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+ { + "type": "text", + "text": "Zichun Wang $^{1}$ , Ying Fu $^{1*}$ , Ji Liu $^{2}$ , Yulun Zhang $^{3}$", + "bbox": [ + 279, + 202, + 686, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1 Beijing Institute of Technology, 2 Baidu Inc., Beijing, China, 3 ETH Zürich", + "bbox": [ + 181, + 220, + 785, + 239 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{wangzichun, fuying}@bit.edu.cn, liuji04@baidu.com, yulun100@gmail.com", + "bbox": [ + 174, + 241, + 790, + 256 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 291, + 312, + 306 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Despite the significant results on synthetic noise under simplified assumptions, most self-supervised denoising methods fail under real noise due to the strong spatial noise correlation, including the advanced self-supervised blind-spot networks (BSNs). For recent methods targeting real-world denoising, they either suffer from ignoring this spatial correlation, or are limited by the destruction of fine textures for under-considering the correlation. In this paper, we present a novel method called LG-BPN for self-supervised real-world denoising, which takes the spatial correlation statistic into our network design for local detail restoration, and also brings the long-range dependencies modeling ability to previously CNN-based BSN methods. First, based on the correlation statistic, we propose a densely-sampled patch-masked convolution module. By taking more neighbor pixels with low noise correlation into account, we enable a denser local receptive field, preserving more useful information for enhanced fine structure recovery. Second, we propose a dilated Transformer block to allow distant context exploitation in BSN. This global perception addresses the intrinsic deficiency of BSN, whose receptive field is constrained by the blind spot requirement, which can not be fully resolved by the previous CNN-based BSNs. These two designs enable LG-BPN to fully exploit both the detailed structure and the global interaction in a blind manner. Extensive results on real-world datasets demonstrate the superior performance of our method. https://github.com/Wang-XiaoDingdd/LGBPN", + "bbox": [ + 75, + 323, + 473, + 746 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 751, + 209, + 767 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Image denoising is a fundamental research topic for low-level vision [7, 36]. Noise can greatly degrade the quality of the captured images, thus bringing adverse impacts on the subsequent downstream tasks [22, 32]. Recently, with the rapid development of neural networks, learning-based methods have shown significant advances compared with traditional model-based algorithms [5, 8, 10, 11].", + "bbox": [ + 75, + 773, + 468, + 878 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/b27ed0159570b1edcbdaf96d72acf305b115b367cbb5dc6f79a263424a1bde4e.jpg", + "image_caption": [ + "SIDD Validation: 0018-0031" + ], + "image_footnote": [], + "bbox": [ + 501, + 290, + 645, + 416 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/3c217f0ae1e494fc5826875b40d017568428768552725441d448cad9a6692e33.jpg", + "image_caption": [ + "DnCNN [36] 31.17/0.778" + ], + "image_footnote": [], + "bbox": [ + 647, + 290, + 725, + 342 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/387de7990b3d7f8fcb55e140b0e7ee5697d3e84e64b595f9e5c33be566e0b966.jpg", + "image_caption": [ + "C2N [15] 28.09/0.706" + ], + "image_footnote": [], + "bbox": [ + 727, + 290, + 805, + 342 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/54cb159d99abf374ec922c6641dff41e987d3df9fda5f3518cebda358842b12d.jpg", + "image_caption": [ + "R2R [26] 30.37/0.770" + ], + "image_footnote": [], + "bbox": [ + 810, + 290, + 890, + 342 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/efa2e6537b61e883a458624c0eff67446678b68c3cd335c88bb079af249ade61.jpg", + "image_caption": [ + "CVF-SID [25] 28.56/0.792" + ], + "image_footnote": [], + "bbox": [ + 647, + 364, + 725, + 415 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/10db8290130deafb867909a0f32c484112c34a1eaa9fc9bcbd8ee21cf35dd7e7.jpg", + "image_caption": [ + "AP-BSN [20] 31.92/0.826", + "Figure 1. Visual comparison of various methods on the SIDD validation [1] dataset. Compared with DnCNN [36], C2N [15] and R2R [15], LG-BPN can be trained in a self-supervised manner without extra data. CVF-SID [25] still contains noise in the output, and AP-BSN [20] suffers from the loss of details." + ], + "image_footnote": [], + "bbox": [ + 727, + 364, + 805, + 415 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/e65ddfd2bd58ee5dcb109fa61f91064e9fd1d38d4afda3279286a1986fca1444.jpg", + "image_caption": [ + "LG-BPN (Ours) 32.76/0.897" + ], + "image_footnote": [], + "bbox": [ + 810, + 364, + 890, + 415 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Unfortunately, learning-based methods often rely on massive labeled image pairs for training [2, 34, 35]. This can not be simply addressed by synthesizing additive white Gaussian noise (AWGN) pairs, since the gap between AWGN and real noise distribution severely degrades their performance in the real world [2, 12]. To this end, several attempts have been made for collecting real-world datasets [1, 4]. Nonetheless, its application is still hindered by the rigorously-controlled and labor-intensive collection procedure. For instance, capturing ground truth images requires long exposure or multiple shots, which is unavailable in complex situations, e.g., dynamic scenes with motion.", + "bbox": [ + 496, + 522, + 892, + 703 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To alleviate the constraint of the large-scale paired dataset, methods without the need for ground truth have attracted increasing attention. The pioneer work Noise2Noise (N2N) [21] uses paired noisy observations for training, which can be applied when clean images are not available. Still, obtaining such noisy pairs under the same scene is less feasible. To make self-supervised methods more practical, researchers seek to learn from one, instead of pairs of observations. Among these methods, blind-spot networks (BSNs) [3, 17, 19, 30] show significant advances to restore clean pixels by utilizing neighbor pixels, with a special blind spot receptive field requirement. Despite their promising results on simple noise such as AWGN, these methods", + "bbox": [ + 496, + 704, + 893, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding Author", + "bbox": [ + 94, + 886, + 223, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "18156", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "usually work under simplified assumptions, e.g., the noise is pixel-wise independent. This obviously does not hold for real noise, where the distribution can be extremely complex and present a strong spatial correlation.", + "bbox": [ + 75, + 90, + 468, + 151 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Accordingly, a few methods have been proposed for self-supervised real noise removal. Recorrupted-to-Recorrupted (R2R) [26] tries to construct noisy-noisy pairs, while it can not be directly applied without extra information, which is not practical in real situations. CVF-SID [25] disentangles the noise components from noisy images, but it assumes the real noise is spatially invariant and ignores the spatial correlation, which contradicts real noise distribution.", + "bbox": [ + 75, + 152, + 467, + 271 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recently, AP-BSN [20] combines pixel-shuffle down-sampling (PD) with the blind spot network (BSN). Though PD can be utilized to meet the noise assumption of BSN, simply combining PD with CNN-based BSN is sub-optimal for dealing with spatially-correlated real noise. It causes damage to local details, thus bringing artifacts to the subsampled images, e.g., aliasing artifact, especially for large PD stride factors [20, 38]. Also, though more advanced designs of BSNs have been proposed [18, 19, 31], CNN-based BSNs fail to capture long-range interactions due to their convolution operator, which is further bounded by the limited receptive field under the blind spot requirement.", + "bbox": [ + 75, + 272, + 467, + 450 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we present a novel method, called LG-BPN, to address these issues on self-supervised real image denoising, including the reliance on extra information, the loss of local structures by noise correlation, and also the lacking of modeling distant pixel interaction. LG-BPN can be directly trained without external information. Furthermore, we ease the destruction of fine textures by carefully considering the spatial correlation in real noise, at the same time injecting long-range interaction by tailoring Transformers to the blind spot network. First, for local information, we introduce a densely-sampled patch-masked convolution (DSPMC) module. Based on the prior statistic of real noise spatial correlation, we take more neighbor pixels into account with a denser receptive field, allowing the network to recover more detailed structures. Second, for global information, we introduce a dilated Transformer block (DTB). Under the special blind spot requirement, this greatly enlarges the receptive field compared with previous CNN-based BSNs, permitting more neighbors to be utilized when predicting the central blind spot pixel. These two designs enable us to fully exploit local and global information, respectively. Extensive studies demonstrate that LG-BPN outperforms other state-of-the-art un-/self-supervised methods on real image denoising, as shown in Figure 1. We summarize our contributions as follows:", + "bbox": [ + 75, + 454, + 467, + 830 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- We present a novel self-supervised method called LG-BPN for real-world image denoising, which can effectively encode both the local detailed structure and the capture of global representation.", + "bbox": [ + 94, + 839, + 467, + 900 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Based on the analysis of real noise spatial correlation, we propose DSPMC module, which takes advantage of the higher sampling density on the neighbor pixels, enabling a denser receptive field for improved local texture recovery.", + "- To establish long-distance dependencies in previous CNN-based BSN methods, we introduce DTB, which aggregates global context while complying with the constraint of blind spot receptive field." + ], + "bbox": [ + 517, + 90, + 890, + 234 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 247, + 640, + 263 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Supervised Image Denoising", + "text_level": 1, + "bbox": [ + 500, + 272, + 754, + 289 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "DnCNN [36] is the first attempt to apply deep learning techniques to the image denoising task, where the training pairs are synthesized by additive white Gaussian noise (AWGN). Following DnCNN, several methods have been proposed for AWGN noise removal. For instance, FFD-Net [37] advances it by taking the noise map as additional input. While achieving superior performance on AWGN removal, recent studies [2, 12] reveal the poor generalization ability of these models when applied to real noise, due to the gap between the noise distribution. The primary obstruction of real image denoising lies in the deficiency of real noisy-clean pairs. To this end, some real-world denoising datasets are collected under carefully considered conditions [1,4]. Based on these datasets, several methods [7, 12] train the network directly on the real image pairs. Despite the decent performance, data collection can be extremely expensive and labor-intensive. Also, it is infeasible to collect clean images under complex scenes containing motion.", + "bbox": [ + 496, + 295, + 890, + 566 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Unsupervised Image Denoising", + "text_level": 1, + "bbox": [ + 500, + 575, + 774, + 590 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Another line of research focuses on the situation where paired data is unavailable, including $i)$ generating pseudo noisy-clean image pairs, $ii)$ generating pseudo noisy-noisy image pairs, and $iii)$ training directly on noisy images.", + "bbox": [ + 496, + 599, + 890, + 657 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Generating pseudo noisy-clean image pairs. In situations where unpaired noisy-clean data is available, generation-based methods seek to synthesize real noise on clean images for aligned training data, which can be used for supervised methods. Inspired by the generative adversarial network (GAN), GCBD [6] synthesizes realistic noisy images to train the denoising network, while its performance is limited by the inaccurate consideration of noise components. UIDNet [31] takes a step further by combining the distilled knowledge of the self-supervised denoising network and extra information from synthetic pairs. C2N [15] considers various noise components in real-world scenarios for more accurate noise synthesis. However, dealing with the gap between unpaired data is still challenging. The mismatch in scene distribution can result in inaccurate generation, thus degrading the quality of synthesized data.", + "bbox": [ + 496, + 659, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "18157", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/25178a5c59a478e3c382af08c3394bcd4db4ca520f47a22ce2b32b9a83c29643.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 94, + 88, + 870, + 262 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/9f880eb70b70951d333d60b0a62ba648a5e70dc3576a7476d4a79aaf5784917d.jpg", + "image_caption": [ + "Figure 2. The overall architecture of LG-BPN. Our method is composed of two branches, aiming at extracting local textures and global interactions, respectively. For each branch, the input first goes through a DSPMC module, then further processed for the deep feature. Finally, the output of two branches is fused for the denoised result." + ], + "image_footnote": [], + "bbox": [ + 98, + 263, + 413, + 400 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/5429102a2b5b49774e3fddb624ef06d5e0ebeb15a7ec31f9d8e8a1e32de8a7e4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 421, + 263, + 867, + 398 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Generating pseudo noisy-noisy image pairs. The semi-supervised method Noise2Noise [21] uses multiple noisy images for training, which can be applied without clean images. However, the acquisition of multiple independent observations under the same scene is still less practical. Therefore, several methods seek to construct noisy-noisy pairs from a single noisy image. Neighbor2Neighbor [14] generates two sub-sampled images under simplified noise assumptions. To handle complex noise distribution in real images, several methods have been proposed, including Noisier2Noise [24], NAC [33] and R2R [26]. Still, these methods either require prior knowledge or are limited by specific constraints, which can be impractical in real situations. Specifically, Noisier2Noise [24] requires noise distribution when synthesizing noisy/noisy pairs. NAC [33] works under the assumption that the noise level is relatively weak. R2R [26] also uses additional information, e.g., noise level function (NLF) and image signal processing (ISP) function.", + "bbox": [ + 75, + 458, + 472, + 731 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Training directly on noisy images. Another type of method follows a self-supervised manner, which can be directly trained on the noisy images and free of synthesizing pseudo image pairs. Noise2Void [17] and Noise2Self [3] propose the self-supervised blind-spot strategy by masking the corresponding central pixel. Laine19 [19] and D-BSN [31] are further proposed for advanced BSN designs, while the convolution-based architecture limits their exploitation for long-range dependencies. To ease the information loss by the blind spot, Blind2Unblind [30] introduces a novel re-visible loss term. Unfortunately, the above-mentioned", + "bbox": [ + 75, + 734, + 472, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "methods work under the assumption that noise is pixel-wise independent, thus inevitably learning identity mapping under spatially-correlated real noise. Towards real image denoising, CVF-SID [25] disentangles the noise components from the clean images, but it assumes the noise is spatially-uncorrelated, which does not match the real noise distribution. Asymmetric pixel shuffle downsampling BSN (APBSN) [20] combines the pixel shuffle downsampling (PD) with a CNN-based BSN [31]. While achieving promising results, local structures are damaged by directly applying the PD operation to the image. Sub-sampled images are corrupted by various artifacts, e.g., aliasing artifacts, which are more pronounced under a large PD stride factor [20,38]. Also, adopting the CNN-based BSN leads to a limited receptive field. Since BSN recovers the central pixels based on its neighbors, fewer available neighbor pixels inevitably lead to performance loss. In summary, this results in the inadequate utilization of information with respect to both local and global contexts. Instead, our method benefits from a denser sampling density for improved local detail extraction, and also enjoys the distant pixel modeling ability for the enlarged receptive field.", + "bbox": [ + 496, + 458, + 890, + 792 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 500, + 797, + 591, + 813 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We first illustrate the overall architecture of LG-BPN in Figure 2, then elaborate on our motivation, and demonstrate our two core designs: DSPMC and DTB.", + "bbox": [ + 496, + 819, + 892, + 864 + ], + "page_idx": 2 + }, + { + "type": "page_footnote", + "text": "1We use 'global' to differentiate from our 'local' branch. Though a more accurate term is 'non-local', we follow the usage of 'global' as [35].", + "bbox": [ + 500, + 875, + 892, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "18158", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/726b069b2cf47f3f86924b2e701730c033e9e128e21d1b41c1d57238be194fdd.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 80, + 88, + 467, + 199 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/d81c5d7a9f2819f82a8d31bd3c5d6f489656508465372038e161c61e0aa37ae8.jpg", + "image_caption": [ + "Figure 3. Comparison of receptive field for the central pixel of APBSN and our method. Green pixels contribute to the restoration of central pixel. Blue pixels represent convolution kernel. We realize a denser receptive field by utilizing more neighbor pixels." + ], + "image_footnote": [], + "bbox": [ + 80, + 202, + 465, + 318 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1. Motivation and Modeling", + "text_level": 1, + "bbox": [ + 76, + 387, + 308, + 404 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Despite the decent results on simple synthetic noise removal, the performance of self-supervised denoising methods declines significantly when dealing with real noise, due to its strong spatial noise correlation. This easily breaks the assumption on which most state-of-the-art methods are based, i.e., noise is pixel-wise independent. These methods assume the clean signal of the central pixel is dependent on neighbors, while the noise is independent instead. Thus under real scenarios, they inevitably misinterpret the spatially-dependent noise as clean signals, and fail to recover the underlying clean images. Consequently, careful consideration of the spatial correlation is a must for self-supervised real noise removal. While the existing methods either struggle with poor results when completely ignoring this correlation, or suffer details loss from ill consideration. For example, AP-BSN [20] meets the assumption of the powerful BSN by adopting PD on the input image. As shown in Figure 3, though this breaks the spatial correlation, the sampling density is dramatically decreased by the PD. This severely degrades the extraction of fine details based on the Nyquist-Shannon sampling theorem, i.e., the fidelity of the results shows a positive correlation to sampling density.", + "bbox": [ + 75, + 411, + 468, + 743 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Besides, though BSN is already adapted for state-of-the-art performance [20], its potential is still heavily hampered by their inherent shortage, i.e., the limit on the receptive field by the masked pixels for avoiding identity mapping. Despite the recent advanced BSN designs [19, 31], CNN-based BSNs are still unable to fully address this issue due to their local convolution operator and fail to model the long-distance dependencies. This adversely affects the perfor", + "bbox": [ + 75, + 744, + 468, + 864 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/85acd48737a79ccc066616a60796bd0dc9ad930f3e492d3001d29781b634da6f.jpg", + "image_caption": [ + "(a) Bar plot of correlation by relative position" + ], + "image_footnote": [], + "bbox": [ + 517, + 87, + 700, + 205 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/820b3f26490cb5c0355ce1fea45ae1b902166381679231d3a5992a1574f6e8a4.jpg", + "image_caption": [ + "(b) High-correlation pixels mask", + "Figure 4. Visualization of spatial correlation in real noise. (a) Bar plot of spatial correlation calculated by the correlation coefficient. Note that we scale the height by log norm for better visualization. The higher bar indicates a stronger correlation. (b) The mask of high-correlation pixels. Locations with 0 mean this pixel is strongly correlated to the central pixel, while 1 means not." + ], + "image_footnote": [], + "bbox": [ + 718, + 93, + 867, + 207 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "mance of BSN, as the number of neighbors around the blind spot used for inferring is dramatically reduced.", + "bbox": [ + 496, + 330, + 890, + 359 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We aim to tackle both of these challenges in our methods. First, we realize better extraction for detailed textures from the perspective of sampling density. As shown in Figure 3, DSPMC enables a denser sampling rate by leveraging more neighbor pixels, which raises the upper limit of reconstruction quality. Second, by tailoring normal Transformers to a blind fashion, DTB is introduced for its powerful global modeling ability to compensate for the limited receptive field of CNN-based BSNs.", + "bbox": [ + 496, + 361, + 892, + 496 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Based on these two modules, we now introduce the overall architecture of our method. As shown in Figure 2, LG-BPN is mainly composed of two branches in parallel, aiming at local and global contexts reconstruction respectively. For the local feature extraction branch, we first apply the $9 \\times 9$ DSPMC module. The densely extracted features are then down-sampled to break the spatial correlation. Then, the feature maps go through dilated convolution with a dilation of 2. For the global branch, the input image first goes through a $21 \\times 21$ DMPMC module with a larger receptive field, which is then processed by DTBs. Finally, the local and global information from the two branches is fused together for the final output.", + "bbox": [ + 496, + 500, + 890, + 696 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Densely-Sampled Patch-Masked Convolution", + "text_level": 1, + "bbox": [ + 500, + 709, + 880, + 726 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Neither adopting a low sample rate nor sampling all neighbor pixels can be an optimal choice for BSN when tacking real noise. In DSPMC, we aim to extract as much local information as possible, at the same time avoiding misinterpretation by these strongly-correlated neighbor pixels. To this end, we start by presenting the relationship between spatial correlation and the relative position, as shown in Figure 4. Following previous works [20, 38], we use Pearson's correlation coefficient to depict the relationship. Specifically, we first obtain the noise map by subtracting the clean images from the noisy images in SIDD medium [1]", + "bbox": [ + 496, + 734, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_footnote", + "text": "2We adopt $9\\times 9$ DSPMC in the local branch. Here, the $11\\times 11$ size is shown for illustration purposes to better compare the receptive field.", + "bbox": [ + 76, + 875, + 467, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "18159", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/9e6ed801c5792a07d6bf9c25f1187cd8da08d3da692c5536265864e39de2b38f.jpg", + "image_caption": [ + "(a) Kernel location during training" + ], + "image_footnote": [], + "bbox": [ + 80, + 90, + 202, + 183 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/2f60473a4421e2fa2e5cf7773538a75814b49d0d71ce915b7ce354803eca9f5b.jpg", + "image_caption": [ + "(b) Shifted kernel location during testing" + ], + "image_footnote": [], + "bbox": [ + 210, + 89, + 334, + 184 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/0226df4140b9d03ab5312a73cb1c4466f94fbf235520d895b7135905d283cda9.jpg", + "image_caption": [ + "(c) Shifted kernel location during testing with dilation", + "Figure 5. Illustration of shifting kernel strategy and dilation of DSPMC. The blue and green points are the kernel locations during training and testing respectively. Yellow arrows indicate the shift direction. This avoids the strongly correlated pixels when training, sampling pixels closer to the center when testing for more details." + ], + "image_footnote": [], + "bbox": [ + 344, + 90, + 467, + 184 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "dataset. Then, correlation coefficient can be calculated by:", + "bbox": [ + 76, + 299, + 460, + 313 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\rho_ {N _ {c e n}, N _ {n e i}} = \\frac {\\operatorname {c o v} \\left(N _ {c e n} , N _ {n e i}\\right)}{\\sigma_ {N _ {c e n}} \\sigma_ {N _ {n e i}}}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 163, + 319, + 468, + 353 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $N_{cen}$ and $N_{cen}$ represent the noise of the central pixel and neighbor pixels respectively. In Figure 4(a), we find that there exist more neighbor pixels which can also be leveraged for prediction. These pixels are not strongly correlated to the center pixel, thus bringing useful information, instead of misinterpretation to BSN. Then, the DSPMC kernel can be calculated as:", + "bbox": [ + 75, + 357, + 468, + 460 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {K} _ {D S P M C} = \\mathbf {K} _ {n} \\odot \\mathbf {M a s k} _ {c o r}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 168, + 469, + 468, + 484 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf{K}_{DSPMC}$ is the kernel of DSPMC, $\\mathbf{K}_n$ is the kernel of the normal convolution, and $\\mathbf{Mask}_{cor}$ is the mask for filtering out highly-correlated pixels shown in Figure 4(b). By integrating this noise distribution prior to sampling locations, our module can effectively take more neighbor pixels while avoiding the strongly correlated pixels. This enables the extracted feature to contain more fine details, and a denser receptive field as well. Also, as shown in Figure 3, since the extracted high-dimension feature already gathers the rich local details, the subsequent feature-level PD can save more useful information compared with the previous image-level PD.", + "bbox": [ + 75, + 489, + 468, + 667 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "However, directly applying this module is not an optimal choice: $i)$ the inference stage requires more details compared with training, so directly using the same architecture can damage high-frequency details [20], $ii)$ a large kernel can cause computational inefficiency.", + "bbox": [ + 75, + 670, + 468, + 744 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Kernel shift strategy. As shown in Figure 5(b), for the first concern, we need to obtain more details while testing, focusing on local detailed information closer to the center pixel. Inspired by the deformable convolution [9], we apply a set of fixed offsets on the kernel for each location, which enforce that the kernels are more gathered in the center:", + "bbox": [ + 75, + 744, + 468, + 834 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {y} \\left(p _ {0}\\right) = \\sum_ {k = 1} ^ {\\mathbf {K}} w _ {k} \\cdot \\mathbf {x} \\left(p _ {0} + p _ {k} + \\Delta p _ {k}\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 142, + 842, + 468, + 883 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\Delta p _ {k} = \\text {R a t i o} * (p _ {k} - p _ {0}),\n$$\n", + "text_format": "latex", + "bbox": [ + 153, + 887, + 333, + 902 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/695d932f9aa4dd65d657b1334a75abadacba3455a1e460a309193ce5816e6cd7.jpg", + "image_caption": [ + "(a) Noisy input", + "Figure 6. The comparison of the feature map visualization of our method and AP-BSN [20] in the training phase. Our feature map shows clearer edges, validating the superiority of local details extraction of DSPMC by imposing denser sampling locations." + ], + "image_footnote": [], + "bbox": [ + 501, + 88, + 622, + 181 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/b1a6cf48ff7abd0b3f8651874629209fc35baad7fd59d9ed3020df0236719c1b.jpg", + "image_caption": [ + "(b) AP-BSN [20]" + ], + "image_footnote": [], + "bbox": [ + 633, + 88, + 754, + 181 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/ff1eec17441fd823b22d1a795b311175dd883e72e15116c50db964942da66b23.jpg", + "image_caption": [ + "(c) LG-BPN (Ours)" + ], + "image_footnote": [], + "bbox": [ + 766, + 88, + 885, + 181 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf{K}$ is the kernel sampling locations, $w_{k}$ is the kernel weight, $\\mathbf{x}(p)$ and $\\mathbf{y}(p)$ denote the features at $p$ in input feature $\\mathbf{x}$ and output feature $\\mathbf{y}$ , and $\\Delta p$ is the applied kernel offset. Ratio is the extent we shift the kernel while testing. By adding offsets to the kernel, we can shrink the kernel and capture finer details while testing.", + "bbox": [ + 496, + 263, + 890, + 354 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Dilation in DSPMC. As shown in Figure 5(c), for the second concern, we further decrease the computational cost by adding dilation to the convolution kernel. This imposed sparsity makes our DSPMC computationally efficient especially for large kernel size, at the same time maintaining the dense receptive field for capturing detailed structures.", + "bbox": [ + 496, + 354, + 890, + 445 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Visualization of the extracted feature map. To validate that our DSPMC module achieves a denser receptive field and is thus better at extracting local high-frequency structures, we present the visualization of the feature map. We select the output feature of the local extraction branch, and the corresponding location in AP-BSN. All channels are averaged and normalized for visualization. As shown in Figure 6, in AP-BSN [20], the local fine texture is damaged due to the insufficient use of neighbor signals. Instead, by leveraging more neighbor pixels, our feature map shows shaper edges and preserves more details.", + "bbox": [ + 496, + 446, + 890, + 611 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Dilated Transformer Block", + "text_level": 1, + "bbox": [ + 500, + 619, + 741, + 635 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The receptive field of BSN is restricted by the imposed blind spots, while the local operator in CNN-based BSNs further prevents it from gathering global interaction. However, under the special blind spot constraint on the receptive field, it is non-trivial to directly introduce normal Transformer blocks to the BSN. Inspired by the D-BSN [31], we aim to design the Transformer block without information exchange between spatially-adjacent pixels, which satisfies the blind spot requirement when combined with DSPMC. Under these requirements, we carefully consider the design of two core components in the Transformer: the self-attention calculation and the feed-forward layer.", + "bbox": [ + 496, + 643, + 890, + 824 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "First, for the self-attention layer, spatial-wise attention enables spatial information exchange and thus does not meet our receptive field requirement. Recently, a grid-like self-attention can meet our requirement [28], while the grid pattern further narrows the receptive field that the blind spot", + "bbox": [ + 496, + 825, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "18160", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/50862906fd61bda8b28d301d511f896fc3fced26f456b3325aac7d550eafa92e.jpg", + "image_caption": [ + "(a) AP-BSN [20]" + ], + "image_footnote": [], + "bbox": [ + 117, + 87, + 254, + 190 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/bab93a1ec28ac9d2b411f20df875127c6c3108ec5e82a6a7237bb12de2f6af8c.jpg", + "image_caption": [ + "(b) LG-BPN (Ours)", + "Figure 7. The comparison of the receptive field between AP-BSN [20] and our method. We calculate the gradient response to the central pixel. The brighter color represents the higher contribution for recovering the central pixel." + ], + "image_footnote": [], + "bbox": [ + 290, + 87, + 426, + 191 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "has reduced. Instead, we adopt channel-wise attention [35] for its unawareness of spatial location and global perception as well. Furthermore, to enhance the local context while preventing information of adjacent pixels, we introduce dilated depth-wise convolution before computing feature similarity. For the input feature $\\mathbf{X}$ , the Query $(\\mathbf{Q})$ , Key $(\\mathbf{K})$ and Value $(\\mathbf{V})$ matrix is thus calculated by $\\mathbf{Q} = g^{Q}(\\mathbf{X})$ , $\\mathbf{K} = g^{K}(\\mathbf{X})$ , $\\mathbf{V} = g^{V}(\\mathbf{X})$ , where $g^{Q}(\\cdot)$ , $g^{K}(\\cdot)$ and $g^{V}(\\cdot)$ denote the dilated $3 \\times 3$ depth-wise convolution. Given the $\\mathbf{Q}$ , $\\mathbf{K}$ and $\\mathbf{V}$ matrix, the channel interaction can be obtained by the dot-product, where the attention map is of size $\\mathbb{R}^{C \\times C}$ , and $C$ is the number of channels. The overall self-attention layer is represented as:", + "bbox": [ + 75, + 276, + 472, + 474 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\operatorname {A t t e n t i o n} (\\mathbf {Q}, \\mathbf {K}, \\mathbf {V}) = \\mathbf {V} \\operatorname {S o f t m a x} (\\mathbf {K Q}), \\\\ \\hat {\\mathbf {X}} = \\operatorname {A t t e n t i o n} (\\mathbf {Q}, \\mathbf {K}, \\mathbf {V}) + \\mathbf {X}, \\tag {4} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 130, + 483, + 468, + 521 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\mathbf{X}$ and $\\hat{\\mathbf{X}}$ denote the input and output features.", + "bbox": [ + 76, + 526, + 428, + 541 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Second, for the feed-forward layer, adjacent information exchange can be simply avoided by adopting $1 \\times 1$ convolutions only. Nonetheless, this fails to capture local context, which can be critical for restoring high-frequency details. We address this issue by also introducing dilation into the normal $3 \\times 3$ convolution in the feed-forward layer. Then, features extracted by dilated depth-wise convolution go through a gating unit for the non-linearity. This gating unit is the element-wise product of two parallel paths, with one of them activated by the GELU unit. The overall process of the feed-forward layer is formulated as:", + "bbox": [ + 75, + 542, + 468, + 708 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathbf {G} ^ {\\mathbf {1}} = g ^ {1} (\\mathrm {L N} (\\mathbf {X})), \\\\ \\mathbf {G} ^ {2} = g ^ {2} (\\mathrm {L N} (\\mathbf {X})), \\tag {5} \\\\ \\hat {\\mathbf {X}} = \\operatorname {G E L U} \\left(\\mathbf {G} ^ {1}\\right) \\odot \\mathbf {G} ^ {2} + \\mathbf {X}, \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 166, + 718, + 468, + 776 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\odot$ is element-wise multiplication, LN denotes layer normalization, $g^{1}(\\cdot)$ and $g^{2}(\\cdot)$ represent the $3\\times 3$ dilated depth-wise convolution. An additional benefit is that, compared to the normal $3\\times 3$ convolution, the introduced dilation can also enlarge the receptive field.", + "bbox": [ + 75, + 779, + 468, + 854 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To prove the effectiveness of the introduced global dependencies, we also plot the receptive field for recovering the central pixel of our method and the CNN-based BSNs", + "bbox": [ + 75, + 854, + 468, + 898 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "in Figure 7. By injecting the long-range interaction into the blind spot network, more neighbor pixels are activated for restoring the central pixels in our method, offering a broader receptive field compared to the previous CNN-based BSNs.", + "bbox": [ + 496, + 90, + 890, + 151 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 165, + 633, + 181 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Dataset and Setup Details", + "text_level": 1, + "bbox": [ + 500, + 190, + 733, + 207 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We train and evaluate our method on two real-world datasets, i.e., SIDD [1] and DND [27]. Note that for the SIDD benchmark dataset and DND benchmark dataset, we submit the output to the website for online evaluation.", + "bbox": [ + 496, + 213, + 890, + 273 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Smartphone Image Denoising Dataset (SIDD) [1] contains paired images for real-world denoising by five smartphone cameras. For training, we use the sRGB images from SIDD-Medium including 320 pairs. For validation and evaluation, we use the sRGB images from the SIDD validation set and benchmark set respectively. Each includes 1280 patches of size $256 \\times 256$ , where the ground truth images are also provided for the validation set.", + "bbox": [ + 496, + 273, + 890, + 393 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Darmstadt Noise Dataset (DND) [27] contains 50 noisy images for benchmarking without the ground truth provided, and the results can only be obtained via the online submission system. Therefore, we enjoy a fully self-supervised manner and directly train our method on the test set without extra eternal data.", + "bbox": [ + 496, + 395, + 890, + 484 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Training Details", + "text_level": 1, + "bbox": [ + 500, + 494, + 661, + 511 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "During training, we keep the same setting as the previous work [20]. Specifically, a batch size of 8 is used in the experiment. We adopt $\\mathcal{L}_1$ loss between ground truth and output for training. The learning rate starts with $1e - 4$ , where Adam optimizer is adopted. The network is trained with 20 epochs until it fully converges. We implement the method in PyTorch 1.8.0, and train our model on the Nvidia RTX 3090. Two metrics are utilized to evaluate the performance of methods, including peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) [29]. The larger value of PSNR and SSIM implies better fidelity.", + "bbox": [ + 496, + 520, + 890, + 686 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Evaluation of Real-world Denoising", + "text_level": 1, + "bbox": [ + 500, + 695, + 808, + 710 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We validate the effectiveness of our method for real-world image denoising on the commonly-used SIDD benchmark dataset and DND benchmark dataset. Table 1 shows the comparison of various methods on SIDD and DND benchmark datasets. Visualization results of several methods addressed in Table 1 on SIDD and DND datasets can be found in Figure 8 and Figure 9. We achieve better results in quantitative and qualitative metrics than previous un-/self-supervised methods. Compared with unsupervised methods trained on unpaired clean-noisy data, LG-BPN does not rely on extra data for synthesizing training pairs, also avoiding the misalignment between the scene distribution. For the", + "bbox": [ + 496, + 719, + 890, + 898 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "18161", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/6aee5393453900883464ddbc3cc933b44f66b1defc36887d4fd750c809a4a0ba.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Type of supervisionTraining dataMethodSIDDDND
PSNRSSIMPSNRSSIM
Non-learning basedNoneBM3D [8]25.650.68534.510.851
WNNM [11]25.780.80934.670.865
SupervisedSynthesized PairsDnCNN [36]23.660.58332.430.790
CBDNet [12]33.280.86838.050.942
AWGN-M [38]33.99*0.896*38.400.945
Real pairsDnCNN [36]35.34*0.885*37.83*0.929*
AINDNet [16]38.840.95139.340.952
RIDNet [2]38.700.95039.250.952
DIDN [34]39.820.97339.620.954
UnsupervisedNoisy-clean pairsGCBD [6]--35.580.922
UIDNet [13]32.480.897--
C2N [15] + DIDN [34]35.350.93736.380.887
D-BSN [31] + MWCNN [23]--37.930.937
Noisy-noisy pairsNoise2Self [3]29.56†0.808†--
NAC [33]--36.200.925
R2R [26]34.780.898--
Single noisy observationNoise2Void [17]27.68†0.668†--
CVF-SID [25]34.710.91736.500.924
AP-BSN [20]35.970.92538.090.937
LG-BPN (Ours)37.280.93638.430.942
", + "bbox": [ + 84, + 88, + 872, + 412 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 1. Quantitative comparison of various methods on SIDD and DND benchmark datasets. Though several supervised methods achieve better results using noisy/clean image pairs, our methods use noisy RGB images only. Results with $\\star$ mean these are reproduced and evaluated by ourselves, since they are not evaluated on the dataset we use in their original paper. The results marked with $\\dagger$ are reported from R2R [26]. Otherwise, we report the official results from SIDD and DND benchmark websites.", + "bbox": [ + 75, + 422, + 893, + 479 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "self-supervised methods, NAC [33] works under the weak noise level assumption, while R2R [26] can not be directly applied to sRGB images without extra NLF and ISP functions, both of which harm their performance in real-world situations. In contrast, LG-BPN can be directly applied and not restricted by these assumptions. For methods leveraging single noisy observations, CVF-SID [25] does not consider the strong spatial correlation property in real noise, thus real noise can not be fully removed as shown in Figure 8. APBSN [20] suffers from inadequate sample locations with a limited receptive field, so details are blurred as shown in Figure 9. Instead, LG-BPN carefully integrates the spatial correlation into the network design, simultaneously modeling distant context dependencies.", + "bbox": [ + 75, + 489, + 472, + 702 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Analysis of the Proposed Method", + "text_level": 1, + "bbox": [ + 76, + 710, + 366, + 727 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Dilation factor in densely-sampled convolution. Directly introducing densely-sample convolution can be computationally expensive. To balance the efficiency and the performance, we further introduce the sparsity to the convolution kernel by adding dilation to the original DSPMC. Figure 5(c) shows the illustration of the dilation.", + "bbox": [ + 75, + 734, + 468, + 824 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To explore the better trade-off between performance and efficiency, we provide ablation studies on the dilation rate for our DSPMC in both local and global extraction branches. As shown in Table 2(a), a dilation of 1 for $9 \\times 9$ DSPMC and 2 for $21 \\times 21$ DSPMC achieve a better balance.", + "bbox": [ + 75, + 825, + 470, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We claim its reason is that the difference in kernel size results in focusing on varied scales of information. This imposes different sensitivity to the dilation, i.e., sampling density. For relatively small $9 \\times 9$ kernels, it focuses more on the local textures, thus adding dilation can notably lower its ability when reconstructing detailed structures. While for the $21 \\times 21$ kernel, the larger kernel size makes it aim at the global context more. Thus, the introduced dilation does not severely harm its global extraction ability, at the same time reducing the computational cost.", + "bbox": [ + 496, + 489, + 890, + 641 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The exploitation of local and global information. LGBPN consists of two branches in parallel. Specifically, we combine the small $9 \\times 9$ DSPMC with dilated convolution and the large $21 \\times 21$ DSPMC with DTB, focusing on local and global context processing respectively. To validate the reasonableness of our network architecture, we conduct ablation studies on these components. Table 2(b) shows the results of different combinations.", + "bbox": [ + 496, + 642, + 890, + 762 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "It can be seen that removing the DSPMC of size $9 \\times 9$ and $21 \\times 21$ in either branch severely degrades the performance. It is on account of the insufficient sampling density, which limits the reconstruction quality according to the Nyquist-Shannon sampling theorem. In this situation, the sampling density is made severely sparse, which causes insufficient utilization of input signals. This performance drop demonstrates the effectiveness of our DSPMC module.", + "bbox": [ + 496, + 763, + 890, + 883 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Furthermore, we validate that the different sizes of", + "bbox": [ + 517, + 885, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "18162", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0a679e6d9787e67073e454372e4316dc7dd5db81d978ec535e32bb7ee5d6f6b8.jpg", + "image_caption": [ + "SIDD benchmark input" + ], + "image_footnote": [], + "bbox": [ + 86, + 87, + 312, + 261 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/5fd3001ca8c868f123c02493662aef0aff464ab8c5563d55c1f64466ae84d6cc.jpg", + "image_caption": [ + "N2V [17]" + ], + "image_footnote": [], + "bbox": [ + 318, + 87, + 454, + 167 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8c7bfe4fbceba170433d10f174e2c80692df33c2a0fe717981480e70c4202e40.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 464, + 87, + 599, + 167 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8ccf2714dd0838b9c5833746fde64282d3a368f84cb232751a0cb21e24d6f892.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 607, + 87, + 743, + 167 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/73f55e134fc87843219db3ac5a30d2e84201cd2d7b77bd346df2f0e7bbb03ee4.jpg", + "image_caption": [ + "C2N [15]" + ], + "image_footnote": [], + "bbox": [ + 751, + 87, + 887, + 167 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/cb2a4def2d50c5b11f6de58d37f068e888e2b679bc27a0d9c6cabcbd57551e6e.jpg", + "image_caption": [ + "R2R [26]", + "Figure 8. Visual quality comparison on SIDD benchmark dataset. Note that the quantitative results are not available." + ], + "image_footnote": [], + "bbox": [ + 318, + 184, + 455, + 261 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ceef7db249ebad747b91a28691e452db1a657a52b0e8b2019ce5b05312235a90.jpg", + "image_caption": [ + "DnCNN [36]", + "CVF-SID [25]" + ], + "image_footnote": [], + "bbox": [ + 462, + 184, + 599, + 261 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/2354a17d50448eee416327728869966eb4b2fe36650f05e308e7b48d914fb28a.jpg", + "image_caption": [ + "AWGN-M [38]", + "AP-BSN [20]" + ], + "image_footnote": [], + "bbox": [ + 607, + 184, + 743, + 261 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/fdcc27c04a5056381699a67b02ff4f5a3b7699c5ad5e73081686ce750930f71f.jpg", + "image_caption": [ + "LG-BPN (Ours)" + ], + "image_footnote": [], + "bbox": [ + 751, + 184, + 887, + 261 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/87197d8ac97094924b3ca41ff80b5099edda4b0f7ad8200bfd6612cfd832959d.jpg", + "table_caption": [], + "table_footnote": [ + "(a) Ablation studies on dilation rates. Different dilation rate combinations are explored on the DSPMC in the local branch and global branch." + ], + "table_body": "
9x9 DSPMC dilation21x21 DSPMC dilationPSNRSSIMFLOPS (G)Params (M)
1137.230.88588.61.35
1237.320.88629.80.45
1337.230.88317.10.26
2136.850.87984.61.23
2236.840.87525.80.39
2336.990.87313.10.20
", + "bbox": [ + 89, + 314, + 542, + 428 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/b604a3461c16fede273a0c47012590c0e90f1ef6635ef7f81b3bde24f050e49e.jpg", + "table_caption": [], + "table_footnote": [ + "(b) Ablation studies on our proposed method. Improvements can be found with our proposed modules and network design." + ], + "table_body": "
MethodPSNRSSIM
w/o 9×9 DSPMC35.820.855
w/o 21×21 DSPMC36.210.869
Replacing Conv with DTB36.900.880
Replacing DTB with Conv36.820.875
w/o kernel shift35.640.857
LG-BPN (Ours)37.320.886
", + "bbox": [ + 575, + 314, + 888, + 428 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 2. The analysis of our method on the SIDD validation dataset. Experimental results prove the effectiveness of our method design.", + "bbox": [ + 83, + 465, + 882, + 479 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/bcb3430696ba746a63a80ccc98ca6bc53819e0615146275f7e1207faed66bab9.jpg", + "image_caption": [ + "DND benchmark input", + "28.50/0.777", + "Figure 9. Visual quality comparison on DND benchmark dataset." + ], + "image_footnote": [], + "bbox": [ + 80, + 492, + 222, + 636 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/434d07212965afcb767e83b940a150db371db9b5d6e6cf67cc54d869b88b220b.jpg", + "image_caption": [ + "NAC [36]" + ], + "image_footnote": [], + "bbox": [ + 223, + 492, + 302, + 554 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b8a44209ca2f0012690a24043573399d397334b484ec772285ddc4c6f907f59e.jpg", + "image_caption": [ + "C2N [15]" + ], + "image_footnote": [], + "bbox": [ + 303, + 492, + 383, + 554 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/23bf0f2d1561402c0cf94079855ff1121f99326c04bad70e52c18b7d12a01774.jpg", + "image_caption": [ + "29.20/0.793", + "AP-BSN [20]", + "32.94/0.889" + ], + "image_footnote": [], + "bbox": [ + 303, + 574, + 383, + 636 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/25f5a632bbf009a3201b5f44afb6b9fc362f7c5a1b9dd77acbdc4af02044b96e.jpg", + "image_caption": [ + "AWGN-M [38]" + ], + "image_footnote": [], + "bbox": [ + 385, + 492, + 465, + 554 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/25ce448dd987ba6d6e07a79f0264c2d2f0b8301c3bb99fc2ca82c104638b3df0.jpg", + "image_caption": [ + "29.26/0.797", + "LG-BPN (Ours)", + "33.37/0.897" + ], + "image_footnote": [], + "bbox": [ + 385, + 574, + 465, + 636 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "DSPMC in local and global feature extraction branches make them focus on various scales of features. Such discrepancy across the scale demands us to treat scale-specific characteristics in a different way. When replacing the dilated convolution in the local branch with our DTB, the lack of local connectivity brings inferior performance. Similarly, when replacing the DTB in the global branch with the dilated convolution, the network is built by convolutions only. It induces a lack of long-range interaction, which greatly limits their recovery quality as well. This proves the superior design of our architecture. By exploiting the locality of convolution with a small DSPMC, also the global dependencies of DTB with a large DSPMC, our architecture enjoys more reasonable exploitation for multi-scale context.", + "bbox": [ + 75, + 688, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The effect of kernel shift strategy. Since the requirement for pixel-wise independent noise is different in training and testing, directly applying the same kernel of the training phase while testing will lose image details [20]. We proposed a kernel shift strategy, as illustrated in Figure 5(b). In Table 2(b), the lack of kernel shift causes $1.68\\mathrm{dB}$ drops, proving the effectiveness of our shifting paradigm.", + "bbox": [ + 498, + 494, + 890, + 602 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 614, + 617, + 628 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we propose LG-BPN for self-supervised real image denoising, aiming to address the details lost by the coarse consideration for real noise correlation, and the lack of global interaction by the inherent constraint on the receptive field for BSN. First, we propose DSPMC to fully preserve the local structures. Owing to a denser receptive field, we ease the destruction of fine textures and can thus better reconstruct details. Second, we propose DTB, injecting distant interactions into the previously CNN-based blind spot networks. Since blind spot networks rely on neighbor signals for predicting, more clues can be provided by activating more neighbor pixels. Extensive results on real-world datasets reveal the superior performance of LG-BPN.", + "bbox": [ + 496, + 638, + 890, + 834 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement This work was supported by the National Natural Science Foundation of China under Grants No. 62171038, No. 61827901, No. 62088101, and No. 62006023.", + "bbox": [ + 496, + 839, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "18163", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Abdelrahman Abdelhamed, Stephen Lin, and Michael S Brown. A high-quality denoising dataset for smartphone cameras. In CVPR, pages 1692-1700, 2018. 1, 2, 4, 6", + "[2] Saeed Anwar and Nick Barnes. Real image denoising with feature attention. 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In AAAI, pages 13074-13081, 2020. 2, 3, 4, 7, 8" + ], + "bbox": [ + 503, + 92, + 890, + 219 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "18165", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/LG-BPN_ Local and Global Blind-Patch Network for Self-Supervised Real-World Denoising/b106948a-bc0f-4862-b17d-1b95904390ce_model.json b/2023/LG-BPN_ Local and Global Blind-Patch Network for Self-Supervised Real-World Denoising/b106948a-bc0f-4862-b17d-1b95904390ce_model.json new file mode 100644 index 0000000000000000000000000000000000000000..457cda3fa4b3203aced932b1f05355b872377c59 --- /dev/null +++ b/2023/LG-BPN_ Local and Global Blind-Patch Network for Self-Supervised Real-World Denoising/b106948a-bc0f-4862-b17d-1b95904390ce_model.json @@ -0,0 +1,2563 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.218, + 0.131, + 0.753, + 0.177 + ], + "angle": 0, + "content": "LG-BPN: Local and Global Blind-Patch Network for Self-Supervised Real-World Denoising" + }, + { + "type": "text", + "bbox": [ + 0.28, + 0.203, + 0.687, + 0.221 + ], + "angle": 0, + "content": "Zichun Wang \\(^{1}\\), Ying Fu \\(^{1*}\\), Ji Liu \\(^{2}\\), Yulun Zhang \\(^{3}\\)" + }, + { + "type": "text", + "bbox": [ + 0.182, + 0.221, + 0.787, + 0.24 + ], + "angle": 0, + "content": "1 Beijing Institute of Technology, 2 Baidu Inc., Beijing, China, 3 ETH Zürich" + }, + { + "type": "text", + "bbox": [ + 0.176, + 0.242, + 0.791, + 0.257 + ], + "angle": 0, + "content": "{wangzichun, fuying}@bit.edu.cn, liuji04@baidu.com, yulun100@gmail.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.292, + 0.313, + 0.308 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.324, + 0.474, + 0.747 + ], + "angle": 0, + "content": "Despite the significant results on synthetic noise under simplified assumptions, most self-supervised denoising methods fail under real noise due to the strong spatial noise correlation, including the advanced self-supervised blind-spot networks (BSNs). For recent methods targeting real-world denoising, they either suffer from ignoring this spatial correlation, or are limited by the destruction of fine textures for under-considering the correlation. In this paper, we present a novel method called LG-BPN for self-supervised real-world denoising, which takes the spatial correlation statistic into our network design for local detail restoration, and also brings the long-range dependencies modeling ability to previously CNN-based BSN methods. First, based on the correlation statistic, we propose a densely-sampled patch-masked convolution module. By taking more neighbor pixels with low noise correlation into account, we enable a denser local receptive field, preserving more useful information for enhanced fine structure recovery. Second, we propose a dilated Transformer block to allow distant context exploitation in BSN. This global perception addresses the intrinsic deficiency of BSN, whose receptive field is constrained by the blind spot requirement, which can not be fully resolved by the previous CNN-based BSNs. These two designs enable LG-BPN to fully exploit both the detailed structure and the global interaction in a blind manner. Extensive results on real-world datasets demonstrate the superior performance of our method. https://github.com/Wang-XiaoDingdd/LGBPN" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.752, + 0.21, + 0.768 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.774, + 0.47, + 0.88 + ], + "angle": 0, + "content": "Image denoising is a fundamental research topic for low-level vision [7, 36]. Noise can greatly degrade the quality of the captured images, thus bringing adverse impacts on the subsequent downstream tasks [22, 32]. Recently, with the rapid development of neural networks, learning-based methods have shown significant advances compared with traditional model-based algorithms [5, 8, 10, 11]." + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.291, + 0.646, + 0.417 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.534, + 0.418, + 0.617, + 0.438 + ], + "angle": 0, + "content": "SIDD Validation: 0018-0031" + }, + { + "type": "image", + "bbox": [ + 0.648, + 0.291, + 0.726, + 0.343 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.657, + 0.344, + 0.718, + 0.364 + ], + "angle": 0, + "content": "DnCNN [36] 31.17/0.778" + }, + { + "type": "image", + "bbox": [ + 0.728, + 0.291, + 0.807, + 0.343 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.74, + 0.344, + 0.797, + 0.364 + ], + "angle": 0, + "content": "C2N [15] 28.09/0.706" + }, + { + "type": "image", + "bbox": [ + 0.812, + 0.291, + 0.891, + 0.343 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.824, + 0.344, + 0.879, + 0.364 + ], + "angle": 0, + "content": "R2R [26] 30.37/0.770" + }, + { + "type": "image", + "bbox": [ + 0.648, + 0.365, + 0.726, + 0.416 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.652, + 0.418, + 0.721, + 0.438 + ], + "angle": 0, + "content": "CVF-SID [25] 28.56/0.792" + }, + { + "type": "image", + "bbox": [ + 0.728, + 0.365, + 0.807, + 0.416 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.737, + 0.418, + 0.799, + 0.438 + ], + "angle": 0, + "content": "AP-BSN [20] 31.92/0.826" + }, + { + "type": "image", + "bbox": [ + 0.811, + 0.365, + 0.891, + 0.416 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.811, + 0.418, + 0.891, + 0.438 + ], + "angle": 0, + "content": "LG-BPN (Ours) 32.76/0.897" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.444, + 0.893, + 0.514 + ], + "angle": 0, + "content": "Figure 1. Visual comparison of various methods on the SIDD validation [1] dataset. Compared with DnCNN [36], C2N [15] and R2R [15], LG-BPN can be trained in a self-supervised manner without extra data. CVF-SID [25] still contains noise in the output, and AP-BSN [20] suffers from the loss of details." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.523, + 0.893, + 0.704 + ], + "angle": 0, + "content": "Unfortunately, learning-based methods often rely on massive labeled image pairs for training [2, 34, 35]. This can not be simply addressed by synthesizing additive white Gaussian noise (AWGN) pairs, since the gap between AWGN and real noise distribution severely degrades their performance in the real world [2, 12]. To this end, several attempts have been made for collecting real-world datasets [1, 4]. Nonetheless, its application is still hindered by the rigorously-controlled and labor-intensive collection procedure. For instance, capturing ground truth images requires long exposure or multiple shots, which is unavailable in complex situations, e.g., dynamic scenes with motion." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.895, + 0.902 + ], + "angle": 0, + "content": "To alleviate the constraint of the large-scale paired dataset, methods without the need for ground truth have attracted increasing attention. The pioneer work Noise2Noise (N2N) [21] uses paired noisy observations for training, which can be applied when clean images are not available. Still, obtaining such noisy pairs under the same scene is less feasible. To make self-supervised methods more practical, researchers seek to learn from one, instead of pairs of observations. Among these methods, blind-spot networks (BSNs) [3, 17, 19, 30] show significant advances to restore clean pixels by utilizing neighbor pixels, with a special blind spot receptive field requirement. Despite their promising results on simple noise such as AWGN, these methods" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.225, + 0.9 + ], + "angle": 0, + "content": "*Corresponding Author" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "18156" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.152 + ], + "angle": 0, + "content": "usually work under simplified assumptions, e.g., the noise is pixel-wise independent. This obviously does not hold for real noise, where the distribution can be extremely complex and present a strong spatial correlation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.153, + 0.468, + 0.272 + ], + "angle": 0, + "content": "Accordingly, a few methods have been proposed for self-supervised real noise removal. Recorrupted-to-Recorrupted (R2R) [26] tries to construct noisy-noisy pairs, while it can not be directly applied without extra information, which is not practical in real situations. CVF-SID [25] disentangles the noise components from noisy images, but it assumes the real noise is spatially invariant and ignores the spatial correlation, which contradicts real noise distribution." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.273, + 0.468, + 0.452 + ], + "angle": 0, + "content": "Recently, AP-BSN [20] combines pixel-shuffle down-sampling (PD) with the blind spot network (BSN). Though PD can be utilized to meet the noise assumption of BSN, simply combining PD with CNN-based BSN is sub-optimal for dealing with spatially-correlated real noise. It causes damage to local details, thus bringing artifacts to the subsampled images, e.g., aliasing artifact, especially for large PD stride factors [20, 38]. Also, though more advanced designs of BSNs have been proposed [18, 19, 31], CNN-based BSNs fail to capture long-range interactions due to their convolution operator, which is further bounded by the limited receptive field under the blind spot requirement." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.455, + 0.468, + 0.831 + ], + "angle": 0, + "content": "In this paper, we present a novel method, called LG-BPN, to address these issues on self-supervised real image denoising, including the reliance on extra information, the loss of local structures by noise correlation, and also the lacking of modeling distant pixel interaction. LG-BPN can be directly trained without external information. Furthermore, we ease the destruction of fine textures by carefully considering the spatial correlation in real noise, at the same time injecting long-range interaction by tailoring Transformers to the blind spot network. First, for local information, we introduce a densely-sampled patch-masked convolution (DSPMC) module. Based on the prior statistic of real noise spatial correlation, we take more neighbor pixels into account with a denser receptive field, allowing the network to recover more detailed structures. Second, for global information, we introduce a dilated Transformer block (DTB). Under the special blind spot requirement, this greatly enlarges the receptive field compared with previous CNN-based BSNs, permitting more neighbors to be utilized when predicting the central blind spot pixel. These two designs enable us to fully exploit local and global information, respectively. Extensive studies demonstrate that LG-BPN outperforms other state-of-the-art un-/self-supervised methods on real image denoising, as shown in Figure 1. We summarize our contributions as follows:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.84, + 0.468, + 0.901 + ], + "angle": 0, + "content": "- We present a novel self-supervised method called LG-BPN for real-world image denoising, which can effectively encode both the local detailed structure and the capture of global representation." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.092, + 0.892, + 0.166 + ], + "angle": 0, + "content": "- Based on the analysis of real noise spatial correlation, we propose DSPMC module, which takes advantage of the higher sampling density on the neighbor pixels, enabling a denser receptive field for improved local texture recovery." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.176, + 0.892, + 0.235 + ], + "angle": 0, + "content": "- To establish long-distance dependencies in previous CNN-based BSN methods, we introduce DTB, which aggregates global context while complying with the constraint of blind spot receptive field." + }, + { + "type": "list", + "bbox": [ + 0.518, + 0.092, + 0.892, + 0.235 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.248, + 0.642, + 0.264 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.273, + 0.755, + 0.29 + ], + "angle": 0, + "content": "2.1. Supervised Image Denoising" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.296, + 0.892, + 0.568 + ], + "angle": 0, + "content": "DnCNN [36] is the first attempt to apply deep learning techniques to the image denoising task, where the training pairs are synthesized by additive white Gaussian noise (AWGN). Following DnCNN, several methods have been proposed for AWGN noise removal. For instance, FFD-Net [37] advances it by taking the noise map as additional input. While achieving superior performance on AWGN removal, recent studies [2, 12] reveal the poor generalization ability of these models when applied to real noise, due to the gap between the noise distribution. The primary obstruction of real image denoising lies in the deficiency of real noisy-clean pairs. To this end, some real-world denoising datasets are collected under carefully considered conditions [1,4]. Based on these datasets, several methods [7, 12] train the network directly on the real image pairs. Despite the decent performance, data collection can be extremely expensive and labor-intensive. Also, it is infeasible to collect clean images under complex scenes containing motion." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.576, + 0.776, + 0.592 + ], + "angle": 0, + "content": "2.2. Unsupervised Image Denoising" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.6, + 0.891, + 0.659 + ], + "angle": 0, + "content": "Another line of research focuses on the situation where paired data is unavailable, including \\( i) \\) generating pseudo noisy-clean image pairs, \\( ii) \\) generating pseudo noisy-noisy image pairs, and \\( iii) \\) training directly on noisy images." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.66, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Generating pseudo noisy-clean image pairs. In situations where unpaired noisy-clean data is available, generation-based methods seek to synthesize real noise on clean images for aligned training data, which can be used for supervised methods. Inspired by the generative adversarial network (GAN), GCBD [6] synthesizes realistic noisy images to train the denoising network, while its performance is limited by the inaccurate consideration of noise components. UIDNet [31] takes a step further by combining the distilled knowledge of the self-supervised denoising network and extra information from synthetic pairs. C2N [15] considers various noise components in real-world scenarios for more accurate noise synthesis. However, dealing with the gap between unpaired data is still challenging. The mismatch in scene distribution can result in inaccurate generation, thus degrading the quality of synthesized data." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18157" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.096, + 0.089, + 0.872, + 0.263 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.099, + 0.264, + 0.415, + 0.401 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.422, + 0.265, + 0.868, + 0.4 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.409, + 0.893, + 0.451 + ], + "angle": 0, + "content": "Figure 2. The overall architecture of LG-BPN. Our method is composed of two branches, aiming at extracting local textures and global interactions, respectively. For each branch, the input first goes through a DSPMC module, then further processed for the deep feature. Finally, the output of two branches is fused for the denoised result." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.459, + 0.473, + 0.732 + ], + "angle": 0, + "content": "Generating pseudo noisy-noisy image pairs. The semi-supervised method Noise2Noise [21] uses multiple noisy images for training, which can be applied without clean images. However, the acquisition of multiple independent observations under the same scene is still less practical. Therefore, several methods seek to construct noisy-noisy pairs from a single noisy image. Neighbor2Neighbor [14] generates two sub-sampled images under simplified noise assumptions. To handle complex noise distribution in real images, several methods have been proposed, including Noisier2Noise [24], NAC [33] and R2R [26]. Still, these methods either require prior knowledge or are limited by specific constraints, which can be impractical in real situations. Specifically, Noisier2Noise [24] requires noise distribution when synthesizing noisy/noisy pairs. NAC [33] works under the assumption that the noise level is relatively weak. R2R [26] also uses additional information, e.g., noise level function (NLF) and image signal processing (ISP) function." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Training directly on noisy images. Another type of method follows a self-supervised manner, which can be directly trained on the noisy images and free of synthesizing pseudo image pairs. Noise2Void [17] and Noise2Self [3] propose the self-supervised blind-spot strategy by masking the corresponding central pixel. Laine19 [19] and D-BSN [31] are further proposed for advanced BSN designs, while the convolution-based architecture limits their exploitation for long-range dependencies. To ease the information loss by the blind spot, Blind2Unblind [30] introduces a novel re-visible loss term. Unfortunately, the above-mentioned" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.459, + 0.892, + 0.793 + ], + "angle": 0, + "content": "methods work under the assumption that noise is pixel-wise independent, thus inevitably learning identity mapping under spatially-correlated real noise. Towards real image denoising, CVF-SID [25] disentangles the noise components from the clean images, but it assumes the noise is spatially-uncorrelated, which does not match the real noise distribution. Asymmetric pixel shuffle downsampling BSN (APBSN) [20] combines the pixel shuffle downsampling (PD) with a CNN-based BSN [31]. While achieving promising results, local structures are damaged by directly applying the PD operation to the image. Sub-sampled images are corrupted by various artifacts, e.g., aliasing artifacts, which are more pronounced under a large PD stride factor [20,38]. Also, adopting the CNN-based BSN leads to a limited receptive field. Since BSN recovers the central pixels based on its neighbors, fewer available neighbor pixels inevitably lead to performance loss. In summary, this results in the inadequate utilization of information with respect to both local and global contexts. Instead, our method benefits from a denser sampling density for improved local detail extraction, and also enjoys the distant pixel modeling ability for the enlarged receptive field." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.798, + 0.593, + 0.814 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.82, + 0.893, + 0.866 + ], + "angle": 0, + "content": "We first illustrate the overall architecture of LG-BPN in Figure 2, then elaborate on our motivation, and demonstrate our two core designs: DSPMC and DTB." + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.875, + 0.893, + 0.901 + ], + "angle": 0, + "content": "1We use 'global' to differentiate from our 'local' branch. Though a more accurate term is 'non-local', we follow the usage of 'global' as [35]." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18158" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.089, + 0.468, + 0.2 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.203, + 0.466, + 0.319 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.32, + 0.471, + 0.378 + ], + "angle": 0, + "content": "Figure 3. Comparison of receptive field for the central pixel of APBSN and our method. Green pixels contribute to the restoration of central pixel. Blue pixels represent convolution kernel. We realize a denser receptive field by utilizing more neighbor pixels." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.388, + 0.31, + 0.405 + ], + "angle": 0, + "content": "3.1. Motivation and Modeling" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.412, + 0.47, + 0.744 + ], + "angle": 0, + "content": "Despite the decent results on simple synthetic noise removal, the performance of self-supervised denoising methods declines significantly when dealing with real noise, due to its strong spatial noise correlation. This easily breaks the assumption on which most state-of-the-art methods are based, i.e., noise is pixel-wise independent. These methods assume the clean signal of the central pixel is dependent on neighbors, while the noise is independent instead. Thus under real scenarios, they inevitably misinterpret the spatially-dependent noise as clean signals, and fail to recover the underlying clean images. Consequently, careful consideration of the spatial correlation is a must for self-supervised real noise removal. While the existing methods either struggle with poor results when completely ignoring this correlation, or suffer details loss from ill consideration. For example, AP-BSN [20] meets the assumption of the powerful BSN by adopting PD on the input image. As shown in Figure 3, though this breaks the spatial correlation, the sampling density is dramatically decreased by the PD. This severely degrades the extraction of fine details based on the Nyquist-Shannon sampling theorem, i.e., the fidelity of the results shows a positive correlation to sampling density." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.745, + 0.47, + 0.866 + ], + "angle": 0, + "content": "Besides, though BSN is already adapted for state-of-the-art performance [20], its potential is still heavily hampered by their inherent shortage, i.e., the limit on the receptive field by the masked pixels for avoiding identity mapping. Despite the recent advanced BSN designs [19, 31], CNN-based BSNs are still unable to fully address this issue due to their local convolution operator and fail to model the long-distance dependencies. This adversely affects the perfor" + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.088, + 0.701, + 0.206 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.519, + 0.209, + 0.701, + 0.234 + ], + "angle": 0, + "content": "(a) Bar plot of correlation by relative position" + }, + { + "type": "image", + "bbox": [ + 0.719, + 0.094, + 0.868, + 0.208 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.72, + 0.21, + 0.869, + 0.233 + ], + "angle": 0, + "content": "(b) High-correlation pixels mask" + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.239, + 0.892, + 0.323 + ], + "angle": 0, + "content": "Figure 4. Visualization of spatial correlation in real noise. (a) Bar plot of spatial correlation calculated by the correlation coefficient. Note that we scale the height by log norm for better visualization. The higher bar indicates a stronger correlation. (b) The mask of high-correlation pixels. Locations with 0 mean this pixel is strongly correlated to the central pixel, while 1 means not." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.331, + 0.892, + 0.361 + ], + "angle": 0, + "content": "mance of BSN, as the number of neighbors around the blind spot used for inferring is dramatically reduced." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.362, + 0.893, + 0.497 + ], + "angle": 0, + "content": "We aim to tackle both of these challenges in our methods. First, we realize better extraction for detailed textures from the perspective of sampling density. As shown in Figure 3, DSPMC enables a denser sampling rate by leveraging more neighbor pixels, which raises the upper limit of reconstruction quality. Second, by tailoring normal Transformers to a blind fashion, DTB is introduced for its powerful global modeling ability to compensate for the limited receptive field of CNN-based BSNs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.5, + 0.892, + 0.697 + ], + "angle": 0, + "content": "Based on these two modules, we now introduce the overall architecture of our method. As shown in Figure 2, LG-BPN is mainly composed of two branches in parallel, aiming at local and global contexts reconstruction respectively. For the local feature extraction branch, we first apply the \\(9 \\times 9\\) DSPMC module. The densely extracted features are then down-sampled to break the spatial correlation. Then, the feature maps go through dilated convolution with a dilation of 2. For the global branch, the input image first goes through a \\(21 \\times 21\\) DMPMC module with a larger receptive field, which is then processed by DTBs. Finally, the local and global information from the two branches is fused together for the final output." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.71, + 0.882, + 0.727 + ], + "angle": 0, + "content": "3.2. Densely-Sampled Patch-Masked Convolution" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Neither adopting a low sample rate nor sampling all neighbor pixels can be an optimal choice for BSN when tacking real noise. In DSPMC, we aim to extract as much local information as possible, at the same time avoiding misinterpretation by these strongly-correlated neighbor pixels. To this end, we start by presenting the relationship between spatial correlation and the relative position, as shown in Figure 4. Following previous works [20, 38], we use Pearson's correlation coefficient to depict the relationship. Specifically, we first obtain the noise map by subtracting the clean images from the noisy images in SIDD medium [1]" + }, + { + "type": "page_footnote", + "bbox": [ + 0.077, + 0.875, + 0.468, + 0.901 + ], + "angle": 0, + "content": "2We adopt \\(9\\times 9\\) DSPMC in the local branch. Here, the \\(11\\times 11\\) size is shown for illustration purposes to better compare the receptive field." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18159" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.091, + 0.203, + 0.184 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.08, + 0.188, + 0.202, + 0.212 + ], + "angle": 0, + "content": "(a) Kernel location during training" + }, + { + "type": "image", + "bbox": [ + 0.212, + 0.09, + 0.336, + 0.185 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.212, + 0.187, + 0.336, + 0.213 + ], + "angle": 0, + "content": "(b) Shifted kernel location during testing" + }, + { + "type": "image", + "bbox": [ + 0.345, + 0.091, + 0.468, + 0.185 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.345, + 0.187, + 0.469, + 0.222 + ], + "angle": 0, + "content": "(c) Shifted kernel location during testing with dilation" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.222, + 0.47, + 0.292 + ], + "angle": 0, + "content": "Figure 5. Illustration of shifting kernel strategy and dilation of DSPMC. The blue and green points are the kernel locations during training and testing respectively. Yellow arrows indicate the shift direction. This avoids the strongly correlated pixels when training, sampling pixels closer to the center when testing for more details." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.3, + 0.462, + 0.314 + ], + "angle": 0, + "content": "dataset. Then, correlation coefficient can be calculated by:" + }, + { + "type": "equation", + "bbox": [ + 0.165, + 0.32, + 0.469, + 0.354 + ], + "angle": 0, + "content": "\\[\n\\rho_ {N _ {c e n}, N _ {n e i}} = \\frac {\\operatorname {c o v} \\left(N _ {c e n} , N _ {n e i}\\right)}{\\sigma_ {N _ {c e n}} \\sigma_ {N _ {n e i}}}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.358, + 0.469, + 0.462 + ], + "angle": 0, + "content": "where \\(N_{cen}\\) and \\(N_{cen}\\) represent the noise of the central pixel and neighbor pixels respectively. In Figure 4(a), we find that there exist more neighbor pixels which can also be leveraged for prediction. These pixels are not strongly correlated to the center pixel, thus bringing useful information, instead of misinterpretation to BSN. Then, the DSPMC kernel can be calculated as:" + }, + { + "type": "equation", + "bbox": [ + 0.169, + 0.47, + 0.469, + 0.485 + ], + "angle": 0, + "content": "\\[\n\\mathbf {K} _ {D S P M C} = \\mathbf {K} _ {n} \\odot \\mathbf {M a s k} _ {c o r}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.49, + 0.469, + 0.669 + ], + "angle": 0, + "content": "where \\(\\mathbf{K}_{DSPMC}\\) is the kernel of DSPMC, \\(\\mathbf{K}_n\\) is the kernel of the normal convolution, and \\(\\mathbf{Mask}_{cor}\\) is the mask for filtering out highly-correlated pixels shown in Figure 4(b). By integrating this noise distribution prior to sampling locations, our module can effectively take more neighbor pixels while avoiding the strongly correlated pixels. This enables the extracted feature to contain more fine details, and a denser receptive field as well. Also, as shown in Figure 3, since the extracted high-dimension feature already gathers the rich local details, the subsequent feature-level PD can save more useful information compared with the previous image-level PD." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.671, + 0.469, + 0.746 + ], + "angle": 0, + "content": "However, directly applying this module is not an optimal choice: \\( i) \\) the inference stage requires more details compared with training, so directly using the same architecture can damage high-frequency details [20], \\( ii) \\) a large kernel can cause computational inefficiency." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.746, + 0.469, + 0.835 + ], + "angle": 0, + "content": "Kernel shift strategy. As shown in Figure 5(b), for the first concern, we need to obtain more details while testing, focusing on local detailed information closer to the center pixel. Inspired by the deformable convolution [9], we apply a set of fixed offsets on the kernel for each location, which enforce that the kernels are more gathered in the center:" + }, + { + "type": "equation", + "bbox": [ + 0.143, + 0.843, + 0.469, + 0.884 + ], + "angle": 0, + "content": "\\[\n\\mathbf {y} \\left(p _ {0}\\right) = \\sum_ {k = 1} ^ {\\mathbf {K}} w _ {k} \\cdot \\mathbf {x} \\left(p _ {0} + p _ {k} + \\Delta p _ {k}\\right), \\tag {3}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.154, + 0.888, + 0.334, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\Delta p _ {k} = \\text {R a t i o} * (p _ {k} - p _ {0}),\n\\]" + }, + { + "type": "image", + "bbox": [ + 0.502, + 0.089, + 0.623, + 0.182 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.521, + 0.184, + 0.603, + 0.196 + ], + "angle": 0, + "content": "(a) Noisy input" + }, + { + "type": "image", + "bbox": [ + 0.635, + 0.089, + 0.755, + 0.182 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.649, + 0.184, + 0.741, + 0.196 + ], + "angle": 0, + "content": "(b) AP-BSN [20]" + }, + { + "type": "image", + "bbox": [ + 0.767, + 0.089, + 0.887, + 0.182 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.775, + 0.184, + 0.88, + 0.196 + ], + "angle": 0, + "content": "(c) LG-BPN (Ours)" + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.201, + 0.892, + 0.258 + ], + "angle": 0, + "content": "Figure 6. The comparison of the feature map visualization of our method and AP-BSN [20] in the training phase. Our feature map shows clearer edges, validating the superiority of local details extraction of DSPMC by imposing denser sampling locations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.265, + 0.892, + 0.355 + ], + "angle": 0, + "content": "where \\(\\mathbf{K}\\) is the kernel sampling locations, \\(w_{k}\\) is the kernel weight, \\(\\mathbf{x}(p)\\) and \\(\\mathbf{y}(p)\\) denote the features at \\(p\\) in input feature \\(\\mathbf{x}\\) and output feature \\(\\mathbf{y}\\), and \\(\\Delta p\\) is the applied kernel offset. Ratio is the extent we shift the kernel while testing. By adding offsets to the kernel, we can shrink the kernel and capture finer details while testing." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.356, + 0.892, + 0.446 + ], + "angle": 0, + "content": "Dilation in DSPMC. As shown in Figure 5(c), for the second concern, we further decrease the computational cost by adding dilation to the convolution kernel. This imposed sparsity makes our DSPMC computationally efficient especially for large kernel size, at the same time maintaining the dense receptive field for capturing detailed structures." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.447, + 0.892, + 0.612 + ], + "angle": 0, + "content": "Visualization of the extracted feature map. To validate that our DSPMC module achieves a denser receptive field and is thus better at extracting local high-frequency structures, we present the visualization of the feature map. We select the output feature of the local extraction branch, and the corresponding location in AP-BSN. All channels are averaged and normalized for visualization. As shown in Figure 6, in AP-BSN [20], the local fine texture is damaged due to the insufficient use of neighbor signals. Instead, by leveraging more neighbor pixels, our feature map shows shaper edges and preserves more details." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.621, + 0.743, + 0.636 + ], + "angle": 0, + "content": "3.3. Dilated Transformer Block" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.645, + 0.892, + 0.825 + ], + "angle": 0, + "content": "The receptive field of BSN is restricted by the imposed blind spots, while the local operator in CNN-based BSNs further prevents it from gathering global interaction. However, under the special blind spot constraint on the receptive field, it is non-trivial to directly introduce normal Transformer blocks to the BSN. Inspired by the D-BSN [31], we aim to design the Transformer block without information exchange between spatially-adjacent pixels, which satisfies the blind spot requirement when combined with DSPMC. Under these requirements, we carefully consider the design of two core components in the Transformer: the self-attention calculation and the feed-forward layer." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.901 + ], + "angle": 0, + "content": "First, for the self-attention layer, spatial-wise attention enables spatial information exchange and thus does not meet our receptive field requirement. Recently, a grid-like self-attention can meet our requirement [28], while the grid pattern further narrows the receptive field that the blind spot" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18160" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.119, + 0.088, + 0.255, + 0.191 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.139, + 0.193, + 0.232, + 0.206 + ], + "angle": 0, + "content": "(a) AP-BSN [20]" + }, + { + "type": "image", + "bbox": [ + 0.291, + 0.088, + 0.428, + 0.192 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.307, + 0.193, + 0.411, + 0.206 + ], + "angle": 0, + "content": "(b) LG-BPN (Ours)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.21, + 0.47, + 0.267 + ], + "angle": 0, + "content": "Figure 7. The comparison of the receptive field between AP-BSN [20] and our method. We calculate the gradient response to the central pixel. The brighter color represents the higher contribution for recovering the central pixel." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.277, + 0.473, + 0.475 + ], + "angle": 0, + "content": "has reduced. Instead, we adopt channel-wise attention [35] for its unawareness of spatial location and global perception as well. Furthermore, to enhance the local context while preventing information of adjacent pixels, we introduce dilated depth-wise convolution before computing feature similarity. For the input feature \\(\\mathbf{X}\\), the Query \\((\\mathbf{Q})\\), Key \\((\\mathbf{K})\\) and Value \\((\\mathbf{V})\\) matrix is thus calculated by \\(\\mathbf{Q} = g^{Q}(\\mathbf{X})\\), \\(\\mathbf{K} = g^{K}(\\mathbf{X})\\), \\(\\mathbf{V} = g^{V}(\\mathbf{X})\\), where \\(g^{Q}(\\cdot)\\), \\(g^{K}(\\cdot)\\) and \\(g^{V}(\\cdot)\\) denote the dilated \\(3 \\times 3\\) depth-wise convolution. Given the \\(\\mathbf{Q}\\), \\(\\mathbf{K}\\) and \\(\\mathbf{V}\\) matrix, the channel interaction can be obtained by the dot-product, where the attention map is of size \\(\\mathbb{R}^{C \\times C}\\), and \\(C\\) is the number of channels. The overall self-attention layer is represented as:" + }, + { + "type": "equation", + "bbox": [ + 0.132, + 0.484, + 0.469, + 0.522 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\operatorname {A t t e n t i o n} (\\mathbf {Q}, \\mathbf {K}, \\mathbf {V}) = \\mathbf {V} \\operatorname {S o f t m a x} (\\mathbf {K Q}), \\\\ \\hat {\\mathbf {X}} = \\operatorname {A t t e n t i o n} (\\mathbf {Q}, \\mathbf {K}, \\mathbf {V}) + \\mathbf {X}, \\tag {4} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.527, + 0.429, + 0.542 + ], + "angle": 0, + "content": "where \\(\\mathbf{X}\\) and \\(\\hat{\\mathbf{X}}\\) denote the input and output features." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.543, + 0.47, + 0.709 + ], + "angle": 0, + "content": "Second, for the feed-forward layer, adjacent information exchange can be simply avoided by adopting \\(1 \\times 1\\) convolutions only. Nonetheless, this fails to capture local context, which can be critical for restoring high-frequency details. We address this issue by also introducing dilation into the normal \\(3 \\times 3\\) convolution in the feed-forward layer. Then, features extracted by dilated depth-wise convolution go through a gating unit for the non-linearity. This gating unit is the element-wise product of two parallel paths, with one of them activated by the GELU unit. The overall process of the feed-forward layer is formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.168, + 0.719, + 0.469, + 0.777 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathbf {G} ^ {\\mathbf {1}} = g ^ {1} (\\mathrm {L N} (\\mathbf {X})), \\\\ \\mathbf {G} ^ {2} = g ^ {2} (\\mathrm {L N} (\\mathbf {X})), \\tag {5} \\\\ \\hat {\\mathbf {X}} = \\operatorname {G E L U} \\left(\\mathbf {G} ^ {1}\\right) \\odot \\mathbf {G} ^ {2} + \\mathbf {X}, \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.469, + 0.855 + ], + "angle": 0, + "content": "where \\(\\odot\\) is element-wise multiplication, LN denotes layer normalization, \\(g^{1}(\\cdot)\\) and \\(g^{2}(\\cdot)\\) represent the \\(3\\times 3\\) dilated depth-wise convolution. An additional benefit is that, compared to the normal \\(3\\times 3\\) convolution, the introduced dilation can also enlarge the receptive field." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.469, + 0.9 + ], + "angle": 0, + "content": "To prove the effectiveness of the introduced global dependencies, we also plot the receptive field for recovering the central pixel of our method and the CNN-based BSNs" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.152 + ], + "angle": 0, + "content": "in Figure 7. By injecting the long-range interaction into the blind spot network, more neighbor pixels are activated for restoring the central pixels in our method, offering a broader receptive field compared to the previous CNN-based BSNs." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.166, + 0.634, + 0.183 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.191, + 0.734, + 0.208 + ], + "angle": 0, + "content": "4.1. Dataset and Setup Details" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.214, + 0.892, + 0.274 + ], + "angle": 0, + "content": "We train and evaluate our method on two real-world datasets, i.e., SIDD [1] and DND [27]. Note that for the SIDD benchmark dataset and DND benchmark dataset, we submit the output to the website for online evaluation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.275, + 0.892, + 0.395 + ], + "angle": 0, + "content": "Smartphone Image Denoising Dataset (SIDD) [1] contains paired images for real-world denoising by five smartphone cameras. For training, we use the sRGB images from SIDD-Medium including 320 pairs. For validation and evaluation, we use the sRGB images from the SIDD validation set and benchmark set respectively. Each includes 1280 patches of size \\(256 \\times 256\\), where the ground truth images are also provided for the validation set." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.396, + 0.892, + 0.485 + ], + "angle": 0, + "content": "Darmstadt Noise Dataset (DND) [27] contains 50 noisy images for benchmarking without the ground truth provided, and the results can only be obtained via the online submission system. Therefore, we enjoy a fully self-supervised manner and directly train our method on the test set without extra eternal data." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.496, + 0.662, + 0.512 + ], + "angle": 0, + "content": "4.2. Training Details" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.521, + 0.892, + 0.687 + ], + "angle": 0, + "content": "During training, we keep the same setting as the previous work [20]. Specifically, a batch size of 8 is used in the experiment. We adopt \\(\\mathcal{L}_1\\) loss between ground truth and output for training. The learning rate starts with \\(1e - 4\\), where Adam optimizer is adopted. The network is trained with 20 epochs until it fully converges. We implement the method in PyTorch 1.8.0, and train our model on the Nvidia RTX 3090. Two metrics are utilized to evaluate the performance of methods, including peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) [29]. The larger value of PSNR and SSIM implies better fidelity." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.696, + 0.81, + 0.712 + ], + "angle": 0, + "content": "4.3. Evaluation of Real-world Denoising" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.892, + 0.9 + ], + "angle": 0, + "content": "We validate the effectiveness of our method for real-world image denoising on the commonly-used SIDD benchmark dataset and DND benchmark dataset. Table 1 shows the comparison of various methods on SIDD and DND benchmark datasets. Visualization results of several methods addressed in Table 1 on SIDD and DND datasets can be found in Figure 8 and Figure 9. We achieve better results in quantitative and qualitative metrics than previous un-/self-supervised methods. Compared with unsupervised methods trained on unpaired clean-noisy data, LG-BPN does not rely on extra data for synthesizing training pairs, also avoiding the misalignment between the scene distribution. For the" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "18161" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.086, + 0.089, + 0.874, + 0.414 + ], + "angle": 0, + "content": "
Type of supervisionTraining dataMethodSIDDDND
PSNRSSIMPSNRSSIM
Non-learning basedNoneBM3D [8]25.650.68534.510.851
WNNM [11]25.780.80934.670.865
SupervisedSynthesized PairsDnCNN [36]23.660.58332.430.790
CBDNet [12]33.280.86838.050.942
AWGN-M [38]33.99*0.896*38.400.945
Real pairsDnCNN [36]35.34*0.885*37.83*0.929*
AINDNet [16]38.840.95139.340.952
RIDNet [2]38.700.95039.250.952
DIDN [34]39.820.97339.620.954
UnsupervisedNoisy-clean pairsGCBD [6]--35.580.922
UIDNet [13]32.480.897--
C2N [15] + DIDN [34]35.350.93736.380.887
D-BSN [31] + MWCNN [23]--37.930.937
Noisy-noisy pairsNoise2Self [3]29.56†0.808†--
NAC [33]--36.200.925
R2R [26]34.780.898--
Single noisy observationNoise2Void [17]27.68†0.668†--
CVF-SID [25]34.710.91736.500.924
AP-BSN [20]35.970.92538.090.937
LG-BPN (Ours)37.280.93638.430.942
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.423, + 0.895, + 0.48 + ], + "angle": 0, + "content": "Table 1. Quantitative comparison of various methods on SIDD and DND benchmark datasets. Though several supervised methods achieve better results using noisy/clean image pairs, our methods use noisy RGB images only. Results with \\(\\star\\) mean these are reproduced and evaluated by ourselves, since they are not evaluated on the dataset we use in their original paper. The results marked with \\(\\dagger\\) are reported from R2R [26]. Otherwise, we report the official results from SIDD and DND benchmark websites." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.491, + 0.473, + 0.703 + ], + "angle": 0, + "content": "self-supervised methods, NAC [33] works under the weak noise level assumption, while R2R [26] can not be directly applied to sRGB images without extra NLF and ISP functions, both of which harm their performance in real-world situations. In contrast, LG-BPN can be directly applied and not restricted by these assumptions. For methods leveraging single noisy observations, CVF-SID [25] does not consider the strong spatial correlation property in real noise, thus real noise can not be fully removed as shown in Figure 8. APBSN [20] suffers from inadequate sample locations with a limited receptive field, so details are blurred as shown in Figure 9. Instead, LG-BPN carefully integrates the spatial correlation into the network design, simultaneously modeling distant context dependencies." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.712, + 0.367, + 0.728 + ], + "angle": 0, + "content": "4.4. Analysis of the Proposed Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.47, + 0.825 + ], + "angle": 0, + "content": "Dilation factor in densely-sampled convolution. Directly introducing densely-sample convolution can be computationally expensive. To balance the efficiency and the performance, we further introduce the sparsity to the convolution kernel by adding dilation to the original DSPMC. Figure 5(c) shows the illustration of the dilation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.471, + 0.901 + ], + "angle": 0, + "content": "To explore the better trade-off between performance and efficiency, we provide ablation studies on the dilation rate for our DSPMC in both local and global extraction branches. As shown in Table 2(a), a dilation of 1 for \\(9 \\times 9\\) DSPMC and 2 for \\(21 \\times 21\\) DSPMC achieve a better balance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.491, + 0.892, + 0.642 + ], + "angle": 0, + "content": "We claim its reason is that the difference in kernel size results in focusing on varied scales of information. This imposes different sensitivity to the dilation, i.e., sampling density. For relatively small \\( 9 \\times 9 \\) kernels, it focuses more on the local textures, thus adding dilation can notably lower its ability when reconstructing detailed structures. While for the \\( 21 \\times 21 \\) kernel, the larger kernel size makes it aim at the global context more. Thus, the introduced dilation does not severely harm its global extraction ability, at the same time reducing the computational cost." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.643, + 0.892, + 0.763 + ], + "angle": 0, + "content": "The exploitation of local and global information. LGBPN consists of two branches in parallel. Specifically, we combine the small \\(9 \\times 9\\) DSPMC with dilated convolution and the large \\(21 \\times 21\\) DSPMC with DTB, focusing on local and global context processing respectively. To validate the reasonableness of our network architecture, we conduct ablation studies on these components. Table 2(b) shows the results of different combinations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.884 + ], + "angle": 0, + "content": "It can be seen that removing the DSPMC of size \\(9 \\times 9\\) and \\(21 \\times 21\\) in either branch severely degrades the performance. It is on account of the insufficient sampling density, which limits the reconstruction quality according to the Nyquist-Shannon sampling theorem. In this situation, the sampling density is made severely sparse, which causes insufficient utilization of input signals. This performance drop demonstrates the effectiveness of our DSPMC module." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.886, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Furthermore, we validate that the different sizes of" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "18162" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.087, + 0.088, + 0.313, + 0.262 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.138, + 0.265, + 0.277, + 0.279 + ], + "angle": 0, + "content": "SIDD benchmark input" + }, + { + "type": "image", + "bbox": [ + 0.319, + 0.088, + 0.455, + 0.168 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.359, + 0.171, + 0.418, + 0.183 + ], + "angle": 0, + "content": "N2V [17]" + }, + { + "type": "image", + "bbox": [ + 0.465, + 0.088, + 0.601, + 0.168 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.493, + 0.171, + 0.572, + 0.184 + ], + "angle": 0, + "content": "DnCNN [36]" + }, + { + "type": "image", + "bbox": [ + 0.608, + 0.088, + 0.745, + 0.168 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.631, + 0.171, + 0.722, + 0.184 + ], + "angle": 0, + "content": "AWGN-M [38]" + }, + { + "type": "image", + "bbox": [ + 0.752, + 0.088, + 0.888, + 0.168 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.791, + 0.171, + 0.85, + 0.183 + ], + "angle": 0, + "content": "C2N [15]" + }, + { + "type": "image", + "bbox": [ + 0.32, + 0.185, + 0.456, + 0.262 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.36, + 0.266, + 0.416, + 0.278 + ], + "angle": 0, + "content": "R2R [26]" + }, + { + "type": "image", + "bbox": [ + 0.464, + 0.185, + 0.601, + 0.262 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.489, + 0.266, + 0.575, + 0.278 + ], + "angle": 0, + "content": "CVF-SID [25]" + }, + { + "type": "image", + "bbox": [ + 0.608, + 0.185, + 0.744, + 0.262 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.636, + 0.266, + 0.717, + 0.278 + ], + "angle": 0, + "content": "AP-BSN [20]" + }, + { + "type": "image", + "bbox": [ + 0.752, + 0.185, + 0.888, + 0.262 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.773, + 0.266, + 0.868, + 0.278 + ], + "angle": 0, + "content": "LG-BPN (Ours)" + }, + { + "type": "image_caption", + "bbox": [ + 0.14, + 0.288, + 0.827, + 0.302 + ], + "angle": 0, + "content": "Figure 8. Visual quality comparison on SIDD benchmark dataset. Note that the quantitative results are not available." + }, + { + "type": "table", + "bbox": [ + 0.091, + 0.315, + 0.544, + 0.429 + ], + "angle": 0, + "content": "
9x9 DSPMC dilation21x21 DSPMC dilationPSNRSSIMFLOPS (G)Params (M)
1137.230.88588.61.35
1237.320.88629.80.45
1337.230.88317.10.26
2136.850.87984.61.23
2236.840.87525.80.39
2336.990.87313.10.20
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.078, + 0.433, + 0.545, + 0.458 + ], + "angle": 0, + "content": "(a) Ablation studies on dilation rates. Different dilation rate combinations are explored on the DSPMC in the local branch and global branch." + }, + { + "type": "table", + "bbox": [ + 0.576, + 0.315, + 0.89, + 0.429 + ], + "angle": 0, + "content": "
MethodPSNRSSIM
w/o 9×9 DSPMC35.820.855
w/o 21×21 DSPMC36.210.869
Replacing Conv with DTB36.900.880
Replacing DTB with Conv36.820.875
w/o kernel shift35.640.857
LG-BPN (Ours)37.320.886
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.561, + 0.435, + 0.89, + 0.46 + ], + "angle": 0, + "content": "(b) Ablation studies on our proposed method. Improvements can be found with our proposed modules and network design." + }, + { + "type": "table_caption", + "bbox": [ + 0.084, + 0.466, + 0.883, + 0.48 + ], + "angle": 0, + "content": "Table 2. The analysis of our method on the SIDD validation dataset. Experimental results prove the effectiveness of our method design." + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.493, + 0.223, + 0.637 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.095, + 0.639, + 0.202, + 0.649 + ], + "angle": 0, + "content": "DND benchmark input" + }, + { + "type": "image", + "bbox": [ + 0.225, + 0.493, + 0.303, + 0.555 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.238, + 0.556, + 0.288, + 0.566 + ], + "angle": 0, + "content": "NAC [36]" + }, + { + "type": "image_caption", + "bbox": [ + 0.235, + 0.566, + 0.292, + 0.575 + ], + "angle": 0, + "content": "28.50/0.777" + }, + { + "type": "image", + "bbox": [ + 0.305, + 0.493, + 0.384, + 0.555 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.321, + 0.556, + 0.367, + 0.566 + ], + "angle": 0, + "content": "C2N [15]" + }, + { + "type": "image_caption", + "bbox": [ + 0.316, + 0.566, + 0.373, + 0.575 + ], + "angle": 0, + "content": "29.20/0.793" + }, + { + "type": "image", + "bbox": [ + 0.305, + 0.575, + 0.384, + 0.637 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.312, + 0.638, + 0.378, + 0.649 + ], + "angle": 0, + "content": "AP-BSN [20]" + }, + { + "type": "image_caption", + "bbox": [ + 0.316, + 0.649, + 0.373, + 0.657 + ], + "angle": 0, + "content": "32.94/0.889" + }, + { + "type": "image", + "bbox": [ + 0.387, + 0.493, + 0.466, + 0.555 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.39, + 0.556, + 0.462, + 0.566 + ], + "angle": 0, + "content": "AWGN-M [38]" + }, + { + "type": "image_caption", + "bbox": [ + 0.396, + 0.566, + 0.455, + 0.575 + ], + "angle": 0, + "content": "29.26/0.797" + }, + { + "type": "image", + "bbox": [ + 0.387, + 0.575, + 0.466, + 0.637 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.386, + 0.638, + 0.467, + 0.649 + ], + "angle": 0, + "content": "LG-BPN (Ours)" + }, + { + "type": "image_caption", + "bbox": [ + 0.398, + 0.649, + 0.456, + 0.658 + ], + "angle": 0, + "content": "33.37/0.897" + }, + { + "type": "image_caption", + "bbox": [ + 0.08, + 0.664, + 0.466, + 0.678 + ], + "angle": 0, + "content": "Figure 9. Visual quality comparison on DND benchmark dataset." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.47, + 0.901 + ], + "angle": 0, + "content": "DSPMC in local and global feature extraction branches make them focus on various scales of features. Such discrepancy across the scale demands us to treat scale-specific characteristics in a different way. When replacing the dilated convolution in the local branch with our DTB, the lack of local connectivity brings inferior performance. Similarly, when replacing the DTB in the global branch with the dilated convolution, the network is built by convolutions only. It induces a lack of long-range interaction, which greatly limits their recovery quality as well. This proves the superior design of our architecture. By exploiting the locality of convolution with a small DSPMC, also the global dependencies of DTB with a large DSPMC, our architecture enjoys more reasonable exploitation for multi-scale context." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.496, + 0.892, + 0.603 + ], + "angle": 0, + "content": "The effect of kernel shift strategy. Since the requirement for pixel-wise independent noise is different in training and testing, directly applying the same kernel of the training phase while testing will lose image details [20]. We proposed a kernel shift strategy, as illustrated in Figure 5(b). In Table 2(b), the lack of kernel shift causes \\(1.68\\mathrm{dB}\\) drops, proving the effectiveness of our shifting paradigm." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.615, + 0.619, + 0.63 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.639, + 0.892, + 0.835 + ], + "angle": 0, + "content": "In this paper, we propose LG-BPN for self-supervised real image denoising, aiming to address the details lost by the coarse consideration for real noise correlation, and the lack of global interaction by the inherent constraint on the receptive field for BSN. First, we propose DSPMC to fully preserve the local structures. Owing to a denser receptive field, we ease the destruction of fine textures and can thus better reconstruct details. Second, we propose DTB, injecting distant interactions into the previously CNN-based blind spot networks. Since blind spot networks rely on neighbor signals for predicting, more clues can be provided by activating more neighbor pixels. Extensive results on real-world datasets reveal the superior performance of LG-BPN." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.899 + ], + "angle": 0, + "content": "Acknowledgement This work was supported by the National Natural Science Foundation of China under Grants No. 62171038, No. 61827901, No. 62088101, and No. 62006023." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "18163" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.469, + 0.156 + ], + "angle": 0, + "content": "[1] Abdelrahman Abdelhamed, Stephen Lin, and Michael S Brown. A high-quality denoising dataset for smartphone cameras. 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For recent methods targeting real-world denoising, they either suffer from ignoring this spatial correlation, or are limited by the destruction of fine textures for under-considering the correlation. In this paper, we present a novel method called LG-BPN for self-supervised real-world denoising, which takes the spatial correlation statistic into our network design for local detail restoration, and also brings the long-range dependencies modeling ability to previously CNN-based BSN methods. First, based on the correlation statistic, we propose a densely-sampled patch-masked convolution module. By taking more neighbor pixels with low noise correlation into account, we enable a denser local receptive field, preserving more useful information for enhanced fine structure recovery. Second, we propose a dilated Transformer block to allow distant context exploitation in BSN. This global perception addresses the intrinsic deficiency of BSN, whose receptive field is constrained by the blind spot requirement, which can not be fully resolved by the previous CNN-based BSNs. These two designs enable LG-BPN to fully exploit both the detailed structure and the global interaction in a blind manner. Extensive results on real-world datasets demonstrate the superior performance of our method. https://github.com/Wang-XiaoDingdd/LGBPN + +# 1. Introduction + +Image denoising is a fundamental research topic for low-level vision [7, 36]. Noise can greatly degrade the quality of the captured images, thus bringing adverse impacts on the subsequent downstream tasks [22, 32]. Recently, with the rapid development of neural networks, learning-based methods have shown significant advances compared with traditional model-based algorithms [5, 8, 10, 11]. + +![](images/b27ed0159570b1edcbdaf96d72acf305b115b367cbb5dc6f79a263424a1bde4e.jpg) +SIDD Validation: 0018-0031 + +![](images/3c217f0ae1e494fc5826875b40d017568428768552725441d448cad9a6692e33.jpg) +DnCNN [36] 31.17/0.778 + +![](images/387de7990b3d7f8fcb55e140b0e7ee5697d3e84e64b595f9e5c33be566e0b966.jpg) +C2N [15] 28.09/0.706 + +![](images/54cb159d99abf374ec922c6641dff41e987d3df9fda5f3518cebda358842b12d.jpg) +R2R [26] 30.37/0.770 + +![](images/efa2e6537b61e883a458624c0eff67446678b68c3cd335c88bb079af249ade61.jpg) +CVF-SID [25] 28.56/0.792 + +![](images/10db8290130deafb867909a0f32c484112c34a1eaa9fc9bcbd8ee21cf35dd7e7.jpg) +AP-BSN [20] 31.92/0.826 +Figure 1. Visual comparison of various methods on the SIDD validation [1] dataset. Compared with DnCNN [36], C2N [15] and R2R [15], LG-BPN can be trained in a self-supervised manner without extra data. CVF-SID [25] still contains noise in the output, and AP-BSN [20] suffers from the loss of details. + +![](images/e65ddfd2bd58ee5dcb109fa61f91064e9fd1d38d4afda3279286a1986fca1444.jpg) +LG-BPN (Ours) 32.76/0.897 + +Unfortunately, learning-based methods often rely on massive labeled image pairs for training [2, 34, 35]. This can not be simply addressed by synthesizing additive white Gaussian noise (AWGN) pairs, since the gap between AWGN and real noise distribution severely degrades their performance in the real world [2, 12]. To this end, several attempts have been made for collecting real-world datasets [1, 4]. Nonetheless, its application is still hindered by the rigorously-controlled and labor-intensive collection procedure. For instance, capturing ground truth images requires long exposure or multiple shots, which is unavailable in complex situations, e.g., dynamic scenes with motion. + +To alleviate the constraint of the large-scale paired dataset, methods without the need for ground truth have attracted increasing attention. The pioneer work Noise2Noise (N2N) [21] uses paired noisy observations for training, which can be applied when clean images are not available. Still, obtaining such noisy pairs under the same scene is less feasible. To make self-supervised methods more practical, researchers seek to learn from one, instead of pairs of observations. Among these methods, blind-spot networks (BSNs) [3, 17, 19, 30] show significant advances to restore clean pixels by utilizing neighbor pixels, with a special blind spot receptive field requirement. Despite their promising results on simple noise such as AWGN, these methods + +usually work under simplified assumptions, e.g., the noise is pixel-wise independent. This obviously does not hold for real noise, where the distribution can be extremely complex and present a strong spatial correlation. + +Accordingly, a few methods have been proposed for self-supervised real noise removal. Recorrupted-to-Recorrupted (R2R) [26] tries to construct noisy-noisy pairs, while it can not be directly applied without extra information, which is not practical in real situations. CVF-SID [25] disentangles the noise components from noisy images, but it assumes the real noise is spatially invariant and ignores the spatial correlation, which contradicts real noise distribution. + +Recently, AP-BSN [20] combines pixel-shuffle down-sampling (PD) with the blind spot network (BSN). Though PD can be utilized to meet the noise assumption of BSN, simply combining PD with CNN-based BSN is sub-optimal for dealing with spatially-correlated real noise. It causes damage to local details, thus bringing artifacts to the subsampled images, e.g., aliasing artifact, especially for large PD stride factors [20, 38]. Also, though more advanced designs of BSNs have been proposed [18, 19, 31], CNN-based BSNs fail to capture long-range interactions due to their convolution operator, which is further bounded by the limited receptive field under the blind spot requirement. + +In this paper, we present a novel method, called LG-BPN, to address these issues on self-supervised real image denoising, including the reliance on extra information, the loss of local structures by noise correlation, and also the lacking of modeling distant pixel interaction. LG-BPN can be directly trained without external information. Furthermore, we ease the destruction of fine textures by carefully considering the spatial correlation in real noise, at the same time injecting long-range interaction by tailoring Transformers to the blind spot network. First, for local information, we introduce a densely-sampled patch-masked convolution (DSPMC) module. Based on the prior statistic of real noise spatial correlation, we take more neighbor pixels into account with a denser receptive field, allowing the network to recover more detailed structures. Second, for global information, we introduce a dilated Transformer block (DTB). Under the special blind spot requirement, this greatly enlarges the receptive field compared with previous CNN-based BSNs, permitting more neighbors to be utilized when predicting the central blind spot pixel. These two designs enable us to fully exploit local and global information, respectively. Extensive studies demonstrate that LG-BPN outperforms other state-of-the-art un-/self-supervised methods on real image denoising, as shown in Figure 1. We summarize our contributions as follows: + +- We present a novel self-supervised method called LG-BPN for real-world image denoising, which can effectively encode both the local detailed structure and the capture of global representation. + +- Based on the analysis of real noise spatial correlation, we propose DSPMC module, which takes advantage of the higher sampling density on the neighbor pixels, enabling a denser receptive field for improved local texture recovery. +- To establish long-distance dependencies in previous CNN-based BSN methods, we introduce DTB, which aggregates global context while complying with the constraint of blind spot receptive field. + +# 2. Related Work + +# 2.1. Supervised Image Denoising + +DnCNN [36] is the first attempt to apply deep learning techniques to the image denoising task, where the training pairs are synthesized by additive white Gaussian noise (AWGN). Following DnCNN, several methods have been proposed for AWGN noise removal. For instance, FFD-Net [37] advances it by taking the noise map as additional input. While achieving superior performance on AWGN removal, recent studies [2, 12] reveal the poor generalization ability of these models when applied to real noise, due to the gap between the noise distribution. The primary obstruction of real image denoising lies in the deficiency of real noisy-clean pairs. To this end, some real-world denoising datasets are collected under carefully considered conditions [1,4]. Based on these datasets, several methods [7, 12] train the network directly on the real image pairs. Despite the decent performance, data collection can be extremely expensive and labor-intensive. Also, it is infeasible to collect clean images under complex scenes containing motion. + +# 2.2. Unsupervised Image Denoising + +Another line of research focuses on the situation where paired data is unavailable, including $i)$ generating pseudo noisy-clean image pairs, $ii)$ generating pseudo noisy-noisy image pairs, and $iii)$ training directly on noisy images. + +Generating pseudo noisy-clean image pairs. In situations where unpaired noisy-clean data is available, generation-based methods seek to synthesize real noise on clean images for aligned training data, which can be used for supervised methods. Inspired by the generative adversarial network (GAN), GCBD [6] synthesizes realistic noisy images to train the denoising network, while its performance is limited by the inaccurate consideration of noise components. UIDNet [31] takes a step further by combining the distilled knowledge of the self-supervised denoising network and extra information from synthetic pairs. C2N [15] considers various noise components in real-world scenarios for more accurate noise synthesis. However, dealing with the gap between unpaired data is still challenging. The mismatch in scene distribution can result in inaccurate generation, thus degrading the quality of synthesized data. + +![](images/25178a5c59a478e3c382af08c3394bcd4db4ca520f47a22ce2b32b9a83c29643.jpg) + +![](images/9f880eb70b70951d333d60b0a62ba648a5e70dc3576a7476d4a79aaf5784917d.jpg) +Figure 2. The overall architecture of LG-BPN. Our method is composed of two branches, aiming at extracting local textures and global interactions, respectively. For each branch, the input first goes through a DSPMC module, then further processed for the deep feature. Finally, the output of two branches is fused for the denoised result. + +![](images/5429102a2b5b49774e3fddb624ef06d5e0ebeb15a7ec31f9d8e8a1e32de8a7e4.jpg) + +Generating pseudo noisy-noisy image pairs. The semi-supervised method Noise2Noise [21] uses multiple noisy images for training, which can be applied without clean images. However, the acquisition of multiple independent observations under the same scene is still less practical. Therefore, several methods seek to construct noisy-noisy pairs from a single noisy image. Neighbor2Neighbor [14] generates two sub-sampled images under simplified noise assumptions. To handle complex noise distribution in real images, several methods have been proposed, including Noisier2Noise [24], NAC [33] and R2R [26]. Still, these methods either require prior knowledge or are limited by specific constraints, which can be impractical in real situations. Specifically, Noisier2Noise [24] requires noise distribution when synthesizing noisy/noisy pairs. NAC [33] works under the assumption that the noise level is relatively weak. R2R [26] also uses additional information, e.g., noise level function (NLF) and image signal processing (ISP) function. + +Training directly on noisy images. Another type of method follows a self-supervised manner, which can be directly trained on the noisy images and free of synthesizing pseudo image pairs. Noise2Void [17] and Noise2Self [3] propose the self-supervised blind-spot strategy by masking the corresponding central pixel. Laine19 [19] and D-BSN [31] are further proposed for advanced BSN designs, while the convolution-based architecture limits their exploitation for long-range dependencies. To ease the information loss by the blind spot, Blind2Unblind [30] introduces a novel re-visible loss term. Unfortunately, the above-mentioned + +methods work under the assumption that noise is pixel-wise independent, thus inevitably learning identity mapping under spatially-correlated real noise. Towards real image denoising, CVF-SID [25] disentangles the noise components from the clean images, but it assumes the noise is spatially-uncorrelated, which does not match the real noise distribution. Asymmetric pixel shuffle downsampling BSN (APBSN) [20] combines the pixel shuffle downsampling (PD) with a CNN-based BSN [31]. While achieving promising results, local structures are damaged by directly applying the PD operation to the image. Sub-sampled images are corrupted by various artifacts, e.g., aliasing artifacts, which are more pronounced under a large PD stride factor [20,38]. Also, adopting the CNN-based BSN leads to a limited receptive field. Since BSN recovers the central pixels based on its neighbors, fewer available neighbor pixels inevitably lead to performance loss. In summary, this results in the inadequate utilization of information with respect to both local and global contexts. Instead, our method benefits from a denser sampling density for improved local detail extraction, and also enjoys the distant pixel modeling ability for the enlarged receptive field. + +# 3. Method + +We first illustrate the overall architecture of LG-BPN in Figure 2, then elaborate on our motivation, and demonstrate our two core designs: DSPMC and DTB. + +![](images/726b069b2cf47f3f86924b2e701730c033e9e128e21d1b41c1d57238be194fdd.jpg) + +![](images/d81c5d7a9f2819f82a8d31bd3c5d6f489656508465372038e161c61e0aa37ae8.jpg) +Figure 3. Comparison of receptive field for the central pixel of APBSN and our method. Green pixels contribute to the restoration of central pixel. Blue pixels represent convolution kernel. We realize a denser receptive field by utilizing more neighbor pixels. + +# 3.1. Motivation and Modeling + +Despite the decent results on simple synthetic noise removal, the performance of self-supervised denoising methods declines significantly when dealing with real noise, due to its strong spatial noise correlation. This easily breaks the assumption on which most state-of-the-art methods are based, i.e., noise is pixel-wise independent. These methods assume the clean signal of the central pixel is dependent on neighbors, while the noise is independent instead. Thus under real scenarios, they inevitably misinterpret the spatially-dependent noise as clean signals, and fail to recover the underlying clean images. Consequently, careful consideration of the spatial correlation is a must for self-supervised real noise removal. While the existing methods either struggle with poor results when completely ignoring this correlation, or suffer details loss from ill consideration. For example, AP-BSN [20] meets the assumption of the powerful BSN by adopting PD on the input image. As shown in Figure 3, though this breaks the spatial correlation, the sampling density is dramatically decreased by the PD. This severely degrades the extraction of fine details based on the Nyquist-Shannon sampling theorem, i.e., the fidelity of the results shows a positive correlation to sampling density. + +Besides, though BSN is already adapted for state-of-the-art performance [20], its potential is still heavily hampered by their inherent shortage, i.e., the limit on the receptive field by the masked pixels for avoiding identity mapping. Despite the recent advanced BSN designs [19, 31], CNN-based BSNs are still unable to fully address this issue due to their local convolution operator and fail to model the long-distance dependencies. This adversely affects the perfor + +![](images/85acd48737a79ccc066616a60796bd0dc9ad930f3e492d3001d29781b634da6f.jpg) +(a) Bar plot of correlation by relative position + +![](images/820b3f26490cb5c0355ce1fea45ae1b902166381679231d3a5992a1574f6e8a4.jpg) +(b) High-correlation pixels mask +Figure 4. Visualization of spatial correlation in real noise. (a) Bar plot of spatial correlation calculated by the correlation coefficient. Note that we scale the height by log norm for better visualization. The higher bar indicates a stronger correlation. (b) The mask of high-correlation pixels. Locations with 0 mean this pixel is strongly correlated to the central pixel, while 1 means not. + +mance of BSN, as the number of neighbors around the blind spot used for inferring is dramatically reduced. + +We aim to tackle both of these challenges in our methods. First, we realize better extraction for detailed textures from the perspective of sampling density. As shown in Figure 3, DSPMC enables a denser sampling rate by leveraging more neighbor pixels, which raises the upper limit of reconstruction quality. Second, by tailoring normal Transformers to a blind fashion, DTB is introduced for its powerful global modeling ability to compensate for the limited receptive field of CNN-based BSNs. + +Based on these two modules, we now introduce the overall architecture of our method. As shown in Figure 2, LG-BPN is mainly composed of two branches in parallel, aiming at local and global contexts reconstruction respectively. For the local feature extraction branch, we first apply the $9 \times 9$ DSPMC module. The densely extracted features are then down-sampled to break the spatial correlation. Then, the feature maps go through dilated convolution with a dilation of 2. For the global branch, the input image first goes through a $21 \times 21$ DMPMC module with a larger receptive field, which is then processed by DTBs. Finally, the local and global information from the two branches is fused together for the final output. + +# 3.2. Densely-Sampled Patch-Masked Convolution + +Neither adopting a low sample rate nor sampling all neighbor pixels can be an optimal choice for BSN when tacking real noise. In DSPMC, we aim to extract as much local information as possible, at the same time avoiding misinterpretation by these strongly-correlated neighbor pixels. To this end, we start by presenting the relationship between spatial correlation and the relative position, as shown in Figure 4. Following previous works [20, 38], we use Pearson's correlation coefficient to depict the relationship. Specifically, we first obtain the noise map by subtracting the clean images from the noisy images in SIDD medium [1] + +![](images/9e6ed801c5792a07d6bf9c25f1187cd8da08d3da692c5536265864e39de2b38f.jpg) +(a) Kernel location during training + +![](images/2f60473a4421e2fa2e5cf7773538a75814b49d0d71ce915b7ce354803eca9f5b.jpg) +(b) Shifted kernel location during testing + +![](images/0226df4140b9d03ab5312a73cb1c4466f94fbf235520d895b7135905d283cda9.jpg) +(c) Shifted kernel location during testing with dilation +Figure 5. Illustration of shifting kernel strategy and dilation of DSPMC. The blue and green points are the kernel locations during training and testing respectively. Yellow arrows indicate the shift direction. This avoids the strongly correlated pixels when training, sampling pixels closer to the center when testing for more details. + +dataset. Then, correlation coefficient can be calculated by: + +$$ +\rho_ {N _ {c e n}, N _ {n e i}} = \frac {\operatorname {c o v} \left(N _ {c e n} , N _ {n e i}\right)}{\sigma_ {N _ {c e n}} \sigma_ {N _ {n e i}}}, \tag {1} +$$ + +where $N_{cen}$ and $N_{cen}$ represent the noise of the central pixel and neighbor pixels respectively. In Figure 4(a), we find that there exist more neighbor pixels which can also be leveraged for prediction. These pixels are not strongly correlated to the center pixel, thus bringing useful information, instead of misinterpretation to BSN. Then, the DSPMC kernel can be calculated as: + +$$ +\mathbf {K} _ {D S P M C} = \mathbf {K} _ {n} \odot \mathbf {M a s k} _ {c o r}, \tag {2} +$$ + +where $\mathbf{K}_{DSPMC}$ is the kernel of DSPMC, $\mathbf{K}_n$ is the kernel of the normal convolution, and $\mathbf{Mask}_{cor}$ is the mask for filtering out highly-correlated pixels shown in Figure 4(b). By integrating this noise distribution prior to sampling locations, our module can effectively take more neighbor pixels while avoiding the strongly correlated pixels. This enables the extracted feature to contain more fine details, and a denser receptive field as well. Also, as shown in Figure 3, since the extracted high-dimension feature already gathers the rich local details, the subsequent feature-level PD can save more useful information compared with the previous image-level PD. + +However, directly applying this module is not an optimal choice: $i)$ the inference stage requires more details compared with training, so directly using the same architecture can damage high-frequency details [20], $ii)$ a large kernel can cause computational inefficiency. + +Kernel shift strategy. As shown in Figure 5(b), for the first concern, we need to obtain more details while testing, focusing on local detailed information closer to the center pixel. Inspired by the deformable convolution [9], we apply a set of fixed offsets on the kernel for each location, which enforce that the kernels are more gathered in the center: + +$$ +\mathbf {y} \left(p _ {0}\right) = \sum_ {k = 1} ^ {\mathbf {K}} w _ {k} \cdot \mathbf {x} \left(p _ {0} + p _ {k} + \Delta p _ {k}\right), \tag {3} +$$ + +$$ +\Delta p _ {k} = \text {R a t i o} * (p _ {k} - p _ {0}), +$$ + +![](images/695d932f9aa4dd65d657b1334a75abadacba3455a1e460a309193ce5816e6cd7.jpg) +(a) Noisy input +Figure 6. The comparison of the feature map visualization of our method and AP-BSN [20] in the training phase. Our feature map shows clearer edges, validating the superiority of local details extraction of DSPMC by imposing denser sampling locations. + +![](images/b1a6cf48ff7abd0b3f8651874629209fc35baad7fd59d9ed3020df0236719c1b.jpg) +(b) AP-BSN [20] + +![](images/ff1eec17441fd823b22d1a795b311175dd883e72e15116c50db964942da66b23.jpg) +(c) LG-BPN (Ours) + +where $\mathbf{K}$ is the kernel sampling locations, $w_{k}$ is the kernel weight, $\mathbf{x}(p)$ and $\mathbf{y}(p)$ denote the features at $p$ in input feature $\mathbf{x}$ and output feature $\mathbf{y}$ , and $\Delta p$ is the applied kernel offset. Ratio is the extent we shift the kernel while testing. By adding offsets to the kernel, we can shrink the kernel and capture finer details while testing. + +Dilation in DSPMC. As shown in Figure 5(c), for the second concern, we further decrease the computational cost by adding dilation to the convolution kernel. This imposed sparsity makes our DSPMC computationally efficient especially for large kernel size, at the same time maintaining the dense receptive field for capturing detailed structures. + +Visualization of the extracted feature map. To validate that our DSPMC module achieves a denser receptive field and is thus better at extracting local high-frequency structures, we present the visualization of the feature map. We select the output feature of the local extraction branch, and the corresponding location in AP-BSN. All channels are averaged and normalized for visualization. As shown in Figure 6, in AP-BSN [20], the local fine texture is damaged due to the insufficient use of neighbor signals. Instead, by leveraging more neighbor pixels, our feature map shows shaper edges and preserves more details. + +# 3.3. Dilated Transformer Block + +The receptive field of BSN is restricted by the imposed blind spots, while the local operator in CNN-based BSNs further prevents it from gathering global interaction. However, under the special blind spot constraint on the receptive field, it is non-trivial to directly introduce normal Transformer blocks to the BSN. Inspired by the D-BSN [31], we aim to design the Transformer block without information exchange between spatially-adjacent pixels, which satisfies the blind spot requirement when combined with DSPMC. Under these requirements, we carefully consider the design of two core components in the Transformer: the self-attention calculation and the feed-forward layer. + +First, for the self-attention layer, spatial-wise attention enables spatial information exchange and thus does not meet our receptive field requirement. Recently, a grid-like self-attention can meet our requirement [28], while the grid pattern further narrows the receptive field that the blind spot + +![](images/50862906fd61bda8b28d301d511f896fc3fced26f456b3325aac7d550eafa92e.jpg) +(a) AP-BSN [20] + +![](images/bab93a1ec28ac9d2b411f20df875127c6c3108ec5e82a6a7237bb12de2f6af8c.jpg) +(b) LG-BPN (Ours) +Figure 7. The comparison of the receptive field between AP-BSN [20] and our method. We calculate the gradient response to the central pixel. The brighter color represents the higher contribution for recovering the central pixel. + +has reduced. Instead, we adopt channel-wise attention [35] for its unawareness of spatial location and global perception as well. Furthermore, to enhance the local context while preventing information of adjacent pixels, we introduce dilated depth-wise convolution before computing feature similarity. For the input feature $\mathbf{X}$ , the Query $(\mathbf{Q})$ , Key $(\mathbf{K})$ and Value $(\mathbf{V})$ matrix is thus calculated by $\mathbf{Q} = g^{Q}(\mathbf{X})$ , $\mathbf{K} = g^{K}(\mathbf{X})$ , $\mathbf{V} = g^{V}(\mathbf{X})$ , where $g^{Q}(\cdot)$ , $g^{K}(\cdot)$ and $g^{V}(\cdot)$ denote the dilated $3 \times 3$ depth-wise convolution. Given the $\mathbf{Q}$ , $\mathbf{K}$ and $\mathbf{V}$ matrix, the channel interaction can be obtained by the dot-product, where the attention map is of size $\mathbb{R}^{C \times C}$ , and $C$ is the number of channels. The overall self-attention layer is represented as: + +$$ +\begin{array}{l} \operatorname {A t t e n t i o n} (\mathbf {Q}, \mathbf {K}, \mathbf {V}) = \mathbf {V} \operatorname {S o f t m a x} (\mathbf {K Q}), \\ \hat {\mathbf {X}} = \operatorname {A t t e n t i o n} (\mathbf {Q}, \mathbf {K}, \mathbf {V}) + \mathbf {X}, \tag {4} \\ \end{array} +$$ + +where $\mathbf{X}$ and $\hat{\mathbf{X}}$ denote the input and output features. + +Second, for the feed-forward layer, adjacent information exchange can be simply avoided by adopting $1 \times 1$ convolutions only. Nonetheless, this fails to capture local context, which can be critical for restoring high-frequency details. We address this issue by also introducing dilation into the normal $3 \times 3$ convolution in the feed-forward layer. Then, features extracted by dilated depth-wise convolution go through a gating unit for the non-linearity. This gating unit is the element-wise product of two parallel paths, with one of them activated by the GELU unit. The overall process of the feed-forward layer is formulated as: + +$$ +\begin{array}{l} \mathbf {G} ^ {\mathbf {1}} = g ^ {1} (\mathrm {L N} (\mathbf {X})), \\ \mathbf {G} ^ {2} = g ^ {2} (\mathrm {L N} (\mathbf {X})), \tag {5} \\ \hat {\mathbf {X}} = \operatorname {G E L U} \left(\mathbf {G} ^ {1}\right) \odot \mathbf {G} ^ {2} + \mathbf {X}, \\ \end{array} +$$ + +where $\odot$ is element-wise multiplication, LN denotes layer normalization, $g^{1}(\cdot)$ and $g^{2}(\cdot)$ represent the $3\times 3$ dilated depth-wise convolution. An additional benefit is that, compared to the normal $3\times 3$ convolution, the introduced dilation can also enlarge the receptive field. + +To prove the effectiveness of the introduced global dependencies, we also plot the receptive field for recovering the central pixel of our method and the CNN-based BSNs + +in Figure 7. By injecting the long-range interaction into the blind spot network, more neighbor pixels are activated for restoring the central pixels in our method, offering a broader receptive field compared to the previous CNN-based BSNs. + +# 4. Experiments + +# 4.1. Dataset and Setup Details + +We train and evaluate our method on two real-world datasets, i.e., SIDD [1] and DND [27]. Note that for the SIDD benchmark dataset and DND benchmark dataset, we submit the output to the website for online evaluation. + +Smartphone Image Denoising Dataset (SIDD) [1] contains paired images for real-world denoising by five smartphone cameras. For training, we use the sRGB images from SIDD-Medium including 320 pairs. For validation and evaluation, we use the sRGB images from the SIDD validation set and benchmark set respectively. Each includes 1280 patches of size $256 \times 256$ , where the ground truth images are also provided for the validation set. + +Darmstadt Noise Dataset (DND) [27] contains 50 noisy images for benchmarking without the ground truth provided, and the results can only be obtained via the online submission system. Therefore, we enjoy a fully self-supervised manner and directly train our method on the test set without extra eternal data. + +# 4.2. Training Details + +During training, we keep the same setting as the previous work [20]. Specifically, a batch size of 8 is used in the experiment. We adopt $\mathcal{L}_1$ loss between ground truth and output for training. The learning rate starts with $1e - 4$ , where Adam optimizer is adopted. The network is trained with 20 epochs until it fully converges. We implement the method in PyTorch 1.8.0, and train our model on the Nvidia RTX 3090. Two metrics are utilized to evaluate the performance of methods, including peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) [29]. The larger value of PSNR and SSIM implies better fidelity. + +# 4.3. Evaluation of Real-world Denoising + +We validate the effectiveness of our method for real-world image denoising on the commonly-used SIDD benchmark dataset and DND benchmark dataset. Table 1 shows the comparison of various methods on SIDD and DND benchmark datasets. Visualization results of several methods addressed in Table 1 on SIDD and DND datasets can be found in Figure 8 and Figure 9. We achieve better results in quantitative and qualitative metrics than previous un-/self-supervised methods. Compared with unsupervised methods trained on unpaired clean-noisy data, LG-BPN does not rely on extra data for synthesizing training pairs, also avoiding the misalignment between the scene distribution. For the + +
Type of supervisionTraining dataMethodSIDDDND
PSNRSSIMPSNRSSIM
Non-learning basedNoneBM3D [8]25.650.68534.510.851
WNNM [11]25.780.80934.670.865
SupervisedSynthesized PairsDnCNN [36]23.660.58332.430.790
CBDNet [12]33.280.86838.050.942
AWGN-M [38]33.99*0.896*38.400.945
Real pairsDnCNN [36]35.34*0.885*37.83*0.929*
AINDNet [16]38.840.95139.340.952
RIDNet [2]38.700.95039.250.952
DIDN [34]39.820.97339.620.954
UnsupervisedNoisy-clean pairsGCBD [6]--35.580.922
UIDNet [13]32.480.897--
C2N [15] + DIDN [34]35.350.93736.380.887
D-BSN [31] + MWCNN [23]--37.930.937
Noisy-noisy pairsNoise2Self [3]29.56†0.808†--
NAC [33]--36.200.925
R2R [26]34.780.898--
Single noisy observationNoise2Void [17]27.68†0.668†--
CVF-SID [25]34.710.91736.500.924
AP-BSN [20]35.970.92538.090.937
LG-BPN (Ours)37.280.93638.430.942
+ +Table 1. Quantitative comparison of various methods on SIDD and DND benchmark datasets. Though several supervised methods achieve better results using noisy/clean image pairs, our methods use noisy RGB images only. Results with $\star$ mean these are reproduced and evaluated by ourselves, since they are not evaluated on the dataset we use in their original paper. The results marked with $\dagger$ are reported from R2R [26]. Otherwise, we report the official results from SIDD and DND benchmark websites. + +self-supervised methods, NAC [33] works under the weak noise level assumption, while R2R [26] can not be directly applied to sRGB images without extra NLF and ISP functions, both of which harm their performance in real-world situations. In contrast, LG-BPN can be directly applied and not restricted by these assumptions. For methods leveraging single noisy observations, CVF-SID [25] does not consider the strong spatial correlation property in real noise, thus real noise can not be fully removed as shown in Figure 8. APBSN [20] suffers from inadequate sample locations with a limited receptive field, so details are blurred as shown in Figure 9. Instead, LG-BPN carefully integrates the spatial correlation into the network design, simultaneously modeling distant context dependencies. + +# 4.4. Analysis of the Proposed Method + +Dilation factor in densely-sampled convolution. Directly introducing densely-sample convolution can be computationally expensive. To balance the efficiency and the performance, we further introduce the sparsity to the convolution kernel by adding dilation to the original DSPMC. Figure 5(c) shows the illustration of the dilation. + +To explore the better trade-off between performance and efficiency, we provide ablation studies on the dilation rate for our DSPMC in both local and global extraction branches. As shown in Table 2(a), a dilation of 1 for $9 \times 9$ DSPMC and 2 for $21 \times 21$ DSPMC achieve a better balance. + +We claim its reason is that the difference in kernel size results in focusing on varied scales of information. This imposes different sensitivity to the dilation, i.e., sampling density. For relatively small $9 \times 9$ kernels, it focuses more on the local textures, thus adding dilation can notably lower its ability when reconstructing detailed structures. While for the $21 \times 21$ kernel, the larger kernel size makes it aim at the global context more. Thus, the introduced dilation does not severely harm its global extraction ability, at the same time reducing the computational cost. + +The exploitation of local and global information. LGBPN consists of two branches in parallel. Specifically, we combine the small $9 \times 9$ DSPMC with dilated convolution and the large $21 \times 21$ DSPMC with DTB, focusing on local and global context processing respectively. To validate the reasonableness of our network architecture, we conduct ablation studies on these components. Table 2(b) shows the results of different combinations. + +It can be seen that removing the DSPMC of size $9 \times 9$ and $21 \times 21$ in either branch severely degrades the performance. It is on account of the insufficient sampling density, which limits the reconstruction quality according to the Nyquist-Shannon sampling theorem. In this situation, the sampling density is made severely sparse, which causes insufficient utilization of input signals. This performance drop demonstrates the effectiveness of our DSPMC module. + +Furthermore, we validate that the different sizes of + +![](images/0a679e6d9787e67073e454372e4316dc7dd5db81d978ec535e32bb7ee5d6f6b8.jpg) +SIDD benchmark input + +![](images/5fd3001ca8c868f123c02493662aef0aff464ab8c5563d55c1f64466ae84d6cc.jpg) +N2V [17] + +![](images/8c7bfe4fbceba170433d10f174e2c80692df33c2a0fe717981480e70c4202e40.jpg) + +![](images/8ccf2714dd0838b9c5833746fde64282d3a368f84cb232751a0cb21e24d6f892.jpg) + +![](images/73f55e134fc87843219db3ac5a30d2e84201cd2d7b77bd346df2f0e7bbb03ee4.jpg) +C2N [15] + +![](images/cb2a4def2d50c5b11f6de58d37f068e888e2b679bc27a0d9c6cabcbd57551e6e.jpg) +R2R [26] +Figure 8. Visual quality comparison on SIDD benchmark dataset. Note that the quantitative results are not available. + +![](images/ceef7db249ebad747b91a28691e452db1a657a52b0e8b2019ce5b05312235a90.jpg) +DnCNN [36] +CVF-SID [25] + +![](images/2354a17d50448eee416327728869966eb4b2fe36650f05e308e7b48d914fb28a.jpg) +AWGN-M [38] +AP-BSN [20] + +![](images/fdcc27c04a5056381699a67b02ff4f5a3b7699c5ad5e73081686ce750930f71f.jpg) +LG-BPN (Ours) + +
9x9 DSPMC dilation21x21 DSPMC dilationPSNRSSIMFLOPS (G)Params (M)
1137.230.88588.61.35
1237.320.88629.80.45
1337.230.88317.10.26
2136.850.87984.61.23
2236.840.87525.80.39
2336.990.87313.10.20
+ +(a) Ablation studies on dilation rates. Different dilation rate combinations are explored on the DSPMC in the local branch and global branch. + +
MethodPSNRSSIM
w/o 9×9 DSPMC35.820.855
w/o 21×21 DSPMC36.210.869
Replacing Conv with DTB36.900.880
Replacing DTB with Conv36.820.875
w/o kernel shift35.640.857
LG-BPN (Ours)37.320.886
+ +(b) Ablation studies on our proposed method. Improvements can be found with our proposed modules and network design. + +Table 2. The analysis of our method on the SIDD validation dataset. Experimental results prove the effectiveness of our method design. + +![](images/bcb3430696ba746a63a80ccc98ca6bc53819e0615146275f7e1207faed66bab9.jpg) +DND benchmark input +28.50/0.777 +Figure 9. Visual quality comparison on DND benchmark dataset. + +![](images/434d07212965afcb767e83b940a150db371db9b5d6e6cf67cc54d869b88b220b.jpg) +NAC [36] + +![](images/b8a44209ca2f0012690a24043573399d397334b484ec772285ddc4c6f907f59e.jpg) +C2N [15] + +![](images/23bf0f2d1561402c0cf94079855ff1121f99326c04bad70e52c18b7d12a01774.jpg) +29.20/0.793 +AP-BSN [20] +32.94/0.889 + +![](images/25f5a632bbf009a3201b5f44afb6b9fc362f7c5a1b9dd77acbdc4af02044b96e.jpg) +AWGN-M [38] + +![](images/25ce448dd987ba6d6e07a79f0264c2d2f0b8301c3bb99fc2ca82c104638b3df0.jpg) +29.26/0.797 +LG-BPN (Ours) +33.37/0.897 + +DSPMC in local and global feature extraction branches make them focus on various scales of features. Such discrepancy across the scale demands us to treat scale-specific characteristics in a different way. When replacing the dilated convolution in the local branch with our DTB, the lack of local connectivity brings inferior performance. Similarly, when replacing the DTB in the global branch with the dilated convolution, the network is built by convolutions only. It induces a lack of long-range interaction, which greatly limits their recovery quality as well. This proves the superior design of our architecture. By exploiting the locality of convolution with a small DSPMC, also the global dependencies of DTB with a large DSPMC, our architecture enjoys more reasonable exploitation for multi-scale context. + +The effect of kernel shift strategy. Since the requirement for pixel-wise independent noise is different in training and testing, directly applying the same kernel of the training phase while testing will lose image details [20]. We proposed a kernel shift strategy, as illustrated in Figure 5(b). In Table 2(b), the lack of kernel shift causes $1.68\mathrm{dB}$ drops, proving the effectiveness of our shifting paradigm. + +# 5. Conclusion + +In this paper, we propose LG-BPN for self-supervised real image denoising, aiming to address the details lost by the coarse consideration for real noise correlation, and the lack of global interaction by the inherent constraint on the receptive field for BSN. First, we propose DSPMC to fully preserve the local structures. Owing to a denser receptive field, we ease the destruction of fine textures and can thus better reconstruct details. Second, we propose DTB, injecting distant interactions into the previously CNN-based blind spot networks. Since blind spot networks rely on neighbor signals for predicting, more clues can be provided by activating more neighbor pixels. Extensive results on real-world datasets reveal the superior performance of LG-BPN. + +Acknowledgement This work was supported by the National Natural Science Foundation of China under Grants No. 62171038, No. 61827901, No. 62088101, and No. 62006023. + +# References + +[1] Abdelrahman Abdelhamed, Stephen Lin, and Michael S Brown. A high-quality denoising dataset for smartphone cameras. In CVPR, pages 1692-1700, 2018. 1, 2, 4, 6 +[2] Saeed Anwar and Nick Barnes. Real image denoising with feature attention. In ICCV, pages 3155-3164, 2019. 1, 2, 7 +[3] Joshua Batson and Loic Royer. Noise2self: Blind denoising by self-supervision. In ICML, pages 524-533, 2019. 1, 3, 7 +[4] Benoit Brummer and Christophe De Vleeschouwer. Natural image noise dataset. In CVPR Workshops, pages 0-0, 2019. 1, 2 +[5] Antoni Buades, Bartomeu Coll, and J-M Morel. A non-local algorithm for image denoising. In CVPR, pages 60-65, 2005. 1 +[6] Jingwen Chen, Jiawei Chen, Hongyang Chao, and Ming Yang. 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Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 613, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 613, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 613, + 287, + 696 + ], + "type": "text", + "content": "Image denoising is a fundamental research topic for low-level vision [7, 36]. Noise can greatly degrade the quality of the captured images, thus bringing adverse impacts on the subsequent downstream tasks [22, 32]. 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Visual comparison of various methods on the SIDD validation [1] dataset. Compared with DnCNN [36], C2N [15] and R2R [15], LG-BPN can be trained in a self-supervised manner without extra data. CVF-SID [25] still contains noise in the output, and AP-BSN [20] suffers from the loss of details." + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "image_caption" + } + ], + "index": 20 + }, + { + "type": "image", + "bbox": [ + 496, + 289, + 545, + 329 + ], + "blocks": [ + { + "bbox": [ + 496, + 289, + 545, + 329 + ], + "lines": [ + { + "bbox": [ + 496, + 289, + 545, + 329 + ], + "spans": [ + { + "bbox": [ + 496, + 289, + 545, + 329 + ], + "type": "image", + "image_path": "e65ddfd2bd58ee5dcb109fa61f91064e9fd1d38d4afda3279286a1986fca1444.jpg" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 496, + 331, + 545, + 346 + ], + "lines": [ + { + "bbox": [ + 496, + 331, + 545, + 346 + ], + "spans": [ + { + "bbox": [ + 496, + 331, + 545, + 346 + ], + "type": "text", + "content": "LG-BPN (Ours) 32.76/0.897" + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_caption" + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 414, + 546, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 414, + 546, + 557 + ], + "spans": [ + { + "bbox": [ + 304, + 414, + 546, + 557 + ], + "type": "text", + "content": "Unfortunately, learning-based methods often rely on massive labeled image pairs for training [2, 34, 35]. This can not be simply addressed by synthesizing additive white Gaussian noise (AWGN) pairs, since the gap between AWGN and real noise distribution severely degrades their performance in the real world [2, 12]. To this end, several attempts have been made for collecting real-world datasets [1, 4]. Nonetheless, its application is still hindered by the rigorously-controlled and labor-intensive collection procedure. For instance, capturing ground truth images requires long exposure or multiple shots, which is unavailable in complex situations, e.g., dynamic scenes with motion." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 304, + 558, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 547, + 714 + ], + "type": "text", + "content": "To alleviate the constraint of the large-scale paired dataset, methods without the need for ground truth have attracted increasing attention. The pioneer work Noise2Noise (N2N) [21] uses paired noisy observations for training, which can be applied when clean images are not available. Still, obtaining such noisy pairs under the same scene is less feasible. To make self-supervised methods more practical, researchers seek to learn from one, instead of pairs of observations. Among these methods, blind-spot networks (BSNs) [3, 17, 19, 30] show significant advances to restore clean pixels by utilizing neighbor pixels, with a special blind spot receptive field requirement. Despite their promising results on simple noise such as AWGN, these methods" + } + ] + } + ], + "index": 26 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 137, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 137, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 137, + 712 + ], + "type": "text", + "content": "*Corresponding Author" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "18156" + } + ] + } + ], + "index": 28 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": "usually work under simplified assumptions, e.g., the noise is pixel-wise independent. This obviously does not hold for real noise, where the distribution can be extremely complex and present a strong spatial correlation." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 121, + 286, + 215 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 121, + 286, + 215 + ], + "spans": [ + { + "bbox": [ + 46, + 121, + 286, + 215 + ], + "type": "text", + "content": "Accordingly, a few methods have been proposed for self-supervised real noise removal. Recorrupted-to-Recorrupted (R2R) [26] tries to construct noisy-noisy pairs, while it can not be directly applied without extra information, which is not practical in real situations. CVF-SID [25] disentangles the noise components from noisy images, but it assumes the real noise is spatially invariant and ignores the spatial correlation, which contradicts real noise distribution." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 216, + 286, + 357 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 216, + 286, + 357 + ], + "spans": [ + { + "bbox": [ + 46, + 216, + 286, + 357 + ], + "type": "text", + "content": "Recently, AP-BSN [20] combines pixel-shuffle down-sampling (PD) with the blind spot network (BSN). Though PD can be utilized to meet the noise assumption of BSN, simply combining PD with CNN-based BSN is sub-optimal for dealing with spatially-correlated real noise. It causes damage to local details, thus bringing artifacts to the subsampled images, e.g., aliasing artifact, especially for large PD stride factors [20, 38]. Also, though more advanced designs of BSNs have been proposed [18, 19, 31], CNN-based BSNs fail to capture long-range interactions due to their convolution operator, which is further bounded by the limited receptive field under the blind spot requirement." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 360, + 286, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 360, + 286, + 658 + ], + "spans": [ + { + "bbox": [ + 46, + 360, + 286, + 658 + ], + "type": "text", + "content": "In this paper, we present a novel method, called LG-BPN, to address these issues on self-supervised real image denoising, including the reliance on extra information, the loss of local structures by noise correlation, and also the lacking of modeling distant pixel interaction. LG-BPN can be directly trained without external information. Furthermore, we ease the destruction of fine textures by carefully considering the spatial correlation in real noise, at the same time injecting long-range interaction by tailoring Transformers to the blind spot network. First, for local information, we introduce a densely-sampled patch-masked convolution (DSPMC) module. Based on the prior statistic of real noise spatial correlation, we take more neighbor pixels into account with a denser receptive field, allowing the network to recover more detailed structures. Second, for global information, we introduce a dilated Transformer block (DTB). Under the special blind spot requirement, this greatly enlarges the receptive field compared with previous CNN-based BSNs, permitting more neighbors to be utilized when predicting the central blind spot pixel. These two designs enable us to fully exploit local and global information, respectively. Extensive studies demonstrate that LG-BPN outperforms other state-of-the-art un-/self-supervised methods on real image denoising, as shown in Figure 1. We summarize our contributions as follows:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 58, + 665, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 665, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 665, + 286, + 713 + ], + "type": "text", + "content": "- We present a novel self-supervised method called LG-BPN for real-world image denoising, which can effectively encode both the local detailed structure and the capture of global representation." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 317, + 72, + 545, + 186 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 317, + 72, + 545, + 131 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 72, + 545, + 131 + ], + "spans": [ + { + "bbox": [ + 317, + 72, + 545, + 131 + ], + "type": "text", + "content": "- Based on the analysis of real noise spatial correlation, we propose DSPMC module, which takes advantage of the higher sampling density on the neighbor pixels, enabling a denser receptive field for improved local texture recovery." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 317, + 139, + 545, + 186 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 139, + 545, + 186 + ], + "spans": [ + { + "bbox": [ + 317, + 139, + 545, + 186 + ], + "type": "text", + "content": "- To establish long-distance dependencies in previous CNN-based BSN methods, we introduce DTB, which aggregates global context while complying with the constraint of blind spot receptive field." + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 196, + 392, + 209 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 196, + 392, + 209 + ], + "spans": [ + { + "bbox": [ + 306, + 196, + 392, + 209 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 216, + 462, + 229 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 216, + 462, + 229 + ], + "spans": [ + { + "bbox": [ + 306, + 216, + 462, + 229 + ], + "type": "text", + "content": "2.1. Supervised Image Denoising" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 234, + 545, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 234, + 545, + 449 + ], + "spans": [ + { + "bbox": [ + 304, + 234, + 545, + 449 + ], + "type": "text", + "content": "DnCNN [36] is the first attempt to apply deep learning techniques to the image denoising task, where the training pairs are synthesized by additive white Gaussian noise (AWGN). Following DnCNN, several methods have been proposed for AWGN noise removal. For instance, FFD-Net [37] advances it by taking the noise map as additional input. While achieving superior performance on AWGN removal, recent studies [2, 12] reveal the poor generalization ability of these models when applied to real noise, due to the gap between the noise distribution. The primary obstruction of real image denoising lies in the deficiency of real noisy-clean pairs. To this end, some real-world denoising datasets are collected under carefully considered conditions [1,4]. Based on these datasets, several methods [7, 12] train the network directly on the real image pairs. Despite the decent performance, data collection can be extremely expensive and labor-intensive. Also, it is infeasible to collect clean images under complex scenes containing motion." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 456, + 474, + 468 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 456, + 474, + 468 + ], + "spans": [ + { + "bbox": [ + 306, + 456, + 474, + 468 + ], + "type": "text", + "content": "2.2. Unsupervised Image Denoising" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 475, + 545, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 475, + 545, + 521 + ], + "spans": [ + { + "bbox": [ + 304, + 475, + 545, + 521 + ], + "type": "text", + "content": "Another line of research focuses on the situation where paired data is unavailable, including " + }, + { + "bbox": [ + 304, + 475, + 545, + 521 + ], + "type": "inline_equation", + "content": "i)" + }, + { + "bbox": [ + 304, + 475, + 545, + 521 + ], + "type": "text", + "content": " generating pseudo noisy-clean image pairs, " + }, + { + "bbox": [ + 304, + 475, + 545, + 521 + ], + "type": "inline_equation", + "content": "ii)" + }, + { + "bbox": [ + 304, + 475, + 545, + 521 + ], + "type": "text", + "content": " generating pseudo noisy-noisy image pairs, and " + }, + { + "bbox": [ + 304, + 475, + 545, + 521 + ], + "type": "inline_equation", + "content": "iii)" + }, + { + "bbox": [ + 304, + 475, + 545, + 521 + ], + "type": "text", + "content": " training directly on noisy images." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "text", + "content": "Generating pseudo noisy-clean image pairs. In situations where unpaired noisy-clean data is available, generation-based methods seek to synthesize real noise on clean images for aligned training data, which can be used for supervised methods. Inspired by the generative adversarial network (GAN), GCBD [6] synthesizes realistic noisy images to train the denoising network, while its performance is limited by the inaccurate consideration of noise components. UIDNet [31] takes a step further by combining the distilled knowledge of the self-supervised denoising network and extra information from synthetic pairs. C2N [15] considers various noise components in real-world scenarios for more accurate noise synthesis. However, dealing with the gap between unpaired data is still challenging. The mismatch in scene distribution can result in inaccurate generation, thus degrading the quality of synthesized data." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18157" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 58, + 70, + 533, + 208 + ], + "blocks": [ + { + "bbox": [ + 58, + 70, + 533, + 208 + ], + "lines": [ + { + "bbox": [ + 58, + 70, + 533, + 208 + ], + "spans": [ + { + "bbox": [ + 58, + 70, + 533, + 208 + ], + "type": "image", + "image_path": "25178a5c59a478e3c382af08c3394bcd4db4ca520f47a22ce2b32b9a83c29643.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 60, + 209, + 253, + 317 + ], + "blocks": [ + { + "bbox": [ + 60, + 209, + 253, + 317 + ], + "lines": [ + { + "bbox": [ + 60, + 209, + 253, + 317 + ], + "spans": [ + { + "bbox": [ + 60, + 209, + 253, + 317 + ], + "type": "image", + "image_path": "9f880eb70b70951d333d60b0a62ba648a5e70dc3576a7476d4a79aaf5784917d.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 323, + 546, + 357 + ], + "lines": [ + { + "bbox": [ + 46, + 323, + 546, + 357 + ], + "spans": [ + { + "bbox": [ + 46, + 323, + 546, + 357 + ], + "type": "text", + "content": "Figure 2. The overall architecture of LG-BPN. Our method is composed of two branches, aiming at extracting local textures and global interactions, respectively. For each branch, the input first goes through a DSPMC module, then further processed for the deep feature. Finally, the output of two branches is fused for the denoised result." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 258, + 209, + 531, + 316 + ], + "blocks": [ + { + "bbox": [ + 258, + 209, + 531, + 316 + ], + "lines": [ + { + "bbox": [ + 258, + 209, + 531, + 316 + ], + "spans": [ + { + "bbox": [ + 258, + 209, + 531, + 316 + ], + "type": "image", + "image_path": "5429102a2b5b49774e3fddb624ef06d5e0ebeb15a7ec31f9d8e8a1e32de8a7e4.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 363, + 289, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 363, + 289, + 579 + ], + "spans": [ + { + "bbox": [ + 46, + 363, + 289, + 579 + ], + "type": "text", + "content": "Generating pseudo noisy-noisy image pairs. The semi-supervised method Noise2Noise [21] uses multiple noisy images for training, which can be applied without clean images. However, the acquisition of multiple independent observations under the same scene is still less practical. Therefore, several methods seek to construct noisy-noisy pairs from a single noisy image. Neighbor2Neighbor [14] generates two sub-sampled images under simplified noise assumptions. To handle complex noise distribution in real images, several methods have been proposed, including Noisier2Noise [24], NAC [33] and R2R [26]. Still, these methods either require prior knowledge or are limited by specific constraints, which can be impractical in real situations. Specifically, Noisier2Noise [24] requires noise distribution when synthesizing noisy/noisy pairs. NAC [33] works under the assumption that the noise level is relatively weak. R2R [26] also uses additional information, e.g., noise level function (NLF) and image signal processing (ISP) function." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "content": "Training directly on noisy images. Another type of method follows a self-supervised manner, which can be directly trained on the noisy images and free of synthesizing pseudo image pairs. Noise2Void [17] and Noise2Self [3] propose the self-supervised blind-spot strategy by masking the corresponding central pixel. Laine19 [19] and D-BSN [31] are further proposed for advanced BSN designs, while the convolution-based architecture limits their exploitation for long-range dependencies. To ease the information loss by the blind spot, Blind2Unblind [30] introduces a novel re-visible loss term. Unfortunately, the above-mentioned" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 363, + 545, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 363, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 363, + 545, + 628 + ], + "type": "text", + "content": "methods work under the assumption that noise is pixel-wise independent, thus inevitably learning identity mapping under spatially-correlated real noise. Towards real image denoising, CVF-SID [25] disentangles the noise components from the clean images, but it assumes the noise is spatially-uncorrelated, which does not match the real noise distribution. Asymmetric pixel shuffle downsampling BSN (APBSN) [20] combines the pixel shuffle downsampling (PD) with a CNN-based BSN [31]. While achieving promising results, local structures are damaged by directly applying the PD operation to the image. Sub-sampled images are corrupted by various artifacts, e.g., aliasing artifacts, which are more pronounced under a large PD stride factor [20,38]. Also, adopting the CNN-based BSN leads to a limited receptive field. Since BSN recovers the central pixels based on its neighbors, fewer available neighbor pixels inevitably lead to performance loss. In summary, this results in the inadequate utilization of information with respect to both local and global contexts. Instead, our method benefits from a denser sampling density for improved local detail extraction, and also enjoys the distant pixel modeling ability for the enlarged receptive field." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 632, + 362, + 644 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 632, + 362, + 644 + ], + "spans": [ + { + "bbox": [ + 306, + 632, + 362, + 644 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 649, + 546, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 649, + 546, + 685 + ], + "spans": [ + { + "bbox": [ + 304, + 649, + 546, + 685 + ], + "type": "text", + "content": "We first illustrate the overall architecture of LG-BPN in Figure 2, then elaborate on our motivation, and demonstrate our two core designs: DSPMC and DTB." + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 306, + 693, + 546, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 693, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 693, + 546, + 713 + ], + "type": "text", + "content": "1We use 'global' to differentiate from our 'local' branch. Though a more accurate term is 'non-local', we follow the usage of 'global' as [35]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18158" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 70, + 286, + 158 + ], + "blocks": [ + { + "bbox": [ + 49, + 70, + 286, + 158 + ], + "lines": [ + { + "bbox": [ + 49, + 70, + 286, + 158 + ], + "spans": [ + { + "bbox": [ + 49, + 70, + 286, + 158 + ], + "type": "image", + "image_path": "726b069b2cf47f3f86924b2e701730c033e9e128e21d1b41c1d57238be194fdd.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 49, + 160, + 285, + 252 + ], + "blocks": [ + { + "bbox": [ + 49, + 160, + 285, + 252 + ], + "lines": [ + { + "bbox": [ + 49, + 160, + 285, + 252 + ], + "spans": [ + { + "bbox": [ + 49, + 160, + 285, + 252 + ], + "type": "image", + "image_path": "d81c5d7a9f2819f82a8d31bd3c5d6f489656508465372038e161c61e0aa37ae8.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 253, + 288, + 299 + ], + "lines": [ + { + "bbox": [ + 46, + 253, + 288, + 299 + ], + "spans": [ + { + "bbox": [ + 46, + 253, + 288, + 299 + ], + "type": "text", + "content": "Figure 3. Comparison of receptive field for the central pixel of APBSN and our method. Green pixels contribute to the restoration of central pixel. Blue pixels represent convolution kernel. We realize a denser receptive field by utilizing more neighbor pixels." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 307, + 189, + 320 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 307, + 189, + 320 + ], + "spans": [ + { + "bbox": [ + 47, + 307, + 189, + 320 + ], + "type": "text", + "content": "3.1. Motivation and Modeling" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 326, + 287, + 589 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 326, + 287, + 589 + ], + "spans": [ + { + "bbox": [ + 46, + 326, + 287, + 589 + ], + "type": "text", + "content": "Despite the decent results on simple synthetic noise removal, the performance of self-supervised denoising methods declines significantly when dealing with real noise, due to its strong spatial noise correlation. This easily breaks the assumption on which most state-of-the-art methods are based, i.e., noise is pixel-wise independent. These methods assume the clean signal of the central pixel is dependent on neighbors, while the noise is independent instead. Thus under real scenarios, they inevitably misinterpret the spatially-dependent noise as clean signals, and fail to recover the underlying clean images. Consequently, careful consideration of the spatial correlation is a must for self-supervised real noise removal. While the existing methods either struggle with poor results when completely ignoring this correlation, or suffer details loss from ill consideration. For example, AP-BSN [20] meets the assumption of the powerful BSN by adopting PD on the input image. As shown in Figure 3, though this breaks the spatial correlation, the sampling density is dramatically decreased by the PD. This severely degrades the extraction of fine details based on the Nyquist-Shannon sampling theorem, i.e., the fidelity of the results shows a positive correlation to sampling density." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 590, + 287, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 590, + 287, + 685 + ], + "spans": [ + { + "bbox": [ + 46, + 590, + 287, + 685 + ], + "type": "text", + "content": "Besides, though BSN is already adapted for state-of-the-art performance [20], its potential is still heavily hampered by their inherent shortage, i.e., the limit on the receptive field by the masked pixels for avoiding identity mapping. Despite the recent advanced BSN designs [19, 31], CNN-based BSNs are still unable to fully address this issue due to their local convolution operator and fail to model the long-distance dependencies. This adversely affects the perfor" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 317, + 69, + 429, + 163 + ], + "blocks": [ + { + "bbox": [ + 317, + 69, + 429, + 163 + ], + "lines": [ + { + "bbox": [ + 317, + 69, + 429, + 163 + ], + "spans": [ + { + "bbox": [ + 317, + 69, + 429, + 163 + ], + "type": "image", + "image_path": "85acd48737a79ccc066616a60796bd0dc9ad930f3e492d3001d29781b634da6f.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 317, + 165, + 429, + 185 + ], + "lines": [ + { + "bbox": [ + 317, + 165, + 429, + 185 + ], + "spans": [ + { + "bbox": [ + 317, + 165, + 429, + 185 + ], + "type": "text", + "content": "(a) Bar plot of correlation by relative position" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 440, + 74, + 531, + 164 + ], + "blocks": [ + { + "bbox": [ + 440, + 74, + 531, + 164 + ], + "lines": [ + { + "bbox": [ + 440, + 74, + 531, + 164 + ], + "spans": [ + { + "bbox": [ + 440, + 74, + 531, + 164 + ], + "type": "image", + "image_path": "820b3f26490cb5c0355ce1fea45ae1b902166381679231d3a5992a1574f6e8a4.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 440, + 166, + 531, + 184 + ], + "lines": [ + { + "bbox": [ + 440, + 166, + 531, + 184 + ], + "spans": [ + { + "bbox": [ + 440, + 166, + 531, + 184 + ], + "type": "text", + "content": "(b) High-correlation pixels mask" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 304, + 189, + 545, + 255 + ], + "lines": [ + { + "bbox": [ + 304, + 189, + 545, + 255 + ], + "spans": [ + { + "bbox": [ + 304, + 189, + 545, + 255 + ], + "type": "text", + "content": "Figure 4. Visualization of spatial correlation in real noise. (a) Bar plot of spatial correlation calculated by the correlation coefficient. Note that we scale the height by log norm for better visualization. The higher bar indicates a stronger correlation. (b) The mask of high-correlation pixels. Locations with 0 mean this pixel is strongly correlated to the central pixel, while 1 means not." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 262, + 545, + 285 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 262, + 545, + 285 + ], + "spans": [ + { + "bbox": [ + 304, + 262, + 545, + 285 + ], + "type": "text", + "content": "mance of BSN, as the number of neighbors around the blind spot used for inferring is dramatically reduced." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 286, + 546, + 393 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 286, + 546, + 393 + ], + "spans": [ + { + "bbox": [ + 304, + 286, + 546, + 393 + ], + "type": "text", + "content": "We aim to tackle both of these challenges in our methods. First, we realize better extraction for detailed textures from the perspective of sampling density. As shown in Figure 3, DSPMC enables a denser sampling rate by leveraging more neighbor pixels, which raises the upper limit of reconstruction quality. Second, by tailoring normal Transformers to a blind fashion, DTB is introduced for its powerful global modeling ability to compensate for the limited receptive field of CNN-based BSNs." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 396, + 545, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 396, + 545, + 552 + ], + "spans": [ + { + "bbox": [ + 304, + 396, + 545, + 552 + ], + "type": "text", + "content": "Based on these two modules, we now introduce the overall architecture of our method. As shown in Figure 2, LG-BPN is mainly composed of two branches in parallel, aiming at local and global contexts reconstruction respectively. For the local feature extraction branch, we first apply the " + }, + { + "bbox": [ + 304, + 396, + 545, + 552 + ], + "type": "inline_equation", + "content": "9 \\times 9" + }, + { + "bbox": [ + 304, + 396, + 545, + 552 + ], + "type": "text", + "content": " DSPMC module. The densely extracted features are then down-sampled to break the spatial correlation. Then, the feature maps go through dilated convolution with a dilation of 2. For the global branch, the input image first goes through a " + }, + { + "bbox": [ + 304, + 396, + 545, + 552 + ], + "type": "inline_equation", + "content": "21 \\times 21" + }, + { + "bbox": [ + 304, + 396, + 545, + 552 + ], + "type": "text", + "content": " DMPMC module with a larger receptive field, which is then processed by DTBs. Finally, the local and global information from the two branches is fused together for the final output." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 562, + 539, + 575 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 562, + 539, + 575 + ], + "spans": [ + { + "bbox": [ + 306, + 562, + 539, + 575 + ], + "type": "text", + "content": "3.2. Densely-Sampled Patch-Masked Convolution" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": "Neither adopting a low sample rate nor sampling all neighbor pixels can be an optimal choice for BSN when tacking real noise. In DSPMC, we aim to extract as much local information as possible, at the same time avoiding misinterpretation by these strongly-correlated neighbor pixels. To this end, we start by presenting the relationship between spatial correlation and the relative position, as shown in Figure 4. Following previous works [20, 38], we use Pearson's correlation coefficient to depict the relationship. Specifically, we first obtain the noise map by subtracting the clean images from the noisy images in SIDD medium [1]" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 47, + 693, + 286, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 693, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 693, + 286, + 713 + ], + "type": "text", + "content": "2We adopt " + }, + { + "bbox": [ + 47, + 693, + 286, + 713 + ], + "type": "inline_equation", + "content": "9\\times 9" + }, + { + "bbox": [ + 47, + 693, + 286, + 713 + ], + "type": "text", + "content": " DSPMC in the local branch. Here, the " + }, + { + "bbox": [ + 47, + 693, + 286, + 713 + ], + "type": "inline_equation", + "content": "11\\times 11" + }, + { + "bbox": [ + 47, + 693, + 286, + 713 + ], + "type": "text", + "content": " size is shown for illustration purposes to better compare the receptive field." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18159" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 72, + 124, + 145 + ], + "blocks": [ + { + "bbox": [ + 49, + 72, + 124, + 145 + ], + "lines": [ + { + "bbox": [ + 49, + 72, + 124, + 145 + ], + "spans": [ + { + "bbox": [ + 49, + 72, + 124, + 145 + ], + "type": "image", + "image_path": "9e6ed801c5792a07d6bf9c25f1187cd8da08d3da692c5536265864e39de2b38f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 48, + 148, + 123, + 167 + ], + "lines": [ + { + "bbox": [ + 48, + 148, + 123, + 167 + ], + "spans": [ + { + "bbox": [ + 48, + 148, + 123, + 167 + ], + "type": "text", + "content": "(a) Kernel location during training" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 129, + 71, + 205, + 146 + ], + "blocks": [ + { + "bbox": [ + 129, + 71, + 205, + 146 + ], + "lines": [ + { + "bbox": [ + 129, + 71, + 205, + 146 + ], + "spans": [ + { + "bbox": [ + 129, + 71, + 205, + 146 + ], + "type": "image", + "image_path": "2f60473a4421e2fa2e5cf7773538a75814b49d0d71ce915b7ce354803eca9f5b.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 129, + 148, + 205, + 168 + ], + "lines": [ + { + "bbox": [ + 129, + 148, + 205, + 168 + ], + "spans": [ + { + "bbox": [ + 129, + 148, + 205, + 168 + ], + "type": "text", + "content": "(b) Shifted kernel location during testing" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 211, + 72, + 286, + 146 + ], + "blocks": [ + { + "bbox": [ + 211, + 72, + 286, + 146 + ], + "lines": [ + { + "bbox": [ + 211, + 72, + 286, + 146 + ], + "spans": [ + { + "bbox": [ + 211, + 72, + 286, + 146 + ], + "type": "image", + "image_path": "0226df4140b9d03ab5312a73cb1c4466f94fbf235520d895b7135905d283cda9.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 211, + 148, + 287, + 175 + ], + "lines": [ + { + "bbox": [ + 211, + 148, + 287, + 175 + ], + "spans": [ + { + "bbox": [ + 211, + 148, + 287, + 175 + ], + "type": "text", + "content": "(c) Shifted kernel location during testing with dilation" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 175, + 287, + 231 + ], + "lines": [ + { + "bbox": [ + 46, + 175, + 287, + 231 + ], + "spans": [ + { + "bbox": [ + 46, + 175, + 287, + 231 + ], + "type": "text", + "content": "Figure 5. Illustration of shifting kernel strategy and dilation of DSPMC. The blue and green points are the kernel locations during training and testing respectively. Yellow arrows indicate the shift direction. This avoids the strongly correlated pixels when training, sampling pixels closer to the center when testing for more details." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 237, + 282, + 248 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 237, + 282, + 248 + ], + "spans": [ + { + "bbox": [ + 47, + 237, + 282, + 248 + ], + "type": "text", + "content": "dataset. Then, correlation coefficient can be calculated by:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 100, + 253, + 287, + 280 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 100, + 253, + 287, + 280 + ], + "spans": [ + { + "bbox": [ + 100, + 253, + 287, + 280 + ], + "type": "interline_equation", + "content": "\\rho_ {N _ {c e n}, N _ {n e i}} = \\frac {\\operatorname {c o v} \\left(N _ {c e n} , N _ {n e i}\\right)}{\\sigma_ {N _ {c e n}} \\sigma_ {N _ {n e i}}}, \\tag {1}", + "image_path": "0d31a4c347e3889b1d3a185be883abd0fd2de0e5813ce4ec1f7ab5592f7ca16a.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 283, + 287, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 283, + 287, + 365 + ], + "spans": [ + { + "bbox": [ + 46, + 283, + 287, + 365 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 283, + 287, + 365 + ], + "type": "inline_equation", + "content": "N_{cen}" + }, + { + "bbox": [ + 46, + 283, + 287, + 365 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 283, + 287, + 365 + ], + "type": "inline_equation", + "content": "N_{cen}" + }, + { + "bbox": [ + 46, + 283, + 287, + 365 + ], + "type": "text", + "content": " represent the noise of the central pixel and neighbor pixels respectively. In Figure 4(a), we find that there exist more neighbor pixels which can also be leveraged for prediction. These pixels are not strongly correlated to the center pixel, thus bringing useful information, instead of misinterpretation to BSN. Then, the DSPMC kernel can be calculated as:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 103, + 372, + 287, + 384 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 103, + 372, + 287, + 384 + ], + "spans": [ + { + "bbox": [ + 103, + 372, + 287, + 384 + ], + "type": "interline_equation", + "content": "\\mathbf {K} _ {D S P M C} = \\mathbf {K} _ {n} \\odot \\mathbf {M a s k} _ {c o r}, \\tag {2}", + "image_path": "8d2a981255cefc73cde6f7aef15379a670edbd86bc5d732a115a9080fa8d2335.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 388, + 287, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 388, + 287, + 529 + ], + "spans": [ + { + "bbox": [ + 46, + 388, + 287, + 529 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 388, + 287, + 529 + ], + "type": "inline_equation", + "content": "\\mathbf{K}_{DSPMC}" + }, + { + "bbox": [ + 46, + 388, + 287, + 529 + ], + "type": "text", + "content": " is the kernel of DSPMC, " + }, + { + "bbox": [ + 46, + 388, + 287, + 529 + ], + "type": "inline_equation", + "content": "\\mathbf{K}_n" + }, + { + "bbox": [ + 46, + 388, + 287, + 529 + ], + "type": "text", + "content": " is the kernel of the normal convolution, and " + }, + { + "bbox": [ + 46, + 388, + 287, + 529 + ], + "type": "inline_equation", + "content": "\\mathbf{Mask}_{cor}" + }, + { + "bbox": [ + 46, + 388, + 287, + 529 + ], + "type": "text", + "content": " is the mask for filtering out highly-correlated pixels shown in Figure 4(b). By integrating this noise distribution prior to sampling locations, our module can effectively take more neighbor pixels while avoiding the strongly correlated pixels. This enables the extracted feature to contain more fine details, and a denser receptive field as well. Also, as shown in Figure 3, since the extracted high-dimension feature already gathers the rich local details, the subsequent feature-level PD can save more useful information compared with the previous image-level PD." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 531, + 287, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 531, + 287, + 590 + ], + "spans": [ + { + "bbox": [ + 46, + 531, + 287, + 590 + ], + "type": "text", + "content": "However, directly applying this module is not an optimal choice: " + }, + { + "bbox": [ + 46, + 531, + 287, + 590 + ], + "type": "inline_equation", + "content": "i)" + }, + { + "bbox": [ + 46, + 531, + 287, + 590 + ], + "type": "text", + "content": " the inference stage requires more details compared with training, so directly using the same architecture can damage high-frequency details [20], " + }, + { + "bbox": [ + 46, + 531, + 287, + 590 + ], + "type": "inline_equation", + "content": "ii)" + }, + { + "bbox": [ + 46, + 531, + 287, + 590 + ], + "type": "text", + "content": " a large kernel can cause computational inefficiency." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 590, + 287, + 661 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 590, + 287, + 661 + ], + "spans": [ + { + "bbox": [ + 46, + 590, + 287, + 661 + ], + "type": "text", + "content": "Kernel shift strategy. As shown in Figure 5(b), for the first concern, we need to obtain more details while testing, focusing on local detailed information closer to the center pixel. Inspired by the deformable convolution [9], we apply a set of fixed offsets on the kernel for each location, which enforce that the kernels are more gathered in the center:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 87, + 667, + 287, + 700 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 87, + 667, + 287, + 700 + ], + "spans": [ + { + "bbox": [ + 87, + 667, + 287, + 700 + ], + "type": "interline_equation", + "content": "\\mathbf {y} \\left(p _ {0}\\right) = \\sum_ {k = 1} ^ {\\mathbf {K}} w _ {k} \\cdot \\mathbf {x} \\left(p _ {0} + p _ {k} + \\Delta p _ {k}\\right), \\tag {3}", + "image_path": "a6efec0d24561070fa892550b4d0a31849267a71f6309200c84f96508f099798.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 94, + 703, + 204, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 94, + 703, + 204, + 715 + ], + "spans": [ + { + "bbox": [ + 94, + 703, + 204, + 715 + ], + "type": "interline_equation", + "content": "\\Delta p _ {k} = \\text {R a t i o} * (p _ {k} - p _ {0}),", + "image_path": "141cfba19574534d6da19d75048239c10f739908219c469b133ba31bea437a80.jpg" + } + ] + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 307, + 70, + 381, + 144 + ], + "blocks": [ + { + "bbox": [ + 307, + 70, + 381, + 144 + ], + "lines": [ + { + "bbox": [ + 307, + 70, + 381, + 144 + ], + "spans": [ + { + "bbox": [ + 307, + 70, + 381, + 144 + ], + "type": "image", + "image_path": "695d932f9aa4dd65d657b1334a75abadacba3455a1e460a309193ce5816e6cd7.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 318, + 145, + 369, + 155 + ], + "lines": [ + { + "bbox": [ + 318, + 145, + 369, + 155 + ], + "spans": [ + { + "bbox": [ + 318, + 145, + 369, + 155 + ], + "type": "text", + "content": "(a) Noisy input" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 304, + 159, + 545, + 204 + ], + "lines": [ + { + "bbox": [ + 304, + 159, + 545, + 204 + ], + "spans": [ + { + "bbox": [ + 304, + 159, + 545, + 204 + ], + "type": "text", + "content": "Figure 6. The comparison of the feature map visualization of our method and AP-BSN [20] in the training phase. Our feature map shows clearer edges, validating the superiority of local details extraction of DSPMC by imposing denser sampling locations." + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_caption" + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 388, + 70, + 462, + 144 + ], + "blocks": [ + { + "bbox": [ + 388, + 70, + 462, + 144 + ], + "lines": [ + { + "bbox": [ + 388, + 70, + 462, + 144 + ], + "spans": [ + { + "bbox": [ + 388, + 70, + 462, + 144 + ], + "type": "image", + "image_path": "b1a6cf48ff7abd0b3f8651874629209fc35baad7fd59d9ed3020df0236719c1b.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 397, + 145, + 453, + 155 + ], + "lines": [ + { + "bbox": [ + 397, + 145, + 453, + 155 + ], + "spans": [ + { + "bbox": [ + 397, + 145, + 453, + 155 + ], + "type": "text", + "content": "(b) AP-BSN [20]" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + } + ], + "index": 18 + }, + { + "type": "image", + "bbox": [ + 469, + 70, + 542, + 144 + ], + "blocks": [ + { + "bbox": [ + 469, + 70, + 542, + 144 + ], + "lines": [ + { + "bbox": [ + 469, + 70, + 542, + 144 + ], + "spans": [ + { + "bbox": [ + 469, + 70, + 542, + 144 + ], + "type": "image", + "image_path": "ff1eec17441fd823b22d1a795b311175dd883e72e15116c50db964942da66b23.jpg" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 474, + 145, + 538, + 155 + ], + "lines": [ + { + "bbox": [ + 474, + 145, + 538, + 155 + ], + "spans": [ + { + "bbox": [ + 474, + 145, + 538, + 155 + ], + "type": "text", + "content": "(c) LG-BPN (Ours)" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_caption" + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 209, + 545, + 281 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 209, + 545, + 281 + ], + "spans": [ + { + "bbox": [ + 304, + 209, + 545, + 281 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 209, + 545, + 281 + ], + "type": "inline_equation", + "content": "\\mathbf{K}" + }, + { + "bbox": [ + 304, + 209, + 545, + 281 + ], + "type": "text", + "content": " is the kernel sampling locations, " + }, + { + "bbox": [ + 304, + 209, + 545, + 281 + ], + "type": "inline_equation", + "content": "w_{k}" + }, + { + "bbox": [ + 304, + 209, + 545, + 281 + ], + "type": "text", + "content": " is the kernel weight, " + }, + { + "bbox": [ + 304, + 209, + 545, + 281 + ], + "type": "inline_equation", + "content": "\\mathbf{x}(p)" + }, + { + "bbox": [ + 304, + 209, + 545, + 281 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 209, + 545, + 281 + ], + "type": "inline_equation", + "content": "\\mathbf{y}(p)" + }, + { + "bbox": [ + 304, + 209, + 545, + 281 + ], + "type": "text", + "content": " denote the features at " + }, + { + "bbox": [ + 304, + 209, + 545, + 281 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 304, + 209, + 545, + 281 + ], + "type": "text", + "content": " in input feature " + }, + { + "bbox": [ + 304, + 209, + 545, + 281 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 304, + 209, + 545, + 281 + ], + "type": "text", + "content": " and output feature " + }, + { + "bbox": [ + 304, + 209, + 545, + 281 + ], + "type": "inline_equation", + "content": "\\mathbf{y}" + }, + { + "bbox": [ + 304, + 209, + 545, + 281 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 209, + 545, + 281 + ], + "type": "inline_equation", + "content": "\\Delta p" + }, + { + "bbox": [ + 304, + 209, + 545, + 281 + ], + "type": "text", + "content": " is the applied kernel offset. Ratio is the extent we shift the kernel while testing. By adding offsets to the kernel, we can shrink the kernel and capture finer details while testing." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 281, + 545, + 353 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 281, + 545, + 353 + ], + "spans": [ + { + "bbox": [ + 304, + 281, + 545, + 353 + ], + "type": "text", + "content": "Dilation in DSPMC. As shown in Figure 5(c), for the second concern, we further decrease the computational cost by adding dilation to the convolution kernel. This imposed sparsity makes our DSPMC computationally efficient especially for large kernel size, at the same time maintaining the dense receptive field for capturing detailed structures." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 354, + 545, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 354, + 545, + 484 + ], + "spans": [ + { + "bbox": [ + 304, + 354, + 545, + 484 + ], + "type": "text", + "content": "Visualization of the extracted feature map. To validate that our DSPMC module achieves a denser receptive field and is thus better at extracting local high-frequency structures, we present the visualization of the feature map. We select the output feature of the local extraction branch, and the corresponding location in AP-BSN. All channels are averaged and normalized for visualization. As shown in Figure 6, in AP-BSN [20], the local fine texture is damaged due to the insufficient use of neighbor signals. Instead, by leveraging more neighbor pixels, our feature map shows shaper edges and preserves more details." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 306, + 491, + 454, + 503 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 491, + 454, + 503 + ], + "spans": [ + { + "bbox": [ + 306, + 491, + 454, + 503 + ], + "type": "text", + "content": "3.3. Dilated Transformer Block" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 304, + 510, + 545, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 545, + 653 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 545, + 653 + ], + "type": "text", + "content": "The receptive field of BSN is restricted by the imposed blind spots, while the local operator in CNN-based BSNs further prevents it from gathering global interaction. However, under the special blind spot constraint on the receptive field, it is non-trivial to directly introduce normal Transformer blocks to the BSN. Inspired by the D-BSN [31], we aim to design the Transformer block without information exchange between spatially-adjacent pixels, which satisfies the blind spot requirement when combined with DSPMC. Under these requirements, we carefully consider the design of two core components in the Transformer: the self-attention calculation and the feed-forward layer." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": "First, for the self-attention layer, spatial-wise attention enables spatial information exchange and thus does not meet our receptive field requirement. Recently, a grid-like self-attention can meet our requirement [28], while the grid pattern further narrows the receptive field that the blind spot" + } + ] + } + ], + "index": 28 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18160" + } + ] + } + ], + "index": 29 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 72, + 69, + 156, + 151 + ], + "blocks": [ + { + "bbox": [ + 72, + 69, + 156, + 151 + ], + "lines": [ + { + "bbox": [ + 72, + 69, + 156, + 151 + ], + "spans": [ + { + "bbox": [ + 72, + 69, + 156, + 151 + ], + "type": "image", + "image_path": "50862906fd61bda8b28d301d511f896fc3fced26f456b3325aac7d550eafa92e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 85, + 152, + 141, + 163 + ], + "lines": [ + { + "bbox": [ + 85, + 152, + 141, + 163 + ], + "spans": [ + { + "bbox": [ + 85, + 152, + 141, + 163 + ], + "type": "text", + "content": "(a) AP-BSN [20]" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 178, + 69, + 261, + 152 + ], + "blocks": [ + { + "bbox": [ + 178, + 69, + 261, + 152 + ], + "lines": [ + { + "bbox": [ + 178, + 69, + 261, + 152 + ], + "spans": [ + { + "bbox": [ + 178, + 69, + 261, + 152 + ], + "type": "image", + "image_path": "bab93a1ec28ac9d2b411f20df875127c6c3108ec5e82a6a7237bb12de2f6af8c.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 187, + 152, + 251, + 163 + ], + "lines": [ + { + "bbox": [ + 187, + 152, + 251, + 163 + ], + "spans": [ + { + "bbox": [ + 187, + 152, + 251, + 163 + ], + "type": "text", + "content": "(b) LG-BPN (Ours)" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 166, + 287, + 211 + ], + "lines": [ + { + "bbox": [ + 46, + 166, + 287, + 211 + ], + "spans": [ + { + "bbox": [ + 46, + 166, + 287, + 211 + ], + "type": "text", + "content": "Figure 7. The comparison of the receptive field between AP-BSN [20] and our method. We calculate the gradient response to the central pixel. The brighter color represents the higher contribution for recovering the central pixel." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 219, + 289, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 219, + 289, + 376 + ], + "spans": [ + { + "bbox": [ + 46, + 219, + 289, + 376 + ], + "type": "text", + "content": "has reduced. Instead, we adopt channel-wise attention [35] for its unawareness of spatial location and global perception as well. Furthermore, to enhance the local context while preventing information of adjacent pixels, we introduce dilated depth-wise convolution before computing feature similarity. For the input feature " + }, + { + "bbox": [ + 46, + 219, + 289, + 376 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 46, + 219, + 289, + 376 + ], + "type": "text", + "content": ", the Query " + }, + { + "bbox": [ + 46, + 219, + 289, + 376 + ], + "type": "inline_equation", + "content": "(\\mathbf{Q})" + }, + { + "bbox": [ + 46, + 219, + 289, + 376 + ], + "type": "text", + "content": ", Key " + }, + { + "bbox": [ + 46, + 219, + 289, + 376 + ], + "type": "inline_equation", + "content": "(\\mathbf{K})" + }, + { + "bbox": [ + 46, + 219, + 289, + 376 + ], + "type": "text", + "content": " and Value " + }, + { + "bbox": [ + 46, + 219, + 289, + 376 + ], + "type": "inline_equation", + "content": "(\\mathbf{V})" + }, + { + "bbox": [ + 46, + 219, + 289, + 376 + ], + "type": "text", + "content": " matrix is thus calculated by " + }, + { + "bbox": [ + 46, + 219, + 289, + 376 + ], + "type": "inline_equation", + "content": "\\mathbf{Q} = g^{Q}(\\mathbf{X})" + }, + { + "bbox": [ + 46, + 219, + 289, + 376 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 219, + 289, + 376 + ], + "type": "inline_equation", + "content": "\\mathbf{K} = g^{K}(\\mathbf{X})" + }, + { + "bbox": [ + 46, + 219, + 289, + 376 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 219, + 289, + 376 + ], + "type": "inline_equation", + "content": "\\mathbf{V} = g^{V}(\\mathbf{X})" + }, + { + "bbox": [ + 46, + 219, + 289, + 376 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 219, + 289, + 376 + ], + "type": "inline_equation", + "content": "g^{Q}(\\cdot)" + }, + { + "bbox": [ + 46, + 219, + 289, + 376 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 219, + 289, + 376 + ], + "type": "inline_equation", + "content": "g^{K}(\\cdot)" + }, + { + "bbox": [ + 46, + 219, + 289, + 376 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 219, + 289, + 376 + ], + "type": "inline_equation", + "content": "g^{V}(\\cdot)" + }, + { + "bbox": [ + 46, + 219, + 289, + 376 + ], + "type": "text", + "content": " denote the dilated " + }, + { + "bbox": [ + 46, + 219, + 289, + 376 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 46, + 219, + 289, + 376 + ], + "type": "text", + "content": " depth-wise convolution. Given the " + }, + { + "bbox": [ + 46, + 219, + 289, + 376 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}" + }, + { + "bbox": [ + 46, + 219, + 289, + 376 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 219, + 289, + 376 + ], + "type": "inline_equation", + "content": "\\mathbf{K}" + }, + { + "bbox": [ + 46, + 219, + 289, + 376 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 219, + 289, + 376 + ], + "type": "inline_equation", + "content": "\\mathbf{V}" + }, + { + "bbox": [ + 46, + 219, + 289, + 376 + ], + "type": "text", + "content": " matrix, the channel interaction can be obtained by the dot-product, where the attention map is of size " + }, + { + "bbox": [ + 46, + 219, + 289, + 376 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{C \\times C}" + }, + { + "bbox": [ + 46, + 219, + 289, + 376 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 219, + 289, + 376 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 219, + 289, + 376 + ], + "type": "text", + "content": " is the number of channels. The overall self-attention layer is represented as:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 80, + 383, + 287, + 413 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 80, + 383, + 287, + 413 + ], + "spans": [ + { + "bbox": [ + 80, + 383, + 287, + 413 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\operatorname {A t t e n t i o n} (\\mathbf {Q}, \\mathbf {K}, \\mathbf {V}) = \\mathbf {V} \\operatorname {S o f t m a x} (\\mathbf {K Q}), \\\\ \\hat {\\mathbf {X}} = \\operatorname {A t t e n t i o n} (\\mathbf {Q}, \\mathbf {K}, \\mathbf {V}) + \\mathbf {X}, \\tag {4} \\\\ \\end{array}", + "image_path": "702e59d3decd030213480498bf3d8de8e78c01a2390cd5f5138691cf9049825b.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 417, + 262, + 429 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 417, + 262, + 429 + ], + "spans": [ + { + "bbox": [ + 47, + 417, + 262, + 429 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 417, + 262, + 429 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 47, + 417, + 262, + 429 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 417, + 262, + 429 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{X}}" + }, + { + "bbox": [ + 47, + 417, + 262, + 429 + ], + "type": "text", + "content": " denote the input and output features." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 430, + 287, + 561 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 430, + 287, + 561 + ], + "spans": [ + { + "bbox": [ + 46, + 430, + 287, + 561 + ], + "type": "text", + "content": "Second, for the feed-forward layer, adjacent information exchange can be simply avoided by adopting " + }, + { + "bbox": [ + 46, + 430, + 287, + 561 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 46, + 430, + 287, + 561 + ], + "type": "text", + "content": " convolutions only. Nonetheless, this fails to capture local context, which can be critical for restoring high-frequency details. We address this issue by also introducing dilation into the normal " + }, + { + "bbox": [ + 46, + 430, + 287, + 561 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 46, + 430, + 287, + 561 + ], + "type": "text", + "content": " convolution in the feed-forward layer. Then, features extracted by dilated depth-wise convolution go through a gating unit for the non-linearity. This gating unit is the element-wise product of two parallel paths, with one of them activated by the GELU unit. The overall process of the feed-forward layer is formulated as:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 102, + 569, + 287, + 615 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 102, + 569, + 287, + 615 + ], + "spans": [ + { + "bbox": [ + 102, + 569, + 287, + 615 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathbf {G} ^ {\\mathbf {1}} = g ^ {1} (\\mathrm {L N} (\\mathbf {X})), \\\\ \\mathbf {G} ^ {2} = g ^ {2} (\\mathrm {L N} (\\mathbf {X})), \\tag {5} \\\\ \\hat {\\mathbf {X}} = \\operatorname {G E L U} \\left(\\mathbf {G} ^ {1}\\right) \\odot \\mathbf {G} ^ {2} + \\mathbf {X}, \\\\ \\end{array}", + "image_path": "f3b711dcb46c1354176f7380e830f647d3665434b4c2a206e478408cc72af531.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 617, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 287, + 677 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 617, + 287, + 677 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 46, + 617, + 287, + 677 + ], + "type": "text", + "content": " is element-wise multiplication, LN denotes layer normalization, " + }, + { + "bbox": [ + 46, + 617, + 287, + 677 + ], + "type": "inline_equation", + "content": "g^{1}(\\cdot)" + }, + { + "bbox": [ + 46, + 617, + 287, + 677 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 617, + 287, + 677 + ], + "type": "inline_equation", + "content": "g^{2}(\\cdot)" + }, + { + "bbox": [ + 46, + 617, + 287, + 677 + ], + "type": "text", + "content": " represent the " + }, + { + "bbox": [ + 46, + 617, + 287, + 677 + ], + "type": "inline_equation", + "content": "3\\times 3" + }, + { + "bbox": [ + 46, + 617, + 287, + 677 + ], + "type": "text", + "content": " dilated depth-wise convolution. An additional benefit is that, compared to the normal " + }, + { + "bbox": [ + 46, + 617, + 287, + 677 + ], + "type": "inline_equation", + "content": "3\\times 3" + }, + { + "bbox": [ + 46, + 617, + 287, + 677 + ], + "type": "text", + "content": " convolution, the introduced dilation can also enlarge the receptive field." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 677, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 712 + ], + "type": "text", + "content": "To prove the effectiveness of the introduced global dependencies, we also plot the receptive field for recovering the central pixel of our method and the CNN-based BSNs" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": "in Figure 7. By injecting the long-range interaction into the blind spot network, more neighbor pixels are activated for restoring the central pixels in our method, offering a broader receptive field compared to the previous CNN-based BSNs." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 131, + 388, + 144 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 131, + 388, + 144 + ], + "spans": [ + { + "bbox": [ + 306, + 131, + 388, + 144 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 151, + 449, + 164 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 151, + 449, + 164 + ], + "spans": [ + { + "bbox": [ + 306, + 151, + 449, + 164 + ], + "type": "text", + "content": "4.1. Dataset and Setup Details" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 169, + 545, + 217 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 169, + 545, + 217 + ], + "spans": [ + { + "bbox": [ + 304, + 169, + 545, + 217 + ], + "type": "text", + "content": "We train and evaluate our method on two real-world datasets, i.e., SIDD [1] and DND [27]. Note that for the SIDD benchmark dataset and DND benchmark dataset, we submit the output to the website for online evaluation." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 217, + 545, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 217, + 545, + 312 + ], + "spans": [ + { + "bbox": [ + 304, + 217, + 545, + 312 + ], + "type": "text", + "content": "Smartphone Image Denoising Dataset (SIDD) [1] contains paired images for real-world denoising by five smartphone cameras. For training, we use the sRGB images from SIDD-Medium including 320 pairs. For validation and evaluation, we use the sRGB images from the SIDD validation set and benchmark set respectively. Each includes 1280 patches of size " + }, + { + "bbox": [ + 304, + 217, + 545, + 312 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 304, + 217, + 545, + 312 + ], + "type": "text", + "content": ", where the ground truth images are also provided for the validation set." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 313, + 545, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 313, + 545, + 384 + ], + "spans": [ + { + "bbox": [ + 304, + 313, + 545, + 384 + ], + "type": "text", + "content": "Darmstadt Noise Dataset (DND) [27] contains 50 noisy images for benchmarking without the ground truth provided, and the results can only be obtained via the online submission system. Therefore, we enjoy a fully self-supervised manner and directly train our method on the test set without extra eternal data." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 392, + 405, + 405 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 392, + 405, + 405 + ], + "spans": [ + { + "bbox": [ + 306, + 392, + 405, + 405 + ], + "type": "text", + "content": "4.2. Training Details" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 412, + 545, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 412, + 545, + 544 + ], + "spans": [ + { + "bbox": [ + 304, + 412, + 545, + 544 + ], + "type": "text", + "content": "During training, we keep the same setting as the previous work [20]. Specifically, a batch size of 8 is used in the experiment. We adopt " + }, + { + "bbox": [ + 304, + 412, + 545, + 544 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_1" + }, + { + "bbox": [ + 304, + 412, + 545, + 544 + ], + "type": "text", + "content": " loss between ground truth and output for training. The learning rate starts with " + }, + { + "bbox": [ + 304, + 412, + 545, + 544 + ], + "type": "inline_equation", + "content": "1e - 4" + }, + { + "bbox": [ + 304, + 412, + 545, + 544 + ], + "type": "text", + "content": ", where Adam optimizer is adopted. The network is trained with 20 epochs until it fully converges. We implement the method in PyTorch 1.8.0, and train our model on the Nvidia RTX 3090. Two metrics are utilized to evaluate the performance of methods, including peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) [29]. The larger value of PSNR and SSIM implies better fidelity." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 551, + 495, + 563 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 551, + 495, + 563 + ], + "spans": [ + { + "bbox": [ + 306, + 551, + 495, + 563 + ], + "type": "text", + "content": "4.3. Evaluation of Real-world Denoising" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 570, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 545, + 712 + ], + "type": "text", + "content": "We validate the effectiveness of our method for real-world image denoising on the commonly-used SIDD benchmark dataset and DND benchmark dataset. Table 1 shows the comparison of various methods on SIDD and DND benchmark datasets. Visualization results of several methods addressed in Table 1 on SIDD and DND datasets can be found in Figure 8 and Figure 9. We achieve better results in quantitative and qualitative metrics than previous un-/self-supervised methods. Compared with unsupervised methods trained on unpaired clean-noisy data, LG-BPN does not rely on extra data for synthesizing training pairs, also avoiding the misalignment between the scene distribution. For the" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18161" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 52, + 70, + 534, + 327 + ], + "blocks": [ + { + "bbox": [ + 52, + 70, + 534, + 327 + ], + "lines": [ + { + "bbox": [ + 52, + 70, + 534, + 327 + ], + "spans": [ + { + "bbox": [ + 52, + 70, + 534, + 327 + ], + "type": "table", + "html": "
Type of supervisionTraining dataMethodSIDDDND
PSNRSSIMPSNRSSIM
Non-learning basedNoneBM3D [8]25.650.68534.510.851
WNNM [11]25.780.80934.670.865
SupervisedSynthesized PairsDnCNN [36]23.660.58332.430.790
CBDNet [12]33.280.86838.050.942
AWGN-M [38]33.99*0.896*38.400.945
Real pairsDnCNN [36]35.34*0.885*37.83*0.929*
AINDNet [16]38.840.95139.340.952
RIDNet [2]38.700.95039.250.952
DIDN [34]39.820.97339.620.954
UnsupervisedNoisy-clean pairsGCBD [6]--35.580.922
UIDNet [13]32.480.897--
C2N [15] + DIDN [34]35.350.93736.380.887
D-BSN [31] + MWCNN [23]--37.930.937
Noisy-noisy pairsNoise2Self [3]29.56†0.808†--
NAC [33]--36.200.925
R2R [26]34.780.898--
Single noisy observationNoise2Void [17]27.68†0.668†--
CVF-SID [25]34.710.91736.500.924
AP-BSN [20]35.970.92538.090.937
LG-BPN (Ours)37.280.93638.430.942
", + "image_path": "6aee5393453900883464ddbc3cc933b44f66b1defc36887d4fd750c809a4a0ba.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 335, + 547, + 380 + ], + "lines": [ + { + "bbox": [ + 46, + 335, + 547, + 380 + ], + "spans": [ + { + "bbox": [ + 46, + 335, + 547, + 380 + ], + "type": "text", + "content": "Table 1. Quantitative comparison of various methods on SIDD and DND benchmark datasets. Though several supervised methods achieve better results using noisy/clean image pairs, our methods use noisy RGB images only. Results with " + }, + { + "bbox": [ + 46, + 335, + 547, + 380 + ], + "type": "inline_equation", + "content": "\\star" + }, + { + "bbox": [ + 46, + 335, + 547, + 380 + ], + "type": "text", + "content": " mean these are reproduced and evaluated by ourselves, since they are not evaluated on the dataset we use in their original paper. The results marked with " + }, + { + "bbox": [ + 46, + 335, + 547, + 380 + ], + "type": "inline_equation", + "content": "\\dagger" + }, + { + "bbox": [ + 46, + 335, + 547, + 380 + ], + "type": "text", + "content": " are reported from R2R [26]. Otherwise, we report the official results from SIDD and DND benchmark websites." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 388, + 289, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 388, + 289, + 556 + ], + "spans": [ + { + "bbox": [ + 46, + 388, + 289, + 556 + ], + "type": "text", + "content": "self-supervised methods, NAC [33] works under the weak noise level assumption, while R2R [26] can not be directly applied to sRGB images without extra NLF and ISP functions, both of which harm their performance in real-world situations. In contrast, LG-BPN can be directly applied and not restricted by these assumptions. For methods leveraging single noisy observations, CVF-SID [25] does not consider the strong spatial correlation property in real noise, thus real noise can not be fully removed as shown in Figure 8. APBSN [20] suffers from inadequate sample locations with a limited receptive field, so details are blurred as shown in Figure 9. Instead, LG-BPN carefully integrates the spatial correlation into the network design, simultaneously modeling distant context dependencies." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 563, + 224, + 576 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 563, + 224, + 576 + ], + "spans": [ + { + "bbox": [ + 47, + 563, + 224, + 576 + ], + "type": "text", + "content": "4.4. Analysis of the Proposed Method" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 582, + 287, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 287, + 653 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 287, + 653 + ], + "type": "text", + "content": "Dilation factor in densely-sampled convolution. Directly introducing densely-sample convolution can be computationally expensive. To balance the efficiency and the performance, we further introduce the sparsity to the convolution kernel by adding dilation to the original DSPMC. Figure 5(c) shows the illustration of the dilation." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 654, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 288, + 713 + ], + "type": "text", + "content": "To explore the better trade-off between performance and efficiency, we provide ablation studies on the dilation rate for our DSPMC in both local and global extraction branches. As shown in Table 2(a), a dilation of 1 for " + }, + { + "bbox": [ + 46, + 654, + 288, + 713 + ], + "type": "inline_equation", + "content": "9 \\times 9" + }, + { + "bbox": [ + 46, + 654, + 288, + 713 + ], + "type": "text", + "content": " DSPMC and 2 for " + }, + { + "bbox": [ + 46, + 654, + 288, + 713 + ], + "type": "inline_equation", + "content": "21 \\times 21" + }, + { + "bbox": [ + 46, + 654, + 288, + 713 + ], + "type": "text", + "content": " DSPMC achieve a better balance." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 388, + 545, + 508 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 388, + 545, + 508 + ], + "spans": [ + { + "bbox": [ + 304, + 388, + 545, + 508 + ], + "type": "text", + "content": "We claim its reason is that the difference in kernel size results in focusing on varied scales of information. This imposes different sensitivity to the dilation, i.e., sampling density. For relatively small " + }, + { + "bbox": [ + 304, + 388, + 545, + 508 + ], + "type": "inline_equation", + "content": "9 \\times 9" + }, + { + "bbox": [ + 304, + 388, + 545, + 508 + ], + "type": "text", + "content": " kernels, it focuses more on the local textures, thus adding dilation can notably lower its ability when reconstructing detailed structures. While for the " + }, + { + "bbox": [ + 304, + 388, + 545, + 508 + ], + "type": "inline_equation", + "content": "21 \\times 21" + }, + { + "bbox": [ + 304, + 388, + 545, + 508 + ], + "type": "text", + "content": " kernel, the larger kernel size makes it aim at the global context more. Thus, the introduced dilation does not severely harm its global extraction ability, at the same time reducing the computational cost." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 509, + 545, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 509, + 545, + 604 + ], + "spans": [ + { + "bbox": [ + 304, + 509, + 545, + 604 + ], + "type": "text", + "content": "The exploitation of local and global information. LGBPN consists of two branches in parallel. Specifically, we combine the small " + }, + { + "bbox": [ + 304, + 509, + 545, + 604 + ], + "type": "inline_equation", + "content": "9 \\times 9" + }, + { + "bbox": [ + 304, + 509, + 545, + 604 + ], + "type": "text", + "content": " DSPMC with dilated convolution and the large " + }, + { + "bbox": [ + 304, + 509, + 545, + 604 + ], + "type": "inline_equation", + "content": "21 \\times 21" + }, + { + "bbox": [ + 304, + 509, + 545, + 604 + ], + "type": "text", + "content": " DSPMC with DTB, focusing on local and global context processing respectively. To validate the reasonableness of our network architecture, we conduct ablation studies on these components. Table 2(b) shows the results of different combinations." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 605, + 545, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 700 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 700 + ], + "type": "text", + "content": "It can be seen that removing the DSPMC of size " + }, + { + "bbox": [ + 304, + 605, + 545, + 700 + ], + "type": "inline_equation", + "content": "9 \\times 9" + }, + { + "bbox": [ + 304, + 605, + 545, + 700 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 605, + 545, + 700 + ], + "type": "inline_equation", + "content": "21 \\times 21" + }, + { + "bbox": [ + 304, + 605, + 545, + 700 + ], + "type": "text", + "content": " in either branch severely degrades the performance. It is on account of the insufficient sampling density, which limits the reconstruction quality according to the Nyquist-Shannon sampling theorem. In this situation, the sampling density is made severely sparse, which causes insufficient utilization of input signals. This performance drop demonstrates the effectiveness of our DSPMC module." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 317, + 701, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 701, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 317, + 701, + 545, + 713 + ], + "type": "text", + "content": "Furthermore, we validate that the different sizes of" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "18162" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 69, + 191, + 207 + ], + "blocks": [ + { + "bbox": [ + 53, + 69, + 191, + 207 + ], + "lines": [ + { + "bbox": [ + 53, + 69, + 191, + 207 + ], + "spans": [ + { + "bbox": [ + 53, + 69, + 191, + 207 + ], + "type": "image", + "image_path": "0a679e6d9787e67073e454372e4316dc7dd5db81d978ec535e32bb7ee5d6f6b8.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 84, + 209, + 169, + 220 + ], + "lines": [ + { + "bbox": [ + 84, + 209, + 169, + 220 + ], + "spans": [ + { + "bbox": [ + 84, + 209, + 169, + 220 + ], + "type": "text", + "content": "SIDD benchmark input" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 195, + 69, + 278, + 133 + ], + "blocks": [ + { + "bbox": [ + 195, + 69, + 278, + 133 + ], + "lines": [ + { + "bbox": [ + 195, + 69, + 278, + 133 + ], + "spans": [ + { + "bbox": [ + 195, + 69, + 278, + 133 + ], + "type": "image", + "image_path": "5fd3001ca8c868f123c02493662aef0aff464ab8c5563d55c1f64466ae84d6cc.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 219, + 135, + 255, + 144 + ], + "lines": [ + { + "bbox": [ + 219, + 135, + 255, + 144 + ], + "spans": [ + { + "bbox": [ + 219, + 135, + 255, + 144 + ], + "type": "text", + "content": "N2V [17]" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 284, + 69, + 367, + 133 + ], + "blocks": [ + { + "bbox": [ + 284, + 69, + 367, + 133 + ], + "lines": [ + { + "bbox": [ + 284, + 69, + 367, + 133 + ], + "spans": [ + { + "bbox": [ + 284, + 69, + 367, + 133 + ], + "type": "image", + "image_path": "8c7bfe4fbceba170433d10f174e2c80692df33c2a0fe717981480e70c4202e40.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 372, + 69, + 455, + 133 + ], + "blocks": [ + { + "bbox": [ + 372, + 69, + 455, + 133 + ], + "lines": [ + { + "bbox": [ + 372, + 69, + 455, + 133 + ], + "spans": [ + { + "bbox": [ + 372, + 69, + 455, + 133 + ], + "type": "image", + "image_path": "8ccf2714dd0838b9c5833746fde64282d3a368f84cb232751a0cb21e24d6f892.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 460, + 69, + 543, + 133 + ], + "blocks": [ + { + "bbox": [ + 460, + 69, + 543, + 133 + ], + "lines": [ + { + "bbox": [ + 460, + 69, + 543, + 133 + ], + "spans": [ + { + "bbox": [ + 460, + 69, + 543, + 133 + ], + "type": "image", + "image_path": "73f55e134fc87843219db3ac5a30d2e84201cd2d7b77bd346df2f0e7bbb03ee4.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 484, + 135, + 520, + 144 + ], + "lines": [ + { + "bbox": [ + 484, + 135, + 520, + 144 + ], + "spans": [ + { + "bbox": [ + 484, + 135, + 520, + 144 + ], + "type": "text", + "content": "C2N [15]" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 195, + 146, + 279, + 207 + ], + "blocks": [ + { + "bbox": [ + 195, + 146, + 279, + 207 + ], + "lines": [ + { + "bbox": [ + 195, + 146, + 279, + 207 + ], + "spans": [ + { + "bbox": [ + 195, + 146, + 279, + 207 + ], + "type": "image", + "image_path": "cb2a4def2d50c5b11f6de58d37f068e888e2b679bc27a0d9c6cabcbd57551e6e.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 220, + 210, + 254, + 220 + ], + "lines": [ + { + "bbox": [ + 220, + 210, + 254, + 220 + ], + "spans": [ + { + "bbox": [ + 220, + 210, + 254, + 220 + ], + "type": "text", + "content": "R2R [26]" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 85, + 228, + 506, + 239 + ], + "lines": [ + { + "bbox": [ + 85, + 228, + 506, + 239 + ], + "spans": [ + { + "bbox": [ + 85, + 228, + 506, + 239 + ], + "type": "text", + "content": "Figure 8. 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9x9 DSPMC dilation21x21 DSPMC dilationPSNRSSIMFLOPS (G)Params (M)
1137.230.88588.61.35
1237.320.88629.80.45
1337.230.88317.10.26
2136.850.87984.61.23
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", + "image_path": "87197d8ac97094924b3ca41ff80b5099edda4b0f7ad8200bfd6612cfd832959d.jpg" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 47, + 342, + 333, + 362 + ], + "lines": [ + { + "bbox": [ + 47, + 342, + 333, + 362 + ], + "spans": [ + { + "bbox": [ + 47, + 342, + 333, + 362 + ], + "type": "text", + "content": "(a) Ablation studies on dilation rates. Different dilation rate combinations are explored on the DSPMC in the local branch and global branch." + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 19 + }, + { + "type": "table", + "bbox": [ + 352, + 249, + 544, + 339 + ], + "blocks": [ + { + "bbox": [ + 352, + 249, + 544, + 339 + ], + "lines": [ + { + "bbox": [ + 352, + 249, + 544, + 339 + ], + "spans": [ + { + "bbox": [ + 352, + 249, + 544, + 339 + ], + "type": "table", + "html": "
MethodPSNRSSIM
w/o 9×9 DSPMC35.820.855
w/o 21×21 DSPMC36.210.869
Replacing Conv with DTB36.900.880
Replacing DTB with Conv36.820.875
w/o kernel shift35.640.857
LG-BPN (Ours)37.320.886
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Such discrepancy across the scale demands us to treat scale-specific characteristics in a different way. When replacing the dilated convolution in the local branch with our DTB, the lack of local connectivity brings inferior performance. Similarly, when replacing the DTB in the global branch with the dilated convolution, the network is built by convolutions only. It induces a lack of long-range interaction, which greatly limits their recovery quality as well. This proves the superior design of our architecture. By exploiting the locality of convolution with a small DSPMC, also the global dependencies of DTB with a large DSPMC, our architecture enjoys more reasonable exploitation for multi-scale context." + } + ] + } + ], + "index": 42 + }, + { + "bbox": [ + 305, + 392, + 545, + 477 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 392, + 545, + 477 + ], + "spans": [ + { + "bbox": [ + 305, + 392, + 545, + 477 + ], + "type": "text", + "content": "The effect of kernel shift strategy. Since the requirement for pixel-wise independent noise is different in training and testing, directly applying the same kernel of the training phase while testing will lose image details [20]. We proposed a kernel shift strategy, as illustrated in Figure 5(b). In Table 2(b), the lack of kernel shift causes " + }, + { + "bbox": [ + 305, + 392, + 545, + 477 + ], + "type": "inline_equation", + "content": "1.68\\mathrm{dB}" + }, + { + "bbox": [ + 305, + 392, + 545, + 477 + ], + "type": "text", + "content": " drops, proving the effectiveness of our shifting paradigm." + } + ] + } + ], + "index": 43 + }, + { + "bbox": [ + 306, + 487, + 378, + 498 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 487, + 378, + 498 + ], + "spans": [ + { + "bbox": [ + 306, + 487, + 378, + 498 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 44 + }, + { + "bbox": [ + 304, + 506, + 545, + 661 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 506, + 545, + 661 + ], + "spans": [ + { + "bbox": [ + 304, + 506, + 545, + 661 + ], + "type": "text", + "content": "In this paper, we propose LG-BPN for self-supervised real image denoising, aiming to address the details lost by the coarse consideration for real noise correlation, and the lack of global interaction by the inherent constraint on the receptive field for BSN. First, we propose DSPMC to fully preserve the local structures. Owing to a denser receptive field, we ease the destruction of fine textures and can thus better reconstruct details. Second, we propose DTB, injecting distant interactions into the previously CNN-based blind spot networks. Since blind spot networks rely on neighbor signals for predicting, more clues can be provided by activating more neighbor pixels. Extensive results on real-world datasets reveal the superior performance of LG-BPN." + } + ] + } + ], + "index": 45 + }, + { + "bbox": [ + 304, + 665, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 712 + ], + "type": "text", + "content": "Acknowledgement This work was supported by the National Natural Science Foundation of China under Grants No. 62171038, No. 61827901, No. 62088101, and No. 62006023." + } + ] + } + ], + "index": 46 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18163" + } + ] + } + ], + "index": 47 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 711 + ], + "type": "list", + "angle": 0, + "index": 18, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "type": "text", + "content": "[1] Abdelrahman Abdelhamed, Stephen Lin, and Michael S Brown. 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In AAAI, pages 13074-13081, 2020. 2, 3, 4, 7, 8" + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "18165" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/LINe_ Out-of-Distribution Detection by Leveraging Important Neurons/7c02f584-1638-4590-ac47-479482d49ca3_content_list.json b/2023/LINe_ Out-of-Distribution Detection by Leveraging Important Neurons/7c02f584-1638-4590-ac47-479482d49ca3_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..d78829403d42e59908b27252871419aa60f934d5 --- /dev/null +++ b/2023/LINe_ Out-of-Distribution Detection by Leveraging Important Neurons/7c02f584-1638-4590-ac47-479482d49ca3_content_list.json @@ -0,0 +1,1502 @@ +[ + { + "type": "text", + "text": "LINE: Out-of-Distribution Detection by Leveraging Important Neurons", + "text_level": 1, + "bbox": [ + 124, + 161, + 843, + 181 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Yong Hyun Ahn $^{1}$ , Gyeong-Moon Park $^{2,*}$ , Seong Tae Kim $^{2,*}$", + "bbox": [ + 250, + 206, + 724, + 223 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ Department of Artificial Intelligence, Kyung Hee University", + "bbox": [ + 243, + 224, + 724, + 240 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{2}$ Department of Computer Science and Engineering, Kyung Hee University", + "bbox": [ + 188, + 240, + 781, + 256 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 288, + 310, + 302 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "It is important to quantify the uncertainty of input samples, especially in mission-critical domains such as autonomous driving and healthcare, where failure predictions on out-of-distribution (OOD) data are likely to cause big problems. OOD detection problem fundamentally begins in that the model cannot express what it is not aware of. Post-hoc OOD detection approaches are widely explored because they do not require an additional re-training process which might degrade the model's performance and increase the training cost. In this study, from the perspective of neurons in the deep layer of the model representing high-level features, we introduce a new aspect for analyzing the difference in model outputs between in-distribution data and OOD data. We propose a novel method, Leveraging Important Neurons (LINe), for post-hoc Out of distribution detection. Shapley value-based pruning reduces the effects of noisy outputs by selecting only high-contribution neurons for predicting specific classes of input data and masking the rest. Activation clipping fixes all values above a certain threshold into the same value, allowing LINe to treat all the class-specific features equally and just consider the difference between the number of activated feature differences between in-distribution and OOD data. Comprehensive experiments verify the effectiveness of the proposed method by outperforming state-of-the-art post-hoc OOD detection methods on CIFAR-10, CIFAR-100, and ImageNet datasets. Code is available on https://github.com/LINE-OOD", + "bbox": [ + 75, + 317, + 472, + 690 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 78, + 715, + 208, + 730 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, deep learning has made tremendous advances in various fields. This advancement has captivated numerous researchers, leading to many attempts to apply deep learning techniques to real-world applications. However, applying these state-of-the-art techniques to real-world applications is often limited for several reasons. One primary obstacle is the presence of unseen classes of samples during", + "bbox": [ + 75, + 739, + 468, + 835 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/f007fd399fdb39b6e1a34f13fee85226bc1601fdf466c7bc336594bcfc4984be.jpg", + "image_caption": [ + "Figure 1. Illustration of the number of activated neuron in the penultimate layer. The distributions of the number of activated neurons from ID (ImageNet [19]) and two OOD datasets (textures [10] and iNaturalist [51]) are presented. We define an activated neuron as one fired with an activation value greater than zero. Most of the neurons are activated when the model receives ID samples but fewer neurons are activated in OOD samples." + ], + "image_footnote": [], + "bbox": [ + 512, + 309, + 863, + 491 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "training. These samples, referred to as out-of-distribution (OOD) data, can compromise a model's stability and, in some cases, severely impair its performance. The inherent characteristics of OOD samples can lead to potentially severe consequences in mission-critical domains, such as autonomous driving and medical applications. So, effectively handling these OOD samples is vital to avoid problems, such as car crashes and misdiagnosis.", + "bbox": [ + 499, + 617, + 890, + 728 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "For OOD detection, numerous techniques have been explored to analyze the distinction between in-distribution (ID) data and OOD data. There are several approaches to OOD detection, including confidence-based methods [7, 11, 16, 19, 29], density-based methods [1, 20, 22-24, 27, 38, 40, 42, 50, 62, 63], and distance-based methods [9, 18, 28, 35, 41, 46, 48, 49, 58]. The post-hoc method is one approach in OOD detection that offers significant advantages in real-world applications as it eliminates the need for a re-training process, which could potentially degrade the model's per", + "bbox": [ + 499, + 728, + 892, + 866 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 95, + 8, + 169, + 45 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 228, + 5, + 815, + 47 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding authors: Gyeong-Moon Park (gmpark@khu.ac.kr) and Seong Tae Kim (st.kim@khu.ac.kr).", + "bbox": [ + 77, + 843, + 468, + 866 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "19852", + "bbox": [ + 465, + 888, + 504, + 898 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "formance and increase training costs [56].", + "bbox": [ + 77, + 126, + 354, + 140 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Post-hoc OOD detection methods [32, 44, 45] employ outputs such as model logits or layer activations, which are typically used for prediction, to calculate OOD scores. These scores allow for the differentiation of ID and OOD data based on the disparities in their respective scores [56]. Enhancing the overall OOD score distribution difference between ID and OOD data is a critical aspect in improving the performance of post-hoc OOD detection methods. Recent studies [44, 45] have found that augmenting the overall difference is contingent upon the capacity to mitigate noisy signals. For example, ReAct [44] demonstrates that OOD data exhibit considerable values in the penultimate layer activation. By truncating these noisy activations, ReAct effectively improves OOD detection performance. Similarly, DICE [45] uncovers the presence of noisy signals that increase the variance of the OOD score distribution. By selectively employing the most salient weights, DICE enhances OOD detection performance while reducing the impact of noisy signals. Minimizing the influence of noisy model outputs is crucial for advancing post-hoc OOD detection performance. In this study, we reveal an additional factor that is also important in the context of OOD detection.", + "bbox": [ + 75, + 143, + 472, + 448 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Figure 1 displays the histogram of the number of activated features in the penultimate layer. We define neurons with activation values greater than zero as activated neurons. As the figure demonstrates, a majority of neurons are activated when the model encounters ID samples. However, for OOD samples, fewer neurons are activated. To understand the primary cause of the observation in Figure 1, we investigate the model from the perspective of neuron-concept association [4,5,21,52]. According to [4], neurons are trained to detect disentangled high-level features in the deep layers of convolutional neural networks (CNNs), and they can even learn new unlabeled abstract concepts from the data [52]. The number of neurons representing these high-level features increases in deeper layers and becomes the most significant amount in the penultimate layer [5]. Since the activation in the penultimate layer represents the presence of these high-level features [4], different input images activate high-level features in varying ways, such as magnitude and patterns. These distinct patterns of activation in the penultimate layer are ultimately used to predict the input image's class. As each class possesses unique characteristics related to high-level concepts, the associated high-level features differ for each class. Consequently, each associated high-level feature can be categorized into one class-specific feature group. The disparity in associated high-level features in neurons results in a difference in penultimate layer activation between ID and OOD samples, which are predicted as the same class. Thus, taking into account the number of activated essential neurons can serve as a useful indicator for distinguishing ID and OOD samples.", + "bbox": [ + 75, + 451, + 472, + 866 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we present a novel post-hoc OOD detection method called Leveraging Important Neurons (LINe). LINe harnesses two crucial aspects: considering the number of activated important neurons and minimizing noisy activations to enhance OOD detection performance. To achieve this, we introduce two powerful techniques within LINe: 1) Shapley-based pruning and 2) activation clipping (AC).", + "bbox": [ + 497, + 126, + 894, + 223 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Shapley value-based pruning is a method that mitigates the influence of noisy outputs by selecting activations essential for inferring input data classes. While several methods exist for identifying important activations, Sun et al. [45] use activation magnitude to determine their importance. However, this approach alone is insufficient for quantifying a neuron's importance. Hence, we employ the Shapley value [43] to more accurately measure each neuron's contribution. Applying the Shapley value concept [43] to neural networks allows us to quantify each neuron's contribution to identifying a specific class. Moreover, neurons with high Shapley values are associated with critical input image features [21]. By leveraging the Shapley value [43], we can identify neurons that represent important high-level features for each class, which are essential for reducing noisy output.", + "bbox": [ + 497, + 223, + 894, + 430 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Activation clipping, a concept introduced in ReAct [44], is another powerful technique. Interpreting activation clipping in terms of class-specific features provides a new understanding of its role in considering the number of activated important neurons for OOD detection. Activation clipping adjusts values exceeding a certain threshold to the threshold value. This modification enables us to account for the differences in the number of activated features between in-distribution and OOD data by treating numerous class-specific features equally. By considering the variation in the number of activated class-specific features, we can effectively augment the overall OOD score difference between ID and OOD data, leading to enhanced performance.", + "bbox": [ + 497, + 430, + 894, + 609 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our key contributions are summarized as follows:", + "bbox": [ + 519, + 609, + 850, + 623 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a simple yet effective post-hoc OOD detection method, named LINe, which uses the Shapley value to rank the contribution of neurons and gives a new inspiration for leveraging selected important class-specific neurons.", + "- We unveil the important factor for improving OOD scoring and show a new way of understanding the role of activation clipping for OOD detection. By applying activation clipping, we can fully consider the number of activated class-specific features and achieve higher OOD detection performance.", + "- Comprehensive experiments have been conducted to verify the effectiveness of the proposed method on the CIFAR-10, CIFAR-100, and ImageNet-1K. Compared to the competitive post-hoc method DICE [45], LINe reduces the FPR95 by up to $14.05\\%$ ." + ], + "bbox": [ + 519, + 630, + 890, + 866 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "19853", + "bbox": [ + 465, + 888, + 504, + 898 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Background and Related Work", + "text_level": 1, + "bbox": [ + 77, + 124, + 363, + 140 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.1. Neuron-Concept Association", + "text_level": 1, + "bbox": [ + 77, + 147, + 332, + 162 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Neuron-concept association methods are a field of study that tries to interpret the internal computation of CNN to a human-understandable concept [3,8,14,37]. Several studies have shown that neurons of shallower layers tend to learn more simple and low-level concepts, such as curves and edges, while deeper layers learn more abstract and high-level concepts, such as arm and face [52, 59, 60]. The methods for quantifying the concept's contribution are also introduced in [12, 14, 33]. Network Dissection [4, 5, 59] assigns each neuron to a concept to quantify its role. Bau et al. [6] investigate the effect of concept-specific neurons by observing the change of concept-related contents in generative models. Recently, Wang et al. [52] show that models can learn abstract concepts like mammal and carnivore, which is not in the label set of training data.", + "bbox": [ + 75, + 168, + 472, + 376 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Shapley Value", + "text_level": 1, + "bbox": [ + 77, + 385, + 223, + 400 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Shapely value [26, 43, 47] is a concept from Game Theory, which evaluates each property's individual and collaborative effects. Studies have been conducted using Shapley value in CNNs to measure each neuron's contribution and interpret models' behaviors [2, 13, 21, 34, 47]. Neuron Shapley [13] sorts the Shapley values to identify the most influential neurons from all hidden layers as image categories. Khazar et al. [21] show neurons that have high Shapley values have high correlations with important features of the input image. Previous studies have inspired us to select important class-specific neurons through the contribution scores calculated from the Shapley value. LINe can effectively eliminate the negative effects of noisy signals by leveraging the selected class-specific neurons.", + "bbox": [ + 75, + 407, + 472, + 602 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.3. Out-of-Distribution Detection", + "text_level": 1, + "bbox": [ + 77, + 609, + 341, + 624 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "ODD detection aims to find inputs with different characteristics from the training data [56]. A lot of research efforts have been devoted to developing an effective method to distinguish OOD inputs from ID inputs. Confidence-based methods perform OOD detection by quantifying OOD scores based on different scoring functions [7,11,16,19,29]. Hendrycks et al. [16] used a maximum softmax probability (MSP) of the model as a baseline confidence-base OOD scoring function. ODIN [30] utilizes perturbation of inputs and temperature scaling on the softmax layer to increase the difference between ID and OOD. To enhance the effectiveness of confidence-based scores, recently, Liu et al. [32] introduced an energy-based score with the theoretical interpretation from a likelihood perspective, which is further adopted in [31, 36, 53] to distinguish ID and OOD samples. Distance-based approaches measure the distance between input sample and typical ID samples or cen", + "bbox": [ + 75, + 632, + 472, + 866 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "troids of them [9, 18, 28, 35, 41, 46, 48, 49, 58]. These approaches are based on simple evidence that OOD samples should have more distance than IDs. Similarly, density-based methods identify OOD samples based on the distribution of the training samples and use density (or likelihood) [1, 20, 22-24, 27, 38, 40, 42, 50, 62, 63].", + "bbox": [ + 497, + 124, + 894, + 209 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "But none of the aforementioned methods consider the number of activated features, which can be a good indicator to distinguish ID and OOD samples. The most similar study to our study is DICE [45]. DICE leverages sparsification to reduce the effect of noisy signals by selectively using salient weights from activation [45]. In this study, we effectively eliminate the outcomes of noisy signals by accurately selecting neurons leveraging the contribution of neurons calculated from Shapley value [21, 43]. In addition, our method performs OOD detection more effectively by considering the number of activated features. The neurons are known to be associated with the concepts, and the activation patterns of neurons in deep layers are different in ID and OOD. This gives a theoretical background for considering the number of activation in OOD detection. To the best of our knowledge, our work is the first study to leverage the neuron contribution based on Shapley value and consider the number of activated features for calculating OOD score.", + "bbox": [ + 497, + 209, + 895, + 458 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 499, + 470, + 591, + 486 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Method Overview", + "text_level": 1, + "bbox": [ + 499, + 495, + 673, + 508 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our method mainly consists of two parts: Activation Clipping and Shapley-based pruning. Activation clipping is a method of clipping each neuron activation to a specific value when the activation value exceeds a particular threshold $(\\delta)$ . Through activation clipping, our method can consider the number of high-level features during calculating OOD scores, which are analyzed in terms of neuron-concept association. Next, Shapley-based pruning eliminates the negative effect of noisy signals by measuring neural contributions of neural networks using important neurons only. We can accurately measure the contribution of each neuron using Shapley value, which is a mathematically grounded method. Also, by applying Shapley value, we can obtain supporting evidence that neurons with large contributions represent critical features for recognizing input image [21]. This allows us to assemble all contributions for each class and select important class-specific neurons representing class-specific features. More details of activation clipping and Shapley-based pruning will be described in Subsection 3.2 and Subsection 3.3. In Subsection 3.4, we will explain the overall method.", + "bbox": [ + 497, + 517, + 895, + 808 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Activation Clipping", + "text_level": 1, + "bbox": [ + 499, + 816, + 690, + 832 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For a pre-trained deep neural network $f_{\\theta}(x)$ parameterized by $\\theta$ , $f_{\\theta}(x)$ encodes an input $x \\in \\mathbb{R}^d$ , where $d$ indicates", + "bbox": [ + 499, + 839, + 894, + 866 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "19854", + "bbox": [ + 465, + 888, + 505, + 898 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/0def9eac921510dc2e6798d6ea7a88f2db213213b6dbff3dd21ad94013718f17.jpg", + "image_caption": [ + "Figure 2. Overall procedure of LINe for calculating OOD score. LINe is composed of mainly three parts. 1) Activation Clipping (AC), 2) Activation Pruning (AP), 3) Weight Pruning (WP). AC limits the magnitude of the activation, which allows LINe to consider the number of activated features. AP uses contribution matrix C, which is precomputed from Shapley value [43]. AP leverages C to select important neurons and mask others. WP uses an adjusted contribution matrix which is obtained from the contribution matrix C. Leveraging AP and WP, LINe can reduce noisy signals effectively." + ], + "image_footnote": [], + "bbox": [ + 82, + 124, + 890, + 437 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "dimension of input $x$ , and predicts a class distribution for $L$ different classes, i.e., $f_{\\theta}(x) \\in \\mathbb{R}^{L}$ . Feature vector from the penultimate layer of the network denotes $h(x) \\in \\mathbb{R}^q$ , where $q$ stands for the dimension of penultimate layer output $h(x)$ . Weight matrix $\\mathbf{W} \\in \\mathbb{R}^{q \\times L}$ weights the importance of each feature in $h(x)$ and transfers to output $f_{\\theta}(x)$ as follows:", + "bbox": [ + 75, + 539, + 472, + 624 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nf _ {\\theta} (x) = \\mathbf {W} ^ {T} h (x) + \\mathbf {b}. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 194, + 640, + 468, + 659 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Activation clipping is applied to the feature vector in the penultimate layer. For each neuron that is activated above a certain threshold, AC limits the magnitude of the activation. As we discussed in Figure 1, the number of activated features in ID and OOD samples are different. By limiting the magnitude of the activation to the same value $\\delta$ , we can treat every activated high-level feature equally, which allows us to consider the number of activated features in the OOD score. This increases the OOD score difference between ID and OOD samples, thereby improving performance.", + "bbox": [ + 75, + 671, + 470, + 810 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For each activation $a_{i}$ in $h(x)$ , penultimate layer feature $h(x)$ can be denoted as $h(x) = [a_1, a_2, \\dots, a_q]$ . With a clipping threshold $\\delta$ , the clipped activation $\\hat{a}_{i}$ can be described as $\\hat{a}_{i} = \\min(a_{i}, \\delta)$ . The clipped feature vector $\\hat{h}(x)$", + "bbox": [ + 75, + 810, + 472, + 868 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "is then,", + "bbox": [ + 500, + 539, + 554, + 552 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {h} (x) = \\left[ \\hat {a} _ {1}, \\hat {a} _ {2}, \\dots , \\hat {a} _ {q} \\right]. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 611, + 554, + 892, + 571 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The model output after AC can be given as:", + "bbox": [ + 500, + 580, + 791, + 595 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nf _ {\\theta} ^ {A C} (x) = \\mathbf {W} ^ {T} \\hat {h} (x) + \\mathbf {b}. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 611, + 605, + 892, + 623 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Shapley-based Pruning", + "text_level": 1, + "bbox": [ + 500, + 636, + 717, + 652 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Shapley-based pruning selectively uses a subset of important neuron activation and weights. To select these subsets, we calculate Shapley value [43] defined by an average of the effect of removing a single unit (e.g., marginal contribution) to all possible combinations of units. However, computing all the combinations of units is computationally expensive and practically infeasible for recent large neural networks. Therefore, we use the Taylor approximation to compute the Shapley value, which is introduced in [21]. For input $x^{l} \\in D$ , where $x^{l}$ denotes the sample of class $l$ from dataset $D$ , a contribution(i.e., Shapley value) of $i$ -th neuron $a_{i}$ in class $l$ , $s_{i}^{l}$ is calculated as", + "bbox": [ + 497, + 658, + 894, + 826 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left. s _ {i} ^ {l} = \\left| f _ {\\theta} \\left(x ^ {l}\\right) - f _ {\\theta} \\left(x ^ {l}; a _ {i} \\leftarrow 0\\right) \\right| = \\left| a _ {i} \\nabla_ {a _ {i}} f _ {\\theta} \\left(x ^ {l}\\right) \\right|. \\right. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 850, + 892, + 870 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "19855", + "bbox": [ + 465, + 888, + 505, + 898 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/0ab4224d979cfb5e7ec58b7c94a41d7e36a54355302b2850f96c7d7d7a592264.jpg", + "image_caption": [ + "Figure 3. Calculation of contribution matrix C." + ], + "image_footnote": [], + "bbox": [ + 80, + 123, + 467, + 246 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3.1 Activation Pruning", + "text_level": 1, + "bbox": [ + 75, + 294, + 265, + 307 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Activation pruning (AP) selectively uses the subset of important neuron activation. Through AP, We can effectively reduce the impact of noisy activation. From the contribution of each neuron $s_i^l$ , which is using obtained from all training data, contribution matrix $\\mathbf{C} \\in \\mathbb{R}^{q \\times L}$ is defined as the class-specific average of all contribution $s_i^l$ . An $(i,l)$ -th entry of contribution matrix $c_{il} \\in \\mathbf{C}$ is defined as:", + "bbox": [ + 75, + 315, + 470, + 412 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {C} _ {i l} = \\frac {1}{n} \\sum^ {n} s _ {i} ^ {l}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 218, + 420, + 468, + 450 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $n$ denotes the number of training images in class $l$ . We select top- $k$ neurons for each class based on the k-largest elements from each column in $\\mathbf{C}$ and define an activation mask matrix $\\mathbf{M}_a \\in \\mathbb{R}^{q \\times L}$ , where we set 1 for the $k$ -largest elements from every column in $\\mathbf{C}$ , otherwise 0. The model output after AP with the predicted class $l$ is given as:", + "bbox": [ + 75, + 457, + 468, + 539 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nf _ {\\theta} ^ {A P} (x) = \\mathbf {W} ^ {T} \\left(\\mathbf {m} _ {l} \\odot h (x)\\right) + \\mathbf {b}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 159, + 548, + 468, + 565 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf{m}_l\\in \\mathbb{R}^q$ indicates $l$ -th column of mask matrix $\\mathbf{M}_a$ and $\\odot$ denotes the element-wise multiplication.", + "bbox": [ + 75, + 574, + 468, + 602 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3.2 Weight Pruning", + "text_level": 1, + "bbox": [ + 75, + 618, + 243, + 632 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Weight pruning (WP) selectively uses the subset of important penultimate layer weights. Through WP, We can effectively reduce the impact of noisy signals due to the overparameterized model. The contribution of neurons is further used to refine the weight matrix as WP. For this purpose, we define a weight contribution matrix for the class $l$ as $\\mathbf{C}_w^l = \\mathbf{c}_l\\odot \\mathbf{W}\\in \\mathbb{R}^{q\\times L}$ where $\\mathbf{c}_1$ indicates the $l$ -th column of contribution matrix $\\mathbf{C}$ . We select top- $k$ weights for each class based on the $k$ -largest elements in $\\mathbf{C}_w^l$ and define a mask matrix for class $l$ as $\\mathbf{M}_w^l\\in \\mathbb{R}^{q\\times L}$ by setting 1 for the $k$ -largest elements in $\\mathbf{C}_w^l$ , otherwise 0. The model output after WP with the predicted class $l$ is given as:", + "bbox": [ + 75, + 639, + 470, + 806 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nf _ {\\theta} ^ {W P} (x) = \\left(\\mathbf {W} \\odot \\mathbf {M} _ {w} ^ {l}\\right) ^ {T} h (x) + \\mathbf {b}. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 156, + 813, + 468, + 831 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "From the Shapley-based AP and WP, we can determine the neurons representing important high-level features for each", + "bbox": [ + 75, + 839, + 470, + 866 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/9a0a2fc7404aa9c3896e94c9b97fe841f045589fa95f00d89115574b96f88458.jpg", + "image_caption": [ + "Figure 4. Calculation of contribution matrix $\\mathbf{C}_{\\mathbf{w}}^{\\mathrm{l}}$ ." + ], + "image_footnote": [], + "bbox": [ + 510, + 124, + 885, + 218 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "class, which play a crucial role in reducing noisy output.", + "bbox": [ + 499, + 266, + 873, + 280 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Leveraging Important Neurons (LINe)", + "text_level": 1, + "bbox": [ + 499, + 302, + 833, + 317 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As already described in the previous Subsection 3.2 and 3.3, there are two ideas to improve the performance of post-hoc OOD detection. One is considering the number of activated high-level features, and the other is reducing noisy signals from less important neurons. LINe achieves both ways to improve post-hoc OOD detection performance through the procedures described above. By adapting LINe to a model, we can effectively increase the overall difference in OOD scores between ID and OOD data. As a result, the model output under LINe with the predicted class $l$ is described as", + "bbox": [ + 497, + 323, + 892, + 475 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nf _ {\\theta} ^ {L I N e} (x) = \\left(\\mathbf {W} \\odot \\mathbf {M} _ {w} ^ {l}\\right) ^ {T} \\left(\\mathbf {m} _ {l} \\odot \\hat {h} (x)\\right) + \\mathbf {b}. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 547, + 483, + 890, + 502 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Please note that there is no parameter change in the model itself and ID classification accuracy can be preserved.", + "bbox": [ + 499, + 512, + 892, + 539 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 551, + 633, + 565 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Comprehensive experiments have been conducted to evaluate our method. In section 4.1, we used the CIFAR [25] benchmark, which is one of the famous benchmarks in OOD studies [32, 44, 45]. In Section 4.2, experiments were conducted based on a large-scale dataset, ImageNet, with various OOD datasets. Section 4.3 analyzes why our method is effective through various ablation experiments.", + "bbox": [ + 497, + 574, + 892, + 671 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Evaluation on CIFAR Benchmarks", + "text_level": 1, + "bbox": [ + 499, + 678, + 806, + 693 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implementation Details. In this experiment, we used 10,000 test images each from CIFAR-10 [25] and CIFAR-100 [25] as ID data, respectively. The model's performance was evaluated using six commonly used OOD datasets as an OOD benchmark. The list of six OOD datasets is as follows: SVHN [39], Textures [10], iSUN [55], LSUN-Crop [57], LSUN-Resize [57], and Places365 [61]. As the pre-trained models, we used DenseNet [17]. As in [45], the models are trained from CIFAR-10 [25] and CIFAR-100 [25] with 50,000 training images respectively. Following [45], the models were trained during 100 epochs with batch size 64, weight decay 0.0001, momentum 0.9, and", + "bbox": [ + 497, + 700, + 894, + 866 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "19856", + "bbox": [ + 465, + 888, + 505, + 898 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/06c8c80117437cd709f1bd501e7477c405902915eeadbb31d2b8c2da579c09cf.jpg", + "table_caption": [ + "Table 1. Comparison on CIFAR benchmarks. Comparison with competitive post-hoc OOD detection methods on CIFAR benchmarks. All values in this table are percentages and averaged over six OOD test datasets. $\\downarrow$ indicates smaller value means better performance and $\\uparrow$ indicates vice versa. Bold numbers are superior results. The overall detail results for each OOD dataset are provided in supplementary material." + ], + "table_footnote": [], + "table_body": "
MethodCIFAR-10CIFAR-100
FPR95 ↓AUROC ↑FPR95 ↓AUROC ↑
MSP [16]48.7392.4680.1374.36
ODIN [30]24.5793.7158.1484.49
Mahalanobis [28]31.4289.1555.3782.73
Energy [32]26.5594.5768.4581.19
ReAct [44]26.4594.9562.2784.47
DICE [45]20.8395.2449.7287.23
DICE + ReAct16.4896.6449.5785.08
LINe (Ours)14.7196.9935.6788.67
", + "bbox": [ + 80, + 223, + 467, + 348 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "start learning rate 0.1. The learning rate was decayed by a factor of 10 at epochs 50, 75, and 90. We used the entire training dataset to estimate the contribution matrix $C$ .", + "bbox": [ + 75, + 372, + 468, + 413 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Comparison. For comparison, we adopted recent post-hoc OOD detection methods: MSP [16], ODIN [30], Mahalanobis distance [28], Energy [32], ReAct [44], and DICE [45]. For all methods, the performances were measured by OOD scores, derived from the same DenseNet model.", + "bbox": [ + 75, + 414, + 468, + 483 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Experimental Results. Table 1 shows the comparisons between LINe and other post-hoc OOD detection methods on CIFAR-10 and CIFAR-100 benchmarks. As shown in the table, our method achieved state-of-the-art performances by outperforming all the other methods on both CIFAR-10 and CIFAR-100 datasets. In CIFAR-100, LINe reduced FPR 95 by $14.05\\%$ compared to the competitive method DICE [45]. In CIFAR-100, LINe achieved an FPR 95 of $14.05\\%$ which was lower than the FPR 95 of DICE [45] $(49.72\\%)$ and DICE + ReAct $(49.57\\%)$ . DICE + ReAct is the method that is implemented by applying ReAct [44] on DICE [45]. DICE [45] removed the noisy signals by using the magnitude of activation and weight. LINe not only removed the noisy signals using class-specific neurons but also considered the number of activations of the high-level feature.", + "bbox": [ + 75, + 486, + 470, + 694 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Evaluation on ImageNet", + "text_level": 1, + "bbox": [ + 77, + 706, + 302, + 721 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation Details. In real-world applications, the model encounters high-resolution images with various scenes and features, and evaluation on a large-scale dataset can provide clues about model performance in a real-world application. Therefore, in this experiment, we evaluated LINe on a large-scale ImageNet dataset. Based on [19], a subset of the four datasets where all the overlapping categories with ImageNet-1k were eliminated was used as OOD datasets. The four OOD datasets are as follows: Textures [10], Places365 [61], iNaturalist [51], and SUN [54]. We", + "bbox": [ + 75, + 728, + 468, + 866 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "used a pre-trained ResNet-50 model [15], which is trained with ImageNet-1k. The entire training dataset was used to estimate the contribution matrix $C$ , and all images were resized to $224 \\times 224$ at test time.", + "bbox": [ + 497, + 126, + 892, + 180 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Experimental Results. In Table 2, we reported the performances of four OOD test datasets respectively. The average results from the four OOD test datasets were also reported. LINe outperformed all baselines including MSP [16], ODIN [30], Mahalanobis distance [28], Energy score [32], ReAct [44], DICE [45], and DICE + ReAct [45]. We compared LINe with Energy [32] first. LINe drastically reduced the FPR95 by $37.71\\%$ , which shows the benefit of leveraging important neurons under the same OOD scoring function. Next, we compared LINe with ReAct [44]. LINe reduced the FPR95 by $10.73\\%$ , which allows us to see the advantages of leveraging important neurons using Shapley value. LINe further outperformed recent DICE [45] and DICE + ReAct by $14.05\\%$ and $6.55\\%$ , respectively. Experimental results showed that the proposed method can be applied to real-world large dataset for OOD detection.", + "bbox": [ + 497, + 181, + 892, + 401 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Ablation Study", + "text_level": 1, + "bbox": [ + 499, + 409, + 653, + 425 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we discuss the effectiveness of each part used in LINe and the detailed differences from other similar approaches. We also analyze the effect of hyperparameters.", + "bbox": [ + 499, + 431, + 892, + 473 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3.1 Ablation Study of LINe on ImageNet", + "text_level": 1, + "bbox": [ + 499, + 489, + 811, + 504 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 3 shows an ablation study over various parts used in LINe. As shown in the table, each part of Shapley-based pruning (AP and WP) improved the performance. Comparing LINE w/o WP with Energy + AC allows us to see the advantages of reducing the noisy activation, which reduces FPR95 by $8.52\\%$ . Next, we compared LINe w/o AP with Energy + AC, which also shows the benefits of reducing noisy weights. Compared to Energy + AC, LINe w/o AP reduced FPR95 by $12.21\\%$ . Finally, we compared LINe w/o AP with DICE + ReAct [45] at Table 2, which allows us to see the benefit of leveraging class-wise contribution under similar circumstances. LINe w/o AP reduced the FPR95 by $4.06\\%$ from $27.25\\%$ to $23.19\\%$ . DICE + ReAct [45] uses activations to select important weights, while LINe w/o AP selects important weights using class-wise contribution derived from the Shapley value [43].", + "bbox": [ + 497, + 511, + 892, + 732 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3.2 Effect of Changing AC Threshold on ImageNet", + "text_level": 1, + "bbox": [ + 499, + 747, + 880, + 763 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In Section 3.2, we discussed the meaning of AC in terms of the neuron-concept association. AC allows us to consider the number of activated high-level features in the penultimate layer. In Table 4, we show various OOD detection performances of the model by changing threshold $\\delta$ . Starting from clipping threshold $\\delta = \\infty$ , the value of FPR95 is the highest in the table. As clipping threshold $\\delta$ becomes", + "bbox": [ + 497, + 769, + 892, + 866 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "19857", + "bbox": [ + 465, + 888, + 505, + 898 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/91ab9adf3a6daa3219358b75dbaa903c1280ec81cf51173dc3a45c52a3f811c5.jpg", + "table_caption": [ + "Table 2. Comparison on ImageNet benchmark. Comparisons with competitive post-hoc OOD detection methods on ImageNet benchmark. All values in this table are percentages and averaged over four OOD test datasets." + ], + "table_footnote": [], + "table_body": "
MethodOOD DatasetsAverage
iNaturalistSUNPlacesTexturesFPR95 ↓ AUROC ↑
FPR95 ↓AUROC ↑FPR95 ↓AUROC ↑FPR95 ↓AUROC ↑FPR95 ↓AUROC ↑FPR95 ↓AUROC ↑
MSP [16]54.9987.7470.8380.8673.9979.7668.0079.6166.9581.99
ODIN [30]47.6689.6660.1584.5967.8981.7850.2385.6256.4885.41
Mahalanobis [28]97.0052.6598.5042.4198.4041.7955.8085.0187.4355.47
Energy [32]55.7289.9559.2685.8964.9282.8653.7285.9958.4186.17
ReAct [44]20.3896.2224.2094.2033.8591.5847.3089.8031.4392.95
DICE [45]25.6394.4935.1590.8346.4987.4831.7290.3034.7590.77
DICE + ReAct [45]18.6496.2425.4593.9436.8690.6728.0792.7427.2593.40
LINe (Ours)12.2697.5619.4895.2628.5292.8522.5494.4420.7095.03
", + "bbox": [ + 80, + 159, + 892, + 300 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/72ccf20ab106c9a821e7ef2458292838051d3cf7f136a1d6d41920ad91b7993c.jpg", + "table_caption": [ + "Table 3. Ablation Study of LINe on ImageNet. Ablation on the effectiveness of Shapley-based pruning used in LINe and comparison with similar approaches. Values are percentages and averaged over OOD datasets. AC, AP, and WP denote activation clipping, activation pruning, and weight pruning, respectively." + ], + "table_footnote": [], + "table_body": "
MethodACAPWPFPR95↓AUROC↑
Energy [32]58.4186.17
Energy + AC✓35.4091.86
LINe w/o WP✓✓26.8893.77
LINe w/o AP✓✓23.1994.57
LINe (Ours)✓✓✓20.7095.03
", + "bbox": [ + 100, + 395, + 448, + 479 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/67b22029c76548d08ecb0167b5f185ce6d992dd7465c97b4c0bc56689aa866d5.jpg", + "table_caption": [ + "Table 4. Ablation on different thresholds $(\\delta)$ of AC. Ablation on the different thresholds $(\\delta)$ of clipping. All values are percentages and averaged over multiple OOD test datasets." + ], + "table_footnote": [], + "table_body": "
Threshold (δ)FPR95 ↓AUROC ↑
δ = 0.141.1888.44
δ = 0.423.4394.79
δ = 0.820.7095.03
δ = 1.021.6994.81
δ = 1.526.9693.99
δ = 2.031.8892.97
δ = ∞ (no AC)44.8889.14
", + "bbox": [ + 147, + 539, + 401, + 649 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "smaller, the OOD detection performance is improved. But at clipping threshold $\\delta < 0.8$ , the OOD detection performance dropped. This is because, as the clipping threshold $\\delta$ approaches 0, all the penultimate output values also approach zero. It is obvious that performance will drop when all the penultimate output values approach zero.", + "bbox": [ + 75, + 671, + 468, + 756 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3.3 Effect of Changing Pruning Percentile on ImageNet", + "text_level": 1, + "bbox": [ + 75, + 774, + 470, + 803 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, we conducted ablation studies on pruning percentiles $(p)$ variation on ImageNet datasets as ID data. In Table 5 we show effect of changing pruning percentile $(p_w$ and $p_a)$ on ImageNet. $p_a$ indicates pruning percentile", + "bbox": [ + 75, + 810, + 470, + 868 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/030c32695dabbf52a8e92890e2dd4f2522aa2bb6b94cbd6e72bd42f15bd4d67b.jpg", + "table_caption": [ + "Table 5. Effect of changing pruning percentile $(p)$ on ImageNet. Ablation on the different pruning percentile $(p_a$ and $p_w)$ of pruning. All values are percentages and averaged over multiple OOD test datasets. $p_a$ denotes pruning percentile for AP, $p_w$ indicates pruning percentile for WP." + ], + "table_footnote": [], + "table_body": "
pa=90pa=70pa=50pa=30pa=10
FPR95 ↓FPR95 ↓FPR95 ↓FPR95 ↓FPR95 ↓
pw=9027.5624.7924.7424.5524.54
pw=7027.4525.9325.8127.4533.32
pw=5033.6927.7826.2825.9027.45
pw=3027.4626.1027.1724.3628.43
pw=1027.6426.7527.7525.4120.70
", + "bbox": [ + 504, + 395, + 895, + 488 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "for AP, $p_w$ indicates pruning percentile for WP. For a fixed WP percentile $p_w$ with extremely high value (e.g., $p_w = 90$ ), the performance tends to increase when the AP percentile $p_a$ falls. Since LINe considers the number of activated features for detecting OOD samples, pruning most of the activations or weights has negatively impacted the performance. A lower pruning percentile is better to leverage differences in the number of activated features between ID and OOD samples. But to restrict the negative effect of noisy signals, we need some portions that can remove the noisy signals. As a result, the model performs the best when the pruning percentile is $p_w = 10$ and $p_a = 10$ on ImageNet.", + "bbox": [ + 497, + 513, + 894, + 680 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3.4 Effect of Changing Pruning Percentile on CIFAR Benchmarks", + "text_level": 1, + "bbox": [ + 499, + 703, + 892, + 730 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In Table 6 and Table 7, we show effect of changing pruning percentile $(p_w$ and $p_a)$ on CIFAR Benchmarks. Both tables show similar tendencies. For all AP percentile $p_a$ , the performance tends to increase when the WP percentile $p_w$ increases. In Table 6, highest performance appeared at $p_w = 90$ and $p_a = 90$ . On the other hand in Table 7, the highest performance appeared at $p_w = 90$ and $p_a = 10$ . This result may seem to conflict with the result in Table 5, our observation in Table 8 can explain the cause of the difference.", + "bbox": [ + 497, + 741, + 892, + 866 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "19858", + "bbox": [ + 465, + 888, + 505, + 898 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/b5d057bb562a244ae4061f512d1209afe999ef6b5716517fb4bd69a834308aa3.jpg", + "table_caption": [ + "Table 6. Effect of changing pruning percentile $(p)$ in CIFAR10. Ablation on the different pruning percentile $(p_a$ and $p_w)$ of pruning. All values are percentages and averaged over multiple OOD test datasets. $p_a$ denotes pruning percentile for AP, $p_w$ indicates pruning percentile for WP." + ], + "table_footnote": [], + "table_body": "
pa=90pa=70pa=50pa=30pa=10
FPR95 ↓FPR95 ↓FPR95 ↓FPR95 ↓FPR95 ↓
pw=9014.7215.0015.0015.0014.99
pw=7014.8015.1215.1215.1215.10
pw=5014.8015.1215.1115.1115.10
pw=3014.8015.1215.1115.1215.10
pw=1014.8015.1315.1315.1215.73
", + "bbox": [ + 80, + 197, + 473, + 291 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/a651343816efac538068c05657ca890a3907de2f558601fdef907f085026aa93.jpg", + "table_caption": [ + "Table 7. Effect of changing pruning percentile $(p)$ in CIFAR100. Ablation on the different pruning percentile $(p_a$ and $p_w)$ of pruning. All values are percentages and averaged over multiple OOD test datasets. $p_a$ denotes pruning percentile for AP, $p_w$ indicates pruning percentile for WP." + ], + "table_footnote": [], + "table_body": "
pa=90pa=70pa=50pa=30pa=10
FPR95↓FPR95↓FPR95↓FPR95↓FPR95↓
pw=9038.7537.8137.8137.7535.67
pw=7038.3739.3040.0739.7540.81
pw=5038.3739.1940.5440.2742.14
pw=3038.3739.1940.6540.2139.32
pw=1038.4039.3140.7640.9138.17
", + "bbox": [ + 80, + 379, + 473, + 472 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/fd0939c6e90fbe7266b0a9a48eada267fdcef2bbb4c9bb7ad16d23c19a2af31f.jpg", + "table_caption": [ + "Table 8. Percentage of class-specific neuron overlap in multiple classes. Difference between the percentage of class-specific neuron overlap in multiple classes on three data sets. For each dataset, we calculated the proportion of very important (top $10\\%$ neurons in more than $o\\%$ of the class. All values are percentages." + ], + "table_footnote": [], + "table_body": "
OverlapCIFAR-10CIFAR-100ImageNet
o = 2024.5626.901.70
o = 3023.390.580.15
", + "bbox": [ + 126, + 561, + 421, + 609 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3.5 Discussion", + "text_level": 1, + "bbox": [ + 77, + 634, + 205, + 646 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In Table 8, we compared the percentage of class-specific neuron overlap in multiple classes on three data sets. For each dataset, we calculated the proportion of very important (top $10\\%$ ) neurons in more than $o\\%$ of the class. These neurons activate in various classes which have semantically different features. Therefore, the higher proportion of these neurons can be seen as an overparameterized model with more numbers of generally activated neurons. These overparameterized models make OOD detection difficult by creating noisy signals, which can be reduced by leveraging AP and WP. To get optimal results from overparameterized models, we can lessen the effect of overparameterized weights with high WP percentile. Also, the effectiveness of considering the number of activated class-specific neurons can be maximized in the low AP percentile as a tendency", + "bbox": [ + 75, + 659, + 468, + 866 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "shown in Table 7. But for a much more overparameterized model, which is shown in Table 6, we need to set high pruning percentile on both $p_w$ and $p_a$ .", + "bbox": [ + 499, + 126, + 892, + 167 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The degree of an overparameterized model can be understood from Section 4.1. We used the same pre-trained model architecture for evaluating CIFAR-10 and CIFAR-100. Of the two models with the same structure, we can intuitively understand that a model trained using a relatively small dataset is more likely to be overparameterized, which can also be observed in Table 8. The proportion of very important (top $10\\%$ ) neurons in more than $30\\%$ of the class(i.e., $o = 30$ ) on CIFAR-10 is the largest compared to other datasets. This observation shows that our pre-trained model used to evaluate CIFAR-10 is more overparameterized than other models we used.", + "bbox": [ + 499, + 168, + 892, + 332 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 348, + 618, + 362 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we propose a powerful OOD Detection method called LINe. LINe adopts a neural-concept association, which only uses important activations and weights selectively by measuring class-wise contribution from the Shapley value. Through LINe, we can effectively reduce the influence of the noise signal and make a difference in the overall OOD score between ID and OOD sample distribution. We conducted extensive experiments to demonstrate that LINe is superior to state-of-the-art OOD detection methods and effective on multiple datasets. From several theoretical studies and insights, we show how our method improves the performance of OOD detection. Our method is effective but has some limitations. It is fundamentally a trade-off relationship that pruning neurons to reduce the noisy output and considers the number of class-specific feature activations. Users have to examine the trade-off considering the degree of overparameterization of the model. We hope that as our study proposes an effective way to view OOD detection from a feature presentation perspective, attempts to understand the behavior of neural networks will be applied to multiple domains to discover other effective methods.", + "bbox": [ + 499, + 372, + 892, + 675 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements", + "text_level": 1, + "bbox": [ + 500, + 690, + 665, + 706 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was supported in part by the Institute of Information and Communications Technology Planning and Evaluation (IITP) grant funded by the Korea Government (MSIT)(No. 2022-0-00078: Explainable Logical Reasoning for Medical Knowledge Generation, No. 2021-0-02068: Artificial Intelligence Innovation Hub, No. RS2022-00155911: Artificial Intelligence Convergence Innovation Human Resources Development (Kyung Hee University)) and by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2021R1G1A1094990).", + "bbox": [ + 499, + 714, + 892, + 866 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "19859", + "bbox": [ + 465, + 888, + 505, + 898 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 124, + 173, + 139 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Davide Abati, Angelo Porrello, Simone Calderara, and Rita Cucchiara. 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In International conference on learning representations, 2018. 1, 3" + ], + "bbox": [ + 78, + 126, + 470, + 475 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "19862", + "bbox": [ + 467, + 888, + 504, + 898 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/LINe_ Out-of-Distribution Detection by Leveraging Important Neurons/7c02f584-1638-4590-ac47-479482d49ca3_model.json b/2023/LINe_ Out-of-Distribution Detection by Leveraging Important Neurons/7c02f584-1638-4590-ac47-479482d49ca3_model.json new file mode 100644 index 0000000000000000000000000000000000000000..22b5058002b5d2fb207da470f578dbb573b269af --- /dev/null +++ b/2023/LINe_ Out-of-Distribution Detection by Leveraging Important Neurons/7c02f584-1638-4590-ac47-479482d49ca3_model.json @@ -0,0 +1,2224 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.096, + 0.009, + 0.171, + 0.046 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.23, + 0.006, + 0.816, + 0.048 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.126, + 0.162, + 0.844, + 0.182 + ], + "angle": 0, + "content": "LINE: Out-of-Distribution Detection by Leveraging Important Neurons" + }, + { + "type": "text", + "bbox": [ + 0.252, + 0.208, + 0.726, + 0.224 + ], + "angle": 0, + "content": "Yong Hyun Ahn\\(^{1}\\), Gyeong-Moon Park\\(^{2,*}\\), Seong Tae Kim\\(^{2,*}\\)" + }, + { + "type": "text", + "bbox": [ + 0.245, + 0.225, + 0.726, + 0.241 + ], + "angle": 0, + "content": "\\(^{1}\\)Department of Artificial Intelligence, Kyung Hee University" + }, + { + "type": "text", + "bbox": [ + 0.189, + 0.241, + 0.782, + 0.257 + ], + "angle": 0, + "content": "\\(^{2}\\)Department of Computer Science and Engineering, Kyung Hee University" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.289, + 0.312, + 0.303 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.318, + 0.473, + 0.692 + ], + "angle": 0, + "content": "It is important to quantify the uncertainty of input samples, especially in mission-critical domains such as autonomous driving and healthcare, where failure predictions on out-of-distribution (OOD) data are likely to cause big problems. OOD detection problem fundamentally begins in that the model cannot express what it is not aware of. Post-hoc OOD detection approaches are widely explored because they do not require an additional re-training process which might degrade the model's performance and increase the training cost. In this study, from the perspective of neurons in the deep layer of the model representing high-level features, we introduce a new aspect for analyzing the difference in model outputs between in-distribution data and OOD data. We propose a novel method, Leveraging Important Neurons (LINe), for post-hoc Out of distribution detection. Shapley value-based pruning reduces the effects of noisy outputs by selecting only high-contribution neurons for predicting specific classes of input data and masking the rest. Activation clipping fixes all values above a certain threshold into the same value, allowing LINe to treat all the class-specific features equally and just consider the difference between the number of activated feature differences between in-distribution and OOD data. Comprehensive experiments verify the effectiveness of the proposed method by outperforming state-of-the-art post-hoc OOD detection methods on CIFAR-10, CIFAR-100, and ImageNet datasets. Code is available on https://github.com/LINE-OOD" + }, + { + "type": "title", + "bbox": [ + 0.079, + 0.717, + 0.209, + 0.731 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.74, + 0.47, + 0.837 + ], + "angle": 0, + "content": "Recently, deep learning has made tremendous advances in various fields. This advancement has captivated numerous researchers, leading to many attempts to apply deep learning techniques to real-world applications. However, applying these state-of-the-art techniques to real-world applications is often limited for several reasons. One primary obstacle is the presence of unseen classes of samples during" + }, + { + "type": "image", + "bbox": [ + 0.513, + 0.31, + 0.865, + 0.492 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.505, + 0.892, + 0.594 + ], + "angle": 0, + "content": "Figure 1. Illustration of the number of activated neuron in the penultimate layer. The distributions of the number of activated neurons from ID (ImageNet [19]) and two OOD datasets (textures [10] and iNaturalist [51]) are presented. We define an activated neuron as one fired with an activation value greater than zero. Most of the neurons are activated when the model receives ID samples but fewer neurons are activated in OOD samples." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.618, + 0.892, + 0.729 + ], + "angle": 0, + "content": "training. These samples, referred to as out-of-distribution (OOD) data, can compromise a model's stability and, in some cases, severely impair its performance. The inherent characteristics of OOD samples can lead to potentially severe consequences in mission-critical domains, such as autonomous driving and medical applications. So, effectively handling these OOD samples is vital to avoid problems, such as car crashes and misdiagnosis." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.73, + 0.893, + 0.868 + ], + "angle": 0, + "content": "For OOD detection, numerous techniques have been explored to analyze the distinction between in-distribution (ID) data and OOD data. There are several approaches to OOD detection, including confidence-based methods [7, 11, 16, 19, 29], density-based methods [1, 20, 22-24, 27, 38, 40, 42, 50, 62, 63], and distance-based methods [9, 18, 28, 35, 41, 46, 48, 49, 58]. The post-hoc method is one approach in OOD detection that offers significant advantages in real-world applications as it eliminates the need for a re-training process, which could potentially degrade the model's per" + }, + { + "type": "page_footnote", + "bbox": [ + 0.078, + 0.844, + 0.47, + 0.867 + ], + "angle": 0, + "content": "*Corresponding authors: Gyeong-Moon Park (gmpark@khu.ac.kr) and Seong Tae Kim (st.kim@khu.ac.kr)." + }, + { + "type": "page_number", + "bbox": [ + 0.467, + 0.889, + 0.505, + 0.899 + ], + "angle": 0, + "content": "19852" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.078, + 0.127, + 0.356, + 0.141 + ], + "angle": 0, + "content": "formance and increase training costs [56]." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.144, + 0.473, + 0.449 + ], + "angle": 0, + "content": "Post-hoc OOD detection methods [32, 44, 45] employ outputs such as model logits or layer activations, which are typically used for prediction, to calculate OOD scores. These scores allow for the differentiation of ID and OOD data based on the disparities in their respective scores [56]. Enhancing the overall OOD score distribution difference between ID and OOD data is a critical aspect in improving the performance of post-hoc OOD detection methods. Recent studies [44, 45] have found that augmenting the overall difference is contingent upon the capacity to mitigate noisy signals. For example, ReAct [44] demonstrates that OOD data exhibit considerable values in the penultimate layer activation. By truncating these noisy activations, ReAct effectively improves OOD detection performance. Similarly, DICE [45] uncovers the presence of noisy signals that increase the variance of the OOD score distribution. By selectively employing the most salient weights, DICE enhances OOD detection performance while reducing the impact of noisy signals. Minimizing the influence of noisy model outputs is crucial for advancing post-hoc OOD detection performance. In this study, we reveal an additional factor that is also important in the context of OOD detection." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.452, + 0.473, + 0.868 + ], + "angle": 0, + "content": "Figure 1 displays the histogram of the number of activated features in the penultimate layer. We define neurons with activation values greater than zero as activated neurons. As the figure demonstrates, a majority of neurons are activated when the model encounters ID samples. However, for OOD samples, fewer neurons are activated. To understand the primary cause of the observation in Figure 1, we investigate the model from the perspective of neuron-concept association [4,5,21,52]. According to [4], neurons are trained to detect disentangled high-level features in the deep layers of convolutional neural networks (CNNs), and they can even learn new unlabeled abstract concepts from the data [52]. The number of neurons representing these high-level features increases in deeper layers and becomes the most significant amount in the penultimate layer [5]. Since the activation in the penultimate layer represents the presence of these high-level features [4], different input images activate high-level features in varying ways, such as magnitude and patterns. These distinct patterns of activation in the penultimate layer are ultimately used to predict the input image's class. As each class possesses unique characteristics related to high-level concepts, the associated high-level features differ for each class. Consequently, each associated high-level feature can be categorized into one class-specific feature group. The disparity in associated high-level features in neurons results in a difference in penultimate layer activation between ID and OOD samples, which are predicted as the same class. Thus, taking into account the number of activated essential neurons can serve as a useful indicator for distinguishing ID and OOD samples." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.127, + 0.895, + 0.224 + ], + "angle": 0, + "content": "In this paper, we present a novel post-hoc OOD detection method called Leveraging Important Neurons (LINe). LINe harnesses two crucial aspects: considering the number of activated important neurons and minimizing noisy activations to enhance OOD detection performance. To achieve this, we introduce two powerful techniques within LINe: 1) Shapley-based pruning and 2) activation clipping (AC)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.224, + 0.895, + 0.431 + ], + "angle": 0, + "content": "Shapley value-based pruning is a method that mitigates the influence of noisy outputs by selecting activations essential for inferring input data classes. While several methods exist for identifying important activations, Sun et al. [45] use activation magnitude to determine their importance. However, this approach alone is insufficient for quantifying a neuron's importance. Hence, we employ the Shapley value [43] to more accurately measure each neuron's contribution. Applying the Shapley value concept [43] to neural networks allows us to quantify each neuron's contribution to identifying a specific class. Moreover, neurons with high Shapley values are associated with critical input image features [21]. By leveraging the Shapley value [43], we can identify neurons that represent important high-level features for each class, which are essential for reducing noisy output." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.431, + 0.895, + 0.61 + ], + "angle": 0, + "content": "Activation clipping, a concept introduced in ReAct [44], is another powerful technique. Interpreting activation clipping in terms of class-specific features provides a new understanding of its role in considering the number of activated important neurons for OOD detection. Activation clipping adjusts values exceeding a certain threshold to the threshold value. This modification enables us to account for the differences in the number of activated features between in-distribution and OOD data by treating numerous class-specific features equally. By considering the variation in the number of activated class-specific features, we can effectively augment the overall OOD score difference between ID and OOD data, leading to enhanced performance." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.611, + 0.851, + 0.624 + ], + "angle": 0, + "content": "Our key contributions are summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.631, + 0.892, + 0.7 + ], + "angle": 0, + "content": "- We propose a simple yet effective post-hoc OOD detection method, named LINe, which uses the Shapley value to rank the contribution of neurons and gives a new inspiration for leveraging selected important class-specific neurons." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.708, + 0.892, + 0.79 + ], + "angle": 0, + "content": "- We unveil the important factor for improving OOD scoring and show a new way of understanding the role of activation clipping for OOD detection. By applying activation clipping, we can fully consider the number of activated class-specific features and achieve higher OOD detection performance." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.799, + 0.892, + 0.868 + ], + "angle": 0, + "content": "- Comprehensive experiments have been conducted to verify the effectiveness of the proposed method on the CIFAR-10, CIFAR-100, and ImageNet-1K. Compared to the competitive post-hoc method DICE [45], LINe reduces the FPR95 by up to \\(14.05\\%\\)." + }, + { + "type": "list", + "bbox": [ + 0.52, + 0.631, + 0.892, + 0.868 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.467, + 0.889, + 0.505, + 0.9 + ], + "angle": 0, + "content": "19853" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.125, + 0.364, + 0.141 + ], + "angle": 0, + "content": "2. Background and Related Work" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.148, + 0.334, + 0.163 + ], + "angle": 0, + "content": "2.1. Neuron-Concept Association" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.17, + 0.473, + 0.378 + ], + "angle": 0, + "content": "Neuron-concept association methods are a field of study that tries to interpret the internal computation of CNN to a human-understandable concept [3,8,14,37]. Several studies have shown that neurons of shallower layers tend to learn more simple and low-level concepts, such as curves and edges, while deeper layers learn more abstract and high-level concepts, such as arm and face [52, 59, 60]. The methods for quantifying the concept's contribution are also introduced in [12, 14, 33]. Network Dissection [4, 5, 59] assigns each neuron to a concept to quantify its role. Bau et al. [6] investigate the effect of concept-specific neurons by observing the change of concept-related contents in generative models. Recently, Wang et al. [52] show that models can learn abstract concepts like mammal and carnivore, which is not in the label set of training data." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.386, + 0.224, + 0.401 + ], + "angle": 0, + "content": "2.2. Shapley Value" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.408, + 0.473, + 0.603 + ], + "angle": 0, + "content": "Shapely value [26, 43, 47] is a concept from Game Theory, which evaluates each property's individual and collaborative effects. Studies have been conducted using Shapley value in CNNs to measure each neuron's contribution and interpret models' behaviors [2, 13, 21, 34, 47]. Neuron Shapley [13] sorts the Shapley values to identify the most influential neurons from all hidden layers as image categories. Khazar et al. [21] show neurons that have high Shapley values have high correlations with important features of the input image. Previous studies have inspired us to select important class-specific neurons through the contribution scores calculated from the Shapley value. LINe can effectively eliminate the negative effects of noisy signals by leveraging the selected class-specific neurons." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.611, + 0.342, + 0.625 + ], + "angle": 0, + "content": "2.3. Out-of-Distribution Detection" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.633, + 0.473, + 0.868 + ], + "angle": 0, + "content": "ODD detection aims to find inputs with different characteristics from the training data [56]. A lot of research efforts have been devoted to developing an effective method to distinguish OOD inputs from ID inputs. Confidence-based methods perform OOD detection by quantifying OOD scores based on different scoring functions [7,11,16,19,29]. Hendrycks et al. [16] used a maximum softmax probability (MSP) of the model as a baseline confidence-base OOD scoring function. ODIN [30] utilizes perturbation of inputs and temperature scaling on the softmax layer to increase the difference between ID and OOD. To enhance the effectiveness of confidence-based scores, recently, Liu et al. [32] introduced an energy-based score with the theoretical interpretation from a likelihood perspective, which is further adopted in [31, 36, 53] to distinguish ID and OOD samples. Distance-based approaches measure the distance between input sample and typical ID samples or cen" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.126, + 0.895, + 0.21 + ], + "angle": 0, + "content": "troids of them [9, 18, 28, 35, 41, 46, 48, 49, 58]. These approaches are based on simple evidence that OOD samples should have more distance than IDs. Similarly, density-based methods identify OOD samples based on the distribution of the training samples and use density (or likelihood) [1, 20, 22-24, 27, 38, 40, 42, 50, 62, 63]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.21, + 0.896, + 0.459 + ], + "angle": 0, + "content": "But none of the aforementioned methods consider the number of activated features, which can be a good indicator to distinguish ID and OOD samples. The most similar study to our study is DICE [45]. DICE leverages sparsification to reduce the effect of noisy signals by selectively using salient weights from activation [45]. In this study, we effectively eliminate the outcomes of noisy signals by accurately selecting neurons leveraging the contribution of neurons calculated from Shapley value [21, 43]. In addition, our method performs OOD detection more effectively by considering the number of activated features. The neurons are known to be associated with the concepts, and the activation patterns of neurons in deep layers are different in ID and OOD. This gives a theoretical background for considering the number of activation in OOD detection. To the best of our knowledge, our work is the first study to leverage the neuron contribution based on Shapley value and consider the number of activated features for calculating OOD score." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.472, + 0.593, + 0.487 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.496, + 0.674, + 0.51 + ], + "angle": 0, + "content": "3.1. Method Overview" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.518, + 0.896, + 0.809 + ], + "angle": 0, + "content": "Our method mainly consists of two parts: Activation Clipping and Shapley-based pruning. Activation clipping is a method of clipping each neuron activation to a specific value when the activation value exceeds a particular threshold \\((\\delta)\\). Through activation clipping, our method can consider the number of high-level features during calculating OOD scores, which are analyzed in terms of neuron-concept association. Next, Shapley-based pruning eliminates the negative effect of noisy signals by measuring neural contributions of neural networks using important neurons only. We can accurately measure the contribution of each neuron using Shapley value, which is a mathematically grounded method. Also, by applying Shapley value, we can obtain supporting evidence that neurons with large contributions represent critical features for recognizing input image [21]. This allows us to assemble all contributions for each class and select important class-specific neurons representing class-specific features. More details of activation clipping and Shapley-based pruning will be described in Subsection 3.2 and Subsection 3.3. In Subsection 3.4, we will explain the overall method." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.818, + 0.691, + 0.833 + ], + "angle": 0, + "content": "3.2. Activation Clipping" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.84, + 0.895, + 0.868 + ], + "angle": 0, + "content": "For a pre-trained deep neural network \\(f_{\\theta}(x)\\) parameterized by \\(\\theta\\), \\(f_{\\theta}(x)\\) encodes an input \\(x \\in \\mathbb{R}^d\\), where \\(d\\) indicates" + }, + { + "type": "page_number", + "bbox": [ + 0.466, + 0.889, + 0.506, + 0.9 + ], + "angle": 0, + "content": "19854" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.126, + 0.891, + 0.438 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.451, + 0.897, + 0.517 + ], + "angle": 0, + "content": "Figure 2. Overall procedure of LINe for calculating OOD score. LINe is composed of mainly three parts. 1) Activation Clipping (AC), 2) Activation Pruning (AP), 3) Weight Pruning (WP). AC limits the magnitude of the activation, which allows LINe to consider the number of activated features. AP uses contribution matrix C, which is precomputed from Shapley value [43]. AP leverages C to select important neurons and mask others. WP uses an adjusted contribution matrix which is obtained from the contribution matrix C. Leveraging AP and WP, LINe can reduce noisy signals effectively." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.54, + 0.473, + 0.625 + ], + "angle": 0, + "content": "dimension of input \\(x\\), and predicts a class distribution for \\(L\\) different classes, i.e., \\(f_{\\theta}(x) \\in \\mathbb{R}^{L}\\). Feature vector from the penultimate layer of the network denotes \\(h(x) \\in \\mathbb{R}^q\\), where \\(q\\) stands for the dimension of penultimate layer output \\(h(x)\\). Weight matrix \\(\\mathbf{W} \\in \\mathbb{R}^{q \\times L}\\) weights the importance of each feature in \\(h(x)\\) and transfers to output \\(f_{\\theta}(x)\\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.196, + 0.642, + 0.47, + 0.66 + ], + "angle": 0, + "content": "\\[\nf _ {\\theta} (x) = \\mathbf {W} ^ {T} h (x) + \\mathbf {b}. \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.672, + 0.472, + 0.811 + ], + "angle": 0, + "content": "Activation clipping is applied to the feature vector in the penultimate layer. For each neuron that is activated above a certain threshold, AC limits the magnitude of the activation. As we discussed in Figure 1, the number of activated features in ID and OOD samples are different. By limiting the magnitude of the activation to the same value \\(\\delta\\), we can treat every activated high-level feature equally, which allows us to consider the number of activated features in the OOD score. This increases the OOD score difference between ID and OOD samples, thereby improving performance." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.812, + 0.473, + 0.869 + ], + "angle": 0, + "content": "For each activation \\(a_{i}\\) in \\(h(x)\\), penultimate layer feature \\(h(x)\\) can be denoted as \\(h(x) = [a_1, a_2, \\dots, a_q]\\). With a clipping threshold \\(\\delta\\), the clipped activation \\(\\hat{a}_{i}\\) can be described as \\(\\hat{a}_{i} = \\min(a_{i}, \\delta)\\). The clipped feature vector \\(\\hat{h}(x)\\)" + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.541, + 0.555, + 0.553 + ], + "angle": 0, + "content": "is then," + }, + { + "type": "equation", + "bbox": [ + 0.612, + 0.555, + 0.894, + 0.573 + ], + "angle": 0, + "content": "\\[\n\\hat {h} (x) = \\left[ \\hat {a} _ {1}, \\hat {a} _ {2}, \\dots , \\hat {a} _ {q} \\right]. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.581, + 0.792, + 0.596 + ], + "angle": 0, + "content": "The model output after AC can be given as:" + }, + { + "type": "equation", + "bbox": [ + 0.612, + 0.606, + 0.893, + 0.624 + ], + "angle": 0, + "content": "\\[\nf _ {\\theta} ^ {A C} (x) = \\mathbf {W} ^ {T} \\hat {h} (x) + \\mathbf {b}. \\tag {3}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.637, + 0.719, + 0.653 + ], + "angle": 0, + "content": "3.3. Shapley-based Pruning" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.659, + 0.895, + 0.827 + ], + "angle": 0, + "content": "Shapley-based pruning selectively uses a subset of important neuron activation and weights. To select these subsets, we calculate Shapley value [43] defined by an average of the effect of removing a single unit (e.g., marginal contribution) to all possible combinations of units. However, computing all the combinations of units is computationally expensive and practically infeasible for recent large neural networks. Therefore, we use the Taylor approximation to compute the Shapley value, which is introduced in [21]. For input \\( x^{l} \\in D \\), where \\( x^{l} \\) denotes the sample of class \\( l \\) from dataset \\( D \\), a contribution(i.e., Shapley value) of \\( i \\)-th neuron \\( a_{i} \\) in class \\( l \\), \\( s_{i}^{l} \\) is calculated as" + }, + { + "type": "equation", + "bbox": [ + 0.52, + 0.851, + 0.894, + 0.871 + ], + "angle": 0, + "content": "\\[\n\\left. s _ {i} ^ {l} = \\left| f _ {\\theta} \\left(x ^ {l}\\right) - f _ {\\theta} \\left(x ^ {l}; a _ {i} \\leftarrow 0\\right) \\right| = \\left| a _ {i} \\nabla_ {a _ {i}} f _ {\\theta} \\left(x ^ {l}\\right) \\right|. \\right. \\tag {4}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.466, + 0.889, + 0.506, + 0.9 + ], + "angle": 0, + "content": "19855" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.124, + 0.468, + 0.247 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.124, + 0.258, + 0.424, + 0.272 + ], + "angle": 0, + "content": "Figure 3. Calculation of contribution matrix C." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.295, + 0.267, + 0.309 + ], + "angle": 0, + "content": "3.3.1 Activation Pruning" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.316, + 0.471, + 0.413 + ], + "angle": 0, + "content": "Activation pruning (AP) selectively uses the subset of important neuron activation. Through AP, We can effectively reduce the impact of noisy activation. From the contribution of each neuron \\( s_i^l \\), which is using obtained from all training data, contribution matrix \\( \\mathbf{C} \\in \\mathbb{R}^{q \\times L} \\) is defined as the class-specific average of all contribution \\( s_i^l \\). An \\( (i,l) \\)-th entry of contribution matrix \\( c_{il} \\in \\mathbf{C} \\) is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.219, + 0.421, + 0.47, + 0.451 + ], + "angle": 0, + "content": "\\[\n\\mathbf {C} _ {i l} = \\frac {1}{n} \\sum^ {n} s _ {i} ^ {l}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.458, + 0.47, + 0.541 + ], + "angle": 0, + "content": "where \\(n\\) denotes the number of training images in class \\(l\\). We select top-\\(k\\) neurons for each class based on the k-largest elements from each column in \\(\\mathbf{C}\\) and define an activation mask matrix \\(\\mathbf{M}_a \\in \\mathbb{R}^{q \\times L}\\), where we set 1 for the \\(k\\)-largest elements from every column in \\(\\mathbf{C}\\), otherwise 0. The model output after AP with the predicted class \\(l\\) is given as:" + }, + { + "type": "equation", + "bbox": [ + 0.161, + 0.549, + 0.47, + 0.567 + ], + "angle": 0, + "content": "\\[\nf _ {\\theta} ^ {A P} (x) = \\mathbf {W} ^ {T} \\left(\\mathbf {m} _ {l} \\odot h (x)\\right) + \\mathbf {b}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.575, + 0.469, + 0.603 + ], + "angle": 0, + "content": "where \\(\\mathbf{m}_l\\in \\mathbb{R}^q\\) indicates \\(l\\)-th column of mask matrix \\(\\mathbf{M}_a\\) and \\(\\odot\\) denotes the element-wise multiplication." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.619, + 0.245, + 0.633 + ], + "angle": 0, + "content": "3.3.2 Weight Pruning" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.64, + 0.471, + 0.807 + ], + "angle": 0, + "content": "Weight pruning (WP) selectively uses the subset of important penultimate layer weights. Through WP, We can effectively reduce the impact of noisy signals due to the overparameterized model. The contribution of neurons is further used to refine the weight matrix as WP. For this purpose, we define a weight contribution matrix for the class \\(l\\) as \\(\\mathbf{C}_w^l = \\mathbf{c}_l\\odot \\mathbf{W}\\in \\mathbb{R}^{q\\times L}\\) where \\(\\mathbf{c}_1\\) indicates the \\(l\\)-th column of contribution matrix \\(\\mathbf{C}\\). We select top-\\(k\\) weights for each class based on the \\(k\\)-largest elements in \\(\\mathbf{C}_w^l\\) and define a mask matrix for class \\(l\\) as \\(\\mathbf{M}_w^l\\in \\mathbb{R}^{q\\times L}\\) by setting 1 for the \\(k\\)-largest elements in \\(\\mathbf{C}_w^l\\), otherwise 0. The model output after WP with the predicted class \\(l\\) is given as:" + }, + { + "type": "equation", + "bbox": [ + 0.157, + 0.814, + 0.47, + 0.832 + ], + "angle": 0, + "content": "\\[\nf _ {\\theta} ^ {W P} (x) = \\left(\\mathbf {W} \\odot \\mathbf {M} _ {w} ^ {l}\\right) ^ {T} h (x) + \\mathbf {b}. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.84, + 0.471, + 0.868 + ], + "angle": 0, + "content": "From the Shapley-based AP and WP, we can determine the neurons representing important high-level features for each" + }, + { + "type": "image", + "bbox": [ + 0.511, + 0.126, + 0.886, + 0.219 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.541, + 0.23, + 0.853, + 0.243 + ], + "angle": 0, + "content": "Figure 4. Calculation of contribution matrix \\( \\mathbf{C}_{\\mathbf{w}}^{\\mathrm{l}} \\)." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.267, + 0.874, + 0.281 + ], + "angle": 0, + "content": "class, which play a crucial role in reducing noisy output." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.303, + 0.834, + 0.318 + ], + "angle": 0, + "content": "3.4. Leveraging Important Neurons (LINe)" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.324, + 0.894, + 0.476 + ], + "angle": 0, + "content": "As already described in the previous Subsection 3.2 and 3.3, there are two ideas to improve the performance of post-hoc OOD detection. One is considering the number of activated high-level features, and the other is reducing noisy signals from less important neurons. LINe achieves both ways to improve post-hoc OOD detection performance through the procedures described above. By adapting LINe to a model, we can effectively increase the overall difference in OOD scores between ID and OOD data. As a result, the model output under LINe with the predicted class \\(l\\) is described as" + }, + { + "type": "equation", + "bbox": [ + 0.549, + 0.485, + 0.892, + 0.503 + ], + "angle": 0, + "content": "\\[\nf _ {\\theta} ^ {L I N e} (x) = \\left(\\mathbf {W} \\odot \\mathbf {M} _ {w} ^ {l}\\right) ^ {T} \\left(\\mathbf {m} _ {l} \\odot \\hat {h} (x)\\right) + \\mathbf {b}. \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.513, + 0.893, + 0.54 + ], + "angle": 0, + "content": "Please note that there is no parameter change in the model itself and ID classification accuracy can be preserved." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.552, + 0.634, + 0.567 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.575, + 0.894, + 0.673 + ], + "angle": 0, + "content": "Comprehensive experiments have been conducted to evaluate our method. In section 4.1, we used the CIFAR [25] benchmark, which is one of the famous benchmarks in OOD studies [32, 44, 45]. In Section 4.2, experiments were conducted based on a large-scale dataset, ImageNet, with various OOD datasets. Section 4.3 analyzes why our method is effective through various ablation experiments." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.68, + 0.807, + 0.694 + ], + "angle": 0, + "content": "4.1. Evaluation on CIFAR Benchmarks" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.701, + 0.895, + 0.868 + ], + "angle": 0, + "content": "Implementation Details. In this experiment, we used 10,000 test images each from CIFAR-10 [25] and CIFAR-100 [25] as ID data, respectively. The model's performance was evaluated using six commonly used OOD datasets as an OOD benchmark. The list of six OOD datasets is as follows: SVHN [39], Textures [10], iSUN [55], LSUN-Crop [57], LSUN-Resize [57], and Places365 [61]. As the pre-trained models, we used DenseNet [17]. As in [45], the models are trained from CIFAR-10 [25] and CIFAR-100 [25] with 50,000 training images respectively. Following [45], the models were trained during 100 epochs with batch size 64, weight decay 0.0001, momentum 0.9, and" + }, + { + "type": "page_number", + "bbox": [ + 0.466, + 0.889, + 0.506, + 0.9 + ], + "angle": 0, + "content": "19856" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.124, + 0.472, + 0.214 + ], + "angle": 0, + "content": "Table 1. Comparison on CIFAR benchmarks. Comparison with competitive post-hoc OOD detection methods on CIFAR benchmarks. All values in this table are percentages and averaged over six OOD test datasets. \\(\\downarrow\\) indicates smaller value means better performance and \\(\\uparrow\\) indicates vice versa. Bold numbers are superior results. The overall detail results for each OOD dataset are provided in supplementary material." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.224, + 0.468, + 0.349 + ], + "angle": 0, + "content": "
MethodCIFAR-10CIFAR-100
FPR95 ↓AUROC ↑FPR95 ↓AUROC ↑
MSP [16]48.7392.4680.1374.36
ODIN [30]24.5793.7158.1484.49
Mahalanobis [28]31.4289.1555.3782.73
Energy [32]26.5594.5768.4581.19
ReAct [44]26.4594.9562.2784.47
DICE [45]20.8395.2449.7287.23
DICE + ReAct16.4896.6449.5785.08
LINe (Ours)14.7196.9935.6788.67
" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.373, + 0.47, + 0.414 + ], + "angle": 0, + "content": "start learning rate 0.1. The learning rate was decayed by a factor of 10 at epochs 50, 75, and 90. We used the entire training dataset to estimate the contribution matrix \\( C \\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.416, + 0.47, + 0.485 + ], + "angle": 0, + "content": "Comparison. For comparison, we adopted recent post-hoc OOD detection methods: MSP [16], ODIN [30], Mahalanobis distance [28], Energy [32], ReAct [44], and DICE [45]. For all methods, the performances were measured by OOD scores, derived from the same DenseNet model." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.487, + 0.471, + 0.695 + ], + "angle": 0, + "content": "Experimental Results. Table 1 shows the comparisons between LINe and other post-hoc OOD detection methods on CIFAR-10 and CIFAR-100 benchmarks. As shown in the table, our method achieved state-of-the-art performances by outperforming all the other methods on both CIFAR-10 and CIFAR-100 datasets. In CIFAR-100, LINe reduced FPR 95 by \\(14.05\\%\\) compared to the competitive method DICE [45]. In CIFAR-100, LINe achieved an FPR 95 of \\(14.05\\%\\) which was lower than the FPR 95 of DICE [45] \\((49.72\\%)\\) and DICE + ReAct \\((49.57\\%)\\). DICE + ReAct is the method that is implemented by applying ReAct [44] on DICE [45]. DICE [45] removed the noisy signals by using the magnitude of activation and weight. LINe not only removed the noisy signals using class-specific neurons but also considered the number of activations of the high-level feature." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.707, + 0.303, + 0.722 + ], + "angle": 0, + "content": "4.2. Evaluation on ImageNet" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.729, + 0.47, + 0.868 + ], + "angle": 0, + "content": "Implementation Details. In real-world applications, the model encounters high-resolution images with various scenes and features, and evaluation on a large-scale dataset can provide clues about model performance in a real-world application. Therefore, in this experiment, we evaluated LINe on a large-scale ImageNet dataset. Based on [19], a subset of the four datasets where all the overlapping categories with ImageNet-1k were eliminated was used as OOD datasets. The four OOD datasets are as follows: Textures [10], Places365 [61], iNaturalist [51], and SUN [54]. We" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.127, + 0.894, + 0.181 + ], + "angle": 0, + "content": "used a pre-trained ResNet-50 model [15], which is trained with ImageNet-1k. The entire training dataset was used to estimate the contribution matrix \\(C\\), and all images were resized to \\(224 \\times 224\\) at test time." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.182, + 0.894, + 0.403 + ], + "angle": 0, + "content": "Experimental Results. In Table 2, we reported the performances of four OOD test datasets respectively. The average results from the four OOD test datasets were also reported. LINe outperformed all baselines including MSP [16], ODIN [30], Mahalanobis distance [28], Energy score [32], ReAct [44], DICE [45], and DICE + ReAct [45]. We compared LINe with Energy [32] first. LINe drastically reduced the FPR95 by \\(37.71\\%\\), which shows the benefit of leveraging important neurons under the same OOD scoring function. Next, we compared LINe with ReAct [44]. LINe reduced the FPR95 by \\(10.73\\%\\), which allows us to see the advantages of leveraging important neurons using Shapley value. LINe further outperformed recent DICE [45] and DICE + ReAct by \\(14.05\\%\\) and \\(6.55\\%\\), respectively. Experimental results showed that the proposed method can be applied to real-world large dataset for OOD detection." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.41, + 0.655, + 0.426 + ], + "angle": 0, + "content": "4.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.432, + 0.894, + 0.474 + ], + "angle": 0, + "content": "In this section, we discuss the effectiveness of each part used in LINe and the detailed differences from other similar approaches. We also analyze the effect of hyperparameters." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.49, + 0.813, + 0.505 + ], + "angle": 0, + "content": "4.3.1 Ablation Study of LINe on ImageNet" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.512, + 0.894, + 0.733 + ], + "angle": 0, + "content": "Table 3 shows an ablation study over various parts used in LINe. As shown in the table, each part of Shapley-based pruning (AP and WP) improved the performance. Comparing LINE w/o WP with Energy + AC allows us to see the advantages of reducing the noisy activation, which reduces FPR95 by \\(8.52\\%\\). Next, we compared LINe w/o AP with Energy + AC, which also shows the benefits of reducing noisy weights. Compared to Energy + AC, LINe w/o AP reduced FPR95 by \\(12.21\\%\\). Finally, we compared LINe w/o AP with DICE + ReAct [45] at Table 2, which allows us to see the benefit of leveraging class-wise contribution under similar circumstances. LINe w/o AP reduced the FPR95 by \\(4.06\\%\\) from \\(27.25\\%\\) to \\(23.19\\%\\). DICE + ReAct [45] uses activations to select important weights, while LINe w/o AP selects important weights using class-wise contribution derived from the Shapley value [43]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.749, + 0.882, + 0.764 + ], + "angle": 0, + "content": "4.3.2 Effect of Changing AC Threshold on ImageNet" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.77, + 0.894, + 0.868 + ], + "angle": 0, + "content": "In Section 3.2, we discussed the meaning of AC in terms of the neuron-concept association. AC allows us to consider the number of activated high-level features in the penultimate layer. In Table 4, we show various OOD detection performances of the model by changing threshold \\(\\delta\\). Starting from clipping threshold \\(\\delta = \\infty\\), the value of FPR95 is the highest in the table. As clipping threshold \\(\\delta\\) becomes" + }, + { + "type": "page_number", + "bbox": [ + 0.466, + 0.889, + 0.506, + 0.9 + ], + "angle": 0, + "content": "19857" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.124, + 0.894, + 0.151 + ], + "angle": 0, + "content": "Table 2. Comparison on ImageNet benchmark. Comparisons with competitive post-hoc OOD detection methods on ImageNet benchmark. All values in this table are percentages and averaged over four OOD test datasets." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.16, + 0.894, + 0.301 + ], + "angle": 0, + "content": "
MethodOOD DatasetsAverage
iNaturalistSUNPlacesTexturesFPR95 ↓ AUROC ↑
FPR95 ↓AUROC ↑FPR95 ↓AUROC ↑FPR95 ↓AUROC ↑FPR95 ↓AUROC ↑FPR95 ↓AUROC ↑
MSP [16]54.9987.7470.8380.8673.9979.7668.0079.6166.9581.99
ODIN [30]47.6689.6660.1584.5967.8981.7850.2385.6256.4885.41
Mahalanobis [28]97.0052.6598.5042.4198.4041.7955.8085.0187.4355.47
Energy [32]55.7289.9559.2685.8964.9282.8653.7285.9958.4186.17
ReAct [44]20.3896.2224.2094.2033.8591.5847.3089.8031.4392.95
DICE [45]25.6394.4935.1590.8346.4987.4831.7290.3034.7590.77
DICE + ReAct [45]18.6496.2425.4593.9436.8690.6728.0792.7427.2593.40
LINe (Ours)12.2697.5619.4895.2628.5292.8522.5494.4420.7095.03
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.321, + 0.471, + 0.386 + ], + "angle": 0, + "content": "Table 3. Ablation Study of LINe on ImageNet. Ablation on the effectiveness of Shapley-based pruning used in LINe and comparison with similar approaches. Values are percentages and averaged over OOD datasets. AC, AP, and WP denote activation clipping, activation pruning, and weight pruning, respectively." + }, + { + "type": "table", + "bbox": [ + 0.101, + 0.396, + 0.449, + 0.48 + ], + "angle": 0, + "content": "
MethodACAPWPFPR95↓AUROC↑
Energy [32]58.4186.17
Energy + AC✓35.4091.86
LINe w/o WP✓✓26.8893.77
LINe w/o AP✓✓23.1994.57
LINe (Ours)✓✓✓20.7095.03
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.493, + 0.471, + 0.532 + ], + "angle": 0, + "content": "Table 4. Ablation on different thresholds \\((\\delta)\\) of AC. Ablation on the different thresholds \\((\\delta)\\) of clipping. All values are percentages and averaged over multiple OOD test datasets." + }, + { + "type": "table", + "bbox": [ + 0.148, + 0.541, + 0.402, + 0.65 + ], + "angle": 0, + "content": "
Threshold (δ)FPR95 ↓AUROC ↑
δ = 0.141.1888.44
δ = 0.423.4394.79
δ = 0.820.7095.03
δ = 1.021.6994.81
δ = 1.526.9693.99
δ = 2.031.8892.97
δ = ∞ (no AC)44.8889.14
" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.673, + 0.47, + 0.757 + ], + "angle": 0, + "content": "smaller, the OOD detection performance is improved. But at clipping threshold \\(\\delta < 0.8\\), the OOD detection performance dropped. This is because, as the clipping threshold \\(\\delta\\) approaches 0, all the penultimate output values also approach zero. It is obvious that performance will drop when all the penultimate output values approach zero." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.775, + 0.471, + 0.804 + ], + "angle": 0, + "content": "4.3.3 Effect of Changing Pruning Percentile on ImageNet" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.812, + 0.471, + 0.869 + ], + "angle": 0, + "content": "In this section, we conducted ablation studies on pruning percentiles \\((p)\\) variation on ImageNet datasets as ID data. In Table 5 we show effect of changing pruning percentile \\((p_w\\) and \\(p_a)\\) on ImageNet. \\(p_a\\) indicates pruning percentile" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.321, + 0.894, + 0.386 + ], + "angle": 0, + "content": "Table 5. Effect of changing pruning percentile \\((p)\\) on ImageNet. Ablation on the different pruning percentile \\((p_a\\) and \\(p_w)\\) of pruning. All values are percentages and averaged over multiple OOD test datasets. \\(p_a\\) denotes pruning percentile for AP, \\(p_w\\) indicates pruning percentile for WP." + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.396, + 0.897, + 0.489 + ], + "angle": 0, + "content": "
pa=90pa=70pa=50pa=30pa=10
FPR95 ↓FPR95 ↓FPR95 ↓FPR95 ↓FPR95 ↓
pw=9027.5624.7924.7424.5524.54
pw=7027.4525.9325.8127.4533.32
pw=5033.6927.7826.2825.9027.45
pw=3027.4626.1027.1724.3628.43
pw=1027.6426.7527.7525.4120.70
" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.514, + 0.895, + 0.681 + ], + "angle": 0, + "content": "for AP, \\( p_w \\) indicates pruning percentile for WP. For a fixed WP percentile \\( p_w \\) with extremely high value (e.g., \\( p_w = 90 \\)), the performance tends to increase when the AP percentile \\( p_a \\) falls. Since LINe considers the number of activated features for detecting OOD samples, pruning most of the activations or weights has negatively impacted the performance. A lower pruning percentile is better to leverage differences in the number of activated features between ID and OOD samples. But to restrict the negative effect of noisy signals, we need some portions that can remove the noisy signals. As a result, the model performs the best when the pruning percentile is \\( p_w = 10 \\) and \\( p_a = 10 \\) on ImageNet." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.705, + 0.894, + 0.731 + ], + "angle": 0, + "content": "4.3.4 Effect of Changing Pruning Percentile on CIFAR Benchmarks" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.743, + 0.894, + 0.868 + ], + "angle": 0, + "content": "In Table 6 and Table 7, we show effect of changing pruning percentile \\((p_w\\) and \\(p_a)\\) on CIFAR Benchmarks. Both tables show similar tendencies. For all AP percentile \\(p_a\\), the performance tends to increase when the WP percentile \\(p_w\\) increases. In Table 6, highest performance appeared at \\(p_w = 90\\) and \\(p_a = 90\\). On the other hand in Table 7, the highest performance appeared at \\(p_w = 90\\) and \\(p_a = 10\\). This result may seem to conflict with the result in Table 5, our observation in Table 8 can explain the cause of the difference." + }, + { + "type": "page_number", + "bbox": [ + 0.466, + 0.889, + 0.506, + 0.9 + ], + "angle": 0, + "content": "19858" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.078, + 0.124, + 0.472, + 0.188 + ], + "angle": 0, + "content": "Table 6. Effect of changing pruning percentile \\((p)\\) in CIFAR10. Ablation on the different pruning percentile \\((p_a\\) and \\(p_w)\\) of pruning. All values are percentages and averaged over multiple OOD test datasets. \\(p_a\\) denotes pruning percentile for AP, \\(p_w\\) indicates pruning percentile for WP." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.198, + 0.474, + 0.292 + ], + "angle": 0, + "content": "
pa=90pa=70pa=50pa=30pa=10
FPR95 ↓FPR95 ↓FPR95 ↓FPR95 ↓FPR95 ↓
pw=9014.7215.0015.0015.0014.99
pw=7014.8015.1215.1215.1215.10
pw=5014.8015.1215.1115.1115.10
pw=3014.8015.1215.1115.1215.10
pw=1014.8015.1315.1315.1215.73
" + }, + { + "type": "table_caption", + "bbox": [ + 0.078, + 0.306, + 0.472, + 0.37 + ], + "angle": 0, + "content": "Table 7. Effect of changing pruning percentile \\((p)\\) in CIFAR100. Ablation on the different pruning percentile \\((p_a\\) and \\(p_w)\\) of pruning. All values are percentages and averaged over multiple OOD test datasets. \\(p_a\\) denotes pruning percentile for AP, \\(p_w\\) indicates pruning percentile for WP." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.38, + 0.474, + 0.473 + ], + "angle": 0, + "content": "
pa=90pa=70pa=50pa=30pa=10
FPR95↓FPR95↓FPR95↓FPR95↓FPR95↓
pw=9038.7537.8137.8137.7535.67
pw=7038.3739.3040.0739.7540.81
pw=5038.3739.1940.5440.2742.14
pw=3038.3739.1940.6540.2139.32
pw=1038.4039.3140.7640.9138.17
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.488, + 0.47, + 0.552 + ], + "angle": 0, + "content": "Table 8. Percentage of class-specific neuron overlap in multiple classes. Difference between the percentage of class-specific neuron overlap in multiple classes on three data sets. For each dataset, we calculated the proportion of very important (top \\(10\\%\\) neurons in more than \\(o\\%\\) of the class. All values are percentages." + }, + { + "type": "table", + "bbox": [ + 0.127, + 0.562, + 0.422, + 0.61 + ], + "angle": 0, + "content": "
OverlapCIFAR-10CIFAR-100ImageNet
o = 2024.5626.901.70
o = 3023.390.580.15
" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.635, + 0.206, + 0.648 + ], + "angle": 0, + "content": "4.3.5 Discussion" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.66, + 0.47, + 0.868 + ], + "angle": 0, + "content": "In Table 8, we compared the percentage of class-specific neuron overlap in multiple classes on three data sets. For each dataset, we calculated the proportion of very important (top \\(10\\%\\)) neurons in more than \\(o\\%\\) of the class. These neurons activate in various classes which have semantically different features. Therefore, the higher proportion of these neurons can be seen as an overparameterized model with more numbers of generally activated neurons. These overparameterized models make OOD detection difficult by creating noisy signals, which can be reduced by leveraging AP and WP. To get optimal results from overparameterized models, we can lessen the effect of overparameterized weights with high WP percentile. Also, the effectiveness of considering the number of activated class-specific neurons can be maximized in the low AP percentile as a tendency" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.127, + 0.894, + 0.168 + ], + "angle": 0, + "content": "shown in Table 7. But for a much more overparameterized model, which is shown in Table 6, we need to set high pruning percentile on both \\( p_w \\) and \\( p_a \\)." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.169, + 0.894, + 0.334 + ], + "angle": 0, + "content": "The degree of an overparameterized model can be understood from Section 4.1. We used the same pre-trained model architecture for evaluating CIFAR-10 and CIFAR-100. Of the two models with the same structure, we can intuitively understand that a model trained using a relatively small dataset is more likely to be overparameterized, which can also be observed in Table 8. The proportion of very important (top \\(10\\%\\)) neurons in more than \\(30\\%\\) of the class(i.e., \\(o = 30\\)) on CIFAR-10 is the largest compared to other datasets. This observation shows that our pre-trained model used to evaluate CIFAR-10 is more overparameterized than other models we used." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.349, + 0.619, + 0.363 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.373, + 0.894, + 0.676 + ], + "angle": 0, + "content": "In this paper, we propose a powerful OOD Detection method called LINe. LINe adopts a neural-concept association, which only uses important activations and weights selectively by measuring class-wise contribution from the Shapley value. Through LINe, we can effectively reduce the influence of the noise signal and make a difference in the overall OOD score between ID and OOD sample distribution. We conducted extensive experiments to demonstrate that LINe is superior to state-of-the-art OOD detection methods and effective on multiple datasets. From several theoretical studies and insights, we show how our method improves the performance of OOD detection. Our method is effective but has some limitations. It is fundamentally a trade-off relationship that pruning neurons to reduce the noisy output and considers the number of class-specific feature activations. Users have to examine the trade-off considering the degree of overparameterization of the model. We hope that as our study proposes an effective way to view OOD detection from a feature presentation perspective, attempts to understand the behavior of neural networks will be applied to multiple domains to discover other effective methods." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.692, + 0.667, + 0.707 + ], + "angle": 0, + "content": "Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.715, + 0.894, + 0.867 + ], + "angle": 0, + "content": "This work was supported in part by the Institute of Information and Communications Technology Planning and Evaluation (IITP) grant funded by the Korea Government (MSIT)(No. 2022-0-00078: Explainable Logical Reasoning for Medical Knowledge Generation, No. 2021-0-02068: Artificial Intelligence Innovation Hub, No. RS2022-00155911: Artificial Intelligence Convergence Innovation Human Resources Development (Kyung Hee University)) and by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2021R1G1A1094990)." + }, + { + "type": "page_number", + "bbox": [ + 0.466, + 0.889, + 0.506, + 0.9 + ], + "angle": 0, + "content": "19859" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.125, + 0.174, + 0.14 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.088, + 0.149, + 0.47, + 0.211 + ], + "angle": 0, + "content": "[1] Davide Abati, Angelo Porrello, Simone Calderara, and Rita Cucchiara. 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In International conference on learning representations, 2018. 1, 3" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.127, + 0.472, + 0.476 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.468, + 0.889, + 0.505, + 0.9 + ], + "angle": 0, + "content": "19862" + } + ] +] \ No newline at end of file diff --git a/2023/LINe_ Out-of-Distribution Detection by Leveraging Important Neurons/7c02f584-1638-4590-ac47-479482d49ca3_origin.pdf b/2023/LINe_ Out-of-Distribution Detection by Leveraging Important Neurons/7c02f584-1638-4590-ac47-479482d49ca3_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..543304452ac94e794c322c9c30c2e2c183ffad88 --- /dev/null +++ b/2023/LINe_ Out-of-Distribution Detection by Leveraging Important Neurons/7c02f584-1638-4590-ac47-479482d49ca3_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:8352eacb5d260fb5fe2005bbb18b83a06f8092c7ab8b939366f61f3c31eb8896 +size 5436517 diff --git a/2023/LINe_ Out-of-Distribution Detection by Leveraging Important Neurons/full.md b/2023/LINe_ Out-of-Distribution Detection by Leveraging Important Neurons/full.md new file mode 100644 index 0000000000000000000000000000000000000000..ba8b1ad52f6287df62fb8a0949efa6e7d82dac2f --- /dev/null +++ b/2023/LINe_ Out-of-Distribution Detection by Leveraging Important Neurons/full.md @@ -0,0 +1,310 @@ +# LINE: Out-of-Distribution Detection by Leveraging Important Neurons + +Yong Hyun Ahn $^{1}$ , Gyeong-Moon Park $^{2,*}$ , Seong Tae Kim $^{2,*}$ + +$^{1}$ Department of Artificial Intelligence, Kyung Hee University + +$^{2}$ Department of Computer Science and Engineering, Kyung Hee University + +# Abstract + +It is important to quantify the uncertainty of input samples, especially in mission-critical domains such as autonomous driving and healthcare, where failure predictions on out-of-distribution (OOD) data are likely to cause big problems. OOD detection problem fundamentally begins in that the model cannot express what it is not aware of. Post-hoc OOD detection approaches are widely explored because they do not require an additional re-training process which might degrade the model's performance and increase the training cost. In this study, from the perspective of neurons in the deep layer of the model representing high-level features, we introduce a new aspect for analyzing the difference in model outputs between in-distribution data and OOD data. We propose a novel method, Leveraging Important Neurons (LINe), for post-hoc Out of distribution detection. Shapley value-based pruning reduces the effects of noisy outputs by selecting only high-contribution neurons for predicting specific classes of input data and masking the rest. Activation clipping fixes all values above a certain threshold into the same value, allowing LINe to treat all the class-specific features equally and just consider the difference between the number of activated feature differences between in-distribution and OOD data. Comprehensive experiments verify the effectiveness of the proposed method by outperforming state-of-the-art post-hoc OOD detection methods on CIFAR-10, CIFAR-100, and ImageNet datasets. Code is available on https://github.com/LINE-OOD + +# 1. Introduction + +Recently, deep learning has made tremendous advances in various fields. This advancement has captivated numerous researchers, leading to many attempts to apply deep learning techniques to real-world applications. However, applying these state-of-the-art techniques to real-world applications is often limited for several reasons. One primary obstacle is the presence of unseen classes of samples during + +![](images/f007fd399fdb39b6e1a34f13fee85226bc1601fdf466c7bc336594bcfc4984be.jpg) +Figure 1. Illustration of the number of activated neuron in the penultimate layer. The distributions of the number of activated neurons from ID (ImageNet [19]) and two OOD datasets (textures [10] and iNaturalist [51]) are presented. We define an activated neuron as one fired with an activation value greater than zero. Most of the neurons are activated when the model receives ID samples but fewer neurons are activated in OOD samples. + +training. These samples, referred to as out-of-distribution (OOD) data, can compromise a model's stability and, in some cases, severely impair its performance. The inherent characteristics of OOD samples can lead to potentially severe consequences in mission-critical domains, such as autonomous driving and medical applications. So, effectively handling these OOD samples is vital to avoid problems, such as car crashes and misdiagnosis. + +For OOD detection, numerous techniques have been explored to analyze the distinction between in-distribution (ID) data and OOD data. There are several approaches to OOD detection, including confidence-based methods [7, 11, 16, 19, 29], density-based methods [1, 20, 22-24, 27, 38, 40, 42, 50, 62, 63], and distance-based methods [9, 18, 28, 35, 41, 46, 48, 49, 58]. The post-hoc method is one approach in OOD detection that offers significant advantages in real-world applications as it eliminates the need for a re-training process, which could potentially degrade the model's per + +formance and increase training costs [56]. + +Post-hoc OOD detection methods [32, 44, 45] employ outputs such as model logits or layer activations, which are typically used for prediction, to calculate OOD scores. These scores allow for the differentiation of ID and OOD data based on the disparities in their respective scores [56]. Enhancing the overall OOD score distribution difference between ID and OOD data is a critical aspect in improving the performance of post-hoc OOD detection methods. Recent studies [44, 45] have found that augmenting the overall difference is contingent upon the capacity to mitigate noisy signals. For example, ReAct [44] demonstrates that OOD data exhibit considerable values in the penultimate layer activation. By truncating these noisy activations, ReAct effectively improves OOD detection performance. Similarly, DICE [45] uncovers the presence of noisy signals that increase the variance of the OOD score distribution. By selectively employing the most salient weights, DICE enhances OOD detection performance while reducing the impact of noisy signals. Minimizing the influence of noisy model outputs is crucial for advancing post-hoc OOD detection performance. In this study, we reveal an additional factor that is also important in the context of OOD detection. + +Figure 1 displays the histogram of the number of activated features in the penultimate layer. We define neurons with activation values greater than zero as activated neurons. As the figure demonstrates, a majority of neurons are activated when the model encounters ID samples. However, for OOD samples, fewer neurons are activated. To understand the primary cause of the observation in Figure 1, we investigate the model from the perspective of neuron-concept association [4,5,21,52]. According to [4], neurons are trained to detect disentangled high-level features in the deep layers of convolutional neural networks (CNNs), and they can even learn new unlabeled abstract concepts from the data [52]. The number of neurons representing these high-level features increases in deeper layers and becomes the most significant amount in the penultimate layer [5]. Since the activation in the penultimate layer represents the presence of these high-level features [4], different input images activate high-level features in varying ways, such as magnitude and patterns. These distinct patterns of activation in the penultimate layer are ultimately used to predict the input image's class. As each class possesses unique characteristics related to high-level concepts, the associated high-level features differ for each class. Consequently, each associated high-level feature can be categorized into one class-specific feature group. The disparity in associated high-level features in neurons results in a difference in penultimate layer activation between ID and OOD samples, which are predicted as the same class. Thus, taking into account the number of activated essential neurons can serve as a useful indicator for distinguishing ID and OOD samples. + +In this paper, we present a novel post-hoc OOD detection method called Leveraging Important Neurons (LINe). LINe harnesses two crucial aspects: considering the number of activated important neurons and minimizing noisy activations to enhance OOD detection performance. To achieve this, we introduce two powerful techniques within LINe: 1) Shapley-based pruning and 2) activation clipping (AC). + +Shapley value-based pruning is a method that mitigates the influence of noisy outputs by selecting activations essential for inferring input data classes. While several methods exist for identifying important activations, Sun et al. [45] use activation magnitude to determine their importance. However, this approach alone is insufficient for quantifying a neuron's importance. Hence, we employ the Shapley value [43] to more accurately measure each neuron's contribution. Applying the Shapley value concept [43] to neural networks allows us to quantify each neuron's contribution to identifying a specific class. Moreover, neurons with high Shapley values are associated with critical input image features [21]. By leveraging the Shapley value [43], we can identify neurons that represent important high-level features for each class, which are essential for reducing noisy output. + +Activation clipping, a concept introduced in ReAct [44], is another powerful technique. Interpreting activation clipping in terms of class-specific features provides a new understanding of its role in considering the number of activated important neurons for OOD detection. Activation clipping adjusts values exceeding a certain threshold to the threshold value. This modification enables us to account for the differences in the number of activated features between in-distribution and OOD data by treating numerous class-specific features equally. By considering the variation in the number of activated class-specific features, we can effectively augment the overall OOD score difference between ID and OOD data, leading to enhanced performance. + +Our key contributions are summarized as follows: + +- We propose a simple yet effective post-hoc OOD detection method, named LINe, which uses the Shapley value to rank the contribution of neurons and gives a new inspiration for leveraging selected important class-specific neurons. +- We unveil the important factor for improving OOD scoring and show a new way of understanding the role of activation clipping for OOD detection. By applying activation clipping, we can fully consider the number of activated class-specific features and achieve higher OOD detection performance. +- Comprehensive experiments have been conducted to verify the effectiveness of the proposed method on the CIFAR-10, CIFAR-100, and ImageNet-1K. Compared to the competitive post-hoc method DICE [45], LINe reduces the FPR95 by up to $14.05\%$ . + +# 2. Background and Related Work + +# 2.1. Neuron-Concept Association + +Neuron-concept association methods are a field of study that tries to interpret the internal computation of CNN to a human-understandable concept [3,8,14,37]. Several studies have shown that neurons of shallower layers tend to learn more simple and low-level concepts, such as curves and edges, while deeper layers learn more abstract and high-level concepts, such as arm and face [52, 59, 60]. The methods for quantifying the concept's contribution are also introduced in [12, 14, 33]. Network Dissection [4, 5, 59] assigns each neuron to a concept to quantify its role. Bau et al. [6] investigate the effect of concept-specific neurons by observing the change of concept-related contents in generative models. Recently, Wang et al. [52] show that models can learn abstract concepts like mammal and carnivore, which is not in the label set of training data. + +# 2.2. Shapley Value + +Shapely value [26, 43, 47] is a concept from Game Theory, which evaluates each property's individual and collaborative effects. Studies have been conducted using Shapley value in CNNs to measure each neuron's contribution and interpret models' behaviors [2, 13, 21, 34, 47]. Neuron Shapley [13] sorts the Shapley values to identify the most influential neurons from all hidden layers as image categories. Khazar et al. [21] show neurons that have high Shapley values have high correlations with important features of the input image. Previous studies have inspired us to select important class-specific neurons through the contribution scores calculated from the Shapley value. LINe can effectively eliminate the negative effects of noisy signals by leveraging the selected class-specific neurons. + +# 2.3. Out-of-Distribution Detection + +ODD detection aims to find inputs with different characteristics from the training data [56]. A lot of research efforts have been devoted to developing an effective method to distinguish OOD inputs from ID inputs. Confidence-based methods perform OOD detection by quantifying OOD scores based on different scoring functions [7,11,16,19,29]. Hendrycks et al. [16] used a maximum softmax probability (MSP) of the model as a baseline confidence-base OOD scoring function. ODIN [30] utilizes perturbation of inputs and temperature scaling on the softmax layer to increase the difference between ID and OOD. To enhance the effectiveness of confidence-based scores, recently, Liu et al. [32] introduced an energy-based score with the theoretical interpretation from a likelihood perspective, which is further adopted in [31, 36, 53] to distinguish ID and OOD samples. Distance-based approaches measure the distance between input sample and typical ID samples or cen + +troids of them [9, 18, 28, 35, 41, 46, 48, 49, 58]. These approaches are based on simple evidence that OOD samples should have more distance than IDs. Similarly, density-based methods identify OOD samples based on the distribution of the training samples and use density (or likelihood) [1, 20, 22-24, 27, 38, 40, 42, 50, 62, 63]. + +But none of the aforementioned methods consider the number of activated features, which can be a good indicator to distinguish ID and OOD samples. The most similar study to our study is DICE [45]. DICE leverages sparsification to reduce the effect of noisy signals by selectively using salient weights from activation [45]. In this study, we effectively eliminate the outcomes of noisy signals by accurately selecting neurons leveraging the contribution of neurons calculated from Shapley value [21, 43]. In addition, our method performs OOD detection more effectively by considering the number of activated features. The neurons are known to be associated with the concepts, and the activation patterns of neurons in deep layers are different in ID and OOD. This gives a theoretical background for considering the number of activation in OOD detection. To the best of our knowledge, our work is the first study to leverage the neuron contribution based on Shapley value and consider the number of activated features for calculating OOD score. + +# 3. Method + +# 3.1. Method Overview + +Our method mainly consists of two parts: Activation Clipping and Shapley-based pruning. Activation clipping is a method of clipping each neuron activation to a specific value when the activation value exceeds a particular threshold $(\delta)$ . Through activation clipping, our method can consider the number of high-level features during calculating OOD scores, which are analyzed in terms of neuron-concept association. Next, Shapley-based pruning eliminates the negative effect of noisy signals by measuring neural contributions of neural networks using important neurons only. We can accurately measure the contribution of each neuron using Shapley value, which is a mathematically grounded method. Also, by applying Shapley value, we can obtain supporting evidence that neurons with large contributions represent critical features for recognizing input image [21]. This allows us to assemble all contributions for each class and select important class-specific neurons representing class-specific features. More details of activation clipping and Shapley-based pruning will be described in Subsection 3.2 and Subsection 3.3. In Subsection 3.4, we will explain the overall method. + +# 3.2. Activation Clipping + +For a pre-trained deep neural network $f_{\theta}(x)$ parameterized by $\theta$ , $f_{\theta}(x)$ encodes an input $x \in \mathbb{R}^d$ , where $d$ indicates + +![](images/0def9eac921510dc2e6798d6ea7a88f2db213213b6dbff3dd21ad94013718f17.jpg) +Figure 2. Overall procedure of LINe for calculating OOD score. LINe is composed of mainly three parts. 1) Activation Clipping (AC), 2) Activation Pruning (AP), 3) Weight Pruning (WP). AC limits the magnitude of the activation, which allows LINe to consider the number of activated features. AP uses contribution matrix C, which is precomputed from Shapley value [43]. AP leverages C to select important neurons and mask others. WP uses an adjusted contribution matrix which is obtained from the contribution matrix C. Leveraging AP and WP, LINe can reduce noisy signals effectively. + +dimension of input $x$ , and predicts a class distribution for $L$ different classes, i.e., $f_{\theta}(x) \in \mathbb{R}^{L}$ . Feature vector from the penultimate layer of the network denotes $h(x) \in \mathbb{R}^q$ , where $q$ stands for the dimension of penultimate layer output $h(x)$ . Weight matrix $\mathbf{W} \in \mathbb{R}^{q \times L}$ weights the importance of each feature in $h(x)$ and transfers to output $f_{\theta}(x)$ as follows: + +$$ +f _ {\theta} (x) = \mathbf {W} ^ {T} h (x) + \mathbf {b}. \tag {1} +$$ + +Activation clipping is applied to the feature vector in the penultimate layer. For each neuron that is activated above a certain threshold, AC limits the magnitude of the activation. As we discussed in Figure 1, the number of activated features in ID and OOD samples are different. By limiting the magnitude of the activation to the same value $\delta$ , we can treat every activated high-level feature equally, which allows us to consider the number of activated features in the OOD score. This increases the OOD score difference between ID and OOD samples, thereby improving performance. + +For each activation $a_{i}$ in $h(x)$ , penultimate layer feature $h(x)$ can be denoted as $h(x) = [a_1, a_2, \dots, a_q]$ . With a clipping threshold $\delta$ , the clipped activation $\hat{a}_{i}$ can be described as $\hat{a}_{i} = \min(a_{i}, \delta)$ . The clipped feature vector $\hat{h}(x)$ + +is then, + +$$ +\hat {h} (x) = \left[ \hat {a} _ {1}, \hat {a} _ {2}, \dots , \hat {a} _ {q} \right]. \tag {2} +$$ + +The model output after AC can be given as: + +$$ +f _ {\theta} ^ {A C} (x) = \mathbf {W} ^ {T} \hat {h} (x) + \mathbf {b}. \tag {3} +$$ + +# 3.3. Shapley-based Pruning + +Shapley-based pruning selectively uses a subset of important neuron activation and weights. To select these subsets, we calculate Shapley value [43] defined by an average of the effect of removing a single unit (e.g., marginal contribution) to all possible combinations of units. However, computing all the combinations of units is computationally expensive and practically infeasible for recent large neural networks. Therefore, we use the Taylor approximation to compute the Shapley value, which is introduced in [21]. For input $x^{l} \in D$ , where $x^{l}$ denotes the sample of class $l$ from dataset $D$ , a contribution(i.e., Shapley value) of $i$ -th neuron $a_{i}$ in class $l$ , $s_{i}^{l}$ is calculated as + +$$ +\left. s _ {i} ^ {l} = \left| f _ {\theta} \left(x ^ {l}\right) - f _ {\theta} \left(x ^ {l}; a _ {i} \leftarrow 0\right) \right| = \left| a _ {i} \nabla_ {a _ {i}} f _ {\theta} \left(x ^ {l}\right) \right|. \right. \tag {4} +$$ + +![](images/0ab4224d979cfb5e7ec58b7c94a41d7e36a54355302b2850f96c7d7d7a592264.jpg) +Figure 3. Calculation of contribution matrix C. + +# 3.3.1 Activation Pruning + +Activation pruning (AP) selectively uses the subset of important neuron activation. Through AP, We can effectively reduce the impact of noisy activation. From the contribution of each neuron $s_i^l$ , which is using obtained from all training data, contribution matrix $\mathbf{C} \in \mathbb{R}^{q \times L}$ is defined as the class-specific average of all contribution $s_i^l$ . An $(i,l)$ -th entry of contribution matrix $c_{il} \in \mathbf{C}$ is defined as: + +$$ +\mathbf {C} _ {i l} = \frac {1}{n} \sum^ {n} s _ {i} ^ {l}, \tag {5} +$$ + +where $n$ denotes the number of training images in class $l$ . We select top- $k$ neurons for each class based on the k-largest elements from each column in $\mathbf{C}$ and define an activation mask matrix $\mathbf{M}_a \in \mathbb{R}^{q \times L}$ , where we set 1 for the $k$ -largest elements from every column in $\mathbf{C}$ , otherwise 0. The model output after AP with the predicted class $l$ is given as: + +$$ +f _ {\theta} ^ {A P} (x) = \mathbf {W} ^ {T} \left(\mathbf {m} _ {l} \odot h (x)\right) + \mathbf {b}, \tag {6} +$$ + +where $\mathbf{m}_l\in \mathbb{R}^q$ indicates $l$ -th column of mask matrix $\mathbf{M}_a$ and $\odot$ denotes the element-wise multiplication. + +# 3.3.2 Weight Pruning + +Weight pruning (WP) selectively uses the subset of important penultimate layer weights. Through WP, We can effectively reduce the impact of noisy signals due to the overparameterized model. The contribution of neurons is further used to refine the weight matrix as WP. For this purpose, we define a weight contribution matrix for the class $l$ as $\mathbf{C}_w^l = \mathbf{c}_l\odot \mathbf{W}\in \mathbb{R}^{q\times L}$ where $\mathbf{c}_1$ indicates the $l$ -th column of contribution matrix $\mathbf{C}$ . We select top- $k$ weights for each class based on the $k$ -largest elements in $\mathbf{C}_w^l$ and define a mask matrix for class $l$ as $\mathbf{M}_w^l\in \mathbb{R}^{q\times L}$ by setting 1 for the $k$ -largest elements in $\mathbf{C}_w^l$ , otherwise 0. The model output after WP with the predicted class $l$ is given as: + +$$ +f _ {\theta} ^ {W P} (x) = \left(\mathbf {W} \odot \mathbf {M} _ {w} ^ {l}\right) ^ {T} h (x) + \mathbf {b}. \tag {7} +$$ + +From the Shapley-based AP and WP, we can determine the neurons representing important high-level features for each + +![](images/9a0a2fc7404aa9c3896e94c9b97fe841f045589fa95f00d89115574b96f88458.jpg) +Figure 4. Calculation of contribution matrix $\mathbf{C}_{\mathbf{w}}^{\mathrm{l}}$ . + +class, which play a crucial role in reducing noisy output. + +# 3.4. Leveraging Important Neurons (LINe) + +As already described in the previous Subsection 3.2 and 3.3, there are two ideas to improve the performance of post-hoc OOD detection. One is considering the number of activated high-level features, and the other is reducing noisy signals from less important neurons. LINe achieves both ways to improve post-hoc OOD detection performance through the procedures described above. By adapting LINe to a model, we can effectively increase the overall difference in OOD scores between ID and OOD data. As a result, the model output under LINe with the predicted class $l$ is described as + +$$ +f _ {\theta} ^ {L I N e} (x) = \left(\mathbf {W} \odot \mathbf {M} _ {w} ^ {l}\right) ^ {T} \left(\mathbf {m} _ {l} \odot \hat {h} (x)\right) + \mathbf {b}. \tag {8} +$$ + +Please note that there is no parameter change in the model itself and ID classification accuracy can be preserved. + +# 4. Experiments + +Comprehensive experiments have been conducted to evaluate our method. In section 4.1, we used the CIFAR [25] benchmark, which is one of the famous benchmarks in OOD studies [32, 44, 45]. In Section 4.2, experiments were conducted based on a large-scale dataset, ImageNet, with various OOD datasets. Section 4.3 analyzes why our method is effective through various ablation experiments. + +# 4.1. Evaluation on CIFAR Benchmarks + +Implementation Details. In this experiment, we used 10,000 test images each from CIFAR-10 [25] and CIFAR-100 [25] as ID data, respectively. The model's performance was evaluated using six commonly used OOD datasets as an OOD benchmark. The list of six OOD datasets is as follows: SVHN [39], Textures [10], iSUN [55], LSUN-Crop [57], LSUN-Resize [57], and Places365 [61]. As the pre-trained models, we used DenseNet [17]. As in [45], the models are trained from CIFAR-10 [25] and CIFAR-100 [25] with 50,000 training images respectively. Following [45], the models were trained during 100 epochs with batch size 64, weight decay 0.0001, momentum 0.9, and + +Table 1. Comparison on CIFAR benchmarks. Comparison with competitive post-hoc OOD detection methods on CIFAR benchmarks. All values in this table are percentages and averaged over six OOD test datasets. $\downarrow$ indicates smaller value means better performance and $\uparrow$ indicates vice versa. Bold numbers are superior results. The overall detail results for each OOD dataset are provided in supplementary material. + +
MethodCIFAR-10CIFAR-100
FPR95 ↓AUROC ↑FPR95 ↓AUROC ↑
MSP [16]48.7392.4680.1374.36
ODIN [30]24.5793.7158.1484.49
Mahalanobis [28]31.4289.1555.3782.73
Energy [32]26.5594.5768.4581.19
ReAct [44]26.4594.9562.2784.47
DICE [45]20.8395.2449.7287.23
DICE + ReAct16.4896.6449.5785.08
LINe (Ours)14.7196.9935.6788.67
+ +start learning rate 0.1. The learning rate was decayed by a factor of 10 at epochs 50, 75, and 90. We used the entire training dataset to estimate the contribution matrix $C$ . + +Comparison. For comparison, we adopted recent post-hoc OOD detection methods: MSP [16], ODIN [30], Mahalanobis distance [28], Energy [32], ReAct [44], and DICE [45]. For all methods, the performances were measured by OOD scores, derived from the same DenseNet model. + +Experimental Results. Table 1 shows the comparisons between LINe and other post-hoc OOD detection methods on CIFAR-10 and CIFAR-100 benchmarks. As shown in the table, our method achieved state-of-the-art performances by outperforming all the other methods on both CIFAR-10 and CIFAR-100 datasets. In CIFAR-100, LINe reduced FPR 95 by $14.05\%$ compared to the competitive method DICE [45]. In CIFAR-100, LINe achieved an FPR 95 of $14.05\%$ which was lower than the FPR 95 of DICE [45] $(49.72\%)$ and DICE + ReAct $(49.57\%)$ . DICE + ReAct is the method that is implemented by applying ReAct [44] on DICE [45]. DICE [45] removed the noisy signals by using the magnitude of activation and weight. LINe not only removed the noisy signals using class-specific neurons but also considered the number of activations of the high-level feature. + +# 4.2. Evaluation on ImageNet + +Implementation Details. In real-world applications, the model encounters high-resolution images with various scenes and features, and evaluation on a large-scale dataset can provide clues about model performance in a real-world application. Therefore, in this experiment, we evaluated LINe on a large-scale ImageNet dataset. Based on [19], a subset of the four datasets where all the overlapping categories with ImageNet-1k were eliminated was used as OOD datasets. The four OOD datasets are as follows: Textures [10], Places365 [61], iNaturalist [51], and SUN [54]. We + +used a pre-trained ResNet-50 model [15], which is trained with ImageNet-1k. The entire training dataset was used to estimate the contribution matrix $C$ , and all images were resized to $224 \times 224$ at test time. + +Experimental Results. In Table 2, we reported the performances of four OOD test datasets respectively. The average results from the four OOD test datasets were also reported. LINe outperformed all baselines including MSP [16], ODIN [30], Mahalanobis distance [28], Energy score [32], ReAct [44], DICE [45], and DICE + ReAct [45]. We compared LINe with Energy [32] first. LINe drastically reduced the FPR95 by $37.71\%$ , which shows the benefit of leveraging important neurons under the same OOD scoring function. Next, we compared LINe with ReAct [44]. LINe reduced the FPR95 by $10.73\%$ , which allows us to see the advantages of leveraging important neurons using Shapley value. LINe further outperformed recent DICE [45] and DICE + ReAct by $14.05\%$ and $6.55\%$ , respectively. Experimental results showed that the proposed method can be applied to real-world large dataset for OOD detection. + +# 4.3. Ablation Study + +In this section, we discuss the effectiveness of each part used in LINe and the detailed differences from other similar approaches. We also analyze the effect of hyperparameters. + +# 4.3.1 Ablation Study of LINe on ImageNet + +Table 3 shows an ablation study over various parts used in LINe. As shown in the table, each part of Shapley-based pruning (AP and WP) improved the performance. Comparing LINE w/o WP with Energy + AC allows us to see the advantages of reducing the noisy activation, which reduces FPR95 by $8.52\%$ . Next, we compared LINe w/o AP with Energy + AC, which also shows the benefits of reducing noisy weights. Compared to Energy + AC, LINe w/o AP reduced FPR95 by $12.21\%$ . Finally, we compared LINe w/o AP with DICE + ReAct [45] at Table 2, which allows us to see the benefit of leveraging class-wise contribution under similar circumstances. LINe w/o AP reduced the FPR95 by $4.06\%$ from $27.25\%$ to $23.19\%$ . DICE + ReAct [45] uses activations to select important weights, while LINe w/o AP selects important weights using class-wise contribution derived from the Shapley value [43]. + +# 4.3.2 Effect of Changing AC Threshold on ImageNet + +In Section 3.2, we discussed the meaning of AC in terms of the neuron-concept association. AC allows us to consider the number of activated high-level features in the penultimate layer. In Table 4, we show various OOD detection performances of the model by changing threshold $\delta$ . Starting from clipping threshold $\delta = \infty$ , the value of FPR95 is the highest in the table. As clipping threshold $\delta$ becomes + +Table 2. Comparison on ImageNet benchmark. Comparisons with competitive post-hoc OOD detection methods on ImageNet benchmark. All values in this table are percentages and averaged over four OOD test datasets. + +
MethodOOD DatasetsAverage
iNaturalistSUNPlacesTexturesFPR95 ↓ AUROC ↑
FPR95 ↓AUROC ↑FPR95 ↓AUROC ↑FPR95 ↓AUROC ↑FPR95 ↓AUROC ↑FPR95 ↓AUROC ↑
MSP [16]54.9987.7470.8380.8673.9979.7668.0079.6166.9581.99
ODIN [30]47.6689.6660.1584.5967.8981.7850.2385.6256.4885.41
Mahalanobis [28]97.0052.6598.5042.4198.4041.7955.8085.0187.4355.47
Energy [32]55.7289.9559.2685.8964.9282.8653.7285.9958.4186.17
ReAct [44]20.3896.2224.2094.2033.8591.5847.3089.8031.4392.95
DICE [45]25.6394.4935.1590.8346.4987.4831.7290.3034.7590.77
DICE + ReAct [45]18.6496.2425.4593.9436.8690.6728.0792.7427.2593.40
LINe (Ours)12.2697.5619.4895.2628.5292.8522.5494.4420.7095.03
+ +Table 3. Ablation Study of LINe on ImageNet. Ablation on the effectiveness of Shapley-based pruning used in LINe and comparison with similar approaches. Values are percentages and averaged over OOD datasets. AC, AP, and WP denote activation clipping, activation pruning, and weight pruning, respectively. + +
MethodACAPWPFPR95↓AUROC↑
Energy [32]58.4186.17
Energy + AC✓35.4091.86
LINe w/o WP✓✓26.8893.77
LINe w/o AP✓✓23.1994.57
LINe (Ours)✓✓✓20.7095.03
+ +Table 4. Ablation on different thresholds $(\delta)$ of AC. Ablation on the different thresholds $(\delta)$ of clipping. All values are percentages and averaged over multiple OOD test datasets. + +
Threshold (δ)FPR95 ↓AUROC ↑
δ = 0.141.1888.44
δ = 0.423.4394.79
δ = 0.820.7095.03
δ = 1.021.6994.81
δ = 1.526.9693.99
δ = 2.031.8892.97
δ = ∞ (no AC)44.8889.14
+ +smaller, the OOD detection performance is improved. But at clipping threshold $\delta < 0.8$ , the OOD detection performance dropped. This is because, as the clipping threshold $\delta$ approaches 0, all the penultimate output values also approach zero. It is obvious that performance will drop when all the penultimate output values approach zero. + +# 4.3.3 Effect of Changing Pruning Percentile on ImageNet + +In this section, we conducted ablation studies on pruning percentiles $(p)$ variation on ImageNet datasets as ID data. In Table 5 we show effect of changing pruning percentile $(p_w$ and $p_a)$ on ImageNet. $p_a$ indicates pruning percentile + +Table 5. Effect of changing pruning percentile $(p)$ on ImageNet. Ablation on the different pruning percentile $(p_a$ and $p_w)$ of pruning. All values are percentages and averaged over multiple OOD test datasets. $p_a$ denotes pruning percentile for AP, $p_w$ indicates pruning percentile for WP. + +
pa=90pa=70pa=50pa=30pa=10
FPR95 ↓FPR95 ↓FPR95 ↓FPR95 ↓FPR95 ↓
pw=9027.5624.7924.7424.5524.54
pw=7027.4525.9325.8127.4533.32
pw=5033.6927.7826.2825.9027.45
pw=3027.4626.1027.1724.3628.43
pw=1027.6426.7527.7525.4120.70
+ +for AP, $p_w$ indicates pruning percentile for WP. For a fixed WP percentile $p_w$ with extremely high value (e.g., $p_w = 90$ ), the performance tends to increase when the AP percentile $p_a$ falls. Since LINe considers the number of activated features for detecting OOD samples, pruning most of the activations or weights has negatively impacted the performance. A lower pruning percentile is better to leverage differences in the number of activated features between ID and OOD samples. But to restrict the negative effect of noisy signals, we need some portions that can remove the noisy signals. As a result, the model performs the best when the pruning percentile is $p_w = 10$ and $p_a = 10$ on ImageNet. + +# 4.3.4 Effect of Changing Pruning Percentile on CIFAR Benchmarks + +In Table 6 and Table 7, we show effect of changing pruning percentile $(p_w$ and $p_a)$ on CIFAR Benchmarks. Both tables show similar tendencies. For all AP percentile $p_a$ , the performance tends to increase when the WP percentile $p_w$ increases. In Table 6, highest performance appeared at $p_w = 90$ and $p_a = 90$ . On the other hand in Table 7, the highest performance appeared at $p_w = 90$ and $p_a = 10$ . This result may seem to conflict with the result in Table 5, our observation in Table 8 can explain the cause of the difference. + +Table 6. Effect of changing pruning percentile $(p)$ in CIFAR10. Ablation on the different pruning percentile $(p_a$ and $p_w)$ of pruning. All values are percentages and averaged over multiple OOD test datasets. $p_a$ denotes pruning percentile for AP, $p_w$ indicates pruning percentile for WP. + +
pa=90pa=70pa=50pa=30pa=10
FPR95 ↓FPR95 ↓FPR95 ↓FPR95 ↓FPR95 ↓
pw=9014.7215.0015.0015.0014.99
pw=7014.8015.1215.1215.1215.10
pw=5014.8015.1215.1115.1115.10
pw=3014.8015.1215.1115.1215.10
pw=1014.8015.1315.1315.1215.73
+ +Table 7. Effect of changing pruning percentile $(p)$ in CIFAR100. Ablation on the different pruning percentile $(p_a$ and $p_w)$ of pruning. All values are percentages and averaged over multiple OOD test datasets. $p_a$ denotes pruning percentile for AP, $p_w$ indicates pruning percentile for WP. + +
pa=90pa=70pa=50pa=30pa=10
FPR95↓FPR95↓FPR95↓FPR95↓FPR95↓
pw=9038.7537.8137.8137.7535.67
pw=7038.3739.3040.0739.7540.81
pw=5038.3739.1940.5440.2742.14
pw=3038.3739.1940.6540.2139.32
pw=1038.4039.3140.7640.9138.17
+ +Table 8. Percentage of class-specific neuron overlap in multiple classes. Difference between the percentage of class-specific neuron overlap in multiple classes on three data sets. For each dataset, we calculated the proportion of very important (top $10\%$ neurons in more than $o\%$ of the class. All values are percentages. + +
OverlapCIFAR-10CIFAR-100ImageNet
o = 2024.5626.901.70
o = 3023.390.580.15
+ +# 4.3.5 Discussion + +In Table 8, we compared the percentage of class-specific neuron overlap in multiple classes on three data sets. For each dataset, we calculated the proportion of very important (top $10\%$ ) neurons in more than $o\%$ of the class. These neurons activate in various classes which have semantically different features. Therefore, the higher proportion of these neurons can be seen as an overparameterized model with more numbers of generally activated neurons. These overparameterized models make OOD detection difficult by creating noisy signals, which can be reduced by leveraging AP and WP. To get optimal results from overparameterized models, we can lessen the effect of overparameterized weights with high WP percentile. Also, the effectiveness of considering the number of activated class-specific neurons can be maximized in the low AP percentile as a tendency + +shown in Table 7. But for a much more overparameterized model, which is shown in Table 6, we need to set high pruning percentile on both $p_w$ and $p_a$ . + +The degree of an overparameterized model can be understood from Section 4.1. We used the same pre-trained model architecture for evaluating CIFAR-10 and CIFAR-100. Of the two models with the same structure, we can intuitively understand that a model trained using a relatively small dataset is more likely to be overparameterized, which can also be observed in Table 8. The proportion of very important (top $10\%$ ) neurons in more than $30\%$ of the class(i.e., $o = 30$ ) on CIFAR-10 is the largest compared to other datasets. This observation shows that our pre-trained model used to evaluate CIFAR-10 is more overparameterized than other models we used. + +# 5. Conclusion + +In this paper, we propose a powerful OOD Detection method called LINe. LINe adopts a neural-concept association, which only uses important activations and weights selectively by measuring class-wise contribution from the Shapley value. Through LINe, we can effectively reduce the influence of the noise signal and make a difference in the overall OOD score between ID and OOD sample distribution. We conducted extensive experiments to demonstrate that LINe is superior to state-of-the-art OOD detection methods and effective on multiple datasets. From several theoretical studies and insights, we show how our method improves the performance of OOD detection. Our method is effective but has some limitations. It is fundamentally a trade-off relationship that pruning neurons to reduce the noisy output and considers the number of class-specific feature activations. Users have to examine the trade-off considering the degree of overparameterization of the model. We hope that as our study proposes an effective way to view OOD detection from a feature presentation perspective, attempts to understand the behavior of neural networks will be applied to multiple domains to discover other effective methods. + +# Acknowledgements + +This work was supported in part by the Institute of Information and Communications Technology Planning and Evaluation (IITP) grant funded by the Korea Government (MSIT)(No. 2022-0-00078: Explainable Logical Reasoning for Medical Knowledge Generation, No. 2021-0-02068: Artificial Intelligence Innovation Hub, No. RS2022-00155911: Artificial Intelligence Convergence Innovation Human Resources Development (Kyung Hee University)) and by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2021R1G1A1094990). + +# References + +[1] Davide Abati, Angelo Porrello, Simone Calderara, and Rita Cucchiara. Latent space autoregression for novelty detection. 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In International conference on learning representations, 2018. 1, 3 \ No newline at end of file diff --git a/2023/LINe_ Out-of-Distribution Detection by Leveraging Important Neurons/images.zip b/2023/LINe_ Out-of-Distribution Detection by Leveraging Important Neurons/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..2e19783b988c978a26ff24b14e753a4c9f03ec63 --- /dev/null +++ b/2023/LINe_ Out-of-Distribution Detection by Leveraging Important Neurons/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:7e7160abc13f658c8e5196cfa9767b26152e40379b638c04908795f6f3a12cdd +size 465006 diff --git a/2023/LINe_ Out-of-Distribution Detection by Leveraging Important Neurons/layout.json b/2023/LINe_ Out-of-Distribution Detection by Leveraging Important Neurons/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..316073abc95afefbd0249f4750832fe43cd98eba --- /dev/null +++ b/2023/LINe_ Out-of-Distribution Detection by Leveraging Important Neurons/layout.json @@ -0,0 +1,9473 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 74, + 136, + 502, + 153 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 74, + 136, + 502, + 153 + ], + "spans": [ + { + "bbox": [ + 74, + 136, + 502, + 153 + ], + "type": "text", + "content": "LINE: Out-of-Distribution Detection by Leveraging Important Neurons" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 149, + 174, + 431, + 188 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 149, + 174, + 431, + 188 + ], + "spans": [ + { + "bbox": [ + 149, + 174, + 431, + 188 + ], + "type": "text", + "content": "Yong Hyun Ahn" + }, + { + "bbox": [ + 149, + 174, + 431, + 188 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 149, + 174, + 431, + 188 + ], + "type": "text", + "content": ", Gyeong-Moon Park" + }, + { + "bbox": [ + 149, + 174, + 431, + 188 + ], + "type": "inline_equation", + "content": "^{2,*}" + }, + { + "bbox": [ + 149, + 174, + 431, + 188 + ], + "type": "text", + "content": ", Seong Tae Kim" + }, + { + "bbox": [ + 149, + 174, + 431, + 188 + ], + "type": "inline_equation", + "content": "^{2,*}" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 145, + 189, + 431, + 202 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 189, + 431, + 202 + ], + "spans": [ + { + "bbox": [ + 145, + 189, + 431, + 202 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 145, + 189, + 431, + 202 + ], + "type": "text", + "content": "Department of Artificial Intelligence, Kyung Hee University" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 112, + 202, + 465, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 112, + 202, + 465, + 216 + ], + "spans": [ + { + "bbox": [ + 112, + 202, + 465, + 216 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 112, + 202, + 465, + 216 + ], + "type": "text", + "content": "Department of Computer Science and Engineering, Kyung Hee University" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 139, + 243, + 185, + 254 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 139, + 243, + 185, + 254 + ], + "spans": [ + { + "bbox": [ + 139, + 243, + 185, + 254 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 45, + 267, + 281, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 267, + 281, + 581 + ], + "spans": [ + { + "bbox": [ + 45, + 267, + 281, + 581 + ], + "type": "text", + "content": "It is important to quantify the uncertainty of input samples, especially in mission-critical domains such as autonomous driving and healthcare, where failure predictions on out-of-distribution (OOD) data are likely to cause big problems. OOD detection problem fundamentally begins in that the model cannot express what it is not aware of. Post-hoc OOD detection approaches are widely explored because they do not require an additional re-training process which might degrade the model's performance and increase the training cost. In this study, from the perspective of neurons in the deep layer of the model representing high-level features, we introduce a new aspect for analyzing the difference in model outputs between in-distribution data and OOD data. We propose a novel method, Leveraging Important Neurons (LINe), for post-hoc Out of distribution detection. Shapley value-based pruning reduces the effects of noisy outputs by selecting only high-contribution neurons for predicting specific classes of input data and masking the rest. Activation clipping fixes all values above a certain threshold into the same value, allowing LINe to treat all the class-specific features equally and just consider the difference between the number of activated feature differences between in-distribution and OOD data. Comprehensive experiments verify the effectiveness of the proposed method by outperforming state-of-the-art post-hoc OOD detection methods on CIFAR-10, CIFAR-100, and ImageNet datasets. Code is available on https://github.com/LINE-OOD" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 602, + 124, + 614 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 602, + 124, + 614 + ], + "spans": [ + { + "bbox": [ + 47, + 602, + 124, + 614 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 45, + 622, + 279, + 703 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 622, + 279, + 703 + ], + "spans": [ + { + "bbox": [ + 45, + 622, + 279, + 703 + ], + "type": "text", + "content": "Recently, deep learning has made tremendous advances in various fields. This advancement has captivated numerous researchers, leading to many attempts to apply deep learning techniques to real-world applications. However, applying these state-of-the-art techniques to real-world applications is often limited for several reasons. One primary obstacle is the presence of unseen classes of samples during" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 305, + 260, + 514, + 413 + ], + "blocks": [ + { + "bbox": [ + 305, + 260, + 514, + 413 + ], + "lines": [ + { + "bbox": [ + 305, + 260, + 514, + 413 + ], + "spans": [ + { + "bbox": [ + 305, + 260, + 514, + 413 + ], + "type": "image", + "image_path": "f007fd399fdb39b6e1a34f13fee85226bc1601fdf466c7bc336594bcfc4984be.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 297, + 424, + 530, + 499 + ], + "lines": [ + { + "bbox": [ + 297, + 424, + 530, + 499 + ], + "spans": [ + { + "bbox": [ + 297, + 424, + 530, + 499 + ], + "type": "text", + "content": "Figure 1. Illustration of the number of activated neuron in the penultimate layer. The distributions of the number of activated neurons from ID (ImageNet [19]) and two OOD datasets (textures [10] and iNaturalist [51]) are presented. We define an activated neuron as one fired with an activation value greater than zero. Most of the neurons are activated when the model receives ID samples but fewer neurons are activated in OOD samples." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 297, + 519, + 530, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 519, + 530, + 613 + ], + "spans": [ + { + "bbox": [ + 297, + 519, + 530, + 613 + ], + "type": "text", + "content": "training. These samples, referred to as out-of-distribution (OOD) data, can compromise a model's stability and, in some cases, severely impair its performance. The inherent characteristics of OOD samples can lead to potentially severe consequences in mission-critical domains, such as autonomous driving and medical applications. So, effectively handling these OOD samples is vital to avoid problems, such as car crashes and misdiagnosis." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 297, + 613, + 531, + 729 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 613, + 531, + 729 + ], + "spans": [ + { + "bbox": [ + 297, + 613, + 531, + 729 + ], + "type": "text", + "content": "For OOD detection, numerous techniques have been explored to analyze the distinction between in-distribution (ID) data and OOD data. There are several approaches to OOD detection, including confidence-based methods [7, 11, 16, 19, 29], density-based methods [1, 20, 22-24, 27, 38, 40, 42, 50, 62, 63], and distance-based methods [9, 18, 28, 35, 41, 46, 48, 49, 58]. The post-hoc method is one approach in OOD detection that offers significant advantages in real-world applications as it eliminates the need for a re-training process, which could potentially degrade the model's per" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 57, + 7, + 101, + 38 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 7, + 101, + 38 + ], + "spans": [ + { + "bbox": [ + 57, + 7, + 101, + 38 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 136, + 5, + 485, + 40 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 136, + 5, + 485, + 40 + ], + "spans": [ + { + "bbox": [ + 136, + 5, + 485, + 40 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 709, + 279, + 729 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 709, + 279, + 729 + ], + "spans": [ + { + "bbox": [ + 46, + 709, + 279, + 729 + ], + "type": "text", + "content": "*Corresponding authors: Gyeong-Moon Park (gmpark@khu.ac.kr) and Seong Tae Kim (st.kim@khu.ac.kr)." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 277, + 747, + 300, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 277, + 747, + 300, + 756 + ], + "spans": [ + { + "bbox": [ + 277, + 747, + 300, + 756 + ], + "type": "text", + "content": "19852" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 595, + 841 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 106, + 211, + 118 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 106, + 211, + 118 + ], + "spans": [ + { + "bbox": [ + 46, + 106, + 211, + 118 + ], + "type": "text", + "content": "formance and increase training costs [56]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 121, + 281, + 377 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 121, + 281, + 377 + ], + "spans": [ + { + "bbox": [ + 45, + 121, + 281, + 377 + ], + "type": "text", + "content": "Post-hoc OOD detection methods [32, 44, 45] employ outputs such as model logits or layer activations, which are typically used for prediction, to calculate OOD scores. These scores allow for the differentiation of ID and OOD data based on the disparities in their respective scores [56]. Enhancing the overall OOD score distribution difference between ID and OOD data is a critical aspect in improving the performance of post-hoc OOD detection methods. Recent studies [44, 45] have found that augmenting the overall difference is contingent upon the capacity to mitigate noisy signals. For example, ReAct [44] demonstrates that OOD data exhibit considerable values in the penultimate layer activation. By truncating these noisy activations, ReAct effectively improves OOD detection performance. Similarly, DICE [45] uncovers the presence of noisy signals that increase the variance of the OOD score distribution. By selectively employing the most salient weights, DICE enhances OOD detection performance while reducing the impact of noisy signals. Minimizing the influence of noisy model outputs is crucial for advancing post-hoc OOD detection performance. In this study, we reveal an additional factor that is also important in the context of OOD detection." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 45, + 380, + 281, + 729 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 380, + 281, + 729 + ], + "spans": [ + { + "bbox": [ + 45, + 380, + 281, + 729 + ], + "type": "text", + "content": "Figure 1 displays the histogram of the number of activated features in the penultimate layer. We define neurons with activation values greater than zero as activated neurons. As the figure demonstrates, a majority of neurons are activated when the model encounters ID samples. However, for OOD samples, fewer neurons are activated. To understand the primary cause of the observation in Figure 1, we investigate the model from the perspective of neuron-concept association [4,5,21,52]. According to [4], neurons are trained to detect disentangled high-level features in the deep layers of convolutional neural networks (CNNs), and they can even learn new unlabeled abstract concepts from the data [52]. The number of neurons representing these high-level features increases in deeper layers and becomes the most significant amount in the penultimate layer [5]. Since the activation in the penultimate layer represents the presence of these high-level features [4], different input images activate high-level features in varying ways, such as magnitude and patterns. These distinct patterns of activation in the penultimate layer are ultimately used to predict the input image's class. As each class possesses unique characteristics related to high-level concepts, the associated high-level features differ for each class. Consequently, each associated high-level feature can be categorized into one class-specific feature group. The disparity in associated high-level features in neurons results in a difference in penultimate layer activation between ID and OOD samples, which are predicted as the same class. Thus, taking into account the number of activated essential neurons can serve as a useful indicator for distinguishing ID and OOD samples." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 296, + 106, + 532, + 188 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 106, + 532, + 188 + ], + "spans": [ + { + "bbox": [ + 296, + 106, + 532, + 188 + ], + "type": "text", + "content": "In this paper, we present a novel post-hoc OOD detection method called Leveraging Important Neurons (LINe). LINe harnesses two crucial aspects: considering the number of activated important neurons and minimizing noisy activations to enhance OOD detection performance. To achieve this, we introduce two powerful techniques within LINe: 1) Shapley-based pruning and 2) activation clipping (AC)." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 296, + 188, + 532, + 362 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 188, + 532, + 362 + ], + "spans": [ + { + "bbox": [ + 296, + 188, + 532, + 362 + ], + "type": "text", + "content": "Shapley value-based pruning is a method that mitigates the influence of noisy outputs by selecting activations essential for inferring input data classes. While several methods exist for identifying important activations, Sun et al. [45] use activation magnitude to determine their importance. However, this approach alone is insufficient for quantifying a neuron's importance. Hence, we employ the Shapley value [43] to more accurately measure each neuron's contribution. Applying the Shapley value concept [43] to neural networks allows us to quantify each neuron's contribution to identifying a specific class. Moreover, neurons with high Shapley values are associated with critical input image features [21]. By leveraging the Shapley value [43], we can identify neurons that represent important high-level features for each class, which are essential for reducing noisy output." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 296, + 362, + 532, + 513 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 362, + 532, + 513 + ], + "spans": [ + { + "bbox": [ + 296, + 362, + 532, + 513 + ], + "type": "text", + "content": "Activation clipping, a concept introduced in ReAct [44], is another powerful technique. Interpreting activation clipping in terms of class-specific features provides a new understanding of its role in considering the number of activated important neurons for OOD detection. Activation clipping adjusts values exceeding a certain threshold to the threshold value. This modification enables us to account for the differences in the number of activated features between in-distribution and OOD data by treating numerous class-specific features equally. By considering the variation in the number of activated class-specific features, we can effectively augment the overall OOD score difference between ID and OOD data, leading to enhanced performance." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 309, + 513, + 506, + 524 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 513, + 506, + 524 + ], + "spans": [ + { + "bbox": [ + 309, + 513, + 506, + 524 + ], + "type": "text", + "content": "Our key contributions are summarized as follows:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 309, + 530, + 530, + 729 + ], + "type": "list", + "angle": 0, + "index": 10, + "blocks": [ + { + "bbox": [ + 309, + 530, + 530, + 588 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 530, + 530, + 588 + ], + "spans": [ + { + "bbox": [ + 309, + 530, + 530, + 588 + ], + "type": "text", + "content": "- We propose a simple yet effective post-hoc OOD detection method, named LINe, which uses the Shapley value to rank the contribution of neurons and gives a new inspiration for leveraging selected important class-specific neurons." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 309, + 595, + 530, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 595, + 530, + 664 + ], + "spans": [ + { + "bbox": [ + 309, + 595, + 530, + 664 + ], + "type": "text", + "content": "- We unveil the important factor for improving OOD scoring and show a new way of understanding the role of activation clipping for OOD detection. By applying activation clipping, we can fully consider the number of activated class-specific features and achieve higher OOD detection performance." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 309, + 671, + 530, + 729 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 671, + 530, + 729 + ], + "spans": [ + { + "bbox": [ + 309, + 671, + 530, + 729 + ], + "type": "text", + "content": "- Comprehensive experiments have been conducted to verify the effectiveness of the proposed method on the CIFAR-10, CIFAR-100, and ImageNet-1K. Compared to the competitive post-hoc method DICE [45], LINe reduces the FPR95 by up to " + }, + { + "bbox": [ + 309, + 671, + 530, + 729 + ], + "type": "inline_equation", + "content": "14.05\\%" + }, + { + "bbox": [ + 309, + 671, + 530, + 729 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 277, + 747, + 300, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 277, + 747, + 300, + 756 + ], + "spans": [ + { + "bbox": [ + 277, + 747, + 300, + 756 + ], + "type": "text", + "content": "19853" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 595, + 841 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 105, + 216, + 118 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 105, + 216, + 118 + ], + "spans": [ + { + "bbox": [ + 46, + 105, + 216, + 118 + ], + "type": "text", + "content": "2. Background and Related Work" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 124, + 198, + 137 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 124, + 198, + 137 + ], + "spans": [ + { + "bbox": [ + 46, + 124, + 198, + 137 + ], + "type": "text", + "content": "2.1. Neuron-Concept Association" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 45, + 142, + 281, + 317 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 142, + 281, + 317 + ], + "spans": [ + { + "bbox": [ + 45, + 142, + 281, + 317 + ], + "type": "text", + "content": "Neuron-concept association methods are a field of study that tries to interpret the internal computation of CNN to a human-understandable concept [3,8,14,37]. Several studies have shown that neurons of shallower layers tend to learn more simple and low-level concepts, such as curves and edges, while deeper layers learn more abstract and high-level concepts, such as arm and face [52, 59, 60]. The methods for quantifying the concept's contribution are also introduced in [12, 14, 33]. Network Dissection [4, 5, 59] assigns each neuron to a concept to quantify its role. Bau et al. [6] investigate the effect of concept-specific neurons by observing the change of concept-related contents in generative models. Recently, Wang et al. [52] show that models can learn abstract concepts like mammal and carnivore, which is not in the label set of training data." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 324, + 133, + 337 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 324, + 133, + 337 + ], + "spans": [ + { + "bbox": [ + 46, + 324, + 133, + 337 + ], + "type": "text", + "content": "2.2. Shapley Value" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 343, + 281, + 507 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 343, + 281, + 507 + ], + "spans": [ + { + "bbox": [ + 45, + 343, + 281, + 507 + ], + "type": "text", + "content": "Shapely value [26, 43, 47] is a concept from Game Theory, which evaluates each property's individual and collaborative effects. Studies have been conducted using Shapley value in CNNs to measure each neuron's contribution and interpret models' behaviors [2, 13, 21, 34, 47]. Neuron Shapley [13] sorts the Shapley values to identify the most influential neurons from all hidden layers as image categories. Khazar et al. [21] show neurons that have high Shapley values have high correlations with important features of the input image. Previous studies have inspired us to select important class-specific neurons through the contribution scores calculated from the Shapley value. LINe can effectively eliminate the negative effects of noisy signals by leveraging the selected class-specific neurons." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 513, + 203, + 525 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 513, + 203, + 525 + ], + "spans": [ + { + "bbox": [ + 46, + 513, + 203, + 525 + ], + "type": "text", + "content": "2.3. Out-of-Distribution Detection" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 532, + 281, + 729 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 532, + 281, + 729 + ], + "spans": [ + { + "bbox": [ + 45, + 532, + 281, + 729 + ], + "type": "text", + "content": "ODD detection aims to find inputs with different characteristics from the training data [56]. A lot of research efforts have been devoted to developing an effective method to distinguish OOD inputs from ID inputs. Confidence-based methods perform OOD detection by quantifying OOD scores based on different scoring functions [7,11,16,19,29]. Hendrycks et al. [16] used a maximum softmax probability (MSP) of the model as a baseline confidence-base OOD scoring function. ODIN [30] utilizes perturbation of inputs and temperature scaling on the softmax layer to increase the difference between ID and OOD. To enhance the effectiveness of confidence-based scores, recently, Liu et al. [32] introduced an energy-based score with the theoretical interpretation from a likelihood perspective, which is further adopted in [31, 36, 53] to distinguish ID and OOD samples. Distance-based approaches measure the distance between input sample and typical ID samples or cen" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 296, + 105, + 532, + 176 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 105, + 532, + 176 + ], + "spans": [ + { + "bbox": [ + 296, + 105, + 532, + 176 + ], + "type": "text", + "content": "troids of them [9, 18, 28, 35, 41, 46, 48, 49, 58]. These approaches are based on simple evidence that OOD samples should have more distance than IDs. Similarly, density-based methods identify OOD samples based on the distribution of the training samples and use density (or likelihood) [1, 20, 22-24, 27, 38, 40, 42, 50, 62, 63]." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 296, + 176, + 533, + 386 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 176, + 533, + 386 + ], + "spans": [ + { + "bbox": [ + 296, + 176, + 533, + 386 + ], + "type": "text", + "content": "But none of the aforementioned methods consider the number of activated features, which can be a good indicator to distinguish ID and OOD samples. The most similar study to our study is DICE [45]. DICE leverages sparsification to reduce the effect of noisy signals by selectively using salient weights from activation [45]. In this study, we effectively eliminate the outcomes of noisy signals by accurately selecting neurons leveraging the contribution of neurons calculated from Shapley value [21, 43]. In addition, our method performs OOD detection more effectively by considering the number of activated features. The neurons are known to be associated with the concepts, and the activation patterns of neurons in deep layers are different in ID and OOD. This gives a theoretical background for considering the number of activation in OOD detection. To the best of our knowledge, our work is the first study to leverage the neuron contribution based on Shapley value and consider the number of activated features for calculating OOD score." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 297, + 396, + 352, + 409 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 396, + 352, + 409 + ], + "spans": [ + { + "bbox": [ + 297, + 396, + 352, + 409 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 297, + 417, + 401, + 428 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 417, + 401, + 428 + ], + "spans": [ + { + "bbox": [ + 297, + 417, + 401, + 428 + ], + "type": "text", + "content": "3.1. Method Overview" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 296, + 435, + 533, + 680 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 435, + 533, + 680 + ], + "spans": [ + { + "bbox": [ + 296, + 435, + 533, + 680 + ], + "type": "text", + "content": "Our method mainly consists of two parts: Activation Clipping and Shapley-based pruning. Activation clipping is a method of clipping each neuron activation to a specific value when the activation value exceeds a particular threshold " + }, + { + "bbox": [ + 296, + 435, + 533, + 680 + ], + "type": "inline_equation", + "content": "(\\delta)" + }, + { + "bbox": [ + 296, + 435, + 533, + 680 + ], + "type": "text", + "content": ". Through activation clipping, our method can consider the number of high-level features during calculating OOD scores, which are analyzed in terms of neuron-concept association. Next, Shapley-based pruning eliminates the negative effect of noisy signals by measuring neural contributions of neural networks using important neurons only. We can accurately measure the contribution of each neuron using Shapley value, which is a mathematically grounded method. Also, by applying Shapley value, we can obtain supporting evidence that neurons with large contributions represent critical features for recognizing input image [21]. This allows us to assemble all contributions for each class and select important class-specific neurons representing class-specific features. More details of activation clipping and Shapley-based pruning will be described in Subsection 3.2 and Subsection 3.3. In Subsection 3.4, we will explain the overall method." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 297, + 687, + 411, + 700 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 687, + 411, + 700 + ], + "spans": [ + { + "bbox": [ + 297, + 687, + 411, + 700 + ], + "type": "text", + "content": "3.2. Activation Clipping" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 297, + 706, + 532, + 729 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 706, + 532, + 729 + ], + "spans": [ + { + "bbox": [ + 297, + 706, + 532, + 729 + ], + "type": "text", + "content": "For a pre-trained deep neural network " + }, + { + "bbox": [ + 297, + 706, + 532, + 729 + ], + "type": "inline_equation", + "content": "f_{\\theta}(x)" + }, + { + "bbox": [ + 297, + 706, + 532, + 729 + ], + "type": "text", + "content": " parameterized by " + }, + { + "bbox": [ + 297, + 706, + 532, + 729 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 297, + 706, + 532, + 729 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 297, + 706, + 532, + 729 + ], + "type": "inline_equation", + "content": "f_{\\theta}(x)" + }, + { + "bbox": [ + 297, + 706, + 532, + 729 + ], + "type": "text", + "content": " encodes an input " + }, + { + "bbox": [ + 297, + 706, + 532, + 729 + ], + "type": "inline_equation", + "content": "x \\in \\mathbb{R}^d" + }, + { + "bbox": [ + 297, + 706, + 532, + 729 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 297, + 706, + 532, + 729 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 297, + 706, + 532, + 729 + ], + "type": "text", + "content": " indicates" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 277, + 747, + 301, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 277, + 747, + 301, + 756 + ], + "spans": [ + { + "bbox": [ + 277, + 747, + 301, + 756 + ], + "type": "text", + "content": "19854" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 595, + 841 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 105, + 530, + 368 + ], + "blocks": [ + { + "bbox": [ + 49, + 105, + 530, + 368 + ], + "lines": [ + { + "bbox": [ + 49, + 105, + 530, + 368 + ], + "spans": [ + { + "bbox": [ + 49, + 105, + 530, + 368 + ], + "type": "image", + "image_path": "0def9eac921510dc2e6798d6ea7a88f2db213213b6dbff3dd21ad94013718f17.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 379, + 533, + 434 + ], + "lines": [ + { + "bbox": [ + 45, + 379, + 533, + 434 + ], + "spans": [ + { + "bbox": [ + 45, + 379, + 533, + 434 + ], + "type": "text", + "content": "Figure 2. Overall procedure of LINe for calculating OOD score. LINe is composed of mainly three parts. 1) Activation Clipping (AC), 2) Activation Pruning (AP), 3) Weight Pruning (WP). AC limits the magnitude of the activation, which allows LINe to consider the number of activated features. AP uses contribution matrix C, which is precomputed from Shapley value [43]. AP leverages C to select important neurons and mask others. WP uses an adjusted contribution matrix which is obtained from the contribution matrix C. Leveraging AP and WP, LINe can reduce noisy signals effectively." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 454, + 281, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 454, + 281, + 525 + ], + "spans": [ + { + "bbox": [ + 45, + 454, + 281, + 525 + ], + "type": "text", + "content": "dimension of input " + }, + { + "bbox": [ + 45, + 454, + 281, + 525 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 45, + 454, + 281, + 525 + ], + "type": "text", + "content": ", and predicts a class distribution for " + }, + { + "bbox": [ + 45, + 454, + 281, + 525 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 45, + 454, + 281, + 525 + ], + "type": "text", + "content": " different classes, i.e., " + }, + { + "bbox": [ + 45, + 454, + 281, + 525 + ], + "type": "inline_equation", + "content": "f_{\\theta}(x) \\in \\mathbb{R}^{L}" + }, + { + "bbox": [ + 45, + 454, + 281, + 525 + ], + "type": "text", + "content": ". 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Weight matrix " + }, + { + "bbox": [ + 45, + 454, + 281, + 525 + ], + "type": "inline_equation", + "content": "\\mathbf{W} \\in \\mathbb{R}^{q \\times L}" + }, + { + "bbox": [ + 45, + 454, + 281, + 525 + ], + "type": "text", + "content": " weights the importance of each feature in " + }, + { + "bbox": [ + 45, + 454, + 281, + 525 + ], + "type": "inline_equation", + "content": "h(x)" + }, + { + "bbox": [ + 45, + 454, + 281, + 525 + ], + "type": "text", + "content": " and transfers to output " + }, + { + "bbox": [ + 45, + 454, + 281, + 525 + ], + "type": "inline_equation", + "content": "f_{\\theta}(x)" + }, + { + "bbox": [ + 45, + 454, + 281, + 525 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 116, + 539, + 279, + 555 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 539, + 279, + 555 + ], + "spans": [ + { + "bbox": [ + 116, + 539, + 279, + 555 + ], + "type": "interline_equation", + "content": "f _ {\\theta} (x) = \\mathbf {W} ^ {T} h (x) + \\mathbf {b}. \\tag {1}", + "image_path": "549c7881dca425a253aa9320902bce4820c2191c126bf48818a45f2070b83fe0.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 565, + 280, + 682 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 565, + 280, + 682 + ], + "spans": [ + { + "bbox": [ + 45, + 565, + 280, + 682 + ], + "type": "text", + "content": "Activation clipping is applied to the feature vector in the penultimate layer. For each neuron that is activated above a certain threshold, AC limits the magnitude of the activation. As we discussed in Figure 1, the number of activated features in ID and OOD samples are different. By limiting the magnitude of the activation to the same value " + }, + { + "bbox": [ + 45, + 565, + 280, + 682 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 45, + 565, + 280, + 682 + ], + "type": "text", + "content": ", we can treat every activated high-level feature equally, which allows us to consider the number of activated features in the OOD score. 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The clipped feature vector " + }, + { + "bbox": [ + 45, + 682, + 281, + 730 + ], + "type": "inline_equation", + "content": "\\hat{h}(x)" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 298, + 454, + 330, + 465 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 454, + 330, + 465 + ], + "spans": [ + { + "bbox": [ + 298, + 454, + 330, + 465 + ], + "type": "text", + "content": "is then," + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 364, + 466, + 531, + 481 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 364, + 466, + 531, + 481 + ], + "spans": [ + { + "bbox": [ + 364, + 466, + 531, + 481 + ], + "type": "interline_equation", + "content": "\\hat {h} (x) = \\left[ \\hat {a} _ {1}, \\hat {a} _ {2}, \\dots , \\hat {a} _ {q} \\right]. \\tag {2}", + "image_path": "0fb27e4af235ab9678cdfd79975129a2c4d3a8d722085f056b05c8e9d284b68d.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 298, + 488, + 471, + 501 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 488, + 471, + 501 + ], + "spans": [ + { + "bbox": [ + 298, + 488, + 471, + 501 + ], + "type": "text", + "content": "The model output after AC can be given as:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 364, + 509, + 531, + 524 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 364, + 509, + 531, + 524 + ], + "spans": [ + { + "bbox": [ + 364, + 509, + 531, + 524 + ], + "type": "interline_equation", + "content": "f _ {\\theta} ^ {A C} (x) = \\mathbf {W} ^ {T} \\hat {h} (x) + \\mathbf {b}. \\tag {3}", + "image_path": "a5c428038cf456c9fc31ade9a5d7d0f20e829d2a0068272f302488869c0aecb0.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 298, + 535, + 427, + 549 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 535, + 427, + 549 + ], + "spans": [ + { + "bbox": [ + 298, + 535, + 427, + 549 + ], + "type": "text", + "content": "3.3. Shapley-based Pruning" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 296, + 554, + 532, + 695 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 554, + 532, + 695 + ], + "spans": [ + { + "bbox": [ + 296, + 554, + 532, + 695 + ], + "type": "text", + "content": "Shapley-based pruning selectively uses a subset of important neuron activation and weights. To select these subsets, we calculate Shapley value [43] defined by an average of the effect of removing a single unit (e.g., marginal contribution) to all possible combinations of units. However, computing all the combinations of units is computationally expensive and practically infeasible for recent large neural networks. Therefore, we use the Taylor approximation to compute the Shapley value, which is introduced in [21]. For input " + }, + { + "bbox": [ + 296, + 554, + 532, + 695 + ], + "type": "inline_equation", + "content": "x^{l} \\in D" + }, + { + "bbox": [ + 296, + 554, + 532, + 695 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 296, + 554, + 532, + 695 + ], + "type": "inline_equation", + "content": "x^{l}" + }, + { + "bbox": [ + 296, + 554, + 532, + 695 + ], + "type": "text", + "content": " denotes the sample of class " + }, + { + "bbox": [ + 296, + 554, + 532, + 695 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 296, + 554, + 532, + 695 + ], + "type": "text", + "content": " from dataset " + }, + { + "bbox": [ + 296, + 554, + 532, + 695 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 296, + 554, + 532, + 695 + ], + "type": "text", + "content": ", a contribution(i.e., Shapley value) of " + }, + { + "bbox": [ + 296, + 554, + 532, + 695 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 296, + 554, + 532, + 695 + ], + "type": "text", + "content": "-th neuron " + }, + { + "bbox": [ + 296, + 554, + 532, + 695 + ], + "type": "inline_equation", + "content": "a_{i}" + }, + { + "bbox": [ + 296, + 554, + 532, + 695 + ], + "type": "text", + "content": " in class " + }, + { + "bbox": [ + 296, + 554, + 532, + 695 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 296, + 554, + 532, + 695 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 296, + 554, + 532, + 695 + ], + "type": "inline_equation", + "content": "s_{i}^{l}" + }, + { + "bbox": [ + 296, + 554, + 532, + 695 + ], + "type": "text", + "content": " is calculated as" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 309, + 715, + 531, + 732 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 715, + 531, + 732 + ], + "spans": [ + { + "bbox": [ + 309, + 715, + 531, + 732 + ], + "type": "interline_equation", + "content": "\\left. s _ {i} ^ {l} = \\left| f _ {\\theta} \\left(x ^ {l}\\right) - f _ {\\theta} \\left(x ^ {l}; a _ {i} \\leftarrow 0\\right) \\right| = \\left| a _ {i} \\nabla_ {a _ {i}} f _ {\\theta} \\left(x ^ {l}\\right) \\right|. \\right. \\tag {4}", + "image_path": "871982b16b3a2634ab4e07204ae48240c5eb5bd7379d42faf9b21387f7318280.jpg" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 277, + 747, + 301, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 277, + 747, + 301, + 756 + ], + "spans": [ + { + "bbox": [ + 277, + 747, + 301, + 756 + ], + "type": "text", + "content": "19855" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 595, + 841 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 104, + 278, + 207 + ], + "blocks": [ + { + "bbox": [ + 48, + 104, + 278, + 207 + ], + "lines": [ + { + "bbox": [ + 48, + 104, + 278, + 207 + ], + "spans": [ + { + "bbox": [ + 48, + 104, + 278, + 207 + ], + "type": "image", + "image_path": "0ab4224d979cfb5e7ec58b7c94a41d7e36a54355302b2850f96c7d7d7a592264.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 73, + 216, + 252, + 228 + ], + "lines": [ + { + "bbox": [ + 73, + 216, + 252, + 228 + ], + "spans": [ + { + "bbox": [ + 73, + 216, + 252, + 228 + ], + "type": "text", + "content": "Figure 3. Calculation of contribution matrix C." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 248, + 158, + 259 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 248, + 158, + 259 + ], + "spans": [ + { + "bbox": [ + 45, + 248, + 158, + 259 + ], + "type": "text", + "content": "3.3.1 Activation Pruning" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 265, + 280, + 347 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 265, + 280, + 347 + ], + "spans": [ + { + "bbox": [ + 45, + 265, + 280, + 347 + ], + "type": "text", + "content": "Activation pruning (AP) selectively uses the subset of important neuron activation. Through AP, We can effectively reduce the impact of noisy activation. 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The model output after AP with the predicted class " + }, + { + "bbox": [ + 45, + 385, + 279, + 454 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 45, + 385, + 279, + 454 + ], + "type": "text", + "content": " is given as:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 95, + 461, + 279, + 476 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 95, + 461, + 279, + 476 + ], + "spans": [ + { + "bbox": [ + 95, + 461, + 279, + 476 + ], + "type": "interline_equation", + "content": "f _ {\\theta} ^ {A P} (x) = \\mathbf {W} ^ {T} \\left(\\mathbf {m} _ {l} \\odot h (x)\\right) + \\mathbf {b}, \\tag {6}", + "image_path": "bc0cffef0618a0a058435c3beb25acd487a4a1a248a9c5a42b4228e0370b1052.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 45, + 483, + 279, + 507 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 483, + 279, + 507 + ], + "spans": [ + { + "bbox": [ + 45, + 483, + 279, + 507 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 45, + 483, + 279, + 507 + ], + "type": "inline_equation", + "content": "\\mathbf{m}_l\\in \\mathbb{R}^q" + }, + { + "bbox": [ + 45, + 483, + 279, + 507 + ], + "type": "text", + "content": " indicates " + }, + { + "bbox": [ + 45, + 483, + 279, + 507 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 45, + 483, + 279, + 507 + ], + "type": "text", + "content": "-th column of mask matrix " + }, + { + "bbox": [ + 45, + 483, + 279, + 507 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_a" + }, + { + "bbox": [ + 45, + 483, + 279, + 507 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 45, + 483, + 279, + 507 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 45, + 483, + 279, + 507 + ], + "type": "text", + "content": " denotes the element-wise multiplication." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 45, + 520, + 145, + 532 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 520, + 145, + 532 + ], + "spans": [ + { + "bbox": [ + 45, + 520, + 145, + 532 + ], + "type": "text", + "content": "3.3.2 Weight Pruning" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 45, + 538, + 280, + 678 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 538, + 280, + 678 + ], + "spans": [ + { + "bbox": [ + 45, + 538, + 280, + 678 + ], + "type": "text", + "content": "Weight pruning (WP) selectively uses the subset of important penultimate layer weights. Through WP, We can effectively reduce the impact of noisy signals due to the overparameterized model. The contribution of neurons is further used to refine the weight matrix as WP. For this purpose, we define a weight contribution matrix for the class " + }, + { + "bbox": [ + 45, + 538, + 280, + 678 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 45, + 538, + 280, + 678 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 45, + 538, + 280, + 678 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_w^l = \\mathbf{c}_l\\odot \\mathbf{W}\\in \\mathbb{R}^{q\\times L}" + }, + { + "bbox": [ + 45, + 538, + 280, + 678 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 45, + 538, + 280, + 678 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_1" + }, + { + "bbox": [ + 45, + 538, + 280, + 678 + ], + "type": "text", + "content": " indicates the " + }, + { + "bbox": [ + 45, + 538, + 280, + 678 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 45, + 538, + 280, + 678 + ], + "type": "text", + "content": "-th column of contribution matrix " + }, + { + "bbox": [ + 45, + 538, + 280, + 678 + ], + "type": "inline_equation", + "content": "\\mathbf{C}" + }, + { + "bbox": [ + 45, + 538, + 280, + 678 + ], + "type": "text", + "content": ". We select top-" + }, + { + "bbox": [ + 45, + 538, + 280, + 678 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 45, + 538, + 280, + 678 + ], + "type": "text", + "content": " weights for each class based on the " + }, + { + "bbox": [ + 45, + 538, + 280, + 678 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 45, + 538, + 280, + 678 + ], + "type": "text", + "content": "-largest elements in " + }, + { + "bbox": [ + 45, + 538, + 280, + 678 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_w^l" + }, + { + "bbox": [ + 45, + 538, + 280, + 678 + ], + "type": "text", + "content": " and define a mask matrix for class " + }, + { + "bbox": [ + 45, + 538, + 280, + 678 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 45, + 538, + 280, + 678 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 45, + 538, + 280, + 678 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_w^l\\in \\mathbb{R}^{q\\times L}" + }, + { + "bbox": [ + 45, + 538, + 280, + 678 + ], + "type": "text", + "content": " by setting 1 for the " + }, + { + "bbox": [ + 45, + 538, + 280, + 678 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 45, + 538, + 280, + 678 + ], + "type": "text", + "content": "-largest elements in " + }, + { + "bbox": [ + 45, + 538, + 280, + 678 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_w^l" + }, + { + "bbox": [ + 45, + 538, + 280, + 678 + ], + "type": "text", + "content": ", otherwise 0. The model output after WP with the predicted class " + }, + { + "bbox": [ + 45, + 538, + 280, + 678 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 45, + 538, + 280, + 678 + ], + "type": "text", + "content": " is given as:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 93, + 684, + 279, + 699 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 93, + 684, + 279, + 699 + ], + "spans": [ + { + "bbox": [ + 93, + 684, + 279, + 699 + ], + "type": "interline_equation", + "content": "f _ {\\theta} ^ {W P} (x) = \\left(\\mathbf {W} \\odot \\mathbf {M} _ {w} ^ {l}\\right) ^ {T} h (x) + \\mathbf {b}. \\tag {7}", + "image_path": "7315adf0e3c08380a873f55b0b035b31212f70da53277bd027a3075a28a454b6.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 45, + 706, + 280, + 729 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 706, + 280, + 729 + ], + "spans": [ + { + "bbox": [ + 45, + 706, + 280, + 729 + ], + "type": "text", + "content": "From the Shapley-based AP and WP, we can determine the neurons representing important high-level features for each" + } + ] + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 304, + 105, + 527, + 184 + ], + "blocks": [ + { + "bbox": [ + 304, + 105, + 527, + 184 + ], + "lines": [ + { + "bbox": [ + 304, + 105, + 527, + 184 + ], + "spans": [ + { + "bbox": [ + 304, + 105, + 527, + 184 + ], + "type": "image", + "image_path": "9a0a2fc7404aa9c3896e94c9b97fe841f045589fa95f00d89115574b96f88458.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 321, + 193, + 507, + 204 + ], + "lines": [ + { + "bbox": [ + 321, + 193, + 507, + 204 + ], + "spans": [ + { + "bbox": [ + 321, + 193, + 507, + 204 + ], + "type": "text", + "content": "Figure 4. Calculation of contribution matrix " + }, + { + "bbox": [ + 321, + 193, + 507, + 204 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_{\\mathbf{w}}^{\\mathrm{l}}" + }, + { + "bbox": [ + 321, + 193, + 507, + 204 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 297, + 224, + 520, + 236 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 224, + 520, + 236 + ], + "spans": [ + { + "bbox": [ + 297, + 224, + 520, + 236 + ], + "type": "text", + "content": "class, which play a crucial role in reducing noisy output." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 297, + 254, + 496, + 267 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 254, + 496, + 267 + ], + "spans": [ + { + "bbox": [ + 297, + 254, + 496, + 267 + ], + "type": "text", + "content": "3.4. Leveraging Important Neurons (LINe)" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 296, + 272, + 531, + 400 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 272, + 531, + 400 + ], + "spans": [ + { + "bbox": [ + 296, + 272, + 531, + 400 + ], + "type": "text", + "content": "As already described in the previous Subsection 3.2 and 3.3, there are two ideas to improve the performance of post-hoc OOD detection. One is considering the number of activated high-level features, and the other is reducing noisy signals from less important neurons. LINe achieves both ways to improve post-hoc OOD detection performance through the procedures described above. By adapting LINe to a model, we can effectively increase the overall difference in OOD scores between ID and OOD data. As a result, the model output under LINe with the predicted class " + }, + { + "bbox": [ + 296, + 272, + 531, + 400 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 296, + 272, + 531, + 400 + ], + "type": "text", + "content": " is described as" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 326, + 407, + 530, + 423 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 407, + 530, + 423 + ], + "spans": [ + { + "bbox": [ + 326, + 407, + 530, + 423 + ], + "type": "interline_equation", + "content": "f _ {\\theta} ^ {L I N e} (x) = \\left(\\mathbf {W} \\odot \\mathbf {M} _ {w} ^ {l}\\right) ^ {T} \\left(\\mathbf {m} _ {l} \\odot \\hat {h} (x)\\right) + \\mathbf {b}. \\tag {8}", + "image_path": "3bcd448ccc3947efb3f7303731ac33aa6fb875b5e0a88955780302786cb62650.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 297, + 431, + 531, + 454 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 431, + 531, + 454 + ], + "spans": [ + { + "bbox": [ + 297, + 431, + 531, + 454 + ], + "type": "text", + "content": "Please note that there is no parameter change in the model itself and ID classification accuracy can be preserved." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 298, + 464, + 377, + 476 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 464, + 377, + 476 + ], + "spans": [ + { + "bbox": [ + 298, + 464, + 377, + 476 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 296, + 483, + 531, + 565 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 483, + 531, + 565 + ], + "spans": [ + { + "bbox": [ + 296, + 483, + 531, + 565 + ], + "type": "text", + "content": "Comprehensive experiments have been conducted to evaluate our method. In section 4.1, we used the CIFAR [25] benchmark, which is one of the famous benchmarks in OOD studies [32, 44, 45]. In Section 4.2, experiments were conducted based on a large-scale dataset, ImageNet, with various OOD datasets. Section 4.3 analyzes why our method is effective through various ablation experiments." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 297, + 571, + 480, + 583 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 571, + 480, + 583 + ], + "spans": [ + { + "bbox": [ + 297, + 571, + 480, + 583 + ], + "type": "text", + "content": "4.1. Evaluation on CIFAR Benchmarks" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 296, + 589, + 532, + 729 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 589, + 532, + 729 + ], + "spans": [ + { + "bbox": [ + 296, + 589, + 532, + 729 + ], + "type": "text", + "content": "Implementation Details. In this experiment, we used 10,000 test images each from CIFAR-10 [25] and CIFAR-100 [25] as ID data, respectively. The model's performance was evaluated using six commonly used OOD datasets as an OOD benchmark. The list of six OOD datasets is as follows: SVHN [39], Textures [10], iSUN [55], LSUN-Crop [57], LSUN-Resize [57], and Places365 [61]. As the pre-trained models, we used DenseNet [17]. As in [45], the models are trained from CIFAR-10 [25] and CIFAR-100 [25] with 50,000 training images respectively. Following [45], the models were trained during 100 epochs with batch size 64, weight decay 0.0001, momentum 0.9, and" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 277, + 747, + 301, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 277, + 747, + 301, + 756 + ], + "spans": [ + { + "bbox": [ + 277, + 747, + 301, + 756 + ], + "type": "text", + "content": "19856" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 595, + 841 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 188, + 278, + 293 + ], + "blocks": [ + { + "bbox": [ + 45, + 104, + 280, + 179 + ], + "lines": [ + { + "bbox": [ + 45, + 104, + 280, + 179 + ], + "spans": [ + { + "bbox": [ + 45, + 104, + 280, + 179 + ], + "type": "text", + "content": "Table 1. Comparison on CIFAR benchmarks. Comparison with competitive post-hoc OOD detection methods on CIFAR benchmarks. All values in this table are percentages and averaged over six OOD test datasets. " + }, + { + "bbox": [ + 45, + 104, + 280, + 179 + ], + "type": "inline_equation", + "content": "\\downarrow" + }, + { + "bbox": [ + 45, + 104, + 280, + 179 + ], + "type": "text", + "content": " indicates smaller value means better performance and " + }, + { + "bbox": [ + 45, + 104, + 280, + 179 + ], + "type": "inline_equation", + "content": "\\uparrow" + }, + { + "bbox": [ + 45, + 104, + 280, + 179 + ], + "type": "text", + "content": " indicates vice versa. Bold numbers are superior results. The overall detail results for each OOD dataset are provided in supplementary material." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 188, + 278, + 293 + ], + "lines": [ + { + "bbox": [ + 48, + 188, + 278, + 293 + ], + "spans": [ + { + "bbox": [ + 48, + 188, + 278, + 293 + ], + "type": "table", + "html": "
MethodCIFAR-10CIFAR-100
FPR95 ↓AUROC ↑FPR95 ↓AUROC ↑
MSP [16]48.7392.4680.1374.36
ODIN [30]24.5793.7158.1484.49
Mahalanobis [28]31.4289.1555.3782.73
Energy [32]26.5594.5768.4581.19
ReAct [44]26.4594.9562.2784.47
DICE [45]20.8395.2449.7287.23
DICE + ReAct16.4896.6449.5785.08
LINe (Ours)14.7196.9935.6788.67
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We used the entire training dataset to estimate the contribution matrix " + }, + { + "bbox": [ + 45, + 313, + 279, + 348 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 45, + 313, + 279, + 348 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 349, + 279, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 349, + 279, + 407 + ], + "spans": [ + { + "bbox": [ + 45, + 349, + 279, + 407 + ], + "type": "text", + "content": "Comparison. For comparison, we adopted recent post-hoc OOD detection methods: MSP [16], ODIN [30], Mahalanobis distance [28], Energy [32], ReAct [44], and DICE [45]. For all methods, the performances were measured by OOD scores, derived from the same DenseNet model." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 409, + 280, + 584 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 409, + 280, + 584 + ], + "spans": [ + { + "bbox": [ + 45, + 409, + 280, + 584 + ], + "type": "text", + "content": "Experimental Results. Table 1 shows the comparisons between LINe and other post-hoc OOD detection methods on CIFAR-10 and CIFAR-100 benchmarks. As shown in the table, our method achieved state-of-the-art performances by outperforming all the other methods on both CIFAR-10 and CIFAR-100 datasets. In CIFAR-100, LINe reduced FPR 95 by " + }, + { + "bbox": [ + 45, + 409, + 280, + 584 + ], + "type": "inline_equation", + "content": "14.05\\%" + }, + { + "bbox": [ + 45, + 409, + 280, + 584 + ], + "type": "text", + "content": " compared to the competitive method DICE [45]. In CIFAR-100, LINe achieved an FPR 95 of " + }, + { + "bbox": [ + 45, + 409, + 280, + 584 + ], + "type": "inline_equation", + "content": "14.05\\%" + }, + { + "bbox": [ + 45, + 409, + 280, + 584 + ], + "type": "text", + "content": " which was lower than the FPR 95 of DICE [45] " + }, + { + "bbox": [ + 45, + 409, + 280, + 584 + ], + "type": "inline_equation", + "content": "(49.72\\%)" + }, + { + "bbox": [ + 45, + 409, + 280, + 584 + ], + "type": "text", + "content": " and DICE + ReAct " + }, + { + "bbox": [ + 45, + 409, + 280, + 584 + ], + "type": "inline_equation", + "content": "(49.57\\%)" + }, + { + "bbox": [ + 45, + 409, + 280, + 584 + ], + "type": "text", + "content": ". DICE + ReAct is the method that is implemented by applying ReAct [44] on DICE [45]. DICE [45] removed the noisy signals by using the magnitude of activation and weight. LINe not only removed the noisy signals using class-specific neurons but also considered the number of activations of the high-level feature." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 594, + 180, + 607 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 180, + 607 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 180, + 607 + ], + "type": "text", + "content": "4.2. Evaluation on ImageNet" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 613, + 279, + 729 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 613, + 279, + 729 + ], + "spans": [ + { + "bbox": [ + 45, + 613, + 279, + 729 + ], + "type": "text", + "content": "Implementation Details. In real-world applications, the model encounters high-resolution images with various scenes and features, and evaluation on a large-scale dataset can provide clues about model performance in a real-world application. Therefore, in this experiment, we evaluated LINe on a large-scale ImageNet dataset. Based on [19], a subset of the four datasets where all the overlapping categories with ImageNet-1k were eliminated was used as OOD datasets. The four OOD datasets are as follows: Textures [10], Places365 [61], iNaturalist [51], and SUN [54]. We" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 296, + 106, + 531, + 152 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 106, + 531, + 152 + ], + "spans": [ + { + "bbox": [ + 296, + 106, + 531, + 152 + ], + "type": "text", + "content": "used a pre-trained ResNet-50 model [15], which is trained with ImageNet-1k. The entire training dataset was used to estimate the contribution matrix " + }, + { + "bbox": [ + 296, + 106, + 531, + 152 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 296, + 106, + 531, + 152 + ], + "type": "text", + "content": ", and all images were resized to " + }, + { + "bbox": [ + 296, + 106, + 531, + 152 + ], + "type": "inline_equation", + "content": "224 \\times 224" + }, + { + "bbox": [ + 296, + 106, + 531, + 152 + ], + "type": "text", + "content": " at test time." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 296, + 153, + 531, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 153, + 531, + 338 + ], + "spans": [ + { + "bbox": [ + 296, + 153, + 531, + 338 + ], + "type": "text", + "content": "Experimental Results. In Table 2, we reported the performances of four OOD test datasets respectively. The average results from the four OOD test datasets were also reported. LINe outperformed all baselines including MSP [16], ODIN [30], Mahalanobis distance [28], Energy score [32], ReAct [44], DICE [45], and DICE + ReAct [45]. We compared LINe with Energy [32] first. LINe drastically reduced the FPR95 by " + }, + { + "bbox": [ + 296, + 153, + 531, + 338 + ], + "type": "inline_equation", + "content": "37.71\\%" + }, + { + "bbox": [ + 296, + 153, + 531, + 338 + ], + "type": "text", + "content": ", which shows the benefit of leveraging important neurons under the same OOD scoring function. Next, we compared LINe with ReAct [44]. LINe reduced the FPR95 by " + }, + { + "bbox": [ + 296, + 153, + 531, + 338 + ], + "type": "inline_equation", + "content": "10.73\\%" + }, + { + "bbox": [ + 296, + 153, + 531, + 338 + ], + "type": "text", + "content": ", which allows us to see the advantages of leveraging important neurons using Shapley value. LINe further outperformed recent DICE [45] and DICE + ReAct by " + }, + { + "bbox": [ + 296, + 153, + 531, + 338 + ], + "type": "inline_equation", + "content": "14.05\\%" + }, + { + "bbox": [ + 296, + 153, + 531, + 338 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 153, + 531, + 338 + ], + "type": "inline_equation", + "content": "6.55\\%" + }, + { + "bbox": [ + 296, + 153, + 531, + 338 + ], + "type": "text", + "content": ", respectively. Experimental results showed that the proposed method can be applied to real-world large dataset for OOD detection." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 297, + 344, + 389, + 358 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 344, + 389, + 358 + ], + "spans": [ + { + "bbox": [ + 297, + 344, + 389, + 358 + ], + "type": "text", + "content": "4.3. Ablation Study" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 297, + 363, + 531, + 398 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 363, + 531, + 398 + ], + "spans": [ + { + "bbox": [ + 297, + 363, + 531, + 398 + ], + "type": "text", + "content": "In this section, we discuss the effectiveness of each part used in LINe and the detailed differences from other similar approaches. We also analyze the effect of hyperparameters." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 297, + 412, + 483, + 424 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 412, + 483, + 424 + ], + "spans": [ + { + "bbox": [ + 297, + 412, + 483, + 424 + ], + "type": "text", + "content": "4.3.1 Ablation Study of LINe on ImageNet" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 296, + 430, + 531, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 430, + 531, + 616 + ], + "spans": [ + { + "bbox": [ + 296, + 430, + 531, + 616 + ], + "type": "text", + "content": "Table 3 shows an ablation study over various parts used in LINe. As shown in the table, each part of Shapley-based pruning (AP and WP) improved the performance. Comparing LINE w/o WP with Energy + AC allows us to see the advantages of reducing the noisy activation, which reduces FPR95 by " + }, + { + "bbox": [ + 296, + 430, + 531, + 616 + ], + "type": "inline_equation", + "content": "8.52\\%" + }, + { + "bbox": [ + 296, + 430, + 531, + 616 + ], + "type": "text", + "content": ". Next, we compared LINe w/o AP with Energy + AC, which also shows the benefits of reducing noisy weights. Compared to Energy + AC, LINe w/o AP reduced FPR95 by " + }, + { + "bbox": [ + 296, + 430, + 531, + 616 + ], + "type": "inline_equation", + "content": "12.21\\%" + }, + { + "bbox": [ + 296, + 430, + 531, + 616 + ], + "type": "text", + "content": ". Finally, we compared LINe w/o AP with DICE + ReAct [45] at Table 2, which allows us to see the benefit of leveraging class-wise contribution under similar circumstances. LINe w/o AP reduced the FPR95 by " + }, + { + "bbox": [ + 296, + 430, + 531, + 616 + ], + "type": "inline_equation", + "content": "4.06\\%" + }, + { + "bbox": [ + 296, + 430, + 531, + 616 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 296, + 430, + 531, + 616 + ], + "type": "inline_equation", + "content": "27.25\\%" + }, + { + "bbox": [ + 296, + 430, + 531, + 616 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 296, + 430, + 531, + 616 + ], + "type": "inline_equation", + "content": "23.19\\%" + }, + { + "bbox": [ + 296, + 430, + 531, + 616 + ], + "type": "text", + "content": ". DICE + ReAct [45] uses activations to select important weights, while LINe w/o AP selects important weights using class-wise contribution derived from the Shapley value [43]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 297, + 629, + 524, + 642 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 629, + 524, + 642 + ], + "spans": [ + { + "bbox": [ + 297, + 629, + 524, + 642 + ], + "type": "text", + "content": "4.3.2 Effect of Changing AC Threshold on ImageNet" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 296, + 647, + 531, + 729 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 647, + 531, + 729 + ], + "spans": [ + { + "bbox": [ + 296, + 647, + 531, + 729 + ], + "type": "text", + "content": "In Section 3.2, we discussed the meaning of AC in terms of the neuron-concept association. AC allows us to consider the number of activated high-level features in the penultimate layer. In Table 4, we show various OOD detection performances of the model by changing threshold " + }, + { + "bbox": [ + 296, + 647, + 531, + 729 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 296, + 647, + 531, + 729 + ], + "type": "text", + "content": ". Starting from clipping threshold " + }, + { + "bbox": [ + 296, + 647, + 531, + 729 + ], + "type": "inline_equation", + "content": "\\delta = \\infty" + }, + { + "bbox": [ + 296, + 647, + 531, + 729 + ], + "type": "text", + "content": ", the value of FPR95 is the highest in the table. As clipping threshold " + }, + { + "bbox": [ + 296, + 647, + 531, + 729 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 296, + 647, + 531, + 729 + ], + "type": "text", + "content": " becomes" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 277, + 747, + 301, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 277, + 747, + 301, + 756 + ], + "spans": [ + { + "bbox": [ + 277, + 747, + 301, + 756 + ], + "type": "text", + "content": "19857" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 595, + 841 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 134, + 531, + 253 + ], + "blocks": [ + { + "bbox": [ + 45, + 104, + 531, + 126 + ], + "lines": [ + { + "bbox": [ + 45, + 104, + 531, + 126 + ], + "spans": [ + { + "bbox": [ + 45, + 104, + 531, + 126 + ], + "type": "text", + "content": "Table 2. Comparison on ImageNet benchmark. Comparisons with competitive post-hoc OOD detection methods on ImageNet benchmark. All values in this table are percentages and averaged over four OOD test datasets." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 134, + 531, + 253 + ], + "lines": [ + { + "bbox": [ + 48, + 134, + 531, + 253 + ], + "spans": [ + { + "bbox": [ + 48, + 134, + 531, + 253 + ], + "type": "table", + "html": "
MethodOOD DatasetsAverage
iNaturalistSUNPlacesTexturesFPR95 ↓ AUROC ↑
FPR95 ↓AUROC ↑FPR95 ↓AUROC ↑FPR95 ↓AUROC ↑FPR95 ↓AUROC ↑FPR95 ↓AUROC ↑
MSP [16]54.9987.7470.8380.8673.9979.7668.0079.6166.9581.99
ODIN [30]47.6689.6660.1584.5967.8981.7850.2385.6256.4885.41
Mahalanobis [28]97.0052.6598.5042.4198.4041.7955.8085.0187.4355.47
Energy [32]55.7289.9559.2685.8964.9282.8653.7285.9958.4186.17
ReAct [44]20.3896.2224.2094.2033.8591.5847.3089.8031.4392.95
DICE [45]25.6394.4935.1590.8346.4987.4831.7290.3034.7590.77
DICE + ReAct [45]18.6496.2425.4593.9436.8690.6728.0792.7427.2593.40
LINe (Ours)12.2697.5619.4895.2628.5292.8522.5494.4420.7095.03
", + "image_path": "91ab9adf3a6daa3219358b75dbaa903c1280ec81cf51173dc3a45c52a3f811c5.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 60, + 333, + 267, + 403 + ], + "blocks": [ + { + "bbox": [ + 45, + 269, + 280, + 324 + ], + "lines": [ + { + "bbox": [ + 45, + 269, + 280, + 324 + ], + "spans": [ + { + "bbox": [ + 45, + 269, + 280, + 324 + ], + "type": "text", + "content": "Table 3. Ablation Study of LINe on ImageNet. Ablation on the effectiveness of Shapley-based pruning used in LINe and comparison with similar approaches. Values are percentages and averaged over OOD datasets. AC, AP, and WP denote activation clipping, activation pruning, and weight pruning, respectively." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 60, + 333, + 267, + 403 + ], + "lines": [ + { + "bbox": [ + 60, + 333, + 267, + 403 + ], + "spans": [ + { + "bbox": [ + 60, + 333, + 267, + 403 + ], + "type": "table", + "html": "
MethodACAPWPFPR95↓AUROC↑
Energy [32]58.4186.17
Energy + AC✓35.4091.86
LINe w/o WP✓✓26.8893.77
LINe w/o AP✓✓23.1994.57
LINe (Ours)✓✓✓20.7095.03
", + "image_path": "72ccf20ab106c9a821e7ef2458292838051d3cf7f136a1d6d41920ad91b7993c.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 88, + 454, + 239, + 546 + ], + "blocks": [ + { + "bbox": [ + 45, + 414, + 280, + 447 + ], + "lines": [ + { + "bbox": [ + 45, + 414, + 280, + 447 + ], + "spans": [ + { + "bbox": [ + 45, + 414, + 280, + 447 + ], + "type": "text", + "content": "Table 4. Ablation on different thresholds " + }, + { + "bbox": [ + 45, + 414, + 280, + 447 + ], + "type": "inline_equation", + "content": "(\\delta)" + }, + { + "bbox": [ + 45, + 414, + 280, + 447 + ], + "type": "text", + "content": " of AC. Ablation on the different thresholds " + }, + { + "bbox": [ + 45, + 414, + 280, + 447 + ], + "type": "inline_equation", + "content": "(\\delta)" + }, + { + "bbox": [ + 45, + 414, + 280, + 447 + ], + "type": "text", + "content": " of clipping. All values are percentages and averaged over multiple OOD test datasets." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 88, + 454, + 239, + 546 + ], + "lines": [ + { + "bbox": [ + 88, + 454, + 239, + 546 + ], + "spans": [ + { + "bbox": [ + 88, + 454, + 239, + 546 + ], + "type": "table", + "html": "
Threshold (δ)FPR95 ↓AUROC ↑
δ = 0.141.1888.44
δ = 0.423.4394.79
δ = 0.820.7095.03
δ = 1.021.6994.81
δ = 1.526.9693.99
δ = 2.031.8892.97
δ = ∞ (no AC)44.8889.14
", + "image_path": "67b22029c76548d08ecb0167b5f185ce6d992dd7465c97b4c0bc56689aa866d5.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 565, + 279, + 636 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 565, + 279, + 636 + ], + "spans": [ + { + "bbox": [ + 45, + 565, + 279, + 636 + ], + "type": "text", + "content": "smaller, the OOD detection performance is improved. But at clipping threshold " + }, + { + "bbox": [ + 45, + 565, + 279, + 636 + ], + "type": "inline_equation", + "content": "\\delta < 0.8" + }, + { + "bbox": [ + 45, + 565, + 279, + 636 + ], + "type": "text", + "content": ", the OOD detection performance dropped. This is because, as the clipping threshold " + }, + { + "bbox": [ + 45, + 565, + 279, + 636 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 45, + 565, + 279, + 636 + ], + "type": "text", + "content": " approaches 0, all the penultimate output values also approach zero. It is obvious that performance will drop when all the penultimate output values approach zero." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 45, + 651, + 280, + 676 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 651, + 280, + 676 + ], + "spans": [ + { + "bbox": [ + 45, + 651, + 280, + 676 + ], + "type": "text", + "content": "4.3.3 Effect of Changing Pruning Percentile on ImageNet" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 45, + 682, + 280, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 682, + 280, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 682, + 280, + 730 + ], + "type": "text", + "content": "In this section, we conducted ablation studies on pruning percentiles " + }, + { + "bbox": [ + 45, + 682, + 280, + 730 + ], + "type": "inline_equation", + "content": "(p)" + }, + { + "bbox": [ + 45, + 682, + 280, + 730 + ], + "type": "text", + "content": " variation on ImageNet datasets as ID data. In Table 5 we show effect of changing pruning percentile " + }, + { + "bbox": [ + 45, + 682, + 280, + 730 + ], + "type": "inline_equation", + "content": "(p_w" + }, + { + "bbox": [ + 45, + 682, + 280, + 730 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 45, + 682, + 280, + 730 + ], + "type": "inline_equation", + "content": "p_a)" + }, + { + "bbox": [ + 45, + 682, + 280, + 730 + ], + "type": "text", + "content": " on ImageNet. " + }, + { + "bbox": [ + 45, + 682, + 280, + 730 + ], + "type": "inline_equation", + "content": "p_a" + }, + { + "bbox": [ + 45, + 682, + 280, + 730 + ], + "type": "text", + "content": " indicates pruning percentile" + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 300, + 333, + 533, + 411 + ], + "blocks": [ + { + "bbox": [ + 297, + 269, + 531, + 324 + ], + "lines": [ + { + "bbox": [ + 297, + 269, + 531, + 324 + ], + "spans": [ + { + "bbox": [ + 297, + 269, + 531, + 324 + ], + "type": "text", + "content": "Table 5. Effect of changing pruning percentile " + }, + { + "bbox": [ + 297, + 269, + 531, + 324 + ], + "type": "inline_equation", + "content": "(p)" + }, + { + "bbox": [ + 297, + 269, + 531, + 324 + ], + "type": "text", + "content": " on ImageNet. Ablation on the different pruning percentile " + }, + { + "bbox": [ + 297, + 269, + 531, + 324 + ], + "type": "inline_equation", + "content": "(p_a" + }, + { + "bbox": [ + 297, + 269, + 531, + 324 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 297, + 269, + 531, + 324 + ], + "type": "inline_equation", + "content": "p_w)" + }, + { + "bbox": [ + 297, + 269, + 531, + 324 + ], + "type": "text", + "content": " of pruning. All values are percentages and averaged over multiple OOD test datasets. " + }, + { + "bbox": [ + 297, + 269, + 531, + 324 + ], + "type": "inline_equation", + "content": "p_a" + }, + { + "bbox": [ + 297, + 269, + 531, + 324 + ], + "type": "text", + "content": " denotes pruning percentile for AP, " + }, + { + "bbox": [ + 297, + 269, + 531, + 324 + ], + "type": "inline_equation", + "content": "p_w" + }, + { + "bbox": [ + 297, + 269, + 531, + 324 + ], + "type": "text", + "content": " indicates pruning percentile for WP." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 300, + 333, + 533, + 411 + ], + "lines": [ + { + "bbox": [ + 300, + 333, + 533, + 411 + ], + "spans": [ + { + "bbox": [ + 300, + 333, + 533, + 411 + ], + "type": "table", + "html": "
pa=90pa=70pa=50pa=30pa=10
FPR95 ↓FPR95 ↓FPR95 ↓FPR95 ↓FPR95 ↓
pw=9027.5624.7924.7424.5524.54
pw=7027.4525.9325.8127.4533.32
pw=5033.6927.7826.2825.9027.45
pw=3027.4626.1027.1724.3628.43
pw=1027.6426.7527.7525.4120.70
", + "image_path": "030c32695dabbf52a8e92890e2dd4f2522aa2bb6b94cbd6e72bd42f15bd4d67b.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 296, + 432, + 532, + 572 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 432, + 532, + 572 + ], + "spans": [ + { + "bbox": [ + 296, + 432, + 532, + 572 + ], + "type": "text", + "content": "for AP, " + }, + { + "bbox": [ + 296, + 432, + 532, + 572 + ], + "type": "inline_equation", + "content": "p_w" + }, + { + "bbox": [ + 296, + 432, + 532, + 572 + ], + "type": "text", + "content": " indicates pruning percentile for WP. For a fixed WP percentile " + }, + { + "bbox": [ + 296, + 432, + 532, + 572 + ], + "type": "inline_equation", + "content": "p_w" + }, + { + "bbox": [ + 296, + 432, + 532, + 572 + ], + "type": "text", + "content": " with extremely high value (e.g., " + }, + { + "bbox": [ + 296, + 432, + 532, + 572 + ], + "type": "inline_equation", + "content": "p_w = 90" + }, + { + "bbox": [ + 296, + 432, + 532, + 572 + ], + "type": "text", + "content": "), the performance tends to increase when the AP percentile " + }, + { + "bbox": [ + 296, + 432, + 532, + 572 + ], + "type": "inline_equation", + "content": "p_a" + }, + { + "bbox": [ + 296, + 432, + 532, + 572 + ], + "type": "text", + "content": " falls. Since LINe considers the number of activated features for detecting OOD samples, pruning most of the activations or weights has negatively impacted the performance. A lower pruning percentile is better to leverage differences in the number of activated features between ID and OOD samples. But to restrict the negative effect of noisy signals, we need some portions that can remove the noisy signals. As a result, the model performs the best when the pruning percentile is " + }, + { + "bbox": [ + 296, + 432, + 532, + 572 + ], + "type": "inline_equation", + "content": "p_w = 10" + }, + { + "bbox": [ + 296, + 432, + 532, + 572 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 432, + 532, + 572 + ], + "type": "inline_equation", + "content": "p_a = 10" + }, + { + "bbox": [ + 296, + 432, + 532, + 572 + ], + "type": "text", + "content": " on ImageNet." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 297, + 592, + 531, + 614 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 592, + 531, + 614 + ], + "spans": [ + { + "bbox": [ + 297, + 592, + 531, + 614 + ], + "type": "text", + "content": "4.3.4 Effect of Changing Pruning Percentile on CIFAR Benchmarks" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 296, + 624, + 531, + 729 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 624, + 531, + 729 + ], + "spans": [ + { + "bbox": [ + 296, + 624, + 531, + 729 + ], + "type": "text", + "content": "In Table 6 and Table 7, we show effect of changing pruning percentile " + }, + { + "bbox": [ + 296, + 624, + 531, + 729 + ], + "type": "inline_equation", + "content": "(p_w" + }, + { + "bbox": [ + 296, + 624, + 531, + 729 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 624, + 531, + 729 + ], + "type": "inline_equation", + "content": "p_a)" + }, + { + "bbox": [ + 296, + 624, + 531, + 729 + ], + "type": "text", + "content": " on CIFAR Benchmarks. Both tables show similar tendencies. For all AP percentile " + }, + { + "bbox": [ + 296, + 624, + 531, + 729 + ], + "type": "inline_equation", + "content": "p_a" + }, + { + "bbox": [ + 296, + 624, + 531, + 729 + ], + "type": "text", + "content": ", the performance tends to increase when the WP percentile " + }, + { + "bbox": [ + 296, + 624, + 531, + 729 + ], + "type": "inline_equation", + "content": "p_w" + }, + { + "bbox": [ + 296, + 624, + 531, + 729 + ], + "type": "text", + "content": " increases. In Table 6, highest performance appeared at " + }, + { + "bbox": [ + 296, + 624, + 531, + 729 + ], + "type": "inline_equation", + "content": "p_w = 90" + }, + { + "bbox": [ + 296, + 624, + 531, + 729 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 624, + 531, + 729 + ], + "type": "inline_equation", + "content": "p_a = 90" + }, + { + "bbox": [ + 296, + 624, + 531, + 729 + ], + "type": "text", + "content": ". On the other hand in Table 7, the highest performance appeared at " + }, + { + "bbox": [ + 296, + 624, + 531, + 729 + ], + "type": "inline_equation", + "content": "p_w = 90" + }, + { + "bbox": [ + 296, + 624, + 531, + 729 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 624, + 531, + 729 + ], + "type": "inline_equation", + "content": "p_a = 10" + }, + { + "bbox": [ + 296, + 624, + 531, + 729 + ], + "type": "text", + "content": ". This result may seem to conflict with the result in Table 5, our observation in Table 8 can explain the cause of the difference." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 277, + 747, + 301, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 277, + 747, + 301, + 756 + ], + "spans": [ + { + "bbox": [ + 277, + 747, + 301, + 756 + ], + "type": "text", + "content": "19858" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 595, + 841 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 166, + 282, + 245 + ], + "blocks": [ + { + "bbox": [ + 46, + 104, + 280, + 158 + ], + "lines": [ + { + "bbox": [ + 46, + 104, + 280, + 158 + ], + "spans": [ + { + "bbox": [ + 46, + 104, + 280, + 158 + ], + "type": "text", + "content": "Table 6. Effect of changing pruning percentile " + }, + { + "bbox": [ + 46, + 104, + 280, + 158 + ], + "type": "inline_equation", + "content": "(p)" + }, + { + "bbox": [ + 46, + 104, + 280, + 158 + ], + "type": "text", + "content": " in CIFAR10. Ablation on the different pruning percentile " + }, + { + "bbox": [ + 46, + 104, + 280, + 158 + ], + "type": "inline_equation", + "content": "(p_a" + }, + { + "bbox": [ + 46, + 104, + 280, + 158 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 104, + 280, + 158 + ], + "type": "inline_equation", + "content": "p_w)" + }, + { + "bbox": [ + 46, + 104, + 280, + 158 + ], + "type": "text", + "content": " of pruning. All values are percentages and averaged over multiple OOD test datasets. " + }, + { + "bbox": [ + 46, + 104, + 280, + 158 + ], + "type": "inline_equation", + "content": "p_a" + }, + { + "bbox": [ + 46, + 104, + 280, + 158 + ], + "type": "text", + "content": " denotes pruning percentile for AP, " + }, + { + "bbox": [ + 46, + 104, + 280, + 158 + ], + "type": "inline_equation", + "content": "p_w" + }, + { + "bbox": [ + 46, + 104, + 280, + 158 + ], + "type": "text", + "content": " indicates pruning percentile for WP." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 166, + 282, + 245 + ], + "lines": [ + { + "bbox": [ + 48, + 166, + 282, + 245 + ], + "spans": [ + { + "bbox": [ + 48, + 166, + 282, + 245 + ], + "type": "table", + "html": "
pa=90pa=70pa=50pa=30pa=10
FPR95 ↓FPR95 ↓FPR95 ↓FPR95 ↓FPR95 ↓
pw=9014.7215.0015.0015.0014.99
pw=7014.8015.1215.1215.1215.10
pw=5014.8015.1215.1115.1115.10
pw=3014.8015.1215.1115.1215.10
pw=1014.8015.1315.1315.1215.73
", + "image_path": "b5d057bb562a244ae4061f512d1209afe999ef6b5716517fb4bd69a834308aa3.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 48, + 319, + 282, + 397 + ], + "blocks": [ + { + "bbox": [ + 46, + 257, + 280, + 311 + ], + "lines": [ + { + "bbox": [ + 46, + 257, + 280, + 311 + ], + "spans": [ + { + "bbox": [ + 46, + 257, + 280, + 311 + ], + "type": "text", + "content": "Table 7. Effect of changing pruning percentile " + }, + { + "bbox": [ + 46, + 257, + 280, + 311 + ], + "type": "inline_equation", + "content": "(p)" + }, + { + "bbox": [ + 46, + 257, + 280, + 311 + ], + "type": "text", + "content": " in CIFAR100. Ablation on the different pruning percentile " + }, + { + "bbox": [ + 46, + 257, + 280, + 311 + ], + "type": "inline_equation", + "content": "(p_a" + }, + { + "bbox": [ + 46, + 257, + 280, + 311 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 257, + 280, + 311 + ], + "type": "inline_equation", + "content": "p_w)" + }, + { + "bbox": [ + 46, + 257, + 280, + 311 + ], + "type": "text", + "content": " of pruning. All values are percentages and averaged over multiple OOD test datasets. " + }, + { + "bbox": [ + 46, + 257, + 280, + 311 + ], + "type": "inline_equation", + "content": "p_a" + }, + { + "bbox": [ + 46, + 257, + 280, + 311 + ], + "type": "text", + "content": " denotes pruning percentile for AP, " + }, + { + "bbox": [ + 46, + 257, + 280, + 311 + ], + "type": "inline_equation", + "content": "p_w" + }, + { + "bbox": [ + 46, + 257, + 280, + 311 + ], + "type": "text", + "content": " indicates pruning percentile for WP." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 319, + 282, + 397 + ], + "lines": [ + { + "bbox": [ + 48, + 319, + 282, + 397 + ], + "spans": [ + { + "bbox": [ + 48, + 319, + 282, + 397 + ], + "type": "table", + "html": "
pa=90pa=70pa=50pa=30pa=10
FPR95↓FPR95↓FPR95↓FPR95↓FPR95↓
pw=9038.7537.8137.8137.7535.67
pw=7038.3739.3040.0739.7540.81
pw=5038.3739.1940.5440.2742.14
pw=3038.3739.1940.6540.2139.32
pw=1038.4039.3140.7640.9138.17
", + "image_path": "a651343816efac538068c05657ca890a3907de2f558601fdef907f085026aa93.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 75, + 472, + 251, + 513 + ], + "blocks": [ + { + "bbox": [ + 45, + 410, + 279, + 464 + ], + "lines": [ + { + "bbox": [ + 45, + 410, + 279, + 464 + ], + "spans": [ + { + "bbox": [ + 45, + 410, + 279, + 464 + ], + "type": "text", + "content": "Table 8. Percentage of class-specific neuron overlap in multiple classes. Difference between the percentage of class-specific neuron overlap in multiple classes on three data sets. For each dataset, we calculated the proportion of very important (top " + }, + { + "bbox": [ + 45, + 410, + 279, + 464 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 45, + 410, + 279, + 464 + ], + "type": "text", + "content": " neurons in more than " + }, + { + "bbox": [ + 45, + 410, + 279, + 464 + ], + "type": "inline_equation", + "content": "o\\%" + }, + { + "bbox": [ + 45, + 410, + 279, + 464 + ], + "type": "text", + "content": " of the class. All values are percentages." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 75, + 472, + 251, + 513 + ], + "lines": [ + { + "bbox": [ + 75, + 472, + 251, + 513 + ], + "spans": [ + { + "bbox": [ + 75, + 472, + 251, + 513 + ], + "type": "table", + "html": "
OverlapCIFAR-10CIFAR-100ImageNet
o = 2024.5626.901.70
o = 3023.390.580.15
", + "image_path": "fd0939c6e90fbe7266b0a9a48eada267fdcef2bbb4c9bb7ad16d23c19a2af31f.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 534, + 122, + 544 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 534, + 122, + 544 + ], + "spans": [ + { + "bbox": [ + 46, + 534, + 122, + 544 + ], + "type": "text", + "content": "4.3.5 Discussion" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 45, + 555, + 279, + 729 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 555, + 279, + 729 + ], + "spans": [ + { + "bbox": [ + 45, + 555, + 279, + 729 + ], + "type": "text", + "content": "In Table 8, we compared the percentage of class-specific neuron overlap in multiple classes on three data sets. For each dataset, we calculated the proportion of very important (top " + }, + { + "bbox": [ + 45, + 555, + 279, + 729 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 45, + 555, + 279, + 729 + ], + "type": "text", + "content": ") neurons in more than " + }, + { + "bbox": [ + 45, + 555, + 279, + 729 + ], + "type": "inline_equation", + "content": "o\\%" + }, + { + "bbox": [ + 45, + 555, + 279, + 729 + ], + "type": "text", + "content": " of the class. These neurons activate in various classes which have semantically different features. Therefore, the higher proportion of these neurons can be seen as an overparameterized model with more numbers of generally activated neurons. These overparameterized models make OOD detection difficult by creating noisy signals, which can be reduced by leveraging AP and WP. To get optimal results from overparameterized models, we can lessen the effect of overparameterized weights with high WP percentile. Also, the effectiveness of considering the number of activated class-specific neurons can be maximized in the low AP percentile as a tendency" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 297, + 106, + 531, + 141 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 106, + 531, + 141 + ], + "spans": [ + { + "bbox": [ + 297, + 106, + 531, + 141 + ], + "type": "text", + "content": "shown in Table 7. But for a much more overparameterized model, which is shown in Table 6, we need to set high pruning percentile on both " + }, + { + "bbox": [ + 297, + 106, + 531, + 141 + ], + "type": "inline_equation", + "content": "p_w" + }, + { + "bbox": [ + 297, + 106, + 531, + 141 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 297, + 106, + 531, + 141 + ], + "type": "inline_equation", + "content": "p_a" + }, + { + "bbox": [ + 297, + 106, + 531, + 141 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 297, + 142, + 531, + 280 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 142, + 531, + 280 + ], + "spans": [ + { + "bbox": [ + 297, + 142, + 531, + 280 + ], + "type": "text", + "content": "The degree of an overparameterized model can be understood from Section 4.1. We used the same pre-trained model architecture for evaluating CIFAR-10 and CIFAR-100. Of the two models with the same structure, we can intuitively understand that a model trained using a relatively small dataset is more likely to be overparameterized, which can also be observed in Table 8. The proportion of very important (top " + }, + { + "bbox": [ + 297, + 142, + 531, + 280 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 297, + 142, + 531, + 280 + ], + "type": "text", + "content": ") neurons in more than " + }, + { + "bbox": [ + 297, + 142, + 531, + 280 + ], + "type": "inline_equation", + "content": "30\\%" + }, + { + "bbox": [ + 297, + 142, + 531, + 280 + ], + "type": "text", + "content": " of the class(i.e., " + }, + { + "bbox": [ + 297, + 142, + 531, + 280 + ], + "type": "inline_equation", + "content": "o = 30" + }, + { + "bbox": [ + 297, + 142, + 531, + 280 + ], + "type": "text", + "content": ") on CIFAR-10 is the largest compared to other datasets. This observation shows that our pre-trained model used to evaluate CIFAR-10 is more overparameterized than other models we used." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 298, + 293, + 368, + 305 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 293, + 368, + 305 + ], + "spans": [ + { + "bbox": [ + 298, + 293, + 368, + 305 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 297, + 313, + 531, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 313, + 531, + 568 + ], + "spans": [ + { + "bbox": [ + 297, + 313, + 531, + 568 + ], + "type": "text", + "content": "In this paper, we propose a powerful OOD Detection method called LINe. LINe adopts a neural-concept association, which only uses important activations and weights selectively by measuring class-wise contribution from the Shapley value. Through LINe, we can effectively reduce the influence of the noise signal and make a difference in the overall OOD score between ID and OOD sample distribution. We conducted extensive experiments to demonstrate that LINe is superior to state-of-the-art OOD detection methods and effective on multiple datasets. From several theoretical studies and insights, we show how our method improves the performance of OOD detection. Our method is effective but has some limitations. It is fundamentally a trade-off relationship that pruning neurons to reduce the noisy output and considers the number of class-specific feature activations. Users have to examine the trade-off considering the degree of overparameterization of the model. We hope that as our study proposes an effective way to view OOD detection from a feature presentation perspective, attempts to understand the behavior of neural networks will be applied to multiple domains to discover other effective methods." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 298, + 581, + 396, + 594 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 581, + 396, + 594 + ], + "spans": [ + { + "bbox": [ + 298, + 581, + 396, + 594 + ], + "type": "text", + "content": "Acknowledgements" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 297, + 601, + 531, + 729 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 601, + 531, + 729 + ], + "spans": [ + { + "bbox": [ + 297, + 601, + 531, + 729 + ], + "type": "text", + "content": "This work was supported in part by the Institute of Information and Communications Technology Planning and Evaluation (IITP) grant funded by the Korea Government (MSIT)(No. 2022-0-00078: Explainable Logical Reasoning for Medical Knowledge Generation, No. 2021-0-02068: Artificial Intelligence Innovation Hub, No. RS2022-00155911: Artificial Intelligence Convergence Innovation Human Resources Development (Kyung Hee University)) and by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2021R1G1A1094990)." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 277, + 747, + 301, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 277, + 747, + 301, + 756 + ], + "spans": [ + { + "bbox": [ + 277, + 747, + 301, + 756 + ], + "type": "text", + "content": "19859" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 595, + 841 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 105, + 103, + 117 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 105, + 103, + 117 + ], + "spans": [ + { + "bbox": [ + 47, + 105, + 103, + 117 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 125, + 280, + 729 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 52, + 125, + 279, + 177 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 125, + 279, + 177 + ], + "spans": [ + { + "bbox": [ + 52, + 125, + 279, + 177 + ], + "type": "text", + "content": "[1] Davide Abati, Angelo Porrello, Simone Calderara, and Rita Cucchiara. 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State-of-the-art methods in weakly supervised affordance grounding often fail to make accurate predictions for objects with complex structures, e.g., chairs and bicycles. To address this, our model (LOCATE) focuses on localizing and transferring features of object parts, which is able to produce more accurate results." + ], + "image_footnote": [], + "bbox": [ + 359, + 368, + 483, + 446 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c0d3d5b7b4a0f5d393701016ab781f7828da21f8f3be109b93020a5a38787020.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 486, + 287, + 611, + 367 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/5d842043f955f85afa58203785110dfa8fc72acc2fca935f774b8e8d99d512e7.jpg", + "image_caption": [ + "Cross-view-AG+ [32]" + ], + "image_footnote": [], + "bbox": [ + 486, + 368, + 611, + 446 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/cd96f218c7b8f4139845c72cc339673dac54c87751bc9de549dd99a87358d5b9.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 614, + 287, + 738, + 367 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/d1b1cc6b687e04fb4fef78952a4c71b646a13db7960d27dd54ba916803b8cba2.jpg", + "image_caption": [ + "LOCATE (Ours)" + ], + "image_footnote": [], + "bbox": [ + 614, + 368, + 738, + 446 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/ff574e1ad8d39e7dcee6c86003e535d285ea80a16d21b80728d76789a439472e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 741, + 289, + 864, + 368 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/0e002d25875712eb3807ec06ac43a6936291a963e550a317d43fd2a2d3e7e98e.jpg", + "image_caption": [ + "GT" + ], + "image_footnote": [], + "bbox": [ + 741, + 369, + 864, + 446 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 520, + 313, + 535 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Humans excel at acquiring knowledge through observation. For example, we can learn to use new tools by watching demonstrations. This skill is fundamental for intelligent systems to interact with the world. A key step to acquire this skill is to identify what part of the object affords each action, which is called affordance grounding. In this paper, we address this problem and propose a framework called LOCATE that can identify matching object parts across images, to transfer knowledge from images where an object is being used (exocentric images used for learning), to images where the object is inactive (egocentric ones used to test). To this end, we first find interaction areas and extract their feature embeddings. Then we learn to aggregate the embeddings into compact prototypes (human, object part, and background), and select the one representing the object part. Finally, we use the selected prototype to guide affordance grounding. We do this in a weakly supervised manner, learning only from image-level affordance and object labels. Extensive experiments demonstrate that our approach outperforms state-of-the-art methods by a large margin on both seen and unseen objects.1", + "bbox": [ + 75, + 545, + 472, + 863 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 500, + 520, + 630, + 535 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "A fundamental skill of humans is learning to interact with objects just by observing someone else performing those interactions [5]. For instance, even if we have never played tennis, we can easily learn where to hold the racket just by looking at a single or few photographs of those interactions. Such learning capabilities are essential for intelligent agents to understand what actions can be performed on a given object. Current visual systems often focus primarily on recognizing what objects are in the scene (passive perception), rather than on how to use objects to achieve certain functions (active interaction). To this end, a growing number of studies [3, 12, 26, 47] have begun to utilize affordance [17] as a medium to bridge the gap between passive perception and active interaction. In computer vision and robotics [2, 20], affordance typically refers to regions of an object that are available to perform a specific action, e.g., a knife handle affords holding, and its blade affords cutting.", + "bbox": [ + 496, + 549, + 890, + 806 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this paper, we focus on the task of affordance grounding, i.e., locating the object regions used for a given action. Previous methods [10, 12, 14, 37, 39] have often treated affordance grounding as a fully supervised semantic segmentation task, which requires costly pixel-level annotations. Instead, we follow the more realistic setting [32, 33, 38]", + "bbox": [ + 496, + 810, + 890, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "1Project page: https://reagan1311.github.io/locate.", + "bbox": [ + 94, + 886, + 452, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "10922", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/b41e5344c1a50842eb5d95db5f1e964ff62fe1903f217b448e107b7f48477ff6.jpg", + "image_caption": [ + "Figure 2. General illustration of LOCATE. We first extract the embeddings under the region of interest where the exocentric interactions are happening, and then split these embeddings into several clusters. In the end, the prototype of the object-part cluster is selected to supervise the egocentric affordance grounding." + ], + "image_footnote": [], + "bbox": [ + 83, + 88, + 472, + 281 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "where the task is learning object affordances by observing human-object interaction images. That is, given some interaction images, such as those in Fig. 2, along with the corresponding label (e.g., \"hold\"), the aim is to learn affordance grounding on the novel instances of that object. This is a weakly-supervised problem setting where only the image-level labels are given without any per-pixel annotations. Concretely, given several third-person human-object interaction images (exocentric) and one target object image (egocentric), our goal is to extract affordance knowledge and cues from exocentric interactions, and perform affordance grounding in the egocentric view by using only affordance labels.", + "bbox": [ + 75, + 397, + 468, + 592 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "There are several key challenges underlying the problem of affordance grounding. The first is due to the nature of the supervision, where only image-level affordance labels are given, being a weakly supervised problem. Here, the system needs to automatically reason about affordance regions just from classification labels. Second, human-object interactions often introduce heavy occlusion of object parts by interacting humans. In other words, the object part that the system needs to predict for a particular affordance (e.g., a mug handle for the \"holding\" affordance) in an exocentric image can often be the part that is occluded (e.g., by hands). Third, interactions are of great diversity. The way humans interact with objects varies across individuals resulting in diverse egocentric interaction images. Lastly, there is a clear domain gap between exocentric and egocentric images where the former have clutter, occlusion etc., and the latter are cleaner (e.g., in Fig. 2). This makes affordance knowledge transfer particularly challenging.", + "bbox": [ + 75, + 595, + 470, + 867 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, we propose a framework called LOCATE that addresses these core challenges by locating the exact", + "bbox": [ + 76, + 869, + 470, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "object parts involved in the interaction from exocentric images and transferring this knowledge to inactive egocentric images. Refer to Fig. 2 for the illustration. Specifically, we first use the class activation mapping (CAM) [51] technique to find the regions of human-object-interaction in exocentric images. Despite being trained for the interaction recognition task, we observe that CAM can generate good localization maps for interaction regions. We then segment this region of interest further into regions corresponding to human, object part, and background. We do this by extracting embeddings and performing k-means clustering to obtain several compact prototypes. Next, we automatically predict which of these prototypes corresponds to the object part relevant to the affordance. To this end, we propose a module named PartSelect that leverages part-aware features and attention maps from a self-supervised vision transformer (DINO-ViT [6]) to obtain the desired prototype. Finally, we use the object-part prototype as a high-level pseudo supervision to guide egocentric affordance grounding.", + "bbox": [ + 496, + 90, + 890, + 378 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our contributions can be summarized as follows. (1) We propose a framework called LOCATE that extracts affordance knowledge from weakly supervised exocentric human-object interactions, and transfers this knowledge to the egocentric image in a localized manner. (2) We introduce a novel module termed PartSelect to pick affordancespecific cues from human-object interactions. The extracted information is then used as explicit supervision to guide affordance grounding on egocentric images. (3) LOCATE achieves state-of-the-art results with far fewer parameters and faster inference speed than previous methods, and is able to locate accurate affordance region for unseen objects. See Fig. 1 for examples of our results and comparison to state-of-the-art.", + "bbox": [ + 496, + 378, + 892, + 589 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 603, + 640, + 619 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Visual Affordance Learning. Affordances are actively studied in robotics and computer vision due to their great potential to bridge the gap between perception and action. In general, affordance-related research in computer vision aims to localize objects or object parts where specific actions can be performed. Earlier work [10, 12, 27, 36] mainly focused on the fully supervised setting. Due to the scarcity of affordance datasets, this work normally required costly manual annotations to construct large-scale datasets [10, 37, 39, 42]. To alleviate the annotation and sensing requirement, new research [33, 38, 41, 42] explored acquiring affordance information in the weakly supervised setting. In particular, Sawatzky et al. [42] proposed a convolutional network to tackle affordance detection using only a few keypoint annotations, and Nagarajan et al. [38] introduced a method to infer the object affordance regions by directly learning from human-object interaction videos. In this work, we also focus on learning affordances from weak", + "bbox": [ + 496, + 628, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "10923", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "supervision, i.e., several human-object interaction images and corresponding image-level affordance labels.", + "bbox": [ + 76, + 90, + 468, + 121 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Weakly Supervised Affordance Grounding. Unlike object localization that aims to find where the object is, in affordance grounding we focus on locating functional regions of objects, which is a more fine-grained localization task. Existing weakly supervised object localization [16, 25, 34, 40, 49, 50] and semantic segmentation methods [8, 9, 28, 48, 52] are mainly based on class activation mapping (CAM) [51], the seminal work that has greatly facilitated the development of weakly supervised learning. Similarly, most affordance grounding research [31, 33, 38] also adopted CAM or its variants [7, 43] to generate activation maps as prediction. However, previous work only used CAM in the inference stage, lacking proper supervision. In contrast, to provide explicit guidance at the training stage, we utilize CAM to produce localization maps in the forward pass and supervise it in a prototypical learning fashion.", + "bbox": [ + 75, + 128, + 470, + 371 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Knowledge Distillation across Domains. Knowledge distillation [23] is a process of transferring knowledge from a network to another, where inputs normally come from the same domain. Recently, many studies [14, 29, 33, 38, 44] have begun to pay more attention to knowledge distillation in different domains. This work transferred representations from the domain with numerous datasets to the other one that typically has low dataset scale and diversity, so that the model can benefit from the large quantity of data in the first domain. For instance, Li et al. [29] proposed a framework to learn egocentric video representations from largescale third-person video datasets, and Luo et al [33] devised a knowledge transfer architecture to transfer affordancespecific features from exocentric view to egocentric view. In this paper, we follow the same setting as [33], using exocentric (third-person) human-object interaction images as the learning target. The objective of this work is to observe where and how humans interact with an object when doing a specific action, and then transfer the knowledge onto the target object.", + "bbox": [ + 75, + 378, + 470, + 680 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Self-supervised Vision Transformer. Self-supervised Vision Transformers (ViT) [13], such as DINO [6], MAE [21], and BEiT [4], have demonstrated immense potential in unsupervised dense prediction tasks. Specifically, the features extracted from the self-attention layer exhibit the ability to separate different objects and generate reliable pseudo segmentation maps without requiring any manual annotations. Building on this property, recent work [15, 18, 19, 35, 45, 46] has achieved exceptional results in unsupervised segmentation and localization. Notably, Amir et al. [1] demonstrated that the pretrained features extracted from DINO-ViT encode fine-grained semantic information, which can yield excellent performance for part co-segmentation and semantic correspondence. Inspired by this work, we leverage DINO", + "bbox": [ + 75, + 688, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "ViT features to identify matching object parts between exocentric and egocentric images.", + "bbox": [ + 498, + 90, + 890, + 121 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 500, + 133, + 591, + 148 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given several exocentric interaction images and one egocentric object image, our goal is to extract affordance-related knowledge from exocentric interactions, and transfer it to egocentric images so that the affordance region can be located even for an inactive object. During training, the only supervision available are image-level affordance labels. In the inference stage, taking an egocentric image and an affordance label as input, the model needs to predict the corresponding affordance region.", + "bbox": [ + 496, + 157, + 890, + 294 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The core idea of our approach is to exclude distracting information, e.g., human and background, when extracting affordance-specific features from the exocentric view, and perform fine-grained part-level knowledge transfer from exocentric images to egocentric ones. To this end, we set up the framework LOCATE to transfer the knowledge in three steps (See Fig. 3). First, we utilize CAM to generate localization maps for exocentric images, and extract corresponding feature embeddings with high activation in the localization maps (Sec. 3.1). Then, we propose PartSelect that leverages part-aware deep features to remove irrelevant information while preserving embeddings that can represent affordance cues (Sec. 3.2). Finally, we use the output from PartSelect to supervise the egocentric affordance grounding in an explicit manner (Sec. 3.3).", + "bbox": [ + 496, + 294, + 892, + 521 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Locating Interaction Regions", + "text_level": 1, + "bbox": [ + 500, + 527, + 761, + 544 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To determine where neural networks focus on for recognition, we adopt the technique of CAM [51] to generate class-aware localization maps, which has been widely used in weakly supervised tasks. The vanilla CAM generates localization maps as a post-processing step that cannot be guided during training. However, our goal is to extract affordance-specific cues from exocentric images, and use these cues as explicit supervision for the egocentric view. Therefore, in order to obtain localization maps during the training phase, we produce class-specific feature maps instead by adding a class-aware convolution layer, which has proven to be identical to the generation process in CAM [50]. Specifically, for input images $\\{I_{exo}, I_{ego}\\}$ ( $I_{exo} = \\{I_1, I_2, \\dots, I_N\\}$ ), we first extract deep features $\\{\\mathcal{F}_{exo}, \\mathcal{F}_{ego}\\} \\in \\mathbb{R}^{D \\times H \\times W}$ using a network $\\phi$ . In our case, $\\phi$ is a self-supervised vision transformer (DINO-ViT), whose features are part-aware and provide good part-level correspondences. We then generate localization maps $\\mathcal{P}$ and classification scores $z$ as follows:", + "bbox": [ + 496, + 551, + 890, + 838 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {P} = \\psi_ {c a m} (\\mathcal {F}) \\in \\mathbb {R} ^ {C \\times H \\times W}, \\quad \\boldsymbol {z} = \\operatorname {G A P} (\\mathcal {P}) \\in \\mathbb {R} ^ {C}, (1)\n$$\n", + "text_format": "latex", + "bbox": [ + 508, + 844, + 890, + 864 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\psi_{cam}$ starts with a projection layer consisting of a feed-forward layer followed by two convolutions to fine", + "bbox": [ + 500, + 869, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "10924", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/55dcdba5ed7f55a397e4b696705f04d172f4613372f98e97ade7196a429b46e6.jpg", + "image_caption": [ + "Figure 3. Overview of the proposed LOCATE framework. It achieves part-level knowledge transfer in three steps: 1) locating interaction regions with $\\psi_{cam}$ (Sec. 3.1), 2) object-part embedding selection with PartSelect (Sec. 3.2), and 3) part-level knowledge transfer with $L_{cos}$ (Sec. 3.3). Details for PartSelect are shown in Fig. 4. At test time, only the egocentric branch is maintained." + ], + "image_footnote": [], + "bbox": [ + 98, + 88, + 872, + 340 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "tune features for the HOI recognition task, i.e., recognizing actions shown in the exocentric images. Then a $1 \\times 1$ class-aware convolution layer is added to yield localization maps, converting the number of channels to $C$ , where $C$ denotes the number of total interaction categories. Therefore, each map $\\mathcal{P}_c \\in \\mathbb{R}^{H \\times W}$ represents the network activation for the $c$ -th interaction. Next, $\\mathcal{P}$ is fed to a global average pooling (GAP) layer to obtain classification scores $z$ , which are used to calculate cross-entropy loss $\\mathcal{L}_{cls}$ for optimization.", + "bbox": [ + 75, + 417, + 468, + 554 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We notice that localization maps for the exocentric branch $\\mathcal{P}_{exo}$ concentrate on the interaction areas, i.e., where the action takes place. Since interaction areas carry strong affordance information, we therefore aim to collect embeddings from the high activation regions in exocentric localization maps. Specifically, we first extract the localization map corresponding to ground-truth class, and conduct min-max normalization to constrain activation values to [0, 1]. After that, we set a threshold $\\tau$ to control the number of extracted embeddings, therefore embeddings with activation value greater than $\\tau$ in the localization map will be extracted from deep features. For multiple exocentric images, embeddings are extracted separately to produce $f_{exo} = [f_1, \\dots, f_N]$ , each $f_n$ containing a different number of embeddings. All embeddings are then concatenated together $f_{exo} \\in \\mathbb{R}^{L \\times D}$ , where $L$ denotes the number of embeddings.", + "bbox": [ + 75, + 556, + 470, + 797 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Object-Part Embedding Selection", + "text_level": 1, + "bbox": [ + 76, + 814, + 372, + 830 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In general, interaction areas are composed of human, object part, and background. Our objective is to eliminate the interference information, and purely deliver embeddings representing the object part to guide the egocentric branch.", + "bbox": [ + 75, + 839, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In consequence, we design PartSelect to choose affordance-related embeddings from exocentric branch. PartSelect is illustrated in Fig. 4a. We first perform k-means clustering to get $K$ compact prototypes $\\pmb{p} \\in \\mathbb{R}^{K \\times D}$ from extracted exocentric embeddings. Next, we compute the cosine distance between each prototype and the egocentric deep features $\\mathcal{F}_{ego}$ to get similarity maps $\\mathcal{S} \\in \\mathbb{R}^{K \\times H \\times W}$ :", + "bbox": [ + 496, + 417, + 892, + 525 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nS ^ {k, u, v} = \\frac {\\boldsymbol {p} _ {k} \\cdot \\mathcal {F} _ {e g o} ^ {u , v}}{\\| \\boldsymbol {p} _ {k} \\| \\| \\mathcal {F} _ {e g o} ^ {u , v} \\|.} \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 614, + 534, + 890, + 569 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Owing to the fine-grained semantic information of DINOViT deep features, embeddings of the same object parts bear high similarity.", + "bbox": [ + 496, + 575, + 890, + 619 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To distinguish which prototype stands for the object part, we aggregate the self-attention maps from the last layer of the DINO-ViT to generate a saliency map $\\mathcal{A} \\in \\mathbb{R}^{H \\times W}$ for the egocentric image. Given the saliency map and similarity maps, we introduce a metric $\\gamma \\in [0,1]$ termed PartIoU to measure if a prototype carries object part information. The PartIoU for the $k$ -th prototype is defined as follows:", + "bbox": [ + 496, + 622, + 892, + 728 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\gamma = \\frac {1}{2} \\frac {\\overline {{\\mathcal {S} _ {k}}} \\cap \\overline {{\\mathcal {A}}}}{\\overline {{\\mathcal {S} _ {k}}}} + \\frac {1}{2} \\frac {\\overline {{\\mathcal {A}}}}{\\overline {{\\mathcal {S} _ {k}}} \\cup \\overline {{\\mathcal {A}}}}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 598, + 738, + 890, + 773 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\overline{S_k}$ , $\\overline{\\mathcal{A}}\\in \\{0,1\\}^{H\\times W}$ are binary masks, we set the threshold as the average of each map to perform binarization. The motivation of PartIoU is fairly straightforward, if $\\overline{S}$ belongs to a portion of $\\overline{\\mathcal{A}}$ , then the intersection of $\\overline{S}$ and $\\overline{\\mathcal{A}}$ should equal $\\overline{S}$ itself, while the union of the two masks should be identical to $\\overline{\\mathcal{A}}$ . Finally, when the maximum PartIoU among $K$ prototypes is above a threshold $\\mu$ , PartS-select will output the prototype with the largest PartIoU as", + "bbox": [ + 496, + 777, + 893, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "10925", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/b6bdd2a99e96e468df6d55aa701ae99027fc247500b7fb7ae083d3f9531f577b.jpg", + "image_caption": [ + "(a) Illustration of PartSelect." + ], + "image_footnote": [], + "bbox": [ + 106, + 90, + 441, + 351 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/b61eff7adeca7c5fe93e08e6d73b1dc0534035dec182ad56266b1c97e1a32270.jpg", + "image_caption": [ + "Exo-image" + ], + "image_footnote": [], + "bbox": [ + 78, + 373, + 176, + 431 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/9c21c273ff5f08fcb07f48183f19798f03878b40cee8258d7ce06ddf92371077.jpg", + "image_caption": [ + "Object Part" + ], + "image_footnote": [], + "bbox": [ + 178, + 373, + 274, + 430 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/f9b649063f7b360addf3c367e34a36274b363a049bf088ae2b616a5babfe53cd.jpg", + "image_caption": [ + "Background", + "Figure 4. (a) PartSelect picks the object-part prototype through clustering and selection, where $\\otimes$ denotes the calculation for PartIOU score. (b) The similarity maps between prototypes and exocentric features confirm our statement that each prototype represents the object part, background, and human." + ], + "image_footnote": [], + "bbox": [ + 274, + 373, + 370, + 430 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/0a262ac6e6253399b37ccb35e8d56cefd730744dfcb93354ead2e6111f57eca0.jpg", + "image_caption": [ + "Human", + "(b) Exocentric similarity maps." + ], + "image_footnote": [], + "bbox": [ + 372, + 373, + 468, + 430 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "the object-part representation. Otherwise, no prototype will be selected for the next step. In Fig. 4b, we visualize the similarity maps between prototypes and exocentric features to demonstrate that the extracted embeddings are clustered into human, object part, and background.", + "bbox": [ + 75, + 579, + 468, + 654 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Part-Level Knowledge Transfer", + "text_level": 1, + "bbox": [ + 76, + 672, + 356, + 690 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "With the help of PartSelect, we find the prototype $f_{op}$ that represents the object part. We then leverage it to perform supervision for egocentric localization maps $\\mathcal{P}_{ego}$ . Concretely, we first perform masked average pooling (MAP) between the normalized localization map and extracted deep features to aggregate into one embedding:", + "bbox": [ + 75, + 700, + 468, + 790 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nf _ {e g o} = \\frac {\\sum_ {u = 1 , v = 1} ^ {W , H} \\mathcal {F} _ {e g o} ^ {u , v} \\mathcal {P} _ {e g o} ^ {t , u , v}}{\\sum_ {i = 1 , j = 1} ^ {W , H} \\mathcal {P} _ {e g o} ^ {t , u , v}} \\in \\mathbb {R} ^ {D}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 145, + 813, + 468, + 856 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $t$ denotes the ground-truth category. Then, a cosine embedding loss is applied to pull the embedding $f_{ego}$ to-", + "bbox": [ + 75, + 869, + 468, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "wards the direction of $f_{op}$ :", + "bbox": [ + 500, + 90, + 676, + 107 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {c o s} = \\max \\left(1 - \\frac {f _ {o p} \\cdot f _ {e g o}}{\\| f _ {o p} \\| \\| f _ {e g o} \\|} - \\alpha , 0\\right), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 560, + 117, + 890, + 152 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "as the two embeddings come from different domains, we thereby add $\\alpha$ as a margin to compensate the domain gap.", + "bbox": [ + 498, + 161, + 890, + 191 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In addition, since the affordance region typically denotes a portion of an object, we can thus impose a geometry loss to regulate its distribution. Inspired by the co-part segmentation work [24], we add a concentration loss to encourage egocentric localization maps to form a concentrated and connected component. The concentration loss is formulated as", + "bbox": [ + 498, + 191, + 890, + 295 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\bar {u} _ {c} = \\sum_ {u, v} u \\cdot \\mathcal {P} _ {e g o} ^ {c, u, v} / z _ {k}, \\bar {v} _ {c} = \\sum_ {u, v} v \\cdot \\mathcal {P} _ {e g o} ^ {c, u, v} / z _ {k}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 524, + 306, + 890, + 339 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {c} = \\sum_ {c} \\sum_ {u, v} \\| \\langle u, v \\rangle - \\langle \\bar {u} _ {c}, \\bar {v} _ {c} \\rangle \\| \\cdot \\mathcal {P} _ {e g o} ^ {c, u, v} / z _ {c}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 544, + 351, + 890, + 383 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\overline{u}_c$ and $\\overline{v}_c$ represents the center of the $c$ -th localization map along axis $u, v$ , and $z_c = \\sum_{u,v} \\mathcal{P}_{ego}^{c,u,v}$ is a normalization term. The concentration loss forces the high activation regions of the localization maps to be close to the geometric center.", + "bbox": [ + 498, + 391, + 890, + 463 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Overall, we train the whole framework in an end-to-end manner, and use the following loss to optimize the model:", + "bbox": [ + 498, + 467, + 890, + 496 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {c l s} + \\lambda_ {c o s} \\mathcal {L} _ {c o s} + \\lambda_ {c} \\mathcal {L} _ {c}, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 593, + 512, + 890, + 527 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\lambda_{cos}$ , and $\\lambda_{c}$ are loss weights that balance the three terms. $\\mathcal{L}_{cls}$ stands for the cross-entropy losses from the two branches. At test time, only the ego branch is maintained, taking an affordance label $t$ and an egocentric image as input, the network extracts the $t$ -th localization map as the prediction of affordance region.", + "bbox": [ + 496, + 536, + 890, + 626 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 641, + 633, + 657 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Experimental Setting", + "text_level": 1, + "bbox": [ + 500, + 666, + 700, + 681 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Dataset and Metrics. We evaluate our method in the Affordance Grounding Dataset (AGD20K) [33], which is the only large-scale image dataset with both exocentric and egocentric views. AGD20K is comprised of 20,061 exocentric images and 3,755 egocentric images, and is annotated with 36 commonly used affordances. Following prior affordance grounding work [14,38], the ground truth of this dataset initially consists of densely annotated points in corresponding affordance regions, and a Gaussian blur is then applied over each point to get final heatmaps. Moreover, AGD20K can be evaluated in two different settings: 1) In the seen setting, object categories in training and test sets are identical. 2) In the unseen setting, there is no object category intersection between training and test sets, e.g., the", + "bbox": [ + 496, + 688, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "10926", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/13e6f102bae368c135f556d5433275327e52b7a2d034b2a1494a287fbeda7a24.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
State-of-the-Art from Relevant TasksSeenUnseen
KLD↓SIM↑NSS↑KLD↓SIM↑NSS↑
Weakly Supervised Object Localization*EIL [34]1.9310.2850.5222.1670.2270.330
SPA [40]5.5280.2210.3577.4250.1690.262
TS-CAM [16]1.8420.2600.3362.1040.2010.151
Weakly Supervised Affordance GroundingHotspots [38]1.7730.2780.6151.9940.2370.577
Cross-view-AG [33]1.5380.3340.9271.7870.2850.829
Cross-view-AG+ [32]1.4890.3420.9811.7650.2790.882
AffCorrs† [18]1.4070.3591.0261.6180.3481.021
LOCATE (Ours)1.2260.4011.1771.4050.3721.157
", + "bbox": [ + 117, + 88, + 854, + 268 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "model observes how humans hold a hammer and anticipates where to hold a knife.", + "bbox": [ + 75, + 333, + 468, + 362 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "As for the metrics, referring to previous affordance grounding work [14, 30, 33, 38], we adopt the commonly used Kullback-Leibler Divergence (KLD), Similarity (SIM), and Normalized Scanpath Saliency (NSS) to evaluate the similarity and correspondence of distributions between ground truth and prediction. Detailed calculation of each metric is shown in the supplementary material.", + "bbox": [ + 75, + 364, + 468, + 470 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation Details. We use the ImageNet [11] pretrained (without supervision) DINO-ViT-S [6] with patch size 16 to generate deep features. In each iteration, N exocentric images along with one egocentric image are taken as input (N is set to 3). Images are first resized to $256 \\times 256$ and then randomly cropped to $224 \\times 224$ followed by random horizontal flipping. SGD with learning rate 1e-3, weight decay 5e-4, and batch size 16 is used for parameter optimization. Loss weight coefficients $(\\lambda_{cos}, \\lambda_c)$ are set to (1, 0.07), and the margin $\\alpha$ is set to 0.5. For the first epoch, we warm up the network without $\\mathcal{L}_{cos}$ , as initial localization maps are not accurate for supervision.", + "bbox": [ + 75, + 474, + 470, + 655 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Comparison to State-of-the-Art", + "text_level": 1, + "bbox": [ + 76, + 665, + 356, + 681 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To conduct a comprehensive comparison, we also display the results of state-of-the-art methods from a relevant task, i.e., weakly supervised object localization. As shown in Table 1, in both seen and unseen settings, LOCATE outperforms all other methods with a considerable margin on all metrics. In particular, compared to the state-of-the-art affordance grounding method Cross-view-AG+ [32], we improve the KLD by $20.4\\%$ , SIM by $33.3\\%$ , and NSS by $31.2\\%$ in the unseen setting. Cross-view-AG+ is an extended version of Cross-view-AG, but still performs the knowledge transfer based on global pooled embeddings at the image level, thus bringing only minor improvement. AffCorrs [18] is a method that focuses on one-shot part affordance grounding, and it also uses the pretrained DINO-ViT", + "bbox": [ + 75, + 688, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/35f7fd74b5a7b54d093f282828dfdd98b85d29fd956c72cc0f67f51dbd6183f7.jpg", + "table_caption": [ + "Table 1. Comparison to state-of-the-arts from relevant tasks on AGD20K dataset. Results of * are taken from [33], and † denotes the adapted AffCorrs. The best and second-best results are highlighted in bold and underlined, respectively (↑/↓ means higher/lower is better)." + ], + "table_footnote": [], + "table_body": "
MethodsParams (M)Time (s)
EIL [34]42.410.019
SPA [40]69.280.081
TS-CAM [16]85.860.023
Hotspots [38]132.640.087
Cross-view-AG [33]120.030.023
Cross-view-AG+ [32]82.270.022
AffCorrs† [18]6.500.205
LOCATE (Ours)6.500.011
", + "bbox": [ + 527, + 330, + 867, + 489 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. Comparison of learnable parameters and inference time. The inference time is evaluated on a 3090Ti GPU. $\\dagger$ denotes the adapted AffCorrs.", + "bbox": [ + 498, + 500, + 890, + 542 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "features to do part matching. However, AffCorrs needs a pixel-level mask as a query, and there is no domain gap during the knowledge transfer. To make AffCorrs comparable in our problem setting, we adapt its structure by replacing the query annotated mask with our CAM estimator. The results verify that AffCorrs can also achieve good performance, but still considerably inferior to LOCATE.", + "bbox": [ + 496, + 563, + 890, + 669 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In Table 2, we make comparisons in terms of model parameters and inference time. Since our framework is built on a frozen small-sized vision transformer (ViT-small), the training process is efficient with a small number of parameters. For example, LOCATE only has $5.4\\%$ of learnable parameters in Cross-view-AG. Additionally, we use a large patch size 16 for the vision transformer, which constrains the input sequence length and greatly reduces computation cost. Therefore, the inference time of LOCATE is also faster than most other methods. By contrast, the adapted AffCorrs runs much slower than LOCATE, as it incorporates an additional CRF post-processing step.", + "bbox": [ + 496, + 671, + 892, + 852 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We further visualize the qualitative comparisons with state-of-the-art affordance grounding methods. As shown in Fig. 5, we compare our results with Hotspots [38], Cross-", + "bbox": [ + 498, + 854, + 893, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "10927", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/311ebddec46f4aede121d2598794e930c3e9c061342e56b0f6575d855b8672b3.jpg", + "image_caption": [ + "Figure 5. Qualitative comparison between our approach and state-of-the-art affordance grounding methods (Hotspots [38], Cross-view-AG [33], and Cross-view-AG+ [32]). For the unseen setting, the displayed objects are not in the training set. For example, the model learns where a motorcycle can be ridden in training, and locates rideable area for the bicycle at test time." + ], + "image_footnote": [], + "bbox": [ + 84, + 89, + 500, + 470 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/04dc063f6e47ca9494caf5b55967368e42503d321f1a2fa5ad1c3384cea64c06.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 514, + 88, + 864, + 469 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "view-AG [33] and Cross-view-AG+ [32]. We observe that the proposed LOCATE can make more concentrated and accurate predictions. Especially for complex objects like bicycles and refrigerators, even in the unseen setting, our method can still locate the saddle of bicycles for riding, and the handle of fridges for opening. In comparison, the results of Cross-view-AG for bicycles are quite noisy. More visualization results are in the supplementary material.", + "bbox": [ + 75, + 556, + 472, + 679 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 693, + 230, + 709 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Knowledge Transfer Manner. We first investigate the impact of knowledge transfer manner. Previous affordance grounding methods [33, 38] simply pull close the global embeddings (produced by global average pooling) of two branches to perform global knowledge transfer (GKT). In contrast, we set up an experiment to implement regional knowledge transfer (RKT), which generates the embeddings via masked average pooling between CAM-produced localization maps and feature maps. The results are shown in Table 3, regional knowledge transfer (RKT) outperforms global knowledge transfer (GKT) on all metrics, demonstrating the effectiveness of filtering irrelevant information.", + "bbox": [ + 75, + 719, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/efb5bb8c950b3b90fa1e0da2b01c83b9e555af9d49dffe6ab8e46fbf2bc83a73.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodSeenUnseen
KLD↓SIM↑NSS↑KLD↓SIM↑NSS↑
GKT1.7320.2670.8101.9710.2210.626
RKT1.5160.3201.0741.8230.2590.850
+ Lc1.4910.3261.0911.7500.2740.948
+S1.2360.3971.1781.4390.3581.130
+S + Lc1.2260.4011.1771.4050.3721.157
", + "bbox": [ + 501, + 553, + 890, + 680 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3. Ablation results of the proposed LOCATE framework. GKT/RKT means global/regional knowledge transfer. $\\mathcal{S}$ denotes PartSelect combined with ${\\mathcal{L}}_{cos}$ ,and ${\\mathcal{L}}_{c}$ is the concentration loss.", + "bbox": [ + 498, + 690, + 890, + 733 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "PartSelect and Concentration Loss. Based on the regional knowledge transfer, we analyze the effect of PartSelect and concentration loss. As shown in Table 3, directly applying the concentration loss $\\mathcal{L}_c$ can only bring marginal improvement. The reason is $\\mathcal{L}_c$ can make egocentric predictions more concentrated, but fail to guide it to focus on the right affordance area. Nonetheless, when adding PartSelect and using cosine embedding loss $\\mathcal{L}_{cos}$ as explicit supervision, the performance is greatly boosted, which proves the effectiveness of the part-level knowledge transfer scheme. In ad", + "bbox": [ + 496, + 750, + 893, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "10928", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/36a9f6af048fa107f3955542288508985f1751d2f41ee59b92806cd1e9707efd.jpg", + "image_caption": [ + "GKT", + "RKT", + "$\\mathrm{RKT} + \\mathcal{S}$", + "$\\mathrm{RKT} + \\mathcal{S} + \\mathcal{L}_c$", + "GT", + "Figure 6. Visualization of the qualitative improvements." + ], + "image_footnote": [], + "bbox": [ + 81, + 90, + 467, + 316 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "dition, to check the qualitative improvement, we visualize the affordance grounding results in Fig. 6. It is clear that GKT tends to locate the wrong affordance area, while RKT can sometimes find the right region, but only give coarse grounding results. After adding PartSelect, the results become much more part-focused, and the concentration loss further makes the grounding maps more robust.", + "bbox": [ + 75, + 359, + 467, + 465 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Number of Prototypes/Exocentric Images. We then explore the impact from the number of prototypes $K$ and exocentric images $N$ . From Fig. 7a, we observe that the model yields the best performance with three prototypes in seen setting, which is consistent with our statement that interaction areas typically consist of human, object part, and background information. While for the unseen setting, $N = 5$ achieves the best results, but improvement is minor. One reason lies in that more prototypes segment objects into more small parts, which boosts the generalization ability. As for the number of exocentric images, we find that more exocentric images can alleviate the impact of interaction diversity and occlusion, thus providing more robust knowledge for the egocentric branch. As shown in Fig. 7b, the model gets largely improved when increasing the number of exocentric images from 1 to 3 in both seen and unseen settings. Finally, we set both $N$ and $K$ to 3.", + "bbox": [ + 75, + 470, + 467, + 728 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Different Feature Extractors. In LOCATE, we employ pretrained DINO features based on ViT, which have been proven to encode high-level semantic information [1]. To investigate the impact of different backbones, we conducted experiments with DINO features trained on the ResNet-50 [22]. From the results in Table 4, we observe that using DINO-ViT features directly (without the proposed PartSelect) can only obtain similar or even inferior results to their ResNet counterpart. After incorporating PartSelect, the results of both backbone features can be improved under the seen setting, but ViT features show better potential in en", + "bbox": [ + 75, + 734, + 467, + 900 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/faf841811f9ddc107d021346d8e1d58b48488ccf5cd95270144381bbedfae89e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 504, + 90, + 885, + 195 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1fee8df9dce98992a513d69bdff480909f04f480bdbac81bb631813fd37e1b49.jpg", + "image_caption": [ + "(a) Number of prototypes $N$", + "(b) Number of exocentric images $K$", + "Figure 7. Ablation study on the number of prototypes and exocentric images (lower is better)." + ], + "image_footnote": [], + "bbox": [ + 504, + 215, + 885, + 321 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/6d8b500180fb2641acf177da367d1a5f24402143c8222b06268fcf54aacadbbd.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
RN-50ViT-S/16PartSelectKLD↓SIM↑NSS↑
Seen✓1.4820.3341.005
✓1.4910.3261.091
✓✓1.4490.3401.021
✓✓1.2260.4011.177
Unseen✓1.7010.2870.962
✓1.7500.2740.948
✓✓1.7070.2870.949
✓✓1.4050.3721.157
", + "bbox": [ + 500, + 393, + 890, + 541 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 4. Ablation study on different feature extractors.", + "bbox": [ + 532, + 551, + 856, + 565 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "hancing the performance due to their part-aware property. In the unseen setting, PartSelect does not yield improvement for ResNet-based features, while ViT features obtain consistent gains.", + "bbox": [ + 496, + 580, + 890, + 641 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 657, + 617, + 672 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we propose a framework named LOCATE to address the weakly supervised affordance grounding task by observing human-object interaction images. Specifically, we first localize where the interaction happens for the exocentric interactions, and then design a module called PartSelect to pick the affordance-specific information from the interaction regions. Finally, we transfer the learned knowledge to the egocentric view to perform affordance grounding with only image-level affordance labels. The proposed LOCATE achieves state-of-the-art results with far fewer parameters and faster inference speed.", + "bbox": [ + 496, + 684, + 890, + 849 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement. This work is supported by the EPSRC, as part of the CDT in Robotics and Autonomous Systems (EP/S023208/1), along with gift funding and the research scholar award from Google.", + "bbox": [ + 496, + 856, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "10929", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Shir Amir, Yossi Gandelsman, Shai Bagon, and Tali Dekel. Deep vit features as dense visual descriptors. ECCVW What is Motion For, 2022. 3, 8", + "[2] Paola Ardón, Éric Pairet, Katrin S Lohan, Subramanian Ramamoorthy, and Ronald Petrick. Affordances in robotic tasks-a survey. arXiv preprint arXiv:2004.07400, 2020.1", + "[3] Paola Ardón, Eric Pairet, Ronald PA Petrick, Subramanian Ramamoorthy, and Katrin S Lohan. 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In CVPR, 2022. 3" + ], + "bbox": [ + 501, + 90, + 890, + 275 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "10931", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/LOCATE_ Localize and Transfer Object Parts for Weakly Supervised Affordance Grounding/c02a6207-738d-48dd-beea-456bd084b930_model.json b/2023/LOCATE_ Localize and Transfer Object Parts for Weakly Supervised Affordance Grounding/c02a6207-738d-48dd-beea-456bd084b930_model.json new file mode 100644 index 0000000000000000000000000000000000000000..529a9f8f3ee88cc724c928f127fd03ac889535c2 --- /dev/null +++ b/2023/LOCATE_ Localize and Transfer Object Parts for Weakly Supervised Affordance Grounding/c02a6207-738d-48dd-beea-456bd084b930_model.json @@ -0,0 +1,2288 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.186, + 0.131, + 0.785, + 0.177 + ], + "angle": 0, + "content": "LOCATE: Localize and Transfer Object Parts for Weakly Supervised Affordance Grounding" + }, + { + "type": "text", + "bbox": [ + 0.203, + 0.203, + 0.271, + 0.221 + ], + "angle": 0, + "content": "Gen Li" + }, + { + "type": "text", + "bbox": [ + 0.306, + 0.203, + 0.434, + 0.222 + ], + "angle": 0, + "content": "Varun Jampani2" + }, + { + "type": "text", + "bbox": [ + 0.468, + 0.204, + 0.573, + 0.222 + ], + "angle": 0, + "content": "Deqing Sun" + }, + { + "type": "text", + "bbox": [ + 0.608, + 0.204, + 0.765, + 0.221 + ], + "angle": 0, + "content": "Laura Sevilla-Lara" + }, + { + "type": "text", + "bbox": [ + 0.305, + 0.238, + 0.667, + 0.257 + ], + "angle": 0, + "content": "1University of Edinburgh 2Google Research" + }, + { + "type": "image", + "bbox": [ + 0.104, + 0.289, + 0.23, + 0.369 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.104, + 0.371, + 0.23, + 0.447 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.133, + 0.449, + 0.207, + 0.461 + ], + "angle": 0, + "content": "Object Image" + }, + { + "type": "image", + "bbox": [ + 0.233, + 0.289, + 0.357, + 0.368 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.233, + 0.369, + 0.357, + 0.447 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.259, + 0.449, + 0.332, + 0.461 + ], + "angle": 0, + "content": "Hotspots [38]" + }, + { + "type": "image", + "bbox": [ + 0.361, + 0.289, + 0.484, + 0.368 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.361, + 0.369, + 0.484, + 0.447 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.367, + 0.449, + 0.478, + 0.461 + ], + "angle": 0, + "content": "Cross-view-AG [33]" + }, + { + "type": "image", + "bbox": [ + 0.487, + 0.289, + 0.612, + 0.368 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.487, + 0.369, + 0.612, + 0.447 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.49, + 0.449, + 0.609, + 0.461 + ], + "angle": 0, + "content": "Cross-view-AG+ [32]" + }, + { + "type": "image", + "bbox": [ + 0.615, + 0.289, + 0.739, + 0.368 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.615, + 0.369, + 0.739, + 0.447 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.632, + 0.449, + 0.723, + 0.461 + ], + "angle": 0, + "content": "LOCATE (Ours)" + }, + { + "type": "image", + "bbox": [ + 0.742, + 0.29, + 0.866, + 0.369 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.742, + 0.37, + 0.866, + 0.447 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.793, + 0.449, + 0.812, + 0.459 + ], + "angle": 0, + "content": "GT" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.466, + 0.894, + 0.508 + ], + "angle": 0, + "content": "Figure 1. State-of-the-art methods in weakly supervised affordance grounding often fail to make accurate predictions for objects with complex structures, e.g., chairs and bicycles. To address this, our model (LOCATE) focuses on localizing and transferring features of object parts, which is able to produce more accurate results." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.521, + 0.314, + 0.536 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.546, + 0.473, + 0.864 + ], + "angle": 0, + "content": "Humans excel at acquiring knowledge through observation. For example, we can learn to use new tools by watching demonstrations. This skill is fundamental for intelligent systems to interact with the world. A key step to acquire this skill is to identify what part of the object affords each action, which is called affordance grounding. In this paper, we address this problem and propose a framework called LOCATE that can identify matching object parts across images, to transfer knowledge from images where an object is being used (exocentric images used for learning), to images where the object is inactive (egocentric ones used to test). To this end, we first find interaction areas and extract their feature embeddings. Then we learn to aggregate the embeddings into compact prototypes (human, object part, and background), and select the one representing the object part. Finally, we use the selected prototype to guide affordance grounding. We do this in a weakly supervised manner, learning only from image-level affordance and object labels. Extensive experiments demonstrate that our approach outperforms state-of-the-art methods by a large margin on both seen and unseen objects.1" + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.521, + 0.631, + 0.536 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.55, + 0.892, + 0.807 + ], + "angle": 0, + "content": "A fundamental skill of humans is learning to interact with objects just by observing someone else performing those interactions [5]. For instance, even if we have never played tennis, we can easily learn where to hold the racket just by looking at a single or few photographs of those interactions. Such learning capabilities are essential for intelligent agents to understand what actions can be performed on a given object. Current visual systems often focus primarily on recognizing what objects are in the scene (passive perception), rather than on how to use objects to achieve certain functions (active interaction). To this end, a growing number of studies [3, 12, 26, 47] have begun to utilize affordance [17] as a medium to bridge the gap between passive perception and active interaction. In computer vision and robotics [2, 20], affordance typically refers to regions of an object that are available to perform a specific action, e.g., a knife handle affords holding, and its blade affords cutting." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.902 + ], + "angle": 0, + "content": "In this paper, we focus on the task of affordance grounding, i.e., locating the object regions used for a given action. Previous methods [10, 12, 14, 37, 39] have often treated affordance grounding as a fully supervised semantic segmentation task, which requires costly pixel-level annotations. Instead, we follow the more realistic setting [32, 33, 38]" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.454, + 0.901 + ], + "angle": 0, + "content": "1Project page: https://reagan1311.github.io/locate." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10922" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.089, + 0.473, + 0.282 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.296, + 0.471, + 0.368 + ], + "angle": 0, + "content": "Figure 2. General illustration of LOCATE. We first extract the embeddings under the region of interest where the exocentric interactions are happening, and then split these embeddings into several clusters. In the end, the prototype of the object-part cluster is selected to supervise the egocentric affordance grounding." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.398, + 0.47, + 0.593 + ], + "angle": 0, + "content": "where the task is learning object affordances by observing human-object interaction images. That is, given some interaction images, such as those in Fig. 2, along with the corresponding label (e.g., \"hold\"), the aim is to learn affordance grounding on the novel instances of that object. This is a weakly-supervised problem setting where only the image-level labels are given without any per-pixel annotations. Concretely, given several third-person human-object interaction images (exocentric) and one target object image (egocentric), our goal is to extract affordance knowledge and cues from exocentric interactions, and perform affordance grounding in the egocentric view by using only affordance labels." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.597, + 0.471, + 0.868 + ], + "angle": 0, + "content": "There are several key challenges underlying the problem of affordance grounding. The first is due to the nature of the supervision, where only image-level affordance labels are given, being a weakly supervised problem. Here, the system needs to automatically reason about affordance regions just from classification labels. Second, human-object interactions often introduce heavy occlusion of object parts by interacting humans. In other words, the object part that the system needs to predict for a particular affordance (e.g., a mug handle for the \"holding\" affordance) in an exocentric image can often be the part that is occluded (e.g., by hands). Third, interactions are of great diversity. The way humans interact with objects varies across individuals resulting in diverse egocentric interaction images. Lastly, there is a clear domain gap between exocentric and egocentric images where the former have clutter, occlusion etc., and the latter are cleaner (e.g., in Fig. 2). This makes affordance knowledge transfer particularly challenging." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.471, + 0.902 + ], + "angle": 0, + "content": "In this work, we propose a framework called LOCATE that addresses these core challenges by locating the exact" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.379 + ], + "angle": 0, + "content": "object parts involved in the interaction from exocentric images and transferring this knowledge to inactive egocentric images. Refer to Fig. 2 for the illustration. Specifically, we first use the class activation mapping (CAM) [51] technique to find the regions of human-object-interaction in exocentric images. Despite being trained for the interaction recognition task, we observe that CAM can generate good localization maps for interaction regions. We then segment this region of interest further into regions corresponding to human, object part, and background. We do this by extracting embeddings and performing k-means clustering to obtain several compact prototypes. Next, we automatically predict which of these prototypes corresponds to the object part relevant to the affordance. To this end, we propose a module named PartSelect that leverages part-aware features and attention maps from a self-supervised vision transformer (DINO-ViT [6]) to obtain the desired prototype. Finally, we use the object-part prototype as a high-level pseudo supervision to guide egocentric affordance grounding." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.379, + 0.893, + 0.59 + ], + "angle": 0, + "content": "Our contributions can be summarized as follows. (1) We propose a framework called LOCATE that extracts affordance knowledge from weakly supervised exocentric human-object interactions, and transfers this knowledge to the egocentric image in a localized manner. (2) We introduce a novel module termed PartSelect to pick affordancespecific cues from human-object interactions. The extracted information is then used as explicit supervision to guide affordance grounding on egocentric images. (3) LOCATE achieves state-of-the-art results with far fewer parameters and faster inference speed than previous methods, and is able to locate accurate affordance region for unseen objects. See Fig. 1 for examples of our results and comparison to state-of-the-art." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.604, + 0.642, + 0.62 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Visual Affordance Learning. Affordances are actively studied in robotics and computer vision due to their great potential to bridge the gap between perception and action. In general, affordance-related research in computer vision aims to localize objects or object parts where specific actions can be performed. Earlier work [10, 12, 27, 36] mainly focused on the fully supervised setting. Due to the scarcity of affordance datasets, this work normally required costly manual annotations to construct large-scale datasets [10, 37, 39, 42]. To alleviate the annotation and sensing requirement, new research [33, 38, 41, 42] explored acquiring affordance information in the weakly supervised setting. In particular, Sawatzky et al. [42] proposed a convolutional network to tackle affordance detection using only a few keypoint annotations, and Nagarajan et al. [38] introduced a method to infer the object affordance regions by directly learning from human-object interaction videos. In this work, we also focus on learning affordances from weak" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10923" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.122 + ], + "angle": 0, + "content": "supervision, i.e., several human-object interaction images and corresponding image-level affordance labels." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.13, + 0.471, + 0.372 + ], + "angle": 0, + "content": "Weakly Supervised Affordance Grounding. Unlike object localization that aims to find where the object is, in affordance grounding we focus on locating functional regions of objects, which is a more fine-grained localization task. Existing weakly supervised object localization [16, 25, 34, 40, 49, 50] and semantic segmentation methods [8, 9, 28, 48, 52] are mainly based on class activation mapping (CAM) [51], the seminal work that has greatly facilitated the development of weakly supervised learning. Similarly, most affordance grounding research [31, 33, 38] also adopted CAM or its variants [7, 43] to generate activation maps as prediction. However, previous work only used CAM in the inference stage, lacking proper supervision. In contrast, to provide explicit guidance at the training stage, we utilize CAM to produce localization maps in the forward pass and supervise it in a prototypical learning fashion." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.379, + 0.471, + 0.681 + ], + "angle": 0, + "content": "Knowledge Distillation across Domains. Knowledge distillation [23] is a process of transferring knowledge from a network to another, where inputs normally come from the same domain. Recently, many studies [14, 29, 33, 38, 44] have begun to pay more attention to knowledge distillation in different domains. This work transferred representations from the domain with numerous datasets to the other one that typically has low dataset scale and diversity, so that the model can benefit from the large quantity of data in the first domain. For instance, Li et al. [29] proposed a framework to learn egocentric video representations from largescale third-person video datasets, and Luo et al [33] devised a knowledge transfer architecture to transfer affordancespecific features from exocentric view to egocentric view. In this paper, we follow the same setting as [33], using exocentric (third-person) human-object interaction images as the learning target. The objective of this work is to observe where and how humans interact with an object when doing a specific action, and then transfer the knowledge onto the target object." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Self-supervised Vision Transformer. Self-supervised Vision Transformers (ViT) [13], such as DINO [6], MAE [21], and BEiT [4], have demonstrated immense potential in unsupervised dense prediction tasks. Specifically, the features extracted from the self-attention layer exhibit the ability to separate different objects and generate reliable pseudo segmentation maps without requiring any manual annotations. Building on this property, recent work [15, 18, 19, 35, 45, 46] has achieved exceptional results in unsupervised segmentation and localization. Notably, Amir et al. [1] demonstrated that the pretrained features extracted from DINO-ViT encode fine-grained semantic information, which can yield excellent performance for part co-segmentation and semantic correspondence. Inspired by this work, we leverage DINO" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.122 + ], + "angle": 0, + "content": "ViT features to identify matching object parts between exocentric and egocentric images." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.134, + 0.593, + 0.15 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.159, + 0.892, + 0.295 + ], + "angle": 0, + "content": "Given several exocentric interaction images and one egocentric object image, our goal is to extract affordance-related knowledge from exocentric interactions, and transfer it to egocentric images so that the affordance region can be located even for an inactive object. During training, the only supervision available are image-level affordance labels. In the inference stage, taking an egocentric image and an affordance label as input, the model needs to predict the corresponding affordance region." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.295, + 0.893, + 0.522 + ], + "angle": 0, + "content": "The core idea of our approach is to exclude distracting information, e.g., human and background, when extracting affordance-specific features from the exocentric view, and perform fine-grained part-level knowledge transfer from exocentric images to egocentric ones. To this end, we set up the framework LOCATE to transfer the knowledge in three steps (See Fig. 3). First, we utilize CAM to generate localization maps for exocentric images, and extract corresponding feature embeddings with high activation in the localization maps (Sec. 3.1). Then, we propose PartSelect that leverages part-aware deep features to remove irrelevant information while preserving embeddings that can represent affordance cues (Sec. 3.2). Finally, we use the output from PartSelect to supervise the egocentric affordance grounding in an explicit manner (Sec. 3.3)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.529, + 0.762, + 0.545 + ], + "angle": 0, + "content": "3.1. Locating Interaction Regions" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.552, + 0.892, + 0.839 + ], + "angle": 0, + "content": "To determine where neural networks focus on for recognition, we adopt the technique of CAM [51] to generate class-aware localization maps, which has been widely used in weakly supervised tasks. The vanilla CAM generates localization maps as a post-processing step that cannot be guided during training. However, our goal is to extract affordance-specific cues from exocentric images, and use these cues as explicit supervision for the egocentric view. Therefore, in order to obtain localization maps during the training phase, we produce class-specific feature maps instead by adding a class-aware convolution layer, which has proven to be identical to the generation process in CAM [50]. Specifically, for input images \\(\\{I_{exo}, I_{ego}\\}\\) (\\(I_{exo} = \\{I_1, I_2, \\dots, I_N\\}\\)), we first extract deep features \\(\\{\\mathcal{F}_{exo}, \\mathcal{F}_{ego}\\} \\in \\mathbb{R}^{D \\times H \\times W}\\) using a network \\(\\phi\\). In our case, \\(\\phi\\) is a self-supervised vision transformer (DINO-ViT), whose features are part-aware and provide good part-level correspondences. We then generate localization maps \\(\\mathcal{P}\\) and classification scores \\(z\\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.509, + 0.845, + 0.892, + 0.865 + ], + "angle": 0, + "content": "\\[\n\\mathcal {P} = \\psi_ {c a m} (\\mathcal {F}) \\in \\mathbb {R} ^ {C \\times H \\times W}, \\quad \\boldsymbol {z} = \\operatorname {G A P} (\\mathcal {P}) \\in \\mathbb {R} ^ {C}, (1)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "where \\(\\psi_{cam}\\) starts with a projection layer consisting of a feed-forward layer followed by two convolutions to fine" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "10924" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.099, + 0.089, + 0.873, + 0.341 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.35, + 0.893, + 0.392 + ], + "angle": 0, + "content": "Figure 3. Overview of the proposed LOCATE framework. It achieves part-level knowledge transfer in three steps: 1) locating interaction regions with \\(\\psi_{cam}\\) (Sec. 3.1), 2) object-part embedding selection with PartSelect (Sec. 3.2), and 3) part-level knowledge transfer with \\(L_{cos}\\) (Sec. 3.3). Details for PartSelect are shown in Fig. 4. At test time, only the egocentric branch is maintained." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.419, + 0.47, + 0.555 + ], + "angle": 0, + "content": "tune features for the HOI recognition task, i.e., recognizing actions shown in the exocentric images. Then a \\(1 \\times 1\\) class-aware convolution layer is added to yield localization maps, converting the number of channels to \\(C\\), where \\(C\\) denotes the number of total interaction categories. Therefore, each map \\(\\mathcal{P}_c \\in \\mathbb{R}^{H \\times W}\\) represents the network activation for the \\(c\\)-th interaction. Next, \\(\\mathcal{P}\\) is fed to a global average pooling (GAP) layer to obtain classification scores \\(z\\), which are used to calculate cross-entropy loss \\(\\mathcal{L}_{cls}\\) for optimization." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.557, + 0.471, + 0.799 + ], + "angle": 0, + "content": "We notice that localization maps for the exocentric branch \\(\\mathcal{P}_{exo}\\) concentrate on the interaction areas, i.e., where the action takes place. Since interaction areas carry strong affordance information, we therefore aim to collect embeddings from the high activation regions in exocentric localization maps. Specifically, we first extract the localization map corresponding to ground-truth class, and conduct min-max normalization to constrain activation values to [0, 1]. After that, we set a threshold \\(\\tau\\) to control the number of extracted embeddings, therefore embeddings with activation value greater than \\(\\tau\\) in the localization map will be extracted from deep features. For multiple exocentric images, embeddings are extracted separately to produce \\(f_{exo} = [f_1, \\dots, f_N]\\), each \\(f_n\\) containing a different number of embeddings. All embeddings are then concatenated together \\(f_{exo} \\in \\mathbb{R}^{L \\times D}\\), where \\(L\\) denotes the number of embeddings." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.815, + 0.373, + 0.831 + ], + "angle": 0, + "content": "3.2. Object-Part Embedding Selection" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.47, + 0.902 + ], + "angle": 0, + "content": "In general, interaction areas are composed of human, object part, and background. Our objective is to eliminate the interference information, and purely deliver embeddings representing the object part to guide the egocentric branch." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.419, + 0.893, + 0.526 + ], + "angle": 0, + "content": "In consequence, we design PartSelect to choose affordance-related embeddings from exocentric branch. PartSelect is illustrated in Fig. 4a. We first perform k-means clustering to get \\(K\\) compact prototypes \\(\\pmb{p} \\in \\mathbb{R}^{K \\times D}\\) from extracted exocentric embeddings. Next, we compute the cosine distance between each prototype and the egocentric deep features \\(\\mathcal{F}_{ego}\\) to get similarity maps \\(\\mathcal{S} \\in \\mathbb{R}^{K \\times H \\times W}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.615, + 0.535, + 0.892, + 0.57 + ], + "angle": 0, + "content": "\\[\nS ^ {k, u, v} = \\frac {\\boldsymbol {p} _ {k} \\cdot \\mathcal {F} _ {e g o} ^ {u , v}}{\\| \\boldsymbol {p} _ {k} \\| \\| \\mathcal {F} _ {e g o} ^ {u , v} \\|.} \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.577, + 0.892, + 0.621 + ], + "angle": 0, + "content": "Owing to the fine-grained semantic information of DINOViT deep features, embeddings of the same object parts bear high similarity." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.623, + 0.893, + 0.729 + ], + "angle": 0, + "content": "To distinguish which prototype stands for the object part, we aggregate the self-attention maps from the last layer of the DINO-ViT to generate a saliency map \\(\\mathcal{A} \\in \\mathbb{R}^{H \\times W}\\) for the egocentric image. Given the saliency map and similarity maps, we introduce a metric \\(\\gamma \\in [0,1]\\) termed PartIoU to measure if a prototype carries object part information. The PartIoU for the \\(k\\)-th prototype is defined as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.599, + 0.739, + 0.892, + 0.774 + ], + "angle": 0, + "content": "\\[\n\\gamma = \\frac {1}{2} \\frac {\\overline {{\\mathcal {S} _ {k}}} \\cap \\overline {{\\mathcal {A}}}}{\\overline {{\\mathcal {S} _ {k}}}} + \\frac {1}{2} \\frac {\\overline {{\\mathcal {A}}}}{\\overline {{\\mathcal {S} _ {k}}} \\cup \\overline {{\\mathcal {A}}}}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.779, + 0.895, + 0.902 + ], + "angle": 0, + "content": "where \\(\\overline{S_k}\\), \\(\\overline{\\mathcal{A}}\\in \\{0,1\\}^{H\\times W}\\) are binary masks, we set the threshold as the average of each map to perform binarization. The motivation of PartIoU is fairly straightforward, if \\(\\overline{S}\\) belongs to a portion of \\(\\overline{\\mathcal{A}}\\), then the intersection of \\(\\overline{S}\\) and \\(\\overline{\\mathcal{A}}\\) should equal \\(\\overline{S}\\) itself, while the union of the two masks should be identical to \\(\\overline{\\mathcal{A}}\\). Finally, when the maximum PartIoU among \\(K\\) prototypes is above a threshold \\(\\mu\\), PartS-select will output the prototype with the largest PartIoU as" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10925" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.107, + 0.092, + 0.442, + 0.352 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.199, + 0.356, + 0.349, + 0.368 + ], + "angle": 0, + "content": "(a) Illustration of PartSelect." + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.374, + 0.177, + 0.432 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.107, + 0.435, + 0.155, + 0.446 + ], + "angle": 0, + "content": "Exo-image" + }, + { + "type": "image", + "bbox": [ + 0.179, + 0.374, + 0.275, + 0.431 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.196, + 0.435, + 0.257, + 0.445 + ], + "angle": 0, + "content": "Object Part" + }, + { + "type": "image", + "bbox": [ + 0.276, + 0.374, + 0.371, + 0.431 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.293, + 0.435, + 0.358, + 0.446 + ], + "angle": 0, + "content": "Background" + }, + { + "type": "image", + "bbox": [ + 0.373, + 0.374, + 0.469, + 0.431 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.401, + 0.435, + 0.441, + 0.444 + ], + "angle": 0, + "content": "Human" + }, + { + "type": "image_caption", + "bbox": [ + 0.192, + 0.452, + 0.356, + 0.465 + ], + "angle": 0, + "content": "(b) Exocentric similarity maps." + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.477, + 0.47, + 0.547 + ], + "angle": 0, + "content": "Figure 4. (a) PartSelect picks the object-part prototype through clustering and selection, where \\(\\otimes\\) denotes the calculation for PartIOU score. (b) The similarity maps between prototypes and exocentric features confirm our statement that each prototype represents the object part, background, and human." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.58, + 0.469, + 0.655 + ], + "angle": 0, + "content": "the object-part representation. Otherwise, no prototype will be selected for the next step. In Fig. 4b, we visualize the similarity maps between prototypes and exocentric features to demonstrate that the extracted embeddings are clustered into human, object part, and background." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.674, + 0.357, + 0.691 + ], + "angle": 0, + "content": "3.3. Part-Level Knowledge Transfer" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.701, + 0.469, + 0.791 + ], + "angle": 0, + "content": "With the help of PartSelect, we find the prototype \\( f_{op} \\) that represents the object part. We then leverage it to perform supervision for egocentric localization maps \\( \\mathcal{P}_{ego} \\). Concretely, we first perform masked average pooling (MAP) between the normalized localization map and extracted deep features to aggregate into one embedding:" + }, + { + "type": "equation", + "bbox": [ + 0.146, + 0.814, + 0.469, + 0.857 + ], + "angle": 0, + "content": "\\[\nf _ {e g o} = \\frac {\\sum_ {u = 1 , v = 1} ^ {W , H} \\mathcal {F} _ {e g o} ^ {u , v} \\mathcal {P} _ {e g o} ^ {t , u , v}}{\\sum_ {i = 1 , j = 1} ^ {W , H} \\mathcal {P} _ {e g o} ^ {t , u , v}} \\in \\mathbb {R} ^ {D}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.469, + 0.903 + ], + "angle": 0, + "content": "where \\( t \\) denotes the ground-truth category. Then, a cosine embedding loss is applied to pull the embedding \\( f_{ego} \\) to-" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.678, + 0.108 + ], + "angle": 0, + "content": "wards the direction of \\( f_{op} \\):" + }, + { + "type": "equation", + "bbox": [ + 0.561, + 0.118, + 0.892, + 0.153 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {c o s} = \\max \\left(1 - \\frac {f _ {o p} \\cdot f _ {e g o}}{\\| f _ {o p} \\| \\| f _ {e g o} \\|} - \\alpha , 0\\right), \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.162, + 0.891, + 0.192 + ], + "angle": 0, + "content": "as the two embeddings come from different domains, we thereby add \\(\\alpha\\) as a margin to compensate the domain gap." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.193, + 0.892, + 0.296 + ], + "angle": 0, + "content": "In addition, since the affordance region typically denotes a portion of an object, we can thus impose a geometry loss to regulate its distribution. Inspired by the co-part segmentation work [24], we add a concentration loss to encourage egocentric localization maps to form a concentrated and connected component. The concentration loss is formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.525, + 0.307, + 0.892, + 0.34 + ], + "angle": 0, + "content": "\\[\n\\bar {u} _ {c} = \\sum_ {u, v} u \\cdot \\mathcal {P} _ {e g o} ^ {c, u, v} / z _ {k}, \\bar {v} _ {c} = \\sum_ {u, v} v \\cdot \\mathcal {P} _ {e g o} ^ {c, u, v} / z _ {k}, \\tag {6}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.545, + 0.352, + 0.892, + 0.385 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {c} = \\sum_ {c} \\sum_ {u, v} \\| \\langle u, v \\rangle - \\langle \\bar {u} _ {c}, \\bar {v} _ {c} \\rangle \\| \\cdot \\mathcal {P} _ {e g o} ^ {c, u, v} / z _ {c}, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.392, + 0.892, + 0.464 + ], + "angle": 0, + "content": "where \\(\\overline{u}_c\\) and \\(\\overline{v}_c\\) represents the center of the \\(c\\)-th localization map along axis \\(u, v\\), and \\(z_c = \\sum_{u,v} \\mathcal{P}_{ego}^{c,u,v}\\) is a normalization term. The concentration loss forces the high activation regions of the localization maps to be close to the geometric center." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.468, + 0.892, + 0.497 + ], + "angle": 0, + "content": "Overall, we train the whole framework in an end-to-end manner, and use the following loss to optimize the model:" + }, + { + "type": "equation", + "bbox": [ + 0.594, + 0.513, + 0.891, + 0.529 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {c l s} + \\lambda_ {c o s} \\mathcal {L} _ {c o s} + \\lambda_ {c} \\mathcal {L} _ {c}, \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.537, + 0.892, + 0.627 + ], + "angle": 0, + "content": "where \\(\\lambda_{cos}\\), and \\(\\lambda_{c}\\) are loss weights that balance the three terms. \\(\\mathcal{L}_{cls}\\) stands for the cross-entropy losses from the two branches. At test time, only the ego branch is maintained, taking an affordance label \\(t\\) and an egocentric image as input, the network extracts the \\(t\\)-th localization map as the prediction of affordance region." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.642, + 0.634, + 0.658 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.667, + 0.701, + 0.683 + ], + "angle": 0, + "content": "4.1. Experimental Setting" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Dataset and Metrics. We evaluate our method in the Affordance Grounding Dataset (AGD20K) [33], which is the only large-scale image dataset with both exocentric and egocentric views. AGD20K is comprised of 20,061 exocentric images and 3,755 egocentric images, and is annotated with 36 commonly used affordances. Following prior affordance grounding work [14,38], the ground truth of this dataset initially consists of densely annotated points in corresponding affordance regions, and a Gaussian blur is then applied over each point to get final heatmaps. Moreover, AGD20K can be evaluated in two different settings: 1) In the seen setting, object categories in training and test sets are identical. 2) In the unseen setting, there is no object category intersection between training and test sets, e.g., the" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10926" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.118, + 0.089, + 0.855, + 0.269 + ], + "angle": 0, + "content": "
State-of-the-Art from Relevant TasksSeenUnseen
KLD↓SIM↑NSS↑KLD↓SIM↑NSS↑
Weakly Supervised Object Localization*EIL [34]1.9310.2850.5222.1670.2270.330
SPA [40]5.5280.2210.3577.4250.1690.262
TS-CAM [16]1.8420.2600.3362.1040.2010.151
Weakly Supervised Affordance GroundingHotspots [38]1.7730.2780.6151.9940.2370.577
Cross-view-AG [33]1.5380.3340.9271.7870.2850.829
Cross-view-AG+ [32]1.4890.3420.9811.7650.2790.882
AffCorrs† [18]1.4070.3591.0261.6180.3481.021
LOCATE (Ours)1.2260.4011.1771.4050.3721.157
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.279, + 0.893, + 0.311 + ], + "angle": 0, + "content": "Table 1. Comparison to state-of-the-arts from relevant tasks on AGD20K dataset. Results of * are taken from [33], and † denotes the adapted AffCorrs. The best and second-best results are highlighted in bold and underlined, respectively (↑/↓ means higher/lower is better)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.334, + 0.47, + 0.363 + ], + "angle": 0, + "content": "model observes how humans hold a hammer and anticipates where to hold a knife." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.365, + 0.47, + 0.472 + ], + "angle": 0, + "content": "As for the metrics, referring to previous affordance grounding work [14, 30, 33, 38], we adopt the commonly used Kullback-Leibler Divergence (KLD), Similarity (SIM), and Normalized Scanpath Saliency (NSS) to evaluate the similarity and correspondence of distributions between ground truth and prediction. Detailed calculation of each metric is shown in the supplementary material." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.475, + 0.471, + 0.656 + ], + "angle": 0, + "content": "Implementation Details. We use the ImageNet [11] pretrained (without supervision) DINO-ViT-S [6] with patch size 16 to generate deep features. In each iteration, N exocentric images along with one egocentric image are taken as input (N is set to 3). Images are first resized to \\(256 \\times 256\\) and then randomly cropped to \\(224 \\times 224\\) followed by random horizontal flipping. SGD with learning rate 1e-3, weight decay 5e-4, and batch size 16 is used for parameter optimization. Loss weight coefficients \\((\\lambda_{cos}, \\lambda_c)\\) are set to (1, 0.07), and the margin \\(\\alpha\\) is set to 0.5. For the first epoch, we warm up the network without \\(\\mathcal{L}_{cos}\\), as initial localization maps are not accurate for supervision." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.666, + 0.357, + 0.683 + ], + "angle": 0, + "content": "4.2. Comparison to State-of-the-Art" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.471, + 0.903 + ], + "angle": 0, + "content": "To conduct a comprehensive comparison, we also display the results of state-of-the-art methods from a relevant task, i.e., weakly supervised object localization. As shown in Table 1, in both seen and unseen settings, LOCATE outperforms all other methods with a considerable margin on all metrics. In particular, compared to the state-of-the-art affordance grounding method Cross-view-AG+ [32], we improve the KLD by \\(20.4\\%\\), SIM by \\(33.3\\%\\), and NSS by \\(31.2\\%\\) in the unseen setting. Cross-view-AG+ is an extended version of Cross-view-AG, but still performs the knowledge transfer based on global pooled embeddings at the image level, thus bringing only minor improvement. AffCorrs [18] is a method that focuses on one-shot part affordance grounding, and it also uses the pretrained DINO-ViT" + }, + { + "type": "table", + "bbox": [ + 0.528, + 0.331, + 0.868, + 0.491 + ], + "angle": 0, + "content": "
MethodsParams (M)Time (s)
EIL [34]42.410.019
SPA [40]69.280.081
TS-CAM [16]85.860.023
Hotspots [38]132.640.087
Cross-view-AG [33]120.030.023
Cross-view-AG+ [32]82.270.022
AffCorrs† [18]6.500.205
LOCATE (Ours)6.500.011
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.501, + 0.892, + 0.543 + ], + "angle": 0, + "content": "Table 2. Comparison of learnable parameters and inference time. The inference time is evaluated on a 3090Ti GPU. \\(\\dagger\\) denotes the adapted AffCorrs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.564, + 0.892, + 0.67 + ], + "angle": 0, + "content": "features to do part matching. However, AffCorrs needs a pixel-level mask as a query, and there is no domain gap during the knowledge transfer. To make AffCorrs comparable in our problem setting, we adapt its structure by replacing the query annotated mask with our CAM estimator. The results verify that AffCorrs can also achieve good performance, but still considerably inferior to LOCATE." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.672, + 0.893, + 0.853 + ], + "angle": 0, + "content": "In Table 2, we make comparisons in terms of model parameters and inference time. Since our framework is built on a frozen small-sized vision transformer (ViT-small), the training process is efficient with a small number of parameters. For example, LOCATE only has \\(5.4\\%\\) of learnable parameters in Cross-view-AG. Additionally, we use a large patch size 16 for the vision transformer, which constrains the input sequence length and greatly reduces computation cost. Therefore, the inference time of LOCATE is also faster than most other methods. By contrast, the adapted AffCorrs runs much slower than LOCATE, as it incorporates an additional CRF post-processing step." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.894, + 0.903 + ], + "angle": 0, + "content": "We further visualize the qualitative comparisons with state-of-the-art affordance grounding methods. As shown in Fig. 5, we compare our results with Hotspots [38], Cross-" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10927" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.086, + 0.09, + 0.501, + 0.471 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.516, + 0.089, + 0.865, + 0.47 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.488, + 0.893, + 0.531 + ], + "angle": 0, + "content": "Figure 5. Qualitative comparison between our approach and state-of-the-art affordance grounding methods (Hotspots [38], Cross-view-AG [33], and Cross-view-AG+ [32]). For the unseen setting, the displayed objects are not in the training set. For example, the model learns where a motorcycle can be ridden in training, and locates rideable area for the bicycle at test time." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.557, + 0.473, + 0.68 + ], + "angle": 0, + "content": "view-AG [33] and Cross-view-AG+ [32]. We observe that the proposed LOCATE can make more concentrated and accurate predictions. Especially for complex objects like bicycles and refrigerators, even in the unseen setting, our method can still locate the saddle of bicycles for riding, and the handle of fridges for opening. In comparison, the results of Cross-view-AG for bicycles are quite noisy. More visualization results are in the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.694, + 0.232, + 0.71 + ], + "angle": 0, + "content": "4.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.472, + 0.903 + ], + "angle": 0, + "content": "Knowledge Transfer Manner. We first investigate the impact of knowledge transfer manner. Previous affordance grounding methods [33, 38] simply pull close the global embeddings (produced by global average pooling) of two branches to perform global knowledge transfer (GKT). In contrast, we set up an experiment to implement regional knowledge transfer (RKT), which generates the embeddings via masked average pooling between CAM-produced localization maps and feature maps. The results are shown in Table 3, regional knowledge transfer (RKT) outperforms global knowledge transfer (GKT) on all metrics, demonstrating the effectiveness of filtering irrelevant information." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.554, + 0.892, + 0.681 + ], + "angle": 0, + "content": "
MethodSeenUnseen
KLD↓SIM↑NSS↑KLD↓SIM↑NSS↑
GKT1.7320.2670.8101.9710.2210.626
RKT1.5160.3201.0741.8230.2590.850
+ Lc1.4910.3261.0911.7500.2740.948
+S1.2360.3971.1781.4390.3581.130
+S + Lc1.2260.4011.1771.4050.3721.157
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.691, + 0.892, + 0.734 + ], + "angle": 0, + "content": "Table 3. Ablation results of the proposed LOCATE framework. GKT/RKT means global/regional knowledge transfer. \\( \\mathcal{S} \\) denotes PartSelect combined with \\( {\\mathcal{L}}_{cos} \\) ,and \\( {\\mathcal{L}}_{c} \\) is the concentration loss." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.895, + 0.903 + ], + "angle": 0, + "content": "PartSelect and Concentration Loss. Based on the regional knowledge transfer, we analyze the effect of PartSelect and concentration loss. As shown in Table 3, directly applying the concentration loss \\(\\mathcal{L}_c\\) can only bring marginal improvement. The reason is \\(\\mathcal{L}_c\\) can make egocentric predictions more concentrated, but fail to guide it to focus on the right affordance area. Nonetheless, when adding PartSelect and using cosine embedding loss \\(\\mathcal{L}_{cos}\\) as explicit supervision, the performance is greatly boosted, which proves the effectiveness of the part-level knowledge transfer scheme. In ad" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "10928" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.104, + 0.076, + 0.132, + 0.086 + ], + "angle": 0, + "content": "GKT" + }, + { + "type": "image_caption", + "bbox": [ + 0.18, + 0.076, + 0.208, + 0.086 + ], + "angle": 0, + "content": "RKT" + }, + { + "type": "image_caption", + "bbox": [ + 0.25, + 0.076, + 0.298, + 0.086 + ], + "angle": 0, + "content": "\\(\\mathrm{RKT} + \\mathcal{S}\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.313, + 0.076, + 0.389, + 0.086 + ], + "angle": 0, + "content": "\\(\\mathrm{RKT} + \\mathcal{S} + \\mathcal{L}_c\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.418, + 0.076, + 0.437, + 0.086 + ], + "angle": 0, + "content": "GT" + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.091, + 0.468, + 0.317 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.106, + 0.329, + 0.439, + 0.343 + ], + "angle": 0, + "content": "Figure 6. Visualization of the qualitative improvements." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.36, + 0.468, + 0.466 + ], + "angle": 0, + "content": "dition, to check the qualitative improvement, we visualize the affordance grounding results in Fig. 6. It is clear that GKT tends to locate the wrong affordance area, while RKT can sometimes find the right region, but only give coarse grounding results. After adding PartSelect, the results become much more part-focused, and the concentration loss further makes the grounding maps more robust." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.472, + 0.468, + 0.729 + ], + "angle": 0, + "content": "Number of Prototypes/Exocentric Images. We then explore the impact from the number of prototypes \\( K \\) and exocentric images \\( N \\). From Fig. 7a, we observe that the model yields the best performance with three prototypes in seen setting, which is consistent with our statement that interaction areas typically consist of human, object part, and background information. While for the unseen setting, \\( N = 5 \\) achieves the best results, but improvement is minor. One reason lies in that more prototypes segment objects into more small parts, which boosts the generalization ability. As for the number of exocentric images, we find that more exocentric images can alleviate the impact of interaction diversity and occlusion, thus providing more robust knowledge for the egocentric branch. As shown in Fig. 7b, the model gets largely improved when increasing the number of exocentric images from 1 to 3 in both seen and unseen settings. Finally, we set both \\( N \\) and \\( K \\) to 3." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Different Feature Extractors. In LOCATE, we employ pretrained DINO features based on ViT, which have been proven to encode high-level semantic information [1]. To investigate the impact of different backbones, we conducted experiments with DINO features trained on the ResNet-50 [22]. From the results in Table 4, we observe that using DINO-ViT features directly (without the proposed PartSelect) can only obtain similar or even inferior results to their ResNet counterpart. After incorporating PartSelect, the results of both backbone features can be improved under the seen setting, but ViT features show better potential in en" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.091, + 0.887, + 0.196 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.621, + 0.201, + 0.772, + 0.214 + ], + "angle": 0, + "content": "(a) Number of prototypes \\(N\\)" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.216, + 0.887, + 0.322 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.602, + 0.326, + 0.792, + 0.338 + ], + "angle": 0, + "content": "(b) Number of exocentric images \\(K\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.35, + 0.892, + 0.379 + ], + "angle": 0, + "content": "Figure 7. Ablation study on the number of prototypes and exocentric images (lower is better)." + }, + { + "type": "table", + "bbox": [ + 0.501, + 0.395, + 0.892, + 0.542 + ], + "angle": 0, + "content": "
RN-50ViT-S/16PartSelectKLD↓SIM↑NSS↑
Seen✓1.4820.3341.005
✓1.4910.3261.091
✓✓1.4490.3401.021
✓✓1.2260.4011.177
Unseen✓1.7010.2870.962
✓1.7500.2740.948
✓✓1.7070.2870.949
✓✓1.4050.3721.157
" + }, + { + "type": "table_caption", + "bbox": [ + 0.533, + 0.552, + 0.857, + 0.566 + ], + "angle": 0, + "content": "Table 4. Ablation study on different feature extractors." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.581, + 0.891, + 0.642 + ], + "angle": 0, + "content": "hancing the performance due to their part-aware property. In the unseen setting, PartSelect does not yield improvement for ResNet-based features, while ViT features obtain consistent gains." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.659, + 0.618, + 0.674 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.685, + 0.892, + 0.851 + ], + "angle": 0, + "content": "In this paper, we propose a framework named LOCATE to address the weakly supervised affordance grounding task by observing human-object interaction images. Specifically, we first localize where the interaction happens for the exocentric interactions, and then design a module called PartSelect to pick the affordance-specific information from the interaction regions. Finally, we transfer the learned knowledge to the egocentric view to perform affordance grounding with only image-level affordance labels. The proposed LOCATE achieves state-of-the-art results with far fewer parameters and faster inference speed." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.857, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Acknowledgement. This work is supported by the EPSRC, as part of the CDT in Robotics and Autonomous Systems (EP/S023208/1), along with gift funding and the research scholar award from Google." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10929" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.156 + ], + "angle": 0, + "content": "[1] Shir Amir, Yossi Gandelsman, Shai Bagon, and Tali Dekel. Deep vit features as dense visual descriptors. ECCVW What is Motion For, 2022. 3, 8" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.157, + 0.47, + 0.2 + ], + "angle": 0, + "content": "[2] Paola Ardón, Éric Pairet, Katrin S Lohan, Subramanian Ramamoorthy, and Ronald Petrick. 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In CVPR, 2022. 3" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.092, + 0.892, + 0.276 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.518, + 0.957 + ], + "angle": 0, + "content": "10931" + } + ] +] \ No newline at end of file diff --git a/2023/LOCATE_ Localize and Transfer Object Parts for Weakly Supervised Affordance Grounding/c02a6207-738d-48dd-beea-456bd084b930_origin.pdf b/2023/LOCATE_ Localize and Transfer Object Parts for Weakly Supervised Affordance Grounding/c02a6207-738d-48dd-beea-456bd084b930_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..ab2f24fccac767413a6009db0969752d0dc21f21 --- /dev/null +++ b/2023/LOCATE_ Localize and Transfer Object Parts for Weakly Supervised Affordance Grounding/c02a6207-738d-48dd-beea-456bd084b930_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:d0ffa89a652739c536dbdcbcdd623b6841d0f30d23407f008a3475cd60a9581c +size 10166682 diff --git a/2023/LOCATE_ Localize and Transfer Object Parts for Weakly Supervised Affordance Grounding/full.md b/2023/LOCATE_ Localize and Transfer Object Parts for Weakly Supervised Affordance Grounding/full.md new file mode 100644 index 0000000000000000000000000000000000000000..38e2a6dbcd9197607f20a3fd9476c068f80b9bbb --- /dev/null +++ b/2023/LOCATE_ Localize and Transfer Object Parts for Weakly Supervised Affordance Grounding/full.md @@ -0,0 +1,318 @@ +# LOCATE: Localize and Transfer Object Parts for Weakly Supervised Affordance Grounding + +Gen Li + +Varun Jampani2 + +Deqing Sun + +Laura Sevilla-Lara + +1University of Edinburgh 2Google Research + +![](images/b15b47d3d32613847aea4be44fbb03e1646cf12d0f3eb3f0cffe79b0aec5579f.jpg) + +![](images/66e5b36c0dfc331a0c47ba82e409e23bad3925130b16b2514b1754fffb8cfe4c.jpg) +Object Image + +![](images/4f7938ae4ab720883a4596a11589bcc1a64b96620ffd3921e21127211e3db242.jpg) + +![](images/3737f22d7ce572070ed3f64d80e5a409640f7c2e4aadb9591d21405870927ce8.jpg) +Hotspots [38] + +![](images/54b2bdfe8ee4dfb1a9ee544244dba47b5da305ed4d4f8de88ffc46922a332bfc.jpg) + +![](images/ff6fb1c8d083d99a4774e9f65fa876d35fd9d356719a85ab9ef8cd356af1f7a3.jpg) +Cross-view-AG [33] +Figure 1. State-of-the-art methods in weakly supervised affordance grounding often fail to make accurate predictions for objects with complex structures, e.g., chairs and bicycles. To address this, our model (LOCATE) focuses on localizing and transferring features of object parts, which is able to produce more accurate results. + +![](images/c0d3d5b7b4a0f5d393701016ab781f7828da21f8f3be109b93020a5a38787020.jpg) + +![](images/5d842043f955f85afa58203785110dfa8fc72acc2fca935f774b8e8d99d512e7.jpg) +Cross-view-AG+ [32] + +![](images/cd96f218c7b8f4139845c72cc339673dac54c87751bc9de549dd99a87358d5b9.jpg) + +![](images/d1b1cc6b687e04fb4fef78952a4c71b646a13db7960d27dd54ba916803b8cba2.jpg) +LOCATE (Ours) + +![](images/ff574e1ad8d39e7dcee6c86003e535d285ea80a16d21b80728d76789a439472e.jpg) + +![](images/0e002d25875712eb3807ec06ac43a6936291a963e550a317d43fd2a2d3e7e98e.jpg) +GT + +# Abstract + +Humans excel at acquiring knowledge through observation. For example, we can learn to use new tools by watching demonstrations. This skill is fundamental for intelligent systems to interact with the world. A key step to acquire this skill is to identify what part of the object affords each action, which is called affordance grounding. In this paper, we address this problem and propose a framework called LOCATE that can identify matching object parts across images, to transfer knowledge from images where an object is being used (exocentric images used for learning), to images where the object is inactive (egocentric ones used to test). To this end, we first find interaction areas and extract their feature embeddings. Then we learn to aggregate the embeddings into compact prototypes (human, object part, and background), and select the one representing the object part. Finally, we use the selected prototype to guide affordance grounding. We do this in a weakly supervised manner, learning only from image-level affordance and object labels. Extensive experiments demonstrate that our approach outperforms state-of-the-art methods by a large margin on both seen and unseen objects.1 + +# 1. Introduction + +A fundamental skill of humans is learning to interact with objects just by observing someone else performing those interactions [5]. For instance, even if we have never played tennis, we can easily learn where to hold the racket just by looking at a single or few photographs of those interactions. Such learning capabilities are essential for intelligent agents to understand what actions can be performed on a given object. Current visual systems often focus primarily on recognizing what objects are in the scene (passive perception), rather than on how to use objects to achieve certain functions (active interaction). To this end, a growing number of studies [3, 12, 26, 47] have begun to utilize affordance [17] as a medium to bridge the gap between passive perception and active interaction. In computer vision and robotics [2, 20], affordance typically refers to regions of an object that are available to perform a specific action, e.g., a knife handle affords holding, and its blade affords cutting. + +In this paper, we focus on the task of affordance grounding, i.e., locating the object regions used for a given action. Previous methods [10, 12, 14, 37, 39] have often treated affordance grounding as a fully supervised semantic segmentation task, which requires costly pixel-level annotations. Instead, we follow the more realistic setting [32, 33, 38] + +![](images/b41e5344c1a50842eb5d95db5f1e964ff62fe1903f217b448e107b7f48477ff6.jpg) +Figure 2. General illustration of LOCATE. We first extract the embeddings under the region of interest where the exocentric interactions are happening, and then split these embeddings into several clusters. In the end, the prototype of the object-part cluster is selected to supervise the egocentric affordance grounding. + +where the task is learning object affordances by observing human-object interaction images. That is, given some interaction images, such as those in Fig. 2, along with the corresponding label (e.g., "hold"), the aim is to learn affordance grounding on the novel instances of that object. This is a weakly-supervised problem setting where only the image-level labels are given without any per-pixel annotations. Concretely, given several third-person human-object interaction images (exocentric) and one target object image (egocentric), our goal is to extract affordance knowledge and cues from exocentric interactions, and perform affordance grounding in the egocentric view by using only affordance labels. + +There are several key challenges underlying the problem of affordance grounding. The first is due to the nature of the supervision, where only image-level affordance labels are given, being a weakly supervised problem. Here, the system needs to automatically reason about affordance regions just from classification labels. Second, human-object interactions often introduce heavy occlusion of object parts by interacting humans. In other words, the object part that the system needs to predict for a particular affordance (e.g., a mug handle for the "holding" affordance) in an exocentric image can often be the part that is occluded (e.g., by hands). Third, interactions are of great diversity. The way humans interact with objects varies across individuals resulting in diverse egocentric interaction images. Lastly, there is a clear domain gap between exocentric and egocentric images where the former have clutter, occlusion etc., and the latter are cleaner (e.g., in Fig. 2). This makes affordance knowledge transfer particularly challenging. + +In this work, we propose a framework called LOCATE that addresses these core challenges by locating the exact + +object parts involved in the interaction from exocentric images and transferring this knowledge to inactive egocentric images. Refer to Fig. 2 for the illustration. Specifically, we first use the class activation mapping (CAM) [51] technique to find the regions of human-object-interaction in exocentric images. Despite being trained for the interaction recognition task, we observe that CAM can generate good localization maps for interaction regions. We then segment this region of interest further into regions corresponding to human, object part, and background. We do this by extracting embeddings and performing k-means clustering to obtain several compact prototypes. Next, we automatically predict which of these prototypes corresponds to the object part relevant to the affordance. To this end, we propose a module named PartSelect that leverages part-aware features and attention maps from a self-supervised vision transformer (DINO-ViT [6]) to obtain the desired prototype. Finally, we use the object-part prototype as a high-level pseudo supervision to guide egocentric affordance grounding. + +Our contributions can be summarized as follows. (1) We propose a framework called LOCATE that extracts affordance knowledge from weakly supervised exocentric human-object interactions, and transfers this knowledge to the egocentric image in a localized manner. (2) We introduce a novel module termed PartSelect to pick affordancespecific cues from human-object interactions. The extracted information is then used as explicit supervision to guide affordance grounding on egocentric images. (3) LOCATE achieves state-of-the-art results with far fewer parameters and faster inference speed than previous methods, and is able to locate accurate affordance region for unseen objects. See Fig. 1 for examples of our results and comparison to state-of-the-art. + +# 2. Related Work + +Visual Affordance Learning. Affordances are actively studied in robotics and computer vision due to their great potential to bridge the gap between perception and action. In general, affordance-related research in computer vision aims to localize objects or object parts where specific actions can be performed. Earlier work [10, 12, 27, 36] mainly focused on the fully supervised setting. Due to the scarcity of affordance datasets, this work normally required costly manual annotations to construct large-scale datasets [10, 37, 39, 42]. To alleviate the annotation and sensing requirement, new research [33, 38, 41, 42] explored acquiring affordance information in the weakly supervised setting. In particular, Sawatzky et al. [42] proposed a convolutional network to tackle affordance detection using only a few keypoint annotations, and Nagarajan et al. [38] introduced a method to infer the object affordance regions by directly learning from human-object interaction videos. In this work, we also focus on learning affordances from weak + +supervision, i.e., several human-object interaction images and corresponding image-level affordance labels. + +Weakly Supervised Affordance Grounding. Unlike object localization that aims to find where the object is, in affordance grounding we focus on locating functional regions of objects, which is a more fine-grained localization task. Existing weakly supervised object localization [16, 25, 34, 40, 49, 50] and semantic segmentation methods [8, 9, 28, 48, 52] are mainly based on class activation mapping (CAM) [51], the seminal work that has greatly facilitated the development of weakly supervised learning. Similarly, most affordance grounding research [31, 33, 38] also adopted CAM or its variants [7, 43] to generate activation maps as prediction. However, previous work only used CAM in the inference stage, lacking proper supervision. In contrast, to provide explicit guidance at the training stage, we utilize CAM to produce localization maps in the forward pass and supervise it in a prototypical learning fashion. + +Knowledge Distillation across Domains. Knowledge distillation [23] is a process of transferring knowledge from a network to another, where inputs normally come from the same domain. Recently, many studies [14, 29, 33, 38, 44] have begun to pay more attention to knowledge distillation in different domains. This work transferred representations from the domain with numerous datasets to the other one that typically has low dataset scale and diversity, so that the model can benefit from the large quantity of data in the first domain. For instance, Li et al. [29] proposed a framework to learn egocentric video representations from largescale third-person video datasets, and Luo et al [33] devised a knowledge transfer architecture to transfer affordancespecific features from exocentric view to egocentric view. In this paper, we follow the same setting as [33], using exocentric (third-person) human-object interaction images as the learning target. The objective of this work is to observe where and how humans interact with an object when doing a specific action, and then transfer the knowledge onto the target object. + +Self-supervised Vision Transformer. Self-supervised Vision Transformers (ViT) [13], such as DINO [6], MAE [21], and BEiT [4], have demonstrated immense potential in unsupervised dense prediction tasks. Specifically, the features extracted from the self-attention layer exhibit the ability to separate different objects and generate reliable pseudo segmentation maps without requiring any manual annotations. Building on this property, recent work [15, 18, 19, 35, 45, 46] has achieved exceptional results in unsupervised segmentation and localization. Notably, Amir et al. [1] demonstrated that the pretrained features extracted from DINO-ViT encode fine-grained semantic information, which can yield excellent performance for part co-segmentation and semantic correspondence. Inspired by this work, we leverage DINO + +ViT features to identify matching object parts between exocentric and egocentric images. + +# 3. Method + +Given several exocentric interaction images and one egocentric object image, our goal is to extract affordance-related knowledge from exocentric interactions, and transfer it to egocentric images so that the affordance region can be located even for an inactive object. During training, the only supervision available are image-level affordance labels. In the inference stage, taking an egocentric image and an affordance label as input, the model needs to predict the corresponding affordance region. + +The core idea of our approach is to exclude distracting information, e.g., human and background, when extracting affordance-specific features from the exocentric view, and perform fine-grained part-level knowledge transfer from exocentric images to egocentric ones. To this end, we set up the framework LOCATE to transfer the knowledge in three steps (See Fig. 3). First, we utilize CAM to generate localization maps for exocentric images, and extract corresponding feature embeddings with high activation in the localization maps (Sec. 3.1). Then, we propose PartSelect that leverages part-aware deep features to remove irrelevant information while preserving embeddings that can represent affordance cues (Sec. 3.2). Finally, we use the output from PartSelect to supervise the egocentric affordance grounding in an explicit manner (Sec. 3.3). + +# 3.1. Locating Interaction Regions + +To determine where neural networks focus on for recognition, we adopt the technique of CAM [51] to generate class-aware localization maps, which has been widely used in weakly supervised tasks. The vanilla CAM generates localization maps as a post-processing step that cannot be guided during training. However, our goal is to extract affordance-specific cues from exocentric images, and use these cues as explicit supervision for the egocentric view. Therefore, in order to obtain localization maps during the training phase, we produce class-specific feature maps instead by adding a class-aware convolution layer, which has proven to be identical to the generation process in CAM [50]. Specifically, for input images $\{I_{exo}, I_{ego}\}$ ( $I_{exo} = \{I_1, I_2, \dots, I_N\}$ ), we first extract deep features $\{\mathcal{F}_{exo}, \mathcal{F}_{ego}\} \in \mathbb{R}^{D \times H \times W}$ using a network $\phi$ . In our case, $\phi$ is a self-supervised vision transformer (DINO-ViT), whose features are part-aware and provide good part-level correspondences. We then generate localization maps $\mathcal{P}$ and classification scores $z$ as follows: + +$$ +\mathcal {P} = \psi_ {c a m} (\mathcal {F}) \in \mathbb {R} ^ {C \times H \times W}, \quad \boldsymbol {z} = \operatorname {G A P} (\mathcal {P}) \in \mathbb {R} ^ {C}, (1) +$$ + +where $\psi_{cam}$ starts with a projection layer consisting of a feed-forward layer followed by two convolutions to fine + +![](images/55dcdba5ed7f55a397e4b696705f04d172f4613372f98e97ade7196a429b46e6.jpg) +Figure 3. Overview of the proposed LOCATE framework. It achieves part-level knowledge transfer in three steps: 1) locating interaction regions with $\psi_{cam}$ (Sec. 3.1), 2) object-part embedding selection with PartSelect (Sec. 3.2), and 3) part-level knowledge transfer with $L_{cos}$ (Sec. 3.3). Details for PartSelect are shown in Fig. 4. At test time, only the egocentric branch is maintained. + +tune features for the HOI recognition task, i.e., recognizing actions shown in the exocentric images. Then a $1 \times 1$ class-aware convolution layer is added to yield localization maps, converting the number of channels to $C$ , where $C$ denotes the number of total interaction categories. Therefore, each map $\mathcal{P}_c \in \mathbb{R}^{H \times W}$ represents the network activation for the $c$ -th interaction. Next, $\mathcal{P}$ is fed to a global average pooling (GAP) layer to obtain classification scores $z$ , which are used to calculate cross-entropy loss $\mathcal{L}_{cls}$ for optimization. + +We notice that localization maps for the exocentric branch $\mathcal{P}_{exo}$ concentrate on the interaction areas, i.e., where the action takes place. Since interaction areas carry strong affordance information, we therefore aim to collect embeddings from the high activation regions in exocentric localization maps. Specifically, we first extract the localization map corresponding to ground-truth class, and conduct min-max normalization to constrain activation values to [0, 1]. After that, we set a threshold $\tau$ to control the number of extracted embeddings, therefore embeddings with activation value greater than $\tau$ in the localization map will be extracted from deep features. For multiple exocentric images, embeddings are extracted separately to produce $f_{exo} = [f_1, \dots, f_N]$ , each $f_n$ containing a different number of embeddings. All embeddings are then concatenated together $f_{exo} \in \mathbb{R}^{L \times D}$ , where $L$ denotes the number of embeddings. + +# 3.2. Object-Part Embedding Selection + +In general, interaction areas are composed of human, object part, and background. Our objective is to eliminate the interference information, and purely deliver embeddings representing the object part to guide the egocentric branch. + +In consequence, we design PartSelect to choose affordance-related embeddings from exocentric branch. PartSelect is illustrated in Fig. 4a. We first perform k-means clustering to get $K$ compact prototypes $\pmb{p} \in \mathbb{R}^{K \times D}$ from extracted exocentric embeddings. Next, we compute the cosine distance between each prototype and the egocentric deep features $\mathcal{F}_{ego}$ to get similarity maps $\mathcal{S} \in \mathbb{R}^{K \times H \times W}$ : + +$$ +S ^ {k, u, v} = \frac {\boldsymbol {p} _ {k} \cdot \mathcal {F} _ {e g o} ^ {u , v}}{\| \boldsymbol {p} _ {k} \| \| \mathcal {F} _ {e g o} ^ {u , v} \|.} \tag {2} +$$ + +Owing to the fine-grained semantic information of DINOViT deep features, embeddings of the same object parts bear high similarity. + +To distinguish which prototype stands for the object part, we aggregate the self-attention maps from the last layer of the DINO-ViT to generate a saliency map $\mathcal{A} \in \mathbb{R}^{H \times W}$ for the egocentric image. Given the saliency map and similarity maps, we introduce a metric $\gamma \in [0,1]$ termed PartIoU to measure if a prototype carries object part information. The PartIoU for the $k$ -th prototype is defined as follows: + +$$ +\gamma = \frac {1}{2} \frac {\overline {{\mathcal {S} _ {k}}} \cap \overline {{\mathcal {A}}}}{\overline {{\mathcal {S} _ {k}}}} + \frac {1}{2} \frac {\overline {{\mathcal {A}}}}{\overline {{\mathcal {S} _ {k}}} \cup \overline {{\mathcal {A}}}}, \tag {3} +$$ + +where $\overline{S_k}$ , $\overline{\mathcal{A}}\in \{0,1\}^{H\times W}$ are binary masks, we set the threshold as the average of each map to perform binarization. The motivation of PartIoU is fairly straightforward, if $\overline{S}$ belongs to a portion of $\overline{\mathcal{A}}$ , then the intersection of $\overline{S}$ and $\overline{\mathcal{A}}$ should equal $\overline{S}$ itself, while the union of the two masks should be identical to $\overline{\mathcal{A}}$ . Finally, when the maximum PartIoU among $K$ prototypes is above a threshold $\mu$ , PartS-select will output the prototype with the largest PartIoU as + +![](images/b6bdd2a99e96e468df6d55aa701ae99027fc247500b7fb7ae083d3f9531f577b.jpg) +(a) Illustration of PartSelect. + +![](images/b61eff7adeca7c5fe93e08e6d73b1dc0534035dec182ad56266b1c97e1a32270.jpg) +Exo-image + +![](images/9c21c273ff5f08fcb07f48183f19798f03878b40cee8258d7ce06ddf92371077.jpg) +Object Part + +![](images/f9b649063f7b360addf3c367e34a36274b363a049bf088ae2b616a5babfe53cd.jpg) +Background +Figure 4. (a) PartSelect picks the object-part prototype through clustering and selection, where $\otimes$ denotes the calculation for PartIOU score. (b) The similarity maps between prototypes and exocentric features confirm our statement that each prototype represents the object part, background, and human. + +![](images/0a262ac6e6253399b37ccb35e8d56cefd730744dfcb93354ead2e6111f57eca0.jpg) +Human +(b) Exocentric similarity maps. + +the object-part representation. Otherwise, no prototype will be selected for the next step. In Fig. 4b, we visualize the similarity maps between prototypes and exocentric features to demonstrate that the extracted embeddings are clustered into human, object part, and background. + +# 3.3. Part-Level Knowledge Transfer + +With the help of PartSelect, we find the prototype $f_{op}$ that represents the object part. We then leverage it to perform supervision for egocentric localization maps $\mathcal{P}_{ego}$ . Concretely, we first perform masked average pooling (MAP) between the normalized localization map and extracted deep features to aggregate into one embedding: + +$$ +f _ {e g o} = \frac {\sum_ {u = 1 , v = 1} ^ {W , H} \mathcal {F} _ {e g o} ^ {u , v} \mathcal {P} _ {e g o} ^ {t , u , v}}{\sum_ {i = 1 , j = 1} ^ {W , H} \mathcal {P} _ {e g o} ^ {t , u , v}} \in \mathbb {R} ^ {D}, \tag {4} +$$ + +where $t$ denotes the ground-truth category. Then, a cosine embedding loss is applied to pull the embedding $f_{ego}$ to- + +wards the direction of $f_{op}$ : + +$$ +\mathcal {L} _ {c o s} = \max \left(1 - \frac {f _ {o p} \cdot f _ {e g o}}{\| f _ {o p} \| \| f _ {e g o} \|} - \alpha , 0\right), \tag {5} +$$ + +as the two embeddings come from different domains, we thereby add $\alpha$ as a margin to compensate the domain gap. + +In addition, since the affordance region typically denotes a portion of an object, we can thus impose a geometry loss to regulate its distribution. Inspired by the co-part segmentation work [24], we add a concentration loss to encourage egocentric localization maps to form a concentrated and connected component. The concentration loss is formulated as + +$$ +\bar {u} _ {c} = \sum_ {u, v} u \cdot \mathcal {P} _ {e g o} ^ {c, u, v} / z _ {k}, \bar {v} _ {c} = \sum_ {u, v} v \cdot \mathcal {P} _ {e g o} ^ {c, u, v} / z _ {k}, \tag {6} +$$ + +$$ +\mathcal {L} _ {c} = \sum_ {c} \sum_ {u, v} \| \langle u, v \rangle - \langle \bar {u} _ {c}, \bar {v} _ {c} \rangle \| \cdot \mathcal {P} _ {e g o} ^ {c, u, v} / z _ {c}, \tag {7} +$$ + +where $\overline{u}_c$ and $\overline{v}_c$ represents the center of the $c$ -th localization map along axis $u, v$ , and $z_c = \sum_{u,v} \mathcal{P}_{ego}^{c,u,v}$ is a normalization term. The concentration loss forces the high activation regions of the localization maps to be close to the geometric center. + +Overall, we train the whole framework in an end-to-end manner, and use the following loss to optimize the model: + +$$ +\mathcal {L} = \mathcal {L} _ {c l s} + \lambda_ {c o s} \mathcal {L} _ {c o s} + \lambda_ {c} \mathcal {L} _ {c}, \tag {8} +$$ + +where $\lambda_{cos}$ , and $\lambda_{c}$ are loss weights that balance the three terms. $\mathcal{L}_{cls}$ stands for the cross-entropy losses from the two branches. At test time, only the ego branch is maintained, taking an affordance label $t$ and an egocentric image as input, the network extracts the $t$ -th localization map as the prediction of affordance region. + +# 4. Experiments + +# 4.1. Experimental Setting + +Dataset and Metrics. We evaluate our method in the Affordance Grounding Dataset (AGD20K) [33], which is the only large-scale image dataset with both exocentric and egocentric views. AGD20K is comprised of 20,061 exocentric images and 3,755 egocentric images, and is annotated with 36 commonly used affordances. Following prior affordance grounding work [14,38], the ground truth of this dataset initially consists of densely annotated points in corresponding affordance regions, and a Gaussian blur is then applied over each point to get final heatmaps. Moreover, AGD20K can be evaluated in two different settings: 1) In the seen setting, object categories in training and test sets are identical. 2) In the unseen setting, there is no object category intersection between training and test sets, e.g., the + +
State-of-the-Art from Relevant TasksSeenUnseen
KLD↓SIM↑NSS↑KLD↓SIM↑NSS↑
Weakly Supervised Object Localization*EIL [34]1.9310.2850.5222.1670.2270.330
SPA [40]5.5280.2210.3577.4250.1690.262
TS-CAM [16]1.8420.2600.3362.1040.2010.151
Weakly Supervised Affordance GroundingHotspots [38]1.7730.2780.6151.9940.2370.577
Cross-view-AG [33]1.5380.3340.9271.7870.2850.829
Cross-view-AG+ [32]1.4890.3420.9811.7650.2790.882
AffCorrs† [18]1.4070.3591.0261.6180.3481.021
LOCATE (Ours)1.2260.4011.1771.4050.3721.157
+ +model observes how humans hold a hammer and anticipates where to hold a knife. + +As for the metrics, referring to previous affordance grounding work [14, 30, 33, 38], we adopt the commonly used Kullback-Leibler Divergence (KLD), Similarity (SIM), and Normalized Scanpath Saliency (NSS) to evaluate the similarity and correspondence of distributions between ground truth and prediction. Detailed calculation of each metric is shown in the supplementary material. + +Implementation Details. We use the ImageNet [11] pretrained (without supervision) DINO-ViT-S [6] with patch size 16 to generate deep features. In each iteration, N exocentric images along with one egocentric image are taken as input (N is set to 3). Images are first resized to $256 \times 256$ and then randomly cropped to $224 \times 224$ followed by random horizontal flipping. SGD with learning rate 1e-3, weight decay 5e-4, and batch size 16 is used for parameter optimization. Loss weight coefficients $(\lambda_{cos}, \lambda_c)$ are set to (1, 0.07), and the margin $\alpha$ is set to 0.5. For the first epoch, we warm up the network without $\mathcal{L}_{cos}$ , as initial localization maps are not accurate for supervision. + +# 4.2. Comparison to State-of-the-Art + +To conduct a comprehensive comparison, we also display the results of state-of-the-art methods from a relevant task, i.e., weakly supervised object localization. As shown in Table 1, in both seen and unseen settings, LOCATE outperforms all other methods with a considerable margin on all metrics. In particular, compared to the state-of-the-art affordance grounding method Cross-view-AG+ [32], we improve the KLD by $20.4\%$ , SIM by $33.3\%$ , and NSS by $31.2\%$ in the unseen setting. Cross-view-AG+ is an extended version of Cross-view-AG, but still performs the knowledge transfer based on global pooled embeddings at the image level, thus bringing only minor improvement. AffCorrs [18] is a method that focuses on one-shot part affordance grounding, and it also uses the pretrained DINO-ViT + +Table 1. Comparison to state-of-the-arts from relevant tasks on AGD20K dataset. Results of * are taken from [33], and † denotes the adapted AffCorrs. The best and second-best results are highlighted in bold and underlined, respectively (↑/↓ means higher/lower is better). + +
MethodsParams (M)Time (s)
EIL [34]42.410.019
SPA [40]69.280.081
TS-CAM [16]85.860.023
Hotspots [38]132.640.087
Cross-view-AG [33]120.030.023
Cross-view-AG+ [32]82.270.022
AffCorrs† [18]6.500.205
LOCATE (Ours)6.500.011
+ +Table 2. Comparison of learnable parameters and inference time. The inference time is evaluated on a 3090Ti GPU. $\dagger$ denotes the adapted AffCorrs. + +features to do part matching. However, AffCorrs needs a pixel-level mask as a query, and there is no domain gap during the knowledge transfer. To make AffCorrs comparable in our problem setting, we adapt its structure by replacing the query annotated mask with our CAM estimator. The results verify that AffCorrs can also achieve good performance, but still considerably inferior to LOCATE. + +In Table 2, we make comparisons in terms of model parameters and inference time. Since our framework is built on a frozen small-sized vision transformer (ViT-small), the training process is efficient with a small number of parameters. For example, LOCATE only has $5.4\%$ of learnable parameters in Cross-view-AG. Additionally, we use a large patch size 16 for the vision transformer, which constrains the input sequence length and greatly reduces computation cost. Therefore, the inference time of LOCATE is also faster than most other methods. By contrast, the adapted AffCorrs runs much slower than LOCATE, as it incorporates an additional CRF post-processing step. + +We further visualize the qualitative comparisons with state-of-the-art affordance grounding methods. As shown in Fig. 5, we compare our results with Hotspots [38], Cross- + +![](images/311ebddec46f4aede121d2598794e930c3e9c061342e56b0f6575d855b8672b3.jpg) +Figure 5. Qualitative comparison between our approach and state-of-the-art affordance grounding methods (Hotspots [38], Cross-view-AG [33], and Cross-view-AG+ [32]). For the unseen setting, the displayed objects are not in the training set. For example, the model learns where a motorcycle can be ridden in training, and locates rideable area for the bicycle at test time. + +![](images/04dc063f6e47ca9494caf5b55967368e42503d321f1a2fa5ad1c3384cea64c06.jpg) + +view-AG [33] and Cross-view-AG+ [32]. We observe that the proposed LOCATE can make more concentrated and accurate predictions. Especially for complex objects like bicycles and refrigerators, even in the unseen setting, our method can still locate the saddle of bicycles for riding, and the handle of fridges for opening. In comparison, the results of Cross-view-AG for bicycles are quite noisy. More visualization results are in the supplementary material. + +# 4.3. Ablation Study + +Knowledge Transfer Manner. We first investigate the impact of knowledge transfer manner. Previous affordance grounding methods [33, 38] simply pull close the global embeddings (produced by global average pooling) of two branches to perform global knowledge transfer (GKT). In contrast, we set up an experiment to implement regional knowledge transfer (RKT), which generates the embeddings via masked average pooling between CAM-produced localization maps and feature maps. The results are shown in Table 3, regional knowledge transfer (RKT) outperforms global knowledge transfer (GKT) on all metrics, demonstrating the effectiveness of filtering irrelevant information. + +
MethodSeenUnseen
KLD↓SIM↑NSS↑KLD↓SIM↑NSS↑
GKT1.7320.2670.8101.9710.2210.626
RKT1.5160.3201.0741.8230.2590.850
+ Lc1.4910.3261.0911.7500.2740.948
+S1.2360.3971.1781.4390.3581.130
+S + Lc1.2260.4011.1771.4050.3721.157
+ +Table 3. Ablation results of the proposed LOCATE framework. GKT/RKT means global/regional knowledge transfer. $\mathcal{S}$ denotes PartSelect combined with ${\mathcal{L}}_{cos}$ ,and ${\mathcal{L}}_{c}$ is the concentration loss. + +PartSelect and Concentration Loss. Based on the regional knowledge transfer, we analyze the effect of PartSelect and concentration loss. As shown in Table 3, directly applying the concentration loss $\mathcal{L}_c$ can only bring marginal improvement. The reason is $\mathcal{L}_c$ can make egocentric predictions more concentrated, but fail to guide it to focus on the right affordance area. Nonetheless, when adding PartSelect and using cosine embedding loss $\mathcal{L}_{cos}$ as explicit supervision, the performance is greatly boosted, which proves the effectiveness of the part-level knowledge transfer scheme. In ad + +![](images/36a9f6af048fa107f3955542288508985f1751d2f41ee59b92806cd1e9707efd.jpg) +GKT +RKT +$\mathrm{RKT} + \mathcal{S}$ +$\mathrm{RKT} + \mathcal{S} + \mathcal{L}_c$ +GT +Figure 6. Visualization of the qualitative improvements. + +dition, to check the qualitative improvement, we visualize the affordance grounding results in Fig. 6. It is clear that GKT tends to locate the wrong affordance area, while RKT can sometimes find the right region, but only give coarse grounding results. After adding PartSelect, the results become much more part-focused, and the concentration loss further makes the grounding maps more robust. + +Number of Prototypes/Exocentric Images. We then explore the impact from the number of prototypes $K$ and exocentric images $N$ . From Fig. 7a, we observe that the model yields the best performance with three prototypes in seen setting, which is consistent with our statement that interaction areas typically consist of human, object part, and background information. While for the unseen setting, $N = 5$ achieves the best results, but improvement is minor. One reason lies in that more prototypes segment objects into more small parts, which boosts the generalization ability. As for the number of exocentric images, we find that more exocentric images can alleviate the impact of interaction diversity and occlusion, thus providing more robust knowledge for the egocentric branch. As shown in Fig. 7b, the model gets largely improved when increasing the number of exocentric images from 1 to 3 in both seen and unseen settings. Finally, we set both $N$ and $K$ to 3. + +Different Feature Extractors. In LOCATE, we employ pretrained DINO features based on ViT, which have been proven to encode high-level semantic information [1]. To investigate the impact of different backbones, we conducted experiments with DINO features trained on the ResNet-50 [22]. From the results in Table 4, we observe that using DINO-ViT features directly (without the proposed PartSelect) can only obtain similar or even inferior results to their ResNet counterpart. After incorporating PartSelect, the results of both backbone features can be improved under the seen setting, but ViT features show better potential in en + +![](images/faf841811f9ddc107d021346d8e1d58b48488ccf5cd95270144381bbedfae89e.jpg) + +![](images/1fee8df9dce98992a513d69bdff480909f04f480bdbac81bb631813fd37e1b49.jpg) +(a) Number of prototypes $N$ +(b) Number of exocentric images $K$ +Figure 7. Ablation study on the number of prototypes and exocentric images (lower is better). + +
RN-50ViT-S/16PartSelectKLD↓SIM↑NSS↑
Seen✓1.4820.3341.005
✓1.4910.3261.091
✓✓1.4490.3401.021
✓✓1.2260.4011.177
Unseen✓1.7010.2870.962
✓1.7500.2740.948
✓✓1.7070.2870.949
✓✓1.4050.3721.157
+ +Table 4. Ablation study on different feature extractors. + +hancing the performance due to their part-aware property. In the unseen setting, PartSelect does not yield improvement for ResNet-based features, while ViT features obtain consistent gains. + +# 5. Conclusion + +In this paper, we propose a framework named LOCATE to address the weakly supervised affordance grounding task by observing human-object interaction images. Specifically, we first localize where the interaction happens for the exocentric interactions, and then design a module called PartSelect to pick the affordance-specific information from the interaction regions. Finally, we transfer the learned knowledge to the egocentric view to perform affordance grounding with only image-level affordance labels. The proposed LOCATE achieves state-of-the-art results with far fewer parameters and faster inference speed. + +Acknowledgement. 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State-of-the-art methods in weakly supervised affordance grounding often fail to make accurate predictions for objects with complex structures, e.g., chairs and bicycles. To address this, our model (LOCATE) focuses on localizing and transferring features of object parts, which is able to produce more accurate results." + } + ] + } + ], + "index": 26, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 298, + 228, + 374, + 291 + ], + "blocks": [ + { + "bbox": [ + 298, + 228, + 374, + 291 + ], + "lines": [ + { + "bbox": [ + 298, + 228, + 374, + 291 + ], + "spans": [ + { + "bbox": [ + 298, + 228, + 374, + 291 + ], + "type": "image", + "image_path": "c0d3d5b7b4a0f5d393701016ab781f7828da21f8f3be109b93020a5a38787020.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 298, + 292, + 374, + 354 + ], + "blocks": [ + { + "bbox": [ + 298, + 292, + 374, + 354 + ], + "lines": [ + { + "bbox": [ + 298, + 292, + 374, + 354 + ], + "spans": [ + { + "bbox": [ + 298, + 292, + 374, + 354 + ], + "type": "image", + "image_path": "5d842043f955f85afa58203785110dfa8fc72acc2fca935f774b8e8d99d512e7.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 299, + 355, + 372, + 365 + ], + "lines": [ + { + "bbox": [ + 299, + 355, + 372, + 365 + ], + "spans": [ + { + "bbox": [ + 299, + 355, + 372, + 365 + ], + "type": "text", + "content": "Cross-view-AG+ [32]" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + } + ], + "index": 18 + }, + { + "type": "image", + "bbox": [ + 376, + 228, + 452, + 291 + ], + "blocks": [ + { + "bbox": [ + 376, + 228, + 452, + 291 + ], + "lines": [ + { + "bbox": [ + 376, + 228, + 452, + 291 + ], + "spans": [ + { + "bbox": [ + 376, + 228, + 452, + 291 + ], + "type": "image", + "image_path": "cd96f218c7b8f4139845c72cc339673dac54c87751bc9de549dd99a87358d5b9.jpg" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_body" + } + ], + "index": 20 + }, + { + "type": "image", + "bbox": [ + 376, + 292, + 452, + 354 + ], + "blocks": [ + { + "bbox": [ + 376, + 292, + 452, + 354 + ], + "lines": [ + { + "bbox": [ + 376, + 292, + 452, + 354 + ], + "spans": [ + { + "bbox": [ + 376, + 292, + 452, + 354 + ], + "type": "image", + "image_path": "d1b1cc6b687e04fb4fef78952a4c71b646a13db7960d27dd54ba916803b8cba2.jpg" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 386, + 355, + 442, + 365 + ], + "lines": [ + { + "bbox": [ + 386, + 355, + 442, + 365 + ], + "spans": [ + { + "bbox": [ + 386, + 355, + 442, + 365 + ], + "type": "text", + "content": "LOCATE (Ours)" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_caption" + } + ], + "index": 21 + }, + { + "type": "image", + "bbox": [ + 454, + 229, + 529, + 292 + ], + "blocks": [ + { + "bbox": [ + 454, + 229, + 529, + 292 + ], + "lines": [ + { + "bbox": [ + 454, + 229, + 529, + 292 + ], + "spans": [ + { + "bbox": [ + 454, + 229, + 529, + 292 + ], + "type": "image", + "image_path": "ff574e1ad8d39e7dcee6c86003e535d285ea80a16d21b80728d76789a439472e.jpg" + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_body" + } + ], + "index": 23 + }, + { + "type": "image", + "bbox": [ + 454, + 293, + 529, + 354 + ], + "blocks": [ + { + "bbox": [ + 454, + 293, + 529, + 354 + ], + "lines": [ + { + "bbox": [ + 454, + 293, + 529, + 354 + ], + "spans": [ + { + "bbox": [ + 454, + 293, + 529, + 354 + ], + "type": "image", + "image_path": "0e002d25875712eb3807ec06ac43a6936291a963e550a317d43fd2a2d3e7e98e.jpg" + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 485, + 355, + 496, + 363 + ], + "lines": [ + { + "bbox": [ + 485, + 355, + 496, + 363 + ], + "spans": [ + { + "bbox": [ + 485, + 355, + 496, + 363 + ], + "type": "text", + "content": "GT" + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "image_caption" + } + ], + "index": 24 + }, + { + "bbox": [ + 143, + 412, + 192, + 424 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 412, + 192, + 424 + ], + "spans": [ + { + "bbox": [ + 143, + 412, + 192, + 424 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 46, + 432, + 289, + 684 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 432, + 289, + 684 + ], + "spans": [ + { + "bbox": [ + 46, + 432, + 289, + 684 + ], + "type": "text", + "content": "Humans excel at acquiring knowledge through observation. For example, we can learn to use new tools by watching demonstrations. This skill is fundamental for intelligent systems to interact with the world. A key step to acquire this skill is to identify what part of the object affords each action, which is called affordance grounding. In this paper, we address this problem and propose a framework called LOCATE that can identify matching object parts across images, to transfer knowledge from images where an object is being used (exocentric images used for learning), to images where the object is inactive (egocentric ones used to test). To this end, we first find interaction areas and extract their feature embeddings. Then we learn to aggregate the embeddings into compact prototypes (human, object part, and background), and select the one representing the object part. Finally, we use the selected prototype to guide affordance grounding. We do this in a weakly supervised manner, learning only from image-level affordance and object labels. Extensive experiments demonstrate that our approach outperforms state-of-the-art methods by a large margin on both seen and unseen objects.1" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 306, + 412, + 386, + 424 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 412, + 386, + 424 + ], + "spans": [ + { + "bbox": [ + 306, + 412, + 386, + 424 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 304, + 435, + 545, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 435, + 545, + 639 + ], + "spans": [ + { + "bbox": [ + 304, + 435, + 545, + 639 + ], + "type": "text", + "content": "A fundamental skill of humans is learning to interact with objects just by observing someone else performing those interactions [5]. For instance, even if we have never played tennis, we can easily learn where to hold the racket just by looking at a single or few photographs of those interactions. Such learning capabilities are essential for intelligent agents to understand what actions can be performed on a given object. Current visual systems often focus primarily on recognizing what objects are in the scene (passive perception), rather than on how to use objects to achieve certain functions (active interaction). To this end, a growing number of studies [3, 12, 26, 47] have begun to utilize affordance [17] as a medium to bridge the gap between passive perception and active interaction. In computer vision and robotics [2, 20], affordance typically refers to regions of an object that are available to perform a specific action, e.g., a knife handle affords holding, and its blade affords cutting." + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 304, + 642, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 714 + ], + "type": "text", + "content": "In this paper, we focus on the task of affordance grounding, i.e., locating the object regions used for a given action. Previous methods [10, 12, 14, 37, 39] have often treated affordance grounding as a fully supervised semantic segmentation task, which requires costly pixel-level annotations. Instead, we follow the more realistic setting [32, 33, 38]" + } + ] + } + ], + "index": 31 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 277, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 277, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 277, + 713 + ], + "type": "text", + "content": "1Project page: https://reagan1311.github.io/locate." + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10922" + } + ] + } + ], + "index": 33 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 70, + 289, + 223 + ], + "blocks": [ + { + "bbox": [ + 51, + 70, + 289, + 223 + ], + "lines": [ + { + "bbox": [ + 51, + 70, + 289, + 223 + ], + "spans": [ + { + "bbox": [ + 51, + 70, + 289, + 223 + ], + "type": "image", + "image_path": "b41e5344c1a50842eb5d95db5f1e964ff62fe1903f217b448e107b7f48477ff6.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 234, + 288, + 291 + ], + "lines": [ + { + "bbox": [ + 46, + 234, + 288, + 291 + ], + "spans": [ + { + "bbox": [ + 46, + 234, + 288, + 291 + ], + "type": "text", + "content": "Figure 2. General illustration of LOCATE. We first extract the embeddings under the region of interest where the exocentric interactions are happening, and then split these embeddings into several clusters. In the end, the prototype of the object-part cluster is selected to supervise the egocentric affordance grounding." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 315, + 287, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 315, + 287, + 469 + ], + "spans": [ + { + "bbox": [ + 46, + 315, + 287, + 469 + ], + "type": "text", + "content": "where the task is learning object affordances by observing human-object interaction images. That is, given some interaction images, such as those in Fig. 2, along with the corresponding label (e.g., \"hold\"), the aim is to learn affordance grounding on the novel instances of that object. This is a weakly-supervised problem setting where only the image-level labels are given without any per-pixel annotations. Concretely, given several third-person human-object interaction images (exocentric) and one target object image (egocentric), our goal is to extract affordance knowledge and cues from exocentric interactions, and perform affordance grounding in the egocentric view by using only affordance labels." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 472, + 288, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 472, + 288, + 687 + ], + "spans": [ + { + "bbox": [ + 46, + 472, + 288, + 687 + ], + "type": "text", + "content": "There are several key challenges underlying the problem of affordance grounding. The first is due to the nature of the supervision, where only image-level affordance labels are given, being a weakly supervised problem. Here, the system needs to automatically reason about affordance regions just from classification labels. Second, human-object interactions often introduce heavy occlusion of object parts by interacting humans. In other words, the object part that the system needs to predict for a particular affordance (e.g., a mug handle for the \"holding\" affordance) in an exocentric image can often be the part that is occluded (e.g., by hands). Third, interactions are of great diversity. The way humans interact with objects varies across individuals resulting in diverse egocentric interaction images. Lastly, there is a clear domain gap between exocentric and egocentric images where the former have clutter, occlusion etc., and the latter are cleaner (e.g., in Fig. 2). This makes affordance knowledge transfer particularly challenging." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "type": "text", + "content": "In this work, we propose a framework called LOCATE that addresses these core challenges by locating the exact" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 72, + 545, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 300 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 300 + ], + "type": "text", + "content": "object parts involved in the interaction from exocentric images and transferring this knowledge to inactive egocentric images. Refer to Fig. 2 for the illustration. Specifically, we first use the class activation mapping (CAM) [51] technique to find the regions of human-object-interaction in exocentric images. Despite being trained for the interaction recognition task, we observe that CAM can generate good localization maps for interaction regions. We then segment this region of interest further into regions corresponding to human, object part, and background. We do this by extracting embeddings and performing k-means clustering to obtain several compact prototypes. Next, we automatically predict which of these prototypes corresponds to the object part relevant to the affordance. To this end, we propose a module named PartSelect that leverages part-aware features and attention maps from a self-supervised vision transformer (DINO-ViT [6]) to obtain the desired prototype. Finally, we use the object-part prototype as a high-level pseudo supervision to guide egocentric affordance grounding." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 300, + 546, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 300, + 546, + 467 + ], + "spans": [ + { + "bbox": [ + 304, + 300, + 546, + 467 + ], + "type": "text", + "content": "Our contributions can be summarized as follows. (1) We propose a framework called LOCATE that extracts affordance knowledge from weakly supervised exocentric human-object interactions, and transfers this knowledge to the egocentric image in a localized manner. (2) We introduce a novel module termed PartSelect to pick affordancespecific cues from human-object interactions. The extracted information is then used as explicit supervision to guide affordance grounding on egocentric images. (3) LOCATE achieves state-of-the-art results with far fewer parameters and faster inference speed than previous methods, and is able to locate accurate affordance region for unseen objects. See Fig. 1 for examples of our results and comparison to state-of-the-art." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 478, + 392, + 491 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 478, + 392, + 491 + ], + "spans": [ + { + "bbox": [ + 306, + 478, + 392, + 491 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 498, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 545, + 713 + ], + "type": "text", + "content": "Visual Affordance Learning. Affordances are actively studied in robotics and computer vision due to their great potential to bridge the gap between perception and action. In general, affordance-related research in computer vision aims to localize objects or object parts where specific actions can be performed. Earlier work [10, 12, 27, 36] mainly focused on the fully supervised setting. Due to the scarcity of affordance datasets, this work normally required costly manual annotations to construct large-scale datasets [10, 37, 39, 42]. To alleviate the annotation and sensing requirement, new research [33, 38, 41, 42] explored acquiring affordance information in the weakly supervised setting. In particular, Sawatzky et al. [42] proposed a convolutional network to tackle affordance detection using only a few keypoint annotations, and Nagarajan et al. [38] introduced a method to infer the object affordance regions by directly learning from human-object interaction videos. In this work, we also focus on learning affordances from weak" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10923" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "content": "supervision, i.e., several human-object interaction images and corresponding image-level affordance labels." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 102, + 288, + 294 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 102, + 288, + 294 + ], + "spans": [ + { + "bbox": [ + 46, + 102, + 288, + 294 + ], + "type": "text", + "content": "Weakly Supervised Affordance Grounding. Unlike object localization that aims to find where the object is, in affordance grounding we focus on locating functional regions of objects, which is a more fine-grained localization task. Existing weakly supervised object localization [16, 25, 34, 40, 49, 50] and semantic segmentation methods [8, 9, 28, 48, 52] are mainly based on class activation mapping (CAM) [51], the seminal work that has greatly facilitated the development of weakly supervised learning. Similarly, most affordance grounding research [31, 33, 38] also adopted CAM or its variants [7, 43] to generate activation maps as prediction. However, previous work only used CAM in the inference stage, lacking proper supervision. In contrast, to provide explicit guidance at the training stage, we utilize CAM to produce localization maps in the forward pass and supervise it in a prototypical learning fashion." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 300, + 288, + 539 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 300, + 288, + 539 + ], + "spans": [ + { + "bbox": [ + 46, + 300, + 288, + 539 + ], + "type": "text", + "content": "Knowledge Distillation across Domains. Knowledge distillation [23] is a process of transferring knowledge from a network to another, where inputs normally come from the same domain. Recently, many studies [14, 29, 33, 38, 44] have begun to pay more attention to knowledge distillation in different domains. This work transferred representations from the domain with numerous datasets to the other one that typically has low dataset scale and diversity, so that the model can benefit from the large quantity of data in the first domain. For instance, Li et al. [29] proposed a framework to learn egocentric video representations from largescale third-person video datasets, and Luo et al [33] devised a knowledge transfer architecture to transfer affordancespecific features from exocentric view to egocentric view. In this paper, we follow the same setting as [33], using exocentric (third-person) human-object interaction images as the learning target. The objective of this work is to observe where and how humans interact with an object when doing a specific action, and then transfer the knowledge onto the target object." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 545, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 287, + 713 + ], + "type": "text", + "content": "Self-supervised Vision Transformer. Self-supervised Vision Transformers (ViT) [13], such as DINO [6], MAE [21], and BEiT [4], have demonstrated immense potential in unsupervised dense prediction tasks. Specifically, the features extracted from the self-attention layer exhibit the ability to separate different objects and generate reliable pseudo segmentation maps without requiring any manual annotations. Building on this property, recent work [15, 18, 19, 35, 45, 46] has achieved exceptional results in unsupervised segmentation and localization. Notably, Amir et al. [1] demonstrated that the pretrained features extracted from DINO-ViT encode fine-grained semantic information, which can yield excellent performance for part co-segmentation and semantic correspondence. Inspired by this work, we leverage DINO" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "content": "ViT features to identify matching object parts between exocentric and egocentric images." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 106, + 362, + 118 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 106, + 362, + 118 + ], + "spans": [ + { + "bbox": [ + 306, + 106, + 362, + 118 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 125, + 545, + 233 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 125, + 545, + 233 + ], + "spans": [ + { + "bbox": [ + 304, + 125, + 545, + 233 + ], + "type": "text", + "content": "Given several exocentric interaction images and one egocentric object image, our goal is to extract affordance-related knowledge from exocentric interactions, and transfer it to egocentric images so that the affordance region can be located even for an inactive object. During training, the only supervision available are image-level affordance labels. In the inference stage, taking an egocentric image and an affordance label as input, the model needs to predict the corresponding affordance region." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 233, + 546, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 233, + 546, + 413 + ], + "spans": [ + { + "bbox": [ + 304, + 233, + 546, + 413 + ], + "type": "text", + "content": "The core idea of our approach is to exclude distracting information, e.g., human and background, when extracting affordance-specific features from the exocentric view, and perform fine-grained part-level knowledge transfer from exocentric images to egocentric ones. To this end, we set up the framework LOCATE to transfer the knowledge in three steps (See Fig. 3). First, we utilize CAM to generate localization maps for exocentric images, and extract corresponding feature embeddings with high activation in the localization maps (Sec. 3.1). Then, we propose PartSelect that leverages part-aware deep features to remove irrelevant information while preserving embeddings that can represent affordance cues (Sec. 3.2). Finally, we use the output from PartSelect to supervise the egocentric affordance grounding in an explicit manner (Sec. 3.3)." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 418, + 466, + 431 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 418, + 466, + 431 + ], + "spans": [ + { + "bbox": [ + 306, + 418, + 466, + 431 + ], + "type": "text", + "content": "3.1. Locating Interaction Regions" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 437, + 545, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 437, + 545, + 664 + ], + "spans": [ + { + "bbox": [ + 304, + 437, + 545, + 664 + ], + "type": "text", + "content": "To determine where neural networks focus on for recognition, we adopt the technique of CAM [51] to generate class-aware localization maps, which has been widely used in weakly supervised tasks. The vanilla CAM generates localization maps as a post-processing step that cannot be guided during training. However, our goal is to extract affordance-specific cues from exocentric images, and use these cues as explicit supervision for the egocentric view. Therefore, in order to obtain localization maps during the training phase, we produce class-specific feature maps instead by adding a class-aware convolution layer, which has proven to be identical to the generation process in CAM [50]. Specifically, for input images " + }, + { + "bbox": [ + 304, + 437, + 545, + 664 + ], + "type": "inline_equation", + "content": "\\{I_{exo}, I_{ego}\\}" + }, + { + "bbox": [ + 304, + 437, + 545, + 664 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 304, + 437, + 545, + 664 + ], + "type": "inline_equation", + "content": "I_{exo} = \\{I_1, I_2, \\dots, I_N\\}" + }, + { + "bbox": [ + 304, + 437, + 545, + 664 + ], + "type": "text", + "content": "), we first extract deep features " + }, + { + "bbox": [ + 304, + 437, + 545, + 664 + ], + "type": "inline_equation", + "content": "\\{\\mathcal{F}_{exo}, \\mathcal{F}_{ego}\\} \\in \\mathbb{R}^{D \\times H \\times W}" + }, + { + "bbox": [ + 304, + 437, + 545, + 664 + ], + "type": "text", + "content": " using a network " + }, + { + "bbox": [ + 304, + 437, + 545, + 664 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 304, + 437, + 545, + 664 + ], + "type": "text", + "content": ". In our case, " + }, + { + "bbox": [ + 304, + 437, + 545, + 664 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 304, + 437, + 545, + 664 + ], + "type": "text", + "content": " is a self-supervised vision transformer (DINO-ViT), whose features are part-aware and provide good part-level correspondences. We then generate localization maps " + }, + { + "bbox": [ + 304, + 437, + 545, + 664 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 304, + 437, + 545, + 664 + ], + "type": "text", + "content": " and classification scores " + }, + { + "bbox": [ + 304, + 437, + 545, + 664 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 304, + 437, + 545, + 664 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 311, + 669, + 545, + 685 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 311, + 669, + 545, + 685 + ], + "spans": [ + { + "bbox": [ + 311, + 669, + 545, + 685 + ], + "type": "interline_equation", + "content": "\\mathcal {P} = \\psi_ {c a m} (\\mathcal {F}) \\in \\mathbb {R} ^ {C \\times H \\times W}, \\quad \\boldsymbol {z} = \\operatorname {G A P} (\\mathcal {P}) \\in \\mathbb {R} ^ {C}, (1)", + "image_path": "96c29a0c9471ef2fa639dc9da1692d333acf69d40673954ff533240b8f090c07.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\psi_{cam}" + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": " starts with a projection layer consisting of a feed-forward layer followed by two convolutions to fine" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "10924" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 60, + 70, + 534, + 270 + ], + "blocks": [ + { + "bbox": [ + 60, + 70, + 534, + 270 + ], + "lines": [ + { + "bbox": [ + 60, + 70, + 534, + 270 + ], + "spans": [ + { + "bbox": [ + 60, + 70, + 534, + 270 + ], + "type": "image", + "image_path": "55dcdba5ed7f55a397e4b696705f04d172f4613372f98e97ade7196a429b46e6.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 277, + 546, + 310 + ], + "lines": [ + { + "bbox": [ + 46, + 277, + 546, + 310 + ], + "spans": [ + { + "bbox": [ + 46, + 277, + 546, + 310 + ], + "type": "text", + "content": "Figure 3. Overview of the proposed LOCATE framework. It achieves part-level knowledge transfer in three steps: 1) locating interaction regions with " + }, + { + "bbox": [ + 46, + 277, + 546, + 310 + ], + "type": "inline_equation", + "content": "\\psi_{cam}" + }, + { + "bbox": [ + 46, + 277, + 546, + 310 + ], + "type": "text", + "content": " (Sec. 3.1), 2) object-part embedding selection with PartSelect (Sec. 3.2), and 3) part-level knowledge transfer with " + }, + { + "bbox": [ + 46, + 277, + 546, + 310 + ], + "type": "inline_equation", + "content": "L_{cos}" + }, + { + "bbox": [ + 46, + 277, + 546, + 310 + ], + "type": "text", + "content": " (Sec. 3.3). Details for PartSelect are shown in Fig. 4. At test time, only the egocentric branch is maintained." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 331, + 287, + 439 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 331, + 287, + 439 + ], + "spans": [ + { + "bbox": [ + 46, + 331, + 287, + 439 + ], + "type": "text", + "content": "tune features for the HOI recognition task, i.e., recognizing actions shown in the exocentric images. Then a " + }, + { + "bbox": [ + 46, + 331, + 287, + 439 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 46, + 331, + 287, + 439 + ], + "type": "text", + "content": " class-aware convolution layer is added to yield localization maps, converting the number of channels to " + }, + { + "bbox": [ + 46, + 331, + 287, + 439 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 331, + 287, + 439 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 331, + 287, + 439 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 331, + 287, + 439 + ], + "type": "text", + "content": " denotes the number of total interaction categories. Therefore, each map " + }, + { + "bbox": [ + 46, + 331, + 287, + 439 + ], + "type": "inline_equation", + "content": "\\mathcal{P}_c \\in \\mathbb{R}^{H \\times W}" + }, + { + "bbox": [ + 46, + 331, + 287, + 439 + ], + "type": "text", + "content": " represents the network activation for the " + }, + { + "bbox": [ + 46, + 331, + 287, + 439 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 331, + 287, + 439 + ], + "type": "text", + "content": "-th interaction. Next, " + }, + { + "bbox": [ + 46, + 331, + 287, + 439 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 46, + 331, + 287, + 439 + ], + "type": "text", + "content": " is fed to a global average pooling (GAP) layer to obtain classification scores " + }, + { + "bbox": [ + 46, + 331, + 287, + 439 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 331, + 287, + 439 + ], + "type": "text", + "content": ", which are used to calculate cross-entropy loss " + }, + { + "bbox": [ + 46, + 331, + 287, + 439 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{cls}" + }, + { + "bbox": [ + 46, + 331, + 287, + 439 + ], + "type": "text", + "content": " for optimization." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 441, + 288, + 632 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 441, + 288, + 632 + ], + "spans": [ + { + "bbox": [ + 46, + 441, + 288, + 632 + ], + "type": "text", + "content": "We notice that localization maps for the exocentric branch " + }, + { + "bbox": [ + 46, + 441, + 288, + 632 + ], + "type": "inline_equation", + "content": "\\mathcal{P}_{exo}" + }, + { + "bbox": [ + 46, + 441, + 288, + 632 + ], + "type": "text", + "content": " concentrate on the interaction areas, i.e., where the action takes place. Since interaction areas carry strong affordance information, we therefore aim to collect embeddings from the high activation regions in exocentric localization maps. Specifically, we first extract the localization map corresponding to ground-truth class, and conduct min-max normalization to constrain activation values to [0, 1]. After that, we set a threshold " + }, + { + "bbox": [ + 46, + 441, + 288, + 632 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 46, + 441, + 288, + 632 + ], + "type": "text", + "content": " to control the number of extracted embeddings, therefore embeddings with activation value greater than " + }, + { + "bbox": [ + 46, + 441, + 288, + 632 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 46, + 441, + 288, + 632 + ], + "type": "text", + "content": " in the localization map will be extracted from deep features. For multiple exocentric images, embeddings are extracted separately to produce " + }, + { + "bbox": [ + 46, + 441, + 288, + 632 + ], + "type": "inline_equation", + "content": "f_{exo} = [f_1, \\dots, f_N]" + }, + { + "bbox": [ + 46, + 441, + 288, + 632 + ], + "type": "text", + "content": ", each " + }, + { + "bbox": [ + 46, + 441, + 288, + 632 + ], + "type": "inline_equation", + "content": "f_n" + }, + { + "bbox": [ + 46, + 441, + 288, + 632 + ], + "type": "text", + "content": " containing a different number of embeddings. All embeddings are then concatenated together " + }, + { + "bbox": [ + 46, + 441, + 288, + 632 + ], + "type": "inline_equation", + "content": "f_{exo} \\in \\mathbb{R}^{L \\times D}" + }, + { + "bbox": [ + 46, + 441, + 288, + 632 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 441, + 288, + 632 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 441, + 288, + 632 + ], + "type": "text", + "content": " denotes the number of embeddings." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 645, + 228, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 645, + 228, + 658 + ], + "spans": [ + { + "bbox": [ + 47, + 645, + 228, + 658 + ], + "type": "text", + "content": "3.2. Object-Part Embedding Selection" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "content": "In general, interaction areas are composed of human, object part, and background. Our objective is to eliminate the interference information, and purely deliver embeddings representing the object part to guide the egocentric branch." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 331, + 546, + 416 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 331, + 546, + 416 + ], + "spans": [ + { + "bbox": [ + 304, + 331, + 546, + 416 + ], + "type": "text", + "content": "In consequence, we design PartSelect to choose affordance-related embeddings from exocentric branch. PartSelect is illustrated in Fig. 4a. We first perform k-means clustering to get " + }, + { + "bbox": [ + 304, + 331, + 546, + 416 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 331, + 546, + 416 + ], + "type": "text", + "content": " compact prototypes " + }, + { + "bbox": [ + 304, + 331, + 546, + 416 + ], + "type": "inline_equation", + "content": "\\pmb{p} \\in \\mathbb{R}^{K \\times D}" + }, + { + "bbox": [ + 304, + 331, + 546, + 416 + ], + "type": "text", + "content": " from extracted exocentric embeddings. Next, we compute the cosine distance between each prototype and the egocentric deep features " + }, + { + "bbox": [ + 304, + 331, + 546, + 416 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{ego}" + }, + { + "bbox": [ + 304, + 331, + 546, + 416 + ], + "type": "text", + "content": " to get similarity maps " + }, + { + "bbox": [ + 304, + 331, + 546, + 416 + ], + "type": "inline_equation", + "content": "\\mathcal{S} \\in \\mathbb{R}^{K \\times H \\times W}" + }, + { + "bbox": [ + 304, + 331, + 546, + 416 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 376, + 423, + 545, + 451 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 376, + 423, + 545, + 451 + ], + "spans": [ + { + "bbox": [ + 376, + 423, + 545, + 451 + ], + "type": "interline_equation", + "content": "S ^ {k, u, v} = \\frac {\\boldsymbol {p} _ {k} \\cdot \\mathcal {F} _ {e g o} ^ {u , v}}{\\| \\boldsymbol {p} _ {k} \\| \\| \\mathcal {F} _ {e g o} ^ {u , v} \\|.} \\tag {2}", + "image_path": "96e6c4fa6fff12179c7c93d81c29fd101559f08e3e768552d5ab643bd62d5178.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 456, + 545, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 456, + 545, + 491 + ], + "spans": [ + { + "bbox": [ + 304, + 456, + 545, + 491 + ], + "type": "text", + "content": "Owing to the fine-grained semantic information of DINOViT deep features, embeddings of the same object parts bear high similarity." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 493, + 546, + 577 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 493, + 546, + 577 + ], + "spans": [ + { + "bbox": [ + 304, + 493, + 546, + 577 + ], + "type": "text", + "content": "To distinguish which prototype stands for the object part, we aggregate the self-attention maps from the last layer of the DINO-ViT to generate a saliency map " + }, + { + "bbox": [ + 304, + 493, + 546, + 577 + ], + "type": "inline_equation", + "content": "\\mathcal{A} \\in \\mathbb{R}^{H \\times W}" + }, + { + "bbox": [ + 304, + 493, + 546, + 577 + ], + "type": "text", + "content": " for the egocentric image. Given the saliency map and similarity maps, we introduce a metric " + }, + { + "bbox": [ + 304, + 493, + 546, + 577 + ], + "type": "inline_equation", + "content": "\\gamma \\in [0,1]" + }, + { + "bbox": [ + 304, + 493, + 546, + 577 + ], + "type": "text", + "content": " termed PartIoU to measure if a prototype carries object part information. The PartIoU for the " + }, + { + "bbox": [ + 304, + 493, + 546, + 577 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 493, + 546, + 577 + ], + "type": "text", + "content": "-th prototype is defined as follows:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 366, + 585, + 545, + 613 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 366, + 585, + 545, + 613 + ], + "spans": [ + { + "bbox": [ + 366, + 585, + 545, + 613 + ], + "type": "interline_equation", + "content": "\\gamma = \\frac {1}{2} \\frac {\\overline {{\\mathcal {S} _ {k}}} \\cap \\overline {{\\mathcal {A}}}}{\\overline {{\\mathcal {S} _ {k}}}} + \\frac {1}{2} \\frac {\\overline {{\\mathcal {A}}}}{\\overline {{\\mathcal {S} _ {k}}} \\cup \\overline {{\\mathcal {A}}}}, \\tag {3}", + "image_path": "2af8f19daaecd2ebb833584322decc38ee4fb6180075c2617f2824917c1953f5.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 616, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 616, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 616, + 547, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 616, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\overline{S_k}" + }, + { + "bbox": [ + 304, + 616, + 547, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 616, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\overline{\\mathcal{A}}\\in \\{0,1\\}^{H\\times W}" + }, + { + "bbox": [ + 304, + 616, + 547, + 714 + ], + "type": "text", + "content": " are binary masks, we set the threshold as the average of each map to perform binarization. The motivation of PartIoU is fairly straightforward, if " + }, + { + "bbox": [ + 304, + 616, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\overline{S}" + }, + { + "bbox": [ + 304, + 616, + 547, + 714 + ], + "type": "text", + "content": " belongs to a portion of " + }, + { + "bbox": [ + 304, + 616, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\overline{\\mathcal{A}}" + }, + { + "bbox": [ + 304, + 616, + 547, + 714 + ], + "type": "text", + "content": ", then the intersection of " + }, + { + "bbox": [ + 304, + 616, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\overline{S}" + }, + { + "bbox": [ + 304, + 616, + 547, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 616, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\overline{\\mathcal{A}}" + }, + { + "bbox": [ + 304, + 616, + 547, + 714 + ], + "type": "text", + "content": " should equal " + }, + { + "bbox": [ + 304, + 616, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\overline{S}" + }, + { + "bbox": [ + 304, + 616, + 547, + 714 + ], + "type": "text", + "content": " itself, while the union of the two masks should be identical to " + }, + { + "bbox": [ + 304, + 616, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\overline{\\mathcal{A}}" + }, + { + "bbox": [ + 304, + 616, + 547, + 714 + ], + "type": "text", + "content": ". Finally, when the maximum PartIoU among " + }, + { + "bbox": [ + 304, + 616, + 547, + 714 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 616, + 547, + 714 + ], + "type": "text", + "content": " prototypes is above a threshold " + }, + { + "bbox": [ + 304, + 616, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 304, + 616, + 547, + 714 + ], + "type": "text", + "content": ", PartS-select will output the prototype with the largest PartIoU as" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10925" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 65, + 72, + 270, + 278 + ], + "blocks": [ + { + "bbox": [ + 65, + 72, + 270, + 278 + ], + "lines": [ + { + "bbox": [ + 65, + 72, + 270, + 278 + ], + "spans": [ + { + "bbox": [ + 65, + 72, + 270, + 278 + ], + "type": "image", + "image_path": "b6bdd2a99e96e468df6d55aa701ae99027fc247500b7fb7ae083d3f9531f577b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 121, + 281, + 213, + 291 + ], + "lines": [ + { + "bbox": [ + 121, + 281, + 213, + 291 + ], + "spans": [ + { + "bbox": [ + 121, + 281, + 213, + 291 + ], + "type": "text", + "content": "(a) Illustration of PartSelect." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 48, + 296, + 108, + 342 + ], + "blocks": [ + { + "bbox": [ + 48, + 296, + 108, + 342 + ], + "lines": [ + { + "bbox": [ + 48, + 296, + 108, + 342 + ], + "spans": [ + { + "bbox": [ + 48, + 296, + 108, + 342 + ], + "type": "image", + "image_path": "b61eff7adeca7c5fe93e08e6d73b1dc0534035dec182ad56266b1c97e1a32270.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 65, + 344, + 94, + 353 + ], + "lines": [ + { + "bbox": [ + 65, + 344, + 94, + 353 + ], + "spans": [ + { + "bbox": [ + 65, + 344, + 94, + 353 + ], + "type": "text", + "content": "Exo-image" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 109, + 296, + 168, + 341 + ], + "blocks": [ + { + "bbox": [ + 109, + 296, + 168, + 341 + ], + "lines": [ + { + "bbox": [ + 109, + 296, + 168, + 341 + ], + "spans": [ + { + "bbox": [ + 109, + 296, + 168, + 341 + ], + "type": "image", + "image_path": "9c21c273ff5f08fcb07f48183f19798f03878b40cee8258d7ce06ddf92371077.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 119, + 344, + 157, + 352 + ], + "lines": [ + { + "bbox": [ + 119, + 344, + 157, + 352 + ], + "spans": [ + { + "bbox": [ + 119, + 344, + 157, + 352 + ], + "type": "text", + "content": "Object Part" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 168, + 296, + 227, + 341 + ], + "blocks": [ + { + "bbox": [ + 168, + 296, + 227, + 341 + ], + "lines": [ + { + "bbox": [ + 168, + 296, + 227, + 341 + ], + "spans": [ + { + "bbox": [ + 168, + 296, + 227, + 341 + ], + "type": "image", + "image_path": "f9b649063f7b360addf3c367e34a36274b363a049bf088ae2b616a5babfe53cd.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 179, + 344, + 219, + 353 + ], + "lines": [ + { + "bbox": [ + 179, + 344, + 219, + 353 + ], + "spans": [ + { + "bbox": [ + 179, + 344, + 219, + 353 + ], + "type": "text", + "content": "Background" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 377, + 287, + 433 + ], + "lines": [ + { + "bbox": [ + 46, + 377, + 287, + 433 + ], + "spans": [ + { + "bbox": [ + 46, + 377, + 287, + 433 + ], + "type": "text", + "content": "Figure 4. (a) PartSelect picks the object-part prototype through clustering and selection, where " + }, + { + "bbox": [ + 46, + 377, + 287, + 433 + ], + "type": "inline_equation", + "content": "\\otimes" + }, + { + "bbox": [ + 46, + 377, + 287, + 433 + ], + "type": "text", + "content": " denotes the calculation for PartIOU score. (b) The similarity maps between prototypes and exocentric features confirm our statement that each prototype represents the object part, background, and human." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 228, + 296, + 287, + 341 + ], + "blocks": [ + { + "bbox": [ + 228, + 296, + 287, + 341 + ], + "lines": [ + { + "bbox": [ + 228, + 296, + 287, + 341 + ], + "spans": [ + { + "bbox": [ + 228, + 296, + 287, + 341 + ], + "type": "image", + "image_path": "0a262ac6e6253399b37ccb35e8d56cefd730744dfcb93354ead2e6111f57eca0.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 245, + 344, + 269, + 351 + ], + "lines": [ + { + "bbox": [ + 245, + 344, + 269, + 351 + ], + "spans": [ + { + "bbox": [ + 245, + 344, + 269, + 351 + ], + "type": "text", + "content": "Human" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 117, + 357, + 217, + 368 + ], + "lines": [ + { + "bbox": [ + 117, + 357, + 217, + 368 + ], + "spans": [ + { + "bbox": [ + 117, + 357, + 217, + 368 + ], + "type": "text", + "content": "(b) Exocentric similarity maps." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 459, + 287, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 459, + 287, + 518 + ], + "spans": [ + { + "bbox": [ + 46, + 459, + 287, + 518 + ], + "type": "text", + "content": "the object-part representation. Otherwise, no prototype will be selected for the next step. In Fig. 4b, we visualize the similarity maps between prototypes and exocentric features to demonstrate that the extracted embeddings are clustered into human, object part, and background." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 533, + 218, + 547 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 533, + 218, + 547 + ], + "spans": [ + { + "bbox": [ + 47, + 533, + 218, + 547 + ], + "type": "text", + "content": "3.3. Part-Level Knowledge Transfer" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 555, + 287, + 626 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 555, + 287, + 626 + ], + "spans": [ + { + "bbox": [ + 46, + 555, + 287, + 626 + ], + "type": "text", + "content": "With the help of PartSelect, we find the prototype " + }, + { + "bbox": [ + 46, + 555, + 287, + 626 + ], + "type": "inline_equation", + "content": "f_{op}" + }, + { + "bbox": [ + 46, + 555, + 287, + 626 + ], + "type": "text", + "content": " that represents the object part. We then leverage it to perform supervision for egocentric localization maps " + }, + { + "bbox": [ + 46, + 555, + 287, + 626 + ], + "type": "inline_equation", + "content": "\\mathcal{P}_{ego}" + }, + { + "bbox": [ + 46, + 555, + 287, + 626 + ], + "type": "text", + "content": ". Concretely, we first perform masked average pooling (MAP) between the normalized localization map and extracted deep features to aggregate into one embedding:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 89, + 644, + 287, + 678 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 89, + 644, + 287, + 678 + ], + "spans": [ + { + "bbox": [ + 89, + 644, + 287, + 678 + ], + "type": "interline_equation", + "content": "f _ {e g o} = \\frac {\\sum_ {u = 1 , v = 1} ^ {W , H} \\mathcal {F} _ {e g o} ^ {u , v} \\mathcal {P} _ {e g o} ^ {t , u , v}}{\\sum_ {i = 1 , j = 1} ^ {W , H} \\mathcal {P} _ {e g o} ^ {t , u , v}} \\in \\mathbb {R} ^ {D}, \\tag {4}", + "image_path": "da58353d05588c4ff4fc391dd5dd37f7276eecf1e8126cb385ff812ae538cf9d.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 46, + 689, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 715 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 689, + 287, + 715 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 689, + 287, + 715 + ], + "type": "text", + "content": " denotes the ground-truth category. Then, a cosine embedding loss is applied to pull the embedding " + }, + { + "bbox": [ + 46, + 689, + 287, + 715 + ], + "type": "inline_equation", + "content": "f_{ego}" + }, + { + "bbox": [ + 46, + 689, + 287, + 715 + ], + "type": "text", + "content": " to-" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 72, + 414, + 85 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 414, + 85 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 414, + 85 + ], + "type": "text", + "content": "wards the direction of " + }, + { + "bbox": [ + 306, + 72, + 414, + 85 + ], + "type": "inline_equation", + "content": "f_{op}" + }, + { + "bbox": [ + 306, + 72, + 414, + 85 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 343, + 93, + 545, + 121 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 343, + 93, + 545, + 121 + ], + "spans": [ + { + "bbox": [ + 343, + 93, + 545, + 121 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {c o s} = \\max \\left(1 - \\frac {f _ {o p} \\cdot f _ {e g o}}{\\| f _ {o p} \\| \\| f _ {e g o} \\|} - \\alpha , 0\\right), \\tag {5}", + "image_path": "954d31f255123ac478d747ab25ff850c97b6397696f787e6215e22aa7ef34152.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 128, + 545, + 152 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 128, + 545, + 152 + ], + "spans": [ + { + "bbox": [ + 305, + 128, + 545, + 152 + ], + "type": "text", + "content": "as the two embeddings come from different domains, we thereby add " + }, + { + "bbox": [ + 305, + 128, + 545, + 152 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 305, + 128, + 545, + 152 + ], + "type": "text", + "content": " as a margin to compensate the domain gap." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 152, + 545, + 234 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 152, + 545, + 234 + ], + "spans": [ + { + "bbox": [ + 305, + 152, + 545, + 234 + ], + "type": "text", + "content": "In addition, since the affordance region typically denotes a portion of an object, we can thus impose a geometry loss to regulate its distribution. Inspired by the co-part segmentation work [24], we add a concentration loss to encourage egocentric localization maps to form a concentrated and connected component. The concentration loss is formulated as" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 321, + 243, + 545, + 269 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 243, + 545, + 269 + ], + "spans": [ + { + "bbox": [ + 321, + 243, + 545, + 269 + ], + "type": "interline_equation", + "content": "\\bar {u} _ {c} = \\sum_ {u, v} u \\cdot \\mathcal {P} _ {e g o} ^ {c, u, v} / z _ {k}, \\bar {v} _ {c} = \\sum_ {u, v} v \\cdot \\mathcal {P} _ {e g o} ^ {c, u, v} / z _ {k}, \\tag {6}", + "image_path": "fabb226a3939ef5fcedf4bd1ce9254278c53c4f1be316205a6aa8270fa914398.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 333, + 278, + 545, + 304 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 333, + 278, + 545, + 304 + ], + "spans": [ + { + "bbox": [ + 333, + 278, + 545, + 304 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {c} = \\sum_ {c} \\sum_ {u, v} \\| \\langle u, v \\rangle - \\langle \\bar {u} _ {c}, \\bar {v} _ {c} \\rangle \\| \\cdot \\mathcal {P} _ {e g o} ^ {c, u, v} / z _ {c}, \\tag {7}", + "image_path": "c80ba10f8627a2eced716d3f8083deac91fb912c5d634c12fc68987abf6495cc.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 305, + 310, + 545, + 367 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 310, + 545, + 367 + ], + "spans": [ + { + "bbox": [ + 305, + 310, + 545, + 367 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 310, + 545, + 367 + ], + "type": "inline_equation", + "content": "\\overline{u}_c" + }, + { + "bbox": [ + 305, + 310, + 545, + 367 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 310, + 545, + 367 + ], + "type": "inline_equation", + "content": "\\overline{v}_c" + }, + { + "bbox": [ + 305, + 310, + 545, + 367 + ], + "type": "text", + "content": " represents the center of the " + }, + { + "bbox": [ + 305, + 310, + 545, + 367 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 305, + 310, + 545, + 367 + ], + "type": "text", + "content": "-th localization map along axis " + }, + { + "bbox": [ + 305, + 310, + 545, + 367 + ], + "type": "inline_equation", + "content": "u, v" + }, + { + "bbox": [ + 305, + 310, + 545, + 367 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 305, + 310, + 545, + 367 + ], + "type": "inline_equation", + "content": "z_c = \\sum_{u,v} \\mathcal{P}_{ego}^{c,u,v}" + }, + { + "bbox": [ + 305, + 310, + 545, + 367 + ], + "type": "text", + "content": " is a normalization term. The concentration loss forces the high activation regions of the localization maps to be close to the geometric center." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 305, + 370, + 545, + 393 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 370, + 545, + 393 + ], + "spans": [ + { + "bbox": [ + 305, + 370, + 545, + 393 + ], + "type": "text", + "content": "Overall, we train the whole framework in an end-to-end manner, and use the following loss to optimize the model:" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 363, + 406, + 545, + 418 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 363, + 406, + 545, + 418 + ], + "spans": [ + { + "bbox": [ + 363, + 406, + 545, + 418 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\mathcal {L} _ {c l s} + \\lambda_ {c o s} \\mathcal {L} _ {c o s} + \\lambda_ {c} \\mathcal {L} _ {c}, \\tag {8}", + "image_path": "6e274dc8b0b291510161028e84ca4802b940eda60b0106b6c6d498d8ced1f68d.jpg" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 304, + 425, + 545, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 425, + 545, + 496 + ], + "spans": [ + { + "bbox": [ + 304, + 425, + 545, + 496 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 425, + 545, + 496 + ], + "type": "inline_equation", + "content": "\\lambda_{cos}" + }, + { + "bbox": [ + 304, + 425, + 545, + 496 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 425, + 545, + 496 + ], + "type": "inline_equation", + "content": "\\lambda_{c}" + }, + { + "bbox": [ + 304, + 425, + 545, + 496 + ], + "type": "text", + "content": " are loss weights that balance the three terms. " + }, + { + "bbox": [ + 304, + 425, + 545, + 496 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{cls}" + }, + { + "bbox": [ + 304, + 425, + 545, + 496 + ], + "type": "text", + "content": " stands for the cross-entropy losses from the two branches. At test time, only the ego branch is maintained, taking an affordance label " + }, + { + "bbox": [ + 304, + 425, + 545, + 496 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 425, + 545, + 496 + ], + "type": "text", + "content": " and an egocentric image as input, the network extracts the " + }, + { + "bbox": [ + 304, + 425, + 545, + 496 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 425, + 545, + 496 + ], + "type": "text", + "content": "-th localization map as the prediction of affordance region." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 306, + 508, + 388, + 521 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 508, + 388, + 521 + ], + "spans": [ + { + "bbox": [ + 306, + 508, + 388, + 521 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 306, + 528, + 429, + 540 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 528, + 429, + 540 + ], + "spans": [ + { + "bbox": [ + 306, + 528, + 429, + 540 + ], + "type": "text", + "content": "4.1. Experimental Setting" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": "Dataset and Metrics. We evaluate our method in the Affordance Grounding Dataset (AGD20K) [33], which is the only large-scale image dataset with both exocentric and egocentric views. AGD20K is comprised of 20,061 exocentric images and 3,755 egocentric images, and is annotated with 36 commonly used affordances. Following prior affordance grounding work [14,38], the ground truth of this dataset initially consists of densely annotated points in corresponding affordance regions, and a Gaussian blur is then applied over each point to get final heatmaps. Moreover, AGD20K can be evaluated in two different settings: 1) In the seen setting, object categories in training and test sets are identical. 2) In the unseen setting, there is no object category intersection between training and test sets, e.g., the" + } + ] + } + ], + "index": 29 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10926" + } + ] + } + ], + "index": 30 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 72, + 70, + 523, + 213 + ], + "blocks": [ + { + "bbox": [ + 72, + 70, + 523, + 213 + ], + "lines": [ + { + "bbox": [ + 72, + 70, + 523, + 213 + ], + "spans": [ + { + "bbox": [ + 72, + 70, + 523, + 213 + ], + "type": "table", + "html": "
State-of-the-Art from Relevant TasksSeenUnseen
KLD↓SIM↑NSS↑KLD↓SIM↑NSS↑
Weakly Supervised Object Localization*EIL [34]1.9310.2850.5222.1670.2270.330
SPA [40]5.5280.2210.3577.4250.1690.262
TS-CAM [16]1.8420.2600.3362.1040.2010.151
Weakly Supervised Affordance GroundingHotspots [38]1.7730.2780.6151.9940.2370.577
Cross-view-AG [33]1.5380.3340.9271.7870.2850.829
Cross-view-AG+ [32]1.4890.3420.9811.7650.2790.882
AffCorrs† [18]1.4070.3591.0261.6180.3481.021
LOCATE (Ours)1.2260.4011.1771.4050.3721.157
", + "image_path": "13e6f102bae368c135f556d5433275327e52b7a2d034b2a1494a287fbeda7a24.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 264, + 287, + 287 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 264, + 287, + 287 + ], + "spans": [ + { + "bbox": [ + 46, + 264, + 287, + 287 + ], + "type": "text", + "content": "model observes how humans hold a hammer and anticipates where to hold a knife." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 289, + 287, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 289, + 287, + 373 + ], + "spans": [ + { + "bbox": [ + 46, + 289, + 287, + 373 + ], + "type": "text", + "content": "As for the metrics, referring to previous affordance grounding work [14, 30, 33, 38], we adopt the commonly used Kullback-Leibler Divergence (KLD), Similarity (SIM), and Normalized Scanpath Saliency (NSS) to evaluate the similarity and correspondence of distributions between ground truth and prediction. Detailed calculation of each metric is shown in the supplementary material." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 376, + 288, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 376, + 288, + 519 + ], + "spans": [ + { + "bbox": [ + 46, + 376, + 288, + 519 + ], + "type": "text", + "content": "Implementation Details. We use the ImageNet [11] pretrained (without supervision) DINO-ViT-S [6] with patch size 16 to generate deep features. In each iteration, N exocentric images along with one egocentric image are taken as input (N is set to 3). Images are first resized to " + }, + { + "bbox": [ + 46, + 376, + 288, + 519 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 46, + 376, + 288, + 519 + ], + "type": "text", + "content": " and then randomly cropped to " + }, + { + "bbox": [ + 46, + 376, + 288, + 519 + ], + "type": "inline_equation", + "content": "224 \\times 224" + }, + { + "bbox": [ + 46, + 376, + 288, + 519 + ], + "type": "text", + "content": " followed by random horizontal flipping. SGD with learning rate 1e-3, weight decay 5e-4, and batch size 16 is used for parameter optimization. Loss weight coefficients " + }, + { + "bbox": [ + 46, + 376, + 288, + 519 + ], + "type": "inline_equation", + "content": "(\\lambda_{cos}, \\lambda_c)" + }, + { + "bbox": [ + 46, + 376, + 288, + 519 + ], + "type": "text", + "content": " are set to (1, 0.07), and the margin " + }, + { + "bbox": [ + 46, + 376, + 288, + 519 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 376, + 288, + 519 + ], + "type": "text", + "content": " is set to 0.5. For the first epoch, we warm up the network without " + }, + { + "bbox": [ + 46, + 376, + 288, + 519 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{cos}" + }, + { + "bbox": [ + 46, + 376, + 288, + 519 + ], + "type": "text", + "content": ", as initial localization maps are not accurate for supervision." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 527, + 218, + 540 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 527, + 218, + 540 + ], + "spans": [ + { + "bbox": [ + 47, + 527, + 218, + 540 + ], + "type": "text", + "content": "4.2. Comparison to State-of-the-Art" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "text", + "content": "To conduct a comprehensive comparison, we also display the results of state-of-the-art methods from a relevant task, i.e., weakly supervised object localization. As shown in Table 1, in both seen and unseen settings, LOCATE outperforms all other methods with a considerable margin on all metrics. In particular, compared to the state-of-the-art affordance grounding method Cross-view-AG+ [32], we improve the KLD by " + }, + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "inline_equation", + "content": "20.4\\%" + }, + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "text", + "content": ", SIM by " + }, + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "inline_equation", + "content": "33.3\\%" + }, + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "text", + "content": ", and NSS by " + }, + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "inline_equation", + "content": "31.2\\%" + }, + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "text", + "content": " in the unseen setting. Cross-view-AG+ is an extended version of Cross-view-AG, but still performs the knowledge transfer based on global pooled embeddings at the image level, thus bringing only minor improvement. AffCorrs [18] is a method that focuses on one-shot part affordance grounding, and it also uses the pretrained DINO-ViT" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 323, + 262, + 531, + 388 + ], + "blocks": [ + { + "bbox": [ + 46, + 220, + 546, + 246 + ], + "lines": [ + { + "bbox": [ + 46, + 220, + 546, + 246 + ], + "spans": [ + { + "bbox": [ + 46, + 220, + 546, + 246 + ], + "type": "text", + "content": "Table 1. Comparison to state-of-the-arts from relevant tasks on AGD20K dataset. Results of * are taken from [33], and † denotes the adapted AffCorrs. The best and second-best results are highlighted in bold and underlined, respectively (↑/↓ means higher/lower is better)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 323, + 262, + 531, + 388 + ], + "lines": [ + { + "bbox": [ + 323, + 262, + 531, + 388 + ], + "spans": [ + { + "bbox": [ + 323, + 262, + 531, + 388 + ], + "type": "table", + "html": "
MethodsParams (M)Time (s)
EIL [34]42.410.019
SPA [40]69.280.081
TS-CAM [16]85.860.023
Hotspots [38]132.640.087
Cross-view-AG [33]120.030.023
Cross-view-AG+ [32]82.270.022
AffCorrs† [18]6.500.205
LOCATE (Ours)6.500.011
", + "image_path": "35f7fd74b5a7b54d093f282828dfdd98b85d29fd956c72cc0f67f51dbd6183f7.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 396, + 545, + 430 + ], + "lines": [ + { + "bbox": [ + 305, + 396, + 545, + 430 + ], + "spans": [ + { + "bbox": [ + 305, + 396, + 545, + 430 + ], + "type": "text", + "content": "Table 2. Comparison of learnable parameters and inference time. The inference time is evaluated on a 3090Ti GPU. " + }, + { + "bbox": [ + 305, + 396, + 545, + 430 + ], + "type": "inline_equation", + "content": "\\dagger" + }, + { + "bbox": [ + 305, + 396, + 545, + 430 + ], + "type": "text", + "content": " denotes the adapted AffCorrs." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 446, + 545, + 530 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 446, + 545, + 530 + ], + "spans": [ + { + "bbox": [ + 304, + 446, + 545, + 530 + ], + "type": "text", + "content": "features to do part matching. However, AffCorrs needs a pixel-level mask as a query, and there is no domain gap during the knowledge transfer. To make AffCorrs comparable in our problem setting, we adapt its structure by replacing the query annotated mask with our CAM estimator. The results verify that AffCorrs can also achieve good performance, but still considerably inferior to LOCATE." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 532, + 546, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 532, + 546, + 675 + ], + "spans": [ + { + "bbox": [ + 304, + 532, + 546, + 675 + ], + "type": "text", + "content": "In Table 2, we make comparisons in terms of model parameters and inference time. Since our framework is built on a frozen small-sized vision transformer (ViT-small), the training process is efficient with a small number of parameters. For example, LOCATE only has " + }, + { + "bbox": [ + 304, + 532, + 546, + 675 + ], + "type": "inline_equation", + "content": "5.4\\%" + }, + { + "bbox": [ + 304, + 532, + 546, + 675 + ], + "type": "text", + "content": " of learnable parameters in Cross-view-AG. Additionally, we use a large patch size 16 for the vision transformer, which constrains the input sequence length and greatly reduces computation cost. Therefore, the inference time of LOCATE is also faster than most other methods. By contrast, the adapted AffCorrs runs much slower than LOCATE, as it incorporates an additional CRF post-processing step." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "type": "text", + "content": "We further visualize the qualitative comparisons with state-of-the-art affordance grounding methods. As shown in Fig. 5, we compare our results with Hotspots [38], Cross-" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10927" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 52, + 71, + 306, + 373 + ], + "blocks": [ + { + "bbox": [ + 52, + 71, + 306, + 373 + ], + "lines": [ + { + "bbox": [ + 52, + 71, + 306, + 373 + ], + "spans": [ + { + "bbox": [ + 52, + 71, + 306, + 373 + ], + "type": "image", + "image_path": "311ebddec46f4aede121d2598794e930c3e9c061342e56b0f6575d855b8672b3.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 386, + 546, + 420 + ], + "lines": [ + { + "bbox": [ + 46, + 386, + 546, + 420 + ], + "spans": [ + { + "bbox": [ + 46, + 386, + 546, + 420 + ], + "type": "text", + "content": "Figure 5. Qualitative comparison between our approach and state-of-the-art affordance grounding methods (Hotspots [38], Cross-view-AG [33], and Cross-view-AG+ [32]). For the unseen setting, the displayed objects are not in the training set. For example, the model learns where a motorcycle can be ridden in training, and locates rideable area for the bicycle at test time." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 315, + 70, + 529, + 372 + ], + "blocks": [ + { + "bbox": [ + 315, + 70, + 529, + 372 + ], + "lines": [ + { + "bbox": [ + 315, + 70, + 529, + 372 + ], + "spans": [ + { + "bbox": [ + 315, + 70, + 529, + 372 + ], + "type": "image", + "image_path": "04dc063f6e47ca9494caf5b55967368e42503d321f1a2fa5ad1c3384cea64c06.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 441, + 289, + 538 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 441, + 289, + 538 + ], + "spans": [ + { + "bbox": [ + 46, + 441, + 289, + 538 + ], + "type": "text", + "content": "view-AG [33] and Cross-view-AG+ [32]. We observe that the proposed LOCATE can make more concentrated and accurate predictions. Especially for complex objects like bicycles and refrigerators, even in the unseen setting, our method can still locate the saddle of bicycles for riding, and the handle of fridges for opening. In comparison, the results of Cross-view-AG for bicycles are quite noisy. More visualization results are in the supplementary material." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 549, + 141, + 562 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 549, + 141, + 562 + ], + "spans": [ + { + "bbox": [ + 47, + 549, + 141, + 562 + ], + "type": "text", + "content": "4.3. Ablation Study" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 570, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 288, + 715 + ], + "type": "text", + "content": "Knowledge Transfer Manner. We first investigate the impact of knowledge transfer manner. Previous affordance grounding methods [33, 38] simply pull close the global embeddings (produced by global average pooling) of two branches to perform global knowledge transfer (GKT). In contrast, we set up an experiment to implement regional knowledge transfer (RKT), which generates the embeddings via masked average pooling between CAM-produced localization maps and feature maps. The results are shown in Table 3, regional knowledge transfer (RKT) outperforms global knowledge transfer (GKT) on all metrics, demonstrating the effectiveness of filtering irrelevant information." + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 307, + 438, + 545, + 539 + ], + "blocks": [ + { + "bbox": [ + 307, + 438, + 545, + 539 + ], + "lines": [ + { + "bbox": [ + 307, + 438, + 545, + 539 + ], + "spans": [ + { + "bbox": [ + 307, + 438, + 545, + 539 + ], + "type": "table", + "html": "
MethodSeenUnseen
KLD↓SIM↑NSS↑KLD↓SIM↑NSS↑
GKT1.7320.2670.8101.9710.2210.626
RKT1.5160.3201.0741.8230.2590.850
+ Lc1.4910.3261.0911.7500.2740.948
+S1.2360.3971.1781.4390.3581.130
+S + Lc1.2260.4011.1771.4050.3721.157
", + "image_path": "efb5bb8c950b3b90fa1e0da2b01c83b9e555af9d49dffe6ab8e46fbf2bc83a73.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 547, + 545, + 581 + ], + "lines": [ + { + "bbox": [ + 305, + 547, + 545, + 581 + ], + "spans": [ + { + "bbox": [ + 305, + 547, + 545, + 581 + ], + "type": "text", + "content": "Table 3. Ablation results of the proposed LOCATE framework. GKT/RKT means global/regional knowledge transfer. " + }, + { + "bbox": [ + 305, + 547, + 545, + 581 + ], + "type": "inline_equation", + "content": "\\mathcal{S}" + }, + { + "bbox": [ + 305, + 547, + 545, + 581 + ], + "type": "text", + "content": " denotes PartSelect combined with " + }, + { + "bbox": [ + 305, + 547, + 545, + 581 + ], + "type": "inline_equation", + "content": "{\\mathcal{L}}_{cos}" + }, + { + "bbox": [ + 305, + 547, + 545, + 581 + ], + "type": "text", + "content": " ,and " + }, + { + "bbox": [ + 305, + 547, + 545, + 581 + ], + "type": "inline_equation", + "content": "{\\mathcal{L}}_{c}" + }, + { + "bbox": [ + 305, + 547, + 545, + 581 + ], + "type": "text", + "content": " is the concentration loss." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "content": "PartSelect and Concentration Loss. Based on the regional knowledge transfer, we analyze the effect of PartSelect and concentration loss. As shown in Table 3, directly applying the concentration loss " + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_c" + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "content": " can only bring marginal improvement. The reason is " + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_c" + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "content": " can make egocentric predictions more concentrated, but fail to guide it to focus on the right affordance area. Nonetheless, when adding PartSelect and using cosine embedding loss " + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{cos}" + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "content": " as explicit supervision, the performance is greatly boosted, which proves the effectiveness of the part-level knowledge transfer scheme. In ad" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "10928" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 72, + 286, + 251 + ], + "blocks": [ + { + "bbox": [ + 63, + 60, + 80, + 68 + ], + "lines": [ + { + "bbox": [ + 63, + 60, + 80, + 68 + ], + "spans": [ + { + "bbox": [ + 63, + 60, + 80, + 68 + ], + "type": "text", + "content": "GKT" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 110, + 60, + 127, + 68 + ], + "lines": [ + { + "bbox": [ + 110, + 60, + 127, + 68 + ], + "spans": [ + { + "bbox": [ + 110, + 60, + 127, + 68 + ], + "type": "text", + "content": "RKT" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 153, + 60, + 182, + 68 + ], + "lines": [ + { + "bbox": [ + 153, + 60, + 182, + 68 + ], + "spans": [ + { + "bbox": [ + 153, + 60, + 182, + 68 + ], + "type": "inline_equation", + "content": "\\mathrm{RKT} + \\mathcal{S}" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 191, + 60, + 238, + 68 + ], + "lines": [ + { + "bbox": [ + 191, + 60, + 238, + 68 + ], + "spans": [ + { + "bbox": [ + 191, + 60, + 238, + 68 + ], + "type": "inline_equation", + "content": "\\mathrm{RKT} + \\mathcal{S} + \\mathcal{L}_c" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 255, + 60, + 267, + 68 + ], + "lines": [ + { + "bbox": [ + 255, + 60, + 267, + 68 + ], + "spans": [ + { + "bbox": [ + 255, + 60, + 267, + 68 + ], + "type": "text", + "content": "GT" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 50, + 72, + 286, + 251 + ], + "lines": [ + { + "bbox": [ + 50, + 72, + 286, + 251 + ], + "spans": [ + { + "bbox": [ + 50, + 72, + 286, + 251 + ], + "type": "image", + "image_path": "36a9f6af048fa107f3955542288508985f1751d2f41ee59b92806cd1e9707efd.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 64, + 260, + 268, + 271 + ], + "lines": [ + { + "bbox": [ + 64, + 260, + 268, + 271 + ], + "spans": [ + { + "bbox": [ + 64, + 260, + 268, + 271 + ], + "type": "text", + "content": "Figure 6. Visualization of the qualitative improvements." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 285, + 286, + 369 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 285, + 286, + 369 + ], + "spans": [ + { + "bbox": [ + 46, + 285, + 286, + 369 + ], + "type": "text", + "content": "dition, to check the qualitative improvement, we visualize the affordance grounding results in Fig. 6. It is clear that GKT tends to locate the wrong affordance area, while RKT can sometimes find the right region, but only give coarse grounding results. After adding PartSelect, the results become much more part-focused, and the concentration loss further makes the grounding maps more robust." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 373, + 286, + 577 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 373, + 286, + 577 + ], + "spans": [ + { + "bbox": [ + 46, + 373, + 286, + 577 + ], + "type": "text", + "content": "Number of Prototypes/Exocentric Images. We then explore the impact from the number of prototypes " + }, + { + "bbox": [ + 46, + 373, + 286, + 577 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 373, + 286, + 577 + ], + "type": "text", + "content": " and exocentric images " + }, + { + "bbox": [ + 46, + 373, + 286, + 577 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 373, + 286, + 577 + ], + "type": "text", + "content": ". From Fig. 7a, we observe that the model yields the best performance with three prototypes in seen setting, which is consistent with our statement that interaction areas typically consist of human, object part, and background information. While for the unseen setting, " + }, + { + "bbox": [ + 46, + 373, + 286, + 577 + ], + "type": "inline_equation", + "content": "N = 5" + }, + { + "bbox": [ + 46, + 373, + 286, + 577 + ], + "type": "text", + "content": " achieves the best results, but improvement is minor. One reason lies in that more prototypes segment objects into more small parts, which boosts the generalization ability. As for the number of exocentric images, we find that more exocentric images can alleviate the impact of interaction diversity and occlusion, thus providing more robust knowledge for the egocentric branch. As shown in Fig. 7b, the model gets largely improved when increasing the number of exocentric images from 1 to 3 in both seen and unseen settings. Finally, we set both " + }, + { + "bbox": [ + 46, + 373, + 286, + 577 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 373, + 286, + 577 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 373, + 286, + 577 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 373, + 286, + 577 + ], + "type": "text", + "content": " to 3." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 582, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 286, + 713 + ], + "type": "text", + "content": "Different Feature Extractors. In LOCATE, we employ pretrained DINO features based on ViT, which have been proven to encode high-level semantic information [1]. To investigate the impact of different backbones, we conducted experiments with DINO features trained on the ResNet-50 [22]. From the results in Table 4, we observe that using DINO-ViT features directly (without the proposed PartSelect) can only obtain similar or even inferior results to their ResNet counterpart. After incorporating PartSelect, the results of both backbone features can be improved under the seen setting, but ViT features show better potential in en" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 309, + 72, + 542, + 155 + ], + "blocks": [ + { + "bbox": [ + 309, + 72, + 542, + 155 + ], + "lines": [ + { + "bbox": [ + 309, + 72, + 542, + 155 + ], + "spans": [ + { + "bbox": [ + 309, + 72, + 542, + 155 + ], + "type": "image", + "image_path": "faf841811f9ddc107d021346d8e1d58b48488ccf5cd95270144381bbedfae89e.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 309, + 171, + 542, + 255 + ], + "blocks": [ + { + "bbox": [ + 380, + 159, + 472, + 169 + ], + "lines": [ + { + "bbox": [ + 380, + 159, + 472, + 169 + ], + "spans": [ + { + "bbox": [ + 380, + 159, + 472, + 169 + ], + "type": "text", + "content": "(a) Number of prototypes " + }, + { + "bbox": [ + 380, + 159, + 472, + 169 + ], + "type": "inline_equation", + "content": "N" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 309, + 171, + 542, + 255 + ], + "lines": [ + { + "bbox": [ + 309, + 171, + 542, + 255 + ], + "spans": [ + { + "bbox": [ + 309, + 171, + 542, + 255 + ], + "type": "image", + "image_path": "1fee8df9dce98992a513d69bdff480909f04f480bdbac81bb631813fd37e1b49.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 368, + 258, + 484, + 267 + ], + "lines": [ + { + "bbox": [ + 368, + 258, + 484, + 267 + ], + "spans": [ + { + "bbox": [ + 368, + 258, + 484, + 267 + ], + "type": "text", + "content": "(b) Number of exocentric images " + }, + { + "bbox": [ + 368, + 258, + 484, + 267 + ], + "type": "inline_equation", + "content": "K" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 306, + 277, + 545, + 300 + ], + "lines": [ + { + "bbox": [ + 306, + 277, + 545, + 300 + ], + "spans": [ + { + "bbox": [ + 306, + 277, + 545, + 300 + ], + "type": "text", + "content": "Figure 7. Ablation study on the number of prototypes and exocentric images (lower is better)." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "type": "table", + "bbox": [ + 306, + 312, + 545, + 429 + ], + "blocks": [ + { + "bbox": [ + 306, + 312, + 545, + 429 + ], + "lines": [ + { + "bbox": [ + 306, + 312, + 545, + 429 + ], + "spans": [ + { + "bbox": [ + 306, + 312, + 545, + 429 + ], + "type": "table", + "html": "
RN-50ViT-S/16PartSelectKLD↓SIM↑NSS↑
Seen✓1.4820.3341.005
✓1.4910.3261.091
✓✓1.4490.3401.021
✓✓1.2260.4011.177
Unseen✓1.7010.2870.962
✓1.7500.2740.948
✓✓1.7070.2870.949
✓✓1.4050.3721.157
", + "image_path": "6d8b500180fb2641acf177da367d1a5f24402143c8222b06268fcf54aacadbbd.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "table_body" + } + ], + "index": 15 + }, + { + "bbox": [ + 326, + 437, + 524, + 448 + ], + "lines": [ + { + "bbox": [ + 326, + 437, + 524, + 448 + ], + "spans": [ + { + "bbox": [ + 326, + 437, + 524, + 448 + ], + "type": "text", + "content": "Table 4. Ablation study on different feature extractors." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 460, + 545, + 508 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 460, + 545, + 508 + ], + "spans": [ + { + "bbox": [ + 304, + 460, + 545, + 508 + ], + "type": "text", + "content": "hancing the performance due to their part-aware property. In the unseen setting, PartSelect does not yield improvement for ResNet-based features, while ViT features obtain consistent gains." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 521, + 378, + 533 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 521, + 378, + 533 + ], + "spans": [ + { + "bbox": [ + 306, + 521, + 378, + 533 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 542, + 545, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 542, + 545, + 673 + ], + "spans": [ + { + "bbox": [ + 304, + 542, + 545, + 673 + ], + "type": "text", + "content": "In this paper, we propose a framework named LOCATE to address the weakly supervised affordance grounding task by observing human-object interaction images. Specifically, we first localize where the interaction happens for the exocentric interactions, and then design a module called PartSelect to pick the affordance-specific information from the interaction regions. Finally, we transfer the learned knowledge to the egocentric view to perform affordance grounding with only image-level affordance labels. The proposed LOCATE achieves state-of-the-art results with far fewer parameters and faster inference speed." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 678, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 678, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 678, + 545, + 713 + ], + "type": "text", + "content": "Acknowledgement. This work is supported by the EPSRC, as part of the CDT in Robotics and Autonomous Systems (EP/S023208/1), along with gift funding and the research scholar award from Google." + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10929" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 714 + ], + "type": "list", + "angle": 0, + "index": 17, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "type": "text", + "content": "[1] Shir Amir, Yossi Gandelsman, Shai Bagon, and Tali Dekel. 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An overview of the LOGO dataset. LOGO is a multi-person long-form video dataset with frame-wise annotations on both action procedures (as shown in the second line) and formations (as shown in the third line, which reflects relations among actors) based on artistic swimming scenarios. It provides a potential for constructing an action quality assessment approach with the ability of modeling group information among actors. Longer video durations also challenge the ability of the method to aggregate long-term temporal information." + ], + "image_footnote": [], + "bbox": [ + 83, + 282, + 890, + 534 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 619, + 313, + 636 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Action quality assessment (AQA) has become an emerging topic since it can be extensively applied in numerous scenarios. However, most existing methods and datasets focus on single-person short-sequence scenes, hindering the application of AQA in more complex situations. To address this issue, we construct a new multi-person long-form video dataset for action quality assessment named LOGO. Distinguished in scenario complexity, our dataset contains 200 videos from 26 artistic swimming events with 8 athletes in each sample along with an average duration of 204.2 seconds. As for richness in annotations, LOGO includes formation labels to depict group information of multiple athletes and detailed annotations on action procedures. Furthermore, we propose a simple yet effective method to model relations among athletes and reason about the potential", + "bbox": [ + 75, + 652, + 472, + 880 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "temporal logic in long-form videos. Specifically, we design a group-aware attention module, which can be easily plugged into existing AQA methods, to enrich the clipwise representations based on contextual group information. To benchmark LOGO, we systematically conduct investigations on the performance of several popular methods in AQA and action segmentation. The results reveal the challenges our dataset brings. Extensive experiments also show that our approach achieves state-of-the-art on the LOGO dataset. The dataset and code will be released at https://github.com/shiyi-zh0408/LOGO.", + "bbox": [ + 500, + 623, + 893, + 789 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 500, + 827, + 632, + 842 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Action quality assessment (AQA) is applicable to many real-world contexts where people evaluate how well a specific action is performed such as sports events [13, 18, 29-", + "bbox": [ + 498, + 854, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* indicates the corresponding author.", + "bbox": [ + 94, + 887, + 290, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "2405", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "table", + "img_path": "images/9b6e0ce25c0eb02a73123e250564124211285a5abdb2e57a8994049f513b7db4.jpg", + "table_caption": [ + "Table 1. Comparisons of LOGO and existing datasets of action quality assessment (upper part of the table) and group activity recognition (lower part of the table). Score indicates the score annotations; Action denotes action types and temporal boundaries; Act.Label indicates the action types of both individuals and groups. Bbox indicates bounding boxes for actors. Formation represents formation annotations. Temp. indicates temporal boundary, Spat. indicates spatial localization." + ], + "table_footnote": [], + "table_body": "
DatasetDurationAvg.Dur.Anno.TypeSamplesEventsForm.Anno.Year
MTL Dive [33]15m,54s6.0sScore1591✘2014
UNLV Dive [31]23m,26s3.8sScore3701✘2017
AQA-7-Dive [29]37m,31s4.1sScore5496✘2019
MTL-AQA [30]96m,29s4.1sAction,Score141216✘2019
Rhythmic Gymnastics [53]26h,23m,20s1m,35sScore10004✘2020
FSD-10 [26]-3-30sAction,Score1484-✘2020
FineDiving [50]3h,30m,0s4.2sAction,Score300030✘2022
Collective Activity [7]--Act.Label44-✘2009
NCAA [35]16h,9m,52s4sBbox,Act.Label11436-✘2016
Volleyball [16]2h,12m,1s1.64sBbox,Act.Label4830-✘2016
FineGym [38]161h,1m,45s45.7sAct.Label,Temp.1268510✘2020
Multisports [25]18h,34m,40s20.9sAct.Label,Temp.,Spat.3200247✘2021
LOGO(Ours)11h,20m,41s3m,24sAction,Formation,Score20026✓(15764)
", + "bbox": [ + 76, + 164, + 893, + 406 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "33, 46], healthcare [28, 39, 55-58], art performances, military parades, and others. Due to the extensive application of AQA, many efforts have been made over the past few years. Although some existing works have achieved promising performances in several simple scenarios, the application of AQA in many situations is still difficult to implement. In the data-driven era, the richness of the dataset largely determines whether the model can be applied to a wide range of scenarios or not. Inspired by this, we reviewed the existing datasets in AQA and concluded that they are not rich enough for the following two reasons:", + "bbox": [ + 75, + 430, + 468, + 597 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Simplicity of Scenarios. We argue that the complexity of the AQA application scenes is reflected in two aspects, the number of people and the duration of the videos. In snowboarding, for example, there is only one performer, while there are multiple actors in a military parade. In diving, the duration is only about 5 seconds, while in artistic swimming and dance performances, the duration of the action reaches several minutes. However, most existing datasets contain a single performer in each sample and many of them collect videos of 3-8s [29-31, 33, 50], which makes it difficult for existing methods to model complex scenes with more actors and longer duration. In such cases, just focusing on how well actions are performed by each individual may be insufficient. Relations among actors should be built, and the potential temporal logic in long-term videos should be modeled.", + "bbox": [ + 75, + 598, + 468, + 838 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Coarse-grained Annotations. Though there have been some long-form video datasets in AQA [49, 53] which provide more complex scenes, they typically contain the score as the only annotation. Such coarse-grained annotation", + "bbox": [ + 75, + 839, + 468, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "makes it difficult for models to learn deeper information, especially in more complex situations. Simply judging action quality via regressing a score for a long-term video could be confusing since we cannot figure out how the model determines whether an action is well-performed or not.", + "bbox": [ + 496, + 430, + 890, + 506 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address these issues, we propose a multi-person long-form video dataset, LOGO (short for LOng-form GrOup). With 8 actors in each sample, LOGO contains videos with an average duration of 204.2s, much longer than most existing datasets in AQA, making the scenes more complex. Besides, as shown in Figure 1, LOGO contains fine-grained annotations including frame-wise action type labels and temporal boundaries of actions for each video. We also devise formation labels to depict relations among actors. Specifically, we use a convex polygon to represent the formation actors perform, which reflects their position information and group information. In general, LOGO is distinguished by its scenario complexity, while it also provides richer annotations compared to most existing datasets in AQA [29-31, 33, 49, 50, 53].", + "bbox": [ + 496, + 508, + 892, + 733 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Furthermore, we build a plug-and-play module, GOAT (short for GrOut-aware ATtention), to bridge the gap between single-person short-sequence scenarios and multiperson long-sequence scenarios. Specifically, in the spatial domain, by building a graph for actors, we model the relations among them. The nodes of this graph represent actors' features extracted from a CNN, and the edges represent the relations among actors. Then we use a graph convolution network (GCN) [19] to model the group features from the graph. The optimized features of the graph then serve as \"queries\" and \"keys\" for GOAT. In the temporal do", + "bbox": [ + 496, + 734, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "2406", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "main, after feature extraction by the video feature backbone, the clip-wise features serve as “values” for GOAT. Instead of fusing the features simply using the average pooling as most previous works [44, 50, 52], GOAT learns the relations among clips and models the temporal features of the long-term videos based on the spatial information in every clip.", + "bbox": [ + 75, + 90, + 468, + 181 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The contributions of this paper can be summarized as: (1) We construct the first multi-person long-form video dataset, LOGO, for action quality assessment. To the best of our knowledge, LOGO stands out for its longer average duration, the larger number of people, and richer annotations when compared to most existing datasets. Experimental results also reveal the challenges our proposed dataset brings. (2) We propose a plug-and-play group-aware module, GOAT, which models the group information and the temporal contextual relations for input videos, bridging the gap between single-person short-sequence scenarios and multi-person long-sequence scenarios. (3) Experimental results demonstrate that our group-aware approach obtains substantial improvements compared to existing methods in AQA and achieves the state-of-the-art.", + "bbox": [ + 75, + 181, + 470, + 407 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 422, + 218, + 436 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Action Quality Assessment. Assessing action quality is an increasingly popular trend in computer vision with wide applications such as video retrieval, instructional video analysis, etc. A wide variety of methods for formulating AQA tasks have been proposed [3, 10, 13, 24, 31, 33, 44, 48, 49, 52, 53]. In long video AQA tasks, actions performed at different times may significantly impact the scores given by experts. However, only a handful of works directly address the problem of long-term video AQA [3, 10, 48, 49, 53]. There are many datasets for AQA, including Diving [29-31, 33, 50], Figure Skating [26, 33], Gymnastic Vault [29, 31], Basketball [3], Fitness [43] and Rhythmic Gymnastics [53]. However, the problem of considering group information in multi-person sports has been relatively unexplored. As shown in Table 1, MIT-Dive [33], UNLV-Dive [31], AQA-7-Dive [29] and Rhythmic Gymnastics [53] only provide action scores, while MTL-AQA [30] FSD-10 [26] and FineDiving [50] only provide action types and scores. To perform AQA in long videos with multi-person, we construct a long-form artistic swimming video dataset, LOGO, with fine-grained frame-wise action and formation labels. Furthermore, we propose a method to model relations among athletes and reason about the potential temporal logic in long-form videos.", + "bbox": [ + 75, + 448, + 468, + 809 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Group Activity Understanding. Group activity understanding, which concentrates on interpreting the collective activity from multi-person behavioral and interaction dynamics, has attracted plenty of work recently. The focus of existing methods has shifted from using shallow handcrafted features [6,8,20,21,36,40] to using deep neural net", + "bbox": [ + 75, + 810, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/23e5da38ac6ef17726fcba3feeb4a04c3a961cb8dd9575ed58174623448bf6f4.jpg", + "image_caption": [ + "Figure 2. A tree structure of LOGO Taxonomy. LOGO organizes both the Actions and Formations annotations hierarchically. The left part shows the Actions categories of Technical and Free events. The right part depicts the formation annotation instances when the group is doing Required, Upper, Lower or Float actions (the right sub-tree of Actions) and not when the group is doing other actions, during which the formations are indistinguishable." + ], + "image_footnote": [], + "bbox": [ + 511, + 92, + 883, + 359 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "works [2,12,15,22,34,45]. Diverse datasets have been proposed to facilitate research in this area, such as the Collective Activity dataset [7], Volleyball dataset [16], etc. However, the methods and datasets mentioned above only stay at the level of group activity recognition; a more profound understanding of group activities should be able to not only find the high-level group activity but also evaluate the quality of group activities, which requires more attention to the quality of collaboration among actors and fine-grained actions of actors. In this paper, LOGO takes the first step towards quality assessment and sets a new benchmark for group activity understanding.", + "bbox": [ + 496, + 482, + 892, + 664 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. The LOGO Dataset", + "text_level": 1, + "bbox": [ + 500, + 676, + 689, + 691 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We propose a new multi-person long-form video dataset with detailed annotations on action and formation, LOGO, to set a new challenging benchmark for AQA. We will introduce it from its construction and annotation in this section.", + "bbox": [ + 496, + 702, + 890, + 762 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Dataset Construction", + "text_level": 1, + "bbox": [ + 500, + 771, + 699, + 786 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Collection. According to the official FINA rules, the same rules, and prescribed movements are used from 2018 until the end of the 2022 World Championships. So we collected the officially designated Technical and Free artistic swimming competitions during this period (2 World Championships, 1 Olympic Games, and 4 World Series). We download competition videos with high resolution, e.g.,", + "bbox": [ + 496, + 794, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "2407", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/a896200b43e7b88c33cd5523ede47483c35d12a4cb29a0b3f1770c0ed43d7100.jpg", + "image_caption": [ + "Figure 3. Statics of LOGO. (a) The score distribution of videos. (b) The action-type distribution of frames." + ], + "image_footnote": [], + "bbox": [ + 80, + 88, + 256, + 233 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/f254d4f53997de152b312ae47b71393a6d36fa2b8ad6b4df031896de34cef704.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 267, + 88, + 464, + 234 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "720p and 1080p, on online video platforms like YouTube. Then we sampled them at 25fps and 1fps sampling rates for fine-grained action and formation labeling. Each official videos provide various content, including three sub-scores, one final score, and frames from different views.", + "bbox": [ + 76, + 286, + 467, + 361 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Lexicon. We construct a fine-grained video dataset organized by temporal structure, which contains action and formation manual annotations, shown in Figure 2. Herein, we design the labeling system with professional artistic swimming athletes to construct a lexicon for annotation, considering FINA rules and the actual scenario of the competitions. In the Technical event, the group size is eight people, the video length is $170 \\pm 15\\mathrm{s}$ , and the actions include Upper, Lower, Float, None, Acrobatic, Cadence, and five Required Elements. Each competition cycle needs to complete five Required Elements, at least two Acrobatic movements, and at least one Cadence action. In the Free events, there are 8 people, the video length is $240 \\pm 15\\mathrm{s}$ , and the actions include Upper, Lower, Float, None, Acrobatic, Cadence, and Free elements. When performing Required, Upper, Lower, and Float, the athletes form neat polygons as in Figure 2.", + "bbox": [ + 76, + 363, + 467, + 604 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Annotation. Given an RGB artistic swimming video, the annotator utilizes our defined lexicon to label each frame with its action and formation. We accomplish the 25fps frame-wise action annotation stage utilizing the COIN annotation toolbox [42] and the 1fps frame-wise formation labels using Labelme. Specifically, we set strict rules defining the boundaries between artistic swimming sequences and the formation marking position and employ eight workers with prior knowledge in the artistic swimming domain to label the dataset frame by frame following the rules. The annotation results of one worker are checked and adjusted by another, which ensures annotation results are double-checked. Under this pipeline, the total time for the annotation process is above 600 hours.", + "bbox": [ + 76, + 606, + 467, + 816 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Dataset Statics", + "text_level": 1, + "bbox": [ + 76, + 830, + 225, + 844 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The LOGO dataset consists of 200 video samples from 26 events with 204.2s average duration and above 11h total duration, covering 3 annotation types, 12 action types,", + "bbox": [ + 76, + 854, + 467, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "and 17 formation types. Figure 3 shows the score and action type distributions among all the events. Table 1 reports more detailed information on the LOGO dataset and compares it with existing AQA datasets and other fine-grained sports datasets. Our dataset differs from existing AQA datasets in the annotation type and dataset scale. Specifically, our dataset includes formation types providing group information and longer videos on sports, helping to evaluate the quality of actions in multiplayer sports quantitatively. Other fine-grained sports datasets cannot be used for assessing action quality due to a lack of action scores. LOGO is the first fine-grained sports video dataset for Group AQA, filling the fine-grained group annotations void in AQA.", + "bbox": [ + 496, + 90, + 890, + 287 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Approach", + "text_level": 1, + "bbox": [ + 498, + 300, + 607, + 316 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Problem Formulation", + "text_level": 1, + "bbox": [ + 500, + 325, + 700, + 339 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Most existing methods in AQA process the output of the video feature backbone using average pooling before regression. It can be represented as:", + "bbox": [ + 498, + 348, + 890, + 393 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {y} = \\mathcal {R} \\left[ \\frac {1}{T} \\sum_ {i = 1} ^ {T} \\mathcal {F} \\left(X _ {i}\\right) | \\Theta \\right], \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 609, + 405, + 890, + 446 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $X_{i}$ denotes the $i$ -th clip of the video. $\\mathcal{F}$ indicates the video feature backbone; $T$ is the number of clips; $\\mathcal{R}$ represents the regression algorithm; $\\Theta$ is the learnable parameters of $\\mathcal{R}$ and $\\hat{y}$ is the predicted score. However, fusing temporal information simply by average pooling in scenes with longer duration may be confusing since there could be redundant or even invalid information in the video. Besides, when dealing with multi-person scenarios, we need to depict the relations among actors. We use group information to fuse the extracted features in the temporal axis, modeling the relations among clips. It can be represented as:", + "bbox": [ + 496, + 455, + 890, + 623 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {y} = \\mathcal {R} \\left[ \\frac {1}{T} \\sum_ {i = 1} ^ {T} f _ {i} | \\Theta \\right], \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 624, + 633, + 890, + 674 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nf _ {i} = \\sum_ {j = 1} ^ {T} \\mathcal {G} \\left(X _ {i}, X _ {j}\\right) \\mathcal {F} \\left(X _ {j}\\right), i = 1 \\dots T, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 566, + 676, + 890, + 720 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{G}(X_i, X_j)$ denotes the weight computed by group features of the $i$ -th clip and the $j$ -th clip; $f_i$ indicates the reconstructed feature of the $i$ -th clip.", + "bbox": [ + 498, + 731, + 890, + 777 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. Group-aware Attention", + "text_level": 1, + "bbox": [ + 500, + 786, + 715, + 801 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "There are two components of GOAT, that is, group-aware GCN and temporal-fusion attention. The overview of our framework is illustrated in Figure 4.", + "bbox": [ + 500, + 810, + 890, + 854 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Group-aware GCN. This component is shown in the right part of Figure 4. We extract the group features by modeling the relations among actors with graphs. Given a", + "bbox": [ + 500, + 854, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "2408", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/274e7339dd3f9da5a3f20567c9f1c6490b6fc32eb601edd0eb4fba13303a3a15.jpg", + "image_caption": [ + "Figure 4. An overview of our group-aware approach for action quality assessment. First, we divide the video into several short clips of equal length. For each clip, we take the middle frame and perform object detection to get the bounding boxes of the actors. Then we send the frame into a CNN to extract the features of the actors. Then we use the feature vector of each actor as the node to construct the relation graph. We use Graph Convolutional Network to enhance the features in the graph, and send the output features into GOAT as “queries” and “keys”. And the “values” are the features obtained from the clip by the video feature backbone such as I3D and video swin-transformer. Thus the aggregation in time can be completed. Finally, the output features are sent into the assessment network to predict the scores." + ], + "image_footnote": [], + "bbox": [ + 81, + 95, + 524, + 289 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/7964c7b1a10d333e0ed932ef186644e76172703c076cb78d96556fde58eda8a6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 529, + 97, + 885, + 289 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "video, we fix it into the given duration via downsampling or upsampling and divide it into several clips of equal length. Then we take three steps to extract the group features. First, we select the middle frame from each clip and build features for the actors. Specifically, we adopt object detection [54] to get bounding boxes of actors. Then, we use Inception-V3 [41] on the frame to get the feature map, to which we apply RoIAlign [14] to extract features for each bounding box. We use a fully connected layer to get a $d$ -dimensional vector from the feature map for each actor. Then we have a $N \\times d$ representation denoted as $G$ for each middle frame, where $N$ denotes the number of actors and $d$ indicates the dimension of feature vectors.", + "bbox": [ + 75, + 406, + 468, + 601 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Second, we build a relation graph with the feature matrix $G$ to model the relations among actors. Concretely, we regard each feature vector of an actor as a node in the graph. We follow the strategy in [47] to build edges among nodes by computing similarities of appearance features and relative location of actors.", + "bbox": [ + 75, + 602, + 468, + 691 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Then, a Graph Convolutional Network (GCN) [19] is adopted to the relation graph to enhance node features by weighted aggregation, which can be represented as:", + "bbox": [ + 75, + 693, + 468, + 739 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nH ^ {(l + 1)} = \\sigma (A H ^ {(l)} W ^ {(l)}), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 184, + 748, + 468, + 767 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $A$ indicates the adjacent matrix; $W^{(l)}$ is the weight matrix in $l$ -th layer; $H^{(l)}$ denotes the features of nodes in $l$ -th layer and $H^{(0)} = G$ . Finally, The group feature vector is extracted by adopting average pooling to the sum of the input and the output features of GCN. The group feature vector of the $i$ -th clip is denoted as $g_{i}$ .", + "bbox": [ + 75, + 777, + 468, + 869 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Temporal-fusion Attention. This component fuses the video embeddings along the temporal axis based on the rep-", + "bbox": [ + 76, + 869, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "resentations from the group-aware GCN. As shown in the left part of Figure 4, for each clip split from the video, we send it into an I3D [4] backbone as most previous works do [44, 50, 52, 53]. We leverage the strong capability of capturing global information of the multi-head attention encoder for learning group-aware video embeddings.", + "bbox": [ + 496, + 406, + 890, + 496 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We denote the I3D features of the video as $\\{\\mathcal{F}(X_i)\\}_{i = 1}^T$ , which serve as the \"value\" of the attention block. And the vectors $\\{g_i\\}_{i = 1}^T$ from group-aware GCN serve as \"query\" and \"key\". The temporal-fusion attention module learns to discover the group feature correspondences among clips, and generates new temporal features in all of them. The module uses the relations of group features among different clips to assign different weights to different temporal features. The above attention learning can be represented as:", + "bbox": [ + 496, + 496, + 892, + 633 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nq ^ {(l)} = W _ {Q} ^ {(l)} q ^ {(l - 1)}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 586, + 642, + 890, + 664 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nk ^ {(l)} = W _ {K} ^ {(l)} k ^ {(l - 1)}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 586, + 666, + 890, + 686 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nW _ {a t t n} ^ {(l)} = \\operatorname {S o f t m a x} \\left(\\frac {q ^ {(l)} k ^ {(l) T}}{\\sqrt {d}}\\right), \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 568, + 688, + 890, + 723 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nv ^ {(l)} = B N \\left[ W _ {a t t n} ^ {(l)} v ^ {(l - 1)} + v ^ {(l - 1)} \\right], \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 586, + 724, + 890, + 744 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $W_{Q}^{(l)}, W_{K}^{(l)}, W_{attn}^{(l)}$ indicate the learnable weights in $l$ -th layer; $q^{(l)}, k^{(l)}, v^{(l)}$ denote the \"query\", \"key\" and \"value\" in $l$ -th layer; $d$ is the dimension of feature vector and $BN$ is the BatchNorm block. Besides, $q^{(0)} = k^{(0)} = \\{g_i\\}_{i=1}^T$ , $v^{(0)} = \\{\\mathcal{F}(X_i)\\}_{i=1}^T$ .", + "bbox": [ + 496, + 756, + 893, + 840 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Formation Detection", + "text_level": 1, + "bbox": [ + 500, + 847, + 694, + 861 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In 4.2, we propose a pipeline to fuse temporal representations based on a kind of spatial information, the group", + "bbox": [ + 498, + 869, + 892, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "2409", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "features. However, such a fusion strategy can also be based on other kinds of spatial features and even without any features by simply using self-attention. To prove the effectiveness of the group features, we devise another kind of spatial features, formation features, to make a comparison.", + "bbox": [ + 75, + 90, + 468, + 165 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Formation Detection Task. As mentioned in Section 3, we use a polygon to depict the formation of actors. As shown in Figure 2, the polygon is represented by several coordinates of some actors but not all of them. So in this task, we need to distinguish whether an actor is the vertex of the polygon or not.", + "bbox": [ + 75, + 167, + 467, + 256 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Formation Detection Algorithm. Inspired by the \"anchor\" in object detection [37], we propose a feasible way to detect the vertexes. Given a picture, we split it into 1024 patches of equal size. For each patch, we set the center point as the \"anchor\". We send the image into Inception-V3 and extract the $d$ -dimensional feature vector with RoIAlign [14] and a fully connected layer for each patch. To represent the absolute position of each patch, we use sine and cosine functions of different frequencies to encode the position of the \"anchor\". We add the $d$ -dimensional positional encodings to the features and send them into a self-attention block to find the relations among different patches and build the $d$ -dimensional formation features for them.", + "bbox": [ + 75, + 257, + 467, + 450 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Then we take two steps to find vertexes. First, for each patch, we judge whether there is a vertex. Second, if there is a vertex, we calculate the relative coordinates of the vertex to the \"anchor\" point. So we detect vertexes by computing:", + "bbox": [ + 75, + 453, + 467, + 513 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {P} = \\left[ \\hat {p} _ {1}, \\dots , \\hat {p} _ {n} \\right], \\quad \\hat {C} = \\left[ \\hat {c} _ {1}, \\dots , \\hat {c} _ {n} \\right], \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 151, + 523, + 467, + 542 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\hat{p}_i\\in \\mathbb{R}$ denotes the confidence of whether there is a vertex in the $i$ -th patch and $\\hat{c}_i\\in \\mathbb{R}^2$ is the relative coordinates of the vertex to the \"anchor\". In this way, the formation detection task is converted to a classification problem and a regression problem. And we respectively use a MLP to predict $\\hat{P}$ and $\\hat{C}$ upon the formation features mentioned above. The object function can be represented as:", + "bbox": [ + 75, + 551, + 467, + 657 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {B C E} = - \\sum_ {i} \\left[ p _ {i} \\log \\hat {p} _ {i} + (1 - p _ {i}) \\log \\left(1 - \\hat {p} _ {i}\\right) \\right], \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 670, + 467, + 699 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {M S E} = \\left\\| C - \\hat {C} \\right\\| ^ {2}. \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 199, + 704, + 467, + 722 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We minimize $\\mathcal{L}_{BCE}$ and $\\mathcal{L}_{MSE}$ to predict the vertexes. The $d$ -dimensional formation features of middle frame in each clip can replace the group features in 4.2 to fuse the temporal information. Relative experiments are conducted in our ablation study.", + "bbox": [ + 75, + 733, + 467, + 808 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 76, + 821, + 207, + 838 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Implementation Details", + "text_level": 1, + "bbox": [ + 76, + 847, + 292, + 862 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Action Quality Assessment. Following [31,49,53], we take two stages to assess action quality: feature extraction", + "bbox": [ + 75, + 869, + 467, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "and score prediction. In the feature extraction stage, we use the I3D model pretrained on Kinetics [4] dataset to extract the 1024-dimensional feature vector for each video clip. Specifically, we sample 5406 frames for each video, split them into 540 snippets, and fed them into I3D. Each snippet contains 16 continuous frames with a stride of 10 frames. In the ablation study, we also use the video swintransformer [27] as the backbone, which is also pretrained on Kinetics. We follow the sampling strategy in [27] to use a temporal stride of 2. The Inception-V3 in 4.2 is pretrained on ImageNet [9] to extract the CNN features. Following [44, 50, 52], we split the dataset into 3:1 for training and testing in all the experiments. We also test our model using the Mindspore [1].", + "bbox": [ + 496, + 90, + 890, + 301 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Action Segmentation. We conduct action segmentation on LOGO with several existing approaches (ASFormer [51], SSTDA [23], MS_TC++ [5], ASRF [17]) to provide a benchmark. We try two backbones to extract frame-wise features: I3D [4] model and video swim-transformer [27] pretrained on Kinetics. For SWIN, we expand the snippet size to 32 frames to extract 1536-dimensional features. In the training stage, we train action segmentation approaches on their default setting.", + "bbox": [ + 496, + 303, + 890, + 438 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Evaluation Metrics", + "text_level": 1, + "bbox": [ + 500, + 449, + 683, + 463 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Action Quality Assessment. Following [44, 50, 52, 53], we comprehensively evaluate our approach to AQA under two metrics, Spearman's rank correlation $(\\rho)$ and relative $\\ell_2$ -distance $(\\mathbf{R} - \\ell_2)$ . Spearman's rank correlation is used to evaluate the rank correlation between the prediction and ground-truth while the relative $\\ell_2$ -distance $(\\mathbf{R} - \\ell_2)$ focuses on the difference of the numerical values.", + "bbox": [ + 496, + 472, + 890, + 577 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Action Segmentation. Following [5, 15, 23, 51], we adopt three widely used evaluation metrics including framewise accuracy (Acc), segmental edit distance and segmental F1 score at overlapping thresholds $10\\%$ , $25\\%$ , and $50\\%$ , denoted by F1@{10, 25, 50} to evaluate the performance of action segmentation approaches.", + "bbox": [ + 496, + 579, + 890, + 670 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.3. Comparison with the State of the Art", + "text_level": 1, + "bbox": [ + 500, + 680, + 820, + 696 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Action Quality Assessment. Table 2 shows the experimental results, which reveal great challenges to performing action quality assessment on the LOGO dataset. With the I3D backbone, the mainstream methods in single-person short-term AQA [44, 50, 52] attain the result of 0.4259, 0.4712, and 0.4518 on Spearman's rank correlation respectively. Besides, the results show that our approach achieves the state-of-the-art. We observe that USDL+GOAT, CoRe+GOAT, and TSA+GOAT consistently improve the performance over the original models. Specifically, our approach respectively obtained $8.48\\%$ , $4.73\\%$ , and $10.12\\%$ improvements on Spearman's rank correlation. Our method also outperforms the previous long-term AQA", + "bbox": [ + 496, + 703, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "2410", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/da839ffdcd1a5d1210e5f69b6d8ef6015827bbe7305bc427a0cdae30b1aa7fd8.jpg", + "image_caption": [ + "Figure 5. The visualization of the output of our proposed GOAT in action quality assessment. We use red stars to denote clips with high weight while using blue stars to represent clips with low weight. Our approach can focus on where the athletes perform effective movements with clear formations while it can also ignore the redundant part such as all actors are under-water." + ], + "image_footnote": [], + "bbox": [ + 81, + 117, + 883, + 328 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/696d78e7440254b07f192445711386fba47f7f806bab45b9a7786a75c77b2803.jpg", + "table_caption": [ + "Table 2. Comparisons of performance with existing AQA methods on LOGO. The higher $\\rho$ ,the lower $\\mathrm{R} - {\\ell }_{2}$ ,the better performance." + ], + "table_footnote": [], + "table_body": "
MethodI3DSWIN
ρ↑R-ℓ2(×100) ↓ρ↑R-ℓ2(×100) ↓
USDL [44]0.42595.73640.47255.0762
CoRe [52]0.47125.40860.50025.9597
TSA [50]0.45185.53260.47514.7778
ACTION-NET [53]0.30575.85810.41015.5693
USDL [44]+GOAT0.46204.87390.53495.0220
CoRe [52]+GOAT0.49355.07160.55994.7626
TSA [50]+GOAT0.48555.39430.48435.4086
", + "bbox": [ + 78, + 416, + 470, + 547 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/618929832b450c6e8ae94e4732749e5cb4daa3bcdc3e13c92d33f9feebe4475b.jpg", + "table_caption": [ + "Table 3. Action segmentation results on LOGO." + ], + "table_footnote": [], + "table_body": "
MethodFeaturesF1@{10,25,50}EditAcc
ASFormer [51]SWIN81.779.871.175.381.0
ASFormer [51]I3D75.171.661.368.273.9
MS_TCN++ [23]SWIN80.878.870.273.580.1
MS_TCN++ [23]I3D72.669.258.566.070.6
SSTDA [5]SWIN77.875.966.370.079.2
SSTDA [5]I3D60.155.744.050.163.4
ASRF [17]SWIN80.879.172.173.280.0
ASRF [17]I3D73.670.559.866.869.8
", + "bbox": [ + 78, + 570, + 467, + 712 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "method [53]. The experimental results illustrate the effectiveness of our proposed module when dealing with multiperson long-term scenarios.", + "bbox": [ + 75, + 718, + 468, + 762 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Action Segmentation. Table 3 presents the experimental results. With the I3D feature, the previous action segmentation methods [5, 17, 23, 51] achieve the result of $73.9\\%$ , $70.6\\%$ , $63.4\\%$ and $69.8\\%$ frame accuracy respectively. And given an identical setting, we see that the SWIN-pretrained feature obtained significant improvement in all five metrics. Table 6 reveals that our method could improve the performance of MS_TC++ and ASFormer and achieve the state-of-the-art with the group information.", + "bbox": [ + 75, + 763, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/324ac265e1e8507b509713a61d6c1c470ca0dfcd3c94a6846a5b083dad0eda62.jpg", + "table_caption": [ + "Table 4. Comparisons of AQA results of CORE and CORE+GOAT based on existing short-term, two-player datasets. @2 means AQA datasets with two-player scenes." + ], + "table_footnote": [], + "table_body": "
DatasetCORE [52]CORE [52]+GOAT
ρ↑R-ℓ2(×100) ↓ρ↑R-ℓ2(×100) ↓
FineDiving [50]@20.89910.37510.90320.3529
TASD-2 [11]@20.91890.78630.93340.7054
AQA-7 [29]@20.90120.73020.93250.6423
", + "bbox": [ + 500, + 430, + 893, + 507 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.4. Generalization of GOAT", + "text_level": 1, + "bbox": [ + 500, + 521, + 723, + 536 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Our method is currently suitable for multi-person scenarios. We select current AQA datasets with two-player scenes (there are only 2 players at most for now) and redivide them according to the number of people. TASD-2 [11] is a dataset collected from synchronized diving events with 2 players in each video. Based on the divided dataset, we obtain results in Table 4, which prove that GOAT can improve the AQA results of two-player scenes in other datasets. These results also demonstrate the generalization of GOAT. Our method can perform well in short-term, two-player scenes.", + "bbox": [ + 496, + 546, + 893, + 699 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.5. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 709, + 653, + 724 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We change the video feature backbone to verify the generality of our approach. Besides, we also try to use other spatial features or simply use self-attention for temporal information fusion to demonstrate the effectiveness of the group features. The experiments also illustrate that our temporal fusion strategy outperforms the average pooling.", + "bbox": [ + 496, + 733, + 892, + 824 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Spatial Features. As shown in Table 5, we conduct experiments utilizing formation features to replace the group embeddings used in GOAT to fuse the temporal representations. The formation features are extracted from the attention block output in the formation detection pipeline men", + "bbox": [ + 496, + 825, + 893, + 902 + ], + "page_idx": 6 + }, + { + "type": "header", + "text": "WorldChampionship2022_free_preliminary_15", + "bbox": [ + 343, + 97, + 647, + 113 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "2411", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ef2df0d15e7a454ef2c53c0d2670d4d448af26e9bebf4d6391b27987b5ba9324.jpg", + "image_caption": [ + "Figure 6. The visualization of the prediction results of our formation detector module. The green polygons represent prediction results and the yellow polygons with blue edges are the ground truth. The results show that our approach can detect the positions of actors and distinguish whether the athlete is the formation vertex or not, which guarantees the reliability of the formation features." + ], + "image_footnote": [], + "bbox": [ + 81, + 90, + 215, + 181 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/9405348331852f45d1f06294cc38ba7a01b2f98cc269d5502d054a7ff3f865b3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 217, + 90, + 349, + 181 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ebe946718bf991d1ab0b2b129fb6311a42628e02577fb7df4078f7ac80a731f7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 351, + 90, + 483, + 181 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/781c3bf082d4f21e5c1f89693a865167526d42ef43a70d3d4b1d603b860c297a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 486, + 90, + 617, + 181 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3604340a74630d551e49b24aff16375af4370d9e50de9ebac1888a0f509818a9.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 619, + 90, + 751, + 181 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/188de8ec2031892b5a3eb1a9664bc12c3dbad7d32e5c63e20ce99fc4e5cb91a9.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 753, + 90, + 888, + 181 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/8e5470a16001f2b580e780b603a35e9736443efb8a4bc5c938da8115f5ed32d8.jpg", + "table_caption": [ + "Table 5. Ablation studies on LOGO. Self. indicates self-attention; Form. indicates using formation features for temporal fusing; AS. means using the action segmentation features for temporal fusing." + ], + "table_footnote": [], + "table_body": "
MethodI3DSWIN
ρ↑R-ℓ2(×100)↓ρ↑R-ℓ2(×100)↓
USDL [44]+Self.0.43354.88980.50784.1305
CoRe [52]+Self.0.43485.60190.52694.5072
TSA [50]+Self.0.45855.03360.47205.7280
USDL [44]+Form.0.43555.76360.53705.0888
CoRe [52]+Form.0.48205.30030.54015.1747
TSA [50]+Form.0.42415.18210.49034.8627
USDL [44]+AS.0.45124.88370.51085.0479
CoRe [52]+AS.0.48255.23930.53644.9102
TSA [50]+AS.0.47725.42030.48295.3561
", + "bbox": [ + 78, + 292, + 470, + 452 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/4a62a090a4d3c7089654c28ec8b47c0d7992049f8147a0f06fdbdb5fc4481470.jpg", + "table_caption": [ + "Table 6. The action segmentation results of existing methods with GOAT on LOGO. +GOAT indicates the method with GOAT." + ], + "table_footnote": [], + "table_body": "
MethodFeaturesF1@{10,25,50}EditAcc
MS_TCN++ [23]+GOATSWIN80.979.070.574.081.1
MS_TCN++ [23]+GOATI3D73.269.959.467.371.7
ASFormer [51]+GOATSWIN82.280.373.675.981.7
ASFormer [51]+GOATI3D75.872.062.168.874.6
", + "bbox": [ + 78, + 491, + 470, + 577 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "tioned in 4.3, which is pretrained on the LOGO dataset by executing formation detection. We also adopt self-attention to replace GOAT, which means we perform our temporal fusion strategy without the assistance of any spatial information. The experimental results show that the formation features outperform the original models and self-attention models but perform worse than the group features in most cases. The results also show that the self-attention models perform better than the original models. Such results of our experiments prove that: (1) Our temporal fusion strategy outperforms the average pooling even without any spatial information. (2) By modeling the spatial information, the performance of our proposed approach is improved. (3) Building the relations among actors, the group features perform better than the formation features.", + "bbox": [ + 75, + 598, + 468, + 823 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Video Feature Backbone. As shown in Table 5 and Table 2. We change the backbone to video swin-transformer (abbreviated as SWIN) and repeat all our experiments. Similar to the results shown in the action segmentation experiments, the methods based on SWIN perform much better", + "bbox": [ + 75, + 824, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "than the methods based on I3D in most cases, which illustrates the effectiveness of SWIN. Besides, except for the case of TSA+Self, the results of our methods substantially outperform the original models based on SWIN, which proves the generality of our approach.", + "bbox": [ + 496, + 246, + 890, + 321 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Asist AQA with Action Segmentation. To assist the AQA task with the action segmentation task (or action labels), we use the backbone features finetuned in the action segmentation task as the input of GOAT in the experiments shown in the lower part of Table 5. The results illustrate that with the help of the segmentation task, the performances of AQA are improved compared with the original methods.", + "bbox": [ + 496, + 323, + 892, + 429 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.6. Visualization", + "text_level": 1, + "bbox": [ + 500, + 440, + 635, + 455 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We visualize the output of GOAT, as shown in Figure 5. It shows that GOAT highlights the part where actors perform effective action with clear formations, demonstrating the effectiveness of our temporal fusion strategy. We also visualize the prediction results of our formation detection module, as shown in Figure 6. It can be seen that our approach can distinguish the vertexes of the formations.", + "bbox": [ + 496, + 464, + 890, + 570 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 585, + 617, + 602 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we construct the first multi-person long-form video dataset, LOGO, for action quality assessment. We also propose a group-aware module, GOAT, to build relations among multiple actors and fuse the temporal representations based on spatial information. Furthermore, the utilization of GOAT in action quality assessment and action segmentation both achieve substantial improvements compared to the existing methods.", + "bbox": [ + 496, + 612, + 890, + 733 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Existing Assets and Personal Data. The videos in LOGO are downloaded from several websites such as YouTube. We are actively connecting with the authors to ensure that appropriate consent has been obtained.", + "bbox": [ + 496, + 734, + 890, + 792 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments. This work was sponsored in part by the National Natural Science Foundation of China (Grant No. 62206153, 62125603), CAAI-Huawei MindSpore Open Fund, Deng Feng Fund, Young Elite Scientists Sponsorship Program by CAST (No. 2022QNRC001), and Shenzhen Stable Supporting Program (WDZC20220818112518001).", + "bbox": [ + 496, + 795, + 892, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "2412", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Mindspore. https://www.mindspore.cn/.6", + "[2] Timur Bagautdinov, Alexandre Alahi, François Fleuret, Pascal Fua, and Silvio Savarese. Social scene understanding: End-to-end multi-person action localization and collective activity recognition. 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Video and accelerometer-based motion analysis for automated surgical skills assessment. *IJCARS*, 13(3):443-455, 2018. 2" + ], + "bbox": [ + 503, + 92, + 890, + 558 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "2414", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/LOGO_ A Long-Form Video Dataset for Group Action Quality Assessment/a2174fdf-969f-47ee-bc14-05e84961929f_model.json b/2023/LOGO_ A Long-Form Video Dataset for Group Action Quality Assessment/a2174fdf-969f-47ee-bc14-05e84961929f_model.json new file mode 100644 index 0000000000000000000000000000000000000000..cc63fc9233d17f69a5daa095c984dca236909120 --- /dev/null +++ b/2023/LOGO_ A Long-Form Video Dataset for Group Action Quality Assessment/a2174fdf-969f-47ee-bc14-05e84961929f_model.json @@ -0,0 +1,2222 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.108, + 0.131, + 0.865, + 0.154 + ], + "angle": 0, + "content": "LOGO: A Long-Form Video Dataset for Group Action Quality Assessment" + }, + { + "type": "text", + "bbox": [ + 0.086, + 0.179, + 0.907, + 0.273 + ], + "angle": 0, + "content": "Shiyi Zhang\\(^{1,2,3}\\), Wenxun Dai\\(^{1}\\), Sujia Wang\\(^{1}\\), Xiangwei Shen\\(^{1}\\), Jiwen Lu\\(^{2,3}\\), Jie Zhou\\(^{2,3}\\), Yansong Tang\\(^{1,*}\\) \n\\(^{1}\\) Shenzhen International Graduate School, Tsinghua University \n\\(^{2}\\) Department of Automation, Tsinghua University \n\\(^{3}\\) Beijing National Research Center for Information Science and Technology \n{shiyi-zh19@mails.,lujiwen@,jzhou@,tang.yansong@sz.}tsinghua.edu.cn" + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.284, + 0.891, + 0.535 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.545, + 0.895, + 0.603 + ], + "angle": 0, + "content": "Figure 1. An overview of the LOGO dataset. LOGO is a multi-person long-form video dataset with frame-wise annotations on both action procedures (as shown in the second line) and formations (as shown in the third line, which reflects relations among actors) based on artistic swimming scenarios. It provides a potential for constructing an action quality assessment approach with the ability of modeling group information among actors. Longer video durations also challenge the ability of the method to aggregate long-term temporal information." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.621, + 0.314, + 0.637 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.654, + 0.473, + 0.881 + ], + "angle": 0, + "content": "Action quality assessment (AQA) has become an emerging topic since it can be extensively applied in numerous scenarios. However, most existing methods and datasets focus on single-person short-sequence scenes, hindering the application of AQA in more complex situations. To address this issue, we construct a new multi-person long-form video dataset for action quality assessment named LOGO. Distinguished in scenario complexity, our dataset contains 200 videos from 26 artistic swimming events with 8 athletes in each sample along with an average duration of 204.2 seconds. As for richness in annotations, LOGO includes formation labels to depict group information of multiple athletes and detailed annotations on action procedures. Furthermore, we propose a simple yet effective method to model relations among athletes and reason about the potential" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.624, + 0.895, + 0.79 + ], + "angle": 0, + "content": "temporal logic in long-form videos. Specifically, we design a group-aware attention module, which can be easily plugged into existing AQA methods, to enrich the clipwise representations based on contextual group information. To benchmark LOGO, we systematically conduct investigations on the performance of several popular methods in AQA and action segmentation. The results reveal the challenges our dataset brings. Extensive experiments also show that our approach achieves state-of-the-art on the LOGO dataset. The dataset and code will be released at https://github.com/shiyi-zh0408/LOGO." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.828, + 0.633, + 0.843 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Action quality assessment (AQA) is applicable to many real-world contexts where people evaluate how well a specific action is performed such as sports events [13, 18, 29-" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.888, + 0.292, + 0.901 + ], + "angle": 0, + "content": "* indicates the corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2405" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.097, + 0.892, + 0.153 + ], + "angle": 0, + "content": "Table 1. Comparisons of LOGO and existing datasets of action quality assessment (upper part of the table) and group activity recognition (lower part of the table). Score indicates the score annotations; Action denotes action types and temporal boundaries; Act.Label indicates the action types of both individuals and groups. Bbox indicates bounding boxes for actors. Formation represents formation annotations. Temp. indicates temporal boundary, Spat. indicates spatial localization." + }, + { + "type": "table", + "bbox": [ + 0.078, + 0.165, + 0.895, + 0.407 + ], + "angle": 0, + "content": "
DatasetDurationAvg.Dur.Anno.TypeSamplesEventsForm.Anno.Year
MTL Dive [33]15m,54s6.0sScore1591✘2014
UNLV Dive [31]23m,26s3.8sScore3701✘2017
AQA-7-Dive [29]37m,31s4.1sScore5496✘2019
MTL-AQA [30]96m,29s4.1sAction,Score141216✘2019
Rhythmic Gymnastics [53]26h,23m,20s1m,35sScore10004✘2020
FSD-10 [26]-3-30sAction,Score1484-✘2020
FineDiving [50]3h,30m,0s4.2sAction,Score300030✘2022
Collective Activity [7]--Act.Label44-✘2009
NCAA [35]16h,9m,52s4sBbox,Act.Label11436-✘2016
Volleyball [16]2h,12m,1s1.64sBbox,Act.Label4830-✘2016
FineGym [38]161h,1m,45s45.7sAct.Label,Temp.1268510✘2020
Multisports [25]18h,34m,40s20.9sAct.Label,Temp.,Spat.3200247✘2021
LOGO(Ours)11h,20m,41s3m,24sAction,Formation,Score20026✓(15764)
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.431, + 0.47, + 0.598 + ], + "angle": 0, + "content": "33, 46], healthcare [28, 39, 55-58], art performances, military parades, and others. Due to the extensive application of AQA, many efforts have been made over the past few years. Although some existing works have achieved promising performances in several simple scenarios, the application of AQA in many situations is still difficult to implement. In the data-driven era, the richness of the dataset largely determines whether the model can be applied to a wide range of scenarios or not. Inspired by this, we reviewed the existing datasets in AQA and concluded that they are not rich enough for the following two reasons:" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.599, + 0.47, + 0.839 + ], + "angle": 0, + "content": "Simplicity of Scenarios. We argue that the complexity of the AQA application scenes is reflected in two aspects, the number of people and the duration of the videos. In snowboarding, for example, there is only one performer, while there are multiple actors in a military parade. In diving, the duration is only about 5 seconds, while in artistic swimming and dance performances, the duration of the action reaches several minutes. However, most existing datasets contain a single performer in each sample and many of them collect videos of 3-8s [29-31, 33, 50], which makes it difficult for existing methods to model complex scenes with more actors and longer duration. In such cases, just focusing on how well actions are performed by each individual may be insufficient. Relations among actors should be built, and the potential temporal logic in long-term videos should be modeled." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Coarse-grained Annotations. Though there have been some long-form video datasets in AQA [49, 53] which provide more complex scenes, they typically contain the score as the only annotation. Such coarse-grained annotation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.431, + 0.892, + 0.507 + ], + "angle": 0, + "content": "makes it difficult for models to learn deeper information, especially in more complex situations. Simply judging action quality via regressing a score for a long-term video could be confusing since we cannot figure out how the model determines whether an action is well-performed or not." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.509, + 0.893, + 0.734 + ], + "angle": 0, + "content": "To address these issues, we propose a multi-person long-form video dataset, LOGO (short for LOng-form GrOup). With 8 actors in each sample, LOGO contains videos with an average duration of 204.2s, much longer than most existing datasets in AQA, making the scenes more complex. Besides, as shown in Figure 1, LOGO contains fine-grained annotations including frame-wise action type labels and temporal boundaries of actions for each video. We also devise formation labels to depict relations among actors. Specifically, we use a convex polygon to represent the formation actors perform, which reflects their position information and group information. In general, LOGO is distinguished by its scenario complexity, while it also provides richer annotations compared to most existing datasets in AQA [29-31, 33, 49, 50, 53]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Furthermore, we build a plug-and-play module, GOAT (short for GrOut-aware ATtention), to bridge the gap between single-person short-sequence scenarios and multiperson long-sequence scenarios. Specifically, in the spatial domain, by building a graph for actors, we model the relations among them. The nodes of this graph represent actors' features extracted from a CNN, and the edges represent the relations among actors. Then we use a graph convolution network (GCN) [19] to model the group features from the graph. The optimized features of the graph then serve as \"queries\" and \"keys\" for GOAT. In the temporal do" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "2406" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.182 + ], + "angle": 0, + "content": "main, after feature extraction by the video feature backbone, the clip-wise features serve as “values” for GOAT. Instead of fusing the features simply using the average pooling as most previous works [44, 50, 52], GOAT learns the relations among clips and models the temporal features of the long-term videos based on the spatial information in every clip." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.183, + 0.471, + 0.409 + ], + "angle": 0, + "content": "The contributions of this paper can be summarized as: (1) We construct the first multi-person long-form video dataset, LOGO, for action quality assessment. To the best of our knowledge, LOGO stands out for its longer average duration, the larger number of people, and richer annotations when compared to most existing datasets. Experimental results also reveal the challenges our proposed dataset brings. (2) We propose a plug-and-play group-aware module, GOAT, which models the group information and the temporal contextual relations for input videos, bridging the gap between single-person short-sequence scenarios and multi-person long-sequence scenarios. (3) Experimental results demonstrate that our group-aware approach obtains substantial improvements compared to existing methods in AQA and achieves the state-of-the-art." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.423, + 0.22, + 0.437 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.449, + 0.47, + 0.81 + ], + "angle": 0, + "content": "Action Quality Assessment. Assessing action quality is an increasingly popular trend in computer vision with wide applications such as video retrieval, instructional video analysis, etc. A wide variety of methods for formulating AQA tasks have been proposed [3, 10, 13, 24, 31, 33, 44, 48, 49, 52, 53]. In long video AQA tasks, actions performed at different times may significantly impact the scores given by experts. However, only a handful of works directly address the problem of long-term video AQA [3, 10, 48, 49, 53]. There are many datasets for AQA, including Diving [29-31, 33, 50], Figure Skating [26, 33], Gymnastic Vault [29, 31], Basketball [3], Fitness [43] and Rhythmic Gymnastics [53]. However, the problem of considering group information in multi-person sports has been relatively unexplored. As shown in Table 1, MIT-Dive [33], UNLV-Dive [31], AQA-7-Dive [29] and Rhythmic Gymnastics [53] only provide action scores, while MTL-AQA [30] FSD-10 [26] and FineDiving [50] only provide action types and scores. To perform AQA in long videos with multi-person, we construct a long-form artistic swimming video dataset, LOGO, with fine-grained frame-wise action and formation labels. Furthermore, we propose a method to model relations among athletes and reason about the potential temporal logic in long-form videos." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Group Activity Understanding. Group activity understanding, which concentrates on interpreting the collective activity from multi-person behavioral and interaction dynamics, has attracted plenty of work recently. The focus of existing methods has shifted from using shallow handcrafted features [6,8,20,21,36,40] to using deep neural net" + }, + { + "type": "image", + "bbox": [ + 0.513, + 0.093, + 0.885, + 0.36 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.376, + 0.892, + 0.474 + ], + "angle": 0, + "content": "Figure 2. A tree structure of LOGO Taxonomy. LOGO organizes both the Actions and Formations annotations hierarchically. The left part shows the Actions categories of Technical and Free events. The right part depicts the formation annotation instances when the group is doing Required, Upper, Lower or Float actions (the right sub-tree of Actions) and not when the group is doing other actions, during which the formations are indistinguishable." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.483, + 0.893, + 0.665 + ], + "angle": 0, + "content": "works [2,12,15,22,34,45]. Diverse datasets have been proposed to facilitate research in this area, such as the Collective Activity dataset [7], Volleyball dataset [16], etc. However, the methods and datasets mentioned above only stay at the level of group activity recognition; a more profound understanding of group activities should be able to not only find the high-level group activity but also evaluate the quality of group activities, which requires more attention to the quality of collaboration among actors and fine-grained actions of actors. In this paper, LOGO takes the first step towards quality assessment and sets a new benchmark for group activity understanding." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.678, + 0.691, + 0.693 + ], + "angle": 0, + "content": "3. The LOGO Dataset" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.703, + 0.892, + 0.763 + ], + "angle": 0, + "content": "We propose a new multi-person long-form video dataset with detailed annotations on action and formation, LOGO, to set a new challenging benchmark for AQA. We will introduce it from its construction and annotation in this section." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.772, + 0.7, + 0.787 + ], + "angle": 0, + "content": "3.1. Dataset Construction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Collection. According to the official FINA rules, the same rules, and prescribed movements are used from 2018 until the end of the 2022 World Championships. So we collected the officially designated Technical and Free artistic swimming competitions during this period (2 World Championships, 1 Olympic Games, and 4 World Series). We download competition videos with high resolution, e.g.," + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2407" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.089, + 0.258, + 0.234 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.268, + 0.089, + 0.465, + 0.235 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.245, + 0.468, + 0.274 + ], + "angle": 0, + "content": "Figure 3. Statics of LOGO. (a) The score distribution of videos. (b) The action-type distribution of frames." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.287, + 0.468, + 0.362 + ], + "angle": 0, + "content": "720p and 1080p, on online video platforms like YouTube. Then we sampled them at 25fps and 1fps sampling rates for fine-grained action and formation labeling. Each official videos provide various content, including three sub-scores, one final score, and frames from different views." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.364, + 0.468, + 0.606 + ], + "angle": 0, + "content": "Lexicon. We construct a fine-grained video dataset organized by temporal structure, which contains action and formation manual annotations, shown in Figure 2. Herein, we design the labeling system with professional artistic swimming athletes to construct a lexicon for annotation, considering FINA rules and the actual scenario of the competitions. In the Technical event, the group size is eight people, the video length is \\(170 \\pm 15\\mathrm{s}\\), and the actions include Upper, Lower, Float, None, Acrobatic, Cadence, and five Required Elements. Each competition cycle needs to complete five Required Elements, at least two Acrobatic movements, and at least one Cadence action. In the Free events, there are 8 people, the video length is \\(240 \\pm 15\\mathrm{s}\\), and the actions include Upper, Lower, Float, None, Acrobatic, Cadence, and Free elements. When performing Required, Upper, Lower, and Float, the athletes form neat polygons as in Figure 2." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.607, + 0.468, + 0.818 + ], + "angle": 0, + "content": "Annotation. Given an RGB artistic swimming video, the annotator utilizes our defined lexicon to label each frame with its action and formation. We accomplish the 25fps frame-wise action annotation stage utilizing the COIN annotation toolbox [42] and the 1fps frame-wise formation labels using Labelme. Specifically, we set strict rules defining the boundaries between artistic swimming sequences and the formation marking position and employ eight workers with prior knowledge in the artistic swimming domain to label the dataset frame by frame following the rules. The annotation results of one worker are checked and adjusted by another, which ensures annotation results are double-checked. Under this pipeline, the total time for the annotation process is above 600 hours." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.831, + 0.227, + 0.845 + ], + "angle": 0, + "content": "3.2. Dataset Statics" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.468, + 0.902 + ], + "angle": 0, + "content": "The LOGO dataset consists of 200 video samples from 26 events with 204.2s average duration and above 11h total duration, covering 3 annotation types, 12 action types," + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.289 + ], + "angle": 0, + "content": "and 17 formation types. Figure 3 shows the score and action type distributions among all the events. Table 1 reports more detailed information on the LOGO dataset and compares it with existing AQA datasets and other fine-grained sports datasets. Our dataset differs from existing AQA datasets in the annotation type and dataset scale. Specifically, our dataset includes formation types providing group information and longer videos on sports, helping to evaluate the quality of actions in multiplayer sports quantitatively. Other fine-grained sports datasets cannot be used for assessing action quality due to a lack of action scores. LOGO is the first fine-grained sports video dataset for Group AQA, filling the fine-grained group annotations void in AQA." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.301, + 0.608, + 0.318 + ], + "angle": 0, + "content": "4. Approach" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.326, + 0.702, + 0.34 + ], + "angle": 0, + "content": "4.1. Problem Formulation" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.349, + 0.892, + 0.395 + ], + "angle": 0, + "content": "Most existing methods in AQA process the output of the video feature backbone using average pooling before regression. It can be represented as:" + }, + { + "type": "equation", + "bbox": [ + 0.61, + 0.406, + 0.892, + 0.448 + ], + "angle": 0, + "content": "\\[\n\\hat {y} = \\mathcal {R} \\left[ \\frac {1}{T} \\sum_ {i = 1} ^ {T} \\mathcal {F} \\left(X _ {i}\\right) | \\Theta \\right], \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.457, + 0.892, + 0.624 + ], + "angle": 0, + "content": "where \\( X_{i} \\) denotes the \\( i \\)-th clip of the video. \\( \\mathcal{F} \\) indicates the video feature backbone; \\( T \\) is the number of clips; \\( \\mathcal{R} \\) represents the regression algorithm; \\( \\Theta \\) is the learnable parameters of \\( \\mathcal{R} \\) and \\( \\hat{y} \\) is the predicted score. However, fusing temporal information simply by average pooling in scenes with longer duration may be confusing since there could be redundant or even invalid information in the video. Besides, when dealing with multi-person scenarios, we need to depict the relations among actors. We use group information to fuse the extracted features in the temporal axis, modeling the relations among clips. It can be represented as:" + }, + { + "type": "equation", + "bbox": [ + 0.625, + 0.634, + 0.892, + 0.675 + ], + "angle": 0, + "content": "\\[\n\\hat {y} = \\mathcal {R} \\left[ \\frac {1}{T} \\sum_ {i = 1} ^ {T} f _ {i} | \\Theta \\right], \\tag {2}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.568, + 0.678, + 0.891, + 0.721 + ], + "angle": 0, + "content": "\\[\nf _ {i} = \\sum_ {j = 1} ^ {T} \\mathcal {G} \\left(X _ {i}, X _ {j}\\right) \\mathcal {F} \\left(X _ {j}\\right), i = 1 \\dots T, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.732, + 0.891, + 0.778 + ], + "angle": 0, + "content": "where \\(\\mathcal{G}(X_i, X_j)\\) denotes the weight computed by group features of the \\(i\\)-th clip and the \\(j\\)-th clip; \\(f_i\\) indicates the reconstructed feature of the \\(i\\)-th clip." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.787, + 0.717, + 0.803 + ], + "angle": 0, + "content": "4.2. Group-aware Attention" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.811, + 0.892, + 0.856 + ], + "angle": 0, + "content": "There are two components of GOAT, that is, group-aware GCN and temporal-fusion attention. The overview of our framework is illustrated in Figure 4." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Group-aware GCN. This component is shown in the right part of Figure 4. We extract the group features by modeling the relations among actors with graphs. Given a" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "2408" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.096, + 0.526, + 0.29 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.53, + 0.098, + 0.887, + 0.29 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.309, + 0.894, + 0.395 + ], + "angle": 0, + "content": "Figure 4. An overview of our group-aware approach for action quality assessment. First, we divide the video into several short clips of equal length. For each clip, we take the middle frame and perform object detection to get the bounding boxes of the actors. Then we send the frame into a CNN to extract the features of the actors. Then we use the feature vector of each actor as the node to construct the relation graph. We use Graph Convolutional Network to enhance the features in the graph, and send the output features into GOAT as “queries” and “keys”. And the “values” are the features obtained from the clip by the video feature backbone such as I3D and video swin-transformer. Thus the aggregation in time can be completed. Finally, the output features are sent into the assessment network to predict the scores." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.407, + 0.47, + 0.602 + ], + "angle": 0, + "content": "video, we fix it into the given duration via downsampling or upsampling and divide it into several clips of equal length. Then we take three steps to extract the group features. First, we select the middle frame from each clip and build features for the actors. Specifically, we adopt object detection [54] to get bounding boxes of actors. Then, we use Inception-V3 [41] on the frame to get the feature map, to which we apply RoIAlign [14] to extract features for each bounding box. We use a fully connected layer to get a \\(d\\)-dimensional vector from the feature map for each actor. Then we have a \\(N \\times d\\) representation denoted as \\(G\\) for each middle frame, where \\(N\\) denotes the number of actors and \\(d\\) indicates the dimension of feature vectors." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.603, + 0.47, + 0.692 + ], + "angle": 0, + "content": "Second, we build a relation graph with the feature matrix \\( G \\) to model the relations among actors. Concretely, we regard each feature vector of an actor as a node in the graph. We follow the strategy in [47] to build edges among nodes by computing similarities of appearance features and relative location of actors." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.694, + 0.47, + 0.74 + ], + "angle": 0, + "content": "Then, a Graph Convolutional Network (GCN) [19] is adopted to the relation graph to enhance node features by weighted aggregation, which can be represented as:" + }, + { + "type": "equation", + "bbox": [ + 0.186, + 0.749, + 0.47, + 0.768 + ], + "angle": 0, + "content": "\\[\nH ^ {(l + 1)} = \\sigma (A H ^ {(l)} W ^ {(l)}), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.779, + 0.47, + 0.87 + ], + "angle": 0, + "content": "where \\(A\\) indicates the adjacent matrix; \\(W^{(l)}\\) is the weight matrix in \\(l\\)-th layer; \\(H^{(l)}\\) denotes the features of nodes in \\(l\\)-th layer and \\(H^{(0)} = G\\). Finally, The group feature vector is extracted by adopting average pooling to the sum of the input and the output features of GCN. The group feature vector of the \\(i\\)-th clip is denoted as \\(g_{i}\\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Temporal-fusion Attention. This component fuses the video embeddings along the temporal axis based on the rep-" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.407, + 0.892, + 0.497 + ], + "angle": 0, + "content": "resentations from the group-aware GCN. As shown in the left part of Figure 4, for each clip split from the video, we send it into an I3D [4] backbone as most previous works do [44, 50, 52, 53]. We leverage the strong capability of capturing global information of the multi-head attention encoder for learning group-aware video embeddings." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.497, + 0.893, + 0.634 + ], + "angle": 0, + "content": "We denote the I3D features of the video as \\(\\{\\mathcal{F}(X_i)\\}_{i = 1}^T\\), which serve as the \"value\" of the attention block. And the vectors \\(\\{g_i\\}_{i = 1}^T\\) from group-aware GCN serve as \"query\" and \"key\". The temporal-fusion attention module learns to discover the group feature correspondences among clips, and generates new temporal features in all of them. The module uses the relations of group features among different clips to assign different weights to different temporal features. The above attention learning can be represented as:" + }, + { + "type": "equation", + "bbox": [ + 0.587, + 0.643, + 0.891, + 0.665 + ], + "angle": 0, + "content": "\\[\nq ^ {(l)} = W _ {Q} ^ {(l)} q ^ {(l - 1)}, \\tag {5}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.588, + 0.667, + 0.891, + 0.687 + ], + "angle": 0, + "content": "\\[\nk ^ {(l)} = W _ {K} ^ {(l)} k ^ {(l - 1)}, \\tag {6}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.57, + 0.689, + 0.891, + 0.724 + ], + "angle": 0, + "content": "\\[\nW _ {a t t n} ^ {(l)} = \\operatorname {S o f t m a x} \\left(\\frac {q ^ {(l)} k ^ {(l) T}}{\\sqrt {d}}\\right), \\tag {7}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.588, + 0.726, + 0.891, + 0.746 + ], + "angle": 0, + "content": "\\[\nv ^ {(l)} = B N \\left[ W _ {a t t n} ^ {(l)} v ^ {(l - 1)} + v ^ {(l - 1)} \\right], \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.757, + 0.894, + 0.841 + ], + "angle": 0, + "content": "where \\( W_{Q}^{(l)}, W_{K}^{(l)}, W_{attn}^{(l)} \\) indicate the learnable weights in \\( l \\)-th layer; \\( q^{(l)}, k^{(l)}, v^{(l)} \\) denote the \"query\", \"key\" and \"value\" in \\( l \\)-th layer; \\( d \\) is the dimension of feature vector and \\( BN \\) is the BatchNorm block. Besides, \\( q^{(0)} = k^{(0)} = \\{g_i\\}_{i=1}^T \\), \\( v^{(0)} = \\{\\mathcal{F}(X_i)\\}_{i=1}^T \\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.848, + 0.696, + 0.862 + ], + "angle": 0, + "content": "4.3. Formation Detection" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.893, + 0.902 + ], + "angle": 0, + "content": "In 4.2, we propose a pipeline to fuse temporal representations based on a kind of spatial information, the group" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2409" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.166 + ], + "angle": 0, + "content": "features. However, such a fusion strategy can also be based on other kinds of spatial features and even without any features by simply using self-attention. To prove the effectiveness of the group features, we devise another kind of spatial features, formation features, to make a comparison." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.168, + 0.468, + 0.257 + ], + "angle": 0, + "content": "Formation Detection Task. As mentioned in Section 3, we use a polygon to depict the formation of actors. As shown in Figure 2, the polygon is represented by several coordinates of some actors but not all of them. So in this task, we need to distinguish whether an actor is the vertex of the polygon or not." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.258, + 0.468, + 0.452 + ], + "angle": 0, + "content": "Formation Detection Algorithm. Inspired by the \"anchor\" in object detection [37], we propose a feasible way to detect the vertexes. Given a picture, we split it into 1024 patches of equal size. For each patch, we set the center point as the \"anchor\". We send the image into Inception-V3 and extract the \\(d\\)-dimensional feature vector with RoIAlign [14] and a fully connected layer for each patch. To represent the absolute position of each patch, we use sine and cosine functions of different frequencies to encode the position of the \"anchor\". We add the \\(d\\)-dimensional positional encodings to the features and send them into a self-attention block to find the relations among different patches and build the \\(d\\)-dimensional formation features for them." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.454, + 0.468, + 0.514 + ], + "angle": 0, + "content": "Then we take two steps to find vertexes. First, for each patch, we judge whether there is a vertex. Second, if there is a vertex, we calculate the relative coordinates of the vertex to the \"anchor\" point. So we detect vertexes by computing:" + }, + { + "type": "equation", + "bbox": [ + 0.153, + 0.524, + 0.468, + 0.543 + ], + "angle": 0, + "content": "\\[\n\\hat {P} = \\left[ \\hat {p} _ {1}, \\dots , \\hat {p} _ {n} \\right], \\quad \\hat {C} = \\left[ \\hat {c} _ {1}, \\dots , \\hat {c} _ {n} \\right], \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.553, + 0.468, + 0.659 + ], + "angle": 0, + "content": "where \\(\\hat{p}_i\\in \\mathbb{R}\\) denotes the confidence of whether there is a vertex in the \\(i\\) -th patch and \\(\\hat{c}_i\\in \\mathbb{R}^2\\) is the relative coordinates of the vertex to the \"anchor\". In this way, the formation detection task is converted to a classification problem and a regression problem. And we respectively use a MLP to predict \\(\\hat{P}\\) and \\(\\hat{C}\\) upon the formation features mentioned above. The object function can be represented as:" + }, + { + "type": "equation", + "bbox": [ + 0.1, + 0.671, + 0.468, + 0.7 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {B C E} = - \\sum_ {i} \\left[ p _ {i} \\log \\hat {p} _ {i} + (1 - p _ {i}) \\log \\left(1 - \\hat {p} _ {i}\\right) \\right], \\tag {10}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.2, + 0.705, + 0.468, + 0.723 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {M S E} = \\left\\| C - \\hat {C} \\right\\| ^ {2}. \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.734, + 0.468, + 0.809 + ], + "angle": 0, + "content": "We minimize \\(\\mathcal{L}_{BCE}\\) and \\(\\mathcal{L}_{MSE}\\) to predict the vertexes. The \\(d\\)-dimensional formation features of middle frame in each clip can replace the group features in 4.2 to fuse the temporal information. Relative experiments are conducted in our ablation study." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.822, + 0.209, + 0.839 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.848, + 0.294, + 0.863 + ], + "angle": 0, + "content": "5.1. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Action Quality Assessment. Following [31,49,53], we take two stages to assess action quality: feature extraction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.303 + ], + "angle": 0, + "content": "and score prediction. In the feature extraction stage, we use the I3D model pretrained on Kinetics [4] dataset to extract the 1024-dimensional feature vector for each video clip. Specifically, we sample 5406 frames for each video, split them into 540 snippets, and fed them into I3D. Each snippet contains 16 continuous frames with a stride of 10 frames. In the ablation study, we also use the video swintransformer [27] as the backbone, which is also pretrained on Kinetics. We follow the sampling strategy in [27] to use a temporal stride of 2. The Inception-V3 in 4.2 is pretrained on ImageNet [9] to extract the CNN features. Following [44, 50, 52], we split the dataset into 3:1 for training and testing in all the experiments. We also test our model using the Mindspore [1]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.304, + 0.892, + 0.439 + ], + "angle": 0, + "content": "Action Segmentation. We conduct action segmentation on LOGO with several existing approaches (ASFormer [51], SSTDA [23], MS_TC++ [5], ASRF [17]) to provide a benchmark. We try two backbones to extract frame-wise features: I3D [4] model and video swim-transformer [27] pretrained on Kinetics. For SWIN, we expand the snippet size to 32 frames to extract 1536-dimensional features. In the training stage, we train action segmentation approaches on their default setting." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.45, + 0.684, + 0.464 + ], + "angle": 0, + "content": "5.2. Evaluation Metrics" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.473, + 0.892, + 0.578 + ], + "angle": 0, + "content": "Action Quality Assessment. Following [44, 50, 52, 53], we comprehensively evaluate our approach to AQA under two metrics, Spearman's rank correlation \\((\\rho)\\) and relative \\(\\ell_2\\)-distance \\((\\mathbf{R} - \\ell_2)\\). Spearman's rank correlation is used to evaluate the rank correlation between the prediction and ground-truth while the relative \\(\\ell_2\\)-distance \\((\\mathbf{R} - \\ell_2)\\) focuses on the difference of the numerical values." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.58, + 0.892, + 0.671 + ], + "angle": 0, + "content": "Action Segmentation. Following [5, 15, 23, 51], we adopt three widely used evaluation metrics including framewise accuracy (Acc), segmental edit distance and segmental F1 score at overlapping thresholds \\(10\\%\\), \\(25\\%\\), and \\(50\\%\\), denoted by F1@{10, 25, 50} to evaluate the performance of action segmentation approaches." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.681, + 0.821, + 0.697 + ], + "angle": 0, + "content": "5.3. Comparison with the State of the Art" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Action Quality Assessment. Table 2 shows the experimental results, which reveal great challenges to performing action quality assessment on the LOGO dataset. With the I3D backbone, the mainstream methods in single-person short-term AQA [44, 50, 52] attain the result of 0.4259, 0.4712, and 0.4518 on Spearman's rank correlation respectively. Besides, the results show that our approach achieves the state-of-the-art. We observe that USDL+GOAT, CoRe+GOAT, and TSA+GOAT consistently improve the performance over the original models. Specifically, our approach respectively obtained \\(8.48\\%\\), \\(4.73\\%\\), and \\(10.12\\%\\) improvements on Spearman's rank correlation. Our method also outperforms the previous long-term AQA" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2410" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.344, + 0.098, + 0.648, + 0.114 + ], + "angle": 0, + "content": "WorldChampionship2022_free_preliminary_15" + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.118, + 0.885, + 0.329 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.332, + 0.895, + 0.376 + ], + "angle": 0, + "content": "Figure 5. The visualization of the output of our proposed GOAT in action quality assessment. We use red stars to denote clips with high weight while using blue stars to represent clips with low weight. Our approach can focus on where the athletes perform effective movements with clear formations while it can also ignore the redundant part such as all actors are under-water." + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.384, + 0.471, + 0.412 + ], + "angle": 0, + "content": "Table 2. Comparisons of performance with existing AQA methods on LOGO. The higher \\( \\rho \\) ,the lower \\( \\mathrm{R} - {\\ell }_{2} \\) ,the better performance." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.417, + 0.472, + 0.548 + ], + "angle": 0, + "content": "
MethodI3DSWIN
ρ↑R-ℓ2(×100) ↓ρ↑R-ℓ2(×100) ↓
USDL [44]0.42595.73640.47255.0762
CoRe [52]0.47125.40860.50025.9597
TSA [50]0.45185.53260.47514.7778
ACTION-NET [53]0.30575.85810.41015.5693
USDL [44]+GOAT0.46204.87390.53495.0220
CoRe [52]+GOAT0.49355.07160.55994.7626
TSA [50]+GOAT0.48555.39430.48435.4086
" + }, + { + "type": "table_caption", + "bbox": [ + 0.13, + 0.551, + 0.416, + 0.565 + ], + "angle": 0, + "content": "Table 3. Action segmentation results on LOGO." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.571, + 0.468, + 0.713 + ], + "angle": 0, + "content": "
MethodFeaturesF1@{10,25,50}EditAcc
ASFormer [51]SWIN81.779.871.175.381.0
ASFormer [51]I3D75.171.661.368.273.9
MS_TCN++ [23]SWIN80.878.870.273.580.1
MS_TCN++ [23]I3D72.669.258.566.070.6
SSTDA [5]SWIN77.875.966.370.079.2
SSTDA [5]I3D60.155.744.050.163.4
ASRF [17]SWIN80.879.172.173.280.0
ASRF [17]I3D73.670.559.866.869.8
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.719, + 0.47, + 0.763 + ], + "angle": 0, + "content": "method [53]. The experimental results illustrate the effectiveness of our proposed module when dealing with multiperson long-term scenarios." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Action Segmentation. Table 3 presents the experimental results. With the I3D feature, the previous action segmentation methods [5, 17, 23, 51] achieve the result of \\(73.9\\%\\), \\(70.6\\%\\), \\(63.4\\%\\) and \\(69.8\\%\\) frame accuracy respectively. And given an identical setting, we see that the SWIN-pretrained feature obtained significant improvement in all five metrics. Table 6 reveals that our method could improve the performance of MS_TC++ and ASFormer and achieve the state-of-the-art with the group information." + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.384, + 0.893, + 0.426 + ], + "angle": 0, + "content": "Table 4. Comparisons of AQA results of CORE and CORE+GOAT based on existing short-term, two-player datasets. @2 means AQA datasets with two-player scenes." + }, + { + "type": "table", + "bbox": [ + 0.501, + 0.431, + 0.894, + 0.508 + ], + "angle": 0, + "content": "
DatasetCORE [52]CORE [52]+GOAT
ρ↑R-ℓ2(×100) ↓ρ↑R-ℓ2(×100) ↓
FineDiving [50]@20.89910.37510.90320.3529
TASD-2 [11]@20.91890.78630.93340.7054
AQA-7 [29]@20.90120.73020.93250.6423
" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.522, + 0.725, + 0.537 + ], + "angle": 0, + "content": "5.4. Generalization of GOAT" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.547, + 0.894, + 0.7 + ], + "angle": 0, + "content": "Our method is currently suitable for multi-person scenarios. We select current AQA datasets with two-player scenes (there are only 2 players at most for now) and redivide them according to the number of people. TASD-2 [11] is a dataset collected from synchronized diving events with 2 players in each video. Based on the divided dataset, we obtain results in Table 4, which prove that GOAT can improve the AQA results of two-player scenes in other datasets. These results also demonstrate the generalization of GOAT. Our method can perform well in short-term, two-player scenes." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.71, + 0.654, + 0.726 + ], + "angle": 0, + "content": "5.5. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.734, + 0.893, + 0.825 + ], + "angle": 0, + "content": "We change the video feature backbone to verify the generality of our approach. Besides, we also try to use other spatial features or simply use self-attention for temporal information fusion to demonstrate the effectiveness of the group features. The experiments also illustrate that our temporal fusion strategy outperforms the average pooling." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.894, + 0.903 + ], + "angle": 0, + "content": "Spatial Features. As shown in Table 5, we conduct experiments utilizing formation features to replace the group embeddings used in GOAT to fuse the temporal representations. The formation features are extracted from the attention block output in the formation detection pipeline men" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "2411" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.091, + 0.216, + 0.183 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.218, + 0.091, + 0.351, + 0.183 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.352, + 0.091, + 0.485, + 0.183 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.487, + 0.091, + 0.619, + 0.183 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.62, + 0.091, + 0.753, + 0.183 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.754, + 0.091, + 0.889, + 0.183 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.192, + 0.895, + 0.234 + ], + "angle": 0, + "content": "Figure 6. The visualization of the prediction results of our formation detector module. The green polygons represent prediction results and the yellow polygons with blue edges are the ground truth. The results show that our approach can detect the positions of actors and distinguish whether the athlete is the formation vertex or not, which guarantees the reliability of the formation features." + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.245, + 0.47, + 0.288 + ], + "angle": 0, + "content": "Table 5. Ablation studies on LOGO. Self. indicates self-attention; Form. indicates using formation features for temporal fusing; AS. means using the action segmentation features for temporal fusing." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.293, + 0.471, + 0.453 + ], + "angle": 0, + "content": "
MethodI3DSWIN
ρ↑R-ℓ2(×100)↓ρ↑R-ℓ2(×100)↓
USDL [44]+Self.0.43354.88980.50784.1305
CoRe [52]+Self.0.43485.60190.52694.5072
TSA [50]+Self.0.45855.03360.47205.7280
USDL [44]+Form.0.43555.76360.53705.0888
CoRe [52]+Form.0.48205.30030.54015.1747
TSA [50]+Form.0.42415.18210.49034.8627
USDL [44]+AS.0.45124.88370.51085.0479
CoRe [52]+AS.0.48255.23930.53644.9102
TSA [50]+AS.0.47725.42030.48295.3561
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.457, + 0.47, + 0.484 + ], + "angle": 0, + "content": "Table 6. The action segmentation results of existing methods with GOAT on LOGO. +GOAT indicates the method with GOAT." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.492, + 0.471, + 0.578 + ], + "angle": 0, + "content": "
MethodFeaturesF1@{10,25,50}EditAcc
MS_TCN++ [23]+GOATSWIN80.979.070.574.081.1
MS_TCN++ [23]+GOATI3D73.269.959.467.371.7
ASFormer [51]+GOATSWIN82.280.373.675.981.7
ASFormer [51]+GOATI3D75.872.062.168.874.6
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.599, + 0.47, + 0.824 + ], + "angle": 0, + "content": "tioned in 4.3, which is pretrained on the LOGO dataset by executing formation detection. We also adopt self-attention to replace GOAT, which means we perform our temporal fusion strategy without the assistance of any spatial information. The experimental results show that the formation features outperform the original models and self-attention models but perform worse than the group features in most cases. The results also show that the self-attention models perform better than the original models. Such results of our experiments prove that: (1) Our temporal fusion strategy outperforms the average pooling even without any spatial information. (2) By modeling the spatial information, the performance of our proposed approach is improved. (3) Building the relations among actors, the group features perform better than the formation features." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Video Feature Backbone. As shown in Table 5 and Table 2. We change the backbone to video swin-transformer (abbreviated as SWIN) and repeat all our experiments. Similar to the results shown in the action segmentation experiments, the methods based on SWIN perform much better" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.247, + 0.892, + 0.323 + ], + "angle": 0, + "content": "than the methods based on I3D in most cases, which illustrates the effectiveness of SWIN. Besides, except for the case of TSA+Self, the results of our methods substantially outperform the original models based on SWIN, which proves the generality of our approach." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.324, + 0.893, + 0.43 + ], + "angle": 0, + "content": "Asist AQA with Action Segmentation. To assist the AQA task with the action segmentation task (or action labels), we use the backbone features finetuned in the action segmentation task as the input of GOAT in the experiments shown in the lower part of Table 5. The results illustrate that with the help of the segmentation task, the performances of AQA are improved compared with the original methods." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.441, + 0.637, + 0.456 + ], + "angle": 0, + "content": "5.6. Visualization" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.465, + 0.892, + 0.571 + ], + "angle": 0, + "content": "We visualize the output of GOAT, as shown in Figure 5. It shows that GOAT highlights the part where actors perform effective action with clear formations, demonstrating the effectiveness of our temporal fusion strategy. We also visualize the prediction results of our formation detection module, as shown in Figure 6. It can be seen that our approach can distinguish the vertexes of the formations." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.587, + 0.619, + 0.603 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.613, + 0.892, + 0.734 + ], + "angle": 0, + "content": "In this paper, we construct the first multi-person long-form video dataset, LOGO, for action quality assessment. We also propose a group-aware module, GOAT, to build relations among multiple actors and fuse the temporal representations based on spatial information. Furthermore, the utilization of GOAT in action quality assessment and action segmentation both achieve substantial improvements compared to the existing methods." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.794 + ], + "angle": 0, + "content": "Existing Assets and Personal Data. The videos in LOGO are downloaded from several websites such as YouTube. We are actively connecting with the authors to ensure that appropriate consent has been obtained." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Acknowledgments. This work was sponsored in part by the National Natural Science Foundation of China (Grant No. 62206153, 62125603), CAAI-Huawei MindSpore Open Fund, Deng Feng Fund, Young Elite Scientists Sponsorship Program by CAST (No. 2022QNRC001), and Shenzhen Stable Supporting Program (WDZC20220818112518001)." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2412" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.105 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.424, + 0.129 + ], + "angle": 0, + "content": "[1] Mindspore. https://www.mindspore.cn/.6" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.131, + 0.469, + 0.186 + ], + "angle": 0, + "content": "[2] Timur Bagautdinov, Alexandre Alahi, François Fleuret, Pascal Fua, and Silvio Savarese. 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Video and accelerometer-based motion analysis for automated surgical skills assessment. *IJCARS*, 13(3):443-455, 2018. 2" + }, + { + "type": "list", + "bbox": [ + 0.504, + 0.093, + 0.892, + 0.559 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "2414" + } + ] +] \ No newline at end of file diff --git a/2023/LOGO_ A Long-Form Video Dataset for Group Action Quality Assessment/a2174fdf-969f-47ee-bc14-05e84961929f_origin.pdf b/2023/LOGO_ A Long-Form Video Dataset for Group Action Quality Assessment/a2174fdf-969f-47ee-bc14-05e84961929f_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..3b53ec73091cd5813be5b66c725962e7b8109b3c --- /dev/null +++ b/2023/LOGO_ A Long-Form Video Dataset for Group Action Quality Assessment/a2174fdf-969f-47ee-bc14-05e84961929f_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:309c5ba8c395e077c03e24dd9bb22ca030bb5b670ca441e795f5062a6a9c0bb5 +size 5953360 diff --git a/2023/LOGO_ A Long-Form Video Dataset for Group Action Quality Assessment/full.md b/2023/LOGO_ A Long-Form Video Dataset for Group Action Quality Assessment/full.md new file mode 100644 index 0000000000000000000000000000000000000000..d465b92b46769af13f4f3fb4c5ff6df3bd170355 --- /dev/null +++ b/2023/LOGO_ A Long-Form Video Dataset for Group Action Quality Assessment/full.md @@ -0,0 +1,327 @@ +# LOGO: A Long-Form Video Dataset for Group Action Quality Assessment + +Shiyi Zhang $^{1,2,3}$ , Wenxun Dai $^{1}$ , Sujia Wang $^{1}$ , Xiangwei Shen $^{1}$ , Jiwen Lu $^{2,3}$ , Jie Zhou $^{2,3}$ , Yansong Tang $^{1,*}$ $^{1}$ Shenzhen International Graduate School, Tsinghua University + $^{2}$ Department of Automation, Tsinghua University + $^{3}$ Beijing National Research Center for Information Science and Technology +{shiyi-zh19@mails.,lujiwen@,jzhou@,tang.yansong@sz.}tsinghua.edu.cn + +![](images/45a698f095dfcaafff4f491ab2670521c738a53a8d1d3efb4657aefaa309e16f.jpg) +Figure 1. An overview of the LOGO dataset. LOGO is a multi-person long-form video dataset with frame-wise annotations on both action procedures (as shown in the second line) and formations (as shown in the third line, which reflects relations among actors) based on artistic swimming scenarios. It provides a potential for constructing an action quality assessment approach with the ability of modeling group information among actors. Longer video durations also challenge the ability of the method to aggregate long-term temporal information. + +# Abstract + +Action quality assessment (AQA) has become an emerging topic since it can be extensively applied in numerous scenarios. However, most existing methods and datasets focus on single-person short-sequence scenes, hindering the application of AQA in more complex situations. To address this issue, we construct a new multi-person long-form video dataset for action quality assessment named LOGO. Distinguished in scenario complexity, our dataset contains 200 videos from 26 artistic swimming events with 8 athletes in each sample along with an average duration of 204.2 seconds. As for richness in annotations, LOGO includes formation labels to depict group information of multiple athletes and detailed annotations on action procedures. Furthermore, we propose a simple yet effective method to model relations among athletes and reason about the potential + +temporal logic in long-form videos. Specifically, we design a group-aware attention module, which can be easily plugged into existing AQA methods, to enrich the clipwise representations based on contextual group information. To benchmark LOGO, we systematically conduct investigations on the performance of several popular methods in AQA and action segmentation. The results reveal the challenges our dataset brings. Extensive experiments also show that our approach achieves state-of-the-art on the LOGO dataset. The dataset and code will be released at https://github.com/shiyi-zh0408/LOGO. + +# 1. Introduction + +Action quality assessment (AQA) is applicable to many real-world contexts where people evaluate how well a specific action is performed such as sports events [13, 18, 29- + +Table 1. Comparisons of LOGO and existing datasets of action quality assessment (upper part of the table) and group activity recognition (lower part of the table). Score indicates the score annotations; Action denotes action types and temporal boundaries; Act.Label indicates the action types of both individuals and groups. Bbox indicates bounding boxes for actors. Formation represents formation annotations. Temp. indicates temporal boundary, Spat. indicates spatial localization. + +
DatasetDurationAvg.Dur.Anno.TypeSamplesEventsForm.Anno.Year
MTL Dive [33]15m,54s6.0sScore1591✘2014
UNLV Dive [31]23m,26s3.8sScore3701✘2017
AQA-7-Dive [29]37m,31s4.1sScore5496✘2019
MTL-AQA [30]96m,29s4.1sAction,Score141216✘2019
Rhythmic Gymnastics [53]26h,23m,20s1m,35sScore10004✘2020
FSD-10 [26]-3-30sAction,Score1484-✘2020
FineDiving [50]3h,30m,0s4.2sAction,Score300030✘2022
Collective Activity [7]--Act.Label44-✘2009
NCAA [35]16h,9m,52s4sBbox,Act.Label11436-✘2016
Volleyball [16]2h,12m,1s1.64sBbox,Act.Label4830-✘2016
FineGym [38]161h,1m,45s45.7sAct.Label,Temp.1268510✘2020
Multisports [25]18h,34m,40s20.9sAct.Label,Temp.,Spat.3200247✘2021
LOGO(Ours)11h,20m,41s3m,24sAction,Formation,Score20026✓(15764)
+ +33, 46], healthcare [28, 39, 55-58], art performances, military parades, and others. Due to the extensive application of AQA, many efforts have been made over the past few years. Although some existing works have achieved promising performances in several simple scenarios, the application of AQA in many situations is still difficult to implement. In the data-driven era, the richness of the dataset largely determines whether the model can be applied to a wide range of scenarios or not. Inspired by this, we reviewed the existing datasets in AQA and concluded that they are not rich enough for the following two reasons: + +Simplicity of Scenarios. We argue that the complexity of the AQA application scenes is reflected in two aspects, the number of people and the duration of the videos. In snowboarding, for example, there is only one performer, while there are multiple actors in a military parade. In diving, the duration is only about 5 seconds, while in artistic swimming and dance performances, the duration of the action reaches several minutes. However, most existing datasets contain a single performer in each sample and many of them collect videos of 3-8s [29-31, 33, 50], which makes it difficult for existing methods to model complex scenes with more actors and longer duration. In such cases, just focusing on how well actions are performed by each individual may be insufficient. Relations among actors should be built, and the potential temporal logic in long-term videos should be modeled. + +Coarse-grained Annotations. Though there have been some long-form video datasets in AQA [49, 53] which provide more complex scenes, they typically contain the score as the only annotation. Such coarse-grained annotation + +makes it difficult for models to learn deeper information, especially in more complex situations. Simply judging action quality via regressing a score for a long-term video could be confusing since we cannot figure out how the model determines whether an action is well-performed or not. + +To address these issues, we propose a multi-person long-form video dataset, LOGO (short for LOng-form GrOup). With 8 actors in each sample, LOGO contains videos with an average duration of 204.2s, much longer than most existing datasets in AQA, making the scenes more complex. Besides, as shown in Figure 1, LOGO contains fine-grained annotations including frame-wise action type labels and temporal boundaries of actions for each video. We also devise formation labels to depict relations among actors. Specifically, we use a convex polygon to represent the formation actors perform, which reflects their position information and group information. In general, LOGO is distinguished by its scenario complexity, while it also provides richer annotations compared to most existing datasets in AQA [29-31, 33, 49, 50, 53]. + +Furthermore, we build a plug-and-play module, GOAT (short for GrOut-aware ATtention), to bridge the gap between single-person short-sequence scenarios and multiperson long-sequence scenarios. Specifically, in the spatial domain, by building a graph for actors, we model the relations among them. The nodes of this graph represent actors' features extracted from a CNN, and the edges represent the relations among actors. Then we use a graph convolution network (GCN) [19] to model the group features from the graph. The optimized features of the graph then serve as "queries" and "keys" for GOAT. In the temporal do + +main, after feature extraction by the video feature backbone, the clip-wise features serve as “values” for GOAT. Instead of fusing the features simply using the average pooling as most previous works [44, 50, 52], GOAT learns the relations among clips and models the temporal features of the long-term videos based on the spatial information in every clip. + +The contributions of this paper can be summarized as: (1) We construct the first multi-person long-form video dataset, LOGO, for action quality assessment. To the best of our knowledge, LOGO stands out for its longer average duration, the larger number of people, and richer annotations when compared to most existing datasets. Experimental results also reveal the challenges our proposed dataset brings. (2) We propose a plug-and-play group-aware module, GOAT, which models the group information and the temporal contextual relations for input videos, bridging the gap between single-person short-sequence scenarios and multi-person long-sequence scenarios. (3) Experimental results demonstrate that our group-aware approach obtains substantial improvements compared to existing methods in AQA and achieves the state-of-the-art. + +# 2. Related Work + +Action Quality Assessment. Assessing action quality is an increasingly popular trend in computer vision with wide applications such as video retrieval, instructional video analysis, etc. A wide variety of methods for formulating AQA tasks have been proposed [3, 10, 13, 24, 31, 33, 44, 48, 49, 52, 53]. In long video AQA tasks, actions performed at different times may significantly impact the scores given by experts. However, only a handful of works directly address the problem of long-term video AQA [3, 10, 48, 49, 53]. There are many datasets for AQA, including Diving [29-31, 33, 50], Figure Skating [26, 33], Gymnastic Vault [29, 31], Basketball [3], Fitness [43] and Rhythmic Gymnastics [53]. However, the problem of considering group information in multi-person sports has been relatively unexplored. As shown in Table 1, MIT-Dive [33], UNLV-Dive [31], AQA-7-Dive [29] and Rhythmic Gymnastics [53] only provide action scores, while MTL-AQA [30] FSD-10 [26] and FineDiving [50] only provide action types and scores. To perform AQA in long videos with multi-person, we construct a long-form artistic swimming video dataset, LOGO, with fine-grained frame-wise action and formation labels. Furthermore, we propose a method to model relations among athletes and reason about the potential temporal logic in long-form videos. + +Group Activity Understanding. Group activity understanding, which concentrates on interpreting the collective activity from multi-person behavioral and interaction dynamics, has attracted plenty of work recently. The focus of existing methods has shifted from using shallow handcrafted features [6,8,20,21,36,40] to using deep neural net + +![](images/23e5da38ac6ef17726fcba3feeb4a04c3a961cb8dd9575ed58174623448bf6f4.jpg) +Figure 2. A tree structure of LOGO Taxonomy. LOGO organizes both the Actions and Formations annotations hierarchically. The left part shows the Actions categories of Technical and Free events. The right part depicts the formation annotation instances when the group is doing Required, Upper, Lower or Float actions (the right sub-tree of Actions) and not when the group is doing other actions, during which the formations are indistinguishable. + +works [2,12,15,22,34,45]. Diverse datasets have been proposed to facilitate research in this area, such as the Collective Activity dataset [7], Volleyball dataset [16], etc. However, the methods and datasets mentioned above only stay at the level of group activity recognition; a more profound understanding of group activities should be able to not only find the high-level group activity but also evaluate the quality of group activities, which requires more attention to the quality of collaboration among actors and fine-grained actions of actors. In this paper, LOGO takes the first step towards quality assessment and sets a new benchmark for group activity understanding. + +# 3. The LOGO Dataset + +We propose a new multi-person long-form video dataset with detailed annotations on action and formation, LOGO, to set a new challenging benchmark for AQA. We will introduce it from its construction and annotation in this section. + +# 3.1. Dataset Construction + +Collection. According to the official FINA rules, the same rules, and prescribed movements are used from 2018 until the end of the 2022 World Championships. So we collected the officially designated Technical and Free artistic swimming competitions during this period (2 World Championships, 1 Olympic Games, and 4 World Series). We download competition videos with high resolution, e.g., + +![](images/a896200b43e7b88c33cd5523ede47483c35d12a4cb29a0b3f1770c0ed43d7100.jpg) +Figure 3. Statics of LOGO. (a) The score distribution of videos. (b) The action-type distribution of frames. + +![](images/f254d4f53997de152b312ae47b71393a6d36fa2b8ad6b4df031896de34cef704.jpg) + +720p and 1080p, on online video platforms like YouTube. Then we sampled them at 25fps and 1fps sampling rates for fine-grained action and formation labeling. Each official videos provide various content, including three sub-scores, one final score, and frames from different views. + +Lexicon. We construct a fine-grained video dataset organized by temporal structure, which contains action and formation manual annotations, shown in Figure 2. Herein, we design the labeling system with professional artistic swimming athletes to construct a lexicon for annotation, considering FINA rules and the actual scenario of the competitions. In the Technical event, the group size is eight people, the video length is $170 \pm 15\mathrm{s}$ , and the actions include Upper, Lower, Float, None, Acrobatic, Cadence, and five Required Elements. Each competition cycle needs to complete five Required Elements, at least two Acrobatic movements, and at least one Cadence action. In the Free events, there are 8 people, the video length is $240 \pm 15\mathrm{s}$ , and the actions include Upper, Lower, Float, None, Acrobatic, Cadence, and Free elements. When performing Required, Upper, Lower, and Float, the athletes form neat polygons as in Figure 2. + +Annotation. Given an RGB artistic swimming video, the annotator utilizes our defined lexicon to label each frame with its action and formation. We accomplish the 25fps frame-wise action annotation stage utilizing the COIN annotation toolbox [42] and the 1fps frame-wise formation labels using Labelme. Specifically, we set strict rules defining the boundaries between artistic swimming sequences and the formation marking position and employ eight workers with prior knowledge in the artistic swimming domain to label the dataset frame by frame following the rules. The annotation results of one worker are checked and adjusted by another, which ensures annotation results are double-checked. Under this pipeline, the total time for the annotation process is above 600 hours. + +# 3.2. Dataset Statics + +The LOGO dataset consists of 200 video samples from 26 events with 204.2s average duration and above 11h total duration, covering 3 annotation types, 12 action types, + +and 17 formation types. Figure 3 shows the score and action type distributions among all the events. Table 1 reports more detailed information on the LOGO dataset and compares it with existing AQA datasets and other fine-grained sports datasets. Our dataset differs from existing AQA datasets in the annotation type and dataset scale. Specifically, our dataset includes formation types providing group information and longer videos on sports, helping to evaluate the quality of actions in multiplayer sports quantitatively. Other fine-grained sports datasets cannot be used for assessing action quality due to a lack of action scores. LOGO is the first fine-grained sports video dataset for Group AQA, filling the fine-grained group annotations void in AQA. + +# 4. Approach + +# 4.1. Problem Formulation + +Most existing methods in AQA process the output of the video feature backbone using average pooling before regression. It can be represented as: + +$$ +\hat {y} = \mathcal {R} \left[ \frac {1}{T} \sum_ {i = 1} ^ {T} \mathcal {F} \left(X _ {i}\right) | \Theta \right], \tag {1} +$$ + +where $X_{i}$ denotes the $i$ -th clip of the video. $\mathcal{F}$ indicates the video feature backbone; $T$ is the number of clips; $\mathcal{R}$ represents the regression algorithm; $\Theta$ is the learnable parameters of $\mathcal{R}$ and $\hat{y}$ is the predicted score. However, fusing temporal information simply by average pooling in scenes with longer duration may be confusing since there could be redundant or even invalid information in the video. Besides, when dealing with multi-person scenarios, we need to depict the relations among actors. We use group information to fuse the extracted features in the temporal axis, modeling the relations among clips. It can be represented as: + +$$ +\hat {y} = \mathcal {R} \left[ \frac {1}{T} \sum_ {i = 1} ^ {T} f _ {i} | \Theta \right], \tag {2} +$$ + +$$ +f _ {i} = \sum_ {j = 1} ^ {T} \mathcal {G} \left(X _ {i}, X _ {j}\right) \mathcal {F} \left(X _ {j}\right), i = 1 \dots T, \tag {3} +$$ + +where $\mathcal{G}(X_i, X_j)$ denotes the weight computed by group features of the $i$ -th clip and the $j$ -th clip; $f_i$ indicates the reconstructed feature of the $i$ -th clip. + +# 4.2. Group-aware Attention + +There are two components of GOAT, that is, group-aware GCN and temporal-fusion attention. The overview of our framework is illustrated in Figure 4. + +Group-aware GCN. This component is shown in the right part of Figure 4. We extract the group features by modeling the relations among actors with graphs. Given a + +![](images/274e7339dd3f9da5a3f20567c9f1c6490b6fc32eb601edd0eb4fba13303a3a15.jpg) +Figure 4. An overview of our group-aware approach for action quality assessment. First, we divide the video into several short clips of equal length. For each clip, we take the middle frame and perform object detection to get the bounding boxes of the actors. Then we send the frame into a CNN to extract the features of the actors. Then we use the feature vector of each actor as the node to construct the relation graph. We use Graph Convolutional Network to enhance the features in the graph, and send the output features into GOAT as “queries” and “keys”. And the “values” are the features obtained from the clip by the video feature backbone such as I3D and video swin-transformer. Thus the aggregation in time can be completed. Finally, the output features are sent into the assessment network to predict the scores. + +![](images/7964c7b1a10d333e0ed932ef186644e76172703c076cb78d96556fde58eda8a6.jpg) + +video, we fix it into the given duration via downsampling or upsampling and divide it into several clips of equal length. Then we take three steps to extract the group features. First, we select the middle frame from each clip and build features for the actors. Specifically, we adopt object detection [54] to get bounding boxes of actors. Then, we use Inception-V3 [41] on the frame to get the feature map, to which we apply RoIAlign [14] to extract features for each bounding box. We use a fully connected layer to get a $d$ -dimensional vector from the feature map for each actor. Then we have a $N \times d$ representation denoted as $G$ for each middle frame, where $N$ denotes the number of actors and $d$ indicates the dimension of feature vectors. + +Second, we build a relation graph with the feature matrix $G$ to model the relations among actors. Concretely, we regard each feature vector of an actor as a node in the graph. We follow the strategy in [47] to build edges among nodes by computing similarities of appearance features and relative location of actors. + +Then, a Graph Convolutional Network (GCN) [19] is adopted to the relation graph to enhance node features by weighted aggregation, which can be represented as: + +$$ +H ^ {(l + 1)} = \sigma (A H ^ {(l)} W ^ {(l)}), \tag {4} +$$ + +where $A$ indicates the adjacent matrix; $W^{(l)}$ is the weight matrix in $l$ -th layer; $H^{(l)}$ denotes the features of nodes in $l$ -th layer and $H^{(0)} = G$ . Finally, The group feature vector is extracted by adopting average pooling to the sum of the input and the output features of GCN. The group feature vector of the $i$ -th clip is denoted as $g_{i}$ . + +Temporal-fusion Attention. This component fuses the video embeddings along the temporal axis based on the rep- + +resentations from the group-aware GCN. As shown in the left part of Figure 4, for each clip split from the video, we send it into an I3D [4] backbone as most previous works do [44, 50, 52, 53]. We leverage the strong capability of capturing global information of the multi-head attention encoder for learning group-aware video embeddings. + +We denote the I3D features of the video as $\{\mathcal{F}(X_i)\}_{i = 1}^T$ , which serve as the "value" of the attention block. And the vectors $\{g_i\}_{i = 1}^T$ from group-aware GCN serve as "query" and "key". The temporal-fusion attention module learns to discover the group feature correspondences among clips, and generates new temporal features in all of them. The module uses the relations of group features among different clips to assign different weights to different temporal features. The above attention learning can be represented as: + +$$ +q ^ {(l)} = W _ {Q} ^ {(l)} q ^ {(l - 1)}, \tag {5} +$$ + +$$ +k ^ {(l)} = W _ {K} ^ {(l)} k ^ {(l - 1)}, \tag {6} +$$ + +$$ +W _ {a t t n} ^ {(l)} = \operatorname {S o f t m a x} \left(\frac {q ^ {(l)} k ^ {(l) T}}{\sqrt {d}}\right), \tag {7} +$$ + +$$ +v ^ {(l)} = B N \left[ W _ {a t t n} ^ {(l)} v ^ {(l - 1)} + v ^ {(l - 1)} \right], \tag {8} +$$ + +where $W_{Q}^{(l)}, W_{K}^{(l)}, W_{attn}^{(l)}$ indicate the learnable weights in $l$ -th layer; $q^{(l)}, k^{(l)}, v^{(l)}$ denote the "query", "key" and "value" in $l$ -th layer; $d$ is the dimension of feature vector and $BN$ is the BatchNorm block. Besides, $q^{(0)} = k^{(0)} = \{g_i\}_{i=1}^T$ , $v^{(0)} = \{\mathcal{F}(X_i)\}_{i=1}^T$ . + +# 4.3. Formation Detection + +In 4.2, we propose a pipeline to fuse temporal representations based on a kind of spatial information, the group + +features. However, such a fusion strategy can also be based on other kinds of spatial features and even without any features by simply using self-attention. To prove the effectiveness of the group features, we devise another kind of spatial features, formation features, to make a comparison. + +Formation Detection Task. As mentioned in Section 3, we use a polygon to depict the formation of actors. As shown in Figure 2, the polygon is represented by several coordinates of some actors but not all of them. So in this task, we need to distinguish whether an actor is the vertex of the polygon or not. + +Formation Detection Algorithm. Inspired by the "anchor" in object detection [37], we propose a feasible way to detect the vertexes. Given a picture, we split it into 1024 patches of equal size. For each patch, we set the center point as the "anchor". We send the image into Inception-V3 and extract the $d$ -dimensional feature vector with RoIAlign [14] and a fully connected layer for each patch. To represent the absolute position of each patch, we use sine and cosine functions of different frequencies to encode the position of the "anchor". We add the $d$ -dimensional positional encodings to the features and send them into a self-attention block to find the relations among different patches and build the $d$ -dimensional formation features for them. + +Then we take two steps to find vertexes. First, for each patch, we judge whether there is a vertex. Second, if there is a vertex, we calculate the relative coordinates of the vertex to the "anchor" point. So we detect vertexes by computing: + +$$ +\hat {P} = \left[ \hat {p} _ {1}, \dots , \hat {p} _ {n} \right], \quad \hat {C} = \left[ \hat {c} _ {1}, \dots , \hat {c} _ {n} \right], \tag {9} +$$ + +where $\hat{p}_i\in \mathbb{R}$ denotes the confidence of whether there is a vertex in the $i$ -th patch and $\hat{c}_i\in \mathbb{R}^2$ is the relative coordinates of the vertex to the "anchor". In this way, the formation detection task is converted to a classification problem and a regression problem. And we respectively use a MLP to predict $\hat{P}$ and $\hat{C}$ upon the formation features mentioned above. The object function can be represented as: + +$$ +\mathcal {L} _ {B C E} = - \sum_ {i} \left[ p _ {i} \log \hat {p} _ {i} + (1 - p _ {i}) \log \left(1 - \hat {p} _ {i}\right) \right], \tag {10} +$$ + +$$ +\mathcal {L} _ {M S E} = \left\| C - \hat {C} \right\| ^ {2}. \tag {11} +$$ + +We minimize $\mathcal{L}_{BCE}$ and $\mathcal{L}_{MSE}$ to predict the vertexes. The $d$ -dimensional formation features of middle frame in each clip can replace the group features in 4.2 to fuse the temporal information. Relative experiments are conducted in our ablation study. + +# 5. Experiments + +# 5.1. Implementation Details + +Action Quality Assessment. Following [31,49,53], we take two stages to assess action quality: feature extraction + +and score prediction. In the feature extraction stage, we use the I3D model pretrained on Kinetics [4] dataset to extract the 1024-dimensional feature vector for each video clip. Specifically, we sample 5406 frames for each video, split them into 540 snippets, and fed them into I3D. Each snippet contains 16 continuous frames with a stride of 10 frames. In the ablation study, we also use the video swintransformer [27] as the backbone, which is also pretrained on Kinetics. We follow the sampling strategy in [27] to use a temporal stride of 2. The Inception-V3 in 4.2 is pretrained on ImageNet [9] to extract the CNN features. Following [44, 50, 52], we split the dataset into 3:1 for training and testing in all the experiments. We also test our model using the Mindspore [1]. + +Action Segmentation. We conduct action segmentation on LOGO with several existing approaches (ASFormer [51], SSTDA [23], MS_TC++ [5], ASRF [17]) to provide a benchmark. We try two backbones to extract frame-wise features: I3D [4] model and video swim-transformer [27] pretrained on Kinetics. For SWIN, we expand the snippet size to 32 frames to extract 1536-dimensional features. In the training stage, we train action segmentation approaches on their default setting. + +# 5.2. Evaluation Metrics + +Action Quality Assessment. Following [44, 50, 52, 53], we comprehensively evaluate our approach to AQA under two metrics, Spearman's rank correlation $(\rho)$ and relative $\ell_2$ -distance $(\mathbf{R} - \ell_2)$ . Spearman's rank correlation is used to evaluate the rank correlation between the prediction and ground-truth while the relative $\ell_2$ -distance $(\mathbf{R} - \ell_2)$ focuses on the difference of the numerical values. + +Action Segmentation. Following [5, 15, 23, 51], we adopt three widely used evaluation metrics including framewise accuracy (Acc), segmental edit distance and segmental F1 score at overlapping thresholds $10\%$ , $25\%$ , and $50\%$ , denoted by F1@{10, 25, 50} to evaluate the performance of action segmentation approaches. + +# 5.3. Comparison with the State of the Art + +Action Quality Assessment. Table 2 shows the experimental results, which reveal great challenges to performing action quality assessment on the LOGO dataset. With the I3D backbone, the mainstream methods in single-person short-term AQA [44, 50, 52] attain the result of 0.4259, 0.4712, and 0.4518 on Spearman's rank correlation respectively. Besides, the results show that our approach achieves the state-of-the-art. We observe that USDL+GOAT, CoRe+GOAT, and TSA+GOAT consistently improve the performance over the original models. Specifically, our approach respectively obtained $8.48\%$ , $4.73\%$ , and $10.12\%$ improvements on Spearman's rank correlation. Our method also outperforms the previous long-term AQA + +![](images/da839ffdcd1a5d1210e5f69b6d8ef6015827bbe7305bc427a0cdae30b1aa7fd8.jpg) +Figure 5. The visualization of the output of our proposed GOAT in action quality assessment. We use red stars to denote clips with high weight while using blue stars to represent clips with low weight. Our approach can focus on where the athletes perform effective movements with clear formations while it can also ignore the redundant part such as all actors are under-water. + +Table 2. Comparisons of performance with existing AQA methods on LOGO. The higher $\rho$ ,the lower $\mathrm{R} - {\ell }_{2}$ ,the better performance. + +
MethodI3DSWIN
ρ↑R-ℓ2(×100) ↓ρ↑R-ℓ2(×100) ↓
USDL [44]0.42595.73640.47255.0762
CoRe [52]0.47125.40860.50025.9597
TSA [50]0.45185.53260.47514.7778
ACTION-NET [53]0.30575.85810.41015.5693
USDL [44]+GOAT0.46204.87390.53495.0220
CoRe [52]+GOAT0.49355.07160.55994.7626
TSA [50]+GOAT0.48555.39430.48435.4086
+ +Table 3. Action segmentation results on LOGO. + +
MethodFeaturesF1@{10,25,50}EditAcc
ASFormer [51]SWIN81.779.871.175.381.0
ASFormer [51]I3D75.171.661.368.273.9
MS_TCN++ [23]SWIN80.878.870.273.580.1
MS_TCN++ [23]I3D72.669.258.566.070.6
SSTDA [5]SWIN77.875.966.370.079.2
SSTDA [5]I3D60.155.744.050.163.4
ASRF [17]SWIN80.879.172.173.280.0
ASRF [17]I3D73.670.559.866.869.8
+ +method [53]. The experimental results illustrate the effectiveness of our proposed module when dealing with multiperson long-term scenarios. + +Action Segmentation. Table 3 presents the experimental results. With the I3D feature, the previous action segmentation methods [5, 17, 23, 51] achieve the result of $73.9\%$ , $70.6\%$ , $63.4\%$ and $69.8\%$ frame accuracy respectively. And given an identical setting, we see that the SWIN-pretrained feature obtained significant improvement in all five metrics. Table 6 reveals that our method could improve the performance of MS_TC++ and ASFormer and achieve the state-of-the-art with the group information. + +Table 4. Comparisons of AQA results of CORE and CORE+GOAT based on existing short-term, two-player datasets. @2 means AQA datasets with two-player scenes. + +
DatasetCORE [52]CORE [52]+GOAT
ρ↑R-ℓ2(×100) ↓ρ↑R-ℓ2(×100) ↓
FineDiving [50]@20.89910.37510.90320.3529
TASD-2 [11]@20.91890.78630.93340.7054
AQA-7 [29]@20.90120.73020.93250.6423
+ +# 5.4. Generalization of GOAT + +Our method is currently suitable for multi-person scenarios. We select current AQA datasets with two-player scenes (there are only 2 players at most for now) and redivide them according to the number of people. TASD-2 [11] is a dataset collected from synchronized diving events with 2 players in each video. Based on the divided dataset, we obtain results in Table 4, which prove that GOAT can improve the AQA results of two-player scenes in other datasets. These results also demonstrate the generalization of GOAT. Our method can perform well in short-term, two-player scenes. + +# 5.5. Ablation Study + +We change the video feature backbone to verify the generality of our approach. Besides, we also try to use other spatial features or simply use self-attention for temporal information fusion to demonstrate the effectiveness of the group features. The experiments also illustrate that our temporal fusion strategy outperforms the average pooling. + +Spatial Features. As shown in Table 5, we conduct experiments utilizing formation features to replace the group embeddings used in GOAT to fuse the temporal representations. The formation features are extracted from the attention block output in the formation detection pipeline men + +![](images/ef2df0d15e7a454ef2c53c0d2670d4d448af26e9bebf4d6391b27987b5ba9324.jpg) +Figure 6. The visualization of the prediction results of our formation detector module. The green polygons represent prediction results and the yellow polygons with blue edges are the ground truth. The results show that our approach can detect the positions of actors and distinguish whether the athlete is the formation vertex or not, which guarantees the reliability of the formation features. + +![](images/9405348331852f45d1f06294cc38ba7a01b2f98cc269d5502d054a7ff3f865b3.jpg) + +![](images/ebe946718bf991d1ab0b2b129fb6311a42628e02577fb7df4078f7ac80a731f7.jpg) + +![](images/781c3bf082d4f21e5c1f89693a865167526d42ef43a70d3d4b1d603b860c297a.jpg) + +![](images/3604340a74630d551e49b24aff16375af4370d9e50de9ebac1888a0f509818a9.jpg) + +![](images/188de8ec2031892b5a3eb1a9664bc12c3dbad7d32e5c63e20ce99fc4e5cb91a9.jpg) + +Table 5. Ablation studies on LOGO. Self. indicates self-attention; Form. indicates using formation features for temporal fusing; AS. means using the action segmentation features for temporal fusing. + +
MethodI3DSWIN
ρ↑R-ℓ2(×100)↓ρ↑R-ℓ2(×100)↓
USDL [44]+Self.0.43354.88980.50784.1305
CoRe [52]+Self.0.43485.60190.52694.5072
TSA [50]+Self.0.45855.03360.47205.7280
USDL [44]+Form.0.43555.76360.53705.0888
CoRe [52]+Form.0.48205.30030.54015.1747
TSA [50]+Form.0.42415.18210.49034.8627
USDL [44]+AS.0.45124.88370.51085.0479
CoRe [52]+AS.0.48255.23930.53644.9102
TSA [50]+AS.0.47725.42030.48295.3561
+ +Table 6. The action segmentation results of existing methods with GOAT on LOGO. +GOAT indicates the method with GOAT. + +
MethodFeaturesF1@{10,25,50}EditAcc
MS_TCN++ [23]+GOATSWIN80.979.070.574.081.1
MS_TCN++ [23]+GOATI3D73.269.959.467.371.7
ASFormer [51]+GOATSWIN82.280.373.675.981.7
ASFormer [51]+GOATI3D75.872.062.168.874.6
+ +tioned in 4.3, which is pretrained on the LOGO dataset by executing formation detection. We also adopt self-attention to replace GOAT, which means we perform our temporal fusion strategy without the assistance of any spatial information. The experimental results show that the formation features outperform the original models and self-attention models but perform worse than the group features in most cases. The results also show that the self-attention models perform better than the original models. Such results of our experiments prove that: (1) Our temporal fusion strategy outperforms the average pooling even without any spatial information. (2) By modeling the spatial information, the performance of our proposed approach is improved. (3) Building the relations among actors, the group features perform better than the formation features. + +Video Feature Backbone. As shown in Table 5 and Table 2. We change the backbone to video swin-transformer (abbreviated as SWIN) and repeat all our experiments. Similar to the results shown in the action segmentation experiments, the methods based on SWIN perform much better + +than the methods based on I3D in most cases, which illustrates the effectiveness of SWIN. Besides, except for the case of TSA+Self, the results of our methods substantially outperform the original models based on SWIN, which proves the generality of our approach. + +Asist AQA with Action Segmentation. To assist the AQA task with the action segmentation task (or action labels), we use the backbone features finetuned in the action segmentation task as the input of GOAT in the experiments shown in the lower part of Table 5. The results illustrate that with the help of the segmentation task, the performances of AQA are improved compared with the original methods. + +# 5.6. Visualization + +We visualize the output of GOAT, as shown in Figure 5. It shows that GOAT highlights the part where actors perform effective action with clear formations, demonstrating the effectiveness of our temporal fusion strategy. We also visualize the prediction results of our formation detection module, as shown in Figure 6. It can be seen that our approach can distinguish the vertexes of the formations. + +# 6. Conclusion + +In this paper, we construct the first multi-person long-form video dataset, LOGO, for action quality assessment. We also propose a group-aware module, GOAT, to build relations among multiple actors and fuse the temporal representations based on spatial information. Furthermore, the utilization of GOAT in action quality assessment and action segmentation both achieve substantial improvements compared to the existing methods. + +Existing Assets and Personal Data. The videos in LOGO are downloaded from several websites such as YouTube. 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In ACM MM, pages 2526–2534, 2020. 2, 3, 5, 6, 7 +[54] Hao Zhang, Feng Li, Shilong Liu, Lei Zhang, Hang Su, Jun Zhu, Lionel M Ni, and Heung-Yeung Shum. Dino: Detr with improved denoising anchor boxes for end-to-end object detection. arXiv preprint arXiv:2203.03605, 2022. 5 +[55] Qiang Zhang and Baoxin Li. Video-based motion expertise analysis in simulation-based surgical training using hierarchical dirichlet process hidden markov model. In MMAR, pages 19-24, 2011. 2 +[56] Qiang Zhang and Baoxin Li. Relative hidden markov models for video-based evaluation of motion skills in surgical training. TPAMI, 37(6):1206-1218, 2014. 2 +[57] Aneeq Zia, Yachna Sharma, Vinay Bettadapura, Eric L Sarin, Mark A Clements, and Irfan Essa. Automated assessment of surgical skills using frequency analysis. In MICCAI, pages 430-438, 2015. 2 +[58] Aneeq Zia, Yachna Sharma, Vinay Bettadapura, Eric L Sarin, and Irfan Essa. Video and accelerometer-based motion analysis for automated surgical skills assessment. *IJCARS*, 13(3):443-455, 2018. 2 \ No newline at end of file diff --git a/2023/LOGO_ A Long-Form Video Dataset for Group Action Quality Assessment/images.zip b/2023/LOGO_ A Long-Form Video Dataset for Group Action Quality Assessment/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..8d6f9670692733880355f56463e9818a42bd0f40 --- /dev/null +++ b/2023/LOGO_ A Long-Form Video Dataset for Group Action Quality Assessment/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:fc5a3a8e3382d3591d31998b21157770e2ce30477f485d0d2130e2bee11e54ca +size 735301 diff --git a/2023/LOGO_ A Long-Form Video Dataset for Group Action Quality Assessment/layout.json b/2023/LOGO_ A Long-Form Video Dataset for Group Action Quality Assessment/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..717f135a20b42a49f02d3f0cce8fad94f501402b --- /dev/null +++ b/2023/LOGO_ A Long-Form Video Dataset for Group Action Quality Assessment/layout.json @@ -0,0 +1,8415 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 66, + 103, + 529, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 103, + 529, + 121 + ], + "spans": [ + { + "bbox": [ + 66, + 103, + 529, + 121 + ], + "type": "text", + "content": "LOGO: A Long-Form Video Dataset for Group Action Quality Assessment" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 52, + 141, + 555, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 141, + 555, + 216 + ], + "spans": [ + { + "bbox": [ + 52, + 141, + 555, + 216 + ], + "type": "text", + "content": "Shiyi Zhang" + }, + { + "bbox": [ + 52, + 141, + 555, + 216 + ], + "type": "inline_equation", + "content": "^{1,2,3}" + }, + { + "bbox": [ + 52, + 141, + 555, + 216 + ], + "type": "text", + "content": ", Wenxun Dai" + }, + { + "bbox": [ + 52, + 141, + 555, + 216 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 52, + 141, + 555, + 216 + ], + "type": "text", + "content": ", Sujia Wang" + }, + { + "bbox": [ + 52, + 141, + 555, + 216 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 52, + 141, + 555, + 216 + ], + "type": "text", + "content": ", Xiangwei Shen" + }, + { + "bbox": [ + 52, + 141, + 555, + 216 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 52, + 141, + 555, + 216 + ], + "type": "text", + "content": ", Jiwen Lu" + }, + { + "bbox": [ + 52, + 141, + 555, + 216 + ], + "type": "inline_equation", + "content": "^{2,3}" + }, + { + "bbox": [ + 52, + 141, + 555, + 216 + ], + "type": "text", + "content": ", Jie Zhou" + }, + { + "bbox": [ + 52, + 141, + 555, + 216 + ], + "type": "inline_equation", + "content": "^{2,3}" + }, + { + "bbox": [ + 52, + 141, + 555, + 216 + ], + "type": "text", + "content": ", Yansong Tang" + }, + { + "bbox": [ + 52, + 141, + 555, + 216 + ], + "type": "inline_equation", + "content": "^{1,*}" + }, + { + "bbox": [ + 52, + 141, + 555, + 216 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 52, + 141, + 555, + 216 + ], + "type": "text", + "content": " Shenzhen International Graduate School, Tsinghua University \n" + }, + { + "bbox": [ + 52, + 141, + 555, + 216 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 52, + 141, + 555, + 216 + ], + "type": "text", + "content": " Department of Automation, Tsinghua University \n" + }, + { + "bbox": [ + 52, + 141, + 555, + 216 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 52, + 141, + 555, + 216 + ], + "type": "text", + "content": " Beijing National Research Center for Information Science and Technology \n{shiyi-zh19@mails.,lujiwen@,jzhou@,tang.yansong@sz.}tsinghua.edu.cn" + } + ] + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 51, + 224, + 545, + 423 + ], + "blocks": [ + { + "bbox": [ + 51, + 224, + 545, + 423 + ], + "lines": [ + { + "bbox": [ + 51, + 224, + 545, + 423 + ], + "spans": [ + { + "bbox": [ + 51, + 224, + 545, + 423 + ], + "type": "image", + "image_path": "45a698f095dfcaafff4f491ab2670521c738a53a8d1d3efb4657aefaa309e16f.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 431, + 547, + 477 + ], + "lines": [ + { + "bbox": [ + 46, + 431, + 547, + 477 + ], + "spans": [ + { + "bbox": [ + 46, + 431, + 547, + 477 + ], + "type": "text", + "content": "Figure 1. An overview of the LOGO dataset. LOGO is a multi-person long-form video dataset with frame-wise annotations on both action procedures (as shown in the second line) and formations (as shown in the third line, which reflects relations among actors) based on artistic swimming scenarios. It provides a potential for constructing an action quality assessment approach with the ability of modeling group information among actors. Longer video durations also challenge the ability of the method to aggregate long-term temporal information." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 491, + 192, + 504 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 491, + 192, + 504 + ], + "spans": [ + { + "bbox": [ + 143, + 491, + 192, + 504 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 517, + 289, + 697 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 517, + 289, + 697 + ], + "spans": [ + { + "bbox": [ + 46, + 517, + 289, + 697 + ], + "type": "text", + "content": "Action quality assessment (AQA) has become an emerging topic since it can be extensively applied in numerous scenarios. However, most existing methods and datasets focus on single-person short-sequence scenes, hindering the application of AQA in more complex situations. To address this issue, we construct a new multi-person long-form video dataset for action quality assessment named LOGO. Distinguished in scenario complexity, our dataset contains 200 videos from 26 artistic swimming events with 8 athletes in each sample along with an average duration of 204.2 seconds. As for richness in annotations, LOGO includes formation labels to depict group information of multiple athletes and detailed annotations on action procedures. Furthermore, we propose a simple yet effective method to model relations among athletes and reason about the potential" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 494, + 547, + 625 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 494, + 547, + 625 + ], + "spans": [ + { + "bbox": [ + 306, + 494, + 547, + 625 + ], + "type": "text", + "content": "temporal logic in long-form videos. Specifically, we design a group-aware attention module, which can be easily plugged into existing AQA methods, to enrich the clipwise representations based on contextual group information. To benchmark LOGO, we systematically conduct investigations on the performance of several popular methods in AQA and action segmentation. The results reveal the challenges our dataset brings. Extensive experiments also show that our approach achieves state-of-the-art on the LOGO dataset. The dataset and code will be released at https://github.com/shiyi-zh0408/LOGO." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 655, + 387, + 667 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 655, + 387, + 667 + ], + "spans": [ + { + "bbox": [ + 306, + 655, + 387, + 667 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "type": "text", + "content": "Action quality assessment (AQA) is applicable to many real-world contexts where people evaluate how well a specific action is performed such as sports events [13, 18, 29-" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 703, + 178, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 703, + 178, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 703, + 178, + 713 + ], + "type": "text", + "content": "* indicates the corresponding author." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2405" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 47, + 130, + 547, + 322 + ], + "blocks": [ + { + "bbox": [ + 47, + 76, + 545, + 121 + ], + "lines": [ + { + "bbox": [ + 47, + 76, + 545, + 121 + ], + "spans": [ + { + "bbox": [ + 47, + 76, + 545, + 121 + ], + "type": "text", + "content": "Table 1. Comparisons of LOGO and existing datasets of action quality assessment (upper part of the table) and group activity recognition (lower part of the table). Score indicates the score annotations; Action denotes action types and temporal boundaries; Act.Label indicates the action types of both individuals and groups. Bbox indicates bounding boxes for actors. Formation represents formation annotations. Temp. indicates temporal boundary, Spat. indicates spatial localization." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 47, + 130, + 547, + 322 + ], + "lines": [ + { + "bbox": [ + 47, + 130, + 547, + 322 + ], + "spans": [ + { + "bbox": [ + 47, + 130, + 547, + 322 + ], + "type": "table", + "html": "
DatasetDurationAvg.Dur.Anno.TypeSamplesEventsForm.Anno.Year
MTL Dive [33]15m,54s6.0sScore1591✘2014
UNLV Dive [31]23m,26s3.8sScore3701✘2017
AQA-7-Dive [29]37m,31s4.1sScore5496✘2019
MTL-AQA [30]96m,29s4.1sAction,Score141216✘2019
Rhythmic Gymnastics [53]26h,23m,20s1m,35sScore10004✘2020
FSD-10 [26]-3-30sAction,Score1484-✘2020
FineDiving [50]3h,30m,0s4.2sAction,Score300030✘2022
Collective Activity [7]--Act.Label44-✘2009
NCAA [35]16h,9m,52s4sBbox,Act.Label11436-✘2016
Volleyball [16]2h,12m,1s1.64sBbox,Act.Label4830-✘2016
FineGym [38]161h,1m,45s45.7sAct.Label,Temp.1268510✘2020
Multisports [25]18h,34m,40s20.9sAct.Label,Temp.,Spat.3200247✘2021
LOGO(Ours)11h,20m,41s3m,24sAction,Formation,Score20026✓(15764)
", + "image_path": "9b6e0ce25c0eb02a73123e250564124211285a5abdb2e57a8994049f513b7db4.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 341, + 287, + 473 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 341, + 287, + 473 + ], + "spans": [ + { + "bbox": [ + 46, + 341, + 287, + 473 + ], + "type": "text", + "content": "33, 46], healthcare [28, 39, 55-58], art performances, military parades, and others. Due to the extensive application of AQA, many efforts have been made over the past few years. Although some existing works have achieved promising performances in several simple scenarios, the application of AQA in many situations is still difficult to implement. In the data-driven era, the richness of the dataset largely determines whether the model can be applied to a wide range of scenarios or not. Inspired by this, we reviewed the existing datasets in AQA and concluded that they are not rich enough for the following two reasons:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 474, + 287, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 474, + 287, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 474, + 287, + 664 + ], + "type": "text", + "content": "Simplicity of Scenarios. We argue that the complexity of the AQA application scenes is reflected in two aspects, the number of people and the duration of the videos. In snowboarding, for example, there is only one performer, while there are multiple actors in a military parade. In diving, the duration is only about 5 seconds, while in artistic swimming and dance performances, the duration of the action reaches several minutes. However, most existing datasets contain a single performer in each sample and many of them collect videos of 3-8s [29-31, 33, 50], which makes it difficult for existing methods to model complex scenes with more actors and longer duration. In such cases, just focusing on how well actions are performed by each individual may be insufficient. Relations among actors should be built, and the potential temporal logic in long-term videos should be modeled." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "content": "Coarse-grained Annotations. Though there have been some long-form video datasets in AQA [49, 53] which provide more complex scenes, they typically contain the score as the only annotation. Such coarse-grained annotation" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 341, + 545, + 401 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 341, + 545, + 401 + ], + "spans": [ + { + "bbox": [ + 304, + 341, + 545, + 401 + ], + "type": "text", + "content": "makes it difficult for models to learn deeper information, especially in more complex situations. Simply judging action quality via regressing a score for a long-term video could be confusing since we cannot figure out how the model determines whether an action is well-performed or not." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 403, + 546, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 403, + 546, + 581 + ], + "spans": [ + { + "bbox": [ + 304, + 403, + 546, + 581 + ], + "type": "text", + "content": "To address these issues, we propose a multi-person long-form video dataset, LOGO (short for LOng-form GrOup). With 8 actors in each sample, LOGO contains videos with an average duration of 204.2s, much longer than most existing datasets in AQA, making the scenes more complex. Besides, as shown in Figure 1, LOGO contains fine-grained annotations including frame-wise action type labels and temporal boundaries of actions for each video. We also devise formation labels to depict relations among actors. Specifically, we use a convex polygon to represent the formation actors perform, which reflects their position information and group information. In general, LOGO is distinguished by its scenario complexity, while it also provides richer annotations compared to most existing datasets in AQA [29-31, 33, 49, 50, 53]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": "Furthermore, we build a plug-and-play module, GOAT (short for GrOut-aware ATtention), to bridge the gap between single-person short-sequence scenarios and multiperson long-sequence scenarios. Specifically, in the spatial domain, by building a graph for actors, we model the relations among them. The nodes of this graph represent actors' features extracted from a CNN, and the edges represent the relations among actors. Then we use a graph convolution network (GCN) [19] to model the group features from the graph. The optimized features of the graph then serve as \"queries\" and \"keys\" for GOAT. In the temporal do" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2406" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "type": "text", + "content": "main, after feature extraction by the video feature backbone, the clip-wise features serve as “values” for GOAT. Instead of fusing the features simply using the average pooling as most previous works [44, 50, 52], GOAT learns the relations among clips and models the temporal features of the long-term videos based on the spatial information in every clip." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 144, + 288, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 144, + 288, + 323 + ], + "spans": [ + { + "bbox": [ + 46, + 144, + 288, + 323 + ], + "type": "text", + "content": "The contributions of this paper can be summarized as: (1) We construct the first multi-person long-form video dataset, LOGO, for action quality assessment. To the best of our knowledge, LOGO stands out for its longer average duration, the larger number of people, and richer annotations when compared to most existing datasets. Experimental results also reveal the challenges our proposed dataset brings. (2) We propose a plug-and-play group-aware module, GOAT, which models the group information and the temporal contextual relations for input videos, bridging the gap between single-person short-sequence scenarios and multi-person long-sequence scenarios. (3) Experimental results demonstrate that our group-aware approach obtains substantial improvements compared to existing methods in AQA and achieves the state-of-the-art." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 335, + 134, + 346 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 335, + 134, + 346 + ], + "spans": [ + { + "bbox": [ + 47, + 335, + 134, + 346 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 355, + 287, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 355, + 287, + 641 + ], + "spans": [ + { + "bbox": [ + 46, + 355, + 287, + 641 + ], + "type": "text", + "content": "Action Quality Assessment. Assessing action quality is an increasingly popular trend in computer vision with wide applications such as video retrieval, instructional video analysis, etc. A wide variety of methods for formulating AQA tasks have been proposed [3, 10, 13, 24, 31, 33, 44, 48, 49, 52, 53]. In long video AQA tasks, actions performed at different times may significantly impact the scores given by experts. However, only a handful of works directly address the problem of long-term video AQA [3, 10, 48, 49, 53]. There are many datasets for AQA, including Diving [29-31, 33, 50], Figure Skating [26, 33], Gymnastic Vault [29, 31], Basketball [3], Fitness [43] and Rhythmic Gymnastics [53]. However, the problem of considering group information in multi-person sports has been relatively unexplored. As shown in Table 1, MIT-Dive [33], UNLV-Dive [31], AQA-7-Dive [29] and Rhythmic Gymnastics [53] only provide action scores, while MTL-AQA [30] FSD-10 [26] and FineDiving [50] only provide action types and scores. To perform AQA in long videos with multi-person, we construct a long-form artistic swimming video dataset, LOGO, with fine-grained frame-wise action and formation labels. Furthermore, we propose a method to model relations among athletes and reason about the potential temporal logic in long-form videos." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 642, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 287, + 713 + ], + "type": "text", + "content": "Group Activity Understanding. Group activity understanding, which concentrates on interpreting the collective activity from multi-person behavioral and interaction dynamics, has attracted plenty of work recently. The focus of existing methods has shifted from using shallow handcrafted features [6,8,20,21,36,40] to using deep neural net" + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 313, + 73, + 541, + 285 + ], + "blocks": [ + { + "bbox": [ + 313, + 73, + 541, + 285 + ], + "lines": [ + { + "bbox": [ + 313, + 73, + 541, + 285 + ], + "spans": [ + { + "bbox": [ + 313, + 73, + 541, + 285 + ], + "type": "image", + "image_path": "23e5da38ac6ef17726fcba3feeb4a04c3a961cb8dd9575ed58174623448bf6f4.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 297, + 545, + 375 + ], + "lines": [ + { + "bbox": [ + 304, + 297, + 545, + 375 + ], + "spans": [ + { + "bbox": [ + 304, + 297, + 545, + 375 + ], + "type": "text", + "content": "Figure 2. A tree structure of LOGO Taxonomy. LOGO organizes both the Actions and Formations annotations hierarchically. The left part shows the Actions categories of Technical and Free events. The right part depicts the formation annotation instances when the group is doing Required, Upper, Lower or Float actions (the right sub-tree of Actions) and not when the group is doing other actions, during which the formations are indistinguishable." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 382, + 546, + 526 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 382, + 546, + 526 + ], + "spans": [ + { + "bbox": [ + 304, + 382, + 546, + 526 + ], + "type": "text", + "content": "works [2,12,15,22,34,45]. Diverse datasets have been proposed to facilitate research in this area, such as the Collective Activity dataset [7], Volleyball dataset [16], etc. However, the methods and datasets mentioned above only stay at the level of group activity recognition; a more profound understanding of group activities should be able to not only find the high-level group activity but also evaluate the quality of group activities, which requires more attention to the quality of collaboration among actors and fine-grained actions of actors. In this paper, LOGO takes the first step towards quality assessment and sets a new benchmark for group activity understanding." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 536, + 422, + 548 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 536, + 422, + 548 + ], + "spans": [ + { + "bbox": [ + 306, + 536, + 422, + 548 + ], + "type": "text", + "content": "3. The LOGO Dataset" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 556, + 545, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 556, + 545, + 604 + ], + "spans": [ + { + "bbox": [ + 304, + 556, + 545, + 604 + ], + "type": "text", + "content": "We propose a new multi-person long-form video dataset with detailed annotations on action and formation, LOGO, to set a new challenging benchmark for AQA. We will introduce it from its construction and annotation in this section." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 611, + 428, + 623 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 611, + 428, + 623 + ], + "spans": [ + { + "bbox": [ + 306, + 611, + 428, + 623 + ], + "type": "text", + "content": "3.1. Dataset Construction" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": "Collection. According to the official FINA rules, the same rules, and prescribed movements are used from 2018 until the end of the 2022 World Championships. So we collected the officially designated Technical and Free artistic swimming competitions during this period (2 World Championships, 1 Olympic Games, and 4 World Series). We download competition videos with high resolution, e.g.," + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2407" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 70, + 157, + 185 + ], + "blocks": [ + { + "bbox": [ + 49, + 70, + 157, + 185 + ], + "lines": [ + { + "bbox": [ + 49, + 70, + 157, + 185 + ], + "spans": [ + { + "bbox": [ + 49, + 70, + 157, + 185 + ], + "type": "image", + "image_path": "a896200b43e7b88c33cd5523ede47483c35d12a4cb29a0b3f1770c0ed43d7100.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 194, + 286, + 217 + ], + "lines": [ + { + "bbox": [ + 47, + 194, + 286, + 217 + ], + "spans": [ + { + "bbox": [ + 47, + 194, + 286, + 217 + ], + "type": "text", + "content": "Figure 3. Statics of LOGO. (a) The score distribution of videos. (b) The action-type distribution of frames." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 164, + 70, + 284, + 186 + ], + "blocks": [ + { + "bbox": [ + 164, + 70, + 284, + 186 + ], + "lines": [ + { + "bbox": [ + 164, + 70, + 284, + 186 + ], + "spans": [ + { + "bbox": [ + 164, + 70, + 284, + 186 + ], + "type": "image", + "image_path": "f254d4f53997de152b312ae47b71393a6d36fa2b8ad6b4df031896de34cef704.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 227, + 286, + 286 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 227, + 286, + 286 + ], + "spans": [ + { + "bbox": [ + 47, + 227, + 286, + 286 + ], + "type": "text", + "content": "720p and 1080p, on online video platforms like YouTube. Then we sampled them at 25fps and 1fps sampling rates for fine-grained action and formation labeling. Each official videos provide various content, including three sub-scores, one final score, and frames from different views." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 288, + 286, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 288, + 286, + 479 + ], + "spans": [ + { + "bbox": [ + 47, + 288, + 286, + 479 + ], + "type": "text", + "content": "Lexicon. We construct a fine-grained video dataset organized by temporal structure, which contains action and formation manual annotations, shown in Figure 2. Herein, we design the labeling system with professional artistic swimming athletes to construct a lexicon for annotation, considering FINA rules and the actual scenario of the competitions. In the Technical event, the group size is eight people, the video length is " + }, + { + "bbox": [ + 47, + 288, + 286, + 479 + ], + "type": "inline_equation", + "content": "170 \\pm 15\\mathrm{s}" + }, + { + "bbox": [ + 47, + 288, + 286, + 479 + ], + "type": "text", + "content": ", and the actions include Upper, Lower, Float, None, Acrobatic, Cadence, and five Required Elements. Each competition cycle needs to complete five Required Elements, at least two Acrobatic movements, and at least one Cadence action. In the Free events, there are 8 people, the video length is " + }, + { + "bbox": [ + 47, + 288, + 286, + 479 + ], + "type": "inline_equation", + "content": "240 \\pm 15\\mathrm{s}" + }, + { + "bbox": [ + 47, + 288, + 286, + 479 + ], + "type": "text", + "content": ", and the actions include Upper, Lower, Float, None, Acrobatic, Cadence, and Free elements. When performing Required, Upper, Lower, and Float, the athletes form neat polygons as in Figure 2." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 480, + 286, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 480, + 286, + 647 + ], + "spans": [ + { + "bbox": [ + 47, + 480, + 286, + 647 + ], + "type": "text", + "content": "Annotation. Given an RGB artistic swimming video, the annotator utilizes our defined lexicon to label each frame with its action and formation. We accomplish the 25fps frame-wise action annotation stage utilizing the COIN annotation toolbox [42] and the 1fps frame-wise formation labels using Labelme. Specifically, we set strict rules defining the boundaries between artistic swimming sequences and the formation marking position and employ eight workers with prior knowledge in the artistic swimming domain to label the dataset frame by frame following the rules. The annotation results of one worker are checked and adjusted by another, which ensures annotation results are double-checked. Under this pipeline, the total time for the annotation process is above 600 hours." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 658, + 138, + 669 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 658, + 138, + 669 + ], + "spans": [ + { + "bbox": [ + 47, + 658, + 138, + 669 + ], + "type": "text", + "content": "3.2. Dataset Statics" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 677, + 286, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 286, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 286, + 714 + ], + "type": "text", + "content": "The LOGO dataset consists of 200 video samples from 26 events with 204.2s average duration and above 11h total duration, covering 3 annotation types, 12 action types," + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "text", + "content": "and 17 formation types. Figure 3 shows the score and action type distributions among all the events. Table 1 reports more detailed information on the LOGO dataset and compares it with existing AQA datasets and other fine-grained sports datasets. Our dataset differs from existing AQA datasets in the annotation type and dataset scale. Specifically, our dataset includes formation types providing group information and longer videos on sports, helping to evaluate the quality of actions in multiplayer sports quantitatively. Other fine-grained sports datasets cannot be used for assessing action quality due to a lack of action scores. LOGO is the first fine-grained sports video dataset for Group AQA, filling the fine-grained group annotations void in AQA." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 238, + 372, + 251 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 238, + 372, + 251 + ], + "spans": [ + { + "bbox": [ + 305, + 238, + 372, + 251 + ], + "type": "text", + "content": "4. 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However, fusing temporal information simply by average pooling in scenes with longer duration may be confusing since there could be redundant or even invalid information in the video. Besides, when dealing with multi-person scenarios, we need to depict the relations among actors. We use group information to fuse the extracted features in the temporal axis, modeling the relations among clips. 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Group-aware Attention" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 642, + 545, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 642, + 545, + 677 + ], + "spans": [ + { + "bbox": [ + 306, + 642, + 545, + 677 + ], + "type": "text", + "content": "There are two components of GOAT, that is, group-aware GCN and temporal-fusion attention. The overview of our framework is illustrated in Figure 4." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 677, + 545, + 713 + ], + "type": "text", + "content": "Group-aware GCN. This component is shown in the right part of Figure 4. We extract the group features by modeling the relations among actors with graphs. Given a" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2408" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 76, + 321, + 229 + ], + "blocks": [ + { + "bbox": [ + 50, + 76, + 321, + 229 + ], + "lines": [ + { + "bbox": [ + 50, + 76, + 321, + 229 + ], + "spans": [ + { + "bbox": [ + 50, + 76, + 321, + 229 + ], + "type": "image", + "image_path": "274e7339dd3f9da5a3f20567c9f1c6490b6fc32eb601edd0eb4fba13303a3a15.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 244, + 547, + 312 + ], + "lines": [ + { + "bbox": [ + 46, + 244, + 547, + 312 + ], + "spans": [ + { + "bbox": [ + 46, + 244, + 547, + 312 + ], + "type": "text", + "content": "Figure 4. An overview of our group-aware approach for action quality assessment. First, we divide the video into several short clips of equal length. For each clip, we take the middle frame and perform object detection to get the bounding boxes of the actors. Then we send the frame into a CNN to extract the features of the actors. Then we use the feature vector of each actor as the node to construct the relation graph. We use Graph Convolutional Network to enhance the features in the graph, and send the output features into GOAT as “queries” and “keys”. And the “values” are the features obtained from the clip by the video feature backbone such as I3D and video swin-transformer. Thus the aggregation in time can be completed. Finally, the output features are sent into the assessment network to predict the scores." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 324, + 77, + 542, + 229 + ], + "blocks": [ + { + "bbox": [ + 324, + 77, + 542, + 229 + ], + "lines": [ + { + "bbox": [ + 324, + 77, + 542, + 229 + ], + "spans": [ + { + "bbox": [ + 324, + 77, + 542, + 229 + ], + "type": "image", + "image_path": "7964c7b1a10d333e0ed932ef186644e76172703c076cb78d96556fde58eda8a6.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 322, + 287, + 476 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 322, + 287, + 476 + ], + "spans": [ + { + "bbox": [ + 46, + 322, + 287, + 476 + ], + "type": "text", + "content": "video, we fix it into the given duration via downsampling or upsampling and divide it into several clips of equal length. Then we take three steps to extract the group features. First, we select the middle frame from each clip and build features for the actors. Specifically, we adopt object detection [54] to get bounding boxes of actors. Then, we use Inception-V3 [41] on the frame to get the feature map, to which we apply RoIAlign [14] to extract features for each bounding box. We use a fully connected layer to get a " + }, + { + "bbox": [ + 46, + 322, + 287, + 476 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 322, + 287, + 476 + ], + "type": "text", + "content": "-dimensional vector from the feature map for each actor. Then we have a " + }, + { + "bbox": [ + 46, + 322, + 287, + 476 + ], + "type": "inline_equation", + "content": "N \\times d" + }, + { + "bbox": [ + 46, + 322, + 287, + 476 + ], + "type": "text", + "content": " representation denoted as " + }, + { + "bbox": [ + 46, + 322, + 287, + 476 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 46, + 322, + 287, + 476 + ], + "type": "text", + "content": " for each middle frame, where " + }, + { + "bbox": [ + 46, + 322, + 287, + 476 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 322, + 287, + 476 + ], + "type": "text", + "content": " denotes the number of actors and " + }, + { + "bbox": [ + 46, + 322, + 287, + 476 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 322, + 287, + 476 + ], + "type": "text", + "content": " indicates the dimension of feature vectors." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 477, + 287, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 477, + 287, + 548 + ], + "spans": [ + { + "bbox": [ + 46, + 477, + 287, + 548 + ], + "type": "text", + "content": "Second, we build a relation graph with the feature matrix " + }, + { + "bbox": [ + 46, + 477, + 287, + 548 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 46, + 477, + 287, + 548 + ], + "type": "text", + "content": " to model the relations among actors. Concretely, we regard each feature vector of an actor as a node in the graph. We follow the strategy in [47] to build edges among nodes by computing similarities of appearance features and relative location of actors." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 549, + 287, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 549, + 287, + 586 + ], + "spans": [ + { + "bbox": [ + 46, + 549, + 287, + 586 + ], + "type": "text", + "content": "Then, a Graph Convolutional Network (GCN) [19] is adopted to the relation graph to enhance node features by weighted aggregation, which can be represented as:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 113, + 593, + 287, + 608 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 113, + 593, + 287, + 608 + ], + "spans": [ + { + "bbox": [ + 113, + 593, + 287, + 608 + ], + "type": "interline_equation", + "content": "H ^ {(l + 1)} = \\sigma (A H ^ {(l)} W ^ {(l)}), \\tag {4}", + "image_path": "3754dc0f92e850cb04162d9b69e5fb4ea6e684de6b5ce6a3bed15592bf418615.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 616, + 287, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 616, + 287, + 689 + ], + "spans": [ + { + "bbox": [ + 46, + 616, + 287, + 689 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 616, + 287, + 689 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 46, + 616, + 287, + 689 + ], + "type": "text", + "content": " indicates the adjacent matrix; " + }, + { + "bbox": [ + 46, + 616, + 287, + 689 + ], + "type": "inline_equation", + "content": "W^{(l)}" + }, + { + "bbox": [ + 46, + 616, + 287, + 689 + ], + "type": "text", + "content": " is the weight matrix in " + }, + { + "bbox": [ + 46, + 616, + 287, + 689 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 46, + 616, + 287, + 689 + ], + "type": "text", + "content": "-th layer; " + }, + { + "bbox": [ + 46, + 616, + 287, + 689 + ], + "type": "inline_equation", + "content": "H^{(l)}" + }, + { + "bbox": [ + 46, + 616, + 287, + 689 + ], + "type": "text", + "content": " denotes the features of nodes in " + }, + { + "bbox": [ + 46, + 616, + 287, + 689 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 46, + 616, + 287, + 689 + ], + "type": "text", + "content": "-th layer and " + }, + { + "bbox": [ + 46, + 616, + 287, + 689 + ], + "type": "inline_equation", + "content": "H^{(0)} = G" + }, + { + "bbox": [ + 46, + 616, + 287, + 689 + ], + "type": "text", + "content": ". Finally, The group feature vector is extracted by adopting average pooling to the sum of the input and the output features of GCN. The group feature vector of the " + }, + { + "bbox": [ + 46, + 616, + 287, + 689 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 616, + 287, + 689 + ], + "type": "text", + "content": "-th clip is denoted as " + }, + { + "bbox": [ + 46, + 616, + 287, + 689 + ], + "type": "inline_equation", + "content": "g_{i}" + }, + { + "bbox": [ + 46, + 616, + 287, + 689 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": "Temporal-fusion Attention. This component fuses the video embeddings along the temporal axis based on the rep-" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 322, + 545, + 393 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 322, + 545, + 393 + ], + "spans": [ + { + "bbox": [ + 304, + 322, + 545, + 393 + ], + "type": "text", + "content": "resentations from the group-aware GCN. As shown in the left part of Figure 4, for each clip split from the video, we send it into an I3D [4] backbone as most previous works do [44, 50, 52, 53]. We leverage the strong capability of capturing global information of the multi-head attention encoder for learning group-aware video embeddings." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 393, + 546, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 393, + 546, + 502 + ], + "spans": [ + { + "bbox": [ + 304, + 393, + 546, + 502 + ], + "type": "text", + "content": "We denote the I3D features of the video as " + }, + { + "bbox": [ + 304, + 393, + 546, + 502 + ], + "type": "inline_equation", + "content": "\\{\\mathcal{F}(X_i)\\}_{i = 1}^T" + }, + { + "bbox": [ + 304, + 393, + 546, + 502 + ], + "type": "text", + "content": ", which serve as the \"value\" of the attention block. And the vectors " + }, + { + "bbox": [ + 304, + 393, + 546, + 502 + ], + "type": "inline_equation", + "content": "\\{g_i\\}_{i = 1}^T" + }, + { + "bbox": [ + 304, + 393, + 546, + 502 + ], + "type": "text", + "content": " from group-aware GCN serve as \"query\" and \"key\". The temporal-fusion attention module learns to discover the group feature correspondences among clips, and generates new temporal features in all of them. The module uses the relations of group features among different clips to assign different weights to different temporal features. The above attention learning can be represented as:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 359, + 509, + 545, + 526 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 359, + 509, + 545, + 526 + ], + "spans": [ + { + "bbox": [ + 359, + 509, + 545, + 526 + ], + "type": "interline_equation", + "content": "q ^ {(l)} = W _ {Q} ^ {(l)} q ^ {(l - 1)}, \\tag {5}", + "image_path": "4906b706d5da34a743789e927bcd98874de49acc0464a6ed7d2e8afd00f780ae.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 359, + 528, + 545, + 544 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 359, + 528, + 545, + 544 + ], + "spans": [ + { + "bbox": [ + 359, + 528, + 545, + 544 + ], + "type": "interline_equation", + "content": "k ^ {(l)} = W _ {K} ^ {(l)} k ^ {(l - 1)}, \\tag {6}", + "image_path": "1f1651d6ba72c495cd696c48953791ece3483cabdaf9d919cf87d5c25aa52e08.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 348, + 545, + 545, + 573 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 348, + 545, + 545, + 573 + ], + "spans": [ + { + "bbox": [ + 348, + 545, + 545, + 573 + ], + "type": "interline_equation", + "content": "W _ {a t t n} ^ {(l)} = \\operatorname {S o f t m a x} \\left(\\frac {q ^ {(l)} k ^ {(l) T}}{\\sqrt {d}}\\right), \\tag {7}", + "image_path": "c60f1993c3ef6bd597184784cbf37c8ebf3785b15d18d46d5c63391500c5e5e3.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 359, + 574, + 545, + 590 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 359, + 574, + 545, + 590 + ], + "spans": [ + { + "bbox": [ + 359, + 574, + 545, + 590 + ], + "type": "interline_equation", + "content": "v ^ {(l)} = B N \\left[ W _ {a t t n} ^ {(l)} v ^ {(l - 1)} + v ^ {(l - 1)} \\right], \\tag {8}", + "image_path": "7c7f992e91bb5098a61c64a72795c3dafb38c17c2ccdeb64793c21aa489522f2.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 599, + 547, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 599, + 547, + 666 + ], + "spans": [ + { + "bbox": [ + 304, + 599, + 547, + 666 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 599, + 547, + 666 + ], + "type": "inline_equation", + "content": "W_{Q}^{(l)}, W_{K}^{(l)}, W_{attn}^{(l)}" + }, + { + "bbox": [ + 304, + 599, + 547, + 666 + ], + "type": "text", + "content": " indicate the learnable weights in " + }, + { + "bbox": [ + 304, + 599, + 547, + 666 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 304, + 599, + 547, + 666 + ], + "type": "text", + "content": "-th layer; " + }, + { + "bbox": [ + 304, + 599, + 547, + 666 + ], + "type": "inline_equation", + "content": "q^{(l)}, k^{(l)}, v^{(l)}" + }, + { + "bbox": [ + 304, + 599, + 547, + 666 + ], + "type": "text", + "content": " denote the \"query\", \"key\" and \"value\" in " + }, + { + "bbox": [ + 304, + 599, + 547, + 666 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 304, + 599, + 547, + 666 + ], + "type": "text", + "content": "-th layer; " + }, + { + "bbox": [ + 304, + 599, + 547, + 666 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 599, + 547, + 666 + ], + "type": "text", + "content": " is the dimension of feature vector and " + }, + { + "bbox": [ + 304, + 599, + 547, + 666 + ], + "type": "inline_equation", + "content": "BN" + }, + { + "bbox": [ + 304, + 599, + 547, + 666 + ], + "type": "text", + "content": " is the BatchNorm block. Besides, " + }, + { + "bbox": [ + 304, + 599, + 547, + 666 + ], + "type": "inline_equation", + "content": "q^{(0)} = k^{(0)} = \\{g_i\\}_{i=1}^T" + }, + { + "bbox": [ + 304, + 599, + 547, + 666 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 599, + 547, + 666 + ], + "type": "inline_equation", + "content": "v^{(0)} = \\{\\mathcal{F}(X_i)\\}_{i=1}^T" + }, + { + "bbox": [ + 304, + 599, + 547, + 666 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 671, + 425, + 682 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 671, + 425, + 682 + ], + "spans": [ + { + "bbox": [ + 306, + 671, + 425, + 682 + ], + "type": "text", + "content": "4.3. Formation Detection" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 689, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 546, + 714 + ], + "type": "text", + "content": "In 4.2, we propose a pipeline to fuse temporal representations based on a kind of spatial information, the group" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2409" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 131 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 131 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 131 + ], + "type": "text", + "content": "features. However, such a fusion strategy can also be based on other kinds of spatial features and even without any features by simply using self-attention. To prove the effectiveness of the group features, we devise another kind of spatial features, formation features, to make a comparison." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 133, + 286, + 203 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 133, + 286, + 203 + ], + "spans": [ + { + "bbox": [ + 46, + 133, + 286, + 203 + ], + "type": "text", + "content": "Formation Detection Task. As mentioned in Section 3, we use a polygon to depict the formation of actors. As shown in Figure 2, the polygon is represented by several coordinates of some actors but not all of them. So in this task, we need to distinguish whether an actor is the vertex of the polygon or not." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 204, + 286, + 357 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 204, + 286, + 357 + ], + "spans": [ + { + "bbox": [ + 46, + 204, + 286, + 357 + ], + "type": "text", + "content": "Formation Detection Algorithm. Inspired by the \"anchor\" in object detection [37], we propose a feasible way to detect the vertexes. Given a picture, we split it into 1024 patches of equal size. For each patch, we set the center point as the \"anchor\". We send the image into Inception-V3 and extract the " + }, + { + "bbox": [ + 46, + 204, + 286, + 357 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 204, + 286, + 357 + ], + "type": "text", + "content": "-dimensional feature vector with RoIAlign [14] and a fully connected layer for each patch. To represent the absolute position of each patch, we use sine and cosine functions of different frequencies to encode the position of the \"anchor\". We add the " + }, + { + "bbox": [ + 46, + 204, + 286, + 357 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 204, + 286, + 357 + ], + "type": "text", + "content": "-dimensional positional encodings to the features and send them into a self-attention block to find the relations among different patches and build the " + }, + { + "bbox": [ + 46, + 204, + 286, + 357 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 204, + 286, + 357 + ], + "type": "text", + "content": "-dimensional formation features for them." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 359, + 286, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 359, + 286, + 407 + ], + "spans": [ + { + "bbox": [ + 46, + 359, + 286, + 407 + ], + "type": "text", + "content": "Then we take two steps to find vertexes. First, for each patch, we judge whether there is a vertex. Second, if there is a vertex, we calculate the relative coordinates of the vertex to the \"anchor\" point. So we detect vertexes by computing:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 93, + 415, + 286, + 430 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 93, + 415, + 286, + 430 + ], + "spans": [ + { + "bbox": [ + 93, + 415, + 286, + 430 + ], + "type": "interline_equation", + "content": "\\hat {P} = \\left[ \\hat {p} _ {1}, \\dots , \\hat {p} _ {n} \\right], \\quad \\hat {C} = \\left[ \\hat {c} _ {1}, \\dots , \\hat {c} _ {n} \\right], \\tag {9}", + "image_path": "cc4749996a855018e32647ede92bc55e5fccb0212349bb740b6a308e71c2633e.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 437, + 286, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 437, + 286, + 521 + ], + "spans": [ + { + "bbox": [ + 46, + 437, + 286, + 521 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 437, + 286, + 521 + ], + "type": "inline_equation", + "content": "\\hat{p}_i\\in \\mathbb{R}" + }, + { + "bbox": [ + 46, + 437, + 286, + 521 + ], + "type": "text", + "content": " denotes the confidence of whether there is a vertex in the " + }, + { + "bbox": [ + 46, + 437, + 286, + 521 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 437, + 286, + 521 + ], + "type": "text", + "content": " -th patch and " + }, + { + "bbox": [ + 46, + 437, + 286, + 521 + ], + "type": "inline_equation", + "content": "\\hat{c}_i\\in \\mathbb{R}^2" + }, + { + "bbox": [ + 46, + 437, + 286, + 521 + ], + "type": "text", + "content": " is the relative coordinates of the vertex to the \"anchor\". In this way, the formation detection task is converted to a classification problem and a regression problem. And we respectively use a MLP to predict " + }, + { + "bbox": [ + 46, + 437, + 286, + 521 + ], + "type": "inline_equation", + "content": "\\hat{P}" + }, + { + "bbox": [ + 46, + 437, + 286, + 521 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 437, + 286, + 521 + ], + "type": "inline_equation", + "content": "\\hat{C}" + }, + { + "bbox": [ + 46, + 437, + 286, + 521 + ], + "type": "text", + "content": " upon the formation features mentioned above. The object function can be represented as:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 61, + 531, + 286, + 554 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 531, + 286, + 554 + ], + "spans": [ + { + "bbox": [ + 61, + 531, + 286, + 554 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {B C E} = - \\sum_ {i} \\left[ p _ {i} \\log \\hat {p} _ {i} + (1 - p _ {i}) \\log \\left(1 - \\hat {p} _ {i}\\right) \\right], \\tag {10}", + "image_path": "101173b4756c214a38097d57856279f0e30baf0d9cccce51c5d9db316c4a8958.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 122, + 558, + 286, + 572 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 122, + 558, + 286, + 572 + ], + "spans": [ + { + "bbox": [ + 122, + 558, + 286, + 572 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {M S E} = \\left\\| C - \\hat {C} \\right\\| ^ {2}. \\tag {11}", + "image_path": "5809f9275d3445d4b888930fe9ec7f13edc8f02a1ded76b23bdea3b1919c2f86.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 581, + 286, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 581, + 286, + 640 + ], + "spans": [ + { + "bbox": [ + 46, + 581, + 286, + 640 + ], + "type": "text", + "content": "We minimize " + }, + { + "bbox": [ + 46, + 581, + 286, + 640 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{BCE}" + }, + { + "bbox": [ + 46, + 581, + 286, + 640 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 581, + 286, + 640 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{MSE}" + }, + { + "bbox": [ + 46, + 581, + 286, + 640 + ], + "type": "text", + "content": " to predict the vertexes. The " + }, + { + "bbox": [ + 46, + 581, + 286, + 640 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 581, + 286, + 640 + ], + "type": "text", + "content": "-dimensional formation features of middle frame in each clip can replace the group features in 4.2 to fuse the temporal information. Relative experiments are conducted in our ablation study." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 651, + 127, + 664 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 651, + 127, + 664 + ], + "spans": [ + { + "bbox": [ + 47, + 651, + 127, + 664 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 671, + 179, + 683 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 671, + 179, + 683 + ], + "spans": [ + { + "bbox": [ + 47, + 671, + 179, + 683 + ], + "type": "text", + "content": "5.1. Implementation Details" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 689, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 286, + 713 + ], + "type": "text", + "content": "Action Quality Assessment. Following [31,49,53], we take two stages to assess action quality: feature extraction" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 72, + 545, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 239 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 239 + ], + "type": "text", + "content": "and score prediction. In the feature extraction stage, we use the I3D model pretrained on Kinetics [4] dataset to extract the 1024-dimensional feature vector for each video clip. Specifically, we sample 5406 frames for each video, split them into 540 snippets, and fed them into I3D. Each snippet contains 16 continuous frames with a stride of 10 frames. In the ablation study, we also use the video swintransformer [27] as the backbone, which is also pretrained on Kinetics. We follow the sampling strategy in [27] to use a temporal stride of 2. The Inception-V3 in 4.2 is pretrained on ImageNet [9] to extract the CNN features. Following [44, 50, 52], we split the dataset into 3:1 for training and testing in all the experiments. We also test our model using the Mindspore [1]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 240, + 545, + 347 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 240, + 545, + 347 + ], + "spans": [ + { + "bbox": [ + 304, + 240, + 545, + 347 + ], + "type": "text", + "content": "Action Segmentation. We conduct action segmentation on LOGO with several existing approaches (ASFormer [51], SSTDA [23], MS_TC++ [5], ASRF [17]) to provide a benchmark. We try two backbones to extract frame-wise features: I3D [4] model and video swim-transformer [27] pretrained on Kinetics. For SWIN, we expand the snippet size to 32 frames to extract 1536-dimensional features. In the training stage, we train action segmentation approaches on their default setting." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 356, + 418, + 367 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 356, + 418, + 367 + ], + "spans": [ + { + "bbox": [ + 306, + 356, + 418, + 367 + ], + "type": "text", + "content": "5.2. Evaluation Metrics" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 374, + 545, + 457 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 374, + 545, + 457 + ], + "spans": [ + { + "bbox": [ + 304, + 374, + 545, + 457 + ], + "type": "text", + "content": "Action Quality Assessment. Following [44, 50, 52, 53], we comprehensively evaluate our approach to AQA under two metrics, Spearman's rank correlation " + }, + { + "bbox": [ + 304, + 374, + 545, + 457 + ], + "type": "inline_equation", + "content": "(\\rho)" + }, + { + "bbox": [ + 304, + 374, + 545, + 457 + ], + "type": "text", + "content": " and relative " + }, + { + "bbox": [ + 304, + 374, + 545, + 457 + ], + "type": "inline_equation", + "content": "\\ell_2" + }, + { + "bbox": [ + 304, + 374, + 545, + 457 + ], + "type": "text", + "content": "-distance " + }, + { + "bbox": [ + 304, + 374, + 545, + 457 + ], + "type": "inline_equation", + "content": "(\\mathbf{R} - \\ell_2)" + }, + { + "bbox": [ + 304, + 374, + 545, + 457 + ], + "type": "text", + "content": ". Spearman's rank correlation is used to evaluate the rank correlation between the prediction and ground-truth while the relative " + }, + { + "bbox": [ + 304, + 374, + 545, + 457 + ], + "type": "inline_equation", + "content": "\\ell_2" + }, + { + "bbox": [ + 304, + 374, + 545, + 457 + ], + "type": "text", + "content": "-distance " + }, + { + "bbox": [ + 304, + 374, + 545, + 457 + ], + "type": "inline_equation", + "content": "(\\mathbf{R} - \\ell_2)" + }, + { + "bbox": [ + 304, + 374, + 545, + 457 + ], + "type": "text", + "content": " focuses on the difference of the numerical values." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 459, + 545, + 531 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 459, + 545, + 531 + ], + "spans": [ + { + "bbox": [ + 304, + 459, + 545, + 531 + ], + "type": "text", + "content": "Action Segmentation. Following [5, 15, 23, 51], we adopt three widely used evaluation metrics including framewise accuracy (Acc), segmental edit distance and segmental F1 score at overlapping thresholds " + }, + { + "bbox": [ + 304, + 459, + 545, + 531 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 304, + 459, + 545, + 531 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 459, + 545, + 531 + ], + "type": "inline_equation", + "content": "25\\%" + }, + { + "bbox": [ + 304, + 459, + 545, + 531 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 459, + 545, + 531 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 304, + 459, + 545, + 531 + ], + "type": "text", + "content": ", denoted by F1@{10, 25, 50} to evaluate the performance of action segmentation approaches." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 539, + 502, + 552 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 539, + 502, + 552 + ], + "spans": [ + { + "bbox": [ + 306, + 539, + 502, + 552 + ], + "type": "text", + "content": "5.3. Comparison with the State of the Art" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 557, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 545, + 713 + ], + "type": "text", + "content": "Action Quality Assessment. Table 2 shows the experimental results, which reveal great challenges to performing action quality assessment on the LOGO dataset. With the I3D backbone, the mainstream methods in single-person short-term AQA [44, 50, 52] attain the result of 0.4259, 0.4712, and 0.4518 on Spearman's rank correlation respectively. Besides, the results show that our approach achieves the state-of-the-art. We observe that USDL+GOAT, CoRe+GOAT, and TSA+GOAT consistently improve the performance over the original models. Specifically, our approach respectively obtained " + }, + { + "bbox": [ + 304, + 557, + 545, + 713 + ], + "type": "inline_equation", + "content": "8.48\\%" + }, + { + "bbox": [ + 304, + 557, + 545, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 557, + 545, + 713 + ], + "type": "inline_equation", + "content": "4.73\\%" + }, + { + "bbox": [ + 304, + 557, + 545, + 713 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 557, + 545, + 713 + ], + "type": "inline_equation", + "content": "10.12\\%" + }, + { + "bbox": [ + 304, + 557, + 545, + 713 + ], + "type": "text", + "content": " improvements on Spearman's rank correlation. Our method also outperforms the previous long-term AQA" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2410" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 93, + 541, + 260 + ], + "blocks": [ + { + "bbox": [ + 50, + 93, + 541, + 260 + ], + "lines": [ + { + "bbox": [ + 50, + 93, + 541, + 260 + ], + "spans": [ + { + "bbox": [ + 50, + 93, + 541, + 260 + ], + "type": "image", + "image_path": "da839ffdcd1a5d1210e5f69b6d8ef6015827bbe7305bc427a0cdae30b1aa7fd8.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 262, + 547, + 297 + ], + "lines": [ + { + "bbox": [ + 46, + 262, + 547, + 297 + ], + "spans": [ + { + "bbox": [ + 46, + 262, + 547, + 297 + ], + "type": "text", + "content": "Figure 5. The visualization of the output of our proposed GOAT in action quality assessment. We use red stars to denote clips with high weight while using blue stars to represent clips with low weight. Our approach can focus on where the athletes perform effective movements with clear formations while it can also ignore the redundant part such as all actors are under-water." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 48, + 330, + 288, + 434 + ], + "blocks": [ + { + "bbox": [ + 47, + 304, + 288, + 326 + ], + "lines": [ + { + "bbox": [ + 47, + 304, + 288, + 326 + ], + "spans": [ + { + "bbox": [ + 47, + 304, + 288, + 326 + ], + "type": "text", + "content": "Table 2. Comparisons of performance with existing AQA methods on LOGO. The higher " + }, + { + "bbox": [ + 47, + 304, + 288, + 326 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 47, + 304, + 288, + 326 + ], + "type": "text", + "content": " ,the lower " + }, + { + "bbox": [ + 47, + 304, + 288, + 326 + ], + "type": "inline_equation", + "content": "\\mathrm{R} - {\\ell }_{2}" + }, + { + "bbox": [ + 47, + 304, + 288, + 326 + ], + "type": "text", + "content": " ,the better performance." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 330, + 288, + 434 + ], + "lines": [ + { + "bbox": [ + 48, + 330, + 288, + 434 + ], + "spans": [ + { + "bbox": [ + 48, + 330, + 288, + 434 + ], + "type": "table", + "html": "
MethodI3DSWIN
ρ↑R-ℓ2(×100) ↓ρ↑R-ℓ2(×100) ↓
USDL [44]0.42595.73640.47255.0762
CoRe [52]0.47125.40860.50025.9597
TSA [50]0.45185.53260.47514.7778
ACTION-NET [53]0.30575.85810.41015.5693
USDL [44]+GOAT0.46204.87390.53495.0220
CoRe [52]+GOAT0.49355.07160.55994.7626
TSA [50]+GOAT0.48555.39430.48435.4086
", + "image_path": "696d78e7440254b07f192445711386fba47f7f806bab45b9a7786a75c77b2803.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 48, + 452, + 286, + 564 + ], + "blocks": [ + { + "bbox": [ + 79, + 436, + 254, + 447 + ], + "lines": [ + { + "bbox": [ + 79, + 436, + 254, + 447 + ], + "spans": [ + { + "bbox": [ + 79, + 436, + 254, + 447 + ], + "type": "text", + "content": "Table 3. Action segmentation results on LOGO." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 452, + 286, + 564 + ], + "lines": [ + { + "bbox": [ + 48, + 452, + 286, + 564 + ], + "spans": [ + { + "bbox": [ + 48, + 452, + 286, + 564 + ], + "type": "table", + "html": "
MethodFeaturesF1@{10,25,50}EditAcc
ASFormer [51]SWIN81.779.871.175.381.0
ASFormer [51]I3D75.171.661.368.273.9
MS_TCN++ [23]SWIN80.878.870.273.580.1
MS_TCN++ [23]I3D72.669.258.566.070.6
SSTDA [5]SWIN77.875.966.370.079.2
SSTDA [5]I3D60.155.744.050.163.4
ASRF [17]SWIN80.879.172.173.280.0
ASRF [17]I3D73.670.559.866.869.8
", + "image_path": "618929832b450c6e8ae94e4732749e5cb4daa3bcdc3e13c92d33f9feebe4475b.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 569, + 287, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 569, + 287, + 604 + ], + "spans": [ + { + "bbox": [ + 46, + 569, + 287, + 604 + ], + "type": "text", + "content": "method [53]. The experimental results illustrate the effectiveness of our proposed module when dealing with multiperson long-term scenarios." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": "Action Segmentation. Table 3 presents the experimental results. With the I3D feature, the previous action segmentation methods [5, 17, 23, 51] achieve the result of " + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "inline_equation", + "content": "73.9\\%" + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "inline_equation", + "content": "70.6\\%" + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "inline_equation", + "content": "63.4\\%" + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "inline_equation", + "content": "69.8\\%" + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": " frame accuracy respectively. And given an identical setting, we see that the SWIN-pretrained feature obtained significant improvement in all five metrics. Table 6 reveals that our method could improve the performance of MS_TC++ and ASFormer and achieve the state-of-the-art with the group information." + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 306, + 341, + 547, + 402 + ], + "blocks": [ + { + "bbox": [ + 305, + 304, + 546, + 337 + ], + "lines": [ + { + "bbox": [ + 305, + 304, + 546, + 337 + ], + "spans": [ + { + "bbox": [ + 305, + 304, + 546, + 337 + ], + "type": "text", + "content": "Table 4. Comparisons of AQA results of CORE and CORE+GOAT based on existing short-term, two-player datasets. @2 means AQA datasets with two-player scenes." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 306, + 341, + 547, + 402 + ], + "lines": [ + { + "bbox": [ + 306, + 341, + 547, + 402 + ], + "spans": [ + { + "bbox": [ + 306, + 341, + 547, + 402 + ], + "type": "table", + "html": "
DatasetCORE [52]CORE [52]+GOAT
ρ↑R-ℓ2(×100) ↓ρ↑R-ℓ2(×100) ↓
FineDiving [50]@20.89910.37510.90320.3529
TASD-2 [11]@20.91890.78630.93340.7054
AQA-7 [29]@20.90120.73020.93250.6423
", + "image_path": "324ac265e1e8507b509713a61d6c1c470ca0dfcd3c94a6846a5b083dad0eda62.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 413, + 443, + 425 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 413, + 443, + 425 + ], + "spans": [ + { + "bbox": [ + 306, + 413, + 443, + 425 + ], + "type": "text", + "content": "5.4. Generalization of GOAT" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 433, + 547, + 554 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 433, + 547, + 554 + ], + "spans": [ + { + "bbox": [ + 304, + 433, + 547, + 554 + ], + "type": "text", + "content": "Our method is currently suitable for multi-person scenarios. We select current AQA datasets with two-player scenes (there are only 2 players at most for now) and redivide them according to the number of people. TASD-2 [11] is a dataset collected from synchronized diving events with 2 players in each video. Based on the divided dataset, we obtain results in Table 4, which prove that GOAT can improve the AQA results of two-player scenes in other datasets. These results also demonstrate the generalization of GOAT. Our method can perform well in short-term, two-player scenes." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 562, + 400, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 562, + 400, + 574 + ], + "spans": [ + { + "bbox": [ + 306, + 562, + 400, + 574 + ], + "type": "text", + "content": "5.5. Ablation Study" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 581, + 546, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 581, + 546, + 653 + ], + "spans": [ + { + "bbox": [ + 304, + 581, + 546, + 653 + ], + "type": "text", + "content": "We change the video feature backbone to verify the generality of our approach. Besides, we also try to use other spatial features or simply use self-attention for temporal information fusion to demonstrate the effectiveness of the group features. The experiments also illustrate that our temporal fusion strategy outperforms the average pooling." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "content": "Spatial Features. As shown in Table 5, we conduct experiments utilizing formation features to replace the group embeddings used in GOAT to fuse the temporal representations. The formation features are extracted from the attention block output in the formation detection pipeline men" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 210, + 77, + 396, + 90 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 210, + 77, + 396, + 90 + ], + "spans": [ + { + "bbox": [ + 210, + 77, + 396, + 90 + ], + "type": "text", + "content": "WorldChampionship2022_free_preliminary_15" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "2411" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 72, + 132, + 144 + ], + "blocks": [ + { + "bbox": [ + 50, + 72, + 132, + 144 + ], + "lines": [ + { + "bbox": [ + 50, + 72, + 132, + 144 + ], + "spans": [ + { + "bbox": [ + 50, + 72, + 132, + 144 + ], + "type": "image", + "image_path": "ef2df0d15e7a454ef2c53c0d2670d4d448af26e9bebf4d6391b27987b5ba9324.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 152, + 547, + 185 + ], + "lines": [ + { + "bbox": [ + 46, + 152, + 547, + 185 + ], + "spans": [ + { + "bbox": [ + 46, + 152, + 547, + 185 + ], + "type": "text", + "content": "Figure 6. The visualization of the prediction results of our formation detector module. The green polygons represent prediction results and the yellow polygons with blue edges are the ground truth. The results show that our approach can detect the positions of actors and distinguish whether the athlete is the formation vertex or not, which guarantees the reliability of the formation features." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 133, + 72, + 214, + 144 + ], + "blocks": [ + { + "bbox": [ + 133, + 72, + 214, + 144 + ], + "lines": [ + { + "bbox": [ + 133, + 72, + 214, + 144 + ], + "spans": [ + { + "bbox": [ + 133, + 72, + 214, + 144 + ], + "type": "image", + "image_path": "9405348331852f45d1f06294cc38ba7a01b2f98cc269d5502d054a7ff3f865b3.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 215, + 72, + 296, + 144 + ], + "blocks": [ + { + "bbox": [ + 215, + 72, + 296, + 144 + ], + "lines": [ + { + "bbox": [ + 215, + 72, + 296, + 144 + ], + "spans": [ + { + "bbox": [ + 215, + 72, + 296, + 144 + ], + "type": "image", + "image_path": "ebe946718bf991d1ab0b2b129fb6311a42628e02577fb7df4078f7ac80a731f7.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 298, + 72, + 378, + 144 + ], + "blocks": [ + { + "bbox": [ + 298, + 72, + 378, + 144 + ], + "lines": [ + { + "bbox": [ + 298, + 72, + 378, + 144 + ], + "spans": [ + { + "bbox": [ + 298, + 72, + 378, + 144 + ], + "type": "image", + "image_path": "781c3bf082d4f21e5c1f89693a865167526d42ef43a70d3d4b1d603b860c297a.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 379, + 72, + 460, + 144 + ], + "blocks": [ + { + "bbox": [ + 379, + 72, + 460, + 144 + ], + "lines": [ + { + "bbox": [ + 379, + 72, + 460, + 144 + ], + "spans": [ + { + "bbox": [ + 379, + 72, + 460, + 144 + ], + "type": "image", + "image_path": "3604340a74630d551e49b24aff16375af4370d9e50de9ebac1888a0f509818a9.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 461, + 72, + 544, + 144 + ], + "blocks": [ + { + "bbox": [ + 461, + 72, + 544, + 144 + ], + "lines": [ + { + "bbox": [ + 461, + 72, + 544, + 144 + ], + "spans": [ + { + "bbox": [ + 461, + 72, + 544, + 144 + ], + "type": "image", + "image_path": "188de8ec2031892b5a3eb1a9664bc12c3dbad7d32e5c63e20ce99fc4e5cb91a9.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 48, + 232, + 288, + 358 + ], + "blocks": [ + { + "bbox": [ + 47, + 194, + 287, + 228 + ], + "lines": [ + { + "bbox": [ + 47, + 194, + 287, + 228 + ], + "spans": [ + { + "bbox": [ + 47, + 194, + 287, + 228 + ], + "type": "text", + "content": "Table 5. Ablation studies on LOGO. Self. indicates self-attention; Form. indicates using formation features for temporal fusing; AS. means using the action segmentation features for temporal fusing." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 232, + 288, + 358 + ], + "lines": [ + { + "bbox": [ + 48, + 232, + 288, + 358 + ], + "spans": [ + { + "bbox": [ + 48, + 232, + 288, + 358 + ], + "type": "table", + "html": "
MethodI3DSWIN
ρ↑R-ℓ2(×100)↓ρ↑R-ℓ2(×100)↓
USDL [44]+Self.0.43354.88980.50784.1305
CoRe [52]+Self.0.43485.60190.52694.5072
TSA [50]+Self.0.45855.03360.47205.7280
USDL [44]+Form.0.43555.76360.53705.0888
CoRe [52]+Form.0.48205.30030.54015.1747
TSA [50]+Form.0.42415.18210.49034.8627
USDL [44]+AS.0.45124.88370.51085.0479
CoRe [52]+AS.0.48255.23930.53644.9102
TSA [50]+AS.0.47725.42030.48295.3561
", + "image_path": "8e5470a16001f2b580e780b603a35e9736443efb8a4bc5c938da8115f5ed32d8.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 48, + 389, + 288, + 457 + ], + "blocks": [ + { + "bbox": [ + 47, + 361, + 287, + 383 + ], + "lines": [ + { + "bbox": [ + 47, + 361, + 287, + 383 + ], + "spans": [ + { + "bbox": [ + 47, + 361, + 287, + 383 + ], + "type": "text", + "content": "Table 6. The action segmentation results of existing methods with GOAT on LOGO. +GOAT indicates the method with GOAT." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 389, + 288, + 457 + ], + "lines": [ + { + "bbox": [ + 48, + 389, + 288, + 457 + ], + "spans": [ + { + "bbox": [ + 48, + 389, + 288, + 457 + ], + "type": "table", + "html": "
MethodFeaturesF1@{10,25,50}EditAcc
MS_TCN++ [23]+GOATSWIN80.979.070.574.081.1
MS_TCN++ [23]+GOATI3D73.269.959.467.371.7
ASFormer [51]+GOATSWIN82.280.373.675.981.7
ASFormer [51]+GOATI3D75.872.062.168.874.6
", + "image_path": "4a62a090a4d3c7089654c28ec8b47c0d7992049f8147a0f06fdbdb5fc4481470.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 474, + 287, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 474, + 287, + 652 + ], + "spans": [ + { + "bbox": [ + 46, + 474, + 287, + 652 + ], + "type": "text", + "content": "tioned in 4.3, which is pretrained on the LOGO dataset by executing formation detection. We also adopt self-attention to replace GOAT, which means we perform our temporal fusion strategy without the assistance of any spatial information. The experimental results show that the formation features outperform the original models and self-attention models but perform worse than the group features in most cases. The results also show that the self-attention models perform better than the original models. Such results of our experiments prove that: (1) Our temporal fusion strategy outperforms the average pooling even without any spatial information. (2) By modeling the spatial information, the performance of our proposed approach is improved. (3) Building the relations among actors, the group features perform better than the formation features." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "text", + "content": "Video Feature Backbone. As shown in Table 5 and Table 2. We change the backbone to video swin-transformer (abbreviated as SWIN) and repeat all our experiments. Similar to the results shown in the action segmentation experiments, the methods based on SWIN perform much better" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 195, + 545, + 255 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 195, + 545, + 255 + ], + "spans": [ + { + "bbox": [ + 304, + 195, + 545, + 255 + ], + "type": "text", + "content": "than the methods based on I3D in most cases, which illustrates the effectiveness of SWIN. Besides, except for the case of TSA+Self, the results of our methods substantially outperform the original models based on SWIN, which proves the generality of our approach." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 256, + 546, + 340 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 256, + 546, + 340 + ], + "spans": [ + { + "bbox": [ + 304, + 256, + 546, + 340 + ], + "type": "text", + "content": "Asist AQA with Action Segmentation. To assist the AQA task with the action segmentation task (or action labels), we use the backbone features finetuned in the action segmentation task as the input of GOAT in the experiments shown in the lower part of Table 5. The results illustrate that with the help of the segmentation task, the performances of AQA are improved compared with the original methods." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 349, + 389, + 361 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 349, + 389, + 361 + ], + "spans": [ + { + "bbox": [ + 306, + 349, + 389, + 361 + ], + "type": "text", + "content": "5.6. Visualization" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 368, + 545, + 452 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 368, + 545, + 452 + ], + "spans": [ + { + "bbox": [ + 304, + 368, + 545, + 452 + ], + "type": "text", + "content": "We visualize the output of GOAT, as shown in Figure 5. It shows that GOAT highlights the part where actors perform effective action with clear formations, demonstrating the effectiveness of our temporal fusion strategy. We also visualize the prediction results of our formation detection module, as shown in Figure 6. It can be seen that our approach can distinguish the vertexes of the formations." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 464, + 378, + 477 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 464, + 378, + 477 + ], + "spans": [ + { + "bbox": [ + 306, + 464, + 378, + 477 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 485, + 545, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 485, + 545, + 581 + ], + "spans": [ + { + "bbox": [ + 304, + 485, + 545, + 581 + ], + "type": "text", + "content": "In this paper, we construct the first multi-person long-form video dataset, LOGO, for action quality assessment. We also propose a group-aware module, GOAT, to build relations among multiple actors and fuse the temporal representations based on spatial information. Furthermore, the utilization of GOAT in action quality assessment and action segmentation both achieve substantial improvements compared to the existing methods." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 582, + 545, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 628 + ], + "type": "text", + "content": "Existing Assets and Personal Data. The videos in LOGO are downloaded from several websites such as YouTube. We are actively connecting with the authors to ensure that appropriate consent has been obtained." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 630, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 546, + 713 + ], + "type": "text", + "content": "Acknowledgments. This work was sponsored in part by the National Natural Science Foundation of China (Grant No. 62206153, 62125603), CAAI-Huawei MindSpore Open Fund, Deng Feng Fund, Young Elite Scientists Sponsorship Program by CAST (No. 2022QNRC001), and Shenzhen Stable Supporting Program (WDZC20220818112518001)." + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2412" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 712 + ], + "type": "list", + "angle": 0, + "index": 18, + "blocks": [ + { + "bbox": [ + 53, + 91, + 259, + 102 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 259, + 102 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 259, + 102 + ], + "type": "text", + "content": "[1] Mindspore. https://www.mindspore.cn/.6" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 53, + 103, + 287, + 147 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 103, + 287, + 147 + ], + "spans": [ + { + "bbox": [ + 53, + 103, + 287, + 147 + ], + "type": "text", + "content": "[2] Timur Bagautdinov, Alexandre Alahi, François Fleuret, Pascal Fua, and Silvio Savarese. 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Video and accelerometer-based motion analysis for automated surgical skills assessment. *IJCARS*, 13(3):443-455, 2018. 2" + } + ] + } + ], + "index": 25 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2414" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/LP-DIF_ Learning Local Pattern-Specific Deep Implicit Function for 3D Objects and Scenes/e23a5c43-ebb5-406b-9d78-64277af6a197_content_list.json b/2023/LP-DIF_ Learning Local Pattern-Specific Deep Implicit Function for 3D Objects and Scenes/e23a5c43-ebb5-406b-9d78-64277af6a197_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..7b31defeb688bd269614b478611bd61d1108d79e --- /dev/null +++ b/2023/LP-DIF_ Learning Local Pattern-Specific Deep Implicit Function for 3D Objects and Scenes/e23a5c43-ebb5-406b-9d78-64277af6a197_content_list.json @@ -0,0 +1,1475 @@ +[ + { + "type": "text", + "text": "LP-DIF: Learning Local Pattern-specific Deep Implicit Function for 3D Objects and Scenes", + "text_level": 1, + "bbox": [ + 84, + 160, + 885, + 201 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Meng Wang1 Yu-Shen Liu1* * Yue Gao1 Kanle Shi2 Yi Fang3 Zhizhong Han4", + "bbox": [ + 131, + 226, + 833, + 245 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ School of Software, BNRist, Tsinghua University, Beijing, China", + "bbox": [ + 243, + 245, + 724, + 261 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{2}$ Kuaishou Technology, Beijing, China", + "bbox": [ + 342, + 261, + 626, + 277 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "3Center for Artificial Intelligence and Robotics, New York University Abu Dhabi, Abu Dhabi, UAE", + "bbox": [ + 124, + 277, + 843, + 292 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{4}$ Department of Computer Science, Wayne State University, Detroit, USA", + "bbox": [ + 216, + 292, + 751, + 309 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{meng_wang, gaoyue, liuyushen}@tsinghua.edu.cn", + "bbox": [ + 280, + 312, + 682, + 326 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "shikanle@kuaishou.com yfang@nyu.edu h312h@wayne.edu", + "bbox": [ + 240, + 328, + 724, + 340 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 372, + 312, + 387 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Deep Implicit Function (DIF) has gained much popularity as an efficient 3D shape representation. To capture geometry details, current mainstream methods divide 3D shapes into local regions and then learn each one with a local latent code via a decoder. Such local methods can capture more local details due to less diversity among local regions than global shapes. Although the diversity of local regions has been decreased compared to global approaches, the diversity in different local regions still poses a challenge in learning an implicit function when treating all regions equally using only a single decoder. What is worse, these local regions often exhibit imbalanced distributions, where certain regions have significantly fewer observations. This leads that fine geometry details could not be preserved well. To solve this problem, we propose a novel Local Pattern-specific Implicit Function, named LP-DIF, to represent a shape with clusters of local regions and multiple decoders, where each decoder only focuses on one cluster of local regions which share a certain pattern. Specifically, we first extract local codes for all regions, and then cluster them into multiple groups in the latent space, where similar regions sharing a common pattern fall into one group. After that, we train multiple decoders for mining local patterns of different groups, which simplifies the learning of fine geometric details by reducing the diversity of local regions seen by each decoder. To further alleviate the data-imbalance problem, we introduce a region re-weighting module to each pattern-specific decoder using a kernel density estimator, which dynamically re-weights the regions during learn", + "bbox": [ + 75, + 404, + 472, + 806 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ing. Our LP-DIF can restore more geometry details, and thus improve the quality of 3D reconstruction. Experiments demonstrate that our method can achieve the state-of-the-art performance over previous methods. Code is available at https://github.com/gtyxyz/lpdfif.", + "bbox": [ + 499, + 374, + 892, + 444 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 500, + 469, + 630, + 484 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Representing 3D shapes is a fundamental problem for many applications in 3D computer vision. Recently, Deep Implicit Function (DIF) [4,22,23,25,28,41] has gained popularity for efficiently learning the representation of 3D objects and scenes. In contrast to directly learning explicit 3D representations [15,30,31] (voxels, point clouds or meshes), DIF aims to train a neural network to learn the binary occupancy function [25] or signed distance function (SDF) [28], as given a query location and an input latent code. Such kind of representation is continuous with arbitrary precision and can handle various topology, which has achieved the state-of-the-art results in several shape reconstruction tasks.", + "bbox": [ + 497, + 492, + 892, + 657 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Existing DIF methods can be roughly classified into two categories: global and local approaches. Most of the early methods [4, 9, 20, 21, 25, 27-29, 35, 37, 40] fall into global approaches. These methods take advantage of one latent code and a single decoder to represent the whole shape. Global approaches often suffer from long training time and low reconstruction accuracy due to the limited capacity of capturing local geometry details. More recently, local approaches [1, 3, 5, 6, 10-12, 17, 19, 34, 36, 38] divide 3D shapes (often divide by 3D grids) into local regions and then learn each one with a local latent code via a decoder, where the decoder shares the geometric similarities among different local regions. Although such local approaches can capture some local details, a large diversity of different local regions still increase the difficulty of learning an implicit function", + "bbox": [ + 497, + 659, + 894, + 866 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 129, + 49, + 200, + 85 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 252, + 48, + 791, + 87 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*The corresponding author is Yu-Shen Liu. This work was supported by National Key R&D Program of China (2022YFC3800600), the National Natural Science Foundation of China (62272263, 62072268), and in part by Tsinghua-Kuaishou Institute of Future Media Data.", + "bbox": [ + 75, + 820, + 470, + 866 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "21856", + "bbox": [ + 463, + 885, + 505, + 897 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/146c79253fa2fb39027cc61808d867306d2668a7062444acaf3e2e8ffca46335.jpg", + "image_caption": [ + "(a) Global DIF", + "(b) Local DIF", + "(c) Ours", + "(d) Reference", + "Figure 1. Visual comparison of 3D shape surface reconstruction. Compared with global DIF (e.g. [28]) and local DIF (e.g. [1]), our method can reconstruct the shape with fine-grained geometric details. Compared with previous methods that treat all local regions equally using a single decoder, we regard a shape as clusters of local regions and mine local patterns with different decoders. This alleviates the difficulty of learning caused by diverse local regions." + ], + "image_footnote": [], + "bbox": [ + 161, + 125, + 803, + 328 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "when treating all regions equally using only a single decoder. In addition, these local regions often exhibit imbalanced distributions, where certain regions have significantly fewer observations, especially in scenes. As a result, fine geometry details of shapes could not be captured well.", + "bbox": [ + 75, + 416, + 468, + 486 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address the above-mentioned problems, we propose a novel Local Pattern-specific Implicit Function, named LP-DIF, for learning 3D shape representation using clusters of local regions with multiple decoders, where each decoder only represents one cluster of local regions which share a certain pattern (geometric features such as facing direction, number of faces, relative positions to the region center). Specifically, we first extract the local latent codes for all local regions divided by 3D grids, and then cluster them into multiple groups in the latent space, where similar regions sharing a common pattern fall into one group. After that, we train a separate pattern-specific decoder for each group of regions, which reduces data-imbalance among different patterns of regions and simplifies the learning of fine geometric details of 3D structures by limiting the diversity of regions seen to each decoder. To further alleviate the region-imbalance problem, we introduce a region reweighting module to each pattern-specific decoder by kernel density estimator, which dynamically re-weights the regions during learning. Our main contributions can be summarized as follows.", + "bbox": [ + 75, + 486, + 468, + 775 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- We propose a novel LP-DIF to learn local pattern-specific deep implicit function of 3D shapes for reconstructing highly detailed geometry. Compared with previous methods that treat all local regions equally using a single decoder, we regard a shape as clusters of local regions and mine local patterns with different de", + "bbox": [ + 95, + 783, + 468, + 866 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "coders. This alleviates the difficulty of learning caused by diverse local regions.", + "bbox": [ + 529, + 416, + 890, + 445 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We introduce a dynamic region re-weighting module, which could provide more focus on less common regions to tackle the data-imbalance problem in each pattern decoder. As a result, the regions with less appearances can be captured more accurately.", + "- Our method could be applied in multiple objects, single complex objects and large scale of scenes. We improve the state-of-the-art accuracy in surface reconstruction under various benchmarks." + ], + "bbox": [ + 517, + 453, + 890, + 586 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Figure 2 illustrates the main differences between DIF, local DIF and our method. For DIF approaches, one global code and a decoder are used for the whole shape. For Local DIF methods, multiple local codes and a shared decoder are used. For our method, multiple clusters of regions are learned with different decoders.", + "bbox": [ + 497, + 596, + 890, + 678 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 499, + 690, + 640, + 705 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In computer vision and graphics, there are two categories of shape representations: explicit representation and implicit representation. Explicit geometric representations [15, 30, 31] such as point clouds, voxels and triangular meshes have been widely used for representing geometries for their simplicity and flexibility. More recently, deep implicit representations [4, 25, 28, 39] have been proposed in the context of shape representation, where the implicit surfaces of geometries are represented as the zero-set of spatial functions with fully connected neural networks. Such kind of representation is continuous with arbitrary precision and", + "bbox": [ + 497, + 714, + 890, + 866 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "21857", + "bbox": [ + 463, + 885, + 504, + 897 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/704e3af13c975e06d5bac373d9a0761951586ceee3a441a67355f23bd5b2cb5a.jpg", + "image_caption": [ + "Figure 2. Comparison between DIF, local DIF and our method. (a) DIF methods leverage one global code and one decoder, often suffer from long training speed and low reconstruction quality due to the limited capacity of capturing local geometry details. (b) Local DIF methods use multiple local codes and one shared decoder, a large diversity of different local regions still increase the difficulty of learning an implicit function when treating all regions equally using only a single decoder. (c) Our method, LP-DIF, for representing a shape with some clusters of local regions and multiple decoders, where each decoder only represents one cluster of local regions which share a certain pattern. (d) Visualization of the clustered local regions." + ], + "image_footnote": [], + "bbox": [ + 161, + 122, + 811, + 334 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "can handle different topology structure, which has achieved the state-of-the-art results in several shape reconstruction task. Implicit representations can be categorized into global and local approaches.", + "bbox": [ + 75, + 442, + 468, + 497 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Global Deep Implicit Shape Representation. In recent years, implicit functions have been introduced into neural networks [25, 28] and show promising results. Early approaches learn one latent code and one single global implicit network to represent the whole shape. For example, DeepSDF [28] learned an implicit function where the network output represents the signed distance of the input point to its nearest surface, where zero-set of the learned function implicitly represents the surface of the shape. Other approaches [25, 29] defined the implicit functions as 3D occupancy probability functions and turned shape representation into a point classification problem. Following these methods, [35, 37] improved the expressiveness of the implicit functions by introducing high frequency signals with periodic activation. [39] proposed to represent the volume density as an implicit function of the signed distance in neural volume rendering for high-quality novel view generation. However, these methods suffer from long training time and low reconstruction accuracy for high resolution data due to the limited capacity of decoder to capture local geometry details.", + "bbox": [ + 75, + 502, + 472, + 792 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Local Deep Implicit Shape Representation. To capture more geometry details, current mainstream methods divide 3D shapes into many local regions and then learn each one with a local latent code via a decoder. Some recent works [1, 29] proposed to divide the whole 3D shape", + "bbox": [ + 75, + 796, + 470, + 866 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "uniformly into 3D grids, where they either assign each local grid with a latent code or trilinearly interpolate local latent codes based on querying location. In LIG [17], this idea was applied to 3D scenes. NGLOD [36] leveraged sparse octree instead of uniform grids to increase efficiency. ACORN [24] proposed to adaptively optimize the coordinate decomposition to achieve higher accuracy in large-scale scenes. DCC-DIF [19] optimized the local latent code learning by introducing dynamic grid positions. IFNet [6] utilized multiple level of latent codes in a hierarchical way. LPI [3] divided the global shape into multiple local parts in latent space to allow easier shape parts learning and blending. PatchNet [38] was proposed to divide a shape into local patches with no fixed structure. Points2surf [10] incorporated local information surrounding each point, but it typically takes a lot of time for point-wise distance calculation. Although such local methods can capture some local details, a large diversity of different local regions still poses an challenge for learning an implicit function when treating all regions equally using only a single decoder. In addition, these local regions often exhibit imbalanced distributions, where certain regions have significantly fewer observations. As a result, fine geometry details could not be captured well. Several methods [8, 13] have been proposed to learn multiple decoders for point deformations, however, their methods cannot be applied in learning implicit representations for shapes. MDIF [5, 33] used multiple levels of decoders in a hierarchical way, however, it did not consider the relationship between local regions. In novel view synthesizing, KiloNeRF [32] utilized thousands of tiny MLPs to represent", + "bbox": [ + 497, + 442, + 895, + 859 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "21858", + "bbox": [ + 463, + 885, + 505, + 897 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "different parts of the scenes. The simple and effective way to introduce multiple decoders is to assign each local region with a decoder, however, it is normally not feasible due to time and space constraint and the prior information of the local regions could not be preserved. In contrast, we introduce clustering for the local regions as a trade-off between reconstruction accuracy and efficiency.", + "bbox": [ + 75, + 125, + 472, + 223 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 77, + 233, + 169, + 248 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given $K$ discrete points $\\mathbf{X} = \\{\\mathbf{x}_k\\}$ and their signed distances $\\mathbf{S} = \\{\\mathbf{s}_k\\}$ from a 3D surface, our goal is to regress a continuous function that outputs the closest signed distance to the 3D surface given a spatial point $\\mathbf{x}$ . To achieve this goal, we propose to learn a local pattern-specific DIF. The architecture of LP-DIF and differences between our LP-DIF and other methods are illustrated in Figure 2. In this section, we first introduce latent embedding learning and local region feature extraction in Sec. 3.1. Then we describe our pattern clustering module in Sec. 3.2. After that we present our pattern decoder with density adaptive re-weighting in Sec. 3.3. At last, we illustrate our training process in Sec. 3.4.", + "bbox": [ + 75, + 256, + 472, + 435 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1. Learning Latent Embedding for Local Regions", + "text_level": 1, + "bbox": [ + 75, + 444, + 468, + 459 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "At the beginning, we choose to train a local DIF network [1, 17] to learn latent embedding for local regions to extract coarse local features for clustering. Local DIF [1, 17] is a special category of DIF, which is defined as a signed distance function $f(\\mathbf{x}, \\mathbf{z})$ modeled with Multilayer Perceptrons (MLP), mapping each query point $\\mathbf{x}$ near a surface to the signed distance domain continuously with condition code $\\mathbf{z}$ . A shape $S$ is defined as the zero level set of $f(\\mathbf{x}, \\mathbf{z})$ :", + "bbox": [ + 75, + 466, + 468, + 577 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {S} = \\left\\{\\mathbf {x} \\in \\mathbb {R} ^ {3} \\mid f _ {\\theta} (\\mathbf {x}, \\mathbf {z}) = 0 \\right\\}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 173, + 587, + 468, + 605 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\theta$ is the parameter of the MLP. To be able to represent multiple shapes in the same time, the condition $\\mathbf{z}$ is optimized for each shape, and the parameter $\\theta$ is shared for all the shapes. Local DIF is defined on partitioned space of shape $S$ . A normalized 3D space is usually partitioned into $d\\times d\\times d$ regions $\\{\\mathbf{B}_i\\} \\subseteq \\mathbb{R}^3$ , $i = 0\\dots N - 1$ . All the regions have their separate codes $\\mathbf{z}_i$ , sharing the same parameter $\\theta$ . The entire surface is defined as:", + "bbox": [ + 75, + 609, + 468, + 720 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {S} = \\left\\{\\mathbf {x} \\in \\mathbb {R} ^ {3} \\mid \\sum f _ {\\theta} (T (\\mathbf {x}), \\mathbf {z} _ {i}) = 0 \\right\\}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 144, + 726, + 468, + 747 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $T(\\mathbf{x})$ is the re-centering function of $\\mathbf{x}$ , which transforms the points in each region to their local coordinates. After training of local DIF, all local regions have their codes $\\mathbf{z}_i$ , which serve as the local features of corresponding regions.", + "bbox": [ + 75, + 755, + 468, + 824 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Code constraint. For DIF methods, it is important to constrain the latent codes of all the regions during training. Traditional Local DIF methods [1, 28] use L2 norm loss on the", + "bbox": [ + 75, + 824, + 468, + 866 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "learned latent codes. However, in our method, we found that L2 norm loss could lead to latent codes being spread randomly in space, which is not good for subsequent clustering and latent code learning. Therefore, we constrain all local latent codes to be distributed within a hyper-sphere. The intuition is to process the latent codes in a way similar to normalizing them before entering the network. We update $\\mathbf{z}$ according to Eq. (3) after every step of learning of $\\mathbf{z}$ .", + "bbox": [ + 497, + 125, + 892, + 248 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {z} _ {i} = \\left\\{ \\begin{array}{c c} \\mathbf {z} _ {i} & i f \\quad | | \\mathbf {z} _ {i} | | \\leq 1 \\\\ \\frac {\\mathbf {z} _ {i}}{| | \\mathbf {z} _ {i} | |} & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 596, + 260, + 890, + 293 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Pattern Clustering", + "text_level": 1, + "bbox": [ + 499, + 299, + 680, + 314 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "After training of the local DIF, each region from the whole set of shapes will be encoded by the condition $\\mathbf{z}_{\\mathrm{ij}}$ for region $\\mathbf{B}_i$ and shape $S_{j}, j = 0\\dots M - 1$ . A shape normally consists of many empty or near-empty regions. To alleviate the influence of these regions, we first remove regions with SDF positive rate (the percentage of positive SDF samples within one local region) out of [0.01, 0.99]. The intuition is that if one region has almost all SDF samples to be positive or negative, this region will be far away from any shape surfaces and need no training. After learning of local DIF, there are regions $\\mathbf{B}_i$ that are learned well with low reconstruction errors, we remove these easy-to-learn regions with error threshold $\\epsilon$ . The remaining regions are aggregated into $P$ clusters by finding the cluster center $\\mathbf{c}_k$ of their condition codes with K-means by optimizing 4. We empirically select $P = 4$ to balance between training speed and accuracy. The clustered local regions are visualized in Figure 2 (d).", + "bbox": [ + 497, + 320, + 892, + 555 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\underset {c _ {k}} {\\operatorname {a r g m i n}} \\sum_ {k = 0} ^ {P} \\sum_ {i = 0} ^ {N} \\sum_ {j = 0} ^ {M} \\left| \\left| \\mathbf {z} _ {\\mathbf {i j}} - \\mathbf {c} _ {\\mathbf {k}} \\right| \\right| ^ {2}. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 584, + 565, + 890, + 605 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Region border consistency. We found that the division of shape and clustering lead to inconsistent surface estimates near the boundaries of local regions. To alleviate this problem, we utilize overlap between close local regions. The $f_{\\theta}(T(\\mathbf{x}, \\mathbf{z}_i))$ near the boundaries (distance less than 0.05) will be averaged by the nearby local regions. The region border consistency is a post-processing procedure. Local regions from all clusters are first processed together back to a whole shape according to their spatial locations.", + "bbox": [ + 497, + 614, + 892, + 739 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Pattern Decoder", + "text_level": 1, + "bbox": [ + 499, + 748, + 663, + 762 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We have multiple pattern decoders to cover each cluster. The structure of each pattern decoder consists of 9-layer MLP and a skip connection. Specifically, local code and query point coordinate are concatenated and fed into MLP, and point coordinate is concatenated again after 4 layers. The output of the network is signed distance to the nearest surface.", + "bbox": [ + 497, + 769, + 890, + 865 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "21859", + "bbox": [ + 463, + 885, + 505, + 897 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/1b87e56e070a0957217c86724bf7f0ff7638d4c5c89329c13395336fe3538719.jpg", + "image_caption": [ + "Figure 3. Pattern decoder with density-adaptive re-weighting. To further alleviate the region-imbalance problem, we introduce a region re-weighting module to each pattern-specific decoder by kernel density estimator, which dynamically re-weights the regions during learning." + ], + "image_footnote": [], + "bbox": [ + 132, + 127, + 410, + 187 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Density-adaptive re-weighting. Among the learned local codes, certain regions may have less appearances than others, and therefore they are usually neglected by the decoder. To recover more details, it is important to focus more on these regions. First we estimate the space density $D$ of local codes based on their density distributions using kernel density estimation. Gaussian kernel is selected with bandwidth $h = 0.35$ . Now we can re-weight region $\\mathbf{B}_i$ with weight $\\omega_i = \\frac{1}{D}$ during loss calculation. There are two ways of re-weighting the regions, fixed and dynamic. In fixed way, we only update the weight once with pre-extracted local codes. In the dynamic way, the re-weighting is applied every time after local codes being updated by the pattern decoder.", + "bbox": [ + 75, + 273, + 468, + 467 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Training", + "text_level": 1, + "bbox": [ + 75, + 473, + 181, + 488 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our LP-DIF is trained in three stages. In the first stage, we extract the features from local regions by learning a coarse local DIF. In the second stage, we cluster the local regions based on their local features. At last, we train multiple pattern decoders on clustered regions. Note that for each pattern decoder, we use simple decoders so we have similar total number of decoder parameters with local DIF. During training, we optimize decoders and latent codes, while during testing, like other auto-decoder methods, we fix all decoders and only optimize latent codes.", + "bbox": [ + 75, + 494, + 468, + 633 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Point sampling. We sample data pairs $(\\mathbf{x}_k, \\mathbf{s}_k)$ from $S_j$ as supervision. $S_j$ is a mesh or point cloud with normals $\\mathbf{n}_k$ . First we sample points along normal directions with normal distribution $N(0, \\theta)$ . Then we sample random points $\\{\\mathbf{x}_k\\}$ and calculate their signed distances $\\{\\mathbf{s}_k\\}$ based on the closest distances.", + "bbox": [ + 75, + 633, + 468, + 714 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Smooth L1 loss. To increase the weight in regions with larger errors, we introduce smooth L1 loss [26], defined by", + "bbox": [ + 75, + 716, + 467, + 744 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {k} ^ {\\text {s d f}} = \\left\\{ \\begin{array}{c c} \\frac {1}{2} \\left(f _ {\\theta} \\left(\\mathbf {x} _ {\\mathbf {k}}\\right) - \\mathbf {s} _ {\\mathbf {k}}\\right) ^ {2} & i f | \\left(f _ {\\theta} \\left(\\mathbf {x} _ {\\mathbf {k}}\\right) - \\mathbf {s} _ {\\mathbf {k}}\\right) | < 1 \\\\ \\left(\\left(f _ {\\theta} \\left(\\mathbf {x} _ {\\mathbf {k}}\\right) - \\mathbf {s} _ {\\mathbf {k}}\\right) - \\frac {1}{2}\\right) & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 82, + 749, + 468, + 792 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Gradient loss. It is important to train a DIF with gradient consistency. We apply constraint on the gradient of each sampled points, denoted as", + "bbox": [ + 75, + 792, + 468, + 833 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {k} ^ {\\operatorname {g r a d}} \\left(\\mathbf {x} _ {\\mathbf {k}}\\right) = e ^ {- \\left(1 0 0 \\mathbf {s} _ {\\mathbf {k}}\\right) ^ {2}} \\left(1 - \\frac {\\left\\langle \\nabla f \\left(\\mathbf {x} _ {\\mathbf {k}}\\right) , \\mathbf {n} _ {\\mathbf {k}} \\right\\rangle}{\\left\\| f \\left(\\mathbf {x} _ {\\mathbf {k}}\\right) \\right\\| \\left\\| \\mathbf {n} _ {\\mathbf {k}} \\right\\|}\\right), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 115, + 839, + 468, + 870 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We use cosine similarity of $\\mathbf{x_k}$ and the normal of its nearest sampled surface point, and make $\\mathbf{x_k}$ closer to the surface have larger influence.", + "bbox": [ + 497, + 125, + 890, + 167 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The total loss function could be formulated as", + "bbox": [ + 517, + 168, + 823, + 180 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL = L _ {s d f} + \\lambda L _ {g r a d}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 623, + 193, + 890, + 209 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\lambda = 1.0$ for all our experiments.", + "bbox": [ + 497, + 219, + 756, + 233 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 497, + 245, + 631, + 261 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We evaluate the effectiveness of our method compared with the state-of-the-art methods on several different aspects: (1) the representation performance on 3D objects dataset, (2) the performance on large-scale synthetic and real scenes data, and (3) reconstruction power on single complex object reconstruction.", + "bbox": [ + 497, + 268, + 890, + 352 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1.3D Objects Dataset Reconstruction", + "text_level": 1, + "bbox": [ + 497, + 361, + 805, + 376 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Dataset and metric. We run the experiments on the ShapeNet dataset [2] with the same settings with [5]. The dataset contains a subset of 13 categories in ShapeNet with train/test splits from [7]. We evaluate geometric reconstruction quality with L2 Chamfer Distance (CD) and F-Score. For L2 Chamfer Distance, we take exactly the same settings as [5]. We sampled 100K signed distances near the surface and 100K signed distances uniformly around the space. We estimate CD using 100,000 randomly sampled points on the ground truth and the reconstructed meshes. Additionally, in all experiments, we compute the F-Score at a threshold of $\\tau$ , as F-Score is a metric less sensitive to outliers. F-Score is the mean of recall (percentage of reconstruction to target distances under $\\tau$ ) and precision (vice versa). For object reconstruction we use $\\tau = 0.01$ . To be consistent with [5], we divide the whole space into $16 \\times 16 \\times 16$ regions. We also compare with NGLOD [36] in ShapeNet150 dataset following their evaluation protocol.", + "bbox": [ + 497, + 382, + 890, + 631 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Quantitative comparison. The comparison results between LP-DIF and other state-of-the-art methods are shown in Table 1. LP-DIF achieves the best performance across all categories in terms of average L2 Chamfer Distance and F-score. Compared with MDIF (auto-decoder branch) [5] and DDC-DIF [19], LP-DIF achieves the best performance in most categories, which shows the representational power of our method for representing multiple objects. As in Table 2, our method performs better than the deepest level of [36]. To test the generalization ability of our method, We train our model on one category (chair) and tested on another (unseen). A subset of the cross-category performance is shown in Table 3. Our method has more accuracy than MDIF [5] in unseen categories (bookshelf). In addition, as local regions share similar feature across categories, the accuracy for seen and unseen categories is almost the same for our method.", + "bbox": [ + 497, + 631, + 892, + 866 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "21860", + "bbox": [ + 463, + 885, + 505, + 897 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/32a35e23db4bb881ccb94bf372c47e99abe343e2ff227f625e6d94028ace12cd.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
CategoryCD Mean ↓F-score ↑
Occ. [29]IMNet [4]L.DIF [5]MDIF [5]DCC-DIF [19]OursOcc [29]IMNet [4]L.DIF [5]MDIF [5]DCC-DIF [19]Ours
airplane0.250.130.0440.0280.0110.011589.891.798.598.699.799.86
bench0.340.220.1210.0520.0170.021185.288.696.096.099.599.64
cabinet0.320.230.0630.0510.1310.040583.289.296.696.696.498.42
car0.580.260.090.0880.2180.033269.382.793.193.092.798.84
chair0.380.430.0420.0350.0370.029480.282.597.797.699.199.43
display0.350.200.0430.0190.0280.025682.389.498.698.799.499.64
lamp1.472.760.7950.7950.3270.018062.973.893.593.597.399.58
rifle0.390.550.0600.0570.0070.006286.181.196.996.999.999.97
sofa0.310.160.2080.0370.0360.026485.289.398.398.499.199.64
speaker0.380.170.0650.0440.1460.042478.189.497.397.396.197.86
table0.310.300.1070.0460.0290.028587.288.696.597.699.399.50
telephone0.190.110.0430.0270.0100.020288.996.599.699.399.699.58
watercraft0.350.390.0750.0670.0420.015680.384.797.497.298.399.70
mean0.430.460.1350.1020.0810.024581.486.796.997.098.299.36
", + "bbox": [ + 117, + 123, + 845, + 281 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/d19dfb05c0aa6f89e5b67305dd2acd00d01fc65a2479f437e3b65d0aac35bd54.jpg", + "table_caption": [ + "Table 1. Surface reconstruction comparison on test set of shapenet in terms of mean L2 chamfer distance (multiplied by 1e3) and F-score." + ], + "table_footnote": [], + "table_body": "
MethodsLOD3 [36]LOD4 [36]LOD5 [36]LP-DIF
CD Mean ↓0.1120.0690.0620.025
", + "bbox": [ + 109, + 317, + 431, + 349 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/1017e647380e0044b953e9eec6573cf6d9038c92f13b6efb32be4805f7a16d7e.jpg", + "table_caption": [ + "Table 2. Comparison in ShapeNet150 with NGLOD [36]." + ], + "table_footnote": [], + "table_body": "
MethodsSofaLampBookshelf
MDIF [5] (seen/unseen) (CD↓)0.0370/-0.7950/-- / 0.0910
LP-DIF (seen/unseen) (CD↓)0.0264/0.02650.0180/0.0185- / 0.0490
", + "bbox": [ + 110, + 377, + 431, + 412 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 3. Cross-category performance in ShapeNet.", + "bbox": [ + 122, + 412, + 423, + 425 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/1ac795f8aa2df2044fb9d9c4d15e9f599740861da61e2f2a0eba107bea23a3de.jpg", + "image_caption": [ + "Figure 4. Visual comparison with OccNet [25], ConvOccNet [29], IFNet [6], and LIG [17], our method could reconstruct more geometry detail on ShapeNet." + ], + "image_footnote": [], + "bbox": [ + 110, + 441, + 431, + 739 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Qualitative comparison. In Figure 4, we visually compared 3D surface reconstruction on Shapenet with other DIF methods [6, 17, 25, 29], from which we find that LP-DIF reconstructs more geometry details while other method tends", + "bbox": [ + 75, + 809, + 470, + 866 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "to lose details on thin structures.", + "bbox": [ + 499, + 321, + 714, + 333 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/e9a1afa6ce592949f5c4c7669eb1664699377f320294735e6c27ebc0a7cb4aaf.jpg", + "image_caption": [ + "Figure 5. Comparison for surface reconstruction on SceneNet with sparse sampling." + ], + "image_footnote": [], + "bbox": [ + 534, + 343, + 855, + 432 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/ef143b81b98a003e766972c0f17faf211d6beda937435ac50c23240464fb1a3d.jpg", + "image_caption": [ + "Figure 6. Comparison for surface reconstruction on 3D Scene dataset with dense sampling." + ], + "image_footnote": [], + "bbox": [ + 514, + 483, + 875, + 654 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2.3D Scene Reconstruction", + "text_level": 1, + "bbox": [ + 499, + 706, + 726, + 720 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Dataset and metric. We conduct our experiments on a synthetic dataset: SceneNet [14], and a real scanned dataset: 3D Scene dataset [42]. As scenes in SceneNet dataset are not watertight, and have many double-sided faces creating conflicting normals, we pre-process SceneNet to watertight using methods from [16]. We drop scenes with empty inner spaces after the watertighting process. We sample a constant density of points according to the area of faces (1000 points per $m^2$ for SceneNet and 10000 points per $m^2$ for 3D Scene dataset). For all the scene-level experiments, we ran", + "bbox": [ + 497, + 726, + 890, + 866 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "21861", + "bbox": [ + 463, + 887, + 502, + 897 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "domly sample 2 million points on the generated mesh and the ground truth mesh when estimating L1 CD, and we use $\\tau = 0.025$ (2.5cm) for F-score. Since data is provided in a physically-meaningful scale, we use world coordinate (meters) for computing CD. Note that these two metrics are not always consistent as CD is more sensitive to outliers. For scene-level experiments, we directly optimize latent codes and decoders on the scenes, and we divide the whole space into $32 \\times 32 \\times 32$ regions.", + "bbox": [ + 75, + 125, + 472, + 249 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Quantitative comparison. The comparison results between LP-DIF and other state-of-the-art methods are shown in Table 4. LP-DIF achieves the best performance across all categories in terms of average L1 Chamfer Distance and F-score both in sparse (Scenenet) and dense (3D SceneNet dataset) sampling settings, which proves better representational power of our method. Compared with scenenet with sparse sampling setting, our method improves more on 3D scenenet dataset with dense sampling settings.", + "bbox": [ + 75, + 250, + 472, + 375 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Qualitative comparison. In Figure 5 and 6, we visually compared 3D surface reconstruction of scene dataset with other DIF methods, from which we find that LP-DIF reconstructs more geometry details and less missing parts than other method.", + "bbox": [ + 75, + 375, + 470, + 444 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Complex 3D Object Reconstruction", + "text_level": 1, + "bbox": [ + 75, + 453, + 386, + 467 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Dataset and metric. For complex 3D object reconstruction, we use Thai Statue, obtained from the Stanford 3D Scanning Repository [18]. It is an intricate statue, which consists of 10 million polygons. Fine details of the statue are challenging to be captured with existing methods. We randomly sample 2 million points on the generated and the ground truth meshes when estimating L1 CD, and we use $\\tau = 0.025$ for F-score. For complex 3D object, we directly optimize latent codes and decoders to fit the shape. For ACORN [24], we train using their official code and extract the reconstructed mesh. [24] is trained for several hours until max octants are reached.", + "bbox": [ + 75, + 475, + 472, + 640 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4078d4d3412b96f7d22e63117b357c42187b42b8375da44352c1e1623a59aa25.jpg", + "image_caption": [ + "Figure 7. Comparison for surface reconstruction on Thai statue. Our result is comparable with ACORN [24] with slightly better details." + ], + "image_footnote": [], + "bbox": [ + 169, + 650, + 374, + 769 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Quantitative comparison. The comparison results between LP-DIF and other state-of-the-art methods are shown in Table 5. LP-DIF achieves the best performance in terms", + "bbox": [ + 75, + 824, + 470, + 866 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "of average L1 Chamfer Distance and F-score for complex 3D object reconstruction.", + "bbox": [ + 497, + 125, + 890, + 153 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Qualitative comparison. In Figure 1, we visually compare 3D surface reconstruction of Thai statue with other DIF methods, where we find that LP-DIF reconstructs much more fine geometry details than other methods. In Figure 7, we compare with ACORN [24]. Our result is comparable with ACORN with slightly better details.", + "bbox": [ + 497, + 154, + 892, + 237 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Ablation Study", + "text_level": 1, + "bbox": [ + 497, + 247, + 653, + 262 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Network capacity and efficiency comparison. We have summarized the number of parameters used in NGLOD (LOD5) [36], LDIF [1], MDIF [5], LIG [17], and our method in Table 6. As in the table, different number of parameters are used and our method utilized the second least total number of parameters. We also tested the performance under the same total number of parameters in Table 7. As in the first two rows of the table, LDIF [1] and our method have the similar total number of parameters, where our method outperforms LDIF [1]. After that, we increase our MLP to 800-dimensional hidden layers to have the similar total number parameters with MDIF [5]. As in the 3-4 rows of the table, the performance of our ablation method is still better than MDIF [5], but is worse than our original decoders. The reason could be that the increased parameters of network makes the optimization of local latent code unstable. The performance of our coarse decoder is also shown in the last row for comparison. We have also compared the computation time on 8 shapes of ShapeNet in Table 8. It takes much more time for NGLOD [36] to train. For L-DIF and LP-DIF, we reported the time needed to reach the same accuracy level. It takes less time for LP-DIF than L-DIF.", + "bbox": [ + 497, + 269, + 892, + 586 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e5d5d84476b626846332cc7324cc1b553b59e8494581b437ba95eab2342942ad.jpg", + "image_caption": [ + "Figure 8. Comparison with random clustering. (a) Replacing the clustering process with random assigning each local region into clusters. (b) Clustering with regards to similarity leads to better performance." + ], + "image_footnote": [], + "bbox": [ + 531, + 598, + 858, + 652 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Ablation on modules. We also conduct a series of experiments on the effectiveness of our modules on Burghers of 3D scenenet dataset. Our baseline is implemented by removing pattern clustering and region re-weighting. First, we separate the whole space into different number of regions (each region has one code), and test the effect of our module under different settings. The results are shown in Table 9, where the baseline model performs better with more local regions and codes, however, more local codes occupy much more space. Our model with $7.63\\mathrm{MB}$ local codes could have similar performance with the baseline", + "bbox": [ + 497, + 714, + 894, + 866 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "21862", + "bbox": [ + 463, + 885, + 505, + 897 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/9ba2d9fb36c088a8be0619bd32e51e834cc8edab8b6fe5e36b9cd37bf0e76c0c.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
CategoryCD Mean ↓F-score ↑SceneCD Mean ↓F-score ↑
LIG [17]OursLIG [17]OursLIG [17]OursLIG [17]Ours
Bathroom0.008250.0063398.5699.66Burghers0.01220.003990.2599.67
Bedroom0.009780.0073096.4199.24Lounge0.01310.003185.4999.72
Office0.014520.0092993.9296.97CopyRoom0.01300.003484.6899.97
Livingroom0.011910.0098796.3998.65StoneWall0.01100.003189.1499.90
Kitchen0.009880.0082596.3698.55TotemPole0.01200.004189.3999.23
Mean0.010650.0081696.4098.67Mean0.01220.003587.7999.70
", + "bbox": [ + 200, + 123, + 766, + 220 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/504d6edcef015e1fd1ae0e20d2b1265204bff857185a0821a4d88cd2fa7211c9.jpg", + "table_caption": [ + "Table 4. Surface reconstruction from sparse point cloud on SceneNet and dense point cloud on 3D SceneNet dataset in terms of mean L1 chamfer distance and F-score." + ], + "table_footnote": [], + "table_body": "
MethodsDeepSDF [28]LIG [17]LDIF baselineOurs
CD Mean ↓0.7400.6030.2110.176
F-score ↑1.313.621.863.6
", + "bbox": [ + 129, + 268, + 413, + 305 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/fe3176ddab5004315cd1b6f18670941cab9971daebc74358f2d390475caea3a4.jpg", + "table_caption": [ + "Table 5. Surface reconstruction comparison on Thai statue in terms of mean L1 chamfer distance and F-score." + ], + "table_footnote": [], + "table_body": "
Methods# Feature Param# Network ParamTotal # Param
LOD5 [36]101225282368510146213
L.DIF [5]524288460993985281
MDIF [5]440321835930118403333
LIG [17]131072227745358817
Ours53248 (coarse) + 2498563745 (coarse) + 463108769957
", + "bbox": [ + 80, + 343, + 484, + 414 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/93a0264de400cbf94e80ae0a664f9aea903808c526bfd55e388c0969592d59a7.jpg", + "table_caption": [ + "Table 6. Network capacity comparison." + ], + "table_footnote": [], + "table_body": "
Methods#Feature Param#Inference ParamTotal # ParamCD (Airplane)↓CD (Bench)↓
L.DIF [5]5242884609939852810.0440.121
Ours303104 (53248 + 249856)466853 (3745 + 463108)7699570.0120.021
MDIF [5]4403218359301184033330.0280.052
Ours-abl-mdif303104 (53248 + 249856)17952293 (3745 + 17948548)182553970.01450.031
Ours-coarse532482689559370.0620.167
", + "bbox": [ + 80, + 441, + 485, + 494 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/327f213f3fdfa08e08d6d7edc549a5f2e59c87b354aa723fabc47f4458df509e.jpg", + "table_caption": [ + "Table 7. Ablation with similar total number of parameters." + ], + "table_footnote": [], + "table_body": "
MethodsStage1Stage 2Stage 3Total
NGLOD [36]---~4000s
LDIF baseline---165s (1.33s ×124epochs)
LP-DIF20s1s141s (2.43s ×58epochs)162s
", + "bbox": [ + 80, + 519, + 484, + 566 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/d1a7dc23eb50f132b179d4773ee91971c01941591add831df4bc3cef2cb6393b.jpg", + "table_caption": [ + "Table 8. Computation efficiency comparison." + ], + "table_footnote": [], + "table_body": "
Methods# of codescode sizeCD Mean ↓F-score ↑
Baseline-3232K7.63 MB0.0055796.78
Baseline-1282097K488 MB0.0038999.65
LP-DIF-3232K7.63 MB0.0039499.67
LP-DIF-1282097K488 MB0.0038799.64
", + "bbox": [ + 149, + 593, + 391, + 638 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/6e7f15c1a117c43bec2d86cd4923c70209d1e153cbeabd3def73f0f1f915164d.jpg", + "table_caption": [ + "Table 9. Ablation study with different number of local codes. Result of the baseline method with different number of local codes are shown in the first two rows. Result of LP-DIF with different number of local codes are shown in the last two rows. Our method can achieve same level of accuracy with much less local codes." + ], + "table_footnote": [], + "table_body": "
MethodsCD Mean↓F-score ↑
Baseline0.0055796.78
LP-DIF w/o clustering0.0044699.52
LP-DIF w/o re-weighting0.0041999.16
LP-DIF0.0039499.67
", + "bbox": [ + 151, + 716, + 391, + 771 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 10. Ablation study on components of our model in terms of mean L1 chamfer distance and F-score.", + "bbox": [ + 75, + 774, + 468, + 799 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "method with 488 MB local codes. After that, we evaluate the effectiveness of our clustering module by replacing it with random assigning cluster indices. As in Figure 8 and", + "bbox": [ + 75, + 824, + 468, + 866 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 6, the performance is deteriorated with random clustering. The possible reason is that randomly separating local regions increases the deviation of some local regions from the cluster centers, causing them to fail in training. Next we evaluate the components of our model by removing them separately. We test two variations: (1) removing the clustering module and re-weight on the whole set of regions, and (2) removing the re-weighting module. The result is shown in Table 10 and Figure 9 (a) - (c), and we find that both modules are helpful for achieving good performance. At last, we test the difference between fixed density estimator and dynamic density estimator. As shown in Figure 9 (d) - (f), dynamic density estimator could reconstruct better geometry details than fixed one.", + "bbox": [ + 497, + 271, + 890, + 465 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/15908933bc6671f5cbd63c4101fb11cf392e1f79d0f157fa5f7d625f635763de.jpg", + "image_caption": [ + "Figure 9. Ablation study on density-adaptive re-weighting. (a) Ours w/o density re-weighting. (b) Ours w/ density re-weighting. (c) Ground truth. (d) Ours w/o density estimator. (e) Ours w/ fixed density estimator. (f) Ours w/ dynamic density estimator." + ], + "image_footnote": [], + "bbox": [ + 591, + 477, + 791, + 605 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 499, + 663, + 618, + 676 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we present LP-DIF, a local pattern-specific deep implicit function for reconstructing highly detailed geometry. Compared with previous methods that treat all local regions equally using a single decoder, we regard a shape as clusters of local regions and mine local patterns with different decoders. This alleviates the difficulty of learning caused by diverse local regions. In addition, we introduce a dynamic region re-weighting module, which could provide more focus on less common regions to tackle the data-imbalance problem in each pattern decoder. As a result, finer details of the local regions are learned more accurately. We demonstrate that our method outperforms the latest methods under various benchmarks.", + "bbox": [ + 497, + 686, + 890, + 865 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "21863", + "bbox": [ + 463, + 885, + 504, + 897 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 124, + 171, + 138 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Rohan Chabra, Jan E Lenssen, Eddy Ilg, Tanner Schmidt, Julian Straub, Steven Lovegrove, and Richard Newcombe. Deep local shapes: Learning local SDF priors for detailed 3d reconstruction. In European Conference on Computer Vision, pages 608-625. Springer, 2020. 1, 2, 3, 4, 7", + "[2] Angel X. Chang, Thomas Funkhouser, Leonidas Guibas, Pat Hanrahan, Qixing Huang, Zimo Li, Silvio Savarese, Manolis Savva, Shuran Song, Hao Su, Jianxiong Xiao, Li Yi, and Fisher Yu. ShapeNet: An Information-Rich 3D Model Repository. 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ACM Transactions on Graphics (ToG), 32(4):1-8, 2013. 6" + ], + "bbox": [ + 502, + 127, + 890, + 448 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "21865", + "bbox": [ + 463, + 885, + 504, + 897 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/LP-DIF_ Learning Local Pattern-Specific Deep Implicit Function for 3D Objects and Scenes/e23a5c43-ebb5-406b-9d78-64277af6a197_model.json b/2023/LP-DIF_ Learning Local Pattern-Specific Deep Implicit Function for 3D Objects and Scenes/e23a5c43-ebb5-406b-9d78-64277af6a197_model.json new file mode 100644 index 0000000000000000000000000000000000000000..6244abbd2ac5ba3b11e16b976bb56542b74ba189 --- /dev/null +++ b/2023/LP-DIF_ Learning Local Pattern-Specific Deep Implicit Function for 3D Objects and Scenes/e23a5c43-ebb5-406b-9d78-64277af6a197_model.json @@ -0,0 +1,2057 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.13, + 0.051, + 0.201, + 0.086 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.253, + 0.049, + 0.793, + 0.088 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.085, + 0.161, + 0.886, + 0.202 + ], + "angle": 0, + "content": "LP-DIF: Learning Local Pattern-specific Deep Implicit Function for 3D Objects and Scenes" + }, + { + "type": "text", + "bbox": [ + 0.132, + 0.228, + 0.834, + 0.246 + ], + "angle": 0, + "content": "Meng Wang1 Yu-Shen Liu1* * Yue Gao1 Kanle Shi2 Yi Fang3 Zhizhong Han4" + }, + { + "type": "text", + "bbox": [ + 0.245, + 0.246, + 0.726, + 0.262 + ], + "angle": 0, + "content": "\\(^{1}\\)School of Software, BNRist, Tsinghua University, Beijing, China" + }, + { + "type": "text", + "bbox": [ + 0.344, + 0.262, + 0.627, + 0.278 + ], + "angle": 0, + "content": "\\(^{2}\\)Kuaishou Technology, Beijing, China" + }, + { + "type": "text", + "bbox": [ + 0.125, + 0.278, + 0.844, + 0.293 + ], + "angle": 0, + "content": "3Center for Artificial Intelligence and Robotics, New York University Abu Dhabi, Abu Dhabi, UAE" + }, + { + "type": "text", + "bbox": [ + 0.218, + 0.293, + 0.752, + 0.31 + ], + "angle": 0, + "content": "\\(^{4}\\)Department of Computer Science, Wayne State University, Detroit, USA" + }, + { + "type": "text", + "bbox": [ + 0.282, + 0.313, + 0.684, + 0.327 + ], + "angle": 0, + "content": "{meng_wang, gaoyue, liuyushen}@tsinghua.edu.cn" + }, + { + "type": "text", + "bbox": [ + 0.241, + 0.329, + 0.725, + 0.342 + ], + "angle": 0, + "content": "shikanle@kuaishou.com yfang@nyu.edu h312h@wayne.edu" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.374, + 0.314, + 0.388 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.405, + 0.473, + 0.807 + ], + "angle": 0, + "content": "Deep Implicit Function (DIF) has gained much popularity as an efficient 3D shape representation. To capture geometry details, current mainstream methods divide 3D shapes into local regions and then learn each one with a local latent code via a decoder. Such local methods can capture more local details due to less diversity among local regions than global shapes. Although the diversity of local regions has been decreased compared to global approaches, the diversity in different local regions still poses a challenge in learning an implicit function when treating all regions equally using only a single decoder. What is worse, these local regions often exhibit imbalanced distributions, where certain regions have significantly fewer observations. This leads that fine geometry details could not be preserved well. To solve this problem, we propose a novel Local Pattern-specific Implicit Function, named LP-DIF, to represent a shape with clusters of local regions and multiple decoders, where each decoder only focuses on one cluster of local regions which share a certain pattern. Specifically, we first extract local codes for all regions, and then cluster them into multiple groups in the latent space, where similar regions sharing a common pattern fall into one group. After that, we train multiple decoders for mining local patterns of different groups, which simplifies the learning of fine geometric details by reducing the diversity of local regions seen by each decoder. To further alleviate the data-imbalance problem, we introduce a region re-weighting module to each pattern-specific decoder using a kernel density estimator, which dynamically re-weights the regions during learn" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.375, + 0.893, + 0.445 + ], + "angle": 0, + "content": "ing. Our LP-DIF can restore more geometry details, and thus improve the quality of 3D reconstruction. Experiments demonstrate that our method can achieve the state-of-the-art performance over previous methods. Code is available at https://github.com/gtyxyz/lpdfif." + }, + { + "type": "title", + "bbox": [ + 0.502, + 0.47, + 0.631, + 0.485 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.494, + 0.893, + 0.659 + ], + "angle": 0, + "content": "Representing 3D shapes is a fundamental problem for many applications in 3D computer vision. Recently, Deep Implicit Function (DIF) [4,22,23,25,28,41] has gained popularity for efficiently learning the representation of 3D objects and scenes. In contrast to directly learning explicit 3D representations [15,30,31] (voxels, point clouds or meshes), DIF aims to train a neural network to learn the binary occupancy function [25] or signed distance function (SDF) [28], as given a query location and an input latent code. Such kind of representation is continuous with arbitrary precision and can handle various topology, which has achieved the state-of-the-art results in several shape reconstruction tasks." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.66, + 0.895, + 0.868 + ], + "angle": 0, + "content": "Existing DIF methods can be roughly classified into two categories: global and local approaches. Most of the early methods [4, 9, 20, 21, 25, 27-29, 35, 37, 40] fall into global approaches. These methods take advantage of one latent code and a single decoder to represent the whole shape. Global approaches often suffer from long training time and low reconstruction accuracy due to the limited capacity of capturing local geometry details. More recently, local approaches [1, 3, 5, 6, 10-12, 17, 19, 34, 36, 38] divide 3D shapes (often divide by 3D grids) into local regions and then learn each one with a local latent code via a decoder, where the decoder shares the geometric similarities among different local regions. Although such local approaches can capture some local details, a large diversity of different local regions still increase the difficulty of learning an implicit function" + }, + { + "type": "page_footnote", + "bbox": [ + 0.076, + 0.821, + 0.471, + 0.867 + ], + "angle": 0, + "content": "*The corresponding author is Yu-Shen Liu. This work was supported by National Key R&D Program of China (2022YFC3800600), the National Natural Science Foundation of China (62272263, 62072268), and in part by Tsinghua-Kuaishou Institute of Future Media Data." + }, + { + "type": "page_number", + "bbox": [ + 0.465, + 0.887, + 0.506, + 0.898 + ], + "angle": 0, + "content": "21856" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.162, + 0.127, + 0.805, + 0.33 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.199, + 0.331, + 0.272, + 0.34 + ], + "angle": 0, + "content": "(a) Global DIF" + }, + { + "type": "image_caption", + "bbox": [ + 0.359, + 0.331, + 0.428, + 0.34 + ], + "angle": 0, + "content": "(b) Local DIF" + }, + { + "type": "image_caption", + "bbox": [ + 0.522, + 0.331, + 0.563, + 0.34 + ], + "angle": 0, + "content": "(c) Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.658, + 0.331, + 0.726, + 0.34 + ], + "angle": 0, + "content": "(d) Reference" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.343, + 0.894, + 0.395 + ], + "angle": 0, + "content": "Figure 1. Visual comparison of 3D shape surface reconstruction. Compared with global DIF (e.g. [28]) and local DIF (e.g. [1]), our method can reconstruct the shape with fine-grained geometric details. Compared with previous methods that treat all local regions equally using a single decoder, we regard a shape as clusters of local regions and mine local patterns with different decoders. This alleviates the difficulty of learning caused by diverse local regions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.418, + 0.469, + 0.487 + ], + "angle": 0, + "content": "when treating all regions equally using only a single decoder. In addition, these local regions often exhibit imbalanced distributions, where certain regions have significantly fewer observations, especially in scenes. As a result, fine geometry details of shapes could not be captured well." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.487, + 0.47, + 0.776 + ], + "angle": 0, + "content": "To address the above-mentioned problems, we propose a novel Local Pattern-specific Implicit Function, named LP-DIF, for learning 3D shape representation using clusters of local regions with multiple decoders, where each decoder only represents one cluster of local regions which share a certain pattern (geometric features such as facing direction, number of faces, relative positions to the region center). Specifically, we first extract the local latent codes for all local regions divided by 3D grids, and then cluster them into multiple groups in the latent space, where similar regions sharing a common pattern fall into one group. After that, we train a separate pattern-specific decoder for each group of regions, which reduces data-imbalance among different patterns of regions and simplifies the learning of fine geometric details of 3D structures by limiting the diversity of regions seen to each decoder. To further alleviate the region-imbalance problem, we introduce a region reweighting module to each pattern-specific decoder by kernel density estimator, which dynamically re-weights the regions during learning. Our main contributions can be summarized as follows." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.784, + 0.47, + 0.867 + ], + "angle": 0, + "content": "- We propose a novel LP-DIF to learn local pattern-specific deep implicit function of 3D shapes for reconstructing highly detailed geometry. Compared with previous methods that treat all local regions equally using a single decoder, we regard a shape as clusters of local regions and mine local patterns with different de" + }, + { + "type": "text", + "bbox": [ + 0.531, + 0.418, + 0.892, + 0.446 + ], + "angle": 0, + "content": "coders. This alleviates the difficulty of learning caused by diverse local regions." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.454, + 0.892, + 0.524 + ], + "angle": 0, + "content": "- We introduce a dynamic region re-weighting module, which could provide more focus on less common regions to tackle the data-imbalance problem in each pattern decoder. As a result, the regions with less appearances can be captured more accurately." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.531, + 0.892, + 0.587 + ], + "angle": 0, + "content": "- Our method could be applied in multiple objects, single complex objects and large scale of scenes. We improve the state-of-the-art accuracy in surface reconstruction under various benchmarks." + }, + { + "type": "list", + "bbox": [ + 0.519, + 0.454, + 0.892, + 0.587 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.597, + 0.892, + 0.679 + ], + "angle": 0, + "content": "Figure 2 illustrates the main differences between DIF, local DIF and our method. For DIF approaches, one global code and a decoder are used for the whole shape. For Local DIF methods, multiple local codes and a shared decoder are used. For our method, multiple clusters of regions are learned with different decoders." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.691, + 0.641, + 0.706 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.715, + 0.892, + 0.867 + ], + "angle": 0, + "content": "In computer vision and graphics, there are two categories of shape representations: explicit representation and implicit representation. Explicit geometric representations [15, 30, 31] such as point clouds, voxels and triangular meshes have been widely used for representing geometries for their simplicity and flexibility. More recently, deep implicit representations [4, 25, 28, 39] have been proposed in the context of shape representation, where the implicit surfaces of geometries are represented as the zero-set of spatial functions with fully connected neural networks. Such kind of representation is continuous with arbitrary precision and" + }, + { + "type": "page_number", + "bbox": [ + 0.465, + 0.887, + 0.505, + 0.898 + ], + "angle": 0, + "content": "21857" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.162, + 0.123, + 0.812, + 0.335 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.342, + 0.896, + 0.419 + ], + "angle": 0, + "content": "Figure 2. Comparison between DIF, local DIF and our method. (a) DIF methods leverage one global code and one decoder, often suffer from long training speed and low reconstruction quality due to the limited capacity of capturing local geometry details. (b) Local DIF methods use multiple local codes and one shared decoder, a large diversity of different local regions still increase the difficulty of learning an implicit function when treating all regions equally using only a single decoder. (c) Our method, LP-DIF, for representing a shape with some clusters of local regions and multiple decoders, where each decoder only represents one cluster of local regions which share a certain pattern. (d) Visualization of the clustered local regions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.443, + 0.47, + 0.498 + ], + "angle": 0, + "content": "can handle different topology structure, which has achieved the state-of-the-art results in several shape reconstruction task. Implicit representations can be categorized into global and local approaches." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.503, + 0.473, + 0.793 + ], + "angle": 0, + "content": "Global Deep Implicit Shape Representation. In recent years, implicit functions have been introduced into neural networks [25, 28] and show promising results. Early approaches learn one latent code and one single global implicit network to represent the whole shape. For example, DeepSDF [28] learned an implicit function where the network output represents the signed distance of the input point to its nearest surface, where zero-set of the learned function implicitly represents the surface of the shape. Other approaches [25, 29] defined the implicit functions as 3D occupancy probability functions and turned shape representation into a point classification problem. Following these methods, [35, 37] improved the expressiveness of the implicit functions by introducing high frequency signals with periodic activation. [39] proposed to represent the volume density as an implicit function of the signed distance in neural volume rendering for high-quality novel view generation. However, these methods suffer from long training time and low reconstruction accuracy for high resolution data due to the limited capacity of decoder to capture local geometry details." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.798, + 0.471, + 0.868 + ], + "angle": 0, + "content": "Local Deep Implicit Shape Representation. To capture more geometry details, current mainstream methods divide 3D shapes into many local regions and then learn each one with a local latent code via a decoder. Some recent works [1, 29] proposed to divide the whole 3D shape" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.443, + 0.896, + 0.86 + ], + "angle": 0, + "content": "uniformly into 3D grids, where they either assign each local grid with a latent code or trilinearly interpolate local latent codes based on querying location. In LIG [17], this idea was applied to 3D scenes. NGLOD [36] leveraged sparse octree instead of uniform grids to increase efficiency. ACORN [24] proposed to adaptively optimize the coordinate decomposition to achieve higher accuracy in large-scale scenes. DCC-DIF [19] optimized the local latent code learning by introducing dynamic grid positions. IFNet [6] utilized multiple level of latent codes in a hierarchical way. LPI [3] divided the global shape into multiple local parts in latent space to allow easier shape parts learning and blending. PatchNet [38] was proposed to divide a shape into local patches with no fixed structure. Points2surf [10] incorporated local information surrounding each point, but it typically takes a lot of time for point-wise distance calculation. Although such local methods can capture some local details, a large diversity of different local regions still poses an challenge for learning an implicit function when treating all regions equally using only a single decoder. In addition, these local regions often exhibit imbalanced distributions, where certain regions have significantly fewer observations. As a result, fine geometry details could not be captured well. Several methods [8, 13] have been proposed to learn multiple decoders for point deformations, however, their methods cannot be applied in learning implicit representations for shapes. MDIF [5, 33] used multiple levels of decoders in a hierarchical way, however, it did not consider the relationship between local regions. In novel view synthesizing, KiloNeRF [32] utilized thousands of tiny MLPs to represent" + }, + { + "type": "page_number", + "bbox": [ + 0.465, + 0.887, + 0.506, + 0.898 + ], + "angle": 0, + "content": "21858" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.126, + 0.473, + 0.224 + ], + "angle": 0, + "content": "different parts of the scenes. The simple and effective way to introduce multiple decoders is to assign each local region with a decoder, however, it is normally not feasible due to time and space constraint and the prior information of the local regions could not be preserved. In contrast, we introduce clustering for the local regions as a trade-off between reconstruction accuracy and efficiency." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.235, + 0.17, + 0.249 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.257, + 0.473, + 0.436 + ], + "angle": 0, + "content": "Given \\(K\\) discrete points \\(\\mathbf{X} = \\{\\mathbf{x}_k\\}\\) and their signed distances \\(\\mathbf{S} = \\{\\mathbf{s}_k\\}\\) from a 3D surface, our goal is to regress a continuous function that outputs the closest signed distance to the 3D surface given a spatial point \\(\\mathbf{x}\\). To achieve this goal, we propose to learn a local pattern-specific DIF. The architecture of LP-DIF and differences between our LP-DIF and other methods are illustrated in Figure 2. In this section, we first introduce latent embedding learning and local region feature extraction in Sec. 3.1. Then we describe our pattern clustering module in Sec. 3.2. After that we present our pattern decoder with density adaptive re-weighting in Sec. 3.3. At last, we illustrate our training process in Sec. 3.4." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.445, + 0.47, + 0.46 + ], + "angle": 0, + "content": "3.1. Learning Latent Embedding for Local Regions" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.467, + 0.47, + 0.578 + ], + "angle": 0, + "content": "At the beginning, we choose to train a local DIF network [1, 17] to learn latent embedding for local regions to extract coarse local features for clustering. Local DIF [1, 17] is a special category of DIF, which is defined as a signed distance function \\( f(\\mathbf{x}, \\mathbf{z}) \\) modeled with Multilayer Perceptrons (MLP), mapping each query point \\( \\mathbf{x} \\) near a surface to the signed distance domain continuously with condition code \\( \\mathbf{z} \\). A shape \\( S \\) is defined as the zero level set of \\( f(\\mathbf{x}, \\mathbf{z}) \\):" + }, + { + "type": "equation", + "bbox": [ + 0.174, + 0.589, + 0.469, + 0.606 + ], + "angle": 0, + "content": "\\[\n\\mathcal {S} = \\left\\{\\mathbf {x} \\in \\mathbb {R} ^ {3} \\mid f _ {\\theta} (\\mathbf {x}, \\mathbf {z}) = 0 \\right\\}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.61, + 0.47, + 0.721 + ], + "angle": 0, + "content": "where \\(\\theta\\) is the parameter of the MLP. To be able to represent multiple shapes in the same time, the condition \\(\\mathbf{z}\\) is optimized for each shape, and the parameter \\(\\theta\\) is shared for all the shapes. Local DIF is defined on partitioned space of shape \\(S\\). A normalized 3D space is usually partitioned into \\(d\\times d\\times d\\) regions \\(\\{\\mathbf{B}_i\\} \\subseteq \\mathbb{R}^3\\), \\(i = 0\\dots N - 1\\). All the regions have their separate codes \\(\\mathbf{z}_i\\), sharing the same parameter \\(\\theta\\). The entire surface is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.145, + 0.728, + 0.469, + 0.748 + ], + "angle": 0, + "content": "\\[\n\\mathcal {S} = \\left\\{\\mathbf {x} \\in \\mathbb {R} ^ {3} \\mid \\sum f _ {\\theta} (T (\\mathbf {x}), \\mathbf {z} _ {i}) = 0 \\right\\}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.756, + 0.469, + 0.825 + ], + "angle": 0, + "content": "where \\( T(\\mathbf{x}) \\) is the re-centering function of \\( \\mathbf{x} \\), which transforms the points in each region to their local coordinates. After training of local DIF, all local regions have their codes \\( \\mathbf{z}_i \\), which serve as the local features of corresponding regions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.469, + 0.867 + ], + "angle": 0, + "content": "Code constraint. For DIF methods, it is important to constrain the latent codes of all the regions during training. Traditional Local DIF methods [1, 28] use L2 norm loss on the" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.126, + 0.894, + 0.249 + ], + "angle": 0, + "content": "learned latent codes. However, in our method, we found that L2 norm loss could lead to latent codes being spread randomly in space, which is not good for subsequent clustering and latent code learning. Therefore, we constrain all local latent codes to be distributed within a hyper-sphere. The intuition is to process the latent codes in a way similar to normalizing them before entering the network. We update \\(\\mathbf{z}\\) according to Eq. (3) after every step of learning of \\(\\mathbf{z}\\)." + }, + { + "type": "equation", + "bbox": [ + 0.597, + 0.261, + 0.892, + 0.294 + ], + "angle": 0, + "content": "\\[\n\\mathbf {z} _ {i} = \\left\\{ \\begin{array}{c c} \\mathbf {z} _ {i} & i f \\quad | | \\mathbf {z} _ {i} | | \\leq 1 \\\\ \\frac {\\mathbf {z} _ {i}}{| | \\mathbf {z} _ {i} | |} & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {3}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.3, + 0.681, + 0.315 + ], + "angle": 0, + "content": "3.2. Pattern Clustering" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.321, + 0.893, + 0.557 + ], + "angle": 0, + "content": "After training of the local DIF, each region from the whole set of shapes will be encoded by the condition \\(\\mathbf{z}_{\\mathrm{ij}}\\) for region \\(\\mathbf{B}_i\\) and shape \\(S_{j}, j = 0\\dots M - 1\\). A shape normally consists of many empty or near-empty regions. To alleviate the influence of these regions, we first remove regions with SDF positive rate (the percentage of positive SDF samples within one local region) out of [0.01, 0.99]. The intuition is that if one region has almost all SDF samples to be positive or negative, this region will be far away from any shape surfaces and need no training. After learning of local DIF, there are regions \\(\\mathbf{B}_i\\) that are learned well with low reconstruction errors, we remove these easy-to-learn regions with error threshold \\(\\epsilon\\). The remaining regions are aggregated into \\(P\\) clusters by finding the cluster center \\(\\mathbf{c}_k\\) of their condition codes with K-means by optimizing 4. We empirically select \\(P = 4\\) to balance between training speed and accuracy. The clustered local regions are visualized in Figure 2 (d)." + }, + { + "type": "equation", + "bbox": [ + 0.585, + 0.566, + 0.892, + 0.606 + ], + "angle": 0, + "content": "\\[\n\\underset {c _ {k}} {\\operatorname {a r g m i n}} \\sum_ {k = 0} ^ {P} \\sum_ {i = 0} ^ {N} \\sum_ {j = 0} ^ {M} \\left| \\left| \\mathbf {z} _ {\\mathbf {i j}} - \\mathbf {c} _ {\\mathbf {k}} \\right| \\right| ^ {2}. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.615, + 0.894, + 0.741 + ], + "angle": 0, + "content": "Region border consistency. We found that the division of shape and clustering lead to inconsistent surface estimates near the boundaries of local regions. To alleviate this problem, we utilize overlap between close local regions. The \\( f_{\\theta}(T(\\mathbf{x}, \\mathbf{z}_i)) \\) near the boundaries (distance less than 0.05) will be averaged by the nearby local regions. The region border consistency is a post-processing procedure. Local regions from all clusters are first processed together back to a whole shape according to their spatial locations." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.749, + 0.664, + 0.763 + ], + "angle": 0, + "content": "3.3. Pattern Decoder" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.77, + 0.892, + 0.866 + ], + "angle": 0, + "content": "We have multiple pattern decoders to cover each cluster. The structure of each pattern decoder consists of 9-layer MLP and a skip connection. Specifically, local code and query point coordinate are concatenated and fed into MLP, and point coordinate is concatenated again after 4 layers. The output of the network is signed distance to the nearest surface." + }, + { + "type": "page_number", + "bbox": [ + 0.465, + 0.887, + 0.506, + 0.898 + ], + "angle": 0, + "content": "21859" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.134, + 0.128, + 0.411, + 0.188 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.189, + 0.471, + 0.253 + ], + "angle": 0, + "content": "Figure 3. Pattern decoder with density-adaptive re-weighting. To further alleviate the region-imbalance problem, we introduce a region re-weighting module to each pattern-specific decoder by kernel density estimator, which dynamically re-weights the regions during learning." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.274, + 0.47, + 0.468 + ], + "angle": 0, + "content": "Density-adaptive re-weighting. Among the learned local codes, certain regions may have less appearances than others, and therefore they are usually neglected by the decoder. To recover more details, it is important to focus more on these regions. First we estimate the space density \\( D \\) of local codes based on their density distributions using kernel density estimation. Gaussian kernel is selected with bandwidth \\( h = 0.35 \\). Now we can re-weight region \\( \\mathbf{B}_i \\) with weight \\( \\omega_i = \\frac{1}{D} \\) during loss calculation. There are two ways of re-weighting the regions, fixed and dynamic. In fixed way, we only update the weight once with pre-extracted local codes. In the dynamic way, the re-weighting is applied every time after local codes being updated by the pattern decoder." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.475, + 0.182, + 0.489 + ], + "angle": 0, + "content": "3.4. Training" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.495, + 0.469, + 0.634 + ], + "angle": 0, + "content": "Our LP-DIF is trained in three stages. In the first stage, we extract the features from local regions by learning a coarse local DIF. In the second stage, we cluster the local regions based on their local features. At last, we train multiple pattern decoders on clustered regions. Note that for each pattern decoder, we use simple decoders so we have similar total number of decoder parameters with local DIF. During training, we optimize decoders and latent codes, while during testing, like other auto-decoder methods, we fix all decoders and only optimize latent codes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.634, + 0.469, + 0.716 + ], + "angle": 0, + "content": "Point sampling. We sample data pairs \\((\\mathbf{x}_k, \\mathbf{s}_k)\\) from \\(S_j\\) as supervision. \\(S_j\\) is a mesh or point cloud with normals \\(\\mathbf{n}_k\\). First we sample points along normal directions with normal distribution \\(N(0, \\theta)\\). Then we sample random points \\(\\{\\mathbf{x}_k\\}\\) and calculate their signed distances \\(\\{\\mathbf{s}_k\\}\\) based on the closest distances." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.717, + 0.468, + 0.745 + ], + "angle": 0, + "content": "Smooth L1 loss. To increase the weight in regions with larger errors, we introduce smooth L1 loss [26], defined by" + }, + { + "type": "equation", + "bbox": [ + 0.084, + 0.75, + 0.469, + 0.793 + ], + "angle": 0, + "content": "\\[\nL _ {k} ^ {\\text {s d f}} = \\left\\{ \\begin{array}{c c} \\frac {1}{2} \\left(f _ {\\theta} \\left(\\mathbf {x} _ {\\mathbf {k}}\\right) - \\mathbf {s} _ {\\mathbf {k}}\\right) ^ {2} & i f | \\left(f _ {\\theta} \\left(\\mathbf {x} _ {\\mathbf {k}}\\right) - \\mathbf {s} _ {\\mathbf {k}}\\right) | < 1 \\\\ \\left(\\left(f _ {\\theta} \\left(\\mathbf {x} _ {\\mathbf {k}}\\right) - \\mathbf {s} _ {\\mathbf {k}}\\right) - \\frac {1}{2}\\right) & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.793, + 0.469, + 0.834 + ], + "angle": 0, + "content": "Gradient loss. It is important to train a DIF with gradient consistency. We apply constraint on the gradient of each sampled points, denoted as" + }, + { + "type": "equation", + "bbox": [ + 0.116, + 0.84, + 0.469, + 0.871 + ], + "angle": 0, + "content": "\\[\nL _ {k} ^ {\\operatorname {g r a d}} \\left(\\mathbf {x} _ {\\mathbf {k}}\\right) = e ^ {- \\left(1 0 0 \\mathbf {s} _ {\\mathbf {k}}\\right) ^ {2}} \\left(1 - \\frac {\\left\\langle \\nabla f \\left(\\mathbf {x} _ {\\mathbf {k}}\\right) , \\mathbf {n} _ {\\mathbf {k}} \\right\\rangle}{\\left\\| f \\left(\\mathbf {x} _ {\\mathbf {k}}\\right) \\right\\| \\left\\| \\mathbf {n} _ {\\mathbf {k}} \\right\\|}\\right), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.127, + 0.892, + 0.168 + ], + "angle": 0, + "content": "We use cosine similarity of \\(\\mathbf{x_k}\\) and the normal of its nearest sampled surface point, and make \\(\\mathbf{x_k}\\) closer to the surface have larger influence." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.169, + 0.824, + 0.181 + ], + "angle": 0, + "content": "The total loss function could be formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.625, + 0.194, + 0.892, + 0.21 + ], + "angle": 0, + "content": "\\[\nL = L _ {s d f} + \\lambda L _ {g r a d}, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.22, + 0.757, + 0.234 + ], + "angle": 0, + "content": "where \\(\\lambda = 1.0\\) for all our experiments." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.246, + 0.632, + 0.262 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.269, + 0.892, + 0.353 + ], + "angle": 0, + "content": "We evaluate the effectiveness of our method compared with the state-of-the-art methods on several different aspects: (1) the representation performance on 3D objects dataset, (2) the performance on large-scale synthetic and real scenes data, and (3) reconstruction power on single complex object reconstruction." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.362, + 0.806, + 0.377 + ], + "angle": 0, + "content": "4.1.3D Objects Dataset Reconstruction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.383, + 0.892, + 0.632 + ], + "angle": 0, + "content": "Dataset and metric. We run the experiments on the ShapeNet dataset [2] with the same settings with [5]. The dataset contains a subset of 13 categories in ShapeNet with train/test splits from [7]. We evaluate geometric reconstruction quality with L2 Chamfer Distance (CD) and F-Score. For L2 Chamfer Distance, we take exactly the same settings as [5]. We sampled 100K signed distances near the surface and 100K signed distances uniformly around the space. We estimate CD using 100,000 randomly sampled points on the ground truth and the reconstructed meshes. Additionally, in all experiments, we compute the F-Score at a threshold of \\(\\tau\\), as F-Score is a metric less sensitive to outliers. F-Score is the mean of recall (percentage of reconstruction to target distances under \\(\\tau\\)) and precision (vice versa). For object reconstruction we use \\(\\tau = 0.01\\). To be consistent with [5], we divide the whole space into \\(16 \\times 16 \\times 16\\) regions. We also compare with NGLOD [36] in ShapeNet150 dataset following their evaluation protocol." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.632, + 0.893, + 0.867 + ], + "angle": 0, + "content": "Quantitative comparison. The comparison results between LP-DIF and other state-of-the-art methods are shown in Table 1. LP-DIF achieves the best performance across all categories in terms of average L2 Chamfer Distance and F-score. Compared with MDIF (auto-decoder branch) [5] and DDC-DIF [19], LP-DIF achieves the best performance in most categories, which shows the representational power of our method for representing multiple objects. As in Table 2, our method performs better than the deepest level of [36]. To test the generalization ability of our method, We train our model on one category (chair) and tested on another (unseen). A subset of the cross-category performance is shown in Table 3. Our method has more accuracy than MDIF [5] in unseen categories (bookshelf). In addition, as local regions share similar feature across categories, the accuracy for seen and unseen categories is almost the same for our method." + }, + { + "type": "page_number", + "bbox": [ + 0.465, + 0.887, + 0.506, + 0.898 + ], + "angle": 0, + "content": "21860" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.119, + 0.124, + 0.846, + 0.282 + ], + "angle": 0, + "content": "
CategoryCD Mean ↓F-score ↑
Occ. [29]IMNet [4]L.DIF [5]MDIF [5]DCC-DIF [19]OursOcc [29]IMNet [4]L.DIF [5]MDIF [5]DCC-DIF [19]Ours
airplane0.250.130.0440.0280.0110.011589.891.798.598.699.799.86
bench0.340.220.1210.0520.0170.021185.288.696.096.099.599.64
cabinet0.320.230.0630.0510.1310.040583.289.296.696.696.498.42
car0.580.260.090.0880.2180.033269.382.793.193.092.798.84
chair0.380.430.0420.0350.0370.029480.282.597.797.699.199.43
display0.350.200.0430.0190.0280.025682.389.498.698.799.499.64
lamp1.472.760.7950.7950.3270.018062.973.893.593.597.399.58
rifle0.390.550.0600.0570.0070.006286.181.196.996.999.999.97
sofa0.310.160.2080.0370.0360.026485.289.398.398.499.199.64
speaker0.380.170.0650.0440.1460.042478.189.497.397.396.197.86
table0.310.300.1070.0460.0290.028587.288.696.597.699.399.50
telephone0.190.110.0430.0270.0100.020288.996.599.699.399.699.58
watercraft0.350.390.0750.0670.0420.015680.384.797.497.298.399.70
mean0.430.460.1350.1020.0810.024581.486.796.997.098.299.36
" + }, + { + "type": "table_caption", + "bbox": [ + 0.078, + 0.284, + 0.891, + 0.297 + ], + "angle": 0, + "content": "Table 1. Surface reconstruction comparison on test set of shapenet in terms of mean L2 chamfer distance (multiplied by 1e3) and F-score." + }, + { + "type": "table", + "bbox": [ + 0.11, + 0.318, + 0.432, + 0.35 + ], + "angle": 0, + "content": "
MethodsLOD3 [36]LOD4 [36]LOD5 [36]LP-DIF
CD Mean ↓0.1120.0690.0620.025
" + }, + { + "type": "table_caption", + "bbox": [ + 0.103, + 0.351, + 0.443, + 0.363 + ], + "angle": 0, + "content": "Table 2. Comparison in ShapeNet150 with NGLOD [36]." + }, + { + "type": "table", + "bbox": [ + 0.111, + 0.378, + 0.432, + 0.413 + ], + "angle": 0, + "content": "
MethodsSofaLampBookshelf
MDIF [5] (seen/unseen) (CD↓)0.0370/-0.7950/-- / 0.0910
LP-DIF (seen/unseen) (CD↓)0.0264/0.02650.0180/0.0185- / 0.0490
" + }, + { + "type": "table_caption", + "bbox": [ + 0.123, + 0.413, + 0.424, + 0.426 + ], + "angle": 0, + "content": "Table 3. Cross-category performance in ShapeNet." + }, + { + "type": "image", + "bbox": [ + 0.111, + 0.442, + 0.432, + 0.741 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.746, + 0.47, + 0.786 + ], + "angle": 0, + "content": "Figure 4. Visual comparison with OccNet [25], ConvOccNet [29], IFNet [6], and LIG [17], our method could reconstruct more geometry detail on ShapeNet." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.471, + 0.868 + ], + "angle": 0, + "content": "Qualitative comparison. In Figure 4, we visually compared 3D surface reconstruction on Shapenet with other DIF methods [6, 17, 25, 29], from which we find that LP-DIF reconstructs more geometry details while other method tends" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.322, + 0.715, + 0.334 + ], + "angle": 0, + "content": "to lose details on thin structures." + }, + { + "type": "image", + "bbox": [ + 0.536, + 0.344, + 0.856, + 0.433 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.433, + 0.891, + 0.457 + ], + "angle": 0, + "content": "Figure 5. Comparison for surface reconstruction on SceneNet with sparse sampling." + }, + { + "type": "image", + "bbox": [ + 0.515, + 0.484, + 0.876, + 0.655 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.656, + 0.891, + 0.682 + ], + "angle": 0, + "content": "Figure 6. Comparison for surface reconstruction on 3D Scene dataset with dense sampling." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.707, + 0.727, + 0.721 + ], + "angle": 0, + "content": "4.2.3D Scene Reconstruction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.728, + 0.892, + 0.867 + ], + "angle": 0, + "content": "Dataset and metric. We conduct our experiments on a synthetic dataset: SceneNet [14], and a real scanned dataset: 3D Scene dataset [42]. As scenes in SceneNet dataset are not watertight, and have many double-sided faces creating conflicting normals, we pre-process SceneNet to watertight using methods from [16]. We drop scenes with empty inner spaces after the watertighting process. We sample a constant density of points according to the area of faces (1000 points per \\( m^2 \\) for SceneNet and 10000 points per \\( m^2 \\) for 3D Scene dataset). For all the scene-level experiments, we ran" + }, + { + "type": "page_number", + "bbox": [ + 0.465, + 0.888, + 0.504, + 0.898 + ], + "angle": 0, + "content": "21861" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.126, + 0.473, + 0.25 + ], + "angle": 0, + "content": "domly sample 2 million points on the generated mesh and the ground truth mesh when estimating L1 CD, and we use \\(\\tau = 0.025\\) (2.5cm) for F-score. Since data is provided in a physically-meaningful scale, we use world coordinate (meters) for computing CD. Note that these two metrics are not always consistent as CD is more sensitive to outliers. For scene-level experiments, we directly optimize latent codes and decoders on the scenes, and we divide the whole space into \\(32 \\times 32 \\times 32\\) regions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.251, + 0.473, + 0.376 + ], + "angle": 0, + "content": "Quantitative comparison. The comparison results between LP-DIF and other state-of-the-art methods are shown in Table 4. LP-DIF achieves the best performance across all categories in terms of average L1 Chamfer Distance and F-score both in sparse (Scenenet) and dense (3D SceneNet dataset) sampling settings, which proves better representational power of our method. Compared with scenenet with sparse sampling setting, our method improves more on 3D scenenet dataset with dense sampling settings." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.376, + 0.471, + 0.445 + ], + "angle": 0, + "content": "Qualitative comparison. In Figure 5 and 6, we visually compared 3D surface reconstruction of scene dataset with other DIF methods, from which we find that LP-DIF reconstructs more geometry details and less missing parts than other method." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.454, + 0.388, + 0.469 + ], + "angle": 0, + "content": "4.3. Complex 3D Object Reconstruction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.476, + 0.473, + 0.641 + ], + "angle": 0, + "content": "Dataset and metric. For complex 3D object reconstruction, we use Thai Statue, obtained from the Stanford 3D Scanning Repository [18]. It is an intricate statue, which consists of 10 million polygons. Fine details of the statue are challenging to be captured with existing methods. We randomly sample 2 million points on the generated and the ground truth meshes when estimating L1 CD, and we use \\(\\tau = 0.025\\) for F-score. For complex 3D object, we directly optimize latent codes and decoders to fit the shape. For ACORN [24], we train using their official code and extract the reconstructed mesh. [24] is trained for several hours until max octants are reached." + }, + { + "type": "image", + "bbox": [ + 0.171, + 0.651, + 0.376, + 0.77 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.77, + 0.47, + 0.808 + ], + "angle": 0, + "content": "Figure 7. Comparison for surface reconstruction on Thai statue. Our result is comparable with ACORN [24] with slightly better details." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.471, + 0.868 + ], + "angle": 0, + "content": "Quantitative comparison. The comparison results between LP-DIF and other state-of-the-art methods are shown in Table 5. LP-DIF achieves the best performance in terms" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.127, + 0.892, + 0.154 + ], + "angle": 0, + "content": "of average L1 Chamfer Distance and F-score for complex 3D object reconstruction." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.155, + 0.894, + 0.238 + ], + "angle": 0, + "content": "Qualitative comparison. In Figure 1, we visually compare 3D surface reconstruction of Thai statue with other DIF methods, where we find that LP-DIF reconstructs much more fine geometry details than other methods. In Figure 7, we compare with ACORN [24]. Our result is comparable with ACORN with slightly better details." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.248, + 0.654, + 0.263 + ], + "angle": 0, + "content": "4.4. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.27, + 0.893, + 0.587 + ], + "angle": 0, + "content": "Network capacity and efficiency comparison. We have summarized the number of parameters used in NGLOD (LOD5) [36], LDIF [1], MDIF [5], LIG [17], and our method in Table 6. As in the table, different number of parameters are used and our method utilized the second least total number of parameters. We also tested the performance under the same total number of parameters in Table 7. As in the first two rows of the table, LDIF [1] and our method have the similar total number of parameters, where our method outperforms LDIF [1]. After that, we increase our MLP to 800-dimensional hidden layers to have the similar total number parameters with MDIF [5]. As in the 3-4 rows of the table, the performance of our ablation method is still better than MDIF [5], but is worse than our original decoders. The reason could be that the increased parameters of network makes the optimization of local latent code unstable. The performance of our coarse decoder is also shown in the last row for comparison. We have also compared the computation time on 8 shapes of ShapeNet in Table 8. It takes much more time for NGLOD [36] to train. For L-DIF and LP-DIF, we reported the time needed to reach the same accuracy level. It takes less time for LP-DIF than L-DIF." + }, + { + "type": "image", + "bbox": [ + 0.532, + 0.599, + 0.859, + 0.653 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.658, + 0.892, + 0.71 + ], + "angle": 0, + "content": "Figure 8. Comparison with random clustering. (a) Replacing the clustering process with random assigning each local region into clusters. (b) Clustering with regards to similarity leads to better performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.715, + 0.895, + 0.868 + ], + "angle": 0, + "content": "Ablation on modules. We also conduct a series of experiments on the effectiveness of our modules on Burghers of 3D scenenet dataset. Our baseline is implemented by removing pattern clustering and region re-weighting. First, we separate the whole space into different number of regions (each region has one code), and test the effect of our module under different settings. The results are shown in Table 9, where the baseline model performs better with more local regions and codes, however, more local codes occupy much more space. Our model with \\(7.63\\mathrm{MB}\\) local codes could have similar performance with the baseline" + }, + { + "type": "page_number", + "bbox": [ + 0.465, + 0.887, + 0.506, + 0.898 + ], + "angle": 0, + "content": "21862" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.201, + 0.124, + 0.768, + 0.221 + ], + "angle": 0, + "content": "
CategoryCD Mean ↓F-score ↑SceneCD Mean ↓F-score ↑
LIG [17]OursLIG [17]OursLIG [17]OursLIG [17]Ours
Bathroom0.008250.0063398.5699.66Burghers0.01220.003990.2599.67
Bedroom0.009780.0073096.4199.24Lounge0.01310.003185.4999.72
Office0.014520.0092993.9296.97CopyRoom0.01300.003484.6899.97
Livingroom0.011910.0098796.3998.65StoneWall0.01100.003189.1499.90
Kitchen0.009880.0082596.3698.55TotemPole0.01200.004189.3999.23
Mean0.010650.0081696.4098.67Mean0.01220.003587.7999.70
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.223, + 0.89, + 0.248 + ], + "angle": 0, + "content": "Table 4. Surface reconstruction from sparse point cloud on SceneNet and dense point cloud on 3D SceneNet dataset in terms of mean L1 chamfer distance and F-score." + }, + { + "type": "table", + "bbox": [ + 0.131, + 0.269, + 0.415, + 0.306 + ], + "angle": 0, + "content": "
MethodsDeepSDF [28]LIG [17]LDIF baselineOurs
CD Mean ↓0.7400.6030.2110.176
F-score ↑1.313.621.863.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.306, + 0.468, + 0.331 + ], + "angle": 0, + "content": "Table 5. Surface reconstruction comparison on Thai statue in terms of mean L1 chamfer distance and F-score." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.344, + 0.485, + 0.415 + ], + "angle": 0, + "content": "
Methods# Feature Param# Network ParamTotal # Param
LOD5 [36]101225282368510146213
L.DIF [5]524288460993985281
MDIF [5]440321835930118403333
LIG [17]131072227745358817
Ours53248 (coarse) + 2498563745 (coarse) + 463108769957
" + }, + { + "type": "table_caption", + "bbox": [ + 0.156, + 0.417, + 0.39, + 0.429 + ], + "angle": 0, + "content": "Table 6. Network capacity comparison." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.442, + 0.486, + 0.495 + ], + "angle": 0, + "content": "
Methods#Feature Param#Inference ParamTotal # ParamCD (Airplane)↓CD (Bench)↓
L.DIF [5]5242884609939852810.0440.121
Ours303104 (53248 + 249856)466853 (3745 + 463108)7699570.0120.021
MDIF [5]4403218359301184033330.0280.052
Ours-abl-mdif303104 (53248 + 249856)17952293 (3745 + 17948548)182553970.01450.031
Ours-coarse532482689559370.0620.167
" + }, + { + "type": "table_caption", + "bbox": [ + 0.1, + 0.495, + 0.446, + 0.507 + ], + "angle": 0, + "content": "Table 7. Ablation with similar total number of parameters." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.52, + 0.485, + 0.567 + ], + "angle": 0, + "content": "
MethodsStage1Stage 2Stage 3Total
NGLOD [36]---~4000s
LDIF baseline---165s (1.33s ×124epochs)
LP-DIF20s1s141s (2.43s ×58epochs)162s
" + }, + { + "type": "table_caption", + "bbox": [ + 0.139, + 0.569, + 0.407, + 0.581 + ], + "angle": 0, + "content": "Table 8. Computation efficiency comparison." + }, + { + "type": "table", + "bbox": [ + 0.151, + 0.595, + 0.393, + 0.64 + ], + "angle": 0, + "content": "
Methods# of codescode sizeCD Mean ↓F-score ↑
Baseline-3232K7.63 MB0.0055796.78
Baseline-1282097K488 MB0.0038999.65
LP-DIF-3232K7.63 MB0.0039499.67
LP-DIF-1282097K488 MB0.0038799.64
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.641, + 0.469, + 0.704 + ], + "angle": 0, + "content": "Table 9. Ablation study with different number of local codes. Result of the baseline method with different number of local codes are shown in the first two rows. Result of LP-DIF with different number of local codes are shown in the last two rows. Our method can achieve same level of accuracy with much less local codes." + }, + { + "type": "table", + "bbox": [ + 0.152, + 0.717, + 0.393, + 0.773 + ], + "angle": 0, + "content": "
MethodsCD Mean↓F-score ↑
Baseline0.0055796.78
LP-DIF w/o clustering0.0044699.52
LP-DIF w/o re-weighting0.0041999.16
LP-DIF0.0039499.67
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.775, + 0.47, + 0.8 + ], + "angle": 0, + "content": "Table 10. Ablation study on components of our model in terms of mean L1 chamfer distance and F-score." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.825, + 0.469, + 0.867 + ], + "angle": 0, + "content": "method with 488 MB local codes. After that, we evaluate the effectiveness of our clustering module by replacing it with random assigning cluster indices. As in Figure 8 and" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.273, + 0.892, + 0.466 + ], + "angle": 0, + "content": "Table 6, the performance is deteriorated with random clustering. The possible reason is that randomly separating local regions increases the deviation of some local regions from the cluster centers, causing them to fail in training. Next we evaluate the components of our model by removing them separately. We test two variations: (1) removing the clustering module and re-weight on the whole set of regions, and (2) removing the re-weighting module. The result is shown in Table 10 and Figure 9 (a) - (c), and we find that both modules are helpful for achieving good performance. At last, we test the difference between fixed density estimator and dynamic density estimator. As shown in Figure 9 (d) - (f), dynamic density estimator could reconstruct better geometry details than fixed one." + }, + { + "type": "image", + "bbox": [ + 0.593, + 0.478, + 0.793, + 0.606 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.607, + 0.892, + 0.658 + ], + "angle": 0, + "content": "Figure 9. Ablation study on density-adaptive re-weighting. (a) Ours w/o density re-weighting. (b) Ours w/ density re-weighting. (c) Ground truth. (d) Ours w/o density estimator. (e) Ours w/ fixed density estimator. (f) Ours w/ dynamic density estimator." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.664, + 0.619, + 0.678 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.687, + 0.892, + 0.866 + ], + "angle": 0, + "content": "In this paper, we present LP-DIF, a local pattern-specific deep implicit function for reconstructing highly detailed geometry. Compared with previous methods that treat all local regions equally using a single decoder, we regard a shape as clusters of local regions and mine local patterns with different decoders. This alleviates the difficulty of learning caused by diverse local regions. In addition, we introduce a dynamic region re-weighting module, which could provide more focus on less common regions to tackle the data-imbalance problem in each pattern decoder. As a result, finer details of the local regions are learned more accurately. We demonstrate that our method outperforms the latest methods under various benchmarks." + }, + { + "type": "page_number", + "bbox": [ + 0.465, + 0.887, + 0.505, + 0.898 + ], + "angle": 0, + "content": "21863" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.125, + 0.173, + 0.139 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.149, + 0.469, + 0.213 + ], + "angle": 0, + "content": "[1] Rohan Chabra, Jan E Lenssen, Eddy Ilg, Tanner Schmidt, Julian Straub, Steven Lovegrove, and Richard Newcombe. Deep local shapes: Learning local SDF priors for detailed 3d reconstruction. In European Conference on Computer Vision, pages 608-625. Springer, 2020. 1, 2, 3, 4, 7" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.215, + 0.469, + 0.303 + ], + "angle": 0, + "content": "[2] Angel X. 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To capture geometry details, current mainstream methods divide 3D shapes into local regions and then learn each one with a local latent code via a decoder. Such local methods can capture more local details due to less diversity among local regions than global shapes. Although the diversity of local regions has been decreased compared to global approaches, the diversity in different local regions still poses a challenge in learning an implicit function when treating all regions equally using only a single decoder. What is worse, these local regions often exhibit imbalanced distributions, where certain regions have significantly fewer observations. This leads that fine geometry details could not be preserved well. To solve this problem, we propose a novel Local Pattern-specific Implicit Function, named LP-DIF, to represent a shape with clusters of local regions and multiple decoders, where each decoder only focuses on one cluster of local regions which share a certain pattern. Specifically, we first extract local codes for all regions, and then cluster them into multiple groups in the latent space, where similar regions sharing a common pattern fall into one group. After that, we train multiple decoders for mining local patterns of different groups, which simplifies the learning of fine geometric details by reducing the diversity of local regions seen by each decoder. To further alleviate the data-imbalance problem, we introduce a region re-weighting module to each pattern-specific decoder using a kernel density estimator, which dynamically re-weights the regions during learn + +ing. Our LP-DIF can restore more geometry details, and thus improve the quality of 3D reconstruction. Experiments demonstrate that our method can achieve the state-of-the-art performance over previous methods. Code is available at https://github.com/gtyxyz/lpdfif. + +# 1. Introduction + +Representing 3D shapes is a fundamental problem for many applications in 3D computer vision. Recently, Deep Implicit Function (DIF) [4,22,23,25,28,41] has gained popularity for efficiently learning the representation of 3D objects and scenes. In contrast to directly learning explicit 3D representations [15,30,31] (voxels, point clouds or meshes), DIF aims to train a neural network to learn the binary occupancy function [25] or signed distance function (SDF) [28], as given a query location and an input latent code. Such kind of representation is continuous with arbitrary precision and can handle various topology, which has achieved the state-of-the-art results in several shape reconstruction tasks. + +Existing DIF methods can be roughly classified into two categories: global and local approaches. Most of the early methods [4, 9, 20, 21, 25, 27-29, 35, 37, 40] fall into global approaches. These methods take advantage of one latent code and a single decoder to represent the whole shape. Global approaches often suffer from long training time and low reconstruction accuracy due to the limited capacity of capturing local geometry details. More recently, local approaches [1, 3, 5, 6, 10-12, 17, 19, 34, 36, 38] divide 3D shapes (often divide by 3D grids) into local regions and then learn each one with a local latent code via a decoder, where the decoder shares the geometric similarities among different local regions. Although such local approaches can capture some local details, a large diversity of different local regions still increase the difficulty of learning an implicit function + +![](images/146c79253fa2fb39027cc61808d867306d2668a7062444acaf3e2e8ffca46335.jpg) +(a) Global DIF +(b) Local DIF +(c) Ours +(d) Reference +Figure 1. Visual comparison of 3D shape surface reconstruction. Compared with global DIF (e.g. [28]) and local DIF (e.g. [1]), our method can reconstruct the shape with fine-grained geometric details. Compared with previous methods that treat all local regions equally using a single decoder, we regard a shape as clusters of local regions and mine local patterns with different decoders. This alleviates the difficulty of learning caused by diverse local regions. + +when treating all regions equally using only a single decoder. In addition, these local regions often exhibit imbalanced distributions, where certain regions have significantly fewer observations, especially in scenes. As a result, fine geometry details of shapes could not be captured well. + +To address the above-mentioned problems, we propose a novel Local Pattern-specific Implicit Function, named LP-DIF, for learning 3D shape representation using clusters of local regions with multiple decoders, where each decoder only represents one cluster of local regions which share a certain pattern (geometric features such as facing direction, number of faces, relative positions to the region center). Specifically, we first extract the local latent codes for all local regions divided by 3D grids, and then cluster them into multiple groups in the latent space, where similar regions sharing a common pattern fall into one group. After that, we train a separate pattern-specific decoder for each group of regions, which reduces data-imbalance among different patterns of regions and simplifies the learning of fine geometric details of 3D structures by limiting the diversity of regions seen to each decoder. To further alleviate the region-imbalance problem, we introduce a region reweighting module to each pattern-specific decoder by kernel density estimator, which dynamically re-weights the regions during learning. Our main contributions can be summarized as follows. + +- We propose a novel LP-DIF to learn local pattern-specific deep implicit function of 3D shapes for reconstructing highly detailed geometry. Compared with previous methods that treat all local regions equally using a single decoder, we regard a shape as clusters of local regions and mine local patterns with different de + +coders. This alleviates the difficulty of learning caused by diverse local regions. + +- We introduce a dynamic region re-weighting module, which could provide more focus on less common regions to tackle the data-imbalance problem in each pattern decoder. As a result, the regions with less appearances can be captured more accurately. +- Our method could be applied in multiple objects, single complex objects and large scale of scenes. We improve the state-of-the-art accuracy in surface reconstruction under various benchmarks. + +Figure 2 illustrates the main differences between DIF, local DIF and our method. For DIF approaches, one global code and a decoder are used for the whole shape. For Local DIF methods, multiple local codes and a shared decoder are used. For our method, multiple clusters of regions are learned with different decoders. + +# 2. Related Work + +In computer vision and graphics, there are two categories of shape representations: explicit representation and implicit representation. Explicit geometric representations [15, 30, 31] such as point clouds, voxels and triangular meshes have been widely used for representing geometries for their simplicity and flexibility. More recently, deep implicit representations [4, 25, 28, 39] have been proposed in the context of shape representation, where the implicit surfaces of geometries are represented as the zero-set of spatial functions with fully connected neural networks. Such kind of representation is continuous with arbitrary precision and + +![](images/704e3af13c975e06d5bac373d9a0761951586ceee3a441a67355f23bd5b2cb5a.jpg) +Figure 2. Comparison between DIF, local DIF and our method. (a) DIF methods leverage one global code and one decoder, often suffer from long training speed and low reconstruction quality due to the limited capacity of capturing local geometry details. (b) Local DIF methods use multiple local codes and one shared decoder, a large diversity of different local regions still increase the difficulty of learning an implicit function when treating all regions equally using only a single decoder. (c) Our method, LP-DIF, for representing a shape with some clusters of local regions and multiple decoders, where each decoder only represents one cluster of local regions which share a certain pattern. (d) Visualization of the clustered local regions. + +can handle different topology structure, which has achieved the state-of-the-art results in several shape reconstruction task. Implicit representations can be categorized into global and local approaches. + +Global Deep Implicit Shape Representation. In recent years, implicit functions have been introduced into neural networks [25, 28] and show promising results. Early approaches learn one latent code and one single global implicit network to represent the whole shape. For example, DeepSDF [28] learned an implicit function where the network output represents the signed distance of the input point to its nearest surface, where zero-set of the learned function implicitly represents the surface of the shape. Other approaches [25, 29] defined the implicit functions as 3D occupancy probability functions and turned shape representation into a point classification problem. Following these methods, [35, 37] improved the expressiveness of the implicit functions by introducing high frequency signals with periodic activation. [39] proposed to represent the volume density as an implicit function of the signed distance in neural volume rendering for high-quality novel view generation. However, these methods suffer from long training time and low reconstruction accuracy for high resolution data due to the limited capacity of decoder to capture local geometry details. + +Local Deep Implicit Shape Representation. To capture more geometry details, current mainstream methods divide 3D shapes into many local regions and then learn each one with a local latent code via a decoder. Some recent works [1, 29] proposed to divide the whole 3D shape + +uniformly into 3D grids, where they either assign each local grid with a latent code or trilinearly interpolate local latent codes based on querying location. In LIG [17], this idea was applied to 3D scenes. NGLOD [36] leveraged sparse octree instead of uniform grids to increase efficiency. ACORN [24] proposed to adaptively optimize the coordinate decomposition to achieve higher accuracy in large-scale scenes. DCC-DIF [19] optimized the local latent code learning by introducing dynamic grid positions. IFNet [6] utilized multiple level of latent codes in a hierarchical way. LPI [3] divided the global shape into multiple local parts in latent space to allow easier shape parts learning and blending. PatchNet [38] was proposed to divide a shape into local patches with no fixed structure. Points2surf [10] incorporated local information surrounding each point, but it typically takes a lot of time for point-wise distance calculation. Although such local methods can capture some local details, a large diversity of different local regions still poses an challenge for learning an implicit function when treating all regions equally using only a single decoder. In addition, these local regions often exhibit imbalanced distributions, where certain regions have significantly fewer observations. As a result, fine geometry details could not be captured well. Several methods [8, 13] have been proposed to learn multiple decoders for point deformations, however, their methods cannot be applied in learning implicit representations for shapes. MDIF [5, 33] used multiple levels of decoders in a hierarchical way, however, it did not consider the relationship between local regions. In novel view synthesizing, KiloNeRF [32] utilized thousands of tiny MLPs to represent + +different parts of the scenes. The simple and effective way to introduce multiple decoders is to assign each local region with a decoder, however, it is normally not feasible due to time and space constraint and the prior information of the local regions could not be preserved. In contrast, we introduce clustering for the local regions as a trade-off between reconstruction accuracy and efficiency. + +# 3. Method + +Given $K$ discrete points $\mathbf{X} = \{\mathbf{x}_k\}$ and their signed distances $\mathbf{S} = \{\mathbf{s}_k\}$ from a 3D surface, our goal is to regress a continuous function that outputs the closest signed distance to the 3D surface given a spatial point $\mathbf{x}$ . To achieve this goal, we propose to learn a local pattern-specific DIF. The architecture of LP-DIF and differences between our LP-DIF and other methods are illustrated in Figure 2. In this section, we first introduce latent embedding learning and local region feature extraction in Sec. 3.1. Then we describe our pattern clustering module in Sec. 3.2. After that we present our pattern decoder with density adaptive re-weighting in Sec. 3.3. At last, we illustrate our training process in Sec. 3.4. + +# 3.1. Learning Latent Embedding for Local Regions + +At the beginning, we choose to train a local DIF network [1, 17] to learn latent embedding for local regions to extract coarse local features for clustering. Local DIF [1, 17] is a special category of DIF, which is defined as a signed distance function $f(\mathbf{x}, \mathbf{z})$ modeled with Multilayer Perceptrons (MLP), mapping each query point $\mathbf{x}$ near a surface to the signed distance domain continuously with condition code $\mathbf{z}$ . A shape $S$ is defined as the zero level set of $f(\mathbf{x}, \mathbf{z})$ : + +$$ +\mathcal {S} = \left\{\mathbf {x} \in \mathbb {R} ^ {3} \mid f _ {\theta} (\mathbf {x}, \mathbf {z}) = 0 \right\}, \tag {1} +$$ + +where $\theta$ is the parameter of the MLP. To be able to represent multiple shapes in the same time, the condition $\mathbf{z}$ is optimized for each shape, and the parameter $\theta$ is shared for all the shapes. Local DIF is defined on partitioned space of shape $S$ . A normalized 3D space is usually partitioned into $d\times d\times d$ regions $\{\mathbf{B}_i\} \subseteq \mathbb{R}^3$ , $i = 0\dots N - 1$ . All the regions have their separate codes $\mathbf{z}_i$ , sharing the same parameter $\theta$ . The entire surface is defined as: + +$$ +\mathcal {S} = \left\{\mathbf {x} \in \mathbb {R} ^ {3} \mid \sum f _ {\theta} (T (\mathbf {x}), \mathbf {z} _ {i}) = 0 \right\}, \tag {2} +$$ + +where $T(\mathbf{x})$ is the re-centering function of $\mathbf{x}$ , which transforms the points in each region to their local coordinates. After training of local DIF, all local regions have their codes $\mathbf{z}_i$ , which serve as the local features of corresponding regions. + +Code constraint. For DIF methods, it is important to constrain the latent codes of all the regions during training. Traditional Local DIF methods [1, 28] use L2 norm loss on the + +learned latent codes. However, in our method, we found that L2 norm loss could lead to latent codes being spread randomly in space, which is not good for subsequent clustering and latent code learning. Therefore, we constrain all local latent codes to be distributed within a hyper-sphere. The intuition is to process the latent codes in a way similar to normalizing them before entering the network. We update $\mathbf{z}$ according to Eq. (3) after every step of learning of $\mathbf{z}$ . + +$$ +\mathbf {z} _ {i} = \left\{ \begin{array}{c c} \mathbf {z} _ {i} & i f \quad | | \mathbf {z} _ {i} | | \leq 1 \\ \frac {\mathbf {z} _ {i}}{| | \mathbf {z} _ {i} | |} & \text {o t h e r w i s e} \end{array} \right. \tag {3} +$$ + +# 3.2. Pattern Clustering + +After training of the local DIF, each region from the whole set of shapes will be encoded by the condition $\mathbf{z}_{\mathrm{ij}}$ for region $\mathbf{B}_i$ and shape $S_{j}, j = 0\dots M - 1$ . A shape normally consists of many empty or near-empty regions. To alleviate the influence of these regions, we first remove regions with SDF positive rate (the percentage of positive SDF samples within one local region) out of [0.01, 0.99]. The intuition is that if one region has almost all SDF samples to be positive or negative, this region will be far away from any shape surfaces and need no training. After learning of local DIF, there are regions $\mathbf{B}_i$ that are learned well with low reconstruction errors, we remove these easy-to-learn regions with error threshold $\epsilon$ . The remaining regions are aggregated into $P$ clusters by finding the cluster center $\mathbf{c}_k$ of their condition codes with K-means by optimizing 4. We empirically select $P = 4$ to balance between training speed and accuracy. The clustered local regions are visualized in Figure 2 (d). + +$$ +\underset {c _ {k}} {\operatorname {a r g m i n}} \sum_ {k = 0} ^ {P} \sum_ {i = 0} ^ {N} \sum_ {j = 0} ^ {M} \left| \left| \mathbf {z} _ {\mathbf {i j}} - \mathbf {c} _ {\mathbf {k}} \right| \right| ^ {2}. \tag {4} +$$ + +Region border consistency. We found that the division of shape and clustering lead to inconsistent surface estimates near the boundaries of local regions. To alleviate this problem, we utilize overlap between close local regions. The $f_{\theta}(T(\mathbf{x}, \mathbf{z}_i))$ near the boundaries (distance less than 0.05) will be averaged by the nearby local regions. The region border consistency is a post-processing procedure. Local regions from all clusters are first processed together back to a whole shape according to their spatial locations. + +# 3.3. Pattern Decoder + +We have multiple pattern decoders to cover each cluster. The structure of each pattern decoder consists of 9-layer MLP and a skip connection. Specifically, local code and query point coordinate are concatenated and fed into MLP, and point coordinate is concatenated again after 4 layers. The output of the network is signed distance to the nearest surface. + +![](images/1b87e56e070a0957217c86724bf7f0ff7638d4c5c89329c13395336fe3538719.jpg) +Figure 3. Pattern decoder with density-adaptive re-weighting. To further alleviate the region-imbalance problem, we introduce a region re-weighting module to each pattern-specific decoder by kernel density estimator, which dynamically re-weights the regions during learning. + +Density-adaptive re-weighting. Among the learned local codes, certain regions may have less appearances than others, and therefore they are usually neglected by the decoder. To recover more details, it is important to focus more on these regions. First we estimate the space density $D$ of local codes based on their density distributions using kernel density estimation. Gaussian kernel is selected with bandwidth $h = 0.35$ . Now we can re-weight region $\mathbf{B}_i$ with weight $\omega_i = \frac{1}{D}$ during loss calculation. There are two ways of re-weighting the regions, fixed and dynamic. In fixed way, we only update the weight once with pre-extracted local codes. In the dynamic way, the re-weighting is applied every time after local codes being updated by the pattern decoder. + +# 3.4. Training + +Our LP-DIF is trained in three stages. In the first stage, we extract the features from local regions by learning a coarse local DIF. In the second stage, we cluster the local regions based on their local features. At last, we train multiple pattern decoders on clustered regions. Note that for each pattern decoder, we use simple decoders so we have similar total number of decoder parameters with local DIF. During training, we optimize decoders and latent codes, while during testing, like other auto-decoder methods, we fix all decoders and only optimize latent codes. + +Point sampling. We sample data pairs $(\mathbf{x}_k, \mathbf{s}_k)$ from $S_j$ as supervision. $S_j$ is a mesh or point cloud with normals $\mathbf{n}_k$ . First we sample points along normal directions with normal distribution $N(0, \theta)$ . Then we sample random points $\{\mathbf{x}_k\}$ and calculate their signed distances $\{\mathbf{s}_k\}$ based on the closest distances. + +Smooth L1 loss. To increase the weight in regions with larger errors, we introduce smooth L1 loss [26], defined by + +$$ +L _ {k} ^ {\text {s d f}} = \left\{ \begin{array}{c c} \frac {1}{2} \left(f _ {\theta} \left(\mathbf {x} _ {\mathbf {k}}\right) - \mathbf {s} _ {\mathbf {k}}\right) ^ {2} & i f | \left(f _ {\theta} \left(\mathbf {x} _ {\mathbf {k}}\right) - \mathbf {s} _ {\mathbf {k}}\right) | < 1 \\ \left(\left(f _ {\theta} \left(\mathbf {x} _ {\mathbf {k}}\right) - \mathbf {s} _ {\mathbf {k}}\right) - \frac {1}{2}\right) & \text {o t h e r w i s e} \end{array} \right. \tag {5} +$$ + +Gradient loss. It is important to train a DIF with gradient consistency. We apply constraint on the gradient of each sampled points, denoted as + +$$ +L _ {k} ^ {\operatorname {g r a d}} \left(\mathbf {x} _ {\mathbf {k}}\right) = e ^ {- \left(1 0 0 \mathbf {s} _ {\mathbf {k}}\right) ^ {2}} \left(1 - \frac {\left\langle \nabla f \left(\mathbf {x} _ {\mathbf {k}}\right) , \mathbf {n} _ {\mathbf {k}} \right\rangle}{\left\| f \left(\mathbf {x} _ {\mathbf {k}}\right) \right\| \left\| \mathbf {n} _ {\mathbf {k}} \right\|}\right), \tag {6} +$$ + +We use cosine similarity of $\mathbf{x_k}$ and the normal of its nearest sampled surface point, and make $\mathbf{x_k}$ closer to the surface have larger influence. + +The total loss function could be formulated as + +$$ +L = L _ {s d f} + \lambda L _ {g r a d}, \tag {7} +$$ + +where $\lambda = 1.0$ for all our experiments. + +# 4. Experiments + +We evaluate the effectiveness of our method compared with the state-of-the-art methods on several different aspects: (1) the representation performance on 3D objects dataset, (2) the performance on large-scale synthetic and real scenes data, and (3) reconstruction power on single complex object reconstruction. + +# 4.1.3D Objects Dataset Reconstruction + +Dataset and metric. We run the experiments on the ShapeNet dataset [2] with the same settings with [5]. The dataset contains a subset of 13 categories in ShapeNet with train/test splits from [7]. We evaluate geometric reconstruction quality with L2 Chamfer Distance (CD) and F-Score. For L2 Chamfer Distance, we take exactly the same settings as [5]. We sampled 100K signed distances near the surface and 100K signed distances uniformly around the space. We estimate CD using 100,000 randomly sampled points on the ground truth and the reconstructed meshes. Additionally, in all experiments, we compute the F-Score at a threshold of $\tau$ , as F-Score is a metric less sensitive to outliers. F-Score is the mean of recall (percentage of reconstruction to target distances under $\tau$ ) and precision (vice versa). For object reconstruction we use $\tau = 0.01$ . To be consistent with [5], we divide the whole space into $16 \times 16 \times 16$ regions. We also compare with NGLOD [36] in ShapeNet150 dataset following their evaluation protocol. + +Quantitative comparison. The comparison results between LP-DIF and other state-of-the-art methods are shown in Table 1. LP-DIF achieves the best performance across all categories in terms of average L2 Chamfer Distance and F-score. Compared with MDIF (auto-decoder branch) [5] and DDC-DIF [19], LP-DIF achieves the best performance in most categories, which shows the representational power of our method for representing multiple objects. As in Table 2, our method performs better than the deepest level of [36]. To test the generalization ability of our method, We train our model on one category (chair) and tested on another (unseen). A subset of the cross-category performance is shown in Table 3. Our method has more accuracy than MDIF [5] in unseen categories (bookshelf). In addition, as local regions share similar feature across categories, the accuracy for seen and unseen categories is almost the same for our method. + +
CategoryCD Mean ↓F-score ↑
Occ. [29]IMNet [4]L.DIF [5]MDIF [5]DCC-DIF [19]OursOcc [29]IMNet [4]L.DIF [5]MDIF [5]DCC-DIF [19]Ours
airplane0.250.130.0440.0280.0110.011589.891.798.598.699.799.86
bench0.340.220.1210.0520.0170.021185.288.696.096.099.599.64
cabinet0.320.230.0630.0510.1310.040583.289.296.696.696.498.42
car0.580.260.090.0880.2180.033269.382.793.193.092.798.84
chair0.380.430.0420.0350.0370.029480.282.597.797.699.199.43
display0.350.200.0430.0190.0280.025682.389.498.698.799.499.64
lamp1.472.760.7950.7950.3270.018062.973.893.593.597.399.58
rifle0.390.550.0600.0570.0070.006286.181.196.996.999.999.97
sofa0.310.160.2080.0370.0360.026485.289.398.398.499.199.64
speaker0.380.170.0650.0440.1460.042478.189.497.397.396.197.86
table0.310.300.1070.0460.0290.028587.288.696.597.699.399.50
telephone0.190.110.0430.0270.0100.020288.996.599.699.399.699.58
watercraft0.350.390.0750.0670.0420.015680.384.797.497.298.399.70
mean0.430.460.1350.1020.0810.024581.486.796.997.098.299.36
+ +Table 1. Surface reconstruction comparison on test set of shapenet in terms of mean L2 chamfer distance (multiplied by 1e3) and F-score. + +
MethodsLOD3 [36]LOD4 [36]LOD5 [36]LP-DIF
CD Mean ↓0.1120.0690.0620.025
+ +Table 2. Comparison in ShapeNet150 with NGLOD [36]. + +
MethodsSofaLampBookshelf
MDIF [5] (seen/unseen) (CD↓)0.0370/-0.7950/-- / 0.0910
LP-DIF (seen/unseen) (CD↓)0.0264/0.02650.0180/0.0185- / 0.0490
+ +Table 3. Cross-category performance in ShapeNet. + +![](images/1ac795f8aa2df2044fb9d9c4d15e9f599740861da61e2f2a0eba107bea23a3de.jpg) +Figure 4. Visual comparison with OccNet [25], ConvOccNet [29], IFNet [6], and LIG [17], our method could reconstruct more geometry detail on ShapeNet. + +Qualitative comparison. In Figure 4, we visually compared 3D surface reconstruction on Shapenet with other DIF methods [6, 17, 25, 29], from which we find that LP-DIF reconstructs more geometry details while other method tends + +to lose details on thin structures. + +![](images/e9a1afa6ce592949f5c4c7669eb1664699377f320294735e6c27ebc0a7cb4aaf.jpg) +Figure 5. Comparison for surface reconstruction on SceneNet with sparse sampling. + +![](images/ef143b81b98a003e766972c0f17faf211d6beda937435ac50c23240464fb1a3d.jpg) +Figure 6. Comparison for surface reconstruction on 3D Scene dataset with dense sampling. + +# 4.2.3D Scene Reconstruction + +Dataset and metric. We conduct our experiments on a synthetic dataset: SceneNet [14], and a real scanned dataset: 3D Scene dataset [42]. As scenes in SceneNet dataset are not watertight, and have many double-sided faces creating conflicting normals, we pre-process SceneNet to watertight using methods from [16]. We drop scenes with empty inner spaces after the watertighting process. We sample a constant density of points according to the area of faces (1000 points per $m^2$ for SceneNet and 10000 points per $m^2$ for 3D Scene dataset). For all the scene-level experiments, we ran + +domly sample 2 million points on the generated mesh and the ground truth mesh when estimating L1 CD, and we use $\tau = 0.025$ (2.5cm) for F-score. Since data is provided in a physically-meaningful scale, we use world coordinate (meters) for computing CD. Note that these two metrics are not always consistent as CD is more sensitive to outliers. For scene-level experiments, we directly optimize latent codes and decoders on the scenes, and we divide the whole space into $32 \times 32 \times 32$ regions. + +Quantitative comparison. The comparison results between LP-DIF and other state-of-the-art methods are shown in Table 4. LP-DIF achieves the best performance across all categories in terms of average L1 Chamfer Distance and F-score both in sparse (Scenenet) and dense (3D SceneNet dataset) sampling settings, which proves better representational power of our method. Compared with scenenet with sparse sampling setting, our method improves more on 3D scenenet dataset with dense sampling settings. + +Qualitative comparison. In Figure 5 and 6, we visually compared 3D surface reconstruction of scene dataset with other DIF methods, from which we find that LP-DIF reconstructs more geometry details and less missing parts than other method. + +# 4.3. Complex 3D Object Reconstruction + +Dataset and metric. For complex 3D object reconstruction, we use Thai Statue, obtained from the Stanford 3D Scanning Repository [18]. It is an intricate statue, which consists of 10 million polygons. Fine details of the statue are challenging to be captured with existing methods. We randomly sample 2 million points on the generated and the ground truth meshes when estimating L1 CD, and we use $\tau = 0.025$ for F-score. For complex 3D object, we directly optimize latent codes and decoders to fit the shape. For ACORN [24], we train using their official code and extract the reconstructed mesh. [24] is trained for several hours until max octants are reached. + +![](images/4078d4d3412b96f7d22e63117b357c42187b42b8375da44352c1e1623a59aa25.jpg) +Figure 7. Comparison for surface reconstruction on Thai statue. Our result is comparable with ACORN [24] with slightly better details. + +Quantitative comparison. The comparison results between LP-DIF and other state-of-the-art methods are shown in Table 5. LP-DIF achieves the best performance in terms + +of average L1 Chamfer Distance and F-score for complex 3D object reconstruction. + +Qualitative comparison. In Figure 1, we visually compare 3D surface reconstruction of Thai statue with other DIF methods, where we find that LP-DIF reconstructs much more fine geometry details than other methods. In Figure 7, we compare with ACORN [24]. Our result is comparable with ACORN with slightly better details. + +# 4.4. Ablation Study + +Network capacity and efficiency comparison. We have summarized the number of parameters used in NGLOD (LOD5) [36], LDIF [1], MDIF [5], LIG [17], and our method in Table 6. As in the table, different number of parameters are used and our method utilized the second least total number of parameters. We also tested the performance under the same total number of parameters in Table 7. As in the first two rows of the table, LDIF [1] and our method have the similar total number of parameters, where our method outperforms LDIF [1]. After that, we increase our MLP to 800-dimensional hidden layers to have the similar total number parameters with MDIF [5]. As in the 3-4 rows of the table, the performance of our ablation method is still better than MDIF [5], but is worse than our original decoders. The reason could be that the increased parameters of network makes the optimization of local latent code unstable. The performance of our coarse decoder is also shown in the last row for comparison. We have also compared the computation time on 8 shapes of ShapeNet in Table 8. It takes much more time for NGLOD [36] to train. For L-DIF and LP-DIF, we reported the time needed to reach the same accuracy level. It takes less time for LP-DIF than L-DIF. + +![](images/e5d5d84476b626846332cc7324cc1b553b59e8494581b437ba95eab2342942ad.jpg) +Figure 8. Comparison with random clustering. (a) Replacing the clustering process with random assigning each local region into clusters. (b) Clustering with regards to similarity leads to better performance. + +Ablation on modules. We also conduct a series of experiments on the effectiveness of our modules on Burghers of 3D scenenet dataset. Our baseline is implemented by removing pattern clustering and region re-weighting. First, we separate the whole space into different number of regions (each region has one code), and test the effect of our module under different settings. The results are shown in Table 9, where the baseline model performs better with more local regions and codes, however, more local codes occupy much more space. Our model with $7.63\mathrm{MB}$ local codes could have similar performance with the baseline + +
CategoryCD Mean ↓F-score ↑SceneCD Mean ↓F-score ↑
LIG [17]OursLIG [17]OursLIG [17]OursLIG [17]Ours
Bathroom0.008250.0063398.5699.66Burghers0.01220.003990.2599.67
Bedroom0.009780.0073096.4199.24Lounge0.01310.003185.4999.72
Office0.014520.0092993.9296.97CopyRoom0.01300.003484.6899.97
Livingroom0.011910.0098796.3998.65StoneWall0.01100.003189.1499.90
Kitchen0.009880.0082596.3698.55TotemPole0.01200.004189.3999.23
Mean0.010650.0081696.4098.67Mean0.01220.003587.7999.70
+ +Table 4. Surface reconstruction from sparse point cloud on SceneNet and dense point cloud on 3D SceneNet dataset in terms of mean L1 chamfer distance and F-score. + +
MethodsDeepSDF [28]LIG [17]LDIF baselineOurs
CD Mean ↓0.7400.6030.2110.176
F-score ↑1.313.621.863.6
+ +Table 5. Surface reconstruction comparison on Thai statue in terms of mean L1 chamfer distance and F-score. + +
Methods# Feature Param# Network ParamTotal # Param
LOD5 [36]101225282368510146213
L.DIF [5]524288460993985281
MDIF [5]440321835930118403333
LIG [17]131072227745358817
Ours53248 (coarse) + 2498563745 (coarse) + 463108769957
+ +Table 6. Network capacity comparison. + +
Methods#Feature Param#Inference ParamTotal # ParamCD (Airplane)↓CD (Bench)↓
L.DIF [5]5242884609939852810.0440.121
Ours303104 (53248 + 249856)466853 (3745 + 463108)7699570.0120.021
MDIF [5]4403218359301184033330.0280.052
Ours-abl-mdif303104 (53248 + 249856)17952293 (3745 + 17948548)182553970.01450.031
Ours-coarse532482689559370.0620.167
+ +Table 7. Ablation with similar total number of parameters. + +
MethodsStage1Stage 2Stage 3Total
NGLOD [36]---~4000s
LDIF baseline---165s (1.33s ×124epochs)
LP-DIF20s1s141s (2.43s ×58epochs)162s
+ +Table 8. Computation efficiency comparison. + +
Methods# of codescode sizeCD Mean ↓F-score ↑
Baseline-3232K7.63 MB0.0055796.78
Baseline-1282097K488 MB0.0038999.65
LP-DIF-3232K7.63 MB0.0039499.67
LP-DIF-1282097K488 MB0.0038799.64
+ +Table 9. Ablation study with different number of local codes. Result of the baseline method with different number of local codes are shown in the first two rows. Result of LP-DIF with different number of local codes are shown in the last two rows. Our method can achieve same level of accuracy with much less local codes. + +
MethodsCD Mean↓F-score ↑
Baseline0.0055796.78
LP-DIF w/o clustering0.0044699.52
LP-DIF w/o re-weighting0.0041999.16
LP-DIF0.0039499.67
+ +Table 10. Ablation study on components of our model in terms of mean L1 chamfer distance and F-score. + +method with 488 MB local codes. After that, we evaluate the effectiveness of our clustering module by replacing it with random assigning cluster indices. As in Figure 8 and + +Table 6, the performance is deteriorated with random clustering. The possible reason is that randomly separating local regions increases the deviation of some local regions from the cluster centers, causing them to fail in training. Next we evaluate the components of our model by removing them separately. We test two variations: (1) removing the clustering module and re-weight on the whole set of regions, and (2) removing the re-weighting module. The result is shown in Table 10 and Figure 9 (a) - (c), and we find that both modules are helpful for achieving good performance. At last, we test the difference between fixed density estimator and dynamic density estimator. As shown in Figure 9 (d) - (f), dynamic density estimator could reconstruct better geometry details than fixed one. + +![](images/15908933bc6671f5cbd63c4101fb11cf392e1f79d0f157fa5f7d625f635763de.jpg) +Figure 9. Ablation study on density-adaptive re-weighting. (a) Ours w/o density re-weighting. (b) Ours w/ density re-weighting. (c) Ground truth. (d) Ours w/o density estimator. (e) Ours w/ fixed density estimator. (f) Ours w/ dynamic density estimator. + +# 5. Conclusion + +In this paper, we present LP-DIF, a local pattern-specific deep implicit function for reconstructing highly detailed geometry. Compared with previous methods that treat all local regions equally using a single decoder, we regard a shape as clusters of local regions and mine local patterns with different decoders. This alleviates the difficulty of learning caused by diverse local regions. 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In Computer Vision-ECCV 2020: 16th European Conference, Glasgow, UK, August 23-28, 2020, Proceedings, Part III 16, pages 523-540. Springer, 2020. 1, 3, 6 +[30] Charles R Qi, Hao Su, Kaichun Mo, and Leonidas J Guibas. PointNet: Deep learning on point sets for 3D classification and segmentation. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 652-660, 2017. 1, 2 +[31] Charles R Qi, Li Yi, Hao Su, and Leonidas J Guibas. Point-net++: Deep hierarchical feature learning on point sets in a metric space. Advances in Neural Information Processing Systems, 2017. 1, 2 +[32] Christian Reiser, Songyou Peng, Yiyi Liao, and Andreas Geiger. Kilonerf: Speeding up neural radiance fields with thousands of tiny mlp's. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 14335-14345, 2021. 3 +[33] Vishwanath Saragadam, Jasper Tan, Guha Balakrishnan, Richard G Baraniuk, and Ashok Veeraraghavan. Miner: Multiscale implicit neural representation. In Computer Vision-ECCV 2022: 17th European Conference, Tel Aviv, Israel, October 23-27, 2022, Proceedings, Part XXIII, pages 318-333. Springer, 2022. 3 +[34] Yawar Siddiqui, Justus Thies, Fangchang Ma, Qi Shan, Matthias Nießner, and Angela Dai. RetrievalFuse: Neural 3D scene reconstruction with a database. International Conference on Computer Vision, 2021. 1 +[35] Vincent Sitzmann, Julien Martel, Alexander Bergman, David Lindell, and Gordon Wetzstein. Implicit neural representations with periodic activation functions. Advances in Neural Information Processing Systems, 33, 2020. 1, 3 +[36] Towaki Takikawa, Joey Litalien, Kangxue Yin, Karsten Kreis, Charles Loop, Derek Nowrouzezahrai, Alec Jacobson, Morgan McGuire, and Sanja Fidler. Neural geometric level of detail: Real-time rendering with implicit 3D shapes. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 11358-11367, 2021. 1, 3, 5, 6, 7, 8 + +[37] Matthew Tancik, Pratul P Srinivasan, Ben Mildenhall, Sara Fridovich-Keil, Nithin Raghavan, Utkarsh Singhal, Ravi Ramamoorthi, Jonathan T Barron, and Ren Ng. Fourier features let networks learn high frequency functions in low dimensional domains. Advances in Neural Information Processing Systems, 2020. 1, 3 +[38] Edgar Tretschk, Ayush Tewari, Vladislav Golyanik, Michael Zollhöfer, Carsten Stoll, and Christian Theobalt. Patchnets: Patch-based generalizable deep implicit 3D shape representations. In European Conference on Computer Vision, pages 293-309. Springer, 2020. 1, 3 +[39] Lior Yariv, Jiatao Gu, Yoni Kasten, and Yaron Lipman. Volume rendering of neural implicit surfaces. Advances in Neural Information Processing Systems, 34, 2021. 2, 3 +[40] Zerong Zheng, Tao Yu, Qionghai Dai, and Yebin Liu. Deep implicit templates for 3D shape representation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 1429-1439, 2021. 1 +[41] Junsheng Zhou, Baorui Ma, Yu-Shen Liu, Yi Fang, and Zhizhong Han. Learning consistency-aware unsigned distance functions progressively from raw point clouds. In Advances in Neural Information Processing Systems, 2022. 1 +[42] Qian-Yi Zhou and Vladlen Koltun. Dense scene reconstruction with points of interest. ACM Transactions on Graphics (ToG), 32(4):1-8, 2013. 6 \ No newline at end of file diff --git a/2023/LP-DIF_ Learning Local Pattern-Specific Deep Implicit Function for 3D Objects and Scenes/images.zip b/2023/LP-DIF_ Learning Local Pattern-Specific Deep Implicit Function for 3D Objects and Scenes/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..8c90abf403623b3776fefd47e8dd116f5b356ed8 --- /dev/null +++ b/2023/LP-DIF_ Learning Local Pattern-Specific Deep Implicit Function for 3D Objects and Scenes/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:1ba2d43beab6bd77cba5085dcb57696f1bbd562c87549f2a96a6e8f85e33061c +size 602743 diff --git a/2023/LP-DIF_ Learning Local Pattern-Specific Deep Implicit Function for 3D Objects and Scenes/layout.json b/2023/LP-DIF_ Learning Local Pattern-Specific Deep Implicit Function for 3D Objects and Scenes/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..b4eecd66e2db58ef07e8aba3b31b97dc49d02c99 --- /dev/null +++ b/2023/LP-DIF_ Learning Local Pattern-Specific Deep Implicit Function for 3D Objects and Scenes/layout.json @@ -0,0 +1,7521 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 50, + 135, + 527, + 170 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 135, + 527, + 170 + ], + "spans": [ + { + "bbox": [ + 50, + 135, + 527, + 170 + ], + "type": "text", + "content": "LP-DIF: Learning Local Pattern-specific Deep Implicit Function for 3D Objects and Scenes" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 78, + 191, + 496, + 207 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 78, + 191, + 496, + 207 + ], + "spans": [ + { + "bbox": [ + 78, + 191, + 496, + 207 + ], + "type": "text", + "content": "Meng Wang1 Yu-Shen Liu1* * Yue Gao1 Kanle Shi2 Yi Fang3 Zhizhong Han4" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 145, + 207, + 431, + 220 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 207, + 431, + 220 + ], + "spans": [ + { + "bbox": [ + 145, + 207, + 431, + 220 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 145, + 207, + 431, + 220 + ], + "type": "text", + "content": "School of Software, BNRist, Tsinghua University, Beijing, China" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 204, + 220, + 373, + 234 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 204, + 220, + 373, + 234 + ], + "spans": [ + { + "bbox": [ + 204, + 220, + 373, + 234 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 204, + 220, + 373, + 234 + ], + "type": "text", + "content": "Kuaishou Technology, Beijing, China" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 74, + 234, + 502, + 246 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 74, + 234, + 502, + 246 + ], + "spans": [ + { + "bbox": [ + 74, + 234, + 502, + 246 + ], + "type": "text", + "content": "3Center for Artificial Intelligence and Robotics, New York University Abu Dhabi, Abu Dhabi, UAE" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 129, + 246, + 447, + 261 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 129, + 246, + 447, + 261 + ], + "spans": [ + { + "bbox": [ + 129, + 246, + 447, + 261 + ], + "type": "inline_equation", + "content": "^{4}" + }, + { + "bbox": [ + 129, + 246, + 447, + 261 + ], + "type": "text", + "content": "Department of Computer Science, Wayne State University, Detroit, USA" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 167, + 263, + 406, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 167, + 263, + 406, + 275 + ], + "spans": [ + { + "bbox": [ + 167, + 263, + 406, + 275 + ], + "type": "text", + "content": "{meng_wang, gaoyue, liuyushen}@tsinghua.edu.cn" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 143, + 277, + 431, + 287 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 277, + 431, + 287 + ], + "spans": [ + { + "bbox": [ + 143, + 277, + 431, + 287 + ], + "type": "text", + "content": "shikanle@kuaishou.com yfang@nyu.edu h312h@wayne.edu" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 139, + 314, + 186, + 326 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 139, + 314, + 186, + 326 + ], + "spans": [ + { + "bbox": [ + 139, + 314, + 186, + 326 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 45, + 341, + 281, + 679 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 341, + 281, + 679 + ], + "spans": [ + { + "bbox": [ + 45, + 341, + 281, + 679 + ], + "type": "text", + "content": "Deep Implicit Function (DIF) has gained much popularity as an efficient 3D shape representation. To capture geometry details, current mainstream methods divide 3D shapes into local regions and then learn each one with a local latent code via a decoder. Such local methods can capture more local details due to less diversity among local regions than global shapes. Although the diversity of local regions has been decreased compared to global approaches, the diversity in different local regions still poses a challenge in learning an implicit function when treating all regions equally using only a single decoder. What is worse, these local regions often exhibit imbalanced distributions, where certain regions have significantly fewer observations. This leads that fine geometry details could not be preserved well. To solve this problem, we propose a novel Local Pattern-specific Implicit Function, named LP-DIF, to represent a shape with clusters of local regions and multiple decoders, where each decoder only focuses on one cluster of local regions which share a certain pattern. Specifically, we first extract local codes for all regions, and then cluster them into multiple groups in the latent space, where similar regions sharing a common pattern fall into one group. After that, we train multiple decoders for mining local patterns of different groups, which simplifies the learning of fine geometric details by reducing the diversity of local regions seen by each decoder. To further alleviate the data-imbalance problem, we introduce a region re-weighting module to each pattern-specific decoder using a kernel density estimator, which dynamically re-weights the regions during learn" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 297, + 315, + 531, + 374 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 315, + 531, + 374 + ], + "spans": [ + { + "bbox": [ + 297, + 315, + 531, + 374 + ], + "type": "text", + "content": "ing. Our LP-DIF can restore more geometry details, and thus improve the quality of 3D reconstruction. Experiments demonstrate that our method can achieve the state-of-the-art performance over previous methods. Code is available at https://github.com/gtyxyz/lpdfif." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 298, + 395, + 375, + 408 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 395, + 375, + 408 + ], + "spans": [ + { + "bbox": [ + 298, + 395, + 375, + 408 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 296, + 415, + 531, + 554 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 415, + 531, + 554 + ], + "spans": [ + { + "bbox": [ + 296, + 415, + 531, + 554 + ], + "type": "text", + "content": "Representing 3D shapes is a fundamental problem for many applications in 3D computer vision. Recently, Deep Implicit Function (DIF) [4,22,23,25,28,41] has gained popularity for efficiently learning the representation of 3D objects and scenes. In contrast to directly learning explicit 3D representations [15,30,31] (voxels, point clouds or meshes), DIF aims to train a neural network to learn the binary occupancy function [25] or signed distance function (SDF) [28], as given a query location and an input latent code. Such kind of representation is continuous with arbitrary precision and can handle various topology, which has achieved the state-of-the-art results in several shape reconstruction tasks." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 296, + 555, + 532, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 555, + 532, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 555, + 532, + 730 + ], + "type": "text", + "content": "Existing DIF methods can be roughly classified into two categories: global and local approaches. Most of the early methods [4, 9, 20, 21, 25, 27-29, 35, 37, 40] fall into global approaches. These methods take advantage of one latent code and a single decoder to represent the whole shape. Global approaches often suffer from long training time and low reconstruction accuracy due to the limited capacity of capturing local geometry details. More recently, local approaches [1, 3, 5, 6, 10-12, 17, 19, 34, 36, 38] divide 3D shapes (often divide by 3D grids) into local regions and then learn each one with a local latent code via a decoder, where the decoder shares the geometric similarities among different local regions. Although such local approaches can capture some local details, a large diversity of different local regions still increase the difficulty of learning an implicit function" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 77, + 42, + 119, + 72 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 42, + 119, + 72 + ], + "spans": [ + { + "bbox": [ + 77, + 42, + 119, + 72 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 150, + 41, + 471, + 74 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 150, + 41, + 471, + 74 + ], + "spans": [ + { + "bbox": [ + 150, + 41, + 471, + 74 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 45, + 691, + 280, + 730 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 691, + 280, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 691, + 280, + 730 + ], + "type": "text", + "content": "*The corresponding author is Yu-Shen Liu. This work was supported by National Key R&D Program of China (2022YFC3800600), the National Natural Science Foundation of China (62272263, 62072268), and in part by Tsinghua-Kuaishou Institute of Future Media Data." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 276, + 746, + 301, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 276, + 746, + 301, + 756 + ], + "spans": [ + { + "bbox": [ + 276, + 746, + 301, + 756 + ], + "type": "text", + "content": "21856" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 96, + 106, + 478, + 277 + ], + "blocks": [ + { + "bbox": [ + 96, + 106, + 478, + 277 + ], + "lines": [ + { + "bbox": [ + 96, + 106, + 478, + 277 + ], + "spans": [ + { + "bbox": [ + 96, + 106, + 478, + 277 + ], + "type": "image", + "image_path": "146c79253fa2fb39027cc61808d867306d2668a7062444acaf3e2e8ffca46335.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 118, + 278, + 161, + 286 + ], + "lines": [ + { + "bbox": [ + 118, + 278, + 161, + 286 + ], + "spans": [ + { + "bbox": [ + 118, + 278, + 161, + 286 + ], + "type": "text", + "content": "(a) Global DIF" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 213, + 278, + 254, + 286 + ], + "lines": [ + { + "bbox": [ + 213, + 278, + 254, + 286 + ], + "spans": [ + { + "bbox": [ + 213, + 278, + 254, + 286 + ], + "type": "text", + "content": "(b) Local DIF" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 310, + 278, + 334, + 286 + ], + "lines": [ + { + "bbox": [ + 310, + 278, + 334, + 286 + ], + "spans": [ + { + "bbox": [ + 310, + 278, + 334, + 286 + ], + "type": "text", + "content": "(c) Ours" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 391, + 278, + 431, + 286 + ], + "lines": [ + { + "bbox": [ + 391, + 278, + 431, + 286 + ], + "spans": [ + { + "bbox": [ + 391, + 278, + 431, + 286 + ], + "type": "text", + "content": "(d) Reference" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 45, + 288, + 531, + 332 + ], + "lines": [ + { + "bbox": [ + 45, + 288, + 531, + 332 + ], + "spans": [ + { + "bbox": [ + 45, + 288, + 531, + 332 + ], + "type": "text", + "content": "Figure 1. Visual comparison of 3D shape surface reconstruction. Compared with global DIF (e.g. [28]) and local DIF (e.g. [1]), our method can reconstruct the shape with fine-grained geometric details. Compared with previous methods that treat all local regions equally using a single decoder, we regard a shape as clusters of local regions and mine local patterns with different decoders. This alleviates the difficulty of learning caused by diverse local regions." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 351, + 279, + 410 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 351, + 279, + 410 + ], + "spans": [ + { + "bbox": [ + 45, + 351, + 279, + 410 + ], + "type": "text", + "content": "when treating all regions equally using only a single decoder. In addition, these local regions often exhibit imbalanced distributions, where certain regions have significantly fewer observations, especially in scenes. As a result, fine geometry details of shapes could not be captured well." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 45, + 410, + 279, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 410, + 279, + 653 + ], + "spans": [ + { + "bbox": [ + 45, + 410, + 279, + 653 + ], + "type": "text", + "content": "To address the above-mentioned problems, we propose a novel Local Pattern-specific Implicit Function, named LP-DIF, for learning 3D shape representation using clusters of local regions with multiple decoders, where each decoder only represents one cluster of local regions which share a certain pattern (geometric features such as facing direction, number of faces, relative positions to the region center). Specifically, we first extract the local latent codes for all local regions divided by 3D grids, and then cluster them into multiple groups in the latent space, where similar regions sharing a common pattern fall into one group. After that, we train a separate pattern-specific decoder for each group of regions, which reduces data-imbalance among different patterns of regions and simplifies the learning of fine geometric details of 3D structures by limiting the diversity of regions seen to each decoder. To further alleviate the region-imbalance problem, we introduce a region reweighting module to each pattern-specific decoder by kernel density estimator, which dynamically re-weights the regions during learning. Our main contributions can be summarized as follows." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 57, + 660, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 660, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 57, + 660, + 279, + 730 + ], + "type": "text", + "content": "- We propose a novel LP-DIF to learn local pattern-specific deep implicit function of 3D shapes for reconstructing highly detailed geometry. Compared with previous methods that treat all local regions equally using a single decoder, we regard a shape as clusters of local regions and mine local patterns with different de" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 315, + 351, + 530, + 375 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 351, + 530, + 375 + ], + "spans": [ + { + "bbox": [ + 315, + 351, + 530, + 375 + ], + "type": "text", + "content": "coders. This alleviates the difficulty of learning caused by diverse local regions." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 308, + 382, + 530, + 494 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 308, + 382, + 530, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 382, + 530, + 441 + ], + "spans": [ + { + "bbox": [ + 308, + 382, + 530, + 441 + ], + "type": "text", + "content": "- We introduce a dynamic region re-weighting module, which could provide more focus on less common regions to tackle the data-imbalance problem in each pattern decoder. As a result, the regions with less appearances can be captured more accurately." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 308, + 447, + 530, + 494 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 447, + 530, + 494 + ], + "spans": [ + { + "bbox": [ + 308, + 447, + 530, + 494 + ], + "type": "text", + "content": "- Our method could be applied in multiple objects, single complex objects and large scale of scenes. We improve the state-of-the-art accuracy in surface reconstruction under various benchmarks." + } + ] + } + ], + "index": 11 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 296, + 502, + 530, + 571 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 502, + 530, + 571 + ], + "spans": [ + { + "bbox": [ + 296, + 502, + 530, + 571 + ], + "type": "text", + "content": "Figure 2 illustrates the main differences between DIF, local DIF and our method. For DIF approaches, one global code and a decoder are used for the whole shape. For Local DIF methods, multiple local codes and a shared decoder are used. For our method, multiple clusters of regions are learned with different decoders." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 297, + 581, + 381, + 594 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 581, + 381, + 594 + ], + "spans": [ + { + "bbox": [ + 297, + 581, + 381, + 594 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 296, + 602, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 602, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 602, + 530, + 730 + ], + "type": "text", + "content": "In computer vision and graphics, there are two categories of shape representations: explicit representation and implicit representation. Explicit geometric representations [15, 30, 31] such as point clouds, voxels and triangular meshes have been widely used for representing geometries for their simplicity and flexibility. More recently, deep implicit representations [4, 25, 28, 39] have been proposed in the context of shape representation, where the implicit surfaces of geometries are represented as the zero-set of spatial functions with fully connected neural networks. Such kind of representation is continuous with arbitrary precision and" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 276, + 746, + 300, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 276, + 746, + 300, + 756 + ], + "spans": [ + { + "bbox": [ + 276, + 746, + 300, + 756 + ], + "type": "text", + "content": "21857" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 96, + 103, + 483, + 282 + ], + "blocks": [ + { + "bbox": [ + 96, + 103, + 483, + 282 + ], + "lines": [ + { + "bbox": [ + 96, + 103, + 483, + 282 + ], + "spans": [ + { + "bbox": [ + 96, + 103, + 483, + 282 + ], + "type": "image", + "image_path": "704e3af13c975e06d5bac373d9a0761951586ceee3a441a67355f23bd5b2cb5a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 287, + 533, + 352 + ], + "lines": [ + { + "bbox": [ + 45, + 287, + 533, + 352 + ], + "spans": [ + { + "bbox": [ + 45, + 287, + 533, + 352 + ], + "type": "text", + "content": "Figure 2. Comparison between DIF, local DIF and our method. (a) DIF methods leverage one global code and one decoder, often suffer from long training speed and low reconstruction quality due to the limited capacity of capturing local geometry details. (b) Local DIF methods use multiple local codes and one shared decoder, a large diversity of different local regions still increase the difficulty of learning an implicit function when treating all regions equally using only a single decoder. (c) Our method, LP-DIF, for representing a shape with some clusters of local regions and multiple decoders, where each decoder only represents one cluster of local regions which share a certain pattern. (d) Visualization of the clustered local regions." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 373, + 279, + 419 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 373, + 279, + 419 + ], + "spans": [ + { + "bbox": [ + 45, + 373, + 279, + 419 + ], + "type": "text", + "content": "can handle different topology structure, which has achieved the state-of-the-art results in several shape reconstruction task. Implicit representations can be categorized into global and local approaches." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 423, + 281, + 667 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 423, + 281, + 667 + ], + "spans": [ + { + "bbox": [ + 45, + 423, + 281, + 667 + ], + "type": "text", + "content": "Global Deep Implicit Shape Representation. In recent years, implicit functions have been introduced into neural networks [25, 28] and show promising results. Early approaches learn one latent code and one single global implicit network to represent the whole shape. For example, DeepSDF [28] learned an implicit function where the network output represents the signed distance of the input point to its nearest surface, where zero-set of the learned function implicitly represents the surface of the shape. Other approaches [25, 29] defined the implicit functions as 3D occupancy probability functions and turned shape representation into a point classification problem. Following these methods, [35, 37] improved the expressiveness of the implicit functions by introducing high frequency signals with periodic activation. [39] proposed to represent the volume density as an implicit function of the signed distance in neural volume rendering for high-quality novel view generation. However, these methods suffer from long training time and low reconstruction accuracy for high resolution data due to the limited capacity of decoder to capture local geometry details." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 671, + 280, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 671, + 280, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 671, + 280, + 730 + ], + "type": "text", + "content": "Local Deep Implicit Shape Representation. To capture more geometry details, current mainstream methods divide 3D shapes into many local regions and then learn each one with a local latent code via a decoder. Some recent works [1, 29] proposed to divide the whole 3D shape" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 296, + 373, + 533, + 724 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 373, + 533, + 724 + ], + "spans": [ + { + "bbox": [ + 296, + 373, + 533, + 724 + ], + "type": "text", + "content": "uniformly into 3D grids, where they either assign each local grid with a latent code or trilinearly interpolate local latent codes based on querying location. In LIG [17], this idea was applied to 3D scenes. NGLOD [36] leveraged sparse octree instead of uniform grids to increase efficiency. ACORN [24] proposed to adaptively optimize the coordinate decomposition to achieve higher accuracy in large-scale scenes. DCC-DIF [19] optimized the local latent code learning by introducing dynamic grid positions. IFNet [6] utilized multiple level of latent codes in a hierarchical way. LPI [3] divided the global shape into multiple local parts in latent space to allow easier shape parts learning and blending. PatchNet [38] was proposed to divide a shape into local patches with no fixed structure. Points2surf [10] incorporated local information surrounding each point, but it typically takes a lot of time for point-wise distance calculation. Although such local methods can capture some local details, a large diversity of different local regions still poses an challenge for learning an implicit function when treating all regions equally using only a single decoder. In addition, these local regions often exhibit imbalanced distributions, where certain regions have significantly fewer observations. As a result, fine geometry details could not be captured well. Several methods [8, 13] have been proposed to learn multiple decoders for point deformations, however, their methods cannot be applied in learning implicit representations for shapes. MDIF [5, 33] used multiple levels of decoders in a hierarchical way, however, it did not consider the relationship between local regions. In novel view synthesizing, KiloNeRF [32] utilized thousands of tiny MLPs to represent" + } + ] + } + ], + "index": 5 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 276, + 746, + 301, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 276, + 746, + 301, + 756 + ], + "spans": [ + { + "bbox": [ + 276, + 746, + 301, + 756 + ], + "type": "text", + "content": "21858" + } + ] + } + ], + "index": 6 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 45, + 106, + 281, + 188 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 106, + 281, + 188 + ], + "spans": [ + { + "bbox": [ + 45, + 106, + 281, + 188 + ], + "type": "text", + "content": "different parts of the scenes. The simple and effective way to introduce multiple decoders is to assign each local region with a decoder, however, it is normally not feasible due to time and space constraint and the prior information of the local regions could not be preserved. In contrast, we introduce clustering for the local regions as a trade-off between reconstruction accuracy and efficiency." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 197, + 101, + 209 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 197, + 101, + 209 + ], + "spans": [ + { + "bbox": [ + 46, + 197, + 101, + 209 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 45, + 216, + 281, + 367 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 216, + 281, + 367 + ], + "spans": [ + { + "bbox": [ + 45, + 216, + 281, + 367 + ], + "type": "text", + "content": "Given " + }, + { + "bbox": [ + 45, + 216, + 281, + 367 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 45, + 216, + 281, + 367 + ], + "type": "text", + "content": " discrete points " + }, + { + "bbox": [ + 45, + 216, + 281, + 367 + ], + "type": "inline_equation", + "content": "\\mathbf{X} = \\{\\mathbf{x}_k\\}" + }, + { + "bbox": [ + 45, + 216, + 281, + 367 + ], + "type": "text", + "content": " and their signed distances " + }, + { + "bbox": [ + 45, + 216, + 281, + 367 + ], + "type": "inline_equation", + "content": "\\mathbf{S} = \\{\\mathbf{s}_k\\}" + }, + { + "bbox": [ + 45, + 216, + 281, + 367 + ], + "type": "text", + "content": " from a 3D surface, our goal is to regress a continuous function that outputs the closest signed distance to the 3D surface given a spatial point " + }, + { + "bbox": [ + 45, + 216, + 281, + 367 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 45, + 216, + 281, + 367 + ], + "type": "text", + "content": ". To achieve this goal, we propose to learn a local pattern-specific DIF. The architecture of LP-DIF and differences between our LP-DIF and other methods are illustrated in Figure 2. In this section, we first introduce latent embedding learning and local region feature extraction in Sec. 3.1. Then we describe our pattern clustering module in Sec. 3.2. After that we present our pattern decoder with density adaptive re-weighting in Sec. 3.3. At last, we illustrate our training process in Sec. 3.4." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 374, + 279, + 387 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 374, + 279, + 387 + ], + "spans": [ + { + "bbox": [ + 45, + 374, + 279, + 387 + ], + "type": "text", + "content": "3.1. Learning Latent Embedding for Local Regions" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 393, + 279, + 486 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 393, + 279, + 486 + ], + "spans": [ + { + "bbox": [ + 45, + 393, + 279, + 486 + ], + "type": "text", + "content": "At the beginning, we choose to train a local DIF network [1, 17] to learn latent embedding for local regions to extract coarse local features for clustering. Local DIF [1, 17] is a special category of DIF, which is defined as a signed distance function " + }, + { + "bbox": [ + 45, + 393, + 279, + 486 + ], + "type": "inline_equation", + "content": "f(\\mathbf{x}, \\mathbf{z})" + }, + { + "bbox": [ + 45, + 393, + 279, + 486 + ], + "type": "text", + "content": " modeled with Multilayer Perceptrons (MLP), mapping each query point " + }, + { + "bbox": [ + 45, + 393, + 279, + 486 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 45, + 393, + 279, + 486 + ], + "type": "text", + "content": " near a surface to the signed distance domain continuously with condition code " + }, + { + "bbox": [ + 45, + 393, + 279, + 486 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 45, + 393, + 279, + 486 + ], + "type": "text", + "content": ". A shape " + }, + { + "bbox": [ + 45, + 393, + 279, + 486 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 45, + 393, + 279, + 486 + ], + "type": "text", + "content": " is defined as the zero level set of " + }, + { + "bbox": [ + 45, + 393, + 279, + 486 + ], + "type": "inline_equation", + "content": "f(\\mathbf{x}, \\mathbf{z})" + }, + { + "bbox": [ + 45, + 393, + 279, + 486 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 103, + 495, + 279, + 510 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 103, + 495, + 279, + 510 + ], + "spans": [ + { + "bbox": [ + 103, + 495, + 279, + 510 + ], + "type": "interline_equation", + "content": "\\mathcal {S} = \\left\\{\\mathbf {x} \\in \\mathbb {R} ^ {3} \\mid f _ {\\theta} (\\mathbf {x}, \\mathbf {z}) = 0 \\right\\}, \\tag {1}", + "image_path": "3786bde4927125a38273e8b938df6cfb16b2c456ebf54d48f2ff3b32932ecd43.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 513, + 279, + 607 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 513, + 279, + 607 + ], + "spans": [ + { + "bbox": [ + 45, + 513, + 279, + 607 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 45, + 513, + 279, + 607 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 45, + 513, + 279, + 607 + ], + "type": "text", + "content": " is the parameter of the MLP. To be able to represent multiple shapes in the same time, the condition " + }, + { + "bbox": [ + 45, + 513, + 279, + 607 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 45, + 513, + 279, + 607 + ], + "type": "text", + "content": " is optimized for each shape, and the parameter " + }, + { + "bbox": [ + 45, + 513, + 279, + 607 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 45, + 513, + 279, + 607 + ], + "type": "text", + "content": " is shared for all the shapes. Local DIF is defined on partitioned space of shape " + }, + { + "bbox": [ + 45, + 513, + 279, + 607 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 45, + 513, + 279, + 607 + ], + "type": "text", + "content": ". A normalized 3D space is usually partitioned into " + }, + { + "bbox": [ + 45, + 513, + 279, + 607 + ], + "type": "inline_equation", + "content": "d\\times d\\times d" + }, + { + "bbox": [ + 45, + 513, + 279, + 607 + ], + "type": "text", + "content": " regions " + }, + { + "bbox": [ + 45, + 513, + 279, + 607 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{B}_i\\} \\subseteq \\mathbb{R}^3" + }, + { + "bbox": [ + 45, + 513, + 279, + 607 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 45, + 513, + 279, + 607 + ], + "type": "inline_equation", + "content": "i = 0\\dots N - 1" + }, + { + "bbox": [ + 45, + 513, + 279, + 607 + ], + "type": "text", + "content": ". All the regions have their separate codes " + }, + { + "bbox": [ + 45, + 513, + 279, + 607 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_i" + }, + { + "bbox": [ + 45, + 513, + 279, + 607 + ], + "type": "text", + "content": ", sharing the same parameter " + }, + { + "bbox": [ + 45, + 513, + 279, + 607 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 45, + 513, + 279, + 607 + ], + "type": "text", + "content": ". The entire surface is defined as:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 86, + 612, + 279, + 629 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 612, + 279, + 629 + ], + "spans": [ + { + "bbox": [ + 86, + 612, + 279, + 629 + ], + "type": "interline_equation", + "content": "\\mathcal {S} = \\left\\{\\mathbf {x} \\in \\mathbb {R} ^ {3} \\mid \\sum f _ {\\theta} (T (\\mathbf {x}), \\mathbf {z} _ {i}) = 0 \\right\\}, \\tag {2}", + "image_path": "445d933ff926e7f29b627d922f8aa49c48d2ae2e0df57b3f956cb829a2eb66a6.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 45, + 636, + 279, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 636, + 279, + 694 + ], + "spans": [ + { + "bbox": [ + 45, + 636, + 279, + 694 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 45, + 636, + 279, + 694 + ], + "type": "inline_equation", + "content": "T(\\mathbf{x})" + }, + { + "bbox": [ + 45, + 636, + 279, + 694 + ], + "type": "text", + "content": " is the re-centering function of " + }, + { + "bbox": [ + 45, + 636, + 279, + 694 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 45, + 636, + 279, + 694 + ], + "type": "text", + "content": ", which transforms the points in each region to their local coordinates. After training of local DIF, all local regions have their codes " + }, + { + "bbox": [ + 45, + 636, + 279, + 694 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_i" + }, + { + "bbox": [ + 45, + 636, + 279, + 694 + ], + "type": "text", + "content": ", which serve as the local features of corresponding regions." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 45, + 694, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 694, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 694, + 279, + 730 + ], + "type": "text", + "content": "Code constraint. For DIF methods, it is important to constrain the latent codes of all the regions during training. Traditional Local DIF methods [1, 28] use L2 norm loss on the" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 296, + 106, + 531, + 209 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 106, + 531, + 209 + ], + "spans": [ + { + "bbox": [ + 296, + 106, + 531, + 209 + ], + "type": "text", + "content": "learned latent codes. However, in our method, we found that L2 norm loss could lead to latent codes being spread randomly in space, which is not good for subsequent clustering and latent code learning. Therefore, we constrain all local latent codes to be distributed within a hyper-sphere. The intuition is to process the latent codes in a way similar to normalizing them before entering the network. We update " + }, + { + "bbox": [ + 296, + 106, + 531, + 209 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 296, + 106, + 531, + 209 + ], + "type": "text", + "content": " according to Eq. (3) after every step of learning of " + }, + { + "bbox": [ + 296, + 106, + 531, + 209 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 296, + 106, + 531, + 209 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 355, + 219, + 530, + 247 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 355, + 219, + 530, + 247 + ], + "spans": [ + { + "bbox": [ + 355, + 219, + 530, + 247 + ], + "type": "interline_equation", + "content": "\\mathbf {z} _ {i} = \\left\\{ \\begin{array}{c c} \\mathbf {z} _ {i} & i f \\quad | | \\mathbf {z} _ {i} | | \\leq 1 \\\\ \\frac {\\mathbf {z} _ {i}}{| | \\mathbf {z} _ {i} | |} & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {3}", + "image_path": "2814d53d64c3f43f7f28a348996daf6000f23d4b9d6170085b371eabe3077775.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 297, + 252, + 405, + 265 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 252, + 405, + 265 + ], + "spans": [ + { + "bbox": [ + 297, + 252, + 405, + 265 + ], + "type": "text", + "content": "3.2. Pattern Clustering" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 296, + 270, + 531, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 270, + 531, + 468 + ], + "spans": [ + { + "bbox": [ + 296, + 270, + 531, + 468 + ], + "type": "text", + "content": "After training of the local DIF, each region from the whole set of shapes will be encoded by the condition " + }, + { + "bbox": [ + 296, + 270, + 531, + 468 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{\\mathrm{ij}}" + }, + { + "bbox": [ + 296, + 270, + 531, + 468 + ], + "type": "text", + "content": " for region " + }, + { + "bbox": [ + 296, + 270, + 531, + 468 + ], + "type": "inline_equation", + "content": "\\mathbf{B}_i" + }, + { + "bbox": [ + 296, + 270, + 531, + 468 + ], + "type": "text", + "content": " and shape " + }, + { + "bbox": [ + 296, + 270, + 531, + 468 + ], + "type": "inline_equation", + "content": "S_{j}, j = 0\\dots M - 1" + }, + { + "bbox": [ + 296, + 270, + 531, + 468 + ], + "type": "text", + "content": ". A shape normally consists of many empty or near-empty regions. To alleviate the influence of these regions, we first remove regions with SDF positive rate (the percentage of positive SDF samples within one local region) out of [0.01, 0.99]. The intuition is that if one region has almost all SDF samples to be positive or negative, this region will be far away from any shape surfaces and need no training. After learning of local DIF, there are regions " + }, + { + "bbox": [ + 296, + 270, + 531, + 468 + ], + "type": "inline_equation", + "content": "\\mathbf{B}_i" + }, + { + "bbox": [ + 296, + 270, + 531, + 468 + ], + "type": "text", + "content": " that are learned well with low reconstruction errors, we remove these easy-to-learn regions with error threshold " + }, + { + "bbox": [ + 296, + 270, + 531, + 468 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 296, + 270, + 531, + 468 + ], + "type": "text", + "content": ". The remaining regions are aggregated into " + }, + { + "bbox": [ + 296, + 270, + 531, + 468 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 296, + 270, + 531, + 468 + ], + "type": "text", + "content": " clusters by finding the cluster center " + }, + { + "bbox": [ + 296, + 270, + 531, + 468 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_k" + }, + { + "bbox": [ + 296, + 270, + 531, + 468 + ], + "type": "text", + "content": " of their condition codes with K-means by optimizing 4. We empirically select " + }, + { + "bbox": [ + 296, + 270, + 531, + 468 + ], + "type": "inline_equation", + "content": "P = 4" + }, + { + "bbox": [ + 296, + 270, + 531, + 468 + ], + "type": "text", + "content": " to balance between training speed and accuracy. The clustered local regions are visualized in Figure 2 (d)." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 348, + 476, + 530, + 510 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 348, + 476, + 530, + 510 + ], + "spans": [ + { + "bbox": [ + 348, + 476, + 530, + 510 + ], + "type": "interline_equation", + "content": "\\underset {c _ {k}} {\\operatorname {a r g m i n}} \\sum_ {k = 0} ^ {P} \\sum_ {i = 0} ^ {N} \\sum_ {j = 0} ^ {M} \\left| \\left| \\mathbf {z} _ {\\mathbf {i j}} - \\mathbf {c} _ {\\mathbf {k}} \\right| \\right| ^ {2}. \\tag {4}", + "image_path": "d6cc577ddaa41a15f69ee22750afbb6837e388f24773d670a56015f403e66189.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 296, + 517, + 531, + 623 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 517, + 531, + 623 + ], + "spans": [ + { + "bbox": [ + 296, + 517, + 531, + 623 + ], + "type": "text", + "content": "Region border consistency. We found that the division of shape and clustering lead to inconsistent surface estimates near the boundaries of local regions. To alleviate this problem, we utilize overlap between close local regions. The " + }, + { + "bbox": [ + 296, + 517, + 531, + 623 + ], + "type": "inline_equation", + "content": "f_{\\theta}(T(\\mathbf{x}, \\mathbf{z}_i))" + }, + { + "bbox": [ + 296, + 517, + 531, + 623 + ], + "type": "text", + "content": " near the boundaries (distance less than 0.05) will be averaged by the nearby local regions. The region border consistency is a post-processing procedure. Local regions from all clusters are first processed together back to a whole shape according to their spatial locations." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 297, + 630, + 395, + 642 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 630, + 395, + 642 + ], + "spans": [ + { + "bbox": [ + 297, + 630, + 395, + 642 + ], + "type": "text", + "content": "3.3. Pattern Decoder" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 296, + 648, + 530, + 729 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 648, + 530, + 729 + ], + "spans": [ + { + "bbox": [ + 296, + 648, + 530, + 729 + ], + "type": "text", + "content": "We have multiple pattern decoders to cover each cluster. The structure of each pattern decoder consists of 9-layer MLP and a skip connection. Specifically, local code and query point coordinate are concatenated and fed into MLP, and point coordinate is concatenated again after 4 layers. The output of the network is signed distance to the nearest surface." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 276, + 746, + 301, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 276, + 746, + 301, + 756 + ], + "spans": [ + { + "bbox": [ + 276, + 746, + 301, + 756 + ], + "type": "text", + "content": "21859" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 79, + 107, + 244, + 158 + ], + "blocks": [ + { + "bbox": [ + 79, + 107, + 244, + 158 + ], + "lines": [ + { + "bbox": [ + 79, + 107, + 244, + 158 + ], + "spans": [ + { + "bbox": [ + 79, + 107, + 244, + 158 + ], + "type": "image", + "image_path": "1b87e56e070a0957217c86724bf7f0ff7638d4c5c89329c13395336fe3538719.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 159, + 280, + 213 + ], + "lines": [ + { + "bbox": [ + 45, + 159, + 280, + 213 + ], + "spans": [ + { + "bbox": [ + 45, + 159, + 280, + 213 + ], + "type": "text", + "content": "Figure 3. Pattern decoder with density-adaptive re-weighting. To further alleviate the region-imbalance problem, we introduce a region re-weighting module to each pattern-specific decoder by kernel density estimator, which dynamically re-weights the regions during learning." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 230, + 279, + 394 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 230, + 279, + 394 + ], + "spans": [ + { + "bbox": [ + 45, + 230, + 279, + 394 + ], + "type": "text", + "content": "Density-adaptive re-weighting. Among the learned local codes, certain regions may have less appearances than others, and therefore they are usually neglected by the decoder. To recover more details, it is important to focus more on these regions. First we estimate the space density " + }, + { + "bbox": [ + 45, + 230, + 279, + 394 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 45, + 230, + 279, + 394 + ], + "type": "text", + "content": " of local codes based on their density distributions using kernel density estimation. Gaussian kernel is selected with bandwidth " + }, + { + "bbox": [ + 45, + 230, + 279, + 394 + ], + "type": "inline_equation", + "content": "h = 0.35" + }, + { + "bbox": [ + 45, + 230, + 279, + 394 + ], + "type": "text", + "content": ". Now we can re-weight region " + }, + { + "bbox": [ + 45, + 230, + 279, + 394 + ], + "type": "inline_equation", + "content": "\\mathbf{B}_i" + }, + { + "bbox": [ + 45, + 230, + 279, + 394 + ], + "type": "text", + "content": " with weight " + }, + { + "bbox": [ + 45, + 230, + 279, + 394 + ], + "type": "inline_equation", + "content": "\\omega_i = \\frac{1}{D}" + }, + { + "bbox": [ + 45, + 230, + 279, + 394 + ], + "type": "text", + "content": " during loss calculation. There are two ways of re-weighting the regions, fixed and dynamic. In fixed way, we only update the weight once with pre-extracted local codes. In the dynamic way, the re-weighting is applied every time after local codes being updated by the pattern decoder." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 399, + 108, + 411 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 399, + 108, + 411 + ], + "spans": [ + { + "bbox": [ + 45, + 399, + 108, + 411 + ], + "type": "text", + "content": "3.4. Training" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 416, + 279, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 416, + 279, + 533 + ], + "spans": [ + { + "bbox": [ + 45, + 416, + 279, + 533 + ], + "type": "text", + "content": "Our LP-DIF is trained in three stages. In the first stage, we extract the features from local regions by learning a coarse local DIF. In the second stage, we cluster the local regions based on their local features. At last, we train multiple pattern decoders on clustered regions. Note that for each pattern decoder, we use simple decoders so we have similar total number of decoder parameters with local DIF. During training, we optimize decoders and latent codes, while during testing, like other auto-decoder methods, we fix all decoders and only optimize latent codes." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 45, + 533, + 279, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 533, + 279, + 602 + ], + "spans": [ + { + "bbox": [ + 45, + 533, + 279, + 602 + ], + "type": "text", + "content": "Point sampling. We sample data pairs " + }, + { + "bbox": [ + 45, + 533, + 279, + 602 + ], + "type": "inline_equation", + "content": "(\\mathbf{x}_k, \\mathbf{s}_k)" + }, + { + "bbox": [ + 45, + 533, + 279, + 602 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 45, + 533, + 279, + 602 + ], + "type": "inline_equation", + "content": "S_j" + }, + { + "bbox": [ + 45, + 533, + 279, + 602 + ], + "type": "text", + "content": " as supervision. " + }, + { + "bbox": [ + 45, + 533, + 279, + 602 + ], + "type": "inline_equation", + "content": "S_j" + }, + { + "bbox": [ + 45, + 533, + 279, + 602 + ], + "type": "text", + "content": " is a mesh or point cloud with normals " + }, + { + "bbox": [ + 45, + 533, + 279, + 602 + ], + "type": "inline_equation", + "content": "\\mathbf{n}_k" + }, + { + "bbox": [ + 45, + 533, + 279, + 602 + ], + "type": "text", + "content": ". First we sample points along normal directions with normal distribution " + }, + { + "bbox": [ + 45, + 533, + 279, + 602 + ], + "type": "inline_equation", + "content": "N(0, \\theta)" + }, + { + "bbox": [ + 45, + 533, + 279, + 602 + ], + "type": "text", + "content": ". Then we sample random points " + }, + { + "bbox": [ + 45, + 533, + 279, + 602 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{x}_k\\}" + }, + { + "bbox": [ + 45, + 533, + 279, + 602 + ], + "type": "text", + "content": " and calculate their signed distances " + }, + { + "bbox": [ + 45, + 533, + 279, + 602 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{s}_k\\}" + }, + { + "bbox": [ + 45, + 533, + 279, + 602 + ], + "type": "text", + "content": " based on the closest distances." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 603, + 278, + 627 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 603, + 278, + 627 + ], + "spans": [ + { + "bbox": [ + 45, + 603, + 278, + 627 + ], + "type": "text", + "content": "Smooth L1 loss. To increase the weight in regions with larger errors, we introduce smooth L1 loss [26], defined by" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 49, + 631, + 279, + 667 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 631, + 279, + 667 + ], + "spans": [ + { + "bbox": [ + 49, + 631, + 279, + 667 + ], + "type": "interline_equation", + "content": "L _ {k} ^ {\\text {s d f}} = \\left\\{ \\begin{array}{c c} \\frac {1}{2} \\left(f _ {\\theta} \\left(\\mathbf {x} _ {\\mathbf {k}}\\right) - \\mathbf {s} _ {\\mathbf {k}}\\right) ^ {2} & i f | \\left(f _ {\\theta} \\left(\\mathbf {x} _ {\\mathbf {k}}\\right) - \\mathbf {s} _ {\\mathbf {k}}\\right) | < 1 \\\\ \\left(\\left(f _ {\\theta} \\left(\\mathbf {x} _ {\\mathbf {k}}\\right) - \\mathbf {s} _ {\\mathbf {k}}\\right) - \\frac {1}{2}\\right) & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {5}", + "image_path": "bfee9292893775c83964c242d46c3697e6a64785cd6afc46486214761bb52e36.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 45, + 667, + 279, + 702 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 667, + 279, + 702 + ], + "spans": [ + { + "bbox": [ + 45, + 667, + 279, + 702 + ], + "type": "text", + "content": "Gradient loss. It is important to train a DIF with gradient consistency. We apply constraint on the gradient of each sampled points, denoted as" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 69, + 707, + 279, + 733 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 707, + 279, + 733 + ], + "spans": [ + { + "bbox": [ + 69, + 707, + 279, + 733 + ], + "type": "interline_equation", + "content": "L _ {k} ^ {\\operatorname {g r a d}} \\left(\\mathbf {x} _ {\\mathbf {k}}\\right) = e ^ {- \\left(1 0 0 \\mathbf {s} _ {\\mathbf {k}}\\right) ^ {2}} \\left(1 - \\frac {\\left\\langle \\nabla f \\left(\\mathbf {x} _ {\\mathbf {k}}\\right) , \\mathbf {n} _ {\\mathbf {k}} \\right\\rangle}{\\left\\| f \\left(\\mathbf {x} _ {\\mathbf {k}}\\right) \\right\\| \\left\\| \\mathbf {n} _ {\\mathbf {k}} \\right\\|}\\right), \\tag {6}", + "image_path": "06c399e89c0622621fceac3cbc2ed3261673aab9dd1771c26e1e5f17a00fa42b.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 296, + 106, + 530, + 141 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 106, + 530, + 141 + ], + "spans": [ + { + "bbox": [ + 296, + 106, + 530, + 141 + ], + "type": "text", + "content": "We use cosine similarity of " + }, + { + "bbox": [ + 296, + 106, + 530, + 141 + ], + "type": "inline_equation", + "content": "\\mathbf{x_k}" + }, + { + "bbox": [ + 296, + 106, + 530, + 141 + ], + "type": "text", + "content": " and the normal of its nearest sampled surface point, and make " + }, + { + "bbox": [ + 296, + 106, + 530, + 141 + ], + "type": "inline_equation", + "content": "\\mathbf{x_k}" + }, + { + "bbox": [ + 296, + 106, + 530, + 141 + ], + "type": "text", + "content": " closer to the surface have larger influence." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 308, + 142, + 490, + 152 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 142, + 490, + 152 + ], + "spans": [ + { + "bbox": [ + 308, + 142, + 490, + 152 + ], + "type": "text", + "content": "The total loss function could be formulated as" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 371, + 163, + 530, + 176 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 371, + 163, + 530, + 176 + ], + "spans": [ + { + "bbox": [ + 371, + 163, + 530, + 176 + ], + "type": "interline_equation", + "content": "L = L _ {s d f} + \\lambda L _ {g r a d}, \\tag {7}", + "image_path": "8a607c803d2a2475f0855533308ee02605fcbbd4edb1672ffdeec1937f6da4b6.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 296, + 185, + 450, + 197 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 185, + 450, + 197 + ], + "spans": [ + { + "bbox": [ + 296, + 185, + 450, + 197 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 296, + 185, + 450, + 197 + ], + "type": "inline_equation", + "content": "\\lambda = 1.0" + }, + { + "bbox": [ + 296, + 185, + 450, + 197 + ], + "type": "text", + "content": " for all our experiments." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 296, + 207, + 376, + 220 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 207, + 376, + 220 + ], + "spans": [ + { + "bbox": [ + 296, + 207, + 376, + 220 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 296, + 226, + 530, + 297 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 226, + 530, + 297 + ], + "spans": [ + { + "bbox": [ + 296, + 226, + 530, + 297 + ], + "type": "text", + "content": "We evaluate the effectiveness of our method compared with the state-of-the-art methods on several different aspects: (1) the representation performance on 3D objects dataset, (2) the performance on large-scale synthetic and real scenes data, and (3) reconstruction power on single complex object reconstruction." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 296, + 304, + 479, + 317 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 304, + 479, + 317 + ], + "spans": [ + { + "bbox": [ + 296, + 304, + 479, + 317 + ], + "type": "text", + "content": "4.1.3D Objects Dataset Reconstruction" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 296, + 322, + 530, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 322, + 530, + 532 + ], + "spans": [ + { + "bbox": [ + 296, + 322, + 530, + 532 + ], + "type": "text", + "content": "Dataset and metric. We run the experiments on the ShapeNet dataset [2] with the same settings with [5]. The dataset contains a subset of 13 categories in ShapeNet with train/test splits from [7]. We evaluate geometric reconstruction quality with L2 Chamfer Distance (CD) and F-Score. For L2 Chamfer Distance, we take exactly the same settings as [5]. We sampled 100K signed distances near the surface and 100K signed distances uniformly around the space. We estimate CD using 100,000 randomly sampled points on the ground truth and the reconstructed meshes. Additionally, in all experiments, we compute the F-Score at a threshold of " + }, + { + "bbox": [ + 296, + 322, + 530, + 532 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 296, + 322, + 530, + 532 + ], + "type": "text", + "content": ", as F-Score is a metric less sensitive to outliers. F-Score is the mean of recall (percentage of reconstruction to target distances under " + }, + { + "bbox": [ + 296, + 322, + 530, + 532 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 296, + 322, + 530, + 532 + ], + "type": "text", + "content": ") and precision (vice versa). For object reconstruction we use " + }, + { + "bbox": [ + 296, + 322, + 530, + 532 + ], + "type": "inline_equation", + "content": "\\tau = 0.01" + }, + { + "bbox": [ + 296, + 322, + 530, + 532 + ], + "type": "text", + "content": ". To be consistent with [5], we divide the whole space into " + }, + { + "bbox": [ + 296, + 322, + 530, + 532 + ], + "type": "inline_equation", + "content": "16 \\times 16 \\times 16" + }, + { + "bbox": [ + 296, + 322, + 530, + 532 + ], + "type": "text", + "content": " regions. We also compare with NGLOD [36] in ShapeNet150 dataset following their evaluation protocol." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 296, + 532, + 531, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 532, + 531, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 532, + 531, + 730 + ], + "type": "text", + "content": "Quantitative comparison. The comparison results between LP-DIF and other state-of-the-art methods are shown in Table 1. LP-DIF achieves the best performance across all categories in terms of average L2 Chamfer Distance and F-score. Compared with MDIF (auto-decoder branch) [5] and DDC-DIF [19], LP-DIF achieves the best performance in most categories, which shows the representational power of our method for representing multiple objects. As in Table 2, our method performs better than the deepest level of [36]. To test the generalization ability of our method, We train our model on one category (chair) and tested on another (unseen). A subset of the cross-category performance is shown in Table 3. Our method has more accuracy than MDIF [5] in unseen categories (bookshelf). In addition, as local regions share similar feature across categories, the accuracy for seen and unseen categories is almost the same for our method." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 276, + 746, + 301, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 276, + 746, + 301, + 756 + ], + "spans": [ + { + "bbox": [ + 276, + 746, + 301, + 756 + ], + "type": "text", + "content": "21860" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 70, + 104, + 503, + 237 + ], + "blocks": [ + { + "bbox": [ + 70, + 104, + 503, + 237 + ], + "lines": [ + { + "bbox": [ + 70, + 104, + 503, + 237 + ], + "spans": [ + { + "bbox": [ + 70, + 104, + 503, + 237 + ], + "type": "table", + "html": "
CategoryCD Mean ↓F-score ↑
Occ. [29]IMNet [4]L.DIF [5]MDIF [5]DCC-DIF [19]OursOcc [29]IMNet [4]L.DIF [5]MDIF [5]DCC-DIF [19]Ours
airplane0.250.130.0440.0280.0110.011589.891.798.598.699.799.86
bench0.340.220.1210.0520.0170.021185.288.696.096.099.599.64
cabinet0.320.230.0630.0510.1310.040583.289.296.696.696.498.42
car0.580.260.090.0880.2180.033269.382.793.193.092.798.84
chair0.380.430.0420.0350.0370.029480.282.597.797.699.199.43
display0.350.200.0430.0190.0280.025682.389.498.698.799.499.64
lamp1.472.760.7950.7950.3270.018062.973.893.593.597.399.58
rifle0.390.550.0600.0570.0070.006286.181.196.996.999.999.97
sofa0.310.160.2080.0370.0360.026485.289.398.398.499.199.64
speaker0.380.170.0650.0440.1460.042478.189.497.397.396.197.86
table0.310.300.1070.0460.0290.028587.288.696.597.699.399.50
telephone0.190.110.0430.0270.0100.020288.996.599.699.399.699.58
watercraft0.350.390.0750.0670.0420.015680.384.797.497.298.399.70
mean0.430.460.1350.1020.0810.024581.486.796.997.098.299.36
", + "image_path": "32a35e23db4bb881ccb94bf372c47e99abe343e2ff227f625e6d94028ace12cd.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 65, + 267, + 257, + 294 + ], + "blocks": [ + { + "bbox": [ + 46, + 239, + 530, + 250 + ], + "lines": [ + { + "bbox": [ + 46, + 239, + 530, + 250 + ], + "spans": [ + { + "bbox": [ + 46, + 239, + 530, + 250 + ], + "type": "text", + "content": "Table 1. Surface reconstruction comparison on test set of shapenet in terms of mean L2 chamfer distance (multiplied by 1e3) and F-score." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 65, + 267, + 257, + 294 + ], + "lines": [ + { + "bbox": [ + 65, + 267, + 257, + 294 + ], + "spans": [ + { + "bbox": [ + 65, + 267, + 257, + 294 + ], + "type": "table", + "html": "
MethodsLOD3 [36]LOD4 [36]LOD5 [36]LP-DIF
CD Mean ↓0.1120.0690.0620.025
", + "image_path": "d19dfb05c0aa6f89e5b67305dd2acd00d01fc65a2479f437e3b65d0aac35bd54.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 66, + 318, + 257, + 347 + ], + "blocks": [ + { + "bbox": [ + 61, + 295, + 263, + 305 + ], + "lines": [ + { + "bbox": [ + 61, + 295, + 263, + 305 + ], + "spans": [ + { + "bbox": [ + 61, + 295, + 263, + 305 + ], + "type": "text", + "content": "Table 2. Comparison in ShapeNet150 with NGLOD [36]." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 66, + 318, + 257, + 347 + ], + "lines": [ + { + "bbox": [ + 66, + 318, + 257, + 347 + ], + "spans": [ + { + "bbox": [ + 66, + 318, + 257, + 347 + ], + "type": "table", + "html": "
MethodsSofaLampBookshelf
MDIF [5] (seen/unseen) (CD↓)0.0370/-0.7950/-- / 0.0910
LP-DIF (seen/unseen) (CD↓)0.0264/0.02650.0180/0.0185- / 0.0490
", + "image_path": "1017e647380e0044b953e9eec6573cf6d9038c92f13b6efb32be4805f7a16d7e.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 73, + 347, + 252, + 358 + ], + "lines": [ + { + "bbox": [ + 73, + 347, + 252, + 358 + ], + "spans": [ + { + "bbox": [ + 73, + 347, + 252, + 358 + ], + "type": "text", + "content": "Table 3. Cross-category performance in ShapeNet." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 66, + 372, + 257, + 623 + ], + "blocks": [ + { + "bbox": [ + 66, + 372, + 257, + 623 + ], + "lines": [ + { + "bbox": [ + 66, + 372, + 257, + 623 + ], + "spans": [ + { + "bbox": [ + 66, + 372, + 257, + 623 + ], + "type": "image", + "image_path": "1ac795f8aa2df2044fb9d9c4d15e9f599740861da61e2f2a0eba107bea23a3de.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 628, + 279, + 661 + ], + "lines": [ + { + "bbox": [ + 45, + 628, + 279, + 661 + ], + "spans": [ + { + "bbox": [ + 45, + 628, + 279, + 661 + ], + "type": "text", + "content": "Figure 4. Visual comparison with OccNet [25], ConvOccNet [29], IFNet [6], and LIG [17], our method could reconstruct more geometry detail on ShapeNet." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 45, + 682, + 280, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 682, + 280, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 682, + 280, + 730 + ], + "type": "text", + "content": "Qualitative comparison. In Figure 4, we visually compared 3D surface reconstruction on Shapenet with other DIF methods [6, 17, 25, 29], from which we find that LP-DIF reconstructs more geometry details while other method tends" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 297, + 271, + 425, + 281 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 271, + 425, + 281 + ], + "spans": [ + { + "bbox": [ + 297, + 271, + 425, + 281 + ], + "type": "text", + "content": "to lose details on thin structures." + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 318, + 289, + 509, + 364 + ], + "blocks": [ + { + "bbox": [ + 318, + 289, + 509, + 364 + ], + "lines": [ + { + "bbox": [ + 318, + 289, + 509, + 364 + ], + "spans": [ + { + "bbox": [ + 318, + 289, + 509, + 364 + ], + "type": "image", + "image_path": "e9a1afa6ce592949f5c4c7669eb1664699377f320294735e6c27ebc0a7cb4aaf.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 297, + 364, + 530, + 384 + ], + "lines": [ + { + "bbox": [ + 297, + 364, + 530, + 384 + ], + "spans": [ + { + "bbox": [ + 297, + 364, + 530, + 384 + ], + "type": "text", + "content": "Figure 5. Comparison for surface reconstruction on SceneNet with sparse sampling." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 306, + 407, + 521, + 551 + ], + "blocks": [ + { + "bbox": [ + 306, + 407, + 521, + 551 + ], + "lines": [ + { + "bbox": [ + 306, + 407, + 521, + 551 + ], + "spans": [ + { + "bbox": [ + 306, + 407, + 521, + 551 + ], + "type": "image", + "image_path": "ef143b81b98a003e766972c0f17faf211d6beda937435ac50c23240464fb1a3d.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 297, + 552, + 530, + 574 + ], + "lines": [ + { + "bbox": [ + 297, + 552, + 530, + 574 + ], + "spans": [ + { + "bbox": [ + 297, + 552, + 530, + 574 + ], + "type": "text", + "content": "Figure 6. Comparison for surface reconstruction on 3D Scene dataset with dense sampling." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 297, + 595, + 432, + 607 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 595, + 432, + 607 + ], + "spans": [ + { + "bbox": [ + 297, + 595, + 432, + 607 + ], + "type": "text", + "content": "4.2.3D Scene Reconstruction" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 296, + 612, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 612, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 612, + 530, + 730 + ], + "type": "text", + "content": "Dataset and metric. We conduct our experiments on a synthetic dataset: SceneNet [14], and a real scanned dataset: 3D Scene dataset [42]. As scenes in SceneNet dataset are not watertight, and have many double-sided faces creating conflicting normals, we pre-process SceneNet to watertight using methods from [16]. We drop scenes with empty inner spaces after the watertighting process. We sample a constant density of points according to the area of faces (1000 points per " + }, + { + "bbox": [ + 296, + 612, + 530, + 730 + ], + "type": "inline_equation", + "content": "m^2" + }, + { + "bbox": [ + 296, + 612, + 530, + 730 + ], + "type": "text", + "content": " for SceneNet and 10000 points per " + }, + { + "bbox": [ + 296, + 612, + 530, + 730 + ], + "type": "inline_equation", + "content": "m^2" + }, + { + "bbox": [ + 296, + 612, + 530, + 730 + ], + "type": "text", + "content": " for 3D Scene dataset). For all the scene-level experiments, we ran" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 276, + 747, + 299, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 276, + 747, + 299, + 756 + ], + "spans": [ + { + "bbox": [ + 276, + 747, + 299, + 756 + ], + "type": "text", + "content": "21861" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 45, + 106, + 281, + 210 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 106, + 281, + 210 + ], + "spans": [ + { + "bbox": [ + 45, + 106, + 281, + 210 + ], + "type": "text", + "content": "domly sample 2 million points on the generated mesh and the ground truth mesh when estimating L1 CD, and we use " + }, + { + "bbox": [ + 45, + 106, + 281, + 210 + ], + "type": "inline_equation", + "content": "\\tau = 0.025" + }, + { + "bbox": [ + 45, + 106, + 281, + 210 + ], + "type": "text", + "content": " (2.5cm) for F-score. Since data is provided in a physically-meaningful scale, we use world coordinate (meters) for computing CD. Note that these two metrics are not always consistent as CD is more sensitive to outliers. For scene-level experiments, we directly optimize latent codes and decoders on the scenes, and we divide the whole space into " + }, + { + "bbox": [ + 45, + 106, + 281, + 210 + ], + "type": "inline_equation", + "content": "32 \\times 32 \\times 32" + }, + { + "bbox": [ + 45, + 106, + 281, + 210 + ], + "type": "text", + "content": " regions." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 211, + 281, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 211, + 281, + 316 + ], + "spans": [ + { + "bbox": [ + 45, + 211, + 281, + 316 + ], + "type": "text", + "content": "Quantitative comparison. The comparison results between LP-DIF and other state-of-the-art methods are shown in Table 4. LP-DIF achieves the best performance across all categories in terms of average L1 Chamfer Distance and F-score both in sparse (Scenenet) and dense (3D SceneNet dataset) sampling settings, which proves better representational power of our method. Compared with scenenet with sparse sampling setting, our method improves more on 3D scenenet dataset with dense sampling settings." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 45, + 316, + 280, + 374 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 316, + 280, + 374 + ], + "spans": [ + { + "bbox": [ + 45, + 316, + 280, + 374 + ], + "type": "text", + "content": "Qualitative comparison. In Figure 5 and 6, we visually compared 3D surface reconstruction of scene dataset with other DIF methods, from which we find that LP-DIF reconstructs more geometry details and less missing parts than other method." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 382, + 230, + 394 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 382, + 230, + 394 + ], + "spans": [ + { + "bbox": [ + 45, + 382, + 230, + 394 + ], + "type": "text", + "content": "4.3. Complex 3D Object Reconstruction" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 400, + 281, + 539 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 400, + 281, + 539 + ], + "spans": [ + { + "bbox": [ + 45, + 400, + 281, + 539 + ], + "type": "text", + "content": "Dataset and metric. For complex 3D object reconstruction, we use Thai Statue, obtained from the Stanford 3D Scanning Repository [18]. It is an intricate statue, which consists of 10 million polygons. Fine details of the statue are challenging to be captured with existing methods. We randomly sample 2 million points on the generated and the ground truth meshes when estimating L1 CD, and we use " + }, + { + "bbox": [ + 45, + 400, + 281, + 539 + ], + "type": "inline_equation", + "content": "\\tau = 0.025" + }, + { + "bbox": [ + 45, + 400, + 281, + 539 + ], + "type": "text", + "content": " for F-score. For complex 3D object, we directly optimize latent codes and decoders to fit the shape. For ACORN [24], we train using their official code and extract the reconstructed mesh. [24] is trained for several hours until max octants are reached." + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 101, + 548, + 223, + 648 + ], + "blocks": [ + { + "bbox": [ + 101, + 548, + 223, + 648 + ], + "lines": [ + { + "bbox": [ + 101, + 548, + 223, + 648 + ], + "spans": [ + { + "bbox": [ + 101, + 548, + 223, + 648 + ], + "type": "image", + "image_path": "4078d4d3412b96f7d22e63117b357c42187b42b8375da44352c1e1623a59aa25.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 648, + 279, + 680 + ], + "lines": [ + { + "bbox": [ + 45, + 648, + 279, + 680 + ], + "spans": [ + { + "bbox": [ + 45, + 648, + 279, + 680 + ], + "type": "text", + "content": "Figure 7. Comparison for surface reconstruction on Thai statue. Our result is comparable with ACORN [24] with slightly better details." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 694, + 280, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 694, + 280, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 694, + 280, + 730 + ], + "type": "text", + "content": "Quantitative comparison. The comparison results between LP-DIF and other state-of-the-art methods are shown in Table 5. LP-DIF achieves the best performance in terms" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 296, + 106, + 530, + 129 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 106, + 530, + 129 + ], + "spans": [ + { + "bbox": [ + 296, + 106, + 530, + 129 + ], + "type": "text", + "content": "of average L1 Chamfer Distance and F-score for complex 3D object reconstruction." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 296, + 130, + 531, + 200 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 130, + 531, + 200 + ], + "spans": [ + { + "bbox": [ + 296, + 130, + 531, + 200 + ], + "type": "text", + "content": "Qualitative comparison. In Figure 1, we visually compare 3D surface reconstruction of Thai statue with other DIF methods, where we find that LP-DIF reconstructs much more fine geometry details than other methods. In Figure 7, we compare with ACORN [24]. Our result is comparable with ACORN with slightly better details." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 296, + 208, + 389, + 221 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 208, + 389, + 221 + ], + "spans": [ + { + "bbox": [ + 296, + 208, + 389, + 221 + ], + "type": "text", + "content": "4.4. Ablation Study" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 296, + 227, + 531, + 494 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 227, + 531, + 494 + ], + "spans": [ + { + "bbox": [ + 296, + 227, + 531, + 494 + ], + "type": "text", + "content": "Network capacity and efficiency comparison. We have summarized the number of parameters used in NGLOD (LOD5) [36], LDIF [1], MDIF [5], LIG [17], and our method in Table 6. As in the table, different number of parameters are used and our method utilized the second least total number of parameters. We also tested the performance under the same total number of parameters in Table 7. As in the first two rows of the table, LDIF [1] and our method have the similar total number of parameters, where our method outperforms LDIF [1]. After that, we increase our MLP to 800-dimensional hidden layers to have the similar total number parameters with MDIF [5]. As in the 3-4 rows of the table, the performance of our ablation method is still better than MDIF [5], but is worse than our original decoders. The reason could be that the increased parameters of network makes the optimization of local latent code unstable. The performance of our coarse decoder is also shown in the last row for comparison. We have also compared the computation time on 8 shapes of ShapeNet in Table 8. It takes much more time for NGLOD [36] to train. For L-DIF and LP-DIF, we reported the time needed to reach the same accuracy level. It takes less time for LP-DIF than L-DIF." + } + ] + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 316, + 504, + 511, + 549 + ], + "blocks": [ + { + "bbox": [ + 316, + 504, + 511, + 549 + ], + "lines": [ + { + "bbox": [ + 316, + 504, + 511, + 549 + ], + "spans": [ + { + "bbox": [ + 316, + 504, + 511, + 549 + ], + "type": "image", + "image_path": "e5d5d84476b626846332cc7324cc1b553b59e8494581b437ba95eab2342942ad.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 297, + 554, + 530, + 597 + ], + "lines": [ + { + "bbox": [ + 297, + 554, + 530, + 597 + ], + "spans": [ + { + "bbox": [ + 297, + 554, + 530, + 597 + ], + "type": "text", + "content": "Figure 8. Comparison with random clustering. (a) Replacing the clustering process with random assigning each local region into clusters. (b) Clustering with regards to similarity leads to better performance." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 296, + 602, + 532, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 602, + 532, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 602, + 532, + 730 + ], + "type": "text", + "content": "Ablation on modules. We also conduct a series of experiments on the effectiveness of our modules on Burghers of 3D scenenet dataset. Our baseline is implemented by removing pattern clustering and region re-weighting. First, we separate the whole space into different number of regions (each region has one code), and test the effect of our module under different settings. The results are shown in Table 9, where the baseline model performs better with more local regions and codes, however, more local codes occupy much more space. Our model with " + }, + { + "bbox": [ + 296, + 602, + 532, + 730 + ], + "type": "inline_equation", + "content": "7.63\\mathrm{MB}" + }, + { + "bbox": [ + 296, + 602, + 532, + 730 + ], + "type": "text", + "content": " local codes could have similar performance with the baseline" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 276, + 746, + 301, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 276, + 746, + 301, + 756 + ], + "spans": [ + { + "bbox": [ + 276, + 746, + 301, + 756 + ], + "type": "text", + "content": "21862" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 119, + 104, + 456, + 186 + ], + "blocks": [ + { + "bbox": [ + 119, + 104, + 456, + 186 + ], + "lines": [ + { + "bbox": [ + 119, + 104, + 456, + 186 + ], + "spans": [ + { + "bbox": [ + 119, + 104, + 456, + 186 + ], + "type": "table", + "html": "
CategoryCD Mean ↓F-score ↑SceneCD Mean ↓F-score ↑
LIG [17]OursLIG [17]OursLIG [17]OursLIG [17]Ours
Bathroom0.008250.0063398.5699.66Burghers0.01220.003990.2599.67
Bedroom0.009780.0073096.4199.24Lounge0.01310.003185.4999.72
Office0.014520.0092993.9296.97CopyRoom0.01300.003484.6899.97
Livingroom0.011910.0098796.3998.65StoneWall0.01100.003189.1499.90
Kitchen0.009880.0082596.3698.55TotemPole0.01200.004189.3999.23
Mean0.010650.0081696.4098.67Mean0.01220.003587.7999.70
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MethodsDeepSDF [28]LIG [17]LDIF baselineOurs
CD Mean ↓0.7400.6030.2110.176
F-score ↑1.313.621.863.6
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Methods# Feature Param# Network ParamTotal # Param
LOD5 [36]101225282368510146213
L.DIF [5]524288460993985281
MDIF [5]440321835930118403333
LIG [17]131072227745358817
Ours53248 (coarse) + 2498563745 (coarse) + 463108769957
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Methods#Feature Param#Inference ParamTotal # ParamCD (Airplane)↓CD (Bench)↓
L.DIF [5]5242884609939852810.0440.121
Ours303104 (53248 + 249856)466853 (3745 + 463108)7699570.0120.021
MDIF [5]4403218359301184033330.0280.052
Ours-abl-mdif303104 (53248 + 249856)17952293 (3745 + 17948548)182553970.01450.031
Ours-coarse532482689559370.0620.167
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MethodsStage1Stage 2Stage 3Total
NGLOD [36]---~4000s
LDIF baseline---165s (1.33s ×124epochs)
LP-DIF20s1s141s (2.43s ×58epochs)162s
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Methods# of codescode sizeCD Mean ↓F-score ↑
Baseline-3232K7.63 MB0.0055796.78
Baseline-1282097K488 MB0.0038999.65
LP-DIF-3232K7.63 MB0.0039499.67
LP-DIF-1282097K488 MB0.0038799.64
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MethodsCD Mean↓F-score ↑
Baseline0.0055796.78
LP-DIF w/o clustering0.0044699.52
LP-DIF w/o re-weighting0.0041999.16
LP-DIF0.0039499.67
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As in Figure 8 and" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 296, + 229, + 530, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 229, + 530, + 392 + ], + "spans": [ + { + "bbox": [ + 296, + 229, + 530, + 392 + ], + "type": "text", + "content": "Table 6, the performance is deteriorated with random clustering. The possible reason is that randomly separating local regions increases the deviation of some local regions from the cluster centers, causing them to fail in training. Next we evaluate the components of our model by removing them separately. We test two variations: (1) removing the clustering module and re-weight on the whole set of regions, and (2) removing the re-weighting module. The result is shown in Table 10 and Figure 9 (a) - (c), and we find that both modules are helpful for achieving good performance. At last, we test the difference between fixed density estimator and dynamic density estimator. As shown in Figure 9 (d) - (f), dynamic density estimator could reconstruct better geometry details than fixed one." + } + ] + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 352, + 402, + 471, + 510 + ], + "blocks": [ + { + "bbox": [ + 352, + 402, + 471, + 510 + ], + "lines": [ + { + "bbox": [ + 352, + 402, + 471, + 510 + ], + "spans": [ + { + "bbox": [ + 352, + 402, + 471, + 510 + ], + "type": "image", + "image_path": "15908933bc6671f5cbd63c4101fb11cf392e1f79d0f157fa5f7d625f635763de.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 296, + 511, + 530, + 554 + ], + "lines": [ + { + "bbox": [ + 296, + 511, + 530, + 554 + ], + "spans": [ + { + "bbox": [ + 296, + 511, + 530, + 554 + ], + "type": "text", + "content": "Figure 9. Ablation study on density-adaptive re-weighting. (a) Ours w/o density re-weighting. (b) Ours w/ density re-weighting. (c) Ground truth. (d) Ours w/o density estimator. (e) Ours w/ fixed density estimator. (f) Ours w/ dynamic density estimator." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 16 + }, + { + "bbox": [ + 297, + 559, + 368, + 570 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 559, + 368, + 570 + ], + "spans": [ + { + "bbox": [ + 297, + 559, + 368, + 570 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 296, + 578, + 530, + 729 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 578, + 530, + 729 + ], + "spans": [ + { + "bbox": [ + 296, + 578, + 530, + 729 + ], + "type": "text", + "content": "In this paper, we present LP-DIF, a local pattern-specific deep implicit function for reconstructing highly detailed geometry. Compared with previous methods that treat all local regions equally using a single decoder, we regard a shape as clusters of local regions and mine local patterns with different decoders. This alleviates the difficulty of learning caused by diverse local regions. In addition, we introduce a dynamic region re-weighting module, which could provide more focus on less common regions to tackle the data-imbalance problem in each pattern decoder. As a result, finer details of the local regions are learned more accurately. 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ACM Transactions on Graphics (ToG), 32(4):1-8, 2013. 6" + } + ] + } + ], + "index": 18 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 276, + 746, + 300, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 276, + 746, + 300, + 756 + ], + "spans": [ + { + "bbox": [ + 276, + 746, + 300, + 756 + ], + "type": "text", + "content": "21865" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/LSTFE-Net_Long Short-Term Feature Enhancement Network for Video Small Object Detection/f85fdbe6-5d06-483d-a4fa-dfa64b2fcc9b_content_list.json b/2023/LSTFE-Net_Long Short-Term Feature Enhancement Network for Video Small Object Detection/f85fdbe6-5d06-483d-a4fa-dfa64b2fcc9b_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..a3dfe558fa37357607a356a2b342b8f30c0029ea --- /dev/null +++ b/2023/LSTFE-Net_Long Short-Term Feature Enhancement Network for Video Small Object Detection/f85fdbe6-5d06-483d-a4fa-dfa64b2fcc9b_content_list.json @@ -0,0 +1,1494 @@ +[ + { + "type": "text", + "text": "LSTFE-Net:Long Short-Term Feature Enhancement Network for Video Small Object Detection", + "text_level": 1, + "bbox": [ + 91, + 128, + 879, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Jinsheng Xiao $^{1}$ , Yuanxu Wu $^{1}$ , Yunhua Chen $^{2*}$ , Shurui Wang $^{1}$ , Zhongyuan Wang $^{1}$ , Jiayi Ma $^{1}$ \n1. Wuhan University, China", + "bbox": [ + 125, + 202, + 841, + 239 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "2. Guangdong University of Technology, China", + "bbox": [ + 297, + 239, + 669, + 257 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{xiaojs,whuwuyuanxu,shuruiwang}@whu.edu.cn，yhchen@gdut.edu.cn", + "bbox": [ + 210, + 258, + 756, + 273 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "wzyhope@163.com, jyma2010@gmail.com", + "bbox": [ + 323, + 277, + 640, + 291 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 325, + 313, + 342 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Video small object detection is a difficult task due to the lack of object information. Recent methods focus on adding more temporal information to obtain more potent high-level features, which often fail to specify the most vital information for small objects, resulting in insufficient or inappropriate features. Since information from frames at different positions contributes differently to small objects, it is not ideal to assume that using one universal method will extract proper features. We find that context information from the long-term frame and temporal information from the short-term frame are two useful cues for video small object detection. To fully utilize these two cues, we propose a long short-term feature enhancement network (LSTFE-Net) for video small object detection. First, we develop a plug-and-play spatio-temporal feature alignment module to create temporal correspondences between the short-term and current frames. Then, we propose a frame selection module to select the long-term frame that can provide the most additional context information. Finally, we propose a long short-term feature aggregation module to fuse long short-term features. Compared to other state-of-the-art methods, our LSTFE-Net achieves $4.4\\%$ absolute boosts in AP on the FL-Drones dataset. More details can be found at https://github.com/xiaojs18/LSTFE-Net.", + "bbox": [ + 73, + 357, + 473, + 720 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 747, + 209, + 763 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Video small object detection plays an important role in many fields such as automatic driving, remote sensing, medical image, and industrial defect detection [26]. However, it is still a difficult task due to the lack of pixel information and the difficulty of feature extraction. Therefore, the topic of how to enhance the features of small objects has attracted great attention [1,7, 16].", + "bbox": [ + 75, + 773, + 468, + 878 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/a0532f6b9398054ab29f50247fdc725cf24463e42bb6fad0ee3e949aca3fa4a8.jpg", + "image_caption": [ + "Figure 1. The architecture of the proposed LSTFE-Net. The current frame (Cur-frame), short-term frames (ST-frames) near the Cur-frame, and long-term frames (LT-frames) sampled from the whole video first go through the feature extraction network. Then the Cur-frame feature and ST-frame features are connected through the spatio-temporal feature alignment module, and the frame selection module searches the background context of LT-frame features. After getting the Proposal-Level (PL) features, the long short-term feature aggregation module finally integrates the long short-term features into the Cur-frame to make feature enhancement. Best viewed in color and zoomed in." + ], + "image_footnote": [], + "bbox": [ + 511, + 323, + 888, + 541 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Some recent works have proved that the improvement of video small object detection performance requires full utilization of information in the temporal dimension. While detecting small objects in the current frame may suffer from many problems such as motion blur, low resolution, and too small size, effective modeling of information from other frames can help address these problems [2, 4, 9, 17]. There is a high similarity in nearby frames because of the strong time continuity between them, so it is natural to emphasize the importance of short-term frames, which are near the current frame. According to FGFA [28] and STSN [2],", + "bbox": [ + 496, + 734, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation.", + "bbox": [ + 236, + 1, + 807, + 21 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "Except for this watermark, it is identical to the accepted version;", + "bbox": [ + 295, + 16, + 751, + 27 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 292, + 30, + 753, + 45 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*The corresponding author", + "bbox": [ + 94, + 887, + 241, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "14613", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "short-term frame features can be aligned and aggregated to provide more useful information for small objects.", + "bbox": [ + 76, + 90, + 468, + 121 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Context information is important for small object detection [16,25]. Because a large number of images are sampled from the same video for the same object, the background context information of the object is single. Additionally, only part of the frames in the video are sampled as current frames (such as 15 frames) while training, which results in the lack of real background context information and reduces the robustness of the training model. Compared to features in a short range, features from the whole video level can be more discriminative and robust [21, 23]. And it is noticed in prior works [9, 23] that more contextual information will be provided when using long-term frames sampled from the whole video.", + "bbox": [ + 75, + 125, + 470, + 319 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The impacts of short-term and long-term frames in detection have been studied in recent methods. However, these methods have obvious disadvantages in both efficiency and accuracy, especially for small objects in videos. Some methods [22, 27, 28] extract information from the short-term frame and exploit the flow model to propagate features across adjacent frames, however, this is expensive because the flow model is hard to construct and transplant. Other methods [21, 23] focus on semantic information from long-term frames and incorporate randomly sampled long-term frames in detection, which causes uncertainty of detection performance and the loss of valuable information. Besides, these methods above cannot figure out the specific information that matters most for small objects from frames. Some methods [21-23, 27, 28] think the information in the video is single and miss considering distinct information from different frames, getting inadequate features. Other methods [3, 5] focus on extracting high-level features from the video which are not suitable for small objects due to their special properties.", + "bbox": [ + 75, + 323, + 470, + 626 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To better mine information from both short-term frames and long-term frames, we propose a long short-term feature enhancement network (LSTFE-Net) for video small object detection. Specifically, the features of short-term frames are expected to correspond to the current frame in a low-cost and effective way, so a spatio-temporal feature alignment module is designed to propagate features across nearby frames. Further, in order to increase the benefit of aligned features while not increasing too much complexity of the model, a spatio-temporal feature aggregation method is also added. The context information is expected to be highlighted from the whole video, prompting a frame selection module to select the long-term frame feature. The goal is to make effective feature enhancement after the features are collected, and the establishment of connections between different features is enforced. A long short-term feature aggregation module is devised to aggregate features from the current frame, the short-term frames, and the long", + "bbox": [ + 75, + 628, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "term frames by stages. The performance of the proposed method is evaluated on the open dataset, and experiment results demonstrate that our method has obvious advantages in video small object detection. The architecture of the network is shown in Fig. 1.", + "bbox": [ + 496, + 90, + 890, + 166 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our main contributions are summarized as follows:", + "bbox": [ + 517, + 167, + 857, + 180 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "(1) An LSTFE-Net is proposed to effectively enhance small object features and improve detection performance.", + "(2) A plug-and-play spatio-temporal feature alignment module is designed for aligning features across adjacent frames. A flexible way to make Pixel-Level feature enhancement for small objects using aligned features is also explored. Combined with the Proposal-Level feature enhancement, this module achieves multi-level enhancement to improve the feature expressiveness. The whole module is easy to transplant and proved to be effective, which reveals its potential ability to benefit most of the works.", + "(3) A frame selection module is proposed to ensure the utilization of high-value input data, and it selects the long-term frame feature with the most context information. This module reinforces the network to automatically look for useful information for small objects, improving its stability and performance in video small object detection.", + "(4) To effectively integrate the long-term frame features and short-term frame features into the current frame, a long short-term feature aggregation module is proposed to aggregate different features in different stages. This enables the relations between Proposal-Level features to be built adaptively based on an attention mechanism, which also means our feature enhancement for small objects can be accomplished in a general and limitless way." + ], + "bbox": [ + 496, + 181, + 890, + 559 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 500, + 573, + 648, + 588 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Object detection from images has achieved considerable success and introduced some leading detectors in recent years. Based on the early proposed detectors, video object detection is intensively studied as a more challenging task. It is proved that exploiting information from other frames can significantly enhance the detection of the current frame, so temporal feature aggregation is gaining attention and introduced into video small object detection.", + "bbox": [ + 496, + 598, + 890, + 718 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Object detection in videos: The appropriate use of the temporal information in the video to increase detection accuracy is a fundamental difficulty in video object detection. Adapting the image object detection algorithm to the video domain is challenging because of the complex spatial and temporal changes in videos. SeqNMS [10], TCN [15], and T-CNN [14] apply post-processing to video object detection to handle the complexities of videos. SeqNMS [10] links bounding boxes from different frames iff their Intersection over Union $(IoU)$ is above some certain threshold and re-ranks those linked boxes; TCN [15] introduces the tubelet components and proposes a temporal convolu", + "bbox": [ + 496, + 719, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "14614", + "bbox": [ + 480, + 945, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "tional neural network to incorporate temporal information, which improves detection performance across frames. TCNN [14] first uses the still-image object detection algorithm to get single frame detection results and associates the results using optical flows. However, none of these methods based on post-processing can be trained end-to-end, and their performance is yet to be improved. Our method, in contrast, directly uses temporal information in videos without post-processing and can be trained end-to-end, which brings great convenience.", + "bbox": [ + 75, + 90, + 470, + 241 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Temporal feature aggregation: Recent works have also focused on ways to aggregate temporal features with different distances from the current frame, including short-term frame and long-term frame features, to enhance the feature of the object. DFF [27] uses a flow field predicted by FlowNet [13] to make the key frame feature align to short-term frames, thus reducing the redundant computation and accelerating the network. Unlike DFF, FGFA [28] mainly employs flow motion to make short-term frame features align to the current frame and then fuses these two kinds of features to improve detection accuracy. MANet [22] achieves the feature calibration module and the feature aggregation module on both pixel-level and instance-level based on FGFA and uses the motion pattern reasoning module to aggregate features from two different levels. Unlike short-term frames, long-term frames are usually sampled from the whole training video. Since there is little time continuity between the long-term frame and the current frame, the fusion of high-level semantic information is paid more attention to. To make more effective feature aggregation, SELSA [23] performs one innovative work by calculating the semantic similarity between current frames and long-term frames. STMN [24] uses the recurrent computation unit as the spatio-temporal memory module to pass semantic information between different frames. While using both local and global features to enhance the features of the current frames, MEGA [3] introduces a memory module to store more temporal features.", + "bbox": [ + 75, + 244, + 470, + 667 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Video small object detection: A few researchers have proposed to improve the detection accuracy of small objects by leveraging temporal information in videos. Motion R-CNN [7] provides additional auxiliary information for small objects based on the frame differencing method and improves small object detection performance in optical remote sensing videos. DogFight [1] proposes to use a two-stage segmentation-based approach employing spatiotemporal attention cues, where objects are localized during the first stage and the object location is tracked and filtered using temporal information during the second stage.", + "bbox": [ + 75, + 670, + 468, + 837 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Although both short-term frame features and long-term frame features have been used to improve detection performance, the information mined from these features is still not enough for them to build strong connections with the", + "bbox": [ + 76, + 839, + 470, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "small object. We focus on several major problems and aim to get more powerful small object features through enhancement. To be specific, while DFF [27] and FGFA [28] require FlowNet which is difficult to construct and transplant, our method uses a plug-and-play spatio-temporal feature alignment module to make feature alignment and Pixel-Level enhancement. Instead of being simply randomly sampled from the video like MEGA [3], the long-term frame in this paper is selected by the frame selection module to enrich context information for small object detection. Unlike the above methods exclusively focusing on exploiting one kind of information from either the short-term frame or the long-term frame [22, 23, 27, 28], we fully consider the various information from both the short-term frame and long-term frame. The high-level features in this paper can work better for small objects than those in [3, 5] because of these purposeful designs.", + "bbox": [ + 496, + 90, + 890, + 348 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methods", + "text_level": 1, + "bbox": [ + 500, + 364, + 598, + 380 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Framework overview", + "text_level": 1, + "bbox": [ + 500, + 391, + 699, + 406 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The architecture of the LSTFE-Net is shown in Fig. 1. Besides the current frame, multiple short-term frames and long-term frames are also sampled from the video and input to the network. The feature extraction network first extracts the frame features of the input. Then different frame features are processed differently according to their characteristics. Because the short-term frames are sampled adjacent to the current frame, there is extensive temporal information between them. A plug-and-play spatio-temporal feature alignment module is designed to make alignment of the current frame feature and short-term frame features using cascaded deformable convolution blocks. This alignment can be described in the form of offsets in convolution, which helps the convolutional neural network sample more features from object regions to precisely enhance the small object of the current frame. The aligned features are further fused into the current frame feature on a low level.", + "bbox": [ + 496, + 415, + 890, + 672 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "It is inappropriate to make feature alignment between the current frame and long-term frames because there is no evident time continuity between them and their object features have great displacement in space. Considering that background context information is crucial and single to small object detection, long-term frames are employed to provide more background context information. It is natural to expect the long-term frames with the most context information to be further used in the network, so a frame selection module is devised. After feature embedding, it selects the long-term frame feature with the lowest similarity to the current frame feature. After the above modules, the Region Proposal Network (RPN) is used to generate proposals and Region of Interest (RoI) Align is applied to make feature extraction, getting the Proposal-Level features of different", + "bbox": [ + 496, + 674, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "14615", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/cf2bcb981c3a1895f9752523f9b7823260324e1254baaa241c4c89a4e3609841.jpg", + "image_caption": [ + "Figure 2. Spatio-temporal feature alignment module. The shortterm frame feature $f_{s}$ is first aligned based on deformable convolution, and then integrated into the current frame feature $f_{t}$ using spatio-temporal feature aggregation. Best viewed in color and zoomed in." + ], + "image_footnote": [], + "bbox": [ + 81, + 90, + 460, + 229 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "frames.", + "text_level": 1, + "bbox": [ + 76, + 338, + 130, + 349 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Effectively integrating long-term frame features and short-term frame features into the current frame feature is also a key part of feature enhancement. To better integrate different kinds of frame features, we divide the long short-term feature aggregation into two stages: long-term feature aggregation and short-term feature aggregation. In the first stage, the feature aggregation between long-term frames and short-term frames is conducted, which provides additional context information for small objects. Next, the feature aggregation between short-term frames and the current frame is carried out in the second stage, and also the location differences between the frames are considered. This module models the relations between Proposal-Level features adaptively and universally, ensuring feature enhancement for small objects. The above algorithms will be introduced in detail in the following sections.", + "bbox": [ + 75, + 352, + 468, + 595 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Spatio-temporal feature alignment module", + "text_level": 1, + "bbox": [ + 76, + 604, + 439, + 619 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "There is a strong similarity between the current frame and the short-term frames. Features of the same object are typically not spatially aligned between frames due to the movement in videos. Hence direct fusion of features between frames will result in feature interference, ghost effects, and even lower detection performance. Deformable convolution [8] learns multiple offsets of the spatial location during convolution. We design a spatio-temporal feature alignment module based on deformable convolution to learn offsets and make feature alignment between frames, and a spatio-temporal feature aggregation module is proposed to conduct Pixel-Level feature enhancement of the current frame. The specific architecture is shown in Fig. 2.", + "bbox": [ + 75, + 628, + 468, + 824 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given a frame $I_{t}$ at time $t$ and a nearby short-term frame $I_{s}$ , let $f_{t}$ and $f_{s}$ indicate spatial features through the feature extraction network from frame $I_{t}$ and $I_{s}$ , as shown in Fig. 2 (a). Suppose the shape of $f_{t}$ or $f_{s}$ is $[C, H, W]$ , where $C$ stands for the channels, $H$ for the height of tensors, and $W$", + "bbox": [ + 76, + 825, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "for the width of tensors. To fuse the features, $f_{t}$ and $f_{s}$ are concatenated to get $f_{cat}$ . Then $f_{cat}$ is fed to a deformable convolutional block, as shown in Fig. 2 (b). The block generates offsets $m_{1} \\in [2 \\times 9, H, W]$ with $3 \\times 3$ convolution, where 9 denotes kernel size $3 \\times 3$ , 2 denotes offsets in two directions: $x$ and $y$ . Finally, $m_{1}$ and $f_{cat}$ are fed to a deformable convolutional layer to get the aligned feature. Our deformable convolutional block is plug-and-play and cascaded, which means multiple blocks can be used in series to make multiple times feature alignments. The final block outputs the final offsets $m_{o}$ , and $m_{o}$ and short-term frame feature $f_{s}$ are fed to a deformable convolutional layer to get the aligned short-term feature $f_{t+s}$ . In general, the temporal information between the current frame and the short-term frame is used to estimate the spatial offset between object features, which is further used to make the short-term frame feature align with the current frame feature.", + "bbox": [ + 496, + 90, + 890, + 347 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To effectively integrate the aligned short-term frame feature into the current frame feature, a spatio-temporal feature aggregation module is designed to make the adaptive information fuse. The adaptive weight can be expressed by formula 1.", + "bbox": [ + 496, + 347, + 890, + 422 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\omega \\left(f _ {t}, f _ {t + s}\\right) = \\rho \\left(l \\left(f _ {t}, f _ {t + s}\\right)\\right) \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 594, + 439, + 890, + 455 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $l$ is a spatio-temporal function that describes spatiotemporal connections between $f_{t}$ and $f_{t + s}$ , and $\\rho$ is the mask function used to calculate the adaptive weight. To fully use temporal information between frames, the frame differencing method is introduced into $l$ , which concatenates $f_{t} - f_{t + s}, f_{t + s} - f_{t}, f_{t}$ , and $f_{t + s}$ into $f_{multi}$ . $f_{multi}$ is then fed to mask function $\\rho$ . It goes through two convolutional layers to squeeze the number of channels and fully fuse the information. To improve the generalization ability of the model, the softmax function is then used to generate the final adaptive weight $\\omega(f_{t}, f_{t + s})$ . As shown in Fig. 2 (c). Finally, the enhanced current frame feature $f$ is computed by", + "bbox": [ + 496, + 463, + 890, + 657 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nf = \\sum_ {f _ {j} \\in \\left(f _ {t}\\right)} \\left\\{\\omega \\left(f _ {t}, f _ {j}\\right) \\otimes f _ {t} \\right\\} \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 594, + 659, + 890, + 694 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $(f_{t})$ denotes a collection of aligned short-term frame features near $f_{t}$ , $\\otimes$ denotes element-wise multiplication. In this paper, multiple short-term frames are sampled, aligned to the current frame, and adaptively integrated into the current frame to enhance the current frame feature on Pixel-Level.", + "bbox": [ + 496, + 700, + 890, + 789 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Frame selection module", + "text_level": 1, + "bbox": [ + 500, + 801, + 718, + 816 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Because a large number of images are sampled in the same video for the same object, the background context information of the object is very similar. Object detection algorithms based on deep learning tend to use this similarity to make the feature enhancement for the current object.", + "bbox": [ + 496, + 825, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "14616", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/64a75970460a4a5226805d560eec08f2398d4a370f4f769c27ec0fd48b3a1749.jpg", + "image_caption": [ + "Figure 3. Frame selection module. The current frame feature $F_{c}$ and $m$ long-term frame features $\\{F_{g}^{i}\\}_{i = 1}^{m}$ first get the feature embedding. Then similarities between them are calculated and finally, the index of the long-term frame with the lowest similarity is output. Best viewed in color and zoomed in." + ], + "image_footnote": [], + "bbox": [ + 83, + 87, + 467, + 209 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "However, this strategy results in the poor generalization performance of the training model, especially for training data with a high degree of similarity. Considering the significance of background context information for small object detection, our network samples long-term frames from the whole video and tries to acquire training frames with more background differences. The frame selection module can select the long-term frame with the lowest similarity to the current frame, which is further used to enrich background context information. The architecture of the frame selection module is shown in Fig. 3.", + "bbox": [ + 75, + 315, + 467, + 479 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Given the current frame feature $F_{c}$ and the sampled long-term frame feature $F_{g}^{i}$ , this module tries to select the long-term frame that is most dissimilar to $F_{c}$ from $m$ candidate long-term frames to be used for Proposal-Level feature aggregation. As a result, this module outputs the index of the long-term frame with the lowest similarity, which can be interpreted as", + "bbox": [ + 75, + 481, + 467, + 585 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\ni n d = \\underset {i \\in [ 1, \\mathrm {m} ]} {\\operatorname {a r g m i n}} \\left\\{S i m \\left(g \\left(F _ {c}\\right), g \\left(F _ {g} ^ {i}\\right)\\right) \\right\\} \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 142, + 598, + 467, + 626 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $ind$ is the index of the selected long-term frame, $Sim$ is the similarity function used to calculate the similarity between different input features, $g$ represents the feature embedding function, $i \\in [1,m]$ indicates the $i^{th}$ candidate long-term frame feature, and $argmin$ is used to calculate the index of the long-term frame with the lowest similarity. Similarity function $Sim$ can be formulated as", + "bbox": [ + 75, + 636, + 467, + 742 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {S i m} (X, Y) = \\frac {X \\cdot Y}{\\sqrt {\\dim}} \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 197, + 752, + 467, + 785 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "According to formula 4, cosine distance is used to calculate the similarity between the current frame feature $g(F_{c})$ and long-term frame feature $g(F_{g}^{i})$ , and dim represents the dimension of the input feature. In formula 3, feature embedding function $g$ incorporates adaptive pooling, dimension reduction, and max pooling, as shown in Fig. 3. Suppose the shape of the input feature $F_{c}$ is $[N,C,H,W]$ , where", + "bbox": [ + 75, + 794, + 467, + 900 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/40a0dc616fe1439cccecfe0900a881081c55cffa8be9bdb6ebecc2ccce84ed2d.jpg", + "image_caption": [ + "Figure 4. Details of long short-term feature aggregation. Input features are first grouped, then make spatio-temporal aggregation, and finally concatenated to get the enhanced feature. The \"Location coding\" is used in the second stage: short-term feature aggregation. Best viewed in color and zoomed in." + ], + "image_footnote": [], + "bbox": [ + 504, + 87, + 885, + 242 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$N, C, H, W$ stands for batch size, channels, height, and width, respectively. The feature is processed by adaptive average pooling on spatial domains and reshaped to a 4D tensor $[N, C, 1, 1]$ to get the global spatial feature of the image. To calculate the similarity more conveniently, the feature then reduces the dimension and is reshaped to the 2D tensor $[N, C]$ , and the most representative feature is selected by max pooling. Finally, the 4D feature $[N, C, H, W]$ is reshaped to 2D $[1, C]$ .", + "bbox": [ + 498, + 349, + 890, + 484 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For selected index ind, the long-term frame feature $F_{g}^{ind}$ has the lowest background context similarity with the current frame feature. In training, it provides more diverse real context information for small object detection.", + "bbox": [ + 498, + 484, + 890, + 546 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Long short-term feature aggregation module", + "text_level": 1, + "bbox": [ + 500, + 558, + 877, + 574 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Short-term frames in the local temporal range are employed in several recent works to enhance the current frame [2, 4, 5]. Nevertheless, only fusing short-term frames can not fully use the information from the whole video and has significant limitations. The long-term frame is therefore introduced to supplement context information. Motivated by the multi-head attention mechanism [12], a long short-term feature aggregation module that conducts feature aggregation on Proposal-Level is proposed. It effectively integrates the long-term frame features and short-term frame features into the current frame features. The long short-term feature aggregation includes two stages: long-term feature aggregation and short-term feature aggregation, the details of long short-term feature aggregation are shown in Fig. 4.", + "bbox": [ + 498, + 582, + 890, + 792 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Long-term feature aggregation: The input of the long-term feature aggregation module is the short-term frame Proposal-Level features $X_{s} \\in [N_{1}, C]$ and the long-term frame Proposal-Level features $X_{g} \\in [N_{2}, C]$ , where $N_{1}$ and $N_{2}$ represent the number of features reserved and $C$ represents the channels of features. To combine information from different channels and subspaces, input features", + "bbox": [ + 498, + 795, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "14617", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "are first divided into $K$ groups. The features after grouping can be formulated as", + "bbox": [ + 75, + 90, + 468, + 119 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nX ^ {k} = X [:, (k - 1) \\frac {C}{K}: k \\frac {C}{K} ] \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 171, + 128, + 468, + 159 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $X$ could be long-term frame Proposal-Level features $X_{g}$ or short-term frame Proposal-Level features $X_{s}$ , $C$ represents the channels of features, $K$ is the number of groups, $k$ means the $k^{th}$ group, and $X^{k}$ denotes the segment of the $k^{th}$ group on the channel dimension. Every group makes spatio-temporal aggregation and is concatenated to each other.", + "bbox": [ + 76, + 167, + 468, + 271 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nX _ {g + s} = \\operatorname {c o n c a t} \\left(\\varphi \\left(X _ {s} ^ {k}, X _ {g} ^ {k}\\right)\\right) \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 171, + 271, + 468, + 292 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $X_{g + s}$ denotes the enhanced short-term frame features, concat denotes concatenation, and the spatiotemporal aggregation function $\\varphi$ effectively aggregates long-term frame features and short-term frame features. $\\varphi$ can be formulated as", + "bbox": [ + 75, + 295, + 468, + 369 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\{ \\begin{array}{l} \\varphi \\left(X _ {s} ^ {k}, X _ {g} ^ {k}\\right) = X _ {s} ^ {k} + \\operatorname {s o f t m a x} (\\omega) \\cdot X _ {g} ^ {k} \\\\ \\omega = \\operatorname {S i m} \\left(\\omega_ {s} \\cdot X _ {s} ^ {k}, \\omega_ {g} \\cdot X _ {g} ^ {k}\\right) + \\operatorname {S i m} \\left(\\mu^ {\\prime}, \\omega_ {g} \\cdot X _ {g} ^ {k}\\right) \\end{array} \\right. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 98, + 377, + 468, + 421 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To obtain a plug-and-play module, the spatio-temporal aggregation function $\\varphi$ utilizes residual connection (as shown in the dotted box in Fig. 4). $X_{g}^{k}$ and $X_{s}^{k}$ are fused in residual function, attention $\\omega$ serves as a correlation weight that consists of two parts: the cosine similarity between short-term frame features and long-term frame features to associate short-term frame and long-term frame, and the cosine similarity between long-term frame features and a group of learnable weights $\\mu^{\\prime}$ to associate different channels of the long-term frame, $\\omega_{s}$ and $\\omega_{g}$ are linear transformation matrixes and also fully connected layers. Definition of Sim is same as formula 4.", + "bbox": [ + 75, + 429, + 468, + 608 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Short-term feature aggregation: Only high-level semantic information of the long-term frame is integrated into the short-term frame during long-term feature aggregation. Considering the strong time continuity between the short-term frame and the current frame, the location information of the short-term frame is also fused into the current frame, as shown in Fig. 4 \"location coding\". Let $r_s = \\{x_s, y_s, h_s, w_s\\}$ be the location information of Regions of Interest (RoIs) in the short-term frame which includes the center point $x_s, y_s$ and height and width $h_s, w_s$ of each RoI, and let $r_c$ be the location information of RoIs in the current frame. The location correlation weight can be represented as", + "bbox": [ + 75, + 609, + 468, + 806 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\{ \\begin{array}{l} \\omega_ {r} = \\operatorname {r e l u} \\left(\\omega_ {c s} \\cdot \\psi \\left(r _ {c}, r _ {s}\\right)\\right) \\\\ \\psi \\left(r _ {c}, r _ {s}\\right) = \\left\\{\\log \\left(\\frac {\\left| x _ {c} - x _ {s} \\right|}{w _ {c}}\\right), \\log \\left(\\frac {\\left| y _ {c} - y _ {s} \\right|}{h _ {c}}\\right), \\log \\left(\\frac {w _ {c}}{w _ {s}}\\right), \\log \\left(\\frac {h _ {c}}{h _ {s}}\\right) \\right\\} \\end{array} \\right. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 86, + 816, + 468, + 861 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\omega_{r}$ denotes location correlation weight, the nonlinear function relu is used to reduce redundant information, $\\omega_{cs}$ is", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "the linear transformation matrix and also a fully connected layer in the network, and $\\psi$ is utilized to code the location information of the current frame and the short-term frame to make the module translation invariant. The correlation weight of short-term feature aggregation can be represented as", + "bbox": [ + 496, + 90, + 890, + 179 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\omega = \\operatorname {S i m} \\left(\\omega_ {c} \\cdot X _ {c} ^ {k}, \\omega_ {g + s} \\cdot X _ {g + s} ^ {k}\\right) \\tag {9} \\\\ + S i m \\left(\\mu^ {\\prime \\prime}, \\omega_ {g + s} \\cdot X _ {g + s} ^ {k}\\right) + \\omega_ {r} ^ {k} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 581, + 186, + 890, + 227 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $X_{c}^{k}$ stands for the current frame Proposal-Level features after grouping, $\\omega_{g+s}$ , $\\omega_{c}$ are fully connected layers used to reshape the feature, $\\omega$ is the adaptive weight including three parts: the cosine similarity between enhanced short-term frame features and current frame features, the cosine similarity between enhanced short-term frame features and a group of learnable weights $\\mu''$ , and the location correlation weight between the current frame and short-term frame after grouping. The other steps of short-term feature aggregation are the same as long-term feature aggregation and needless to be described again.", + "bbox": [ + 496, + 244, + 890, + 411 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 434, + 630, + 452 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Experiment Setup", + "text_level": 1, + "bbox": [ + 500, + 463, + 674, + 479 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets and Evaluation Setup: We conduct experiments on ImageNet-VID [20] and FL-Drones [19]. ImageNet-VID is a widely used large-scale benchmark for video object detection, which contains 3862 videos in the training set, 555 videos in the validation set, and a total of 30 categories. $mAP$ is used for evaluation on ImageNet-VID. To evaluate the performance of the proposed method on video small object detection, we also make use of the FL-Drones dataset consisting of 14 videos and 38948 frames. The flying drones in the dataset can be regarded as small objects because the average size of annotated drones is $25 \\times 16$ and the frame resolutions are $640 \\times 480$ and $752 \\times 480$ . This dataset is quite challenging due to the extreme illumination and relatively small size. According to the author [19], half of the data is used for training, and the other half is used for testing. And $AP$ is used as the evaluation metric for FL-Drones since it is a video dataset for small objects.", + "bbox": [ + 496, + 489, + 890, + 744 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation Details: The proposed algorithm is trained and tested using 4 16GB NVIDIA Tesla V100. The baseline used in this paper is Faster R-CNN. Following the multi-task loss in baseline, the whole network is optimized with both classification and regression losses. SGD is selected as the optimizer and the model is trained for 120000 iterations on ImageNet-VID and 66000 iterations on FLDrones. The learning rate is set to 0.001 and updated using WarmupMultiStepLR [18], which means the model first has 500 warm-up iterations to improve stability.", + "bbox": [ + 496, + 750, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "14618", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Comparison with state-of-the-art", + "text_level": 1, + "bbox": [ + 76, + 90, + 366, + 107 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ImageNet-VID dataset: Comparison results on this dataset are shown in Table 1. All algorithms adopt the same feature extraction network to be compared fairly, and the results of the state-of-the-art works are collected from published papers.", + "bbox": [ + 75, + 114, + 468, + 189 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/1c3beae9af59108acce164794d07074516bba2916aa5656fdea57d470d5f6497.jpg", + "table_caption": [ + "Table 1. Quantitative results on the ImageNet-VID dataset $(\\%)$" + ], + "table_footnote": [], + "table_body": "
MethodBackbonemAP
FGFA [28]ResNet10176.3
STMN [24]ResNet10180.5
LongRange [21]ResNet10181.0
D&T [6]ResNet10175.8
MANet [22]ResNet10178.1
STSN [2]ResNet10178.9
RDN [5]ResNet10181.8
SELSA [23]ResNet10180.3
MEGA [3]ResNet10182.9
LSTFE-NetResNet10183.4
", + "bbox": [ + 130, + 241, + 411, + 412 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "It is obvious that our method outperforms other state-of-the-art methods and achieves the highest $mAP$ of $83.4\\%$ . Results show that the LSTFE-Net can better collect the information from long-term and short-term frames and enhance the feature.", + "bbox": [ + 75, + 441, + 468, + 516 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "FL-Drones dataset: As a video dataset for small objects, few results of other classical methods can be found on this dataset which means we need to conduct experiments using these methods ourselves. For a more comprehensive comparison, ResNet50 and ResNet101 are respectively used as the feature extraction network for analysis. The results are shown in Table 2.", + "bbox": [ + 75, + 517, + 468, + 622 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "According to Table 2, our method achieves the best small object detection performance no matter what the feature extraction network is. Our LSTFE-Net obtains the highest $AP$ of $37.8\\%$ and outperforms the strongest competitor TransVOD by $0.9\\%$ $AP$ when ResNet50 is used. For ResNet101, our LSTFE-Net achieves an $AP$ of $46.8\\%$ , $4.4\\%$ higher than MEGA. Fig. 5 shows some qualitative comparison results of our LSTFE-Net versus other state-of-the-art works.", + "bbox": [ + 75, + 623, + 468, + 758 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Ablation Studies", + "text_level": 1, + "bbox": [ + 76, + 770, + 240, + 786 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We conduct ablation studies to validate the effectiveness of each component in our model on the FL-Drones dataset.", + "bbox": [ + 75, + 794, + 468, + 824 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Spatio-temporal feature alignment module: $k$ cascaded deformable convolutional blocks are applied in this module, and experiments are conducted in this section to study the influence of the value of $k$ on spatio-temporal modeling. The short-term frame and the long-term frame", + "bbox": [ + 75, + 825, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/80cff4ca2be9f9b452b57355e0596c58ba92d0568f8ae2b6896f4d28d88a8cc3.jpg", + "table_caption": [ + "Table 2. Quantitative results on the FL-Drones dataset $(\\%)$" + ], + "table_footnote": [], + "table_body": "
MethodAP
ResNet50ResNet101
DFF [27]19.522.4
FGFA [28]21.224.5
TransVOD [11]36.935.2
RDN [5]35.942.1
MEGA [3]36.542.4
LSTFE-Net37.846.8
", + "bbox": [ + 542, + 126, + 846, + 252 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c716b97fdffa670b87afa3fd9767e467661aec5e2c481364a473601c88bd4537.jpg", + "image_caption": [ + "Figure 5. Qualitative comparison of our LSTFE-Net versus other state-of-the-art works. Blue boxes represent the detection. Best viewed in color and zoomed in." + ], + "image_footnote": [], + "bbox": [ + 503, + 280, + 890, + 494 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/20065713fc65ae40845cd87ba3dacea2f335b3b4a2c209547a86c3fa55e55941.jpg", + "table_caption": [ + "Table 3. Ablation study of the spatio-temporal feature alignment module(%)" + ], + "table_footnote": [], + "table_body": "
BackboneAP
k = 0ResNet10142.1
k = 1ResNet10145.4
k = 2ResNet10139.4
k = 3ResNet10139.3
", + "bbox": [ + 591, + 612, + 797, + 694 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "are first added to the baseline, and then the value of $k$ is adjusted. Results are shown in Table 3:", + "bbox": [ + 498, + 732, + 890, + 761 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3 shows that the network achieves an $AP$ of $42.1\\%$ if the spatio-temporal feature alignment module is not used. When $k = 1$ , $AP$ increases by $3.3\\%$ to $45.4\\%$ . As $k$ increases from 1 to 3, $AP$ decreases gradually. To explore the reasons for the decreasing detection performance, the offset matrixes with different values of $k$ are visualized, as shown in Fig. 6.", + "bbox": [ + 496, + 763, + 890, + 868 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The offset matrix with $k = 1$ is visualized in Fig. 6(b), where it is obvious that offsets are generally larger at the", + "bbox": [ + 500, + 869, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "14619", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f965767d00c9061d02480474ea5217f7997862226bebc0cd533793b1a349952c.jpg", + "image_caption": [ + "(a)input" + ], + "image_footnote": [], + "bbox": [ + 81, + 90, + 171, + 143 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7d87939a2af6bb33c80a82a80c491710e427e793f3d2ac2c41bda10d2884ccb9.jpg", + "image_caption": [ + "(b) $k = 1$" + ], + "image_footnote": [], + "bbox": [ + 174, + 90, + 264, + 143 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/10bd77638127979172d8313cca09bf2afe8c95757d278debd5e7588d0c13a47a.jpg", + "image_caption": [ + "(c) $k = 2$", + "Figure 6. Visualization of offset matrix. The deeper the color, the larger the offset." + ], + "image_footnote": [], + "bbox": [ + 272, + 90, + 362, + 143 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f8ea147d93d7c710195b2d094361312a3bd565b6d5ca71949228355dc9eeabe2.jpg", + "image_caption": [ + "(d) $k = 3$" + ], + "image_footnote": [], + "bbox": [ + 372, + 90, + 460, + 143 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/f02b7127a8ca20a80e7dfddd5ea04f7a8bd4795fe4355fddf2d26293f16eebe7.jpg", + "table_caption": [ + "Table 4. Ablation study of frame selection module $(\\%)$" + ], + "table_footnote": [], + "table_body": "
Number of long-term framesBackboneAP
Long-term framesFrame selection
1ResNet10129.529.9
2ResNet10135.135.9
3ResNet10133.934.8
4ResNet10129.630.7
", + "bbox": [ + 83, + 253, + 464, + 329 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "moving target and smaller in the stationary background area. This indicates that the network can better model the correlation between the same object of different frames. With the increase of $k$ , temporal information is mixed up, which makes the offset learned by the spatio-temporal feature alignment module gradually disordered. When $k = 3$ , the offset matrix can hardly represent the relationship between frames. Adding the offset in the convolution will hinder the normal extraction of features and make the detection result worse.", + "bbox": [ + 75, + 368, + 467, + 518 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Frame selection module: The detection results before and after using the frame selection module are compared. To emphasize the impact of the frame selection module, the number of short-term frames is set to 0. After $m$ long-term frames are sampled, additional $2m$ frames are then sampled and $m$ frames are selected by the frame selection module. The results are shown in Table 4:", + "bbox": [ + 75, + 520, + 467, + 625 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 4 demonstrates how the number of long-term frames will affect the detection performance of small objects. The promotion effects of the frame selection module vary for different numbers of sampled long-term frames. When there are 4 sampled frames, $AP$ improves most $(1.1\\%)$ . And when the number of sampled frames is 2, $AP$ improves by $0.8\\%$ to $35.9\\%$ (highest).", + "bbox": [ + 75, + 627, + 467, + 733 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Long short-term feature aggregation module: In this section, concatenation is used as a simple feature aggregation method to be compared. The only difference between short-term feature aggregation and long-term feature aggregation is the utilization of location coding, so the contribution of location coding is verified. Short-term frames and long-term frames are first added to the baseline, and then simple feature aggregation, long short-term feature aggregation without location coding, and long short-term feature aggregation are used for experiments separately. The results are shown in Table 5.", + "bbox": [ + 75, + 734, + 467, + 898 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/261b130bbc98aa6338b86b24b2528758b295bf621fab338c9b4bd6f0ccd24e5b.jpg", + "table_caption": [ + "Table 5. Ablation study of long short-term feature aggregation module $(\\%)$" + ], + "table_footnote": [], + "table_body": "
MethodBackboneAP
simple feature aggregationResNet10139.9
long short-term feature aggregation without location codingResNet10141.2
long short-term feature aggregationResNet10142.1
", + "bbox": [ + 532, + 140, + 857, + 208 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 5 shows that the simple feature aggregation method obtains an $AP$ of $39.9\\%$ , while the proposed long short-term feature aggregation method can improve $AP$ to $42.1\\%$ . Additionally, the $AP$ drops to $41.2\\%$ when the location coding is removed, which means that the location coding can bring a gain of $0.9\\% AP$ .", + "bbox": [ + 496, + 244, + 890, + 335 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 351, + 617, + 366 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "For small objects, we propose an LSTFE-Net to enhance the feature with two important sources of information from the video. A spatio-temporal feature alignment module is proposed to model the temporal information between the short-term frame and the current frame. It uses deformable convolution to make connections between objects of different frames, and conducts feature enhancement on Pixel-Level. Considering that the background context information of the object is single, the frame selection module is used to select the long-term frame with the most distinct feature from the current frame, which is further used to enrich the vital context information for small object detection. To effectively fuse the features of different types of frames, we develop a long short-term feature aggregation module, where context information from the long-term frames and the temporal information from the short-term frames are incorporated into the current frame by stages. Experiments are carried out on ImageNet-VID and FL-Drones to compare our method with other state-of-the-art methods and conduct ablation studies. The results show that the proposed method achieves superior small object detection performance in videos.", + "bbox": [ + 496, + 376, + 890, + 708 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement", + "text_level": 1, + "bbox": [ + 500, + 723, + 658, + 739 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work is supported by National Natural Science Foundation of China (U1903214), Major Science and Technology Projects of Jilin Province (20210301030GX), Natural Science Foundation of Guangdong Province (2021A1515012233)", + "bbox": [ + 496, + 748, + 890, + 818 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 500, + 832, + 596, + 848 + ], + "page_idx": 7 + }, + { + "type": "ref_text", + "text": "[1] Muhammad Waseem Ashraf, Waqas Sultani, and Mubarak Shah. Dogfight: Detecting drones from drones videos. 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In Proceedings of the IEEE international conference on computer vision, pages 408-417, 2017. 1, 2, 3, 7" + ], + "bbox": [ + 78, + 90, + 468, + 273 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "14622", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/LSTFE-Net_Long Short-Term Feature Enhancement Network for Video Small Object Detection/f85fdbe6-5d06-483d-a4fa-dfa64b2fcc9b_model.json b/2023/LSTFE-Net_Long Short-Term Feature Enhancement Network for Video Small Object Detection/f85fdbe6-5d06-483d-a4fa-dfa64b2fcc9b_model.json new file mode 100644 index 0000000000000000000000000000000000000000..6e9a23d8c70e916e82a02ca1ea72209a84d5b41c --- /dev/null +++ b/2023/LSTFE-Net_Long Short-Term Feature Enhancement Network for Video Small Object Detection/f85fdbe6-5d06-483d-a4fa-dfa64b2fcc9b_model.json @@ -0,0 +1,1903 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.002, + 0.808, + 0.022 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation." + }, + { + "type": "header", + "bbox": [ + 0.297, + 0.017, + 0.752, + 0.028 + ], + "angle": 0, + "content": "Except for this watermark, it is identical to the accepted version;" + }, + { + "type": "header", + "bbox": [ + 0.294, + 0.031, + 0.754, + 0.046 + ], + "angle": 0, + "content": "the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.092, + 0.13, + 0.88, + 0.178 + ], + "angle": 0, + "content": "LSTFE-Net:Long Short-Term Feature Enhancement Network for Video Small Object Detection" + }, + { + "type": "text", + "bbox": [ + 0.126, + 0.203, + 0.842, + 0.24 + ], + "angle": 0, + "content": "Jinsheng Xiao\\(^{1}\\), Yuanxu Wu\\(^{1}\\), Yunhua Chen\\(^{2*}\\), Shurui Wang\\(^{1}\\), Zhongyuan Wang\\(^{1}\\), Jiayi Ma\\(^{1}\\) \n1. Wuhan University, China" + }, + { + "type": "text", + "bbox": [ + 0.299, + 0.24, + 0.671, + 0.258 + ], + "angle": 0, + "content": "2. Guangdong University of Technology, China" + }, + { + "type": "text", + "bbox": [ + 0.212, + 0.259, + 0.758, + 0.275 + ], + "angle": 0, + "content": "{xiaojs,whuwuyuanxu,shuruiwang}@whu.edu.cn，yhchen@gdut.edu.cn" + }, + { + "type": "text", + "bbox": [ + 0.324, + 0.278, + 0.642, + 0.292 + ], + "angle": 0, + "content": "wzyhope@163.com, jyma2010@gmail.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.327, + 0.314, + 0.343 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.358, + 0.474, + 0.722 + ], + "angle": 0, + "content": "Video small object detection is a difficult task due to the lack of object information. Recent methods focus on adding more temporal information to obtain more potent high-level features, which often fail to specify the most vital information for small objects, resulting in insufficient or inappropriate features. Since information from frames at different positions contributes differently to small objects, it is not ideal to assume that using one universal method will extract proper features. We find that context information from the long-term frame and temporal information from the short-term frame are two useful cues for video small object detection. To fully utilize these two cues, we propose a long short-term feature enhancement network (LSTFE-Net) for video small object detection. First, we develop a plug-and-play spatio-temporal feature alignment module to create temporal correspondences between the short-term and current frames. Then, we propose a frame selection module to select the long-term frame that can provide the most additional context information. Finally, we propose a long short-term feature aggregation module to fuse long short-term features. Compared to other state-of-the-art methods, our LSTFE-Net achieves \\(4.4\\%\\) absolute boosts in AP on the FL-Drones dataset. More details can be found at https://github.com/xiaojs18/LSTFE-Net." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.748, + 0.21, + 0.765 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.774, + 0.47, + 0.88 + ], + "angle": 0, + "content": "Video small object detection plays an important role in many fields such as automatic driving, remote sensing, medical image, and industrial defect detection [26]. However, it is still a difficult task due to the lack of pixel information and the difficulty of feature extraction. Therefore, the topic of how to enhance the features of small objects has attracted great attention [1,7, 16]." + }, + { + "type": "image", + "bbox": [ + 0.513, + 0.324, + 0.889, + 0.542 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.552, + 0.895, + 0.706 + ], + "angle": 0, + "content": "Figure 1. The architecture of the proposed LSTFE-Net. The current frame (Cur-frame), short-term frames (ST-frames) near the Cur-frame, and long-term frames (LT-frames) sampled from the whole video first go through the feature extraction network. Then the Cur-frame feature and ST-frame features are connected through the spatio-temporal feature alignment module, and the frame selection module searches the background context of LT-frame features. After getting the Proposal-Level (PL) features, the long short-term feature aggregation module finally integrates the long short-term features into the Cur-frame to make feature enhancement. Best viewed in color and zoomed in." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Some recent works have proved that the improvement of video small object detection performance requires full utilization of information in the temporal dimension. While detecting small objects in the current frame may suffer from many problems such as motion blur, low resolution, and too small size, effective modeling of information from other frames can help address these problems [2, 4, 9, 17]. There is a high similarity in nearby frames because of the strong time continuity between them, so it is natural to emphasize the importance of short-term frames, which are near the current frame. According to FGFA [28] and STSN [2]," + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.888, + 0.242, + 0.901 + ], + "angle": 0, + "content": "*The corresponding author" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14613" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.122 + ], + "angle": 0, + "content": "short-term frame features can be aligned and aggregated to provide more useful information for small objects." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.125, + 0.471, + 0.32 + ], + "angle": 0, + "content": "Context information is important for small object detection [16,25]. Because a large number of images are sampled from the same video for the same object, the background context information of the object is single. Additionally, only part of the frames in the video are sampled as current frames (such as 15 frames) while training, which results in the lack of real background context information and reduces the robustness of the training model. Compared to features in a short range, features from the whole video level can be more discriminative and robust [21, 23]. And it is noticed in prior works [9, 23] that more contextual information will be provided when using long-term frames sampled from the whole video." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.324, + 0.471, + 0.627 + ], + "angle": 0, + "content": "The impacts of short-term and long-term frames in detection have been studied in recent methods. However, these methods have obvious disadvantages in both efficiency and accuracy, especially for small objects in videos. Some methods [22, 27, 28] extract information from the short-term frame and exploit the flow model to propagate features across adjacent frames, however, this is expensive because the flow model is hard to construct and transplant. Other methods [21, 23] focus on semantic information from long-term frames and incorporate randomly sampled long-term frames in detection, which causes uncertainty of detection performance and the loss of valuable information. Besides, these methods above cannot figure out the specific information that matters most for small objects from frames. Some methods [21-23, 27, 28] think the information in the video is single and miss considering distinct information from different frames, getting inadequate features. Other methods [3, 5] focus on extracting high-level features from the video which are not suitable for small objects due to their special properties." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.629, + 0.47, + 0.901 + ], + "angle": 0, + "content": "To better mine information from both short-term frames and long-term frames, we propose a long short-term feature enhancement network (LSTFE-Net) for video small object detection. Specifically, the features of short-term frames are expected to correspond to the current frame in a low-cost and effective way, so a spatio-temporal feature alignment module is designed to propagate features across nearby frames. Further, in order to increase the benefit of aligned features while not increasing too much complexity of the model, a spatio-temporal feature aggregation method is also added. The context information is expected to be highlighted from the whole video, prompting a frame selection module to select the long-term frame feature. The goal is to make effective feature enhancement after the features are collected, and the establishment of connections between different features is enforced. A long short-term feature aggregation module is devised to aggregate features from the current frame, the short-term frames, and the long" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.167 + ], + "angle": 0, + "content": "term frames by stages. The performance of the proposed method is evaluated on the open dataset, and experiment results demonstrate that our method has obvious advantages in video small object detection. The architecture of the network is shown in Fig. 1." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.168, + 0.859, + 0.181 + ], + "angle": 0, + "content": "Our main contributions are summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.183, + 0.891, + 0.213 + ], + "angle": 0, + "content": "(1) An LSTFE-Net is proposed to effectively enhance small object features and improve detection performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.213, + 0.892, + 0.348 + ], + "angle": 0, + "content": "(2) A plug-and-play spatio-temporal feature alignment module is designed for aligning features across adjacent frames. A flexible way to make Pixel-Level feature enhancement for small objects using aligned features is also explored. Combined with the Proposal-Level feature enhancement, this module achieves multi-level enhancement to improve the feature expressiveness. The whole module is easy to transplant and proved to be effective, which reveals its potential ability to benefit most of the works." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.349, + 0.892, + 0.439 + ], + "angle": 0, + "content": "(3) A frame selection module is proposed to ensure the utilization of high-value input data, and it selects the long-term frame feature with the most context information. This module reinforces the network to automatically look for useful information for small objects, improving its stability and performance in video small object detection." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.44, + 0.892, + 0.56 + ], + "angle": 0, + "content": "(4) To effectively integrate the long-term frame features and short-term frame features into the current frame, a long short-term feature aggregation module is proposed to aggregate different features in different stages. This enables the relations between Proposal-Level features to be built adaptively based on an attention mechanism, which also means our feature enhancement for small objects can be accomplished in a general and limitless way." + }, + { + "type": "list", + "bbox": [ + 0.498, + 0.183, + 0.892, + 0.56 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.574, + 0.65, + 0.589 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.892, + 0.719 + ], + "angle": 0, + "content": "Object detection from images has achieved considerable success and introduced some leading detectors in recent years. Based on the early proposed detectors, video object detection is intensively studied as a more challenging task. It is proved that exploiting information from other frames can significantly enhance the detection of the current frame, so temporal feature aggregation is gaining attention and introduced into video small object detection." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Object detection in videos: The appropriate use of the temporal information in the video to increase detection accuracy is a fundamental difficulty in video object detection. Adapting the image object detection algorithm to the video domain is challenging because of the complex spatial and temporal changes in videos. SeqNMS [10], TCN [15], and T-CNN [14] apply post-processing to video object detection to handle the complexities of videos. SeqNMS [10] links bounding boxes from different frames iff their Intersection over Union \\((IoU)\\) is above some certain threshold and re-ranks those linked boxes; TCN [15] introduces the tubelet components and proposes a temporal convolu" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.52, + 0.957 + ], + "angle": 0, + "content": "14614" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.471, + 0.242 + ], + "angle": 0, + "content": "tional neural network to incorporate temporal information, which improves detection performance across frames. TCNN [14] first uses the still-image object detection algorithm to get single frame detection results and associates the results using optical flows. However, none of these methods based on post-processing can be trained end-to-end, and their performance is yet to be improved. Our method, in contrast, directly uses temporal information in videos without post-processing and can be trained end-to-end, which brings great convenience." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.246, + 0.471, + 0.668 + ], + "angle": 0, + "content": "Temporal feature aggregation: Recent works have also focused on ways to aggregate temporal features with different distances from the current frame, including short-term frame and long-term frame features, to enhance the feature of the object. DFF [27] uses a flow field predicted by FlowNet [13] to make the key frame feature align to short-term frames, thus reducing the redundant computation and accelerating the network. Unlike DFF, FGFA [28] mainly employs flow motion to make short-term frame features align to the current frame and then fuses these two kinds of features to improve detection accuracy. MANet [22] achieves the feature calibration module and the feature aggregation module on both pixel-level and instance-level based on FGFA and uses the motion pattern reasoning module to aggregate features from two different levels. Unlike short-term frames, long-term frames are usually sampled from the whole training video. Since there is little time continuity between the long-term frame and the current frame, the fusion of high-level semantic information is paid more attention to. To make more effective feature aggregation, SELSA [23] performs one innovative work by calculating the semantic similarity between current frames and long-term frames. STMN [24] uses the recurrent computation unit as the spatio-temporal memory module to pass semantic information between different frames. While using both local and global features to enhance the features of the current frames, MEGA [3] introduces a memory module to store more temporal features." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.671, + 0.47, + 0.838 + ], + "angle": 0, + "content": "Video small object detection: A few researchers have proposed to improve the detection accuracy of small objects by leveraging temporal information in videos. Motion R-CNN [7] provides additional auxiliary information for small objects based on the frame differencing method and improves small object detection performance in optical remote sensing videos. DogFight [1] proposes to use a two-stage segmentation-based approach employing spatiotemporal attention cues, where objects are localized during the first stage and the object location is tracked and filtered using temporal information during the second stage." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.84, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Although both short-term frame features and long-term frame features have been used to improve detection performance, the information mined from these features is still not enough for them to build strong connections with the" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.349 + ], + "angle": 0, + "content": "small object. We focus on several major problems and aim to get more powerful small object features through enhancement. To be specific, while DFF [27] and FGFA [28] require FlowNet which is difficult to construct and transplant, our method uses a plug-and-play spatio-temporal feature alignment module to make feature alignment and Pixel-Level enhancement. Instead of being simply randomly sampled from the video like MEGA [3], the long-term frame in this paper is selected by the frame selection module to enrich context information for small object detection. Unlike the above methods exclusively focusing on exploiting one kind of information from either the short-term frame or the long-term frame [22, 23, 27, 28], we fully consider the various information from both the short-term frame and long-term frame. The high-level features in this paper can work better for small objects than those in [3, 5] because of these purposeful designs." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.366, + 0.599, + 0.381 + ], + "angle": 0, + "content": "3. Methods" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.392, + 0.7, + 0.407 + ], + "angle": 0, + "content": "3.1. Framework overview" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.416, + 0.892, + 0.673 + ], + "angle": 0, + "content": "The architecture of the LSTFE-Net is shown in Fig. 1. Besides the current frame, multiple short-term frames and long-term frames are also sampled from the video and input to the network. The feature extraction network first extracts the frame features of the input. Then different frame features are processed differently according to their characteristics. Because the short-term frames are sampled adjacent to the current frame, there is extensive temporal information between them. A plug-and-play spatio-temporal feature alignment module is designed to make alignment of the current frame feature and short-term frame features using cascaded deformable convolution blocks. This alignment can be described in the form of offsets in convolution, which helps the convolutional neural network sample more features from object regions to precisely enhance the small object of the current frame. The aligned features are further fused into the current frame feature on a low level." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.892, + 0.901 + ], + "angle": 0, + "content": "It is inappropriate to make feature alignment between the current frame and long-term frames because there is no evident time continuity between them and their object features have great displacement in space. Considering that background context information is crucial and single to small object detection, long-term frames are employed to provide more background context information. It is natural to expect the long-term frames with the most context information to be further used in the network, so a frame selection module is devised. After feature embedding, it selects the long-term frame feature with the lowest similarity to the current frame feature. After the above modules, the Region Proposal Network (RPN) is used to generate proposals and Region of Interest (RoI) Align is applied to make feature extraction, getting the Proposal-Level features of different" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14615" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.092, + 0.462, + 0.23 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.241, + 0.47, + 0.31 + ], + "angle": 0, + "content": "Figure 2. Spatio-temporal feature alignment module. The shortterm frame feature \\( f_{s} \\) is first aligned based on deformable convolution, and then integrated into the current frame feature \\( f_{t} \\) using spatio-temporal feature aggregation. Best viewed in color and zoomed in." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.339, + 0.131, + 0.351 + ], + "angle": 0, + "content": "frames." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.353, + 0.47, + 0.596 + ], + "angle": 0, + "content": "Effectively integrating long-term frame features and short-term frame features into the current frame feature is also a key part of feature enhancement. To better integrate different kinds of frame features, we divide the long short-term feature aggregation into two stages: long-term feature aggregation and short-term feature aggregation. In the first stage, the feature aggregation between long-term frames and short-term frames is conducted, which provides additional context information for small objects. Next, the feature aggregation between short-term frames and the current frame is carried out in the second stage, and also the location differences between the frames are considered. This module models the relations between Proposal-Level features adaptively and universally, ensuring feature enhancement for small objects. The above algorithms will be introduced in detail in the following sections." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.606, + 0.441, + 0.621 + ], + "angle": 0, + "content": "3.2. Spatio-temporal feature alignment module" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.629, + 0.469, + 0.825 + ], + "angle": 0, + "content": "There is a strong similarity between the current frame and the short-term frames. Features of the same object are typically not spatially aligned between frames due to the movement in videos. Hence direct fusion of features between frames will result in feature interference, ghost effects, and even lower detection performance. Deformable convolution [8] learns multiple offsets of the spatial location during convolution. We design a spatio-temporal feature alignment module based on deformable convolution to learn offsets and make feature alignment between frames, and a spatio-temporal feature aggregation module is proposed to conduct Pixel-Level feature enhancement of the current frame. The specific architecture is shown in Fig. 2." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.826, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Given a frame \\(I_{t}\\) at time \\(t\\) and a nearby short-term frame \\(I_{s}\\), let \\(f_{t}\\) and \\(f_{s}\\) indicate spatial features through the feature extraction network from frame \\(I_{t}\\) and \\(I_{s}\\), as shown in Fig. 2 (a). Suppose the shape of \\(f_{t}\\) or \\(f_{s}\\) is \\([C, H, W]\\), where \\(C\\) stands for the channels, \\(H\\) for the height of tensors, and \\(W\\)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.348 + ], + "angle": 0, + "content": "for the width of tensors. To fuse the features, \\( f_{t} \\) and \\( f_{s} \\) are concatenated to get \\( f_{cat} \\). Then \\( f_{cat} \\) is fed to a deformable convolutional block, as shown in Fig. 2 (b). The block generates offsets \\( m_{1} \\in [2 \\times 9, H, W] \\) with \\( 3 \\times 3 \\) convolution, where 9 denotes kernel size \\( 3 \\times 3 \\), 2 denotes offsets in two directions: \\( x \\) and \\( y \\). Finally, \\( m_{1} \\) and \\( f_{cat} \\) are fed to a deformable convolutional layer to get the aligned feature. Our deformable convolutional block is plug-and-play and cascaded, which means multiple blocks can be used in series to make multiple times feature alignments. The final block outputs the final offsets \\( m_{o} \\), and \\( m_{o} \\) and short-term frame feature \\( f_{s} \\) are fed to a deformable convolutional layer to get the aligned short-term feature \\( f_{t+s} \\). In general, the temporal information between the current frame and the short-term frame is used to estimate the spatial offset between object features, which is further used to make the short-term frame feature align with the current frame feature." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.348, + 0.892, + 0.424 + ], + "angle": 0, + "content": "To effectively integrate the aligned short-term frame feature into the current frame feature, a spatio-temporal feature aggregation module is designed to make the adaptive information fuse. The adaptive weight can be expressed by formula 1." + }, + { + "type": "equation", + "bbox": [ + 0.595, + 0.44, + 0.892, + 0.457 + ], + "angle": 0, + "content": "\\[\n\\omega \\left(f _ {t}, f _ {t + s}\\right) = \\rho \\left(l \\left(f _ {t}, f _ {t + s}\\right)\\right) \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.464, + 0.892, + 0.659 + ], + "angle": 0, + "content": "where \\(l\\) is a spatio-temporal function that describes spatiotemporal connections between \\(f_{t}\\) and \\(f_{t + s}\\), and \\(\\rho\\) is the mask function used to calculate the adaptive weight. To fully use temporal information between frames, the frame differencing method is introduced into \\(l\\), which concatenates \\(f_{t} - f_{t + s}, f_{t + s} - f_{t}, f_{t}\\), and \\(f_{t + s}\\) into \\(f_{multi}\\). \\(f_{multi}\\) is then fed to mask function \\(\\rho\\). It goes through two convolutional layers to squeeze the number of channels and fully fuse the information. To improve the generalization ability of the model, the softmax function is then used to generate the final adaptive weight \\(\\omega(f_{t}, f_{t + s})\\). As shown in Fig. 2 (c). Finally, the enhanced current frame feature \\(f\\) is computed by" + }, + { + "type": "equation", + "bbox": [ + 0.595, + 0.66, + 0.891, + 0.695 + ], + "angle": 0, + "content": "\\[\nf = \\sum_ {f _ {j} \\in \\left(f _ {t}\\right)} \\left\\{\\omega \\left(f _ {t}, f _ {j}\\right) \\otimes f _ {t} \\right\\} \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.701, + 0.892, + 0.79 + ], + "angle": 0, + "content": "where \\((f_{t})\\) denotes a collection of aligned short-term frame features near \\(f_{t}\\), \\(\\otimes\\) denotes element-wise multiplication. In this paper, multiple short-term frames are sampled, aligned to the current frame, and adaptively integrated into the current frame to enhance the current frame feature on Pixel-Level." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.802, + 0.72, + 0.817 + ], + "angle": 0, + "content": "3.3. Frame selection module" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Because a large number of images are sampled in the same video for the same object, the background context information of the object is very similar. Object detection algorithms based on deep learning tend to use this similarity to make the feature enhancement for the current object." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "14616" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.088, + 0.468, + 0.21 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.219, + 0.47, + 0.289 + ], + "angle": 0, + "content": "Figure 3. Frame selection module. The current frame feature \\( F_{c} \\) and \\( m \\) long-term frame features \\( \\{F_{g}^{i}\\}_{i = 1}^{m} \\) first get the feature embedding. Then similarities between them are calculated and finally, the index of the long-term frame with the lowest similarity is output. Best viewed in color and zoomed in." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.316, + 0.468, + 0.481 + ], + "angle": 0, + "content": "However, this strategy results in the poor generalization performance of the training model, especially for training data with a high degree of similarity. Considering the significance of background context information for small object detection, our network samples long-term frames from the whole video and tries to acquire training frames with more background differences. The frame selection module can select the long-term frame with the lowest similarity to the current frame, which is further used to enrich background context information. The architecture of the frame selection module is shown in Fig. 3." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.482, + 0.468, + 0.587 + ], + "angle": 0, + "content": "Given the current frame feature \\( F_{c} \\) and the sampled long-term frame feature \\( F_{g}^{i} \\), this module tries to select the long-term frame that is most dissimilar to \\( F_{c} \\) from \\( m \\) candidate long-term frames to be used for Proposal-Level feature aggregation. As a result, this module outputs the index of the long-term frame with the lowest similarity, which can be interpreted as" + }, + { + "type": "equation", + "bbox": [ + 0.143, + 0.599, + 0.468, + 0.627 + ], + "angle": 0, + "content": "\\[\ni n d = \\underset {i \\in [ 1, \\mathrm {m} ]} {\\operatorname {a r g m i n}} \\left\\{S i m \\left(g \\left(F _ {c}\\right), g \\left(F _ {g} ^ {i}\\right)\\right) \\right\\} \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.637, + 0.468, + 0.743 + ], + "angle": 0, + "content": "where \\( ind \\) is the index of the selected long-term frame, \\( Sim \\) is the similarity function used to calculate the similarity between different input features, \\( g \\) represents the feature embedding function, \\( i \\in [1,m] \\) indicates the \\( i^{th} \\) candidate long-term frame feature, and \\( argmin \\) is used to calculate the index of the long-term frame with the lowest similarity. Similarity function \\( Sim \\) can be formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.198, + 0.753, + 0.468, + 0.786 + ], + "angle": 0, + "content": "\\[\n\\operatorname {S i m} (X, Y) = \\frac {X \\cdot Y}{\\sqrt {\\dim}} \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.468, + 0.901 + ], + "angle": 0, + "content": "According to formula 4, cosine distance is used to calculate the similarity between the current frame feature \\( g(F_{c}) \\) and long-term frame feature \\( g(F_{g}^{i}) \\), and dim represents the dimension of the input feature. In formula 3, feature embedding function \\( g \\) incorporates adaptive pooling, dimension reduction, and max pooling, as shown in Fig. 3. Suppose the shape of the input feature \\( F_{c} \\) is \\([N,C,H,W]\\), where" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.088, + 0.887, + 0.243 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.252, + 0.892, + 0.322 + ], + "angle": 0, + "content": "Figure 4. Details of long short-term feature aggregation. Input features are first grouped, then make spatio-temporal aggregation, and finally concatenated to get the enhanced feature. The \"Location coding\" is used in the second stage: short-term feature aggregation. Best viewed in color and zoomed in." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.35, + 0.892, + 0.486 + ], + "angle": 0, + "content": "\\(N, C, H, W\\) stands for batch size, channels, height, and width, respectively. The feature is processed by adaptive average pooling on spatial domains and reshaped to a 4D tensor \\([N, C, 1, 1]\\) to get the global spatial feature of the image. To calculate the similarity more conveniently, the feature then reduces the dimension and is reshaped to the 2D tensor \\([N, C]\\), and the most representative feature is selected by max pooling. Finally, the 4D feature \\([N, C, H, W]\\) is reshaped to 2D \\([1, C]\\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.486, + 0.892, + 0.547 + ], + "angle": 0, + "content": "For selected index ind, the long-term frame feature \\( F_{g}^{ind} \\) has the lowest background context similarity with the current frame feature. In training, it provides more diverse real context information for small object detection." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.559, + 0.878, + 0.575 + ], + "angle": 0, + "content": "3.4. Long short-term feature aggregation module" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.583, + 0.892, + 0.794 + ], + "angle": 0, + "content": "Short-term frames in the local temporal range are employed in several recent works to enhance the current frame [2, 4, 5]. Nevertheless, only fusing short-term frames can not fully use the information from the whole video and has significant limitations. The long-term frame is therefore introduced to supplement context information. Motivated by the multi-head attention mechanism [12], a long short-term feature aggregation module that conducts feature aggregation on Proposal-Level is proposed. It effectively integrates the long-term frame features and short-term frame features into the current frame features. The long short-term feature aggregation includes two stages: long-term feature aggregation and short-term feature aggregation, the details of long short-term feature aggregation are shown in Fig. 4." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.796, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Long-term feature aggregation: The input of the long-term feature aggregation module is the short-term frame Proposal-Level features \\( X_{s} \\in [N_{1}, C] \\) and the long-term frame Proposal-Level features \\( X_{g} \\in [N_{2}, C] \\), where \\( N_{1} \\) and \\( N_{2} \\) represent the number of features reserved and \\( C \\) represents the channels of features. To combine information from different channels and subspaces, input features" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14617" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.121 + ], + "angle": 0, + "content": "are first divided into \\(K\\) groups. The features after grouping can be formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.172, + 0.129, + 0.469, + 0.16 + ], + "angle": 0, + "content": "\\[\nX ^ {k} = X [:, (k - 1) \\frac {C}{K}: k \\frac {C}{K} ] \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.168, + 0.469, + 0.272 + ], + "angle": 0, + "content": "where \\( X \\) could be long-term frame Proposal-Level features \\( X_{g} \\) or short-term frame Proposal-Level features \\( X_{s} \\), \\( C \\) represents the channels of features, \\( K \\) is the number of groups, \\( k \\) means the \\( k^{th} \\) group, and \\( X^{k} \\) denotes the segment of the \\( k^{th} \\) group on the channel dimension. Every group makes spatio-temporal aggregation and is concatenated to each other." + }, + { + "type": "equation", + "bbox": [ + 0.172, + 0.272, + 0.469, + 0.293 + ], + "angle": 0, + "content": "\\[\nX _ {g + s} = \\operatorname {c o n c a t} \\left(\\varphi \\left(X _ {s} ^ {k}, X _ {g} ^ {k}\\right)\\right) \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.296, + 0.469, + 0.371 + ], + "angle": 0, + "content": "where \\( X_{g + s} \\) denotes the enhanced short-term frame features, concat denotes concatenation, and the spatiotemporal aggregation function \\( \\varphi \\) effectively aggregates long-term frame features and short-term frame features. \\( \\varphi \\) can be formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.099, + 0.378, + 0.469, + 0.422 + ], + "angle": 0, + "content": "\\[\n\\left\\{ \\begin{array}{l} \\varphi \\left(X _ {s} ^ {k}, X _ {g} ^ {k}\\right) = X _ {s} ^ {k} + \\operatorname {s o f t m a x} (\\omega) \\cdot X _ {g} ^ {k} \\\\ \\omega = \\operatorname {S i m} \\left(\\omega_ {s} \\cdot X _ {s} ^ {k}, \\omega_ {g} \\cdot X _ {g} ^ {k}\\right) + \\operatorname {S i m} \\left(\\mu^ {\\prime}, \\omega_ {g} \\cdot X _ {g} ^ {k}\\right) \\end{array} \\right. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.43, + 0.469, + 0.609 + ], + "angle": 0, + "content": "To obtain a plug-and-play module, the spatio-temporal aggregation function \\(\\varphi\\) utilizes residual connection (as shown in the dotted box in Fig. 4). \\(X_{g}^{k}\\) and \\(X_{s}^{k}\\) are fused in residual function, attention \\(\\omega\\) serves as a correlation weight that consists of two parts: the cosine similarity between short-term frame features and long-term frame features to associate short-term frame and long-term frame, and the cosine similarity between long-term frame features and a group of learnable weights \\(\\mu^{\\prime}\\) to associate different channels of the long-term frame, \\(\\omega_{s}\\) and \\(\\omega_{g}\\) are linear transformation matrixes and also fully connected layers. Definition of Sim is same as formula 4." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.611, + 0.469, + 0.807 + ], + "angle": 0, + "content": "Short-term feature aggregation: Only high-level semantic information of the long-term frame is integrated into the short-term frame during long-term feature aggregation. Considering the strong time continuity between the short-term frame and the current frame, the location information of the short-term frame is also fused into the current frame, as shown in Fig. 4 \"location coding\". Let \\( r_s = \\{x_s, y_s, h_s, w_s\\} \\) be the location information of Regions of Interest (RoIs) in the short-term frame which includes the center point \\( x_s, y_s \\) and height and width \\( h_s, w_s \\) of each RoI, and let \\( r_c \\) be the location information of RoIs in the current frame. The location correlation weight can be represented as" + }, + { + "type": "equation", + "bbox": [ + 0.088, + 0.817, + 0.469, + 0.862 + ], + "angle": 0, + "content": "\\[\n\\left\\{ \\begin{array}{l} \\omega_ {r} = \\operatorname {r e l u} \\left(\\omega_ {c s} \\cdot \\psi \\left(r _ {c}, r _ {s}\\right)\\right) \\\\ \\psi \\left(r _ {c}, r _ {s}\\right) = \\left\\{\\log \\left(\\frac {\\left| x _ {c} - x _ {s} \\right|}{w _ {c}}\\right), \\log \\left(\\frac {\\left| y _ {c} - y _ {s} \\right|}{h _ {c}}\\right), \\log \\left(\\frac {w _ {c}}{w _ {s}}\\right), \\log \\left(\\frac {h _ {c}}{h _ {s}}\\right) \\right\\} \\end{array} \\right. \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "where \\(\\omega_{r}\\) denotes location correlation weight, the nonlinear function relu is used to reduce redundant information, \\(\\omega_{cs}\\) is" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.18 + ], + "angle": 0, + "content": "the linear transformation matrix and also a fully connected layer in the network, and \\(\\psi\\) is utilized to code the location information of the current frame and the short-term frame to make the module translation invariant. The correlation weight of short-term feature aggregation can be represented as" + }, + { + "type": "equation", + "bbox": [ + 0.583, + 0.188, + 0.892, + 0.228 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\omega = \\operatorname {S i m} \\left(\\omega_ {c} \\cdot X _ {c} ^ {k}, \\omega_ {g + s} \\cdot X _ {g + s} ^ {k}\\right) \\tag {9} \\\\ + S i m \\left(\\mu^ {\\prime \\prime}, \\omega_ {g + s} \\cdot X _ {g + s} ^ {k}\\right) + \\omega_ {r} ^ {k} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.245, + 0.892, + 0.412 + ], + "angle": 0, + "content": "where \\( X_{c}^{k} \\) stands for the current frame Proposal-Level features after grouping, \\( \\omega_{g+s} \\), \\( \\omega_{c} \\) are fully connected layers used to reshape the feature, \\( \\omega \\) is the adaptive weight including three parts: the cosine similarity between enhanced short-term frame features and current frame features, the cosine similarity between enhanced short-term frame features and a group of learnable weights \\( \\mu'' \\), and the location correlation weight between the current frame and short-term frame after grouping. The other steps of short-term feature aggregation are the same as long-term feature aggregation and needless to be described again." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.435, + 0.632, + 0.453 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.464, + 0.676, + 0.48 + ], + "angle": 0, + "content": "4.1. Experiment Setup" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.49, + 0.892, + 0.746 + ], + "angle": 0, + "content": "Datasets and Evaluation Setup: We conduct experiments on ImageNet-VID [20] and FL-Drones [19]. ImageNet-VID is a widely used large-scale benchmark for video object detection, which contains 3862 videos in the training set, 555 videos in the validation set, and a total of 30 categories. \\( mAP \\) is used for evaluation on ImageNet-VID. To evaluate the performance of the proposed method on video small object detection, we also make use of the FL-Drones dataset consisting of 14 videos and 38948 frames. The flying drones in the dataset can be regarded as small objects because the average size of annotated drones is \\( 25 \\times 16 \\) and the frame resolutions are \\( 640 \\times 480 \\) and \\( 752 \\times 480 \\). This dataset is quite challenging due to the extreme illumination and relatively small size. According to the author [19], half of the data is used for training, and the other half is used for testing. And \\( AP \\) is used as the evaluation metric for FL-Drones since it is a video dataset for small objects." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Implementation Details: The proposed algorithm is trained and tested using 4 16GB NVIDIA Tesla V100. The baseline used in this paper is Faster R-CNN. Following the multi-task loss in baseline, the whole network is optimized with both classification and regression losses. SGD is selected as the optimizer and the model is trained for 120000 iterations on ImageNet-VID and 66000 iterations on FLDrones. The learning rate is set to 0.001 and updated using WarmupMultiStepLR [18], which means the model first has 500 warm-up iterations to improve stability." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14618" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.077, + 0.091, + 0.367, + 0.108 + ], + "angle": 0, + "content": "4.2. Comparison with state-of-the-art" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.115, + 0.47, + 0.19 + ], + "angle": 0, + "content": "ImageNet-VID dataset: Comparison results on this dataset are shown in Table 1. All algorithms adopt the same feature extraction network to be compared fairly, and the results of the state-of-the-art works are collected from published papers." + }, + { + "type": "table_caption", + "bbox": [ + 0.084, + 0.204, + 0.462, + 0.219 + ], + "angle": 0, + "content": "Table 1. Quantitative results on the ImageNet-VID dataset \\((\\%)\\)" + }, + { + "type": "table", + "bbox": [ + 0.132, + 0.242, + 0.413, + 0.414 + ], + "angle": 0, + "content": "
MethodBackbonemAP
FGFA [28]ResNet10176.3
STMN [24]ResNet10180.5
LongRange [21]ResNet10181.0
D&T [6]ResNet10175.8
MANet [22]ResNet10178.1
STSN [2]ResNet10178.9
RDN [5]ResNet10181.8
SELSA [23]ResNet10180.3
MEGA [3]ResNet10182.9
LSTFE-NetResNet10183.4
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.442, + 0.47, + 0.517 + ], + "angle": 0, + "content": "It is obvious that our method outperforms other state-of-the-art methods and achieves the highest \\( mAP \\) of \\( 83.4\\% \\). Results show that the LSTFE-Net can better collect the information from long-term and short-term frames and enhance the feature." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.518, + 0.47, + 0.623 + ], + "angle": 0, + "content": "FL-Drones dataset: As a video dataset for small objects, few results of other classical methods can be found on this dataset which means we need to conduct experiments using these methods ourselves. For a more comprehensive comparison, ResNet50 and ResNet101 are respectively used as the feature extraction network for analysis. The results are shown in Table 2." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.624, + 0.47, + 0.759 + ], + "angle": 0, + "content": "According to Table 2, our method achieves the best small object detection performance no matter what the feature extraction network is. Our LSTFE-Net obtains the highest \\(AP\\) of \\(37.8\\%\\) and outperforms the strongest competitor TransVOD by \\(0.9\\%\\) \\(AP\\) when ResNet50 is used. For ResNet101, our LSTFE-Net achieves an \\(AP\\) of \\(46.8\\%\\), \\(4.4\\%\\) higher than MEGA. Fig. 5 shows some qualitative comparison results of our LSTFE-Net versus other state-of-the-art works." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.771, + 0.241, + 0.787 + ], + "angle": 0, + "content": "4.3. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.469, + 0.825 + ], + "angle": 0, + "content": "We conduct ablation studies to validate the effectiveness of each component in our model on the FL-Drones dataset." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Spatio-temporal feature alignment module: \\( k \\) cascaded deformable convolutional blocks are applied in this module, and experiments are conducted in this section to study the influence of the value of \\( k \\) on spatio-temporal modeling. The short-term frame and the long-term frame" + }, + { + "type": "table_caption", + "bbox": [ + 0.52, + 0.09, + 0.872, + 0.104 + ], + "angle": 0, + "content": "Table 2. Quantitative results on the FL-Drones dataset \\((\\%)\\)" + }, + { + "type": "table", + "bbox": [ + 0.543, + 0.127, + 0.847, + 0.253 + ], + "angle": 0, + "content": "
MethodAP
ResNet50ResNet101
DFF [27]19.522.4
FGFA [28]21.224.5
TransVOD [11]36.935.2
RDN [5]35.942.1
MEGA [3]36.542.4
LSTFE-Net37.846.8
" + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.281, + 0.891, + 0.495 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.503, + 0.892, + 0.545 + ], + "angle": 0, + "content": "Figure 5. Qualitative comparison of our LSTFE-Net versus other state-of-the-art works. Blue boxes represent the detection. Best viewed in color and zoomed in." + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.562, + 0.892, + 0.589 + ], + "angle": 0, + "content": "Table 3. Ablation study of the spatio-temporal feature alignment module(%)" + }, + { + "type": "table", + "bbox": [ + 0.593, + 0.613, + 0.798, + 0.695 + ], + "angle": 0, + "content": "
BackboneAP
k = 0ResNet10142.1
k = 1ResNet10145.4
k = 2ResNet10139.4
k = 3ResNet10139.3
" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.733, + 0.891, + 0.762 + ], + "angle": 0, + "content": "are first added to the baseline, and then the value of \\( k \\) is adjusted. Results are shown in Table 3:" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.764, + 0.892, + 0.869 + ], + "angle": 0, + "content": "Table 3 shows that the network achieves an \\(AP\\) of \\(42.1\\%\\) if the spatio-temporal feature alignment module is not used. When \\(k = 1\\), \\(AP\\) increases by \\(3.3\\%\\) to \\(45.4\\%\\). As \\(k\\) increases from 1 to 3, \\(AP\\) decreases gradually. To explore the reasons for the decreasing detection performance, the offset matrixes with different values of \\(k\\) are visualized, as shown in Fig. 6." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The offset matrix with \\( k = 1 \\) is visualized in Fig. 6(b), where it is obvious that offsets are generally larger at the" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14619" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.092, + 0.172, + 0.145 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.117, + 0.149, + 0.146, + 0.157 + ], + "angle": 0, + "content": "(a)input" + }, + { + "type": "image", + "bbox": [ + 0.176, + 0.092, + 0.266, + 0.145 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.206, + 0.149, + 0.235, + 0.157 + ], + "angle": 0, + "content": "(b) \\( k = 1 \\)" + }, + { + "type": "image", + "bbox": [ + 0.274, + 0.092, + 0.364, + 0.145 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.304, + 0.148, + 0.334, + 0.157 + ], + "angle": 0, + "content": "(c) \\( k = 2 \\)" + }, + { + "type": "image", + "bbox": [ + 0.373, + 0.092, + 0.461, + 0.145 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.402, + 0.148, + 0.432, + 0.157 + ], + "angle": 0, + "content": "(d) \\( k = 3 \\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.172, + 0.468, + 0.199 + ], + "angle": 0, + "content": "Figure 6. Visualization of offset matrix. The deeper the color, the larger the offset." + }, + { + "type": "table_caption", + "bbox": [ + 0.108, + 0.217, + 0.438, + 0.232 + ], + "angle": 0, + "content": "Table 4. Ablation study of frame selection module \\((\\%)\\)" + }, + { + "type": "table", + "bbox": [ + 0.084, + 0.254, + 0.465, + 0.33 + ], + "angle": 0, + "content": "
Number of long-term framesBackboneAP
Long-term framesFrame selection
1ResNet10129.529.9
2ResNet10135.135.9
3ResNet10133.934.8
4ResNet10129.630.7
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.369, + 0.468, + 0.519 + ], + "angle": 0, + "content": "moving target and smaller in the stationary background area. This indicates that the network can better model the correlation between the same object of different frames. With the increase of \\( k \\), temporal information is mixed up, which makes the offset learned by the spatio-temporal feature alignment module gradually disordered. When \\( k = 3 \\), the offset matrix can hardly represent the relationship between frames. Adding the offset in the convolution will hinder the normal extraction of features and make the detection result worse." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.521, + 0.468, + 0.626 + ], + "angle": 0, + "content": "Frame selection module: The detection results before and after using the frame selection module are compared. To emphasize the impact of the frame selection module, the number of short-term frames is set to 0. After \\( m \\) long-term frames are sampled, additional \\( 2m \\) frames are then sampled and \\( m \\) frames are selected by the frame selection module. The results are shown in Table 4:" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.628, + 0.468, + 0.734 + ], + "angle": 0, + "content": "Table 4 demonstrates how the number of long-term frames will affect the detection performance of small objects. The promotion effects of the frame selection module vary for different numbers of sampled long-term frames. When there are 4 sampled frames, \\(AP\\) improves most \\((1.1\\%)\\). And when the number of sampled frames is 2, \\(AP\\) improves by \\(0.8\\%\\) to \\(35.9\\%\\) (highest)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.468, + 0.9 + ], + "angle": 0, + "content": "Long short-term feature aggregation module: In this section, concatenation is used as a simple feature aggregation method to be compared. The only difference between short-term feature aggregation and long-term feature aggregation is the utilization of location coding, so the contribution of location coding is verified. Short-term frames and long-term frames are first added to the baseline, and then simple feature aggregation, long short-term feature aggregation without location coding, and long short-term feature aggregation are used for experiments separately. The results are shown in Table 5." + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.09, + 0.892, + 0.117 + ], + "angle": 0, + "content": "Table 5. Ablation study of long short-term feature aggregation module \\((\\%)\\)" + }, + { + "type": "table", + "bbox": [ + 0.534, + 0.141, + 0.859, + 0.209 + ], + "angle": 0, + "content": "
MethodBackboneAP
simple feature aggregationResNet10139.9
long short-term feature aggregation without location codingResNet10141.2
long short-term feature aggregationResNet10142.1
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.246, + 0.892, + 0.337 + ], + "angle": 0, + "content": "Table 5 shows that the simple feature aggregation method obtains an \\(AP\\) of \\(39.9\\%\\), while the proposed long short-term feature aggregation method can improve \\(AP\\) to \\(42.1\\%\\). Additionally, the \\(AP\\) drops to \\(41.2\\%\\) when the location coding is removed, which means that the location coding can bring a gain of \\(0.9\\% AP\\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.352, + 0.619, + 0.367 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.377, + 0.892, + 0.709 + ], + "angle": 0, + "content": "For small objects, we propose an LSTFE-Net to enhance the feature with two important sources of information from the video. A spatio-temporal feature alignment module is proposed to model the temporal information between the short-term frame and the current frame. It uses deformable convolution to make connections between objects of different frames, and conducts feature enhancement on Pixel-Level. Considering that the background context information of the object is single, the frame selection module is used to select the long-term frame with the most distinct feature from the current frame, which is further used to enrich the vital context information for small object detection. To effectively fuse the features of different types of frames, we develop a long short-term feature aggregation module, where context information from the long-term frames and the temporal information from the short-term frames are incorporated into the current frame by stages. Experiments are carried out on ImageNet-VID and FL-Drones to compare our method with other state-of-the-art methods and conduct ablation studies. The results show that the proposed method achieves superior small object detection performance in videos." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.724, + 0.66, + 0.74 + ], + "angle": 0, + "content": "Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.749, + 0.892, + 0.819 + ], + "angle": 0, + "content": "This work is supported by National Natural Science Foundation of China (U1903214), Major Science and Technology Projects of Jilin Province (20210301030GX), Natural Science Foundation of Guangdong Province (2021A1515012233)" + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.833, + 0.597, + 0.849 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.508, + 0.859, + 0.892, + 0.901 + ], + "angle": 0, + "content": "[1] Muhammad Waseem Ashraf, Waqas Sultani, and Mubarak Shah. Dogfight: Detecting drones from drones videos. 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Wuhan University, China + +2. Guangdong University of Technology, China + +{xiaojs,whuwuyuanxu,shuruiwang}@whu.edu.cn，yhchen@gdut.edu.cn + +wzyhope@163.com, jyma2010@gmail.com + +# Abstract + +Video small object detection is a difficult task due to the lack of object information. Recent methods focus on adding more temporal information to obtain more potent high-level features, which often fail to specify the most vital information for small objects, resulting in insufficient or inappropriate features. Since information from frames at different positions contributes differently to small objects, it is not ideal to assume that using one universal method will extract proper features. We find that context information from the long-term frame and temporal information from the short-term frame are two useful cues for video small object detection. To fully utilize these two cues, we propose a long short-term feature enhancement network (LSTFE-Net) for video small object detection. First, we develop a plug-and-play spatio-temporal feature alignment module to create temporal correspondences between the short-term and current frames. Then, we propose a frame selection module to select the long-term frame that can provide the most additional context information. Finally, we propose a long short-term feature aggregation module to fuse long short-term features. Compared to other state-of-the-art methods, our LSTFE-Net achieves $4.4\%$ absolute boosts in AP on the FL-Drones dataset. More details can be found at https://github.com/xiaojs18/LSTFE-Net. + +# 1. Introduction + +Video small object detection plays an important role in many fields such as automatic driving, remote sensing, medical image, and industrial defect detection [26]. However, it is still a difficult task due to the lack of pixel information and the difficulty of feature extraction. Therefore, the topic of how to enhance the features of small objects has attracted great attention [1,7, 16]. + +![](images/a0532f6b9398054ab29f50247fdc725cf24463e42bb6fad0ee3e949aca3fa4a8.jpg) +Figure 1. The architecture of the proposed LSTFE-Net. The current frame (Cur-frame), short-term frames (ST-frames) near the Cur-frame, and long-term frames (LT-frames) sampled from the whole video first go through the feature extraction network. Then the Cur-frame feature and ST-frame features are connected through the spatio-temporal feature alignment module, and the frame selection module searches the background context of LT-frame features. After getting the Proposal-Level (PL) features, the long short-term feature aggregation module finally integrates the long short-term features into the Cur-frame to make feature enhancement. Best viewed in color and zoomed in. + +Some recent works have proved that the improvement of video small object detection performance requires full utilization of information in the temporal dimension. While detecting small objects in the current frame may suffer from many problems such as motion blur, low resolution, and too small size, effective modeling of information from other frames can help address these problems [2, 4, 9, 17]. There is a high similarity in nearby frames because of the strong time continuity between them, so it is natural to emphasize the importance of short-term frames, which are near the current frame. According to FGFA [28] and STSN [2], + +short-term frame features can be aligned and aggregated to provide more useful information for small objects. + +Context information is important for small object detection [16,25]. Because a large number of images are sampled from the same video for the same object, the background context information of the object is single. Additionally, only part of the frames in the video are sampled as current frames (such as 15 frames) while training, which results in the lack of real background context information and reduces the robustness of the training model. Compared to features in a short range, features from the whole video level can be more discriminative and robust [21, 23]. And it is noticed in prior works [9, 23] that more contextual information will be provided when using long-term frames sampled from the whole video. + +The impacts of short-term and long-term frames in detection have been studied in recent methods. However, these methods have obvious disadvantages in both efficiency and accuracy, especially for small objects in videos. Some methods [22, 27, 28] extract information from the short-term frame and exploit the flow model to propagate features across adjacent frames, however, this is expensive because the flow model is hard to construct and transplant. Other methods [21, 23] focus on semantic information from long-term frames and incorporate randomly sampled long-term frames in detection, which causes uncertainty of detection performance and the loss of valuable information. Besides, these methods above cannot figure out the specific information that matters most for small objects from frames. Some methods [21-23, 27, 28] think the information in the video is single and miss considering distinct information from different frames, getting inadequate features. Other methods [3, 5] focus on extracting high-level features from the video which are not suitable for small objects due to their special properties. + +To better mine information from both short-term frames and long-term frames, we propose a long short-term feature enhancement network (LSTFE-Net) for video small object detection. Specifically, the features of short-term frames are expected to correspond to the current frame in a low-cost and effective way, so a spatio-temporal feature alignment module is designed to propagate features across nearby frames. Further, in order to increase the benefit of aligned features while not increasing too much complexity of the model, a spatio-temporal feature aggregation method is also added. The context information is expected to be highlighted from the whole video, prompting a frame selection module to select the long-term frame feature. The goal is to make effective feature enhancement after the features are collected, and the establishment of connections between different features is enforced. A long short-term feature aggregation module is devised to aggregate features from the current frame, the short-term frames, and the long + +term frames by stages. The performance of the proposed method is evaluated on the open dataset, and experiment results demonstrate that our method has obvious advantages in video small object detection. The architecture of the network is shown in Fig. 1. + +Our main contributions are summarized as follows: + +(1) An LSTFE-Net is proposed to effectively enhance small object features and improve detection performance. +(2) A plug-and-play spatio-temporal feature alignment module is designed for aligning features across adjacent frames. A flexible way to make Pixel-Level feature enhancement for small objects using aligned features is also explored. Combined with the Proposal-Level feature enhancement, this module achieves multi-level enhancement to improve the feature expressiveness. The whole module is easy to transplant and proved to be effective, which reveals its potential ability to benefit most of the works. +(3) A frame selection module is proposed to ensure the utilization of high-value input data, and it selects the long-term frame feature with the most context information. This module reinforces the network to automatically look for useful information for small objects, improving its stability and performance in video small object detection. +(4) To effectively integrate the long-term frame features and short-term frame features into the current frame, a long short-term feature aggregation module is proposed to aggregate different features in different stages. This enables the relations between Proposal-Level features to be built adaptively based on an attention mechanism, which also means our feature enhancement for small objects can be accomplished in a general and limitless way. + +# 2. Related Works + +Object detection from images has achieved considerable success and introduced some leading detectors in recent years. Based on the early proposed detectors, video object detection is intensively studied as a more challenging task. It is proved that exploiting information from other frames can significantly enhance the detection of the current frame, so temporal feature aggregation is gaining attention and introduced into video small object detection. + +Object detection in videos: The appropriate use of the temporal information in the video to increase detection accuracy is a fundamental difficulty in video object detection. Adapting the image object detection algorithm to the video domain is challenging because of the complex spatial and temporal changes in videos. SeqNMS [10], TCN [15], and T-CNN [14] apply post-processing to video object detection to handle the complexities of videos. SeqNMS [10] links bounding boxes from different frames iff their Intersection over Union $(IoU)$ is above some certain threshold and re-ranks those linked boxes; TCN [15] introduces the tubelet components and proposes a temporal convolu + +tional neural network to incorporate temporal information, which improves detection performance across frames. TCNN [14] first uses the still-image object detection algorithm to get single frame detection results and associates the results using optical flows. However, none of these methods based on post-processing can be trained end-to-end, and their performance is yet to be improved. Our method, in contrast, directly uses temporal information in videos without post-processing and can be trained end-to-end, which brings great convenience. + +Temporal feature aggregation: Recent works have also focused on ways to aggregate temporal features with different distances from the current frame, including short-term frame and long-term frame features, to enhance the feature of the object. DFF [27] uses a flow field predicted by FlowNet [13] to make the key frame feature align to short-term frames, thus reducing the redundant computation and accelerating the network. Unlike DFF, FGFA [28] mainly employs flow motion to make short-term frame features align to the current frame and then fuses these two kinds of features to improve detection accuracy. MANet [22] achieves the feature calibration module and the feature aggregation module on both pixel-level and instance-level based on FGFA and uses the motion pattern reasoning module to aggregate features from two different levels. Unlike short-term frames, long-term frames are usually sampled from the whole training video. Since there is little time continuity between the long-term frame and the current frame, the fusion of high-level semantic information is paid more attention to. To make more effective feature aggregation, SELSA [23] performs one innovative work by calculating the semantic similarity between current frames and long-term frames. STMN [24] uses the recurrent computation unit as the spatio-temporal memory module to pass semantic information between different frames. While using both local and global features to enhance the features of the current frames, MEGA [3] introduces a memory module to store more temporal features. + +Video small object detection: A few researchers have proposed to improve the detection accuracy of small objects by leveraging temporal information in videos. Motion R-CNN [7] provides additional auxiliary information for small objects based on the frame differencing method and improves small object detection performance in optical remote sensing videos. DogFight [1] proposes to use a two-stage segmentation-based approach employing spatiotemporal attention cues, where objects are localized during the first stage and the object location is tracked and filtered using temporal information during the second stage. + +Although both short-term frame features and long-term frame features have been used to improve detection performance, the information mined from these features is still not enough for them to build strong connections with the + +small object. We focus on several major problems and aim to get more powerful small object features through enhancement. To be specific, while DFF [27] and FGFA [28] require FlowNet which is difficult to construct and transplant, our method uses a plug-and-play spatio-temporal feature alignment module to make feature alignment and Pixel-Level enhancement. Instead of being simply randomly sampled from the video like MEGA [3], the long-term frame in this paper is selected by the frame selection module to enrich context information for small object detection. Unlike the above methods exclusively focusing on exploiting one kind of information from either the short-term frame or the long-term frame [22, 23, 27, 28], we fully consider the various information from both the short-term frame and long-term frame. The high-level features in this paper can work better for small objects than those in [3, 5] because of these purposeful designs. + +# 3. Methods + +# 3.1. Framework overview + +The architecture of the LSTFE-Net is shown in Fig. 1. Besides the current frame, multiple short-term frames and long-term frames are also sampled from the video and input to the network. The feature extraction network first extracts the frame features of the input. Then different frame features are processed differently according to their characteristics. Because the short-term frames are sampled adjacent to the current frame, there is extensive temporal information between them. A plug-and-play spatio-temporal feature alignment module is designed to make alignment of the current frame feature and short-term frame features using cascaded deformable convolution blocks. This alignment can be described in the form of offsets in convolution, which helps the convolutional neural network sample more features from object regions to precisely enhance the small object of the current frame. The aligned features are further fused into the current frame feature on a low level. + +It is inappropriate to make feature alignment between the current frame and long-term frames because there is no evident time continuity between them and their object features have great displacement in space. Considering that background context information is crucial and single to small object detection, long-term frames are employed to provide more background context information. It is natural to expect the long-term frames with the most context information to be further used in the network, so a frame selection module is devised. After feature embedding, it selects the long-term frame feature with the lowest similarity to the current frame feature. After the above modules, the Region Proposal Network (RPN) is used to generate proposals and Region of Interest (RoI) Align is applied to make feature extraction, getting the Proposal-Level features of different + +![](images/cf2bcb981c3a1895f9752523f9b7823260324e1254baaa241c4c89a4e3609841.jpg) +Figure 2. Spatio-temporal feature alignment module. The shortterm frame feature $f_{s}$ is first aligned based on deformable convolution, and then integrated into the current frame feature $f_{t}$ using spatio-temporal feature aggregation. Best viewed in color and zoomed in. + +# frames. + +Effectively integrating long-term frame features and short-term frame features into the current frame feature is also a key part of feature enhancement. To better integrate different kinds of frame features, we divide the long short-term feature aggregation into two stages: long-term feature aggregation and short-term feature aggregation. In the first stage, the feature aggregation between long-term frames and short-term frames is conducted, which provides additional context information for small objects. Next, the feature aggregation between short-term frames and the current frame is carried out in the second stage, and also the location differences between the frames are considered. This module models the relations between Proposal-Level features adaptively and universally, ensuring feature enhancement for small objects. The above algorithms will be introduced in detail in the following sections. + +# 3.2. Spatio-temporal feature alignment module + +There is a strong similarity between the current frame and the short-term frames. Features of the same object are typically not spatially aligned between frames due to the movement in videos. Hence direct fusion of features between frames will result in feature interference, ghost effects, and even lower detection performance. Deformable convolution [8] learns multiple offsets of the spatial location during convolution. We design a spatio-temporal feature alignment module based on deformable convolution to learn offsets and make feature alignment between frames, and a spatio-temporal feature aggregation module is proposed to conduct Pixel-Level feature enhancement of the current frame. The specific architecture is shown in Fig. 2. + +Given a frame $I_{t}$ at time $t$ and a nearby short-term frame $I_{s}$ , let $f_{t}$ and $f_{s}$ indicate spatial features through the feature extraction network from frame $I_{t}$ and $I_{s}$ , as shown in Fig. 2 (a). Suppose the shape of $f_{t}$ or $f_{s}$ is $[C, H, W]$ , where $C$ stands for the channels, $H$ for the height of tensors, and $W$ + +for the width of tensors. To fuse the features, $f_{t}$ and $f_{s}$ are concatenated to get $f_{cat}$ . Then $f_{cat}$ is fed to a deformable convolutional block, as shown in Fig. 2 (b). The block generates offsets $m_{1} \in [2 \times 9, H, W]$ with $3 \times 3$ convolution, where 9 denotes kernel size $3 \times 3$ , 2 denotes offsets in two directions: $x$ and $y$ . Finally, $m_{1}$ and $f_{cat}$ are fed to a deformable convolutional layer to get the aligned feature. Our deformable convolutional block is plug-and-play and cascaded, which means multiple blocks can be used in series to make multiple times feature alignments. The final block outputs the final offsets $m_{o}$ , and $m_{o}$ and short-term frame feature $f_{s}$ are fed to a deformable convolutional layer to get the aligned short-term feature $f_{t+s}$ . In general, the temporal information between the current frame and the short-term frame is used to estimate the spatial offset between object features, which is further used to make the short-term frame feature align with the current frame feature. + +To effectively integrate the aligned short-term frame feature into the current frame feature, a spatio-temporal feature aggregation module is designed to make the adaptive information fuse. The adaptive weight can be expressed by formula 1. + +$$ +\omega \left(f _ {t}, f _ {t + s}\right) = \rho \left(l \left(f _ {t}, f _ {t + s}\right)\right) \tag {1} +$$ + +where $l$ is a spatio-temporal function that describes spatiotemporal connections between $f_{t}$ and $f_{t + s}$ , and $\rho$ is the mask function used to calculate the adaptive weight. To fully use temporal information between frames, the frame differencing method is introduced into $l$ , which concatenates $f_{t} - f_{t + s}, f_{t + s} - f_{t}, f_{t}$ , and $f_{t + s}$ into $f_{multi}$ . $f_{multi}$ is then fed to mask function $\rho$ . It goes through two convolutional layers to squeeze the number of channels and fully fuse the information. To improve the generalization ability of the model, the softmax function is then used to generate the final adaptive weight $\omega(f_{t}, f_{t + s})$ . As shown in Fig. 2 (c). Finally, the enhanced current frame feature $f$ is computed by + +$$ +f = \sum_ {f _ {j} \in \left(f _ {t}\right)} \left\{\omega \left(f _ {t}, f _ {j}\right) \otimes f _ {t} \right\} \tag {2} +$$ + +where $(f_{t})$ denotes a collection of aligned short-term frame features near $f_{t}$ , $\otimes$ denotes element-wise multiplication. In this paper, multiple short-term frames are sampled, aligned to the current frame, and adaptively integrated into the current frame to enhance the current frame feature on Pixel-Level. + +# 3.3. Frame selection module + +Because a large number of images are sampled in the same video for the same object, the background context information of the object is very similar. Object detection algorithms based on deep learning tend to use this similarity to make the feature enhancement for the current object. + +![](images/64a75970460a4a5226805d560eec08f2398d4a370f4f769c27ec0fd48b3a1749.jpg) +Figure 3. Frame selection module. The current frame feature $F_{c}$ and $m$ long-term frame features $\{F_{g}^{i}\}_{i = 1}^{m}$ first get the feature embedding. Then similarities between them are calculated and finally, the index of the long-term frame with the lowest similarity is output. Best viewed in color and zoomed in. + +However, this strategy results in the poor generalization performance of the training model, especially for training data with a high degree of similarity. Considering the significance of background context information for small object detection, our network samples long-term frames from the whole video and tries to acquire training frames with more background differences. The frame selection module can select the long-term frame with the lowest similarity to the current frame, which is further used to enrich background context information. The architecture of the frame selection module is shown in Fig. 3. + +Given the current frame feature $F_{c}$ and the sampled long-term frame feature $F_{g}^{i}$ , this module tries to select the long-term frame that is most dissimilar to $F_{c}$ from $m$ candidate long-term frames to be used for Proposal-Level feature aggregation. As a result, this module outputs the index of the long-term frame with the lowest similarity, which can be interpreted as + +$$ +i n d = \underset {i \in [ 1, \mathrm {m} ]} {\operatorname {a r g m i n}} \left\{S i m \left(g \left(F _ {c}\right), g \left(F _ {g} ^ {i}\right)\right) \right\} \tag {3} +$$ + +where $ind$ is the index of the selected long-term frame, $Sim$ is the similarity function used to calculate the similarity between different input features, $g$ represents the feature embedding function, $i \in [1,m]$ indicates the $i^{th}$ candidate long-term frame feature, and $argmin$ is used to calculate the index of the long-term frame with the lowest similarity. Similarity function $Sim$ can be formulated as + +$$ +\operatorname {S i m} (X, Y) = \frac {X \cdot Y}{\sqrt {\dim}} \tag {4} +$$ + +According to formula 4, cosine distance is used to calculate the similarity between the current frame feature $g(F_{c})$ and long-term frame feature $g(F_{g}^{i})$ , and dim represents the dimension of the input feature. In formula 3, feature embedding function $g$ incorporates adaptive pooling, dimension reduction, and max pooling, as shown in Fig. 3. Suppose the shape of the input feature $F_{c}$ is $[N,C,H,W]$ , where + +![](images/40a0dc616fe1439cccecfe0900a881081c55cffa8be9bdb6ebecc2ccce84ed2d.jpg) +Figure 4. Details of long short-term feature aggregation. Input features are first grouped, then make spatio-temporal aggregation, and finally concatenated to get the enhanced feature. The "Location coding" is used in the second stage: short-term feature aggregation. Best viewed in color and zoomed in. + +$N, C, H, W$ stands for batch size, channels, height, and width, respectively. The feature is processed by adaptive average pooling on spatial domains and reshaped to a 4D tensor $[N, C, 1, 1]$ to get the global spatial feature of the image. To calculate the similarity more conveniently, the feature then reduces the dimension and is reshaped to the 2D tensor $[N, C]$ , and the most representative feature is selected by max pooling. Finally, the 4D feature $[N, C, H, W]$ is reshaped to 2D $[1, C]$ . + +For selected index ind, the long-term frame feature $F_{g}^{ind}$ has the lowest background context similarity with the current frame feature. In training, it provides more diverse real context information for small object detection. + +# 3.4. Long short-term feature aggregation module + +Short-term frames in the local temporal range are employed in several recent works to enhance the current frame [2, 4, 5]. Nevertheless, only fusing short-term frames can not fully use the information from the whole video and has significant limitations. The long-term frame is therefore introduced to supplement context information. Motivated by the multi-head attention mechanism [12], a long short-term feature aggregation module that conducts feature aggregation on Proposal-Level is proposed. It effectively integrates the long-term frame features and short-term frame features into the current frame features. The long short-term feature aggregation includes two stages: long-term feature aggregation and short-term feature aggregation, the details of long short-term feature aggregation are shown in Fig. 4. + +Long-term feature aggregation: The input of the long-term feature aggregation module is the short-term frame Proposal-Level features $X_{s} \in [N_{1}, C]$ and the long-term frame Proposal-Level features $X_{g} \in [N_{2}, C]$ , where $N_{1}$ and $N_{2}$ represent the number of features reserved and $C$ represents the channels of features. To combine information from different channels and subspaces, input features + +are first divided into $K$ groups. The features after grouping can be formulated as + +$$ +X ^ {k} = X [:, (k - 1) \frac {C}{K}: k \frac {C}{K} ] \tag {5} +$$ + +where $X$ could be long-term frame Proposal-Level features $X_{g}$ or short-term frame Proposal-Level features $X_{s}$ , $C$ represents the channels of features, $K$ is the number of groups, $k$ means the $k^{th}$ group, and $X^{k}$ denotes the segment of the $k^{th}$ group on the channel dimension. Every group makes spatio-temporal aggregation and is concatenated to each other. + +$$ +X _ {g + s} = \operatorname {c o n c a t} \left(\varphi \left(X _ {s} ^ {k}, X _ {g} ^ {k}\right)\right) \tag {6} +$$ + +where $X_{g + s}$ denotes the enhanced short-term frame features, concat denotes concatenation, and the spatiotemporal aggregation function $\varphi$ effectively aggregates long-term frame features and short-term frame features. $\varphi$ can be formulated as + +$$ +\left\{ \begin{array}{l} \varphi \left(X _ {s} ^ {k}, X _ {g} ^ {k}\right) = X _ {s} ^ {k} + \operatorname {s o f t m a x} (\omega) \cdot X _ {g} ^ {k} \\ \omega = \operatorname {S i m} \left(\omega_ {s} \cdot X _ {s} ^ {k}, \omega_ {g} \cdot X _ {g} ^ {k}\right) + \operatorname {S i m} \left(\mu^ {\prime}, \omega_ {g} \cdot X _ {g} ^ {k}\right) \end{array} \right. \tag {7} +$$ + +To obtain a plug-and-play module, the spatio-temporal aggregation function $\varphi$ utilizes residual connection (as shown in the dotted box in Fig. 4). $X_{g}^{k}$ and $X_{s}^{k}$ are fused in residual function, attention $\omega$ serves as a correlation weight that consists of two parts: the cosine similarity between short-term frame features and long-term frame features to associate short-term frame and long-term frame, and the cosine similarity between long-term frame features and a group of learnable weights $\mu^{\prime}$ to associate different channels of the long-term frame, $\omega_{s}$ and $\omega_{g}$ are linear transformation matrixes and also fully connected layers. Definition of Sim is same as formula 4. + +Short-term feature aggregation: Only high-level semantic information of the long-term frame is integrated into the short-term frame during long-term feature aggregation. Considering the strong time continuity between the short-term frame and the current frame, the location information of the short-term frame is also fused into the current frame, as shown in Fig. 4 "location coding". Let $r_s = \{x_s, y_s, h_s, w_s\}$ be the location information of Regions of Interest (RoIs) in the short-term frame which includes the center point $x_s, y_s$ and height and width $h_s, w_s$ of each RoI, and let $r_c$ be the location information of RoIs in the current frame. The location correlation weight can be represented as + +$$ +\left\{ \begin{array}{l} \omega_ {r} = \operatorname {r e l u} \left(\omega_ {c s} \cdot \psi \left(r _ {c}, r _ {s}\right)\right) \\ \psi \left(r _ {c}, r _ {s}\right) = \left\{\log \left(\frac {\left| x _ {c} - x _ {s} \right|}{w _ {c}}\right), \log \left(\frac {\left| y _ {c} - y _ {s} \right|}{h _ {c}}\right), \log \left(\frac {w _ {c}}{w _ {s}}\right), \log \left(\frac {h _ {c}}{h _ {s}}\right) \right\} \end{array} \right. \tag {8} +$$ + +where $\omega_{r}$ denotes location correlation weight, the nonlinear function relu is used to reduce redundant information, $\omega_{cs}$ is + +the linear transformation matrix and also a fully connected layer in the network, and $\psi$ is utilized to code the location information of the current frame and the short-term frame to make the module translation invariant. The correlation weight of short-term feature aggregation can be represented as + +$$ +\begin{array}{l} \omega = \operatorname {S i m} \left(\omega_ {c} \cdot X _ {c} ^ {k}, \omega_ {g + s} \cdot X _ {g + s} ^ {k}\right) \tag {9} \\ + S i m \left(\mu^ {\prime \prime}, \omega_ {g + s} \cdot X _ {g + s} ^ {k}\right) + \omega_ {r} ^ {k} \\ \end{array} +$$ + +where $X_{c}^{k}$ stands for the current frame Proposal-Level features after grouping, $\omega_{g+s}$ , $\omega_{c}$ are fully connected layers used to reshape the feature, $\omega$ is the adaptive weight including three parts: the cosine similarity between enhanced short-term frame features and current frame features, the cosine similarity between enhanced short-term frame features and a group of learnable weights $\mu''$ , and the location correlation weight between the current frame and short-term frame after grouping. The other steps of short-term feature aggregation are the same as long-term feature aggregation and needless to be described again. + +# 4. Experiments + +# 4.1. Experiment Setup + +Datasets and Evaluation Setup: We conduct experiments on ImageNet-VID [20] and FL-Drones [19]. ImageNet-VID is a widely used large-scale benchmark for video object detection, which contains 3862 videos in the training set, 555 videos in the validation set, and a total of 30 categories. $mAP$ is used for evaluation on ImageNet-VID. To evaluate the performance of the proposed method on video small object detection, we also make use of the FL-Drones dataset consisting of 14 videos and 38948 frames. The flying drones in the dataset can be regarded as small objects because the average size of annotated drones is $25 \times 16$ and the frame resolutions are $640 \times 480$ and $752 \times 480$ . This dataset is quite challenging due to the extreme illumination and relatively small size. According to the author [19], half of the data is used for training, and the other half is used for testing. And $AP$ is used as the evaluation metric for FL-Drones since it is a video dataset for small objects. + +Implementation Details: The proposed algorithm is trained and tested using 4 16GB NVIDIA Tesla V100. The baseline used in this paper is Faster R-CNN. Following the multi-task loss in baseline, the whole network is optimized with both classification and regression losses. SGD is selected as the optimizer and the model is trained for 120000 iterations on ImageNet-VID and 66000 iterations on FLDrones. The learning rate is set to 0.001 and updated using WarmupMultiStepLR [18], which means the model first has 500 warm-up iterations to improve stability. + +# 4.2. Comparison with state-of-the-art + +ImageNet-VID dataset: Comparison results on this dataset are shown in Table 1. All algorithms adopt the same feature extraction network to be compared fairly, and the results of the state-of-the-art works are collected from published papers. + +Table 1. Quantitative results on the ImageNet-VID dataset $(\%)$ + +
MethodBackbonemAP
FGFA [28]ResNet10176.3
STMN [24]ResNet10180.5
LongRange [21]ResNet10181.0
D&T [6]ResNet10175.8
MANet [22]ResNet10178.1
STSN [2]ResNet10178.9
RDN [5]ResNet10181.8
SELSA [23]ResNet10180.3
MEGA [3]ResNet10182.9
LSTFE-NetResNet10183.4
+ +It is obvious that our method outperforms other state-of-the-art methods and achieves the highest $mAP$ of $83.4\%$ . Results show that the LSTFE-Net can better collect the information from long-term and short-term frames and enhance the feature. + +FL-Drones dataset: As a video dataset for small objects, few results of other classical methods can be found on this dataset which means we need to conduct experiments using these methods ourselves. For a more comprehensive comparison, ResNet50 and ResNet101 are respectively used as the feature extraction network for analysis. The results are shown in Table 2. + +According to Table 2, our method achieves the best small object detection performance no matter what the feature extraction network is. Our LSTFE-Net obtains the highest $AP$ of $37.8\%$ and outperforms the strongest competitor TransVOD by $0.9\%$ $AP$ when ResNet50 is used. For ResNet101, our LSTFE-Net achieves an $AP$ of $46.8\%$ , $4.4\%$ higher than MEGA. Fig. 5 shows some qualitative comparison results of our LSTFE-Net versus other state-of-the-art works. + +# 4.3. Ablation Studies + +We conduct ablation studies to validate the effectiveness of each component in our model on the FL-Drones dataset. + +Spatio-temporal feature alignment module: $k$ cascaded deformable convolutional blocks are applied in this module, and experiments are conducted in this section to study the influence of the value of $k$ on spatio-temporal modeling. The short-term frame and the long-term frame + +Table 2. Quantitative results on the FL-Drones dataset $(\%)$ + +
MethodAP
ResNet50ResNet101
DFF [27]19.522.4
FGFA [28]21.224.5
TransVOD [11]36.935.2
RDN [5]35.942.1
MEGA [3]36.542.4
LSTFE-Net37.846.8
+ +![](images/c716b97fdffa670b87afa3fd9767e467661aec5e2c481364a473601c88bd4537.jpg) +Figure 5. Qualitative comparison of our LSTFE-Net versus other state-of-the-art works. Blue boxes represent the detection. Best viewed in color and zoomed in. + +Table 3. Ablation study of the spatio-temporal feature alignment module(%) + +
BackboneAP
k = 0ResNet10142.1
k = 1ResNet10145.4
k = 2ResNet10139.4
k = 3ResNet10139.3
+ +are first added to the baseline, and then the value of $k$ is adjusted. Results are shown in Table 3: + +Table 3 shows that the network achieves an $AP$ of $42.1\%$ if the spatio-temporal feature alignment module is not used. When $k = 1$ , $AP$ increases by $3.3\%$ to $45.4\%$ . As $k$ increases from 1 to 3, $AP$ decreases gradually. To explore the reasons for the decreasing detection performance, the offset matrixes with different values of $k$ are visualized, as shown in Fig. 6. + +The offset matrix with $k = 1$ is visualized in Fig. 6(b), where it is obvious that offsets are generally larger at the + +![](images/f965767d00c9061d02480474ea5217f7997862226bebc0cd533793b1a349952c.jpg) +(a)input + +![](images/7d87939a2af6bb33c80a82a80c491710e427e793f3d2ac2c41bda10d2884ccb9.jpg) +(b) $k = 1$ + +![](images/10bd77638127979172d8313cca09bf2afe8c95757d278debd5e7588d0c13a47a.jpg) +(c) $k = 2$ +Figure 6. Visualization of offset matrix. The deeper the color, the larger the offset. + +![](images/f8ea147d93d7c710195b2d094361312a3bd565b6d5ca71949228355dc9eeabe2.jpg) +(d) $k = 3$ + +Table 4. Ablation study of frame selection module $(\%)$ + +
Number of long-term framesBackboneAP
Long-term framesFrame selection
1ResNet10129.529.9
2ResNet10135.135.9
3ResNet10133.934.8
4ResNet10129.630.7
+ +moving target and smaller in the stationary background area. This indicates that the network can better model the correlation between the same object of different frames. With the increase of $k$ , temporal information is mixed up, which makes the offset learned by the spatio-temporal feature alignment module gradually disordered. When $k = 3$ , the offset matrix can hardly represent the relationship between frames. Adding the offset in the convolution will hinder the normal extraction of features and make the detection result worse. + +Frame selection module: The detection results before and after using the frame selection module are compared. To emphasize the impact of the frame selection module, the number of short-term frames is set to 0. After $m$ long-term frames are sampled, additional $2m$ frames are then sampled and $m$ frames are selected by the frame selection module. The results are shown in Table 4: + +Table 4 demonstrates how the number of long-term frames will affect the detection performance of small objects. The promotion effects of the frame selection module vary for different numbers of sampled long-term frames. When there are 4 sampled frames, $AP$ improves most $(1.1\%)$ . And when the number of sampled frames is 2, $AP$ improves by $0.8\%$ to $35.9\%$ (highest). + +Long short-term feature aggregation module: In this section, concatenation is used as a simple feature aggregation method to be compared. The only difference between short-term feature aggregation and long-term feature aggregation is the utilization of location coding, so the contribution of location coding is verified. Short-term frames and long-term frames are first added to the baseline, and then simple feature aggregation, long short-term feature aggregation without location coding, and long short-term feature aggregation are used for experiments separately. The results are shown in Table 5. + +Table 5. Ablation study of long short-term feature aggregation module $(\%)$ + +
MethodBackboneAP
simple feature aggregationResNet10139.9
long short-term feature aggregation without location codingResNet10141.2
long short-term feature aggregationResNet10142.1
+ +Table 5 shows that the simple feature aggregation method obtains an $AP$ of $39.9\%$ , while the proposed long short-term feature aggregation method can improve $AP$ to $42.1\%$ . Additionally, the $AP$ drops to $41.2\%$ when the location coding is removed, which means that the location coding can bring a gain of $0.9\% AP$ . + +# 5. Conclusion + +For small objects, we propose an LSTFE-Net to enhance the feature with two important sources of information from the video. A spatio-temporal feature alignment module is proposed to model the temporal information between the short-term frame and the current frame. It uses deformable convolution to make connections between objects of different frames, and conducts feature enhancement on Pixel-Level. Considering that the background context information of the object is single, the frame selection module is used to select the long-term frame with the most distinct feature from the current frame, which is further used to enrich the vital context information for small object detection. To effectively fuse the features of different types of frames, we develop a long short-term feature aggregation module, where context information from the long-term frames and the temporal information from the short-term frames are incorporated into the current frame by stages. Experiments are carried out on ImageNet-VID and FL-Drones to compare our method with other state-of-the-art methods and conduct ablation studies. The results show that the proposed method achieves superior small object detection performance in videos. + +# Acknowledgement + +This work is supported by National Natural Science Foundation of China (U1903214), Major Science and Technology Projects of Jilin Province (20210301030GX), Natural Science Foundation of Guangdong Province (2021A1515012233) + +# References + +[1] Muhammad Waseem Ashraf, Waqas Sultani, and Mubarak Shah. Dogfight: Detecting drones from drones videos. In Proceedings of the IEEE/CVF Conference on Computer Vi + +sion and Pattern Recognition, pages 7067-7076, 2021. 1, 3 +[2] Gedas Bertasius, Lorenzo Torresani, and Jianbo Shi. Object detection in video with spatiotemporal sampling networks. In Proceedings of the European Conference on Computer Vision (ECCV), pages 331-346, 2018. 1, 5, 7 +[3] Yihong Chen, Yue Cao, Han Hu, and Liwei Wang. Memory enhanced global-local aggregation for video object detection. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 13668-13677, 2022. 1 +[27] Xizhou Zhu, Jifeng Dai, Lu Yuan, and Yichen Wei. Towards high performance video object detection. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 7210-7218, 2018. 2, 3, 7 +[28] Xizhou Zhu, Yujie Wang, Jifeng Dai, Lu Yuan, and Yichen Wei. Flow-guided feature aggregation for video object detection. In Proceedings of the IEEE international conference on computer vision, pages 408-417, 2017. 1, 2, 3, 7 \ No newline at end of file diff --git a/2023/LSTFE-Net_Long Short-Term Feature Enhancement Network for Video Small Object Detection/images.zip b/2023/LSTFE-Net_Long Short-Term Feature Enhancement Network for Video Small Object Detection/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..44aeaa66fd730cdeb5842eb15127179da48357ae --- /dev/null +++ b/2023/LSTFE-Net_Long Short-Term Feature Enhancement Network for Video Small Object Detection/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:b68d15fdfdca799cc757bdf0b9581119981e361151a1eeac3a9a2a7fefd718e8 +size 354163 diff --git a/2023/LSTFE-Net_Long Short-Term Feature Enhancement Network for Video Small Object Detection/layout.json b/2023/LSTFE-Net_Long Short-Term Feature Enhancement Network for Video Small Object Detection/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..a1ed4b2b2a0d7648d1e8988d72618295d4d85e0b --- /dev/null +++ b/2023/LSTFE-Net_Long Short-Term Feature Enhancement Network for Video Small Object Detection/layout.json @@ -0,0 +1,9085 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 56, + 102, + 538, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 102, + 538, + 140 + ], + "spans": [ + { + "bbox": [ + 56, + 102, + 538, + 140 + ], + "type": "text", + "content": "LSTFE-Net:Long Short-Term Feature Enhancement Network for Video Small Object Detection" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 77, + 160, + 515, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 160, + 515, + 190 + ], + "spans": [ + { + "bbox": [ + 77, + 160, + 515, + 190 + ], + "type": "text", + "content": "Jinsheng Xiao" + }, + { + "bbox": [ + 77, + 160, + 515, + 190 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 77, + 160, + 515, + 190 + ], + "type": "text", + "content": ", Yuanxu Wu" + }, + { + "bbox": [ + 77, + 160, + 515, + 190 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 77, + 160, + 515, + 190 + ], + "type": "text", + "content": ", Yunhua Chen" + }, + { + "bbox": [ + 77, + 160, + 515, + 190 + ], + "type": "inline_equation", + "content": "^{2*}" + }, + { + "bbox": [ + 77, + 160, + 515, + 190 + ], + "type": "text", + "content": ", Shurui Wang" + }, + { + "bbox": [ + 77, + 160, + 515, + 190 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 77, + 160, + 515, + 190 + ], + "type": "text", + "content": ", Zhongyuan Wang" + }, + { + "bbox": [ + 77, + 160, + 515, + 190 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 77, + 160, + 515, + 190 + ], + "type": "text", + "content": ", Jiayi Ma" + }, + { + "bbox": [ + 77, + 160, + 515, + 190 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 77, + 160, + 515, + 190 + ], + "type": "text", + "content": " \n1. Wuhan University, China" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 182, + 190, + 410, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 182, + 190, + 410, + 204 + ], + "spans": [ + { + "bbox": [ + 182, + 190, + 410, + 204 + ], + "type": "text", + "content": "2. Guangdong University of Technology, China" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 129, + 205, + 463, + 217 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 129, + 205, + 463, + 217 + ], + "spans": [ + { + "bbox": [ + 129, + 205, + 463, + 217 + ], + "type": "text", + "content": "{xiaojs,whuwuyuanxu,shuruiwang}@whu.edu.cn，yhchen@gdut.edu.cn" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 198, + 220, + 392, + 231 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 198, + 220, + 392, + 231 + ], + "spans": [ + { + "bbox": [ + 198, + 220, + 392, + 231 + ], + "type": "text", + "content": "wzyhope@163.com, jyma2010@gmail.com" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 143, + 258, + 192, + 271 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 258, + 192, + 271 + ], + "spans": [ + { + "bbox": [ + 143, + 258, + 192, + 271 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 45, + 283, + 290, + 571 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 283, + 290, + 571 + ], + "spans": [ + { + "bbox": [ + 45, + 283, + 290, + 571 + ], + "type": "text", + "content": "Video small object detection is a difficult task due to the lack of object information. Recent methods focus on adding more temporal information to obtain more potent high-level features, which often fail to specify the most vital information for small objects, resulting in insufficient or inappropriate features. Since information from frames at different positions contributes differently to small objects, it is not ideal to assume that using one universal method will extract proper features. We find that context information from the long-term frame and temporal information from the short-term frame are two useful cues for video small object detection. To fully utilize these two cues, we propose a long short-term feature enhancement network (LSTFE-Net) for video small object detection. First, we develop a plug-and-play spatio-temporal feature alignment module to create temporal correspondences between the short-term and current frames. Then, we propose a frame selection module to select the long-term frame that can provide the most additional context information. Finally, we propose a long short-term feature aggregation module to fuse long short-term features. Compared to other state-of-the-art methods, our LSTFE-Net achieves " + }, + { + "bbox": [ + 45, + 283, + 290, + 571 + ], + "type": "inline_equation", + "content": "4.4\\%" + }, + { + "bbox": [ + 45, + 283, + 290, + 571 + ], + "type": "text", + "content": " absolute boosts in AP on the FL-Drones dataset. More details can be found at https://github.com/xiaojs18/LSTFE-Net." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 592, + 128, + 605 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 592, + 128, + 605 + ], + "spans": [ + { + "bbox": [ + 47, + 592, + 128, + 605 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 613, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 613, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 613, + 287, + 696 + ], + "type": "text", + "content": "Video small object detection plays an important role in many fields such as automatic driving, remote sensing, medical image, and industrial defect detection [26]. However, it is still a difficult task due to the lack of pixel information and the difficulty of feature extraction. Therefore, the topic of how to enhance the features of small objects has attracted great attention [1,7, 16]." + } + ] + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 313, + 256, + 544, + 429 + ], + "blocks": [ + { + "bbox": [ + 313, + 256, + 544, + 429 + ], + "lines": [ + { + "bbox": [ + 313, + 256, + 544, + 429 + ], + "spans": [ + { + "bbox": [ + 313, + 256, + 544, + 429 + ], + "type": "image", + "image_path": "a0532f6b9398054ab29f50247fdc725cf24463e42bb6fad0ee3e949aca3fa4a8.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 437, + 547, + 559 + ], + "lines": [ + { + "bbox": [ + 304, + 437, + 547, + 559 + ], + "spans": [ + { + "bbox": [ + 304, + 437, + 547, + 559 + ], + "type": "text", + "content": "Figure 1. The architecture of the proposed LSTFE-Net. The current frame (Cur-frame), short-term frames (ST-frames) near the Cur-frame, and long-term frames (LT-frames) sampled from the whole video first go through the feature extraction network. Then the Cur-frame feature and ST-frame features are connected through the spatio-temporal feature alignment module, and the frame selection module searches the background context of LT-frame features. After getting the Proposal-Level (PL) features, the long short-term feature aggregation module finally integrates the long short-term features into the Cur-frame to make feature enhancement. Best viewed in color and zoomed in." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "content": "Some recent works have proved that the improvement of video small object detection performance requires full utilization of information in the temporal dimension. While detecting small objects in the current frame may suffer from many problems such as motion blur, low resolution, and too small size, effective modeling of information from other frames can help address these problems [2, 4, 9, 17]. There is a high similarity in nearby frames because of the strong time continuity between them, so it is natural to emphasize the importance of short-term frames, which are near the current frame. According to FGFA [28] and STSN [2]," + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 1, + 494, + 17 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 1, + 494, + 17 + ], + "spans": [ + { + "bbox": [ + 145, + 1, + 494, + 17 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 181, + 13, + 460, + 22 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 181, + 13, + 460, + 22 + ], + "spans": [ + { + "bbox": [ + 181, + 13, + 460, + 22 + ], + "type": "text", + "content": "Except for this watermark, it is identical to the accepted version;" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 179, + 24, + 461, + 36 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 179, + 24, + 461, + 36 + ], + "spans": [ + { + "bbox": [ + 179, + 24, + 461, + 36 + ], + "type": "text", + "content": "the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 58, + 703, + 148, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 703, + 148, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 703, + 148, + 713 + ], + "type": "text", + "content": "*The corresponding author" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14613" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "content": "short-term frame features can be aligned and aggregated to provide more useful information for small objects." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 99, + 288, + 253 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 99, + 288, + 253 + ], + "spans": [ + { + "bbox": [ + 46, + 99, + 288, + 253 + ], + "type": "text", + "content": "Context information is important for small object detection [16,25]. Because a large number of images are sampled from the same video for the same object, the background context information of the object is single. Additionally, only part of the frames in the video are sampled as current frames (such as 15 frames) while training, which results in the lack of real background context information and reduces the robustness of the training model. Compared to features in a short range, features from the whole video level can be more discriminative and robust [21, 23]. And it is noticed in prior works [9, 23] that more contextual information will be provided when using long-term frames sampled from the whole video." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 256, + 288, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 256, + 288, + 496 + ], + "spans": [ + { + "bbox": [ + 46, + 256, + 288, + 496 + ], + "type": "text", + "content": "The impacts of short-term and long-term frames in detection have been studied in recent methods. However, these methods have obvious disadvantages in both efficiency and accuracy, especially for small objects in videos. Some methods [22, 27, 28] extract information from the short-term frame and exploit the flow model to propagate features across adjacent frames, however, this is expensive because the flow model is hard to construct and transplant. Other methods [21, 23] focus on semantic information from long-term frames and incorporate randomly sampled long-term frames in detection, which causes uncertainty of detection performance and the loss of valuable information. Besides, these methods above cannot figure out the specific information that matters most for small objects from frames. Some methods [21-23, 27, 28] think the information in the video is single and miss considering distinct information from different frames, getting inadequate features. Other methods [3, 5] focus on extracting high-level features from the video which are not suitable for small objects due to their special properties." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 498, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 287, + 713 + ], + "type": "text", + "content": "To better mine information from both short-term frames and long-term frames, we propose a long short-term feature enhancement network (LSTFE-Net) for video small object detection. Specifically, the features of short-term frames are expected to correspond to the current frame in a low-cost and effective way, so a spatio-temporal feature alignment module is designed to propagate features across nearby frames. Further, in order to increase the benefit of aligned features while not increasing too much complexity of the model, a spatio-temporal feature aggregation method is also added. The context information is expected to be highlighted from the whole video, prompting a frame selection module to select the long-term frame feature. The goal is to make effective feature enhancement after the features are collected, and the establishment of connections between different features is enforced. A long short-term feature aggregation module is devised to aggregate features from the current frame, the short-term frames, and the long" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 72, + 545, + 132 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 132 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 132 + ], + "type": "text", + "content": "term frames by stages. The performance of the proposed method is evaluated on the open dataset, and experiment results demonstrate that our method has obvious advantages in video small object detection. The architecture of the network is shown in Fig. 1." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 317, + 133, + 525, + 143 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 133, + 525, + 143 + ], + "spans": [ + { + "bbox": [ + 317, + 133, + 525, + 143 + ], + "type": "text", + "content": "Our main contributions are summarized as follows:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 144, + 545, + 443 + ], + "type": "list", + "angle": 0, + "index": 10, + "blocks": [ + { + "bbox": [ + 305, + 144, + 545, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 144, + 545, + 168 + ], + "spans": [ + { + "bbox": [ + 305, + 144, + 545, + 168 + ], + "type": "text", + "content": "(1) An LSTFE-Net is proposed to effectively enhance small object features and improve detection performance." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 168, + 545, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 168, + 545, + 275 + ], + "spans": [ + { + "bbox": [ + 304, + 168, + 545, + 275 + ], + "type": "text", + "content": "(2) A plug-and-play spatio-temporal feature alignment module is designed for aligning features across adjacent frames. A flexible way to make Pixel-Level feature enhancement for small objects using aligned features is also explored. Combined with the Proposal-Level feature enhancement, this module achieves multi-level enhancement to improve the feature expressiveness. The whole module is easy to transplant and proved to be effective, which reveals its potential ability to benefit most of the works." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 276, + 545, + 347 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 276, + 545, + 347 + ], + "spans": [ + { + "bbox": [ + 304, + 276, + 545, + 347 + ], + "type": "text", + "content": "(3) A frame selection module is proposed to ensure the utilization of high-value input data, and it selects the long-term frame feature with the most context information. This module reinforces the network to automatically look for useful information for small objects, improving its stability and performance in video small object detection." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 348, + 545, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 348, + 545, + 443 + ], + "spans": [ + { + "bbox": [ + 304, + 348, + 545, + 443 + ], + "type": "text", + "content": "(4) To effectively integrate the long-term frame features and short-term frame features into the current frame, a long short-term feature aggregation module is proposed to aggregate different features in different stages. This enables the relations between Proposal-Level features to be built adaptively based on an attention mechanism, which also means our feature enhancement for small objects can be accomplished in a general and limitless way." + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 454, + 397, + 466 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 454, + 397, + 466 + ], + "spans": [ + { + "bbox": [ + 306, + 454, + 397, + 466 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 474, + 545, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 545, + 569 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 545, + 569 + ], + "type": "text", + "content": "Object detection from images has achieved considerable success and introduced some leading detectors in recent years. Based on the early proposed detectors, video object detection is intensively studied as a more challenging task. It is proved that exploiting information from other frames can significantly enhance the detection of the current frame, so temporal feature aggregation is gaining attention and introduced into video small object detection." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": "Object detection in videos: The appropriate use of the temporal information in the video to increase detection accuracy is a fundamental difficulty in video object detection. Adapting the image object detection algorithm to the video domain is challenging because of the complex spatial and temporal changes in videos. SeqNMS [10], TCN [15], and T-CNN [14] apply post-processing to video object detection to handle the complexities of videos. SeqNMS [10] links bounding boxes from different frames iff their Intersection over Union " + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "inline_equation", + "content": "(IoU)" + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": " is above some certain threshold and re-ranks those linked boxes; TCN [15] introduces the tubelet components and proposes a temporal convolu" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "text", + "content": "14614" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 191 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 191 + ], + "type": "text", + "content": "tional neural network to incorporate temporal information, which improves detection performance across frames. TCNN [14] first uses the still-image object detection algorithm to get single frame detection results and associates the results using optical flows. However, none of these methods based on post-processing can be trained end-to-end, and their performance is yet to be improved. Our method, in contrast, directly uses temporal information in videos without post-processing and can be trained end-to-end, which brings great convenience." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 194, + 288, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 194, + 288, + 529 + ], + "spans": [ + { + "bbox": [ + 46, + 194, + 288, + 529 + ], + "type": "text", + "content": "Temporal feature aggregation: Recent works have also focused on ways to aggregate temporal features with different distances from the current frame, including short-term frame and long-term frame features, to enhance the feature of the object. DFF [27] uses a flow field predicted by FlowNet [13] to make the key frame feature align to short-term frames, thus reducing the redundant computation and accelerating the network. Unlike DFF, FGFA [28] mainly employs flow motion to make short-term frame features align to the current frame and then fuses these two kinds of features to improve detection accuracy. MANet [22] achieves the feature calibration module and the feature aggregation module on both pixel-level and instance-level based on FGFA and uses the motion pattern reasoning module to aggregate features from two different levels. Unlike short-term frames, long-term frames are usually sampled from the whole training video. Since there is little time continuity between the long-term frame and the current frame, the fusion of high-level semantic information is paid more attention to. To make more effective feature aggregation, SELSA [23] performs one innovative work by calculating the semantic similarity between current frames and long-term frames. STMN [24] uses the recurrent computation unit as the spatio-temporal memory module to pass semantic information between different frames. While using both local and global features to enhance the features of the current frames, MEGA [3] introduces a memory module to store more temporal features." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 531, + 287, + 663 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 531, + 287, + 663 + ], + "spans": [ + { + "bbox": [ + 46, + 531, + 287, + 663 + ], + "type": "text", + "content": "Video small object detection: A few researchers have proposed to improve the detection accuracy of small objects by leveraging temporal information in videos. Motion R-CNN [7] provides additional auxiliary information for small objects based on the frame differencing method and improves small object detection performance in optical remote sensing videos. DogFight [1] proposes to use a two-stage segmentation-based approach employing spatiotemporal attention cues, where objects are localized during the first stage and the object location is tracked and filtered using temporal information during the second stage." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 665, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 665, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 665, + 288, + 713 + ], + "type": "text", + "content": "Although both short-term frame features and long-term frame features have been used to improve detection performance, the information mined from these features is still not enough for them to build strong connections with the" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 72, + 545, + 276 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 276 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 276 + ], + "type": "text", + "content": "small object. We focus on several major problems and aim to get more powerful small object features through enhancement. To be specific, while DFF [27] and FGFA [28] require FlowNet which is difficult to construct and transplant, our method uses a plug-and-play spatio-temporal feature alignment module to make feature alignment and Pixel-Level enhancement. Instead of being simply randomly sampled from the video like MEGA [3], the long-term frame in this paper is selected by the frame selection module to enrich context information for small object detection. Unlike the above methods exclusively focusing on exploiting one kind of information from either the short-term frame or the long-term frame [22, 23, 27, 28], we fully consider the various information from both the short-term frame and long-term frame. The high-level features in this paper can work better for small objects than those in [3, 5] because of these purposeful designs." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 289, + 366, + 301 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 289, + 366, + 301 + ], + "spans": [ + { + "bbox": [ + 306, + 289, + 366, + 301 + ], + "type": "text", + "content": "3. Methods" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 310, + 428, + 322 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 310, + 428, + 322 + ], + "spans": [ + { + "bbox": [ + 306, + 310, + 428, + 322 + ], + "type": "text", + "content": "3.1. Framework overview" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 329, + 545, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 329, + 545, + 533 + ], + "spans": [ + { + "bbox": [ + 304, + 329, + 545, + 533 + ], + "type": "text", + "content": "The architecture of the LSTFE-Net is shown in Fig. 1. Besides the current frame, multiple short-term frames and long-term frames are also sampled from the video and input to the network. The feature extraction network first extracts the frame features of the input. Then different frame features are processed differently according to their characteristics. Because the short-term frames are sampled adjacent to the current frame, there is extensive temporal information between them. A plug-and-play spatio-temporal feature alignment module is designed to make alignment of the current frame feature and short-term frame features using cascaded deformable convolution blocks. This alignment can be described in the form of offsets in convolution, which helps the convolutional neural network sample more features from object regions to precisely enhance the small object of the current frame. The aligned features are further fused into the current frame feature on a low level." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": "It is inappropriate to make feature alignment between the current frame and long-term frames because there is no evident time continuity between them and their object features have great displacement in space. Considering that background context information is crucial and single to small object detection, long-term frames are employed to provide more background context information. It is natural to expect the long-term frames with the most context information to be further used in the network, so a frame selection module is devised. After feature embedding, it selects the long-term frame feature with the lowest similarity to the current frame feature. After the above modules, the Region Proposal Network (RPN) is used to generate proposals and Region of Interest (RoI) Align is applied to make feature extraction, getting the Proposal-Level features of different" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14615" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 72, + 282, + 182 + ], + "blocks": [ + { + "bbox": [ + 50, + 72, + 282, + 182 + ], + "lines": [ + { + "bbox": [ + 50, + 72, + 282, + 182 + ], + "spans": [ + { + "bbox": [ + 50, + 72, + 282, + 182 + ], + "type": "image", + "image_path": "cf2bcb981c3a1895f9752523f9b7823260324e1254baaa241c4c89a4e3609841.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 190, + 287, + 245 + ], + "lines": [ + { + "bbox": [ + 46, + 190, + 287, + 245 + ], + "spans": [ + { + "bbox": [ + 46, + 190, + 287, + 245 + ], + "type": "text", + "content": "Figure 2. Spatio-temporal feature alignment module. The shortterm frame feature " + }, + { + "bbox": [ + 46, + 190, + 287, + 245 + ], + "type": "inline_equation", + "content": "f_{s}" + }, + { + "bbox": [ + 46, + 190, + 287, + 245 + ], + "type": "text", + "content": " is first aligned based on deformable convolution, and then integrated into the current frame feature " + }, + { + "bbox": [ + 46, + 190, + 287, + 245 + ], + "type": "inline_equation", + "content": "f_{t}" + }, + { + "bbox": [ + 46, + 190, + 287, + 245 + ], + "type": "text", + "content": " using spatio-temporal feature aggregation. Best viewed in color and zoomed in." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 268, + 80, + 277 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 268, + 80, + 277 + ], + "spans": [ + { + "bbox": [ + 47, + 268, + 80, + 277 + ], + "type": "text", + "content": "frames." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 279, + 287, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 279, + 287, + 472 + ], + "spans": [ + { + "bbox": [ + 46, + 279, + 287, + 472 + ], + "type": "text", + "content": "Effectively integrating long-term frame features and short-term frame features into the current frame feature is also a key part of feature enhancement. To better integrate different kinds of frame features, we divide the long short-term feature aggregation into two stages: long-term feature aggregation and short-term feature aggregation. In the first stage, the feature aggregation between long-term frames and short-term frames is conducted, which provides additional context information for small objects. Next, the feature aggregation between short-term frames and the current frame is carried out in the second stage, and also the location differences between the frames are considered. This module models the relations between Proposal-Level features adaptively and universally, ensuring feature enhancement for small objects. The above algorithms will be introduced in detail in the following sections." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 479, + 269, + 491 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 479, + 269, + 491 + ], + "spans": [ + { + "bbox": [ + 47, + 479, + 269, + 491 + ], + "type": "text", + "content": "3.2. Spatio-temporal feature alignment module" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 498, + 287, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 287, + 653 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 287, + 653 + ], + "type": "text", + "content": "There is a strong similarity between the current frame and the short-term frames. Features of the same object are typically not spatially aligned between frames due to the movement in videos. Hence direct fusion of features between frames will result in feature interference, ghost effects, and even lower detection performance. Deformable convolution [8] learns multiple offsets of the spatial location during convolution. We design a spatio-temporal feature alignment module based on deformable convolution to learn offsets and make feature alignment between frames, and a spatio-temporal feature aggregation module is proposed to conduct Pixel-Level feature enhancement of the current frame. The specific architecture is shown in Fig. 2." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 654, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 654, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 654, + 287, + 714 + ], + "type": "text", + "content": "Given a frame " + }, + { + "bbox": [ + 47, + 654, + 287, + 714 + ], + "type": "inline_equation", + "content": "I_{t}" + }, + { + "bbox": [ + 47, + 654, + 287, + 714 + ], + "type": "text", + "content": " at time " + }, + { + "bbox": [ + 47, + 654, + 287, + 714 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 47, + 654, + 287, + 714 + ], + "type": "text", + "content": " and a nearby short-term frame " + }, + { + "bbox": [ + 47, + 654, + 287, + 714 + ], + "type": "inline_equation", + "content": "I_{s}" + }, + { + "bbox": [ + 47, + 654, + 287, + 714 + ], + "type": "text", + "content": ", let " + }, + { + "bbox": [ + 47, + 654, + 287, + 714 + ], + "type": "inline_equation", + "content": "f_{t}" + }, + { + "bbox": [ + 47, + 654, + 287, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 654, + 287, + 714 + ], + "type": "inline_equation", + "content": "f_{s}" + }, + { + "bbox": [ + 47, + 654, + 287, + 714 + ], + "type": "text", + "content": " indicate spatial features through the feature extraction network from frame " + }, + { + "bbox": [ + 47, + 654, + 287, + 714 + ], + "type": "inline_equation", + "content": "I_{t}" + }, + { + "bbox": [ + 47, + 654, + 287, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 654, + 287, + 714 + ], + "type": "inline_equation", + "content": "I_{s}" + }, + { + "bbox": [ + 47, + 654, + 287, + 714 + ], + "type": "text", + "content": ", as shown in Fig. 2 (a). Suppose the shape of " + }, + { + "bbox": [ + 47, + 654, + 287, + 714 + ], + "type": "inline_equation", + "content": "f_{t}" + }, + { + "bbox": [ + 47, + 654, + 287, + 714 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 47, + 654, + 287, + 714 + ], + "type": "inline_equation", + "content": "f_{s}" + }, + { + "bbox": [ + 47, + 654, + 287, + 714 + ], + "type": "text", + "content": " is " + }, + { + "bbox": [ + 47, + 654, + 287, + 714 + ], + "type": "inline_equation", + "content": "[C, H, W]" + }, + { + "bbox": [ + 47, + 654, + 287, + 714 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 47, + 654, + 287, + 714 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 47, + 654, + 287, + 714 + ], + "type": "text", + "content": " stands for the channels, " + }, + { + "bbox": [ + 47, + 654, + 287, + 714 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 47, + 654, + 287, + 714 + ], + "type": "text", + "content": " for the height of tensors, and " + }, + { + "bbox": [ + 47, + 654, + 287, + 714 + ], + "type": "inline_equation", + "content": "W" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 545, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 275 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 275 + ], + "type": "text", + "content": "for the width of tensors. To fuse the features, " + }, + { + "bbox": [ + 304, + 72, + 545, + 275 + ], + "type": "inline_equation", + "content": "f_{t}" + }, + { + "bbox": [ + 304, + 72, + 545, + 275 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 72, + 545, + 275 + ], + "type": "inline_equation", + "content": "f_{s}" + }, + { + "bbox": [ + 304, + 72, + 545, + 275 + ], + "type": "text", + "content": " are concatenated to get " + }, + { + "bbox": [ + 304, + 72, + 545, + 275 + ], + "type": "inline_equation", + "content": "f_{cat}" + }, + { + "bbox": [ + 304, + 72, + 545, + 275 + ], + "type": "text", + "content": ". Then " + }, + { + "bbox": [ + 304, + 72, + 545, + 275 + ], + "type": "inline_equation", + "content": "f_{cat}" + }, + { + "bbox": [ + 304, + 72, + 545, + 275 + ], + "type": "text", + "content": " is fed to a deformable convolutional block, as shown in Fig. 2 (b). The block generates offsets " + }, + { + "bbox": [ + 304, + 72, + 545, + 275 + ], + "type": "inline_equation", + "content": "m_{1} \\in [2 \\times 9, H, W]" + }, + { + "bbox": [ + 304, + 72, + 545, + 275 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 304, + 72, + 545, + 275 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 304, + 72, + 545, + 275 + ], + "type": "text", + "content": " convolution, where 9 denotes kernel size " + }, + { + "bbox": [ + 304, + 72, + 545, + 275 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 304, + 72, + 545, + 275 + ], + "type": "text", + "content": ", 2 denotes offsets in two directions: " + }, + { + "bbox": [ + 304, + 72, + 545, + 275 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 72, + 545, + 275 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 72, + 545, + 275 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 304, + 72, + 545, + 275 + ], + "type": "text", + "content": ". Finally, " + }, + { + "bbox": [ + 304, + 72, + 545, + 275 + ], + "type": "inline_equation", + "content": "m_{1}" + }, + { + "bbox": [ + 304, + 72, + 545, + 275 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 72, + 545, + 275 + ], + "type": "inline_equation", + "content": "f_{cat}" + }, + { + "bbox": [ + 304, + 72, + 545, + 275 + ], + "type": "text", + "content": " are fed to a deformable convolutional layer to get the aligned feature. Our deformable convolutional block is plug-and-play and cascaded, which means multiple blocks can be used in series to make multiple times feature alignments. The final block outputs the final offsets " + }, + { + "bbox": [ + 304, + 72, + 545, + 275 + ], + "type": "inline_equation", + "content": "m_{o}" + }, + { + "bbox": [ + 304, + 72, + 545, + 275 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 72, + 545, + 275 + ], + "type": "inline_equation", + "content": "m_{o}" + }, + { + "bbox": [ + 304, + 72, + 545, + 275 + ], + "type": "text", + "content": " and short-term frame feature " + }, + { + "bbox": [ + 304, + 72, + 545, + 275 + ], + "type": "inline_equation", + "content": "f_{s}" + }, + { + "bbox": [ + 304, + 72, + 545, + 275 + ], + "type": "text", + "content": " are fed to a deformable convolutional layer to get the aligned short-term feature " + }, + { + "bbox": [ + 304, + 72, + 545, + 275 + ], + "type": "inline_equation", + "content": "f_{t+s}" + }, + { + "bbox": [ + 304, + 72, + 545, + 275 + ], + "type": "text", + "content": ". In general, the temporal information between the current frame and the short-term frame is used to estimate the spatial offset between object features, which is further used to make the short-term frame feature align with the current frame feature." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 275, + 545, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 275, + 545, + 335 + ], + "spans": [ + { + "bbox": [ + 304, + 275, + 545, + 335 + ], + "type": "text", + "content": "To effectively integrate the aligned short-term frame feature into the current frame feature, a spatio-temporal feature aggregation module is designed to make the adaptive information fuse. The adaptive weight can be expressed by formula 1." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 364, + 348, + 545, + 361 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 364, + 348, + 545, + 361 + ], + "spans": [ + { + "bbox": [ + 364, + 348, + 545, + 361 + ], + "type": "interline_equation", + "content": "\\omega \\left(f _ {t}, f _ {t + s}\\right) = \\rho \\left(l \\left(f _ {t}, f _ {t + s}\\right)\\right) \\tag {1}", + "image_path": "70cb54ee2892c791c94fd4303dabe9d1893db48f9a349b6d556dbfd6d79fbb79.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 367, + 545, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 367, + 545, + 521 + ], + "spans": [ + { + "bbox": [ + 304, + 367, + 545, + 521 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 367, + 545, + 521 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 304, + 367, + 545, + 521 + ], + "type": "text", + "content": " is a spatio-temporal function that describes spatiotemporal connections between " + }, + { + "bbox": [ + 304, + 367, + 545, + 521 + ], + "type": "inline_equation", + "content": "f_{t}" + }, + { + "bbox": [ + 304, + 367, + 545, + 521 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 367, + 545, + 521 + ], + "type": "inline_equation", + "content": "f_{t + s}" + }, + { + "bbox": [ + 304, + 367, + 545, + 521 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 367, + 545, + 521 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 304, + 367, + 545, + 521 + ], + "type": "text", + "content": " is the mask function used to calculate the adaptive weight. To fully use temporal information between frames, the frame differencing method is introduced into " + }, + { + "bbox": [ + 304, + 367, + 545, + 521 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 304, + 367, + 545, + 521 + ], + "type": "text", + "content": ", which concatenates " + }, + { + "bbox": [ + 304, + 367, + 545, + 521 + ], + "type": "inline_equation", + "content": "f_{t} - f_{t + s}, f_{t + s} - f_{t}, f_{t}" + }, + { + "bbox": [ + 304, + 367, + 545, + 521 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 367, + 545, + 521 + ], + "type": "inline_equation", + "content": "f_{t + s}" + }, + { + "bbox": [ + 304, + 367, + 545, + 521 + ], + "type": "text", + "content": " into " + }, + { + "bbox": [ + 304, + 367, + 545, + 521 + ], + "type": "inline_equation", + "content": "f_{multi}" + }, + { + "bbox": [ + 304, + 367, + 545, + 521 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 367, + 545, + 521 + ], + "type": "inline_equation", + "content": "f_{multi}" + }, + { + "bbox": [ + 304, + 367, + 545, + 521 + ], + "type": "text", + "content": " is then fed to mask function " + }, + { + "bbox": [ + 304, + 367, + 545, + 521 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 304, + 367, + 545, + 521 + ], + "type": "text", + "content": ". It goes through two convolutional layers to squeeze the number of channels and fully fuse the information. To improve the generalization ability of the model, the softmax function is then used to generate the final adaptive weight " + }, + { + "bbox": [ + 304, + 367, + 545, + 521 + ], + "type": "inline_equation", + "content": "\\omega(f_{t}, f_{t + s})" + }, + { + "bbox": [ + 304, + 367, + 545, + 521 + ], + "type": "text", + "content": ". As shown in Fig. 2 (c). Finally, the enhanced current frame feature " + }, + { + "bbox": [ + 304, + 367, + 545, + 521 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 367, + 545, + 521 + ], + "type": "text", + "content": " is computed by" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 364, + 522, + 545, + 550 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 364, + 522, + 545, + 550 + ], + "spans": [ + { + "bbox": [ + 364, + 522, + 545, + 550 + ], + "type": "interline_equation", + "content": "f = \\sum_ {f _ {j} \\in \\left(f _ {t}\\right)} \\left\\{\\omega \\left(f _ {t}, f _ {j}\\right) \\otimes f _ {t} \\right\\} \\tag {2}", + "image_path": "1a9cb1a79ef29510ff421c9717f4ceab261beb9e7f30b478dc641a23e6afcb52.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 555, + 545, + 625 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 555, + 545, + 625 + ], + "spans": [ + { + "bbox": [ + 304, + 555, + 545, + 625 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 555, + 545, + 625 + ], + "type": "inline_equation", + "content": "(f_{t})" + }, + { + "bbox": [ + 304, + 555, + 545, + 625 + ], + "type": "text", + "content": " denotes a collection of aligned short-term frame features near " + }, + { + "bbox": [ + 304, + 555, + 545, + 625 + ], + "type": "inline_equation", + "content": "f_{t}" + }, + { + "bbox": [ + 304, + 555, + 545, + 625 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 555, + 545, + 625 + ], + "type": "inline_equation", + "content": "\\otimes" + }, + { + "bbox": [ + 304, + 555, + 545, + 625 + ], + "type": "text", + "content": " denotes element-wise multiplication. In this paper, multiple short-term frames are sampled, aligned to the current frame, and adaptively integrated into the current frame to enhance the current frame feature on Pixel-Level." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 635, + 440, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 635, + 440, + 647 + ], + "spans": [ + { + "bbox": [ + 306, + 635, + 440, + 647 + ], + "type": "text", + "content": "3.3. Frame selection module" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": "Because a large number of images are sampled in the same video for the same object, the background context information of the object is very similar. Object detection algorithms based on deep learning tend to use this similarity to make the feature enhancement for the current object." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "14616" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 69, + 286, + 166 + ], + "blocks": [ + { + "bbox": [ + 51, + 69, + 286, + 166 + ], + "lines": [ + { + "bbox": [ + 51, + 69, + 286, + 166 + ], + "spans": [ + { + "bbox": [ + 51, + 69, + 286, + 166 + ], + "type": "image", + "image_path": "64a75970460a4a5226805d560eec08f2398d4a370f4f769c27ec0fd48b3a1749.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 173, + 287, + 228 + ], + "lines": [ + { + "bbox": [ + 46, + 173, + 287, + 228 + ], + "spans": [ + { + "bbox": [ + 46, + 173, + 287, + 228 + ], + "type": "text", + "content": "Figure 3. Frame selection module. The current frame feature " + }, + { + "bbox": [ + 46, + 173, + 287, + 228 + ], + "type": "inline_equation", + "content": "F_{c}" + }, + { + "bbox": [ + 46, + 173, + 287, + 228 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 173, + 287, + 228 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 173, + 287, + 228 + ], + "type": "text", + "content": " long-term frame features " + }, + { + "bbox": [ + 46, + 173, + 287, + 228 + ], + "type": "inline_equation", + "content": "\\{F_{g}^{i}\\}_{i = 1}^{m}" + }, + { + "bbox": [ + 46, + 173, + 287, + 228 + ], + "type": "text", + "content": " first get the feature embedding. Then similarities between them are calculated and finally, the index of the long-term frame with the lowest similarity is output. Best viewed in color and zoomed in." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 250, + 286, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 250, + 286, + 380 + ], + "spans": [ + { + "bbox": [ + 46, + 250, + 286, + 380 + ], + "type": "text", + "content": "However, this strategy results in the poor generalization performance of the training model, especially for training data with a high degree of similarity. Considering the significance of background context information for small object detection, our network samples long-term frames from the whole video and tries to acquire training frames with more background differences. The frame selection module can select the long-term frame with the lowest similarity to the current frame, which is further used to enrich background context information. The architecture of the frame selection module is shown in Fig. 3." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 381, + 286, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 381, + 286, + 464 + ], + "spans": [ + { + "bbox": [ + 46, + 381, + 286, + 464 + ], + "type": "text", + "content": "Given the current frame feature " + }, + { + "bbox": [ + 46, + 381, + 286, + 464 + ], + "type": "inline_equation", + "content": "F_{c}" + }, + { + "bbox": [ + 46, + 381, + 286, + 464 + ], + "type": "text", + "content": " and the sampled long-term frame feature " + }, + { + "bbox": [ + 46, + 381, + 286, + 464 + ], + "type": "inline_equation", + "content": "F_{g}^{i}" + }, + { + "bbox": [ + 46, + 381, + 286, + 464 + ], + "type": "text", + "content": ", this module tries to select the long-term frame that is most dissimilar to " + }, + { + "bbox": [ + 46, + 381, + 286, + 464 + ], + "type": "inline_equation", + "content": "F_{c}" + }, + { + "bbox": [ + 46, + 381, + 286, + 464 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 46, + 381, + 286, + 464 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 381, + 286, + 464 + ], + "type": "text", + "content": " candidate long-term frames to be used for Proposal-Level feature aggregation. As a result, this module outputs the index of the long-term frame with the lowest similarity, which can be interpreted as" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 87, + 474, + 286, + 496 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 87, + 474, + 286, + 496 + ], + "spans": [ + { + "bbox": [ + 87, + 474, + 286, + 496 + ], + "type": "interline_equation", + "content": "i n d = \\underset {i \\in [ 1, \\mathrm {m} ]} {\\operatorname {a r g m i n}} \\left\\{S i m \\left(g \\left(F _ {c}\\right), g \\left(F _ {g} ^ {i}\\right)\\right) \\right\\} \\tag {3}", + "image_path": "2c9a8b18fba7c65ce513ffb01c24d81031da493fb0b97e8101502767b65b2f5f.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 504, + 286, + 588 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 504, + 286, + 588 + ], + "spans": [ + { + "bbox": [ + 46, + 504, + 286, + 588 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 504, + 286, + 588 + ], + "type": "inline_equation", + "content": "ind" + }, + { + "bbox": [ + 46, + 504, + 286, + 588 + ], + "type": "text", + "content": " is the index of the selected long-term frame, " + }, + { + "bbox": [ + 46, + 504, + 286, + 588 + ], + "type": "inline_equation", + "content": "Sim" + }, + { + "bbox": [ + 46, + 504, + 286, + 588 + ], + "type": "text", + "content": " is the similarity function used to calculate the similarity between different input features, " + }, + { + "bbox": [ + 46, + 504, + 286, + 588 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 46, + 504, + 286, + 588 + ], + "type": "text", + "content": " represents the feature embedding function, " + }, + { + "bbox": [ + 46, + 504, + 286, + 588 + ], + "type": "inline_equation", + "content": "i \\in [1,m]" + }, + { + "bbox": [ + 46, + 504, + 286, + 588 + ], + "type": "text", + "content": " indicates the " + }, + { + "bbox": [ + 46, + 504, + 286, + 588 + ], + "type": "inline_equation", + "content": "i^{th}" + }, + { + "bbox": [ + 46, + 504, + 286, + 588 + ], + "type": "text", + "content": " candidate long-term frame feature, and " + }, + { + "bbox": [ + 46, + 504, + 286, + 588 + ], + "type": "inline_equation", + "content": "argmin" + }, + { + "bbox": [ + 46, + 504, + 286, + 588 + ], + "type": "text", + "content": " is used to calculate the index of the long-term frame with the lowest similarity. Similarity function " + }, + { + "bbox": [ + 46, + 504, + 286, + 588 + ], + "type": "inline_equation", + "content": "Sim" + }, + { + "bbox": [ + 46, + 504, + 286, + 588 + ], + "type": "text", + "content": " can be formulated as" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 121, + 596, + 286, + 622 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 121, + 596, + 286, + 622 + ], + "spans": [ + { + "bbox": [ + 121, + 596, + 286, + 622 + ], + "type": "interline_equation", + "content": "\\operatorname {S i m} (X, Y) = \\frac {X \\cdot Y}{\\sqrt {\\dim}} \\tag {4}", + "image_path": "0ecb0c54d1aad80932dc09cb8308dd91115d2e35a1f7c2da236b02329f6b4ef2.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 629, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 286, + 713 + ], + "type": "text", + "content": "According to formula 4, cosine distance is used to calculate the similarity between the current frame feature " + }, + { + "bbox": [ + 46, + 629, + 286, + 713 + ], + "type": "inline_equation", + "content": "g(F_{c})" + }, + { + "bbox": [ + 46, + 629, + 286, + 713 + ], + "type": "text", + "content": " and long-term frame feature " + }, + { + "bbox": [ + 46, + 629, + 286, + 713 + ], + "type": "inline_equation", + "content": "g(F_{g}^{i})" + }, + { + "bbox": [ + 46, + 629, + 286, + 713 + ], + "type": "text", + "content": ", and dim represents the dimension of the input feature. In formula 3, feature embedding function " + }, + { + "bbox": [ + 46, + 629, + 286, + 713 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 46, + 629, + 286, + 713 + ], + "type": "text", + "content": " incorporates adaptive pooling, dimension reduction, and max pooling, as shown in Fig. 3. Suppose the shape of the input feature " + }, + { + "bbox": [ + 46, + 629, + 286, + 713 + ], + "type": "inline_equation", + "content": "F_{c}" + }, + { + "bbox": [ + 46, + 629, + 286, + 713 + ], + "type": "text", + "content": " is " + }, + { + "bbox": [ + 46, + 629, + 286, + 713 + ], + "type": "inline_equation", + "content": "[N,C,H,W]" + }, + { + "bbox": [ + 46, + 629, + 286, + 713 + ], + "type": "text", + "content": ", where" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 309, + 69, + 542, + 192 + ], + "blocks": [ + { + "bbox": [ + 309, + 69, + 542, + 192 + ], + "lines": [ + { + "bbox": [ + 309, + 69, + 542, + 192 + ], + "spans": [ + { + "bbox": [ + 309, + 69, + 542, + 192 + ], + "type": "image", + "image_path": "40a0dc616fe1439cccecfe0900a881081c55cffa8be9bdb6ebecc2ccce84ed2d.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 199, + 545, + 255 + ], + "lines": [ + { + "bbox": [ + 305, + 199, + 545, + 255 + ], + "spans": [ + { + "bbox": [ + 305, + 199, + 545, + 255 + ], + "type": "text", + "content": "Figure 4. Details of long short-term feature aggregation. Input features are first grouped, then make spatio-temporal aggregation, and finally concatenated to get the enhanced feature. The \"Location coding\" is used in the second stage: short-term feature aggregation. Best viewed in color and zoomed in." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 277, + 545, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 277, + 545, + 384 + ], + "spans": [ + { + "bbox": [ + 305, + 277, + 545, + 384 + ], + "type": "inline_equation", + "content": "N, C, H, W" + }, + { + "bbox": [ + 305, + 277, + 545, + 384 + ], + "type": "text", + "content": " stands for batch size, channels, height, and width, respectively. The feature is processed by adaptive average pooling on spatial domains and reshaped to a 4D tensor " + }, + { + "bbox": [ + 305, + 277, + 545, + 384 + ], + "type": "inline_equation", + "content": "[N, C, 1, 1]" + }, + { + "bbox": [ + 305, + 277, + 545, + 384 + ], + "type": "text", + "content": " to get the global spatial feature of the image. To calculate the similarity more conveniently, the feature then reduces the dimension and is reshaped to the 2D tensor " + }, + { + "bbox": [ + 305, + 277, + 545, + 384 + ], + "type": "inline_equation", + "content": "[N, C]" + }, + { + "bbox": [ + 305, + 277, + 545, + 384 + ], + "type": "text", + "content": ", and the most representative feature is selected by max pooling. Finally, the 4D feature " + }, + { + "bbox": [ + 305, + 277, + 545, + 384 + ], + "type": "inline_equation", + "content": "[N, C, H, W]" + }, + { + "bbox": [ + 305, + 277, + 545, + 384 + ], + "type": "text", + "content": " is reshaped to 2D " + }, + { + "bbox": [ + 305, + 277, + 545, + 384 + ], + "type": "inline_equation", + "content": "[1, C]" + }, + { + "bbox": [ + 305, + 277, + 545, + 384 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 384, + 545, + 433 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 384, + 545, + 433 + ], + "spans": [ + { + "bbox": [ + 305, + 384, + 545, + 433 + ], + "type": "text", + "content": "For selected index ind, the long-term frame feature " + }, + { + "bbox": [ + 305, + 384, + 545, + 433 + ], + "type": "inline_equation", + "content": "F_{g}^{ind}" + }, + { + "bbox": [ + 305, + 384, + 545, + 433 + ], + "type": "text", + "content": " has the lowest background context similarity with the current frame feature. In training, it provides more diverse real context information for small object detection." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 442, + 537, + 455 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 442, + 537, + 455 + ], + "spans": [ + { + "bbox": [ + 306, + 442, + 537, + 455 + ], + "type": "text", + "content": "3.4. Long short-term feature aggregation module" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 461, + 545, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 461, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 305, + 461, + 545, + 628 + ], + "type": "text", + "content": "Short-term frames in the local temporal range are employed in several recent works to enhance the current frame [2, 4, 5]. Nevertheless, only fusing short-term frames can not fully use the information from the whole video and has significant limitations. The long-term frame is therefore introduced to supplement context information. Motivated by the multi-head attention mechanism [12], a long short-term feature aggregation module that conducts feature aggregation on Proposal-Level is proposed. It effectively integrates the long-term frame features and short-term frame features into the current frame features. The long short-term feature aggregation includes two stages: long-term feature aggregation and short-term feature aggregation, the details of long short-term feature aggregation are shown in Fig. 4." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 630, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 630, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 630, + 545, + 713 + ], + "type": "text", + "content": "Long-term feature aggregation: The input of the long-term feature aggregation module is the short-term frame Proposal-Level features " + }, + { + "bbox": [ + 305, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "X_{s} \\in [N_{1}, C]" + }, + { + "bbox": [ + 305, + 630, + 545, + 713 + ], + "type": "text", + "content": " and the long-term frame Proposal-Level features " + }, + { + "bbox": [ + 305, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "X_{g} \\in [N_{2}, C]" + }, + { + "bbox": [ + 305, + 630, + 545, + 713 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 305, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "N_{1}" + }, + { + "bbox": [ + 305, + 630, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "N_{2}" + }, + { + "bbox": [ + 305, + 630, + 545, + 713 + ], + "type": "text", + "content": " represent the number of features reserved and " + }, + { + "bbox": [ + 305, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 305, + 630, + 545, + 713 + ], + "type": "text", + "content": " represents the channels of features. To combine information from different channels and subspaces, input features" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14617" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "content": "are first divided into " + }, + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "content": " groups. The features after grouping can be formulated as" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 102, + 287, + 126 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 102, + 287, + 126 + ], + "spans": [ + { + "bbox": [ + 105, + 102, + 287, + 126 + ], + "type": "interline_equation", + "content": "X ^ {k} = X [:, (k - 1) \\frac {C}{K}: k \\frac {C}{K} ] \\tag {5}", + "image_path": "8deaa7dd6c25f79f2df41c55ffbbdcf4264e3d3a0485cbc7ec3394b474cc766e.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 133, + 287, + 215 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 133, + 287, + 215 + ], + "spans": [ + { + "bbox": [ + 47, + 133, + 287, + 215 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 133, + 287, + 215 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 47, + 133, + 287, + 215 + ], + "type": "text", + "content": " could be long-term frame Proposal-Level features " + }, + { + "bbox": [ + 47, + 133, + 287, + 215 + ], + "type": "inline_equation", + "content": "X_{g}" + }, + { + "bbox": [ + 47, + 133, + 287, + 215 + ], + "type": "text", + "content": " or short-term frame Proposal-Level features " + }, + { + "bbox": [ + 47, + 133, + 287, + 215 + ], + "type": "inline_equation", + "content": "X_{s}" + }, + { + "bbox": [ + 47, + 133, + 287, + 215 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 133, + 287, + 215 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 47, + 133, + 287, + 215 + ], + "type": "text", + "content": " represents the channels of features, " + }, + { + "bbox": [ + 47, + 133, + 287, + 215 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 47, + 133, + 287, + 215 + ], + "type": "text", + "content": " is the number of groups, " + }, + { + "bbox": [ + 47, + 133, + 287, + 215 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 47, + 133, + 287, + 215 + ], + "type": "text", + "content": " means the " + }, + { + "bbox": [ + 47, + 133, + 287, + 215 + ], + "type": "inline_equation", + "content": "k^{th}" + }, + { + "bbox": [ + 47, + 133, + 287, + 215 + ], + "type": "text", + "content": " group, and " + }, + { + "bbox": [ + 47, + 133, + 287, + 215 + ], + "type": "inline_equation", + "content": "X^{k}" + }, + { + "bbox": [ + 47, + 133, + 287, + 215 + ], + "type": "text", + "content": " denotes the segment of the " + }, + { + "bbox": [ + 47, + 133, + 287, + 215 + ], + "type": "inline_equation", + "content": "k^{th}" + }, + { + "bbox": [ + 47, + 133, + 287, + 215 + ], + "type": "text", + "content": " group on the channel dimension. Every group makes spatio-temporal aggregation and is concatenated to each other." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 215, + 287, + 232 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 215, + 287, + 232 + ], + "spans": [ + { + "bbox": [ + 105, + 215, + 287, + 232 + ], + "type": "interline_equation", + "content": "X _ {g + s} = \\operatorname {c o n c a t} \\left(\\varphi \\left(X _ {s} ^ {k}, X _ {g} ^ {k}\\right)\\right) \\tag {6}", + "image_path": "00f2c1ec1a477013e01f13b28253accdd4278fb5304ce8c3dffc6be43053ced6.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 234, + 287, + 293 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 234, + 287, + 293 + ], + "spans": [ + { + "bbox": [ + 46, + 234, + 287, + 293 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 234, + 287, + 293 + ], + "type": "inline_equation", + "content": "X_{g + s}" + }, + { + "bbox": [ + 46, + 234, + 287, + 293 + ], + "type": "text", + "content": " denotes the enhanced short-term frame features, concat denotes concatenation, and the spatiotemporal aggregation function " + }, + { + "bbox": [ + 46, + 234, + 287, + 293 + ], + "type": "inline_equation", + "content": "\\varphi" + }, + { + "bbox": [ + 46, + 234, + 287, + 293 + ], + "type": "text", + "content": " effectively aggregates long-term frame features and short-term frame features. " + }, + { + "bbox": [ + 46, + 234, + 287, + 293 + ], + "type": "inline_equation", + "content": "\\varphi" + }, + { + "bbox": [ + 46, + 234, + 287, + 293 + ], + "type": "text", + "content": " can be formulated as" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 60, + 299, + 287, + 334 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 60, + 299, + 287, + 334 + ], + "spans": [ + { + "bbox": [ + 60, + 299, + 287, + 334 + ], + "type": "interline_equation", + "content": "\\left\\{ \\begin{array}{l} \\varphi \\left(X _ {s} ^ {k}, X _ {g} ^ {k}\\right) = X _ {s} ^ {k} + \\operatorname {s o f t m a x} (\\omega) \\cdot X _ {g} ^ {k} \\\\ \\omega = \\operatorname {S i m} \\left(\\omega_ {s} \\cdot X _ {s} ^ {k}, \\omega_ {g} \\cdot X _ {g} ^ {k}\\right) + \\operatorname {S i m} \\left(\\mu^ {\\prime}, \\omega_ {g} \\cdot X _ {g} ^ {k}\\right) \\end{array} \\right. \\tag {7}", + "image_path": "e41eff6df7c3c209a010430f3a42f353aa7eb9c9092fe15c00da1f7d4d8e98cb.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 340, + 287, + 482 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 340, + 287, + 482 + ], + "spans": [ + { + "bbox": [ + 46, + 340, + 287, + 482 + ], + "type": "text", + "content": "To obtain a plug-and-play module, the spatio-temporal aggregation function " + }, + { + "bbox": [ + 46, + 340, + 287, + 482 + ], + "type": "inline_equation", + "content": "\\varphi" + }, + { + "bbox": [ + 46, + 340, + 287, + 482 + ], + "type": "text", + "content": " utilizes residual connection (as shown in the dotted box in Fig. 4). " + }, + { + "bbox": [ + 46, + 340, + 287, + 482 + ], + "type": "inline_equation", + "content": "X_{g}^{k}" + }, + { + "bbox": [ + 46, + 340, + 287, + 482 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 340, + 287, + 482 + ], + "type": "inline_equation", + "content": "X_{s}^{k}" + }, + { + "bbox": [ + 46, + 340, + 287, + 482 + ], + "type": "text", + "content": " are fused in residual function, attention " + }, + { + "bbox": [ + 46, + 340, + 287, + 482 + ], + "type": "inline_equation", + "content": "\\omega" + }, + { + "bbox": [ + 46, + 340, + 287, + 482 + ], + "type": "text", + "content": " serves as a correlation weight that consists of two parts: the cosine similarity between short-term frame features and long-term frame features to associate short-term frame and long-term frame, and the cosine similarity between long-term frame features and a group of learnable weights " + }, + { + "bbox": [ + 46, + 340, + 287, + 482 + ], + "type": "inline_equation", + "content": "\\mu^{\\prime}" + }, + { + "bbox": [ + 46, + 340, + 287, + 482 + ], + "type": "text", + "content": " to associate different channels of the long-term frame, " + }, + { + "bbox": [ + 46, + 340, + 287, + 482 + ], + "type": "inline_equation", + "content": "\\omega_{s}" + }, + { + "bbox": [ + 46, + 340, + 287, + 482 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 340, + 287, + 482 + ], + "type": "inline_equation", + "content": "\\omega_{g}" + }, + { + "bbox": [ + 46, + 340, + 287, + 482 + ], + "type": "text", + "content": " are linear transformation matrixes and also fully connected layers. Definition of Sim is same as formula 4." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 483, + 287, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 483, + 287, + 639 + ], + "spans": [ + { + "bbox": [ + 46, + 483, + 287, + 639 + ], + "type": "text", + "content": "Short-term feature aggregation: Only high-level semantic information of the long-term frame is integrated into the short-term frame during long-term feature aggregation. Considering the strong time continuity between the short-term frame and the current frame, the location information of the short-term frame is also fused into the current frame, as shown in Fig. 4 \"location coding\". Let " + }, + { + "bbox": [ + 46, + 483, + 287, + 639 + ], + "type": "inline_equation", + "content": "r_s = \\{x_s, y_s, h_s, w_s\\}" + }, + { + "bbox": [ + 46, + 483, + 287, + 639 + ], + "type": "text", + "content": " be the location information of Regions of Interest (RoIs) in the short-term frame which includes the center point " + }, + { + "bbox": [ + 46, + 483, + 287, + 639 + ], + "type": "inline_equation", + "content": "x_s, y_s" + }, + { + "bbox": [ + 46, + 483, + 287, + 639 + ], + "type": "text", + "content": " and height and width " + }, + { + "bbox": [ + 46, + 483, + 287, + 639 + ], + "type": "inline_equation", + "content": "h_s, w_s" + }, + { + "bbox": [ + 46, + 483, + 287, + 639 + ], + "type": "text", + "content": " of each RoI, and let " + }, + { + "bbox": [ + 46, + 483, + 287, + 639 + ], + "type": "inline_equation", + "content": "r_c" + }, + { + "bbox": [ + 46, + 483, + 287, + 639 + ], + "type": "text", + "content": " be the location information of RoIs in the current frame. The location correlation weight can be represented as" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 53, + 647, + 287, + 682 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 647, + 287, + 682 + ], + "spans": [ + { + "bbox": [ + 53, + 647, + 287, + 682 + ], + "type": "interline_equation", + "content": "\\left\\{ \\begin{array}{l} \\omega_ {r} = \\operatorname {r e l u} \\left(\\omega_ {c s} \\cdot \\psi \\left(r _ {c}, r _ {s}\\right)\\right) \\\\ \\psi \\left(r _ {c}, r _ {s}\\right) = \\left\\{\\log \\left(\\frac {\\left| x _ {c} - x _ {s} \\right|}{w _ {c}}\\right), \\log \\left(\\frac {\\left| y _ {c} - y _ {s} \\right|}{h _ {c}}\\right), \\log \\left(\\frac {w _ {c}}{w _ {s}}\\right), \\log \\left(\\frac {h _ {c}}{h _ {s}}\\right) \\right\\} \\end{array} \\right. \\tag {8}", + "image_path": "3332442db999efd56c48419e03e902f94b701a1f1144b852bb47879d4074c819.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\omega_{r}" + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": " denotes location correlation weight, the nonlinear function relu is used to reduce redundant information, " + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\omega_{cs}" + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": " is" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 72, + 545, + 142 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 142 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 142 + ], + "type": "text", + "content": "the linear transformation matrix and also a fully connected layer in the network, and " + }, + { + "bbox": [ + 304, + 72, + 545, + 142 + ], + "type": "inline_equation", + "content": "\\psi" + }, + { + "bbox": [ + 304, + 72, + 545, + 142 + ], + "type": "text", + "content": " is utilized to code the location information of the current frame and the short-term frame to make the module translation invariant. The correlation weight of short-term feature aggregation can be represented as" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 356, + 148, + 545, + 180 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 356, + 148, + 545, + 180 + ], + "spans": [ + { + "bbox": [ + 356, + 148, + 545, + 180 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\omega = \\operatorname {S i m} \\left(\\omega_ {c} \\cdot X _ {c} ^ {k}, \\omega_ {g + s} \\cdot X _ {g + s} ^ {k}\\right) \\tag {9} \\\\ + S i m \\left(\\mu^ {\\prime \\prime}, \\omega_ {g + s} \\cdot X _ {g + s} ^ {k}\\right) + \\omega_ {r} ^ {k} \\\\ \\end{array}", + "image_path": "9d2cc892fb361a053c7af2666bd88714a8553c11a545bc8a0e79d4d9dd7c2fef.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 194, + 545, + 326 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 194, + 545, + 326 + ], + "spans": [ + { + "bbox": [ + 304, + 194, + 545, + 326 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 194, + 545, + 326 + ], + "type": "inline_equation", + "content": "X_{c}^{k}" + }, + { + "bbox": [ + 304, + 194, + 545, + 326 + ], + "type": "text", + "content": " stands for the current frame Proposal-Level features after grouping, " + }, + { + "bbox": [ + 304, + 194, + 545, + 326 + ], + "type": "inline_equation", + "content": "\\omega_{g+s}" + }, + { + "bbox": [ + 304, + 194, + 545, + 326 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 194, + 545, + 326 + ], + "type": "inline_equation", + "content": "\\omega_{c}" + }, + { + "bbox": [ + 304, + 194, + 545, + 326 + ], + "type": "text", + "content": " are fully connected layers used to reshape the feature, " + }, + { + "bbox": [ + 304, + 194, + 545, + 326 + ], + "type": "inline_equation", + "content": "\\omega" + }, + { + "bbox": [ + 304, + 194, + 545, + 326 + ], + "type": "text", + "content": " is the adaptive weight including three parts: the cosine similarity between enhanced short-term frame features and current frame features, the cosine similarity between enhanced short-term frame features and a group of learnable weights " + }, + { + "bbox": [ + 304, + 194, + 545, + 326 + ], + "type": "inline_equation", + "content": "\\mu''" + }, + { + "bbox": [ + 304, + 194, + 545, + 326 + ], + "type": "text", + "content": ", and the location correlation weight between the current frame and short-term frame after grouping. The other steps of short-term feature aggregation are the same as long-term feature aggregation and needless to be described again." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 344, + 386, + 358 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 344, + 386, + 358 + ], + "spans": [ + { + "bbox": [ + 306, + 344, + 386, + 358 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 367, + 413, + 380 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 367, + 413, + 380 + ], + "spans": [ + { + "bbox": [ + 306, + 367, + 413, + 380 + ], + "type": "text", + "content": "4.1. Experiment Setup" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 388, + 545, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 388, + 545, + 590 + ], + "spans": [ + { + "bbox": [ + 304, + 388, + 545, + 590 + ], + "type": "text", + "content": "Datasets and Evaluation Setup: We conduct experiments on ImageNet-VID [20] and FL-Drones [19]. ImageNet-VID is a widely used large-scale benchmark for video object detection, which contains 3862 videos in the training set, 555 videos in the validation set, and a total of 30 categories. " + }, + { + "bbox": [ + 304, + 388, + 545, + 590 + ], + "type": "inline_equation", + "content": "mAP" + }, + { + "bbox": [ + 304, + 388, + 545, + 590 + ], + "type": "text", + "content": " is used for evaluation on ImageNet-VID. To evaluate the performance of the proposed method on video small object detection, we also make use of the FL-Drones dataset consisting of 14 videos and 38948 frames. The flying drones in the dataset can be regarded as small objects because the average size of annotated drones is " + }, + { + "bbox": [ + 304, + 388, + 545, + 590 + ], + "type": "inline_equation", + "content": "25 \\times 16" + }, + { + "bbox": [ + 304, + 388, + 545, + 590 + ], + "type": "text", + "content": " and the frame resolutions are " + }, + { + "bbox": [ + 304, + 388, + 545, + 590 + ], + "type": "inline_equation", + "content": "640 \\times 480" + }, + { + "bbox": [ + 304, + 388, + 545, + 590 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 388, + 545, + 590 + ], + "type": "inline_equation", + "content": "752 \\times 480" + }, + { + "bbox": [ + 304, + 388, + 545, + 590 + ], + "type": "text", + "content": ". This dataset is quite challenging due to the extreme illumination and relatively small size. According to the author [19], half of the data is used for training, and the other half is used for testing. And " + }, + { + "bbox": [ + 304, + 388, + 545, + 590 + ], + "type": "inline_equation", + "content": "AP" + }, + { + "bbox": [ + 304, + 388, + 545, + 590 + ], + "type": "text", + "content": " is used as the evaluation metric for FL-Drones since it is a video dataset for small objects." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": "Implementation Details: The proposed algorithm is trained and tested using 4 16GB NVIDIA Tesla V100. The baseline used in this paper is Faster R-CNN. Following the multi-task loss in baseline, the whole network is optimized with both classification and regression losses. SGD is selected as the optimizer and the model is trained for 120000 iterations on ImageNet-VID and 66000 iterations on FLDrones. The learning rate is set to 0.001 and updated using WarmupMultiStepLR [18], which means the model first has 500 warm-up iterations to improve stability." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "14618" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 224, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 224, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 224, + 85 + ], + "type": "text", + "content": "4.2. Comparison with state-of-the-art" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 91, + 287, + 150 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 91, + 287, + 150 + ], + "spans": [ + { + "bbox": [ + 46, + 91, + 287, + 150 + ], + "type": "text", + "content": "ImageNet-VID dataset: Comparison results on this dataset are shown in Table 1. All algorithms adopt the same feature extraction network to be compared fairly, and the results of the state-of-the-art works are collected from published papers." + } + ] + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 80, + 191, + 252, + 327 + ], + "blocks": [ + { + "bbox": [ + 51, + 161, + 282, + 173 + ], + "lines": [ + { + "bbox": [ + 51, + 161, + 282, + 173 + ], + "spans": [ + { + "bbox": [ + 51, + 161, + 282, + 173 + ], + "type": "text", + "content": "Table 1. Quantitative results on the ImageNet-VID dataset " + }, + { + "bbox": [ + 51, + 161, + 282, + 173 + ], + "type": "inline_equation", + "content": "(\\%)" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 80, + 191, + 252, + 327 + ], + "lines": [ + { + "bbox": [ + 80, + 191, + 252, + 327 + ], + "spans": [ + { + "bbox": [ + 80, + 191, + 252, + 327 + ], + "type": "table", + "html": "
MethodBackbonemAP
FGFA [28]ResNet10176.3
STMN [24]ResNet10180.5
LongRange [21]ResNet10181.0
D&T [6]ResNet10175.8
MANet [22]ResNet10178.1
STSN [2]ResNet10178.9
RDN [5]ResNet10181.8
SELSA [23]ResNet10180.3
MEGA [3]ResNet10182.9
LSTFE-NetResNet10183.4
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Results show that the LSTFE-Net can better collect the information from long-term and short-term frames and enhance the feature." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 410, + 287, + 493 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 410, + 287, + 493 + ], + "spans": [ + { + "bbox": [ + 46, + 410, + 287, + 493 + ], + "type": "text", + "content": "FL-Drones dataset: As a video dataset for small objects, few results of other classical methods can be found on this dataset which means we need to conduct experiments using these methods ourselves. For a more comprehensive comparison, ResNet50 and ResNet101 are respectively used as the feature extraction network for analysis. The results are shown in Table 2." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 494, + 287, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 494, + 287, + 601 + ], + "spans": [ + { + "bbox": [ + 46, + 494, + 287, + 601 + ], + "type": "text", + "content": "According to Table 2, our method achieves the best small object detection performance no matter what the feature extraction network is. Our LSTFE-Net obtains the highest " + }, + { + "bbox": [ + 46, + 494, + 287, + 601 + ], + "type": "inline_equation", + "content": "AP" + }, + { + "bbox": [ + 46, + 494, + 287, + 601 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 46, + 494, + 287, + 601 + ], + "type": "inline_equation", + "content": "37.8\\%" + }, + { + "bbox": [ + 46, + 494, + 287, + 601 + ], + "type": "text", + "content": " and outperforms the strongest competitor TransVOD by " + }, + { + "bbox": [ + 46, + 494, + 287, + 601 + ], + "type": "inline_equation", + "content": "0.9\\%" + }, + { + "bbox": [ + 46, + 494, + 287, + 601 + ], + "type": "inline_equation", + "content": "AP" + }, + { + "bbox": [ + 46, + 494, + 287, + 601 + ], + "type": "text", + "content": " when ResNet50 is used. For ResNet101, our LSTFE-Net achieves an " + }, + { + "bbox": [ + 46, + 494, + 287, + 601 + ], + "type": "inline_equation", + "content": "AP" + }, + { + "bbox": [ + 46, + 494, + 287, + 601 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 46, + 494, + 287, + 601 + ], + "type": "inline_equation", + "content": "46.8\\%" + }, + { + "bbox": [ + 46, + 494, + 287, + 601 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 494, + 287, + 601 + ], + "type": "inline_equation", + "content": "4.4\\%" + }, + { + "bbox": [ + 46, + 494, + 287, + 601 + ], + "type": "text", + "content": " higher than MEGA. Fig. 5 shows some qualitative comparison results of our LSTFE-Net versus other state-of-the-art works." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 610, + 147, + 623 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 610, + 147, + 623 + ], + "spans": [ + { + "bbox": [ + 47, + 610, + 147, + 623 + ], + "type": "text", + "content": "4.3. Ablation Studies" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 629, + 287, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 287, + 653 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 287, + 653 + ], + "type": "text", + "content": "We conduct ablation studies to validate the effectiveness of each component in our model on the FL-Drones dataset." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "text", + "content": "Spatio-temporal feature alignment module: " + }, + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "text", + "content": " cascaded deformable convolutional blocks are applied in this module, and experiments are conducted in this section to study the influence of the value of " + }, + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "text", + "content": " on spatio-temporal modeling. The short-term frame and the long-term frame" + } + ] + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 332, + 100, + 518, + 200 + ], + "blocks": [ + { + "bbox": [ + 318, + 71, + 533, + 82 + ], + "lines": [ + { + "bbox": [ + 318, + 71, + 533, + 82 + ], + "spans": [ + { + "bbox": [ + 318, + 71, + 533, + 82 + ], + "type": "text", + "content": "Table 2. Quantitative results on the FL-Drones dataset " + }, + { + "bbox": [ + 318, + 71, + 533, + 82 + ], + "type": "inline_equation", + "content": "(\\%)" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 332, + 100, + 518, + 200 + ], + "lines": [ + { + "bbox": [ + 332, + 100, + 518, + 200 + ], + "spans": [ + { + "bbox": [ + 332, + 100, + 518, + 200 + ], + "type": "table", + "html": "
MethodAP
ResNet50ResNet101
DFF [27]19.522.4
FGFA [28]21.224.5
TransVOD [11]36.935.2
RDN [5]35.942.1
MEGA [3]36.542.4
LSTFE-Net37.846.8
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BackboneAP
k = 0ResNet10142.1
k = 1ResNet10145.4
k = 2ResNet10139.4
k = 3ResNet10139.3
", + "image_path": "20065713fc65ae40845cd87ba3dacea2f335b3b4a2c209547a86c3fa55e55941.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "table_body" + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 580, + 545, + 603 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 580, + 545, + 603 + ], + "spans": [ + { + "bbox": [ + 305, + 580, + 545, + 603 + ], + "type": "text", + "content": "are first added to the baseline, and then the value of " + }, + { + "bbox": [ + 305, + 580, + 545, + 603 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 305, + 580, + 545, + 603 + ], + "type": "text", + "content": " is adjusted. Results are shown in Table 3:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 605, + 545, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 688 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 688 + ], + "type": "text", + "content": "Table 3 shows that the network achieves an " + }, + { + "bbox": [ + 304, + 605, + 545, + 688 + ], + "type": "inline_equation", + "content": "AP" + }, + { + "bbox": [ + 304, + 605, + 545, + 688 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 304, + 605, + 545, + 688 + ], + "type": "inline_equation", + "content": "42.1\\%" + }, + { + "bbox": [ + 304, + 605, + 545, + 688 + ], + "type": "text", + "content": " if the spatio-temporal feature alignment module is not used. When " + }, + { + "bbox": [ + 304, + 605, + 545, + 688 + ], + "type": "inline_equation", + "content": "k = 1" + }, + { + "bbox": [ + 304, + 605, + 545, + 688 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 605, + 545, + 688 + ], + "type": "inline_equation", + "content": "AP" + }, + { + "bbox": [ + 304, + 605, + 545, + 688 + ], + "type": "text", + "content": " increases by " + }, + { + "bbox": [ + 304, + 605, + 545, + 688 + ], + "type": "inline_equation", + "content": "3.3\\%" + }, + { + "bbox": [ + 304, + 605, + 545, + 688 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 605, + 545, + 688 + ], + "type": "inline_equation", + "content": "45.4\\%" + }, + { + "bbox": [ + 304, + 605, + 545, + 688 + ], + "type": "text", + "content": ". As " + }, + { + "bbox": [ + 304, + 605, + 545, + 688 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 605, + 545, + 688 + ], + "type": "text", + "content": " increases from 1 to 3, " + }, + { + "bbox": [ + 304, + 605, + 545, + 688 + ], + "type": "inline_equation", + "content": "AP" + }, + { + "bbox": [ + 304, + 605, + 545, + 688 + ], + "type": "text", + "content": " decreases gradually. To explore the reasons for the decreasing detection performance, the offset matrixes with different values of " + }, + { + "bbox": [ + 304, + 605, + 545, + 688 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 605, + 545, + 688 + ], + "type": "text", + "content": " are visualized, as shown in Fig. 6." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": "The offset matrix with " + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "inline_equation", + "content": "k = 1" + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": " is visualized in Fig. 6(b), where it is obvious that offsets are generally larger at the" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14619" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 72, + 105, + 114 + ], + "blocks": [ + { + "bbox": [ + 50, + 72, + 105, + 114 + ], + "lines": [ + { + "bbox": [ + 50, + 72, + 105, + 114 + ], + "spans": [ + { + "bbox": [ + 50, + 72, + 105, + 114 + ], + "type": "image", + "image_path": "f965767d00c9061d02480474ea5217f7997862226bebc0cd533793b1a349952c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 71, + 118, + 89, + 124 + ], + "lines": [ + { + "bbox": [ + 71, + 118, + 89, + 124 + ], + "spans": [ + { + "bbox": [ + 71, + 118, + 89, + 124 + ], + "type": "text", + "content": "(a)input" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 107, + 72, + 162, + 114 + ], + "blocks": [ + { + "bbox": [ + 107, + 72, + 162, + 114 + ], + "lines": [ + { + "bbox": [ + 107, + 72, + 162, + 114 + ], + "spans": [ + { + "bbox": [ + 107, + 72, + 162, + 114 + ], + "type": "image", + "image_path": "7d87939a2af6bb33c80a82a80c491710e427e793f3d2ac2c41bda10d2884ccb9.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 126, + 118, + 143, + 124 + ], + "lines": [ + { + "bbox": [ + 126, + 118, + 143, + 124 + ], + "spans": [ + { + "bbox": [ + 126, + 118, + 143, + 124 + ], + "type": "text", + "content": "(b) " + }, + { + "bbox": [ + 126, + 118, + 143, + 124 + ], + "type": "inline_equation", + "content": "k = 1" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 167, + 72, + 222, + 114 + ], + "blocks": [ + { + "bbox": [ + 167, + 72, + 222, + 114 + ], + "lines": [ + { + "bbox": [ + 167, + 72, + 222, + 114 + ], + "spans": [ + { + "bbox": [ + 167, + 72, + 222, + 114 + ], + "type": "image", + "image_path": "10bd77638127979172d8313cca09bf2afe8c95757d278debd5e7588d0c13a47a.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 186, + 117, + 204, + 124 + ], + "lines": [ + { + "bbox": [ + 186, + 117, + 204, + 124 + ], + "spans": [ + { + "bbox": [ + 186, + 117, + 204, + 124 + ], + "type": "text", + "content": "(c) " + }, + { + "bbox": [ + 186, + 117, + 204, + 124 + ], + "type": "inline_equation", + "content": "k = 2" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 47, + 136, + 286, + 157 + ], + "lines": [ + { + "bbox": [ + 47, + 136, + 286, + 157 + ], + "spans": [ + { + "bbox": [ + 47, + 136, + 286, + 157 + ], + "type": "text", + "content": "Figure 6. Visualization of offset matrix. The deeper the color, the larger the offset." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 228, + 72, + 282, + 114 + ], + "blocks": [ + { + "bbox": [ + 228, + 72, + 282, + 114 + ], + "lines": [ + { + "bbox": [ + 228, + 72, + 282, + 114 + ], + "spans": [ + { + "bbox": [ + 228, + 72, + 282, + 114 + ], + "type": "image", + "image_path": "f8ea147d93d7c710195b2d094361312a3bd565b6d5ca71949228355dc9eeabe2.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 246, + 117, + 264, + 124 + ], + "lines": [ + { + "bbox": [ + 246, + 117, + 264, + 124 + ], + "spans": [ + { + "bbox": [ + 246, + 117, + 264, + 124 + ], + "type": "text", + "content": "(d) " + }, + { + "bbox": [ + 246, + 117, + 264, + 124 + ], + "type": "inline_equation", + "content": "k = 3" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 51, + 201, + 284, + 261 + ], + "blocks": [ + { + "bbox": [ + 66, + 171, + 268, + 183 + ], + "lines": [ + { + "bbox": [ + 66, + 171, + 268, + 183 + ], + "spans": [ + { + "bbox": [ + 66, + 171, + 268, + 183 + ], + "type": "text", + "content": "Table 4. Ablation study of frame selection module " + }, + { + "bbox": [ + 66, + 171, + 268, + 183 + ], + "type": "inline_equation", + "content": "(\\%)" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 51, + 201, + 284, + 261 + ], + "lines": [ + { + "bbox": [ + 51, + 201, + 284, + 261 + ], + "spans": [ + { + "bbox": [ + 51, + 201, + 284, + 261 + ], + "type": "table", + "html": "
Number of long-term framesBackboneAP
Long-term framesFrame selection
1ResNet10129.529.9
2ResNet10135.135.9
3ResNet10133.934.8
4ResNet10129.630.7
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When " + }, + { + "bbox": [ + 46, + 292, + 286, + 411 + ], + "type": "inline_equation", + "content": "k = 3" + }, + { + "bbox": [ + 46, + 292, + 286, + 411 + ], + "type": "text", + "content": ", the offset matrix can hardly represent the relationship between frames. Adding the offset in the convolution will hinder the normal extraction of features and make the detection result worse." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 412, + 286, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 412, + 286, + 495 + ], + "spans": [ + { + "bbox": [ + 46, + 412, + 286, + 495 + ], + "type": "text", + "content": "Frame selection module: The detection results before and after using the frame selection module are compared. To emphasize the impact of the frame selection module, the number of short-term frames is set to 0. After " + }, + { + "bbox": [ + 46, + 412, + 286, + 495 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 412, + 286, + 495 + ], + "type": "text", + "content": " long-term frames are sampled, additional " + }, + { + "bbox": [ + 46, + 412, + 286, + 495 + ], + "type": "inline_equation", + "content": "2m" + }, + { + "bbox": [ + 46, + 412, + 286, + 495 + ], + "type": "text", + "content": " frames are then sampled and " + }, + { + "bbox": [ + 46, + 412, + 286, + 495 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 412, + 286, + 495 + ], + "type": "text", + "content": " frames are selected by the frame selection module. The results are shown in Table 4:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 497, + 286, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 497, + 286, + 581 + ], + "spans": [ + { + "bbox": [ + 46, + 497, + 286, + 581 + ], + "type": "text", + "content": "Table 4 demonstrates how the number of long-term frames will affect the detection performance of small objects. The promotion effects of the frame selection module vary for different numbers of sampled long-term frames. When there are 4 sampled frames, " + }, + { + "bbox": [ + 46, + 497, + 286, + 581 + ], + "type": "inline_equation", + "content": "AP" + }, + { + "bbox": [ + 46, + 497, + 286, + 581 + ], + "type": "text", + "content": " improves most " + }, + { + "bbox": [ + 46, + 497, + 286, + 581 + ], + "type": "inline_equation", + "content": "(1.1\\%)" + }, + { + "bbox": [ + 46, + 497, + 286, + 581 + ], + "type": "text", + "content": ". And when the number of sampled frames is 2, " + }, + { + "bbox": [ + 46, + 497, + 286, + 581 + ], + "type": "inline_equation", + "content": "AP" + }, + { + "bbox": [ + 46, + 497, + 286, + 581 + ], + "type": "text", + "content": " improves by " + }, + { + "bbox": [ + 46, + 497, + 286, + 581 + ], + "type": "inline_equation", + "content": "0.8\\%" + }, + { + "bbox": [ + 46, + 497, + 286, + 581 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 497, + 286, + 581 + ], + "type": "inline_equation", + "content": "35.9\\%" + }, + { + "bbox": [ + 46, + 497, + 286, + 581 + ], + "type": "text", + "content": " (highest)." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 582, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 286, + 712 + ], + "type": "text", + "content": "Long short-term feature aggregation module: In this section, concatenation is used as a simple feature aggregation method to be compared. The only difference between short-term feature aggregation and long-term feature aggregation is the utilization of location coding, so the contribution of location coding is verified. Short-term frames and long-term frames are first added to the baseline, and then simple feature aggregation, long short-term feature aggregation without location coding, and long short-term feature aggregation are used for experiments separately. The results are shown in Table 5." + } + ] + } + ], + "index": 14 + }, + { + "type": "table", + "bbox": [ + 326, + 111, + 525, + 165 + ], + "blocks": [ + { + "bbox": [ + 305, + 71, + 545, + 92 + ], + "lines": [ + { + "bbox": [ + 305, + 71, + 545, + 92 + ], + "spans": [ + { + "bbox": [ + 305, + 71, + 545, + 92 + ], + "type": "text", + "content": "Table 5. Ablation study of long short-term feature aggregation module " + }, + { + "bbox": [ + 305, + 71, + 545, + 92 + ], + "type": "inline_equation", + "content": "(\\%)" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 326, + 111, + 525, + 165 + ], + "lines": [ + { + "bbox": [ + 326, + 111, + 525, + 165 + ], + "spans": [ + { + "bbox": [ + 326, + 111, + 525, + 165 + ], + "type": "table", + "html": "
MethodBackboneAP
simple feature aggregationResNet10139.9
long short-term feature aggregation without location codingResNet10141.2
long short-term feature aggregationResNet10142.1
", + "image_path": "261b130bbc98aa6338b86b24b2528758b295bf621fab338c9b4bd6f0ccd24e5b.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "table_body" + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 194, + 545, + 266 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 194, + 545, + 266 + ], + "spans": [ + { + "bbox": [ + 304, + 194, + 545, + 266 + ], + "type": "text", + "content": "Table 5 shows that the simple feature aggregation method obtains an " + }, + { + "bbox": [ + 304, + 194, + 545, + 266 + ], + "type": "inline_equation", + "content": "AP" + }, + { + "bbox": [ + 304, + 194, + 545, + 266 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 304, + 194, + 545, + 266 + ], + "type": "inline_equation", + "content": "39.9\\%" + }, + { + "bbox": [ + 304, + 194, + 545, + 266 + ], + "type": "text", + "content": ", while the proposed long short-term feature aggregation method can improve " + }, + { + "bbox": [ + 304, + 194, + 545, + 266 + ], + "type": "inline_equation", + "content": "AP" + }, + { + "bbox": [ + 304, + 194, + 545, + 266 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 194, + 545, + 266 + ], + "type": "inline_equation", + "content": "42.1\\%" + }, + { + "bbox": [ + 304, + 194, + 545, + 266 + ], + "type": "text", + "content": ". Additionally, the " + }, + { + "bbox": [ + 304, + 194, + 545, + 266 + ], + "type": "inline_equation", + "content": "AP" + }, + { + "bbox": [ + 304, + 194, + 545, + 266 + ], + "type": "text", + "content": " drops to " + }, + { + "bbox": [ + 304, + 194, + 545, + 266 + ], + "type": "inline_equation", + "content": "41.2\\%" + }, + { + "bbox": [ + 304, + 194, + 545, + 266 + ], + "type": "text", + "content": " when the location coding is removed, which means that the location coding can bring a gain of " + }, + { + "bbox": [ + 304, + 194, + 545, + 266 + ], + "type": "inline_equation", + "content": "0.9\\% AP" + }, + { + "bbox": [ + 304, + 194, + 545, + 266 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 278, + 378, + 290 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 278, + 378, + 290 + ], + "spans": [ + { + "bbox": [ + 306, + 278, + 378, + 290 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 298, + 545, + 561 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 298, + 545, + 561 + ], + "spans": [ + { + "bbox": [ + 304, + 298, + 545, + 561 + ], + "type": "text", + "content": "For small objects, we propose an LSTFE-Net to enhance the feature with two important sources of information from the video. A spatio-temporal feature alignment module is proposed to model the temporal information between the short-term frame and the current frame. It uses deformable convolution to make connections between objects of different frames, and conducts feature enhancement on Pixel-Level. Considering that the background context information of the object is single, the frame selection module is used to select the long-term frame with the most distinct feature from the current frame, which is further used to enrich the vital context information for small object detection. To effectively fuse the features of different types of frames, we develop a long short-term feature aggregation module, where context information from the long-term frames and the temporal information from the short-term frames are incorporated into the current frame by stages. Experiments are carried out on ImageNet-VID and FL-Drones to compare our method with other state-of-the-art methods and conduct ablation studies. The results show that the proposed method achieves superior small object detection performance in videos." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 573, + 403, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 573, + 403, + 586 + ], + "spans": [ + { + "bbox": [ + 306, + 573, + 403, + 586 + ], + "type": "text", + "content": "Acknowledgement" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 593, + 545, + 648 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 593, + 545, + 648 + ], + "spans": [ + { + "bbox": [ + 304, + 593, + 545, + 648 + ], + "type": "text", + "content": "This work is supported by National Natural Science Foundation of China (U1903214), Major Science and Technology Projects of Jilin Province (20210301030GX), Natural Science Foundation of Guangdong Province (2021A1515012233)" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 659, + 365, + 672 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 659, + 365, + 672 + ], + "spans": [ + { + "bbox": [ + 306, + 659, + 365, + 672 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 310, + 680, + 545, + 713 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 680, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 310, + 680, + 545, + 713 + ], + "type": "text", + "content": "[1] Muhammad Waseem Ashraf, Waqas Sultani, and Mubarak Shah. 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Expert Systems with Applications, 211:118665, 2023. 2" + } + ] + } + ], + "index": 25 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "14621" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 8 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 72, + 287, + 217 + ], + "type": "list", + "angle": 0, + "index": 3, + "blocks": [ + { + "bbox": [ + 48, + 72, + 287, + 127 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 72, + 287, + 127 + ], + "spans": [ + { + "bbox": [ + 48, + 72, + 287, + 127 + ], + "type": "text", + "content": "[26] Chenhongyi Yang, Zehao Huang, and Naiyan Wang. Querydet: Cascaded sparse query for accelerating high-resolution small object detection. 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In Proceedings of the IEEE international conference on computer vision, pages 408-417, 2017. 1, 2, 3, 7" + } + ] + } + ], + "index": 2 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "14622" + } + ] + } + ], + "index": 4 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/LVQAC_ Lattice Vector Quantization Coupled With Spatially Adaptive Companding for Efficient Learned Image Compression/7db2f3f4-b386-46ae-b0d0-6d14527e76a1_content_list.json b/2023/LVQAC_ Lattice Vector Quantization Coupled With Spatially Adaptive Companding for Efficient Learned Image Compression/7db2f3f4-b386-46ae-b0d0-6d14527e76a1_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..000fed419d64bc1171fc0f68be71a86cd6030992 --- /dev/null +++ b/2023/LVQAC_ Lattice Vector Quantization Coupled With Spatially Adaptive Companding for Efficient Learned Image Compression/7db2f3f4-b386-46ae-b0d0-6d14527e76a1_content_list.json @@ -0,0 +1,1615 @@ +[ + { + "type": "text", + "text": "LVQAC: Lattice Vector Quantization Coupled with Spatially Adaptive Compa nding for Efficient Learned Image Compression", + "text_level": 1, + "bbox": [ + 129, + 128, + 841, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Xi Zhang \nShanghai Jiao Tong University \nzhangxi_19930818@sjtu.edu.cn", + "bbox": [ + 241, + 204, + 488, + 257 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Xiaolin Wu \nMcMaster University \nxwu@ece.mcmaster.ca", + "bbox": [ + 550, + 204, + 723, + 256 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 291, + 313, + 306 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, numerous end-to-end optimized image compression neural networks have been developed and proved themselves as leaders in rate-distortion performance. The main strength of these learnt compression methods is in powerful nonlinear analysis and synthesis transforms that can be facilitated by deep neural networks. However, out of operational expediency, most of these end-to-end methods adopt uniform scalar quantizers rather than vector quantizers, which are information-theoretically optimal. In this paper, we present a novel Lattice Vector Quantization scheme coupled with a spatially Adaptive Companding (LVQAC) mapping. LVQ can better exploit the inter-feature dependencies than scalar uniform quantization while being computationally almost as simple as the latter. Moreover, to improve the adaptability of LVQ to source statistics, we couple a spatially adaptive companding (AC) mapping with LVQ. The resulting LVQAC design can be easily embedded into any end-to-end optimized image compression system. Extensive experiments demonstrate that for any end-to-end CNN image compression models, replacing uniform quantizer by LVQAC achieves better rate-distortion performance without significantly increasing the model complexity.", + "bbox": [ + 75, + 324, + 473, + 657 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 690, + 209, + 705 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In the past five years, the research on end-to-end CNN image compression has made steady progress and led to the birth of a new class of image compression methods [1, 3, 4, 8, 21, 25, 26, 34-36, 40-44]. The CNN compression can now match and even exceed the rate-distortion performance of the previous best image compression methods [6, 33, 37, 45], which operate in the traditional paradigm of linear transform, quantization and entropy coding.", + "bbox": [ + 75, + 717, + 468, + 838 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The advantages of the CNN approach of data compression come from the nonlinearity of its analysis and synthesis transforms of the autoencoder architecture, the end-to-end joint optimization of the nonlinear transforms, uni", + "bbox": [ + 75, + 839, + 468, + 901 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "form quantization of the latent space and conditional entropy coding (context-based arithmetic coding) of quantized features.", + "bbox": [ + 496, + 292, + 890, + 337 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Apparently, using uniform scalar quantizer in the above CNN image compression framework is motivated by operational expediency more than other considerations. Only at very high bit rate uniform quantization can approach the rate-distortion optimality [15]. It is very difficult to directly adopt and optimize a vector quantizer (VQ) in the end-to-end CNN architecture design for data compression, because VQ is a discrete decision process and it is not compatible with variational backpropagation that is necessary to the end-to-end CNN training. In [1], Agustsson et al. tried to circumvent the difficulty by a so-called soft-to-hard vector quantization scheme. Their technique is a soft (continuous) relaxation of discrete computations of VQ and entropy so that their effects can be approximated in the end-to-end training. However, in [1] the quantization centers are optimized along with the other modules, which make the whole system quite cumbersome and more difficult to train. In this paper, we propose a novel Lattice Vector Quantization scheme coupled with a spatially Adaptive Companding (LVQAC) mapping. LVQ can better exploit the inter-feature dependencies than scalar uniform quantization while being computationally almost as simple as the latter. Even if the features to be compressed are statistically independent, LVQ is still a more efficient coding strategy than scalar uniform quantization. This is because the former offers a more efficient covering of high-dimensional space than the latter, as proven by the theory of sphere packings, lattices and groups [11]. Moreover, to improve the adaptability of LVQ to source statistics, we couple a spatially adaptive companding mapping with LVQ. The resulting LVQAC design is computationally as simple and as amenable to the end-to-end training of the CNN compression model as in the originally proposed framework of [3].", + "bbox": [ + 496, + 339, + 892, + 838 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Consequently, for any end-to-end CNN image compression models, replacing uniform quantizer by LVQAC achieves better rate-distortion performance without significantly increasing the model complexity; the simpler", + "bbox": [ + 496, + 839, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "10239", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "the context-sensitive entropy model, the greater the performance gain. For instance, the checkerboard context model [18] has recently been proposed to speed up the decoding process, but it hurts the R-D performance slightly. By incorporating LVQAC into the end-to-end compression CNN with a checkerboard context model, we can achieve the same performance as the counterpart CNN using a far more expensive auto-regressive context model. This is because uniform scalar quantization needs a more complex model to compensate for its coding inefficiency, whereas LVQAC does not.", + "bbox": [ + 75, + 90, + 472, + 257 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Overview of Learned Image Compression and Related Work", + "text_level": 1, + "bbox": [ + 76, + 268, + 468, + 303 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Balle et al. [3] pioneered the end-to-end CNN model for image compression. Their network design is still shaped by the legacy of classical three-step signal compression algorithms; namely, transform, quantization and entropy coding. The greatest advantage of the CNN approach over the classical one comes from replacing linear transforms of the latter by more powerful and complex nonlinear transforms, which is the distinctive prowess of deep neural networks. Specifically, in the end-to-end image compression CNNs, an image vector $\\pmb{x} \\in \\mathbb{R}^N$ is mapped to a latent code space via a parametric nonlinear analysis transform, $\\pmb{y} = g_{a}(\\pmb{x};\\pmb{\\theta}_{g})$ . Then this representation is quantized, yielding a discrete-valued vector $\\hat{\\pmb{y}} = Q(\\pmb{y}) \\in \\mathbb{Z}^{M}$ which can be losslessly compressed using entropy coding algorithms such as arithmetic coding [31, 38] and transmitted as a sequence of bits. On the other side, the decoder recovers $\\hat{\\pmb{y}}$ from the compressed codes, and subjects it to a parametric nonlinear synthesis transform $g_{s}(\\hat{\\pmb{y}};\\phi_{g})$ to build the reconstructed image $\\hat{\\pmb{x}}$ . The nonlinear parametric transform $g_{a}(\\pmb{x};\\pmb{\\theta}_{g})$ and $g_{s}(\\pmb{x};\\phi_{g})$ are implemented by convolutional neural networks and the parameters $\\pmb{\\theta}_{g}$ and $\\phi_{g}$ are learned over a large amount of natural images.", + "bbox": [ + 75, + 311, + 472, + 648 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The training goal is to minimize the expected length of the bitstream as well as the expected distortion of the reconstructed image with respect to the original image, giving rise to a rate-distortion optimization problem:", + "bbox": [ + 75, + 648, + 470, + 709 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {m i n i m i z e} R + \\lambda \\cdot D\n$$\n", + "text_format": "latex", + "bbox": [ + 143, + 718, + 287, + 731 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\nR = \\mathbb {E} _ {\\boldsymbol {x} \\sim p _ {x}} \\left[ - \\log_ {2} p _ {\\tilde {y}} \\left(Q \\left(g _ {a} (\\boldsymbol {x})\\right)\\right) \\right] \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 145, + 734, + 468, + 753 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\nD = \\lambda \\cdot \\mathbb {E} _ {\\boldsymbol {x} \\sim p _ {x}} [ d (\\boldsymbol {x}, g _ {s} (Q (g _ {a} (\\boldsymbol {x})))) ]\n$$\n", + "text_format": "latex", + "bbox": [ + 145, + 753, + 400, + 772 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "where $\\lambda$ is the Lagrange multiplier that determines the desired rate-distortion trade-off, $p_x$ is the (unknown) distribution of source images and $p_{\\hat{y}}$ is a discrete entropy model. $Q(\\cdot)$ represents quantization, implemented as rounding to the nearest integer in most of the end-to-end compression papers. The first term (representing rate) corresponds to the cross entropy between the marginal distribution of the latent and the learned entropy model, which is minimized", + "bbox": [ + 75, + 779, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "when the two distributions are identical. The second term (distortion) corresponds to the reconstructed error between the original image and the reconstructed image.", + "bbox": [ + 496, + 90, + 890, + 136 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In most of the published end-to-end image compression CNNs, uniform scalar quantizer instead of vector quantizer (VQ) is adopted as the quantization function $Q(\\cdot)$ in Eq. 1, That is,", + "bbox": [ + 496, + 137, + 893, + 196 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {y} _ {i} = Q \\left(y _ {i}\\right) = \\operatorname {r o u n d} \\left(y _ {i}\\right) \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 612, + 200, + 890, + 217 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "where index $i$ runs over all elements of the vectors, including channels and spatial locations. Note that both terms in Eq. 1 depend on the quantized values, and the derivatives of the quantization function are zero almost everywhere, causing gradient descent problem. To allow optimization via stochastic gradient descent, a relaxation technique is used to replace the quantizer with an additive i.i.d. uniform noise $\\Delta y_{i}$ , which has the same width as the quantization bins (one):", + "bbox": [ + 496, + 227, + 893, + 362 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {y} _ {i} = y _ {i} + \\Delta y _ {i}, \\Delta y _ {i} \\in \\mathcal {U} \\left(- \\frac {1}{2}, \\frac {1}{2}\\right). \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 578, + 364, + 890, + 391 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Very few articles [1, 46] studied vector quantization in end-to-end image compression networks. Agustsson et al. [1] proposed a so-called soft-to-hard vector quantization module to bridge the nearest neighbor decision process of VQ and variational backpropagation that is necessary for the end-to-end CNN training. Their technique is a soft (continuous) relaxation of branching operation of VQ so that the VQ effects can be approximated in the end-to-end training. Zhu et al. [46] proposed a probabilistic vector quantization with cascaded estimation to estimate means and covariances. However, the optimization goal of [46] only contains the distortion term, ignoring the vital design requirement of coding rates.", + "bbox": [ + 496, + 400, + 890, + 595 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "After the pioneering work of Balle et al. [3], many other end-to-end compression methods have been proposed to further improve the R-D performances by introducing more complex nonlinear transforms and more efficient context entropy models.", + "bbox": [ + 496, + 598, + 890, + 672 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Rippel et al. [2, 30] proposed to learn the distribution of images using adversarial training to achieve better perceptual quality at extremely low bit rate. Johnston et al. [19] published a spatially adaptive bit allocation algorithm that efficiently uses a limited number of bits to encode visually complex image regions. Li et al. [23] developed a method to allocate the content-aware bit rate under the guidance of a content-weighted importance map. Some papers focused on investigating the adaptive context model for entropy estimation to achieve a better trade-off between reconstruction errors and required bits (entropy), including [4, 21, 25, 26], among which the CNN methods of [21, 26] are the first to outperform BPG in PSNR. Choi et al. [9] published a novel variable-rate learned image compression framework with a conditional auto-encoder. Cheng et al. [8] proposed", + "bbox": [ + 496, + 674, + 893, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "10240", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "to use discretized Gaussian Mixture Likelihoods to parameterize the distributions of latent codes and achieved a more accurate and flexible entropy model. Lin et al. [24] proposed a novel spatial recurrent neural network for end-to-end image compression. The block based LSTM is utilized in spatial RNN to fully exploit spatial redundancy. Minnen et al. [27] introduced two enhancements, channel-conditioning and latent residual prediction, that lead to network architectures with better rate-distortion performance than existing context-adaptive models while minimizing serial processing. Zhang et al. [41] proposed a deep learning system for attention-guided dual-layer image compression (AGDL) by introducing a novel idea of critical pixel set.", + "bbox": [ + 75, + 90, + 472, + 287 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "More recently, He et al. [18] proposed a parallelizable checkerboard context model to speed up the decoding process in the end-to-end image compression. Yanget al. [39] proposed slimmable compressive autoencoders (SlimCAEs), where rate (R) and distortion (D) are jointly optimized for different capacities. Gao et al. [14] proposed to conduct neural image compression via Attentional Multi-scale Back Projection and Frequency Decomposition. Kim et al. [20] proposed a novel entropy model called Information Transformer (Informer) that exploits both global and local information in a content-dependent manner using an attention mechanism. He et al. [17] proposed the uneven channel-conditional adaptive coding, motivated by the observation of energy compaction in learned image compression. Cheng et al. [7] proposed to optimize the image compression algorithm to be noise-aware as joint denoising and compression to resolve the noisy image compression problem. There are some other papers [22, 28, 32] focused on the content adaptive approaches by updating the encoder-side component in the inference time to improve the coding performance.", + "bbox": [ + 75, + 287, + 472, + 604 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Design of LVQAC", + "text_level": 1, + "bbox": [ + 76, + 616, + 253, + 633 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The main contribution of this work is to replace the uniform scalar quantization of feature values by the new LVQAC module outlined in the introduction, in the end-to-end design of compression CNNs. The LVQAC module is composed of a lattice vector quantizer (LVQ) and a spatially adaptive companding (AC) mapping. LVQ, also known as poor man's VQ, is computationally almost as simple as scalar uniform quantization, but it enjoys higher coding efficiency thanks to more efficient spatial covering property of LVQ [10].", + "bbox": [ + 75, + 642, + 468, + 792 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In addition, we couple LVQ with another compression technique of adaptive companding to improve the adaptability of LVQ to source statistics.", + "bbox": [ + 75, + 792, + 468, + 839 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Lattice Vector Quantization", + "text_level": 1, + "bbox": [ + 76, + 847, + 328, + 863 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Let $\\{\\pmb{u}_1, \\dots, \\pmb{u}_n\\}$ be a set of linearly independent vectors in $\\mathbb{R}^n$ , which is the $n$ -dimensional basis generating a lattice", + "bbox": [ + 76, + 869, + 468, + 901 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/8ec5810670b82ac7221f79f98b2c543857331c7d1b820022a225d0c06f482735.jpg", + "image_caption": [ + "(a) Square lattice $Z_{2}$ .", + "Figure 1. Two-dimensional square lattice $Z_{2}$ and hexagonal lattice $A_{2}$ and their Voronoi cells." + ], + "image_footnote": [], + "bbox": [ + 506, + 89, + 687, + 229 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/196b596517796f4fd63481d9aec6856ec8484d94aae8a4c1c2dced7ad38fea7f.jpg", + "image_caption": [ + "(b) Hexagonal lattice $A_{2}$ ." + ], + "image_footnote": [], + "bbox": [ + 702, + 89, + 885, + 229 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "$\\Lambda$ $\\Lambda$ consists of all points of the form", + "bbox": [ + 500, + 309, + 751, + 324 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {z} = \\sum_ {i = 1} ^ {n} c _ {i} \\boldsymbol {u} _ {i}, c _ {i} \\in \\mathbb {Z}. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 622, + 333, + 890, + 369 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Let $\\mathbf{U} = (\\mathbf{u}_1, \\dots, \\mathbf{u}_n)$ be the lattice generator matrix. Any vector of the lattice can be represented as $z = c\\mathbf{U}, c = (c_1, \\dots, c_n)$ , thus a lattice can be defined as:", + "bbox": [ + 498, + 378, + 890, + 424 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nz \\triangleq \\left\\{z \\in \\mathbb {R} ^ {n}: z = c U, c \\in \\mathbb {Z} ^ {n} \\right\\}. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 581, + 431, + 890, + 450 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The Voronoi cell of a lattice point $z \\in \\Lambda$ is defined as", + "bbox": [ + 500, + 458, + 854, + 473 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nV (z) \\triangleq \\left\\{\\boldsymbol {x} \\in \\mathbb {R} ^ {n}: | | \\boldsymbol {x} - z | | \\leq | | \\boldsymbol {x} - \\hat {z} | |, \\forall \\hat {z} \\in \\Lambda \\right\\}. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 506, + 481, + 890, + 500 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The above structure is that of lattice vector quantization [15, 16]. The LVQ codewords are the centroids of the Voronoi polyhedrons which are of the same size and shape.", + "bbox": [ + 498, + 507, + 890, + 551 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Fig. 1 depicts the concept of LVQ. It shows two examples: the two-dimensional square lattice (integer lattice) $Z_{2}$ and the hexagonal lattice $A_{2}$ , together with their Voronoi cells. The generator matrix for $Z_{2}$ lattice and $A_{2}$ lattice are as follows:", + "bbox": [ + 498, + 551, + 890, + 626 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {U} _ {Z _ {2}} = \\left( \\begin{array}{c c} 1 & 0 \\\\ 0 & 1 \\end{array} \\right), \\quad \\boldsymbol {U} _ {A _ {2}} = \\left( \\begin{array}{c c} 1 & 0 \\\\ 1 / 2 & \\sqrt {3} / 2 \\end{array} \\right). \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 545, + 633, + 890, + 667 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In fact, the square lattice $Z_{2}$ is equivalent to the simple uniform scalar quantizer. The hexagonal lattice $A_{2}$ , however, offers a more efficient covering of 2D space than the square lattice $Z_{2}$ . Therefore, LVQ with the hexagonal lattice codebook offers higher coding efficiency than the square lattice codebook. It is noteworthy that the hexagonal lattice is the optimal lattice for two-dimensional space [13] but it can not be directly applied to the situation of three or higher dimensional space.", + "bbox": [ + 496, + 672, + 890, + 809 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For our task of quantizing CNN feature vectors, the dimensionality of the problem is much higher than two. In the interest of low complexity and dimension independence, we choose the diamond lattice (also known as body centred lattice) instead of more complex lattice structures. The generator matrix of the $n$ -dimensional diamond lattice is", + "bbox": [ + 496, + 810, + 890, + 898 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "10241", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/df55aad6c1fa2dfe2ab3cf3c1df0562d87b515a41d7b1e55e1a0faf0b60a4057.jpg", + "image_caption": [ + "Figure 2. Left: Two codebooks used in diamond lattice quantization. The first codebook (blue one) is a square lattice and the second codebook (yellow one) is obtained by shifting the first codebook by $1/2$ quantization stride in each dimension. Right: Two-dimensional diamond lattice codebook. It can be obtained by shifting the square lattice like the left." + ], + "image_footnote": [], + "bbox": [ + 145, + 97, + 823, + 329 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {U} = \\left( \\begin{array}{c c c c c c c} 1 & 0 & 0 & 0 & \\dots & 0 & 0 \\\\ 1 / 2 & - 1 / 2 & 0 & 0 & \\dots & 0 & 0 \\\\ 0 & 1 / 2 & - 1 / 2 & 0 & \\dots & 0 & 0 \\\\ & \\vdots & & & \\ddots & \\vdots \\\\ 0 & 0 & 0 & 0 & \\dots & - 1 / 2 & 0 \\\\ 0 & 0 & 0 & 0 & \\dots & 1 / 2 & - 1 / 2 \\end{array} \\right). \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 91, + 436, + 468, + 539 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "An example of two-dimensional diamond lattice is shown in Fig. 2.", + "bbox": [ + 76, + 542, + 468, + 571 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The lattice vector quantization process can be decomposed into two scalar quantizations with respective codebooks plus one argmin operation. The first codebook is a square lattice and the second codebook is obtained by shifting the first codebook by $1/2$ quantization stride in each dimension, as shown in Fig. 2. Specifically, for $z$ to be quantized, instead of doing the regular vector quantization (computing distances between $z$ and all centroids and select the nearest one), we do twice scalar quantizations to each element of $z$ based on two codebooks and get two quantized vectors $\\hat{z}_1$ and $\\hat{z}_2$ . We choose the closer one as the lattice quantized result $\\hat{z}$ , that is", + "bbox": [ + 75, + 571, + 470, + 753 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {z} = \\underset {\\boldsymbol {q} = \\{\\hat {\\boldsymbol {z}} _ {1}, \\hat {\\boldsymbol {z}} _ {2} \\}} {\\arg \\min } \\| \\boldsymbol {z} - \\boldsymbol {q} \\|. \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 192, + 763, + 468, + 792 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As arg min operation is not compatible with backpropagation, we instead use its soft relaxation which is proposed in [1]. The relaxation can be written as", + "bbox": [ + 76, + 801, + 470, + 848 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {z} = \\phi_ {a} \\hat {z} _ {1} + \\phi_ {b} \\hat {z} _ {2}. \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 210, + 858, + 468, + 875 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where the weights $(\\phi_{a},\\phi_{b})$ are obtained by applying soft", + "bbox": [ + 76, + 885, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "max on the distances from $z$ to $\\hat{z}_1$ and $\\hat{z}_2$ , that is:", + "bbox": [ + 500, + 412, + 828, + 429 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left(\\phi_ {a}, \\phi_ {b}\\right) = \\Psi (- \\sigma [ \\| z - \\hat {z} _ {1} \\|, \\| z - \\hat {z} _ {2} \\| ]), \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 539, + 441, + 890, + 458 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\Psi$ is the softmax function, $\\sigma$ controls the degree of relaxation (or called hardness of the soft assignment as in the original paper).", + "bbox": [ + 498, + 470, + 892, + 516 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Specifically, given the latent representation $\\pmb{y} \\in \\mathbb{R}^{h \\times w \\times c}$ with $c$ channels and $h \\times w$ size, we apply the lattice quantization operation $\\pmb{Q}_l(\\cdot)$ on the latent vector for each spatial location $\\{\\pmb{y}_j \\in \\mathbb{R}^c, 1 \\leq j \\leq hw\\}$ , so the lattice quantized latent representation is:", + "bbox": [ + 498, + 517, + 893, + 594 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\boldsymbol {y}} = \\left\\{\\boldsymbol {Q} _ {l} (\\boldsymbol {y} _ {j}), \\boldsymbol {y} _ {j} \\in \\mathbb {R} ^ {c}, 1 \\leq j \\leq h w \\right\\}. \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 568, + 606, + 890, + 625 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "It is noteworthy that in addition to transmitting the index of quantized representation, we also need to transmit extra bits to identify the selected codebook besides the quantized vectors, but the bitrate of codebook selection is negligible. As the lattice quantization is done to the latent vector for each spatial location, all elements in each spatial location share the same codebook. Thus the codebook only varies with spatial location. For a given image of size $h \\times w \\times 3$ , the extracted latent representation will be of size $\\frac{h}{16} \\times \\frac{w}{16} \\times c$ and the codebook selection information will be of size $\\frac{h}{16} \\times \\frac{w}{16}$ with 1-bit precision. The extra bitrate for codebook selection is less than 0.004 bpp even without binary compression.", + "bbox": [ + 498, + 636, + 892, + 835 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Spatially Adaptive Companding", + "text_level": 1, + "bbox": [ + 500, + 845, + 784, + 864 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To further improve coding efficiency, we propose a spatially adaptive companding mapping to be coupled with the", + "bbox": [ + 500, + 869, + 892, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "10242", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "LVQ module to boost its adaptation to source statistics. Instead of adopting a universal companding to all elements over channels and spatial locations, we choose to learn different companding functions for different spatial locations. To reduce the difficulty of learning and also guarantee the inference speed, we restrict the companding to the form of A-law function. For a given input $x$ , the equation for A-law encoding is as follows:", + "bbox": [ + 75, + 90, + 472, + 212 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nF (x) = \\operatorname {s g n} (x) \\left\\{ \\begin{array}{l l} \\frac {A | x |}{1 + \\ln (A)}, & | x | < \\frac {1}{A} \\\\ \\frac {1 + \\ln (A | x |)}{1 + \\ln (A)}, & \\frac {1}{A} \\leq | x | \\leq 1 \\end{array} \\right. \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 237, + 468, + 316 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $A$ is the scale parameter. A-law decoding is given by the inverse function:", + "bbox": [ + 75, + 328, + 468, + 359 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nF ^ {- 1} (y) = \\operatorname {s g n} (y) \\left\\{ \\begin{array}{l l} \\frac {| y | (1 + \\ln (A))}{A}, & | y | < \\frac {1}{1 + \\ln (A)} \\\\ \\frac {e ^ {- 1 + | y | (1 + \\ln (A))}}{A}, & \\frac {1}{1 + \\ln (A)} \\leq | x | \\leq 1 \\end{array} \\right. \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 383, + 483, + 477 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The A-law function and its inverse are both continuous and derivative, which implies that they can be embedded into the end-to-end optimization system.", + "bbox": [ + 75, + 479, + 468, + 523 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Specifically, we learn different scale parameters $A$ for different spatial locations and apply the unique learned A-law companding to all elements at the same location. Learning of scale parameters $A$ is implemented by a shallow convolution network $h$ , which consists of several convolution layers. It takes the latent representation $y$ as input; and predicts the optimal scale parameters of A-law functions for different spatial locations, $\\pmb{a} = h(\\pmb{y})$ . Then we apply these learned A-law companding functions $f(F; \\pmb{a})$ on the latent representations to scale it to the ideal dynamic range for better quantization performance. In the other side, after decoding $\\hat{\\pmb{y}}$ from bitstream, the inverse A-law companding $f^{-1}(F^{-1}; \\pmb{a})$ is applied on $\\hat{\\pmb{y}}$ to scale it to the original dynamic range.", + "bbox": [ + 75, + 525, + 468, + 736 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Given the proposed lattice vector quantization module and spatially adaptive companding mapping, the optimization goal should be rewritten to:", + "bbox": [ + 75, + 737, + 468, + 782 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\text {m i n i m i z e} R + \\lambda \\cdot D\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 796, + 238, + 810 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nR = \\mathbb {E} _ {\\boldsymbol {x} \\sim p _ {x}} \\left[ - \\log_ {2} p _ {i j} \\left(\\boldsymbol {Q} _ {l} \\left(\\boldsymbol {f} \\left(g _ {a} (\\boldsymbol {x})\\right)\\right)\\right) \\right] \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 815, + 468, + 833 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nD = \\lambda \\cdot \\mathbb {E} _ {\\boldsymbol {x} \\sim p _ {x}} \\left[ \\right. d \\left( \\right.\\boldsymbol {x}, g _ {s} \\left(\\boldsymbol {f} ^ {- 1} \\left(\\boldsymbol {Q} _ {l} \\left(\\boldsymbol {f} \\left(g _ {a} (\\boldsymbol {x})\\right)\\right)\\right)\\right)\\left. \\right]\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 835, + 419, + 854 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $Q_{l}$ is the proposed LVQ module, $\\pmb{f}$ and $\\pmb{f}^{-1}$ are the learned spatially adaptive A-law function and its inverse.", + "bbox": [ + 75, + 869, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 90, + 633, + 107 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We conduct extensive experiments to systematically evaluate and analyze the effectiveness of the proposed LVQAC scheme. Specifically, we select two representative end-to-end CNN compression architectures Cheng2020 [8] and Minnen2018 [26] and replace their uniform scalar quantizers by the proposed LVQAC module to demonstrate the superiority of LVQAC. We show the R-D performance comparisons between the models with uniform scalar quantization and LVQAC for each architecture, and also provide visual comparisons. Besides, the encoding and decoding latencies are tabulated to validate the computational efficiency of LVQAC. Other analyses such as an ablation study on the effects of each component of LVQAC are further given.", + "bbox": [ + 496, + 114, + 893, + 325 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Dataset and Training Details", + "text_level": 1, + "bbox": [ + 500, + 333, + 756, + 349 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The training dataset consists of the largest 8000 images picked from ImageNet [12], following the previous work [17]. Training images are then random-cropped to $512 \\times 512$ and batched into 16. We train each model using the Adam optimizer with $\\beta - 1 = 0.9$ , $\\beta_{2} = 0.999$ . Each model is trained with an initial learning rate $10^{-4}$ for 2000 epochs (1M iterations), and then we decay the learning rate to $10^{-5}$ for another 100-epoch training. Tests involve two image sets: Kodak (24 images) and CLIC Professional valid set (41 images). The network and the proposed LVQAC module are both implemented in PyTorch [29] and CompressAI [5]. All experiments are conducted with four RTX 2080ti GPUs.", + "bbox": [ + 496, + 356, + 893, + 551 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Rate-Distortion Performance", + "text_level": 1, + "bbox": [ + 500, + 560, + 759, + 574 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We evaluate our LVQAC scheme based on two representative published architectures Cheng2020 [8] and Minnen2018 [26]. The reason for choosing these two architectures is that they are the milestones in the end-to-end optimized image compression area, as Minnen2018 [26] is the first learning-based method to outperform BPG in PSNR metric and Cheng2020 [8] is the first work to achieve comparable performance with latest compression standard Versatile Video Coding (VVC) regarding PSNR. These two architectures were originally proposed with an autoregressive (serial) context model. To fully explore the potentiality of LVQAC, we consider the two architectures with two different context models, namely the autoregressive context model and checkerboard context model [18]. For each architecture, given two different context models, we do not change any other architectures except by replacing the uniform scalar quantizer with the proposed LVQAC scheme. We implement the two representative models coupled with uniform scalar quantizer and LVQAC, respectively. The Lagrange multipliers are set to $\\lambda = \\{0.0016, 0.0032, 0.0075, 0.015, 0.03, 0.045\\}$ .", + "bbox": [ + 496, + 583, + 893, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "10243", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/89a47f5278b5977825875dfcdfbe75f2cf6cef4d1c395a67ae3eae9aa80721e3.jpg", + "image_caption": [ + "(a) Cheng2020 [8], Kodak." + ], + "image_footnote": [], + "bbox": [ + 99, + 111, + 444, + 304 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/be765997b7a421dfbd86b7da879f4924ce21fe8ff0bdb6cd00499bdd2ce95fa0.jpg", + "image_caption": [ + "(b) Minnen2018 [26], Kodak." + ], + "image_footnote": [], + "bbox": [ + 511, + 111, + 856, + 304 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/f94aa754ff1ab2e46bd0a1d8dc3b40ecc276a3dad9461b7ea448765e9d738562.jpg", + "image_caption": [ + "Figure 3. Rate-distortion curves on Kodak dataset. All models are optimized for MSE.", + "(a) Cheng2020 [8], CLIC Pro.", + "Figure 4. Rate-distortion curves on CLIC Pro dataset. All models are optimized for MSE." + ], + "image_footnote": [], + "bbox": [ + 99, + 369, + 439, + 563 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/0960480bdd6aefe09d5705f08fb31b4a7707138565543b4ba750a801d2c177dd.jpg", + "image_caption": [ + "(b) Minnen2018 [26], CLIC Pro." + ], + "image_footnote": [], + "bbox": [ + 511, + 371, + 852, + 563 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Fig. 3 and Fig. 4 graphically presents the rate-distortion behaviors of different methods on Kodak and CLIC Pro datasets in PSNR metric. We can see that for any architecture, no matter with autoregressive or checkerboard context model, replacing uniform quantizer by LVQAC achieves better rate-distortion performance. Besides, LVQAC brings greater performance gain when coupled with the checkerboard context model than being coupled with the autoregressive context model. The CNN model adopted LVQAC + checkerboard context model can achieve a similar performance as the counterpart CNN using a far more expensive autoregressive context model + uniform scalar quantizer, yet the former is much lighter and faster than the latter. We show the detailed computational complexity of LVQAC in subsection 4.4. We can also find that LVQAC can bring more performance gain at the low bit rate than at the high bit rate. This is expected as uniform quantization can approach the rate-distortion optimality at very high bit rate [15].", + "bbox": [ + 76, + 628, + 472, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Visual Comparison", + "text_level": 1, + "bbox": [ + 500, + 627, + 684, + 643 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We also provide visual comparisons to demonstrate the effectiveness of the proposed LVQAC scheme. Fig. 5, 6 and 7 show the visual results of different methods, including BPG, Cheng2020 with scalar quantizer, Cheng2002 with LVQAC and the Ground Truth. We pick three images 'kodim01.png', 'kodim07.png' and 'kodim10.png' from Kodak dataset to show the comparisons. The bit rates of all methods are adjusted to the same level for the fairness. In Fig. 5, LVQAC can preserve the sharper edges on doors than uniform scalar quantizer. In Fig. 6, LVQAC also achieves richer and clearer textures on flowers over uniform scalar quantizer. Another interesting observation is that the faint lines in Fig. 7 are both removed by BPG and scalar quantizer, but LVQAC can preserve such features. These observations reveal that the end-to-end CNN compression model coupled with LVQAC can produce much sharper edges and", + "bbox": [ + 496, + 659, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "10244", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/352f5bd22f9bef7d6cdfe2448cdf95c20a6d67a8fe46c74edfdc9daf10044943.jpg", + "image_caption": [ + "(a) BPG" + ], + "image_footnote": [], + "bbox": [ + 80, + 88, + 274, + 195 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/066af03a15da9916d208aca95fb7d77ff5b5566a65d7021945c9e60a3052f50f.jpg", + "image_caption": [ + "(b) Cheng2020, Scalar" + ], + "image_footnote": [], + "bbox": [ + 282, + 88, + 480, + 196 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3eae9b47cb71b38d4e246e01ec1f4b34c09b09b57ad402bf753b39967dad87e9.jpg", + "image_caption": [ + "(c) Cheng2020, LVQAC" + ], + "image_footnote": [], + "bbox": [ + 488, + 88, + 686, + 196 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6b60879132a2e91616eab4828261cbda81de5ca31e5376e90d3da132f7c19aca.jpg", + "image_caption": [ + "(d) Ground Truth" + ], + "image_footnote": [], + "bbox": [ + 694, + 88, + 890, + 196 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/26a1be0f0fed15ee28142d8973fd26defc87e0e957c0286ccffdbd77f64d4e24.jpg", + "image_caption": [ + "(a) BPG" + ], + "image_footnote": [], + "bbox": [ + 80, + 250, + 274, + 358 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8c0a548c630c1ecdec11c4b9fadb0d7edc76c52df90f0e1a98bf8c1c11fcfa13.jpg", + "image_caption": [ + "Figure 5. Visual comparisons of different methods on 'kodim01.png' from Kodak dataset.", + "(b) Cheng2020, Scalar" + ], + "image_footnote": [], + "bbox": [ + 282, + 250, + 480, + 358 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2e9501b79c430ded00fea7eec2f2af9adbf04a0afcfc4a465b6ca1cb95ea8a25.jpg", + "image_caption": [ + "(c) Cheng2020, LVQAC" + ], + "image_footnote": [], + "bbox": [ + 488, + 250, + 686, + 358 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e1e6d725b2bdd5ed4911cff76fdb306b22d1c99a62767e378972193b87d6bb0d.jpg", + "image_caption": [ + "(d) Ground Truth" + ], + "image_footnote": [], + "bbox": [ + 694, + 250, + 890, + 358 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d4bcf25305e24c72dcf83a55bf2cd733d9d63e29ad745684f4d440db247a187c.jpg", + "image_caption": [ + "Figure 6. Visual comparisons of different methods on 'kodim07.png' from Kodak dataset.", + "(a) BPG", + "Figure 7. Visual comparisons of different methods on 'kodim10.png' from Kodak dataset." + ], + "image_footnote": [], + "bbox": [ + 80, + 412, + 274, + 640 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/acf5a728a081b3c0a0564829fe3dcd9eef6473a0ba9c73b026cfc4fd4b919afe.jpg", + "image_caption": [ + "(b) Cheng2020, Scalar" + ], + "image_footnote": [], + "bbox": [ + 282, + 412, + 480, + 640 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ae93e15e28c994be5fcfd08822edd5f36c14194b25d7e41e38af9df1445d5cf9.jpg", + "image_caption": [ + "(c) Cheng2020, LVQAC" + ], + "image_footnote": [], + "bbox": [ + 488, + 412, + 686, + 640 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4c105ef06e31692cdc158441df1a7a6f270337b17fb5bb74d31321a5d7b7ab3d.jpg", + "image_caption": [ + "(d) Ground Truth" + ], + "image_footnote": [], + "bbox": [ + 694, + 412, + 890, + 640 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "clearer textures than the counterpart CNN coupled with scalar quantizer. We present more high-resolution visual examples in the supplementary material.", + "bbox": [ + 75, + 708, + 468, + 753 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Encoding and Decoding Latency", + "text_level": 1, + "bbox": [ + 76, + 768, + 362, + 786 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We provide a detailed analysis of encoding and decoding latency in this subsection. Specifically, we evaluate the inference latency of end-to-end CNN compression models with different quantizers: uniform scalar quantizer and the proposed LVQAC. Table 1 tabulate the encoding time and decoding time of different architectures coupled with scalar quantizer and LVQAC. We can see that, for the ar", + "bbox": [ + 75, + 794, + 468, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "chitecture Cheng2020 with checkerboard context, LVQAC only increases the encoding time by about $15\\%$ and the decoding time by about $5\\%$ , yet improves the performance to the same level as that using autoregressive context. It is noteworthy that the decoding time of the model using autoregressive context is two orders of magnitude higher than that of the checkerboard context. For the architecture Cheng2020 with autoregressive context model, the increase of encoding time is about $17\\%$ , and the increase of decoding time is negligible due to the huge base $(>10^{3})$ . Similar observations can be obtained on the Minnen2018 architecture. These observations reveal that replacing uniform quantizer", + "bbox": [ + 496, + 708, + 893, + 890 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "10245", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/4e487e94344639d264330595c19bf213742cef4ff61ca3146b10dc3fdfe7ee7b.jpg", + "table_caption": [ + "Table 1. BD-Rates and inference times of different methods. The BD-Rate data is calculated relative to VVC (YUV 444) from PSNR-BPP curve on Kodak. [A] represents the autoregressive context model, [C] represents the checkerboard context model." + ], + "table_footnote": [], + "table_body": "
ArchitectureContext + QuantizerBD-Rate (%)Enc. Time (ms)Dec. Time (ms)
Cheng2020 [8][A] + LVQAC3.1248.65>103
[A] + Scalar3.3541.42>103
[C] + LVQAC3.3952.6655.84
[C] + Scalar3.8945.4353.01
Minnen2018 [26][A] + LVQAC14.7525.87>103
[A] + Scalar14.9218.14>103
[C] + LVQAC16.1726.2327.10
[C] + Scalar20.0018.8424.52
", + "bbox": [ + 151, + 128, + 818, + 297 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "by LVQAC can achieve better rate-distortion performance without significantly increasing the model complexity; the simpler the context-sensitive entropy model, the greater the performance gain.", + "bbox": [ + 75, + 316, + 470, + 380 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 386, + 230, + 402 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To investigate the impacts of the proposed LVQAC scheme, we conduct an ablation study to investigate the importance of each component in the proposed LVQAC scheme. We experiment progressively to explore the respective contribution of the lattice vector quantization module and spatially adaptive companding module. Specifically, we progressively add LVQ and AC modules into the network and test the coding performance. Table 2 shows the results of the ablation study. It can be seen that lattice vector quantization and spatially adaptive companding contribute almost equally to the performance gain.", + "bbox": [ + 75, + 409, + 470, + 575 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.6. Limitation", + "text_level": 1, + "bbox": [ + 76, + 583, + 194, + 598 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The main limitation of this work relies on that it is difficult to know the optimal lattice structure for any given dimension. In this paper, we choose the diamond lattice structure due to its simplicity and easy extension to any dimension. However, even though diamond lattice is not the optimal lattice structure in the vast majority of cases, it is still much more efficient than uniform scalar quantizer without significantly increasing the model complexity. Another limitation of LVQAC is that if the context model is complex and powerful enough, such as an autoregressive context, then the gain brought by LVQAC will be very limited. Thus the application of LVQAC may be restricted to those lightweight end-to-end CNN compression models.", + "bbox": [ + 75, + 606, + 468, + 803 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion and Future Work", + "text_level": 1, + "bbox": [ + 76, + 814, + 346, + 830 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we present a novel Lattice Vector Quantization scheme coupled with a spatially Adaptive Companding (LVQAC) mapping. LVQ can better exploit the inter-feature dependencies than scalar uniform quantization while being", + "bbox": [ + 75, + 839, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/5c15d4daf88f5bc746ae49603561dd0a815148fbc598ed114b7c05dcfe489006.jpg", + "table_caption": [ + "Table 2. Results of the progressive ablation study. The BD-Rate data is calculated relative to VVC (YUV 444) from PSNR-BPP curve on Kodak. [A] represents the autoregressive context model, [C] represents the checkerboard context model." + ], + "table_footnote": [], + "table_body": "
ArchitectureContext + QuantizerBD-Rate
Cheng2020 [8][A] + LVQ + AC3.12
[A] + LVQ3.24
[A] + Scalar + AC3.30
[A] + Scalar3.35
[C] + LVQ + AC3.39
[C] + LVQ3.68
[C] + Scalar + AC3.82
[C] + Scalar3.89
Minnen2018 [26][A] + LVQ + AC14.75
[A] + LVQ14.86
[A] + Scalar + AC14.88
[A] + Scalar14.92
[C] + LVQ + AC16.17
[C] + LVQ18.43
[C] + Scalar + AC19.29
[C] + Scalar20.00
", + "bbox": [ + 503, + 382, + 887, + 696 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "computationally almost as simple as the latter. Moreover, to improve the adaptability of LVQ to source statistics, we couple a spatially adaptive companding (AC) mapping with LVQ. The resulting LVQAC design can be easily embedded into any end-to-end optimized image compression system. Extensive experiments demonstrate that for any end-to-end CNN image compression models, replacing uniform quantizer by LVQAC achieves better rate-distortion performance without significantly increasing the model complexity. Future work will focus on exploring the optimal lattice vector quantizer for a given dimension and how to embed it into the end-to-end image compression system.", + "bbox": [ + 496, + 719, + 893, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "10246", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Eirikur Agustsson, Fabian Mentzer, Michael Tschannen, Lukas Cavigelli, Radu Timofte, Luca Benini, and Luc Van Gool. Soft-to-hard vector quantization for end-to-end learning compressible representations. In Advances in Neural Information Processing Systems 30, pages 1141-1151, 2017. 1, 2, 4", + "[2] Eirikur Agustsson, Michael Tschannen, Fabian Mentzer, Radu Timofte, and Luc Van Gool. Generative adversarial networks for extreme learned image compression. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 17612-17621, 2022. 2" + ], + "bbox": [ + 501, + 92, + 890, + 458 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "10248", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/LVQAC_ Lattice Vector Quantization Coupled With Spatially Adaptive Companding for Efficient Learned Image Compression/7db2f3f4-b386-46ae-b0d0-6d14527e76a1_model.json b/2023/LVQAC_ Lattice Vector Quantization Coupled With Spatially Adaptive Companding for Efficient Learned Image Compression/7db2f3f4-b386-46ae-b0d0-6d14527e76a1_model.json new file mode 100644 index 0000000000000000000000000000000000000000..cd6ea44e81d967757ecc082fc284841500e0e0c2 --- /dev/null +++ b/2023/LVQAC_ Lattice Vector Quantization Coupled With Spatially Adaptive Companding for Efficient Learned Image Compression/7db2f3f4-b386-46ae-b0d0-6d14527e76a1_model.json @@ -0,0 +1,2277 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.13, + 0.13, + 0.842, + 0.177 + ], + "angle": 0, + "content": "LVQAC: Lattice Vector Quantization Coupled with Spatially Adaptive Compa nding for Efficient Learned Image Compression" + }, + { + "type": "text", + "bbox": [ + 0.243, + 0.205, + 0.49, + 0.258 + ], + "angle": 0, + "content": "Xi Zhang \nShanghai Jiao Tong University \nzhangxi_19930818@sjtu.edu.cn" + }, + { + "type": "text", + "bbox": [ + 0.552, + 0.205, + 0.725, + 0.257 + ], + "angle": 0, + "content": "Xiaolin Wu \nMcMaster University \nxwu@ece.mcmaster.ca" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.292, + 0.314, + 0.308 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.325, + 0.474, + 0.658 + ], + "angle": 0, + "content": "Recently, numerous end-to-end optimized image compression neural networks have been developed and proved themselves as leaders in rate-distortion performance. The main strength of these learnt compression methods is in powerful nonlinear analysis and synthesis transforms that can be facilitated by deep neural networks. However, out of operational expediency, most of these end-to-end methods adopt uniform scalar quantizers rather than vector quantizers, which are information-theoretically optimal. In this paper, we present a novel Lattice Vector Quantization scheme coupled with a spatially Adaptive Companding (LVQAC) mapping. LVQ can better exploit the inter-feature dependencies than scalar uniform quantization while being computationally almost as simple as the latter. Moreover, to improve the adaptability of LVQ to source statistics, we couple a spatially adaptive companding (AC) mapping with LVQ. The resulting LVQAC design can be easily embedded into any end-to-end optimized image compression system. Extensive experiments demonstrate that for any end-to-end CNN image compression models, replacing uniform quantizer by LVQAC achieves better rate-distortion performance without significantly increasing the model complexity." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.691, + 0.21, + 0.707 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.718, + 0.47, + 0.839 + ], + "angle": 0, + "content": "In the past five years, the research on end-to-end CNN image compression has made steady progress and led to the birth of a new class of image compression methods [1, 3, 4, 8, 21, 25, 26, 34-36, 40-44]. The CNN compression can now match and even exceed the rate-distortion performance of the previous best image compression methods [6, 33, 37, 45], which operate in the traditional paradigm of linear transform, quantization and entropy coding." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.47, + 0.902 + ], + "angle": 0, + "content": "The advantages of the CNN approach of data compression come from the nonlinearity of its analysis and synthesis transforms of the autoencoder architecture, the end-to-end joint optimization of the nonlinear transforms, uni" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.293, + 0.892, + 0.338 + ], + "angle": 0, + "content": "form quantization of the latent space and conditional entropy coding (context-based arithmetic coding) of quantized features." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.34, + 0.893, + 0.839 + ], + "angle": 0, + "content": "Apparently, using uniform scalar quantizer in the above CNN image compression framework is motivated by operational expediency more than other considerations. Only at very high bit rate uniform quantization can approach the rate-distortion optimality [15]. It is very difficult to directly adopt and optimize a vector quantizer (VQ) in the end-to-end CNN architecture design for data compression, because VQ is a discrete decision process and it is not compatible with variational backpropagation that is necessary to the end-to-end CNN training. In [1], Agustsson et al. tried to circumvent the difficulty by a so-called soft-to-hard vector quantization scheme. Their technique is a soft (continuous) relaxation of discrete computations of VQ and entropy so that their effects can be approximated in the end-to-end training. However, in [1] the quantization centers are optimized along with the other modules, which make the whole system quite cumbersome and more difficult to train. In this paper, we propose a novel Lattice Vector Quantization scheme coupled with a spatially Adaptive Companding (LVQAC) mapping. LVQ can better exploit the inter-feature dependencies than scalar uniform quantization while being computationally almost as simple as the latter. Even if the features to be compressed are statistically independent, LVQ is still a more efficient coding strategy than scalar uniform quantization. This is because the former offers a more efficient covering of high-dimensional space than the latter, as proven by the theory of sphere packings, lattices and groups [11]. Moreover, to improve the adaptability of LVQ to source statistics, we couple a spatially adaptive companding mapping with LVQ. The resulting LVQAC design is computationally as simple and as amenable to the end-to-end training of the CNN compression model as in the originally proposed framework of [3]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Consequently, for any end-to-end CNN image compression models, replacing uniform quantizer by LVQAC achieves better rate-distortion performance without significantly increasing the model complexity; the simpler" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "10239" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.258 + ], + "angle": 0, + "content": "the context-sensitive entropy model, the greater the performance gain. For instance, the checkerboard context model [18] has recently been proposed to speed up the decoding process, but it hurts the R-D performance slightly. By incorporating LVQAC into the end-to-end compression CNN with a checkerboard context model, we can achieve the same performance as the counterpart CNN using a far more expensive auto-regressive context model. This is because uniform scalar quantization needs a more complex model to compensate for its coding inefficiency, whereas LVQAC does not." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.27, + 0.47, + 0.304 + ], + "angle": 0, + "content": "2. Overview of Learned Image Compression and Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.313, + 0.473, + 0.649 + ], + "angle": 0, + "content": "Balle et al. [3] pioneered the end-to-end CNN model for image compression. Their network design is still shaped by the legacy of classical three-step signal compression algorithms; namely, transform, quantization and entropy coding. The greatest advantage of the CNN approach over the classical one comes from replacing linear transforms of the latter by more powerful and complex nonlinear transforms, which is the distinctive prowess of deep neural networks. Specifically, in the end-to-end image compression CNNs, an image vector \\( \\pmb{x} \\in \\mathbb{R}^N \\) is mapped to a latent code space via a parametric nonlinear analysis transform, \\( \\pmb{y} = g_{a}(\\pmb{x};\\pmb{\\theta}_{g}) \\). Then this representation is quantized, yielding a discrete-valued vector \\( \\hat{\\pmb{y}} = Q(\\pmb{y}) \\in \\mathbb{Z}^{M} \\) which can be losslessly compressed using entropy coding algorithms such as arithmetic coding [31, 38] and transmitted as a sequence of bits. On the other side, the decoder recovers \\( \\hat{\\pmb{y}} \\) from the compressed codes, and subjects it to a parametric nonlinear synthesis transform \\( g_{s}(\\hat{\\pmb{y}};\\phi_{g}) \\) to build the reconstructed image \\( \\hat{\\pmb{x}} \\). The nonlinear parametric transform \\( g_{a}(\\pmb{x};\\pmb{\\theta}_{g}) \\) and \\( g_{s}(\\pmb{x};\\phi_{g}) \\) are implemented by convolutional neural networks and the parameters \\( \\pmb{\\theta}_{g} \\) and \\( \\phi_{g} \\) are learned over a large amount of natural images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.65, + 0.472, + 0.71 + ], + "angle": 0, + "content": "The training goal is to minimize the expected length of the bitstream as well as the expected distortion of the reconstructed image with respect to the original image, giving rise to a rate-distortion optimization problem:" + }, + { + "type": "equation", + "bbox": [ + 0.145, + 0.719, + 0.289, + 0.732 + ], + "angle": 0, + "content": "\\[\n\\operatorname {m i n i m i z e} R + \\lambda \\cdot D\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.146, + 0.736, + 0.469, + 0.754 + ], + "angle": 0, + "content": "\\[\nR = \\mathbb {E} _ {\\boldsymbol {x} \\sim p _ {x}} \\left[ - \\log_ {2} p _ {\\tilde {y}} \\left(Q \\left(g _ {a} (\\boldsymbol {x})\\right)\\right) \\right] \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.146, + 0.755, + 0.401, + 0.773 + ], + "angle": 0, + "content": "\\[\nD = \\lambda \\cdot \\mathbb {E} _ {\\boldsymbol {x} \\sim p _ {x}} [ d (\\boldsymbol {x}, g _ {s} (Q (g _ {a} (\\boldsymbol {x})))) ]\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.47, + 0.901 + ], + "angle": 0, + "content": "where \\(\\lambda\\) is the Lagrange multiplier that determines the desired rate-distortion trade-off, \\(p_x\\) is the (unknown) distribution of source images and \\(p_{\\hat{y}}\\) is a discrete entropy model. \\(Q(\\cdot)\\) represents quantization, implemented as rounding to the nearest integer in most of the end-to-end compression papers. The first term (representing rate) corresponds to the cross entropy between the marginal distribution of the latent and the learned entropy model, which is minimized" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.137 + ], + "angle": 0, + "content": "when the two distributions are identical. The second term (distortion) corresponds to the reconstructed error between the original image and the reconstructed image." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.138, + 0.894, + 0.197 + ], + "angle": 0, + "content": "In most of the published end-to-end image compression CNNs, uniform scalar quantizer instead of vector quantizer (VQ) is adopted as the quantization function \\( Q(\\cdot) \\) in Eq. 1, That is," + }, + { + "type": "equation", + "bbox": [ + 0.613, + 0.201, + 0.892, + 0.218 + ], + "angle": 0, + "content": "\\[\n\\hat {y} _ {i} = Q \\left(y _ {i}\\right) = \\operatorname {r o u n d} \\left(y _ {i}\\right) \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.228, + 0.895, + 0.363 + ], + "angle": 0, + "content": "where index \\( i \\) runs over all elements of the vectors, including channels and spatial locations. Note that both terms in Eq. 1 depend on the quantized values, and the derivatives of the quantization function are zero almost everywhere, causing gradient descent problem. To allow optimization via stochastic gradient descent, a relaxation technique is used to replace the quantizer with an additive i.i.d. uniform noise \\( \\Delta y_{i} \\), which has the same width as the quantization bins (one):" + }, + { + "type": "equation", + "bbox": [ + 0.58, + 0.365, + 0.892, + 0.392 + ], + "angle": 0, + "content": "\\[\n\\tilde {y} _ {i} = y _ {i} + \\Delta y _ {i}, \\Delta y _ {i} \\in \\mathcal {U} \\left(- \\frac {1}{2}, \\frac {1}{2}\\right). \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.401, + 0.892, + 0.597 + ], + "angle": 0, + "content": "Very few articles [1, 46] studied vector quantization in end-to-end image compression networks. Agustsson et al. [1] proposed a so-called soft-to-hard vector quantization module to bridge the nearest neighbor decision process of VQ and variational backpropagation that is necessary for the end-to-end CNN training. Their technique is a soft (continuous) relaxation of branching operation of VQ so that the VQ effects can be approximated in the end-to-end training. Zhu et al. [46] proposed a probabilistic vector quantization with cascaded estimation to estimate means and covariances. However, the optimization goal of [46] only contains the distortion term, ignoring the vital design requirement of coding rates." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.892, + 0.673 + ], + "angle": 0, + "content": "After the pioneering work of Balle et al. [3], many other end-to-end compression methods have been proposed to further improve the R-D performances by introducing more complex nonlinear transforms and more efficient context entropy models." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Rippel et al. [2, 30] proposed to learn the distribution of images using adversarial training to achieve better perceptual quality at extremely low bit rate. Johnston et al. [19] published a spatially adaptive bit allocation algorithm that efficiently uses a limited number of bits to encode visually complex image regions. Li et al. [23] developed a method to allocate the content-aware bit rate under the guidance of a content-weighted importance map. Some papers focused on investigating the adaptive context model for entropy estimation to achieve a better trade-off between reconstruction errors and required bits (entropy), including [4, 21, 25, 26], among which the CNN methods of [21, 26] are the first to outperform BPG in PSNR. Choi et al. [9] published a novel variable-rate learned image compression framework with a conditional auto-encoder. Cheng et al. [8] proposed" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "10240" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.288 + ], + "angle": 0, + "content": "to use discretized Gaussian Mixture Likelihoods to parameterize the distributions of latent codes and achieved a more accurate and flexible entropy model. Lin et al. [24] proposed a novel spatial recurrent neural network for end-to-end image compression. The block based LSTM is utilized in spatial RNN to fully exploit spatial redundancy. Minnen et al. [27] introduced two enhancements, channel-conditioning and latent residual prediction, that lead to network architectures with better rate-distortion performance than existing context-adaptive models while minimizing serial processing. Zhang et al. [41] proposed a deep learning system for attention-guided dual-layer image compression (AGDL) by introducing a novel idea of critical pixel set." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.288, + 0.473, + 0.606 + ], + "angle": 0, + "content": "More recently, He et al. [18] proposed a parallelizable checkerboard context model to speed up the decoding process in the end-to-end image compression. Yanget al. [39] proposed slimmable compressive autoencoders (SlimCAEs), where rate (R) and distortion (D) are jointly optimized for different capacities. Gao et al. [14] proposed to conduct neural image compression via Attentional Multi-scale Back Projection and Frequency Decomposition. Kim et al. [20] proposed a novel entropy model called Information Transformer (Informer) that exploits both global and local information in a content-dependent manner using an attention mechanism. He et al. [17] proposed the uneven channel-conditional adaptive coding, motivated by the observation of energy compaction in learned image compression. Cheng et al. [7] proposed to optimize the image compression algorithm to be noise-aware as joint denoising and compression to resolve the noisy image compression problem. There are some other papers [22, 28, 32] focused on the content adaptive approaches by updating the encoder-side component in the inference time to improve the coding performance." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.617, + 0.254, + 0.635 + ], + "angle": 0, + "content": "3. Design of LVQAC" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.643, + 0.47, + 0.793 + ], + "angle": 0, + "content": "The main contribution of this work is to replace the uniform scalar quantization of feature values by the new LVQAC module outlined in the introduction, in the end-to-end design of compression CNNs. The LVQAC module is composed of a lattice vector quantizer (LVQ) and a spatially adaptive companding (AC) mapping. LVQ, also known as poor man's VQ, is computationally almost as simple as scalar uniform quantization, but it enjoys higher coding efficiency thanks to more efficient spatial covering property of LVQ [10]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.794, + 0.47, + 0.84 + ], + "angle": 0, + "content": "In addition, we couple LVQ with another compression technique of adaptive companding to improve the adaptability of LVQ to source statistics." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.848, + 0.329, + 0.864 + ], + "angle": 0, + "content": "3.1. Lattice Vector Quantization" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Let \\(\\{\\pmb{u}_1, \\dots, \\pmb{u}_n\\}\\) be a set of linearly independent vectors in \\(\\mathbb{R}^n\\), which is the \\(n\\)-dimensional basis generating a lattice" + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.09, + 0.689, + 0.231 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.539, + 0.233, + 0.653, + 0.246 + ], + "angle": 0, + "content": "(a) Square lattice \\(Z_{2}\\)." + }, + { + "type": "image", + "bbox": [ + 0.704, + 0.09, + 0.887, + 0.231 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.729, + 0.233, + 0.863, + 0.246 + ], + "angle": 0, + "content": "(b) Hexagonal lattice \\(A_{2}\\)." + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.257, + 0.892, + 0.285 + ], + "angle": 0, + "content": "Figure 1. Two-dimensional square lattice \\( Z_{2} \\) and hexagonal lattice \\( A_{2} \\) and their Voronoi cells." + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.31, + 0.753, + 0.325 + ], + "angle": 0, + "content": "\\(\\Lambda\\) \\(\\Lambda\\) consists of all points of the form" + }, + { + "type": "equation", + "bbox": [ + 0.623, + 0.334, + 0.892, + 0.371 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {z} = \\sum_ {i = 1} ^ {n} c _ {i} \\boldsymbol {u} _ {i}, c _ {i} \\in \\mathbb {Z}. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.379, + 0.892, + 0.425 + ], + "angle": 0, + "content": "Let \\( \\mathbf{U} = (\\mathbf{u}_1, \\dots, \\mathbf{u}_n) \\) be the lattice generator matrix. Any vector of the lattice can be represented as \\( z = c\\mathbf{U}, c = (c_1, \\dots, c_n) \\), thus a lattice can be defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.583, + 0.433, + 0.892, + 0.451 + ], + "angle": 0, + "content": "\\[\nz \\triangleq \\left\\{z \\in \\mathbb {R} ^ {n}: z = c U, c \\in \\mathbb {Z} ^ {n} \\right\\}. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.459, + 0.855, + 0.474 + ], + "angle": 0, + "content": "The Voronoi cell of a lattice point \\(z \\in \\Lambda\\) is defined as" + }, + { + "type": "equation", + "bbox": [ + 0.508, + 0.482, + 0.891, + 0.5 + ], + "angle": 0, + "content": "\\[\nV (z) \\triangleq \\left\\{\\boldsymbol {x} \\in \\mathbb {R} ^ {n}: | | \\boldsymbol {x} - z | | \\leq | | \\boldsymbol {x} - \\hat {z} | |, \\forall \\hat {z} \\in \\Lambda \\right\\}. \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.508, + 0.891, + 0.553 + ], + "angle": 0, + "content": "The above structure is that of lattice vector quantization [15, 16]. The LVQ codewords are the centroids of the Voronoi polyhedrons which are of the same size and shape." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.553, + 0.892, + 0.627 + ], + "angle": 0, + "content": "Fig. 1 depicts the concept of LVQ. It shows two examples: the two-dimensional square lattice (integer lattice) \\( Z_{2} \\) and the hexagonal lattice \\( A_{2} \\), together with their Voronoi cells. The generator matrix for \\( Z_{2} \\) lattice and \\( A_{2} \\) lattice are as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.547, + 0.634, + 0.892, + 0.668 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {U} _ {Z _ {2}} = \\left( \\begin{array}{c c} 1 & 0 \\\\ 0 & 1 \\end{array} \\right), \\quad \\boldsymbol {U} _ {A _ {2}} = \\left( \\begin{array}{c c} 1 & 0 \\\\ 1 / 2 & \\sqrt {3} / 2 \\end{array} \\right). \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.674, + 0.892, + 0.81 + ], + "angle": 0, + "content": "In fact, the square lattice \\( Z_{2} \\) is equivalent to the simple uniform scalar quantizer. The hexagonal lattice \\( A_{2} \\), however, offers a more efficient covering of 2D space than the square lattice \\( Z_{2} \\). Therefore, LVQ with the hexagonal lattice codebook offers higher coding efficiency than the square lattice codebook. It is noteworthy that the hexagonal lattice is the optimal lattice for two-dimensional space [13] but it can not be directly applied to the situation of three or higher dimensional space." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.9 + ], + "angle": 0, + "content": "For our task of quantizing CNN feature vectors, the dimensionality of the problem is much higher than two. In the interest of low complexity and dimension independence, we choose the diamond lattice (also known as body centred lattice) instead of more complex lattice structures. The generator matrix of the \\(n\\)-dimensional diamond lattice is" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "10241" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.146, + 0.098, + 0.825, + 0.33 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.345, + 0.895, + 0.389 + ], + "angle": 0, + "content": "Figure 2. Left: Two codebooks used in diamond lattice quantization. The first codebook (blue one) is a square lattice and the second codebook (yellow one) is obtained by shifting the first codebook by \\(1/2\\) quantization stride in each dimension. Right: Two-dimensional diamond lattice codebook. It can be obtained by shifting the square lattice like the left." + }, + { + "type": "equation", + "bbox": [ + 0.093, + 0.437, + 0.47, + 0.54 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {U} = \\left( \\begin{array}{c c c c c c c} 1 & 0 & 0 & 0 & \\dots & 0 & 0 \\\\ 1 / 2 & - 1 / 2 & 0 & 0 & \\dots & 0 & 0 \\\\ 0 & 1 / 2 & - 1 / 2 & 0 & \\dots & 0 & 0 \\\\ & \\vdots & & & \\ddots & \\vdots \\\\ 0 & 0 & 0 & 0 & \\dots & - 1 / 2 & 0 \\\\ 0 & 0 & 0 & 0 & \\dots & 1 / 2 & - 1 / 2 \\end{array} \\right). \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.543, + 0.47, + 0.572 + ], + "angle": 0, + "content": "An example of two-dimensional diamond lattice is shown in Fig. 2." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.573, + 0.471, + 0.754 + ], + "angle": 0, + "content": "The lattice vector quantization process can be decomposed into two scalar quantizations with respective codebooks plus one argmin operation. The first codebook is a square lattice and the second codebook is obtained by shifting the first codebook by \\(1/2\\) quantization stride in each dimension, as shown in Fig. 2. Specifically, for \\(z\\) to be quantized, instead of doing the regular vector quantization (computing distances between \\(z\\) and all centroids and select the nearest one), we do twice scalar quantizations to each element of \\(z\\) based on two codebooks and get two quantized vectors \\(\\hat{z}_1\\) and \\(\\hat{z}_2\\). We choose the closer one as the lattice quantized result \\(\\hat{z}\\), that is" + }, + { + "type": "equation", + "bbox": [ + 0.194, + 0.765, + 0.47, + 0.793 + ], + "angle": 0, + "content": "\\[\n\\hat {z} = \\underset {\\boldsymbol {q} = \\{\\hat {\\boldsymbol {z}} _ {1}, \\hat {\\boldsymbol {z}} _ {2} \\}} {\\arg \\min } \\| \\boldsymbol {z} - \\boldsymbol {q} \\|. \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.802, + 0.471, + 0.849 + ], + "angle": 0, + "content": "As arg min operation is not compatible with backpropagation, we instead use its soft relaxation which is proposed in [1]. The relaxation can be written as" + }, + { + "type": "equation", + "bbox": [ + 0.211, + 0.859, + 0.469, + 0.875 + ], + "angle": 0, + "content": "\\[\n\\hat {z} = \\phi_ {a} \\hat {z} _ {1} + \\phi_ {b} \\hat {z} _ {2}. \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.886, + 0.47, + 0.902 + ], + "angle": 0, + "content": "where the weights \\((\\phi_{a},\\phi_{b})\\) are obtained by applying soft" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.414, + 0.829, + 0.43 + ], + "angle": 0, + "content": "max on the distances from \\(z\\) to \\(\\hat{z}_1\\) and \\(\\hat{z}_2\\), that is:" + }, + { + "type": "equation", + "bbox": [ + 0.54, + 0.442, + 0.892, + 0.459 + ], + "angle": 0, + "content": "\\[\n\\left(\\phi_ {a}, \\phi_ {b}\\right) = \\Psi (- \\sigma [ \\| z - \\hat {z} _ {1} \\|, \\| z - \\hat {z} _ {2} \\| ]), \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.471, + 0.893, + 0.517 + ], + "angle": 0, + "content": "where \\(\\Psi\\) is the softmax function, \\(\\sigma\\) controls the degree of relaxation (or called hardness of the soft assignment as in the original paper)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.518, + 0.894, + 0.595 + ], + "angle": 0, + "content": "Specifically, given the latent representation \\(\\pmb{y} \\in \\mathbb{R}^{h \\times w \\times c}\\) with \\(c\\) channels and \\(h \\times w\\) size, we apply the lattice quantization operation \\(\\pmb{Q}_l(\\cdot)\\) on the latent vector for each spatial location \\(\\{\\pmb{y}_j \\in \\mathbb{R}^c, 1 \\leq j \\leq hw\\}\\), so the lattice quantized latent representation is:" + }, + { + "type": "equation", + "bbox": [ + 0.57, + 0.607, + 0.892, + 0.625 + ], + "angle": 0, + "content": "\\[\n\\hat {\\boldsymbol {y}} = \\left\\{\\boldsymbol {Q} _ {l} (\\boldsymbol {y} _ {j}), \\boldsymbol {y} _ {j} \\in \\mathbb {R} ^ {c}, 1 \\leq j \\leq h w \\right\\}. \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.637, + 0.893, + 0.837 + ], + "angle": 0, + "content": "It is noteworthy that in addition to transmitting the index of quantized representation, we also need to transmit extra bits to identify the selected codebook besides the quantized vectors, but the bitrate of codebook selection is negligible. As the lattice quantization is done to the latent vector for each spatial location, all elements in each spatial location share the same codebook. Thus the codebook only varies with spatial location. For a given image of size \\( h \\times w \\times 3 \\), the extracted latent representation will be of size \\( \\frac{h}{16} \\times \\frac{w}{16} \\times c \\) and the codebook selection information will be of size \\( \\frac{h}{16} \\times \\frac{w}{16} \\) with 1-bit precision. The extra bitrate for codebook selection is less than 0.004 bpp even without binary compression." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.847, + 0.785, + 0.865 + ], + "angle": 0, + "content": "3.2. Spatially Adaptive Companding" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.893, + 0.902 + ], + "angle": 0, + "content": "To further improve coding efficiency, we propose a spatially adaptive companding mapping to be coupled with the" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "10242" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.213 + ], + "angle": 0, + "content": "LVQ module to boost its adaptation to source statistics. Instead of adopting a universal companding to all elements over channels and spatial locations, we choose to learn different companding functions for different spatial locations. To reduce the difficulty of learning and also guarantee the inference speed, we restrict the companding to the form of A-law function. For a given input \\( x \\), the equation for A-law encoding is as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.091, + 0.238, + 0.47, + 0.318 + ], + "angle": 0, + "content": "\\[\nF (x) = \\operatorname {s g n} (x) \\left\\{ \\begin{array}{l l} \\frac {A | x |}{1 + \\ln (A)}, & | x | < \\frac {1}{A} \\\\ \\frac {1 + \\ln (A | x |)}{1 + \\ln (A)}, & \\frac {1}{A} \\leq | x | \\leq 1 \\end{array} \\right. \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.329, + 0.47, + 0.36 + ], + "angle": 0, + "content": "where \\(A\\) is the scale parameter. A-law decoding is given by the inverse function:" + }, + { + "type": "equation", + "bbox": [ + 0.078, + 0.384, + 0.485, + 0.478 + ], + "angle": 0, + "content": "\\[\nF ^ {- 1} (y) = \\operatorname {s g n} (y) \\left\\{ \\begin{array}{l l} \\frac {| y | (1 + \\ln (A))}{A}, & | y | < \\frac {1}{1 + \\ln (A)} \\\\ \\frac {e ^ {- 1 + | y | (1 + \\ln (A))}}{A}, & \\frac {1}{1 + \\ln (A)} \\leq | x | \\leq 1 \\end{array} \\right. \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.48, + 0.47, + 0.525 + ], + "angle": 0, + "content": "The A-law function and its inverse are both continuous and derivative, which implies that they can be embedded into the end-to-end optimization system." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.526, + 0.47, + 0.737 + ], + "angle": 0, + "content": "Specifically, we learn different scale parameters \\( A \\) for different spatial locations and apply the unique learned A-law companding to all elements at the same location. Learning of scale parameters \\( A \\) is implemented by a shallow convolution network \\( h \\), which consists of several convolution layers. It takes the latent representation \\( y \\) as input; and predicts the optimal scale parameters of A-law functions for different spatial locations, \\( \\pmb{a} = h(\\pmb{y}) \\). Then we apply these learned A-law companding functions \\( f(F; \\pmb{a}) \\) on the latent representations to scale it to the ideal dynamic range for better quantization performance. In the other side, after decoding \\( \\hat{\\pmb{y}} \\) from bitstream, the inverse A-law companding \\( f^{-1}(F^{-1}; \\pmb{a}) \\) is applied on \\( \\hat{\\pmb{y}} \\) to scale it to the original dynamic range." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.738, + 0.47, + 0.784 + ], + "angle": 0, + "content": "Given the proposed lattice vector quantization module and spatially adaptive companding mapping, the optimization goal should be rewritten to:" + }, + { + "type": "equation", + "bbox": [ + 0.1, + 0.797, + 0.24, + 0.811 + ], + "angle": 0, + "content": "\\[\n\\text {m i n i m i z e} R + \\lambda \\cdot D\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.1, + 0.816, + 0.469, + 0.834 + ], + "angle": 0, + "content": "\\[\nR = \\mathbb {E} _ {\\boldsymbol {x} \\sim p _ {x}} \\left[ - \\log_ {2} p _ {i j} \\left(\\boldsymbol {Q} _ {l} \\left(\\boldsymbol {f} \\left(g _ {a} (\\boldsymbol {x})\\right)\\right)\\right) \\right] \\tag {15}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.1, + 0.836, + 0.42, + 0.855 + ], + "angle": 0, + "content": "\\[\nD = \\lambda \\cdot \\mathbb {E} _ {\\boldsymbol {x} \\sim p _ {x}} \\left[ \\right. d \\left( \\right.\\boldsymbol {x}, g _ {s} \\left(\\boldsymbol {f} ^ {- 1} \\left(\\boldsymbol {Q} _ {l} \\left(\\boldsymbol {f} \\left(g _ {a} (\\boldsymbol {x})\\right)\\right)\\right)\\right)\\left. \\right]\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.87, + 0.469, + 0.901 + ], + "angle": 0, + "content": "where \\(Q_{l}\\) is the proposed LVQ module, \\(\\pmb{f}\\) and \\(\\pmb{f}^{-1}\\) are the learned spatially adaptive A-law function and its inverse." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.091, + 0.634, + 0.108 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.115, + 0.895, + 0.327 + ], + "angle": 0, + "content": "We conduct extensive experiments to systematically evaluate and analyze the effectiveness of the proposed LVQAC scheme. Specifically, we select two representative end-to-end CNN compression architectures Cheng2020 [8] and Minnen2018 [26] and replace their uniform scalar quantizers by the proposed LVQAC module to demonstrate the superiority of LVQAC. We show the R-D performance comparisons between the models with uniform scalar quantization and LVQAC for each architecture, and also provide visual comparisons. Besides, the encoding and decoding latencies are tabulated to validate the computational efficiency of LVQAC. Other analyses such as an ablation study on the effects of each component of LVQAC are further given." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.334, + 0.757, + 0.35 + ], + "angle": 0, + "content": "4.1. Dataset and Training Details" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.357, + 0.895, + 0.553 + ], + "angle": 0, + "content": "The training dataset consists of the largest 8000 images picked from ImageNet [12], following the previous work [17]. Training images are then random-cropped to \\(512 \\times 512\\) and batched into 16. We train each model using the Adam optimizer with \\(\\beta - 1 = 0.9\\), \\(\\beta_{2} = 0.999\\). Each model is trained with an initial learning rate \\(10^{-4}\\) for 2000 epochs (1M iterations), and then we decay the learning rate to \\(10^{-5}\\) for another 100-epoch training. Tests involve two image sets: Kodak (24 images) and CLIC Professional valid set (41 images). The network and the proposed LVQAC module are both implemented in PyTorch [29] and CompressAI [5]. All experiments are conducted with four RTX 2080ti GPUs." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.561, + 0.761, + 0.575 + ], + "angle": 0, + "content": "4.2. Rate-Distortion Performance" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.584, + 0.895, + 0.903 + ], + "angle": 0, + "content": "We evaluate our LVQAC scheme based on two representative published architectures Cheng2020 [8] and Minnen2018 [26]. The reason for choosing these two architectures is that they are the milestones in the end-to-end optimized image compression area, as Minnen2018 [26] is the first learning-based method to outperform BPG in PSNR metric and Cheng2020 [8] is the first work to achieve comparable performance with latest compression standard Versatile Video Coding (VVC) regarding PSNR. These two architectures were originally proposed with an autoregressive (serial) context model. To fully explore the potentiality of LVQAC, we consider the two architectures with two different context models, namely the autoregressive context model and checkerboard context model [18]. For each architecture, given two different context models, we do not change any other architectures except by replacing the uniform scalar quantizer with the proposed LVQAC scheme. We implement the two representative models coupled with uniform scalar quantizer and LVQAC, respectively. The Lagrange multipliers are set to \\(\\lambda = \\{0.0016, 0.0032, 0.0075, 0.015, 0.03, 0.045\\}\\)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10243" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.101, + 0.112, + 0.445, + 0.305 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.208, + 0.312, + 0.351, + 0.324 + ], + "angle": 0, + "content": "(a) Cheng2020 [8], Kodak." + }, + { + "type": "image", + "bbox": [ + 0.513, + 0.112, + 0.857, + 0.305 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.614, + 0.312, + 0.769, + 0.324 + ], + "angle": 0, + "content": "(b) Minnen2018 [26], Kodak." + }, + { + "type": "image_caption", + "bbox": [ + 0.227, + 0.337, + 0.741, + 0.351 + ], + "angle": 0, + "content": "Figure 3. Rate-distortion curves on Kodak dataset. All models are optimized for MSE." + }, + { + "type": "image", + "bbox": [ + 0.101, + 0.371, + 0.441, + 0.564 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.199, + 0.57, + 0.359, + 0.583 + ], + "angle": 0, + "content": "(a) Cheng2020 [8], CLIC Pro." + }, + { + "type": "image", + "bbox": [ + 0.513, + 0.372, + 0.853, + 0.564 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.605, + 0.57, + 0.778, + 0.583 + ], + "angle": 0, + "content": "(b) Minnen2018 [26], CLIC Pro." + }, + { + "type": "image_caption", + "bbox": [ + 0.218, + 0.595, + 0.75, + 0.61 + ], + "angle": 0, + "content": "Figure 4. Rate-distortion curves on CLIC Pro dataset. All models are optimized for MSE." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.629, + 0.473, + 0.902 + ], + "angle": 0, + "content": "Fig. 3 and Fig. 4 graphically presents the rate-distortion behaviors of different methods on Kodak and CLIC Pro datasets in PSNR metric. We can see that for any architecture, no matter with autoregressive or checkerboard context model, replacing uniform quantizer by LVQAC achieves better rate-distortion performance. Besides, LVQAC brings greater performance gain when coupled with the checkerboard context model than being coupled with the autoregressive context model. The CNN model adopted LVQAC + checkerboard context model can achieve a similar performance as the counterpart CNN using a far more expensive autoregressive context model + uniform scalar quantizer, yet the former is much lighter and faster than the latter. We show the detailed computational complexity of LVQAC in subsection 4.4. We can also find that LVQAC can bring more performance gain at the low bit rate than at the high bit rate. This is expected as uniform quantization can approach the rate-distortion optimality at very high bit rate [15]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.628, + 0.685, + 0.644 + ], + "angle": 0, + "content": "4.3. Visual Comparison" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.66, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We also provide visual comparisons to demonstrate the effectiveness of the proposed LVQAC scheme. Fig. 5, 6 and 7 show the visual results of different methods, including BPG, Cheng2020 with scalar quantizer, Cheng2002 with LVQAC and the Ground Truth. We pick three images 'kodim01.png', 'kodim07.png' and 'kodim10.png' from Kodak dataset to show the comparisons. The bit rates of all methods are adjusted to the same level for the fairness. In Fig. 5, LVQAC can preserve the sharper edges on doors than uniform scalar quantizer. In Fig. 6, LVQAC also achieves richer and clearer textures on flowers over uniform scalar quantizer. Another interesting observation is that the faint lines in Fig. 7 are both removed by BPG and scalar quantizer, but LVQAC can preserve such features. These observations reveal that the end-to-end CNN compression model coupled with LVQAC can produce much sharper edges and" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10244" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.089, + 0.276, + 0.196 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.155, + 0.199, + 0.201, + 0.21 + ], + "angle": 0, + "content": "(a) BPG" + }, + { + "type": "image", + "bbox": [ + 0.284, + 0.089, + 0.482, + 0.197 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.324, + 0.199, + 0.443, + 0.211 + ], + "angle": 0, + "content": "(b) Cheng2020, Scalar" + }, + { + "type": "image", + "bbox": [ + 0.49, + 0.089, + 0.687, + 0.197 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.523, + 0.199, + 0.653, + 0.211 + ], + "angle": 0, + "content": "(c) Cheng2020, LVQAC" + }, + { + "type": "image", + "bbox": [ + 0.696, + 0.089, + 0.892, + 0.197 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.747, + 0.199, + 0.839, + 0.21 + ], + "angle": 0, + "content": "(d) Ground Truth" + }, + { + "type": "image_caption", + "bbox": [ + 0.218, + 0.223, + 0.751, + 0.238 + ], + "angle": 0, + "content": "Figure 5. Visual comparisons of different methods on 'kodim01.png' from Kodak dataset." + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.251, + 0.276, + 0.359 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.156, + 0.361, + 0.201, + 0.372 + ], + "angle": 0, + "content": "(a) BPG" + }, + { + "type": "image", + "bbox": [ + 0.284, + 0.251, + 0.482, + 0.359 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.324, + 0.361, + 0.443, + 0.373 + ], + "angle": 0, + "content": "(b) Cheng2020, Scalar" + }, + { + "type": "image", + "bbox": [ + 0.49, + 0.251, + 0.687, + 0.359 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.523, + 0.361, + 0.653, + 0.373 + ], + "angle": 0, + "content": "(c) Cheng2020, LVQAC" + }, + { + "type": "image", + "bbox": [ + 0.696, + 0.251, + 0.892, + 0.359 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.747, + 0.361, + 0.839, + 0.372 + ], + "angle": 0, + "content": "(d) Ground Truth" + }, + { + "type": "image_caption", + "bbox": [ + 0.218, + 0.385, + 0.75, + 0.4 + ], + "angle": 0, + "content": "Figure 6. Visual comparisons of different methods on 'kodim07.png' from Kodak dataset." + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.414, + 0.276, + 0.641 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.156, + 0.644, + 0.201, + 0.655 + ], + "angle": 0, + "content": "(a) BPG" + }, + { + "type": "image", + "bbox": [ + 0.284, + 0.413, + 0.482, + 0.641 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.324, + 0.644, + 0.443, + 0.655 + ], + "angle": 0, + "content": "(b) Cheng2020, Scalar" + }, + { + "type": "image", + "bbox": [ + 0.49, + 0.413, + 0.687, + 0.641 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.523, + 0.643, + 0.653, + 0.655 + ], + "angle": 0, + "content": "(c) Cheng2020, LVQAC" + }, + { + "type": "image", + "bbox": [ + 0.696, + 0.413, + 0.892, + 0.641 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.747, + 0.643, + 0.839, + 0.655 + ], + "angle": 0, + "content": "(d) Ground Truth" + }, + { + "type": "image_caption", + "bbox": [ + 0.218, + 0.667, + 0.751, + 0.682 + ], + "angle": 0, + "content": "Figure 7. Visual comparisons of different methods on 'kodim10.png' from Kodak dataset." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.709, + 0.47, + 0.755 + ], + "angle": 0, + "content": "clearer textures than the counterpart CNN coupled with scalar quantizer. We present more high-resolution visual examples in the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.77, + 0.363, + 0.787 + ], + "angle": 0, + "content": "4.4. Encoding and Decoding Latency" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.47, + 0.903 + ], + "angle": 0, + "content": "We provide a detailed analysis of encoding and decoding latency in this subsection. Specifically, we evaluate the inference latency of end-to-end CNN compression models with different quantizers: uniform scalar quantizer and the proposed LVQAC. Table 1 tabulate the encoding time and decoding time of different architectures coupled with scalar quantizer and LVQAC. We can see that, for the ar" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.709, + 0.894, + 0.891 + ], + "angle": 0, + "content": "chitecture Cheng2020 with checkerboard context, LVQAC only increases the encoding time by about \\(15\\%\\) and the decoding time by about \\(5\\%\\), yet improves the performance to the same level as that using autoregressive context. It is noteworthy that the decoding time of the model using autoregressive context is two orders of magnitude higher than that of the checkerboard context. For the architecture Cheng2020 with autoregressive context model, the increase of encoding time is about \\(17\\%\\), and the increase of decoding time is negligible due to the huge base \\((>10^{3})\\). Similar observations can be obtained on the Minnen2018 architecture. These observations reveal that replacing uniform quantizer" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10245" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.894, + 0.119 + ], + "angle": 0, + "content": "Table 1. BD-Rates and inference times of different methods. The BD-Rate data is calculated relative to VVC (YUV 444) from PSNR-BPP curve on Kodak. [A] represents the autoregressive context model, [C] represents the checkerboard context model." + }, + { + "type": "table", + "bbox": [ + 0.152, + 0.129, + 0.819, + 0.299 + ], + "angle": 0, + "content": "
ArchitectureContext + QuantizerBD-Rate (%)Enc. Time (ms)Dec. Time (ms)
Cheng2020 [8][A] + LVQAC3.1248.65>103
[A] + Scalar3.3541.42>103
[C] + LVQAC3.3952.6655.84
[C] + Scalar3.8945.4353.01
Minnen2018 [26][A] + LVQAC14.7525.87>103
[A] + Scalar14.9218.14>103
[C] + LVQAC16.1726.2327.10
[C] + Scalar20.0018.8424.52
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.318, + 0.471, + 0.381 + ], + "angle": 0, + "content": "by LVQAC can achieve better rate-distortion performance without significantly increasing the model complexity; the simpler the context-sensitive entropy model, the greater the performance gain." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.387, + 0.231, + 0.403 + ], + "angle": 0, + "content": "4.5. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.41, + 0.472, + 0.577 + ], + "angle": 0, + "content": "To investigate the impacts of the proposed LVQAC scheme, we conduct an ablation study to investigate the importance of each component in the proposed LVQAC scheme. We experiment progressively to explore the respective contribution of the lattice vector quantization module and spatially adaptive companding module. Specifically, we progressively add LVQ and AC modules into the network and test the coding performance. Table 2 shows the results of the ablation study. It can be seen that lattice vector quantization and spatially adaptive companding contribute almost equally to the performance gain." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.584, + 0.196, + 0.599 + ], + "angle": 0, + "content": "4.6. Limitation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.607, + 0.47, + 0.804 + ], + "angle": 0, + "content": "The main limitation of this work relies on that it is difficult to know the optimal lattice structure for any given dimension. In this paper, we choose the diamond lattice structure due to its simplicity and easy extension to any dimension. However, even though diamond lattice is not the optimal lattice structure in the vast majority of cases, it is still much more efficient than uniform scalar quantizer without significantly increasing the model complexity. Another limitation of LVQAC is that if the context model is complex and powerful enough, such as an autoregressive context, then the gain brought by LVQAC will be very limited. Thus the application of LVQAC may be restricted to those lightweight end-to-end CNN compression models." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.815, + 0.348, + 0.832 + ], + "angle": 0, + "content": "5. Conclusion and Future Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.903 + ], + "angle": 0, + "content": "In this paper, we present a novel Lattice Vector Quantization scheme coupled with a spatially Adaptive Companding (LVQAC) mapping. LVQ can better exploit the inter-feature dependencies than scalar uniform quantization while being" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.317, + 0.894, + 0.373 + ], + "angle": 0, + "content": "Table 2. Results of the progressive ablation study. The BD-Rate data is calculated relative to VVC (YUV 444) from PSNR-BPP curve on Kodak. [A] represents the autoregressive context model, [C] represents the checkerboard context model." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.383, + 0.888, + 0.698 + ], + "angle": 0, + "content": "
ArchitectureContext + QuantizerBD-Rate
Cheng2020 [8][A] + LVQ + AC3.12
[A] + LVQ3.24
[A] + Scalar + AC3.30
[A] + Scalar3.35
[C] + LVQ + AC3.39
[C] + LVQ3.68
[C] + Scalar + AC3.82
[C] + Scalar3.89
Minnen2018 [26][A] + LVQ + AC14.75
[A] + LVQ14.86
[A] + Scalar + AC14.88
[A] + Scalar14.92
[C] + LVQ + AC16.17
[C] + LVQ18.43
[C] + Scalar + AC19.29
[C] + Scalar20.00
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.895, + 0.903 + ], + "angle": 0, + "content": "computationally almost as simple as the latter. Moreover, to improve the adaptability of LVQ to source statistics, we couple a spatially adaptive companding (AC) mapping with LVQ. The resulting LVQAC design can be easily embedded into any end-to-end optimized image compression system. Extensive experiments demonstrate that for any end-to-end CNN image compression models, replacing uniform quantizer by LVQAC achieves better rate-distortion performance without significantly increasing the model complexity. Future work will focus on exploring the optimal lattice vector quantizer for a given dimension and how to embed it into the end-to-end image compression system." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "10246" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.175, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.197 + ], + "angle": 0, + "content": "[1] Eirikur Agustsson, Fabian Mentzer, Michael Tschannen, Lukas Cavigelli, Radu Timofte, Luca Benini, and Luc Van Gool. Soft-to-hard vector quantization for end-to-end learning compressible representations. 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The main strength of these learnt compression methods is in powerful nonlinear analysis and synthesis transforms that can be facilitated by deep neural networks. However, out of operational expediency, most of these end-to-end methods adopt uniform scalar quantizers rather than vector quantizers, which are information-theoretically optimal. In this paper, we present a novel Lattice Vector Quantization scheme coupled with a spatially Adaptive Companding (LVQAC) mapping. LVQ can better exploit the inter-feature dependencies than scalar uniform quantization while being computationally almost as simple as the latter. Moreover, to improve the adaptability of LVQ to source statistics, we couple a spatially adaptive companding (AC) mapping with LVQ. The resulting LVQAC design can be easily embedded into any end-to-end optimized image compression system. Extensive experiments demonstrate that for any end-to-end CNN image compression models, replacing uniform quantizer by LVQAC achieves better rate-distortion performance without significantly increasing the model complexity. + +# 1. Introduction + +In the past five years, the research on end-to-end CNN image compression has made steady progress and led to the birth of a new class of image compression methods [1, 3, 4, 8, 21, 25, 26, 34-36, 40-44]. The CNN compression can now match and even exceed the rate-distortion performance of the previous best image compression methods [6, 33, 37, 45], which operate in the traditional paradigm of linear transform, quantization and entropy coding. + +The advantages of the CNN approach of data compression come from the nonlinearity of its analysis and synthesis transforms of the autoencoder architecture, the end-to-end joint optimization of the nonlinear transforms, uni + +form quantization of the latent space and conditional entropy coding (context-based arithmetic coding) of quantized features. + +Apparently, using uniform scalar quantizer in the above CNN image compression framework is motivated by operational expediency more than other considerations. Only at very high bit rate uniform quantization can approach the rate-distortion optimality [15]. It is very difficult to directly adopt and optimize a vector quantizer (VQ) in the end-to-end CNN architecture design for data compression, because VQ is a discrete decision process and it is not compatible with variational backpropagation that is necessary to the end-to-end CNN training. In [1], Agustsson et al. tried to circumvent the difficulty by a so-called soft-to-hard vector quantization scheme. Their technique is a soft (continuous) relaxation of discrete computations of VQ and entropy so that their effects can be approximated in the end-to-end training. However, in [1] the quantization centers are optimized along with the other modules, which make the whole system quite cumbersome and more difficult to train. In this paper, we propose a novel Lattice Vector Quantization scheme coupled with a spatially Adaptive Companding (LVQAC) mapping. LVQ can better exploit the inter-feature dependencies than scalar uniform quantization while being computationally almost as simple as the latter. Even if the features to be compressed are statistically independent, LVQ is still a more efficient coding strategy than scalar uniform quantization. This is because the former offers a more efficient covering of high-dimensional space than the latter, as proven by the theory of sphere packings, lattices and groups [11]. Moreover, to improve the adaptability of LVQ to source statistics, we couple a spatially adaptive companding mapping with LVQ. The resulting LVQAC design is computationally as simple and as amenable to the end-to-end training of the CNN compression model as in the originally proposed framework of [3]. + +Consequently, for any end-to-end CNN image compression models, replacing uniform quantizer by LVQAC achieves better rate-distortion performance without significantly increasing the model complexity; the simpler + +the context-sensitive entropy model, the greater the performance gain. For instance, the checkerboard context model [18] has recently been proposed to speed up the decoding process, but it hurts the R-D performance slightly. By incorporating LVQAC into the end-to-end compression CNN with a checkerboard context model, we can achieve the same performance as the counterpart CNN using a far more expensive auto-regressive context model. This is because uniform scalar quantization needs a more complex model to compensate for its coding inefficiency, whereas LVQAC does not. + +# 2. Overview of Learned Image Compression and Related Work + +Balle et al. [3] pioneered the end-to-end CNN model for image compression. Their network design is still shaped by the legacy of classical three-step signal compression algorithms; namely, transform, quantization and entropy coding. The greatest advantage of the CNN approach over the classical one comes from replacing linear transforms of the latter by more powerful and complex nonlinear transforms, which is the distinctive prowess of deep neural networks. Specifically, in the end-to-end image compression CNNs, an image vector $\pmb{x} \in \mathbb{R}^N$ is mapped to a latent code space via a parametric nonlinear analysis transform, $\pmb{y} = g_{a}(\pmb{x};\pmb{\theta}_{g})$ . Then this representation is quantized, yielding a discrete-valued vector $\hat{\pmb{y}} = Q(\pmb{y}) \in \mathbb{Z}^{M}$ which can be losslessly compressed using entropy coding algorithms such as arithmetic coding [31, 38] and transmitted as a sequence of bits. On the other side, the decoder recovers $\hat{\pmb{y}}$ from the compressed codes, and subjects it to a parametric nonlinear synthesis transform $g_{s}(\hat{\pmb{y}};\phi_{g})$ to build the reconstructed image $\hat{\pmb{x}}$ . The nonlinear parametric transform $g_{a}(\pmb{x};\pmb{\theta}_{g})$ and $g_{s}(\pmb{x};\phi_{g})$ are implemented by convolutional neural networks and the parameters $\pmb{\theta}_{g}$ and $\phi_{g}$ are learned over a large amount of natural images. + +The training goal is to minimize the expected length of the bitstream as well as the expected distortion of the reconstructed image with respect to the original image, giving rise to a rate-distortion optimization problem: + +$$ +\operatorname {m i n i m i z e} R + \lambda \cdot D +$$ + +$$ +R = \mathbb {E} _ {\boldsymbol {x} \sim p _ {x}} \left[ - \log_ {2} p _ {\tilde {y}} \left(Q \left(g _ {a} (\boldsymbol {x})\right)\right) \right] \tag {1} +$$ + +$$ +D = \lambda \cdot \mathbb {E} _ {\boldsymbol {x} \sim p _ {x}} [ d (\boldsymbol {x}, g _ {s} (Q (g _ {a} (\boldsymbol {x})))) ] +$$ + +where $\lambda$ is the Lagrange multiplier that determines the desired rate-distortion trade-off, $p_x$ is the (unknown) distribution of source images and $p_{\hat{y}}$ is a discrete entropy model. $Q(\cdot)$ represents quantization, implemented as rounding to the nearest integer in most of the end-to-end compression papers. The first term (representing rate) corresponds to the cross entropy between the marginal distribution of the latent and the learned entropy model, which is minimized + +when the two distributions are identical. The second term (distortion) corresponds to the reconstructed error between the original image and the reconstructed image. + +In most of the published end-to-end image compression CNNs, uniform scalar quantizer instead of vector quantizer (VQ) is adopted as the quantization function $Q(\cdot)$ in Eq. 1, That is, + +$$ +\hat {y} _ {i} = Q \left(y _ {i}\right) = \operatorname {r o u n d} \left(y _ {i}\right) \tag {2} +$$ + +where index $i$ runs over all elements of the vectors, including channels and spatial locations. Note that both terms in Eq. 1 depend on the quantized values, and the derivatives of the quantization function are zero almost everywhere, causing gradient descent problem. To allow optimization via stochastic gradient descent, a relaxation technique is used to replace the quantizer with an additive i.i.d. uniform noise $\Delta y_{i}$ , which has the same width as the quantization bins (one): + +$$ +\tilde {y} _ {i} = y _ {i} + \Delta y _ {i}, \Delta y _ {i} \in \mathcal {U} \left(- \frac {1}{2}, \frac {1}{2}\right). \tag {3} +$$ + +Very few articles [1, 46] studied vector quantization in end-to-end image compression networks. Agustsson et al. [1] proposed a so-called soft-to-hard vector quantization module to bridge the nearest neighbor decision process of VQ and variational backpropagation that is necessary for the end-to-end CNN training. Their technique is a soft (continuous) relaxation of branching operation of VQ so that the VQ effects can be approximated in the end-to-end training. Zhu et al. [46] proposed a probabilistic vector quantization with cascaded estimation to estimate means and covariances. However, the optimization goal of [46] only contains the distortion term, ignoring the vital design requirement of coding rates. + +After the pioneering work of Balle et al. [3], many other end-to-end compression methods have been proposed to further improve the R-D performances by introducing more complex nonlinear transforms and more efficient context entropy models. + +Rippel et al. [2, 30] proposed to learn the distribution of images using adversarial training to achieve better perceptual quality at extremely low bit rate. Johnston et al. [19] published a spatially adaptive bit allocation algorithm that efficiently uses a limited number of bits to encode visually complex image regions. Li et al. [23] developed a method to allocate the content-aware bit rate under the guidance of a content-weighted importance map. Some papers focused on investigating the adaptive context model for entropy estimation to achieve a better trade-off between reconstruction errors and required bits (entropy), including [4, 21, 25, 26], among which the CNN methods of [21, 26] are the first to outperform BPG in PSNR. Choi et al. [9] published a novel variable-rate learned image compression framework with a conditional auto-encoder. Cheng et al. [8] proposed + +to use discretized Gaussian Mixture Likelihoods to parameterize the distributions of latent codes and achieved a more accurate and flexible entropy model. Lin et al. [24] proposed a novel spatial recurrent neural network for end-to-end image compression. The block based LSTM is utilized in spatial RNN to fully exploit spatial redundancy. Minnen et al. [27] introduced two enhancements, channel-conditioning and latent residual prediction, that lead to network architectures with better rate-distortion performance than existing context-adaptive models while minimizing serial processing. Zhang et al. [41] proposed a deep learning system for attention-guided dual-layer image compression (AGDL) by introducing a novel idea of critical pixel set. + +More recently, He et al. [18] proposed a parallelizable checkerboard context model to speed up the decoding process in the end-to-end image compression. Yanget al. [39] proposed slimmable compressive autoencoders (SlimCAEs), where rate (R) and distortion (D) are jointly optimized for different capacities. Gao et al. [14] proposed to conduct neural image compression via Attentional Multi-scale Back Projection and Frequency Decomposition. Kim et al. [20] proposed a novel entropy model called Information Transformer (Informer) that exploits both global and local information in a content-dependent manner using an attention mechanism. He et al. [17] proposed the uneven channel-conditional adaptive coding, motivated by the observation of energy compaction in learned image compression. Cheng et al. [7] proposed to optimize the image compression algorithm to be noise-aware as joint denoising and compression to resolve the noisy image compression problem. There are some other papers [22, 28, 32] focused on the content adaptive approaches by updating the encoder-side component in the inference time to improve the coding performance. + +# 3. Design of LVQAC + +The main contribution of this work is to replace the uniform scalar quantization of feature values by the new LVQAC module outlined in the introduction, in the end-to-end design of compression CNNs. The LVQAC module is composed of a lattice vector quantizer (LVQ) and a spatially adaptive companding (AC) mapping. LVQ, also known as poor man's VQ, is computationally almost as simple as scalar uniform quantization, but it enjoys higher coding efficiency thanks to more efficient spatial covering property of LVQ [10]. + +In addition, we couple LVQ with another compression technique of adaptive companding to improve the adaptability of LVQ to source statistics. + +# 3.1. Lattice Vector Quantization + +Let $\{\pmb{u}_1, \dots, \pmb{u}_n\}$ be a set of linearly independent vectors in $\mathbb{R}^n$ , which is the $n$ -dimensional basis generating a lattice + +![](images/8ec5810670b82ac7221f79f98b2c543857331c7d1b820022a225d0c06f482735.jpg) +(a) Square lattice $Z_{2}$ . +Figure 1. Two-dimensional square lattice $Z_{2}$ and hexagonal lattice $A_{2}$ and their Voronoi cells. + +![](images/196b596517796f4fd63481d9aec6856ec8484d94aae8a4c1c2dced7ad38fea7f.jpg) +(b) Hexagonal lattice $A_{2}$ . + +$\Lambda$ $\Lambda$ consists of all points of the form + +$$ +\boldsymbol {z} = \sum_ {i = 1} ^ {n} c _ {i} \boldsymbol {u} _ {i}, c _ {i} \in \mathbb {Z}. \tag {4} +$$ + +Let $\mathbf{U} = (\mathbf{u}_1, \dots, \mathbf{u}_n)$ be the lattice generator matrix. Any vector of the lattice can be represented as $z = c\mathbf{U}, c = (c_1, \dots, c_n)$ , thus a lattice can be defined as: + +$$ +z \triangleq \left\{z \in \mathbb {R} ^ {n}: z = c U, c \in \mathbb {Z} ^ {n} \right\}. \tag {5} +$$ + +The Voronoi cell of a lattice point $z \in \Lambda$ is defined as + +$$ +V (z) \triangleq \left\{\boldsymbol {x} \in \mathbb {R} ^ {n}: | | \boldsymbol {x} - z | | \leq | | \boldsymbol {x} - \hat {z} | |, \forall \hat {z} \in \Lambda \right\}. \tag {6} +$$ + +The above structure is that of lattice vector quantization [15, 16]. The LVQ codewords are the centroids of the Voronoi polyhedrons which are of the same size and shape. + +Fig. 1 depicts the concept of LVQ. It shows two examples: the two-dimensional square lattice (integer lattice) $Z_{2}$ and the hexagonal lattice $A_{2}$ , together with their Voronoi cells. The generator matrix for $Z_{2}$ lattice and $A_{2}$ lattice are as follows: + +$$ +\boldsymbol {U} _ {Z _ {2}} = \left( \begin{array}{c c} 1 & 0 \\ 0 & 1 \end{array} \right), \quad \boldsymbol {U} _ {A _ {2}} = \left( \begin{array}{c c} 1 & 0 \\ 1 / 2 & \sqrt {3} / 2 \end{array} \right). \tag {7} +$$ + +In fact, the square lattice $Z_{2}$ is equivalent to the simple uniform scalar quantizer. The hexagonal lattice $A_{2}$ , however, offers a more efficient covering of 2D space than the square lattice $Z_{2}$ . Therefore, LVQ with the hexagonal lattice codebook offers higher coding efficiency than the square lattice codebook. It is noteworthy that the hexagonal lattice is the optimal lattice for two-dimensional space [13] but it can not be directly applied to the situation of three or higher dimensional space. + +For our task of quantizing CNN feature vectors, the dimensionality of the problem is much higher than two. In the interest of low complexity and dimension independence, we choose the diamond lattice (also known as body centred lattice) instead of more complex lattice structures. The generator matrix of the $n$ -dimensional diamond lattice is + +![](images/df55aad6c1fa2dfe2ab3cf3c1df0562d87b515a41d7b1e55e1a0faf0b60a4057.jpg) +Figure 2. Left: Two codebooks used in diamond lattice quantization. The first codebook (blue one) is a square lattice and the second codebook (yellow one) is obtained by shifting the first codebook by $1/2$ quantization stride in each dimension. Right: Two-dimensional diamond lattice codebook. It can be obtained by shifting the square lattice like the left. + +$$ +\boldsymbol {U} = \left( \begin{array}{c c c c c c c} 1 & 0 & 0 & 0 & \dots & 0 & 0 \\ 1 / 2 & - 1 / 2 & 0 & 0 & \dots & 0 & 0 \\ 0 & 1 / 2 & - 1 / 2 & 0 & \dots & 0 & 0 \\ & \vdots & & & \ddots & \vdots \\ 0 & 0 & 0 & 0 & \dots & - 1 / 2 & 0 \\ 0 & 0 & 0 & 0 & \dots & 1 / 2 & - 1 / 2 \end{array} \right). \tag {8} +$$ + +An example of two-dimensional diamond lattice is shown in Fig. 2. + +The lattice vector quantization process can be decomposed into two scalar quantizations with respective codebooks plus one argmin operation. The first codebook is a square lattice and the second codebook is obtained by shifting the first codebook by $1/2$ quantization stride in each dimension, as shown in Fig. 2. Specifically, for $z$ to be quantized, instead of doing the regular vector quantization (computing distances between $z$ and all centroids and select the nearest one), we do twice scalar quantizations to each element of $z$ based on two codebooks and get two quantized vectors $\hat{z}_1$ and $\hat{z}_2$ . We choose the closer one as the lattice quantized result $\hat{z}$ , that is + +$$ +\hat {z} = \underset {\boldsymbol {q} = \{\hat {\boldsymbol {z}} _ {1}, \hat {\boldsymbol {z}} _ {2} \}} {\arg \min } \| \boldsymbol {z} - \boldsymbol {q} \|. \tag {9} +$$ + +As arg min operation is not compatible with backpropagation, we instead use its soft relaxation which is proposed in [1]. The relaxation can be written as + +$$ +\hat {z} = \phi_ {a} \hat {z} _ {1} + \phi_ {b} \hat {z} _ {2}. \tag {10} +$$ + +where the weights $(\phi_{a},\phi_{b})$ are obtained by applying soft + +max on the distances from $z$ to $\hat{z}_1$ and $\hat{z}_2$ , that is: + +$$ +\left(\phi_ {a}, \phi_ {b}\right) = \Psi (- \sigma [ \| z - \hat {z} _ {1} \|, \| z - \hat {z} _ {2} \| ]), \tag {11} +$$ + +where $\Psi$ is the softmax function, $\sigma$ controls the degree of relaxation (or called hardness of the soft assignment as in the original paper). + +Specifically, given the latent representation $\pmb{y} \in \mathbb{R}^{h \times w \times c}$ with $c$ channels and $h \times w$ size, we apply the lattice quantization operation $\pmb{Q}_l(\cdot)$ on the latent vector for each spatial location $\{\pmb{y}_j \in \mathbb{R}^c, 1 \leq j \leq hw\}$ , so the lattice quantized latent representation is: + +$$ +\hat {\boldsymbol {y}} = \left\{\boldsymbol {Q} _ {l} (\boldsymbol {y} _ {j}), \boldsymbol {y} _ {j} \in \mathbb {R} ^ {c}, 1 \leq j \leq h w \right\}. \tag {12} +$$ + +It is noteworthy that in addition to transmitting the index of quantized representation, we also need to transmit extra bits to identify the selected codebook besides the quantized vectors, but the bitrate of codebook selection is negligible. As the lattice quantization is done to the latent vector for each spatial location, all elements in each spatial location share the same codebook. Thus the codebook only varies with spatial location. For a given image of size $h \times w \times 3$ , the extracted latent representation will be of size $\frac{h}{16} \times \frac{w}{16} \times c$ and the codebook selection information will be of size $\frac{h}{16} \times \frac{w}{16}$ with 1-bit precision. The extra bitrate for codebook selection is less than 0.004 bpp even without binary compression. + +# 3.2. Spatially Adaptive Companding + +To further improve coding efficiency, we propose a spatially adaptive companding mapping to be coupled with the + +LVQ module to boost its adaptation to source statistics. Instead of adopting a universal companding to all elements over channels and spatial locations, we choose to learn different companding functions for different spatial locations. To reduce the difficulty of learning and also guarantee the inference speed, we restrict the companding to the form of A-law function. For a given input $x$ , the equation for A-law encoding is as follows: + +$$ +F (x) = \operatorname {s g n} (x) \left\{ \begin{array}{l l} \frac {A | x |}{1 + \ln (A)}, & | x | < \frac {1}{A} \\ \frac {1 + \ln (A | x |)}{1 + \ln (A)}, & \frac {1}{A} \leq | x | \leq 1 \end{array} \right. \tag {13} +$$ + +where $A$ is the scale parameter. A-law decoding is given by the inverse function: + +$$ +F ^ {- 1} (y) = \operatorname {s g n} (y) \left\{ \begin{array}{l l} \frac {| y | (1 + \ln (A))}{A}, & | y | < \frac {1}{1 + \ln (A)} \\ \frac {e ^ {- 1 + | y | (1 + \ln (A))}}{A}, & \frac {1}{1 + \ln (A)} \leq | x | \leq 1 \end{array} \right. \tag {14} +$$ + +The A-law function and its inverse are both continuous and derivative, which implies that they can be embedded into the end-to-end optimization system. + +Specifically, we learn different scale parameters $A$ for different spatial locations and apply the unique learned A-law companding to all elements at the same location. Learning of scale parameters $A$ is implemented by a shallow convolution network $h$ , which consists of several convolution layers. It takes the latent representation $y$ as input; and predicts the optimal scale parameters of A-law functions for different spatial locations, $\pmb{a} = h(\pmb{y})$ . Then we apply these learned A-law companding functions $f(F; \pmb{a})$ on the latent representations to scale it to the ideal dynamic range for better quantization performance. In the other side, after decoding $\hat{\pmb{y}}$ from bitstream, the inverse A-law companding $f^{-1}(F^{-1}; \pmb{a})$ is applied on $\hat{\pmb{y}}$ to scale it to the original dynamic range. + +Given the proposed lattice vector quantization module and spatially adaptive companding mapping, the optimization goal should be rewritten to: + +$$ +\text {m i n i m i z e} R + \lambda \cdot D +$$ + +$$ +R = \mathbb {E} _ {\boldsymbol {x} \sim p _ {x}} \left[ - \log_ {2} p _ {i j} \left(\boldsymbol {Q} _ {l} \left(\boldsymbol {f} \left(g _ {a} (\boldsymbol {x})\right)\right)\right) \right] \tag {15} +$$ + +$$ +D = \lambda \cdot \mathbb {E} _ {\boldsymbol {x} \sim p _ {x}} \left[ \right. d \left( \right.\boldsymbol {x}, g _ {s} \left(\boldsymbol {f} ^ {- 1} \left(\boldsymbol {Q} _ {l} \left(\boldsymbol {f} \left(g _ {a} (\boldsymbol {x})\right)\right)\right)\right)\left. \right] +$$ + +where $Q_{l}$ is the proposed LVQ module, $\pmb{f}$ and $\pmb{f}^{-1}$ are the learned spatially adaptive A-law function and its inverse. + +# 4. Experiments + +We conduct extensive experiments to systematically evaluate and analyze the effectiveness of the proposed LVQAC scheme. Specifically, we select two representative end-to-end CNN compression architectures Cheng2020 [8] and Minnen2018 [26] and replace their uniform scalar quantizers by the proposed LVQAC module to demonstrate the superiority of LVQAC. We show the R-D performance comparisons between the models with uniform scalar quantization and LVQAC for each architecture, and also provide visual comparisons. Besides, the encoding and decoding latencies are tabulated to validate the computational efficiency of LVQAC. Other analyses such as an ablation study on the effects of each component of LVQAC are further given. + +# 4.1. Dataset and Training Details + +The training dataset consists of the largest 8000 images picked from ImageNet [12], following the previous work [17]. Training images are then random-cropped to $512 \times 512$ and batched into 16. We train each model using the Adam optimizer with $\beta - 1 = 0.9$ , $\beta_{2} = 0.999$ . Each model is trained with an initial learning rate $10^{-4}$ for 2000 epochs (1M iterations), and then we decay the learning rate to $10^{-5}$ for another 100-epoch training. Tests involve two image sets: Kodak (24 images) and CLIC Professional valid set (41 images). The network and the proposed LVQAC module are both implemented in PyTorch [29] and CompressAI [5]. All experiments are conducted with four RTX 2080ti GPUs. + +# 4.2. Rate-Distortion Performance + +We evaluate our LVQAC scheme based on two representative published architectures Cheng2020 [8] and Minnen2018 [26]. The reason for choosing these two architectures is that they are the milestones in the end-to-end optimized image compression area, as Minnen2018 [26] is the first learning-based method to outperform BPG in PSNR metric and Cheng2020 [8] is the first work to achieve comparable performance with latest compression standard Versatile Video Coding (VVC) regarding PSNR. These two architectures were originally proposed with an autoregressive (serial) context model. To fully explore the potentiality of LVQAC, we consider the two architectures with two different context models, namely the autoregressive context model and checkerboard context model [18]. For each architecture, given two different context models, we do not change any other architectures except by replacing the uniform scalar quantizer with the proposed LVQAC scheme. We implement the two representative models coupled with uniform scalar quantizer and LVQAC, respectively. The Lagrange multipliers are set to $\lambda = \{0.0016, 0.0032, 0.0075, 0.015, 0.03, 0.045\}$ . + +![](images/89a47f5278b5977825875dfcdfbe75f2cf6cef4d1c395a67ae3eae9aa80721e3.jpg) +(a) Cheng2020 [8], Kodak. + +![](images/be765997b7a421dfbd86b7da879f4924ce21fe8ff0bdb6cd00499bdd2ce95fa0.jpg) +(b) Minnen2018 [26], Kodak. + +![](images/f94aa754ff1ab2e46bd0a1d8dc3b40ecc276a3dad9461b7ea448765e9d738562.jpg) +Figure 3. Rate-distortion curves on Kodak dataset. All models are optimized for MSE. +(a) Cheng2020 [8], CLIC Pro. +Figure 4. Rate-distortion curves on CLIC Pro dataset. All models are optimized for MSE. + +![](images/0960480bdd6aefe09d5705f08fb31b4a7707138565543b4ba750a801d2c177dd.jpg) +(b) Minnen2018 [26], CLIC Pro. + +Fig. 3 and Fig. 4 graphically presents the rate-distortion behaviors of different methods on Kodak and CLIC Pro datasets in PSNR metric. We can see that for any architecture, no matter with autoregressive or checkerboard context model, replacing uniform quantizer by LVQAC achieves better rate-distortion performance. Besides, LVQAC brings greater performance gain when coupled with the checkerboard context model than being coupled with the autoregressive context model. The CNN model adopted LVQAC + checkerboard context model can achieve a similar performance as the counterpart CNN using a far more expensive autoregressive context model + uniform scalar quantizer, yet the former is much lighter and faster than the latter. We show the detailed computational complexity of LVQAC in subsection 4.4. We can also find that LVQAC can bring more performance gain at the low bit rate than at the high bit rate. This is expected as uniform quantization can approach the rate-distortion optimality at very high bit rate [15]. + +# 4.3. Visual Comparison + +We also provide visual comparisons to demonstrate the effectiveness of the proposed LVQAC scheme. Fig. 5, 6 and 7 show the visual results of different methods, including BPG, Cheng2020 with scalar quantizer, Cheng2002 with LVQAC and the Ground Truth. We pick three images 'kodim01.png', 'kodim07.png' and 'kodim10.png' from Kodak dataset to show the comparisons. The bit rates of all methods are adjusted to the same level for the fairness. In Fig. 5, LVQAC can preserve the sharper edges on doors than uniform scalar quantizer. In Fig. 6, LVQAC also achieves richer and clearer textures on flowers over uniform scalar quantizer. Another interesting observation is that the faint lines in Fig. 7 are both removed by BPG and scalar quantizer, but LVQAC can preserve such features. These observations reveal that the end-to-end CNN compression model coupled with LVQAC can produce much sharper edges and + +![](images/352f5bd22f9bef7d6cdfe2448cdf95c20a6d67a8fe46c74edfdc9daf10044943.jpg) +(a) BPG + +![](images/066af03a15da9916d208aca95fb7d77ff5b5566a65d7021945c9e60a3052f50f.jpg) +(b) Cheng2020, Scalar + +![](images/3eae9b47cb71b38d4e246e01ec1f4b34c09b09b57ad402bf753b39967dad87e9.jpg) +(c) Cheng2020, LVQAC + +![](images/6b60879132a2e91616eab4828261cbda81de5ca31e5376e90d3da132f7c19aca.jpg) +(d) Ground Truth + +![](images/26a1be0f0fed15ee28142d8973fd26defc87e0e957c0286ccffdbd77f64d4e24.jpg) +(a) BPG + +![](images/8c0a548c630c1ecdec11c4b9fadb0d7edc76c52df90f0e1a98bf8c1c11fcfa13.jpg) +Figure 5. Visual comparisons of different methods on 'kodim01.png' from Kodak dataset. +(b) Cheng2020, Scalar + +![](images/2e9501b79c430ded00fea7eec2f2af9adbf04a0afcfc4a465b6ca1cb95ea8a25.jpg) +(c) Cheng2020, LVQAC + +![](images/e1e6d725b2bdd5ed4911cff76fdb306b22d1c99a62767e378972193b87d6bb0d.jpg) +(d) Ground Truth + +![](images/d4bcf25305e24c72dcf83a55bf2cd733d9d63e29ad745684f4d440db247a187c.jpg) +Figure 6. Visual comparisons of different methods on 'kodim07.png' from Kodak dataset. +(a) BPG +Figure 7. Visual comparisons of different methods on 'kodim10.png' from Kodak dataset. + +![](images/acf5a728a081b3c0a0564829fe3dcd9eef6473a0ba9c73b026cfc4fd4b919afe.jpg) +(b) Cheng2020, Scalar + +![](images/ae93e15e28c994be5fcfd08822edd5f36c14194b25d7e41e38af9df1445d5cf9.jpg) +(c) Cheng2020, LVQAC + +![](images/4c105ef06e31692cdc158441df1a7a6f270337b17fb5bb74d31321a5d7b7ab3d.jpg) +(d) Ground Truth + +clearer textures than the counterpart CNN coupled with scalar quantizer. We present more high-resolution visual examples in the supplementary material. + +# 4.4. Encoding and Decoding Latency + +We provide a detailed analysis of encoding and decoding latency in this subsection. Specifically, we evaluate the inference latency of end-to-end CNN compression models with different quantizers: uniform scalar quantizer and the proposed LVQAC. Table 1 tabulate the encoding time and decoding time of different architectures coupled with scalar quantizer and LVQAC. We can see that, for the ar + +chitecture Cheng2020 with checkerboard context, LVQAC only increases the encoding time by about $15\%$ and the decoding time by about $5\%$ , yet improves the performance to the same level as that using autoregressive context. It is noteworthy that the decoding time of the model using autoregressive context is two orders of magnitude higher than that of the checkerboard context. For the architecture Cheng2020 with autoregressive context model, the increase of encoding time is about $17\%$ , and the increase of decoding time is negligible due to the huge base $(>10^{3})$ . Similar observations can be obtained on the Minnen2018 architecture. These observations reveal that replacing uniform quantizer + +Table 1. BD-Rates and inference times of different methods. The BD-Rate data is calculated relative to VVC (YUV 444) from PSNR-BPP curve on Kodak. [A] represents the autoregressive context model, [C] represents the checkerboard context model. + +
ArchitectureContext + QuantizerBD-Rate (%)Enc. Time (ms)Dec. Time (ms)
Cheng2020 [8][A] + LVQAC3.1248.65>103
[A] + Scalar3.3541.42>103
[C] + LVQAC3.3952.6655.84
[C] + Scalar3.8945.4353.01
Minnen2018 [26][A] + LVQAC14.7525.87>103
[A] + Scalar14.9218.14>103
[C] + LVQAC16.1726.2327.10
[C] + Scalar20.0018.8424.52
+ +by LVQAC can achieve better rate-distortion performance without significantly increasing the model complexity; the simpler the context-sensitive entropy model, the greater the performance gain. + +# 4.5. Ablation Study + +To investigate the impacts of the proposed LVQAC scheme, we conduct an ablation study to investigate the importance of each component in the proposed LVQAC scheme. We experiment progressively to explore the respective contribution of the lattice vector quantization module and spatially adaptive companding module. Specifically, we progressively add LVQ and AC modules into the network and test the coding performance. Table 2 shows the results of the ablation study. It can be seen that lattice vector quantization and spatially adaptive companding contribute almost equally to the performance gain. + +# 4.6. Limitation + +The main limitation of this work relies on that it is difficult to know the optimal lattice structure for any given dimension. In this paper, we choose the diamond lattice structure due to its simplicity and easy extension to any dimension. However, even though diamond lattice is not the optimal lattice structure in the vast majority of cases, it is still much more efficient than uniform scalar quantizer without significantly increasing the model complexity. Another limitation of LVQAC is that if the context model is complex and powerful enough, such as an autoregressive context, then the gain brought by LVQAC will be very limited. Thus the application of LVQAC may be restricted to those lightweight end-to-end CNN compression models. + +# 5. Conclusion and Future Work + +In this paper, we present a novel Lattice Vector Quantization scheme coupled with a spatially Adaptive Companding (LVQAC) mapping. LVQ can better exploit the inter-feature dependencies than scalar uniform quantization while being + +Table 2. Results of the progressive ablation study. The BD-Rate data is calculated relative to VVC (YUV 444) from PSNR-BPP curve on Kodak. [A] represents the autoregressive context model, [C] represents the checkerboard context model. + +
ArchitectureContext + QuantizerBD-Rate
Cheng2020 [8][A] + LVQ + AC3.12
[A] + LVQ3.24
[A] + Scalar + AC3.30
[A] + Scalar3.35
[C] + LVQ + AC3.39
[C] + LVQ3.68
[C] + Scalar + AC3.82
[C] + Scalar3.89
Minnen2018 [26][A] + LVQ + AC14.75
[A] + LVQ14.86
[A] + Scalar + AC14.88
[A] + Scalar14.92
[C] + LVQ + AC16.17
[C] + LVQ18.43
[C] + Scalar + AC19.29
[C] + Scalar20.00
+ +computationally almost as simple as the latter. Moreover, to improve the adaptability of LVQ to source statistics, we couple a spatially adaptive companding (AC) mapping with LVQ. The resulting LVQAC design can be easily embedded into any end-to-end optimized image compression system. Extensive experiments demonstrate that for any end-to-end CNN image compression models, replacing uniform quantizer by LVQAC achieves better rate-distortion performance without significantly increasing the model complexity. Future work will focus on exploring the optimal lattice vector quantizer for a given dimension and how to embed it into the end-to-end image compression system. + +# References + +[1] Eirikur Agustsson, Fabian Mentzer, Michael Tschannen, Lukas Cavigelli, Radu Timofte, Luca Benini, and Luc Van Gool. Soft-to-hard vector quantization for end-to-end learning compressible representations. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 17612-17621, 2022. 2 \ No newline at end of file diff --git a/2023/LVQAC_ Lattice Vector Quantization Coupled With Spatially Adaptive Companding for Efficient Learned Image Compression/images.zip b/2023/LVQAC_ Lattice Vector Quantization Coupled With Spatially Adaptive Companding for Efficient Learned Image Compression/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..68792c16009777c670a67f6bd42fd956c83cd728 --- /dev/null +++ b/2023/LVQAC_ Lattice Vector Quantization Coupled With Spatially Adaptive Companding for Efficient Learned Image Compression/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:139b6fceea4a3097d1ef3880be9e158f0ac609fb94d055156e35aecf04762f7f +size 557639 diff --git a/2023/LVQAC_ Lattice Vector Quantization Coupled With Spatially Adaptive Companding for Efficient Learned Image Compression/layout.json b/2023/LVQAC_ Lattice Vector Quantization Coupled With Spatially Adaptive Companding for Efficient Learned Image Compression/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..bc7d849cb5d80057e95c5916670f6175bdbd5329 --- /dev/null +++ b/2023/LVQAC_ Lattice Vector Quantization Coupled With Spatially Adaptive Companding for Efficient Learned Image Compression/layout.json @@ -0,0 +1,8738 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 79, + 102, + 515, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 79, + 102, + 515, + 140 + ], + "spans": [ + { + "bbox": [ + 79, + 102, + 515, + 140 + ], + "type": "text", + "content": "LVQAC: Lattice Vector Quantization Coupled with Spatially Adaptive Compa nding for Efficient Learned Image Compression" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 148, + 162, + 299, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 148, + 162, + 299, + 204 + ], + "spans": [ + { + "bbox": [ + 148, + 162, + 299, + 204 + ], + "type": "text", + "content": "Xi Zhang \nShanghai Jiao Tong University \nzhangxi_19930818@sjtu.edu.cn" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 337, + 162, + 443, + 203 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 337, + 162, + 443, + 203 + ], + "spans": [ + { + "bbox": [ + 337, + 162, + 443, + 203 + ], + "type": "text", + "content": "Xiaolin Wu \nMcMaster University \nxwu@ece.mcmaster.ca" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 231, + 192, + 243 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 231, + 192, + 243 + ], + "spans": [ + { + "bbox": [ + 143, + 231, + 192, + 243 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 257, + 290, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 257, + 290, + 521 + ], + "spans": [ + { + "bbox": [ + 46, + 257, + 290, + 521 + ], + "type": "text", + "content": "Recently, numerous end-to-end optimized image compression neural networks have been developed and proved themselves as leaders in rate-distortion performance. The main strength of these learnt compression methods is in powerful nonlinear analysis and synthesis transforms that can be facilitated by deep neural networks. However, out of operational expediency, most of these end-to-end methods adopt uniform scalar quantizers rather than vector quantizers, which are information-theoretically optimal. In this paper, we present a novel Lattice Vector Quantization scheme coupled with a spatially Adaptive Companding (LVQAC) mapping. LVQ can better exploit the inter-feature dependencies than scalar uniform quantization while being computationally almost as simple as the latter. Moreover, to improve the adaptability of LVQ to source statistics, we couple a spatially adaptive companding (AC) mapping with LVQ. The resulting LVQAC design can be easily embedded into any end-to-end optimized image compression system. Extensive experiments demonstrate that for any end-to-end CNN image compression models, replacing uniform quantizer by LVQAC achieves better rate-distortion performance without significantly increasing the model complexity." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 547, + 128, + 559 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 547, + 128, + 559 + ], + "spans": [ + { + "bbox": [ + 47, + 547, + 128, + 559 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 568, + 287, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 568, + 287, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 568, + 287, + 664 + ], + "type": "text", + "content": "In the past five years, the research on end-to-end CNN image compression has made steady progress and led to the birth of a new class of image compression methods [1, 3, 4, 8, 21, 25, 26, 34-36, 40-44]. The CNN compression can now match and even exceed the rate-distortion performance of the previous best image compression methods [6, 33, 37, 45], which operate in the traditional paradigm of linear transform, quantization and entropy coding." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "content": "The advantages of the CNN approach of data compression come from the nonlinearity of its analysis and synthesis transforms of the autoencoder architecture, the end-to-end joint optimization of the nonlinear transforms, uni" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 232, + 545, + 267 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 232, + 545, + 267 + ], + "spans": [ + { + "bbox": [ + 304, + 232, + 545, + 267 + ], + "type": "text", + "content": "form quantization of the latent space and conditional entropy coding (context-based arithmetic coding) of quantized features." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 269, + 546, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 269, + 546, + 664 + ], + "spans": [ + { + "bbox": [ + 304, + 269, + 546, + 664 + ], + "type": "text", + "content": "Apparently, using uniform scalar quantizer in the above CNN image compression framework is motivated by operational expediency more than other considerations. Only at very high bit rate uniform quantization can approach the rate-distortion optimality [15]. It is very difficult to directly adopt and optimize a vector quantizer (VQ) in the end-to-end CNN architecture design for data compression, because VQ is a discrete decision process and it is not compatible with variational backpropagation that is necessary to the end-to-end CNN training. In [1], Agustsson et al. tried to circumvent the difficulty by a so-called soft-to-hard vector quantization scheme. Their technique is a soft (continuous) relaxation of discrete computations of VQ and entropy so that their effects can be approximated in the end-to-end training. However, in [1] the quantization centers are optimized along with the other modules, which make the whole system quite cumbersome and more difficult to train. In this paper, we propose a novel Lattice Vector Quantization scheme coupled with a spatially Adaptive Companding (LVQAC) mapping. LVQ can better exploit the inter-feature dependencies than scalar uniform quantization while being computationally almost as simple as the latter. Even if the features to be compressed are statistically independent, LVQ is still a more efficient coding strategy than scalar uniform quantization. This is because the former offers a more efficient covering of high-dimensional space than the latter, as proven by the theory of sphere packings, lattices and groups [11]. Moreover, to improve the adaptability of LVQ to source statistics, we couple a spatially adaptive companding mapping with LVQ. The resulting LVQAC design is computationally as simple and as amenable to the end-to-end training of the CNN compression model as in the originally proposed framework of [3]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "content": "Consequently, for any end-to-end CNN image compression models, replacing uniform quantizer by LVQAC achieves better rate-distortion performance without significantly increasing the model complexity; the simpler" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "10239" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": "the context-sensitive entropy model, the greater the performance gain. For instance, the checkerboard context model [18] has recently been proposed to speed up the decoding process, but it hurts the R-D performance slightly. By incorporating LVQAC into the end-to-end compression CNN with a checkerboard context model, we can achieve the same performance as the counterpart CNN using a far more expensive auto-regressive context model. This is because uniform scalar quantization needs a more complex model to compensate for its coding inefficiency, whereas LVQAC does not." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 213, + 287, + 240 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 213, + 287, + 240 + ], + "spans": [ + { + "bbox": [ + 47, + 213, + 287, + 240 + ], + "type": "text", + "content": "2. Overview of Learned Image Compression and Related Work" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 247, + 289, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 247, + 289, + 514 + ], + "spans": [ + { + "bbox": [ + 46, + 247, + 289, + 514 + ], + "type": "text", + "content": "Balle et al. [3] pioneered the end-to-end CNN model for image compression. Their network design is still shaped by the legacy of classical three-step signal compression algorithms; namely, transform, quantization and entropy coding. The greatest advantage of the CNN approach over the classical one comes from replacing linear transforms of the latter by more powerful and complex nonlinear transforms, which is the distinctive prowess of deep neural networks. 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" + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "inline_equation", + "content": "Q(\\cdot)" + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "content": " represents quantization, implemented as rounding to the nearest integer in most of the end-to-end compression papers. The first term (representing rate) corresponds to the cross entropy between the marginal distribution of the latent and the learned entropy model, which is minimized" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "type": "text", + "content": "when the two distributions are identical. The second term (distortion) corresponds to the reconstructed error between the original image and the reconstructed image." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 109, + 547, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 109, + 547, + 156 + ], + "spans": [ + { + "bbox": [ + 304, + 109, + 547, + 156 + ], + "type": "text", + "content": "In most of the published end-to-end image compression CNNs, uniform scalar quantizer instead of vector quantizer (VQ) is adopted as the quantization function " + }, + { + "bbox": [ + 304, + 109, + 547, + 156 + ], + "type": "inline_equation", + "content": "Q(\\cdot)" + }, + { + "bbox": [ + 304, + 109, + 547, + 156 + ], + "type": "text", + "content": " in Eq. 1, That is," + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 375, + 159, + 545, + 172 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 375, + 159, + 545, + 172 + ], + "spans": [ + { + "bbox": [ + 375, + 159, + 545, + 172 + ], + "type": "interline_equation", + "content": "\\hat {y} _ {i} = Q \\left(y _ {i}\\right) = \\operatorname {r o u n d} \\left(y _ {i}\\right) \\tag {2}", + "image_path": "0c095868bedd7e4d683e1c0e0027a5368fe7afabaea9b4cb6c23640e2caba238.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 180, + 547, + 287 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 180, + 547, + 287 + ], + "spans": [ + { + "bbox": [ + 304, + 180, + 547, + 287 + ], + "type": "text", + "content": "where index " + }, + { + "bbox": [ + 304, + 180, + 547, + 287 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 180, + 547, + 287 + ], + "type": "text", + "content": " runs over all elements of the vectors, including channels and spatial locations. Note that both terms in Eq. 1 depend on the quantized values, and the derivatives of the quantization function are zero almost everywhere, causing gradient descent problem. To allow optimization via stochastic gradient descent, a relaxation technique is used to replace the quantizer with an additive i.i.d. uniform noise " + }, + { + "bbox": [ + 304, + 180, + 547, + 287 + ], + "type": "inline_equation", + "content": "\\Delta y_{i}" + }, + { + "bbox": [ + 304, + 180, + 547, + 287 + ], + "type": "text", + "content": ", which has the same width as the quantization bins (one):" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 354, + 289, + 545, + 310 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 354, + 289, + 545, + 310 + ], + "spans": [ + { + "bbox": [ + 354, + 289, + 545, + 310 + ], + "type": "interline_equation", + "content": "\\tilde {y} _ {i} = y _ {i} + \\Delta y _ {i}, \\Delta y _ {i} \\in \\mathcal {U} \\left(- \\frac {1}{2}, \\frac {1}{2}\\right). \\tag {3}", + "image_path": "4c730ef1dd57e8ad20907769392a759663bf95e1029ef587deffd09bb24bacaa.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 317, + 545, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 317, + 545, + 472 + ], + "spans": [ + { + "bbox": [ + 304, + 317, + 545, + 472 + ], + "type": "text", + "content": "Very few articles [1, 46] studied vector quantization in end-to-end image compression networks. Agustsson et al. [1] proposed a so-called soft-to-hard vector quantization module to bridge the nearest neighbor decision process of VQ and variational backpropagation that is necessary for the end-to-end CNN training. Their technique is a soft (continuous) relaxation of branching operation of VQ so that the VQ effects can be approximated in the end-to-end training. Zhu et al. [46] proposed a probabilistic vector quantization with cascaded estimation to estimate means and covariances. However, the optimization goal of [46] only contains the distortion term, ignoring the vital design requirement of coding rates." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 474, + 545, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 545, + 533 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 545, + 533 + ], + "type": "text", + "content": "After the pioneering work of Balle et al. [3], many other end-to-end compression methods have been proposed to further improve the R-D performances by introducing more complex nonlinear transforms and more efficient context entropy models." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 534, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 547, + 713 + ], + "type": "text", + "content": "Rippel et al. [2, 30] proposed to learn the distribution of images using adversarial training to achieve better perceptual quality at extremely low bit rate. Johnston et al. [19] published a spatially adaptive bit allocation algorithm that efficiently uses a limited number of bits to encode visually complex image regions. Li et al. [23] developed a method to allocate the content-aware bit rate under the guidance of a content-weighted importance map. Some papers focused on investigating the adaptive context model for entropy estimation to achieve a better trade-off between reconstruction errors and required bits (entropy), including [4, 21, 25, 26], among which the CNN methods of [21, 26] are the first to outperform BPG in PSNR. Choi et al. [9] published a novel variable-rate learned image compression framework with a conditional auto-encoder. Cheng et al. [8] proposed" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "10240" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": "to use discretized Gaussian Mixture Likelihoods to parameterize the distributions of latent codes and achieved a more accurate and flexible entropy model. Lin et al. [24] proposed a novel spatial recurrent neural network for end-to-end image compression. The block based LSTM is utilized in spatial RNN to fully exploit spatial redundancy. Minnen et al. [27] introduced two enhancements, channel-conditioning and latent residual prediction, that lead to network architectures with better rate-distortion performance than existing context-adaptive models while minimizing serial processing. Zhang et al. [41] proposed a deep learning system for attention-guided dual-layer image compression (AGDL) by introducing a novel idea of critical pixel set." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 228, + 289, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 228, + 289, + 479 + ], + "spans": [ + { + "bbox": [ + 46, + 228, + 289, + 479 + ], + "type": "text", + "content": "More recently, He et al. [18] proposed a parallelizable checkerboard context model to speed up the decoding process in the end-to-end image compression. Yanget al. [39] proposed slimmable compressive autoencoders (SlimCAEs), where rate (R) and distortion (D) are jointly optimized for different capacities. Gao et al. [14] proposed to conduct neural image compression via Attentional Multi-scale Back Projection and Frequency Decomposition. Kim et al. [20] proposed a novel entropy model called Information Transformer (Informer) that exploits both global and local information in a content-dependent manner using an attention mechanism. He et al. [17] proposed the uneven channel-conditional adaptive coding, motivated by the observation of energy compaction in learned image compression. Cheng et al. [7] proposed to optimize the image compression algorithm to be noise-aware as joint denoising and compression to resolve the noisy image compression problem. There are some other papers [22, 28, 32] focused on the content adaptive approaches by updating the encoder-side component in the inference time to improve the coding performance." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 488, + 155, + 502 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 488, + 155, + 502 + ], + "spans": [ + { + "bbox": [ + 47, + 488, + 155, + 502 + ], + "type": "text", + "content": "3. Design of LVQAC" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 509, + 287, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 509, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 509, + 287, + 628 + ], + "type": "text", + "content": "The main contribution of this work is to replace the uniform scalar quantization of feature values by the new LVQAC module outlined in the introduction, in the end-to-end design of compression CNNs. The LVQAC module is composed of a lattice vector quantizer (LVQ) and a spatially adaptive companding (AC) mapping. 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Lattice Vector Quantization" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": "Let " + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\{\\pmb{u}_1, \\dots, \\pmb{u}_n\\}" + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": " be a set of linearly independent vectors in " + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^n" + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": ", which is the " + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": "-dimensional basis generating a lattice" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 310, + 71, + 421, + 182 + ], + "blocks": [ + { + "bbox": [ + 310, + 71, + 421, + 182 + ], + "lines": [ + { + "bbox": [ + 310, + 71, + 421, + 182 + ], + "spans": [ + { + "bbox": [ + 310, + 71, + 421, + 182 + ], + "type": "image", + "image_path": "8ec5810670b82ac7221f79f98b2c543857331c7d1b820022a225d0c06f482735.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 329, + 184, + 399, + 194 + ], + "lines": [ + { + "bbox": [ + 329, + 184, + 399, + 194 + ], + "spans": [ + { + "bbox": [ + 329, + 184, + 399, + 194 + ], + "type": "text", + "content": "(a) Square lattice " + }, + { + "bbox": [ + 329, + 184, + 399, + 194 + ], + "type": "inline_equation", + "content": "Z_{2}" + }, + { + "bbox": [ + 329, + 184, + 399, + 194 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 306, + 203, + 545, + 225 + ], + "lines": [ + { + "bbox": [ + 306, + 203, + 545, + 225 + ], + "spans": [ + { + "bbox": [ + 306, + 203, + 545, + 225 + ], + "type": "text", + "content": "Figure 1. Two-dimensional square lattice " + }, + { + "bbox": [ + 306, + 203, + 545, + 225 + ], + "type": "inline_equation", + "content": "Z_{2}" + }, + { + "bbox": [ + 306, + 203, + 545, + 225 + ], + "type": "text", + "content": " and hexagonal lattice " + }, + { + "bbox": [ + 306, + 203, + 545, + 225 + ], + "type": "inline_equation", + "content": "A_{2}" + }, + { + "bbox": [ + 306, + 203, + 545, + 225 + ], + "type": "text", + "content": " and their Voronoi cells." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 430, + 71, + 542, + 182 + ], + "blocks": [ + { + "bbox": [ + 430, + 71, + 542, + 182 + ], + "lines": [ + { + "bbox": [ + 430, + 71, + 542, + 182 + ], + "spans": [ + { + "bbox": [ + 430, + 71, + 542, + 182 + ], + "type": "image", + "image_path": "196b596517796f4fd63481d9aec6856ec8484d94aae8a4c1c2dced7ad38fea7f.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 446, + 184, + 528, + 194 + ], + "lines": [ + { + "bbox": [ + 446, + 184, + 528, + 194 + ], + "spans": [ + { + "bbox": [ + 446, + 184, + 528, + 194 + ], + "type": "text", + "content": "(b) Hexagonal lattice " + }, + { + "bbox": [ + 446, + 184, + 528, + 194 + ], + "type": "inline_equation", + "content": "A_{2}" + }, + { + "bbox": [ + 446, + 184, + 528, + 194 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 245, + 460, + 257 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 245, + 460, + 257 + ], + "spans": [ + { + "bbox": [ + 306, + 245, + 460, + 257 + ], + "type": "inline_equation", + "content": "\\Lambda" + }, + { + "bbox": [ + 306, + 245, + 460, + 257 + ], + "type": "inline_equation", + "content": "\\Lambda" + }, + { + "bbox": [ + 306, + 245, + 460, + 257 + ], + "type": "text", + "content": " consists of all points of the form" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 381, + 264, + 545, + 293 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 381, + 264, + 545, + 293 + ], + "spans": [ + { + "bbox": [ + 381, + 264, + 545, + 293 + ], + "type": "interline_equation", + "content": "\\boldsymbol {z} = \\sum_ {i = 1} ^ {n} c _ {i} \\boldsymbol {u} _ {i}, c _ {i} \\in \\mathbb {Z}. \\tag {4}", + "image_path": "2c6070672904d242d07c3012a2a7cf196c63dd68b89b622551553fbcaa91ecd4.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 300, + 545, + 336 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 300, + 545, + 336 + ], + "spans": [ + { + "bbox": [ + 305, + 300, + 545, + 336 + ], + "type": "text", + "content": "Let " + }, + { + "bbox": [ + 305, + 300, + 545, + 336 + ], + "type": "inline_equation", + "content": "\\mathbf{U} = (\\mathbf{u}_1, \\dots, \\mathbf{u}_n)" + }, + { + "bbox": [ + 305, + 300, + 545, + 336 + ], + "type": "text", + "content": " be the lattice generator matrix. Any vector of the lattice can be represented as " + }, + { + "bbox": [ + 305, + 300, + 545, + 336 + ], + "type": "inline_equation", + "content": "z = c\\mathbf{U}, c = (c_1, \\dots, c_n)" + }, + { + "bbox": [ + 305, + 300, + 545, + 336 + ], + "type": "text", + "content": ", thus a lattice can be defined as:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 356, + 342, + 545, + 357 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 356, + 342, + 545, + 357 + ], + "spans": [ + { + "bbox": [ + 356, + 342, + 545, + 357 + ], + "type": "interline_equation", + "content": "z \\triangleq \\left\\{z \\in \\mathbb {R} ^ {n}: z = c U, c \\in \\mathbb {Z} ^ {n} \\right\\}. \\tag {5}", + "image_path": "b569d0051d6a9cdb4fb92afedd8b32c4627ea70f40e2e19810b9df930c91048b.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 363, + 523, + 375 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 363, + 523, + 375 + ], + "spans": [ + { + "bbox": [ + 306, + 363, + 523, + 375 + ], + "type": "text", + "content": "The Voronoi cell of a lattice point " + }, + { + "bbox": [ + 306, + 363, + 523, + 375 + ], + "type": "inline_equation", + "content": "z \\in \\Lambda" + }, + { + "bbox": [ + 306, + 363, + 523, + 375 + ], + "type": "text", + "content": " is defined as" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 310, + 381, + 545, + 396 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 381, + 545, + 396 + ], + "spans": [ + { + "bbox": [ + 310, + 381, + 545, + 396 + ], + "type": "interline_equation", + "content": "V (z) \\triangleq \\left\\{\\boldsymbol {x} \\in \\mathbb {R} ^ {n}: | | \\boldsymbol {x} - z | | \\leq | | \\boldsymbol {x} - \\hat {z} | |, \\forall \\hat {z} \\in \\Lambda \\right\\}. \\tag {6}", + "image_path": "13614c459b2bed926e643d0371305acf22672289726dff37a932dff241072037.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 402, + 545, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 402, + 545, + 437 + ], + "spans": [ + { + "bbox": [ + 305, + 402, + 545, + 437 + ], + "type": "text", + "content": "The above structure is that of lattice vector quantization [15, 16]. The LVQ codewords are the centroids of the Voronoi polyhedrons which are of the same size and shape." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 437, + 545, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 437, + 545, + 496 + ], + "spans": [ + { + "bbox": [ + 305, + 437, + 545, + 496 + ], + "type": "text", + "content": "Fig. 1 depicts the concept of LVQ. It shows two examples: the two-dimensional square lattice (integer lattice) " + }, + { + "bbox": [ + 305, + 437, + 545, + 496 + ], + "type": "inline_equation", + "content": "Z_{2}" + }, + { + "bbox": [ + 305, + 437, + 545, + 496 + ], + "type": "text", + "content": " and the hexagonal lattice " + }, + { + "bbox": [ + 305, + 437, + 545, + 496 + ], + "type": "inline_equation", + "content": "A_{2}" + }, + { + "bbox": [ + 305, + 437, + 545, + 496 + ], + "type": "text", + "content": ", together with their Voronoi cells. The generator matrix for " + }, + { + "bbox": [ + 305, + 437, + 545, + 496 + ], + "type": "inline_equation", + "content": "Z_{2}" + }, + { + "bbox": [ + 305, + 437, + 545, + 496 + ], + "type": "text", + "content": " lattice and " + }, + { + "bbox": [ + 305, + 437, + 545, + 496 + ], + "type": "inline_equation", + "content": "A_{2}" + }, + { + "bbox": [ + 305, + 437, + 545, + 496 + ], + "type": "text", + "content": " lattice are as follows:" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 334, + 502, + 545, + 529 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 334, + 502, + 545, + 529 + ], + "spans": [ + { + "bbox": [ + 334, + 502, + 545, + 529 + ], + "type": "interline_equation", + "content": "\\boldsymbol {U} _ {Z _ {2}} = \\left( \\begin{array}{c c} 1 & 0 \\\\ 0 & 1 \\end{array} \\right), \\quad \\boldsymbol {U} _ {A _ {2}} = \\left( \\begin{array}{c c} 1 & 0 \\\\ 1 / 2 & \\sqrt {3} / 2 \\end{array} \\right). \\tag {7}", + "image_path": "d8fc62d5f3bde58f115424de21fba3d1893a2f0cdfb900f810531aea5e34d7b0.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 533, + 545, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 545, + 641 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 545, + 641 + ], + "type": "text", + "content": "In fact, the square lattice " + }, + { + "bbox": [ + 304, + 533, + 545, + 641 + ], + "type": "inline_equation", + "content": "Z_{2}" + }, + { + "bbox": [ + 304, + 533, + 545, + 641 + ], + "type": "text", + "content": " is equivalent to the simple uniform scalar quantizer. The hexagonal lattice " + }, + { + "bbox": [ + 304, + 533, + 545, + 641 + ], + "type": "inline_equation", + "content": "A_{2}" + }, + { + "bbox": [ + 304, + 533, + 545, + 641 + ], + "type": "text", + "content": ", however, offers a more efficient covering of 2D space than the square lattice " + }, + { + "bbox": [ + 304, + 533, + 545, + 641 + ], + "type": "inline_equation", + "content": "Z_{2}" + }, + { + "bbox": [ + 304, + 533, + 545, + 641 + ], + "type": "text", + "content": ". Therefore, LVQ with the hexagonal lattice codebook offers higher coding efficiency than the square lattice codebook. It is noteworthy that the hexagonal lattice is the optimal lattice for two-dimensional space [13] but it can not be directly applied to the situation of three or higher dimensional space." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 642, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 712 + ], + "type": "text", + "content": "For our task of quantizing CNN feature vectors, the dimensionality of the problem is much higher than two. In the interest of low complexity and dimension independence, we choose the diamond lattice (also known as body centred lattice) instead of more complex lattice structures. The generator matrix of the " + }, + { + "bbox": [ + 304, + 642, + 545, + 712 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 642, + 545, + 712 + ], + "type": "text", + "content": "-dimensional diamond lattice is" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10241" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 89, + 77, + 504, + 261 + ], + "blocks": [ + { + "bbox": [ + 89, + 77, + 504, + 261 + ], + "lines": [ + { + "bbox": [ + 89, + 77, + 504, + 261 + ], + "spans": [ + { + "bbox": [ + 89, + 77, + 504, + 261 + ], + "type": "image", + "image_path": "df55aad6c1fa2dfe2ab3cf3c1df0562d87b515a41d7b1e55e1a0faf0b60a4057.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 273, + 547, + 308 + ], + "lines": [ + { + "bbox": [ + 46, + 273, + 547, + 308 + ], + "spans": [ + { + "bbox": [ + 46, + 273, + 547, + 308 + ], + "type": "text", + "content": "Figure 2. Left: Two codebooks used in diamond lattice quantization. The first codebook (blue one) is a square lattice and the second codebook (yellow one) is obtained by shifting the first codebook by " + }, + { + "bbox": [ + 46, + 273, + 547, + 308 + ], + "type": "inline_equation", + "content": "1/2" + }, + { + "bbox": [ + 46, + 273, + 547, + 308 + ], + "type": "text", + "content": " quantization stride in each dimension. Right: Two-dimensional diamond lattice codebook. It can be obtained by shifting the square lattice like the left." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 346, + 287, + 427 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 346, + 287, + 427 + ], + "spans": [ + { + "bbox": [ + 56, + 346, + 287, + 427 + ], + "type": "interline_equation", + "content": "\\boldsymbol {U} = \\left( \\begin{array}{c c c c c c c} 1 & 0 & 0 & 0 & \\dots & 0 & 0 \\\\ 1 / 2 & - 1 / 2 & 0 & 0 & \\dots & 0 & 0 \\\\ 0 & 1 / 2 & - 1 / 2 & 0 & \\dots & 0 & 0 \\\\ & \\vdots & & & \\ddots & \\vdots \\\\ 0 & 0 & 0 & 0 & \\dots & - 1 / 2 & 0 \\\\ 0 & 0 & 0 & 0 & \\dots & 1 / 2 & - 1 / 2 \\end{array} \\right). \\tag {8}", + "image_path": "6171121c10001f1ebc36c652ffbf2055434f57529465c5b7a52657bcfffee546.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 430, + 287, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 430, + 287, + 453 + ], + "spans": [ + { + "bbox": [ + 47, + 430, + 287, + 453 + ], + "type": "text", + "content": "An example of two-dimensional diamond lattice is shown in Fig. 2." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 453, + 288, + 597 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 453, + 288, + 597 + ], + "spans": [ + { + "bbox": [ + 46, + 453, + 288, + 597 + ], + "type": "text", + "content": "The lattice vector quantization process can be decomposed into two scalar quantizations with respective codebooks plus one argmin operation. The first codebook is a square lattice and the second codebook is obtained by shifting the first codebook by " + }, + { + "bbox": [ + 46, + 453, + 288, + 597 + ], + "type": "inline_equation", + "content": "1/2" + }, + { + "bbox": [ + 46, + 453, + 288, + 597 + ], + "type": "text", + "content": " quantization stride in each dimension, as shown in Fig. 2. Specifically, for " + }, + { + "bbox": [ + 46, + 453, + 288, + 597 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 453, + 288, + 597 + ], + "type": "text", + "content": " to be quantized, instead of doing the regular vector quantization (computing distances between " + }, + { + "bbox": [ + 46, + 453, + 288, + 597 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 453, + 288, + 597 + ], + "type": "text", + "content": " and all centroids and select the nearest one), we do twice scalar quantizations to each element of " + }, + { + "bbox": [ + 46, + 453, + 288, + 597 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 453, + 288, + 597 + ], + "type": "text", + "content": " based on two codebooks and get two quantized vectors " + }, + { + "bbox": [ + 46, + 453, + 288, + 597 + ], + "type": "inline_equation", + "content": "\\hat{z}_1" + }, + { + "bbox": [ + 46, + 453, + 288, + 597 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 453, + 288, + 597 + ], + "type": "inline_equation", + "content": "\\hat{z}_2" + }, + { + "bbox": [ + 46, + 453, + 288, + 597 + ], + "type": "text", + "content": ". We choose the closer one as the lattice quantized result " + }, + { + "bbox": [ + 46, + 453, + 288, + 597 + ], + "type": "inline_equation", + "content": "\\hat{z}" + }, + { + "bbox": [ + 46, + 453, + 288, + 597 + ], + "type": "text", + "content": ", that is" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 118, + 605, + 287, + 628 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 118, + 605, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 118, + 605, + 287, + 628 + ], + "type": "interline_equation", + "content": "\\hat {z} = \\underset {\\boldsymbol {q} = \\{\\hat {\\boldsymbol {z}} _ {1}, \\hat {\\boldsymbol {z}} _ {2} \\}} {\\arg \\min } \\| \\boldsymbol {z} - \\boldsymbol {q} \\|. \\tag {9}", + "image_path": "399b018ef2fee39e2db120af876834b4428c6fe3f98953c94567abc54e7b4408.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 635, + 288, + 672 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 635, + 288, + 672 + ], + "spans": [ + { + "bbox": [ + 47, + 635, + 288, + 672 + ], + "type": "text", + "content": "As arg min operation is not compatible with backpropagation, we instead use its soft relaxation which is proposed in [1]. The relaxation can be written as" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 129, + 680, + 287, + 693 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 129, + 680, + 287, + 693 + ], + "spans": [ + { + "bbox": [ + 129, + 680, + 287, + 693 + ], + "type": "interline_equation", + "content": "\\hat {z} = \\phi_ {a} \\hat {z} _ {1} + \\phi_ {b} \\hat {z} _ {2}. \\tag {10}", + "image_path": "b792c981d12fb668c413b7fd7625ea9d8ac1e69f95f7c967f8f9dbcb8149e8bf.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 701, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 701, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 701, + 287, + 714 + ], + "type": "text", + "content": "where the weights " + }, + { + "bbox": [ + 47, + 701, + 287, + 714 + ], + "type": "inline_equation", + "content": "(\\phi_{a},\\phi_{b})" + }, + { + "bbox": [ + 47, + 701, + 287, + 714 + ], + "type": "text", + "content": " are obtained by applying soft" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 327, + 507, + 340 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 327, + 507, + 340 + ], + "spans": [ + { + "bbox": [ + 306, + 327, + 507, + 340 + ], + "type": "text", + "content": "max on the distances from " + }, + { + "bbox": [ + 306, + 327, + 507, + 340 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 306, + 327, + 507, + 340 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 306, + 327, + 507, + 340 + ], + "type": "inline_equation", + "content": "\\hat{z}_1" + }, + { + "bbox": [ + 306, + 327, + 507, + 340 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 327, + 507, + 340 + ], + "type": "inline_equation", + "content": "\\hat{z}_2" + }, + { + "bbox": [ + 306, + 327, + 507, + 340 + ], + "type": "text", + "content": ", that is:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 330, + 350, + 545, + 363 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 330, + 350, + 545, + 363 + ], + "spans": [ + { + "bbox": [ + 330, + 350, + 545, + 363 + ], + "type": "interline_equation", + "content": "\\left(\\phi_ {a}, \\phi_ {b}\\right) = \\Psi (- \\sigma [ \\| z - \\hat {z} _ {1} \\|, \\| z - \\hat {z} _ {2} \\| ]), \\tag {11}", + "image_path": "6162bb39c0c6418a78f09818397aa8166b6d7f33d2a9cc7b11e16a5f3d04181c.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 373, + 546, + 409 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 373, + 546, + 409 + ], + "spans": [ + { + "bbox": [ + 305, + 373, + 546, + 409 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 373, + 546, + 409 + ], + "type": "inline_equation", + "content": "\\Psi" + }, + { + "bbox": [ + 305, + 373, + 546, + 409 + ], + "type": "text", + "content": " is the softmax function, " + }, + { + "bbox": [ + 305, + 373, + 546, + 409 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 305, + 373, + 546, + 409 + ], + "type": "text", + "content": " controls the degree of relaxation (or called hardness of the soft assignment as in the original paper)." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 410, + 547, + 471 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 410, + 547, + 471 + ], + "spans": [ + { + "bbox": [ + 305, + 410, + 547, + 471 + ], + "type": "text", + "content": "Specifically, given the latent representation " + }, + { + "bbox": [ + 305, + 410, + 547, + 471 + ], + "type": "inline_equation", + "content": "\\pmb{y} \\in \\mathbb{R}^{h \\times w \\times c}" + }, + { + "bbox": [ + 305, + 410, + 547, + 471 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 305, + 410, + 547, + 471 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 305, + 410, + 547, + 471 + ], + "type": "text", + "content": " channels and " + }, + { + "bbox": [ + 305, + 410, + 547, + 471 + ], + "type": "inline_equation", + "content": "h \\times w" + }, + { + "bbox": [ + 305, + 410, + 547, + 471 + ], + "type": "text", + "content": " size, we apply the lattice quantization operation " + }, + { + "bbox": [ + 305, + 410, + 547, + 471 + ], + "type": "inline_equation", + "content": "\\pmb{Q}_l(\\cdot)" + }, + { + "bbox": [ + 305, + 410, + 547, + 471 + ], + "type": "text", + "content": " on the latent vector for each spatial location " + }, + { + "bbox": [ + 305, + 410, + 547, + 471 + ], + "type": "inline_equation", + "content": "\\{\\pmb{y}_j \\in \\mathbb{R}^c, 1 \\leq j \\leq hw\\}" + }, + { + "bbox": [ + 305, + 410, + 547, + 471 + ], + "type": "text", + "content": ", so the lattice quantized latent representation is:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 348, + 480, + 545, + 495 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 348, + 480, + 545, + 495 + ], + "spans": [ + { + "bbox": [ + 348, + 480, + 545, + 495 + ], + "type": "interline_equation", + "content": "\\hat {\\boldsymbol {y}} = \\left\\{\\boldsymbol {Q} _ {l} (\\boldsymbol {y} _ {j}), \\boldsymbol {y} _ {j} \\in \\mathbb {R} ^ {c}, 1 \\leq j \\leq h w \\right\\}. \\tag {12}", + "image_path": "cf0dc2aa0538cce7c169adc1663fa92576f3f4ed9dd2a7391c51d9fcbbfece02.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 504, + 546, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 504, + 546, + 662 + ], + "spans": [ + { + "bbox": [ + 305, + 504, + 546, + 662 + ], + "type": "text", + "content": "It is noteworthy that in addition to transmitting the index of quantized representation, we also need to transmit extra bits to identify the selected codebook besides the quantized vectors, but the bitrate of codebook selection is negligible. As the lattice quantization is done to the latent vector for each spatial location, all elements in each spatial location share the same codebook. Thus the codebook only varies with spatial location. For a given image of size " + }, + { + "bbox": [ + 305, + 504, + 546, + 662 + ], + "type": "inline_equation", + "content": "h \\times w \\times 3" + }, + { + "bbox": [ + 305, + 504, + 546, + 662 + ], + "type": "text", + "content": ", the extracted latent representation will be of size " + }, + { + "bbox": [ + 305, + 504, + 546, + 662 + ], + "type": "inline_equation", + "content": "\\frac{h}{16} \\times \\frac{w}{16} \\times c" + }, + { + "bbox": [ + 305, + 504, + 546, + 662 + ], + "type": "text", + "content": " and the codebook selection information will be of size " + }, + { + "bbox": [ + 305, + 504, + 546, + 662 + ], + "type": "inline_equation", + "content": "\\frac{h}{16} \\times \\frac{w}{16}" + }, + { + "bbox": [ + 305, + 504, + 546, + 662 + ], + "type": "text", + "content": " with 1-bit precision. The extra bitrate for codebook selection is less than 0.004 bpp even without binary compression." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 670, + 480, + 685 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 670, + 480, + 685 + ], + "spans": [ + { + "bbox": [ + 306, + 670, + 480, + 685 + ], + "type": "text", + "content": "3.2. Spatially Adaptive Companding" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 689, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 546, + 714 + ], + "type": "text", + "content": "To further improve coding efficiency, we propose a spatially adaptive companding mapping to be coupled with the" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "10242" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "content": "LVQ module to boost its adaptation to source statistics. Instead of adopting a universal companding to all elements over channels and spatial locations, we choose to learn different companding functions for different spatial locations. To reduce the difficulty of learning and also guarantee the inference speed, we restrict the companding to the form of A-law function. For a given input " + }, + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "content": ", the equation for A-law encoding is as follows:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 188, + 287, + 251 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 188, + 287, + 251 + ], + "spans": [ + { + "bbox": [ + 55, + 188, + 287, + 251 + ], + "type": "interline_equation", + "content": "F (x) = \\operatorname {s g n} (x) \\left\\{ \\begin{array}{l l} \\frac {A | x |}{1 + \\ln (A)}, & | x | < \\frac {1}{A} \\\\ \\frac {1 + \\ln (A | x |)}{1 + \\ln (A)}, & \\frac {1}{A} \\leq | x | \\leq 1 \\end{array} \\right. \\tag {13}", + "image_path": "00ad9e7ee9aacce8d3a2c7f32c9b6b794eef8e4d862e27425fa320e899cb593d.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 260, + 287, + 285 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 260, + 287, + 285 + ], + "spans": [ + { + "bbox": [ + 46, + 260, + 287, + 285 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 260, + 287, + 285 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 46, + 260, + 287, + 285 + ], + "type": "text", + "content": " is the scale parameter. A-law decoding is given by the inverse function:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 304, + 296, + 378 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 304, + 296, + 378 + ], + "spans": [ + { + "bbox": [ + 47, + 304, + 296, + 378 + ], + "type": "interline_equation", + "content": "F ^ {- 1} (y) = \\operatorname {s g n} (y) \\left\\{ \\begin{array}{l l} \\frac {| y | (1 + \\ln (A))}{A}, & | y | < \\frac {1}{1 + \\ln (A)} \\\\ \\frac {e ^ {- 1 + | y | (1 + \\ln (A))}}{A}, & \\frac {1}{1 + \\ln (A)} \\leq | x | \\leq 1 \\end{array} \\right. \\tag {14}", + "image_path": "77c87b6e0ab26079d81d7b474d00e5914ceac9b1bba71e2b0eb852a3c86b26c9.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 380, + 287, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 380, + 287, + 415 + ], + "spans": [ + { + "bbox": [ + 46, + 380, + 287, + 415 + ], + "type": "text", + "content": "The A-law function and its inverse are both continuous and derivative, which implies that they can be embedded into the end-to-end optimization system." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 416, + 287, + 583 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 416, + 287, + 583 + ], + "spans": [ + { + "bbox": [ + 46, + 416, + 287, + 583 + ], + "type": "text", + "content": "Specifically, we learn different scale parameters " + }, + { + "bbox": [ + 46, + 416, + 287, + 583 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 46, + 416, + 287, + 583 + ], + "type": "text", + "content": " for different spatial locations and apply the unique learned A-law companding to all elements at the same location. Learning of scale parameters " + }, + { + "bbox": [ + 46, + 416, + 287, + 583 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 46, + 416, + 287, + 583 + ], + "type": "text", + "content": " is implemented by a shallow convolution network " + }, + { + "bbox": [ + 46, + 416, + 287, + 583 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 46, + 416, + 287, + 583 + ], + "type": "text", + "content": ", which consists of several convolution layers. It takes the latent representation " + }, + { + "bbox": [ + 46, + 416, + 287, + 583 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 416, + 287, + 583 + ], + "type": "text", + "content": " as input; and predicts the optimal scale parameters of A-law functions for different spatial locations, " + }, + { + "bbox": [ + 46, + 416, + 287, + 583 + ], + "type": "inline_equation", + "content": "\\pmb{a} = h(\\pmb{y})" + }, + { + "bbox": [ + 46, + 416, + 287, + 583 + ], + "type": "text", + "content": ". Then we apply these learned A-law companding functions " + }, + { + "bbox": [ + 46, + 416, + 287, + 583 + ], + "type": "inline_equation", + "content": "f(F; \\pmb{a})" + }, + { + "bbox": [ + 46, + 416, + 287, + 583 + ], + "type": "text", + "content": " on the latent representations to scale it to the ideal dynamic range for better quantization performance. In the other side, after decoding " + }, + { + "bbox": [ + 46, + 416, + 287, + 583 + ], + "type": "inline_equation", + "content": "\\hat{\\pmb{y}}" + }, + { + "bbox": [ + 46, + 416, + 287, + 583 + ], + "type": "text", + "content": " from bitstream, the inverse A-law companding " + }, + { + "bbox": [ + 46, + 416, + 287, + 583 + ], + "type": "inline_equation", + "content": "f^{-1}(F^{-1}; \\pmb{a})" + }, + { + "bbox": [ + 46, + 416, + 287, + 583 + ], + "type": "text", + "content": " is applied on " + }, + { + "bbox": [ + 46, + 416, + 287, + 583 + ], + "type": "inline_equation", + "content": "\\hat{\\pmb{y}}" + }, + { + "bbox": [ + 46, + 416, + 287, + 583 + ], + "type": "text", + "content": " to scale it to the original dynamic range." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 584, + 287, + 620 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 584, + 287, + 620 + ], + "spans": [ + { + "bbox": [ + 46, + 584, + 287, + 620 + ], + "type": "text", + "content": "Given the proposed lattice vector quantization module and spatially adaptive companding mapping, the optimization goal should be rewritten to:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 61, + 631, + 146, + 642 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 631, + 146, + 642 + ], + "spans": [ + { + "bbox": [ + 61, + 631, + 146, + 642 + ], + "type": "interline_equation", + "content": "\\text {m i n i m i z e} R + \\lambda \\cdot D", + "image_path": "533036184ccc5221cf6ba7daefcbf88bb263d081870867d4f63dfac811dde4cd.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 61, + 646, + 287, + 660 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 646, + 287, + 660 + ], + "spans": [ + { + "bbox": [ + 61, + 646, + 287, + 660 + ], + "type": "interline_equation", + "content": "R = \\mathbb {E} _ {\\boldsymbol {x} \\sim p _ {x}} \\left[ - \\log_ {2} p _ {i j} \\left(\\boldsymbol {Q} _ {l} \\left(\\boldsymbol {f} \\left(g _ {a} (\\boldsymbol {x})\\right)\\right)\\right) \\right] \\tag {15}", + "image_path": "3d51d5489b2326009b0d0cd775adb96a2ab3297aa08d9eedc7c46e722537110a.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 61, + 662, + 257, + 677 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 662, + 257, + 677 + ], + "spans": [ + { + "bbox": [ + 61, + 662, + 257, + 677 + ], + "type": "interline_equation", + "content": "D = \\lambda \\cdot \\mathbb {E} _ {\\boldsymbol {x} \\sim p _ {x}} \\left[ \\right. d \\left( \\right.\\boldsymbol {x}, g _ {s} \\left(\\boldsymbol {f} ^ {- 1} \\left(\\boldsymbol {Q} _ {l} \\left(\\boldsymbol {f} \\left(g _ {a} (\\boldsymbol {x})\\right)\\right)\\right)\\right)\\left. \\right]", + "image_path": "e875bc15d0e6cca94fcd27190e61ceb303d10fd7b2cd32893c47ec7c5fad5f00.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "inline_equation", + "content": "Q_{l}" + }, + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "content": " is the proposed LVQ module, " + }, + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\pmb{f}" + }, + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\pmb{f}^{-1}" + }, + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "content": " are the learned spatially adaptive A-law function and its inverse." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 72, + 388, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 388, + 85 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 388, + 85 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 91, + 547, + 258 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 91, + 547, + 258 + ], + "spans": [ + { + "bbox": [ + 304, + 91, + 547, + 258 + ], + "type": "text", + "content": "We conduct extensive experiments to systematically evaluate and analyze the effectiveness of the proposed LVQAC scheme. Specifically, we select two representative end-to-end CNN compression architectures Cheng2020 [8] and Minnen2018 [26] and replace their uniform scalar quantizers by the proposed LVQAC module to demonstrate the superiority of LVQAC. We show the R-D performance comparisons between the models with uniform scalar quantization and LVQAC for each architecture, and also provide visual comparisons. Besides, the encoding and decoding latencies are tabulated to validate the computational efficiency of LVQAC. Other analyses such as an ablation study on the effects of each component of LVQAC are further given." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 264, + 463, + 277 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 264, + 463, + 277 + ], + "spans": [ + { + "bbox": [ + 306, + 264, + 463, + 277 + ], + "type": "text", + "content": "4.1. Dataset and Training Details" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 282, + 547, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 282, + 547, + 437 + ], + "spans": [ + { + "bbox": [ + 304, + 282, + 547, + 437 + ], + "type": "text", + "content": "The training dataset consists of the largest 8000 images picked from ImageNet [12], following the previous work [17]. Training images are then random-cropped to " + }, + { + "bbox": [ + 304, + 282, + 547, + 437 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 304, + 282, + 547, + 437 + ], + "type": "text", + "content": " and batched into 16. We train each model using the Adam optimizer with " + }, + { + "bbox": [ + 304, + 282, + 547, + 437 + ], + "type": "inline_equation", + "content": "\\beta - 1 = 0.9" + }, + { + "bbox": [ + 304, + 282, + 547, + 437 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 282, + 547, + 437 + ], + "type": "inline_equation", + "content": "\\beta_{2} = 0.999" + }, + { + "bbox": [ + 304, + 282, + 547, + 437 + ], + "type": "text", + "content": ". Each model is trained with an initial learning rate " + }, + { + "bbox": [ + 304, + 282, + 547, + 437 + ], + "type": "inline_equation", + "content": "10^{-4}" + }, + { + "bbox": [ + 304, + 282, + 547, + 437 + ], + "type": "text", + "content": " for 2000 epochs (1M iterations), and then we decay the learning rate to " + }, + { + "bbox": [ + 304, + 282, + 547, + 437 + ], + "type": "inline_equation", + "content": "10^{-5}" + }, + { + "bbox": [ + 304, + 282, + 547, + 437 + ], + "type": "text", + "content": " for another 100-epoch training. Tests involve two image sets: Kodak (24 images) and CLIC Professional valid set (41 images). The network and the proposed LVQAC module are both implemented in PyTorch [29] and CompressAI [5]. All experiments are conducted with four RTX 2080ti GPUs." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 444, + 465, + 455 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 444, + 465, + 455 + ], + "spans": [ + { + "bbox": [ + 306, + 444, + 465, + 455 + ], + "type": "text", + "content": "4.2. Rate-Distortion Performance" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 462, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 462, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 462, + 547, + 715 + ], + "type": "text", + "content": "We evaluate our LVQAC scheme based on two representative published architectures Cheng2020 [8] and Minnen2018 [26]. The reason for choosing these two architectures is that they are the milestones in the end-to-end optimized image compression area, as Minnen2018 [26] is the first learning-based method to outperform BPG in PSNR metric and Cheng2020 [8] is the first work to achieve comparable performance with latest compression standard Versatile Video Coding (VVC) regarding PSNR. These two architectures were originally proposed with an autoregressive (serial) context model. To fully explore the potentiality of LVQAC, we consider the two architectures with two different context models, namely the autoregressive context model and checkerboard context model [18]. For each architecture, given two different context models, we do not change any other architectures except by replacing the uniform scalar quantizer with the proposed LVQAC scheme. We implement the two representative models coupled with uniform scalar quantizer and LVQAC, respectively. The Lagrange multipliers are set to " + }, + { + "bbox": [ + 304, + 462, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\lambda = \\{0.0016, 0.0032, 0.0075, 0.015, 0.03, 0.045\\}" + }, + { + "bbox": [ + 304, + 462, + 547, + 715 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10243" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 88, + 272, + 241 + ], + "blocks": [ + { + "bbox": [ + 61, + 88, + 272, + 241 + ], + "lines": [ + { + "bbox": [ + 61, + 88, + 272, + 241 + ], + "spans": [ + { + "bbox": [ + 61, + 88, + 272, + 241 + ], + "type": "image", + "image_path": "89a47f5278b5977825875dfcdfbe75f2cf6cef4d1c395a67ae3eae9aa80721e3.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 127, + 247, + 214, + 256 + ], + "lines": [ + { + "bbox": [ + 127, + 247, + 214, + 256 + ], + "spans": [ + { + "bbox": [ + 127, + 247, + 214, + 256 + ], + "type": "text", + "content": "(a) Cheng2020 [8], Kodak." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 313, + 88, + 524, + 241 + ], + "blocks": [ + { + "bbox": [ + 313, + 88, + 524, + 241 + ], + "lines": [ + { + "bbox": [ + 313, + 88, + 524, + 241 + ], + "spans": [ + { + "bbox": [ + 313, + 88, + 524, + 241 + ], + "type": "image", + "image_path": "be765997b7a421dfbd86b7da879f4924ce21fe8ff0bdb6cd00499bdd2ce95fa0.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 375, + 247, + 470, + 256 + ], + "lines": [ + { + "bbox": [ + 375, + 247, + 470, + 256 + ], + "spans": [ + { + "bbox": [ + 375, + 247, + 470, + 256 + ], + "type": "text", + "content": "(b) Minnen2018 [26], Kodak." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 61, + 293, + 269, + 446 + ], + "blocks": [ + { + "bbox": [ + 138, + 266, + 453, + 277 + ], + "lines": [ + { + "bbox": [ + 138, + 266, + 453, + 277 + ], + "spans": [ + { + "bbox": [ + 138, + 266, + 453, + 277 + ], + "type": "text", + "content": "Figure 3. Rate-distortion curves on Kodak dataset. All models are optimized for MSE." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 61, + 293, + 269, + 446 + ], + "lines": [ + { + "bbox": [ + 61, + 293, + 269, + 446 + ], + "spans": [ + { + "bbox": [ + 61, + 293, + 269, + 446 + ], + "type": "image", + "image_path": "f94aa754ff1ab2e46bd0a1d8dc3b40ecc276a3dad9461b7ea448765e9d738562.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 121, + 451, + 219, + 461 + ], + "lines": [ + { + "bbox": [ + 121, + 451, + 219, + 461 + ], + "spans": [ + { + "bbox": [ + 121, + 451, + 219, + 461 + ], + "type": "text", + "content": "(a) Cheng2020 [8], CLIC Pro." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 133, + 471, + 459, + 483 + ], + "lines": [ + { + "bbox": [ + 133, + 471, + 459, + 483 + ], + "spans": [ + { + "bbox": [ + 133, + 471, + 459, + 483 + ], + "type": "text", + "content": "Figure 4. Rate-distortion curves on CLIC Pro dataset. All models are optimized for MSE." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 313, + 294, + 522, + 446 + ], + "blocks": [ + { + "bbox": [ + 313, + 294, + 522, + 446 + ], + "lines": [ + { + "bbox": [ + 313, + 294, + 522, + 446 + ], + "spans": [ + { + "bbox": [ + 313, + 294, + 522, + 446 + ], + "type": "image", + "image_path": "0960480bdd6aefe09d5705f08fb31b4a7707138565543b4ba750a801d2c177dd.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 370, + 451, + 476, + 461 + ], + "lines": [ + { + "bbox": [ + 370, + 451, + 476, + 461 + ], + "spans": [ + { + "bbox": [ + 370, + 451, + 476, + 461 + ], + "type": "text", + "content": "(b) Minnen2018 [26], CLIC Pro." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 498, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 498, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 498, + 289, + 714 + ], + "type": "text", + "content": "Fig. 3 and Fig. 4 graphically presents the rate-distortion behaviors of different methods on Kodak and CLIC Pro datasets in PSNR metric. We can see that for any architecture, no matter with autoregressive or checkerboard context model, replacing uniform quantizer by LVQAC achieves better rate-distortion performance. Besides, LVQAC brings greater performance gain when coupled with the checkerboard context model than being coupled with the autoregressive context model. The CNN model adopted LVQAC + checkerboard context model can achieve a similar performance as the counterpart CNN using a far more expensive autoregressive context model + uniform scalar quantizer, yet the former is much lighter and faster than the latter. We show the detailed computational complexity of LVQAC in subsection 4.4. We can also find that LVQAC can bring more performance gain at the low bit rate than at the high bit rate. This is expected as uniform quantization can approach the rate-distortion optimality at very high bit rate [15]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 497, + 419, + 510 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 497, + 419, + 510 + ], + "spans": [ + { + "bbox": [ + 306, + 497, + 419, + 510 + ], + "type": "text", + "content": "4.3. Visual Comparison" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "text", + "content": "We also provide visual comparisons to demonstrate the effectiveness of the proposed LVQAC scheme. Fig. 5, 6 and 7 show the visual results of different methods, including BPG, Cheng2020 with scalar quantizer, Cheng2002 with LVQAC and the Ground Truth. We pick three images 'kodim01.png', 'kodim07.png' and 'kodim10.png' from Kodak dataset to show the comparisons. The bit rates of all methods are adjusted to the same level for the fairness. In Fig. 5, LVQAC can preserve the sharper edges on doors than uniform scalar quantizer. In Fig. 6, LVQAC also achieves richer and clearer textures on flowers over uniform scalar quantizer. Another interesting observation is that the faint lines in Fig. 7 are both removed by BPG and scalar quantizer, but LVQAC can preserve such features. These observations reveal that the end-to-end CNN compression model coupled with LVQAC can produce much sharper edges and" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10244" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 70, + 168, + 155 + ], + "blocks": [ + { + "bbox": [ + 49, + 70, + 168, + 155 + ], + "lines": [ + { + "bbox": [ + 49, + 70, + 168, + 155 + ], + "spans": [ + { + "bbox": [ + 49, + 70, + 168, + 155 + ], + "type": "image", + "image_path": "352f5bd22f9bef7d6cdfe2448cdf95c20a6d67a8fe46c74edfdc9daf10044943.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 94, + 157, + 123, + 166 + ], + "lines": [ + { + "bbox": [ + 94, + 157, + 123, + 166 + ], + "spans": [ + { + "bbox": [ + 94, + 157, + 123, + 166 + ], + "type": "text", + "content": "(a) BPG" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 173, + 70, + 294, + 156 + ], + "blocks": [ + { + "bbox": [ + 173, + 70, + 294, + 156 + ], + "lines": [ + { + "bbox": [ + 173, + 70, + 294, + 156 + ], + "spans": [ + { + "bbox": [ + 173, + 70, + 294, + 156 + ], + "type": "image", + "image_path": "066af03a15da9916d208aca95fb7d77ff5b5566a65d7021945c9e60a3052f50f.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 198, + 157, + 271, + 167 + ], + "lines": [ + { + "bbox": [ + 198, + 157, + 271, + 167 + ], + "spans": [ + { + "bbox": [ + 198, + 157, + 271, + 167 + ], + "type": "text", + "content": "(b) Cheng2020, Scalar" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 299, + 70, + 420, + 156 + ], + "blocks": [ + { + "bbox": [ + 299, + 70, + 420, + 156 + ], + "lines": [ + { + "bbox": [ + 299, + 70, + 420, + 156 + ], + "spans": [ + { + "bbox": [ + 299, + 70, + 420, + 156 + ], + "type": "image", + "image_path": "3eae9b47cb71b38d4e246e01ec1f4b34c09b09b57ad402bf753b39967dad87e9.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 320, + 157, + 399, + 167 + ], + "lines": [ + { + "bbox": [ + 320, + 157, + 399, + 167 + ], + "spans": [ + { + "bbox": [ + 320, + 157, + 399, + 167 + ], + "type": "text", + "content": "(c) Cheng2020, LVQAC" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 425, + 70, + 545, + 156 + ], + "blocks": [ + { + "bbox": [ + 425, + 70, + 545, + 156 + ], + "lines": [ + { + "bbox": [ + 425, + 70, + 545, + 156 + ], + "spans": [ + { + "bbox": [ + 425, + 70, + 545, + 156 + ], + "type": "image", + "image_path": "6b60879132a2e91616eab4828261cbda81de5ca31e5376e90d3da132f7c19aca.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 457, + 157, + 513, + 166 + ], + "lines": [ + { + "bbox": [ + 457, + 157, + 513, + 166 + ], + "spans": [ + { + "bbox": [ + 457, + 157, + 513, + 166 + ], + "type": "text", + "content": "(d) Ground Truth" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 49, + 198, + 168, + 284 + ], + "blocks": [ + { + "bbox": [ + 49, + 198, + 168, + 284 + ], + "lines": [ + { + "bbox": [ + 49, + 198, + 168, + 284 + ], + "spans": [ + { + "bbox": [ + 49, + 198, + 168, + 284 + ], + "type": "image", + "image_path": "26a1be0f0fed15ee28142d8973fd26defc87e0e957c0286ccffdbd77f64d4e24.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 95, + 285, + 123, + 294 + ], + "lines": [ + { + "bbox": [ + 95, + 285, + 123, + 294 + ], + "spans": [ + { + "bbox": [ + 95, + 285, + 123, + 294 + ], + "type": "text", + "content": "(a) BPG" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 173, + 198, + 294, + 284 + ], + "blocks": [ + { + "bbox": [ + 133, + 176, + 459, + 188 + ], + "lines": [ + { + "bbox": [ + 133, + 176, + 459, + 188 + ], + "spans": [ + { + "bbox": [ + 133, + 176, + 459, + 188 + ], + "type": "text", + "content": "Figure 5. Visual comparisons of different methods on 'kodim01.png' from Kodak dataset." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 173, + 198, + 294, + 284 + ], + "lines": [ + { + "bbox": [ + 173, + 198, + 294, + 284 + ], + "spans": [ + { + "bbox": [ + 173, + 198, + 294, + 284 + ], + "type": "image", + "image_path": "8c0a548c630c1ecdec11c4b9fadb0d7edc76c52df90f0e1a98bf8c1c11fcfa13.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 198, + 285, + 271, + 295 + ], + "lines": [ + { + "bbox": [ + 198, + 285, + 271, + 295 + ], + "spans": [ + { + "bbox": [ + 198, + 285, + 271, + 295 + ], + "type": "text", + "content": "(b) Cheng2020, Scalar" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 299, + 198, + 420, + 284 + ], + "blocks": [ + { + "bbox": [ + 299, + 198, + 420, + 284 + ], + "lines": [ + { + "bbox": [ + 299, + 198, + 420, + 284 + ], + "spans": [ + { + "bbox": [ + 299, + 198, + 420, + 284 + ], + "type": "image", + "image_path": "2e9501b79c430ded00fea7eec2f2af9adbf04a0afcfc4a465b6ca1cb95ea8a25.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 320, + 285, + 399, + 295 + ], + "lines": [ + { + "bbox": [ + 320, + 285, + 399, + 295 + ], + "spans": [ + { + "bbox": [ + 320, + 285, + 399, + 295 + ], + "type": "text", + "content": "(c) Cheng2020, LVQAC" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 425, + 198, + 545, + 284 + ], + "blocks": [ + { + "bbox": [ + 425, + 198, + 545, + 284 + ], + "lines": [ + { + "bbox": [ + 425, + 198, + 545, + 284 + ], + "spans": [ + { + "bbox": [ + 425, + 198, + 545, + 284 + ], + "type": "image", + "image_path": "e1e6d725b2bdd5ed4911cff76fdb306b22d1c99a62767e378972193b87d6bb0d.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 457, + 285, + 513, + 294 + ], + "lines": [ + { + "bbox": [ + 457, + 285, + 513, + 294 + ], + "spans": [ + { + "bbox": [ + 457, + 285, + 513, + 294 + ], + "type": "text", + "content": "(d) Ground Truth" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 49, + 327, + 168, + 507 + ], + "blocks": [ + { + "bbox": [ + 133, + 304, + 459, + 316 + ], + "lines": [ + { + "bbox": [ + 133, + 304, + 459, + 316 + ], + "spans": [ + { + "bbox": [ + 133, + 304, + 459, + 316 + ], + "type": "text", + "content": "Figure 6. Visual comparisons of different methods on 'kodim07.png' from Kodak dataset." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 49, + 327, + 168, + 507 + ], + "lines": [ + { + "bbox": [ + 49, + 327, + 168, + 507 + ], + "spans": [ + { + "bbox": [ + 49, + 327, + 168, + 507 + ], + "type": "image", + "image_path": "d4bcf25305e24c72dcf83a55bf2cd733d9d63e29ad745684f4d440db247a187c.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 95, + 510, + 123, + 518 + ], + "lines": [ + { + "bbox": [ + 95, + 510, + 123, + 518 + ], + "spans": [ + { + "bbox": [ + 95, + 510, + 123, + 518 + ], + "type": "text", + "content": "(a) BPG" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 133, + 528, + 459, + 540 + ], + "lines": [ + { + "bbox": [ + 133, + 528, + 459, + 540 + ], + "spans": [ + { + "bbox": [ + 133, + 528, + 459, + 540 + ], + "type": "text", + "content": "Figure 7. Visual comparisons of different methods on 'kodim10.png' from Kodak dataset." + } + ] + } + ], + "index": 26, + "angle": 0, + "type": "image_caption" + } + ], + "index": 18 + }, + { + "type": "image", + "bbox": [ + 173, + 327, + 294, + 507 + ], + "blocks": [ + { + "bbox": [ + 173, + 327, + 294, + 507 + ], + "lines": [ + { + "bbox": [ + 173, + 327, + 294, + 507 + ], + "spans": [ + { + "bbox": [ + 173, + 327, + 294, + 507 + ], + "type": "image", + "image_path": "acf5a728a081b3c0a0564829fe3dcd9eef6473a0ba9c73b026cfc4fd4b919afe.jpg" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 198, + 510, + 271, + 518 + ], + "lines": [ + { + "bbox": [ + 198, + 510, + 271, + 518 + ], + "spans": [ + { + "bbox": [ + 198, + 510, + 271, + 518 + ], + "type": "text", + "content": "(b) Cheng2020, Scalar" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_caption" + } + ], + "index": 20 + }, + { + "type": "image", + "bbox": [ + 299, + 327, + 420, + 507 + ], + "blocks": [ + { + "bbox": [ + 299, + 327, + 420, + 507 + ], + "lines": [ + { + "bbox": [ + 299, + 327, + 420, + 507 + ], + "spans": [ + { + "bbox": [ + 299, + 327, + 420, + 507 + ], + "type": "image", + "image_path": "ae93e15e28c994be5fcfd08822edd5f36c14194b25d7e41e38af9df1445d5cf9.jpg" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 320, + 509, + 399, + 518 + ], + "lines": [ + { + "bbox": [ + 320, + 509, + 399, + 518 + ], + "spans": [ + { + "bbox": [ + 320, + 509, + 399, + 518 + ], + "type": "text", + "content": "(c) Cheng2020, LVQAC" + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_caption" + } + ], + "index": 22 + }, + { + "type": "image", + "bbox": [ + 425, + 327, + 545, + 507 + ], + "blocks": [ + { + "bbox": [ + 425, + 327, + 545, + 507 + ], + "lines": [ + { + "bbox": [ + 425, + 327, + 545, + 507 + ], + "spans": [ + { + "bbox": [ + 425, + 327, + 545, + 507 + ], + "type": "image", + "image_path": "4c105ef06e31692cdc158441df1a7a6f270337b17fb5bb74d31321a5d7b7ab3d.jpg" + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 457, + 509, + 513, + 518 + ], + "lines": [ + { + "bbox": [ + 457, + 509, + 513, + 518 + ], + "spans": [ + { + "bbox": [ + 457, + 509, + 513, + 518 + ], + "type": "text", + "content": "(d) Ground Truth" + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "image_caption" + } + ], + "index": 24 + }, + { + "bbox": [ + 46, + 561, + 287, + 597 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 561, + 287, + 597 + ], + "spans": [ + { + "bbox": [ + 46, + 561, + 287, + 597 + ], + "type": "text", + "content": "clearer textures than the counterpart CNN coupled with scalar quantizer. We present more high-resolution visual examples in the supplementary material." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 47, + 609, + 222, + 623 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 609, + 222, + 623 + ], + "spans": [ + { + "bbox": [ + 47, + 609, + 222, + 623 + ], + "type": "text", + "content": "4.4. Encoding and Decoding Latency" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "content": "We provide a detailed analysis of encoding and decoding latency in this subsection. Specifically, we evaluate the inference latency of end-to-end CNN compression models with different quantizers: uniform scalar quantizer and the proposed LVQAC. Table 1 tabulate the encoding time and decoding time of different architectures coupled with scalar quantizer and LVQAC. We can see that, for the ar" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 304, + 561, + 547, + 705 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 561, + 547, + 705 + ], + "spans": [ + { + "bbox": [ + 304, + 561, + 547, + 705 + ], + "type": "text", + "content": "chitecture Cheng2020 with checkerboard context, LVQAC only increases the encoding time by about " + }, + { + "bbox": [ + 304, + 561, + 547, + 705 + ], + "type": "inline_equation", + "content": "15\\%" + }, + { + "bbox": [ + 304, + 561, + 547, + 705 + ], + "type": "text", + "content": " and the decoding time by about " + }, + { + "bbox": [ + 304, + 561, + 547, + 705 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 304, + 561, + 547, + 705 + ], + "type": "text", + "content": ", yet improves the performance to the same level as that using autoregressive context. It is noteworthy that the decoding time of the model using autoregressive context is two orders of magnitude higher than that of the checkerboard context. For the architecture Cheng2020 with autoregressive context model, the increase of encoding time is about " + }, + { + "bbox": [ + 304, + 561, + 547, + 705 + ], + "type": "inline_equation", + "content": "17\\%" + }, + { + "bbox": [ + 304, + 561, + 547, + 705 + ], + "type": "text", + "content": ", and the increase of decoding time is negligible due to the huge base " + }, + { + "bbox": [ + 304, + 561, + 547, + 705 + ], + "type": "inline_equation", + "content": "(>10^{3})" + }, + { + "bbox": [ + 304, + 561, + 547, + 705 + ], + "type": "text", + "content": ". Similar observations can be obtained on the Minnen2018 architecture. These observations reveal that replacing uniform quantizer" + } + ] + } + ], + "index": 30 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10245" + } + ] + } + ], + "index": 31 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 93, + 102, + 501, + 236 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 547, + 94 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 547, + 94 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 547, + 94 + ], + "type": "text", + "content": "Table 1. BD-Rates and inference times of different methods. The BD-Rate data is calculated relative to VVC (YUV 444) from PSNR-BPP curve on Kodak. [A] represents the autoregressive context model, [C] represents the checkerboard context model." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 93, + 102, + 501, + 236 + ], + "lines": [ + { + "bbox": [ + 93, + 102, + 501, + 236 + ], + "spans": [ + { + "bbox": [ + 93, + 102, + 501, + 236 + ], + "type": "table", + "html": "
ArchitectureContext + QuantizerBD-Rate (%)Enc. Time (ms)Dec. Time (ms)
Cheng2020 [8][A] + LVQAC3.1248.65>103
[A] + Scalar3.3541.42>103
[C] + LVQAC3.3952.6655.84
[C] + Scalar3.8945.4353.01
Minnen2018 [26][A] + LVQAC14.7525.87>103
[A] + Scalar14.9218.14>103
[C] + LVQAC16.1726.2327.10
[C] + Scalar20.0018.8424.52
", + "image_path": "4e487e94344639d264330595c19bf213742cef4ff61ca3146b10dc3fdfe7ee7b.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 251, + 288, + 301 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 251, + 288, + 301 + ], + "spans": [ + { + "bbox": [ + 46, + 251, + 288, + 301 + ], + "type": "text", + "content": "by LVQAC can achieve better rate-distortion performance without significantly increasing the model complexity; the simpler the context-sensitive entropy model, the greater the performance gain." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 306, + 141, + 319 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 306, + 141, + 319 + ], + "spans": [ + { + "bbox": [ + 47, + 306, + 141, + 319 + ], + "type": "text", + "content": "4.5. Ablation Study" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 324, + 288, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 324, + 288, + 456 + ], + "spans": [ + { + "bbox": [ + 46, + 324, + 288, + 456 + ], + "type": "text", + "content": "To investigate the impacts of the proposed LVQAC scheme, we conduct an ablation study to investigate the importance of each component in the proposed LVQAC scheme. We experiment progressively to explore the respective contribution of the lattice vector quantization module and spatially adaptive companding module. Specifically, we progressively add LVQ and AC modules into the network and test the coding performance. Table 2 shows the results of the ablation study. It can be seen that lattice vector quantization and spatially adaptive companding contribute almost equally to the performance gain." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 462, + 119, + 474 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 462, + 119, + 474 + ], + "spans": [ + { + "bbox": [ + 47, + 462, + 119, + 474 + ], + "type": "text", + "content": "4.6. Limitation" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 480, + 287, + 636 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 480, + 287, + 636 + ], + "spans": [ + { + "bbox": [ + 46, + 480, + 287, + 636 + ], + "type": "text", + "content": "The main limitation of this work relies on that it is difficult to know the optimal lattice structure for any given dimension. In this paper, we choose the diamond lattice structure due to its simplicity and easy extension to any dimension. However, even though diamond lattice is not the optimal lattice structure in the vast majority of cases, it is still much more efficient than uniform scalar quantizer without significantly increasing the model complexity. Another limitation of LVQAC is that if the context model is complex and powerful enough, such as an autoregressive context, then the gain brought by LVQAC will be very limited. Thus the application of LVQAC may be restricted to those lightweight end-to-end CNN compression models." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 645, + 212, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 645, + 212, + 658 + ], + "spans": [ + { + "bbox": [ + 47, + 645, + 212, + 658 + ], + "type": "text", + "content": "5. Conclusion and Future Work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": "In this paper, we present a novel Lattice Vector Quantization scheme coupled with a spatially Adaptive Companding (LVQAC) mapping. LVQ can better exploit the inter-feature dependencies than scalar uniform quantization while being" + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 308, + 303, + 543, + 552 + ], + "blocks": [ + { + "bbox": [ + 305, + 251, + 547, + 295 + ], + "lines": [ + { + "bbox": [ + 305, + 251, + 547, + 295 + ], + "spans": [ + { + "bbox": [ + 305, + 251, + 547, + 295 + ], + "type": "text", + "content": "Table 2. Results of the progressive ablation study. The BD-Rate data is calculated relative to VVC (YUV 444) from PSNR-BPP curve on Kodak. [A] represents the autoregressive context model, [C] represents the checkerboard context model." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 303, + 543, + 552 + ], + "lines": [ + { + "bbox": [ + 308, + 303, + 543, + 552 + ], + "spans": [ + { + "bbox": [ + 308, + 303, + 543, + 552 + ], + "type": "table", + "html": "
ArchitectureContext + QuantizerBD-Rate
Cheng2020 [8][A] + LVQ + AC3.12
[A] + LVQ3.24
[A] + Scalar + AC3.30
[A] + Scalar3.35
[C] + LVQ + AC3.39
[C] + LVQ3.68
[C] + Scalar + AC3.82
[C] + Scalar3.89
Minnen2018 [26][A] + LVQ + AC14.75
[A] + LVQ14.86
[A] + Scalar + AC14.88
[A] + Scalar14.92
[C] + LVQ + AC16.17
[C] + LVQ18.43
[C] + Scalar + AC19.29
[C] + Scalar20.00
", + "image_path": "5c15d4daf88f5bc746ae49603561dd0a815148fbc598ed114b7c05dcfe489006.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "content": "computationally almost as simple as the latter. Moreover, to improve the adaptability of LVQ to source statistics, we couple a spatially adaptive companding (AC) mapping with LVQ. The resulting LVQAC design can be easily embedded into any end-to-end optimized image compression system. Extensive experiments demonstrate that for any end-to-end CNN image compression models, replacing uniform quantizer by LVQAC achieves better rate-distortion performance without significantly increasing the model complexity. Future work will focus on exploring the optimal lattice vector quantizer for a given dimension and how to embed it into the end-to-end image compression system." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "10246" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 156 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 156 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 156 + ], + "type": "text", + "content": "[1] Eirikur Agustsson, Fabian Mentzer, Michael Tschannen, Lukas Cavigelli, Radu Timofte, Luca Benini, and Luc Van Gool. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 17612-17621, 2022. 2" + } + ] + } + ], + "index": 20 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10248" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Label Information Bottleneck for Label Enhancement/17915eba-e6e6-4f83-bad7-de11a7a573e3_content_list.json b/2023/Label Information Bottleneck for Label Enhancement/17915eba-e6e6-4f83-bad7-de11a7a573e3_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..d8629774a9471b9a7720ca650131abe56ebd1371 --- /dev/null +++ b/2023/Label Information Bottleneck for Label Enhancement/17915eba-e6e6-4f83-bad7-de11a7a573e3_content_list.json @@ -0,0 +1,2009 @@ +[ + { + "type": "text", + "text": "Label Information Bottleneck for Label Enhancement", + "text_level": 1, + "bbox": [ + 210, + 130, + 756, + 150 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Qinghai Zheng $^{1}$ , Jihua Zhu $^{2*}$ , Haoyu Tang $^{3}$", + "bbox": [ + 308, + 179, + 658, + 199 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1College of Computer and Data Science, Fuzhou University, China", + "bbox": [ + 220, + 198, + 748, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{2}$ School of Software Engineering, Xi'an Jiaotong University, Xi'an, China", + "bbox": [ + 192, + 215, + 776, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{3}$ School of Software, Shandong University, Jinan, China", + "bbox": [ + 263, + 233, + 705, + 251 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 286, + 313, + 301 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this work, we focus on the challenging problem of Label Enhancement (LE), which aims to exactly recover label distributions from logical labels, and present a novel Label Information Bottleneck (LIB) method for LE. For the recovery process of label distributions, the label irrelevant information contained in the dataset may lead to unsatisfactory recovery performance. To address this limitation, we make efforts to excavate the essential label relevant information to improve the recovery performance. Our method formulates the LE problem as the following two joint processes: 1) learning the representation with the essential label relevant information, 2) recovering label distributions based on the learned representation. The label relevant information can be excavated based on the \"bottleneck\" formed by the learned representation. Significantly, both the label relevant information about the label assignments and the label relevant information about the label gaps can be explored in our method. Evaluation experiments conducted on several benchmark label distribution learning datasets verify the effectiveness and competitiveness of LIB. Our source codes are available at https://github.com/qinghai-zheng/LIBLE", + "bbox": [ + 75, + 318, + 473, + 650 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 681, + 209, + 698 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Learning with label ambiguity is important in computer vision and machine learning. Different from the traditional Multi-Label Learning (MLL), which employs multiple logical labels to annotate one instance to address the label ambiguity issue [20], Label Distribution Learning (LDL) considers the relative importance of different labels and draws much attention in recent years [6,8,14,18,26]. By distinguishing the description degrees of all labels, LDL annotates one instance with a label distribution. Therefore, LDL is a more general learning paradigm, MLL can be regarded as a special case of LDL [8,10,12].", + "bbox": [ + 75, + 708, + 468, + 875 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, many LDL methods are proposed and achieve great success in practice [3, 9, 14, 18]. Instances with exact label distributions are vital for the training process of LDL methods. Nevertheless, annotating instances with label distributions is time-consuming [24, 28]. We take the label distribution annotation process of SJAFFE dataset for example here. SJAFFE dataset is the facial expression dataset, which contains 213 grayscale images collected from 10 Japanese female models, each facial expression image is rated by 60 persons on 6 basic emotions, including happiness, surprise, sadness, fear, anger, and disgust, with a five-level scale from 1 - 5, the higher value indicates the higher emotion intensity. Consequently, the average score of each emotion is served as the emotion label distribution [14, 28]. Clearly, the above annotation process is costly and it is unpractical to annotate data with label distributions manually, especially when the number of data is large. Fortunately, most existing datasets in the field of computer vision and machine learning are annotated by single-label or multi-labels [7, 29], therefore, a highly recommended promising solution is Label Enhancement (LE), which attempts to recover the desired label distributions exactly from existing logical labels [24, 28, 32].", + "bbox": [ + 500, + 287, + 892, + 619 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Driven by the urgent requirement of obtaining label distributions and the convenience of LE, some LE methods are proposed in recent years [5, 7, 11, 13, 15, 17, 21, 24, 28, 29]. Given a dataset $\\mathbf{X} = \\{\\pmb{x}_1, \\pmb{x}_2, \\dots, \\pmb{x}_n\\} \\in \\mathbb{R}^{q \\times n}$ , in which $q$ and $n$ denote the number of dimensions and the number of instances, the potential label set is $\\{y_1, y_2, \\dots, y_c\\}$ . The available logical labels and the desired distribution labels of $\\mathbf{X}$ are separately indicated by $\\mathbf{L} = \\{l_1, l_2, \\dots, l_n\\}$ and $\\mathbf{D} = \\{d_1, d_2, \\dots, d_n\\}$ , where $l_i$ and $d_i$ are:", + "bbox": [ + 498, + 619, + 893, + 756 + ], + "page_idx": 0 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {l} _ {i} = \\left(l _ {i} ^ {y _ {1}}, l _ {i} ^ {y _ {2}}, \\dots , l _ {i} ^ {y _ {c}}\\right) ^ {T}, \\boldsymbol {d} _ {i} = \\left(d _ {i} ^ {y _ {1}}, d _ {i} ^ {y _ {2}}, \\dots , d _ {i} ^ {y _ {c}}\\right) ^ {T}. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 509, + 762, + 892, + 781 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To be specific, LE aims to recover $D$ based on the information provided by $X$ and $L$ . For most existing LE methods, their objectives can be concisely summarized as follows:", + "bbox": [ + 498, + 787, + 890, + 833 + ], + "page_idx": 0 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\theta} \\| f _ {\\theta} (\\boldsymbol {X}) - \\boldsymbol {L} \\| _ {F} ^ {2} + \\gamma r e g (f _ {\\theta} (\\boldsymbol {X})), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 563, + 839, + 890, + 864 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "in which $\\pmb{D} = f_{\\theta}(\\pmb{X})$ , $f_{\\theta}(\\cdot)$ indicates the mapping from $\\pmb{X}$ to $\\pmb{D}$ , $reg(\\cdot)$ denotes the regularization function, and $\\gamma$", + "bbox": [ + 500, + 869, + 892, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author, E-mail: zhujh@xjtu.edu.cn", + "bbox": [ + 94, + 886, + 367, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "7497", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/938d1516c60e7eae4d0f313b03c47b436a880ccd51e138931954df05b4858467.jpg", + "image_caption": [ + "Figure 1. Illustration of label relevant information. Excavating the essential label relevant information directly is challenging and we adopt a indirect way here. We jointly investigate the information about the assignments of labels to the instance and the information about the label gaps between logical labels and label distributions. Given the $i$ -th instance $\\pmb{x}_i$ , the label gap of the $y_j$ label is $\\delta_i^{y_j} = l_i^{y_j} - d_i^{y_j}$ . The information contained in $l_i^{y_j}$ and $\\delta_i^{y_j}$ can be amalgamated to form the essential label relevant information. In other words, we employ $l_i^{y_j}$ to explore the label relevant information about the label assignments and $\\delta_i^{y_j}$ to excavate the label relevant information about the label gaps. To a certain degree, the combination of $\\delta_i^{y_j}$ and $l_i^{y_j}$ is equivalent to $d_i^{y_j}$ . As depicted here, $l_i^{y_j}$ indicates that $y_1$ and $y_3$ are related labels and $\\delta_i^{y_j}$ provides the importance of $y_1$ and $y_3$ ." + ], + "image_footnote": [], + "bbox": [ + 133, + 88, + 410, + 276 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "is the trade-off parameter. Most existing LE methods vary in $reg(\\cdot)$ . For example, GLLE [28] calculates the distance-based similarity matrix of data and employs the smoothness assumption [33] to construct $reg(\\cdot)$ ; LESC [24] considers the global sample correlations and introduces the low-rank constraint as the regularization; PNLR [13] leverages $reg(\\cdot)$ to maintain positive and negative label relations during the recovery process. Although a remarkable progress can be made by aforementioned methods, they ignore the label irrelevant information contained in $X$ , which prevents the further improvement of recovery results. For example, in the LE task of recovering facial age label distributions, the label irrelevant information, such as peculiarities information, cast shadows information, and occlusions information, may result in the incorrect mapping process of $f_{\\theta}(\\cdot)$ and the unsuitable regularization of $reg(\\cdot)$ , eventually leads to the unsatisfactory recovery performance.", + "bbox": [ + 75, + 507, + 468, + 763 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To overcome the aforementioned limitation, we present a Label Information Bottleneck (LIB) method for LE. Concretely, the core idea of LIB is to learn the latent representation $\\pmb{H}$ , which preserves the maximum label relevant information, from $\\pmb{X}$ , and jointly recovers the label distributions based on the latent representation. For the LE problem, the label relevant information is the information that describes the description degrees of labels. It is tough to explore the label relevant information directly. As shown in Fig. 1, we", + "bbox": [ + 75, + 765, + 470, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "decompose the label relevant information into two components, namely the assignments of labels to the instance and the label gaps between label distributions and logical labels. Inspired by Information Bottleneck (IB) [25], LIB utilizes the existing logical labels to explore the information about the assignments of labels to the instance. Unlike simply employing the original IB on the LE task, our method further considers the information about the label gaps between label distributions and logical labels. It is noteworthy that the above two components of the label relevant information are jointly explored in our method, and that is why we term the proposed method Label Information Bottleneck (LIB). The main contributions can be summarized as follows:", + "bbox": [ + 496, + 90, + 890, + 287 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We decompose the label relevant information into the information about the assignments of labels to instance and the information about the label gaps between logical labels, both of which can be jointly explored during the learning process of our method.", + "- We introduce a novel LE method, termed LIB, which excavates the label relevant information to exactly recover the label distributions. Based on the original IB, which explores the label assignments information for LE, LIB further explores the label gaps information.", + "- We verify the effectiveness of LIB by performing extensive experiments on several datasets. Experimental results show that the proposed method can achieve the competitive performance, compared to state-of-the-art LE methods." + ], + "bbox": [ + 514, + 294, + 890, + 537 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 550, + 640, + 566 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Label Enhancement", + "text_level": 1, + "bbox": [ + 500, + 575, + 689, + 589 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To recover the label distributions from the existing logical labels, many efforts are made recently [24, 28]. In general, most existing LE methods can be roughly divided into two categories, namely, algorithm adaptation and specialized algorithm [8, 24].", + "bbox": [ + 496, + 598, + 890, + 672 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Algorithm adaptation extends some existing methods to achieve the goal of LE [5, 15]. For example, FCM [5] recovers the label distributions by utilizing the fuzzy clustering and fuzzy relabeling. To be specific, FCM utilizes the fuzzy C-means clustering to get different clusters and cluster prototypes, then obtains membership degrees of each instance with respect to different cluster prototypes, finally annotates all instances with label distributions by employing the fuzzy composition and softmax normalization. KM [15] leverages the fuzzy SVM to achieve the membership function. During the recovery process, KM separates instances into two clusters and employs the nonlinear function to get the radius and distances between centers and kernelized instances, and then gets the label distributions with the help of the softmax normalization.", + "bbox": [ + 496, + 674, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "7498", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Specialized algorithm is specially designed to deal with the LE problem. Most existing LE methods belong to the category of specialized algorithm and have the basic objective Eq. (2). By using different constraints, different methods adopt different $reg(\\cdot)$ in Eq. (2). For example, based on the assumption that instances closed in the feature space are more likely to share the same label, GLLE [28] employs the following local graph information in the feature space to boost the recovery performance:", + "bbox": [ + 75, + 90, + 472, + 227 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nq _ {i, j} = \\left\\{ \\begin{array}{l} \\exp \\left(- \\frac {\\left\\| \\boldsymbol {x} _ {i} - \\boldsymbol {x} _ {j} \\right\\| ^ {2}}{2 \\varepsilon^ {2}}\\right), \\text {i f} \\boldsymbol {x} _ {j} \\in k (i), \\\\ 0, \\text {o t h e r w i s e}, \\end{array} \\right. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 114, + 236, + 468, + 296 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $k(i)$ denotes the $k$ -nearest neighbours of $\\pmb{x}_i$ . $reg(\\cdot)$ in GLLE is constructed as follows:", + "bbox": [ + 76, + 306, + 468, + 335 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nr e g \\left(f _ {\\theta} (\\boldsymbol {X})\\right) = \\sum_ {i, j} q _ {i, j} \\left\\| f _ {\\theta} \\left(\\boldsymbol {x} _ {i}\\right) - f _ {\\theta} \\left(\\boldsymbol {x} _ {j}\\right) \\right\\| _ {2} ^ {2}. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 122, + 343, + 468, + 377 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Unlike GLLE, LESC [24] considers the global graph information and uses the low-rank representation learning [19]:", + "bbox": [ + 76, + 385, + 468, + 417 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\boldsymbol {G}, \\boldsymbol {E}} \\| \\boldsymbol {G} \\| _ {*} + \\lambda_ {2} \\| \\boldsymbol {E} \\| _ {2, 1}, \\text {s . t . ,} \\boldsymbol {X} = \\boldsymbol {X} \\boldsymbol {G} + \\boldsymbol {E}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 114, + 430, + 468, + 454 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $G$ indicates the low-rank representation of instances in the feature space. The regularization function in LESC is written as follows:", + "bbox": [ + 76, + 458, + 468, + 503 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nr e g (f _ {\\theta} (\\pmb {X})) = \\| f _ {\\theta} (\\pmb {X}) - f _ {\\theta} (\\pmb {X}) \\pmb {G} \\| _ {F} ^ {2}. \\qquad (6)\n$$\n", + "text_format": "latex", + "bbox": [ + 138, + 512, + 468, + 532 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For these aforementioned LE methods, they all neglect the label irrelevant information contained in $X$ , the negative effect of which can result in the unsatisfactory recovery results. Taking the recovery of facial emotion label distributions for example, the inaccurate graph information would be obtained in GLLE and LESSC with the presence of label irrelevant information, such as the identity information, hindering the further improvement of recovery results.", + "bbox": [ + 75, + 541, + 468, + 662 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Information Bottleneck", + "text_level": 1, + "bbox": [ + 76, + 670, + 294, + 686 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Information bottleneck (IB) [1, 25, 25] is an information theoretic principle, which describes the relevant information in data formally. To be concrete, IB has the following objective:", + "bbox": [ + 75, + 693, + 468, + 753 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\boldsymbol {B}} - I (\\boldsymbol {B}, \\boldsymbol {C}), \\text {s . t .}, I (\\boldsymbol {A}, \\boldsymbol {B}) \\leqslant I _ {c}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 143, + 763, + 468, + 787 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $I(\\cdot, \\cdot)$ measures the mutual information and $I_{c}$ is the information constraint. Clearly, IB aims to learn the representation $\\pmb{B}$ , which preserves the relevant information about $\\pmb{C}$ , from $\\pmb{A}$ . Considering the scenario of LE, it is natural to get the following formula:", + "bbox": [ + 76, + 795, + 468, + 872 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\boldsymbol {H}} - I (\\boldsymbol {H}, \\boldsymbol {L}), \\text {s . t .}, I (\\boldsymbol {X}, \\boldsymbol {H}) \\leqslant I _ {c}. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 142, + 882, + 468, + 904 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/3a32c40ca8c4da719214278990048c1ffa7bc42cc60e02604ce68f7b852dc16f.jpg", + "image_caption": [ + "Figure 2. Framework of the proposed LIB. Since the way that directly explores the label relevant information is challenging, LIB decomposes the label relevant information into two components, namely the assignments of labels to the instance and the label gaps between label distributions and logical labels, and adopts an indirect path, which explores the information about label assignments and label gaps simultaneously. By minimizing $\\mathcal{L}_{as}$ , LIB explores the information about assignments of labels to the instance. Meanwhile, by minimizing $\\mathcal{L}_{gap}$ , LIB explores the information about the label gaps between logical labels and label distributions. Consequently, the label relevant information can be effectively explored and the label distributions can be exactly recovered." + ], + "image_footnote": [], + "bbox": [ + 517, + 88, + 877, + 268 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As discussed in Section 1, the information merely about the assignments of labels to the instance can be explored based on Eq. (8), which neglects the vital information about the label gaps between logical labels and label distributions.", + "bbox": [ + 496, + 469, + 890, + 529 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Recently, IB has been successfully utilized in many real-world applications [1, 2, 22, 27, 30, 31]. To the best of our knowledge, the method introduced in this paper is the first work that leverages IB to deal with the LE problem. More notably, rather than using IB simply (as shown in Eq. (8)), our method conducts more in-depth exploration to exactly recover label distributions based on IB.", + "bbox": [ + 496, + 530, + 890, + 635 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. The Proposed Method", + "text_level": 1, + "bbox": [ + 500, + 647, + 710, + 666 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. The Objective Construction", + "text_level": 1, + "bbox": [ + 500, + 672, + 750, + 689 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Generally, the basic idea can be written as follows:", + "bbox": [ + 517, + 696, + 854, + 710 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\boldsymbol {H}} \\mathcal {L} _ {a s} + \\alpha \\mathcal {L} _ {g a p}, \\text {s . t .}, I (\\boldsymbol {X}, \\boldsymbol {H}) \\leqslant I _ {c}, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 542, + 720, + 890, + 743 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_{as}$ excavates the information about the assignments of labels to the instance, $\\mathcal{L}_{gap}$ investigates the information about the label gaps between the logical labels and distribution labels, $\\alpha$ is the trade-off parameter, the constraint aims to remove the label irrelevant information. The framework of our method is depicted in Fig. 2. It's worth noting that employing the original IB for LE merely explores the information about the label assignments. While our LIB makes attempts to capture the information about both the label assignments and the description degrees of labels.", + "bbox": [ + 496, + 750, + 890, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "7499", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1.1 Label assignments information modeling", + "text_level": 1, + "bbox": [ + 76, + 90, + 410, + 107 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For $\\mathcal{L}_{as}$ , inspired by IB, we have the following formula:", + "bbox": [ + 76, + 114, + 447, + 130 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {a s} = - I (\\boldsymbol {H}, \\boldsymbol {L}). \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 207, + 138, + 468, + 154 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "According to the concept of mutual information, $\\mathcal{L}_{as}$ can be rewritten out in full as follows:", + "bbox": [ + 76, + 162, + 468, + 191 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {a s} = - \\sum_ {\\boldsymbol {h}} \\sum_ {\\boldsymbol {l}} p (\\boldsymbol {h}, \\boldsymbol {l}) \\log \\frac {p (\\boldsymbol {l} | \\boldsymbol {h})}{p (\\boldsymbol {l})}. \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 150, + 196, + 468, + 234 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For the convenience of optimization, we introduce the variational approximation $q(\\boldsymbol{l}|\\boldsymbol{h})$ to $p(\\boldsymbol{l}|\\boldsymbol{h})$ . Since both the Kullback Leibler divergence and the entropy are positive:", + "bbox": [ + 76, + 242, + 468, + 287 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\operatorname {K L} \\left(p (\\boldsymbol {l} | \\boldsymbol {h}) | | q (\\boldsymbol {l} | \\boldsymbol {h})\\right) = \\sum_ {\\boldsymbol {l}} p (\\boldsymbol {l} | \\boldsymbol {h}) \\log \\frac {p (\\boldsymbol {l} | \\boldsymbol {h})}{q (\\boldsymbol {l} | \\boldsymbol {h})} \\geqslant 0 (12) \\\\ \\Rightarrow \\sum_ {\\boldsymbol {l}} p (\\boldsymbol {l} | \\boldsymbol {h}) \\log p (\\boldsymbol {l} | \\boldsymbol {h}) \\geqslant \\sum_ {\\boldsymbol {l}} p (\\boldsymbol {l} | \\boldsymbol {h}) \\log q (\\boldsymbol {l} | \\boldsymbol {h}), \\\\ \\mathbb {E} _ {p (\\boldsymbol {l})} [ - \\log p (\\boldsymbol {l}) ] = - \\sum_ {\\boldsymbol {l}} p (\\boldsymbol {l}) \\log p (\\boldsymbol {l}) \\geqslant 0, (13) \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 94, + 294, + 468, + 407 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "based on Markov chain that $L\\gets X\\to H$ , we can get:", + "bbox": [ + 76, + 411, + 446, + 426 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL _ {a s} \\leqslant - \\sum_ {\\boldsymbol {x}} \\sum_ {l} \\sum_ {\\boldsymbol {h}} p (\\boldsymbol {x}, l) p (\\boldsymbol {h} | \\boldsymbol {x}) \\log q (l | \\boldsymbol {h}). \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 104, + 434, + 468, + 465 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1.2 Label gaps information modeling", + "text_level": 1, + "bbox": [ + 76, + 481, + 362, + 497 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To investigate the label-relevant information about the description degrees of labels, we introduce the label gaps between logical labels and label distributions $\\pmb{\\Delta}$ , and consider the conditional self-information, i.e., $I(\\Delta | H)$ . Therefore, we construct $\\mathcal{L}_{gap}^{1}$ as follows:", + "bbox": [ + 76, + 505, + 468, + 580 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {g a p} = I (\\boldsymbol {\\Delta} | \\boldsymbol {H}) = - \\log p (\\boldsymbol {\\Delta} | \\boldsymbol {H}) \\\\ = - \\sum_ {\\delta} \\sum_ {\\boldsymbol {h}} \\log p (\\boldsymbol {\\delta} | \\boldsymbol {h}) \\tag {15} \\\\ = - \\sum_ {l} \\sum_ {\\boldsymbol {h}} \\log p (\\boldsymbol {l} - \\hat {\\boldsymbol {d}} | \\boldsymbol {h}). \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 153, + 589, + 468, + 676 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\delta = l - \\hat{d},\\hat{d}$ is the label distribution recovered in our method.", + "bbox": [ + 76, + 685, + 468, + 715 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1.3 Label irrelevant information modeling", + "text_level": 1, + "bbox": [ + 76, + 734, + 398, + 750 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Regarding the label irrelevant information, LIB employs the constraint in Eq. (9) to discard it during the learning process. $I(\\mathbf{X},\\mathbf{H})$ can be formulated as follows:", + "bbox": [ + 76, + 757, + 468, + 803 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nI (\\boldsymbol {X}, \\boldsymbol {H}) = \\sum_ {\\boldsymbol {x}} \\sum_ {\\boldsymbol {h}} p (\\boldsymbol {x}, \\boldsymbol {h}) \\log \\frac {p (\\boldsymbol {h} \\mid \\boldsymbol {x})}{p (\\boldsymbol {h})}. \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 135, + 811, + 468, + 848 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Since it is difficult to calculate $p(h)$ directly, we also introduce the variational approximation $q(h)$ to $p(h)$ . Similar to Eq. (12), based on $\\mathrm{KL}(p(h)||q(h)) \\geqslant 0$ , we have:", + "bbox": [ + 498, + 90, + 890, + 137 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\sum_ {\\boldsymbol {h}} p (\\boldsymbol {h}) \\log p (\\boldsymbol {h}) \\geqslant \\sum_ {\\boldsymbol {h}} p (\\boldsymbol {h}) \\log q (\\boldsymbol {h}). \\tag {17}\n$$\n", + "text_format": "latex", + "bbox": [ + 563, + 148, + 890, + 181 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Subsequently, the following formula can be written:", + "bbox": [ + 500, + 191, + 841, + 208 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} I (\\boldsymbol {X}, \\boldsymbol {H}) \\leqslant \\sum_ {\\boldsymbol {x}} \\sum_ {\\boldsymbol {h}} p (\\boldsymbol {x}, \\boldsymbol {h}) \\log \\frac {p (\\boldsymbol {h} | \\boldsymbol {x})}{q (\\boldsymbol {h})} \\tag {18} \\\\ = \\sum_ {\\boldsymbol {x}} \\sum_ {\\boldsymbol {l}} p (\\boldsymbol {x}, \\boldsymbol {l}) \\operatorname {K L} (p (\\boldsymbol {h} | \\boldsymbol {x}) | | q (\\boldsymbol {h})). \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 524, + 219, + 890, + 290 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1.4 Objective of LIB", + "text_level": 1, + "bbox": [ + 500, + 311, + 669, + 325 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "By employing the Lagrange multiplier method and combining Eq. (9), (14), (15), and (18), we have:", + "bbox": [ + 498, + 335, + 890, + 367 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} = \\mathcal {L} _ {a s} + \\alpha \\mathcal {L} _ {g a p} + \\beta I (\\boldsymbol {X}, \\boldsymbol {H}) \\\\ \\leqslant - \\sum_ {\\boldsymbol {x}} \\sum_ {\\boldsymbol {l}} \\sum_ {\\boldsymbol {h}} p (\\boldsymbol {x}, \\boldsymbol {l}) p (\\boldsymbol {h} | \\boldsymbol {x}, \\boldsymbol {l}) \\log q (\\boldsymbol {l} | \\boldsymbol {h}) \\\\ - \\alpha \\sum_ {\\boldsymbol {l}} \\sum_ {\\boldsymbol {h}} \\log p (\\boldsymbol {l} - \\hat {\\boldsymbol {d}} | \\boldsymbol {h}) \\tag {19} \\\\ + \\beta \\sum_ {\\boldsymbol {x}} \\sum_ {\\boldsymbol {l}} p (\\boldsymbol {x}, \\boldsymbol {l}) \\operatorname {K L} (p (\\boldsymbol {h} | \\boldsymbol {x}) | | q (\\boldsymbol {h})). \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 529, + 378, + 890, + 500 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\beta$ is the Lagrange multiplier. Considering the bound of $\\mathcal{L}$ and using the empirical Monte Carlo approximation of sampling [23], we have the following objective of LIB:", + "bbox": [ + 498, + 511, + 890, + 556 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {L I B} = \\frac {1}{n} \\sum_ {i = 1} ^ {n} \\left[ - \\sum_ {\\boldsymbol {h}} p (\\boldsymbol {h} | \\boldsymbol {x} _ {i}) \\log q \\left(\\boldsymbol {l} _ {i} \\mid \\boldsymbol {h}\\right) \\right. \\tag {20} \\\\ + \\beta \\operatorname {K L} (p (\\boldsymbol {h} | \\boldsymbol {x} _ {i}) | | q (\\boldsymbol {h})) ] - \\alpha \\sum_ {\\boldsymbol {l}} \\sum_ {\\boldsymbol {h}} \\log p (\\boldsymbol {l} - \\hat {\\boldsymbol {d}} | \\boldsymbol {h}). \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 506, + 569, + 890, + 643 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. The Optimization of LIB", + "text_level": 1, + "bbox": [ + 500, + 656, + 725, + 672 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To minimize the objective of $\\mathcal{L}_{LIB}$ , we use the reparameterization trick [16, 23]. For $p(\\boldsymbol{h}|\\boldsymbol{x})$ , we assume that:", + "bbox": [ + 500, + 680, + 888, + 710 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\np (\\boldsymbol {h} | \\boldsymbol {x}) \\sim \\mathcal {N} \\left(\\boldsymbol {\\mu} _ {\\boldsymbol {h} | \\boldsymbol {x}}, \\boldsymbol {\\sigma} _ {\\boldsymbol {h} | \\boldsymbol {x}} ^ {2} \\boldsymbol {I}\\right), \\tag {21}\n$$\n", + "text_format": "latex", + "bbox": [ + 599, + 722, + 890, + 741 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\pmb{\\mu}_{h|\\pmb{x}}$ and $\\sigma_{h|x}$ are obtained by using the encoder network $f_{\\theta_{en}}(\\cdot)$ , i.e., $\\pmb{\\mu}_{h|x} = f_{\\theta_{en}}^{\\pmb{\\mu}}(\\pmb{x})$ and $\\pmb{\\sigma}_{h|x} = f_{\\theta_{en}}^{\\pmb{\\sigma}}(\\pmb{x})$ . Subsequently, we have that:", + "bbox": [ + 498, + 753, + 890, + 799 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {h} = \\mu_ {\\boldsymbol {h} | \\boldsymbol {x}} + \\sigma_ {\\boldsymbol {h} | \\boldsymbol {x}} \\odot \\epsilon , \\tag {22}\n$$\n", + "text_format": "latex", + "bbox": [ + 617, + 811, + 890, + 828 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\epsilon \\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I})$ and $\\odot$ is the element-wise product. For $q(l|h)$ , we assume:", + "bbox": [ + 500, + 840, + 890, + 871 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nq (\\boldsymbol {l} | \\boldsymbol {h}) \\sim \\mathcal {N} \\left(\\boldsymbol {\\mu} _ {\\boldsymbol {l} | \\boldsymbol {h}}, \\boldsymbol {I}\\right), \\tag {23}\n$$\n", + "text_format": "latex", + "bbox": [ + 620, + 883, + 890, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_footnote", + "text": "It can be also interpreted and derived from the view of the probability distribution: $\\max_{\\Delta} \\log p(\\pmb{H}, \\pmb{\\Delta}) \\Rightarrow \\max_{\\Delta} \\log p(\\pmb{\\Delta}|\\pmb{H}) + \\log p(\\pmb{H}) \\Rightarrow \\max_{\\Delta} \\log p(\\pmb{\\Delta}|\\pmb{H})$ . We appreciate reviewers for their helpful comments.", + "bbox": [ + 76, + 854, + 468, + 905 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "7500", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\pmb{\\mu}_{l|\\pmb{h}}$ is learned by using the decoder network $f_{\\theta_{de}}(\\cdot)$ , namely, $\\pmb{\\mu}_{l|\\pmb{h}} = f_{\\theta_{de}}(\\pmb{h})$ . For $q(\\pmb{h})$ , we assume that:", + "bbox": [ + 76, + 90, + 468, + 122 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nq (\\boldsymbol {h}) \\sim \\mathcal {N} (\\boldsymbol {0}, \\boldsymbol {I}). \\tag {24}\n$$\n", + "text_format": "latex", + "bbox": [ + 212, + 133, + 468, + 150 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For $p(\\boldsymbol{l} - \\hat{\\boldsymbol{d}}|\\boldsymbol{h})$ , the following assumption is adopted:", + "bbox": [ + 76, + 160, + 429, + 176 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\np (\\boldsymbol {l} - \\hat {\\boldsymbol {d}} | \\boldsymbol {h}) \\sim \\mathcal {N} (\\boldsymbol {0}, \\sigma_ {\\delta | \\boldsymbol {h}} ^ {2} \\boldsymbol {I}), \\tag {25}\n$$\n", + "text_format": "latex", + "bbox": [ + 176, + 186, + 468, + 207 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\sigma_{\\delta|\\pmb{h}}$ can be achieved by introducing the gap deviation network $f_{\\theta_{gd}}(\\cdot)$ , i.e., $\\sigma_{\\delta|\\pmb{h}} = f_{\\theta_{gd}}(\\pmb{h})$ . For the recovered label distribution $\\hat{\\pmb{d}}$ , we introduce the label distribution network $f_{\\theta_{ld}}(\\cdot)$ and has the following formula:", + "bbox": [ + 76, + 215, + 468, + 280 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\boldsymbol {d}} = f _ {\\theta_ {l d}} (\\boldsymbol {h}). \\tag {26}\n$$\n", + "text_format": "latex", + "bbox": [ + 227, + 291, + 468, + 310 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Consequently, based on Eq. (21)-(26), we have:", + "bbox": [ + 96, + 321, + 411, + 335 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\min _ {\\theta_ {e n}, \\theta_ {d e}, \\theta_ {g d}, \\theta_ {l d}} \\mathcal {L} _ {L I B} \\\\ \\Rightarrow \\min _ {\\theta_ {e n}, \\theta_ {d e}, \\theta_ {g d}, \\theta_ {l d}} \\frac {1}{n} \\sum_ {\\boldsymbol {l}} \\left[ \\frac {1}{2} \\| \\boldsymbol {\\mu} _ {\\boldsymbol {l} | \\boldsymbol {h}} - \\boldsymbol {l} \\| _ {2} ^ {2} \\right. (27) \\\\ \\left. + \\alpha \\left(\\frac {1}{2} (\\boldsymbol {l} - \\hat {\\boldsymbol {d}}) ^ {T} \\left(\\boldsymbol {\\sigma} _ {\\delta | h} ^ {- 2} \\boldsymbol {I}\\right) (\\boldsymbol {l} - \\hat {\\boldsymbol {d}}) + \\log \\det \\left(\\boldsymbol {\\sigma} _ {\\delta | h} ^ {2} \\boldsymbol {I}\\right)\\right) \\right] (27) \\\\ + \\frac {\\beta}{2} \\sum_ {\\boldsymbol {x}} \\left[ \\boldsymbol {\\mu} _ {\\boldsymbol {h} | \\boldsymbol {x}} ^ {T} \\boldsymbol {\\mu} _ {\\boldsymbol {h} | \\boldsymbol {x}} + \\operatorname {t r} \\left(\\boldsymbol {\\sigma} _ {\\boldsymbol {h} | \\boldsymbol {x}} ^ {2} \\boldsymbol {I}\\right) - \\log \\det \\left(\\boldsymbol {\\sigma} _ {\\boldsymbol {h} | \\boldsymbol {x}} ^ {2} \\boldsymbol {I}\\right) \\right]. \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 86, + 348, + 468, + 478 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "When the problem of Eq. (27) is optimized, we can effectively recover the desired label distributions. To be specific, given $\\{\\pmb {X},\\pmb {L}\\}$ , we can obtain $\\pmb{H}$ according to Eq. (22) and achieve the recovery results based on Eq. (26), namely, $\\hat{\\pmb{D}} = f_{\\theta_{ld}}(\\pmb {H})$", + "bbox": [ + 76, + 488, + 468, + 565 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Comparison with Existing LE Methods", + "text_level": 1, + "bbox": [ + 76, + 574, + 413, + 590 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The main difference between LIB and existing methods is that our method deals with the problem of LE from the perspective of information bottleneck. Considering the first term in Eq. (2), it aims to minimize $\\| \\pmb{d} - \\pmb{l} \\|_2^2$ under the assumption that information in the label distributions is inherited from the initial logical labels [24, 28, 29]. For LIB, the more reasonable term:", + "bbox": [ + 75, + 597, + 468, + 702 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {1}{2} (\\boldsymbol {l} - \\hat {\\boldsymbol {d}}) ^ {T} \\left(\\boldsymbol {\\sigma} _ {\\delta | \\boldsymbol {h}} ^ {- 2} \\boldsymbol {I}\\right) (\\boldsymbol {l} - \\hat {\\boldsymbol {d}}) + \\log \\det \\left(\\boldsymbol {\\sigma} _ {\\delta | \\boldsymbol {h}} ^ {2} \\boldsymbol {I}\\right) \\tag {28}\n$$\n", + "text_format": "latex", + "bbox": [ + 109, + 710, + 468, + 739 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "which can be deduced by excavating the label relevant information about the label gaps between logical labels and label distributions.", + "bbox": [ + 76, + 750, + 468, + 792 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Besides, we compare our method with the recently proposed LEVI [29] further. Although the objectives of LEVI and LIB are somewhat similar in form, they are essentially different as follows: 1) LIB makes attempts from the perspective of information bottleneck, while LEVI from the view of variational inference; 2) The formulas of LEVI and LIB are just partially similar in form, since the variational", + "bbox": [ + 75, + 795, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/b8fc22ff8d03ffdbe392752561742bc16c11c78c2797a900539a2b010ada9df1.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Dataset# dimension q# instance n# labels c
Artificialtoy326013
Movie186977555
SBU-3DFE24325006
SJAFFE2432136
Yeast-alpha24246518
Yeast-cdc24246515
Yeast-cold2424654
Yeast-diau2424657
Yeast-dtt2424654
Yeast-elu24246514
Yeast-heat2424656
Yeast-spo2424656
Yeast-spo52424653
Yeast-spoem2424652
", + "bbox": [ + 542, + 88, + 854, + 276 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 1. Details of datasets. The numbers of dimension $q$ , instance $n$ , and labels $c$ are provided here.", + "bbox": [ + 498, + 287, + 890, + 315 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "inference is employed as the optimization tool in LIB. The details of these two formulas are totally different; 3) LEVI requires an extra regularizer, i.e., $\\| d - l\\| _2^2$ to constrain the recovery process, while LIB achieves $d$ based on the more reasonable term, i.e., Eq. (28).", + "bbox": [ + 498, + 343, + 890, + 419 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 434, + 630, + 452 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To verify the effectiveness and competitiveness of LIB, extensive experiments are conducted in this section.", + "bbox": [ + 498, + 460, + 890, + 489 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 500, + 502, + 689, + 518 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As shown in Table 1, we use both one toy dataset and 13 real-world datasets for evaluation $^2$ . For the toy dataset, i.e., Artificial dataset, it is utilized to vividly show the recovery performance [28]. Movie dataset is collected from movies, SBU-3DFE and SJAFFE datasets are two facial expression datasets. Yeast datasets (alpha to spoem) are collected from 10 biological experiments on the budding yeast genes [4]. It is important to note that only the ground-truth label distributions are provided by these datasets. Therefore, we adopt the binarization strategy, which is also used in existing LE works [24, 28, 29], to ensure the consistency of evaluation.", + "bbox": [ + 496, + 526, + 890, + 691 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We compare our method LIB to 7 LE methods, including FCM [5], KM [15], LP [17], ML [11], GLLE [28], LESC [24], and LEVI [29]. The first two methods belong to the algorithm adaption, and the rest methods are specialized algorithms. For the sake of fairness, we utilize the parameter settings recommended in their original works. Specifically, for FCM, we set the parameter $\\beta = 2$ . For KM, we leverage the Gaussian kernel. For LP, we set the parameter $\\alpha = 0.5$ . For ML, we set the number of neighbors $k = c + 1$ . For GLLE, we select $\\lambda$ from $\\{0.01, 0.1, \\dots, 100\\}$ and set the number of neighbors $k$ to $c + 1$ . For LESC, $\\lambda_{1}$ and $\\lambda_{2}$ are selected from $\\{0.0001, 0.1, \\dots, 10\\}$ . For LEVI, MLPs with", + "bbox": [ + 496, + 693, + 890, + 875 + ], + "page_idx": 4 + }, + { + "type": "page_footnote", + "text": "$^{2}$ http://palm.seu.edu.cn/xgeng/LDL/index.htm", + "bbox": [ + 514, + 886, + 764, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "7501", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "two hidden layers and softmax activation functions are utilized, and the results are reported after 150 training epochs. For LIB, we select $\\alpha$ and $\\beta$ from $\\{0.001, 0.01, \\dots, 10\\}$ , and the fully connected networks with 3 layers and sigmoid activation function are leveraged in the proposed method.", + "bbox": [ + 75, + 90, + 468, + 166 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To evaluate the recovery performance, we adopt 6 metrics, namely Chebyshev, Canberra, Clark, Kullback-Leibler, Cosine, and Intersection [8,24,28]. Given the ground-truth label distribution $\\pmb{d}$ and the recovered label distribution $\\hat{\\pmb{d}}$ , the first four metrics and the rest two metrics respectively measure the distance and similarity between $\\pmb{d}$ and $\\hat{\\pmb{d}}$ :", + "bbox": [ + 75, + 167, + 470, + 257 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nD _ {\\text {C h e b y s h e v}} (\\boldsymbol {d}, \\hat {\\boldsymbol {d}}) = \\max _ {i} \\left| d ^ {y _ {i}} - \\hat {d} ^ {y _ {i}} \\right|, \\tag {29}\n$$\n", + "text_format": "latex", + "bbox": [ + 142, + 261, + 468, + 287 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nD _ {\\text {C a n b e r r a}} (\\boldsymbol {d}, \\hat {\\boldsymbol {d}}) = \\sum_ {i = 1} ^ {c} \\frac {\\left| d ^ {y _ {i}} - \\hat {d} ^ {y _ {i}} \\right|}{d ^ {y _ {i}} + \\hat {d} ^ {y _ {i}}}, \\tag {30}\n$$\n", + "text_format": "latex", + "bbox": [ + 153, + 289, + 468, + 337 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nD _ {\\text {C l a r k}} (\\boldsymbol {d}, \\hat {\\boldsymbol {d}}) = \\sqrt {\\sum_ {i = 1} ^ {c} \\frac {\\left(d ^ {y _ {i}} - \\hat {d} ^ {y _ {i}}\\right) ^ {2}}{\\left(d ^ {y _ {i}} + \\hat {d} ^ {y _ {i}}\\right) ^ {2}}}, \\tag {31}\n$$\n", + "text_format": "latex", + "bbox": [ + 147, + 340, + 468, + 402 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nD _ {\\text {K u l l b a c k - L e i b l e r}} (\\boldsymbol {d}, \\hat {\\boldsymbol {d}}) = \\sum_ {i = 1} ^ {c} d ^ {y _ {i}} \\ln \\frac {d ^ {y _ {i}}}{\\hat {d} ^ {y _ {i}}}, \\tag {32}\n$$\n", + "text_format": "latex", + "bbox": [ + 135, + 405, + 468, + 444 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nS _ {\\text {C o s i n e}} (\\boldsymbol {d}, \\hat {\\boldsymbol {d}}) = \\frac {\\sum_ {i = 1} ^ {c} d ^ {y _ {i}} \\hat {d} ^ {y _ {i}}}{\\sqrt {\\sum_ {i = 1} ^ {c} \\left(d ^ {y _ {i}}\\right) ^ {2}} \\sqrt {\\sum_ {i = 1} ^ {c} \\left(\\hat {d} ^ {y _ {i}}\\right) ^ {2}}}, \\tag {33}\n$$\n", + "text_format": "latex", + "bbox": [ + 112, + 448, + 468, + 521 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nS _ {\\text {I n t e r s e c t i o n}} (\\boldsymbol {d}, \\hat {\\boldsymbol {d}}) = \\sum_ {i = 1} ^ {c} \\min \\left(d ^ {y _ {i}}, \\hat {d} ^ {y _ {i}}\\right). \\tag {34}\n$$\n", + "text_format": "latex", + "bbox": [ + 135, + 523, + 468, + 561 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The smaller values of distance metric and similarity metric indicate the better and the worse results, respectively.", + "bbox": [ + 75, + 566, + 468, + 598 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Visualization Results on Toy Dataset", + "text_level": 1, + "bbox": [ + 76, + 604, + 393, + 622 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The recovery results on the Artificial dataset are vividly presented in Fig. 3, which shows the three-dimensional label distributions by the RGB color channels separately. The more similar the color patterns of the recovered results and the ground-truth are, the better the recovery results are.", + "bbox": [ + 75, + 628, + 468, + 703 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "It can be seen that FCM, GLLE, LESC, LEVI, and LIB can obtain the similar color pattern, while KM, LP, and ML are incapable to obtain the promising recovery performance on Artificial dataset. Regarding the visualization results of FCM, GLLE, LESC, LEVI, and LIB, the color pattern that is most close to the ground-truth is achieved by our LIB.", + "bbox": [ + 75, + 704, + 468, + 794 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Comparison Results on Real-world Datasets", + "text_level": 1, + "bbox": [ + 76, + 801, + 450, + 816 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We provide the detailed comparison results on 13 real-world datasets in Table 2. Overall, LIB has the competitive recovery performance. We have the following observations: 1) Compared with FCM and KM, which belong to the category of algorithm adaption, remarkable improvements can", + "bbox": [ + 76, + 824, + 468, + 901 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/433cd0f9051a1ea30701968a1eed431fdc486563dec9da9be3ad48ccbe4e63ab.jpg", + "image_caption": [ + "(a) FCM" + ], + "image_footnote": [], + "bbox": [ + 504, + 92, + 629, + 162 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/b47102f6ed3a8907aa6d3e729f478a653bdfd10d16dca6ad1c91b57de938260f.jpg", + "image_caption": [ + "(b) KM" + ], + "image_footnote": [], + "bbox": [ + 633, + 93, + 756, + 162 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/e131d1d7a6778ee2032f789d3b789003607c3efdf066d1201b74f22c1ee45e27.jpg", + "image_caption": [ + "(c) LP" + ], + "image_footnote": [], + "bbox": [ + 763, + 93, + 888, + 162 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/6652292ecd2846730a922ac31fdde7d33229d0af6e55f276355a7d68c9e502d2.jpg", + "image_caption": [ + "(d) ML" + ], + "image_footnote": [], + "bbox": [ + 503, + 181, + 627, + 253 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/2cc8d1196705731916bf47035a1299ac48def00bafb6812363a368384ebccb43.jpg", + "image_caption": [ + "(e) GLLE" + ], + "image_footnote": [], + "bbox": [ + 633, + 181, + 756, + 253 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/e1a94e21c97ea76a259bb4b7315e2e656fbb374d356e905c00fc823f5473279e.jpg", + "image_caption": [ + "(f) LESC" + ], + "image_footnote": [], + "bbox": [ + 763, + 181, + 888, + 253 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/a9a05937edda45c20123f3ada7b3d3ec0b8d821261fdced91e8c84e1a651f414.jpg", + "image_caption": [ + "(g) LEVI" + ], + "image_footnote": [], + "bbox": [ + 501, + 273, + 629, + 342 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/7ebfd869fe40c74bb516122a9b70b79ff705dbf7f854098c1c35277b22db6a84.jpg", + "image_caption": [ + "(h) LIB" + ], + "image_footnote": [], + "bbox": [ + 633, + 273, + 756, + 342 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/a76eb77437031a722c2e3032e06efe562cf7b59739b4b2e601ac4ba0559c5330.jpg", + "image_caption": [ + "(i) Ground-truth", + "Figure 3. Visualization results of the label distributions recovered by different methods ((a)-(h)) and the ground-truth ((i)) on Artificial dataset. (Best viewed in color.)" + ], + "image_footnote": [], + "bbox": [ + 763, + 273, + 888, + 342 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "be achieved by our method; 2) Compared with the methods belonging to the category of specialized algorithm, LIB can also obtain better recovery results in most cases. For example, LIB obtains the best recovery results on Movie datasets in all metrics. Moreover, although LESC can obtain slightly favorable results in some cases, the corresponding recovery results of LIB are also promising and competitive. The underlying reason may be that LESC further considers the sample correlations during the recovery process; 3) The recovery performance of all methods can be roughly ranked as LIB>LESC≈LEV1>GLLE>LP≈FCM>ML>KM. We can conclude that LIB is suitable for the LE problem. The underlying reason for the significant improvement is that the label relevant information, including the information about label assignments and the information about label gaps, can be effectively investigated by LIB.", + "bbox": [ + 496, + 439, + 890, + 681 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.4. Analysis and Discussion of LIB", + "text_level": 1, + "bbox": [ + 500, + 691, + 774, + 708 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We analyze the parameter sensitivity of LIB firstly, and then we conduct the ablation studies as well.", + "bbox": [ + 500, + 717, + 890, + 746 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.4.1 Sensitivity of LIB", + "text_level": 1, + "bbox": [ + 500, + 768, + 676, + 784 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In the proposed method, we choose the values of $\\alpha$ and $\\beta$ from $\\{0.001, 0.01, \\dots, 10\\}$ . To show the parameter sensitivity of LIB, we conduct experiments on SBU-3DFE datasets with different values of $\\alpha$ and $\\beta$ . Regarding the dimension of the learned latent representation, we set it to 256 for all datasets. The experimental results in metrics of Chebyshev distance, Cosine coefficient, and Intersection similarity are", + "bbox": [ + 496, + 794, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "7502", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/c2c45932273bcac0010d9b0fbd1438bd72d4eadbfd04a8fc9ba2cb061db91805.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MetricChebyshev ↓Clark ↓
MethodFCMKMLPMLGLLELESCLEVLIBFCMKMLPMLGLLELESCLEVLIB
Movie0.2300.2340.1610.1640.1220.1210.1100.1070.8591.7660.9131.1400.5690.5640.5510.517
SUB-3DFE0.1350.2380.1230.2330.1260.1220.0950.0940.4821.9070.5801.8480.3910.3780.3030.297
SJAFFE0.1320.2140.1070.1860.0870.0690.0750.0710.5221.8740.5021.5190.3770.2760.2900.262
Yeast-alpha0.0440.0630.0400.0570.0200.0150.0120.0170.8213.1531.1853.0880.3370.2530.3190.275
Yeast-cdc0.0510.0760.0420.0710.0220.0190.0160.0170.7392.8851.0142.8250.3060.2510.3230.242
Yeast-cold0.1410.2520.1370.2420.0660.0560.0820.0540.4331.4720.5031.4400.1760.1520.2690.146
Yeast-diau0.1240.1520.0990.1480.0530.0420.0440.0490.8381.8860.7881.8440.2960.2240.2950.273
Yeast-dtt0.0970.2570.1280.2440.0520.0430.0840.0340.3291.4770.4991.4460.1430.1190.2940.092
Yeast-elu0.0520.0780.0440.0720.0230.0190.0170.0180.5792.7680.9732.7110.2950.2410.3170.224
Yeast-heat0.1690.1750.0860.1650.0490.0460.0520.0390.5801.8020.5681.7640.2130.1990.2880.165
Yeast-spo0.1300.1750.0900.1710.0620.0600.0550.0530.5201.8110.5581.7680.2660.2580.2770.224
Yeast-spo50.1620.2770.1140.2730.0990.0920.0910.0760.3951.0590.2741.0360.1970.1850.2090.158
Yeast-sopem0.2330.4080.1630.4030.0880.0870.1150.0690.4011.0280.2721.0040.1320.1290.1820.104
Avg.Rank6.0778.0005.0006.8463.7692.3082.4631.5385.3858.0005.6157.0003.3851.9233.4621.231
MetricCanberra ↓
MethodFCMKMLPMLGLLELESCLEVLIBFCMKMLPMLGLLELESCLEVLIB
Movie1.6643.4441.7201.9341.0451.0340.9740.9200.3810.4520.1770.2180.1230.1200.0820.077
SUB-3DFE1.0204.1211.2454.0010.8200.7990.6370.6110.0940.6030.1050.5650.0690.0640.0420.041
SJAFFE1.0814.0101.0643.1380.7810.5610.6000.5310.1070.5580.0770.3910.0500.0290.0320.027
Yeast-alpha2.88311.8094.54411.6031.1340.8461.2490.8930.1000.6300.1210.6020.0130.0080.0110.009
Yeast-cdc2.4159.8753.6449.6950.9590.7651,1480.7470.0910.6300.1110.6010.0140.0100.0140.008
Yeast-cold0.7342.5660.9242.5190.3050.2630.5010.2500.1130.5860.1030.5560.0190.0150.0350.012
Yeast-diau1.8954.2611.7484.1800.6710.4800.6890.6210.1590.5380.1270.5090.0270.0170.0230.022
Yeast-dtt0.5012.5940.9412.5490.2480.2060.5620.1580.0650.6170.1030.5860.0130.0100.0420.005
Yeast-elu1.6899.1103.3818.9490.9020.7271.0930.6700.0590.6170.1090.5890.0130.0090.0140.008
Yeast-heat1.1573.8491.2933.7790.4300.4010.6460.3270.1470.5860.0890.5560.0170.0150.0270.011
Yeast-spo0.9983.8541.2313.7720.5480.5330.6050.4540.1100.5620.0840.5320.0290.0280.0250.019
Yeast-spo50.5631.3820.4011.3550.3050.2840.3110.2410.1230.3340.0420.3170.0340.0310.0280.021
Yeast-sopem0.5341.2530.3651.2260.1830.1800.2480.1440.2080.5310.0670.5030.0270.0270.0360.018
Avg.Rank5.2318.0005.6927.0003.2312.003.6921.1545.6928.0005.3856.9233.4622.1543.0771.154
MetricCosine ↑
MethodFCMKMLPMLGLLELESCLEVLIBFCMKMLPMLGLLELESCLEVLIB
Movie0.7730.8800.9290.9190.9360.9370.9540.9550.6770.6490.7780.7790.8310.8330.8490.859
SUB-3DFE0.9120.8120.9220.8150.9270.9320.9560.9580.8270.5790.8100.5870.8500.8550.8820.887
SJAFFE0.9060.8270.9410.8570.9580.9730.9690.9740.8210.5930.8370.6610.8720.9050.8970.909
Yeast-alpha0.9220.7510.9110.7560.9870.9920.9890.9920.8440.5320.7740.5370.9380.9530.9320.951
Yeast-cdc0.9290.7540.9160.7590.9870.9910.9870.9920.8470.5330.7790.5380.9370.9500.9250.951
Yeast-heat0.9220.7790.9250.7840.9820.9860.9700.9880.8330.5590.7940.5650.9240.9350.8810.938
Yeast-diau0.8820.7990.9150.8030.9750.9850.9800.9790.7600.5880.7880.5930.9060.9330.9080.913
Yeast-dtt0.9590.7590.9210.7630.9880.9910.9650.9950.8940.5410.7860.5460.9390.9490.8660.961
Yeast-elu0.9500.7580.9180.7630.9870.9910.9870.9920.8830.5390.7820.5440.9360.9490.9240.952
Yeast-heat0.8830.7790.9320.7830.9840.9860.9770.9900.8070.5590.8050.5640.9290.9340.8970.946
Yeast-spo0.9090.8000.9390.8030.9740.9750.9780.9820.8360.5750.8190.5800.9090.9120.9030.925
Yeast-spo50.9220.8820.9690.8840.9710.9740.9790.9830.8380.7240.8860.7270.9010.9080.9090.924
Yeast-sopem0.8780.8120.9500.8150.9780.9780.9720.9850.7670.5920.8370.5970.9120.9130.8850.931
Avg.Rank5.8467.9235.3086.9233.4622.1542.9231.2315.3858.0005.6926.8463.3852.0073.4621.154
", + "bbox": [ + 93, + 87, + 879, + 691 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2. Recovery results on 13 real-world datasets. $\\downarrow$ indicates that \"the smaller the better\" and $\\uparrow$ means that \"the larger the better\". The average ranks (Avg.Rank) on all datasets are also reported for all methods. We highlight the best recovery results.", + "bbox": [ + 75, + 704, + 893, + 733 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "provided in Fig. 4. It can be observed that LIB method can get promising recovery results and is robust with respect to different values of $\\alpha$ and $\\beta$ in a large range.", + "bbox": [ + 75, + 758, + 470, + 805 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4.2 Ablation studies of LIB", + "text_level": 1, + "bbox": [ + 76, + 829, + 294, + 844 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The ablation studies are conducted to further verify the effectiveness of introducing the label information bottleneck framework for LE. In the proposed objective Eq. (9), $\\mathcal{L}_{as}$", + "bbox": [ + 75, + 854, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "and $\\mathcal{L}_{gap}$ explore the label assignments information and label gaps information during the recovery process. As can be observed from Eq. (14) and Eq. (15), only the latent representation $\\pmb{H}$ can be learned if we employ $\\mathcal{L}_{as}$ merely during the recovery process. Consequently, considering the goal of LE, we compare the proposed LIB with the method termed $\\mathrm{LIB}_{gap}$ , which only employs $\\mathcal{L}_{gap}$ to achieve the recovery results. In other words, $\\mathrm{LIB}_{gap}$ investigates the label gaps information in the case of not considering the label assign-", + "bbox": [ + 496, + 758, + 893, + 897 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "7503", + "bbox": [ + 482, + 944, + 514, + 957 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7ef24d8fd4faa580c9270dd65e2459ad9d4679736da1f0a0f8156d2ee573bfa2.jpg", + "image_caption": [ + "(a) Chebyshev" + ], + "image_footnote": [], + "bbox": [ + 133, + 92, + 367, + 231 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/54dd238b4658d45bbbff76f97a3d612fb0c01a3613d942ea96b4ec9f9463c5ca.jpg", + "image_caption": [ + "(b) Cosine $\\uparrow$", + "Figure 4. The recovery results in metrics of (a) Chebyshev distance, (b) Cosine coefficient, and (c) Intersection similarity with different values of $\\alpha$ and $\\beta$ . $\\downarrow$ indicates that \"the smaller the better\" and $\\uparrow$ means that \"the larger the better\". The experimental results demonstrate that LIB is robust with respect to different values of $\\lambda$ and $\\beta$ . (Best viewed in color.)" + ], + "image_footnote": [], + "bbox": [ + 372, + 95, + 594, + 229 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ad1e900b56aeffddfa362eb0bfa0ad711e7773bba0a5057ec1eac85267f4c772.jpg", + "image_caption": [ + "(c) Intersection $\\uparrow$" + ], + "image_footnote": [], + "bbox": [ + 607, + 95, + 836, + 229 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/2210f1252640a11bb5fe6ed47a41775a3e142e013459e346771775be0ac06e87.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MetricChebyshev ↓Clark ↓Canberra ↓Kullback-Leibler ↓Cosine ↑Intersection ↑
MethodLIBgapLIBLIBgapLIBLIBgapLIBLIBgapLIBLIBgapLIBLIBgapLIB
Movie0.1200.1070.5630.5171.0290.9200.0990.0770.9380.9550.8340.859
SUB-3DFE0.1300.0940.3950.2970.8490.6110.0790.0410.9230.9580.8460.887
SJAFFE0.1130.0710.3910.2620.8160.5310.0660.0270.9380.9730.8600.909
Yeast-alpha0.0180.0170.2810.2750.9200.8930.0100.0090.9910.9920.9500.951
Yeast-cdc0.0190.0170.2540.2420.7820.7470.0090.0080.9910.9920.9480.951
Yeast-cold0.0610.0170.1620.1460.2800.2500.0160.0120.9850.9880.9300.938
Yeast-diau0.0500.0490.2880.2730.6590.6210.0250.0220.9770.9790.9080.913
Yeast-dtt0.0450.0340.1240.0920.2170.1580.0100.0050.9910.9950.9460.961
Yeast-elu0.0190.0180.2370.2240.7140.6700.0090.0080.9920.9920.9490.952
Yeast-heat0.0450.0390.1930.1650.3880.3270.0140.0110.9860.9900.9360.946
Yeast-spo0.0590.0530.2530.2240.5230.4540.0250.0190.9760.9820.9140.925
Yeast-spo50.0970.0760.1930.1580.3000.2410.0320.0210.9710.9830.9030.924
Yeast-sopem0.0880.0690.1300.1040.1810.1440.0270.0180.9770.9850.9120.931
", + "bbox": [ + 135, + 314, + 841, + 517 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 3. Recovery results of $\\mathrm{LIB}_{gap}$ and LIB on 13 real-world datasets. $\\downarrow$ indicates that \"the smaller the better\" and $\\uparrow$ means that \"the larger the better\". We highlight the best recovery results.", + "bbox": [ + 75, + 526, + 892, + 555 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ments information during the recovery process.", + "bbox": [ + 76, + 582, + 390, + 597 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To be specific, $\\mathrm{LIB}_{gap}$ has with the following objective:", + "bbox": [ + 96, + 597, + 464, + 613 + ], + "page_idx": 7 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\theta_ {g d}, \\theta_ {l d}} \\frac {1}{2} \\sum_ {\\boldsymbol {x}} \\left[ (\\boldsymbol {l} - \\hat {\\boldsymbol {d}}) ^ {T} \\left(\\boldsymbol {\\sigma} _ {\\delta | \\boldsymbol {x}} ^ {- 2} \\boldsymbol {I}\\right) (\\boldsymbol {l} - \\hat {\\boldsymbol {d}}) + \\log \\det \\left(\\boldsymbol {\\sigma} _ {\\delta | \\boldsymbol {x}} ^ {2} \\boldsymbol {I}\\right) \\right]. \\tag {35}\n$$\n", + "text_format": "latex", + "bbox": [ + 81, + 625, + 468, + 672 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Notably, $\\sigma_{\\delta |x} = f_{\\theta_{gd}}(x)$ and $\\hat{\\pmb{d}} = f_{\\theta_{ld}}(\\pmb {x})$ , which are different from the objective Eq. (27) utilized in LIB. Only the partial label relevant information, i.e., the information about the label gaps, is explored in $\\mathrm{LIB}_{gap}$", + "bbox": [ + 75, + 672, + 468, + 734 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 3 provides the recovery results of $\\mathrm{LIB}_{gap}$ and LIB. It can be observed that LIB outperforms $\\mathrm{LIB}_{gap}$ in all cases. Compared with LIB, $\\mathrm{LIB}_{gap}$ merely makes the effort to explore the label gap information to boost the recovery performance, while LIB excavates both the information about the label assignments and the information about the label gaps jointly. Therefore, the promising recovery performance can be achieved by LIB. Furthermore, according to the results provided in Table 2 and 3, the recovery results of $\\mathrm{LIB}_{gap}$ seem to be competitive, which also indicates that the exploration of information about label gaps is beneficial for LE.", + "bbox": [ + 75, + 734, + 470, + 901 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 580, + 619, + 595 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we present a new perspective to deal with the Label Enhancement (LE) problem and introduce the novel Label Information Bottleneck (LIB) method. The label relevant information is decomposed into the information about label assignments and the information about label gaps. Consequently, our method transform the LE problem into simultaneously learning the latent representation and modeling the label gaps. Extensive experiments carried on both the toy dataset and real-world datasets verify the competitiveness of LIB.", + "bbox": [ + 496, + 604, + 892, + 756 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments", + "text_level": 1, + "bbox": [ + 500, + 768, + 660, + 787 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was supported by the National Key R&D Program of China under Grant 2020AAA0109602; the Education and Research Foundation for Middle-aged and Young Teacher of Fujian Province under Grant JAT220005; the National Natural Science Foundation of China (NSFC) under Grant 62206156; Alibaba Group through Alibaba Innovative Research Program, No.21169774.", + "bbox": [ + 496, + 794, + 893, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "7504", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] A Alemi, Ian Fischer, J Dillon, and Kevin Murphy. 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PhD thesis, Carnegie Mellon University, language technologies institute, 2005. 2" + ], + "bbox": [ + 78, + 90, + 468, + 330 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "7506", + "bbox": [ + 482, + 945, + 516, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Label Information Bottleneck for Label Enhancement/17915eba-e6e6-4f83-bad7-de11a7a573e3_model.json b/2023/Label Information Bottleneck for Label Enhancement/17915eba-e6e6-4f83-bad7-de11a7a573e3_model.json new file mode 100644 index 0000000000000000000000000000000000000000..9eaa49f17f32114a56ac2ed0f6b58b0741c408ab --- /dev/null +++ b/2023/Label Information Bottleneck for Label Enhancement/17915eba-e6e6-4f83-bad7-de11a7a573e3_model.json @@ -0,0 +1,2442 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.212, + 0.131, + 0.758, + 0.151 + ], + "angle": 0, + "content": "Label Information Bottleneck for Label Enhancement" + }, + { + "type": "text", + "bbox": [ + 0.31, + 0.18, + 0.659, + 0.2 + ], + "angle": 0, + "content": "Qinghai Zheng\\(^{1}\\), Jihua Zhu\\(^{2*}\\), Haoyu Tang\\(^{3}\\)" + }, + { + "type": "text", + "bbox": [ + 0.222, + 0.199, + 0.749, + 0.217 + ], + "angle": 0, + "content": "1College of Computer and Data Science, Fuzhou University, China" + }, + { + "type": "text", + "bbox": [ + 0.194, + 0.217, + 0.777, + 0.234 + ], + "angle": 0, + "content": "\\(^{2}\\)School of Software Engineering, Xi'an Jiaotong University, Xi'an, China" + }, + { + "type": "text", + "bbox": [ + 0.264, + 0.234, + 0.706, + 0.252 + ], + "angle": 0, + "content": "\\(^{3}\\)School of Software, Shandong University, Jinan, China" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.287, + 0.314, + 0.303 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.319, + 0.474, + 0.651 + ], + "angle": 0, + "content": "In this work, we focus on the challenging problem of Label Enhancement (LE), which aims to exactly recover label distributions from logical labels, and present a novel Label Information Bottleneck (LIB) method for LE. For the recovery process of label distributions, the label irrelevant information contained in the dataset may lead to unsatisfactory recovery performance. To address this limitation, we make efforts to excavate the essential label relevant information to improve the recovery performance. Our method formulates the LE problem as the following two joint processes: 1) learning the representation with the essential label relevant information, 2) recovering label distributions based on the learned representation. The label relevant information can be excavated based on the \"bottleneck\" formed by the learned representation. Significantly, both the label relevant information about the label assignments and the label relevant information about the label gaps can be explored in our method. Evaluation experiments conducted on several benchmark label distribution learning datasets verify the effectiveness and competitiveness of LIB. Our source codes are available at https://github.com/qinghai-zheng/LIBLE" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.682, + 0.21, + 0.699 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.709, + 0.47, + 0.875 + ], + "angle": 0, + "content": "Learning with label ambiguity is important in computer vision and machine learning. Different from the traditional Multi-Label Learning (MLL), which employs multiple logical labels to annotate one instance to address the label ambiguity issue [20], Label Distribution Learning (LDL) considers the relative importance of different labels and draws much attention in recent years [6,8,14,18,26]. By distinguishing the description degrees of all labels, LDL annotates one instance with a label distribution. Therefore, LDL is a more general learning paradigm, MLL can be regarded as a special case of LDL [8,10,12]." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.288, + 0.893, + 0.621 + ], + "angle": 0, + "content": "Recently, many LDL methods are proposed and achieve great success in practice [3, 9, 14, 18]. Instances with exact label distributions are vital for the training process of LDL methods. Nevertheless, annotating instances with label distributions is time-consuming [24, 28]. We take the label distribution annotation process of SJAFFE dataset for example here. SJAFFE dataset is the facial expression dataset, which contains 213 grayscale images collected from 10 Japanese female models, each facial expression image is rated by 60 persons on 6 basic emotions, including happiness, surprise, sadness, fear, anger, and disgust, with a five-level scale from 1 - 5, the higher value indicates the higher emotion intensity. Consequently, the average score of each emotion is served as the emotion label distribution [14, 28]. Clearly, the above annotation process is costly and it is unpractical to annotate data with label distributions manually, especially when the number of data is large. Fortunately, most existing datasets in the field of computer vision and machine learning are annotated by single-label or multi-labels [7, 29], therefore, a highly recommended promising solution is Label Enhancement (LE), which attempts to recover the desired label distributions exactly from existing logical labels [24, 28, 32]." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.621, + 0.894, + 0.757 + ], + "angle": 0, + "content": "Driven by the urgent requirement of obtaining label distributions and the convenience of LE, some LE methods are proposed in recent years [5, 7, 11, 13, 15, 17, 21, 24, 28, 29]. Given a dataset \\( \\mathbf{X} = \\{\\pmb{x}_1, \\pmb{x}_2, \\dots, \\pmb{x}_n\\} \\in \\mathbb{R}^{q \\times n} \\), in which \\( q \\) and \\( n \\) denote the number of dimensions and the number of instances, the potential label set is \\( \\{y_1, y_2, \\dots, y_c\\} \\). The available logical labels and the desired distribution labels of \\( \\mathbf{X} \\) are separately indicated by \\( \\mathbf{L} = \\{l_1, l_2, \\dots, l_n\\} \\) and \\( \\mathbf{D} = \\{d_1, d_2, \\dots, d_n\\} \\), where \\( l_i \\) and \\( d_i \\) are:" + }, + { + "type": "equation", + "bbox": [ + 0.51, + 0.763, + 0.893, + 0.782 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {l} _ {i} = \\left(l _ {i} ^ {y _ {1}}, l _ {i} ^ {y _ {2}}, \\dots , l _ {i} ^ {y _ {c}}\\right) ^ {T}, \\boldsymbol {d} _ {i} = \\left(d _ {i} ^ {y _ {1}}, d _ {i} ^ {y _ {2}}, \\dots , d _ {i} ^ {y _ {c}}\\right) ^ {T}. \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.788, + 0.892, + 0.834 + ], + "angle": 0, + "content": "To be specific, LE aims to recover \\( D \\) based on the information provided by \\( X \\) and \\( L \\). For most existing LE methods, their objectives can be concisely summarized as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.564, + 0.84, + 0.892, + 0.865 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\theta} \\| f _ {\\theta} (\\boldsymbol {X}) - \\boldsymbol {L} \\| _ {F} ^ {2} + \\gamma r e g (f _ {\\theta} (\\boldsymbol {X})), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.87, + 0.893, + 0.903 + ], + "angle": 0, + "content": "in which \\( \\pmb{D} = f_{\\theta}(\\pmb{X}) \\), \\( f_{\\theta}(\\cdot) \\) indicates the mapping from \\( \\pmb{X} \\) to \\( \\pmb{D} \\), \\( reg(\\cdot) \\) denotes the regularization function, and \\( \\gamma \\)" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.368, + 0.901 + ], + "angle": 0, + "content": "*Corresponding author, E-mail: zhujh@xjtu.edu.cn" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7497" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.134, + 0.089, + 0.411, + 0.277 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.287, + 0.473, + 0.481 + ], + "angle": 0, + "content": "Figure 1. Illustration of label relevant information. Excavating the essential label relevant information directly is challenging and we adopt a indirect way here. We jointly investigate the information about the assignments of labels to the instance and the information about the label gaps between logical labels and label distributions. Given the \\(i\\)-th instance \\(\\pmb{x}_i\\), the label gap of the \\(y_j\\) label is \\(\\delta_i^{y_j} = l_i^{y_j} - d_i^{y_j}\\). The information contained in \\(l_i^{y_j}\\) and \\(\\delta_i^{y_j}\\) can be amalgamated to form the essential label relevant information. In other words, we employ \\(l_i^{y_j}\\) to explore the label relevant information about the label assignments and \\(\\delta_i^{y_j}\\) to excavate the label relevant information about the label gaps. To a certain degree, the combination of \\(\\delta_i^{y_j}\\) and \\(l_i^{y_j}\\) is equivalent to \\(d_i^{y_j}\\). As depicted here, \\(l_i^{y_j}\\) indicates that \\(y_1\\) and \\(y_3\\) are related labels and \\(\\delta_i^{y_j}\\) provides the importance of \\(y_1\\) and \\(y_3\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.508, + 0.47, + 0.765 + ], + "angle": 0, + "content": "is the trade-off parameter. Most existing LE methods vary in \\( reg(\\cdot) \\). For example, GLLE [28] calculates the distance-based similarity matrix of data and employs the smoothness assumption [33] to construct \\( reg(\\cdot) \\); LESC [24] considers the global sample correlations and introduces the low-rank constraint as the regularization; PNLR [13] leverages \\( reg(\\cdot) \\) to maintain positive and negative label relations during the recovery process. Although a remarkable progress can be made by aforementioned methods, they ignore the label irrelevant information contained in \\( X \\), which prevents the further improvement of recovery results. For example, in the LE task of recovering facial age label distributions, the label irrelevant information, such as peculiarities information, cast shadows information, and occlusions information, may result in the incorrect mapping process of \\( f_{\\theta}(\\cdot) \\) and the unsuitable regularization of \\( reg(\\cdot) \\), eventually leads to the unsatisfactory recovery performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.766, + 0.471, + 0.903 + ], + "angle": 0, + "content": "To overcome the aforementioned limitation, we present a Label Information Bottleneck (LIB) method for LE. Concretely, the core idea of LIB is to learn the latent representation \\( \\pmb{H} \\), which preserves the maximum label relevant information, from \\( \\pmb{X} \\), and jointly recovers the label distributions based on the latent representation. For the LE problem, the label relevant information is the information that describes the description degrees of labels. It is tough to explore the label relevant information directly. As shown in Fig. 1, we" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.288 + ], + "angle": 0, + "content": "decompose the label relevant information into two components, namely the assignments of labels to the instance and the label gaps between label distributions and logical labels. Inspired by Information Bottleneck (IB) [25], LIB utilizes the existing logical labels to explore the information about the assignments of labels to the instance. Unlike simply employing the original IB on the LE task, our method further considers the information about the label gaps between label distributions and logical labels. It is noteworthy that the above two components of the label relevant information are jointly explored in our method, and that is why we term the proposed method Label Information Bottleneck (LIB). The main contributions can be summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.516, + 0.295, + 0.892, + 0.371 + ], + "angle": 0, + "content": "- We decompose the label relevant information into the information about the assignments of labels to instance and the information about the label gaps between logical labels, both of which can be jointly explored during the learning process of our method." + }, + { + "type": "text", + "bbox": [ + 0.517, + 0.379, + 0.892, + 0.456 + ], + "angle": 0, + "content": "- We introduce a novel LE method, termed LIB, which excavates the label relevant information to exactly recover the label distributions. Based on the original IB, which explores the label assignments information for LE, LIB further explores the label gaps information." + }, + { + "type": "text", + "bbox": [ + 0.517, + 0.463, + 0.892, + 0.538 + ], + "angle": 0, + "content": "- We verify the effectiveness of LIB by performing extensive experiments on several datasets. Experimental results show that the proposed method can achieve the competitive performance, compared to state-of-the-art LE methods." + }, + { + "type": "list", + "bbox": [ + 0.516, + 0.295, + 0.892, + 0.538 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.551, + 0.642, + 0.567 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.576, + 0.691, + 0.59 + ], + "angle": 0, + "content": "2.1. Label Enhancement" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.891, + 0.674 + ], + "angle": 0, + "content": "To recover the label distributions from the existing logical labels, many efforts are made recently [24, 28]. In general, most existing LE methods can be roughly divided into two categories, namely, algorithm adaptation and specialized algorithm [8, 24]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Algorithm adaptation extends some existing methods to achieve the goal of LE [5, 15]. For example, FCM [5] recovers the label distributions by utilizing the fuzzy clustering and fuzzy relabeling. To be specific, FCM utilizes the fuzzy C-means clustering to get different clusters and cluster prototypes, then obtains membership degrees of each instance with respect to different cluster prototypes, finally annotates all instances with label distributions by employing the fuzzy composition and softmax normalization. KM [15] leverages the fuzzy SVM to achieve the membership function. During the recovery process, KM separates instances into two clusters and employs the nonlinear function to get the radius and distances between centers and kernelized instances, and then gets the label distributions with the help of the softmax normalization." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7498" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.228 + ], + "angle": 0, + "content": "Specialized algorithm is specially designed to deal with the LE problem. Most existing LE methods belong to the category of specialized algorithm and have the basic objective Eq. (2). By using different constraints, different methods adopt different \\( reg(\\cdot) \\) in Eq. (2). For example, based on the assumption that instances closed in the feature space are more likely to share the same label, GLLE [28] employs the following local graph information in the feature space to boost the recovery performance:" + }, + { + "type": "equation", + "bbox": [ + 0.115, + 0.237, + 0.47, + 0.297 + ], + "angle": 0, + "content": "\\[\nq _ {i, j} = \\left\\{ \\begin{array}{l} \\exp \\left(- \\frac {\\left\\| \\boldsymbol {x} _ {i} - \\boldsymbol {x} _ {j} \\right\\| ^ {2}}{2 \\varepsilon^ {2}}\\right), \\text {i f} \\boldsymbol {x} _ {j} \\in k (i), \\\\ 0, \\text {o t h e r w i s e}, \\end{array} \\right. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.307, + 0.47, + 0.336 + ], + "angle": 0, + "content": "where \\(k(i)\\) denotes the \\(k\\)-nearest neighbours of \\(\\pmb{x}_i\\). \\(reg(\\cdot)\\) in GLLE is constructed as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.124, + 0.344, + 0.47, + 0.378 + ], + "angle": 0, + "content": "\\[\nr e g \\left(f _ {\\theta} (\\boldsymbol {X})\\right) = \\sum_ {i, j} q _ {i, j} \\left\\| f _ {\\theta} \\left(\\boldsymbol {x} _ {i}\\right) - f _ {\\theta} \\left(\\boldsymbol {x} _ {j}\\right) \\right\\| _ {2} ^ {2}. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.386, + 0.47, + 0.418 + ], + "angle": 0, + "content": "Unlike GLLE, LESC [24] considers the global graph information and uses the low-rank representation learning [19]:" + }, + { + "type": "equation", + "bbox": [ + 0.116, + 0.431, + 0.469, + 0.455 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\boldsymbol {G}, \\boldsymbol {E}} \\| \\boldsymbol {G} \\| _ {*} + \\lambda_ {2} \\| \\boldsymbol {E} \\| _ {2, 1}, \\text {s . t . ,} \\boldsymbol {X} = \\boldsymbol {X} \\boldsymbol {G} + \\boldsymbol {E}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.459, + 0.47, + 0.504 + ], + "angle": 0, + "content": "where \\( G \\) indicates the low-rank representation of instances in the feature space. The regularization function in LESC is written as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.14, + 0.513, + 0.47, + 0.534 + ], + "angle": 0, + "content": "\\[\nr e g (f _ {\\theta} (\\pmb {X})) = \\| f _ {\\theta} (\\pmb {X}) - f _ {\\theta} (\\pmb {X}) \\pmb {G} \\| _ {F} ^ {2}. \\qquad (6)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.542, + 0.47, + 0.664 + ], + "angle": 0, + "content": "For these aforementioned LE methods, they all neglect the label irrelevant information contained in \\( X \\), the negative effect of which can result in the unsatisfactory recovery results. Taking the recovery of facial emotion label distributions for example, the inaccurate graph information would be obtained in GLLE and LESSC with the presence of label irrelevant information, such as the identity information, hindering the further improvement of recovery results." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.671, + 0.295, + 0.687 + ], + "angle": 0, + "content": "2.2. Information Bottleneck" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.694, + 0.47, + 0.755 + ], + "angle": 0, + "content": "Information bottleneck (IB) [1, 25, 25] is an information theoretic principle, which describes the relevant information in data formally. To be concrete, IB has the following objective:" + }, + { + "type": "equation", + "bbox": [ + 0.145, + 0.765, + 0.469, + 0.788 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\boldsymbol {B}} - I (\\boldsymbol {B}, \\boldsymbol {C}), \\text {s . t .}, I (\\boldsymbol {A}, \\boldsymbol {B}) \\leqslant I _ {c}, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.796, + 0.47, + 0.873 + ], + "angle": 0, + "content": "where \\(I(\\cdot, \\cdot)\\) measures the mutual information and \\(I_{c}\\) is the information constraint. Clearly, IB aims to learn the representation \\(\\pmb{B}\\), which preserves the relevant information about \\(\\pmb{C}\\), from \\(\\pmb{A}\\). Considering the scenario of LE, it is natural to get the following formula:" + }, + { + "type": "equation", + "bbox": [ + 0.143, + 0.883, + 0.47, + 0.905 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\boldsymbol {H}} - I (\\boldsymbol {H}, \\boldsymbol {L}), \\text {s . t .}, I (\\boldsymbol {X}, \\boldsymbol {H}) \\leqslant I _ {c}. \\tag {8}\n\\]" + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.089, + 0.878, + 0.27 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.279, + 0.892, + 0.448 + ], + "angle": 0, + "content": "Figure 2. Framework of the proposed LIB. Since the way that directly explores the label relevant information is challenging, LIB decomposes the label relevant information into two components, namely the assignments of labels to the instance and the label gaps between label distributions and logical labels, and adopts an indirect path, which explores the information about label assignments and label gaps simultaneously. By minimizing \\(\\mathcal{L}_{as}\\), LIB explores the information about assignments of labels to the instance. Meanwhile, by minimizing \\(\\mathcal{L}_{gap}\\), LIB explores the information about the label gaps between logical labels and label distributions. Consequently, the label relevant information can be effectively explored and the label distributions can be exactly recovered." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.47, + 0.892, + 0.53 + ], + "angle": 0, + "content": "As discussed in Section 1, the information merely about the assignments of labels to the instance can be explored based on Eq. (8), which neglects the vital information about the label gaps between logical labels and label distributions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.531, + 0.892, + 0.636 + ], + "angle": 0, + "content": "Recently, IB has been successfully utilized in many real-world applications [1, 2, 22, 27, 30, 31]. To the best of our knowledge, the method introduced in this paper is the first work that leverages IB to deal with the LE problem. More notably, rather than using IB simply (as shown in Eq. (8)), our method conducts more in-depth exploration to exactly recover label distributions based on IB." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.648, + 0.712, + 0.667 + ], + "angle": 0, + "content": "3. The Proposed Method" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.673, + 0.75, + 0.69 + ], + "angle": 0, + "content": "3.1. The Objective Construction" + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.697, + 0.856, + 0.712 + ], + "angle": 0, + "content": "Generally, the basic idea can be written as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.543, + 0.721, + 0.892, + 0.744 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\boldsymbol {H}} \\mathcal {L} _ {a s} + \\alpha \\mathcal {L} _ {g a p}, \\text {s . t .}, I (\\boldsymbol {X}, \\boldsymbol {H}) \\leqslant I _ {c}, \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.902 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_{as}\\) excavates the information about the assignments of labels to the instance, \\(\\mathcal{L}_{gap}\\) investigates the information about the label gaps between the logical labels and distribution labels, \\(\\alpha\\) is the trade-off parameter, the constraint aims to remove the label irrelevant information. The framework of our method is depicted in Fig. 2. It's worth noting that employing the original IB for LE merely explores the information about the label assignments. While our LIB makes attempts to capture the information about both the label assignments and the description degrees of labels." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7499" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.077, + 0.092, + 0.411, + 0.108 + ], + "angle": 0, + "content": "3.1.1 Label assignments information modeling" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.115, + 0.448, + 0.131 + ], + "angle": 0, + "content": "For \\(\\mathcal{L}_{as}\\), inspired by IB, we have the following formula:" + }, + { + "type": "equation", + "bbox": [ + 0.209, + 0.139, + 0.469, + 0.155 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {a s} = - I (\\boldsymbol {H}, \\boldsymbol {L}). \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.164, + 0.469, + 0.193 + ], + "angle": 0, + "content": "According to the concept of mutual information, \\(\\mathcal{L}_{as}\\) can be rewritten out in full as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.151, + 0.198, + 0.469, + 0.236 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {a s} = - \\sum_ {\\boldsymbol {h}} \\sum_ {\\boldsymbol {l}} p (\\boldsymbol {h}, \\boldsymbol {l}) \\log \\frac {p (\\boldsymbol {l} | \\boldsymbol {h})}{p (\\boldsymbol {l})}. \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.243, + 0.469, + 0.289 + ], + "angle": 0, + "content": "For the convenience of optimization, we introduce the variational approximation \\( q(\\boldsymbol{l}|\\boldsymbol{h}) \\) to \\( p(\\boldsymbol{l}|\\boldsymbol{h}) \\). Since both the Kullback Leibler divergence and the entropy are positive:" + }, + { + "type": "equation", + "bbox": [ + 0.096, + 0.295, + 0.469, + 0.408 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\operatorname {K L} \\left(p (\\boldsymbol {l} | \\boldsymbol {h}) | | q (\\boldsymbol {l} | \\boldsymbol {h})\\right) = \\sum_ {\\boldsymbol {l}} p (\\boldsymbol {l} | \\boldsymbol {h}) \\log \\frac {p (\\boldsymbol {l} | \\boldsymbol {h})}{q (\\boldsymbol {l} | \\boldsymbol {h})} \\geqslant 0 (12) \\\\ \\Rightarrow \\sum_ {\\boldsymbol {l}} p (\\boldsymbol {l} | \\boldsymbol {h}) \\log p (\\boldsymbol {l} | \\boldsymbol {h}) \\geqslant \\sum_ {\\boldsymbol {l}} p (\\boldsymbol {l} | \\boldsymbol {h}) \\log q (\\boldsymbol {l} | \\boldsymbol {h}), \\\\ \\mathbb {E} _ {p (\\boldsymbol {l})} [ - \\log p (\\boldsymbol {l}) ] = - \\sum_ {\\boldsymbol {l}} p (\\boldsymbol {l}) \\log p (\\boldsymbol {l}) \\geqslant 0, (13) \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.412, + 0.447, + 0.428 + ], + "angle": 0, + "content": "based on Markov chain that \\(L\\gets X\\to H\\) , we can get:" + }, + { + "type": "equation", + "bbox": [ + 0.105, + 0.435, + 0.469, + 0.467 + ], + "angle": 0, + "content": "\\[\nL _ {a s} \\leqslant - \\sum_ {\\boldsymbol {x}} \\sum_ {l} \\sum_ {\\boldsymbol {h}} p (\\boldsymbol {x}, l) p (\\boldsymbol {h} | \\boldsymbol {x}) \\log q (l | \\boldsymbol {h}). \\tag {14}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.482, + 0.364, + 0.498 + ], + "angle": 0, + "content": "3.1.2 Label gaps information modeling" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.506, + 0.469, + 0.582 + ], + "angle": 0, + "content": "To investigate the label-relevant information about the description degrees of labels, we introduce the label gaps between logical labels and label distributions \\(\\pmb{\\Delta}\\), and consider the conditional self-information, i.e., \\(I(\\Delta | H)\\). Therefore, we construct \\(\\mathcal{L}_{gap}^{1}\\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.154, + 0.59, + 0.469, + 0.677 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {g a p} = I (\\boldsymbol {\\Delta} | \\boldsymbol {H}) = - \\log p (\\boldsymbol {\\Delta} | \\boldsymbol {H}) \\\\ = - \\sum_ {\\delta} \\sum_ {\\boldsymbol {h}} \\log p (\\boldsymbol {\\delta} | \\boldsymbol {h}) \\tag {15} \\\\ = - \\sum_ {l} \\sum_ {\\boldsymbol {h}} \\log p (\\boldsymbol {l} - \\hat {\\boldsymbol {d}} | \\boldsymbol {h}). \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.686, + 0.469, + 0.716 + ], + "angle": 0, + "content": "where \\(\\delta = l - \\hat{d},\\hat{d}\\) is the label distribution recovered in our method." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.735, + 0.4, + 0.751 + ], + "angle": 0, + "content": "3.1.3 Label irrelevant information modeling" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.758, + 0.469, + 0.804 + ], + "angle": 0, + "content": "Regarding the label irrelevant information, LIB employs the constraint in Eq. (9) to discard it during the learning process. \\( I(\\mathbf{X},\\mathbf{H}) \\) can be formulated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.137, + 0.812, + 0.469, + 0.849 + ], + "angle": 0, + "content": "\\[\nI (\\boldsymbol {X}, \\boldsymbol {H}) = \\sum_ {\\boldsymbol {x}} \\sum_ {\\boldsymbol {h}} p (\\boldsymbol {x}, \\boldsymbol {h}) \\log \\frac {p (\\boldsymbol {h} \\mid \\boldsymbol {x})}{p (\\boldsymbol {h})}. \\tag {16}\n\\]" + }, + { + "type": "page_footnote", + "bbox": [ + 0.077, + 0.856, + 0.469, + 0.906 + ], + "angle": 0, + "content": "It can be also interpreted and derived from the view of the probability distribution: \\(\\max_{\\Delta} \\log p(\\pmb{H}, \\pmb{\\Delta}) \\Rightarrow \\max_{\\Delta} \\log p(\\pmb{\\Delta}|\\pmb{H}) + \\log p(\\pmb{H}) \\Rightarrow \\max_{\\Delta} \\log p(\\pmb{\\Delta}|\\pmb{H})\\). We appreciate reviewers for their helpful comments." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.138 + ], + "angle": 0, + "content": "Since it is difficult to calculate \\( p(h) \\) directly, we also introduce the variational approximation \\( q(h) \\) to \\( p(h) \\). Similar to Eq. (12), based on \\( \\mathrm{KL}(p(h)||q(h)) \\geqslant 0 \\), we have:" + }, + { + "type": "equation", + "bbox": [ + 0.564, + 0.15, + 0.892, + 0.182 + ], + "angle": 0, + "content": "\\[\n\\sum_ {\\boldsymbol {h}} p (\\boldsymbol {h}) \\log p (\\boldsymbol {h}) \\geqslant \\sum_ {\\boldsymbol {h}} p (\\boldsymbol {h}) \\log q (\\boldsymbol {h}). \\tag {17}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.193, + 0.843, + 0.209 + ], + "angle": 0, + "content": "Subsequently, the following formula can be written:" + }, + { + "type": "equation", + "bbox": [ + 0.525, + 0.22, + 0.892, + 0.291 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} I (\\boldsymbol {X}, \\boldsymbol {H}) \\leqslant \\sum_ {\\boldsymbol {x}} \\sum_ {\\boldsymbol {h}} p (\\boldsymbol {x}, \\boldsymbol {h}) \\log \\frac {p (\\boldsymbol {h} | \\boldsymbol {x})}{q (\\boldsymbol {h})} \\tag {18} \\\\ = \\sum_ {\\boldsymbol {x}} \\sum_ {\\boldsymbol {l}} p (\\boldsymbol {x}, \\boldsymbol {l}) \\operatorname {K L} (p (\\boldsymbol {h} | \\boldsymbol {x}) | | q (\\boldsymbol {h})). \\\\ \\end{array}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.312, + 0.671, + 0.327 + ], + "angle": 0, + "content": "3.1.4 Objective of LIB" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.337, + 0.892, + 0.368 + ], + "angle": 0, + "content": "By employing the Lagrange multiplier method and combining Eq. (9), (14), (15), and (18), we have:" + }, + { + "type": "equation", + "bbox": [ + 0.53, + 0.38, + 0.891, + 0.5 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} = \\mathcal {L} _ {a s} + \\alpha \\mathcal {L} _ {g a p} + \\beta I (\\boldsymbol {X}, \\boldsymbol {H}) \\\\ \\leqslant - \\sum_ {\\boldsymbol {x}} \\sum_ {\\boldsymbol {l}} \\sum_ {\\boldsymbol {h}} p (\\boldsymbol {x}, \\boldsymbol {l}) p (\\boldsymbol {h} | \\boldsymbol {x}, \\boldsymbol {l}) \\log q (\\boldsymbol {l} | \\boldsymbol {h}) \\\\ - \\alpha \\sum_ {\\boldsymbol {l}} \\sum_ {\\boldsymbol {h}} \\log p (\\boldsymbol {l} - \\hat {\\boldsymbol {d}} | \\boldsymbol {h}) \\tag {19} \\\\ + \\beta \\sum_ {\\boldsymbol {x}} \\sum_ {\\boldsymbol {l}} p (\\boldsymbol {x}, \\boldsymbol {l}) \\operatorname {K L} (p (\\boldsymbol {h} | \\boldsymbol {x}) | | q (\\boldsymbol {h})). \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.512, + 0.892, + 0.558 + ], + "angle": 0, + "content": "where \\(\\beta\\) is the Lagrange multiplier. Considering the bound of \\(\\mathcal{L}\\) and using the empirical Monte Carlo approximation of sampling [23], we have the following objective of LIB:" + }, + { + "type": "equation", + "bbox": [ + 0.508, + 0.57, + 0.891, + 0.644 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {L I B} = \\frac {1}{n} \\sum_ {i = 1} ^ {n} \\left[ - \\sum_ {\\boldsymbol {h}} p (\\boldsymbol {h} | \\boldsymbol {x} _ {i}) \\log q \\left(\\boldsymbol {l} _ {i} \\mid \\boldsymbol {h}\\right) \\right. \\tag {20} \\\\ + \\beta \\operatorname {K L} (p (\\boldsymbol {h} | \\boldsymbol {x} _ {i}) | | q (\\boldsymbol {h})) ] - \\alpha \\sum_ {\\boldsymbol {l}} \\sum_ {\\boldsymbol {h}} \\log p (\\boldsymbol {l} - \\hat {\\boldsymbol {d}} | \\boldsymbol {h}). \\\\ \\end{array}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.657, + 0.727, + 0.673 + ], + "angle": 0, + "content": "3.2. The Optimization of LIB" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.681, + 0.89, + 0.711 + ], + "angle": 0, + "content": "To minimize the objective of \\(\\mathcal{L}_{LIB}\\), we use the reparameterization trick [16, 23]. For \\(p(\\boldsymbol{h}|\\boldsymbol{x})\\), we assume that:" + }, + { + "type": "equation", + "bbox": [ + 0.6, + 0.723, + 0.891, + 0.742 + ], + "angle": 0, + "content": "\\[\np (\\boldsymbol {h} | \\boldsymbol {x}) \\sim \\mathcal {N} \\left(\\boldsymbol {\\mu} _ {\\boldsymbol {h} | \\boldsymbol {x}}, \\boldsymbol {\\sigma} _ {\\boldsymbol {h} | \\boldsymbol {x}} ^ {2} \\boldsymbol {I}\\right), \\tag {21}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.754, + 0.892, + 0.8 + ], + "angle": 0, + "content": "where \\(\\pmb{\\mu}_{h|\\pmb{x}}\\) and \\(\\sigma_{h|x}\\) are obtained by using the encoder network \\(f_{\\theta_{en}}(\\cdot)\\), i.e., \\(\\pmb{\\mu}_{h|x} = f_{\\theta_{en}}^{\\pmb{\\mu}}(\\pmb{x})\\) and \\(\\pmb{\\sigma}_{h|x} = f_{\\theta_{en}}^{\\pmb{\\sigma}}(\\pmb{x})\\). Subsequently, we have that:" + }, + { + "type": "equation", + "bbox": [ + 0.618, + 0.813, + 0.891, + 0.829 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {h} = \\mu_ {\\boldsymbol {h} | \\boldsymbol {x}} + \\sigma_ {\\boldsymbol {h} | \\boldsymbol {x}} \\odot \\epsilon , \\tag {22}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.842, + 0.891, + 0.872 + ], + "angle": 0, + "content": "where \\(\\epsilon \\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I})\\) and \\(\\odot\\) is the element-wise product. For \\(q(l|h)\\), we assume:" + }, + { + "type": "equation", + "bbox": [ + 0.622, + 0.885, + 0.891, + 0.903 + ], + "angle": 0, + "content": "\\[\nq (\\boldsymbol {l} | \\boldsymbol {h}) \\sim \\mathcal {N} \\left(\\boldsymbol {\\mu} _ {\\boldsymbol {l} | \\boldsymbol {h}}, \\boldsymbol {I}\\right), \\tag {23}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7500" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.123 + ], + "angle": 0, + "content": "where \\(\\pmb{\\mu}_{l|\\pmb{h}}\\) is learned by using the decoder network \\(f_{\\theta_{de}}(\\cdot)\\), namely, \\(\\pmb{\\mu}_{l|\\pmb{h}} = f_{\\theta_{de}}(\\pmb{h})\\). For \\(q(\\pmb{h})\\), we assume that:" + }, + { + "type": "equation", + "bbox": [ + 0.214, + 0.134, + 0.469, + 0.151 + ], + "angle": 0, + "content": "\\[\nq (\\boldsymbol {h}) \\sim \\mathcal {N} (\\boldsymbol {0}, \\boldsymbol {I}). \\tag {24}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.161, + 0.43, + 0.178 + ], + "angle": 0, + "content": "For \\(p(\\boldsymbol{l} - \\hat{\\boldsymbol{d}}|\\boldsymbol{h})\\), the following assumption is adopted:" + }, + { + "type": "equation", + "bbox": [ + 0.178, + 0.187, + 0.469, + 0.208 + ], + "angle": 0, + "content": "\\[\np (\\boldsymbol {l} - \\hat {\\boldsymbol {d}} | \\boldsymbol {h}) \\sim \\mathcal {N} (\\boldsymbol {0}, \\sigma_ {\\delta | \\boldsymbol {h}} ^ {2} \\boldsymbol {I}), \\tag {25}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.217, + 0.469, + 0.281 + ], + "angle": 0, + "content": "where \\(\\sigma_{\\delta|\\pmb{h}}\\) can be achieved by introducing the gap deviation network \\(f_{\\theta_{gd}}(\\cdot)\\), i.e., \\(\\sigma_{\\delta|\\pmb{h}} = f_{\\theta_{gd}}(\\pmb{h})\\). For the recovered label distribution \\(\\hat{\\pmb{d}}\\), we introduce the label distribution network \\(f_{\\theta_{ld}}(\\cdot)\\) and has the following formula:" + }, + { + "type": "equation", + "bbox": [ + 0.228, + 0.292, + 0.469, + 0.311 + ], + "angle": 0, + "content": "\\[\n\\hat {\\boldsymbol {d}} = f _ {\\theta_ {l d}} (\\boldsymbol {h}). \\tag {26}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.322, + 0.412, + 0.337 + ], + "angle": 0, + "content": "Consequently, based on Eq. (21)-(26), we have:" + }, + { + "type": "equation", + "bbox": [ + 0.088, + 0.349, + 0.469, + 0.479 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\min _ {\\theta_ {e n}, \\theta_ {d e}, \\theta_ {g d}, \\theta_ {l d}} \\mathcal {L} _ {L I B} \\\\ \\Rightarrow \\min _ {\\theta_ {e n}, \\theta_ {d e}, \\theta_ {g d}, \\theta_ {l d}} \\frac {1}{n} \\sum_ {\\boldsymbol {l}} \\left[ \\frac {1}{2} \\| \\boldsymbol {\\mu} _ {\\boldsymbol {l} | \\boldsymbol {h}} - \\boldsymbol {l} \\| _ {2} ^ {2} \\right. (27) \\\\ \\left. + \\alpha \\left(\\frac {1}{2} (\\boldsymbol {l} - \\hat {\\boldsymbol {d}}) ^ {T} \\left(\\boldsymbol {\\sigma} _ {\\delta | h} ^ {- 2} \\boldsymbol {I}\\right) (\\boldsymbol {l} - \\hat {\\boldsymbol {d}}) + \\log \\det \\left(\\boldsymbol {\\sigma} _ {\\delta | h} ^ {2} \\boldsymbol {I}\\right)\\right) \\right] (27) \\\\ + \\frac {\\beta}{2} \\sum_ {\\boldsymbol {x}} \\left[ \\boldsymbol {\\mu} _ {\\boldsymbol {h} | \\boldsymbol {x}} ^ {T} \\boldsymbol {\\mu} _ {\\boldsymbol {h} | \\boldsymbol {x}} + \\operatorname {t r} \\left(\\boldsymbol {\\sigma} _ {\\boldsymbol {h} | \\boldsymbol {x}} ^ {2} \\boldsymbol {I}\\right) - \\log \\det \\left(\\boldsymbol {\\sigma} _ {\\boldsymbol {h} | \\boldsymbol {x}} ^ {2} \\boldsymbol {I}\\right) \\right]. \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.489, + 0.469, + 0.566 + ], + "angle": 0, + "content": "When the problem of Eq. (27) is optimized, we can effectively recover the desired label distributions. To be specific, given \\(\\{\\pmb {X},\\pmb {L}\\}\\), we can obtain \\(\\pmb{H}\\) according to Eq. (22) and achieve the recovery results based on Eq. (26), namely, \\(\\hat{\\pmb{D}} = f_{\\theta_{ld}}(\\pmb {H})\\)" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.575, + 0.414, + 0.591 + ], + "angle": 0, + "content": "3.3. Comparison with Existing LE Methods" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.598, + 0.469, + 0.703 + ], + "angle": 0, + "content": "The main difference between LIB and existing methods is that our method deals with the problem of LE from the perspective of information bottleneck. Considering the first term in Eq. (2), it aims to minimize \\( \\| \\pmb{d} - \\pmb{l} \\|_2^2 \\) under the assumption that information in the label distributions is inherited from the initial logical labels [24, 28, 29]. For LIB, the more reasonable term:" + }, + { + "type": "equation", + "bbox": [ + 0.11, + 0.711, + 0.469, + 0.741 + ], + "angle": 0, + "content": "\\[\n\\frac {1}{2} (\\boldsymbol {l} - \\hat {\\boldsymbol {d}}) ^ {T} \\left(\\boldsymbol {\\sigma} _ {\\delta | \\boldsymbol {h}} ^ {- 2} \\boldsymbol {I}\\right) (\\boldsymbol {l} - \\hat {\\boldsymbol {d}}) + \\log \\det \\left(\\boldsymbol {\\sigma} _ {\\delta | \\boldsymbol {h}} ^ {2} \\boldsymbol {I}\\right) \\tag {28}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.75, + 0.469, + 0.794 + ], + "angle": 0, + "content": "which can be deduced by excavating the label relevant information about the label gaps between logical labels and label distributions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Besides, we compare our method with the recently proposed LEVI [29] further. Although the objectives of LEVI and LIB are somewhat similar in form, they are essentially different as follows: 1) LIB makes attempts from the perspective of information bottleneck, while LEVI from the view of variational inference; 2) The formulas of LEVI and LIB are just partially similar in form, since the variational" + }, + { + "type": "table", + "bbox": [ + 0.544, + 0.089, + 0.855, + 0.277 + ], + "angle": 0, + "content": "
Dataset# dimension q# instance n# labels c
Artificialtoy326013
Movie186977555
SBU-3DFE24325006
SJAFFE2432136
Yeast-alpha24246518
Yeast-cdc24246515
Yeast-cold2424654
Yeast-diau2424657
Yeast-dtt2424654
Yeast-elu24246514
Yeast-heat2424656
Yeast-spo2424656
Yeast-spo52424653
Yeast-spoem2424652
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.288, + 0.892, + 0.316 + ], + "angle": 0, + "content": "Table 1. Details of datasets. The numbers of dimension \\( q \\), instance \\( n \\), and labels \\( c \\) are provided here." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.344, + 0.892, + 0.42 + ], + "angle": 0, + "content": "inference is employed as the optimization tool in LIB. The details of these two formulas are totally different; 3) LEVI requires an extra regularizer, i.e., \\(\\| d - l\\| _2^2\\) to constrain the recovery process, while LIB achieves \\(d\\) based on the more reasonable term, i.e., Eq. (28)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.435, + 0.632, + 0.453 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.461, + 0.891, + 0.491 + ], + "angle": 0, + "content": "To verify the effectiveness and competitiveness of LIB, extensive experiments are conducted in this section." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.503, + 0.691, + 0.52 + ], + "angle": 0, + "content": "4.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.527, + 0.892, + 0.693 + ], + "angle": 0, + "content": "As shown in Table 1, we use both one toy dataset and 13 real-world datasets for evaluation\\(^2\\). For the toy dataset, i.e., Artificial dataset, it is utilized to vividly show the recovery performance [28]. Movie dataset is collected from movies, SBU-3DFE and SJAFFE datasets are two facial expression datasets. Yeast datasets (alpha to spoem) are collected from 10 biological experiments on the budding yeast genes [4]. It is important to note that only the ground-truth label distributions are provided by these datasets. Therefore, we adopt the binarization strategy, which is also used in existing LE works [24, 28, 29], to ensure the consistency of evaluation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.694, + 0.892, + 0.876 + ], + "angle": 0, + "content": "We compare our method LIB to 7 LE methods, including FCM [5], KM [15], LP [17], ML [11], GLLE [28], LESC [24], and LEVI [29]. The first two methods belong to the algorithm adaption, and the rest methods are specialized algorithms. For the sake of fairness, we utilize the parameter settings recommended in their original works. Specifically, for FCM, we set the parameter \\(\\beta = 2\\). For KM, we leverage the Gaussian kernel. For LP, we set the parameter \\(\\alpha = 0.5\\). For ML, we set the number of neighbors \\(k = c + 1\\). For GLLE, we select \\(\\lambda\\) from \\(\\{0.01, 0.1, \\dots, 100\\}\\) and set the number of neighbors \\(k\\) to \\(c + 1\\). For LESC, \\(\\lambda_{1}\\) and \\(\\lambda_{2}\\) are selected from \\(\\{0.0001, 0.1, \\dots, 10\\}\\). For LEVI, MLPs with" + }, + { + "type": "page_footnote", + "bbox": [ + 0.516, + 0.887, + 0.765, + 0.901 + ], + "angle": 0, + "content": "\\(^{2}\\)http://palm.seu.edu.cn/xgeng/LDL/index.htm" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "7501" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.167 + ], + "angle": 0, + "content": "two hidden layers and softmax activation functions are utilized, and the results are reported after 150 training epochs. For LIB, we select \\(\\alpha\\) and \\(\\beta\\) from \\(\\{0.001, 0.01, \\dots, 10\\}\\), and the fully connected networks with 3 layers and sigmoid activation function are leveraged in the proposed method." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.168, + 0.471, + 0.258 + ], + "angle": 0, + "content": "To evaluate the recovery performance, we adopt 6 metrics, namely Chebyshev, Canberra, Clark, Kullback-Leibler, Cosine, and Intersection [8,24,28]. Given the ground-truth label distribution \\( \\pmb{d} \\) and the recovered label distribution \\( \\hat{\\pmb{d}} \\), the first four metrics and the rest two metrics respectively measure the distance and similarity between \\( \\pmb{d} \\) and \\( \\hat{\\pmb{d}} \\):" + }, + { + "type": "equation", + "bbox": [ + 0.143, + 0.262, + 0.47, + 0.289 + ], + "angle": 0, + "content": "\\[\nD _ {\\text {C h e b y s h e v}} (\\boldsymbol {d}, \\hat {\\boldsymbol {d}}) = \\max _ {i} \\left| d ^ {y _ {i}} - \\hat {d} ^ {y _ {i}} \\right|, \\tag {29}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.154, + 0.29, + 0.469, + 0.338 + ], + "angle": 0, + "content": "\\[\nD _ {\\text {C a n b e r r a}} (\\boldsymbol {d}, \\hat {\\boldsymbol {d}}) = \\sum_ {i = 1} ^ {c} \\frac {\\left| d ^ {y _ {i}} - \\hat {d} ^ {y _ {i}} \\right|}{d ^ {y _ {i}} + \\hat {d} ^ {y _ {i}}}, \\tag {30}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.148, + 0.341, + 0.469, + 0.404 + ], + "angle": 0, + "content": "\\[\nD _ {\\text {C l a r k}} (\\boldsymbol {d}, \\hat {\\boldsymbol {d}}) = \\sqrt {\\sum_ {i = 1} ^ {c} \\frac {\\left(d ^ {y _ {i}} - \\hat {d} ^ {y _ {i}}\\right) ^ {2}}{\\left(d ^ {y _ {i}} + \\hat {d} ^ {y _ {i}}\\right) ^ {2}}}, \\tag {31}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.136, + 0.406, + 0.469, + 0.445 + ], + "angle": 0, + "content": "\\[\nD _ {\\text {K u l l b a c k - L e i b l e r}} (\\boldsymbol {d}, \\hat {\\boldsymbol {d}}) = \\sum_ {i = 1} ^ {c} d ^ {y _ {i}} \\ln \\frac {d ^ {y _ {i}}}{\\hat {d} ^ {y _ {i}}}, \\tag {32}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.114, + 0.449, + 0.469, + 0.522 + ], + "angle": 0, + "content": "\\[\nS _ {\\text {C o s i n e}} (\\boldsymbol {d}, \\hat {\\boldsymbol {d}}) = \\frac {\\sum_ {i = 1} ^ {c} d ^ {y _ {i}} \\hat {d} ^ {y _ {i}}}{\\sqrt {\\sum_ {i = 1} ^ {c} \\left(d ^ {y _ {i}}\\right) ^ {2}} \\sqrt {\\sum_ {i = 1} ^ {c} \\left(\\hat {d} ^ {y _ {i}}\\right) ^ {2}}}, \\tag {33}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.136, + 0.525, + 0.469, + 0.563 + ], + "angle": 0, + "content": "\\[\nS _ {\\text {I n t e r s e c t i o n}} (\\boldsymbol {d}, \\hat {\\boldsymbol {d}}) = \\sum_ {i = 1} ^ {c} \\min \\left(d ^ {y _ {i}}, \\hat {d} ^ {y _ {i}}\\right). \\tag {34}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.568, + 0.469, + 0.599 + ], + "angle": 0, + "content": "The smaller values of distance metric and similarity metric indicate the better and the worse results, respectively." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.606, + 0.394, + 0.623 + ], + "angle": 0, + "content": "4.2. Visualization Results on Toy Dataset" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.629, + 0.469, + 0.704 + ], + "angle": 0, + "content": "The recovery results on the Artificial dataset are vividly presented in Fig. 3, which shows the three-dimensional label distributions by the RGB color channels separately. The more similar the color patterns of the recovered results and the ground-truth are, the better the recovery results are." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.47, + 0.795 + ], + "angle": 0, + "content": "It can be seen that FCM, GLLE, LESC, LEVI, and LIB can obtain the similar color pattern, while KM, LP, and ML are incapable to obtain the promising recovery performance on Artificial dataset. Regarding the visualization results of FCM, GLLE, LESC, LEVI, and LIB, the color pattern that is most close to the ground-truth is achieved by our LIB." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.802, + 0.452, + 0.818 + ], + "angle": 0, + "content": "4.3. Comparison Results on Real-world Datasets" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.825, + 0.469, + 0.902 + ], + "angle": 0, + "content": "We provide the detailed comparison results on 13 real-world datasets in Table 2. Overall, LIB has the competitive recovery performance. We have the following observations: 1) Compared with FCM and KM, which belong to the category of algorithm adaption, remarkable improvements can" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.093, + 0.63, + 0.163 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.543, + 0.166, + 0.591, + 0.178 + ], + "angle": 0, + "content": "(a) FCM" + }, + { + "type": "image", + "bbox": [ + 0.635, + 0.094, + 0.758, + 0.163 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.675, + 0.166, + 0.718, + 0.178 + ], + "angle": 0, + "content": "(b) KM" + }, + { + "type": "image", + "bbox": [ + 0.764, + 0.094, + 0.89, + 0.163 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.808, + 0.166, + 0.845, + 0.178 + ], + "angle": 0, + "content": "(c) LP" + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.183, + 0.629, + 0.254 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.547, + 0.256, + 0.588, + 0.268 + ], + "angle": 0, + "content": "(d) ML" + }, + { + "type": "image", + "bbox": [ + 0.635, + 0.183, + 0.757, + 0.254 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.671, + 0.256, + 0.724, + 0.268 + ], + "angle": 0, + "content": "(e) GLLE" + }, + { + "type": "image", + "bbox": [ + 0.764, + 0.183, + 0.889, + 0.254 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.801, + 0.256, + 0.852, + 0.268 + ], + "angle": 0, + "content": "(f) LESC" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.274, + 0.63, + 0.343 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.542, + 0.346, + 0.593, + 0.358 + ], + "angle": 0, + "content": "(g) LEVI" + }, + { + "type": "image", + "bbox": [ + 0.635, + 0.274, + 0.758, + 0.343 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.676, + 0.345, + 0.718, + 0.358 + ], + "angle": 0, + "content": "(h) LIB" + }, + { + "type": "image", + "bbox": [ + 0.764, + 0.274, + 0.889, + 0.343 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.783, + 0.345, + 0.871, + 0.358 + ], + "angle": 0, + "content": "(i) Ground-truth" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.37, + 0.892, + 0.412 + ], + "angle": 0, + "content": "Figure 3. Visualization results of the label distributions recovered by different methods ((a)-(h)) and the ground-truth ((i)) on Artificial dataset. (Best viewed in color.)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.44, + 0.892, + 0.682 + ], + "angle": 0, + "content": "be achieved by our method; 2) Compared with the methods belonging to the category of specialized algorithm, LIB can also obtain better recovery results in most cases. For example, LIB obtains the best recovery results on Movie datasets in all metrics. Moreover, although LESC can obtain slightly favorable results in some cases, the corresponding recovery results of LIB are also promising and competitive. The underlying reason may be that LESC further considers the sample correlations during the recovery process; 3) The recovery performance of all methods can be roughly ranked as LIB>LESC≈LEV1>GLLE>LP≈FCM>ML>KM. We can conclude that LIB is suitable for the LE problem. The underlying reason for the significant improvement is that the label relevant information, including the information about label assignments and the information about label gaps, can be effectively investigated by LIB." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.693, + 0.776, + 0.709 + ], + "angle": 0, + "content": "4.4. Analysis and Discussion of LIB" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.718, + 0.892, + 0.747 + ], + "angle": 0, + "content": "We analyze the parameter sensitivity of LIB firstly, and then we conduct the ablation studies as well." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.77, + 0.677, + 0.785 + ], + "angle": 0, + "content": "4.4.1 Sensitivity of LIB" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In the proposed method, we choose the values of \\(\\alpha\\) and \\(\\beta\\) from \\(\\{0.001, 0.01, \\dots, 10\\}\\). To show the parameter sensitivity of LIB, we conduct experiments on SBU-3DFE datasets with different values of \\(\\alpha\\) and \\(\\beta\\). Regarding the dimension of the learned latent representation, we set it to 256 for all datasets. The experimental results in metrics of Chebyshev distance, Cosine coefficient, and Intersection similarity are" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7502" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.094, + 0.088, + 0.88, + 0.693 + ], + "angle": 0, + "content": "
MetricChebyshev ↓Clark ↓
MethodFCMKMLPMLGLLELESCLEVLIBFCMKMLPMLGLLELESCLEVLIB
Movie0.2300.2340.1610.1640.1220.1210.1100.1070.8591.7660.9131.1400.5690.5640.5510.517
SUB-3DFE0.1350.2380.1230.2330.1260.1220.0950.0940.4821.9070.5801.8480.3910.3780.3030.297
SJAFFE0.1320.2140.1070.1860.0870.0690.0750.0710.5221.8740.5021.5190.3770.2760.2900.262
Yeast-alpha0.0440.0630.0400.0570.0200.0150.0120.0170.8213.1531.1853.0880.3370.2530.3190.275
Yeast-cdc0.0510.0760.0420.0710.0220.0190.0160.0170.7392.8851.0142.8250.3060.2510.3230.242
Yeast-cold0.1410.2520.1370.2420.0660.0560.0820.0540.4331.4720.5031.4400.1760.1520.2690.146
Yeast-diau0.1240.1520.0990.1480.0530.0420.0440.0490.8381.8860.7881.8440.2960.2240.2950.273
Yeast-dtt0.0970.2570.1280.2440.0520.0430.0840.0340.3291.4770.4991.4460.1430.1190.2940.092
Yeast-elu0.0520.0780.0440.0720.0230.0190.0170.0180.5792.7680.9732.7110.2950.2410.3170.224
Yeast-heat0.1690.1750.0860.1650.0490.0460.0520.0390.5801.8020.5681.7640.2130.1990.2880.165
Yeast-spo0.1300.1750.0900.1710.0620.0600.0550.0530.5201.8110.5581.7680.2660.2580.2770.224
Yeast-spo50.1620.2770.1140.2730.0990.0920.0910.0760.3951.0590.2741.0360.1970.1850.2090.158
Yeast-sopem0.2330.4080.1630.4030.0880.0870.1150.0690.4011.0280.2721.0040.1320.1290.1820.104
Avg.Rank6.0778.0005.0006.8463.7692.3082.4631.5385.3858.0005.6157.0003.3851.9233.4621.231
MetricCanberra ↓
MethodFCMKMLPMLGLLELESCLEVLIBFCMKMLPMLGLLELESCLEVLIB
Movie1.6643.4441.7201.9341.0451.0340.9740.9200.3810.4520.1770.2180.1230.1200.0820.077
SUB-3DFE1.0204.1211.2454.0010.8200.7990.6370.6110.0940.6030.1050.5650.0690.0640.0420.041
SJAFFE1.0814.0101.0643.1380.7810.5610.6000.5310.1070.5580.0770.3910.0500.0290.0320.027
Yeast-alpha2.88311.8094.54411.6031.1340.8461.2490.8930.1000.6300.1210.6020.0130.0080.0110.009
Yeast-cdc2.4159.8753.6449.6950.9590.7651,1480.7470.0910.6300.1110.6010.0140.0100.0140.008
Yeast-cold0.7342.5660.9242.5190.3050.2630.5010.2500.1130.5860.1030.5560.0190.0150.0350.012
Yeast-diau1.8954.2611.7484.1800.6710.4800.6890.6210.1590.5380.1270.5090.0270.0170.0230.022
Yeast-dtt0.5012.5940.9412.5490.2480.2060.5620.1580.0650.6170.1030.5860.0130.0100.0420.005
Yeast-elu1.6899.1103.3818.9490.9020.7271.0930.6700.0590.6170.1090.5890.0130.0090.0140.008
Yeast-heat1.1573.8491.2933.7790.4300.4010.6460.3270.1470.5860.0890.5560.0170.0150.0270.011
Yeast-spo0.9983.8541.2313.7720.5480.5330.6050.4540.1100.5620.0840.5320.0290.0280.0250.019
Yeast-spo50.5631.3820.4011.3550.3050.2840.3110.2410.1230.3340.0420.3170.0340.0310.0280.021
Yeast-sopem0.5341.2530.3651.2260.1830.1800.2480.1440.2080.5310.0670.5030.0270.0270.0360.018
Avg.Rank5.2318.0005.6927.0003.2312.003.6921.1545.6928.0005.3856.9233.4622.1543.0771.154
MetricCosine ↑
MethodFCMKMLPMLGLLELESCLEVLIBFCMKMLPMLGLLELESCLEVLIB
Movie0.7730.8800.9290.9190.9360.9370.9540.9550.6770.6490.7780.7790.8310.8330.8490.859
SUB-3DFE0.9120.8120.9220.8150.9270.9320.9560.9580.8270.5790.8100.5870.8500.8550.8820.887
SJAFFE0.9060.8270.9410.8570.9580.9730.9690.9740.8210.5930.8370.6610.8720.9050.8970.909
Yeast-alpha0.9220.7510.9110.7560.9870.9920.9890.9920.8440.5320.7740.5370.9380.9530.9320.951
Yeast-cdc0.9290.7540.9160.7590.9870.9910.9870.9920.8470.5330.7790.5380.9370.9500.9250.951
Yeast-heat0.9220.7790.9250.7840.9820.9860.9700.9880.8330.5590.7940.5650.9240.9350.8810.938
Yeast-diau0.8820.7990.9150.8030.9750.9850.9800.9790.7600.5880.7880.5930.9060.9330.9080.913
Yeast-dtt0.9590.7590.9210.7630.9880.9910.9650.9950.8940.5410.7860.5460.9390.9490.8660.961
Yeast-elu0.9500.7580.9180.7630.9870.9910.9870.9920.8830.5390.7820.5440.9360.9490.9240.952
Yeast-heat0.8830.7790.9320.7830.9840.9860.9770.9900.8070.5590.8050.5640.9290.9340.8970.946
Yeast-spo0.9090.8000.9390.8030.9740.9750.9780.9820.8360.5750.8190.5800.9090.9120.9030.925
Yeast-spo50.9220.8820.9690.8840.9710.9740.9790.9830.8380.7240.8860.7270.9010.9080.9090.924
Yeast-sopem0.8780.8120.9500.8150.9780.9780.9720.9850.7670.5920.8370.5970.9120.9130.8850.931
Avg.Rank5.8467.9235.3086.9233.4622.1542.9231.2315.3858.0005.6926.8463.3852.0073.4621.154
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.705, + 0.895, + 0.734 + ], + "angle": 0, + "content": "Table 2. Recovery results on 13 real-world datasets. \\( \\downarrow \\) indicates that \"the smaller the better\" and \\( \\uparrow \\) means that \"the larger the better\". The average ranks (Avg.Rank) on all datasets are also reported for all methods. We highlight the best recovery results." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.759, + 0.471, + 0.806 + ], + "angle": 0, + "content": "provided in Fig. 4. It can be observed that LIB method can get promising recovery results and is robust with respect to different values of \\(\\alpha\\) and \\(\\beta\\) in a large range." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.83, + 0.295, + 0.845 + ], + "angle": 0, + "content": "4.4.2 Ablation studies of LIB" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.471, + 0.903 + ], + "angle": 0, + "content": "The ablation studies are conducted to further verify the effectiveness of introducing the label information bottleneck framework for LE. In the proposed objective Eq. (9), \\(\\mathcal{L}_{as}\\)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.759, + 0.895, + 0.898 + ], + "angle": 0, + "content": "and \\(\\mathcal{L}_{gap}\\) explore the label assignments information and label gaps information during the recovery process. As can be observed from Eq. (14) and Eq. (15), only the latent representation \\(\\pmb{H}\\) can be learned if we employ \\(\\mathcal{L}_{as}\\) merely during the recovery process. Consequently, considering the goal of LE, we compare the proposed LIB with the method termed \\(\\mathrm{LIB}_{gap}\\), which only employs \\(\\mathcal{L}_{gap}\\) to achieve the recovery results. In other words, \\(\\mathrm{LIB}_{gap}\\) investigates the label gaps information in the case of not considering the label assign-" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.958 + ], + "angle": 0, + "content": "7503" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.134, + 0.093, + 0.368, + 0.232 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.203, + 0.235, + 0.292, + 0.248 + ], + "angle": 0, + "content": "(a) Chebyshev" + }, + { + "type": "image", + "bbox": [ + 0.373, + 0.096, + 0.596, + 0.23 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.452, + 0.233, + 0.52, + 0.246 + ], + "angle": 0, + "content": "(b) Cosine \\(\\uparrow\\)" + }, + { + "type": "image", + "bbox": [ + 0.609, + 0.096, + 0.837, + 0.231 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.678, + 0.234, + 0.771, + 0.246 + ], + "angle": 0, + "content": "(c) Intersection \\(\\uparrow\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.259, + 0.895, + 0.302 + ], + "angle": 0, + "content": "Figure 4. The recovery results in metrics of (a) Chebyshev distance, (b) Cosine coefficient, and (c) Intersection similarity with different values of \\(\\alpha\\) and \\(\\beta\\). \\(\\downarrow\\) indicates that \"the smaller the better\" and \\(\\uparrow\\) means that \"the larger the better\". The experimental results demonstrate that LIB is robust with respect to different values of \\(\\lambda\\) and \\(\\beta\\). (Best viewed in color.)" + }, + { + "type": "table", + "bbox": [ + 0.136, + 0.315, + 0.842, + 0.518 + ], + "angle": 0, + "content": "
MetricChebyshev ↓Clark ↓Canberra ↓Kullback-Leibler ↓Cosine ↑Intersection ↑
MethodLIBgapLIBLIBgapLIBLIBgapLIBLIBgapLIBLIBgapLIBLIBgapLIB
Movie0.1200.1070.5630.5171.0290.9200.0990.0770.9380.9550.8340.859
SUB-3DFE0.1300.0940.3950.2970.8490.6110.0790.0410.9230.9580.8460.887
SJAFFE0.1130.0710.3910.2620.8160.5310.0660.0270.9380.9730.8600.909
Yeast-alpha0.0180.0170.2810.2750.9200.8930.0100.0090.9910.9920.9500.951
Yeast-cdc0.0190.0170.2540.2420.7820.7470.0090.0080.9910.9920.9480.951
Yeast-cold0.0610.0170.1620.1460.2800.2500.0160.0120.9850.9880.9300.938
Yeast-diau0.0500.0490.2880.2730.6590.6210.0250.0220.9770.9790.9080.913
Yeast-dtt0.0450.0340.1240.0920.2170.1580.0100.0050.9910.9950.9460.961
Yeast-elu0.0190.0180.2370.2240.7140.6700.0090.0080.9920.9920.9490.952
Yeast-heat0.0450.0390.1930.1650.3880.3270.0140.0110.9860.9900.9360.946
Yeast-spo0.0590.0530.2530.2240.5230.4540.0250.0190.9760.9820.9140.925
Yeast-spo50.0970.0760.1930.1580.3000.2410.0320.0210.9710.9830.9030.924
Yeast-sopem0.0880.0690.1300.1040.1810.1440.0270.0180.9770.9850.9120.931
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.527, + 0.893, + 0.556 + ], + "angle": 0, + "content": "Table 3. Recovery results of \\( \\mathrm{LIB}_{gap} \\) and LIB on 13 real-world datasets. \\( \\downarrow \\) indicates that \"the smaller the better\" and \\( \\uparrow \\) means that \"the larger the better\". We highlight the best recovery results." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.583, + 0.391, + 0.598 + ], + "angle": 0, + "content": "ments information during the recovery process." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.598, + 0.465, + 0.614 + ], + "angle": 0, + "content": "To be specific, \\(\\mathrm{LIB}_{gap}\\) has with the following objective:" + }, + { + "type": "equation", + "bbox": [ + 0.082, + 0.626, + 0.469, + 0.673 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\theta_ {g d}, \\theta_ {l d}} \\frac {1}{2} \\sum_ {\\boldsymbol {x}} \\left[ (\\boldsymbol {l} - \\hat {\\boldsymbol {d}}) ^ {T} \\left(\\boldsymbol {\\sigma} _ {\\delta | \\boldsymbol {x}} ^ {- 2} \\boldsymbol {I}\\right) (\\boldsymbol {l} - \\hat {\\boldsymbol {d}}) + \\log \\det \\left(\\boldsymbol {\\sigma} _ {\\delta | \\boldsymbol {x}} ^ {2} \\boldsymbol {I}\\right) \\right]. \\tag {35}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.673, + 0.47, + 0.735 + ], + "angle": 0, + "content": "Notably, \\(\\sigma_{\\delta |x} = f_{\\theta_{gd}}(x)\\) and \\(\\hat{\\pmb{d}} = f_{\\theta_{ld}}(\\pmb {x})\\) , which are different from the objective Eq. (27) utilized in LIB. Only the partial label relevant information, i.e., the information about the label gaps, is explored in \\(\\mathrm{LIB}_{gap}\\)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Table 3 provides the recovery results of \\(\\mathrm{LIB}_{gap}\\) and LIB. It can be observed that LIB outperforms \\(\\mathrm{LIB}_{gap}\\) in all cases. Compared with LIB, \\(\\mathrm{LIB}_{gap}\\) merely makes the effort to explore the label gap information to boost the recovery performance, while LIB excavates both the information about the label assignments and the information about the label gaps jointly. Therefore, the promising recovery performance can be achieved by LIB. Furthermore, according to the results provided in Table 2 and 3, the recovery results of \\(\\mathrm{LIB}_{gap}\\) seem to be competitive, which also indicates that the exploration of information about label gaps is beneficial for LE." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.581, + 0.62, + 0.597 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.606, + 0.893, + 0.757 + ], + "angle": 0, + "content": "In this paper, we present a new perspective to deal with the Label Enhancement (LE) problem and introduce the novel Label Information Bottleneck (LIB) method. The label relevant information is decomposed into the information about label assignments and the information about label gaps. Consequently, our method transform the LE problem into simultaneously learning the latent representation and modeling the label gaps. Extensive experiments carried on both the toy dataset and real-world datasets verify the competitiveness of LIB." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.77, + 0.661, + 0.788 + ], + "angle": 0, + "content": "Acknowledgments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.894, + 0.903 + ], + "angle": 0, + "content": "This work was supported by the National Key R&D Program of China under Grant 2020AAA0109602; the Education and Research Foundation for Middle-aged and Young Teacher of Fujian Province under Grant JAT220005; the National Natural Science Foundation of China (NSFC) under Grant 62206156; Alibaba Group through Alibaba Innovative Research Program, No.21169774." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7504" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.156 + ], + "angle": 0, + "content": "[1] A Alemi, Ian Fischer, J Dillon, and Kevin Murphy. 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PhD thesis, Carnegie Mellon University, language technologies institute, 2005. 2" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.47, + 0.332 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.517, + 0.956 + ], + "angle": 0, + "content": "7506" + } + ] +] \ No newline at end of file diff --git a/2023/Label Information Bottleneck for Label Enhancement/17915eba-e6e6-4f83-bad7-de11a7a573e3_origin.pdf b/2023/Label Information Bottleneck for Label Enhancement/17915eba-e6e6-4f83-bad7-de11a7a573e3_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..96aab4dc274be809d8b5618a23acd4888b70e26a --- /dev/null +++ b/2023/Label Information Bottleneck for Label Enhancement/17915eba-e6e6-4f83-bad7-de11a7a573e3_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:37c65a2c2cb462caf2fa8c61e0e709266fb5ac93beb4fe7562a3ca19c3221a57 +size 2956982 diff --git a/2023/Label Information Bottleneck for Label Enhancement/full.md b/2023/Label Information Bottleneck for Label Enhancement/full.md new file mode 100644 index 0000000000000000000000000000000000000000..1fc820f7c48d40e15f54444e4a0204738c2bb4eb --- /dev/null +++ b/2023/Label Information Bottleneck for Label Enhancement/full.md @@ -0,0 +1,420 @@ +# Label Information Bottleneck for Label Enhancement + +Qinghai Zheng $^{1}$ , Jihua Zhu $^{2*}$ , Haoyu Tang $^{3}$ + +1College of Computer and Data Science, Fuzhou University, China + +$^{2}$ School of Software Engineering, Xi'an Jiaotong University, Xi'an, China + +$^{3}$ School of Software, Shandong University, Jinan, China + +# Abstract + +In this work, we focus on the challenging problem of Label Enhancement (LE), which aims to exactly recover label distributions from logical labels, and present a novel Label Information Bottleneck (LIB) method for LE. For the recovery process of label distributions, the label irrelevant information contained in the dataset may lead to unsatisfactory recovery performance. To address this limitation, we make efforts to excavate the essential label relevant information to improve the recovery performance. Our method formulates the LE problem as the following two joint processes: 1) learning the representation with the essential label relevant information, 2) recovering label distributions based on the learned representation. The label relevant information can be excavated based on the "bottleneck" formed by the learned representation. Significantly, both the label relevant information about the label assignments and the label relevant information about the label gaps can be explored in our method. Evaluation experiments conducted on several benchmark label distribution learning datasets verify the effectiveness and competitiveness of LIB. Our source codes are available at https://github.com/qinghai-zheng/LIBLE + +# 1. Introduction + +Learning with label ambiguity is important in computer vision and machine learning. Different from the traditional Multi-Label Learning (MLL), which employs multiple logical labels to annotate one instance to address the label ambiguity issue [20], Label Distribution Learning (LDL) considers the relative importance of different labels and draws much attention in recent years [6,8,14,18,26]. By distinguishing the description degrees of all labels, LDL annotates one instance with a label distribution. Therefore, LDL is a more general learning paradigm, MLL can be regarded as a special case of LDL [8,10,12]. + +Recently, many LDL methods are proposed and achieve great success in practice [3, 9, 14, 18]. Instances with exact label distributions are vital for the training process of LDL methods. Nevertheless, annotating instances with label distributions is time-consuming [24, 28]. We take the label distribution annotation process of SJAFFE dataset for example here. SJAFFE dataset is the facial expression dataset, which contains 213 grayscale images collected from 10 Japanese female models, each facial expression image is rated by 60 persons on 6 basic emotions, including happiness, surprise, sadness, fear, anger, and disgust, with a five-level scale from 1 - 5, the higher value indicates the higher emotion intensity. Consequently, the average score of each emotion is served as the emotion label distribution [14, 28]. Clearly, the above annotation process is costly and it is unpractical to annotate data with label distributions manually, especially when the number of data is large. Fortunately, most existing datasets in the field of computer vision and machine learning are annotated by single-label or multi-labels [7, 29], therefore, a highly recommended promising solution is Label Enhancement (LE), which attempts to recover the desired label distributions exactly from existing logical labels [24, 28, 32]. + +Driven by the urgent requirement of obtaining label distributions and the convenience of LE, some LE methods are proposed in recent years [5, 7, 11, 13, 15, 17, 21, 24, 28, 29]. Given a dataset $\mathbf{X} = \{\pmb{x}_1, \pmb{x}_2, \dots, \pmb{x}_n\} \in \mathbb{R}^{q \times n}$ , in which $q$ and $n$ denote the number of dimensions and the number of instances, the potential label set is $\{y_1, y_2, \dots, y_c\}$ . The available logical labels and the desired distribution labels of $\mathbf{X}$ are separately indicated by $\mathbf{L} = \{l_1, l_2, \dots, l_n\}$ and $\mathbf{D} = \{d_1, d_2, \dots, d_n\}$ , where $l_i$ and $d_i$ are: + +$$ +\boldsymbol {l} _ {i} = \left(l _ {i} ^ {y _ {1}}, l _ {i} ^ {y _ {2}}, \dots , l _ {i} ^ {y _ {c}}\right) ^ {T}, \boldsymbol {d} _ {i} = \left(d _ {i} ^ {y _ {1}}, d _ {i} ^ {y _ {2}}, \dots , d _ {i} ^ {y _ {c}}\right) ^ {T}. \tag {1} +$$ + +To be specific, LE aims to recover $D$ based on the information provided by $X$ and $L$ . For most existing LE methods, their objectives can be concisely summarized as follows: + +$$ +\min _ {\theta} \| f _ {\theta} (\boldsymbol {X}) - \boldsymbol {L} \| _ {F} ^ {2} + \gamma r e g (f _ {\theta} (\boldsymbol {X})), \tag {2} +$$ + +in which $\pmb{D} = f_{\theta}(\pmb{X})$ , $f_{\theta}(\cdot)$ indicates the mapping from $\pmb{X}$ to $\pmb{D}$ , $reg(\cdot)$ denotes the regularization function, and $\gamma$ + +![](images/938d1516c60e7eae4d0f313b03c47b436a880ccd51e138931954df05b4858467.jpg) +Figure 1. Illustration of label relevant information. Excavating the essential label relevant information directly is challenging and we adopt a indirect way here. We jointly investigate the information about the assignments of labels to the instance and the information about the label gaps between logical labels and label distributions. Given the $i$ -th instance $\pmb{x}_i$ , the label gap of the $y_j$ label is $\delta_i^{y_j} = l_i^{y_j} - d_i^{y_j}$ . The information contained in $l_i^{y_j}$ and $\delta_i^{y_j}$ can be amalgamated to form the essential label relevant information. In other words, we employ $l_i^{y_j}$ to explore the label relevant information about the label assignments and $\delta_i^{y_j}$ to excavate the label relevant information about the label gaps. To a certain degree, the combination of $\delta_i^{y_j}$ and $l_i^{y_j}$ is equivalent to $d_i^{y_j}$ . As depicted here, $l_i^{y_j}$ indicates that $y_1$ and $y_3$ are related labels and $\delta_i^{y_j}$ provides the importance of $y_1$ and $y_3$ . + +is the trade-off parameter. Most existing LE methods vary in $reg(\cdot)$ . For example, GLLE [28] calculates the distance-based similarity matrix of data and employs the smoothness assumption [33] to construct $reg(\cdot)$ ; LESC [24] considers the global sample correlations and introduces the low-rank constraint as the regularization; PNLR [13] leverages $reg(\cdot)$ to maintain positive and negative label relations during the recovery process. Although a remarkable progress can be made by aforementioned methods, they ignore the label irrelevant information contained in $X$ , which prevents the further improvement of recovery results. For example, in the LE task of recovering facial age label distributions, the label irrelevant information, such as peculiarities information, cast shadows information, and occlusions information, may result in the incorrect mapping process of $f_{\theta}(\cdot)$ and the unsuitable regularization of $reg(\cdot)$ , eventually leads to the unsatisfactory recovery performance. + +To overcome the aforementioned limitation, we present a Label Information Bottleneck (LIB) method for LE. Concretely, the core idea of LIB is to learn the latent representation $\pmb{H}$ , which preserves the maximum label relevant information, from $\pmb{X}$ , and jointly recovers the label distributions based on the latent representation. For the LE problem, the label relevant information is the information that describes the description degrees of labels. It is tough to explore the label relevant information directly. As shown in Fig. 1, we + +decompose the label relevant information into two components, namely the assignments of labels to the instance and the label gaps between label distributions and logical labels. Inspired by Information Bottleneck (IB) [25], LIB utilizes the existing logical labels to explore the information about the assignments of labels to the instance. Unlike simply employing the original IB on the LE task, our method further considers the information about the label gaps between label distributions and logical labels. It is noteworthy that the above two components of the label relevant information are jointly explored in our method, and that is why we term the proposed method Label Information Bottleneck (LIB). The main contributions can be summarized as follows: + +- We decompose the label relevant information into the information about the assignments of labels to instance and the information about the label gaps between logical labels, both of which can be jointly explored during the learning process of our method. +- We introduce a novel LE method, termed LIB, which excavates the label relevant information to exactly recover the label distributions. Based on the original IB, which explores the label assignments information for LE, LIB further explores the label gaps information. +- We verify the effectiveness of LIB by performing extensive experiments on several datasets. Experimental results show that the proposed method can achieve the competitive performance, compared to state-of-the-art LE methods. + +# 2. Related Work + +# 2.1. Label Enhancement + +To recover the label distributions from the existing logical labels, many efforts are made recently [24, 28]. In general, most existing LE methods can be roughly divided into two categories, namely, algorithm adaptation and specialized algorithm [8, 24]. + +Algorithm adaptation extends some existing methods to achieve the goal of LE [5, 15]. For example, FCM [5] recovers the label distributions by utilizing the fuzzy clustering and fuzzy relabeling. To be specific, FCM utilizes the fuzzy C-means clustering to get different clusters and cluster prototypes, then obtains membership degrees of each instance with respect to different cluster prototypes, finally annotates all instances with label distributions by employing the fuzzy composition and softmax normalization. KM [15] leverages the fuzzy SVM to achieve the membership function. During the recovery process, KM separates instances into two clusters and employs the nonlinear function to get the radius and distances between centers and kernelized instances, and then gets the label distributions with the help of the softmax normalization. + +Specialized algorithm is specially designed to deal with the LE problem. Most existing LE methods belong to the category of specialized algorithm and have the basic objective Eq. (2). By using different constraints, different methods adopt different $reg(\cdot)$ in Eq. (2). For example, based on the assumption that instances closed in the feature space are more likely to share the same label, GLLE [28] employs the following local graph information in the feature space to boost the recovery performance: + +$$ +q _ {i, j} = \left\{ \begin{array}{l} \exp \left(- \frac {\left\| \boldsymbol {x} _ {i} - \boldsymbol {x} _ {j} \right\| ^ {2}}{2 \varepsilon^ {2}}\right), \text {i f} \boldsymbol {x} _ {j} \in k (i), \\ 0, \text {o t h e r w i s e}, \end{array} \right. \tag {3} +$$ + +where $k(i)$ denotes the $k$ -nearest neighbours of $\pmb{x}_i$ . $reg(\cdot)$ in GLLE is constructed as follows: + +$$ +r e g \left(f _ {\theta} (\boldsymbol {X})\right) = \sum_ {i, j} q _ {i, j} \left\| f _ {\theta} \left(\boldsymbol {x} _ {i}\right) - f _ {\theta} \left(\boldsymbol {x} _ {j}\right) \right\| _ {2} ^ {2}. \tag {4} +$$ + +Unlike GLLE, LESC [24] considers the global graph information and uses the low-rank representation learning [19]: + +$$ +\min _ {\boldsymbol {G}, \boldsymbol {E}} \| \boldsymbol {G} \| _ {*} + \lambda_ {2} \| \boldsymbol {E} \| _ {2, 1}, \text {s . t . ,} \boldsymbol {X} = \boldsymbol {X} \boldsymbol {G} + \boldsymbol {E}, \tag {5} +$$ + +where $G$ indicates the low-rank representation of instances in the feature space. The regularization function in LESC is written as follows: + +$$ +r e g (f _ {\theta} (\pmb {X})) = \| f _ {\theta} (\pmb {X}) - f _ {\theta} (\pmb {X}) \pmb {G} \| _ {F} ^ {2}. \qquad (6) +$$ + +For these aforementioned LE methods, they all neglect the label irrelevant information contained in $X$ , the negative effect of which can result in the unsatisfactory recovery results. Taking the recovery of facial emotion label distributions for example, the inaccurate graph information would be obtained in GLLE and LESSC with the presence of label irrelevant information, such as the identity information, hindering the further improvement of recovery results. + +# 2.2. Information Bottleneck + +Information bottleneck (IB) [1, 25, 25] is an information theoretic principle, which describes the relevant information in data formally. To be concrete, IB has the following objective: + +$$ +\min _ {\boldsymbol {B}} - I (\boldsymbol {B}, \boldsymbol {C}), \text {s . t .}, I (\boldsymbol {A}, \boldsymbol {B}) \leqslant I _ {c}, \tag {7} +$$ + +where $I(\cdot, \cdot)$ measures the mutual information and $I_{c}$ is the information constraint. Clearly, IB aims to learn the representation $\pmb{B}$ , which preserves the relevant information about $\pmb{C}$ , from $\pmb{A}$ . Considering the scenario of LE, it is natural to get the following formula: + +$$ +\min _ {\boldsymbol {H}} - I (\boldsymbol {H}, \boldsymbol {L}), \text {s . t .}, I (\boldsymbol {X}, \boldsymbol {H}) \leqslant I _ {c}. \tag {8} +$$ + +![](images/3a32c40ca8c4da719214278990048c1ffa7bc42cc60e02604ce68f7b852dc16f.jpg) +Figure 2. Framework of the proposed LIB. Since the way that directly explores the label relevant information is challenging, LIB decomposes the label relevant information into two components, namely the assignments of labels to the instance and the label gaps between label distributions and logical labels, and adopts an indirect path, which explores the information about label assignments and label gaps simultaneously. By minimizing $\mathcal{L}_{as}$ , LIB explores the information about assignments of labels to the instance. Meanwhile, by minimizing $\mathcal{L}_{gap}$ , LIB explores the information about the label gaps between logical labels and label distributions. Consequently, the label relevant information can be effectively explored and the label distributions can be exactly recovered. + +As discussed in Section 1, the information merely about the assignments of labels to the instance can be explored based on Eq. (8), which neglects the vital information about the label gaps between logical labels and label distributions. + +Recently, IB has been successfully utilized in many real-world applications [1, 2, 22, 27, 30, 31]. To the best of our knowledge, the method introduced in this paper is the first work that leverages IB to deal with the LE problem. More notably, rather than using IB simply (as shown in Eq. (8)), our method conducts more in-depth exploration to exactly recover label distributions based on IB. + +# 3. The Proposed Method + +# 3.1. The Objective Construction + +Generally, the basic idea can be written as follows: + +$$ +\min _ {\boldsymbol {H}} \mathcal {L} _ {a s} + \alpha \mathcal {L} _ {g a p}, \text {s . t .}, I (\boldsymbol {X}, \boldsymbol {H}) \leqslant I _ {c}, \tag {9} +$$ + +where $\mathcal{L}_{as}$ excavates the information about the assignments of labels to the instance, $\mathcal{L}_{gap}$ investigates the information about the label gaps between the logical labels and distribution labels, $\alpha$ is the trade-off parameter, the constraint aims to remove the label irrelevant information. The framework of our method is depicted in Fig. 2. It's worth noting that employing the original IB for LE merely explores the information about the label assignments. While our LIB makes attempts to capture the information about both the label assignments and the description degrees of labels. + +# 3.1.1 Label assignments information modeling + +For $\mathcal{L}_{as}$ , inspired by IB, we have the following formula: + +$$ +\mathcal {L} _ {a s} = - I (\boldsymbol {H}, \boldsymbol {L}). \tag {10} +$$ + +According to the concept of mutual information, $\mathcal{L}_{as}$ can be rewritten out in full as follows: + +$$ +\mathcal {L} _ {a s} = - \sum_ {\boldsymbol {h}} \sum_ {\boldsymbol {l}} p (\boldsymbol {h}, \boldsymbol {l}) \log \frac {p (\boldsymbol {l} | \boldsymbol {h})}{p (\boldsymbol {l})}. \tag {11} +$$ + +For the convenience of optimization, we introduce the variational approximation $q(\boldsymbol{l}|\boldsymbol{h})$ to $p(\boldsymbol{l}|\boldsymbol{h})$ . Since both the Kullback Leibler divergence and the entropy are positive: + +$$ +\begin{array}{l} \operatorname {K L} \left(p (\boldsymbol {l} | \boldsymbol {h}) | | q (\boldsymbol {l} | \boldsymbol {h})\right) = \sum_ {\boldsymbol {l}} p (\boldsymbol {l} | \boldsymbol {h}) \log \frac {p (\boldsymbol {l} | \boldsymbol {h})}{q (\boldsymbol {l} | \boldsymbol {h})} \geqslant 0 (12) \\ \Rightarrow \sum_ {\boldsymbol {l}} p (\boldsymbol {l} | \boldsymbol {h}) \log p (\boldsymbol {l} | \boldsymbol {h}) \geqslant \sum_ {\boldsymbol {l}} p (\boldsymbol {l} | \boldsymbol {h}) \log q (\boldsymbol {l} | \boldsymbol {h}), \\ \mathbb {E} _ {p (\boldsymbol {l})} [ - \log p (\boldsymbol {l}) ] = - \sum_ {\boldsymbol {l}} p (\boldsymbol {l}) \log p (\boldsymbol {l}) \geqslant 0, (13) \\ \end{array} +$$ + +based on Markov chain that $L\gets X\to H$ , we can get: + +$$ +L _ {a s} \leqslant - \sum_ {\boldsymbol {x}} \sum_ {l} \sum_ {\boldsymbol {h}} p (\boldsymbol {x}, l) p (\boldsymbol {h} | \boldsymbol {x}) \log q (l | \boldsymbol {h}). \tag {14} +$$ + +# 3.1.2 Label gaps information modeling + +To investigate the label-relevant information about the description degrees of labels, we introduce the label gaps between logical labels and label distributions $\pmb{\Delta}$ , and consider the conditional self-information, i.e., $I(\Delta | H)$ . Therefore, we construct $\mathcal{L}_{gap}^{1}$ as follows: + +$$ +\begin{array}{l} \mathcal {L} _ {g a p} = I (\boldsymbol {\Delta} | \boldsymbol {H}) = - \log p (\boldsymbol {\Delta} | \boldsymbol {H}) \\ = - \sum_ {\delta} \sum_ {\boldsymbol {h}} \log p (\boldsymbol {\delta} | \boldsymbol {h}) \tag {15} \\ = - \sum_ {l} \sum_ {\boldsymbol {h}} \log p (\boldsymbol {l} - \hat {\boldsymbol {d}} | \boldsymbol {h}). \\ \end{array} +$$ + +where $\delta = l - \hat{d},\hat{d}$ is the label distribution recovered in our method. + +# 3.1.3 Label irrelevant information modeling + +Regarding the label irrelevant information, LIB employs the constraint in Eq. (9) to discard it during the learning process. $I(\mathbf{X},\mathbf{H})$ can be formulated as follows: + +$$ +I (\boldsymbol {X}, \boldsymbol {H}) = \sum_ {\boldsymbol {x}} \sum_ {\boldsymbol {h}} p (\boldsymbol {x}, \boldsymbol {h}) \log \frac {p (\boldsymbol {h} \mid \boldsymbol {x})}{p (\boldsymbol {h})}. \tag {16} +$$ + +Since it is difficult to calculate $p(h)$ directly, we also introduce the variational approximation $q(h)$ to $p(h)$ . Similar to Eq. (12), based on $\mathrm{KL}(p(h)||q(h)) \geqslant 0$ , we have: + +$$ +\sum_ {\boldsymbol {h}} p (\boldsymbol {h}) \log p (\boldsymbol {h}) \geqslant \sum_ {\boldsymbol {h}} p (\boldsymbol {h}) \log q (\boldsymbol {h}). \tag {17} +$$ + +Subsequently, the following formula can be written: + +$$ +\begin{array}{l} I (\boldsymbol {X}, \boldsymbol {H}) \leqslant \sum_ {\boldsymbol {x}} \sum_ {\boldsymbol {h}} p (\boldsymbol {x}, \boldsymbol {h}) \log \frac {p (\boldsymbol {h} | \boldsymbol {x})}{q (\boldsymbol {h})} \tag {18} \\ = \sum_ {\boldsymbol {x}} \sum_ {\boldsymbol {l}} p (\boldsymbol {x}, \boldsymbol {l}) \operatorname {K L} (p (\boldsymbol {h} | \boldsymbol {x}) | | q (\boldsymbol {h})). \\ \end{array} +$$ + +# 3.1.4 Objective of LIB + +By employing the Lagrange multiplier method and combining Eq. (9), (14), (15), and (18), we have: + +$$ +\begin{array}{l} \mathcal {L} = \mathcal {L} _ {a s} + \alpha \mathcal {L} _ {g a p} + \beta I (\boldsymbol {X}, \boldsymbol {H}) \\ \leqslant - \sum_ {\boldsymbol {x}} \sum_ {\boldsymbol {l}} \sum_ {\boldsymbol {h}} p (\boldsymbol {x}, \boldsymbol {l}) p (\boldsymbol {h} | \boldsymbol {x}, \boldsymbol {l}) \log q (\boldsymbol {l} | \boldsymbol {h}) \\ - \alpha \sum_ {\boldsymbol {l}} \sum_ {\boldsymbol {h}} \log p (\boldsymbol {l} - \hat {\boldsymbol {d}} | \boldsymbol {h}) \tag {19} \\ + \beta \sum_ {\boldsymbol {x}} \sum_ {\boldsymbol {l}} p (\boldsymbol {x}, \boldsymbol {l}) \operatorname {K L} (p (\boldsymbol {h} | \boldsymbol {x}) | | q (\boldsymbol {h})). \\ \end{array} +$$ + +where $\beta$ is the Lagrange multiplier. Considering the bound of $\mathcal{L}$ and using the empirical Monte Carlo approximation of sampling [23], we have the following objective of LIB: + +$$ +\begin{array}{l} \mathcal {L} _ {L I B} = \frac {1}{n} \sum_ {i = 1} ^ {n} \left[ - \sum_ {\boldsymbol {h}} p (\boldsymbol {h} | \boldsymbol {x} _ {i}) \log q \left(\boldsymbol {l} _ {i} \mid \boldsymbol {h}\right) \right. \tag {20} \\ + \beta \operatorname {K L} (p (\boldsymbol {h} | \boldsymbol {x} _ {i}) | | q (\boldsymbol {h})) ] - \alpha \sum_ {\boldsymbol {l}} \sum_ {\boldsymbol {h}} \log p (\boldsymbol {l} - \hat {\boldsymbol {d}} | \boldsymbol {h}). \\ \end{array} +$$ + +# 3.2. The Optimization of LIB + +To minimize the objective of $\mathcal{L}_{LIB}$ , we use the reparameterization trick [16, 23]. For $p(\boldsymbol{h}|\boldsymbol{x})$ , we assume that: + +$$ +p (\boldsymbol {h} | \boldsymbol {x}) \sim \mathcal {N} \left(\boldsymbol {\mu} _ {\boldsymbol {h} | \boldsymbol {x}}, \boldsymbol {\sigma} _ {\boldsymbol {h} | \boldsymbol {x}} ^ {2} \boldsymbol {I}\right), \tag {21} +$$ + +where $\pmb{\mu}_{h|\pmb{x}}$ and $\sigma_{h|x}$ are obtained by using the encoder network $f_{\theta_{en}}(\cdot)$ , i.e., $\pmb{\mu}_{h|x} = f_{\theta_{en}}^{\pmb{\mu}}(\pmb{x})$ and $\pmb{\sigma}_{h|x} = f_{\theta_{en}}^{\pmb{\sigma}}(\pmb{x})$ . Subsequently, we have that: + +$$ +\boldsymbol {h} = \mu_ {\boldsymbol {h} | \boldsymbol {x}} + \sigma_ {\boldsymbol {h} | \boldsymbol {x}} \odot \epsilon , \tag {22} +$$ + +where $\epsilon \sim \mathcal{N}(\mathbf{0},\mathbf{I})$ and $\odot$ is the element-wise product. For $q(l|h)$ , we assume: + +$$ +q (\boldsymbol {l} | \boldsymbol {h}) \sim \mathcal {N} \left(\boldsymbol {\mu} _ {\boldsymbol {l} | \boldsymbol {h}}, \boldsymbol {I}\right), \tag {23} +$$ + +where $\pmb{\mu}_{l|\pmb{h}}$ is learned by using the decoder network $f_{\theta_{de}}(\cdot)$ , namely, $\pmb{\mu}_{l|\pmb{h}} = f_{\theta_{de}}(\pmb{h})$ . For $q(\pmb{h})$ , we assume that: + +$$ +q (\boldsymbol {h}) \sim \mathcal {N} (\boldsymbol {0}, \boldsymbol {I}). \tag {24} +$$ + +For $p(\boldsymbol{l} - \hat{\boldsymbol{d}}|\boldsymbol{h})$ , the following assumption is adopted: + +$$ +p (\boldsymbol {l} - \hat {\boldsymbol {d}} | \boldsymbol {h}) \sim \mathcal {N} (\boldsymbol {0}, \sigma_ {\delta | \boldsymbol {h}} ^ {2} \boldsymbol {I}), \tag {25} +$$ + +where $\sigma_{\delta|\pmb{h}}$ can be achieved by introducing the gap deviation network $f_{\theta_{gd}}(\cdot)$ , i.e., $\sigma_{\delta|\pmb{h}} = f_{\theta_{gd}}(\pmb{h})$ . For the recovered label distribution $\hat{\pmb{d}}$ , we introduce the label distribution network $f_{\theta_{ld}}(\cdot)$ and has the following formula: + +$$ +\hat {\boldsymbol {d}} = f _ {\theta_ {l d}} (\boldsymbol {h}). \tag {26} +$$ + +Consequently, based on Eq. (21)-(26), we have: + +$$ +\begin{array}{l} \min _ {\theta_ {e n}, \theta_ {d e}, \theta_ {g d}, \theta_ {l d}} \mathcal {L} _ {L I B} \\ \Rightarrow \min _ {\theta_ {e n}, \theta_ {d e}, \theta_ {g d}, \theta_ {l d}} \frac {1}{n} \sum_ {\boldsymbol {l}} \left[ \frac {1}{2} \| \boldsymbol {\mu} _ {\boldsymbol {l} | \boldsymbol {h}} - \boldsymbol {l} \| _ {2} ^ {2} \right. (27) \\ \left. + \alpha \left(\frac {1}{2} (\boldsymbol {l} - \hat {\boldsymbol {d}}) ^ {T} \left(\boldsymbol {\sigma} _ {\delta | h} ^ {- 2} \boldsymbol {I}\right) (\boldsymbol {l} - \hat {\boldsymbol {d}}) + \log \det \left(\boldsymbol {\sigma} _ {\delta | h} ^ {2} \boldsymbol {I}\right)\right) \right] (27) \\ + \frac {\beta}{2} \sum_ {\boldsymbol {x}} \left[ \boldsymbol {\mu} _ {\boldsymbol {h} | \boldsymbol {x}} ^ {T} \boldsymbol {\mu} _ {\boldsymbol {h} | \boldsymbol {x}} + \operatorname {t r} \left(\boldsymbol {\sigma} _ {\boldsymbol {h} | \boldsymbol {x}} ^ {2} \boldsymbol {I}\right) - \log \det \left(\boldsymbol {\sigma} _ {\boldsymbol {h} | \boldsymbol {x}} ^ {2} \boldsymbol {I}\right) \right]. \\ \end{array} +$$ + +When the problem of Eq. (27) is optimized, we can effectively recover the desired label distributions. To be specific, given $\{\pmb {X},\pmb {L}\}$ , we can obtain $\pmb{H}$ according to Eq. (22) and achieve the recovery results based on Eq. (26), namely, $\hat{\pmb{D}} = f_{\theta_{ld}}(\pmb {H})$ + +# 3.3. Comparison with Existing LE Methods + +The main difference between LIB and existing methods is that our method deals with the problem of LE from the perspective of information bottleneck. Considering the first term in Eq. (2), it aims to minimize $\| \pmb{d} - \pmb{l} \|_2^2$ under the assumption that information in the label distributions is inherited from the initial logical labels [24, 28, 29]. For LIB, the more reasonable term: + +$$ +\frac {1}{2} (\boldsymbol {l} - \hat {\boldsymbol {d}}) ^ {T} \left(\boldsymbol {\sigma} _ {\delta | \boldsymbol {h}} ^ {- 2} \boldsymbol {I}\right) (\boldsymbol {l} - \hat {\boldsymbol {d}}) + \log \det \left(\boldsymbol {\sigma} _ {\delta | \boldsymbol {h}} ^ {2} \boldsymbol {I}\right) \tag {28} +$$ + +which can be deduced by excavating the label relevant information about the label gaps between logical labels and label distributions. + +Besides, we compare our method with the recently proposed LEVI [29] further. Although the objectives of LEVI and LIB are somewhat similar in form, they are essentially different as follows: 1) LIB makes attempts from the perspective of information bottleneck, while LEVI from the view of variational inference; 2) The formulas of LEVI and LIB are just partially similar in form, since the variational + +
Dataset# dimension q# instance n# labels c
Artificialtoy326013
Movie186977555
SBU-3DFE24325006
SJAFFE2432136
Yeast-alpha24246518
Yeast-cdc24246515
Yeast-cold2424654
Yeast-diau2424657
Yeast-dtt2424654
Yeast-elu24246514
Yeast-heat2424656
Yeast-spo2424656
Yeast-spo52424653
Yeast-spoem2424652
+ +Table 1. Details of datasets. The numbers of dimension $q$ , instance $n$ , and labels $c$ are provided here. + +inference is employed as the optimization tool in LIB. The details of these two formulas are totally different; 3) LEVI requires an extra regularizer, i.e., $\| d - l\| _2^2$ to constrain the recovery process, while LIB achieves $d$ based on the more reasonable term, i.e., Eq. (28). + +# 4. Experiments + +To verify the effectiveness and competitiveness of LIB, extensive experiments are conducted in this section. + +# 4.1. Experimental Setup + +As shown in Table 1, we use both one toy dataset and 13 real-world datasets for evaluation $^2$ . For the toy dataset, i.e., Artificial dataset, it is utilized to vividly show the recovery performance [28]. Movie dataset is collected from movies, SBU-3DFE and SJAFFE datasets are two facial expression datasets. Yeast datasets (alpha to spoem) are collected from 10 biological experiments on the budding yeast genes [4]. It is important to note that only the ground-truth label distributions are provided by these datasets. Therefore, we adopt the binarization strategy, which is also used in existing LE works [24, 28, 29], to ensure the consistency of evaluation. + +We compare our method LIB to 7 LE methods, including FCM [5], KM [15], LP [17], ML [11], GLLE [28], LESC [24], and LEVI [29]. The first two methods belong to the algorithm adaption, and the rest methods are specialized algorithms. For the sake of fairness, we utilize the parameter settings recommended in their original works. Specifically, for FCM, we set the parameter $\beta = 2$ . For KM, we leverage the Gaussian kernel. For LP, we set the parameter $\alpha = 0.5$ . For ML, we set the number of neighbors $k = c + 1$ . For GLLE, we select $\lambda$ from $\{0.01, 0.1, \dots, 100\}$ and set the number of neighbors $k$ to $c + 1$ . For LESC, $\lambda_{1}$ and $\lambda_{2}$ are selected from $\{0.0001, 0.1, \dots, 10\}$ . For LEVI, MLPs with + +two hidden layers and softmax activation functions are utilized, and the results are reported after 150 training epochs. For LIB, we select $\alpha$ and $\beta$ from $\{0.001, 0.01, \dots, 10\}$ , and the fully connected networks with 3 layers and sigmoid activation function are leveraged in the proposed method. + +To evaluate the recovery performance, we adopt 6 metrics, namely Chebyshev, Canberra, Clark, Kullback-Leibler, Cosine, and Intersection [8,24,28]. Given the ground-truth label distribution $\pmb{d}$ and the recovered label distribution $\hat{\pmb{d}}$ , the first four metrics and the rest two metrics respectively measure the distance and similarity between $\pmb{d}$ and $\hat{\pmb{d}}$ : + +$$ +D _ {\text {C h e b y s h e v}} (\boldsymbol {d}, \hat {\boldsymbol {d}}) = \max _ {i} \left| d ^ {y _ {i}} - \hat {d} ^ {y _ {i}} \right|, \tag {29} +$$ + +$$ +D _ {\text {C a n b e r r a}} (\boldsymbol {d}, \hat {\boldsymbol {d}}) = \sum_ {i = 1} ^ {c} \frac {\left| d ^ {y _ {i}} - \hat {d} ^ {y _ {i}} \right|}{d ^ {y _ {i}} + \hat {d} ^ {y _ {i}}}, \tag {30} +$$ + +$$ +D _ {\text {C l a r k}} (\boldsymbol {d}, \hat {\boldsymbol {d}}) = \sqrt {\sum_ {i = 1} ^ {c} \frac {\left(d ^ {y _ {i}} - \hat {d} ^ {y _ {i}}\right) ^ {2}}{\left(d ^ {y _ {i}} + \hat {d} ^ {y _ {i}}\right) ^ {2}}}, \tag {31} +$$ + +$$ +D _ {\text {K u l l b a c k - L e i b l e r}} (\boldsymbol {d}, \hat {\boldsymbol {d}}) = \sum_ {i = 1} ^ {c} d ^ {y _ {i}} \ln \frac {d ^ {y _ {i}}}{\hat {d} ^ {y _ {i}}}, \tag {32} +$$ + +$$ +S _ {\text {C o s i n e}} (\boldsymbol {d}, \hat {\boldsymbol {d}}) = \frac {\sum_ {i = 1} ^ {c} d ^ {y _ {i}} \hat {d} ^ {y _ {i}}}{\sqrt {\sum_ {i = 1} ^ {c} \left(d ^ {y _ {i}}\right) ^ {2}} \sqrt {\sum_ {i = 1} ^ {c} \left(\hat {d} ^ {y _ {i}}\right) ^ {2}}}, \tag {33} +$$ + +$$ +S _ {\text {I n t e r s e c t i o n}} (\boldsymbol {d}, \hat {\boldsymbol {d}}) = \sum_ {i = 1} ^ {c} \min \left(d ^ {y _ {i}}, \hat {d} ^ {y _ {i}}\right). \tag {34} +$$ + +The smaller values of distance metric and similarity metric indicate the better and the worse results, respectively. + +# 4.2. Visualization Results on Toy Dataset + +The recovery results on the Artificial dataset are vividly presented in Fig. 3, which shows the three-dimensional label distributions by the RGB color channels separately. The more similar the color patterns of the recovered results and the ground-truth are, the better the recovery results are. + +It can be seen that FCM, GLLE, LESC, LEVI, and LIB can obtain the similar color pattern, while KM, LP, and ML are incapable to obtain the promising recovery performance on Artificial dataset. Regarding the visualization results of FCM, GLLE, LESC, LEVI, and LIB, the color pattern that is most close to the ground-truth is achieved by our LIB. + +# 4.3. Comparison Results on Real-world Datasets + +We provide the detailed comparison results on 13 real-world datasets in Table 2. Overall, LIB has the competitive recovery performance. We have the following observations: 1) Compared with FCM and KM, which belong to the category of algorithm adaption, remarkable improvements can + +![](images/433cd0f9051a1ea30701968a1eed431fdc486563dec9da9be3ad48ccbe4e63ab.jpg) +(a) FCM + +![](images/b47102f6ed3a8907aa6d3e729f478a653bdfd10d16dca6ad1c91b57de938260f.jpg) +(b) KM + +![](images/e131d1d7a6778ee2032f789d3b789003607c3efdf066d1201b74f22c1ee45e27.jpg) +(c) LP + +![](images/6652292ecd2846730a922ac31fdde7d33229d0af6e55f276355a7d68c9e502d2.jpg) +(d) ML + +![](images/2cc8d1196705731916bf47035a1299ac48def00bafb6812363a368384ebccb43.jpg) +(e) GLLE + +![](images/e1a94e21c97ea76a259bb4b7315e2e656fbb374d356e905c00fc823f5473279e.jpg) +(f) LESC + +![](images/a9a05937edda45c20123f3ada7b3d3ec0b8d821261fdced91e8c84e1a651f414.jpg) +(g) LEVI + +![](images/7ebfd869fe40c74bb516122a9b70b79ff705dbf7f854098c1c35277b22db6a84.jpg) +(h) LIB + +![](images/a76eb77437031a722c2e3032e06efe562cf7b59739b4b2e601ac4ba0559c5330.jpg) +(i) Ground-truth +Figure 3. Visualization results of the label distributions recovered by different methods ((a)-(h)) and the ground-truth ((i)) on Artificial dataset. (Best viewed in color.) + +be achieved by our method; 2) Compared with the methods belonging to the category of specialized algorithm, LIB can also obtain better recovery results in most cases. For example, LIB obtains the best recovery results on Movie datasets in all metrics. Moreover, although LESC can obtain slightly favorable results in some cases, the corresponding recovery results of LIB are also promising and competitive. The underlying reason may be that LESC further considers the sample correlations during the recovery process; 3) The recovery performance of all methods can be roughly ranked as LIB>LESC≈LEV1>GLLE>LP≈FCM>ML>KM. We can conclude that LIB is suitable for the LE problem. The underlying reason for the significant improvement is that the label relevant information, including the information about label assignments and the information about label gaps, can be effectively investigated by LIB. + +# 4.4. Analysis and Discussion of LIB + +We analyze the parameter sensitivity of LIB firstly, and then we conduct the ablation studies as well. + +# 4.4.1 Sensitivity of LIB + +In the proposed method, we choose the values of $\alpha$ and $\beta$ from $\{0.001, 0.01, \dots, 10\}$ . To show the parameter sensitivity of LIB, we conduct experiments on SBU-3DFE datasets with different values of $\alpha$ and $\beta$ . Regarding the dimension of the learned latent representation, we set it to 256 for all datasets. The experimental results in metrics of Chebyshev distance, Cosine coefficient, and Intersection similarity are + +
MetricChebyshev ↓Clark ↓
MethodFCMKMLPMLGLLELESCLEVLIBFCMKMLPMLGLLELESCLEVLIB
Movie0.2300.2340.1610.1640.1220.1210.1100.1070.8591.7660.9131.1400.5690.5640.5510.517
SUB-3DFE0.1350.2380.1230.2330.1260.1220.0950.0940.4821.9070.5801.8480.3910.3780.3030.297
SJAFFE0.1320.2140.1070.1860.0870.0690.0750.0710.5221.8740.5021.5190.3770.2760.2900.262
Yeast-alpha0.0440.0630.0400.0570.0200.0150.0120.0170.8213.1531.1853.0880.3370.2530.3190.275
Yeast-cdc0.0510.0760.0420.0710.0220.0190.0160.0170.7392.8851.0142.8250.3060.2510.3230.242
Yeast-cold0.1410.2520.1370.2420.0660.0560.0820.0540.4331.4720.5031.4400.1760.1520.2690.146
Yeast-diau0.1240.1520.0990.1480.0530.0420.0440.0490.8381.8860.7881.8440.2960.2240.2950.273
Yeast-dtt0.0970.2570.1280.2440.0520.0430.0840.0340.3291.4770.4991.4460.1430.1190.2940.092
Yeast-elu0.0520.0780.0440.0720.0230.0190.0170.0180.5792.7680.9732.7110.2950.2410.3170.224
Yeast-heat0.1690.1750.0860.1650.0490.0460.0520.0390.5801.8020.5681.7640.2130.1990.2880.165
Yeast-spo0.1300.1750.0900.1710.0620.0600.0550.0530.5201.8110.5581.7680.2660.2580.2770.224
Yeast-spo50.1620.2770.1140.2730.0990.0920.0910.0760.3951.0590.2741.0360.1970.1850.2090.158
Yeast-sopem0.2330.4080.1630.4030.0880.0870.1150.0690.4011.0280.2721.0040.1320.1290.1820.104
Avg.Rank6.0778.0005.0006.8463.7692.3082.4631.5385.3858.0005.6157.0003.3851.9233.4621.231
MetricCanberra ↓
MethodFCMKMLPMLGLLELESCLEVLIBFCMKMLPMLGLLELESCLEVLIB
Movie1.6643.4441.7201.9341.0451.0340.9740.9200.3810.4520.1770.2180.1230.1200.0820.077
SUB-3DFE1.0204.1211.2454.0010.8200.7990.6370.6110.0940.6030.1050.5650.0690.0640.0420.041
SJAFFE1.0814.0101.0643.1380.7810.5610.6000.5310.1070.5580.0770.3910.0500.0290.0320.027
Yeast-alpha2.88311.8094.54411.6031.1340.8461.2490.8930.1000.6300.1210.6020.0130.0080.0110.009
Yeast-cdc2.4159.8753.6449.6950.9590.7651,1480.7470.0910.6300.1110.6010.0140.0100.0140.008
Yeast-cold0.7342.5660.9242.5190.3050.2630.5010.2500.1130.5860.1030.5560.0190.0150.0350.012
Yeast-diau1.8954.2611.7484.1800.6710.4800.6890.6210.1590.5380.1270.5090.0270.0170.0230.022
Yeast-dtt0.5012.5940.9412.5490.2480.2060.5620.1580.0650.6170.1030.5860.0130.0100.0420.005
Yeast-elu1.6899.1103.3818.9490.9020.7271.0930.6700.0590.6170.1090.5890.0130.0090.0140.008
Yeast-heat1.1573.8491.2933.7790.4300.4010.6460.3270.1470.5860.0890.5560.0170.0150.0270.011
Yeast-spo0.9983.8541.2313.7720.5480.5330.6050.4540.1100.5620.0840.5320.0290.0280.0250.019
Yeast-spo50.5631.3820.4011.3550.3050.2840.3110.2410.1230.3340.0420.3170.0340.0310.0280.021
Yeast-sopem0.5341.2530.3651.2260.1830.1800.2480.1440.2080.5310.0670.5030.0270.0270.0360.018
Avg.Rank5.2318.0005.6927.0003.2312.003.6921.1545.6928.0005.3856.9233.4622.1543.0771.154
MetricCosine ↑
MethodFCMKMLPMLGLLELESCLEVLIBFCMKMLPMLGLLELESCLEVLIB
Movie0.7730.8800.9290.9190.9360.9370.9540.9550.6770.6490.7780.7790.8310.8330.8490.859
SUB-3DFE0.9120.8120.9220.8150.9270.9320.9560.9580.8270.5790.8100.5870.8500.8550.8820.887
SJAFFE0.9060.8270.9410.8570.9580.9730.9690.9740.8210.5930.8370.6610.8720.9050.8970.909
Yeast-alpha0.9220.7510.9110.7560.9870.9920.9890.9920.8440.5320.7740.5370.9380.9530.9320.951
Yeast-cdc0.9290.7540.9160.7590.9870.9910.9870.9920.8470.5330.7790.5380.9370.9500.9250.951
Yeast-heat0.9220.7790.9250.7840.9820.9860.9700.9880.8330.5590.7940.5650.9240.9350.8810.938
Yeast-diau0.8820.7990.9150.8030.9750.9850.9800.9790.7600.5880.7880.5930.9060.9330.9080.913
Yeast-dtt0.9590.7590.9210.7630.9880.9910.9650.9950.8940.5410.7860.5460.9390.9490.8660.961
Yeast-elu0.9500.7580.9180.7630.9870.9910.9870.9920.8830.5390.7820.5440.9360.9490.9240.952
Yeast-heat0.8830.7790.9320.7830.9840.9860.9770.9900.8070.5590.8050.5640.9290.9340.8970.946
Yeast-spo0.9090.8000.9390.8030.9740.9750.9780.9820.8360.5750.8190.5800.9090.9120.9030.925
Yeast-spo50.9220.8820.9690.8840.9710.9740.9790.9830.8380.7240.8860.7270.9010.9080.9090.924
Yeast-sopem0.8780.8120.9500.8150.9780.9780.9720.9850.7670.5920.8370.5970.9120.9130.8850.931
Avg.Rank5.8467.9235.3086.9233.4622.1542.9231.2315.3858.0005.6926.8463.3852.0073.4621.154
+ +Table 2. Recovery results on 13 real-world datasets. $\downarrow$ indicates that "the smaller the better" and $\uparrow$ means that "the larger the better". The average ranks (Avg.Rank) on all datasets are also reported for all methods. We highlight the best recovery results. + +provided in Fig. 4. It can be observed that LIB method can get promising recovery results and is robust with respect to different values of $\alpha$ and $\beta$ in a large range. + +# 4.4.2 Ablation studies of LIB + +The ablation studies are conducted to further verify the effectiveness of introducing the label information bottleneck framework for LE. In the proposed objective Eq. (9), $\mathcal{L}_{as}$ + +and $\mathcal{L}_{gap}$ explore the label assignments information and label gaps information during the recovery process. As can be observed from Eq. (14) and Eq. (15), only the latent representation $\pmb{H}$ can be learned if we employ $\mathcal{L}_{as}$ merely during the recovery process. Consequently, considering the goal of LE, we compare the proposed LIB with the method termed $\mathrm{LIB}_{gap}$ , which only employs $\mathcal{L}_{gap}$ to achieve the recovery results. In other words, $\mathrm{LIB}_{gap}$ investigates the label gaps information in the case of not considering the label assign- + +![](images/7ef24d8fd4faa580c9270dd65e2459ad9d4679736da1f0a0f8156d2ee573bfa2.jpg) +(a) Chebyshev + +![](images/54dd238b4658d45bbbff76f97a3d612fb0c01a3613d942ea96b4ec9f9463c5ca.jpg) +(b) Cosine $\uparrow$ +Figure 4. The recovery results in metrics of (a) Chebyshev distance, (b) Cosine coefficient, and (c) Intersection similarity with different values of $\alpha$ and $\beta$ . $\downarrow$ indicates that "the smaller the better" and $\uparrow$ means that "the larger the better". The experimental results demonstrate that LIB is robust with respect to different values of $\lambda$ and $\beta$ . (Best viewed in color.) + +![](images/ad1e900b56aeffddfa362eb0bfa0ad711e7773bba0a5057ec1eac85267f4c772.jpg) +(c) Intersection $\uparrow$ + +
MetricChebyshev ↓Clark ↓Canberra ↓Kullback-Leibler ↓Cosine ↑Intersection ↑
MethodLIBgapLIBLIBgapLIBLIBgapLIBLIBgapLIBLIBgapLIBLIBgapLIB
Movie0.1200.1070.5630.5171.0290.9200.0990.0770.9380.9550.8340.859
SUB-3DFE0.1300.0940.3950.2970.8490.6110.0790.0410.9230.9580.8460.887
SJAFFE0.1130.0710.3910.2620.8160.5310.0660.0270.9380.9730.8600.909
Yeast-alpha0.0180.0170.2810.2750.9200.8930.0100.0090.9910.9920.9500.951
Yeast-cdc0.0190.0170.2540.2420.7820.7470.0090.0080.9910.9920.9480.951
Yeast-cold0.0610.0170.1620.1460.2800.2500.0160.0120.9850.9880.9300.938
Yeast-diau0.0500.0490.2880.2730.6590.6210.0250.0220.9770.9790.9080.913
Yeast-dtt0.0450.0340.1240.0920.2170.1580.0100.0050.9910.9950.9460.961
Yeast-elu0.0190.0180.2370.2240.7140.6700.0090.0080.9920.9920.9490.952
Yeast-heat0.0450.0390.1930.1650.3880.3270.0140.0110.9860.9900.9360.946
Yeast-spo0.0590.0530.2530.2240.5230.4540.0250.0190.9760.9820.9140.925
Yeast-spo50.0970.0760.1930.1580.3000.2410.0320.0210.9710.9830.9030.924
Yeast-sopem0.0880.0690.1300.1040.1810.1440.0270.0180.9770.9850.9120.931
+ +Table 3. Recovery results of $\mathrm{LIB}_{gap}$ and LIB on 13 real-world datasets. $\downarrow$ indicates that "the smaller the better" and $\uparrow$ means that "the larger the better". We highlight the best recovery results. + +ments information during the recovery process. + +To be specific, $\mathrm{LIB}_{gap}$ has with the following objective: + +$$ +\min _ {\theta_ {g d}, \theta_ {l d}} \frac {1}{2} \sum_ {\boldsymbol {x}} \left[ (\boldsymbol {l} - \hat {\boldsymbol {d}}) ^ {T} \left(\boldsymbol {\sigma} _ {\delta | \boldsymbol {x}} ^ {- 2} \boldsymbol {I}\right) (\boldsymbol {l} - \hat {\boldsymbol {d}}) + \log \det \left(\boldsymbol {\sigma} _ {\delta | \boldsymbol {x}} ^ {2} \boldsymbol {I}\right) \right]. \tag {35} +$$ + +Notably, $\sigma_{\delta |x} = f_{\theta_{gd}}(x)$ and $\hat{\pmb{d}} = f_{\theta_{ld}}(\pmb {x})$ , which are different from the objective Eq. (27) utilized in LIB. Only the partial label relevant information, i.e., the information about the label gaps, is explored in $\mathrm{LIB}_{gap}$ + +Table 3 provides the recovery results of $\mathrm{LIB}_{gap}$ and LIB. It can be observed that LIB outperforms $\mathrm{LIB}_{gap}$ in all cases. Compared with LIB, $\mathrm{LIB}_{gap}$ merely makes the effort to explore the label gap information to boost the recovery performance, while LIB excavates both the information about the label assignments and the information about the label gaps jointly. Therefore, the promising recovery performance can be achieved by LIB. Furthermore, according to the results provided in Table 2 and 3, the recovery results of $\mathrm{LIB}_{gap}$ seem to be competitive, which also indicates that the exploration of information about label gaps is beneficial for LE. + +# 5. Conclusion + +In this paper, we present a new perspective to deal with the Label Enhancement (LE) problem and introduce the novel Label Information Bottleneck (LIB) method. The label relevant information is decomposed into the information about label assignments and the information about label gaps. Consequently, our method transform the LE problem into simultaneously learning the latent representation and modeling the label gaps. Extensive experiments carried on both the toy dataset and real-world datasets verify the competitiveness of LIB. + +# Acknowledgments + +This work was supported by the National Key R&D Program of China under Grant 2020AAA0109602; the Education and Research Foundation for Middle-aged and Young Teacher of Fujian Province under Grant JAT220005; the National Natural Science Foundation of China (NSFC) under Grant 62206156; Alibaba Group through Alibaba Innovative Research Program, No.21169774. + +# References + +[1] A Alemi, Ian Fischer, J Dillon, and Kevin Murphy. Deep variational information bottleneck int. In Conf. on Learning Representations, 2017. 3 +[2] Rana Ali Amjad and Bernhard C Geiger. Learning representations for neural network-based classification using the information bottleneck principle. IEEE transactions on pattern analysis and machine intelligence, 42(9):2225-2239, 2019. 3 +[3] Shikai Chen, Jianfeng Wang, Yuedong Chen, Zhongchao Shi, Xin Geng, and Yong Rui. 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PhD thesis, Carnegie Mellon University, language technologies institute, 2005. 2 \ No newline at end of file diff --git a/2023/Label Information Bottleneck for Label Enhancement/images.zip b/2023/Label Information Bottleneck for Label Enhancement/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..ea7a4e34dabe71dc01593d708fc46cbc0295229d --- /dev/null +++ b/2023/Label Information Bottleneck for Label Enhancement/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:a11b92f42b817397829a0ae4958d927e88362a05d1e1247fa34a835cbebd1d83 +size 966132 diff --git a/2023/Label Information Bottleneck for Label Enhancement/layout.json b/2023/Label Information Bottleneck for Label Enhancement/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..5ff1f8cf65b537f23ef667c693ea8032d170737d --- /dev/null +++ b/2023/Label Information Bottleneck for Label Enhancement/layout.json @@ -0,0 +1,10741 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 129, + 103, + 463, + 119 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 129, + 103, + 463, + 119 + ], + "spans": [ + { + "bbox": [ + 129, + 103, + 463, + 119 + ], + "type": "text", + "content": "Label Information Bottleneck for Label Enhancement" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 189, + 142, + 403, + 158 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 189, + 142, + 403, + 158 + ], + "spans": [ + { + "bbox": [ + 189, + 142, + 403, + 158 + ], + "type": "text", + "content": "Qinghai Zheng" + }, + { + "bbox": [ + 189, + 142, + 403, + 158 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 189, + 142, + 403, + 158 + ], + "type": "text", + "content": ", Jihua Zhu" + }, + { + "bbox": [ + 189, + 142, + 403, + 158 + ], + "type": "inline_equation", + "content": "^{2*}" + }, + { + "bbox": [ + 189, + 142, + 403, + 158 + ], + "type": "text", + "content": ", Haoyu Tang" + }, + { + "bbox": [ + 189, + 142, + 403, + 158 + ], + "type": "inline_equation", + "content": "^{3}" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 135, + 157, + 458, + 171 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 135, + 157, + 458, + 171 + ], + "spans": [ + { + "bbox": [ + 135, + 157, + 458, + 171 + ], + "type": "text", + "content": "1College of Computer and Data Science, Fuzhou University, China" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 118, + 171, + 475, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 118, + 171, + 475, + 185 + ], + "spans": [ + { + "bbox": [ + 118, + 171, + 475, + 185 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 118, + 171, + 475, + 185 + ], + "type": "text", + "content": "School of Software Engineering, Xi'an Jiaotong University, Xi'an, China" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 161, + 185, + 432, + 199 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 161, + 185, + 432, + 199 + ], + "spans": [ + { + "bbox": [ + 161, + 185, + 432, + 199 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 161, + 185, + 432, + 199 + ], + "type": "text", + "content": "School of Software, Shandong University, Jinan, China" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 143, + 227, + 192, + 239 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 227, + 192, + 239 + ], + "spans": [ + { + "bbox": [ + 143, + 227, + 192, + 239 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 252, + 290, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 252, + 290, + 515 + ], + "spans": [ + { + "bbox": [ + 46, + 252, + 290, + 515 + ], + "type": "text", + "content": "In this work, we focus on the challenging problem of Label Enhancement (LE), which aims to exactly recover label distributions from logical labels, and present a novel Label Information Bottleneck (LIB) method for LE. For the recovery process of label distributions, the label irrelevant information contained in the dataset may lead to unsatisfactory recovery performance. To address this limitation, we make efforts to excavate the essential label relevant information to improve the recovery performance. Our method formulates the LE problem as the following two joint processes: 1) learning the representation with the essential label relevant information, 2) recovering label distributions based on the learned representation. The label relevant information can be excavated based on the \"bottleneck\" formed by the learned representation. Significantly, both the label relevant information about the label assignments and the label relevant information about the label gaps can be explored in our method. Evaluation experiments conducted on several benchmark label distribution learning datasets verify the effectiveness and competitiveness of LIB. Our source codes are available at https://github.com/qinghai-zheng/LIBLE" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 540, + 128, + 553 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 540, + 128, + 553 + ], + "spans": [ + { + "bbox": [ + 47, + 540, + 128, + 553 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 561, + 287, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 561, + 287, + 693 + ], + "spans": [ + { + "bbox": [ + 46, + 561, + 287, + 693 + ], + "type": "text", + "content": "Learning with label ambiguity is important in computer vision and machine learning. Different from the traditional Multi-Label Learning (MLL), which employs multiple logical labels to annotate one instance to address the label ambiguity issue [20], Label Distribution Learning (LDL) considers the relative importance of different labels and draws much attention in recent years [6,8,14,18,26]. By distinguishing the description degrees of all labels, LDL annotates one instance with a label distribution. Therefore, LDL is a more general learning paradigm, MLL can be regarded as a special case of LDL [8,10,12]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 228, + 546, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 228, + 546, + 491 + ], + "spans": [ + { + "bbox": [ + 306, + 228, + 546, + 491 + ], + "type": "text", + "content": "Recently, many LDL methods are proposed and achieve great success in practice [3, 9, 14, 18]. Instances with exact label distributions are vital for the training process of LDL methods. Nevertheless, annotating instances with label distributions is time-consuming [24, 28]. We take the label distribution annotation process of SJAFFE dataset for example here. SJAFFE dataset is the facial expression dataset, which contains 213 grayscale images collected from 10 Japanese female models, each facial expression image is rated by 60 persons on 6 basic emotions, including happiness, surprise, sadness, fear, anger, and disgust, with a five-level scale from 1 - 5, the higher value indicates the higher emotion intensity. Consequently, the average score of each emotion is served as the emotion label distribution [14, 28]. Clearly, the above annotation process is costly and it is unpractical to annotate data with label distributions manually, especially when the number of data is large. Fortunately, most existing datasets in the field of computer vision and machine learning are annotated by single-label or multi-labels [7, 29], therefore, a highly recommended promising solution is Label Enhancement (LE), which attempts to recover the desired label distributions exactly from existing logical labels [24, 28, 32]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 491, + 547, + 599 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 491, + 547, + 599 + ], + "spans": [ + { + "bbox": [ + 305, + 491, + 547, + 599 + ], + "type": "text", + "content": "Driven by the urgent requirement of obtaining label distributions and the convenience of LE, some LE methods are proposed in recent years [5, 7, 11, 13, 15, 17, 21, 24, 28, 29]. Given a dataset " + }, + { + "bbox": [ + 305, + 491, + 547, + 599 + ], + "type": "inline_equation", + "content": "\\mathbf{X} = \\{\\pmb{x}_1, \\pmb{x}_2, \\dots, \\pmb{x}_n\\} \\in \\mathbb{R}^{q \\times n}" + }, + { + "bbox": [ + 305, + 491, + 547, + 599 + ], + "type": "text", + "content": ", in which " + }, + { + "bbox": [ + 305, + 491, + 547, + 599 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 305, + 491, + 547, + 599 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 491, + 547, + 599 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 305, + 491, + 547, + 599 + ], + "type": "text", + "content": " denote the number of dimensions and the number of instances, the potential label set is " + }, + { + "bbox": [ + 305, + 491, + 547, + 599 + ], + "type": "inline_equation", + "content": "\\{y_1, y_2, \\dots, y_c\\}" + }, + { + "bbox": [ + 305, + 491, + 547, + 599 + ], + "type": "text", + "content": ". The available logical labels and the desired distribution labels of " + }, + { + "bbox": [ + 305, + 491, + 547, + 599 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 305, + 491, + 547, + 599 + ], + "type": "text", + "content": " are separately indicated by " + }, + { + "bbox": [ + 305, + 491, + 547, + 599 + ], + "type": "inline_equation", + "content": "\\mathbf{L} = \\{l_1, l_2, \\dots, l_n\\}" + }, + { + "bbox": [ + 305, + 491, + 547, + 599 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 491, + 547, + 599 + ], + "type": "inline_equation", + "content": "\\mathbf{D} = \\{d_1, d_2, \\dots, d_n\\}" + }, + { + "bbox": [ + 305, + 491, + 547, + 599 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 305, + 491, + 547, + 599 + ], + "type": "inline_equation", + "content": "l_i" + }, + { + "bbox": [ + 305, + 491, + 547, + 599 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 491, + 547, + 599 + ], + "type": "inline_equation", + "content": "d_i" + }, + { + "bbox": [ + 305, + 491, + 547, + 599 + ], + "type": "text", + "content": " are:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 312, + 604, + 546, + 619 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 604, + 546, + 619 + ], + "spans": [ + { + "bbox": [ + 312, + 604, + 546, + 619 + ], + "type": "interline_equation", + "content": "\\boldsymbol {l} _ {i} = \\left(l _ {i} ^ {y _ {1}}, l _ {i} ^ {y _ {2}}, \\dots , l _ {i} ^ {y _ {c}}\\right) ^ {T}, \\boldsymbol {d} _ {i} = \\left(d _ {i} ^ {y _ {1}}, d _ {i} ^ {y _ {2}}, \\dots , d _ {i} ^ {y _ {c}}\\right) ^ {T}. \\tag {1}", + "image_path": "a89e3c0c4adbd4b8f0a024bc939bed89793420598b24ea231a4ecdf82fd33efd.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 624, + 545, + 660 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 624, + 545, + 660 + ], + "spans": [ + { + "bbox": [ + 305, + 624, + 545, + 660 + ], + "type": "text", + "content": "To be specific, LE aims to recover " + }, + { + "bbox": [ + 305, + 624, + 545, + 660 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 305, + 624, + 545, + 660 + ], + "type": "text", + "content": " based on the information provided by " + }, + { + "bbox": [ + 305, + 624, + 545, + 660 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 305, + 624, + 545, + 660 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 624, + 545, + 660 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 305, + 624, + 545, + 660 + ], + "type": "text", + "content": ". For most existing LE methods, their objectives can be concisely summarized as follows:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 345, + 665, + 545, + 685 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 345, + 665, + 545, + 685 + ], + "spans": [ + { + "bbox": [ + 345, + 665, + 545, + 685 + ], + "type": "interline_equation", + "content": "\\min _ {\\theta} \\| f _ {\\theta} (\\boldsymbol {X}) - \\boldsymbol {L} \\| _ {F} ^ {2} + \\gamma r e g (f _ {\\theta} (\\boldsymbol {X})), \\tag {2}", + "image_path": "1c7b057d01605dfab9845daebac82a5b887dac5ad6be395055d7d05f825b32c1.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 689, + 546, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 546, + 715 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 546, + 715 + ], + "type": "text", + "content": "in which " + }, + { + "bbox": [ + 306, + 689, + 546, + 715 + ], + "type": "inline_equation", + "content": "\\pmb{D} = f_{\\theta}(\\pmb{X})" + }, + { + "bbox": [ + 306, + 689, + 546, + 715 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 306, + 689, + 546, + 715 + ], + "type": "inline_equation", + "content": "f_{\\theta}(\\cdot)" + }, + { + "bbox": [ + 306, + 689, + 546, + 715 + ], + "type": "text", + "content": " indicates the mapping from " + }, + { + "bbox": [ + 306, + 689, + 546, + 715 + ], + "type": "inline_equation", + "content": "\\pmb{X}" + }, + { + "bbox": [ + 306, + 689, + 546, + 715 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 306, + 689, + 546, + 715 + ], + "type": "inline_equation", + "content": "\\pmb{D}" + }, + { + "bbox": [ + 306, + 689, + 546, + 715 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 306, + 689, + 546, + 715 + ], + "type": "inline_equation", + "content": "reg(\\cdot)" + }, + { + "bbox": [ + 306, + 689, + 546, + 715 + ], + "type": "text", + "content": " denotes the regularization function, and " + }, + { + "bbox": [ + 306, + 689, + 546, + 715 + ], + "type": "inline_equation", + "content": "\\gamma" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 225, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 225, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 225, + 713 + ], + "type": "text", + "content": "*Corresponding author, E-mail: zhujh@xjtu.edu.cn" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7497" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 82, + 70, + 251, + 219 + ], + "blocks": [ + { + "bbox": [ + 82, + 70, + 251, + 219 + ], + "lines": [ + { + "bbox": [ + 82, + 70, + 251, + 219 + ], + "spans": [ + { + "bbox": [ + 82, + 70, + 251, + 219 + ], + "type": "image", + "image_path": "938d1516c60e7eae4d0f313b03c47b436a880ccd51e138931954df05b4858467.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 227, + 289, + 380 + ], + "lines": [ + { + "bbox": [ + 46, + 227, + 289, + 380 + ], + "spans": [ + { + "bbox": [ + 46, + 227, + 289, + 380 + ], + "type": "text", + "content": "Figure 1. Illustration of label relevant information. Excavating the essential label relevant information directly is challenging and we adopt a indirect way here. We jointly investigate the information about the assignments of labels to the instance and the information about the label gaps between logical labels and label distributions. Given the " + }, + { + "bbox": [ + 46, + 227, + 289, + 380 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 227, + 289, + 380 + ], + "type": "text", + "content": "-th instance " + }, + { + "bbox": [ + 46, + 227, + 289, + 380 + ], + "type": "inline_equation", + "content": "\\pmb{x}_i" + }, + { + "bbox": [ + 46, + 227, + 289, + 380 + ], + "type": "text", + "content": ", the label gap of the " + }, + { + "bbox": [ + 46, + 227, + 289, + 380 + ], + "type": "inline_equation", + "content": "y_j" + }, + { + "bbox": [ + 46, + 227, + 289, + 380 + ], + "type": "text", + "content": " label is " + }, + { + "bbox": [ + 46, + 227, + 289, + 380 + ], + "type": "inline_equation", + "content": "\\delta_i^{y_j} = l_i^{y_j} - d_i^{y_j}" + }, + { + "bbox": [ + 46, + 227, + 289, + 380 + ], + "type": "text", + "content": ". The information contained in " + }, + { + "bbox": [ + 46, + 227, + 289, + 380 + ], + "type": "inline_equation", + "content": "l_i^{y_j}" + }, + { + "bbox": [ + 46, + 227, + 289, + 380 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 227, + 289, + 380 + ], + "type": "inline_equation", + "content": "\\delta_i^{y_j}" + }, + { + "bbox": [ + 46, + 227, + 289, + 380 + ], + "type": "text", + "content": " can be amalgamated to form the essential label relevant information. In other words, we employ " + }, + { + "bbox": [ + 46, + 227, + 289, + 380 + ], + "type": "inline_equation", + "content": "l_i^{y_j}" + }, + { + "bbox": [ + 46, + 227, + 289, + 380 + ], + "type": "text", + "content": " to explore the label relevant information about the label assignments and " + }, + { + "bbox": [ + 46, + 227, + 289, + 380 + ], + "type": "inline_equation", + "content": "\\delta_i^{y_j}" + }, + { + "bbox": [ + 46, + 227, + 289, + 380 + ], + "type": "text", + "content": " to excavate the label relevant information about the label gaps. To a certain degree, the combination of " + }, + { + "bbox": [ + 46, + 227, + 289, + 380 + ], + "type": "inline_equation", + "content": "\\delta_i^{y_j}" + }, + { + "bbox": [ + 46, + 227, + 289, + 380 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 227, + 289, + 380 + ], + "type": "inline_equation", + "content": "l_i^{y_j}" + }, + { + "bbox": [ + 46, + 227, + 289, + 380 + ], + "type": "text", + "content": " is equivalent to " + }, + { + "bbox": [ + 46, + 227, + 289, + 380 + ], + "type": "inline_equation", + "content": "d_i^{y_j}" + }, + { + "bbox": [ + 46, + 227, + 289, + 380 + ], + "type": "text", + "content": ". As depicted here, " + }, + { + "bbox": [ + 46, + 227, + 289, + 380 + ], + "type": "inline_equation", + "content": "l_i^{y_j}" + }, + { + "bbox": [ + 46, + 227, + 289, + 380 + ], + "type": "text", + "content": " indicates that " + }, + { + "bbox": [ + 46, + 227, + 289, + 380 + ], + "type": "inline_equation", + "content": "y_1" + }, + { + "bbox": [ + 46, + 227, + 289, + 380 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 227, + 289, + 380 + ], + "type": "inline_equation", + "content": "y_3" + }, + { + "bbox": [ + 46, + 227, + 289, + 380 + ], + "type": "text", + "content": " are related labels and " + }, + { + "bbox": [ + 46, + 227, + 289, + 380 + ], + "type": "inline_equation", + "content": "\\delta_i^{y_j}" + }, + { + "bbox": [ + 46, + 227, + 289, + 380 + ], + "type": "text", + "content": " provides the importance of " + }, + { + "bbox": [ + 46, + 227, + 289, + 380 + ], + "type": "inline_equation", + "content": "y_1" + }, + { + "bbox": [ + 46, + 227, + 289, + 380 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 227, + 289, + 380 + ], + "type": "inline_equation", + "content": "y_3" + }, + { + "bbox": [ + 46, + 227, + 289, + 380 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 402, + 287, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 402, + 287, + 605 + ], + "spans": [ + { + "bbox": [ + 46, + 402, + 287, + 605 + ], + "type": "text", + "content": "is the trade-off parameter. Most existing LE methods vary in " + }, + { + "bbox": [ + 46, + 402, + 287, + 605 + ], + "type": "inline_equation", + "content": "reg(\\cdot)" + }, + { + "bbox": [ + 46, + 402, + 287, + 605 + ], + "type": "text", + "content": ". For example, GLLE [28] calculates the distance-based similarity matrix of data and employs the smoothness assumption [33] to construct " + }, + { + "bbox": [ + 46, + 402, + 287, + 605 + ], + "type": "inline_equation", + "content": "reg(\\cdot)" + }, + { + "bbox": [ + 46, + 402, + 287, + 605 + ], + "type": "text", + "content": "; LESC [24] considers the global sample correlations and introduces the low-rank constraint as the regularization; PNLR [13] leverages " + }, + { + "bbox": [ + 46, + 402, + 287, + 605 + ], + "type": "inline_equation", + "content": "reg(\\cdot)" + }, + { + "bbox": [ + 46, + 402, + 287, + 605 + ], + "type": "text", + "content": " to maintain positive and negative label relations during the recovery process. Although a remarkable progress can be made by aforementioned methods, they ignore the label irrelevant information contained in " + }, + { + "bbox": [ + 46, + 402, + 287, + 605 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 46, + 402, + 287, + 605 + ], + "type": "text", + "content": ", which prevents the further improvement of recovery results. For example, in the LE task of recovering facial age label distributions, the label irrelevant information, such as peculiarities information, cast shadows information, and occlusions information, may result in the incorrect mapping process of " + }, + { + "bbox": [ + 46, + 402, + 287, + 605 + ], + "type": "inline_equation", + "content": "f_{\\theta}(\\cdot)" + }, + { + "bbox": [ + 46, + 402, + 287, + 605 + ], + "type": "text", + "content": " and the unsuitable regularization of " + }, + { + "bbox": [ + 46, + 402, + 287, + 605 + ], + "type": "inline_equation", + "content": "reg(\\cdot)" + }, + { + "bbox": [ + 46, + 402, + 287, + 605 + ], + "type": "text", + "content": ", eventually leads to the unsatisfactory recovery performance." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 606, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 606, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 606, + 288, + 715 + ], + "type": "text", + "content": "To overcome the aforementioned limitation, we present a Label Information Bottleneck (LIB) method for LE. Concretely, the core idea of LIB is to learn the latent representation " + }, + { + "bbox": [ + 46, + 606, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\pmb{H}" + }, + { + "bbox": [ + 46, + 606, + 288, + 715 + ], + "type": "text", + "content": ", which preserves the maximum label relevant information, from " + }, + { + "bbox": [ + 46, + 606, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\pmb{X}" + }, + { + "bbox": [ + 46, + 606, + 288, + 715 + ], + "type": "text", + "content": ", and jointly recovers the label distributions based on the latent representation. For the LE problem, the label relevant information is the information that describes the description degrees of labels. It is tough to explore the label relevant information directly. As shown in Fig. 1, we" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "text", + "content": "decompose the label relevant information into two components, namely the assignments of labels to the instance and the label gaps between label distributions and logical labels. Inspired by Information Bottleneck (IB) [25], LIB utilizes the existing logical labels to explore the information about the assignments of labels to the instance. Unlike simply employing the original IB on the LE task, our method further considers the information about the label gaps between label distributions and logical labels. It is noteworthy that the above two components of the label relevant information are jointly explored in our method, and that is why we term the proposed method Label Information Bottleneck (LIB). The main contributions can be summarized as follows:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 315, + 233, + 545, + 426 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 315, + 233, + 545, + 293 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 233, + 545, + 293 + ], + "spans": [ + { + "bbox": [ + 315, + 233, + 545, + 293 + ], + "type": "text", + "content": "- We decompose the label relevant information into the information about the assignments of labels to instance and the information about the label gaps between logical labels, both of which can be jointly explored during the learning process of our method." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 316, + 300, + 545, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 300, + 545, + 361 + ], + "spans": [ + { + "bbox": [ + 316, + 300, + 545, + 361 + ], + "type": "text", + "content": "- We introduce a novel LE method, termed LIB, which excavates the label relevant information to exactly recover the label distributions. Based on the original IB, which explores the label assignments information for LE, LIB further explores the label gaps information." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 316, + 366, + 545, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 366, + 545, + 426 + ], + "spans": [ + { + "bbox": [ + 316, + 366, + 545, + 426 + ], + "type": "text", + "content": "- We verify the effectiveness of LIB by performing extensive experiments on several datasets. Experimental results show that the proposed method can achieve the competitive performance, compared to state-of-the-art LE methods." + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 436, + 392, + 449 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 436, + 392, + 449 + ], + "spans": [ + { + "bbox": [ + 306, + 436, + 392, + 449 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 456, + 422, + 467 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 456, + 422, + 467 + ], + "spans": [ + { + "bbox": [ + 306, + 456, + 422, + 467 + ], + "type": "text", + "content": "2.1. Label Enhancement" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 474, + 545, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 545, + 533 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 545, + 533 + ], + "type": "text", + "content": "To recover the label distributions from the existing logical labels, many efforts are made recently [24, 28]. In general, most existing LE methods can be roughly divided into two categories, namely, algorithm adaptation and specialized algorithm [8, 24]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": "Algorithm adaptation extends some existing methods to achieve the goal of LE [5, 15]. For example, FCM [5] recovers the label distributions by utilizing the fuzzy clustering and fuzzy relabeling. To be specific, FCM utilizes the fuzzy C-means clustering to get different clusters and cluster prototypes, then obtains membership degrees of each instance with respect to different cluster prototypes, finally annotates all instances with label distributions by employing the fuzzy composition and softmax normalization. KM [15] leverages the fuzzy SVM to achieve the membership function. During the recovery process, KM separates instances into two clusters and employs the nonlinear function to get the radius and distances between centers and kernelized instances, and then gets the label distributions with the help of the softmax normalization." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7498" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 180 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 180 + ], + "type": "text", + "content": "Specialized algorithm is specially designed to deal with the LE problem. Most existing LE methods belong to the category of specialized algorithm and have the basic objective Eq. (2). By using different constraints, different methods adopt different " + }, + { + "bbox": [ + 46, + 72, + 289, + 180 + ], + "type": "inline_equation", + "content": "reg(\\cdot)" + }, + { + "bbox": [ + 46, + 72, + 289, + 180 + ], + "type": "text", + "content": " in Eq. (2). For example, based on the assumption that instances closed in the feature space are more likely to share the same label, GLLE [28] employs the following local graph information in the feature space to boost the recovery performance:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 70, + 187, + 287, + 235 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 187, + 287, + 235 + ], + "spans": [ + { + "bbox": [ + 70, + 187, + 287, + 235 + ], + "type": "interline_equation", + "content": "q _ {i, j} = \\left\\{ \\begin{array}{l} \\exp \\left(- \\frac {\\left\\| \\boldsymbol {x} _ {i} - \\boldsymbol {x} _ {j} \\right\\| ^ {2}}{2 \\varepsilon^ {2}}\\right), \\text {i f} \\boldsymbol {x} _ {j} \\in k (i), \\\\ 0, \\text {o t h e r w i s e}, \\end{array} \\right. \\tag {3}", + "image_path": "f59acff4aecc6b2e91162d828f2fe16e287c00845ae523261be35b8f35f81386.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 243, + 287, + 266 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 243, + 287, + 266 + ], + "spans": [ + { + "bbox": [ + 47, + 243, + 287, + 266 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 243, + 287, + 266 + ], + "type": "inline_equation", + "content": "k(i)" + }, + { + "bbox": [ + 47, + 243, + 287, + 266 + ], + "type": "text", + "content": " denotes the " + }, + { + "bbox": [ + 47, + 243, + 287, + 266 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 47, + 243, + 287, + 266 + ], + "type": "text", + "content": "-nearest neighbours of " + }, + { + "bbox": [ + 47, + 243, + 287, + 266 + ], + "type": "inline_equation", + "content": "\\pmb{x}_i" + }, + { + "bbox": [ + 47, + 243, + 287, + 266 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 47, + 243, + 287, + 266 + ], + "type": "inline_equation", + "content": "reg(\\cdot)" + }, + { + "bbox": [ + 47, + 243, + 287, + 266 + ], + "type": "text", + "content": " in GLLE is constructed as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 75, + 272, + 287, + 299 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 75, + 272, + 287, + 299 + ], + "spans": [ + { + "bbox": [ + 75, + 272, + 287, + 299 + ], + "type": "interline_equation", + "content": "r e g \\left(f _ {\\theta} (\\boldsymbol {X})\\right) = \\sum_ {i, j} q _ {i, j} \\left\\| f _ {\\theta} \\left(\\boldsymbol {x} _ {i}\\right) - f _ {\\theta} \\left(\\boldsymbol {x} _ {j}\\right) \\right\\| _ {2} ^ {2}. \\tag {4}", + "image_path": "e28e5591e2e346fcf5999a24b5db81f0a87d5f1973f1d908698994558e3b0bed.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 305, + 287, + 331 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 305, + 287, + 331 + ], + "spans": [ + { + "bbox": [ + 47, + 305, + 287, + 331 + ], + "type": "text", + "content": "Unlike GLLE, LESC [24] considers the global graph information and uses the low-rank representation learning [19]:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 70, + 341, + 287, + 360 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 341, + 287, + 360 + ], + "spans": [ + { + "bbox": [ + 70, + 341, + 287, + 360 + ], + "type": "interline_equation", + "content": "\\min _ {\\boldsymbol {G}, \\boldsymbol {E}} \\| \\boldsymbol {G} \\| _ {*} + \\lambda_ {2} \\| \\boldsymbol {E} \\| _ {2, 1}, \\text {s . t . ,} \\boldsymbol {X} = \\boldsymbol {X} \\boldsymbol {G} + \\boldsymbol {E}, \\tag {5}", + "image_path": "08658c738c3a4d6867a95236b1f4ba631a1349bf052cb6ab7a2675530886f997.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 363, + 287, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 363, + 287, + 399 + ], + "spans": [ + { + "bbox": [ + 47, + 363, + 287, + 399 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 363, + 287, + 399 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 47, + 363, + 287, + 399 + ], + "type": "text", + "content": " indicates the low-rank representation of instances in the feature space. The regularization function in LESC is written as follows:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 85, + 406, + 287, + 422 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 406, + 287, + 422 + ], + "spans": [ + { + "bbox": [ + 85, + 406, + 287, + 422 + ], + "type": "interline_equation", + "content": "r e g (f _ {\\theta} (\\pmb {X})) = \\| f _ {\\theta} (\\pmb {X}) - f _ {\\theta} (\\pmb {X}) \\pmb {G} \\| _ {F} ^ {2}. \\qquad (6)", + "image_path": "f59d9f69a0eafa6d8d54e3f1188a2020f88193f12aee71d345a7c2aac280f72c.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 429, + 287, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 429, + 287, + 525 + ], + "spans": [ + { + "bbox": [ + 46, + 429, + 287, + 525 + ], + "type": "text", + "content": "For these aforementioned LE methods, they all neglect the label irrelevant information contained in " + }, + { + "bbox": [ + 46, + 429, + 287, + 525 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 46, + 429, + 287, + 525 + ], + "type": "text", + "content": ", the negative effect of which can result in the unsatisfactory recovery results. Taking the recovery of facial emotion label distributions for example, the inaccurate graph information would be obtained in GLLE and LESSC with the presence of label irrelevant information, such as the identity information, hindering the further improvement of recovery results." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 531, + 180, + 544 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 531, + 180, + 544 + ], + "spans": [ + { + "bbox": [ + 47, + 531, + 180, + 544 + ], + "type": "text", + "content": "2.2. Information Bottleneck" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 549, + 287, + 597 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 549, + 287, + 597 + ], + "spans": [ + { + "bbox": [ + 46, + 549, + 287, + 597 + ], + "type": "text", + "content": "Information bottleneck (IB) [1, 25, 25] is an information theoretic principle, which describes the relevant information in data formally. To be concrete, IB has the following objective:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 88, + 605, + 287, + 624 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 88, + 605, + 287, + 624 + ], + "spans": [ + { + "bbox": [ + 88, + 605, + 287, + 624 + ], + "type": "interline_equation", + "content": "\\min _ {\\boldsymbol {B}} - I (\\boldsymbol {B}, \\boldsymbol {C}), \\text {s . t .}, I (\\boldsymbol {A}, \\boldsymbol {B}) \\leqslant I _ {c}, \\tag {7}", + "image_path": "e78cfa830147556d5b578b64c095e42b325000d72916434915884660eb390e6e.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 630, + 287, + 691 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 630, + 287, + 691 + ], + "spans": [ + { + "bbox": [ + 47, + 630, + 287, + 691 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 630, + 287, + 691 + ], + "type": "inline_equation", + "content": "I(\\cdot, \\cdot)" + }, + { + "bbox": [ + 47, + 630, + 287, + 691 + ], + "type": "text", + "content": " measures the mutual information and " + }, + { + "bbox": [ + 47, + 630, + 287, + 691 + ], + "type": "inline_equation", + "content": "I_{c}" + }, + { + "bbox": [ + 47, + 630, + 287, + 691 + ], + "type": "text", + "content": " is the information constraint. Clearly, IB aims to learn the representation " + }, + { + "bbox": [ + 47, + 630, + 287, + 691 + ], + "type": "inline_equation", + "content": "\\pmb{B}" + }, + { + "bbox": [ + 47, + 630, + 287, + 691 + ], + "type": "text", + "content": ", which preserves the relevant information about " + }, + { + "bbox": [ + 47, + 630, + 287, + 691 + ], + "type": "inline_equation", + "content": "\\pmb{C}" + }, + { + "bbox": [ + 47, + 630, + 287, + 691 + ], + "type": "text", + "content": ", from " + }, + { + "bbox": [ + 47, + 630, + 287, + 691 + ], + "type": "inline_equation", + "content": "\\pmb{A}" + }, + { + "bbox": [ + 47, + 630, + 287, + 691 + ], + "type": "text", + "content": ". Considering the scenario of LE, it is natural to get the following formula:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 87, + 699, + 287, + 716 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 87, + 699, + 287, + 716 + ], + "spans": [ + { + "bbox": [ + 87, + 699, + 287, + 716 + ], + "type": "interline_equation", + "content": "\\min _ {\\boldsymbol {H}} - I (\\boldsymbol {H}, \\boldsymbol {L}), \\text {s . t .}, I (\\boldsymbol {X}, \\boldsymbol {H}) \\leqslant I _ {c}. \\tag {8}", + "image_path": "75c885cb789d8cccda6d24663dca45de37440c5ffee903ad2729fcf0658f9168.jpg" + } + ] + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 317, + 70, + 537, + 213 + ], + "blocks": [ + { + "bbox": [ + 317, + 70, + 537, + 213 + ], + "lines": [ + { + "bbox": [ + 317, + 70, + 537, + 213 + ], + "spans": [ + { + "bbox": [ + 317, + 70, + 537, + 213 + ], + "type": "image", + "image_path": "3a32c40ca8c4da719214278990048c1ffa7bc42cc60e02604ce68f7b852dc16f.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 220, + 545, + 354 + ], + "lines": [ + { + "bbox": [ + 304, + 220, + 545, + 354 + ], + "spans": [ + { + "bbox": [ + 304, + 220, + 545, + 354 + ], + "type": "text", + "content": "Figure 2. Framework of the proposed LIB. Since the way that directly explores the label relevant information is challenging, LIB decomposes the label relevant information into two components, namely the assignments of labels to the instance and the label gaps between label distributions and logical labels, and adopts an indirect path, which explores the information about label assignments and label gaps simultaneously. By minimizing " + }, + { + "bbox": [ + 304, + 220, + 545, + 354 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{as}" + }, + { + "bbox": [ + 304, + 220, + 545, + 354 + ], + "type": "text", + "content": ", LIB explores the information about assignments of labels to the instance. Meanwhile, by minimizing " + }, + { + "bbox": [ + 304, + 220, + 545, + 354 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{gap}" + }, + { + "bbox": [ + 304, + 220, + 545, + 354 + ], + "type": "text", + "content": ", LIB explores the information about the label gaps between logical labels and label distributions. Consequently, the label relevant information can be effectively explored and the label distributions can be exactly recovered." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 372, + 545, + 419 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 372, + 545, + 419 + ], + "spans": [ + { + "bbox": [ + 304, + 372, + 545, + 419 + ], + "type": "text", + "content": "As discussed in Section 1, the information merely about the assignments of labels to the instance can be explored based on Eq. (8), which neglects the vital information about the label gaps between logical labels and label distributions." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 420, + 545, + 503 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 420, + 545, + 503 + ], + "spans": [ + { + "bbox": [ + 304, + 420, + 545, + 503 + ], + "type": "text", + "content": "Recently, IB has been successfully utilized in many real-world applications [1, 2, 22, 27, 30, 31]. To the best of our knowledge, the method introduced in this paper is the first work that leverages IB to deal with the LE problem. More notably, rather than using IB simply (as shown in Eq. (8)), our method conducts more in-depth exploration to exactly recover label distributions based on IB." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 513, + 435, + 528 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 513, + 435, + 528 + ], + "spans": [ + { + "bbox": [ + 306, + 513, + 435, + 528 + ], + "type": "text", + "content": "3. The Proposed Method" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 533, + 459, + 546 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 533, + 459, + 546 + ], + "spans": [ + { + "bbox": [ + 306, + 533, + 459, + 546 + ], + "type": "text", + "content": "3.1. The Objective Construction" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 317, + 552, + 523, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 552, + 523, + 563 + ], + "spans": [ + { + "bbox": [ + 317, + 552, + 523, + 563 + ], + "type": "text", + "content": "Generally, the basic idea can be written as follows:" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 332, + 571, + 545, + 589 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 332, + 571, + 545, + 589 + ], + "spans": [ + { + "bbox": [ + 332, + 571, + 545, + 589 + ], + "type": "interline_equation", + "content": "\\min _ {\\boldsymbol {H}} \\mathcal {L} _ {a s} + \\alpha \\mathcal {L} _ {g a p}, \\text {s . t .}, I (\\boldsymbol {X}, \\boldsymbol {H}) \\leqslant I _ {c}, \\tag {9}", + "image_path": "f02910056d1a8fc9361b5fad17f926c59b3f169103949a1016dbccc809a05459.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 594, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 594, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{as}" + }, + { + "bbox": [ + 304, + 594, + 545, + 714 + ], + "type": "text", + "content": " excavates the information about the assignments of labels to the instance, " + }, + { + "bbox": [ + 304, + 594, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{gap}" + }, + { + "bbox": [ + 304, + 594, + 545, + 714 + ], + "type": "text", + "content": " investigates the information about the label gaps between the logical labels and distribution labels, " + }, + { + "bbox": [ + 304, + 594, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 594, + 545, + 714 + ], + "type": "text", + "content": " is the trade-off parameter, the constraint aims to remove the label irrelevant information. The framework of our method is depicted in Fig. 2. It's worth noting that employing the original IB for LE merely explores the information about the label assignments. While our LIB makes attempts to capture the information about both the label assignments and the description degrees of labels." + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7499" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 251, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 251, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 251, + 85 + ], + "type": "text", + "content": "3.1.1 Label assignments information modeling" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 91, + 274, + 103 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 91, + 274, + 103 + ], + "spans": [ + { + "bbox": [ + 47, + 91, + 274, + 103 + ], + "type": "text", + "content": "For " + }, + { + "bbox": [ + 47, + 91, + 274, + 103 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{as}" + }, + { + "bbox": [ + 47, + 91, + 274, + 103 + ], + "type": "text", + "content": ", inspired by IB, we have the following formula:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 127, + 110, + 287, + 122 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 127, + 110, + 287, + 122 + ], + "spans": [ + { + "bbox": [ + 127, + 110, + 287, + 122 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {a s} = - I (\\boldsymbol {H}, \\boldsymbol {L}). \\tag {10}", + "image_path": "0b515dca7a4554c3cfc7dec3df788a1ba35c6225f3635e08b4d4caf9e9631298.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 129, + 287, + 152 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 129, + 287, + 152 + ], + "spans": [ + { + "bbox": [ + 47, + 129, + 287, + 152 + ], + "type": "text", + "content": "According to the concept of mutual information, " + }, + { + "bbox": [ + 47, + 129, + 287, + 152 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{as}" + }, + { + "bbox": [ + 47, + 129, + 287, + 152 + ], + "type": "text", + "content": " can be rewritten out in full as follows:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 92, + 156, + 287, + 186 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 92, + 156, + 287, + 186 + ], + "spans": [ + { + "bbox": [ + 92, + 156, + 287, + 186 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {a s} = - \\sum_ {\\boldsymbol {h}} \\sum_ {\\boldsymbol {l}} p (\\boldsymbol {h}, \\boldsymbol {l}) \\log \\frac {p (\\boldsymbol {l} | \\boldsymbol {h})}{p (\\boldsymbol {l})}. \\tag {11}", + "image_path": "1eec44a5bb0ec667d6e6991a7e31af45840011d7e98987a6663ab522c6f8d141.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 192, + 287, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 192, + 287, + 228 + ], + "spans": [ + { + "bbox": [ + 47, + 192, + 287, + 228 + ], + "type": "text", + "content": "For the convenience of optimization, we introduce the variational approximation " + }, + { + "bbox": [ + 47, + 192, + 287, + 228 + ], + "type": "inline_equation", + "content": "q(\\boldsymbol{l}|\\boldsymbol{h})" + }, + { + "bbox": [ + 47, + 192, + 287, + 228 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 47, + 192, + 287, + 228 + ], + "type": "inline_equation", + "content": "p(\\boldsymbol{l}|\\boldsymbol{h})" + }, + { + "bbox": [ + 47, + 192, + 287, + 228 + ], + "type": "text", + "content": ". Since both the Kullback Leibler divergence and the entropy are positive:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 58, + 233, + 287, + 323 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 233, + 287, + 323 + ], + "spans": [ + { + "bbox": [ + 58, + 233, + 287, + 323 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\operatorname {K L} \\left(p (\\boldsymbol {l} | \\boldsymbol {h}) | | q (\\boldsymbol {l} | \\boldsymbol {h})\\right) = \\sum_ {\\boldsymbol {l}} p (\\boldsymbol {l} | \\boldsymbol {h}) \\log \\frac {p (\\boldsymbol {l} | \\boldsymbol {h})}{q (\\boldsymbol {l} | \\boldsymbol {h})} \\geqslant 0 (12) \\\\ \\Rightarrow \\sum_ {\\boldsymbol {l}} p (\\boldsymbol {l} | \\boldsymbol {h}) \\log p (\\boldsymbol {l} | \\boldsymbol {h}) \\geqslant \\sum_ {\\boldsymbol {l}} p (\\boldsymbol {l} | \\boldsymbol {h}) \\log q (\\boldsymbol {l} | \\boldsymbol {h}), \\\\ \\mathbb {E} _ {p (\\boldsymbol {l})} [ - \\log p (\\boldsymbol {l}) ] = - \\sum_ {\\boldsymbol {l}} p (\\boldsymbol {l}) \\log p (\\boldsymbol {l}) \\geqslant 0, (13) \\\\ \\end{array}", + "image_path": "e52c5e16877306033bc6defabf4e73e6106846873c9be1109915b711b85b5dd2.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 326, + 273, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 326, + 273, + 338 + ], + "spans": [ + { + "bbox": [ + 47, + 326, + 273, + 338 + ], + "type": "text", + "content": "based on Markov chain that " + }, + { + "bbox": [ + 47, + 326, + 273, + 338 + ], + "type": "inline_equation", + "content": "L\\gets X\\to H" + }, + { + "bbox": [ + 47, + 326, + 273, + 338 + ], + "type": "text", + "content": " , we can get:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 64, + 344, + 287, + 369 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 64, + 344, + 287, + 369 + ], + "spans": [ + { + "bbox": [ + 64, + 344, + 287, + 369 + ], + "type": "interline_equation", + "content": "L _ {a s} \\leqslant - \\sum_ {\\boldsymbol {x}} \\sum_ {l} \\sum_ {\\boldsymbol {h}} p (\\boldsymbol {x}, l) p (\\boldsymbol {h} | \\boldsymbol {x}) \\log q (l | \\boldsymbol {h}). \\tag {14}", + "image_path": "f2cbf09d29ddf596b0a0dbddb6e7f796ea46fd18f247d713f1a608b0be68d259.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 381, + 222, + 394 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 381, + 222, + 394 + ], + "spans": [ + { + "bbox": [ + 47, + 381, + 222, + 394 + ], + "type": "text", + "content": "3.1.2 Label gaps information modeling" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 400, + 287, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 400, + 287, + 460 + ], + "spans": [ + { + "bbox": [ + 47, + 400, + 287, + 460 + ], + "type": "text", + "content": "To investigate the label-relevant information about the description degrees of labels, we introduce the label gaps between logical labels and label distributions " + }, + { + "bbox": [ + 47, + 400, + 287, + 460 + ], + "type": "inline_equation", + "content": "\\pmb{\\Delta}" + }, + { + "bbox": [ + 47, + 400, + 287, + 460 + ], + "type": "text", + "content": ", and consider the conditional self-information, i.e., " + }, + { + "bbox": [ + 47, + 400, + 287, + 460 + ], + "type": "inline_equation", + "content": "I(\\Delta | H)" + }, + { + "bbox": [ + 47, + 400, + 287, + 460 + ], + "type": "text", + "content": ". Therefore, we construct " + }, + { + "bbox": [ + 47, + 400, + 287, + 460 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{gap}^{1}" + }, + { + "bbox": [ + 47, + 400, + 287, + 460 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 94, + 467, + 287, + 536 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 94, + 467, + 287, + 536 + ], + "spans": [ + { + "bbox": [ + 94, + 467, + 287, + 536 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {g a p} = I (\\boldsymbol {\\Delta} | \\boldsymbol {H}) = - \\log p (\\boldsymbol {\\Delta} | \\boldsymbol {H}) \\\\ = - \\sum_ {\\delta} \\sum_ {\\boldsymbol {h}} \\log p (\\boldsymbol {\\delta} | \\boldsymbol {h}) \\tag {15} \\\\ = - \\sum_ {l} \\sum_ {\\boldsymbol {h}} \\log p (\\boldsymbol {l} - \\hat {\\boldsymbol {d}} | \\boldsymbol {h}). \\\\ \\end{array}", + "image_path": "c8416da1a81c37c36bf0410f5fab804588bb447f2de3074252ea04d226d61d58.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 543, + 287, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 543, + 287, + 567 + ], + "spans": [ + { + "bbox": [ + 47, + 543, + 287, + 567 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 543, + 287, + 567 + ], + "type": "inline_equation", + "content": "\\delta = l - \\hat{d},\\hat{d}" + }, + { + "bbox": [ + 47, + 543, + 287, + 567 + ], + "type": "text", + "content": " is the label distribution recovered in our method." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 582, + 244, + 594 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 582, + 244, + 594 + ], + "spans": [ + { + "bbox": [ + 47, + 582, + 244, + 594 + ], + "type": "text", + "content": "3.1.3 Label irrelevant information modeling" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 47, + 600, + 287, + 636 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 600, + 287, + 636 + ], + "spans": [ + { + "bbox": [ + 47, + 600, + 287, + 636 + ], + "type": "text", + "content": "Regarding the label irrelevant information, LIB employs the constraint in Eq. (9) to discard it during the learning process. " + }, + { + "bbox": [ + 47, + 600, + 287, + 636 + ], + "type": "inline_equation", + "content": "I(\\mathbf{X},\\mathbf{H})" + }, + { + "bbox": [ + 47, + 600, + 287, + 636 + ], + "type": "text", + "content": " can be formulated as follows:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 83, + 643, + 287, + 672 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 643, + 287, + 672 + ], + "spans": [ + { + "bbox": [ + 83, + 643, + 287, + 672 + ], + "type": "interline_equation", + "content": "I (\\boldsymbol {X}, \\boldsymbol {H}) = \\sum_ {\\boldsymbol {x}} \\sum_ {\\boldsymbol {h}} p (\\boldsymbol {x}, \\boldsymbol {h}) \\log \\frac {p (\\boldsymbol {h} \\mid \\boldsymbol {x})}{p (\\boldsymbol {h})}. \\tag {16}", + "image_path": "20284ee5e8e4f33fc339e680affea4ae1c165c6873480553c7183d69f44101ce.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "content": "Since it is difficult to calculate " + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "inline_equation", + "content": "p(h)" + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "content": " directly, we also introduce the variational approximation " + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "inline_equation", + "content": "q(h)" + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "inline_equation", + "content": "p(h)" + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "content": ". Similar to Eq. (12), based on " + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "inline_equation", + "content": "\\mathrm{KL}(p(h)||q(h)) \\geqslant 0" + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "content": ", we have:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 345, + 118, + 545, + 144 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 345, + 118, + 545, + 144 + ], + "spans": [ + { + "bbox": [ + 345, + 118, + 545, + 144 + ], + "type": "interline_equation", + "content": "\\sum_ {\\boldsymbol {h}} p (\\boldsymbol {h}) \\log p (\\boldsymbol {h}) \\geqslant \\sum_ {\\boldsymbol {h}} p (\\boldsymbol {h}) \\log q (\\boldsymbol {h}). \\tag {17}", + "image_path": "6b1d74cef2008f0896c841880b5b63fbc407e7c27a44814f1f79e49f0d84e730.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 152, + 515, + 165 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 152, + 515, + 165 + ], + "spans": [ + { + "bbox": [ + 306, + 152, + 515, + 165 + ], + "type": "text", + "content": "Subsequently, the following formula can be written:" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 321, + 174, + 545, + 230 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 174, + 545, + 230 + ], + "spans": [ + { + "bbox": [ + 321, + 174, + 545, + 230 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} I (\\boldsymbol {X}, \\boldsymbol {H}) \\leqslant \\sum_ {\\boldsymbol {x}} \\sum_ {\\boldsymbol {h}} p (\\boldsymbol {x}, \\boldsymbol {h}) \\log \\frac {p (\\boldsymbol {h} | \\boldsymbol {x})}{q (\\boldsymbol {h})} \\tag {18} \\\\ = \\sum_ {\\boldsymbol {x}} \\sum_ {\\boldsymbol {l}} p (\\boldsymbol {x}, \\boldsymbol {l}) \\operatorname {K L} (p (\\boldsymbol {h} | \\boldsymbol {x}) | | q (\\boldsymbol {h})). \\\\ \\end{array}", + "image_path": "2bdc15cee26c553359ede8cc6919cda4cea221fca0e2e47deb022bffbf3ffbc4.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 247, + 410, + 258 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 247, + 410, + 258 + ], + "spans": [ + { + "bbox": [ + 306, + 247, + 410, + 258 + ], + "type": "text", + "content": "3.1.4 Objective of LIB" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 305, + 266, + 545, + 291 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 266, + 545, + 291 + ], + "spans": [ + { + "bbox": [ + 305, + 266, + 545, + 291 + ], + "type": "text", + "content": "By employing the Lagrange multiplier method and combining Eq. (9), (14), (15), and (18), we have:" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 324, + 300, + 545, + 396 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 324, + 300, + 545, + 396 + ], + "spans": [ + { + "bbox": [ + 324, + 300, + 545, + 396 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} = \\mathcal {L} _ {a s} + \\alpha \\mathcal {L} _ {g a p} + \\beta I (\\boldsymbol {X}, \\boldsymbol {H}) \\\\ \\leqslant - \\sum_ {\\boldsymbol {x}} \\sum_ {\\boldsymbol {l}} \\sum_ {\\boldsymbol {h}} p (\\boldsymbol {x}, \\boldsymbol {l}) p (\\boldsymbol {h} | \\boldsymbol {x}, \\boldsymbol {l}) \\log q (\\boldsymbol {l} | \\boldsymbol {h}) \\\\ - \\alpha \\sum_ {\\boldsymbol {l}} \\sum_ {\\boldsymbol {h}} \\log p (\\boldsymbol {l} - \\hat {\\boldsymbol {d}} | \\boldsymbol {h}) \\tag {19} \\\\ + \\beta \\sum_ {\\boldsymbol {x}} \\sum_ {\\boldsymbol {l}} p (\\boldsymbol {x}, \\boldsymbol {l}) \\operatorname {K L} (p (\\boldsymbol {h} | \\boldsymbol {x}) | | q (\\boldsymbol {h})). \\\\ \\end{array}", + "image_path": "d30d81b83aa41001ee6457c8fdaf2597d14c9fc8e2fb98c02353599be63cf1e5.jpg" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 305, + 405, + 545, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 405, + 545, + 441 + ], + "spans": [ + { + "bbox": [ + 305, + 405, + 545, + 441 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 405, + 545, + 441 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 305, + 405, + 545, + 441 + ], + "type": "text", + "content": " is the Lagrange multiplier. Considering the bound of " + }, + { + "bbox": [ + 305, + 405, + 545, + 441 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 305, + 405, + 545, + 441 + ], + "type": "text", + "content": " and using the empirical Monte Carlo approximation of sampling [23], we have the following objective of LIB:" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 310, + 451, + 545, + 510 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 451, + 545, + 510 + ], + "spans": [ + { + "bbox": [ + 310, + 451, + 545, + 510 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {L I B} = \\frac {1}{n} \\sum_ {i = 1} ^ {n} \\left[ - \\sum_ {\\boldsymbol {h}} p (\\boldsymbol {h} | \\boldsymbol {x} _ {i}) \\log q \\left(\\boldsymbol {l} _ {i} \\mid \\boldsymbol {h}\\right) \\right. \\tag {20} \\\\ + \\beta \\operatorname {K L} (p (\\boldsymbol {h} | \\boldsymbol {x} _ {i}) | | q (\\boldsymbol {h})) ] - \\alpha \\sum_ {\\boldsymbol {l}} \\sum_ {\\boldsymbol {h}} \\log p (\\boldsymbol {l} - \\hat {\\boldsymbol {d}} | \\boldsymbol {h}). \\\\ \\end{array}", + "image_path": "8dfc0c07a1cde19299fd74457ee0928958c028b5b56ffae96264db4caa61461b.jpg" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 306, + 520, + 444, + 533 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 520, + 444, + 533 + ], + "spans": [ + { + "bbox": [ + 306, + 520, + 444, + 533 + ], + "type": "text", + "content": "3.2. The Optimization of LIB" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 306, + 539, + 544, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 539, + 544, + 563 + ], + "spans": [ + { + "bbox": [ + 306, + 539, + 544, + 563 + ], + "type": "text", + "content": "To minimize the objective of " + }, + { + "bbox": [ + 306, + 539, + 544, + 563 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{LIB}" + }, + { + "bbox": [ + 306, + 539, + 544, + 563 + ], + "type": "text", + "content": ", we use the reparameterization trick [16, 23]. For " + }, + { + "bbox": [ + 306, + 539, + 544, + 563 + ], + "type": "inline_equation", + "content": "p(\\boldsymbol{h}|\\boldsymbol{x})" + }, + { + "bbox": [ + 306, + 539, + 544, + 563 + ], + "type": "text", + "content": ", we assume that:" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 367, + 572, + 545, + 587 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 367, + 572, + 545, + 587 + ], + "spans": [ + { + "bbox": [ + 367, + 572, + 545, + 587 + ], + "type": "interline_equation", + "content": "p (\\boldsymbol {h} | \\boldsymbol {x}) \\sim \\mathcal {N} \\left(\\boldsymbol {\\mu} _ {\\boldsymbol {h} | \\boldsymbol {x}}, \\boldsymbol {\\sigma} _ {\\boldsymbol {h} | \\boldsymbol {x}} ^ {2} \\boldsymbol {I}\\right), \\tag {21}", + "image_path": "0e9efe4fec6930085ace46d2c9bcd158bdc30705705a4f398f1c50fc2ef3c387.jpg" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 305, + 597, + 545, + 633 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 597, + 545, + 633 + ], + "spans": [ + { + "bbox": [ + 305, + 597, + 545, + 633 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 597, + 545, + 633 + ], + "type": "inline_equation", + "content": "\\pmb{\\mu}_{h|\\pmb{x}}" + }, + { + "bbox": [ + 305, + 597, + 545, + 633 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 597, + 545, + 633 + ], + "type": "inline_equation", + "content": "\\sigma_{h|x}" + }, + { + "bbox": [ + 305, + 597, + 545, + 633 + ], + "type": "text", + "content": " are obtained by using the encoder network " + }, + { + "bbox": [ + 305, + 597, + 545, + 633 + ], + "type": "inline_equation", + "content": "f_{\\theta_{en}}(\\cdot)" + }, + { + "bbox": [ + 305, + 597, + 545, + 633 + ], + "type": "text", + "content": ", i.e., " + }, + { + "bbox": [ + 305, + 597, + 545, + 633 + ], + "type": "inline_equation", + "content": "\\pmb{\\mu}_{h|x} = f_{\\theta_{en}}^{\\pmb{\\mu}}(\\pmb{x})" + }, + { + "bbox": [ + 305, + 597, + 545, + 633 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 597, + 545, + 633 + ], + "type": "inline_equation", + "content": "\\pmb{\\sigma}_{h|x} = f_{\\theta_{en}}^{\\pmb{\\sigma}}(\\pmb{x})" + }, + { + "bbox": [ + 305, + 597, + 545, + 633 + ], + "type": "text", + "content": ". Subsequently, we have that:" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 378, + 643, + 545, + 656 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 378, + 643, + 545, + 656 + ], + "spans": [ + { + "bbox": [ + 378, + 643, + 545, + 656 + ], + "type": "interline_equation", + "content": "\\boldsymbol {h} = \\mu_ {\\boldsymbol {h} | \\boldsymbol {x}} + \\sigma_ {\\boldsymbol {h} | \\boldsymbol {x}} \\odot \\epsilon , \\tag {22}", + "image_path": "e6f3849f200772649b726b4915375455dcbb8500dc2e1af341b5eceb3cc40045.jpg" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 306, + 666, + 545, + 690 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 666, + 545, + 690 + ], + "spans": [ + { + "bbox": [ + 306, + 666, + 545, + 690 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 666, + 545, + 690 + ], + "type": "inline_equation", + "content": "\\epsilon \\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I})" + }, + { + "bbox": [ + 306, + 666, + 545, + 690 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 666, + 545, + 690 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 306, + 666, + 545, + 690 + ], + "type": "text", + "content": " is the element-wise product. For " + }, + { + "bbox": [ + 306, + 666, + 545, + 690 + ], + "type": "inline_equation", + "content": "q(l|h)" + }, + { + "bbox": [ + 306, + 666, + 545, + 690 + ], + "type": "text", + "content": ", we assume:" + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 380, + 700, + 545, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 380, + 700, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 380, + 700, + 545, + 715 + ], + "type": "interline_equation", + "content": "q (\\boldsymbol {l} | \\boldsymbol {h}) \\sim \\mathcal {N} \\left(\\boldsymbol {\\mu} _ {\\boldsymbol {l} | \\boldsymbol {h}}, \\boldsymbol {I}\\right), \\tag {23}", + "image_path": "edb127d0901793703431997c76e9d8480d9b8a761cbbd65577550bc107d096bb.jpg" + } + ] + } + ], + "index": 32 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 47, + 677, + 287, + 717 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 717 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 717 + ], + "type": "text", + "content": "It can be also interpreted and derived from the view of the probability distribution: " + }, + { + "bbox": [ + 47, + 677, + 287, + 717 + ], + "type": "inline_equation", + "content": "\\max_{\\Delta} \\log p(\\pmb{H}, \\pmb{\\Delta}) \\Rightarrow \\max_{\\Delta} \\log p(\\pmb{\\Delta}|\\pmb{H}) + \\log p(\\pmb{H}) \\Rightarrow \\max_{\\Delta} \\log p(\\pmb{\\Delta}|\\pmb{H})" + }, + { + "bbox": [ + 47, + 677, + 287, + 717 + ], + "type": "text", + "content": ". We appreciate reviewers for their helpful comments." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7500" + } + ] + } + ], + "index": 33 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 97 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 97 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 97 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 72, + 287, + 97 + ], + "type": "inline_equation", + "content": "\\pmb{\\mu}_{l|\\pmb{h}}" + }, + { + "bbox": [ + 47, + 72, + 287, + 97 + ], + "type": "text", + "content": " is learned by using the decoder network " + }, + { + "bbox": [ + 47, + 72, + 287, + 97 + ], + "type": "inline_equation", + "content": "f_{\\theta_{de}}(\\cdot)" + }, + { + "bbox": [ + 47, + 72, + 287, + 97 + ], + "type": "text", + "content": ", namely, " + }, + { + "bbox": [ + 47, + 72, + 287, + 97 + ], + "type": "inline_equation", + "content": "\\pmb{\\mu}_{l|\\pmb{h}} = f_{\\theta_{de}}(\\pmb{h})" + }, + { + "bbox": [ + 47, + 72, + 287, + 97 + ], + "type": "text", + "content": ". For " + }, + { + "bbox": [ + 47, + 72, + 287, + 97 + ], + "type": "inline_equation", + "content": "q(\\pmb{h})" + }, + { + "bbox": [ + 47, + 72, + 287, + 97 + ], + "type": "text", + "content": ", we assume that:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 130, + 106, + 287, + 119 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 130, + 106, + 287, + 119 + ], + "spans": [ + { + "bbox": [ + 130, + 106, + 287, + 119 + ], + "type": "interline_equation", + "content": "q (\\boldsymbol {h}) \\sim \\mathcal {N} (\\boldsymbol {0}, \\boldsymbol {I}). \\tag {24}", + "image_path": "9b655722e3e8de3934ce93641de2ce88a2381424f3d704f78d0eca6441392568.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 127, + 263, + 140 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 127, + 263, + 140 + ], + "spans": [ + { + "bbox": [ + 47, + 127, + 263, + 140 + ], + "type": "text", + "content": "For " + }, + { + "bbox": [ + 47, + 127, + 263, + 140 + ], + "type": "inline_equation", + "content": "p(\\boldsymbol{l} - \\hat{\\boldsymbol{d}}|\\boldsymbol{h})" + }, + { + "bbox": [ + 47, + 127, + 263, + 140 + ], + "type": "text", + "content": ", the following assumption is adopted:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 108, + 148, + 287, + 164 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 148, + 287, + 164 + ], + "spans": [ + { + "bbox": [ + 108, + 148, + 287, + 164 + ], + "type": "interline_equation", + "content": "p (\\boldsymbol {l} - \\hat {\\boldsymbol {d}} | \\boldsymbol {h}) \\sim \\mathcal {N} (\\boldsymbol {0}, \\sigma_ {\\delta | \\boldsymbol {h}} ^ {2} \\boldsymbol {I}), \\tag {25}", + "image_path": "52290d4b06276b9210e944099a36fb57a50d51e22e324de9e9cbbeb7404fc680.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 171, + 287, + 222 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 171, + 287, + 222 + ], + "spans": [ + { + "bbox": [ + 47, + 171, + 287, + 222 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 171, + 287, + 222 + ], + "type": "inline_equation", + "content": "\\sigma_{\\delta|\\pmb{h}}" + }, + { + "bbox": [ + 47, + 171, + 287, + 222 + ], + "type": "text", + "content": " can be achieved by introducing the gap deviation network " + }, + { + "bbox": [ + 47, + 171, + 287, + 222 + ], + "type": "inline_equation", + "content": "f_{\\theta_{gd}}(\\cdot)" + }, + { + "bbox": [ + 47, + 171, + 287, + 222 + ], + "type": "text", + "content": ", i.e., " + }, + { + "bbox": [ + 47, + 171, + 287, + 222 + ], + "type": "inline_equation", + "content": "\\sigma_{\\delta|\\pmb{h}} = f_{\\theta_{gd}}(\\pmb{h})" + }, + { + "bbox": [ + 47, + 171, + 287, + 222 + ], + "type": "text", + "content": ". For the recovered label distribution " + }, + { + "bbox": [ + 47, + 171, + 287, + 222 + ], + "type": "inline_equation", + "content": "\\hat{\\pmb{d}}" + }, + { + "bbox": [ + 47, + 171, + 287, + 222 + ], + "type": "text", + "content": ", we introduce the label distribution network " + }, + { + "bbox": [ + 47, + 171, + 287, + 222 + ], + "type": "inline_equation", + "content": "f_{\\theta_{ld}}(\\cdot)" + }, + { + "bbox": [ + 47, + 171, + 287, + 222 + ], + "type": "text", + "content": " and has the following formula:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 139, + 231, + 287, + 246 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 139, + 231, + 287, + 246 + ], + "spans": [ + { + "bbox": [ + 139, + 231, + 287, + 246 + ], + "type": "interline_equation", + "content": "\\hat {\\boldsymbol {d}} = f _ {\\theta_ {l d}} (\\boldsymbol {h}). \\tag {26}", + "image_path": "9558eb1b25856010e278a49a75ac3d3c525bb00a4c987027c48ecf4365efb64b.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 59, + 255, + 252, + 266 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 255, + 252, + 266 + ], + "spans": [ + { + "bbox": [ + 59, + 255, + 252, + 266 + ], + "type": "text", + "content": "Consequently, based on Eq. (21)-(26), we have:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 53, + 276, + 287, + 379 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 276, + 287, + 379 + ], + "spans": [ + { + "bbox": [ + 53, + 276, + 287, + 379 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\min _ {\\theta_ {e n}, \\theta_ {d e}, \\theta_ {g d}, \\theta_ {l d}} \\mathcal {L} _ {L I B} \\\\ \\Rightarrow \\min _ {\\theta_ {e n}, \\theta_ {d e}, \\theta_ {g d}, \\theta_ {l d}} \\frac {1}{n} \\sum_ {\\boldsymbol {l}} \\left[ \\frac {1}{2} \\| \\boldsymbol {\\mu} _ {\\boldsymbol {l} | \\boldsymbol {h}} - \\boldsymbol {l} \\| _ {2} ^ {2} \\right. (27) \\\\ \\left. + \\alpha \\left(\\frac {1}{2} (\\boldsymbol {l} - \\hat {\\boldsymbol {d}}) ^ {T} \\left(\\boldsymbol {\\sigma} _ {\\delta | h} ^ {- 2} \\boldsymbol {I}\\right) (\\boldsymbol {l} - \\hat {\\boldsymbol {d}}) + \\log \\det \\left(\\boldsymbol {\\sigma} _ {\\delta | h} ^ {2} \\boldsymbol {I}\\right)\\right) \\right] (27) \\\\ + \\frac {\\beta}{2} \\sum_ {\\boldsymbol {x}} \\left[ \\boldsymbol {\\mu} _ {\\boldsymbol {h} | \\boldsymbol {x}} ^ {T} \\boldsymbol {\\mu} _ {\\boldsymbol {h} | \\boldsymbol {x}} + \\operatorname {t r} \\left(\\boldsymbol {\\sigma} _ {\\boldsymbol {h} | \\boldsymbol {x}} ^ {2} \\boldsymbol {I}\\right) - \\log \\det \\left(\\boldsymbol {\\sigma} _ {\\boldsymbol {h} | \\boldsymbol {x}} ^ {2} \\boldsymbol {I}\\right) \\right]. \\\\ \\end{array}", + "image_path": "af81e61dc079f961c31fd35588e7b04e8105f83b4d6d7fe78e5b03667cbacb46.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 387, + 287, + 448 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 387, + 287, + 448 + ], + "spans": [ + { + "bbox": [ + 47, + 387, + 287, + 448 + ], + "type": "text", + "content": "When the problem of Eq. (27) is optimized, we can effectively recover the desired label distributions. To be specific, given " + }, + { + "bbox": [ + 47, + 387, + 287, + 448 + ], + "type": "inline_equation", + "content": "\\{\\pmb {X},\\pmb {L}\\}" + }, + { + "bbox": [ + 47, + 387, + 287, + 448 + ], + "type": "text", + "content": ", we can obtain " + }, + { + "bbox": [ + 47, + 387, + 287, + 448 + ], + "type": "inline_equation", + "content": "\\pmb{H}" + }, + { + "bbox": [ + 47, + 387, + 287, + 448 + ], + "type": "text", + "content": " according to Eq. (22) and achieve the recovery results based on Eq. (26), namely, " + }, + { + "bbox": [ + 47, + 387, + 287, + 448 + ], + "type": "inline_equation", + "content": "\\hat{\\pmb{D}} = f_{\\theta_{ld}}(\\pmb {H})" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 455, + 253, + 468 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 455, + 253, + 468 + ], + "spans": [ + { + "bbox": [ + 47, + 455, + 253, + 468 + ], + "type": "text", + "content": "3.3. Comparison with Existing LE Methods" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 473, + 287, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 473, + 287, + 556 + ], + "spans": [ + { + "bbox": [ + 46, + 473, + 287, + 556 + ], + "type": "text", + "content": "The main difference between LIB and existing methods is that our method deals with the problem of LE from the perspective of information bottleneck. Considering the first term in Eq. (2), it aims to minimize " + }, + { + "bbox": [ + 46, + 473, + 287, + 556 + ], + "type": "inline_equation", + "content": "\\| \\pmb{d} - \\pmb{l} \\|_2^2" + }, + { + "bbox": [ + 46, + 473, + 287, + 556 + ], + "type": "text", + "content": " under the assumption that information in the label distributions is inherited from the initial logical labels [24, 28, 29]. For LIB, the more reasonable term:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 67, + 563, + 287, + 586 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 563, + 287, + 586 + ], + "spans": [ + { + "bbox": [ + 67, + 563, + 287, + 586 + ], + "type": "interline_equation", + "content": "\\frac {1}{2} (\\boldsymbol {l} - \\hat {\\boldsymbol {d}}) ^ {T} \\left(\\boldsymbol {\\sigma} _ {\\delta | \\boldsymbol {h}} ^ {- 2} \\boldsymbol {I}\\right) (\\boldsymbol {l} - \\hat {\\boldsymbol {d}}) + \\log \\det \\left(\\boldsymbol {\\sigma} _ {\\delta | \\boldsymbol {h}} ^ {2} \\boldsymbol {I}\\right) \\tag {28}", + "image_path": "c5db7c11fe218a9c65f8aca7648c19c326f26270bc9cf60e944b54157a66aa12.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 594, + 287, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 594, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 47, + 594, + 287, + 628 + ], + "type": "text", + "content": "which can be deduced by excavating the label relevant information about the label gaps between logical labels and label distributions." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "text", + "content": "Besides, we compare our method with the recently proposed LEVI [29] further. Although the objectives of LEVI and LIB are somewhat similar in form, they are essentially different as follows: 1) LIB makes attempts from the perspective of information bottleneck, while LEVI from the view of variational inference; 2) The formulas of LEVI and LIB are just partially similar in form, since the variational" + } + ] + } + ], + "index": 13 + }, + { + "type": "table", + "bbox": [ + 332, + 70, + 523, + 219 + ], + "blocks": [ + { + "bbox": [ + 332, + 70, + 523, + 219 + ], + "lines": [ + { + "bbox": [ + 332, + 70, + 523, + 219 + ], + "spans": [ + { + "bbox": [ + 332, + 70, + 523, + 219 + ], + "type": "table", + "html": "
Dataset# dimension q# instance n# labels c
Artificialtoy326013
Movie186977555
SBU-3DFE24325006
SJAFFE2432136
Yeast-alpha24246518
Yeast-cdc24246515
Yeast-cold2424654
Yeast-diau2424657
Yeast-dtt2424654
Yeast-elu24246514
Yeast-heat2424656
Yeast-spo2424656
Yeast-spo52424653
Yeast-spoem2424652
", + "image_path": "b8fc22ff8d03ffdbe392752561742bc16c11c78c2797a900539a2b010ada9df1.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "table_body" + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 228, + 545, + 250 + ], + "lines": [ + { + "bbox": [ + 305, + 228, + 545, + 250 + ], + "spans": [ + { + "bbox": [ + 305, + 228, + 545, + 250 + ], + "type": "text", + "content": "Table 1. Details of datasets. The numbers of dimension " + }, + { + "bbox": [ + 305, + 228, + 545, + 250 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 305, + 228, + 545, + 250 + ], + "type": "text", + "content": ", instance " + }, + { + "bbox": [ + 305, + 228, + 545, + 250 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 305, + 228, + 545, + 250 + ], + "type": "text", + "content": ", and labels " + }, + { + "bbox": [ + 305, + 228, + 545, + 250 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 305, + 228, + 545, + 250 + ], + "type": "text", + "content": " are provided here." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 272, + 545, + 332 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 272, + 545, + 332 + ], + "spans": [ + { + "bbox": [ + 305, + 272, + 545, + 332 + ], + "type": "text", + "content": "inference is employed as the optimization tool in LIB. The details of these two formulas are totally different; 3) LEVI requires an extra regularizer, i.e., " + }, + { + "bbox": [ + 305, + 272, + 545, + 332 + ], + "type": "inline_equation", + "content": "\\| d - l\\| _2^2" + }, + { + "bbox": [ + 305, + 272, + 545, + 332 + ], + "type": "text", + "content": " to constrain the recovery process, while LIB achieves " + }, + { + "bbox": [ + 305, + 272, + 545, + 332 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 305, + 272, + 545, + 332 + ], + "type": "text", + "content": " based on the more reasonable term, i.e., Eq. (28)." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 344, + 386, + 358 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 344, + 386, + 358 + ], + "spans": [ + { + "bbox": [ + 306, + 344, + 386, + 358 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 365, + 545, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 365, + 545, + 388 + ], + "spans": [ + { + "bbox": [ + 305, + 365, + 545, + 388 + ], + "type": "text", + "content": "To verify the effectiveness and competitiveness of LIB, extensive experiments are conducted in this section." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 398, + 422, + 411 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 398, + 422, + 411 + ], + "spans": [ + { + "bbox": [ + 306, + 398, + 422, + 411 + ], + "type": "text", + "content": "4.1. Experimental Setup" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 417, + 545, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 417, + 545, + 548 + ], + "spans": [ + { + "bbox": [ + 304, + 417, + 545, + 548 + ], + "type": "text", + "content": "As shown in Table 1, we use both one toy dataset and 13 real-world datasets for evaluation" + }, + { + "bbox": [ + 304, + 417, + 545, + 548 + ], + "type": "inline_equation", + "content": "^2" + }, + { + "bbox": [ + 304, + 417, + 545, + 548 + ], + "type": "text", + "content": ". For the toy dataset, i.e., Artificial dataset, it is utilized to vividly show the recovery performance [28]. Movie dataset is collected from movies, SBU-3DFE and SJAFFE datasets are two facial expression datasets. Yeast datasets (alpha to spoem) are collected from 10 biological experiments on the budding yeast genes [4]. It is important to note that only the ground-truth label distributions are provided by these datasets. Therefore, we adopt the binarization strategy, which is also used in existing LE works [24, 28, 29], to ensure the consistency of evaluation." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 549, + 545, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 549, + 545, + 693 + ], + "spans": [ + { + "bbox": [ + 304, + 549, + 545, + 693 + ], + "type": "text", + "content": "We compare our method LIB to 7 LE methods, including FCM [5], KM [15], LP [17], ML [11], GLLE [28], LESC [24], and LEVI [29]. The first two methods belong to the algorithm adaption, and the rest methods are specialized algorithms. For the sake of fairness, we utilize the parameter settings recommended in their original works. Specifically, for FCM, we set the parameter " + }, + { + "bbox": [ + 304, + 549, + 545, + 693 + ], + "type": "inline_equation", + "content": "\\beta = 2" + }, + { + "bbox": [ + 304, + 549, + 545, + 693 + ], + "type": "text", + "content": ". For KM, we leverage the Gaussian kernel. For LP, we set the parameter " + }, + { + "bbox": [ + 304, + 549, + 545, + 693 + ], + "type": "inline_equation", + "content": "\\alpha = 0.5" + }, + { + "bbox": [ + 304, + 549, + 545, + 693 + ], + "type": "text", + "content": ". For ML, we set the number of neighbors " + }, + { + "bbox": [ + 304, + 549, + 545, + 693 + ], + "type": "inline_equation", + "content": "k = c + 1" + }, + { + "bbox": [ + 304, + 549, + 545, + 693 + ], + "type": "text", + "content": ". For GLLE, we select " + }, + { + "bbox": [ + 304, + 549, + 545, + 693 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 304, + 549, + 545, + 693 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 304, + 549, + 545, + 693 + ], + "type": "inline_equation", + "content": "\\{0.01, 0.1, \\dots, 100\\}" + }, + { + "bbox": [ + 304, + 549, + 545, + 693 + ], + "type": "text", + "content": " and set the number of neighbors " + }, + { + "bbox": [ + 304, + 549, + 545, + 693 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 549, + 545, + 693 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 549, + 545, + 693 + ], + "type": "inline_equation", + "content": "c + 1" + }, + { + "bbox": [ + 304, + 549, + 545, + 693 + ], + "type": "text", + "content": ". For LESC, " + }, + { + "bbox": [ + 304, + 549, + 545, + 693 + ], + "type": "inline_equation", + "content": "\\lambda_{1}" + }, + { + "bbox": [ + 304, + 549, + 545, + 693 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 549, + 545, + 693 + ], + "type": "inline_equation", + "content": "\\lambda_{2}" + }, + { + "bbox": [ + 304, + 549, + 545, + 693 + ], + "type": "text", + "content": " are selected from " + }, + { + "bbox": [ + 304, + 549, + 545, + 693 + ], + "type": "inline_equation", + "content": "\\{0.0001, 0.1, \\dots, 10\\}" + }, + { + "bbox": [ + 304, + 549, + 545, + 693 + ], + "type": "text", + "content": ". For LEVI, MLPs with" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 315, + 702, + 468, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 702, + 468, + 713 + ], + "spans": [ + { + "bbox": [ + 315, + 702, + 468, + 713 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 315, + 702, + 468, + 713 + ], + "type": "text", + "content": "http://palm.seu.edu.cn/xgeng/LDL/index.htm" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "7501" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 132 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 132 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 132 + ], + "type": "text", + "content": "two hidden layers and softmax activation functions are utilized, and the results are reported after 150 training epochs. For LIB, we select " + }, + { + "bbox": [ + 46, + 72, + 287, + 132 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 72, + 287, + 132 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 72, + 287, + 132 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 72, + 287, + 132 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 46, + 72, + 287, + 132 + ], + "type": "inline_equation", + "content": "\\{0.001, 0.01, \\dots, 10\\}" + }, + { + "bbox": [ + 46, + 72, + 287, + 132 + ], + "type": "text", + "content": ", and the fully connected networks with 3 layers and sigmoid activation function are leveraged in the proposed method." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 133, + 288, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 133, + 288, + 204 + ], + "spans": [ + { + "bbox": [ + 46, + 133, + 288, + 204 + ], + "type": "text", + "content": "To evaluate the recovery performance, we adopt 6 metrics, namely Chebyshev, Canberra, Clark, Kullback-Leibler, Cosine, and Intersection [8,24,28]. Given the ground-truth label distribution " + }, + { + "bbox": [ + 46, + 133, + 288, + 204 + ], + "type": "inline_equation", + "content": "\\pmb{d}" + }, + { + "bbox": [ + 46, + 133, + 288, + 204 + ], + "type": "text", + "content": " and the recovered label distribution " + }, + { + "bbox": [ + 46, + 133, + 288, + 204 + ], + "type": "inline_equation", + "content": "\\hat{\\pmb{d}}" + }, + { + "bbox": [ + 46, + 133, + 288, + 204 + ], + "type": "text", + "content": ", the first four metrics and the rest two metrics respectively measure the distance and similarity between " + }, + { + "bbox": [ + 46, + 133, + 288, + 204 + ], + "type": "inline_equation", + "content": "\\pmb{d}" + }, + { + "bbox": [ + 46, + 133, + 288, + 204 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 133, + 288, + 204 + ], + "type": "inline_equation", + "content": "\\hat{\\pmb{d}}" + }, + { + "bbox": [ + 46, + 133, + 288, + 204 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 87, + 207, + 287, + 228 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 87, + 207, + 287, + 228 + ], + "spans": [ + { + "bbox": [ + 87, + 207, + 287, + 228 + ], + "type": "interline_equation", + "content": "D _ {\\text {C h e b y s h e v}} (\\boldsymbol {d}, \\hat {\\boldsymbol {d}}) = \\max _ {i} \\left| d ^ {y _ {i}} - \\hat {d} ^ {y _ {i}} \\right|, \\tag {29}", + "image_path": "144530233183a57c2c45c34349a7518724bfbb2382b49242c0969c19f2267c0c.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 94, + 229, + 287, + 267 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 94, + 229, + 287, + 267 + ], + "spans": [ + { + "bbox": [ + 94, + 229, + 287, + 267 + ], + "type": "interline_equation", + "content": "D _ {\\text {C a n b e r r a}} (\\boldsymbol {d}, \\hat {\\boldsymbol {d}}) = \\sum_ {i = 1} ^ {c} \\frac {\\left| d ^ {y _ {i}} - \\hat {d} ^ {y _ {i}} \\right|}{d ^ {y _ {i}} + \\hat {d} ^ {y _ {i}}}, \\tag {30}", + "image_path": "68f7e41d1cb57e08f62c88b896ae57832e7292e68c0d1f833fe01571b83a31bf.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 90, + 270, + 287, + 319 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 90, + 270, + 287, + 319 + ], + "spans": [ + { + "bbox": [ + 90, + 270, + 287, + 319 + ], + "type": "interline_equation", + "content": "D _ {\\text {C l a r k}} (\\boldsymbol {d}, \\hat {\\boldsymbol {d}}) = \\sqrt {\\sum_ {i = 1} ^ {c} \\frac {\\left(d ^ {y _ {i}} - \\hat {d} ^ {y _ {i}}\\right) ^ {2}}{\\left(d ^ {y _ {i}} + \\hat {d} ^ {y _ {i}}\\right) ^ {2}}}, \\tag {31}", + "image_path": "5fd179068b01ec8c9b3e1cdb0a54b9d66180c584b54836b8c57b57c0453ec587.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 83, + 321, + 287, + 352 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 321, + 287, + 352 + ], + "spans": [ + { + "bbox": [ + 83, + 321, + 287, + 352 + ], + "type": "interline_equation", + "content": "D _ {\\text {K u l l b a c k - L e i b l e r}} (\\boldsymbol {d}, \\hat {\\boldsymbol {d}}) = \\sum_ {i = 1} ^ {c} d ^ {y _ {i}} \\ln \\frac {d ^ {y _ {i}}}{\\hat {d} ^ {y _ {i}}}, \\tag {32}", + "image_path": "a4a2c67b2f0c4ab4859a63201ffb8305563470840bc3a167178ad00a41e9ecf5.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 69, + 355, + 287, + 413 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 355, + 287, + 413 + ], + "spans": [ + { + "bbox": [ + 69, + 355, + 287, + 413 + ], + "type": "interline_equation", + "content": "S _ {\\text {C o s i n e}} (\\boldsymbol {d}, \\hat {\\boldsymbol {d}}) = \\frac {\\sum_ {i = 1} ^ {c} d ^ {y _ {i}} \\hat {d} ^ {y _ {i}}}{\\sqrt {\\sum_ {i = 1} ^ {c} \\left(d ^ {y _ {i}}\\right) ^ {2}} \\sqrt {\\sum_ {i = 1} ^ {c} \\left(\\hat {d} ^ {y _ {i}}\\right) ^ {2}}}, \\tag {33}", + "image_path": "fb8ec6db081c2417fffaa9fbe3f51f65532df4eaa6929b6ab0b932a1e5e1a25d.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 83, + 415, + 287, + 445 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 415, + 287, + 445 + ], + "spans": [ + { + "bbox": [ + 83, + 415, + 287, + 445 + ], + "type": "interline_equation", + "content": "S _ {\\text {I n t e r s e c t i o n}} (\\boldsymbol {d}, \\hat {\\boldsymbol {d}}) = \\sum_ {i = 1} ^ {c} \\min \\left(d ^ {y _ {i}}, \\hat {d} ^ {y _ {i}}\\right). \\tag {34}", + "image_path": "8e060ce8018401ccfe92953f03f87f6a3f780dedc47c8749872c4b78d9e78f48.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 449, + 287, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 449, + 287, + 474 + ], + "spans": [ + { + "bbox": [ + 46, + 449, + 287, + 474 + ], + "type": "text", + "content": "The smaller values of distance metric and similarity metric indicate the better and the worse results, respectively." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 479, + 241, + 493 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 479, + 241, + 493 + ], + "spans": [ + { + "bbox": [ + 47, + 479, + 241, + 493 + ], + "type": "text", + "content": "4.2. Visualization Results on Toy Dataset" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 498, + 287, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 287, + 557 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 287, + 557 + ], + "type": "text", + "content": "The recovery results on the Artificial dataset are vividly presented in Fig. 3, which shows the three-dimensional label distributions by the RGB color channels separately. The more similar the color patterns of the recovered results and the ground-truth are, the better the recovery results are." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 558, + 287, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 287, + 629 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 287, + 629 + ], + "type": "text", + "content": "It can be seen that FCM, GLLE, LESC, LEVI, and LIB can obtain the similar color pattern, while KM, LP, and ML are incapable to obtain the promising recovery performance on Artificial dataset. Regarding the visualization results of FCM, GLLE, LESC, LEVI, and LIB, the color pattern that is most close to the ground-truth is achieved by our LIB." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 635, + 276, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 635, + 276, + 647 + ], + "spans": [ + { + "bbox": [ + 47, + 635, + 276, + 647 + ], + "type": "text", + "content": "4.3. Comparison Results on Real-world Datasets" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 653, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 653, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 653, + 287, + 714 + ], + "type": "text", + "content": "We provide the detailed comparison results on 13 real-world datasets in Table 2. Overall, LIB has the competitive recovery performance. We have the following observations: 1) Compared with FCM and KM, which belong to the category of algorithm adaption, remarkable improvements can" + } + ] + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 309, + 73, + 385, + 129 + ], + "blocks": [ + { + "bbox": [ + 309, + 73, + 385, + 129 + ], + "lines": [ + { + "bbox": [ + 309, + 73, + 385, + 129 + ], + "spans": [ + { + "bbox": [ + 309, + 73, + 385, + 129 + ], + "type": "image", + "image_path": "433cd0f9051a1ea30701968a1eed431fdc486563dec9da9be3ad48ccbe4e63ab.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 332, + 131, + 361, + 140 + ], + "lines": [ + { + "bbox": [ + 332, + 131, + 361, + 140 + ], + "spans": [ + { + "bbox": [ + 332, + 131, + 361, + 140 + ], + "type": "text", + "content": "(a) FCM" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 388, + 74, + 463, + 129 + ], + "blocks": [ 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"a9a05937edda45c20123f3ada7b3d3ec0b8d821261fdced91e8c84e1a651f414.jpg" + } + ] + } + ], + "index": 26, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 331, + 274, + 362, + 283 + ], + "lines": [ + { + "bbox": [ + 331, + 274, + 362, + 283 + ], + "spans": [ + { + "bbox": [ + 331, + 274, + 362, + 283 + ], + "type": "text", + "content": "(g) LEVI" + } + ] + } + ], + "index": 27, + "angle": 0, + "type": "image_caption" + } + ], + "index": 26 + }, + { + "type": "image", + "bbox": [ + 388, + 217, + 463, + 271 + ], + "blocks": [ + { + "bbox": [ + 388, + 217, + 463, + 271 + ], + "lines": [ + { + "bbox": [ + 388, + 217, + 463, + 271 + ], + "spans": [ + { + "bbox": [ + 388, + 217, + 463, + 271 + ], + "type": "image", + "image_path": "7ebfd869fe40c74bb516122a9b70b79ff705dbf7f854098c1c35277b22db6a84.jpg" + } + ] + } + ], + "index": 28, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 413, + 273, + 439, + 283 + ], + "lines": [ + { + "bbox": [ + 413, + 273, + 439, + 283 + ], + "spans": [ + { + "bbox": [ + 413, + 273, + 439, + 283 + ], + "type": "text", + "content": "(h) LIB" + } + ] + } + ], + "index": 29, + "angle": 0, + "type": "image_caption" + } + ], + "index": 28 + }, + { + "type": "image", + "bbox": [ + 467, + 217, + 544, + 271 + ], + "blocks": [ + { + "bbox": [ + 467, + 217, + 544, + 271 + ], + "lines": [ + { + "bbox": [ + 467, + 217, + 544, + 271 + ], + "spans": [ + { + "bbox": [ + 467, + 217, + 544, + 271 + ], + "type": "image", + "image_path": "a76eb77437031a722c2e3032e06efe562cf7b59739b4b2e601ac4ba0559c5330.jpg" + } + ] + } + ], + "index": 30, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 479, + 273, + 533, + 283 + ], + "lines": [ + { + "bbox": [ + 479, + 273, + 533, + 283 + ], + "spans": [ + { + "bbox": [ + 479, + 273, + 533, + 283 + ], + "type": "text", + "content": "(i) Ground-truth" + } + ] + } + ], + "index": 31, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 305, + 293, + 545, + 326 + ], + "lines": [ + { + "bbox": [ + 305, + 293, + 545, + 326 + ], + "spans": [ + { + "bbox": [ + 305, + 293, + 545, + 326 + ], + "type": "text", + "content": "Figure 3. Visualization results of the label distributions recovered by different methods ((a)-(h)) and the ground-truth ((i)) on Artificial dataset. (Best viewed in color.)" + } + ] + } + ], + "index": 32, + "angle": 0, + "type": "image_caption" + } + ], + "index": 30 + }, + { + "bbox": [ + 304, + 348, + 545, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 348, + 545, + 540 + ], + "spans": [ + { + "bbox": [ + 304, + 348, + 545, + 540 + ], + "type": "text", + "content": "be achieved by our method; 2) Compared with the methods belonging to the category of specialized algorithm, LIB can also obtain better recovery results in most cases. For example, LIB obtains the best recovery results on Movie datasets in all metrics. Moreover, although LESC can obtain slightly favorable results in some cases, the corresponding recovery results of LIB are also promising and competitive. The underlying reason may be that LESC further considers the sample correlations during the recovery process; 3) The recovery performance of all methods can be roughly ranked as LIB>LESC≈LEV1>GLLE>LP≈FCM>ML>KM. We can conclude that LIB is suitable for the LE problem. The underlying reason for the significant improvement is that the label relevant information, including the information about label assignments and the information about label gaps, can be effectively investigated by LIB." + } + ] + } + ], + "index": 33 + }, + { + "bbox": [ + 306, + 548, + 474, + 561 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 548, + 474, + 561 + ], + "spans": [ + { + "bbox": [ + 306, + 548, + 474, + 561 + ], + "type": "text", + "content": "4.4. Analysis and Discussion of LIB" + } + ] + } + ], + "index": 34 + }, + { + "bbox": [ + 306, + 568, + 545, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 568, + 545, + 591 + ], + "spans": [ + { + "bbox": [ + 306, + 568, + 545, + 591 + ], + "type": "text", + "content": "We analyze the parameter sensitivity of LIB firstly, and then we conduct the ablation studies as well." + } + ] + } + ], + "index": 35 + }, + { + "bbox": [ + 306, + 609, + 414, + 621 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 609, + 414, + 621 + ], + "spans": [ + { + "bbox": [ + 306, + 609, + 414, + 621 + ], + "type": "text", + "content": "4.4.1 Sensitivity of LIB" + } + ] + } + ], + "index": 36 + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": "In the proposed method, we choose the values of " + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\{0.001, 0.01, \\dots, 10\\}" + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": ". To show the parameter sensitivity of LIB, we conduct experiments on SBU-3DFE datasets with different values of " + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": ". Regarding the dimension of the learned latent representation, we set it to 256 for all datasets. The experimental results in metrics of Chebyshev distance, Cosine coefficient, and Intersection similarity are" + } + ] + } + ], + "index": 37 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7502" + } + ] + } + ], + "index": 38 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 57, + 69, + 538, + 548 + ], + "blocks": [ + { + "bbox": [ + 57, + 69, + 538, + 548 + ], + "lines": [ + { + "bbox": [ + 57, + 69, + 538, + 548 + ], + "spans": [ + { + "bbox": [ + 57, + 69, + 538, + 548 + ], + "type": "table", + "html": "
MetricChebyshev ↓Clark ↓
MethodFCMKMLPMLGLLELESCLEVLIBFCMKMLPMLGLLELESCLEVLIB
Movie0.2300.2340.1610.1640.1220.1210.1100.1070.8591.7660.9131.1400.5690.5640.5510.517
SUB-3DFE0.1350.2380.1230.2330.1260.1220.0950.0940.4821.9070.5801.8480.3910.3780.3030.297
SJAFFE0.1320.2140.1070.1860.0870.0690.0750.0710.5221.8740.5021.5190.3770.2760.2900.262
Yeast-alpha0.0440.0630.0400.0570.0200.0150.0120.0170.8213.1531.1853.0880.3370.2530.3190.275
Yeast-cdc0.0510.0760.0420.0710.0220.0190.0160.0170.7392.8851.0142.8250.3060.2510.3230.242
Yeast-cold0.1410.2520.1370.2420.0660.0560.0820.0540.4331.4720.5031.4400.1760.1520.2690.146
Yeast-diau0.1240.1520.0990.1480.0530.0420.0440.0490.8381.8860.7881.8440.2960.2240.2950.273
Yeast-dtt0.0970.2570.1280.2440.0520.0430.0840.0340.3291.4770.4991.4460.1430.1190.2940.092
Yeast-elu0.0520.0780.0440.0720.0230.0190.0170.0180.5792.7680.9732.7110.2950.2410.3170.224
Yeast-heat0.1690.1750.0860.1650.0490.0460.0520.0390.5801.8020.5681.7640.2130.1990.2880.165
Yeast-spo0.1300.1750.0900.1710.0620.0600.0550.0530.5201.8110.5581.7680.2660.2580.2770.224
Yeast-spo50.1620.2770.1140.2730.0990.0920.0910.0760.3951.0590.2741.0360.1970.1850.2090.158
Yeast-sopem0.2330.4080.1630.4030.0880.0870.1150.0690.4011.0280.2721.0040.1320.1290.1820.104
Avg.Rank6.0778.0005.0006.8463.7692.3082.4631.5385.3858.0005.6157.0003.3851.9233.4621.231
MetricCanberra ↓
MethodFCMKMLPMLGLLELESCLEVLIBFCMKMLPMLGLLELESCLEVLIB
Movie1.6643.4441.7201.9341.0451.0340.9740.9200.3810.4520.1770.2180.1230.1200.0820.077
SUB-3DFE1.0204.1211.2454.0010.8200.7990.6370.6110.0940.6030.1050.5650.0690.0640.0420.041
SJAFFE1.0814.0101.0643.1380.7810.5610.6000.5310.1070.5580.0770.3910.0500.0290.0320.027
Yeast-alpha2.88311.8094.54411.6031.1340.8461.2490.8930.1000.6300.1210.6020.0130.0080.0110.009
Yeast-cdc2.4159.8753.6449.6950.9590.7651,1480.7470.0910.6300.1110.6010.0140.0100.0140.008
Yeast-cold0.7342.5660.9242.5190.3050.2630.5010.2500.1130.5860.1030.5560.0190.0150.0350.012
Yeast-diau1.8954.2611.7484.1800.6710.4800.6890.6210.1590.5380.1270.5090.0270.0170.0230.022
Yeast-dtt0.5012.5940.9412.5490.2480.2060.5620.1580.0650.6170.1030.5860.0130.0100.0420.005
Yeast-elu1.6899.1103.3818.9490.9020.7271.0930.6700.0590.6170.1090.5890.0130.0090.0140.008
Yeast-heat1.1573.8491.2933.7790.4300.4010.6460.3270.1470.5860.0890.5560.0170.0150.0270.011
Yeast-spo0.9983.8541.2313.7720.5480.5330.6050.4540.1100.5620.0840.5320.0290.0280.0250.019
Yeast-spo50.5631.3820.4011.3550.3050.2840.3110.2410.1230.3340.0420.3170.0340.0310.0280.021
Yeast-sopem0.5341.2530.3651.2260.1830.1800.2480.1440.2080.5310.0670.5030.0270.0270.0360.018
Avg.Rank5.2318.0005.6927.0003.2312.003.6921.1545.6928.0005.3856.9233.4622.1543.0771.154
MetricCosine ↑
MethodFCMKMLPMLGLLELESCLEVLIBFCMKMLPMLGLLELESCLEVLIB
Movie0.7730.8800.9290.9190.9360.9370.9540.9550.6770.6490.7780.7790.8310.8330.8490.859
SUB-3DFE0.9120.8120.9220.8150.9270.9320.9560.9580.8270.5790.8100.5870.8500.8550.8820.887
SJAFFE0.9060.8270.9410.8570.9580.9730.9690.9740.8210.5930.8370.6610.8720.9050.8970.909
Yeast-alpha0.9220.7510.9110.7560.9870.9920.9890.9920.8440.5320.7740.5370.9380.9530.9320.951
Yeast-cdc0.9290.7540.9160.7590.9870.9910.9870.9920.8470.5330.7790.5380.9370.9500.9250.951
Yeast-heat0.9220.7790.9250.7840.9820.9860.9700.9880.8330.5590.7940.5650.9240.9350.8810.938
Yeast-diau0.8820.7990.9150.8030.9750.9850.9800.9790.7600.5880.7880.5930.9060.9330.9080.913
Yeast-dtt0.9590.7590.9210.7630.9880.9910.9650.9950.8940.5410.7860.5460.9390.9490.8660.961
Yeast-elu0.9500.7580.9180.7630.9870.9910.9870.9920.8830.5390.7820.5440.9360.9490.9240.952
Yeast-heat0.8830.7790.9320.7830.9840.9860.9770.9900.8070.5590.8050.5640.9290.9340.8970.946
Yeast-spo0.9090.8000.9390.8030.9740.9750.9780.9820.8360.5750.8190.5800.9090.9120.9030.925
Yeast-spo50.9220.8820.9690.8840.9710.9740.9790.9830.8380.7240.8860.7270.9010.9080.9090.924
Yeast-sopem0.8780.8120.9500.8150.9780.9780.9720.9850.7670.5920.8370.5970.9120.9130.8850.931
Avg.Rank5.8467.9235.3086.9233.4622.1542.9231.2315.3858.0005.6926.8463.3852.0073.4621.154
", + "image_path": "c2c45932273bcac0010d9b0fbd1438bd72d4eadbfd04a8fc9ba2cb061db91805.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 558, + 547, + 581 + ], + "lines": [ + { + "bbox": [ + 46, + 558, + 547, + 581 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 547, + 581 + ], + "type": "text", + "content": "Table 2. Recovery results on 13 real-world datasets. " + }, + { + "bbox": [ + 46, + 558, + 547, + 581 + ], + "type": "inline_equation", + "content": "\\downarrow" + }, + { + "bbox": [ + 46, + 558, + 547, + 581 + ], + "type": "text", + "content": " indicates that \"the smaller the better\" and " + }, + { + "bbox": [ + 46, + 558, + 547, + 581 + ], + "type": "inline_equation", + "content": "\\uparrow" + }, + { + "bbox": [ + 46, + 558, + 547, + 581 + ], + "type": "text", + "content": " means that \"the larger the better\". The average ranks (Avg.Rank) on all datasets are also reported for all methods. We highlight the best recovery results." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 601, + 288, + 638 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 601, + 288, + 638 + ], + "spans": [ + { + "bbox": [ + 46, + 601, + 288, + 638 + ], + "type": "text", + "content": "provided in Fig. 4. It can be observed that LIB method can get promising recovery results and is robust with respect to different values of " + }, + { + "bbox": [ + 46, + 601, + 288, + 638 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 601, + 288, + 638 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 601, + 288, + 638 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 601, + 288, + 638 + ], + "type": "text", + "content": " in a large range." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 657, + 180, + 669 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 657, + 180, + 669 + ], + "spans": [ + { + "bbox": [ + 47, + 657, + 180, + 669 + ], + "type": "text", + "content": "4.4.2 Ablation studies of LIB" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "content": "The ablation studies are conducted to further verify the effectiveness of introducing the label information bottleneck framework for LE. In the proposed objective Eq. (9), " + }, + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{as}" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 601, + 547, + 711 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 601, + 547, + 711 + ], + "spans": [ + { + "bbox": [ + 304, + 601, + 547, + 711 + ], + "type": "text", + "content": "and " + }, + { + "bbox": [ + 304, + 601, + 547, + 711 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{gap}" + }, + { + "bbox": [ + 304, + 601, + 547, + 711 + ], + "type": "text", + "content": " explore the label assignments information and label gaps information during the recovery process. As can be observed from Eq. (14) and Eq. (15), only the latent representation " + }, + { + "bbox": [ + 304, + 601, + 547, + 711 + ], + "type": "inline_equation", + "content": "\\pmb{H}" + }, + { + "bbox": [ + 304, + 601, + 547, + 711 + ], + "type": "text", + "content": " can be learned if we employ " + }, + { + "bbox": [ + 304, + 601, + 547, + 711 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{as}" + }, + { + "bbox": [ + 304, + 601, + 547, + 711 + ], + "type": "text", + "content": " merely during the recovery process. Consequently, considering the goal of LE, we compare the proposed LIB with the method termed " + }, + { + "bbox": [ + 304, + 601, + 547, + 711 + ], + "type": "inline_equation", + "content": "\\mathrm{LIB}_{gap}" + }, + { + "bbox": [ + 304, + 601, + 547, + 711 + ], + "type": "text", + "content": ", which only employs " + }, + { + "bbox": [ + 304, + 601, + 547, + 711 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{gap}" + }, + { + "bbox": [ + 304, + 601, + 547, + 711 + ], + "type": "text", + "content": " to achieve the recovery results. In other words, " + }, + { + "bbox": [ + 304, + 601, + 547, + 711 + ], + "type": "inline_equation", + "content": "\\mathrm{LIB}_{gap}" + }, + { + "bbox": [ + 304, + 601, + 547, + 711 + ], + "type": "text", + "content": " investigates the label gaps information in the case of not considering the label assign-" + } + ] + } + ], + "index": 5 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 758 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 758 + ], + "type": "text", + "content": "7503" + } + ] + } + ], + "index": 6 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 82, + 73, + 225, + 183 + ], + "blocks": [ + { + "bbox": [ + 82, + 73, + 225, + 183 + ], + "lines": [ + { + "bbox": [ + 82, + 73, + 225, + 183 + ], + "spans": [ + { + "bbox": [ + 82, + 73, + 225, + 183 + ], + "type": "image", + "image_path": "7ef24d8fd4faa580c9270dd65e2459ad9d4679736da1f0a0f8156d2ee573bfa2.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 124, + 186, + 178, + 196 + ], + "lines": [ + { + "bbox": [ + 124, + 186, + 178, + 196 + ], + "spans": [ + { + "bbox": [ + 124, + 186, + 178, + 196 + ], + "type": "text", + "content": "(a) Chebyshev" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 228, + 76, + 364, + 182 + ], + "blocks": [ + { + "bbox": [ + 228, + 76, + 364, + 182 + ], + "lines": [ + { + "bbox": [ + 228, + 76, + 364, + 182 + ], + "spans": [ + { + "bbox": [ + 228, + 76, + 364, + 182 + ], + "type": "image", + "image_path": "54dd238b4658d45bbbff76f97a3d612fb0c01a3613d942ea96b4ec9f9463c5ca.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 276, + 184, + 318, + 194 + ], + "lines": [ + { + "bbox": [ + 276, + 184, + 318, + 194 + ], + "spans": [ + { + "bbox": [ + 276, + 184, + 318, + 194 + ], + "type": "text", + "content": "(b) Cosine " + }, + { + "bbox": [ + 276, + 184, + 318, + 194 + ], + "type": "inline_equation", + "content": "\\uparrow" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 205, + 547, + 239 + ], + "lines": [ + { + "bbox": [ + 46, + 205, + 547, + 239 + ], + "spans": [ + { + "bbox": [ + 46, + 205, + 547, + 239 + ], + "type": "text", + "content": "Figure 4. The recovery results in metrics of (a) Chebyshev distance, (b) Cosine coefficient, and (c) Intersection similarity with different values of " + }, + { + "bbox": [ + 46, + 205, + 547, + 239 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 205, + 547, + 239 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 205, + 547, + 239 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 205, + 547, + 239 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 46, + 205, + 547, + 239 + ], + "type": "inline_equation", + "content": "\\downarrow" + }, + { + "bbox": [ + 46, + 205, + 547, + 239 + ], + "type": "text", + "content": " indicates that \"the smaller the better\" and " + }, + { + "bbox": [ + 46, + 205, + 547, + 239 + ], + "type": "inline_equation", + "content": "\\uparrow" + }, + { + "bbox": [ + 46, + 205, + 547, + 239 + ], + "type": "text", + "content": " means that \"the larger the better\". The experimental results demonstrate that LIB is robust with respect to different values of " + }, + { + "bbox": [ + 46, + 205, + 547, + 239 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 46, + 205, + 547, + 239 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 205, + 547, + 239 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 205, + 547, + 239 + ], + "type": "text", + "content": ". (Best viewed in color.)" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 372, + 76, + 512, + 182 + ], + "blocks": [ + { + "bbox": [ + 372, + 76, + 512, + 182 + ], + "lines": [ + { + "bbox": [ + 372, + 76, + 512, + 182 + ], + "spans": [ + { + "bbox": [ + 372, + 76, + 512, + 182 + ], + "type": "image", + "image_path": "ad1e900b56aeffddfa362eb0bfa0ad711e7773bba0a5057ec1eac85267f4c772.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 414, + 185, + 471, + 194 + ], + "lines": [ + { + "bbox": [ + 414, + 185, + 471, + 194 + ], + "spans": [ + { + "bbox": [ + 414, + 185, + 471, + 194 + ], + "type": "text", + "content": "(c) Intersection " + }, + { + "bbox": [ + 414, + 185, + 471, + 194 + ], + "type": "inline_equation", + "content": "\\uparrow" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 83, + 249, + 515, + 410 + ], + "blocks": [ + { + "bbox": [ + 83, + 249, + 515, + 410 + ], + "lines": [ + { + "bbox": [ + 83, + 249, + 515, + 410 + ], + "spans": [ + { + "bbox": [ + 83, + 249, + 515, + 410 + ], + "type": "table", + "html": "
MetricChebyshev ↓Clark ↓Canberra ↓Kullback-Leibler ↓Cosine ↑Intersection ↑
MethodLIBgapLIBLIBgapLIBLIBgapLIBLIBgapLIBLIBgapLIBLIBgapLIB
Movie0.1200.1070.5630.5171.0290.9200.0990.0770.9380.9550.8340.859
SUB-3DFE0.1300.0940.3950.2970.8490.6110.0790.0410.9230.9580.8460.887
SJAFFE0.1130.0710.3910.2620.8160.5310.0660.0270.9380.9730.8600.909
Yeast-alpha0.0180.0170.2810.2750.9200.8930.0100.0090.9910.9920.9500.951
Yeast-cdc0.0190.0170.2540.2420.7820.7470.0090.0080.9910.9920.9480.951
Yeast-cold0.0610.0170.1620.1460.2800.2500.0160.0120.9850.9880.9300.938
Yeast-diau0.0500.0490.2880.2730.6590.6210.0250.0220.9770.9790.9080.913
Yeast-dtt0.0450.0340.1240.0920.2170.1580.0100.0050.9910.9950.9460.961
Yeast-elu0.0190.0180.2370.2240.7140.6700.0090.0080.9920.9920.9490.952
Yeast-heat0.0450.0390.1930.1650.3880.3270.0140.0110.9860.9900.9360.946
Yeast-spo0.0590.0530.2530.2240.5230.4540.0250.0190.9760.9820.9140.925
Yeast-spo50.0970.0760.1930.1580.3000.2410.0320.0210.9710.9830.9030.924
Yeast-sopem0.0880.0690.1300.1040.1810.1440.0270.0180.9770.9850.9120.931
", + "image_path": "2210f1252640a11bb5fe6ed47a41775a3e142e013459e346771775be0ac06e87.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 417, + 546, + 440 + ], + "lines": [ + { + "bbox": [ + 46, + 417, + 546, + 440 + ], + "spans": [ + { + "bbox": [ + 46, + 417, + 546, + 440 + ], + "type": "text", + "content": "Table 3. Recovery results of " + }, + { + "bbox": [ + 46, + 417, + 546, + 440 + ], + "type": "inline_equation", + "content": "\\mathrm{LIB}_{gap}" + }, + { + "bbox": [ + 46, + 417, + 546, + 440 + ], + "type": "text", + "content": " and LIB on 13 real-world datasets. " + }, + { + "bbox": [ + 46, + 417, + 546, + 440 + ], + "type": "inline_equation", + "content": "\\downarrow" + }, + { + "bbox": [ + 46, + 417, + 546, + 440 + ], + "type": "text", + "content": " indicates that \"the smaller the better\" and " + }, + { + "bbox": [ + 46, + 417, + 546, + 440 + ], + "type": "inline_equation", + "content": "\\uparrow" + }, + { + "bbox": [ + 46, + 417, + 546, + 440 + ], + "type": "text", + "content": " means that \"the larger the better\". We highlight the best recovery results." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 47, + 461, + 239, + 473 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 461, + 239, + 473 + ], + "spans": [ + { + "bbox": [ + 47, + 461, + 239, + 473 + ], + "type": "text", + "content": "ments information during the recovery process." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 59, + 473, + 284, + 486 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 473, + 284, + 486 + ], + "spans": [ + { + "bbox": [ + 59, + 473, + 284, + 486 + ], + "type": "text", + "content": "To be specific, " + }, + { + "bbox": [ + 59, + 473, + 284, + 486 + ], + "type": "inline_equation", + "content": "\\mathrm{LIB}_{gap}" + }, + { + "bbox": [ + 59, + 473, + 284, + 486 + ], + "type": "text", + "content": " has with the following objective:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 50, + 495, + 287, + 533 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 495, + 287, + 533 + ], + "spans": [ + { + "bbox": [ + 50, + 495, + 287, + 533 + ], + "type": "interline_equation", + "content": "\\min _ {\\theta_ {g d}, \\theta_ {l d}} \\frac {1}{2} \\sum_ {\\boldsymbol {x}} \\left[ (\\boldsymbol {l} - \\hat {\\boldsymbol {d}}) ^ {T} \\left(\\boldsymbol {\\sigma} _ {\\delta | \\boldsymbol {x}} ^ {- 2} \\boldsymbol {I}\\right) (\\boldsymbol {l} - \\hat {\\boldsymbol {d}}) + \\log \\det \\left(\\boldsymbol {\\sigma} _ {\\delta | \\boldsymbol {x}} ^ {2} \\boldsymbol {I}\\right) \\right]. \\tag {35}", + "image_path": "d7cb34e9881b3b86f6f7e243b8593f139f4b3d11b973e63a9fd6cea4b48fcdb0.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 533, + 287, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 533, + 287, + 582 + ], + "spans": [ + { + "bbox": [ + 46, + 533, + 287, + 582 + ], + "type": "text", + "content": "Notably, " + }, + { + "bbox": [ + 46, + 533, + 287, + 582 + ], + "type": "inline_equation", + "content": "\\sigma_{\\delta |x} = f_{\\theta_{gd}}(x)" + }, + { + "bbox": [ + 46, + 533, + 287, + 582 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 533, + 287, + 582 + ], + "type": "inline_equation", + "content": "\\hat{\\pmb{d}} = f_{\\theta_{ld}}(\\pmb {x})" + }, + { + "bbox": [ + 46, + 533, + 287, + 582 + ], + "type": "text", + "content": " , which are different from the objective Eq. (27) utilized in LIB. Only the partial label relevant information, i.e., the information about the label gaps, is explored in " + }, + { + "bbox": [ + 46, + 533, + 287, + 582 + ], + "type": "inline_equation", + "content": "\\mathrm{LIB}_{gap}" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "text", + "content": "Table 3 provides the recovery results of " + }, + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathrm{LIB}_{gap}" + }, + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "text", + "content": " and LIB. It can be observed that LIB outperforms " + }, + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathrm{LIB}_{gap}" + }, + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "text", + "content": " in all cases. Compared with LIB, " + }, + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathrm{LIB}_{gap}" + }, + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "text", + "content": " merely makes the effort to explore the label gap information to boost the recovery performance, while LIB excavates both the information about the label assignments and the information about the label gaps jointly. Therefore, the promising recovery performance can be achieved by LIB. Furthermore, according to the results provided in Table 2 and 3, the recovery results of " + }, + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathrm{LIB}_{gap}" + }, + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "text", + "content": " seem to be competitive, which also indicates that the exploration of information about label gaps is beneficial for LE." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 460, + 379, + 472 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 460, + 379, + 472 + ], + "spans": [ + { + "bbox": [ + 306, + 460, + 379, + 472 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 479, + 546, + 599 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 479, + 546, + 599 + ], + "spans": [ + { + "bbox": [ + 304, + 479, + 546, + 599 + ], + "type": "text", + "content": "In this paper, we present a new perspective to deal with the Label Enhancement (LE) problem and introduce the novel Label Information Bottleneck (LIB) method. The label relevant information is decomposed into the information about label assignments and the information about label gaps. Consequently, our method transform the LE problem into simultaneously learning the latent representation and modeling the label gaps. Extensive experiments carried on both the toy dataset and real-world datasets verify the competitiveness of LIB." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 609, + 404, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 609, + 404, + 624 + ], + "spans": [ + { + "bbox": [ + 306, + 609, + 404, + 624 + ], + "type": "text", + "content": "Acknowledgments" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "type": "text", + "content": "This work was supported by the National Key R&D Program of China under Grant 2020AAA0109602; the Education and Research Foundation for Middle-aged and Young Teacher of Fujian Province under Grant JAT220005; the National Natural Science Foundation of China (NSFC) under Grant 62206156; Alibaba Group through Alibaba Innovative Research Program, No.21169774." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7504" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 714 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "type": "text", + "content": "[1] A Alemi, Ian Fischer, J Dillon, and Kevin Murphy. 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PhD thesis, Carnegie Mellon University, language technologies institute, 2005. 2" + } + ] + } + ], + "index": 3 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 316, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 316, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 316, + 757 + ], + "type": "text", + "content": "7506" + } + ] + } + ], + "index": 5 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Label-Free Liver Tumor Segmentation/13c17228-4f2d-4f7f-be2f-fb50e22321a7_content_list.json b/2023/Label-Free Liver Tumor Segmentation/13c17228-4f2d-4f7f-be2f-fb50e22321a7_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..7f6060a068991a3be7f9bf6f30fdcf74cc87e89b --- /dev/null +++ b/2023/Label-Free Liver Tumor Segmentation/13c17228-4f2d-4f7f-be2f-fb50e22321a7_content_list.json @@ -0,0 +1,1518 @@ +[ + { + "type": "text", + "text": "Label-Free Liver Tumor Segmentation", + "text_level": 1, + "bbox": [ + 295, + 122, + 699, + 142 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Qixin Hu1 Yixiong Chen2 Junfei Xiao3 Shuwen Sun4 Jieneng Chen3 Alan Yuille3 Zongwei Zhou3,*", + "bbox": [ + 252, + 168, + 742, + 202 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1Huazhong University of Science and Technology \n2The Chinese University of Hong Kong – Shenzhen \n3Johns Hopkins University \n4The First Affiliated Hospital of Nanjing Medical University", + "bbox": [ + 252, + 211, + 742, + 278 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Code and Visual Turing Test: https://github.com/MrGiovanni/SyntheticTumors", + "bbox": [ + 253, + 285, + 734, + 298 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 240, + 332, + 319, + 346 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We demonstrate that AI models can accurately segment liver tumors without the need for manual annotation by using synthetic tumors in CT scans. Our synthetic tumors have two intriguing advantages: (I) realistic in shape and texture, which even medical professionals can confuse with real tumors; (II) effective for training AI models, which can perform liver tumor segmentation similarly to the model trained on real tumors—this result is exciting because no existing work, using synthetic tumors only, has thus far reached a similar or even close performance to real tumors. This result also implies that manual efforts for annotating tumors voxel by voxel (which took years to create) can be significantly reduced in the future. Moreover, our synthetic tumors can automatically generate many examples of small (or even tiny) synthetic tumors and have the potential to improve the success rate of detecting small liver tumors, which is critical for detecting the early stages of cancer. In addition to enriching the training data, our synthesizing strategy also enables us to rigorously assess the AI robustness.", + "bbox": [ + 78, + 362, + 482, + 632 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 78, + 659, + 215, + 673 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Artificial intelligence (AI) has dominated medical image segmentation [21,26,73-75], but training an AI model (e.g., U-Net [48]) often requires a large number of annotations. Annotating medical images is not only expensive and time-consuming, but also requires extensive medical expertise, and sometimes needs the assistance of radiology reports and biopsy results to achieve annotation accuracy [12, 52, 59, 69-71]. Due to its high annotation cost, only roughly 200 CT scans with annotated liver tumors are publicly available (provided by LiTS [5]) for training and testing models.", + "bbox": [ + 78, + 683, + 482, + 826 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To minimize annotation expenses, generating synthetic tumors is an emerging research topic. Early attempts include, but only limited to, synthesizing COVID-19 infections [41,63], lung nodules [19] abdominal tumors [27], diabetic lesions [57], and brain tumors [60]. However, the synthetic tumors in those studies appear very different from the real tumors; due to this, AI models trained using synthetic tumors perform significantly worse than those trained using real tumors. What makes synthesizing tumors so hard? There are several important factors: shape, intensity, size, location, and texture. In this paper, we handcraft a strategy to synthesize liver tumors in abdominal CT scans. Our key novelties include (i) location without collision with vessels, (ii) texture with scaled-up Gaussian noise, and (iii) shape generated from distorted ellipsoids. These three aspects are proposed according to the clinical knowledge of liver tumors (detailed in §3.2). The resulting synthetic tumors are realistic—even medical professionals usually confuse them with real tumors in the visual examination (Figure 1; Table 2). In addition, the model trained on our synthetic tumors achieves a Dice Similarity Coefficient (DSC) of $59.81\\%$ for segmenting real liver tumors, whereas AI trained on real tumors obtains a DSC of $57.63\\%$ (Figure 2), showing that synthetic tumors have the potential to be used as an alternative to real tumors in training AI models.", + "bbox": [ + 512, + 332, + 917, + 688 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "These results are exciting because using synthetic tumors only, no previous work has thus far reached a similar (or even close) performance to the model trained on real tumors [24]. Moreover, our synthesizing strategy can exhaustively generate tumors with desired locations, sizes, shapes, textures, and intensities, which are not limited to a fixed finite-size training set (the well-known limitation of the conventional training paradigm [65]). For example, it is hard to collect sufficient training examples with small tumors. It is because early-stage tumors may not cause symptoms, which can delay detection, and these tumors are rela", + "bbox": [ + 510, + 690, + 917, + 847 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 95, + 8, + 171, + 45 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 228, + 5, + 818, + 47 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author: Zongwei Zhou (zzhou82@jh.edu)", + "bbox": [ + 97, + 834, + 415, + 846 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "7422", + "bbox": [ + 468, + 877, + 500, + 888 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/cf4cc99d4fa6b841d334d1bbfcf9e2a3a4c60d7cc68b9c0e7cde4218b878eb9d.jpg", + "image_caption": [ + "Figure 1. [Better viewed in color and zoomed in for details] Can you tell which liver tumors are real and which are fake? The answers are provided in Appendix. We have recruited two medical professionals with at least six years of experience to distinguish fake tumors, generated by our method, from the real ones (namely, Visual Turing Test). Our synthetic tumors have passed the Visual Turing Test on both two medical professionals (<50% fake tumors were picked out). More importantly, using our label-free synthetic tumors, AI models can segment real tumors with performance similar to the AI models trained on real tumors with expensive, detailed, per-voxel annotation." + ], + "image_footnote": [], + "bbox": [ + 80, + 80, + 357, + 284 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/459d7d9eeec18ffd4d652325cc5aff60b191ec6ccdc81eb771dda2a319d2fc3c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 361, + 80, + 636, + 284 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/c9afb121b735b92dcd609dd30719b360158b9db12c091532460f3e457ae94cc5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 638, + 80, + 915, + 284 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "tively small and exhibit subtle abnormal textures that make it difficult for radiologists to manually delineate the tumor boundaries. In contrast, our synthesis strategy can generate a large number of examples featuring small tumors. The key contribution of ours is a synthetic tumor generator, which offers five advantages as summarized below.", + "bbox": [ + 78, + 386, + 482, + 470 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. The synthesis strategy embeds medical knowledge into an executable program, enabling the generation of realistic tumors through the collaboration of radiologists and computer scientists (§5.1; Table 2; Figure 3).", + "2. The entire training stage requires no annotation cost, and the resulting model significantly outperforms previous unsupervised anomaly segmentation approaches and tumor synthesis strategies (§5.2; Table 3).", + "3. The AI model trained on synthetic tumors can achieve similar performance to AI models trained on real tumors with per-voxel annotation in real tumors segmentation, and can be generalized to CT scans with healthy liver and scans from other hospitals (§5.3; Figure 4).", + "4. The synthesis strategy can generate a variety of tumors for model training, including those at small, medium, and large scales, and therefore have the potential to detect small tumors and facilitate the early detection of liver cancer (§5.4; Figure 5).", + "5. The synthesis strategy allows for straightforward manipulation of parameters such as tumor location, size, texture, shape, and intensity, providing a comprehensive test-bed for evaluating AI models under out-of-distribution scenarios (§5.5; Figure 6)." + ], + "bbox": [ + 90, + 482, + 482, + 847 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "These results have the potential to stimulate a shift in the tumor segmentation training paradigm, as illustrated in Figure 2, from label-intensive to label-free AI development for tumor segmentation. Our ultimate goal is to train AI models for tumor segmentation without using manual annotation—this study makes a significant step towards it.", + "bbox": [ + 512, + 386, + 917, + 472 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 512, + 488, + 660, + 504 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Unsupervised anomaly segmentation. Anomaly segmentation is a challenging application area, especially for medical diagnosis [29, 62] and industrial defect detection [4, 25]. Compared with their supervised counterparts, unsupervised methods raises more attention for their low cost and scalability. The general unsupervised anomaly detection setting is to train with normal samples only, without any anomalous data, and no image-level annotation or pixel-level annotation is provided [30, 51, 53]. Under the unsupervised setting, some previous works use self-organizing maps for unsupervised anomaly detection [34, 44] and Huang et al. [25] introduced gradient magnitude similarity and structured similarity index losses in addition to mean square error to compute the loss of image reconstruction. Evidenced in Table 3, our label-free synthetic tumors achieve a significantly better performance in unsupervised tumor segmentation than some of the most recent work in this area.", + "bbox": [ + 512, + 514, + 917, + 755 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Tumor synthesis. Successful works about tumor synthesis include polyp detection from colonoscopy videos [54], COVID-19 detection from Chest CT [41, 63], diabetic lesion detection from retinal images [57], cancer detection from fluorescence microscopy images [23], and brain tumor detection from MRI [60]. However, these works are", + "bbox": [ + 512, + 762, + 917, + 847 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "7423", + "bbox": [ + 468, + 877, + 500, + 889 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/5d9456019ee18e458ad32a53f99543dac400a2e0a9f1ff8c3bd145a7d16b4077.jpg", + "image_caption": [ + "Figure 2. The paradigm shift from label-intensive to label-free tumor segmentation in this work. AI trained on synthetic tumors can segment liver tumors as accurately as AI trained on real tumors. The performance is measured on real tumors using Dice Similarity Coefficient (DSC) and Normalized Surface Distance (NSD)." + ], + "image_footnote": [], + "bbox": [ + 80, + 80, + 478, + 259 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "restricted to the types of tumors, and other diseases, that are fairly easy to visually identify in CT scans. Most recently, Zhang et al. [67] synthesized liver and brain tumors for pre-training and adapted the model to tumor segmentation within the same organ under a low-annotation regime. The manually crafted \"counterfeit\" tumors in the related work appear very differently from real tumors. As a result, AI algorithms, trained on synthetic tumors, may work well in detecting synthetic tumors in the test set but fail to recognize the actual tumors (evidenced in Table 3). We tackle these limitations by integrating radiologists in the tumor synthesis study for feedback ( $\\S 3.2$ ). This enables us to understand deeply about tumors, and in turn, benefit in developing AI algorithms to segment them more accurately.", + "bbox": [ + 75, + 359, + 484, + 558 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Generalization from synthetic to real domains. The problem of domain generalization was introduced [6] for zero-shot adaptation to data with a domain gap. Specifically, the goal is to make a model using data from a single or multiple related source domain(s) while achieving great generalization ability well to any target domain(s) [58, 68]. In this paper, evaluating the model generalization ability on real data is of great importance to justify whether our tumor generator is powerful enough. Domain generalization has been widely studied in multiple computer vision tasks like object recognition [33, 35], semantic segmentation [56, 64] and medical imaging [37, 38]. As deep learning models are data hungry and annotated data are very expensive, how to train a model with synthetic data but generalize well to real data has been targeted in some previous works [8, 9, 13] and some datasets [10, 14, 46, 47, 49] are created for benchmark and further exploring. While previous works focus on preserving the transferable knowledge learned from synthetic data, our paper aims to prove that our tumor generator is powerful enough to generate tumors with reasonable domain gap", + "bbox": [ + 75, + 562, + 482, + 850 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "and that our model has outstanding generalization ability to detect real tumors (detailed in Section 5.3).", + "bbox": [ + 512, + 85, + 917, + 115 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 512, + 127, + 606, + 142 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Tumor Generation", + "text_level": 1, + "bbox": [ + 512, + 151, + 700, + 166 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To localize the liver, we first apply the pre-trained nnU-Net1 to the CT scans. With a coarse location of the liver available, we then develop a sequence of morphological image-processing operations to synthesize realistic tumors within the liver (see Figure 3). The tumor generation consists of four steps: (1) location selection, (2) texture generation, (3) shape generation, and (4) post-processing.", + "bbox": [ + 512, + 174, + 917, + 274 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Location selection. The first step is to select a proper location for the tumor. This step is crucial because liver tumors usually do not allow any vessels (e.g., hepatic vein, portal vein, and inferior vena cava) to pass through them. To avoid the blood vessels, we first conduct vessel segmentation through the voxel value thresholding [16]. The segmented vessel mask is given by the following equation:", + "bbox": [ + 512, + 277, + 917, + 379 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nv (x, y, z) = \\left\\{ \\begin{array}{l} 1, f ^ {\\prime} (x, y, z) > T, l (x, y, z) = 1 \\\\ 0, \\text {o t h e r w i s e} \\end{array} , \\right. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 526, + 388, + 917, + 420 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $f'(x,y,z)$ is the smoothed CT scan, $f'(x,y,z) = f(x,y,z) \\otimes g(x,y,z;\\sigma_a)$ , by applying a Gaussian filter $g(x,y,z;\\sigma_a)$ with standard deviation $\\sigma_a$ to the original CT scans $f(x,y,z)$ ; $\\otimes$ is the standard image filtering operator. Smoothing can effectively eliminate noise caused by CT reconstruction. The threshold $T$ is set to a value slightly greater than the mean Hounsfield Unit (HU) of the liver.", + "bbox": [ + 512, + 430, + 917, + 531 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nT = \\overline {{f (x , y , z) \\odot l (x , y , z)}} + b, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 605, + 541, + 917, + 560 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $l(x,y,z)$ is the liver mask (background $\\equiv 0$ , liver $= 1$ - $\\odot$ is point-wise multiplication, and $b$ is a hyperparameter.", + "bbox": [ + 512, + 569, + 914, + 598 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "With the vessel mask, one can detect whether a chosen location is at risk of making a tumor collide with vessels. After proposing a random location $(X,Y,Z) \\in \\{x,y,z \\mid l(x,y,z) = 1\\}$ , we conduct the collision detection by judging whether there are blood vessels within the range of tumor radius $r$ . If $\\exists v(x,y,z) = 1, \\forall x \\in [X - r,X + r]$ , $y \\in [Y - r,Y + r]$ , $z \\in [Z - r,Z + r]$ , there is a risk of collision, so the location needs to be re-selected. This process iterates until a tumor location $(x_t,y_t,z_t)$ without collision is found. With the desirable tumor location, we are able to generate the tumor texture and shape.", + "bbox": [ + 512, + 598, + 917, + 755 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Texture generation. The HU values of liver and tumor textures follow the Gaussian distributions. To obtain realistic tumor textures, we first generate a 3D Gaussian noise with", + "bbox": [ + 512, + 758, + 917, + 802 + ], + "page_idx": 2 + }, + { + "type": "page_footnote", + "text": "1The off-the-shield, pre-trained nnU-Net [26] for liver segmentation can be downloaded here, which can achieve an average DSC of $95\\%$ on unseen CT scans (sufficient for a coarse localization of the liver).", + "bbox": [ + 512, + 810, + 917, + 847 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "7424", + "bbox": [ + 468, + 877, + 500, + 889 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/bccd8d0cce9a76b64823110ce9ffc09b0bff95cba3eab064dbd1d77156001f42.jpg", + "image_caption": [ + "Figure 3. Liver tumor generation. After randomly selecting a location that avoids the vessels, we generate a Gaussian texture and deformed ellipsoidal shape for a tumor. Then, the texture and shape are combined and placed in the selected location. In addition, we take another two post-processing steps to make a generated tumor more realistic: (1) tumor edge expansion by local scaling warping; (2) capsular generation by brightening the tumor edge. Four steps, in light green, are only used for Visual Turing Test (not for training)." + ], + "image_footnote": [], + "bbox": [ + 80, + 80, + 917, + 225 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "the predefined mean HU intensity $\\mu_t$ and the same standard deviation $\\sigma_p$ as the hepatic parenchyma (the liver area excluding vessels), $T(x,y,z) \\sim \\mathcal{N}(\\mu_t, \\sigma_p)$ . Since the random Gaussian noise is usually too sharp as the texture for the tumor, we soften the texture by scaling it up with spline interpolation of the order 3 (cubic interpolation) on $x, y, z$ directions. The scaled-up texture is denoted as $T'(x,y,z)$ in this work, we want it exhibits graininess close to the hepatic parenchyma. The scaling factor $\\eta \\in [1,\\infty)$ determines how rough the generated grain feels. $\\eta = 1$ means the Gaussian texture is not scaled, resulting in large value fluctuation between adjacent voxels. Larger $\\eta$ brings greater graininess, which may be similar to the real tumor texture. Finally, considering the tomography imaging quality, we further blur the texture with Gaussian filter $g(x,y,z; \\sigma_b)$", + "bbox": [ + 77, + 311, + 484, + 525 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nT ^ {\\prime \\prime} (x, y, z) = T ^ {\\prime} (x, y, z) \\otimes g (x, y, z; \\sigma_ {b}), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 136, + 533, + 480, + 550 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\sigma_{b}$ is the standard deviation. After blurring, the texture resembles those generated by real imaging.", + "bbox": [ + 78, + 558, + 482, + 589 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Shape generation. Most tumors grow from the centers and gradually swell, making small tumors (i.e., $r < 20mm$ ) nearly spherical. This motivates us to generate tumor-like shapes with ellipsoids. We randomly sample the half-axis lengths of the ellipsoid for $x, y, z$ directions from a uniform distribution $U(0.75r, 1.25r)$ , and place the generated ellipsoid mask centered at $(x_t, y_t, z_t)$ . For a generated ellipsoid tumor mask $t(x, y, z)$ (background=0, tumor=1), and with the same shape as the scanning volume $f(x, y, z)$ , elastic deformations [45, 48], controlled by $\\sigma_e$ , are applied to enrich its diversity. The deformed tumor mask is more similar to the naturally grown tumors in appearance than simple ellipsoids. In addition, it can also improve the model's robustness by learning the shape-semantic invariance. The deformed tumor mask is denoted as $t'(x, y, z)$ . In order to make the transition between the generated tumor and the surrounding liver parenchyma more natural, we finally blur the mask by applying a Gaussian filter $g(x, y, z; \\sigma_c)$ with", + "bbox": [ + 77, + 590, + 482, + 848 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "the standard deviation $\\sigma_{c}$ . To be more specifically, we obtain blur shape $t''(x,y,z) = t'(x,y,z)\\otimes g(x,y,z;\\sigma_c)$ .", + "bbox": [ + 512, + 311, + 917, + 341 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Post-processing. The first step of post-processing is placing the tumor on the scanning volume $f(x,y,z)$ and corresponding liver mask $l(x,y,z)$ . Assuming the tumor mask array $t''(x,y,z)$ and the texture array $T''(x,y,z)$ have the same shape as $f(x,y,z)$ and $l(x,y,z)$ . We can obtain new scanning volume with tumor through equation", + "bbox": [ + 512, + 344, + 917, + 431 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nf ^ {\\prime} (x, y, z) = \\left(1 - t ^ {\\prime \\prime} (x, y, z)\\right) \\odot f (x, y, z) + \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 563, + 441, + 917, + 458 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nt ^ {\\prime \\prime} (x, y, z) \\odot T ^ {\\prime \\prime} (x, y, z).\n$$\n", + "text_format": "latex", + "bbox": [ + 652, + 458, + 825, + 476 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For the new mask with the tumor (bg=0,liver=1,tumor=2), it can be synthesized with $l'(x,y,z) = l(x,y,z) + t''(x,y,z)$ . After placing the tumor, we adopt another two steps to make the generated tumor more realistic to medical professionals. They aim to simulate mass effect and the capsule appearance, respectively. Mass effect means the expanding tumor pushes its surrounding tissue apart. If the tumor grows large enough, it will compress the surrounding blood vessels to make them bend, or even cause the edge of the nearby liver to bulge. Local scaling warping [18] is chosen in this work to implement mass effect. It remaps pixels in a circle to be nearer to the circumference. For a pixel with a distance $\\gamma$ to the circle center, the remapped pixel distance $\\gamma'$ is", + "bbox": [ + 512, + 488, + 917, + 674 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\gamma^ {\\prime} = \\left(1 - \\left(1 - \\frac {\\gamma}{\\gamma_ {m a x}}\\right) ^ {2} \\cdot \\frac {I}{1 0 0}\\right) \\cdot \\gamma , \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 579, + 684, + 917, + 722 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\gamma_{max}$ is the radius of the expanded circular area, $I\\in [0,100]$ is a hyper-parameter for controlling the expansion intensity. Larger $I$ leads to stronger warping. Note that when $I = 0$ , the remapping reduces to the identity function $\\gamma^{\\prime} = \\gamma$ . The remapping procedure is conducted on both scanning and mask volumes. After warping, they are named $f^{\\prime \\prime}(x,y,z)$ and $l^{\\prime \\prime}(x,y,z)$ . The latter one (liver/tumor segmentation label) is now ready for the subsequent training.", + "bbox": [ + 512, + 733, + 917, + 848 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "7425", + "bbox": [ + 468, + 877, + 500, + 889 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/9fb4690189eff08bc6d1348b19f8260f1181ca8612c5492317e10c6b78985b1e.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
parametervalueparametervalue
σa0.5 + 0.025σpμtU(30,μp-10)
σb0.6ηU(1.1,1.5)
σcU(0.6,1.2)γmax1.3r
σd0.8I30
b15(lb,ub)(0.4,0.7)
d120
", + "bbox": [ + 80, + 82, + 484, + 167 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Finally, we simulate the capsule appearance by brightening the tumor edge. The edge area can be obtained by", + "bbox": [ + 78, + 266, + 482, + 296 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\ne (x, y, z) = \\left\\{ \\begin{array}{l} 1, t ^ {\\prime \\prime} (x, y, z) \\in [ l b, u b ] \\\\ 0, \\text {o t h e r w i s e} \\end{array} , \\right. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 137, + 305, + 480, + 338 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $lb$ and $ub$ are the lower bound and upper bound for filtering the edge from tumor mask. Then we increase HU intensity of the blurred edge area to simulate the capsule", + "bbox": [ + 78, + 344, + 482, + 390 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\ne ^ {\\prime} (x, y, z) = e (x, y, z) \\otimes g (x, y, z; \\sigma_ {d}), \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 144, + 399, + 480, + 416 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nf ^ {\\prime \\prime \\prime} (x, y, z) = f ^ {\\prime \\prime} (x, y, z) + d \\cdot e (x, y, z), \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 137, + 425, + 480, + 441 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $d$ is the pre-defined HU intensity difference between a tumor and its capsule. The new scanning volume $f^{\\prime \\prime \\prime}(x,y,z)$ is now ready for training or Turing test. The parameters we use are shown in Table 1. Visualization examples can be found in Appendix Figures 8-10.", + "bbox": [ + 78, + 447, + 482, + 519 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.2. Clinical Knowledge about Liver Tumors", + "text_level": 1, + "bbox": [ + 78, + 526, + 433, + 542 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "This work focuses on generating hepatocellular carcinomas (tumor grown from liver cells). After the contrast injection, the clinical examination process of liver is divided into three phases, arterial phase (30s after injection), portal venous phase (60-70s after injection), and delay phase (3min after injection). Typically, only the first two phases are used for detecting hepatocellular carcinomas, and the tumor HU intensity value in different stages distributes differently. The mean attenuation measurement of the lesions in the hepatic arterial phase was 111 HU (range, 32-207 HU), and it decreased in the portal venous phase to a mean of 106 HU (range, 36-162 HU). There was a mean difference of 26 HU (range, -44 to 146 HU) between the lesion and liver in the arterial phase. On average, the hepatocellular carcinomas measured 11 HU (range, -98 to 61 HU) less than the adjacent liver parenchyma in the portal venous phase [32]. The distributional characteristics help us determine the generated mean tumor HU values.", + "bbox": [ + 77, + 548, + 482, + 804 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The location, shape, and number of tumors depend on how severe the hepatocellular carcinomas are according to the standardized guidance of the Liver Imaging Reporting", + "bbox": [ + 78, + 804, + 482, + 848 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/b0ee0fc22e64d635c1281b5bb84d02b231446f0d9b7d858aa74a6af712fe6654.jpg", + "table_caption": [ + "Table 1. Hyper-parameters. $\\mu_p, \\sigma_p$ are the mean and standard deviation of the hepatic parenchyma. The values are adjusted by (1) feedback from clinicians based on the clinical prior knowledge about liver tumors ( $\\S 3.2$ ) and (2) visual assessment between the real and synthetic tumors ( $\\S 5.1$ )." + ], + "table_footnote": [ + "1The junior professional achieves an Accuracy, Sensitivity, and Specificity of 26.5%, 27.6%, and 25.0%. One CT scan is marked unsure.", + "2The senior professional achieves an Accuracy, Sensitivity, and Specificity of $71.0\\%$ $63.2\\%$ ,and $83.3\\%$ . 19 CT scans are marked unsure." + ], + "table_body": "
junior professionalsenior professional
real (P)synt (N)real (P)synt (N)
truthreal (P)515102
synt (N)218712
", + "bbox": [ + 517, + 82, + 915, + 131 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 2. Results of Visual Turing Test. The test has been performed on two medical professionals with 6-year and 15-year experience. Each professional is given 50 CT scans, some of which contain real tumors and the others contain synthetic ones. The professional can mark each CT scan as real, synthetic, or unsure. \"Synt\" denotes synthetic tumors, $P$ and $N$ indicate positive and negative classes for computing Sensitivity and Specificity.", + "bbox": [ + 512, + 181, + 917, + 274 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "and Data System (LI-RADS) [42]. Milder carcinomas usually lead to smaller, fewer spherical lesions. Only one small tumor emerges in most cases. While multi-focal lesions, which means scattered small tumors, only appear in seldom cases. Severe carcinomas usually present a satellite lesion, a large lesion surrounded by a cluster of small lesions. The large central lesion also takes on a more irregular shape than small lesions. And also, larger tumors usually display evident mass effects, accompanied by capsule appearances that separate the tumor from the liver parenchyma.", + "bbox": [ + 512, + 298, + 917, + 441 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 512, + 454, + 650, + 469 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets. Detailed per-voxel annotations for liver tumors are provided in LiTS [5]. The volume of liver tumors ranges from $38\\mathrm{mm}^3$ to $349~\\mathrm{cm}^3$ , and the radius of tumors is in the range of [2, 44]mm. We perform 5-fold cross-validation, following the same split as in Tang et al. [55]. An AI model (e.g. U-Net) is trained on 101 CT scans with annotated liver and liver tumors. For comparison, a dataset of 116 CT scans with healthy livers is assembled from CHAOS [28] (20 CT scans), BTCV [31] (47 CT scans), Pancreas-CT [50] (38 CT scans) and health subjects in LiTS (11 CT scans). We then generate tumors in these scans on the fly, resulting in enormous image-label pairs of synthetic tumors for training the AI model. We generate five levels of tumor sizes for model training; the parameters and examples can be found in Appendix Table 6 and Figure 11.", + "bbox": [ + 512, + 478, + 917, + 690 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Evaluation metrics. Tumor segmentation performance was evaluated by Dice similarity coefficient (DSC) and Normalized Surface Dice (NSD) with $2\\mathrm{mm}$ tolerance; tumor detection performance was evaluated by Sensitivity and Specificity. For all the metrics above, $95\\%$ CIs were calculated and the $p$ -value cutoff of less than 0.05 was used for defining statistical significance.", + "bbox": [ + 512, + 695, + 917, + 795 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implementation. Our codes are implemented based on the MONAI $^2$ framework for both U-Net and Swin UN-", + "bbox": [ + 512, + 799, + 917, + 826 + ], + "page_idx": 4 + }, + { + "type": "page_footnote", + "text": "2https://monai.io/", + "bbox": [ + 531, + 833, + 633, + 846 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "7426", + "bbox": [ + 468, + 877, + 500, + 888 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/6b04bef74393f73aabf0fed8d194730d4ad1dc23d183b0486ca987e0465903b2.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
tumorsmethodarchitecturelabeled / unlabeled CTsDSC (%) [95% CI]NSD (%) [95% CI]
nonePatchCore [51]Wide-Resnet50-2 [66]0 / 11615.97 [11.86–20.09]16.43 [10.42–22.44]
nonef-AnoGAN [53]Customized [3]0 / 11619.00 [13.88–24.11]16.94 [11.97–21.91]
noneVAE [30]Customized [3]0 / 11624.63 [19.83–29.44]23.63 [18.44–28.83]
syntYao et al. [63]U-Net [48]0 / 11632.79 [28.66–36.92]31.28 [26.87–35.70]
realfully-supervisedU-Net101 / 057.51 [52.24–62.79]58.04 [52.56–63.52]
syntlabel-free (ours)U-Net0 / 11659.77 [54.54–64.99]61.29 [56.12–66.47]
", + "bbox": [ + 85, + 82, + 910, + 167 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 3. Comparison with state-of-the-art methods, 5-fold cross-validation. We compare our methods with other unsupervised anomaly segmentation baselines, tumor synthesis strategies, and fully-supervised methods. Our method significantly outperforms all other state-of-the-art unsupervised baseline methods and even surpasses the fully-supervised method with detailed pixel-wise annotation.", + "bbox": [ + 78, + 175, + 915, + 216 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "ETR. Input images are clipped with the window range of [-21,189] and then normalized to have zero mean and unit standard deviation. Random patches of $96 \\times 96 \\times 96$ were cropped from 3D image volumes during training. All models are trained for 4,000 epochs, and the base learning rate is 0.0002. The batch size is two per GPU. We adopt the linear warmup strategy and the cosine annealing learning rate schedule. For inference, we use the sliding window strategy by setting the overlapping area ratio to 0.75.", + "bbox": [ + 78, + 241, + 480, + 368 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Results & Discussion", + "text_level": 1, + "bbox": [ + 80, + 381, + 284, + 395 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Using 116 CT scans from Pancreas-CT, CHAOS, and BTCV with our label-free tumor generator, we outperformed all those methods on the LiTS benchmark, wherein previous methods used 101 CT scans and annotations from LiTS.", + "bbox": [ + 78, + 404, + 480, + 462 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Clinical Validation using Visual Turing Test", + "text_level": 1, + "bbox": [ + 80, + 469, + 458, + 483 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We conduct the Visual Turing Test [15] on 50 CT scans, where 20 scans are with real tumors from LiTS, and the remaining 30 scans are healthy livers from WORD [40] with synthetic tumors. Two professionals with different experience levels take part in this test. They can inspect each sample in 3D view, which means continuous variation of slice sequence can be observed by scrolling the mouse. This is an important setting for the test because some important tumor characteristics are not obvious in a 2D view (e.g., vessel collision). In the test, professionals can label each sample as real, synthetic or unsure. When calculating the performance metrics, only the samples with definite results are counted.", + "bbox": [ + 78, + 491, + 480, + 661 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The testing results are shown in Table 2. For junior professionals with 6-year experience, definite judgments of 49 out of 50 samples are given. All of the accuracy, sensitivity, and specificity are below $30\\%$ , which means the generated samples succeed in confusing the junior professional. In particular, the sensitivity of $27.6\\%$ means that the rest $72.4\\%$ synthetic samples are mistakenly regarded as real samples. The result verifies that our synthesis method can generate realistic tumors. According to the results given by the senior professional with 15-year experience, $36.8\\%$ synthetic samples seemed to be real, indicating that nearly half of the generated samples can tease senior professionals. Noteworthy, the senior professional only gives 19 judg-", + "bbox": [ + 78, + 663, + 480, + 847 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "ments among all 30 synthetic samples. Adding up misjudged samples and uncertain samples, a total of 18 out of 30 generated samples have confused him/her.", + "bbox": [ + 512, + 241, + 917, + 282 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Comparison with State-of-the-art Methods", + "text_level": 1, + "bbox": [ + 512, + 294, + 885, + 310 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We compare our label-free tumor synthesis strategy with several prominent unsupervised tumor segmentation methods designed for both natural and medical images, such as PatchCore [51], f-AnoGAN [53], VAE [3], and the method proposed by Yao et al. [63]. To enhance the performance of these baseline methods, we focus solely on the liver region for training and testing to minimize noise caused by extraneous information. Table 3 shows that all the previous unsupervised methods exhibit suboptimal performance in segmenting real liver tumors. In contrast, our label-free tumor synthesis—a novel approach to unsupervised tumor segmentation—significantly outperforms all these methods, achieving a DSC of $59.77\\%$ and an NSD of $61.29\\%$ . On the other hand, the model trained on real tumors using fully supervised learning achieves a DSC of $57.51\\%$ and an NSD of $58.04\\%$ . These results highlight the potential of a paradigm shift from label-intensive to label-free tumor segmentation.", + "bbox": [ + 512, + 318, + 915, + 558 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.3. Generalization to Different Models and Data", + "text_level": 1, + "bbox": [ + 512, + 571, + 900, + 586 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We verify the generalizability of synthetic tumors using Swin UNETR [20], including its Tiny, Small, and Base variants. Figure 4 shows that the model trained on real tumors performs slightly better than that on synthetic tumors, but there is no statistical difference between the two results as the $p$ -value is greater than 0.05. In addition to evaluating the models on the LiTS dataset, we assess their domain generalization ability using data from other datasets (i.e., MSD-Pancreas, MSD-Spleen, MSD-Colon). As shown in the right panel of Figure 4, our model trained with healthy data collected from 3 different datasets shows better robustness than the model trained on real data only from LiTS,", + "bbox": [ + 512, + 594, + 915, + 765 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "${}^{3}$ Swin UNETR is a hybrid segmentation architecture,which integrates the benefits of both U-Net [48] and Transformer [11,39]. We select Swin UNETR because it is very competitive and has ranked first in numerous public benchmarks [55], including liver tumor segmentation (MSD-Liver).", + "bbox": [ + 512, + 777, + 915, + 822 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "4We first selected the tumor-free scans from these datasets and then had radiologists review each one of the scans to dismiss the diseased liver.", + "bbox": [ + 515, + 824, + 915, + 846 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "7427", + "bbox": [ + 468, + 877, + 500, + 888 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/acd1c70ce7ca7f4e3aca5bb17376701925c04bf24104cc14b31dae718b9a2e6e.jpg", + "image_caption": [ + "Figure 4. Generalization to different models and data. Training U-Net on synthetic liver tumors outperforms as well as training it on real tumors with per-voxel annotation (see Table 3). We further examine this observation using Swin UNETR [55], including its variance of Tiny (Param = 4.0M), Small (Param = 15.7M), and Base (Param = 62.1M). The DSC, NSD, and Sensitivity scores are evaluated on the LiTS datasets. The detailed results of 5-fold cross-validation are reported in Appendix Table 5. Moreover, the model trained on synthetic tumors can also be generalized to CT scans with the healthy liver across datasets (e.g. MSD-Pancreas, MSD-Spleen, and MSD-Colon [2]), generating fewer false positives and yielding a higher Specificity compared with the model trained on real tumors." + ], + "image_footnote": [], + "bbox": [ + 78, + 80, + 236, + 212 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/9b7a049c0ee2b4a4b9c16012dbca91b2ae888121b0e41fce5237d5fb730ded05.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 240, + 80, + 401, + 212 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7ef46a8ad207f9b6dae4481bcd50f56f7d8786f54672c16b20bbe8bb8cd212f6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 406, + 85, + 571, + 212 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2dc891781a030f9c32a21e0624e82f54b2140b138bb4581e79681f22933a978e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 628, + 80, + 917, + 212 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f226e584f863496fa1b364d1cd1df314b3adedd9266c7130f6d6a0208e6b7f73.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 82, + 323, + 480, + 451 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/bcdc686bf2c103371b12dc6af136a8fe1b6a985896188e58ca33a386f5b7cbb8.jpg", + "image_caption": [ + "Figure 5. Small tumor detection. The upper panel presents two examples of small tumors and the segmentation results. For both models trained on real and synthetic tumors, the false negatives are mostly smaller than $10\\mathrm{mm}$ . The lower panel presents the tumor detection rate. The model trained on synthetic tumors could detect tumors as small as $2\\mathrm{mm}$ ." + ], + "image_footnote": [], + "bbox": [ + 82, + 456, + 475, + 532 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "while achieving much higher Specificity on the three external datasets. It is noteworthy that higher Specificity (fewer false positives) is crucial in clinical applications as it reduces the number of patients subjected to invasive diagnostic procedures and their associated costs [7,36,61].", + "bbox": [ + 77, + 645, + 482, + 715 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.4. Potential in Small Tumor Detection", + "text_level": 1, + "bbox": [ + 78, + 725, + 394, + 739 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Early detection of small tumors is essential for prompt cancer diagnosis, but such cases are scarce in real datasets because most patients remain asymptomatic during the early stages. AI models trained on these datasets exhibit reduced detection sensitivity for small tumors (radius $< 5\\mathrm{mm}$ ) compared with larger tumors (radius $>5\\mathrm{mm}$ ), displaying sensitivities of $52.0\\%$ and $91.6\\%$ , respectively.", + "bbox": [ + 77, + 747, + 482, + 847 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Thus, an advanced tumor generator could create synthetic data containing various tumor sizes for training and testing models, addressing the size imbalance issue found in real data. The lower panel of Figure 5 presents quantitative tumor detection performance stratified by tumor size, and the upper panel presents two cases with small tumors for qualitative comparison. Evidently, AI models (trained solely on synthetic data) outperform those trained on real tumors in detecting and segmenting small tumors in the liver. The results indicate that the generation of copious amounts of synthetic small tumors can improve the efficacy of models in detecting real small tumors, thereby playing a crucial role in the early detection of cancer.", + "bbox": [ + 510, + 326, + 917, + 510 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.5. Controllable Robustness Benchmark", + "text_level": 1, + "bbox": [ + 512, + 524, + 840, + 539 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Standard evaluation in medical imaging is limited to determining the effectiveness of AI in detecting tumors. This is because the number of annotated tumors in the existing test datasets is not big enough to be representative of the tumors that occur in real organs and, in particular, contains only a limited number of very small tumors. We show that synthetic tumors can serve as an accessible and comprehensive source for rigorously evaluating AI's performance in detecting tumors at a variety of different sizes and locations with the organs. To be specific, our tumor generator can synthesize liver tumors varying in five dimensions, i.e. location, size, shape, intensity, and texture, by tuning hyperparameters in the tumor generation pipeline. Taking five different options in each dimension, our tumor generator could create $25(5\\times 5)$ variants for each single CT scan. Generating a large number of synthetic tumors during testing enables us to find failure scenarios of current AI models. After locating the worst cases of AI, we can synthesize and include worst-case tumors in the training set and fine-tune AI algorithms. Figure 6 illustrates the out-of-distribution (o.o.d.) benchmark created by synthetic tumors, wherein", + "bbox": [ + 510, + 548, + 917, + 847 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "7428", + "bbox": [ + 468, + 877, + 500, + 888 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f392a587b03c869a4a7c0d2384530146cb40560f1b216601ad51b8b221aadd09.jpg", + "image_caption": [ + "Figure 6. Controllable benchmark for robust evaluation. UNet++ [72], nnU-Net [26], and Swin UNETR [55] are very competitive segmentation models in the medical domain. However, their limitations of tumor segmentation are not fully revealed due to the lack of sufficient testing images (only 70 CT scans are available for testing in MSD Task03 [1]). On the contrary, synthetic tumors enable us to perform an extensive evaluation of these models in segmenting liver tumors that vary from different conditions, i.e. shape, size, texture, intensity, and location. We downloaded the checkpoints of these models trained on LiTS, and evaluated them on synthetic tumors. Synthetic tumors were generated using different parameters, where $\\mu$ and $\\sigma$ denote mean and standard deviation, respectively. Our findings indicate that these public models exhibit robustness to variations in tumor shape, location, and texture, but they are sensitive to tumor size and intensity. Specifically, these models are prone to errors when encountering tumors that are smaller or larger than those in the training set, or when faced with differing Hounsfield Unit (HU) values, which may be attributable to contrast enhancement." + ], + "image_footnote": [], + "bbox": [ + 80, + 80, + 915, + 261 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/b66716394349be0ffe58ce366f788d3ef1c8ab6245f545c8b545e334ca114983.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
tiny sizeelastic deformationedge blurringall tumors DSC (%)small tumors det Sen. (%)
✓43.926.4
✓✓47.151.3
✓✓50.354.1
✓✓52.633.4
✓✓✓55.161.8
", + "bbox": [ + 87, + 411, + 475, + 495 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 4. Ablation study on shape generation. The quality of synthesized tumors influences model performance to a certain degree, emphasizing the importance of each component in our proposed method (§3; Figure 3). The quality assessment of generated tumors is in Appendix Figure 11. Moreover, generating tiny synthetic tumors positively impacts the sensitivity of small tumors.", + "bbox": [ + 78, + 505, + 480, + 583 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "we evaluate several state-of-the-art models (trained on public datasets). These models show good robustness in the shape, location, and texture dimensions but are sensitive to tumors of extreme sizes and intensities.", + "bbox": [ + 78, + 612, + 480, + 668 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.6. Ablation Study on Shape Generation", + "text_level": 1, + "bbox": [ + 78, + 681, + 406, + 697 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To show the importance of each step in tumor generation, we design ablation studies focusing on shape generation and synthesizing small tumors. We evaluate the models trained with different incomplete settings of synthetic strategies on two aspects: all tumor segmentation and small tumor detection. As shown in Table 4, the performance would be much poorer without synthesizing small tumors, edge blurring or elastic deformation in the shape generation. The reasons are simple: (1) without elastic deformation and edge blurring steps for shape generation (shown in Figure 3), the syn", + "bbox": [ + 78, + 703, + 480, + 847 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "thetic tumors can be extremely unrealistic (i.e. the edge is sharp and shape can only be ellipsoid). Several examples are provided in Appendix Figure 12. (2) The model doesn't have the generalization ability to small tumors (radius $< 5\\mathrm{mm}$ ) when the training set does not have them.", + "bbox": [ + 512, + 414, + 917, + 486 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 512, + 495, + 636, + 511 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we have developed an effective strategy to synthesize liver tumors. With zero manual annotation, we verify that the AI model trained on synthetic tumors can perform similarly to the ones trained on real tumors in the LiTS dataset (which took months to create). This reveals the great potential for the use of synthesis tumors to train AI models on larger-scale healthy CT datasets (which are much easier to obtain than CT scans with liver tumors). Furthermore, synthetic tumors allow us to assess AI's capability of detecting tumors of varying locations, sizes, shapes, intensities, textures, and stages in CT scans. In the future, we will consider generative adversarial nets (GANs) [17,19], Diffusion Models [22] and possibly improved with 3D geometry models like NeRF [43] to generate better tumor texture.", + "bbox": [ + 512, + 520, + 917, + 718 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements. This work was supported by the Lustgarten Foundation for Pancreatic Cancer Research and partially by the Patrick J. McGovern Foundation Award. We appreciate the effort of the MONAI Team to provide open-source code for the community. We thank Yucheng Tang, Huimiao Chen, Bowen Li, Jessica Han, and Wenxuan Li for their constructive suggestions; thank Camille Torrico and Alexa Delaney for improving the writing of this paper. 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Springer, 2019. 1" + ], + "bbox": [ + 515, + 86, + 915, + 445 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "7432", + "bbox": [ + 468, + 878, + 500, + 887 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Label-Free Liver Tumor Segmentation/13c17228-4f2d-4f7f-be2f-fb50e22321a7_model.json b/2023/Label-Free Liver Tumor Segmentation/13c17228-4f2d-4f7f-be2f-fb50e22321a7_model.json new file mode 100644 index 0000000000000000000000000000000000000000..5b00ecbd79d5fd55b2434788538299f16bb06285 --- /dev/null +++ b/2023/Label-Free Liver Tumor Segmentation/13c17228-4f2d-4f7f-be2f-fb50e22321a7_model.json @@ -0,0 +1,2378 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.096, + 0.009, + 0.172, + 0.046 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.23, + 0.006, + 0.819, + 0.048 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.297, + 0.123, + 0.7, + 0.143 + ], + "angle": 0, + "content": "Label-Free Liver Tumor Segmentation" + }, + { + "type": "text", + "bbox": [ + 0.253, + 0.169, + 0.744, + 0.203 + ], + "angle": 0, + "content": "Qixin Hu1 Yixiong Chen2 Junfei Xiao3 Shuwen Sun4 Jieneng Chen3 Alan Yuille3 Zongwei Zhou3,*" + }, + { + "type": "text", + "bbox": [ + 0.253, + 0.212, + 0.744, + 0.279 + ], + "angle": 0, + "content": "1Huazhong University of Science and Technology \n2The Chinese University of Hong Kong – Shenzhen \n3Johns Hopkins University \n4The First Affiliated Hospital of Nanjing Medical University" + }, + { + "type": "text", + "bbox": [ + 0.255, + 0.286, + 0.735, + 0.299 + ], + "angle": 0, + "content": "Code and Visual Turing Test: https://github.com/MrGiovanni/SyntheticTumors" + }, + { + "type": "title", + "bbox": [ + 0.242, + 0.333, + 0.321, + 0.347 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.079, + 0.363, + 0.483, + 0.633 + ], + "angle": 0, + "content": "We demonstrate that AI models can accurately segment liver tumors without the need for manual annotation by using synthetic tumors in CT scans. Our synthetic tumors have two intriguing advantages: (I) realistic in shape and texture, which even medical professionals can confuse with real tumors; (II) effective for training AI models, which can perform liver tumor segmentation similarly to the model trained on real tumors—this result is exciting because no existing work, using synthetic tumors only, has thus far reached a similar or even close performance to real tumors. This result also implies that manual efforts for annotating tumors voxel by voxel (which took years to create) can be significantly reduced in the future. Moreover, our synthetic tumors can automatically generate many examples of small (or even tiny) synthetic tumors and have the potential to improve the success rate of detecting small liver tumors, which is critical for detecting the early stages of cancer. In addition to enriching the training data, our synthesizing strategy also enables us to rigorously assess the AI robustness." + }, + { + "type": "title", + "bbox": [ + 0.08, + 0.66, + 0.216, + 0.674 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.079, + 0.684, + 0.483, + 0.827 + ], + "angle": 0, + "content": "Artificial intelligence (AI) has dominated medical image segmentation [21,26,73-75], but training an AI model (e.g., U-Net [48]) often requires a large number of annotations. Annotating medical images is not only expensive and time-consuming, but also requires extensive medical expertise, and sometimes needs the assistance of radiology reports and biopsy results to achieve annotation accuracy [12, 52, 59, 69-71]. Due to its high annotation cost, only roughly 200 CT scans with annotated liver tumors are publicly available (provided by LiTS [5]) for training and testing models." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.334, + 0.918, + 0.689 + ], + "angle": 0, + "content": "To minimize annotation expenses, generating synthetic tumors is an emerging research topic. Early attempts include, but only limited to, synthesizing COVID-19 infections [41,63], lung nodules [19] abdominal tumors [27], diabetic lesions [57], and brain tumors [60]. However, the synthetic tumors in those studies appear very different from the real tumors; due to this, AI models trained using synthetic tumors perform significantly worse than those trained using real tumors. What makes synthesizing tumors so hard? There are several important factors: shape, intensity, size, location, and texture. In this paper, we handcraft a strategy to synthesize liver tumors in abdominal CT scans. Our key novelties include (i) location without collision with vessels, (ii) texture with scaled-up Gaussian noise, and (iii) shape generated from distorted ellipsoids. These three aspects are proposed according to the clinical knowledge of liver tumors (detailed in §3.2). The resulting synthetic tumors are realistic—even medical professionals usually confuse them with real tumors in the visual examination (Figure 1; Table 2). In addition, the model trained on our synthetic tumors achieves a Dice Similarity Coefficient (DSC) of \\(59.81\\%\\) for segmenting real liver tumors, whereas AI trained on real tumors obtains a DSC of \\(57.63\\%\\) (Figure 2), showing that synthetic tumors have the potential to be used as an alternative to real tumors in training AI models." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.691, + 0.918, + 0.848 + ], + "angle": 0, + "content": "These results are exciting because using synthetic tumors only, no previous work has thus far reached a similar (or even close) performance to the model trained on real tumors [24]. Moreover, our synthesizing strategy can exhaustively generate tumors with desired locations, sizes, shapes, textures, and intensities, which are not limited to a fixed finite-size training set (the well-known limitation of the conventional training paradigm [65]). For example, it is hard to collect sufficient training examples with small tumors. It is because early-stage tumors may not cause symptoms, which can delay detection, and these tumors are rela" + }, + { + "type": "page_footnote", + "bbox": [ + 0.098, + 0.835, + 0.416, + 0.847 + ], + "angle": 0, + "content": "*Corresponding author: Zongwei Zhou (zzhou82@jh.edu)" + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.878, + 0.501, + 0.889 + ], + "angle": 0, + "content": "7422" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.082, + 0.359, + 0.285 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.362, + 0.082, + 0.637, + 0.285 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.64, + 0.082, + 0.917, + 0.285 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.078, + 0.296, + 0.919, + 0.364 + ], + "angle": 0, + "content": "Figure 1. [Better viewed in color and zoomed in for details] Can you tell which liver tumors are real and which are fake? The answers are provided in Appendix. We have recruited two medical professionals with at least six years of experience to distinguish fake tumors, generated by our method, from the real ones (namely, Visual Turing Test). Our synthetic tumors have passed the Visual Turing Test on both two medical professionals (<50% fake tumors were picked out). More importantly, using our label-free synthetic tumors, AI models can segment real tumors with performance similar to the AI models trained on real tumors with expensive, detailed, per-voxel annotation." + }, + { + "type": "text", + "bbox": [ + 0.079, + 0.387, + 0.483, + 0.472 + ], + "angle": 0, + "content": "tively small and exhibit subtle abnormal textures that make it difficult for radiologists to manually delineate the tumor boundaries. In contrast, our synthesis strategy can generate a large number of examples featuring small tumors. The key contribution of ours is a synthetic tumor generator, which offers five advantages as summarized below." + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.483, + 0.483, + 0.542 + ], + "angle": 0, + "content": "1. The synthesis strategy embeds medical knowledge into an executable program, enabling the generation of realistic tumors through the collaboration of radiologists and computer scientists (§5.1; Table 2; Figure 3)." + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.55, + 0.483, + 0.608 + ], + "angle": 0, + "content": "2. The entire training stage requires no annotation cost, and the resulting model significantly outperforms previous unsupervised anomaly segmentation approaches and tumor synthesis strategies (§5.2; Table 3)." + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.616, + 0.483, + 0.687 + ], + "angle": 0, + "content": "3. The AI model trained on synthetic tumors can achieve similar performance to AI models trained on real tumors with per-voxel annotation in real tumors segmentation, and can be generalized to CT scans with healthy liver and scans from other hospitals (§5.3; Figure 4)." + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.696, + 0.483, + 0.768 + ], + "angle": 0, + "content": "4. The synthesis strategy can generate a variety of tumors for model training, including those at small, medium, and large scales, and therefore have the potential to detect small tumors and facilitate the early detection of liver cancer (§5.4; Figure 5)." + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.776, + 0.483, + 0.848 + ], + "angle": 0, + "content": "5. The synthesis strategy allows for straightforward manipulation of parameters such as tumor location, size, texture, shape, and intensity, providing a comprehensive test-bed for evaluating AI models under out-of-distribution scenarios (§5.5; Figure 6)." + }, + { + "type": "list", + "bbox": [ + 0.092, + 0.483, + 0.483, + 0.848 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.387, + 0.918, + 0.473 + ], + "angle": 0, + "content": "These results have the potential to stimulate a shift in the tumor segmentation training paradigm, as illustrated in Figure 2, from label-intensive to label-free AI development for tumor segmentation. Our ultimate goal is to train AI models for tumor segmentation without using manual annotation—this study makes a significant step towards it." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.489, + 0.661, + 0.505 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.515, + 0.918, + 0.756 + ], + "angle": 0, + "content": "Unsupervised anomaly segmentation. Anomaly segmentation is a challenging application area, especially for medical diagnosis [29, 62] and industrial defect detection [4, 25]. Compared with their supervised counterparts, unsupervised methods raises more attention for their low cost and scalability. The general unsupervised anomaly detection setting is to train with normal samples only, without any anomalous data, and no image-level annotation or pixel-level annotation is provided [30, 51, 53]. Under the unsupervised setting, some previous works use self-organizing maps for unsupervised anomaly detection [34, 44] and Huang et al. [25] introduced gradient magnitude similarity and structured similarity index losses in addition to mean square error to compute the loss of image reconstruction. Evidenced in Table 3, our label-free synthetic tumors achieve a significantly better performance in unsupervised tumor segmentation than some of the most recent work in this area." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.763, + 0.918, + 0.848 + ], + "angle": 0, + "content": "Tumor synthesis. Successful works about tumor synthesis include polyp detection from colonoscopy videos [54], COVID-19 detection from Chest CT [41, 63], diabetic lesion detection from retinal images [57], cancer detection from fluorescence microscopy images [23], and brain tumor detection from MRI [60]. However, these works are" + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.878, + 0.502, + 0.89 + ], + "angle": 0, + "content": "7423" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.082, + 0.479, + 0.26 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.078, + 0.269, + 0.487, + 0.337 + ], + "angle": 0, + "content": "Figure 2. The paradigm shift from label-intensive to label-free tumor segmentation in this work. AI trained on synthetic tumors can segment liver tumors as accurately as AI trained on real tumors. The performance is measured on real tumors using Dice Similarity Coefficient (DSC) and Normalized Surface Distance (NSD)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.36, + 0.485, + 0.56 + ], + "angle": 0, + "content": "restricted to the types of tumors, and other diseases, that are fairly easy to visually identify in CT scans. Most recently, Zhang et al. [67] synthesized liver and brain tumors for pre-training and adapted the model to tumor segmentation within the same organ under a low-annotation regime. The manually crafted \"counterfeit\" tumors in the related work appear very differently from real tumors. As a result, AI algorithms, trained on synthetic tumors, may work well in detecting synthetic tumors in the test set but fail to recognize the actual tumors (evidenced in Table 3). We tackle these limitations by integrating radiologists in the tumor synthesis study for feedback (\\(\\S 3.2\\)). This enables us to understand deeply about tumors, and in turn, benefit in developing AI algorithms to segment them more accurately." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.563, + 0.484, + 0.851 + ], + "angle": 0, + "content": "Generalization from synthetic to real domains. The problem of domain generalization was introduced [6] for zero-shot adaptation to data with a domain gap. Specifically, the goal is to make a model using data from a single or multiple related source domain(s) while achieving great generalization ability well to any target domain(s) [58, 68]. In this paper, evaluating the model generalization ability on real data is of great importance to justify whether our tumor generator is powerful enough. Domain generalization has been widely studied in multiple computer vision tasks like object recognition [33, 35], semantic segmentation [56, 64] and medical imaging [37, 38]. As deep learning models are data hungry and annotated data are very expensive, how to train a model with synthetic data but generalize well to real data has been targeted in some previous works [8, 9, 13] and some datasets [10, 14, 46, 47, 49] are created for benchmark and further exploring. While previous works focus on preserving the transferable knowledge learned from synthetic data, our paper aims to prove that our tumor generator is powerful enough to generate tumors with reasonable domain gap" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.086, + 0.918, + 0.116 + ], + "angle": 0, + "content": "and that our model has outstanding generalization ability to detect real tumors (detailed in Section 5.3)." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.128, + 0.608, + 0.143 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.152, + 0.702, + 0.167 + ], + "angle": 0, + "content": "3.1. Tumor Generation" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.175, + 0.918, + 0.275 + ], + "angle": 0, + "content": "To localize the liver, we first apply the pre-trained nnU-Net1 to the CT scans. With a coarse location of the liver available, we then develop a sequence of morphological image-processing operations to synthesize realistic tumors within the liver (see Figure 3). The tumor generation consists of four steps: (1) location selection, (2) texture generation, (3) shape generation, and (4) post-processing." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.278, + 0.918, + 0.38 + ], + "angle": 0, + "content": "Location selection. The first step is to select a proper location for the tumor. This step is crucial because liver tumors usually do not allow any vessels (e.g., hepatic vein, portal vein, and inferior vena cava) to pass through them. To avoid the blood vessels, we first conduct vessel segmentation through the voxel value thresholding [16]. The segmented vessel mask is given by the following equation:" + }, + { + "type": "equation", + "bbox": [ + 0.527, + 0.389, + 0.918, + 0.422 + ], + "angle": 0, + "content": "\\[\nv (x, y, z) = \\left\\{ \\begin{array}{l} 1, f ^ {\\prime} (x, y, z) > T, l (x, y, z) = 1 \\\\ 0, \\text {o t h e r w i s e} \\end{array} , \\right. \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.431, + 0.918, + 0.532 + ], + "angle": 0, + "content": "where \\( f'(x,y,z) \\) is the smoothed CT scan, \\( f'(x,y,z) = f(x,y,z) \\otimes g(x,y,z;\\sigma_a) \\), by applying a Gaussian filter \\( g(x,y,z;\\sigma_a) \\) with standard deviation \\( \\sigma_a \\) to the original CT scans \\( f(x,y,z) \\); \\( \\otimes \\) is the standard image filtering operator. Smoothing can effectively eliminate noise caused by CT reconstruction. The threshold \\( T \\) is set to a value slightly greater than the mean Hounsfield Unit (HU) of the liver." + }, + { + "type": "equation", + "bbox": [ + 0.606, + 0.542, + 0.918, + 0.561 + ], + "angle": 0, + "content": "\\[\nT = \\overline {{f (x , y , z) \\odot l (x , y , z)}} + b, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.57, + 0.915, + 0.599 + ], + "angle": 0, + "content": "where \\(l(x,y,z)\\) is the liver mask (background \\(\\equiv 0\\) , liver \\(= 1\\) - \\(\\odot\\) is point-wise multiplication, and \\(b\\) is a hyperparameter." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.599, + 0.918, + 0.756 + ], + "angle": 0, + "content": "With the vessel mask, one can detect whether a chosen location is at risk of making a tumor collide with vessels. After proposing a random location \\((X,Y,Z) \\in \\{x,y,z \\mid l(x,y,z) = 1\\}\\), we conduct the collision detection by judging whether there are blood vessels within the range of tumor radius \\(r\\). If \\(\\exists v(x,y,z) = 1, \\forall x \\in [X - r,X + r]\\), \\(y \\in [Y - r,Y + r]\\), \\(z \\in [Z - r,Z + r]\\), there is a risk of collision, so the location needs to be re-selected. This process iterates until a tumor location \\((x_t,y_t,z_t)\\) without collision is found. With the desirable tumor location, we are able to generate the tumor texture and shape." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.759, + 0.918, + 0.803 + ], + "angle": 0, + "content": "Texture generation. The HU values of liver and tumor textures follow the Gaussian distributions. To obtain realistic tumor textures, we first generate a 3D Gaussian noise with" + }, + { + "type": "page_footnote", + "bbox": [ + 0.513, + 0.812, + 0.918, + 0.848 + ], + "angle": 0, + "content": "1The off-the-shield, pre-trained nnU-Net [26] for liver segmentation can be downloaded here, which can achieve an average DSC of \\(95\\%\\) on unseen CT scans (sufficient for a coarse localization of the liver)." + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.878, + 0.502, + 0.89 + ], + "angle": 0, + "content": "7424" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.082, + 0.919, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.078, + 0.234, + 0.921, + 0.289 + ], + "angle": 0, + "content": "Figure 3. Liver tumor generation. After randomly selecting a location that avoids the vessels, we generate a Gaussian texture and deformed ellipsoidal shape for a tumor. Then, the texture and shape are combined and placed in the selected location. In addition, we take another two post-processing steps to make a generated tumor more realistic: (1) tumor edge expansion by local scaling warping; (2) capsular generation by brightening the tumor edge. Four steps, in light green, are only used for Visual Turing Test (not for training)." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.312, + 0.485, + 0.526 + ], + "angle": 0, + "content": "the predefined mean HU intensity \\(\\mu_t\\) and the same standard deviation \\(\\sigma_p\\) as the hepatic parenchyma (the liver area excluding vessels), \\(T(x,y,z) \\sim \\mathcal{N}(\\mu_t, \\sigma_p)\\). Since the random Gaussian noise is usually too sharp as the texture for the tumor, we soften the texture by scaling it up with spline interpolation of the order 3 (cubic interpolation) on \\(x, y, z\\) directions. The scaled-up texture is denoted as \\(T'(x,y,z)\\) in this work, we want it exhibits graininess close to the hepatic parenchyma. The scaling factor \\(\\eta \\in [1,\\infty)\\) determines how rough the generated grain feels. \\(\\eta = 1\\) means the Gaussian texture is not scaled, resulting in large value fluctuation between adjacent voxels. Larger \\(\\eta\\) brings greater graininess, which may be similar to the real tumor texture. Finally, considering the tomography imaging quality, we further blur the texture with Gaussian filter \\(g(x,y,z; \\sigma_b)\\)" + }, + { + "type": "equation", + "bbox": [ + 0.137, + 0.535, + 0.482, + 0.551 + ], + "angle": 0, + "content": "\\[\nT ^ {\\prime \\prime} (x, y, z) = T ^ {\\prime} (x, y, z) \\otimes g (x, y, z; \\sigma_ {b}), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.079, + 0.56, + 0.483, + 0.59 + ], + "angle": 0, + "content": "where \\(\\sigma_{b}\\) is the standard deviation. After blurring, the texture resembles those generated by real imaging." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.592, + 0.484, + 0.849 + ], + "angle": 0, + "content": "Shape generation. Most tumors grow from the centers and gradually swell, making small tumors (i.e., \\( r < 20mm \\)) nearly spherical. This motivates us to generate tumor-like shapes with ellipsoids. We randomly sample the half-axis lengths of the ellipsoid for \\( x, y, z \\) directions from a uniform distribution \\( U(0.75r, 1.25r) \\), and place the generated ellipsoid mask centered at \\( (x_t, y_t, z_t) \\). For a generated ellipsoid tumor mask \\( t(x, y, z) \\) (background=0, tumor=1), and with the same shape as the scanning volume \\( f(x, y, z) \\), elastic deformations [45, 48], controlled by \\( \\sigma_e \\), are applied to enrich its diversity. The deformed tumor mask is more similar to the naturally grown tumors in appearance than simple ellipsoids. In addition, it can also improve the model's robustness by learning the shape-semantic invariance. The deformed tumor mask is denoted as \\( t'(x, y, z) \\). In order to make the transition between the generated tumor and the surrounding liver parenchyma more natural, we finally blur the mask by applying a Gaussian filter \\( g(x, y, z; \\sigma_c) \\) with" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.312, + 0.918, + 0.342 + ], + "angle": 0, + "content": "the standard deviation \\(\\sigma_{c}\\). To be more specifically, we obtain blur shape \\(t''(x,y,z) = t'(x,y,z)\\otimes g(x,y,z;\\sigma_c)\\)." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.345, + 0.918, + 0.432 + ], + "angle": 0, + "content": "Post-processing. The first step of post-processing is placing the tumor on the scanning volume \\( f(x,y,z) \\) and corresponding liver mask \\( l(x,y,z) \\). Assuming the tumor mask array \\( t''(x,y,z) \\) and the texture array \\( T''(x,y,z) \\) have the same shape as \\( f(x,y,z) \\) and \\( l(x,y,z) \\). We can obtain new scanning volume with tumor through equation" + }, + { + "type": "equation", + "bbox": [ + 0.564, + 0.442, + 0.918, + 0.459 + ], + "angle": 0, + "content": "\\[\nf ^ {\\prime} (x, y, z) = \\left(1 - t ^ {\\prime \\prime} (x, y, z)\\right) \\odot f (x, y, z) + \\tag {4}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.653, + 0.46, + 0.826, + 0.477 + ], + "angle": 0, + "content": "\\[\nt ^ {\\prime \\prime} (x, y, z) \\odot T ^ {\\prime \\prime} (x, y, z).\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.489, + 0.919, + 0.675 + ], + "angle": 0, + "content": "For the new mask with the tumor (bg=0,liver=1,tumor=2), it can be synthesized with \\( l'(x,y,z) = l(x,y,z) + t''(x,y,z) \\). After placing the tumor, we adopt another two steps to make the generated tumor more realistic to medical professionals. They aim to simulate mass effect and the capsule appearance, respectively. Mass effect means the expanding tumor pushes its surrounding tissue apart. If the tumor grows large enough, it will compress the surrounding blood vessels to make them bend, or even cause the edge of the nearby liver to bulge. Local scaling warping [18] is chosen in this work to implement mass effect. It remaps pixels in a circle to be nearer to the circumference. For a pixel with a distance \\( \\gamma \\) to the circle center, the remapped pixel distance \\( \\gamma' \\) is" + }, + { + "type": "equation", + "bbox": [ + 0.581, + 0.685, + 0.918, + 0.723 + ], + "angle": 0, + "content": "\\[\n\\gamma^ {\\prime} = \\left(1 - \\left(1 - \\frac {\\gamma}{\\gamma_ {m a x}}\\right) ^ {2} \\cdot \\frac {I}{1 0 0}\\right) \\cdot \\gamma , \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.734, + 0.919, + 0.849 + ], + "angle": 0, + "content": "where \\(\\gamma_{max}\\) is the radius of the expanded circular area, \\(I\\in [0,100]\\) is a hyper-parameter for controlling the expansion intensity. Larger \\(I\\) leads to stronger warping. Note that when \\(I = 0\\), the remapping reduces to the identity function \\(\\gamma^{\\prime} = \\gamma\\). The remapping procedure is conducted on both scanning and mask volumes. After warping, they are named \\(f^{\\prime \\prime}(x,y,z)\\) and \\(l^{\\prime \\prime}(x,y,z)\\). The latter one (liver/tumor segmentation label) is now ready for the subsequent training." + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.878, + 0.502, + 0.89 + ], + "angle": 0, + "content": "7425" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.083, + 0.485, + 0.168 + ], + "angle": 0, + "content": "
parametervalueparametervalue
σa0.5 + 0.025σpμtU(30,μp-10)
σb0.6ηU(1.1,1.5)
σcU(0.6,1.2)γmax1.3r
σd0.8I30
b15(lb,ub)(0.4,0.7)
d120
" + }, + { + "type": "table_caption", + "bbox": [ + 0.079, + 0.177, + 0.483, + 0.243 + ], + "angle": 0, + "content": "Table 1. Hyper-parameters. \\(\\mu_p, \\sigma_p\\) are the mean and standard deviation of the hepatic parenchyma. The values are adjusted by (1) feedback from clinicians based on the clinical prior knowledge about liver tumors (\\(\\S 3.2\\)) and (2) visual assessment between the real and synthetic tumors (\\(\\S 5.1\\))." + }, + { + "type": "text", + "bbox": [ + 0.079, + 0.267, + 0.483, + 0.297 + ], + "angle": 0, + "content": "Finally, we simulate the capsule appearance by brightening the tumor edge. The edge area can be obtained by" + }, + { + "type": "equation", + "bbox": [ + 0.138, + 0.306, + 0.482, + 0.339 + ], + "angle": 0, + "content": "\\[\ne (x, y, z) = \\left\\{ \\begin{array}{l} 1, t ^ {\\prime \\prime} (x, y, z) \\in [ l b, u b ] \\\\ 0, \\text {o t h e r w i s e} \\end{array} , \\right. \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.079, + 0.346, + 0.484, + 0.391 + ], + "angle": 0, + "content": "where \\( lb \\) and \\( ub \\) are the lower bound and upper bound for filtering the edge from tumor mask. Then we increase HU intensity of the blurred edge area to simulate the capsule" + }, + { + "type": "equation", + "bbox": [ + 0.145, + 0.4, + 0.482, + 0.417 + ], + "angle": 0, + "content": "\\[\ne ^ {\\prime} (x, y, z) = e (x, y, z) \\otimes g (x, y, z; \\sigma_ {d}), \\tag {7}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.138, + 0.426, + 0.482, + 0.442 + ], + "angle": 0, + "content": "\\[\nf ^ {\\prime \\prime \\prime} (x, y, z) = f ^ {\\prime \\prime} (x, y, z) + d \\cdot e (x, y, z), \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.079, + 0.448, + 0.484, + 0.52 + ], + "angle": 0, + "content": "where \\(d\\) is the pre-defined HU intensity difference between a tumor and its capsule. The new scanning volume \\(f^{\\prime \\prime \\prime}(x,y,z)\\) is now ready for training or Turing test. The parameters we use are shown in Table 1. Visualization examples can be found in Appendix Figures 8-10." + }, + { + "type": "title", + "bbox": [ + 0.08, + 0.527, + 0.434, + 0.543 + ], + "angle": 0, + "content": "3.2. Clinical Knowledge about Liver Tumors" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.549, + 0.483, + 0.805 + ], + "angle": 0, + "content": "This work focuses on generating hepatocellular carcinomas (tumor grown from liver cells). After the contrast injection, the clinical examination process of liver is divided into three phases, arterial phase (30s after injection), portal venous phase (60-70s after injection), and delay phase (3min after injection). Typically, only the first two phases are used for detecting hepatocellular carcinomas, and the tumor HU intensity value in different stages distributes differently. The mean attenuation measurement of the lesions in the hepatic arterial phase was 111 HU (range, 32-207 HU), and it decreased in the portal venous phase to a mean of 106 HU (range, 36-162 HU). There was a mean difference of 26 HU (range, -44 to 146 HU) between the lesion and liver in the arterial phase. On average, the hepatocellular carcinomas measured 11 HU (range, -98 to 61 HU) less than the adjacent liver parenchyma in the portal venous phase [32]. The distributional characteristics help us determine the generated mean tumor HU values." + }, + { + "type": "text", + "bbox": [ + 0.079, + 0.806, + 0.484, + 0.849 + ], + "angle": 0, + "content": "The location, shape, and number of tumors depend on how severe the hepatocellular carcinomas are according to the standardized guidance of the Liver Imaging Reporting" + }, + { + "type": "table", + "bbox": [ + 0.518, + 0.083, + 0.916, + 0.133 + ], + "angle": 0, + "content": "
junior professionalsenior professional
real (P)synt (N)real (P)synt (N)
truthreal (P)515102
synt (N)218712
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.536, + 0.134, + 0.915, + 0.153 + ], + "angle": 0, + "content": "1The junior professional achieves an Accuracy, Sensitivity, and Specificity of 26.5%, 27.6%, and 25.0%. One CT scan is marked unsure." + }, + { + "type": "table_footnote", + "bbox": [ + 0.539, + 0.153, + 0.915, + 0.172 + ], + "angle": 0, + "content": "2The senior professional achieves an Accuracy, Sensitivity, and Specificity of \\(71.0\\%\\) \\(63.2\\%\\) ,and \\(83.3\\%\\) . 19 CT scans are marked unsure." + }, + { + "type": "list", + "bbox": [ + 0.536, + 0.134, + 0.915, + 0.172 + ], + "angle": 0, + "content": null + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.182, + 0.918, + 0.275 + ], + "angle": 0, + "content": "Table 2. Results of Visual Turing Test. The test has been performed on two medical professionals with 6-year and 15-year experience. Each professional is given 50 CT scans, some of which contain real tumors and the others contain synthetic ones. The professional can mark each CT scan as real, synthetic, or unsure. \"Synt\" denotes synthetic tumors, \\( P \\) and \\( N \\) indicate positive and negative classes for computing Sensitivity and Specificity." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.299, + 0.918, + 0.442 + ], + "angle": 0, + "content": "and Data System (LI-RADS) [42]. Milder carcinomas usually lead to smaller, fewer spherical lesions. Only one small tumor emerges in most cases. While multi-focal lesions, which means scattered small tumors, only appear in seldom cases. Severe carcinomas usually present a satellite lesion, a large lesion surrounded by a cluster of small lesions. The large central lesion also takes on a more irregular shape than small lesions. And also, larger tumors usually display evident mass effects, accompanied by capsule appearances that separate the tumor from the liver parenchyma." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.455, + 0.651, + 0.47 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.479, + 0.918, + 0.692 + ], + "angle": 0, + "content": "Datasets. Detailed per-voxel annotations for liver tumors are provided in LiTS [5]. The volume of liver tumors ranges from \\(38\\mathrm{mm}^3\\) to \\(349~\\mathrm{cm}^3\\), and the radius of tumors is in the range of [2, 44]mm. We perform 5-fold cross-validation, following the same split as in Tang et al. [55]. An AI model (e.g. U-Net) is trained on 101 CT scans with annotated liver and liver tumors. For comparison, a dataset of 116 CT scans with healthy livers is assembled from CHAOS [28] (20 CT scans), BTCV [31] (47 CT scans), Pancreas-CT [50] (38 CT scans) and health subjects in LiTS (11 CT scans). We then generate tumors in these scans on the fly, resulting in enormous image-label pairs of synthetic tumors for training the AI model. We generate five levels of tumor sizes for model training; the parameters and examples can be found in Appendix Table 6 and Figure 11." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.696, + 0.918, + 0.796 + ], + "angle": 0, + "content": "Evaluation metrics. Tumor segmentation performance was evaluated by Dice similarity coefficient (DSC) and Normalized Surface Dice (NSD) with \\(2\\mathrm{mm}\\) tolerance; tumor detection performance was evaluated by Sensitivity and Specificity. For all the metrics above, \\(95\\%\\) CIs were calculated and the \\(p\\)-value cutoff of less than 0.05 was used for defining statistical significance." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.8, + 0.918, + 0.827 + ], + "angle": 0, + "content": "Implementation. Our codes are implemented based on the MONAI\\(^2\\) framework for both U-Net and Swin UN-" + }, + { + "type": "page_footnote", + "bbox": [ + 0.532, + 0.834, + 0.634, + 0.847 + ], + "angle": 0, + "content": "2https://monai.io/" + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.878, + 0.502, + 0.889 + ], + "angle": 0, + "content": "7426" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.086, + 0.083, + 0.911, + 0.168 + ], + "angle": 0, + "content": "
tumorsmethodarchitecturelabeled / unlabeled CTsDSC (%) [95% CI]NSD (%) [95% CI]
nonePatchCore [51]Wide-Resnet50-2 [66]0 / 11615.97 [11.86–20.09]16.43 [10.42–22.44]
nonef-AnoGAN [53]Customized [3]0 / 11619.00 [13.88–24.11]16.94 [11.97–21.91]
noneVAE [30]Customized [3]0 / 11624.63 [19.83–29.44]23.63 [18.44–28.83]
syntYao et al. [63]U-Net [48]0 / 11632.79 [28.66–36.92]31.28 [26.87–35.70]
realfully-supervisedU-Net101 / 057.51 [52.24–62.79]58.04 [52.56–63.52]
syntlabel-free (ours)U-Net0 / 11659.77 [54.54–64.99]61.29 [56.12–66.47]
" + }, + { + "type": "table_caption", + "bbox": [ + 0.08, + 0.177, + 0.917, + 0.217 + ], + "angle": 0, + "content": "Table 3. Comparison with state-of-the-art methods, 5-fold cross-validation. We compare our methods with other unsupervised anomaly segmentation baselines, tumor synthesis strategies, and fully-supervised methods. Our method significantly outperforms all other state-of-the-art unsupervised baseline methods and even surpasses the fully-supervised method with detailed pixel-wise annotation." + }, + { + "type": "text", + "bbox": [ + 0.079, + 0.242, + 0.482, + 0.369 + ], + "angle": 0, + "content": "ETR. Input images are clipped with the window range of [-21,189] and then normalized to have zero mean and unit standard deviation. Random patches of \\( 96 \\times 96 \\times 96 \\) were cropped from 3D image volumes during training. All models are trained for 4,000 epochs, and the base learning rate is 0.0002. The batch size is two per GPU. We adopt the linear warmup strategy and the cosine annealing learning rate schedule. For inference, we use the sliding window strategy by setting the overlapping area ratio to 0.75." + }, + { + "type": "title", + "bbox": [ + 0.081, + 0.382, + 0.285, + 0.397 + ], + "angle": 0, + "content": "5. Results & Discussion" + }, + { + "type": "text", + "bbox": [ + 0.08, + 0.405, + 0.482, + 0.463 + ], + "angle": 0, + "content": "Using 116 CT scans from Pancreas-CT, CHAOS, and BTCV with our label-free tumor generator, we outperformed all those methods on the LiTS benchmark, wherein previous methods used 101 CT scans and annotations from LiTS." + }, + { + "type": "title", + "bbox": [ + 0.081, + 0.47, + 0.46, + 0.485 + ], + "angle": 0, + "content": "5.1. Clinical Validation using Visual Turing Test" + }, + { + "type": "text", + "bbox": [ + 0.08, + 0.492, + 0.482, + 0.662 + ], + "angle": 0, + "content": "We conduct the Visual Turing Test [15] on 50 CT scans, where 20 scans are with real tumors from LiTS, and the remaining 30 scans are healthy livers from WORD [40] with synthetic tumors. Two professionals with different experience levels take part in this test. They can inspect each sample in 3D view, which means continuous variation of slice sequence can be observed by scrolling the mouse. This is an important setting for the test because some important tumor characteristics are not obvious in a 2D view (e.g., vessel collision). In the test, professionals can label each sample as real, synthetic or unsure. When calculating the performance metrics, only the samples with definite results are counted." + }, + { + "type": "text", + "bbox": [ + 0.079, + 0.664, + 0.482, + 0.848 + ], + "angle": 0, + "content": "The testing results are shown in Table 2. For junior professionals with 6-year experience, definite judgments of 49 out of 50 samples are given. All of the accuracy, sensitivity, and specificity are below \\(30\\%\\), which means the generated samples succeed in confusing the junior professional. In particular, the sensitivity of \\(27.6\\%\\) means that the rest \\(72.4\\%\\) synthetic samples are mistakenly regarded as real samples. The result verifies that our synthesis method can generate realistic tumors. According to the results given by the senior professional with 15-year experience, \\(36.8\\%\\) synthetic samples seemed to be real, indicating that nearly half of the generated samples can tease senior professionals. Noteworthy, the senior professional only gives 19 judg-" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.242, + 0.918, + 0.284 + ], + "angle": 0, + "content": "ments among all 30 synthetic samples. Adding up misjudged samples and uncertain samples, a total of 18 out of 30 generated samples have confused him/her." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.296, + 0.887, + 0.311 + ], + "angle": 0, + "content": "5.2. Comparison with State-of-the-art Methods" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.319, + 0.917, + 0.56 + ], + "angle": 0, + "content": "We compare our label-free tumor synthesis strategy with several prominent unsupervised tumor segmentation methods designed for both natural and medical images, such as PatchCore [51], f-AnoGAN [53], VAE [3], and the method proposed by Yao et al. [63]. To enhance the performance of these baseline methods, we focus solely on the liver region for training and testing to minimize noise caused by extraneous information. Table 3 shows that all the previous unsupervised methods exhibit suboptimal performance in segmenting real liver tumors. In contrast, our label-free tumor synthesis—a novel approach to unsupervised tumor segmentation—significantly outperforms all these methods, achieving a DSC of \\(59.77\\%\\) and an NSD of \\(61.29\\%\\). On the other hand, the model trained on real tumors using fully supervised learning achieves a DSC of \\(57.51\\%\\) and an NSD of \\(58.04\\%\\). These results highlight the potential of a paradigm shift from label-intensive to label-free tumor segmentation." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.572, + 0.902, + 0.587 + ], + "angle": 0, + "content": "5.3. Generalization to Different Models and Data" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.595, + 0.917, + 0.766 + ], + "angle": 0, + "content": "We verify the generalizability of synthetic tumors using Swin UNETR [20], including its Tiny, Small, and Base variants. Figure 4 shows that the model trained on real tumors performs slightly better than that on synthetic tumors, but there is no statistical difference between the two results as the \\( p \\)-value is greater than 0.05. In addition to evaluating the models on the LiTS dataset, we assess their domain generalization ability using data from other datasets (i.e., MSD-Pancreas, MSD-Spleen, MSD-Colon). As shown in the right panel of Figure 4, our model trained with healthy data collected from 3 different datasets shows better robustness than the model trained on real data only from LiTS," + }, + { + "type": "page_footnote", + "bbox": [ + 0.513, + 0.778, + 0.916, + 0.824 + ], + "angle": 0, + "content": "\\( {}^{3} \\) Swin UNETR is a hybrid segmentation architecture,which integrates the benefits of both U-Net [48] and Transformer [11,39]. We select Swin UNETR because it is very competitive and has ranked first in numerous public benchmarks [55], including liver tumor segmentation (MSD-Liver)." + }, + { + "type": "page_footnote", + "bbox": [ + 0.516, + 0.825, + 0.917, + 0.847 + ], + "angle": 0, + "content": "4We first selected the tumor-free scans from these datasets and then had radiologists review each one of the scans to dismiss the diseased liver." + }, + { + "type": "list", + "bbox": [ + 0.513, + 0.778, + 0.917, + 0.847 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.878, + 0.501, + 0.889 + ], + "angle": 0, + "content": "7427" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.08, + 0.082, + 0.237, + 0.214 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.242, + 0.081, + 0.402, + 0.213 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.407, + 0.086, + 0.573, + 0.213 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.63, + 0.082, + 0.918, + 0.214 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.078, + 0.223, + 0.917, + 0.302 + ], + "angle": 0, + "content": "Figure 4. Generalization to different models and data. Training U-Net on synthetic liver tumors outperforms as well as training it on real tumors with per-voxel annotation (see Table 3). We further examine this observation using Swin UNETR [55], including its variance of Tiny (Param = 4.0M), Small (Param = 15.7M), and Base (Param = 62.1M). The DSC, NSD, and Sensitivity scores are evaluated on the LiTS datasets. The detailed results of 5-fold cross-validation are reported in Appendix Table 5. Moreover, the model trained on synthetic tumors can also be generalized to CT scans with the healthy liver across datasets (e.g. MSD-Pancreas, MSD-Spleen, and MSD-Colon [2]), generating fewer false positives and yielding a higher Specificity compared with the model trained on real tumors." + }, + { + "type": "image", + "bbox": [ + 0.083, + 0.324, + 0.482, + 0.452 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.457, + 0.477, + 0.533 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.078, + 0.542, + 0.483, + 0.62 + ], + "angle": 0, + "content": "Figure 5. Small tumor detection. The upper panel presents two examples of small tumors and the segmentation results. For both models trained on real and synthetic tumors, the false negatives are mostly smaller than \\(10\\mathrm{mm}\\). The lower panel presents the tumor detection rate. The model trained on synthetic tumors could detect tumors as small as \\(2\\mathrm{mm}\\)." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.646, + 0.483, + 0.716 + ], + "angle": 0, + "content": "while achieving much higher Specificity on the three external datasets. It is noteworthy that higher Specificity (fewer false positives) is crucial in clinical applications as it reduces the number of patients subjected to invasive diagnostic procedures and their associated costs [7,36,61]." + }, + { + "type": "title", + "bbox": [ + 0.08, + 0.726, + 0.395, + 0.74 + ], + "angle": 0, + "content": "5.4. Potential in Small Tumor Detection" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.748, + 0.483, + 0.848 + ], + "angle": 0, + "content": "Early detection of small tumors is essential for prompt cancer diagnosis, but such cases are scarce in real datasets because most patients remain asymptomatic during the early stages. AI models trained on these datasets exhibit reduced detection sensitivity for small tumors (radius \\(< 5\\mathrm{mm}\\)) compared with larger tumors (radius \\(>5\\mathrm{mm}\\)), displaying sensitivities of \\(52.0\\%\\) and \\(91.6\\%\\), respectively." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.327, + 0.918, + 0.511 + ], + "angle": 0, + "content": "Thus, an advanced tumor generator could create synthetic data containing various tumor sizes for training and testing models, addressing the size imbalance issue found in real data. The lower panel of Figure 5 presents quantitative tumor detection performance stratified by tumor size, and the upper panel presents two cases with small tumors for qualitative comparison. Evidently, AI models (trained solely on synthetic data) outperform those trained on real tumors in detecting and segmenting small tumors in the liver. The results indicate that the generation of copious amounts of synthetic small tumors can improve the efficacy of models in detecting real small tumors, thereby playing a crucial role in the early detection of cancer." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.525, + 0.842, + 0.54 + ], + "angle": 0, + "content": "5.5. Controllable Robustness Benchmark" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.549, + 0.918, + 0.848 + ], + "angle": 0, + "content": "Standard evaluation in medical imaging is limited to determining the effectiveness of AI in detecting tumors. This is because the number of annotated tumors in the existing test datasets is not big enough to be representative of the tumors that occur in real organs and, in particular, contains only a limited number of very small tumors. We show that synthetic tumors can serve as an accessible and comprehensive source for rigorously evaluating AI's performance in detecting tumors at a variety of different sizes and locations with the organs. To be specific, our tumor generator can synthesize liver tumors varying in five dimensions, i.e. location, size, shape, intensity, and texture, by tuning hyperparameters in the tumor generation pipeline. Taking five different options in each dimension, our tumor generator could create \\(25(5\\times 5)\\) variants for each single CT scan. Generating a large number of synthetic tumors during testing enables us to find failure scenarios of current AI models. After locating the worst cases of AI, we can synthesize and include worst-case tumors in the training set and fine-tune AI algorithms. Figure 6 illustrates the out-of-distribution (o.o.d.) benchmark created by synthetic tumors, wherein" + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.878, + 0.502, + 0.889 + ], + "angle": 0, + "content": "7428" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.082, + 0.917, + 0.262 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.078, + 0.272, + 0.919, + 0.39 + ], + "angle": 0, + "content": "Figure 6. Controllable benchmark for robust evaluation. UNet++ [72], nnU-Net [26], and Swin UNETR [55] are very competitive segmentation models in the medical domain. However, their limitations of tumor segmentation are not fully revealed due to the lack of sufficient testing images (only 70 CT scans are available for testing in MSD Task03 [1]). On the contrary, synthetic tumors enable us to perform an extensive evaluation of these models in segmenting liver tumors that vary from different conditions, i.e. shape, size, texture, intensity, and location. We downloaded the checkpoints of these models trained on LiTS, and evaluated them on synthetic tumors. Synthetic tumors were generated using different parameters, where \\(\\mu\\) and \\(\\sigma\\) denote mean and standard deviation, respectively. Our findings indicate that these public models exhibit robustness to variations in tumor shape, location, and texture, but they are sensitive to tumor size and intensity. Specifically, these models are prone to errors when encountering tumors that are smaller or larger than those in the training set, or when faced with differing Hounsfield Unit (HU) values, which may be attributable to contrast enhancement." + }, + { + "type": "table", + "bbox": [ + 0.088, + 0.412, + 0.476, + 0.496 + ], + "angle": 0, + "content": "
tiny sizeelastic deformationedge blurringall tumors DSC (%)small tumors det Sen. (%)
✓43.926.4
✓✓47.151.3
✓✓50.354.1
✓✓52.633.4
✓✓✓55.161.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.079, + 0.506, + 0.482, + 0.584 + ], + "angle": 0, + "content": "Table 4. Ablation study on shape generation. The quality of synthesized tumors influences model performance to a certain degree, emphasizing the importance of each component in our proposed method (§3; Figure 3). The quality assessment of generated tumors is in Appendix Figure 11. Moreover, generating tiny synthetic tumors positively impacts the sensitivity of small tumors." + }, + { + "type": "text", + "bbox": [ + 0.079, + 0.613, + 0.482, + 0.669 + ], + "angle": 0, + "content": "we evaluate several state-of-the-art models (trained on public datasets). These models show good robustness in the shape, location, and texture dimensions but are sensitive to tumors of extreme sizes and intensities." + }, + { + "type": "title", + "bbox": [ + 0.08, + 0.682, + 0.407, + 0.698 + ], + "angle": 0, + "content": "5.6. Ablation Study on Shape Generation" + }, + { + "type": "text", + "bbox": [ + 0.079, + 0.705, + 0.482, + 0.848 + ], + "angle": 0, + "content": "To show the importance of each step in tumor generation, we design ablation studies focusing on shape generation and synthesizing small tumors. We evaluate the models trained with different incomplete settings of synthetic strategies on two aspects: all tumor segmentation and small tumor detection. As shown in Table 4, the performance would be much poorer without synthesizing small tumors, edge blurring or elastic deformation in the shape generation. The reasons are simple: (1) without elastic deformation and edge blurring steps for shape generation (shown in Figure 3), the syn" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.415, + 0.918, + 0.487 + ], + "angle": 0, + "content": "thetic tumors can be extremely unrealistic (i.e. the edge is sharp and shape can only be ellipsoid). Several examples are provided in Appendix Figure 12. (2) The model doesn't have the generalization ability to small tumors (radius \\(< 5\\mathrm{mm}\\)) when the training set does not have them." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.497, + 0.637, + 0.512 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.521, + 0.918, + 0.719 + ], + "angle": 0, + "content": "In this paper, we have developed an effective strategy to synthesize liver tumors. With zero manual annotation, we verify that the AI model trained on synthetic tumors can perform similarly to the ones trained on real tumors in the LiTS dataset (which took months to create). This reveals the great potential for the use of synthesis tumors to train AI models on larger-scale healthy CT datasets (which are much easier to obtain than CT scans with liver tumors). Furthermore, synthetic tumors allow us to assess AI's capability of detecting tumors of varying locations, sizes, shapes, intensities, textures, and stages in CT scans. In the future, we will consider generative adversarial nets (GANs) [17,19], Diffusion Models [22] and possibly improved with 3D geometry models like NeRF [43] to generate better tumor texture." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.72, + 0.918, + 0.848 + ], + "angle": 0, + "content": "Acknowledgements. This work was supported by the Lustgarten Foundation for Pancreatic Cancer Research and partially by the Patrick J. McGovern Foundation Award. We appreciate the effort of the MONAI Team to provide open-source code for the community. We thank Yucheng Tang, Huimiao Chen, Bowen Li, Jessica Han, and Wenxuan Li for their constructive suggestions; thank Camille Torrico and Alexa Delaney for improving the writing of this paper. Paper content is covered by patents pending." + }, + { + "type": "page_number", + "bbox": [ + 0.469, + 0.878, + 0.502, + 0.889 + ], + "angle": 0, + "content": "7429" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.082, + 0.085, + 0.179, + 0.1 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.089, + 0.109, + 0.484, + 0.174 + ], + "angle": 0, + "content": "[1] Michela Antonelli, Annika Reinke, Spyridon Bakas, Keyvan Farahani, Annette Kopp-Schneider, Bennett A Landman, Geert Litjens, Bjoern Menze, Olaf Ronneberger, Ronald M Summers, et al. The medical segmentation decathlon. Nature communications, 13(1):1-13, 2022. 8" + }, + { + "type": "ref_text", + "bbox": [ + 0.089, + 0.176, + 0.484, + 0.24 + ], + "angle": 0, + "content": "[2] Michela Antonelli, Annika Reinke, Spyridon Bakas, Keyvan Farahani, Bennett A Landman, Geert Litjens, Bjoern Menze, Olaf Ronneberger, Ronald M Summers, Bram van Ginneken, et al. 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Our synthetic tumors have two intriguing advantages: (I) realistic in shape and texture, which even medical professionals can confuse with real tumors; (II) effective for training AI models, which can perform liver tumor segmentation similarly to the model trained on real tumors—this result is exciting because no existing work, using synthetic tumors only, has thus far reached a similar or even close performance to real tumors. This result also implies that manual efforts for annotating tumors voxel by voxel (which took years to create) can be significantly reduced in the future. Moreover, our synthetic tumors can automatically generate many examples of small (or even tiny) synthetic tumors and have the potential to improve the success rate of detecting small liver tumors, which is critical for detecting the early stages of cancer. In addition to enriching the training data, our synthesizing strategy also enables us to rigorously assess the AI robustness. + +# 1. Introduction + +Artificial intelligence (AI) has dominated medical image segmentation [21,26,73-75], but training an AI model (e.g., U-Net [48]) often requires a large number of annotations. Annotating medical images is not only expensive and time-consuming, but also requires extensive medical expertise, and sometimes needs the assistance of radiology reports and biopsy results to achieve annotation accuracy [12, 52, 59, 69-71]. Due to its high annotation cost, only roughly 200 CT scans with annotated liver tumors are publicly available (provided by LiTS [5]) for training and testing models. + +To minimize annotation expenses, generating synthetic tumors is an emerging research topic. Early attempts include, but only limited to, synthesizing COVID-19 infections [41,63], lung nodules [19] abdominal tumors [27], diabetic lesions [57], and brain tumors [60]. However, the synthetic tumors in those studies appear very different from the real tumors; due to this, AI models trained using synthetic tumors perform significantly worse than those trained using real tumors. What makes synthesizing tumors so hard? There are several important factors: shape, intensity, size, location, and texture. In this paper, we handcraft a strategy to synthesize liver tumors in abdominal CT scans. Our key novelties include (i) location without collision with vessels, (ii) texture with scaled-up Gaussian noise, and (iii) shape generated from distorted ellipsoids. These three aspects are proposed according to the clinical knowledge of liver tumors (detailed in §3.2). The resulting synthetic tumors are realistic—even medical professionals usually confuse them with real tumors in the visual examination (Figure 1; Table 2). In addition, the model trained on our synthetic tumors achieves a Dice Similarity Coefficient (DSC) of $59.81\%$ for segmenting real liver tumors, whereas AI trained on real tumors obtains a DSC of $57.63\%$ (Figure 2), showing that synthetic tumors have the potential to be used as an alternative to real tumors in training AI models. + +These results are exciting because using synthetic tumors only, no previous work has thus far reached a similar (or even close) performance to the model trained on real tumors [24]. Moreover, our synthesizing strategy can exhaustively generate tumors with desired locations, sizes, shapes, textures, and intensities, which are not limited to a fixed finite-size training set (the well-known limitation of the conventional training paradigm [65]). For example, it is hard to collect sufficient training examples with small tumors. It is because early-stage tumors may not cause symptoms, which can delay detection, and these tumors are rela + +![](images/cf4cc99d4fa6b841d334d1bbfcf9e2a3a4c60d7cc68b9c0e7cde4218b878eb9d.jpg) +Figure 1. [Better viewed in color and zoomed in for details] Can you tell which liver tumors are real and which are fake? The answers are provided in Appendix. We have recruited two medical professionals with at least six years of experience to distinguish fake tumors, generated by our method, from the real ones (namely, Visual Turing Test). Our synthetic tumors have passed the Visual Turing Test on both two medical professionals (<50% fake tumors were picked out). More importantly, using our label-free synthetic tumors, AI models can segment real tumors with performance similar to the AI models trained on real tumors with expensive, detailed, per-voxel annotation. + +![](images/459d7d9eeec18ffd4d652325cc5aff60b191ec6ccdc81eb771dda2a319d2fc3c.jpg) + +![](images/c9afb121b735b92dcd609dd30719b360158b9db12c091532460f3e457ae94cc5.jpg) + +tively small and exhibit subtle abnormal textures that make it difficult for radiologists to manually delineate the tumor boundaries. In contrast, our synthesis strategy can generate a large number of examples featuring small tumors. The key contribution of ours is a synthetic tumor generator, which offers five advantages as summarized below. + +1. The synthesis strategy embeds medical knowledge into an executable program, enabling the generation of realistic tumors through the collaboration of radiologists and computer scientists (§5.1; Table 2; Figure 3). +2. The entire training stage requires no annotation cost, and the resulting model significantly outperforms previous unsupervised anomaly segmentation approaches and tumor synthesis strategies (§5.2; Table 3). +3. The AI model trained on synthetic tumors can achieve similar performance to AI models trained on real tumors with per-voxel annotation in real tumors segmentation, and can be generalized to CT scans with healthy liver and scans from other hospitals (§5.3; Figure 4). +4. The synthesis strategy can generate a variety of tumors for model training, including those at small, medium, and large scales, and therefore have the potential to detect small tumors and facilitate the early detection of liver cancer (§5.4; Figure 5). +5. The synthesis strategy allows for straightforward manipulation of parameters such as tumor location, size, texture, shape, and intensity, providing a comprehensive test-bed for evaluating AI models under out-of-distribution scenarios (§5.5; Figure 6). + +These results have the potential to stimulate a shift in the tumor segmentation training paradigm, as illustrated in Figure 2, from label-intensive to label-free AI development for tumor segmentation. Our ultimate goal is to train AI models for tumor segmentation without using manual annotation—this study makes a significant step towards it. + +# 2. Related Work + +Unsupervised anomaly segmentation. Anomaly segmentation is a challenging application area, especially for medical diagnosis [29, 62] and industrial defect detection [4, 25]. Compared with their supervised counterparts, unsupervised methods raises more attention for their low cost and scalability. The general unsupervised anomaly detection setting is to train with normal samples only, without any anomalous data, and no image-level annotation or pixel-level annotation is provided [30, 51, 53]. Under the unsupervised setting, some previous works use self-organizing maps for unsupervised anomaly detection [34, 44] and Huang et al. [25] introduced gradient magnitude similarity and structured similarity index losses in addition to mean square error to compute the loss of image reconstruction. Evidenced in Table 3, our label-free synthetic tumors achieve a significantly better performance in unsupervised tumor segmentation than some of the most recent work in this area. + +Tumor synthesis. Successful works about tumor synthesis include polyp detection from colonoscopy videos [54], COVID-19 detection from Chest CT [41, 63], diabetic lesion detection from retinal images [57], cancer detection from fluorescence microscopy images [23], and brain tumor detection from MRI [60]. However, these works are + +![](images/5d9456019ee18e458ad32a53f99543dac400a2e0a9f1ff8c3bd145a7d16b4077.jpg) +Figure 2. The paradigm shift from label-intensive to label-free tumor segmentation in this work. AI trained on synthetic tumors can segment liver tumors as accurately as AI trained on real tumors. The performance is measured on real tumors using Dice Similarity Coefficient (DSC) and Normalized Surface Distance (NSD). + +restricted to the types of tumors, and other diseases, that are fairly easy to visually identify in CT scans. Most recently, Zhang et al. [67] synthesized liver and brain tumors for pre-training and adapted the model to tumor segmentation within the same organ under a low-annotation regime. The manually crafted "counterfeit" tumors in the related work appear very differently from real tumors. As a result, AI algorithms, trained on synthetic tumors, may work well in detecting synthetic tumors in the test set but fail to recognize the actual tumors (evidenced in Table 3). We tackle these limitations by integrating radiologists in the tumor synthesis study for feedback ( $\S 3.2$ ). This enables us to understand deeply about tumors, and in turn, benefit in developing AI algorithms to segment them more accurately. + +Generalization from synthetic to real domains. The problem of domain generalization was introduced [6] for zero-shot adaptation to data with a domain gap. Specifically, the goal is to make a model using data from a single or multiple related source domain(s) while achieving great generalization ability well to any target domain(s) [58, 68]. In this paper, evaluating the model generalization ability on real data is of great importance to justify whether our tumor generator is powerful enough. Domain generalization has been widely studied in multiple computer vision tasks like object recognition [33, 35], semantic segmentation [56, 64] and medical imaging [37, 38]. As deep learning models are data hungry and annotated data are very expensive, how to train a model with synthetic data but generalize well to real data has been targeted in some previous works [8, 9, 13] and some datasets [10, 14, 46, 47, 49] are created for benchmark and further exploring. While previous works focus on preserving the transferable knowledge learned from synthetic data, our paper aims to prove that our tumor generator is powerful enough to generate tumors with reasonable domain gap + +and that our model has outstanding generalization ability to detect real tumors (detailed in Section 5.3). + +# 3. Method + +# 3.1. Tumor Generation + +To localize the liver, we first apply the pre-trained nnU-Net1 to the CT scans. With a coarse location of the liver available, we then develop a sequence of morphological image-processing operations to synthesize realistic tumors within the liver (see Figure 3). The tumor generation consists of four steps: (1) location selection, (2) texture generation, (3) shape generation, and (4) post-processing. + +Location selection. The first step is to select a proper location for the tumor. This step is crucial because liver tumors usually do not allow any vessels (e.g., hepatic vein, portal vein, and inferior vena cava) to pass through them. To avoid the blood vessels, we first conduct vessel segmentation through the voxel value thresholding [16]. The segmented vessel mask is given by the following equation: + +$$ +v (x, y, z) = \left\{ \begin{array}{l} 1, f ^ {\prime} (x, y, z) > T, l (x, y, z) = 1 \\ 0, \text {o t h e r w i s e} \end{array} , \right. \tag {1} +$$ + +where $f'(x,y,z)$ is the smoothed CT scan, $f'(x,y,z) = f(x,y,z) \otimes g(x,y,z;\sigma_a)$ , by applying a Gaussian filter $g(x,y,z;\sigma_a)$ with standard deviation $\sigma_a$ to the original CT scans $f(x,y,z)$ ; $\otimes$ is the standard image filtering operator. Smoothing can effectively eliminate noise caused by CT reconstruction. The threshold $T$ is set to a value slightly greater than the mean Hounsfield Unit (HU) of the liver. + +$$ +T = \overline {{f (x , y , z) \odot l (x , y , z)}} + b, \tag {2} +$$ + +where $l(x,y,z)$ is the liver mask (background $\equiv 0$ , liver $= 1$ - $\odot$ is point-wise multiplication, and $b$ is a hyperparameter. + +With the vessel mask, one can detect whether a chosen location is at risk of making a tumor collide with vessels. After proposing a random location $(X,Y,Z) \in \{x,y,z \mid l(x,y,z) = 1\}$ , we conduct the collision detection by judging whether there are blood vessels within the range of tumor radius $r$ . If $\exists v(x,y,z) = 1, \forall x \in [X - r,X + r]$ , $y \in [Y - r,Y + r]$ , $z \in [Z - r,Z + r]$ , there is a risk of collision, so the location needs to be re-selected. This process iterates until a tumor location $(x_t,y_t,z_t)$ without collision is found. With the desirable tumor location, we are able to generate the tumor texture and shape. + +Texture generation. The HU values of liver and tumor textures follow the Gaussian distributions. To obtain realistic tumor textures, we first generate a 3D Gaussian noise with + +![](images/bccd8d0cce9a76b64823110ce9ffc09b0bff95cba3eab064dbd1d77156001f42.jpg) +Figure 3. Liver tumor generation. After randomly selecting a location that avoids the vessels, we generate a Gaussian texture and deformed ellipsoidal shape for a tumor. Then, the texture and shape are combined and placed in the selected location. In addition, we take another two post-processing steps to make a generated tumor more realistic: (1) tumor edge expansion by local scaling warping; (2) capsular generation by brightening the tumor edge. Four steps, in light green, are only used for Visual Turing Test (not for training). + +the predefined mean HU intensity $\mu_t$ and the same standard deviation $\sigma_p$ as the hepatic parenchyma (the liver area excluding vessels), $T(x,y,z) \sim \mathcal{N}(\mu_t, \sigma_p)$ . Since the random Gaussian noise is usually too sharp as the texture for the tumor, we soften the texture by scaling it up with spline interpolation of the order 3 (cubic interpolation) on $x, y, z$ directions. The scaled-up texture is denoted as $T'(x,y,z)$ in this work, we want it exhibits graininess close to the hepatic parenchyma. The scaling factor $\eta \in [1,\infty)$ determines how rough the generated grain feels. $\eta = 1$ means the Gaussian texture is not scaled, resulting in large value fluctuation between adjacent voxels. Larger $\eta$ brings greater graininess, which may be similar to the real tumor texture. Finally, considering the tomography imaging quality, we further blur the texture with Gaussian filter $g(x,y,z; \sigma_b)$ + +$$ +T ^ {\prime \prime} (x, y, z) = T ^ {\prime} (x, y, z) \otimes g (x, y, z; \sigma_ {b}), \tag {3} +$$ + +where $\sigma_{b}$ is the standard deviation. After blurring, the texture resembles those generated by real imaging. + +Shape generation. Most tumors grow from the centers and gradually swell, making small tumors (i.e., $r < 20mm$ ) nearly spherical. This motivates us to generate tumor-like shapes with ellipsoids. We randomly sample the half-axis lengths of the ellipsoid for $x, y, z$ directions from a uniform distribution $U(0.75r, 1.25r)$ , and place the generated ellipsoid mask centered at $(x_t, y_t, z_t)$ . For a generated ellipsoid tumor mask $t(x, y, z)$ (background=0, tumor=1), and with the same shape as the scanning volume $f(x, y, z)$ , elastic deformations [45, 48], controlled by $\sigma_e$ , are applied to enrich its diversity. The deformed tumor mask is more similar to the naturally grown tumors in appearance than simple ellipsoids. In addition, it can also improve the model's robustness by learning the shape-semantic invariance. The deformed tumor mask is denoted as $t'(x, y, z)$ . In order to make the transition between the generated tumor and the surrounding liver parenchyma more natural, we finally blur the mask by applying a Gaussian filter $g(x, y, z; \sigma_c)$ with + +the standard deviation $\sigma_{c}$ . To be more specifically, we obtain blur shape $t''(x,y,z) = t'(x,y,z)\otimes g(x,y,z;\sigma_c)$ . + +Post-processing. The first step of post-processing is placing the tumor on the scanning volume $f(x,y,z)$ and corresponding liver mask $l(x,y,z)$ . Assuming the tumor mask array $t''(x,y,z)$ and the texture array $T''(x,y,z)$ have the same shape as $f(x,y,z)$ and $l(x,y,z)$ . We can obtain new scanning volume with tumor through equation + +$$ +f ^ {\prime} (x, y, z) = \left(1 - t ^ {\prime \prime} (x, y, z)\right) \odot f (x, y, z) + \tag {4} +$$ + +$$ +t ^ {\prime \prime} (x, y, z) \odot T ^ {\prime \prime} (x, y, z). +$$ + +For the new mask with the tumor (bg=0,liver=1,tumor=2), it can be synthesized with $l'(x,y,z) = l(x,y,z) + t''(x,y,z)$ . After placing the tumor, we adopt another two steps to make the generated tumor more realistic to medical professionals. They aim to simulate mass effect and the capsule appearance, respectively. Mass effect means the expanding tumor pushes its surrounding tissue apart. If the tumor grows large enough, it will compress the surrounding blood vessels to make them bend, or even cause the edge of the nearby liver to bulge. Local scaling warping [18] is chosen in this work to implement mass effect. It remaps pixels in a circle to be nearer to the circumference. For a pixel with a distance $\gamma$ to the circle center, the remapped pixel distance $\gamma'$ is + +$$ +\gamma^ {\prime} = \left(1 - \left(1 - \frac {\gamma}{\gamma_ {m a x}}\right) ^ {2} \cdot \frac {I}{1 0 0}\right) \cdot \gamma , \tag {5} +$$ + +where $\gamma_{max}$ is the radius of the expanded circular area, $I\in [0,100]$ is a hyper-parameter for controlling the expansion intensity. Larger $I$ leads to stronger warping. Note that when $I = 0$ , the remapping reduces to the identity function $\gamma^{\prime} = \gamma$ . The remapping procedure is conducted on both scanning and mask volumes. After warping, they are named $f^{\prime \prime}(x,y,z)$ and $l^{\prime \prime}(x,y,z)$ . The latter one (liver/tumor segmentation label) is now ready for the subsequent training. + +
parametervalueparametervalue
σa0.5 + 0.025σpμtU(30,μp-10)
σb0.6ηU(1.1,1.5)
σcU(0.6,1.2)γmax1.3r
σd0.8I30
b15(lb,ub)(0.4,0.7)
d120
+ +Finally, we simulate the capsule appearance by brightening the tumor edge. The edge area can be obtained by + +$$ +e (x, y, z) = \left\{ \begin{array}{l} 1, t ^ {\prime \prime} (x, y, z) \in [ l b, u b ] \\ 0, \text {o t h e r w i s e} \end{array} , \right. \tag {6} +$$ + +where $lb$ and $ub$ are the lower bound and upper bound for filtering the edge from tumor mask. Then we increase HU intensity of the blurred edge area to simulate the capsule + +$$ +e ^ {\prime} (x, y, z) = e (x, y, z) \otimes g (x, y, z; \sigma_ {d}), \tag {7} +$$ + +$$ +f ^ {\prime \prime \prime} (x, y, z) = f ^ {\prime \prime} (x, y, z) + d \cdot e (x, y, z), \tag {8} +$$ + +where $d$ is the pre-defined HU intensity difference between a tumor and its capsule. The new scanning volume $f^{\prime \prime \prime}(x,y,z)$ is now ready for training or Turing test. The parameters we use are shown in Table 1. Visualization examples can be found in Appendix Figures 8-10. + +# 3.2. Clinical Knowledge about Liver Tumors + +This work focuses on generating hepatocellular carcinomas (tumor grown from liver cells). After the contrast injection, the clinical examination process of liver is divided into three phases, arterial phase (30s after injection), portal venous phase (60-70s after injection), and delay phase (3min after injection). Typically, only the first two phases are used for detecting hepatocellular carcinomas, and the tumor HU intensity value in different stages distributes differently. The mean attenuation measurement of the lesions in the hepatic arterial phase was 111 HU (range, 32-207 HU), and it decreased in the portal venous phase to a mean of 106 HU (range, 36-162 HU). There was a mean difference of 26 HU (range, -44 to 146 HU) between the lesion and liver in the arterial phase. On average, the hepatocellular carcinomas measured 11 HU (range, -98 to 61 HU) less than the adjacent liver parenchyma in the portal venous phase [32]. The distributional characteristics help us determine the generated mean tumor HU values. + +The location, shape, and number of tumors depend on how severe the hepatocellular carcinomas are according to the standardized guidance of the Liver Imaging Reporting + +Table 1. Hyper-parameters. $\mu_p, \sigma_p$ are the mean and standard deviation of the hepatic parenchyma. The values are adjusted by (1) feedback from clinicians based on the clinical prior knowledge about liver tumors ( $\S 3.2$ ) and (2) visual assessment between the real and synthetic tumors ( $\S 5.1$ ). + +
junior professionalsenior professional
real (P)synt (N)real (P)synt (N)
truthreal (P)515102
synt (N)218712
+ +1The junior professional achieves an Accuracy, Sensitivity, and Specificity of 26.5%, 27.6%, and 25.0%. One CT scan is marked unsure. +2The senior professional achieves an Accuracy, Sensitivity, and Specificity of $71.0\%$ $63.2\%$ ,and $83.3\%$ . 19 CT scans are marked unsure. + +Table 2. Results of Visual Turing Test. The test has been performed on two medical professionals with 6-year and 15-year experience. Each professional is given 50 CT scans, some of which contain real tumors and the others contain synthetic ones. The professional can mark each CT scan as real, synthetic, or unsure. "Synt" denotes synthetic tumors, $P$ and $N$ indicate positive and negative classes for computing Sensitivity and Specificity. + +and Data System (LI-RADS) [42]. Milder carcinomas usually lead to smaller, fewer spherical lesions. Only one small tumor emerges in most cases. While multi-focal lesions, which means scattered small tumors, only appear in seldom cases. Severe carcinomas usually present a satellite lesion, a large lesion surrounded by a cluster of small lesions. The large central lesion also takes on a more irregular shape than small lesions. And also, larger tumors usually display evident mass effects, accompanied by capsule appearances that separate the tumor from the liver parenchyma. + +# 4. Experiments + +Datasets. Detailed per-voxel annotations for liver tumors are provided in LiTS [5]. The volume of liver tumors ranges from $38\mathrm{mm}^3$ to $349~\mathrm{cm}^3$ , and the radius of tumors is in the range of [2, 44]mm. We perform 5-fold cross-validation, following the same split as in Tang et al. [55]. An AI model (e.g. U-Net) is trained on 101 CT scans with annotated liver and liver tumors. For comparison, a dataset of 116 CT scans with healthy livers is assembled from CHAOS [28] (20 CT scans), BTCV [31] (47 CT scans), Pancreas-CT [50] (38 CT scans) and health subjects in LiTS (11 CT scans). We then generate tumors in these scans on the fly, resulting in enormous image-label pairs of synthetic tumors for training the AI model. We generate five levels of tumor sizes for model training; the parameters and examples can be found in Appendix Table 6 and Figure 11. + +Evaluation metrics. Tumor segmentation performance was evaluated by Dice similarity coefficient (DSC) and Normalized Surface Dice (NSD) with $2\mathrm{mm}$ tolerance; tumor detection performance was evaluated by Sensitivity and Specificity. For all the metrics above, $95\%$ CIs were calculated and the $p$ -value cutoff of less than 0.05 was used for defining statistical significance. + +Implementation. Our codes are implemented based on the MONAI $^2$ framework for both U-Net and Swin UN- + +
tumorsmethodarchitecturelabeled / unlabeled CTsDSC (%) [95% CI]NSD (%) [95% CI]
nonePatchCore [51]Wide-Resnet50-2 [66]0 / 11615.97 [11.86–20.09]16.43 [10.42–22.44]
nonef-AnoGAN [53]Customized [3]0 / 11619.00 [13.88–24.11]16.94 [11.97–21.91]
noneVAE [30]Customized [3]0 / 11624.63 [19.83–29.44]23.63 [18.44–28.83]
syntYao et al. [63]U-Net [48]0 / 11632.79 [28.66–36.92]31.28 [26.87–35.70]
realfully-supervisedU-Net101 / 057.51 [52.24–62.79]58.04 [52.56–63.52]
syntlabel-free (ours)U-Net0 / 11659.77 [54.54–64.99]61.29 [56.12–66.47]
+ +Table 3. Comparison with state-of-the-art methods, 5-fold cross-validation. We compare our methods with other unsupervised anomaly segmentation baselines, tumor synthesis strategies, and fully-supervised methods. Our method significantly outperforms all other state-of-the-art unsupervised baseline methods and even surpasses the fully-supervised method with detailed pixel-wise annotation. + +ETR. Input images are clipped with the window range of [-21,189] and then normalized to have zero mean and unit standard deviation. Random patches of $96 \times 96 \times 96$ were cropped from 3D image volumes during training. All models are trained for 4,000 epochs, and the base learning rate is 0.0002. The batch size is two per GPU. We adopt the linear warmup strategy and the cosine annealing learning rate schedule. For inference, we use the sliding window strategy by setting the overlapping area ratio to 0.75. + +# 5. Results & Discussion + +Using 116 CT scans from Pancreas-CT, CHAOS, and BTCV with our label-free tumor generator, we outperformed all those methods on the LiTS benchmark, wherein previous methods used 101 CT scans and annotations from LiTS. + +# 5.1. Clinical Validation using Visual Turing Test + +We conduct the Visual Turing Test [15] on 50 CT scans, where 20 scans are with real tumors from LiTS, and the remaining 30 scans are healthy livers from WORD [40] with synthetic tumors. Two professionals with different experience levels take part in this test. They can inspect each sample in 3D view, which means continuous variation of slice sequence can be observed by scrolling the mouse. This is an important setting for the test because some important tumor characteristics are not obvious in a 2D view (e.g., vessel collision). In the test, professionals can label each sample as real, synthetic or unsure. When calculating the performance metrics, only the samples with definite results are counted. + +The testing results are shown in Table 2. For junior professionals with 6-year experience, definite judgments of 49 out of 50 samples are given. All of the accuracy, sensitivity, and specificity are below $30\%$ , which means the generated samples succeed in confusing the junior professional. In particular, the sensitivity of $27.6\%$ means that the rest $72.4\%$ synthetic samples are mistakenly regarded as real samples. The result verifies that our synthesis method can generate realistic tumors. According to the results given by the senior professional with 15-year experience, $36.8\%$ synthetic samples seemed to be real, indicating that nearly half of the generated samples can tease senior professionals. Noteworthy, the senior professional only gives 19 judg- + +ments among all 30 synthetic samples. Adding up misjudged samples and uncertain samples, a total of 18 out of 30 generated samples have confused him/her. + +# 5.2. Comparison with State-of-the-art Methods + +We compare our label-free tumor synthesis strategy with several prominent unsupervised tumor segmentation methods designed for both natural and medical images, such as PatchCore [51], f-AnoGAN [53], VAE [3], and the method proposed by Yao et al. [63]. To enhance the performance of these baseline methods, we focus solely on the liver region for training and testing to minimize noise caused by extraneous information. Table 3 shows that all the previous unsupervised methods exhibit suboptimal performance in segmenting real liver tumors. In contrast, our label-free tumor synthesis—a novel approach to unsupervised tumor segmentation—significantly outperforms all these methods, achieving a DSC of $59.77\%$ and an NSD of $61.29\%$ . On the other hand, the model trained on real tumors using fully supervised learning achieves a DSC of $57.51\%$ and an NSD of $58.04\%$ . These results highlight the potential of a paradigm shift from label-intensive to label-free tumor segmentation. + +# 5.3. Generalization to Different Models and Data + +We verify the generalizability of synthetic tumors using Swin UNETR [20], including its Tiny, Small, and Base variants. Figure 4 shows that the model trained on real tumors performs slightly better than that on synthetic tumors, but there is no statistical difference between the two results as the $p$ -value is greater than 0.05. In addition to evaluating the models on the LiTS dataset, we assess their domain generalization ability using data from other datasets (i.e., MSD-Pancreas, MSD-Spleen, MSD-Colon). As shown in the right panel of Figure 4, our model trained with healthy data collected from 3 different datasets shows better robustness than the model trained on real data only from LiTS, + +![](images/acd1c70ce7ca7f4e3aca5bb17376701925c04bf24104cc14b31dae718b9a2e6e.jpg) +Figure 4. Generalization to different models and data. Training U-Net on synthetic liver tumors outperforms as well as training it on real tumors with per-voxel annotation (see Table 3). We further examine this observation using Swin UNETR [55], including its variance of Tiny (Param = 4.0M), Small (Param = 15.7M), and Base (Param = 62.1M). The DSC, NSD, and Sensitivity scores are evaluated on the LiTS datasets. The detailed results of 5-fold cross-validation are reported in Appendix Table 5. Moreover, the model trained on synthetic tumors can also be generalized to CT scans with the healthy liver across datasets (e.g. MSD-Pancreas, MSD-Spleen, and MSD-Colon [2]), generating fewer false positives and yielding a higher Specificity compared with the model trained on real tumors. + +![](images/9b7a049c0ee2b4a4b9c16012dbca91b2ae888121b0e41fce5237d5fb730ded05.jpg) + +![](images/7ef46a8ad207f9b6dae4481bcd50f56f7d8786f54672c16b20bbe8bb8cd212f6.jpg) + +![](images/2dc891781a030f9c32a21e0624e82f54b2140b138bb4581e79681f22933a978e.jpg) + +![](images/f226e584f863496fa1b364d1cd1df314b3adedd9266c7130f6d6a0208e6b7f73.jpg) + +![](images/bcdc686bf2c103371b12dc6af136a8fe1b6a985896188e58ca33a386f5b7cbb8.jpg) +Figure 5. Small tumor detection. The upper panel presents two examples of small tumors and the segmentation results. For both models trained on real and synthetic tumors, the false negatives are mostly smaller than $10\mathrm{mm}$ . The lower panel presents the tumor detection rate. The model trained on synthetic tumors could detect tumors as small as $2\mathrm{mm}$ . + +while achieving much higher Specificity on the three external datasets. It is noteworthy that higher Specificity (fewer false positives) is crucial in clinical applications as it reduces the number of patients subjected to invasive diagnostic procedures and their associated costs [7,36,61]. + +# 5.4. Potential in Small Tumor Detection + +Early detection of small tumors is essential for prompt cancer diagnosis, but such cases are scarce in real datasets because most patients remain asymptomatic during the early stages. AI models trained on these datasets exhibit reduced detection sensitivity for small tumors (radius $< 5\mathrm{mm}$ ) compared with larger tumors (radius $>5\mathrm{mm}$ ), displaying sensitivities of $52.0\%$ and $91.6\%$ , respectively. + +Thus, an advanced tumor generator could create synthetic data containing various tumor sizes for training and testing models, addressing the size imbalance issue found in real data. The lower panel of Figure 5 presents quantitative tumor detection performance stratified by tumor size, and the upper panel presents two cases with small tumors for qualitative comparison. Evidently, AI models (trained solely on synthetic data) outperform those trained on real tumors in detecting and segmenting small tumors in the liver. The results indicate that the generation of copious amounts of synthetic small tumors can improve the efficacy of models in detecting real small tumors, thereby playing a crucial role in the early detection of cancer. + +# 5.5. Controllable Robustness Benchmark + +Standard evaluation in medical imaging is limited to determining the effectiveness of AI in detecting tumors. This is because the number of annotated tumors in the existing test datasets is not big enough to be representative of the tumors that occur in real organs and, in particular, contains only a limited number of very small tumors. We show that synthetic tumors can serve as an accessible and comprehensive source for rigorously evaluating AI's performance in detecting tumors at a variety of different sizes and locations with the organs. To be specific, our tumor generator can synthesize liver tumors varying in five dimensions, i.e. location, size, shape, intensity, and texture, by tuning hyperparameters in the tumor generation pipeline. Taking five different options in each dimension, our tumor generator could create $25(5\times 5)$ variants for each single CT scan. Generating a large number of synthetic tumors during testing enables us to find failure scenarios of current AI models. After locating the worst cases of AI, we can synthesize and include worst-case tumors in the training set and fine-tune AI algorithms. Figure 6 illustrates the out-of-distribution (o.o.d.) benchmark created by synthetic tumors, wherein + +![](images/f392a587b03c869a4a7c0d2384530146cb40560f1b216601ad51b8b221aadd09.jpg) +Figure 6. Controllable benchmark for robust evaluation. UNet++ [72], nnU-Net [26], and Swin UNETR [55] are very competitive segmentation models in the medical domain. However, their limitations of tumor segmentation are not fully revealed due to the lack of sufficient testing images (only 70 CT scans are available for testing in MSD Task03 [1]). On the contrary, synthetic tumors enable us to perform an extensive evaluation of these models in segmenting liver tumors that vary from different conditions, i.e. shape, size, texture, intensity, and location. We downloaded the checkpoints of these models trained on LiTS, and evaluated them on synthetic tumors. Synthetic tumors were generated using different parameters, where $\mu$ and $\sigma$ denote mean and standard deviation, respectively. Our findings indicate that these public models exhibit robustness to variations in tumor shape, location, and texture, but they are sensitive to tumor size and intensity. Specifically, these models are prone to errors when encountering tumors that are smaller or larger than those in the training set, or when faced with differing Hounsfield Unit (HU) values, which may be attributable to contrast enhancement. + +
tiny sizeelastic deformationedge blurringall tumors DSC (%)small tumors det Sen. (%)
✓43.926.4
✓✓47.151.3
✓✓50.354.1
✓✓52.633.4
✓✓✓55.161.8
+ +Table 4. Ablation study on shape generation. The quality of synthesized tumors influences model performance to a certain degree, emphasizing the importance of each component in our proposed method (§3; Figure 3). The quality assessment of generated tumors is in Appendix Figure 11. Moreover, generating tiny synthetic tumors positively impacts the sensitivity of small tumors. + +we evaluate several state-of-the-art models (trained on public datasets). These models show good robustness in the shape, location, and texture dimensions but are sensitive to tumors of extreme sizes and intensities. + +# 5.6. Ablation Study on Shape Generation + +To show the importance of each step in tumor generation, we design ablation studies focusing on shape generation and synthesizing small tumors. We evaluate the models trained with different incomplete settings of synthetic strategies on two aspects: all tumor segmentation and small tumor detection. As shown in Table 4, the performance would be much poorer without synthesizing small tumors, edge blurring or elastic deformation in the shape generation. The reasons are simple: (1) without elastic deformation and edge blurring steps for shape generation (shown in Figure 3), the syn + +thetic tumors can be extremely unrealistic (i.e. the edge is sharp and shape can only be ellipsoid). Several examples are provided in Appendix Figure 12. (2) The model doesn't have the generalization ability to small tumors (radius $< 5\mathrm{mm}$ ) when the training set does not have them. + +# 6. Conclusion + +In this paper, we have developed an effective strategy to synthesize liver tumors. With zero manual annotation, we verify that the AI model trained on synthetic tumors can perform similarly to the ones trained on real tumors in the LiTS dataset (which took months to create). This reveals the great potential for the use of synthesis tumors to train AI models on larger-scale healthy CT datasets (which are much easier to obtain than CT scans with liver tumors). Furthermore, synthetic tumors allow us to assess AI's capability of detecting tumors of varying locations, sizes, shapes, intensities, textures, and stages in CT scans. In the future, we will consider generative adversarial nets (GANs) [17,19], Diffusion Models [22] and possibly improved with 3D geometry models like NeRF [43] to generate better tumor texture. + +Acknowledgements. This work was supported by the Lustgarten Foundation for Pancreatic Cancer Research and partially by the Patrick J. McGovern Foundation Award. We appreciate the effort of the MONAI Team to provide open-source code for the community. We thank Yucheng Tang, Huimiao Chen, Bowen Li, Jessica Han, and Wenxuan Li for their constructive suggestions; thank Camille Torrico and Alexa Delaney for improving the writing of this paper. 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Springer, 2019. 1 \ No newline at end of file diff --git a/2023/Label-Free Liver Tumor Segmentation/images.zip b/2023/Label-Free Liver Tumor Segmentation/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..a75ee793ec9f32dfb50a5c7ca4da643e042817fb --- /dev/null +++ b/2023/Label-Free Liver Tumor Segmentation/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:44d245b7bec8c95e356c4ead42bcf75064845ddbec9df5a44d69e2d45c620384 +size 570642 diff --git a/2023/Label-Free Liver Tumor Segmentation/layout.json b/2023/Label-Free Liver Tumor Segmentation/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..a826c0cd2a105dca10438e760b5abae2c1ce8032 --- /dev/null +++ b/2023/Label-Free Liver Tumor Segmentation/layout.json @@ -0,0 +1,9125 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 176, + 103, + 416, + 120 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 176, + 103, + 416, + 120 + ], + "spans": [ + { + "bbox": [ + 176, + 103, + 416, + 120 + ], + "type": "text", + "content": "Label-Free Liver Tumor Segmentation" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 150, + 142, + 442, + 170 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 150, + 142, + 442, + 170 + ], + "spans": [ + { + "bbox": [ + 150, + 142, + 442, + 170 + ], + "type": "text", + "content": "Qixin Hu1 Yixiong Chen2 Junfei Xiao3 Shuwen Sun4 Jieneng Chen3 Alan Yuille3 Zongwei Zhou3,*" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 150, + 178, + 442, + 234 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 150, + 178, + 442, + 234 + ], + "spans": [ + { + "bbox": [ + 150, + 178, + 442, + 234 + ], + "type": "text", + "content": "1Huazhong University of Science and Technology \n2The Chinese University of Hong Kong – Shenzhen \n3Johns Hopkins University \n4The First Affiliated Hospital of Nanjing Medical University" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 151, + 240, + 437, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 151, + 240, + 437, + 251 + ], + "spans": [ + { + "bbox": [ + 151, + 240, + 437, + 251 + ], + "type": "text", + "content": "Code and Visual Turing Test: https://github.com/MrGiovanni/SyntheticTumors" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 143, + 280, + 190, + 291 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 280, + 190, + 291 + ], + "spans": [ + { + "bbox": [ + 143, + 280, + 190, + 291 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 305, + 287, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 305, + 287, + 532 + ], + "spans": [ + { + "bbox": [ + 47, + 305, + 287, + 532 + ], + "type": "text", + "content": "We demonstrate that AI models can accurately segment liver tumors without the need for manual annotation by using synthetic tumors in CT scans. Our synthetic tumors have two intriguing advantages: (I) realistic in shape and texture, which even medical professionals can confuse with real tumors; (II) effective for training AI models, which can perform liver tumor segmentation similarly to the model trained on real tumors—this result is exciting because no existing work, using synthetic tumors only, has thus far reached a similar or even close performance to real tumors. This result also implies that manual efforts for annotating tumors voxel by voxel (which took years to create) can be significantly reduced in the future. Moreover, our synthetic tumors can automatically generate many examples of small (or even tiny) synthetic tumors and have the potential to improve the success rate of detecting small liver tumors, which is critical for detecting the early stages of cancer. In addition to enriching the training data, our synthesizing strategy also enables us to rigorously assess the AI robustness." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 555, + 128, + 566 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 555, + 128, + 566 + ], + "spans": [ + { + "bbox": [ + 47, + 555, + 128, + 566 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 575, + 287, + 695 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 575, + 287, + 695 + ], + "spans": [ + { + "bbox": [ + 47, + 575, + 287, + 695 + ], + "type": "text", + "content": "Artificial intelligence (AI) has dominated medical image segmentation [21,26,73-75], but training an AI model (e.g., U-Net [48]) often requires a large number of annotations. Annotating medical images is not only expensive and time-consuming, but also requires extensive medical expertise, and sometimes needs the assistance of radiology reports and biopsy results to achieve annotation accuracy [12, 52, 59, 69-71]. Due to its high annotation cost, only roughly 200 CT scans with annotated liver tumors are publicly available (provided by LiTS [5]) for training and testing models." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 280, + 546, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 280, + 546, + 579 + ], + "spans": [ + { + "bbox": [ + 305, + 280, + 546, + 579 + ], + "type": "text", + "content": "To minimize annotation expenses, generating synthetic tumors is an emerging research topic. Early attempts include, but only limited to, synthesizing COVID-19 infections [41,63], lung nodules [19] abdominal tumors [27], diabetic lesions [57], and brain tumors [60]. However, the synthetic tumors in those studies appear very different from the real tumors; due to this, AI models trained using synthetic tumors perform significantly worse than those trained using real tumors. What makes synthesizing tumors so hard? There are several important factors: shape, intensity, size, location, and texture. In this paper, we handcraft a strategy to synthesize liver tumors in abdominal CT scans. Our key novelties include (i) location without collision with vessels, (ii) texture with scaled-up Gaussian noise, and (iii) shape generated from distorted ellipsoids. These three aspects are proposed according to the clinical knowledge of liver tumors (detailed in §3.2). The resulting synthetic tumors are realistic—even medical professionals usually confuse them with real tumors in the visual examination (Figure 1; Table 2). In addition, the model trained on our synthetic tumors achieves a Dice Similarity Coefficient (DSC) of " + }, + { + "bbox": [ + 305, + 280, + 546, + 579 + ], + "type": "inline_equation", + "content": "59.81\\%" + }, + { + "bbox": [ + 305, + 280, + 546, + 579 + ], + "type": "text", + "content": " for segmenting real liver tumors, whereas AI trained on real tumors obtains a DSC of " + }, + { + "bbox": [ + 305, + 280, + 546, + 579 + ], + "type": "inline_equation", + "content": "57.63\\%" + }, + { + "bbox": [ + 305, + 280, + 546, + 579 + ], + "type": "text", + "content": " (Figure 2), showing that synthetic tumors have the potential to be used as an alternative to real tumors in training AI models." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 581, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 581, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 581, + 546, + 713 + ], + "type": "text", + "content": "These results are exciting because using synthetic tumors only, no previous work has thus far reached a similar (or even close) performance to the model trained on real tumors [24]. Moreover, our synthesizing strategy can exhaustively generate tumors with desired locations, sizes, shapes, textures, and intensities, which are not limited to a fixed finite-size training set (the well-known limitation of the conventional training paradigm [65]). For example, it is hard to collect sufficient training examples with small tumors. It is because early-stage tumors may not cause symptoms, which can delay detection, and these tumors are rela" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 57, + 7, + 102, + 38 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 7, + 102, + 38 + ], + "spans": [ + { + "bbox": [ + 57, + 7, + 102, + 38 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 136, + 5, + 487, + 40 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 136, + 5, + 487, + 40 + ], + "spans": [ + { + "bbox": [ + 136, + 5, + 487, + 40 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 247, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 247, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 247, + 712 + ], + "type": "text", + "content": "*Corresponding author: Zongwei Zhou (zzhou82@jh.edu)" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 279, + 738, + 298, + 747 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 738, + 298, + 747 + ], + "spans": [ + { + "bbox": [ + 279, + 738, + 298, + 747 + ], + "type": "text", + "content": "7422" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 595, + 841 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 68, + 213, + 239 + ], + "blocks": [ + { + "bbox": [ + 48, + 68, + 213, + 239 + ], + "lines": [ + { + "bbox": [ + 48, + 68, + 213, + 239 + ], + "spans": [ + { + "bbox": [ + 48, + 68, + 213, + 239 + ], + "type": "image", + "image_path": "cf4cc99d4fa6b841d334d1bbfcf9e2a3a4c60d7cc68b9c0e7cde4218b878eb9d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 248, + 546, + 306 + ], + "lines": [ + { + "bbox": [ + 46, + 248, + 546, + 306 + ], + "spans": [ + { + "bbox": [ + 46, + 248, + 546, + 306 + ], + "type": "text", + "content": "Figure 1. [Better viewed in color and zoomed in for details] Can you tell which liver tumors are real and which are fake? The answers are provided in Appendix. We have recruited two medical professionals with at least six years of experience to distinguish fake tumors, generated by our method, from the real ones (namely, Visual Turing Test). Our synthetic tumors have passed the Visual Turing Test on both two medical professionals (<50% fake tumors were picked out). More importantly, using our label-free synthetic tumors, AI models can segment real tumors with performance similar to the AI models trained on real tumors with expensive, detailed, per-voxel annotation." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 215, + 68, + 379, + 239 + ], + "blocks": [ + { + "bbox": [ + 215, + 68, + 379, + 239 + ], + "lines": [ + { + "bbox": [ + 215, + 68, + 379, + 239 + ], + "spans": [ + { + "bbox": [ + 215, + 68, + 379, + 239 + ], + "type": "image", + "image_path": "459d7d9eeec18ffd4d652325cc5aff60b191ec6ccdc81eb771dda2a319d2fc3c.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 380, + 68, + 545, + 239 + ], + "blocks": [ + { + "bbox": [ + 380, + 68, + 545, + 239 + ], + "lines": [ + { + "bbox": [ + 380, + 68, + 545, + 239 + ], + "spans": [ + { + "bbox": [ + 380, + 68, + 545, + 239 + ], + "type": "image", + "image_path": "c9afb121b735b92dcd609dd30719b360158b9db12c091532460f3e457ae94cc5.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 325, + 287, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 325, + 287, + 396 + ], + "spans": [ + { + "bbox": [ + 47, + 325, + 287, + 396 + ], + "type": "text", + "content": "tively small and exhibit subtle abnormal textures that make it difficult for radiologists to manually delineate the tumor boundaries. In contrast, our synthesis strategy can generate a large number of examples featuring small tumors. The key contribution of ours is a synthetic tumor generator, which offers five advantages as summarized below." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 54, + 406, + 287, + 713 + ], + "type": "list", + "angle": 0, + "index": 10, + "blocks": [ + { + "bbox": [ + 55, + 406, + 287, + 455 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 406, + 287, + 455 + ], + "spans": [ + { + "bbox": [ + 55, + 406, + 287, + 455 + ], + "type": "text", + "content": "1. The synthesis strategy embeds medical knowledge into an executable program, enabling the generation of realistic tumors through the collaboration of radiologists and computer scientists (§5.1; Table 2; Figure 3)." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 54, + 462, + 287, + 511 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 462, + 287, + 511 + ], + "spans": [ + { + "bbox": [ + 54, + 462, + 287, + 511 + ], + "type": "text", + "content": "2. The entire training stage requires no annotation cost, and the resulting model significantly outperforms previous unsupervised anomaly segmentation approaches and tumor synthesis strategies (§5.2; Table 3)." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 54, + 518, + 287, + 577 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 518, + 287, + 577 + ], + "spans": [ + { + "bbox": [ + 54, + 518, + 287, + 577 + ], + "type": "text", + "content": "3. The AI model trained on synthetic tumors can achieve similar performance to AI models trained on real tumors with per-voxel annotation in real tumors segmentation, and can be generalized to CT scans with healthy liver and scans from other hospitals (§5.3; Figure 4)." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 54, + 585, + 287, + 645 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 585, + 287, + 645 + ], + "spans": [ + { + "bbox": [ + 54, + 585, + 287, + 645 + ], + "type": "text", + "content": "4. The synthesis strategy can generate a variety of tumors for model training, including those at small, medium, and large scales, and therefore have the potential to detect small tumors and facilitate the early detection of liver cancer (§5.4; Figure 5)." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 54, + 652, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 652, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 54, + 652, + 287, + 713 + ], + "type": "text", + "content": "5. The synthesis strategy allows for straightforward manipulation of parameters such as tumor location, size, texture, shape, and intensity, providing a comprehensive test-bed for evaluating AI models under out-of-distribution scenarios (§5.5; Figure 6)." + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 305, + 325, + 546, + 397 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 325, + 546, + 397 + ], + "spans": [ + { + "bbox": [ + 305, + 325, + 546, + 397 + ], + "type": "text", + "content": "These results have the potential to stimulate a shift in the tumor segmentation training paradigm, as illustrated in Figure 2, from label-intensive to label-free AI development for tumor segmentation. Our ultimate goal is to train AI models for tumor segmentation without using manual annotation—this study makes a significant step towards it." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 411, + 393, + 424 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 411, + 393, + 424 + ], + "spans": [ + { + "bbox": [ + 305, + 411, + 393, + 424 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 433, + 546, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 433, + 546, + 635 + ], + "spans": [ + { + "bbox": [ + 305, + 433, + 546, + 635 + ], + "type": "text", + "content": "Unsupervised anomaly segmentation. Anomaly segmentation is a challenging application area, especially for medical diagnosis [29, 62] and industrial defect detection [4, 25]. Compared with their supervised counterparts, unsupervised methods raises more attention for their low cost and scalability. The general unsupervised anomaly detection setting is to train with normal samples only, without any anomalous data, and no image-level annotation or pixel-level annotation is provided [30, 51, 53]. Under the unsupervised setting, some previous works use self-organizing maps for unsupervised anomaly detection [34, 44] and Huang et al. [25] introduced gradient magnitude similarity and structured similarity index losses in addition to mean square error to compute the loss of image reconstruction. Evidenced in Table 3, our label-free synthetic tumors achieve a significantly better performance in unsupervised tumor segmentation than some of the most recent work in this area." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 641, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 641, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 641, + 546, + 713 + ], + "type": "text", + "content": "Tumor synthesis. Successful works about tumor synthesis include polyp detection from colonoscopy videos [54], COVID-19 detection from Chest CT [41, 63], diabetic lesion detection from retinal images [57], cancer detection from fluorescence microscopy images [23], and brain tumor detection from MRI [60]. However, these works are" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 738, + 298, + 748 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 738, + 298, + 748 + ], + "spans": [ + { + "bbox": [ + 279, + 738, + 298, + 748 + ], + "type": "text", + "content": "7423" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 595, + 841 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 68, + 285, + 218 + ], + "blocks": [ + { + "bbox": [ + 48, + 68, + 285, + 218 + ], + "lines": [ + { + "bbox": [ + 48, + 68, + 285, + 218 + ], + "spans": [ + { + "bbox": [ + 48, + 68, + 285, + 218 + ], + "type": "image", + "image_path": "5d9456019ee18e458ad32a53f99543dac400a2e0a9f1ff8c3bd145a7d16b4077.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 226, + 289, + 283 + ], + "lines": [ + { + "bbox": [ + 46, + 226, + 289, + 283 + ], + "spans": [ + { + "bbox": [ + 46, + 226, + 289, + 283 + ], + "type": "text", + "content": "Figure 2. The paradigm shift from label-intensive to label-free tumor segmentation in this work. AI trained on synthetic tumors can segment liver tumors as accurately as AI trained on real tumors. The performance is measured on real tumors using Dice Similarity Coefficient (DSC) and Normalized Surface Distance (NSD)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 302, + 288, + 470 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 302, + 288, + 470 + ], + "spans": [ + { + "bbox": [ + 45, + 302, + 288, + 470 + ], + "type": "text", + "content": "restricted to the types of tumors, and other diseases, that are fairly easy to visually identify in CT scans. Most recently, Zhang et al. [67] synthesized liver and brain tumors for pre-training and adapted the model to tumor segmentation within the same organ under a low-annotation regime. The manually crafted \"counterfeit\" tumors in the related work appear very differently from real tumors. As a result, AI algorithms, trained on synthetic tumors, may work well in detecting synthetic tumors in the test set but fail to recognize the actual tumors (evidenced in Table 3). We tackle these limitations by integrating radiologists in the tumor synthesis study for feedback (" + }, + { + "bbox": [ + 45, + 302, + 288, + 470 + ], + "type": "inline_equation", + "content": "\\S 3.2" + }, + { + "bbox": [ + 45, + 302, + 288, + 470 + ], + "type": "text", + "content": "). This enables us to understand deeply about tumors, and in turn, benefit in developing AI algorithms to segment them more accurately." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 473, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 473, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 45, + 473, + 287, + 715 + ], + "type": "text", + "content": "Generalization from synthetic to real domains. The problem of domain generalization was introduced [6] for zero-shot adaptation to data with a domain gap. Specifically, the goal is to make a model using data from a single or multiple related source domain(s) while achieving great generalization ability well to any target domain(s) [58, 68]. In this paper, evaluating the model generalization ability on real data is of great importance to justify whether our tumor generator is powerful enough. Domain generalization has been widely studied in multiple computer vision tasks like object recognition [33, 35], semantic segmentation [56, 64] and medical imaging [37, 38]. As deep learning models are data hungry and annotated data are very expensive, how to train a model with synthetic data but generalize well to real data has been targeted in some previous works [8, 9, 13] and some datasets [10, 14, 46, 47, 49] are created for benchmark and further exploring. While previous works focus on preserving the transferable knowledge learned from synthetic data, our paper aims to prove that our tumor generator is powerful enough to generate tumors with reasonable domain gap" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 305, + 72, + 546, + 97 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 546, + 97 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 546, + 97 + ], + "type": "text", + "content": "and that our model has outstanding generalization ability to detect real tumors (detailed in Section 5.3)." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 305, + 107, + 361, + 120 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 107, + 361, + 120 + ], + "spans": [ + { + "bbox": [ + 305, + 107, + 361, + 120 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 127, + 417, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 127, + 417, + 140 + ], + "spans": [ + { + "bbox": [ + 305, + 127, + 417, + 140 + ], + "type": "text", + "content": "3.1. Tumor Generation" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 147, + 546, + 231 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 147, + 546, + 231 + ], + "spans": [ + { + "bbox": [ + 305, + 147, + 546, + 231 + ], + "type": "text", + "content": "To localize the liver, we first apply the pre-trained nnU-Net1 to the CT scans. With a coarse location of the liver available, we then develop a sequence of morphological image-processing operations to synthesize realistic tumors within the liver (see Figure 3). The tumor generation consists of four steps: (1) location selection, (2) texture generation, (3) shape generation, and (4) post-processing." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 233, + 546, + 319 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 233, + 546, + 319 + ], + "spans": [ + { + "bbox": [ + 305, + 233, + 546, + 319 + ], + "type": "text", + "content": "Location selection. The first step is to select a proper location for the tumor. This step is crucial because liver tumors usually do not allow any vessels (e.g., hepatic vein, portal vein, and inferior vena cava) to pass through them. To avoid the blood vessels, we first conduct vessel segmentation through the voxel value thresholding [16]. The segmented vessel mask is given by the following equation:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 327, + 546, + 354 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 327, + 546, + 354 + ], + "spans": [ + { + "bbox": [ + 313, + 327, + 546, + 354 + ], + "type": "interline_equation", + "content": "v (x, y, z) = \\left\\{ \\begin{array}{l} 1, f ^ {\\prime} (x, y, z) > T, l (x, y, z) = 1 \\\\ 0, \\text {o t h e r w i s e} \\end{array} , \\right. \\tag {1}", + "image_path": "f3f5751b8cbb79d99b48cf70038ac6d6fba3460579019727c4f271471d3756eb.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 362, + 546, + 447 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 362, + 546, + 447 + ], + "spans": [ + { + "bbox": [ + 305, + 362, + 546, + 447 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 362, + 546, + 447 + ], + "type": "inline_equation", + "content": "f'(x,y,z)" + }, + { + "bbox": [ + 305, + 362, + 546, + 447 + ], + "type": "text", + "content": " is the smoothed CT scan, " + }, + { + "bbox": [ + 305, + 362, + 546, + 447 + ], + "type": "inline_equation", + "content": "f'(x,y,z) = f(x,y,z) \\otimes g(x,y,z;\\sigma_a)" + }, + { + "bbox": [ + 305, + 362, + 546, + 447 + ], + "type": "text", + "content": ", by applying a Gaussian filter " + }, + { + "bbox": [ + 305, + 362, + 546, + 447 + ], + "type": "inline_equation", + "content": "g(x,y,z;\\sigma_a)" + }, + { + "bbox": [ + 305, + 362, + 546, + 447 + ], + "type": "text", + "content": " with standard deviation " + }, + { + "bbox": [ + 305, + 362, + 546, + 447 + ], + "type": "inline_equation", + "content": "\\sigma_a" + }, + { + "bbox": [ + 305, + 362, + 546, + 447 + ], + "type": "text", + "content": " to the original CT scans " + }, + { + "bbox": [ + 305, + 362, + 546, + 447 + ], + "type": "inline_equation", + "content": "f(x,y,z)" + }, + { + "bbox": [ + 305, + 362, + 546, + 447 + ], + "type": "text", + "content": "; " + }, + { + "bbox": [ + 305, + 362, + 546, + 447 + ], + "type": "inline_equation", + "content": "\\otimes" + }, + { + "bbox": [ + 305, + 362, + 546, + 447 + ], + "type": "text", + "content": " is the standard image filtering operator. Smoothing can effectively eliminate noise caused by CT reconstruction. The threshold " + }, + { + "bbox": [ + 305, + 362, + 546, + 447 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 305, + 362, + 546, + 447 + ], + "type": "text", + "content": " is set to a value slightly greater than the mean Hounsfield Unit (HU) of the liver." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 360, + 455, + 546, + 471 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 360, + 455, + 546, + 471 + ], + "spans": [ + { + "bbox": [ + 360, + 455, + 546, + 471 + ], + "type": "interline_equation", + "content": "T = \\overline {{f (x , y , z) \\odot l (x , y , z)}} + b, \\tag {2}", + "image_path": "a67e0b1956b1816c10cc14b7d1774b001241d08c2b4fb33762b98d72d04d4ce1.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 479, + 544, + 503 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 479, + 544, + 503 + ], + "spans": [ + { + "bbox": [ + 305, + 479, + 544, + 503 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 479, + 544, + 503 + ], + "type": "inline_equation", + "content": "l(x,y,z)" + }, + { + "bbox": [ + 305, + 479, + 544, + 503 + ], + "type": "text", + "content": " is the liver mask (background " + }, + { + "bbox": [ + 305, + 479, + 544, + 503 + ], + "type": "inline_equation", + "content": "\\equiv 0" + }, + { + "bbox": [ + 305, + 479, + 544, + 503 + ], + "type": "text", + "content": " , liver " + }, + { + "bbox": [ + 305, + 479, + 544, + 503 + ], + "type": "inline_equation", + "content": "= 1" + }, + { + "bbox": [ + 305, + 479, + 544, + 503 + ], + "type": "text", + "content": " - " + }, + { + "bbox": [ + 305, + 479, + 544, + 503 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 305, + 479, + 544, + 503 + ], + "type": "text", + "content": " is point-wise multiplication, and " + }, + { + "bbox": [ + 305, + 479, + 544, + 503 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 305, + 479, + 544, + 503 + ], + "type": "text", + "content": " is a hyperparameter." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 503, + 546, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 503, + 546, + 635 + ], + "spans": [ + { + "bbox": [ + 305, + 503, + 546, + 635 + ], + "type": "text", + "content": "With the vessel mask, one can detect whether a chosen location is at risk of making a tumor collide with vessels. After proposing a random location " + }, + { + "bbox": [ + 305, + 503, + 546, + 635 + ], + "type": "inline_equation", + "content": "(X,Y,Z) \\in \\{x,y,z \\mid l(x,y,z) = 1\\}" + }, + { + "bbox": [ + 305, + 503, + 546, + 635 + ], + "type": "text", + "content": ", we conduct the collision detection by judging whether there are blood vessels within the range of tumor radius " + }, + { + "bbox": [ + 305, + 503, + 546, + 635 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 305, + 503, + 546, + 635 + ], + "type": "text", + "content": ". If " + }, + { + "bbox": [ + 305, + 503, + 546, + 635 + ], + "type": "inline_equation", + "content": "\\exists v(x,y,z) = 1, \\forall x \\in [X - r,X + r]" + }, + { + "bbox": [ + 305, + 503, + 546, + 635 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 503, + 546, + 635 + ], + "type": "inline_equation", + "content": "y \\in [Y - r,Y + r]" + }, + { + "bbox": [ + 305, + 503, + 546, + 635 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 503, + 546, + 635 + ], + "type": "inline_equation", + "content": "z \\in [Z - r,Z + r]" + }, + { + "bbox": [ + 305, + 503, + 546, + 635 + ], + "type": "text", + "content": ", there is a risk of collision, so the location needs to be re-selected. This process iterates until a tumor location " + }, + { + "bbox": [ + 305, + 503, + 546, + 635 + ], + "type": "inline_equation", + "content": "(x_t,y_t,z_t)" + }, + { + "bbox": [ + 305, + 503, + 546, + 635 + ], + "type": "text", + "content": " without collision is found. With the desirable tumor location, we are able to generate the tumor texture and shape." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 638, + 546, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 638, + 546, + 675 + ], + "spans": [ + { + "bbox": [ + 305, + 638, + 546, + 675 + ], + "type": "text", + "content": "Texture generation. The HU values of liver and tumor textures follow the Gaussian distributions. To obtain realistic tumor textures, we first generate a 3D Gaussian noise with" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 305, + 682, + 546, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 682, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 682, + 546, + 713 + ], + "type": "text", + "content": "1The off-the-shield, pre-trained nnU-Net [26] for liver segmentation can be downloaded here, which can achieve an average DSC of " + }, + { + "bbox": [ + 305, + 682, + 546, + 713 + ], + "type": "inline_equation", + "content": "95\\%" + }, + { + "bbox": [ + 305, + 682, + 546, + 713 + ], + "type": "text", + "content": " on unseen CT scans (sufficient for a coarse localization of the liver)." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 279, + 738, + 298, + 748 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 738, + 298, + 748 + ], + "spans": [ + { + "bbox": [ + 279, + 738, + 298, + 748 + ], + "type": "text", + "content": "7424" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 595, + 841 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 68, + 546, + 190 + ], + "blocks": [ + { + "bbox": [ + 48, + 68, + 546, + 190 + ], + "lines": [ + { + "bbox": [ + 48, + 68, + 546, + 190 + ], + "spans": [ + { + "bbox": [ + 48, + 68, + 546, + 190 + ], + "type": "image", + "image_path": "bccd8d0cce9a76b64823110ce9ffc09b0bff95cba3eab064dbd1d77156001f42.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 196, + 547, + 243 + ], + "lines": [ + { + "bbox": [ + 46, + 196, + 547, + 243 + ], + "spans": [ + { + "bbox": [ + 46, + 196, + 547, + 243 + ], + "type": "text", + "content": "Figure 3. Liver tumor generation. After randomly selecting a location that avoids the vessels, we generate a Gaussian texture and deformed ellipsoidal shape for a tumor. Then, the texture and shape are combined and placed in the selected location. In addition, we take another two post-processing steps to make a generated tumor more realistic: (1) tumor edge expansion by local scaling warping; (2) capsular generation by brightening the tumor edge. Four steps, in light green, are only used for Visual Turing Test (not for training)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 262, + 288, + 442 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 262, + 288, + 442 + ], + "spans": [ + { + "bbox": [ + 46, + 262, + 288, + 442 + ], + "type": "text", + "content": "the predefined mean HU intensity " + }, + { + "bbox": [ + 46, + 262, + 288, + 442 + ], + "type": "inline_equation", + "content": "\\mu_t" + }, + { + "bbox": [ + 46, + 262, + 288, + 442 + ], + "type": "text", + "content": " and the same standard deviation " + }, + { + "bbox": [ + 46, + 262, + 288, + 442 + ], + "type": "inline_equation", + "content": "\\sigma_p" + }, + { + "bbox": [ + 46, + 262, + 288, + 442 + ], + "type": "text", + "content": " as the hepatic parenchyma (the liver area excluding vessels), " + }, + { + "bbox": [ + 46, + 262, + 288, + 442 + ], + "type": "inline_equation", + "content": "T(x,y,z) \\sim \\mathcal{N}(\\mu_t, \\sigma_p)" + }, + { + "bbox": [ + 46, + 262, + 288, + 442 + ], + "type": "text", + "content": ". Since the random Gaussian noise is usually too sharp as the texture for the tumor, we soften the texture by scaling it up with spline interpolation of the order 3 (cubic interpolation) on " + }, + { + "bbox": [ + 46, + 262, + 288, + 442 + ], + "type": "inline_equation", + "content": "x, y, z" + }, + { + "bbox": [ + 46, + 262, + 288, + 442 + ], + "type": "text", + "content": " directions. The scaled-up texture is denoted as " + }, + { + "bbox": [ + 46, + 262, + 288, + 442 + ], + "type": "inline_equation", + "content": "T'(x,y,z)" + }, + { + "bbox": [ + 46, + 262, + 288, + 442 + ], + "type": "text", + "content": " in this work, we want it exhibits graininess close to the hepatic parenchyma. The scaling factor " + }, + { + "bbox": [ + 46, + 262, + 288, + 442 + ], + "type": "inline_equation", + "content": "\\eta \\in [1,\\infty)" + }, + { + "bbox": [ + 46, + 262, + 288, + 442 + ], + "type": "text", + "content": " determines how rough the generated grain feels. " + }, + { + "bbox": [ + 46, + 262, + 288, + 442 + ], + "type": "inline_equation", + "content": "\\eta = 1" + }, + { + "bbox": [ + 46, + 262, + 288, + 442 + ], + "type": "text", + "content": " means the Gaussian texture is not scaled, resulting in large value fluctuation between adjacent voxels. Larger " + }, + { + "bbox": [ + 46, + 262, + 288, + 442 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 46, + 262, + 288, + 442 + ], + "type": "text", + "content": " brings greater graininess, which may be similar to the real tumor texture. Finally, considering the tomography imaging quality, we further blur the texture with Gaussian filter " + }, + { + "bbox": [ + 46, + 262, + 288, + 442 + ], + "type": "inline_equation", + "content": "g(x,y,z; \\sigma_b)" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 81, + 449, + 286, + 463 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 81, + 449, + 286, + 463 + ], + "spans": [ + { + "bbox": [ + 81, + 449, + 286, + 463 + ], + "type": "interline_equation", + "content": "T ^ {\\prime \\prime} (x, y, z) = T ^ {\\prime} (x, y, z) \\otimes g (x, y, z; \\sigma_ {b}), \\tag {3}", + "image_path": "35c8474042936874173df0cb218ce60b9318f9abd5c1cd5739036a7082ddc7eb.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 470, + 287, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 470, + 287, + 496 + ], + "spans": [ + { + "bbox": [ + 47, + 470, + 287, + 496 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 470, + 287, + 496 + ], + "type": "inline_equation", + "content": "\\sigma_{b}" + }, + { + "bbox": [ + 47, + 470, + 287, + 496 + ], + "type": "text", + "content": " is the standard deviation. After blurring, the texture resembles those generated by real imaging." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 497, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 497, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 497, + 287, + 714 + ], + "type": "text", + "content": "Shape generation. Most tumors grow from the centers and gradually swell, making small tumors (i.e., " + }, + { + "bbox": [ + 46, + 497, + 287, + 714 + ], + "type": "inline_equation", + "content": "r < 20mm" + }, + { + "bbox": [ + 46, + 497, + 287, + 714 + ], + "type": "text", + "content": ") nearly spherical. This motivates us to generate tumor-like shapes with ellipsoids. We randomly sample the half-axis lengths of the ellipsoid for " + }, + { + "bbox": [ + 46, + 497, + 287, + 714 + ], + "type": "inline_equation", + "content": "x, y, z" + }, + { + "bbox": [ + 46, + 497, + 287, + 714 + ], + "type": "text", + "content": " directions from a uniform distribution " + }, + { + "bbox": [ + 46, + 497, + 287, + 714 + ], + "type": "inline_equation", + "content": "U(0.75r, 1.25r)" + }, + { + "bbox": [ + 46, + 497, + 287, + 714 + ], + "type": "text", + "content": ", and place the generated ellipsoid mask centered at " + }, + { + "bbox": [ + 46, + 497, + 287, + 714 + ], + "type": "inline_equation", + "content": "(x_t, y_t, z_t)" + }, + { + "bbox": [ + 46, + 497, + 287, + 714 + ], + "type": "text", + "content": ". For a generated ellipsoid tumor mask " + }, + { + "bbox": [ + 46, + 497, + 287, + 714 + ], + "type": "inline_equation", + "content": "t(x, y, z)" + }, + { + "bbox": [ + 46, + 497, + 287, + 714 + ], + "type": "text", + "content": " (background=0, tumor=1), and with the same shape as the scanning volume " + }, + { + "bbox": [ + 46, + 497, + 287, + 714 + ], + "type": "inline_equation", + "content": "f(x, y, z)" + }, + { + "bbox": [ + 46, + 497, + 287, + 714 + ], + "type": "text", + "content": ", elastic deformations [45, 48], controlled by " + }, + { + "bbox": [ + 46, + 497, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\sigma_e" + }, + { + "bbox": [ + 46, + 497, + 287, + 714 + ], + "type": "text", + "content": ", are applied to enrich its diversity. The deformed tumor mask is more similar to the naturally grown tumors in appearance than simple ellipsoids. In addition, it can also improve the model's robustness by learning the shape-semantic invariance. The deformed tumor mask is denoted as " + }, + { + "bbox": [ + 46, + 497, + 287, + 714 + ], + "type": "inline_equation", + "content": "t'(x, y, z)" + }, + { + "bbox": [ + 46, + 497, + 287, + 714 + ], + "type": "text", + "content": ". In order to make the transition between the generated tumor and the surrounding liver parenchyma more natural, we finally blur the mask by applying a Gaussian filter " + }, + { + "bbox": [ + 46, + 497, + 287, + 714 + ], + "type": "inline_equation", + "content": "g(x, y, z; \\sigma_c)" + }, + { + "bbox": [ + 46, + 497, + 287, + 714 + ], + "type": "text", + "content": " with" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 262, + 546, + 287 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 262, + 546, + 287 + ], + "spans": [ + { + "bbox": [ + 305, + 262, + 546, + 287 + ], + "type": "text", + "content": "the standard deviation " + }, + { + "bbox": [ + 305, + 262, + 546, + 287 + ], + "type": "inline_equation", + "content": "\\sigma_{c}" + }, + { + "bbox": [ + 305, + 262, + 546, + 287 + ], + "type": "text", + "content": ". To be more specifically, we obtain blur shape " + }, + { + "bbox": [ + 305, + 262, + 546, + 287 + ], + "type": "inline_equation", + "content": "t''(x,y,z) = t'(x,y,z)\\otimes g(x,y,z;\\sigma_c)" + }, + { + "bbox": [ + 305, + 262, + 546, + 287 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 290, + 546, + 363 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 290, + 546, + 363 + ], + "spans": [ + { + "bbox": [ + 305, + 290, + 546, + 363 + ], + "type": "text", + "content": "Post-processing. The first step of post-processing is placing the tumor on the scanning volume " + }, + { + "bbox": [ + 305, + 290, + 546, + 363 + ], + "type": "inline_equation", + "content": "f(x,y,z)" + }, + { + "bbox": [ + 305, + 290, + 546, + 363 + ], + "type": "text", + "content": " and corresponding liver mask " + }, + { + "bbox": [ + 305, + 290, + 546, + 363 + ], + "type": "inline_equation", + "content": "l(x,y,z)" + }, + { + "bbox": [ + 305, + 290, + 546, + 363 + ], + "type": "text", + "content": ". Assuming the tumor mask array " + }, + { + "bbox": [ + 305, + 290, + 546, + 363 + ], + "type": "inline_equation", + "content": "t''(x,y,z)" + }, + { + "bbox": [ + 305, + 290, + 546, + 363 + ], + "type": "text", + "content": " and the texture array " + }, + { + "bbox": [ + 305, + 290, + 546, + 363 + ], + "type": "inline_equation", + "content": "T''(x,y,z)" + }, + { + "bbox": [ + 305, + 290, + 546, + 363 + ], + "type": "text", + "content": " have the same shape as " + }, + { + "bbox": [ + 305, + 290, + 546, + 363 + ], + "type": "inline_equation", + "content": "f(x,y,z)" + }, + { + "bbox": [ + 305, + 290, + 546, + 363 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 290, + 546, + 363 + ], + "type": "inline_equation", + "content": "l(x,y,z)" + }, + { + "bbox": [ + 305, + 290, + 546, + 363 + ], + "type": "text", + "content": ". We can obtain new scanning volume with tumor through equation" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 335, + 371, + 546, + 386 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 335, + 371, + 546, + 386 + ], + "spans": [ + { + "bbox": [ + 335, + 371, + 546, + 386 + ], + "type": "interline_equation", + "content": "f ^ {\\prime} (x, y, z) = \\left(1 - t ^ {\\prime \\prime} (x, y, z)\\right) \\odot f (x, y, z) + \\tag {4}", + "image_path": "dd4690b970fef3c2ef5a745f5e28afe2ded846e60e55c640b2995854e801bbce.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 388, + 386, + 491, + 401 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 388, + 386, + 491, + 401 + ], + "spans": [ + { + "bbox": [ + 388, + 386, + 491, + 401 + ], + "type": "interline_equation", + "content": "t ^ {\\prime \\prime} (x, y, z) \\odot T ^ {\\prime \\prime} (x, y, z).", + "image_path": "d95bf43faf82a8894591e33a8ef812f3735bfa130df71ace9e9523c37132e9fd.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 411, + 546, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 411, + 546, + 567 + ], + "spans": [ + { + "bbox": [ + 305, + 411, + 546, + 567 + ], + "type": "text", + "content": "For the new mask with the tumor (bg=0,liver=1,tumor=2), it can be synthesized with " + }, + { + "bbox": [ + 305, + 411, + 546, + 567 + ], + "type": "inline_equation", + "content": "l'(x,y,z) = l(x,y,z) + t''(x,y,z)" + }, + { + "bbox": [ + 305, + 411, + 546, + 567 + ], + "type": "text", + "content": ". After placing the tumor, we adopt another two steps to make the generated tumor more realistic to medical professionals. They aim to simulate mass effect and the capsule appearance, respectively. Mass effect means the expanding tumor pushes its surrounding tissue apart. If the tumor grows large enough, it will compress the surrounding blood vessels to make them bend, or even cause the edge of the nearby liver to bulge. Local scaling warping [18] is chosen in this work to implement mass effect. It remaps pixels in a circle to be nearer to the circumference. For a pixel with a distance " + }, + { + "bbox": [ + 305, + 411, + 546, + 567 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 305, + 411, + 546, + 567 + ], + "type": "text", + "content": " to the circle center, the remapped pixel distance " + }, + { + "bbox": [ + 305, + 411, + 546, + 567 + ], + "type": "inline_equation", + "content": "\\gamma'" + }, + { + "bbox": [ + 305, + 411, + 546, + 567 + ], + "type": "text", + "content": " is" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 345, + 576, + 546, + 608 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 345, + 576, + 546, + 608 + ], + "spans": [ + { + "bbox": [ + 345, + 576, + 546, + 608 + ], + "type": "interline_equation", + "content": "\\gamma^ {\\prime} = \\left(1 - \\left(1 - \\frac {\\gamma}{\\gamma_ {m a x}}\\right) ^ {2} \\cdot \\frac {I}{1 0 0}\\right) \\cdot \\gamma , \\tag {5}", + "image_path": "7161085a858bb47a5c0a23d69cfe802315ac11244ab9208b25be14272d587670.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 617, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 617, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 617, + 546, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 617, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\gamma_{max}" + }, + { + "bbox": [ + 305, + 617, + 546, + 714 + ], + "type": "text", + "content": " is the radius of the expanded circular area, " + }, + { + "bbox": [ + 305, + 617, + 546, + 714 + ], + "type": "inline_equation", + "content": "I\\in [0,100]" + }, + { + "bbox": [ + 305, + 617, + 546, + 714 + ], + "type": "text", + "content": " is a hyper-parameter for controlling the expansion intensity. Larger " + }, + { + "bbox": [ + 305, + 617, + 546, + 714 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 305, + 617, + 546, + 714 + ], + "type": "text", + "content": " leads to stronger warping. Note that when " + }, + { + "bbox": [ + 305, + 617, + 546, + 714 + ], + "type": "inline_equation", + "content": "I = 0" + }, + { + "bbox": [ + 305, + 617, + 546, + 714 + ], + "type": "text", + "content": ", the remapping reduces to the identity function " + }, + { + "bbox": [ + 305, + 617, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\gamma^{\\prime} = \\gamma" + }, + { + "bbox": [ + 305, + 617, + 546, + 714 + ], + "type": "text", + "content": ". The remapping procedure is conducted on both scanning and mask volumes. After warping, they are named " + }, + { + "bbox": [ + 305, + 617, + 546, + 714 + ], + "type": "inline_equation", + "content": "f^{\\prime \\prime}(x,y,z)" + }, + { + "bbox": [ + 305, + 617, + 546, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 617, + 546, + 714 + ], + "type": "inline_equation", + "content": "l^{\\prime \\prime}(x,y,z)" + }, + { + "bbox": [ + 305, + 617, + 546, + 714 + ], + "type": "text", + "content": ". The latter one (liver/tumor segmentation label) is now ready for the subsequent training." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 738, + 298, + 748 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 738, + 298, + 748 + ], + "spans": [ + { + "bbox": [ + 279, + 738, + 298, + 748 + ], + "type": "text", + "content": "7425" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 595, + 841 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 69, + 288, + 141 + ], + "blocks": [ + { + "bbox": [ + 48, + 69, + 288, + 141 + ], + "lines": [ + { + "bbox": [ + 48, + 69, + 288, + 141 + ], + "spans": [ + { + "bbox": [ + 48, + 69, + 288, + 141 + ], + "type": "table", + "html": "
parametervalueparametervalue
σa0.5 + 0.025σpμtU(30,μp-10)
σb0.6ηU(1.1,1.5)
σcU(0.6,1.2)γmax1.3r
σd0.8I30
b15(lb,ub)(0.4,0.7)
d120
", + "image_path": "9fb4690189eff08bc6d1348b19f8260f1181ca8612c5492317e10c6b78985b1e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 224, + 287, + 249 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 224, + 287, + 249 + ], + "spans": [ + { + "bbox": [ + 47, + 224, + 287, + 249 + ], + "type": "text", + "content": "Finally, we simulate the capsule appearance by brightening the tumor edge. The edge area can be obtained by" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 82, + 257, + 286, + 285 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 82, + 257, + 286, + 285 + ], + "spans": [ + { + "bbox": [ + 82, + 257, + 286, + 285 + ], + "type": "interline_equation", + "content": "e (x, y, z) = \\left\\{ \\begin{array}{l} 1, t ^ {\\prime \\prime} (x, y, z) \\in [ l b, u b ] \\\\ 0, \\text {o t h e r w i s e} \\end{array} , \\right. \\tag {6}", + "image_path": "da3a0868320aeb5f37c3af2bd98f0cfddb68b728bb8e704ca5bb757c0e2d4fea.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 290, + 287, + 328 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 290, + 287, + 328 + ], + "spans": [ + { + "bbox": [ + 47, + 290, + 287, + 328 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 290, + 287, + 328 + ], + "type": "inline_equation", + "content": "lb" + }, + { + "bbox": [ + 47, + 290, + 287, + 328 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 290, + 287, + 328 + ], + "type": "inline_equation", + "content": "ub" + }, + { + "bbox": [ + 47, + 290, + 287, + 328 + ], + "type": "text", + "content": " are the lower bound and upper bound for filtering the edge from tumor mask. Then we increase HU intensity of the blurred edge area to simulate the capsule" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 86, + 336, + 286, + 350 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 336, + 286, + 350 + ], + "spans": [ + { + "bbox": [ + 86, + 336, + 286, + 350 + ], + "type": "interline_equation", + "content": "e ^ {\\prime} (x, y, z) = e (x, y, z) \\otimes g (x, y, z; \\sigma_ {d}), \\tag {7}", + "image_path": "59b4573b76f4744bbcb697587869c4b5b8d09ee6e26807b21b35655e77d3a00b.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 82, + 358, + 286, + 371 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 82, + 358, + 286, + 371 + ], + "spans": [ + { + "bbox": [ + 82, + 358, + 286, + 371 + ], + "type": "interline_equation", + "content": "f ^ {\\prime \\prime \\prime} (x, y, z) = f ^ {\\prime \\prime} (x, y, z) + d \\cdot e (x, y, z), \\tag {8}", + "image_path": "46ebee4bdb37fec2dfb1eb9fe99950d1942ab281524616220fe465e58e76654e.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 376, + 287, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 376, + 287, + 437 + ], + "spans": [ + { + "bbox": [ + 47, + 376, + 287, + 437 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 376, + 287, + 437 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 47, + 376, + 287, + 437 + ], + "type": "text", + "content": " is the pre-defined HU intensity difference between a tumor and its capsule. The new scanning volume " + }, + { + "bbox": [ + 47, + 376, + 287, + 437 + ], + "type": "inline_equation", + "content": "f^{\\prime \\prime \\prime}(x,y,z)" + }, + { + "bbox": [ + 47, + 376, + 287, + 437 + ], + "type": "text", + "content": " is now ready for training or Turing test. The parameters we use are shown in Table 1. Visualization examples can be found in Appendix Figures 8-10." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 443, + 258, + 456 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 443, + 258, + 456 + ], + "spans": [ + { + "bbox": [ + 47, + 443, + 258, + 456 + ], + "type": "text", + "content": "3.2. Clinical Knowledge about Liver Tumors" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 461, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 461, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 461, + 287, + 677 + ], + "type": "text", + "content": "This work focuses on generating hepatocellular carcinomas (tumor grown from liver cells). After the contrast injection, the clinical examination process of liver is divided into three phases, arterial phase (30s after injection), portal venous phase (60-70s after injection), and delay phase (3min after injection). Typically, only the first two phases are used for detecting hepatocellular carcinomas, and the tumor HU intensity value in different stages distributes differently. The mean attenuation measurement of the lesions in the hepatic arterial phase was 111 HU (range, 32-207 HU), and it decreased in the portal venous phase to a mean of 106 HU (range, 36-162 HU). There was a mean difference of 26 HU (range, -44 to 146 HU) between the lesion and liver in the arterial phase. On average, the hepatocellular carcinomas measured 11 HU (range, -98 to 61 HU) less than the adjacent liver parenchyma in the portal venous phase [32]. The distributional characteristics help us determine the generated mean tumor HU values." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "text", + "content": "The location, shape, and number of tumors depend on how severe the hepatocellular carcinomas are according to the standardized guidance of the Liver Imaging Reporting" + } + ] + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 308, + 69, + 545, + 111 + ], + "blocks": [ + { + "bbox": [ + 47, + 148, + 287, + 204 + ], + "lines": [ + { + "bbox": [ + 47, + 148, + 287, + 204 + ], + "spans": [ + { + "bbox": [ + 47, + 148, + 287, + 204 + ], + "type": "text", + "content": "Table 1. Hyper-parameters. " + }, + { + "bbox": [ + 47, + 148, + 287, + 204 + ], + "type": "inline_equation", + "content": "\\mu_p, \\sigma_p" + }, + { + "bbox": [ + 47, + 148, + 287, + 204 + ], + "type": "text", + "content": " are the mean and standard deviation of the hepatic parenchyma. The values are adjusted by (1) feedback from clinicians based on the clinical prior knowledge about liver tumors (" + }, + { + "bbox": [ + 47, + 148, + 287, + 204 + ], + "type": "inline_equation", + "content": "\\S 3.2" + }, + { + "bbox": [ + 47, + 148, + 287, + 204 + ], + "type": "text", + "content": ") and (2) visual assessment between the real and synthetic tumors (" + }, + { + "bbox": [ + 47, + 148, + 287, + 204 + ], + "type": "inline_equation", + "content": "\\S 5.1" + }, + { + "bbox": [ + 47, + 148, + 287, + 204 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 69, + 545, + 111 + ], + "lines": [ + { + "bbox": [ + 308, + 69, + 545, + 111 + ], + "spans": [ + { + "bbox": [ + 308, + 69, + 545, + 111 + ], + "type": "table", + "html": "
junior professionalsenior professional
real (P)synt (N)real (P)synt (N)
truthreal (P)515102
synt (N)218712
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One CT scan is marked unsure." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_footnote" + }, + { + "bbox": [ + 320, + 128, + 544, + 144 + ], + "lines": [ + { + "bbox": [ + 320, + 128, + 544, + 144 + ], + "spans": [ + { + "bbox": [ + 320, + 128, + 544, + 144 + ], + "type": "text", + "content": "2The senior professional achieves an Accuracy, Sensitivity, and Specificity of " + }, + { + "bbox": [ + 320, + 128, + 544, + 144 + ], + "type": "inline_equation", + "content": "71.0\\%" + }, + { + "bbox": [ + 320, + 128, + 544, + 144 + ], + "type": "inline_equation", + "content": "63.2\\%" + }, + { + "bbox": [ + 320, + 128, + 544, + 144 + ], + "type": "text", + "content": " ,and " + }, + { + "bbox": [ + 320, + 128, + 544, + 144 + ], + "type": "inline_equation", + "content": "83.3\\%" + }, + { + "bbox": [ + 320, + 128, + 544, + 144 + ], + "type": "text", + "content": " . 19 CT scans are marked unsure." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 153, + 546, + 231 + ], + "lines": [ + { + "bbox": [ + 305, + 153, + 546, + 231 + ], + "spans": [ + { + "bbox": [ + 305, + 153, + 546, + 231 + ], + "type": "text", + "content": "Table 2. Results of Visual Turing Test. The test has been performed on two medical professionals with 6-year and 15-year experience. Each professional is given 50 CT scans, some of which contain real tumors and the others contain synthetic ones. The professional can mark each CT scan as real, synthetic, or unsure. \"Synt\" denotes synthetic tumors, " + }, + { + "bbox": [ + 305, + 153, + 546, + 231 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 305, + 153, + 546, + 231 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 153, + 546, + 231 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 305, + 153, + 546, + 231 + ], + "type": "text", + "content": " indicate positive and negative classes for computing Sensitivity and Specificity." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 251, + 546, + 371 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 251, + 546, + 371 + ], + "spans": [ + { + "bbox": [ + 305, + 251, + 546, + 371 + ], + "type": "text", + "content": "and Data System (LI-RADS) [42]. Milder carcinomas usually lead to smaller, fewer spherical lesions. Only one small tumor emerges in most cases. While multi-focal lesions, which means scattered small tumors, only appear in seldom cases. Severe carcinomas usually present a satellite lesion, a large lesion surrounded by a cluster of small lesions. The large central lesion also takes on a more irregular shape than small lesions. And also, larger tumors usually display evident mass effects, accompanied by capsule appearances that separate the tumor from the liver parenchyma." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 382, + 387, + 395 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 382, + 387, + 395 + ], + "spans": [ + { + "bbox": [ + 305, + 382, + 387, + 395 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 402, + 546, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 402, + 546, + 581 + ], + "spans": [ + { + "bbox": [ + 305, + 402, + 546, + 581 + ], + "type": "text", + "content": "Datasets. Detailed per-voxel annotations for liver tumors are provided in LiTS [5]. The volume of liver tumors ranges from " + }, + { + "bbox": [ + 305, + 402, + 546, + 581 + ], + "type": "inline_equation", + "content": "38\\mathrm{mm}^3" + }, + { + "bbox": [ + 305, + 402, + 546, + 581 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 305, + 402, + 546, + 581 + ], + "type": "inline_equation", + "content": "349~\\mathrm{cm}^3" + }, + { + "bbox": [ + 305, + 402, + 546, + 581 + ], + "type": "text", + "content": ", and the radius of tumors is in the range of [2, 44]mm. We perform 5-fold cross-validation, following the same split as in Tang et al. [55]. An AI model (e.g. U-Net) is trained on 101 CT scans with annotated liver and liver tumors. For comparison, a dataset of 116 CT scans with healthy livers is assembled from CHAOS [28] (20 CT scans), BTCV [31] (47 CT scans), Pancreas-CT [50] (38 CT scans) and health subjects in LiTS (11 CT scans). We then generate tumors in these scans on the fly, resulting in enormous image-label pairs of synthetic tumors for training the AI model. We generate five levels of tumor sizes for model training; the parameters and examples can be found in Appendix Table 6 and Figure 11." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 585, + 546, + 669 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 585, + 546, + 669 + ], + "spans": [ + { + "bbox": [ + 305, + 585, + 546, + 669 + ], + "type": "text", + "content": "Evaluation metrics. Tumor segmentation performance was evaluated by Dice similarity coefficient (DSC) and Normalized Surface Dice (NSD) with " + }, + { + "bbox": [ + 305, + 585, + 546, + 669 + ], + "type": "inline_equation", + "content": "2\\mathrm{mm}" + }, + { + "bbox": [ + 305, + 585, + 546, + 669 + ], + "type": "text", + "content": " tolerance; tumor detection performance was evaluated by Sensitivity and Specificity. For all the metrics above, " + }, + { + "bbox": [ + 305, + 585, + 546, + 669 + ], + "type": "inline_equation", + "content": "95\\%" + }, + { + "bbox": [ + 305, + 585, + 546, + 669 + ], + "type": "text", + "content": " CIs were calculated and the " + }, + { + "bbox": [ + 305, + 585, + 546, + 669 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 305, + 585, + 546, + 669 + ], + "type": "text", + "content": "-value cutoff of less than 0.05 was used for defining statistical significance." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 672, + 546, + 695 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 672, + 546, + 695 + ], + "spans": [ + { + "bbox": [ + 305, + 672, + 546, + 695 + ], + "type": "text", + "content": "Implementation. Our codes are implemented based on the MONAI" + }, + { + "bbox": [ + 305, + 672, + 546, + 695 + ], + "type": "inline_equation", + "content": "^2" + }, + { + "bbox": [ + 305, + 672, + 546, + 695 + ], + "type": "text", + "content": " framework for both U-Net and Swin UN-" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 316, + 701, + 377, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 701, + 377, + 712 + ], + "spans": [ + { + "bbox": [ + 316, + 701, + 377, + 712 + ], + "type": "text", + "content": "2https://monai.io/" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 279, + 738, + 298, + 747 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 738, + 298, + 747 + ], + "spans": [ + { + "bbox": [ + 279, + 738, + 298, + 747 + ], + "type": "text", + "content": "7426" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 595, + 841 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 51, + 69, + 542, + 141 + ], + "blocks": [ + { + "bbox": [ + 51, + 69, + 542, + 141 + ], + "lines": [ + { + "bbox": [ + 51, + 69, + 542, + 141 + ], + "spans": [ + { + "bbox": [ + 51, + 69, + 542, + 141 + ], + "type": "table", + "html": "
tumorsmethodarchitecturelabeled / unlabeled CTsDSC (%) [95% CI]NSD (%) [95% CI]
nonePatchCore [51]Wide-Resnet50-2 [66]0 / 11615.97 [11.86–20.09]16.43 [10.42–22.44]
nonef-AnoGAN [53]Customized [3]0 / 11619.00 [13.88–24.11]16.94 [11.97–21.91]
noneVAE [30]Customized [3]0 / 11624.63 [19.83–29.44]23.63 [18.44–28.83]
syntYao et al. [63]U-Net [48]0 / 11632.79 [28.66–36.92]31.28 [26.87–35.70]
realfully-supervisedU-Net101 / 057.51 [52.24–62.79]58.04 [52.56–63.52]
syntlabel-free (ours)U-Net0 / 11659.77 [54.54–64.99]61.29 [56.12–66.47]
", + "image_path": "6b04bef74393f73aabf0fed8d194730d4ad1dc23d183b0486ca987e0465903b2.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 148, + 545, + 182 + ], + "lines": [ + { + "bbox": [ + 47, + 148, + 545, + 182 + ], + "spans": [ + { + "bbox": [ + 47, + 148, + 545, + 182 + ], + "type": "text", + "content": "Table 3. Comparison with state-of-the-art methods, 5-fold cross-validation. We compare our methods with other unsupervised anomaly segmentation baselines, tumor synthesis strategies, and fully-supervised methods. Our method significantly outperforms all other state-of-the-art unsupervised baseline methods and even surpasses the fully-supervised method with detailed pixel-wise annotation." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 47, + 203, + 286, + 310 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 203, + 286, + 310 + ], + "spans": [ + { + "bbox": [ + 47, + 203, + 286, + 310 + ], + "type": "text", + "content": "ETR. Input images are clipped with the window range of [-21,189] and then normalized to have zero mean and unit standard deviation. Random patches of " + }, + { + "bbox": [ + 47, + 203, + 286, + 310 + ], + "type": "inline_equation", + "content": "96 \\times 96 \\times 96" + }, + { + "bbox": [ + 47, + 203, + 286, + 310 + ], + "type": "text", + "content": " were cropped from 3D image volumes during training. All models are trained for 4,000 epochs, and the base learning rate is 0.0002. The batch size is two per GPU. We adopt the linear warmup strategy and the cosine annealing learning rate schedule. For inference, we use the sliding window strategy by setting the overlapping area ratio to 0.75." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 48, + 321, + 169, + 333 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 321, + 169, + 333 + ], + "spans": [ + { + "bbox": [ + 48, + 321, + 169, + 333 + ], + "type": "text", + "content": "5. Results & Discussion" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 340, + 286, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 340, + 286, + 389 + ], + "spans": [ + { + "bbox": [ + 47, + 340, + 286, + 389 + ], + "type": "text", + "content": "Using 116 CT scans from Pancreas-CT, CHAOS, and BTCV with our label-free tumor generator, we outperformed all those methods on the LiTS benchmark, wherein previous methods used 101 CT scans and annotations from LiTS." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 48, + 395, + 273, + 407 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 395, + 273, + 407 + ], + "spans": [ + { + "bbox": [ + 48, + 395, + 273, + 407 + ], + "type": "text", + "content": "5.1. Clinical Validation using Visual Turing Test" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 413, + 286, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 413, + 286, + 556 + ], + "spans": [ + { + "bbox": [ + 47, + 413, + 286, + 556 + ], + "type": "text", + "content": "We conduct the Visual Turing Test [15] on 50 CT scans, where 20 scans are with real tumors from LiTS, and the remaining 30 scans are healthy livers from WORD [40] with synthetic tumors. Two professionals with different experience levels take part in this test. They can inspect each sample in 3D view, which means continuous variation of slice sequence can be observed by scrolling the mouse. This is an important setting for the test because some important tumor characteristics are not obvious in a 2D view (e.g., vessel collision). In the test, professionals can label each sample as real, synthetic or unsure. When calculating the performance metrics, only the samples with definite results are counted." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 558, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 558, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 558, + 286, + 713 + ], + "type": "text", + "content": "The testing results are shown in Table 2. For junior professionals with 6-year experience, definite judgments of 49 out of 50 samples are given. All of the accuracy, sensitivity, and specificity are below " + }, + { + "bbox": [ + 47, + 558, + 286, + 713 + ], + "type": "inline_equation", + "content": "30\\%" + }, + { + "bbox": [ + 47, + 558, + 286, + 713 + ], + "type": "text", + "content": ", which means the generated samples succeed in confusing the junior professional. In particular, the sensitivity of " + }, + { + "bbox": [ + 47, + 558, + 286, + 713 + ], + "type": "inline_equation", + "content": "27.6\\%" + }, + { + "bbox": [ + 47, + 558, + 286, + 713 + ], + "type": "text", + "content": " means that the rest " + }, + { + "bbox": [ + 47, + 558, + 286, + 713 + ], + "type": "inline_equation", + "content": "72.4\\%" + }, + { + "bbox": [ + 47, + 558, + 286, + 713 + ], + "type": "text", + "content": " synthetic samples are mistakenly regarded as real samples. The result verifies that our synthesis method can generate realistic tumors. According to the results given by the senior professional with 15-year experience, " + }, + { + "bbox": [ + 47, + 558, + 286, + 713 + ], + "type": "inline_equation", + "content": "36.8\\%" + }, + { + "bbox": [ + 47, + 558, + 286, + 713 + ], + "type": "text", + "content": " synthetic samples seemed to be real, indicating that nearly half of the generated samples can tease senior professionals. Noteworthy, the senior professional only gives 19 judg-" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 203, + 546, + 238 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 203, + 546, + 238 + ], + "spans": [ + { + "bbox": [ + 305, + 203, + 546, + 238 + ], + "type": "text", + "content": "ments among all 30 synthetic samples. Adding up misjudged samples and uncertain samples, a total of 18 out of 30 generated samples have confused him/her." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 248, + 527, + 261 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 248, + 527, + 261 + ], + "spans": [ + { + "bbox": [ + 305, + 248, + 527, + 261 + ], + "type": "text", + "content": "5.2. Comparison with State-of-the-art Methods" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 268, + 545, + 470 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 268, + 545, + 470 + ], + "spans": [ + { + "bbox": [ + 305, + 268, + 545, + 470 + ], + "type": "text", + "content": "We compare our label-free tumor synthesis strategy with several prominent unsupervised tumor segmentation methods designed for both natural and medical images, such as PatchCore [51], f-AnoGAN [53], VAE [3], and the method proposed by Yao et al. [63]. To enhance the performance of these baseline methods, we focus solely on the liver region for training and testing to minimize noise caused by extraneous information. Table 3 shows that all the previous unsupervised methods exhibit suboptimal performance in segmenting real liver tumors. In contrast, our label-free tumor synthesis—a novel approach to unsupervised tumor segmentation—significantly outperforms all these methods, achieving a DSC of " + }, + { + "bbox": [ + 305, + 268, + 545, + 470 + ], + "type": "inline_equation", + "content": "59.77\\%" + }, + { + "bbox": [ + 305, + 268, + 545, + 470 + ], + "type": "text", + "content": " and an NSD of " + }, + { + "bbox": [ + 305, + 268, + 545, + 470 + ], + "type": "inline_equation", + "content": "61.29\\%" + }, + { + "bbox": [ + 305, + 268, + 545, + 470 + ], + "type": "text", + "content": ". On the other hand, the model trained on real tumors using fully supervised learning achieves a DSC of " + }, + { + "bbox": [ + 305, + 268, + 545, + 470 + ], + "type": "inline_equation", + "content": "57.51\\%" + }, + { + "bbox": [ + 305, + 268, + 545, + 470 + ], + "type": "text", + "content": " and an NSD of " + }, + { + "bbox": [ + 305, + 268, + 545, + 470 + ], + "type": "inline_equation", + "content": "58.04\\%" + }, + { + "bbox": [ + 305, + 268, + 545, + 470 + ], + "type": "text", + "content": ". These results highlight the potential of a paradigm shift from label-intensive to label-free tumor segmentation." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 481, + 536, + 493 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 481, + 536, + 493 + ], + "spans": [ + { + "bbox": [ + 305, + 481, + 536, + 493 + ], + "type": "text", + "content": "5.3. Generalization to Different Models and Data" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 500, + 545, + 644 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 500, + 545, + 644 + ], + "spans": [ + { + "bbox": [ + 305, + 500, + 545, + 644 + ], + "type": "text", + "content": "We verify the generalizability of synthetic tumors using Swin UNETR [20], including its Tiny, Small, and Base variants. Figure 4 shows that the model trained on real tumors performs slightly better than that on synthetic tumors, but there is no statistical difference between the two results as the " + }, + { + "bbox": [ + 305, + 500, + 545, + 644 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 305, + 500, + 545, + 644 + ], + "type": "text", + "content": "-value is greater than 0.05. In addition to evaluating the models on the LiTS dataset, we assess their domain generalization ability using data from other datasets (i.e., MSD-Pancreas, MSD-Spleen, MSD-Colon). As shown in the right panel of Figure 4, our model trained with healthy data collected from 3 different datasets shows better robustness than the model trained on real data only from LiTS," + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 305, + 654, + 545, + 692 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 654, + 545, + 692 + ], + "spans": [ + { + "bbox": [ + 305, + 654, + 545, + 692 + ], + "type": "inline_equation", + "content": "{}^{3}" + }, + { + "bbox": [ + 305, + 654, + 545, + 692 + ], + "type": "text", + "content": " Swin UNETR is a hybrid segmentation architecture,which integrates the benefits of both U-Net [48] and Transformer [11,39]. We select Swin UNETR because it is very competitive and has ranked first in numerous public benchmarks [55], including liver tumor segmentation (MSD-Liver)." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 307, + 693, + 545, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 693, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 307, + 693, + 545, + 712 + ], + "type": "text", + "content": "4We first selected the tumor-free scans from these datasets and then had radiologists review each one of the scans to dismiss the diseased liver." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 279, + 738, + 298, + 747 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 738, + 298, + 747 + ], + "spans": [ + { + "bbox": [ + 279, + 738, + 298, + 747 + ], + "type": "text", + "content": "7427" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 595, + 841 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 68, + 141, + 179 + ], + "blocks": [ + { + "bbox": [ + 47, + 68, + 141, + 179 + ], + "lines": [ + { + "bbox": [ + 47, + 68, + 141, + 179 + ], + "spans": [ + { + "bbox": [ + 47, + 68, + 141, + 179 + ], + "type": "image", + "image_path": "acd1c70ce7ca7f4e3aca5bb17376701925c04bf24104cc14b31dae718b9a2e6e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 187, + 545, + 253 + ], + "lines": [ + { + "bbox": [ + 46, + 187, + 545, + 253 + ], + "spans": [ + { + "bbox": [ + 46, + 187, + 545, + 253 + ], + "type": "text", + "content": "Figure 4. Generalization to different models and data. Training U-Net on synthetic liver tumors outperforms as well as training it on real tumors with per-voxel annotation (see Table 3). We further examine this observation using Swin UNETR [55], including its variance of Tiny (Param = 4.0M), Small (Param = 15.7M), and Base (Param = 62.1M). The DSC, NSD, and Sensitivity scores are evaluated on the LiTS datasets. The detailed results of 5-fold cross-validation are reported in Appendix Table 5. Moreover, the model trained on synthetic tumors can also be generalized to CT scans with the healthy liver across datasets (e.g. MSD-Pancreas, MSD-Spleen, and MSD-Colon [2]), generating fewer false positives and yielding a higher Specificity compared with the model trained on real tumors." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 143, + 68, + 239, + 179 + ], + "blocks": [ + { + "bbox": [ + 143, + 68, + 239, + 179 + ], + "lines": [ + { + "bbox": [ + 143, + 68, + 239, + 179 + ], + "spans": [ + { + "bbox": [ + 143, + 68, + 239, + 179 + ], + "type": "image", + "image_path": "9b7a049c0ee2b4a4b9c16012dbca91b2ae888121b0e41fce5237d5fb730ded05.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 242, + 72, + 340, + 179 + ], + "blocks": [ + { + "bbox": [ + 242, + 72, + 340, + 179 + ], + "lines": [ + { + "bbox": [ + 242, + 72, + 340, + 179 + ], + "spans": [ + { + "bbox": [ + 242, + 72, + 340, + 179 + ], + "type": "image", + "image_path": "7ef46a8ad207f9b6dae4481bcd50f56f7d8786f54672c16b20bbe8bb8cd212f6.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 374, + 68, + 546, + 179 + ], + "blocks": [ + { + "bbox": [ + 374, + 68, + 546, + 179 + ], + "lines": [ + { + "bbox": [ + 374, + 68, + 546, + 179 + ], + "spans": [ + { + "bbox": [ + 374, + 68, + 546, + 179 + ], + "type": "image", + "image_path": "2dc891781a030f9c32a21e0624e82f54b2140b138bb4581e79681f22933a978e.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 49, + 272, + 286, + 380 + ], + "blocks": [ + { + "bbox": [ + 49, + 272, + 286, + 380 + ], + "lines": [ + { + "bbox": [ + 49, + 272, + 286, + 380 + ], + "spans": [ + { + "bbox": [ + 49, + 272, + 286, + 380 + ], + "type": "image", + "image_path": "f226e584f863496fa1b364d1cd1df314b3adedd9266c7130f6d6a0208e6b7f73.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 49, + 384, + 283, + 448 + ], + "blocks": [ + { + "bbox": [ + 49, + 384, + 283, + 448 + ], + "lines": [ + { + "bbox": [ + 49, + 384, + 283, + 448 + ], + "spans": [ + { + "bbox": [ + 49, + 384, + 283, + 448 + ], + "type": "image", + "image_path": "bcdc686bf2c103371b12dc6af136a8fe1b6a985896188e58ca33a386f5b7cbb8.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 455, + 287, + 521 + ], + "lines": [ + { + "bbox": [ + 46, + 455, + 287, + 521 + ], + "spans": [ + { + "bbox": [ + 46, + 455, + 287, + 521 + ], + "type": "text", + "content": "Figure 5. Small tumor detection. The upper panel presents two examples of small tumors and the segmentation results. For both models trained on real and synthetic tumors, the false negatives are mostly smaller than " + }, + { + "bbox": [ + 46, + 455, + 287, + 521 + ], + "type": "inline_equation", + "content": "10\\mathrm{mm}" + }, + { + "bbox": [ + 46, + 455, + 287, + 521 + ], + "type": "text", + "content": ". The lower panel presents the tumor detection rate. The model trained on synthetic tumors could detect tumors as small as " + }, + { + "bbox": [ + 46, + 455, + 287, + 521 + ], + "type": "inline_equation", + "content": "2\\mathrm{mm}" + }, + { + "bbox": [ + 46, + 455, + 287, + 521 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 543, + 287, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 543, + 287, + 602 + ], + "spans": [ + { + "bbox": [ + 46, + 543, + 287, + 602 + ], + "type": "text", + "content": "while achieving much higher Specificity on the three external datasets. It is noteworthy that higher Specificity (fewer false positives) is crucial in clinical applications as it reduces the number of patients subjected to invasive diagnostic procedures and their associated costs [7,36,61]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 610, + 235, + 622 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 610, + 235, + 622 + ], + "spans": [ + { + "bbox": [ + 47, + 610, + 235, + 622 + ], + "type": "text", + "content": "5.4. Potential in Small Tumor Detection" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "content": "Early detection of small tumors is essential for prompt cancer diagnosis, but such cases are scarce in real datasets because most patients remain asymptomatic during the early stages. AI models trained on these datasets exhibit reduced detection sensitivity for small tumors (radius " + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "inline_equation", + "content": "< 5\\mathrm{mm}" + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "content": ") compared with larger tumors (radius " + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "inline_equation", + "content": ">5\\mathrm{mm}" + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "content": "), displaying sensitivities of " + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "inline_equation", + "content": "52.0\\%" + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "inline_equation", + "content": "91.6\\%" + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "content": ", respectively." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 275, + 546, + 429 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 275, + 546, + 429 + ], + "spans": [ + { + "bbox": [ + 304, + 275, + 546, + 429 + ], + "type": "text", + "content": "Thus, an advanced tumor generator could create synthetic data containing various tumor sizes for training and testing models, addressing the size imbalance issue found in real data. The lower panel of Figure 5 presents quantitative tumor detection performance stratified by tumor size, and the upper panel presents two cases with small tumors for qualitative comparison. Evidently, AI models (trained solely on synthetic data) outperform those trained on real tumors in detecting and segmenting small tumors in the liver. The results indicate that the generation of copious amounts of synthetic small tumors can improve the efficacy of models in detecting real small tumors, thereby playing a crucial role in the early detection of cancer." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 441, + 500, + 454 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 441, + 500, + 454 + ], + "spans": [ + { + "bbox": [ + 305, + 441, + 500, + 454 + ], + "type": "text", + "content": "5.5. Controllable Robustness Benchmark" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 461, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 461, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 461, + 546, + 713 + ], + "type": "text", + "content": "Standard evaluation in medical imaging is limited to determining the effectiveness of AI in detecting tumors. This is because the number of annotated tumors in the existing test datasets is not big enough to be representative of the tumors that occur in real organs and, in particular, contains only a limited number of very small tumors. We show that synthetic tumors can serve as an accessible and comprehensive source for rigorously evaluating AI's performance in detecting tumors at a variety of different sizes and locations with the organs. To be specific, our tumor generator can synthesize liver tumors varying in five dimensions, i.e. location, size, shape, intensity, and texture, by tuning hyperparameters in the tumor generation pipeline. Taking five different options in each dimension, our tumor generator could create " + }, + { + "bbox": [ + 304, + 461, + 546, + 713 + ], + "type": "inline_equation", + "content": "25(5\\times 5)" + }, + { + "bbox": [ + 304, + 461, + 546, + 713 + ], + "type": "text", + "content": " variants for each single CT scan. Generating a large number of synthetic tumors during testing enables us to find failure scenarios of current AI models. After locating the worst cases of AI, we can synthesize and include worst-case tumors in the training set and fine-tune AI algorithms. Figure 6 illustrates the out-of-distribution (o.o.d.) benchmark created by synthetic tumors, wherein" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 738, + 298, + 747 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 738, + 298, + 747 + ], + "spans": [ + { + "bbox": [ + 279, + 738, + 298, + 747 + ], + "type": "text", + "content": "7428" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 595, + 841 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 68, + 545, + 220 + ], + "blocks": [ + { + "bbox": [ + 48, + 68, + 545, + 220 + ], + "lines": [ + { + "bbox": [ + 48, + 68, + 545, + 220 + ], + "spans": [ + { + "bbox": [ + 48, + 68, + 545, + 220 + ], + "type": "image", + "image_path": "f392a587b03c869a4a7c0d2384530146cb40560f1b216601ad51b8b221aadd09.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 228, + 546, + 327 + ], + "lines": [ + { + "bbox": [ + 46, + 228, + 546, + 327 + ], + "spans": [ + { + "bbox": [ + 46, + 228, + 546, + 327 + ], + "type": "text", + "content": "Figure 6. Controllable benchmark for robust evaluation. UNet++ [72], nnU-Net [26], and Swin UNETR [55] are very competitive segmentation models in the medical domain. However, their limitations of tumor segmentation are not fully revealed due to the lack of sufficient testing images (only 70 CT scans are available for testing in MSD Task03 [1]). On the contrary, synthetic tumors enable us to perform an extensive evaluation of these models in segmenting liver tumors that vary from different conditions, i.e. shape, size, texture, intensity, and location. We downloaded the checkpoints of these models trained on LiTS, and evaluated them on synthetic tumors. Synthetic tumors were generated using different parameters, where " + }, + { + "bbox": [ + 46, + 228, + 546, + 327 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 46, + 228, + 546, + 327 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 228, + 546, + 327 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 46, + 228, + 546, + 327 + ], + "type": "text", + "content": " denote mean and standard deviation, respectively. Our findings indicate that these public models exhibit robustness to variations in tumor shape, location, and texture, but they are sensitive to tumor size and intensity. Specifically, these models are prone to errors when encountering tumors that are smaller or larger than those in the training set, or when faced with differing Hounsfield Unit (HU) values, which may be attributable to contrast enhancement." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 52, + 346, + 283, + 417 + ], + "blocks": [ + { + "bbox": [ + 52, + 346, + 283, + 417 + ], + "lines": [ + { + "bbox": [ + 52, + 346, + 283, + 417 + ], + "spans": [ + { + "bbox": [ + 52, + 346, + 283, + 417 + ], + "type": "table", + "html": "
tiny sizeelastic deformationedge blurringall tumors DSC (%)small tumors det Sen. (%)
✓43.926.4
✓✓47.151.3
✓✓50.354.1
✓✓52.633.4
✓✓✓55.161.8
", + "image_path": "b66716394349be0ffe58ce366f788d3ef1c8ab6245f545c8b545e334ca114983.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 425, + 286, + 491 + ], + "lines": [ + { + "bbox": [ + 47, + 425, + 286, + 491 + ], + "spans": [ + { + "bbox": [ + 47, + 425, + 286, + 491 + ], + "type": "text", + "content": "Table 4. Ablation study on shape generation. The quality of synthesized tumors influences model performance to a certain degree, emphasizing the importance of each component in our proposed method (§3; Figure 3). The quality assessment of generated tumors is in Appendix Figure 11. Moreover, generating tiny synthetic tumors positively impacts the sensitivity of small tumors." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 47, + 515, + 286, + 562 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 515, + 286, + 562 + ], + "spans": [ + { + "bbox": [ + 47, + 515, + 286, + 562 + ], + "type": "text", + "content": "we evaluate several state-of-the-art models (trained on public datasets). These models show good robustness in the shape, location, and texture dimensions but are sensitive to tumors of extreme sizes and intensities." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 573, + 242, + 587 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 573, + 242, + 587 + ], + "spans": [ + { + "bbox": [ + 47, + 573, + 242, + 587 + ], + "type": "text", + "content": "5.6. Ablation Study on Shape Generation" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 592, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 592, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 592, + 286, + 713 + ], + "type": "text", + "content": "To show the importance of each step in tumor generation, we design ablation studies focusing on shape generation and synthesizing small tumors. We evaluate the models trained with different incomplete settings of synthetic strategies on two aspects: all tumor segmentation and small tumor detection. As shown in Table 4, the performance would be much poorer without synthesizing small tumors, edge blurring or elastic deformation in the shape generation. The reasons are simple: (1) without elastic deformation and edge blurring steps for shape generation (shown in Figure 3), the syn" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 349, + 546, + 409 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 349, + 546, + 409 + ], + "spans": [ + { + "bbox": [ + 305, + 349, + 546, + 409 + ], + "type": "text", + "content": "thetic tumors can be extremely unrealistic (i.e. the edge is sharp and shape can only be ellipsoid). Several examples are provided in Appendix Figure 12. (2) The model doesn't have the generalization ability to small tumors (radius " + }, + { + "bbox": [ + 305, + 349, + 546, + 409 + ], + "type": "inline_equation", + "content": "< 5\\mathrm{mm}" + }, + { + "bbox": [ + 305, + 349, + 546, + 409 + ], + "type": "text", + "content": ") when the training set does not have them." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 417, + 379, + 430 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 417, + 379, + 430 + ], + "spans": [ + { + "bbox": [ + 305, + 417, + 379, + 430 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 438, + 546, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 438, + 546, + 604 + ], + "spans": [ + { + "bbox": [ + 305, + 438, + 546, + 604 + ], + "type": "text", + "content": "In this paper, we have developed an effective strategy to synthesize liver tumors. With zero manual annotation, we verify that the AI model trained on synthetic tumors can perform similarly to the ones trained on real tumors in the LiTS dataset (which took months to create). This reveals the great potential for the use of synthesis tumors to train AI models on larger-scale healthy CT datasets (which are much easier to obtain than CT scans with liver tumors). Furthermore, synthetic tumors allow us to assess AI's capability of detecting tumors of varying locations, sizes, shapes, intensities, textures, and stages in CT scans. In the future, we will consider generative adversarial nets (GANs) [17,19], Diffusion Models [22] and possibly improved with 3D geometry models like NeRF [43] to generate better tumor texture." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 605, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 605, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 605, + 546, + 713 + ], + "type": "text", + "content": "Acknowledgements. This work was supported by the Lustgarten Foundation for Pancreatic Cancer Research and partially by the Patrick J. McGovern Foundation Award. We appreciate the effort of the MONAI Team to provide open-source code for the community. We thank Yucheng Tang, Huimiao Chen, Bowen Li, Jessica Han, and Wenxuan Li for their constructive suggestions; thank Camille Torrico and Alexa Delaney for improving the writing of this paper. 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Springer, 2019. 1" + } + ] + } + ], + "index": 21 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 279, + 739, + 298, + 746 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 279, + 739, + 298, + 746 + ], + "spans": [ + { + "bbox": [ + 279, + 739, + 298, + 746 + ], + "type": "text", + "content": "7432" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 595, + 841 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Language Adaptive Weight Generation for Multi-Task Visual Grounding/09bf5769-e1b7-4520-b426-6463f773ed2a_content_list.json b/2023/Language Adaptive Weight Generation for Multi-Task Visual Grounding/09bf5769-e1b7-4520-b426-6463f773ed2a_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..6c49f8188a594be60b5fc840310e9699f70203d4 --- /dev/null +++ b/2023/Language Adaptive Weight Generation for Multi-Task Visual Grounding/09bf5769-e1b7-4520-b426-6463f773ed2a_content_list.json @@ -0,0 +1,1431 @@ +[ + { + "type": "text", + "text": "Language Adaptive Weight Generation for Multi-task Visual Grounding", + "text_level": 1, + "bbox": [ + 119, + 130, + 851, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Wei Su1 Peihan Miao1 Huanzhang Dou1 Gaoang Wang4 Liang Qiao1,3 Zheyang Li1,3 Xi Li1,2,5*", + "bbox": [ + 238, + 178, + 730, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ Zhejiang University $^{2}$ Shanghai AI Laboratory $^{3}$ Hikvision Research Institute $^{4}$ Zhejiang University-University of Illinois Urbana-Champaign Institute, Zhejiang University $^{5}$ Shanghai Institute for Advanced Study of Zhejiang University", + "bbox": [ + 117, + 215, + 849, + 270 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{weisuzju, peihan.miao, hzdou, qiaoliang, xilizju}@zju.edu.cn gaoangwang@intl.zju.edu.cn, lizheyang@hikvision.com", + "bbox": [ + 215, + 271, + 754, + 305 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 339, + 313, + 354 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Although the impressive performance in visual grounding, the prevailing approaches usually exploit the visual backbone in a passive way, i.e., the visual backbone extracts features with fixed weights without expression-related hints. The passive perception may lead to mismatches (e.g., redundant and missing), limiting further performance improvement. Ideally, the visual backbone should actively extract visual features since the expressions already provide the blueprint of desired visual features. The active perception can take expressions as priors to extract relevant visual features, which can effectively alleviate the mismatches. Inspired by this, we propose an active perception Visual Grounding framework based on Language Adaptive Weights, called VG-LAW. The visual backbone serves as an expression-specific feature extractor through dynamic weights generated for various expressions. Benefiting from the specific and relevant visual features extracted from the language-aware visual backbone, VG-LAW does not require additional modules for cross-modal interaction. Along with a neat multi-task head, VG-LAW can be competent in referring expression comprehension and segmentation jointly. Extensive experiments on four representative datasets, i.e., RefCOCO, RefCOCO+, RefCOCOg, and ReferItGame, validate the effectiveness of the proposed framework and demonstrate state-of-the-art performance.", + "bbox": [ + 75, + 369, + 473, + 750 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 791, + 209, + 806 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Visual grounding (such as referring expression comprehension [4, 23, 42, 45, 46, 48, 50], referring expression segmentation [6, 14, 17, 23, 32, 33, 44], and phrase grounding [4, 23, 50]) aims to detect or segment the specific object", + "bbox": [ + 75, + 816, + 468, + 878 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/f421886bb36a673d7a513c149a6d4ce2bf47e6eb3dd0c85999c73f1f4e4e42b4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 504, + 335, + 890, + 415 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/2e0b9c00a8a0e117cba7ffd3d29b229fbae1371bbd7d7f717de2d107c3b9081b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 503, + 417, + 890, + 500 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/71fde5d9edeacf11803b0fca155864d891e4a9aba332999927d3dd7c1caad168.jpg", + "image_caption": [ + "Figure 1. The comparison of visual grounding frameworks. (a) The visual and linguistic backbone independently extracts features, which are fused through cross-modal interaction. (b) Additional designed modules are inserted into the visual backbone to modulate visual features using linguistic features. (c) VG-LAW can generate language-adaptive weights for the visual backbone and directly output referred objects through our designed multitask head without additional cross-modal interaction modules." + ], + "image_footnote": [], + "bbox": [ + 504, + 500, + 890, + 580 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "based on a given natural language description. Compared to general object detection [38] or instance segmentation [11], which can only locate objects within a predefined and fixed category set, visual grounding is more flexible and purposeful. Free-formed language descriptions can specify specific visual properties of the target object, such as categories, attributes, relationships with other objects, relative/absolute positions, and etc.", + "bbox": [ + 496, + 732, + 893, + 853 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Due to the similarity with detection tasks, previous visual grounding approaches [23, 33, 46, 50] usually follow the general object detection frameworks [1, 11, 37], and pay", + "bbox": [ + 498, + 854, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* corresponding author.", + "bbox": [ + 94, + 887, + 218, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "10857", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/1ca2784989b575d0aa9823600577ec9f26dccd958f4887a1120b72dfca877a76.jpg", + "image_caption": [ + "Figure 2. Attention visualization of the visual backbone with different weights. (a) input image, (b) visual backbone with fixed weights, (c) and (d) visual backbone with weights generated for \"white bird\" and \"right bird\", respectively." + ], + "image_footnote": [], + "bbox": [ + 81, + 88, + 176, + 152 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/8fc0e0d4a8e3ab11886591230a7ec982c84f17decf4b205e9c8d622e09a14490.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 179, + 88, + 272, + 152 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/339a3a4390dc637070b3f728727aae1a56ba654d9bd1cec0ea620c4494b8a843.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 276, + 88, + 370, + 152 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/d05fba495222e7bba79e0f5bdb1e0deb46d101fb4507b3bd60e6b8b3c5a74073.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 372, + 88, + 465, + 152 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "attention to the design of cross-modal interaction modules. Despite achieving impressive performance, the visual backbone is not well explored. Concretely, the visual backbone passively extracts visual features with fixed architecture and weights, regardless of the referring expressions, as illustrated in Fig. 1 (a). Such passive feature extraction may lead to mismatches between the extracted visual features and those required for various referring expressions, such as missing or redundant features. Taking Fig. 2 as an example, the fixed visual backbone has an inherent preference for the image, as shown in Fig. 2 (b), which may be irrelevant to the referring expression \"white bird\". Ideally, the visual backbone should take full advantage of expressions, as the expressions can provide information and tendencies about the desired visual features.", + "bbox": [ + 75, + 248, + 468, + 474 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Several methods have noticed this phenomenon and proposed corresponding solutions, such as QRNet [45], and LAVT [44]. Both methods achieve the expression-aware visual feature extraction by inserting carefully designed interaction modules (such as QD-ATT [45], and PWAN [44]) into the visual backbone, as illustrated in Fig. 1 (b). Concretely, visual features are first extracted and then adjusted using QD-ATT (channel and spatial attention) or PWAM (transformer-based pixel-word attention) in QRNet and LAVT at the end of each stage, respectively. Although performance improvement with adjusted visual features, the extract-then-adjust paradigm inevitably contains a large number of feature-extraction components with fixed weights, e.g., the components belonging to the original visual backbone in QRNet and LAVT. Considering that the architecture and weights jointly determine the function of the visual backbone, this paper adopts a simpler and fine-grained scheme that modifies the function of the visual backbone with language-adaptive weights, as illustrated in Fig. 1 (c). Different from the extract-then-adjust paradigm used by QRNet and LAVT, the visual backbone equipped with language-adaptive weights can directly extract expression-relevant visual features without additional feature-adjustment modules.", + "bbox": [ + 75, + 476, + 470, + 838 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we propose an active perception Visual Grounding framework based on Language Adaptive Weights, called VG-LAW. It can dynamically adjust the behavior of the visual backbone by injecting the informa", + "bbox": [ + 75, + 839, + 468, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "tion of referring expressions into the weights. Specifically, VG-LAW first obtains the specific language-adaptive weights for the visual backbone through two successive processes of linguistic feature aggregation and weight generation. Then, the language-aware visual backbone can extract expression-relevant visual features without manually modifying the visual backbone architecture. Since the extracted visual features are highly expression-relevant, cross-modal interaction modules are not required for further cross-modal fusion, and the entire network architecture is more streamlined. Furthermore, based on the expression-relevant features, we propose a lightweight but neat multitask prediction head for jointly referring expression comprehension (REC) and referring expression segmentation (RES) tasks. Extensive experiments on RefCOCO [47], RefCOCO+ [47], RefCOCOg [36], and ReferItGame [19] datasets demonstrate the effectiveness of our method, which achieves state-of-the-art performance.", + "bbox": [ + 496, + 90, + 890, + 362 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The main contributions can be summarized as follows:", + "bbox": [ + 519, + 364, + 879, + 377 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose an active perception visual grounding framework based on the language adaptive weights, called VG-LAW, which can actively extract expression-relevant visual features without manually modifying the visual backbone architecture.", + "- Benefiting from the active perception of visual feature extraction, we can directly utilize our proposed neat but efficient multi-task head for REC and RES tasks jointly without carefully designed cross-modal interaction modules.", + "- Extensive experiments demonstrate the effectiveness of our framework, which achieves state-of-the-art performance on four widely used datasets, i.e., RefCOCO, RefCOCO+, RefCOCOg, and ReferItGame." + ], + "bbox": [ + 519, + 391, + 890, + 628 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 654, + 640, + 669 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Referring Expression Comprehension", + "text_level": 1, + "bbox": [ + 500, + 680, + 823, + 696 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Referring expression comprehension (REC) [4,13,30,42, 43,46,48-50] aims to generate a bounding box in an image specified by a given referring expression. Early researchers explore REC through a two-stage framework [13,29,30,46], where region proposals [38] are first extracted and then ranked according to their similarity scores with referring expressions. To alleviate the speed and accuracy issues of the region proposals in the two-stage framework, simpler and faster one-stage methods [42, 43, 49] based on dense anchors are proposed. Recently, transformer-based methods [4,12,18,48,50] can effectively capture intra- and intermodality context and achieve better performance, benefiting from the self-attention mechanism [40].", + "bbox": [ + 496, + 703, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "10858", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/a703d02f7d5868bfed0c1ceeb01394285b2a3c7abd582d6bb353ad615a30a456.jpg", + "image_caption": [ + "Figure 3. The overall architecture of our proposed VG-LAW framework. It consists of four components: (1) Linguistic Backbone, which extracts linguistic features from free-formed referring expressions, (2) Language Adaptive Weight Generator, which generates dynamic weights for the visual backbone conditioned on specific expressions, (3) Visual Backbone, which extracts visual features from the raw image and its behavior can be modified by language-adaptive weights, and (4) Multi-task Head, which predicts the bounding box and mask of referred object jointly. $\\otimes$ represents the matrix multiplication." + ], + "image_footnote": [], + "bbox": [ + 81, + 88, + 890, + 287 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Referring Expression Segmentation", + "text_level": 1, + "bbox": [ + 76, + 393, + 387, + 411 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Similar to REC, referring expression segmentation (RES) [6, 9, 14, 15, 17, 20, 23, 32, 44, 50] aims to predict a precise pixel-wise binary mask corresponding to the given referring expression. The pioneering work [14] proposes to generate segmentation masks for natural language expressions by concatenating the visual and linguistic features and mixing these two modal features with fully convolutional classifiers. Follow-up solutions [9, 15, 17, 32] propose various attention mechanisms to perform cross-modal interaction to generate a high-resolution segmentation map. Recent studies [6, 20, 23, 44, 50], like REC, leverage transformer [40] to realize cross-modal interaction and achieve excellent performance. All these methods achieve cross-modal interaction by either adjusting the inputs or modifying the architectures with fixed network weights.", + "bbox": [ + 75, + 419, + 473, + 647 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.3. Dynamic Weight Networks", + "text_level": 1, + "bbox": [ + 76, + 662, + 321, + 680 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Several works [3, 10, 16, 24, 41] have investigated dynamic weight networks, where given inputs adaptively generate the weights of the network. According to the way of dynamic weight generation, the current methods can be roughly divided into three categories. (1) Dynamic weights are directly generated using fully-connected layers with learnable embeddings [10] or intermediate features [16] as input. (2) Weights are computed as the weighted sum of a set of learnable weights [3, 22, 41], which can also be regarded as the mixture-of-experts and may suffer from challenging joint optimization. (3) The weights are analyzed from the perspective of matrix decomposition [24], and the final dynamic weights are generated by calculating the multiplication of several matrices.", + "bbox": [ + 75, + 688, + 472, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 500, + 393, + 591, + 409 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we will introduce the active perception framework for multi-task visual grounding, including the language-adaptive weight generation, multi-task prediction head, and training objectives.", + "bbox": [ + 496, + 420, + 893, + 482 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Overview", + "text_level": 1, + "bbox": [ + 500, + 496, + 609, + 510 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The extraction of visual features by the visual backbone in the manner of passive perception may cause mismatch problems, which can lead to suboptimal performance despite subsequent carefully designed cross-modal interaction modules. Considering that expressions already provide a blueprint for the desired visual features, we propose an active perception visual grounding framework based on the language adaptive weights, called VG-LAW, as illustrated in Fig. 3. In this framework, the visual backbone can actively extract expression-relevant visual features using language-adaptive weights, without needing to manually modify the visual backbone architecture or elaborately design additional cross-modal interaction modules.", + "bbox": [ + 496, + 521, + 893, + 717 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Specifically, the VG-LAW framework consists of four components, i.e., linguistic backbone, language adaptive weight generator, visual backbone, and multi-task head. Given a referring expression, the $N$ -layer BERT-based [5] linguistic backbone tokenizes the expressions, prepends a [CLS] token, and extracts linguistic features $F_{l} \\in \\mathbb{R}^{L \\times d_{l}}$ where $L$ and $d_{l}$ represent the token numbers and dimension of linguistic features, respectively. The linguistic features $F_{l}$ are then fed to the language adaptive weight generator to generate weights for the transformer-based visual backbone. Next, given an image $I \\in \\mathbb{R}^{3 \\times H \\times W}$ , the expression-aware visual features $F_{v} \\in \\mathbb{R}^{C \\times \\frac{H}{s} \\times \\frac{W}{s}}$ can be extracted by", + "bbox": [ + 496, + 719, + 895, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "10859", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/31f51d04e7bac8198c5dbaf947fd750cd127876a9384ff4286c57e5b18885fc2.jpg", + "image_caption": [ + "Figure 4. The detailed architecture for language adaptive weight generation. The upper part shows the architecture of the adapted ViT block in the visual backbone, and the lower part shows the linguistic feature aggregation and weight generation." + ], + "image_footnote": [], + "bbox": [ + 86, + 90, + 460, + 315 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "the visual backbone, where $C$ and $s$ represent the channel number and stride of the visual features, respectively. Finally, we pass the linguistic features $F_{l}^{1} \\in \\mathbb{R}^{\\bar{d}_{l}}$ represented by the [CLS] token and the visual features to the multi-task head, which predicts the bounding box and mask of the referred object for REC and RES, respectively.", + "bbox": [ + 75, + 409, + 468, + 501 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Language Adaptive Weight Generation", + "text_level": 1, + "bbox": [ + 76, + 510, + 413, + 526 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "After extracting linguistic features, language-adaptive weights are generated to guide the active perception of the visual backbone. The process of language adaptive weight generation has two stages, i.e., the layer-wise linguistic feature aggregation and the weight generation.", + "bbox": [ + 75, + 532, + 468, + 609 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Linguistic Feature Aggregation. Considering the referring expressions correspond to a different number of linguistic tokens and each layer of the visual backbone may prefer different linguistic tokens, we try to aggregate linguistic features with fixed sizes for each layer independently. Inspired by the multi-head attention mechanism [40], we introduce a learnable layer-specific embedding $e_i \\in \\mathbb{R}^{d_l}$ for each layer $i$ of the visual backbone to extract layer-specific linguistic features dynamically, which can improve the model flexibility at negligible cost. The calculation is performed on $G$ groups. For each group $g$ , the token-wise attention $\\alpha_i^g \\in [0,1]^L$ is assigned to the normalized dot product of $e_i^g$ and $F_l^g$ , which is denoted as:", + "bbox": [ + 75, + 628, + 468, + 825 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\alpha_ {i} ^ {g} = \\mathrm {S o f t m a x} ([ e _ {i} ^ {g} \\cdot F _ {l} ^ {g, 1}, e _ {i} ^ {g} \\cdot F _ {l} ^ {g, 2}, \\dots , e _ {i} ^ {g} \\cdot F _ {l} ^ {g, L} ]). (1)\n$$\n", + "text_format": "latex", + "bbox": [ + 86, + 837, + 468, + 858 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Then, the aggregated linguistic feature $h_0^i \\in \\mathbb{R}^{d_l}$ can be derived by concatenating $h_0^{i,g} = \\sum_{j=1}^{L} \\alpha_i^{g,j} F_l^{g,j}$ .", + "bbox": [ + 75, + 867, + 468, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Finally, we use a fully-connected layer (FC) to reduce the dimension of the aggregated linguistic features for the $i$ -th layer of the visual backbone, which is indicated as:", + "bbox": [ + 498, + 90, + 890, + 136 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nh _ {1} ^ {i} = \\delta \\left(W _ {1} ^ {i} h _ {0} ^ {i}\\right), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 640, + 148, + 890, + 165 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $W_1^i \\in \\mathbb{R}^{d_l \\times d_h}$ is used to reducing the dimension to $d_h = d_l / r$ , and $r$ is the reduction ratio. $\\delta$ refers to the GeLU activation function.", + "bbox": [ + 498, + 176, + 890, + 220 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Weight Generation. To guide the active perception of the visual backbone, we generate language-adaptive weights for producing the query $X_{q}$ , key $X_{k}$ , and value $X_{v}$ in the visual backbone conditioned on referring expressions, which can be represented as:", + "bbox": [ + 498, + 241, + 890, + 316 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nX _ {q} = \\theta (X; W _ {q}), X _ {k} = \\theta (X; W _ {k}), X _ {v} = \\theta (X; W _ {v}), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 509, + 328, + 890, + 345 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\theta (\\cdot ;W)$ indicates the linear projection operation parameterized by $W$ , and $X$ represents the input visual features. $W_{q},W_{k},W_{v}\\in \\mathbb{R}^{d_{out}\\times d_{in}}$ are the dynamic projection weights used to generate the query, key, and value, respectively. $d_{in}$ and $d_{out}$ are the dimension of feature $X$ and query/key/value, respectively.", + "bbox": [ + 498, + 356, + 890, + 446 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Considering the large number $d_{out} \\times d_{in}$ of the dynamic weights, it is unaffordable to directly generate weights using fully-connected layers like Hypernetworks [10]. The DynamicConv [3] and CondConv [41] can alleviate this problem by generating weights with weighted summation of $K$ static kernels but can increase the parameter number by $K$ -times and suffer from challenging joint optimization. Inspired by the dynamic channel fusion [24], we try to generate dynamic weights following the matrix decomposition paradigm. Taking the $i$ -th ViT block as an example, which can be formulated as:", + "bbox": [ + 496, + 448, + 890, + 612 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left[ W _ {q} ^ {i}, W _ {k} ^ {i}, W _ {v} ^ {i} \\right] = W _ {0} ^ {i} + P \\Phi \\left(h _ {1} ^ {i}\\right) Q ^ {T}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 573, + 625, + 890, + 643 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $W_0^i \\in \\mathbb{R}^{d_{out} \\times d_{in}}$ is the layer-specific static learnable weights. $P \\in \\mathbb{R}^{d_{out} \\times d_w}$ and $Q \\in \\mathbb{R}^{d_{in} \\times d_w}$ are also static learnable weights, but sharable across all ViT blocks to reduce the parameter numbers and prevent the model from overfitting. $\\Phi(h_1^i)$ is a fully-connected layer, which produces a dynamic matrix of shape $d_w \\times d_w$ with aggregated linguistic features $h_1^i$ as input.", + "bbox": [ + 496, + 655, + 890, + 763 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Multi-task Head", + "text_level": 1, + "bbox": [ + 500, + 771, + 663, + 786 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Different from the previous methods [6,23,42,45,46,49, 50], which require carefully designed cross-modal interaction modules, VG-LAW can obtain expression-relevant visual features extracted by the language-aware visual backbone without additional cross-modal interaction modules. Through our proposed neat but efficient multi-task head, we can utilize the visual and linguistic features to predict", + "bbox": [ + 496, + 794, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "10860", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "the bounding box for REC and the segmentation mask for RES. Concretely, there are two branches in the multi-task head for REC and RES, respectively.", + "bbox": [ + 75, + 90, + 468, + 136 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For the REC branch, we apply direct coordinate regression to predict the bounding box of referred object. To pool the 2- $d$ visual features along the spatial dimension, we propose a language adaptive pooling module (LAP), which aggregates visual features using language-adaptive attention. Specifically, the visual features $\\{F_v^{i,j}\\} \\in \\mathbb{R}^{C\\times \\frac{H}{s}\\times \\frac{W}{s}}$ and linguistic feature $F_{l}^{1}\\in \\mathbb{R}^{d_{l}}$ are firstly projected to the lower-dimension space $\\mathbb{R}^k$ , and the attention weights $A\\in \\mathbb{R}_{\\frac{H}{s}\\times \\frac{W}{s}}$ are calculated as dot-product similarity followed by Softmax normalization. Then, the visual features are aggregated by calculating the weighted sum with attention weights $A$ . Finally, the aggregated visual features are fed to a three-layer fully-connected layer, and the Sigmoid function is used to predict the referred bounding box $\\hat{b} = (\\hat{x},\\hat{y},\\hat{w},\\hat{h})$ .", + "bbox": [ + 75, + 136, + 468, + 362 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For the RES branch, we apply binary classification to each visual feature along the spatial dimension to predict segmentation masks for referred objects. Specifically, the visual features $F_{v}$ are first up-sampled to $\\hat{F}_v\\in \\mathbb{R}^{d_l\\times \\frac{H}{4}\\times \\frac{W}{4}}$ with successive transposed convolutions. Then, the intermediate segmentation map $\\bar{s}\\in \\mathbb{R}^{\\frac{H}{4}\\times \\frac{W}{4}}$ can be obtained by using linear projection $\\theta (\\cdot ;W)$ on each visual feature. Following the language adaptive weight paradigm, we also use dynamic rather than fixed weights by simply setting $W = F_l^1$ . Finally, the full-resolution segmentation mask $\\hat{s}\\in \\mathbb{R}^{H\\times W}$ is derived by simply up-sample $\\bar{s}$ using bilinear interpolation, followed by the Sigmoid function.", + "bbox": [ + 75, + 363, + 470, + 544 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Training Objectives", + "text_level": 1, + "bbox": [ + 76, + 551, + 264, + 566 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The VG-LAW framework can be optimized end-to-end for multi-task visual grounding. For REC, given the predicted bounding box $\\hat{b} = (\\hat{x},\\hat{y},\\hat{w},\\hat{h})$ and the ground truth $b = (x,y,w,h)$ , the detection loss function is defined as follows:", + "bbox": [ + 75, + 574, + 468, + 648 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {d e t}} = \\lambda_ {L 1} \\mathcal {L} _ {L 1} (b, \\hat {b}) + \\lambda_ {g i o u} \\mathcal {L} _ {g i o u} (b, \\hat {b}), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 133, + 656, + 468, + 674 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_{L1}(\\cdot, \\cdot)$ and $\\mathcal{L}_{giou}(\\cdot, \\cdot)$ represent L1 loss and Generalized IoU loss [39], respectively, and $\\lambda_{L1}$ and $\\lambda_{giou}$ are the relative weights to control the two detection loss functions. For RES, given the predicted mask $\\hat{s}$ and the ground-truth $s$ , the segmentation loss function is defined as follows:", + "bbox": [ + 75, + 680, + 468, + 755 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {s e g}} = \\lambda_ {\\text {f o c a l}} \\mathcal {L} _ {\\text {f o c a l}} (s, \\hat {s}) + \\lambda_ {\\text {d i c e}} \\mathcal {L} _ {\\text {d i c e}} (s, \\hat {s}), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 119, + 763, + 468, + 781 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_{focal}(\\cdot, \\cdot)$ and $\\mathcal{L}_{dice}(\\cdot, \\cdot)$ represent focal loss [27] and DICE/F-1 loss [35], respectively, and $\\lambda_{focal}$ and $\\lambda_{dice}$ are the relative weights to control the two segmentation loss functions. Our framework can be seamlessly used for joint training of REC and RES, and its joint training loss function is defined as follows:", + "bbox": [ + 75, + 786, + 468, + 876 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {t o t a l}} = \\mathcal {L} _ {\\text {d e t}} + \\mathcal {L} _ {\\text {s e g}}. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 196, + 885, + 468, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The trained model performs well for language-guided detection and segmentation. The experimental analysis of the whole framework will be elaborated in Sec. 4.", + "bbox": [ + 498, + 90, + 890, + 135 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 498, + 147, + 630, + 165 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we will give a detailed experimental analysis of the whole framework, including the datasets, evaluation protocol, implementation details, comparisons with the state-of-the-art methods, and ablation analysis.", + "bbox": [ + 496, + 172, + 890, + 233 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Datasets and Evaluation Protocol", + "text_level": 1, + "bbox": [ + 498, + 239, + 790, + 255 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets. To verify the effectiveness of our method, we conduct experiments on the widely used RefCOCO [47], RefCOCO+ [47], RefCOCOg [34], and ReferItGame [19] datasets. RefCOCO, RefCOCO+, and RefCOCOg are collected from MS-COCO [28]. RefCOCO and RefCOCO+, which are collected in interactive games, can be divided into train, val, testA, and testB sets. Compared to RefCOCO, the expressions of RefCOCO+ contain more attributes than absolute locations. Unlike RefCOCO and RefCOCO+, RefCOCOg collected by Amazon Mechanical Turk has a longer length of 8.4 words, including the attribute and location of referents. Following a common version of split [36], RefCOCOg has train, val, and test sets. In addition, ReferItGame collected from SAIAPR-12 [8] contains train and test sets. Each sample in the above datasets contains its corresponding bounding box and mask.", + "bbox": [ + 496, + 263, + 890, + 505 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Evaluation Protocol. Following the previous works [23, 33, 50], we use Prec@0.5 and mIoU to evaluate the performance of REC and RES, respectively. For Prec@0.5, the predicted bounding box is considered correct if the intersection-over-union (IoU) with the ground-truth bounding box is greater than 0.5. mIoU represents the IoU between the prediction and ground truth averaged across all test samples.", + "bbox": [ + 496, + 522, + 890, + 643 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Implementation Details", + "text_level": 1, + "bbox": [ + 498, + 650, + 715, + 666 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Training. The resolution of the input image is resized to $448 \\times 448$ . ViT-Base [7] is used as the visual backbone, and we follow the adaptation introduced by ViTDet [25] to adapt the visual backbone to higher-resolution images. The visual backbone is pre-trained using Mask R-CNN [11] on MS-COCO [28], where overlapping images of the val/test sets are excluded. The $W_0^i$ and $\\Phi(h_1^i)$ in Eq. (4) are initialized with the corresponding pre-trained weights of the visual backbone and zeros, respectively. The maximum length of referring expression is set to 40, and the uncased base of six-layer BERT [5] as the linguistic backbone is used to generate linguistic features. $\\lambda_{L1}$ and $\\lambda_{giou}$ are set to 1. $\\lambda_{focal}$ and $\\lambda_{dice}$ are set to 4. The reduction ratio $r$ is set to 16. The initial learning rate for the visual and linguistic backbone is 4e-5, and the initial learning rate for the", + "bbox": [ + 496, + 674, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "10861", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/06e9bac9514b6dfa99a32ee8dbc7d9700f35be97397f7c5ed98dab4dfa7246ad.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodsVenueVisual BackboneMulti-taskRefCOCORefCOCO+RefCOCOgReferItGame test
valtestAtestBvaltestAtestBvaltest
Two-stage:
MAttNet [46]CVPR18RN101X76.6581.1469.9965.3371.6256.0266.5867.2729.04
RvG-Tree [13]TPAMI19RN101X75.0678.6169.8563.5167.4556.6666.9566.51-
CM-A-E [30]CVPR19RN101X78.3583.1471.3268.0973.6558.0367.9968.67-
Ref-NMS [2]AAAI21RN101X80.7084.0076.0468.2573.6859.4270.5570.62-
One-stage:
FAOA [43]ICCV19DN53X72.5474.3568.5056.8160.2349.6061.3360.3660.67
ReSC-Large [42]ECCV20DN53X77.6380.4572.3063.5968.3656.8167.3067.2064.60
MCN [33]CVPR20DN53✓80.0882.2974.9867.1672.8657.3166.4666.01-
RealGIN [49]TNNLS21DN53X77.2578.7072.1062.7867.1754.2162.7562.33-
PLV-FPN* [26]TIP22RN101X81.9384.9976.2571.2077.4061.0870.4571.0871.77
Transformer-based:
TransVG [4]ICCV21RN101X81.0282.7278.3564.8270.7056.9468.6767.7370.73
RefTR* [23]NeurIPS21RN101✓82.2385.5976.5771.5875.9662.1669.4169.4071.42
SeqTR [50]ECCV22DN53X81.2385.0076.0868.8275.3758.7871.3571.5869.66
Word2Pix [48]TNNLS22RN101X81.2084.3978.1269.7476.1161.2470.8171.34-
YORO [12]ECCVW22-X82.9085.6077.4073.5078.6064.9073.4074.3071.90
QRNet [45]CVPR22Swin-SX84.0185.8582.3472.9476.1763.8171.8973.0374.61
Ours:
VG-LAW-ViT-BX86.0688.5682.8775.7480.3266.6975.3175.9576.60
VG-LAW-ViT-B✓86.6289.3283.1676.3781.0467.5076.9076.9677.22
", + "bbox": [ + 76, + 88, + 898, + 438 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/61bbb9e6fb2eb50e7dbc26be8da994ff57408040e09abbf0aefadd16172a7644.jpg", + "table_caption": [ + "Table 1. Comparison with state-of-the-art methods on RefCOCO [47], RefCOCO+ [47], RefCOCOg [36] and ReferItGame [19] for REC task. The visual backbone is pre-trained on MS-COCO [28], where overlapping images of the val/test sets are excluded. * represents ImageNet [21] pre-training. RN101, DN53, Swin-S, and ViT-B are shorthand for the ResNet101, DarkNet53, Swin-Transformer Small, and ViT Base, respectively. We highlight the best and second best performance in the red and blue colors." + ], + "table_footnote": [], + "table_body": "
MethodsVenueVisual BackboneMulti-taskRefCOCORefCOCO+RefCOCOg
valtestAtestBvaltestAtestBvaltest
CGAN [32]MM20DN53X64.8668.0462.0751.0355.5144.0654.4054.25
MCN [33]CVPR20DN53✓62.4464.2059.7150.6254.9944.6949.2249.40
LTS [17]CVPR21DN53X65.4367.7663.0854.2158.3248.0254.4054.25
VLT [50]ICCV21DN53X65.6568.2962.7355.5059.2049.3652.9956.65
RefTR* [23]NeurIPS21RN101✓70.5673.4966.5761.0864.6952.7358.7358.51
SeqTR [50]ECCV22DN53X67.2669.7964.1254.1458.9348.1955.6755.64
LAVT* [44]CVPR22Swin-BX74.4676.8970.9465.8170.9759.2363.6263.66
Ours:
VG-LAW-ViT-BX75.0577.3671.6966.6170.3058.1465.3665.13
VG-LAW-ViT-B✓75.6277.5172.8966.6370.3858.8965.6366.08
", + "bbox": [ + 142, + 516, + 828, + 700 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. Comparison with state-of-the-art methods on RefCOCO [47], RefCOCO+ [47], and RefCOCOg [36] for RES task. The visual backbone is pre-trained on MS-COCO [28], where overlapping images of the val/test sets are excluded. * represents ImageNet [21] pre-training. RN101, DN53, Swin-B, and ViT-B are shorthand for the ResNet101, DarkNet53, Swin-Transformer Base, and ViT Base, respectively. We highlight the best and second best performance in the red and blue colors.", + "bbox": [ + 75, + 709, + 892, + 767 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "remaining components is 4e-4. The model is end-to-end optimized by AdamW [31] for 90 epochs with a batch size of 256, where weight decay is set to 1e-4, and the learning rate is reduced by a factor of 10 after 60 epochs. Data augmentation operation includes random horizontal flips. We implement our framework using PyTorch and conduct experiments with NVIDIA A100 GPUs.", + "bbox": [ + 75, + 792, + 470, + 898 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Inference. At inference time, the input image is resized to $448 \\times 448$ , and the maximum length of referring expressions is set to 40. Following the previous method [33], We set the threshold to 0.35 to realize the binarization of the RES prediction. Without any post-processing operation, our framework directly outputs bounding boxes and segmentation maps specified by referring expressions.", + "bbox": [ + 496, + 792, + 893, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "10862", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/e718842e9dc933811d396986013a8a741d114979614c013f1ab4e76fa0a8f1ef.jpg", + "image_caption": [ + "Figure 5. Comparison of accuracy under different lengths of referring expression on RefCOCOg-test. ReSC [42], TransVG [4], Word2Pix [48], and the proposed VG-LAW are compared." + ], + "image_footnote": [], + "bbox": [ + 102, + 93, + 444, + 270 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Comparisons with State-of-the-art Methods", + "text_level": 1, + "bbox": [ + 76, + 353, + 447, + 369 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To estimate the effectiveness of the proposed VG-LAW framework, we conduct quantitative experiments on four widely used datasets, i.e., RefCOCO [47], RefCOCO+ [47], RefCOCOg [34], and ReferItGame [19].", + "bbox": [ + 75, + 376, + 468, + 439 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "REC Task. For the REC task, we compare the performance with state-of-the-art REC methods, including the two-stage methods [2, 13, 30, 46], one-stage methods [26, 33, 42, 43, 49], and transformer-based methods [4, 12, 23, 45, 48, 50]. The main results are summarized to Tab. 1. It can be observed that VG-LAW achieves a significant performance improvement compared to the state-of-the-art two-stage method Ref-NMS [2] and one-stage method PLV-FPN [26]. When comparing to the transformer-based method QRNet [45], which modified the visual backbone by inserting language-aware spatial and channel attention modules, our method has better performance with $+2.62\\% / +3.47\\% / +0.82\\%$ on RefCOCO, $+3.43\\% / +4.87\\% / +3.69\\%$ on RefCOCO+, $+5.01\\% / +3.93\\%$ on RefCOCOg, and $+2.61\\%$ on ReferItGame. QRNet [45] follows the TransVG [4] framework, both of which use the transformer encoder-based cross-modal interaction module. Compared to them, VG-LAW achieves better performance without complex cross-modal interaction modules. Furthermore, our method significantly outperforms MCN [33] and RefTR [23] based on joint training of REC and RES.", + "bbox": [ + 75, + 457, + 470, + 775 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "RES Task. For the RES task, we compare the performance with state-of-the-art methods [6,17,23,32,33,44,50], and the main results are summarized to Tab. 2. Compared with state-of-the-art RES method LAVT [44], VG-LAW achieves better $mIoU$ with $+1.16\\% / +0.62\\% / +1.95\\%$ on RefCOCO, $+2.01\\% / +2.42\\%$ on RefCOCOg, and comparable $mIoU$ with $+0.82\\% / -0.59\\% / -0.34\\%$ on RefCOCO+.", + "bbox": [ + 75, + 794, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/883776ab57b09b2069ca094279e6a9703540d1b6ecdd88d61be5b08815a8925f.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
LAWGLAPMTHPrec@0.5(%)
✓74.89
✓74.37
✓✓76.60
✓✓✓77.22
", + "bbox": [ + 553, + 88, + 841, + 188 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3. Ablation experiments on ReferItGame [19] to evaluate the proposed language adaptive weight generation (LAWG), language adaptive pooling (LAP), and multi-task head (MTH).", + "bbox": [ + 498, + 199, + 890, + 241 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "When comparing the models trained with or without multi-task settings, it can also be observed that consistent performance gains are achieved across all the datasets and splits. As REC can provide localization information of the referred object, such coarse-grained supervision can slightly improve the segmentation accuracy in RES.", + "bbox": [ + 498, + 268, + 890, + 359 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Analysis of Referring Expression Length. As the visual backbone in VG-LAW extracts features purely perceptually, it is of concern whether it can handle long and complex referring expressions. ReSC [42] reveals that one-stage methods may ignore detailed descriptions in complex referring expressions and lead to poor performance. Following that, we evaluate the REC performance on referring expressions of different lengths, as illustrated in Fig. 5. VG-LAW performs better than ReSC, TransVG [4] and Word2Pix [48], with no significant performance degradation when the length of referring expressions varies from 6-7 to $11+$ .", + "bbox": [ + 498, + 378, + 890, + 545 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Ablation Analysis", + "text_level": 1, + "bbox": [ + 500, + 556, + 671, + 571 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To validate the effectiveness of our proposed modules, i.e. language-adaptive weight generation, language-adaptive pooling, and multi-task head, we conduct ablation experiments on the REC dataset of ReferItGame, which is summarized in Tab. 3. When only using the LAWG, the visual features are pooled with global average pooling, and when only using the LAP, the visual backbone has fixed architecture and weights. When only using the LAWG or the LAP, it can be observed that the model already achieves $74.89\\%$ and $74.37\\%$ , respectively, which is close to the $74.61\\%$ reported by QRNet [45]. When combined with the LAWG and LAP, further improvements can be brought by LAWG and LAP with $+2.23\\%$ and $+1.71\\%$ , respectively. Benefiting from the auxiliary supervision of RES, our model equipped with the multi-task head can localize the referred objects better and achieve $77.22\\%$ .", + "bbox": [ + 498, + 579, + 890, + 820 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.5. Qualitative Results", + "text_level": 1, + "bbox": [ + 500, + 830, + 681, + 847 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The qualitative results of the four datasets are shown in Fig. 6. It can be observed that our model can successfully locate and segment the referred objects, and the attention of", + "bbox": [ + 498, + 854, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "10863", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/60f13a15c23dcc097354103c325bfc86b86a4fa8a9404a5fd2edde0901309009.jpg", + "image_caption": [ + "Figure 6. Qualitative results on the RefCOCO [47], RefCOCO+ [47], RefCOCOg [34], and ReferItGame [19] datasets. Each dataset shows two examples. From left to right: the input image, the ground truth of REC and RES, the prediction of VG-LAW, and the attention of the visual backbone with language-adaptive weights." + ], + "image_footnote": [], + "bbox": [ + 89, + 89, + 883, + 406 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6924d1d9e7c0fb578033c5acf10f16f4dbc9539dffcc2b70facc3d2c1ae76048.jpg", + "image_caption": [ + "Figure 7. Wordcloud visualization of words assigned to the first and second halves of the visual backbone." + ], + "image_footnote": [], + "bbox": [ + 89, + 483, + 264, + 585 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6889d45355f4cd056702b3e009912c6fefc0f245803fbf5271b3ef83084ca52f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 281, + 484, + 455, + 585 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "the visual backbone can focus on the most relevant image regions, demonstrating the effectiveness of using language adaptive weights. Taking the results on ReferItGame as an example, the visual backbone can dynamically filter out irrelevant regions for different expressions. For instance, when the \"purple curtain\" is referred to, the regions related to the \"the painting/photo on the wall\" are ignored.", + "bbox": [ + 75, + 656, + 468, + 763 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In addition, we count the scores of words assigned to the first and second halves of the visual backbone, as shown in Fig. 7. The scores are calculated by averaging attention score $\\alpha_{i}$ in Eq. (1) for each word, followed by softmax normalization along the layer dimension. It can be observed that the shallow layers tend to the words describing individuals, such as the categories \"velvet\" and \"yacht\", and the deep layers tend to the words about contexts, such as the ordinal number \"2nd\" and the position \"right\".", + "bbox": [ + 75, + 763, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusions and Limitations", + "text_level": 1, + "bbox": [ + 500, + 484, + 767, + 500 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we propose an active perception framework VG-LAW for visual grounding, based on the language adaptive weights. VG-LAW can directly inject the information of referring expressions into the weights of the visual backbone without modifying its architecture. Equipped with the proposed neat yet efficient multi-task head, VG-LAW achieves state-of-the-art performance for REC and RES tasks on widely used datasets. The limitations of our method are two-fold: (1) VG-LAW is weak in interpretability, and the entire reasoning process is implicit, which makes it difficult to understand how the reasoning process works, and (2) the multi-task head predicts one instance at a time, which limits its application in phrase grounding.", + "bbox": [ + 496, + 511, + 890, + 708 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Acknowledgments", + "text_level": 1, + "bbox": [ + 500, + 723, + 679, + 739 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work is supported in part by National Key Research and Development Program of China under Grant 2020AAA0107400, National Natural Science Foundation of China under Grant U20A20222, National Science Foundation for Distinguished Young Scholars under Grant 62225605, Ant Group through CCF-Ant Research Fund, and sponsored by CCF-AFSG Research Fund, CAAI-HUAWEI MindSpore Open Fund, CCF-Zhipu AI Large Model Fund (CCF-Zhipu202302) as well as Hikvision Cooperation Fund.", + "bbox": [ + 496, + 750, + 892, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "10864", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Nicolas Carion, Francisco Massa, Gabriel Synnaeve, Nicolas Usunier, Alexander Kirillov, and Sergey Zagoruyko. 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Seqtr: A simple yet universal network for visual grounding. arXiv preprint arXiv:2203.16265, 2022. 1, 2, 3, 4, 5, 6, 7" + ], + "bbox": [ + 501, + 90, + 890, + 329 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "10866", + "bbox": [ + 480, + 945, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Language Adaptive Weight Generation for Multi-Task Visual Grounding/09bf5769-e1b7-4520-b426-6463f773ed2a_model.json b/2023/Language Adaptive Weight Generation for Multi-Task Visual Grounding/09bf5769-e1b7-4520-b426-6463f773ed2a_model.json new file mode 100644 index 0000000000000000000000000000000000000000..d2f906bbb0a83904b09700f9f40dc2d0c507fe36 --- /dev/null +++ b/2023/Language Adaptive Weight Generation for Multi-Task Visual Grounding/09bf5769-e1b7-4520-b426-6463f773ed2a_model.json @@ -0,0 +1,1980 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.12, + 0.131, + 0.852, + 0.154 + ], + "angle": 0, + "content": "Language Adaptive Weight Generation for Multi-task Visual Grounding" + }, + { + "type": "text", + "bbox": [ + 0.24, + 0.179, + 0.731, + 0.217 + ], + "angle": 0, + "content": "Wei Su1 Peihan Miao1 Huanzhang Dou1 Gaoang Wang4 Liang Qiao1,3 Zheyang Li1,3 Xi Li1,2,5*" + }, + { + "type": "text", + "bbox": [ + 0.119, + 0.217, + 0.851, + 0.271 + ], + "angle": 0, + "content": "\\(^{1}\\)Zhejiang University \\(^{2}\\)Shanghai AI Laboratory \\(^{3}\\)Hikvision Research Institute \\(^{4}\\)Zhejiang University-University of Illinois Urbana-Champaign Institute, Zhejiang University \\(^{5}\\)Shanghai Institute for Advanced Study of Zhejiang University" + }, + { + "type": "text", + "bbox": [ + 0.216, + 0.272, + 0.756, + 0.306 + ], + "angle": 0, + "content": "{weisuzju, peihan.miao, hzdou, qiaoliang, xilizju}@zju.edu.cn gaoangwang@intl.zju.edu.cn, lizheyang@hikvision.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.34, + 0.314, + 0.356 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.371, + 0.474, + 0.751 + ], + "angle": 0, + "content": "Although the impressive performance in visual grounding, the prevailing approaches usually exploit the visual backbone in a passive way, i.e., the visual backbone extracts features with fixed weights without expression-related hints. The passive perception may lead to mismatches (e.g., redundant and missing), limiting further performance improvement. Ideally, the visual backbone should actively extract visual features since the expressions already provide the blueprint of desired visual features. The active perception can take expressions as priors to extract relevant visual features, which can effectively alleviate the mismatches. Inspired by this, we propose an active perception Visual Grounding framework based on Language Adaptive Weights, called VG-LAW. The visual backbone serves as an expression-specific feature extractor through dynamic weights generated for various expressions. Benefiting from the specific and relevant visual features extracted from the language-aware visual backbone, VG-LAW does not require additional modules for cross-modal interaction. Along with a neat multi-task head, VG-LAW can be competent in referring expression comprehension and segmentation jointly. Extensive experiments on four representative datasets, i.e., RefCOCO, RefCOCO+, RefCOCOg, and ReferItGame, validate the effectiveness of the proposed framework and demonstrate state-of-the-art performance." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.792, + 0.21, + 0.808 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.818, + 0.47, + 0.88 + ], + "angle": 0, + "content": "Visual grounding (such as referring expression comprehension [4, 23, 42, 45, 46, 48, 50], referring expression segmentation [6, 14, 17, 23, 32, 33, 44], and phrase grounding [4, 23, 50]) aims to detect or segment the specific object" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.337, + 0.892, + 0.416 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.418, + 0.892, + 0.5 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.506, + 0.501, + 0.892, + 0.582 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.592, + 0.895, + 0.704 + ], + "angle": 0, + "content": "Figure 1. The comparison of visual grounding frameworks. (a) The visual and linguistic backbone independently extracts features, which are fused through cross-modal interaction. (b) Additional designed modules are inserted into the visual backbone to modulate visual features using linguistic features. (c) VG-LAW can generate language-adaptive weights for the visual backbone and directly output referred objects through our designed multitask head without additional cross-modal interaction modules." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.733, + 0.894, + 0.854 + ], + "angle": 0, + "content": "based on a given natural language description. Compared to general object detection [38] or instance segmentation [11], which can only locate objects within a predefined and fixed category set, visual grounding is more flexible and purposeful. Free-formed language descriptions can specify specific visual properties of the target object, such as categories, attributes, relationships with other objects, relative/absolute positions, and etc." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.894, + 0.903 + ], + "angle": 0, + "content": "Due to the similarity with detection tasks, previous visual grounding approaches [23, 33, 46, 50] usually follow the general object detection frameworks [1, 11, 37], and pay" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.888, + 0.22, + 0.901 + ], + "angle": 0, + "content": "* corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10857" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.083, + 0.089, + 0.177, + 0.153 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.18, + 0.089, + 0.274, + 0.153 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.277, + 0.089, + 0.371, + 0.153 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.373, + 0.089, + 0.467, + 0.153 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.164, + 0.47, + 0.22 + ], + "angle": 0, + "content": "Figure 2. Attention visualization of the visual backbone with different weights. (a) input image, (b) visual backbone with fixed weights, (c) and (d) visual backbone with weights generated for \"white bird\" and \"right bird\", respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.249, + 0.47, + 0.475 + ], + "angle": 0, + "content": "attention to the design of cross-modal interaction modules. Despite achieving impressive performance, the visual backbone is not well explored. Concretely, the visual backbone passively extracts visual features with fixed architecture and weights, regardless of the referring expressions, as illustrated in Fig. 1 (a). Such passive feature extraction may lead to mismatches between the extracted visual features and those required for various referring expressions, such as missing or redundant features. Taking Fig. 2 as an example, the fixed visual backbone has an inherent preference for the image, as shown in Fig. 2 (b), which may be irrelevant to the referring expression \"white bird\". Ideally, the visual backbone should take full advantage of expressions, as the expressions can provide information and tendencies about the desired visual features." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.477, + 0.471, + 0.839 + ], + "angle": 0, + "content": "Several methods have noticed this phenomenon and proposed corresponding solutions, such as QRNet [45], and LAVT [44]. Both methods achieve the expression-aware visual feature extraction by inserting carefully designed interaction modules (such as QD-ATT [45], and PWAN [44]) into the visual backbone, as illustrated in Fig. 1 (b). Concretely, visual features are first extracted and then adjusted using QD-ATT (channel and spatial attention) or PWAM (transformer-based pixel-word attention) in QRNet and LAVT at the end of each stage, respectively. Although performance improvement with adjusted visual features, the extract-then-adjust paradigm inevitably contains a large number of feature-extraction components with fixed weights, e.g., the components belonging to the original visual backbone in QRNet and LAVT. Considering that the architecture and weights jointly determine the function of the visual backbone, this paper adopts a simpler and fine-grained scheme that modifies the function of the visual backbone with language-adaptive weights, as illustrated in Fig. 1 (c). Different from the extract-then-adjust paradigm used by QRNet and LAVT, the visual backbone equipped with language-adaptive weights can directly extract expression-relevant visual features without additional feature-adjustment modules." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.47, + 0.902 + ], + "angle": 0, + "content": "In this paper, we propose an active perception Visual Grounding framework based on Language Adaptive Weights, called VG-LAW. It can dynamically adjust the behavior of the visual backbone by injecting the informa" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.363 + ], + "angle": 0, + "content": "tion of referring expressions into the weights. Specifically, VG-LAW first obtains the specific language-adaptive weights for the visual backbone through two successive processes of linguistic feature aggregation and weight generation. Then, the language-aware visual backbone can extract expression-relevant visual features without manually modifying the visual backbone architecture. Since the extracted visual features are highly expression-relevant, cross-modal interaction modules are not required for further cross-modal fusion, and the entire network architecture is more streamlined. Furthermore, based on the expression-relevant features, we propose a lightweight but neat multitask prediction head for jointly referring expression comprehension (REC) and referring expression segmentation (RES) tasks. Extensive experiments on RefCOCO [47], RefCOCO+ [47], RefCOCOg [36], and ReferItGame [19] datasets demonstrate the effectiveness of our method, which achieves state-of-the-art performance." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.365, + 0.88, + 0.378 + ], + "angle": 0, + "content": "The main contributions can be summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.392, + 0.892, + 0.467 + ], + "angle": 0, + "content": "- We propose an active perception visual grounding framework based on the language adaptive weights, called VG-LAW, which can actively extract expression-relevant visual features without manually modifying the visual backbone architecture." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.48, + 0.892, + 0.554 + ], + "angle": 0, + "content": "- Benefiting from the active perception of visual feature extraction, we can directly utilize our proposed neat but efficient multi-task head for REC and RES tasks jointly without carefully designed cross-modal interaction modules." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.568, + 0.892, + 0.629 + ], + "angle": 0, + "content": "- Extensive experiments demonstrate the effectiveness of our framework, which achieves state-of-the-art performance on four widely used datasets, i.e., RefCOCO, RefCOCO+, RefCOCOg, and ReferItGame." + }, + { + "type": "list", + "bbox": [ + 0.52, + 0.392, + 0.892, + 0.629 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.655, + 0.641, + 0.67 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.681, + 0.825, + 0.697 + ], + "angle": 0, + "content": "2.1. Referring Expression Comprehension" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Referring expression comprehension (REC) [4,13,30,42, 43,46,48-50] aims to generate a bounding box in an image specified by a given referring expression. Early researchers explore REC through a two-stage framework [13,29,30,46], where region proposals [38] are first extracted and then ranked according to their similarity scores with referring expressions. To alleviate the speed and accuracy issues of the region proposals in the two-stage framework, simpler and faster one-stage methods [42, 43, 49] based on dense anchors are proposed. Recently, transformer-based methods [4,12,18,48,50] can effectively capture intra- and intermodality context and achieve better performance, benefiting from the self-attention mechanism [40]." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10858" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.089, + 0.891, + 0.288 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.299, + 0.896, + 0.373 + ], + "angle": 0, + "content": "Figure 3. The overall architecture of our proposed VG-LAW framework. It consists of four components: (1) Linguistic Backbone, which extracts linguistic features from free-formed referring expressions, (2) Language Adaptive Weight Generator, which generates dynamic weights for the visual backbone conditioned on specific expressions, (3) Visual Backbone, which extracts visual features from the raw image and its behavior can be modified by language-adaptive weights, and (4) Multi-task Head, which predicts the bounding box and mask of referred object jointly. \\(\\otimes\\) represents the matrix multiplication." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.395, + 0.388, + 0.412 + ], + "angle": 0, + "content": "2.2. Referring Expression Segmentation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.42, + 0.475, + 0.648 + ], + "angle": 0, + "content": "Similar to REC, referring expression segmentation (RES) [6, 9, 14, 15, 17, 20, 23, 32, 44, 50] aims to predict a precise pixel-wise binary mask corresponding to the given referring expression. The pioneering work [14] proposes to generate segmentation masks for natural language expressions by concatenating the visual and linguistic features and mixing these two modal features with fully convolutional classifiers. Follow-up solutions [9, 15, 17, 32] propose various attention mechanisms to perform cross-modal interaction to generate a high-resolution segmentation map. Recent studies [6, 20, 23, 44, 50], like REC, leverage transformer [40] to realize cross-modal interaction and achieve excellent performance. All these methods achieve cross-modal interaction by either adjusting the inputs or modifying the architectures with fixed network weights." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.664, + 0.322, + 0.681 + ], + "angle": 0, + "content": "2.3. Dynamic Weight Networks" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Several works [3, 10, 16, 24, 41] have investigated dynamic weight networks, where given inputs adaptively generate the weights of the network. According to the way of dynamic weight generation, the current methods can be roughly divided into three categories. (1) Dynamic weights are directly generated using fully-connected layers with learnable embeddings [10] or intermediate features [16] as input. (2) Weights are computed as the weighted sum of a set of learnable weights [3, 22, 41], which can also be regarded as the mixture-of-experts and may suffer from challenging joint optimization. (3) The weights are analyzed from the perspective of matrix decomposition [24], and the final dynamic weights are generated by calculating the multiplication of several matrices." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.394, + 0.593, + 0.41 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.421, + 0.895, + 0.483 + ], + "angle": 0, + "content": "In this section, we will introduce the active perception framework for multi-task visual grounding, including the language-adaptive weight generation, multi-task prediction head, and training objectives." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.497, + 0.611, + 0.511 + ], + "angle": 0, + "content": "3.1. Overview" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.522, + 0.895, + 0.718 + ], + "angle": 0, + "content": "The extraction of visual features by the visual backbone in the manner of passive perception may cause mismatch problems, which can lead to suboptimal performance despite subsequent carefully designed cross-modal interaction modules. Considering that expressions already provide a blueprint for the desired visual features, we propose an active perception visual grounding framework based on the language adaptive weights, called VG-LAW, as illustrated in Fig. 3. In this framework, the visual backbone can actively extract expression-relevant visual features using language-adaptive weights, without needing to manually modify the visual backbone architecture or elaborately design additional cross-modal interaction modules." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.896, + 0.903 + ], + "angle": 0, + "content": "Specifically, the VG-LAW framework consists of four components, i.e., linguistic backbone, language adaptive weight generator, visual backbone, and multi-task head. Given a referring expression, the \\(N\\)-layer BERT-based [5] linguistic backbone tokenizes the expressions, prepends a [CLS] token, and extracts linguistic features \\(F_{l} \\in \\mathbb{R}^{L \\times d_{l}}\\) where \\(L\\) and \\(d_{l}\\) represent the token numbers and dimension of linguistic features, respectively. The linguistic features \\(F_{l}\\) are then fed to the language adaptive weight generator to generate weights for the transformer-based visual backbone. Next, given an image \\(I \\in \\mathbb{R}^{3 \\times H \\times W}\\), the expression-aware visual features \\(F_{v} \\in \\mathbb{R}^{C \\times \\frac{H}{s} \\times \\frac{W}{s}}\\) can be extracted by" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "10859" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.087, + 0.092, + 0.462, + 0.316 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.327, + 0.471, + 0.385 + ], + "angle": 0, + "content": "Figure 4. The detailed architecture for language adaptive weight generation. The upper part shows the architecture of the adapted ViT block in the visual backbone, and the lower part shows the linguistic feature aggregation and weight generation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.41, + 0.47, + 0.502 + ], + "angle": 0, + "content": "the visual backbone, where \\( C \\) and \\( s \\) represent the channel number and stride of the visual features, respectively. Finally, we pass the linguistic features \\( F_{l}^{1} \\in \\mathbb{R}^{\\bar{d}_{l}} \\) represented by the [CLS] token and the visual features to the multi-task head, which predicts the bounding box and mask of the referred object for REC and RES, respectively." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.511, + 0.415, + 0.527 + ], + "angle": 0, + "content": "3.2. Language Adaptive Weight Generation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.534, + 0.47, + 0.61 + ], + "angle": 0, + "content": "After extracting linguistic features, language-adaptive weights are generated to guide the active perception of the visual backbone. The process of language adaptive weight generation has two stages, i.e., the layer-wise linguistic feature aggregation and the weight generation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.629, + 0.47, + 0.827 + ], + "angle": 0, + "content": "Linguistic Feature Aggregation. Considering the referring expressions correspond to a different number of linguistic tokens and each layer of the visual backbone may prefer different linguistic tokens, we try to aggregate linguistic features with fixed sizes for each layer independently. Inspired by the multi-head attention mechanism [40], we introduce a learnable layer-specific embedding \\( e_i \\in \\mathbb{R}^{d_l} \\) for each layer \\( i \\) of the visual backbone to extract layer-specific linguistic features dynamically, which can improve the model flexibility at negligible cost. The calculation is performed on \\( G \\) groups. For each group \\( g \\), the token-wise attention \\( \\alpha_i^g \\in [0,1]^L \\) is assigned to the normalized dot product of \\( e_i^g \\) and \\( F_l^g \\), which is denoted as:" + }, + { + "type": "equation", + "bbox": [ + 0.088, + 0.838, + 0.47, + 0.859 + ], + "angle": 0, + "content": "\\[\n\\alpha_ {i} ^ {g} = \\mathrm {S o f t m a x} ([ e _ {i} ^ {g} \\cdot F _ {l} ^ {g, 1}, e _ {i} ^ {g} \\cdot F _ {l} ^ {g, 2}, \\dots , e _ {i} ^ {g} \\cdot F _ {l} ^ {g, L} ]). (1)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.868, + 0.469, + 0.904 + ], + "angle": 0, + "content": "Then, the aggregated linguistic feature \\( h_0^i \\in \\mathbb{R}^{d_l} \\) can be derived by concatenating \\( h_0^{i,g} = \\sum_{j=1}^{L} \\alpha_i^{g,j} F_l^{g,j} \\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.137 + ], + "angle": 0, + "content": "Finally, we use a fully-connected layer (FC) to reduce the dimension of the aggregated linguistic features for the \\(i\\)-th layer of the visual backbone, which is indicated as:" + }, + { + "type": "equation", + "bbox": [ + 0.642, + 0.149, + 0.892, + 0.166 + ], + "angle": 0, + "content": "\\[\nh _ {1} ^ {i} = \\delta \\left(W _ {1} ^ {i} h _ {0} ^ {i}\\right), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.177, + 0.892, + 0.222 + ], + "angle": 0, + "content": "where \\( W_1^i \\in \\mathbb{R}^{d_l \\times d_h} \\) is used to reducing the dimension to \\( d_h = d_l / r \\), and \\( r \\) is the reduction ratio. \\( \\delta \\) refers to the GeLU activation function." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.242, + 0.892, + 0.317 + ], + "angle": 0, + "content": "Weight Generation. To guide the active perception of the visual backbone, we generate language-adaptive weights for producing the query \\( X_{q} \\), key \\( X_{k} \\), and value \\( X_{v} \\) in the visual backbone conditioned on referring expressions, which can be represented as:" + }, + { + "type": "equation", + "bbox": [ + 0.511, + 0.329, + 0.892, + 0.347 + ], + "angle": 0, + "content": "\\[\nX _ {q} = \\theta (X; W _ {q}), X _ {k} = \\theta (X; W _ {k}), X _ {v} = \\theta (X; W _ {v}), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.357, + 0.892, + 0.448 + ], + "angle": 0, + "content": "where \\(\\theta (\\cdot ;W)\\) indicates the linear projection operation parameterized by \\(W\\), and \\(X\\) represents the input visual features. \\(W_{q},W_{k},W_{v}\\in \\mathbb{R}^{d_{out}\\times d_{in}}\\) are the dynamic projection weights used to generate the query, key, and value, respectively. \\(d_{in}\\) and \\(d_{out}\\) are the dimension of feature \\(X\\) and query/key/value, respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.449, + 0.892, + 0.613 + ], + "angle": 0, + "content": "Considering the large number \\(d_{out} \\times d_{in}\\) of the dynamic weights, it is unaffordable to directly generate weights using fully-connected layers like Hypernetworks [10]. The DynamicConv [3] and CondConv [41] can alleviate this problem by generating weights with weighted summation of \\(K\\) static kernels but can increase the parameter number by \\(K\\)-times and suffer from challenging joint optimization. Inspired by the dynamic channel fusion [24], we try to generate dynamic weights following the matrix decomposition paradigm. Taking the \\(i\\)-th ViT block as an example, which can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.574, + 0.625, + 0.892, + 0.645 + ], + "angle": 0, + "content": "\\[\n\\left[ W _ {q} ^ {i}, W _ {k} ^ {i}, W _ {v} ^ {i} \\right] = W _ {0} ^ {i} + P \\Phi \\left(h _ {1} ^ {i}\\right) Q ^ {T}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.656, + 0.892, + 0.764 + ], + "angle": 0, + "content": "where \\( W_0^i \\in \\mathbb{R}^{d_{out} \\times d_{in}} \\) is the layer-specific static learnable weights. \\( P \\in \\mathbb{R}^{d_{out} \\times d_w} \\) and \\( Q \\in \\mathbb{R}^{d_{in} \\times d_w} \\) are also static learnable weights, but sharable across all ViT blocks to reduce the parameter numbers and prevent the model from overfitting. \\( \\Phi(h_1^i) \\) is a fully-connected layer, which produces a dynamic matrix of shape \\( d_w \\times d_w \\) with aggregated linguistic features \\( h_1^i \\) as input." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.772, + 0.664, + 0.787 + ], + "angle": 0, + "content": "3.3. Multi-task Head" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Different from the previous methods [6,23,42,45,46,49, 50], which require carefully designed cross-modal interaction modules, VG-LAW can obtain expression-relevant visual features extracted by the language-aware visual backbone without additional cross-modal interaction modules. Through our proposed neat but efficient multi-task head, we can utilize the visual and linguistic features to predict" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10860" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.137 + ], + "angle": 0, + "content": "the bounding box for REC and the segmentation mask for RES. Concretely, there are two branches in the multi-task head for REC and RES, respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.137, + 0.47, + 0.363 + ], + "angle": 0, + "content": "For the REC branch, we apply direct coordinate regression to predict the bounding box of referred object. To pool the 2- \\(d\\) visual features along the spatial dimension, we propose a language adaptive pooling module (LAP), which aggregates visual features using language-adaptive attention. Specifically, the visual features \\(\\{F_v^{i,j}\\} \\in \\mathbb{R}^{C\\times \\frac{H}{s}\\times \\frac{W}{s}}\\) and linguistic feature \\(F_{l}^{1}\\in \\mathbb{R}^{d_{l}}\\) are firstly projected to the lower-dimension space \\(\\mathbb{R}^k\\), and the attention weights \\(A\\in \\mathbb{R}_{\\frac{H}{s}\\times \\frac{W}{s}}\\) are calculated as dot-product similarity followed by Softmax normalization. Then, the visual features are aggregated by calculating the weighted sum with attention weights \\(A\\). Finally, the aggregated visual features are fed to a three-layer fully-connected layer, and the Sigmoid function is used to predict the referred bounding box \\(\\hat{b} = (\\hat{x},\\hat{y},\\hat{w},\\hat{h})\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.364, + 0.471, + 0.545 + ], + "angle": 0, + "content": "For the RES branch, we apply binary classification to each visual feature along the spatial dimension to predict segmentation masks for referred objects. Specifically, the visual features \\(F_{v}\\) are first up-sampled to \\(\\hat{F}_v\\in \\mathbb{R}^{d_l\\times \\frac{H}{4}\\times \\frac{W}{4}}\\) with successive transposed convolutions. Then, the intermediate segmentation map \\(\\bar{s}\\in \\mathbb{R}^{\\frac{H}{4}\\times \\frac{W}{4}}\\) can be obtained by using linear projection \\(\\theta (\\cdot ;W)\\) on each visual feature. Following the language adaptive weight paradigm, we also use dynamic rather than fixed weights by simply setting \\(W = F_l^1\\). Finally, the full-resolution segmentation mask \\(\\hat{s}\\in \\mathbb{R}^{H\\times W}\\) is derived by simply up-sample \\(\\bar{s}\\) using bilinear interpolation, followed by the Sigmoid function." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.552, + 0.266, + 0.568 + ], + "angle": 0, + "content": "3.4. Training Objectives" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.575, + 0.469, + 0.65 + ], + "angle": 0, + "content": "The VG-LAW framework can be optimized end-to-end for multi-task visual grounding. For REC, given the predicted bounding box \\(\\hat{b} = (\\hat{x},\\hat{y},\\hat{w},\\hat{h})\\) and the ground truth \\(b = (x,y,w,h)\\), the detection loss function is defined as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.135, + 0.657, + 0.469, + 0.675 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {d e t}} = \\lambda_ {L 1} \\mathcal {L} _ {L 1} (b, \\hat {b}) + \\lambda_ {g i o u} \\mathcal {L} _ {g i o u} (b, \\hat {b}), \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.681, + 0.469, + 0.756 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_{L1}(\\cdot, \\cdot)\\) and \\(\\mathcal{L}_{giou}(\\cdot, \\cdot)\\) represent L1 loss and Generalized IoU loss [39], respectively, and \\(\\lambda_{L1}\\) and \\(\\lambda_{giou}\\) are the relative weights to control the two detection loss functions. For RES, given the predicted mask \\(\\hat{s}\\) and the ground-truth \\(s\\), the segmentation loss function is defined as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.12, + 0.765, + 0.469, + 0.782 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {s e g}} = \\lambda_ {\\text {f o c a l}} \\mathcal {L} _ {\\text {f o c a l}} (s, \\hat {s}) + \\lambda_ {\\text {d i c e}} \\mathcal {L} _ {\\text {d i c e}} (s, \\hat {s}), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.787, + 0.469, + 0.877 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_{focal}(\\cdot, \\cdot)\\) and \\(\\mathcal{L}_{dice}(\\cdot, \\cdot)\\) represent focal loss [27] and DICE/F-1 loss [35], respectively, and \\(\\lambda_{focal}\\) and \\(\\lambda_{dice}\\) are the relative weights to control the two segmentation loss functions. Our framework can be seamlessly used for joint training of REC and RES, and its joint training loss function is defined as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.197, + 0.886, + 0.469, + 0.903 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {t o t a l}} = \\mathcal {L} _ {\\text {d e t}} + \\mathcal {L} _ {\\text {s e g}}. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.136 + ], + "angle": 0, + "content": "The trained model performs well for language-guided detection and segmentation. The experimental analysis of the whole framework will be elaborated in Sec. 4." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.148, + 0.632, + 0.166 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.174, + 0.892, + 0.234 + ], + "angle": 0, + "content": "In this section, we will give a detailed experimental analysis of the whole framework, including the datasets, evaluation protocol, implementation details, comparisons with the state-of-the-art methods, and ablation analysis." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.241, + 0.792, + 0.256 + ], + "angle": 0, + "content": "4.1. Datasets and Evaluation Protocol" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.265, + 0.892, + 0.506 + ], + "angle": 0, + "content": "Datasets. To verify the effectiveness of our method, we conduct experiments on the widely used RefCOCO [47], RefCOCO+ [47], RefCOCOg [34], and ReferItGame [19] datasets. RefCOCO, RefCOCO+, and RefCOCOg are collected from MS-COCO [28]. RefCOCO and RefCOCO+, which are collected in interactive games, can be divided into train, val, testA, and testB sets. Compared to RefCOCO, the expressions of RefCOCO+ contain more attributes than absolute locations. Unlike RefCOCO and RefCOCO+, RefCOCOg collected by Amazon Mechanical Turk has a longer length of 8.4 words, including the attribute and location of referents. Following a common version of split [36], RefCOCOg has train, val, and test sets. In addition, ReferItGame collected from SAIAPR-12 [8] contains train and test sets. Each sample in the above datasets contains its corresponding bounding box and mask." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.523, + 0.892, + 0.644 + ], + "angle": 0, + "content": "Evaluation Protocol. Following the previous works [23, 33, 50], we use Prec@0.5 and mIoU to evaluate the performance of REC and RES, respectively. For Prec@0.5, the predicted bounding box is considered correct if the intersection-over-union (IoU) with the ground-truth bounding box is greater than 0.5. mIoU represents the IoU between the prediction and ground truth averaged across all test samples." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.651, + 0.716, + 0.667 + ], + "angle": 0, + "content": "4.2. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Training. The resolution of the input image is resized to \\(448 \\times 448\\). ViT-Base [7] is used as the visual backbone, and we follow the adaptation introduced by ViTDet [25] to adapt the visual backbone to higher-resolution images. The visual backbone is pre-trained using Mask R-CNN [11] on MS-COCO [28], where overlapping images of the val/test sets are excluded. The \\(W_0^i\\) and \\(\\Phi(h_1^i)\\) in Eq. (4) are initialized with the corresponding pre-trained weights of the visual backbone and zeros, respectively. The maximum length of referring expression is set to 40, and the uncased base of six-layer BERT [5] as the linguistic backbone is used to generate linguistic features. \\(\\lambda_{L1}\\) and \\(\\lambda_{giou}\\) are set to 1. \\(\\lambda_{focal}\\) and \\(\\lambda_{dice}\\) are set to 4. The reduction ratio \\(r\\) is set to 16. The initial learning rate for the visual and linguistic backbone is 4e-5, and the initial learning rate for the" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "10861" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.078, + 0.089, + 0.899, + 0.439 + ], + "angle": 0, + "content": "
MethodsVenueVisual BackboneMulti-taskRefCOCORefCOCO+RefCOCOgReferItGame test
valtestAtestBvaltestAtestBvaltest
Two-stage:
MAttNet [46]CVPR18RN101X76.6581.1469.9965.3371.6256.0266.5867.2729.04
RvG-Tree [13]TPAMI19RN101X75.0678.6169.8563.5167.4556.6666.9566.51-
CM-A-E [30]CVPR19RN101X78.3583.1471.3268.0973.6558.0367.9968.67-
Ref-NMS [2]AAAI21RN101X80.7084.0076.0468.2573.6859.4270.5570.62-
One-stage:
FAOA [43]ICCV19DN53X72.5474.3568.5056.8160.2349.6061.3360.3660.67
ReSC-Large [42]ECCV20DN53X77.6380.4572.3063.5968.3656.8167.3067.2064.60
MCN [33]CVPR20DN53✓80.0882.2974.9867.1672.8657.3166.4666.01-
RealGIN [49]TNNLS21DN53X77.2578.7072.1062.7867.1754.2162.7562.33-
PLV-FPN* [26]TIP22RN101X81.9384.9976.2571.2077.4061.0870.4571.0871.77
Transformer-based:
TransVG [4]ICCV21RN101X81.0282.7278.3564.8270.7056.9468.6767.7370.73
RefTR* [23]NeurIPS21RN101✓82.2385.5976.5771.5875.9662.1669.4169.4071.42
SeqTR [50]ECCV22DN53X81.2385.0076.0868.8275.3758.7871.3571.5869.66
Word2Pix [48]TNNLS22RN101X81.2084.3978.1269.7476.1161.2470.8171.34-
YORO [12]ECCVW22-X82.9085.6077.4073.5078.6064.9073.4074.3071.90
QRNet [45]CVPR22Swin-SX84.0185.8582.3472.9476.1763.8171.8973.0374.61
Ours:
VG-LAW-ViT-BX86.0688.5682.8775.7480.3266.6975.3175.9576.60
VG-LAW-ViT-B✓86.6289.3283.1676.3781.0467.5076.9076.9677.22
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.448, + 0.894, + 0.507 + ], + "angle": 0, + "content": "Table 1. Comparison with state-of-the-art methods on RefCOCO [47], RefCOCO+ [47], RefCOCOg [36] and ReferItGame [19] for REC task. The visual backbone is pre-trained on MS-COCO [28], where overlapping images of the val/test sets are excluded. * represents ImageNet [21] pre-training. RN101, DN53, Swin-S, and ViT-B are shorthand for the ResNet101, DarkNet53, Swin-Transformer Small, and ViT Base, respectively. We highlight the best and second best performance in the red and blue colors." + }, + { + "type": "table", + "bbox": [ + 0.143, + 0.517, + 0.83, + 0.701 + ], + "angle": 0, + "content": "
MethodsVenueVisual BackboneMulti-taskRefCOCORefCOCO+RefCOCOg
valtestAtestBvaltestAtestBvaltest
CGAN [32]MM20DN53X64.8668.0462.0751.0355.5144.0654.4054.25
MCN [33]CVPR20DN53✓62.4464.2059.7150.6254.9944.6949.2249.40
LTS [17]CVPR21DN53X65.4367.7663.0854.2158.3248.0254.4054.25
VLT [50]ICCV21DN53X65.6568.2962.7355.5059.2049.3652.9956.65
RefTR* [23]NeurIPS21RN101✓70.5673.4966.5761.0864.6952.7358.7358.51
SeqTR [50]ECCV22DN53X67.2669.7964.1254.1458.9348.1955.6755.64
LAVT* [44]CVPR22Swin-BX74.4676.8970.9465.8170.9759.2363.6263.66
Ours:
VG-LAW-ViT-BX75.0577.3671.6966.6170.3058.1465.3665.13
VG-LAW-ViT-B✓75.6277.5172.8966.6370.3858.8965.6366.08
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.71, + 0.893, + 0.768 + ], + "angle": 0, + "content": "Table 2. Comparison with state-of-the-art methods on RefCOCO [47], RefCOCO+ [47], and RefCOCOg [36] for RES task. The visual backbone is pre-trained on MS-COCO [28], where overlapping images of the val/test sets are excluded. * represents ImageNet [21] pre-training. RN101, DN53, Swin-B, and ViT-B are shorthand for the ResNet101, DarkNet53, Swin-Transformer Base, and ViT Base, respectively. We highlight the best and second best performance in the red and blue colors." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.793, + 0.471, + 0.899 + ], + "angle": 0, + "content": "remaining components is 4e-4. The model is end-to-end optimized by AdamW [31] for 90 epochs with a batch size of 256, where weight decay is set to 1e-4, and the learning rate is reduced by a factor of 10 after 60 epochs. Data augmentation operation includes random horizontal flips. We implement our framework using PyTorch and conduct experiments with NVIDIA A100 GPUs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.793, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Inference. At inference time, the input image is resized to \\(448 \\times 448\\), and the maximum length of referring expressions is set to 40. Following the previous method [33], We set the threshold to 0.35 to realize the binarization of the RES prediction. Without any post-processing operation, our framework directly outputs bounding boxes and segmentation maps specified by referring expressions." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "10862" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.104, + 0.094, + 0.445, + 0.271 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.285, + 0.47, + 0.328 + ], + "angle": 0, + "content": "Figure 5. Comparison of accuracy under different lengths of referring expression on RefCOCOg-test. ReSC [42], TransVG [4], Word2Pix [48], and the proposed VG-LAW are compared." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.354, + 0.449, + 0.37 + ], + "angle": 0, + "content": "4.3. Comparisons with State-of-the-art Methods" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.377, + 0.47, + 0.44 + ], + "angle": 0, + "content": "To estimate the effectiveness of the proposed VG-LAW framework, we conduct quantitative experiments on four widely used datasets, i.e., RefCOCO [47], RefCOCO+ [47], RefCOCOg [34], and ReferItGame [19]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.458, + 0.471, + 0.776 + ], + "angle": 0, + "content": "REC Task. For the REC task, we compare the performance with state-of-the-art REC methods, including the two-stage methods [2, 13, 30, 46], one-stage methods [26, 33, 42, 43, 49], and transformer-based methods [4, 12, 23, 45, 48, 50]. The main results are summarized to Tab. 1. It can be observed that VG-LAW achieves a significant performance improvement compared to the state-of-the-art two-stage method Ref-NMS [2] and one-stage method PLV-FPN [26]. When comparing to the transformer-based method QRNet [45], which modified the visual backbone by inserting language-aware spatial and channel attention modules, our method has better performance with \\(+2.62\\% / +3.47\\% / +0.82\\%\\) on RefCOCO, \\(+3.43\\% / +4.87\\% / +3.69\\%\\) on RefCOCO+, \\(+5.01\\% / +3.93\\%\\) on RefCOCOg, and \\(+2.61\\%\\) on ReferItGame. QRNet [45] follows the TransVG [4] framework, both of which use the transformer encoder-based cross-modal interaction module. Compared to them, VG-LAW achieves better performance without complex cross-modal interaction modules. Furthermore, our method significantly outperforms MCN [33] and RefTR [23] based on joint training of REC and RES." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.47, + 0.901 + ], + "angle": 0, + "content": "RES Task. For the RES task, we compare the performance with state-of-the-art methods [6,17,23,32,33,44,50], and the main results are summarized to Tab. 2. Compared with state-of-the-art RES method LAVT [44], VG-LAW achieves better \\(mIoU\\) with \\(+1.16\\% / +0.62\\% / +1.95\\%\\) on RefCOCO, \\(+2.01\\% / +2.42\\%\\) on RefCOCOg, and comparable \\(mIoU\\) with \\(+0.82\\% / -0.59\\% / -0.34\\%\\) on RefCOCO+." + }, + { + "type": "table", + "bbox": [ + 0.554, + 0.089, + 0.842, + 0.189 + ], + "angle": 0, + "content": "
LAWGLAPMTHPrec@0.5(%)
✓74.89
✓74.37
✓✓76.60
✓✓✓77.22
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.2, + 0.892, + 0.242 + ], + "angle": 0, + "content": "Table 3. Ablation experiments on ReferItGame [19] to evaluate the proposed language adaptive weight generation (LAWG), language adaptive pooling (LAP), and multi-task head (MTH)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.269, + 0.892, + 0.36 + ], + "angle": 0, + "content": "When comparing the models trained with or without multi-task settings, it can also be observed that consistent performance gains are achieved across all the datasets and splits. As REC can provide localization information of the referred object, such coarse-grained supervision can slightly improve the segmentation accuracy in RES." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.38, + 0.892, + 0.546 + ], + "angle": 0, + "content": "Analysis of Referring Expression Length. As the visual backbone in VG-LAW extracts features purely perceptually, it is of concern whether it can handle long and complex referring expressions. ReSC [42] reveals that one-stage methods may ignore detailed descriptions in complex referring expressions and lead to poor performance. Following that, we evaluate the REC performance on referring expressions of different lengths, as illustrated in Fig. 5. VG-LAW performs better than ReSC, TransVG [4] and Word2Pix [48], with no significant performance degradation when the length of referring expressions varies from 6-7 to \\(11+\\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.557, + 0.673, + 0.573 + ], + "angle": 0, + "content": "4.4. Ablation Analysis" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.58, + 0.892, + 0.821 + ], + "angle": 0, + "content": "To validate the effectiveness of our proposed modules, i.e. language-adaptive weight generation, language-adaptive pooling, and multi-task head, we conduct ablation experiments on the REC dataset of ReferItGame, which is summarized in Tab. 3. When only using the LAWG, the visual features are pooled with global average pooling, and when only using the LAP, the visual backbone has fixed architecture and weights. When only using the LAWG or the LAP, it can be observed that the model already achieves \\(74.89\\%\\) and \\(74.37\\%\\), respectively, which is close to the \\(74.61\\%\\) reported by QRNet [45]. When combined with the LAWG and LAP, further improvements can be brought by LAWG and LAP with \\(+2.23\\%\\) and \\(+1.71\\%\\), respectively. Benefiting from the auxiliary supervision of RES, our model equipped with the multi-task head can localize the referred objects better and achieve \\(77.22\\%\\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.832, + 0.683, + 0.848 + ], + "angle": 0, + "content": "4.5. Qualitative Results" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The qualitative results of the four datasets are shown in Fig. 6. It can be observed that our model can successfully locate and segment the referred objects, and the attention of" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10863" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.09, + 0.09, + 0.885, + 0.407 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.418, + 0.893, + 0.461 + ], + "angle": 0, + "content": "Figure 6. Qualitative results on the RefCOCO [47], RefCOCO+ [47], RefCOCOg [34], and ReferItGame [19] datasets. Each dataset shows two examples. From left to right: the input image, the ground truth of REC and RES, the prediction of VG-LAW, and the attention of the visual backbone with language-adaptive weights." + }, + { + "type": "image", + "bbox": [ + 0.091, + 0.484, + 0.266, + 0.587 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.282, + 0.485, + 0.457, + 0.587 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.599, + 0.47, + 0.626 + ], + "angle": 0, + "content": "Figure 7. Wordcloud visualization of words assigned to the first and second halves of the visual backbone." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.657, + 0.47, + 0.764 + ], + "angle": 0, + "content": "the visual backbone can focus on the most relevant image regions, demonstrating the effectiveness of using language adaptive weights. Taking the results on ReferItGame as an example, the visual backbone can dynamically filter out irrelevant regions for different expressions. For instance, when the \"purple curtain\" is referred to, the regions related to the \"the painting/photo on the wall\" are ignored." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.471, + 0.903 + ], + "angle": 0, + "content": "In addition, we count the scores of words assigned to the first and second halves of the visual backbone, as shown in Fig. 7. The scores are calculated by averaging attention score \\(\\alpha_{i}\\) in Eq. (1) for each word, followed by softmax normalization along the layer dimension. It can be observed that the shallow layers tend to the words describing individuals, such as the categories \"velvet\" and \"yacht\", and the deep layers tend to the words about contexts, such as the ordinal number \"2nd\" and the position \"right\"." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.485, + 0.769, + 0.501 + ], + "angle": 0, + "content": "5. Conclusions and Limitations" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.512, + 0.892, + 0.709 + ], + "angle": 0, + "content": "In this paper, we propose an active perception framework VG-LAW for visual grounding, based on the language adaptive weights. VG-LAW can directly inject the information of referring expressions into the weights of the visual backbone without modifying its architecture. Equipped with the proposed neat yet efficient multi-task head, VG-LAW achieves state-of-the-art performance for REC and RES tasks on widely used datasets. The limitations of our method are two-fold: (1) VG-LAW is weak in interpretability, and the entire reasoning process is implicit, which makes it difficult to understand how the reasoning process works, and (2) the multi-task head predicts one instance at a time, which limits its application in phrase grounding." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.724, + 0.68, + 0.741 + ], + "angle": 0, + "content": "6. Acknowledgments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.893, + 0.901 + ], + "angle": 0, + "content": "This work is supported in part by National Key Research and Development Program of China under Grant 2020AAA0107400, National Natural Science Foundation of China under Grant U20A20222, National Science Foundation for Distinguished Young Scholars under Grant 62225605, Ant Group through CCF-Ant Research Fund, and sponsored by CCF-AFSG Research Fund, CAAI-HUAWEI MindSpore Open Fund, CCF-Zhipu AI Large Model Fund (CCF-Zhipu202302) as well as Hikvision Cooperation Fund." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10864" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.175, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.169 + ], + "angle": 0, + "content": "[1] Nicolas Carion, Francisco Massa, Gabriel Synnaeve, Nicolas Usunier, Alexander Kirillov, and Sergey Zagoruyko. 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Seqtr: A simple yet universal network for visual grounding. arXiv preprint arXiv:2203.16265, 2022. 1, 2, 3, 4, 5, 6, 7" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.092, + 0.892, + 0.33 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.52, + 0.957 + ], + "angle": 0, + "content": "10866" + } + ] +] \ No newline at end of file diff --git a/2023/Language Adaptive Weight Generation for Multi-Task Visual Grounding/09bf5769-e1b7-4520-b426-6463f773ed2a_origin.pdf b/2023/Language Adaptive Weight Generation for Multi-Task Visual Grounding/09bf5769-e1b7-4520-b426-6463f773ed2a_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..f0f80bd2184f622ccdd4154d458f0c2911fce459 --- /dev/null +++ b/2023/Language Adaptive Weight Generation for Multi-Task Visual Grounding/09bf5769-e1b7-4520-b426-6463f773ed2a_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:99e2333c6337845e8c41bedec8adfc5cf623d6b7226a273044ec764a9fa8e076 +size 1204828 diff --git a/2023/Language Adaptive Weight Generation for Multi-Task Visual Grounding/full.md b/2023/Language Adaptive Weight Generation for Multi-Task Visual Grounding/full.md new file mode 100644 index 0000000000000000000000000000000000000000..9d5b56b1d4c38cb4f5c1f99fce66fcb404cea02e --- /dev/null +++ b/2023/Language Adaptive Weight Generation for Multi-Task Visual Grounding/full.md @@ -0,0 +1,278 @@ +# Language Adaptive Weight Generation for Multi-task Visual Grounding + +Wei Su1 Peihan Miao1 Huanzhang Dou1 Gaoang Wang4 Liang Qiao1,3 Zheyang Li1,3 Xi Li1,2,5* + +$^{1}$ Zhejiang University $^{2}$ Shanghai AI Laboratory $^{3}$ Hikvision Research Institute $^{4}$ Zhejiang University-University of Illinois Urbana-Champaign Institute, Zhejiang University $^{5}$ Shanghai Institute for Advanced Study of Zhejiang University + +{weisuzju, peihan.miao, hzdou, qiaoliang, xilizju}@zju.edu.cn gaoangwang@intl.zju.edu.cn, lizheyang@hikvision.com + +# Abstract + +Although the impressive performance in visual grounding, the prevailing approaches usually exploit the visual backbone in a passive way, i.e., the visual backbone extracts features with fixed weights without expression-related hints. The passive perception may lead to mismatches (e.g., redundant and missing), limiting further performance improvement. Ideally, the visual backbone should actively extract visual features since the expressions already provide the blueprint of desired visual features. The active perception can take expressions as priors to extract relevant visual features, which can effectively alleviate the mismatches. Inspired by this, we propose an active perception Visual Grounding framework based on Language Adaptive Weights, called VG-LAW. The visual backbone serves as an expression-specific feature extractor through dynamic weights generated for various expressions. Benefiting from the specific and relevant visual features extracted from the language-aware visual backbone, VG-LAW does not require additional modules for cross-modal interaction. Along with a neat multi-task head, VG-LAW can be competent in referring expression comprehension and segmentation jointly. Extensive experiments on four representative datasets, i.e., RefCOCO, RefCOCO+, RefCOCOg, and ReferItGame, validate the effectiveness of the proposed framework and demonstrate state-of-the-art performance. + +# 1. Introduction + +Visual grounding (such as referring expression comprehension [4, 23, 42, 45, 46, 48, 50], referring expression segmentation [6, 14, 17, 23, 32, 33, 44], and phrase grounding [4, 23, 50]) aims to detect or segment the specific object + +![](images/f421886bb36a673d7a513c149a6d4ce2bf47e6eb3dd0c85999c73f1f4e4e42b4.jpg) + +![](images/2e0b9c00a8a0e117cba7ffd3d29b229fbae1371bbd7d7f717de2d107c3b9081b.jpg) + +![](images/71fde5d9edeacf11803b0fca155864d891e4a9aba332999927d3dd7c1caad168.jpg) +Figure 1. The comparison of visual grounding frameworks. (a) The visual and linguistic backbone independently extracts features, which are fused through cross-modal interaction. (b) Additional designed modules are inserted into the visual backbone to modulate visual features using linguistic features. (c) VG-LAW can generate language-adaptive weights for the visual backbone and directly output referred objects through our designed multitask head without additional cross-modal interaction modules. + +based on a given natural language description. Compared to general object detection [38] or instance segmentation [11], which can only locate objects within a predefined and fixed category set, visual grounding is more flexible and purposeful. Free-formed language descriptions can specify specific visual properties of the target object, such as categories, attributes, relationships with other objects, relative/absolute positions, and etc. + +Due to the similarity with detection tasks, previous visual grounding approaches [23, 33, 46, 50] usually follow the general object detection frameworks [1, 11, 37], and pay + +![](images/1ca2784989b575d0aa9823600577ec9f26dccd958f4887a1120b72dfca877a76.jpg) +Figure 2. Attention visualization of the visual backbone with different weights. (a) input image, (b) visual backbone with fixed weights, (c) and (d) visual backbone with weights generated for "white bird" and "right bird", respectively. + +![](images/8fc0e0d4a8e3ab11886591230a7ec982c84f17decf4b205e9c8d622e09a14490.jpg) + +![](images/339a3a4390dc637070b3f728727aae1a56ba654d9bd1cec0ea620c4494b8a843.jpg) + +![](images/d05fba495222e7bba79e0f5bdb1e0deb46d101fb4507b3bd60e6b8b3c5a74073.jpg) + +attention to the design of cross-modal interaction modules. Despite achieving impressive performance, the visual backbone is not well explored. Concretely, the visual backbone passively extracts visual features with fixed architecture and weights, regardless of the referring expressions, as illustrated in Fig. 1 (a). Such passive feature extraction may lead to mismatches between the extracted visual features and those required for various referring expressions, such as missing or redundant features. Taking Fig. 2 as an example, the fixed visual backbone has an inherent preference for the image, as shown in Fig. 2 (b), which may be irrelevant to the referring expression "white bird". Ideally, the visual backbone should take full advantage of expressions, as the expressions can provide information and tendencies about the desired visual features. + +Several methods have noticed this phenomenon and proposed corresponding solutions, such as QRNet [45], and LAVT [44]. Both methods achieve the expression-aware visual feature extraction by inserting carefully designed interaction modules (such as QD-ATT [45], and PWAN [44]) into the visual backbone, as illustrated in Fig. 1 (b). Concretely, visual features are first extracted and then adjusted using QD-ATT (channel and spatial attention) or PWAM (transformer-based pixel-word attention) in QRNet and LAVT at the end of each stage, respectively. Although performance improvement with adjusted visual features, the extract-then-adjust paradigm inevitably contains a large number of feature-extraction components with fixed weights, e.g., the components belonging to the original visual backbone in QRNet and LAVT. Considering that the architecture and weights jointly determine the function of the visual backbone, this paper adopts a simpler and fine-grained scheme that modifies the function of the visual backbone with language-adaptive weights, as illustrated in Fig. 1 (c). Different from the extract-then-adjust paradigm used by QRNet and LAVT, the visual backbone equipped with language-adaptive weights can directly extract expression-relevant visual features without additional feature-adjustment modules. + +In this paper, we propose an active perception Visual Grounding framework based on Language Adaptive Weights, called VG-LAW. It can dynamically adjust the behavior of the visual backbone by injecting the informa + +tion of referring expressions into the weights. Specifically, VG-LAW first obtains the specific language-adaptive weights for the visual backbone through two successive processes of linguistic feature aggregation and weight generation. Then, the language-aware visual backbone can extract expression-relevant visual features without manually modifying the visual backbone architecture. Since the extracted visual features are highly expression-relevant, cross-modal interaction modules are not required for further cross-modal fusion, and the entire network architecture is more streamlined. Furthermore, based on the expression-relevant features, we propose a lightweight but neat multitask prediction head for jointly referring expression comprehension (REC) and referring expression segmentation (RES) tasks. Extensive experiments on RefCOCO [47], RefCOCO+ [47], RefCOCOg [36], and ReferItGame [19] datasets demonstrate the effectiveness of our method, which achieves state-of-the-art performance. + +The main contributions can be summarized as follows: + +- We propose an active perception visual grounding framework based on the language adaptive weights, called VG-LAW, which can actively extract expression-relevant visual features without manually modifying the visual backbone architecture. +- Benefiting from the active perception of visual feature extraction, we can directly utilize our proposed neat but efficient multi-task head for REC and RES tasks jointly without carefully designed cross-modal interaction modules. +- Extensive experiments demonstrate the effectiveness of our framework, which achieves state-of-the-art performance on four widely used datasets, i.e., RefCOCO, RefCOCO+, RefCOCOg, and ReferItGame. + +# 2. Related Work + +# 2.1. Referring Expression Comprehension + +Referring expression comprehension (REC) [4,13,30,42, 43,46,48-50] aims to generate a bounding box in an image specified by a given referring expression. Early researchers explore REC through a two-stage framework [13,29,30,46], where region proposals [38] are first extracted and then ranked according to their similarity scores with referring expressions. To alleviate the speed and accuracy issues of the region proposals in the two-stage framework, simpler and faster one-stage methods [42, 43, 49] based on dense anchors are proposed. Recently, transformer-based methods [4,12,18,48,50] can effectively capture intra- and intermodality context and achieve better performance, benefiting from the self-attention mechanism [40]. + +![](images/a703d02f7d5868bfed0c1ceeb01394285b2a3c7abd582d6bb353ad615a30a456.jpg) +Figure 3. The overall architecture of our proposed VG-LAW framework. It consists of four components: (1) Linguistic Backbone, which extracts linguistic features from free-formed referring expressions, (2) Language Adaptive Weight Generator, which generates dynamic weights for the visual backbone conditioned on specific expressions, (3) Visual Backbone, which extracts visual features from the raw image and its behavior can be modified by language-adaptive weights, and (4) Multi-task Head, which predicts the bounding box and mask of referred object jointly. $\otimes$ represents the matrix multiplication. + +# 2.2. Referring Expression Segmentation + +Similar to REC, referring expression segmentation (RES) [6, 9, 14, 15, 17, 20, 23, 32, 44, 50] aims to predict a precise pixel-wise binary mask corresponding to the given referring expression. The pioneering work [14] proposes to generate segmentation masks for natural language expressions by concatenating the visual and linguistic features and mixing these two modal features with fully convolutional classifiers. Follow-up solutions [9, 15, 17, 32] propose various attention mechanisms to perform cross-modal interaction to generate a high-resolution segmentation map. Recent studies [6, 20, 23, 44, 50], like REC, leverage transformer [40] to realize cross-modal interaction and achieve excellent performance. All these methods achieve cross-modal interaction by either adjusting the inputs or modifying the architectures with fixed network weights. + +# 2.3. Dynamic Weight Networks + +Several works [3, 10, 16, 24, 41] have investigated dynamic weight networks, where given inputs adaptively generate the weights of the network. According to the way of dynamic weight generation, the current methods can be roughly divided into three categories. (1) Dynamic weights are directly generated using fully-connected layers with learnable embeddings [10] or intermediate features [16] as input. (2) Weights are computed as the weighted sum of a set of learnable weights [3, 22, 41], which can also be regarded as the mixture-of-experts and may suffer from challenging joint optimization. (3) The weights are analyzed from the perspective of matrix decomposition [24], and the final dynamic weights are generated by calculating the multiplication of several matrices. + +# 3. Method + +In this section, we will introduce the active perception framework for multi-task visual grounding, including the language-adaptive weight generation, multi-task prediction head, and training objectives. + +# 3.1. Overview + +The extraction of visual features by the visual backbone in the manner of passive perception may cause mismatch problems, which can lead to suboptimal performance despite subsequent carefully designed cross-modal interaction modules. Considering that expressions already provide a blueprint for the desired visual features, we propose an active perception visual grounding framework based on the language adaptive weights, called VG-LAW, as illustrated in Fig. 3. In this framework, the visual backbone can actively extract expression-relevant visual features using language-adaptive weights, without needing to manually modify the visual backbone architecture or elaborately design additional cross-modal interaction modules. + +Specifically, the VG-LAW framework consists of four components, i.e., linguistic backbone, language adaptive weight generator, visual backbone, and multi-task head. Given a referring expression, the $N$ -layer BERT-based [5] linguistic backbone tokenizes the expressions, prepends a [CLS] token, and extracts linguistic features $F_{l} \in \mathbb{R}^{L \times d_{l}}$ where $L$ and $d_{l}$ represent the token numbers and dimension of linguistic features, respectively. The linguistic features $F_{l}$ are then fed to the language adaptive weight generator to generate weights for the transformer-based visual backbone. Next, given an image $I \in \mathbb{R}^{3 \times H \times W}$ , the expression-aware visual features $F_{v} \in \mathbb{R}^{C \times \frac{H}{s} \times \frac{W}{s}}$ can be extracted by + +![](images/31f51d04e7bac8198c5dbaf947fd750cd127876a9384ff4286c57e5b18885fc2.jpg) +Figure 4. The detailed architecture for language adaptive weight generation. The upper part shows the architecture of the adapted ViT block in the visual backbone, and the lower part shows the linguistic feature aggregation and weight generation. + +the visual backbone, where $C$ and $s$ represent the channel number and stride of the visual features, respectively. Finally, we pass the linguistic features $F_{l}^{1} \in \mathbb{R}^{\bar{d}_{l}}$ represented by the [CLS] token and the visual features to the multi-task head, which predicts the bounding box and mask of the referred object for REC and RES, respectively. + +# 3.2. Language Adaptive Weight Generation + +After extracting linguistic features, language-adaptive weights are generated to guide the active perception of the visual backbone. The process of language adaptive weight generation has two stages, i.e., the layer-wise linguistic feature aggregation and the weight generation. + +Linguistic Feature Aggregation. Considering the referring expressions correspond to a different number of linguistic tokens and each layer of the visual backbone may prefer different linguistic tokens, we try to aggregate linguistic features with fixed sizes for each layer independently. Inspired by the multi-head attention mechanism [40], we introduce a learnable layer-specific embedding $e_i \in \mathbb{R}^{d_l}$ for each layer $i$ of the visual backbone to extract layer-specific linguistic features dynamically, which can improve the model flexibility at negligible cost. The calculation is performed on $G$ groups. For each group $g$ , the token-wise attention $\alpha_i^g \in [0,1]^L$ is assigned to the normalized dot product of $e_i^g$ and $F_l^g$ , which is denoted as: + +$$ +\alpha_ {i} ^ {g} = \mathrm {S o f t m a x} ([ e _ {i} ^ {g} \cdot F _ {l} ^ {g, 1}, e _ {i} ^ {g} \cdot F _ {l} ^ {g, 2}, \dots , e _ {i} ^ {g} \cdot F _ {l} ^ {g, L} ]). (1) +$$ + +Then, the aggregated linguistic feature $h_0^i \in \mathbb{R}^{d_l}$ can be derived by concatenating $h_0^{i,g} = \sum_{j=1}^{L} \alpha_i^{g,j} F_l^{g,j}$ . + +Finally, we use a fully-connected layer (FC) to reduce the dimension of the aggregated linguistic features for the $i$ -th layer of the visual backbone, which is indicated as: + +$$ +h _ {1} ^ {i} = \delta \left(W _ {1} ^ {i} h _ {0} ^ {i}\right), \tag {2} +$$ + +where $W_1^i \in \mathbb{R}^{d_l \times d_h}$ is used to reducing the dimension to $d_h = d_l / r$ , and $r$ is the reduction ratio. $\delta$ refers to the GeLU activation function. + +Weight Generation. To guide the active perception of the visual backbone, we generate language-adaptive weights for producing the query $X_{q}$ , key $X_{k}$ , and value $X_{v}$ in the visual backbone conditioned on referring expressions, which can be represented as: + +$$ +X _ {q} = \theta (X; W _ {q}), X _ {k} = \theta (X; W _ {k}), X _ {v} = \theta (X; W _ {v}), \tag {3} +$$ + +where $\theta (\cdot ;W)$ indicates the linear projection operation parameterized by $W$ , and $X$ represents the input visual features. $W_{q},W_{k},W_{v}\in \mathbb{R}^{d_{out}\times d_{in}}$ are the dynamic projection weights used to generate the query, key, and value, respectively. $d_{in}$ and $d_{out}$ are the dimension of feature $X$ and query/key/value, respectively. + +Considering the large number $d_{out} \times d_{in}$ of the dynamic weights, it is unaffordable to directly generate weights using fully-connected layers like Hypernetworks [10]. The DynamicConv [3] and CondConv [41] can alleviate this problem by generating weights with weighted summation of $K$ static kernels but can increase the parameter number by $K$ -times and suffer from challenging joint optimization. Inspired by the dynamic channel fusion [24], we try to generate dynamic weights following the matrix decomposition paradigm. Taking the $i$ -th ViT block as an example, which can be formulated as: + +$$ +\left[ W _ {q} ^ {i}, W _ {k} ^ {i}, W _ {v} ^ {i} \right] = W _ {0} ^ {i} + P \Phi \left(h _ {1} ^ {i}\right) Q ^ {T}, \tag {4} +$$ + +where $W_0^i \in \mathbb{R}^{d_{out} \times d_{in}}$ is the layer-specific static learnable weights. $P \in \mathbb{R}^{d_{out} \times d_w}$ and $Q \in \mathbb{R}^{d_{in} \times d_w}$ are also static learnable weights, but sharable across all ViT blocks to reduce the parameter numbers and prevent the model from overfitting. $\Phi(h_1^i)$ is a fully-connected layer, which produces a dynamic matrix of shape $d_w \times d_w$ with aggregated linguistic features $h_1^i$ as input. + +# 3.3. Multi-task Head + +Different from the previous methods [6,23,42,45,46,49, 50], which require carefully designed cross-modal interaction modules, VG-LAW can obtain expression-relevant visual features extracted by the language-aware visual backbone without additional cross-modal interaction modules. Through our proposed neat but efficient multi-task head, we can utilize the visual and linguistic features to predict + +the bounding box for REC and the segmentation mask for RES. Concretely, there are two branches in the multi-task head for REC and RES, respectively. + +For the REC branch, we apply direct coordinate regression to predict the bounding box of referred object. To pool the 2- $d$ visual features along the spatial dimension, we propose a language adaptive pooling module (LAP), which aggregates visual features using language-adaptive attention. Specifically, the visual features $\{F_v^{i,j}\} \in \mathbb{R}^{C\times \frac{H}{s}\times \frac{W}{s}}$ and linguistic feature $F_{l}^{1}\in \mathbb{R}^{d_{l}}$ are firstly projected to the lower-dimension space $\mathbb{R}^k$ , and the attention weights $A\in \mathbb{R}_{\frac{H}{s}\times \frac{W}{s}}$ are calculated as dot-product similarity followed by Softmax normalization. Then, the visual features are aggregated by calculating the weighted sum with attention weights $A$ . Finally, the aggregated visual features are fed to a three-layer fully-connected layer, and the Sigmoid function is used to predict the referred bounding box $\hat{b} = (\hat{x},\hat{y},\hat{w},\hat{h})$ . + +For the RES branch, we apply binary classification to each visual feature along the spatial dimension to predict segmentation masks for referred objects. Specifically, the visual features $F_{v}$ are first up-sampled to $\hat{F}_v\in \mathbb{R}^{d_l\times \frac{H}{4}\times \frac{W}{4}}$ with successive transposed convolutions. Then, the intermediate segmentation map $\bar{s}\in \mathbb{R}^{\frac{H}{4}\times \frac{W}{4}}$ can be obtained by using linear projection $\theta (\cdot ;W)$ on each visual feature. Following the language adaptive weight paradigm, we also use dynamic rather than fixed weights by simply setting $W = F_l^1$ . Finally, the full-resolution segmentation mask $\hat{s}\in \mathbb{R}^{H\times W}$ is derived by simply up-sample $\bar{s}$ using bilinear interpolation, followed by the Sigmoid function. + +# 3.4. Training Objectives + +The VG-LAW framework can be optimized end-to-end for multi-task visual grounding. For REC, given the predicted bounding box $\hat{b} = (\hat{x},\hat{y},\hat{w},\hat{h})$ and the ground truth $b = (x,y,w,h)$ , the detection loss function is defined as follows: + +$$ +\mathcal {L} _ {\text {d e t}} = \lambda_ {L 1} \mathcal {L} _ {L 1} (b, \hat {b}) + \lambda_ {g i o u} \mathcal {L} _ {g i o u} (b, \hat {b}), \tag {5} +$$ + +where $\mathcal{L}_{L1}(\cdot, \cdot)$ and $\mathcal{L}_{giou}(\cdot, \cdot)$ represent L1 loss and Generalized IoU loss [39], respectively, and $\lambda_{L1}$ and $\lambda_{giou}$ are the relative weights to control the two detection loss functions. For RES, given the predicted mask $\hat{s}$ and the ground-truth $s$ , the segmentation loss function is defined as follows: + +$$ +\mathcal {L} _ {\text {s e g}} = \lambda_ {\text {f o c a l}} \mathcal {L} _ {\text {f o c a l}} (s, \hat {s}) + \lambda_ {\text {d i c e}} \mathcal {L} _ {\text {d i c e}} (s, \hat {s}), \tag {6} +$$ + +where $\mathcal{L}_{focal}(\cdot, \cdot)$ and $\mathcal{L}_{dice}(\cdot, \cdot)$ represent focal loss [27] and DICE/F-1 loss [35], respectively, and $\lambda_{focal}$ and $\lambda_{dice}$ are the relative weights to control the two segmentation loss functions. Our framework can be seamlessly used for joint training of REC and RES, and its joint training loss function is defined as follows: + +$$ +\mathcal {L} _ {\text {t o t a l}} = \mathcal {L} _ {\text {d e t}} + \mathcal {L} _ {\text {s e g}}. \tag {7} +$$ + +The trained model performs well for language-guided detection and segmentation. The experimental analysis of the whole framework will be elaborated in Sec. 4. + +# 4. Experiments + +In this section, we will give a detailed experimental analysis of the whole framework, including the datasets, evaluation protocol, implementation details, comparisons with the state-of-the-art methods, and ablation analysis. + +# 4.1. Datasets and Evaluation Protocol + +Datasets. To verify the effectiveness of our method, we conduct experiments on the widely used RefCOCO [47], RefCOCO+ [47], RefCOCOg [34], and ReferItGame [19] datasets. RefCOCO, RefCOCO+, and RefCOCOg are collected from MS-COCO [28]. RefCOCO and RefCOCO+, which are collected in interactive games, can be divided into train, val, testA, and testB sets. Compared to RefCOCO, the expressions of RefCOCO+ contain more attributes than absolute locations. Unlike RefCOCO and RefCOCO+, RefCOCOg collected by Amazon Mechanical Turk has a longer length of 8.4 words, including the attribute and location of referents. Following a common version of split [36], RefCOCOg has train, val, and test sets. In addition, ReferItGame collected from SAIAPR-12 [8] contains train and test sets. Each sample in the above datasets contains its corresponding bounding box and mask. + +Evaluation Protocol. Following the previous works [23, 33, 50], we use Prec@0.5 and mIoU to evaluate the performance of REC and RES, respectively. For Prec@0.5, the predicted bounding box is considered correct if the intersection-over-union (IoU) with the ground-truth bounding box is greater than 0.5. mIoU represents the IoU between the prediction and ground truth averaged across all test samples. + +# 4.2. Implementation Details + +Training. The resolution of the input image is resized to $448 \times 448$ . ViT-Base [7] is used as the visual backbone, and we follow the adaptation introduced by ViTDet [25] to adapt the visual backbone to higher-resolution images. The visual backbone is pre-trained using Mask R-CNN [11] on MS-COCO [28], where overlapping images of the val/test sets are excluded. The $W_0^i$ and $\Phi(h_1^i)$ in Eq. (4) are initialized with the corresponding pre-trained weights of the visual backbone and zeros, respectively. The maximum length of referring expression is set to 40, and the uncased base of six-layer BERT [5] as the linguistic backbone is used to generate linguistic features. $\lambda_{L1}$ and $\lambda_{giou}$ are set to 1. $\lambda_{focal}$ and $\lambda_{dice}$ are set to 4. The reduction ratio $r$ is set to 16. The initial learning rate for the visual and linguistic backbone is 4e-5, and the initial learning rate for the + +
MethodsVenueVisual BackboneMulti-taskRefCOCORefCOCO+RefCOCOgReferItGame test
valtestAtestBvaltestAtestBvaltest
Two-stage:
MAttNet [46]CVPR18RN101X76.6581.1469.9965.3371.6256.0266.5867.2729.04
RvG-Tree [13]TPAMI19RN101X75.0678.6169.8563.5167.4556.6666.9566.51-
CM-A-E [30]CVPR19RN101X78.3583.1471.3268.0973.6558.0367.9968.67-
Ref-NMS [2]AAAI21RN101X80.7084.0076.0468.2573.6859.4270.5570.62-
One-stage:
FAOA [43]ICCV19DN53X72.5474.3568.5056.8160.2349.6061.3360.3660.67
ReSC-Large [42]ECCV20DN53X77.6380.4572.3063.5968.3656.8167.3067.2064.60
MCN [33]CVPR20DN53✓80.0882.2974.9867.1672.8657.3166.4666.01-
RealGIN [49]TNNLS21DN53X77.2578.7072.1062.7867.1754.2162.7562.33-
PLV-FPN* [26]TIP22RN101X81.9384.9976.2571.2077.4061.0870.4571.0871.77
Transformer-based:
TransVG [4]ICCV21RN101X81.0282.7278.3564.8270.7056.9468.6767.7370.73
RefTR* [23]NeurIPS21RN101✓82.2385.5976.5771.5875.9662.1669.4169.4071.42
SeqTR [50]ECCV22DN53X81.2385.0076.0868.8275.3758.7871.3571.5869.66
Word2Pix [48]TNNLS22RN101X81.2084.3978.1269.7476.1161.2470.8171.34-
YORO [12]ECCVW22-X82.9085.6077.4073.5078.6064.9073.4074.3071.90
QRNet [45]CVPR22Swin-SX84.0185.8582.3472.9476.1763.8171.8973.0374.61
Ours:
VG-LAW-ViT-BX86.0688.5682.8775.7480.3266.6975.3175.9576.60
VG-LAW-ViT-B✓86.6289.3283.1676.3781.0467.5076.9076.9677.22
+ +Table 1. Comparison with state-of-the-art methods on RefCOCO [47], RefCOCO+ [47], RefCOCOg [36] and ReferItGame [19] for REC task. The visual backbone is pre-trained on MS-COCO [28], where overlapping images of the val/test sets are excluded. * represents ImageNet [21] pre-training. RN101, DN53, Swin-S, and ViT-B are shorthand for the ResNet101, DarkNet53, Swin-Transformer Small, and ViT Base, respectively. We highlight the best and second best performance in the red and blue colors. + +
MethodsVenueVisual BackboneMulti-taskRefCOCORefCOCO+RefCOCOg
valtestAtestBvaltestAtestBvaltest
CGAN [32]MM20DN53X64.8668.0462.0751.0355.5144.0654.4054.25
MCN [33]CVPR20DN53✓62.4464.2059.7150.6254.9944.6949.2249.40
LTS [17]CVPR21DN53X65.4367.7663.0854.2158.3248.0254.4054.25
VLT [50]ICCV21DN53X65.6568.2962.7355.5059.2049.3652.9956.65
RefTR* [23]NeurIPS21RN101✓70.5673.4966.5761.0864.6952.7358.7358.51
SeqTR [50]ECCV22DN53X67.2669.7964.1254.1458.9348.1955.6755.64
LAVT* [44]CVPR22Swin-BX74.4676.8970.9465.8170.9759.2363.6263.66
Ours:
VG-LAW-ViT-BX75.0577.3671.6966.6170.3058.1465.3665.13
VG-LAW-ViT-B✓75.6277.5172.8966.6370.3858.8965.6366.08
+ +Table 2. Comparison with state-of-the-art methods on RefCOCO [47], RefCOCO+ [47], and RefCOCOg [36] for RES task. The visual backbone is pre-trained on MS-COCO [28], where overlapping images of the val/test sets are excluded. * represents ImageNet [21] pre-training. RN101, DN53, Swin-B, and ViT-B are shorthand for the ResNet101, DarkNet53, Swin-Transformer Base, and ViT Base, respectively. We highlight the best and second best performance in the red and blue colors. + +remaining components is 4e-4. The model is end-to-end optimized by AdamW [31] for 90 epochs with a batch size of 256, where weight decay is set to 1e-4, and the learning rate is reduced by a factor of 10 after 60 epochs. Data augmentation operation includes random horizontal flips. We implement our framework using PyTorch and conduct experiments with NVIDIA A100 GPUs. + +Inference. At inference time, the input image is resized to $448 \times 448$ , and the maximum length of referring expressions is set to 40. Following the previous method [33], We set the threshold to 0.35 to realize the binarization of the RES prediction. Without any post-processing operation, our framework directly outputs bounding boxes and segmentation maps specified by referring expressions. + +![](images/e718842e9dc933811d396986013a8a741d114979614c013f1ab4e76fa0a8f1ef.jpg) +Figure 5. Comparison of accuracy under different lengths of referring expression on RefCOCOg-test. ReSC [42], TransVG [4], Word2Pix [48], and the proposed VG-LAW are compared. + +# 4.3. Comparisons with State-of-the-art Methods + +To estimate the effectiveness of the proposed VG-LAW framework, we conduct quantitative experiments on four widely used datasets, i.e., RefCOCO [47], RefCOCO+ [47], RefCOCOg [34], and ReferItGame [19]. + +REC Task. For the REC task, we compare the performance with state-of-the-art REC methods, including the two-stage methods [2, 13, 30, 46], one-stage methods [26, 33, 42, 43, 49], and transformer-based methods [4, 12, 23, 45, 48, 50]. The main results are summarized to Tab. 1. It can be observed that VG-LAW achieves a significant performance improvement compared to the state-of-the-art two-stage method Ref-NMS [2] and one-stage method PLV-FPN [26]. When comparing to the transformer-based method QRNet [45], which modified the visual backbone by inserting language-aware spatial and channel attention modules, our method has better performance with $+2.62\% / +3.47\% / +0.82\%$ on RefCOCO, $+3.43\% / +4.87\% / +3.69\%$ on RefCOCO+, $+5.01\% / +3.93\%$ on RefCOCOg, and $+2.61\%$ on ReferItGame. QRNet [45] follows the TransVG [4] framework, both of which use the transformer encoder-based cross-modal interaction module. Compared to them, VG-LAW achieves better performance without complex cross-modal interaction modules. Furthermore, our method significantly outperforms MCN [33] and RefTR [23] based on joint training of REC and RES. + +RES Task. For the RES task, we compare the performance with state-of-the-art methods [6,17,23,32,33,44,50], and the main results are summarized to Tab. 2. Compared with state-of-the-art RES method LAVT [44], VG-LAW achieves better $mIoU$ with $+1.16\% / +0.62\% / +1.95\%$ on RefCOCO, $+2.01\% / +2.42\%$ on RefCOCOg, and comparable $mIoU$ with $+0.82\% / -0.59\% / -0.34\%$ on RefCOCO+. + +
LAWGLAPMTHPrec@0.5(%)
✓74.89
✓74.37
✓✓76.60
✓✓✓77.22
+ +Table 3. Ablation experiments on ReferItGame [19] to evaluate the proposed language adaptive weight generation (LAWG), language adaptive pooling (LAP), and multi-task head (MTH). + +When comparing the models trained with or without multi-task settings, it can also be observed that consistent performance gains are achieved across all the datasets and splits. As REC can provide localization information of the referred object, such coarse-grained supervision can slightly improve the segmentation accuracy in RES. + +Analysis of Referring Expression Length. As the visual backbone in VG-LAW extracts features purely perceptually, it is of concern whether it can handle long and complex referring expressions. ReSC [42] reveals that one-stage methods may ignore detailed descriptions in complex referring expressions and lead to poor performance. Following that, we evaluate the REC performance on referring expressions of different lengths, as illustrated in Fig. 5. VG-LAW performs better than ReSC, TransVG [4] and Word2Pix [48], with no significant performance degradation when the length of referring expressions varies from 6-7 to $11+$ . + +# 4.4. Ablation Analysis + +To validate the effectiveness of our proposed modules, i.e. language-adaptive weight generation, language-adaptive pooling, and multi-task head, we conduct ablation experiments on the REC dataset of ReferItGame, which is summarized in Tab. 3. When only using the LAWG, the visual features are pooled with global average pooling, and when only using the LAP, the visual backbone has fixed architecture and weights. When only using the LAWG or the LAP, it can be observed that the model already achieves $74.89\%$ and $74.37\%$ , respectively, which is close to the $74.61\%$ reported by QRNet [45]. When combined with the LAWG and LAP, further improvements can be brought by LAWG and LAP with $+2.23\%$ and $+1.71\%$ , respectively. Benefiting from the auxiliary supervision of RES, our model equipped with the multi-task head can localize the referred objects better and achieve $77.22\%$ . + +# 4.5. Qualitative Results + +The qualitative results of the four datasets are shown in Fig. 6. It can be observed that our model can successfully locate and segment the referred objects, and the attention of + +![](images/60f13a15c23dcc097354103c325bfc86b86a4fa8a9404a5fd2edde0901309009.jpg) +Figure 6. Qualitative results on the RefCOCO [47], RefCOCO+ [47], RefCOCOg [34], and ReferItGame [19] datasets. Each dataset shows two examples. From left to right: the input image, the ground truth of REC and RES, the prediction of VG-LAW, and the attention of the visual backbone with language-adaptive weights. + +![](images/6924d1d9e7c0fb578033c5acf10f16f4dbc9539dffcc2b70facc3d2c1ae76048.jpg) +Figure 7. Wordcloud visualization of words assigned to the first and second halves of the visual backbone. + +![](images/6889d45355f4cd056702b3e009912c6fefc0f245803fbf5271b3ef83084ca52f.jpg) + +the visual backbone can focus on the most relevant image regions, demonstrating the effectiveness of using language adaptive weights. Taking the results on ReferItGame as an example, the visual backbone can dynamically filter out irrelevant regions for different expressions. For instance, when the "purple curtain" is referred to, the regions related to the "the painting/photo on the wall" are ignored. + +In addition, we count the scores of words assigned to the first and second halves of the visual backbone, as shown in Fig. 7. The scores are calculated by averaging attention score $\alpha_{i}$ in Eq. (1) for each word, followed by softmax normalization along the layer dimension. It can be observed that the shallow layers tend to the words describing individuals, such as the categories "velvet" and "yacht", and the deep layers tend to the words about contexts, such as the ordinal number "2nd" and the position "right". + +# 5. Conclusions and Limitations + +In this paper, we propose an active perception framework VG-LAW for visual grounding, based on the language adaptive weights. VG-LAW can directly inject the information of referring expressions into the weights of the visual backbone without modifying its architecture. Equipped with the proposed neat yet efficient multi-task head, VG-LAW achieves state-of-the-art performance for REC and RES tasks on widely used datasets. The limitations of our method are two-fold: (1) VG-LAW is weak in interpretability, and the entire reasoning process is implicit, which makes it difficult to understand how the reasoning process works, and (2) the multi-task head predicts one instance at a time, which limits its application in phrase grounding. + +# 6. Acknowledgments + +This work is supported in part by National Key Research and Development Program of China under Grant 2020AAA0107400, National Natural Science Foundation of China under Grant U20A20222, National Science Foundation for Distinguished Young Scholars under Grant 62225605, Ant Group through CCF-Ant Research Fund, and sponsored by CCF-AFSG Research Fund, CAAI-HUAWEI MindSpore Open Fund, CCF-Zhipu AI Large Model Fund (CCF-Zhipu202302) as well as Hikvision Cooperation Fund. + +# References + +[1] Nicolas Carion, Francisco Massa, Gabriel Synnaeve, Nicolas Usunier, Alexander Kirillov, and Sergey Zagoruyko. End-to-end object detection with transformers. 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In ICCV, pages 4683-4693, 2019. 2, 6, 7 +[44] Zhao Yang, Jiaqi Wang, Yansong Tang, Kai Chen, Hengshuang Zhao, and Philip HS Torr. Lavt: Language-aware vision transformer for referring image segmentation. In CVPR, pages 18155-18165, 2022. 1, 2, 3, 6, 7 +[45] Jiabo Ye, Junfeng Tian, Ming Yan, Xiaoshan Yang, Xuwu Wang, Ji Zhang, Liang He, and Xin Lin. Shifting more attention to visual backbone: Query-modulated refinement networks for end-to-end visual grounding. In CVPR, pages 15502-15512, 2022. 1, 2, 4, 6, 7 +[46] Licheng Yu, Zhe Lin, Xiaohui Shen, Jimei Yang, Xin Lu, Mohit Bansal, and Tamara L Berg. Mattnet: Modular attention network for referring expression comprehension. In CVPR, pages 1307-1315, 2018. 1, 2, 4, 6, 7 + +[47] Licheng Yu, Patrick Poirson, Shan Yang, Alexander C Berg, and Tamara L Berg. Modeling context in referring expressions. In ECCV, pages 69–85, 2016. 2, 5, 6, 7, 8 +[48] Heng Zhao, Joey Tianyi Zhou, and Yew-Soon Ong. Word2pix: Word to pixel cross-attention transformer in visual grounding. IEEE Trans. Neural Networks and Learning Systems., 2022. 1, 2, 6, 7 +[49] Yiyi Zhou, Rongrong Ji, Gen Luo, Xiaoshuai Sun, Jinsong Su, Xinghao Ding, Chia-Wen Lin, and Qi Tian. A real-time global inference network for one-stage referring expression comprehension. IEEE Trans. Neural Networks and Learning Systems., 2021. 2, 4, 6, 7 +[50] Chaoyang Zhu, Yiyi Zhou, Yunhang Shen, Gen Luo, Xingjia Pan, Mingbao Lin, Chao Chen, Liujuan Cao, Xiaoshuai Sun, and Rongrong Ji. Seqtr: A simple yet universal network for visual grounding. arXiv preprint arXiv:2203.16265, 2022. 1, 2, 3, 4, 5, 6, 7 \ No newline at end of file diff --git a/2023/Language Adaptive Weight Generation for Multi-Task Visual Grounding/images.zip b/2023/Language Adaptive Weight Generation for Multi-Task Visual Grounding/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..313538686ea78d50d735dca9725aad01ef75c23e --- /dev/null +++ b/2023/Language Adaptive Weight Generation for Multi-Task Visual Grounding/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:b199a4b2b9eb05c8b1e357c32ecc310cd336e4c137b0e6e11a0b6cac6516f1b8 +size 694858 diff --git a/2023/Language Adaptive Weight Generation for Multi-Task Visual Grounding/layout.json b/2023/Language Adaptive Weight Generation for Multi-Task Visual Grounding/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..ee9b7dd4fa7bac74f119bdd9d7e366ba585fc87d --- /dev/null +++ b/2023/Language Adaptive Weight Generation for Multi-Task Visual Grounding/layout.json @@ -0,0 +1,8127 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 73, + 103, + 521, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 73, + 103, + 521, + 121 + ], + "spans": [ + { + "bbox": [ + 73, + 103, + 521, + 121 + ], + "type": "text", + "content": "Language Adaptive Weight Generation for Multi-task Visual Grounding" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 146, + 141, + 447, + 171 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 141, + 447, + 171 + ], + "spans": [ + { + "bbox": [ + 146, + 141, + 447, + 171 + ], + "type": "text", + "content": "Wei Su1 Peihan Miao1 Huanzhang Dou1 Gaoang Wang4 Liang Qiao1,3 Zheyang Li1,3 Xi Li1,2,5*" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 72, + 171, + 520, + 214 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 72, + 171, + 520, + 214 + ], + "spans": [ + { + "bbox": [ + 72, + 171, + 520, + 214 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 72, + 171, + 520, + 214 + ], + "type": "text", + "content": "Zhejiang University " + }, + { + "bbox": [ + 72, + 171, + 520, + 214 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 72, + 171, + 520, + 214 + ], + "type": "text", + "content": "Shanghai AI Laboratory " + }, + { + "bbox": [ + 72, + 171, + 520, + 214 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 72, + 171, + 520, + 214 + ], + "type": "text", + "content": "Hikvision Research Institute " + }, + { + "bbox": [ + 72, + 171, + 520, + 214 + ], + "type": "inline_equation", + "content": "^{4}" + }, + { + "bbox": [ + 72, + 171, + 520, + 214 + ], + "type": "text", + "content": "Zhejiang University-University of Illinois Urbana-Champaign Institute, Zhejiang University " + }, + { + "bbox": [ + 72, + 171, + 520, + 214 + ], + "type": "inline_equation", + "content": "^{5}" + }, + { + "bbox": [ + 72, + 171, + 520, + 214 + ], + "type": "text", + "content": "Shanghai Institute for Advanced Study of Zhejiang University" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 132, + 215, + 462, + 242 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 132, + 215, + 462, + 242 + ], + "spans": [ + { + "bbox": [ + 132, + 215, + 462, + 242 + ], + "type": "text", + "content": "{weisuzju, peihan.miao, hzdou, qiaoliang, xilizju}@zju.edu.cn gaoangwang@intl.zju.edu.cn, lizheyang@hikvision.com" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 143, + 269, + 192, + 281 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 269, + 192, + 281 + ], + "spans": [ + { + "bbox": [ + 143, + 269, + 192, + 281 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 293, + 290, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 293, + 290, + 594 + ], + "spans": [ + { + "bbox": [ + 46, + 293, + 290, + 594 + ], + "type": "text", + "content": "Although the impressive performance in visual grounding, the prevailing approaches usually exploit the visual backbone in a passive way, i.e., the visual backbone extracts features with fixed weights without expression-related hints. The passive perception may lead to mismatches (e.g., redundant and missing), limiting further performance improvement. Ideally, the visual backbone should actively extract visual features since the expressions already provide the blueprint of desired visual features. The active perception can take expressions as priors to extract relevant visual features, which can effectively alleviate the mismatches. Inspired by this, we propose an active perception Visual Grounding framework based on Language Adaptive Weights, called VG-LAW. The visual backbone serves as an expression-specific feature extractor through dynamic weights generated for various expressions. Benefiting from the specific and relevant visual features extracted from the language-aware visual backbone, VG-LAW does not require additional modules for cross-modal interaction. Along with a neat multi-task head, VG-LAW can be competent in referring expression comprehension and segmentation jointly. Extensive experiments on four representative datasets, i.e., RefCOCO, RefCOCO+, RefCOCOg, and ReferItGame, validate the effectiveness of the proposed framework and demonstrate state-of-the-art performance." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 627, + 128, + 639 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 627, + 128, + 639 + ], + "spans": [ + { + "bbox": [ + 47, + 627, + 128, + 639 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 647, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 647, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 647, + 287, + 696 + ], + "type": "text", + "content": "Visual grounding (such as referring expression comprehension [4, 23, 42, 45, 46, 48, 50], referring expression segmentation [6, 14, 17, 23, 32, 33, 44], and phrase grounding [4, 23, 50]) aims to detect or segment the specific object" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 309, + 266, + 545, + 329 + ], + "blocks": [ + { + "bbox": [ + 309, + 266, + 545, + 329 + ], + "lines": [ + { + "bbox": [ + 309, + 266, + 545, + 329 + ], + "spans": [ + { + "bbox": [ + 309, + 266, + 545, + 329 + ], + "type": "image", + "image_path": "f421886bb36a673d7a513c149a6d4ce2bf47e6eb3dd0c85999c73f1f4e4e42b4.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 308, + 331, + 545, + 396 + ], + "blocks": [ + { + "bbox": [ + 308, + 331, + 545, + 396 + ], + "lines": [ + { + "bbox": [ + 308, + 331, + 545, + 396 + ], + "spans": [ + { + "bbox": [ + 308, + 331, + 545, + 396 + ], + "type": "image", + "image_path": "2e0b9c00a8a0e117cba7ffd3d29b229fbae1371bbd7d7f717de2d107c3b9081b.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 309, + 396, + 545, + 460 + ], + "blocks": [ + { + "bbox": [ + 309, + 396, + 545, + 460 + ], + "lines": [ + { + "bbox": [ + 309, + 396, + 545, + 460 + ], + "spans": [ + { + "bbox": [ + 309, + 396, + 545, + 460 + ], + "type": "image", + "image_path": "71fde5d9edeacf11803b0fca155864d891e4a9aba332999927d3dd7c1caad168.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 468, + 547, + 557 + ], + "lines": [ + { + "bbox": [ + 304, + 468, + 547, + 557 + ], + "spans": [ + { + "bbox": [ + 304, + 468, + 547, + 557 + ], + "type": "text", + "content": "Figure 1. The comparison of visual grounding frameworks. (a) The visual and linguistic backbone independently extracts features, which are fused through cross-modal interaction. (b) Additional designed modules are inserted into the visual backbone to modulate visual features using linguistic features. (c) VG-LAW can generate language-adaptive weights for the visual backbone and directly output referred objects through our designed multitask head without additional cross-modal interaction modules." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 580, + 547, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 580, + 547, + 676 + ], + "spans": [ + { + "bbox": [ + 304, + 580, + 547, + 676 + ], + "type": "text", + "content": "based on a given natural language description. Compared to general object detection [38] or instance segmentation [11], which can only locate objects within a predefined and fixed category set, visual grounding is more flexible and purposeful. Free-formed language descriptions can specify specific visual properties of the target object, such as categories, attributes, relationships with other objects, relative/absolute positions, and etc." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "type": "text", + "content": "Due to the similarity with detection tasks, previous visual grounding approaches [23, 33, 46, 50] usually follow the general object detection frameworks [1, 11, 37], and pay" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 703, + 134, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 703, + 134, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 703, + 134, + 713 + ], + "type": "text", + "content": "* corresponding author." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10857" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 70, + 108, + 121 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 108, + 121 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 108, + 121 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 108, + 121 + ], + "type": "image", + "image_path": "1ca2784989b575d0aa9823600577ec9f26dccd958f4887a1120b72dfca877a76.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 129, + 287, + 174 + ], + "lines": [ + { + "bbox": [ + 47, + 129, + 287, + 174 + ], + "spans": [ + { + "bbox": [ + 47, + 129, + 287, + 174 + ], + "type": "text", + "content": "Figure 2. Attention visualization of the visual backbone with different weights. (a) input image, (b) visual backbone with fixed weights, (c) and (d) visual backbone with weights generated for \"white bird\" and \"right bird\", respectively." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 110, + 70, + 167, + 121 + ], + "blocks": [ + { + "bbox": [ + 110, + 70, + 167, + 121 + ], + "lines": [ + { + "bbox": [ + 110, + 70, + 167, + 121 + ], + "spans": [ + { + "bbox": [ + 110, + 70, + 167, + 121 + ], + "type": "image", + "image_path": "8fc0e0d4a8e3ab11886591230a7ec982c84f17decf4b205e9c8d622e09a14490.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 169, + 70, + 227, + 121 + ], + "blocks": [ + { + "bbox": [ + 169, + 70, + 227, + 121 + ], + "lines": [ + { + "bbox": [ + 169, + 70, + 227, + 121 + ], + "spans": [ + { + "bbox": [ + 169, + 70, + 227, + 121 + ], + "type": "image", + "image_path": "339a3a4390dc637070b3f728727aae1a56ba654d9bd1cec0ea620c4494b8a843.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 228, + 70, + 285, + 121 + ], + "blocks": [ + { + "bbox": [ + 228, + 70, + 285, + 121 + ], + "lines": [ + { + "bbox": [ + 228, + 70, + 285, + 121 + ], + "spans": [ + { + "bbox": [ + 228, + 70, + 285, + 121 + ], + "type": "image", + "image_path": "d05fba495222e7bba79e0f5bdb1e0deb46d101fb4507b3bd60e6b8b3c5a74073.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 197, + 287, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 197, + 287, + 376 + ], + "spans": [ + { + "bbox": [ + 46, + 197, + 287, + 376 + ], + "type": "text", + "content": "attention to the design of cross-modal interaction modules. Despite achieving impressive performance, the visual backbone is not well explored. Concretely, the visual backbone passively extracts visual features with fixed architecture and weights, regardless of the referring expressions, as illustrated in Fig. 1 (a). Such passive feature extraction may lead to mismatches between the extracted visual features and those required for various referring expressions, such as missing or redundant features. Taking Fig. 2 as an example, the fixed visual backbone has an inherent preference for the image, as shown in Fig. 2 (b), which may be irrelevant to the referring expression \"white bird\". Ideally, the visual backbone should take full advantage of expressions, as the expressions can provide information and tendencies about the desired visual features." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 377, + 288, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 377, + 288, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 377, + 288, + 664 + ], + "type": "text", + "content": "Several methods have noticed this phenomenon and proposed corresponding solutions, such as QRNet [45], and LAVT [44]. Both methods achieve the expression-aware visual feature extraction by inserting carefully designed interaction modules (such as QD-ATT [45], and PWAN [44]) into the visual backbone, as illustrated in Fig. 1 (b). Concretely, visual features are first extracted and then adjusted using QD-ATT (channel and spatial attention) or PWAM (transformer-based pixel-word attention) in QRNet and LAVT at the end of each stage, respectively. Although performance improvement with adjusted visual features, the extract-then-adjust paradigm inevitably contains a large number of feature-extraction components with fixed weights, e.g., the components belonging to the original visual backbone in QRNet and LAVT. Considering that the architecture and weights jointly determine the function of the visual backbone, this paper adopts a simpler and fine-grained scheme that modifies the function of the visual backbone with language-adaptive weights, as illustrated in Fig. 1 (c). Different from the extract-then-adjust paradigm used by QRNet and LAVT, the visual backbone equipped with language-adaptive weights can directly extract expression-relevant visual features without additional feature-adjustment modules." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "content": "In this paper, we propose an active perception Visual Grounding framework based on Language Adaptive Weights, called VG-LAW. It can dynamically adjust the behavior of the visual backbone by injecting the informa" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 72, + 545, + 287 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 287 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 287 + ], + "type": "text", + "content": "tion of referring expressions into the weights. Specifically, VG-LAW first obtains the specific language-adaptive weights for the visual backbone through two successive processes of linguistic feature aggregation and weight generation. Then, the language-aware visual backbone can extract expression-relevant visual features without manually modifying the visual backbone architecture. Since the extracted visual features are highly expression-relevant, cross-modal interaction modules are not required for further cross-modal fusion, and the entire network architecture is more streamlined. Furthermore, based on the expression-relevant features, we propose a lightweight but neat multitask prediction head for jointly referring expression comprehension (REC) and referring expression segmentation (RES) tasks. Extensive experiments on RefCOCO [47], RefCOCO+ [47], RefCOCOg [36], and ReferItGame [19] datasets demonstrate the effectiveness of our method, which achieves state-of-the-art performance." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 318, + 289, + 538, + 299 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 289, + 538, + 299 + ], + "spans": [ + { + "bbox": [ + 318, + 289, + 538, + 299 + ], + "type": "text", + "content": "The main contributions can be summarized as follows:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 318, + 310, + 545, + 498 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 318, + 310, + 545, + 369 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 310, + 545, + 369 + ], + "spans": [ + { + "bbox": [ + 318, + 310, + 545, + 369 + ], + "type": "text", + "content": "- We propose an active perception visual grounding framework based on the language adaptive weights, called VG-LAW, which can actively extract expression-relevant visual features without manually modifying the visual backbone architecture." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 318, + 380, + 545, + 438 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 380, + 545, + 438 + ], + "spans": [ + { + "bbox": [ + 318, + 380, + 545, + 438 + ], + "type": "text", + "content": "- Benefiting from the active perception of visual feature extraction, we can directly utilize our proposed neat but efficient multi-task head for REC and RES tasks jointly without carefully designed cross-modal interaction modules." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 318, + 449, + 545, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 449, + 545, + 498 + ], + "spans": [ + { + "bbox": [ + 318, + 449, + 545, + 498 + ], + "type": "text", + "content": "- Extensive experiments demonstrate the effectiveness of our framework, which achieves state-of-the-art performance on four widely used datasets, i.e., RefCOCO, RefCOCO+, RefCOCOg, and ReferItGame." + } + ] + } + ], + "index": 12 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 518, + 392, + 530 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 518, + 392, + 530 + ], + "spans": [ + { + "bbox": [ + 306, + 518, + 392, + 530 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 539, + 504, + 552 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 539, + 504, + 552 + ], + "spans": [ + { + "bbox": [ + 306, + 539, + 504, + 552 + ], + "type": "text", + "content": "2.1. Referring Expression Comprehension" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 557, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 545, + 713 + ], + "type": "text", + "content": "Referring expression comprehension (REC) [4,13,30,42, 43,46,48-50] aims to generate a bounding box in an image specified by a given referring expression. Early researchers explore REC through a two-stage framework [13,29,30,46], where region proposals [38] are first extracted and then ranked according to their similarity scores with referring expressions. To alleviate the speed and accuracy issues of the region proposals in the two-stage framework, simpler and faster one-stage methods [42, 43, 49] based on dense anchors are proposed. Recently, transformer-based methods [4,12,18,48,50] can effectively capture intra- and intermodality context and achieve better performance, benefiting from the self-attention mechanism [40]." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10858" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 70, + 545, + 228 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 545, + 228 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 545, + 228 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 545, + 228 + ], + "type": "image", + "image_path": "a703d02f7d5868bfed0c1ceeb01394285b2a3c7abd582d6bb353ad615a30a456.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 236, + 548, + 295 + ], + "lines": [ + { + "bbox": [ + 46, + 236, + 548, + 295 + ], + "spans": [ + { + "bbox": [ + 46, + 236, + 548, + 295 + ], + "type": "text", + "content": "Figure 3. The overall architecture of our proposed VG-LAW framework. It consists of four components: (1) Linguistic Backbone, which extracts linguistic features from free-formed referring expressions, (2) Language Adaptive Weight Generator, which generates dynamic weights for the visual backbone conditioned on specific expressions, (3) Visual Backbone, which extracts visual features from the raw image and its behavior can be modified by language-adaptive weights, and (4) Multi-task Head, which predicts the bounding box and mask of referred object jointly. " + }, + { + "bbox": [ + 46, + 236, + 548, + 295 + ], + "type": "inline_equation", + "content": "\\otimes" + }, + { + "bbox": [ + 46, + 236, + 548, + 295 + ], + "type": "text", + "content": " represents the matrix multiplication." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 312, + 237, + 326 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 312, + 237, + 326 + ], + "spans": [ + { + "bbox": [ + 47, + 312, + 237, + 326 + ], + "type": "text", + "content": "2.2. Referring Expression Segmentation" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 332, + 290, + 513 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 332, + 290, + 513 + ], + "spans": [ + { + "bbox": [ + 46, + 332, + 290, + 513 + ], + "type": "text", + "content": "Similar to REC, referring expression segmentation (RES) [6, 9, 14, 15, 17, 20, 23, 32, 44, 50] aims to predict a precise pixel-wise binary mask corresponding to the given referring expression. The pioneering work [14] proposes to generate segmentation masks for natural language expressions by concatenating the visual and linguistic features and mixing these two modal features with fully convolutional classifiers. Follow-up solutions [9, 15, 17, 32] propose various attention mechanisms to perform cross-modal interaction to generate a high-resolution segmentation map. Recent studies [6, 20, 23, 44, 50], like REC, leverage transformer [40] to realize cross-modal interaction and achieve excellent performance. All these methods achieve cross-modal interaction by either adjusting the inputs or modifying the architectures with fixed network weights." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 525, + 197, + 539 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 525, + 197, + 539 + ], + "spans": [ + { + "bbox": [ + 47, + 525, + 197, + 539 + ], + "type": "text", + "content": "2.3. Dynamic Weight Networks" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 545, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 289, + 715 + ], + "type": "text", + "content": "Several works [3, 10, 16, 24, 41] have investigated dynamic weight networks, where given inputs adaptively generate the weights of the network. According to the way of dynamic weight generation, the current methods can be roughly divided into three categories. (1) Dynamic weights are directly generated using fully-connected layers with learnable embeddings [10] or intermediate features [16] as input. (2) Weights are computed as the weighted sum of a set of learnable weights [3, 22, 41], which can also be regarded as the mixture-of-experts and may suffer from challenging joint optimization. (3) The weights are analyzed from the perspective of matrix decomposition [24], and the final dynamic weights are generated by calculating the multiplication of several matrices." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 312, + 362, + 324 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 312, + 362, + 324 + ], + "spans": [ + { + "bbox": [ + 306, + 312, + 362, + 324 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 333, + 547, + 382 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 333, + 547, + 382 + ], + "spans": [ + { + "bbox": [ + 304, + 333, + 547, + 382 + ], + "type": "text", + "content": "In this section, we will introduce the active perception framework for multi-task visual grounding, including the language-adaptive weight generation, multi-task prediction head, and training objectives." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 393, + 373, + 404 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 393, + 373, + 404 + ], + "spans": [ + { + "bbox": [ + 306, + 393, + 373, + 404 + ], + "type": "text", + "content": "3.1. Overview" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 413, + 547, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 413, + 547, + 568 + ], + "spans": [ + { + "bbox": [ + 304, + 413, + 547, + 568 + ], + "type": "text", + "content": "The extraction of visual features by the visual backbone in the manner of passive perception may cause mismatch problems, which can lead to suboptimal performance despite subsequent carefully designed cross-modal interaction modules. Considering that expressions already provide a blueprint for the desired visual features, we propose an active perception visual grounding framework based on the language adaptive weights, called VG-LAW, as illustrated in Fig. 3. In this framework, the visual backbone can actively extract expression-relevant visual features using language-adaptive weights, without needing to manually modify the visual backbone architecture or elaborately design additional cross-modal interaction modules." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 570, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 548, + 715 + ], + "type": "text", + "content": "Specifically, the VG-LAW framework consists of four components, i.e., linguistic backbone, language adaptive weight generator, visual backbone, and multi-task head. Given a referring expression, the " + }, + { + "bbox": [ + 304, + 570, + 548, + 715 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 570, + 548, + 715 + ], + "type": "text", + "content": "-layer BERT-based [5] linguistic backbone tokenizes the expressions, prepends a [CLS] token, and extracts linguistic features " + }, + { + "bbox": [ + 304, + 570, + 548, + 715 + ], + "type": "inline_equation", + "content": "F_{l} \\in \\mathbb{R}^{L \\times d_{l}}" + }, + { + "bbox": [ + 304, + 570, + 548, + 715 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 570, + 548, + 715 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 304, + 570, + 548, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 570, + 548, + 715 + ], + "type": "inline_equation", + "content": "d_{l}" + }, + { + "bbox": [ + 304, + 570, + 548, + 715 + ], + "type": "text", + "content": " represent the token numbers and dimension of linguistic features, respectively. The linguistic features " + }, + { + "bbox": [ + 304, + 570, + 548, + 715 + ], + "type": "inline_equation", + "content": "F_{l}" + }, + { + "bbox": [ + 304, + 570, + 548, + 715 + ], + "type": "text", + "content": " are then fed to the language adaptive weight generator to generate weights for the transformer-based visual backbone. Next, given an image " + }, + { + "bbox": [ + 304, + 570, + 548, + 715 + ], + "type": "inline_equation", + "content": "I \\in \\mathbb{R}^{3 \\times H \\times W}" + }, + { + "bbox": [ + 304, + 570, + 548, + 715 + ], + "type": "text", + "content": ", the expression-aware visual features " + }, + { + "bbox": [ + 304, + 570, + 548, + 715 + ], + "type": "inline_equation", + "content": "F_{v} \\in \\mathbb{R}^{C \\times \\frac{H}{s} \\times \\frac{W}{s}}" + }, + { + "bbox": [ + 304, + 570, + 548, + 715 + ], + "type": "text", + "content": " can be extracted by" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "10859" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 72, + 282, + 250 + ], + "blocks": [ + { + "bbox": [ + 53, + 72, + 282, + 250 + ], + "lines": [ + { + "bbox": [ + 53, + 72, + 282, + 250 + ], + "spans": [ + { + "bbox": [ + 53, + 72, + 282, + 250 + ], + "type": "image", + "image_path": "31f51d04e7bac8198c5dbaf947fd750cd127876a9384ff4286c57e5b18885fc2.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 258, + 288, + 304 + ], + "lines": [ + { + "bbox": [ + 46, + 258, + 288, + 304 + ], + "spans": [ + { + "bbox": [ + 46, + 258, + 288, + 304 + ], + "type": "text", + "content": "Figure 4. The detailed architecture for language adaptive weight generation. The upper part shows the architecture of the adapted ViT block in the visual backbone, and the lower part shows the linguistic feature aggregation and weight generation." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 324, + 287, + 397 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 324, + 287, + 397 + ], + "spans": [ + { + "bbox": [ + 46, + 324, + 287, + 397 + ], + "type": "text", + "content": "the visual backbone, where " + }, + { + "bbox": [ + 46, + 324, + 287, + 397 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 324, + 287, + 397 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 324, + 287, + 397 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 46, + 324, + 287, + 397 + ], + "type": "text", + "content": " represent the channel number and stride of the visual features, respectively. Finally, we pass the linguistic features " + }, + { + "bbox": [ + 46, + 324, + 287, + 397 + ], + "type": "inline_equation", + "content": "F_{l}^{1} \\in \\mathbb{R}^{\\bar{d}_{l}}" + }, + { + "bbox": [ + 46, + 324, + 287, + 397 + ], + "type": "text", + "content": " represented by the [CLS] token and the visual features to the multi-task head, which predicts the bounding box and mask of the referred object for REC and RES, respectively." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 404, + 253, + 417 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 404, + 253, + 417 + ], + "spans": [ + { + "bbox": [ + 47, + 404, + 253, + 417 + ], + "type": "text", + "content": "3.2. Language Adaptive Weight Generation" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 422, + 287, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 422, + 287, + 483 + ], + "spans": [ + { + "bbox": [ + 46, + 422, + 287, + 483 + ], + "type": "text", + "content": "After extracting linguistic features, language-adaptive weights are generated to guide the active perception of the visual backbone. The process of language adaptive weight generation has two stages, i.e., the layer-wise linguistic feature aggregation and the weight generation." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 498, + 287, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 287, + 654 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 287, + 654 + ], + "type": "text", + "content": "Linguistic Feature Aggregation. Considering the referring expressions correspond to a different number of linguistic tokens and each layer of the visual backbone may prefer different linguistic tokens, we try to aggregate linguistic features with fixed sizes for each layer independently. Inspired by the multi-head attention mechanism [40], we introduce a learnable layer-specific embedding " + }, + { + "bbox": [ + 46, + 498, + 287, + 654 + ], + "type": "inline_equation", + "content": "e_i \\in \\mathbb{R}^{d_l}" + }, + { + "bbox": [ + 46, + 498, + 287, + 654 + ], + "type": "text", + "content": " for each layer " + }, + { + "bbox": [ + 46, + 498, + 287, + 654 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 498, + 287, + 654 + ], + "type": "text", + "content": " of the visual backbone to extract layer-specific linguistic features dynamically, which can improve the model flexibility at negligible cost. The calculation is performed on " + }, + { + "bbox": [ + 46, + 498, + 287, + 654 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 46, + 498, + 287, + 654 + ], + "type": "text", + "content": " groups. For each group " + }, + { + "bbox": [ + 46, + 498, + 287, + 654 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 46, + 498, + 287, + 654 + ], + "type": "text", + "content": ", the token-wise attention " + }, + { + "bbox": [ + 46, + 498, + 287, + 654 + ], + "type": "inline_equation", + "content": "\\alpha_i^g \\in [0,1]^L" + }, + { + "bbox": [ + 46, + 498, + 287, + 654 + ], + "type": "text", + "content": " is assigned to the normalized dot product of " + }, + { + "bbox": [ + 46, + 498, + 287, + 654 + ], + "type": "inline_equation", + "content": "e_i^g" + }, + { + "bbox": [ + 46, + 498, + 287, + 654 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 498, + 287, + 654 + ], + "type": "inline_equation", + "content": "F_l^g" + }, + { + "bbox": [ + 46, + 498, + 287, + 654 + ], + "type": "text", + "content": ", which is denoted as:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 53, + 663, + 287, + 680 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 663, + 287, + 680 + ], + "spans": [ + { + "bbox": [ + 53, + 663, + 287, + 680 + ], + "type": "interline_equation", + "content": "\\alpha_ {i} ^ {g} = \\mathrm {S o f t m a x} ([ e _ {i} ^ {g} \\cdot F _ {l} ^ {g, 1}, e _ {i} ^ {g} \\cdot F _ {l} ^ {g, 2}, \\dots , e _ {i} ^ {g} \\cdot F _ {l} ^ {g, L} ]). (1)", + "image_path": "f34d251375e7db5536a6f606a8e0ec2b208caeb2222f4c4bba1adbf49c76e723.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 687, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 687, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 687, + 287, + 715 + ], + "type": "text", + "content": "Then, the aggregated linguistic feature " + }, + { + "bbox": [ + 46, + 687, + 287, + 715 + ], + "type": "inline_equation", + "content": "h_0^i \\in \\mathbb{R}^{d_l}" + }, + { + "bbox": [ + 46, + 687, + 287, + 715 + ], + "type": "text", + "content": " can be derived by concatenating " + }, + { + "bbox": [ + 46, + 687, + 287, + 715 + ], + "type": "inline_equation", + "content": "h_0^{i,g} = \\sum_{j=1}^{L} \\alpha_i^{g,j} F_l^{g,j}" + }, + { + "bbox": [ + 46, + 687, + 287, + 715 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "type": "text", + "content": "Finally, we use a fully-connected layer (FC) to reduce the dimension of the aggregated linguistic features for the " + }, + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "type": "text", + "content": "-th layer of the visual backbone, which is indicated as:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 392, + 118, + 545, + 131 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 392, + 118, + 545, + 131 + ], + "spans": [ + { + "bbox": [ + 392, + 118, + 545, + 131 + ], + "type": "interline_equation", + "content": "h _ {1} ^ {i} = \\delta \\left(W _ {1} ^ {i} h _ {0} ^ {i}\\right), \\tag {2}", + "image_path": "94bd7b6ed2bb24e4898557516e91fedff218cd306ee0b67538d216d9346c1682.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 140, + 545, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 140, + 545, + 175 + ], + "spans": [ + { + "bbox": [ + 305, + 140, + 545, + 175 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 140, + 545, + 175 + ], + "type": "inline_equation", + "content": "W_1^i \\in \\mathbb{R}^{d_l \\times d_h}" + }, + { + "bbox": [ + 305, + 140, + 545, + 175 + ], + "type": "text", + "content": " is used to reducing the dimension to " + }, + { + "bbox": [ + 305, + 140, + 545, + 175 + ], + "type": "inline_equation", + "content": "d_h = d_l / r" + }, + { + "bbox": [ + 305, + 140, + 545, + 175 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 305, + 140, + 545, + 175 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 305, + 140, + 545, + 175 + ], + "type": "text", + "content": " is the reduction ratio. " + }, + { + "bbox": [ + 305, + 140, + 545, + 175 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 305, + 140, + 545, + 175 + ], + "type": "text", + "content": " refers to the GeLU activation function." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 191, + 545, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 191, + 545, + 251 + ], + "spans": [ + { + "bbox": [ + 305, + 191, + 545, + 251 + ], + "type": "text", + "content": "Weight Generation. To guide the active perception of the visual backbone, we generate language-adaptive weights for producing the query " + }, + { + "bbox": [ + 305, + 191, + 545, + 251 + ], + "type": "inline_equation", + "content": "X_{q}" + }, + { + "bbox": [ + 305, + 191, + 545, + 251 + ], + "type": "text", + "content": ", key " + }, + { + "bbox": [ + 305, + 191, + 545, + 251 + ], + "type": "inline_equation", + "content": "X_{k}" + }, + { + "bbox": [ + 305, + 191, + 545, + 251 + ], + "type": "text", + "content": ", and value " + }, + { + "bbox": [ + 305, + 191, + 545, + 251 + ], + "type": "inline_equation", + "content": "X_{v}" + }, + { + "bbox": [ + 305, + 191, + 545, + 251 + ], + "type": "text", + "content": " in the visual backbone conditioned on referring expressions, which can be represented as:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 312, + 260, + 545, + 274 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 260, + 545, + 274 + ], + "spans": [ + { + "bbox": [ + 312, + 260, + 545, + 274 + ], + "type": "interline_equation", + "content": "X _ {q} = \\theta (X; W _ {q}), X _ {k} = \\theta (X; W _ {k}), X _ {v} = \\theta (X; W _ {v}), \\tag {3}", + "image_path": "0946b5c1c2a4051cbb4ef3604fff0d3907288bfab6ce45d9f6737170c02e187d.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 282, + 545, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 282, + 545, + 354 + ], + "spans": [ + { + "bbox": [ + 305, + 282, + 545, + 354 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 282, + 545, + 354 + ], + "type": "inline_equation", + "content": "\\theta (\\cdot ;W)" + }, + { + "bbox": [ + 305, + 282, + 545, + 354 + ], + "type": "text", + "content": " indicates the linear projection operation parameterized by " + }, + { + "bbox": [ + 305, + 282, + 545, + 354 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 305, + 282, + 545, + 354 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 305, + 282, + 545, + 354 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 305, + 282, + 545, + 354 + ], + "type": "text", + "content": " represents the input visual features. " + }, + { + "bbox": [ + 305, + 282, + 545, + 354 + ], + "type": "inline_equation", + "content": "W_{q},W_{k},W_{v}\\in \\mathbb{R}^{d_{out}\\times d_{in}}" + }, + { + "bbox": [ + 305, + 282, + 545, + 354 + ], + "type": "text", + "content": " are the dynamic projection weights used to generate the query, key, and value, respectively. " + }, + { + "bbox": [ + 305, + 282, + 545, + 354 + ], + "type": "inline_equation", + "content": "d_{in}" + }, + { + "bbox": [ + 305, + 282, + 545, + 354 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 282, + 545, + 354 + ], + "type": "inline_equation", + "content": "d_{out}" + }, + { + "bbox": [ + 305, + 282, + 545, + 354 + ], + "type": "text", + "content": " are the dimension of feature " + }, + { + "bbox": [ + 305, + 282, + 545, + 354 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 305, + 282, + 545, + 354 + ], + "type": "text", + "content": " and query/key/value, respectively." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 355, + 545, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 355, + 545, + 485 + ], + "spans": [ + { + "bbox": [ + 304, + 355, + 545, + 485 + ], + "type": "text", + "content": "Considering the large number " + }, + { + "bbox": [ + 304, + 355, + 545, + 485 + ], + "type": "inline_equation", + "content": "d_{out} \\times d_{in}" + }, + { + "bbox": [ + 304, + 355, + 545, + 485 + ], + "type": "text", + "content": " of the dynamic weights, it is unaffordable to directly generate weights using fully-connected layers like Hypernetworks [10]. The DynamicConv [3] and CondConv [41] can alleviate this problem by generating weights with weighted summation of " + }, + { + "bbox": [ + 304, + 355, + 545, + 485 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 355, + 545, + 485 + ], + "type": "text", + "content": " static kernels but can increase the parameter number by " + }, + { + "bbox": [ + 304, + 355, + 545, + 485 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 355, + 545, + 485 + ], + "type": "text", + "content": "-times and suffer from challenging joint optimization. Inspired by the dynamic channel fusion [24], we try to generate dynamic weights following the matrix decomposition paradigm. Taking the " + }, + { + "bbox": [ + 304, + 355, + 545, + 485 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 355, + 545, + 485 + ], + "type": "text", + "content": "-th ViT block as an example, which can be formulated as:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 351, + 495, + 545, + 510 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 351, + 495, + 545, + 510 + ], + "spans": [ + { + "bbox": [ + 351, + 495, + 545, + 510 + ], + "type": "interline_equation", + "content": "\\left[ W _ {q} ^ {i}, W _ {k} ^ {i}, W _ {v} ^ {i} \\right] = W _ {0} ^ {i} + P \\Phi \\left(h _ {1} ^ {i}\\right) Q ^ {T}, \\tag {4}", + "image_path": "ee4303e7365173e7357caded0ae37e50d2d7b6575eaae96b7f3301a02a37e7f7.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 519, + 545, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 519, + 545, + 605 + ], + "spans": [ + { + "bbox": [ + 304, + 519, + 545, + 605 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 519, + 545, + 605 + ], + "type": "inline_equation", + "content": "W_0^i \\in \\mathbb{R}^{d_{out} \\times d_{in}}" + }, + { + "bbox": [ + 304, + 519, + 545, + 605 + ], + "type": "text", + "content": " is the layer-specific static learnable weights. " + }, + { + "bbox": [ + 304, + 519, + 545, + 605 + ], + "type": "inline_equation", + "content": "P \\in \\mathbb{R}^{d_{out} \\times d_w}" + }, + { + "bbox": [ + 304, + 519, + 545, + 605 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 519, + 545, + 605 + ], + "type": "inline_equation", + "content": "Q \\in \\mathbb{R}^{d_{in} \\times d_w}" + }, + { + "bbox": [ + 304, + 519, + 545, + 605 + ], + "type": "text", + "content": " are also static learnable weights, but sharable across all ViT blocks to reduce the parameter numbers and prevent the model from overfitting. " + }, + { + "bbox": [ + 304, + 519, + 545, + 605 + ], + "type": "inline_equation", + "content": "\\Phi(h_1^i)" + }, + { + "bbox": [ + 304, + 519, + 545, + 605 + ], + "type": "text", + "content": " is a fully-connected layer, which produces a dynamic matrix of shape " + }, + { + "bbox": [ + 304, + 519, + 545, + 605 + ], + "type": "inline_equation", + "content": "d_w \\times d_w" + }, + { + "bbox": [ + 304, + 519, + 545, + 605 + ], + "type": "text", + "content": " with aggregated linguistic features " + }, + { + "bbox": [ + 304, + 519, + 545, + 605 + ], + "type": "inline_equation", + "content": "h_1^i" + }, + { + "bbox": [ + 304, + 519, + 545, + 605 + ], + "type": "text", + "content": " as input." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 611, + 406, + 623 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 611, + 406, + 623 + ], + "spans": [ + { + "bbox": [ + 306, + 611, + 406, + 623 + ], + "type": "text", + "content": "3.3. Multi-task Head" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": "Different from the previous methods [6,23,42,45,46,49, 50], which require carefully designed cross-modal interaction modules, VG-LAW can obtain expression-relevant visual features extracted by the language-aware visual backbone without additional cross-modal interaction modules. Through our proposed neat but efficient multi-task head, we can utilize the visual and linguistic features to predict" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10860" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "content": "the bounding box for REC and the segmentation mask for RES. Concretely, there are two branches in the multi-task head for REC and RES, respectively." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 108, + 287, + 287 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 108, + 287, + 287 + ], + "spans": [ + { + "bbox": [ + 46, + 108, + 287, + 287 + ], + "type": "text", + "content": "For the REC branch, we apply direct coordinate regression to predict the bounding box of referred object. To pool the 2- " + }, + { + "bbox": [ + 46, + 108, + 287, + 287 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 108, + 287, + 287 + ], + "type": "text", + "content": " visual features along the spatial dimension, we propose a language adaptive pooling module (LAP), which aggregates visual features using language-adaptive attention. Specifically, the visual features " + }, + { + "bbox": [ + 46, + 108, + 287, + 287 + ], + "type": "inline_equation", + "content": "\\{F_v^{i,j}\\} \\in \\mathbb{R}^{C\\times \\frac{H}{s}\\times \\frac{W}{s}}" + }, + { + "bbox": [ + 46, + 108, + 287, + 287 + ], + "type": "text", + "content": " and linguistic feature " + }, + { + "bbox": [ + 46, + 108, + 287, + 287 + ], + "type": "inline_equation", + "content": "F_{l}^{1}\\in \\mathbb{R}^{d_{l}}" + }, + { + "bbox": [ + 46, + 108, + 287, + 287 + ], + "type": "text", + "content": " are firstly projected to the lower-dimension space " + }, + { + "bbox": [ + 46, + 108, + 287, + 287 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^k" + }, + { + "bbox": [ + 46, + 108, + 287, + 287 + ], + "type": "text", + "content": ", and the attention weights " + }, + { + "bbox": [ + 46, + 108, + 287, + 287 + ], + "type": "inline_equation", + "content": "A\\in \\mathbb{R}_{\\frac{H}{s}\\times \\frac{W}{s}}" + }, + { + "bbox": [ + 46, + 108, + 287, + 287 + ], + "type": "text", + "content": " are calculated as dot-product similarity followed by Softmax normalization. Then, the visual features are aggregated by calculating the weighted sum with attention weights " + }, + { + "bbox": [ + 46, + 108, + 287, + 287 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 46, + 108, + 287, + 287 + ], + "type": "text", + "content": ". Finally, the aggregated visual features are fed to a three-layer fully-connected layer, and the Sigmoid function is used to predict the referred bounding box " + }, + { + "bbox": [ + 46, + 108, + 287, + 287 + ], + "type": "inline_equation", + "content": "\\hat{b} = (\\hat{x},\\hat{y},\\hat{w},\\hat{h})" + }, + { + "bbox": [ + 46, + 108, + 287, + 287 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 288, + 288, + 431 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 288, + 288, + 431 + ], + "spans": [ + { + "bbox": [ + 46, + 288, + 288, + 431 + ], + "type": "text", + "content": "For the RES branch, we apply binary classification to each visual feature along the spatial dimension to predict segmentation masks for referred objects. Specifically, the visual features " + }, + { + "bbox": [ + 46, + 288, + 288, + 431 + ], + "type": "inline_equation", + "content": "F_{v}" + }, + { + "bbox": [ + 46, + 288, + 288, + 431 + ], + "type": "text", + "content": " are first up-sampled to " + }, + { + "bbox": [ + 46, + 288, + 288, + 431 + ], + "type": "inline_equation", + "content": "\\hat{F}_v\\in \\mathbb{R}^{d_l\\times \\frac{H}{4}\\times \\frac{W}{4}}" + }, + { + "bbox": [ + 46, + 288, + 288, + 431 + ], + "type": "text", + "content": " with successive transposed convolutions. Then, the intermediate segmentation map " + }, + { + "bbox": [ + 46, + 288, + 288, + 431 + ], + "type": "inline_equation", + "content": "\\bar{s}\\in \\mathbb{R}^{\\frac{H}{4}\\times \\frac{W}{4}}" + }, + { + "bbox": [ + 46, + 288, + 288, + 431 + ], + "type": "text", + "content": " can be obtained by using linear projection " + }, + { + "bbox": [ + 46, + 288, + 288, + 431 + ], + "type": "inline_equation", + "content": "\\theta (\\cdot ;W)" + }, + { + "bbox": [ + 46, + 288, + 288, + 431 + ], + "type": "text", + "content": " on each visual feature. Following the language adaptive weight paradigm, we also use dynamic rather than fixed weights by simply setting " + }, + { + "bbox": [ + 46, + 288, + 288, + 431 + ], + "type": "inline_equation", + "content": "W = F_l^1" + }, + { + "bbox": [ + 46, + 288, + 288, + 431 + ], + "type": "text", + "content": ". Finally, the full-resolution segmentation mask " + }, + { + "bbox": [ + 46, + 288, + 288, + 431 + ], + "type": "inline_equation", + "content": "\\hat{s}\\in \\mathbb{R}^{H\\times W}" + }, + { + "bbox": [ + 46, + 288, + 288, + 431 + ], + "type": "text", + "content": " is derived by simply up-sample " + }, + { + "bbox": [ + 46, + 288, + 288, + 431 + ], + "type": "inline_equation", + "content": "\\bar{s}" + }, + { + "bbox": [ + 46, + 288, + 288, + 431 + ], + "type": "text", + "content": " using bilinear interpolation, followed by the Sigmoid function." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 437, + 162, + 449 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 437, + 162, + 449 + ], + "spans": [ + { + "bbox": [ + 47, + 437, + 162, + 449 + ], + "type": "text", + "content": "3.4. Training Objectives" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 455, + 287, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 455, + 287, + 514 + ], + "spans": [ + { + "bbox": [ + 46, + 455, + 287, + 514 + ], + "type": "text", + "content": "The VG-LAW framework can be optimized end-to-end for multi-task visual grounding. For REC, given the predicted bounding box " + }, + { + "bbox": [ + 46, + 455, + 287, + 514 + ], + "type": "inline_equation", + "content": "\\hat{b} = (\\hat{x},\\hat{y},\\hat{w},\\hat{h})" + }, + { + "bbox": [ + 46, + 455, + 287, + 514 + ], + "type": "text", + "content": " and the ground truth " + }, + { + "bbox": [ + 46, + 455, + 287, + 514 + ], + "type": "inline_equation", + "content": "b = (x,y,w,h)" + }, + { + "bbox": [ + 46, + 455, + 287, + 514 + ], + "type": "text", + "content": ", the detection loss function is defined as follows:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 82, + 520, + 287, + 534 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 82, + 520, + 287, + 534 + ], + "spans": [ + { + "bbox": [ + 82, + 520, + 287, + 534 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {d e t}} = \\lambda_ {L 1} \\mathcal {L} _ {L 1} (b, \\hat {b}) + \\lambda_ {g i o u} \\mathcal {L} _ {g i o u} (b, \\hat {b}), \\tag {5}", + "image_path": "b5997f00d3bc11c5d6080a031028d510ae6a7d71bf3975bf0b0bdb19088e935e.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 539, + 287, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 539, + 287, + 598 + ], + "spans": [ + { + "bbox": [ + 46, + 539, + 287, + 598 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 539, + 287, + 598 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{L1}(\\cdot, \\cdot)" + }, + { + "bbox": [ + 46, + 539, + 287, + 598 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 539, + 287, + 598 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{giou}(\\cdot, \\cdot)" + }, + { + "bbox": [ + 46, + 539, + 287, + 598 + ], + "type": "text", + "content": " represent L1 loss and Generalized IoU loss [39], respectively, and " + }, + { + "bbox": [ + 46, + 539, + 287, + 598 + ], + "type": "inline_equation", + "content": "\\lambda_{L1}" + }, + { + "bbox": [ + 46, + 539, + 287, + 598 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 539, + 287, + 598 + ], + "type": "inline_equation", + "content": "\\lambda_{giou}" + }, + { + "bbox": [ + 46, + 539, + 287, + 598 + ], + "type": "text", + "content": " are the relative weights to control the two detection loss functions. For RES, given the predicted mask " + }, + { + "bbox": [ + 46, + 539, + 287, + 598 + ], + "type": "inline_equation", + "content": "\\hat{s}" + }, + { + "bbox": [ + 46, + 539, + 287, + 598 + ], + "type": "text", + "content": " and the ground-truth " + }, + { + "bbox": [ + 46, + 539, + 287, + 598 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 46, + 539, + 287, + 598 + ], + "type": "text", + "content": ", the segmentation loss function is defined as follows:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 73, + 605, + 287, + 619 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 73, + 605, + 287, + 619 + ], + "spans": [ + { + "bbox": [ + 73, + 605, + 287, + 619 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {s e g}} = \\lambda_ {\\text {f o c a l}} \\mathcal {L} _ {\\text {f o c a l}} (s, \\hat {s}) + \\lambda_ {\\text {d i c e}} \\mathcal {L} _ {\\text {d i c e}} (s, \\hat {s}), \\tag {6}", + "image_path": "a0fd6cee06a69a792cd62de54529947bd74dbac55a0478484ca3247247dc0a57.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 623, + 287, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 623, + 287, + 694 + ], + "spans": [ + { + "bbox": [ + 46, + 623, + 287, + 694 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 623, + 287, + 694 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{focal}(\\cdot, \\cdot)" + }, + { + "bbox": [ + 46, + 623, + 287, + 694 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 623, + 287, + 694 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{dice}(\\cdot, \\cdot)" + }, + { + "bbox": [ + 46, + 623, + 287, + 694 + ], + "type": "text", + "content": " represent focal loss [27] and DICE/F-1 loss [35], respectively, and " + }, + { + "bbox": [ + 46, + 623, + 287, + 694 + ], + "type": "inline_equation", + "content": "\\lambda_{focal}" + }, + { + "bbox": [ + 46, + 623, + 287, + 694 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 623, + 287, + 694 + ], + "type": "inline_equation", + "content": "\\lambda_{dice}" + }, + { + "bbox": [ + 46, + 623, + 287, + 694 + ], + "type": "text", + "content": " are the relative weights to control the two segmentation loss functions. Our framework can be seamlessly used for joint training of REC and RES, and its joint training loss function is defined as follows:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 120, + 701, + 287, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 120, + 701, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 120, + 701, + 287, + 715 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {t o t a l}} = \\mathcal {L} _ {\\text {d e t}} + \\mathcal {L} _ {\\text {s e g}}. \\tag {7}", + "image_path": "f3d2197fb2184efbab44b795aa2b3943528f48086f0005be7203e980fb08d62d.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 72, + 545, + 107 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 107 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 107 + ], + "type": "text", + "content": "The trained model performs well for language-guided detection and segmentation. The experimental analysis of the whole framework will be elaborated in Sec. 4." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 117, + 386, + 131 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 117, + 386, + 131 + ], + "spans": [ + { + "bbox": [ + 305, + 117, + 386, + 131 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 137, + 545, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 137, + 545, + 185 + ], + "spans": [ + { + "bbox": [ + 304, + 137, + 545, + 185 + ], + "type": "text", + "content": "In this section, we will give a detailed experimental analysis of the whole framework, including the datasets, evaluation protocol, implementation details, comparisons with the state-of-the-art methods, and ablation analysis." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 190, + 484, + 202 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 190, + 484, + 202 + ], + "spans": [ + { + "bbox": [ + 305, + 190, + 484, + 202 + ], + "type": "text", + "content": "4.1. Datasets and Evaluation Protocol" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 209, + 545, + 400 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 209, + 545, + 400 + ], + "spans": [ + { + "bbox": [ + 304, + 209, + 545, + 400 + ], + "type": "text", + "content": "Datasets. To verify the effectiveness of our method, we conduct experiments on the widely used RefCOCO [47], RefCOCO+ [47], RefCOCOg [34], and ReferItGame [19] datasets. RefCOCO, RefCOCO+, and RefCOCOg are collected from MS-COCO [28]. RefCOCO and RefCOCO+, which are collected in interactive games, can be divided into train, val, testA, and testB sets. Compared to RefCOCO, the expressions of RefCOCO+ contain more attributes than absolute locations. Unlike RefCOCO and RefCOCO+, RefCOCOg collected by Amazon Mechanical Turk has a longer length of 8.4 words, including the attribute and location of referents. Following a common version of split [36], RefCOCOg has train, val, and test sets. In addition, ReferItGame collected from SAIAPR-12 [8] contains train and test sets. Each sample in the above datasets contains its corresponding bounding box and mask." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 414, + 545, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 414, + 545, + 510 + ], + "spans": [ + { + "bbox": [ + 304, + 414, + 545, + 510 + ], + "type": "text", + "content": "Evaluation Protocol. Following the previous works [23, 33, 50], we use Prec@0.5 and mIoU to evaluate the performance of REC and RES, respectively. For Prec@0.5, the predicted bounding box is considered correct if the intersection-over-union (IoU) with the ground-truth bounding box is greater than 0.5. mIoU represents the IoU between the prediction and ground truth averaged across all test samples." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 515, + 438, + 528 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 515, + 438, + 528 + ], + "spans": [ + { + "bbox": [ + 305, + 515, + 438, + 528 + ], + "type": "text", + "content": "4.2. Implementation Details" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": "Training. The resolution of the input image is resized to " + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "448 \\times 448" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": ". ViT-Base [7] is used as the visual backbone, and we follow the adaptation introduced by ViTDet [25] to adapt the visual backbone to higher-resolution images. The visual backbone is pre-trained using Mask R-CNN [11] on MS-COCO [28], where overlapping images of the val/test sets are excluded. The " + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "W_0^i" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\Phi(h_1^i)" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": " in Eq. (4) are initialized with the corresponding pre-trained weights of the visual backbone and zeros, respectively. The maximum length of referring expression is set to 40, and the uncased base of six-layer BERT [5] as the linguistic backbone is used to generate linguistic features. " + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\lambda_{L1}" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\lambda_{giou}" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": " are set to 1. " + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\lambda_{focal}" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\lambda_{dice}" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": " are set to 4. The reduction ratio " + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": " is set to 16. The initial learning rate for the visual and linguistic backbone is 4e-5, and the initial learning rate for the" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10861" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 47, + 70, + 550, + 347 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 550, + 347 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 550, + 347 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 550, + 347 + ], + "type": "table", + "html": "
MethodsVenueVisual BackboneMulti-taskRefCOCORefCOCO+RefCOCOgReferItGame test
valtestAtestBvaltestAtestBvaltest
Two-stage:
MAttNet [46]CVPR18RN101X76.6581.1469.9965.3371.6256.0266.5867.2729.04
RvG-Tree [13]TPAMI19RN101X75.0678.6169.8563.5167.4556.6666.9566.51-
CM-A-E [30]CVPR19RN101X78.3583.1471.3268.0973.6558.0367.9968.67-
Ref-NMS [2]AAAI21RN101X80.7084.0076.0468.2573.6859.4270.5570.62-
One-stage:
FAOA [43]ICCV19DN53X72.5474.3568.5056.8160.2349.6061.3360.3660.67
ReSC-Large [42]ECCV20DN53X77.6380.4572.3063.5968.3656.8167.3067.2064.60
MCN [33]CVPR20DN53✓80.0882.2974.9867.1672.8657.3166.4666.01-
RealGIN [49]TNNLS21DN53X77.2578.7072.1062.7867.1754.2162.7562.33-
PLV-FPN* [26]TIP22RN101X81.9384.9976.2571.2077.4061.0870.4571.0871.77
Transformer-based:
TransVG [4]ICCV21RN101X81.0282.7278.3564.8270.7056.9468.6767.7370.73
RefTR* [23]NeurIPS21RN101✓82.2385.5976.5771.5875.9662.1669.4169.4071.42
SeqTR [50]ECCV22DN53X81.2385.0076.0868.8275.3758.7871.3571.5869.66
Word2Pix [48]TNNLS22RN101X81.2084.3978.1269.7476.1161.2470.8171.34-
YORO [12]ECCVW22-X82.9085.6077.4073.5078.6064.9073.4074.3071.90
QRNet [45]CVPR22Swin-SX84.0185.8582.3472.9476.1763.8171.8973.0374.61
Ours:
VG-LAW-ViT-BX86.0688.5682.8775.7480.3266.6975.3175.9576.60
VG-LAW-ViT-B✓86.6289.3283.1676.3781.0467.5076.9076.9677.22
", + "image_path": "06e9bac9514b6dfa99a32ee8dbc7d9700f35be97397f7c5ed98dab4dfa7246ad.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 87, + 409, + 507, + 555 + ], + "blocks": [ + { + "bbox": [ + 46, + 354, + 547, + 401 + ], + "lines": [ + { + "bbox": [ + 46, + 354, + 547, + 401 + ], + "spans": [ + { + "bbox": [ + 46, + 354, + 547, + 401 + ], + "type": "text", + "content": "Table 1. Comparison with state-of-the-art methods on RefCOCO [47], RefCOCO+ [47], RefCOCOg [36] and ReferItGame [19] for REC task. The visual backbone is pre-trained on MS-COCO [28], where overlapping images of the val/test sets are excluded. * represents ImageNet [21] pre-training. RN101, DN53, Swin-S, and ViT-B are shorthand for the ResNet101, DarkNet53, Swin-Transformer Small, and ViT Base, respectively. We highlight the best and second best performance in the red and blue colors." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 87, + 409, + 507, + 555 + ], + "lines": [ + { + "bbox": [ + 87, + 409, + 507, + 555 + ], + "spans": [ + { + "bbox": [ + 87, + 409, + 507, + 555 + ], + "type": "table", + "html": "
MethodsVenueVisual BackboneMulti-taskRefCOCORefCOCO+RefCOCOg
valtestAtestBvaltestAtestBvaltest
CGAN [32]MM20DN53X64.8668.0462.0751.0355.5144.0654.4054.25
MCN [33]CVPR20DN53✓62.4464.2059.7150.6254.9944.6949.2249.40
LTS [17]CVPR21DN53X65.4367.7663.0854.2158.3248.0254.4054.25
VLT [50]ICCV21DN53X65.6568.2962.7355.5059.2049.3652.9956.65
RefTR* [23]NeurIPS21RN101✓70.5673.4966.5761.0864.6952.7358.7358.51
SeqTR [50]ECCV22DN53X67.2669.7964.1254.1458.9348.1955.6755.64
LAVT* [44]CVPR22Swin-BX74.4676.8970.9465.8170.9759.2363.6263.66
Ours:
VG-LAW-ViT-BX75.0577.3671.6966.6170.3058.1465.3665.13
VG-LAW-ViT-B✓75.6277.5172.8966.6370.3858.8965.6366.08
", + "image_path": "61bbb9e6fb2eb50e7dbc26be8da994ff57408040e09abbf0aefadd16172a7644.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 562, + 546, + 608 + ], + "lines": [ + { + "bbox": [ + 46, + 562, + 546, + 608 + ], + "spans": [ + { + "bbox": [ + 46, + 562, + 546, + 608 + ], + "type": "text", + "content": "Table 2. Comparison with state-of-the-art methods on RefCOCO [47], RefCOCO+ [47], and RefCOCOg [36] for RES task. The visual backbone is pre-trained on MS-COCO [28], where overlapping images of the val/test sets are excluded. * represents ImageNet [21] pre-training. RN101, DN53, Swin-B, and ViT-B are shorthand for the ResNet101, DarkNet53, Swin-Transformer Base, and ViT Base, respectively. We highlight the best and second best performance in the red and blue colors." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 628, + 288, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 628, + 288, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 628, + 288, + 712 + ], + "type": "text", + "content": "remaining components is 4e-4. The model is end-to-end optimized by AdamW [31] for 90 epochs with a batch size of 256, where weight decay is set to 1e-4, and the learning rate is reduced by a factor of 10 after 60 epochs. Data augmentation operation includes random horizontal flips. We implement our framework using PyTorch and conduct experiments with NVIDIA A100 GPUs." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 628, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 628, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 628, + 547, + 713 + ], + "type": "text", + "content": "Inference. At inference time, the input image is resized to " + }, + { + "bbox": [ + 304, + 628, + 547, + 713 + ], + "type": "inline_equation", + "content": "448 \\times 448" + }, + { + "bbox": [ + 304, + 628, + 547, + 713 + ], + "type": "text", + "content": ", and the maximum length of referring expressions is set to 40. Following the previous method [33], We set the threshold to 0.35 to realize the binarization of the RES prediction. Without any post-processing operation, our framework directly outputs bounding boxes and segmentation maps specified by referring expressions." + } + ] + } + ], + "index": 5 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "10862" + } + ] + } + ], + "index": 6 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 63, + 74, + 272, + 214 + ], + "blocks": [ + { + "bbox": [ + 63, + 74, + 272, + 214 + ], + "lines": [ + { + "bbox": [ + 63, + 74, + 272, + 214 + ], + "spans": [ + { + "bbox": [ + 63, + 74, + 272, + 214 + ], + "type": "image", + "image_path": "e718842e9dc933811d396986013a8a741d114979614c013f1ab4e76fa0a8f1ef.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 225, + 287, + 259 + ], + "lines": [ + { + "bbox": [ + 46, + 225, + 287, + 259 + ], + "spans": [ + { + "bbox": [ + 46, + 225, + 287, + 259 + ], + "type": "text", + "content": "Figure 5. Comparison of accuracy under different lengths of referring expression on RefCOCOg-test. ReSC [42], TransVG [4], Word2Pix [48], and the proposed VG-LAW are compared." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 280, + 274, + 293 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 280, + 274, + 293 + ], + "spans": [ + { + "bbox": [ + 47, + 280, + 274, + 293 + ], + "type": "text", + "content": "4.3. Comparisons with State-of-the-art Methods" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 298, + 287, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 298, + 287, + 348 + ], + "spans": [ + { + "bbox": [ + 46, + 298, + 287, + 348 + ], + "type": "text", + "content": "To estimate the effectiveness of the proposed VG-LAW framework, we conduct quantitative experiments on four widely used datasets, i.e., RefCOCO [47], RefCOCO+ [47], RefCOCOg [34], and ReferItGame [19]." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 362, + 288, + 614 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 362, + 288, + 614 + ], + "spans": [ + { + "bbox": [ + 46, + 362, + 288, + 614 + ], + "type": "text", + "content": "REC Task. For the REC task, we compare the performance with state-of-the-art REC methods, including the two-stage methods [2, 13, 30, 46], one-stage methods [26, 33, 42, 43, 49], and transformer-based methods [4, 12, 23, 45, 48, 50]. The main results are summarized to Tab. 1. It can be observed that VG-LAW achieves a significant performance improvement compared to the state-of-the-art two-stage method Ref-NMS [2] and one-stage method PLV-FPN [26]. When comparing to the transformer-based method QRNet [45], which modified the visual backbone by inserting language-aware spatial and channel attention modules, our method has better performance with " + }, + { + "bbox": [ + 46, + 362, + 288, + 614 + ], + "type": "inline_equation", + "content": "+2.62\\% / +3.47\\% / +0.82\\%" + }, + { + "bbox": [ + 46, + 362, + 288, + 614 + ], + "type": "text", + "content": " on RefCOCO, " + }, + { + "bbox": [ + 46, + 362, + 288, + 614 + ], + "type": "inline_equation", + "content": "+3.43\\% / +4.87\\% / +3.69\\%" + }, + { + "bbox": [ + 46, + 362, + 288, + 614 + ], + "type": "text", + "content": " on RefCOCO+, " + }, + { + "bbox": [ + 46, + 362, + 288, + 614 + ], + "type": "inline_equation", + "content": "+5.01\\% / +3.93\\%" + }, + { + "bbox": [ + 46, + 362, + 288, + 614 + ], + "type": "text", + "content": " on RefCOCOg, and " + }, + { + "bbox": [ + 46, + 362, + 288, + 614 + ], + "type": "inline_equation", + "content": "+2.61\\%" + }, + { + "bbox": [ + 46, + 362, + 288, + 614 + ], + "type": "text", + "content": " on ReferItGame. QRNet [45] follows the TransVG [4] framework, both of which use the transformer encoder-based cross-modal interaction module. Compared to them, VG-LAW achieves better performance without complex cross-modal interaction modules. Furthermore, our method significantly outperforms MCN [33] and RefTR [23] based on joint training of REC and RES." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "content": "RES Task. For the RES task, we compare the performance with state-of-the-art methods [6,17,23,32,33,44,50], and the main results are summarized to Tab. 2. Compared with state-of-the-art RES method LAVT [44], VG-LAW achieves better " + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "inline_equation", + "content": "mIoU" + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "inline_equation", + "content": "+1.16\\% / +0.62\\% / +1.95\\%" + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "content": " on RefCOCO, " + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "inline_equation", + "content": "+2.01\\% / +2.42\\%" + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "content": " on RefCOCOg, and comparable " + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "inline_equation", + "content": "mIoU" + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "inline_equation", + "content": "+0.82\\% / -0.59\\% / -0.34\\%" + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "content": " on RefCOCO+." + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 339, + 70, + 515, + 149 + ], + "blocks": [ + { + "bbox": [ + 339, + 70, + 515, + 149 + ], + "lines": [ + { + "bbox": [ + 339, + 70, + 515, + 149 + ], + "spans": [ + { + "bbox": [ + 339, + 70, + 515, + 149 + ], + "type": "table", + "html": "
LAWGLAPMTHPrec@0.5(%)
✓74.89
✓74.37
✓✓76.60
✓✓✓77.22
", + "image_path": "883776ab57b09b2069ca094279e6a9703540d1b6ecdd88d61be5b08815a8925f.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 158, + 545, + 191 + ], + "lines": [ + { + "bbox": [ + 305, + 158, + 545, + 191 + ], + "spans": [ + { + "bbox": [ + 305, + 158, + 545, + 191 + ], + "type": "text", + "content": "Table 3. Ablation experiments on ReferItGame [19] to evaluate the proposed language adaptive weight generation (LAWG), language adaptive pooling (LAP), and multi-task head (MTH)." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 213, + 545, + 285 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 213, + 545, + 285 + ], + "spans": [ + { + "bbox": [ + 305, + 213, + 545, + 285 + ], + "type": "text", + "content": "When comparing the models trained with or without multi-task settings, it can also be observed that consistent performance gains are achieved across all the datasets and splits. As REC can provide localization information of the referred object, such coarse-grained supervision can slightly improve the segmentation accuracy in RES." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 300, + 545, + 432 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 300, + 545, + 432 + ], + "spans": [ + { + "bbox": [ + 305, + 300, + 545, + 432 + ], + "type": "text", + "content": "Analysis of Referring Expression Length. As the visual backbone in VG-LAW extracts features purely perceptually, it is of concern whether it can handle long and complex referring expressions. ReSC [42] reveals that one-stage methods may ignore detailed descriptions in complex referring expressions and lead to poor performance. Following that, we evaluate the REC performance on referring expressions of different lengths, as illustrated in Fig. 5. VG-LAW performs better than ReSC, TransVG [4] and Word2Pix [48], with no significant performance degradation when the length of referring expressions varies from 6-7 to " + }, + { + "bbox": [ + 305, + 300, + 545, + 432 + ], + "type": "inline_equation", + "content": "11+" + }, + { + "bbox": [ + 305, + 300, + 545, + 432 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 441, + 411, + 453 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 441, + 411, + 453 + ], + "spans": [ + { + "bbox": [ + 306, + 441, + 411, + 453 + ], + "type": "text", + "content": "4.4. Ablation Analysis" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 459, + 545, + 650 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 459, + 545, + 650 + ], + "spans": [ + { + "bbox": [ + 305, + 459, + 545, + 650 + ], + "type": "text", + "content": "To validate the effectiveness of our proposed modules, i.e. language-adaptive weight generation, language-adaptive pooling, and multi-task head, we conduct ablation experiments on the REC dataset of ReferItGame, which is summarized in Tab. 3. When only using the LAWG, the visual features are pooled with global average pooling, and when only using the LAP, the visual backbone has fixed architecture and weights. When only using the LAWG or the LAP, it can be observed that the model already achieves " + }, + { + "bbox": [ + 305, + 459, + 545, + 650 + ], + "type": "inline_equation", + "content": "74.89\\%" + }, + { + "bbox": [ + 305, + 459, + 545, + 650 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 459, + 545, + 650 + ], + "type": "inline_equation", + "content": "74.37\\%" + }, + { + "bbox": [ + 305, + 459, + 545, + 650 + ], + "type": "text", + "content": ", respectively, which is close to the " + }, + { + "bbox": [ + 305, + 459, + 545, + 650 + ], + "type": "inline_equation", + "content": "74.61\\%" + }, + { + "bbox": [ + 305, + 459, + 545, + 650 + ], + "type": "text", + "content": " reported by QRNet [45]. When combined with the LAWG and LAP, further improvements can be brought by LAWG and LAP with " + }, + { + "bbox": [ + 305, + 459, + 545, + 650 + ], + "type": "inline_equation", + "content": "+2.23\\%" + }, + { + "bbox": [ + 305, + 459, + 545, + 650 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 459, + 545, + 650 + ], + "type": "inline_equation", + "content": "+1.71\\%" + }, + { + "bbox": [ + 305, + 459, + 545, + 650 + ], + "type": "text", + "content": ", respectively. Benefiting from the auxiliary supervision of RES, our model equipped with the multi-task head can localize the referred objects better and achieve " + }, + { + "bbox": [ + 305, + 459, + 545, + 650 + ], + "type": "inline_equation", + "content": "77.22\\%" + }, + { + "bbox": [ + 305, + 459, + 545, + 650 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 658, + 417, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 658, + 417, + 671 + ], + "spans": [ + { + "bbox": [ + 306, + 658, + 417, + 671 + ], + "type": "text", + "content": "4.5. Qualitative Results" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "content": "The qualitative results of the four datasets are shown in Fig. 6. It can be observed that our model can successfully locate and segment the referred objects, and the attention of" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10863" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 55, + 71, + 541, + 322 + ], + "blocks": [ + { + "bbox": [ + 55, + 71, + 541, + 322 + ], + "lines": [ + { + "bbox": [ + 55, + 71, + 541, + 322 + ], + "spans": [ + { + "bbox": [ + 55, + 71, + 541, + 322 + ], + "type": "image", + "image_path": "60f13a15c23dcc097354103c325bfc86b86a4fa8a9404a5fd2edde0901309009.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 331, + 546, + 365 + ], + "lines": [ + { + "bbox": [ + 46, + 331, + 546, + 365 + ], + "spans": [ + { + "bbox": [ + 46, + 331, + 546, + 365 + ], + "type": "text", + "content": "Figure 6. Qualitative results on the RefCOCO [47], RefCOCO+ [47], RefCOCOg [34], and ReferItGame [19] datasets. Each dataset shows two examples. From left to right: the input image, the ground truth of REC and RES, the prediction of VG-LAW, and the attention of the visual backbone with language-adaptive weights." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 55, + 383, + 162, + 464 + ], + "blocks": [ + { + "bbox": [ + 55, + 383, + 162, + 464 + ], + "lines": [ + { + "bbox": [ + 55, + 383, + 162, + 464 + ], + "spans": [ + { + "bbox": [ + 55, + 383, + 162, + 464 + ], + "type": "image", + "image_path": "6924d1d9e7c0fb578033c5acf10f16f4dbc9539dffcc2b70facc3d2c1ae76048.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 474, + 287, + 495 + ], + "lines": [ + { + "bbox": [ + 47, + 474, + 287, + 495 + ], + "spans": [ + { + "bbox": [ + 47, + 474, + 287, + 495 + ], + "type": "text", + "content": "Figure 7. Wordcloud visualization of words assigned to the first and second halves of the visual backbone." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 172, + 384, + 279, + 464 + ], + "blocks": [ + { + "bbox": [ + 172, + 384, + 279, + 464 + ], + "lines": [ + { + "bbox": [ + 172, + 384, + 279, + 464 + ], + "spans": [ + { + "bbox": [ + 172, + 384, + 279, + 464 + ], + "type": "image", + "image_path": "6889d45355f4cd056702b3e009912c6fefc0f245803fbf5271b3ef83084ca52f.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 520, + 287, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 520, + 287, + 605 + ], + "spans": [ + { + "bbox": [ + 46, + 520, + 287, + 605 + ], + "type": "text", + "content": "the visual backbone can focus on the most relevant image regions, demonstrating the effectiveness of using language adaptive weights. Taking the results on ReferItGame as an example, the visual backbone can dynamically filter out irrelevant regions for different expressions. For instance, when the \"purple curtain\" is referred to, the regions related to the \"the painting/photo on the wall\" are ignored." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": "In addition, we count the scores of words assigned to the first and second halves of the visual backbone, as shown in Fig. 7. The scores are calculated by averaging attention score " + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\alpha_{i}" + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": " in Eq. (1) for each word, followed by softmax normalization along the layer dimension. It can be observed that the shallow layers tend to the words describing individuals, such as the categories \"velvet\" and \"yacht\", and the deep layers tend to the words about contexts, such as the ordinal number \"2nd\" and the position \"right\"." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 384, + 470, + 396 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 384, + 470, + 396 + ], + "spans": [ + { + "bbox": [ + 306, + 384, + 470, + 396 + ], + "type": "text", + "content": "5. Conclusions and Limitations" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 405, + 545, + 561 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 405, + 545, + 561 + ], + "spans": [ + { + "bbox": [ + 304, + 405, + 545, + 561 + ], + "type": "text", + "content": "In this paper, we propose an active perception framework VG-LAW for visual grounding, based on the language adaptive weights. VG-LAW can directly inject the information of referring expressions into the weights of the visual backbone without modifying its architecture. Equipped with the proposed neat yet efficient multi-task head, VG-LAW achieves state-of-the-art performance for REC and RES tasks on widely used datasets. The limitations of our method are two-fold: (1) VG-LAW is weak in interpretability, and the entire reasoning process is implicit, which makes it difficult to understand how the reasoning process works, and (2) the multi-task head predicts one instance at a time, which limits its application in phrase grounding." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 573, + 416, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 573, + 416, + 586 + ], + "spans": [ + { + "bbox": [ + 306, + 573, + 416, + 586 + ], + "type": "text", + "content": "6. Acknowledgments" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "text", + "content": "This work is supported in part by National Key Research and Development Program of China under Grant 2020AAA0107400, National Natural Science Foundation of China under Grant U20A20222, National Science Foundation for Distinguished Young Scholars under Grant 62225605, Ant Group through CCF-Ant Research Fund, and sponsored by CCF-AFSG Research Fund, CAAI-HUAWEI MindSpore Open Fund, CCF-Zhipu AI Large Model Fund (CCF-Zhipu202302) as well as Hikvision Cooperation Fund." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10864" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 713 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 133 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 133 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 133 + ], + "type": "text", + "content": "[1] Nicolas Carion, Francisco Massa, Gabriel Synnaeve, Nicolas Usunier, Alexander Kirillov, and Sergey Zagoruyko. 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Seqtr: A simple yet universal network for visual grounding. arXiv preprint arXiv:2203.16265, 2022. 1, 2, 3, 4, 5, 6, 7" + } + ] + } + ], + "index": 19 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "text", + "content": "10866" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Language in a Bottle_ Language Model Guided Concept Bottlenecks for Interpretable Image Classification/b8f072ca-77d7-4ea7-aa8e-47b49a1b8d4b_content_list.json b/2023/Language in a Bottle_ Language Model Guided Concept Bottlenecks for Interpretable Image Classification/b8f072ca-77d7-4ea7-aa8e-47b49a1b8d4b_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..2b6cb125cfffb3c83bd328c462e0538e1a716692 --- /dev/null +++ b/2023/Language in a Bottle_ Language Model Guided Concept Bottlenecks for Interpretable Image Classification/b8f072ca-77d7-4ea7-aa8e-47b49a1b8d4b_content_list.json @@ -0,0 +1,1816 @@ +[ + { + "type": "text", + "text": "Language in a Bottle: Language Model Guided Concept Bottlenecks for Interpretable Image Classification", + "text_level": 1, + "bbox": [ + 140, + 130, + 828, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Yue Yang, Artemis Panagopoulou, Shenghao Zhou, Daniel Jin, Chris Callison-Burch, Mark Yatskar University of Pennsylvania", + "bbox": [ + 235, + 203, + 733, + 256 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{yueyang1, artemisp, shzhou2, jindan, ccb, myatskar}@seas.upenn.edu", + "bbox": [ + 184, + 258, + 777, + 273 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 308, + 313, + 325 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Concept Bottleneck Models (CBM) are inherently interpretable models that factor model decisions into human-readable concepts. They allow people to easily understand why a model is failing, a critical feature for high-stakes applications. CBMs require manually specified concepts and often under-perform their black box counterparts, preventing their broad adoption. We address these shortcomings and are first to show how to construct high-performance CBMs without manual specification of similar accuracy to black box models. Our approach, Language Guided Bottlenecks (LaBo), leverages a language model, GPT-3, to define a large space of possible bottlenecks. Given a problem domain, LaBo uses GPT-3 to produce factual sentences about categories to form candidate concepts. LaBo efficiently searches possible bottlenecks through a novel submodular utility that promotes the selection of discriminative and diverse information. Ultimately, GPT-3's sentential concepts can be aligned to images using CLIP, to form a bottleneck layer. Experiments demonstrate that LaBo is a highly effective prior for concepts important to visual recognition. In the evaluation with 11 diverse datasets, LaBo bottlenecks excel at few-shot classification: they are $11.7\\%$ more accurate than black box linear probes at 1 shot and comparable with more data. Overall, LaBo demonstrates that inherently interpretable models can be widely applied at similar, or better, performance than black box approaches.1", + "bbox": [ + 76, + 340, + 473, + 734 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 761, + 209, + 777 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "As deep learning systems improve, their applicability to critical domains is hampered because of a lack of transparency. Efforts to address this have largely focused on post-hoc explanations [47, 54, 72]. Such explanations can be problematic because they may be incomplete or unfaithful with respect to the model's computations [49]. Models", + "bbox": [ + 76, + 787, + 470, + 878 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/3fc95e6605ad9afb030fa06ad63b42f2342bef796caf7c2950867a55beb5efcb.jpg", + "image_caption": [ + "Figure 1. Our proposed high-performance Concept Bottleneck Model alleviates the need for human-designed concepts by prompting large language models (LLMs) such as GPT-3 [4]." + ], + "image_footnote": [], + "bbox": [ + 504, + 306, + 890, + 431 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "can also be designed to be inherently interpretable, but it is believed that such models will perform more poorly than their black box alternatives [16]. In this work, we provide evidence to the contrary. We show how to construct high-performance interpretable-by-design classifiers by combining a language model, GPT-3 [4], and a language-vision model, CLIP [44].", + "bbox": [ + 496, + 501, + 893, + 607 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Our method builds on Concept Bottleneck Models (CBM) [25], which construct predictors through a linear combination of human-designed concepts. For example, as seen in Figure 1, a qualified person can design concepts, such as \"nape color,\" as intermediate targets for a black box model before classifying a bird. CBMs provide abstractions that people can use to understand errors or intervene on, contributing to increased trust.", + "bbox": [ + 496, + 609, + 893, + 731 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Application of CBMs is limited because they require costly attribute annotations by domain experts and often under-perform their black box counterparts. In contexts where CBM performance is competitive with black box alternatives, interpretability properties are sacrificed [34, 70]. To address both of these challenges, we propose to build systems that automatically construct CBMs.", + "bbox": [ + 496, + 732, + 893, + 838 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Our Language Model Guided Concept Bottleneck Model (LaBo), Figure 2, allows for the automatic construction of high-performance CBMs for arbitrary classification problems without concept annotations. Large language models", + "bbox": [ + 496, + 839, + 893, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "$^{1}$ Code and data are available at https://github.com/YueYANG1996/LaBo", + "bbox": [ + 94, + 886, + 468, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "19187", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/2e14f5129572f4a18e139a0c44fe81cd78931d81488b23059e1180d938b8b073.jpg", + "image_caption": [ + "Figure 2. We present an overview of our Language-Model-Guided Concept Bottleneck Model (LaBo), which is interpretable by design image classification system. First, we prompt the large language model (GPT-3) to generate candidate concepts (Sec 3.4). Second, we employ a submodular function to select concepts from all candidates to construct the bottleneck (Sec 3.2). Third, we apply a pretrained alignment model (CLIP) to obtain the embeddings of concepts and images, which is used to compute concept scores. Finally, we train a linear function in which the weight $W$ denotes the concept-class association user to predict targets based on concept scores (Sec 3.3)." + ], + "image_footnote": [], + "bbox": [ + 102, + 88, + 872, + 378 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "(LLMs) contain significant world knowledge [21, 42, 61], that can be elicited by inputting a string prefix and allowing LLMs to complete the string (prompting). For example, in Figure 1, GPT-3 is prompted about sparrows and completes with information such as \"brown head with white stripes.\" LaBo leverages this by constructing bottlenecks where the concepts are such GPT-3 generated sentences. Since our concepts are textual, we use CLIP to score their presence in an image and form a bottleneck layer out of these scores.", + "bbox": [ + 75, + 474, + 473, + 609 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "A key advantage of LaBo is the ability to control the selection of concepts in the bottleneck by generating candidates from the language model. We develop selection principles targeting both interpretability and classification accuracy. For example, we prefer smaller bottlenecks that include shorter sentences that do not include class names. Furthermore, to maximize performance, we prefer attributes that CLIP can easily recognize and are highly discriminative. To account for appearance variation, we select attributes that cover a variety of information and are not repetitive. We formulate these factors into a novel sub-modular criterion that allows us to select good bottlenecks efficiently [38].", + "bbox": [ + 75, + 612, + 470, + 792 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We have evaluated LaBo-created bottlenecks on 11 diverse image classification tasks, spanning recognition of common objects [11,26] to skin tumors [64]. fine-grained types [3, 32, 39, 67], textures [10], actions [59], skin tumors [64], and satellite photographed objects [8].2 Our", + "bbox": [ + 75, + 795, + 470, + 872 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "main finding is that LaBo is a highly effective prior for what concepts to look for, especially in low data regimes. In evaluations comparing with linear probes, LaBo outperforms by as much as $11.7\\%$ at 1-shot and marginally underperforms given larger data settings. Averaged over many dataset sizes, LaBo bottlenecks are $1.5\\%$ more accurate than linear probes. In comparison to modifications of CBMs that improve performance by circumventing the bottleneck [70], we achieve similar or better results without breaking the CBM abstraction. In extensive ablations, we study key trade-offs in bottleneck design and show our selection criteria are crucial and highlight several other critical design choices.", + "bbox": [ + 496, + 474, + 893, + 654 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Human evaluations indicate that our bottlenecks are largely understandable, visual, and factual. Finally, annotators find our GPT-3 sourced bottlenecks are more factual and groundable than those constructed from WordNet or Wikipedia sentences. Overall, our experiments demonstrate that automatically designed CBMs can be as effective as black box models while maintaining critical factors contributing to their interpretability.", + "bbox": [ + 496, + 655, + 895, + 777 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 789, + 640, + 806 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Broadly, interpretability methods fall into two categories:", + "bbox": [ + 517, + 815, + 893, + 830 + ], + "page_idx": 1 + }, + { + "type": "page_footnote", + "text": "3 when creating candidate attributes. This is largely done to overcome problems of word sense. For example, when naively prompted to produce knowledge about the flower \"bird of paradise\" GPT-3 yields information about birds instead of flowers. In general, specialization here was also minimal. See appendix for prompts.", + "bbox": [ + 500, + 839, + 893, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_footnote", + "text": "2The only dataset specialization we perform is prompt tuning for GPT-", + "bbox": [ + 94, + 886, + 470, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "19188", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "post-hoc and by design. While ours is an instance of the latter, post-hoc methods have the advantage of not imposing any model constraints. For example, Gradient-weighted Class Activation Mapping approaches [2, 19, 36, 54] trace network gradients to identify the input areas that guide predictions. Similarly, Explanation Generation methods [17, 23, 40, 57] require models to produce explanations for visual tasks by conditioning their predictions on captioning models and [18, 41] incorporate visual evidence to ground explanations.", + "bbox": [ + 75, + 90, + 472, + 227 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Despite their advantages, there is no guarantee that post-hoc methods faithfully represent model reasoning [49]. In contrast, our work falls under interpretable by design methods, which constrain explanations to align with the model's reasoning. For example, Prototype methods [6,37,51,58,66] optimize a metric space that guides classification by computing distances to prototype representations of each class. While such methods identify important regions in the input for classification, they still require featurized region representations that obfuscate the semantic content of the region.", + "bbox": [ + 75, + 229, + 473, + 381 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "This work extends another family of interpretable by design methods known as Concept Bottleneck Models [25, 52]. Following early attempts in few shot learning [27] and attribute learning [50, 68], CBMs predict targets by linearly combining an intermediate layer of human-understandable attributes. Recently, Computational Derivation Learning (CompDL) [71] proposed a CBM architecture that applies a linear layer over CLIP scores between human expert designed concepts and images to predict targets in the context of an evaluation framework to measure how well CLIP grounds concepts. CBMs generally suffer from the need for costly class description annotations and lower performance compared to end-to-end counterparts. Post-hoc Concept Bottleneck (PCBM) [70] was proposed to fill these two gaps by leveraging information from a static knowledge base, such as ConceptNet [60], and adding a residual connection from image features to the final prediction to improve accuracy [70]. However, PCBMs cannot be expanded to larger-scale (e.g., ImageNet [11]) or domain-specific tasks (e.g., fine-grained [32]) because knowledge bases have limited coverage. In addition, they include a residual predictor, which effectively ensembles CBM with an end-to-end model, undermining interpretability.", + "bbox": [ + 75, + 382, + 473, + 731 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Inspired by previous work on using textual knowledge to guide vision models [5,22,48,55], we circumvent the requirement for external knowledge bases, and instead query LLMs to collect concepts. We remove the need for direct mapping from image features to targets by fully automating the extraction and filtering of LLM knowledge. Our model surpasses end-to-end models in few shot scenarios and achieves comparable performance in large data settings, while concurrent work [35] only evaluates on zero-shot settings.", + "bbox": [ + 75, + 732, + 470, + 868 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our work capitalizes on improvements in vision-language pretraining from earlier BERT-based models", + "bbox": [ + 76, + 869, + 472, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "[7, 30, 31, 62] to more scalable contrastive architectures [20, 28, 44, 69], which are very effective for few shot image classification [9, 63].", + "bbox": [ + 496, + 90, + 893, + 136 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our work can be viewed as interpretability-focused prompt tuning of CLIP [44]. Significant efforts have been devoted to prompting vision language models [12, 14, 29, 43, 46, 73, 74]. These focus on searching over text prompts to improve classification performance, and resemble earlier techniques in LLM prompt tuning [15, 53, 56].", + "bbox": [ + 496, + 136, + 893, + 227 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 500, + 232, + 591, + 247 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Figure 2 presents an overview of our method. Our model prompts a large language model, GPT-3 [4] to generate a set of candidate concepts for each class (Section 3.4). We employ submodular optimization to greedily select a subset of concepts for each class such that we maximize discriminability and diversity (Section 3.2). We then align the selected concepts to images using CLIP [44]. We apply a linear layer over the similarity scores of concepts and images to learn a weight matrix representing the importance of each concept in the final classification. This weight matrix is initialized using a language model prior from GPT-3 (Section 3.3).", + "bbox": [ + 496, + 257, + 893, + 425 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Problem Formulation", + "text_level": 1, + "bbox": [ + 500, + 431, + 702, + 446 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Consider a training set of image-label pairs $\\mathcal{D} = \\{(i,y)\\}$ where $i$ is the image and $y\\in \\mathcal{V}$ , is a label from a set of $N$ classes. Suppose we have a pretrained multimodal alignment model (e.g., CLIP [44]), which has an image encoder $\\mathcal{I}$ and a text encoder $\\mathcal{T}$ . $\\mathcal{I}$ and $\\mathcal{T}$ can map images and text into the shared feature space, respectively. The dot product of the image and text features reflects the alignment score between the two modalities. We extract the features of all images in $\\mathcal{D}$ as $\\pmb{x} = \\mathcal{I}(i)\\in \\mathbb{R}^d$ , and the dataset can be represented as $\\mathcal{D} = \\{(x,y)\\}$ . Let $S$ be the superset of candidate textual concepts generated from language models. We use a submodular function $\\mathcal{F}$ to select a bottleneck, $C$ , where $C\\subseteq S$ , made of $N_{C}$ concepts, $C = \\{c_1,c_2,\\dots ,c_{N_C}\\}$ . We can construct a bottleneck embedding, $\\pmb{E}_{C}\\in \\mathbb{R}^{N_{C}\\times d}$ , and each row of $\\pmb{E}_{C}$ is the text feature $\\mathcal{T}(c)\\in \\mathbb{R}^d$ of a concept $c$ extracted by the text encoder $\\mathcal{T}$ .", + "bbox": [ + 496, + 455, + 893, + 696 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Concept bottleneck models produce a prediction by composing two functions, $\\hat{y} = f\\left(g(\\boldsymbol{x},\\boldsymbol{E}_C)\\right)$ , in which $g: \\mathbb{R}^d \\to \\mathbb{R}^{N_C}$ maps the image feature to a score for every element of the bottleneck and $f: \\mathbb{R}^{N_C} \\to \\mathcal{V}$ makes the final prediction on the label space given the concept scores. In our setting, we find a bottleneck $C$ and appropriate $f$ by solving the following minimization problem:", + "bbox": [ + 496, + 696, + 893, + 804 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {f, C} \\underset {(\\boldsymbol {x}, y) \\sim \\mathcal {D}} {\\mathbb {E}} \\left[ \\mathcal {L} \\left(f (g (\\boldsymbol {x}, \\boldsymbol {E} _ {C})) , y\\right) \\right] - \\mathcal {F} (C, \\mathcal {D}) \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 811, + 893, + 845 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "in which $\\mathcal{L}(\\hat{y}, y)$ is the cross-entropy loss on the label prediction and $\\mathcal{F}(C, \\mathcal{D})$ is the quality of the bottleneck as measured by the submodular function. In practice, we optimize", + "bbox": [ + 496, + 854, + 893, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "19189", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "sequentially: we first find a high scoring $C$ under $\\mathcal{F}$ . Then, we use the dot product of image and concept embeddings as $g$ . Finally, we find an $f$ that minimizes $\\mathcal{L}$ . In the following sections, we will illustrate how we: construct the submodular function $\\mathcal{F}$ to select a subset of concepts $C$ from the candidates $S$ (Section 3.2) and learn $f$ (Section 3.3).", + "bbox": [ + 75, + 90, + 472, + 183 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Submodular Concept Selection", + "text_level": 1, + "bbox": [ + 76, + 189, + 352, + 207 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We create a superset of candidate concepts, $S$ , out of class-specific subsets. For every label $y \\in \\mathcal{V}$ , we construct $S_y$ by prompting a language model to produce textual knowledge about $y$ (Section 3.4). Instead of directly choosing $N_C$ concepts from $S$ , we select $k$ concepts for each class, such that $N \\times k = N_C$ , to ensure each class has an equal number of relevant concepts in the bottleneck.", + "bbox": [ + 75, + 212, + 470, + 318 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We employ submodular optimization [1] to select a subset $C_y \\subseteq S_y$ , $|C_y| = k$ . Specifically, we need to design a score function $\\mathcal{F}: 2^{|S_y|} \\to \\mathbb{R}$ to evaluate the utility of the subset. Submodular functions should satisfy the diminishing returns property. If a submodular function is monotone, a greedy algorithm [38] can be used to find a solution within a constant factor of the optimal one. We propose the following monotone submodular function to select the subset $C_y$ from the candidate set $S_y$ :", + "bbox": [ + 75, + 319, + 468, + 455 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {F} \\left(C _ {y}\\right) = \\underbrace {\\alpha \\cdot \\sum_ {c \\in C _ {y}} D (c)} _ {\\text {d i s c r i m i n a b i l i t y}} + \\underbrace {\\beta \\cdot \\sum_ {c _ {1} \\in S _ {y}} \\max _ {c _ {2} \\in C _ {y}} \\phi \\left(c _ {1} , c _ {2}\\right)} _ {\\text {c o v e r a g e}}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 91, + 463, + 468, + 518 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $D(c)$ denotes the discriminability score of the concept $c$ and $\\phi(\\cdot)$ is the intra-concept similarity. Generally, the first term tends to select more informative concepts, and the second term ensures the subset has good coverage of the candidate set. The hyperparameters $\\alpha$ and $\\beta$ control the weights of the two sub-functions. Here we present how to compute these two scores:", + "bbox": [ + 75, + 526, + 468, + 632 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Discriminability Score. We introduce a discriminability score to encourage the selection of concepts that are aligned with many images in class $y$ , but few images in other classes. We first define the similarity score $Sim(y, c)$ between a class and concept by taking the mean of the dot product between the images and text features:", + "bbox": [ + 75, + 638, + 468, + 729 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {S i m} (y, c) = \\frac {1}{| \\mathcal {X} _ {y} |} \\sum_ {\\boldsymbol {x} \\in \\mathcal {X} _ {y}} \\boldsymbol {x} \\cdot \\mathcal {T} (c) ^ {\\top}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 153, + 737, + 468, + 773 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{X}_y$ is the set of training images labeled with $y^6$ and $\\mathcal{T}$ is the text encoder. We define the normalized class association, which measures the conditional likelihood of aligning", + "bbox": [ + 76, + 784, + 470, + 830 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "${}^{3}$ diminishing returns property means $\\forall A \\subseteq B \\subseteq V \\smallsetminus v$ ,we have $\\mathcal{F}\\left( {A + \\{ v\\} }\\right) - \\mathcal{F}\\left( A\\right) \\geq \\mathcal{F}\\left( {B + \\{ v\\} }\\right) - \\mathcal{F}\\left( B\\right)$ .", + "4 A submodular function is monotone if $\\forall A\\subseteq B,\\mathcal{F}(A)\\leq \\mathcal{F}(B)$", + "5 Any linear combination of submodular functions is still submodular.", + "$^6$ In $N$ -way- $K$ -shot setting, $|\\mathcal{X}_y| = K$ ." + ], + "bbox": [ + 76, + 837, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "featurized images of a class given a concept's textual embedding, $\\overline{Sim}(y|c) = Sim(y, c) / \\sum_{y' \\in \\mathcal{Y}} Sim(y', c)$ , and compute its negative entropy:", + "bbox": [ + 496, + 90, + 893, + 137 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nD (c) = \\sum_ {y ^ {\\prime} \\in Y} \\overline {{S i m}} \\left(y ^ {\\prime} | c\\right) \\cdot \\log \\left(\\overline {{S i m}} \\left(y ^ {\\prime} | c\\right)\\right) \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 547, + 143, + 893, + 179 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Maximizing $D(c)$ will result in the selection of concepts that have peaked $\\overline{Sim}(y|c)$ , indicating that a concept is strongly associated with only a few classes.", + "bbox": [ + 496, + 186, + 892, + 233 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "**Coverage Score.** The second term of equation 2 is a minimax facility location function that tries to minimize the maximum distance between each element in the subset and the candidate set. For distance, we use the cosine between the features of the two concepts extracted by the text encoder: $\\phi(c_1, c_2) = \\cos(\\mathcal{T}(c_1), \\mathcal{T}(c_2))$ . A high coverage score yields a diverse bottleneck that covers different possible appearances for a target class.", + "bbox": [ + 496, + 239, + 893, + 359 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Optimize Class-concept Association", + "text_level": 1, + "bbox": [ + 498, + 369, + 808, + 386 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this section, we explain how we compute $g$ (the concept predictor) and learn $f$ (the label predictor) of the bottleneck.", + "bbox": [ + 496, + 392, + 893, + 422 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Predict the Concept Scores. The concept predictor $g$ is not learned in our method because the alignment model we use can measure the correlation between image and text through dot product. We treat the dot product of input image feature $\\mathbf{x}$ and the concept space $\\mathbf{E}_C$ defined in Section 3.2 as $g$ : $g(\\mathbf{x},\\mathbf{E}_C) = \\mathbf{x}\\cdot \\mathbf{E}_C^\\top$ , where $g(\\mathbf{x},\\mathbf{E}_C)\\in \\mathbb{R}^{N_C}$ , and each element is the score of image $\\mathbf{x}$ on a concept.", + "bbox": [ + 496, + 429, + 893, + 534 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Concept Weight Matrix. We learn a linear function for the label predictor $f$ that maps from concept scores to the final prediction. Intuitively, these weights encode the affinity of the concept to the class, allowing the model to represent that classes depend differently on the same concept. To normalize the class-concept association distributed over the weight matrix, we regularize the matrix with the softmax activation function. Concretely, we learn a concept weight matrix $\\mathbf{W} \\in \\mathbb{R}^{N \\times N_C}$ , that is used for prediction: $\\hat{y} = \\operatorname{argmax}\\left(g(\\mathbf{x},\\mathbf{E}_C)\\cdot \\sigma (\\mathbf{W})^\\top\\right)$ , in which $\\sigma (\\cdot)$ is the softmax activation which is applied along the concepts axis: $\\mathbf{W}_{y,c} = e^{\\mathbf{W}_{y,c}} / \\sum_{y'\\in \\mathcal{Y}}e^{\\mathbf{W}_{y',c}}$ .", + "bbox": [ + 496, + 540, + 893, + 731 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Initializing the Weight Matrix with Language Priors. Previous work trains the concept weight matrix freely from scratch, which is not feasible in low-resource scenarios where we don't have enough data to learn the weight effectively. To extend the application of CBM to few-shot image classification, we consider biasing the weights toward the initial association from the language model used to propose concepts. If a concept $c$ was present in $C_y$ , we initialize the elements of $W$ corresponding to the weight between class $y$ and concept $c$ to a higher value before optimization: $W_{y,c} = 1$ , if $c \\in C_y$ , otherwise 0.", + "bbox": [ + 496, + 734, + 893, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "19190", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/cab6e18d0b4713fa07be2038a79ada4a5bb5079d80e4e782168bdca96a1302ab.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 91, + 89, + 285, + 186 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/95ae922ab0beff4f2bd2c069ceaead5e1d3b868188cdcdb62a672297402f832d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 292, + 90, + 483, + 186 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/c7c7fbe41ee988e069cc9f92f4dadeef073393894dba3e65caed51ff05b297b3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 486, + 90, + 676, + 186 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/f75c5d68d878ae0cc98fdf6aefe8a698b9b5b3429473a057bbc9a7c865595883.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 684, + 90, + 875, + 186 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/7c508b006b2256322ca4a4a9beb98f8241cce6277e946f0caf0b6ab81e836749.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 89, + 189, + 284, + 286 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/6d5b506bba6c3f41d04cd446e0c1b81445fd7fcfdb21d7033703739a70ae4335.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 290, + 189, + 482, + 285 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/4bfc0fbb948348a53f2b18b931c228e3abc191ab257e212a8ea62645790b9de9.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 488, + 189, + 679, + 285 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/5c91390af6045150b79120ac020c8c65ed88889c19056f593f443249b275a1fe.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 686, + 189, + 879, + 285 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/fd61017ebc5cc7e6b60a2da0ebd60e02cc515a8ffa579300dda9a0f0d602890c.jpg", + "image_caption": [ + "Figure 3. Test accuracy $(\\%)$ comparison between LaBo and Linear Probe on 11 datasets. The x-axis represents the number of labeled images." + ], + "image_footnote": [], + "bbox": [ + 89, + 289, + 282, + 386 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/98298d1b9030a3b048a8439b85ce4629274823dbf1ab98bb6052dbbaa00218c1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 290, + 289, + 482, + 386 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/1cdf808641182b78ac6c614f478dd536ed20ac80f45b88fb3c3a2b8089bcd393.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 488, + 289, + 679, + 386 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/0be002c05e48125fd576a388d9debfe3a3675b923a4da0c8c6890863fe0f6680.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 686, + 289, + 879, + 386 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Prepare the Candidates", + "text_level": 1, + "bbox": [ + 76, + 428, + 294, + 445 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To collect the candidates $S$ to feed into our model, we prompt GPT-3 to generate relevant sentences by incorporating the class name in 5 templates shown in supplementary materials. For example, as shown in the top-left of Figure 2, we prompt GPT-3 by asking \"describe what the axolotl looks like\", and the GPT-3 returns a sentence about the target class. We obtain 500 sentences for each class and automatically split these sentences into shorter concepts using a T5 model [45] fine-tuned on a small set of annotated sentence-concept pairs. We use string match to identify and remove class name tokens in each concept. (see supplementary)", + "bbox": [ + 75, + 452, + 472, + 619 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experimental Setup", + "text_level": 1, + "bbox": [ + 76, + 633, + 269, + 652 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We evaluate our method on a diverse set of 11 datasets (Section 4.1) and compare it to its end-to-end counterpart and other interpretable CBM methods (Section 4.2).", + "bbox": [ + 75, + 660, + 468, + 707 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Dataset", + "text_level": 1, + "bbox": [ + 76, + 717, + 171, + 732 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We select a comprehensive benchmark of 11 image classification datasets spanning a diverse set of domains, including (1) Common objects: ImageNet [11], CIFAR-10 and CIFAR-100 [26]; (2) Fine-grained objects: Food-101 [3], FGVC-Aircraft [32], Flower-102 [39], CUB-200-2011 [67]; (3) Actions: UCF-101 [59]; (4) Textures: DTD [10]; (5) Skin tumors: HAM10000 [64] and (6) Satellite images: RE-SISC45 [8]. We use train/dev/test splits for all the datasets.", + "bbox": [ + 75, + 741, + 472, + 863 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Detailed statistics are presented in the supplementary material. We follow the few-shot evaluation protocol proposed by CLIP [44] with 1, 2, 4, 8, and 16 images randomly sampled from the training set for each class. We also evaluate in the fully-supervised setting where we train on all available images. For all experiments, we report the test accuracy.", + "bbox": [ + 500, + 429, + 893, + 521 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Baselines", + "text_level": 1, + "bbox": [ + 500, + 527, + 607, + 542 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We compare our model, LaBo, with black-box linear probing and two interpretable methods.", + "bbox": [ + 500, + 550, + 890, + 580 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Linear Probe Following previous evaluations on CBM [25, 70], linear probing serves as our primary baseline for comparison. We follow the implementation of CLIP [44] by training the scikit-learn's L-BFGS logistic regression with a hyperparameter sweep on the L2 regularization weight.", + "bbox": [ + 500, + 585, + 893, + 662 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "PCBM Post-hoc Concept Bottleneck Model [70] designs a residual modeling step that directly maps the original image embedding into the label space. PCBM treats the attributes of each class in ConceptNet [60] as concepts.", + "bbox": [ + 500, + 667, + 890, + 728 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "CompDL Compositional Derivation Learning [71] learns a linear layer over CLIP similarity scores between human-designed class descriptions and images to predict targets.", + "bbox": [ + 500, + 733, + 893, + 779 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Implementation Details", + "text_level": 1, + "bbox": [ + 500, + 786, + 715, + 801 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We prompt GPT-3-text-davinci-002 to generate concepts. The CLIP model is adapted from OpenAI's public repo with ViT-L/14 as the default vision backbone. We only use CLIP-RN50 as the backbone when comparing with PCBM, and ViT-B/32 with CompDL for a fair comparison. We implement the submodular function using the apricot package and", + "bbox": [ + 500, + 809, + 893, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_footnote", + "text": "7We use the same set of prompts for all datasets except UCF-101 since it is very different to describe an action.", + "bbox": [ + 75, + 875, + 468, + 898 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "19191", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/f2c720bbdd667c70516874296d022a748b1e5c91062cc01fa5feb12bd691ee4c.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Method124816FullAvg
Linear Probe51.6965.1372.3377.3881.5387.3872.57
LaBo (Ours)63.3568.1072.0876.1979.1185.7274.09
", + "bbox": [ + 78, + 88, + 465, + 128 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/3b1a31d9aa0cf58705828821791542144527b72ce5ea2685d39df3003d21552f.jpg", + "table_caption": [ + "Table 1. Mean accuracy across all datasets, at different shots ." + ], + "table_footnote": [], + "table_body": "
Methodw/ end-to-endCIFAR-10CIFAR-100
PCBM [70]✗84.556.0
LaBo (Ours)✗87.969.1
PCBM-h [70]✓87.669.9
Linear Probe✓88.870.1
", + "bbox": [ + 96, + 162, + 444, + 231 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/b843391b81534a82cfd50580b7cf8ffd553f5218b9c1a990095a8e6b85316b92.jpg", + "table_caption": [ + "Table 2. Test accuracy comparison between LaBo and Post-hoc Concept Bottleneck Model (PCBM) on CIFAR-10 and CIFAR-100. \"w/ end-to-end\" denotes whether the model employs an end-to-end residual predictor from image features to targets." + ], + "table_footnote": [], + "table_body": "
Methodw/ manual concepts15Full
CompDL [71]✓13.633.252.6
LaBo (Ours)✗35.155.771.8
Linear Probe-28.455.475.5
", + "bbox": [ + 96, + 306, + 444, + 363 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "set the default number of concepts selected for each class to 50. To train the linear function, we use the Pytorch-lightning library with Adam [24] optimizer. We tune the batch size, learning rate, and submodular weights on the development set. Model checkpoints with the highest validation accuracy are evaluated on the test set. We list the hyperparameters for all datasets and shots in the supplementary material.", + "bbox": [ + 75, + 402, + 468, + 508 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Evaluation", + "text_level": 1, + "bbox": [ + 76, + 522, + 192, + 537 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Main Results", + "text_level": 1, + "bbox": [ + 76, + 546, + 215, + 561 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We compare LaBo's performance with a linear probe and other interpretable baselines to evaluate if we can maintain black box accuracy without sacrificing interpretability.", + "bbox": [ + 75, + 569, + 468, + 614 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Comparison with End-to-End Model. One of our goals is to close the performance gap between interpretable and black box models. Table 1 reports the mean test accuracy of LaBo and the linear probe on 11 datasets. LaBo significantly outperforms the end-to-end model when little data is available and continues to be competitive as the number of data increases. On average, LaBo surpasses the linear probe by $1.5\\%$ . Figure 3 provides analytic performance comparisons between LaBo and Linear Probe on each dataset.", + "bbox": [ + 75, + 621, + 468, + 756 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In general, LaBo's performance depends on the quality of knowledge extracted from GPT-3. For common categories, GPT-3 contains high-quality knowledge allowing substantial improvement over linear probes. For some fine-grained datasets, such as Flower-102, GPT-3's knowledge is largely non-visual, as seen in Figure 7. In such cases, specialized language models could be used to improve LaBo.", + "bbox": [ + 75, + 757, + 470, + 864 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Comparison with other Interpretable Methods. Table 2 compares LaBo's performance with PCBM and Linear Probe.", + "bbox": [ + 75, + 869, + 472, + 902 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/912b6a39462ebfc18b84b7b9959560cd94efa0e52570e5a691b9fe43ef03047c.jpg", + "table_caption": [ + "Table 3. LaBo and CompDL evaluated on CUB for 1/5/full shots." + ], + "table_footnote": [], + "table_body": "
n. of concepts per class (k)n. of shots
124816Full
141.8952.4561.7665.9969.6178.95
552.5461.1367.2272.9075.6283.83
1058.0064.5969.9074.5077.4384.66
2561.7266.3371.3975.2879.0485.26
5063.0367.7971.8876.0879.1085.71
", + "bbox": [ + 509, + 89, + 880, + 179 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/6b4fdd65c0bb8a547a9b7aa52e8efc4d46c5998aa9fdefa7325b80ec3b71bd34.jpg", + "table_caption": [ + "Table 4. Ablation results on bottleneck sizes. We vary the sizes of the bottlenecks and report the average performance on 11 datasets." + ], + "table_footnote": [], + "table_body": "
Selection Methodn. of shots
124816Full
RANDOM59.2464.7170.4274.0778.2985.06
SIMILARITY54.5961.4267.1772.6677.3284.88
COVERAGE59.7365.9370.8274.7178.9085.60
DISCRIM60.9966.4970.9374.8177.9085.31
SUBMODULAR63.0367.7971.8876.0879.1085.71
", + "bbox": [ + 509, + 229, + 879, + 321 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 5. Ablation results on concept selection methods. We report mean test accuracy on 11 datasets.", + "bbox": [ + 498, + 330, + 890, + 359 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "LaBo outperforms PCBM by $3.4\\%$ on CIFAR-10 and $13.1\\%$ on CIFAR-100. LaBo maintains comparable performance to PCBM with a residual predictor (PCBM-h), without circumventing the bottleneck. In Table 3, LaBo is more accurate than CompDL [71] without manually constructed concepts.", + "bbox": [ + 496, + 375, + 893, + 452 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 460, + 653, + 477 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We evaluate the importance of each of our model's components on final performance. Specifically, we compare results with different concept selection methods, language and random weight initialization, and bottleneck sizes.", + "bbox": [ + 496, + 484, + 893, + 544 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Concept Selection Methods. We compare our submodular function with four concept selection methods: (1) RANDOM: we randomly sample a subset of concepts from the candidates for each class; (2) SIMILARITY: we select the top concepts ranked by their similarity scores with the class calculated by equation 3; (3) COVERAGE: we only consider the coverage score for concept selection; (4) DISCRIM: we only consider the discriminability score for concept selection. As shown in Table 5, our submodular function, which jointly optimizes coverage and discriminability, achieves the best performance across different numbers of shots. We notice that using coverage or discriminability alone still outperforms using similarity between the class and random selection. The selection method plays an important role in all data settings, but its impact decreases with more supervision.", + "bbox": [ + 496, + 551, + 893, + 779 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Initialization with Language Priors. We deactivate the LM initialization and use random initialization instead. Figure 4 shows that the LM prior is more important for low shot settings since there is less signal to guide concept importance.", + "bbox": [ + 496, + 786, + 893, + 848 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Bottleneck Size. In Table 4, we compare performance for different bottleneck sizes ranging from 1 to 50 concepts selected by the submodular function. Larger bottlenecks are", + "bbox": [ + 496, + 854, + 893, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "19192", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/0119f7d29c86bd03b71d85f73d27c4d7af0978206d2b036d3749cb3a36bc3c76.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 81, + 90, + 464, + 214 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3624ddebc571049301334d5df1533a6845a8c8a713f793f61492167663562a24.jpg", + "image_caption": [ + "Figure 4. Language Prior vs. Random Weight initialization average over all datasets." + ], + "image_footnote": [], + "bbox": [ + 80, + 263, + 455, + 330 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c6fb465506d9be5bc5f6cf94848a554873e448ee2b1935ee398f593fcf70c3f5.jpg", + "image_caption": [ + "Figure 5. Human evaluation on Factuality and Groundability for different bottlenecks on ImageNet. \"w/o Submod\" denotes without submodular function, i.e., random concept selection. \"w/o LM\" denotes no language prior weight initialization." + ], + "image_footnote": [], + "bbox": [ + 81, + 335, + 455, + 402 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "usually better, but with more data, similar performance is achievable with smaller bottlenecks.", + "bbox": [ + 75, + 489, + 468, + 518 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Human Evaluation", + "text_level": 1, + "bbox": [ + 76, + 540, + 261, + 555 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "It is important for interpretability that the vision-language alignment model correctly grounds concepts to images. For example, if a concept \"usually round\" ranks both circles and stripes highly, the name of the attribute does not faithfully represent the computation. In addition, it is important that the automatically generated concept bottlenecks factually correspond to the class they describe. To this end, we introduce two metrics to evaluate the quality of our concept bottleneck items: (1) Factuality measures how accurate the concepts are in describing their designated class by requiring annotators to judge whether they describe ground truth images, and (2) Groundability measures how consistent the vision-language model grounding of the concepts to images with human interpretations by requiring annotators to judge their applicability on the top-10 images ranked by CLIP alignment scores.", + "bbox": [ + 75, + 564, + 472, + 806 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Setup. Both metrics are computed by asking annotators to select images that describe a highly ranked concept in our bottlenecks. Formally, the two metrics are represented by:", + "bbox": [ + 75, + 815, + 470, + 861 + ], + "page_idx": 6 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {F a c t u a l i t y} (c) = \\frac {\\text {n u m b e r o f i m a g e s s e l e c t e d}}{k \\text {g r o u n d t r u t h i m a g e s o f t h e c l a s s}}\n$$\n", + "text_format": "latex", + "bbox": [ + 102, + 871, + 442, + 905 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f5e280be94cb40596c8c872c1314b682666101190e60c04f802ff934bf96cc70.jpg", + "image_caption": [ + "Figure 6. Percentage of invalid concepts identified by humans for different bottlenecks on ImageNet. Lower percentage is better." + ], + "image_footnote": [], + "bbox": [ + 504, + 90, + 883, + 215 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/10427b7ef4fe9ee2f62a156555ac447c86dc97b0e2bda8ab5df939636c3891d3.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MetricsLaBow/o Submodw/o LM
Factuality (%) ↑24.022.814.1
Groundability (%) ↑14.122.520.2
Non Visual (%) ↓4.85.65.8
Non Sensical (%) ↓8.09.68.7
Unknown Vocab (%) ↓10.210.510.7
", + "bbox": [ + 506, + 260, + 879, + 349 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 6. Average human evaluation results of LaBo on 11 datasets. We also evaluate LaBo by removing the submodular function (w/o Submod) and language model priors (w/o LM).", + "bbox": [ + 498, + 359, + 893, + 402 + ], + "page_idx": 6 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {G r o u n d a b i l i t y} (c) = \\frac {\\text {n u m b e r o f i m a g e s s e l e c t e d}}{\\text {t o p - k a l i n g e d i m a g e s o f t h e c o n c e p t}}\n$$\n", + "text_format": "latex", + "bbox": [ + 506, + 417, + 880, + 450 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "where we set $k = 10$ . In addition to the two main metrics, we ask the annotator to select whether the concept is non-visual, nonsensical, or contains unknown vocabulary. We randomly sample 20 classes for each dataset and evaluate the top 5 concepts (ranked by the weights of the linear function) for each class, 100 concepts per dataset. We release our human evaluation task on Amazon Mechanical Turk and collect three annotations for each concept. More details on the task and the results can be found in the supplement.", + "bbox": [ + 496, + 455, + 893, + 593 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Baselines. We evaluate the bottlenecks under full supervision and compare them with two main baselines: (1) LaBo (w/o Submod), which randomly selects the concepts instead of using the submodular function, and (2) LaBo (w/o LM), which initializes the concept weight matrix randomly without leveraging the priors of the language model. For ImageNet, we add two additional baselines using human-written text: (1) WordNet [13] definitions and (2) Wikipedia sentences [22]. We adopt the same preprocessing pipeline as LaBo to extract concepts from human-written resources and utilize the submodular function to select the bottlenecks.", + "bbox": [ + 496, + 599, + 893, + 766 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results. Figure 5 shows the evaluation on ImageNet, and we observe that LaBo has significantly higher Factuality and Groundability than human-written text. We further observe that removing components from our system (submodular and LM Prior) hurt both human evaluation metrics, indicating their collective importance in our system. In addition, Figure", + "bbox": [ + 496, + 773, + 893, + 866 + ], + "page_idx": 6 + }, + { + "type": "page_footnote", + "text": "With the only exception of Factuality for Flower-102 where we set $k = 8$ because there are not enough images in the dev set.", + "bbox": [ + 500, + 875, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "19193", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/63f4c1c9f91fe571378bf210603bfbca39c25ce029f12ca88a53339cc7f4c2d1.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Class NameTop-3 ConceptsClass NameTop-3 ConceptsClass NameTop-3 ConceptsClass NameTop-3 Concepts
ImageNetbadger1. short legs and long body make it an excellent diggerant1. black and red stingerhammer1.long, thin tool with a wooden handlewater buffalo1. large head with short, curved horns
2. black-and-white striped fur2. black-and-white striped fur2. small, black insect with six legs2. small, black insect with six legs2. great tool for pounding object2. great tool for pounding object2. heaviest living species of bovid2. heaviest living species of bovid
3. coat is very shaggy3. coat is very shaggy3. long, slender antennae that it uses to smell and touch3. long, slender antennae that it uses to smell and touch3. used to pound on surfaces3. used to pound on surfaces3. huge, dark-colored animal3. huge, dark-colored animal
CUBeared grebe1. black and white plumage that is striking in the sunlighthorned lark1. black line running through yellow facewhite pelican1. long neck and bill make it look like a giant swanarctic tern1. breeds in greenland, iceland, and northern russia
2. black body with a long, slender neck2. black body with a long, slender neck2. head is black with a white horn on each side2. head is black with a white horn on each side2. large, white bird with black wings2. large, white bird with black wings2. large, white birds2. black and white markings
3. red and black bill3. red and black bill3. black horn on each side of their head3. black horn on each side of their head3. bill is huge and yellow3. bill is huge and yellow3. bill is huge and yellow3. small white bird with a black cap
Flowerwater lily1. depicted in artworks of ponds and waterfallbarbeton daisy1. scientific name for the flower is taraxacum officinalmarigold1. central disc with smaller floretstiger lily1. long, protruding stamen
2. member of the nymphaceae family2. member of the nymphaceae family2. named after the city of barberton2. named after the city of barberton2. have a slightly furry texture2. have a slightly furry texture2. have a slightly furry texture2. orange with black spots and stripes
3. lily pads float3. lily pads float3. member of the daisy family3. member of the daisy family3. bold and vibrant color palette3. bold and vibrant color palette3. bold and vibrant color palette3. bold and vibrant color palette
UCF-101archery1. grip bow tightly in their left handdrumming1. blur as they fly over the drumssurfing1. deep blue colorlong jump1. get out of sandpit
2. focused and concentrated on their task2. focused and concentrated on their task2. sitting on a stool in front of a drum set2. sitting on a stool in front of a drum set2. tans contrast with the white of their boards2. tans contrast with the white of their boards2. tans contrast with the white of their boards2. series of movements starting from a standing position
3. keep bow and arrows in safe and dry place when not in use3. keep bow and arrows in safe and dry place when not in use3. position the drumstick so it is resting on your index finger3. position the drumstick so it is resting on your index finger3. sending a spray of water into the air3. sending a spray of water into the air3. person tucks their knees up to chest3. person tucks their knees up to chest
HAM100000dermatofibroma1. generally not painfulmelanoma1. dark brown or black in colormelanocytic nevi1. color is tanbenign lesions1. color ranges from light brown to black
2. red, brown, or purple in color2. red, brown, or purple in color2. large and dark2. large and dark2. dark brown or black color2. dark brown or black color2. dark brown or black color2. rough or scaly texture
3. thin white halo around them3. thin white halo around them3. flesh-colored, brown, or black3. flesh-colored, brown, or black3. small, round, and slightly raised3. small, round, and slightly raised3. small, round, and slightly raised3. dark brown or black
", + "bbox": [ + 83, + 89, + 885, + 483 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Figure 7. Several example bottlenecks generated by LaBo. The top-3 concepts, ranked by their weights in the linear function, for randomly selected classes, paired with a random image from the class, across 6 datasets.", + "bbox": [ + 75, + 494, + 892, + 523 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6 shows that LaBo has significantly fewer invalid concepts than other baselines. Table 6 summarizes the average human evaluation results over the 11 datasets9. On average, we observe a trade-off between Factuality and Groundability. Increasing coverage and discriminability leads to more variable and specific concepts that CLIP finds more difficult to ground. This could be due to challenges in capturing composite concepts [33, 71]. For individual analysis of the datasets, refer to the supplementary material. Finally, Figure 7 shows several CBMs we constructed. Across many types of tasks, the bottlenecks are largely coherent, factual, and groundable by CLIP.", + "bbox": [ + 75, + 539, + 472, + 720 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion and Limitation", + "text_level": 1, + "bbox": [ + 76, + 734, + 326, + 750 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Overall, our approach demonstrates that the accuracy and interpretability of vision systems may be less at odds than previously believed. Leveraging LLMs was crucial, as they encode important visual knowledge. In the future, our approach can easily be enriched with new factors that capture different priors on bottleneck construction. The limits of knowledge in GPT-3 are not known, but likely there are", + "bbox": [ + 75, + 760, + 468, + 864 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "domains where prompting generates few useful facts. Even in contexts where GPT-3 can generate useful information, our method depends on CLIP being able to recognize those aspects in images. The alignment between GPT-3 and CLIP likely does not hold for all cases. Future work could focus on dynamically prompting GPT-3 to make this coupling more robust. Finally, our work depends on large models trained at scales that are not currently reproducible. It is possible unrevealed aspects of training by OpenAI will require a reevaluation of our claims.", + "bbox": [ + 496, + 539, + 893, + 690 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements", + "text_level": 1, + "bbox": [ + 500, + 707, + 666, + 724 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This research is based upon work supported in part by the DARPA KAIROS Program (contract FA8750-19-2-1004), the DARPA LwLL Program (contract FA8750-19-2-0201), the IARPA BETTER Program (contract 2019-19051600004), the IARPA HIATUS Program (contract 2022-22072200005), the NSF (Award 1928631), and an AI2 Young Investigator Award. Approved for Public Release, Distribution Unlimited. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies, either expressed or implied, of ODNI, DARPA, IARPA, NSF, or the U.S. Government.", + "bbox": [ + 496, + 734, + 893, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_footnote", + "text": "The low resolution of CIFAR images partially affects those metrics since annotators have greater difficulty in completing the task.", + "bbox": [ + 76, + 875, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "19194", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Francis Bach. 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International Journal of Computer Vision, 130(9):2337-2348, 2022, 3, 12, 14" + ], + "bbox": [ + 501, + 92, + 893, + 502 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "19197", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Language in a Bottle_ Language Model Guided Concept Bottlenecks for Interpretable Image Classification/b8f072ca-77d7-4ea7-aa8e-47b49a1b8d4b_model.json b/2023/Language in a Bottle_ Language Model Guided Concept Bottlenecks for Interpretable Image Classification/b8f072ca-77d7-4ea7-aa8e-47b49a1b8d4b_model.json new file mode 100644 index 0000000000000000000000000000000000000000..59ddd58db453e1008636d669134908ed981ddba6 --- /dev/null +++ b/2023/Language in a Bottle_ Language Model Guided Concept Bottlenecks for Interpretable Image Classification/b8f072ca-77d7-4ea7-aa8e-47b49a1b8d4b_model.json @@ -0,0 +1,2631 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.142, + 0.131, + 0.83, + 0.177 + ], + "angle": 0, + "content": "Language in a Bottle: Language Model Guided Concept Bottlenecks for Interpretable Image Classification" + }, + { + "type": "text", + "bbox": [ + 0.236, + 0.204, + 0.735, + 0.257 + ], + "angle": 0, + "content": "Yue Yang, Artemis Panagopoulou, Shenghao Zhou, Daniel Jin, Chris Callison-Burch, Mark Yatskar University of Pennsylvania" + }, + { + "type": "text", + "bbox": [ + 0.186, + 0.26, + 0.778, + 0.275 + ], + "angle": 0, + "content": "{yueyang1, artemisp, shzhou2, jindan, ccb, myatskar}@seas.upenn.edu" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.309, + 0.314, + 0.326 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.341, + 0.474, + 0.735 + ], + "angle": 0, + "content": "Concept Bottleneck Models (CBM) are inherently interpretable models that factor model decisions into human-readable concepts. They allow people to easily understand why a model is failing, a critical feature for high-stakes applications. CBMs require manually specified concepts and often under-perform their black box counterparts, preventing their broad adoption. We address these shortcomings and are first to show how to construct high-performance CBMs without manual specification of similar accuracy to black box models. Our approach, Language Guided Bottlenecks (LaBo), leverages a language model, GPT-3, to define a large space of possible bottlenecks. Given a problem domain, LaBo uses GPT-3 to produce factual sentences about categories to form candidate concepts. LaBo efficiently searches possible bottlenecks through a novel submodular utility that promotes the selection of discriminative and diverse information. Ultimately, GPT-3's sentential concepts can be aligned to images using CLIP, to form a bottleneck layer. Experiments demonstrate that LaBo is a highly effective prior for concepts important to visual recognition. In the evaluation with 11 diverse datasets, LaBo bottlenecks excel at few-shot classification: they are \\(11.7\\%\\) more accurate than black box linear probes at 1 shot and comparable with more data. Overall, LaBo demonstrates that inherently interpretable models can be widely applied at similar, or better, performance than black box approaches.1" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.762, + 0.21, + 0.779 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.788, + 0.471, + 0.879 + ], + "angle": 0, + "content": "As deep learning systems improve, their applicability to critical domains is hampered because of a lack of transparency. Efforts to address this have largely focused on post-hoc explanations [47, 54, 72]. Such explanations can be problematic because they may be incomplete or unfaithful with respect to the model's computations [49]. Models" + }, + { + "type": "image", + "bbox": [ + 0.506, + 0.308, + 0.892, + 0.433 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.444, + 0.895, + 0.486 + ], + "angle": 0, + "content": "Figure 1. Our proposed high-performance Concept Bottleneck Model alleviates the need for human-designed concepts by prompting large language models (LLMs) such as GPT-3 [4]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.502, + 0.895, + 0.608 + ], + "angle": 0, + "content": "can also be designed to be inherently interpretable, but it is believed that such models will perform more poorly than their black box alternatives [16]. In this work, we provide evidence to the contrary. We show how to construct high-performance interpretable-by-design classifiers by combining a language model, GPT-3 [4], and a language-vision model, CLIP [44]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.61, + 0.895, + 0.732 + ], + "angle": 0, + "content": "Our method builds on Concept Bottleneck Models (CBM) [25], which construct predictors through a linear combination of human-designed concepts. For example, as seen in Figure 1, a qualified person can design concepts, such as \"nape color,\" as intermediate targets for a black box model before classifying a bird. CBMs provide abstractions that people can use to understand errors or intervene on, contributing to increased trust." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.733, + 0.895, + 0.839 + ], + "angle": 0, + "content": "Application of CBMs is limited because they require costly attribute annotations by domain experts and often under-perform their black box counterparts. In contexts where CBM performance is competitive with black box alternatives, interpretability properties are sacrificed [34, 70]. To address both of these challenges, we propose to build systems that automatically construct CBMs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Our Language Model Guided Concept Bottleneck Model (LaBo), Figure 2, allows for the automatic construction of high-performance CBMs for arbitrary classification problems without concept annotations. Large language models" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.47, + 0.9 + ], + "angle": 0, + "content": "\\(^{1}\\)Code and data are available at https://github.com/YueYANG1996/LaBo" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19187" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.104, + 0.089, + 0.873, + 0.38 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.389, + 0.895, + 0.461 + ], + "angle": 0, + "content": "Figure 2. We present an overview of our Language-Model-Guided Concept Bottleneck Model (LaBo), which is interpretable by design image classification system. First, we prompt the large language model (GPT-3) to generate candidate concepts (Sec 3.4). Second, we employ a submodular function to select concepts from all candidates to construct the bottleneck (Sec 3.2). Third, we apply a pretrained alignment model (CLIP) to obtain the embeddings of concepts and images, which is used to compute concept scores. Finally, we train a linear function in which the weight \\( W \\) denotes the concept-class association user to predict targets based on concept scores (Sec 3.3)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.475, + 0.475, + 0.61 + ], + "angle": 0, + "content": "(LLMs) contain significant world knowledge [21, 42, 61], that can be elicited by inputting a string prefix and allowing LLMs to complete the string (prompting). For example, in Figure 1, GPT-3 is prompted about sparrows and completes with information such as \"brown head with white stripes.\" LaBo leverages this by constructing bottlenecks where the concepts are such GPT-3 generated sentences. Since our concepts are textual, we use CLIP to score their presence in an image and form a bottleneck layer out of these scores." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.613, + 0.472, + 0.794 + ], + "angle": 0, + "content": "A key advantage of LaBo is the ability to control the selection of concepts in the bottleneck by generating candidates from the language model. We develop selection principles targeting both interpretability and classification accuracy. For example, we prefer smaller bottlenecks that include shorter sentences that do not include class names. Furthermore, to maximize performance, we prefer attributes that CLIP can easily recognize and are highly discriminative. To account for appearance variation, we select attributes that cover a variety of information and are not repetitive. We formulate these factors into a novel sub-modular criterion that allows us to select good bottlenecks efficiently [38]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.472, + 0.873 + ], + "angle": 0, + "content": "We have evaluated LaBo-created bottlenecks on 11 diverse image classification tasks, spanning recognition of common objects [11,26] to skin tumors [64]. fine-grained types [3, 32, 39, 67], textures [10], actions [59], skin tumors [64], and satellite photographed objects [8].2 Our" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.475, + 0.895, + 0.655 + ], + "angle": 0, + "content": "main finding is that LaBo is a highly effective prior for what concepts to look for, especially in low data regimes. In evaluations comparing with linear probes, LaBo outperforms by as much as \\(11.7\\%\\) at 1-shot and marginally underperforms given larger data settings. Averaged over many dataset sizes, LaBo bottlenecks are \\(1.5\\%\\) more accurate than linear probes. In comparison to modifications of CBMs that improve performance by circumventing the bottleneck [70], we achieve similar or better results without breaking the CBM abstraction. In extensive ablations, we study key trade-offs in bottleneck design and show our selection criteria are crucial and highlight several other critical design choices." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.656, + 0.897, + 0.779 + ], + "angle": 0, + "content": "Human evaluations indicate that our bottlenecks are largely understandable, visual, and factual. Finally, annotators find our GPT-3 sourced bottlenecks are more factual and groundable than those constructed from WordNet or Wikipedia sentences. Overall, our experiments demonstrate that automatically designed CBMs can be as effective as black box models while maintaining critical factors contributing to their interpretability." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.79, + 0.642, + 0.807 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.816, + 0.895, + 0.832 + ], + "angle": 0, + "content": "Broadly, interpretability methods fall into two categories:" + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.84, + 0.895, + 0.901 + ], + "angle": 0, + "content": "3 when creating candidate attributes. This is largely done to overcome problems of word sense. For example, when naively prompted to produce knowledge about the flower \"bird of paradise\" GPT-3 yields information about birds instead of flowers. In general, specialization here was also minimal. See appendix for prompts." + }, + { + "type": "page_footnote", + "bbox": [ + 0.095, + 0.887, + 0.472, + 0.902 + ], + "angle": 0, + "content": "2The only dataset specialization we perform is prompt tuning for GPT-" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "19188" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.228 + ], + "angle": 0, + "content": "post-hoc and by design. While ours is an instance of the latter, post-hoc methods have the advantage of not imposing any model constraints. For example, Gradient-weighted Class Activation Mapping approaches [2, 19, 36, 54] trace network gradients to identify the input areas that guide predictions. Similarly, Explanation Generation methods [17, 23, 40, 57] require models to produce explanations for visual tasks by conditioning their predictions on captioning models and [18, 41] incorporate visual evidence to ground explanations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.23, + 0.474, + 0.382 + ], + "angle": 0, + "content": "Despite their advantages, there is no guarantee that post-hoc methods faithfully represent model reasoning [49]. In contrast, our work falls under interpretable by design methods, which constrain explanations to align with the model's reasoning. For example, Prototype methods [6,37,51,58,66] optimize a metric space that guides classification by computing distances to prototype representations of each class. While such methods identify important regions in the input for classification, they still require featurized region representations that obfuscate the semantic content of the region." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.383, + 0.474, + 0.732 + ], + "angle": 0, + "content": "This work extends another family of interpretable by design methods known as Concept Bottleneck Models [25, 52]. Following early attempts in few shot learning [27] and attribute learning [50, 68], CBMs predict targets by linearly combining an intermediate layer of human-understandable attributes. Recently, Computational Derivation Learning (CompDL) [71] proposed a CBM architecture that applies a linear layer over CLIP scores between human expert designed concepts and images to predict targets in the context of an evaluation framework to measure how well CLIP grounds concepts. CBMs generally suffer from the need for costly class description annotations and lower performance compared to end-to-end counterparts. Post-hoc Concept Bottleneck (PCBM) [70] was proposed to fill these two gaps by leveraging information from a static knowledge base, such as ConceptNet [60], and adding a residual connection from image features to the final prediction to improve accuracy [70]. However, PCBMs cannot be expanded to larger-scale (e.g., ImageNet [11]) or domain-specific tasks (e.g., fine-grained [32]) because knowledge bases have limited coverage. In addition, they include a residual predictor, which effectively ensembles CBM with an end-to-end model, undermining interpretability." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.733, + 0.472, + 0.869 + ], + "angle": 0, + "content": "Inspired by previous work on using textual knowledge to guide vision models [5,22,48,55], we circumvent the requirement for external knowledge bases, and instead query LLMs to collect concepts. We remove the need for direct mapping from image features to targets by fully automating the extraction and filtering of LLM knowledge. Our model surpasses end-to-end models in few shot scenarios and achieves comparable performance in large data settings, while concurrent work [35] only evaluates on zero-shot settings." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.473, + 0.902 + ], + "angle": 0, + "content": "Our work capitalizes on improvements in vision-language pretraining from earlier BERT-based models" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.894, + 0.137 + ], + "angle": 0, + "content": "[7, 30, 31, 62] to more scalable contrastive architectures [20, 28, 44, 69], which are very effective for few shot image classification [9, 63]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.137, + 0.895, + 0.228 + ], + "angle": 0, + "content": "Our work can be viewed as interpretability-focused prompt tuning of CLIP [44]. Significant efforts have been devoted to prompting vision language models [12, 14, 29, 43, 46, 73, 74]. These focus on searching over text prompts to improve classification performance, and resemble earlier techniques in LLM prompt tuning [15, 53, 56]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.233, + 0.593, + 0.248 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.258, + 0.895, + 0.426 + ], + "angle": 0, + "content": "Figure 2 presents an overview of our method. Our model prompts a large language model, GPT-3 [4] to generate a set of candidate concepts for each class (Section 3.4). We employ submodular optimization to greedily select a subset of concepts for each class such that we maximize discriminability and diversity (Section 3.2). We then align the selected concepts to images using CLIP [44]. We apply a linear layer over the similarity scores of concepts and images to learn a weight matrix representing the importance of each concept in the final classification. This weight matrix is initialized using a language model prior from GPT-3 (Section 3.3)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.433, + 0.704, + 0.448 + ], + "angle": 0, + "content": "3.1. Problem Formulation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.456, + 0.895, + 0.698 + ], + "angle": 0, + "content": "Consider a training set of image-label pairs \\(\\mathcal{D} = \\{(i,y)\\}\\) where \\(i\\) is the image and \\(y\\in \\mathcal{V}\\), is a label from a set of \\(N\\) classes. Suppose we have a pretrained multimodal alignment model (e.g., CLIP [44]), which has an image encoder \\(\\mathcal{I}\\) and a text encoder \\(\\mathcal{T}\\). \\(\\mathcal{I}\\) and \\(\\mathcal{T}\\) can map images and text into the shared feature space, respectively. The dot product of the image and text features reflects the alignment score between the two modalities. We extract the features of all images in \\(\\mathcal{D}\\) as \\(\\pmb{x} = \\mathcal{I}(i)\\in \\mathbb{R}^d\\), and the dataset can be represented as \\(\\mathcal{D} = \\{(x,y)\\}\\). Let \\(S\\) be the superset of candidate textual concepts generated from language models. We use a submodular function \\(\\mathcal{F}\\) to select a bottleneck, \\(C\\), where \\(C\\subseteq S\\), made of \\(N_{C}\\) concepts, \\(C = \\{c_1,c_2,\\dots ,c_{N_C}\\}\\). We can construct a bottleneck embedding, \\(\\pmb{E}_{C}\\in \\mathbb{R}^{N_{C}\\times d}\\), and each row of \\(\\pmb{E}_{C}\\) is the text feature \\(\\mathcal{T}(c)\\in \\mathbb{R}^d\\) of a concept \\(c\\) extracted by the text encoder \\(\\mathcal{T}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.698, + 0.895, + 0.805 + ], + "angle": 0, + "content": "Concept bottleneck models produce a prediction by composing two functions, \\(\\hat{y} = f\\left(g(\\boldsymbol{x},\\boldsymbol{E}_C)\\right)\\), in which \\(g: \\mathbb{R}^d \\to \\mathbb{R}^{N_C}\\) maps the image feature to a score for every element of the bottleneck and \\(f: \\mathbb{R}^{N_C} \\to \\mathcal{V}\\) makes the final prediction on the label space given the concept scores. In our setting, we find a bottleneck \\(C\\) and appropriate \\(f\\) by solving the following minimization problem:" + }, + { + "type": "equation", + "bbox": [ + 0.52, + 0.812, + 0.895, + 0.847 + ], + "angle": 0, + "content": "\\[\n\\min _ {f, C} \\underset {(\\boldsymbol {x}, y) \\sim \\mathcal {D}} {\\mathbb {E}} \\left[ \\mathcal {L} \\left(f (g (\\boldsymbol {x}, \\boldsymbol {E} _ {C})) , y\\right) \\right] - \\mathcal {F} (C, \\mathcal {D}) \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.895, + 0.902 + ], + "angle": 0, + "content": "in which \\(\\mathcal{L}(\\hat{y}, y)\\) is the cross-entropy loss on the label prediction and \\(\\mathcal{F}(C, \\mathcal{D})\\) is the quality of the bottleneck as measured by the submodular function. In practice, we optimize" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "19189" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.184 + ], + "angle": 0, + "content": "sequentially: we first find a high scoring \\( C \\) under \\( \\mathcal{F} \\). Then, we use the dot product of image and concept embeddings as \\( g \\). Finally, we find an \\( f \\) that minimizes \\( \\mathcal{L} \\). In the following sections, we will illustrate how we: construct the submodular function \\( \\mathcal{F} \\) to select a subset of concepts \\( C \\) from the candidates \\( S \\) (Section 3.2) and learn \\( f \\) (Section 3.3)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.19, + 0.353, + 0.208 + ], + "angle": 0, + "content": "3.2. Submodular Concept Selection" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.213, + 0.471, + 0.319 + ], + "angle": 0, + "content": "We create a superset of candidate concepts, \\( S \\), out of class-specific subsets. For every label \\( y \\in \\mathcal{V} \\), we construct \\( S_y \\) by prompting a language model to produce textual knowledge about \\( y \\) (Section 3.4). Instead of directly choosing \\( N_C \\) concepts from \\( S \\), we select \\( k \\) concepts for each class, such that \\( N \\times k = N_C \\), to ensure each class has an equal number of relevant concepts in the bottleneck." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.32, + 0.47, + 0.456 + ], + "angle": 0, + "content": "We employ submodular optimization [1] to select a subset \\( C_y \\subseteq S_y \\), \\( |C_y| = k \\). Specifically, we need to design a score function \\( \\mathcal{F}: 2^{|S_y|} \\to \\mathbb{R} \\) to evaluate the utility of the subset. Submodular functions should satisfy the diminishing returns property. If a submodular function is monotone, a greedy algorithm [38] can be used to find a solution within a constant factor of the optimal one. We propose the following monotone submodular function to select the subset \\( C_y \\) from the candidate set \\( S_y \\):" + }, + { + "type": "equation", + "bbox": [ + 0.092, + 0.464, + 0.47, + 0.519 + ], + "angle": 0, + "content": "\\[\n\\mathcal {F} \\left(C _ {y}\\right) = \\underbrace {\\alpha \\cdot \\sum_ {c \\in C _ {y}} D (c)} _ {\\text {d i s c r i m i n a b i l i t y}} + \\underbrace {\\beta \\cdot \\sum_ {c _ {1} \\in S _ {y}} \\max _ {c _ {2} \\in C _ {y}} \\phi \\left(c _ {1} , c _ {2}\\right)} _ {\\text {c o v e r a g e}}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.527, + 0.47, + 0.633 + ], + "angle": 0, + "content": "where \\( D(c) \\) denotes the discriminability score of the concept \\( c \\) and \\( \\phi(\\cdot) \\) is the intra-concept similarity. Generally, the first term tends to select more informative concepts, and the second term ensures the subset has good coverage of the candidate set. The hyperparameters \\( \\alpha \\) and \\( \\beta \\) control the weights of the two sub-functions. Here we present how to compute these two scores:" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.64, + 0.47, + 0.731 + ], + "angle": 0, + "content": "Discriminability Score. We introduce a discriminability score to encourage the selection of concepts that are aligned with many images in class \\( y \\), but few images in other classes. We first define the similarity score \\( Sim(y, c) \\) between a class and concept by taking the mean of the dot product between the images and text features:" + }, + { + "type": "equation", + "bbox": [ + 0.154, + 0.738, + 0.47, + 0.775 + ], + "angle": 0, + "content": "\\[\n\\operatorname {S i m} (y, c) = \\frac {1}{| \\mathcal {X} _ {y} |} \\sum_ {\\boldsymbol {x} \\in \\mathcal {X} _ {y}} \\boldsymbol {x} \\cdot \\mathcal {T} (c) ^ {\\top}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.785, + 0.471, + 0.831 + ], + "angle": 0, + "content": "where \\(\\mathcal{X}_y\\) is the set of training images labeled with \\(y^6\\) and \\(\\mathcal{T}\\) is the text encoder. We define the normalized class association, which measures the conditional likelihood of aligning" + }, + { + "type": "ref_text", + "bbox": [ + 0.078, + 0.838, + 0.47, + 0.864 + ], + "angle": 0, + "content": "\\( {}^{3} \\) diminishing returns property means \\( \\forall A \\subseteq B \\subseteq V \\smallsetminus v \\) ,we have \\( \\mathcal{F}\\left( {A + \\{ v\\} }\\right) - \\mathcal{F}\\left( A\\right) \\geq \\mathcal{F}\\left( {B + \\{ v\\} }\\right) - \\mathcal{F}\\left( B\\right) \\) ." + }, + { + "type": "ref_text", + "bbox": [ + 0.096, + 0.864, + 0.449, + 0.876 + ], + "angle": 0, + "content": "4 A submodular function is monotone if \\(\\forall A\\subseteq B,\\mathcal{F}(A)\\leq \\mathcal{F}(B)\\)" + }, + { + "type": "ref_text", + "bbox": [ + 0.096, + 0.876, + 0.461, + 0.888 + ], + "angle": 0, + "content": "5 Any linear combination of submodular functions is still submodular." + }, + { + "type": "ref_text", + "bbox": [ + 0.096, + 0.888, + 0.305, + 0.901 + ], + "angle": 0, + "content": "\\(^6\\)In \\(N\\)-way-\\(K\\)-shot setting, \\(|\\mathcal{X}_y| = K\\)." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.838, + 0.47, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.894, + 0.138 + ], + "angle": 0, + "content": "featurized images of a class given a concept's textual embedding, \\(\\overline{Sim}(y|c) = Sim(y, c) / \\sum_{y' \\in \\mathcal{Y}} Sim(y', c)\\), and compute its negative entropy:" + }, + { + "type": "equation", + "bbox": [ + 0.548, + 0.145, + 0.894, + 0.18 + ], + "angle": 0, + "content": "\\[\nD (c) = \\sum_ {y ^ {\\prime} \\in Y} \\overline {{S i m}} \\left(y ^ {\\prime} | c\\right) \\cdot \\log \\left(\\overline {{S i m}} \\left(y ^ {\\prime} | c\\right)\\right) \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.188, + 0.893, + 0.234 + ], + "angle": 0, + "content": "Maximizing \\( D(c) \\) will result in the selection of concepts that have peaked \\( \\overline{Sim}(y|c) \\), indicating that a concept is strongly associated with only a few classes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.24, + 0.895, + 0.361 + ], + "angle": 0, + "content": "**Coverage Score.** The second term of equation 2 is a minimax facility location function that tries to minimize the maximum distance between each element in the subset and the candidate set. For distance, we use the cosine between the features of the two concepts extracted by the text encoder: \\(\\phi(c_1, c_2) = \\cos(\\mathcal{T}(c_1), \\mathcal{T}(c_2))\\). A high coverage score yields a diverse bottleneck that covers different possible appearances for a target class." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.37, + 0.81, + 0.387 + ], + "angle": 0, + "content": "3.3. Optimize Class-concept Association" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.393, + 0.894, + 0.424 + ], + "angle": 0, + "content": "In this section, we explain how we compute \\( g \\) (the concept predictor) and learn \\( f \\) (the label predictor) of the bottleneck." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.43, + 0.894, + 0.535 + ], + "angle": 0, + "content": "Predict the Concept Scores. The concept predictor \\( g \\) is not learned in our method because the alignment model we use can measure the correlation between image and text through dot product. We treat the dot product of input image feature \\( \\mathbf{x} \\) and the concept space \\( \\mathbf{E}_C \\) defined in Section 3.2 as \\( g \\): \\( g(\\mathbf{x},\\mathbf{E}_C) = \\mathbf{x}\\cdot \\mathbf{E}_C^\\top \\), where \\( g(\\mathbf{x},\\mathbf{E}_C)\\in \\mathbb{R}^{N_C} \\), and each element is the score of image \\( \\mathbf{x} \\) on a concept." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.541, + 0.895, + 0.732 + ], + "angle": 0, + "content": "Concept Weight Matrix. We learn a linear function for the label predictor \\( f \\) that maps from concept scores to the final prediction. Intuitively, these weights encode the affinity of the concept to the class, allowing the model to represent that classes depend differently on the same concept. To normalize the class-concept association distributed over the weight matrix, we regularize the matrix with the softmax activation function. Concretely, we learn a concept weight matrix \\( \\mathbf{W} \\in \\mathbb{R}^{N \\times N_C} \\), that is used for prediction: \\( \\hat{y} = \\operatorname{argmax}\\left(g(\\mathbf{x},\\mathbf{E}_C)\\cdot \\sigma (\\mathbf{W})^\\top\\right) \\), in which \\( \\sigma (\\cdot) \\) is the softmax activation which is applied along the concepts axis: \\( \\mathbf{W}_{y,c} = e^{\\mathbf{W}_{y,c}} / \\sum_{y'\\in \\mathcal{Y}}e^{\\mathbf{W}_{y',c}} \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Initializing the Weight Matrix with Language Priors. Previous work trains the concept weight matrix freely from scratch, which is not feasible in low-resource scenarios where we don't have enough data to learn the weight effectively. To extend the application of CBM to few-shot image classification, we consider biasing the weights toward the initial association from the language model used to propose concepts. If a concept \\( c \\) was present in \\( C_y \\), we initialize the elements of \\( W \\) corresponding to the weight between class \\( y \\) and concept \\( c \\) to a higher value before optimization: \\( W_{y,c} = 1 \\), if \\( c \\in C_y \\), otherwise 0." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "19190" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.092, + 0.09, + 0.287, + 0.187 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.293, + 0.091, + 0.484, + 0.187 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.487, + 0.091, + 0.678, + 0.187 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.685, + 0.091, + 0.877, + 0.187 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.091, + 0.19, + 0.285, + 0.287 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.291, + 0.19, + 0.483, + 0.286 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.489, + 0.19, + 0.681, + 0.286 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.687, + 0.19, + 0.88, + 0.286 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.091, + 0.29, + 0.284, + 0.387 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.291, + 0.29, + 0.483, + 0.387 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.489, + 0.29, + 0.681, + 0.387 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.687, + 0.29, + 0.88, + 0.387 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.4, + 0.891, + 0.415 + ], + "angle": 0, + "content": "Figure 3. Test accuracy \\((\\%)\\) comparison between LaBo and Linear Probe on 11 datasets. The x-axis represents the number of labeled images." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.429, + 0.295, + 0.446 + ], + "angle": 0, + "content": "3.4. Prepare the Candidates" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.453, + 0.473, + 0.621 + ], + "angle": 0, + "content": "To collect the candidates \\( S \\) to feed into our model, we prompt GPT-3 to generate relevant sentences by incorporating the class name in 5 templates shown in supplementary materials. For example, as shown in the top-left of Figure 2, we prompt GPT-3 by asking \"describe what the axolotl looks like\", and the GPT-3 returns a sentence about the target class. We obtain 500 sentences for each class and automatically split these sentences into shorter concepts using a T5 model [45] fine-tuned on a small set of annotated sentence-concept pairs. We use string match to identify and remove class name tokens in each concept. (see supplementary)" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.635, + 0.27, + 0.654 + ], + "angle": 0, + "content": "4. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.661, + 0.47, + 0.708 + ], + "angle": 0, + "content": "We evaluate our method on a diverse set of 11 datasets (Section 4.1) and compare it to its end-to-end counterpart and other interpretable CBM methods (Section 4.2)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.718, + 0.173, + 0.733 + ], + "angle": 0, + "content": "4.1. Dataset" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.742, + 0.473, + 0.864 + ], + "angle": 0, + "content": "We select a comprehensive benchmark of 11 image classification datasets spanning a diverse set of domains, including (1) Common objects: ImageNet [11], CIFAR-10 and CIFAR-100 [26]; (2) Fine-grained objects: Food-101 [3], FGVC-Aircraft [32], Flower-102 [39], CUB-200-2011 [67]; (3) Actions: UCF-101 [59]; (4) Textures: DTD [10]; (5) Skin tumors: HAM10000 [64] and (6) Satellite images: RE-SISC45 [8]. We use train/dev/test splits for all the datasets." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.43, + 0.894, + 0.522 + ], + "angle": 0, + "content": "Detailed statistics are presented in the supplementary material. We follow the few-shot evaluation protocol proposed by CLIP [44] with 1, 2, 4, 8, and 16 images randomly sampled from the training set for each class. We also evaluate in the fully-supervised setting where we train on all available images. For all experiments, we report the test accuracy." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.528, + 0.608, + 0.543 + ], + "angle": 0, + "content": "4.2. Baselines" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.551, + 0.892, + 0.582 + ], + "angle": 0, + "content": "We compare our model, LaBo, with black-box linear probing and two interpretable methods." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.587, + 0.894, + 0.664 + ], + "angle": 0, + "content": "Linear Probe Following previous evaluations on CBM [25, 70], linear probing serves as our primary baseline for comparison. We follow the implementation of CLIP [44] by training the scikit-learn's L-BFGS logistic regression with a hyperparameter sweep on the L2 regularization weight." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.668, + 0.892, + 0.729 + ], + "angle": 0, + "content": "PCBM Post-hoc Concept Bottleneck Model [70] designs a residual modeling step that directly maps the original image embedding into the label space. PCBM treats the attributes of each class in ConceptNet [60] as concepts." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.734, + 0.894, + 0.78 + ], + "angle": 0, + "content": "CompDL Compositional Derivation Learning [71] learns a linear layer over CLIP similarity scores between human-designed class descriptions and images to predict targets." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.787, + 0.717, + 0.803 + ], + "angle": 0, + "content": "4.3. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.81, + 0.895, + 0.902 + ], + "angle": 0, + "content": "We prompt GPT-3-text-davinci-002 to generate concepts. The CLIP model is adapted from OpenAI's public repo with ViT-L/14 as the default vision backbone. We only use CLIP-RN50 as the backbone when comparing with PCBM, and ViT-B/32 with CompDL for a fair comparison. We implement the submodular function using the apricot package and" + }, + { + "type": "page_footnote", + "bbox": [ + 0.076, + 0.875, + 0.47, + 0.9 + ], + "angle": 0, + "content": "7We use the same set of prompts for all datasets except UCF-101 since it is very different to describe an action." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "19191" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.08, + 0.089, + 0.466, + 0.129 + ], + "angle": 0, + "content": "
Method124816FullAvg
Linear Probe51.6965.1372.3377.3881.5387.3872.57
LaBo (Ours)63.3568.1072.0876.1979.1185.7274.09
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.14, + 0.455, + 0.153 + ], + "angle": 0, + "content": "Table 1. Mean accuracy across all datasets, at different shots ." + }, + { + "type": "table", + "bbox": [ + 0.098, + 0.163, + 0.446, + 0.232 + ], + "angle": 0, + "content": "
Methodw/ end-to-endCIFAR-10CIFAR-100
PCBM [70]✗84.556.0
LaBo (Ours)✗87.969.1
PCBM-h [70]✓87.669.9
Linear Probe✓88.870.1
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.243, + 0.47, + 0.299 + ], + "angle": 0, + "content": "Table 2. Test accuracy comparison between LaBo and Post-hoc Concept Bottleneck Model (PCBM) on CIFAR-10 and CIFAR-100. \"w/ end-to-end\" denotes whether the model employs an end-to-end residual predictor from image features to targets." + }, + { + "type": "table", + "bbox": [ + 0.098, + 0.307, + 0.446, + 0.364 + ], + "angle": 0, + "content": "
Methodw/ manual concepts15Full
CompDL [71]✓13.633.252.6
LaBo (Ours)✗35.155.771.8
Linear Probe-28.455.475.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.078, + 0.375, + 0.468, + 0.388 + ], + "angle": 0, + "content": "Table 3. LaBo and CompDL evaluated on CUB for 1/5/full shots." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.404, + 0.469, + 0.509 + ], + "angle": 0, + "content": "set the default number of concepts selected for each class to 50. To train the linear function, we use the Pytorch-lightning library with Adam [24] optimizer. We tune the batch size, learning rate, and submodular weights on the development set. Model checkpoints with the highest validation accuracy are evaluated on the test set. We list the hyperparameters for all datasets and shots in the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.523, + 0.194, + 0.538 + ], + "angle": 0, + "content": "5. Evaluation" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.547, + 0.216, + 0.562 + ], + "angle": 0, + "content": "5.1. Main Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.57, + 0.47, + 0.616 + ], + "angle": 0, + "content": "We compare LaBo's performance with a linear probe and other interpretable baselines to evaluate if we can maintain black box accuracy without sacrificing interpretability." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.622, + 0.47, + 0.757 + ], + "angle": 0, + "content": "Comparison with End-to-End Model. One of our goals is to close the performance gap between interpretable and black box models. Table 1 reports the mean test accuracy of LaBo and the linear probe on 11 datasets. LaBo significantly outperforms the end-to-end model when little data is available and continues to be competitive as the number of data increases. On average, LaBo surpasses the linear probe by \\(1.5\\%\\). Figure 3 provides analytic performance comparisons between LaBo and Linear Probe on each dataset." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.758, + 0.471, + 0.865 + ], + "angle": 0, + "content": "In general, LaBo's performance depends on the quality of knowledge extracted from GPT-3. For common categories, GPT-3 contains high-quality knowledge allowing substantial improvement over linear probes. For some fine-grained datasets, such as Flower-102, GPT-3's knowledge is largely non-visual, as seen in Figure 7. In such cases, specialized language models could be used to improve LaBo." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Comparison with other Interpretable Methods. Table 2 compares LaBo's performance with PCBM and Linear Probe." + }, + { + "type": "table", + "bbox": [ + 0.51, + 0.09, + 0.882, + 0.18 + ], + "angle": 0, + "content": "
n. of concepts per class (k)n. of shots
124816Full
141.8952.4561.7665.9969.6178.95
552.5461.1367.2272.9075.6283.83
1058.0064.5969.9074.5077.4384.66
2561.7266.3371.3975.2879.0485.26
5063.0367.7971.8876.0879.1085.71
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.192, + 0.894, + 0.22 + ], + "angle": 0, + "content": "Table 4. Ablation results on bottleneck sizes. We vary the sizes of the bottlenecks and report the average performance on 11 datasets." + }, + { + "type": "table", + "bbox": [ + 0.51, + 0.231, + 0.88, + 0.322 + ], + "angle": 0, + "content": "
Selection Methodn. of shots
124816Full
RANDOM59.2464.7170.4274.0778.2985.06
SIMILARITY54.5961.4267.1772.6677.3284.88
COVERAGE59.7365.9370.8274.7178.9085.60
DISCRIM60.9966.4970.9374.8177.9085.31
SUBMODULAR63.0367.7971.8876.0879.1085.71
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.332, + 0.892, + 0.36 + ], + "angle": 0, + "content": "Table 5. Ablation results on concept selection methods. We report mean test accuracy on 11 datasets." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.376, + 0.894, + 0.453 + ], + "angle": 0, + "content": "LaBo outperforms PCBM by \\(3.4\\%\\) on CIFAR-10 and \\(13.1\\%\\) on CIFAR-100. LaBo maintains comparable performance to PCBM with a residual predictor (PCBM-h), without circumventing the bottleneck. In Table 3, LaBo is more accurate than CompDL [71] without manually constructed concepts." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.461, + 0.654, + 0.478 + ], + "angle": 0, + "content": "5.2. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.485, + 0.894, + 0.545 + ], + "angle": 0, + "content": "We evaluate the importance of each of our model's components on final performance. Specifically, we compare results with different concept selection methods, language and random weight initialization, and bottleneck sizes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.553, + 0.895, + 0.78 + ], + "angle": 0, + "content": "Concept Selection Methods. We compare our submodular function with four concept selection methods: (1) RANDOM: we randomly sample a subset of concepts from the candidates for each class; (2) SIMILARITY: we select the top concepts ranked by their similarity scores with the class calculated by equation 3; (3) COVERAGE: we only consider the coverage score for concept selection; (4) DISCRIM: we only consider the discriminability score for concept selection. As shown in Table 5, our submodular function, which jointly optimizes coverage and discriminability, achieves the best performance across different numbers of shots. We notice that using coverage or discriminability alone still outperforms using similarity between the class and random selection. The selection method plays an important role in all data settings, but its impact decreases with more supervision." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.787, + 0.894, + 0.849 + ], + "angle": 0, + "content": "Initialization with Language Priors. We deactivate the LM initialization and use random initialization instead. Figure 4 shows that the LM prior is more important for low shot settings since there is less signal to guide concept importance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Bottleneck Size. In Table 4, we compare performance for different bottleneck sizes ranging from 1 to 50 concepts selected by the submodular function. Larger bottlenecks are" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "19192" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.092, + 0.465, + 0.215 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.23, + 0.47, + 0.259 + ], + "angle": 0, + "content": "Figure 4. Language Prior vs. Random Weight initialization average over all datasets." + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.265, + 0.456, + 0.332 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.337, + 0.456, + 0.404 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.417, + 0.473, + 0.475 + ], + "angle": 0, + "content": "Figure 5. Human evaluation on Factuality and Groundability for different bottlenecks on ImageNet. \"w/o Submod\" denotes without submodular function, i.e., random concept selection. \"w/o LM\" denotes no language prior weight initialization." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.49, + 0.47, + 0.52 + ], + "angle": 0, + "content": "usually better, but with more data, similar performance is achievable with smaller bottlenecks." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.541, + 0.262, + 0.556 + ], + "angle": 0, + "content": "5.3. Human Evaluation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.565, + 0.473, + 0.807 + ], + "angle": 0, + "content": "It is important for interpretability that the vision-language alignment model correctly grounds concepts to images. For example, if a concept \"usually round\" ranks both circles and stripes highly, the name of the attribute does not faithfully represent the computation. In addition, it is important that the automatically generated concept bottlenecks factually correspond to the class they describe. To this end, we introduce two metrics to evaluate the quality of our concept bottleneck items: (1) Factuality measures how accurate the concepts are in describing their designated class by requiring annotators to judge whether they describe ground truth images, and (2) Groundability measures how consistent the vision-language model grounding of the concepts to images with human interpretations by requiring annotators to judge their applicability on the top-10 images ranked by CLIP alignment scores." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.816, + 0.471, + 0.862 + ], + "angle": 0, + "content": "Setup. Both metrics are computed by asking annotators to select images that describe a highly ranked concept in our bottlenecks. Formally, the two metrics are represented by:" + }, + { + "type": "equation", + "bbox": [ + 0.104, + 0.872, + 0.443, + 0.906 + ], + "angle": 0, + "content": "\\[\n\\operatorname {F a c t u a l i t y} (c) = \\frac {\\text {n u m b e r o f i m a g e s s e l e c t e d}}{k \\text {g r o u n d t r u t h i m a g e s o f t h e c l a s s}}\n\\]" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.092, + 0.885, + 0.216 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.23, + 0.892, + 0.259 + ], + "angle": 0, + "content": "Figure 6. Percentage of invalid concepts identified by humans for different bottlenecks on ImageNet. Lower percentage is better." + }, + { + "type": "table", + "bbox": [ + 0.508, + 0.261, + 0.88, + 0.35 + ], + "angle": 0, + "content": "
MetricsLaBow/o Submodw/o LM
Factuality (%) ↑24.022.814.1
Groundability (%) ↑14.122.520.2
Non Visual (%) ↓4.85.65.8
Non Sensical (%) ↓8.09.68.7
Unknown Vocab (%) ↓10.210.510.7
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.36, + 0.894, + 0.403 + ], + "angle": 0, + "content": "Table 6. Average human evaluation results of LaBo on 11 datasets. We also evaluate LaBo by removing the submodular function (w/o Submod) and language model priors (w/o LM)." + }, + { + "type": "equation", + "bbox": [ + 0.508, + 0.418, + 0.882, + 0.451 + ], + "angle": 0, + "content": "\\[\n\\operatorname {G r o u n d a b i l i t y} (c) = \\frac {\\text {n u m b e r o f i m a g e s s e l e c t e d}}{\\text {t o p - k a l i n g e d i m a g e s o f t h e c o n c e p t}}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.457, + 0.895, + 0.594 + ], + "angle": 0, + "content": "where we set \\( k = 10 \\). In addition to the two main metrics, we ask the annotator to select whether the concept is non-visual, nonsensical, or contains unknown vocabulary. We randomly sample 20 classes for each dataset and evaluate the top 5 concepts (ranked by the weights of the linear function) for each class, 100 concepts per dataset. We release our human evaluation task on Amazon Mechanical Turk and collect three annotations for each concept. More details on the task and the results can be found in the supplement." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.601, + 0.895, + 0.767 + ], + "angle": 0, + "content": "Baselines. We evaluate the bottlenecks under full supervision and compare them with two main baselines: (1) LaBo (w/o Submod), which randomly selects the concepts instead of using the submodular function, and (2) LaBo (w/o LM), which initializes the concept weight matrix randomly without leveraging the priors of the language model. For ImageNet, we add two additional baselines using human-written text: (1) WordNet [13] definitions and (2) Wikipedia sentences [22]. We adopt the same preprocessing pipeline as LaBo to extract concepts from human-written resources and utilize the submodular function to select the bottlenecks." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.775, + 0.894, + 0.867 + ], + "angle": 0, + "content": "Results. Figure 5 shows the evaluation on ImageNet, and we observe that LaBo has significantly higher Factuality and Groundability than human-written text. We further observe that removing components from our system (submodular and LM Prior) hurt both human evaluation metrics, indicating their collective importance in our system. In addition, Figure" + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.875, + 0.892, + 0.901 + ], + "angle": 0, + "content": "With the only exception of Factuality for Flower-102 where we set \\( k = 8 \\) because there are not enough images in the dev set." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19193" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.084, + 0.09, + 0.887, + 0.484 + ], + "angle": 0, + "content": "
Class NameTop-3 ConceptsClass NameTop-3 ConceptsClass NameTop-3 ConceptsClass NameTop-3 Concepts
ImageNetbadger1. short legs and long body make it an excellent diggerant1. black and red stingerhammer1.long, thin tool with a wooden handlewater buffalo1. large head with short, curved horns
2. black-and-white striped fur2. black-and-white striped fur2. small, black insect with six legs2. small, black insect with six legs2. great tool for pounding object2. great tool for pounding object2. heaviest living species of bovid2. heaviest living species of bovid
3. coat is very shaggy3. coat is very shaggy3. long, slender antennae that it uses to smell and touch3. long, slender antennae that it uses to smell and touch3. used to pound on surfaces3. used to pound on surfaces3. huge, dark-colored animal3. huge, dark-colored animal
CUBeared grebe1. black and white plumage that is striking in the sunlighthorned lark1. black line running through yellow facewhite pelican1. long neck and bill make it look like a giant swanarctic tern1. breeds in greenland, iceland, and northern russia
2. black body with a long, slender neck2. black body with a long, slender neck2. head is black with a white horn on each side2. head is black with a white horn on each side2. large, white bird with black wings2. large, white bird with black wings2. large, white birds2. black and white markings
3. red and black bill3. red and black bill3. black horn on each side of their head3. black horn on each side of their head3. bill is huge and yellow3. bill is huge and yellow3. bill is huge and yellow3. small white bird with a black cap
Flowerwater lily1. depicted in artworks of ponds and waterfallbarbeton daisy1. scientific name for the flower is taraxacum officinalmarigold1. central disc with smaller floretstiger lily1. long, protruding stamen
2. member of the nymphaceae family2. member of the nymphaceae family2. named after the city of barberton2. named after the city of barberton2. have a slightly furry texture2. have a slightly furry texture2. have a slightly furry texture2. orange with black spots and stripes
3. lily pads float3. lily pads float3. member of the daisy family3. member of the daisy family3. bold and vibrant color palette3. bold and vibrant color palette3. bold and vibrant color palette3. bold and vibrant color palette
UCF-101archery1. grip bow tightly in their left handdrumming1. blur as they fly over the drumssurfing1. deep blue colorlong jump1. get out of sandpit
2. focused and concentrated on their task2. focused and concentrated on their task2. sitting on a stool in front of a drum set2. sitting on a stool in front of a drum set2. tans contrast with the white of their boards2. tans contrast with the white of their boards2. tans contrast with the white of their boards2. series of movements starting from a standing position
3. keep bow and arrows in safe and dry place when not in use3. keep bow and arrows in safe and dry place when not in use3. position the drumstick so it is resting on your index finger3. position the drumstick so it is resting on your index finger3. sending a spray of water into the air3. sending a spray of water into the air3. person tucks their knees up to chest3. person tucks their knees up to chest
HAM100000dermatofibroma1. generally not painfulmelanoma1. dark brown or black in colormelanocytic nevi1. color is tanbenign lesions1. color ranges from light brown to black
2. red, brown, or purple in color2. red, brown, or purple in color2. large and dark2. large and dark2. dark brown or black color2. dark brown or black color2. dark brown or black color2. rough or scaly texture
3. thin white halo around them3. thin white halo around them3. flesh-colored, brown, or black3. flesh-colored, brown, or black3. small, round, and slightly raised3. small, round, and slightly raised3. small, round, and slightly raised3. dark brown or black
" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.496, + 0.893, + 0.525 + ], + "angle": 0, + "content": "Figure 7. Several example bottlenecks generated by LaBo. The top-3 concepts, ranked by their weights in the linear function, for randomly selected classes, paired with a random image from the class, across 6 datasets." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.54, + 0.473, + 0.722 + ], + "angle": 0, + "content": "6 shows that LaBo has significantly fewer invalid concepts than other baselines. Table 6 summarizes the average human evaluation results over the 11 datasets9. On average, we observe a trade-off between Factuality and Groundability. Increasing coverage and discriminability leads to more variable and specific concepts that CLIP finds more difficult to ground. This could be due to challenges in capturing composite concepts [33, 71]. For individual analysis of the datasets, refer to the supplementary material. Finally, Figure 7 shows several CBMs we constructed. Across many types of tasks, the bottlenecks are largely coherent, factual, and groundable by CLIP." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.735, + 0.327, + 0.751 + ], + "angle": 0, + "content": "6. Conclusion and Limitation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.761, + 0.47, + 0.866 + ], + "angle": 0, + "content": "Overall, our approach demonstrates that the accuracy and interpretability of vision systems may be less at odds than previously believed. Leveraging LLMs was crucial, as they encode important visual knowledge. In the future, our approach can easily be enriched with new factors that capture different priors on bottleneck construction. The limits of knowledge in GPT-3 are not known, but likely there are" + }, + { + "type": "page_footnote", + "bbox": [ + 0.077, + 0.875, + 0.469, + 0.901 + ], + "angle": 0, + "content": "The low resolution of CIFAR images partially affects those metrics since annotators have greater difficulty in completing the task." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.54, + 0.895, + 0.691 + ], + "angle": 0, + "content": "domains where prompting generates few useful facts. Even in contexts where GPT-3 can generate useful information, our method depends on CLIP being able to recognize those aspects in images. The alignment between GPT-3 and CLIP likely does not hold for all cases. Future work could focus on dynamically prompting GPT-3 to make this coupling more robust. Finally, our work depends on large models trained at scales that are not currently reproducible. It is possible unrevealed aspects of training by OpenAI will require a reevaluation of our claims." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.708, + 0.667, + 0.725 + ], + "angle": 0, + "content": "Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.895, + 0.901 + ], + "angle": 0, + "content": "This research is based upon work supported in part by the DARPA KAIROS Program (contract FA8750-19-2-1004), the DARPA LwLL Program (contract FA8750-19-2-0201), the IARPA BETTER Program (contract 2019-19051600004), the IARPA HIATUS Program (contract 2022-22072200005), the NSF (Award 1928631), and an AI2 Young Investigator Award. Approved for Public Release, Distribution Unlimited. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies, either expressed or implied, of ODNI, DARPA, IARPA, NSF, or the U.S. Government." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19194" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.117, + 0.472, + 0.159 + ], + "angle": 0, + "content": "[1] Francis Bach. Convex analysis and optimization with submodular functions: a tutorial. arXiv preprint arXiv:1010.4207, 2010.4" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.163, + 0.472, + 0.233 + ], + "angle": 0, + "content": "[2] David Bau, Bolei Zhou, Aditya Khosla, Aude Oliva, and Antonio Torralba. Network dissection: Quantifying interpretability of deep visual representations. 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They allow people to easily understand why a model is failing, a critical feature for high-stakes applications. CBMs require manually specified concepts and often under-perform their black box counterparts, preventing their broad adoption. We address these shortcomings and are first to show how to construct high-performance CBMs without manual specification of similar accuracy to black box models. Our approach, Language Guided Bottlenecks (LaBo), leverages a language model, GPT-3, to define a large space of possible bottlenecks. Given a problem domain, LaBo uses GPT-3 to produce factual sentences about categories to form candidate concepts. LaBo efficiently searches possible bottlenecks through a novel submodular utility that promotes the selection of discriminative and diverse information. Ultimately, GPT-3's sentential concepts can be aligned to images using CLIP, to form a bottleneck layer. Experiments demonstrate that LaBo is a highly effective prior for concepts important to visual recognition. In the evaluation with 11 diverse datasets, LaBo bottlenecks excel at few-shot classification: they are $11.7\%$ more accurate than black box linear probes at 1 shot and comparable with more data. Overall, LaBo demonstrates that inherently interpretable models can be widely applied at similar, or better, performance than black box approaches.1 + +# 1. Introduction + +As deep learning systems improve, their applicability to critical domains is hampered because of a lack of transparency. Efforts to address this have largely focused on post-hoc explanations [47, 54, 72]. Such explanations can be problematic because they may be incomplete or unfaithful with respect to the model's computations [49]. Models + +![](images/3fc95e6605ad9afb030fa06ad63b42f2342bef796caf7c2950867a55beb5efcb.jpg) +Figure 1. Our proposed high-performance Concept Bottleneck Model alleviates the need for human-designed concepts by prompting large language models (LLMs) such as GPT-3 [4]. + +can also be designed to be inherently interpretable, but it is believed that such models will perform more poorly than their black box alternatives [16]. In this work, we provide evidence to the contrary. We show how to construct high-performance interpretable-by-design classifiers by combining a language model, GPT-3 [4], and a language-vision model, CLIP [44]. + +Our method builds on Concept Bottleneck Models (CBM) [25], which construct predictors through a linear combination of human-designed concepts. For example, as seen in Figure 1, a qualified person can design concepts, such as "nape color," as intermediate targets for a black box model before classifying a bird. CBMs provide abstractions that people can use to understand errors or intervene on, contributing to increased trust. + +Application of CBMs is limited because they require costly attribute annotations by domain experts and often under-perform their black box counterparts. In contexts where CBM performance is competitive with black box alternatives, interpretability properties are sacrificed [34, 70]. To address both of these challenges, we propose to build systems that automatically construct CBMs. + +Our Language Model Guided Concept Bottleneck Model (LaBo), Figure 2, allows for the automatic construction of high-performance CBMs for arbitrary classification problems without concept annotations. Large language models + +![](images/2e14f5129572f4a18e139a0c44fe81cd78931d81488b23059e1180d938b8b073.jpg) +Figure 2. We present an overview of our Language-Model-Guided Concept Bottleneck Model (LaBo), which is interpretable by design image classification system. First, we prompt the large language model (GPT-3) to generate candidate concepts (Sec 3.4). Second, we employ a submodular function to select concepts from all candidates to construct the bottleneck (Sec 3.2). Third, we apply a pretrained alignment model (CLIP) to obtain the embeddings of concepts and images, which is used to compute concept scores. Finally, we train a linear function in which the weight $W$ denotes the concept-class association user to predict targets based on concept scores (Sec 3.3). + +(LLMs) contain significant world knowledge [21, 42, 61], that can be elicited by inputting a string prefix and allowing LLMs to complete the string (prompting). For example, in Figure 1, GPT-3 is prompted about sparrows and completes with information such as "brown head with white stripes." LaBo leverages this by constructing bottlenecks where the concepts are such GPT-3 generated sentences. Since our concepts are textual, we use CLIP to score their presence in an image and form a bottleneck layer out of these scores. + +A key advantage of LaBo is the ability to control the selection of concepts in the bottleneck by generating candidates from the language model. We develop selection principles targeting both interpretability and classification accuracy. For example, we prefer smaller bottlenecks that include shorter sentences that do not include class names. Furthermore, to maximize performance, we prefer attributes that CLIP can easily recognize and are highly discriminative. To account for appearance variation, we select attributes that cover a variety of information and are not repetitive. We formulate these factors into a novel sub-modular criterion that allows us to select good bottlenecks efficiently [38]. + +We have evaluated LaBo-created bottlenecks on 11 diverse image classification tasks, spanning recognition of common objects [11,26] to skin tumors [64]. fine-grained types [3, 32, 39, 67], textures [10], actions [59], skin tumors [64], and satellite photographed objects [8].2 Our + +main finding is that LaBo is a highly effective prior for what concepts to look for, especially in low data regimes. In evaluations comparing with linear probes, LaBo outperforms by as much as $11.7\%$ at 1-shot and marginally underperforms given larger data settings. Averaged over many dataset sizes, LaBo bottlenecks are $1.5\%$ more accurate than linear probes. In comparison to modifications of CBMs that improve performance by circumventing the bottleneck [70], we achieve similar or better results without breaking the CBM abstraction. In extensive ablations, we study key trade-offs in bottleneck design and show our selection criteria are crucial and highlight several other critical design choices. + +Human evaluations indicate that our bottlenecks are largely understandable, visual, and factual. Finally, annotators find our GPT-3 sourced bottlenecks are more factual and groundable than those constructed from WordNet or Wikipedia sentences. Overall, our experiments demonstrate that automatically designed CBMs can be as effective as black box models while maintaining critical factors contributing to their interpretability. + +# 2. Related Work + +Broadly, interpretability methods fall into two categories: + +post-hoc and by design. While ours is an instance of the latter, post-hoc methods have the advantage of not imposing any model constraints. For example, Gradient-weighted Class Activation Mapping approaches [2, 19, 36, 54] trace network gradients to identify the input areas that guide predictions. Similarly, Explanation Generation methods [17, 23, 40, 57] require models to produce explanations for visual tasks by conditioning their predictions on captioning models and [18, 41] incorporate visual evidence to ground explanations. + +Despite their advantages, there is no guarantee that post-hoc methods faithfully represent model reasoning [49]. In contrast, our work falls under interpretable by design methods, which constrain explanations to align with the model's reasoning. For example, Prototype methods [6,37,51,58,66] optimize a metric space that guides classification by computing distances to prototype representations of each class. While such methods identify important regions in the input for classification, they still require featurized region representations that obfuscate the semantic content of the region. + +This work extends another family of interpretable by design methods known as Concept Bottleneck Models [25, 52]. Following early attempts in few shot learning [27] and attribute learning [50, 68], CBMs predict targets by linearly combining an intermediate layer of human-understandable attributes. Recently, Computational Derivation Learning (CompDL) [71] proposed a CBM architecture that applies a linear layer over CLIP scores between human expert designed concepts and images to predict targets in the context of an evaluation framework to measure how well CLIP grounds concepts. CBMs generally suffer from the need for costly class description annotations and lower performance compared to end-to-end counterparts. Post-hoc Concept Bottleneck (PCBM) [70] was proposed to fill these two gaps by leveraging information from a static knowledge base, such as ConceptNet [60], and adding a residual connection from image features to the final prediction to improve accuracy [70]. However, PCBMs cannot be expanded to larger-scale (e.g., ImageNet [11]) or domain-specific tasks (e.g., fine-grained [32]) because knowledge bases have limited coverage. In addition, they include a residual predictor, which effectively ensembles CBM with an end-to-end model, undermining interpretability. + +Inspired by previous work on using textual knowledge to guide vision models [5,22,48,55], we circumvent the requirement for external knowledge bases, and instead query LLMs to collect concepts. We remove the need for direct mapping from image features to targets by fully automating the extraction and filtering of LLM knowledge. Our model surpasses end-to-end models in few shot scenarios and achieves comparable performance in large data settings, while concurrent work [35] only evaluates on zero-shot settings. + +Our work capitalizes on improvements in vision-language pretraining from earlier BERT-based models + +[7, 30, 31, 62] to more scalable contrastive architectures [20, 28, 44, 69], which are very effective for few shot image classification [9, 63]. + +Our work can be viewed as interpretability-focused prompt tuning of CLIP [44]. Significant efforts have been devoted to prompting vision language models [12, 14, 29, 43, 46, 73, 74]. These focus on searching over text prompts to improve classification performance, and resemble earlier techniques in LLM prompt tuning [15, 53, 56]. + +# 3. Method + +Figure 2 presents an overview of our method. Our model prompts a large language model, GPT-3 [4] to generate a set of candidate concepts for each class (Section 3.4). We employ submodular optimization to greedily select a subset of concepts for each class such that we maximize discriminability and diversity (Section 3.2). We then align the selected concepts to images using CLIP [44]. We apply a linear layer over the similarity scores of concepts and images to learn a weight matrix representing the importance of each concept in the final classification. This weight matrix is initialized using a language model prior from GPT-3 (Section 3.3). + +# 3.1. Problem Formulation + +Consider a training set of image-label pairs $\mathcal{D} = \{(i,y)\}$ where $i$ is the image and $y\in \mathcal{V}$ , is a label from a set of $N$ classes. Suppose we have a pretrained multimodal alignment model (e.g., CLIP [44]), which has an image encoder $\mathcal{I}$ and a text encoder $\mathcal{T}$ . $\mathcal{I}$ and $\mathcal{T}$ can map images and text into the shared feature space, respectively. The dot product of the image and text features reflects the alignment score between the two modalities. We extract the features of all images in $\mathcal{D}$ as $\pmb{x} = \mathcal{I}(i)\in \mathbb{R}^d$ , and the dataset can be represented as $\mathcal{D} = \{(x,y)\}$ . Let $S$ be the superset of candidate textual concepts generated from language models. We use a submodular function $\mathcal{F}$ to select a bottleneck, $C$ , where $C\subseteq S$ , made of $N_{C}$ concepts, $C = \{c_1,c_2,\dots ,c_{N_C}\}$ . We can construct a bottleneck embedding, $\pmb{E}_{C}\in \mathbb{R}^{N_{C}\times d}$ , and each row of $\pmb{E}_{C}$ is the text feature $\mathcal{T}(c)\in \mathbb{R}^d$ of a concept $c$ extracted by the text encoder $\mathcal{T}$ . + +Concept bottleneck models produce a prediction by composing two functions, $\hat{y} = f\left(g(\boldsymbol{x},\boldsymbol{E}_C)\right)$ , in which $g: \mathbb{R}^d \to \mathbb{R}^{N_C}$ maps the image feature to a score for every element of the bottleneck and $f: \mathbb{R}^{N_C} \to \mathcal{V}$ makes the final prediction on the label space given the concept scores. In our setting, we find a bottleneck $C$ and appropriate $f$ by solving the following minimization problem: + +$$ +\min _ {f, C} \underset {(\boldsymbol {x}, y) \sim \mathcal {D}} {\mathbb {E}} \left[ \mathcal {L} \left(f (g (\boldsymbol {x}, \boldsymbol {E} _ {C})) , y\right) \right] - \mathcal {F} (C, \mathcal {D}) \tag {1} +$$ + +in which $\mathcal{L}(\hat{y}, y)$ is the cross-entropy loss on the label prediction and $\mathcal{F}(C, \mathcal{D})$ is the quality of the bottleneck as measured by the submodular function. In practice, we optimize + +sequentially: we first find a high scoring $C$ under $\mathcal{F}$ . Then, we use the dot product of image and concept embeddings as $g$ . Finally, we find an $f$ that minimizes $\mathcal{L}$ . In the following sections, we will illustrate how we: construct the submodular function $\mathcal{F}$ to select a subset of concepts $C$ from the candidates $S$ (Section 3.2) and learn $f$ (Section 3.3). + +# 3.2. Submodular Concept Selection + +We create a superset of candidate concepts, $S$ , out of class-specific subsets. For every label $y \in \mathcal{V}$ , we construct $S_y$ by prompting a language model to produce textual knowledge about $y$ (Section 3.4). Instead of directly choosing $N_C$ concepts from $S$ , we select $k$ concepts for each class, such that $N \times k = N_C$ , to ensure each class has an equal number of relevant concepts in the bottleneck. + +We employ submodular optimization [1] to select a subset $C_y \subseteq S_y$ , $|C_y| = k$ . Specifically, we need to design a score function $\mathcal{F}: 2^{|S_y|} \to \mathbb{R}$ to evaluate the utility of the subset. Submodular functions should satisfy the diminishing returns property. If a submodular function is monotone, a greedy algorithm [38] can be used to find a solution within a constant factor of the optimal one. We propose the following monotone submodular function to select the subset $C_y$ from the candidate set $S_y$ : + +$$ +\mathcal {F} \left(C _ {y}\right) = \underbrace {\alpha \cdot \sum_ {c \in C _ {y}} D (c)} _ {\text {d i s c r i m i n a b i l i t y}} + \underbrace {\beta \cdot \sum_ {c _ {1} \in S _ {y}} \max _ {c _ {2} \in C _ {y}} \phi \left(c _ {1} , c _ {2}\right)} _ {\text {c o v e r a g e}}, \tag {2} +$$ + +where $D(c)$ denotes the discriminability score of the concept $c$ and $\phi(\cdot)$ is the intra-concept similarity. Generally, the first term tends to select more informative concepts, and the second term ensures the subset has good coverage of the candidate set. The hyperparameters $\alpha$ and $\beta$ control the weights of the two sub-functions. Here we present how to compute these two scores: + +Discriminability Score. We introduce a discriminability score to encourage the selection of concepts that are aligned with many images in class $y$ , but few images in other classes. We first define the similarity score $Sim(y, c)$ between a class and concept by taking the mean of the dot product between the images and text features: + +$$ +\operatorname {S i m} (y, c) = \frac {1}{| \mathcal {X} _ {y} |} \sum_ {\boldsymbol {x} \in \mathcal {X} _ {y}} \boldsymbol {x} \cdot \mathcal {T} (c) ^ {\top}, \tag {3} +$$ + +where $\mathcal{X}_y$ is the set of training images labeled with $y^6$ and $\mathcal{T}$ is the text encoder. We define the normalized class association, which measures the conditional likelihood of aligning + +${}^{3}$ diminishing returns property means $\forall A \subseteq B \subseteq V \smallsetminus v$ ,we have $\mathcal{F}\left( {A + \{ v\} }\right) - \mathcal{F}\left( A\right) \geq \mathcal{F}\left( {B + \{ v\} }\right) - \mathcal{F}\left( B\right)$ . +4 A submodular function is monotone if $\forall A\subseteq B,\mathcal{F}(A)\leq \mathcal{F}(B)$ +5 Any linear combination of submodular functions is still submodular. +$^6$ In $N$ -way- $K$ -shot setting, $|\mathcal{X}_y| = K$ . + +featurized images of a class given a concept's textual embedding, $\overline{Sim}(y|c) = Sim(y, c) / \sum_{y' \in \mathcal{Y}} Sim(y', c)$ , and compute its negative entropy: + +$$ +D (c) = \sum_ {y ^ {\prime} \in Y} \overline {{S i m}} \left(y ^ {\prime} | c\right) \cdot \log \left(\overline {{S i m}} \left(y ^ {\prime} | c\right)\right) \tag {4} +$$ + +Maximizing $D(c)$ will result in the selection of concepts that have peaked $\overline{Sim}(y|c)$ , indicating that a concept is strongly associated with only a few classes. + +**Coverage Score.** The second term of equation 2 is a minimax facility location function that tries to minimize the maximum distance between each element in the subset and the candidate set. For distance, we use the cosine between the features of the two concepts extracted by the text encoder: $\phi(c_1, c_2) = \cos(\mathcal{T}(c_1), \mathcal{T}(c_2))$ . A high coverage score yields a diverse bottleneck that covers different possible appearances for a target class. + +# 3.3. Optimize Class-concept Association + +In this section, we explain how we compute $g$ (the concept predictor) and learn $f$ (the label predictor) of the bottleneck. + +Predict the Concept Scores. The concept predictor $g$ is not learned in our method because the alignment model we use can measure the correlation between image and text through dot product. We treat the dot product of input image feature $\mathbf{x}$ and the concept space $\mathbf{E}_C$ defined in Section 3.2 as $g$ : $g(\mathbf{x},\mathbf{E}_C) = \mathbf{x}\cdot \mathbf{E}_C^\top$ , where $g(\mathbf{x},\mathbf{E}_C)\in \mathbb{R}^{N_C}$ , and each element is the score of image $\mathbf{x}$ on a concept. + +Concept Weight Matrix. We learn a linear function for the label predictor $f$ that maps from concept scores to the final prediction. Intuitively, these weights encode the affinity of the concept to the class, allowing the model to represent that classes depend differently on the same concept. To normalize the class-concept association distributed over the weight matrix, we regularize the matrix with the softmax activation function. Concretely, we learn a concept weight matrix $\mathbf{W} \in \mathbb{R}^{N \times N_C}$ , that is used for prediction: $\hat{y} = \operatorname{argmax}\left(g(\mathbf{x},\mathbf{E}_C)\cdot \sigma (\mathbf{W})^\top\right)$ , in which $\sigma (\cdot)$ is the softmax activation which is applied along the concepts axis: $\mathbf{W}_{y,c} = e^{\mathbf{W}_{y,c}} / \sum_{y'\in \mathcal{Y}}e^{\mathbf{W}_{y',c}}$ . + +Initializing the Weight Matrix with Language Priors. Previous work trains the concept weight matrix freely from scratch, which is not feasible in low-resource scenarios where we don't have enough data to learn the weight effectively. To extend the application of CBM to few-shot image classification, we consider biasing the weights toward the initial association from the language model used to propose concepts. If a concept $c$ was present in $C_y$ , we initialize the elements of $W$ corresponding to the weight between class $y$ and concept $c$ to a higher value before optimization: $W_{y,c} = 1$ , if $c \in C_y$ , otherwise 0. + +![](images/cab6e18d0b4713fa07be2038a79ada4a5bb5079d80e4e782168bdca96a1302ab.jpg) + +![](images/95ae922ab0beff4f2bd2c069ceaead5e1d3b868188cdcdb62a672297402f832d.jpg) + +![](images/c7c7fbe41ee988e069cc9f92f4dadeef073393894dba3e65caed51ff05b297b3.jpg) + +![](images/f75c5d68d878ae0cc98fdf6aefe8a698b9b5b3429473a057bbc9a7c865595883.jpg) + +![](images/7c508b006b2256322ca4a4a9beb98f8241cce6277e946f0caf0b6ab81e836749.jpg) + +![](images/6d5b506bba6c3f41d04cd446e0c1b81445fd7fcfdb21d7033703739a70ae4335.jpg) + +![](images/4bfc0fbb948348a53f2b18b931c228e3abc191ab257e212a8ea62645790b9de9.jpg) + +![](images/5c91390af6045150b79120ac020c8c65ed88889c19056f593f443249b275a1fe.jpg) + +![](images/fd61017ebc5cc7e6b60a2da0ebd60e02cc515a8ffa579300dda9a0f0d602890c.jpg) +Figure 3. Test accuracy $(\%)$ comparison between LaBo and Linear Probe on 11 datasets. The x-axis represents the number of labeled images. + +![](images/98298d1b9030a3b048a8439b85ce4629274823dbf1ab98bb6052dbbaa00218c1.jpg) + +![](images/1cdf808641182b78ac6c614f478dd536ed20ac80f45b88fb3c3a2b8089bcd393.jpg) + +![](images/0be002c05e48125fd576a388d9debfe3a3675b923a4da0c8c6890863fe0f6680.jpg) + +# 3.4. Prepare the Candidates + +To collect the candidates $S$ to feed into our model, we prompt GPT-3 to generate relevant sentences by incorporating the class name in 5 templates shown in supplementary materials. For example, as shown in the top-left of Figure 2, we prompt GPT-3 by asking "describe what the axolotl looks like", and the GPT-3 returns a sentence about the target class. We obtain 500 sentences for each class and automatically split these sentences into shorter concepts using a T5 model [45] fine-tuned on a small set of annotated sentence-concept pairs. We use string match to identify and remove class name tokens in each concept. (see supplementary) + +# 4. Experimental Setup + +We evaluate our method on a diverse set of 11 datasets (Section 4.1) and compare it to its end-to-end counterpart and other interpretable CBM methods (Section 4.2). + +# 4.1. Dataset + +We select a comprehensive benchmark of 11 image classification datasets spanning a diverse set of domains, including (1) Common objects: ImageNet [11], CIFAR-10 and CIFAR-100 [26]; (2) Fine-grained objects: Food-101 [3], FGVC-Aircraft [32], Flower-102 [39], CUB-200-2011 [67]; (3) Actions: UCF-101 [59]; (4) Textures: DTD [10]; (5) Skin tumors: HAM10000 [64] and (6) Satellite images: RE-SISC45 [8]. We use train/dev/test splits for all the datasets. + +Detailed statistics are presented in the supplementary material. We follow the few-shot evaluation protocol proposed by CLIP [44] with 1, 2, 4, 8, and 16 images randomly sampled from the training set for each class. We also evaluate in the fully-supervised setting where we train on all available images. For all experiments, we report the test accuracy. + +# 4.2. Baselines + +We compare our model, LaBo, with black-box linear probing and two interpretable methods. + +Linear Probe Following previous evaluations on CBM [25, 70], linear probing serves as our primary baseline for comparison. We follow the implementation of CLIP [44] by training the scikit-learn's L-BFGS logistic regression with a hyperparameter sweep on the L2 regularization weight. + +PCBM Post-hoc Concept Bottleneck Model [70] designs a residual modeling step that directly maps the original image embedding into the label space. PCBM treats the attributes of each class in ConceptNet [60] as concepts. + +CompDL Compositional Derivation Learning [71] learns a linear layer over CLIP similarity scores between human-designed class descriptions and images to predict targets. + +# 4.3. Implementation Details + +We prompt GPT-3-text-davinci-002 to generate concepts. The CLIP model is adapted from OpenAI's public repo with ViT-L/14 as the default vision backbone. We only use CLIP-RN50 as the backbone when comparing with PCBM, and ViT-B/32 with CompDL for a fair comparison. We implement the submodular function using the apricot package and + +
Method124816FullAvg
Linear Probe51.6965.1372.3377.3881.5387.3872.57
LaBo (Ours)63.3568.1072.0876.1979.1185.7274.09
+ +Table 1. Mean accuracy across all datasets, at different shots . + +
Methodw/ end-to-endCIFAR-10CIFAR-100
PCBM [70]✗84.556.0
LaBo (Ours)✗87.969.1
PCBM-h [70]✓87.669.9
Linear Probe✓88.870.1
+ +Table 2. Test accuracy comparison between LaBo and Post-hoc Concept Bottleneck Model (PCBM) on CIFAR-10 and CIFAR-100. "w/ end-to-end" denotes whether the model employs an end-to-end residual predictor from image features to targets. + +
Methodw/ manual concepts15Full
CompDL [71]✓13.633.252.6
LaBo (Ours)✗35.155.771.8
Linear Probe-28.455.475.5
+ +set the default number of concepts selected for each class to 50. To train the linear function, we use the Pytorch-lightning library with Adam [24] optimizer. We tune the batch size, learning rate, and submodular weights on the development set. Model checkpoints with the highest validation accuracy are evaluated on the test set. We list the hyperparameters for all datasets and shots in the supplementary material. + +# 5. Evaluation + +# 5.1. Main Results + +We compare LaBo's performance with a linear probe and other interpretable baselines to evaluate if we can maintain black box accuracy without sacrificing interpretability. + +Comparison with End-to-End Model. One of our goals is to close the performance gap between interpretable and black box models. Table 1 reports the mean test accuracy of LaBo and the linear probe on 11 datasets. LaBo significantly outperforms the end-to-end model when little data is available and continues to be competitive as the number of data increases. On average, LaBo surpasses the linear probe by $1.5\%$ . Figure 3 provides analytic performance comparisons between LaBo and Linear Probe on each dataset. + +In general, LaBo's performance depends on the quality of knowledge extracted from GPT-3. For common categories, GPT-3 contains high-quality knowledge allowing substantial improvement over linear probes. For some fine-grained datasets, such as Flower-102, GPT-3's knowledge is largely non-visual, as seen in Figure 7. In such cases, specialized language models could be used to improve LaBo. + +Comparison with other Interpretable Methods. Table 2 compares LaBo's performance with PCBM and Linear Probe. + +Table 3. LaBo and CompDL evaluated on CUB for 1/5/full shots. + +
n. of concepts per class (k)n. of shots
124816Full
141.8952.4561.7665.9969.6178.95
552.5461.1367.2272.9075.6283.83
1058.0064.5969.9074.5077.4384.66
2561.7266.3371.3975.2879.0485.26
5063.0367.7971.8876.0879.1085.71
+ +Table 4. Ablation results on bottleneck sizes. We vary the sizes of the bottlenecks and report the average performance on 11 datasets. + +
Selection Methodn. of shots
124816Full
RANDOM59.2464.7170.4274.0778.2985.06
SIMILARITY54.5961.4267.1772.6677.3284.88
COVERAGE59.7365.9370.8274.7178.9085.60
DISCRIM60.9966.4970.9374.8177.9085.31
SUBMODULAR63.0367.7971.8876.0879.1085.71
+ +Table 5. Ablation results on concept selection methods. We report mean test accuracy on 11 datasets. + +LaBo outperforms PCBM by $3.4\%$ on CIFAR-10 and $13.1\%$ on CIFAR-100. LaBo maintains comparable performance to PCBM with a residual predictor (PCBM-h), without circumventing the bottleneck. In Table 3, LaBo is more accurate than CompDL [71] without manually constructed concepts. + +# 5.2. Ablation Study + +We evaluate the importance of each of our model's components on final performance. Specifically, we compare results with different concept selection methods, language and random weight initialization, and bottleneck sizes. + +Concept Selection Methods. We compare our submodular function with four concept selection methods: (1) RANDOM: we randomly sample a subset of concepts from the candidates for each class; (2) SIMILARITY: we select the top concepts ranked by their similarity scores with the class calculated by equation 3; (3) COVERAGE: we only consider the coverage score for concept selection; (4) DISCRIM: we only consider the discriminability score for concept selection. As shown in Table 5, our submodular function, which jointly optimizes coverage and discriminability, achieves the best performance across different numbers of shots. We notice that using coverage or discriminability alone still outperforms using similarity between the class and random selection. The selection method plays an important role in all data settings, but its impact decreases with more supervision. + +Initialization with Language Priors. We deactivate the LM initialization and use random initialization instead. Figure 4 shows that the LM prior is more important for low shot settings since there is less signal to guide concept importance. + +Bottleneck Size. In Table 4, we compare performance for different bottleneck sizes ranging from 1 to 50 concepts selected by the submodular function. Larger bottlenecks are + +![](images/0119f7d29c86bd03b71d85f73d27c4d7af0978206d2b036d3749cb3a36bc3c76.jpg) + +![](images/3624ddebc571049301334d5df1533a6845a8c8a713f793f61492167663562a24.jpg) +Figure 4. Language Prior vs. Random Weight initialization average over all datasets. + +![](images/c6fb465506d9be5bc5f6cf94848a554873e448ee2b1935ee398f593fcf70c3f5.jpg) +Figure 5. Human evaluation on Factuality and Groundability for different bottlenecks on ImageNet. "w/o Submod" denotes without submodular function, i.e., random concept selection. "w/o LM" denotes no language prior weight initialization. + +usually better, but with more data, similar performance is achievable with smaller bottlenecks. + +# 5.3. Human Evaluation + +It is important for interpretability that the vision-language alignment model correctly grounds concepts to images. For example, if a concept "usually round" ranks both circles and stripes highly, the name of the attribute does not faithfully represent the computation. In addition, it is important that the automatically generated concept bottlenecks factually correspond to the class they describe. To this end, we introduce two metrics to evaluate the quality of our concept bottleneck items: (1) Factuality measures how accurate the concepts are in describing their designated class by requiring annotators to judge whether they describe ground truth images, and (2) Groundability measures how consistent the vision-language model grounding of the concepts to images with human interpretations by requiring annotators to judge their applicability on the top-10 images ranked by CLIP alignment scores. + +Setup. Both metrics are computed by asking annotators to select images that describe a highly ranked concept in our bottlenecks. Formally, the two metrics are represented by: + +$$ +\operatorname {F a c t u a l i t y} (c) = \frac {\text {n u m b e r o f i m a g e s s e l e c t e d}}{k \text {g r o u n d t r u t h i m a g e s o f t h e c l a s s}} +$$ + +![](images/f5e280be94cb40596c8c872c1314b682666101190e60c04f802ff934bf96cc70.jpg) +Figure 6. Percentage of invalid concepts identified by humans for different bottlenecks on ImageNet. Lower percentage is better. + +
MetricsLaBow/o Submodw/o LM
Factuality (%) ↑24.022.814.1
Groundability (%) ↑14.122.520.2
Non Visual (%) ↓4.85.65.8
Non Sensical (%) ↓8.09.68.7
Unknown Vocab (%) ↓10.210.510.7
+ +Table 6. Average human evaluation results of LaBo on 11 datasets. We also evaluate LaBo by removing the submodular function (w/o Submod) and language model priors (w/o LM). + +$$ +\operatorname {G r o u n d a b i l i t y} (c) = \frac {\text {n u m b e r o f i m a g e s s e l e c t e d}}{\text {t o p - k a l i n g e d i m a g e s o f t h e c o n c e p t}} +$$ + +where we set $k = 10$ . In addition to the two main metrics, we ask the annotator to select whether the concept is non-visual, nonsensical, or contains unknown vocabulary. We randomly sample 20 classes for each dataset and evaluate the top 5 concepts (ranked by the weights of the linear function) for each class, 100 concepts per dataset. We release our human evaluation task on Amazon Mechanical Turk and collect three annotations for each concept. More details on the task and the results can be found in the supplement. + +Baselines. We evaluate the bottlenecks under full supervision and compare them with two main baselines: (1) LaBo (w/o Submod), which randomly selects the concepts instead of using the submodular function, and (2) LaBo (w/o LM), which initializes the concept weight matrix randomly without leveraging the priors of the language model. For ImageNet, we add two additional baselines using human-written text: (1) WordNet [13] definitions and (2) Wikipedia sentences [22]. We adopt the same preprocessing pipeline as LaBo to extract concepts from human-written resources and utilize the submodular function to select the bottlenecks. + +Results. Figure 5 shows the evaluation on ImageNet, and we observe that LaBo has significantly higher Factuality and Groundability than human-written text. We further observe that removing components from our system (submodular and LM Prior) hurt both human evaluation metrics, indicating their collective importance in our system. In addition, Figure + +
Class NameTop-3 ConceptsClass NameTop-3 ConceptsClass NameTop-3 ConceptsClass NameTop-3 Concepts
ImageNetbadger1. short legs and long body make it an excellent diggerant1. black and red stingerhammer1.long, thin tool with a wooden handlewater buffalo1. large head with short, curved horns
2. black-and-white striped fur2. black-and-white striped fur2. small, black insect with six legs2. small, black insect with six legs2. great tool for pounding object2. great tool for pounding object2. heaviest living species of bovid2. heaviest living species of bovid
3. coat is very shaggy3. coat is very shaggy3. long, slender antennae that it uses to smell and touch3. long, slender antennae that it uses to smell and touch3. used to pound on surfaces3. used to pound on surfaces3. huge, dark-colored animal3. huge, dark-colored animal
CUBeared grebe1. black and white plumage that is striking in the sunlighthorned lark1. black line running through yellow facewhite pelican1. long neck and bill make it look like a giant swanarctic tern1. breeds in greenland, iceland, and northern russia
2. black body with a long, slender neck2. black body with a long, slender neck2. head is black with a white horn on each side2. head is black with a white horn on each side2. large, white bird with black wings2. large, white bird with black wings2. large, white birds2. black and white markings
3. red and black bill3. red and black bill3. black horn on each side of their head3. black horn on each side of their head3. bill is huge and yellow3. bill is huge and yellow3. bill is huge and yellow3. small white bird with a black cap
Flowerwater lily1. depicted in artworks of ponds and waterfallbarbeton daisy1. scientific name for the flower is taraxacum officinalmarigold1. central disc with smaller floretstiger lily1. long, protruding stamen
2. member of the nymphaceae family2. member of the nymphaceae family2. named after the city of barberton2. named after the city of barberton2. have a slightly furry texture2. have a slightly furry texture2. have a slightly furry texture2. orange with black spots and stripes
3. lily pads float3. lily pads float3. member of the daisy family3. member of the daisy family3. bold and vibrant color palette3. bold and vibrant color palette3. bold and vibrant color palette3. bold and vibrant color palette
UCF-101archery1. grip bow tightly in their left handdrumming1. blur as they fly over the drumssurfing1. deep blue colorlong jump1. get out of sandpit
2. focused and concentrated on their task2. focused and concentrated on their task2. sitting on a stool in front of a drum set2. sitting on a stool in front of a drum set2. tans contrast with the white of their boards2. tans contrast with the white of their boards2. tans contrast with the white of their boards2. series of movements starting from a standing position
3. keep bow and arrows in safe and dry place when not in use3. keep bow and arrows in safe and dry place when not in use3. position the drumstick so it is resting on your index finger3. position the drumstick so it is resting on your index finger3. sending a spray of water into the air3. sending a spray of water into the air3. person tucks their knees up to chest3. person tucks their knees up to chest
HAM100000dermatofibroma1. generally not painfulmelanoma1. dark brown or black in colormelanocytic nevi1. color is tanbenign lesions1. color ranges from light brown to black
2. red, brown, or purple in color2. red, brown, or purple in color2. large and dark2. large and dark2. dark brown or black color2. dark brown or black color2. dark brown or black color2. rough or scaly texture
3. thin white halo around them3. thin white halo around them3. flesh-colored, brown, or black3. flesh-colored, brown, or black3. small, round, and slightly raised3. small, round, and slightly raised3. small, round, and slightly raised3. dark brown or black
+ +Figure 7. Several example bottlenecks generated by LaBo. The top-3 concepts, ranked by their weights in the linear function, for randomly selected classes, paired with a random image from the class, across 6 datasets. + +6 shows that LaBo has significantly fewer invalid concepts than other baselines. Table 6 summarizes the average human evaluation results over the 11 datasets9. On average, we observe a trade-off between Factuality and Groundability. Increasing coverage and discriminability leads to more variable and specific concepts that CLIP finds more difficult to ground. This could be due to challenges in capturing composite concepts [33, 71]. For individual analysis of the datasets, refer to the supplementary material. Finally, Figure 7 shows several CBMs we constructed. Across many types of tasks, the bottlenecks are largely coherent, factual, and groundable by CLIP. + +# 6. Conclusion and Limitation + +Overall, our approach demonstrates that the accuracy and interpretability of vision systems may be less at odds than previously believed. Leveraging LLMs was crucial, as they encode important visual knowledge. In the future, our approach can easily be enriched with new factors that capture different priors on bottleneck construction. The limits of knowledge in GPT-3 are not known, but likely there are + +domains where prompting generates few useful facts. Even in contexts where GPT-3 can generate useful information, our method depends on CLIP being able to recognize those aspects in images. The alignment between GPT-3 and CLIP likely does not hold for all cases. Future work could focus on dynamically prompting GPT-3 to make this coupling more robust. Finally, our work depends on large models trained at scales that are not currently reproducible. It is possible unrevealed aspects of training by OpenAI will require a reevaluation of our claims. + +# Acknowledgements + +This research is based upon work supported in part by the DARPA KAIROS Program (contract FA8750-19-2-1004), the DARPA LwLL Program (contract FA8750-19-2-0201), the IARPA BETTER Program (contract 2019-19051600004), the IARPA HIATUS Program (contract 2022-22072200005), the NSF (Award 1928631), and an AI2 Young Investigator Award. Approved for Public Release, Distribution Unlimited. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies, either expressed or implied, of ODNI, DARPA, IARPA, NSF, or the U.S. Government. + +# References + +[1] Francis Bach. Convex analysis and optimization with submodular functions: a tutorial. arXiv preprint arXiv:1010.4207, 2010.4 +[2] David Bau, Bolei Zhou, Aditya Khosla, Aude Oliva, and Antonio Torralba. 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They allow people to easily understand why a model is failing, a critical feature for high-stakes applications. CBMs require manually specified concepts and often under-perform their black box counterparts, preventing their broad adoption. We address these shortcomings and are first to show how to construct high-performance CBMs without manual specification of similar accuracy to black box models. Our approach, Language Guided Bottlenecks (LaBo), leverages a language model, GPT-3, to define a large space of possible bottlenecks. Given a problem domain, LaBo uses GPT-3 to produce factual sentences about categories to form candidate concepts. LaBo efficiently searches possible bottlenecks through a novel submodular utility that promotes the selection of discriminative and diverse information. Ultimately, GPT-3's sentential concepts can be aligned to images using CLIP, to form a bottleneck layer. 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Our proposed high-performance Concept Bottleneck Model alleviates the need for human-designed concepts by prompting large language models (LLMs) such as GPT-3 [4]." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 397, + 547, + 481 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 397, + 547, + 481 + ], + "spans": [ + { + "bbox": [ + 304, + 397, + 547, + 481 + ], + "type": "text", + "content": "can also be designed to be inherently interpretable, but it is believed that such models will perform more poorly than their black box alternatives [16]. In this work, we provide evidence to the contrary. We show how to construct high-performance interpretable-by-design classifiers by combining a language model, GPT-3 [4], and a language-vision model, CLIP [44]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 483, + 547, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 483, + 547, + 579 + ], + "spans": [ + { + "bbox": [ + 304, + 483, + 547, + 579 + ], + "type": "text", + "content": "Our method builds on Concept Bottleneck Models (CBM) [25], which construct predictors through a linear combination of human-designed concepts. For example, as seen in Figure 1, a qualified person can design concepts, such as \"nape color,\" as intermediate targets for a black box model before classifying a bird. CBMs provide abstractions that people can use to understand errors or intervene on, contributing to increased trust." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 580, + 547, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 580, + 547, + 664 + ], + "spans": [ + { + "bbox": [ + 304, + 580, + 547, + 664 + ], + "type": "text", + "content": "Application of CBMs is limited because they require costly attribute annotations by domain experts and often under-perform their black box counterparts. In contexts where CBM performance is competitive with black box alternatives, interpretability properties are sacrificed [34, 70]. To address both of these challenges, we propose to build systems that automatically construct CBMs." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 665, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 714 + ], + "type": "text", + "content": "Our Language Model Guided Concept Bottleneck Model (LaBo), Figure 2, allows for the automatic construction of high-performance CBMs for arbitrary classification problems without concept annotations. Large language models" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 287, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 287, + 712 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 58, + 702, + 287, + 712 + ], + "type": "text", + "content": "Code and data are available at https://github.com/YueYANG1996/LaBo" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19187" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 63, + 70, + 534, + 300 + ], + "blocks": [ + { + "bbox": [ + 63, + 70, + 534, + 300 + ], + "lines": [ + { + "bbox": [ + 63, + 70, + 534, + 300 + ], + "spans": [ + { + "bbox": [ + 63, + 70, + 534, + 300 + ], + "type": "image", + "image_path": "2e14f5129572f4a18e139a0c44fe81cd78931d81488b23059e1180d938b8b073.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 308, + 547, + 365 + ], + "lines": [ + { + "bbox": [ + 46, + 308, + 547, + 365 + ], + "spans": [ + { + "bbox": [ + 46, + 308, + 547, + 365 + ], + "type": "text", + "content": "Figure 2. We present an overview of our Language-Model-Guided Concept Bottleneck Model (LaBo), which is interpretable by design image classification system. First, we prompt the large language model (GPT-3) to generate candidate concepts (Sec 3.4). Second, we employ a submodular function to select concepts from all candidates to construct the bottleneck (Sec 3.2). Third, we apply a pretrained alignment model (CLIP) to obtain the embeddings of concepts and images, which is used to compute concept scores. Finally, we train a linear function in which the weight " + }, + { + "bbox": [ + 46, + 308, + 547, + 365 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 46, + 308, + 547, + 365 + ], + "type": "text", + "content": " denotes the concept-class association user to predict targets based on concept scores (Sec 3.3)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 376, + 290, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 376, + 290, + 483 + ], + "spans": [ + { + "bbox": [ + 46, + 376, + 290, + 483 + ], + "type": "text", + "content": "(LLMs) contain significant world knowledge [21, 42, 61], that can be elicited by inputting a string prefix and allowing LLMs to complete the string (prompting). For example, in Figure 1, GPT-3 is prompted about sparrows and completes with information such as \"brown head with white stripes.\" LaBo leverages this by constructing bottlenecks where the concepts are such GPT-3 generated sentences. Since our concepts are textual, we use CLIP to score their presence in an image and form a bottleneck layer out of these scores." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 485, + 288, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 485, + 288, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 485, + 288, + 628 + ], + "type": "text", + "content": "A key advantage of LaBo is the ability to control the selection of concepts in the bottleneck by generating candidates from the language model. We develop selection principles targeting both interpretability and classification accuracy. For example, we prefer smaller bottlenecks that include shorter sentences that do not include class names. Furthermore, to maximize performance, we prefer attributes that CLIP can easily recognize and are highly discriminative. To account for appearance variation, we select attributes that cover a variety of information and are not repetitive. We formulate these factors into a novel sub-modular criterion that allows us to select good bottlenecks efficiently [38]." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 630, + 288, + 691 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 288, + 691 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 288, + 691 + ], + "type": "text", + "content": "We have evaluated LaBo-created bottlenecks on 11 diverse image classification tasks, spanning recognition of common objects [11,26] to skin tumors [64]. fine-grained types [3, 32, 39, 67], textures [10], actions [59], skin tumors [64], and satellite photographed objects [8].2 Our" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 376, + 547, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 376, + 547, + 518 + ], + "spans": [ + { + "bbox": [ + 304, + 376, + 547, + 518 + ], + "type": "text", + "content": "main finding is that LaBo is a highly effective prior for what concepts to look for, especially in low data regimes. In evaluations comparing with linear probes, LaBo outperforms by as much as " + }, + { + "bbox": [ + 304, + 376, + 547, + 518 + ], + "type": "inline_equation", + "content": "11.7\\%" + }, + { + "bbox": [ + 304, + 376, + 547, + 518 + ], + "type": "text", + "content": " at 1-shot and marginally underperforms given larger data settings. Averaged over many dataset sizes, LaBo bottlenecks are " + }, + { + "bbox": [ + 304, + 376, + 547, + 518 + ], + "type": "inline_equation", + "content": "1.5\\%" + }, + { + "bbox": [ + 304, + 376, + 547, + 518 + ], + "type": "text", + "content": " more accurate than linear probes. In comparison to modifications of CBMs that improve performance by circumventing the bottleneck [70], we achieve similar or better results without breaking the CBM abstraction. In extensive ablations, we study key trade-offs in bottleneck design and show our selection criteria are crucial and highlight several other critical design choices." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 519, + 548, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 519, + 548, + 616 + ], + "spans": [ + { + "bbox": [ + 304, + 519, + 548, + 616 + ], + "type": "text", + "content": "Human evaluations indicate that our bottlenecks are largely understandable, visual, and factual. Finally, annotators find our GPT-3 sourced bottlenecks are more factual and groundable than those constructed from WordNet or Wikipedia sentences. Overall, our experiments demonstrate that automatically designed CBMs can be as effective as black box models while maintaining critical factors contributing to their interpretability." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 625, + 392, + 639 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 625, + 392, + 639 + ], + "spans": [ + { + "bbox": [ + 306, + 625, + 392, + 639 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 317, + 646, + 547, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 646, + 547, + 658 + ], + "spans": [ + { + "bbox": [ + 317, + 646, + 547, + 658 + ], + "type": "text", + "content": "Broadly, interpretability methods fall into two categories:" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 306, + 665, + 547, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 665, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 665, + 547, + 713 + ], + "type": "text", + "content": "3 when creating candidate attributes. This is largely done to overcome problems of word sense. For example, when naively prompted to produce knowledge about the flower \"bird of paradise\" GPT-3 yields information about birds instead of flowers. In general, specialization here was also minimal. See appendix for prompts." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 58, + 702, + 288, + 714 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 288, + 714 + ], + "type": "text", + "content": "2The only dataset specialization we perform is prompt tuning for GPT-" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "19188" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 180 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 180 + ], + "type": "text", + "content": "post-hoc and by design. While ours is an instance of the latter, post-hoc methods have the advantage of not imposing any model constraints. For example, Gradient-weighted Class Activation Mapping approaches [2, 19, 36, 54] trace network gradients to identify the input areas that guide predictions. Similarly, Explanation Generation methods [17, 23, 40, 57] require models to produce explanations for visual tasks by conditioning their predictions on captioning models and [18, 41] incorporate visual evidence to ground explanations." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 182, + 290, + 302 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 182, + 290, + 302 + ], + "spans": [ + { + "bbox": [ + 46, + 182, + 290, + 302 + ], + "type": "text", + "content": "Despite their advantages, there is no guarantee that post-hoc methods faithfully represent model reasoning [49]. In contrast, our work falls under interpretable by design methods, which constrain explanations to align with the model's reasoning. For example, Prototype methods [6,37,51,58,66] optimize a metric space that guides classification by computing distances to prototype representations of each class. While such methods identify important regions in the input for classification, they still require featurized region representations that obfuscate the semantic content of the region." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 303, + 290, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 303, + 290, + 579 + ], + "spans": [ + { + "bbox": [ + 46, + 303, + 290, + 579 + ], + "type": "text", + "content": "This work extends another family of interpretable by design methods known as Concept Bottleneck Models [25, 52]. Following early attempts in few shot learning [27] and attribute learning [50, 68], CBMs predict targets by linearly combining an intermediate layer of human-understandable attributes. Recently, Computational Derivation Learning (CompDL) [71] proposed a CBM architecture that applies a linear layer over CLIP scores between human expert designed concepts and images to predict targets in the context of an evaluation framework to measure how well CLIP grounds concepts. CBMs generally suffer from the need for costly class description annotations and lower performance compared to end-to-end counterparts. Post-hoc Concept Bottleneck (PCBM) [70] was proposed to fill these two gaps by leveraging information from a static knowledge base, such as ConceptNet [60], and adding a residual connection from image features to the final prediction to improve accuracy [70]. However, PCBMs cannot be expanded to larger-scale (e.g., ImageNet [11]) or domain-specific tasks (e.g., fine-grained [32]) because knowledge bases have limited coverage. In addition, they include a residual predictor, which effectively ensembles CBM with an end-to-end model, undermining interpretability." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 580, + 288, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 580, + 288, + 688 + ], + "spans": [ + { + "bbox": [ + 46, + 580, + 288, + 688 + ], + "type": "text", + "content": "Inspired by previous work on using textual knowledge to guide vision models [5,22,48,55], we circumvent the requirement for external knowledge bases, and instead query LLMs to collect concepts. We remove the need for direct mapping from image features to targets by fully automating the extraction and filtering of LLM knowledge. Our model surpasses end-to-end models in few shot scenarios and achieves comparable performance in large data settings, while concurrent work [35] only evaluates on zero-shot settings." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 689, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 289, + 714 + ], + "type": "text", + "content": "Our work capitalizes on improvements in vision-language pretraining from earlier BERT-based models" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 72, + 547, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 108 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 108 + ], + "type": "text", + "content": "[7, 30, 31, 62] to more scalable contrastive architectures [20, 28, 44, 69], which are very effective for few shot image classification [9, 63]." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 108, + 547, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 108, + 547, + 180 + ], + "spans": [ + { + "bbox": [ + 304, + 108, + 547, + 180 + ], + "type": "text", + "content": "Our work can be viewed as interpretability-focused prompt tuning of CLIP [44]. Significant efforts have been devoted to prompting vision language models [12, 14, 29, 43, 46, 73, 74]. These focus on searching over text prompts to improve classification performance, and resemble earlier techniques in LLM prompt tuning [15, 53, 56]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 184, + 362, + 196 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 184, + 362, + 196 + ], + "spans": [ + { + "bbox": [ + 306, + 184, + 362, + 196 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 204, + 547, + 337 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 204, + 547, + 337 + ], + "spans": [ + { + "bbox": [ + 304, + 204, + 547, + 337 + ], + "type": "text", + "content": "Figure 2 presents an overview of our method. Our model prompts a large language model, GPT-3 [4] to generate a set of candidate concepts for each class (Section 3.4). We employ submodular optimization to greedily select a subset of concepts for each class such that we maximize discriminability and diversity (Section 3.2). We then align the selected concepts to images using CLIP [44]. We apply a linear layer over the similarity scores of concepts and images to learn a weight matrix representing the importance of each concept in the final classification. This weight matrix is initialized using a language model prior from GPT-3 (Section 3.3)." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 342, + 430, + 354 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 342, + 430, + 354 + ], + "spans": [ + { + "bbox": [ + 306, + 342, + 430, + 354 + ], + "type": "text", + "content": "3.1. Problem Formulation" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 361, + 547, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 361, + 547, + 552 + ], + "spans": [ + { + "bbox": [ + 304, + 361, + 547, + 552 + ], + "type": "text", + "content": "Consider a training set of image-label pairs " + }, + { + "bbox": [ + 304, + 361, + 547, + 552 + ], + "type": "inline_equation", + "content": "\\mathcal{D} = \\{(i,y)\\}" + }, + { + "bbox": [ + 304, + 361, + 547, + 552 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 361, + 547, + 552 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 361, + 547, + 552 + ], + "type": "text", + "content": " is the image and " + }, + { + "bbox": [ + 304, + 361, + 547, + 552 + ], + "type": "inline_equation", + "content": "y\\in \\mathcal{V}" + }, + { + "bbox": [ + 304, + 361, + 547, + 552 + ], + "type": "text", + "content": ", is a label from a set of " + }, + { + "bbox": [ + 304, + 361, + 547, + 552 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 361, + 547, + 552 + ], + "type": "text", + "content": " classes. Suppose we have a pretrained multimodal alignment model (e.g., CLIP [44]), which has an image encoder " + }, + { + "bbox": [ + 304, + 361, + 547, + 552 + ], + "type": "inline_equation", + "content": "\\mathcal{I}" + }, + { + "bbox": [ + 304, + 361, + 547, + 552 + ], + "type": "text", + "content": " and a text encoder " + }, + { + "bbox": [ + 304, + 361, + 547, + 552 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 304, + 361, + 547, + 552 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 361, + 547, + 552 + ], + "type": "inline_equation", + "content": "\\mathcal{I}" + }, + { + "bbox": [ + 304, + 361, + 547, + 552 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 361, + 547, + 552 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 304, + 361, + 547, + 552 + ], + "type": "text", + "content": " can map images and text into the shared feature space, respectively. The dot product of the image and text features reflects the alignment score between the two modalities. We extract the features of all images in " + }, + { + "bbox": [ + 304, + 361, + 547, + 552 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 304, + 361, + 547, + 552 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 304, + 361, + 547, + 552 + ], + "type": "inline_equation", + "content": "\\pmb{x} = \\mathcal{I}(i)\\in \\mathbb{R}^d" + }, + { + "bbox": [ + 304, + 361, + 547, + 552 + ], + "type": "text", + "content": ", and the dataset can be represented as " + }, + { + "bbox": [ + 304, + 361, + 547, + 552 + ], + "type": "inline_equation", + "content": "\\mathcal{D} = \\{(x,y)\\}" + }, + { + "bbox": [ + 304, + 361, + 547, + 552 + ], + "type": "text", + "content": ". Let " + }, + { + "bbox": [ + 304, + 361, + 547, + 552 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 361, + 547, + 552 + ], + "type": "text", + "content": " be the superset of candidate textual concepts generated from language models. We use a submodular function " + }, + { + "bbox": [ + 304, + 361, + 547, + 552 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 304, + 361, + 547, + 552 + ], + "type": "text", + "content": " to select a bottleneck, " + }, + { + "bbox": [ + 304, + 361, + 547, + 552 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 304, + 361, + 547, + 552 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 361, + 547, + 552 + ], + "type": "inline_equation", + "content": "C\\subseteq S" + }, + { + "bbox": [ + 304, + 361, + 547, + 552 + ], + "type": "text", + "content": ", made of " + }, + { + "bbox": [ + 304, + 361, + 547, + 552 + ], + "type": "inline_equation", + "content": "N_{C}" + }, + { + "bbox": [ + 304, + 361, + 547, + 552 + ], + "type": "text", + "content": " concepts, " + }, + { + "bbox": [ + 304, + 361, + 547, + 552 + ], + "type": "inline_equation", + "content": "C = \\{c_1,c_2,\\dots ,c_{N_C}\\}" + }, + { + "bbox": [ + 304, + 361, + 547, + 552 + ], + "type": "text", + "content": ". We can construct a bottleneck embedding, " + }, + { + "bbox": [ + 304, + 361, + 547, + 552 + ], + "type": "inline_equation", + "content": "\\pmb{E}_{C}\\in \\mathbb{R}^{N_{C}\\times d}" + }, + { + "bbox": [ + 304, + 361, + 547, + 552 + ], + "type": "text", + "content": ", and each row of " + }, + { + "bbox": [ + 304, + 361, + 547, + 552 + ], + "type": "inline_equation", + "content": "\\pmb{E}_{C}" + }, + { + "bbox": [ + 304, + 361, + 547, + 552 + ], + "type": "text", + "content": " is the text feature " + }, + { + "bbox": [ + 304, + 361, + 547, + 552 + ], + "type": "inline_equation", + "content": "\\mathcal{T}(c)\\in \\mathbb{R}^d" + }, + { + "bbox": [ + 304, + 361, + 547, + 552 + ], + "type": "text", + "content": " of a concept " + }, + { + "bbox": [ + 304, + 361, + 547, + 552 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 361, + 547, + 552 + ], + "type": "text", + "content": " extracted by the text encoder " + }, + { + "bbox": [ + 304, + 361, + 547, + 552 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 304, + 361, + 547, + 552 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 552, + 547, + 637 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 552, + 547, + 637 + ], + "spans": [ + { + "bbox": [ + 304, + 552, + 547, + 637 + ], + "type": "text", + "content": "Concept bottleneck models produce a prediction by composing two functions, " + }, + { + "bbox": [ + 304, + 552, + 547, + 637 + ], + "type": "inline_equation", + "content": "\\hat{y} = f\\left(g(\\boldsymbol{x},\\boldsymbol{E}_C)\\right)" + }, + { + "bbox": [ + 304, + 552, + 547, + 637 + ], + "type": "text", + "content": ", in which " + }, + { + "bbox": [ + 304, + 552, + 547, + 637 + ], + "type": "inline_equation", + "content": "g: \\mathbb{R}^d \\to \\mathbb{R}^{N_C}" + }, + { + "bbox": [ + 304, + 552, + 547, + 637 + ], + "type": "text", + "content": " maps the image feature to a score for every element of the bottleneck and " + }, + { + "bbox": [ + 304, + 552, + 547, + 637 + ], + "type": "inline_equation", + "content": "f: \\mathbb{R}^{N_C} \\to \\mathcal{V}" + }, + { + "bbox": [ + 304, + 552, + 547, + 637 + ], + "type": "text", + "content": " makes the final prediction on the label space given the concept scores. In our setting, we find a bottleneck " + }, + { + "bbox": [ + 304, + 552, + 547, + 637 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 304, + 552, + 547, + 637 + ], + "type": "text", + "content": " and appropriate " + }, + { + "bbox": [ + 304, + 552, + 547, + 637 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 552, + 547, + 637 + ], + "type": "text", + "content": " by solving the following minimization problem:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 318, + 643, + 547, + 670 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 643, + 547, + 670 + ], + "spans": [ + { + "bbox": [ + 318, + 643, + 547, + 670 + ], + "type": "interline_equation", + "content": "\\min _ {f, C} \\underset {(\\boldsymbol {x}, y) \\sim \\mathcal {D}} {\\mathbb {E}} \\left[ \\mathcal {L} \\left(f (g (\\boldsymbol {x}, \\boldsymbol {E} _ {C})) , y\\right) \\right] - \\mathcal {F} (C, \\mathcal {D}) \\tag {1}", + "image_path": "7fb4ba9d8be4157a80bd724e71adf709bcf0683bdcda9a2bda1ec2c5a3594c2b.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 677, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 547, + 714 + ], + "type": "text", + "content": "in which " + }, + { + "bbox": [ + 304, + 677, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{L}(\\hat{y}, y)" + }, + { + "bbox": [ + 304, + 677, + 547, + 714 + ], + "type": "text", + "content": " is the cross-entropy loss on the label prediction and " + }, + { + "bbox": [ + 304, + 677, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{F}(C, \\mathcal{D})" + }, + { + "bbox": [ + 304, + 677, + 547, + 714 + ], + "type": "text", + "content": " is the quality of the bottleneck as measured by the submodular function. In practice, we optimize" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "19189" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "type": "text", + "content": "sequentially: we first find a high scoring " + }, + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "type": "text", + "content": " under " + }, + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "type": "text", + "content": ". Then, we use the dot product of image and concept embeddings as " + }, + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "type": "text", + "content": ". Finally, we find an " + }, + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "type": "text", + "content": " that minimizes " + }, + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "type": "text", + "content": ". In the following sections, we will illustrate how we: construct the submodular function " + }, + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "type": "text", + "content": " to select a subset of concepts " + }, + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "type": "text", + "content": " from the candidates " + }, + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "type": "text", + "content": " (Section 3.2) and learn " + }, + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "type": "text", + "content": " (Section 3.3)." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 150, + 216, + 164 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 150, + 216, + 164 + ], + "spans": [ + { + "bbox": [ + 47, + 150, + 216, + 164 + ], + "type": "text", + "content": "3.2. Submodular Concept Selection" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 168, + 288, + 252 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 168, + 288, + 252 + ], + "spans": [ + { + "bbox": [ + 46, + 168, + 288, + 252 + ], + "type": "text", + "content": "We create a superset of candidate concepts, " + }, + { + "bbox": [ + 46, + 168, + 288, + 252 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 168, + 288, + 252 + ], + "type": "text", + "content": ", out of class-specific subsets. For every label " + }, + { + "bbox": [ + 46, + 168, + 288, + 252 + ], + "type": "inline_equation", + "content": "y \\in \\mathcal{V}" + }, + { + "bbox": [ + 46, + 168, + 288, + 252 + ], + "type": "text", + "content": ", we construct " + }, + { + "bbox": [ + 46, + 168, + 288, + 252 + ], + "type": "inline_equation", + "content": "S_y" + }, + { + "bbox": [ + 46, + 168, + 288, + 252 + ], + "type": "text", + "content": " by prompting a language model to produce textual knowledge about " + }, + { + "bbox": [ + 46, + 168, + 288, + 252 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 168, + 288, + 252 + ], + "type": "text", + "content": " (Section 3.4). Instead of directly choosing " + }, + { + "bbox": [ + 46, + 168, + 288, + 252 + ], + "type": "inline_equation", + "content": "N_C" + }, + { + "bbox": [ + 46, + 168, + 288, + 252 + ], + "type": "text", + "content": " concepts from " + }, + { + "bbox": [ + 46, + 168, + 288, + 252 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 168, + 288, + 252 + ], + "type": "text", + "content": ", we select " + }, + { + "bbox": [ + 46, + 168, + 288, + 252 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 168, + 288, + 252 + ], + "type": "text", + "content": " concepts for each class, such that " + }, + { + "bbox": [ + 46, + 168, + 288, + 252 + ], + "type": "inline_equation", + "content": "N \\times k = N_C" + }, + { + "bbox": [ + 46, + 168, + 288, + 252 + ], + "type": "text", + "content": ", to ensure each class has an equal number of relevant concepts in the bottleneck." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 253, + 287, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 253, + 287, + 361 + ], + "spans": [ + { + "bbox": [ + 46, + 253, + 287, + 361 + ], + "type": "text", + "content": "We employ submodular optimization [1] to select a subset " + }, + { + "bbox": [ + 46, + 253, + 287, + 361 + ], + "type": "inline_equation", + "content": "C_y \\subseteq S_y" + }, + { + "bbox": [ + 46, + 253, + 287, + 361 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 253, + 287, + 361 + ], + "type": "inline_equation", + "content": "|C_y| = k" + }, + { + "bbox": [ + 46, + 253, + 287, + 361 + ], + "type": "text", + "content": ". Specifically, we need to design a score function " + }, + { + "bbox": [ + 46, + 253, + 287, + 361 + ], + "type": "inline_equation", + "content": "\\mathcal{F}: 2^{|S_y|} \\to \\mathbb{R}" + }, + { + "bbox": [ + 46, + 253, + 287, + 361 + ], + "type": "text", + "content": " to evaluate the utility of the subset. Submodular functions should satisfy the diminishing returns property. If a submodular function is monotone, a greedy algorithm [38] can be used to find a solution within a constant factor of the optimal one. We propose the following monotone submodular function to select the subset " + }, + { + "bbox": [ + 46, + 253, + 287, + 361 + ], + "type": "inline_equation", + "content": "C_y" + }, + { + "bbox": [ + 46, + 253, + 287, + 361 + ], + "type": "text", + "content": " from the candidate set " + }, + { + "bbox": [ + 46, + 253, + 287, + 361 + ], + "type": "inline_equation", + "content": "S_y" + }, + { + "bbox": [ + 46, + 253, + 287, + 361 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 56, + 367, + 287, + 411 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 367, + 287, + 411 + ], + "spans": [ + { + "bbox": [ + 56, + 367, + 287, + 411 + ], + "type": "interline_equation", + "content": "\\mathcal {F} \\left(C _ {y}\\right) = \\underbrace {\\alpha \\cdot \\sum_ {c \\in C _ {y}} D (c)} _ {\\text {d i s c r i m i n a b i l i t y}} + \\underbrace {\\beta \\cdot \\sum_ {c _ {1} \\in S _ {y}} \\max _ {c _ {2} \\in C _ {y}} \\phi \\left(c _ {1} , c _ {2}\\right)} _ {\\text {c o v e r a g e}}, \\tag {2}", + "image_path": "8761d3ca8f186fc9acd365b07f9a83d70a94f7f9b53a1c8be580fb6f0868cf67.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 417, + 287, + 501 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 417, + 287, + 501 + ], + "spans": [ + { + "bbox": [ + 46, + 417, + 287, + 501 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 417, + 287, + 501 + ], + "type": "inline_equation", + "content": "D(c)" + }, + { + "bbox": [ + 46, + 417, + 287, + 501 + ], + "type": "text", + "content": " denotes the discriminability score of the concept " + }, + { + "bbox": [ + 46, + 417, + 287, + 501 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 417, + 287, + 501 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 417, + 287, + 501 + ], + "type": "inline_equation", + "content": "\\phi(\\cdot)" + }, + { + "bbox": [ + 46, + 417, + 287, + 501 + ], + "type": "text", + "content": " is the intra-concept similarity. Generally, the first term tends to select more informative concepts, and the second term ensures the subset has good coverage of the candidate set. The hyperparameters " + }, + { + "bbox": [ + 46, + 417, + 287, + 501 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 417, + 287, + 501 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 417, + 287, + 501 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 417, + 287, + 501 + ], + "type": "text", + "content": " control the weights of the two sub-functions. Here we present how to compute these two scores:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 506, + 287, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 506, + 287, + 578 + ], + "spans": [ + { + "bbox": [ + 46, + 506, + 287, + 578 + ], + "type": "text", + "content": "Discriminability Score. We introduce a discriminability score to encourage the selection of concepts that are aligned with many images in class " + }, + { + "bbox": [ + 46, + 506, + 287, + 578 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 506, + 287, + 578 + ], + "type": "text", + "content": ", but few images in other classes. We first define the similarity score " + }, + { + "bbox": [ + 46, + 506, + 287, + 578 + ], + "type": "inline_equation", + "content": "Sim(y, c)" + }, + { + "bbox": [ + 46, + 506, + 287, + 578 + ], + "type": "text", + "content": " between a class and concept by taking the mean of the dot product between the images and text features:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 94, + 584, + 287, + 613 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 94, + 584, + 287, + 613 + ], + "spans": [ + { + "bbox": [ + 94, + 584, + 287, + 613 + ], + "type": "interline_equation", + "content": "\\operatorname {S i m} (y, c) = \\frac {1}{| \\mathcal {X} _ {y} |} \\sum_ {\\boldsymbol {x} \\in \\mathcal {X} _ {y}} \\boldsymbol {x} \\cdot \\mathcal {T} (c) ^ {\\top}, \\tag {3}", + "image_path": "00badc9ecdb75bbf07fdf6da460ac690ad75668e2df02aa91acffb0b3378f938.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 621, + 288, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 621, + 288, + 658 + ], + "spans": [ + { + "bbox": [ + 47, + 621, + 288, + 658 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 621, + 288, + 658 + ], + "type": "inline_equation", + "content": "\\mathcal{X}_y" + }, + { + "bbox": [ + 47, + 621, + 288, + 658 + ], + "type": "text", + "content": " is the set of training images labeled with " + }, + { + "bbox": [ + 47, + 621, + 288, + 658 + ], + "type": "inline_equation", + "content": "y^6" + }, + { + "bbox": [ + 47, + 621, + 288, + 658 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 621, + 288, + 658 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 47, + 621, + 288, + 658 + ], + "type": "text", + "content": " is the text encoder. We define the normalized class association, which measures the conditional likelihood of aligning" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 663, + 287, + 713 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 47, + 663, + 287, + 684 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 663, + 287, + 684 + ], + "spans": [ + { + "bbox": [ + 47, + 663, + 287, + 684 + ], + "type": "inline_equation", + "content": "{}^{3}" + }, + { + "bbox": [ + 47, + 663, + 287, + 684 + ], + "type": "text", + "content": " diminishing returns property means " + }, + { + "bbox": [ + 47, + 663, + 287, + 684 + ], + "type": "inline_equation", + "content": "\\forall A \\subseteq B \\subseteq V \\smallsetminus v" + }, + { + "bbox": [ + 47, + 663, + 287, + 684 + ], + "type": "text", + "content": " ,we have " + }, + { + "bbox": [ + 47, + 663, + 287, + 684 + ], + "type": "inline_equation", + "content": "\\mathcal{F}\\left( {A + \\{ v\\} }\\right) - \\mathcal{F}\\left( A\\right) \\geq \\mathcal{F}\\left( {B + \\{ v\\} }\\right) - \\mathcal{F}\\left( B\\right)" + }, + { + "bbox": [ + 47, + 663, + 287, + 684 + ], + "type": "text", + "content": " ." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 58, + 684, + 274, + 693 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 684, + 274, + 693 + ], + "spans": [ + { + "bbox": [ + 58, + 684, + 274, + 693 + ], + "type": "text", + "content": "4 A submodular function is monotone if " + }, + { + "bbox": [ + 58, + 684, + 274, + 693 + ], + "type": "inline_equation", + "content": "\\forall A\\subseteq B,\\mathcal{F}(A)\\leq \\mathcal{F}(B)" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 58, + 693, + 282, + 703 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 693, + 282, + 703 + ], + "spans": [ + { + "bbox": [ + 58, + 693, + 282, + 703 + ], + "type": "text", + "content": "5 Any linear combination of submodular functions is still submodular." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 58, + 703, + 186, + 713 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 703, + 186, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 703, + 186, + 713 + ], + "type": "inline_equation", + "content": "^6" + }, + { + "bbox": [ + 58, + 703, + 186, + 713 + ], + "type": "text", + "content": "In " + }, + { + "bbox": [ + 58, + 703, + 186, + 713 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 58, + 703, + 186, + 713 + ], + "type": "text", + "content": "-way-" + }, + { + "bbox": [ + 58, + 703, + 186, + 713 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 58, + 703, + 186, + 713 + ], + "type": "text", + "content": "-shot setting, " + }, + { + "bbox": [ + 58, + 703, + 186, + 713 + ], + "type": "inline_equation", + "content": "|\\mathcal{X}_y| = K" + }, + { + "bbox": [ + 58, + 703, + 186, + 713 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12 + } + ], + "sub_type": "ref_text" + }, + { + "bbox": [ + 304, + 72, + 547, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 109 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 109 + ], + "type": "text", + "content": "featurized images of a class given a concept's textual embedding, " + }, + { + "bbox": [ + 304, + 72, + 547, + 109 + ], + "type": "inline_equation", + "content": "\\overline{Sim}(y|c) = Sim(y, c) / \\sum_{y' \\in \\mathcal{Y}} Sim(y', c)" + }, + { + "bbox": [ + 304, + 72, + 547, + 109 + ], + "type": "text", + "content": ", and compute its negative entropy:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 335, + 114, + 547, + 142 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 335, + 114, + 547, + 142 + ], + "spans": [ + { + "bbox": [ + 335, + 114, + 547, + 142 + ], + "type": "interline_equation", + "content": "D (c) = \\sum_ {y ^ {\\prime} \\in Y} \\overline {{S i m}} \\left(y ^ {\\prime} | c\\right) \\cdot \\log \\left(\\overline {{S i m}} \\left(y ^ {\\prime} | c\\right)\\right) \\tag {4}", + "image_path": "cbba950cfcedd5055a4813dcaddeb9f10509aa565374c201775a1d062f0f4d3c.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 148, + 546, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 148, + 546, + 185 + ], + "spans": [ + { + "bbox": [ + 304, + 148, + 546, + 185 + ], + "type": "text", + "content": "Maximizing " + }, + { + "bbox": [ + 304, + 148, + 546, + 185 + ], + "type": "inline_equation", + "content": "D(c)" + }, + { + "bbox": [ + 304, + 148, + 546, + 185 + ], + "type": "text", + "content": " will result in the selection of concepts that have peaked " + }, + { + "bbox": [ + 304, + 148, + 546, + 185 + ], + "type": "inline_equation", + "content": "\\overline{Sim}(y|c)" + }, + { + "bbox": [ + 304, + 148, + 546, + 185 + ], + "type": "text", + "content": ", indicating that a concept is strongly associated with only a few classes." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 190, + 547, + 285 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 190, + 547, + 285 + ], + "spans": [ + { + "bbox": [ + 304, + 190, + 547, + 285 + ], + "type": "text", + "content": "**Coverage Score.** The second term of equation 2 is a minimax facility location function that tries to minimize the maximum distance between each element in the subset and the candidate set. For distance, we use the cosine between the features of the two concepts extracted by the text encoder: " + }, + { + "bbox": [ + 304, + 190, + 547, + 285 + ], + "type": "inline_equation", + "content": "\\phi(c_1, c_2) = \\cos(\\mathcal{T}(c_1), \\mathcal{T}(c_2))" + }, + { + "bbox": [ + 304, + 190, + 547, + 285 + ], + "type": "text", + "content": ". A high coverage score yields a diverse bottleneck that covers different possible appearances for a target class." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 293, + 495, + 306 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 293, + 495, + 306 + ], + "spans": [ + { + "bbox": [ + 305, + 293, + 495, + 306 + ], + "type": "text", + "content": "3.3. Optimize Class-concept Association" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 311, + 547, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 311, + 547, + 335 + ], + "spans": [ + { + "bbox": [ + 304, + 311, + 547, + 335 + ], + "type": "text", + "content": "In this section, we explain how we compute " + }, + { + "bbox": [ + 304, + 311, + 547, + 335 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 304, + 311, + 547, + 335 + ], + "type": "text", + "content": " (the concept predictor) and learn " + }, + { + "bbox": [ + 304, + 311, + 547, + 335 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 311, + 547, + 335 + ], + "type": "text", + "content": " (the label predictor) of the bottleneck." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 340, + 547, + 423 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 340, + 547, + 423 + ], + "spans": [ + { + "bbox": [ + 304, + 340, + 547, + 423 + ], + "type": "text", + "content": "Predict the Concept Scores. The concept predictor " + }, + { + "bbox": [ + 304, + 340, + 547, + 423 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 304, + 340, + 547, + 423 + ], + "type": "text", + "content": " is not learned in our method because the alignment model we use can measure the correlation between image and text through dot product. We treat the dot product of input image feature " + }, + { + "bbox": [ + 304, + 340, + 547, + 423 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 304, + 340, + 547, + 423 + ], + "type": "text", + "content": " and the concept space " + }, + { + "bbox": [ + 304, + 340, + 547, + 423 + ], + "type": "inline_equation", + "content": "\\mathbf{E}_C" + }, + { + "bbox": [ + 304, + 340, + 547, + 423 + ], + "type": "text", + "content": " defined in Section 3.2 as " + }, + { + "bbox": [ + 304, + 340, + 547, + 423 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 304, + 340, + 547, + 423 + ], + "type": "text", + "content": ": " + }, + { + "bbox": [ + 304, + 340, + 547, + 423 + ], + "type": "inline_equation", + "content": "g(\\mathbf{x},\\mathbf{E}_C) = \\mathbf{x}\\cdot \\mathbf{E}_C^\\top" + }, + { + "bbox": [ + 304, + 340, + 547, + 423 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 340, + 547, + 423 + ], + "type": "inline_equation", + "content": "g(\\mathbf{x},\\mathbf{E}_C)\\in \\mathbb{R}^{N_C}" + }, + { + "bbox": [ + 304, + 340, + 547, + 423 + ], + "type": "text", + "content": ", and each element is the score of image " + }, + { + "bbox": [ + 304, + 340, + 547, + 423 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 304, + 340, + 547, + 423 + ], + "type": "text", + "content": " on a concept." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 428, + 547, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 428, + 547, + 579 + ], + "spans": [ + { + "bbox": [ + 304, + 428, + 547, + 579 + ], + "type": "text", + "content": "Concept Weight Matrix. We learn a linear function for the label predictor " + }, + { + "bbox": [ + 304, + 428, + 547, + 579 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 428, + 547, + 579 + ], + "type": "text", + "content": " that maps from concept scores to the final prediction. Intuitively, these weights encode the affinity of the concept to the class, allowing the model to represent that classes depend differently on the same concept. To normalize the class-concept association distributed over the weight matrix, we regularize the matrix with the softmax activation function. Concretely, we learn a concept weight matrix " + }, + { + "bbox": [ + 304, + 428, + 547, + 579 + ], + "type": "inline_equation", + "content": "\\mathbf{W} \\in \\mathbb{R}^{N \\times N_C}" + }, + { + "bbox": [ + 304, + 428, + 547, + 579 + ], + "type": "text", + "content": ", that is used for prediction: " + }, + { + "bbox": [ + 304, + 428, + 547, + 579 + ], + "type": "inline_equation", + "content": "\\hat{y} = \\operatorname{argmax}\\left(g(\\mathbf{x},\\mathbf{E}_C)\\cdot \\sigma (\\mathbf{W})^\\top\\right)" + }, + { + "bbox": [ + 304, + 428, + 547, + 579 + ], + "type": "text", + "content": ", in which " + }, + { + "bbox": [ + 304, + 428, + 547, + 579 + ], + "type": "inline_equation", + "content": "\\sigma (\\cdot)" + }, + { + "bbox": [ + 304, + 428, + 547, + 579 + ], + "type": "text", + "content": " is the softmax activation which is applied along the concepts axis: " + }, + { + "bbox": [ + 304, + 428, + 547, + 579 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_{y,c} = e^{\\mathbf{W}_{y,c}} / \\sum_{y'\\in \\mathcal{Y}}e^{\\mathbf{W}_{y',c}}" + }, + { + "bbox": [ + 304, + 428, + 547, + 579 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "content": "Initializing the Weight Matrix with Language Priors. Previous work trains the concept weight matrix freely from scratch, which is not feasible in low-resource scenarios where we don't have enough data to learn the weight effectively. To extend the application of CBM to few-shot image classification, we consider biasing the weights toward the initial association from the language model used to propose concepts. If a concept " + }, + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "content": " was present in " + }, + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "inline_equation", + "content": "C_y" + }, + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "content": ", we initialize the elements of " + }, + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "content": " corresponding to the weight between class " + }, + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "content": " and concept " + }, + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "content": " to a higher value before optimization: " + }, + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "inline_equation", + "content": "W_{y,c} = 1" + }, + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "content": ", if " + }, + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "inline_equation", + "content": "c \\in C_y" + }, + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "content": ", otherwise 0." + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "19190" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 71, + 175, + 148 + ], + 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Test accuracy " + }, + { + "bbox": [ + 46, + 316, + 545, + 328 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 46, + 316, + 545, + 328 + ], + "type": "text", + "content": " comparison between LaBo and Linear Probe on 11 datasets. The x-axis represents the number of labeled images." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 178, + 229, + 295, + 306 + ], + "blocks": [ + { + "bbox": [ + 178, + 229, + 295, + 306 + ], + "lines": [ + { + "bbox": [ + 178, + 229, + 295, + 306 + ], + "spans": [ + { + "bbox": [ + 178, + 229, + 295, + 306 + ], + "type": "image", + "image_path": "98298d1b9030a3b048a8439b85ce4629274823dbf1ab98bb6052dbbaa00218c1.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 299, + 229, + 416, + 306 + ], + "blocks": [ + { + "bbox": [ + 299, + 229, + 416, + 306 + ], + "lines": [ + { + "bbox": [ + 299, + 229, + 416, + 306 + ], + "spans": [ + { + "bbox": [ + 299, + 229, + 416, + 306 + ], + "type": "image", + "image_path": "1cdf808641182b78ac6c614f478dd536ed20ac80f45b88fb3c3a2b8089bcd393.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 420, + 229, + 538, + 306 + ], + "blocks": [ + { + "bbox": [ + 420, + 229, + 538, + 306 + ], + "lines": [ + { + "bbox": [ + 420, + 229, + 538, + 306 + ], + "spans": [ + { + "bbox": [ + 420, + 229, + 538, + 306 + ], + "type": "image", + "image_path": "0be002c05e48125fd576a388d9debfe3a3675b923a4da0c8c6890863fe0f6680.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 339, + 180, + 353 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 339, + 180, + 353 + ], + "spans": [ + { + "bbox": [ + 47, + 339, + 180, + 353 + ], + "type": "text", + "content": "3.4. Prepare the Candidates" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 358, + 289, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 358, + 289, + 491 + ], + "spans": [ + { + "bbox": [ + 46, + 358, + 289, + 491 + ], + "type": "text", + "content": "To collect the candidates " + }, + { + "bbox": [ + 46, + 358, + 289, + 491 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 358, + 289, + 491 + ], + "type": "text", + "content": " to feed into our model, we prompt GPT-3 to generate relevant sentences by incorporating the class name in 5 templates shown in supplementary materials. For example, as shown in the top-left of Figure 2, we prompt GPT-3 by asking \"describe what the axolotl looks like\", and the GPT-3 returns a sentence about the target class. We obtain 500 sentences for each class and automatically split these sentences into shorter concepts using a T5 model [45] fine-tuned on a small set of annotated sentence-concept pairs. We use string match to identify and remove class name tokens in each concept. (see supplementary)" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 47, + 502, + 165, + 517 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 502, + 165, + 517 + ], + "spans": [ + { + "bbox": [ + 47, + 502, + 165, + 517 + ], + "type": "text", + "content": "4. Experimental Setup" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 46, + 523, + 287, + 560 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 523, + 287, + 560 + ], + "spans": [ + { + "bbox": [ + 46, + 523, + 287, + 560 + ], + "type": "text", + "content": "We evaluate our method on a diverse set of 11 datasets (Section 4.1) and compare it to its end-to-end counterpart and other interpretable CBM methods (Section 4.2)." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 47, + 568, + 105, + 580 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 568, + 105, + 580 + ], + "spans": [ + { + "bbox": [ + 47, + 568, + 105, + 580 + ], + "type": "text", + "content": "4.1. Dataset" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 46, + 587, + 289, + 684 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 587, + 289, + 684 + ], + "spans": [ + { + "bbox": [ + 46, + 587, + 289, + 684 + ], + "type": "text", + "content": "We select a comprehensive benchmark of 11 image classification datasets spanning a diverse set of domains, including (1) Common objects: ImageNet [11], CIFAR-10 and CIFAR-100 [26]; (2) Fine-grained objects: Food-101 [3], FGVC-Aircraft [32], Flower-102 [39], CUB-200-2011 [67]; (3) Actions: UCF-101 [59]; (4) Textures: DTD [10]; (5) Skin tumors: HAM10000 [64] and (6) Satellite images: RE-SISC45 [8]. We use train/dev/test splits for all the datasets." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 340, + 547, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 340, + 547, + 413 + ], + "spans": [ + { + "bbox": [ + 306, + 340, + 547, + 413 + ], + "type": "text", + "content": "Detailed statistics are presented in the supplementary material. We follow the few-shot evaluation protocol proposed by CLIP [44] with 1, 2, 4, 8, and 16 images randomly sampled from the training set for each class. We also evaluate in the fully-supervised setting where we train on all available images. For all experiments, we report the test accuracy." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 418, + 372, + 430 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 418, + 372, + 430 + ], + "spans": [ + { + "bbox": [ + 306, + 418, + 372, + 430 + ], + "type": "text", + "content": "4.2. Baselines" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 436, + 545, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 436, + 545, + 460 + ], + "spans": [ + { + "bbox": [ + 306, + 436, + 545, + 460 + ], + "type": "text", + "content": "We compare our model, LaBo, with black-box linear probing and two interpretable methods." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 464, + 547, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 464, + 547, + 525 + ], + "spans": [ + { + "bbox": [ + 306, + 464, + 547, + 525 + ], + "type": "text", + "content": "Linear Probe Following previous evaluations on CBM [25, 70], linear probing serves as our primary baseline for comparison. We follow the implementation of CLIP [44] by training the scikit-learn's L-BFGS logistic regression with a hyperparameter sweep on the L2 regularization weight." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 306, + 529, + 545, + 577 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 529, + 545, + 577 + ], + "spans": [ + { + "bbox": [ + 306, + 529, + 545, + 577 + ], + "type": "text", + "content": "PCBM Post-hoc Concept Bottleneck Model [70] designs a residual modeling step that directly maps the original image embedding into the label space. PCBM treats the attributes of each class in ConceptNet [60] as concepts." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 306, + 581, + 547, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 581, + 547, + 617 + ], + "spans": [ + { + "bbox": [ + 306, + 581, + 547, + 617 + ], + "type": "text", + "content": "CompDL Compositional Derivation Learning [71] learns a linear layer over CLIP similarity scores between human-designed class descriptions and images to predict targets." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 306, + 623, + 438, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 623, + 438, + 635 + ], + "spans": [ + { + "bbox": [ + 306, + 623, + 438, + 635 + ], + "type": "text", + "content": "4.3. Implementation Details" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 306, + 641, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 641, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 641, + 547, + 714 + ], + "type": "text", + "content": "We prompt GPT-3-text-davinci-002 to generate concepts. The CLIP model is adapted from OpenAI's public repo with ViT-L/14 as the default vision backbone. We only use CLIP-RN50 as the backbone when comparing with PCBM, and ViT-B/32 with CompDL for a fair comparison. We implement the submodular function using the apricot package and" + } + ] + } + ], + "index": 26 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 46, + 693, + 287, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 693, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 693, + 287, + 712 + ], + "type": "text", + "content": "7We use the same set of prompts for all datasets except UCF-101 since it is very different to describe an action." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19191" + } + ] + } + ], + "index": 28 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 70, + 285, + 102 + ], + "blocks": [ + { + "bbox": [ + 48, + 70, + 285, + 102 + ], + "lines": [ + { + "bbox": [ + 48, + 70, + 285, + 102 + ], + "spans": [ + { + "bbox": [ + 48, + 70, + 285, + 102 + ], + "type": "table", + "html": "
Method124816FullAvg
Linear Probe51.6965.1372.3377.3881.5387.3872.57
LaBo (Ours)63.3568.1072.0876.1979.1185.7274.09
", + "image_path": "f2c720bbdd667c70516874296d022a748b1e5c91062cc01fa5feb12bd691ee4c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 59, + 129, + 272, + 183 + ], + "blocks": [ + { + "bbox": [ + 55, + 110, + 278, + 121 + ], + "lines": [ + { + "bbox": [ + 55, + 110, + 278, + 121 + ], + "spans": [ + { + "bbox": [ + 55, + 110, + 278, + 121 + ], + "type": "text", + "content": "Table 1. Mean accuracy across all datasets, at different shots ." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 59, + 129, + 272, + 183 + ], + "lines": [ + { + "bbox": [ + 59, + 129, + 272, + 183 + ], + "spans": [ + { + "bbox": [ + 59, + 129, + 272, + 183 + ], + "type": "table", + "html": "
Methodw/ end-to-endCIFAR-10CIFAR-100
PCBM [70]✗84.556.0
LaBo (Ours)✗87.969.1
PCBM-h [70]✓87.669.9
Linear Probe✓88.870.1
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Methodw/ manual concepts15Full
CompDL [71]✓13.633.252.6
LaBo (Ours)✗35.155.771.8
Linear Probe-28.455.475.5
", + "image_path": "b843391b81534a82cfd50580b7cf8ffd553f5218b9c1a990095a8e6b85316b92.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 319, + 287, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 319, + 287, + 403 + ], + "spans": [ + { + "bbox": [ + 46, + 319, + 287, + 403 + ], + "type": "text", + "content": "set the default number of concepts selected for each class to 50. To train the linear function, we use the Pytorch-lightning library with Adam [24] optimizer. We tune the batch size, learning rate, and submodular weights on the development set. Model checkpoints with the highest validation accuracy are evaluated on the test set. We list the hyperparameters for all datasets and shots in the supplementary material." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 414, + 118, + 426 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 414, + 118, + 426 + ], + "spans": [ + { + "bbox": [ + 47, + 414, + 118, + 426 + ], + "type": "text", + "content": "5. Evaluation" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 433, + 132, + 445 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 433, + 132, + 445 + ], + "spans": [ + { + "bbox": [ + 47, + 433, + 132, + 445 + ], + "type": "text", + "content": "5.1. Main Results" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 451, + 287, + 487 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 451, + 287, + 487 + ], + "spans": [ + { + "bbox": [ + 46, + 451, + 287, + 487 + ], + "type": "text", + "content": "We compare LaBo's performance with a linear probe and other interpretable baselines to evaluate if we can maintain black box accuracy without sacrificing interpretability." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 492, + 287, + 599 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 492, + 287, + 599 + ], + "spans": [ + { + "bbox": [ + 46, + 492, + 287, + 599 + ], + "type": "text", + "content": "Comparison with End-to-End Model. One of our goals is to close the performance gap between interpretable and black box models. Table 1 reports the mean test accuracy of LaBo and the linear probe on 11 datasets. LaBo significantly outperforms the end-to-end model when little data is available and continues to be competitive as the number of data increases. On average, LaBo surpasses the linear probe by " + }, + { + "bbox": [ + 46, + 492, + 287, + 599 + ], + "type": "inline_equation", + "content": "1.5\\%" + }, + { + "bbox": [ + 46, + 492, + 287, + 599 + ], + "type": "text", + "content": ". Figure 3 provides analytic performance comparisons between LaBo and Linear Probe on each dataset." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 600, + 288, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 600, + 288, + 685 + ], + "spans": [ + { + "bbox": [ + 46, + 600, + 288, + 685 + ], + "type": "text", + "content": "In general, LaBo's performance depends on the quality of knowledge extracted from GPT-3. For common categories, GPT-3 contains high-quality knowledge allowing substantial improvement over linear probes. For some fine-grained datasets, such as Flower-102, GPT-3's knowledge is largely non-visual, as seen in Figure 7. In such cases, specialized language models could be used to improve LaBo." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 689, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 289, + 715 + ], + "type": "text", + "content": "Comparison with other Interpretable Methods. Table 2 compares LaBo's performance with PCBM and Linear Probe." + } + ] + } + ], + "index": 12 + }, + { + "type": "table", + "bbox": [ + 312, + 71, + 539, + 142 + ], + "blocks": [ + { + "bbox": [ + 47, + 297, + 286, + 307 + ], + "lines": [ + { + "bbox": [ + 47, + 297, + 286, + 307 + ], + "spans": [ + { + "bbox": [ + 47, + 297, + 286, + 307 + ], + "type": "text", + "content": "Table 3. LaBo and CompDL evaluated on CUB for 1/5/full shots." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 312, + 71, + 539, + 142 + ], + "lines": [ + { + "bbox": [ + 312, + 71, + 539, + 142 + ], + "spans": [ + { + "bbox": [ + 312, + 71, + 539, + 142 + ], + "type": "table", + "html": "
n. of concepts per class (k)n. of shots
124816Full
141.8952.4561.7665.9969.6178.95
552.5461.1367.2272.9075.6283.83
1058.0064.5969.9074.5077.4384.66
2561.7266.3371.3975.2879.0485.26
5063.0367.7971.8876.0879.1085.71
", + "image_path": "912b6a39462ebfc18b84b7b9959560cd94efa0e52570e5a691b9fe43ef03047c.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_body" + } + ], + "index": 13 + }, + { + "type": "table", + "bbox": [ + 312, + 182, + 538, + 255 + ], + "blocks": [ + { + "bbox": [ + 305, + 152, + 547, + 174 + ], + "lines": [ + { + "bbox": [ + 305, + 152, + 547, + 174 + ], + "spans": [ + { + "bbox": [ + 305, + 152, + 547, + 174 + ], + "type": "text", + "content": "Table 4. Ablation results on bottleneck sizes. We vary the sizes of the bottlenecks and report the average performance on 11 datasets." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 312, + 182, + 538, + 255 + ], + "lines": [ + { + "bbox": [ + 312, + 182, + 538, + 255 + ], + "spans": [ + { + "bbox": [ + 312, + 182, + 538, + 255 + ], + "type": "table", + "html": "
Selection Methodn. of shots
124816Full
RANDOM59.2464.7170.4274.0778.2985.06
SIMILARITY54.5961.4267.1772.6677.3284.88
COVERAGE59.7365.9370.8274.7178.9085.60
DISCRIM60.9966.4970.9374.8177.9085.31
SUBMODULAR63.0367.7971.8876.0879.1085.71
", + "image_path": "6b4fdd65c0bb8a547a9b7aa52e8efc4d46c5998aa9fdefa7325b80ec3b71bd34.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "table_body" + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 262, + 545, + 285 + ], + "lines": [ + { + "bbox": [ + 305, + 262, + 545, + 285 + ], + "spans": [ + { + "bbox": [ + 305, + 262, + 545, + 285 + ], + "type": "text", + "content": "Table 5. Ablation results on concept selection methods. We report mean test accuracy on 11 datasets." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 297, + 547, + 358 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 297, + 547, + 358 + ], + "spans": [ + { + "bbox": [ + 304, + 297, + 547, + 358 + ], + "type": "text", + "content": "LaBo outperforms PCBM by " + }, + { + "bbox": [ + 304, + 297, + 547, + 358 + ], + "type": "inline_equation", + "content": "3.4\\%" + }, + { + "bbox": [ + 304, + 297, + 547, + 358 + ], + "type": "text", + "content": " on CIFAR-10 and " + }, + { + "bbox": [ + 304, + 297, + 547, + 358 + ], + "type": "inline_equation", + "content": "13.1\\%" + }, + { + "bbox": [ + 304, + 297, + 547, + 358 + ], + "type": "text", + "content": " on CIFAR-100. LaBo maintains comparable performance to PCBM with a residual predictor (PCBM-h), without circumventing the bottleneck. In Table 3, LaBo is more accurate than CompDL [71] without manually constructed concepts." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 365, + 400, + 378 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 365, + 400, + 378 + ], + "spans": [ + { + "bbox": [ + 306, + 365, + 400, + 378 + ], + "type": "text", + "content": "5.2. Ablation Study" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 384, + 547, + 431 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 384, + 547, + 431 + ], + "spans": [ + { + "bbox": [ + 304, + 384, + 547, + 431 + ], + "type": "text", + "content": "We evaluate the importance of each of our model's components on final performance. Specifically, we compare results with different concept selection methods, language and random weight initialization, and bottleneck sizes." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 437, + 547, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 437, + 547, + 617 + ], + "spans": [ + { + "bbox": [ + 304, + 437, + 547, + 617 + ], + "type": "text", + "content": "Concept Selection Methods. We compare our submodular function with four concept selection methods: (1) RANDOM: we randomly sample a subset of concepts from the candidates for each class; (2) SIMILARITY: we select the top concepts ranked by their similarity scores with the class calculated by equation 3; (3) COVERAGE: we only consider the coverage score for concept selection; (4) DISCRIM: we only consider the discriminability score for concept selection. As shown in Table 5, our submodular function, which jointly optimizes coverage and discriminability, achieves the best performance across different numbers of shots. We notice that using coverage or discriminability alone still outperforms using similarity between the class and random selection. The selection method plays an important role in all data settings, but its impact decreases with more supervision." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 623, + 547, + 672 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 623, + 547, + 672 + ], + "spans": [ + { + "bbox": [ + 304, + 623, + 547, + 672 + ], + "type": "text", + "content": "Initialization with Language Priors. We deactivate the LM initialization and use random initialization instead. Figure 4 shows that the LM prior is more important for low shot settings since there is less signal to guide concept importance." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "type": "text", + "content": "Bottleneck Size. In Table 4, we compare performance for different bottleneck sizes ranging from 1 to 50 concepts selected by the submodular function. Larger bottlenecks are" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "19192" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 72, + 284, + 170 + ], + "blocks": [ + { + "bbox": [ + 50, + 72, + 284, + 170 + ], + "lines": [ + { + "bbox": [ + 50, + 72, + 284, + 170 + ], + "spans": [ + { + "bbox": [ + 50, + 72, + 284, + 170 + ], + "type": "image", + "image_path": "0119f7d29c86bd03b71d85f73d27c4d7af0978206d2b036d3749cb3a36bc3c76.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 49, + 209, + 279, + 262 + ], + "blocks": [ + { + "bbox": [ + 46, + 182, + 287, + 205 + ], + "lines": [ + { + "bbox": [ + 46, + 182, + 287, + 205 + ], + "spans": [ + { + "bbox": [ + 46, + 182, + 287, + 205 + ], + "type": "text", + "content": "Figure 4. Language Prior vs. Random Weight initialization average over all datasets." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 49, + 209, + 279, + 262 + ], + "lines": [ + { + "bbox": [ + 49, + 209, + 279, + 262 + ], + "spans": [ + { + "bbox": [ + 49, + 209, + 279, + 262 + ], + "type": "image", + "image_path": "3624ddebc571049301334d5df1533a6845a8c8a713f793f61492167663562a24.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 50, + 266, + 279, + 319 + ], + "blocks": [ + { + "bbox": [ + 50, + 266, + 279, + 319 + ], + "lines": [ + { + "bbox": [ + 50, + 266, + 279, + 319 + ], + "spans": [ + { + "bbox": [ + 50, + 266, + 279, + 319 + ], + "type": "image", + "image_path": "c6fb465506d9be5bc5f6cf94848a554873e448ee2b1935ee398f593fcf70c3f5.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 330, + 289, + 376 + ], + "lines": [ + { + "bbox": [ + 46, + 330, + 289, + 376 + ], + "spans": [ + { + "bbox": [ + 46, + 330, + 289, + 376 + ], + "type": "text", + "content": "Figure 5. Human evaluation on Factuality and Groundability for different bottlenecks on ImageNet. \"w/o Submod\" denotes without submodular function, i.e., random concept selection. \"w/o LM\" denotes no language prior weight initialization." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 388, + 287, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 388, + 287, + 411 + ], + "spans": [ + { + "bbox": [ + 46, + 388, + 287, + 411 + ], + "type": "text", + "content": "usually better, but with more data, similar performance is achievable with smaller bottlenecks." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 428, + 160, + 440 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 428, + 160, + 440 + ], + "spans": [ + { + "bbox": [ + 47, + 428, + 160, + 440 + ], + "type": "text", + "content": "5.3. Human Evaluation" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 447, + 289, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 447, + 289, + 639 + ], + "spans": [ + { + "bbox": [ + 46, + 447, + 289, + 639 + ], + "type": "text", + "content": "It is important for interpretability that the vision-language alignment model correctly grounds concepts to images. For example, if a concept \"usually round\" ranks both circles and stripes highly, the name of the attribute does not faithfully represent the computation. In addition, it is important that the automatically generated concept bottlenecks factually correspond to the class they describe. To this end, we introduce two metrics to evaluate the quality of our concept bottleneck items: (1) Factuality measures how accurate the concepts are in describing their designated class by requiring annotators to judge whether they describe ground truth images, and (2) Groundability measures how consistent the vision-language model grounding of the concepts to images with human interpretations by requiring annotators to judge their applicability on the top-10 images ranked by CLIP alignment scores." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 646, + 288, + 682 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 646, + 288, + 682 + ], + "spans": [ + { + "bbox": [ + 46, + 646, + 288, + 682 + ], + "type": "text", + "content": "Setup. Both metrics are computed by asking annotators to select images that describe a highly ranked concept in our bottlenecks. Formally, the two metrics are represented by:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 63, + 690, + 271, + 717 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 690, + 271, + 717 + ], + "spans": [ + { + "bbox": [ + 63, + 690, + 271, + 717 + ], + "type": "interline_equation", + "content": "\\operatorname {F a c t u a l i t y} (c) = \\frac {\\text {n u m b e r o f i m a g e s s e l e c t e d}}{k \\text {g r o u n d t r u t h i m a g e s o f t h e c l a s s}}", + "image_path": "df9aeec00e74744d774802afbbc07fc182664bde42df8e6f43d7b5e5c14ea350.jpg" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 309, + 72, + 541, + 171 + ], + "blocks": [ + { + "bbox": [ + 309, + 72, + 541, + 171 + ], + "lines": [ + { + "bbox": [ + 309, + 72, + 541, + 171 + ], + "spans": [ + { + "bbox": [ + 309, + 72, + 541, + 171 + ], + "type": "image", + "image_path": "f5e280be94cb40596c8c872c1314b682666101190e60c04f802ff934bf96cc70.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 182, + 545, + 205 + ], + "lines": [ + { + "bbox": [ + 305, + 182, + 545, + 205 + ], + "spans": [ + { + "bbox": [ + 305, + 182, + 545, + 205 + ], + "type": "text", + "content": "Figure 6. Percentage of invalid concepts identified by humans for different bottlenecks on ImageNet. Lower percentage is better." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 310, + 206, + 538, + 277 + ], + "blocks": [ + { + "bbox": [ + 310, + 206, + 538, + 277 + ], + "lines": [ + { + "bbox": [ + 310, + 206, + 538, + 277 + ], + "spans": [ + { + "bbox": [ + 310, + 206, + 538, + 277 + ], + "type": "table", + "html": "
MetricsLaBow/o Submodw/o LM
Factuality (%) ↑24.022.814.1
Groundability (%) ↑14.122.520.2
Non Visual (%) ↓4.85.65.8
Non Sensical (%) ↓8.09.68.7
Unknown Vocab (%) ↓10.210.510.7
", + "image_path": "10427b7ef4fe9ee2f62a156555ac447c86dc97b0e2bda8ab5df939636c3891d3.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 285, + 547, + 319 + ], + "lines": [ + { + "bbox": [ + 305, + 285, + 547, + 319 + ], + "spans": [ + { + "bbox": [ + 305, + 285, + 547, + 319 + ], + "type": "text", + "content": "Table 6. Average human evaluation results of LaBo on 11 datasets. We also evaluate LaBo by removing the submodular function (w/o Submod) and language model priors (w/o LM)." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 310, + 331, + 539, + 357 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 331, + 539, + 357 + ], + "spans": [ + { + "bbox": [ + 310, + 331, + 539, + 357 + ], + "type": "interline_equation", + "content": "\\operatorname {G r o u n d a b i l i t y} (c) = \\frac {\\text {n u m b e r o f i m a g e s s e l e c t e d}}{\\text {t o p - k a l i n g e d i m a g e s o f t h e c o n c e p t}}", + "image_path": "9e74e8cd7539d68c845b4a1c2f17baf9bcffa8e8ec6eea19553b97b1e637241b.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 361, + 547, + 470 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 361, + 547, + 470 + ], + "spans": [ + { + "bbox": [ + 304, + 361, + 547, + 470 + ], + "type": "text", + "content": "where we set " + }, + { + "bbox": [ + 304, + 361, + 547, + 470 + ], + "type": "inline_equation", + "content": "k = 10" + }, + { + "bbox": [ + 304, + 361, + 547, + 470 + ], + "type": "text", + "content": ". In addition to the two main metrics, we ask the annotator to select whether the concept is non-visual, nonsensical, or contains unknown vocabulary. We randomly sample 20 classes for each dataset and evaluate the top 5 concepts (ranked by the weights of the linear function) for each class, 100 concepts per dataset. We release our human evaluation task on Amazon Mechanical Turk and collect three annotations for each concept. More details on the task and the results can be found in the supplement." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 475, + 547, + 607 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 475, + 547, + 607 + ], + "spans": [ + { + "bbox": [ + 304, + 475, + 547, + 607 + ], + "type": "text", + "content": "Baselines. We evaluate the bottlenecks under full supervision and compare them with two main baselines: (1) LaBo (w/o Submod), which randomly selects the concepts instead of using the submodular function, and (2) LaBo (w/o LM), which initializes the concept weight matrix randomly without leveraging the priors of the language model. For ImageNet, we add two additional baselines using human-written text: (1) WordNet [13] definitions and (2) Wikipedia sentences [22]. We adopt the same preprocessing pipeline as LaBo to extract concepts from human-written resources and utilize the submodular function to select the bottlenecks." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 613, + 547, + 686 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 613, + 547, + 686 + ], + "spans": [ + { + "bbox": [ + 304, + 613, + 547, + 686 + ], + "type": "text", + "content": "Results. Figure 5 shows the evaluation on ImageNet, and we observe that LaBo has significantly higher Factuality and Groundability than human-written text. We further observe that removing components from our system (submodular and LM Prior) hurt both human evaluation metrics, indicating their collective importance in our system. In addition, Figure" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "text", + "content": "With the only exception of Factuality for Flower-102 where we set " + }, + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "inline_equation", + "content": "k = 8" + }, + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "text", + "content": " because there are not enough images in the dev set." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19193" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 51, + 71, + 542, + 383 + ], + "blocks": [ + { + "bbox": [ + 51, + 71, + 542, + 383 + ], + "lines": [ + { + "bbox": [ + 51, + 71, + 542, + 383 + ], + "spans": [ + { + "bbox": [ + 51, + 71, + 542, + 383 + ], + "type": "table", + "html": "
Class NameTop-3 ConceptsClass NameTop-3 ConceptsClass NameTop-3 ConceptsClass NameTop-3 Concepts
ImageNetbadger1. short legs and long body make it an excellent diggerant1. black and red stingerhammer1.long, thin tool with a wooden handlewater buffalo1. large head with short, curved horns
2. black-and-white striped fur2. black-and-white striped fur2. small, black insect with six legs2. small, black insect with six legs2. great tool for pounding object2. great tool for pounding object2. heaviest living species of bovid2. heaviest living species of bovid
3. coat is very shaggy3. coat is very shaggy3. long, slender antennae that it uses to smell and touch3. long, slender antennae that it uses to smell and touch3. used to pound on surfaces3. used to pound on surfaces3. huge, dark-colored animal3. huge, dark-colored animal
CUBeared grebe1. black and white plumage that is striking in the sunlighthorned lark1. black line running through yellow facewhite pelican1. long neck and bill make it look like a giant swanarctic tern1. breeds in greenland, iceland, and northern russia
2. black body with a long, slender neck2. black body with a long, slender neck2. head is black with a white horn on each side2. head is black with a white horn on each side2. large, white bird with black wings2. large, white bird with black wings2. large, white birds2. black and white markings
3. red and black bill3. red and black bill3. black horn on each side of their head3. black horn on each side of their head3. bill is huge and yellow3. bill is huge and yellow3. bill is huge and yellow3. small white bird with a black cap
Flowerwater lily1. depicted in artworks of ponds and waterfallbarbeton daisy1. scientific name for the flower is taraxacum officinalmarigold1. central disc with smaller floretstiger lily1. long, protruding stamen
2. member of the nymphaceae family2. member of the nymphaceae family2. named after the city of barberton2. named after the city of barberton2. have a slightly furry texture2. have a slightly furry texture2. have a slightly furry texture2. orange with black spots and stripes
3. lily pads float3. lily pads float3. member of the daisy family3. member of the daisy family3. bold and vibrant color palette3. bold and vibrant color palette3. bold and vibrant color palette3. bold and vibrant color palette
UCF-101archery1. grip bow tightly in their left handdrumming1. blur as they fly over the drumssurfing1. deep blue colorlong jump1. get out of sandpit
2. focused and concentrated on their task2. focused and concentrated on their task2. sitting on a stool in front of a drum set2. sitting on a stool in front of a drum set2. tans contrast with the white of their boards2. tans contrast with the white of their boards2. tans contrast with the white of their boards2. series of movements starting from a standing position
3. keep bow and arrows in safe and dry place when not in use3. keep bow and arrows in safe and dry place when not in use3. position the drumstick so it is resting on your index finger3. position the drumstick so it is resting on your index finger3. sending a spray of water into the air3. sending a spray of water into the air3. person tucks their knees up to chest3. person tucks their knees up to chest
HAM100000dermatofibroma1. generally not painfulmelanoma1. dark brown or black in colormelanocytic nevi1. color is tanbenign lesions1. color ranges from light brown to black
2. red, brown, or purple in color2. red, brown, or purple in color2. large and dark2. large and dark2. dark brown or black color2. dark brown or black color2. dark brown or black color2. rough or scaly texture
3. thin white halo around them3. thin white halo around them3. flesh-colored, brown, or black3. flesh-colored, brown, or black3. small, round, and slightly raised3. small, round, and slightly raised3. small, round, and slightly raised3. dark brown or black
", + "image_path": "63f4c1c9f91fe571378bf210603bfbca39c25ce029f12ca88a53339cc7f4c2d1.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 392, + 546, + 415 + ], + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 392, + 546, + 415 + ], + "spans": [ + { + "bbox": [ + 46, + 392, + 546, + 415 + ], + "type": "text", + "content": "Figure 7. Several example bottlenecks generated by LaBo. The top-3 concepts, ranked by their weights in the linear function, for randomly selected classes, paired with a random image from the class, across 6 datasets." + } + ] + } + ], + "index": 1, + "type": "text" + }, + { + "bbox": [ + 46, + 427, + 289, + 571 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 427, + 289, + 571 + ], + "spans": [ + { + "bbox": [ + 46, + 427, + 289, + 571 + ], + "type": "text", + "content": "6 shows that LaBo has significantly fewer invalid concepts than other baselines. Table 6 summarizes the average human evaluation results over the 11 datasets9. On average, we observe a trade-off between Factuality and Groundability. Increasing coverage and discriminability leads to more variable and specific concepts that CLIP finds more difficult to ground. This could be due to challenges in capturing composite concepts [33, 71]. For individual analysis of the datasets, refer to the supplementary material. Finally, Figure 7 shows several CBMs we constructed. Across many types of tasks, the bottlenecks are largely coherent, factual, and groundable by CLIP." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 582, + 200, + 594 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 582, + 200, + 594 + ], + "spans": [ + { + "bbox": [ + 47, + 582, + 200, + 594 + ], + "type": "text", + "content": "6. Conclusion and Limitation" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 602, + 287, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 602, + 287, + 685 + ], + "spans": [ + { + "bbox": [ + 46, + 602, + 287, + 685 + ], + "type": "text", + "content": "Overall, our approach demonstrates that the accuracy and interpretability of vision systems may be less at odds than previously believed. Leveraging LLMs was crucial, as they encode important visual knowledge. In the future, our approach can easily be enriched with new factors that capture different priors on bottleneck construction. The limits of knowledge in GPT-3 are not known, but likely there are" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 427, + 547, + 547 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 427, + 547, + 547 + ], + "spans": [ + { + "bbox": [ + 304, + 427, + 547, + 547 + ], + "type": "text", + "content": "domains where prompting generates few useful facts. Even in contexts where GPT-3 can generate useful information, our method depends on CLIP being able to recognize those aspects in images. The alignment between GPT-3 and CLIP likely does not hold for all cases. Future work could focus on dynamically prompting GPT-3 to make this coupling more robust. Finally, our work depends on large models trained at scales that are not currently reproducible. It is possible unrevealed aspects of training by OpenAI will require a reevaluation of our claims." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 560, + 408, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 560, + 408, + 574 + ], + "spans": [ + { + "bbox": [ + 306, + 560, + 408, + 574 + ], + "type": "text", + "content": "Acknowledgements" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "type": "text", + "content": "This research is based upon work supported in part by the DARPA KAIROS Program (contract FA8750-19-2-1004), the DARPA LwLL Program (contract FA8750-19-2-0201), the IARPA BETTER Program (contract 2019-19051600004), the IARPA HIATUS Program (contract 2022-22072200005), the NSF (Award 1928631), and an AI2 Young Investigator Award. Approved for Public Release, Distribution Unlimited. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies, either expressed or implied, of ODNI, DARPA, IARPA, NSF, or the U.S. Government." + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 47, + 693, + 287, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 693, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 693, + 287, + 713 + ], + "type": "text", + "content": "The low resolution of CIFAR images partially affects those metrics since annotators have greater difficulty in completing the task." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19194" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 92, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 53, + 92, + 288, + 125 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 92, + 288, + 125 + ], + "spans": [ + { + "bbox": [ + 53, + 92, + 288, + 125 + ], + "type": "text", + "content": "[1] Francis Bach. 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International Journal of Computer Vision, 130(9):2337-2348, 2022, 3, 12, 14" + } + ] + } + ], + "index": 22 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "19197" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Language-Guided Audio-Visual Source Separation via Trimodal Consistency/8ed77a3b-731a-4b06-bbf1-882c057c335a_content_list.json b/2023/Language-Guided Audio-Visual Source Separation via Trimodal Consistency/8ed77a3b-731a-4b06-bbf1-882c057c335a_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..d6295a184778d7dd66c54a3d8813064967bb3d66 --- /dev/null +++ b/2023/Language-Guided Audio-Visual Source Separation via Trimodal Consistency/8ed77a3b-731a-4b06-bbf1-882c057c335a_content_list.json @@ -0,0 +1,1316 @@ +[ + { + "type": "text", + "text": "Language-Guided Audio-Visual Source Separation via Trimodal Consistency", + "text_level": 1, + "bbox": [ + 98, + 130, + 870, + 154 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Reuben Tan $^{1}$ Arijit Ray $^{1}$ Andrea Burns $^{1}$ Bryan A. Plummer $^{1}$ Justin Salamon $^{2}$ Oriol Nieto $^{2}$ Bryan Russell $^{2}$ Kate Saenko $^{1,3}$", + "bbox": [ + 125, + 179, + 821, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ Boston University, $^{2}$ Adobe Research, $^{3}$ MIT-IBM Watson AI Lab, IBM Research $\\{\\mathrm{rxtan}, \\mathrm{aburns4}, \\mathrm{array}, \\mathrm{bplum}, \\mathrm{saenko}\\} @ \\mathrm{bu.edu}, \\{\\mathrm{salamon}, \\mathrm{onieto}, \\mathrm{brussell}\\} @ \\mathrm{adobe.com}$", + "bbox": [ + 125, + 215, + 849, + 251 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 286, + 313, + 301 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We propose a self-supervised approach for learning to perform audio source separation in videos based on natural language queries, using only unlabeled video and audio pairs as training data. A key challenge in this task is learning to associate the linguistic description of a sound-emitting object to its visual features and the corresponding components of the audio waveform, all without access to annotations during training. To overcome this challenge, we adapt off-the-shelf vision-language foundation models to provide pseudo-target supervision via two novel loss functions and encourage a stronger alignment between the audio, visual and natural language modalities. During inference, our approach can separate sounds given text, video and audio input, or given text and audio input alone. We demonstrate the effectiveness of our self-supervised approach on three audio-visual separation datasets, including MUSIC, SOLOS and AudioSet, where we outperform state-of-the-art strongly supervised approaches despite not using object detectors or text labels during training. Our project page including publicly available code can be found at https://cs-people.bu.edu/rxtan/projects/VAST.", + "bbox": [ + 75, + 316, + 473, + 636 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 662, + 209, + 679 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Our everyday audiovisual world is composed of many visible sound sources, often with multiple sources layering on top of one another. For example, consider the video of the guitar and cello musicians playing together in Fig. 1. The two instruments have distinct timbres, and the musicians play non-unison, but complementary melodies. Despite hearing both instruments simultaneously, humans have an innate ability to identify and isolate the melody of a single source object. In this paper, we define the corresponding machine task as follows: given a natural language query that selects a sounding object, such as \"person playing a guitar\", separate its sound source from the input audio waveform and localize it in the input video, without any supervision.", + "bbox": [ + 75, + 688, + 468, + 885 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "This task is challenging. First, there is no approach for", + "bbox": [ + 96, + 885, + 468, + 900 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/68108733d5c101bf1df27531a94da84ff7f5cbe67f7d812940ec1f642c799a95.jpg", + "image_caption": [ + "Figure 1. We propose to separate and localize audio sources based on a natural language query, by learning to align the modalities on completely unlabeled videos. In comparison, prior audio-visual sound separation approaches require object label supervision." + ], + "image_footnote": [], + "bbox": [ + 506, + 286, + 888, + 619 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "associating the linguistic description of a sound-emitting object to its visual features and the corresponding components of the audio waveform without access to annotations during training. Existing audio-visual methods [5, 14, 41] do not generalize to natural language queries due to their dependence on discrete object class labels. Second, an ideal solution would jointly identify and localize sound-emitting objects in videos as well as separate the corresponding components in the audio waveform without strong supervision. Although prior audio-visual work has demonstrated the benefits of aligning relevant object regions in the video with their corresponding sounds [5, 14], these approaches require strong supervision including object label", + "bbox": [ + 496, + 703, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "10575", + "bbox": [ + 478, + 924, + 517, + 936 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "and bounding box annotations (see Fig. 1 top). Overcoming these challenges would enable important downstream applications including holistic video understanding [33], embodied AI [6], and bidirectional audio-to-video retrieval [38].", + "bbox": [ + 75, + 90, + 467, + 150 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address these challenges, we make the following contributions. First, we propose Video-Audio Separation through Text (VAST), a self-supervised approach that leverages large vision-language \"foundation\" models [20, 26] to provide pseudo-supervision for learning the alignment between the three modalities: audio, video and natural language. Our key insight is to learn a strong transitive relation from audio to natural language using vision as an intermediary modality, while preserving the alignment between the visual and natural language modalities embodied by the foundation models. However, just using the visual representations of these foundation models in existing AV separation approaches does not preserve the transitive relationships between the three modalities (Sec. 4.1).", + "bbox": [ + 75, + 152, + 467, + 361 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our second contribution introduces two novel multimodal alignment objectives that encourage the learnt audio representations to encode the semantics of captions and infer the latent transitive relation between the three modalities. While natural language can express a large and varied range of visual concepts for audio separation in videos, the absence of captions in unlabeled videos during training poses a significant challenge in our self-supervised formulation. To learn the transitive alignment, we adapt a foundation model to extract latent captions from unlabeled videos. Intuitively, the latent captions are representations that express the visual concepts present in the videos. Third, we introduce a Multiple Instance Learning formulation to learn to perform audio separation at the video region level since we do not have prior information on relevant objects or their locations in the videos during training.", + "bbox": [ + 75, + 363, + 467, + 603 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Finally, we demonstrate the effectiveness of our proposed VAST approach through extensive evaluations on the audio source separation task on the SOLOS [24], MUSIC [41], and AudioSet [15] datasets. We show that our self-supervised approach outperforms strongly-supervised state-of-the-art approaches without using labels during training by leveraging the capability of vision-language foundation models. More importantly, we demonstrate that VAST learns to use language queries for audio separation despite not training with ground-truth language supervision.", + "bbox": [ + 75, + 604, + 467, + 755 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 768, + 217, + 784 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Audio-only source separation. The goal of audio-only source separation is to use the aural cues present in the input audio waveform to separate the individual components. Conventional audio signal processing techniques rely on strong assumptions such as the number of sources in the audio waveforms to compute non-negative matrix factorization [3, 10, 37] of audio spectrograms. Deep learn-", + "bbox": [ + 75, + 794, + 467, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ing methods commonly adopt the self-supervised 'mix-and-separate' strategy where multiple audio sources are combined into a synthetic mixture and then predict a spectrogram mask to retrieve queried audio components [5, 14, 41]. Multimodal source separation. Recent work in audiotext [21, 22] and audio-visual [5, 7, 14, 40, 41] separation also use the 'mix-and-separate' strategy to train a decoder to predict a spectrogram mask based on natural language and video queries, respectively. In the case of the former, state-of-the-art approaches can either accept a single object label [5, 14, 41] or free-form natural language queries [21, 22]. Existing audio-visual source separation approaches often rely on training object detectors with strong supervision from bounding box annotations to localize objects of interest before learning to perform source separation at the object-level. In contrast, our proposed approach does not rely on pretrained object detectors or object labels in the training videos. The Sound of Pixels (SOP) model is the most similar in spirit to our proposed approach since it does not rely on object detectors. Instead, it learns to perform sound separation based on a video-level representation during training. Our VAST approach is also similar to the Voiceformer [28] approach which aims to separate speech from multiple speakers using a combination of audio, visual and language inputs. In contrast to our approach, their approach requires ground-truth text transcripts for training. Finally, the task is also similar in nature to that of sound localization in videos [9, 19].", + "bbox": [ + 496, + 90, + 890, + 512 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Multimodal representation learning. One key challenge is grounding information from the text and/or audio modalities in the video frames [2, 5, 14, 35]. Since annotating video datasets is a costly process, prior work has investigated self-supervised pretraining methods on unlabeled videos [17, 36]. This often involves utilizing complementary information from the audio, text and visual modalities [39] to learn robust representations that can generalize to downstream tasks such as action recognition [1, 25, 32] and text-to-video retrieval [2, 23]. These approaches often use large-scale pretraining datasets such as Kinetics-400 / 600 [4] and HowTo100M [23] before finetuning linear probes for target tasks and datasets. Recent work has also focused on prompting multimodal foundation models such as CLIP [26] and ALIGN [20] to adapt them to new tasks ranging from open-vocabulary object detection [16] to domain adaptation [13] without modifying their parameters.", + "bbox": [ + 496, + 513, + 890, + 771 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Video-Audio Separation through Text", + "text_level": 1, + "bbox": [ + 500, + 784, + 836, + 801 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Given a set of unlabeled videos and their audio tracks, we strive to learn a self-supervised model that separates an audio source given a natural language query and, optionally, an accompanying video. This goal requires a model to learn a strong alignment between the audio, vision, and language modalities. To this end, we propose a novel Audio-Visual", + "bbox": [ + 496, + 810, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "10576", + "bbox": [ + 480, + 924, + 517, + 935 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/233e18ac7f6b45bfd83a69d99e27b47d231936652dd3e70aee42fe7ebb02c341.jpg", + "image_caption": [ + "Figure 2. Training overview of our proposed VAST approach. We introduce tri-modal (Section 3.1) and audio-language (Section 3.1) consistency objectives to learn the latent alignment between the audio, video and language modalities. Furthermore, we adopt a prior mask prediction loss [41] (Section 3.2) to guide the training of our mask prediction decoder." + ], + "image_footnote": [], + "bbox": [ + 81, + 90, + 467, + 220 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Separation through Text (VAST) approach that learns an effective representation for audio-visual source separation, as well as a strong alignment between the audio and language modalities for audio-text source separation (see Figure 2 for an overview). To learn this representation, we exploit the strong joint visual-semantic alignment embodied in pretrained vision-language foundation models by encouraging our model to learn a direct projection function for audio inputs into their joint embedding space (Section 3.1). Our key insight is to use videos as an intermediary modality to learn a transitive alignment between the audio and language modalities. Since the visual and language modalities are already aligned, learning a strong correspondence between audio and vision should also provide an alignment between audio and language through videos via transitivity.", + "bbox": [ + 75, + 337, + 468, + 565 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Despite the intuitiveness of this idea, our experiments will show that using the visual representations of existing audio-visual foundation models does not help them learn the above-mentioned transitive alignment. To address this limitation, we introduce our novel tri-modal and audiolanguage consistency alignment objectives (Figure 2). The tri-modal objective encourages the model to maximize the semantic consistency between all three modalities by using videos as the intermediary modality and the audiolanguage objective helps to further improve the transitive alignment between audio and natural language. We leverage vision-and-language foundation models to infer latent captions that correspond to the audio components without text annotations, thus providing pseudo-language supervision (Section 3.1). In addition, we adopt the \"mix-and-separate\" strategy [41] to train our audio separation model, where the audio from multiple videos are mixed and then separated using only the video's visual information. For an input audio waveform $A$ , we apply a Short-Time Fourier Transform (STFT) to obtain its magnitude spectrogram $A^S$ and phase $A^{\\mathrm{phase}}$ . Our learning objective only makes use of $A^S$ , which encodes how the magnitude of the audio fre", + "bbox": [ + 75, + 568, + 470, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "quencies changes over time. We reconstruct the predicted waveform by applying the inverse STFT on the predicted spectrogram using the original phase $A^{\\mathrm{phase}}$ . We describe our VAST audio separation model $\\mathcal{M}$ in Section 3.2.", + "bbox": [ + 496, + 90, + 890, + 151 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Alignment between audio, language and video", + "text_level": 1, + "bbox": [ + 498, + 159, + 887, + 176 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "A standard method to learn a strong alignment between the audio, language and vision modalities is to maximize the pairwise similarities of their input representations using a contrastive learning formulation [1, 23]. However, learning this alignment necessitates the presence of labels that indicate ground-truth correspondences between these modalities. In our self-supervised setting, the unlabeled videos only provide noisy labels of audio-visual pairings but do not contain text labels. To circumvent this limitation, we propose to extract latent captions, which are pseudo-words that encode the visual concepts in videos with language semantics. Prior work [8, 11] has demonstrated that the rich visualsemantic alignment in vision-language foundation models can be adapted to extract latent word representations that convey the semantics of their conditioning images. Inspired by this insight, we introduce the novel idea of using latent captions to identify sound-emitting object candidates in unlabeled videos for training, thereby allowing us to train without prior knowledge of existing objects in the videos.", + "bbox": [ + 496, + 183, + 890, + 469 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Latent captions. We perform \"textual inversion\" [8, 11, 12] where we adapt the CLIP language encoder to express the visual concepts of a video in the form of an encoded learnable parameter. Instead of introducing new concepts into the vocabulary of these models which require their parameters to be updated, we search for their latent language representations through a visual reconstruction objective. This objective is based on the key insight that the final learnt latent captions should be expressive enough to convey the visual semantics of the video. While it is also possible to use the visual frame representations as latent captions, we reason that learning them as outputs of the language encoder will help a model generalize better to language queries during inference. For a given video $V$ , we encode its center frame $V_{center}$ as: $f_{center}^{V} = g^{V}(V_{center})$ , where $g^{V}$ is the embedding function of the CLIP visual encoder. Then, we replace the token embeddings used for language queries with a learnable parameter $p$ and encode it as: $g^{L}(p)$ , where $g^{L}$ is the embedding function of the CLIP language encoder. We optimize the weights of $p$ by maximizing the cosine similarity between $f_{center}^{V}$ and $g^{L}(p)$ :", + "bbox": [ + 496, + 470, + 890, + 787 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\np ^ {*} \\in \\underset {p} {\\arg \\max } \\operatorname {s i m} \\left(f _ {\\text {c e n t e r}} ^ {V}, g ^ {L} (p)\\right) \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 575, + 794, + 890, + 821 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\text{sim}(x, y) = x^T y / (\\| x \\| \\| y \\|)$ and $||.||$ denotes the $L_2$ norm operator. Let $C^* = g^L(p^*)$ be the latent caption. We illustrate this operation in the supplemental. In theory, $C^*$ is analogous to a representation of a description of the frame and may replace ground-truth annotations effectively.", + "bbox": [ + 496, + 824, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "10577", + "bbox": [ + 480, + 925, + 517, + 936 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/01092bb17ba79431dd2336a332e39fff85153ce19d70c72c0255de9066463350.jpg", + "image_caption": [ + "Figure 3. Audio-language and tri-modal consistency alignment objectives. (a) The audio-language objective aims to maximize the semantic similarity between the predicted audio and its latent caption. (b) In the tri-modal consistency objective, we compute normalized probability distributions over the spatiotemporal regions based on cosine similarity scores (colored frame patches) with respect to the predicted audio and latent captions. $K$ and $Q$ denote the key and query terminology that is used in self-attention. Intuitively, this objective encourages agreement between where the latent caption and predicted audio is occurring in the video." + ], + "image_footnote": [], + "bbox": [ + 98, + 85, + 447, + 257 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/04b53d6f981850088658e98b7e6e169e860182829137576eae7d7edbe1b880a7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 460, + 85, + 875, + 257 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Our audio-language and tri-modal consistency alignment objectives are based on our reasoning that well-separated audio sources should be semantically consistent with the visual concepts that guide their separation as well as their text labels. Given an input video $V$ of $T$ frames $V = \\{V_{1},\\dots V_{T}\\}$ and an audio spectrogram $A^S\\in \\mathbb{R}^{F\\times N}$ with $F$ frequency bins and $N$ STFT time frames, our model predicts a separated audio spectrogram $\\hat{A}^S\\in \\mathbb{R}^{F\\times N}$ . We extract a latent representation for the predicted spectrogram: $\\hat{f}^A = \\mathcal{M}_\\theta (\\hat{A}^S)\\in \\mathbb{R}^D$ where $\\mathcal{M}$ denotes our audio separation model. For each video, we use its encoded predicted spectrogram and latent caption to provide pseudo-language supervision in our alignment objectives detailed below.", + "bbox": [ + 75, + 345, + 472, + 542 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Audio-language consistency loss. To encourage our audio encoder to learn audio representations that are effective for separating sound components when conditioned on either text or video queries, we aim to maximize the pairwise similarities between all three modalities. The key insight is that the audio sources that are well-separated by the visual concepts in a video should have a strong semantic relevance to its latent caption which express the same concepts in natural language (Figure 3a). Theoretically, this is similar to the self-supervised multimodal learning objective of maximizing the similarity between the representations of an image and its corresponding caption as well as the dissimilarity of non-corresponding captions. In lieu of ground-truth object labels, we can maximize the alignment between the predicted audio representations and the latent captions over the entire vocabulary of captions $\\mathcal{X}$ :", + "bbox": [ + 75, + 547, + 468, + 790 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {A u b i o - l a n g u a g e}} = - \\log \\left(\\frac {\\exp \\left(\\hat {f} ^ {A} \\cdot C ^ {*} / \\tau\\right)}{\\sum_ {x \\in \\mathcal {X}} \\exp \\left(\\hat {f} ^ {A} \\cdot x / \\tau\\right)}\\right) \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 801, + 468, + 843 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\tau$ is the temperature.", + "bbox": [ + 76, + 854, + 261, + 869 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "However, the problem of false negatives has been well-documented in image-text datasets, where captions for", + "bbox": [ + 75, + 869, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "some images may be relevant to other images but are treated erroneously as negatives. Since we are training on unlabeled videos, we account for the high likelihood that some videos may contain similar sounding objects by using a lower weight for this objective. Intuitively, this weighting helps to alleviate the effect of false negatives and prevent it from introducing a lot of noise during training.", + "bbox": [ + 496, + 345, + 890, + 452 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Tri-modal consistency loss. While the audio-language consistency objective facilitates improving the alignment between audio sources and their corresponding latent captions, it does not provide a straightforward solution to disregard false negatives in its contrastive formulation. To address this issue, we further introduce a softer tri-modal alignment constraint which exploits the implicit localization capability of vision-language foundation models for supervision without requiring any negative samples. Specifically, we propose to use the intermediary visual modality to encourage well-separated audio components to be grounded correctly in the relevant spatiotemporal regions of a video. Prior work [29, 42] has demonstrated that the CLIP model can be engineered to extract a segmentation map based on natural language queries. Inspired by this finding, we use the latent captions to provide pseudo-target attention maps.", + "bbox": [ + 496, + 457, + 892, + 699 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Our intuition is that enforcing a soft constraint on the predicted spectrograms such that they can be mapped to similar relevant regions as determined by the latent captions will encourage the model to implicitly learn the transitive alignment between the audio and language modalities. Let $P_{Att}(A, b) = \\sigma(A \\cdot b)$ to be the attention operation where $\\sigma(z)_i = z_i / \\sum_j z_j$ is the softmax function. For a given video $V$ , we extract a set of spatiotemporal region representations by encoding each frame separately. Specifically, we encode the $t$ -th frame as: $f_t^V = g_\\theta^V(V_t)$ , where $f_t^V \\in \\mathbb{R}^{HW\\times D}$ , where $H$ and $W$ are the downsampled height and width of the input video. Then, we compute a probability distribution of similarity scores over the set of", + "bbox": [ + 496, + 704, + 893, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "10578", + "bbox": [ + 480, + 924, + 517, + 935 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/95ab4d675e65384b6fc447fc88566d8912775f176319f6f5db0448fa0dfb2443.jpg", + "image_caption": [ + "Audio-Language Separation Model $\\mathcal{M}_{\\mathcal{A}\\mathcal{L}}$", + "Figure 4. Spectrogram mask prediction. During inference, our model is able to separate audio sources using video or language queries despite training without ground-truth text annotations. We note that we only use unlabeled videos during training. We illustrate the audio-visual separation mode $\\mathcal{M}_{AV}$ in the supplemental." + ], + "image_footnote": [], + "bbox": [ + 81, + 102, + 483, + 214 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "spatial region features with respect to its latent caption $C^*$ for the $t$ -th frame: $P_{VC}^{t} = P_{Att}(f_{t}^{V}, C^{*}) \\in \\mathbb{R}^{HW \\times 1}$ . Next, we compute a similar distribution over the region features of the $t$ -th frame with respect to the encoded audio representation of the masked spectrogram: $P_{VA}^{t} = P_{Att}(f_{t}^{V}, \\hat{f}^{A}) \\in \\mathbb{R}^{HW \\times 1}$ . We encourage the predicted audio representation to be similar to that of the latent caption by minimizing the Kullback-Leibler (KL) divergence between both attention distributions over the set of all time steps in a video $\\mathcal{T}$ :", + "bbox": [ + 75, + 313, + 468, + 450 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {T r i m o d a l}} = \\mathbb {E} _ {t \\sim \\mathcal {T}} \\left[ \\sum_ {x = 1} ^ {H W} P _ {V C} ^ {t} (x) \\log \\frac {P _ {V C} ^ {t} (x)}{P _ {V A} ^ {t} (x)} \\right], \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 114, + 455, + 468, + 500 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $P_{VA}^{t}(x)$ denotes the audio-video attention distribution over the $t$ -frame of the $x$ -th spatial region.", + "bbox": [ + 76, + 505, + 468, + 536 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.2. Audio Separation Model", + "text_level": 1, + "bbox": [ + 76, + 542, + 302, + 559 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We introduce two audio separation models $\\mathcal{M}_{AL}$ and $\\mathcal{M}_{AV}$ which share the same audio model parameters for separating audio sources. $\\mathcal{M}_{AL}$ (Figure 4) infers a spectrogram mask based on a language query while $\\mathcal{M}_{AV}$ (shown in supplemental) conditions its prediction on the input video. We adopt the U-Net [31] model as the audio component in $\\mathcal{M}_{AL}$ and $\\mathcal{M}_{AV}$ , which has been demonstrated by prior work [14, 41] to be effective at audio source separation, and the CLIP visual and language encoders to exploit its learnt visual-semantic alignment. The U-Net model comprises an encoder $\\mathcal{E}$ and a decoder $\\mathcal{D}$ . Given an input audio spectrogram $A^S$ , the encoder $\\mathcal{E}$ applies a series of downsampling convolutional layers to output a set of bottleneck features: $f^A = \\mathcal{E}(A^S)$ , $f^A \\in \\mathbb{R}^{H^A \\times W^A \\times D}$ , where $H^A$ and $W^A$ denote the height and width of the downsampled spectrogram, respectively.", + "bbox": [ + 75, + 566, + 468, + 809 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Given a natural language query $L \\in \\mathbb{R}^{N_w}$ where $N_{w}$ is the number of words, we extract its representation $f^L \\in \\mathbb{R}^{1\\times D}$ using the text encoder: $f^L = g^L (L)$ . We stress that language queries with ground-truth object labels are only used during inference. Then, we tile the language representation by the factor $H^{A}W^{A}$ and concatenate with the", + "bbox": [ + 75, + 809, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "audio bottleneck representations along the channel dimension: $f^{AL} = \\text{concat}(f^A, \\text{tile}(f^L))$ , where $f^{AL}$ has the dimensions $\\mathbb{R}^{H^A \\times W^A \\times 2D}$ . We pass the concatenated representations into the decoder $\\mathcal{D}$ consisting of a series of upsampling convolutional layers to generate a real-valued ratio mask: $\\hat{M} = \\mathcal{D}(f^{AL}) \\in \\mathbb{R}^{F \\times N}$ . To predict the separated audio source, each element of the mask is multiplied with the corresponding location in the input spectrogram: $\\hat{A}^S = \\hat{M} \\odot A^S$ , where $\\odot$ denotes the Hadamard product.", + "bbox": [ + 496, + 90, + 890, + 229 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Video and Multiple Instance Learning for mask prediction. Since language annotations are not used during training, we train only with unlabeled videos. During training, as well as inference on audio-visual separation, we use the CLIP visual encoder to extract a set of language-grounded spatiotemporal region representations $f^{V} \\in \\mathbb{R}^{T \\times H \\times W \\times D}$ . Similarly, we can perform the same mask inference operation using videos by using the representation of each spatiotemporal region representation interchangeably in place of the language representation. This interchangeability is due to the fact that the CLIP representations project the video to the joint vision-language embedding space.", + "bbox": [ + 496, + 231, + 890, + 412 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Prior work [14] has demonstrated the advantages of performing audio-visual separation at the object level for videos with multiple objects. In the absence of object detectors and labels, we propose an MIL formulation, where all spatiotemporal regions in the input video are treated as positive candidates. Specifically, given a spatiotemporal grid of region representations extracted from the visual encoder as defined in this section, we predict a spectrogram mask $\\hat{M}_j$ for the $j$ -th region. Finally, we aggregate them over all regions to obtain a spectrogram mask for the entire video:", + "bbox": [ + 496, + 412, + 890, + 564 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {M} = \\frac {1}{T} \\sum_ {j = 1} ^ {T H W} \\hat {M} _ {j}. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 617, + 570, + 890, + 599 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Intuitively, this formulation encourages the model to learn to identify the salient regions with sounding objects for audio separation. We obtain the predicted mask for each frame by computing the sum of the predicted masks over all spatial regions and average the predicted masks over the temporal dimension since we reason that a sounding object should have similar prediction masks across frames. We adopt the self-supervised 'mix-and-separate' learning objective [14, 41] to train our model for predicting spectrogram masks. In this formulation, audio from two or more videos are mixed and the goal is to use the visual information of a video to separate its audio component. This setting allows us to generate pseudo-target masks for training supervision. We compute $\\mathcal{L}_{mask}$ as the L1 loss between the pseudo-target and predicted ratio masks [41]. Please refer to the supplemental for details of our spatiotemporal region representation, audio-visual separation model and $\\mathcal{L}_{mask}$ . The final objective function is computed as:", + "bbox": [ + 496, + 604, + 890, + 876 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\lambda_ {1} \\mathcal {L} _ {\\text {m a s k}} + \\lambda_ {2} \\mathcal {L} _ {\\text {T r i m o d a l}} + \\lambda_ {3} \\mathcal {L} _ {\\text {A u s i o - l a n g u a g e}} \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 539, + 885, + 890, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "10579", + "bbox": [ + 480, + 925, + 517, + 936 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/b07fe8755e91e8684aa2fdcdc41158bd3112776bbed4ccfff296ca70c72514ff.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodObject detectors# Region proposalsSolosDuets
NSDR ↑SIR ↑SAR ↑NSDR ↑SIR ↑SAR ↑
Co-Separation [14]Yes27.3813.7010.827.4213.8110.60
AVSGS [5]Yes429.0414.4512.2410.2515.6012.82
Sound-of-Pixels [41]NoNone7.3011.9011.906.059.8110.61
AV-Mix-and-Separate [14]NoNone3.166.748.893.237.019.14
NMF-MFCC [34]NoNone0.925.686.840.925.686.84
VAST (Ours)NoNone7.9813.9212.358.0813.9711.33
", + "bbox": [ + 109, + 88, + 859, + 214 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Audio-visual source separation on MUSIC. We report results on videos that contain one instrument (solos) and two instruments (duets). Despite not training with object bounding boxes, VAST performs competitively with state-of-the-art detection-based approaches.", + "bbox": [ + 75, + 224, + 893, + 253 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\lambda_{1},\\lambda_{2}$ and $\\lambda_{3}$ denote the weights for the mask, tri-modal and audio-language consistency losses, respectively.", + "bbox": [ + 75, + 266, + 470, + 297 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 311, + 209, + 329 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We evaluate the effectiveness of our proposed VAST approach on audio-text and audio-visual source separation in videos. To perform fair comparison to prior work, we conduct experiments on the SOLOS [24], MUSIC [41] and AudioSet [15] datasets. We refer readers to the supplemental for additional implementation and dataset details. Given a language query containing a prompt template and an object, the goal of audio-text source separation is to extract its corresponding sound component from an audio input, which is often comprised of a mixture of sounds emitted by various objects. Similarly, in audio-visual source separation, a model has to leverage the visual information in the input video to extract its corresponding sound component and align it with the relevant video pixels.", + "bbox": [ + 73, + 337, + 468, + 547 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation metrics. We adopt the Normalized Signal-to-Distortion Ratio (NSDR), Signal-to-Interference Ratio (SIR) and Signal-to-Artifact Ratio (SAR) [27, 30]. NSDR computes the difference between the SDR of the predicted and mixed audio with respect to the ground-truth waveforms, which measures the sound quality of the separated audios. SIR measures the amount of contamination from other audio sources in the predicted audio. Finally, SAR measures the amount of artifacts in the predicted audio.", + "bbox": [ + 75, + 549, + 468, + 686 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Quantitative results", + "text_level": 1, + "bbox": [ + 76, + 695, + 266, + 710 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We compare our approach to the following baselines. Similar to our approach, Sound of Pixels (SOP) [41] does not require object detectors but learns to perform video-level separation. We also implement the AV-Mix-and-separate baseline from [14] with the same audio-visual separation model as ours but is trained to perform video-level separation and without our alignment objectives. The off-the-shelf NMF-MFCC [34] baseline performs audio separation using non-negative matrix factorization (NMF) and Mel frequency cepstrum coefficients (MFCC). Next, we also compare to Co-Separation [14] that learns to perform audio separation at the object-level by relying on object de", + "bbox": [ + 75, + 719, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "tectors. Last but not least, we include AVSGS [5] that also relies on a high number of object proposals to construct a spatiotemporal scene graph to reason about context.", + "bbox": [ + 496, + 266, + 890, + 311 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Audio-visual source separation on MUSIC. We report the results of our evaluation under two settings in Table 1. In the first setting, each video contains only a single instrument while the 'duet' setting includes videos that contain two different instruments. To begin, our VAST approach outperforms SOP by a large margin despite not relying on object detectors too. As shown in Table 4, we show that this performance gain is not due to just replacing ImageNet-pretrained Resnet18 [18] visual representations with those of the CLIP model since it leads to a large drop in performance. We hypothesize that SOP does not learn a direct projection of the audio inputs used in source separation into the CLIP embedding space. In contrast, VAST facilitates a better adaptation of the learnt audio representations to the CLIP embedding. We also found it important to modify CLIP's self-attention (see supp.). We observe that VAST outperforms AV-Mix-and-Separate by significantly, particularly under the duet setting. This suggests that performing region-level audio separation provides more capacity for the model to reason about multiple sounding objects in videos.", + "bbox": [ + 496, + 316, + 892, + 619 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "More significantly, we observe that our approach outperforms the Co-Separation approach [14], which relies on object labels in the videos. Since Co-Separation uses a high confidence region proposal for each instrument to localize relevant regions, our improvements over it suggest that our latent captions are able to express multiple visual concepts that are present in the video. Last but not least, our approach is also comparable to AVSGS even without scene graph reasoning modules. The latter constructs a spatiotemporal visual scene graph over a large number of region proposals to reason about context between detected objects. We note that their audio-visual scene graph component can be combined with our VAST approach to possibly improve performance but is beyond the scope of this work.", + "bbox": [ + 496, + 625, + 893, + 835 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Audio-visual source separation on SOLOS. While the videos in the SOLOS dataset generally have less background noise than those of the MUSIC dataset, we see in Table 2 that AV-Mix-and-Separate and NMF-MFCC are still", + "bbox": [ + 496, + 839, + 893, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "10580", + "bbox": [ + 480, + 925, + 519, + 936 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/35d49d6cfd849bc2a9bac6d95e049952981b7751e289548d6419b92ba4bb363f.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodObject detectorsNSDR ↑SIR ↑SAR ↑
Co-Separation [14]Yes7.1112.0910.05
AVSGS [5]Yes9.2014.0512.17
Sound-of-Pixels [41]No6.2810.8410.13
AV-Mix-and-Sep [14]No2.945.818.33
NMF-MFCC [34]No0.684.755.12
VAST (Ours)No8.5814.1612.35
", + "bbox": [ + 78, + 88, + 486, + 212 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/8e510848a34918119dc421506fb8e881ca3eb74c2b29f51e4275aba7ec817cdd.jpg", + "table_caption": [ + "Table 2. Audio-visual source separation results on the SOLOS dataset. Similar to the results in Table 1, we see that VAST significantly closes the gap with object detection-based approaches." + ], + "table_footnote": [], + "table_body": "
MethodObject detectorsNSDR ↑SIR ↑SAR ↑
Co-Separation [14]Yes4.267.0713.00
AVSGS [5]Yes5.288.2713.04
Sound-of-Pixels [41]No1.663.5811.50
AV-Mix-and-Sep [14]No1.683.3012.20
NMF-MFCC [34]No0.254.195.78
VAST (Ours)No4.157.6213.20
", + "bbox": [ + 78, + 277, + 485, + 402 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/b9353952369106a2dfcc0566d21fea7852b87c1f2efc763946a3f8fb757951a2.jpg", + "table_caption": [ + "Table 3. Audio-visual source separation results on AudioSet. VAST generalizes much better to the noisier AudioSet dataset than Sound-of-Pixels which also does not use object detections." + ], + "table_footnote": [], + "table_body": "
ModelVisual encoderNSDR ↑SIR ↑SAR ↑
SOP [41]ImageNet6.2810.8410.13
SOP [41]CLIP4.428.368.21
OursCLIP8.5814.1612.35
", + "bbox": [ + 78, + 474, + 475, + 541 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "unable to generalize to the cleaner audio signals. Similar to the reported performance on the MUSIC dataset, we also observe that VAST is comparable to the strongly supervised AVSGS approach on the SOLOS dataset. One possible reason behind the lower performance of AVSGS on videos with single instrument is that it is less critical to reason about context for videos with a single sounding object. Our better performance as compared to Co-Separation suggests that learning to perform audio separation at the coarse video region level under an MIL formulation can serve as an effective replacement for training object detectors. These results also indicate the great promise of latent captions in replacing ground-truth object annotations for supervision.", + "bbox": [ + 75, + 611, + 468, + 808 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Audio-visual source separation on AudioSet. Finally, we report the results of our evaluation on the AudioSet dataset in Table 3. AudioSet has been documented by prior work [14] to be much noisier than the videos in the other two datasets, which explains the lower performance across all approaches. Unlike the SOP model, we observe that our", + "bbox": [ + 75, + 810, + 468, + 901 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/9209bdad0c7491341a26c55dc7a38de778b416bd98b5d79da36af4a9808064c3.jpg", + "table_caption": [ + "Table 4. Using CLIP visual features in SOP model on the SOLOS dataset. Using CLIP visual features naively in existing methods results in a drop in performance." + ], + "table_footnote": [], + "table_body": "
LAudio-languageLTrimodalNSDR ↑SIR ↑SAR ↑
XX5.4710.5510.95
✓X8.0813.7412.18
X✓8.1013.8411.79
✓✓8.5814.1612.35
", + "bbox": [ + 506, + 88, + 883, + 167 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/3f36a5a8b69779738732e1e5212e64ffc2a4ac00d7e8dc9ef1bed997c7974d98.jpg", + "table_caption": [ + "Table 5. Ablation of our audio-language and tri-modal consistency alignment objectives on SOLOs. The alignment objectives help to improve audio-visual separation performance." + ], + "table_footnote": [], + "table_body": "
# tokensNSDR ↑SIR ↑SAR ↑
17.3111.3411.71
27.6713.0711.45
38.5814.1612.35
48.0213.3911.53
", + "bbox": [ + 558, + 234, + 831, + 314 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 6. Ablation over number of learnable tokens on SOLOS. Using more learnable tokens generally improves performance.", + "bbox": [ + 496, + 325, + 890, + 354 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "training approach is more robust to noise in the dataset where the sounding object may not always be visible.", + "bbox": [ + 496, + 363, + 890, + 393 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.1.1 Model Analysis", + "text_level": 1, + "bbox": [ + 500, + 402, + 661, + 417 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Ablation of $\\mathcal{L}_{\\mathrm{Trimodal}}$ and $\\mathcal{L}_{\\mathrm{Audio - language}}$ . Table 5 provides an ablation over our audio-language and tri-modal consistency losses. Despite being trained on a larger and more diverse set of visual concepts, we find the CLIP visual representations alone do not encourage the audio encoder to learn a strong alignment between the audio and vision modalities (row 1). We observe the importance of our proposed alignment objectives where adding one or the other leads to a significant improvement in audio separation performance. Due to multiple training videos containing similar instruments, it is likely that we are treating some latent captions as false negative samples for each video in the audio-language consistency objective. However, we see that the consistency objective is still beneficial towards audio separation.", + "bbox": [ + 496, + 426, + 890, + 638 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Number of learnable token embeddings in latent captions. We report the results of our ablation over the number of learnable token parameters used in the extraction of latent captions in Table 6. We observe that increasing the number of learnable tokens generally helps to improve the performance, although using 4 tokens hurts performance slightly. We hypothesize that a higher number of learnable tokens provide more capacity for the CLIP language model to express multiple visual concepts that are present in the videos. This finding suggests that using more tokens may be beneficial for videos with more complex visual scenes.", + "bbox": [ + 496, + 638, + 890, + 805 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Audio-language source separation", + "text_level": 1, + "bbox": [ + 500, + 816, + 795, + 832 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Finally, we evaluate the capability of our trained model to separate audio components based on natural language queries in Table 7. We construct each query using the template 'person playing a {instrument}''. We stress that we", + "bbox": [ + 496, + 839, + 890, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "10581", + "bbox": [ + 480, + 926, + 517, + 936 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/9789259e90894b46a5bcb610ead0d6dac3c82ccc78dcd0ef869ded6a76456c84.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Query ModalityAlignment objectivesSOLOSMUSICAudioset
NSDR ↑SIR ↑SAR ↑NSDR ↑SIR ↑SAR ↑NSDR ↑SIR ↑SAR ↑
LanguageNo-3.052.793.77-3.672.513.41-5.021.9814.94
LanguageYes6.9212.0710.416.4511.1810.772.364.7110.28
", + "bbox": [ + 78, + 88, + 893, + 154 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 7. Audio-text separation with natural language queries. We evaluate our model, that is trained only on unlabeled videos, on the task of audio-text separation. Note that we do not compare to other audio-visual separation baselines since there is no straightforward way to adapt them for language queries. We compare our full VAST model to a variant that is only trained with the mask prediction loss.", + "bbox": [ + 75, + 162, + 893, + 205 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "only train on unlabeled videos without text supervision. To begin, we compare our VAST model to a variant that is trained without our alignment objectives. Note that we do not compare to other audio-visual approaches since there is no straightforward way to adapt them for language queries. As evidenced by the significant performance gap between both variants, our alignment losses are integral to learning a strong transitive alignment between the audio and language modalities. This finding suggests that just learning an alignment between the audio and visual modalities does not result in a transitive relationship between the audio and natural language modalities.", + "bbox": [ + 75, + 219, + 472, + 400 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Additionally, for effective sound source separation given either video or text inputs, we hypothesize that it is critical to learn an audio encoder E that is well-aligned with CLIP's vision-language embedding. Note that the same shared audio encoder $\\mathcal{E}$ encodes both mixed and predicted audio sources. Thus, it can also be used as a general audio encoder and the decoder $\\mathcal{D}$ can condition its separation process on either language or video queries. Lastly, we observe that our alignment objectives are still insufficient for closing the performance gap between audio-text and audio-visual separation (Tables 1, 2 and 3) completely. This observation indicates that future work is needed for further improving the latent alignment between all three modalities.", + "bbox": [ + 75, + 401, + 472, + 597 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3. Qualitative results", + "text_level": 1, + "bbox": [ + 76, + 604, + 254, + 619 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Predicted audio-to-video attention visualizations. To evaluate the semantic consistency between the predicted audio sources and the visual cues that guide the separation process, we plot the attention map between the encoded predicted spectrograms and their corresponding video frames (Section 3.1) in Figure 5. We observe that VAST helps the model to learn to ground the audio source in the video pixels despite not requiring bounding box supervision.", + "bbox": [ + 75, + 628, + 468, + 750 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Predicted outputs of language-based audio separation. Finally, we present an example of how different language queries affect the separation performance for the same audio input in Figure 6. Significantly, despite not relying on text annotations for training supervision, our model can separate audio components based on free-form language queries. This demonstrates the effectiveness of our proposed idea to substitute ground-truth text annotations with latent captions during training. Additionally, we also observe that providing more context in the language query (e.g., \"violin\" versus", + "bbox": [ + 75, + 750, + 470, + 901 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/09abd40468bc959b6f7293d65f16ac6cadb7f4e2b8b9301e7fea933a46683ac3.jpg", + "image_caption": [ + "Figure 5. Predicted audio attention in videos. Our consistency objectives help the model to localize the relevant regions more accurately without prior knowledge of sounding object locations." + ], + "image_footnote": [], + "bbox": [ + 504, + 218, + 908, + 329 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d28ed4712836791b135c5de9dfe4c08bf0ba2ce58b539832fd5bf6860d638fbb.jpg", + "image_caption": [ + "Figure 6. Predicted audio spectrograms with language queries. Interestingly, we see that including visually grounded adjectives in the queries affects the quality of the separated audio sources." + ], + "image_footnote": [], + "bbox": [ + 503, + 382, + 908, + 604 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "\"person playing a violin\") can lead to improved separations.", + "bbox": [ + 500, + 656, + 890, + 671 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 678, + 617, + 694 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In summary, we introduce a self-supervised approach for learning to separate audio based on a language query, or a video. In the absence of object labels, we propose to extract latent captions to provide pseudo-language supervision. Furthermore, we introduce the novel tri-modal and audio-language alignment objectives that use the latent captions to improve the alignment of the audio, language and video modalities. By reducing the training need for object labels, our work opens up the possibility of large-scale pretraining on unlabeled videos with diverse visual concepts.", + "bbox": [ + 496, + 704, + 890, + 854 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements: This material is based upon work supported, in part, by DARPA under agreement number HR00112020054 and a gift from Adobe Research.", + "bbox": [ + 498, + 854, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "10582", + "bbox": [ + 480, + 926, + 517, + 936 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Hassan Akbari, Liangzhe Yuan, Rui Qian, Wei-Hong Chuang, Shih-Fu Chang, Yin Cui, and Boqing Gong. Vatt: Transformers for multimodal self-supervised learning from raw video, audio and text. 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Denseclip: Extract free dense labels from clip. arXiv preprint arXiv:2112.01071, 2021. 4" + ], + "bbox": [ + 501, + 92, + 890, + 470 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "10584", + "bbox": [ + 480, + 926, + 519, + 936 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Language-Guided Audio-Visual Source Separation via Trimodal Consistency/8ed77a3b-731a-4b06-bbf1-882c057c335a_model.json b/2023/Language-Guided Audio-Visual Source Separation via Trimodal Consistency/8ed77a3b-731a-4b06-bbf1-882c057c335a_model.json new file mode 100644 index 0000000000000000000000000000000000000000..2b8968d414e6d467b6c20465c24245afa41699f6 --- /dev/null +++ b/2023/Language-Guided Audio-Visual Source Separation via Trimodal Consistency/8ed77a3b-731a-4b06-bbf1-882c057c335a_model.json @@ -0,0 +1,1804 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.099, + 0.131, + 0.872, + 0.155 + ], + "angle": 0, + "content": "Language-Guided Audio-Visual Source Separation via Trimodal Consistency" + }, + { + "type": "text", + "bbox": [ + 0.127, + 0.18, + 0.822, + 0.217 + ], + "angle": 0, + "content": "Reuben Tan\\(^{1}\\) Arijit Ray\\(^{1}\\) Andrea Burns\\(^{1}\\) Bryan A. Plummer\\(^{1}\\) Justin Salamon\\(^{2}\\) Oriol Nieto\\(^{2}\\) Bryan Russell\\(^{2}\\) Kate Saenko\\(^{1,3}\\)" + }, + { + "type": "text", + "bbox": [ + 0.126, + 0.217, + 0.851, + 0.252 + ], + "angle": 0, + "content": "\\(^{1}\\)Boston University, \\(^{2}\\)Adobe Research, \\(^{3}\\)MIT-IBM Watson AI Lab, IBM Research \\(\\{\\mathrm{rxtan}, \\mathrm{aburns4}, \\mathrm{array}, \\mathrm{bplum}, \\mathrm{saenko}\\} @ \\mathrm{bu.edu}, \\{\\mathrm{salamon}, \\mathrm{onieto}, \\mathrm{brussell}\\} @ \\mathrm{adobe.com}\\)" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.287, + 0.314, + 0.303 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.318, + 0.474, + 0.637 + ], + "angle": 0, + "content": "We propose a self-supervised approach for learning to perform audio source separation in videos based on natural language queries, using only unlabeled video and audio pairs as training data. A key challenge in this task is learning to associate the linguistic description of a sound-emitting object to its visual features and the corresponding components of the audio waveform, all without access to annotations during training. To overcome this challenge, we adapt off-the-shelf vision-language foundation models to provide pseudo-target supervision via two novel loss functions and encourage a stronger alignment between the audio, visual and natural language modalities. During inference, our approach can separate sounds given text, video and audio input, or given text and audio input alone. We demonstrate the effectiveness of our self-supervised approach on three audio-visual separation datasets, including MUSIC, SOLOS and AudioSet, where we outperform state-of-the-art strongly supervised approaches despite not using object detectors or text labels during training. Our project page including publicly available code can be found at https://cs-people.bu.edu/rxtan/projects/VAST." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.664, + 0.21, + 0.68 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.47, + 0.886 + ], + "angle": 0, + "content": "Our everyday audiovisual world is composed of many visible sound sources, often with multiple sources layering on top of one another. For example, consider the video of the guitar and cello musicians playing together in Fig. 1. The two instruments have distinct timbres, and the musicians play non-unison, but complementary melodies. Despite hearing both instruments simultaneously, humans have an innate ability to identify and isolate the melody of a single source object. In this paper, we define the corresponding machine task as follows: given a natural language query that selects a sounding object, such as \"person playing a guitar\", separate its sound source from the input audio waveform and localize it in the input video, without any supervision." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.886, + 0.47, + 0.901 + ], + "angle": 0, + "content": "This task is challenging. First, there is no approach for" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.287, + 0.889, + 0.621 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.632, + 0.895, + 0.689 + ], + "angle": 0, + "content": "Figure 1. We propose to separate and localize audio sources based on a natural language query, by learning to align the modalities on completely unlabeled videos. In comparison, prior audio-visual sound separation approaches require object label supervision." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.895, + 0.903 + ], + "angle": 0, + "content": "associating the linguistic description of a sound-emitting object to its visual features and the corresponding components of the audio waveform without access to annotations during training. Existing audio-visual methods [5, 14, 41] do not generalize to natural language queries due to their dependence on discrete object class labels. Second, an ideal solution would jointly identify and localize sound-emitting objects in videos as well as separate the corresponding components in the audio waveform without strong supervision. Although prior audio-visual work has demonstrated the benefits of aligning relevant object regions in the video with their corresponding sounds [5, 14], these approaches require strong supervision including object label" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.925, + 0.519, + 0.937 + ], + "angle": 0, + "content": "10575" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.468, + 0.151 + ], + "angle": 0, + "content": "and bounding box annotations (see Fig. 1 top). Overcoming these challenges would enable important downstream applications including holistic video understanding [33], embodied AI [6], and bidirectional audio-to-video retrieval [38]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.153, + 0.468, + 0.362 + ], + "angle": 0, + "content": "To address these challenges, we make the following contributions. First, we propose Video-Audio Separation through Text (VAST), a self-supervised approach that leverages large vision-language \"foundation\" models [20, 26] to provide pseudo-supervision for learning the alignment between the three modalities: audio, video and natural language. Our key insight is to learn a strong transitive relation from audio to natural language using vision as an intermediary modality, while preserving the alignment between the visual and natural language modalities embodied by the foundation models. However, just using the visual representations of these foundation models in existing AV separation approaches does not preserve the transitive relationships between the three modalities (Sec. 4.1)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.364, + 0.468, + 0.604 + ], + "angle": 0, + "content": "Our second contribution introduces two novel multimodal alignment objectives that encourage the learnt audio representations to encode the semantics of captions and infer the latent transitive relation between the three modalities. While natural language can express a large and varied range of visual concepts for audio separation in videos, the absence of captions in unlabeled videos during training poses a significant challenge in our self-supervised formulation. To learn the transitive alignment, we adapt a foundation model to extract latent captions from unlabeled videos. Intuitively, the latent captions are representations that express the visual concepts present in the videos. Third, we introduce a Multiple Instance Learning formulation to learn to perform audio separation at the video region level since we do not have prior information on relevant objects or their locations in the videos during training." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.606, + 0.468, + 0.756 + ], + "angle": 0, + "content": "Finally, we demonstrate the effectiveness of our proposed VAST approach through extensive evaluations on the audio source separation task on the SOLOS [24], MUSIC [41], and AudioSet [15] datasets. We show that our self-supervised approach outperforms strongly-supervised state-of-the-art approaches without using labels during training by leveraging the capability of vision-language foundation models. More importantly, we demonstrate that VAST learns to use language queries for audio separation despite not training with ground-truth language supervision." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.77, + 0.218, + 0.785 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Audio-only source separation. The goal of audio-only source separation is to use the aural cues present in the input audio waveform to separate the individual components. Conventional audio signal processing techniques rely on strong assumptions such as the number of sources in the audio waveforms to compute non-negative matrix factorization [3, 10, 37] of audio spectrograms. Deep learn-" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.513 + ], + "angle": 0, + "content": "ing methods commonly adopt the self-supervised 'mix-and-separate' strategy where multiple audio sources are combined into a synthetic mixture and then predict a spectrogram mask to retrieve queried audio components [5, 14, 41]. Multimodal source separation. Recent work in audiotext [21, 22] and audio-visual [5, 7, 14, 40, 41] separation also use the 'mix-and-separate' strategy to train a decoder to predict a spectrogram mask based on natural language and video queries, respectively. In the case of the former, state-of-the-art approaches can either accept a single object label [5, 14, 41] or free-form natural language queries [21, 22]. Existing audio-visual source separation approaches often rely on training object detectors with strong supervision from bounding box annotations to localize objects of interest before learning to perform source separation at the object-level. In contrast, our proposed approach does not rely on pretrained object detectors or object labels in the training videos. The Sound of Pixels (SOP) model is the most similar in spirit to our proposed approach since it does not rely on object detectors. Instead, it learns to perform sound separation based on a video-level representation during training. Our VAST approach is also similar to the Voiceformer [28] approach which aims to separate speech from multiple speakers using a combination of audio, visual and language inputs. In contrast to our approach, their approach requires ground-truth text transcripts for training. Finally, the task is also similar in nature to that of sound localization in videos [9, 19]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.515, + 0.892, + 0.772 + ], + "angle": 0, + "content": "Multimodal representation learning. One key challenge is grounding information from the text and/or audio modalities in the video frames [2, 5, 14, 35]. Since annotating video datasets is a costly process, prior work has investigated self-supervised pretraining methods on unlabeled videos [17, 36]. This often involves utilizing complementary information from the audio, text and visual modalities [39] to learn robust representations that can generalize to downstream tasks such as action recognition [1, 25, 32] and text-to-video retrieval [2, 23]. These approaches often use large-scale pretraining datasets such as Kinetics-400 / 600 [4] and HowTo100M [23] before finetuning linear probes for target tasks and datasets. Recent work has also focused on prompting multimodal foundation models such as CLIP [26] and ALIGN [20] to adapt them to new tasks ranging from open-vocabulary object detection [16] to domain adaptation [13] without modifying their parameters." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.785, + 0.838, + 0.802 + ], + "angle": 0, + "content": "3. Video-Audio Separation through Text" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Given a set of unlabeled videos and their audio tracks, we strive to learn a self-supervised model that separates an audio source given a natural language query and, optionally, an accompanying video. This goal requires a model to learn a strong alignment between the audio, vision, and language modalities. To this end, we propose a novel Audio-Visual" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.925, + 0.519, + 0.936 + ], + "angle": 0, + "content": "10576" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.091, + 0.468, + 0.222 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.233, + 0.47, + 0.318 + ], + "angle": 0, + "content": "Figure 2. Training overview of our proposed VAST approach. We introduce tri-modal (Section 3.1) and audio-language (Section 3.1) consistency objectives to learn the latent alignment between the audio, video and language modalities. Furthermore, we adopt a prior mask prediction loss [41] (Section 3.2) to guide the training of our mask prediction decoder." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.338, + 0.47, + 0.566 + ], + "angle": 0, + "content": "Separation through Text (VAST) approach that learns an effective representation for audio-visual source separation, as well as a strong alignment between the audio and language modalities for audio-text source separation (see Figure 2 for an overview). To learn this representation, we exploit the strong joint visual-semantic alignment embodied in pretrained vision-language foundation models by encouraging our model to learn a direct projection function for audio inputs into their joint embedding space (Section 3.1). Our key insight is to use videos as an intermediary modality to learn a transitive alignment between the audio and language modalities. Since the visual and language modalities are already aligned, learning a strong correspondence between audio and vision should also provide an alignment between audio and language through videos via transitivity." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.569, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Despite the intuitiveness of this idea, our experiments will show that using the visual representations of existing audio-visual foundation models does not help them learn the above-mentioned transitive alignment. To address this limitation, we introduce our novel tri-modal and audiolanguage consistency alignment objectives (Figure 2). The tri-modal objective encourages the model to maximize the semantic consistency between all three modalities by using videos as the intermediary modality and the audiolanguage objective helps to further improve the transitive alignment between audio and natural language. We leverage vision-and-language foundation models to infer latent captions that correspond to the audio components without text annotations, thus providing pseudo-language supervision (Section 3.1). In addition, we adopt the \"mix-and-separate\" strategy [41] to train our audio separation model, where the audio from multiple videos are mixed and then separated using only the video's visual information. For an input audio waveform \\( A \\), we apply a Short-Time Fourier Transform (STFT) to obtain its magnitude spectrogram \\( A^S \\) and phase \\( A^{\\mathrm{phase}} \\). Our learning objective only makes use of \\( A^S \\), which encodes how the magnitude of the audio fre" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.152 + ], + "angle": 0, + "content": "quencies changes over time. We reconstruct the predicted waveform by applying the inverse STFT on the predicted spectrogram using the original phase \\( A^{\\mathrm{phase}} \\). We describe our VAST audio separation model \\( \\mathcal{M} \\) in Section 3.2." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.16, + 0.888, + 0.177 + ], + "angle": 0, + "content": "3.1. Alignment between audio, language and video" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.184, + 0.892, + 0.47 + ], + "angle": 0, + "content": "A standard method to learn a strong alignment between the audio, language and vision modalities is to maximize the pairwise similarities of their input representations using a contrastive learning formulation [1, 23]. However, learning this alignment necessitates the presence of labels that indicate ground-truth correspondences between these modalities. In our self-supervised setting, the unlabeled videos only provide noisy labels of audio-visual pairings but do not contain text labels. To circumvent this limitation, we propose to extract latent captions, which are pseudo-words that encode the visual concepts in videos with language semantics. Prior work [8, 11] has demonstrated that the rich visualsemantic alignment in vision-language foundation models can be adapted to extract latent word representations that convey the semantics of their conditioning images. Inspired by this insight, we introduce the novel idea of using latent captions to identify sound-emitting object candidates in unlabeled videos for training, thereby allowing us to train without prior knowledge of existing objects in the videos." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.471, + 0.892, + 0.789 + ], + "angle": 0, + "content": "Latent captions. We perform \"textual inversion\" [8, 11, 12] where we adapt the CLIP language encoder to express the visual concepts of a video in the form of an encoded learnable parameter. Instead of introducing new concepts into the vocabulary of these models which require their parameters to be updated, we search for their latent language representations through a visual reconstruction objective. This objective is based on the key insight that the final learnt latent captions should be expressive enough to convey the visual semantics of the video. While it is also possible to use the visual frame representations as latent captions, we reason that learning them as outputs of the language encoder will help a model generalize better to language queries during inference. For a given video \\( V \\), we encode its center frame \\( V_{center} \\) as: \\( f_{center}^{V} = g^{V}(V_{center}) \\), where \\( g^{V} \\) is the embedding function of the CLIP visual encoder. Then, we replace the token embeddings used for language queries with a learnable parameter \\( p \\) and encode it as: \\( g^{L}(p) \\), where \\( g^{L} \\) is the embedding function of the CLIP language encoder. We optimize the weights of \\( p \\) by maximizing the cosine similarity between \\( f_{center}^{V} \\) and \\( g^{L}(p) \\):" + }, + { + "type": "equation", + "bbox": [ + 0.576, + 0.795, + 0.891, + 0.822 + ], + "angle": 0, + "content": "\\[\np ^ {*} \\in \\underset {p} {\\arg \\max } \\operatorname {s i m} \\left(f _ {\\text {c e n t e r}} ^ {V}, g ^ {L} (p)\\right) \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.892, + 0.901 + ], + "angle": 0, + "content": "where \\( \\text{sim}(x, y) = x^T y / (\\| x \\| \\| y \\|) \\) and \\( ||.|| \\) denotes the \\( L_2 \\) norm operator. Let \\( C^* = g^L(p^*) \\) be the latent caption. We illustrate this operation in the supplemental. In theory, \\( C^* \\) is analogous to a representation of a description of the frame and may replace ground-truth annotations effectively." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.926, + 0.519, + 0.938 + ], + "angle": 0, + "content": "10577" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.099, + 0.087, + 0.448, + 0.258 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.461, + 0.087, + 0.877, + 0.258 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.263, + 0.894, + 0.334 + ], + "angle": 0, + "content": "Figure 3. Audio-language and tri-modal consistency alignment objectives. (a) The audio-language objective aims to maximize the semantic similarity between the predicted audio and its latent caption. (b) In the tri-modal consistency objective, we compute normalized probability distributions over the spatiotemporal regions based on cosine similarity scores (colored frame patches) with respect to the predicted audio and latent captions. \\( K \\) and \\( Q \\) denote the key and query terminology that is used in self-attention. Intuitively, this objective encourages agreement between where the latent caption and predicted audio is occurring in the video." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.347, + 0.473, + 0.543 + ], + "angle": 0, + "content": "Our audio-language and tri-modal consistency alignment objectives are based on our reasoning that well-separated audio sources should be semantically consistent with the visual concepts that guide their separation as well as their text labels. Given an input video \\(V\\) of \\(T\\) frames \\(V = \\{V_{1},\\dots V_{T}\\}\\) and an audio spectrogram \\(A^S\\in \\mathbb{R}^{F\\times N}\\) with \\(F\\) frequency bins and \\(N\\) STFT time frames, our model predicts a separated audio spectrogram \\(\\hat{A}^S\\in \\mathbb{R}^{F\\times N}\\). We extract a latent representation for the predicted spectrogram: \\(\\hat{f}^A = \\mathcal{M}_\\theta (\\hat{A}^S)\\in \\mathbb{R}^D\\) where \\(\\mathcal{M}\\) denotes our audio separation model. For each video, we use its encoded predicted spectrogram and latent caption to provide pseudo-language supervision in our alignment objectives detailed below." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.549, + 0.47, + 0.791 + ], + "angle": 0, + "content": "Audio-language consistency loss. To encourage our audio encoder to learn audio representations that are effective for separating sound components when conditioned on either text or video queries, we aim to maximize the pairwise similarities between all three modalities. The key insight is that the audio sources that are well-separated by the visual concepts in a video should have a strong semantic relevance to its latent caption which express the same concepts in natural language (Figure 3a). Theoretically, this is similar to the self-supervised multimodal learning objective of maximizing the similarity between the representations of an image and its corresponding caption as well as the dissimilarity of non-corresponding captions. In lieu of ground-truth object labels, we can maximize the alignment between the predicted audio representations and the latent captions over the entire vocabulary of captions \\(\\mathcal{X}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.101, + 0.802, + 0.47, + 0.844 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {A u b i o - l a n g u a g e}} = - \\log \\left(\\frac {\\exp \\left(\\hat {f} ^ {A} \\cdot C ^ {*} / \\tau\\right)}{\\sum_ {x \\in \\mathcal {X}} \\exp \\left(\\hat {f} ^ {A} \\cdot x / \\tau\\right)}\\right) \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.855, + 0.262, + 0.87 + ], + "angle": 0, + "content": "where \\(\\tau\\) is the temperature." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "However, the problem of false negatives has been well-documented in image-text datasets, where captions for" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.347, + 0.892, + 0.453 + ], + "angle": 0, + "content": "some images may be relevant to other images but are treated erroneously as negatives. Since we are training on unlabeled videos, we account for the high likelihood that some videos may contain similar sounding objects by using a lower weight for this objective. Intuitively, this weighting helps to alleviate the effect of false negatives and prevent it from introducing a lot of noise during training." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.458, + 0.893, + 0.7 + ], + "angle": 0, + "content": "Tri-modal consistency loss. While the audio-language consistency objective facilitates improving the alignment between audio sources and their corresponding latent captions, it does not provide a straightforward solution to disregard false negatives in its contrastive formulation. To address this issue, we further introduce a softer tri-modal alignment constraint which exploits the implicit localization capability of vision-language foundation models for supervision without requiring any negative samples. Specifically, we propose to use the intermediary visual modality to encourage well-separated audio components to be grounded correctly in the relevant spatiotemporal regions of a video. Prior work [29, 42] has demonstrated that the CLIP model can be engineered to extract a segmentation map based on natural language queries. Inspired by this finding, we use the latent captions to provide pseudo-target attention maps." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Our intuition is that enforcing a soft constraint on the predicted spectrograms such that they can be mapped to similar relevant regions as determined by the latent captions will encourage the model to implicitly learn the transitive alignment between the audio and language modalities. Let \\( P_{Att}(A, b) = \\sigma(A \\cdot b) \\) to be the attention operation where \\( \\sigma(z)_i = z_i / \\sum_j z_j \\) is the softmax function. For a given video \\( V \\), we extract a set of spatiotemporal region representations by encoding each frame separately. Specifically, we encode the \\( t \\)-th frame as: \\( f_t^V = g_\\theta^V(V_t) \\), where \\( f_t^V \\in \\mathbb{R}^{HW\\times D} \\), where \\( H \\) and \\( W \\) are the downsampled height and width of the input video. Then, we compute a probability distribution of similarity scores over the set of" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.925, + 0.519, + 0.936 + ], + "angle": 0, + "content": "10578" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.148, + 0.089, + 0.411, + 0.102 + ], + "angle": 0, + "content": "Audio-Language Separation Model \\(\\mathcal{M}_{\\mathcal{A}\\mathcal{L}}\\)" + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.103, + 0.485, + 0.215 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.228, + 0.471, + 0.298 + ], + "angle": 0, + "content": "Figure 4. Spectrogram mask prediction. During inference, our model is able to separate audio sources using video or language queries despite training without ground-truth text annotations. We note that we only use unlabeled videos during training. We illustrate the audio-visual separation mode \\(\\mathcal{M}_{AV}\\) in the supplemental." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.314, + 0.47, + 0.451 + ], + "angle": 0, + "content": "spatial region features with respect to its latent caption \\(C^*\\) for the \\(t\\)-th frame: \\(P_{VC}^{t} = P_{Att}(f_{t}^{V}, C^{*}) \\in \\mathbb{R}^{HW \\times 1}\\). Next, we compute a similar distribution over the region features of the \\(t\\)-th frame with respect to the encoded audio representation of the masked spectrogram: \\(P_{VA}^{t} = P_{Att}(f_{t}^{V}, \\hat{f}^{A}) \\in \\mathbb{R}^{HW \\times 1}\\). We encourage the predicted audio representation to be similar to that of the latent caption by minimizing the Kullback-Leibler (KL) divergence between both attention distributions over the set of all time steps in a video \\(\\mathcal{T}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.116, + 0.457, + 0.469, + 0.5 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {T r i m o d a l}} = \\mathbb {E} _ {t \\sim \\mathcal {T}} \\left[ \\sum_ {x = 1} ^ {H W} P _ {V C} ^ {t} (x) \\log \\frac {P _ {V C} ^ {t} (x)}{P _ {V A} ^ {t} (x)} \\right], \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.506, + 0.469, + 0.537 + ], + "angle": 0, + "content": "where \\(P_{VA}^{t}(x)\\) denotes the audio-video attention distribution over the \\(t\\)-frame of the \\(x\\)-th spatial region." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.544, + 0.303, + 0.56 + ], + "angle": 0, + "content": "3.2. Audio Separation Model" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.567, + 0.47, + 0.81 + ], + "angle": 0, + "content": "We introduce two audio separation models \\(\\mathcal{M}_{AL}\\) and \\(\\mathcal{M}_{AV}\\) which share the same audio model parameters for separating audio sources. \\(\\mathcal{M}_{AL}\\) (Figure 4) infers a spectrogram mask based on a language query while \\(\\mathcal{M}_{AV}\\) (shown in supplemental) conditions its prediction on the input video. We adopt the U-Net [31] model as the audio component in \\(\\mathcal{M}_{AL}\\) and \\(\\mathcal{M}_{AV}\\), which has been demonstrated by prior work [14, 41] to be effective at audio source separation, and the CLIP visual and language encoders to exploit its learnt visual-semantic alignment. The U-Net model comprises an encoder \\(\\mathcal{E}\\) and a decoder \\(\\mathcal{D}\\). Given an input audio spectrogram \\(A^S\\), the encoder \\(\\mathcal{E}\\) applies a series of downsampling convolutional layers to output a set of bottleneck features: \\(f^A = \\mathcal{E}(A^S)\\), \\(f^A \\in \\mathbb{R}^{H^A \\times W^A \\times D}\\), where \\(H^A\\) and \\(W^A\\) denote the height and width of the downsampled spectrogram, respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Given a natural language query \\(L \\in \\mathbb{R}^{N_w}\\) where \\(N_{w}\\) is the number of words, we extract its representation \\(f^L \\in \\mathbb{R}^{1\\times D}\\) using the text encoder: \\(f^L = g^L (L)\\). We stress that language queries with ground-truth object labels are only used during inference. Then, we tile the language representation by the factor \\(H^{A}W^{A}\\) and concatenate with the" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.231 + ], + "angle": 0, + "content": "audio bottleneck representations along the channel dimension: \\( f^{AL} = \\text{concat}(f^A, \\text{tile}(f^L)) \\), where \\( f^{AL} \\) has the dimensions \\( \\mathbb{R}^{H^A \\times W^A \\times 2D} \\). We pass the concatenated representations into the decoder \\( \\mathcal{D} \\) consisting of a series of upsampling convolutional layers to generate a real-valued ratio mask: \\( \\hat{M} = \\mathcal{D}(f^{AL}) \\in \\mathbb{R}^{F \\times N} \\). To predict the separated audio source, each element of the mask is multiplied with the corresponding location in the input spectrogram: \\( \\hat{A}^S = \\hat{M} \\odot A^S \\), where \\( \\odot \\) denotes the Hadamard product." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.232, + 0.892, + 0.414 + ], + "angle": 0, + "content": "Video and Multiple Instance Learning for mask prediction. Since language annotations are not used during training, we train only with unlabeled videos. During training, as well as inference on audio-visual separation, we use the CLIP visual encoder to extract a set of language-grounded spatiotemporal region representations \\( f^{V} \\in \\mathbb{R}^{T \\times H \\times W \\times D} \\). Similarly, we can perform the same mask inference operation using videos by using the representation of each spatiotemporal region representation interchangeably in place of the language representation. This interchangeability is due to the fact that the CLIP representations project the video to the joint vision-language embedding space." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.414, + 0.892, + 0.565 + ], + "angle": 0, + "content": "Prior work [14] has demonstrated the advantages of performing audio-visual separation at the object level for videos with multiple objects. In the absence of object detectors and labels, we propose an MIL formulation, where all spatiotemporal regions in the input video are treated as positive candidates. Specifically, given a spatiotemporal grid of region representations extracted from the visual encoder as defined in this section, we predict a spectrogram mask \\(\\hat{M}_j\\) for the \\(j\\)-th region. Finally, we aggregate them over all regions to obtain a spectrogram mask for the entire video:" + }, + { + "type": "equation", + "bbox": [ + 0.619, + 0.571, + 0.891, + 0.6 + ], + "angle": 0, + "content": "\\[\n\\hat {M} = \\frac {1}{T} \\sum_ {j = 1} ^ {T H W} \\hat {M} _ {j}. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.606, + 0.892, + 0.877 + ], + "angle": 0, + "content": "Intuitively, this formulation encourages the model to learn to identify the salient regions with sounding objects for audio separation. We obtain the predicted mask for each frame by computing the sum of the predicted masks over all spatial regions and average the predicted masks over the temporal dimension since we reason that a sounding object should have similar prediction masks across frames. We adopt the self-supervised 'mix-and-separate' learning objective [14, 41] to train our model for predicting spectrogram masks. In this formulation, audio from two or more videos are mixed and the goal is to use the visual information of a video to separate its audio component. This setting allows us to generate pseudo-target masks for training supervision. We compute \\(\\mathcal{L}_{mask}\\) as the L1 loss between the pseudo-target and predicted ratio masks [41]. Please refer to the supplemental for details of our spatiotemporal region representation, audio-visual separation model and \\(\\mathcal{L}_{mask}\\). The final objective function is computed as:" + }, + { + "type": "equation", + "bbox": [ + 0.54, + 0.886, + 0.891, + 0.902 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\lambda_ {1} \\mathcal {L} _ {\\text {m a s k}} + \\lambda_ {2} \\mathcal {L} _ {\\text {T r i m o d a l}} + \\lambda_ {3} \\mathcal {L} _ {\\text {A u s i o - l a n g u a g e}} \\tag {5}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.926, + 0.519, + 0.938 + ], + "angle": 0, + "content": "10579" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.11, + 0.089, + 0.86, + 0.215 + ], + "angle": 0, + "content": "
MethodObject detectors# Region proposalsSolosDuets
NSDR ↑SIR ↑SAR ↑NSDR ↑SIR ↑SAR ↑
Co-Separation [14]Yes27.3813.7010.827.4213.8110.60
AVSGS [5]Yes429.0414.4512.2410.2515.6012.82
Sound-of-Pixels [41]NoNone7.3011.9011.906.059.8110.61
AV-Mix-and-Separate [14]NoNone3.166.748.893.237.019.14
NMF-MFCC [34]NoNone0.925.686.840.925.686.84
VAST (Ours)NoNone7.9813.9212.358.0813.9711.33
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.225, + 0.894, + 0.255 + ], + "angle": 0, + "content": "Table 1. Audio-visual source separation on MUSIC. We report results on videos that contain one instrument (solos) and two instruments (duets). Despite not training with object bounding boxes, VAST performs competitively with state-of-the-art detection-based approaches." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.267, + 0.471, + 0.299 + ], + "angle": 0, + "content": "where \\(\\lambda_{1},\\lambda_{2}\\) and \\(\\lambda_{3}\\) denote the weights for the mask, tri-modal and audio-language consistency losses, respectively." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.312, + 0.21, + 0.33 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.338, + 0.47, + 0.549 + ], + "angle": 0, + "content": "We evaluate the effectiveness of our proposed VAST approach on audio-text and audio-visual source separation in videos. To perform fair comparison to prior work, we conduct experiments on the SOLOS [24], MUSIC [41] and AudioSet [15] datasets. We refer readers to the supplemental for additional implementation and dataset details. Given a language query containing a prompt template and an object, the goal of audio-text source separation is to extract its corresponding sound component from an audio input, which is often comprised of a mixture of sounds emitted by various objects. Similarly, in audio-visual source separation, a model has to leverage the visual information in the input video to extract its corresponding sound component and align it with the relevant video pixels." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.55, + 0.47, + 0.688 + ], + "angle": 0, + "content": "Evaluation metrics. We adopt the Normalized Signal-to-Distortion Ratio (NSDR), Signal-to-Interference Ratio (SIR) and Signal-to-Artifact Ratio (SAR) [27, 30]. NSDR computes the difference between the SDR of the predicted and mixed audio with respect to the ground-truth waveforms, which measures the sound quality of the separated audios. SIR measures the amount of contamination from other audio sources in the predicted audio. Finally, SAR measures the amount of artifacts in the predicted audio." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.696, + 0.267, + 0.712 + ], + "angle": 0, + "content": "4.1. Quantitative results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.471, + 0.903 + ], + "angle": 0, + "content": "We compare our approach to the following baselines. Similar to our approach, Sound of Pixels (SOP) [41] does not require object detectors but learns to perform video-level separation. We also implement the AV-Mix-and-separate baseline from [14] with the same audio-visual separation model as ours but is trained to perform video-level separation and without our alignment objectives. The off-the-shelf NMF-MFCC [34] baseline performs audio separation using non-negative matrix factorization (NMF) and Mel frequency cepstrum coefficients (MFCC). Next, we also compare to Co-Separation [14] that learns to perform audio separation at the object-level by relying on object de" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.267, + 0.892, + 0.313 + ], + "angle": 0, + "content": "tectors. Last but not least, we include AVSGS [5] that also relies on a high number of object proposals to construct a spatiotemporal scene graph to reason about context." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.317, + 0.893, + 0.62 + ], + "angle": 0, + "content": "Audio-visual source separation on MUSIC. We report the results of our evaluation under two settings in Table 1. In the first setting, each video contains only a single instrument while the 'duet' setting includes videos that contain two different instruments. To begin, our VAST approach outperforms SOP by a large margin despite not relying on object detectors too. As shown in Table 4, we show that this performance gain is not due to just replacing ImageNet-pretrained Resnet18 [18] visual representations with those of the CLIP model since it leads to a large drop in performance. We hypothesize that SOP does not learn a direct projection of the audio inputs used in source separation into the CLIP embedding space. In contrast, VAST facilitates a better adaptation of the learnt audio representations to the CLIP embedding. We also found it important to modify CLIP's self-attention (see supp.). We observe that VAST outperforms AV-Mix-and-Separate by significantly, particularly under the duet setting. This suggests that performing region-level audio separation provides more capacity for the model to reason about multiple sounding objects in videos." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.625, + 0.894, + 0.837 + ], + "angle": 0, + "content": "More significantly, we observe that our approach outperforms the Co-Separation approach [14], which relies on object labels in the videos. Since Co-Separation uses a high confidence region proposal for each instrument to localize relevant regions, our improvements over it suggest that our latent captions are able to express multiple visual concepts that are present in the video. Last but not least, our approach is also comparable to AVSGS even without scene graph reasoning modules. The latter constructs a spatiotemporal visual scene graph over a large number of region proposals to reason about context between detected objects. We note that their audio-visual scene graph component can be combined with our VAST approach to possibly improve performance but is beyond the scope of this work." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.894, + 0.903 + ], + "angle": 0, + "content": "Audio-visual source separation on SOLOS. While the videos in the SOLOS dataset generally have less background noise than those of the MUSIC dataset, we see in Table 2 that AV-Mix-and-Separate and NMF-MFCC are still" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.926, + 0.521, + 0.938 + ], + "angle": 0, + "content": "10580" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.079, + 0.089, + 0.487, + 0.213 + ], + "angle": 0, + "content": "
MethodObject detectorsNSDR ↑SIR ↑SAR ↑
Co-Separation [14]Yes7.1112.0910.05
AVSGS [5]Yes9.2014.0512.17
Sound-of-Pixels [41]No6.2810.8410.13
AV-Mix-and-Sep [14]No2.945.818.33
NMF-MFCC [34]No0.684.755.12
VAST (Ours)No8.5814.1612.35
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.225, + 0.47, + 0.268 + ], + "angle": 0, + "content": "Table 2. Audio-visual source separation results on the SOLOS dataset. Similar to the results in Table 1, we see that VAST significantly closes the gap with object detection-based approaches." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.279, + 0.486, + 0.404 + ], + "angle": 0, + "content": "
MethodObject detectorsNSDR ↑SIR ↑SAR ↑
Co-Separation [14]Yes4.267.0713.00
AVSGS [5]Yes5.288.2713.04
Sound-of-Pixels [41]No1.663.5811.50
AV-Mix-and-Sep [14]No1.683.3012.20
NMF-MFCC [34]No0.254.195.78
VAST (Ours)No4.157.6213.20
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.415, + 0.47, + 0.457 + ], + "angle": 0, + "content": "Table 3. Audio-visual source separation results on AudioSet. VAST generalizes much better to the noisier AudioSet dataset than Sound-of-Pixels which also does not use object detections." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.476, + 0.476, + 0.542 + ], + "angle": 0, + "content": "
ModelVisual encoderNSDR ↑SIR ↑SAR ↑
SOP [41]ImageNet6.2810.8410.13
SOP [41]CLIP4.428.368.21
OursCLIP8.5814.1612.35
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.551, + 0.47, + 0.595 + ], + "angle": 0, + "content": "Table 4. Using CLIP visual features in SOP model on the SOLOS dataset. Using CLIP visual features naively in existing methods results in a drop in performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.612, + 0.47, + 0.809 + ], + "angle": 0, + "content": "unable to generalize to the cleaner audio signals. Similar to the reported performance on the MUSIC dataset, we also observe that VAST is comparable to the strongly supervised AVSGS approach on the SOLOS dataset. One possible reason behind the lower performance of AVSGS on videos with single instrument is that it is less critical to reason about context for videos with a single sounding object. Our better performance as compared to Co-Separation suggests that learning to perform audio separation at the coarse video region level under an MIL formulation can serve as an effective replacement for training object detectors. These results also indicate the great promise of latent captions in replacing ground-truth object annotations for supervision." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Audio-visual source separation on AudioSet. Finally, we report the results of our evaluation on the AudioSet dataset in Table 3. AudioSet has been documented by prior work [14] to be much noisier than the videos in the other two datasets, which explains the lower performance across all approaches. Unlike the SOP model, we observe that our" + }, + { + "type": "table", + "bbox": [ + 0.508, + 0.089, + 0.885, + 0.168 + ], + "angle": 0, + "content": "
LAudio-languageLTrimodalNSDR ↑SIR ↑SAR ↑
XX5.4710.5510.95
✓X8.0813.7412.18
X✓8.1013.8411.79
✓✓8.5814.1612.35
" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.179, + 0.892, + 0.222 + ], + "angle": 0, + "content": "Table 5. Ablation of our audio-language and tri-modal consistency alignment objectives on SOLOs. The alignment objectives help to improve audio-visual separation performance." + }, + { + "type": "table", + "bbox": [ + 0.56, + 0.236, + 0.833, + 0.315 + ], + "angle": 0, + "content": "
# tokensNSDR ↑SIR ↑SAR ↑
17.3111.3411.71
27.6713.0711.45
38.5814.1612.35
48.0213.3911.53
" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.326, + 0.892, + 0.356 + ], + "angle": 0, + "content": "Table 6. Ablation over number of learnable tokens on SOLOS. Using more learnable tokens generally improves performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.364, + 0.892, + 0.395 + ], + "angle": 0, + "content": "training approach is more robust to noise in the dataset where the sounding object may not always be visible." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.403, + 0.663, + 0.418 + ], + "angle": 0, + "content": "4.1.1 Model Analysis" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.428, + 0.892, + 0.639 + ], + "angle": 0, + "content": "Ablation of \\(\\mathcal{L}_{\\mathrm{Trimodal}}\\) and \\(\\mathcal{L}_{\\mathrm{Audio - language}}\\). Table 5 provides an ablation over our audio-language and tri-modal consistency losses. Despite being trained on a larger and more diverse set of visual concepts, we find the CLIP visual representations alone do not encourage the audio encoder to learn a strong alignment between the audio and vision modalities (row 1). We observe the importance of our proposed alignment objectives where adding one or the other leads to a significant improvement in audio separation performance. Due to multiple training videos containing similar instruments, it is likely that we are treating some latent captions as false negative samples for each video in the audio-language consistency objective. However, we see that the consistency objective is still beneficial towards audio separation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.64, + 0.892, + 0.806 + ], + "angle": 0, + "content": "Number of learnable token embeddings in latent captions. We report the results of our ablation over the number of learnable token parameters used in the extraction of latent captions in Table 6. We observe that increasing the number of learnable tokens generally helps to improve the performance, although using 4 tokens hurts performance slightly. We hypothesize that a higher number of learnable tokens provide more capacity for the CLIP language model to express multiple visual concepts that are present in the videos. This finding suggests that using more tokens may be beneficial for videos with more complex visual scenes." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.817, + 0.797, + 0.833 + ], + "angle": 0, + "content": "4.2. Audio-language source separation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.903 + ], + "angle": 0, + "content": "Finally, we evaluate the capability of our trained model to separate audio components based on natural language queries in Table 7. We construct each query using the template 'person playing a {instrument}''. We stress that we" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.927, + 0.518, + 0.938 + ], + "angle": 0, + "content": "10581" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.079, + 0.089, + 0.894, + 0.155 + ], + "angle": 0, + "content": "
Query ModalityAlignment objectivesSOLOSMUSICAudioset
NSDR ↑SIR ↑SAR ↑NSDR ↑SIR ↑SAR ↑NSDR ↑SIR ↑SAR ↑
LanguageNo-3.052.793.77-3.672.513.41-5.021.9814.94
LanguageYes6.9212.0710.416.4511.1810.772.364.7110.28
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.164, + 0.895, + 0.207 + ], + "angle": 0, + "content": "Table 7. Audio-text separation with natural language queries. We evaluate our model, that is trained only on unlabeled videos, on the task of audio-text separation. Note that we do not compare to other audio-visual separation baselines since there is no straightforward way to adapt them for language queries. We compare our full VAST model to a variant that is only trained with the mask prediction loss." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.22, + 0.473, + 0.401 + ], + "angle": 0, + "content": "only train on unlabeled videos without text supervision. To begin, we compare our VAST model to a variant that is trained without our alignment objectives. Note that we do not compare to other audio-visual approaches since there is no straightforward way to adapt them for language queries. As evidenced by the significant performance gap between both variants, our alignment losses are integral to learning a strong transitive alignment between the audio and language modalities. This finding suggests that just learning an alignment between the audio and visual modalities does not result in a transitive relationship between the audio and natural language modalities." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.402, + 0.473, + 0.598 + ], + "angle": 0, + "content": "Additionally, for effective sound source separation given either video or text inputs, we hypothesize that it is critical to learn an audio encoder E that is well-aligned with CLIP's vision-language embedding. Note that the same shared audio encoder \\(\\mathcal{E}\\) encodes both mixed and predicted audio sources. Thus, it can also be used as a general audio encoder and the decoder \\(\\mathcal{D}\\) can condition its separation process on either language or video queries. Lastly, we observe that our alignment objectives are still insufficient for closing the performance gap between audio-text and audio-visual separation (Tables 1, 2 and 3) completely. This observation indicates that future work is needed for further improving the latent alignment between all three modalities." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.606, + 0.255, + 0.621 + ], + "angle": 0, + "content": "4.3. Qualitative results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.629, + 0.47, + 0.75 + ], + "angle": 0, + "content": "Predicted audio-to-video attention visualizations. To evaluate the semantic consistency between the predicted audio sources and the visual cues that guide the separation process, we plot the attention map between the encoded predicted spectrograms and their corresponding video frames (Section 3.1) in Figure 5. We observe that VAST helps the model to learn to ground the audio source in the video pixels despite not requiring bounding box supervision." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.751, + 0.472, + 0.902 + ], + "angle": 0, + "content": "Predicted outputs of language-based audio separation. Finally, we present an example of how different language queries affect the separation performance for the same audio input in Figure 6. Significantly, despite not relying on text annotations for training supervision, our model can separate audio components based on free-form language queries. This demonstrates the effectiveness of our proposed idea to substitute ground-truth text annotations with latent captions during training. Additionally, we also observe that providing more context in the language query (e.g., \"violin\" versus" + }, + { + "type": "image", + "bbox": [ + 0.506, + 0.219, + 0.91, + 0.33 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.338, + 0.895, + 0.38 + ], + "angle": 0, + "content": "Figure 5. Predicted audio attention in videos. Our consistency objectives help the model to localize the relevant regions more accurately without prior knowledge of sounding object locations." + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.383, + 0.91, + 0.605 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.607, + 0.895, + 0.648 + ], + "angle": 0, + "content": "Figure 6. Predicted audio spectrograms with language queries. Interestingly, we see that including visually grounded adjectives in the queries affects the quality of the separated audio sources." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.657, + 0.892, + 0.672 + ], + "angle": 0, + "content": "\"person playing a violin\") can lead to improved separations." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.679, + 0.619, + 0.695 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.892, + 0.856 + ], + "angle": 0, + "content": "In summary, we introduce a self-supervised approach for learning to separate audio based on a language query, or a video. In the absence of object labels, we propose to extract latent captions to provide pseudo-language supervision. Furthermore, we introduce the novel tri-modal and audio-language alignment objectives that use the latent captions to improve the alignment of the audio, language and video modalities. By reducing the training need for object labels, our work opens up the possibility of large-scale pretraining on unlabeled videos with diverse visual concepts." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Acknowledgements: This material is based upon work supported, in part, by DARPA under agreement number HR00112020054 and a gift from Adobe Research." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.927, + 0.519, + 0.938 + ], + "angle": 0, + "content": "10582" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.184 + ], + "angle": 0, + "content": "[1] Hassan Akbari, Liangzhe Yuan, Rui Qian, Wei-Hong Chuang, Shih-Fu Chang, Yin Cui, and Boqing Gong. Vatt: Transformers for multimodal self-supervised learning from raw video, audio and text. 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Denseclip: Extract free dense labels from clip. arXiv preprint arXiv:2112.01071, 2021. 4" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.472 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.927, + 0.52, + 0.938 + ], + "angle": 0, + "content": "10584" + } + ] +] \ No newline at end of file diff --git a/2023/Language-Guided Audio-Visual Source Separation via Trimodal Consistency/8ed77a3b-731a-4b06-bbf1-882c057c335a_origin.pdf b/2023/Language-Guided Audio-Visual Source Separation via Trimodal Consistency/8ed77a3b-731a-4b06-bbf1-882c057c335a_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..c85decda78d5c97b79a4a4a1b282333ccbc2a876 --- /dev/null +++ b/2023/Language-Guided Audio-Visual Source Separation via Trimodal Consistency/8ed77a3b-731a-4b06-bbf1-882c057c335a_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:ea5963cc4b4082d5b774aecf0d63f89a4654d65630ba0eddf3752f66cea4ad1c +size 1337500 diff --git a/2023/Language-Guided Audio-Visual Source Separation via Trimodal Consistency/full.md b/2023/Language-Guided Audio-Visual Source Separation via Trimodal Consistency/full.md new file mode 100644 index 0000000000000000000000000000000000000000..17da7317b3b6bec8c5542428464e0210bfbb4653 --- /dev/null +++ b/2023/Language-Guided Audio-Visual Source Separation via Trimodal Consistency/full.md @@ -0,0 +1,255 @@ +# Language-Guided Audio-Visual Source Separation via Trimodal Consistency + +Reuben Tan $^{1}$ Arijit Ray $^{1}$ Andrea Burns $^{1}$ Bryan A. Plummer $^{1}$ Justin Salamon $^{2}$ Oriol Nieto $^{2}$ Bryan Russell $^{2}$ Kate Saenko $^{1,3}$ + +$^{1}$ Boston University, $^{2}$ Adobe Research, $^{3}$ MIT-IBM Watson AI Lab, IBM Research $\{\mathrm{rxtan}, \mathrm{aburns4}, \mathrm{array}, \mathrm{bplum}, \mathrm{saenko}\} @ \mathrm{bu.edu}, \{\mathrm{salamon}, \mathrm{onieto}, \mathrm{brussell}\} @ \mathrm{adobe.com}$ + +# Abstract + +We propose a self-supervised approach for learning to perform audio source separation in videos based on natural language queries, using only unlabeled video and audio pairs as training data. A key challenge in this task is learning to associate the linguistic description of a sound-emitting object to its visual features and the corresponding components of the audio waveform, all without access to annotations during training. To overcome this challenge, we adapt off-the-shelf vision-language foundation models to provide pseudo-target supervision via two novel loss functions and encourage a stronger alignment between the audio, visual and natural language modalities. During inference, our approach can separate sounds given text, video and audio input, or given text and audio input alone. We demonstrate the effectiveness of our self-supervised approach on three audio-visual separation datasets, including MUSIC, SOLOS and AudioSet, where we outperform state-of-the-art strongly supervised approaches despite not using object detectors or text labels during training. Our project page including publicly available code can be found at https://cs-people.bu.edu/rxtan/projects/VAST. + +# 1. Introduction + +Our everyday audiovisual world is composed of many visible sound sources, often with multiple sources layering on top of one another. For example, consider the video of the guitar and cello musicians playing together in Fig. 1. The two instruments have distinct timbres, and the musicians play non-unison, but complementary melodies. Despite hearing both instruments simultaneously, humans have an innate ability to identify and isolate the melody of a single source object. In this paper, we define the corresponding machine task as follows: given a natural language query that selects a sounding object, such as "person playing a guitar", separate its sound source from the input audio waveform and localize it in the input video, without any supervision. + +This task is challenging. First, there is no approach for + +![](images/68108733d5c101bf1df27531a94da84ff7f5cbe67f7d812940ec1f642c799a95.jpg) +Figure 1. We propose to separate and localize audio sources based on a natural language query, by learning to align the modalities on completely unlabeled videos. In comparison, prior audio-visual sound separation approaches require object label supervision. + +associating the linguistic description of a sound-emitting object to its visual features and the corresponding components of the audio waveform without access to annotations during training. Existing audio-visual methods [5, 14, 41] do not generalize to natural language queries due to their dependence on discrete object class labels. Second, an ideal solution would jointly identify and localize sound-emitting objects in videos as well as separate the corresponding components in the audio waveform without strong supervision. Although prior audio-visual work has demonstrated the benefits of aligning relevant object regions in the video with their corresponding sounds [5, 14], these approaches require strong supervision including object label + +and bounding box annotations (see Fig. 1 top). Overcoming these challenges would enable important downstream applications including holistic video understanding [33], embodied AI [6], and bidirectional audio-to-video retrieval [38]. + +To address these challenges, we make the following contributions. First, we propose Video-Audio Separation through Text (VAST), a self-supervised approach that leverages large vision-language "foundation" models [20, 26] to provide pseudo-supervision for learning the alignment between the three modalities: audio, video and natural language. Our key insight is to learn a strong transitive relation from audio to natural language using vision as an intermediary modality, while preserving the alignment between the visual and natural language modalities embodied by the foundation models. However, just using the visual representations of these foundation models in existing AV separation approaches does not preserve the transitive relationships between the three modalities (Sec. 4.1). + +Our second contribution introduces two novel multimodal alignment objectives that encourage the learnt audio representations to encode the semantics of captions and infer the latent transitive relation between the three modalities. While natural language can express a large and varied range of visual concepts for audio separation in videos, the absence of captions in unlabeled videos during training poses a significant challenge in our self-supervised formulation. To learn the transitive alignment, we adapt a foundation model to extract latent captions from unlabeled videos. Intuitively, the latent captions are representations that express the visual concepts present in the videos. Third, we introduce a Multiple Instance Learning formulation to learn to perform audio separation at the video region level since we do not have prior information on relevant objects or their locations in the videos during training. + +Finally, we demonstrate the effectiveness of our proposed VAST approach through extensive evaluations on the audio source separation task on the SOLOS [24], MUSIC [41], and AudioSet [15] datasets. We show that our self-supervised approach outperforms strongly-supervised state-of-the-art approaches without using labels during training by leveraging the capability of vision-language foundation models. More importantly, we demonstrate that VAST learns to use language queries for audio separation despite not training with ground-truth language supervision. + +# 2. Related Work + +Audio-only source separation. The goal of audio-only source separation is to use the aural cues present in the input audio waveform to separate the individual components. Conventional audio signal processing techniques rely on strong assumptions such as the number of sources in the audio waveforms to compute non-negative matrix factorization [3, 10, 37] of audio spectrograms. Deep learn- + +ing methods commonly adopt the self-supervised 'mix-and-separate' strategy where multiple audio sources are combined into a synthetic mixture and then predict a spectrogram mask to retrieve queried audio components [5, 14, 41]. Multimodal source separation. Recent work in audiotext [21, 22] and audio-visual [5, 7, 14, 40, 41] separation also use the 'mix-and-separate' strategy to train a decoder to predict a spectrogram mask based on natural language and video queries, respectively. In the case of the former, state-of-the-art approaches can either accept a single object label [5, 14, 41] or free-form natural language queries [21, 22]. Existing audio-visual source separation approaches often rely on training object detectors with strong supervision from bounding box annotations to localize objects of interest before learning to perform source separation at the object-level. In contrast, our proposed approach does not rely on pretrained object detectors or object labels in the training videos. The Sound of Pixels (SOP) model is the most similar in spirit to our proposed approach since it does not rely on object detectors. Instead, it learns to perform sound separation based on a video-level representation during training. Our VAST approach is also similar to the Voiceformer [28] approach which aims to separate speech from multiple speakers using a combination of audio, visual and language inputs. In contrast to our approach, their approach requires ground-truth text transcripts for training. Finally, the task is also similar in nature to that of sound localization in videos [9, 19]. + +Multimodal representation learning. One key challenge is grounding information from the text and/or audio modalities in the video frames [2, 5, 14, 35]. Since annotating video datasets is a costly process, prior work has investigated self-supervised pretraining methods on unlabeled videos [17, 36]. This often involves utilizing complementary information from the audio, text and visual modalities [39] to learn robust representations that can generalize to downstream tasks such as action recognition [1, 25, 32] and text-to-video retrieval [2, 23]. These approaches often use large-scale pretraining datasets such as Kinetics-400 / 600 [4] and HowTo100M [23] before finetuning linear probes for target tasks and datasets. Recent work has also focused on prompting multimodal foundation models such as CLIP [26] and ALIGN [20] to adapt them to new tasks ranging from open-vocabulary object detection [16] to domain adaptation [13] without modifying their parameters. + +# 3. Video-Audio Separation through Text + +Given a set of unlabeled videos and their audio tracks, we strive to learn a self-supervised model that separates an audio source given a natural language query and, optionally, an accompanying video. This goal requires a model to learn a strong alignment between the audio, vision, and language modalities. To this end, we propose a novel Audio-Visual + +![](images/233e18ac7f6b45bfd83a69d99e27b47d231936652dd3e70aee42fe7ebb02c341.jpg) +Figure 2. Training overview of our proposed VAST approach. We introduce tri-modal (Section 3.1) and audio-language (Section 3.1) consistency objectives to learn the latent alignment between the audio, video and language modalities. Furthermore, we adopt a prior mask prediction loss [41] (Section 3.2) to guide the training of our mask prediction decoder. + +Separation through Text (VAST) approach that learns an effective representation for audio-visual source separation, as well as a strong alignment between the audio and language modalities for audio-text source separation (see Figure 2 for an overview). To learn this representation, we exploit the strong joint visual-semantic alignment embodied in pretrained vision-language foundation models by encouraging our model to learn a direct projection function for audio inputs into their joint embedding space (Section 3.1). Our key insight is to use videos as an intermediary modality to learn a transitive alignment between the audio and language modalities. Since the visual and language modalities are already aligned, learning a strong correspondence between audio and vision should also provide an alignment between audio and language through videos via transitivity. + +Despite the intuitiveness of this idea, our experiments will show that using the visual representations of existing audio-visual foundation models does not help them learn the above-mentioned transitive alignment. To address this limitation, we introduce our novel tri-modal and audiolanguage consistency alignment objectives (Figure 2). The tri-modal objective encourages the model to maximize the semantic consistency between all three modalities by using videos as the intermediary modality and the audiolanguage objective helps to further improve the transitive alignment between audio and natural language. We leverage vision-and-language foundation models to infer latent captions that correspond to the audio components without text annotations, thus providing pseudo-language supervision (Section 3.1). In addition, we adopt the "mix-and-separate" strategy [41] to train our audio separation model, where the audio from multiple videos are mixed and then separated using only the video's visual information. For an input audio waveform $A$ , we apply a Short-Time Fourier Transform (STFT) to obtain its magnitude spectrogram $A^S$ and phase $A^{\mathrm{phase}}$ . Our learning objective only makes use of $A^S$ , which encodes how the magnitude of the audio fre + +quencies changes over time. We reconstruct the predicted waveform by applying the inverse STFT on the predicted spectrogram using the original phase $A^{\mathrm{phase}}$ . We describe our VAST audio separation model $\mathcal{M}$ in Section 3.2. + +# 3.1. Alignment between audio, language and video + +A standard method to learn a strong alignment between the audio, language and vision modalities is to maximize the pairwise similarities of their input representations using a contrastive learning formulation [1, 23]. However, learning this alignment necessitates the presence of labels that indicate ground-truth correspondences between these modalities. In our self-supervised setting, the unlabeled videos only provide noisy labels of audio-visual pairings but do not contain text labels. To circumvent this limitation, we propose to extract latent captions, which are pseudo-words that encode the visual concepts in videos with language semantics. Prior work [8, 11] has demonstrated that the rich visualsemantic alignment in vision-language foundation models can be adapted to extract latent word representations that convey the semantics of their conditioning images. Inspired by this insight, we introduce the novel idea of using latent captions to identify sound-emitting object candidates in unlabeled videos for training, thereby allowing us to train without prior knowledge of existing objects in the videos. + +Latent captions. We perform "textual inversion" [8, 11, 12] where we adapt the CLIP language encoder to express the visual concepts of a video in the form of an encoded learnable parameter. Instead of introducing new concepts into the vocabulary of these models which require their parameters to be updated, we search for their latent language representations through a visual reconstruction objective. This objective is based on the key insight that the final learnt latent captions should be expressive enough to convey the visual semantics of the video. While it is also possible to use the visual frame representations as latent captions, we reason that learning them as outputs of the language encoder will help a model generalize better to language queries during inference. For a given video $V$ , we encode its center frame $V_{center}$ as: $f_{center}^{V} = g^{V}(V_{center})$ , where $g^{V}$ is the embedding function of the CLIP visual encoder. Then, we replace the token embeddings used for language queries with a learnable parameter $p$ and encode it as: $g^{L}(p)$ , where $g^{L}$ is the embedding function of the CLIP language encoder. We optimize the weights of $p$ by maximizing the cosine similarity between $f_{center}^{V}$ and $g^{L}(p)$ : + +$$ +p ^ {*} \in \underset {p} {\arg \max } \operatorname {s i m} \left(f _ {\text {c e n t e r}} ^ {V}, g ^ {L} (p)\right) \tag {1} +$$ + +where $\text{sim}(x, y) = x^T y / (\| x \| \| y \|)$ and $||.||$ denotes the $L_2$ norm operator. Let $C^* = g^L(p^*)$ be the latent caption. We illustrate this operation in the supplemental. In theory, $C^*$ is analogous to a representation of a description of the frame and may replace ground-truth annotations effectively. + +![](images/01092bb17ba79431dd2336a332e39fff85153ce19d70c72c0255de9066463350.jpg) +Figure 3. Audio-language and tri-modal consistency alignment objectives. (a) The audio-language objective aims to maximize the semantic similarity between the predicted audio and its latent caption. (b) In the tri-modal consistency objective, we compute normalized probability distributions over the spatiotemporal regions based on cosine similarity scores (colored frame patches) with respect to the predicted audio and latent captions. $K$ and $Q$ denote the key and query terminology that is used in self-attention. Intuitively, this objective encourages agreement between where the latent caption and predicted audio is occurring in the video. + +![](images/04b53d6f981850088658e98b7e6e169e860182829137576eae7d7edbe1b880a7.jpg) + +Our audio-language and tri-modal consistency alignment objectives are based on our reasoning that well-separated audio sources should be semantically consistent with the visual concepts that guide their separation as well as their text labels. Given an input video $V$ of $T$ frames $V = \{V_{1},\dots V_{T}\}$ and an audio spectrogram $A^S\in \mathbb{R}^{F\times N}$ with $F$ frequency bins and $N$ STFT time frames, our model predicts a separated audio spectrogram $\hat{A}^S\in \mathbb{R}^{F\times N}$ . We extract a latent representation for the predicted spectrogram: $\hat{f}^A = \mathcal{M}_\theta (\hat{A}^S)\in \mathbb{R}^D$ where $\mathcal{M}$ denotes our audio separation model. For each video, we use its encoded predicted spectrogram and latent caption to provide pseudo-language supervision in our alignment objectives detailed below. + +Audio-language consistency loss. To encourage our audio encoder to learn audio representations that are effective for separating sound components when conditioned on either text or video queries, we aim to maximize the pairwise similarities between all three modalities. The key insight is that the audio sources that are well-separated by the visual concepts in a video should have a strong semantic relevance to its latent caption which express the same concepts in natural language (Figure 3a). Theoretically, this is similar to the self-supervised multimodal learning objective of maximizing the similarity between the representations of an image and its corresponding caption as well as the dissimilarity of non-corresponding captions. In lieu of ground-truth object labels, we can maximize the alignment between the predicted audio representations and the latent captions over the entire vocabulary of captions $\mathcal{X}$ : + +$$ +\mathcal {L} _ {\text {A u b i o - l a n g u a g e}} = - \log \left(\frac {\exp \left(\hat {f} ^ {A} \cdot C ^ {*} / \tau\right)}{\sum_ {x \in \mathcal {X}} \exp \left(\hat {f} ^ {A} \cdot x / \tau\right)}\right) \tag {2} +$$ + +where $\tau$ is the temperature. + +However, the problem of false negatives has been well-documented in image-text datasets, where captions for + +some images may be relevant to other images but are treated erroneously as negatives. Since we are training on unlabeled videos, we account for the high likelihood that some videos may contain similar sounding objects by using a lower weight for this objective. Intuitively, this weighting helps to alleviate the effect of false negatives and prevent it from introducing a lot of noise during training. + +Tri-modal consistency loss. While the audio-language consistency objective facilitates improving the alignment between audio sources and their corresponding latent captions, it does not provide a straightforward solution to disregard false negatives in its contrastive formulation. To address this issue, we further introduce a softer tri-modal alignment constraint which exploits the implicit localization capability of vision-language foundation models for supervision without requiring any negative samples. Specifically, we propose to use the intermediary visual modality to encourage well-separated audio components to be grounded correctly in the relevant spatiotemporal regions of a video. Prior work [29, 42] has demonstrated that the CLIP model can be engineered to extract a segmentation map based on natural language queries. Inspired by this finding, we use the latent captions to provide pseudo-target attention maps. + +Our intuition is that enforcing a soft constraint on the predicted spectrograms such that they can be mapped to similar relevant regions as determined by the latent captions will encourage the model to implicitly learn the transitive alignment between the audio and language modalities. Let $P_{Att}(A, b) = \sigma(A \cdot b)$ to be the attention operation where $\sigma(z)_i = z_i / \sum_j z_j$ is the softmax function. For a given video $V$ , we extract a set of spatiotemporal region representations by encoding each frame separately. Specifically, we encode the $t$ -th frame as: $f_t^V = g_\theta^V(V_t)$ , where $f_t^V \in \mathbb{R}^{HW\times D}$ , where $H$ and $W$ are the downsampled height and width of the input video. Then, we compute a probability distribution of similarity scores over the set of + +![](images/95ab4d675e65384b6fc447fc88566d8912775f176319f6f5db0448fa0dfb2443.jpg) +Audio-Language Separation Model $\mathcal{M}_{\mathcal{A}\mathcal{L}}$ +Figure 4. Spectrogram mask prediction. During inference, our model is able to separate audio sources using video or language queries despite training without ground-truth text annotations. We note that we only use unlabeled videos during training. We illustrate the audio-visual separation mode $\mathcal{M}_{AV}$ in the supplemental. + +spatial region features with respect to its latent caption $C^*$ for the $t$ -th frame: $P_{VC}^{t} = P_{Att}(f_{t}^{V}, C^{*}) \in \mathbb{R}^{HW \times 1}$ . Next, we compute a similar distribution over the region features of the $t$ -th frame with respect to the encoded audio representation of the masked spectrogram: $P_{VA}^{t} = P_{Att}(f_{t}^{V}, \hat{f}^{A}) \in \mathbb{R}^{HW \times 1}$ . We encourage the predicted audio representation to be similar to that of the latent caption by minimizing the Kullback-Leibler (KL) divergence between both attention distributions over the set of all time steps in a video $\mathcal{T}$ : + +$$ +\mathcal {L} _ {\text {T r i m o d a l}} = \mathbb {E} _ {t \sim \mathcal {T}} \left[ \sum_ {x = 1} ^ {H W} P _ {V C} ^ {t} (x) \log \frac {P _ {V C} ^ {t} (x)}{P _ {V A} ^ {t} (x)} \right], \tag {3} +$$ + +where $P_{VA}^{t}(x)$ denotes the audio-video attention distribution over the $t$ -frame of the $x$ -th spatial region. + +# 3.2. Audio Separation Model + +We introduce two audio separation models $\mathcal{M}_{AL}$ and $\mathcal{M}_{AV}$ which share the same audio model parameters for separating audio sources. $\mathcal{M}_{AL}$ (Figure 4) infers a spectrogram mask based on a language query while $\mathcal{M}_{AV}$ (shown in supplemental) conditions its prediction on the input video. We adopt the U-Net [31] model as the audio component in $\mathcal{M}_{AL}$ and $\mathcal{M}_{AV}$ , which has been demonstrated by prior work [14, 41] to be effective at audio source separation, and the CLIP visual and language encoders to exploit its learnt visual-semantic alignment. The U-Net model comprises an encoder $\mathcal{E}$ and a decoder $\mathcal{D}$ . Given an input audio spectrogram $A^S$ , the encoder $\mathcal{E}$ applies a series of downsampling convolutional layers to output a set of bottleneck features: $f^A = \mathcal{E}(A^S)$ , $f^A \in \mathbb{R}^{H^A \times W^A \times D}$ , where $H^A$ and $W^A$ denote the height and width of the downsampled spectrogram, respectively. + +Given a natural language query $L \in \mathbb{R}^{N_w}$ where $N_{w}$ is the number of words, we extract its representation $f^L \in \mathbb{R}^{1\times D}$ using the text encoder: $f^L = g^L (L)$ . We stress that language queries with ground-truth object labels are only used during inference. Then, we tile the language representation by the factor $H^{A}W^{A}$ and concatenate with the + +audio bottleneck representations along the channel dimension: $f^{AL} = \text{concat}(f^A, \text{tile}(f^L))$ , where $f^{AL}$ has the dimensions $\mathbb{R}^{H^A \times W^A \times 2D}$ . We pass the concatenated representations into the decoder $\mathcal{D}$ consisting of a series of upsampling convolutional layers to generate a real-valued ratio mask: $\hat{M} = \mathcal{D}(f^{AL}) \in \mathbb{R}^{F \times N}$ . To predict the separated audio source, each element of the mask is multiplied with the corresponding location in the input spectrogram: $\hat{A}^S = \hat{M} \odot A^S$ , where $\odot$ denotes the Hadamard product. + +Video and Multiple Instance Learning for mask prediction. Since language annotations are not used during training, we train only with unlabeled videos. During training, as well as inference on audio-visual separation, we use the CLIP visual encoder to extract a set of language-grounded spatiotemporal region representations $f^{V} \in \mathbb{R}^{T \times H \times W \times D}$ . Similarly, we can perform the same mask inference operation using videos by using the representation of each spatiotemporal region representation interchangeably in place of the language representation. This interchangeability is due to the fact that the CLIP representations project the video to the joint vision-language embedding space. + +Prior work [14] has demonstrated the advantages of performing audio-visual separation at the object level for videos with multiple objects. In the absence of object detectors and labels, we propose an MIL formulation, where all spatiotemporal regions in the input video are treated as positive candidates. Specifically, given a spatiotemporal grid of region representations extracted from the visual encoder as defined in this section, we predict a spectrogram mask $\hat{M}_j$ for the $j$ -th region. Finally, we aggregate them over all regions to obtain a spectrogram mask for the entire video: + +$$ +\hat {M} = \frac {1}{T} \sum_ {j = 1} ^ {T H W} \hat {M} _ {j}. \tag {4} +$$ + +Intuitively, this formulation encourages the model to learn to identify the salient regions with sounding objects for audio separation. We obtain the predicted mask for each frame by computing the sum of the predicted masks over all spatial regions and average the predicted masks over the temporal dimension since we reason that a sounding object should have similar prediction masks across frames. We adopt the self-supervised 'mix-and-separate' learning objective [14, 41] to train our model for predicting spectrogram masks. In this formulation, audio from two or more videos are mixed and the goal is to use the visual information of a video to separate its audio component. This setting allows us to generate pseudo-target masks for training supervision. We compute $\mathcal{L}_{mask}$ as the L1 loss between the pseudo-target and predicted ratio masks [41]. Please refer to the supplemental for details of our spatiotemporal region representation, audio-visual separation model and $\mathcal{L}_{mask}$ . The final objective function is computed as: + +$$ +\mathcal {L} = \lambda_ {1} \mathcal {L} _ {\text {m a s k}} + \lambda_ {2} \mathcal {L} _ {\text {T r i m o d a l}} + \lambda_ {3} \mathcal {L} _ {\text {A u s i o - l a n g u a g e}} \tag {5} +$$ + +
MethodObject detectors# Region proposalsSolosDuets
NSDR ↑SIR ↑SAR ↑NSDR ↑SIR ↑SAR ↑
Co-Separation [14]Yes27.3813.7010.827.4213.8110.60
AVSGS [5]Yes429.0414.4512.2410.2515.6012.82
Sound-of-Pixels [41]NoNone7.3011.9011.906.059.8110.61
AV-Mix-and-Separate [14]NoNone3.166.748.893.237.019.14
NMF-MFCC [34]NoNone0.925.686.840.925.686.84
VAST (Ours)NoNone7.9813.9212.358.0813.9711.33
+ +Table 1. Audio-visual source separation on MUSIC. We report results on videos that contain one instrument (solos) and two instruments (duets). Despite not training with object bounding boxes, VAST performs competitively with state-of-the-art detection-based approaches. + +where $\lambda_{1},\lambda_{2}$ and $\lambda_{3}$ denote the weights for the mask, tri-modal and audio-language consistency losses, respectively. + +# 4. Experiments + +We evaluate the effectiveness of our proposed VAST approach on audio-text and audio-visual source separation in videos. To perform fair comparison to prior work, we conduct experiments on the SOLOS [24], MUSIC [41] and AudioSet [15] datasets. We refer readers to the supplemental for additional implementation and dataset details. Given a language query containing a prompt template and an object, the goal of audio-text source separation is to extract its corresponding sound component from an audio input, which is often comprised of a mixture of sounds emitted by various objects. Similarly, in audio-visual source separation, a model has to leverage the visual information in the input video to extract its corresponding sound component and align it with the relevant video pixels. + +Evaluation metrics. We adopt the Normalized Signal-to-Distortion Ratio (NSDR), Signal-to-Interference Ratio (SIR) and Signal-to-Artifact Ratio (SAR) [27, 30]. NSDR computes the difference between the SDR of the predicted and mixed audio with respect to the ground-truth waveforms, which measures the sound quality of the separated audios. SIR measures the amount of contamination from other audio sources in the predicted audio. Finally, SAR measures the amount of artifacts in the predicted audio. + +# 4.1. Quantitative results + +We compare our approach to the following baselines. Similar to our approach, Sound of Pixels (SOP) [41] does not require object detectors but learns to perform video-level separation. We also implement the AV-Mix-and-separate baseline from [14] with the same audio-visual separation model as ours but is trained to perform video-level separation and without our alignment objectives. The off-the-shelf NMF-MFCC [34] baseline performs audio separation using non-negative matrix factorization (NMF) and Mel frequency cepstrum coefficients (MFCC). Next, we also compare to Co-Separation [14] that learns to perform audio separation at the object-level by relying on object de + +tectors. Last but not least, we include AVSGS [5] that also relies on a high number of object proposals to construct a spatiotemporal scene graph to reason about context. + +Audio-visual source separation on MUSIC. We report the results of our evaluation under two settings in Table 1. In the first setting, each video contains only a single instrument while the 'duet' setting includes videos that contain two different instruments. To begin, our VAST approach outperforms SOP by a large margin despite not relying on object detectors too. As shown in Table 4, we show that this performance gain is not due to just replacing ImageNet-pretrained Resnet18 [18] visual representations with those of the CLIP model since it leads to a large drop in performance. We hypothesize that SOP does not learn a direct projection of the audio inputs used in source separation into the CLIP embedding space. In contrast, VAST facilitates a better adaptation of the learnt audio representations to the CLIP embedding. We also found it important to modify CLIP's self-attention (see supp.). We observe that VAST outperforms AV-Mix-and-Separate by significantly, particularly under the duet setting. This suggests that performing region-level audio separation provides more capacity for the model to reason about multiple sounding objects in videos. + +More significantly, we observe that our approach outperforms the Co-Separation approach [14], which relies on object labels in the videos. Since Co-Separation uses a high confidence region proposal for each instrument to localize relevant regions, our improvements over it suggest that our latent captions are able to express multiple visual concepts that are present in the video. Last but not least, our approach is also comparable to AVSGS even without scene graph reasoning modules. The latter constructs a spatiotemporal visual scene graph over a large number of region proposals to reason about context between detected objects. We note that their audio-visual scene graph component can be combined with our VAST approach to possibly improve performance but is beyond the scope of this work. + +Audio-visual source separation on SOLOS. While the videos in the SOLOS dataset generally have less background noise than those of the MUSIC dataset, we see in Table 2 that AV-Mix-and-Separate and NMF-MFCC are still + +
MethodObject detectorsNSDR ↑SIR ↑SAR ↑
Co-Separation [14]Yes7.1112.0910.05
AVSGS [5]Yes9.2014.0512.17
Sound-of-Pixels [41]No6.2810.8410.13
AV-Mix-and-Sep [14]No2.945.818.33
NMF-MFCC [34]No0.684.755.12
VAST (Ours)No8.5814.1612.35
+ +Table 2. Audio-visual source separation results on the SOLOS dataset. Similar to the results in Table 1, we see that VAST significantly closes the gap with object detection-based approaches. + +
MethodObject detectorsNSDR ↑SIR ↑SAR ↑
Co-Separation [14]Yes4.267.0713.00
AVSGS [5]Yes5.288.2713.04
Sound-of-Pixels [41]No1.663.5811.50
AV-Mix-and-Sep [14]No1.683.3012.20
NMF-MFCC [34]No0.254.195.78
VAST (Ours)No4.157.6213.20
+ +Table 3. Audio-visual source separation results on AudioSet. VAST generalizes much better to the noisier AudioSet dataset than Sound-of-Pixels which also does not use object detections. + +
ModelVisual encoderNSDR ↑SIR ↑SAR ↑
SOP [41]ImageNet6.2810.8410.13
SOP [41]CLIP4.428.368.21
OursCLIP8.5814.1612.35
+ +unable to generalize to the cleaner audio signals. Similar to the reported performance on the MUSIC dataset, we also observe that VAST is comparable to the strongly supervised AVSGS approach on the SOLOS dataset. One possible reason behind the lower performance of AVSGS on videos with single instrument is that it is less critical to reason about context for videos with a single sounding object. Our better performance as compared to Co-Separation suggests that learning to perform audio separation at the coarse video region level under an MIL formulation can serve as an effective replacement for training object detectors. These results also indicate the great promise of latent captions in replacing ground-truth object annotations for supervision. + +Audio-visual source separation on AudioSet. Finally, we report the results of our evaluation on the AudioSet dataset in Table 3. AudioSet has been documented by prior work [14] to be much noisier than the videos in the other two datasets, which explains the lower performance across all approaches. Unlike the SOP model, we observe that our + +Table 4. Using CLIP visual features in SOP model on the SOLOS dataset. Using CLIP visual features naively in existing methods results in a drop in performance. + +
LAudio-languageLTrimodalNSDR ↑SIR ↑SAR ↑
XX5.4710.5510.95
✓X8.0813.7412.18
X✓8.1013.8411.79
✓✓8.5814.1612.35
+ +Table 5. Ablation of our audio-language and tri-modal consistency alignment objectives on SOLOs. The alignment objectives help to improve audio-visual separation performance. + +
# tokensNSDR ↑SIR ↑SAR ↑
17.3111.3411.71
27.6713.0711.45
38.5814.1612.35
48.0213.3911.53
+ +Table 6. Ablation over number of learnable tokens on SOLOS. Using more learnable tokens generally improves performance. + +training approach is more robust to noise in the dataset where the sounding object may not always be visible. + +# 4.1.1 Model Analysis + +Ablation of $\mathcal{L}_{\mathrm{Trimodal}}$ and $\mathcal{L}_{\mathrm{Audio - language}}$ . Table 5 provides an ablation over our audio-language and tri-modal consistency losses. Despite being trained on a larger and more diverse set of visual concepts, we find the CLIP visual representations alone do not encourage the audio encoder to learn a strong alignment between the audio and vision modalities (row 1). We observe the importance of our proposed alignment objectives where adding one or the other leads to a significant improvement in audio separation performance. Due to multiple training videos containing similar instruments, it is likely that we are treating some latent captions as false negative samples for each video in the audio-language consistency objective. However, we see that the consistency objective is still beneficial towards audio separation. + +Number of learnable token embeddings in latent captions. We report the results of our ablation over the number of learnable token parameters used in the extraction of latent captions in Table 6. We observe that increasing the number of learnable tokens generally helps to improve the performance, although using 4 tokens hurts performance slightly. We hypothesize that a higher number of learnable tokens provide more capacity for the CLIP language model to express multiple visual concepts that are present in the videos. This finding suggests that using more tokens may be beneficial for videos with more complex visual scenes. + +# 4.2. Audio-language source separation + +Finally, we evaluate the capability of our trained model to separate audio components based on natural language queries in Table 7. We construct each query using the template 'person playing a {instrument}''. We stress that we + +
Query ModalityAlignment objectivesSOLOSMUSICAudioset
NSDR ↑SIR ↑SAR ↑NSDR ↑SIR ↑SAR ↑NSDR ↑SIR ↑SAR ↑
LanguageNo-3.052.793.77-3.672.513.41-5.021.9814.94
LanguageYes6.9212.0710.416.4511.1810.772.364.7110.28
+ +Table 7. Audio-text separation with natural language queries. We evaluate our model, that is trained only on unlabeled videos, on the task of audio-text separation. Note that we do not compare to other audio-visual separation baselines since there is no straightforward way to adapt them for language queries. We compare our full VAST model to a variant that is only trained with the mask prediction loss. + +only train on unlabeled videos without text supervision. To begin, we compare our VAST model to a variant that is trained without our alignment objectives. Note that we do not compare to other audio-visual approaches since there is no straightforward way to adapt them for language queries. As evidenced by the significant performance gap between both variants, our alignment losses are integral to learning a strong transitive alignment between the audio and language modalities. This finding suggests that just learning an alignment between the audio and visual modalities does not result in a transitive relationship between the audio and natural language modalities. + +Additionally, for effective sound source separation given either video or text inputs, we hypothesize that it is critical to learn an audio encoder E that is well-aligned with CLIP's vision-language embedding. Note that the same shared audio encoder $\mathcal{E}$ encodes both mixed and predicted audio sources. Thus, it can also be used as a general audio encoder and the decoder $\mathcal{D}$ can condition its separation process on either language or video queries. Lastly, we observe that our alignment objectives are still insufficient for closing the performance gap between audio-text and audio-visual separation (Tables 1, 2 and 3) completely. This observation indicates that future work is needed for further improving the latent alignment between all three modalities. + +# 4.3. Qualitative results + +Predicted audio-to-video attention visualizations. To evaluate the semantic consistency between the predicted audio sources and the visual cues that guide the separation process, we plot the attention map between the encoded predicted spectrograms and their corresponding video frames (Section 3.1) in Figure 5. We observe that VAST helps the model to learn to ground the audio source in the video pixels despite not requiring bounding box supervision. + +Predicted outputs of language-based audio separation. Finally, we present an example of how different language queries affect the separation performance for the same audio input in Figure 6. Significantly, despite not relying on text annotations for training supervision, our model can separate audio components based on free-form language queries. This demonstrates the effectiveness of our proposed idea to substitute ground-truth text annotations with latent captions during training. Additionally, we also observe that providing more context in the language query (e.g., "violin" versus + +![](images/09abd40468bc959b6f7293d65f16ac6cadb7f4e2b8b9301e7fea933a46683ac3.jpg) +Figure 5. Predicted audio attention in videos. Our consistency objectives help the model to localize the relevant regions more accurately without prior knowledge of sounding object locations. + +![](images/d28ed4712836791b135c5de9dfe4c08bf0ba2ce58b539832fd5bf6860d638fbb.jpg) +Figure 6. Predicted audio spectrograms with language queries. Interestingly, we see that including visually grounded adjectives in the queries affects the quality of the separated audio sources. + +"person playing a violin") can lead to improved separations. + +# 5. Conclusion + +In summary, we introduce a self-supervised approach for learning to separate audio based on a language query, or a video. In the absence of object labels, we propose to extract latent captions to provide pseudo-language supervision. 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A key challenge in this task is learning to associate the linguistic description of a sound-emitting object to its visual features and the corresponding components of the audio waveform, all without access to annotations during training. To overcome this challenge, we adapt off-the-shelf vision-language foundation models to provide pseudo-target supervision via two novel loss functions and encourage a stronger alignment between the audio, visual and natural language modalities. During inference, our approach can separate sounds given text, video and audio input, or given text and audio input alone. We demonstrate the effectiveness of our self-supervised approach on three audio-visual separation datasets, including MUSIC, SOLOS and AudioSet, where we outperform state-of-the-art strongly supervised approaches despite not using object detectors or text labels during training. Our project page including publicly available code can be found at https://cs-people.bu.edu/rxtan/projects/VAST." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 525, + 128, + 538 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 525, + 128, + 538 + ], + "spans": [ + { + "bbox": [ + 47, + 525, + 128, + 538 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 545, + 287, + 701 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 287, + 701 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 287, + 701 + ], + "type": "text", + "content": "Our everyday audiovisual world is composed of many visible sound sources, often with multiple sources layering on top of one another. For example, consider the video of the guitar and cello musicians playing together in Fig. 1. The two instruments have distinct timbres, and the musicians play non-unison, but complementary melodies. Despite hearing both instruments simultaneously, humans have an innate ability to identify and isolate the melody of a single source object. In this paper, we define the corresponding machine task as follows: given a natural language query that selects a sounding object, such as \"person playing a guitar\", separate its sound source from the input audio waveform and localize it in the input video, without any supervision." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 59, + 701, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 701, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 59, + 701, + 287, + 713 + ], + "type": "text", + "content": "This task is challenging. First, there is no approach for" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 310, + 227, + 544, + 491 + ], + "blocks": [ + { + "bbox": [ + 310, + 227, + 544, + 491 + ], + "lines": [ + { + "bbox": [ + 310, + 227, + 544, + 491 + ], + "spans": [ + { + "bbox": [ + 310, + 227, + 544, + 491 + ], + "type": "image", + "image_path": "68108733d5c101bf1df27531a94da84ff7f5cbe67f7d812940ec1f642c799a95.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 500, + 547, + 545 + ], + "lines": [ + { + "bbox": [ + 305, + 500, + 547, + 545 + ], + "spans": [ + { + "bbox": [ + 305, + 500, + 547, + 545 + ], + "type": "text", + "content": "Figure 1. We propose to separate and localize audio sources based on a natural language query, by learning to align the modalities on completely unlabeled videos. In comparison, prior audio-visual sound separation approaches require object label supervision." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 557, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 547, + 715 + ], + "type": "text", + "content": "associating the linguistic description of a sound-emitting object to its visual features and the corresponding components of the audio waveform without access to annotations during training. Existing audio-visual methods [5, 14, 41] do not generalize to natural language queries due to their dependence on discrete object class labels. Second, an ideal solution would jointly identify and localize sound-emitting objects in videos as well as separate the corresponding components in the audio waveform without strong supervision. Although prior audio-visual work has demonstrated the benefits of aligning relevant object regions in the video with their corresponding sounds [5, 14], these approaches require strong supervision including object label" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 293, + 732, + 317, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 732, + 317, + 742 + ], + "spans": [ + { + "bbox": [ + 293, + 732, + 317, + 742 + ], + "type": "text", + "content": "10575" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 286, + 119 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 286, + 119 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 286, + 119 + ], + "type": "text", + "content": "and bounding box annotations (see Fig. 1 top). Overcoming these challenges would enable important downstream applications including holistic video understanding [33], embodied AI [6], and bidirectional audio-to-video retrieval [38]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 121, + 286, + 286 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 121, + 286, + 286 + ], + "spans": [ + { + "bbox": [ + 46, + 121, + 286, + 286 + ], + "type": "text", + "content": "To address these challenges, we make the following contributions. First, we propose Video-Audio Separation through Text (VAST), a self-supervised approach that leverages large vision-language \"foundation\" models [20, 26] to provide pseudo-supervision for learning the alignment between the three modalities: audio, video and natural language. Our key insight is to learn a strong transitive relation from audio to natural language using vision as an intermediary modality, while preserving the alignment between the visual and natural language modalities embodied by the foundation models. However, just using the visual representations of these foundation models in existing AV separation approaches does not preserve the transitive relationships between the three modalities (Sec. 4.1)." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 288, + 286, + 478 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 288, + 286, + 478 + ], + "spans": [ + { + "bbox": [ + 46, + 288, + 286, + 478 + ], + "type": "text", + "content": "Our second contribution introduces two novel multimodal alignment objectives that encourage the learnt audio representations to encode the semantics of captions and infer the latent transitive relation between the three modalities. While natural language can express a large and varied range of visual concepts for audio separation in videos, the absence of captions in unlabeled videos during training poses a significant challenge in our self-supervised formulation. To learn the transitive alignment, we adapt a foundation model to extract latent captions from unlabeled videos. Intuitively, the latent captions are representations that express the visual concepts present in the videos. Third, we introduce a Multiple Instance Learning formulation to learn to perform audio separation at the video region level since we do not have prior information on relevant objects or their locations in the videos during training." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 479, + 286, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 479, + 286, + 598 + ], + "spans": [ + { + "bbox": [ + 46, + 479, + 286, + 598 + ], + "type": "text", + "content": "Finally, we demonstrate the effectiveness of our proposed VAST approach through extensive evaluations on the audio source separation task on the SOLOS [24], MUSIC [41], and AudioSet [15] datasets. We show that our self-supervised approach outperforms strongly-supervised state-of-the-art approaches without using labels during training by leveraging the capability of vision-language foundation models. More importantly, we demonstrate that VAST learns to use language queries for audio separation despite not training with ground-truth language supervision." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 609, + 133, + 621 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 609, + 133, + 621 + ], + "spans": [ + { + "bbox": [ + 47, + 609, + 133, + 621 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 629, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 286, + 713 + ], + "type": "text", + "content": "Audio-only source separation. The goal of audio-only source separation is to use the aural cues present in the input audio waveform to separate the individual components. Conventional audio signal processing techniques rely on strong assumptions such as the number of sources in the audio waveforms to compute non-negative matrix factorization [3, 10, 37] of audio spectrograms. Deep learn-" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 545, + 406 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 406 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 406 + ], + "type": "text", + "content": "ing methods commonly adopt the self-supervised 'mix-and-separate' strategy where multiple audio sources are combined into a synthetic mixture and then predict a spectrogram mask to retrieve queried audio components [5, 14, 41]. Multimodal source separation. Recent work in audiotext [21, 22] and audio-visual [5, 7, 14, 40, 41] separation also use the 'mix-and-separate' strategy to train a decoder to predict a spectrogram mask based on natural language and video queries, respectively. In the case of the former, state-of-the-art approaches can either accept a single object label [5, 14, 41] or free-form natural language queries [21, 22]. Existing audio-visual source separation approaches often rely on training object detectors with strong supervision from bounding box annotations to localize objects of interest before learning to perform source separation at the object-level. In contrast, our proposed approach does not rely on pretrained object detectors or object labels in the training videos. The Sound of Pixels (SOP) model is the most similar in spirit to our proposed approach since it does not rely on object detectors. Instead, it learns to perform sound separation based on a video-level representation during training. Our VAST approach is also similar to the Voiceformer [28] approach which aims to separate speech from multiple speakers using a combination of audio, visual and language inputs. In contrast to our approach, their approach requires ground-truth text transcripts for training. Finally, the task is also similar in nature to that of sound localization in videos [9, 19]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 407, + 545, + 611 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 407, + 545, + 611 + ], + "spans": [ + { + "bbox": [ + 304, + 407, + 545, + 611 + ], + "type": "text", + "content": "Multimodal representation learning. One key challenge is grounding information from the text and/or audio modalities in the video frames [2, 5, 14, 35]. Since annotating video datasets is a costly process, prior work has investigated self-supervised pretraining methods on unlabeled videos [17, 36]. This often involves utilizing complementary information from the audio, text and visual modalities [39] to learn robust representations that can generalize to downstream tasks such as action recognition [1, 25, 32] and text-to-video retrieval [2, 23]. These approaches often use large-scale pretraining datasets such as Kinetics-400 / 600 [4] and HowTo100M [23] before finetuning linear probes for target tasks and datasets. Recent work has also focused on prompting multimodal foundation models such as CLIP [26] and ALIGN [20] to adapt them to new tasks ranging from open-vocabulary object detection [16] to domain adaptation [13] without modifying their parameters." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 621, + 512, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 621, + 512, + 635 + ], + "spans": [ + { + "bbox": [ + 306, + 621, + 512, + 635 + ], + "type": "text", + "content": "3. Video-Audio Separation through Text" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": "Given a set of unlabeled videos and their audio tracks, we strive to learn a self-supervised model that separates an audio source given a natural language query and, optionally, an accompanying video. This goal requires a model to learn a strong alignment between the audio, vision, and language modalities. To this end, we propose a novel Audio-Visual" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 732, + 317, + 741 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 732, + 317, + 741 + ], + "spans": [ + { + "bbox": [ + 294, + 732, + 317, + 741 + ], + "type": "text", + "content": "10576" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 72, + 286, + 175 + ], + "blocks": [ + { + "bbox": [ + 50, + 72, + 286, + 175 + ], + "lines": [ + { + "bbox": [ + 50, + 72, + 286, + 175 + ], + "spans": [ + { + "bbox": [ + 50, + 72, + 286, + 175 + ], + "type": "image", + "image_path": "233e18ac7f6b45bfd83a69d99e27b47d231936652dd3e70aee42fe7ebb02c341.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 184, + 287, + 251 + ], + "lines": [ + { + "bbox": [ + 46, + 184, + 287, + 251 + ], + "spans": [ + { + "bbox": [ + 46, + 184, + 287, + 251 + ], + "type": "text", + "content": "Figure 2. Training overview of our proposed VAST approach. We introduce tri-modal (Section 3.1) and audio-language (Section 3.1) consistency objectives to learn the latent alignment between the audio, video and language modalities. Furthermore, we adopt a prior mask prediction loss [41] (Section 3.2) to guide the training of our mask prediction decoder." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 267, + 287, + 448 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 267, + 287, + 448 + ], + "spans": [ + { + "bbox": [ + 46, + 267, + 287, + 448 + ], + "type": "text", + "content": "Separation through Text (VAST) approach that learns an effective representation for audio-visual source separation, as well as a strong alignment between the audio and language modalities for audio-text source separation (see Figure 2 for an overview). To learn this representation, we exploit the strong joint visual-semantic alignment embodied in pretrained vision-language foundation models by encouraging our model to learn a direct projection function for audio inputs into their joint embedding space (Section 3.1). Our key insight is to use videos as an intermediary modality to learn a transitive alignment between the audio and language modalities. Since the visual and language modalities are already aligned, learning a strong correspondence between audio and vision should also provide an alignment between audio and language through videos via transitivity." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 450, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 450, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 450, + 288, + 713 + ], + "type": "text", + "content": "Despite the intuitiveness of this idea, our experiments will show that using the visual representations of existing audio-visual foundation models does not help them learn the above-mentioned transitive alignment. To address this limitation, we introduce our novel tri-modal and audiolanguage consistency alignment objectives (Figure 2). The tri-modal objective encourages the model to maximize the semantic consistency between all three modalities by using videos as the intermediary modality and the audiolanguage objective helps to further improve the transitive alignment between audio and natural language. We leverage vision-and-language foundation models to infer latent captions that correspond to the audio components without text annotations, thus providing pseudo-language supervision (Section 3.1). In addition, we adopt the \"mix-and-separate\" strategy [41] to train our audio separation model, where the audio from multiple videos are mixed and then separated using only the video's visual information. For an input audio waveform " + }, + { + "bbox": [ + 46, + 450, + 288, + 713 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 46, + 450, + 288, + 713 + ], + "type": "text", + "content": ", we apply a Short-Time Fourier Transform (STFT) to obtain its magnitude spectrogram " + }, + { + "bbox": [ + 46, + 450, + 288, + 713 + ], + "type": "inline_equation", + "content": "A^S" + }, + { + "bbox": [ + 46, + 450, + 288, + 713 + ], + "type": "text", + "content": " and phase " + }, + { + "bbox": [ + 46, + 450, + 288, + 713 + ], + "type": "inline_equation", + "content": "A^{\\mathrm{phase}}" + }, + { + "bbox": [ + 46, + 450, + 288, + 713 + ], + "type": "text", + "content": ". Our learning objective only makes use of " + }, + { + "bbox": [ + 46, + 450, + 288, + 713 + ], + "type": "inline_equation", + "content": "A^S" + }, + { + "bbox": [ + 46, + 450, + 288, + 713 + ], + "type": "text", + "content": ", which encodes how the magnitude of the audio fre" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": "quencies changes over time. We reconstruct the predicted waveform by applying the inverse STFT on the predicted spectrogram using the original phase " + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "inline_equation", + "content": "A^{\\mathrm{phase}}" + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": ". We describe our VAST audio separation model " + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": " in Section 3.2." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 305, + 126, + 543, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 126, + 543, + 140 + ], + "spans": [ + { + "bbox": [ + 305, + 126, + 543, + 140 + ], + "type": "text", + "content": "3.1. Alignment between audio, language and video" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 145, + 545, + 372 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 145, + 545, + 372 + ], + "spans": [ + { + "bbox": [ + 304, + 145, + 545, + 372 + ], + "type": "text", + "content": "A standard method to learn a strong alignment between the audio, language and vision modalities is to maximize the pairwise similarities of their input representations using a contrastive learning formulation [1, 23]. However, learning this alignment necessitates the presence of labels that indicate ground-truth correspondences between these modalities. In our self-supervised setting, the unlabeled videos only provide noisy labels of audio-visual pairings but do not contain text labels. To circumvent this limitation, we propose to extract latent captions, which are pseudo-words that encode the visual concepts in videos with language semantics. Prior work [8, 11] has demonstrated that the rich visualsemantic alignment in vision-language foundation models can be adapted to extract latent word representations that convey the semantics of their conditioning images. Inspired by this insight, we introduce the novel idea of using latent captions to identify sound-emitting object candidates in unlabeled videos for training, thereby allowing us to train without prior knowledge of existing objects in the videos." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 373, + 545, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 373, + 545, + 624 + ], + "spans": [ + { + "bbox": [ + 304, + 373, + 545, + 624 + ], + "type": "text", + "content": "Latent captions. We perform \"textual inversion\" [8, 11, 12] where we adapt the CLIP language encoder to express the visual concepts of a video in the form of an encoded learnable parameter. Instead of introducing new concepts into the vocabulary of these models which require their parameters to be updated, we search for their latent language representations through a visual reconstruction objective. This objective is based on the key insight that the final learnt latent captions should be expressive enough to convey the visual semantics of the video. While it is also possible to use the visual frame representations as latent captions, we reason that learning them as outputs of the language encoder will help a model generalize better to language queries during inference. For a given video " + }, + { + "bbox": [ + 304, + 373, + 545, + 624 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 304, + 373, + 545, + 624 + ], + "type": "text", + "content": ", we encode its center frame " + }, + { + "bbox": [ + 304, + 373, + 545, + 624 + ], + "type": "inline_equation", + "content": "V_{center}" + }, + { + "bbox": [ + 304, + 373, + 545, + 624 + ], + "type": "text", + "content": " as: " + }, + { + "bbox": [ + 304, + 373, + 545, + 624 + ], + "type": "inline_equation", + "content": "f_{center}^{V} = g^{V}(V_{center})" + }, + { + "bbox": [ + 304, + 373, + 545, + 624 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 373, + 545, + 624 + ], + "type": "inline_equation", + "content": "g^{V}" + }, + { + "bbox": [ + 304, + 373, + 545, + 624 + ], + "type": "text", + "content": " is the embedding function of the CLIP visual encoder. Then, we replace the token embeddings used for language queries with a learnable parameter " + }, + { + "bbox": [ + 304, + 373, + 545, + 624 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 304, + 373, + 545, + 624 + ], + "type": "text", + "content": " and encode it as: " + }, + { + "bbox": [ + 304, + 373, + 545, + 624 + ], + "type": "inline_equation", + "content": "g^{L}(p)" + }, + { + "bbox": [ + 304, + 373, + 545, + 624 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 373, + 545, + 624 + ], + "type": "inline_equation", + "content": "g^{L}" + }, + { + "bbox": [ + 304, + 373, + 545, + 624 + ], + "type": "text", + "content": " is the embedding function of the CLIP language encoder. We optimize the weights of " + }, + { + "bbox": [ + 304, + 373, + 545, + 624 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 304, + 373, + 545, + 624 + ], + "type": "text", + "content": " by maximizing the cosine similarity between " + }, + { + "bbox": [ + 304, + 373, + 545, + 624 + ], + "type": "inline_equation", + "content": "f_{center}^{V}" + }, + { + "bbox": [ + 304, + 373, + 545, + 624 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 373, + 545, + 624 + ], + "type": "inline_equation", + "content": "g^{L}(p)" + }, + { + "bbox": [ + 304, + 373, + 545, + 624 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 352, + 629, + 545, + 651 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 352, + 629, + 545, + 651 + ], + "spans": [ + { + "bbox": [ + 352, + 629, + 545, + 651 + ], + "type": "interline_equation", + "content": "p ^ {*} \\in \\underset {p} {\\arg \\max } \\operatorname {s i m} \\left(f _ {\\text {c e n t e r}} ^ {V}, g ^ {L} (p)\\right) \\tag {1}", + "image_path": "9c2f2541e00191c721d96b10ba7051b0dbf6b35bebf7258016144176ab52632b.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\text{sim}(x, y) = x^T y / (\\| x \\| \\| y \\|)" + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "inline_equation", + "content": "||.||" + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "content": " denotes the " + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "inline_equation", + "content": "L_2" + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "content": " norm operator. Let " + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "inline_equation", + "content": "C^* = g^L(p^*)" + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "content": " be the latent caption. We illustrate this operation in the supplemental. In theory, " + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "inline_equation", + "content": "C^*" + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "content": " is analogous to a representation of a description of the frame and may replace ground-truth annotations effectively." + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 733, + 317, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 733, + 317, + 742 + ], + "spans": [ + { + "bbox": [ + 294, + 733, + 317, + 742 + ], + "type": "text", + "content": "10577" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 60, + 68, + 274, + 204 + ], + "blocks": [ + { + "bbox": [ + 60, + 68, + 274, + 204 + ], + "lines": [ + { + "bbox": [ + 60, + 68, + 274, + 204 + ], + "spans": [ + { + "bbox": [ + 60, + 68, + 274, + 204 + ], + "type": "image", + "image_path": "01092bb17ba79431dd2336a332e39fff85153ce19d70c72c0255de9066463350.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 208, + 547, + 264 + ], + "lines": [ + { + "bbox": [ + 46, + 208, + 547, + 264 + ], + "spans": [ + { + "bbox": [ + 46, + 208, + 547, + 264 + ], + "type": "text", + "content": "Figure 3. Audio-language and tri-modal consistency alignment objectives. (a) The audio-language objective aims to maximize the semantic similarity between the predicted audio and its latent caption. (b) In the tri-modal consistency objective, we compute normalized probability distributions over the spatiotemporal regions based on cosine similarity scores (colored frame patches) with respect to the predicted audio and latent captions. " + }, + { + "bbox": [ + 46, + 208, + 547, + 264 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 208, + 547, + 264 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 208, + 547, + 264 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 46, + 208, + 547, + 264 + ], + "type": "text", + "content": " denote the key and query terminology that is used in self-attention. Intuitively, this objective encourages agreement between where the latent caption and predicted audio is occurring in the video." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 282, + 68, + 536, + 204 + ], + "blocks": [ + { + "bbox": [ + 282, + 68, + 536, + 204 + ], + "lines": [ + { + "bbox": [ + 282, + 68, + 536, + 204 + ], + "spans": [ + { + "bbox": [ + 282, + 68, + 536, + 204 + ], + "type": "image", + "image_path": "04b53d6f981850088658e98b7e6e169e860182829137576eae7d7edbe1b880a7.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 274, + 289, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 274, + 289, + 430 + ], + "spans": [ + { + "bbox": [ + 46, + 274, + 289, + 430 + ], + "type": "text", + "content": "Our audio-language and tri-modal consistency alignment objectives are based on our reasoning that well-separated audio sources should be semantically consistent with the visual concepts that guide their separation as well as their text labels. Given an input video " + }, + { + "bbox": [ + 46, + 274, + 289, + 430 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 46, + 274, + 289, + 430 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 46, + 274, + 289, + 430 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 274, + 289, + 430 + ], + "type": "text", + "content": " frames " + }, + { + "bbox": [ + 46, + 274, + 289, + 430 + ], + "type": "inline_equation", + "content": "V = \\{V_{1},\\dots V_{T}\\}" + }, + { + "bbox": [ + 46, + 274, + 289, + 430 + ], + "type": "text", + "content": " and an audio spectrogram " + }, + { + "bbox": [ + 46, + 274, + 289, + 430 + ], + "type": "inline_equation", + "content": "A^S\\in \\mathbb{R}^{F\\times N}" + }, + { + "bbox": [ + 46, + 274, + 289, + 430 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 46, + 274, + 289, + 430 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 46, + 274, + 289, + 430 + ], + "type": "text", + "content": " frequency bins and " + }, + { + "bbox": [ + 46, + 274, + 289, + 430 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 274, + 289, + 430 + ], + "type": "text", + "content": " STFT time frames, our model predicts a separated audio spectrogram " + }, + { + "bbox": [ + 46, + 274, + 289, + 430 + ], + "type": "inline_equation", + "content": "\\hat{A}^S\\in \\mathbb{R}^{F\\times N}" + }, + { + "bbox": [ + 46, + 274, + 289, + 430 + ], + "type": "text", + "content": ". We extract a latent representation for the predicted spectrogram: " + }, + { + "bbox": [ + 46, + 274, + 289, + 430 + ], + "type": "inline_equation", + "content": "\\hat{f}^A = \\mathcal{M}_\\theta (\\hat{A}^S)\\in \\mathbb{R}^D" + }, + { + "bbox": [ + 46, + 274, + 289, + 430 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 46, + 274, + 289, + 430 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 46, + 274, + 289, + 430 + ], + "type": "text", + "content": " denotes our audio separation model. For each video, we use its encoded predicted spectrogram and latent caption to provide pseudo-language supervision in our alignment objectives detailed below." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 434, + 287, + 626 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 434, + 287, + 626 + ], + "spans": [ + { + "bbox": [ + 46, + 434, + 287, + 626 + ], + "type": "text", + "content": "Audio-language consistency loss. To encourage our audio encoder to learn audio representations that are effective for separating sound components when conditioned on either text or video queries, we aim to maximize the pairwise similarities between all three modalities. The key insight is that the audio sources that are well-separated by the visual concepts in a video should have a strong semantic relevance to its latent caption which express the same concepts in natural language (Figure 3a). Theoretically, this is similar to the self-supervised multimodal learning objective of maximizing the similarity between the representations of an image and its corresponding caption as well as the dissimilarity of non-corresponding captions. In lieu of ground-truth object labels, we can maximize the alignment between the predicted audio representations and the latent captions over the entire vocabulary of captions " + }, + { + "bbox": [ + 46, + 434, + 287, + 626 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 46, + 434, + 287, + 626 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 61, + 635, + 287, + 668 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 635, + 287, + 668 + ], + "spans": [ + { + "bbox": [ + 61, + 635, + 287, + 668 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {A u b i o - l a n g u a g e}} = - \\log \\left(\\frac {\\exp \\left(\\hat {f} ^ {A} \\cdot C ^ {*} / \\tau\\right)}{\\sum_ {x \\in \\mathcal {X}} \\exp \\left(\\hat {f} ^ {A} \\cdot x / \\tau\\right)}\\right) \\tag {2}", + "image_path": "649b4a5702fd08b4fc2b06d83909148f14a7c0761192d828c661fe2042e8c742.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 677, + 160, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 160, + 689 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 160, + 689 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 677, + 160, + 689 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 47, + 677, + 160, + 689 + ], + "type": "text", + "content": " is the temperature." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "content": "However, the problem of false negatives has been well-documented in image-text datasets, where captions for" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 274, + 545, + 358 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 274, + 545, + 358 + ], + "spans": [ + { + "bbox": [ + 304, + 274, + 545, + 358 + ], + "type": "text", + "content": "some images may be relevant to other images but are treated erroneously as negatives. Since we are training on unlabeled videos, we account for the high likelihood that some videos may contain similar sounding objects by using a lower weight for this objective. Intuitively, this weighting helps to alleviate the effect of false negatives and prevent it from introducing a lot of noise during training." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 362, + 546, + 554 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 362, + 546, + 554 + ], + "spans": [ + { + "bbox": [ + 304, + 362, + 546, + 554 + ], + "type": "text", + "content": "Tri-modal consistency loss. While the audio-language consistency objective facilitates improving the alignment between audio sources and their corresponding latent captions, it does not provide a straightforward solution to disregard false negatives in its contrastive formulation. To address this issue, we further introduce a softer tri-modal alignment constraint which exploits the implicit localization capability of vision-language foundation models for supervision without requiring any negative samples. Specifically, we propose to use the intermediary visual modality to encourage well-separated audio components to be grounded correctly in the relevant spatiotemporal regions of a video. Prior work [29, 42] has demonstrated that the CLIP model can be engineered to extract a segmentation map based on natural language queries. Inspired by this finding, we use the latent captions to provide pseudo-target attention maps." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 558, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 547, + 713 + ], + "type": "text", + "content": "Our intuition is that enforcing a soft constraint on the predicted spectrograms such that they can be mapped to similar relevant regions as determined by the latent captions will encourage the model to implicitly learn the transitive alignment between the audio and language modalities. Let " + }, + { + "bbox": [ + 304, + 558, + 547, + 713 + ], + "type": "inline_equation", + "content": "P_{Att}(A, b) = \\sigma(A \\cdot b)" + }, + { + "bbox": [ + 304, + 558, + 547, + 713 + ], + "type": "text", + "content": " to be the attention operation where " + }, + { + "bbox": [ + 304, + 558, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\sigma(z)_i = z_i / \\sum_j z_j" + }, + { + "bbox": [ + 304, + 558, + 547, + 713 + ], + "type": "text", + "content": " is the softmax function. For a given video " + }, + { + "bbox": [ + 304, + 558, + 547, + 713 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 304, + 558, + 547, + 713 + ], + "type": "text", + "content": ", we extract a set of spatiotemporal region representations by encoding each frame separately. Specifically, we encode the " + }, + { + "bbox": [ + 304, + 558, + 547, + 713 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 558, + 547, + 713 + ], + "type": "text", + "content": "-th frame as: " + }, + { + "bbox": [ + 304, + 558, + 547, + 713 + ], + "type": "inline_equation", + "content": "f_t^V = g_\\theta^V(V_t)" + }, + { + "bbox": [ + 304, + 558, + 547, + 713 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 558, + 547, + 713 + ], + "type": "inline_equation", + "content": "f_t^V \\in \\mathbb{R}^{HW\\times D}" + }, + { + "bbox": [ + 304, + 558, + 547, + 713 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 558, + 547, + 713 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 304, + 558, + 547, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 558, + 547, + 713 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 304, + 558, + 547, + 713 + ], + "type": "text", + "content": " are the downsampled height and width of the input video. Then, we compute a probability distribution of similarity scores over the set of" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 732, + 317, + 741 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 732, + 317, + 741 + ], + "spans": [ + { + "bbox": [ + 294, + 732, + 317, + 741 + ], + "type": "text", + "content": "10578" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 81, + 296, + 170 + ], + "blocks": [ + { + "bbox": [ + 90, + 70, + 251, + 80 + ], + "lines": [ + { + "bbox": [ + 90, + 70, + 251, + 80 + ], + "spans": [ + { + "bbox": [ + 90, + 70, + 251, + 80 + ], + "type": "text", + "content": "Audio-Language Separation Model " + }, + { + "bbox": [ + 90, + 70, + 251, + 80 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{\\mathcal{A}\\mathcal{L}}" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 50, + 81, + 296, + 170 + ], + "lines": [ + { + "bbox": [ + 50, + 81, + 296, + 170 + ], + "spans": [ + { + "bbox": [ + 50, + 81, + 296, + 170 + ], + "type": "image", + "image_path": "95ab4d675e65384b6fc447fc88566d8912775f176319f6f5db0448fa0dfb2443.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 180, + 288, + 236 + ], + "lines": [ + { + "bbox": [ + 46, + 180, + 288, + 236 + ], + "spans": [ + { + "bbox": [ + 46, + 180, + 288, + 236 + ], + "type": "text", + "content": "Figure 4. Spectrogram mask prediction. During inference, our model is able to separate audio sources using video or language queries despite training without ground-truth text annotations. We note that we only use unlabeled videos during training. We illustrate the audio-visual separation mode " + }, + { + "bbox": [ + 46, + 180, + 288, + 236 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{AV}" + }, + { + "bbox": [ + 46, + 180, + 288, + 236 + ], + "type": "text", + "content": " in the supplemental." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 248, + 287, + 357 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 248, + 287, + 357 + ], + "spans": [ + { + "bbox": [ + 46, + 248, + 287, + 357 + ], + "type": "text", + "content": "spatial region features with respect to its latent caption " + }, + { + "bbox": [ + 46, + 248, + 287, + 357 + ], + "type": "inline_equation", + "content": "C^*" + }, + { + "bbox": [ + 46, + 248, + 287, + 357 + ], + "type": "text", + "content": " for the " + }, + { + "bbox": [ + 46, + 248, + 287, + 357 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 248, + 287, + 357 + ], + "type": "text", + "content": "-th frame: " + }, + { + "bbox": [ + 46, + 248, + 287, + 357 + ], + "type": "inline_equation", + "content": "P_{VC}^{t} = P_{Att}(f_{t}^{V}, C^{*}) \\in \\mathbb{R}^{HW \\times 1}" + }, + { + "bbox": [ + 46, + 248, + 287, + 357 + ], + "type": "text", + "content": ". Next, we compute a similar distribution over the region features of the " + }, + { + "bbox": [ + 46, + 248, + 287, + 357 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 248, + 287, + 357 + ], + "type": "text", + "content": "-th frame with respect to the encoded audio representation of the masked spectrogram: " + }, + { + "bbox": [ + 46, + 248, + 287, + 357 + ], + "type": "inline_equation", + "content": "P_{VA}^{t} = P_{Att}(f_{t}^{V}, \\hat{f}^{A}) \\in \\mathbb{R}^{HW \\times 1}" + }, + { + "bbox": [ + 46, + 248, + 287, + 357 + ], + "type": "text", + "content": ". We encourage the predicted audio representation to be similar to that of the latent caption by minimizing the Kullback-Leibler (KL) divergence between both attention distributions over the set of all time steps in a video " + }, + { + "bbox": [ + 46, + 248, + 287, + 357 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 46, + 248, + 287, + 357 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 70, + 361, + 287, + 396 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 361, + 287, + 396 + ], + "spans": [ + { + "bbox": [ + 70, + 361, + 287, + 396 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {T r i m o d a l}} = \\mathbb {E} _ {t \\sim \\mathcal {T}} \\left[ \\sum_ {x = 1} ^ {H W} P _ {V C} ^ {t} (x) \\log \\frac {P _ {V C} ^ {t} (x)}{P _ {V A} ^ {t} (x)} \\right], \\tag {3}", + "image_path": "79551bc3cb77af09bc815d7fe11c9341089bae1f52200c2a41d42941907bf60d.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 400, + 287, + 425 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 400, + 287, + 425 + ], + "spans": [ + { + "bbox": [ + 47, + 400, + 287, + 425 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 400, + 287, + 425 + ], + "type": "inline_equation", + "content": "P_{VA}^{t}(x)" + }, + { + "bbox": [ + 47, + 400, + 287, + 425 + ], + "type": "text", + "content": " denotes the audio-video attention distribution over the " + }, + { + "bbox": [ + 47, + 400, + 287, + 425 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 47, + 400, + 287, + 425 + ], + "type": "text", + "content": "-frame of the " + }, + { + "bbox": [ + 47, + 400, + 287, + 425 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 47, + 400, + 287, + 425 + ], + "type": "text", + "content": "-th spatial region." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 430, + 185, + 443 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 430, + 185, + 443 + ], + "spans": [ + { + "bbox": [ + 47, + 430, + 185, + 443 + ], + "type": "text", + "content": "3.2. Audio Separation Model" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 449, + 287, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 449, + 287, + 641 + ], + "spans": [ + { + "bbox": [ + 46, + 449, + 287, + 641 + ], + "type": "text", + "content": "We introduce two audio separation models " + }, + { + "bbox": [ + 46, + 449, + 287, + 641 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{AL}" + }, + { + "bbox": [ + 46, + 449, + 287, + 641 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 449, + 287, + 641 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{AV}" + }, + { + "bbox": [ + 46, + 449, + 287, + 641 + ], + "type": "text", + "content": " which share the same audio model parameters for separating audio sources. " + }, + { + "bbox": [ + 46, + 449, + 287, + 641 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{AL}" + }, + { + "bbox": [ + 46, + 449, + 287, + 641 + ], + "type": "text", + "content": " (Figure 4) infers a spectrogram mask based on a language query while " + }, + { + "bbox": [ + 46, + 449, + 287, + 641 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{AV}" + }, + { + "bbox": [ + 46, + 449, + 287, + 641 + ], + "type": "text", + "content": " (shown in supplemental) conditions its prediction on the input video. We adopt the U-Net [31] model as the audio component in " + }, + { + "bbox": [ + 46, + 449, + 287, + 641 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{AL}" + }, + { + "bbox": [ + 46, + 449, + 287, + 641 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 449, + 287, + 641 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{AV}" + }, + { + "bbox": [ + 46, + 449, + 287, + 641 + ], + "type": "text", + "content": ", which has been demonstrated by prior work [14, 41] to be effective at audio source separation, and the CLIP visual and language encoders to exploit its learnt visual-semantic alignment. The U-Net model comprises an encoder " + }, + { + "bbox": [ + 46, + 449, + 287, + 641 + ], + "type": "inline_equation", + "content": "\\mathcal{E}" + }, + { + "bbox": [ + 46, + 449, + 287, + 641 + ], + "type": "text", + "content": " and a decoder " + }, + { + "bbox": [ + 46, + 449, + 287, + 641 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 46, + 449, + 287, + 641 + ], + "type": "text", + "content": ". Given an input audio spectrogram " + }, + { + "bbox": [ + 46, + 449, + 287, + 641 + ], + "type": "inline_equation", + "content": "A^S" + }, + { + "bbox": [ + 46, + 449, + 287, + 641 + ], + "type": "text", + "content": ", the encoder " + }, + { + "bbox": [ + 46, + 449, + 287, + 641 + ], + "type": "inline_equation", + "content": "\\mathcal{E}" + }, + { + "bbox": [ + 46, + 449, + 287, + 641 + ], + "type": "text", + "content": " applies a series of downsampling convolutional layers to output a set of bottleneck features: " + }, + { + "bbox": [ + 46, + 449, + 287, + 641 + ], + "type": "inline_equation", + "content": "f^A = \\mathcal{E}(A^S)" + }, + { + "bbox": [ + 46, + 449, + 287, + 641 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 449, + 287, + 641 + ], + "type": "inline_equation", + "content": "f^A \\in \\mathbb{R}^{H^A \\times W^A \\times D}" + }, + { + "bbox": [ + 46, + 449, + 287, + 641 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 449, + 287, + 641 + ], + "type": "inline_equation", + "content": "H^A" + }, + { + "bbox": [ + 46, + 449, + 287, + 641 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 449, + 287, + 641 + ], + "type": "inline_equation", + "content": "W^A" + }, + { + "bbox": [ + 46, + 449, + 287, + 641 + ], + "type": "text", + "content": " denote the height and width of the downsampled spectrogram, respectively." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "type": "text", + "content": "Given a natural language query " + }, + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "type": "inline_equation", + "content": "L \\in \\mathbb{R}^{N_w}" + }, + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "type": "inline_equation", + "content": "N_{w}" + }, + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "type": "text", + "content": " is the number of words, we extract its representation " + }, + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "type": "inline_equation", + "content": "f^L \\in \\mathbb{R}^{1\\times D}" + }, + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "type": "text", + "content": " using the text encoder: " + }, + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "type": "inline_equation", + "content": "f^L = g^L (L)" + }, + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "type": "text", + "content": ". We stress that language queries with ground-truth object labels are only used during inference. Then, we tile the language representation by the factor " + }, + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "type": "inline_equation", + "content": "H^{A}W^{A}" + }, + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "type": "text", + "content": " and concatenate with the" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 72, + 545, + 182 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 182 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 182 + ], + "type": "text", + "content": "audio bottleneck representations along the channel dimension: " + }, + { + "bbox": [ + 304, + 72, + 545, + 182 + ], + "type": "inline_equation", + "content": "f^{AL} = \\text{concat}(f^A, \\text{tile}(f^L))" + }, + { + "bbox": [ + 304, + 72, + 545, + 182 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 72, + 545, + 182 + ], + "type": "inline_equation", + "content": "f^{AL}" + }, + { + "bbox": [ + 304, + 72, + 545, + 182 + ], + "type": "text", + "content": " has the dimensions " + }, + { + "bbox": [ + 304, + 72, + 545, + 182 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{H^A \\times W^A \\times 2D}" + }, + { + "bbox": [ + 304, + 72, + 545, + 182 + ], + "type": "text", + "content": ". We pass the concatenated representations into the decoder " + }, + { + "bbox": [ + 304, + 72, + 545, + 182 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 304, + 72, + 545, + 182 + ], + "type": "text", + "content": " consisting of a series of upsampling convolutional layers to generate a real-valued ratio mask: " + }, + { + "bbox": [ + 304, + 72, + 545, + 182 + ], + "type": "inline_equation", + "content": "\\hat{M} = \\mathcal{D}(f^{AL}) \\in \\mathbb{R}^{F \\times N}" + }, + { + "bbox": [ + 304, + 72, + 545, + 182 + ], + "type": "text", + "content": ". To predict the separated audio source, each element of the mask is multiplied with the corresponding location in the input spectrogram: " + }, + { + "bbox": [ + 304, + 72, + 545, + 182 + ], + "type": "inline_equation", + "content": "\\hat{A}^S = \\hat{M} \\odot A^S" + }, + { + "bbox": [ + 304, + 72, + 545, + 182 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 72, + 545, + 182 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 304, + 72, + 545, + 182 + ], + "type": "text", + "content": " denotes the Hadamard product." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 183, + 545, + 327 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 183, + 545, + 327 + ], + "spans": [ + { + "bbox": [ + 304, + 183, + 545, + 327 + ], + "type": "text", + "content": "Video and Multiple Instance Learning for mask prediction. Since language annotations are not used during training, we train only with unlabeled videos. During training, as well as inference on audio-visual separation, we use the CLIP visual encoder to extract a set of language-grounded spatiotemporal region representations " + }, + { + "bbox": [ + 304, + 183, + 545, + 327 + ], + "type": "inline_equation", + "content": "f^{V} \\in \\mathbb{R}^{T \\times H \\times W \\times D}" + }, + { + "bbox": [ + 304, + 183, + 545, + 327 + ], + "type": "text", + "content": ". Similarly, we can perform the same mask inference operation using videos by using the representation of each spatiotemporal region representation interchangeably in place of the language representation. This interchangeability is due to the fact that the CLIP representations project the video to the joint vision-language embedding space." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 327, + 545, + 447 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 327, + 545, + 447 + ], + "spans": [ + { + "bbox": [ + 304, + 327, + 545, + 447 + ], + "type": "text", + "content": "Prior work [14] has demonstrated the advantages of performing audio-visual separation at the object level for videos with multiple objects. In the absence of object detectors and labels, we propose an MIL formulation, where all spatiotemporal regions in the input video are treated as positive candidates. Specifically, given a spatiotemporal grid of region representations extracted from the visual encoder as defined in this section, we predict a spectrogram mask " + }, + { + "bbox": [ + 304, + 327, + 545, + 447 + ], + "type": "inline_equation", + "content": "\\hat{M}_j" + }, + { + "bbox": [ + 304, + 327, + 545, + 447 + ], + "type": "text", + "content": " for the " + }, + { + "bbox": [ + 304, + 327, + 545, + 447 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 304, + 327, + 545, + 447 + ], + "type": "text", + "content": "-th region. Finally, we aggregate them over all regions to obtain a spectrogram mask for the entire video:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 378, + 452, + 545, + 475 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 378, + 452, + 545, + 475 + ], + "spans": [ + { + "bbox": [ + 378, + 452, + 545, + 475 + ], + "type": "interline_equation", + "content": "\\hat {M} = \\frac {1}{T} \\sum_ {j = 1} ^ {T H W} \\hat {M} _ {j}. \\tag {4}", + "image_path": "287557de7ae94cef1f98eabc338f5852eb2cf4c1f025d65f7c07ea7ad62c6d9d.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 479, + 545, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 479, + 545, + 694 + ], + "spans": [ + { + "bbox": [ + 304, + 479, + 545, + 694 + ], + "type": "text", + "content": "Intuitively, this formulation encourages the model to learn to identify the salient regions with sounding objects for audio separation. We obtain the predicted mask for each frame by computing the sum of the predicted masks over all spatial regions and average the predicted masks over the temporal dimension since we reason that a sounding object should have similar prediction masks across frames. We adopt the self-supervised 'mix-and-separate' learning objective [14, 41] to train our model for predicting spectrogram masks. In this formulation, audio from two or more videos are mixed and the goal is to use the visual information of a video to separate its audio component. This setting allows us to generate pseudo-target masks for training supervision. We compute " + }, + { + "bbox": [ + 304, + 479, + 545, + 694 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{mask}" + }, + { + "bbox": [ + 304, + 479, + 545, + 694 + ], + "type": "text", + "content": " as the L1 loss between the pseudo-target and predicted ratio masks [41]. Please refer to the supplemental for details of our spatiotemporal region representation, audio-visual separation model and " + }, + { + "bbox": [ + 304, + 479, + 545, + 694 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{mask}" + }, + { + "bbox": [ + 304, + 479, + 545, + 694 + ], + "type": "text", + "content": ". The final objective function is computed as:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 330, + 701, + 545, + 714 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 330, + 701, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 330, + 701, + 545, + 714 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\lambda_ {1} \\mathcal {L} _ {\\text {m a s k}} + \\lambda_ {2} \\mathcal {L} _ {\\text {T r i m o d a l}} + \\lambda_ {3} \\mathcal {L} _ {\\text {A u s i o - l a n g u a g e}} \\tag {5}", + "image_path": "3d18f4f78da86e21bce0c9cb8247713f023b4920418258715c4b5c37ebec331d.jpg" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 733, + 317, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 733, + 317, + 742 + ], + "spans": [ + { + "bbox": [ + 294, + 733, + 317, + 742 + ], + "type": "text", + "content": "10579" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 67, + 70, + 526, + 170 + ], + "blocks": [ + { + "bbox": [ + 67, + 70, + 526, + 170 + ], + "lines": [ + { + "bbox": [ + 67, + 70, + 526, + 170 + ], + "spans": [ + { + "bbox": [ + 67, + 70, + 526, + 170 + ], + "type": "table", + "html": "
MethodObject detectors# Region proposalsSolosDuets
NSDR ↑SIR ↑SAR ↑NSDR ↑SIR ↑SAR ↑
Co-Separation [14]Yes27.3813.7010.827.4213.8110.60
AVSGS [5]Yes429.0414.4512.2410.2515.6012.82
Sound-of-Pixels [41]NoNone7.3011.9011.906.059.8110.61
AV-Mix-and-Separate [14]NoNone3.166.748.893.237.019.14
NMF-MFCC [34]NoNone0.925.686.840.925.686.84
VAST (Ours)NoNone7.9813.9212.358.0813.9711.33
", + "image_path": "b07fe8755e91e8684aa2fdcdc41158bd3112776bbed4ccfff296ca70c72514ff.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 178, + 547, + 201 + ], + "lines": [ + { + "bbox": [ + 46, + 178, + 547, + 201 + ], + "spans": [ + { + "bbox": [ + 46, + 178, + 547, + 201 + ], + "type": "text", + "content": "Table 1. Audio-visual source separation on MUSIC. We report results on videos that contain one instrument (solos) and two instruments (duets). Despite not training with object bounding boxes, VAST performs competitively with state-of-the-art detection-based approaches." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 211, + 288, + 236 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 211, + 288, + 236 + ], + "spans": [ + { + "bbox": [ + 46, + 211, + 288, + 236 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 211, + 288, + 236 + ], + "type": "inline_equation", + "content": "\\lambda_{1},\\lambda_{2}" + }, + { + "bbox": [ + 46, + 211, + 288, + 236 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 211, + 288, + 236 + ], + "type": "inline_equation", + "content": "\\lambda_{3}" + }, + { + "bbox": [ + 46, + 211, + 288, + 236 + ], + "type": "text", + "content": " denote the weights for the mask, tri-modal and audio-language consistency losses, respectively." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 247, + 128, + 261 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 247, + 128, + 261 + ], + "spans": [ + { + "bbox": [ + 47, + 247, + 128, + 261 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 267, + 287, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 267, + 287, + 434 + ], + "spans": [ + { + "bbox": [ + 45, + 267, + 287, + 434 + ], + "type": "text", + "content": "We evaluate the effectiveness of our proposed VAST approach on audio-text and audio-visual source separation in videos. To perform fair comparison to prior work, we conduct experiments on the SOLOS [24], MUSIC [41] and AudioSet [15] datasets. We refer readers to the supplemental for additional implementation and dataset details. Given a language query containing a prompt template and an object, the goal of audio-text source separation is to extract its corresponding sound component from an audio input, which is often comprised of a mixture of sounds emitted by various objects. Similarly, in audio-visual source separation, a model has to leverage the visual information in the input video to extract its corresponding sound component and align it with the relevant video pixels." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 435, + 287, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 435, + 287, + 544 + ], + "spans": [ + { + "bbox": [ + 46, + 435, + 287, + 544 + ], + "type": "text", + "content": "Evaluation metrics. We adopt the Normalized Signal-to-Distortion Ratio (NSDR), Signal-to-Interference Ratio (SIR) and Signal-to-Artifact Ratio (SAR) [27, 30]. NSDR computes the difference between the SDR of the predicted and mixed audio with respect to the ground-truth waveforms, which measures the sound quality of the separated audios. SIR measures the amount of contamination from other audio sources in the predicted audio. Finally, SAR measures the amount of artifacts in the predicted audio." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 551, + 163, + 563 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 551, + 163, + 563 + ], + "spans": [ + { + "bbox": [ + 47, + 551, + 163, + 563 + ], + "type": "text", + "content": "4.1. Quantitative results" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 570, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 288, + 715 + ], + "type": "text", + "content": "We compare our approach to the following baselines. Similar to our approach, Sound of Pixels (SOP) [41] does not require object detectors but learns to perform video-level separation. We also implement the AV-Mix-and-separate baseline from [14] with the same audio-visual separation model as ours but is trained to perform video-level separation and without our alignment objectives. The off-the-shelf NMF-MFCC [34] baseline performs audio separation using non-negative matrix factorization (NMF) and Mel frequency cepstrum coefficients (MFCC). Next, we also compare to Co-Separation [14] that learns to perform audio separation at the object-level by relying on object de" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 211, + 545, + 247 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 211, + 545, + 247 + ], + "spans": [ + { + "bbox": [ + 304, + 211, + 545, + 247 + ], + "type": "text", + "content": "tectors. Last but not least, we include AVSGS [5] that also relies on a high number of object proposals to construct a spatiotemporal scene graph to reason about context." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 251, + 546, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 251, + 546, + 491 + ], + "spans": [ + { + "bbox": [ + 304, + 251, + 546, + 491 + ], + "type": "text", + "content": "Audio-visual source separation on MUSIC. We report the results of our evaluation under two settings in Table 1. In the first setting, each video contains only a single instrument while the 'duet' setting includes videos that contain two different instruments. To begin, our VAST approach outperforms SOP by a large margin despite not relying on object detectors too. As shown in Table 4, we show that this performance gain is not due to just replacing ImageNet-pretrained Resnet18 [18] visual representations with those of the CLIP model since it leads to a large drop in performance. We hypothesize that SOP does not learn a direct projection of the audio inputs used in source separation into the CLIP embedding space. In contrast, VAST facilitates a better adaptation of the learnt audio representations to the CLIP embedding. We also found it important to modify CLIP's self-attention (see supp.). We observe that VAST outperforms AV-Mix-and-Separate by significantly, particularly under the duet setting. This suggests that performing region-level audio separation provides more capacity for the model to reason about multiple sounding objects in videos." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 495, + 547, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 495, + 547, + 662 + ], + "spans": [ + { + "bbox": [ + 304, + 495, + 547, + 662 + ], + "type": "text", + "content": "More significantly, we observe that our approach outperforms the Co-Separation approach [14], which relies on object labels in the videos. Since Co-Separation uses a high confidence region proposal for each instrument to localize relevant regions, our improvements over it suggest that our latent captions are able to express multiple visual concepts that are present in the video. Last but not least, our approach is also comparable to AVSGS even without scene graph reasoning modules. The latter constructs a spatiotemporal visual scene graph over a large number of region proposals to reason about context between detected objects. We note that their audio-visual scene graph component can be combined with our VAST approach to possibly improve performance but is beyond the scope of this work." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "content": "Audio-visual source separation on SOLOS. While the videos in the SOLOS dataset generally have less background noise than those of the MUSIC dataset, we see in Table 2 that AV-Mix-and-Separate and NMF-MFCC are still" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 733, + 318, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 733, + 318, + 742 + ], + "spans": [ + { + "bbox": [ + 294, + 733, + 318, + 742 + ], + "type": "text", + "content": "10580" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 70, + 298, + 168 + ], + "blocks": [ + { + "bbox": [ + 48, + 70, + 298, + 168 + ], + "lines": [ + { + "bbox": [ + 48, + 70, + 298, + 168 + ], + "spans": [ + { + "bbox": [ + 48, + 70, + 298, + 168 + ], + "type": "table", + "html": "
MethodObject detectorsNSDR ↑SIR ↑SAR ↑
Co-Separation [14]Yes7.1112.0910.05
AVSGS [5]Yes9.2014.0512.17
Sound-of-Pixels [41]No6.2810.8410.13
AV-Mix-and-Sep [14]No2.945.818.33
NMF-MFCC [34]No0.684.755.12
VAST (Ours)No8.5814.1612.35
", + "image_path": "35d49d6cfd849bc2a9bac6d95e049952981b7751e289548d6419b92ba4bb363f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 48, + 220, + 297, + 319 + ], + "blocks": [ + { + "bbox": [ + 47, + 178, + 287, + 212 + ], + "lines": [ + { + "bbox": [ + 47, + 178, + 287, + 212 + ], + "spans": [ + { + "bbox": [ + 47, + 178, + 287, + 212 + ], + "type": "text", + "content": "Table 2. Audio-visual source separation results on the SOLOS dataset. Similar to the results in Table 1, we see that VAST significantly closes the gap with object detection-based approaches." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 220, + 297, + 319 + ], + "lines": [ + { + "bbox": [ + 48, + 220, + 297, + 319 + ], + "spans": [ + { + "bbox": [ + 48, + 220, + 297, + 319 + ], + "type": "table", + "html": "
MethodObject detectorsNSDR ↑SIR ↑SAR ↑
Co-Separation [14]Yes4.267.0713.00
AVSGS [5]Yes5.288.2713.04
Sound-of-Pixels [41]No1.663.5811.50
AV-Mix-and-Sep [14]No1.683.3012.20
NMF-MFCC [34]No0.254.195.78
VAST (Ours)No4.157.6213.20
", + "image_path": "8e510848a34918119dc421506fb8e881ca3eb74c2b29f51e4275aba7ec817cdd.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 48, + 376, + 291, + 429 + ], + "blocks": [ + { + "bbox": [ + 47, + 328, + 287, + 361 + ], + "lines": [ + { + "bbox": [ + 47, + 328, + 287, + 361 + ], + "spans": [ + { + "bbox": [ + 47, + 328, + 287, + 361 + ], + "type": "text", + "content": "Table 3. Audio-visual source separation results on AudioSet. VAST generalizes much better to the noisier AudioSet dataset than Sound-of-Pixels which also does not use object detections." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 376, + 291, + 429 + ], + "lines": [ + { + "bbox": [ + 48, + 376, + 291, + 429 + ], + "spans": [ + { + "bbox": [ + 48, + 376, + 291, + 429 + ], + "type": "table", + "html": "
ModelVisual encoderNSDR ↑SIR ↑SAR ↑
SOP [41]ImageNet6.2810.8410.13
SOP [41]CLIP4.428.368.21
OursCLIP8.5814.1612.35
", + "image_path": "b9353952369106a2dfcc0566d21fea7852b87c1f2efc763946a3f8fb757951a2.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 484, + 287, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 484, + 287, + 640 + ], + "spans": [ + { + "bbox": [ + 46, + 484, + 287, + 640 + ], + "type": "text", + "content": "unable to generalize to the cleaner audio signals. Similar to the reported performance on the MUSIC dataset, we also observe that VAST is comparable to the strongly supervised AVSGS approach on the SOLOS dataset. One possible reason behind the lower performance of AVSGS on videos with single instrument is that it is less critical to reason about context for videos with a single sounding object. Our better performance as compared to Co-Separation suggests that learning to perform audio separation at the coarse video region level under an MIL formulation can serve as an effective replacement for training object detectors. These results also indicate the great promise of latent captions in replacing ground-truth object annotations for supervision." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 642, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 287, + 714 + ], + "type": "text", + "content": "Audio-visual source separation on AudioSet. Finally, we report the results of our evaluation on the AudioSet dataset in Table 3. AudioSet has been documented by prior work [14] to be much noisier than the videos in the other two datasets, which explains the lower performance across all approaches. Unlike the SOP model, we observe that our" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 310, + 70, + 541, + 133 + ], + "blocks": [ + { + "bbox": [ + 47, + 436, + 287, + 471 + ], + "lines": [ + { + "bbox": [ + 47, + 436, + 287, + 471 + ], + "spans": [ + { + "bbox": [ + 47, + 436, + 287, + 471 + ], + "type": "text", + "content": "Table 4. Using CLIP visual features in SOP model on the SOLOS dataset. Using CLIP visual features naively in existing methods results in a drop in performance." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 310, + 70, + 541, + 133 + ], + "lines": [ + { + "bbox": [ + 310, + 70, + 541, + 133 + ], + "spans": [ + { + "bbox": [ + 310, + 70, + 541, + 133 + ], + "type": "table", + "html": "
LAudio-languageLTrimodalNSDR ↑SIR ↑SAR ↑
XX5.4710.5510.95
✓X8.0813.7412.18
X✓8.1013.8411.79
✓✓8.5814.1612.35
", + "image_path": "9209bdad0c7491341a26c55dc7a38de778b416bd98b5d79da36af4a9808064c3.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 342, + 186, + 509, + 249 + ], + "blocks": [ + { + "bbox": [ + 304, + 141, + 545, + 175 + ], + "lines": [ + { + "bbox": [ + 304, + 141, + 545, + 175 + ], + "spans": [ + { + "bbox": [ + 304, + 141, + 545, + 175 + ], + "type": "text", + "content": "Table 5. Ablation of our audio-language and tri-modal consistency alignment objectives on SOLOs. The alignment objectives help to improve audio-visual separation performance." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 342, + 186, + 509, + 249 + ], + "lines": [ + { + "bbox": [ + 342, + 186, + 509, + 249 + ], + "spans": [ + { + "bbox": [ + 342, + 186, + 509, + 249 + ], + "type": "table", + "html": "
# tokensNSDR ↑SIR ↑SAR ↑
17.3111.3411.71
27.6713.0711.45
38.5814.1612.35
48.0213.3911.53
", + "image_path": "3f36a5a8b69779738732e1e5212e64ffc2a4ac00d7e8dc9ef1bed997c7974d98.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 258, + 545, + 281 + ], + "lines": [ + { + "bbox": [ + 304, + 258, + 545, + 281 + ], + "spans": [ + { + "bbox": [ + 304, + 258, + 545, + 281 + ], + "type": "text", + "content": "Table 6. Ablation over number of learnable tokens on SOLOS. Using more learnable tokens generally improves performance." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 288, + 545, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 288, + 545, + 312 + ], + "spans": [ + { + "bbox": [ + 304, + 288, + 545, + 312 + ], + "type": "text", + "content": "training approach is more robust to noise in the dataset where the sounding object may not always be visible." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 319, + 405, + 331 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 319, + 405, + 331 + ], + "spans": [ + { + "bbox": [ + 306, + 319, + 405, + 331 + ], + "type": "text", + "content": "4.1.1 Model Analysis" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 338, + 545, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 338, + 545, + 506 + ], + "spans": [ + { + "bbox": [ + 304, + 338, + 545, + 506 + ], + "type": "text", + "content": "Ablation of " + }, + { + "bbox": [ + 304, + 338, + 545, + 506 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{Trimodal}}" + }, + { + "bbox": [ + 304, + 338, + 545, + 506 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 338, + 545, + 506 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{Audio - language}}" + }, + { + "bbox": [ + 304, + 338, + 545, + 506 + ], + "type": "text", + "content": ". Table 5 provides an ablation over our audio-language and tri-modal consistency losses. Despite being trained on a larger and more diverse set of visual concepts, we find the CLIP visual representations alone do not encourage the audio encoder to learn a strong alignment between the audio and vision modalities (row 1). We observe the importance of our proposed alignment objectives where adding one or the other leads to a significant improvement in audio separation performance. Due to multiple training videos containing similar instruments, it is likely that we are treating some latent captions as false negative samples for each video in the audio-language consistency objective. However, we see that the consistency objective is still beneficial towards audio separation." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 506, + 545, + 638 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 506, + 545, + 638 + ], + "spans": [ + { + "bbox": [ + 304, + 506, + 545, + 638 + ], + "type": "text", + "content": "Number of learnable token embeddings in latent captions. We report the results of our ablation over the number of learnable token parameters used in the extraction of latent captions in Table 6. We observe that increasing the number of learnable tokens generally helps to improve the performance, although using 4 tokens hurts performance slightly. We hypothesize that a higher number of learnable tokens provide more capacity for the CLIP language model to express multiple visual concepts that are present in the videos. This finding suggests that using more tokens may be beneficial for videos with more complex visual scenes." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 647, + 487, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 647, + 487, + 659 + ], + "spans": [ + { + "bbox": [ + 306, + 647, + 487, + 659 + ], + "type": "text", + "content": "4.2. Audio-language source separation" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 665, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 715 + ], + "type": "text", + "content": "Finally, we evaluate the capability of our trained model to separate audio components based on natural language queries in Table 7. We construct each query using the template 'person playing a {instrument}''. We stress that we" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 734, + 317, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 734, + 317, + 742 + ], + "spans": [ + { + "bbox": [ + 294, + 734, + 317, + 742 + ], + "type": "text", + "content": "10581" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 70, + 547, + 122 + ], + "blocks": [ + { + "bbox": [ + 48, + 70, + 547, + 122 + ], + "lines": [ + { + "bbox": [ + 48, + 70, + 547, + 122 + ], + "spans": [ + { + "bbox": [ + 48, + 70, + 547, + 122 + ], + "type": "table", + "html": "
Query ModalityAlignment objectivesSOLOSMUSICAudioset
NSDR ↑SIR ↑SAR ↑NSDR ↑SIR ↑SAR ↑NSDR ↑SIR ↑SAR ↑
LanguageNo-3.052.793.77-3.672.513.41-5.021.9814.94
LanguageYes6.9212.0710.416.4511.1810.772.364.7110.28
", + "image_path": "9789259e90894b46a5bcb610ead0d6dac3c82ccc78dcd0ef869ded6a76456c84.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 129, + 547, + 163 + ], + "lines": [ + { + "bbox": [ + 46, + 129, + 547, + 163 + ], + "spans": [ + { + "bbox": [ + 46, + 129, + 547, + 163 + ], + "type": "text", + "content": "Table 7. Audio-text separation with natural language queries. We evaluate our model, that is trained only on unlabeled videos, on the task of audio-text separation. Note that we do not compare to other audio-visual separation baselines since there is no straightforward way to adapt them for language queries. We compare our full VAST model to a variant that is only trained with the mask prediction loss." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 174, + 289, + 317 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 174, + 289, + 317 + ], + "spans": [ + { + "bbox": [ + 46, + 174, + 289, + 317 + ], + "type": "text", + "content": "only train on unlabeled videos without text supervision. To begin, we compare our VAST model to a variant that is trained without our alignment objectives. Note that we do not compare to other audio-visual approaches since there is no straightforward way to adapt them for language queries. As evidenced by the significant performance gap between both variants, our alignment losses are integral to learning a strong transitive alignment between the audio and language modalities. This finding suggests that just learning an alignment between the audio and visual modalities does not result in a transitive relationship between the audio and natural language modalities." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 318, + 289, + 473 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 318, + 289, + 473 + ], + "spans": [ + { + "bbox": [ + 46, + 318, + 289, + 473 + ], + "type": "text", + "content": "Additionally, for effective sound source separation given either video or text inputs, we hypothesize that it is critical to learn an audio encoder E that is well-aligned with CLIP's vision-language embedding. Note that the same shared audio encoder " + }, + { + "bbox": [ + 46, + 318, + 289, + 473 + ], + "type": "inline_equation", + "content": "\\mathcal{E}" + }, + { + "bbox": [ + 46, + 318, + 289, + 473 + ], + "type": "text", + "content": " encodes both mixed and predicted audio sources. Thus, it can also be used as a general audio encoder and the decoder " + }, + { + "bbox": [ + 46, + 318, + 289, + 473 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 46, + 318, + 289, + 473 + ], + "type": "text", + "content": " can condition its separation process on either language or video queries. Lastly, we observe that our alignment objectives are still insufficient for closing the performance gap between audio-text and audio-visual separation (Tables 1, 2 and 3) completely. This observation indicates that future work is needed for further improving the latent alignment between all three modalities." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 479, + 156, + 491 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 479, + 156, + 491 + ], + "spans": [ + { + "bbox": [ + 47, + 479, + 156, + 491 + ], + "type": "text", + "content": "4.3. Qualitative results" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 498, + 287, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 287, + 594 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 287, + 594 + ], + "type": "text", + "content": "Predicted audio-to-video attention visualizations. To evaluate the semantic consistency between the predicted audio sources and the visual cues that guide the separation process, we plot the attention map between the encoded predicted spectrograms and their corresponding video frames (Section 3.1) in Figure 5. We observe that VAST helps the model to learn to ground the audio source in the video pixels despite not requiring bounding box supervision." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": "Predicted outputs of language-based audio separation. Finally, we present an example of how different language queries affect the separation performance for the same audio input in Figure 6. Significantly, despite not relying on text annotations for training supervision, our model can separate audio components based on free-form language queries. This demonstrates the effectiveness of our proposed idea to substitute ground-truth text annotations with latent captions during training. Additionally, we also observe that providing more context in the language query (e.g., \"violin\" versus" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 309, + 173, + 556, + 261 + ], + "blocks": [ + { + "bbox": [ + 309, + 173, + 556, + 261 + ], + "lines": [ + { + "bbox": [ + 309, + 173, + 556, + 261 + ], + "spans": [ + { + "bbox": [ + 309, + 173, + 556, + 261 + ], + "type": "image", + "image_path": "09abd40468bc959b6f7293d65f16ac6cadb7f4e2b8b9301e7fea933a46683ac3.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 267, + 547, + 300 + ], + "lines": [ + { + "bbox": [ + 305, + 267, + 547, + 300 + ], + "spans": [ + { + "bbox": [ + 305, + 267, + 547, + 300 + ], + "type": "text", + "content": "Figure 5. Predicted audio attention in videos. Our consistency objectives help the model to localize the relevant regions more accurately without prior knowledge of sounding object locations." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 308, + 303, + 556, + 479 + ], + "blocks": [ + { + "bbox": [ + 308, + 303, + 556, + 479 + ], + "lines": [ + { + "bbox": [ + 308, + 303, + 556, + 479 + ], + "spans": [ + { + "bbox": [ + 308, + 303, + 556, + 479 + ], + "type": "image", + "image_path": "d28ed4712836791b135c5de9dfe4c08bf0ba2ce58b539832fd5bf6860d638fbb.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 480, + 547, + 513 + ], + "lines": [ + { + "bbox": [ + 305, + 480, + 547, + 513 + ], + "spans": [ + { + "bbox": [ + 305, + 480, + 547, + 513 + ], + "type": "text", + "content": "Figure 6. Predicted audio spectrograms with language queries. Interestingly, we see that including visually grounded adjectives in the queries affects the quality of the separated audio sources." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 520, + 545, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 520, + 545, + 532 + ], + "spans": [ + { + "bbox": [ + 306, + 520, + 545, + 532 + ], + "type": "text", + "content": "\"person playing a violin\") can lead to improved separations." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 537, + 378, + 550 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 537, + 378, + 550 + ], + "spans": [ + { + "bbox": [ + 306, + 537, + 378, + 550 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 558, + 545, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 545, + 677 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 545, + 677 + ], + "type": "text", + "content": "In summary, we introduce a self-supervised approach for learning to separate audio based on a language query, or a video. In the absence of object labels, we propose to extract latent captions to provide pseudo-language supervision. Furthermore, we introduce the novel tri-modal and audio-language alignment objectives that use the latent captions to improve the alignment of the audio, language and video modalities. By reducing the training need for object labels, our work opens up the possibility of large-scale pretraining on unlabeled videos with diverse visual concepts." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "content": "Acknowledgements: This material is based upon work supported, in part, by DARPA under agreement number HR00112020054 and a gift from Adobe Research." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 734, + 317, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 734, + 317, + 742 + ], + "spans": [ + { + "bbox": [ + 294, + 734, + 317, + 742 + ], + "type": "text", + "content": "10582" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 712 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "text", + "content": "[1] Hassan Akbari, Liangzhe Yuan, Rui Qian, Wei-Hong Chuang, Shih-Fu Chang, Yin Cui, and Boqing Gong. 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A key challenge of this problem setting is that existing music video datasets provide the needed (video, music) training pairs, but lack text descriptions of the music. This work addresses this challenge with the following three contributions. First, we propose a text-synthesis approach that relies on an analogy-based prompting procedure to generate natural language music descriptions from a large-scale language model (BLOOM-176B) given pre-trained music tagger outputs and a small number of human text descriptions. Second, we use these synthesized music descriptions to train a new trimodal model, which fuses text and video input representations to query music samples. For training, we introduce a text dropout regularization mechanism which we show is critical to model performance. Our model design allows for the retrieved music audio to agree with the two input modalities by matching visual style depicted in the video and musical genre, mood, or instrumentation described in the natural language query. Third, to evaluate our approach, we collect a testing dataset for our problem by annotating a subset of 4k clips from the YT8M-MusicVideo dataset with natural language music descriptions which we make publicly available. We show that our approach can match or exceed the performance of prior methods on video-to-music retrieval while significantly improving retrieval accuracy when using text guidance.", + "bbox": [ + 75, + 340, + 473, + 763 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 791, + 207, + 806 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "A key part of the video editing process for creators is choosing a musical soundtrack. Especially given the rise of short-form videos on social media platforms, automated music recommendation systems have become an increas", + "bbox": [ + 75, + 816, + 468, + 878 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/b410e7da8c50994ec6d0dd92b0fbab8aef819159ddc2843c499124260ceaa06e.jpg", + "image_caption": [ + "Language-Guided Music Retrieval", + "Figure 1. Language-guided music retrieval. Our ViML model takes a video and text prompt as input to retrieve a suitable music track from a database. The model learns to fuse video and language representations in order to guide retrieval. Notice how our approach retrieves audio matching both the video and language content. For the same video query (top two rows), we can change the music style to match the language query, and for the same Upbeat pop query (bottom two rows) we can change the vocalist to match the video content. To fully appreciate our results, please view and listen to the companion video on our website." + ], + "image_footnote": [], + "bbox": [ + 508, + 332, + 879, + 601 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ingly common and important part of video editing applications. While these systems can be helpful for finding relevant music, they often provide limited capability for user control over the types of music recommended. In previous work, music is retrieved based solely on the visual content and style from a video [32, 37]. However, music itself can convey critical information about how a video should", + "bbox": [ + 496, + 794, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Work done as an intern with Adobe Research", + "bbox": [ + 94, + 886, + 341, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "14784", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "be perceived. Music selection alone can transform a visual scene into one that is perceived as happy, scary, or sad1. As a result, the lack of user input capability to describe a target music for an inputted video is a key limitation on the utility of current music recommendation methods.", + "bbox": [ + 75, + 90, + 468, + 165 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, we propose a more flexible music-for-video recommendation approach that allows a user to guide recommendations towards specific musical attributes including mood, genre, or instrumentation, illustrated in Figure 1. To maximize flexibility and user convenience, we propose to take user musical attribute descriptions in the form of free-form natural language (e.g., \"Folk music with guitar\" in Figure 1). There are two key challenges in learning a model for language-guided music recommendation for video. First, while there are datasets which include music+text [5,7,19,30] or music+video [1], there are no available datasets which include music, video, and text together. Further, the existing datasets that do include text and music focus on a limited vocabulary of tags rather than free-form text. Second, previous works have explored jointly learning visual, audio, and text embeddings [2-4, 34, 47], and without careful regularization, a network can overfit and possibly learn to ignore one of the input modalities. We seek to train a model that keeps the information flow through the network and does not ignore one of the modalities.", + "bbox": [ + 73, + 167, + 470, + 467 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In order to meet the challenges outlined above, our work makes the following contributions:", + "bbox": [ + 76, + 469, + 468, + 498 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "(1) We propose a new approach to automatically generate natural language descriptions for a music video dataset. This approach combines a pre-trained music tagger with a large-scale language model to output natural language descriptions for any music clip, illustrated in Figure 2 (left). First, the tagger predicts tags from a pre-defined vocabulary describing musical genre, mood, or instrumentation. Second, these predicted tags, together with their probabilities, are converted into a rich natural language description for the music video using a carefully designed large-scale language model prompting procedure based on analogies with a small number of human-provided text descriptions (i.e., $A$ (tags): $A'$ (description)): $B$ (tags): $B'$ (description)), where $A$ and $B$ are music tags automatically provided by the tagger, $A'$ is a human-provided text description, and $B'$ is the natural language description output by the large-scale language model.", + "bbox": [ + 75, + 500, + 468, + 755 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "(2) We propose a Transformer-based model architecture with a video-text fusion module. Our model, which we call Video to Music with Language (ViML), is able to retrieve music that matches both the visual content/style of the input video and described musical genre, mood, and instrumentation in the natural language query. Similar to prior work [16, 28, 39], we find that training with text dropout as a regularization mechanism is critical to achieve music re", + "bbox": [ + 75, + 756, + 468, + 876 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "trieval performance improvements from added text inputs.", + "bbox": [ + 500, + 90, + 883, + 106 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "(3) We release a dataset of 4000 high quality text annotations for clips from a subset of the YT8M-MusicVideo dataset [1] to evaluate language-guided music recommendation. We show that our method can achieve substantial improvements over prior works on music retrieval when incorporating text inputs. Moreover, our model can match or even exceed performance of baseline music-for-video recommendation models when the text input is ignored.", + "bbox": [ + 496, + 107, + 890, + 229 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 246, + 640, + 262 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Music and language. There are numerous music tagging datasets which contain tags specifying attributes like mood, genre, or instrumentation [5, 7, 19, 30], and several works have studied training automated music taggers from such datasets [10, 20, 22, 31, 43, 44]. Beyond these methods constrained to limited tag vocabularies, some works also have studied jointly embedding music and free-form natural language [9, 14, 27, 44]. However, none of these approaches incorporate the video modality.", + "bbox": [ + 496, + 273, + 890, + 409 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Music recommendation for video. Others have investigated automatic recommendation of music based on style and content of an input video [13, 24, 32, 37, 49]. Prétet et al. [32] build on previous self-supervised methods [13] by incorporating learned audio features instead of handcrafted features. More recently, Surís et al. [37] propose the MVPt model which employs a self-supervised contrastive loss and Transformer [38] architecture to greatly improve the long-range temporal context modeling in order to retrieve suitable music for a given input video. However, none of these approaches incorporate the natural language modality which we focus on in this work.", + "bbox": [ + 496, + 417, + 890, + 598 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Video, audio, & language. While a wide variety of works have explored audio-visual or vision-language topics, a smaller number focus on jointly embedding video, audio, and language [2, 4, 12, 34, 45, 47]. Specifically, Alayrac et al. [3] investigate how best to combine audio and video with text representations. The VATT model [2] is a fully end-to-end tri-modal model capable of using a single shared Transformer backbone across modalities. Lastly, two recent methods [12, 45] extend CLIP [33] to jointly embed audio. While relevant, all of these approaches share a common focus on \"environmental\" or \"everyday\" sounds rather than music, and they lack the long-range temporal context modeling critical for music recommendation as a result. In addition, none of these works address a downstream problem of using two modalities in combination (video, text) to query results from another (music).", + "bbox": [ + 496, + 604, + 890, + 847 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Few-shot language model prompting. Recent large language models have shown significant success at a wide variety of few-shot or zero-shot tasks from those related to read-", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_footnote", + "text": "1https://www.youtube.com/watch?v=iSkJFs7myn0", + "bbox": [ + 94, + 886, + 441, + 898 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "14785", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/3b6e4248c61330880dab9607fb42b4681137d6ab3322bd02f33d4ed07f6f4805.jpg", + "image_caption": [ + "I. prompt2text Synthesis" + ], + "image_footnote": [], + "bbox": [ + 76, + 111, + 459, + 371 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/ba3a248b43d1b98e3b4d60d399e1c311a7be63e0523093139b5a0c8d59846429.jpg", + "image_caption": [ + "II. data2text Synthesis", + "Figure 2. Overview of three text synthesis approaches explored in our work. All rely on tag predictions from a pretrained music tagger model. We highlight output text from each method in green, inputs from the tagger in blue font, and inputs from a human annotator in red font. Left: We introduce the prompt2tags approach for generating natural language descriptions given automatically predicted music tags and a small set of human descriptions. We ask a large language model (BLOOM-176B) to complete an analogy task ( $A:A^{\\prime}::B:B^{\\prime}$ ) between music tags ( $A,B$ ) and descriptions ( $A^{\\prime},B^{\\prime}$ ). Top right: The data2text pipeline inserts sampled tags into randomly selected template sentences corresponding to each tag category. The Zero-shot D2T model [17] then orders, aggregates, and compresses these templates into a final output description. Bottom right: The tags approach involves direct concatenation of high confidence tags to form the text description of the music." + ], + "image_footnote": [], + "bbox": [ + 472, + 111, + 890, + 369 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "ing comprehension and QA [8,41], to reasoning [18,42], or even data augmentation [11,40,46]. A few works have extended this success to multimodal applications. For example, Zeng et al. [48] show that language models can solve video understanding or image captioning tasks by reformulating these problems as reading comprehension or QA tasks with inputs from large visual or audio models. Other works have used language models to help with generating or retrieving text annotations for multimodal tasks [25] or in robotic planning [15,35]. In this work, we propose a completely new application of few-shot language query modeling: generating free-form musical text descriptions from music tags.", + "bbox": [ + 75, + 531, + 472, + 728 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Approach", + "text_level": 1, + "bbox": [ + 76, + 739, + 187, + 757 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our goal is to train a pair of feature encoders $f^{vt}$ and $f^m$ which are capable of predicting the similarity $s(f^{vt},f^{m})$ between an input pair of video and musical text description $(v,t)$ and a music clip $m$ , as illustrated in Figure 3. To train such a model in a supervised manner, it is necessary to have a dataset of corresponding triplets $(v,m,t)$ . While large-scale datasets of videos with paired music are available, it is difficult to find datasets which also contain high-quality natural language descriptions of the paired music tracks. As a", + "bbox": [ + 75, + 763, + 470, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "result, we investigate a synthesis approach based on a model $G$ which generates text descriptions from available structured data in the form of music tags for each music track. In the following sections, we first discuss the musical description synthesis approach $G$ before describing an approach to train a language-guided video-to-music recommendation model.", + "bbox": [ + 496, + 531, + 893, + 637 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Synthesizing Text Descriptions for Music", + "text_level": 1, + "bbox": [ + 498, + 648, + 851, + 666 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Suppose that we are given a set of video and music audio pairs $(v_{i},m_{i})$ and that we also have access to structured data $d_{i}\\in \\mathcal{T}^{D}$ which describe the music $m_{i}$ . In our case, this structured data consists of musical tags with confidence. Each music track $m_{i}$ may be described by a free-form human text description $t_i\\in \\mathcal{T}^T$ . However, it can be prohibitively expensive to obtain high-quality human descriptions on a large scale. Instead, we propose to synthesize such text descriptions using a generator $G:\\mathcal{T}^D\\to \\mathcal{T}^T$ which maps structured data describing an audio track to the space of natural human descriptions.", + "bbox": [ + 496, + 672, + 890, + 839 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The goals of such a mapping function $G$ are that: (i) a predicted output $\\tilde{t}_i = G(d_i)$ should preserve the semantic meaning contained within the structured data $d_i$ corresponding to a specific musical track and (ii) the distribu", + "bbox": [ + 496, + 839, + 893, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "14786", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "tion of predicted outputs $\\tilde{t}_i$ should follow the distribution of ground truth human text annotations $t_i\\in \\mathcal{T}^T$ . Training a fully supervised model to be the generator function $G$ would require a large quantity of human text descriptions. Instead, we explore zero-shot or few-shot approaches to obtain a generator function $G$ . In particular, we describe three approaches that all use the automatically predicted music tags: a prompt2text approach which relies entirely on careful few-shot prompting of a pretrained language model, a zero-shot data2text approach which rephrases tem-. plated sentences using pretrained language models, and a zero-shot tags baseline that represents the music track description directly via the set of automatically obtained tags. Details are given next.", + "bbox": [ + 75, + 90, + 472, + 303 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "I. Few-shot prompt2text approach. We first explore whether the full mapping function $G$ can be encompassed by a single large language model through careful few-shot prompting. This approach relies on a small set of example human-provided descriptions $t_0, \\dots, t_N$ where $t_i \\sim \\mathcal{T}^T$ . We assume that for each example $t_i$ , we also have a paired structured data output $d_i$ , provided by the automatic music tagger, which describes the same audio track. Unlike prior prompt-based data augmentation works [11, 40, 46] which aim for an unconditional generator $G$ , we aim to generate text data $\\tilde{t}_i \\sim G(d_i)$ conditioned on structured data $d_i$ such that it follows the distribution of human sentences $\\tilde{t}_i \\in \\mathcal{T}^T$ .", + "bbox": [ + 75, + 311, + 472, + 493 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As shown in Figure 2 (left), the structured data output $d_{i}$ is converted to text form via a template, and a set of pairs $(d_0,t_0),\\dots,(d_k,t_k)$ are used to form $k$ input/output components in the prompt. The final segment of the prompt is the structured data $d_{i}$ corresponding to a new music track. Given $d_{i}$ , the model will attempt to output a description $t_i$ following the mapping $\\mathcal{T}^D\\to \\mathcal{T}^T$ suggested by the example inputs. For text generation in this setting, we use the BLOOM-176B [6] model which is trained on a highly diverse 1.5TB text corpus.", + "bbox": [ + 75, + 496, + 472, + 648 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given that the prompt2text allows for the greatest freedom in generation, the model can more easily generate a diverse set of text resembling the target distribution $\\mathcal{T}^T$ . The prompt2text approach is also very flexible as large language models like BLOOM can handle a variety of different structured data inputs such as both tags and their confidence predictions. However, the model may also be less likely to preserve semantic meaning from structured data.", + "bbox": [ + 75, + 648, + 472, + 772 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "II. Zero-shot data2text approach. The second setting that we propose involves a data-to-text generation process which is illustrated in Figure 2 (top right). At a high level, the goal of this method is to insert structured tag data into predefined template sentences and rephrase these template sentences using a language model while preserving original semantic meaning. We begin with the tags predicted for each music track and grouped into genre, mood, and in-", + "bbox": [ + 75, + 779, + 472, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "strument categories. We define a set of category-specific templates in the form of short sentences with placeholders for tags. We randomly sample a template sentence for each category, and fill the template with the high-confidence predicted tags for that category. To form these sentences into more natural free-form descriptions, we make use of pretrained large language models. Specifically, we follow the Zero-shot D2T approach [17], which consists of ordering, aggregation, and compression modules built on pretrained RoBERTa [26] and BART [23] language models. The pipeline components first set the order of the individual filled template sentences and assign which sentences should be combined into a single sentence. Next, the compression module uses a generative text model to rewrite the input sentences based on the ordering and aggregation specifications. The module aims to rephrase the information while preserving semantic meaning. Because this D2T pipeline makes use of models that are pre-trained on large, general text corpus, we find these modules to perform well at generating music descriptions in a zero-shot manner.", + "bbox": [ + 496, + 90, + 893, + 393 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "III. tags approach. The final setting we use involves a simple concatenation of predicted tags. We take the set of top filtered predicted tags for each music track (this set typically numbers around 10-15 tags total). We then randomly shuffle these tags to prevent model dependence on ordering and concatenate all of the tags into a comma-separated list of musical descriptions (e.g., \"synthesizer keyboard, electronic drumset, pop, dance, synth bass, electronic, happy, electric guitar, frantic, dynamic\"). While this approach strongly preserves the semantic meaning, it fails to generate text with diverse vocabulary and form which would well represent the human annotation distribution $\\mathcal{T}^T$ .", + "bbox": [ + 496, + 400, + 893, + 583 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Text Dropout for Music Retrieval Training", + "text_level": 1, + "bbox": [ + 498, + 595, + 864, + 613 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The objective here is to retrieve music track $m$ matching a query video $v$ and a natural language query $t$ describing the target music track. This is a challenging task as the model has to fuse together information from both the input video and the input language query to then find a semantically appropriate music track. Moreover, the difference in granularity between audio/video and text can significantly hinder training. We design a tri-modal approach, dubbed ViML, for this task and introduce text dropout to address the granularity issue. In a similar manner to the way dropout prevents overfitting by reducing co-adaptation between individual neurons [36], text dropout serves to avoid overfitting to the text inputs and prevent co-adaptations between the video and text encoders. The approach is illustrated in Figure 3 and details of model architecture, loss, and text dropout are given next.", + "bbox": [ + 496, + 619, + 893, + 864 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Model architecture. Our model is trained on a set of (video, music, text) pairings, $(v,m,t)$ , corresponding to a", + "bbox": [ + 498, + 869, + 893, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "14787", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/8fca2012f333f4998b41c9df6d947c1aeffe76c1f6f663331b5364daf9f3d0ea.jpg", + "image_caption": [ + "Figure 3. Our proposed ViML model embeds inputs from three modalities (video, text, and audio) into an embedding space. We extract base features using DeepSim [20] for music input and from CLIP [33] for video frames and text descriptions. These base features are inputted to Transformer encoders for each modality. The video and text features are combined with a fusion module to enable querying of music in a shared embedding space. Finally, we employ text dropout to address the difference in granularity between the three modalities. Since video is a more complex input modality, text dropout forces an improved video representation by preventing co-adaptation of the video and text representations." + ], + "image_footnote": [], + "bbox": [ + 84, + 88, + 475, + 239 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "music video clip $v$ , which has been labeled with a generated text description $t$ of its music track $m$ , as outlined in Section 3.1. We transform these inputs into base features $x^{v} = g^{v}(v)$ for visual video features, $x^{m} = g^{m}(m)$ for music features, and $x^{t} = g^{t}(t)$ for text features using pretrained large-scale encoders $g^{v}, g^{m}$ , and $g^{t}$ which are frozen during training.", + "bbox": [ + 75, + 441, + 468, + 547 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Each base feature representation $x$ is of dimension $n \\times d$ , where $n$ is the length of the temporal sequence of base features representing a video clip and $d$ is the dimension of the base feature. We note that while our model is capable of handling a sequence of temporal text descriptions similar to music or video, we obtain only a track-level text description in practice meaning that $n = 1$ for text.", + "bbox": [ + 75, + 547, + 468, + 654 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our tri-modal model consists of three separate modules corresponding to each modality $f^v, f^m, f^t$ , and a fourth fusion module $f^{vt}$ to combine video and text representations. The modules take respective base features and output embeddings $y^v = f^v(x^v)$ , $y^m = f^m(x^m)$ , $y^t = f^t(x^t)$ . The fusion model outputs a fused embedding from the video and text embeddings $y^{vt} = f^{vt}(y^v, y^t)$ .", + "bbox": [ + 75, + 654, + 468, + 760 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Fusion loss. For training, we use an InfoNCE loss [29] between music and fused video-text embeddings:", + "bbox": [ + 76, + 766, + 468, + 796 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {v t \\rightarrow m} = - \\frac {1}{| \\mathcal {D} |} \\sum_ {i \\in \\mathcal {D}} \\frac {\\exp \\left(s \\left(y _ {i} ^ {v t} , y _ {i} ^ {m}\\right) / \\tau\\right)}{\\sum_ {j \\in \\mathcal {D}} \\exp \\left(s \\left(y _ {i} ^ {v t} , y _ {j} ^ {m}\\right) / \\tau\\right)} \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 102, + 806, + 468, + 844 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $s$ is a similarity function, $\\mathcal{D}$ is a batch of data, and $\\tau$ is a temperature hyperparameter we set as $\\tau = 0.03$ . For our similarity metric, we use the cosine similarity defined as", + "bbox": [ + 76, + 854, + 470, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$s(x,y) = x^{T}y / (\\| x\\| \\cdot \\| y\\|)$ . We note that the loss $\\mathcal{L}_{vt\\to m}$ is not symmetric as negatives are sampled from music embeddings only. So that our loss is symmetric, we instead train with the summed loss $\\mathcal{L}_{m,vt} = \\mathcal{L}_{vt\\to m} + \\mathcal{L}_{m\\to vt}$ .", + "bbox": [ + 498, + 90, + 890, + 152 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Text dropout. To address difficulties posed by the difference in granularity between audio/video and text, we introduce text dropout as a regularization mechanism. With probability $p$ , we set the input text embedding $x^{t}$ to a specific value $x^{\\mathrm{NULL}}$ . In practice, we assign this $x^{\\mathrm{NULL}}$ input as the embedding produced by the pretrained $g^{t}$ model for an empty string. However, using a zero vector as $x^{\\mathrm{NULL}}$ works similarly. In addition to improving the performance of music retrieval from text and video together, training with text dropout yields a model which also performs well at retrieval from video alone by removing dependence on text inputs.", + "bbox": [ + 496, + 165, + 890, + 332 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Implementation Details", + "text_level": 1, + "bbox": [ + 500, + 364, + 718, + 380 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Music tag generation. The key first step to our text generation process is obtaining the structured data describing each musical track. To do this, we use a music tagger trained on a dataset of music tracks manually annotated with a fixed predefined vocabulary of tags [20, 21]. Specifically, the tagger predicts confidence for 41 instrument tags, 20 genre tags, and 28 mood tags. We aggregate these predictions at the clip or track level, and we filter the subsequent set based on confidence, keeping only those above a particular threshold (0.3 in our experiments).", + "bbox": [ + 496, + 395, + 890, + 546 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "ViML Model. Following MVPt [37], we employ the Transformer architecture [38] for our music and video encoders $f^{m}$ and $f^{v}$ . Transformers play a key role in improving model performance by encoding long-term context from video and music clips. We also use a similar two-layer Transformer architecture for our text encoder $f^{t}$ and the video-text fusion layer $f^{vt}$ . However, we find that other fusion module architectures such as a single linear layer yield similar results. Please see our supplemental for study of fusion module architectures.", + "bbox": [ + 496, + 560, + 890, + 710 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For base features, we use CLIP [33] to encode representations for video frames and text inputs, and DeepSim [20] to encode music. Following communication with the authors of [37], we split the video into 10-second segments and compute a feature for each segment by averaging CLIP embedding features computed at 6 frames per second. We compute 512 dimensional CLIP embedding features using OpenAI's CLIP ViT-B/32 model. We encode all input base features into embeddings of size $d = 256$ using a linear projection layer for each modality. We also select $d = 256$ as the output dimension for encoded video, text, music, and fused video-text representations from our model.", + "bbox": [ + 496, + 719, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "14788", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/26d34da65764ee63c650328268a9966d651ee8ffb33498e7dd84ba2e5e3e95f9.jpg", + "image_caption": [ + "A faint, simple acoustic piece of singing by a female vocalist with an acoustic guitar with a fast-paced strumming pattern in a closed room recorded live. great for singing along." + ], + "image_footnote": [], + "bbox": [ + 86, + 89, + 235, + 150 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/a44e8944cdd14fd98ef12e71036428c04340efaaacd782a2e0c0939cedf4eb87.jpg", + "image_caption": [ + "Hip-hop track with a dark synth pad with male aggressive rapping along with a chipmunk voice." + ], + "image_footnote": [], + "bbox": [ + 250, + 90, + 398, + 150 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/90785c2cd564d647b1e9203f9e3b776c7923cdd50386a5385cae3531e8a0c6fb.jpg", + "image_caption": [ + "Instrumental track featuring an ambient pad and bell-like sounds. Seems to be a film score." + ], + "image_footnote": [], + "bbox": [ + 413, + 89, + 560, + 148 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/708cbc86d95aa369ecd3b5f8487ca12b1c8b721f113494d73d9c29dbf7a92e8d.jpg", + "image_caption": [ + "A cover version of Elvis Presley's pop song featuring male and female vocals and piano layers. Sounds like a confession in love." + ], + "image_footnote": [], + "bbox": [ + 575, + 89, + 723, + 148 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/39adebe7b99f06214b14ae190f04f74fd45a09ed4e29209785f8cf2317608765.jpg", + "image_caption": [ + "Punjabi track with multiple vocals and other instruments that's great for traditional marriage celebrations.", + "Figure 4. Example annotations from our collected YouTube8M-MusicTextClips dataset. Each example shows a frame from the 10sec source video clip from which audio was extracted for annotation. Note that annotators were only provided audio from the music video, so the annotation describes the music, but not the corresponding video. Each example in the figure contains a hyperlink to the corresponding YT8M source video with timestamp at the start of the 10sec target clip. Hover over the video frame image and click to follow the link." + ], + "image_footnote": [], + "bbox": [ + 735, + 90, + 885, + 150 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 329, + 209, + 345 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we report our experimental settings and results. First, we describe our datasets and the evaluation protocol in Sec. 4.1. Next, we investigate tag-based video-to-music retrieval, comparing against state-of-the-art video-to-music retrieval methods in Sec. 4.2. In Sec. 4.3, we evaluate performance of video-to-music retrieval guided by free-form text annotations. Finally, we perform ablation studies to measure the influence of text dropout in Sec. 4.4.", + "bbox": [ + 75, + 356, + 468, + 477 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Datasets and Evaluation Protocol", + "text_level": 1, + "bbox": [ + 76, + 489, + 369, + 505 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "YT8M-MusicVideo. In all of our experiments, we train models using the YT8M-MusicVideo dataset which includes around 100k videos with the \"music video\" tag from the much larger YouTube8M dataset [1]. We synthesize tags and a natural language text describing the music track of each video for the full dataset using the approaches described in Sec. 3.1. We also use the test split of YT8M-MusicVideo to evaluate tag-based retrieval in Sec. 4.2.", + "bbox": [ + 75, + 515, + 468, + 636 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "YT8M-MusicTextClips. In addition to the full YT8M-MusicVideo dataset, we also annotate a 4,000 sample subset of clips from YT8M-MusicVideo with human-provided text descriptions of the music track accompanying each video. To create these annotations, we sample 10 second audio clips from the middle of each music video, and we ask human annotators to describe the music they hear after listening to the audio clip. Thus, an annotation describes only the music from a YT8M sample, and the annotators do not see the corresponding video. Example annotations are shown in Figure 4 with links to the starting timestamp of the 10sec clips in corresponding YouTube videos. This annotated set is meant mainly for evaluation. As a result, the annotations are split into a larger set of 3,000 samples from the test set of YT8M-MusicVideo and a smaller set of 1,000 samples from the train set of YT8M-MusicVideo which we use as examples in the few-shot prompt2text synthesis process. We", + "bbox": [ + 75, + 643, + 470, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "make the annotated text descriptions publicly available at our companion website2.", + "bbox": [ + 498, + 330, + 890, + 359 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation Set-up and Metrics. We evaluate music retrieval performance consistently with previous works [32, 37]. However, in our case, a query can be either a video alone or a video and corresponding text annotation together. For each query, we compute feature similarity between the query and a pool of N music tracks (we set $\\mathrm{N} = 2000$ in the track-level setting and $\\mathrm{N} = 500$ for evaluation on clips). The pool contains a single ground truth music track corresponding to the input query (the positive example) with the remaining music tracks in the pool being non-matching (i.e., negative examples). We rank the music tracks in a query's pool by feature similarity, and find the rank of the query's ground truth matching music track (the positive example). We then compute Recall@K (shortened to R@K) for $\\mathrm{K} = 1,5,10$ and Median Rank, calculating the average of each of these metrics across the full set of test queries.", + "bbox": [ + 496, + 367, + 892, + 609 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Tag-Based Retrieval", + "text_level": 1, + "bbox": [ + 500, + 617, + 691, + 633 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For our first set of experiments, we explore the setting of tag-based retrieval. Here the goal is to retrieve a music track given a query video together with a set of tags from a predefined vocabulary, such as \"happy\", \"piano\" and \"jazz\". This setting could be practically interesting in some applications, e.g., tag-based search. To address this setting, we train our model on text synthesized with the tags approach. In these experiments, we train a track-level model and perform retrieval on a track-level in a manner consistent with prior work [32, 37]. To directly compare results with prior work, we perform retrieval on the full YT8M test set consisting of around 10K samples. As shown in Table 1, we include three baselines: the model proposed by Pretét et al. [32], the MVPt model [37], and an improved version of MVPt that we call MVPt+, where we tune the temperature", + "bbox": [ + 496, + 640, + 893, + 867 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "2https://www.danielbmckee.com/language-guided-music-for-video/index.html", + "bbox": [ + 500, + 875, + 890, + 898 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "14789", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/1fd3809481d1a1722c55004f6590aecf19d6cf56ee8ead66f782fcd7c513d3b3.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodTrain TextQuery Text InputMedian Rank ↓R@1 ↑R@5 ↑R@10 ↑
a. Pretét et al. [32]--2340.763.425.90
b. MVPt [37]--136.0924.9141.89
c. MVPt+ [37]--527.9350.6460.68
d. ViML (ours)tags-329.4362.4975.40
e. ViML (ours)tagstags249.4981.6189.41
f. Chance10000.050.250.50
", + "bbox": [ + 140, + 88, + 831, + 218 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/08aa241214cbace9e509410f6c70d9032d4277089a5edd16bd5f96b6850cbebd.jpg", + "table_caption": [ + "Table 1. Tag-based music retrieval on full YouTube8M-MusicVideo test set. We compare ViML against prior methods on video to music retrieval without tag queries (row d.). We also evaluate ViML on video+text to music retrieval using (synthetic) tags at test time (row e.). The text descriptions for both training and evaluation are generated with the tags approach for these experiments." + ], + "table_footnote": [], + "table_body": "
MethodTrain TextMR ↓R@1 ↑R@5 ↑R@10 ↑
a. MVPt+-1712.2029.4340.46
b. ViMLtags1511.9530.3442.62
c. ViMLdata2text1313.6133.9446.24
d. ViMLprompt2text1214.0935.0447.88
Chance2500.201.002.00
", + "bbox": [ + 86, + 292, + 455, + 386 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2. Music retrieval with free-form natural language on YT8M-MusicTextClips test set. All methods which take text input are evaluated on the human text annotations as queries. Since the $\\mathrm{MVPt + }$ model does not take text inputs, it is evaluated on music retrieval from video alone for the same set of 3k video clips. MR is median rank.", + "bbox": [ + 75, + 396, + 470, + 479 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "parameter $\\tau$ in the InfoNCE loss to 0.03. This change leads to further significant improvement in performance.", + "bbox": [ + 75, + 507, + 468, + 537 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Next, we introduce our model (ViML) trained on data generated from the tags approach. We evaluate our ViML model in two settings. First, we evaluate without input texts at test time (an empty text input is used instead). Second, we evaluate with text inputs at test time. As we do not have track-level human-provided music tag annotations for the full YT8M MusicVideo split, we evaluate the track-level model on synthetically generated tags using our tags approach. While a model trained on the tags synthesized data may not generalize to out-of-domain free-form text inputs, the tag-based prompting can be a convenient way to guide music retrieval with key desired attributes (for example \"female vocalist, guitar, happy\"). The tag-based retrieval we report can serve as an upper bound for this type of user tag-guided retrieval since the tag-based text for testing comes from the same music tagger model we used to synthesize training data.", + "bbox": [ + 75, + 537, + 468, + 794 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Evaluating our model with synthetic tags leads to a very substantial performance increase over $\\mathrm{MVPt + }$ of 20-30 points in each recall metric. Interestingly, our ViML model evaluated without text at test time not only matches the video-to-music retrieval performance of $\\mathrm{MVT + }$ but substantially improves over $\\mathrm{MVPt + }$ , especially in Recall@5 and Recall@10. This performance increase is not simply", + "bbox": [ + 75, + 795, + 468, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "a result of added parameters in the fusion layer, as a fusion module consisting of only a single linear layer yields similar results (see our supplemental for further details). This result suggests that training jointly with the text domain can lead to improvements in the video and audio representations. We hypothesize that the joint training with language helps to disentangle the video-audio space into semantically meaningful dimensions corresponding to the provided tags as well as helps to suppress non-relevant dimensions, e.g., corresponding to presence/absence of some non-relevant objects.", + "bbox": [ + 496, + 296, + 893, + 464 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Free-Form Natural Language Retrieval", + "text_level": 1, + "bbox": [ + 498, + 469, + 841, + 486 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "For the next experiments, we turn to retrieval with free-form natural language inputs. The goal is, given an input video and a query free-form natural language description, to retrieve a relevant music track. For this setting, we evaluate on testing videos from the YT8M-MusicTextClips dataset which contains free-form human text annotations describing the music corresponding to each video in the dataset.", + "bbox": [ + 496, + 493, + 893, + 599 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In these experiments, we use a similar protocol to the \"segment-level\" setting reported by Surís et al. [37], but our input video includes only a 30sec clip surrounding the 10sec of audio labeled by a human annotator. In contrast, a model had access to a large context spanning the full source video in the previous segment-level setting reported by Surís et al. [37]. We note that retrieval in this setting is significantly more difficult than the segment-level setting in [37] or the track-level setting reported in 4.2 due to the limited context. However, such retrieval is of particular interest given the rise of short-form video in social media and entertainment.", + "bbox": [ + 496, + 599, + 893, + 763 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results are summarized in Table 2. Our baseline is an $\\mathrm{MVPt + }$ model which has been trained on 30sec segments (training $\\mathrm{MVPt + }$ on full videos and testing on 30sec clips causes a much more severe drop in performance). We next report music retrieval using video and free-form human text descriptions as input queries to our ViML model. In Table 2, we report three variants trained on YT8M music videos with text synthesized by each of the three approaches described in Sec. 3.1. The model trained with our first tags syn", + "bbox": [ + 496, + 765, + 893, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "14790", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/988d3d13ac6d255be374ff5603600f5b1066672ddda85cf30ea9122b12542c1f.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodTrain TextDropoutText InputsMedian Rank ↓R@1 ↑R@5 ↑R@10 ↑
a. MVPt+---1712.2029.4340.46
b. MVT-Fuseprompt2textX-209.9426.4237.01
c. MVT-Fuseprompt2textXhuman1511.4530.4542.77
d. MVT-Fuseprompt2text✓-1612.2730.3441.51
e. MVT-Fuseprompt2text✓human1214.0935.0447.88
", + "bbox": [ + 119, + 88, + 849, + 202 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 3. Influence of training with text dropout on retrieval performance. Evaluated on the YT8M-MusicTextClips test set.", + "bbox": [ + 107, + 212, + 859, + 226 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "thesis baseline (b.) provides substantial improvement over retrieval with MVPt+ using only video (a.). Next, we evaluate the data2text approach (c.) which generates more natural phrases while strictly preserving tag semantics. This approach provides a consistent improvement over the ViML tags variant (b.). Finally, our prompt2text approach (d.) leads to the best performance showing that large language models prove to be strong annotators on this task with careful few-shot prompting.", + "bbox": [ + 75, + 253, + 468, + 388 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Qualitative results. In Figure 5, we provide qualitative retrieval results for examples in YouTube8M-MusicTextClips. In the first example, both models retrieve tracks that match the style and beat of the input video well. However, only the ViML can match the correct musical style by using the input text. In the second example, only the ViML result correctly matches the desired music genre and the mood of the video.", + "bbox": [ + 75, + 388, + 468, + 508 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Analysis of Text Dropout", + "text_level": 1, + "bbox": [ + 76, + 520, + 303, + 536 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In Table 3, we compare the performance of our ViML model trained on prompt2text descriptions with and without text dropout. We evaluate this model on music retrieval in two settings: (i) using only video (inputting empty text, rows b. and d.) as a query and (ii) using both video and human text descriptions together as a query (rows c. and e.). As expected, adding text dropout during training (d.) improves the performance of retrieval using only video (b.). However, interestingly, text dropout also substantially improves performance when the query includes natural language (e. vs. c.), suggesting that text dropout is a very useful regularization technique in the multimodal setting. We find that without text dropout, training begins to plateau early as the model starts overfitting to the training text inputs. Since video is a much richer and more complex modality, forcing more attention to this modality during training improves learning. We find that the dropout technique is most effective at high rates of dropout in the range 0.8-0.95, and we use a dropout rate of 0.8 in all of our experiments.", + "bbox": [ + 75, + 542, + 468, + 830 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 76, + 844, + 194, + 859 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this work, we introduced an approach to allow language-guided music recommendation for video. We pro", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a42e9433edd4f88644cf28bd04206e9bdc09b63631896fc451fcdf26405c6ddf.jpg", + "image_caption": [ + "Video+Language Query" + ], + "image_footnote": [ + "Electronic dance pop track that has male vocals and a pulsating rhythm. Best for nightclubs." + ], + "bbox": [ + 527, + 294, + 637, + 343 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/be85c7822299996c12fffff5fdce48f650f520de0a97d303f9cd2fb9e452bf01.jpg", + "image_caption": [ + "Retrieved Music" + ], + "image_footnote": [ + "MVPt+" + ], + "bbox": [ + 676, + 297, + 718, + 319 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/261b27073dfa5642a1c3ede328d58644cdde152942df7c76ebfe1b203fd9d996.jpg", + "image_caption": [], + "image_footnote": [ + "ViML", + "Percussive Latin music with a male vocalist, synth line, and Cumbia beat aligned with video." + ], + "bbox": [ + 794, + 297, + 836, + 318 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/bcb8781ae7de8317048b3da2bc962b9945d7c9224bffcaba165ac220e6454d89.jpg", + "image_caption": [ + "Figure 5. Qualitative results on YouTube8M-MusicTextClips test set. We compare music retrieval quality for two examples using the $\\mathrm{MVPt + }$ model and our ViML model. The column on the left includes a frame from the input video and the input text description describing the target music. The $\\mathrm{MVPt + }$ model takes only the video as an input while the ViML model takes both video and corresponding text. The two columns on the right contain retrieved music for $\\mathrm{MVPt + }$ and ViML respectively. Please see results in the companion video on our website." + ], + "image_footnote": [ + "Male rap song in a foreign language with hip-hop beats and electronic music that gives a freestyle vibe to it." + ], + "bbox": [ + 524, + 400, + 633, + 449 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/af413976f812c87bdc2cd1103714c9b174da864d2f1191c3c20591c73fc31147.jpg", + "image_caption": [], + "image_footnote": [ + "Upbeat jazzy melody played on a saxophone over rhythmic electronic bass beats." + ], + "bbox": [ + 676, + 407, + 718, + 429 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/17736ab6a375ecbd561282ed5e457386c467a7dc539312db5babb89410490356.jpg", + "image_caption": [], + "image_footnote": [ + "Energetic electronic party song with male vocals over rising synth layers and claps aligned with video.", + "French rap song with processed male vocals, thumping drum beats, and synth pad effects." + ], + "bbox": [ + 794, + 407, + 836, + 429 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "posed a model, ViML, which fuses text and video inputs to find music matching both domains and introduced the text dropout technique to improve training. To obtain data for training, we proposed a free-form music description synthesis approach using a large language model (BLOOM-176B) and outputs from a pretrained music tagger. Our results show that large language models provide a powerful tool for training data synthesis in domains where text data is limited but other structured data is available. To evaluate our method, we also introduced a new dataset, YouTube8M-MusicTextClips, which includes high quality free-form human descriptions of the music in YT8M videos. There are many exciting directions to build upon this work including allowing more fine-grained control over specific music attributes or language-guided audio-video generation.", + "bbox": [ + 496, + 672, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "14791", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Sami Abu-El-Haija, Nisarg Kothari, Joonseok Lee, Paul Natsev, George Toderici, Balakrishnan Varadarajan, and Sudheendra Vijayanarasimhan. Youtube-8m: A large-scale video classification benchmark. arXiv preprint arXiv:1609.08675, 2016. 2, 6", + "[2] Hassan Akbari, Liangzhe Yuan, Rui Qian, Wei-Hong Chuang, Shih-Fu Chang, Yin Cui, and Boqing Gong. Vatt: Transformers for multimodal self-supervised learning from raw video, audio and text. 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IEEE, 2018. 2" + ], + "bbox": [ + 501, + 92, + 890, + 837 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "14793", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Language-Guided Music Recommendation for Video via Prompt Analogies/c0941191-f1a3-4b4b-84fc-4169036b56b1_model.json b/2023/Language-Guided Music Recommendation for Video via Prompt Analogies/c0941191-f1a3-4b4b-84fc-4169036b56b1_model.json new file mode 100644 index 0000000000000000000000000000000000000000..75b08e1df0e482c735667b584ed516afddd24af8 --- /dev/null +++ b/2023/Language-Guided Music Recommendation for Video via Prompt Analogies/c0941191-f1a3-4b4b-84fc-4169036b56b1_model.json @@ -0,0 +1,2167 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.108, + 0.131, + 0.865, + 0.155 + ], + "angle": 0, + "content": "Language-Guided Music Recommendation for Video via Prompt Analogies" + }, + { + "type": "text", + "bbox": [ + 0.189, + 0.18, + 0.324, + 0.198 + ], + "angle": 0, + "content": "Daniel McKee1*" + }, + { + "type": "text", + "bbox": [ + 0.349, + 0.181, + 0.479, + 0.198 + ], + "angle": 0, + "content": "Justin Salamon2" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.181, + 0.62, + 0.199 + ], + "angle": 0, + "content": "Josef Sivic2,3" + }, + { + "type": "text", + "bbox": [ + 0.654, + 0.182, + 0.775, + 0.199 + ], + "angle": 0, + "content": "Bryan Russell" + }, + { + "type": "text", + "bbox": [ + 0.23, + 0.203, + 0.826, + 0.239 + ], + "angle": 0, + "content": "1University of Illinois at Urbana-Champaign 2Adobe Research Institute of Informatics, Robotics and Cybernetics, Czech Technical University" + }, + { + "type": "text", + "bbox": [ + 0.102, + 0.242, + 0.291, + 0.256 + ], + "angle": 0, + "content": "dbmckee2@illinois.edu" + }, + { + "type": "text", + "bbox": [ + 0.319, + 0.242, + 0.471, + 0.255 + ], + "angle": 0, + "content": "salamon@adobe.com" + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.242, + 0.67, + 0.256 + ], + "angle": 0, + "content": "josef.sivic@cvut.cz" + }, + { + "type": "text", + "bbox": [ + 0.698, + 0.242, + 0.86, + 0.256 + ], + "angle": 0, + "content": "brussell@adobe.com" + }, + { + "type": "text", + "bbox": [ + 0.215, + 0.26, + 0.751, + 0.274 + ], + "angle": 0, + "content": "https://www.danielbmckee.com/language-guided-music-for-video" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.309, + 0.314, + 0.325 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.341, + 0.474, + 0.765 + ], + "angle": 0, + "content": "We propose a method to recommend music for an input video while allowing a user to guide music selection with free-form natural language. A key challenge of this problem setting is that existing music video datasets provide the needed (video, music) training pairs, but lack text descriptions of the music. This work addresses this challenge with the following three contributions. First, we propose a text-synthesis approach that relies on an analogy-based prompting procedure to generate natural language music descriptions from a large-scale language model (BLOOM-176B) given pre-trained music tagger outputs and a small number of human text descriptions. Second, we use these synthesized music descriptions to train a new trimodal model, which fuses text and video input representations to query music samples. For training, we introduce a text dropout regularization mechanism which we show is critical to model performance. Our model design allows for the retrieved music audio to agree with the two input modalities by matching visual style depicted in the video and musical genre, mood, or instrumentation described in the natural language query. Third, to evaluate our approach, we collect a testing dataset for our problem by annotating a subset of 4k clips from the YT8M-MusicVideo dataset with natural language music descriptions which we make publicly available. We show that our approach can match or exceed the performance of prior methods on video-to-music retrieval while significantly improving retrieval accuracy when using text guidance." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.792, + 0.208, + 0.807 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.818, + 0.47, + 0.879 + ], + "angle": 0, + "content": "A key part of the video editing process for creators is choosing a musical soundtrack. Especially given the rise of short-form videos on social media platforms, automated music recommendation systems have become an increas" + }, + { + "type": "image_caption", + "bbox": [ + 0.594, + 0.313, + 0.803, + 0.326 + ], + "angle": 0, + "content": "Language-Guided Music Retrieval" + }, + { + "type": "image", + "bbox": [ + 0.509, + 0.333, + 0.88, + 0.602 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.615, + 0.895, + 0.756 + ], + "angle": 0, + "content": "Figure 1. Language-guided music retrieval. Our ViML model takes a video and text prompt as input to retrieve a suitable music track from a database. The model learns to fuse video and language representations in order to guide retrieval. Notice how our approach retrieves audio matching both the video and language content. For the same video query (top two rows), we can change the music style to match the language query, and for the same Upbeat pop query (bottom two rows) we can change the vocalist to match the video content. To fully appreciate our results, please view and listen to the companion video on our website." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.895, + 0.903 + ], + "angle": 0, + "content": "ingly common and important part of video editing applications. While these systems can be helpful for finding relevant music, they often provide limited capability for user control over the types of music recommended. In previous work, music is retrieved based solely on the visual content and style from a video [32, 37]. However, music itself can convey critical information about how a video should" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.342, + 0.9 + ], + "angle": 0, + "content": "*Work done as an intern with Adobe Research" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "14784" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.166 + ], + "angle": 0, + "content": "be perceived. Music selection alone can transform a visual scene into one that is perceived as happy, scary, or sad1. As a result, the lack of user input capability to describe a target music for an inputted video is a key limitation on the utility of current music recommendation methods." + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.168, + 0.471, + 0.468 + ], + "angle": 0, + "content": "In this work, we propose a more flexible music-for-video recommendation approach that allows a user to guide recommendations towards specific musical attributes including mood, genre, or instrumentation, illustrated in Figure 1. To maximize flexibility and user convenience, we propose to take user musical attribute descriptions in the form of free-form natural language (e.g., \"Folk music with guitar\" in Figure 1). There are two key challenges in learning a model for language-guided music recommendation for video. First, while there are datasets which include music+text [5,7,19,30] or music+video [1], there are no available datasets which include music, video, and text together. Further, the existing datasets that do include text and music focus on a limited vocabulary of tags rather than free-form text. Second, previous works have explored jointly learning visual, audio, and text embeddings [2-4, 34, 47], and without careful regularization, a network can overfit and possibly learn to ignore one of the input modalities. We seek to train a model that keeps the information flow through the network and does not ignore one of the modalities." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.47, + 0.47, + 0.499 + ], + "angle": 0, + "content": "In order to meet the challenges outlined above, our work makes the following contributions:" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.5, + 0.47, + 0.756 + ], + "angle": 0, + "content": "(1) We propose a new approach to automatically generate natural language descriptions for a music video dataset. This approach combines a pre-trained music tagger with a large-scale language model to output natural language descriptions for any music clip, illustrated in Figure 2 (left). First, the tagger predicts tags from a pre-defined vocabulary describing musical genre, mood, or instrumentation. Second, these predicted tags, together with their probabilities, are converted into a rich natural language description for the music video using a carefully designed large-scale language model prompting procedure based on analogies with a small number of human-provided text descriptions (i.e., \\( A \\) (tags): \\( A' \\) (description)): \\( B \\) (tags): \\( B' \\) (description)), where \\( A \\) and \\( B \\) are music tags automatically provided by the tagger, \\( A' \\) is a human-provided text description, and \\( B' \\) is the natural language description output by the large-scale language model." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.757, + 0.47, + 0.877 + ], + "angle": 0, + "content": "(2) We propose a Transformer-based model architecture with a video-text fusion module. Our model, which we call Video to Music with Language (ViML), is able to retrieve music that matches both the visual content/style of the input video and described musical genre, mood, and instrumentation in the natural language query. Similar to prior work [16, 28, 39], we find that training with text dropout as a regularization mechanism is critical to achieve music re" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.884, + 0.107 + ], + "angle": 0, + "content": "trieval performance improvements from added text inputs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.108, + 0.892, + 0.23 + ], + "angle": 0, + "content": "(3) We release a dataset of 4000 high quality text annotations for clips from a subset of the YT8M-MusicVideo dataset [1] to evaluate language-guided music recommendation. We show that our method can achieve substantial improvements over prior works on music retrieval when incorporating text inputs. Moreover, our model can match or even exceed performance of baseline music-for-video recommendation models when the text input is ignored." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.247, + 0.642, + 0.263 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.274, + 0.892, + 0.41 + ], + "angle": 0, + "content": "Music and language. There are numerous music tagging datasets which contain tags specifying attributes like mood, genre, or instrumentation [5, 7, 19, 30], and several works have studied training automated music taggers from such datasets [10, 20, 22, 31, 43, 44]. Beyond these methods constrained to limited tag vocabularies, some works also have studied jointly embedding music and free-form natural language [9, 14, 27, 44]. However, none of these approaches incorporate the video modality." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.418, + 0.892, + 0.599 + ], + "angle": 0, + "content": "Music recommendation for video. Others have investigated automatic recommendation of music based on style and content of an input video [13, 24, 32, 37, 49]. Prétet et al. [32] build on previous self-supervised methods [13] by incorporating learned audio features instead of handcrafted features. More recently, Surís et al. [37] propose the MVPt model which employs a self-supervised contrastive loss and Transformer [38] architecture to greatly improve the long-range temporal context modeling in order to retrieve suitable music for a given input video. However, none of these approaches incorporate the natural language modality which we focus on in this work." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.606, + 0.892, + 0.848 + ], + "angle": 0, + "content": "Video, audio, & language. While a wide variety of works have explored audio-visual or vision-language topics, a smaller number focus on jointly embedding video, audio, and language [2, 4, 12, 34, 45, 47]. Specifically, Alayrac et al. [3] investigate how best to combine audio and video with text representations. The VATT model [2] is a fully end-to-end tri-modal model capable of using a single shared Transformer backbone across modalities. Lastly, two recent methods [12, 45] extend CLIP [33] to jointly embed audio. While relevant, all of these approaches share a common focus on \"environmental\" or \"everyday\" sounds rather than music, and they lack the long-range temporal context modeling critical for music recommendation as a result. In addition, none of these works address a downstream problem of using two modalities in combination (video, text) to query results from another (music)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Few-shot language model prompting. Recent large language models have shown significant success at a wide variety of few-shot or zero-shot tasks from those related to read-" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.442, + 0.9 + ], + "angle": 0, + "content": "1https://www.youtube.com/watch?v=iSkJFs7myn0" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14785" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.173, + 0.095, + 0.351, + 0.108 + ], + "angle": 0, + "content": "I. prompt2text Synthesis" + }, + { + "type": "image", + "bbox": [ + 0.078, + 0.112, + 0.46, + 0.372 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.59, + 0.096, + 0.754, + 0.109 + ], + "angle": 0, + "content": "II. data2text Synthesis" + }, + { + "type": "image", + "bbox": [ + 0.473, + 0.112, + 0.891, + 0.371 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.382, + 0.895, + 0.493 + ], + "angle": 0, + "content": "Figure 2. Overview of three text synthesis approaches explored in our work. All rely on tag predictions from a pretrained music tagger model. We highlight output text from each method in green, inputs from the tagger in blue font, and inputs from a human annotator in red font. Left: We introduce the prompt2tags approach for generating natural language descriptions given automatically predicted music tags and a small set of human descriptions. We ask a large language model (BLOOM-176B) to complete an analogy task (\\(A:A^{\\prime}::B:B^{\\prime}\\)) between music tags (\\(A,B\\)) and descriptions (\\(A^{\\prime},B^{\\prime}\\)). Top right: The data2text pipeline inserts sampled tags into randomly selected template sentences corresponding to each tag category. The Zero-shot D2T model [17] then orders, aggregates, and compresses these templates into a final output description. Bottom right: The tags approach involves direct concatenation of high confidence tags to form the text description of the music." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.532, + 0.473, + 0.729 + ], + "angle": 0, + "content": "ing comprehension and QA [8,41], to reasoning [18,42], or even data augmentation [11,40,46]. A few works have extended this success to multimodal applications. For example, Zeng et al. [48] show that language models can solve video understanding or image captioning tasks by reformulating these problems as reading comprehension or QA tasks with inputs from large visual or audio models. Other works have used language models to help with generating or retrieving text annotations for multimodal tasks [25] or in robotic planning [15,35]. In this work, we propose a completely new application of few-shot language query modeling: generating free-form musical text descriptions from music tags." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.74, + 0.188, + 0.758 + ], + "angle": 0, + "content": "3. Approach" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.472, + 0.903 + ], + "angle": 0, + "content": "Our goal is to train a pair of feature encoders \\( f^{vt} \\) and \\( f^m \\) which are capable of predicting the similarity \\( s(f^{vt},f^{m}) \\) between an input pair of video and musical text description \\( (v,t) \\) and a music clip \\( m \\), as illustrated in Figure 3. To train such a model in a supervised manner, it is necessary to have a dataset of corresponding triplets \\( (v,m,t) \\). While large-scale datasets of videos with paired music are available, it is difficult to find datasets which also contain high-quality natural language descriptions of the paired music tracks. As a" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.532, + 0.895, + 0.638 + ], + "angle": 0, + "content": "result, we investigate a synthesis approach based on a model \\( G \\) which generates text descriptions from available structured data in the form of music tags for each music track. In the following sections, we first discuss the musical description synthesis approach \\( G \\) before describing an approach to train a language-guided video-to-music recommendation model." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.65, + 0.852, + 0.667 + ], + "angle": 0, + "content": "3.1. Synthesizing Text Descriptions for Music" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.674, + 0.892, + 0.84 + ], + "angle": 0, + "content": "Suppose that we are given a set of video and music audio pairs \\((v_{i},m_{i})\\) and that we also have access to structured data \\(d_{i}\\in \\mathcal{T}^{D}\\) which describe the music \\(m_{i}\\). In our case, this structured data consists of musical tags with confidence. Each music track \\(m_{i}\\) may be described by a free-form human text description \\(t_i\\in \\mathcal{T}^T\\). However, it can be prohibitively expensive to obtain high-quality human descriptions on a large scale. Instead, we propose to synthesize such text descriptions using a generator \\(G:\\mathcal{T}^D\\to \\mathcal{T}^T\\) which maps structured data describing an audio track to the space of natural human descriptions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.895, + 0.903 + ], + "angle": 0, + "content": "The goals of such a mapping function \\( G \\) are that: (i) a predicted output \\( \\tilde{t}_i = G(d_i) \\) should preserve the semantic meaning contained within the structured data \\( d_i \\) corresponding to a specific musical track and (ii) the distribu" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "14786" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.473, + 0.304 + ], + "angle": 0, + "content": "tion of predicted outputs \\(\\tilde{t}_i\\) should follow the distribution of ground truth human text annotations \\(t_i\\in \\mathcal{T}^T\\). Training a fully supervised model to be the generator function \\(G\\) would require a large quantity of human text descriptions. Instead, we explore zero-shot or few-shot approaches to obtain a generator function \\(G\\). In particular, we describe three approaches that all use the automatically predicted music tags: a prompt2text approach which relies entirely on careful few-shot prompting of a pretrained language model, a zero-shot data2text approach which rephrases tem-. plated sentences using pretrained language models, and a zero-shot tags baseline that represents the music track description directly via the set of automatically obtained tags. Details are given next." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.312, + 0.473, + 0.494 + ], + "angle": 0, + "content": "I. Few-shot prompt2text approach. We first explore whether the full mapping function \\( G \\) can be encompassed by a single large language model through careful few-shot prompting. This approach relies on a small set of example human-provided descriptions \\( t_0, \\dots, t_N \\) where \\( t_i \\sim \\mathcal{T}^T \\). We assume that for each example \\( t_i \\), we also have a paired structured data output \\( d_i \\), provided by the automatic music tagger, which describes the same audio track. Unlike prior prompt-based data augmentation works [11, 40, 46] which aim for an unconditional generator \\( G \\), we aim to generate text data \\( \\tilde{t}_i \\sim G(d_i) \\) conditioned on structured data \\( d_i \\) such that it follows the distribution of human sentences \\( \\tilde{t}_i \\in \\mathcal{T}^T \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.497, + 0.473, + 0.649 + ], + "angle": 0, + "content": "As shown in Figure 2 (left), the structured data output \\( d_{i} \\) is converted to text form via a template, and a set of pairs \\( (d_0,t_0),\\dots,(d_k,t_k) \\) are used to form \\( k \\) input/output components in the prompt. The final segment of the prompt is the structured data \\( d_{i} \\) corresponding to a new music track. Given \\( d_{i} \\), the model will attempt to output a description \\( t_i \\) following the mapping \\( \\mathcal{T}^D\\to \\mathcal{T}^T \\) suggested by the example inputs. For text generation in this setting, we use the BLOOM-176B [6] model which is trained on a highly diverse 1.5TB text corpus." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.65, + 0.473, + 0.773 + ], + "angle": 0, + "content": "Given that the prompt2text allows for the greatest freedom in generation, the model can more easily generate a diverse set of text resembling the target distribution \\(\\mathcal{T}^T\\). The prompt2text approach is also very flexible as large language models like BLOOM can handle a variety of different structured data inputs such as both tags and their confidence predictions. However, the model may also be less likely to preserve semantic meaning from structured data." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.473, + 0.903 + ], + "angle": 0, + "content": "II. Zero-shot data2text approach. The second setting that we propose involves a data-to-text generation process which is illustrated in Figure 2 (top right). At a high level, the goal of this method is to insert structured tag data into predefined template sentences and rephrase these template sentences using a language model while preserving original semantic meaning. We begin with the tags predicted for each music track and grouped into genre, mood, and in-" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.395 + ], + "angle": 0, + "content": "strument categories. We define a set of category-specific templates in the form of short sentences with placeholders for tags. We randomly sample a template sentence for each category, and fill the template with the high-confidence predicted tags for that category. To form these sentences into more natural free-form descriptions, we make use of pretrained large language models. Specifically, we follow the Zero-shot D2T approach [17], which consists of ordering, aggregation, and compression modules built on pretrained RoBERTa [26] and BART [23] language models. The pipeline components first set the order of the individual filled template sentences and assign which sentences should be combined into a single sentence. Next, the compression module uses a generative text model to rewrite the input sentences based on the ordering and aggregation specifications. The module aims to rephrase the information while preserving semantic meaning. Because this D2T pipeline makes use of models that are pre-trained on large, general text corpus, we find these modules to perform well at generating music descriptions in a zero-shot manner." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.401, + 0.895, + 0.584 + ], + "angle": 0, + "content": "III. tags approach. The final setting we use involves a simple concatenation of predicted tags. We take the set of top filtered predicted tags for each music track (this set typically numbers around 10-15 tags total). We then randomly shuffle these tags to prevent model dependence on ordering and concatenate all of the tags into a comma-separated list of musical descriptions (e.g., \"synthesizer keyboard, electronic drumset, pop, dance, synth bass, electronic, happy, electric guitar, frantic, dynamic\"). While this approach strongly preserves the semantic meaning, it fails to generate text with diverse vocabulary and form which would well represent the human annotation distribution \\(\\mathcal{T}^T\\)." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.597, + 0.866, + 0.614 + ], + "angle": 0, + "content": "3.2. Text Dropout for Music Retrieval Training" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.621, + 0.895, + 0.865 + ], + "angle": 0, + "content": "The objective here is to retrieve music track \\( m \\) matching a query video \\( v \\) and a natural language query \\( t \\) describing the target music track. This is a challenging task as the model has to fuse together information from both the input video and the input language query to then find a semantically appropriate music track. Moreover, the difference in granularity between audio/video and text can significantly hinder training. We design a tri-modal approach, dubbed ViML, for this task and introduce text dropout to address the granularity issue. In a similar manner to the way dropout prevents overfitting by reducing co-adaptation between individual neurons [36], text dropout serves to avoid overfitting to the text inputs and prevent co-adaptations between the video and text encoders. The approach is illustrated in Figure 3 and details of model architecture, loss, and text dropout are given next." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Model architecture. Our model is trained on a set of (video, music, text) pairings, \\((v,m,t)\\), corresponding to a" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "14787" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.086, + 0.089, + 0.477, + 0.241 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.252, + 0.473, + 0.406 + ], + "angle": 0, + "content": "Figure 3. Our proposed ViML model embeds inputs from three modalities (video, text, and audio) into an embedding space. We extract base features using DeepSim [20] for music input and from CLIP [33] for video frames and text descriptions. These base features are inputted to Transformer encoders for each modality. The video and text features are combined with a fusion module to enable querying of music in a shared embedding space. Finally, we employ text dropout to address the difference in granularity between the three modalities. Since video is a more complex input modality, text dropout forces an improved video representation by preventing co-adaptation of the video and text representations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.443, + 0.47, + 0.548 + ], + "angle": 0, + "content": "music video clip \\( v \\), which has been labeled with a generated text description \\( t \\) of its music track \\( m \\), as outlined in Section 3.1. We transform these inputs into base features \\( x^{v} = g^{v}(v) \\) for visual video features, \\( x^{m} = g^{m}(m) \\) for music features, and \\( x^{t} = g^{t}(t) \\) for text features using pretrained large-scale encoders \\( g^{v}, g^{m} \\), and \\( g^{t} \\) which are frozen during training." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.549, + 0.47, + 0.655 + ], + "angle": 0, + "content": "Each base feature representation \\( x \\) is of dimension \\( n \\times d \\), where \\( n \\) is the length of the temporal sequence of base features representing a video clip and \\( d \\) is the dimension of the base feature. We note that while our model is capable of handling a sequence of temporal text descriptions similar to music or video, we obtain only a track-level text description in practice meaning that \\( n = 1 \\) for text." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.655, + 0.47, + 0.761 + ], + "angle": 0, + "content": "Our tri-modal model consists of three separate modules corresponding to each modality \\( f^v, f^m, f^t \\), and a fourth fusion module \\( f^{vt} \\) to combine video and text representations. The modules take respective base features and output embeddings \\( y^v = f^v(x^v) \\), \\( y^m = f^m(x^m) \\), \\( y^t = f^t(x^t) \\). The fusion model outputs a fused embedding from the video and text embeddings \\( y^{vt} = f^{vt}(y^v, y^t) \\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.767, + 0.47, + 0.797 + ], + "angle": 0, + "content": "Fusion loss. For training, we use an InfoNCE loss [29] between music and fused video-text embeddings:" + }, + { + "type": "equation", + "bbox": [ + 0.104, + 0.808, + 0.47, + 0.845 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {v t \\rightarrow m} = - \\frac {1}{| \\mathcal {D} |} \\sum_ {i \\in \\mathcal {D}} \\frac {\\exp \\left(s \\left(y _ {i} ^ {v t} , y _ {i} ^ {m}\\right) / \\tau\\right)}{\\sum_ {j \\in \\mathcal {D}} \\exp \\left(s \\left(y _ {i} ^ {v t} , y _ {j} ^ {m}\\right) / \\tau\\right)} \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.471, + 0.902 + ], + "angle": 0, + "content": "where \\( s \\) is a similarity function, \\( \\mathcal{D} \\) is a batch of data, and \\( \\tau \\) is a temperature hyperparameter we set as \\( \\tau = 0.03 \\). For our similarity metric, we use the cosine similarity defined as" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.091, + 0.892, + 0.153 + ], + "angle": 0, + "content": "\\(s(x,y) = x^{T}y / (\\| x\\| \\cdot \\| y\\|)\\). We note that the loss \\(\\mathcal{L}_{vt\\to m}\\) is not symmetric as negatives are sampled from music embeddings only. So that our loss is symmetric, we instead train with the summed loss \\(\\mathcal{L}_{m,vt} = \\mathcal{L}_{vt\\to m} + \\mathcal{L}_{m\\to vt}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.166, + 0.892, + 0.333 + ], + "angle": 0, + "content": "Text dropout. To address difficulties posed by the difference in granularity between audio/video and text, we introduce text dropout as a regularization mechanism. With probability \\( p \\), we set the input text embedding \\( x^{t} \\) to a specific value \\( x^{\\mathrm{NULL}} \\). In practice, we assign this \\( x^{\\mathrm{NULL}} \\) input as the embedding produced by the pretrained \\( g^{t} \\) model for an empty string. However, using a zero vector as \\( x^{\\mathrm{NULL}} \\) works similarly. In addition to improving the performance of music retrieval from text and video together, training with text dropout yields a model which also performs well at retrieval from video alone by removing dependence on text inputs." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.365, + 0.719, + 0.381 + ], + "angle": 0, + "content": "3.3. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.396, + 0.892, + 0.547 + ], + "angle": 0, + "content": "Music tag generation. The key first step to our text generation process is obtaining the structured data describing each musical track. To do this, we use a music tagger trained on a dataset of music tracks manually annotated with a fixed predefined vocabulary of tags [20, 21]. Specifically, the tagger predicts confidence for 41 instrument tags, 20 genre tags, and 28 mood tags. We aggregate these predictions at the clip or track level, and we filter the subsequent set based on confidence, keeping only those above a particular threshold (0.3 in our experiments)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.561, + 0.892, + 0.711 + ], + "angle": 0, + "content": "ViML Model. Following MVPt [37], we employ the Transformer architecture [38] for our music and video encoders \\( f^{m} \\) and \\( f^{v} \\). Transformers play a key role in improving model performance by encoding long-term context from video and music clips. We also use a similar two-layer Transformer architecture for our text encoder \\( f^{t} \\) and the video-text fusion layer \\( f^{vt} \\). However, we find that other fusion module architectures such as a single linear layer yield similar results. Please see our supplemental for study of fusion module architectures." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.892, + 0.901 + ], + "angle": 0, + "content": "For base features, we use CLIP [33] to encode representations for video frames and text inputs, and DeepSim [20] to encode music. Following communication with the authors of [37], we split the video into 10-second segments and compute a feature for each segment by averaging CLIP embedding features computed at 6 frames per second. We compute 512 dimensional CLIP embedding features using OpenAI's CLIP ViT-B/32 model. We encode all input base features into embeddings of size \\( d = 256 \\) using a linear projection layer for each modality. We also select \\( d = 256 \\) as the output dimension for encoded video, text, music, and fused video-text representations from our model." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14788" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.088, + 0.09, + 0.236, + 0.151 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.078, + 0.153, + 0.236, + 0.237 + ], + "angle": 0, + "content": "A faint, simple acoustic piece of singing by a female vocalist with an acoustic guitar with a fast-paced strumming pattern in a closed room recorded live. great for singing along." + }, + { + "type": "image", + "bbox": [ + 0.25, + 0.091, + 0.399, + 0.151 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.242, + 0.153, + 0.399, + 0.201 + ], + "angle": 0, + "content": "Hip-hop track with a dark synth pad with male aggressive rapping along with a chipmunk voice." + }, + { + "type": "image", + "bbox": [ + 0.414, + 0.09, + 0.561, + 0.15 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.404, + 0.153, + 0.562, + 0.2 + ], + "angle": 0, + "content": "Instrumental track featuring an ambient pad and bell-like sounds. Seems to be a film score." + }, + { + "type": "image", + "bbox": [ + 0.576, + 0.09, + 0.724, + 0.15 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.567, + 0.153, + 0.724, + 0.212 + ], + "angle": 0, + "content": "A cover version of Elvis Presley's pop song featuring male and female vocals and piano layers. Sounds like a confession in love." + }, + { + "type": "image", + "bbox": [ + 0.736, + 0.091, + 0.887, + 0.151 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.729, + 0.153, + 0.887, + 0.212 + ], + "angle": 0, + "content": "Punjabi track with multiple vocals and other instruments that's great for traditional marriage celebrations." + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.249, + 0.895, + 0.306 + ], + "angle": 0, + "content": "Figure 4. Example annotations from our collected YouTube8M-MusicTextClips dataset. Each example shows a frame from the 10sec source video clip from which audio was extracted for annotation. Note that annotators were only provided audio from the music video, so the annotation describes the music, but not the corresponding video. Each example in the figure contains a hyperlink to the corresponding YT8M source video with timestamp at the start of the 10sec target clip. Hover over the video frame image and click to follow the link." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.33, + 0.21, + 0.347 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.357, + 0.47, + 0.478 + ], + "angle": 0, + "content": "In this section, we report our experimental settings and results. First, we describe our datasets and the evaluation protocol in Sec. 4.1. Next, we investigate tag-based video-to-music retrieval, comparing against state-of-the-art video-to-music retrieval methods in Sec. 4.2. In Sec. 4.3, we evaluate performance of video-to-music retrieval guided by free-form text annotations. Finally, we perform ablation studies to measure the influence of text dropout in Sec. 4.4." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.491, + 0.37, + 0.506 + ], + "angle": 0, + "content": "4.1. Datasets and Evaluation Protocol" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.516, + 0.47, + 0.637 + ], + "angle": 0, + "content": "YT8M-MusicVideo. In all of our experiments, we train models using the YT8M-MusicVideo dataset which includes around 100k videos with the \"music video\" tag from the much larger YouTube8M dataset [1]. We synthesize tags and a natural language text describing the music track of each video for the full dataset using the approaches described in Sec. 3.1. We also use the test split of YT8M-MusicVideo to evaluate tag-based retrieval in Sec. 4.2." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.644, + 0.471, + 0.902 + ], + "angle": 0, + "content": "YT8M-MusicTextClips. In addition to the full YT8M-MusicVideo dataset, we also annotate a 4,000 sample subset of clips from YT8M-MusicVideo with human-provided text descriptions of the music track accompanying each video. To create these annotations, we sample 10 second audio clips from the middle of each music video, and we ask human annotators to describe the music they hear after listening to the audio clip. Thus, an annotation describes only the music from a YT8M sample, and the annotators do not see the corresponding video. Example annotations are shown in Figure 4 with links to the starting timestamp of the 10sec clips in corresponding YouTube videos. This annotated set is meant mainly for evaluation. As a result, the annotations are split into a larger set of 3,000 samples from the test set of YT8M-MusicVideo and a smaller set of 1,000 samples from the train set of YT8M-MusicVideo which we use as examples in the few-shot prompt2text synthesis process. We" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.332, + 0.892, + 0.361 + ], + "angle": 0, + "content": "make the annotated text descriptions publicly available at our companion website2." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.368, + 0.893, + 0.61 + ], + "angle": 0, + "content": "Evaluation Set-up and Metrics. We evaluate music retrieval performance consistently with previous works [32, 37]. However, in our case, a query can be either a video alone or a video and corresponding text annotation together. For each query, we compute feature similarity between the query and a pool of N music tracks (we set \\( \\mathrm{N} = 2000 \\) in the track-level setting and \\( \\mathrm{N} = 500 \\) for evaluation on clips). The pool contains a single ground truth music track corresponding to the input query (the positive example) with the remaining music tracks in the pool being non-matching (i.e., negative examples). We rank the music tracks in a query's pool by feature similarity, and find the rank of the query's ground truth matching music track (the positive example). We then compute Recall@K (shortened to R@K) for \\( \\mathrm{K} = 1,5,10 \\) and Median Rank, calculating the average of each of these metrics across the full set of test queries." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.618, + 0.692, + 0.634 + ], + "angle": 0, + "content": "4.2. Tag-Based Retrieval" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.641, + 0.895, + 0.868 + ], + "angle": 0, + "content": "For our first set of experiments, we explore the setting of tag-based retrieval. Here the goal is to retrieve a music track given a query video together with a set of tags from a predefined vocabulary, such as \"happy\", \"piano\" and \"jazz\". This setting could be practically interesting in some applications, e.g., tag-based search. To address this setting, we train our model on text synthesized with the tags approach. In these experiments, we train a track-level model and perform retrieval on a track-level in a manner consistent with prior work [32, 37]. To directly compare results with prior work, we perform retrieval on the full YT8M test set consisting of around 10K samples. As shown in Table 1, we include three baselines: the model proposed by Pretét et al. [32], the MVPt model [37], and an improved version of MVPt that we call MVPt+, where we tune the temperature" + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.875, + 0.892, + 0.9 + ], + "angle": 0, + "content": "2https://www.danielbmckee.com/language-guided-music-for-video/index.html" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14789" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.141, + 0.089, + 0.832, + 0.219 + ], + "angle": 0, + "content": "
MethodTrain TextQuery Text InputMedian Rank ↓R@1 ↑R@5 ↑R@10 ↑
a. Pretét et al. [32]--2340.763.425.90
b. MVPt [37]--136.0924.9141.89
c. MVPt+ [37]--527.9350.6460.68
d. ViML (ours)tags-329.4362.4975.40
e. ViML (ours)tagstags249.4981.6189.41
f. Chance10000.050.250.50
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.228, + 0.895, + 0.272 + ], + "angle": 0, + "content": "Table 1. Tag-based music retrieval on full YouTube8M-MusicVideo test set. We compare ViML against prior methods on video to music retrieval without tag queries (row d.). We also evaluate ViML on video+text to music retrieval using (synthetic) tags at test time (row e.). The text descriptions for both training and evaluation are generated with the tags approach for these experiments." + }, + { + "type": "table", + "bbox": [ + 0.088, + 0.294, + 0.457, + 0.387 + ], + "angle": 0, + "content": "
MethodTrain TextMR ↓R@1 ↑R@5 ↑R@10 ↑
a. MVPt+-1712.2029.4340.46
b. ViMLtags1511.9530.3442.62
c. ViMLdata2text1313.6133.9446.24
d. ViMLprompt2text1214.0935.0447.88
Chance2500.201.002.00
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.397, + 0.472, + 0.48 + ], + "angle": 0, + "content": "Table 2. Music retrieval with free-form natural language on YT8M-MusicTextClips test set. All methods which take text input are evaluated on the human text annotations as queries. Since the \\(\\mathrm{MVPt + }\\) model does not take text inputs, it is evaluated on music retrieval from video alone for the same set of 3k video clips. MR is median rank." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.508, + 0.47, + 0.539 + ], + "angle": 0, + "content": "parameter \\(\\tau\\) in the InfoNCE loss to 0.03. This change leads to further significant improvement in performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.539, + 0.47, + 0.795 + ], + "angle": 0, + "content": "Next, we introduce our model (ViML) trained on data generated from the tags approach. We evaluate our ViML model in two settings. First, we evaluate without input texts at test time (an empty text input is used instead). Second, we evaluate with text inputs at test time. As we do not have track-level human-provided music tag annotations for the full YT8M MusicVideo split, we evaluate the track-level model on synthetically generated tags using our tags approach. While a model trained on the tags synthesized data may not generalize to out-of-domain free-form text inputs, the tag-based prompting can be a convenient way to guide music retrieval with key desired attributes (for example \"female vocalist, guitar, happy\"). The tag-based retrieval we report can serve as an upper bound for this type of user tag-guided retrieval since the tag-based text for testing comes from the same music tagger model we used to synthesize training data." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Evaluating our model with synthetic tags leads to a very substantial performance increase over \\(\\mathrm{MVPt + }\\) of 20-30 points in each recall metric. Interestingly, our ViML model evaluated without text at test time not only matches the video-to-music retrieval performance of \\(\\mathrm{MVT + }\\) but substantially improves over \\(\\mathrm{MVPt + }\\), especially in Recall@5 and Recall@10. This performance increase is not simply" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.297, + 0.895, + 0.465 + ], + "angle": 0, + "content": "a result of added parameters in the fusion layer, as a fusion module consisting of only a single linear layer yields similar results (see our supplemental for further details). This result suggests that training jointly with the text domain can lead to improvements in the video and audio representations. We hypothesize that the joint training with language helps to disentangle the video-audio space into semantically meaningful dimensions corresponding to the provided tags as well as helps to suppress non-relevant dimensions, e.g., corresponding to presence/absence of some non-relevant objects." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.47, + 0.842, + 0.487 + ], + "angle": 0, + "content": "4.3. Free-Form Natural Language Retrieval" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.494, + 0.895, + 0.6 + ], + "angle": 0, + "content": "For the next experiments, we turn to retrieval with free-form natural language inputs. The goal is, given an input video and a query free-form natural language description, to retrieve a relevant music track. For this setting, we evaluate on testing videos from the YT8M-MusicTextClips dataset which contains free-form human text annotations describing the music corresponding to each video in the dataset." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.6, + 0.895, + 0.765 + ], + "angle": 0, + "content": "In these experiments, we use a similar protocol to the \"segment-level\" setting reported by Surís et al. [37], but our input video includes only a 30sec clip surrounding the 10sec of audio labeled by a human annotator. In contrast, a model had access to a large context spanning the full source video in the previous segment-level setting reported by Surís et al. [37]. We note that retrieval in this setting is significantly more difficult than the segment-level setting in [37] or the track-level setting reported in 4.2 due to the limited context. However, such retrieval is of particular interest given the rise of short-form video in social media and entertainment." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.766, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Results are summarized in Table 2. Our baseline is an \\(\\mathrm{MVPt + }\\) model which has been trained on 30sec segments (training \\(\\mathrm{MVPt + }\\) on full videos and testing on 30sec clips causes a much more severe drop in performance). We next report music retrieval using video and free-form human text descriptions as input queries to our ViML model. In Table 2, we report three variants trained on YT8M music videos with text synthesized by each of the three approaches described in Sec. 3.1. The model trained with our first tags syn" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "14790" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.12, + 0.089, + 0.851, + 0.203 + ], + "angle": 0, + "content": "
MethodTrain TextDropoutText InputsMedian Rank ↓R@1 ↑R@5 ↑R@10 ↑
a. MVPt+---1712.2029.4340.46
b. MVT-Fuseprompt2textX-209.9426.4237.01
c. MVT-Fuseprompt2textXhuman1511.4530.4542.77
d. MVT-Fuseprompt2text✓-1612.2730.3441.51
e. MVT-Fuseprompt2text✓human1214.0935.0447.88
" + }, + { + "type": "table_caption", + "bbox": [ + 0.108, + 0.213, + 0.86, + 0.227 + ], + "angle": 0, + "content": "Table 3. Influence of training with text dropout on retrieval performance. Evaluated on the YT8M-MusicTextClips test set." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.254, + 0.469, + 0.389 + ], + "angle": 0, + "content": "thesis baseline (b.) provides substantial improvement over retrieval with MVPt+ using only video (a.). Next, we evaluate the data2text approach (c.) which generates more natural phrases while strictly preserving tag semantics. This approach provides a consistent improvement over the ViML tags variant (b.). Finally, our prompt2text approach (d.) leads to the best performance showing that large language models prove to be strong annotators on this task with careful few-shot prompting." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.39, + 0.469, + 0.51 + ], + "angle": 0, + "content": "Qualitative results. In Figure 5, we provide qualitative retrieval results for examples in YouTube8M-MusicTextClips. In the first example, both models retrieve tracks that match the style and beat of the input video well. However, only the ViML can match the correct musical style by using the input text. In the second example, only the ViML result correctly matches the desired music genre and the mood of the video." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.521, + 0.305, + 0.537 + ], + "angle": 0, + "content": "4.4. Analysis of Text Dropout" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.544, + 0.47, + 0.831 + ], + "angle": 0, + "content": "In Table 3, we compare the performance of our ViML model trained on prompt2text descriptions with and without text dropout. We evaluate this model on music retrieval in two settings: (i) using only video (inputting empty text, rows b. and d.) as a query and (ii) using both video and human text descriptions together as a query (rows c. and e.). As expected, adding text dropout during training (d.) improves the performance of retrieval using only video (b.). However, interestingly, text dropout also substantially improves performance when the query includes natural language (e. vs. c.), suggesting that text dropout is a very useful regularization technique in the multimodal setting. We find that without text dropout, training begins to plateau early as the model starts overfitting to the training text inputs. Since video is a much richer and more complex modality, forcing more attention to this modality during training improves learning. We find that the dropout technique is most effective at high rates of dropout in the range 0.8-0.95, and we use a dropout rate of 0.8 in all of our experiments." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.845, + 0.195, + 0.86 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "In this work, we introduced an approach to allow language-guided music recommendation for video. We pro" + }, + { + "type": "image_caption", + "bbox": [ + 0.508, + 0.257, + 0.648, + 0.271 + ], + "angle": 0, + "content": "Video+Language Query" + }, + { + "type": "image", + "bbox": [ + 0.529, + 0.295, + 0.638, + 0.344 + ], + "angle": 0, + "content": null + }, + { + "type": "image_footnote", + "bbox": [ + 0.512, + 0.347, + 0.644, + 0.385 + ], + "angle": 0, + "content": "Electronic dance pop track that has male vocals and a pulsating rhythm. Best for nightclubs." + }, + { + "type": "image_caption", + "bbox": [ + 0.729, + 0.259, + 0.825, + 0.269 + ], + "angle": 0, + "content": "Retrieved Music" + }, + { + "type": "image_footnote", + "bbox": [ + 0.699, + 0.275, + 0.738, + 0.284 + ], + "angle": 0, + "content": "MVPt+" + }, + { + "type": "image_footnote", + "bbox": [ + 0.819, + 0.275, + 0.85, + 0.284 + ], + "angle": 0, + "content": "ViML" + }, + { + "type": "image", + "bbox": [ + 0.677, + 0.299, + 0.72, + 0.32 + ], + "angle": 0, + "content": null + }, + { + "type": "image_footnote", + "bbox": [ + 0.67, + 0.33, + 0.772, + 0.375 + ], + "angle": 0, + "content": "Percussive Latin music with a male vocalist, synth line, and Cumbia beat aligned with video." + }, + { + "type": "image", + "bbox": [ + 0.795, + 0.299, + 0.838, + 0.319 + ], + "angle": 0, + "content": null + }, + { + "type": "image_footnote", + "bbox": [ + 0.785, + 0.33, + 0.882, + 0.377 + ], + "angle": 0, + "content": "Energetic electronic party song with male vocals over rising synth layers and claps aligned with video." + }, + { + "type": "image", + "bbox": [ + 0.525, + 0.401, + 0.635, + 0.45 + ], + "angle": 0, + "content": null + }, + { + "type": "image_footnote", + "bbox": [ + 0.512, + 0.454, + 0.649, + 0.491 + ], + "angle": 0, + "content": "Male rap song in a foreign language with hip-hop beats and electronic music that gives a freestyle vibe to it." + }, + { + "type": "image", + "bbox": [ + 0.677, + 0.408, + 0.72, + 0.43 + ], + "angle": 0, + "content": null + }, + { + "type": "image_footnote", + "bbox": [ + 0.669, + 0.442, + 0.768, + 0.479 + ], + "angle": 0, + "content": "Upbeat jazzy melody played on a saxophone over rhythmic electronic bass beats." + }, + { + "type": "image", + "bbox": [ + 0.795, + 0.409, + 0.838, + 0.43 + ], + "angle": 0, + "content": null + }, + { + "type": "image_footnote", + "bbox": [ + 0.786, + 0.442, + 0.885, + 0.48 + ], + "angle": 0, + "content": "French rap song with processed male vocals, thumping drum beats, and synth pad effects." + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.509, + 0.892, + 0.634 + ], + "angle": 0, + "content": "Figure 5. Qualitative results on YouTube8M-MusicTextClips test set. We compare music retrieval quality for two examples using the \\(\\mathrm{MVPt + }\\) model and our ViML model. The column on the left includes a frame from the input video and the input text description describing the target music. The \\(\\mathrm{MVPt + }\\) model takes only the video as an input while the ViML model takes both video and corresponding text. The two columns on the right contain retrieved music for \\(\\mathrm{MVPt + }\\) and ViML respectively. Please see results in the companion video on our website." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.673, + 0.892, + 0.9 + ], + "angle": 0, + "content": "posed a model, ViML, which fuses text and video inputs to find music matching both domains and introduced the text dropout technique to improve training. To obtain data for training, we proposed a free-form music description synthesis approach using a large language model (BLOOM-176B) and outputs from a pretrained music tagger. Our results show that large language models provide a powerful tool for training data synthesis in domains where text data is limited but other structured data is available. To evaluate our method, we also introduced a new dataset, YouTube8M-MusicTextClips, which includes high quality free-form human descriptions of the music in YT8M videos. There are many exciting directions to build upon this work including allowing more fine-grained control over specific music attributes or language-guided audio-video generation." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "14791" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.185 + ], + "angle": 0, + "content": "[1] Sami Abu-El-Haija, Nisarg Kothari, Joonseok Lee, Paul Natsev, George Toderici, Balakrishnan Varadarajan, and Sudheendra Vijayanarasimhan. Youtube-8m: A large-scale video classification benchmark. arXiv preprint arXiv:1609.08675, 2016. 2, 6" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.187, + 0.472, + 0.257 + ], + "angle": 0, + "content": "[2] Hassan Akbari, Liangzhe Yuan, Rui Qian, Wei-Hong Chuang, Shih-Fu Chang, Yin Cui, and Boqing Gong. 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IEEE, 2018. 2" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.838 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.956 + ], + "angle": 0, + "content": "14793" + } + ] +] \ No newline at end of file diff --git a/2023/Language-Guided Music Recommendation for Video via Prompt Analogies/c0941191-f1a3-4b4b-84fc-4169036b56b1_origin.pdf b/2023/Language-Guided Music Recommendation for Video via Prompt Analogies/c0941191-f1a3-4b4b-84fc-4169036b56b1_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..c2c65c93f8c498fc9b788106c13be25e476a05c7 --- /dev/null +++ b/2023/Language-Guided Music Recommendation for Video via Prompt Analogies/c0941191-f1a3-4b4b-84fc-4169036b56b1_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:20741c6c9b635207b3494fe074cf1731ae5fa27fa68b0b93fb3cbb1859411559 +size 9226004 diff --git a/2023/Language-Guided Music Recommendation for Video via Prompt Analogies/full.md b/2023/Language-Guided Music Recommendation for Video via Prompt Analogies/full.md new file mode 100644 index 0000000000000000000000000000000000000000..75e23674c0a990bf66e960f2e9fbf82f84ecdb8c --- /dev/null +++ b/2023/Language-Guided Music Recommendation for Video via Prompt Analogies/full.md @@ -0,0 +1,284 @@ +# Language-Guided Music Recommendation for Video via Prompt Analogies + +Daniel McKee1* + +Justin Salamon2 + +Josef Sivic2,3 + +Bryan Russell + +1University of Illinois at Urbana-Champaign 2Adobe Research Institute of Informatics, Robotics and Cybernetics, Czech Technical University + +dbmckee2@illinois.edu + +salamon@adobe.com + +josef.sivic@cvut.cz + +brussell@adobe.com + +https://www.danielbmckee.com/language-guided-music-for-video + +# Abstract + +We propose a method to recommend music for an input video while allowing a user to guide music selection with free-form natural language. A key challenge of this problem setting is that existing music video datasets provide the needed (video, music) training pairs, but lack text descriptions of the music. This work addresses this challenge with the following three contributions. First, we propose a text-synthesis approach that relies on an analogy-based prompting procedure to generate natural language music descriptions from a large-scale language model (BLOOM-176B) given pre-trained music tagger outputs and a small number of human text descriptions. Second, we use these synthesized music descriptions to train a new trimodal model, which fuses text and video input representations to query music samples. For training, we introduce a text dropout regularization mechanism which we show is critical to model performance. Our model design allows for the retrieved music audio to agree with the two input modalities by matching visual style depicted in the video and musical genre, mood, or instrumentation described in the natural language query. Third, to evaluate our approach, we collect a testing dataset for our problem by annotating a subset of 4k clips from the YT8M-MusicVideo dataset with natural language music descriptions which we make publicly available. We show that our approach can match or exceed the performance of prior methods on video-to-music retrieval while significantly improving retrieval accuracy when using text guidance. + +# 1. Introduction + +A key part of the video editing process for creators is choosing a musical soundtrack. Especially given the rise of short-form videos on social media platforms, automated music recommendation systems have become an increas + +![](images/b410e7da8c50994ec6d0dd92b0fbab8aef819159ddc2843c499124260ceaa06e.jpg) +Language-Guided Music Retrieval +Figure 1. Language-guided music retrieval. Our ViML model takes a video and text prompt as input to retrieve a suitable music track from a database. The model learns to fuse video and language representations in order to guide retrieval. Notice how our approach retrieves audio matching both the video and language content. For the same video query (top two rows), we can change the music style to match the language query, and for the same Upbeat pop query (bottom two rows) we can change the vocalist to match the video content. To fully appreciate our results, please view and listen to the companion video on our website. + +ingly common and important part of video editing applications. While these systems can be helpful for finding relevant music, they often provide limited capability for user control over the types of music recommended. In previous work, music is retrieved based solely on the visual content and style from a video [32, 37]. However, music itself can convey critical information about how a video should + +be perceived. Music selection alone can transform a visual scene into one that is perceived as happy, scary, or sad1. As a result, the lack of user input capability to describe a target music for an inputted video is a key limitation on the utility of current music recommendation methods. + +In this work, we propose a more flexible music-for-video recommendation approach that allows a user to guide recommendations towards specific musical attributes including mood, genre, or instrumentation, illustrated in Figure 1. To maximize flexibility and user convenience, we propose to take user musical attribute descriptions in the form of free-form natural language (e.g., "Folk music with guitar" in Figure 1). There are two key challenges in learning a model for language-guided music recommendation for video. First, while there are datasets which include music+text [5,7,19,30] or music+video [1], there are no available datasets which include music, video, and text together. Further, the existing datasets that do include text and music focus on a limited vocabulary of tags rather than free-form text. Second, previous works have explored jointly learning visual, audio, and text embeddings [2-4, 34, 47], and without careful regularization, a network can overfit and possibly learn to ignore one of the input modalities. We seek to train a model that keeps the information flow through the network and does not ignore one of the modalities. + +In order to meet the challenges outlined above, our work makes the following contributions: + +(1) We propose a new approach to automatically generate natural language descriptions for a music video dataset. This approach combines a pre-trained music tagger with a large-scale language model to output natural language descriptions for any music clip, illustrated in Figure 2 (left). First, the tagger predicts tags from a pre-defined vocabulary describing musical genre, mood, or instrumentation. Second, these predicted tags, together with their probabilities, are converted into a rich natural language description for the music video using a carefully designed large-scale language model prompting procedure based on analogies with a small number of human-provided text descriptions (i.e., $A$ (tags): $A'$ (description)): $B$ (tags): $B'$ (description)), where $A$ and $B$ are music tags automatically provided by the tagger, $A'$ is a human-provided text description, and $B'$ is the natural language description output by the large-scale language model. + +(2) We propose a Transformer-based model architecture with a video-text fusion module. Our model, which we call Video to Music with Language (ViML), is able to retrieve music that matches both the visual content/style of the input video and described musical genre, mood, and instrumentation in the natural language query. Similar to prior work [16, 28, 39], we find that training with text dropout as a regularization mechanism is critical to achieve music re + +trieval performance improvements from added text inputs. + +(3) We release a dataset of 4000 high quality text annotations for clips from a subset of the YT8M-MusicVideo dataset [1] to evaluate language-guided music recommendation. We show that our method can achieve substantial improvements over prior works on music retrieval when incorporating text inputs. Moreover, our model can match or even exceed performance of baseline music-for-video recommendation models when the text input is ignored. + +# 2. Related Work + +Music and language. There are numerous music tagging datasets which contain tags specifying attributes like mood, genre, or instrumentation [5, 7, 19, 30], and several works have studied training automated music taggers from such datasets [10, 20, 22, 31, 43, 44]. Beyond these methods constrained to limited tag vocabularies, some works also have studied jointly embedding music and free-form natural language [9, 14, 27, 44]. However, none of these approaches incorporate the video modality. + +Music recommendation for video. Others have investigated automatic recommendation of music based on style and content of an input video [13, 24, 32, 37, 49]. Prétet et al. [32] build on previous self-supervised methods [13] by incorporating learned audio features instead of handcrafted features. More recently, Surís et al. [37] propose the MVPt model which employs a self-supervised contrastive loss and Transformer [38] architecture to greatly improve the long-range temporal context modeling in order to retrieve suitable music for a given input video. However, none of these approaches incorporate the natural language modality which we focus on in this work. + +Video, audio, & language. While a wide variety of works have explored audio-visual or vision-language topics, a smaller number focus on jointly embedding video, audio, and language [2, 4, 12, 34, 45, 47]. Specifically, Alayrac et al. [3] investigate how best to combine audio and video with text representations. The VATT model [2] is a fully end-to-end tri-modal model capable of using a single shared Transformer backbone across modalities. Lastly, two recent methods [12, 45] extend CLIP [33] to jointly embed audio. While relevant, all of these approaches share a common focus on "environmental" or "everyday" sounds rather than music, and they lack the long-range temporal context modeling critical for music recommendation as a result. In addition, none of these works address a downstream problem of using two modalities in combination (video, text) to query results from another (music). + +Few-shot language model prompting. Recent large language models have shown significant success at a wide variety of few-shot or zero-shot tasks from those related to read- + +![](images/3b6e4248c61330880dab9607fb42b4681137d6ab3322bd02f33d4ed07f6f4805.jpg) +I. prompt2text Synthesis + +![](images/ba3a248b43d1b98e3b4d60d399e1c311a7be63e0523093139b5a0c8d59846429.jpg) +II. data2text Synthesis +Figure 2. Overview of three text synthesis approaches explored in our work. All rely on tag predictions from a pretrained music tagger model. We highlight output text from each method in green, inputs from the tagger in blue font, and inputs from a human annotator in red font. Left: We introduce the prompt2tags approach for generating natural language descriptions given automatically predicted music tags and a small set of human descriptions. We ask a large language model (BLOOM-176B) to complete an analogy task ( $A:A^{\prime}::B:B^{\prime}$ ) between music tags ( $A,B$ ) and descriptions ( $A^{\prime},B^{\prime}$ ). Top right: The data2text pipeline inserts sampled tags into randomly selected template sentences corresponding to each tag category. The Zero-shot D2T model [17] then orders, aggregates, and compresses these templates into a final output description. Bottom right: The tags approach involves direct concatenation of high confidence tags to form the text description of the music. + +ing comprehension and QA [8,41], to reasoning [18,42], or even data augmentation [11,40,46]. A few works have extended this success to multimodal applications. For example, Zeng et al. [48] show that language models can solve video understanding or image captioning tasks by reformulating these problems as reading comprehension or QA tasks with inputs from large visual or audio models. Other works have used language models to help with generating or retrieving text annotations for multimodal tasks [25] or in robotic planning [15,35]. In this work, we propose a completely new application of few-shot language query modeling: generating free-form musical text descriptions from music tags. + +# 3. Approach + +Our goal is to train a pair of feature encoders $f^{vt}$ and $f^m$ which are capable of predicting the similarity $s(f^{vt},f^{m})$ between an input pair of video and musical text description $(v,t)$ and a music clip $m$ , as illustrated in Figure 3. To train such a model in a supervised manner, it is necessary to have a dataset of corresponding triplets $(v,m,t)$ . While large-scale datasets of videos with paired music are available, it is difficult to find datasets which also contain high-quality natural language descriptions of the paired music tracks. As a + +result, we investigate a synthesis approach based on a model $G$ which generates text descriptions from available structured data in the form of music tags for each music track. In the following sections, we first discuss the musical description synthesis approach $G$ before describing an approach to train a language-guided video-to-music recommendation model. + +# 3.1. Synthesizing Text Descriptions for Music + +Suppose that we are given a set of video and music audio pairs $(v_{i},m_{i})$ and that we also have access to structured data $d_{i}\in \mathcal{T}^{D}$ which describe the music $m_{i}$ . In our case, this structured data consists of musical tags with confidence. Each music track $m_{i}$ may be described by a free-form human text description $t_i\in \mathcal{T}^T$ . However, it can be prohibitively expensive to obtain high-quality human descriptions on a large scale. Instead, we propose to synthesize such text descriptions using a generator $G:\mathcal{T}^D\to \mathcal{T}^T$ which maps structured data describing an audio track to the space of natural human descriptions. + +The goals of such a mapping function $G$ are that: (i) a predicted output $\tilde{t}_i = G(d_i)$ should preserve the semantic meaning contained within the structured data $d_i$ corresponding to a specific musical track and (ii) the distribu + +tion of predicted outputs $\tilde{t}_i$ should follow the distribution of ground truth human text annotations $t_i\in \mathcal{T}^T$ . Training a fully supervised model to be the generator function $G$ would require a large quantity of human text descriptions. Instead, we explore zero-shot or few-shot approaches to obtain a generator function $G$ . In particular, we describe three approaches that all use the automatically predicted music tags: a prompt2text approach which relies entirely on careful few-shot prompting of a pretrained language model, a zero-shot data2text approach which rephrases tem-. plated sentences using pretrained language models, and a zero-shot tags baseline that represents the music track description directly via the set of automatically obtained tags. Details are given next. + +I. Few-shot prompt2text approach. We first explore whether the full mapping function $G$ can be encompassed by a single large language model through careful few-shot prompting. This approach relies on a small set of example human-provided descriptions $t_0, \dots, t_N$ where $t_i \sim \mathcal{T}^T$ . We assume that for each example $t_i$ , we also have a paired structured data output $d_i$ , provided by the automatic music tagger, which describes the same audio track. Unlike prior prompt-based data augmentation works [11, 40, 46] which aim for an unconditional generator $G$ , we aim to generate text data $\tilde{t}_i \sim G(d_i)$ conditioned on structured data $d_i$ such that it follows the distribution of human sentences $\tilde{t}_i \in \mathcal{T}^T$ . + +As shown in Figure 2 (left), the structured data output $d_{i}$ is converted to text form via a template, and a set of pairs $(d_0,t_0),\dots,(d_k,t_k)$ are used to form $k$ input/output components in the prompt. The final segment of the prompt is the structured data $d_{i}$ corresponding to a new music track. Given $d_{i}$ , the model will attempt to output a description $t_i$ following the mapping $\mathcal{T}^D\to \mathcal{T}^T$ suggested by the example inputs. For text generation in this setting, we use the BLOOM-176B [6] model which is trained on a highly diverse 1.5TB text corpus. + +Given that the prompt2text allows for the greatest freedom in generation, the model can more easily generate a diverse set of text resembling the target distribution $\mathcal{T}^T$ . The prompt2text approach is also very flexible as large language models like BLOOM can handle a variety of different structured data inputs such as both tags and their confidence predictions. However, the model may also be less likely to preserve semantic meaning from structured data. + +II. Zero-shot data2text approach. The second setting that we propose involves a data-to-text generation process which is illustrated in Figure 2 (top right). At a high level, the goal of this method is to insert structured tag data into predefined template sentences and rephrase these template sentences using a language model while preserving original semantic meaning. We begin with the tags predicted for each music track and grouped into genre, mood, and in- + +strument categories. We define a set of category-specific templates in the form of short sentences with placeholders for tags. We randomly sample a template sentence for each category, and fill the template with the high-confidence predicted tags for that category. To form these sentences into more natural free-form descriptions, we make use of pretrained large language models. Specifically, we follow the Zero-shot D2T approach [17], which consists of ordering, aggregation, and compression modules built on pretrained RoBERTa [26] and BART [23] language models. The pipeline components first set the order of the individual filled template sentences and assign which sentences should be combined into a single sentence. Next, the compression module uses a generative text model to rewrite the input sentences based on the ordering and aggregation specifications. The module aims to rephrase the information while preserving semantic meaning. Because this D2T pipeline makes use of models that are pre-trained on large, general text corpus, we find these modules to perform well at generating music descriptions in a zero-shot manner. + +III. tags approach. The final setting we use involves a simple concatenation of predicted tags. We take the set of top filtered predicted tags for each music track (this set typically numbers around 10-15 tags total). We then randomly shuffle these tags to prevent model dependence on ordering and concatenate all of the tags into a comma-separated list of musical descriptions (e.g., "synthesizer keyboard, electronic drumset, pop, dance, synth bass, electronic, happy, electric guitar, frantic, dynamic"). While this approach strongly preserves the semantic meaning, it fails to generate text with diverse vocabulary and form which would well represent the human annotation distribution $\mathcal{T}^T$ . + +# 3.2. Text Dropout for Music Retrieval Training + +The objective here is to retrieve music track $m$ matching a query video $v$ and a natural language query $t$ describing the target music track. This is a challenging task as the model has to fuse together information from both the input video and the input language query to then find a semantically appropriate music track. Moreover, the difference in granularity between audio/video and text can significantly hinder training. We design a tri-modal approach, dubbed ViML, for this task and introduce text dropout to address the granularity issue. In a similar manner to the way dropout prevents overfitting by reducing co-adaptation between individual neurons [36], text dropout serves to avoid overfitting to the text inputs and prevent co-adaptations between the video and text encoders. The approach is illustrated in Figure 3 and details of model architecture, loss, and text dropout are given next. + +Model architecture. Our model is trained on a set of (video, music, text) pairings, $(v,m,t)$ , corresponding to a + +![](images/8fca2012f333f4998b41c9df6d947c1aeffe76c1f6f663331b5364daf9f3d0ea.jpg) +Figure 3. Our proposed ViML model embeds inputs from three modalities (video, text, and audio) into an embedding space. We extract base features using DeepSim [20] for music input and from CLIP [33] for video frames and text descriptions. These base features are inputted to Transformer encoders for each modality. The video and text features are combined with a fusion module to enable querying of music in a shared embedding space. Finally, we employ text dropout to address the difference in granularity between the three modalities. Since video is a more complex input modality, text dropout forces an improved video representation by preventing co-adaptation of the video and text representations. + +music video clip $v$ , which has been labeled with a generated text description $t$ of its music track $m$ , as outlined in Section 3.1. We transform these inputs into base features $x^{v} = g^{v}(v)$ for visual video features, $x^{m} = g^{m}(m)$ for music features, and $x^{t} = g^{t}(t)$ for text features using pretrained large-scale encoders $g^{v}, g^{m}$ , and $g^{t}$ which are frozen during training. + +Each base feature representation $x$ is of dimension $n \times d$ , where $n$ is the length of the temporal sequence of base features representing a video clip and $d$ is the dimension of the base feature. We note that while our model is capable of handling a sequence of temporal text descriptions similar to music or video, we obtain only a track-level text description in practice meaning that $n = 1$ for text. + +Our tri-modal model consists of three separate modules corresponding to each modality $f^v, f^m, f^t$ , and a fourth fusion module $f^{vt}$ to combine video and text representations. The modules take respective base features and output embeddings $y^v = f^v(x^v)$ , $y^m = f^m(x^m)$ , $y^t = f^t(x^t)$ . The fusion model outputs a fused embedding from the video and text embeddings $y^{vt} = f^{vt}(y^v, y^t)$ . + +Fusion loss. For training, we use an InfoNCE loss [29] between music and fused video-text embeddings: + +$$ +\mathcal {L} _ {v t \rightarrow m} = - \frac {1}{| \mathcal {D} |} \sum_ {i \in \mathcal {D}} \frac {\exp \left(s \left(y _ {i} ^ {v t} , y _ {i} ^ {m}\right) / \tau\right)}{\sum_ {j \in \mathcal {D}} \exp \left(s \left(y _ {i} ^ {v t} , y _ {j} ^ {m}\right) / \tau\right)} \tag {1} +$$ + +where $s$ is a similarity function, $\mathcal{D}$ is a batch of data, and $\tau$ is a temperature hyperparameter we set as $\tau = 0.03$ . For our similarity metric, we use the cosine similarity defined as + +$s(x,y) = x^{T}y / (\| x\| \cdot \| y\|)$ . We note that the loss $\mathcal{L}_{vt\to m}$ is not symmetric as negatives are sampled from music embeddings only. So that our loss is symmetric, we instead train with the summed loss $\mathcal{L}_{m,vt} = \mathcal{L}_{vt\to m} + \mathcal{L}_{m\to vt}$ . + +Text dropout. To address difficulties posed by the difference in granularity between audio/video and text, we introduce text dropout as a regularization mechanism. With probability $p$ , we set the input text embedding $x^{t}$ to a specific value $x^{\mathrm{NULL}}$ . In practice, we assign this $x^{\mathrm{NULL}}$ input as the embedding produced by the pretrained $g^{t}$ model for an empty string. However, using a zero vector as $x^{\mathrm{NULL}}$ works similarly. In addition to improving the performance of music retrieval from text and video together, training with text dropout yields a model which also performs well at retrieval from video alone by removing dependence on text inputs. + +# 3.3. Implementation Details + +Music tag generation. The key first step to our text generation process is obtaining the structured data describing each musical track. To do this, we use a music tagger trained on a dataset of music tracks manually annotated with a fixed predefined vocabulary of tags [20, 21]. Specifically, the tagger predicts confidence for 41 instrument tags, 20 genre tags, and 28 mood tags. We aggregate these predictions at the clip or track level, and we filter the subsequent set based on confidence, keeping only those above a particular threshold (0.3 in our experiments). + +ViML Model. Following MVPt [37], we employ the Transformer architecture [38] for our music and video encoders $f^{m}$ and $f^{v}$ . Transformers play a key role in improving model performance by encoding long-term context from video and music clips. We also use a similar two-layer Transformer architecture for our text encoder $f^{t}$ and the video-text fusion layer $f^{vt}$ . However, we find that other fusion module architectures such as a single linear layer yield similar results. Please see our supplemental for study of fusion module architectures. + +For base features, we use CLIP [33] to encode representations for video frames and text inputs, and DeepSim [20] to encode music. Following communication with the authors of [37], we split the video into 10-second segments and compute a feature for each segment by averaging CLIP embedding features computed at 6 frames per second. We compute 512 dimensional CLIP embedding features using OpenAI's CLIP ViT-B/32 model. We encode all input base features into embeddings of size $d = 256$ using a linear projection layer for each modality. We also select $d = 256$ as the output dimension for encoded video, text, music, and fused video-text representations from our model. + +![](images/26d34da65764ee63c650328268a9966d651ee8ffb33498e7dd84ba2e5e3e95f9.jpg) +A faint, simple acoustic piece of singing by a female vocalist with an acoustic guitar with a fast-paced strumming pattern in a closed room recorded live. great for singing along. + +![](images/a44e8944cdd14fd98ef12e71036428c04340efaaacd782a2e0c0939cedf4eb87.jpg) +Hip-hop track with a dark synth pad with male aggressive rapping along with a chipmunk voice. + +![](images/90785c2cd564d647b1e9203f9e3b776c7923cdd50386a5385cae3531e8a0c6fb.jpg) +Instrumental track featuring an ambient pad and bell-like sounds. Seems to be a film score. + +![](images/708cbc86d95aa369ecd3b5f8487ca12b1c8b721f113494d73d9c29dbf7a92e8d.jpg) +A cover version of Elvis Presley's pop song featuring male and female vocals and piano layers. Sounds like a confession in love. + +![](images/39adebe7b99f06214b14ae190f04f74fd45a09ed4e29209785f8cf2317608765.jpg) +Punjabi track with multiple vocals and other instruments that's great for traditional marriage celebrations. +Figure 4. Example annotations from our collected YouTube8M-MusicTextClips dataset. Each example shows a frame from the 10sec source video clip from which audio was extracted for annotation. Note that annotators were only provided audio from the music video, so the annotation describes the music, but not the corresponding video. Each example in the figure contains a hyperlink to the corresponding YT8M source video with timestamp at the start of the 10sec target clip. Hover over the video frame image and click to follow the link. + +# 4. Experiments + +In this section, we report our experimental settings and results. First, we describe our datasets and the evaluation protocol in Sec. 4.1. Next, we investigate tag-based video-to-music retrieval, comparing against state-of-the-art video-to-music retrieval methods in Sec. 4.2. In Sec. 4.3, we evaluate performance of video-to-music retrieval guided by free-form text annotations. Finally, we perform ablation studies to measure the influence of text dropout in Sec. 4.4. + +# 4.1. Datasets and Evaluation Protocol + +YT8M-MusicVideo. In all of our experiments, we train models using the YT8M-MusicVideo dataset which includes around 100k videos with the "music video" tag from the much larger YouTube8M dataset [1]. We synthesize tags and a natural language text describing the music track of each video for the full dataset using the approaches described in Sec. 3.1. We also use the test split of YT8M-MusicVideo to evaluate tag-based retrieval in Sec. 4.2. + +YT8M-MusicTextClips. In addition to the full YT8M-MusicVideo dataset, we also annotate a 4,000 sample subset of clips from YT8M-MusicVideo with human-provided text descriptions of the music track accompanying each video. To create these annotations, we sample 10 second audio clips from the middle of each music video, and we ask human annotators to describe the music they hear after listening to the audio clip. Thus, an annotation describes only the music from a YT8M sample, and the annotators do not see the corresponding video. Example annotations are shown in Figure 4 with links to the starting timestamp of the 10sec clips in corresponding YouTube videos. This annotated set is meant mainly for evaluation. As a result, the annotations are split into a larger set of 3,000 samples from the test set of YT8M-MusicVideo and a smaller set of 1,000 samples from the train set of YT8M-MusicVideo which we use as examples in the few-shot prompt2text synthesis process. We + +make the annotated text descriptions publicly available at our companion website2. + +Evaluation Set-up and Metrics. We evaluate music retrieval performance consistently with previous works [32, 37]. However, in our case, a query can be either a video alone or a video and corresponding text annotation together. For each query, we compute feature similarity between the query and a pool of N music tracks (we set $\mathrm{N} = 2000$ in the track-level setting and $\mathrm{N} = 500$ for evaluation on clips). The pool contains a single ground truth music track corresponding to the input query (the positive example) with the remaining music tracks in the pool being non-matching (i.e., negative examples). We rank the music tracks in a query's pool by feature similarity, and find the rank of the query's ground truth matching music track (the positive example). We then compute Recall@K (shortened to R@K) for $\mathrm{K} = 1,5,10$ and Median Rank, calculating the average of each of these metrics across the full set of test queries. + +# 4.2. Tag-Based Retrieval + +For our first set of experiments, we explore the setting of tag-based retrieval. Here the goal is to retrieve a music track given a query video together with a set of tags from a predefined vocabulary, such as "happy", "piano" and "jazz". This setting could be practically interesting in some applications, e.g., tag-based search. To address this setting, we train our model on text synthesized with the tags approach. In these experiments, we train a track-level model and perform retrieval on a track-level in a manner consistent with prior work [32, 37]. To directly compare results with prior work, we perform retrieval on the full YT8M test set consisting of around 10K samples. As shown in Table 1, we include three baselines: the model proposed by Pretét et al. [32], the MVPt model [37], and an improved version of MVPt that we call MVPt+, where we tune the temperature + +
MethodTrain TextQuery Text InputMedian Rank ↓R@1 ↑R@5 ↑R@10 ↑
a. Pretét et al. [32]--2340.763.425.90
b. MVPt [37]--136.0924.9141.89
c. MVPt+ [37]--527.9350.6460.68
d. ViML (ours)tags-329.4362.4975.40
e. ViML (ours)tagstags249.4981.6189.41
f. Chance10000.050.250.50
+ +Table 1. Tag-based music retrieval on full YouTube8M-MusicVideo test set. We compare ViML against prior methods on video to music retrieval without tag queries (row d.). We also evaluate ViML on video+text to music retrieval using (synthetic) tags at test time (row e.). The text descriptions for both training and evaluation are generated with the tags approach for these experiments. + +
MethodTrain TextMR ↓R@1 ↑R@5 ↑R@10 ↑
a. MVPt+-1712.2029.4340.46
b. ViMLtags1511.9530.3442.62
c. ViMLdata2text1313.6133.9446.24
d. ViMLprompt2text1214.0935.0447.88
Chance2500.201.002.00
+ +Table 2. Music retrieval with free-form natural language on YT8M-MusicTextClips test set. All methods which take text input are evaluated on the human text annotations as queries. Since the $\mathrm{MVPt + }$ model does not take text inputs, it is evaluated on music retrieval from video alone for the same set of 3k video clips. MR is median rank. + +parameter $\tau$ in the InfoNCE loss to 0.03. This change leads to further significant improvement in performance. + +Next, we introduce our model (ViML) trained on data generated from the tags approach. We evaluate our ViML model in two settings. First, we evaluate without input texts at test time (an empty text input is used instead). Second, we evaluate with text inputs at test time. As we do not have track-level human-provided music tag annotations for the full YT8M MusicVideo split, we evaluate the track-level model on synthetically generated tags using our tags approach. While a model trained on the tags synthesized data may not generalize to out-of-domain free-form text inputs, the tag-based prompting can be a convenient way to guide music retrieval with key desired attributes (for example "female vocalist, guitar, happy"). The tag-based retrieval we report can serve as an upper bound for this type of user tag-guided retrieval since the tag-based text for testing comes from the same music tagger model we used to synthesize training data. + +Evaluating our model with synthetic tags leads to a very substantial performance increase over $\mathrm{MVPt + }$ of 20-30 points in each recall metric. Interestingly, our ViML model evaluated without text at test time not only matches the video-to-music retrieval performance of $\mathrm{MVT + }$ but substantially improves over $\mathrm{MVPt + }$ , especially in Recall@5 and Recall@10. This performance increase is not simply + +a result of added parameters in the fusion layer, as a fusion module consisting of only a single linear layer yields similar results (see our supplemental for further details). This result suggests that training jointly with the text domain can lead to improvements in the video and audio representations. We hypothesize that the joint training with language helps to disentangle the video-audio space into semantically meaningful dimensions corresponding to the provided tags as well as helps to suppress non-relevant dimensions, e.g., corresponding to presence/absence of some non-relevant objects. + +# 4.3. Free-Form Natural Language Retrieval + +For the next experiments, we turn to retrieval with free-form natural language inputs. The goal is, given an input video and a query free-form natural language description, to retrieve a relevant music track. For this setting, we evaluate on testing videos from the YT8M-MusicTextClips dataset which contains free-form human text annotations describing the music corresponding to each video in the dataset. + +In these experiments, we use a similar protocol to the "segment-level" setting reported by Surís et al. [37], but our input video includes only a 30sec clip surrounding the 10sec of audio labeled by a human annotator. In contrast, a model had access to a large context spanning the full source video in the previous segment-level setting reported by Surís et al. [37]. We note that retrieval in this setting is significantly more difficult than the segment-level setting in [37] or the track-level setting reported in 4.2 due to the limited context. However, such retrieval is of particular interest given the rise of short-form video in social media and entertainment. + +Results are summarized in Table 2. Our baseline is an $\mathrm{MVPt + }$ model which has been trained on 30sec segments (training $\mathrm{MVPt + }$ on full videos and testing on 30sec clips causes a much more severe drop in performance). We next report music retrieval using video and free-form human text descriptions as input queries to our ViML model. In Table 2, we report three variants trained on YT8M music videos with text synthesized by each of the three approaches described in Sec. 3.1. The model trained with our first tags syn + +
MethodTrain TextDropoutText InputsMedian Rank ↓R@1 ↑R@5 ↑R@10 ↑
a. MVPt+---1712.2029.4340.46
b. MVT-Fuseprompt2textX-209.9426.4237.01
c. MVT-Fuseprompt2textXhuman1511.4530.4542.77
d. MVT-Fuseprompt2text✓-1612.2730.3441.51
e. MVT-Fuseprompt2text✓human1214.0935.0447.88
+ +Table 3. Influence of training with text dropout on retrieval performance. Evaluated on the YT8M-MusicTextClips test set. + +thesis baseline (b.) provides substantial improvement over retrieval with MVPt+ using only video (a.). Next, we evaluate the data2text approach (c.) which generates more natural phrases while strictly preserving tag semantics. This approach provides a consistent improvement over the ViML tags variant (b.). Finally, our prompt2text approach (d.) leads to the best performance showing that large language models prove to be strong annotators on this task with careful few-shot prompting. + +Qualitative results. In Figure 5, we provide qualitative retrieval results for examples in YouTube8M-MusicTextClips. In the first example, both models retrieve tracks that match the style and beat of the input video well. However, only the ViML can match the correct musical style by using the input text. In the second example, only the ViML result correctly matches the desired music genre and the mood of the video. + +# 4.4. Analysis of Text Dropout + +In Table 3, we compare the performance of our ViML model trained on prompt2text descriptions with and without text dropout. We evaluate this model on music retrieval in two settings: (i) using only video (inputting empty text, rows b. and d.) as a query and (ii) using both video and human text descriptions together as a query (rows c. and e.). As expected, adding text dropout during training (d.) improves the performance of retrieval using only video (b.). However, interestingly, text dropout also substantially improves performance when the query includes natural language (e. vs. c.), suggesting that text dropout is a very useful regularization technique in the multimodal setting. We find that without text dropout, training begins to plateau early as the model starts overfitting to the training text inputs. Since video is a much richer and more complex modality, forcing more attention to this modality during training improves learning. We find that the dropout technique is most effective at high rates of dropout in the range 0.8-0.95, and we use a dropout rate of 0.8 in all of our experiments. + +# 5. Conclusion + +In this work, we introduced an approach to allow language-guided music recommendation for video. We pro + +Video+Language Query +![](images/a42e9433edd4f88644cf28bd04206e9bdc09b63631896fc451fcdf26405c6ddf.jpg) +Electronic dance pop track that has male vocals and a pulsating rhythm. Best for nightclubs. + +Retrieved Music +![](images/be85c7822299996c12fffff5fdce48f650f520de0a97d303f9cd2fb9e452bf01.jpg) +MVPt+ + +![](images/261b27073dfa5642a1c3ede328d58644cdde152942df7c76ebfe1b203fd9d996.jpg) +ViML +Percussive Latin music with a male vocalist, synth line, and Cumbia beat aligned with video. + +Figure 5. Qualitative results on YouTube8M-MusicTextClips test set. We compare music retrieval quality for two examples using the $\mathrm{MVPt + }$ model and our ViML model. The column on the left includes a frame from the input video and the input text description describing the target music. The $\mathrm{MVPt + }$ model takes only the video as an input while the ViML model takes both video and corresponding text. The two columns on the right contain retrieved music for $\mathrm{MVPt + }$ and ViML respectively. Please see results in the companion video on our website. +![](images/bcb8781ae7de8317048b3da2bc962b9945d7c9224bffcaba165ac220e6454d89.jpg) +Male rap song in a foreign language with hip-hop beats and electronic music that gives a freestyle vibe to it. + +![](images/af413976f812c87bdc2cd1103714c9b174da864d2f1191c3c20591c73fc31147.jpg) +Upbeat jazzy melody played on a saxophone over rhythmic electronic bass beats. + +![](images/17736ab6a375ecbd561282ed5e457386c467a7dc539312db5babb89410490356.jpg) +Energetic electronic party song with male vocals over rising synth layers and claps aligned with video. +French rap song with processed male vocals, thumping drum beats, and synth pad effects. + +posed a model, ViML, which fuses text and video inputs to find music matching both domains and introduced the text dropout technique to improve training. To obtain data for training, we proposed a free-form music description synthesis approach using a large language model (BLOOM-176B) and outputs from a pretrained music tagger. Our results show that large language models provide a powerful tool for training data synthesis in domains where text data is limited but other structured data is available. To evaluate our method, we also introduced a new dataset, YouTube8M-MusicTextClips, which includes high quality free-form human descriptions of the music in YT8M videos. There are many exciting directions to build upon this work including allowing more fine-grained control over specific music attributes or language-guided audio-video generation. + +# References + +[1] Sami Abu-El-Haija, Nisarg Kothari, Joonseok Lee, Paul Natsev, George Toderici, Balakrishnan Varadarajan, and Sudheendra Vijayanarasimhan. 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video while allowing a user to guide music selection with free-form natural language. A key challenge of this problem setting is that existing music video datasets provide the needed (video, music) training pairs, but lack text descriptions of the music. This work addresses this challenge with the following three contributions. First, we propose a text-synthesis approach that relies on an analogy-based prompting procedure to generate natural language music descriptions from a large-scale language model (BLOOM-176B) given pre-trained music tagger outputs and a small number of human text descriptions. Second, we use these synthesized music descriptions to train a new trimodal model, which fuses text and video input representations to query music samples. For training, we introduce a text dropout regularization mechanism which we show is critical to model performance. Our model design allows for the retrieved music audio to agree with the two input modalities by matching visual style depicted in the video and musical genre, mood, or instrumentation described in the natural language query. Third, to evaluate our approach, we collect a testing dataset for our problem by annotating a subset of 4k clips from the YT8M-MusicVideo dataset with natural language music descriptions which we make publicly available. We show that our approach can match or exceed the performance of prior methods on video-to-music retrieval while significantly improving retrieval accuracy when using text guidance." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 47, + 627, + 127, + 639 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 627, + 127, + 639 + ], + "spans": [ + { + "bbox": [ + 47, + 627, + 127, + 639 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 46, + 647, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 647, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 647, + 287, + 696 + ], + "type": "text", + "content": "A key part of the video editing process for creators is choosing a musical soundtrack. Especially given the rise of short-form videos on social media platforms, automated music recommendation systems have become an increas" + } + ] + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 311, + 263, + 538, + 476 + ], + "blocks": [ + { + "bbox": [ + 363, + 247, + 491, + 258 + ], + "lines": [ + { + "bbox": [ + 363, + 247, + 491, + 258 + ], + "spans": [ + { + "bbox": [ + 363, + 247, + 491, + 258 + ], + "type": "text", + "content": "Language-Guided Music Retrieval" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 311, + 263, + 538, + 476 + ], + "lines": [ + { + "bbox": [ + 311, + 263, + 538, + 476 + ], + "spans": [ + { + "bbox": [ + 311, + 263, + 538, + 476 + ], + "type": "image", + "image_path": "b410e7da8c50994ec6d0dd92b0fbab8aef819159ddc2843c499124260ceaa06e.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 487, + 547, + 598 + ], + "lines": [ + { + "bbox": [ + 304, + 487, + 547, + 598 + ], + "spans": [ + { + "bbox": [ + 304, + 487, + 547, + 598 + ], + "type": "text", + "content": "Figure 1. Language-guided music retrieval. Our ViML model takes a video and text prompt as input to retrieve a suitable music track from a database. The model learns to fuse video and language representations in order to guide retrieval. Notice how our approach retrieves audio matching both the video and language content. For the same video query (top two rows), we can change the music style to match the language query, and for the same Upbeat pop query (bottom two rows) we can change the vocalist to match the video content. To fully appreciate our results, please view and listen to the companion video on our website." + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "type": "text", + "content": "ingly common and important part of video editing applications. While these systems can be helpful for finding relevant music, they often provide limited capability for user control over the types of music recommended. In previous work, music is retrieved based solely on the visual content and style from a video [32, 37]. However, music itself can convey critical information about how a video should" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 209, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 209, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 209, + 712 + ], + "type": "text", + "content": "*Work done as an intern with Adobe Research" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "14784" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 131 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 131 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 131 + ], + "type": "text", + "content": "be perceived. Music selection alone can transform a visual scene into one that is perceived as happy, scary, or sad1. As a result, the lack of user input capability to describe a target music for an inputted video is a key limitation on the utility of current music recommendation methods." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 133, + 288, + 370 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 133, + 288, + 370 + ], + "spans": [ + { + "bbox": [ + 45, + 133, + 288, + 370 + ], + "type": "text", + "content": "In this work, we propose a more flexible music-for-video recommendation approach that allows a user to guide recommendations towards specific musical attributes including mood, genre, or instrumentation, illustrated in Figure 1. To maximize flexibility and user convenience, we propose to take user musical attribute descriptions in the form of free-form natural language (e.g., \"Folk music with guitar\" in Figure 1). There are two key challenges in learning a model for language-guided music recommendation for video. First, while there are datasets which include music+text [5,7,19,30] or music+video [1], there are no available datasets which include music, video, and text together. Further, the existing datasets that do include text and music focus on a limited vocabulary of tags rather than free-form text. Second, previous works have explored jointly learning visual, audio, and text embeddings [2-4, 34, 47], and without careful regularization, a network can overfit and possibly learn to ignore one of the input modalities. We seek to train a model that keeps the information flow through the network and does not ignore one of the modalities." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 372, + 287, + 395 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 372, + 287, + 395 + ], + "spans": [ + { + "bbox": [ + 47, + 372, + 287, + 395 + ], + "type": "text", + "content": "In order to meet the challenges outlined above, our work makes the following contributions:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 396, + 287, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 396, + 287, + 598 + ], + "spans": [ + { + "bbox": [ + 46, + 396, + 287, + 598 + ], + "type": "text", + "content": "(1) We propose a new approach to automatically generate natural language descriptions for a music video dataset. This approach combines a pre-trained music tagger with a large-scale language model to output natural language descriptions for any music clip, illustrated in Figure 2 (left). First, the tagger predicts tags from a pre-defined vocabulary describing musical genre, mood, or instrumentation. Second, these predicted tags, together with their probabilities, are converted into a rich natural language description for the music video using a carefully designed large-scale language model prompting procedure based on analogies with a small number of human-provided text descriptions (i.e., " + }, + { + "bbox": [ + 46, + 396, + 287, + 598 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 46, + 396, + 287, + 598 + ], + "type": "text", + "content": " (tags): " + }, + { + "bbox": [ + 46, + 396, + 287, + 598 + ], + "type": "inline_equation", + "content": "A'" + }, + { + "bbox": [ + 46, + 396, + 287, + 598 + ], + "type": "text", + "content": " (description)): " + }, + { + "bbox": [ + 46, + 396, + 287, + 598 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 46, + 396, + 287, + 598 + ], + "type": "text", + "content": " (tags): " + }, + { + "bbox": [ + 46, + 396, + 287, + 598 + ], + "type": "inline_equation", + "content": "B'" + }, + { + "bbox": [ + 46, + 396, + 287, + 598 + ], + "type": "text", + "content": " (description)), where " + }, + { + "bbox": [ + 46, + 396, + 287, + 598 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 46, + 396, + 287, + 598 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 396, + 287, + 598 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 46, + 396, + 287, + 598 + ], + "type": "text", + "content": " are music tags automatically provided by the tagger, " + }, + { + "bbox": [ + 46, + 396, + 287, + 598 + ], + "type": "inline_equation", + "content": "A'" + }, + { + "bbox": [ + 46, + 396, + 287, + 598 + ], + "type": "text", + "content": " is a human-provided text description, and " + }, + { + "bbox": [ + 46, + 396, + 287, + 598 + ], + "type": "inline_equation", + "content": "B'" + }, + { + "bbox": [ + 46, + 396, + 287, + 598 + ], + "type": "text", + "content": " is the natural language description output by the large-scale language model." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 599, + 287, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 599, + 287, + 694 + ], + "spans": [ + { + "bbox": [ + 46, + 599, + 287, + 694 + ], + "type": "text", + "content": "(2) We propose a Transformer-based model architecture with a video-text fusion module. Our model, which we call Video to Music with Language (ViML), is able to retrieve music that matches both the visual content/style of the input video and described musical genre, mood, and instrumentation in the natural language query. Similar to prior work [16, 28, 39], we find that training with text dropout as a regularization mechanism is critical to achieve music re" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 72, + 541, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 541, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 541, + 84 + ], + "type": "text", + "content": "trieval performance improvements from added text inputs." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 85, + 545, + 182 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 85, + 545, + 182 + ], + "spans": [ + { + "bbox": [ + 304, + 85, + 545, + 182 + ], + "type": "text", + "content": "(3) We release a dataset of 4000 high quality text annotations for clips from a subset of the YT8M-MusicVideo dataset [1] to evaluate language-guided music recommendation. We show that our method can achieve substantial improvements over prior works on music retrieval when incorporating text inputs. Moreover, our model can match or even exceed performance of baseline music-for-video recommendation models when the text input is ignored." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 195, + 392, + 208 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 195, + 392, + 208 + ], + "spans": [ + { + "bbox": [ + 306, + 195, + 392, + 208 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 217, + 545, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 217, + 545, + 324 + ], + "spans": [ + { + "bbox": [ + 304, + 217, + 545, + 324 + ], + "type": "text", + "content": "Music and language. There are numerous music tagging datasets which contain tags specifying attributes like mood, genre, or instrumentation [5, 7, 19, 30], and several works have studied training automated music taggers from such datasets [10, 20, 22, 31, 43, 44]. Beyond these methods constrained to limited tag vocabularies, some works also have studied jointly embedding music and free-form natural language [9, 14, 27, 44]. However, none of these approaches incorporate the video modality." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 331, + 545, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 331, + 545, + 474 + ], + "spans": [ + { + "bbox": [ + 304, + 331, + 545, + 474 + ], + "type": "text", + "content": "Music recommendation for video. Others have investigated automatic recommendation of music based on style and content of an input video [13, 24, 32, 37, 49]. Prétet et al. [32] build on previous self-supervised methods [13] by incorporating learned audio features instead of handcrafted features. More recently, Surís et al. [37] propose the MVPt model which employs a self-supervised contrastive loss and Transformer [38] architecture to greatly improve the long-range temporal context modeling in order to retrieve suitable music for a given input video. However, none of these approaches incorporate the natural language modality which we focus on in this work." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 479, + 545, + 671 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 479, + 545, + 671 + ], + "spans": [ + { + "bbox": [ + 304, + 479, + 545, + 671 + ], + "type": "text", + "content": "Video, audio, & language. While a wide variety of works have explored audio-visual or vision-language topics, a smaller number focus on jointly embedding video, audio, and language [2, 4, 12, 34, 45, 47]. Specifically, Alayrac et al. [3] investigate how best to combine audio and video with text representations. The VATT model [2] is a fully end-to-end tri-modal model capable of using a single shared Transformer backbone across modalities. Lastly, two recent methods [12, 45] extend CLIP [33] to jointly embed audio. While relevant, all of these approaches share a common focus on \"environmental\" or \"everyday\" sounds rather than music, and they lack the long-range temporal context modeling critical for music recommendation as a result. In addition, none of these works address a downstream problem of using two modalities in combination (video, text) to query results from another (music)." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": "Few-shot language model prompting. Recent large language models have shown significant success at a wide variety of few-shot or zero-shot tasks from those related to read-" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 58, + 702, + 270, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 270, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 270, + 712 + ], + "type": "text", + "content": "1https://www.youtube.com/watch?v=iSkJFs7myn0" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14785" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 88, + 281, + 294 + ], + "blocks": [ + { + "bbox": [ + 105, + 75, + 214, + 85 + ], + "lines": [ + { + "bbox": [ + 105, + 75, + 214, + 85 + ], + "spans": [ + { + "bbox": [ + 105, + 75, + 214, + 85 + ], + "type": "text", + "content": "I. prompt2text Synthesis" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 47, + 88, + 281, + 294 + ], + "lines": [ + { + "bbox": [ + 47, + 88, + 281, + 294 + ], + "spans": [ + { + "bbox": [ + 47, + 88, + 281, + 294 + ], + "type": "image", + "image_path": "3b6e4248c61330880dab9607fb42b4681137d6ab3322bd02f33d4ed07f6f4805.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 289, + 88, + 545, + 293 + ], + "blocks": [ + { + "bbox": [ + 361, + 76, + 461, + 86 + ], + "lines": [ + { + "bbox": [ + 361, + 76, + 461, + 86 + ], + "spans": [ + { + "bbox": [ + 361, + 76, + 461, + 86 + ], + "type": "text", + "content": "II. data2text Synthesis" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 289, + 88, + 545, + 293 + ], + "lines": [ + { + "bbox": [ + 289, + 88, + 545, + 293 + ], + "spans": [ + { + "bbox": [ + 289, + 88, + 545, + 293 + ], + "type": "image", + "image_path": "ba3a248b43d1b98e3b4d60d399e1c311a7be63e0523093139b5a0c8d59846429.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 302, + 547, + 390 + ], + "lines": [ + { + "bbox": [ + 45, + 302, + 547, + 390 + ], + "spans": [ + { + "bbox": [ + 45, + 302, + 547, + 390 + ], + "type": "text", + "content": "Figure 2. Overview of three text synthesis approaches explored in our work. All rely on tag predictions from a pretrained music tagger model. We highlight output text from each method in green, inputs from the tagger in blue font, and inputs from a human annotator in red font. Left: We introduce the prompt2tags approach for generating natural language descriptions given automatically predicted music tags and a small set of human descriptions. We ask a large language model (BLOOM-176B) to complete an analogy task (" + }, + { + "bbox": [ + 45, + 302, + 547, + 390 + ], + "type": "inline_equation", + "content": "A:A^{\\prime}::B:B^{\\prime}" + }, + { + "bbox": [ + 45, + 302, + 547, + 390 + ], + "type": "text", + "content": ") between music tags (" + }, + { + "bbox": [ + 45, + 302, + 547, + 390 + ], + "type": "inline_equation", + "content": "A,B" + }, + { + "bbox": [ + 45, + 302, + 547, + 390 + ], + "type": "text", + "content": ") and descriptions (" + }, + { + "bbox": [ + 45, + 302, + 547, + 390 + ], + "type": "inline_equation", + "content": "A^{\\prime},B^{\\prime}" + }, + { + "bbox": [ + 45, + 302, + 547, + 390 + ], + "type": "text", + "content": "). Top right: The data2text pipeline inserts sampled tags into randomly selected template sentences corresponding to each tag category. The Zero-shot D2T model [17] then orders, aggregates, and compresses these templates into a final output description. Bottom right: The tags approach involves direct concatenation of high confidence tags to form the text description of the music." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 421, + 289, + 577 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 421, + 289, + 577 + ], + "spans": [ + { + "bbox": [ + 46, + 421, + 289, + 577 + ], + "type": "text", + "content": "ing comprehension and QA [8,41], to reasoning [18,42], or even data augmentation [11,40,46]. A few works have extended this success to multimodal applications. For example, Zeng et al. [48] show that language models can solve video understanding or image captioning tasks by reformulating these problems as reading comprehension or QA tasks with inputs from large visual or audio models. Other works have used language models to help with generating or retrieving text annotations for multimodal tasks [25] or in robotic planning [15,35]. In this work, we propose a completely new application of few-shot language query modeling: generating free-form musical text descriptions from music tags." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 586, + 115, + 600 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 586, + 115, + 600 + ], + "spans": [ + { + "bbox": [ + 47, + 586, + 115, + 600 + ], + "type": "text", + "content": "3. Approach" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": "Our goal is to train a pair of feature encoders " + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "inline_equation", + "content": "f^{vt}" + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "inline_equation", + "content": "f^m" + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": " which are capable of predicting the similarity " + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "inline_equation", + "content": "s(f^{vt},f^{m})" + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": " between an input pair of video and musical text description " + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "inline_equation", + "content": "(v,t)" + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": " and a music clip " + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": ", as illustrated in Figure 3. To train such a model in a supervised manner, it is necessary to have a dataset of corresponding triplets " + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "inline_equation", + "content": "(v,m,t)" + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": ". While large-scale datasets of videos with paired music are available, it is difficult to find datasets which also contain high-quality natural language descriptions of the paired music tracks. As a" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 421, + 547, + 505 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 421, + 547, + 505 + ], + "spans": [ + { + "bbox": [ + 304, + 421, + 547, + 505 + ], + "type": "text", + "content": "result, we investigate a synthesis approach based on a model " + }, + { + "bbox": [ + 304, + 421, + 547, + 505 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 304, + 421, + 547, + 505 + ], + "type": "text", + "content": " which generates text descriptions from available structured data in the form of music tags for each music track. In the following sections, we first discuss the musical description synthesis approach " + }, + { + "bbox": [ + 304, + 421, + 547, + 505 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 304, + 421, + 547, + 505 + ], + "type": "text", + "content": " before describing an approach to train a language-guided video-to-music recommendation model." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 514, + 521, + 528 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 514, + 521, + 528 + ], + "spans": [ + { + "bbox": [ + 305, + 514, + 521, + 528 + ], + "type": "text", + "content": "3.1. Synthesizing Text Descriptions for Music" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 533, + 545, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 545, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 545, + 665 + ], + "type": "text", + "content": "Suppose that we are given a set of video and music audio pairs " + }, + { + "bbox": [ + 304, + 533, + 545, + 665 + ], + "type": "inline_equation", + "content": "(v_{i},m_{i})" + }, + { + "bbox": [ + 304, + 533, + 545, + 665 + ], + "type": "text", + "content": " and that we also have access to structured data " + }, + { + "bbox": [ + 304, + 533, + 545, + 665 + ], + "type": "inline_equation", + "content": "d_{i}\\in \\mathcal{T}^{D}" + }, + { + "bbox": [ + 304, + 533, + 545, + 665 + ], + "type": "text", + "content": " which describe the music " + }, + { + "bbox": [ + 304, + 533, + 545, + 665 + ], + "type": "inline_equation", + "content": "m_{i}" + }, + { + "bbox": [ + 304, + 533, + 545, + 665 + ], + "type": "text", + "content": ". In our case, this structured data consists of musical tags with confidence. Each music track " + }, + { + "bbox": [ + 304, + 533, + 545, + 665 + ], + "type": "inline_equation", + "content": "m_{i}" + }, + { + "bbox": [ + 304, + 533, + 545, + 665 + ], + "type": "text", + "content": " may be described by a free-form human text description " + }, + { + "bbox": [ + 304, + 533, + 545, + 665 + ], + "type": "inline_equation", + "content": "t_i\\in \\mathcal{T}^T" + }, + { + "bbox": [ + 304, + 533, + 545, + 665 + ], + "type": "text", + "content": ". However, it can be prohibitively expensive to obtain high-quality human descriptions on a large scale. Instead, we propose to synthesize such text descriptions using a generator " + }, + { + "bbox": [ + 304, + 533, + 545, + 665 + ], + "type": "inline_equation", + "content": "G:\\mathcal{T}^D\\to \\mathcal{T}^T" + }, + { + "bbox": [ + 304, + 533, + 545, + 665 + ], + "type": "text", + "content": " which maps structured data describing an audio track to the space of natural human descriptions." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "content": "The goals of such a mapping function " + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "content": " are that: (i) a predicted output " + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\tilde{t}_i = G(d_i)" + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "content": " should preserve the semantic meaning contained within the structured data " + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "inline_equation", + "content": "d_i" + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "content": " corresponding to a specific musical track and (ii) the distribu" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "14786" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "text", + "content": "tion of predicted outputs " + }, + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "inline_equation", + "content": "\\tilde{t}_i" + }, + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "text", + "content": " should follow the distribution of ground truth human text annotations " + }, + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "inline_equation", + "content": "t_i\\in \\mathcal{T}^T" + }, + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "text", + "content": ". Training a fully supervised model to be the generator function " + }, + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "text", + "content": " would require a large quantity of human text descriptions. Instead, we explore zero-shot or few-shot approaches to obtain a generator function " + }, + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "text", + "content": ". In particular, we describe three approaches that all use the automatically predicted music tags: a prompt2text approach which relies entirely on careful few-shot prompting of a pretrained language model, a zero-shot data2text approach which rephrases tem-. plated sentences using pretrained language models, and a zero-shot tags baseline that represents the music track description directly via the set of automatically obtained tags. Details are given next." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 247, + 289, + 391 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 247, + 289, + 391 + ], + "spans": [ + { + "bbox": [ + 46, + 247, + 289, + 391 + ], + "type": "text", + "content": "I. Few-shot prompt2text approach. We first explore whether the full mapping function " + }, + { + "bbox": [ + 46, + 247, + 289, + 391 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 46, + 247, + 289, + 391 + ], + "type": "text", + "content": " can be encompassed by a single large language model through careful few-shot prompting. This approach relies on a small set of example human-provided descriptions " + }, + { + "bbox": [ + 46, + 247, + 289, + 391 + ], + "type": "inline_equation", + "content": "t_0, \\dots, t_N" + }, + { + "bbox": [ + 46, + 247, + 289, + 391 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 46, + 247, + 289, + 391 + ], + "type": "inline_equation", + "content": "t_i \\sim \\mathcal{T}^T" + }, + { + "bbox": [ + 46, + 247, + 289, + 391 + ], + "type": "text", + "content": ". We assume that for each example " + }, + { + "bbox": [ + 46, + 247, + 289, + 391 + ], + "type": "inline_equation", + "content": "t_i" + }, + { + "bbox": [ + 46, + 247, + 289, + 391 + ], + "type": "text", + "content": ", we also have a paired structured data output " + }, + { + "bbox": [ + 46, + 247, + 289, + 391 + ], + "type": "inline_equation", + "content": "d_i" + }, + { + "bbox": [ + 46, + 247, + 289, + 391 + ], + "type": "text", + "content": ", provided by the automatic music tagger, which describes the same audio track. Unlike prior prompt-based data augmentation works [11, 40, 46] which aim for an unconditional generator " + }, + { + "bbox": [ + 46, + 247, + 289, + 391 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 46, + 247, + 289, + 391 + ], + "type": "text", + "content": ", we aim to generate text data " + }, + { + "bbox": [ + 46, + 247, + 289, + 391 + ], + "type": "inline_equation", + "content": "\\tilde{t}_i \\sim G(d_i)" + }, + { + "bbox": [ + 46, + 247, + 289, + 391 + ], + "type": "text", + "content": " conditioned on structured data " + }, + { + "bbox": [ + 46, + 247, + 289, + 391 + ], + "type": "inline_equation", + "content": "d_i" + }, + { + "bbox": [ + 46, + 247, + 289, + 391 + ], + "type": "text", + "content": " such that it follows the distribution of human sentences " + }, + { + "bbox": [ + 46, + 247, + 289, + 391 + ], + "type": "inline_equation", + "content": "\\tilde{t}_i \\in \\mathcal{T}^T" + }, + { + "bbox": [ + 46, + 247, + 289, + 391 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 393, + 289, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 393, + 289, + 514 + ], + "spans": [ + { + "bbox": [ + 46, + 393, + 289, + 514 + ], + "type": "text", + "content": "As shown in Figure 2 (left), the structured data output " + }, + { + "bbox": [ + 46, + 393, + 289, + 514 + ], + "type": "inline_equation", + "content": "d_{i}" + }, + { + "bbox": [ + 46, + 393, + 289, + 514 + ], + "type": "text", + "content": " is converted to text form via a template, and a set of pairs " + }, + { + "bbox": [ + 46, + 393, + 289, + 514 + ], + "type": "inline_equation", + "content": "(d_0,t_0),\\dots,(d_k,t_k)" + }, + { + "bbox": [ + 46, + 393, + 289, + 514 + ], + "type": "text", + "content": " are used to form " + }, + { + "bbox": [ + 46, + 393, + 289, + 514 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 393, + 289, + 514 + ], + "type": "text", + "content": " input/output components in the prompt. The final segment of the prompt is the structured data " + }, + { + "bbox": [ + 46, + 393, + 289, + 514 + ], + "type": "inline_equation", + "content": "d_{i}" + }, + { + "bbox": [ + 46, + 393, + 289, + 514 + ], + "type": "text", + "content": " corresponding to a new music track. Given " + }, + { + "bbox": [ + 46, + 393, + 289, + 514 + ], + "type": "inline_equation", + "content": "d_{i}" + }, + { + "bbox": [ + 46, + 393, + 289, + 514 + ], + "type": "text", + "content": ", the model will attempt to output a description " + }, + { + "bbox": [ + 46, + 393, + 289, + 514 + ], + "type": "inline_equation", + "content": "t_i" + }, + { + "bbox": [ + 46, + 393, + 289, + 514 + ], + "type": "text", + "content": " following the mapping " + }, + { + "bbox": [ + 46, + 393, + 289, + 514 + ], + "type": "inline_equation", + "content": "\\mathcal{T}^D\\to \\mathcal{T}^T" + }, + { + "bbox": [ + 46, + 393, + 289, + 514 + ], + "type": "text", + "content": " suggested by the example inputs. For text generation in this setting, we use the BLOOM-176B [6] model which is trained on a highly diverse 1.5TB text corpus." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 514, + 289, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 514, + 289, + 612 + ], + "spans": [ + { + "bbox": [ + 46, + 514, + 289, + 612 + ], + "type": "text", + "content": "Given that the prompt2text allows for the greatest freedom in generation, the model can more easily generate a diverse set of text resembling the target distribution " + }, + { + "bbox": [ + 46, + 514, + 289, + 612 + ], + "type": "inline_equation", + "content": "\\mathcal{T}^T" + }, + { + "bbox": [ + 46, + 514, + 289, + 612 + ], + "type": "text", + "content": ". The prompt2text approach is also very flexible as large language models like BLOOM can handle a variety of different structured data inputs such as both tags and their confidence predictions. However, the model may also be less likely to preserve semantic meaning from structured data." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "text", + "content": "II. Zero-shot data2text approach. The second setting that we propose involves a data-to-text generation process which is illustrated in Figure 2 (top right). At a high level, the goal of this method is to insert structured tag data into predefined template sentences and rephrase these template sentences using a language model while preserving original semantic meaning. We begin with the tags predicted for each music track and grouped into genre, mood, and in-" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 72, + 547, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 312 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 312 + ], + "type": "text", + "content": "strument categories. We define a set of category-specific templates in the form of short sentences with placeholders for tags. We randomly sample a template sentence for each category, and fill the template with the high-confidence predicted tags for that category. To form these sentences into more natural free-form descriptions, we make use of pretrained large language models. Specifically, we follow the Zero-shot D2T approach [17], which consists of ordering, aggregation, and compression modules built on pretrained RoBERTa [26] and BART [23] language models. The pipeline components first set the order of the individual filled template sentences and assign which sentences should be combined into a single sentence. Next, the compression module uses a generative text model to rewrite the input sentences based on the ordering and aggregation specifications. The module aims to rephrase the information while preserving semantic meaning. Because this D2T pipeline makes use of models that are pre-trained on large, general text corpus, we find these modules to perform well at generating music descriptions in a zero-shot manner." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 317, + 547, + 462 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 317, + 547, + 462 + ], + "spans": [ + { + "bbox": [ + 304, + 317, + 547, + 462 + ], + "type": "text", + "content": "III. tags approach. The final setting we use involves a simple concatenation of predicted tags. We take the set of top filtered predicted tags for each music track (this set typically numbers around 10-15 tags total). We then randomly shuffle these tags to prevent model dependence on ordering and concatenate all of the tags into a comma-separated list of musical descriptions (e.g., \"synthesizer keyboard, electronic drumset, pop, dance, synth bass, electronic, happy, electric guitar, frantic, dynamic\"). While this approach strongly preserves the semantic meaning, it fails to generate text with diverse vocabulary and form which would well represent the human annotation distribution " + }, + { + "bbox": [ + 304, + 317, + 547, + 462 + ], + "type": "inline_equation", + "content": "\\mathcal{T}^T" + }, + { + "bbox": [ + 304, + 317, + 547, + 462 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 472, + 529, + 486 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 472, + 529, + 486 + ], + "spans": [ + { + "bbox": [ + 305, + 472, + 529, + 486 + ], + "type": "text", + "content": "3.2. Text Dropout for Music Retrieval Training" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 491, + 547, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 491, + 547, + 685 + ], + "spans": [ + { + "bbox": [ + 304, + 491, + 547, + 685 + ], + "type": "text", + "content": "The objective here is to retrieve music track " + }, + { + "bbox": [ + 304, + 491, + 547, + 685 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 491, + 547, + 685 + ], + "type": "text", + "content": " matching a query video " + }, + { + "bbox": [ + 304, + 491, + 547, + 685 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 304, + 491, + 547, + 685 + ], + "type": "text", + "content": " and a natural language query " + }, + { + "bbox": [ + 304, + 491, + 547, + 685 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 491, + 547, + 685 + ], + "type": "text", + "content": " describing the target music track. This is a challenging task as the model has to fuse together information from both the input video and the input language query to then find a semantically appropriate music track. Moreover, the difference in granularity between audio/video and text can significantly hinder training. We design a tri-modal approach, dubbed ViML, for this task and introduce text dropout to address the granularity issue. In a similar manner to the way dropout prevents overfitting by reducing co-adaptation between individual neurons [36], text dropout serves to avoid overfitting to the text inputs and prevent co-adaptations between the video and text encoders. The approach is illustrated in Figure 3 and details of model architecture, loss, and text dropout are given next." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 689, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 547, + 715 + ], + "type": "text", + "content": "Model architecture. Our model is trained on a set of (video, music, text) pairings, " + }, + { + "bbox": [ + 305, + 689, + 547, + 715 + ], + "type": "inline_equation", + "content": "(v,m,t)" + }, + { + "bbox": [ + 305, + 689, + 547, + 715 + ], + "type": "text", + "content": ", corresponding to a" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "14787" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 52, + 70, + 291, + 190 + ], + "blocks": [ + { + "bbox": [ + 52, + 70, + 291, + 190 + ], + "lines": [ + { + "bbox": [ + 52, + 70, + 291, + 190 + ], + "spans": [ + { + "bbox": [ + 52, + 70, + 291, + 190 + ], + "type": "image", + "image_path": "8fca2012f333f4998b41c9df6d947c1aeffe76c1f6f663331b5364daf9f3d0ea.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 199, + 289, + 321 + ], + "lines": [ + { + "bbox": [ + 46, + 199, + 289, + 321 + ], + "spans": [ + { + "bbox": [ + 46, + 199, + 289, + 321 + ], + "type": "text", + "content": "Figure 3. Our proposed ViML model embeds inputs from three modalities (video, text, and audio) into an embedding space. We extract base features using DeepSim [20] for music input and from CLIP [33] for video frames and text descriptions. These base features are inputted to Transformer encoders for each modality. The video and text features are combined with a fusion module to enable querying of music in a shared embedding space. Finally, we employ text dropout to address the difference in granularity between the three modalities. Since video is a more complex input modality, text dropout forces an improved video representation by preventing co-adaptation of the video and text representations." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 350, + 287, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 350, + 287, + 434 + ], + "spans": [ + { + "bbox": [ + 46, + 350, + 287, + 434 + ], + "type": "text", + "content": "music video clip " + }, + { + "bbox": [ + 46, + 350, + 287, + 434 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 46, + 350, + 287, + 434 + ], + "type": "text", + "content": ", which has been labeled with a generated text description " + }, + { + "bbox": [ + 46, + 350, + 287, + 434 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 350, + 287, + 434 + ], + "type": "text", + "content": " of its music track " + }, + { + "bbox": [ + 46, + 350, + 287, + 434 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 350, + 287, + 434 + ], + "type": "text", + "content": ", as outlined in Section 3.1. We transform these inputs into base features " + }, + { + "bbox": [ + 46, + 350, + 287, + 434 + ], + "type": "inline_equation", + "content": "x^{v} = g^{v}(v)" + }, + { + "bbox": [ + 46, + 350, + 287, + 434 + ], + "type": "text", + "content": " for visual video features, " + }, + { + "bbox": [ + 46, + 350, + 287, + 434 + ], + "type": "inline_equation", + "content": "x^{m} = g^{m}(m)" + }, + { + "bbox": [ + 46, + 350, + 287, + 434 + ], + "type": "text", + "content": " for music features, and " + }, + { + "bbox": [ + 46, + 350, + 287, + 434 + ], + "type": "inline_equation", + "content": "x^{t} = g^{t}(t)" + }, + { + "bbox": [ + 46, + 350, + 287, + 434 + ], + "type": "text", + "content": " for text features using pretrained large-scale encoders " + }, + { + "bbox": [ + 46, + 350, + 287, + 434 + ], + "type": "inline_equation", + "content": "g^{v}, g^{m}" + }, + { + "bbox": [ + 46, + 350, + 287, + 434 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 350, + 287, + 434 + ], + "type": "inline_equation", + "content": "g^{t}" + }, + { + "bbox": [ + 46, + 350, + 287, + 434 + ], + "type": "text", + "content": " which are frozen during training." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 434, + 287, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 434, + 287, + 518 + ], + "spans": [ + { + "bbox": [ + 46, + 434, + 287, + 518 + ], + "type": "text", + "content": "Each base feature representation " + }, + { + "bbox": [ + 46, + 434, + 287, + 518 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 434, + 287, + 518 + ], + "type": "text", + "content": " is of dimension " + }, + { + "bbox": [ + 46, + 434, + 287, + 518 + ], + "type": "inline_equation", + "content": "n \\times d" + }, + { + "bbox": [ + 46, + 434, + 287, + 518 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 434, + 287, + 518 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 434, + 287, + 518 + ], + "type": "text", + "content": " is the length of the temporal sequence of base features representing a video clip and " + }, + { + "bbox": [ + 46, + 434, + 287, + 518 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 434, + 287, + 518 + ], + "type": "text", + "content": " is the dimension of the base feature. We note that while our model is capable of handling a sequence of temporal text descriptions similar to music or video, we obtain only a track-level text description in practice meaning that " + }, + { + "bbox": [ + 46, + 434, + 287, + 518 + ], + "type": "inline_equation", + "content": "n = 1" + }, + { + "bbox": [ + 46, + 434, + 287, + 518 + ], + "type": "text", + "content": " for text." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 518, + 287, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 518, + 287, + 602 + ], + "spans": [ + { + "bbox": [ + 46, + 518, + 287, + 602 + ], + "type": "text", + "content": "Our tri-modal model consists of three separate modules corresponding to each modality " + }, + { + "bbox": [ + 46, + 518, + 287, + 602 + ], + "type": "inline_equation", + "content": "f^v, f^m, f^t" + }, + { + "bbox": [ + 46, + 518, + 287, + 602 + ], + "type": "text", + "content": ", and a fourth fusion module " + }, + { + "bbox": [ + 46, + 518, + 287, + 602 + ], + "type": "inline_equation", + "content": "f^{vt}" + }, + { + "bbox": [ + 46, + 518, + 287, + 602 + ], + "type": "text", + "content": " to combine video and text representations. The modules take respective base features and output embeddings " + }, + { + "bbox": [ + 46, + 518, + 287, + 602 + ], + "type": "inline_equation", + "content": "y^v = f^v(x^v)" + }, + { + "bbox": [ + 46, + 518, + 287, + 602 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 518, + 287, + 602 + ], + "type": "inline_equation", + "content": "y^m = f^m(x^m)" + }, + { + "bbox": [ + 46, + 518, + 287, + 602 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 518, + 287, + 602 + ], + "type": "inline_equation", + "content": "y^t = f^t(x^t)" + }, + { + "bbox": [ + 46, + 518, + 287, + 602 + ], + "type": "text", + "content": ". The fusion model outputs a fused embedding from the video and text embeddings " + }, + { + "bbox": [ + 46, + 518, + 287, + 602 + ], + "type": "inline_equation", + "content": "y^{vt} = f^{vt}(y^v, y^t)" + }, + { + "bbox": [ + 46, + 518, + 287, + 602 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 607, + 287, + 631 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 607, + 287, + 631 + ], + "spans": [ + { + "bbox": [ + 47, + 607, + 287, + 631 + ], + "type": "text", + "content": "Fusion loss. For training, we use an InfoNCE loss [29] between music and fused video-text embeddings:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 63, + 639, + 287, + 669 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 639, + 287, + 669 + ], + "spans": [ + { + "bbox": [ + 63, + 639, + 287, + 669 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {v t \\rightarrow m} = - \\frac {1}{| \\mathcal {D} |} \\sum_ {i \\in \\mathcal {D}} \\frac {\\exp \\left(s \\left(y _ {i} ^ {v t} , y _ {i} ^ {m}\\right) / \\tau\\right)}{\\sum_ {j \\in \\mathcal {D}} \\exp \\left(s \\left(y _ {i} ^ {v t} , y _ {j} ^ {m}\\right) / \\tau\\right)} \\tag {1}", + "image_path": "b42480c2cf50fd3eaf0105148e821708fa823d5501974b26f73f4fd92c56511e.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 677, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 288, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 677, + 288, + 714 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 47, + 677, + 288, + 714 + ], + "type": "text", + "content": " is a similarity function, " + }, + { + "bbox": [ + 47, + 677, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 47, + 677, + 288, + 714 + ], + "type": "text", + "content": " is a batch of data, and " + }, + { + "bbox": [ + 47, + 677, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 47, + 677, + 288, + 714 + ], + "type": "text", + "content": " is a temperature hyperparameter we set as " + }, + { + "bbox": [ + 47, + 677, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\tau = 0.03" + }, + { + "bbox": [ + 47, + 677, + 288, + 714 + ], + "type": "text", + "content": ". For our similarity metric, we use the cosine similarity defined as" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 72, + 545, + 121 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 121 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 121 + ], + "type": "inline_equation", + "content": "s(x,y) = x^{T}y / (\\| x\\| \\cdot \\| y\\|)" + }, + { + "bbox": [ + 305, + 72, + 545, + 121 + ], + "type": "text", + "content": ". We note that the loss " + }, + { + "bbox": [ + 305, + 72, + 545, + 121 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{vt\\to m}" + }, + { + "bbox": [ + 305, + 72, + 545, + 121 + ], + "type": "text", + "content": " is not symmetric as negatives are sampled from music embeddings only. So that our loss is symmetric, we instead train with the summed loss " + }, + { + "bbox": [ + 305, + 72, + 545, + 121 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{m,vt} = \\mathcal{L}_{vt\\to m} + \\mathcal{L}_{m\\to vt}" + }, + { + "bbox": [ + 305, + 72, + 545, + 121 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 131, + 545, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 131, + 545, + 263 + ], + "spans": [ + { + "bbox": [ + 304, + 131, + 545, + 263 + ], + "type": "text", + "content": "Text dropout. To address difficulties posed by the difference in granularity between audio/video and text, we introduce text dropout as a regularization mechanism. With probability " + }, + { + "bbox": [ + 304, + 131, + 545, + 263 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 304, + 131, + 545, + 263 + ], + "type": "text", + "content": ", we set the input text embedding " + }, + { + "bbox": [ + 304, + 131, + 545, + 263 + ], + "type": "inline_equation", + "content": "x^{t}" + }, + { + "bbox": [ + 304, + 131, + 545, + 263 + ], + "type": "text", + "content": " to a specific value " + }, + { + "bbox": [ + 304, + 131, + 545, + 263 + ], + "type": "inline_equation", + "content": "x^{\\mathrm{NULL}}" + }, + { + "bbox": [ + 304, + 131, + 545, + 263 + ], + "type": "text", + "content": ". In practice, we assign this " + }, + { + "bbox": [ + 304, + 131, + 545, + 263 + ], + "type": "inline_equation", + "content": "x^{\\mathrm{NULL}}" + }, + { + "bbox": [ + 304, + 131, + 545, + 263 + ], + "type": "text", + "content": " input as the embedding produced by the pretrained " + }, + { + "bbox": [ + 304, + 131, + 545, + 263 + ], + "type": "inline_equation", + "content": "g^{t}" + }, + { + "bbox": [ + 304, + 131, + 545, + 263 + ], + "type": "text", + "content": " model for an empty string. However, using a zero vector as " + }, + { + "bbox": [ + 304, + 131, + 545, + 263 + ], + "type": "inline_equation", + "content": "x^{\\mathrm{NULL}}" + }, + { + "bbox": [ + 304, + 131, + 545, + 263 + ], + "type": "text", + "content": " works similarly. In addition to improving the performance of music retrieval from text and video together, training with text dropout yields a model which also performs well at retrieval from video alone by removing dependence on text inputs." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 289, + 440, + 301 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 289, + 440, + 301 + ], + "spans": [ + { + "bbox": [ + 306, + 289, + 440, + 301 + ], + "type": "text", + "content": "3.3. Implementation Details" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 313, + 545, + 433 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 313, + 545, + 433 + ], + "spans": [ + { + "bbox": [ + 304, + 313, + 545, + 433 + ], + "type": "text", + "content": "Music tag generation. The key first step to our text generation process is obtaining the structured data describing each musical track. To do this, we use a music tagger trained on a dataset of music tracks manually annotated with a fixed predefined vocabulary of tags [20, 21]. Specifically, the tagger predicts confidence for 41 instrument tags, 20 genre tags, and 28 mood tags. We aggregate these predictions at the clip or track level, and we filter the subsequent set based on confidence, keeping only those above a particular threshold (0.3 in our experiments)." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 444, + 545, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 444, + 545, + 563 + ], + "spans": [ + { + "bbox": [ + 304, + 444, + 545, + 563 + ], + "type": "text", + "content": "ViML Model. Following MVPt [37], we employ the Transformer architecture [38] for our music and video encoders " + }, + { + "bbox": [ + 304, + 444, + 545, + 563 + ], + "type": "inline_equation", + "content": "f^{m}" + }, + { + "bbox": [ + 304, + 444, + 545, + 563 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 444, + 545, + 563 + ], + "type": "inline_equation", + "content": "f^{v}" + }, + { + "bbox": [ + 304, + 444, + 545, + 563 + ], + "type": "text", + "content": ". Transformers play a key role in improving model performance by encoding long-term context from video and music clips. We also use a similar two-layer Transformer architecture for our text encoder " + }, + { + "bbox": [ + 304, + 444, + 545, + 563 + ], + "type": "inline_equation", + "content": "f^{t}" + }, + { + "bbox": [ + 304, + 444, + 545, + 563 + ], + "type": "text", + "content": " and the video-text fusion layer " + }, + { + "bbox": [ + 304, + 444, + 545, + 563 + ], + "type": "inline_equation", + "content": "f^{vt}" + }, + { + "bbox": [ + 304, + 444, + 545, + 563 + ], + "type": "text", + "content": ". However, we find that other fusion module architectures such as a single linear layer yield similar results. Please see our supplemental for study of fusion module architectures." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": "For base features, we use CLIP [33] to encode representations for video frames and text inputs, and DeepSim [20] to encode music. Following communication with the authors of [37], we split the video into 10-second segments and compute a feature for each segment by averaging CLIP embedding features computed at 6 frames per second. We compute 512 dimensional CLIP embedding features using OpenAI's CLIP ViT-B/32 model. We encode all input base features into embeddings of size " + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "inline_equation", + "content": "d = 256" + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": " using a linear projection layer for each modality. We also select " + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "inline_equation", + "content": "d = 256" + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": " as the output dimension for encoded video, text, music, and fused video-text representations from our model." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14788" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 71, + 144, + 119 + ], + "blocks": [ + { + "bbox": [ + 53, + 71, + 144, + 119 + ], + "lines": [ + { + "bbox": [ + 53, + 71, + 144, + 119 + ], + "spans": [ + { + "bbox": [ + 53, + 71, + 144, + 119 + ], + "type": "image", + "image_path": "26d34da65764ee63c650328268a9966d651ee8ffb33498e7dd84ba2e5e3e95f9.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 121, + 144, + 187 + ], + "lines": [ + { + "bbox": [ + 47, + 121, + 144, + 187 + ], + "spans": [ + { + "bbox": [ + 47, + 121, + 144, + 187 + ], + "type": "text", + "content": "A faint, simple acoustic piece of singing by a female vocalist with an acoustic guitar with a fast-paced strumming pattern in a closed room recorded live. great for singing along." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 153, + 72, + 244, + 119 + ], + "blocks": [ + { + "bbox": [ + 153, + 72, + 244, + 119 + ], + "lines": [ + { + "bbox": [ + 153, + 72, + 244, + 119 + ], + "spans": [ + { + "bbox": [ + 153, + 72, + 244, + 119 + ], + "type": "image", + "image_path": "a44e8944cdd14fd98ef12e71036428c04340efaaacd782a2e0c0939cedf4eb87.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 148, + 121, + 244, + 159 + ], + "lines": [ + { + "bbox": [ + 148, + 121, + 244, + 159 + ], + "spans": [ + { + "bbox": [ + 148, + 121, + 244, + 159 + ], + "type": "text", + "content": "Hip-hop track with a dark synth pad with male aggressive rapping along with a chipmunk voice." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 253, + 71, + 343, + 118 + ], + "blocks": [ + { + "bbox": [ + 253, + 71, + 343, + 118 + ], + "lines": [ + { + "bbox": [ + 253, + 71, + 343, + 118 + ], + "spans": [ + { + "bbox": [ + 253, + 71, + 343, + 118 + ], + "type": "image", + "image_path": "90785c2cd564d647b1e9203f9e3b776c7923cdd50386a5385cae3531e8a0c6fb.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 247, + 121, + 343, + 158 + ], + "lines": [ + { + "bbox": [ + 247, + 121, + 343, + 158 + ], + "spans": [ + { + "bbox": [ + 247, + 121, + 343, + 158 + ], + "type": "text", + "content": "Instrumental track featuring an ambient pad and bell-like sounds. Seems to be a film score." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 352, + 71, + 443, + 118 + ], + "blocks": [ + { + "bbox": [ + 352, + 71, + 443, + 118 + ], + "lines": [ + { + "bbox": [ + 352, + 71, + 443, + 118 + ], + "spans": [ + { + "bbox": [ + 352, + 71, + 443, + 118 + ], + "type": "image", + "image_path": "708cbc86d95aa369ecd3b5f8487ca12b1c8b721f113494d73d9c29dbf7a92e8d.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 347, + 121, + 443, + 167 + ], + "lines": [ + { + "bbox": [ + 347, + 121, + 443, + 167 + ], + "spans": [ + { + "bbox": [ + 347, + 121, + 443, + 167 + ], + "type": "text", + "content": "A cover version of Elvis Presley's pop song featuring male and female vocals and piano layers. Sounds like a confession in love." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 450, + 72, + 542, + 119 + ], + "blocks": [ + { + "bbox": [ + 450, + 72, + 542, + 119 + ], + "lines": [ + { + "bbox": [ + 450, + 72, + 542, + 119 + ], + "spans": [ + { + "bbox": [ + 450, + 72, + 542, + 119 + ], + "type": "image", + "image_path": "39adebe7b99f06214b14ae190f04f74fd45a09ed4e29209785f8cf2317608765.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 446, + 121, + 542, + 167 + ], + "lines": [ + { + "bbox": [ + 446, + 121, + 542, + 167 + ], + "spans": [ + { + "bbox": [ + 446, + 121, + 542, + 167 + ], + "type": "text", + "content": "Punjabi track with multiple vocals and other instruments that's great for traditional marriage celebrations." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 197, + 547, + 242 + ], + "lines": [ + { + "bbox": [ + 46, + 197, + 547, + 242 + ], + "spans": [ + { + "bbox": [ + 46, + 197, + 547, + 242 + ], + "type": "text", + "content": "Figure 4. Example annotations from our collected YouTube8M-MusicTextClips dataset. Each example shows a frame from the 10sec source video clip from which audio was extracted for annotation. Note that annotators were only provided audio from the music video, so the annotation describes the music, but not the corresponding video. Each example in the figure contains a hyperlink to the corresponding YT8M source video with timestamp at the start of the 10sec target clip. Hover over the video frame image and click to follow the link." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 261, + 128, + 274 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 261, + 128, + 274 + ], + "spans": [ + { + "bbox": [ + 47, + 261, + 128, + 274 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 282, + 287, + 378 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 282, + 287, + 378 + ], + "spans": [ + { + "bbox": [ + 46, + 282, + 287, + 378 + ], + "type": "text", + "content": "In this section, we report our experimental settings and results. First, we describe our datasets and the evaluation protocol in Sec. 4.1. Next, we investigate tag-based video-to-music retrieval, comparing against state-of-the-art video-to-music retrieval methods in Sec. 4.2. In Sec. 4.3, we evaluate performance of video-to-music retrieval guided by free-form text annotations. Finally, we perform ablation studies to measure the influence of text dropout in Sec. 4.4." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 388, + 226, + 400 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 388, + 226, + 400 + ], + "spans": [ + { + "bbox": [ + 47, + 388, + 226, + 400 + ], + "type": "text", + "content": "4.1. Datasets and Evaluation Protocol" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 408, + 287, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 408, + 287, + 504 + ], + "spans": [ + { + "bbox": [ + 46, + 408, + 287, + 504 + ], + "type": "text", + "content": "YT8M-MusicVideo. In all of our experiments, we train models using the YT8M-MusicVideo dataset which includes around 100k videos with the \"music video\" tag from the much larger YouTube8M dataset [1]. We synthesize tags and a natural language text describing the music track of each video for the full dataset using the approaches described in Sec. 3.1. We also use the test split of YT8M-MusicVideo to evaluate tag-based retrieval in Sec. 4.2." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 510, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 288, + 714 + ], + "type": "text", + "content": "YT8M-MusicTextClips. In addition to the full YT8M-MusicVideo dataset, we also annotate a 4,000 sample subset of clips from YT8M-MusicVideo with human-provided text descriptions of the music track accompanying each video. To create these annotations, we sample 10 second audio clips from the middle of each music video, and we ask human annotators to describe the music they hear after listening to the audio clip. Thus, an annotation describes only the music from a YT8M sample, and the annotators do not see the corresponding video. Example annotations are shown in Figure 4 with links to the starting timestamp of the 10sec clips in corresponding YouTube videos. This annotated set is meant mainly for evaluation. As a result, the annotations are split into a larger set of 3,000 samples from the test set of YT8M-MusicVideo and a smaller set of 1,000 samples from the train set of YT8M-MusicVideo which we use as examples in the few-shot prompt2text synthesis process. We" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 262, + 545, + 285 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 262, + 545, + 285 + ], + "spans": [ + { + "bbox": [ + 305, + 262, + 545, + 285 + ], + "type": "text", + "content": "make the annotated text descriptions publicly available at our companion website2." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 291, + 546, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 291, + 546, + 483 + ], + "spans": [ + { + "bbox": [ + 304, + 291, + 546, + 483 + ], + "type": "text", + "content": "Evaluation Set-up and Metrics. We evaluate music retrieval performance consistently with previous works [32, 37]. However, in our case, a query can be either a video alone or a video and corresponding text annotation together. For each query, we compute feature similarity between the query and a pool of N music tracks (we set " + }, + { + "bbox": [ + 304, + 291, + 546, + 483 + ], + "type": "inline_equation", + "content": "\\mathrm{N} = 2000" + }, + { + "bbox": [ + 304, + 291, + 546, + 483 + ], + "type": "text", + "content": " in the track-level setting and " + }, + { + "bbox": [ + 304, + 291, + 546, + 483 + ], + "type": "inline_equation", + "content": "\\mathrm{N} = 500" + }, + { + "bbox": [ + 304, + 291, + 546, + 483 + ], + "type": "text", + "content": " for evaluation on clips). The pool contains a single ground truth music track corresponding to the input query (the positive example) with the remaining music tracks in the pool being non-matching (i.e., negative examples). We rank the music tracks in a query's pool by feature similarity, and find the rank of the query's ground truth matching music track (the positive example). We then compute Recall@K (shortened to R@K) for " + }, + { + "bbox": [ + 304, + 291, + 546, + 483 + ], + "type": "inline_equation", + "content": "\\mathrm{K} = 1,5,10" + }, + { + "bbox": [ + 304, + 291, + 546, + 483 + ], + "type": "text", + "content": " and Median Rank, calculating the average of each of these metrics across the full set of test queries." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 489, + 423, + 502 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 489, + 423, + 502 + ], + "spans": [ + { + "bbox": [ + 306, + 489, + 423, + 502 + ], + "type": "text", + "content": "4.2. Tag-Based Retrieval" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 507, + 547, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 507, + 547, + 687 + ], + "spans": [ + { + "bbox": [ + 304, + 507, + 547, + 687 + ], + "type": "text", + "content": "For our first set of experiments, we explore the setting of tag-based retrieval. Here the goal is to retrieve a music track given a query video together with a set of tags from a predefined vocabulary, such as \"happy\", \"piano\" and \"jazz\". This setting could be practically interesting in some applications, e.g., tag-based search. To address this setting, we train our model on text synthesized with the tags approach. In these experiments, we train a track-level model and perform retrieval on a track-level in a manner consistent with prior work [32, 37]. To directly compare results with prior work, we perform retrieval on the full YT8M test set consisting of around 10K samples. As shown in Table 1, we include three baselines: the model proposed by Pretét et al. [32], the MVPt model [37], and an improved version of MVPt that we call MVPt+, where we tune the temperature" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 306, + 693, + 545, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 693, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 306, + 693, + 545, + 712 + ], + "type": "text", + "content": "2https://www.danielbmckee.com/language-guided-music-for-video/index.html" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14789" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 86, + 70, + 509, + 173 + ], + "blocks": [ + { + "bbox": [ + 86, + 70, + 509, + 173 + ], + "lines": [ + { + "bbox": [ + 86, + 70, + 509, + 173 + ], + "spans": [ + { + "bbox": [ + 86, + 70, + 509, + 173 + ], + "type": "table", + "html": "
MethodTrain TextQuery Text InputMedian Rank ↓R@1 ↑R@5 ↑R@10 ↑
a. Pretét et al. [32]--2340.763.425.90
b. MVPt [37]--136.0924.9141.89
c. MVPt+ [37]--527.9350.6460.68
d. ViML (ours)tags-329.4362.4975.40
e. ViML (ours)tagstags249.4981.6189.41
f. Chance10000.050.250.50
", + "image_path": "1fd3809481d1a1722c55004f6590aecf19d6cf56ee8ead66f782fcd7c513d3b3.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 53, + 232, + 279, + 306 + ], + "blocks": [ + { + "bbox": [ + 46, + 180, + 547, + 215 + ], + "lines": [ + { + "bbox": [ + 46, + 180, + 547, + 215 + ], + "spans": [ + { + "bbox": [ + 46, + 180, + 547, + 215 + ], + "type": "text", + "content": "Table 1. Tag-based music retrieval on full YouTube8M-MusicVideo test set. We compare ViML against prior methods on video to music retrieval without tag queries (row d.). We also evaluate ViML on video+text to music retrieval using (synthetic) tags at test time (row e.). The text descriptions for both training and evaluation are generated with the tags approach for these experiments." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 53, + 232, + 279, + 306 + ], + "lines": [ + { + "bbox": [ + 53, + 232, + 279, + 306 + ], + "spans": [ + { + "bbox": [ + 53, + 232, + 279, + 306 + ], + "type": "table", + "html": "
MethodTrain TextMR ↓R@1 ↑R@5 ↑R@10 ↑
a. MVPt+-1712.2029.4340.46
b. ViMLtags1511.9530.3442.62
c. ViMLdata2text1313.6133.9446.24
d. ViMLprompt2text1214.0935.0447.88
Chance2500.201.002.00
", + "image_path": "08aa241214cbace9e509410f6c70d9032d4277089a5edd16bd5f96b6850cbebd.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 314, + 288, + 380 + ], + "lines": [ + { + "bbox": [ + 46, + 314, + 288, + 380 + ], + "spans": [ + { + "bbox": [ + 46, + 314, + 288, + 380 + ], + "type": "text", + "content": "Table 2. Music retrieval with free-form natural language on YT8M-MusicTextClips test set. All methods which take text input are evaluated on the human text annotations as queries. Since the " + }, + { + "bbox": [ + 46, + 314, + 288, + 380 + ], + "type": "inline_equation", + "content": "\\mathrm{MVPt + }" + }, + { + "bbox": [ + 46, + 314, + 288, + 380 + ], + "type": "text", + "content": " model does not take text inputs, it is evaluated on music retrieval from video alone for the same set of 3k video clips. MR is median rank." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 402, + 287, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 402, + 287, + 426 + ], + "spans": [ + { + "bbox": [ + 46, + 402, + 287, + 426 + ], + "type": "text", + "content": "parameter " + }, + { + "bbox": [ + 46, + 402, + 287, + 426 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 46, + 402, + 287, + 426 + ], + "type": "text", + "content": " in the InfoNCE loss to 0.03. This change leads to further significant improvement in performance." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 426, + 287, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 426, + 287, + 629 + ], + "spans": [ + { + "bbox": [ + 46, + 426, + 287, + 629 + ], + "type": "text", + "content": "Next, we introduce our model (ViML) trained on data generated from the tags approach. We evaluate our ViML model in two settings. First, we evaluate without input texts at test time (an empty text input is used instead). Second, we evaluate with text inputs at test time. As we do not have track-level human-provided music tag annotations for the full YT8M MusicVideo split, we evaluate the track-level model on synthetically generated tags using our tags approach. While a model trained on the tags synthesized data may not generalize to out-of-domain free-form text inputs, the tag-based prompting can be a convenient way to guide music retrieval with key desired attributes (for example \"female vocalist, guitar, happy\"). The tag-based retrieval we report can serve as an upper bound for this type of user tag-guided retrieval since the tag-based text for testing comes from the same music tagger model we used to synthesize training data." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 630, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 287, + 715 + ], + "type": "text", + "content": "Evaluating our model with synthetic tags leads to a very substantial performance increase over " + }, + { + "bbox": [ + 46, + 630, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathrm{MVPt + }" + }, + { + "bbox": [ + 46, + 630, + 287, + 715 + ], + "type": "text", + "content": " of 20-30 points in each recall metric. Interestingly, our ViML model evaluated without text at test time not only matches the video-to-music retrieval performance of " + }, + { + "bbox": [ + 46, + 630, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathrm{MVT + }" + }, + { + "bbox": [ + 46, + 630, + 287, + 715 + ], + "type": "text", + "content": " but substantially improves over " + }, + { + "bbox": [ + 46, + 630, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathrm{MVPt + }" + }, + { + "bbox": [ + 46, + 630, + 287, + 715 + ], + "type": "text", + "content": ", especially in Recall@5 and Recall@10. This performance increase is not simply" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 235, + 547, + 368 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 235, + 547, + 368 + ], + "spans": [ + { + "bbox": [ + 304, + 235, + 547, + 368 + ], + "type": "text", + "content": "a result of added parameters in the fusion layer, as a fusion module consisting of only a single linear layer yields similar results (see our supplemental for further details). This result suggests that training jointly with the text domain can lead to improvements in the video and audio representations. We hypothesize that the joint training with language helps to disentangle the video-audio space into semantically meaningful dimensions corresponding to the provided tags as well as helps to suppress non-relevant dimensions, e.g., corresponding to presence/absence of some non-relevant objects." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 372, + 515, + 385 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 372, + 515, + 385 + ], + "spans": [ + { + "bbox": [ + 305, + 372, + 515, + 385 + ], + "type": "text", + "content": "4.3. Free-Form Natural Language Retrieval" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 391, + 547, + 475 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 391, + 547, + 475 + ], + "spans": [ + { + "bbox": [ + 304, + 391, + 547, + 475 + ], + "type": "text", + "content": "For the next experiments, we turn to retrieval with free-form natural language inputs. The goal is, given an input video and a query free-form natural language description, to retrieve a relevant music track. For this setting, we evaluate on testing videos from the YT8M-MusicTextClips dataset which contains free-form human text annotations describing the music corresponding to each video in the dataset." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 475, + 547, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 475, + 547, + 605 + ], + "spans": [ + { + "bbox": [ + 304, + 475, + 547, + 605 + ], + "type": "text", + "content": "In these experiments, we use a similar protocol to the \"segment-level\" setting reported by Surís et al. [37], but our input video includes only a 30sec clip surrounding the 10sec of audio labeled by a human annotator. In contrast, a model had access to a large context spanning the full source video in the previous segment-level setting reported by Surís et al. [37]. We note that retrieval in this setting is significantly more difficult than the segment-level setting in [37] or the track-level setting reported in 4.2 due to the limited context. However, such retrieval is of particular interest given the rise of short-form video in social media and entertainment." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 606, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 606, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 606, + 547, + 715 + ], + "type": "text", + "content": "Results are summarized in Table 2. Our baseline is an " + }, + { + "bbox": [ + 304, + 606, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathrm{MVPt + }" + }, + { + "bbox": [ + 304, + 606, + 547, + 715 + ], + "type": "text", + "content": " model which has been trained on 30sec segments (training " + }, + { + "bbox": [ + 304, + 606, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathrm{MVPt + }" + }, + { + "bbox": [ + 304, + 606, + 547, + 715 + ], + "type": "text", + "content": " on full videos and testing on 30sec clips causes a much more severe drop in performance). We next report music retrieval using video and free-form human text descriptions as input queries to our ViML model. In Table 2, we report three variants trained on YT8M music videos with text synthesized by each of the three approaches described in Sec. 3.1. The model trained with our first tags syn" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "14790" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 73, + 70, + 520, + 160 + ], + "blocks": [ + { + "bbox": [ + 73, + 70, + 520, + 160 + ], + "lines": [ + { + "bbox": [ + 73, + 70, + 520, + 160 + ], + "spans": [ + { + "bbox": [ + 73, + 70, + 520, + 160 + ], + "type": "table", + "html": "
MethodTrain TextDropoutText InputsMedian Rank ↓R@1 ↑R@5 ↑R@10 ↑
a. MVPt+---1712.2029.4340.46
b. MVT-Fuseprompt2textX-209.9426.4237.01
c. MVT-Fuseprompt2textXhuman1511.4530.4542.77
d. MVT-Fuseprompt2text✓-1612.2730.3441.51
e. MVT-Fuseprompt2text✓human1214.0935.0447.88
", + "image_path": "988d3d13ac6d255be374ff5603600f5b1066672ddda85cf30ea9122b12542c1f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 66, + 168, + 526, + 179 + ], + "lines": [ + { + "bbox": [ + 66, + 168, + 526, + 179 + ], + "spans": [ + { + "bbox": [ + 66, + 168, + 526, + 179 + ], + "type": "text", + "content": "Table 3. Influence of training with text dropout on retrieval performance. Evaluated on the YT8M-MusicTextClips test set." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 201, + 287, + 308 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 201, + 287, + 308 + ], + "spans": [ + { + "bbox": [ + 46, + 201, + 287, + 308 + ], + "type": "text", + "content": "thesis baseline (b.) provides substantial improvement over retrieval with MVPt+ using only video (a.). Next, we evaluate the data2text approach (c.) which generates more natural phrases while strictly preserving tag semantics. This approach provides a consistent improvement over the ViML tags variant (b.). Finally, our prompt2text approach (d.) leads to the best performance showing that large language models prove to be strong annotators on this task with careful few-shot prompting." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 308, + 287, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 308, + 287, + 403 + ], + "spans": [ + { + "bbox": [ + 46, + 308, + 287, + 403 + ], + "type": "text", + "content": "Qualitative results. In Figure 5, we provide qualitative retrieval results for examples in YouTube8M-MusicTextClips. In the first example, both models retrieve tracks that match the style and beat of the input video well. However, only the ViML can match the correct musical style by using the input text. In the second example, only the ViML result correctly matches the desired music genre and the mood of the video." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 412, + 186, + 425 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 412, + 186, + 425 + ], + "spans": [ + { + "bbox": [ + 47, + 412, + 186, + 425 + ], + "type": "text", + "content": "4.4. Analysis of Text Dropout" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 430, + 287, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 430, + 287, + 658 + ], + "spans": [ + { + "bbox": [ + 46, + 430, + 287, + 658 + ], + "type": "text", + "content": "In Table 3, we compare the performance of our ViML model trained on prompt2text descriptions with and without text dropout. We evaluate this model on music retrieval in two settings: (i) using only video (inputting empty text, rows b. and d.) as a query and (ii) using both video and human text descriptions together as a query (rows c. and e.). As expected, adding text dropout during training (d.) improves the performance of retrieval using only video (b.). However, interestingly, text dropout also substantially improves performance when the query includes natural language (e. vs. c.), suggesting that text dropout is a very useful regularization technique in the multimodal setting. We find that without text dropout, training begins to plateau early as the model starts overfitting to the training text inputs. Since video is a much richer and more complex modality, forcing more attention to this modality during training improves learning. We find that the dropout technique is most effective at high rates of dropout in the range 0.8-0.95, and we use a dropout rate of 0.8 in all of our experiments." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 669, + 119, + 681 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 669, + 119, + 681 + ], + "spans": [ + { + "bbox": [ + 47, + 669, + 119, + 681 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "In this work, we introduced an approach to allow language-guided music recommendation for video. We pro" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 323, + 233, + 390, + 272 + ], + "blocks": [ + { + "bbox": [ + 310, + 203, + 396, + 214 + ], + "lines": [ + { + "bbox": [ + 310, + 203, + 396, + 214 + ], + "spans": [ + { + "bbox": [ + 310, + 203, + 396, + 214 + ], + "type": "text", + "content": "Video+Language Query" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 323, + 233, + 390, + 272 + ], + "lines": [ + { + "bbox": [ + 323, + 233, + 390, + 272 + ], + "spans": [ + { + "bbox": [ + 323, + 233, + 390, + 272 + ], + "type": "image", + "image_path": "a42e9433edd4f88644cf28bd04206e9bdc09b63631896fc451fcdf26405c6ddf.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 274, + 394, + 304 + ], + "lines": [ + { + "bbox": [ + 313, + 274, + 394, + 304 + ], + "spans": [ + { + "bbox": [ + 313, + 274, + 394, + 304 + ], + "type": "text", + "content": "Electronic dance pop track that has male vocals and a pulsating rhythm. Best for nightclubs." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_footnote" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 414, + 236, + 440, + 253 + ], + "blocks": [ + { + "bbox": [ + 446, + 205, + 504, + 213 + ], + "lines": [ + { + "bbox": [ + 446, + 205, + 504, + 213 + ], + "spans": [ + { + "bbox": [ + 446, + 205, + 504, + 213 + ], + "type": "text", + "content": "Retrieved Music" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 427, + 217, + 451, + 224 + ], + "lines": [ + { + "bbox": [ + 427, + 217, + 451, + 224 + ], + "spans": [ + { + "bbox": [ + 427, + 217, + 451, + 224 + ], + "type": "text", + "content": "MVPt+" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_footnote" + }, + { + "bbox": [ + 414, + 236, + 440, + 253 + ], + "lines": [ + { + "bbox": [ + 414, + 236, + 440, + 253 + ], + "spans": [ + { + "bbox": [ + 414, + 236, + 440, + 253 + ], + "type": "image", + "image_path": "be85c7822299996c12fffff5fdce48f650f520de0a97d303f9cd2fb9e452bf01.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 486, + 236, + 512, + 252 + ], + "blocks": [ + { + "bbox": [ + 501, + 217, + 520, + 224 + ], + "lines": [ + { + "bbox": [ + 501, + 217, + 520, + 224 + ], + "spans": [ + { + "bbox": [ + 501, + 217, + 520, + 224 + ], + "type": "text", + "content": "ViML" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_footnote" + }, + { + "bbox": [ + 410, + 261, + 472, + 297 + ], + "lines": [ + { + "bbox": [ + 410, + 261, + 472, + 297 + ], + "spans": [ + { + "bbox": [ + 410, + 261, + 472, + 297 + ], + "type": "text", + "content": "Percussive Latin music with a male vocalist, synth line, and Cumbia beat aligned with video." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_footnote" + }, + { + "bbox": [ + 486, + 236, + 512, + 252 + ], + "lines": [ + { + "bbox": [ + 486, + 236, + 512, + 252 + ], + "spans": [ + { + "bbox": [ + 486, + 236, + 512, + 252 + ], + "type": "image", + "image_path": "261b27073dfa5642a1c3ede328d58644cdde152942df7c76ebfe1b203fd9d996.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 321, + 317, + 388, + 356 + ], + "blocks": [ + { + "bbox": [ + 321, + 317, + 388, + 356 + ], + "lines": [ + { + "bbox": [ + 321, + 317, + 388, + 356 + ], + "spans": [ + { + "bbox": [ + 321, + 317, + 388, + 356 + ], + "type": "image", + "image_path": "bcb8781ae7de8317048b3da2bc962b9945d7c9224bffcaba165ac220e6454d89.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 359, + 397, + 388 + ], + "lines": [ + { + "bbox": [ + 313, + 359, + 397, + 388 + ], + "spans": [ + { + "bbox": [ + 313, + 359, + 397, + 388 + ], + "type": "text", + "content": "Male rap song in a foreign language with hip-hop beats and electronic music that gives a freestyle vibe to it." + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_footnote" + }, + { + "bbox": [ + 304, + 403, + 545, + 502 + ], + "lines": [ + { + "bbox": [ + 304, + 403, + 545, + 502 + ], + "spans": [ + { + "bbox": [ + 304, + 403, + 545, + 502 + ], + "type": "text", + "content": "Figure 5. Qualitative results on YouTube8M-MusicTextClips test set. We compare music retrieval quality for two examples using the " + }, + { + "bbox": [ + 304, + 403, + 545, + 502 + ], + "type": "inline_equation", + "content": "\\mathrm{MVPt + }" + }, + { + "bbox": [ + 304, + 403, + 545, + 502 + ], + "type": "text", + "content": " model and our ViML model. The column on the left includes a frame from the input video and the input text description describing the target music. The " + }, + { + "bbox": [ + 304, + 403, + 545, + 502 + ], + "type": "inline_equation", + "content": "\\mathrm{MVPt + }" + }, + { + "bbox": [ + 304, + 403, + 545, + 502 + ], + "type": "text", + "content": " model takes only the video as an input while the ViML model takes both video and corresponding text. The two columns on the right contain retrieved music for " + }, + { + "bbox": [ + 304, + 403, + 545, + 502 + ], + "type": "inline_equation", + "content": "\\mathrm{MVPt + }" + }, + { + "bbox": [ + 304, + 403, + 545, + 502 + ], + "type": "text", + "content": " and ViML respectively. Please see results in the companion video on our website." + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "image_caption" + } + ], + "index": 18 + }, + { + "type": "image", + "bbox": [ + 414, + 323, + 440, + 340 + ], + "blocks": [ + { + "bbox": [ + 414, + 323, + 440, + 340 + ], + "lines": [ + { + "bbox": [ + 414, + 323, + 440, + 340 + ], + "spans": [ + { + "bbox": [ + 414, + 323, + 440, + 340 + ], + "type": "image", + "image_path": "af413976f812c87bdc2cd1103714c9b174da864d2f1191c3c20591c73fc31147.jpg" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 409, + 350, + 470, + 379 + ], + "lines": [ + { + "bbox": [ + 409, + 350, + 470, + 379 + ], + "spans": [ + { + "bbox": [ + 409, + 350, + 470, + 379 + ], + "type": "text", + "content": "Upbeat jazzy melody played on a saxophone over rhythmic electronic bass beats." + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_footnote" + } + ], + "index": 20 + }, + { + "type": "image", + "bbox": [ + 486, + 323, + 512, + 340 + ], + "blocks": [ + { + "bbox": [ + 480, + 261, + 539, + 298 + ], + "lines": [ + { + "bbox": [ + 480, + 261, + 539, + 298 + ], + "spans": [ + { + "bbox": [ + 480, + 261, + 539, + 298 + ], + "type": "text", + "content": "Energetic electronic party song with male vocals over rising synth layers and claps aligned with video." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_footnote" + }, + { + "bbox": [ + 486, + 323, + 512, + 340 + ], + "lines": [ + { + "bbox": [ + 486, + 323, + 512, + 340 + ], + "spans": [ + { + "bbox": [ + 486, + 323, + 512, + 340 + ], + "type": "image", + "image_path": "17736ab6a375ecbd561282ed5e457386c467a7dc539312db5babb89410490356.jpg" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 481, + 350, + 541, + 380 + ], + "lines": [ + { + "bbox": [ + 481, + 350, + 541, + 380 + ], + "spans": [ + { + "bbox": [ + 481, + 350, + 541, + 380 + ], + "type": "text", + "content": "French rap song with processed male vocals, thumping drum beats, and synth pad effects." + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_footnote" + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 533, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 545, + 712 + ], + "type": "text", + "content": "posed a model, ViML, which fuses text and video inputs to find music matching both domains and introduced the text dropout technique to improve training. To obtain data for training, we proposed a free-form music description synthesis approach using a large language model (BLOOM-176B) and outputs from a pretrained music tagger. Our results show that large language models provide a powerful tool for training data synthesis in domains where text data is limited but other structured data is available. To evaluate our method, we also introduced a new dataset, YouTube8M-MusicTextClips, which includes high quality free-form human descriptions of the music in YT8M videos. There are many exciting directions to build upon this work including allowing more fine-grained control over specific music attributes or language-guided audio-video generation." + } + ] + } + ], + "index": 25 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14791" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 712 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 146 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 146 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 146 + ], + "type": "text", + "content": "[1] Sami Abu-El-Haija, Nisarg Kothari, Joonseok Lee, Paul Natsev, George Toderici, Balakrishnan Varadarajan, and Sudheendra Vijayanarasimhan. 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IEEE, 2018. 2" + } + ] + } + ], + "index": 24 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14793" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Large-Capacity and Flexible Video Steganography via Invertible Neural Network/e548c867-6b1a-4988-b551-f9862e60583c_content_list.json b/2023/Large-Capacity and Flexible Video Steganography via Invertible Neural Network/e548c867-6b1a-4988-b551-f9862e60583c_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..666ca384d6ba1e7770aa5d2cf907540cde1bd4a3 --- /dev/null +++ b/2023/Large-Capacity and Flexible Video Steganography via Invertible Neural Network/e548c867-6b1a-4988-b551-f9862e60583c_content_list.json @@ -0,0 +1,1738 @@ +[ + { + "type": "text", + "text": "Large-capacity and Flexible Video Steganography via Invertible Neural Network", + "text_level": 1, + "bbox": [ + 78, + 130, + 890, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Chong Mou1, Youmin Xu1, Jiechong Song1, Chen Zhao2, Bernard Ghanem2, Jian Zhang1,3,*", + "bbox": [ + 119, + 179, + 846, + 199 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1Peking University Shenzhen Graduate School, Shenzhen, China", + "bbox": [ + 228, + 198, + 740, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{2}$ King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia", + "bbox": [ + 135, + 215, + 833, + 232 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{3}$ Peng Cheng Laboratory, Shenzhen, China", + "bbox": [ + 315, + 233, + 655, + 251 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{eechongm, youmin.xu}@stu.pku.edu.cn; {songjiechong, zhangjian.sz}@pku.edu.cn;", + "bbox": [ + 140, + 253, + 823, + 268 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{chen.zhao, Bernard.Ghanem}@kaust.edu.sa", + "bbox": [ + 303, + 272, + 656, + 286 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 321, + 313, + 338 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Video steganography is the art of unobtrusively concealing secret data in a cover video and then recovering the secret data through a decoding protocol at the receiver end. Although several attempts have been made, most of them are limited to low-capacity and fixed steganography. To rectify these weaknesses, we propose a Large-capacity and Flexible Video Steganography Network (LF-VSN) in this paper. For large-capacity, we present a reversible pipeline to perform multiple videos hiding and recovering through a single invertible neural network (INN). Our method can hide/recover 7 secret videos in/from 1 cover video with promising performance. For flexibility, we propose a key-controllable scheme, enabling different receivers to recover particular secret videos from the same cover video through specific keys. Moreover, we further improve the flexibility by proposing a scalable strategy in multiple videos hiding, which can hide variable numbers of secret videos in a cover video with a single model and a single training session. Extensive experiments demonstrate that with the significant improvement of the video steganography performance, our proposed LF-VSN has high security, large hiding capacity, and flexibility. The source code is available at https://github.com/MC-E/LF-VSN.", + "bbox": [ + 76, + 353, + 473, + 700 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 729, + 209, + 744 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Steganography [10] is the technology of hiding some secret data into an inconspicuous cover medium to generate a stego output, which only allows the authorized receiver to recover the secret information. Unauthorized people can only access the content of the plain cover medium, and hard", + "bbox": [ + 75, + 753, + 468, + 830 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "to detect the existence of secret data. In the current digital world, image and video are commonly used covers, widely applied in digital communication [27], copyright protection [36], information certification [31], e-commerce [26], and many other practical fields [10, 12].", + "bbox": [ + 500, + 323, + 890, + 398 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Traditional video steganography methods usually hide messages in the spatial domain or transform domain by manual design. Video steganography in the spatial domain means embedding is done directly to the pixel values of video frames. Least significant bits (LSB) [8,45] is the most well-known spatial-domain method, replacing the $n$ least significant bits of the cover image with the most significant $n$ bits of the secret data. Many researchers have used LSB replacement [6] and LSB matching [34] for video steganography. The transform-domain hiding [5, 17, 39] is done by modifying certain frequency coefficients of the transformed frames. For instance, [44] proposed a video steganography technique by manipulating the quantized coefficients of DCT (Discrete Cosine Transformation). [9] proposed to compare the DWT (Discrete Wavelet Transformation) coefficients of the secret image and the cover video for hiding. However, these traditional methods have low hiding capacity and invisibility, easily being cracked by steganalysis methods [15, 28, 33].", + "bbox": [ + 496, + 400, + 892, + 686 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, some deep-learning methods were proposed to improve the hiding capacity and performance. Early works are presented in image steganography. Baluja [3, 4] proposed the first deep-learning method to hide a full-size image into another image. Recently, [21, 32] proposed designing the steganography model as an invertible neural network (INN) [13, 14] to perform image hiding and recovering with a single model. For video steganography, Khare et al. [22] first utilized back propagation neural networks to improve the performance of the LSB-based scheme. [43] is the first deep-learning method to hide a video into another video. Unfortunately, it simply aims to hide the residual across adjacent frames in a frame-by-frame manner, and it requires several separate steps to complete the video hiding and re", + "bbox": [ + 496, + 689, + 893, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author. This work was supported by the King Abdulah University of Science and Technology (KAUST) Office of Sponsored Research through the Visual Computing Center (VCC) funding, SDAIA-KAUST Center of Excellence in Data Science and Artificial Intelligence, and Shenzhen Research Project JCYJ20220531093215035.", + "bbox": [ + 75, + 839, + 468, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "22606", + "bbox": [ + 478, + 945, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/ece7fba48046d09cb4437851ad802dd0312c5d95783eaf91fe9d68359f2e20b5.jpg", + "image_caption": [ + "Figure 1. Illustration of our large-capacity and flexible video steganography network (LF-VSN). Our LF-VSN reversibly solves multiple videos hiding and recovering with a single model and the same parameters. It has large-capacity, key-controllable and scalable advantages." + ], + "image_footnote": [], + "bbox": [ + 86, + 85, + 885, + 334 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "covering. [35] utilize 3D-CNN to explore the temporal correlation in video hiding. However, it utilizes two separated 3D UNet to perform hiding and recovering, and it has high model complexity (367.2 million parameters). While video steganography has achieved impressive success in terms of hiding capacity to hide a full-size video, the more challenging multiple videos hiding has hardly been studied. Also, the steganography pipeline is rigid.", + "bbox": [ + 75, + 383, + 468, + 503 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we study the large-capacity and flexible video steganography, as shown in Fig. 1. Concretely, we propose a reversible video steganography pipeline, achieving large capacity to hide/recover multiple secret videos in/from a cover video. At the same time, our model complexity is also attractive by combining several weight-sharing designs. The flexibility of our method is twofold. First, we propose a key-controllable scheme, enabling different receivers to recover particular secret videos with specific keys. Second, we propose a scalable strategy, which can hide variable numbers of secret videos into a cover video with a single model and a single training session. To summarize, this work has the following contributions:", + "bbox": [ + 75, + 505, + 470, + 700 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a large-capacity video steganography method, which can hide/recover multiple (up to 7) secret videos in/from a cover video. Our hiding and recovering are fully reversible via a single INN.", + "- We propose a key-controllable scheme with which different receivers can recover particular secret videos from the same cover video via specific keys.", + "- We propose a scalable embedding module, utilizing a single model and a single training session to satisfy different requirements for the number of secret videos hidden in a cover video.", + "- Extensive experiments demonstrate that our proposed" + ], + "bbox": [ + 94, + 705, + 468, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "method achieves state-of-the-art performance with large hiding capacity and flexibility.", + "bbox": [ + 531, + 383, + 890, + 414 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 428, + 640, + 444 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Video Steganography", + "text_level": 1, + "bbox": [ + 500, + 453, + 700, + 470 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Steganography can date back to the 15th century, whose goal is to encode a secret message in some transport mediums and covertly communicate with a potential receiver who knows the decoding protocol to recover the secret message. Since the human visual system is less sensitive to small changes in digital media, especially digital videos. Video steganography is becoming an important research area in various data-hiding technologies [10].", + "bbox": [ + 496, + 477, + 890, + 598 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Traditional video steganography methods usually performed hiding and recovering in the spatial domain, e.g., Pixel Value Differencing (PVD) [20, 40] and Least Significant Bits (LSB) [6, 34, 41]. PVD embeds the secret data in the difference value of two adjacent pixels. In [40], a PVD-based video steganography system is proposed to embed the secret data in a compressed domain of the cover medium. [20] utilized enhanced pixel-value differencing (EPVD) to improve the video steganography performance. LSB methods work by replacing the $n$ least significant bits of the cover data with the most significant $n$ bits of the secret information. [41] utilized LSB replacement technique to hide secret text in grayscale video frames. To enhance the security in LSB-based methods, [2] shuffled the secret data and embedded the index of correct order into the cover video. In addition to spatial-domain methods, some transformed domain methods [9, 44] were proposed to perform hiding by modifying certain frequency coefficients of the transformed cover video. For instance, [44] proposed a video steganography technique by manipulating the quantized coefficients", + "bbox": [ + 496, + 599, + 892, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "22607", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "of DCT transformation. [9] proposed to compare the DWT transformation coefficients of the secret image and the cover video for hiding. Nevertheless, the above traditional methods have low hiding capacity and invisibility, easily producing artificial markings and being cracked by steganalysis methods [15, 28, 33].", + "bbox": [ + 75, + 90, + 468, + 181 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Motivated by the success of deep learning, some deep-learning methods were proposed. [16] introduced GAN to steganography, showing that the adversarial training scheme can improve hiding security. [49] improve the hiding quality by utilizing two independent adversarial networks to critique the video quality and optimize for robustness. [25] studied the lossless steganography below 3 bits per pixel (bpp) hiding. [38] embedded the secret data in the wavelet transform coefficients of the video frames. The above methods focus more on the robustness of low-capacity hiding. One of the important applications of low-capacity steganography is watermarking [1, 42, 52], in which the secret bit string represents the sign of the owner. Some deep-learning methods were proposed for large-capacity hiding. [3, 4] first explored hiding a full-size image into another image. [21, 32] proposed a cheaper pipeline by implementing image hiding and recovering with a single invertible neural network (INN) [13, 14]. Compared with image hiding, video hiding is a more challenging task, requiring a larger hiding capacity. [43] first studied to hide/recover a video in/from another video. However, this method simply hides the residual across adjacent frames in a frame-by-frame manner. [35] explores the temporal correlation by 3D CNN in video steganography. However, it utilizes two separate 3D UNet to perform hiding and recovering and has high model complexity (367.2M model parameters). These previous works demonstrate that deep networks have great potential in video hiding, inspiring us to study the more challenging task of multiple and flexible video hiding.", + "bbox": [ + 75, + 181, + 470, + 621 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Invertible Neural Nerwork", + "text_level": 1, + "bbox": [ + 76, + 633, + 318, + 648 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Since the concept of invertible neural network (INN) was proposed in [13, 14], INN has attracted more and more attention due to its pure invertible pipeline. Pioneering research on INN can be seen in image generation tasks. For instance, Glow [24] utilized INN to construct an invertible mapping between the latent variable $\\mathbf{z}$ and nature images $\\mathbf{x}$ . Specifically, the generative process $\\mathbf{x} = f_{\\theta}(\\mathbf{z})$ given a latent variable can be specified by an INN architecture $f_{\\theta}$ . The direct access to the inverse mapping $\\mathbf{z} = f_{\\theta}^{-1}(\\mathbf{x})$ makes inference much cheaper. Up to now, INN has been studied in several vision tasks (e.g., image rescaling [19, 46], image restoration [29, 30], image coloring [51], and video temporal action localization [50]) and presents promising performance.", + "bbox": [ + 75, + 657, + 468, + 867 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The architecture of INN needs to be carefully designed to guarantee the invertibility. Commonly, INN is composed", + "bbox": [ + 76, + 869, + 470, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "of several invertible blocks, e.g., the coupling layer [13]. Given the input $\\mathbf{h}$ , the coupling layer first splits $\\mathbf{h}$ into two parts $(\\mathbf{h}_1$ and $\\mathbf{h}_2)$ along the channel axis. Then they undergo the affine transformations with the affine parameters generated by each other:", + "bbox": [ + 496, + 90, + 890, + 167 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{c} \\hat {\\mathbf {h}} _ {1} = \\mathbf {h} _ {1} \\cdot \\psi_ {1} (\\mathbf {h} _ {2}) + \\phi_ {1} (\\mathbf {h} _ {2}) \\\\ \\hat {\\quad} \\quad \\hat {\\quad} \\quad \\hat {\\quad} \\quad \\hat {\\quad} \\quad \\hat {\\quad} \\quad \\hat {\\quad} \\quad \\hat {\\quad} \\quad \\hat {\\quad} \\quad \\hat {\\quad} \\quad \\hat {\\quad} \\quad \\hat {\\quad} \\quad \\hat {\\quad} \\quad \\hat {\\quad} \\quad \\hat {\\quad} \\quad \\end{array} \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 596, + 169, + 890, + 194 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathbf {h}} _ {2} = \\mathbf {h} _ {2} \\cdot \\psi_ {2} (\\hat {\\mathbf {h}} _ {1}) + \\phi_ {2} (\\hat {\\mathbf {h}} _ {1}),\n$$\n", + "text_format": "latex", + "bbox": [ + 596, + 191, + 792, + 208 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\psi (\\cdot)$ and $\\phi (\\cdot)$ are arbitrary functions. $\\hat{\\mathbf{h}}_1$ and $\\hat{\\mathbf{h}}_2$ are the outputs of the coupling layer. Correspondingly, the inverse process is defined as:", + "bbox": [ + 496, + 217, + 890, + 262 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {h} _ {1} = \\frac {\\hat {\\mathbf {h}} _ {1} - \\phi_ {1} \\left(\\mathbf {h} _ {2}\\right)}{\\psi_ {1} \\left(\\mathbf {h} _ {2}\\right)}; \\quad \\mathbf {h} _ {2} = \\frac {\\hat {\\mathbf {h}} _ {2} - \\phi_ {2} \\left(\\hat {\\mathbf {h}} _ {1}\\right)}{\\psi_ {2} \\left(\\hat {\\mathbf {h}} _ {1}\\right)}. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 544, + 263, + 890, + 301 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this paper, we employ the reversible forward and backward processes of INN to perform multiple videos hiding and recovering, respectively. We further improve INN to explore flexible video steganography.", + "bbox": [ + 496, + 306, + 890, + 368 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 500, + 378, + 633, + 395 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Overview", + "text_level": 1, + "bbox": [ + 500, + 402, + 609, + 417 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "An overview of our LF-VSN is presented in Fig. 2. Specifically, given $N_{s}$ secret videos $\\mathbf{x}_{se} = \\{\\mathbf{x}_{se}(n)\\}_{n=1}^{N_{s}}$ and a cover video $\\mathbf{x}_{co}$ , the forward hiding is operated group-by-group through a sliding window, traversing each video from head to tail. After hiding, a stego video $\\mathbf{x}_{st}$ is produced, ostensibly indistinguishable from $\\mathbf{x}_{co}$ to ensure that $\\mathbf{x}_{se}$ is undetectable. In the backward recovering, a channel-wise broadcasting operation $(\\mathbb{R}^{3\\times W\\times H}\\xrightarrow{\\text{copy}}\\mathbb{R}^{3L\\times W\\times H})$ copies each stego frame in the channel dimension to form the reversed input. During recovering, multiple secret videos are recovered frame-by-frame in parallel. It is worth noting that the forward hiding and backward recovering share the same model architecture and parameters.", + "bbox": [ + 496, + 426, + 890, + 625 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Steganography Input and Output Design", + "text_level": 1, + "bbox": [ + 500, + 632, + 849, + 648 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "At the beginning of each hiding step, a fusion module is applied to fuse frames in each group to take advantage of the inner temporal correlation. Considering that it is easy to produce texture artifacts and color distortion when hiding in the spatial dimension [15, 21], we perform the fusion by a frequency concatenation. Specifically, given the $j$ -th cover group $\\mathbf{X}_{co\\otimes j} \\in \\mathbb{R}^{L \\times 3 \\times W \\times H}$ and secret groups $\\{\\mathbf{X}_{se\\otimes j}(n) \\in \\mathbb{R}^{L \\times 3 \\times W \\times H}\\}_{n=1}^{N_s}$ (each contains $L$ frames), we adopt Haar discrete wavelet transform (DWT) to split each frame into four frequency bands (i.e., LL, HL, LH, HH). In each frame group, we concatenate the part in the same frequency band from different frames in the channel dimension and then concatenate these four bands in order of frequency magnitude, producing the final secret input $\\{\\mathbf{X}_{se\\otimes j}(n) \\in \\mathbb{R}^{12L_s \\times \\frac{W}{2} \\times \\frac{H}{2}}\\}_{n=1}^{N_s}$ and cover input $\\mathbf{X}_{co\\otimes j} \\in \\mathbb{R}^{12L_c \\times \\frac{W}{2} \\times \\frac{H}{2}}$ . The output of the forward", + "bbox": [ + 496, + 655, + 890, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "22608", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/6e7b99436d6eba7190b1c8dc626ad8f702a65acf40db4880f7eb3c1d55fe71cc.jpg", + "image_caption": [ + "Figure 2. Network architecture of our LF-VSN. It is composed of several invertible blocks. In the forward hiding process, multiple secret videos are hidden in a cover video to generate a stego video, together with redundancy. In the backward recovering process, the stego video and predicted redundancy are fed to the reverse data flow of the same network with the same parameters to recover secret videos." + ], + "image_footnote": [], + "bbox": [ + 83, + 88, + 885, + 314 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "hiding comprises a stego group $\\mathbf{X}_{st\\oplus j}$ and several redundancy groups $\\{\\mathbf{X}_{re\\oplus j}(n)\\}_{n = 1}^{N_s}$ . $\\mathbf{X}_{st\\oplus j}$ is converted from the frequency domain to the spatial domain by a frequency separation, i.e., the inverse of the frequency concatenation. $\\mathbf{X}_{re\\oplus j}(n)$ represents the redundancy of the $\\mathbf{X}_{se\\oplus j}(n)$ that does not need to be hidden and will be discarded. In our LF-VSN, we utilize the adjacent frames to cooperate with hiding the central frame. Thus, we only output the central stego frame in each hiding step. The backward recovering is similarly operated in the frequency domain and converted to the spatial domain at the output.", + "bbox": [ + 75, + 376, + 473, + 544 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Invertible Block", + "text_level": 1, + "bbox": [ + 76, + 555, + 238, + 569 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As shown in Fig. 2, our hiding and recovering have reverse information flow constructed by several invertible blocks (IBs). The architecture of IB is presented in Fig. 3. Concretely, in the $k$ -th IB, there are two branches to process the input cover group $\\mathbf{X}_{co\\otimes j}^k$ and secret groups $\\{\\mathbf{X}_{se\\otimes j}^k(n)\\}_{n=1}^{N_s}$ , respectively. Several interaction pathways between these two branches construct the invertible projection. We use an additive transformation to project the cover branch and employ an enhanced affine transformation to project the secret branch. The transformation parameters are generated from each other. Here we utilize weight-sharing modules $(\\eta_k^1(\\cdot)$ and $\\phi_k^1(\\cdot))$ to extract features from all secret groups, producing a feature set $\\{\\mathbf{F}_{se}^k(n)\\}_{n=1}^{N_s} = \\{\\phi_k(\\eta_k(\\mathbf{X}_{se\\otimes j}^k(n)))\\}_{n=1}^{N_s}$ . $\\eta_k^i(\\cdot)$ and $\\phi_k^i(\\cdot)$ ( $i = 1, 2, 3$ ) refer to a $3 \\times 3$ convolution layer and a five-layer dense block [18], respectively. Then, we concatenate $\\mathbf{F}_{se}^k$ in the channel dimension and pass through an aggregation module $\\xi_k(\\cdot)$ to generate the transformation parameters of the cover branch. Note that $\\xi_k(\\cdot)$ is optional in different cases. In our fixed hiding, $\\xi_k(\\cdot)$ is a $3 \\times 3$ convolution layer, and it is a scalable embedding module in our scalable hiding. The", + "bbox": [ + 75, + 579, + 473, + 901 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/9f014d1ed1fd758b8c31cb2c9f8242ba4121159af2d9fe9f7858fb2e6d835a74.jpg", + "image_caption": [ + "Figure 3. Illustration of the architecture of our invertible block. The dashed line refers to weight sharing." + ], + "image_footnote": [], + "bbox": [ + 516, + 372, + 870, + 545 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "transformation parameters of the secret branch are generated from $\\mathbf{X}_{co\\otimes j}^{k}$ and shared among different secret groups. Thus, in the $k$ -th invertible block, the bijection of the forward propagation in Eq. (1) is reformulated as:", + "bbox": [ + 498, + 599, + 890, + 659 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {X} _ {c o \\circledast j} ^ {k + 1} = \\mathbf {X} _ {c o \\circledast j} ^ {k} + \\xi_ {k} \\left(\\left| \\left| \\phi_ {k} ^ {1} \\left(\\eta_ {k} ^ {1} \\left(\\mathbf {X} _ {s e \\circledast j} ^ {k} (n)\\right)\\right) \\right| \\right| _ {n = 1} ^ {N _ {s}}\\right)\n$$\n", + "text_format": "latex", + "bbox": [ + 532, + 678, + 838, + 696 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\{\\mathbf {X} _ {s e \\circledast j} ^ {k + 1} (n) \\right\\} _ {n = 1} ^ {N _ {s}} = \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 535, + 698, + 890, + 715 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {X} _ {s e \\circledast j} ^ {k} (n) \\cdot \\exp \\left(\\phi_ {k} ^ {2} \\left(\\eta_ {k} ^ {2} \\left(\\mathbf {X} _ {c o \\circledast j}\\right)\\right)\\right) + \\phi_ {k} ^ {3} \\left(\\eta_ {k} ^ {3} \\left(\\mathbf {X} _ {c o \\circledast j} ^ {k + 1}\\right)\\right),\n$$\n", + "text_format": "latex", + "bbox": [ + 535, + 717, + 857, + 736 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $||\\cdot ||$ refers to the channel-wise concatenation. $\\exp (\\cdot)$ is the Exponential function. Accordingly, the backward propagation is defined as:", + "bbox": [ + 500, + 753, + 890, + 801 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\{\\mathbf {X} _ {s e \\circledast j} ^ {k} (n) \\} _ {n = 1} ^ {N _ {s}} =\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 819, + 638, + 835 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left(\\mathbf {X} _ {s e \\circledast j} ^ {k + 1} (n) - \\phi_ {k} ^ {3} \\left(\\eta_ {k} ^ {3} \\left(\\mathbf {X} _ {c o \\circledast j} ^ {k + 1}\\right)\\right)\\right) \\cdot \\exp \\left(- \\phi_ {k} ^ {2} \\left(\\eta_ {k} ^ {2} \\left(\\mathbf {X} _ {c o \\circledast j} ^ {k + 1}\\right)\\right)\\right) \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 516, + 838, + 890, + 857 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {X} _ {c o \\circledast j} ^ {k} = \\mathbf {X} _ {c o \\circledast j} ^ {k + 1} - \\xi_ {k} \\left(\\left| \\left| \\phi_ {k} ^ {1} \\left(\\eta_ {k} ^ {1} \\left(\\mathbf {X} _ {s e \\circledast j} ^ {k} (n)\\right)\\right) \\right| \\right| n = _ {1}\\right).\n$$\n", + "text_format": "latex", + "bbox": [ + 516, + 859, + 823, + 877 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "22609", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/cc032df3fcba499771314ec39f29bf85660d6f70b314ca805cd06b0a4af5542a.jpg", + "image_caption": [ + "(a) w/o key" + ], + "image_footnote": [], + "bbox": [ + 96, + 88, + 240, + 328 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/592f922e462c47501c993e5d02a1ebdaf6fce91c620aed164ee810bd6238b721.jpg", + "image_caption": [ + "(b) w key", + "Figure 4. The architecture of our redundancy prediction module (RPM). It has two model settings: (a) RPM without (w/o) key controlling; (b) RPM with (w) key controlling." + ], + "image_footnote": [], + "bbox": [ + 243, + 88, + 446, + 329 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Redundancy Prediction Module (RPM) & Key-controllable Design", + "text_level": 1, + "bbox": [ + 76, + 407, + 468, + 439 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As illustrated previously, we retain the stego part and discard the redundancy information in the forward hiding. Therefore, we need to prepare a suitable redundancy in the backward process to utilize the reversibility of INN to reconstruct the forward input (i.e., secret and cover). In different tasks, most INN-based methods [21,24,32,46] constrain the generated redundancy information to obey the Gaussian distribution and utilize random Gaussian sampling to approximate this part in the backward process. Nevertheless, such random sampling lacks data specificity and adaptivity. In our LF-VSN, we predict the redundancy information from the stego group through a redundancy prediction module (RPM), as shown in Fig. 4(a). It is composed of several residual blocks (RB) without the Batch Normalization layer.", + "bbox": [ + 75, + 446, + 468, + 657 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this paper, we present a novel extension of RPM to construct key-controllable video steganography, with which we can hide multiple secret videos in a cover video and recover a secret video conditioned on a specific key. The architecture is shown in Fig. 4(b). Given the index $n_{key}$ of a secret video $\\mathbf{X}_{se}(n_{key})$ , a specific key is generated by a key encoder, which is composed of several fully connected (FC) layers. The key is then fed into a FC layer at the end of each RB in RPM to generate a condition vector with $2C_{rpm}$ channels, which is divided into two modulation vectors $\\alpha, \\beta \\in \\mathbb{R}^{C_{rpm} \\times 1 \\times 1}$ in the channel dimension. $C_{rpm}$ is the feature channel of each RB in RPM. Then we modulate the output feature $\\mathbf{F}_{rpm}$ of each RB as $\\mathbf{F}_{rpm} \\cdot \\alpha + \\beta$ . In the training process, we constrain the recovered output the same as the $n_{key}$ -th secret video (i.e., $\\mathbf{X}_{se}(n_{key})$ ). More details can be found in Sec. 3.6.", + "bbox": [ + 75, + 659, + 470, + 900 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/41a82ca31f5611c1a2f1be94b449e1290b70820da587d341dc6dcca6abbd7ca1.jpg", + "image_caption": [ + "Figure 5. Illustration of our scalable embedding module. It takes the input feature map with scalable channels $C_{in} \\in [1, C]$ and produces output features with fixed channels $C_{out}$ ." + ], + "image_footnote": [], + "bbox": [ + 521, + 87, + 870, + 244 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5. Scalable Embedding Module", + "text_level": 1, + "bbox": [ + 500, + 304, + 756, + 320 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The scalable design is used to handle the case where there are different requirements for the number of secret videos hidden in a cover video. It is succinctly designed on the feature aggregation part $\\xi_{k}(\\cdot)$ in each IB, as shown in Fig. 3. The illustration of our scalable embedding module is presented in Fig. 5. It can be regarded as a special convolution layer, whose dimension of the convolution kernel can be changed according to the input. All convolution kernels $\\widetilde{\\mathbf{M}}$ with different dimensions are parameter-shared from the same base kernel $\\mathbf{M}$ . Technically, given the input feature $\\mathbf{F}_{in} \\in \\mathbb{R}^{C_{in} \\times W \\times H}$ , we truncate a convolution kernel $\\widetilde{\\mathbf{M}} \\in \\mathbb{R}^{C_{in} \\times C_{out} \\times k \\times k}$ from $\\mathbf{M} \\in \\mathbb{R}^{C \\times C_{out} \\times k \\times k}$ to match the input dimension and then perform convolution: $\\mathbf{F}_{out} = \\widetilde{\\mathbf{M}} * \\mathbf{F}_{in}$ . In this way, the training of $\\mathbf{M}$ is completed through the training of all sub-kernels $\\widetilde{\\mathbf{M}}$ .", + "bbox": [ + 496, + 327, + 890, + 561 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.6. Loss Function", + "text_level": 1, + "bbox": [ + 500, + 568, + 643, + 580 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In our LF-VSN, the loss function is used to constrain two parts, i.e., forward hiding and backward recovering. The forward hiding is to hide multiple secret videos in the cover video. The generated stego video $\\mathbf{X}_{st}$ should be undetectable to secret videos and as similar as possible to the cover video. Therefore, we constrain $\\mathbf{X}_{st}$ to be the same as the cover video $\\mathbf{X}_{co}$ :", + "bbox": [ + 496, + 590, + 890, + 696 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {f} = \\left| \\left| \\mathbf {X} _ {s t \\circledast j} [ I _ {c} ] - \\mathbf {X} _ {c o \\circledast j} [ I _ {c} ] \\right| \\right| _ {2} ^ {2}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 581, + 703, + 890, + 720 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $||\\cdot ||_2^2$ donates the $\\ell_{2}$ norm. $I_{c}$ is the index of the central frame in each group. In the backward recovering, there are two patterns: with and without key controlling. In both patterns, we aim to recover the secret information from the cover video. The difference stands between recovering a specific secret video and all secret videos. In the pattern without key controlling, the loss function is defined as:", + "bbox": [ + 496, + 728, + 890, + 834 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {b} = \\sum_ {n = 1} ^ {N _ {s}} \\left| \\left| \\hat {\\mathbf {X}} _ {s e \\otimes j} (n) [ I _ {c} ] - \\mathbf {X} _ {s e \\otimes j} (n) [ I _ {c} ] \\right| \\right| _ {2} ^ {2} + \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 540, + 840, + 890, + 882 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\left. \\left\\| \\hat {\\mathbf {X}} _ {c o \\circledast j} [ I _ {c} ] - \\mathbf {X} _ {c o \\circledast j} [ I _ {c} ] \\right\\| _ {2} ^ {2}, \\right.\n$$\n", + "text_format": "latex", + "bbox": [ + 663, + 883, + 849, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "22610", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/519e63c8cc0ee51757efebc0ae2c9842869728f51b57783b2b66be2167889bf4.jpg", + "table_caption": [ + "Table 1. Quantitative comparison (PSNR/SSIM) on Vimeo-T200. The best and second-best results are highlighted and underlined. Our LF-VSN achieves the best performance in stego and secret quality with acceptable complexity." + ], + "table_footnote": [], + "table_body": "
Weng et al. [43]Baluja [4]ISN [32]HiNet [21]RIIS [47]PIH [11]LF-VSN (Ours)
Stego29.43/0.86234.14/0.86042.08/0.96542.09/0.96243.50/0.951-45.17/0.980
Secret32.08/0.89935.21/0.93142.11/0.98444.44/0.99144.08/0.96436.48/0.93948.39/0.996
Params.42.57M2.65M3.00M4.05M8.15M0.67M7.40M
", + "bbox": [ + 78, + 121, + 890, + 195 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/5edf7612f72e303b37f54afab1af67f0600541a198020664c1e5003ec605a6fe.jpg", + "image_caption": [ + "GroundTruth" + ], + "image_footnote": [], + "bbox": [ + 78, + 210, + 295, + 387 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/2e06b67db7e1c87b81b87fddb8ea26a3c2534136fc47b68279580d0d91cb42f2.jpg", + "image_caption": [ + "ISN [32]" + ], + "image_footnote": [], + "bbox": [ + 297, + 210, + 493, + 386 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/4a464cd1601957c3bd6076400432db39866a12746f0d8588aaa0a721d6a340d8.jpg", + "image_caption": [ + "PIH [11]" + ], + "image_footnote": [], + "bbox": [ + 495, + 210, + 692, + 386 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/b953141990d3b37beeede203b5e9278f261af3c8f1cd52b7b1ee1d761ff847cb.jpg", + "image_caption": [ + "LF-VSN (Ours)" + ], + "image_footnote": [], + "bbox": [ + 694, + 210, + 890, + 386 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/0881958a1e084788ce362c46e312216f6868689ff41837c9c42dab9bd760b4d0.jpg", + "image_caption": [ + "Figure 6. Visual comparison between our LF-VSN, ISN [32], and PIH [11] in 4 videos Steganography. We present the secret reconstruction results of video 2 and video 4. Our LF-VSN produces better result with intact color and details." + ], + "image_footnote": [], + "bbox": [ + 78, + 453, + 176, + 502 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/8a6fcf07325bde8d2b8bf81ed7281c1eb58240a8159619f9fc1b0518ac95816a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 178, + 453, + 272, + 502 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/7f98b5d3875eec21f5decf7c829584721d34b32ff0c6b344e805563a74626d07.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 274, + 453, + 370, + 502 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/9bdd5c4db0f50ace30887c4c2f016833e4e4ab9dbd1cedea2a0be7d8a3e1c3be.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 372, + 453, + 468, + 502 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/197238f0a1402abc7c0df756ad9204c10b7181a79c08cf575798671dcb3a5d3e.jpg", + "image_caption": [ + "Xco", + "Xst" + ], + "image_footnote": [], + "bbox": [ + 78, + 518, + 176, + 565 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/fad5ccf6cae1afd8d9b7feda6dc7832d75b9ce66a369a8a151693247bb8eb256.jpg", + "image_caption": [ + "$\\mathbf{X}_{se}(3)$", + "$\\hat{\\mathbf{X}}_{se}(3)$" + ], + "image_footnote": [], + "bbox": [ + 178, + 518, + 272, + 565 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/192070a4258cc36348f3528a938ff453569c7f8d7948b57f9bed5e5e79385f4c.jpg", + "image_caption": [ + "$\\mathbf{X}_{se}(5)$", + "$\\hat{\\mathbf{X}}_{se}(5)$", + "Figure 7. Visualization of our LF-VSN in 7 videos steganography, showing promising performance in such an extreme case." + ], + "image_footnote": [], + "bbox": [ + 274, + 518, + 370, + 566 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/3af70c6d91b41cb00700ab9c663413d0f2c93c916a46210af47eacd4fe8f1263.jpg", + "image_caption": [ + "$\\mathbf{X}_{se}(7)$", + "$\\hat{\\mathbf{X}}_{se}(7)$" + ], + "image_footnote": [], + "bbox": [ + 372, + 518, + 468, + 566 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\hat{\\mathbf{X}}_{se}$ and $\\hat{\\mathbf{X}}_{co}$ represent the recovered secret and cover videos. In the pattern with key controlling, the loss function is defined to guarantee that the key generated from the video index $n_{key}$ can only recover the $n_{key}$ -th secret video. Thus, the loss function is reformulated as:", + "bbox": [ + 75, + 640, + 468, + 715 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {b} = \\left| \\right| \\frac {1}{N _ {s}} \\sum_ {n = 1} ^ {N _ {s}} \\hat {\\mathbf {X}} _ {s e * j} (n) [ I _ {c} ] - \\mathbf {X} _ {s e * j} \\left(n _ {k e y}\\right) [ I _ {c} ] \\left| \\right| _ {2} ^ {2} + \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 84, + 720, + 468, + 762 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\left| \\left| \\hat {\\mathbf {X}} _ {c o * j} [ I _ {c} ] - \\mathbf {X} _ {c o * j} [ I _ {c} ] \\right| \\right| _ {2} ^ {2}.\n$$\n", + "text_format": "latex", + "bbox": [ + 254, + 765, + 439, + 785 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We optimize our LF-VSN by minimizing the forward loss function $\\mathcal{L}_f$ and backward loss function $\\mathcal{L}_b$ as:", + "bbox": [ + 76, + 791, + 468, + 821 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {f} + \\lambda \\mathcal {L} _ {b}, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 217, + 830, + 468, + 847 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\lambda$ is a hyper-parameter to make a trade-off between forward hiding and backward recovering. We set $\\lambda = 4$ to balance these two loss portions.", + "bbox": [ + 75, + 854, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiment", + "text_level": 1, + "bbox": [ + 500, + 454, + 624, + 470 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Implementation Details", + "text_level": 1, + "bbox": [ + 500, + 479, + 715, + 494 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this work, we adopt the training set of Vimeo90K [48] to train our LF-VSN. Each sequence has a fixed spatial resolution of $448 \\times 256$ . During training, we randomly crop training videos to $144 \\times 144$ with random horizontal and vertical flipping to make a data augmentation. We use Adam optimizer [23], with $\\beta_{1} = 0.9$ , $\\beta_{2} = 0.5$ . We set the batch size as 16. The weight decay factor is set as $1 \\times 10^{-12}$ . We use an initial learning rate of $1 \\times 10^{-4}$ , which will decrease by half for every $30K$ iterations. The number of total iterations is set as $250K$ . The training process can be completed on one NVIDIA Tesla V100 GPU within 3 days. For testing, we select 200 sequences from the testing set of Vimeo-90K, denoted as Vimeo-T200 in this paper.", + "bbox": [ + 496, + 503, + 890, + 700 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Comparison Against Other Methods", + "text_level": 1, + "bbox": [ + 500, + 710, + 815, + 726 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Here we compare our LF-VSN with other methods on single video steganography and challenging multiple videos steganography. The evaluation includes the stego quality in forward hiding and the secret quality in backward recovering. For single video steganography, we compare our LF-VSN with some well-known methods [4, 43] and recent proposed methods [11, 21, 32, 47]. Note that PIH [11] highlighted the need to quantize the stego image from the floating-point format of $32 \\times 3$ to $8 \\times 3$ bits per pixel. But PIH just added the quantization to the compared methods without retraining. Here we retrain HiNet [21] with", + "bbox": [ + 496, + 734, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "22611", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/a68027af20d71226084dd5c728c980fdf83c8169179b27c95718e895da9c753a.jpg", + "table_caption": [ + "Table 2. Multiple videos steganography comparison (PSNR) of our LF-VSN, ISN [32], and PIH [11] on Vimeo-T200 test set. Our LF-VSN can hide/recover 7 videos with promising performance." + ], + "table_footnote": [], + "table_body": "
Videos234567
ISNStego37.6036.4132.5631.46--
Secret41.4738.7633.4233.39--
PIHStego------
Secret35.9534.9634.20---
OursStego40.9738.5537.5536.5735.6835.01
Secret44.2442.2740.2138.8836.9435.71
", + "bbox": [ + 80, + 135, + 464, + 244 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/cd2d8536f5456b32d1eede040957847c24656fbfae6f3845ce7622bd086f7f9e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 81, + 247, + 207, + 305 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2e2140616dc4ac970d985e45a53f9981a3454debacb6ebf2a4396eda21e8117f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 209, + 247, + 334, + 305 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/eb20884d44a37ad8d311c3914a55b3fb7a3f2623def279c756e3e3445102a438.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 334, + 247, + 460, + 305 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/befbac94ca57960ca6a150cc3b947b99a8f6d0a34ad1cca944249df6281463f3.jpg", + "image_caption": [ + "Key $2^{*}$ recovered Key $4^{*}$ recovered Key $6^{*}$ recovered", + "Figure 8. Visualization of our key-controllable scheme in 6 videos steganography. In the second and third rows, we use the correct and wrong (*) keys of 2, 4, 6 to recover secret videos, respectively." + ], + "image_footnote": [], + "bbox": [ + 80, + 309, + 462, + 449 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "quantization to make a more fair comparison. Thus, its performance may be slightly higher than that reported in PIH. ISN [32], RIIS [47] and PIH were originally designed with quantization, which can be directly compared. Tab. 1 presents that our method achieves the best performance on stego and secret while maintaining acceptable complexity.", + "bbox": [ + 75, + 521, + 468, + 611 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "For multiple videos steganography, ISN [32] and PIH [11] studied how to hide multiple secret images in a cover image, which can be competitive counterparts of our LF-VSN. ISN can hide up to 5 secret images into 1 cover image, and PIH can hide 4 secret images. The comparison in Tab. 3 shows the better performance of our LF-VSN. Even in the 7 videos hiding, our method still has promising stego and secret quality ( $>35dB$ ). We present the visual comparison of different methods in 4 videos steganography in Fig. 6. Obviously, ISN has color distortion, and PIH has a loss of details. By contrast, our LF-VSN can recover high-fidelity results. We also present the secret and stego quality of our LF-VSN in 7 videos hiding in Fig. 7. These videos are from DAVIS [37] dataset. One can see that our LF-VSN has promising performance in such an extreme case.", + "bbox": [ + 75, + 611, + 468, + 838 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Key-controllable Video Steganography", + "text_level": 1, + "bbox": [ + 76, + 847, + 410, + 864 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Hiding multiple secret videos in a cover video is challenging; doing so for different receivers is even more dif", + "bbox": [ + 76, + 869, + 468, + 902 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/4ddd794d9609e2739194b833e5c70b3739347d3cfbe229f41ba1341e78084820.jpg", + "table_caption": [ + "Table 3. Performance comparison between controllable (C) and non-controllable (NC) video steganography of our LF-VSN." + ], + "table_footnote": [], + "table_body": "
Num. videos246
Stego (NC/C)40.97/38.6737.55/34.4135.68/30.48
Secret (NC/C)44.24/41.0440.21/37.1536.94/31.95
", + "bbox": [ + 503, + 121, + 880, + 172 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/91d41fbb871065915eeca5e54f02a643a859328875254b8450e7cc0c8dad6373.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 501, + 176, + 694, + 330 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c7b7255671297442a71885073d141d73e166bda2824c888410ce2a7edc235ddb.jpg", + "image_caption": [ + "Figure 9. Performance comparison between our scalable and fixed design in multiple videos steganography." + ], + "image_footnote": [], + "bbox": [ + 697, + 176, + 885, + 332 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ficult. In this paper, we present a key-controllable scheme in multiple videos steganography. It enables different receivers to recover particular secret videos through specific keys. The comparison in Tab. 3 presents that our controllable scheme still has a large hiding capacity (up to 6 videos) with attractive performance ( $>30dB$ ). The visualization of recovering quality is presented in the second row of Fig. 8, showing the high-quality and key-controllable results of our LF-VSN in multiple videos steganography.", + "bbox": [ + 496, + 380, + 890, + 516 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We also study the security of our controlling scheme, i.e., the key is sensitive and model-specific. Here we take two sets of parameters, producing from the 250K and 240K iterations in the same training process. We use the key produced by one model (*) to recover the secret video hidden by another. The result in the third row of Fig. 8 presents that the wrong key has no controlling and recovering ability. Thus, our key-controllable scheme not only has the controlling function but also enhances data security.", + "bbox": [ + 496, + 516, + 892, + 652 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Scalable Video Steganography", + "text_level": 1, + "bbox": [ + 498, + 662, + 769, + 679 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this paper, we present a scalable scheme in multiple videos steganography. It can hide a variable number of secret videos into a cover video with a single model. We evaluate the performance of our scalable design and compare it with the fixed version in Tab. 9. Obviously, our method has an attractive performance ( $>31dB$ ) in hiding a variable number (up to 7) of secret videos into a cover video by a single model. The performance degradation compared to fixed version is acceptable. With this design, a single model can satisfy multiple steganography demands.", + "bbox": [ + 496, + 686, + 890, + 838 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.5. Steganographic Analysis", + "text_level": 1, + "bbox": [ + 500, + 845, + 725, + 863 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The data security is one of the most important concerns in steganography. In this section, we evaluate the anti", + "bbox": [ + 498, + 869, + 890, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "22612", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/c93439b7fb072c288b3c6670c4b0644e6a34dbe029fa4d5d33d3b427da13a914.jpg", + "table_caption": [ + "Table 4. The ablation study of different components in our LF-VSN. It includes the sliding window size, number of invertible blocks (IB), frequency concatenation (FreqCat), and redundancy prediction module (RPM)." + ], + "table_footnote": [], + "table_body": "
Num. videos246333
Window size13513513533 (ours)333
Num. IB1616161616161616161216201616
FreqCat✓✓✓✓✓✓✓✓✓✓✓✓✓×
RPM✓✓✓✓✓✓✓✓✓✓✓✓×✓
Stego39.6440.9741.0836.4137.5537.8634.4735.4635.9638.0338.5538.9138.2836.85
Secret42.9744.2444.4337.6740.2140.4235.1136.8339.9741.9942.2742.4041.6940.36
", + "bbox": [ + 76, + 116, + 885, + 212 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/25d4c48d9297d58fb3cf320eac39139b6cbb9eb1f27c2352bf3524cb06e95300.jpg", + "image_caption": [ + "Figure 10. Statistics-based steganalysis by StegExpose [7]. The closer the detection accuracy is to $50\\%$ , the higher the security is." + ], + "image_footnote": [], + "bbox": [ + 104, + 224, + 434, + 435 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "steganalysis ability of different methods, which stands for the possibility of detecting stego frames from nature frames by steganalysis tools. We utilize the StegExpose [7] to attack different steganography methods. The detection set is built by mixing stego and cover with equal proportions. We vary the detection thresholds in a wide range in StegExpose and draw the receiver operating characteristic (ROC) curve in Fig. 10. Note that the ideal case represents that the detector has a $50\\%$ probability of detecting stego from an equally mixed cover and stego, the same as random sampling. Therefore, the closer the curve is to the ideal case, the higher the security is. Obviously, the stego frames generated by our LF-VSN are harder to be detected than other methods. Even in the multiple videos (e.g., 2 and 4 videos) hiding, our method can still achieve attractive performance, demonstrating the higher data security of our LF-VSN.", + "bbox": [ + 75, + 483, + 468, + 724 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.6. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 739, + 230, + 755 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this subsection, we present the ablation study in Tab. 4 to investigate the effect of different components in our LF-VSN. The experiments are conducted on Vimeo-T200.", + "bbox": [ + 75, + 763, + 468, + 808 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Sliding window size. In this paper, we utilize the temporal correlation within each frame group to improve the video steganography performance. To demonstrate the effectiveness, we evaluate the performance of our LF-VSN with the window size $L = \\{1,3,5\\}$ in 2,4,and 6 videos steganography. The results in Tab. 4 present that the temporal corre", + "bbox": [ + 75, + 809, + 468, + 901 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "lation has obvious performance gains to the multiple videos steganography. Considering the model complexity, we set the sliding window size as 3 in our LF-VSN.", + "bbox": [ + 496, + 228, + 890, + 272 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Number of invertible blocks (IB). As mentioned above, our LF-VSN is composed of several IBs. To investigate the effectiveness of IB, we evaluate the performance of our LF-VSN with the number of IB being 12, 16, and 20. The results in Tab. 4 present that the performance increases with the number of IB. To make a trade-off between performance and complexity, we utilize 16 IBs in our LF-VSN.", + "bbox": [ + 496, + 273, + 890, + 378 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Frequency concatenation (FreqCat). In our LF-VSN, we use the DWT transform to merge each input group in the frequency domain. To demonstrate the effectiveness, we replace this operation with direct channel-wise concatenation. Tab. 4 presents that there are $1.7dB$ and $1.91dB$ gains of FreqCat on stego and secret quality in 3 videos steganography. The possible reason is that DWT transform can separate the low-frequency and high-frequency sub-bands, making it more effective for information fusion and hiding.", + "bbox": [ + 496, + 378, + 890, + 513 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Redundancy prediction module (RPM). In our LF-VSN, we employ RPM to predict the redundancy in the backward process instead of randomly sampling. To demonstrate the effectiveness of RPM, we replace this module with a random Gaussian sampling. The result in Tab. 4 shows that RPM can be used not only to design key-controllable steganography, but also to improve performance.", + "bbox": [ + 496, + 513, + 890, + 621 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 633, + 617, + 648 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we propose a large-capacity and flexible video steganography network (LF-VSN). The novelty of our method is twofold. First, our LF-VSN has a large hiding capacity, with which we can hide 7 secret videos into a cover video and then recover them well $(>35dB)$ . Second, we explore the flexibility in multiple videos steganography by proposing a key-controllable scheme and a scalable design. Specifically, our key-controllable scheme can enable different receivers to recover particular secret videos through specific keys. Also, the key controlling is sensitive and model-specific, which can enhance data security. Our scalable design further improves the flexibility to hide a variable number of secret videos into a cover video with a single model. Extensive experiments demonstrate that our proposed LF-VSN has state-of-the-art performance with high security, large hiding capacity, and flexibility.", + "bbox": [ + 496, + 659, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "22613", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Mahdi Ahmadi, Alireza Norouzi, Nader Karimi, Shadrokh Samavi, and Ali Emami. ReDMark: Framework for residual diffusion watermarking based on deep networks. Expert Systems with Applications, 146:113157, 2020. 3", + "[2] R Balaji and Garewal Naveen. Secure data transmission using video steganography. In 2011 IEEE International Conference on Electro/Information Technology, pages 1-5, 2011. 2", + "[3] Shumeet Baluja. Hiding images in plain sight: Deep steganography. 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In Proceedings of the European Conference on Computer Vision (ECCV), pages 657–672, 2018. 3" + ], + "bbox": [ + 501, + 92, + 890, + 556 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "22615", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Large-Capacity and Flexible Video Steganography via Invertible Neural Network/e548c867-6b1a-4988-b551-f9862e60583c_model.json b/2023/Large-Capacity and Flexible Video Steganography via Invertible Neural Network/e548c867-6b1a-4988-b551-f9862e60583c_model.json new file mode 100644 index 0000000000000000000000000000000000000000..c0b1a27758a18e0ed83774f8817f55d0ec48deb4 --- /dev/null +++ b/2023/Large-Capacity and Flexible Video Steganography via Invertible Neural Network/e548c867-6b1a-4988-b551-f9862e60583c_model.json @@ -0,0 +1,2497 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.079, + 0.131, + 0.892, + 0.153 + ], + "angle": 0, + "content": "Large-capacity and Flexible Video Steganography via Invertible Neural Network" + }, + { + "type": "text", + "bbox": [ + 0.12, + 0.18, + 0.847, + 0.2 + ], + "angle": 0, + "content": "Chong Mou1, Youmin Xu1, Jiechong Song1, Chen Zhao2, Bernard Ghanem2, Jian Zhang1,3,*" + }, + { + "type": "text", + "bbox": [ + 0.23, + 0.199, + 0.741, + 0.216 + ], + "angle": 0, + "content": "1Peking University Shenzhen Graduate School, Shenzhen, China" + }, + { + "type": "text", + "bbox": [ + 0.137, + 0.216, + 0.834, + 0.233 + ], + "angle": 0, + "content": "\\(^{2}\\)King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia" + }, + { + "type": "text", + "bbox": [ + 0.316, + 0.234, + 0.656, + 0.252 + ], + "angle": 0, + "content": "\\(^{3}\\)Peng Cheng Laboratory, Shenzhen, China" + }, + { + "type": "text", + "bbox": [ + 0.142, + 0.254, + 0.825, + 0.27 + ], + "angle": 0, + "content": "{eechongm, youmin.xu}@stu.pku.edu.cn; {songjiechong, zhangjian.sz}@pku.edu.cn;" + }, + { + "type": "text", + "bbox": [ + 0.305, + 0.273, + 0.658, + 0.287 + ], + "angle": 0, + "content": "{chen.zhao, Bernard.Ghanem}@kaust.edu.sa" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.322, + 0.314, + 0.339 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.354, + 0.474, + 0.701 + ], + "angle": 0, + "content": "Video steganography is the art of unobtrusively concealing secret data in a cover video and then recovering the secret data through a decoding protocol at the receiver end. Although several attempts have been made, most of them are limited to low-capacity and fixed steganography. To rectify these weaknesses, we propose a Large-capacity and Flexible Video Steganography Network (LF-VSN) in this paper. For large-capacity, we present a reversible pipeline to perform multiple videos hiding and recovering through a single invertible neural network (INN). Our method can hide/recover 7 secret videos in/from 1 cover video with promising performance. For flexibility, we propose a key-controllable scheme, enabling different receivers to recover particular secret videos from the same cover video through specific keys. Moreover, we further improve the flexibility by proposing a scalable strategy in multiple videos hiding, which can hide variable numbers of secret videos in a cover video with a single model and a single training session. Extensive experiments demonstrate that with the significant improvement of the video steganography performance, our proposed LF-VSN has high security, large hiding capacity, and flexibility. The source code is available at https://github.com/MC-E/LF-VSN." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.73, + 0.21, + 0.745 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.755, + 0.47, + 0.831 + ], + "angle": 0, + "content": "Steganography [10] is the technology of hiding some secret data into an inconspicuous cover medium to generate a stego output, which only allows the authorized receiver to recover the secret information. Unauthorized people can only access the content of the plain cover medium, and hard" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.324, + 0.892, + 0.399 + ], + "angle": 0, + "content": "to detect the existence of secret data. In the current digital world, image and video are commonly used covers, widely applied in digital communication [27], copyright protection [36], information certification [31], e-commerce [26], and many other practical fields [10, 12]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.401, + 0.893, + 0.688 + ], + "angle": 0, + "content": "Traditional video steganography methods usually hide messages in the spatial domain or transform domain by manual design. Video steganography in the spatial domain means embedding is done directly to the pixel values of video frames. Least significant bits (LSB) [8,45] is the most well-known spatial-domain method, replacing the \\( n \\) least significant bits of the cover image with the most significant \\( n \\) bits of the secret data. Many researchers have used LSB replacement [6] and LSB matching [34] for video steganography. The transform-domain hiding [5, 17, 39] is done by modifying certain frequency coefficients of the transformed frames. For instance, [44] proposed a video steganography technique by manipulating the quantized coefficients of DCT (Discrete Cosine Transformation). [9] proposed to compare the DWT (Discrete Wavelet Transformation) coefficients of the secret image and the cover video for hiding. However, these traditional methods have low hiding capacity and invisibility, easily being cracked by steganalysis methods [15, 28, 33]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.69, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Recently, some deep-learning methods were proposed to improve the hiding capacity and performance. Early works are presented in image steganography. Baluja [3, 4] proposed the first deep-learning method to hide a full-size image into another image. Recently, [21, 32] proposed designing the steganography model as an invertible neural network (INN) [13, 14] to perform image hiding and recovering with a single model. For video steganography, Khare et al. [22] first utilized back propagation neural networks to improve the performance of the LSB-based scheme. [43] is the first deep-learning method to hide a video into another video. Unfortunately, it simply aims to hide the residual across adjacent frames in a frame-by-frame manner, and it requires several separate steps to complete the video hiding and re" + }, + { + "type": "page_footnote", + "bbox": [ + 0.076, + 0.84, + 0.47, + 0.901 + ], + "angle": 0, + "content": "*Corresponding author. This work was supported by the King Abdulah University of Science and Technology (KAUST) Office of Sponsored Research through the Visual Computing Center (VCC) funding, SDAIA-KAUST Center of Excellence in Data Science and Artificial Intelligence, and Shenzhen Research Project JCYJ20220531093215035." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.946, + 0.521, + 0.957 + ], + "angle": 0, + "content": "22606" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.087, + 0.087, + 0.887, + 0.335 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.342, + 0.895, + 0.373 + ], + "angle": 0, + "content": "Figure 1. Illustration of our large-capacity and flexible video steganography network (LF-VSN). Our LF-VSN reversibly solves multiple videos hiding and recovering with a single model and the same parameters. It has large-capacity, key-controllable and scalable advantages." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.384, + 0.47, + 0.505 + ], + "angle": 0, + "content": "covering. [35] utilize 3D-CNN to explore the temporal correlation in video hiding. However, it utilizes two separated 3D UNet to perform hiding and recovering, and it has high model complexity (367.2 million parameters). While video steganography has achieved impressive success in terms of hiding capacity to hide a full-size video, the more challenging multiple videos hiding has hardly been studied. Also, the steganography pipeline is rigid." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.506, + 0.471, + 0.701 + ], + "angle": 0, + "content": "In this paper, we study the large-capacity and flexible video steganography, as shown in Fig. 1. Concretely, we propose a reversible video steganography pipeline, achieving large capacity to hide/recover multiple secret videos in/from a cover video. At the same time, our model complexity is also attractive by combining several weight-sharing designs. The flexibility of our method is twofold. First, we propose a key-controllable scheme, enabling different receivers to recover particular secret videos with specific keys. Second, we propose a scalable strategy, which can hide variable numbers of secret videos into a cover video with a single model and a single training session. To summarize, this work has the following contributions:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.706, + 0.47, + 0.766 + ], + "angle": 0, + "content": "- We propose a large-capacity video steganography method, which can hide/recover multiple (up to 7) secret videos in/from a cover video. Our hiding and recovering are fully reversible via a single INN." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.771, + 0.469, + 0.817 + ], + "angle": 0, + "content": "- We propose a key-controllable scheme with which different receivers can recover particular secret videos from the same cover video via specific keys." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.821, + 0.469, + 0.88 + ], + "angle": 0, + "content": "- We propose a scalable embedding module, utilizing a single model and a single training session to satisfy different requirements for the number of secret videos hidden in a cover video." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.886, + 0.469, + 0.902 + ], + "angle": 0, + "content": "- Extensive experiments demonstrate that our proposed" + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.706, + 0.47, + 0.902 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.532, + 0.384, + 0.892, + 0.415 + ], + "angle": 0, + "content": "method achieves state-of-the-art performance with large hiding capacity and flexibility." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.429, + 0.642, + 0.445 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.454, + 0.702, + 0.471 + ], + "angle": 0, + "content": "2.1. Video Steganography" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.478, + 0.892, + 0.599 + ], + "angle": 0, + "content": "Steganography can date back to the 15th century, whose goal is to encode a secret message in some transport mediums and covertly communicate with a potential receiver who knows the decoding protocol to recover the secret message. Since the human visual system is less sensitive to small changes in digital media, especially digital videos. Video steganography is becoming an important research area in various data-hiding technologies [10]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.6, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Traditional video steganography methods usually performed hiding and recovering in the spatial domain, e.g., Pixel Value Differencing (PVD) [20, 40] and Least Significant Bits (LSB) [6, 34, 41]. PVD embeds the secret data in the difference value of two adjacent pixels. In [40], a PVD-based video steganography system is proposed to embed the secret data in a compressed domain of the cover medium. [20] utilized enhanced pixel-value differencing (EPVD) to improve the video steganography performance. LSB methods work by replacing the \\( n \\) least significant bits of the cover data with the most significant \\( n \\) bits of the secret information. [41] utilized LSB replacement technique to hide secret text in grayscale video frames. To enhance the security in LSB-based methods, [2] shuffled the secret data and embedded the index of correct order into the cover video. In addition to spatial-domain methods, some transformed domain methods [9, 44] were proposed to perform hiding by modifying certain frequency coefficients of the transformed cover video. For instance, [44] proposed a video steganography technique by manipulating the quantized coefficients" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "22607" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.47, + 0.182 + ], + "angle": 0, + "content": "of DCT transformation. [9] proposed to compare the DWT transformation coefficients of the secret image and the cover video for hiding. Nevertheless, the above traditional methods have low hiding capacity and invisibility, easily producing artificial markings and being cracked by steganalysis methods [15, 28, 33]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.183, + 0.471, + 0.622 + ], + "angle": 0, + "content": "Motivated by the success of deep learning, some deep-learning methods were proposed. [16] introduced GAN to steganography, showing that the adversarial training scheme can improve hiding security. [49] improve the hiding quality by utilizing two independent adversarial networks to critique the video quality and optimize for robustness. [25] studied the lossless steganography below 3 bits per pixel (bpp) hiding. [38] embedded the secret data in the wavelet transform coefficients of the video frames. The above methods focus more on the robustness of low-capacity hiding. One of the important applications of low-capacity steganography is watermarking [1, 42, 52], in which the secret bit string represents the sign of the owner. Some deep-learning methods were proposed for large-capacity hiding. [3, 4] first explored hiding a full-size image into another image. [21, 32] proposed a cheaper pipeline by implementing image hiding and recovering with a single invertible neural network (INN) [13, 14]. Compared with image hiding, video hiding is a more challenging task, requiring a larger hiding capacity. [43] first studied to hide/recover a video in/from another video. However, this method simply hides the residual across adjacent frames in a frame-by-frame manner. [35] explores the temporal correlation by 3D CNN in video steganography. However, it utilizes two separate 3D UNet to perform hiding and recovering and has high model complexity (367.2M model parameters). These previous works demonstrate that deep networks have great potential in video hiding, inspiring us to study the more challenging task of multiple and flexible video hiding." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.634, + 0.32, + 0.649 + ], + "angle": 0, + "content": "2.2. Invertible Neural Nerwork" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.658, + 0.47, + 0.868 + ], + "angle": 0, + "content": "Since the concept of invertible neural network (INN) was proposed in [13, 14], INN has attracted more and more attention due to its pure invertible pipeline. Pioneering research on INN can be seen in image generation tasks. For instance, Glow [24] utilized INN to construct an invertible mapping between the latent variable \\(\\mathbf{z}\\) and nature images \\(\\mathbf{x}\\). Specifically, the generative process \\(\\mathbf{x} = f_{\\theta}(\\mathbf{z})\\) given a latent variable can be specified by an INN architecture \\(f_{\\theta}\\). The direct access to the inverse mapping \\(\\mathbf{z} = f_{\\theta}^{-1}(\\mathbf{x})\\) makes inference much cheaper. Up to now, INN has been studied in several vision tasks (e.g., image rescaling [19, 46], image restoration [29, 30], image coloring [51], and video temporal action localization [50]) and presents promising performance." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.471, + 0.902 + ], + "angle": 0, + "content": "The architecture of INN needs to be carefully designed to guarantee the invertibility. Commonly, INN is composed" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.168 + ], + "angle": 0, + "content": "of several invertible blocks, e.g., the coupling layer [13]. Given the input \\(\\mathbf{h}\\), the coupling layer first splits \\(\\mathbf{h}\\) into two parts \\((\\mathbf{h}_1\\) and \\(\\mathbf{h}_2)\\) along the channel axis. Then they undergo the affine transformations with the affine parameters generated by each other:" + }, + { + "type": "equation", + "bbox": [ + 0.598, + 0.17, + 0.892, + 0.195 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{c} \\hat {\\mathbf {h}} _ {1} = \\mathbf {h} _ {1} \\cdot \\psi_ {1} (\\mathbf {h} _ {2}) + \\phi_ {1} (\\mathbf {h} _ {2}) \\\\ \\hat {\\quad} \\quad \\hat {\\quad} \\quad \\hat {\\quad} \\quad \\hat {\\quad} \\quad \\hat {\\quad} \\quad \\hat {\\quad} \\quad \\hat {\\quad} \\quad \\hat {\\quad} \\quad \\hat {\\quad} \\quad \\hat {\\quad} \\quad \\hat {\\quad} \\quad \\hat {\\quad} \\quad \\hat {\\quad} \\quad \\hat {\\quad} \\quad \\end{array} \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.598, + 0.192, + 0.794, + 0.209 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathbf {h}} _ {2} = \\mathbf {h} _ {2} \\cdot \\psi_ {2} (\\hat {\\mathbf {h}} _ {1}) + \\phi_ {2} (\\hat {\\mathbf {h}} _ {1}),\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.218, + 0.892, + 0.263 + ], + "angle": 0, + "content": "where \\(\\psi (\\cdot)\\) and \\(\\phi (\\cdot)\\) are arbitrary functions. \\(\\hat{\\mathbf{h}}_1\\) and \\(\\hat{\\mathbf{h}}_2\\) are the outputs of the coupling layer. Correspondingly, the inverse process is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.545, + 0.265, + 0.892, + 0.303 + ], + "angle": 0, + "content": "\\[\n\\mathbf {h} _ {1} = \\frac {\\hat {\\mathbf {h}} _ {1} - \\phi_ {1} \\left(\\mathbf {h} _ {2}\\right)}{\\psi_ {1} \\left(\\mathbf {h} _ {2}\\right)}; \\quad \\mathbf {h} _ {2} = \\frac {\\hat {\\mathbf {h}} _ {2} - \\phi_ {2} \\left(\\hat {\\mathbf {h}} _ {1}\\right)}{\\psi_ {2} \\left(\\hat {\\mathbf {h}} _ {1}\\right)}. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.307, + 0.892, + 0.369 + ], + "angle": 0, + "content": "In this paper, we employ the reversible forward and backward processes of INN to perform multiple videos hiding and recovering, respectively. We further improve INN to explore flexible video steganography." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.38, + 0.635, + 0.396 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.404, + 0.611, + 0.419 + ], + "angle": 0, + "content": "3.1. Overview" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.427, + 0.892, + 0.626 + ], + "angle": 0, + "content": "An overview of our LF-VSN is presented in Fig. 2. Specifically, given \\( N_{s} \\) secret videos \\( \\mathbf{x}_{se} = \\{\\mathbf{x}_{se}(n)\\}_{n=1}^{N_{s}} \\) and a cover video \\( \\mathbf{x}_{co} \\), the forward hiding is operated group-by-group through a sliding window, traversing each video from head to tail. After hiding, a stego video \\( \\mathbf{x}_{st} \\) is produced, ostensibly indistinguishable from \\( \\mathbf{x}_{co} \\) to ensure that \\( \\mathbf{x}_{se} \\) is undetectable. In the backward recovering, a channel-wise broadcasting operation \\( (\\mathbb{R}^{3\\times W\\times H}\\xrightarrow{\\text{copy}}\\mathbb{R}^{3L\\times W\\times H}) \\) copies each stego frame in the channel dimension to form the reversed input. During recovering, multiple secret videos are recovered frame-by-frame in parallel. It is worth noting that the forward hiding and backward recovering share the same model architecture and parameters." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.633, + 0.85, + 0.65 + ], + "angle": 0, + "content": "3.2. Steganography Input and Output Design" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.656, + 0.892, + 0.903 + ], + "angle": 0, + "content": "At the beginning of each hiding step, a fusion module is applied to fuse frames in each group to take advantage of the inner temporal correlation. Considering that it is easy to produce texture artifacts and color distortion when hiding in the spatial dimension [15, 21], we perform the fusion by a frequency concatenation. Specifically, given the \\(j\\)-th cover group \\(\\mathbf{X}_{co\\otimes j} \\in \\mathbb{R}^{L \\times 3 \\times W \\times H}\\) and secret groups \\(\\{\\mathbf{X}_{se\\otimes j}(n) \\in \\mathbb{R}^{L \\times 3 \\times W \\times H}\\}_{n=1}^{N_s}\\) (each contains \\(L\\) frames), we adopt Haar discrete wavelet transform (DWT) to split each frame into four frequency bands (i.e., LL, HL, LH, HH). In each frame group, we concatenate the part in the same frequency band from different frames in the channel dimension and then concatenate these four bands in order of frequency magnitude, producing the final secret input \\(\\{\\mathbf{X}_{se\\otimes j}(n) \\in \\mathbb{R}^{12L_s \\times \\frac{W}{2} \\times \\frac{H}{2}}\\}_{n=1}^{N_s}\\) and cover input \\(\\mathbf{X}_{co\\otimes j} \\in \\mathbb{R}^{12L_c \\times \\frac{W}{2} \\times \\frac{H}{2}}\\). The output of the forward" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "22608" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.089, + 0.887, + 0.315 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.32, + 0.895, + 0.364 + ], + "angle": 0, + "content": "Figure 2. Network architecture of our LF-VSN. It is composed of several invertible blocks. In the forward hiding process, multiple secret videos are hidden in a cover video to generate a stego video, together with redundancy. In the backward recovering process, the stego video and predicted redundancy are fed to the reverse data flow of the same network with the same parameters to recover secret videos." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.377, + 0.474, + 0.545 + ], + "angle": 0, + "content": "hiding comprises a stego group \\(\\mathbf{X}_{st\\oplus j}\\) and several redundancy groups \\(\\{\\mathbf{X}_{re\\oplus j}(n)\\}_{n = 1}^{N_s}\\). \\(\\mathbf{X}_{st\\oplus j}\\) is converted from the frequency domain to the spatial domain by a frequency separation, i.e., the inverse of the frequency concatenation. \\(\\mathbf{X}_{re\\oplus j}(n)\\) represents the redundancy of the \\(\\mathbf{X}_{se\\oplus j}(n)\\) that does not need to be hidden and will be discarded. In our LF-VSN, we utilize the adjacent frames to cooperate with hiding the central frame. Thus, we only output the central stego frame in each hiding step. The backward recovering is similarly operated in the frequency domain and converted to the spatial domain at the output." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.556, + 0.24, + 0.57 + ], + "angle": 0, + "content": "3.3. Invertible Block" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.58, + 0.474, + 0.902 + ], + "angle": 0, + "content": "As shown in Fig. 2, our hiding and recovering have reverse information flow constructed by several invertible blocks (IBs). The architecture of IB is presented in Fig. 3. Concretely, in the \\(k\\)-th IB, there are two branches to process the input cover group \\(\\mathbf{X}_{co\\otimes j}^k\\) and secret groups \\(\\{\\mathbf{X}_{se\\otimes j}^k(n)\\}_{n=1}^{N_s}\\), respectively. Several interaction pathways between these two branches construct the invertible projection. We use an additive transformation to project the cover branch and employ an enhanced affine transformation to project the secret branch. The transformation parameters are generated from each other. Here we utilize weight-sharing modules \\((\\eta_k^1(\\cdot)\\) and \\(\\phi_k^1(\\cdot))\\) to extract features from all secret groups, producing a feature set \\(\\{\\mathbf{F}_{se}^k(n)\\}_{n=1}^{N_s} = \\{\\phi_k(\\eta_k(\\mathbf{X}_{se\\otimes j}^k(n)))\\}_{n=1}^{N_s}\\). \\(\\eta_k^i(\\cdot)\\) and \\(\\phi_k^i(\\cdot)\\) (\\(i = 1, 2, 3\\)) refer to a \\(3 \\times 3\\) convolution layer and a five-layer dense block [18], respectively. Then, we concatenate \\(\\mathbf{F}_{se}^k\\) in the channel dimension and pass through an aggregation module \\(\\xi_k(\\cdot)\\) to generate the transformation parameters of the cover branch. Note that \\(\\xi_k(\\cdot)\\) is optional in different cases. In our fixed hiding, \\(\\xi_k(\\cdot)\\) is a \\(3 \\times 3\\) convolution layer, and it is a scalable embedding module in our scalable hiding. The" + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.373, + 0.871, + 0.546 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.55, + 0.892, + 0.58 + ], + "angle": 0, + "content": "Figure 3. Illustration of the architecture of our invertible block. The dashed line refers to weight sharing." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.6, + 0.892, + 0.66 + ], + "angle": 0, + "content": "transformation parameters of the secret branch are generated from \\(\\mathbf{X}_{co\\otimes j}^{k}\\) and shared among different secret groups. Thus, in the \\(k\\)-th invertible block, the bijection of the forward propagation in Eq. (1) is reformulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.533, + 0.679, + 0.839, + 0.697 + ], + "angle": 0, + "content": "\\[\n\\mathbf {X} _ {c o \\circledast j} ^ {k + 1} = \\mathbf {X} _ {c o \\circledast j} ^ {k} + \\xi_ {k} \\left(\\left| \\left| \\phi_ {k} ^ {1} \\left(\\eta_ {k} ^ {1} \\left(\\mathbf {X} _ {s e \\circledast j} ^ {k} (n)\\right)\\right) \\right| \\right| _ {n = 1} ^ {N _ {s}}\\right)\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.536, + 0.699, + 0.892, + 0.716 + ], + "angle": 0, + "content": "\\[\n\\left\\{\\mathbf {X} _ {s e \\circledast j} ^ {k + 1} (n) \\right\\} _ {n = 1} ^ {N _ {s}} = \\tag {3}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.536, + 0.718, + 0.858, + 0.737 + ], + "angle": 0, + "content": "\\[\n\\mathbf {X} _ {s e \\circledast j} ^ {k} (n) \\cdot \\exp \\left(\\phi_ {k} ^ {2} \\left(\\eta_ {k} ^ {2} \\left(\\mathbf {X} _ {c o \\circledast j}\\right)\\right)\\right) + \\phi_ {k} ^ {3} \\left(\\eta_ {k} ^ {3} \\left(\\mathbf {X} _ {c o \\circledast j} ^ {k + 1}\\right)\\right),\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.755, + 0.892, + 0.802 + ], + "angle": 0, + "content": "where \\(||\\cdot ||\\) refers to the channel-wise concatenation. \\(\\exp (\\cdot)\\) is the Exponential function. Accordingly, the backward propagation is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.516, + 0.82, + 0.639, + 0.837 + ], + "angle": 0, + "content": "\\[\n\\{\\mathbf {X} _ {s e \\circledast j} ^ {k} (n) \\} _ {n = 1} ^ {N _ {s}} =\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.517, + 0.839, + 0.892, + 0.858 + ], + "angle": 0, + "content": "\\[\n\\left(\\mathbf {X} _ {s e \\circledast j} ^ {k + 1} (n) - \\phi_ {k} ^ {3} \\left(\\eta_ {k} ^ {3} \\left(\\mathbf {X} _ {c o \\circledast j} ^ {k + 1}\\right)\\right)\\right) \\cdot \\exp \\left(- \\phi_ {k} ^ {2} \\left(\\eta_ {k} ^ {2} \\left(\\mathbf {X} _ {c o \\circledast j} ^ {k + 1}\\right)\\right)\\right) \\tag {4}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.517, + 0.86, + 0.825, + 0.878 + ], + "angle": 0, + "content": "\\[\n\\mathbf {X} _ {c o \\circledast j} ^ {k} = \\mathbf {X} _ {c o \\circledast j} ^ {k + 1} - \\xi_ {k} \\left(\\left| \\left| \\phi_ {k} ^ {1} \\left(\\eta_ {k} ^ {1} \\left(\\mathbf {X} _ {s e \\circledast j} ^ {k} (n)\\right)\\right) \\right| \\right| n = _ {1}\\right).\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "22609" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.098, + 0.089, + 0.241, + 0.329 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.132, + 0.334, + 0.205, + 0.347 + ], + "angle": 0, + "content": "(a) w/o key" + }, + { + "type": "image", + "bbox": [ + 0.244, + 0.089, + 0.447, + 0.33 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.312, + 0.334, + 0.375, + 0.347 + ], + "angle": 0, + "content": "(b) w key" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.351, + 0.47, + 0.394 + ], + "angle": 0, + "content": "Figure 4. The architecture of our redundancy prediction module (RPM). It has two model settings: (a) RPM without (w/o) key controlling; (b) RPM with (w) key controlling." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.408, + 0.469, + 0.44 + ], + "angle": 0, + "content": "3.4. Redundancy Prediction Module (RPM) & Key-controllable Design" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.447, + 0.47, + 0.658 + ], + "angle": 0, + "content": "As illustrated previously, we retain the stego part and discard the redundancy information in the forward hiding. Therefore, we need to prepare a suitable redundancy in the backward process to utilize the reversibility of INN to reconstruct the forward input (i.e., secret and cover). In different tasks, most INN-based methods [21,24,32,46] constrain the generated redundancy information to obey the Gaussian distribution and utilize random Gaussian sampling to approximate this part in the backward process. Nevertheless, such random sampling lacks data specificity and adaptivity. In our LF-VSN, we predict the redundancy information from the stego group through a redundancy prediction module (RPM), as shown in Fig. 4(a). It is composed of several residual blocks (RB) without the Batch Normalization layer." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.66, + 0.471, + 0.901 + ], + "angle": 0, + "content": "In this paper, we present a novel extension of RPM to construct key-controllable video steganography, with which we can hide multiple secret videos in a cover video and recover a secret video conditioned on a specific key. The architecture is shown in Fig. 4(b). Given the index \\( n_{key} \\) of a secret video \\( \\mathbf{X}_{se}(n_{key}) \\), a specific key is generated by a key encoder, which is composed of several fully connected (FC) layers. The key is then fed into a FC layer at the end of each RB in RPM to generate a condition vector with \\( 2C_{rpm} \\) channels, which is divided into two modulation vectors \\( \\alpha, \\beta \\in \\mathbb{R}^{C_{rpm} \\times 1 \\times 1} \\) in the channel dimension. \\( C_{rpm} \\) is the feature channel of each RB in RPM. Then we modulate the output feature \\( \\mathbf{F}_{rpm} \\) of each RB as \\( \\mathbf{F}_{rpm} \\cdot \\alpha + \\beta \\). In the training process, we constrain the recovered output the same as the \\( n_{key} \\)-th secret video (i.e., \\( \\mathbf{X}_{se}(n_{key}) \\)). More details can be found in Sec. 3.6." + }, + { + "type": "image", + "bbox": [ + 0.522, + 0.088, + 0.872, + 0.245 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.253, + 0.892, + 0.296 + ], + "angle": 0, + "content": "Figure 5. Illustration of our scalable embedding module. It takes the input feature map with scalable channels \\( C_{in} \\in [1, C] \\) and produces output features with fixed channels \\( C_{out} \\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.305, + 0.757, + 0.321 + ], + "angle": 0, + "content": "3.5. Scalable Embedding Module" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.328, + 0.892, + 0.562 + ], + "angle": 0, + "content": "The scalable design is used to handle the case where there are different requirements for the number of secret videos hidden in a cover video. It is succinctly designed on the feature aggregation part \\(\\xi_{k}(\\cdot)\\) in each IB, as shown in Fig. 3. The illustration of our scalable embedding module is presented in Fig. 5. It can be regarded as a special convolution layer, whose dimension of the convolution kernel can be changed according to the input. All convolution kernels \\(\\widetilde{\\mathbf{M}}\\) with different dimensions are parameter-shared from the same base kernel \\(\\mathbf{M}\\). Technically, given the input feature \\(\\mathbf{F}_{in} \\in \\mathbb{R}^{C_{in} \\times W \\times H}\\), we truncate a convolution kernel \\(\\widetilde{\\mathbf{M}} \\in \\mathbb{R}^{C_{in} \\times C_{out} \\times k \\times k}\\) from \\(\\mathbf{M} \\in \\mathbb{R}^{C \\times C_{out} \\times k \\times k}\\) to match the input dimension and then perform convolution: \\(\\mathbf{F}_{out} = \\widetilde{\\mathbf{M}} * \\mathbf{F}_{in}\\). In this way, the training of \\(\\mathbf{M}\\) is completed through the training of all sub-kernels \\(\\widetilde{\\mathbf{M}}\\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.569, + 0.645, + 0.582 + ], + "angle": 0, + "content": "3.6. Loss Function" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.592, + 0.892, + 0.697 + ], + "angle": 0, + "content": "In our LF-VSN, the loss function is used to constrain two parts, i.e., forward hiding and backward recovering. The forward hiding is to hide multiple secret videos in the cover video. The generated stego video \\(\\mathbf{X}_{st}\\) should be undetectable to secret videos and as similar as possible to the cover video. Therefore, we constrain \\(\\mathbf{X}_{st}\\) to be the same as the cover video \\(\\mathbf{X}_{co}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.582, + 0.704, + 0.891, + 0.722 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {f} = \\left| \\left| \\mathbf {X} _ {s t \\circledast j} [ I _ {c} ] - \\mathbf {X} _ {c o \\circledast j} [ I _ {c} ] \\right| \\right| _ {2} ^ {2}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.729, + 0.892, + 0.835 + ], + "angle": 0, + "content": "where \\(||\\cdot ||_2^2\\) donates the \\(\\ell_{2}\\) norm. \\(I_{c}\\) is the index of the central frame in each group. In the backward recovering, there are two patterns: with and without key controlling. In both patterns, we aim to recover the secret information from the cover video. The difference stands between recovering a specific secret video and all secret videos. In the pattern without key controlling, the loss function is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.541, + 0.842, + 0.892, + 0.883 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {b} = \\sum_ {n = 1} ^ {N _ {s}} \\left| \\left| \\hat {\\mathbf {X}} _ {s e \\otimes j} (n) [ I _ {c} ] - \\mathbf {X} _ {s e \\otimes j} (n) [ I _ {c} ] \\right| \\right| _ {2} ^ {2} + \\tag {6}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.664, + 0.885, + 0.85, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\left. \\left\\| \\hat {\\mathbf {X}} _ {c o \\circledast j} [ I _ {c} ] - \\mathbf {X} _ {c o \\circledast j} [ I _ {c} ] \\right\\| _ {2} ^ {2}, \\right.\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "22610" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.892, + 0.118 + ], + "angle": 0, + "content": "Table 1. Quantitative comparison (PSNR/SSIM) on Vimeo-T200. The best and second-best results are highlighted and underlined. Our LF-VSN achieves the best performance in stego and secret quality with acceptable complexity." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.122, + 0.892, + 0.196 + ], + "angle": 0, + "content": "
Weng et al. [43]Baluja [4]ISN [32]HiNet [21]RIIS [47]PIH [11]LF-VSN (Ours)
Stego29.43/0.86234.14/0.86042.08/0.96542.09/0.96243.50/0.951-45.17/0.980
Secret32.08/0.89935.21/0.93142.11/0.98444.44/0.99144.08/0.96436.48/0.93948.39/0.996
Params.42.57M2.65M3.00M4.05M8.15M0.67M7.40M
" + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.212, + 0.297, + 0.388 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.155, + 0.391, + 0.242, + 0.404 + ], + "angle": 0, + "content": "GroundTruth" + }, + { + "type": "image", + "bbox": [ + 0.298, + 0.212, + 0.495, + 0.387 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.367, + 0.39, + 0.426, + 0.405 + ], + "angle": 0, + "content": "ISN [32]" + }, + { + "type": "image", + "bbox": [ + 0.496, + 0.212, + 0.694, + 0.387 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.565, + 0.39, + 0.624, + 0.405 + ], + "angle": 0, + "content": "PIH [11]" + }, + { + "type": "image", + "bbox": [ + 0.695, + 0.212, + 0.892, + 0.387 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.739, + 0.39, + 0.846, + 0.404 + ], + "angle": 0, + "content": "LF-VSN (Ours)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.409, + 0.893, + 0.437 + ], + "angle": 0, + "content": "Figure 6. Visual comparison between our LF-VSN, ISN [32], and PIH [11] in 4 videos Steganography. We present the secret reconstruction results of video 2 and video 4. Our LF-VSN produces better result with intact color and details." + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.454, + 0.177, + 0.503 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.114, + 0.506, + 0.142, + 0.519 + ], + "angle": 0, + "content": "Xco" + }, + { + "type": "image", + "bbox": [ + 0.179, + 0.454, + 0.274, + 0.503 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.2, + 0.505, + 0.249, + 0.519 + ], + "angle": 0, + "content": "\\(\\mathbf{X}_{se}(3)\\)" + }, + { + "type": "image", + "bbox": [ + 0.276, + 0.454, + 0.371, + 0.503 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.298, + 0.505, + 0.346, + 0.519 + ], + "angle": 0, + "content": "\\(\\mathbf{X}_{se}(5)\\)" + }, + { + "type": "image", + "bbox": [ + 0.373, + 0.454, + 0.469, + 0.503 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.395, + 0.505, + 0.445, + 0.519 + ], + "angle": 0, + "content": "\\(\\mathbf{X}_{se}(7)\\)" + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.519, + 0.177, + 0.566 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.114, + 0.57, + 0.141, + 0.584 + ], + "angle": 0, + "content": "Xst" + }, + { + "type": "image", + "bbox": [ + 0.179, + 0.519, + 0.274, + 0.566 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.2, + 0.57, + 0.249, + 0.586 + ], + "angle": 0, + "content": "\\(\\hat{\\mathbf{X}}_{se}(3)\\)" + }, + { + "type": "image", + "bbox": [ + 0.276, + 0.519, + 0.371, + 0.567 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.298, + 0.57, + 0.346, + 0.586 + ], + "angle": 0, + "content": "\\(\\hat{\\mathbf{X}}_{se}(5)\\)" + }, + { + "type": "image", + "bbox": [ + 0.373, + 0.519, + 0.469, + 0.567 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.395, + 0.57, + 0.445, + 0.586 + ], + "angle": 0, + "content": "\\(\\hat{\\mathbf{X}}_{se}(7)\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.597, + 0.469, + 0.625 + ], + "angle": 0, + "content": "Figure 7. Visualization of our LF-VSN in 7 videos steganography, showing promising performance in such an extreme case." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.641, + 0.47, + 0.716 + ], + "angle": 0, + "content": "where \\(\\hat{\\mathbf{X}}_{se}\\) and \\(\\hat{\\mathbf{X}}_{co}\\) represent the recovered secret and cover videos. In the pattern with key controlling, the loss function is defined to guarantee that the key generated from the video index \\(n_{key}\\) can only recover the \\(n_{key}\\)-th secret video. Thus, the loss function is reformulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.085, + 0.722, + 0.469, + 0.763 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {b} = \\left| \\right| \\frac {1}{N _ {s}} \\sum_ {n = 1} ^ {N _ {s}} \\hat {\\mathbf {X}} _ {s e * j} (n) [ I _ {c} ] - \\mathbf {X} _ {s e * j} \\left(n _ {k e y}\\right) [ I _ {c} ] \\left| \\right| _ {2} ^ {2} + \\tag {7}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.255, + 0.766, + 0.44, + 0.786 + ], + "angle": 0, + "content": "\\[\n\\left| \\left| \\hat {\\mathbf {X}} _ {c o * j} [ I _ {c} ] - \\mathbf {X} _ {c o * j} [ I _ {c} ] \\right| \\right| _ {2} ^ {2}.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.792, + 0.469, + 0.823 + ], + "angle": 0, + "content": "We optimize our LF-VSN by minimizing the forward loss function \\(\\mathcal{L}_f\\) and backward loss function \\(\\mathcal{L}_b\\) as:" + }, + { + "type": "equation", + "bbox": [ + 0.218, + 0.831, + 0.469, + 0.848 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {f} + \\lambda \\mathcal {L} _ {b}, \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.469, + 0.901 + ], + "angle": 0, + "content": "where \\(\\lambda\\) is a hyper-parameter to make a trade-off between forward hiding and backward recovering. We set \\(\\lambda = 4\\) to balance these two loss portions." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.455, + 0.625, + 0.472 + ], + "angle": 0, + "content": "4. Experiment" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.48, + 0.717, + 0.496 + ], + "angle": 0, + "content": "4.1. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.504, + 0.892, + 0.701 + ], + "angle": 0, + "content": "In this work, we adopt the training set of Vimeo90K [48] to train our LF-VSN. Each sequence has a fixed spatial resolution of \\( 448 \\times 256 \\). During training, we randomly crop training videos to \\( 144 \\times 144 \\) with random horizontal and vertical flipping to make a data augmentation. We use Adam optimizer [23], with \\( \\beta_{1} = 0.9 \\), \\( \\beta_{2} = 0.5 \\). We set the batch size as 16. The weight decay factor is set as \\( 1 \\times 10^{-12} \\). We use an initial learning rate of \\( 1 \\times 10^{-4} \\), which will decrease by half for every \\( 30K \\) iterations. The number of total iterations is set as \\( 250K \\). The training process can be completed on one NVIDIA Tesla V100 GPU within 3 days. For testing, we select 200 sequences from the testing set of Vimeo-90K, denoted as Vimeo-T200 in this paper." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.711, + 0.816, + 0.727 + ], + "angle": 0, + "content": "4.2. Comparison Against Other Methods" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Here we compare our LF-VSN with other methods on single video steganography and challenging multiple videos steganography. The evaluation includes the stego quality in forward hiding and the secret quality in backward recovering. For single video steganography, we compare our LF-VSN with some well-known methods [4, 43] and recent proposed methods [11, 21, 32, 47]. Note that PIH [11] highlighted the need to quantize the stego image from the floating-point format of \\(32 \\times 3\\) to \\(8 \\times 3\\) bits per pixel. But PIH just added the quantization to the compared methods without retraining. Here we retrain HiNet [21] with" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "22611" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.473, + 0.132 + ], + "angle": 0, + "content": "Table 2. Multiple videos steganography comparison (PSNR) of our LF-VSN, ISN [32], and PIH [11] on Vimeo-T200 test set. Our LF-VSN can hide/recover 7 videos with promising performance." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.136, + 0.465, + 0.246 + ], + "angle": 0, + "content": "
Videos234567
ISNStego37.6036.4132.5631.46--
Secret41.4738.7633.4233.39--
PIHStego------
Secret35.9534.9634.20---
OursStego40.9738.5537.5536.5735.6835.01
Secret44.2442.2740.2138.8836.9435.71
" + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.248, + 0.208, + 0.306 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.21, + 0.248, + 0.335, + 0.306 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.336, + 0.248, + 0.462, + 0.306 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.31, + 0.464, + 0.45 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.086, + 0.454, + 0.46, + 0.469 + ], + "angle": 0, + "content": "Key \\(2^{*}\\) recovered Key \\(4^{*}\\) recovered Key \\(6^{*}\\) recovered" + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.471, + 0.47, + 0.514 + ], + "angle": 0, + "content": "Figure 8. Visualization of our key-controllable scheme in 6 videos steganography. In the second and third rows, we use the correct and wrong (*) keys of 2, 4, 6 to recover secret videos, respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.522, + 0.469, + 0.612 + ], + "angle": 0, + "content": "quantization to make a more fair comparison. Thus, its performance may be slightly higher than that reported in PIH. ISN [32], RIIS [47] and PIH were originally designed with quantization, which can be directly compared. Tab. 1 presents that our method achieves the best performance on stego and secret while maintaining acceptable complexity." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.612, + 0.47, + 0.839 + ], + "angle": 0, + "content": "For multiple videos steganography, ISN [32] and PIH [11] studied how to hide multiple secret images in a cover image, which can be competitive counterparts of our LF-VSN. ISN can hide up to 5 secret images into 1 cover image, and PIH can hide 4 secret images. The comparison in Tab. 3 shows the better performance of our LF-VSN. Even in the 7 videos hiding, our method still has promising stego and secret quality (\\(>35dB\\)). We present the visual comparison of different methods in 4 videos steganography in Fig. 6. Obviously, ISN has color distortion, and PIH has a loss of details. By contrast, our LF-VSN can recover high-fidelity results. We also present the secret and stego quality of our LF-VSN in 7 videos hiding in Fig. 7. These videos are from DAVIS [37] dataset. One can see that our LF-VSN has promising performance in such an extreme case." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.848, + 0.411, + 0.865 + ], + "angle": 0, + "content": "4.3. Key-controllable Video Steganography" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Hiding multiple secret videos in a cover video is challenging; doing so for different receivers is even more dif" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.089, + 0.894, + 0.118 + ], + "angle": 0, + "content": "Table 3. Performance comparison between controllable (C) and non-controllable (NC) video steganography of our LF-VSN." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.122, + 0.882, + 0.173 + ], + "angle": 0, + "content": "
Num. videos246
Stego (NC/C)40.97/38.6737.55/34.4135.68/30.48
Secret (NC/C)44.24/41.0440.21/37.1536.94/31.95
" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.178, + 0.695, + 0.332 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.699, + 0.178, + 0.886, + 0.333 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.338, + 0.893, + 0.368 + ], + "angle": 0, + "content": "Figure 9. Performance comparison between our scalable and fixed design in multiple videos steganography." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.381, + 0.892, + 0.517 + ], + "angle": 0, + "content": "ficult. In this paper, we present a key-controllable scheme in multiple videos steganography. It enables different receivers to recover particular secret videos through specific keys. The comparison in Tab. 3 presents that our controllable scheme still has a large hiding capacity (up to 6 videos) with attractive performance (\\(>30dB\\)). The visualization of recovering quality is presented in the second row of Fig. 8, showing the high-quality and key-controllable results of our LF-VSN in multiple videos steganography." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.517, + 0.893, + 0.654 + ], + "angle": 0, + "content": "We also study the security of our controlling scheme, i.e., the key is sensitive and model-specific. Here we take two sets of parameters, producing from the 250K and 240K iterations in the same training process. We use the key produced by one model (*) to recover the secret video hidden by another. The result in the third row of Fig. 8 presents that the wrong key has no controlling and recovering ability. Thus, our key-controllable scheme not only has the controlling function but also enhances data security." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.663, + 0.771, + 0.68 + ], + "angle": 0, + "content": "4.4. Scalable Video Steganography" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.687, + 0.892, + 0.839 + ], + "angle": 0, + "content": "In this paper, we present a scalable scheme in multiple videos steganography. It can hide a variable number of secret videos into a cover video with a single model. We evaluate the performance of our scalable design and compare it with the fixed version in Tab. 9. Obviously, our method has an attractive performance (\\(>31dB\\)) in hiding a variable number (up to 7) of secret videos into a cover video by a single model. The performance degradation compared to fixed version is acceptable. With this design, a single model can satisfy multiple steganography demands." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.847, + 0.727, + 0.864 + ], + "angle": 0, + "content": "4.5. Steganographic Analysis" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "The data security is one of the most important concerns in steganography. In this section, we evaluate the anti" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "22612" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.892, + 0.117 + ], + "angle": 0, + "content": "Table 4. The ablation study of different components in our LF-VSN. It includes the sliding window size, number of invertible blocks (IB), frequency concatenation (FreqCat), and redundancy prediction module (RPM)." + }, + { + "type": "table", + "bbox": [ + 0.078, + 0.117, + 0.887, + 0.213 + ], + "angle": 0, + "content": "
Num. videos246333
Window size13513513533 (ours)333
Num. IB1616161616161616161216201616
FreqCat✓✓✓✓✓✓✓✓✓✓✓✓✓×
RPM✓✓✓✓✓✓✓✓✓✓✓✓×✓
Stego39.6440.9741.0836.4137.5537.8634.4735.4635.9638.0338.5538.9138.2836.85
Secret42.9744.2444.4337.6740.2140.4235.1136.8339.9741.9942.2742.4041.6940.36
" + }, + { + "type": "image", + "bbox": [ + 0.105, + 0.226, + 0.436, + 0.436 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.44, + 0.47, + 0.469 + ], + "angle": 0, + "content": "Figure 10. Statistics-based steganalysis by StegExpose [7]. The closer the detection accuracy is to \\(50\\%\\), the higher the security is." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.484, + 0.47, + 0.726 + ], + "angle": 0, + "content": "steganalysis ability of different methods, which stands for the possibility of detecting stego frames from nature frames by steganalysis tools. We utilize the StegExpose [7] to attack different steganography methods. The detection set is built by mixing stego and cover with equal proportions. We vary the detection thresholds in a wide range in StegExpose and draw the receiver operating characteristic (ROC) curve in Fig. 10. Note that the ideal case represents that the detector has a \\(50\\%\\) probability of detecting stego from an equally mixed cover and stego, the same as random sampling. Therefore, the closer the curve is to the ideal case, the higher the security is. Obviously, the stego frames generated by our LF-VSN are harder to be detected than other methods. Even in the multiple videos (e.g., 2 and 4 videos) hiding, our method can still achieve attractive performance, demonstrating the higher data security of our LF-VSN." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.74, + 0.231, + 0.756 + ], + "angle": 0, + "content": "4.6. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.764, + 0.469, + 0.809 + ], + "angle": 0, + "content": "In this subsection, we present the ablation study in Tab. 4 to investigate the effect of different components in our LF-VSN. The experiments are conducted on Vimeo-T200." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.469, + 0.902 + ], + "angle": 0, + "content": "Sliding window size. In this paper, we utilize the temporal correlation within each frame group to improve the video steganography performance. To demonstrate the effectiveness, we evaluate the performance of our LF-VSN with the window size \\( L = \\{1,3,5\\} \\) in 2,4,and 6 videos steganography. The results in Tab. 4 present that the temporal corre" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.229, + 0.892, + 0.273 + ], + "angle": 0, + "content": "lation has obvious performance gains to the multiple videos steganography. Considering the model complexity, we set the sliding window size as 3 in our LF-VSN." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.274, + 0.892, + 0.379 + ], + "angle": 0, + "content": "Number of invertible blocks (IB). As mentioned above, our LF-VSN is composed of several IBs. To investigate the effectiveness of IB, we evaluate the performance of our LF-VSN with the number of IB being 12, 16, and 20. The results in Tab. 4 present that the performance increases with the number of IB. To make a trade-off between performance and complexity, we utilize 16 IBs in our LF-VSN." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.379, + 0.892, + 0.515 + ], + "angle": 0, + "content": "Frequency concatenation (FreqCat). In our LF-VSN, we use the DWT transform to merge each input group in the frequency domain. To demonstrate the effectiveness, we replace this operation with direct channel-wise concatenation. Tab. 4 presents that there are \\(1.7dB\\) and \\(1.91dB\\) gains of FreqCat on stego and secret quality in 3 videos steganography. The possible reason is that DWT transform can separate the low-frequency and high-frequency sub-bands, making it more effective for information fusion and hiding." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.515, + 0.892, + 0.622 + ], + "angle": 0, + "content": "Redundancy prediction module (RPM). In our LF-VSN, we employ RPM to predict the redundancy in the backward process instead of randomly sampling. To demonstrate the effectiveness of RPM, we replace this module with a random Gaussian sampling. The result in Tab. 4 shows that RPM can be used not only to design key-controllable steganography, but also to improve performance." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.634, + 0.619, + 0.65 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.66, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In this paper, we propose a large-capacity and flexible video steganography network (LF-VSN). The novelty of our method is twofold. First, our LF-VSN has a large hiding capacity, with which we can hide 7 secret videos into a cover video and then recover them well \\((>35dB)\\). Second, we explore the flexibility in multiple videos steganography by proposing a key-controllable scheme and a scalable design. Specifically, our key-controllable scheme can enable different receivers to recover particular secret videos through specific keys. Also, the key controlling is sensitive and model-specific, which can enhance data security. Our scalable design further improves the flexibility to hide a variable number of secret videos into a cover video with a single model. Extensive experiments demonstrate that our proposed LF-VSN has state-of-the-art performance with high security, large hiding capacity, and flexibility." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "22613" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.105 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.171 + ], + "angle": 0, + "content": "[1] Mahdi Ahmadi, Alireza Norouzi, Nader Karimi, Shadrokh Samavi, and Ali Emami. ReDMark: Framework for residual diffusion watermarking based on deep networks. Expert Systems with Applications, 146:113157, 2020. 3" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.172, + 0.47, + 0.224 + ], + "angle": 0, + "content": "[2] R Balaji and Garewal Naveen. Secure data transmission using video steganography. 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Although several attempts have been made, most of them are limited to low-capacity and fixed steganography. To rectify these weaknesses, we propose a Large-capacity and Flexible Video Steganography Network (LF-VSN) in this paper. For large-capacity, we present a reversible pipeline to perform multiple videos hiding and recovering through a single invertible neural network (INN). Our method can hide/recover 7 secret videos in/from 1 cover video with promising performance. For flexibility, we propose a key-controllable scheme, enabling different receivers to recover particular secret videos from the same cover video through specific keys. Moreover, we further improve the flexibility by proposing a scalable strategy in multiple videos hiding, which can hide variable numbers of secret videos in a cover video with a single model and a single training session. Extensive experiments demonstrate that with the significant improvement of the video steganography performance, our proposed LF-VSN has high security, large hiding capacity, and flexibility. The source code is available at https://github.com/MC-E/LF-VSN. + +# 1. Introduction + +Steganography [10] is the technology of hiding some secret data into an inconspicuous cover medium to generate a stego output, which only allows the authorized receiver to recover the secret information. Unauthorized people can only access the content of the plain cover medium, and hard + +to detect the existence of secret data. In the current digital world, image and video are commonly used covers, widely applied in digital communication [27], copyright protection [36], information certification [31], e-commerce [26], and many other practical fields [10, 12]. + +Traditional video steganography methods usually hide messages in the spatial domain or transform domain by manual design. Video steganography in the spatial domain means embedding is done directly to the pixel values of video frames. Least significant bits (LSB) [8,45] is the most well-known spatial-domain method, replacing the $n$ least significant bits of the cover image with the most significant $n$ bits of the secret data. Many researchers have used LSB replacement [6] and LSB matching [34] for video steganography. The transform-domain hiding [5, 17, 39] is done by modifying certain frequency coefficients of the transformed frames. For instance, [44] proposed a video steganography technique by manipulating the quantized coefficients of DCT (Discrete Cosine Transformation). [9] proposed to compare the DWT (Discrete Wavelet Transformation) coefficients of the secret image and the cover video for hiding. However, these traditional methods have low hiding capacity and invisibility, easily being cracked by steganalysis methods [15, 28, 33]. + +Recently, some deep-learning methods were proposed to improve the hiding capacity and performance. Early works are presented in image steganography. Baluja [3, 4] proposed the first deep-learning method to hide a full-size image into another image. Recently, [21, 32] proposed designing the steganography model as an invertible neural network (INN) [13, 14] to perform image hiding and recovering with a single model. For video steganography, Khare et al. [22] first utilized back propagation neural networks to improve the performance of the LSB-based scheme. [43] is the first deep-learning method to hide a video into another video. Unfortunately, it simply aims to hide the residual across adjacent frames in a frame-by-frame manner, and it requires several separate steps to complete the video hiding and re + +![](images/ece7fba48046d09cb4437851ad802dd0312c5d95783eaf91fe9d68359f2e20b5.jpg) +Figure 1. Illustration of our large-capacity and flexible video steganography network (LF-VSN). Our LF-VSN reversibly solves multiple videos hiding and recovering with a single model and the same parameters. It has large-capacity, key-controllable and scalable advantages. + +covering. [35] utilize 3D-CNN to explore the temporal correlation in video hiding. However, it utilizes two separated 3D UNet to perform hiding and recovering, and it has high model complexity (367.2 million parameters). While video steganography has achieved impressive success in terms of hiding capacity to hide a full-size video, the more challenging multiple videos hiding has hardly been studied. Also, the steganography pipeline is rigid. + +In this paper, we study the large-capacity and flexible video steganography, as shown in Fig. 1. Concretely, we propose a reversible video steganography pipeline, achieving large capacity to hide/recover multiple secret videos in/from a cover video. At the same time, our model complexity is also attractive by combining several weight-sharing designs. The flexibility of our method is twofold. First, we propose a key-controllable scheme, enabling different receivers to recover particular secret videos with specific keys. Second, we propose a scalable strategy, which can hide variable numbers of secret videos into a cover video with a single model and a single training session. To summarize, this work has the following contributions: + +- We propose a large-capacity video steganography method, which can hide/recover multiple (up to 7) secret videos in/from a cover video. Our hiding and recovering are fully reversible via a single INN. +- We propose a key-controllable scheme with which different receivers can recover particular secret videos from the same cover video via specific keys. +- We propose a scalable embedding module, utilizing a single model and a single training session to satisfy different requirements for the number of secret videos hidden in a cover video. +- Extensive experiments demonstrate that our proposed + +method achieves state-of-the-art performance with large hiding capacity and flexibility. + +# 2. Related Work + +# 2.1. Video Steganography + +Steganography can date back to the 15th century, whose goal is to encode a secret message in some transport mediums and covertly communicate with a potential receiver who knows the decoding protocol to recover the secret message. Since the human visual system is less sensitive to small changes in digital media, especially digital videos. Video steganography is becoming an important research area in various data-hiding technologies [10]. + +Traditional video steganography methods usually performed hiding and recovering in the spatial domain, e.g., Pixel Value Differencing (PVD) [20, 40] and Least Significant Bits (LSB) [6, 34, 41]. PVD embeds the secret data in the difference value of two adjacent pixels. In [40], a PVD-based video steganography system is proposed to embed the secret data in a compressed domain of the cover medium. [20] utilized enhanced pixel-value differencing (EPVD) to improve the video steganography performance. LSB methods work by replacing the $n$ least significant bits of the cover data with the most significant $n$ bits of the secret information. [41] utilized LSB replacement technique to hide secret text in grayscale video frames. To enhance the security in LSB-based methods, [2] shuffled the secret data and embedded the index of correct order into the cover video. In addition to spatial-domain methods, some transformed domain methods [9, 44] were proposed to perform hiding by modifying certain frequency coefficients of the transformed cover video. For instance, [44] proposed a video steganography technique by manipulating the quantized coefficients + +of DCT transformation. [9] proposed to compare the DWT transformation coefficients of the secret image and the cover video for hiding. Nevertheless, the above traditional methods have low hiding capacity and invisibility, easily producing artificial markings and being cracked by steganalysis methods [15, 28, 33]. + +Motivated by the success of deep learning, some deep-learning methods were proposed. [16] introduced GAN to steganography, showing that the adversarial training scheme can improve hiding security. [49] improve the hiding quality by utilizing two independent adversarial networks to critique the video quality and optimize for robustness. [25] studied the lossless steganography below 3 bits per pixel (bpp) hiding. [38] embedded the secret data in the wavelet transform coefficients of the video frames. The above methods focus more on the robustness of low-capacity hiding. One of the important applications of low-capacity steganography is watermarking [1, 42, 52], in which the secret bit string represents the sign of the owner. Some deep-learning methods were proposed for large-capacity hiding. [3, 4] first explored hiding a full-size image into another image. [21, 32] proposed a cheaper pipeline by implementing image hiding and recovering with a single invertible neural network (INN) [13, 14]. Compared with image hiding, video hiding is a more challenging task, requiring a larger hiding capacity. [43] first studied to hide/recover a video in/from another video. However, this method simply hides the residual across adjacent frames in a frame-by-frame manner. [35] explores the temporal correlation by 3D CNN in video steganography. However, it utilizes two separate 3D UNet to perform hiding and recovering and has high model complexity (367.2M model parameters). These previous works demonstrate that deep networks have great potential in video hiding, inspiring us to study the more challenging task of multiple and flexible video hiding. + +# 2.2. Invertible Neural Nerwork + +Since the concept of invertible neural network (INN) was proposed in [13, 14], INN has attracted more and more attention due to its pure invertible pipeline. Pioneering research on INN can be seen in image generation tasks. For instance, Glow [24] utilized INN to construct an invertible mapping between the latent variable $\mathbf{z}$ and nature images $\mathbf{x}$ . Specifically, the generative process $\mathbf{x} = f_{\theta}(\mathbf{z})$ given a latent variable can be specified by an INN architecture $f_{\theta}$ . The direct access to the inverse mapping $\mathbf{z} = f_{\theta}^{-1}(\mathbf{x})$ makes inference much cheaper. Up to now, INN has been studied in several vision tasks (e.g., image rescaling [19, 46], image restoration [29, 30], image coloring [51], and video temporal action localization [50]) and presents promising performance. + +The architecture of INN needs to be carefully designed to guarantee the invertibility. Commonly, INN is composed + +of several invertible blocks, e.g., the coupling layer [13]. Given the input $\mathbf{h}$ , the coupling layer first splits $\mathbf{h}$ into two parts $(\mathbf{h}_1$ and $\mathbf{h}_2)$ along the channel axis. Then they undergo the affine transformations with the affine parameters generated by each other: + +$$ +\begin{array}{c} \hat {\mathbf {h}} _ {1} = \mathbf {h} _ {1} \cdot \psi_ {1} (\mathbf {h} _ {2}) + \phi_ {1} (\mathbf {h} _ {2}) \\ \hat {\quad} \quad \hat {\quad} \quad \hat {\quad} \quad \hat {\quad} \quad \hat {\quad} \quad \hat {\quad} \quad \hat {\quad} \quad \hat {\quad} \quad \hat {\quad} \quad \hat {\quad} \quad \hat {\quad} \quad \hat {\quad} \quad \hat {\quad} \quad \hat {\quad} \quad \end{array} \tag {1} +$$ + +$$ +\hat {\mathbf {h}} _ {2} = \mathbf {h} _ {2} \cdot \psi_ {2} (\hat {\mathbf {h}} _ {1}) + \phi_ {2} (\hat {\mathbf {h}} _ {1}), +$$ + +where $\psi (\cdot)$ and $\phi (\cdot)$ are arbitrary functions. $\hat{\mathbf{h}}_1$ and $\hat{\mathbf{h}}_2$ are the outputs of the coupling layer. Correspondingly, the inverse process is defined as: + +$$ +\mathbf {h} _ {1} = \frac {\hat {\mathbf {h}} _ {1} - \phi_ {1} \left(\mathbf {h} _ {2}\right)}{\psi_ {1} \left(\mathbf {h} _ {2}\right)}; \quad \mathbf {h} _ {2} = \frac {\hat {\mathbf {h}} _ {2} - \phi_ {2} \left(\hat {\mathbf {h}} _ {1}\right)}{\psi_ {2} \left(\hat {\mathbf {h}} _ {1}\right)}. \tag {2} +$$ + +In this paper, we employ the reversible forward and backward processes of INN to perform multiple videos hiding and recovering, respectively. We further improve INN to explore flexible video steganography. + +# 3. Methodology + +# 3.1. Overview + +An overview of our LF-VSN is presented in Fig. 2. Specifically, given $N_{s}$ secret videos $\mathbf{x}_{se} = \{\mathbf{x}_{se}(n)\}_{n=1}^{N_{s}}$ and a cover video $\mathbf{x}_{co}$ , the forward hiding is operated group-by-group through a sliding window, traversing each video from head to tail. After hiding, a stego video $\mathbf{x}_{st}$ is produced, ostensibly indistinguishable from $\mathbf{x}_{co}$ to ensure that $\mathbf{x}_{se}$ is undetectable. In the backward recovering, a channel-wise broadcasting operation $(\mathbb{R}^{3\times W\times H}\xrightarrow{\text{copy}}\mathbb{R}^{3L\times W\times H})$ copies each stego frame in the channel dimension to form the reversed input. During recovering, multiple secret videos are recovered frame-by-frame in parallel. It is worth noting that the forward hiding and backward recovering share the same model architecture and parameters. + +# 3.2. Steganography Input and Output Design + +At the beginning of each hiding step, a fusion module is applied to fuse frames in each group to take advantage of the inner temporal correlation. Considering that it is easy to produce texture artifacts and color distortion when hiding in the spatial dimension [15, 21], we perform the fusion by a frequency concatenation. Specifically, given the $j$ -th cover group $\mathbf{X}_{co\otimes j} \in \mathbb{R}^{L \times 3 \times W \times H}$ and secret groups $\{\mathbf{X}_{se\otimes j}(n) \in \mathbb{R}^{L \times 3 \times W \times H}\}_{n=1}^{N_s}$ (each contains $L$ frames), we adopt Haar discrete wavelet transform (DWT) to split each frame into four frequency bands (i.e., LL, HL, LH, HH). In each frame group, we concatenate the part in the same frequency band from different frames in the channel dimension and then concatenate these four bands in order of frequency magnitude, producing the final secret input $\{\mathbf{X}_{se\otimes j}(n) \in \mathbb{R}^{12L_s \times \frac{W}{2} \times \frac{H}{2}}\}_{n=1}^{N_s}$ and cover input $\mathbf{X}_{co\otimes j} \in \mathbb{R}^{12L_c \times \frac{W}{2} \times \frac{H}{2}}$ . The output of the forward + +![](images/6e7b99436d6eba7190b1c8dc626ad8f702a65acf40db4880f7eb3c1d55fe71cc.jpg) +Figure 2. Network architecture of our LF-VSN. It is composed of several invertible blocks. In the forward hiding process, multiple secret videos are hidden in a cover video to generate a stego video, together with redundancy. In the backward recovering process, the stego video and predicted redundancy are fed to the reverse data flow of the same network with the same parameters to recover secret videos. + +hiding comprises a stego group $\mathbf{X}_{st\oplus j}$ and several redundancy groups $\{\mathbf{X}_{re\oplus j}(n)\}_{n = 1}^{N_s}$ . $\mathbf{X}_{st\oplus j}$ is converted from the frequency domain to the spatial domain by a frequency separation, i.e., the inverse of the frequency concatenation. $\mathbf{X}_{re\oplus j}(n)$ represents the redundancy of the $\mathbf{X}_{se\oplus j}(n)$ that does not need to be hidden and will be discarded. In our LF-VSN, we utilize the adjacent frames to cooperate with hiding the central frame. Thus, we only output the central stego frame in each hiding step. The backward recovering is similarly operated in the frequency domain and converted to the spatial domain at the output. + +# 3.3. Invertible Block + +As shown in Fig. 2, our hiding and recovering have reverse information flow constructed by several invertible blocks (IBs). The architecture of IB is presented in Fig. 3. Concretely, in the $k$ -th IB, there are two branches to process the input cover group $\mathbf{X}_{co\otimes j}^k$ and secret groups $\{\mathbf{X}_{se\otimes j}^k(n)\}_{n=1}^{N_s}$ , respectively. Several interaction pathways between these two branches construct the invertible projection. We use an additive transformation to project the cover branch and employ an enhanced affine transformation to project the secret branch. The transformation parameters are generated from each other. Here we utilize weight-sharing modules $(\eta_k^1(\cdot)$ and $\phi_k^1(\cdot))$ to extract features from all secret groups, producing a feature set $\{\mathbf{F}_{se}^k(n)\}_{n=1}^{N_s} = \{\phi_k(\eta_k(\mathbf{X}_{se\otimes j}^k(n)))\}_{n=1}^{N_s}$ . $\eta_k^i(\cdot)$ and $\phi_k^i(\cdot)$ ( $i = 1, 2, 3$ ) refer to a $3 \times 3$ convolution layer and a five-layer dense block [18], respectively. Then, we concatenate $\mathbf{F}_{se}^k$ in the channel dimension and pass through an aggregation module $\xi_k(\cdot)$ to generate the transformation parameters of the cover branch. Note that $\xi_k(\cdot)$ is optional in different cases. In our fixed hiding, $\xi_k(\cdot)$ is a $3 \times 3$ convolution layer, and it is a scalable embedding module in our scalable hiding. The + +![](images/9f014d1ed1fd758b8c31cb2c9f8242ba4121159af2d9fe9f7858fb2e6d835a74.jpg) +Figure 3. Illustration of the architecture of our invertible block. The dashed line refers to weight sharing. + +transformation parameters of the secret branch are generated from $\mathbf{X}_{co\otimes j}^{k}$ and shared among different secret groups. Thus, in the $k$ -th invertible block, the bijection of the forward propagation in Eq. (1) is reformulated as: + +$$ +\mathbf {X} _ {c o \circledast j} ^ {k + 1} = \mathbf {X} _ {c o \circledast j} ^ {k} + \xi_ {k} \left(\left| \left| \phi_ {k} ^ {1} \left(\eta_ {k} ^ {1} \left(\mathbf {X} _ {s e \circledast j} ^ {k} (n)\right)\right) \right| \right| _ {n = 1} ^ {N _ {s}}\right) +$$ + +$$ +\left\{\mathbf {X} _ {s e \circledast j} ^ {k + 1} (n) \right\} _ {n = 1} ^ {N _ {s}} = \tag {3} +$$ + +$$ +\mathbf {X} _ {s e \circledast j} ^ {k} (n) \cdot \exp \left(\phi_ {k} ^ {2} \left(\eta_ {k} ^ {2} \left(\mathbf {X} _ {c o \circledast j}\right)\right)\right) + \phi_ {k} ^ {3} \left(\eta_ {k} ^ {3} \left(\mathbf {X} _ {c o \circledast j} ^ {k + 1}\right)\right), +$$ + +where $||\cdot ||$ refers to the channel-wise concatenation. $\exp (\cdot)$ is the Exponential function. Accordingly, the backward propagation is defined as: + +$$ +\{\mathbf {X} _ {s e \circledast j} ^ {k} (n) \} _ {n = 1} ^ {N _ {s}} = +$$ + +$$ +\left(\mathbf {X} _ {s e \circledast j} ^ {k + 1} (n) - \phi_ {k} ^ {3} \left(\eta_ {k} ^ {3} \left(\mathbf {X} _ {c o \circledast j} ^ {k + 1}\right)\right)\right) \cdot \exp \left(- \phi_ {k} ^ {2} \left(\eta_ {k} ^ {2} \left(\mathbf {X} _ {c o \circledast j} ^ {k + 1}\right)\right)\right) \tag {4} +$$ + +$$ +\mathbf {X} _ {c o \circledast j} ^ {k} = \mathbf {X} _ {c o \circledast j} ^ {k + 1} - \xi_ {k} \left(\left| \left| \phi_ {k} ^ {1} \left(\eta_ {k} ^ {1} \left(\mathbf {X} _ {s e \circledast j} ^ {k} (n)\right)\right) \right| \right| n = _ {1}\right). +$$ + +![](images/cc032df3fcba499771314ec39f29bf85660d6f70b314ca805cd06b0a4af5542a.jpg) +(a) w/o key + +![](images/592f922e462c47501c993e5d02a1ebdaf6fce91c620aed164ee810bd6238b721.jpg) +(b) w key +Figure 4. The architecture of our redundancy prediction module (RPM). It has two model settings: (a) RPM without (w/o) key controlling; (b) RPM with (w) key controlling. + +# 3.4. Redundancy Prediction Module (RPM) & Key-controllable Design + +As illustrated previously, we retain the stego part and discard the redundancy information in the forward hiding. Therefore, we need to prepare a suitable redundancy in the backward process to utilize the reversibility of INN to reconstruct the forward input (i.e., secret and cover). In different tasks, most INN-based methods [21,24,32,46] constrain the generated redundancy information to obey the Gaussian distribution and utilize random Gaussian sampling to approximate this part in the backward process. Nevertheless, such random sampling lacks data specificity and adaptivity. In our LF-VSN, we predict the redundancy information from the stego group through a redundancy prediction module (RPM), as shown in Fig. 4(a). It is composed of several residual blocks (RB) without the Batch Normalization layer. + +In this paper, we present a novel extension of RPM to construct key-controllable video steganography, with which we can hide multiple secret videos in a cover video and recover a secret video conditioned on a specific key. The architecture is shown in Fig. 4(b). Given the index $n_{key}$ of a secret video $\mathbf{X}_{se}(n_{key})$ , a specific key is generated by a key encoder, which is composed of several fully connected (FC) layers. The key is then fed into a FC layer at the end of each RB in RPM to generate a condition vector with $2C_{rpm}$ channels, which is divided into two modulation vectors $\alpha, \beta \in \mathbb{R}^{C_{rpm} \times 1 \times 1}$ in the channel dimension. $C_{rpm}$ is the feature channel of each RB in RPM. Then we modulate the output feature $\mathbf{F}_{rpm}$ of each RB as $\mathbf{F}_{rpm} \cdot \alpha + \beta$ . In the training process, we constrain the recovered output the same as the $n_{key}$ -th secret video (i.e., $\mathbf{X}_{se}(n_{key})$ ). More details can be found in Sec. 3.6. + +![](images/41a82ca31f5611c1a2f1be94b449e1290b70820da587d341dc6dcca6abbd7ca1.jpg) +Figure 5. Illustration of our scalable embedding module. It takes the input feature map with scalable channels $C_{in} \in [1, C]$ and produces output features with fixed channels $C_{out}$ . + +# 3.5. Scalable Embedding Module + +The scalable design is used to handle the case where there are different requirements for the number of secret videos hidden in a cover video. It is succinctly designed on the feature aggregation part $\xi_{k}(\cdot)$ in each IB, as shown in Fig. 3. The illustration of our scalable embedding module is presented in Fig. 5. It can be regarded as a special convolution layer, whose dimension of the convolution kernel can be changed according to the input. All convolution kernels $\widetilde{\mathbf{M}}$ with different dimensions are parameter-shared from the same base kernel $\mathbf{M}$ . Technically, given the input feature $\mathbf{F}_{in} \in \mathbb{R}^{C_{in} \times W \times H}$ , we truncate a convolution kernel $\widetilde{\mathbf{M}} \in \mathbb{R}^{C_{in} \times C_{out} \times k \times k}$ from $\mathbf{M} \in \mathbb{R}^{C \times C_{out} \times k \times k}$ to match the input dimension and then perform convolution: $\mathbf{F}_{out} = \widetilde{\mathbf{M}} * \mathbf{F}_{in}$ . In this way, the training of $\mathbf{M}$ is completed through the training of all sub-kernels $\widetilde{\mathbf{M}}$ . + +# 3.6. Loss Function + +In our LF-VSN, the loss function is used to constrain two parts, i.e., forward hiding and backward recovering. The forward hiding is to hide multiple secret videos in the cover video. The generated stego video $\mathbf{X}_{st}$ should be undetectable to secret videos and as similar as possible to the cover video. Therefore, we constrain $\mathbf{X}_{st}$ to be the same as the cover video $\mathbf{X}_{co}$ : + +$$ +\mathcal {L} _ {f} = \left| \left| \mathbf {X} _ {s t \circledast j} [ I _ {c} ] - \mathbf {X} _ {c o \circledast j} [ I _ {c} ] \right| \right| _ {2} ^ {2}, \tag {5} +$$ + +where $||\cdot ||_2^2$ donates the $\ell_{2}$ norm. $I_{c}$ is the index of the central frame in each group. In the backward recovering, there are two patterns: with and without key controlling. In both patterns, we aim to recover the secret information from the cover video. The difference stands between recovering a specific secret video and all secret videos. In the pattern without key controlling, the loss function is defined as: + +$$ +\mathcal {L} _ {b} = \sum_ {n = 1} ^ {N _ {s}} \left| \left| \hat {\mathbf {X}} _ {s e \otimes j} (n) [ I _ {c} ] - \mathbf {X} _ {s e \otimes j} (n) [ I _ {c} ] \right| \right| _ {2} ^ {2} + \tag {6} +$$ + +$$ +\left. \left\| \hat {\mathbf {X}} _ {c o \circledast j} [ I _ {c} ] - \mathbf {X} _ {c o \circledast j} [ I _ {c} ] \right\| _ {2} ^ {2}, \right. +$$ + +Table 1. Quantitative comparison (PSNR/SSIM) on Vimeo-T200. The best and second-best results are highlighted and underlined. Our LF-VSN achieves the best performance in stego and secret quality with acceptable complexity. + +
Weng et al. [43]Baluja [4]ISN [32]HiNet [21]RIIS [47]PIH [11]LF-VSN (Ours)
Stego29.43/0.86234.14/0.86042.08/0.96542.09/0.96243.50/0.951-45.17/0.980
Secret32.08/0.89935.21/0.93142.11/0.98444.44/0.99144.08/0.96436.48/0.93948.39/0.996
Params.42.57M2.65M3.00M4.05M8.15M0.67M7.40M
+ +![](images/5edf7612f72e303b37f54afab1af67f0600541a198020664c1e5003ec605a6fe.jpg) +GroundTruth + +![](images/2e06b67db7e1c87b81b87fddb8ea26a3c2534136fc47b68279580d0d91cb42f2.jpg) +ISN [32] + +![](images/4a464cd1601957c3bd6076400432db39866a12746f0d8588aaa0a721d6a340d8.jpg) +PIH [11] + +![](images/b953141990d3b37beeede203b5e9278f261af3c8f1cd52b7b1ee1d761ff847cb.jpg) +LF-VSN (Ours) + +![](images/0881958a1e084788ce362c46e312216f6868689ff41837c9c42dab9bd760b4d0.jpg) +Figure 6. Visual comparison between our LF-VSN, ISN [32], and PIH [11] in 4 videos Steganography. We present the secret reconstruction results of video 2 and video 4. Our LF-VSN produces better result with intact color and details. + +![](images/8a6fcf07325bde8d2b8bf81ed7281c1eb58240a8159619f9fc1b0518ac95816a.jpg) + +![](images/7f98b5d3875eec21f5decf7c829584721d34b32ff0c6b344e805563a74626d07.jpg) + +![](images/9bdd5c4db0f50ace30887c4c2f016833e4e4ab9dbd1cedea2a0be7d8a3e1c3be.jpg) + +![](images/197238f0a1402abc7c0df756ad9204c10b7181a79c08cf575798671dcb3a5d3e.jpg) +Xco +Xst + +![](images/fad5ccf6cae1afd8d9b7feda6dc7832d75b9ce66a369a8a151693247bb8eb256.jpg) +$\mathbf{X}_{se}(3)$ +$\hat{\mathbf{X}}_{se}(3)$ + +![](images/192070a4258cc36348f3528a938ff453569c7f8d7948b57f9bed5e5e79385f4c.jpg) +$\mathbf{X}_{se}(5)$ +$\hat{\mathbf{X}}_{se}(5)$ +Figure 7. Visualization of our LF-VSN in 7 videos steganography, showing promising performance in such an extreme case. + +![](images/3af70c6d91b41cb00700ab9c663413d0f2c93c916a46210af47eacd4fe8f1263.jpg) +$\mathbf{X}_{se}(7)$ +$\hat{\mathbf{X}}_{se}(7)$ + +where $\hat{\mathbf{X}}_{se}$ and $\hat{\mathbf{X}}_{co}$ represent the recovered secret and cover videos. In the pattern with key controlling, the loss function is defined to guarantee that the key generated from the video index $n_{key}$ can only recover the $n_{key}$ -th secret video. Thus, the loss function is reformulated as: + +$$ +\mathcal {L} _ {b} = \left| \right| \frac {1}{N _ {s}} \sum_ {n = 1} ^ {N _ {s}} \hat {\mathbf {X}} _ {s e * j} (n) [ I _ {c} ] - \mathbf {X} _ {s e * j} \left(n _ {k e y}\right) [ I _ {c} ] \left| \right| _ {2} ^ {2} + \tag {7} +$$ + +$$ +\left| \left| \hat {\mathbf {X}} _ {c o * j} [ I _ {c} ] - \mathbf {X} _ {c o * j} [ I _ {c} ] \right| \right| _ {2} ^ {2}. +$$ + +We optimize our LF-VSN by minimizing the forward loss function $\mathcal{L}_f$ and backward loss function $\mathcal{L}_b$ as: + +$$ +\mathcal {L} = \mathcal {L} _ {f} + \lambda \mathcal {L} _ {b}, \tag {8} +$$ + +where $\lambda$ is a hyper-parameter to make a trade-off between forward hiding and backward recovering. We set $\lambda = 4$ to balance these two loss portions. + +# 4. Experiment + +# 4.1. Implementation Details + +In this work, we adopt the training set of Vimeo90K [48] to train our LF-VSN. Each sequence has a fixed spatial resolution of $448 \times 256$ . During training, we randomly crop training videos to $144 \times 144$ with random horizontal and vertical flipping to make a data augmentation. We use Adam optimizer [23], with $\beta_{1} = 0.9$ , $\beta_{2} = 0.5$ . We set the batch size as 16. The weight decay factor is set as $1 \times 10^{-12}$ . We use an initial learning rate of $1 \times 10^{-4}$ , which will decrease by half for every $30K$ iterations. The number of total iterations is set as $250K$ . The training process can be completed on one NVIDIA Tesla V100 GPU within 3 days. For testing, we select 200 sequences from the testing set of Vimeo-90K, denoted as Vimeo-T200 in this paper. + +# 4.2. Comparison Against Other Methods + +Here we compare our LF-VSN with other methods on single video steganography and challenging multiple videos steganography. The evaluation includes the stego quality in forward hiding and the secret quality in backward recovering. For single video steganography, we compare our LF-VSN with some well-known methods [4, 43] and recent proposed methods [11, 21, 32, 47]. Note that PIH [11] highlighted the need to quantize the stego image from the floating-point format of $32 \times 3$ to $8 \times 3$ bits per pixel. But PIH just added the quantization to the compared methods without retraining. Here we retrain HiNet [21] with + +Table 2. Multiple videos steganography comparison (PSNR) of our LF-VSN, ISN [32], and PIH [11] on Vimeo-T200 test set. Our LF-VSN can hide/recover 7 videos with promising performance. + +
Videos234567
ISNStego37.6036.4132.5631.46--
Secret41.4738.7633.4233.39--
PIHStego------
Secret35.9534.9634.20---
OursStego40.9738.5537.5536.5735.6835.01
Secret44.2442.2740.2138.8836.9435.71
+ +![](images/cd2d8536f5456b32d1eede040957847c24656fbfae6f3845ce7622bd086f7f9e.jpg) + +![](images/2e2140616dc4ac970d985e45a53f9981a3454debacb6ebf2a4396eda21e8117f.jpg) + +![](images/eb20884d44a37ad8d311c3914a55b3fb7a3f2623def279c756e3e3445102a438.jpg) + +![](images/befbac94ca57960ca6a150cc3b947b99a8f6d0a34ad1cca944249df6281463f3.jpg) +Key $2^{*}$ recovered Key $4^{*}$ recovered Key $6^{*}$ recovered +Figure 8. Visualization of our key-controllable scheme in 6 videos steganography. In the second and third rows, we use the correct and wrong (*) keys of 2, 4, 6 to recover secret videos, respectively. + +quantization to make a more fair comparison. Thus, its performance may be slightly higher than that reported in PIH. ISN [32], RIIS [47] and PIH were originally designed with quantization, which can be directly compared. Tab. 1 presents that our method achieves the best performance on stego and secret while maintaining acceptable complexity. + +For multiple videos steganography, ISN [32] and PIH [11] studied how to hide multiple secret images in a cover image, which can be competitive counterparts of our LF-VSN. ISN can hide up to 5 secret images into 1 cover image, and PIH can hide 4 secret images. The comparison in Tab. 3 shows the better performance of our LF-VSN. Even in the 7 videos hiding, our method still has promising stego and secret quality ( $>35dB$ ). We present the visual comparison of different methods in 4 videos steganography in Fig. 6. Obviously, ISN has color distortion, and PIH has a loss of details. By contrast, our LF-VSN can recover high-fidelity results. We also present the secret and stego quality of our LF-VSN in 7 videos hiding in Fig. 7. These videos are from DAVIS [37] dataset. One can see that our LF-VSN has promising performance in such an extreme case. + +# 4.3. Key-controllable Video Steganography + +Hiding multiple secret videos in a cover video is challenging; doing so for different receivers is even more dif + +Table 3. Performance comparison between controllable (C) and non-controllable (NC) video steganography of our LF-VSN. + +
Num. videos246
Stego (NC/C)40.97/38.6737.55/34.4135.68/30.48
Secret (NC/C)44.24/41.0440.21/37.1536.94/31.95
+ +![](images/91d41fbb871065915eeca5e54f02a643a859328875254b8450e7cc0c8dad6373.jpg) + +![](images/c7b7255671297442a71885073d141d73e166bda2824c888410ce2a7edc235ddb.jpg) +Figure 9. Performance comparison between our scalable and fixed design in multiple videos steganography. + +ficult. In this paper, we present a key-controllable scheme in multiple videos steganography. It enables different receivers to recover particular secret videos through specific keys. The comparison in Tab. 3 presents that our controllable scheme still has a large hiding capacity (up to 6 videos) with attractive performance ( $>30dB$ ). The visualization of recovering quality is presented in the second row of Fig. 8, showing the high-quality and key-controllable results of our LF-VSN in multiple videos steganography. + +We also study the security of our controlling scheme, i.e., the key is sensitive and model-specific. Here we take two sets of parameters, producing from the 250K and 240K iterations in the same training process. We use the key produced by one model (*) to recover the secret video hidden by another. The result in the third row of Fig. 8 presents that the wrong key has no controlling and recovering ability. Thus, our key-controllable scheme not only has the controlling function but also enhances data security. + +# 4.4. Scalable Video Steganography + +In this paper, we present a scalable scheme in multiple videos steganography. It can hide a variable number of secret videos into a cover video with a single model. We evaluate the performance of our scalable design and compare it with the fixed version in Tab. 9. Obviously, our method has an attractive performance ( $>31dB$ ) in hiding a variable number (up to 7) of secret videos into a cover video by a single model. The performance degradation compared to fixed version is acceptable. With this design, a single model can satisfy multiple steganography demands. + +# 4.5. Steganographic Analysis + +The data security is one of the most important concerns in steganography. In this section, we evaluate the anti + +Table 4. The ablation study of different components in our LF-VSN. It includes the sliding window size, number of invertible blocks (IB), frequency concatenation (FreqCat), and redundancy prediction module (RPM). + +
Num. videos246333
Window size13513513533 (ours)333
Num. IB1616161616161616161216201616
FreqCat✓✓✓✓✓✓✓✓✓✓✓✓✓×
RPM✓✓✓✓✓✓✓✓✓✓✓✓×✓
Stego39.6440.9741.0836.4137.5537.8634.4735.4635.9638.0338.5538.9138.2836.85
Secret42.9744.2444.4337.6740.2140.4235.1136.8339.9741.9942.2742.4041.6940.36
+ +![](images/25d4c48d9297d58fb3cf320eac39139b6cbb9eb1f27c2352bf3524cb06e95300.jpg) +Figure 10. Statistics-based steganalysis by StegExpose [7]. The closer the detection accuracy is to $50\%$ , the higher the security is. + +steganalysis ability of different methods, which stands for the possibility of detecting stego frames from nature frames by steganalysis tools. We utilize the StegExpose [7] to attack different steganography methods. The detection set is built by mixing stego and cover with equal proportions. We vary the detection thresholds in a wide range in StegExpose and draw the receiver operating characteristic (ROC) curve in Fig. 10. Note that the ideal case represents that the detector has a $50\%$ probability of detecting stego from an equally mixed cover and stego, the same as random sampling. Therefore, the closer the curve is to the ideal case, the higher the security is. Obviously, the stego frames generated by our LF-VSN are harder to be detected than other methods. Even in the multiple videos (e.g., 2 and 4 videos) hiding, our method can still achieve attractive performance, demonstrating the higher data security of our LF-VSN. + +# 4.6. Ablation Study + +In this subsection, we present the ablation study in Tab. 4 to investigate the effect of different components in our LF-VSN. The experiments are conducted on Vimeo-T200. + +Sliding window size. In this paper, we utilize the temporal correlation within each frame group to improve the video steganography performance. To demonstrate the effectiveness, we evaluate the performance of our LF-VSN with the window size $L = \{1,3,5\}$ in 2,4,and 6 videos steganography. The results in Tab. 4 present that the temporal corre + +lation has obvious performance gains to the multiple videos steganography. Considering the model complexity, we set the sliding window size as 3 in our LF-VSN. + +Number of invertible blocks (IB). As mentioned above, our LF-VSN is composed of several IBs. To investigate the effectiveness of IB, we evaluate the performance of our LF-VSN with the number of IB being 12, 16, and 20. The results in Tab. 4 present that the performance increases with the number of IB. To make a trade-off between performance and complexity, we utilize 16 IBs in our LF-VSN. + +Frequency concatenation (FreqCat). In our LF-VSN, we use the DWT transform to merge each input group in the frequency domain. To demonstrate the effectiveness, we replace this operation with direct channel-wise concatenation. Tab. 4 presents that there are $1.7dB$ and $1.91dB$ gains of FreqCat on stego and secret quality in 3 videos steganography. The possible reason is that DWT transform can separate the low-frequency and high-frequency sub-bands, making it more effective for information fusion and hiding. + +Redundancy prediction module (RPM). In our LF-VSN, we employ RPM to predict the redundancy in the backward process instead of randomly sampling. To demonstrate the effectiveness of RPM, we replace this module with a random Gaussian sampling. The result in Tab. 4 shows that RPM can be used not only to design key-controllable steganography, but also to improve performance. + +# 5. Conclusion + +In this paper, we propose a large-capacity and flexible video steganography network (LF-VSN). The novelty of our method is twofold. First, our LF-VSN has a large hiding capacity, with which we can hide 7 secret videos into a cover video and then recover them well $(>35dB)$ . Second, we explore the flexibility in multiple videos steganography by proposing a key-controllable scheme and a scalable design. Specifically, our key-controllable scheme can enable different receivers to recover particular secret videos through specific keys. Also, the key controlling is sensitive and model-specific, which can enhance data security. 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In Proceedings of the European Conference on Computer Vision (ECCV), pages 657–672, 2018. 3 \ No newline at end of file diff --git a/2023/Large-Capacity and Flexible Video Steganography via Invertible Neural Network/images.zip b/2023/Large-Capacity and Flexible Video Steganography via Invertible Neural Network/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..7b9e82832b27b7653bb795498da0e04861ded6d3 --- /dev/null +++ b/2023/Large-Capacity and Flexible Video Steganography via Invertible Neural Network/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:1731792cba840a2db150a7ec01efe30fbdd09f5c019e34ea7cf70f1d93ecac2c +size 770606 diff --git a/2023/Large-Capacity and Flexible Video Steganography via Invertible Neural Network/layout.json b/2023/Large-Capacity and Flexible Video Steganography via Invertible Neural Network/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..b06ff666a0a9eccf1a0c7c62d0cde2f92dc06a4a --- /dev/null +++ b/2023/Large-Capacity and Flexible Video Steganography via Invertible Neural Network/layout.json @@ -0,0 +1,10033 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 48, + 103, + 545, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 103, + 545, + 121 + ], + "spans": [ + { + "bbox": [ + 48, + 103, + 545, + 121 + ], + "type": "text", + "content": "Large-capacity and Flexible Video Steganography via Invertible Neural Network" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 73, + 142, + 518, + 158 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 73, + 142, + 518, + 158 + ], + "spans": [ + { + "bbox": [ + 73, + 142, + 518, + 158 + ], + "type": "text", + "content": "Chong Mou1, Youmin Xu1, Jiechong Song1, Chen Zhao2, Bernard Ghanem2, Jian Zhang1,3,*" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 140, + 157, + 453, + 171 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 140, + 157, + 453, + 171 + ], + "spans": [ + { + "bbox": [ + 140, + 157, + 453, + 171 + ], + "type": "text", + "content": "1Peking University Shenzhen Graduate School, Shenzhen, China" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 83, + 171, + 510, + 184 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 171, + 510, + 184 + ], + "spans": [ + { + "bbox": [ + 83, + 171, + 510, + 184 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 83, + 171, + 510, + 184 + ], + "type": "text", + "content": "King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 193, + 185, + 401, + 199 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 193, + 185, + 401, + 199 + ], + "spans": [ + { + "bbox": [ + 193, + 185, + 401, + 199 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 193, + 185, + 401, + 199 + ], + "type": "text", + "content": "Peng Cheng Laboratory, Shenzhen, China" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 86, + 201, + 504, + 213 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 201, + 504, + 213 + ], + "spans": [ + { + "bbox": [ + 86, + 201, + 504, + 213 + ], + "type": "text", + "content": "{eechongm, youmin.xu}@stu.pku.edu.cn; {songjiechong, zhangjian.sz}@pku.edu.cn;" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 186, + 216, + 402, + 227 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 186, + 216, + 402, + 227 + ], + "spans": [ + { + "bbox": [ + 186, + 216, + 402, + 227 + ], + "type": "text", + "content": "{chen.zhao, Bernard.Ghanem}@kaust.edu.sa" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 143, + 255, + 192, + 268 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 255, + 192, + 268 + ], + "spans": [ + { + "bbox": [ + 143, + 255, + 192, + 268 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 280, + 290, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 280, + 290, + 555 + ], + "spans": [ + { + "bbox": [ + 47, + 280, + 290, + 555 + ], + "type": "text", + "content": "Video steganography is the art of unobtrusively concealing secret data in a cover video and then recovering the secret data through a decoding protocol at the receiver end. Although several attempts have been made, most of them are limited to low-capacity and fixed steganography. To rectify these weaknesses, we propose a Large-capacity and Flexible Video Steganography Network (LF-VSN) in this paper. For large-capacity, we present a reversible pipeline to perform multiple videos hiding and recovering through a single invertible neural network (INN). Our method can hide/recover 7 secret videos in/from 1 cover video with promising performance. For flexibility, we propose a key-controllable scheme, enabling different receivers to recover particular secret videos from the same cover video through specific keys. Moreover, we further improve the flexibility by proposing a scalable strategy in multiple videos hiding, which can hide variable numbers of secret videos in a cover video with a single model and a single training session. Extensive experiments demonstrate that with the significant improvement of the video steganography performance, our proposed LF-VSN has high security, large hiding capacity, and flexibility. The source code is available at https://github.com/MC-E/LF-VSN." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 578, + 128, + 590 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 578, + 128, + 590 + ], + "spans": [ + { + "bbox": [ + 47, + 578, + 128, + 590 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 597, + 287, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 597, + 287, + 658 + ], + "spans": [ + { + "bbox": [ + 46, + 597, + 287, + 658 + ], + "type": "text", + "content": "Steganography [10] is the technology of hiding some secret data into an inconspicuous cover medium to generate a stego output, which only allows the authorized receiver to recover the secret information. Unauthorized people can only access the content of the plain cover medium, and hard" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 256, + 545, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 256, + 545, + 316 + ], + "spans": [ + { + "bbox": [ + 306, + 256, + 545, + 316 + ], + "type": "text", + "content": "to detect the existence of secret data. In the current digital world, image and video are commonly used covers, widely applied in digital communication [27], copyright protection [36], information certification [31], e-commerce [26], and many other practical fields [10, 12]." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 317, + 546, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 317, + 546, + 544 + ], + "spans": [ + { + "bbox": [ + 304, + 317, + 546, + 544 + ], + "type": "text", + "content": "Traditional video steganography methods usually hide messages in the spatial domain or transform domain by manual design. Video steganography in the spatial domain means embedding is done directly to the pixel values of video frames. Least significant bits (LSB) [8,45] is the most well-known spatial-domain method, replacing the " + }, + { + "bbox": [ + 304, + 317, + 546, + 544 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 317, + 546, + 544 + ], + "type": "text", + "content": " least significant bits of the cover image with the most significant " + }, + { + "bbox": [ + 304, + 317, + 546, + 544 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 317, + 546, + 544 + ], + "type": "text", + "content": " bits of the secret data. Many researchers have used LSB replacement [6] and LSB matching [34] for video steganography. The transform-domain hiding [5, 17, 39] is done by modifying certain frequency coefficients of the transformed frames. For instance, [44] proposed a video steganography technique by manipulating the quantized coefficients of DCT (Discrete Cosine Transformation). [9] proposed to compare the DWT (Discrete Wavelet Transformation) coefficients of the secret image and the cover video for hiding. However, these traditional methods have low hiding capacity and invisibility, easily being cracked by steganalysis methods [15, 28, 33]." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 546, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 546, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 546, + 547, + 714 + ], + "type": "text", + "content": "Recently, some deep-learning methods were proposed to improve the hiding capacity and performance. Early works are presented in image steganography. Baluja [3, 4] proposed the first deep-learning method to hide a full-size image into another image. Recently, [21, 32] proposed designing the steganography model as an invertible neural network (INN) [13, 14] to perform image hiding and recovering with a single model. For video steganography, Khare et al. [22] first utilized back propagation neural networks to improve the performance of the LSB-based scheme. [43] is the first deep-learning method to hide a video into another video. Unfortunately, it simply aims to hide the residual across adjacent frames in a frame-by-frame manner, and it requires several separate steps to complete the video hiding and re" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "content": "*Corresponding author. This work was supported by the King Abdulah University of Science and Technology (KAUST) Office of Sponsored Research through the Visual Computing Center (VCC) funding, SDAIA-KAUST Center of Excellence in Data Science and Artificial Intelligence, and Shenzhen Research Project JCYJ20220531093215035." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "text", + "content": "22606" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 68, + 542, + 265 + ], + "blocks": [ + { + "bbox": [ + 53, + 68, + 542, + 265 + ], + "lines": [ + { + "bbox": [ + 53, + 68, + 542, + 265 + ], + "spans": [ + { + "bbox": [ + 53, + 68, + 542, + 265 + ], + "type": "image", + "image_path": "ece7fba48046d09cb4437851ad802dd0312c5d95783eaf91fe9d68359f2e20b5.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 270, + 547, + 295 + ], + "lines": [ + { + "bbox": [ + 46, + 270, + 547, + 295 + ], + "spans": [ + { + "bbox": [ + 46, + 270, + 547, + 295 + ], + "type": "text", + "content": "Figure 1. Illustration of our large-capacity and flexible video steganography network (LF-VSN). Our LF-VSN reversibly solves multiple videos hiding and recovering with a single model and the same parameters. It has large-capacity, key-controllable and scalable advantages." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 304, + 287, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 304, + 287, + 399 + ], + "spans": [ + { + "bbox": [ + 46, + 304, + 287, + 399 + ], + "type": "text", + "content": "covering. [35] utilize 3D-CNN to explore the temporal correlation in video hiding. However, it utilizes two separated 3D UNet to perform hiding and recovering, and it has high model complexity (367.2 million parameters). While video steganography has achieved impressive success in terms of hiding capacity to hide a full-size video, the more challenging multiple videos hiding has hardly been studied. Also, the steganography pipeline is rigid." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 400, + 288, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 400, + 288, + 555 + ], + "spans": [ + { + "bbox": [ + 46, + 400, + 288, + 555 + ], + "type": "text", + "content": "In this paper, we study the large-capacity and flexible video steganography, as shown in Fig. 1. Concretely, we propose a reversible video steganography pipeline, achieving large capacity to hide/recover multiple secret videos in/from a cover video. At the same time, our model complexity is also attractive by combining several weight-sharing designs. The flexibility of our method is twofold. First, we propose a key-controllable scheme, enabling different receivers to recover particular secret videos with specific keys. Second, we propose a scalable strategy, which can hide variable numbers of secret videos into a cover video with a single model and a single training session. To summarize, this work has the following contributions:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 58, + 559, + 287, + 714 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 58, + 559, + 287, + 606 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 559, + 287, + 606 + ], + "spans": [ + { + "bbox": [ + 58, + 559, + 287, + 606 + ], + "type": "text", + "content": "- We propose a large-capacity video steganography method, which can hide/recover multiple (up to 7) secret videos in/from a cover video. Our hiding and recovering are fully reversible via a single INN." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 58, + 610, + 287, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 610, + 287, + 647 + ], + "spans": [ + { + "bbox": [ + 58, + 610, + 287, + 647 + ], + "type": "text", + "content": "- We propose a key-controllable scheme with which different receivers can recover particular secret videos from the same cover video via specific keys." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 58, + 650, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 650, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 58, + 650, + 287, + 696 + ], + "type": "text", + "content": "- We propose a scalable embedding module, utilizing a single model and a single training session to satisfy different requirements for the number of secret videos hidden in a cover video." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 58, + 701, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 701, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 58, + 701, + 287, + 714 + ], + "type": "text", + "content": "- Extensive experiments demonstrate that our proposed" + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 325, + 304, + 545, + 328 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 325, + 304, + 545, + 328 + ], + "spans": [ + { + "bbox": [ + 325, + 304, + 545, + 328 + ], + "type": "text", + "content": "method achieves state-of-the-art performance with large hiding capacity and flexibility." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 339, + 392, + 352 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 339, + 392, + 352 + ], + "spans": [ + { + "bbox": [ + 306, + 339, + 392, + 352 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 359, + 429, + 373 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 359, + 429, + 373 + ], + "spans": [ + { + "bbox": [ + 306, + 359, + 429, + 373 + ], + "type": "text", + "content": "2.1. Video Steganography" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 378, + 545, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 378, + 545, + 474 + ], + "spans": [ + { + "bbox": [ + 304, + 378, + 545, + 474 + ], + "type": "text", + "content": "Steganography can date back to the 15th century, whose goal is to encode a secret message in some transport mediums and covertly communicate with a potential receiver who knows the decoding protocol to recover the secret message. Since the human visual system is less sensitive to small changes in digital media, especially digital videos. Video steganography is becoming an important research area in various data-hiding technologies [10]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 475, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 475, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 475, + 546, + 713 + ], + "type": "text", + "content": "Traditional video steganography methods usually performed hiding and recovering in the spatial domain, e.g., Pixel Value Differencing (PVD) [20, 40] and Least Significant Bits (LSB) [6, 34, 41]. PVD embeds the secret data in the difference value of two adjacent pixels. In [40], a PVD-based video steganography system is proposed to embed the secret data in a compressed domain of the cover medium. [20] utilized enhanced pixel-value differencing (EPVD) to improve the video steganography performance. LSB methods work by replacing the " + }, + { + "bbox": [ + 304, + 475, + 546, + 713 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 475, + 546, + 713 + ], + "type": "text", + "content": " least significant bits of the cover data with the most significant " + }, + { + "bbox": [ + 304, + 475, + 546, + 713 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 475, + 546, + 713 + ], + "type": "text", + "content": " bits of the secret information. [41] utilized LSB replacement technique to hide secret text in grayscale video frames. To enhance the security in LSB-based methods, [2] shuffled the secret data and embedded the index of correct order into the cover video. In addition to spatial-domain methods, some transformed domain methods [9, 44] were proposed to perform hiding by modifying certain frequency coefficients of the transformed cover video. For instance, [44] proposed a video steganography technique by manipulating the quantized coefficients" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "22607" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "type": "text", + "content": "of DCT transformation. [9] proposed to compare the DWT transformation coefficients of the secret image and the cover video for hiding. Nevertheless, the above traditional methods have low hiding capacity and invisibility, easily producing artificial markings and being cracked by steganalysis methods [15, 28, 33]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 144, + 288, + 492 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 144, + 288, + 492 + ], + "spans": [ + { + "bbox": [ + 46, + 144, + 288, + 492 + ], + "type": "text", + "content": "Motivated by the success of deep learning, some deep-learning methods were proposed. [16] introduced GAN to steganography, showing that the adversarial training scheme can improve hiding security. [49] improve the hiding quality by utilizing two independent adversarial networks to critique the video quality and optimize for robustness. [25] studied the lossless steganography below 3 bits per pixel (bpp) hiding. [38] embedded the secret data in the wavelet transform coefficients of the video frames. The above methods focus more on the robustness of low-capacity hiding. One of the important applications of low-capacity steganography is watermarking [1, 42, 52], in which the secret bit string represents the sign of the owner. Some deep-learning methods were proposed for large-capacity hiding. [3, 4] first explored hiding a full-size image into another image. [21, 32] proposed a cheaper pipeline by implementing image hiding and recovering with a single invertible neural network (INN) [13, 14]. Compared with image hiding, video hiding is a more challenging task, requiring a larger hiding capacity. [43] first studied to hide/recover a video in/from another video. However, this method simply hides the residual across adjacent frames in a frame-by-frame manner. [35] explores the temporal correlation by 3D CNN in video steganography. However, it utilizes two separate 3D UNet to perform hiding and recovering and has high model complexity (367.2M model parameters). These previous works demonstrate that deep networks have great potential in video hiding, inspiring us to study the more challenging task of multiple and flexible video hiding." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 502, + 195, + 514 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 502, + 195, + 514 + ], + "spans": [ + { + "bbox": [ + 47, + 502, + 195, + 514 + ], + "type": "text", + "content": "2.2. Invertible Neural Nerwork" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 521, + 287, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 287, + 687 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 287, + 687 + ], + "type": "text", + "content": "Since the concept of invertible neural network (INN) was proposed in [13, 14], INN has attracted more and more attention due to its pure invertible pipeline. Pioneering research on INN can be seen in image generation tasks. For instance, Glow [24] utilized INN to construct an invertible mapping between the latent variable " + }, + { + "bbox": [ + 46, + 521, + 287, + 687 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 46, + 521, + 287, + 687 + ], + "type": "text", + "content": " and nature images " + }, + { + "bbox": [ + 46, + 521, + 287, + 687 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 46, + 521, + 287, + 687 + ], + "type": "text", + "content": ". Specifically, the generative process " + }, + { + "bbox": [ + 46, + 521, + 287, + 687 + ], + "type": "inline_equation", + "content": "\\mathbf{x} = f_{\\theta}(\\mathbf{z})" + }, + { + "bbox": [ + 46, + 521, + 287, + 687 + ], + "type": "text", + "content": " given a latent variable can be specified by an INN architecture " + }, + { + "bbox": [ + 46, + 521, + 287, + 687 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 46, + 521, + 287, + 687 + ], + "type": "text", + "content": ". The direct access to the inverse mapping " + }, + { + "bbox": [ + 46, + 521, + 287, + 687 + ], + "type": "inline_equation", + "content": "\\mathbf{z} = f_{\\theta}^{-1}(\\mathbf{x})" + }, + { + "bbox": [ + 46, + 521, + 287, + 687 + ], + "type": "text", + "content": " makes inference much cheaper. Up to now, INN has been studied in several vision tasks (e.g., image rescaling [19, 46], image restoration [29, 30], image coloring [51], and video temporal action localization [50]) and presents promising performance." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "type": "text", + "content": "The architecture of INN needs to be carefully designed to guarantee the invertibility. Commonly, INN is composed" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": "of several invertible blocks, e.g., the coupling layer [13]. Given the input " + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "inline_equation", + "content": "\\mathbf{h}" + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": ", the coupling layer first splits " + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "inline_equation", + "content": "\\mathbf{h}" + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": " into two parts " + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "inline_equation", + "content": "(\\mathbf{h}_1" + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "inline_equation", + "content": "\\mathbf{h}_2)" + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": " along the channel axis. Then they undergo the affine transformations with the affine parameters generated by each other:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 365, + 134, + 545, + 154 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 365, + 134, + 545, + 154 + ], + "spans": [ + { + "bbox": [ + 365, + 134, + 545, + 154 + ], + "type": "interline_equation", + "content": "\\begin{array}{c} \\hat {\\mathbf {h}} _ {1} = \\mathbf {h} _ {1} \\cdot \\psi_ {1} (\\mathbf {h} _ {2}) + \\phi_ {1} (\\mathbf {h} _ {2}) \\\\ \\hat {\\quad} \\quad \\hat {\\quad} \\quad \\hat {\\quad} \\quad \\hat {\\quad} \\quad \\hat {\\quad} \\quad \\hat {\\quad} \\quad \\hat {\\quad} \\quad \\hat {\\quad} \\quad \\hat {\\quad} \\quad \\hat {\\quad} \\quad \\hat {\\quad} \\quad \\hat {\\quad} \\quad \\hat {\\quad} \\quad \\hat {\\quad} \\quad \\end{array} \\tag {1}", + "image_path": "a9728e3c84a9ff4a7a075267649726c8b167e207204694a9c2569351e5a39732.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 365, + 152, + 485, + 165 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 365, + 152, + 485, + 165 + ], + "spans": [ + { + "bbox": [ + 365, + 152, + 485, + 165 + ], + "type": "interline_equation", + "content": "\\hat {\\mathbf {h}} _ {2} = \\mathbf {h} _ {2} \\cdot \\psi_ {2} (\\hat {\\mathbf {h}} _ {1}) + \\phi_ {2} (\\hat {\\mathbf {h}} _ {1}),", + "image_path": "1487e25e38ca4c03c525dbcd785ef62ab7a9b505fab23d57002d7ed497eb0ea8.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 172, + 545, + 208 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 172, + 545, + 208 + ], + "spans": [ + { + "bbox": [ + 304, + 172, + 545, + 208 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 172, + 545, + 208 + ], + "type": "inline_equation", + "content": "\\psi (\\cdot)" + }, + { + "bbox": [ + 304, + 172, + 545, + 208 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 172, + 545, + 208 + ], + "type": "inline_equation", + "content": "\\phi (\\cdot)" + }, + { + "bbox": [ + 304, + 172, + 545, + 208 + ], + "type": "text", + "content": " are arbitrary functions. " + }, + { + "bbox": [ + 304, + 172, + 545, + 208 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{h}}_1" + }, + { + "bbox": [ + 304, + 172, + 545, + 208 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 172, + 545, + 208 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{h}}_2" + }, + { + "bbox": [ + 304, + 172, + 545, + 208 + ], + "type": "text", + "content": " are the outputs of the coupling layer. Correspondingly, the inverse process is defined as:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 333, + 209, + 545, + 239 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 333, + 209, + 545, + 239 + ], + "spans": [ + { + "bbox": [ + 333, + 209, + 545, + 239 + ], + "type": "interline_equation", + "content": "\\mathbf {h} _ {1} = \\frac {\\hat {\\mathbf {h}} _ {1} - \\phi_ {1} \\left(\\mathbf {h} _ {2}\\right)}{\\psi_ {1} \\left(\\mathbf {h} _ {2}\\right)}; \\quad \\mathbf {h} _ {2} = \\frac {\\hat {\\mathbf {h}} _ {2} - \\phi_ {2} \\left(\\hat {\\mathbf {h}} _ {1}\\right)}{\\psi_ {2} \\left(\\hat {\\mathbf {h}} _ {1}\\right)}. \\tag {2}", + "image_path": "430094d7291b6a3142273f31e8cf8084338a7cfa1deaa21a26fcd2f649496118.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 243, + 545, + 292 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 243, + 545, + 292 + ], + "spans": [ + { + "bbox": [ + 304, + 243, + 545, + 292 + ], + "type": "text", + "content": "In this paper, we employ the reversible forward and backward processes of INN to perform multiple videos hiding and recovering, respectively. We further improve INN to explore flexible video steganography." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 300, + 388, + 313 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 300, + 388, + 313 + ], + "spans": [ + { + "bbox": [ + 306, + 300, + 388, + 313 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 319, + 373, + 331 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 319, + 373, + 331 + ], + "spans": [ + { + "bbox": [ + 306, + 319, + 373, + 331 + ], + "type": "text", + "content": "3.1. Overview" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 338, + 545, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 338, + 545, + 495 + ], + "spans": [ + { + "bbox": [ + 304, + 338, + 545, + 495 + ], + "type": "text", + "content": "An overview of our LF-VSN is presented in Fig. 2. Specifically, given " + }, + { + "bbox": [ + 304, + 338, + 545, + 495 + ], + "type": "inline_equation", + "content": "N_{s}" + }, + { + "bbox": [ + 304, + 338, + 545, + 495 + ], + "type": "text", + "content": " secret videos " + }, + { + "bbox": [ + 304, + 338, + 545, + 495 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{se} = \\{\\mathbf{x}_{se}(n)\\}_{n=1}^{N_{s}}" + }, + { + "bbox": [ + 304, + 338, + 545, + 495 + ], + "type": "text", + "content": " and a cover video " + }, + { + "bbox": [ + 304, + 338, + 545, + 495 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{co}" + }, + { + "bbox": [ + 304, + 338, + 545, + 495 + ], + "type": "text", + "content": ", the forward hiding is operated group-by-group through a sliding window, traversing each video from head to tail. After hiding, a stego video " + }, + { + "bbox": [ + 304, + 338, + 545, + 495 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{st}" + }, + { + "bbox": [ + 304, + 338, + 545, + 495 + ], + "type": "text", + "content": " is produced, ostensibly indistinguishable from " + }, + { + "bbox": [ + 304, + 338, + 545, + 495 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{co}" + }, + { + "bbox": [ + 304, + 338, + 545, + 495 + ], + "type": "text", + "content": " to ensure that " + }, + { + "bbox": [ + 304, + 338, + 545, + 495 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{se}" + }, + { + "bbox": [ + 304, + 338, + 545, + 495 + ], + "type": "text", + "content": " is undetectable. In the backward recovering, a channel-wise broadcasting operation " + }, + { + "bbox": [ + 304, + 338, + 545, + 495 + ], + "type": "inline_equation", + "content": "(\\mathbb{R}^{3\\times W\\times H}\\xrightarrow{\\text{copy}}\\mathbb{R}^{3L\\times W\\times H})" + }, + { + "bbox": [ + 304, + 338, + 545, + 495 + ], + "type": "text", + "content": " copies each stego frame in the channel dimension to form the reversed input. During recovering, multiple secret videos are recovered frame-by-frame in parallel. It is worth noting that the forward hiding and backward recovering share the same model architecture and parameters." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 501, + 520, + 514 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 501, + 520, + 514 + ], + "spans": [ + { + "bbox": [ + 306, + 501, + 520, + 514 + ], + "type": "text", + "content": "3.2. Steganography Input and Output Design" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 519, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 519, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 519, + 545, + 715 + ], + "type": "text", + "content": "At the beginning of each hiding step, a fusion module is applied to fuse frames in each group to take advantage of the inner temporal correlation. Considering that it is easy to produce texture artifacts and color distortion when hiding in the spatial dimension [15, 21], we perform the fusion by a frequency concatenation. Specifically, given the " + }, + { + "bbox": [ + 304, + 519, + 545, + 715 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 304, + 519, + 545, + 715 + ], + "type": "text", + "content": "-th cover group " + }, + { + "bbox": [ + 304, + 519, + 545, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_{co\\otimes j} \\in \\mathbb{R}^{L \\times 3 \\times W \\times H}" + }, + { + "bbox": [ + 304, + 519, + 545, + 715 + ], + "type": "text", + "content": " and secret groups " + }, + { + "bbox": [ + 304, + 519, + 545, + 715 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{X}_{se\\otimes j}(n) \\in \\mathbb{R}^{L \\times 3 \\times W \\times H}\\}_{n=1}^{N_s}" + }, + { + "bbox": [ + 304, + 519, + 545, + 715 + ], + "type": "text", + "content": " (each contains " + }, + { + "bbox": [ + 304, + 519, + 545, + 715 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 304, + 519, + 545, + 715 + ], + "type": "text", + "content": " frames), we adopt Haar discrete wavelet transform (DWT) to split each frame into four frequency bands (i.e., LL, HL, LH, HH). In each frame group, we concatenate the part in the same frequency band from different frames in the channel dimension and then concatenate these four bands in order of frequency magnitude, producing the final secret input " + }, + { + "bbox": [ + 304, + 519, + 545, + 715 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{X}_{se\\otimes j}(n) \\in \\mathbb{R}^{12L_s \\times \\frac{W}{2} \\times \\frac{H}{2}}\\}_{n=1}^{N_s}" + }, + { + "bbox": [ + 304, + 519, + 545, + 715 + ], + "type": "text", + "content": " and cover input " + }, + { + "bbox": [ + 304, + 519, + 545, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_{co\\otimes j} \\in \\mathbb{R}^{12L_c \\times \\frac{W}{2} \\times \\frac{H}{2}}" + }, + { + "bbox": [ + 304, + 519, + 545, + 715 + ], + "type": "text", + "content": ". The output of the forward" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "22608" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 70, + 542, + 249 + ], + "blocks": [ + { + "bbox": [ + 51, + 70, + 542, + 249 + ], + "lines": [ + { + "bbox": [ + 51, + 70, + 542, + 249 + ], + "spans": [ + { + "bbox": [ + 51, + 70, + 542, + 249 + ], + "type": "image", + "image_path": "6e7b99436d6eba7190b1c8dc626ad8f702a65acf40db4880f7eb3c1d55fe71cc.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 253, + 547, + 288 + ], + "lines": [ + { + "bbox": [ + 46, + 253, + 547, + 288 + ], + "spans": [ + { + "bbox": [ + 46, + 253, + 547, + 288 + ], + "type": "text", + "content": "Figure 2. Network architecture of our LF-VSN. It is composed of several invertible blocks. In the forward hiding process, multiple secret videos are hidden in a cover video to generate a stego video, together with redundancy. In the backward recovering process, the stego video and predicted redundancy are fed to the reverse data flow of the same network with the same parameters to recover secret videos." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 298, + 290, + 431 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 298, + 290, + 431 + ], + "spans": [ + { + "bbox": [ + 46, + 298, + 290, + 431 + ], + "type": "text", + "content": "hiding comprises a stego group " + }, + { + "bbox": [ + 46, + 298, + 290, + 431 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_{st\\oplus j}" + }, + { + "bbox": [ + 46, + 298, + 290, + 431 + ], + "type": "text", + "content": " and several redundancy groups " + }, + { + "bbox": [ + 46, + 298, + 290, + 431 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{X}_{re\\oplus j}(n)\\}_{n = 1}^{N_s}" + }, + { + "bbox": [ + 46, + 298, + 290, + 431 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 46, + 298, + 290, + 431 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_{st\\oplus j}" + }, + { + "bbox": [ + 46, + 298, + 290, + 431 + ], + "type": "text", + "content": " is converted from the frequency domain to the spatial domain by a frequency separation, i.e., the inverse of the frequency concatenation. " + }, + { + "bbox": [ + 46, + 298, + 290, + 431 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_{re\\oplus j}(n)" + }, + { + "bbox": [ + 46, + 298, + 290, + 431 + ], + "type": "text", + "content": " represents the redundancy of the " + }, + { + "bbox": [ + 46, + 298, + 290, + 431 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_{se\\oplus j}(n)" + }, + { + "bbox": [ + 46, + 298, + 290, + 431 + ], + "type": "text", + "content": " that does not need to be hidden and will be discarded. In our LF-VSN, we utilize the adjacent frames to cooperate with hiding the central frame. Thus, we only output the central stego frame in each hiding step. The backward recovering is similarly operated in the frequency domain and converted to the spatial domain at the output." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 440, + 146, + 451 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 440, + 146, + 451 + ], + "spans": [ + { + "bbox": [ + 47, + 440, + 146, + 451 + ], + "type": "text", + "content": "3.3. Invertible Block" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 459, + 290, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 459, + 290, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 459, + 290, + 714 + ], + "type": "text", + "content": "As shown in Fig. 2, our hiding and recovering have reverse information flow constructed by several invertible blocks (IBs). The architecture of IB is presented in Fig. 3. Concretely, in the " + }, + { + "bbox": [ + 46, + 459, + 290, + 714 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 459, + 290, + 714 + ], + "type": "text", + "content": "-th IB, there are two branches to process the input cover group " + }, + { + "bbox": [ + 46, + 459, + 290, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_{co\\otimes j}^k" + }, + { + "bbox": [ + 46, + 459, + 290, + 714 + ], + "type": "text", + "content": " and secret groups " + }, + { + "bbox": [ + 46, + 459, + 290, + 714 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{X}_{se\\otimes j}^k(n)\\}_{n=1}^{N_s}" + }, + { + "bbox": [ + 46, + 459, + 290, + 714 + ], + "type": "text", + "content": ", respectively. Several interaction pathways between these two branches construct the invertible projection. We use an additive transformation to project the cover branch and employ an enhanced affine transformation to project the secret branch. The transformation parameters are generated from each other. Here we utilize weight-sharing modules " + }, + { + "bbox": [ + 46, + 459, + 290, + 714 + ], + "type": "inline_equation", + "content": "(\\eta_k^1(\\cdot)" + }, + { + "bbox": [ + 46, + 459, + 290, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 459, + 290, + 714 + ], + "type": "inline_equation", + "content": "\\phi_k^1(\\cdot))" + }, + { + "bbox": [ + 46, + 459, + 290, + 714 + ], + "type": "text", + "content": " to extract features from all secret groups, producing a feature set " + }, + { + "bbox": [ + 46, + 459, + 290, + 714 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{F}_{se}^k(n)\\}_{n=1}^{N_s} = \\{\\phi_k(\\eta_k(\\mathbf{X}_{se\\otimes j}^k(n)))\\}_{n=1}^{N_s}" + }, + { + "bbox": [ + 46, + 459, + 290, + 714 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 46, + 459, + 290, + 714 + ], + "type": "inline_equation", + "content": "\\eta_k^i(\\cdot)" + }, + { + "bbox": [ + 46, + 459, + 290, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 459, + 290, + 714 + ], + "type": "inline_equation", + "content": "\\phi_k^i(\\cdot)" + }, + { + "bbox": [ + 46, + 459, + 290, + 714 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 46, + 459, + 290, + 714 + ], + "type": "inline_equation", + "content": "i = 1, 2, 3" + }, + { + "bbox": [ + 46, + 459, + 290, + 714 + ], + "type": "text", + "content": ") refer to a " + }, + { + "bbox": [ + 46, + 459, + 290, + 714 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 46, + 459, + 290, + 714 + ], + "type": "text", + "content": " convolution layer and a five-layer dense block [18], respectively. Then, we concatenate " + }, + { + "bbox": [ + 46, + 459, + 290, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{se}^k" + }, + { + "bbox": [ + 46, + 459, + 290, + 714 + ], + "type": "text", + "content": " in the channel dimension and pass through an aggregation module " + }, + { + "bbox": [ + 46, + 459, + 290, + 714 + ], + "type": "inline_equation", + "content": "\\xi_k(\\cdot)" + }, + { + "bbox": [ + 46, + 459, + 290, + 714 + ], + "type": "text", + "content": " to generate the transformation parameters of the cover branch. Note that " + }, + { + "bbox": [ + 46, + 459, + 290, + 714 + ], + "type": "inline_equation", + "content": "\\xi_k(\\cdot)" + }, + { + "bbox": [ + 46, + 459, + 290, + 714 + ], + "type": "text", + "content": " is optional in different cases. In our fixed hiding, " + }, + { + "bbox": [ + 46, + 459, + 290, + 714 + ], + "type": "inline_equation", + "content": "\\xi_k(\\cdot)" + }, + { + "bbox": [ + 46, + 459, + 290, + 714 + ], + "type": "text", + "content": " is a " + }, + { + "bbox": [ + 46, + 459, + 290, + 714 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 46, + 459, + 290, + 714 + ], + "type": "text", + "content": " convolution layer, and it is a scalable embedding module in our scalable hiding. The" + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 316, + 295, + 533, + 432 + ], + "blocks": [ + { + "bbox": [ + 316, + 295, + 533, + 432 + ], + "lines": [ + { + "bbox": [ + 316, + 295, + 533, + 432 + ], + "spans": [ + { + "bbox": [ + 316, + 295, + 533, + 432 + ], + "type": "image", + "image_path": "9f014d1ed1fd758b8c31cb2c9f8242ba4121159af2d9fe9f7858fb2e6d835a74.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 435, + 545, + 459 + ], + "lines": [ + { + "bbox": [ + 305, + 435, + 545, + 459 + ], + "spans": [ + { + "bbox": [ + 305, + 435, + 545, + 459 + ], + "type": "text", + "content": "Figure 3. Illustration of the architecture of our invertible block. The dashed line refers to weight sharing." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 475, + 545, + 522 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 475, + 545, + 522 + ], + "spans": [ + { + "bbox": [ + 305, + 475, + 545, + 522 + ], + "type": "text", + "content": "transformation parameters of the secret branch are generated from " + }, + { + "bbox": [ + 305, + 475, + 545, + 522 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_{co\\otimes j}^{k}" + }, + { + "bbox": [ + 305, + 475, + 545, + 522 + ], + "type": "text", + "content": " and shared among different secret groups. Thus, in the " + }, + { + "bbox": [ + 305, + 475, + 545, + 522 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 305, + 475, + 545, + 522 + ], + "type": "text", + "content": "-th invertible block, the bijection of the forward propagation in Eq. (1) is reformulated as:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 326, + 537, + 513, + 552 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 537, + 513, + 552 + ], + "spans": [ + { + "bbox": [ + 326, + 537, + 513, + 552 + ], + "type": "interline_equation", + "content": "\\mathbf {X} _ {c o \\circledast j} ^ {k + 1} = \\mathbf {X} _ {c o \\circledast j} ^ {k} + \\xi_ {k} \\left(\\left| \\left| \\phi_ {k} ^ {1} \\left(\\eta_ {k} ^ {1} \\left(\\mathbf {X} _ {s e \\circledast j} ^ {k} (n)\\right)\\right) \\right| \\right| _ {n = 1} ^ {N _ {s}}\\right)", + "image_path": "5fd88a70ee049110228fbaf51606015d6e5b55b0003355bc183ebf840abfb77c.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 328, + 553, + 545, + 567 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 328, + 553, + 545, + 567 + ], + "spans": [ + { + "bbox": [ + 328, + 553, + 545, + 567 + ], + "type": "interline_equation", + "content": "\\left\\{\\mathbf {X} _ {s e \\circledast j} ^ {k + 1} (n) \\right\\} _ {n = 1} ^ {N _ {s}} = \\tag {3}", + "image_path": "c60a9d1e467d966ad911c301f5c92d008182db01ce8ef70b6f036f0ae1051b4b.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 328, + 568, + 525, + 583 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 328, + 568, + 525, + 583 + ], + "spans": [ + { + "bbox": [ + 328, + 568, + 525, + 583 + ], + "type": "interline_equation", + "content": "\\mathbf {X} _ {s e \\circledast j} ^ {k} (n) \\cdot \\exp \\left(\\phi_ {k} ^ {2} \\left(\\eta_ {k} ^ {2} \\left(\\mathbf {X} _ {c o \\circledast j}\\right)\\right)\\right) + \\phi_ {k} ^ {3} \\left(\\eta_ {k} ^ {3} \\left(\\mathbf {X} _ {c o \\circledast j} ^ {k + 1}\\right)\\right),", + "image_path": "40564b3d6c8bfda140c04cffd7dd7ccb02104a85205a9ecaa4dd51b4d815293d.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 597, + 545, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 597, + 545, + 635 + ], + "spans": [ + { + "bbox": [ + 306, + 597, + 545, + 635 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 597, + 545, + 635 + ], + "type": "inline_equation", + "content": "||\\cdot ||" + }, + { + "bbox": [ + 306, + 597, + 545, + 635 + ], + "type": "text", + "content": " refers to the channel-wise concatenation. " + }, + { + "bbox": [ + 306, + 597, + 545, + 635 + ], + "type": "inline_equation", + "content": "\\exp (\\cdot)" + }, + { + "bbox": [ + 306, + 597, + 545, + 635 + ], + "type": "text", + "content": " is the Exponential function. Accordingly, the backward propagation is defined as:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 315, + 649, + 391, + 662 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 649, + 391, + 662 + ], + "spans": [ + { + "bbox": [ + 315, + 649, + 391, + 662 + ], + "type": "interline_equation", + "content": "\\{\\mathbf {X} _ {s e \\circledast j} ^ {k} (n) \\} _ {n = 1} ^ {N _ {s}} =", + "image_path": "81bd550cff94788f613c8ef7cac651a2ce95c65aba19d7162d468f0d0af19577.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 316, + 664, + 545, + 679 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 664, + 545, + 679 + ], + "spans": [ + { + "bbox": [ + 316, + 664, + 545, + 679 + ], + "type": "interline_equation", + "content": "\\left(\\mathbf {X} _ {s e \\circledast j} ^ {k + 1} (n) - \\phi_ {k} ^ {3} \\left(\\eta_ {k} ^ {3} \\left(\\mathbf {X} _ {c o \\circledast j} ^ {k + 1}\\right)\\right)\\right) \\cdot \\exp \\left(- \\phi_ {k} ^ {2} \\left(\\eta_ {k} ^ {2} \\left(\\mathbf {X} _ {c o \\circledast j} ^ {k + 1}\\right)\\right)\\right) \\tag {4}", + "image_path": "623c2167914da1d39ab852683fc45b4216b6d7a1d560b29d27bd2427ec367752.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 316, + 681, + 504, + 695 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 681, + 504, + 695 + ], + "spans": [ + { + "bbox": [ + 316, + 681, + 504, + 695 + ], + "type": "interline_equation", + "content": "\\mathbf {X} _ {c o \\circledast j} ^ {k} = \\mathbf {X} _ {c o \\circledast j} ^ {k + 1} - \\xi_ {k} \\left(\\left| \\left| \\phi_ {k} ^ {1} \\left(\\eta_ {k} ^ {1} \\left(\\mathbf {X} _ {s e \\circledast j} ^ {k} (n)\\right)\\right) \\right| \\right| n = _ {1}\\right).", + "image_path": "73214973561f952f40f107a5a96b254da2fe16478f83ca005a05009153042d48.jpg" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "22609" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 59, + 70, + 147, + 260 + ], + "blocks": [ + { + "bbox": [ + 59, + 70, + 147, + 260 + ], + "lines": [ + { + "bbox": [ + 59, + 70, + 147, + 260 + ], + "spans": [ + { + "bbox": [ + 59, + 70, + 147, + 260 + ], + "type": "image", + "image_path": "cc032df3fcba499771314ec39f29bf85660d6f70b314ca805cd06b0a4af5542a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 80, + 264, + 125, + 274 + ], + "lines": [ + { + "bbox": [ + 80, + 264, + 125, + 274 + ], + "spans": [ + { + "bbox": [ + 80, + 264, + 125, + 274 + ], + "type": "text", + "content": "(a) w/o key" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 149, + 70, + 273, + 261 + ], + "blocks": [ + { + "bbox": [ + 149, + 70, + 273, + 261 + ], + "lines": [ + { + "bbox": [ + 149, + 70, + 273, + 261 + ], + "spans": [ + { + "bbox": [ + 149, + 70, + 273, + 261 + ], + "type": "image", + "image_path": "592f922e462c47501c993e5d02a1ebdaf6fce91c620aed164ee810bd6238b721.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 190, + 264, + 229, + 274 + ], + "lines": [ + { + "bbox": [ + 190, + 264, + 229, + 274 + ], + "spans": [ + { + "bbox": [ + 190, + 264, + 229, + 274 + ], + "type": "text", + "content": "(b) w key" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 277, + 287, + 312 + ], + "lines": [ + { + "bbox": [ + 46, + 277, + 287, + 312 + ], + "spans": [ + { + "bbox": [ + 46, + 277, + 287, + 312 + ], + "type": "text", + "content": "Figure 4. The architecture of our redundancy prediction module (RPM). It has two model settings: (a) RPM without (w/o) key controlling; (b) RPM with (w) key controlling." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 323, + 287, + 348 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 323, + 287, + 348 + ], + "spans": [ + { + "bbox": [ + 47, + 323, + 287, + 348 + ], + "type": "text", + "content": "3.4. Redundancy Prediction Module (RPM) & Key-controllable Design" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 354, + 287, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 354, + 287, + 521 + ], + "spans": [ + { + "bbox": [ + 46, + 354, + 287, + 521 + ], + "type": "text", + "content": "As illustrated previously, we retain the stego part and discard the redundancy information in the forward hiding. Therefore, we need to prepare a suitable redundancy in the backward process to utilize the reversibility of INN to reconstruct the forward input (i.e., secret and cover). In different tasks, most INN-based methods [21,24,32,46] constrain the generated redundancy information to obey the Gaussian distribution and utilize random Gaussian sampling to approximate this part in the backward process. Nevertheless, such random sampling lacks data specificity and adaptivity. In our LF-VSN, we predict the redundancy information from the stego group through a redundancy prediction module (RPM), as shown in Fig. 4(a). It is composed of several residual blocks (RB) without the Batch Normalization layer." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 522, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 522, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 522, + 288, + 713 + ], + "type": "text", + "content": "In this paper, we present a novel extension of RPM to construct key-controllable video steganography, with which we can hide multiple secret videos in a cover video and recover a secret video conditioned on a specific key. The architecture is shown in Fig. 4(b). Given the index " + }, + { + "bbox": [ + 46, + 522, + 288, + 713 + ], + "type": "inline_equation", + "content": "n_{key}" + }, + { + "bbox": [ + 46, + 522, + 288, + 713 + ], + "type": "text", + "content": " of a secret video " + }, + { + "bbox": [ + 46, + 522, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_{se}(n_{key})" + }, + { + "bbox": [ + 46, + 522, + 288, + 713 + ], + "type": "text", + "content": ", a specific key is generated by a key encoder, which is composed of several fully connected (FC) layers. The key is then fed into a FC layer at the end of each RB in RPM to generate a condition vector with " + }, + { + "bbox": [ + 46, + 522, + 288, + 713 + ], + "type": "inline_equation", + "content": "2C_{rpm}" + }, + { + "bbox": [ + 46, + 522, + 288, + 713 + ], + "type": "text", + "content": " channels, which is divided into two modulation vectors " + }, + { + "bbox": [ + 46, + 522, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\alpha, \\beta \\in \\mathbb{R}^{C_{rpm} \\times 1 \\times 1}" + }, + { + "bbox": [ + 46, + 522, + 288, + 713 + ], + "type": "text", + "content": " in the channel dimension. " + }, + { + "bbox": [ + 46, + 522, + 288, + 713 + ], + "type": "inline_equation", + "content": "C_{rpm}" + }, + { + "bbox": [ + 46, + 522, + 288, + 713 + ], + "type": "text", + "content": " is the feature channel of each RB in RPM. Then we modulate the output feature " + }, + { + "bbox": [ + 46, + 522, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{rpm}" + }, + { + "bbox": [ + 46, + 522, + 288, + 713 + ], + "type": "text", + "content": " of each RB as " + }, + { + "bbox": [ + 46, + 522, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{rpm} \\cdot \\alpha + \\beta" + }, + { + "bbox": [ + 46, + 522, + 288, + 713 + ], + "type": "text", + "content": ". In the training process, we constrain the recovered output the same as the " + }, + { + "bbox": [ + 46, + 522, + 288, + 713 + ], + "type": "inline_equation", + "content": "n_{key}" + }, + { + "bbox": [ + 46, + 522, + 288, + 713 + ], + "type": "text", + "content": "-th secret video (i.e., " + }, + { + "bbox": [ + 46, + 522, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_{se}(n_{key})" + }, + { + "bbox": [ + 46, + 522, + 288, + 713 + ], + "type": "text", + "content": "). More details can be found in Sec. 3.6." + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 319, + 69, + 533, + 194 + ], + "blocks": [ + { + "bbox": [ + 319, + 69, + 533, + 194 + ], + "lines": [ + { + "bbox": [ + 319, + 69, + 533, + 194 + ], + "spans": [ + { + "bbox": [ + 319, + 69, + 533, + 194 + ], + "type": "image", + "image_path": "41a82ca31f5611c1a2f1be94b449e1290b70820da587d341dc6dcca6abbd7ca1.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 200, + 545, + 234 + ], + "lines": [ + { + "bbox": [ + 305, + 200, + 545, + 234 + ], + "spans": [ + { + "bbox": [ + 305, + 200, + 545, + 234 + ], + "type": "text", + "content": "Figure 5. Illustration of our scalable embedding module. It takes the input feature map with scalable channels " + }, + { + "bbox": [ + 305, + 200, + 545, + 234 + ], + "type": "inline_equation", + "content": "C_{in} \\in [1, C]" + }, + { + "bbox": [ + 305, + 200, + 545, + 234 + ], + "type": "text", + "content": " and produces output features with fixed channels " + }, + { + "bbox": [ + 305, + 200, + 545, + 234 + ], + "type": "inline_equation", + "content": "C_{out}" + }, + { + "bbox": [ + 305, + 200, + 545, + 234 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 241, + 463, + 254 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 241, + 463, + 254 + ], + "spans": [ + { + "bbox": [ + 306, + 241, + 463, + 254 + ], + "type": "text", + "content": "3.5. Scalable Embedding Module" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 259, + 545, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 259, + 545, + 445 + ], + "spans": [ + { + "bbox": [ + 304, + 259, + 545, + 445 + ], + "type": "text", + "content": "The scalable design is used to handle the case where there are different requirements for the number of secret videos hidden in a cover video. It is succinctly designed on the feature aggregation part " + }, + { + "bbox": [ + 304, + 259, + 545, + 445 + ], + "type": "inline_equation", + "content": "\\xi_{k}(\\cdot)" + }, + { + "bbox": [ + 304, + 259, + 545, + 445 + ], + "type": "text", + "content": " in each IB, as shown in Fig. 3. The illustration of our scalable embedding module is presented in Fig. 5. It can be regarded as a special convolution layer, whose dimension of the convolution kernel can be changed according to the input. All convolution kernels " + }, + { + "bbox": [ + 304, + 259, + 545, + 445 + ], + "type": "inline_equation", + "content": "\\widetilde{\\mathbf{M}}" + }, + { + "bbox": [ + 304, + 259, + 545, + 445 + ], + "type": "text", + "content": " with different dimensions are parameter-shared from the same base kernel " + }, + { + "bbox": [ + 304, + 259, + 545, + 445 + ], + "type": "inline_equation", + "content": "\\mathbf{M}" + }, + { + "bbox": [ + 304, + 259, + 545, + 445 + ], + "type": "text", + "content": ". Technically, given the input feature " + }, + { + "bbox": [ + 304, + 259, + 545, + 445 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{in} \\in \\mathbb{R}^{C_{in} \\times W \\times H}" + }, + { + "bbox": [ + 304, + 259, + 545, + 445 + ], + "type": "text", + "content": ", we truncate a convolution kernel " + }, + { + "bbox": [ + 304, + 259, + 545, + 445 + ], + "type": "inline_equation", + "content": "\\widetilde{\\mathbf{M}} \\in \\mathbb{R}^{C_{in} \\times C_{out} \\times k \\times k}" + }, + { + "bbox": [ + 304, + 259, + 545, + 445 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 304, + 259, + 545, + 445 + ], + "type": "inline_equation", + "content": "\\mathbf{M} \\in \\mathbb{R}^{C \\times C_{out} \\times k \\times k}" + }, + { + "bbox": [ + 304, + 259, + 545, + 445 + ], + "type": "text", + "content": " to match the input dimension and then perform convolution: " + }, + { + "bbox": [ + 304, + 259, + 545, + 445 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{out} = \\widetilde{\\mathbf{M}} * \\mathbf{F}_{in}" + }, + { + "bbox": [ + 304, + 259, + 545, + 445 + ], + "type": "text", + "content": ". In this way, the training of " + }, + { + "bbox": [ + 304, + 259, + 545, + 445 + ], + "type": "inline_equation", + "content": "\\mathbf{M}" + }, + { + "bbox": [ + 304, + 259, + 545, + 445 + ], + "type": "text", + "content": " is completed through the training of all sub-kernels " + }, + { + "bbox": [ + 304, + 259, + 545, + 445 + ], + "type": "inline_equation", + "content": "\\widetilde{\\mathbf{M}}" + }, + { + "bbox": [ + 304, + 259, + 545, + 445 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 450, + 394, + 460 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 450, + 394, + 460 + ], + "spans": [ + { + "bbox": [ + 306, + 450, + 394, + 460 + ], + "type": "text", + "content": "3.6. Loss Function" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 468, + 545, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 468, + 545, + 552 + ], + "spans": [ + { + "bbox": [ + 304, + 468, + 545, + 552 + ], + "type": "text", + "content": "In our LF-VSN, the loss function is used to constrain two parts, i.e., forward hiding and backward recovering. The forward hiding is to hide multiple secret videos in the cover video. The generated stego video " + }, + { + "bbox": [ + 304, + 468, + 545, + 552 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_{st}" + }, + { + "bbox": [ + 304, + 468, + 545, + 552 + ], + "type": "text", + "content": " should be undetectable to secret videos and as similar as possible to the cover video. Therefore, we constrain " + }, + { + "bbox": [ + 304, + 468, + 545, + 552 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_{st}" + }, + { + "bbox": [ + 304, + 468, + 545, + 552 + ], + "type": "text", + "content": " to be the same as the cover video " + }, + { + "bbox": [ + 304, + 468, + 545, + 552 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_{co}" + }, + { + "bbox": [ + 304, + 468, + 545, + 552 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 356, + 557, + 545, + 571 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 356, + 557, + 545, + 571 + ], + "spans": [ + { + "bbox": [ + 356, + 557, + 545, + 571 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {f} = \\left| \\left| \\mathbf {X} _ {s t \\circledast j} [ I _ {c} ] - \\mathbf {X} _ {c o \\circledast j} [ I _ {c} ] \\right| \\right| _ {2} ^ {2}, \\tag {5}", + "image_path": "e032bb353d02a8436f8b26b3cf3aa536cf72d0e48eb3f0af78238c43cff76250.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 577, + 545, + 661 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 577, + 545, + 661 + ], + "spans": [ + { + "bbox": [ + 304, + 577, + 545, + 661 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 577, + 545, + 661 + ], + "type": "inline_equation", + "content": "||\\cdot ||_2^2" + }, + { + "bbox": [ + 304, + 577, + 545, + 661 + ], + "type": "text", + "content": " donates the " + }, + { + "bbox": [ + 304, + 577, + 545, + 661 + ], + "type": "inline_equation", + "content": "\\ell_{2}" + }, + { + "bbox": [ + 304, + 577, + 545, + 661 + ], + "type": "text", + "content": " norm. 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Quantitative comparison (PSNR/SSIM) on Vimeo-T200. The best and second-best results are highlighted and underlined. Our LF-VSN achieves the best performance in stego and secret quality with acceptable complexity." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 96, + 545, + 155 + ], + "lines": [ + { + "bbox": [ + 48, + 96, + 545, + 155 + ], + "spans": [ + { + "bbox": [ + 48, + 96, + 545, + 155 + ], + "type": "table", + "html": "
Weng et al. [43]Baluja [4]ISN [32]HiNet [21]RIIS [47]PIH [11]LF-VSN (Ours)
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Visual comparison between our LF-VSN, ISN [32], and PIH [11] in 4 videos Steganography. We present the secret reconstruction results of video 2 and video 4. 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In the pattern with key controlling, the loss function is defined to guarantee that the key generated from the video index " + }, + { + "bbox": [ + 46, + 507, + 287, + 567 + ], + "type": "inline_equation", + "content": "n_{key}" + }, + { + "bbox": [ + 46, + 507, + 287, + 567 + ], + "type": "text", + "content": " can only recover the " + }, + { + "bbox": [ + 46, + 507, + 287, + 567 + ], + "type": "inline_equation", + "content": "n_{key}" + }, + { + "bbox": [ + 46, + 507, + 287, + 567 + ], + "type": "text", + "content": "-th secret video. Thus, the loss function is reformulated as:" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 52, + 571, + 287, + 604 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 571, + 287, + 604 + ], + "spans": [ + { + "bbox": [ + 52, + 571, + 287, + 604 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {b} = \\left| \\right| \\frac {1}{N _ {s}} \\sum_ {n = 1} ^ {N _ {s}} \\hat {\\mathbf {X}} _ {s e * j} (n) [ I _ {c} ] - \\mathbf {X} _ {s e * j} \\left(n _ {k e y}\\right) [ I _ {c} ] \\left| \\right| _ {2} ^ {2} + \\tag {7}", + "image_path": "ee755ba1ec40cd0f6ab9fea8a8131cea18a9e2c03b76ecc4136681d7ec2a0826.jpg" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 156, + 606, + 269, + 622 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 156, + 606, + 269, + 622 + ], + "spans": [ + { + "bbox": [ + 156, + 606, + 269, + 622 + ], + "type": "interline_equation", + "content": "\\left| \\left| \\hat {\\mathbf {X}} _ {c o * j} [ I _ {c} ] - \\mathbf {X} _ {c o * j} [ I _ {c} ] \\right| \\right| _ {2} ^ {2}.", + "image_path": "c0d40c906c1f9dcf5e562d6b3c64aefaaac313e53549cd3d04619e34d20b1922.jpg" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 47, + 627, + 287, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 627, + 287, + 651 + ], + "spans": [ + { + "bbox": [ + 47, + 627, + 287, + 651 + ], + "type": "text", + "content": "We optimize our LF-VSN by minimizing the forward loss function " + }, + { + "bbox": [ + 47, + 627, + 287, + 651 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_f" + }, + { + "bbox": [ + 47, + 627, + 287, + 651 + ], + "type": "text", + "content": " and backward loss function " + }, + { + "bbox": [ + 47, + 627, + 287, + 651 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_b" + }, + { + "bbox": [ + 47, + 627, + 287, + 651 + ], + "type": "text", + "content": " as:" + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 133, + 658, + 287, + 671 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 133, + 658, + 287, + 671 + ], + "spans": [ + { + "bbox": [ + 133, + 658, + 287, + 671 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\mathcal {L} _ {f} + \\lambda \\mathcal {L} _ {b}, \\tag {8}", + "image_path": "6ca77f6644523beedd35dfdca6f30fea2dcbc190616a3f213d0667cb4102cda9.jpg" + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": " is a hyper-parameter to make a trade-off between forward hiding and backward recovering. We set " + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\lambda = 4" + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": " to balance these two loss portions." + } + ] + } + ], + "index": 33 + }, + { + "bbox": [ + 306, + 360, + 382, + 373 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 360, + 382, + 373 + ], + "spans": [ + { + "bbox": [ + 306, + 360, + 382, + 373 + ], + "type": "text", + "content": "4. Experiment" + } + ] + } + ], + "index": 34 + }, + { + "bbox": [ + 306, + 380, + 438, + 392 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 380, + 438, + 392 + ], + "spans": [ + { + "bbox": [ + 306, + 380, + 438, + 392 + ], + "type": "text", + "content": "4.1. Implementation Details" + } + ] + } + ], + "index": 35 + }, + { + "bbox": [ + 304, + 399, + 545, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 399, + 545, + 555 + ], + "spans": [ + { + "bbox": [ + 304, + 399, + 545, + 555 + ], + "type": "text", + "content": "In this work, we adopt the training set of Vimeo90K [48] to train our LF-VSN. Each sequence has a fixed spatial resolution of " + }, + { + "bbox": [ + 304, + 399, + 545, + 555 + ], + "type": "inline_equation", + "content": "448 \\times 256" + }, + { + "bbox": [ + 304, + 399, + 545, + 555 + ], + "type": "text", + "content": ". During training, we randomly crop training videos to " + }, + { + "bbox": [ + 304, + 399, + 545, + 555 + ], + "type": "inline_equation", + "content": "144 \\times 144" + }, + { + "bbox": [ + 304, + 399, + 545, + 555 + ], + "type": "text", + "content": " with random horizontal and vertical flipping to make a data augmentation. We use Adam optimizer [23], with " + }, + { + "bbox": [ + 304, + 399, + 545, + 555 + ], + "type": "inline_equation", + "content": "\\beta_{1} = 0.9" + }, + { + "bbox": [ + 304, + 399, + 545, + 555 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 399, + 545, + 555 + ], + "type": "inline_equation", + "content": "\\beta_{2} = 0.5" + }, + { + "bbox": [ + 304, + 399, + 545, + 555 + ], + "type": "text", + "content": ". We set the batch size as 16. The weight decay factor is set as " + }, + { + "bbox": [ + 304, + 399, + 545, + 555 + ], + "type": "inline_equation", + "content": "1 \\times 10^{-12}" + }, + { + "bbox": [ + 304, + 399, + 545, + 555 + ], + "type": "text", + "content": ". We use an initial learning rate of " + }, + { + "bbox": [ + 304, + 399, + 545, + 555 + ], + "type": "inline_equation", + "content": "1 \\times 10^{-4}" + }, + { + "bbox": [ + 304, + 399, + 545, + 555 + ], + "type": "text", + "content": ", which will decrease by half for every " + }, + { + "bbox": [ + 304, + 399, + 545, + 555 + ], + "type": "inline_equation", + "content": "30K" + }, + { + "bbox": [ + 304, + 399, + 545, + 555 + ], + "type": "text", + "content": " iterations. The number of total iterations is set as " + }, + { + "bbox": [ + 304, + 399, + 545, + 555 + ], + "type": "inline_equation", + "content": "250K" + }, + { + "bbox": [ + 304, + 399, + 545, + 555 + ], + "type": "text", + "content": ". The training process can be completed on one NVIDIA Tesla V100 GPU within 3 days. For testing, we select 200 sequences from the testing set of Vimeo-90K, denoted as Vimeo-T200 in this paper." + } + ] + } + ], + "index": 36 + }, + { + "bbox": [ + 306, + 563, + 499, + 575 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 563, + 499, + 575 + ], + "spans": [ + { + "bbox": [ + 306, + 563, + 499, + 575 + ], + "type": "text", + "content": "4.2. Comparison Against Other Methods" + } + ] + } + ], + "index": 37 + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": "Here we compare our LF-VSN with other methods on single video steganography and challenging multiple videos steganography. The evaluation includes the stego quality in forward hiding and the secret quality in backward recovering. For single video steganography, we compare our LF-VSN with some well-known methods [4, 43] and recent proposed methods [11, 21, 32, 47]. Note that PIH [11] highlighted the need to quantize the stego image from the floating-point format of " + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "inline_equation", + "content": "32 \\times 3" + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "inline_equation", + "content": "8 \\times 3" + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": " bits per pixel. But PIH just added the quantization to the compared methods without retraining. Here we retrain HiNet [21] with" + } + ] + } + ], + "index": 38 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22611" + } + ] + } + ], + "index": 39 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 49, + 107, + 284, + 194 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 289, + 104 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 289, + 104 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 289, + 104 + ], + "type": "text", + "content": "Table 2. Multiple videos steganography comparison (PSNR) of our LF-VSN, ISN [32], and PIH [11] on Vimeo-T200 test set. Our LF-VSN can hide/recover 7 videos with promising performance." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 49, + 107, + 284, + 194 + ], + "lines": [ + { + "bbox": [ + 49, + 107, + 284, + 194 + ], + "spans": [ + { + "bbox": [ + 49, + 107, + 284, + 194 + ], + "type": "table", + "html": "
Videos234567
ISNStego37.6036.4132.5631.46--
Secret41.4738.7633.4233.39--
PIHStego------
Secret35.9534.9634.20---
OursStego40.9738.5537.5536.5735.6835.01
Secret44.2442.2740.2138.8836.9435.71
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Visualization of our key-controllable scheme in 6 videos steganography. In the second and third rows, we use the correct and wrong (*) keys of 2, 4, 6 to recover secret videos, respectively." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 413, + 287, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 413, + 287, + 484 + ], + "spans": [ + { + "bbox": [ + 46, + 413, + 287, + 484 + ], + "type": "text", + "content": "quantization to make a more fair comparison. Thus, its performance may be slightly higher than that reported in PIH. ISN [32], RIIS [47] and PIH were originally designed with quantization, which can be directly compared. Tab. 1 presents that our method achieves the best performance on stego and secret while maintaining acceptable complexity." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 484, + 287, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 484, + 287, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 484, + 287, + 664 + ], + "type": "text", + "content": "For multiple videos steganography, ISN [32] and PIH [11] studied how to hide multiple secret images in a cover image, which can be competitive counterparts of our LF-VSN. ISN can hide up to 5 secret images into 1 cover image, and PIH can hide 4 secret images. The comparison in Tab. 3 shows the better performance of our LF-VSN. Even in the 7 videos hiding, our method still has promising stego and secret quality (" + }, + { + "bbox": [ + 46, + 484, + 287, + 664 + ], + "type": "inline_equation", + "content": ">35dB" + }, + { + "bbox": [ + 46, + 484, + 287, + 664 + ], + "type": "text", + "content": "). We present the visual comparison of different methods in 4 videos steganography in Fig. 6. Obviously, ISN has color distortion, and PIH has a loss of details. By contrast, our LF-VSN can recover high-fidelity results. We also present the secret and stego quality of our LF-VSN in 7 videos hiding in Fig. 7. These videos are from DAVIS [37] dataset. One can see that our LF-VSN has promising performance in such an extreme case." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 671, + 251, + 685 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 671, + 251, + 685 + ], + "spans": [ + { + "bbox": [ + 47, + 671, + 251, + 685 + ], + "type": "text", + "content": "4.3. Key-controllable Video Steganography" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "content": "Hiding multiple secret videos in a cover video is challenging; doing so for different receivers is even more dif" + } + ] + } + ], + "index": 11 + }, + { + "type": "table", + "bbox": [ + 308, + 96, + 539, + 137 + ], + "blocks": [ + { + "bbox": [ + 305, + 70, + 547, + 93 + ], + "lines": [ + { + "bbox": [ + 305, + 70, + 547, + 93 + ], + "spans": [ + { + "bbox": [ + 305, + 70, + 547, + 93 + ], + "type": "text", + "content": "Table 3. Performance comparison between controllable (C) and non-controllable (NC) video steganography of our LF-VSN." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 96, + 539, + 137 + ], + "lines": [ + { + "bbox": [ + 308, + 96, + 539, + 137 + ], + "spans": [ + { + "bbox": [ + 308, + 96, + 539, + 137 + ], + "type": "table", + "html": "
Num. videos246
Stego (NC/C)40.97/38.6737.55/34.4135.68/30.48
Secret (NC/C)44.24/41.0440.21/37.1536.94/31.95
", + "image_path": "4ddd794d9609e2739194b833e5c70b3739347d3cfbe229f41ba1341e78084820.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_body" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 307, + 140, + 425, + 262 + ], + "blocks": [ + { + "bbox": [ + 307, + 140, + 425, + 262 + ], + "lines": [ + { + "bbox": [ + 307, + 140, + 425, + 262 + ], + "spans": [ + { + "bbox": [ + 307, + 140, + 425, + 262 + ], + "type": "image", + "image_path": "91d41fbb871065915eeca5e54f02a643a859328875254b8450e7cc0c8dad6373.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 427, + 140, + 542, + 263 + ], + "blocks": [ + { + "bbox": [ + 427, + 140, + 542, + 263 + ], + "lines": [ + { + "bbox": [ + 427, + 140, + 542, + 263 + ], + "spans": [ + { + "bbox": [ + 427, + 140, + 542, + 263 + ], + "type": "image", + "image_path": "c7b7255671297442a71885073d141d73e166bda2824c888410ce2a7edc235ddb.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 267, + 546, + 291 + ], + "lines": [ + { + "bbox": [ + 305, + 267, + 546, + 291 + ], + "spans": [ + { + "bbox": [ + 305, + 267, + 546, + 291 + ], + "type": "text", + "content": "Figure 9. Performance comparison between our scalable and fixed design in multiple videos steganography." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 301, + 545, + 409 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 301, + 545, + 409 + ], + "spans": [ + { + "bbox": [ + 304, + 301, + 545, + 409 + ], + "type": "text", + "content": "ficult. In this paper, we present a key-controllable scheme in multiple videos steganography. It enables different receivers to recover particular secret videos through specific keys. The comparison in Tab. 3 presents that our controllable scheme still has a large hiding capacity (up to 6 videos) with attractive performance (" + }, + { + "bbox": [ + 304, + 301, + 545, + 409 + ], + "type": "inline_equation", + "content": ">30dB" + }, + { + "bbox": [ + 304, + 301, + 545, + 409 + ], + "type": "text", + "content": "). The visualization of recovering quality is presented in the second row of Fig. 8, showing the high-quality and key-controllable results of our LF-VSN in multiple videos steganography." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 409, + 546, + 517 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 409, + 546, + 517 + ], + "spans": [ + { + "bbox": [ + 304, + 409, + 546, + 517 + ], + "type": "text", + "content": "We also study the security of our controlling scheme, i.e., the key is sensitive and model-specific. Here we take two sets of parameters, producing from the 250K and 240K iterations in the same training process. We use the key produced by one model (*) to recover the secret video hidden by another. The result in the third row of Fig. 8 presents that the wrong key has no controlling and recovering ability. Thus, our key-controllable scheme not only has the controlling function but also enhances data security." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 525, + 471, + 538 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 525, + 471, + 538 + ], + "spans": [ + { + "bbox": [ + 305, + 525, + 471, + 538 + ], + "type": "text", + "content": "4.4. Scalable Video Steganography" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 544, + 545, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 544, + 545, + 664 + ], + "spans": [ + { + "bbox": [ + 304, + 544, + 545, + 664 + ], + "type": "text", + "content": "In this paper, we present a scalable scheme in multiple videos steganography. It can hide a variable number of secret videos into a cover video with a single model. We evaluate the performance of our scalable design and compare it with the fixed version in Tab. 9. Obviously, our method has an attractive performance (" + }, + { + "bbox": [ + 304, + 544, + 545, + 664 + ], + "type": "inline_equation", + "content": ">31dB" + }, + { + "bbox": [ + 304, + 544, + 545, + 664 + ], + "type": "text", + "content": ") in hiding a variable number (up to 7) of secret videos into a cover video by a single model. The performance degradation compared to fixed version is acceptable. With this design, a single model can satisfy multiple steganography demands." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 670, + 444, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 670, + 444, + 684 + ], + "spans": [ + { + "bbox": [ + 306, + 670, + 444, + 684 + ], + "type": "text", + "content": "4.5. Steganographic Analysis" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "content": "The data security is one of the most important concerns in steganography. In this section, we evaluate the anti" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "22612" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 47, + 92, + 542, + 168 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 545, + 92 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 545, + 92 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 545, + 92 + ], + "type": "text", + "content": "Table 4. The ablation study of different components in our LF-VSN. It includes the sliding window size, number of invertible blocks (IB), frequency concatenation (FreqCat), and redundancy prediction module (RPM)." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 47, + 92, + 542, + 168 + ], + "lines": [ + { + "bbox": [ + 47, + 92, + 542, + 168 + ], + "spans": [ + { + "bbox": [ + 47, + 92, + 542, + 168 + ], + "type": "table", + "html": "
Num. videos246333
Window size13513513533 (ours)333
Num. IB1616161616161616161216201616
FreqCat✓✓✓✓✓✓✓✓✓✓✓✓✓×
RPM✓✓✓✓✓✓✓✓✓✓✓✓×✓
Stego39.6440.9741.0836.4137.5537.8634.4735.4635.9638.0338.5538.9138.2836.85
Secret42.9744.2444.4337.6740.2140.4235.1136.8339.9741.9942.2742.4041.6940.36
", + "image_path": "c93439b7fb072c288b3c6670c4b0644e6a34dbe029fa4d5d33d3b427da13a914.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 64, + 178, + 266, + 345 + ], + "blocks": [ + { + "bbox": [ + 64, + 178, + 266, + 345 + ], + "lines": [ + { + "bbox": [ + 64, + 178, + 266, + 345 + ], + "spans": [ + { + "bbox": [ + 64, + 178, + 266, + 345 + ], + "type": "image", + "image_path": "25d4c48d9297d58fb3cf320eac39139b6cbb9eb1f27c2352bf3524cb06e95300.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 348, + 287, + 371 + ], + "lines": [ + { + "bbox": [ + 46, + 348, + 287, + 371 + ], + "spans": [ + { + "bbox": [ + 46, + 348, + 287, + 371 + ], + "type": "text", + "content": "Figure 10. Statistics-based steganalysis by StegExpose [7]. The closer the detection accuracy is to " + }, + { + "bbox": [ + 46, + 348, + 287, + 371 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 46, + 348, + 287, + 371 + ], + "type": "text", + "content": ", the higher the security is." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 383, + 287, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 383, + 287, + 574 + ], + "spans": [ + { + "bbox": [ + 46, + 383, + 287, + 574 + ], + "type": "text", + "content": "steganalysis ability of different methods, which stands for the possibility of detecting stego frames from nature frames by steganalysis tools. We utilize the StegExpose [7] to attack different steganography methods. The detection set is built by mixing stego and cover with equal proportions. We vary the detection thresholds in a wide range in StegExpose and draw the receiver operating characteristic (ROC) curve in Fig. 10. Note that the ideal case represents that the detector has a " + }, + { + "bbox": [ + 46, + 383, + 287, + 574 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 46, + 383, + 287, + 574 + ], + "type": "text", + "content": " probability of detecting stego from an equally mixed cover and stego, the same as random sampling. Therefore, the closer the curve is to the ideal case, the higher the security is. Obviously, the stego frames generated by our LF-VSN are harder to be detected than other methods. Even in the multiple videos (e.g., 2 and 4 videos) hiding, our method can still achieve attractive performance, demonstrating the higher data security of our LF-VSN." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 586, + 141, + 598 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 586, + 141, + 598 + ], + "spans": [ + { + "bbox": [ + 47, + 586, + 141, + 598 + ], + "type": "text", + "content": "4.6. Ablation Study" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 605, + 287, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 640 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 640 + ], + "type": "text", + "content": "In this subsection, we present the ablation study in Tab. 4 to investigate the effect of different components in our LF-VSN. The experiments are conducted on Vimeo-T200." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 641, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 287, + 714 + ], + "type": "text", + "content": "Sliding window size. In this paper, we utilize the temporal correlation within each frame group to improve the video steganography performance. To demonstrate the effectiveness, we evaluate the performance of our LF-VSN with the window size " + }, + { + "bbox": [ + 46, + 641, + 287, + 714 + ], + "type": "inline_equation", + "content": "L = \\{1,3,5\\}" + }, + { + "bbox": [ + 46, + 641, + 287, + 714 + ], + "type": "text", + "content": " in 2,4,and 6 videos steganography. The results in Tab. 4 present that the temporal corre" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 181, + 545, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 181, + 545, + 216 + ], + "spans": [ + { + "bbox": [ + 304, + 181, + 545, + 216 + ], + "type": "text", + "content": "lation has obvious performance gains to the multiple videos steganography. Considering the model complexity, we set the sliding window size as 3 in our LF-VSN." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 217, + 545, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 217, + 545, + 300 + ], + "spans": [ + { + "bbox": [ + 304, + 217, + 545, + 300 + ], + "type": "text", + "content": "Number of invertible blocks (IB). As mentioned above, our LF-VSN is composed of several IBs. To investigate the effectiveness of IB, we evaluate the performance of our LF-VSN with the number of IB being 12, 16, and 20. The results in Tab. 4 present that the performance increases with the number of IB. To make a trade-off between performance and complexity, we utilize 16 IBs in our LF-VSN." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 300, + 545, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 300, + 545, + 407 + ], + "spans": [ + { + "bbox": [ + 304, + 300, + 545, + 407 + ], + "type": "text", + "content": "Frequency concatenation (FreqCat). In our LF-VSN, we use the DWT transform to merge each input group in the frequency domain. To demonstrate the effectiveness, we replace this operation with direct channel-wise concatenation. Tab. 4 presents that there are " + }, + { + "bbox": [ + 304, + 300, + 545, + 407 + ], + "type": "inline_equation", + "content": "1.7dB" + }, + { + "bbox": [ + 304, + 300, + 545, + 407 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 300, + 545, + 407 + ], + "type": "inline_equation", + "content": "1.91dB" + }, + { + "bbox": [ + 304, + 300, + 545, + 407 + ], + "type": "text", + "content": " gains of FreqCat on stego and secret quality in 3 videos steganography. The possible reason is that DWT transform can separate the low-frequency and high-frequency sub-bands, making it more effective for information fusion and hiding." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 407, + 545, + 492 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 407, + 545, + 492 + ], + "spans": [ + { + "bbox": [ + 304, + 407, + 545, + 492 + ], + "type": "text", + "content": "Redundancy prediction module (RPM). In our LF-VSN, we employ RPM to predict the redundancy in the backward process instead of randomly sampling. To demonstrate the effectiveness of RPM, we replace this module with a random Gaussian sampling. The result in Tab. 4 shows that RPM can be used not only to design key-controllable steganography, but also to improve performance." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 502, + 378, + 514 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 502, + 378, + 514 + ], + "spans": [ + { + "bbox": [ + 306, + 502, + 378, + 514 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "text", + "content": "In this paper, we propose a large-capacity and flexible video steganography network (LF-VSN). The novelty of our method is twofold. First, our LF-VSN has a large hiding capacity, with which we can hide 7 secret videos into a cover video and then recover them well " + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "inline_equation", + "content": "(>35dB)" + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "text", + "content": ". Second, we explore the flexibility in multiple videos steganography by proposing a key-controllable scheme and a scalable design. Specifically, our key-controllable scheme can enable different receivers to recover particular secret videos through specific keys. Also, the key controlling is sensitive and model-specific, which can enhance data security. Our scalable design further improves the flexibility to hide a variable number of secret videos into a cover video with a single model. Extensive experiments demonstrate that our proposed LF-VSN has state-of-the-art performance with high security, large hiding capacity, and flexibility." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22613" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 713 + ], + "type": "list", + "angle": 0, + "index": 17, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "text", + "content": "[1] Mahdi Ahmadi, Alireza Norouzi, Nader Karimi, Shadrokh Samavi, and Ali Emami. 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In Proceedings of the European Conference on Computer Vision (ECCV), pages 657–672, 2018. 3" + } + ] + } + ], + "index": 23 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22615" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Large-Scale Training Data Search for Object Re-Identification/ba5e79f5-4095-4a3d-aee6-38393b11d227_content_list.json b/2023/Large-Scale Training Data Search for Object Re-Identification/ba5e79f5-4095-4a3d-aee6-38393b11d227_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..c446f333e931e8bb85bd4699d9b29c95b774ee93 --- /dev/null +++ b/2023/Large-Scale Training Data Search for Object Re-Identification/ba5e79f5-4095-4a3d-aee6-38393b11d227_content_list.json @@ -0,0 +1,1820 @@ +[ + { + "type": "text", + "text": "Large-scale Training Data Search for Object Re-identification", + "text_level": 1, + "bbox": [ + 173, + 130, + 795, + 151 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Yue Yao $^{1}$ Tom Gedeon $^{2}$ Liang Zheng $^{1}$ $^{1}$ Australian National University \n $^{2}$ Curtin University \n{first name(second name)}@{anu | curtin}.edu.au", + "bbox": [ + 272, + 179, + 694, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 268, + 312, + 282 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We consider a scenario where we have access to the target domain, but cannot afford on-the-fly training data annotation, and instead would like to construct an alternative training set from a large-scale data pool such that a competitive model can be obtained. We propose a search and pruning (SnP) solution to this training data search problem, tailored to object re-identification (re-ID), an application aiming to match the same object captured by different cameras. Specifically, the search stage identifies and merges clusters of source identities which exhibit similar distributions with the target domain. The second stage, subject to a budget, then selects identities and their images from the Stage I output, to control the size of the resulting training set for efficient training. The two steps provide us with training sets $80\\%$ smaller than the source pool while achieving a similar or even higher re-ID accuracy. These training sets are also shown to be superior to a few existing search methods such as random sampling and greedy sampling under the same budget on training data size. If we release the budget, training sets resulting from the first stage alone allow even higher re-ID accuracy. We provide interesting discussions on the specificity of our method to the re-ID problem and particularly its role in bridging the re-ID domain gap. The code is available at https://github.com/yorkeyao/SnP", + "bbox": [ + 75, + 301, + 473, + 680 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 708, + 207, + 723 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The success of a deep learning-based object re-ID relies on one of its critical prerequisites: the labeled training data. To achieve high accuracy, typically a massive amount of data needs to be used to train deep learning models. However, creating large-scale object re-ID training data with manual labels is expensive. Furthermore, collecting training data that contributes to the high test accuracy of the trained model is even more challenging. Recent years have seen a large amount of datasets proposed and a significant increase in the data size of a single dataset. For example, the Rand-Person [37] dataset has 8000 identities, which is more than", + "bbox": [ + 75, + 734, + 468, + 900 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/3f02dee31ef16b43195c1fd29f4ff799834f4c4963e4a27f07d682d29f9abef4.jpg", + "image_caption": [ + "Figure 1. We present a search and pruning (SnP) solution to the training data search problem in object re-ID. The source data pool is 1 order of magnitude larger than existing re-ID training sets in terms of the number of images and the number of identities. When the target is AlicePerson [1], from the source pool, our method (SnP) results in a training set $80\\%$ smaller than the source pool while achieving a similar or even higher re-ID accuracy. The searched training set is also superior to existing individual training sets such as Market-1501 [54], Duke [55], and MSMT [45]." + ], + "image_footnote": [], + "bbox": [ + 500, + 268, + 893, + 474 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$6\\times$ larger than the previous PersonX [37] dataset.", + "bbox": [ + 500, + 654, + 826, + 670 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "However, these datasets generally have their own dataset bias, making the model trained on one dataset unable to generalize well to another. For example, depending on the filming scenario, different person re-ID datasets generally have biases on camera positions, human races, and clothing style. Such dataset biases usually lead to model bias, which results in the model's difficulty performing well in an unseen filming scenario. To address this, many try to improve learning algorithms, including domain adaptation and domain generalization methods [2, 10, 27, 33, 35, 56]. Whereas these algorithms are well-studied and have proven successful in many re-ID applications, deciding what kind of data to use for training the re-ID model is still an open research problem, and has received relatively little attention in the community. We argue that this is a crucial problem", + "bbox": [ + 496, + 674, + 893, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "15568", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "to be answered in light of the ever-increasing scale of the available datasets.", + "bbox": [ + 76, + 90, + 468, + 119 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we introduce SnP, a search and pruning solution for sampling an efficient re-ID training set to a target domain. SnP is designed for the scenario in that we have a target dataset that does not have labeled training data. Our collected source pool, in replace, provides suitable labeled data to train a competitive model. Specifically, given a user-specified budget (e.g., maximum desired data size), we sample a subset of the source pool, which satisfies the budget requirement and desirably has high-quality data to train deep learning models. This scenario is especially helpful for deploying a re-ID system for unknown test environments, as it is difficult to manually label a training set for these new environments. We note that due to the absence of an indistribution training set, the searched data are directly used for training the re-ID model rather than pre-training.", + "bbox": [ + 75, + 121, + 468, + 347 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In particular, we combine several popular re-ID datasets into a source pool, and represent each image in the pool with features. Those features are extracted from an Imagenet-pretrained model [39]. The images with features are stored on the dataserver to serve as a gallery. When there is a query from the target, we extract the feature of the query image, and search in the gallery for similar images on a feature level. Specifically, in the search stage, we calculate feature-level distance, i.e., Fréchet Inception Distance (FID) [16]. Given the constraint of a budget, we select the most representative samples in the pruning stage, based on the outputs from the search stage. This limits the size of the constructed training set and enables efficient training.", + "bbox": [ + 75, + 348, + 468, + 542 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Combining search and pruning, we construct a training dataset that empirically shows significant accuracy improvements on several object re-ID targets, compared to the baselines. Without budget constraints, our searched training sets allow higher re-ID accuracy than the complete source pool, due to its target-specificity. With budget constraints, the pruned training set still achieves comparable or better performance than the source pool. The proposed SnP is demonstrated to be superior to random or greedy sampling. We show in Fig. 1 that the training set constructed by SnP leads to the best performance on the target compared to the others. We provide discussions on the specificity of our method and its role in bridging the re-ID domain gap.", + "bbox": [ + 75, + 545, + 468, + 741 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 753, + 218, + 768 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Active learning gradually searches over unlabeled data to find samples to be labeled by the oracle [32]. It is an iterative training process, where data search is performed at each iteration to train a task model. Our task is different from active learning. First, active learning is designed to acquire a training set and train models gradually. This requires multiple real training processes which are computationally expensive. In comparison, we directly search the", + "bbox": [ + 75, + 779, + 468, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "whole training set all at once. Then the searched training set is used for model training. Second, many active learning methods require access to the target task model to provide selection metrics, e.g., uncertainty-based metrics [9, 12, 14, 49]. Our task does not require task model information, in other words, a real training process, during the process of the training set search. Thus enabling a fast training data retrial.", + "bbox": [ + 496, + 90, + 890, + 210 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Neural data server is the closest inspiring work [32,48]. They also aim to search training data all at once from a large database. However, compared with us, firstly, [48] and [32] are designed for searching pretraining data rather than direct training data. Such a design is understandable as they are mainly for the classification task. Searching direct training data require careful class alignment. In comparison, We are targeting the re-ID task, where its training set can have a different class from the target, and then be directly used for training models. Furthermore, [48] and [32] require unsupervised pretrained experts to measure the domain gap. While we do not require so, which saves extraction time and simplify the solution.", + "bbox": [ + 496, + 212, + 890, + 407 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Transfer learning is a long-standing problem for re-ID tasks, and many attempts on learning algorithms have been made to reduce the effect of domain gap [7, 26, 29, 30, 42]. Common strategies contain feature-level [24] and pseudolabel based [10, 35, 56] domain adaptation, and domain generalization [2, 27, 33]. In this paper, we focus on training data that is orthogonal to existing training algorithms. To be shown in experiments, together with some domain adaptation (i.e., pseudo-label) methods, SnP can achieve higher re-ID accuracy.", + "bbox": [ + 496, + 407, + 890, + 558 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Learning to generate synthetic training data. Data simulation is also an inexpensive alternative to increasing a training set scale while providing accurate image labels [23, 37, 50-52]. These methods aim to lower the domain gap between synthetic data and real data by searching a set of parameters that control the 3D rendering process [50, 51]. In comparison, our search is not conducted on predefined parameters but on data directly. This enables more direct research on how to form a good training set.", + "bbox": [ + 496, + 560, + 890, + 694 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Object re-ID has received increasing attention in the past few years, and many effective systems have been proposed [17, 40, 44, 57]. In this paper, we study object re-ID datasets rather than algorithms. Depending on the camera condition, location and environment, existing object re-ID datasets usually have their own distinct characteristics or bias [36, 37, 51]. We show details in §3.", + "bbox": [ + 496, + 696, + 890, + 801 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Motivation: Tackling Target Bias", + "text_level": 1, + "bbox": [ + 500, + 814, + 802, + 832 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Data bias commonly exists in the re-ID datasets (for examples see below) [25, 43, 47, 52], and it becomes problematic when the training and testing have different biases. Given a target domain with a certain bias, we aim to find", + "bbox": [ + 496, + 840, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "15569", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/85e89a870fddef36ebf6bb2bebbd0609762d4256e5dd995677438f516bc981ae.jpg", + "image_caption": [ + "(A) Viewpoint bias." + ], + "image_footnote": [], + "bbox": [ + 76, + 88, + 215, + 215 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/a38897acaf08fd0cb84072c027e3a53597ab16098d41b4351a564f2db12659a1.jpg", + "image_caption": [ + "(B) Human races & clothing style bias." + ], + "image_footnote": [], + "bbox": [ + 223, + 95, + 473, + 212 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/c7feef806e2f346f77af55e4b4038163cbb18637dc9bf77baa11e296d8ee3817.jpg", + "image_caption": [ + "(C) Vehicle model bias.", + "CityFlow AliceVehicle", + "Figure 2. Dataset bias in existing object re-ID datasets. (A) Viewpoint distribution of different re-ID datasets. Each blue dot indicates a sample filmed from a specific viewpoint. Compared with the bi-modal viewpoint distribution in Market camera 1, Duke camera 4 has more diverse viewpoints. (B) Different human races and clothing styles of different person re-ID datasets. (C) Different vehicle makes in different datasets. For example, taxis in VeRi are unlikely to be found in CityFlow. (D) Different backgrounds in different datasets. We show a city background in AliceVehicle versus an urban background in CityFlow. To tackle such bias in the target domain, we design an automatic way to generate a training set with similar distribution or bias." + ], + "image_footnote": [], + "bbox": [ + 478, + 88, + 709, + 212 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/44b52121b55ef6183548c4d6baec7c02d51ed317f3b87cb7573faac0f3d3869a.jpg", + "image_caption": [ + "(D) Background bias." + ], + "image_footnote": [], + "bbox": [ + 753, + 97, + 890, + 212 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "a target-specific training set that has similar distribution or bias. Depending on the filming scenario, there are four major types of data biases in existing re-ID datasets. We show examples of each type in Fig. 2.", + "bbox": [ + 75, + 340, + 468, + 401 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Viewpoint. Viewpoint bias applies to generic objects, including persons and vehicles. We visualize the viewpoint distributions of two representative person re-ID datasets in Fig. 2(A), i.e., Market-1501 [54] (denoted as Market) and Duke-reID [55] (denoted as Duke) $^{1}$ .", + "bbox": [ + 75, + 402, + 468, + 477 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Human races and clothing style. Subject to the places where the data is collected, identities in the person re-ID datasets can have distinctive patterns. We show in Fig. 2(B) that the humans in Market and Duke datasets evince different races and clothing styles.", + "bbox": [ + 75, + 479, + 468, + 556 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Vehicle model. Similar to the identity bias (i.e., human races and clothing style) in person re-ID, the vehicle identities in vehicle re-ID also hold distinct patterns across different datasets. We show examples in Fig. 2(C) using the VeRi [22] (denoted as VeRi) and the CityFlow [41].", + "bbox": [ + 75, + 556, + 468, + 633 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Background. Background bias exists in both person and vehicle re-ID datasets, which is similar to viewpoint bias. Fig. 2(D) compares the background difference of images from two different vehicle re-ID datasets.", + "bbox": [ + 75, + 635, + 468, + 694 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Method", + "text_level": 1, + "bbox": [ + 76, + 714, + 168, + 729 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given a target unlabeled dataset, we aim to construct a source labeled dataset that has minimal data bias inconsistencies with the target, under certain budget constraints. It induces the model trained on the source to show good performance on the target. To achieve the construction of the source (training) dataset, we propose the search and pruning (SnP) framework.", + "bbox": [ + 75, + 741, + 468, + 847 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.1. Overview", + "text_level": 1, + "bbox": [ + 500, + 340, + 609, + 354 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We denote the target set as $\\mathcal{D}_T = \\{(x_i, y_i)\\}_{i \\in [m_t]}$ where $m_t$ indicates the number of image-label pairs in the target and $[m_t] = \\{1, 2, \\dots, m_t\\}$ . It follows the distribution $p_T$ , i.e., $\\mathcal{D}_T \\sim p_T$ . Let $\\mathcal{D}_S$ be the source set to be constructed under a budget $b$ . The budget is specified by the number of identities $n$ and the number of images $m$ allowed in $\\mathcal{D}_S$ , denoted as $b = (n, m)$ . A high budget can lead to an unwanted increase in the training cost, in terms of either training time or model size.", + "bbox": [ + 496, + 363, + 890, + 498 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To construct the training set $\\mathcal{D}_S$ , we create a source pool $S$ , which is a collection of multiple object re-ID datasets. It is represented as $\\mathcal{S} = \\mathcal{D}_S^1 \\cup \\mathcal{D}_S^2 \\dots \\cup \\mathcal{D}_S^K$ . Here each $\\mathcal{D}_S^k$ , $k \\in [K]$ , indicates the $k$ -th source re-ID dataset. Given the source pool, we firstly build a subset $\\mathbf{S}^*$ of $S$ regardless of the budget constraint. Let $h_{\\mathbf{S}}$ be a model $h$ trained on an arbitrary dataset $\\mathbf{S}$ . The prediction risk of $h_{\\mathbf{S}}$ on the test sample $\\mathbf{x}$ with ground truth label $y$ is computed as $\\ell(h_{\\mathbf{S}}(\\mathbf{x}), y)$ . We build $\\mathbf{S}^*$ by ensuring that the model $h_{\\mathbf{S}^*}$ has minimized risk on $\\mathcal{D}_T$ , i.e.,", + "bbox": [ + 496, + 500, + 892, + 651 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {S} ^ {*} = \\underset {\\mathbf {S} \\in 2 ^ {\\mathcal {S}}} {\\arg \\min } \\mathbb {E} _ {\\boldsymbol {x}, y \\sim p _ {T}} [ \\ell (h _ {\\mathbf {S}} (\\boldsymbol {x}), y) ]. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 570, + 662, + 890, + 689 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We apply target-specific search in $\\S 4.3$ to construct $\\mathbf{S}^*$ .", + "bbox": [ + 498, + 700, + 861, + 715 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "It can be seen that the construction of $\\mathbf{S}^*$ does not take the budget constraint $b = (n,m)$ into consideration, which is otherwise important in reality. Therefore, we build the training set $\\mathcal{D}_S$ by pruning $\\mathbf{S}^*$ to comprise no more than $n$ identities and no more than $m$ images. Details of the budgeted pruning process are introduced in §4.4.", + "bbox": [ + 496, + 715, + 890, + 806 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.2. Correlation Study", + "text_level": 1, + "bbox": [ + 500, + 816, + 674, + 832 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In order to know how to obtain $\\mathbf{S}^*$ , we conduct the correlation study to learn the relationships between the dataset bias differences (i.e., domain gap measured in measured in FID [16]), the number of IDs and the training set quality", + "bbox": [ + 496, + 839, + 890, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_footnote", + "text": "1 We understand that it is no longer encouraged to use the Duke dataset. In fact, we are not using it individually for algorithm design, but moving forward to find solutions to replace such individual use.", + "bbox": [ + 65, + 862, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "15570", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/2a3242a888d6e628385a210dfc0483cf239b4d7aec9db7019f0357bf25ebba48.jpg", + "image_caption": [ + "(A)" + ], + "image_footnote": [], + "bbox": [ + 78, + 95, + 272, + 194 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/8eb5124e0d5072eca73300f6c3e1f30d10592752a11112fabc3d7d566083f37a.jpg", + "image_caption": [ + "(B)" + ], + "image_footnote": [], + "bbox": [ + 276, + 95, + 468, + 194 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/f4ff4c5f224b0ba5b7257a28eb64c01fd89e9e47218c2b4dd5097c830c381911.jpg", + "image_caption": [ + "(C)" + ], + "image_footnote": [], + "bbox": [ + 472, + 95, + 663, + 195 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/9fbe779324bef4ae9c790d71aa054062c27cc92bc7b7ccf54d47468668af96be.jpg", + "image_caption": [ + "(D)" + ], + "image_footnote": [], + "bbox": [ + 666, + 95, + 893, + 194 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/f1c0f0830b733c47196b0821b8afa00322e4ae95e42f9575abbc2af59af72d70.jpg", + "image_caption": [ + "Figure 3. Relationships between the domain gap (measured using FID), the number of ID and the rank-1 accuracy on the target. Top: correlations when AlicePerson [1] is targeted. Bottom: correlations when AliceVehicle [1] is targeted. The Pearson correlation is used to measure the relationship between them. (A) FID vs. the rank-1 accuracy. They have a relatively strong negative correlation $(\\leq -0.636)$ . (B) The number of ID vs. the rank-1 accuracy. There exists a positive correlation but such a correlation is not stable. (C) FID vs. number of ID. The correlation is weak between them. (D) The joint influence of FID and the number of ID on rank-1 accuracy. The top left corner, i.e., training sets that have low FID scores and a large number of IDs have high rank-1 accuracy on the target." + ], + "image_footnote": [], + "bbox": [ + 76, + 200, + 271, + 301 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/487740c39563801ab57d1df38cf269ac9cf04cc926b47ae3d40a96d619d0ec5f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 277, + 200, + 470, + 301 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/332360379e510586ba1b7373b517b68553dda192f400b169b8f70de6a73e5ee7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 472, + 200, + 665, + 301 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/8a97d263163a9c8e433021dec219dc24e6dfbf99fd661aa6cdae23429d36ac20.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 665, + 200, + 893, + 301 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "(i.e., rank-1 test accuracy with the model trained on the such training set). Shown in Fig. 3, in each subfigure, each point represents a training set, which is clustered from the source pool. For each training set, we calculate its domain gap to the target domain, count its number of IDs, and evaluate the rank-1 accuracy. We use the Pearson correlation coefficient $(\\gamma)$ [5] to measure the correlation between them. The Pearson correlation coefficients range from $[-1, 1]$ . A value closer to -1 or 1 indicates a stronger negative or positive correlation, respectively, and 0 implies no correlation.", + "bbox": [ + 75, + 412, + 468, + 563 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "From this Fig. 3(A), we observe a relatively strong negative correlation between domain gap and rank-1 accuracy. This indicates minimizing the domain gap between the source and target is highly likely to improve training set quality, i.e., test set rank-1 accuracy. From this Fig. 3(B), we observe a positive but unstable correlation between the number of ID and the rank-1 accuracy. For example, when AlicePerson is targeted, they have a relatively strong positive correlation (0.720). However, such correlation is only 0.383 when AliceVehicle is targeted. Fig. 3(C) shows the correlation between FID and the number of ID is weak. They are independent factors that influence training set quality. Fig. 3(D) shows the joint influence of FID and the number of ID on the training set quality. The top left corner, i.e., training sets that have a low domain gap to the target and a large number of IDs are of high quality, thereby can train a model that has higher rank-1 accuracy on the target.", + "bbox": [ + 75, + 564, + 468, + 821 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.3. Target-specific Subset Search", + "text_level": 1, + "bbox": [ + 76, + 828, + 338, + 845 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The theory of domain adaptation [3] states that:", + "bbox": [ + 96, + 852, + 410, + 867 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\varepsilon_ {T} (h) < \\varepsilon_ {S} (h) + \\frac {1}{2} d _ {\\mathcal {H} \\Delta \\mathcal {H}} (\\mathbf {S}, \\mathcal {D} _ {T}). \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 151, + 875, + 468, + 905 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Here $h \\in \\mathcal{H}$ represents the hypothesis function (i.e., the model). $\\varepsilon_T(h)$ is the risk of model $h$ on the target set $\\mathcal{D}_T$ , while $\\varepsilon_S(h)$ is its risk on the source set $\\mathbf{S}$ . $d_{\\mathcal{H}\\Delta \\mathcal{H}}(\\mathbf{S},\\mathcal{D}_T)$ is the unlabelled $\\mathcal{H}\\Delta \\mathcal{H}$ divergence [3] between $\\mathbf{S}$ and $\\mathcal{D}_T$ . Equation 2 shows that the target risk $\\varepsilon_T(h)$ is upper bounded by $d_{\\mathcal{H}\\Delta \\mathcal{H}}(\\mathbf{S},\\mathcal{D}_T)$ .", + "bbox": [ + 496, + 412, + 890, + 503 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In the common practice of feature-level domain adaptation, the source training set $\\mathbf{S}$ is fixed while the joint feature extraction model is used to minimize $d_{\\mathcal{H}\\Delta \\mathcal{H}}(\\mathbf{S},\\mathcal{D}_T)$ [24]. In our design, the feature extraction model is fixed instead. To minimize $\\varepsilon_T(h)$ , the problem is reformulated as", + "bbox": [ + 496, + 503, + 890, + 579 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {S} ^ {*} = \\underset {\\mathbf {S} \\in 2 ^ {S}} {\\arg \\min } d _ {\\mathcal {H} \\Delta \\mathcal {H}} (\\mathbf {S}, \\mathcal {D} _ {T}). \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 594, + 590, + 890, + 616 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Generally, $d_{\\mathcal{H}\\Delta \\mathcal{H}}(\\mathbf{S}^*,\\mathcal{D}_T)$ is difficult to compute, but many alternatives exist in the literature [24]. We use Fréchet Inception Distance (FID) [16], which is defined as:", + "bbox": [ + 496, + 627, + 890, + 672 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {F I D} \\left(\\mathbf {S} ^ {*}, \\mathcal {D} _ {T}\\right) = \\left\\| \\boldsymbol {\\mu} _ {s} - \\boldsymbol {\\mu} _ {t} \\right\\| _ {2} ^ {2} + \\operatorname {T r} \\left(\\boldsymbol {\\Sigma} _ {s} + \\boldsymbol {\\Sigma} _ {t} - 2 \\left(\\boldsymbol {\\Sigma} _ {s} \\boldsymbol {\\Sigma} _ {t}\\right) ^ {\\frac {1}{2}}\\right). \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 498, + 683, + 890, + 715 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In Eq. 4, $\\pmb{\\mu}_s \\in \\mathbb{R}^d$ and $\\pmb{\\Sigma}_s \\in \\mathbb{R}^{d \\times d}$ are the mean and covariance matrix of the image descriptors of $\\mathbf{S}^*$ , respectively. $\\pmb{\\mu}_t$ and $\\pmb{\\Sigma}_t$ are those of $\\mathcal{D}_T$ . $\\mathrm{Tr}(.)$ represents the trace of a square matrix. $d$ is the dimension of the image descriptors. Consequently, the objective function is reduced as,", + "bbox": [ + 496, + 715, + 890, + 792 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {S} ^ {*} = \\underset {\\mathbf {S} \\in 2 ^ {S}} {\\arg \\min } \\operatorname {F I D} (\\mathbf {S}, \\mathcal {D} _ {T}). \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 602, + 804, + 890, + 829 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We build $\\mathbf{S}^*$ with the greedy algorithm below.", + "bbox": [ + 500, + 839, + 803, + 854 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Firstly, we divide the entire dataset $S$ into $J$ clusters $\\{\\mathbf{S}^1,\\dots ,\\mathbf{S}^J\\}$ , as shown in Fig. 4 (A). Specifically, we average all image descriptors that belong to the same identity,", + "bbox": [ + 500, + 854, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "15571", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/550f7f9130ef0d238482804da2357bdf01fa32fe6107cbe7c538322486f72196.jpg", + "image_caption": [ + "Figure 4. Workflow of the proposed SnP method. We are given sources composed of $K$ existing datasets. From these sources, we aim to construct a training set, which satisfies the budget of no more than $n$ IDs and $m$ images. To achieve this, we perform (A) target-specific subset search to obtain a subset $\\mathbf{S}^*$ with similar distributions to the target, then perform (B) budgeted pruning to select $n$ IDs and $m$ representative images, forming the final training set." + ], + "image_footnote": [], + "bbox": [ + 76, + 74, + 472, + 207 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "and use this ID-averaged descriptor to represent all corresponding images. Afterwards, we cluster the ID-averaged features into $J$ groups using the k-means method [20]. Each subset $\\mathbf{S}^j$ , $j \\in [J]$ , is composed of all images with the corresponding IDs in that group. Secondly, we calculate the FID between each subset $\\mathbf{S}^j$ and the target $\\mathcal{D}_T$ , and sort $\\{\\mathrm{FID}(\\mathbf{S}^j, \\mathcal{D}_T)\\}_{j \\in [J]}$ in ascending order. To build $\\mathbf{S}^*$ , we keep adding the subsets with lower FID to $\\mathbf{S}^*$ until $\\mathrm{FID}(\\mathbf{S}^*, \\mathcal{D}_T)$ stops to decrease. This indicates that the constructed $\\mathbf{S}^*$ holds the minimum FID to the target set. Algorithm 1 summarizes the above procedures. We empirically demonstrate in Fig. 5 that, the subset $\\mathbf{S}^*$ with the minimum $\\mathrm{FID}(\\mathbf{S}^*, \\mathcal{D}_T)$ results in the model to produce highest accuracy on the target dataset.", + "bbox": [ + 75, + 325, + 468, + 537 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.4. Budget-constrained Pruning", + "text_level": 1, + "bbox": [ + 76, + 545, + 331, + 561 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Using the target-specific subset search, we construct a candidate training set $\\mathbf{S}^*$ . Yet, it can violate the budget constraint of $b = (n,m)$ , which prefers the training set to include no more than $n$ identities and no more than $m$ images. Let $\\mathcal{Y}(\\mathbf{S}^*) = \\{y^1,y^2,\\dots ,y^a\\}$ , be the set of unique identities in $\\mathbf{S}^*$ , and $s(y^{i})$ , $i\\in [a]$ be the set of all images with identity $y^{i}$ . Generally, we have $a\\geq n$ . To get the training set $\\mathcal{D}_S$ under budget $b$ , we randomly sample a subset $\\pmb{y}$ of $n$ identities from $\\mathcal{V}$ . All images with identities in $\\pmb{y}$ are combined to form a subset $\\hat{\\mathbf{s}} = \\{s(y^{i})|y^{i}\\in \\pmb{y}\\}$ . We also initialize $\\mathcal{D}_S$ by random sampling a seed image from each $s(y^{i})$ , $y^{i}\\in \\pmb{y}$ . This guarantees $\\mathcal{D}_S$ to cover all the identities in the subset $\\hat{\\mathbf{s}}$ .", + "bbox": [ + 75, + 569, + 468, + 763 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Suppose the number of images in $\\hat{\\mathbf{s}}$ is larger than $m$ . We construct $\\mathcal{D}_S$ by sampling images iteratively from $\\hat{\\mathbf{s}}$ until $|\\mathcal{D}_S| = m$ . To ensure similar performance between the model trained on $D_S$ and the model trained on $\\hat{\\mathbf{s}}$ , we minimize the risk differences between them,", + "bbox": [ + 76, + 765, + 468, + 839 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {D} _ {S} = \\underset {\\mathcal {D} _ {S} \\in 2 ^ {\\hat {\\mathbf {s}}}} {\\arg \\min } \\left| L \\left(h _ {\\hat {\\mathbf {s}}} (\\boldsymbol {x}), y\\right) - L \\left(h _ {\\mathcal {D} _ {S}} (\\boldsymbol {x}), y\\right) \\right|. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 116, + 849, + 468, + 876 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$L(h_{\\mathfrak{S}}(\\pmb {x}),y)$ and $L(h_{\\mathcal{D}_S}(\\pmb {x}),y)$ are the respective risks of", + "bbox": [ + 76, + 885, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/cbd3cafd8d5ffff9631f38858ef53a273e088b9bcf38fab0cee5e21193a9f60b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 500, + 85, + 694, + 202 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/68125579b3a7c9e7c3dbc06d8cbe5714e4d414fc1cec6b56561b90f4ab35bd84.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 705, + 88, + 893, + 202 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/38c74062262b2f662e50409935f11fb4d4d75bc83382d9d28c32263fa2a17613.jpg", + "image_caption": [ + "Figure 5. Performance of constructed training set at different iterations on the target set. We greedily add clustered subset to form $\\mathbf{S}^*$ which has the smallest domain gap to the target $\\mathcal{D}_T$ . During this process, we have relatively high FID and low accuracy at (A). Gradually, we reach situation (B) of the smallest domain gap and highest accuracy. After (B), adding subsets leads to an increase in the domain gap, and the accuracy drops, e.g., (C). To study the correlation between FID and mAP during the search process, we hope to eliminate the impact of dataset size. Thus we use the same number of IDs from the searched set (i.e., $2\\%$ ID)." + ], + "image_footnote": [], + "bbox": [ + 517, + 209, + 888, + 325 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "model $h$ on the dataset $\\hat{\\mathbf{s}}$ and $\\mathcal{D}_S$ . For simplicity, we define the risk of model $h$ on an arbitrary dataset $\\mathbf{S}$ as", + "bbox": [ + 498, + 497, + 888, + 527 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL \\left(h _ {\\mathbf {S}} (\\boldsymbol {x}), y\\right) = \\frac {1}{| \\mathbf {S} |} \\sum_ {\\left(\\boldsymbol {x} _ {i}, y _ {i}\\right) \\in \\mathbf {S}} \\ell \\left(h _ {\\mathbf {S}} \\left(\\boldsymbol {x} _ {i}\\right), y _ {i}\\right). \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 552, + 534, + 890, + 571 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As in Eq. 1, $\\ell(h_{\\mathbf{S}}(\\pmb{x}_i), y_i)$ is the risk on individual samples.", + "bbox": [ + 500, + 580, + 888, + 595 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "From the theory of core set [31], if $\\mathcal{D}_S$ is the $\\delta_s$ cover of the set $\\hat{\\mathbf{s}}$ and shares the same number of classes with $\\hat{\\mathbf{s}}$ , the risk difference between model $h_{\\hat{\\mathbf{s}}}$ and $h_{\\mathcal{D}_S}$ is bounded by", + "bbox": [ + 498, + 597, + 890, + 642 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\left| L \\left(h _ {\\hat {\\mathbf {s}}} (\\boldsymbol {x}), y\\right) - L \\left(h _ {\\mathcal {D} _ {S}} (\\boldsymbol {x}), y\\right) \\right| \\leq \\mathcal {O} \\left(\\delta_ {s}\\right) + \\mathcal {O} \\left(\\frac {1}{\\sqrt {| \\mathcal {D} _ {S} |}}\\right). \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 508, + 648, + 890, + 683 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$\\delta_{s}$ is the radius of the cover, and $\\mathcal{O}(\\delta_s)$ is a polynomial function over $\\delta_{s}$ . The problem can be reduced as a K-center problem [11] by optimizing $\\mathcal{O}(\\delta_s)$ . We apply a 2-approximation algorithm [46] to iteratively find optimal samples in $\\hat{\\mathbf{s}}$ and add to $\\mathcal{D}_S$ . Specifically, each optimal sample $\\mathbf{z}^*$ is computed as", + "bbox": [ + 498, + 690, + 890, + 781 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {z} ^ {*} = \\underset {\\mathbf {z} _ {i} \\in \\hat {\\mathbf {s}} \\backslash \\mathcal {D} _ {\\mathcal {S}}} {\\arg \\max } \\underset {\\mathbf {z} _ {j} \\in \\mathcal {D} _ {\\mathcal {S}}} {\\min } \\| f (\\boldsymbol {x} _ {i}) - f (\\boldsymbol {x} _ {j}) \\| _ {2}, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 558, + 789, + 890, + 815 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf{z} = (\\pmb{x},y)$ , and $f(\\pmb{x})$ represents the descriptor of an image $\\pmb{x}$ . Equation 9 relates to the furthest point sampling method [8], which enables the most representative samples from a dataset to be selected. We summarize the pruning process in Algorithm 2.", + "bbox": [ + 496, + 824, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "15572", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Algorithm 1 Target-specific Subset Search" + ], + "code_body": "1: Input: Source pool $S$ , target set $\\mathcal{D}_T$ , and the number of clusters $J$ . \n2: Begin: \n3: Cluster $(S, J) \\longrightarrow \\{\\mathbf{S}^1, \\dots, \\mathbf{S}^J\\}$ \n4: $\\mathbf{s} = \\emptyset, \\epsilon = \\infty, \\mathbf{S}^* = \\emptyset$ \n5: $\\mathcal{I} = \\text{argsort}(\\{\\text{FID}(\\mathbf{S}^j, \\mathcal{D}_T)\\}_{j \\in [J]}) \\triangleright$ Ascending \n6: for $j$ in $\\mathcal{I}$ do \n7: $\\mathbf{s} = \\mathbf{s} \\cup \\mathbf{S}^j$ \n8: if FID(s, T) < $\\epsilon$ then \n9: $\\epsilon = \\text{FID}(\\mathbf{s}, \\mathcal{D}_T)$ \n10: $\\mathbf{S}^* = \\mathbf{s}$ \n11: return S*", + "bbox": [ + 78, + 107, + 468, + 292 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.5. Discussion", + "text_level": 1, + "bbox": [ + 76, + 319, + 192, + 333 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "What to prune first, ID or image? In our design, we select the IDs first and then images, aiming to build a dataset that has a small domain gap to target and is meanwhile in small-scale. Selecting the images first and then IDs is possible. However, it leads to a significant increase in the time complexity. As shown in Algorithm 2, the most time-consuming part of our algorithm is the FPS for finding image core sets, which takes $\\mathcal{O}(m|\\hat{\\mathbf{s}}|)$ . If we select images first, the time complexity becomes $\\mathcal{O}(m|\\mathbf{S}^*|)$ , which is significantly higher than $\\mathcal{O}(m|\\hat{\\mathbf{s}}|)$ as $|\\mathbf{S}^*| \\gg |\\hat{\\mathbf{s}}|$ .", + "bbox": [ + 75, + 342, + 468, + 493 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Is SnP applicable to tasks beyond object re-ID? It is possible to apply our search and pruning (SnP) framework to other tasks, e.g., classification. Yet, achieving this requires the SnP algorithm to be partially redesigned. The reason is that, in object re-ID, the major domain gap comes from the class difference, i.e., IDs. However, such a gap does not exist in the classification tasks as the train/val/test datasets always share the same classes. Therefore, our current design of selecting similar IDs for similar distributions is not directly applicable, and has to be adapted.", + "bbox": [ + 75, + 494, + 468, + 645 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiment", + "text_level": 1, + "bbox": [ + 76, + 659, + 200, + 676 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We evaluate the effectiveness of SnP on person re-ID and vehicle re-ID. In both tasks, given target data, we use the SnP pipeline to find a training set that has a similar distribution to the target and simultaneously meets a budget.", + "bbox": [ + 75, + 685, + 468, + 746 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Source and Target Datasets", + "text_level": 1, + "bbox": [ + 76, + 756, + 321, + 771 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Person re-ID. We create the source pool for person re-ID using 10 public datasets, including Market [54], Duke [55], MSMT17 [45] (denoted as MSMT), CUHK03 [19], RAiD [6], PersonX [37], UnrealPerson [52], RandPerson [43], PKU-Reid [28] and VIPeR [4]. Those datasets cover both synthetic and real-world data. Ten re-ID datasets constitute a source pool that contains in total of 15,060 IDs and 399,715 images.", + "bbox": [ + 75, + 779, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Algorithm 2 Budgeted Pruning" + ], + "code_body": "1: Input: Initial source set $\\mathbf{S}^*$ , budget $b = (n, m)$ . \n2: Begin: \n3: $\\pmb{y} = \\mathcal{U}(\\mathcal{V}(\\mathbf{S}^*), n)$ ▷ Sample n IDs \n4: $\\hat{\\mathbf{s}} = \\{\\pmb{s}(y_i) | y_i \\in \\pmb{y}\\}$ \n5: $\\mathcal{D}_S = \\{\\mathcal{U}(\\mathbf{s}(y^i), 1) | y_i \\in \\pmb{y}\\}$ \n6: if $|\\hat{\\mathbf{s}}| > m$ then ▷ Sample m images \n7: repeat \n8: $\\mathbf{z}^* = \\arg\\max_{\\mathbf{z}_i \\in \\hat{\\mathbf{s}} \\setminus \\mathcal{D}_S} \\min_{\\mathbf{z}_j \\in \\mathcal{D}_S} \\|\\pmb{x}_i - \\pmb{x}_j\\|_2$ \n9: $\\mathcal{D}_S = \\mathcal{D}_S \\cup \\{\\mathbf{z}^*\\}$ \n10: until $|\\mathcal{D}_S| = m$ \n11: else \n12: $\\mathcal{D}_S = \\hat{\\mathbf{s}}$ \n13: return $\\mathcal{D}_S$", + "bbox": [ + 500, + 107, + 890, + 323 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We use two real-world datasets as targets: AlicePerson [1] and Market [54]. Specifically, AlicePerson is specially designed for domain adaptation as it contains unlabeled training images. Note that in Market, the label for its training set is not be used. When Market is the target, Market training set is excluded from the source pool.", + "bbox": [ + 496, + 349, + 890, + 439 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Vehicle re-ID. For vehicle re-ID, we create the source pool by combining 8 datasets, which are VeRi [22], CityFlow [41], VehicleID [21], VeRi-Wild [25], VehicleX [50], Stanford Cars [18], PKU-vd1 [47] and PKU-vd2 [47]. It totally has 156,512 IDs and 1,284,272 images.", + "bbox": [ + 496, + 441, + 890, + 516 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "AliceVehicle [1] and VeRi [22] are separately used as the target domains. Similar to AlicePerson, AliceVehicle is also designed for domain adaptation. When VeRi is the target, the VeRi training set is excluded from the source pool.", + "bbox": [ + 496, + 517, + 890, + 577 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation protocol. For object re-ID, we use mean average precision (mAP) and cumulative match curve (CMC) scores to measure system accuracy, e.g., \"rank-1\" and \"rank-5\". \"rank-1\" denotes the success rate of finding the true match in the first rank, and \"rank-5\" means the success rate of ranking at least one true match within top-5 matches.", + "bbox": [ + 496, + 579, + 890, + 667 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Results", + "text_level": 1, + "bbox": [ + 500, + 680, + 591, + 694 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "SnP framework vs. random sampling and greedy sampling. Given a target domain, the SnP framework allows us to construct a budgeted dataset with a similar distribution. We show the superiority of SnP framework in Table 1. After sampling target-specific data with SnP, we train the subsequent re-ID model with the sampled target-specific data only. In Table 1, we compare the sampled dataset with those created by greedy sampling and random sampling. Random sampling means we randomly select IDs according to the uniform distribution. For greedy sampling, we reproduce [48]. Specifically, We assign each ID a score, which is calculated using FID. IDs will then be selected greedily from the lowest FID value to the highest FID value.", + "bbox": [ + 496, + 704, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "15573", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/751fb430d8d7a9f2004cd36a958c71b2f4aff0db52e662907e2eab8bff668265.jpg", + "table_caption": [ + "Table 1. Comparing different methods in training data search: SnP, random sampling, and greedy sampling. We set the budget as $2\\%$ , $5\\%$ , and $20\\%$ of the total source IDs. We use four targets: AlicePerson, Market, AliceVehicle and VeRi. The task model is IDE [53]. FID, rank-1 accuracy $(\\%)$ , and mAP $(\\%)$ are reported." + ], + "table_footnote": [], + "table_body": "
Training dataPerson re-ID targetsVehicle re-ID targets
AlicePersonMarketAliceVehicleVeRi
FID↓R1↑mAP↑FID↓R1↑mAP↑FID↓R1↑mAP↑FID↓R1↑mAP↑
Source pool81.6738.9617.6237.5355.5530.6243.9530.4714.6424.3955.9025.03
Searched60.9548.1925.5130.4261.4934.4023.4446.7825.4617.9274.1341.71
Pruned2% IDsRandom80.0623.679.8039.0340.7719.5445.9731.3512.8724.6867.1626.48
Greedy [48]61.7833.2215.1034.4342.1919.3538.5131.8212.9129.5366.5726.24
SnP60.4238.2318.1731.2944.8021.6523.4838.4817.7917.7069.9631.10
5% IDsRandom81.4133.1614.4939.6547.3923.9744.5236.3614.1725.2770.3830.44
Greedy [48]61.0144.6322.8131.6349.1724.7732.4841.3217.7726.0671.2332.53
SnP60.6447.2625.4530.3751.9626.5623.9244.5821.7918.0972.0536.01
20% IDsRandom79.3338.1017.7938.6353.1528.3943.9040.8918.1324.4368.7134.10
Greedy [48]63.1546.7422.6532.4253.5328.1924.1544.5822.8218.7471.0438.07
SnP61.8747.2025.3630.5857.1433.0923.4746.0725.2417.9373.4840.75
", + "bbox": [ + 78, + 142, + 893, + 319 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/4b5981b914d268dc894e5d91acdfa7b2a1f4e0e5d5499c02cb71e23c7b3ba721.jpg", + "table_caption": [ + "Table 2. The effectiveness of the target-specific subset search. mAP $(\\%)$ and CMC scores are reported. \"R1\" and \"R5\" denote rank-1 accuracy $(\\%)$ and rank-5 accuracy $(\\%)$ , respectively." + ], + "table_footnote": [], + "table_body": "
AlicePersonAliceVehicle
Training dataR1R5mAPTraining dataR1R5mAP
Market [54]32.8952.5416.06VeRi [22]30.6943.6611.05
Duke [55]23.2741.138.59CityFlow [41]23.9536.007.45
MSMT [45]31.2952.7915.08VehicleID [21]16.329.134.73
PersonX [37]16.0827.426.41VehicleX [50]18.8532.188.89
Source pool38.9657.4817.62Source pool30.4748.3314.64
Searched48.1967.5725.51Searched46.7864.4125.46
", + "bbox": [ + 78, + 385, + 468, + 488 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "From the results shown in Table 1 and Table 3, we observe that training sets selected using SnP achieve consistently lower domain gap to the target and higher re-ID accuracy than those found by random sampling and greedy sampling. For example, when creating a training set with only $2\\%$ source IDs for AlicePerson as the target, SnP results in -19.64 and -1.36 improvement in FID value, and $+14.56\\%$ and $+5.01\\%$ improvement in rank-1 accuracy over using random sampling and greedy sampling, respectively. When sampling training set with $2\\%$ of the source IDs for AliceVehicle as the target, the rank-1 accuracy improvement is $+7.13\\%$ and $+6.66\\%$ , respectively.", + "bbox": [ + 75, + 506, + 468, + 686 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effectiveness of the search step. We analyze this step in Table 1 and Table 2. In this search process that poses no limit on the number of IDs and images, we aim to identify and merge clusters of source identities that exhibit similar distributions with the target. We show the searched datasets contribute to improved accuracy over the entire data pool. For example, for AlicePerson, we observe a $+9.23\\%$ improvement in rank-1 accuracy over the entire data pool. We further show the searched data is superior to individual training sets in Table 2. For example, when AliceVehicle is our target, we show our searched dataset results in $+16.09\\%$ , $+22.83\\%$ , $+30.48\\%$ , $+27.93\\%$ higher rank-1 accuracy than VeRi, CityFlow, VehicleID, and VehicleX, respectively.", + "bbox": [ + 75, + 688, + 468, + 883 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Of note, accuracy under this application scenario is usu", + "bbox": [ + 96, + 885, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/9dc27d660f6ad20d298239ec64d3a4df245f7d7eff05bf922ba191bb8564eafe.jpg", + "table_caption": [ + "Table 3. The superiority of SnP over random sampling and greedy sampling, when different direct transfer and pseudu-label re-ID models are used. We report accuracy when $2\\%$ IDs are selected for target AicerPerson. Notations and evaluation metrics are the same as those in the previous table." + ], + "table_footnote": [], + "table_body": "
TypeModelTraining dataR1R5mAP
Direct TransferIDE [53]Random23.6742.329.80
Greedy [48]33.2254.4515.10
SnP38.2358.4018.17
PCB [38]Random24.7941.609.91
Greedy [48]29.0746.0112.59
SnP32.4349.9015.18
TransReid [15]Random52.0469.7328.47
Greedy [48]63.7380.2441.88
SnP64.3180.4642.74
Pseudo-labelingUDA [34]Random32.1754.6715.32
Greedy [48]36.4752.0617.34
SnP41.4155.7420.47
MMT [13]Random35.9451.9117.25
Greedy [48]38.6456.4821.18
SnP43.3660.3823.34
", + "bbox": [ + 501, + 412, + 888, + 612 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ally lower than that produced by in-distribution training sets. This difference is understandable, because searched data have a relatively lower resemblance to the target data compared with in-distribution training sets. That said, annotating in-distribution training sets is usually expensive, especially considering the complex, specific and ever-changing target environments, where creating a training set on-the-fly with good performance is of practical value.", + "bbox": [ + 496, + 628, + 890, + 748 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effectiveness of the pruning step is analyzed in Table 1 and Fig. 7. Pruning aims to find a subset that has no more than $n$ IDs and $m$ images. From Table 1 and Fig. 7, admittedly, the pruning of both IDs and images will lead to an accuracy decrease. For example, when the target is AlicePerson, if we select $2\\%$ IDs, there is a $-9.23\\%$ decrease in rank-1 accuracy. From Fig. 7, when the target is AlicePerson, if we further select $40\\%$ images, there is a $-9.96\\%$ decrease in rank-1 accuracy. However, even though only $2\\%$ IDs are used, rank-1 accuracy obtained from the pruned", + "bbox": [ + 496, + 750, + 893, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "15574", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2cf4282a82d532cc3d6c0a24bb732c846e31a980858d1d976e39c6880e33f93e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 86, + 92, + 135, + 186 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/880bb195f29531e50c689e4880c92244ccc7b484fa9acafb7aeb4a9d2061a18d.jpg", + "image_caption": [ + "(A) AlicePerson as Target" + ], + "image_footnote": [], + "bbox": [ + 155, + 92, + 468, + 186 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/713c29398d2c352ac7b57c6608a9cf992709ad485d19da4e6165dda58ceaa6e3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 475, + 93, + 517, + 186 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/19ac4343920cf44e3125c76b59cc3b760e288c48b82eb2f152d1e066309c3eaf.jpg", + "image_caption": [ + "(C) AliceVehicle as Target" + ], + "image_footnote": [], + "bbox": [ + 531, + 93, + 890, + 186 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1eefac88a398c5e503b9634e8dab309da7206a00500eb84f3ae1a1cfd7733add.jpg", + "image_caption": [ + "Figure 6. Composition statistics and images samples of searched training sets. For each subfigure (A), (B), (C) and (D), the columns on the left presents unlabeled target samples; columns the middle provide samples of the searched training set; the pie chart Community-verified icon Verified on the right shows composition statistics of the searched training set." + ], + "image_footnote": [], + "bbox": [ + 89, + 205, + 135, + 297 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/65059450bca16183eb99c56940ea48b32f5b58d6bbbb37fb41855b88cb5e7f39.jpg", + "image_caption": [ + "(B) Market as Target" + ], + "image_footnote": [], + "bbox": [ + 156, + 205, + 248, + 299 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/efd25f39ad81c51d8df974d30eb473228ade052696164ea519b2883e8fc68bcd.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 250, + 205, + 468, + 300 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0d6d2f5aef430e2e73fdb2b91548e9b32d66e456d573d294f4ddaa13fd6c85dd.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 475, + 205, + 517, + 299 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/bbb19cb863fbf2ff27693bd4506e25361454eb051baeb0b6346dfdeff9717f51.jpg", + "image_caption": [ + "(D) VeRi as Target" + ], + "image_footnote": [], + "bbox": [ + 532, + 205, + 888, + 300 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/be4208034c5a783fb7163eb872a5667893bcf9fc966bb04381adfaeadc58ee22.jpg", + "image_caption": [ + "(A) AlicePerson", + "Figure 7. Comparing FPS with random sampling. The search step provides us with $2\\%$ of the source IDs. We further select various ratios of images from these IDs. Four different targets are used, and rank-1 accuracy is the evaluation metric. Score is averaged over three runs." + ], + "image_footnote": [], + "bbox": [ + 76, + 393, + 284, + 503 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/fae4df5605549642b98ece0a33cea56fac4d8b58c24f98136494ec85db14e4d2.jpg", + "image_caption": [ + "(B) Market" + ], + "image_footnote": [], + "bbox": [ + 292, + 393, + 488, + 503 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/581f466d061d35169b464e8ffe407120042db86bf5f22f9957507aa09061bfd4.jpg", + "image_caption": [ + "(C) Alice Vehicle" + ], + "image_footnote": [], + "bbox": [ + 495, + 393, + 689, + 503 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a47c41604d10dd733f5a88f55fdfd2cd4511c8ab151dec146e120247c71bca7c.jpg", + "image_caption": [ + "(D) VeRi" + ], + "image_footnote": [], + "bbox": [ + 696, + 393, + 892, + 503 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "training data is still competitive over the source pool, which is just $-0.73\\%$ lower than the source pool. It shows the pruning method significantly reduces the training set scale while being able to train a model of reasonable accuracy.", + "bbox": [ + 75, + 555, + 468, + 617 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Composition of searched training sets. We visualize four examples in in Fig. 6. It is clear that searched training sets have different compositions under different targets. If we use AlicePerson as the target, in the searched training set, images from Market and Duke take up $68\\%$ and $26\\%$ , respectively. In comparison, when using Market as the target, the resulting training set contains, $43\\%$ images from UnrealPerson, and $34\\%$ from MSMT. An interesting observation is that synthetic data (UnrealPerson) has a major role under Market as the target. It demonstrates the potential use of synthetic data for real-world target domains.", + "bbox": [ + 75, + 622, + 468, + 787 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Comparison between FPS and random sampling. Both can be used for sampling images resulting from the search step. In Fig. 7, we sample different ratios of the images resulting from the search step. We observe FPS is consistently superior to random sampling, under different selection ratios and targets. Improvement of FPS over random sampling first increase and then decreases, with peak", + "bbox": [ + 75, + 794, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "improvement happening at the $30 - 60\\%$ ratio.", + "bbox": [ + 500, + 556, + 795, + 571 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 584, + 617, + 599 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This paper studies the training data set search problem, for object re-ID applications. Under a certain budget, we aim to find a target-specific training set that gives a competitive re-ID model. We show our method is overall superior to existing strategies such as random sampling and greedy sampling in terms of accuracy on the target domain. We analyze various components in the SnP system and find them to be stable under various source pools and targets. We also point out the correlation between domain gap, dataset size, and training set quality, and would like to further study the data-centric problems in the community.", + "bbox": [ + 496, + 609, + 890, + 776 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Acknowledgement", + "text_level": 1, + "bbox": [ + 500, + 789, + 679, + 806 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was supported in part by the ARC Discovery Early Career Researcher Award (DE200101283), the ARC Discovery Project (DP210102801), Oracle Cloud credits, and related resources provided by Oracle for Research. 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Scalable person re-identification: A benchmark. In Proceedings of the IEEE International Conference on Computer Vision, 2015. 1, 3, 6, 7", + "[55] Zhedong Zheng, Liang Zheng, and Yi Yang. Unlabeled samples generated by gan improve the person re-identification baseline in vitro. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 3754–3762, 2017. 1, 3, 6, 7", + "[56] Zhun Zhong, Liang Zheng, Zhiming Luo, Shaozi Li, and Yi Yang. Invariance matters: Exemplar memory for domain adaptive person re-identification. In Proceedings of IEEE Conference on Computer Vision and Pattern Recognition, 2019. 1, 2", + "[57] Yi Zhou and Ling Shao. Aware attentive multi-view inference for vehicle re-identification. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2018. 2" + ], + "bbox": [ + 78, + 90, + 470, + 345 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "15578", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Large-Scale Training Data Search for Object Re-Identification/ba5e79f5-4095-4a3d-aee6-38393b11d227_model.json b/2023/Large-Scale Training Data Search for Object Re-Identification/ba5e79f5-4095-4a3d-aee6-38393b11d227_model.json new file mode 100644 index 0000000000000000000000000000000000000000..7d4b8b49f3cc40b5c48d93792e51dee3fceecfd6 --- /dev/null +++ b/2023/Large-Scale Training Data Search for Object Re-Identification/ba5e79f5-4095-4a3d-aee6-38393b11d227_model.json @@ -0,0 +1,2587 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.174, + 0.131, + 0.797, + 0.152 + ], + "angle": 0, + "content": "Large-scale Training Data Search for Object Re-identification" + }, + { + "type": "text", + "bbox": [ + 0.273, + 0.18, + 0.696, + 0.234 + ], + "angle": 0, + "content": "Yue Yao\\(^{1}\\) Tom Gedeon\\(^{2}\\) Liang Zheng\\(^{1}\\) \n\\(^{1}\\)Australian National University \n\\(^{2}\\)Curtin University \n{first name(second name)}@{anu | curtin}.edu.au" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.269, + 0.313, + 0.284 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.302, + 0.474, + 0.681 + ], + "angle": 0, + "content": "We consider a scenario where we have access to the target domain, but cannot afford on-the-fly training data annotation, and instead would like to construct an alternative training set from a large-scale data pool such that a competitive model can be obtained. We propose a search and pruning (SnP) solution to this training data search problem, tailored to object re-identification (re-ID), an application aiming to match the same object captured by different cameras. Specifically, the search stage identifies and merges clusters of source identities which exhibit similar distributions with the target domain. The second stage, subject to a budget, then selects identities and their images from the Stage I output, to control the size of the resulting training set for efficient training. The two steps provide us with training sets \\(80\\%\\) smaller than the source pool while achieving a similar or even higher re-ID accuracy. These training sets are also shown to be superior to a few existing search methods such as random sampling and greedy sampling under the same budget on training data size. If we release the budget, training sets resulting from the first stage alone allow even higher re-ID accuracy. We provide interesting discussions on the specificity of our method to the re-ID problem and particularly its role in bridging the re-ID domain gap. The code is available at https://github.com/yorkeyao/SnP" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.709, + 0.208, + 0.724 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.47, + 0.901 + ], + "angle": 0, + "content": "The success of a deep learning-based object re-ID relies on one of its critical prerequisites: the labeled training data. To achieve high accuracy, typically a massive amount of data needs to be used to train deep learning models. However, creating large-scale object re-ID training data with manual labels is expensive. Furthermore, collecting training data that contributes to the high test accuracy of the trained model is even more challenging. Recent years have seen a large amount of datasets proposed and a significant increase in the data size of a single dataset. For example, the Rand-Person [37] dataset has 8000 identities, which is more than" + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.269, + 0.895, + 0.476 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.496, + 0.895, + 0.622 + ], + "angle": 0, + "content": "Figure 1. We present a search and pruning (SnP) solution to the training data search problem in object re-ID. The source data pool is 1 order of magnitude larger than existing re-ID training sets in terms of the number of images and the number of identities. When the target is AlicePerson [1], from the source pool, our method (SnP) results in a training set \\(80\\%\\) smaller than the source pool while achieving a similar or even higher re-ID accuracy. The searched training set is also superior to existing individual training sets such as Market-1501 [54], Duke [55], and MSMT [45]." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.655, + 0.828, + 0.671 + ], + "angle": 0, + "content": "\\(6\\times\\) larger than the previous PersonX [37] dataset." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.895, + 0.901 + ], + "angle": 0, + "content": "However, these datasets generally have their own dataset bias, making the model trained on one dataset unable to generalize well to another. For example, depending on the filming scenario, different person re-ID datasets generally have biases on camera positions, human races, and clothing style. Such dataset biases usually lead to model bias, which results in the model's difficulty performing well in an unseen filming scenario. To address this, many try to improve learning algorithms, including domain adaptation and domain generalization methods [2, 10, 27, 33, 35, 56]. Whereas these algorithms are well-studied and have proven successful in many re-ID applications, deciding what kind of data to use for training the re-ID model is still an open research problem, and has received relatively little attention in the community. We argue that this is a crucial problem" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15568" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.121 + ], + "angle": 0, + "content": "to be answered in light of the ever-increasing scale of the available datasets." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.122, + 0.47, + 0.348 + ], + "angle": 0, + "content": "In this paper, we introduce SnP, a search and pruning solution for sampling an efficient re-ID training set to a target domain. SnP is designed for the scenario in that we have a target dataset that does not have labeled training data. Our collected source pool, in replace, provides suitable labeled data to train a competitive model. Specifically, given a user-specified budget (e.g., maximum desired data size), we sample a subset of the source pool, which satisfies the budget requirement and desirably has high-quality data to train deep learning models. This scenario is especially helpful for deploying a re-ID system for unknown test environments, as it is difficult to manually label a training set for these new environments. We note that due to the absence of an indistribution training set, the searched data are directly used for training the re-ID model rather than pre-training." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.349, + 0.47, + 0.544 + ], + "angle": 0, + "content": "In particular, we combine several popular re-ID datasets into a source pool, and represent each image in the pool with features. Those features are extracted from an Imagenet-pretrained model [39]. The images with features are stored on the dataserver to serve as a gallery. When there is a query from the target, we extract the feature of the query image, and search in the gallery for similar images on a feature level. Specifically, in the search stage, we calculate feature-level distance, i.e., Fréchet Inception Distance (FID) [16]. Given the constraint of a budget, we select the most representative samples in the pruning stage, based on the outputs from the search stage. This limits the size of the constructed training set and enables efficient training." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.546, + 0.47, + 0.742 + ], + "angle": 0, + "content": "Combining search and pruning, we construct a training dataset that empirically shows significant accuracy improvements on several object re-ID targets, compared to the baselines. Without budget constraints, our searched training sets allow higher re-ID accuracy than the complete source pool, due to its target-specificity. With budget constraints, the pruned training set still achieves comparable or better performance than the source pool. The proposed SnP is demonstrated to be superior to random or greedy sampling. We show in Fig. 1 that the training set constructed by SnP leads to the best performance on the target compared to the others. We provide discussions on the specificity of our method and its role in bridging the re-ID domain gap." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.755, + 0.22, + 0.77 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Active learning gradually searches over unlabeled data to find samples to be labeled by the oracle [32]. It is an iterative training process, where data search is performed at each iteration to train a task model. Our task is different from active learning. First, active learning is designed to acquire a training set and train models gradually. This requires multiple real training processes which are computationally expensive. In comparison, we directly search the" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.212 + ], + "angle": 0, + "content": "whole training set all at once. Then the searched training set is used for model training. Second, many active learning methods require access to the target task model to provide selection metrics, e.g., uncertainty-based metrics [9, 12, 14, 49]. Our task does not require task model information, in other words, a real training process, during the process of the training set search. Thus enabling a fast training data retrial." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.213, + 0.892, + 0.408 + ], + "angle": 0, + "content": "Neural data server is the closest inspiring work [32,48]. They also aim to search training data all at once from a large database. However, compared with us, firstly, [48] and [32] are designed for searching pretraining data rather than direct training data. Such a design is understandable as they are mainly for the classification task. Searching direct training data require careful class alignment. In comparison, We are targeting the re-ID task, where its training set can have a different class from the target, and then be directly used for training models. Furthermore, [48] and [32] require unsupervised pretrained experts to measure the domain gap. While we do not require so, which saves extraction time and simplify the solution." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.409, + 0.892, + 0.559 + ], + "angle": 0, + "content": "Transfer learning is a long-standing problem for re-ID tasks, and many attempts on learning algorithms have been made to reduce the effect of domain gap [7, 26, 29, 30, 42]. Common strategies contain feature-level [24] and pseudolabel based [10, 35, 56] domain adaptation, and domain generalization [2, 27, 33]. In this paper, we focus on training data that is orthogonal to existing training algorithms. To be shown in experiments, together with some domain adaptation (i.e., pseudo-label) methods, SnP can achieve higher re-ID accuracy." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.561, + 0.892, + 0.695 + ], + "angle": 0, + "content": "Learning to generate synthetic training data. Data simulation is also an inexpensive alternative to increasing a training set scale while providing accurate image labels [23, 37, 50-52]. These methods aim to lower the domain gap between synthetic data and real data by searching a set of parameters that control the 3D rendering process [50, 51]. In comparison, our search is not conducted on predefined parameters but on data directly. This enables more direct research on how to form a good training set." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.697, + 0.892, + 0.802 + ], + "angle": 0, + "content": "Object re-ID has received increasing attention in the past few years, and many effective systems have been proposed [17, 40, 44, 57]. In this paper, we study object re-ID datasets rather than algorithms. Depending on the camera condition, location and environment, existing object re-ID datasets usually have their own distinct characteristics or bias [36, 37, 51]. We show details in §3." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.815, + 0.803, + 0.833 + ], + "angle": 0, + "content": "3. Motivation: Tackling Target Bias" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.841, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Data bias commonly exists in the re-ID datasets (for examples see below) [25, 43, 47, 52], and it becomes problematic when the training and testing have different biases. Given a target domain with a certain bias, we aim to find" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "15569" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.089, + 0.216, + 0.216 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.099, + 0.218, + 0.206, + 0.231 + ], + "angle": 0, + "content": "(A) Viewpoint bias." + }, + { + "type": "image", + "bbox": [ + 0.224, + 0.097, + 0.475, + 0.213 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.253, + 0.219, + 0.461, + 0.232 + ], + "angle": 0, + "content": "(B) Human races & clothing style bias." + }, + { + "type": "image", + "bbox": [ + 0.48, + 0.089, + 0.71, + 0.213 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.538, + 0.218, + 0.664, + 0.23 + ], + "angle": 0, + "content": "(C) Vehicle model bias." + }, + { + "type": "image_caption", + "bbox": [ + 0.721, + 0.096, + 0.738, + 0.213 + ], + "angle": 270, + "content": "CityFlow AliceVehicle" + }, + { + "type": "image", + "bbox": [ + 0.754, + 0.098, + 0.892, + 0.213 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.761, + 0.218, + 0.877, + 0.23 + ], + "angle": 0, + "content": "(D) Background bias." + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.244, + 0.894, + 0.327 + ], + "angle": 0, + "content": "Figure 2. Dataset bias in existing object re-ID datasets. (A) Viewpoint distribution of different re-ID datasets. Each blue dot indicates a sample filmed from a specific viewpoint. Compared with the bi-modal viewpoint distribution in Market camera 1, Duke camera 4 has more diverse viewpoints. (B) Different human races and clothing styles of different person re-ID datasets. (C) Different vehicle makes in different datasets. For example, taxis in VeRi are unlikely to be found in CityFlow. (D) Different backgrounds in different datasets. We show a city background in AliceVehicle versus an urban background in CityFlow. To tackle such bias in the target domain, we design an automatic way to generate a training set with similar distribution or bias." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.342, + 0.47, + 0.402 + ], + "angle": 0, + "content": "a target-specific training set that has similar distribution or bias. Depending on the filming scenario, there are four major types of data biases in existing re-ID datasets. We show examples of each type in Fig. 2." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.403, + 0.47, + 0.478 + ], + "angle": 0, + "content": "Viewpoint. Viewpoint bias applies to generic objects, including persons and vehicles. We visualize the viewpoint distributions of two representative person re-ID datasets in Fig. 2(A), i.e., Market-1501 [54] (denoted as Market) and Duke-reID [55] (denoted as Duke)\\(^{1}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.481, + 0.47, + 0.557 + ], + "angle": 0, + "content": "Human races and clothing style. Subject to the places where the data is collected, identities in the person re-ID datasets can have distinctive patterns. We show in Fig. 2(B) that the humans in Market and Duke datasets evince different races and clothing styles." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.558, + 0.47, + 0.634 + ], + "angle": 0, + "content": "Vehicle model. Similar to the identity bias (i.e., human races and clothing style) in person re-ID, the vehicle identities in vehicle re-ID also hold distinct patterns across different datasets. We show examples in Fig. 2(C) using the VeRi [22] (denoted as VeRi) and the CityFlow [41]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.636, + 0.47, + 0.695 + ], + "angle": 0, + "content": "Background. Background bias exists in both person and vehicle re-ID datasets, which is similar to viewpoint bias. Fig. 2(D) compares the background difference of images from two different vehicle re-ID datasets." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.715, + 0.169, + 0.73 + ], + "angle": 0, + "content": "4. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.742, + 0.47, + 0.848 + ], + "angle": 0, + "content": "Given a target unlabeled dataset, we aim to construct a source labeled dataset that has minimal data bias inconsistencies with the target, under certain budget constraints. It induces the model trained on the source to show good performance on the target. To achieve the construction of the source (training) dataset, we propose the search and pruning (SnP) framework." + }, + { + "type": "page_footnote", + "bbox": [ + 0.066, + 0.863, + 0.47, + 0.901 + ], + "angle": 0, + "content": "1 We understand that it is no longer encouraged to use the Duke dataset. In fact, we are not using it individually for algorithm design, but moving forward to find solutions to replace such individual use." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.341, + 0.611, + 0.355 + ], + "angle": 0, + "content": "4.1. Overview" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.364, + 0.892, + 0.499 + ], + "angle": 0, + "content": "We denote the target set as \\(\\mathcal{D}_T = \\{(x_i, y_i)\\}_{i \\in [m_t]}\\) where \\(m_t\\) indicates the number of image-label pairs in the target and \\([m_t] = \\{1, 2, \\dots, m_t\\}\\). It follows the distribution \\(p_T\\), i.e., \\(\\mathcal{D}_T \\sim p_T\\). Let \\(\\mathcal{D}_S\\) be the source set to be constructed under a budget \\(b\\). The budget is specified by the number of identities \\(n\\) and the number of images \\(m\\) allowed in \\(\\mathcal{D}_S\\), denoted as \\(b = (n, m)\\). A high budget can lead to an unwanted increase in the training cost, in terms of either training time or model size." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.501, + 0.893, + 0.652 + ], + "angle": 0, + "content": "To construct the training set \\(\\mathcal{D}_S\\), we create a source pool \\(S\\), which is a collection of multiple object re-ID datasets. It is represented as \\(\\mathcal{S} = \\mathcal{D}_S^1 \\cup \\mathcal{D}_S^2 \\dots \\cup \\mathcal{D}_S^K\\). Here each \\(\\mathcal{D}_S^k\\), \\(k \\in [K]\\), indicates the \\(k\\)-th source re-ID dataset. Given the source pool, we firstly build a subset \\(\\mathbf{S}^*\\) of \\(S\\) regardless of the budget constraint. Let \\(h_{\\mathbf{S}}\\) be a model \\(h\\) trained on an arbitrary dataset \\(\\mathbf{S}\\). The prediction risk of \\(h_{\\mathbf{S}}\\) on the test sample \\(\\mathbf{x}\\) with ground truth label \\(y\\) is computed as \\(\\ell(h_{\\mathbf{S}}(\\mathbf{x}), y)\\). We build \\(\\mathbf{S}^*\\) by ensuring that the model \\(h_{\\mathbf{S}^*}\\) has minimized risk on \\(\\mathcal{D}_T\\), i.e.," + }, + { + "type": "equation", + "bbox": [ + 0.571, + 0.664, + 0.892, + 0.69 + ], + "angle": 0, + "content": "\\[\n\\mathbf {S} ^ {*} = \\underset {\\mathbf {S} \\in 2 ^ {\\mathcal {S}}} {\\arg \\min } \\mathbb {E} _ {\\boldsymbol {x}, y \\sim p _ {T}} [ \\ell (h _ {\\mathbf {S}} (\\boldsymbol {x}), y) ]. \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.701, + 0.862, + 0.716 + ], + "angle": 0, + "content": "We apply target-specific search in \\(\\S 4.3\\) to construct \\(\\mathbf{S}^*\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.717, + 0.892, + 0.807 + ], + "angle": 0, + "content": "It can be seen that the construction of \\(\\mathbf{S}^*\\) does not take the budget constraint \\(b = (n,m)\\) into consideration, which is otherwise important in reality. Therefore, we build the training set \\(\\mathcal{D}_S\\) by pruning \\(\\mathbf{S}^*\\) to comprise no more than \\(n\\) identities and no more than \\(m\\) images. Details of the budgeted pruning process are introduced in §4.4." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.817, + 0.676, + 0.833 + ], + "angle": 0, + "content": "4.2. Correlation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.902 + ], + "angle": 0, + "content": "In order to know how to obtain \\(\\mathbf{S}^*\\), we conduct the correlation study to learn the relationships between the dataset bias differences (i.e., domain gap measured in measured in FID [16]), the number of IDs and the training set quality" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15570" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.178, + 0.088, + 0.197, + 0.098 + ], + "angle": 0, + "content": "(A)" + }, + { + "type": "image", + "bbox": [ + 0.079, + 0.097, + 0.273, + 0.195 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.377, + 0.089, + 0.396, + 0.098 + ], + "angle": 0, + "content": "(B)" + }, + { + "type": "image", + "bbox": [ + 0.277, + 0.097, + 0.47, + 0.195 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.571, + 0.089, + 0.589, + 0.098 + ], + "angle": 0, + "content": "(C)" + }, + { + "type": "image", + "bbox": [ + 0.473, + 0.097, + 0.665, + 0.196 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.771, + 0.089, + 0.79, + 0.098 + ], + "angle": 0, + "content": "(D)" + }, + { + "type": "image", + "bbox": [ + 0.667, + 0.097, + 0.894, + 0.195 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.078, + 0.202, + 0.272, + 0.302 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.278, + 0.202, + 0.471, + 0.302 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.473, + 0.202, + 0.666, + 0.302 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.666, + 0.202, + 0.894, + 0.302 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.316, + 0.894, + 0.4 + ], + "angle": 0, + "content": "Figure 3. Relationships between the domain gap (measured using FID), the number of ID and the rank-1 accuracy on the target. Top: correlations when AlicePerson [1] is targeted. Bottom: correlations when AliceVehicle [1] is targeted. The Pearson correlation is used to measure the relationship between them. (A) FID vs. the rank-1 accuracy. They have a relatively strong negative correlation \\((\\leq -0.636)\\). (B) The number of ID vs. the rank-1 accuracy. There exists a positive correlation but such a correlation is not stable. (C) FID vs. number of ID. The correlation is weak between them. (D) The joint influence of FID and the number of ID on rank-1 accuracy. The top left corner, i.e., training sets that have low FID scores and a large number of IDs have high rank-1 accuracy on the target." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.414, + 0.469, + 0.564 + ], + "angle": 0, + "content": "(i.e., rank-1 test accuracy with the model trained on the such training set). Shown in Fig. 3, in each subfigure, each point represents a training set, which is clustered from the source pool. For each training set, we calculate its domain gap to the target domain, count its number of IDs, and evaluate the rank-1 accuracy. We use the Pearson correlation coefficient \\((\\gamma)\\) [5] to measure the correlation between them. The Pearson correlation coefficients range from \\([-1, 1]\\). A value closer to -1 or 1 indicates a stronger negative or positive correlation, respectively, and 0 implies no correlation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.565, + 0.47, + 0.822 + ], + "angle": 0, + "content": "From this Fig. 3(A), we observe a relatively strong negative correlation between domain gap and rank-1 accuracy. This indicates minimizing the domain gap between the source and target is highly likely to improve training set quality, i.e., test set rank-1 accuracy. From this Fig. 3(B), we observe a positive but unstable correlation between the number of ID and the rank-1 accuracy. For example, when AlicePerson is targeted, they have a relatively strong positive correlation (0.720). However, such correlation is only 0.383 when AliceVehicle is targeted. Fig. 3(C) shows the correlation between FID and the number of ID is weak. They are independent factors that influence training set quality. Fig. 3(D) shows the joint influence of FID and the number of ID on the training set quality. The top left corner, i.e., training sets that have a low domain gap to the target and a large number of IDs are of high quality, thereby can train a model that has higher rank-1 accuracy on the target." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.829, + 0.339, + 0.846 + ], + "angle": 0, + "content": "4.3. Target-specific Subset Search" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.853, + 0.411, + 0.868 + ], + "angle": 0, + "content": "The theory of domain adaptation [3] states that:" + }, + { + "type": "equation", + "bbox": [ + 0.153, + 0.876, + 0.47, + 0.906 + ], + "angle": 0, + "content": "\\[\n\\varepsilon_ {T} (h) < \\varepsilon_ {S} (h) + \\frac {1}{2} d _ {\\mathcal {H} \\Delta \\mathcal {H}} (\\mathbf {S}, \\mathcal {D} _ {T}). \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.414, + 0.892, + 0.505 + ], + "angle": 0, + "content": "Here \\( h \\in \\mathcal{H} \\) represents the hypothesis function (i.e., the model). \\( \\varepsilon_T(h) \\) is the risk of model \\( h \\) on the target set \\( \\mathcal{D}_T \\), while \\( \\varepsilon_S(h) \\) is its risk on the source set \\( \\mathbf{S} \\). \\( d_{\\mathcal{H}\\Delta \\mathcal{H}}(\\mathbf{S},\\mathcal{D}_T) \\) is the unlabelled \\( \\mathcal{H}\\Delta \\mathcal{H} \\) divergence [3] between \\( \\mathbf{S} \\) and \\( \\mathcal{D}_T \\). Equation 2 shows that the target risk \\( \\varepsilon_T(h) \\) is upper bounded by \\( d_{\\mathcal{H}\\Delta \\mathcal{H}}(\\mathbf{S},\\mathcal{D}_T) \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.505, + 0.892, + 0.58 + ], + "angle": 0, + "content": "In the common practice of feature-level domain adaptation, the source training set \\(\\mathbf{S}\\) is fixed while the joint feature extraction model is used to minimize \\(d_{\\mathcal{H}\\Delta \\mathcal{H}}(\\mathbf{S},\\mathcal{D}_T)\\) [24]. In our design, the feature extraction model is fixed instead. To minimize \\(\\varepsilon_T(h)\\), the problem is reformulated as" + }, + { + "type": "equation", + "bbox": [ + 0.595, + 0.591, + 0.891, + 0.617 + ], + "angle": 0, + "content": "\\[\n\\mathbf {S} ^ {*} = \\underset {\\mathbf {S} \\in 2 ^ {S}} {\\arg \\min } d _ {\\mathcal {H} \\Delta \\mathcal {H}} (\\mathbf {S}, \\mathcal {D} _ {T}). \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.628, + 0.891, + 0.674 + ], + "angle": 0, + "content": "Generally, \\(d_{\\mathcal{H}\\Delta \\mathcal{H}}(\\mathbf{S}^*,\\mathcal{D}_T)\\) is difficult to compute, but many alternatives exist in the literature [24]. We use Fréchet Inception Distance (FID) [16], which is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.499, + 0.684, + 0.891, + 0.717 + ], + "angle": 0, + "content": "\\[\n\\operatorname {F I D} \\left(\\mathbf {S} ^ {*}, \\mathcal {D} _ {T}\\right) = \\left\\| \\boldsymbol {\\mu} _ {s} - \\boldsymbol {\\mu} _ {t} \\right\\| _ {2} ^ {2} + \\operatorname {T r} \\left(\\boldsymbol {\\Sigma} _ {s} + \\boldsymbol {\\Sigma} _ {t} - 2 \\left(\\boldsymbol {\\Sigma} _ {s} \\boldsymbol {\\Sigma} _ {t}\\right) ^ {\\frac {1}{2}}\\right). \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.717, + 0.892, + 0.793 + ], + "angle": 0, + "content": "In Eq. 4, \\(\\pmb{\\mu}_s \\in \\mathbb{R}^d\\) and \\(\\pmb{\\Sigma}_s \\in \\mathbb{R}^{d \\times d}\\) are the mean and covariance matrix of the image descriptors of \\(\\mathbf{S}^*\\), respectively. \\(\\pmb{\\mu}_t\\) and \\(\\pmb{\\Sigma}_t\\) are those of \\(\\mathcal{D}_T\\). \\(\\mathrm{Tr}(.)\\) represents the trace of a square matrix. \\(d\\) is the dimension of the image descriptors. Consequently, the objective function is reduced as," + }, + { + "type": "equation", + "bbox": [ + 0.603, + 0.805, + 0.891, + 0.83 + ], + "angle": 0, + "content": "\\[\n\\mathbf {S} ^ {*} = \\underset {\\mathbf {S} \\in 2 ^ {S}} {\\arg \\min } \\operatorname {F I D} (\\mathbf {S}, \\mathcal {D} _ {T}). \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.84, + 0.805, + 0.856 + ], + "angle": 0, + "content": "We build \\(\\mathbf{S}^*\\) with the greedy algorithm below." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Firstly, we divide the entire dataset \\(S\\) into \\(J\\) clusters \\(\\{\\mathbf{S}^1,\\dots ,\\mathbf{S}^J\\}\\), as shown in Fig. 4 (A). Specifically, we average all image descriptors that belong to the same identity," + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "15571" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.075, + 0.473, + 0.208 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.217, + 0.47, + 0.314 + ], + "angle": 0, + "content": "Figure 4. Workflow of the proposed SnP method. We are given sources composed of \\( K \\) existing datasets. From these sources, we aim to construct a training set, which satisfies the budget of no more than \\( n \\) IDs and \\( m \\) images. To achieve this, we perform (A) target-specific subset search to obtain a subset \\( \\mathbf{S}^* \\) with similar distributions to the target, then perform (B) budgeted pruning to select \\( n \\) IDs and \\( m \\) representative images, forming the final training set." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.327, + 0.47, + 0.538 + ], + "angle": 0, + "content": "and use this ID-averaged descriptor to represent all corresponding images. Afterwards, we cluster the ID-averaged features into \\( J \\) groups using the k-means method [20]. Each subset \\( \\mathbf{S}^j \\), \\( j \\in [J] \\), is composed of all images with the corresponding IDs in that group. Secondly, we calculate the FID between each subset \\( \\mathbf{S}^j \\) and the target \\( \\mathcal{D}_T \\), and sort \\( \\{\\mathrm{FID}(\\mathbf{S}^j, \\mathcal{D}_T)\\}_{j \\in [J]} \\) in ascending order. To build \\( \\mathbf{S}^* \\), we keep adding the subsets with lower FID to \\( \\mathbf{S}^* \\) until \\( \\mathrm{FID}(\\mathbf{S}^*, \\mathcal{D}_T) \\) stops to decrease. This indicates that the constructed \\( \\mathbf{S}^* \\) holds the minimum FID to the target set. Algorithm 1 summarizes the above procedures. We empirically demonstrate in Fig. 5 that, the subset \\( \\mathbf{S}^* \\) with the minimum \\( \\mathrm{FID}(\\mathbf{S}^*, \\mathcal{D}_T) \\) results in the model to produce highest accuracy on the target dataset." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.546, + 0.332, + 0.563 + ], + "angle": 0, + "content": "4.4. Budget-constrained Pruning" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.57, + 0.47, + 0.765 + ], + "angle": 0, + "content": "Using the target-specific subset search, we construct a candidate training set \\(\\mathbf{S}^*\\). Yet, it can violate the budget constraint of \\(b = (n,m)\\), which prefers the training set to include no more than \\(n\\) identities and no more than \\(m\\) images. Let \\(\\mathcal{Y}(\\mathbf{S}^*) = \\{y^1,y^2,\\dots ,y^a\\}\\), be the set of unique identities in \\(\\mathbf{S}^*\\), and \\(s(y^{i})\\), \\(i\\in [a]\\) be the set of all images with identity \\(y^{i}\\). Generally, we have \\(a\\geq n\\). To get the training set \\(\\mathcal{D}_S\\) under budget \\(b\\), we randomly sample a subset \\(\\pmb{y}\\) of \\(n\\) identities from \\(\\mathcal{V}\\). All images with identities in \\(\\pmb{y}\\) are combined to form a subset \\(\\hat{\\mathbf{s}} = \\{s(y^{i})|y^{i}\\in \\pmb{y}\\}\\). We also initialize \\(\\mathcal{D}_S\\) by random sampling a seed image from each \\(s(y^{i})\\), \\(y^{i}\\in \\pmb{y}\\). This guarantees \\(\\mathcal{D}_S\\) to cover all the identities in the subset \\(\\hat{\\mathbf{s}}\\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.766, + 0.469, + 0.84 + ], + "angle": 0, + "content": "Suppose the number of images in \\(\\hat{\\mathbf{s}}\\) is larger than \\(m\\). We construct \\(\\mathcal{D}_S\\) by sampling images iteratively from \\(\\hat{\\mathbf{s}}\\) until \\(|\\mathcal{D}_S| = m\\). To ensure similar performance between the model trained on \\(D_S\\) and the model trained on \\(\\hat{\\mathbf{s}}\\), we minimize the risk differences between them," + }, + { + "type": "equation", + "bbox": [ + 0.117, + 0.85, + 0.469, + 0.877 + ], + "angle": 0, + "content": "\\[\n\\mathcal {D} _ {S} = \\underset {\\mathcal {D} _ {S} \\in 2 ^ {\\hat {\\mathbf {s}}}} {\\arg \\min } \\left| L \\left(h _ {\\hat {\\mathbf {s}}} (\\boldsymbol {x}), y\\right) - L \\left(h _ {\\mathcal {D} _ {S}} (\\boldsymbol {x}), y\\right) \\right|. \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.886, + 0.47, + 0.902 + ], + "angle": 0, + "content": "\\(L(h_{\\mathfrak{S}}(\\pmb {x}),y)\\) and \\(L(h_{\\mathcal{D}_S}(\\pmb {x}),y)\\) are the respective risks of" + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.087, + 0.695, + 0.203 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.706, + 0.089, + 0.894, + 0.203 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.519, + 0.21, + 0.89, + 0.327 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.348, + 0.892, + 0.486 + ], + "angle": 0, + "content": "Figure 5. Performance of constructed training set at different iterations on the target set. We greedily add clustered subset to form \\(\\mathbf{S}^*\\) which has the smallest domain gap to the target \\(\\mathcal{D}_T\\). During this process, we have relatively high FID and low accuracy at (A). Gradually, we reach situation (B) of the smallest domain gap and highest accuracy. After (B), adding subsets leads to an increase in the domain gap, and the accuracy drops, e.g., (C). To study the correlation between FID and mAP during the search process, we hope to eliminate the impact of dataset size. Thus we use the same number of IDs from the searched set (i.e., \\(2\\%\\) ID)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.498, + 0.89, + 0.528 + ], + "angle": 0, + "content": "model \\(h\\) on the dataset \\(\\hat{\\mathbf{s}}\\) and \\(\\mathcal{D}_S\\). For simplicity, we define the risk of model \\(h\\) on an arbitrary dataset \\(\\mathbf{S}\\) as" + }, + { + "type": "equation", + "bbox": [ + 0.553, + 0.535, + 0.891, + 0.573 + ], + "angle": 0, + "content": "\\[\nL \\left(h _ {\\mathbf {S}} (\\boldsymbol {x}), y\\right) = \\frac {1}{| \\mathbf {S} |} \\sum_ {\\left(\\boldsymbol {x} _ {i}, y _ {i}\\right) \\in \\mathbf {S}} \\ell \\left(h _ {\\mathbf {S}} \\left(\\boldsymbol {x} _ {i}\\right), y _ {i}\\right). \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.582, + 0.89, + 0.597 + ], + "angle": 0, + "content": "As in Eq. 1, \\(\\ell(h_{\\mathbf{S}}(\\pmb{x}_i), y_i)\\) is the risk on individual samples." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.598, + 0.891, + 0.643 + ], + "angle": 0, + "content": "From the theory of core set [31], if \\(\\mathcal{D}_S\\) is the \\(\\delta_s\\) cover of the set \\(\\hat{\\mathbf{s}}\\) and shares the same number of classes with \\(\\hat{\\mathbf{s}}\\), the risk difference between model \\(h_{\\hat{\\mathbf{s}}}\\) and \\(h_{\\mathcal{D}_S}\\) is bounded by" + }, + { + "type": "equation", + "bbox": [ + 0.509, + 0.65, + 0.891, + 0.684 + ], + "angle": 0, + "content": "\\[\n\\left| L \\left(h _ {\\hat {\\mathbf {s}}} (\\boldsymbol {x}), y\\right) - L \\left(h _ {\\mathcal {D} _ {S}} (\\boldsymbol {x}), y\\right) \\right| \\leq \\mathcal {O} \\left(\\delta_ {s}\\right) + \\mathcal {O} \\left(\\frac {1}{\\sqrt {| \\mathcal {D} _ {S} |}}\\right). \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.691, + 0.891, + 0.782 + ], + "angle": 0, + "content": "\\(\\delta_{s}\\) is the radius of the cover, and \\(\\mathcal{O}(\\delta_s)\\) is a polynomial function over \\(\\delta_{s}\\). The problem can be reduced as a K-center problem [11] by optimizing \\(\\mathcal{O}(\\delta_s)\\). We apply a 2-approximation algorithm [46] to iteratively find optimal samples in \\(\\hat{\\mathbf{s}}\\) and add to \\(\\mathcal{D}_S\\). Specifically, each optimal sample \\(\\mathbf{z}^*\\) is computed as" + }, + { + "type": "equation", + "bbox": [ + 0.559, + 0.79, + 0.891, + 0.816 + ], + "angle": 0, + "content": "\\[\n\\mathbf {z} ^ {*} = \\underset {\\mathbf {z} _ {i} \\in \\hat {\\mathbf {s}} \\backslash \\mathcal {D} _ {\\mathcal {S}}} {\\arg \\max } \\underset {\\mathbf {z} _ {j} \\in \\mathcal {D} _ {\\mathcal {S}}} {\\min } \\| f (\\boldsymbol {x} _ {i}) - f (\\boldsymbol {x} _ {j}) \\| _ {2}, \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.892, + 0.901 + ], + "angle": 0, + "content": "where \\(\\mathbf{z} = (\\pmb{x},y)\\), and \\(f(\\pmb{x})\\) represents the descriptor of an image \\(\\pmb{x}\\). Equation 9 relates to the furthest point sampling method [8], which enables the most representative samples from a dataset to be selected. We summarize the pruning process in Algorithm 2." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15572" + } + ], + [ + { + "type": "code_caption", + "bbox": [ + 0.08, + 0.092, + 0.362, + 0.106 + ], + "angle": 0, + "content": "Algorithm 1 Target-specific Subset Search" + }, + { + "type": "algorithm", + "bbox": [ + 0.08, + 0.108, + 0.47, + 0.294 + ], + "angle": 0, + "content": "1: Input: Source pool \\(S\\), target set \\(\\mathcal{D}_T\\), and the number of clusters \\(J\\). \n2: Begin: \n3: Cluster \\((S, J) \\longrightarrow \\{\\mathbf{S}^1, \\dots, \\mathbf{S}^J\\}\\) \n4: \\(\\mathbf{s} = \\emptyset, \\epsilon = \\infty, \\mathbf{S}^* = \\emptyset\\) \n5: \\(\\mathcal{I} = \\text{argsort}(\\{\\text{FID}(\\mathbf{S}^j, \\mathcal{D}_T)\\}_{j \\in [J]}) \\triangleright\\) Ascending \n6: for \\(j\\) in \\(\\mathcal{I}\\) do \n7: \\(\\mathbf{s} = \\mathbf{s} \\cup \\mathbf{S}^j\\) \n8: if FID(s, T) < \\(\\epsilon\\) then \n9: \\(\\epsilon = \\text{FID}(\\mathbf{s}, \\mathcal{D}_T)\\) \n10: \\(\\mathbf{S}^* = \\mathbf{s}\\) \n11: return S*" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.32, + 0.194, + 0.334 + ], + "angle": 0, + "content": "4.5. Discussion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.343, + 0.469, + 0.494 + ], + "angle": 0, + "content": "What to prune first, ID or image? In our design, we select the IDs first and then images, aiming to build a dataset that has a small domain gap to target and is meanwhile in small-scale. Selecting the images first and then IDs is possible. However, it leads to a significant increase in the time complexity. As shown in Algorithm 2, the most time-consuming part of our algorithm is the FPS for finding image core sets, which takes \\(\\mathcal{O}(m|\\hat{\\mathbf{s}}|)\\). If we select images first, the time complexity becomes \\(\\mathcal{O}(m|\\mathbf{S}^*|)\\), which is significantly higher than \\(\\mathcal{O}(m|\\hat{\\mathbf{s}}|)\\) as \\(|\\mathbf{S}^*| \\gg |\\hat{\\mathbf{s}}|\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.495, + 0.469, + 0.646 + ], + "angle": 0, + "content": "Is SnP applicable to tasks beyond object re-ID? It is possible to apply our search and pruning (SnP) framework to other tasks, e.g., classification. Yet, achieving this requires the SnP algorithm to be partially redesigned. The reason is that, in object re-ID, the major domain gap comes from the class difference, i.e., IDs. However, such a gap does not exist in the classification tasks as the train/val/test datasets always share the same classes. Therefore, our current design of selecting similar IDs for similar distributions is not directly applicable, and has to be adapted." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.66, + 0.201, + 0.677 + ], + "angle": 0, + "content": "5. Experiment" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.686, + 0.469, + 0.747 + ], + "angle": 0, + "content": "We evaluate the effectiveness of SnP on person re-ID and vehicle re-ID. In both tasks, given target data, we use the SnP pipeline to find a training set that has a similar distribution to the target and simultaneously meets a budget." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.757, + 0.323, + 0.772 + ], + "angle": 0, + "content": "5.1. Source and Target Datasets" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Person re-ID. We create the source pool for person re-ID using 10 public datasets, including Market [54], Duke [55], MSMT17 [45] (denoted as MSMT), CUHK03 [19], RAiD [6], PersonX [37], UnrealPerson [52], RandPerson [43], PKU-Reid [28] and VIPeR [4]. Those datasets cover both synthetic and real-world data. Ten re-ID datasets constitute a source pool that contains in total of 15,060 IDs and 399,715 images." + }, + { + "type": "code_caption", + "bbox": [ + 0.502, + 0.092, + 0.712, + 0.106 + ], + "angle": 0, + "content": "Algorithm 2 Budgeted Pruning" + }, + { + "type": "algorithm", + "bbox": [ + 0.501, + 0.108, + 0.892, + 0.324 + ], + "angle": 0, + "content": "1: Input: Initial source set \\(\\mathbf{S}^*\\), budget \\(b = (n, m)\\). \n2: Begin: \n3: \\(\\pmb{y} = \\mathcal{U}(\\mathcal{V}(\\mathbf{S}^*), n)\\) ▷ Sample n IDs \n4: \\(\\hat{\\mathbf{s}} = \\{\\pmb{s}(y_i) | y_i \\in \\pmb{y}\\}\\) \n5: \\(\\mathcal{D}_S = \\{\\mathcal{U}(\\mathbf{s}(y^i), 1) | y_i \\in \\pmb{y}\\}\\) \n6: if \\(|\\hat{\\mathbf{s}}| > m\\) then ▷ Sample m images \n7: repeat \n8: \\(\\mathbf{z}^* = \\arg\\max_{\\mathbf{z}_i \\in \\hat{\\mathbf{s}} \\setminus \\mathcal{D}_S} \\min_{\\mathbf{z}_j \\in \\mathcal{D}_S} \\|\\pmb{x}_i - \\pmb{x}_j\\|_2\\) \n9: \\(\\mathcal{D}_S = \\mathcal{D}_S \\cup \\{\\mathbf{z}^*\\}\\) \n10: until \\(|\\mathcal{D}_S| = m\\) \n11: else \n12: \\(\\mathcal{D}_S = \\hat{\\mathbf{s}}\\) \n13: return \\(\\mathcal{D}_S\\)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.351, + 0.892, + 0.44 + ], + "angle": 0, + "content": "We use two real-world datasets as targets: AlicePerson [1] and Market [54]. Specifically, AlicePerson is specially designed for domain adaptation as it contains unlabeled training images. Note that in Market, the label for its training set is not be used. When Market is the target, Market training set is excluded from the source pool." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.442, + 0.892, + 0.517 + ], + "angle": 0, + "content": "Vehicle re-ID. For vehicle re-ID, we create the source pool by combining 8 datasets, which are VeRi [22], CityFlow [41], VehicleID [21], VeRi-Wild [25], VehicleX [50], Stanford Cars [18], PKU-vd1 [47] and PKU-vd2 [47]. It totally has 156,512 IDs and 1,284,272 images." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.518, + 0.892, + 0.578 + ], + "angle": 0, + "content": "AliceVehicle [1] and VeRi [22] are separately used as the target domains. Similar to AlicePerson, AliceVehicle is also designed for domain adaptation. When VeRi is the target, the VeRi training set is excluded from the source pool." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.58, + 0.892, + 0.669 + ], + "angle": 0, + "content": "Evaluation protocol. For object re-ID, we use mean average precision (mAP) and cumulative match curve (CMC) scores to measure system accuracy, e.g., \"rank-1\" and \"rank-5\". \"rank-1\" denotes the success rate of finding the true match in the first rank, and \"rank-5\" means the success rate of ranking at least one true match within top-5 matches." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.681, + 0.592, + 0.695 + ], + "angle": 0, + "content": "5.2. Results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.892, + 0.901 + ], + "angle": 0, + "content": "SnP framework vs. random sampling and greedy sampling. Given a target domain, the SnP framework allows us to construct a budgeted dataset with a similar distribution. We show the superiority of SnP framework in Table 1. After sampling target-specific data with SnP, we train the subsequent re-ID model with the sampled target-specific data only. In Table 1, we compare the sampled dataset with those created by greedy sampling and random sampling. Random sampling means we randomly select IDs according to the uniform distribution. For greedy sampling, we reproduce [48]. Specifically, We assign each ID a score, which is calculated using FID. IDs will then be selected greedily from the lowest FID value to the highest FID value." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "15573" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.895, + 0.133 + ], + "angle": 0, + "content": "Table 1. Comparing different methods in training data search: SnP, random sampling, and greedy sampling. We set the budget as \\(2\\%\\), \\(5\\%\\), and \\(20\\%\\) of the total source IDs. We use four targets: AlicePerson, Market, AliceVehicle and VeRi. The task model is IDE [53]. FID, rank-1 accuracy \\((\\%)\\), and mAP \\((\\%)\\) are reported." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.143, + 0.894, + 0.32 + ], + "angle": 0, + "content": "
Training dataPerson re-ID targetsVehicle re-ID targets
AlicePersonMarketAliceVehicleVeRi
FID↓R1↑mAP↑FID↓R1↑mAP↑FID↓R1↑mAP↑FID↓R1↑mAP↑
Source pool81.6738.9617.6237.5355.5530.6243.9530.4714.6424.3955.9025.03
Searched60.9548.1925.5130.4261.4934.4023.4446.7825.4617.9274.1341.71
Pruned2% IDsRandom80.0623.679.8039.0340.7719.5445.9731.3512.8724.6867.1626.48
Greedy [48]61.7833.2215.1034.4342.1919.3538.5131.8212.9129.5366.5726.24
SnP60.4238.2318.1731.2944.8021.6523.4838.4817.7917.7069.9631.10
5% IDsRandom81.4133.1614.4939.6547.3923.9744.5236.3614.1725.2770.3830.44
Greedy [48]61.0144.6322.8131.6349.1724.7732.4841.3217.7726.0671.2332.53
SnP60.6447.2625.4530.3751.9626.5623.9244.5821.7918.0972.0536.01
20% IDsRandom79.3338.1017.7938.6353.1528.3943.9040.8918.1324.4368.7134.10
Greedy [48]63.1546.7422.6532.4253.5328.1924.1544.5822.8218.7471.0438.07
SnP61.8747.2025.3630.5857.1433.0923.4746.0725.2417.9373.4840.75
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.332, + 0.472, + 0.375 + ], + "angle": 0, + "content": "Table 2. The effectiveness of the target-specific subset search. mAP \\((\\%)\\) and CMC scores are reported. \"R1\" and \"R5\" denote rank-1 accuracy \\((\\%)\\) and rank-5 accuracy \\((\\%)\\), respectively." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.386, + 0.47, + 0.489 + ], + "angle": 0, + "content": "
AlicePersonAliceVehicle
Training dataR1R5mAPTraining dataR1R5mAP
Market [54]32.8952.5416.06VeRi [22]30.6943.6611.05
Duke [55]23.2741.138.59CityFlow [41]23.9536.007.45
MSMT [45]31.2952.7915.08VehicleID [21]16.329.134.73
PersonX [37]16.0827.426.41VehicleX [50]18.8532.188.89
Source pool38.9657.4817.62Source pool30.4748.3314.64
Searched48.1967.5725.51Searched46.7864.4125.46
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.507, + 0.47, + 0.688 + ], + "angle": 0, + "content": "From the results shown in Table 1 and Table 3, we observe that training sets selected using SnP achieve consistently lower domain gap to the target and higher re-ID accuracy than those found by random sampling and greedy sampling. For example, when creating a training set with only \\(2\\%\\) source IDs for AlicePerson as the target, SnP results in -19.64 and -1.36 improvement in FID value, and \\(+14.56\\%\\) and \\(+5.01\\%\\) improvement in rank-1 accuracy over using random sampling and greedy sampling, respectively. When sampling training set with \\(2\\%\\) of the source IDs for AliceVehicle as the target, the rank-1 accuracy improvement is \\(+7.13\\%\\) and \\(+6.66\\%\\), respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.47, + 0.884 + ], + "angle": 0, + "content": "Effectiveness of the search step. We analyze this step in Table 1 and Table 2. In this search process that poses no limit on the number of IDs and images, we aim to identify and merge clusters of source identities that exhibit similar distributions with the target. We show the searched datasets contribute to improved accuracy over the entire data pool. For example, for AlicePerson, we observe a \\(+9.23\\%\\) improvement in rank-1 accuracy over the entire data pool. We further show the searched data is superior to individual training sets in Table 2. For example, when AliceVehicle is our target, we show our searched dataset results in \\(+16.09\\%\\), \\(+22.83\\%\\), \\(+30.48\\%\\), \\(+27.93\\%\\) higher rank-1 accuracy than VeRi, CityFlow, VehicleID, and VehicleX, respectively." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.886, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Of note, accuracy under this application scenario is usu" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.332, + 0.895, + 0.403 + ], + "angle": 0, + "content": "Table 3. The superiority of SnP over random sampling and greedy sampling, when different direct transfer and pseudu-label re-ID models are used. We report accuracy when \\(2\\%\\) IDs are selected for target AicerPerson. Notations and evaluation metrics are the same as those in the previous table." + }, + { + "type": "table", + "bbox": [ + 0.503, + 0.413, + 0.89, + 0.613 + ], + "angle": 0, + "content": "
TypeModelTraining dataR1R5mAP
Direct TransferIDE [53]Random23.6742.329.80
Greedy [48]33.2254.4515.10
SnP38.2358.4018.17
PCB [38]Random24.7941.609.91
Greedy [48]29.0746.0112.59
SnP32.4349.9015.18
TransReid [15]Random52.0469.7328.47
Greedy [48]63.7380.2441.88
SnP64.3180.4642.74
Pseudo-labelingUDA [34]Random32.1754.6715.32
Greedy [48]36.4752.0617.34
SnP41.4155.7420.47
MMT [13]Random35.9451.9117.25
Greedy [48]38.6456.4821.18
SnP43.3660.3823.34
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.892, + 0.749 + ], + "angle": 0, + "content": "ally lower than that produced by in-distribution training sets. This difference is understandable, because searched data have a relatively lower resemblance to the target data compared with in-distribution training sets. That said, annotating in-distribution training sets is usually expensive, especially considering the complex, specific and ever-changing target environments, where creating a training set on-the-fly with good performance is of practical value." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Effectiveness of the pruning step is analyzed in Table 1 and Fig. 7. Pruning aims to find a subset that has no more than \\( n \\) IDs and \\( m \\) images. From Table 1 and Fig. 7, admittedly, the pruning of both IDs and images will lead to an accuracy decrease. For example, when the target is AlicePerson, if we select \\( 2\\% \\) IDs, there is a \\( -9.23\\% \\) decrease in rank-1 accuracy. From Fig. 7, when the target is AlicePerson, if we further select \\( 40\\% \\) images, there is a \\( -9.96\\% \\) decrease in rank-1 accuracy. However, even though only \\( 2\\% \\) IDs are used, rank-1 accuracy obtained from the pruned" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "15574" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.088, + 0.093, + 0.136, + 0.187 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.156, + 0.093, + 0.47, + 0.187 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.223, + 0.188, + 0.352, + 0.2 + ], + "angle": 0, + "content": "(A) AlicePerson as Target" + }, + { + "type": "image", + "bbox": [ + 0.476, + 0.094, + 0.518, + 0.187 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.532, + 0.094, + 0.891, + 0.188 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.633, + 0.189, + 0.765, + 0.201 + ], + "angle": 0, + "content": "(C) AliceVehicle as Target" + }, + { + "type": "image", + "bbox": [ + 0.09, + 0.207, + 0.137, + 0.299 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.157, + 0.206, + 0.249, + 0.3 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.251, + 0.206, + 0.47, + 0.301 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.238, + 0.303, + 0.343, + 0.314 + ], + "angle": 0, + "content": "(B) Market as Target" + }, + { + "type": "image", + "bbox": [ + 0.476, + 0.207, + 0.518, + 0.3 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.533, + 0.206, + 0.889, + 0.301 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.649, + 0.304, + 0.743, + 0.315 + ], + "angle": 0, + "content": "(D) VeRi as Target" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.327, + 0.893, + 0.369 + ], + "angle": 0, + "content": "Figure 6. Composition statistics and images samples of searched training sets. For each subfigure (A), (B), (C) and (D), the columns on the left presents unlabeled target samples; columns the middle provide samples of the searched training set; the pie chart Community-verified icon Verified on the right shows composition statistics of the searched training set." + }, + { + "type": "image_caption", + "bbox": [ + 0.15, + 0.382, + 0.23, + 0.393 + ], + "angle": 0, + "content": "(A) AlicePerson" + }, + { + "type": "image", + "bbox": [ + 0.078, + 0.394, + 0.285, + 0.504 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.367, + 0.382, + 0.424, + 0.393 + ], + "angle": 0, + "content": "(B) Market" + }, + { + "type": "image", + "bbox": [ + 0.294, + 0.394, + 0.489, + 0.504 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.554, + 0.382, + 0.638, + 0.393 + ], + "angle": 0, + "content": "(C) Alice Vehicle" + }, + { + "type": "image", + "bbox": [ + 0.496, + 0.394, + 0.691, + 0.504 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.773, + 0.383, + 0.818, + 0.394 + ], + "angle": 0, + "content": "(D) VeRi" + }, + { + "type": "image", + "bbox": [ + 0.697, + 0.395, + 0.893, + 0.504 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.514, + 0.89, + 0.543 + ], + "angle": 0, + "content": "Figure 7. Comparing FPS with random sampling. The search step provides us with \\(2\\%\\) of the source IDs. We further select various ratios of images from these IDs. Four different targets are used, and rank-1 accuracy is the evaluation metric. Score is averaged over three runs." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.556, + 0.469, + 0.618 + ], + "angle": 0, + "content": "training data is still competitive over the source pool, which is just \\(-0.73\\%\\) lower than the source pool. It shows the pruning method significantly reduces the training set scale while being able to train a model of reasonable accuracy." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.623, + 0.469, + 0.789 + ], + "angle": 0, + "content": "Composition of searched training sets. We visualize four examples in in Fig. 6. It is clear that searched training sets have different compositions under different targets. If we use AlicePerson as the target, in the searched training set, images from Market and Duke take up \\(68\\%\\) and \\(26\\%\\), respectively. In comparison, when using Market as the target, the resulting training set contains, \\(43\\%\\) images from UnrealPerson, and \\(34\\%\\) from MSMT. An interesting observation is that synthetic data (UnrealPerson) has a major role under Market as the target. It demonstrates the potential use of synthetic data for real-world target domains." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Comparison between FPS and random sampling. Both can be used for sampling images resulting from the search step. In Fig. 7, we sample different ratios of the images resulting from the search step. We observe FPS is consistently superior to random sampling, under different selection ratios and targets. Improvement of FPS over random sampling first increase and then decreases, with peak" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.557, + 0.796, + 0.572 + ], + "angle": 0, + "content": "improvement happening at the \\(30 - 60\\%\\) ratio." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.585, + 0.618, + 0.601 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.61, + 0.892, + 0.777 + ], + "angle": 0, + "content": "This paper studies the training data set search problem, for object re-ID applications. Under a certain budget, we aim to find a target-specific training set that gives a competitive re-ID model. We show our method is overall superior to existing strategies such as random sampling and greedy sampling in terms of accuracy on the target domain. We analyze various components in the SnP system and find them to be stable under various source pools and targets. We also point out the correlation between domain gap, dataset size, and training set quality, and would like to further study the data-centric problems in the community." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.79, + 0.68, + 0.807 + ], + "angle": 0, + "content": "7. Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.815, + 0.892, + 0.892 + ], + "angle": 0, + "content": "This work was supported in part by the ARC Discovery Early Career Researcher Award (DE200101283), the ARC Discovery Project (DP210102801), Oracle Cloud credits, and related resources provided by Oracle for Research. 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We propose a search and pruning (SnP) solution to this training data search problem, tailored to object re-identification (re-ID), an application aiming to match the same object captured by different cameras. Specifically, the search stage identifies and merges clusters of source identities which exhibit similar distributions with the target domain. The second stage, subject to a budget, then selects identities and their images from the Stage I output, to control the size of the resulting training set for efficient training. The two steps provide us with training sets $80\%$ smaller than the source pool while achieving a similar or even higher re-ID accuracy. These training sets are also shown to be superior to a few existing search methods such as random sampling and greedy sampling under the same budget on training data size. If we release the budget, training sets resulting from the first stage alone allow even higher re-ID accuracy. We provide interesting discussions on the specificity of our method to the re-ID problem and particularly its role in bridging the re-ID domain gap. The code is available at https://github.com/yorkeyao/SnP + +# 1. Introduction + +The success of a deep learning-based object re-ID relies on one of its critical prerequisites: the labeled training data. To achieve high accuracy, typically a massive amount of data needs to be used to train deep learning models. However, creating large-scale object re-ID training data with manual labels is expensive. Furthermore, collecting training data that contributes to the high test accuracy of the trained model is even more challenging. Recent years have seen a large amount of datasets proposed and a significant increase in the data size of a single dataset. For example, the Rand-Person [37] dataset has 8000 identities, which is more than + +![](images/3f02dee31ef16b43195c1fd29f4ff799834f4c4963e4a27f07d682d29f9abef4.jpg) +Figure 1. We present a search and pruning (SnP) solution to the training data search problem in object re-ID. The source data pool is 1 order of magnitude larger than existing re-ID training sets in terms of the number of images and the number of identities. When the target is AlicePerson [1], from the source pool, our method (SnP) results in a training set $80\%$ smaller than the source pool while achieving a similar or even higher re-ID accuracy. The searched training set is also superior to existing individual training sets such as Market-1501 [54], Duke [55], and MSMT [45]. + +$6\times$ larger than the previous PersonX [37] dataset. + +However, these datasets generally have their own dataset bias, making the model trained on one dataset unable to generalize well to another. For example, depending on the filming scenario, different person re-ID datasets generally have biases on camera positions, human races, and clothing style. Such dataset biases usually lead to model bias, which results in the model's difficulty performing well in an unseen filming scenario. To address this, many try to improve learning algorithms, including domain adaptation and domain generalization methods [2, 10, 27, 33, 35, 56]. Whereas these algorithms are well-studied and have proven successful in many re-ID applications, deciding what kind of data to use for training the re-ID model is still an open research problem, and has received relatively little attention in the community. We argue that this is a crucial problem + +to be answered in light of the ever-increasing scale of the available datasets. + +In this paper, we introduce SnP, a search and pruning solution for sampling an efficient re-ID training set to a target domain. SnP is designed for the scenario in that we have a target dataset that does not have labeled training data. Our collected source pool, in replace, provides suitable labeled data to train a competitive model. Specifically, given a user-specified budget (e.g., maximum desired data size), we sample a subset of the source pool, which satisfies the budget requirement and desirably has high-quality data to train deep learning models. This scenario is especially helpful for deploying a re-ID system for unknown test environments, as it is difficult to manually label a training set for these new environments. We note that due to the absence of an indistribution training set, the searched data are directly used for training the re-ID model rather than pre-training. + +In particular, we combine several popular re-ID datasets into a source pool, and represent each image in the pool with features. Those features are extracted from an Imagenet-pretrained model [39]. The images with features are stored on the dataserver to serve as a gallery. When there is a query from the target, we extract the feature of the query image, and search in the gallery for similar images on a feature level. Specifically, in the search stage, we calculate feature-level distance, i.e., Fréchet Inception Distance (FID) [16]. Given the constraint of a budget, we select the most representative samples in the pruning stage, based on the outputs from the search stage. This limits the size of the constructed training set and enables efficient training. + +Combining search and pruning, we construct a training dataset that empirically shows significant accuracy improvements on several object re-ID targets, compared to the baselines. Without budget constraints, our searched training sets allow higher re-ID accuracy than the complete source pool, due to its target-specificity. With budget constraints, the pruned training set still achieves comparable or better performance than the source pool. The proposed SnP is demonstrated to be superior to random or greedy sampling. We show in Fig. 1 that the training set constructed by SnP leads to the best performance on the target compared to the others. We provide discussions on the specificity of our method and its role in bridging the re-ID domain gap. + +# 2. Related Work + +Active learning gradually searches over unlabeled data to find samples to be labeled by the oracle [32]. It is an iterative training process, where data search is performed at each iteration to train a task model. Our task is different from active learning. First, active learning is designed to acquire a training set and train models gradually. This requires multiple real training processes which are computationally expensive. In comparison, we directly search the + +whole training set all at once. Then the searched training set is used for model training. Second, many active learning methods require access to the target task model to provide selection metrics, e.g., uncertainty-based metrics [9, 12, 14, 49]. Our task does not require task model information, in other words, a real training process, during the process of the training set search. Thus enabling a fast training data retrial. + +Neural data server is the closest inspiring work [32,48]. They also aim to search training data all at once from a large database. However, compared with us, firstly, [48] and [32] are designed for searching pretraining data rather than direct training data. Such a design is understandable as they are mainly for the classification task. Searching direct training data require careful class alignment. In comparison, We are targeting the re-ID task, where its training set can have a different class from the target, and then be directly used for training models. Furthermore, [48] and [32] require unsupervised pretrained experts to measure the domain gap. While we do not require so, which saves extraction time and simplify the solution. + +Transfer learning is a long-standing problem for re-ID tasks, and many attempts on learning algorithms have been made to reduce the effect of domain gap [7, 26, 29, 30, 42]. Common strategies contain feature-level [24] and pseudolabel based [10, 35, 56] domain adaptation, and domain generalization [2, 27, 33]. In this paper, we focus on training data that is orthogonal to existing training algorithms. To be shown in experiments, together with some domain adaptation (i.e., pseudo-label) methods, SnP can achieve higher re-ID accuracy. + +Learning to generate synthetic training data. Data simulation is also an inexpensive alternative to increasing a training set scale while providing accurate image labels [23, 37, 50-52]. These methods aim to lower the domain gap between synthetic data and real data by searching a set of parameters that control the 3D rendering process [50, 51]. In comparison, our search is not conducted on predefined parameters but on data directly. This enables more direct research on how to form a good training set. + +Object re-ID has received increasing attention in the past few years, and many effective systems have been proposed [17, 40, 44, 57]. In this paper, we study object re-ID datasets rather than algorithms. Depending on the camera condition, location and environment, existing object re-ID datasets usually have their own distinct characteristics or bias [36, 37, 51]. We show details in §3. + +# 3. Motivation: Tackling Target Bias + +Data bias commonly exists in the re-ID datasets (for examples see below) [25, 43, 47, 52], and it becomes problematic when the training and testing have different biases. Given a target domain with a certain bias, we aim to find + +![](images/85e89a870fddef36ebf6bb2bebbd0609762d4256e5dd995677438f516bc981ae.jpg) +(A) Viewpoint bias. + +![](images/a38897acaf08fd0cb84072c027e3a53597ab16098d41b4351a564f2db12659a1.jpg) +(B) Human races & clothing style bias. + +![](images/c7feef806e2f346f77af55e4b4038163cbb18637dc9bf77baa11e296d8ee3817.jpg) +(C) Vehicle model bias. +CityFlow AliceVehicle +Figure 2. Dataset bias in existing object re-ID datasets. (A) Viewpoint distribution of different re-ID datasets. Each blue dot indicates a sample filmed from a specific viewpoint. Compared with the bi-modal viewpoint distribution in Market camera 1, Duke camera 4 has more diverse viewpoints. (B) Different human races and clothing styles of different person re-ID datasets. (C) Different vehicle makes in different datasets. For example, taxis in VeRi are unlikely to be found in CityFlow. (D) Different backgrounds in different datasets. We show a city background in AliceVehicle versus an urban background in CityFlow. To tackle such bias in the target domain, we design an automatic way to generate a training set with similar distribution or bias. + +![](images/44b52121b55ef6183548c4d6baec7c02d51ed317f3b87cb7573faac0f3d3869a.jpg) +(D) Background bias. + +a target-specific training set that has similar distribution or bias. Depending on the filming scenario, there are four major types of data biases in existing re-ID datasets. We show examples of each type in Fig. 2. + +Viewpoint. Viewpoint bias applies to generic objects, including persons and vehicles. We visualize the viewpoint distributions of two representative person re-ID datasets in Fig. 2(A), i.e., Market-1501 [54] (denoted as Market) and Duke-reID [55] (denoted as Duke) $^{1}$ . + +Human races and clothing style. Subject to the places where the data is collected, identities in the person re-ID datasets can have distinctive patterns. We show in Fig. 2(B) that the humans in Market and Duke datasets evince different races and clothing styles. + +Vehicle model. Similar to the identity bias (i.e., human races and clothing style) in person re-ID, the vehicle identities in vehicle re-ID also hold distinct patterns across different datasets. We show examples in Fig. 2(C) using the VeRi [22] (denoted as VeRi) and the CityFlow [41]. + +Background. Background bias exists in both person and vehicle re-ID datasets, which is similar to viewpoint bias. Fig. 2(D) compares the background difference of images from two different vehicle re-ID datasets. + +# 4. Method + +Given a target unlabeled dataset, we aim to construct a source labeled dataset that has minimal data bias inconsistencies with the target, under certain budget constraints. It induces the model trained on the source to show good performance on the target. To achieve the construction of the source (training) dataset, we propose the search and pruning (SnP) framework. + +# 4.1. Overview + +We denote the target set as $\mathcal{D}_T = \{(x_i, y_i)\}_{i \in [m_t]}$ where $m_t$ indicates the number of image-label pairs in the target and $[m_t] = \{1, 2, \dots, m_t\}$ . It follows the distribution $p_T$ , i.e., $\mathcal{D}_T \sim p_T$ . Let $\mathcal{D}_S$ be the source set to be constructed under a budget $b$ . The budget is specified by the number of identities $n$ and the number of images $m$ allowed in $\mathcal{D}_S$ , denoted as $b = (n, m)$ . A high budget can lead to an unwanted increase in the training cost, in terms of either training time or model size. + +To construct the training set $\mathcal{D}_S$ , we create a source pool $S$ , which is a collection of multiple object re-ID datasets. It is represented as $\mathcal{S} = \mathcal{D}_S^1 \cup \mathcal{D}_S^2 \dots \cup \mathcal{D}_S^K$ . Here each $\mathcal{D}_S^k$ , $k \in [K]$ , indicates the $k$ -th source re-ID dataset. Given the source pool, we firstly build a subset $\mathbf{S}^*$ of $S$ regardless of the budget constraint. Let $h_{\mathbf{S}}$ be a model $h$ trained on an arbitrary dataset $\mathbf{S}$ . The prediction risk of $h_{\mathbf{S}}$ on the test sample $\mathbf{x}$ with ground truth label $y$ is computed as $\ell(h_{\mathbf{S}}(\mathbf{x}), y)$ . We build $\mathbf{S}^*$ by ensuring that the model $h_{\mathbf{S}^*}$ has minimized risk on $\mathcal{D}_T$ , i.e., + +$$ +\mathbf {S} ^ {*} = \underset {\mathbf {S} \in 2 ^ {\mathcal {S}}} {\arg \min } \mathbb {E} _ {\boldsymbol {x}, y \sim p _ {T}} [ \ell (h _ {\mathbf {S}} (\boldsymbol {x}), y) ]. \tag {1} +$$ + +We apply target-specific search in $\S 4.3$ to construct $\mathbf{S}^*$ . + +It can be seen that the construction of $\mathbf{S}^*$ does not take the budget constraint $b = (n,m)$ into consideration, which is otherwise important in reality. Therefore, we build the training set $\mathcal{D}_S$ by pruning $\mathbf{S}^*$ to comprise no more than $n$ identities and no more than $m$ images. Details of the budgeted pruning process are introduced in §4.4. + +# 4.2. Correlation Study + +In order to know how to obtain $\mathbf{S}^*$ , we conduct the correlation study to learn the relationships between the dataset bias differences (i.e., domain gap measured in measured in FID [16]), the number of IDs and the training set quality + +![](images/2a3242a888d6e628385a210dfc0483cf239b4d7aec9db7019f0357bf25ebba48.jpg) +(A) + +![](images/8eb5124e0d5072eca73300f6c3e1f30d10592752a11112fabc3d7d566083f37a.jpg) +(B) + +![](images/f4ff4c5f224b0ba5b7257a28eb64c01fd89e9e47218c2b4dd5097c830c381911.jpg) +(C) + +![](images/9fbe779324bef4ae9c790d71aa054062c27cc92bc7b7ccf54d47468668af96be.jpg) +(D) + +![](images/f1c0f0830b733c47196b0821b8afa00322e4ae95e42f9575abbc2af59af72d70.jpg) +Figure 3. Relationships between the domain gap (measured using FID), the number of ID and the rank-1 accuracy on the target. Top: correlations when AlicePerson [1] is targeted. Bottom: correlations when AliceVehicle [1] is targeted. The Pearson correlation is used to measure the relationship between them. (A) FID vs. the rank-1 accuracy. They have a relatively strong negative correlation $(\leq -0.636)$ . (B) The number of ID vs. the rank-1 accuracy. There exists a positive correlation but such a correlation is not stable. (C) FID vs. number of ID. The correlation is weak between them. (D) The joint influence of FID and the number of ID on rank-1 accuracy. The top left corner, i.e., training sets that have low FID scores and a large number of IDs have high rank-1 accuracy on the target. + +![](images/487740c39563801ab57d1df38cf269ac9cf04cc926b47ae3d40a96d619d0ec5f.jpg) + +![](images/332360379e510586ba1b7373b517b68553dda192f400b169b8f70de6a73e5ee7.jpg) + +![](images/8a97d263163a9c8e433021dec219dc24e6dfbf99fd661aa6cdae23429d36ac20.jpg) + +(i.e., rank-1 test accuracy with the model trained on the such training set). Shown in Fig. 3, in each subfigure, each point represents a training set, which is clustered from the source pool. For each training set, we calculate its domain gap to the target domain, count its number of IDs, and evaluate the rank-1 accuracy. We use the Pearson correlation coefficient $(\gamma)$ [5] to measure the correlation between them. The Pearson correlation coefficients range from $[-1, 1]$ . A value closer to -1 or 1 indicates a stronger negative or positive correlation, respectively, and 0 implies no correlation. + +From this Fig. 3(A), we observe a relatively strong negative correlation between domain gap and rank-1 accuracy. This indicates minimizing the domain gap between the source and target is highly likely to improve training set quality, i.e., test set rank-1 accuracy. From this Fig. 3(B), we observe a positive but unstable correlation between the number of ID and the rank-1 accuracy. For example, when AlicePerson is targeted, they have a relatively strong positive correlation (0.720). However, such correlation is only 0.383 when AliceVehicle is targeted. Fig. 3(C) shows the correlation between FID and the number of ID is weak. They are independent factors that influence training set quality. Fig. 3(D) shows the joint influence of FID and the number of ID on the training set quality. The top left corner, i.e., training sets that have a low domain gap to the target and a large number of IDs are of high quality, thereby can train a model that has higher rank-1 accuracy on the target. + +# 4.3. Target-specific Subset Search + +The theory of domain adaptation [3] states that: + +$$ +\varepsilon_ {T} (h) < \varepsilon_ {S} (h) + \frac {1}{2} d _ {\mathcal {H} \Delta \mathcal {H}} (\mathbf {S}, \mathcal {D} _ {T}). \tag {2} +$$ + +Here $h \in \mathcal{H}$ represents the hypothesis function (i.e., the model). $\varepsilon_T(h)$ is the risk of model $h$ on the target set $\mathcal{D}_T$ , while $\varepsilon_S(h)$ is its risk on the source set $\mathbf{S}$ . $d_{\mathcal{H}\Delta \mathcal{H}}(\mathbf{S},\mathcal{D}_T)$ is the unlabelled $\mathcal{H}\Delta \mathcal{H}$ divergence [3] between $\mathbf{S}$ and $\mathcal{D}_T$ . Equation 2 shows that the target risk $\varepsilon_T(h)$ is upper bounded by $d_{\mathcal{H}\Delta \mathcal{H}}(\mathbf{S},\mathcal{D}_T)$ . + +In the common practice of feature-level domain adaptation, the source training set $\mathbf{S}$ is fixed while the joint feature extraction model is used to minimize $d_{\mathcal{H}\Delta \mathcal{H}}(\mathbf{S},\mathcal{D}_T)$ [24]. In our design, the feature extraction model is fixed instead. To minimize $\varepsilon_T(h)$ , the problem is reformulated as + +$$ +\mathbf {S} ^ {*} = \underset {\mathbf {S} \in 2 ^ {S}} {\arg \min } d _ {\mathcal {H} \Delta \mathcal {H}} (\mathbf {S}, \mathcal {D} _ {T}). \tag {3} +$$ + +Generally, $d_{\mathcal{H}\Delta \mathcal{H}}(\mathbf{S}^*,\mathcal{D}_T)$ is difficult to compute, but many alternatives exist in the literature [24]. We use Fréchet Inception Distance (FID) [16], which is defined as: + +$$ +\operatorname {F I D} \left(\mathbf {S} ^ {*}, \mathcal {D} _ {T}\right) = \left\| \boldsymbol {\mu} _ {s} - \boldsymbol {\mu} _ {t} \right\| _ {2} ^ {2} + \operatorname {T r} \left(\boldsymbol {\Sigma} _ {s} + \boldsymbol {\Sigma} _ {t} - 2 \left(\boldsymbol {\Sigma} _ {s} \boldsymbol {\Sigma} _ {t}\right) ^ {\frac {1}{2}}\right). \tag {4} +$$ + +In Eq. 4, $\pmb{\mu}_s \in \mathbb{R}^d$ and $\pmb{\Sigma}_s \in \mathbb{R}^{d \times d}$ are the mean and covariance matrix of the image descriptors of $\mathbf{S}^*$ , respectively. $\pmb{\mu}_t$ and $\pmb{\Sigma}_t$ are those of $\mathcal{D}_T$ . $\mathrm{Tr}(.)$ represents the trace of a square matrix. $d$ is the dimension of the image descriptors. Consequently, the objective function is reduced as, + +$$ +\mathbf {S} ^ {*} = \underset {\mathbf {S} \in 2 ^ {S}} {\arg \min } \operatorname {F I D} (\mathbf {S}, \mathcal {D} _ {T}). \tag {5} +$$ + +We build $\mathbf{S}^*$ with the greedy algorithm below. + +Firstly, we divide the entire dataset $S$ into $J$ clusters $\{\mathbf{S}^1,\dots ,\mathbf{S}^J\}$ , as shown in Fig. 4 (A). Specifically, we average all image descriptors that belong to the same identity, + +![](images/550f7f9130ef0d238482804da2357bdf01fa32fe6107cbe7c538322486f72196.jpg) +Figure 4. Workflow of the proposed SnP method. We are given sources composed of $K$ existing datasets. From these sources, we aim to construct a training set, which satisfies the budget of no more than $n$ IDs and $m$ images. To achieve this, we perform (A) target-specific subset search to obtain a subset $\mathbf{S}^*$ with similar distributions to the target, then perform (B) budgeted pruning to select $n$ IDs and $m$ representative images, forming the final training set. + +and use this ID-averaged descriptor to represent all corresponding images. Afterwards, we cluster the ID-averaged features into $J$ groups using the k-means method [20]. Each subset $\mathbf{S}^j$ , $j \in [J]$ , is composed of all images with the corresponding IDs in that group. Secondly, we calculate the FID between each subset $\mathbf{S}^j$ and the target $\mathcal{D}_T$ , and sort $\{\mathrm{FID}(\mathbf{S}^j, \mathcal{D}_T)\}_{j \in [J]}$ in ascending order. To build $\mathbf{S}^*$ , we keep adding the subsets with lower FID to $\mathbf{S}^*$ until $\mathrm{FID}(\mathbf{S}^*, \mathcal{D}_T)$ stops to decrease. This indicates that the constructed $\mathbf{S}^*$ holds the minimum FID to the target set. Algorithm 1 summarizes the above procedures. We empirically demonstrate in Fig. 5 that, the subset $\mathbf{S}^*$ with the minimum $\mathrm{FID}(\mathbf{S}^*, \mathcal{D}_T)$ results in the model to produce highest accuracy on the target dataset. + +# 4.4. Budget-constrained Pruning + +Using the target-specific subset search, we construct a candidate training set $\mathbf{S}^*$ . Yet, it can violate the budget constraint of $b = (n,m)$ , which prefers the training set to include no more than $n$ identities and no more than $m$ images. Let $\mathcal{Y}(\mathbf{S}^*) = \{y^1,y^2,\dots ,y^a\}$ , be the set of unique identities in $\mathbf{S}^*$ , and $s(y^{i})$ , $i\in [a]$ be the set of all images with identity $y^{i}$ . Generally, we have $a\geq n$ . To get the training set $\mathcal{D}_S$ under budget $b$ , we randomly sample a subset $\pmb{y}$ of $n$ identities from $\mathcal{V}$ . All images with identities in $\pmb{y}$ are combined to form a subset $\hat{\mathbf{s}} = \{s(y^{i})|y^{i}\in \pmb{y}\}$ . We also initialize $\mathcal{D}_S$ by random sampling a seed image from each $s(y^{i})$ , $y^{i}\in \pmb{y}$ . This guarantees $\mathcal{D}_S$ to cover all the identities in the subset $\hat{\mathbf{s}}$ . + +Suppose the number of images in $\hat{\mathbf{s}}$ is larger than $m$ . We construct $\mathcal{D}_S$ by sampling images iteratively from $\hat{\mathbf{s}}$ until $|\mathcal{D}_S| = m$ . To ensure similar performance between the model trained on $D_S$ and the model trained on $\hat{\mathbf{s}}$ , we minimize the risk differences between them, + +$$ +\mathcal {D} _ {S} = \underset {\mathcal {D} _ {S} \in 2 ^ {\hat {\mathbf {s}}}} {\arg \min } \left| L \left(h _ {\hat {\mathbf {s}}} (\boldsymbol {x}), y\right) - L \left(h _ {\mathcal {D} _ {S}} (\boldsymbol {x}), y\right) \right|. \tag {6} +$$ + +$L(h_{\mathfrak{S}}(\pmb {x}),y)$ and $L(h_{\mathcal{D}_S}(\pmb {x}),y)$ are the respective risks of + +![](images/cbd3cafd8d5ffff9631f38858ef53a273e088b9bcf38fab0cee5e21193a9f60b.jpg) + +![](images/68125579b3a7c9e7c3dbc06d8cbe5714e4d414fc1cec6b56561b90f4ab35bd84.jpg) + +![](images/38c74062262b2f662e50409935f11fb4d4d75bc83382d9d28c32263fa2a17613.jpg) +Figure 5. Performance of constructed training set at different iterations on the target set. We greedily add clustered subset to form $\mathbf{S}^*$ which has the smallest domain gap to the target $\mathcal{D}_T$ . During this process, we have relatively high FID and low accuracy at (A). Gradually, we reach situation (B) of the smallest domain gap and highest accuracy. After (B), adding subsets leads to an increase in the domain gap, and the accuracy drops, e.g., (C). To study the correlation between FID and mAP during the search process, we hope to eliminate the impact of dataset size. Thus we use the same number of IDs from the searched set (i.e., $2\%$ ID). + +model $h$ on the dataset $\hat{\mathbf{s}}$ and $\mathcal{D}_S$ . For simplicity, we define the risk of model $h$ on an arbitrary dataset $\mathbf{S}$ as + +$$ +L \left(h _ {\mathbf {S}} (\boldsymbol {x}), y\right) = \frac {1}{| \mathbf {S} |} \sum_ {\left(\boldsymbol {x} _ {i}, y _ {i}\right) \in \mathbf {S}} \ell \left(h _ {\mathbf {S}} \left(\boldsymbol {x} _ {i}\right), y _ {i}\right). \tag {7} +$$ + +As in Eq. 1, $\ell(h_{\mathbf{S}}(\pmb{x}_i), y_i)$ is the risk on individual samples. + +From the theory of core set [31], if $\mathcal{D}_S$ is the $\delta_s$ cover of the set $\hat{\mathbf{s}}$ and shares the same number of classes with $\hat{\mathbf{s}}$ , the risk difference between model $h_{\hat{\mathbf{s}}}$ and $h_{\mathcal{D}_S}$ is bounded by + +$$ +\left| L \left(h _ {\hat {\mathbf {s}}} (\boldsymbol {x}), y\right) - L \left(h _ {\mathcal {D} _ {S}} (\boldsymbol {x}), y\right) \right| \leq \mathcal {O} \left(\delta_ {s}\right) + \mathcal {O} \left(\frac {1}{\sqrt {| \mathcal {D} _ {S} |}}\right). \tag {8} +$$ + +$\delta_{s}$ is the radius of the cover, and $\mathcal{O}(\delta_s)$ is a polynomial function over $\delta_{s}$ . The problem can be reduced as a K-center problem [11] by optimizing $\mathcal{O}(\delta_s)$ . We apply a 2-approximation algorithm [46] to iteratively find optimal samples in $\hat{\mathbf{s}}$ and add to $\mathcal{D}_S$ . Specifically, each optimal sample $\mathbf{z}^*$ is computed as + +$$ +\mathbf {z} ^ {*} = \underset {\mathbf {z} _ {i} \in \hat {\mathbf {s}} \backslash \mathcal {D} _ {\mathcal {S}}} {\arg \max } \underset {\mathbf {z} _ {j} \in \mathcal {D} _ {\mathcal {S}}} {\min } \| f (\boldsymbol {x} _ {i}) - f (\boldsymbol {x} _ {j}) \| _ {2}, \tag {9} +$$ + +where $\mathbf{z} = (\pmb{x},y)$ , and $f(\pmb{x})$ represents the descriptor of an image $\pmb{x}$ . Equation 9 relates to the furthest point sampling method [8], which enables the most representative samples from a dataset to be selected. We summarize the pruning process in Algorithm 2. + +Algorithm 1 Target-specific Subset Search +1: Input: Source pool $S$ , target set $\mathcal{D}_T$ , and the number of clusters $J$ . +2: Begin: +3: Cluster $(S, J) \longrightarrow \{\mathbf{S}^1, \dots, \mathbf{S}^J\}$ +4: $\mathbf{s} = \emptyset, \epsilon = \infty, \mathbf{S}^* = \emptyset$ +5: $\mathcal{I} = \text{argsort}(\{\text{FID}(\mathbf{S}^j, \mathcal{D}_T)\}_{j \in [J]}) \triangleright$ Ascending +6: for $j$ in $\mathcal{I}$ do +7: $\mathbf{s} = \mathbf{s} \cup \mathbf{S}^j$ +8: if FID(s, T) < $\epsilon$ then +9: $\epsilon = \text{FID}(\mathbf{s}, \mathcal{D}_T)$ +10: $\mathbf{S}^* = \mathbf{s}$ +11: return S* + +# 4.5. Discussion + +What to prune first, ID or image? In our design, we select the IDs first and then images, aiming to build a dataset that has a small domain gap to target and is meanwhile in small-scale. Selecting the images first and then IDs is possible. However, it leads to a significant increase in the time complexity. As shown in Algorithm 2, the most time-consuming part of our algorithm is the FPS for finding image core sets, which takes $\mathcal{O}(m|\hat{\mathbf{s}}|)$ . If we select images first, the time complexity becomes $\mathcal{O}(m|\mathbf{S}^*|)$ , which is significantly higher than $\mathcal{O}(m|\hat{\mathbf{s}}|)$ as $|\mathbf{S}^*| \gg |\hat{\mathbf{s}}|$ . + +Is SnP applicable to tasks beyond object re-ID? It is possible to apply our search and pruning (SnP) framework to other tasks, e.g., classification. Yet, achieving this requires the SnP algorithm to be partially redesigned. The reason is that, in object re-ID, the major domain gap comes from the class difference, i.e., IDs. However, such a gap does not exist in the classification tasks as the train/val/test datasets always share the same classes. Therefore, our current design of selecting similar IDs for similar distributions is not directly applicable, and has to be adapted. + +# 5. Experiment + +We evaluate the effectiveness of SnP on person re-ID and vehicle re-ID. In both tasks, given target data, we use the SnP pipeline to find a training set that has a similar distribution to the target and simultaneously meets a budget. + +# 5.1. Source and Target Datasets + +Person re-ID. We create the source pool for person re-ID using 10 public datasets, including Market [54], Duke [55], MSMT17 [45] (denoted as MSMT), CUHK03 [19], RAiD [6], PersonX [37], UnrealPerson [52], RandPerson [43], PKU-Reid [28] and VIPeR [4]. Those datasets cover both synthetic and real-world data. Ten re-ID datasets constitute a source pool that contains in total of 15,060 IDs and 399,715 images. + +Algorithm 2 Budgeted Pruning +1: Input: Initial source set $\mathbf{S}^*$ , budget $b = (n, m)$ . +2: Begin: +3: $\pmb{y} = \mathcal{U}(\mathcal{V}(\mathbf{S}^*), n)$ ▷ Sample n IDs +4: $\hat{\mathbf{s}} = \{\pmb{s}(y_i) | y_i \in \pmb{y}\}$ +5: $\mathcal{D}_S = \{\mathcal{U}(\mathbf{s}(y^i), 1) | y_i \in \pmb{y}\}$ +6: if $|\hat{\mathbf{s}}| > m$ then ▷ Sample m images +7: repeat +8: $\mathbf{z}^* = \arg\max_{\mathbf{z}_i \in \hat{\mathbf{s}} \setminus \mathcal{D}_S} \min_{\mathbf{z}_j \in \mathcal{D}_S} \|\pmb{x}_i - \pmb{x}_j\|_2$ +9: $\mathcal{D}_S = \mathcal{D}_S \cup \{\mathbf{z}^*\}$ +10: until $|\mathcal{D}_S| = m$ +11: else +12: $\mathcal{D}_S = \hat{\mathbf{s}}$ +13: return $\mathcal{D}_S$ + +We use two real-world datasets as targets: AlicePerson [1] and Market [54]. Specifically, AlicePerson is specially designed for domain adaptation as it contains unlabeled training images. Note that in Market, the label for its training set is not be used. When Market is the target, Market training set is excluded from the source pool. + +Vehicle re-ID. For vehicle re-ID, we create the source pool by combining 8 datasets, which are VeRi [22], CityFlow [41], VehicleID [21], VeRi-Wild [25], VehicleX [50], Stanford Cars [18], PKU-vd1 [47] and PKU-vd2 [47]. It totally has 156,512 IDs and 1,284,272 images. + +AliceVehicle [1] and VeRi [22] are separately used as the target domains. Similar to AlicePerson, AliceVehicle is also designed for domain adaptation. When VeRi is the target, the VeRi training set is excluded from the source pool. + +Evaluation protocol. For object re-ID, we use mean average precision (mAP) and cumulative match curve (CMC) scores to measure system accuracy, e.g., "rank-1" and "rank-5". "rank-1" denotes the success rate of finding the true match in the first rank, and "rank-5" means the success rate of ranking at least one true match within top-5 matches. + +# 5.2. Results + +SnP framework vs. random sampling and greedy sampling. Given a target domain, the SnP framework allows us to construct a budgeted dataset with a similar distribution. We show the superiority of SnP framework in Table 1. After sampling target-specific data with SnP, we train the subsequent re-ID model with the sampled target-specific data only. In Table 1, we compare the sampled dataset with those created by greedy sampling and random sampling. Random sampling means we randomly select IDs according to the uniform distribution. For greedy sampling, we reproduce [48]. Specifically, We assign each ID a score, which is calculated using FID. IDs will then be selected greedily from the lowest FID value to the highest FID value. + +Table 1. Comparing different methods in training data search: SnP, random sampling, and greedy sampling. We set the budget as $2\%$ , $5\%$ , and $20\%$ of the total source IDs. We use four targets: AlicePerson, Market, AliceVehicle and VeRi. The task model is IDE [53]. FID, rank-1 accuracy $(\%)$ , and mAP $(\%)$ are reported. + +
Training dataPerson re-ID targetsVehicle re-ID targets
AlicePersonMarketAliceVehicleVeRi
FID↓R1↑mAP↑FID↓R1↑mAP↑FID↓R1↑mAP↑FID↓R1↑mAP↑
Source pool81.6738.9617.6237.5355.5530.6243.9530.4714.6424.3955.9025.03
Searched60.9548.1925.5130.4261.4934.4023.4446.7825.4617.9274.1341.71
Pruned2% IDsRandom80.0623.679.8039.0340.7719.5445.9731.3512.8724.6867.1626.48
Greedy [48]61.7833.2215.1034.4342.1919.3538.5131.8212.9129.5366.5726.24
SnP60.4238.2318.1731.2944.8021.6523.4838.4817.7917.7069.9631.10
5% IDsRandom81.4133.1614.4939.6547.3923.9744.5236.3614.1725.2770.3830.44
Greedy [48]61.0144.6322.8131.6349.1724.7732.4841.3217.7726.0671.2332.53
SnP60.6447.2625.4530.3751.9626.5623.9244.5821.7918.0972.0536.01
20% IDsRandom79.3338.1017.7938.6353.1528.3943.9040.8918.1324.4368.7134.10
Greedy [48]63.1546.7422.6532.4253.5328.1924.1544.5822.8218.7471.0438.07
SnP61.8747.2025.3630.5857.1433.0923.4746.0725.2417.9373.4840.75
+ +Table 2. The effectiveness of the target-specific subset search. mAP $(\%)$ and CMC scores are reported. "R1" and "R5" denote rank-1 accuracy $(\%)$ and rank-5 accuracy $(\%)$ , respectively. + +
AlicePersonAliceVehicle
Training dataR1R5mAPTraining dataR1R5mAP
Market [54]32.8952.5416.06VeRi [22]30.6943.6611.05
Duke [55]23.2741.138.59CityFlow [41]23.9536.007.45
MSMT [45]31.2952.7915.08VehicleID [21]16.329.134.73
PersonX [37]16.0827.426.41VehicleX [50]18.8532.188.89
Source pool38.9657.4817.62Source pool30.4748.3314.64
Searched48.1967.5725.51Searched46.7864.4125.46
+ +From the results shown in Table 1 and Table 3, we observe that training sets selected using SnP achieve consistently lower domain gap to the target and higher re-ID accuracy than those found by random sampling and greedy sampling. For example, when creating a training set with only $2\%$ source IDs for AlicePerson as the target, SnP results in -19.64 and -1.36 improvement in FID value, and $+14.56\%$ and $+5.01\%$ improvement in rank-1 accuracy over using random sampling and greedy sampling, respectively. When sampling training set with $2\%$ of the source IDs for AliceVehicle as the target, the rank-1 accuracy improvement is $+7.13\%$ and $+6.66\%$ , respectively. + +Effectiveness of the search step. We analyze this step in Table 1 and Table 2. In this search process that poses no limit on the number of IDs and images, we aim to identify and merge clusters of source identities that exhibit similar distributions with the target. We show the searched datasets contribute to improved accuracy over the entire data pool. For example, for AlicePerson, we observe a $+9.23\%$ improvement in rank-1 accuracy over the entire data pool. We further show the searched data is superior to individual training sets in Table 2. For example, when AliceVehicle is our target, we show our searched dataset results in $+16.09\%$ , $+22.83\%$ , $+30.48\%$ , $+27.93\%$ higher rank-1 accuracy than VeRi, CityFlow, VehicleID, and VehicleX, respectively. + +Of note, accuracy under this application scenario is usu + +Table 3. The superiority of SnP over random sampling and greedy sampling, when different direct transfer and pseudu-label re-ID models are used. We report accuracy when $2\%$ IDs are selected for target AicerPerson. Notations and evaluation metrics are the same as those in the previous table. + +
TypeModelTraining dataR1R5mAP
Direct TransferIDE [53]Random23.6742.329.80
Greedy [48]33.2254.4515.10
SnP38.2358.4018.17
PCB [38]Random24.7941.609.91
Greedy [48]29.0746.0112.59
SnP32.4349.9015.18
TransReid [15]Random52.0469.7328.47
Greedy [48]63.7380.2441.88
SnP64.3180.4642.74
Pseudo-labelingUDA [34]Random32.1754.6715.32
Greedy [48]36.4752.0617.34
SnP41.4155.7420.47
MMT [13]Random35.9451.9117.25
Greedy [48]38.6456.4821.18
SnP43.3660.3823.34
+ +ally lower than that produced by in-distribution training sets. This difference is understandable, because searched data have a relatively lower resemblance to the target data compared with in-distribution training sets. That said, annotating in-distribution training sets is usually expensive, especially considering the complex, specific and ever-changing target environments, where creating a training set on-the-fly with good performance is of practical value. + +Effectiveness of the pruning step is analyzed in Table 1 and Fig. 7. Pruning aims to find a subset that has no more than $n$ IDs and $m$ images. From Table 1 and Fig. 7, admittedly, the pruning of both IDs and images will lead to an accuracy decrease. For example, when the target is AlicePerson, if we select $2\%$ IDs, there is a $-9.23\%$ decrease in rank-1 accuracy. From Fig. 7, when the target is AlicePerson, if we further select $40\%$ images, there is a $-9.96\%$ decrease in rank-1 accuracy. However, even though only $2\%$ IDs are used, rank-1 accuracy obtained from the pruned + +![](images/2cf4282a82d532cc3d6c0a24bb732c846e31a980858d1d976e39c6880e33f93e.jpg) + +![](images/880bb195f29531e50c689e4880c92244ccc7b484fa9acafb7aeb4a9d2061a18d.jpg) +(A) AlicePerson as Target + +![](images/713c29398d2c352ac7b57c6608a9cf992709ad485d19da4e6165dda58ceaa6e3.jpg) + +![](images/19ac4343920cf44e3125c76b59cc3b760e288c48b82eb2f152d1e066309c3eaf.jpg) +(C) AliceVehicle as Target + +![](images/1eefac88a398c5e503b9634e8dab309da7206a00500eb84f3ae1a1cfd7733add.jpg) +Figure 6. Composition statistics and images samples of searched training sets. For each subfigure (A), (B), (C) and (D), the columns on the left presents unlabeled target samples; columns the middle provide samples of the searched training set; the pie chart Community-verified icon Verified on the right shows composition statistics of the searched training set. + +![](images/65059450bca16183eb99c56940ea48b32f5b58d6bbbb37fb41855b88cb5e7f39.jpg) +(B) Market as Target + +![](images/efd25f39ad81c51d8df974d30eb473228ade052696164ea519b2883e8fc68bcd.jpg) + +![](images/0d6d2f5aef430e2e73fdb2b91548e9b32d66e456d573d294f4ddaa13fd6c85dd.jpg) + +![](images/bbb19cb863fbf2ff27693bd4506e25361454eb051baeb0b6346dfdeff9717f51.jpg) +(D) VeRi as Target + +![](images/be4208034c5a783fb7163eb872a5667893bcf9fc966bb04381adfaeadc58ee22.jpg) +(A) AlicePerson +Figure 7. Comparing FPS with random sampling. The search step provides us with $2\%$ of the source IDs. We further select various ratios of images from these IDs. Four different targets are used, and rank-1 accuracy is the evaluation metric. Score is averaged over three runs. + +![](images/fae4df5605549642b98ece0a33cea56fac4d8b58c24f98136494ec85db14e4d2.jpg) +(B) Market + +![](images/581f466d061d35169b464e8ffe407120042db86bf5f22f9957507aa09061bfd4.jpg) +(C) Alice Vehicle + +![](images/a47c41604d10dd733f5a88f55fdfd2cd4511c8ab151dec146e120247c71bca7c.jpg) +(D) VeRi + +training data is still competitive over the source pool, which is just $-0.73\%$ lower than the source pool. It shows the pruning method significantly reduces the training set scale while being able to train a model of reasonable accuracy. + +Composition of searched training sets. We visualize four examples in in Fig. 6. It is clear that searched training sets have different compositions under different targets. If we use AlicePerson as the target, in the searched training set, images from Market and Duke take up $68\%$ and $26\%$ , respectively. In comparison, when using Market as the target, the resulting training set contains, $43\%$ images from UnrealPerson, and $34\%$ from MSMT. An interesting observation is that synthetic data (UnrealPerson) has a major role under Market as the target. It demonstrates the potential use of synthetic data for real-world target domains. + +Comparison between FPS and random sampling. Both can be used for sampling images resulting from the search step. In Fig. 7, we sample different ratios of the images resulting from the search step. We observe FPS is consistently superior to random sampling, under different selection ratios and targets. Improvement of FPS over random sampling first increase and then decreases, with peak + +improvement happening at the $30 - 60\%$ ratio. + +# 6. Conclusion + +This paper studies the training data set search problem, for object re-ID applications. Under a certain budget, we aim to find a target-specific training set that gives a competitive re-ID model. We show our method is overall superior to existing strategies such as random sampling and greedy sampling in terms of accuracy on the target domain. We analyze various components in the SnP system and find them to be stable under various source pools and targets. We also point out the correlation between domain gap, dataset size, and training set quality, and would like to further study the data-centric problems in the community. + +# 7. Acknowledgement + +This work was supported in part by the ARC Discovery Early Career Researcher Award (DE200101283), the ARC Discovery Project (DP210102801), Oracle Cloud credits, and related resources provided by Oracle for Research. We thank Dr. Lei Huan for her help in general in paper editing. + +# References + +[1] Alice benchmark. https://competitions.codalab.org/competitions/27739?secret_key=289a61c4-4566-4431-89e2-be09ab16b848.1,4,6 +[2] Yan Bai, Jile Jiao, Wang Ce, Jun Liu, Yihang Lou, Xuetao Feng, and Ling-Yu Duan. 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We propose a search and pruning (SnP) solution to this training data search problem, tailored to object re-identification (re-ID), an application aiming to match the same object captured by different cameras. Specifically, the search stage identifies and merges clusters of source identities which exhibit similar distributions with the target domain. The second stage, subject to a budget, then selects identities and their images from the Stage I output, to control the size of the resulting training set for efficient training. The two steps provide us with training sets " + }, + { + "bbox": [ + 46, + 239, + 290, + 539 + ], + "type": "inline_equation", + "content": "80\\%" + }, + { + "bbox": [ + 46, + 239, + 290, + 539 + ], + "type": "text", + "content": " smaller than the source pool while achieving a similar or even higher re-ID accuracy. These training sets are also shown to be superior to a few existing search methods such as random sampling and greedy sampling under the same budget on training data size. If we release the budget, training sets resulting from the first stage alone allow even higher re-ID accuracy. We provide interesting discussions on the specificity of our method to the re-ID problem and particularly its role in bridging the re-ID domain gap. The code is available at https://github.com/yorkeyao/SnP" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 561, + 127, + 573 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 561, + 127, + 573 + ], + "spans": [ + { + "bbox": [ + 47, + 561, + 127, + 573 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "text", + "content": "The success of a deep learning-based object re-ID relies on one of its critical prerequisites: the labeled training data. To achieve high accuracy, typically a massive amount of data needs to be used to train deep learning models. However, creating large-scale object re-ID training data with manual labels is expensive. Furthermore, collecting training data that contributes to the high test accuracy of the trained model is even more challenging. Recent years have seen a large amount of datasets proposed and a significant increase in the data size of a single dataset. For example, the Rand-Person [37] dataset has 8000 identities, which is more than" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 306, + 213, + 547, + 376 + ], + "blocks": [ + { + "bbox": [ + 306, + 213, + 547, + 376 + ], + "lines": [ + { + "bbox": [ + 306, + 213, + 547, + 376 + ], + "spans": [ + { + "bbox": [ + 306, + 213, + 547, + 376 + ], + "type": "image", + "image_path": "3f02dee31ef16b43195c1fd29f4ff799834f4c4963e4a27f07d682d29f9abef4.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 392, + 547, + 492 + ], + "lines": [ + { + "bbox": [ + 304, + 392, + 547, + 492 + ], + "spans": [ + { + "bbox": [ + 304, + 392, + 547, + 492 + ], + "type": "text", + "content": "Figure 1. We present a search and pruning (SnP) solution to the training data search problem in object re-ID. The source data pool is 1 order of magnitude larger than existing re-ID training sets in terms of the number of images and the number of identities. When the target is AlicePerson [1], from the source pool, our method (SnP) results in a training set " + }, + { + "bbox": [ + 304, + 392, + 547, + 492 + ], + "type": "inline_equation", + "content": "80\\%" + }, + { + "bbox": [ + 304, + 392, + 547, + 492 + ], + "type": "text", + "content": " smaller than the source pool while achieving a similar or even higher re-ID accuracy. The searched training set is also superior to existing individual training sets such as Market-1501 [54], Duke [55], and MSMT [45]." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 518, + 506, + 531 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 518, + 506, + 531 + ], + "spans": [ + { + "bbox": [ + 306, + 518, + 506, + 531 + ], + "type": "inline_equation", + "content": "6\\times" + }, + { + "bbox": [ + 306, + 518, + 506, + 531 + ], + "type": "text", + "content": " larger than the previous PersonX [37] dataset." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 534, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 547, + 713 + ], + "type": "text", + "content": "However, these datasets generally have their own dataset bias, making the model trained on one dataset unable to generalize well to another. For example, depending on the filming scenario, different person re-ID datasets generally have biases on camera positions, human races, and clothing style. Such dataset biases usually lead to model bias, which results in the model's difficulty performing well in an unseen filming scenario. To address this, many try to improve learning algorithms, including domain adaptation and domain generalization methods [2, 10, 27, 33, 35, 56]. Whereas these algorithms are well-studied and have proven successful in many re-ID applications, deciding what kind of data to use for training the re-ID model is still an open research problem, and has received relatively little attention in the community. We argue that this is a crucial problem" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15568" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 95 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 95 + ], + "type": "text", + "content": "to be answered in light of the ever-increasing scale of the available datasets." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 96, + 287, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 96, + 287, + 275 + ], + "spans": [ + { + "bbox": [ + 46, + 96, + 287, + 275 + ], + "type": "text", + "content": "In this paper, we introduce SnP, a search and pruning solution for sampling an efficient re-ID training set to a target domain. SnP is designed for the scenario in that we have a target dataset that does not have labeled training data. Our collected source pool, in replace, provides suitable labeled data to train a competitive model. Specifically, given a user-specified budget (e.g., maximum desired data size), we sample a subset of the source pool, which satisfies the budget requirement and desirably has high-quality data to train deep learning models. This scenario is especially helpful for deploying a re-ID system for unknown test environments, as it is difficult to manually label a training set for these new environments. We note that due to the absence of an indistribution training set, the searched data are directly used for training the re-ID model rather than pre-training." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 276, + 287, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 276, + 287, + 430 + ], + "spans": [ + { + "bbox": [ + 46, + 276, + 287, + 430 + ], + "type": "text", + "content": "In particular, we combine several popular re-ID datasets into a source pool, and represent each image in the pool with features. Those features are extracted from an Imagenet-pretrained model [39]. The images with features are stored on the dataserver to serve as a gallery. When there is a query from the target, we extract the feature of the query image, and search in the gallery for similar images on a feature level. Specifically, in the search stage, we calculate feature-level distance, i.e., Fréchet Inception Distance (FID) [16]. Given the constraint of a budget, we select the most representative samples in the pruning stage, based on the outputs from the search stage. This limits the size of the constructed training set and enables efficient training." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 432, + 287, + 587 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 432, + 287, + 587 + ], + "spans": [ + { + "bbox": [ + 46, + 432, + 287, + 587 + ], + "type": "text", + "content": "Combining search and pruning, we construct a training dataset that empirically shows significant accuracy improvements on several object re-ID targets, compared to the baselines. Without budget constraints, our searched training sets allow higher re-ID accuracy than the complete source pool, due to its target-specificity. With budget constraints, the pruned training set still achieves comparable or better performance than the source pool. The proposed SnP is demonstrated to be superior to random or greedy sampling. We show in Fig. 1 that the training set constructed by SnP leads to the best performance on the target compared to the others. We provide discussions on the specificity of our method and its role in bridging the re-ID domain gap." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 597, + 134, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 597, + 134, + 609 + ], + "spans": [ + { + "bbox": [ + 47, + 597, + 134, + 609 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "type": "text", + "content": "Active learning gradually searches over unlabeled data to find samples to be labeled by the oracle [32]. It is an iterative training process, where data search is performed at each iteration to train a task model. Our task is different from active learning. First, active learning is designed to acquire a training set and train models gradually. This requires multiple real training processes which are computationally expensive. In comparison, we directly search the" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "text", + "content": "whole training set all at once. Then the searched training set is used for model training. Second, many active learning methods require access to the target task model to provide selection metrics, e.g., uncertainty-based metrics [9, 12, 14, 49]. Our task does not require task model information, in other words, a real training process, during the process of the training set search. Thus enabling a fast training data retrial." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 168, + 545, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 168, + 545, + 323 + ], + "spans": [ + { + "bbox": [ + 304, + 168, + 545, + 323 + ], + "type": "text", + "content": "Neural data server is the closest inspiring work [32,48]. They also aim to search training data all at once from a large database. However, compared with us, firstly, [48] and [32] are designed for searching pretraining data rather than direct training data. Such a design is understandable as they are mainly for the classification task. Searching direct training data require careful class alignment. In comparison, We are targeting the re-ID task, where its training set can have a different class from the target, and then be directly used for training models. Furthermore, [48] and [32] require unsupervised pretrained experts to measure the domain gap. While we do not require so, which saves extraction time and simplify the solution." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 323, + 545, + 442 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 323, + 545, + 442 + ], + "spans": [ + { + "bbox": [ + 304, + 323, + 545, + 442 + ], + "type": "text", + "content": "Transfer learning is a long-standing problem for re-ID tasks, and many attempts on learning algorithms have been made to reduce the effect of domain gap [7, 26, 29, 30, 42]. Common strategies contain feature-level [24] and pseudolabel based [10, 35, 56] domain adaptation, and domain generalization [2, 27, 33]. In this paper, we focus on training data that is orthogonal to existing training algorithms. To be shown in experiments, together with some domain adaptation (i.e., pseudo-label) methods, SnP can achieve higher re-ID accuracy." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 444, + 545, + 550 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 444, + 545, + 550 + ], + "spans": [ + { + "bbox": [ + 304, + 444, + 545, + 550 + ], + "type": "text", + "content": "Learning to generate synthetic training data. Data simulation is also an inexpensive alternative to increasing a training set scale while providing accurate image labels [23, 37, 50-52]. These methods aim to lower the domain gap between synthetic data and real data by searching a set of parameters that control the 3D rendering process [50, 51]. In comparison, our search is not conducted on predefined parameters but on data directly. This enables more direct research on how to form a good training set." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 552, + 545, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 552, + 545, + 635 + ], + "spans": [ + { + "bbox": [ + 304, + 552, + 545, + 635 + ], + "type": "text", + "content": "Object re-ID has received increasing attention in the past few years, and many effective systems have been proposed [17, 40, 44, 57]. In this paper, we study object re-ID datasets rather than algorithms. Depending on the camera condition, location and environment, existing object re-ID datasets usually have their own distinct characteristics or bias [36, 37, 51]. We show details in §3." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 645, + 491, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 645, + 491, + 659 + ], + "spans": [ + { + "bbox": [ + 306, + 645, + 491, + 659 + ], + "type": "text", + "content": "3. Motivation: Tackling Target Bias" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 666, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 666, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 666, + 545, + 713 + ], + "type": "text", + "content": "Data bias commonly exists in the re-ID datasets (for examples see below) [25, 43, 47, 52], and it becomes problematic when the training and testing have different biases. Given a target domain with a certain bias, we aim to find" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "15569" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 70, + 132, + 171 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 132, + 171 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 132, + 171 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 132, + 171 + ], + "type": "image", + "image_path": "85e89a870fddef36ebf6bb2bebbd0609762d4256e5dd995677438f516bc981ae.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 60, + 172, + 126, + 182 + ], + "lines": [ + { + "bbox": [ + 60, + 172, + 126, + 182 + ], + "spans": [ + { + "bbox": [ + 60, + 172, + 126, + 182 + ], + "type": "text", + "content": "(A) Viewpoint bias." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 137, + 76, + 290, + 168 + ], + "blocks": [ + { + "bbox": [ + 137, + 76, + 290, + 168 + ], + "lines": [ + { + "bbox": [ + 137, + 76, + 290, + 168 + ], + "spans": [ + { + "bbox": [ + 137, + 76, + 290, + 168 + ], + "type": "image", + "image_path": "a38897acaf08fd0cb84072c027e3a53597ab16098d41b4351a564f2db12659a1.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 154, + 173, + 282, + 183 + ], + "lines": [ + { + "bbox": [ + 154, + 173, + 282, + 183 + ], + "spans": [ + { + "bbox": [ + 154, + 173, + 282, + 183 + ], + "type": "text", + "content": "(B) Human races & clothing style bias." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 293, + 70, + 434, + 168 + ], + "blocks": [ + { + "bbox": [ + 293, + 70, + 434, + 168 + ], + "lines": [ + { + "bbox": [ + 293, + 70, + 434, + 168 + ], + "spans": [ + { + "bbox": [ + 293, + 70, + 434, + 168 + ], + "type": "image", + "image_path": "c7feef806e2f346f77af55e4b4038163cbb18637dc9bf77baa11e296d8ee3817.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 329, + 172, + 406, + 182 + ], + "lines": [ + { + "bbox": [ + 329, + 172, + 406, + 182 + ], + "spans": [ + { + "bbox": [ + 329, + 172, + 406, + 182 + ], + "type": "text", + "content": "(C) Vehicle model bias." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 441, + 76, + 451, + 168 + ], + "lines": [ + { + "bbox": [ + 441, + 76, + 451, + 168 + ], + "spans": [ + { + "bbox": [ + 441, + 76, + 451, + 168 + ], + "type": "text", + "content": "CityFlow AliceVehicle" + } + ] + } + ], + "index": 6, + "angle": 270, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 193, + 547, + 258 + ], + "lines": [ + { + "bbox": [ + 46, + 193, + 547, + 258 + ], + "spans": [ + { + "bbox": [ + 46, + 193, + 547, + 258 + ], + "type": "text", + "content": "Figure 2. Dataset bias in existing object re-ID datasets. (A) Viewpoint distribution of different re-ID datasets. Each blue dot indicates a sample filmed from a specific viewpoint. Compared with the bi-modal viewpoint distribution in Market camera 1, Duke camera 4 has more diverse viewpoints. (B) Different human races and clothing styles of different person re-ID datasets. (C) Different vehicle makes in different datasets. For example, taxis in VeRi are unlikely to be found in CityFlow. (D) Different backgrounds in different datasets. We show a city background in AliceVehicle versus an urban background in CityFlow. To tackle such bias in the target domain, we design an automatic way to generate a training set with similar distribution or bias." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 461, + 77, + 545, + 168 + ], + "blocks": [ + { + "bbox": [ + 461, + 77, + 545, + 168 + ], + "lines": [ + { + "bbox": [ + 461, + 77, + 545, + 168 + ], + "spans": [ + { + "bbox": [ + 461, + 77, + 545, + 168 + ], + "type": "image", + "image_path": "44b52121b55ef6183548c4d6baec7c02d51ed317f3b87cb7573faac0f3d3869a.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 465, + 172, + 536, + 182 + ], + "lines": [ + { + "bbox": [ + 465, + 172, + 536, + 182 + ], + "spans": [ + { + "bbox": [ + 465, + 172, + 536, + 182 + ], + "type": "text", + "content": "(D) Background bias." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 270, + 287, + 318 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 270, + 287, + 318 + ], + "spans": [ + { + "bbox": [ + 46, + 270, + 287, + 318 + ], + "type": "text", + "content": "a target-specific training set that has similar distribution or bias. Depending on the filming scenario, there are four major types of data biases in existing re-ID datasets. We show examples of each type in Fig. 2." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 319, + 287, + 378 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 319, + 287, + 378 + ], + "spans": [ + { + "bbox": [ + 46, + 319, + 287, + 378 + ], + "type": "text", + "content": "Viewpoint. Viewpoint bias applies to generic objects, including persons and vehicles. We visualize the viewpoint distributions of two representative person re-ID datasets in Fig. 2(A), i.e., Market-1501 [54] (denoted as Market) and Duke-reID [55] (denoted as Duke)" + }, + { + "bbox": [ + 46, + 319, + 287, + 378 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 46, + 319, + 287, + 378 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 380, + 287, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 380, + 287, + 441 + ], + "spans": [ + { + "bbox": [ + 46, + 380, + 287, + 441 + ], + "type": "text", + "content": "Human races and clothing style. Subject to the places where the data is collected, identities in the person re-ID datasets can have distinctive patterns. We show in Fig. 2(B) that the humans in Market and Duke datasets evince different races and clothing styles." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 441, + 287, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 441, + 287, + 502 + ], + "spans": [ + { + "bbox": [ + 46, + 441, + 287, + 502 + ], + "type": "text", + "content": "Vehicle model. Similar to the identity bias (i.e., human races and clothing style) in person re-ID, the vehicle identities in vehicle re-ID also hold distinct patterns across different datasets. We show examples in Fig. 2(C) using the VeRi [22] (denoted as VeRi) and the CityFlow [41]." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 503, + 287, + 550 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 503, + 287, + 550 + ], + "spans": [ + { + "bbox": [ + 46, + 503, + 287, + 550 + ], + "type": "text", + "content": "Background. Background bias exists in both person and vehicle re-ID datasets, which is similar to viewpoint bias. Fig. 2(D) compares the background difference of images from two different vehicle re-ID datasets." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 47, + 566, + 103, + 578 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 566, + 103, + 578 + ], + "spans": [ + { + "bbox": [ + 47, + 566, + 103, + 578 + ], + "type": "text", + "content": "4. Method" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 46, + 587, + 287, + 671 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 587, + 287, + 671 + ], + "spans": [ + { + "bbox": [ + 46, + 587, + 287, + 671 + ], + "type": "text", + "content": "Given a target unlabeled dataset, we aim to construct a source labeled dataset that has minimal data bias inconsistencies with the target, under certain budget constraints. It induces the model trained on the source to show good performance on the target. To achieve the construction of the source (training) dataset, we propose the search and pruning (SnP) framework." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 270, + 373, + 281 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 270, + 373, + 281 + ], + "spans": [ + { + "bbox": [ + 306, + 270, + 373, + 281 + ], + "type": "text", + "content": "4.1. Overview" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 288, + 545, + 395 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 288, + 545, + 395 + ], + "spans": [ + { + "bbox": [ + 304, + 288, + 545, + 395 + ], + "type": "text", + "content": "We denote the target set as " + }, + { + "bbox": [ + 304, + 288, + 545, + 395 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_T = \\{(x_i, y_i)\\}_{i \\in [m_t]}" + }, + { + "bbox": [ + 304, + 288, + 545, + 395 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 288, + 545, + 395 + ], + "type": "inline_equation", + "content": "m_t" + }, + { + "bbox": [ + 304, + 288, + 545, + 395 + ], + "type": "text", + "content": " indicates the number of image-label pairs in the target and " + }, + { + "bbox": [ + 304, + 288, + 545, + 395 + ], + "type": "inline_equation", + "content": "[m_t] = \\{1, 2, \\dots, m_t\\}" + }, + { + "bbox": [ + 304, + 288, + 545, + 395 + ], + "type": "text", + "content": ". It follows the distribution " + }, + { + "bbox": [ + 304, + 288, + 545, + 395 + ], + "type": "inline_equation", + "content": "p_T" + }, + { + "bbox": [ + 304, + 288, + 545, + 395 + ], + "type": "text", + "content": ", i.e., " + }, + { + "bbox": [ + 304, + 288, + 545, + 395 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_T \\sim p_T" + }, + { + "bbox": [ + 304, + 288, + 545, + 395 + ], + "type": "text", + "content": ". Let " + }, + { + "bbox": [ + 304, + 288, + 545, + 395 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_S" + }, + { + "bbox": [ + 304, + 288, + 545, + 395 + ], + "type": "text", + "content": " be the source set to be constructed under a budget " + }, + { + "bbox": [ + 304, + 288, + 545, + 395 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 304, + 288, + 545, + 395 + ], + "type": "text", + "content": ". The budget is specified by the number of identities " + }, + { + "bbox": [ + 304, + 288, + 545, + 395 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 288, + 545, + 395 + ], + "type": "text", + "content": " and the number of images " + }, + { + "bbox": [ + 304, + 288, + 545, + 395 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 288, + 545, + 395 + ], + "type": "text", + "content": " allowed in " + }, + { + "bbox": [ + 304, + 288, + 545, + 395 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_S" + }, + { + "bbox": [ + 304, + 288, + 545, + 395 + ], + "type": "text", + "content": ", denoted as " + }, + { + "bbox": [ + 304, + 288, + 545, + 395 + ], + "type": "inline_equation", + "content": "b = (n, m)" + }, + { + "bbox": [ + 304, + 288, + 545, + 395 + ], + "type": "text", + "content": ". A high budget can lead to an unwanted increase in the training cost, in terms of either training time or model size." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 396, + 546, + 516 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 396, + 546, + 516 + ], + "spans": [ + { + "bbox": [ + 304, + 396, + 546, + 516 + ], + "type": "text", + "content": "To construct the training set " + }, + { + "bbox": [ + 304, + 396, + 546, + 516 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_S" + }, + { + "bbox": [ + 304, + 396, + 546, + 516 + ], + "type": "text", + "content": ", we create a source pool " + }, + { + "bbox": [ + 304, + 396, + 546, + 516 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 396, + 546, + 516 + ], + "type": "text", + "content": ", which is a collection of multiple object re-ID datasets. It is represented as " + }, + { + "bbox": [ + 304, + 396, + 546, + 516 + ], + "type": "inline_equation", + "content": "\\mathcal{S} = \\mathcal{D}_S^1 \\cup \\mathcal{D}_S^2 \\dots \\cup \\mathcal{D}_S^K" + }, + { + "bbox": [ + 304, + 396, + 546, + 516 + ], + "type": "text", + "content": ". Here each " + }, + { + "bbox": [ + 304, + 396, + 546, + 516 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_S^k" + }, + { + "bbox": [ + 304, + 396, + 546, + 516 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 396, + 546, + 516 + ], + "type": "inline_equation", + "content": "k \\in [K]" + }, + { + "bbox": [ + 304, + 396, + 546, + 516 + ], + "type": "text", + "content": ", indicates the " + }, + { + "bbox": [ + 304, + 396, + 546, + 516 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 396, + 546, + 516 + ], + "type": "text", + "content": "-th source re-ID dataset. Given the source pool, we firstly build a subset " + }, + { + "bbox": [ + 304, + 396, + 546, + 516 + ], + "type": "inline_equation", + "content": "\\mathbf{S}^*" + }, + { + "bbox": [ + 304, + 396, + 546, + 516 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 304, + 396, + 546, + 516 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 396, + 546, + 516 + ], + "type": "text", + "content": " regardless of the budget constraint. Let " + }, + { + "bbox": [ + 304, + 396, + 546, + 516 + ], + "type": "inline_equation", + "content": "h_{\\mathbf{S}}" + }, + { + "bbox": [ + 304, + 396, + 546, + 516 + ], + "type": "text", + "content": " be a model " + }, + { + "bbox": [ + 304, + 396, + 546, + 516 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 304, + 396, + 546, + 516 + ], + "type": "text", + "content": " trained on an arbitrary dataset " + }, + { + "bbox": [ + 304, + 396, + 546, + 516 + ], + "type": "inline_equation", + "content": "\\mathbf{S}" + }, + { + "bbox": [ + 304, + 396, + 546, + 516 + ], + "type": "text", + "content": ". The prediction risk of " + }, + { + "bbox": [ + 304, + 396, + 546, + 516 + ], + "type": "inline_equation", + "content": "h_{\\mathbf{S}}" + }, + { + "bbox": [ + 304, + 396, + 546, + 516 + ], + "type": "text", + "content": " on the test sample " + }, + { + "bbox": [ + 304, + 396, + 546, + 516 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 304, + 396, + 546, + 516 + ], + "type": "text", + "content": " with ground truth label " + }, + { + "bbox": [ + 304, + 396, + 546, + 516 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 304, + 396, + 546, + 516 + ], + "type": "text", + "content": " is computed as " + }, + { + "bbox": [ + 304, + 396, + 546, + 516 + ], + "type": "inline_equation", + "content": "\\ell(h_{\\mathbf{S}}(\\mathbf{x}), y)" + }, + { + "bbox": [ + 304, + 396, + 546, + 516 + ], + "type": "text", + "content": ". We build " + }, + { + "bbox": [ + 304, + 396, + 546, + 516 + ], + "type": "inline_equation", + "content": "\\mathbf{S}^*" + }, + { + "bbox": [ + 304, + 396, + 546, + 516 + ], + "type": "text", + "content": " by ensuring that the model " + }, + { + "bbox": [ + 304, + 396, + 546, + 516 + ], + "type": "inline_equation", + "content": "h_{\\mathbf{S}^*}" + }, + { + "bbox": [ + 304, + 396, + 546, + 516 + ], + "type": "text", + "content": " has minimized risk on " + }, + { + "bbox": [ + 304, + 396, + 546, + 516 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_T" + }, + { + "bbox": [ + 304, + 396, + 546, + 516 + ], + "type": "text", + "content": ", i.e.," + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 349, + 525, + 545, + 546 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 349, + 525, + 545, + 546 + ], + "spans": [ + { + "bbox": [ + 349, + 525, + 545, + 546 + ], + "type": "interline_equation", + "content": "\\mathbf {S} ^ {*} = \\underset {\\mathbf {S} \\in 2 ^ {\\mathcal {S}}} {\\arg \\min } \\mathbb {E} _ {\\boldsymbol {x}, y \\sim p _ {T}} [ \\ell (h _ {\\mathbf {S}} (\\boldsymbol {x}), y) ]. \\tag {1}", + "image_path": "aaf39aa4b04fb65040c3e2b9b4f9650847aa73ef05bf4502e28b88a2d5d074f2.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 305, + 555, + 527, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 555, + 527, + 567 + ], + "spans": [ + { + "bbox": [ + 305, + 555, + 527, + 567 + ], + "type": "text", + "content": "We apply target-specific search in " + }, + { + "bbox": [ + 305, + 555, + 527, + 567 + ], + "type": "inline_equation", + "content": "\\S 4.3" + }, + { + "bbox": [ + 305, + 555, + 527, + 567 + ], + "type": "text", + "content": " to construct " + }, + { + "bbox": [ + 305, + 555, + 527, + 567 + ], + "type": "inline_equation", + "content": "\\mathbf{S}^*" + }, + { + "bbox": [ + 305, + 555, + 527, + 567 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 567, + 545, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 567, + 545, + 639 + ], + "spans": [ + { + "bbox": [ + 304, + 567, + 545, + 639 + ], + "type": "text", + "content": "It can be seen that the construction of " + }, + { + "bbox": [ + 304, + 567, + 545, + 639 + ], + "type": "inline_equation", + "content": "\\mathbf{S}^*" + }, + { + "bbox": [ + 304, + 567, + 545, + 639 + ], + "type": "text", + "content": " does not take the budget constraint " + }, + { + "bbox": [ + 304, + 567, + 545, + 639 + ], + "type": "inline_equation", + "content": "b = (n,m)" + }, + { + "bbox": [ + 304, + 567, + 545, + 639 + ], + "type": "text", + "content": " into consideration, which is otherwise important in reality. Therefore, we build the training set " + }, + { + "bbox": [ + 304, + 567, + 545, + 639 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_S" + }, + { + "bbox": [ + 304, + 567, + 545, + 639 + ], + "type": "text", + "content": " by pruning " + }, + { + "bbox": [ + 304, + 567, + 545, + 639 + ], + "type": "inline_equation", + "content": "\\mathbf{S}^*" + }, + { + "bbox": [ + 304, + 567, + 545, + 639 + ], + "type": "text", + "content": " to comprise no more than " + }, + { + "bbox": [ + 304, + 567, + 545, + 639 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 567, + 545, + 639 + ], + "type": "text", + "content": " identities and no more than " + }, + { + "bbox": [ + 304, + 567, + 545, + 639 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 567, + 545, + 639 + ], + "type": "text", + "content": " images. Details of the budgeted pruning process are introduced in §4.4." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 306, + 647, + 413, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 647, + 413, + 659 + ], + "spans": [ + { + "bbox": [ + 306, + 647, + 413, + 659 + ], + "type": "text", + "content": "4.2. Correlation Study" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 665, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 714 + ], + "type": "text", + "content": "In order to know how to obtain " + }, + { + "bbox": [ + 304, + 665, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{S}^*" + }, + { + "bbox": [ + 304, + 665, + 545, + 714 + ], + "type": "text", + "content": ", we conduct the correlation study to learn the relationships between the dataset bias differences (i.e., domain gap measured in measured in FID [16]), the number of IDs and the training set quality" + } + ] + } + ], + "index": 25 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 40, + 683, + 287, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 40, + 683, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 40, + 683, + 287, + 713 + ], + "type": "text", + "content": "1 We understand that it is no longer encouraged to use the Duke dataset. In fact, we are not using it individually for algorithm design, but moving forward to find solutions to replace such individual use." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15570" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 76, + 167, + 154 + ], + "blocks": [ + { + "bbox": [ + 108, + 69, + 120, + 77 + ], + "lines": [ + { + "bbox": [ + 108, + 69, + 120, + 77 + ], + "spans": [ + { + "bbox": [ + 108, + 69, + 120, + 77 + ], + "type": "text", + "content": "(A)" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 48, + 76, + 167, + 154 + ], + "lines": [ + { + "bbox": [ + 48, + 76, + 167, + 154 + ], + "spans": [ + { + "bbox": [ + 48, + 76, + 167, + 154 + ], + "type": "image", + "image_path": "2a3242a888d6e628385a210dfc0483cf239b4d7aec9db7019f0357bf25ebba48.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 169, + 76, + 287, + 154 + ], + "blocks": [ + { + "bbox": [ + 230, + 70, + 242, + 77 + ], + "lines": [ + { + "bbox": [ + 230, + 70, + 242, + 77 + ], + "spans": [ + { + "bbox": [ + 230, + 70, + 242, + 77 + ], + "type": "text", + "content": "(B)" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 169, + 76, + 287, + 154 + ], + "lines": [ + { + "bbox": [ + 169, + 76, + 287, + 154 + ], + "spans": [ + { + "bbox": [ + 169, + 76, + 287, + 154 + ], + "type": "image", + "image_path": "8eb5124e0d5072eca73300f6c3e1f30d10592752a11112fabc3d7d566083f37a.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 289, + 76, + 406, + 155 + ], + "blocks": [ + { + "bbox": [ + 349, + 70, + 360, + 77 + ], + "lines": [ + { + "bbox": [ + 349, + 70, + 360, + 77 + ], + "spans": [ + { + "bbox": [ + 349, + 70, + 360, + 77 + ], + "type": "text", + "content": "(C)" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 289, + 76, + 406, + 155 + ], + "lines": [ + { + "bbox": [ + 289, + 76, + 406, + 155 + ], + "spans": [ + { + "bbox": [ + 289, + 76, + 406, + 155 + ], + "type": "image", + "image_path": "f4ff4c5f224b0ba5b7257a28eb64c01fd89e9e47218c2b4dd5097c830c381911.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 408, + 76, + 547, + 154 + ], + "blocks": [ + { + "bbox": [ + 471, + 70, + 483, + 77 + ], + "lines": [ + { + "bbox": [ + 471, + 70, + 483, + 77 + ], + "spans": [ + { + "bbox": [ + 471, + 70, + 483, + 77 + ], + "type": "text", + "content": "(D)" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 408, + 76, + 547, + 154 + ], + "lines": [ + { + "bbox": [ + 408, + 76, + 547, + 154 + ], + "spans": [ + { + "bbox": [ + 408, + 76, + 547, + 154 + ], + "type": "image", + "image_path": "9fbe779324bef4ae9c790d71aa054062c27cc92bc7b7ccf54d47468668af96be.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 47, + 159, + 166, + 239 + ], + "blocks": [ + { + "bbox": [ + 47, + 159, + 166, + 239 + ], + "lines": [ + { + "bbox": [ + 47, + 159, + 166, + 239 + ], + "spans": [ + { + "bbox": [ + 47, + 159, + 166, + 239 + ], + "type": "image", + "image_path": "f1c0f0830b733c47196b0821b8afa00322e4ae95e42f9575abbc2af59af72d70.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 250, + 547, + 316 + ], + "lines": [ + { + "bbox": [ + 46, + 250, + 547, + 316 + ], + "spans": [ + { + "bbox": [ + 46, + 250, + 547, + 316 + ], + "type": "text", + "content": "Figure 3. Relationships between the domain gap (measured using FID), the number of ID and the rank-1 accuracy on the target. Top: correlations when AlicePerson [1] is targeted. Bottom: correlations when AliceVehicle [1] is targeted. The Pearson correlation is used to measure the relationship between them. (A) FID vs. the rank-1 accuracy. They have a relatively strong negative correlation " + }, + { + "bbox": [ + 46, + 250, + 547, + 316 + ], + "type": "inline_equation", + "content": "(\\leq -0.636)" + }, + { + "bbox": [ + 46, + 250, + 547, + 316 + ], + "type": "text", + "content": ". (B) The number of ID vs. the rank-1 accuracy. There exists a positive correlation but such a correlation is not stable. (C) FID vs. number of ID. The correlation is weak between them. (D) The joint influence of FID and the number of ID on rank-1 accuracy. The top left corner, i.e., training sets that have low FID scores and a large number of IDs have high rank-1 accuracy on the target." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 170, + 159, + 288, + 239 + ], + "blocks": [ + { + "bbox": [ + 170, + 159, + 288, + 239 + ], + "lines": [ + { + "bbox": [ + 170, + 159, + 288, + 239 + ], + "spans": [ + { + "bbox": [ + 170, + 159, + 288, + 239 + ], + "type": "image", + "image_path": "487740c39563801ab57d1df38cf269ac9cf04cc926b47ae3d40a96d619d0ec5f.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 289, + 159, + 407, + 239 + ], + "blocks": [ + { + "bbox": [ + 289, + 159, + 407, + 239 + ], + "lines": [ + { + "bbox": [ + 289, + 159, + 407, + 239 + ], + "spans": [ + { + "bbox": [ + 289, + 159, + 407, + 239 + ], + "type": "image", + "image_path": "332360379e510586ba1b7373b517b68553dda192f400b169b8f70de6a73e5ee7.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 407, + 159, + 547, + 239 + ], + "blocks": [ + { + "bbox": [ + 407, + 159, + 547, + 239 + ], + "lines": [ + { + "bbox": [ + 407, + 159, + 547, + 239 + ], + "spans": [ + { + "bbox": [ + 407, + 159, + 547, + 239 + ], + "type": "image", + "image_path": "8a97d263163a9c8e433021dec219dc24e6dfbf99fd661aa6cdae23429d36ac20.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 327, + 287, + 446 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 327, + 287, + 446 + ], + "spans": [ + { + "bbox": [ + 46, + 327, + 287, + 446 + ], + "type": "text", + "content": "(i.e., rank-1 test accuracy with the model trained on the such training set). Shown in Fig. 3, in each subfigure, each point represents a training set, which is clustered from the source pool. For each training set, we calculate its domain gap to the target domain, count its number of IDs, and evaluate the rank-1 accuracy. We use the Pearson correlation coefficient " + }, + { + "bbox": [ + 46, + 327, + 287, + 446 + ], + "type": "inline_equation", + "content": "(\\gamma)" + }, + { + "bbox": [ + 46, + 327, + 287, + 446 + ], + "type": "text", + "content": " [5] to measure the correlation between them. The Pearson correlation coefficients range from " + }, + { + "bbox": [ + 46, + 327, + 287, + 446 + ], + "type": "inline_equation", + "content": "[-1, 1]" + }, + { + "bbox": [ + 46, + 327, + 287, + 446 + ], + "type": "text", + "content": ". A value closer to -1 or 1 indicates a stronger negative or positive correlation, respectively, and 0 implies no correlation." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 447, + 287, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 447, + 287, + 651 + ], + "spans": [ + { + "bbox": [ + 46, + 447, + 287, + 651 + ], + "type": "text", + "content": "From this Fig. 3(A), we observe a relatively strong negative correlation between domain gap and rank-1 accuracy. This indicates minimizing the domain gap between the source and target is highly likely to improve training set quality, i.e., test set rank-1 accuracy. From this Fig. 3(B), we observe a positive but unstable correlation between the number of ID and the rank-1 accuracy. For example, when AlicePerson is targeted, they have a relatively strong positive correlation (0.720). However, such correlation is only 0.383 when AliceVehicle is targeted. Fig. 3(C) shows the correlation between FID and the number of ID is weak. They are independent factors that influence training set quality. Fig. 3(D) shows the joint influence of FID and the number of ID on the training set quality. The top left corner, i.e., training sets that have a low domain gap to the target and a large number of IDs are of high quality, thereby can train a model that has higher rank-1 accuracy on the target." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 47, + 656, + 207, + 670 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 656, + 207, + 670 + ], + "spans": [ + { + "bbox": [ + 47, + 656, + 207, + 670 + ], + "type": "text", + "content": "4.3. Target-specific Subset Search" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 59, + 675, + 251, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 675, + 251, + 687 + ], + "spans": [ + { + "bbox": [ + 59, + 675, + 251, + 687 + ], + "type": "text", + "content": "The theory of domain adaptation [3] states that:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 93, + 693, + 287, + 717 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 93, + 693, + 287, + 717 + ], + "spans": [ + { + "bbox": [ + 93, + 693, + 287, + 717 + ], + "type": "interline_equation", + "content": "\\varepsilon_ {T} (h) < \\varepsilon_ {S} (h) + \\frac {1}{2} d _ {\\mathcal {H} \\Delta \\mathcal {H}} (\\mathbf {S}, \\mathcal {D} _ {T}). \\tag {2}", + "image_path": "0167f2fc0c5aaac2283902822f1d03001564b5b235297c68202f37b09a9a081e.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 327, + 545, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 327, + 545, + 399 + ], + "spans": [ + { + "bbox": [ + 304, + 327, + 545, + 399 + ], + "type": "text", + "content": "Here " + }, + { + "bbox": [ + 304, + 327, + 545, + 399 + ], + "type": "inline_equation", + "content": "h \\in \\mathcal{H}" + }, + { + "bbox": [ + 304, + 327, + 545, + 399 + ], + "type": "text", + "content": " represents the hypothesis function (i.e., the model). " + }, + { + "bbox": [ + 304, + 327, + 545, + 399 + ], + "type": "inline_equation", + "content": "\\varepsilon_T(h)" + }, + { + "bbox": [ + 304, + 327, + 545, + 399 + ], + "type": "text", + "content": " is the risk of model " + }, + { + "bbox": [ + 304, + 327, + 545, + 399 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 304, + 327, + 545, + 399 + ], + "type": "text", + "content": " on the target set " + }, + { + "bbox": [ + 304, + 327, + 545, + 399 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_T" + }, + { + "bbox": [ + 304, + 327, + 545, + 399 + ], + "type": "text", + "content": ", while " + }, + { + "bbox": [ + 304, + 327, + 545, + 399 + ], + "type": "inline_equation", + "content": "\\varepsilon_S(h)" + }, + { + "bbox": [ + 304, + 327, + 545, + 399 + ], + "type": "text", + "content": " is its risk on the source set " + }, + { + "bbox": [ + 304, + 327, + 545, + 399 + ], + "type": "inline_equation", + "content": "\\mathbf{S}" + }, + { + "bbox": [ + 304, + 327, + 545, + 399 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 327, + 545, + 399 + ], + "type": "inline_equation", + "content": "d_{\\mathcal{H}\\Delta \\mathcal{H}}(\\mathbf{S},\\mathcal{D}_T)" + }, + { + "bbox": [ + 304, + 327, + 545, + 399 + ], + "type": "text", + "content": " is the unlabelled " + }, + { + "bbox": [ + 304, + 327, + 545, + 399 + ], + "type": "inline_equation", + "content": "\\mathcal{H}\\Delta \\mathcal{H}" + }, + { + "bbox": [ + 304, + 327, + 545, + 399 + ], + "type": "text", + "content": " divergence [3] between " + }, + { + "bbox": [ + 304, + 327, + 545, + 399 + ], + "type": "inline_equation", + "content": "\\mathbf{S}" + }, + { + "bbox": [ + 304, + 327, + 545, + 399 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 327, + 545, + 399 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_T" + }, + { + "bbox": [ + 304, + 327, + 545, + 399 + ], + "type": "text", + "content": ". Equation 2 shows that the target risk " + }, + { + "bbox": [ + 304, + 327, + 545, + 399 + ], + "type": "inline_equation", + "content": "\\varepsilon_T(h)" + }, + { + "bbox": [ + 304, + 327, + 545, + 399 + ], + "type": "text", + "content": " is upper bounded by " + }, + { + "bbox": [ + 304, + 327, + 545, + 399 + ], + "type": "inline_equation", + "content": "d_{\\mathcal{H}\\Delta \\mathcal{H}}(\\mathbf{S},\\mathcal{D}_T)" + }, + { + "bbox": [ + 304, + 327, + 545, + 399 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 399, + 545, + 459 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 399, + 545, + 459 + ], + "spans": [ + { + "bbox": [ + 304, + 399, + 545, + 459 + ], + "type": "text", + "content": "In the common practice of feature-level domain adaptation, the source training set " + }, + { + "bbox": [ + 304, + 399, + 545, + 459 + ], + "type": "inline_equation", + "content": "\\mathbf{S}" + }, + { + "bbox": [ + 304, + 399, + 545, + 459 + ], + "type": "text", + "content": " is fixed while the joint feature extraction model is used to minimize " + }, + { + "bbox": [ + 304, + 399, + 545, + 459 + ], + "type": "inline_equation", + "content": "d_{\\mathcal{H}\\Delta \\mathcal{H}}(\\mathbf{S},\\mathcal{D}_T)" + }, + { + "bbox": [ + 304, + 399, + 545, + 459 + ], + "type": "text", + "content": " [24]. In our design, the feature extraction model is fixed instead. To minimize " + }, + { + "bbox": [ + 304, + 399, + 545, + 459 + ], + "type": "inline_equation", + "content": "\\varepsilon_T(h)" + }, + { + "bbox": [ + 304, + 399, + 545, + 459 + ], + "type": "text", + "content": ", the problem is reformulated as" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 364, + 468, + 545, + 488 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 364, + 468, + 545, + 488 + ], + "spans": [ + { + "bbox": [ + 364, + 468, + 545, + 488 + ], + "type": "interline_equation", + "content": "\\mathbf {S} ^ {*} = \\underset {\\mathbf {S} \\in 2 ^ {S}} {\\arg \\min } d _ {\\mathcal {H} \\Delta \\mathcal {H}} (\\mathbf {S}, \\mathcal {D} _ {T}). \\tag {3}", + "image_path": "b7fe14a8cd585dd2faf2227c91d6203e365b96d2381deedb87721693e28026bc.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 497, + 545, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 497, + 545, + 533 + ], + "spans": [ + { + "bbox": [ + 304, + 497, + 545, + 533 + ], + "type": "text", + "content": "Generally, " + }, + { + "bbox": [ + 304, + 497, + 545, + 533 + ], + "type": "inline_equation", + "content": "d_{\\mathcal{H}\\Delta \\mathcal{H}}(\\mathbf{S}^*,\\mathcal{D}_T)" + }, + { + "bbox": [ + 304, + 497, + 545, + 533 + ], + "type": "text", + "content": " is difficult to compute, but many alternatives exist in the literature [24]. We use Fréchet Inception Distance (FID) [16], which is defined as:" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 305, + 541, + 545, + 567 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 541, + 545, + 567 + ], + "spans": [ + { + "bbox": [ + 305, + 541, + 545, + 567 + ], + "type": "interline_equation", + "content": "\\operatorname {F I D} \\left(\\mathbf {S} ^ {*}, \\mathcal {D} _ {T}\\right) = \\left\\| \\boldsymbol {\\mu} _ {s} - \\boldsymbol {\\mu} _ {t} \\right\\| _ {2} ^ {2} + \\operatorname {T r} \\left(\\boldsymbol {\\Sigma} _ {s} + \\boldsymbol {\\Sigma} _ {t} - 2 \\left(\\boldsymbol {\\Sigma} _ {s} \\boldsymbol {\\Sigma} _ {t}\\right) ^ {\\frac {1}{2}}\\right). \\tag {4}", + "image_path": "214944e13bc36dc97a9b6a980ce5fd31037fc75d61d85f3dac9164fc6e776217.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 567, + 545, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 567, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 567, + 545, + 628 + ], + "type": "text", + "content": "In Eq. 4, " + }, + { + "bbox": [ + 304, + 567, + 545, + 628 + ], + "type": "inline_equation", + "content": "\\pmb{\\mu}_s \\in \\mathbb{R}^d" + }, + { + "bbox": [ + 304, + 567, + 545, + 628 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 567, + 545, + 628 + ], + "type": "inline_equation", + "content": "\\pmb{\\Sigma}_s \\in \\mathbb{R}^{d \\times d}" + }, + { + "bbox": [ + 304, + 567, + 545, + 628 + ], + "type": "text", + "content": " are the mean and covariance matrix of the image descriptors of " + }, + { + "bbox": [ + 304, + 567, + 545, + 628 + ], + "type": "inline_equation", + "content": "\\mathbf{S}^*" + }, + { + "bbox": [ + 304, + 567, + 545, + 628 + ], + "type": "text", + "content": ", respectively. " + }, + { + "bbox": [ + 304, + 567, + 545, + 628 + ], + "type": "inline_equation", + "content": "\\pmb{\\mu}_t" + }, + { + "bbox": [ + 304, + 567, + 545, + 628 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 567, + 545, + 628 + ], + "type": "inline_equation", + "content": "\\pmb{\\Sigma}_t" + }, + { + "bbox": [ + 304, + 567, + 545, + 628 + ], + "type": "text", + "content": " are those of " + }, + { + "bbox": [ + 304, + 567, + 545, + 628 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_T" + }, + { + "bbox": [ + 304, + 567, + 545, + 628 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 567, + 545, + 628 + ], + "type": "inline_equation", + "content": "\\mathrm{Tr}(.)" + }, + { + "bbox": [ + 304, + 567, + 545, + 628 + ], + "type": "text", + "content": " represents the trace of a square matrix. " + }, + { + "bbox": [ + 304, + 567, + 545, + 628 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 567, + 545, + 628 + ], + "type": "text", + "content": " is the dimension of the image descriptors. Consequently, the objective function is reduced as," + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 369, + 637, + 545, + 657 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 369, + 637, + 545, + 657 + ], + "spans": [ + { + "bbox": [ + 369, + 637, + 545, + 657 + ], + "type": "interline_equation", + "content": "\\mathbf {S} ^ {*} = \\underset {\\mathbf {S} \\in 2 ^ {S}} {\\arg \\min } \\operatorname {F I D} (\\mathbf {S}, \\mathcal {D} _ {T}). \\tag {5}", + "image_path": "8398daf53e3e1c96d7041c9ff9b7a55e0b05e4f078998c624263ea3b0814adc2.jpg" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 306, + 665, + 492, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 665, + 492, + 677 + ], + "spans": [ + { + "bbox": [ + 306, + 665, + 492, + 677 + ], + "type": "text", + "content": "We build " + }, + { + "bbox": [ + 306, + 665, + 492, + 677 + ], + "type": "inline_equation", + "content": "\\mathbf{S}^*" + }, + { + "bbox": [ + 306, + 665, + 492, + 677 + ], + "type": "text", + "content": " with the greedy algorithm below." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 306, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 677, + 545, + 713 + ], + "type": "text", + "content": "Firstly, we divide the entire dataset " + }, + { + "bbox": [ + 306, + 677, + 545, + 713 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 306, + 677, + 545, + 713 + ], + "type": "text", + "content": " into " + }, + { + "bbox": [ + 306, + 677, + 545, + 713 + ], + "type": "inline_equation", + "content": "J" + }, + { + "bbox": [ + 306, + 677, + 545, + 713 + ], + "type": "text", + "content": " clusters " + }, + { + "bbox": [ + 306, + 677, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{S}^1,\\dots ,\\mathbf{S}^J\\}" + }, + { + "bbox": [ + 306, + 677, + 545, + 713 + ], + "type": "text", + "content": ", as shown in Fig. 4 (A). Specifically, we average all image descriptors that belong to the same identity," + } + ] + } + ], + "index": 26 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15571" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 59, + 289, + 164 + ], + "blocks": [ + { + "bbox": [ + 47, + 59, + 289, + 164 + ], + "lines": [ + { + "bbox": [ + 47, + 59, + 289, + 164 + ], + "spans": [ + { + "bbox": [ + 47, + 59, + 289, + 164 + ], + "type": "image", + "image_path": "550f7f9130ef0d238482804da2357bdf01fa32fe6107cbe7c538322486f72196.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 171, + 287, + 248 + ], + "lines": [ + { + "bbox": [ + 46, + 171, + 287, + 248 + ], + "spans": [ + { + "bbox": [ + 46, + 171, + 287, + 248 + ], + "type": "text", + "content": "Figure 4. Workflow of the proposed SnP method. We are given sources composed of " + }, + { + "bbox": [ + 46, + 171, + 287, + 248 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 171, + 287, + 248 + ], + "type": "text", + "content": " existing datasets. From these sources, we aim to construct a training set, which satisfies the budget of no more than " + }, + { + "bbox": [ + 46, + 171, + 287, + 248 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 171, + 287, + 248 + ], + "type": "text", + "content": " IDs and " + }, + { + "bbox": [ + 46, + 171, + 287, + 248 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 171, + 287, + 248 + ], + "type": "text", + "content": " images. To achieve this, we perform (A) target-specific subset search to obtain a subset " + }, + { + "bbox": [ + 46, + 171, + 287, + 248 + ], + "type": "inline_equation", + "content": "\\mathbf{S}^*" + }, + { + "bbox": [ + 46, + 171, + 287, + 248 + ], + "type": "text", + "content": " with similar distributions to the target, then perform (B) budgeted pruning to select " + }, + { + "bbox": [ + 46, + 171, + 287, + 248 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 171, + 287, + 248 + ], + "type": "text", + "content": " IDs and " + }, + { + "bbox": [ + 46, + 171, + 287, + 248 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 171, + 287, + 248 + ], + "type": "text", + "content": " representative images, forming the final training set." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 258, + 287, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 258, + 287, + 426 + ], + "spans": [ + { + "bbox": [ + 46, + 258, + 287, + 426 + ], + "type": "text", + "content": "and use this ID-averaged descriptor to represent all corresponding images. Afterwards, we cluster the ID-averaged features into " + }, + { + "bbox": [ + 46, + 258, + 287, + 426 + ], + "type": "inline_equation", + "content": "J" + }, + { + "bbox": [ + 46, + 258, + 287, + 426 + ], + "type": "text", + "content": " groups using the k-means method [20]. Each subset " + }, + { + "bbox": [ + 46, + 258, + 287, + 426 + ], + "type": "inline_equation", + "content": "\\mathbf{S}^j" + }, + { + "bbox": [ + 46, + 258, + 287, + 426 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 258, + 287, + 426 + ], + "type": "inline_equation", + "content": "j \\in [J]" + }, + { + "bbox": [ + 46, + 258, + 287, + 426 + ], + "type": "text", + "content": ", is composed of all images with the corresponding IDs in that group. Secondly, we calculate the FID between each subset " + }, + { + "bbox": [ + 46, + 258, + 287, + 426 + ], + "type": "inline_equation", + "content": "\\mathbf{S}^j" + }, + { + "bbox": [ + 46, + 258, + 287, + 426 + ], + "type": "text", + "content": " and the target " + }, + { + "bbox": [ + 46, + 258, + 287, + 426 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_T" + }, + { + "bbox": [ + 46, + 258, + 287, + 426 + ], + "type": "text", + "content": ", and sort " + }, + { + "bbox": [ + 46, + 258, + 287, + 426 + ], + "type": "inline_equation", + "content": "\\{\\mathrm{FID}(\\mathbf{S}^j, \\mathcal{D}_T)\\}_{j \\in [J]}" + }, + { + "bbox": [ + 46, + 258, + 287, + 426 + ], + "type": "text", + "content": " in ascending order. To build " + }, + { + "bbox": [ + 46, + 258, + 287, + 426 + ], + "type": "inline_equation", + "content": "\\mathbf{S}^*" + }, + { + "bbox": [ + 46, + 258, + 287, + 426 + ], + "type": "text", + "content": ", we keep adding the subsets with lower FID to " + }, + { + "bbox": [ + 46, + 258, + 287, + 426 + ], + "type": "inline_equation", + "content": "\\mathbf{S}^*" + }, + { + "bbox": [ + 46, + 258, + 287, + 426 + ], + "type": "text", + "content": " until " + }, + { + "bbox": [ + 46, + 258, + 287, + 426 + ], + "type": "inline_equation", + "content": "\\mathrm{FID}(\\mathbf{S}^*, \\mathcal{D}_T)" + }, + { + "bbox": [ + 46, + 258, + 287, + 426 + ], + "type": "text", + "content": " stops to decrease. This indicates that the constructed " + }, + { + "bbox": [ + 46, + 258, + 287, + 426 + ], + "type": "inline_equation", + "content": "\\mathbf{S}^*" + }, + { + "bbox": [ + 46, + 258, + 287, + 426 + ], + "type": "text", + "content": " holds the minimum FID to the target set. Algorithm 1 summarizes the above procedures. We empirically demonstrate in Fig. 5 that, the subset " + }, + { + "bbox": [ + 46, + 258, + 287, + 426 + ], + "type": "inline_equation", + "content": "\\mathbf{S}^*" + }, + { + "bbox": [ + 46, + 258, + 287, + 426 + ], + "type": "text", + "content": " with the minimum " + }, + { + "bbox": [ + 46, + 258, + 287, + 426 + ], + "type": "inline_equation", + "content": "\\mathrm{FID}(\\mathbf{S}^*, \\mathcal{D}_T)" + }, + { + "bbox": [ + 46, + 258, + 287, + 426 + ], + "type": "text", + "content": " results in the model to produce highest accuracy on the target dataset." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 432, + 203, + 445 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 432, + 203, + 445 + ], + "spans": [ + { + "bbox": [ + 47, + 432, + 203, + 445 + ], + "type": "text", + "content": "4.4. Budget-constrained Pruning" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 451, + 287, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 451, + 287, + 605 + ], + "spans": [ + { + "bbox": [ + 46, + 451, + 287, + 605 + ], + "type": "text", + "content": "Using the target-specific subset search, we construct a candidate training set " + }, + { + "bbox": [ + 46, + 451, + 287, + 605 + ], + "type": "inline_equation", + "content": "\\mathbf{S}^*" + }, + { + "bbox": [ + 46, + 451, + 287, + 605 + ], + "type": "text", + "content": ". Yet, it can violate the budget constraint of " + }, + { + "bbox": [ + 46, + 451, + 287, + 605 + ], + "type": "inline_equation", + "content": "b = (n,m)" + }, + { + "bbox": [ + 46, + 451, + 287, + 605 + ], + "type": "text", + "content": ", which prefers the training set to include no more than " + }, + { + "bbox": [ + 46, + 451, + 287, + 605 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 451, + 287, + 605 + ], + "type": "text", + "content": " identities and no more than " + }, + { + "bbox": [ + 46, + 451, + 287, + 605 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 451, + 287, + 605 + ], + "type": "text", + "content": " images. Let " + }, + { + "bbox": [ + 46, + 451, + 287, + 605 + ], + "type": "inline_equation", + "content": "\\mathcal{Y}(\\mathbf{S}^*) = \\{y^1,y^2,\\dots ,y^a\\}" + }, + { + "bbox": [ + 46, + 451, + 287, + 605 + ], + "type": "text", + "content": ", be the set of unique identities in " + }, + { + "bbox": [ + 46, + 451, + 287, + 605 + ], + "type": "inline_equation", + "content": "\\mathbf{S}^*" + }, + { + "bbox": [ + 46, + 451, + 287, + 605 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 451, + 287, + 605 + ], + "type": "inline_equation", + "content": "s(y^{i})" + }, + { + "bbox": [ + 46, + 451, + 287, + 605 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 451, + 287, + 605 + ], + "type": "inline_equation", + "content": "i\\in [a]" + }, + { + "bbox": [ + 46, + 451, + 287, + 605 + ], + "type": "text", + "content": " be the set of all images with identity " + }, + { + "bbox": [ + 46, + 451, + 287, + 605 + ], + "type": "inline_equation", + "content": "y^{i}" + }, + { + "bbox": [ + 46, + 451, + 287, + 605 + ], + "type": "text", + "content": ". Generally, we have " + }, + { + "bbox": [ + 46, + 451, + 287, + 605 + ], + "type": "inline_equation", + "content": "a\\geq n" + }, + { + "bbox": [ + 46, + 451, + 287, + 605 + ], + "type": "text", + "content": ". To get the training set " + }, + { + "bbox": [ + 46, + 451, + 287, + 605 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_S" + }, + { + "bbox": [ + 46, + 451, + 287, + 605 + ], + "type": "text", + "content": " under budget " + }, + { + "bbox": [ + 46, + 451, + 287, + 605 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 46, + 451, + 287, + 605 + ], + "type": "text", + "content": ", we randomly sample a subset " + }, + { + "bbox": [ + 46, + 451, + 287, + 605 + ], + "type": "inline_equation", + "content": "\\pmb{y}" + }, + { + "bbox": [ + 46, + 451, + 287, + 605 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 46, + 451, + 287, + 605 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 451, + 287, + 605 + ], + "type": "text", + "content": " identities from " + }, + { + "bbox": [ + 46, + 451, + 287, + 605 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 46, + 451, + 287, + 605 + ], + "type": "text", + "content": ". All images with identities in " + }, + { + "bbox": [ + 46, + 451, + 287, + 605 + ], + "type": "inline_equation", + "content": "\\pmb{y}" + }, + { + "bbox": [ + 46, + 451, + 287, + 605 + ], + "type": "text", + "content": " are combined to form a subset " + }, + { + "bbox": [ + 46, + 451, + 287, + 605 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{s}} = \\{s(y^{i})|y^{i}\\in \\pmb{y}\\}" + }, + { + "bbox": [ + 46, + 451, + 287, + 605 + ], + "type": "text", + "content": ". We also initialize " + }, + { + "bbox": [ + 46, + 451, + 287, + 605 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_S" + }, + { + "bbox": [ + 46, + 451, + 287, + 605 + ], + "type": "text", + "content": " by random sampling a seed image from each " + }, + { + "bbox": [ + 46, + 451, + 287, + 605 + ], + "type": "inline_equation", + "content": "s(y^{i})" + }, + { + "bbox": [ + 46, + 451, + 287, + 605 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 451, + 287, + 605 + ], + "type": "inline_equation", + "content": "y^{i}\\in \\pmb{y}" + }, + { + "bbox": [ + 46, + 451, + 287, + 605 + ], + "type": "text", + "content": ". This guarantees " + }, + { + "bbox": [ + 46, + 451, + 287, + 605 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_S" + }, + { + "bbox": [ + 46, + 451, + 287, + 605 + ], + "type": "text", + "content": " to cover all the identities in the subset " + }, + { + "bbox": [ + 46, + 451, + 287, + 605 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{s}}" + }, + { + "bbox": [ + 46, + 451, + 287, + 605 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 606, + 287, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 606, + 287, + 665 + ], + "spans": [ + { + "bbox": [ + 47, + 606, + 287, + 665 + ], + "type": "text", + "content": "Suppose the number of images in " + }, + { + "bbox": [ + 47, + 606, + 287, + 665 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{s}}" + }, + { + "bbox": [ + 47, + 606, + 287, + 665 + ], + "type": "text", + "content": " is larger than " + }, + { + "bbox": [ + 47, + 606, + 287, + 665 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 47, + 606, + 287, + 665 + ], + "type": "text", + "content": ". We construct " + }, + { + "bbox": [ + 47, + 606, + 287, + 665 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_S" + }, + { + "bbox": [ + 47, + 606, + 287, + 665 + ], + "type": "text", + "content": " by sampling images iteratively from " + }, + { + "bbox": [ + 47, + 606, + 287, + 665 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{s}}" + }, + { + "bbox": [ + 47, + 606, + 287, + 665 + ], + "type": "text", + "content": " until " + }, + { + "bbox": [ + 47, + 606, + 287, + 665 + ], + "type": "inline_equation", + "content": "|\\mathcal{D}_S| = m" + }, + { + "bbox": [ + 47, + 606, + 287, + 665 + ], + "type": "text", + "content": ". To ensure similar performance between the model trained on " + }, + { + "bbox": [ + 47, + 606, + 287, + 665 + ], + "type": "inline_equation", + "content": "D_S" + }, + { + "bbox": [ + 47, + 606, + 287, + 665 + ], + "type": "text", + "content": " and the model trained on " + }, + { + "bbox": [ + 47, + 606, + 287, + 665 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{s}}" + }, + { + "bbox": [ + 47, + 606, + 287, + 665 + ], + "type": "text", + "content": ", we minimize the risk differences between them," + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 71, + 673, + 287, + 694 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 71, + 673, + 287, + 694 + ], + "spans": [ + { + "bbox": [ + 71, + 673, + 287, + 694 + ], + "type": "interline_equation", + "content": "\\mathcal {D} _ {S} = \\underset {\\mathcal {D} _ {S} \\in 2 ^ {\\hat {\\mathbf {s}}}} {\\arg \\min } \\left| L \\left(h _ {\\hat {\\mathbf {s}}} (\\boldsymbol {x}), y\\right) - L \\left(h _ {\\mathcal {D} _ {S}} (\\boldsymbol {x}), y\\right) \\right|. \\tag {6}", + "image_path": "694dce6df2e93420b9c8f1cb0cd67b3500b56e6e64814f896ba01e00c5a65a06.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 701, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 701, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 701, + 287, + 714 + ], + "type": "inline_equation", + "content": "L(h_{\\mathfrak{S}}(\\pmb {x}),y)" + }, + { + "bbox": [ + 47, + 701, + 287, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 701, + 287, + 714 + ], + "type": "inline_equation", + "content": "L(h_{\\mathcal{D}_S}(\\pmb {x}),y)" + }, + { + "bbox": [ + 47, + 701, + 287, + 714 + ], + "type": "text", + "content": " are the respective risks of" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 306, + 68, + 425, + 160 + ], + "blocks": [ + { + "bbox": [ + 306, + 68, + 425, + 160 + ], + "lines": [ + { + "bbox": [ + 306, + 68, + 425, + 160 + ], + "spans": [ + { + "bbox": [ + 306, + 68, + 425, + 160 + ], + "type": "image", + "image_path": "cbd3cafd8d5ffff9631f38858ef53a273e088b9bcf38fab0cee5e21193a9f60b.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 432, + 70, + 547, + 160 + ], + "blocks": [ + { + "bbox": [ + 432, + 70, + 547, + 160 + ], + "lines": [ + { + "bbox": [ + 432, + 70, + 547, + 160 + ], + "spans": [ + { + "bbox": [ + 432, + 70, + 547, + 160 + ], + "type": "image", + "image_path": "68125579b3a7c9e7c3dbc06d8cbe5714e4d414fc1cec6b56561b90f4ab35bd84.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 317, + 166, + 544, + 258 + ], + "blocks": [ + { + "bbox": [ + 317, + 166, + 544, + 258 + ], + "lines": [ + { + "bbox": [ + 317, + 166, + 544, + 258 + ], + "spans": [ + { + "bbox": [ + 317, + 166, + 544, + 258 + ], + "type": "image", + "image_path": "38c74062262b2f662e50409935f11fb4d4d75bc83382d9d28c32263fa2a17613.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 275, + 545, + 384 + ], + "lines": [ + { + "bbox": [ + 304, + 275, + 545, + 384 + ], + "spans": [ + { + "bbox": [ + 304, + 275, + 545, + 384 + ], + "type": "text", + "content": "Figure 5. Performance of constructed training set at different iterations on the target set. We greedily add clustered subset to form " + }, + { + "bbox": [ + 304, + 275, + 545, + 384 + ], + "type": "inline_equation", + "content": "\\mathbf{S}^*" + }, + { + "bbox": [ + 304, + 275, + 545, + 384 + ], + "type": "text", + "content": " which has the smallest domain gap to the target " + }, + { + "bbox": [ + 304, + 275, + 545, + 384 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_T" + }, + { + "bbox": [ + 304, + 275, + 545, + 384 + ], + "type": "text", + "content": ". During this process, we have relatively high FID and low accuracy at (A). Gradually, we reach situation (B) of the smallest domain gap and highest accuracy. After (B), adding subsets leads to an increase in the domain gap, and the accuracy drops, e.g., (C). To study the correlation between FID and mAP during the search process, we hope to eliminate the impact of dataset size. Thus we use the same number of IDs from the searched set (i.e., " + }, + { + "bbox": [ + 304, + 275, + 545, + 384 + ], + "type": "inline_equation", + "content": "2\\%" + }, + { + "bbox": [ + 304, + 275, + 545, + 384 + ], + "type": "text", + "content": " ID)." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 394, + 544, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 394, + 544, + 418 + ], + "spans": [ + { + "bbox": [ + 305, + 394, + 544, + 418 + ], + "type": "text", + "content": "model " + }, + { + "bbox": [ + 305, + 394, + 544, + 418 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 305, + 394, + 544, + 418 + ], + "type": "text", + "content": " on the dataset " + }, + { + "bbox": [ + 305, + 394, + 544, + 418 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{s}}" + }, + { + "bbox": [ + 305, + 394, + 544, + 418 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 394, + 544, + 418 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_S" + }, + { + "bbox": [ + 305, + 394, + 544, + 418 + ], + "type": "text", + "content": ". For simplicity, we define the risk of model " + }, + { + "bbox": [ + 305, + 394, + 544, + 418 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 305, + 394, + 544, + 418 + ], + "type": "text", + "content": " on an arbitrary dataset " + }, + { + "bbox": [ + 305, + 394, + 544, + 418 + ], + "type": "inline_equation", + "content": "\\mathbf{S}" + }, + { + "bbox": [ + 305, + 394, + 544, + 418 + ], + "type": "text", + "content": " as" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 338, + 423, + 545, + 453 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 338, + 423, + 545, + 453 + ], + "spans": [ + { + "bbox": [ + 338, + 423, + 545, + 453 + ], + "type": "interline_equation", + "content": "L \\left(h _ {\\mathbf {S}} (\\boldsymbol {x}), y\\right) = \\frac {1}{| \\mathbf {S} |} \\sum_ {\\left(\\boldsymbol {x} _ {i}, y _ {i}\\right) \\in \\mathbf {S}} \\ell \\left(h _ {\\mathbf {S}} \\left(\\boldsymbol {x} _ {i}\\right), y _ {i}\\right). \\tag {7}", + "image_path": "5109cd95531826d655398739276d27e2a3dc964dd9f998073ac6572334486ef5.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 460, + 544, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 460, + 544, + 472 + ], + "spans": [ + { + "bbox": [ + 306, + 460, + 544, + 472 + ], + "type": "text", + "content": "As in Eq. 1, " + }, + { + "bbox": [ + 306, + 460, + 544, + 472 + ], + "type": "inline_equation", + "content": "\\ell(h_{\\mathbf{S}}(\\pmb{x}_i), y_i)" + }, + { + "bbox": [ + 306, + 460, + 544, + 472 + ], + "type": "text", + "content": " is the risk on individual samples." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 473, + 545, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 473, + 545, + 509 + ], + "spans": [ + { + "bbox": [ + 305, + 473, + 545, + 509 + ], + "type": "text", + "content": "From the theory of core set [31], if " + }, + { + "bbox": [ + 305, + 473, + 545, + 509 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_S" + }, + { + "bbox": [ + 305, + 473, + 545, + 509 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 305, + 473, + 545, + 509 + ], + "type": "inline_equation", + "content": "\\delta_s" + }, + { + "bbox": [ + 305, + 473, + 545, + 509 + ], + "type": "text", + "content": " cover of the set " + }, + { + "bbox": [ + 305, + 473, + 545, + 509 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{s}}" + }, + { + "bbox": [ + 305, + 473, + 545, + 509 + ], + "type": "text", + "content": " and shares the same number of classes with " + }, + { + "bbox": [ + 305, + 473, + 545, + 509 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{s}}" + }, + { + "bbox": [ + 305, + 473, + 545, + 509 + ], + "type": "text", + "content": ", the risk difference between model " + }, + { + "bbox": [ + 305, + 473, + 545, + 509 + ], + "type": "inline_equation", + "content": "h_{\\hat{\\mathbf{s}}}" + }, + { + "bbox": [ + 305, + 473, + 545, + 509 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 473, + 545, + 509 + ], + "type": "inline_equation", + "content": "h_{\\mathcal{D}_S}" + }, + { + "bbox": [ + 305, + 473, + 545, + 509 + ], + "type": "text", + "content": " is bounded by" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 311, + 514, + 545, + 541 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 311, + 514, + 545, + 541 + ], + "spans": [ + { + "bbox": [ + 311, + 514, + 545, + 541 + ], + "type": "interline_equation", + "content": "\\left| L \\left(h _ {\\hat {\\mathbf {s}}} (\\boldsymbol {x}), y\\right) - L \\left(h _ {\\mathcal {D} _ {S}} (\\boldsymbol {x}), y\\right) \\right| \\leq \\mathcal {O} \\left(\\delta_ {s}\\right) + \\mathcal {O} \\left(\\frac {1}{\\sqrt {| \\mathcal {D} _ {S} |}}\\right). \\tag {8}", + "image_path": "5d303f4491b88e756e6c99b1b3a525dd6c89919e2b44919ac58574da6978efbb.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 547, + 545, + 619 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 547, + 545, + 619 + ], + "spans": [ + { + "bbox": [ + 305, + 547, + 545, + 619 + ], + "type": "inline_equation", + "content": "\\delta_{s}" + }, + { + "bbox": [ + 305, + 547, + 545, + 619 + ], + "type": "text", + "content": " is the radius of the cover, and " + }, + { + "bbox": [ + 305, + 547, + 545, + 619 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(\\delta_s)" + }, + { + "bbox": [ + 305, + 547, + 545, + 619 + ], + "type": "text", + "content": " is a polynomial function over " + }, + { + "bbox": [ + 305, + 547, + 545, + 619 + ], + "type": "inline_equation", + "content": "\\delta_{s}" + }, + { + "bbox": [ + 305, + 547, + 545, + 619 + ], + "type": "text", + "content": ". The problem can be reduced as a K-center problem [11] by optimizing " + }, + { + "bbox": [ + 305, + 547, + 545, + 619 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(\\delta_s)" + }, + { + "bbox": [ + 305, + 547, + 545, + 619 + ], + "type": "text", + "content": ". We apply a 2-approximation algorithm [46] to iteratively find optimal samples in " + }, + { + "bbox": [ + 305, + 547, + 545, + 619 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{s}}" + }, + { + "bbox": [ + 305, + 547, + 545, + 619 + ], + "type": "text", + "content": " and add to " + }, + { + "bbox": [ + 305, + 547, + 545, + 619 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_S" + }, + { + "bbox": [ + 305, + 547, + 545, + 619 + ], + "type": "text", + "content": ". Specifically, each optimal sample " + }, + { + "bbox": [ + 305, + 547, + 545, + 619 + ], + "type": "inline_equation", + "content": "\\mathbf{z}^*" + }, + { + "bbox": [ + 305, + 547, + 545, + 619 + ], + "type": "text", + "content": " is computed as" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 342, + 625, + 545, + 646 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 342, + 625, + 545, + 646 + ], + "spans": [ + { + "bbox": [ + 342, + 625, + 545, + 646 + ], + "type": "interline_equation", + "content": "\\mathbf {z} ^ {*} = \\underset {\\mathbf {z} _ {i} \\in \\hat {\\mathbf {s}} \\backslash \\mathcal {D} _ {\\mathcal {S}}} {\\arg \\max } \\underset {\\mathbf {z} _ {j} \\in \\mathcal {D} _ {\\mathcal {S}}} {\\min } \\| f (\\boldsymbol {x} _ {i}) - f (\\boldsymbol {x} _ {j}) \\| _ {2}, \\tag {9}", + "image_path": "ac9d55393ef5395c7de5b2d35e40b13a8ef3f8777133a46d5e0f0d4c5e7d0699.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{z} = (\\pmb{x},y)" + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "inline_equation", + "content": "f(\\pmb{x})" + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "content": " represents the descriptor of an image " + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\pmb{x}" + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "content": ". Equation 9 relates to the furthest point sampling method [8], which enables the most representative samples from a dataset to be selected. We summarize the pruning process in Algorithm 2." + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "15572" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "code", + "bbox": [ + 48, + 85, + 287, + 232 + ], + "blocks": [ + { + "bbox": [ + 48, + 72, + 221, + 83 + ], + "lines": [ + { + "bbox": [ + 48, + 72, + 221, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 72, + 221, + 83 + ], + "type": "text", + "content": "Algorithm 1 Target-specific Subset Search" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 48, + 85, + 287, + 232 + ], + "lines": [ + { + "bbox": [ + 48, + 85, + 287, + 232 + ], + "spans": [ + { + "bbox": [ + 48, + 85, + 287, + 232 + ], + "type": "text", + "content": "1: Input: Source pool " + }, + { + "bbox": [ + 48, + 85, + 287, + 232 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 48, + 85, + 287, + 232 + ], + "type": "text", + "content": ", target set " + }, + { + "bbox": [ + 48, + 85, + 287, + 232 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_T" + }, + { + "bbox": [ + 48, + 85, + 287, + 232 + ], + "type": "text", + "content": ", and the number of clusters " + }, + { + "bbox": [ + 48, + 85, + 287, + 232 + ], + "type": "inline_equation", + "content": "J" + }, + { + "bbox": [ + 48, + 85, + 287, + 232 + ], + "type": "text", + "content": ". \n2: Begin: \n3: Cluster " + }, + { + "bbox": [ + 48, + 85, + 287, + 232 + ], + "type": "inline_equation", + "content": "(S, J) \\longrightarrow \\{\\mathbf{S}^1, \\dots, \\mathbf{S}^J\\}" + }, + { + "bbox": [ + 48, + 85, + 287, + 232 + ], + "type": "text", + "content": " \n4: " + }, + { + "bbox": [ + 48, + 85, + 287, + 232 + ], + "type": "inline_equation", + "content": "\\mathbf{s} = \\emptyset, \\epsilon = \\infty, \\mathbf{S}^* = \\emptyset" + }, + { + "bbox": [ + 48, + 85, + 287, + 232 + ], + "type": "text", + "content": " \n5: " + }, + { + "bbox": [ + 48, + 85, + 287, + 232 + ], + "type": "inline_equation", + "content": "\\mathcal{I} = \\text{argsort}(\\{\\text{FID}(\\mathbf{S}^j, \\mathcal{D}_T)\\}_{j \\in [J]}) \\triangleright" + }, + { + "bbox": [ + 48, + 85, + 287, + 232 + ], + "type": "text", + "content": " Ascending \n6: for " + }, + { + "bbox": [ + 48, + 85, + 287, + 232 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 48, + 85, + 287, + 232 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 48, + 85, + 287, + 232 + ], + "type": "inline_equation", + "content": "\\mathcal{I}" + }, + { + "bbox": [ + 48, + 85, + 287, + 232 + ], + "type": "text", + "content": " do \n7: " + }, + { + "bbox": [ + 48, + 85, + 287, + 232 + ], + "type": "inline_equation", + "content": "\\mathbf{s} = \\mathbf{s} \\cup \\mathbf{S}^j" + }, + { + "bbox": [ + 48, + 85, + 287, + 232 + ], + "type": "text", + "content": " \n8: if FID(s, T) < " + }, + { + "bbox": [ + 48, + 85, + 287, + 232 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 48, + 85, + 287, + 232 + ], + "type": "text", + "content": " then \n9: " + }, + { + "bbox": [ + 48, + 85, + 287, + 232 + ], + "type": "inline_equation", + "content": "\\epsilon = \\text{FID}(\\mathbf{s}, \\mathcal{D}_T)" + }, + { + "bbox": [ + 48, + 85, + 287, + 232 + ], + "type": "text", + "content": " \n10: " + }, + { + "bbox": [ + 48, + 85, + 287, + 232 + ], + "type": "inline_equation", + "content": "\\mathbf{S}^* = \\mathbf{s}" + }, + { + "bbox": [ + 48, + 85, + 287, + 232 + ], + "type": "text", + "content": " \n11: return S*" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "code_body" + } + ], + "index": 1, + "sub_type": "algorithm" + }, + { + "bbox": [ + 47, + 253, + 118, + 264 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 253, + 118, + 264 + ], + "spans": [ + { + "bbox": [ + 47, + 253, + 118, + 264 + ], + "type": "text", + "content": "4.5. Discussion" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 271, + 287, + 391 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 271, + 287, + 391 + ], + "spans": [ + { + "bbox": [ + 46, + 271, + 287, + 391 + ], + "type": "text", + "content": "What to prune first, ID or image? In our design, we select the IDs first and then images, aiming to build a dataset that has a small domain gap to target and is meanwhile in small-scale. Selecting the images first and then IDs is possible. However, it leads to a significant increase in the time complexity. As shown in Algorithm 2, the most time-consuming part of our algorithm is the FPS for finding image core sets, which takes " + }, + { + "bbox": [ + 46, + 271, + 287, + 391 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(m|\\hat{\\mathbf{s}}|)" + }, + { + "bbox": [ + 46, + 271, + 287, + 391 + ], + "type": "text", + "content": ". If we select images first, the time complexity becomes " + }, + { + "bbox": [ + 46, + 271, + 287, + 391 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(m|\\mathbf{S}^*|)" + }, + { + "bbox": [ + 46, + 271, + 287, + 391 + ], + "type": "text", + "content": ", which is significantly higher than " + }, + { + "bbox": [ + 46, + 271, + 287, + 391 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(m|\\hat{\\mathbf{s}}|)" + }, + { + "bbox": [ + 46, + 271, + 287, + 391 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 46, + 271, + 287, + 391 + ], + "type": "inline_equation", + "content": "|\\mathbf{S}^*| \\gg |\\hat{\\mathbf{s}}|" + }, + { + "bbox": [ + 46, + 271, + 287, + 391 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 392, + 287, + 511 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 392, + 287, + 511 + ], + "spans": [ + { + "bbox": [ + 46, + 392, + 287, + 511 + ], + "type": "text", + "content": "Is SnP applicable to tasks beyond object re-ID? It is possible to apply our search and pruning (SnP) framework to other tasks, e.g., classification. Yet, achieving this requires the SnP algorithm to be partially redesigned. The reason is that, in object re-ID, the major domain gap comes from the class difference, i.e., IDs. However, such a gap does not exist in the classification tasks as the train/val/test datasets always share the same classes. Therefore, our current design of selecting similar IDs for similar distributions is not directly applicable, and has to be adapted." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 522, + 123, + 536 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 522, + 123, + 536 + ], + "spans": [ + { + "bbox": [ + 47, + 522, + 123, + 536 + ], + "type": "text", + "content": "5. Experiment" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 543, + 287, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 543, + 287, + 591 + ], + "spans": [ + { + "bbox": [ + 46, + 543, + 287, + 591 + ], + "type": "text", + "content": "We evaluate the effectiveness of SnP on person re-ID and vehicle re-ID. In both tasks, given target data, we use the SnP pipeline to find a training set that has a similar distribution to the target and simultaneously meets a budget." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 599, + 197, + 611 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 599, + 197, + 611 + ], + "spans": [ + { + "bbox": [ + 47, + 599, + 197, + 611 + ], + "type": "text", + "content": "5.1. Source and Target Datasets" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "content": "Person re-ID. We create the source pool for person re-ID using 10 public datasets, including Market [54], Duke [55], MSMT17 [45] (denoted as MSMT), CUHK03 [19], RAiD [6], PersonX [37], UnrealPerson [52], RandPerson [43], PKU-Reid [28] and VIPeR [4]. Those datasets cover both synthetic and real-world data. Ten re-ID datasets constitute a source pool that contains in total of 15,060 IDs and 399,715 images." + } + ] + } + ], + "index": 8 + }, + { + "type": "code", + "bbox": [ + 306, + 85, + 545, + 256 + ], + "blocks": [ + { + "bbox": [ + 307, + 72, + 435, + 83 + ], + "lines": [ + { + "bbox": [ + 307, + 72, + 435, + 83 + ], + "spans": [ + { + "bbox": [ + 307, + 72, + 435, + 83 + ], + "type": "text", + "content": "Algorithm 2 Budgeted Pruning" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 306, + 85, + 545, + 256 + ], + "lines": [ + { + "bbox": [ + 306, + 85, + 545, + 256 + ], + "spans": [ + { + "bbox": [ + 306, + 85, + 545, + 256 + ], + "type": "text", + "content": "1: Input: Initial source set " + }, + { + "bbox": [ + 306, + 85, + 545, + 256 + ], + "type": "inline_equation", + "content": "\\mathbf{S}^*" + }, + { + "bbox": [ + 306, + 85, + 545, + 256 + ], + "type": "text", + "content": ", budget " + }, + { + "bbox": [ + 306, + 85, + 545, + 256 + ], + "type": "inline_equation", + "content": "b = (n, m)" + }, + { + "bbox": [ + 306, + 85, + 545, + 256 + ], + "type": "text", + "content": ". \n2: Begin: \n3: " + }, + { + "bbox": [ + 306, + 85, + 545, + 256 + ], + "type": "inline_equation", + "content": "\\pmb{y} = \\mathcal{U}(\\mathcal{V}(\\mathbf{S}^*), n)" + }, + { + "bbox": [ + 306, + 85, + 545, + 256 + ], + "type": "text", + "content": " ▷ Sample n IDs \n4: " + }, + { + "bbox": [ + 306, + 85, + 545, + 256 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{s}} = \\{\\pmb{s}(y_i) | y_i \\in \\pmb{y}\\}" + }, + { + "bbox": [ + 306, + 85, + 545, + 256 + ], + "type": "text", + "content": " \n5: " + }, + { + "bbox": [ + 306, + 85, + 545, + 256 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_S = \\{\\mathcal{U}(\\mathbf{s}(y^i), 1) | y_i \\in \\pmb{y}\\}" + }, + { + "bbox": [ + 306, + 85, + 545, + 256 + ], + "type": "text", + "content": " \n6: if " + }, + { + "bbox": [ + 306, + 85, + 545, + 256 + ], + "type": "inline_equation", + "content": "|\\hat{\\mathbf{s}}| > m" + }, + { + "bbox": [ + 306, + 85, + 545, + 256 + ], + "type": "text", + "content": " then ▷ Sample m images \n7: repeat \n8: " + }, + { + "bbox": [ + 306, + 85, + 545, + 256 + ], + "type": "inline_equation", + "content": "\\mathbf{z}^* = \\arg\\max_{\\mathbf{z}_i \\in \\hat{\\mathbf{s}} \\setminus \\mathcal{D}_S} \\min_{\\mathbf{z}_j \\in \\mathcal{D}_S} \\|\\pmb{x}_i - \\pmb{x}_j\\|_2" + }, + { + "bbox": [ + 306, + 85, + 545, + 256 + ], + "type": "text", + "content": " \n9: " + }, + { + "bbox": [ + 306, + 85, + 545, + 256 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_S = \\mathcal{D}_S \\cup \\{\\mathbf{z}^*\\}" + }, + { + "bbox": [ + 306, + 85, + 545, + 256 + ], + "type": "text", + "content": " \n10: until " + }, + { + "bbox": [ + 306, + 85, + 545, + 256 + ], + "type": "inline_equation", + "content": "|\\mathcal{D}_S| = m" + }, + { + "bbox": [ + 306, + 85, + 545, + 256 + ], + "type": "text", + "content": " \n11: else \n12: " + }, + { + "bbox": [ + 306, + 85, + 545, + 256 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_S = \\hat{\\mathbf{s}}" + }, + { + "bbox": [ + 306, + 85, + 545, + 256 + ], + "type": "text", + "content": " \n13: return " + }, + { + "bbox": [ + 306, + 85, + 545, + 256 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_S" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "code_body" + } + ], + "index": 10, + "sub_type": "algorithm" + }, + { + "bbox": [ + 304, + 277, + 545, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 277, + 545, + 348 + ], + "spans": [ + { + "bbox": [ + 304, + 277, + 545, + 348 + ], + "type": "text", + "content": "We use two real-world datasets as targets: AlicePerson [1] and Market [54]. Specifically, AlicePerson is specially designed for domain adaptation as it contains unlabeled training images. Note that in Market, the label for its training set is not be used. When Market is the target, Market training set is excluded from the source pool." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 350, + 545, + 409 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 350, + 545, + 409 + ], + "spans": [ + { + "bbox": [ + 304, + 350, + 545, + 409 + ], + "type": "text", + "content": "Vehicle re-ID. For vehicle re-ID, we create the source pool by combining 8 datasets, which are VeRi [22], CityFlow [41], VehicleID [21], VeRi-Wild [25], VehicleX [50], Stanford Cars [18], PKU-vd1 [47] and PKU-vd2 [47]. It totally has 156,512 IDs and 1,284,272 images." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 410, + 545, + 457 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 410, + 545, + 457 + ], + "spans": [ + { + "bbox": [ + 304, + 410, + 545, + 457 + ], + "type": "text", + "content": "AliceVehicle [1] and VeRi [22] are separately used as the target domains. Similar to AlicePerson, AliceVehicle is also designed for domain adaptation. When VeRi is the target, the VeRi training set is excluded from the source pool." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 459, + 545, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 459, + 545, + 529 + ], + "spans": [ + { + "bbox": [ + 304, + 459, + 545, + 529 + ], + "type": "text", + "content": "Evaluation protocol. For object re-ID, we use mean average precision (mAP) and cumulative match curve (CMC) scores to measure system accuracy, e.g., \"rank-1\" and \"rank-5\". \"rank-1\" denotes the success rate of finding the true match in the first rank, and \"rank-5\" means the success rate of ranking at least one true match within top-5 matches." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 539, + 362, + 550 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 539, + 362, + 550 + ], + "spans": [ + { + "bbox": [ + 306, + 539, + 362, + 550 + ], + "type": "text", + "content": "5.2. Results" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "content": "SnP framework vs. random sampling and greedy sampling. Given a target domain, the SnP framework allows us to construct a budgeted dataset with a similar distribution. We show the superiority of SnP framework in Table 1. After sampling target-specific data with SnP, we train the subsequent re-ID model with the sampled target-specific data only. In Table 1, we compare the sampled dataset with those created by greedy sampling and random sampling. Random sampling means we randomly select IDs according to the uniform distribution. For greedy sampling, we reproduce [48]. Specifically, We assign each ID a score, which is calculated using FID. IDs will then be selected greedily from the lowest FID value to the highest FID value." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15573" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 113, + 547, + 253 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "text", + "content": "Table 1. Comparing different methods in training data search: SnP, random sampling, and greedy sampling. We set the budget as " + }, + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "inline_equation", + "content": "2\\%" + }, + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "text", + "content": " of the total source IDs. We use four targets: AlicePerson, Market, AliceVehicle and VeRi. The task model is IDE [53]. FID, rank-1 accuracy " + }, + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "text", + "content": ", and mAP " + }, + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "text", + "content": " are reported." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 113, + 547, + 253 + ], + "lines": [ + { + "bbox": [ + 48, + 113, + 547, + 253 + ], + "spans": [ + { + "bbox": [ + 48, + 113, + 547, + 253 + ], + "type": "table", + "html": "
Training dataPerson re-ID targetsVehicle re-ID targets
AlicePersonMarketAliceVehicleVeRi
FID↓R1↑mAP↑FID↓R1↑mAP↑FID↓R1↑mAP↑FID↓R1↑mAP↑
Source pool81.6738.9617.6237.5355.5530.6243.9530.4714.6424.3955.9025.03
Searched60.9548.1925.5130.4261.4934.4023.4446.7825.4617.9274.1341.71
Pruned2% IDsRandom80.0623.679.8039.0340.7719.5445.9731.3512.8724.6867.1626.48
Greedy [48]61.7833.2215.1034.4342.1919.3538.5131.8212.9129.5366.5726.24
SnP60.4238.2318.1731.2944.8021.6523.4838.4817.7917.7069.9631.10
5% IDsRandom81.4133.1614.4939.6547.3923.9744.5236.3614.1725.2770.3830.44
Greedy [48]61.0144.6322.8131.6349.1724.7732.4841.3217.7726.0671.2332.53
SnP60.6447.2625.4530.3751.9626.5623.9244.5821.7918.0972.0536.01
20% IDsRandom79.3338.1017.7938.6353.1528.3943.9040.8918.1324.4368.7134.10
Greedy [48]63.1546.7422.6532.4253.5328.1924.1544.5822.8218.7471.0438.07
SnP61.8747.2025.3630.5857.1433.0923.4746.0725.2417.9373.4840.75
", + "image_path": "751fb430d8d7a9f2004cd36a958c71b2f4aff0db52e662907e2eab8bff668265.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 48, + 305, + 287, + 387 + ], + "blocks": [ + { + "bbox": [ + 46, + 262, + 288, + 297 + ], + "lines": [ + { + "bbox": [ + 46, + 262, + 288, + 297 + ], + "spans": [ + { + "bbox": [ + 46, + 262, + 288, + 297 + ], + "type": "text", + "content": "Table 2. The effectiveness of the target-specific subset search. mAP " + }, + { + "bbox": [ + 46, + 262, + 288, + 297 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 46, + 262, + 288, + 297 + ], + "type": "text", + "content": " and CMC scores are reported. \"R1\" and \"R5\" denote rank-1 accuracy " + }, + { + "bbox": [ + 46, + 262, + 288, + 297 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 46, + 262, + 288, + 297 + ], + "type": "text", + "content": " and rank-5 accuracy " + }, + { + "bbox": [ + 46, + 262, + 288, + 297 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 46, + 262, + 288, + 297 + ], + "type": "text", + "content": ", respectively." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 305, + 287, + 387 + ], + "lines": [ + { + "bbox": [ + 48, + 305, + 287, + 387 + ], + "spans": [ + { + "bbox": [ + 48, + 305, + 287, + 387 + ], + "type": "table", + "html": "
AlicePersonAliceVehicle
Training dataR1R5mAPTraining dataR1R5mAP
Market [54]32.8952.5416.06VeRi [22]30.6943.6611.05
Duke [55]23.2741.138.59CityFlow [41]23.9536.007.45
MSMT [45]31.2952.7915.08VehicleID [21]16.329.134.73
PersonX [37]16.0827.426.41VehicleX [50]18.8532.188.89
Source pool38.9657.4817.62Source pool30.4748.3314.64
Searched48.1967.5725.51Searched46.7864.4125.46
", + "image_path": "4b5981b914d268dc894e5d91acdfa7b2a1f4e0e5d5499c02cb71e23c7b3ba721.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 401, + 287, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 401, + 287, + 544 + ], + "spans": [ + { + "bbox": [ + 46, + 401, + 287, + 544 + ], + "type": "text", + "content": "From the results shown in Table 1 and Table 3, we observe that training sets selected using SnP achieve consistently lower domain gap to the target and higher re-ID accuracy than those found by random sampling and greedy sampling. For example, when creating a training set with only " + }, + { + "bbox": [ + 46, + 401, + 287, + 544 + ], + "type": "inline_equation", + "content": "2\\%" + }, + { + "bbox": [ + 46, + 401, + 287, + 544 + ], + "type": "text", + "content": " source IDs for AlicePerson as the target, SnP results in -19.64 and -1.36 improvement in FID value, and " + }, + { + "bbox": [ + 46, + 401, + 287, + 544 + ], + "type": "inline_equation", + "content": "+14.56\\%" + }, + { + "bbox": [ + 46, + 401, + 287, + 544 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 401, + 287, + 544 + ], + "type": "inline_equation", + "content": "+5.01\\%" + }, + { + "bbox": [ + 46, + 401, + 287, + 544 + ], + "type": "text", + "content": " improvement in rank-1 accuracy over using random sampling and greedy sampling, respectively. When sampling training set with " + }, + { + "bbox": [ + 46, + 401, + 287, + 544 + ], + "type": "inline_equation", + "content": "2\\%" + }, + { + "bbox": [ + 46, + 401, + 287, + 544 + ], + "type": "text", + "content": " of the source IDs for AliceVehicle as the target, the rank-1 accuracy improvement is " + }, + { + "bbox": [ + 46, + 401, + 287, + 544 + ], + "type": "inline_equation", + "content": "+7.13\\%" + }, + { + "bbox": [ + 46, + 401, + 287, + 544 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 401, + 287, + 544 + ], + "type": "inline_equation", + "content": "+6.66\\%" + }, + { + "bbox": [ + 46, + 401, + 287, + 544 + ], + "type": "text", + "content": ", respectively." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 545, + 287, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 287, + 700 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 287, + 700 + ], + "type": "text", + "content": "Effectiveness of the search step. We analyze this step in Table 1 and Table 2. In this search process that poses no limit on the number of IDs and images, we aim to identify and merge clusters of source identities that exhibit similar distributions with the target. We show the searched datasets contribute to improved accuracy over the entire data pool. For example, for AlicePerson, we observe a " + }, + { + "bbox": [ + 46, + 545, + 287, + 700 + ], + "type": "inline_equation", + "content": "+9.23\\%" + }, + { + "bbox": [ + 46, + 545, + 287, + 700 + ], + "type": "text", + "content": " improvement in rank-1 accuracy over the entire data pool. We further show the searched data is superior to individual training sets in Table 2. For example, when AliceVehicle is our target, we show our searched dataset results in " + }, + { + "bbox": [ + 46, + 545, + 287, + 700 + ], + "type": "inline_equation", + "content": "+16.09\\%" + }, + { + "bbox": [ + 46, + 545, + 287, + 700 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 545, + 287, + 700 + ], + "type": "inline_equation", + "content": "+22.83\\%" + }, + { + "bbox": [ + 46, + 545, + 287, + 700 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 545, + 287, + 700 + ], + "type": "inline_equation", + "content": "+30.48\\%" + }, + { + "bbox": [ + 46, + 545, + 287, + 700 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 545, + 287, + 700 + ], + "type": "inline_equation", + "content": "+27.93\\%" + }, + { + "bbox": [ + 46, + 545, + 287, + 700 + ], + "type": "text", + "content": " higher rank-1 accuracy than VeRi, CityFlow, VehicleID, and VehicleX, respectively." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 59, + 701, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 701, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 59, + 701, + 287, + 713 + ], + "type": "text", + "content": "Of note, accuracy under this application scenario is usu" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 307, + 327, + 544, + 485 + ], + "blocks": [ + { + "bbox": [ + 305, + 262, + 547, + 319 + ], + "lines": [ + { + "bbox": [ + 305, + 262, + 547, + 319 + ], + "spans": [ + { + "bbox": [ + 305, + 262, + 547, + 319 + ], + "type": "text", + "content": "Table 3. The superiority of SnP over random sampling and greedy sampling, when different direct transfer and pseudu-label re-ID models are used. We report accuracy when " + }, + { + "bbox": [ + 305, + 262, + 547, + 319 + ], + "type": "inline_equation", + "content": "2\\%" + }, + { + "bbox": [ + 305, + 262, + 547, + 319 + ], + "type": "text", + "content": " IDs are selected for target AicerPerson. Notations and evaluation metrics are the same as those in the previous table." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 327, + 544, + 485 + ], + "lines": [ + { + "bbox": [ + 307, + 327, + 544, + 485 + ], + "spans": [ + { + "bbox": [ + 307, + 327, + 544, + 485 + ], + "type": "table", + "html": "
TypeModelTraining dataR1R5mAP
Direct TransferIDE [53]Random23.6742.329.80
Greedy [48]33.2254.4515.10
SnP38.2358.4018.17
PCB [38]Random24.7941.609.91
Greedy [48]29.0746.0112.59
SnP32.4349.9015.18
TransReid [15]Random52.0469.7328.47
Greedy [48]63.7380.2441.88
SnP64.3180.4642.74
Pseudo-labelingUDA [34]Random32.1754.6715.32
Greedy [48]36.4752.0617.34
SnP41.4155.7420.47
MMT [13]Random35.9451.9117.25
Greedy [48]38.6456.4821.18
SnP43.3660.3823.34
", + "image_path": "9dc27d660f6ad20d298239ec64d3a4df245f7d7eff05bf922ba191bb8564eafe.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 498, + 545, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 545, + 593 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 545, + 593 + ], + "type": "text", + "content": "ally lower than that produced by in-distribution training sets. This difference is understandable, because searched data have a relatively lower resemblance to the target data compared with in-distribution training sets. That said, annotating in-distribution training sets is usually expensive, especially considering the complex, specific and ever-changing target environments, where creating a training set on-the-fly with good performance is of practical value." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "text", + "content": "Effectiveness of the pruning step is analyzed in Table 1 and Fig. 7. Pruning aims to find a subset that has no more than " + }, + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "text", + "content": " IDs and " + }, + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "text", + "content": " images. From Table 1 and Fig. 7, admittedly, the pruning of both IDs and images will lead to an accuracy decrease. For example, when the target is AlicePerson, if we select " + }, + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "inline_equation", + "content": "2\\%" + }, + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "text", + "content": " IDs, there is a " + }, + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "inline_equation", + "content": "-9.23\\%" + }, + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "text", + "content": " decrease in rank-1 accuracy. From Fig. 7, when the target is AlicePerson, if we further select " + }, + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "inline_equation", + "content": "40\\%" + }, + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "text", + "content": " images, there is a " + }, + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "inline_equation", + "content": "-9.96\\%" + }, + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "text", + "content": " decrease in rank-1 accuracy. However, even though only " + }, + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "inline_equation", + "content": "2\\%" + }, + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "text", + "content": " IDs are used, rank-1 accuracy obtained from the pruned" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "15574" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 73, + 83, + 148 + ], + "blocks": [ + { + "bbox": [ + 53, + 73, + 83, + 148 + ], + "lines": [ + { + "bbox": [ + 53, + 73, + 83, + 148 + ], + "spans": [ + { + "bbox": [ + 53, + 73, + 83, + 148 + ], + "type": "image", + "image_path": "2cf4282a82d532cc3d6c0a24bb732c846e31a980858d1d976e39c6880e33f93e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 95, + 73, + 287, + 148 + ], + "blocks": [ + { + "bbox": [ + 95, + 73, + 287, + 148 + ], + "lines": [ + { + "bbox": [ + 95, + 73, + 287, + 148 + ], + "spans": [ + { + "bbox": [ + 95, + 73, + 287, + 148 + ], + "type": "image", + "image_path": "880bb195f29531e50c689e4880c92244ccc7b484fa9acafb7aeb4a9d2061a18d.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 136, + 148, + 215, + 158 + ], + "lines": [ + { + "bbox": [ + 136, + 148, + 215, + 158 + ], + "spans": [ + { + "bbox": [ + 136, + 148, + 215, + 158 + ], + "type": "text", + "content": "(A) AlicePerson as Target" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 291, + 74, + 317, + 148 + ], + "blocks": [ + { + "bbox": [ + 291, + 74, + 317, + 148 + ], + "lines": [ + { + "bbox": [ + 291, + 74, + 317, + 148 + ], + "spans": [ + { + "bbox": [ + 291, + 74, + 317, + 148 + ], + "type": "image", + "image_path": "713c29398d2c352ac7b57c6608a9cf992709ad485d19da4e6165dda58ceaa6e3.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 325, + 74, + 545, + 148 + ], + "blocks": [ + { + "bbox": [ + 325, + 74, + 545, + 148 + ], + "lines": [ + { + "bbox": [ + 325, + 74, + 545, + 148 + ], + "spans": [ + { + "bbox": [ + 325, + 74, + 545, + 148 + ], + "type": "image", + "image_path": "19ac4343920cf44e3125c76b59cc3b760e288c48b82eb2f152d1e066309c3eaf.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 387, + 149, + 468, + 159 + ], + "lines": [ + { + "bbox": [ + 387, + 149, + 468, + 159 + ], + "spans": [ + { + "bbox": [ + 387, + 149, + 468, + 159 + ], + "type": "text", + "content": "(C) AliceVehicle as Target" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 55, + 163, + 83, + 236 + ], + "blocks": [ + { + "bbox": [ + 55, + 163, + 83, + 236 + ], + "lines": [ + { + "bbox": [ + 55, + 163, + 83, + 236 + ], + "spans": [ + { + "bbox": [ + 55, + 163, + 83, + 236 + ], + "type": "image", + "image_path": "1eefac88a398c5e503b9634e8dab309da7206a00500eb84f3ae1a1cfd7733add.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 258, + 546, + 292 + ], + "lines": [ + { + "bbox": [ + 46, + 258, + 546, + 292 + ], + "spans": [ + { + "bbox": [ + 46, + 258, + 546, + 292 + ], + "type": "text", + "content": "Figure 6. Composition statistics and images samples of searched training sets. For each subfigure (A), (B), (C) and (D), the columns on the left presents unlabeled target samples; columns the middle provide samples of the searched training set; the pie chart Community-verified icon Verified on the right shows composition statistics of the searched training set." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 96, + 163, + 152, + 237 + ], + "blocks": [ + { + "bbox": [ + 96, + 163, + 152, + 237 + ], + "lines": [ + { + "bbox": [ + 96, + 163, + 152, + 237 + ], + "spans": [ + { + "bbox": [ + 96, + 163, + 152, + 237 + ], + "type": "image", + "image_path": "65059450bca16183eb99c56940ea48b32f5b58d6bbbb37fb41855b88cb5e7f39.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 145, + 239, + 209, + 248 + ], + "lines": [ + { + "bbox": [ + 145, + 239, + 209, + 248 + ], + "spans": [ + { + "bbox": [ + 145, + 239, + 209, + 248 + ], + "type": "text", + "content": "(B) Market as Target" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 153, + 163, + 287, + 238 + ], + "blocks": [ + { + "bbox": [ + 153, + 163, + 287, + 238 + ], + "lines": [ + { + "bbox": [ + 153, + 163, + 287, + 238 + ], + "spans": [ + { + "bbox": [ + 153, + 163, + 287, + 238 + ], + "type": "image", + "image_path": "efd25f39ad81c51d8df974d30eb473228ade052696164ea519b2883e8fc68bcd.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 291, + 163, + 317, + 237 + ], + "blocks": [ + { + "bbox": [ + 291, + 163, + 317, + 237 + ], + "lines": [ + { + "bbox": [ + 291, + 163, + 317, + 237 + ], + "spans": [ + { + "bbox": [ + 291, + 163, + 317, + 237 + ], + "type": "image", + "image_path": "0d6d2f5aef430e2e73fdb2b91548e9b32d66e456d573d294f4ddaa13fd6c85dd.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 326, + 163, + 544, + 238 + ], + "blocks": [ + { + "bbox": [ + 326, + 163, + 544, + 238 + ], + "lines": [ + { + "bbox": [ + 326, + 163, + 544, + 238 + ], + "spans": [ + { + "bbox": [ + 326, + 163, + 544, + 238 + ], + "type": "image", + "image_path": "bbb19cb863fbf2ff27693bd4506e25361454eb051baeb0b6346dfdeff9717f51.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 397, + 240, + 454, + 249 + ], + "lines": [ + { + "bbox": [ + 397, + 240, + 454, + 249 + ], + "spans": [ + { + "bbox": [ + 397, + 240, + 454, + 249 + ], + "type": "text", + "content": "(D) VeRi as Target" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 47, + 312, + 174, + 399 + ], + "blocks": [ + { + "bbox": [ + 91, + 302, + 140, + 311 + ], + "lines": [ + { + "bbox": [ + 91, + 302, + 140, + 311 + ], + "spans": [ + { + "bbox": [ + 91, + 302, + 140, + 311 + ], + "type": "text", + "content": "(A) AlicePerson" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 47, + 312, + 174, + 399 + ], + "lines": [ + { + "bbox": [ + 47, + 312, + 174, + 399 + ], + "spans": [ + { + "bbox": [ + 47, + 312, + 174, + 399 + ], + "type": "image", + "image_path": "be4208034c5a783fb7163eb872a5667893bcf9fc966bb04381adfaeadc58ee22.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 407, + 544, + 430 + ], + "lines": [ + { + "bbox": [ + 46, + 407, + 544, + 430 + ], + "spans": [ + { + "bbox": [ + 46, + 407, + 544, + 430 + ], + "type": "text", + "content": "Figure 7. Comparing FPS with random sampling. The search step provides us with " + }, + { + "bbox": [ + 46, + 407, + 544, + 430 + ], + "type": "inline_equation", + "content": "2\\%" + }, + { + "bbox": [ + 46, + 407, + 544, + 430 + ], + "type": "text", + "content": " of the source IDs. We further select various ratios of images from these IDs. Four different targets are used, and rank-1 accuracy is the evaluation metric. Score is averaged over three runs." + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 179, + 312, + 299, + 399 + ], + "blocks": [ + { + "bbox": [ + 224, + 302, + 259, + 311 + ], + "lines": [ + { + "bbox": [ + 224, + 302, + 259, + 311 + ], + "spans": [ + { + "bbox": [ + 224, + 302, + 259, + 311 + ], + "type": "text", + "content": "(B) Market" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 179, + 312, + 299, + 399 + ], + "lines": [ + { + "bbox": [ + 179, + 312, + 299, + 399 + ], + "spans": [ + { + "bbox": [ + 179, + 312, + 299, + 399 + ], + "type": "image", + "image_path": "fae4df5605549642b98ece0a33cea56fac4d8b58c24f98136494ec85db14e4d2.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 303, + 312, + 422, + 399 + ], + "blocks": [ + { + "bbox": [ + 339, + 302, + 390, + 311 + ], + "lines": [ + { + "bbox": [ + 339, + 302, + 390, + 311 + ], + "spans": [ + { + "bbox": [ + 339, + 302, + 390, + 311 + ], + "type": "text", + "content": "(C) Alice Vehicle" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 303, + 312, + 422, + 399 + ], + "lines": [ + { + "bbox": [ + 303, + 312, + 422, + 399 + ], + "spans": [ + { + "bbox": [ + 303, + 312, + 422, + 399 + ], + "type": "image", + "image_path": "581f466d061d35169b464e8ffe407120042db86bf5f22f9957507aa09061bfd4.jpg" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_body" + } + ], + "index": 19 + }, + { + "type": "image", + "bbox": [ + 426, + 312, + 546, + 399 + ], + "blocks": [ + { + "bbox": [ + 473, + 303, + 500, + 312 + ], + "lines": [ + { + "bbox": [ + 473, + 303, + 500, + 312 + ], + "spans": [ + { + "bbox": [ + 473, + 303, + 500, + 312 + ], + "type": "text", + "content": "(D) VeRi" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 426, + 312, + 546, + 399 + ], + "lines": [ + { + "bbox": [ + 426, + 312, + 546, + 399 + ], + "spans": [ + { + "bbox": [ + 426, + 312, + 546, + 399 + ], + "type": "image", + "image_path": "a47c41604d10dd733f5a88f55fdfd2cd4511c8ab151dec146e120247c71bca7c.jpg" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_body" + } + ], + "index": 21 + }, + { + "bbox": [ + 46, + 440, + 287, + 489 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 440, + 287, + 489 + ], + "spans": [ + { + "bbox": [ + 46, + 440, + 287, + 489 + ], + "type": "text", + "content": "training data is still competitive over the source pool, which is just " + }, + { + "bbox": [ + 46, + 440, + 287, + 489 + ], + "type": "inline_equation", + "content": "-0.73\\%" + }, + { + "bbox": [ + 46, + 440, + 287, + 489 + ], + "type": "text", + "content": " lower than the source pool. It shows the pruning method significantly reduces the training set scale while being able to train a model of reasonable accuracy." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 46, + 493, + 287, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 493, + 287, + 624 + ], + "spans": [ + { + "bbox": [ + 46, + 493, + 287, + 624 + ], + "type": "text", + "content": "Composition of searched training sets. We visualize four examples in in Fig. 6. It is clear that searched training sets have different compositions under different targets. If we use AlicePerson as the target, in the searched training set, images from Market and Duke take up " + }, + { + "bbox": [ + 46, + 493, + 287, + 624 + ], + "type": "inline_equation", + "content": "68\\%" + }, + { + "bbox": [ + 46, + 493, + 287, + 624 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 493, + 287, + 624 + ], + "type": "inline_equation", + "content": "26\\%" + }, + { + "bbox": [ + 46, + 493, + 287, + 624 + ], + "type": "text", + "content": ", respectively. In comparison, when using Market as the target, the resulting training set contains, " + }, + { + "bbox": [ + 46, + 493, + 287, + 624 + ], + "type": "inline_equation", + "content": "43\\%" + }, + { + "bbox": [ + 46, + 493, + 287, + 624 + ], + "type": "text", + "content": " images from UnrealPerson, and " + }, + { + "bbox": [ + 46, + 493, + 287, + 624 + ], + "type": "inline_equation", + "content": "34\\%" + }, + { + "bbox": [ + 46, + 493, + 287, + 624 + ], + "type": "text", + "content": " from MSMT. An interesting observation is that synthetic data (UnrealPerson) has a major role under Market as the target. It demonstrates the potential use of synthetic data for real-world target domains." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "content": "Comparison between FPS and random sampling. Both can be used for sampling images resulting from the search step. In Fig. 7, we sample different ratios of the images resulting from the search step. We observe FPS is consistently superior to random sampling, under different selection ratios and targets. Improvement of FPS over random sampling first increase and then decreases, with peak" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 306, + 441, + 487, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 441, + 487, + 453 + ], + "spans": [ + { + "bbox": [ + 306, + 441, + 487, + 453 + ], + "type": "text", + "content": "improvement happening at the " + }, + { + "bbox": [ + 306, + 441, + 487, + 453 + ], + "type": "inline_equation", + "content": "30 - 60\\%" + }, + { + "bbox": [ + 306, + 441, + 487, + 453 + ], + "type": "text", + "content": " ratio." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 306, + 463, + 378, + 475 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 463, + 378, + 475 + ], + "spans": [ + { + "bbox": [ + 306, + 463, + 378, + 475 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 304, + 483, + 545, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 483, + 545, + 615 + ], + "spans": [ + { + "bbox": [ + 304, + 483, + 545, + 615 + ], + "type": "text", + "content": "This paper studies the training data set search problem, for object re-ID applications. Under a certain budget, we aim to find a target-specific training set that gives a competitive re-ID model. We show our method is overall superior to existing strategies such as random sampling and greedy sampling in terms of accuracy on the target domain. We analyze various components in the SnP system and find them to be stable under various source pools and targets. We also point out the correlation between domain gap, dataset size, and training set quality, and would like to further study the data-centric problems in the community." + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 306, + 625, + 416, + 639 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 625, + 416, + 639 + ], + "spans": [ + { + "bbox": [ + 306, + 625, + 416, + 639 + ], + "type": "text", + "content": "7. Acknowledgement" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 304, + 645, + 545, + 706 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 645, + 545, + 706 + ], + "spans": [ + { + "bbox": [ + 304, + 645, + 545, + 706 + ], + "type": "text", + "content": "This work was supported in part by the ARC Discovery Early Career Researcher Award (DE200101283), the ARC Discovery Project (DP210102801), Oracle Cloud credits, and related resources provided by Oracle for Research. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2018. 2" + } + ] + } + ], + "index": 3 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "15578" + } + ] + } + ], + "index": 5 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/LargeKernel3D_ Scaling Up Kernels in 3D Sparse CNNs/55787f59-b334-48a8-9764-98d4fb45ca63_content_list.json b/2023/LargeKernel3D_ Scaling Up Kernels in 3D Sparse CNNs/55787f59-b334-48a8-9764-98d4fb45ca63_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..6a7d2e37a119850beff36759331134b174c36e13 --- /dev/null +++ b/2023/LargeKernel3D_ Scaling Up Kernels in 3D Sparse CNNs/55787f59-b334-48a8-9764-98d4fb45ca63_content_list.json @@ -0,0 +1,1666 @@ +[ + { + "type": "text", + "text": "LargeKernel3D: Scaling up Kernels in 3D Sparse CNNs", + "text_level": 1, + "bbox": [ + 202, + 130, + 767, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Yukang Chen $^{1*}$ Jianhui Liu $^{2*}$ Xiangyu Zhang $^{3}$ Xiaojuan Qi $^{2}$ Jiaya Jia $^{1,4}$ $^{1}$ The Chinese University of Hong Kong $^{2}$ The University of Hong Kong $^{3}$ MEGVII $^{4}$ SmartMore", + "bbox": [ + 101, + 179, + 862, + 223 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 257, + 313, + 273 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recent advance in 2D CNNs has revealed that large kernels are important. However, when directly applying large convolutional kernels in 3D CNNs, severe difficulties are met, where those successful module designs in 2D become surprisingly ineffective on 3D networks, including the popular depth-wise convolution. To address this vital challenge, we instead propose the spatial-wise partition convolution and its large-kernel module. As a result, it avoids the optimization and efficiency issues of naive 3D large kernels. Our large-kernel 3D CNN network, LargeKernel3D, yields notable improvement in 3D tasks of semantic segmentation and object detection. It achieves $73.9\\%$ mIoU on the ScanNetv2 semantic segmentation and $72.8\\%$ NDS nuScenes object detection benchmarks, ranking $1^{st}$ on the nuScenes LIDAR leaderboard. The performance further boosts to $74.2\\%$ NDS with a simple multi-modal fusion. In addition, LargeKernel3D can be scaled to $17\\times 17\\times 17$ kernel size on Waymo 3D object detection. For the first time, we show that large kernels are feasible and essential for 3D visual tasks. Our code and models is available at github.com/dvlab-research/LargeKernel3D.", + "bbox": [ + 75, + 290, + 473, + 608 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 637, + 209, + 652 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "3D Sparse convolutional neural networks (CNNs) have been widely used as feature extractors in 3D tasks, e.g., semantic segmentation [9,24] and object detection [55,65,75]. The advantages of efficiency and convenient usage ensure its important role in various applications, such as autonomous driving and robotics. However, 3D sparse CNNs are recently challenged by transformer-based methods [45,46,79], mainly from the aspect of building effective receptive fields. Both global and local [21,45] self-attention mechanisms are able to capture context information from a large spatial scope. 2D Vision Transformers (ViTs) also emphasize their advantages in modeling long-range dependencies [20,42,51]. In contrast, common 3D sparse CNNs are limited in this regard. It is because the receptive fields", + "bbox": [ + 75, + 662, + 470, + 876 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "of default 3D sparse CNN are constrained by small kernel sizes and spatial disconnection of sparse features (due to the property of submanifold sparse convolution [25]).", + "bbox": [ + 500, + 258, + 890, + 305 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Literature about 2D CNNs [18, 43, 62] presents a series of methods, combined with large kernels, to enlarge the receptive fields and model capacity. ConvNeXt [43] employs $7 \\times 7$ depth-wise convolution as a strong design, combing with other training techniques to challenge its Swin Transformer counterpart [42]. RepLKNet [18] pursues extremely large kernel sizes of $31 \\times 31$ to boost the performance of different tasks. To ensure the effectiveness of RepLKNet [18], additional factors, including depth-wise convolution, are also required. Other work [27] also emphasizes the importance of depth-wise convolution. Due to differences between 3D and 2D tasks, these methods, however, are found not a good solution for 3D sparse CNNs.", + "bbox": [ + 496, + 306, + 892, + 503 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We first analyze the difficulties of 3D large-kernel CNN design in two aspects. The first challenge is efficiency. It is easy to understand that 3D convolution is with the cubic kernel size and computation increases fast. For example, the model size increases $10+$ times when kernels change from $3 \\times 3 \\times 3$ to $7 \\times 7 \\times 7$ . The second difficulty exists in the optimization procedure. 3D datasets may contain only thousands of scenes, which cannot match 2D image benchmarks [15, 40] in terms of scales. In addition, 3D point clouds or voxels are sparse, instead of dense images. Thus, it might be insufficient to optimize the proliferated parameters of large kernels and leads to over-fitting.", + "bbox": [ + 496, + 505, + 893, + 686 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this paper, we propose spatial-wise partition convolution as the 3D large-kernel design. It is a new family of group convolution by sharing weights among spatially adjacent locations, rather than depth-wise convolution [29] of channel-level groups. As shown in Fig. 1, spatial-wise partition convolution remaps a large kernel $(e.g., 7 \\times 7)$ as a small one $(e.g., 3 \\times 3)$ via grouping spatial neighbors, while the absolutely large spatial size remains unchanged. With regard to the efficiency issue, it occupies few model sizes to keep parameters the same as those of small kernels. Moreover, it takes less latency, compared with plain large kernel counterparts. As for the optimization challenge, weight-sharing among spatial dimensions gives parameters more chance to update and overcome the over-fitting issue.", + "bbox": [ + 496, + 689, + 893, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Equal Contribution.", + "bbox": [ + 94, + 886, + 209, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "13488", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/7012f8da40b09801a0e5e833a2187f227f43c1f5e91081c6cb18774651966b7d.jpg", + "image_caption": [ + "Small-kernel sparse conv" + ], + "image_footnote": [], + "bbox": [ + 80, + 88, + 330, + 224 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/cea45d776185dfeb745398c2de74993d87bd89446abaa5826adbbd15361d6f16.jpg", + "image_caption": [ + "Large-kernel sparse conv", + "Figure 1. Sparse convolutions with different kernels. Small-kernel sparse convolution gathers features in a local area. It is efficient but discards sufficient information flow due to feature disconnection and the small scope. Large-kernel sparse convolution is capable of capturing long-range information, at the price of a large number of parameters and computation. Our proposed spatial-wise partition convolution uses large kernel sizes, and shares weights among local neighbors for efficiency. We show 2D features for the simplicity sake." + ], + "image_footnote": [], + "bbox": [ + 346, + 88, + 609, + 224 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/64ace8631b92f635a6d6c2bcd90919523a388b114de5b4a09b66e5602dd7d47b.jpg", + "image_caption": [ + "Spatial-wise partition conv" + ], + "image_footnote": [], + "bbox": [ + 625, + 88, + 890, + 224 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To increase the detail-capturing ability of large kernels [18], we introduce position embeddings for spatial-wise group convolution. It makes notable effects for large kernel sizes. We name the proposed block as spatial-wise large-kernel convolution (SW-LK Conv). We compare the efficiency between plain 3D submanifold sparse convolution and ours, as shown in Tab. 1. Both parameters and latency of the baseline increases dramatically, as its kernel size becomes larger, while ours is far more efficient.", + "bbox": [ + 75, + 348, + 468, + 484 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "SW-LK Conv can readily replace plain convolution layers in existing 3D convolutional networks. We establish large-kernel backbone networks LargeKernel3D on existing 3D semantic segmentation [9] and object detection [16, 75] networks. It achieves notable improvement upon state-of-the-art methods [9, 16, 75], with a small model complexity overhead. Extensive experiments validate our effectiveness on large-scale benchmarks, including ScanNetv2 [13], nuScenes [4], and Waymo [57]. For object detection, LargeKernel3D achieves $72.8\\%$ NDS on nuScenes, ranking $\\mathbf{1}^{st}$ on the nuScenes LIDAR leaderboard. Without bells and whistles, it further improves to $74.2\\%$ NDS in a simple voxel-wise multi-modal fusion manner. More importantly, it is scalable to $17\\times 17\\times 17$ kernel sizes on the large-scale Waymo 3D object detection.", + "bbox": [ + 75, + 484, + 468, + 712 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We visualize the Effective Receptive Fields (ERFs) of plain 3D CNNs and our LargeKernel3D in Fig. 2. It shows that deep small-kernel networks are also constrained by limited ERFs, since sparse features are spatially disconnected. Note that our large-kernel networks elegantly resolve this issue. For the first time, we show that large-kernel CNN designs become effective on essential 3D visual tasks.", + "bbox": [ + 75, + 713, + 468, + 819 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 837, + 218, + 852 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Convolutional Large-kernel Networks Large-kernel setting has been commonly used in 2D convolutional net", + "bbox": [ + 75, + 869, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "works [18, 43, 68]. ConvNeXt [43] combines various training techniques and large kernel sizes, to compete with Swin Transformer [42]. RepLKNet [18] is a specific work that focuses on large-kernel designs. It reveals that the large kernel sizes are more beneficial to tasks of object detection and semantic segmentation than image classification. GCNs [47] also show improvement from large-kernel designs on semantic segmentation. There are methods approximating large kernel sizes using implicit techniques, including Fourier domain transformation [52], and continuous functions [53]. Other methods change kernel shapes to enlarge receptive fields using dilated convolutions [5, 76], deformable convolutions [14, 81] and active convolutions [31]. These schemes sparsify kernels, and is hard to capture the original sparse features in 3D deep learning.", + "bbox": [ + 496, + 348, + 890, + 575 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3D Feature Extractors A key challenge in 3D tasks [32,38] is to learn effective representation from the sparse and non-uniformed 3D geometric data, e.g., point clouds. In general, there are two kinds of 3D feature extractors. The first is to learn on point cloud directly, using a series of PointNet networks [48, 49]. The sampling and grouping operations in PointNet++ [49] are also time-consuming. Followups [46, 79] use grid-sampling or scene-partition to save computation in each forward and combine results from multiple runs. The second is to process point clouds with voxelization and apply 3D sparse CNNs. Due to its efficiency advantages, this stream of methods has been widely used in various 3D tasks, such as 3D segmentation [9-11, 33] and backbone networks in 3D object detectors [16, 26, 55, 64].", + "bbox": [ + 496, + 582, + 890, + 792 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The spatial group convolution (SGC) [78] is relevant to the proposed spatial-wise partition convolution. SGC is originally designed for the task of 3D scene completion. They both conduct the partition operation spatially. The difference is also essential and clear. Our method partition kernel weighs while SGC splits input features into groups. In terms of targets, SGC focuses more on efficiency improve", + "bbox": [ + 496, + 795, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "13489", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "table", + "img_path": "images/39aa5bb89c62206e710d3422070dcf674f6301eeb1e5edfdf2f9053594d98205.jpg", + "table_caption": [ + "Table 1. Efficiency comparison between plain 3D sparse convolution and our SW-LK Conv. The baseline is a submanifold sparse convolutional layer with input and output channels 16. The input data is a sparse tensor with 80,000 voxels randomly scattered and batch size 1. We test all latencies on a single 2080Ti GPU by an average of 10 times running, after a warm-up start of additional 10 times." + ], + "table_footnote": [], + "table_body": "
Kernel Size3×3×35×5×57×7×79×9×911×11×1113×13×1315×15×1517×17×17
PlainParams6.9 K32.0 K87.8 K186.6 K340.7 K562.4 K864.0 K1.3 M
Latency2.5 ms4.2 ms8.9 ms17.5 ms31.1 ms55.1 ms81.1 ms106.3 ms
OursParams-8.9 K12.4 K18.6 K28.2 K42.1 K60.9 K85.5 K
Latency-3.4 ms3.9 ms4.8 ms6.2 ms8.4 ms11.4 ms15.8 ms
", + "bbox": [ + 89, + 141, + 877, + 224 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "ment by changing feature sparsity in each spatial group, while our method is to facilitate large kernels in 3D tasks. Further analysis and comparisons are given in experiments.", + "bbox": [ + 75, + 260, + 470, + 306 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Vision Transformer Vision transformers that conduct attention computation in local areas or windows share a similar spirit with large-kernel models [18]. Swin Transformers [42] capture features in shifted windows with sizes from 7 to 12. Its variants [19, 41] show that larger window sizes are beneficial to performance. Focal Transformer [71] captures fine-grained local attention with adaptive patch sizes. SST [21] and Stratified Transformer [34] apply window-based self-attention on 3D detection and segmentation.", + "bbox": [ + 75, + 311, + 468, + 450 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Position Encoding Since the self-attention in transformers is permutation-equivalent, position encoding is well-designed for imbuing the network with the position information. It can be grouped into two streams of absolute and relative position encoding. For the first group, positions are encoded in a precise manner. Specifically, encoding [63] is generated with the sinusoidal functions of different frequencies. They are then added to the input. In contrast, relative position encoding [54] takes the relative relationship into consideration. It can naturally handle longer sequences and is more scalable. Most work [3, 50, 66, 73] computes the relative distance between tokens and applies implicit encoding using learnable transformations. Besides, the literature [12] shows that convolution with padding can provide effective relative position information for relative position encoding. In addition to transformers, the recent work [72] also shows that position embedding is beneficial to the CNNs with fourier transformation.", + "bbox": [ + 75, + 455, + 468, + 728 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Considering that our spatial-wise partition convolution divides the kernel into different portions in pursuit of higher efficiency. The position information may be blurred due to weight sharing in each portion. We thus use relative position encoding as a bias to supplement the lost position information. More details are provided in Sec. 4.", + "bbox": [ + 75, + 729, + 468, + 821 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Revisiting 3D Sparse CNNs", + "text_level": 1, + "bbox": [ + 76, + 837, + 333, + 854 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Preliminary 3D sparse CNNs consist of 3D sparse convolutions, which are typically regular and submanifold sparse", + "bbox": [ + 75, + 869, + 470, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "convolutions [25]. We formulate 3D sparse convolutions in Eq. (1). Given a set of sparse input features $\\{\\mathbf{x}_{p\\in P}\\}$ with a number of $c_{\\mathrm{in}}$ channels, the position of each feature $p\\in P$ sparsely distributes in 3D space. We process these features by a convolution with kernel weights $\\mathbf{w}\\in \\mathbb{R}^{|K| \\times c_{\\mathrm{in}} \\times c_{\\mathrm{out}}}$ . For example, in the 3D coordinate space, $\\mathbf{w}$ contains $c_{\\mathrm{in}} \\times c_{\\mathrm{out}}$ spatial kernels with size 3 and $|K| = 27$ . The convolution process at the output position $\\bar{p}$ is represented as", + "bbox": [ + 496, + 260, + 893, + 397 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {y} _ {\\bar {p}} = \\sum_ {k \\in K} \\mathrm {w} _ {k} \\cdot \\mathrm {x} _ {\\bar {p} + k}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 620, + 407, + 890, + 440 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $k$ is an 3D offset distance from $\\bar{p}$ . $\\bar{p} + k$ is the location around center $\\bar{p}$ . It enumerates all discrete locations in the kernel space $K$ where sparse features $\\mathbf{x}_{\\bar{p} + k}$ exist.", + "bbox": [ + 496, + 449, + 893, + 497 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Convolution Types Regular sparse convolutions enlarge their output positions by dilating each input position $p \\in P$ to the kernel shape $K$ . It dramatically decreases feature density and increases the computational burden. Thus, regular sparse convolutions with stride 2 are only employed at the first layer in each stage for down-sampling. Submanifold sparse convolutions, in contrast, fix their output positions $\\bar{p}$ identical to input positions $p \\in P$ , which preserves the computation cost at low levels. Please refer to the original paper [25] for more details.", + "bbox": [ + 496, + 501, + 893, + 652 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Due to the efficiency advantage, submanifold sparse convolutions dominate most layers of 3D CNNs, except for the down-sampling layers. However, limited by the small local scope, it misses sufficient information flow for the spatially disconnected features. Increasing kernel sizes becomes a potential solution to relieve this issue.", + "bbox": [ + 496, + 652, + 893, + 743 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Obstacles in 3D Large Kernels Efficiency is the first issue in 3D large-kernel CNNs. When we increase kernel sizes, the amount of parameters and computational burden grows much faster than those of 2D CNNs. For instance, the parameter amount in one 3D convolutional layer increases from $27 \\cdot C_{in \\cdot out}$ to $343 \\cdot c_{in} \\cdot c_{out}$ , given its kernel size changing from 3 to 7. It is thus clear that naively enlarging 3D kernels is unreasonable.", + "bbox": [ + 496, + 750, + 893, + 869 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Optimization difficulty is the second obstacle. The booming parameters require sufficient data for learning. How-", + "bbox": [ + 496, + 869, + 893, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "13490", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/8f4373936a081c48af3a50c9f77409e663af35690da8ce009898d2a09f2324bf.jpg", + "image_caption": [ + "(a) Plain 3D CNN" + ], + "image_footnote": [], + "bbox": [ + 80, + 89, + 230, + 186 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/90ca9a1279931199f5c1b34c13b953d2f94afa692ea8e8f87c5fd04ea3b59ca0.jpg", + "image_caption": [ + "(b) Plain 3D CNN - 2x" + ], + "image_footnote": [], + "bbox": [ + 230, + 90, + 379, + 186 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/9d2afaa194ef9ec7eea68f981ef69034c946b11a49d48e3f2d7d94fd49e98b55.jpg", + "image_caption": [ + "(c) LargeKernel3D", + "Figure 2. Effective Receptive Fields (ERF) of plain 3D CNN, plain 3D CNN - $2 \\times$ , and our LargeKernel3D for 3D object detection. The plain 3D CNN backbone has insufficient ERF size, which hardly covers a nearby car. Plain 3D CNN - $2 \\times$ is a deeper version with its layers doubled in each stage. More layers help little in ERF, as the disconnection between sparse features. Our LargeKernel3D obtains large ERF at both the object centers (left) and edges (right), capturing context information. More illustrations are provided in the appendix. The figure is best viewed in color and by zoom-in." + ], + "image_footnote": [], + "bbox": [ + 379, + 90, + 529, + 186 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/bc9ae4b31ba796d0c855e673deeb60a0c624ad6ceeb8ab53d47c48cacc87c6ab.jpg", + "image_caption": [ + "Feature of interest" + ], + "image_footnote": [], + "bbox": [ + 534, + 90, + 771, + 186 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/29e089707ad2b981be90e1ac90c16b08cabc705cb82ee42a70005524220d3b3a.jpg", + "image_caption": [ + "Magnitude of ERF" + ], + "image_footnote": [], + "bbox": [ + 771, + 90, + 888, + 186 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "ever, 3D datasets are commonly not in that large scale as 2D benchmarks. For example, ImageNet [15] contains millions of images, while 3D datasets commonly contain only no more than one thousand scenes. The over-fitting issue gradually deteriorates the performance when increasing kernel sizes from $3 \\times 3 \\times 3$ to $7 \\times 7 \\times 7$ in MinkowskiNet-34 [9].", + "bbox": [ + 75, + 321, + 467, + 412 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Previous 2D knowledge is not helpful in 3D large-kernel CNNs. Recent 2D methods [18, 43] show some helpful components in large-kernel CNNs, including depth-wise convolutions [29], layer normalization [1], GELU [28] activation. We examine these popular components and find that they are either ineffective or even harmful in 3D CNNs. To demonstrate this finding, we use MinkowskiNet-34 [9] to benchmark and train on the 3D semantic segmentation dataset of ScanNetv2 [13]. We change the original activation function from ReLU to GELU, batch normalization to layer normalization, and plain convolution to depth-wise operation, respectively. Directly using these components makes the final system yield performance drop on both small and large kernel networks. It requires us to seek other ways to construct 3D large-kernel CNNs.", + "bbox": [ + 75, + 412, + 467, + 640 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. 3D Large-kernel Convolutional Network", + "text_level": 1, + "bbox": [ + 76, + 654, + 437, + 671 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Spatial-wise Partition Convolution", + "text_level": 1, + "bbox": [ + 76, + 680, + 377, + 695 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "A standard convolution kernel can be viewed as a 3D matrix, which consists of input channels $C_{\\mathrm{in}}$ , output channels $C_{\\mathrm{out}}$ , and the spatial kernel dimension $|K|$ . Taking kernel size as $k$ , the volume of spatial kernel dimension $|K| = k \\times k$ for 2D convolutions and $k \\times k \\times k$ for 3D convolutions. Depth-wise convolutions share weights along channel dimensions, where group numbers equal to input channels. Point-wise convolutions fix kernel size as 1, which is common as a conjunction layer to depth-wise convolutions to adjust output channels.", + "bbox": [ + 75, + 703, + 467, + 853 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Different from 2D methods, which rely on depthwise convolutions for performance boosting [27, 43] and accuracy-FLOPs trade-offs [18], we empirically find that", + "bbox": [ + 75, + 854, + 467, + 900 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/6e602c8795741cc5cc6ecc030aa488440413ecefcbf2e328442422ba2e6a648c.jpg", + "image_caption": [ + "Figure 3. Illustration on spatial-wise partition convolution. In the plain large-kernel convolution, due to the sparsity of input features, only a small proportion of weights are involved and updated in each training step. The spatial-wise partition convolution relieves this issue by sharing weights among spatial neighbors. It increases the chance for weights to be optimized. During inference, we reformulate the spatial-wise partition convolutions into small ones, with feature assignment in a large scope." + ], + "image_footnote": [], + "bbox": [ + 503, + 320, + 792, + 422 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/eb332a305d5b6a514cb12c507458607ae072f4338c1daca62578f81b37087a71.jpg", + "image_caption": [ + "feature" + ], + "image_footnote": [], + "bbox": [ + 823, + 325, + 839, + 335 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/297098d66294db1a446494caf032616047ac976bf79953b61e557dc28900cad8.jpg", + "image_caption": [ + "weight" + ], + "image_footnote": [], + "bbox": [ + 823, + 347, + 844, + 362 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/e5f5173fb694520f7d92b37a01f8d0d9707b714a396416337803e50819d98c57.jpg", + "image_caption": [ + "group", + "assign" + ], + "image_footnote": [], + "bbox": [ + 818, + 372, + 849, + 397 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/0020c31d6aa5fe563383023250eaa512b46318323c5bf1fd3d324024d14aa3be.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 818, + 407, + 836, + 417 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "depth-wise convolutions are not beneficial to 3D tasks, no matter whether point-wise convolutions are included.", + "bbox": [ + 498, + 592, + 888, + 621 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We instead propose spatial-wise partition convolution for 3D large-kernel CNNs. It shares weights among spatial dimension $K$ on convolutional kernels, instead of among channel dimension. It is also different from SGC [78], which partitions spatial groups on input features. Specially, in Eq. (1), $w_{k}$ shares the same values in a local area $k \\in K$ . We thus group the original large-kernel convolution from $7 \\times 7$ into $3 \\times 3$ , by sharing weights among spatial neighbors. Spatial-wise partition convolution is specially designed for 3D tasks and has the following advantages in terms of efficiency and performance.", + "bbox": [ + 496, + 625, + 890, + 792 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Regarding efficiency, when naively enlarging the kernel size from $3 \\times 3 \\times 3$ to $7 \\times 7 \\times 7$ on MinkowskiNet-34 [9], both model size and latency have a sharp increase by multiple times. In contrast, our spatial-wise partition convolution avoids increasing parameters and introduces limited latency overhead. The advantage of our method over plain large kernels attributes to the specific implementation of sparse", + "bbox": [ + 496, + 795, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "13491", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/a71e09d5a750e504684d67c2d222f2532206e293c0b72fa47f4ad4548a7f4fcc.jpg", + "image_caption": [ + "Input & Weight" + ], + "image_footnote": [], + "bbox": [ + 117, + 90, + 240, + 186 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/bba440df8df5086009492dd08de536228cb53b44260915b5a4f79bba292fa875.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 256, + 128, + 290, + 152 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/f21bf1001bad0c6cfbc2680ad24c2b895eb89c3058b81e4435fc802a93b6a022.jpg", + "image_caption": [ + "Position Encodings" + ], + "image_footnote": [], + "bbox": [ + 308, + 93, + 431, + 186 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/6d57a0400b83600c0c4d93bf62896aef93de291d47707f20ce88cef87ba8f6b2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 449, + 126, + 490, + 152 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/37659452c43261793e96a5d9aed1fd48507de048b76bc2b5d0e060cf63478652.jpg", + "image_caption": [ + "Output & Weight" + ], + "image_footnote": [], + "bbox": [ + 508, + 94, + 627, + 186 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/aaeaaca078c9d53f1150a74f595190e6f0fa75329a638660ff568122d065a23b.jpg", + "image_caption": [ + "Sparse feature" + ], + "image_footnote": [], + "bbox": [ + 686, + 97, + 704, + 109 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/e5c02c82c9d8f99cd794fc38494989db12c351fc8407a63fae44dee0c0f438c5.jpg", + "image_caption": [ + "Conv weight" + ], + "image_footnote": [], + "bbox": [ + 686, + 116, + 709, + 131 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/1b0cba53db37c124ef02e54263dd5b7679f7ac08dad302d7fc74235082b76c5b.jpg", + "image_caption": [ + "Position encoding" + ], + "image_footnote": [], + "bbox": [ + 686, + 141, + 709, + 157 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/74d9a1316e66b36722b961b932360297b24a07ddb10e61e6235837b96fcfef0a.jpg", + "image_caption": [ + "Spatial-wise group", + "Figure 4. Structure of spatial-wise large-kernel convolution (SW-LK Conv). It consists of a large-kernel spatial-wise partition convolution and a learnable position embedding. The position embedding is used to make up the detail-capturing ability of large kernels." + ], + "image_footnote": [], + "bbox": [ + 679, + 165, + 718, + 194 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "convolution. For a spatial-wise partition convolution, we directly use the small-kernel layer during inference, and enlarge its feature-assign areas to the large-kernel scope. As shown in Fig. 3, thanks to the weight-sharing operation, it much saves the multiplication, e.g., from 343 to 27 times. We implement this operation upon the open-sourced spconv library and omit the details here. Tab. 4 shows that our implementation on spatial-wise partition convolution is far more efficient than the plain large-kernel baseline. The optimization difficulty of large-kernel CNNs is relieved with the help of spatial-wise partition convolutions, which constrains model sizes to a limited number. It avoids requiring a large amount of data for training and the over-fitting issue.", + "bbox": [ + 75, + 284, + 472, + 479 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Kernel-wise Position Encoding", + "text_level": 1, + "bbox": [ + 76, + 497, + 348, + 513 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Considering that the spatial-wise partition convolution is designed in a sharing weights manner against the spatial sparsity. Although this design is efficient, there is still an issue: voxels within an area share the same weight, which results in local details blurred. This phenomenon is further amplified with an increase of kernel sizes. To address this problem, we propose the kernel-wise position embedding. We illustrate this design in Fig. 4.", + "bbox": [ + 75, + 523, + 468, + 645 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Particularly, we initialize position weights $\\mathrm{e} \\in \\mathbb{R}^{K \\times c_{\\mathrm{in}}}$ , which corresponds to the convolution kernel. During the convolution process, we let the input features query the position weights of the equivalent position and add them together. This process modifies Eq. (1) to", + "bbox": [ + 75, + 646, + 468, + 723 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {y} _ {\\bar {p}} = \\sum_ {k \\in K} \\mathrm {w} _ {k} \\cdot \\left(\\mathrm {x} _ {\\bar {p} + k} + \\mathrm {e} _ {k}\\right). \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 173, + 744, + 468, + 779 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "This simple design essentially adds bias with relative position information to the input features. There is almost no extra calculation and additional parameters. It is a decent solution to the position insensitivity problem caused by sharing weights, especially for the extremely large kernels, e.g., $17 \\times 17 \\times 17$ . For more experimental results and details, please refer to the Sec. 5.", + "bbox": [ + 75, + 794, + 470, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Large-kernel Architecture", + "text_level": 1, + "bbox": [ + 498, + 282, + 738, + 299 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Following the above designs and observations, we now describe the architectures of our large-kernel 3D CNNs. We readily replace the plain 3D submanifold sparse convolution [25] layers with our SW-LK Conv in existing 3D backbones for semantic segmentation and object detection.", + "bbox": [ + 496, + 306, + 890, + 381 + ], + "page_idx": 4 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "3D Semantic Segmentation The architectures of LargeKernel3D for 3D semantic segmentation resemble MinkowskiNet [9], including 1 stem layer and 8 stages. The stem layer is a $5 \\times 5 \\times 5$ submanifold convolution. The first 4 stages account for down-sampling and the last 4 stages are for up-sampling. As for the U-Net structure, the first 4 features are concatenated into the up-sampling stages. We replace the original layers in MinkowskiNet-34 [9] by SW-LK Convs, where spatial-wise $7 \\times 7 \\times 7$ convolutions is grouped into $3 \\times 3 \\times 3$ splits. By default, other hyper-parameters, including channels and block numbers, follow MinkowskiNet-34 [9].", + "3D Object Detection The typical backbone networks in 3D object detectors [16, 55, 75] consist of 1 stem layer and 4 stages. A $3 \\times 3 \\times 3$ submanifold convolution [25] layer serves as the stem. In each stage, except for the first one, there is a sparse convolutional layer with stride 2 for down-sampling. We substitute other plain blocks with SW-LK Convs. For models on nuScenes dataset, we find that $7 \\times 7 \\times 7$ kernel sizes are enough. They both use the $3 \\times 3 \\times 3$ spatial-wise groups. For models on Waymo dataset, kernel sizes are scalable to $17 \\times 17 \\times 17$ . We remain the last stage of backbone network as the original, because receptive fields have already been sufficiently enlarged in the front stages. We keep these hyper-parameters unchanged by the default settings in baseline detectors [16, 75]. We include these detailed numbers in appendix." + ], + "bbox": [ + 496, + 387, + 893, + 801 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 500, + 816, + 632, + 832 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.1. Experimental Setting", + "text_level": 1, + "bbox": [ + 500, + 840, + 699, + 857 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3D Semantic Segmentation ScanNetv2 [13] is a large-scale benchmark in 3D semantic segmentation. It con", + "bbox": [ + 500, + 869, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "13492", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/1fac9e476e3e811296d0be5c01abc9e394ff00adcc3db50b72628029bfa9eea5.jpg", + "table_caption": [ + "Table 2. Ablations on various techniques and kernel sizes on MinkowskiNet-34 and ScanNetv2. LN denotes the layer normalization. DW Conv denotes the depth-wise convolution." + ], + "table_footnote": [], + "table_body": "
KernelBaseline+GELU+LN+DW Conv+PWOurs
3×3×371.770.266.870.670.7-
7×7×768.668.465.068.768.773.5
", + "bbox": [ + 81, + 143, + 468, + 185 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/055e648c3037fa0c7eef7984670f3ddc0d196866769e0ede887dc7b05a821719.jpg", + "table_caption": [ + "Table 3. Ablations on group convolution on ScanNetv2." + ], + "table_footnote": [], + "table_body": "
KernelBaselineGroup 24816DWOurs
3x3x371.771.571.270.770.670.6-
7x7x768.668.869.268.868.768.773.5
", + "bbox": [ + 81, + 239, + 468, + 282 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/c0e963d82a172d7d1a9eeb033f8afda4868ac32c74e61a1c484ca6a989b5e03a.jpg", + "table_caption": [ + "Table 4. Comparisons with relevant convolutional schemes on ScanNetv2. Baseline is a MinkowskiNet-34 network. All models listed are trained in the same training hyper-parameters." + ], + "table_footnote": [], + "table_body": "
MethodParamsFLOPsLatencymIoU
Baseline37.9 M182.8 G108 ms71.7
+ Kernel 5×5×5170.3M537.5 G212 ms70.7
+ Kernel 7×7×7465.0M1089.5 G487 ms68.6
Dilate conv37.9M100.1 G98 ms64.6
Pooling + Dilate37.9M183.2 G115 msnan
Spatial group [78]37.9M127.2 G96 ms70.0
Deformable conv42.5M250.1 G238 ms72.0
LargeKernel3D-T38.4M171.4 G111 ms72.8
LargeKernel3D40.2M240.0 G145 ms73.5
", + "bbox": [ + 81, + 364, + 468, + 507 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/0397193a099f125e35616423be7ad15283e4d8e29999685de29817be9a405248.jpg", + "table_caption": [ + "Table 5. Results on other backbone networks andScanNetv2." + ], + "table_footnote": [], + "table_body": "
ModelBaseline+OursΔ
MinkowskiNet-14 [9]67.069.7+2.7
MinkowskiNet-18 [9]69.571.5+2.0
SparseConvNet [24]69.371.2+1.9
", + "bbox": [ + 98, + 561, + 449, + 627 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "tains 1,201 indoor RGB-D scenes for training, 312 scenes for validation, and 100 scenes for testing. Semantic labels in 20 categories are annotated. We train our models with the default settings in MinkowskiNet [9], including training hyper-parameters and data augmentations. We evaluate models in the mean Intersection over Union (mIoU) metric. Detailed experimental settings, including network structures and training details, are listed in the appendix.", + "bbox": [ + 75, + 666, + 468, + 787 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3D Object Detection nuScenes, and Waymo are all popular 3D object detection benchmarks. nuScenes is a large dataset and contains 1,000 driving sequences in total. Among them, there are 700 scenes split for training, 150 scenes for validation, and 150 scenes for testing. It contains LIDAR, camera, and radar sources with a complete $360^{\\circ}$ environment. We evaluate our methods on both LIDAR-only and LIDAR-", + "bbox": [ + 75, + 794, + 470, + 901 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/89d684f59419ed57c39b9181fcbd30157e001b7497cfb61498e834c6b02eaad3.jpg", + "table_caption": [ + "Table 6. Effects of the spatial-wise partition manners on SW-LK Conv and ScanNetv2. Center group means the size of central area. Shifting is to translate the center position by 1 in all 3 dimensions." + ], + "table_footnote": [], + "table_body": "
Center group1×1×11×1×13×3×35×5×5
ShiftingX✓XX
mIoU73.566.870.668.2
", + "bbox": [ + 501, + 142, + 890, + 196 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/7fc7c8ef730b291a98ba8f2048a05832f95c04096b8dd4e76c94b2daa3ab9850.jpg", + "table_caption": [ + "Table 7. Improvement over various kernel sizes on LargeKernel3D upon CenterPoint, training on 1/5 Waymo training set and evaluate on the validation set. $\\Delta$ means the improvement from the kernel 3 baseline. L1 and L2 means LEVEL_1 and LEVEL_2 mAP." + ], + "table_footnote": [], + "table_body": "
KernelVehiclePedestrianCyclist
L1L2L1L2L1L2
Baseline70.962.971.563.569.166.5
7×7×771.963.871.763.770.467.8
11×11×1172.264.271.863.970.268.3
15×15×1572.764.673.865.870.868.2
17×17×1773.265.174.166.071.068.1
Δ2.3↑2.2↑2.6↑2.5↑1.9↑1.6↑
", + "bbox": [ + 504, + 292, + 890, + 416 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/d2d23d68d3adc2407a576eb8ecee6069996309380c22e486e6df00cc4f4b2581.jpg", + "table_caption": [ + "Table 8. Effects of position embedding (PE) in the mAP of vehicle detection on Waymo validation set." + ], + "table_footnote": [], + "table_body": "
KernelPELatencyLEVEL_1LEVEL_2
3×3×3-109 ms70.962.9
7×7×7×120 ms71.663.4
✓122 ms71.963.8
17×17×17×158 ms71.563.3
✓164 ms73.265.1
", + "bbox": [ + 503, + 483, + 883, + 579 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "RGB fusion settings. The main evaluation metrics are mAP and nuScenes detection score (NDS). Waymo [57] dataset also contains 1,000 sequences in total, with 798 for training and 202 for validation. For Waymo dataset, we use 1/5 training data for the ablation study and full training set for main results. Results in Waymo are evaluated on difficulty LEVEL_1 and LEVEL_2 objects. In experiments, we validate our networks on state-of-the-art detection framework of CenterPoint [75] on nuScenes [4] and Waymo [57].", + "bbox": [ + 496, + 617, + 890, + 755 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Ablation Studies", + "text_level": 1, + "bbox": [ + 500, + 763, + 663, + 780 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Usefulness of 2D CNN Techniques We first validate the techniques that have proven effective on 2D CNNs, including layer normalization [1], depth-wise convolution [29, 43], and GeLU [28]. We conduct experiments on MinkowskiNet-34 [9] on the ScanNet [13] semantic segmentation dataset, as shown in Tab. 2. Kernel $7 \\times 7 \\times 7$ means modifying kernel sizes in all stages to 7. All these", + "bbox": [ + 496, + 794, + 890, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "13493", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/4dbdff16721225f4cb43c9228674951291d379eb43d63d67e21c0035bc6ba270.jpg", + "table_caption": [ + "Table 9. Comparison with other methods on nuScenes test split. $\\ddagger$ means flipping and rotation testing-time augmentations." + ], + "table_footnote": [], + "table_body": "
MethodNDSmAPCarTruckBusTrailerC.V.PedMotBycT.C.Bar
PointPillars [35]45.330.568.423.028.223.44.159.727.41.130.838.9
3DSSD [74]56.442.681.247.261.430.512.670.236.08.631.147.9
CBGS [80]63.352.881.148.554.942.910.580.151.522.370.965.7
CenterPoint [75]65.558.084.651.060.253.217.583.453.728.776.770.9
HotSpotNet [7]66.059.383.150.956.453.323.081.363.536.673.071.6
CVCNET [6]66.658.282.649.559.451.116.283.061.838.869.769.7
UVTR-L [37]69.763.986.352.262.859.733.784.568.841.174.774.9
VISTA [17]69.863.084.455.163.754.225.182.870.045.478.571.4
Focals Conv [8]70.063.886.756.367.759.523.887.564.536.381.474.1
TransFusion-L [2]70.265.586.256.766.358.828.286.168.344.282.078.2
LargeKernel3D70.665.485.553.864.459.529.785.972.746.879.975.5
LargeKernel3D‡72.868.786.758.567.762.731.988.577.154.982.376.6
LargeKernel3D-F‡74.271.287.760.169.366.034.389.481.360.286.777.4
", + "bbox": [ + 81, + 114, + 893, + 354 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "techniques bring no obvious benefit to baseline networks. In contrast, SW-LK Conv introduces clear improvement upon these strong networks. We also show the effects of group convolution with different group numbers in Tab. 3.", + "bbox": [ + 75, + 392, + 470, + 452 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparisons with Relevant Schemes We compare both performance and efficiency in Tab. 4 using various existing schemes to enlarge receptive fields. Dilated Conv [5] contains $3 \\times 3 \\times 3$ kernel parameters. It dilates to $7 \\times 7 \\times 7$ spatial sizes. Pooling + Dilated Conv inserts a 3D average pooling layer before the dilated convolutions to enlarge receptive fields. Spatial group conv is implemented, following the settings in the original paper [78]. We extend Deformable Conv [14] to 3D offset prediction, following [61]. Latencies are measured on an NVIDIA 2080ti GPU. It shows that none of these related schemes present better performance than the baseline. One reason for the low performance of dilation and deformable convolutions is that they tend to factorize the original dense kernels into sparse ones, which cause more information loss when applied to sparse 3D features than their 2D counterparts. Our LargeKernel3D achieves the best performance among these methods. In addition, we also build a tiny version, LargeKernel3D-T, which has half channel numbers in the last two stages. It introduces almost no additional computation overhead to baseline, but still has notable performance improvement. Except for the MinkowskiNet-34, we also show our effects on other backbone networks in Tab. 5.", + "bbox": [ + 75, + 465, + 468, + 811 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Spatial-wise Group Partition Manner We ablate the effects of different spatial-wise group partition manners in Tab. 6. We study the size of central groups and center shifting. This ablation study is conducted on the LargeKernel3D and the Scannetv2 dataset. We find that both large central", + "bbox": [ + 75, + 824, + 468, + 902 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/8a69a9215f18f03f6f49b66477e2d718d9a85d9d5055fad5a28ec97eef435b8b.jpg", + "table_caption": [ + "Table 10. Comparison on ScanNetv2 mIoU on 3D semantic segmentation. † Sliding-window testing." + ], + "table_footnote": [], + "table_body": "
MethodLatencyvaltest
PointCNN [36]--45.8
PointNet++ [49]-53.555.7
RandLA-Net [30]--64.5
PointConv [67]80 ms61.066.6
PointASNL [69]-63.566.6
KPConv [61]-69.268.6
FusionNet [77]--68.8
Point Transformer† [79]1012 ms70.6-
Fast Point Transformer [46]298 ms72.1-
SparseConvNet [24]-69.372.5
Stratified Transformer† [34]1624 ms74.373.7
MinkowskiNet-34108 ms71.7
+ LargeKernel3D14573.573.9
", + "bbox": [ + 503, + 429, + 883, + 650 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "sizes and center shifting hurt the performance. As the center sizes enlarge from $1 \\times 1 \\times 1$ to $5 \\times 5 \\times 5$ , the accuracy sharply drops. Because submanifold sparse convolution [25] always aligns each individual voxel feature at its kernel center, we suppose that central features should maintain distinct and clean. Therefore, we keep the center size as $1 \\times 1 \\times 1$ without shifting, as a default setting.", + "bbox": [ + 496, + 680, + 890, + 787 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Further Enlarging Kernel Sizes We show that LargeKernel3D is scalable to kernel sizes $17 \\times 17 \\times 17$ on the outdoor dataset Waymo [57] in Tab. 7 with baseline kernel $3 \\times 3 \\times 3$ . Models in this ablation are trained on $1/5$ training data and evaluated on the full validation set. Results with full training data are compared in Tab. 11. It shows that the mAP on all categories increases by around $2\\%$ . This setting demon-", + "bbox": [ + 496, + 794, + 892, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "13494", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/21a9c9b0b8471b765b0ea2be022ad6b821bf8c405a97c032ca418046d04f4747.jpg", + "table_caption": [ + "Table 11. Performance of vehicle detection on the Waymo val split. All models listed take LIDAR-only input and single frames, without any test-time augmentations or model ensemble." + ], + "table_footnote": [], + "table_body": "
MethodLEVEL_13D AP / APHLEVEL_23D AP / APH
VoTr-SSD [45]68.99 / 68.3960.22 / 59.69
PointPillars [75]72.08 / 71.5363.55 / 63.06
SECOND [70]72.27 / 71.6963.85 / 63.33
RangeDet [23]72.85 / 72.3364.03 / 63.57
SST [22]74.22 / 73.7765.47 / 65.07
VoTr-TSD [45]74.95 / 74.2565.91 / 65.29
RSN [59]75.1 / 74.666.0 / 65.5
Voxel RCNN [16]75.59 / ——66.59 / ——
LIDAR-RCNN [39]76.0 / 75.568.3 / 67.9
SST [22]76.22 / 75.7968.04 / 67.64
Pyramid RCNN [44]76.30 / 75.6867.23 / 66.68
Part-A2-Net [56]77.05 / 76.5168.47 / 67.14
PV-RCNN [55]77.51 / 76.8968.98 / 68.41
SWFormer [58]69.2 / 68.880.9 / 72.7
CenterPoint [75]76.59 / 76.0568.85 / 68.35
+ LargeKernel3D78.07 / 77.6169.81 / 69.38
", + "bbox": [ + 83, + 143, + 464, + 422 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "strates that a large-scale dataset is a key to unlocking the potential and capability of large kernel methods. In addition, we also try to extend the kernel size to $19 \\times 19 \\times 19$ , but obtain no further gains.", + "bbox": [ + 75, + 465, + 468, + 527 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effects of Position Embedding In LargeKernel3D, position embedding is introduced to relieve the feature-blurring issue caused by weight-sharing. We ablate its effects in Tab. 8, in terms of both latency and performance. Position embedding introduces limited latency overhead on both kernel $7 \\times 7 \\times 7$ and $17 \\times 17 \\times 17$ models. In terms of performance, its effects on the $7 \\times 7 \\times 7$ model are a bit marginal, but essential on the $17 \\times 17 \\times 17$ model, which has larger kernel sizes and suffers from feature blurring.", + "bbox": [ + 75, + 532, + 468, + 670 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Shrinking Kernels During Inference For the spatial-wise partition convolution, we can shrink kernels into small ones during inference. As shown in Tab. 4, the latency of LargeKernel3D is $145\\mathrm{ms}$ on ScanNetv2. It degrades to $514\\mathrm{ms}$ with the same $73.5\\%$ mIoU, if we disable shrinking.", + "bbox": [ + 75, + 676, + 468, + 753 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.3. Main Results", + "text_level": 1, + "bbox": [ + 76, + 763, + 215, + 779 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "3D Semantic Segmentation We make comparisons with other 3D semantic segmentation methods on the ScanNetv2 dataset in Tab. 10. Our method surpasses others on test split. MinkowskiNet [9] is already a state-of-the-art method in ScanNetv2. Our SW-LK Conv further improves its performance. Our method is also superior to transformer-based methods [46,79]. Stratified Transformer [34] uses a sliding-", + "bbox": [ + 75, + 794, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "window testing technique† and splits integrated scenes into overlapped parts. The method tests each part one by one and then ensembles results together, taking hours on evaluation. Moreover, our results are better on the test split.", + "bbox": [ + 496, + 90, + 890, + 152 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "3D Object Detection We compare our LargeKernel3D upon CenterPoint [75] with previous methods on the test split of the nuScenes [4] dataset in Tab. 9. LargeKernel3D improves CenterPoint [75] to $70.6\\%$ and $72.8\\%$ NDS, with and without test augmentation, both outperforming other LIDAR methods. The multi-modal modal LargeKernel3D-F further improves to $74.2\\%$ NDS and $71.2\\%$ mAP. The fusion module directly follows a simple painting-based manner [8]. Results on the val split is shown in the appendix.", + "bbox": [ + 496, + 159, + 890, + 297 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We also show the effectiveness of LargeKernel3D model on the vehicle detection of Waymo [57] validation set in Tab. 11. The kernel size of LargeKernel3D is $17 \\times 17 \\times 17$ . LargeKernel3D improves the vehicle performance of CenterPoint [75] by around $1.5\\%$ LEVEL_1 AP / APH. Models listed take single-frame LIDAR data without any test-time augmentations or ensemble. It also performs better than other methods. We use CenterPoint [75] to keep consistency to the nuScenes benchmark. Note that LargeKernel3D has the potential to achieve further performance if equipped with stronger detection heads [55].", + "bbox": [ + 496, + 297, + 893, + 465 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion and Discussion", + "text_level": 1, + "bbox": [ + 500, + 486, + 748, + 502 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We have studied large-kernel designs for 3D convolutional networks, which have essential differences from the solutions in 2D CNNs. We present spatial-wise partition convolution (SW Conv) that is specifically designed for 3D large kernels. It effectively resolves the efficiency and optimization issues in plain 3D large-kernel CNNs. Based on this design, we further propose the SW-LK Conv and the corresponding LargeKernel3D for 3D semantic segmentation and object detection. Our 3D large-kernel networks achieve decent improvement on both semantic segmentation and object detection tasks. For the first time, we show that 3D large kernels can be realized efficiently and effectively. We expect our findings to advance further development of 3D networks. Additional experiments and limitation analysis are provided in the appendix.", + "bbox": [ + 496, + 513, + 890, + 741 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitations LargeKernel3D mainly relies on hand-designed spatial kernel sizes in 3D semantic segmentation and object detection benchmarks. These sizes might be suboptimal for other datasets or tasks, depending on the overall scene sizes and data sparsity. Other search-based techniques [60] might be helpful, which we will try latter.", + "bbox": [ + 496, + 747, + 890, + 839 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement. This work is supported by Shenzhen Science and Technology Program (KQTD20210811090149095), Hong Kong Research Grant Council - Early Career Scheme (No. 27209621), and General Research Fund Scheme (No. 17202422).", + "bbox": [ + 496, + 844, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "13495", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Lei Jimmy Ba, Jamie Ryan Kiros, and Geoffrey E. Hinton. Layer normalization. CoRR, abs/1607.06450, 2016. 4, 6", + "[2] Xuyang Bai, Zeyu Hu, Xinge Zhu, Qingqiu Huang, Yilun Chen, Hongbo Fu, and Chiew-Lan Tai. Transfusion: Robust lidar-camera fusion for 3d object detection with transformers. CoRR, abs/2203.11496, 2022. 7", + "[3] Irwan Bello, Barret Zoph, Ashish Vaswani, Jonathon Shlens, and Quoc V Le. 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In CVPR, pages 9308-9316, 2019. 2" + ], + "bbox": [ + 501, + 92, + 890, + 489 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "13498", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/LargeKernel3D_ Scaling Up Kernels in 3D Sparse CNNs/55787f59-b334-48a8-9764-98d4fb45ca63_model.json b/2023/LargeKernel3D_ Scaling Up Kernels in 3D Sparse CNNs/55787f59-b334-48a8-9764-98d4fb45ca63_model.json new file mode 100644 index 0000000000000000000000000000000000000000..ae68e6ba174d544d9bc6add39ce7d7b9c594d8fe --- /dev/null +++ b/2023/LargeKernel3D_ Scaling Up Kernels in 3D Sparse CNNs/55787f59-b334-48a8-9764-98d4fb45ca63_model.json @@ -0,0 +1,2730 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.204, + 0.131, + 0.768, + 0.154 + ], + "angle": 0, + "content": "LargeKernel3D: Scaling up Kernels in 3D Sparse CNNs" + }, + { + "type": "text", + "bbox": [ + 0.102, + 0.18, + 0.864, + 0.224 + ], + "angle": 0, + "content": "Yukang Chen\\(^{1*}\\) Jianhui Liu\\(^{2*}\\) Xiangyu Zhang\\(^{3}\\) Xiaojuan Qi\\(^{2}\\) Jiaya Jia\\(^{1,4}\\) \n\\(^{1}\\)The Chinese University of Hong Kong \\(^{2}\\)The University of Hong Kong \\(^{3}\\)MEGVII \\(^{4}\\)SmartMore" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.258, + 0.314, + 0.274 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.291, + 0.474, + 0.609 + ], + "angle": 0, + "content": "Recent advance in 2D CNNs has revealed that large kernels are important. However, when directly applying large convolutional kernels in 3D CNNs, severe difficulties are met, where those successful module designs in 2D become surprisingly ineffective on 3D networks, including the popular depth-wise convolution. To address this vital challenge, we instead propose the spatial-wise partition convolution and its large-kernel module. As a result, it avoids the optimization and efficiency issues of naive 3D large kernels. Our large-kernel 3D CNN network, LargeKernel3D, yields notable improvement in 3D tasks of semantic segmentation and object detection. It achieves \\(73.9\\%\\) mIoU on the ScanNetv2 semantic segmentation and \\(72.8\\%\\) NDS nuScenes object detection benchmarks, ranking \\(1^{st}\\) on the nuScenes LIDAR leaderboard. The performance further boosts to \\(74.2\\%\\) NDS with a simple multi-modal fusion. In addition, LargeKernel3D can be scaled to \\(17\\times 17\\times 17\\) kernel size on Waymo 3D object detection. For the first time, we show that large kernels are feasible and essential for 3D visual tasks. Our code and models is available at github.com/dvlab-research/LargeKernel3D." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.638, + 0.21, + 0.654 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.664, + 0.471, + 0.877 + ], + "angle": 0, + "content": "3D Sparse convolutional neural networks (CNNs) have been widely used as feature extractors in 3D tasks, e.g., semantic segmentation [9,24] and object detection [55,65,75]. The advantages of efficiency and convenient usage ensure its important role in various applications, such as autonomous driving and robotics. However, 3D sparse CNNs are recently challenged by transformer-based methods [45,46,79], mainly from the aspect of building effective receptive fields. Both global and local [21,45] self-attention mechanisms are able to capture context information from a large spatial scope. 2D Vision Transformers (ViTs) also emphasize their advantages in modeling long-range dependencies [20,42,51]. In contrast, common 3D sparse CNNs are limited in this regard. It is because the receptive fields" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.259, + 0.892, + 0.306 + ], + "angle": 0, + "content": "of default 3D sparse CNN are constrained by small kernel sizes and spatial disconnection of sparse features (due to the property of submanifold sparse convolution [25])." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.308, + 0.893, + 0.504 + ], + "angle": 0, + "content": "Literature about 2D CNNs [18, 43, 62] presents a series of methods, combined with large kernels, to enlarge the receptive fields and model capacity. ConvNeXt [43] employs \\(7 \\times 7\\) depth-wise convolution as a strong design, combing with other training techniques to challenge its Swin Transformer counterpart [42]. RepLKNet [18] pursues extremely large kernel sizes of \\(31 \\times 31\\) to boost the performance of different tasks. To ensure the effectiveness of RepLKNet [18], additional factors, including depth-wise convolution, are also required. Other work [27] also emphasizes the importance of depth-wise convolution. Due to differences between 3D and 2D tasks, these methods, however, are found not a good solution for 3D sparse CNNs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.506, + 0.895, + 0.688 + ], + "angle": 0, + "content": "We first analyze the difficulties of 3D large-kernel CNN design in two aspects. The first challenge is efficiency. It is easy to understand that 3D convolution is with the cubic kernel size and computation increases fast. For example, the model size increases \\(10+\\) times when kernels change from \\(3 \\times 3 \\times 3\\) to \\(7 \\times 7 \\times 7\\). The second difficulty exists in the optimization procedure. 3D datasets may contain only thousands of scenes, which cannot match 2D image benchmarks [15, 40] in terms of scales. In addition, 3D point clouds or voxels are sparse, instead of dense images. Thus, it might be insufficient to optimize the proliferated parameters of large kernels and leads to over-fitting." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.69, + 0.895, + 0.901 + ], + "angle": 0, + "content": "In this paper, we propose spatial-wise partition convolution as the 3D large-kernel design. It is a new family of group convolution by sharing weights among spatially adjacent locations, rather than depth-wise convolution [29] of channel-level groups. As shown in Fig. 1, spatial-wise partition convolution remaps a large kernel \\((e.g., 7 \\times 7)\\) as a small one \\((e.g., 3 \\times 3)\\) via grouping spatial neighbors, while the absolutely large spatial size remains unchanged. With regard to the efficiency issue, it occupies few model sizes to keep parameters the same as those of small kernels. Moreover, it takes less latency, compared with plain large kernel counterparts. As for the optimization challenge, weight-sharing among spatial dimensions gives parameters more chance to update and overcome the over-fitting issue." + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.21, + 0.9 + ], + "angle": 0, + "content": "*Equal Contribution." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "13488" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.089, + 0.331, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.131, + 0.228, + 0.276, + 0.242 + ], + "angle": 0, + "content": "Small-kernel sparse conv" + }, + { + "type": "image", + "bbox": [ + 0.347, + 0.089, + 0.611, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.404, + 0.228, + 0.549, + 0.242 + ], + "angle": 0, + "content": "Large-kernel sparse conv" + }, + { + "type": "image", + "bbox": [ + 0.627, + 0.089, + 0.891, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.681, + 0.228, + 0.836, + 0.242 + ], + "angle": 0, + "content": "Spatial-wise partition conv" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.254, + 0.894, + 0.311 + ], + "angle": 0, + "content": "Figure 1. Sparse convolutions with different kernels. Small-kernel sparse convolution gathers features in a local area. It is efficient but discards sufficient information flow due to feature disconnection and the small scope. Large-kernel sparse convolution is capable of capturing long-range information, at the price of a large number of parameters and computation. Our proposed spatial-wise partition convolution uses large kernel sizes, and shares weights among local neighbors for efficiency. We show 2D features for the simplicity sake." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.349, + 0.47, + 0.485 + ], + "angle": 0, + "content": "To increase the detail-capturing ability of large kernels [18], we introduce position embeddings for spatial-wise group convolution. It makes notable effects for large kernel sizes. We name the proposed block as spatial-wise large-kernel convolution (SW-LK Conv). We compare the efficiency between plain 3D submanifold sparse convolution and ours, as shown in Tab. 1. Both parameters and latency of the baseline increases dramatically, as its kernel size becomes larger, while ours is far more efficient." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.486, + 0.47, + 0.713 + ], + "angle": 0, + "content": "SW-LK Conv can readily replace plain convolution layers in existing 3D convolutional networks. We establish large-kernel backbone networks LargeKernel3D on existing 3D semantic segmentation [9] and object detection [16, 75] networks. It achieves notable improvement upon state-of-the-art methods [9, 16, 75], with a small model complexity overhead. Extensive experiments validate our effectiveness on large-scale benchmarks, including ScanNetv2 [13], nuScenes [4], and Waymo [57]. For object detection, LargeKernel3D achieves \\(72.8\\%\\) NDS on nuScenes, ranking \\(\\mathbf{1}^{st}\\) on the nuScenes LIDAR leaderboard. Without bells and whistles, it further improves to \\(74.2\\%\\) NDS in a simple voxel-wise multi-modal fusion manner. More importantly, it is scalable to \\(17\\times 17\\times 17\\) kernel sizes on the large-scale Waymo 3D object detection." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.714, + 0.47, + 0.82 + ], + "angle": 0, + "content": "We visualize the Effective Receptive Fields (ERFs) of plain 3D CNNs and our LargeKernel3D in Fig. 2. It shows that deep small-kernel networks are also constrained by limited ERFs, since sparse features are spatially disconnected. Note that our large-kernel networks elegantly resolve this issue. For the first time, we show that large-kernel CNN designs become effective on essential 3D visual tasks." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.838, + 0.219, + 0.853 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Convolutional Large-kernel Networks Large-kernel setting has been commonly used in 2D convolutional net" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.349, + 0.892, + 0.577 + ], + "angle": 0, + "content": "works [18, 43, 68]. ConvNeXt [43] combines various training techniques and large kernel sizes, to compete with Swin Transformer [42]. RepLKNet [18] is a specific work that focuses on large-kernel designs. It reveals that the large kernel sizes are more beneficial to tasks of object detection and semantic segmentation than image classification. GCNs [47] also show improvement from large-kernel designs on semantic segmentation. There are methods approximating large kernel sizes using implicit techniques, including Fourier domain transformation [52], and continuous functions [53]. Other methods change kernel shapes to enlarge receptive fields using dilated convolutions [5, 76], deformable convolutions [14, 81] and active convolutions [31]. These schemes sparsify kernels, and is hard to capture the original sparse features in 3D deep learning." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.583, + 0.892, + 0.794 + ], + "angle": 0, + "content": "3D Feature Extractors A key challenge in 3D tasks [32,38] is to learn effective representation from the sparse and non-uniformed 3D geometric data, e.g., point clouds. In general, there are two kinds of 3D feature extractors. The first is to learn on point cloud directly, using a series of PointNet networks [48, 49]. The sampling and grouping operations in PointNet++ [49] are also time-consuming. Followups [46, 79] use grid-sampling or scene-partition to save computation in each forward and combine results from multiple runs. The second is to process point clouds with voxelization and apply 3D sparse CNNs. Due to its efficiency advantages, this stream of methods has been widely used in various 3D tasks, such as 3D segmentation [9-11, 33] and backbone networks in 3D object detectors [16, 26, 55, 64]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The spatial group convolution (SGC) [78] is relevant to the proposed spatial-wise partition convolution. SGC is originally designed for the task of 3D scene completion. They both conduct the partition operation spatially. The difference is also essential and clear. Our method partition kernel weighs while SGC splits input features into groups. In terms of targets, SGC focuses more on efficiency improve" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13489" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.895, + 0.134 + ], + "angle": 0, + "content": "Table 1. Efficiency comparison between plain 3D sparse convolution and our SW-LK Conv. The baseline is a submanifold sparse convolutional layer with input and output channels 16. The input data is a sparse tensor with 80,000 voxels randomly scattered and batch size 1. We test all latencies on a single 2080Ti GPU by an average of 10 times running, after a warm-up start of additional 10 times." + }, + { + "type": "table", + "bbox": [ + 0.09, + 0.142, + 0.878, + 0.226 + ], + "angle": 0, + "content": "
Kernel Size3×3×35×5×57×7×79×9×911×11×1113×13×1315×15×1517×17×17
PlainParams6.9 K32.0 K87.8 K186.6 K340.7 K562.4 K864.0 K1.3 M
Latency2.5 ms4.2 ms8.9 ms17.5 ms31.1 ms55.1 ms81.1 ms106.3 ms
OursParams-8.9 K12.4 K18.6 K28.2 K42.1 K60.9 K85.5 K
Latency-3.4 ms3.9 ms4.8 ms6.2 ms8.4 ms11.4 ms15.8 ms
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.261, + 0.471, + 0.308 + ], + "angle": 0, + "content": "ment by changing feature sparsity in each spatial group, while our method is to facilitate large kernels in 3D tasks. Further analysis and comparisons are given in experiments." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.313, + 0.47, + 0.451 + ], + "angle": 0, + "content": "Vision Transformer Vision transformers that conduct attention computation in local areas or windows share a similar spirit with large-kernel models [18]. Swin Transformers [42] capture features in shifted windows with sizes from 7 to 12. Its variants [19, 41] show that larger window sizes are beneficial to performance. Focal Transformer [71] captures fine-grained local attention with adaptive patch sizes. SST [21] and Stratified Transformer [34] apply window-based self-attention on 3D detection and segmentation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.457, + 0.47, + 0.729 + ], + "angle": 0, + "content": "Position Encoding Since the self-attention in transformers is permutation-equivalent, position encoding is well-designed for imbuing the network with the position information. It can be grouped into two streams of absolute and relative position encoding. For the first group, positions are encoded in a precise manner. Specifically, encoding [63] is generated with the sinusoidal functions of different frequencies. They are then added to the input. In contrast, relative position encoding [54] takes the relative relationship into consideration. It can naturally handle longer sequences and is more scalable. Most work [3, 50, 66, 73] computes the relative distance between tokens and applies implicit encoding using learnable transformations. Besides, the literature [12] shows that convolution with padding can provide effective relative position information for relative position encoding. In addition to transformers, the recent work [72] also shows that position embedding is beneficial to the CNNs with fourier transformation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.73, + 0.47, + 0.822 + ], + "angle": 0, + "content": "Considering that our spatial-wise partition convolution divides the kernel into different portions in pursuit of higher efficiency. The position information may be blurred due to weight sharing in each portion. We thus use relative position encoding as a bias to supplement the lost position information. More details are provided in Sec. 4." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.838, + 0.334, + 0.856 + ], + "angle": 0, + "content": "3. Revisiting 3D Sparse CNNs" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Preliminary 3D sparse CNNs consist of 3D sparse convolutions, which are typically regular and submanifold sparse" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.261, + 0.895, + 0.398 + ], + "angle": 0, + "content": "convolutions [25]. We formulate 3D sparse convolutions in Eq. (1). Given a set of sparse input features \\(\\{\\mathbf{x}_{p\\in P}\\}\\) with a number of \\(c_{\\mathrm{in}}\\) channels, the position of each feature \\(p\\in P\\) sparsely distributes in 3D space. We process these features by a convolution with kernel weights \\(\\mathbf{w}\\in \\mathbb{R}^{|K| \\times c_{\\mathrm{in}} \\times c_{\\mathrm{out}}}\\). For example, in the 3D coordinate space, \\(\\mathbf{w}\\) contains \\(c_{\\mathrm{in}} \\times c_{\\mathrm{out}}\\) spatial kernels with size 3 and \\(|K| = 27\\). The convolution process at the output position \\(\\bar{p}\\) is represented as" + }, + { + "type": "equation", + "bbox": [ + 0.622, + 0.408, + 0.892, + 0.441 + ], + "angle": 0, + "content": "\\[\n\\mathrm {y} _ {\\bar {p}} = \\sum_ {k \\in K} \\mathrm {w} _ {k} \\cdot \\mathrm {x} _ {\\bar {p} + k}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.45, + 0.895, + 0.498 + ], + "angle": 0, + "content": "where \\( k \\) is an 3D offset distance from \\( \\bar{p} \\). \\( \\bar{p} + k \\) is the location around center \\( \\bar{p} \\). It enumerates all discrete locations in the kernel space \\( K \\) where sparse features \\( \\mathbf{x}_{\\bar{p} + k} \\) exist." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.502, + 0.895, + 0.653 + ], + "angle": 0, + "content": "Convolution Types Regular sparse convolutions enlarge their output positions by dilating each input position \\( p \\in P \\) to the kernel shape \\( K \\). It dramatically decreases feature density and increases the computational burden. Thus, regular sparse convolutions with stride 2 are only employed at the first layer in each stage for down-sampling. Submanifold sparse convolutions, in contrast, fix their output positions \\( \\bar{p} \\) identical to input positions \\( p \\in P \\), which preserves the computation cost at low levels. Please refer to the original paper [25] for more details." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.653, + 0.895, + 0.744 + ], + "angle": 0, + "content": "Due to the efficiency advantage, submanifold sparse convolutions dominate most layers of 3D CNNs, except for the down-sampling layers. However, limited by the small local scope, it misses sufficient information flow for the spatially disconnected features. Increasing kernel sizes becomes a potential solution to relieve this issue." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.895, + 0.87 + ], + "angle": 0, + "content": "Obstacles in 3D Large Kernels Efficiency is the first issue in 3D large-kernel CNNs. When we increase kernel sizes, the amount of parameters and computational burden grows much faster than those of 2D CNNs. For instance, the parameter amount in one 3D convolutional layer increases from \\(27 \\cdot C_{in \\cdot out}\\) to \\(343 \\cdot c_{in} \\cdot c_{out}\\), given its kernel size changing from 3 to 7. It is thus clear that naively enlarging 3D kernels is unreasonable." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.871, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Optimization difficulty is the second obstacle. The booming parameters require sufficient data for learning. How-" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "13490" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.09, + 0.231, + 0.188 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.107, + 0.19, + 0.205, + 0.201 + ], + "angle": 0, + "content": "(a) Plain 3D CNN" + }, + { + "type": "image", + "bbox": [ + 0.231, + 0.091, + 0.38, + 0.188 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.245, + 0.19, + 0.365, + 0.202 + ], + "angle": 0, + "content": "(b) Plain 3D CNN - 2x" + }, + { + "type": "image", + "bbox": [ + 0.38, + 0.091, + 0.531, + 0.188 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.405, + 0.19, + 0.505, + 0.203 + ], + "angle": 0, + "content": "(c) LargeKernel3D" + }, + { + "type": "image", + "bbox": [ + 0.535, + 0.091, + 0.772, + 0.188 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.554, + 0.19, + 0.665, + 0.201 + ], + "angle": 0, + "content": "Feature of interest" + }, + { + "type": "image", + "bbox": [ + 0.772, + 0.091, + 0.89, + 0.188 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.784, + 0.19, + 0.883, + 0.202 + ], + "angle": 0, + "content": "Magnitude of ERF" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.214, + 0.894, + 0.284 + ], + "angle": 0, + "content": "Figure 2. Effective Receptive Fields (ERF) of plain 3D CNN, plain 3D CNN - \\(2 \\times\\), and our LargeKernel3D for 3D object detection. The plain 3D CNN backbone has insufficient ERF size, which hardly covers a nearby car. Plain 3D CNN - \\(2 \\times\\) is a deeper version with its layers doubled in each stage. More layers help little in ERF, as the disconnection between sparse features. Our LargeKernel3D obtains large ERF at both the object centers (left) and edges (right), capturing context information. More illustrations are provided in the appendix. The figure is best viewed in color and by zoom-in." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.323, + 0.468, + 0.413 + ], + "angle": 0, + "content": "ever, 3D datasets are commonly not in that large scale as 2D benchmarks. For example, ImageNet [15] contains millions of images, while 3D datasets commonly contain only no more than one thousand scenes. The over-fitting issue gradually deteriorates the performance when increasing kernel sizes from \\(3 \\times 3 \\times 3\\) to \\(7 \\times 7 \\times 7\\) in MinkowskiNet-34 [9]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.414, + 0.468, + 0.641 + ], + "angle": 0, + "content": "Previous 2D knowledge is not helpful in 3D large-kernel CNNs. Recent 2D methods [18, 43] show some helpful components in large-kernel CNNs, including depth-wise convolutions [29], layer normalization [1], GELU [28] activation. We examine these popular components and find that they are either ineffective or even harmful in 3D CNNs. To demonstrate this finding, we use MinkowskiNet-34 [9] to benchmark and train on the 3D semantic segmentation dataset of ScanNetv2 [13]. We change the original activation function from ReLU to GELU, batch normalization to layer normalization, and plain convolution to depth-wise operation, respectively. Directly using these components makes the final system yield performance drop on both small and large kernel networks. It requires us to seek other ways to construct 3D large-kernel CNNs." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.655, + 0.439, + 0.672 + ], + "angle": 0, + "content": "4. 3D Large-kernel Convolutional Network" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.681, + 0.378, + 0.696 + ], + "angle": 0, + "content": "4.1. Spatial-wise Partition Convolution" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.704, + 0.468, + 0.854 + ], + "angle": 0, + "content": "A standard convolution kernel can be viewed as a 3D matrix, which consists of input channels \\( C_{\\mathrm{in}} \\), output channels \\( C_{\\mathrm{out}} \\), and the spatial kernel dimension \\( |K| \\). Taking kernel size as \\( k \\), the volume of spatial kernel dimension \\( |K| = k \\times k \\) for 2D convolutions and \\( k \\times k \\times k \\) for 3D convolutions. Depth-wise convolutions share weights along channel dimensions, where group numbers equal to input channels. Point-wise convolutions fix kernel size as 1, which is common as a conjunction layer to depth-wise convolutions to adjust output channels." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Different from 2D methods, which rely on depthwise convolutions for performance boosting [27, 43] and accuracy-FLOPs trade-offs [18], we empirically find that" + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.321, + 0.793, + 0.424 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.825, + 0.327, + 0.841, + 0.337 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.853, + 0.327, + 0.89, + 0.336 + ], + "angle": 0, + "content": "feature" + }, + { + "type": "image", + "bbox": [ + 0.825, + 0.348, + 0.845, + 0.363 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.854, + 0.35, + 0.89, + 0.361 + ], + "angle": 0, + "content": "weight" + }, + { + "type": "image", + "bbox": [ + 0.819, + 0.373, + 0.851, + 0.398 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.854, + 0.381, + 0.885, + 0.39 + ], + "angle": 0, + "content": "group" + }, + { + "type": "image", + "bbox": [ + 0.819, + 0.409, + 0.838, + 0.419 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.853, + 0.409, + 0.886, + 0.418 + ], + "angle": 0, + "content": "assign" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.436, + 0.892, + 0.547 + ], + "angle": 0, + "content": "Figure 3. Illustration on spatial-wise partition convolution. In the plain large-kernel convolution, due to the sparsity of input features, only a small proportion of weights are involved and updated in each training step. The spatial-wise partition convolution relieves this issue by sharing weights among spatial neighbors. It increases the chance for weights to be optimized. During inference, we reformulate the spatial-wise partition convolutions into small ones, with feature assignment in a large scope." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.593, + 0.89, + 0.622 + ], + "angle": 0, + "content": "depth-wise convolutions are not beneficial to 3D tasks, no matter whether point-wise convolutions are included." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.626, + 0.892, + 0.793 + ], + "angle": 0, + "content": "We instead propose spatial-wise partition convolution for 3D large-kernel CNNs. It shares weights among spatial dimension \\( K \\) on convolutional kernels, instead of among channel dimension. It is also different from SGC [78], which partitions spatial groups on input features. Specially, in Eq. (1), \\( w_{k} \\) shares the same values in a local area \\( k \\in K \\). We thus group the original large-kernel convolution from \\( 7 \\times 7 \\) into \\( 3 \\times 3 \\), by sharing weights among spatial neighbors. Spatial-wise partition convolution is specially designed for 3D tasks and has the following advantages in terms of efficiency and performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Regarding efficiency, when naively enlarging the kernel size from \\(3 \\times 3 \\times 3\\) to \\(7 \\times 7 \\times 7\\) on MinkowskiNet-34 [9], both model size and latency have a sharp increase by multiple times. In contrast, our spatial-wise partition convolution avoids increasing parameters and introduces limited latency overhead. The advantage of our method over plain large kernels attributes to the specific implementation of sparse" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "13491" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.119, + 0.092, + 0.241, + 0.187 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.133, + 0.19, + 0.228, + 0.204 + ], + "angle": 0, + "content": "Input & Weight" + }, + { + "type": "image", + "bbox": [ + 0.258, + 0.129, + 0.291, + 0.154 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.31, + 0.094, + 0.432, + 0.187 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.315, + 0.19, + 0.429, + 0.204 + ], + "angle": 0, + "content": "Position Encodings" + }, + { + "type": "image", + "bbox": [ + 0.45, + 0.127, + 0.491, + 0.153 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.509, + 0.095, + 0.629, + 0.187 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.517, + 0.19, + 0.619, + 0.205 + ], + "angle": 0, + "content": "Output & Weight" + }, + { + "type": "image", + "bbox": [ + 0.687, + 0.098, + 0.705, + 0.11 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.72, + 0.098, + 0.809, + 0.111 + ], + "angle": 0, + "content": "Sparse feature" + }, + { + "type": "image", + "bbox": [ + 0.687, + 0.117, + 0.71, + 0.132 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.722, + 0.118, + 0.799, + 0.132 + ], + "angle": 0, + "content": "Conv weight" + }, + { + "type": "image", + "bbox": [ + 0.687, + 0.142, + 0.71, + 0.158 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.723, + 0.144, + 0.832, + 0.157 + ], + "angle": 0, + "content": "Position encoding" + }, + { + "type": "image", + "bbox": [ + 0.681, + 0.166, + 0.719, + 0.195 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.723, + 0.172, + 0.835, + 0.185 + ], + "angle": 0, + "content": "Spatial-wise group" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.217, + 0.892, + 0.245 + ], + "angle": 0, + "content": "Figure 4. Structure of spatial-wise large-kernel convolution (SW-LK Conv). It consists of a large-kernel spatial-wise partition convolution and a learnable position embedding. The position embedding is used to make up the detail-capturing ability of large kernels." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.285, + 0.473, + 0.481 + ], + "angle": 0, + "content": "convolution. For a spatial-wise partition convolution, we directly use the small-kernel layer during inference, and enlarge its feature-assign areas to the large-kernel scope. As shown in Fig. 3, thanks to the weight-sharing operation, it much saves the multiplication, e.g., from 343 to 27 times. We implement this operation upon the open-sourced spconv library and omit the details here. Tab. 4 shows that our implementation on spatial-wise partition convolution is far more efficient than the plain large-kernel baseline. The optimization difficulty of large-kernel CNNs is relieved with the help of spatial-wise partition convolutions, which constrains model sizes to a limited number. It avoids requiring a large amount of data for training and the over-fitting issue." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.498, + 0.349, + 0.515 + ], + "angle": 0, + "content": "4.2. Kernel-wise Position Encoding" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.524, + 0.47, + 0.646 + ], + "angle": 0, + "content": "Considering that the spatial-wise partition convolution is designed in a sharing weights manner against the spatial sparsity. Although this design is efficient, there is still an issue: voxels within an area share the same weight, which results in local details blurred. This phenomenon is further amplified with an increase of kernel sizes. To address this problem, we propose the kernel-wise position embedding. We illustrate this design in Fig. 4." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.647, + 0.47, + 0.724 + ], + "angle": 0, + "content": "Particularly, we initialize position weights \\(\\mathrm{e} \\in \\mathbb{R}^{K \\times c_{\\mathrm{in}}}\\), which corresponds to the convolution kernel. During the convolution process, we let the input features query the position weights of the equivalent position and add them together. This process modifies Eq. (1) to" + }, + { + "type": "equation", + "bbox": [ + 0.174, + 0.746, + 0.47, + 0.78 + ], + "angle": 0, + "content": "\\[\n\\mathrm {y} _ {\\bar {p}} = \\sum_ {k \\in K} \\mathrm {w} _ {k} \\cdot \\left(\\mathrm {x} _ {\\bar {p} + k} + \\mathrm {e} _ {k}\\right). \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.471, + 0.901 + ], + "angle": 0, + "content": "This simple design essentially adds bias with relative position information to the input features. There is almost no extra calculation and additional parameters. It is a decent solution to the position insensitivity problem caused by sharing weights, especially for the extremely large kernels, e.g., \\(17 \\times 17 \\times 17\\). For more experimental results and details, please refer to the Sec. 5." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.284, + 0.74, + 0.3 + ], + "angle": 0, + "content": "4.3. Large-kernel Architecture" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.307, + 0.892, + 0.382 + ], + "angle": 0, + "content": "Following the above designs and observations, we now describe the architectures of our large-kernel 3D CNNs. We readily replace the plain 3D submanifold sparse convolution [25] layers with our SW-LK Conv in existing 3D backbones for semantic segmentation and object detection." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.388, + 0.893, + 0.57 + ], + "angle": 0, + "content": "3D Semantic Segmentation The architectures of LargeKernel3D for 3D semantic segmentation resemble MinkowskiNet [9], including 1 stem layer and 8 stages. The stem layer is a \\(5 \\times 5 \\times 5\\) submanifold convolution. The first 4 stages account for down-sampling and the last 4 stages are for up-sampling. As for the U-Net structure, the first 4 features are concatenated into the up-sampling stages. We replace the original layers in MinkowskiNet-34 [9] by SW-LK Convs, where spatial-wise \\(7 \\times 7 \\times 7\\) convolutions is grouped into \\(3 \\times 3 \\times 3\\) splits. By default, other hyper-parameters, including channels and block numbers, follow MinkowskiNet-34 [9]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.576, + 0.895, + 0.803 + ], + "angle": 0, + "content": "3D Object Detection The typical backbone networks in 3D object detectors [16, 55, 75] consist of 1 stem layer and 4 stages. A \\(3 \\times 3 \\times 3\\) submanifold convolution [25] layer serves as the stem. In each stage, except for the first one, there is a sparse convolutional layer with stride 2 for down-sampling. We substitute other plain blocks with SW-LK Convs. For models on nuScenes dataset, we find that \\(7 \\times 7 \\times 7\\) kernel sizes are enough. They both use the \\(3 \\times 3 \\times 3\\) spatial-wise groups. For models on Waymo dataset, kernel sizes are scalable to \\(17 \\times 17 \\times 17\\). We remain the last stage of backbone network as the original, because receptive fields have already been sufficiently enlarged in the front stages. We keep these hyper-parameters unchanged by the default settings in baseline detectors [16, 75]. We include these detailed numbers in appendix." + }, + { + "type": "list", + "bbox": [ + 0.498, + 0.388, + 0.895, + 0.803 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.817, + 0.633, + 0.833 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.841, + 0.7, + 0.858 + ], + "angle": 0, + "content": "5.1. Experimental Setting" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "3D Semantic Segmentation ScanNetv2 [13] is a large-scale benchmark in 3D semantic segmentation. It con" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13492" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.472, + 0.132 + ], + "angle": 0, + "content": "Table 2. Ablations on various techniques and kernel sizes on MinkowskiNet-34 and ScanNetv2. LN denotes the layer normalization. DW Conv denotes the depth-wise convolution." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.144, + 0.47, + 0.186 + ], + "angle": 0, + "content": "
KernelBaseline+GELU+LN+DW Conv+PWOurs
3×3×371.770.266.870.670.7-
7×7×768.668.465.068.768.773.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.106, + 0.213, + 0.439, + 0.228 + ], + "angle": 0, + "content": "Table 3. Ablations on group convolution on ScanNetv2." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.24, + 0.469, + 0.283 + ], + "angle": 0, + "content": "
KernelBaselineGroup 24816DWOurs
3x3x371.771.571.270.770.670.6-
7x7x768.668.869.268.868.768.773.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.312, + 0.47, + 0.355 + ], + "angle": 0, + "content": "Table 4. Comparisons with relevant convolutional schemes on ScanNetv2. Baseline is a MinkowskiNet-34 network. All models listed are trained in the same training hyper-parameters." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.366, + 0.469, + 0.508 + ], + "angle": 0, + "content": "
MethodParamsFLOPsLatencymIoU
Baseline37.9 M182.8 G108 ms71.7
+ Kernel 5×5×5170.3M537.5 G212 ms70.7
+ Kernel 7×7×7465.0M1089.5 G487 ms68.6
Dilate conv37.9M100.1 G98 ms64.6
Pooling + Dilate37.9M183.2 G115 msnan
Spatial group [78]37.9M127.2 G96 ms70.0
Deformable conv42.5M250.1 G238 ms72.0
LargeKernel3D-T38.4M171.4 G111 ms72.8
LargeKernel3D40.2M240.0 G145 ms73.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.093, + 0.537, + 0.454, + 0.551 + ], + "angle": 0, + "content": "Table 5. Results on other backbone networks andScanNetv2." + }, + { + "type": "table", + "bbox": [ + 0.099, + 0.563, + 0.45, + 0.628 + ], + "angle": 0, + "content": "
ModelBaseline+OursΔ
MinkowskiNet-14 [9]67.069.7+2.7
MinkowskiNet-18 [9]69.571.5+2.0
SparseConvNet [24]69.371.2+1.9
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.667, + 0.47, + 0.789 + ], + "angle": 0, + "content": "tains 1,201 indoor RGB-D scenes for training, 312 scenes for validation, and 100 scenes for testing. Semantic labels in 20 categories are annotated. We train our models with the default settings in MinkowskiNet [9], including training hyper-parameters and data augmentations. We evaluate models in the mean Intersection over Union (mIoU) metric. Detailed experimental settings, including network structures and training details, are listed in the appendix." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.471, + 0.902 + ], + "angle": 0, + "content": "3D Object Detection nuScenes, and Waymo are all popular 3D object detection benchmarks. nuScenes is a large dataset and contains 1,000 driving sequences in total. Among them, there are 700 scenes split for training, 150 scenes for validation, and 150 scenes for testing. It contains LIDAR, camera, and radar sources with a complete \\(360^{\\circ}\\) environment. We evaluate our methods on both LIDAR-only and LIDAR-" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.089, + 0.892, + 0.132 + ], + "angle": 0, + "content": "Table 6. Effects of the spatial-wise partition manners on SW-LK Conv and ScanNetv2. Center group means the size of central area. Shifting is to translate the center position by 1 in all 3 dimensions." + }, + { + "type": "table", + "bbox": [ + 0.503, + 0.143, + 0.892, + 0.197 + ], + "angle": 0, + "content": "
Center group1×1×11×1×13×3×35×5×5
ShiftingX✓XX
mIoU73.566.870.668.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.224, + 0.892, + 0.28 + ], + "angle": 0, + "content": "Table 7. Improvement over various kernel sizes on LargeKernel3D upon CenterPoint, training on 1/5 Waymo training set and evaluate on the validation set. \\(\\Delta\\) means the improvement from the kernel 3 baseline. L1 and L2 means LEVEL_1 and LEVEL_2 mAP." + }, + { + "type": "table", + "bbox": [ + 0.506, + 0.293, + 0.892, + 0.417 + ], + "angle": 0, + "content": "
KernelVehiclePedestrianCyclist
L1L2L1L2L1L2
Baseline70.962.971.563.569.166.5
7×7×771.963.871.763.770.467.8
11×11×1172.264.271.863.970.268.3
15×15×1572.764.673.865.870.868.2
17×17×1773.265.174.166.071.068.1
Δ2.3↑2.2↑2.6↑2.5↑1.9↑1.6↑
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.444, + 0.892, + 0.472 + ], + "angle": 0, + "content": "Table 8. Effects of position embedding (PE) in the mAP of vehicle detection on Waymo validation set." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.484, + 0.885, + 0.58 + ], + "angle": 0, + "content": "
KernelPELatencyLEVEL_1LEVEL_2
3×3×3-109 ms70.962.9
7×7×7×120 ms71.663.4
✓122 ms71.963.8
17×17×17×158 ms71.563.3
✓164 ms73.265.1
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.618, + 0.892, + 0.756 + ], + "angle": 0, + "content": "RGB fusion settings. The main evaluation metrics are mAP and nuScenes detection score (NDS). Waymo [57] dataset also contains 1,000 sequences in total, with 798 for training and 202 for validation. For Waymo dataset, we use 1/5 training data for the ablation study and full training set for main results. Results in Waymo are evaluated on difficulty LEVEL_1 and LEVEL_2 objects. In experiments, we validate our networks on state-of-the-art detection framework of CenterPoint [75] on nuScenes [4] and Waymo [57]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.765, + 0.665, + 0.781 + ], + "angle": 0, + "content": "5.2. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.892, + 0.903 + ], + "angle": 0, + "content": "Usefulness of 2D CNN Techniques We first validate the techniques that have proven effective on 2D CNNs, including layer normalization [1], depth-wise convolution [29, 43], and GeLU [28]. We conduct experiments on MinkowskiNet-34 [9] on the ScanNet [13] semantic segmentation dataset, as shown in Tab. 2. Kernel \\(7 \\times 7 \\times 7\\) means modifying kernel sizes in all stages to 7. All these" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13493" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.124, + 0.09, + 0.844, + 0.105 + ], + "angle": 0, + "content": "Table 9. Comparison with other methods on nuScenes test split. \\( \\ddagger \\) means flipping and rotation testing-time augmentations." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.116, + 0.895, + 0.355 + ], + "angle": 0, + "content": "
MethodNDSmAPCarTruckBusTrailerC.V.PedMotBycT.C.Bar
PointPillars [35]45.330.568.423.028.223.44.159.727.41.130.838.9
3DSSD [74]56.442.681.247.261.430.512.670.236.08.631.147.9
CBGS [80]63.352.881.148.554.942.910.580.151.522.370.965.7
CenterPoint [75]65.558.084.651.060.253.217.583.453.728.776.770.9
HotSpotNet [7]66.059.383.150.956.453.323.081.363.536.673.071.6
CVCNET [6]66.658.282.649.559.451.116.283.061.838.869.769.7
UVTR-L [37]69.763.986.352.262.859.733.784.568.841.174.774.9
VISTA [17]69.863.084.455.163.754.225.182.870.045.478.571.4
Focals Conv [8]70.063.886.756.367.759.523.887.564.536.381.474.1
TransFusion-L [2]70.265.586.256.766.358.828.286.168.344.282.078.2
LargeKernel3D70.665.485.553.864.459.529.785.972.746.879.975.5
LargeKernel3D‡72.868.786.758.567.762.731.988.577.154.982.376.6
LargeKernel3D-F‡74.271.287.760.169.366.034.389.481.360.286.777.4
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.393, + 0.471, + 0.453 + ], + "angle": 0, + "content": "techniques bring no obvious benefit to baseline networks. In contrast, SW-LK Conv introduces clear improvement upon these strong networks. We also show the effects of group convolution with different group numbers in Tab. 3." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.466, + 0.47, + 0.812 + ], + "angle": 0, + "content": "Comparisons with Relevant Schemes We compare both performance and efficiency in Tab. 4 using various existing schemes to enlarge receptive fields. Dilated Conv [5] contains \\(3 \\times 3 \\times 3\\) kernel parameters. It dilates to \\(7 \\times 7 \\times 7\\) spatial sizes. Pooling + Dilated Conv inserts a 3D average pooling layer before the dilated convolutions to enlarge receptive fields. Spatial group conv is implemented, following the settings in the original paper [78]. We extend Deformable Conv [14] to 3D offset prediction, following [61]. Latencies are measured on an NVIDIA 2080ti GPU. It shows that none of these related schemes present better performance than the baseline. One reason for the low performance of dilation and deformable convolutions is that they tend to factorize the original dense kernels into sparse ones, which cause more information loss when applied to sparse 3D features than their 2D counterparts. Our LargeKernel3D achieves the best performance among these methods. In addition, we also build a tiny version, LargeKernel3D-T, which has half channel numbers in the last two stages. It introduces almost no additional computation overhead to baseline, but still has notable performance improvement. Except for the MinkowskiNet-34, we also show our effects on other backbone networks in Tab. 5." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Spatial-wise Group Partition Manner We ablate the effects of different spatial-wise group partition manners in Tab. 6. We study the size of central groups and center shifting. This ablation study is conducted on the LargeKernel3D and the Scannetv2 dataset. We find that both large central" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.39, + 0.892, + 0.419 + ], + "angle": 0, + "content": "Table 10. Comparison on ScanNetv2 mIoU on 3D semantic segmentation. † Sliding-window testing." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.43, + 0.885, + 0.651 + ], + "angle": 0, + "content": "
MethodLatencyvaltest
PointCNN [36]--45.8
PointNet++ [49]-53.555.7
RandLA-Net [30]--64.5
PointConv [67]80 ms61.066.6
PointASNL [69]-63.566.6
KPConv [61]-69.268.6
FusionNet [77]--68.8
Point Transformer† [79]1012 ms70.6-
Fast Point Transformer [46]298 ms72.1-
SparseConvNet [24]-69.372.5
Stratified Transformer† [34]1624 ms74.373.7
MinkowskiNet-34108 ms71.7
+ LargeKernel3D14573.573.9
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.681, + 0.892, + 0.788 + ], + "angle": 0, + "content": "sizes and center shifting hurt the performance. As the center sizes enlarge from \\(1 \\times 1 \\times 1\\) to \\(5 \\times 5 \\times 5\\), the accuracy sharply drops. Because submanifold sparse convolution [25] always aligns each individual voxel feature at its kernel center, we suppose that central features should maintain distinct and clean. Therefore, we keep the center size as \\(1 \\times 1 \\times 1\\) without shifting, as a default setting." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.893, + 0.903 + ], + "angle": 0, + "content": "Further Enlarging Kernel Sizes We show that LargeKernel3D is scalable to kernel sizes \\(17 \\times 17 \\times 17\\) on the outdoor dataset Waymo [57] in Tab. 7 with baseline kernel \\(3 \\times 3 \\times 3\\). Models in this ablation are trained on \\(1/5\\) training data and evaluated on the full validation set. Results with full training data are compared in Tab. 11. It shows that the mAP on all categories increases by around \\(2\\%\\). This setting demon-" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "13494" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.472, + 0.132 + ], + "angle": 0, + "content": "Table 11. Performance of vehicle detection on the Waymo val split. All models listed take LIDAR-only input and single frames, without any test-time augmentations or model ensemble." + }, + { + "type": "table", + "bbox": [ + 0.084, + 0.144, + 0.465, + 0.424 + ], + "angle": 0, + "content": "
MethodLEVEL_13D AP / APHLEVEL_23D AP / APH
VoTr-SSD [45]68.99 / 68.3960.22 / 59.69
PointPillars [75]72.08 / 71.5363.55 / 63.06
SECOND [70]72.27 / 71.6963.85 / 63.33
RangeDet [23]72.85 / 72.3364.03 / 63.57
SST [22]74.22 / 73.7765.47 / 65.07
VoTr-TSD [45]74.95 / 74.2565.91 / 65.29
RSN [59]75.1 / 74.666.0 / 65.5
Voxel RCNN [16]75.59 / ——66.59 / ——
LIDAR-RCNN [39]76.0 / 75.568.3 / 67.9
SST [22]76.22 / 75.7968.04 / 67.64
Pyramid RCNN [44]76.30 / 75.6867.23 / 66.68
Part-A2-Net [56]77.05 / 76.5168.47 / 67.14
PV-RCNN [55]77.51 / 76.8968.98 / 68.41
SWFormer [58]69.2 / 68.880.9 / 72.7
CenterPoint [75]76.59 / 76.0568.85 / 68.35
+ LargeKernel3D78.07 / 77.6169.81 / 69.38
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.466, + 0.47, + 0.528 + ], + "angle": 0, + "content": "strates that a large-scale dataset is a key to unlocking the potential and capability of large kernel methods. In addition, we also try to extend the kernel size to \\(19 \\times 19 \\times 19\\), but obtain no further gains." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.534, + 0.47, + 0.671 + ], + "angle": 0, + "content": "Effects of Position Embedding In LargeKernel3D, position embedding is introduced to relieve the feature-blurring issue caused by weight-sharing. We ablate its effects in Tab. 8, in terms of both latency and performance. Position embedding introduces limited latency overhead on both kernel \\(7 \\times 7 \\times 7\\) and \\(17 \\times 17 \\times 17\\) models. In terms of performance, its effects on the \\(7 \\times 7 \\times 7\\) model are a bit marginal, but essential on the \\(17 \\times 17 \\times 17\\) model, which has larger kernel sizes and suffers from feature blurring." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.677, + 0.47, + 0.754 + ], + "angle": 0, + "content": "Shrinking Kernels During Inference For the spatial-wise partition convolution, we can shrink kernels into small ones during inference. As shown in Tab. 4, the latency of LargeKernel3D is \\(145\\mathrm{ms}\\) on ScanNetv2. It degrades to \\(514\\mathrm{ms}\\) with the same \\(73.5\\%\\) mIoU, if we disable shrinking." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.765, + 0.216, + 0.78 + ], + "angle": 0, + "content": "5.3. Main Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.471, + 0.903 + ], + "angle": 0, + "content": "3D Semantic Segmentation We make comparisons with other 3D semantic segmentation methods on the ScanNetv2 dataset in Tab. 10. Our method surpasses others on test split. MinkowskiNet [9] is already a state-of-the-art method in ScanNetv2. Our SW-LK Conv further improves its performance. Our method is also superior to transformer-based methods [46,79]. Stratified Transformer [34] uses a sliding-" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.153 + ], + "angle": 0, + "content": "window testing technique† and splits integrated scenes into overlapped parts. The method tests each part one by one and then ensembles results together, taking hours on evaluation. Moreover, our results are better on the test split." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.16, + 0.892, + 0.298 + ], + "angle": 0, + "content": "3D Object Detection We compare our LargeKernel3D upon CenterPoint [75] with previous methods on the test split of the nuScenes [4] dataset in Tab. 9. LargeKernel3D improves CenterPoint [75] to \\(70.6\\%\\) and \\(72.8\\%\\) NDS, with and without test augmentation, both outperforming other LIDAR methods. The multi-modal modal LargeKernel3D-F further improves to \\(74.2\\%\\) NDS and \\(71.2\\%\\) mAP. The fusion module directly follows a simple painting-based manner [8]. Results on the val split is shown in the appendix." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.299, + 0.895, + 0.466 + ], + "angle": 0, + "content": "We also show the effectiveness of LargeKernel3D model on the vehicle detection of Waymo [57] validation set in Tab. 11. The kernel size of LargeKernel3D is \\(17 \\times 17 \\times 17\\). LargeKernel3D improves the vehicle performance of CenterPoint [75] by around \\(1.5\\%\\) LEVEL_1 AP / APH. Models listed take single-frame LIDAR data without any test-time augmentations or ensemble. It also performs better than other methods. We use CenterPoint [75] to keep consistency to the nuScenes benchmark. Note that LargeKernel3D has the potential to achieve further performance if equipped with stronger detection heads [55]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.487, + 0.749, + 0.503 + ], + "angle": 0, + "content": "6. Conclusion and Discussion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.515, + 0.892, + 0.742 + ], + "angle": 0, + "content": "We have studied large-kernel designs for 3D convolutional networks, which have essential differences from the solutions in 2D CNNs. We present spatial-wise partition convolution (SW Conv) that is specifically designed for 3D large kernels. It effectively resolves the efficiency and optimization issues in plain 3D large-kernel CNNs. Based on this design, we further propose the SW-LK Conv and the corresponding LargeKernel3D for 3D semantic segmentation and object detection. Our 3D large-kernel networks achieve decent improvement on both semantic segmentation and object detection tasks. For the first time, we show that 3D large kernels can be realized efficiently and effectively. We expect our findings to advance further development of 3D networks. Additional experiments and limitation analysis are provided in the appendix." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.748, + 0.892, + 0.84 + ], + "angle": 0, + "content": "Limitations LargeKernel3D mainly relies on hand-designed spatial kernel sizes in 3D semantic segmentation and object detection benchmarks. These sizes might be suboptimal for other datasets or tasks, depending on the overall scene sizes and data sparsity. Other search-based techniques [60] might be helpful, which we will try latter." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.845, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Acknowledgement. This work is supported by Shenzhen Science and Technology Program (KQTD20210811090149095), Hong Kong Research Grant Council - Early Career Scheme (No. 27209621), and General Research Fund Scheme (No. 17202422)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13495" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.117, + 0.468, + 0.144 + ], + "angle": 0, + "content": "[1] Lei Jimmy Ba, Jamie Ryan Kiros, and Geoffrey E. Hinton. Layer normalization. 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However, when directly applying large convolutional kernels in 3D CNNs, severe difficulties are met, where those successful module designs in 2D become surprisingly ineffective on 3D networks, including the popular depth-wise convolution. To address this vital challenge, we instead propose the spatial-wise partition convolution and its large-kernel module. As a result, it avoids the optimization and efficiency issues of naive 3D large kernels. Our large-kernel 3D CNN network, LargeKernel3D, yields notable improvement in 3D tasks of semantic segmentation and object detection. It achieves $73.9\%$ mIoU on the ScanNetv2 semantic segmentation and $72.8\%$ NDS nuScenes object detection benchmarks, ranking $1^{st}$ on the nuScenes LIDAR leaderboard. The performance further boosts to $74.2\%$ NDS with a simple multi-modal fusion. In addition, LargeKernel3D can be scaled to $17\times 17\times 17$ kernel size on Waymo 3D object detection. For the first time, we show that large kernels are feasible and essential for 3D visual tasks. Our code and models is available at github.com/dvlab-research/LargeKernel3D. + +# 1. Introduction + +3D Sparse convolutional neural networks (CNNs) have been widely used as feature extractors in 3D tasks, e.g., semantic segmentation [9,24] and object detection [55,65,75]. The advantages of efficiency and convenient usage ensure its important role in various applications, such as autonomous driving and robotics. However, 3D sparse CNNs are recently challenged by transformer-based methods [45,46,79], mainly from the aspect of building effective receptive fields. Both global and local [21,45] self-attention mechanisms are able to capture context information from a large spatial scope. 2D Vision Transformers (ViTs) also emphasize their advantages in modeling long-range dependencies [20,42,51]. In contrast, common 3D sparse CNNs are limited in this regard. It is because the receptive fields + +of default 3D sparse CNN are constrained by small kernel sizes and spatial disconnection of sparse features (due to the property of submanifold sparse convolution [25]). + +Literature about 2D CNNs [18, 43, 62] presents a series of methods, combined with large kernels, to enlarge the receptive fields and model capacity. ConvNeXt [43] employs $7 \times 7$ depth-wise convolution as a strong design, combing with other training techniques to challenge its Swin Transformer counterpart [42]. RepLKNet [18] pursues extremely large kernel sizes of $31 \times 31$ to boost the performance of different tasks. To ensure the effectiveness of RepLKNet [18], additional factors, including depth-wise convolution, are also required. Other work [27] also emphasizes the importance of depth-wise convolution. Due to differences between 3D and 2D tasks, these methods, however, are found not a good solution for 3D sparse CNNs. + +We first analyze the difficulties of 3D large-kernel CNN design in two aspects. The first challenge is efficiency. It is easy to understand that 3D convolution is with the cubic kernel size and computation increases fast. For example, the model size increases $10+$ times when kernels change from $3 \times 3 \times 3$ to $7 \times 7 \times 7$ . The second difficulty exists in the optimization procedure. 3D datasets may contain only thousands of scenes, which cannot match 2D image benchmarks [15, 40] in terms of scales. In addition, 3D point clouds or voxels are sparse, instead of dense images. Thus, it might be insufficient to optimize the proliferated parameters of large kernels and leads to over-fitting. + +In this paper, we propose spatial-wise partition convolution as the 3D large-kernel design. It is a new family of group convolution by sharing weights among spatially adjacent locations, rather than depth-wise convolution [29] of channel-level groups. As shown in Fig. 1, spatial-wise partition convolution remaps a large kernel $(e.g., 7 \times 7)$ as a small one $(e.g., 3 \times 3)$ via grouping spatial neighbors, while the absolutely large spatial size remains unchanged. With regard to the efficiency issue, it occupies few model sizes to keep parameters the same as those of small kernels. Moreover, it takes less latency, compared with plain large kernel counterparts. As for the optimization challenge, weight-sharing among spatial dimensions gives parameters more chance to update and overcome the over-fitting issue. + +![](images/7012f8da40b09801a0e5e833a2187f227f43c1f5e91081c6cb18774651966b7d.jpg) +Small-kernel sparse conv + +![](images/cea45d776185dfeb745398c2de74993d87bd89446abaa5826adbbd15361d6f16.jpg) +Large-kernel sparse conv +Figure 1. Sparse convolutions with different kernels. Small-kernel sparse convolution gathers features in a local area. It is efficient but discards sufficient information flow due to feature disconnection and the small scope. Large-kernel sparse convolution is capable of capturing long-range information, at the price of a large number of parameters and computation. Our proposed spatial-wise partition convolution uses large kernel sizes, and shares weights among local neighbors for efficiency. We show 2D features for the simplicity sake. + +![](images/64ace8631b92f635a6d6c2bcd90919523a388b114de5b4a09b66e5602dd7d47b.jpg) +Spatial-wise partition conv + +To increase the detail-capturing ability of large kernels [18], we introduce position embeddings for spatial-wise group convolution. It makes notable effects for large kernel sizes. We name the proposed block as spatial-wise large-kernel convolution (SW-LK Conv). We compare the efficiency between plain 3D submanifold sparse convolution and ours, as shown in Tab. 1. Both parameters and latency of the baseline increases dramatically, as its kernel size becomes larger, while ours is far more efficient. + +SW-LK Conv can readily replace plain convolution layers in existing 3D convolutional networks. We establish large-kernel backbone networks LargeKernel3D on existing 3D semantic segmentation [9] and object detection [16, 75] networks. It achieves notable improvement upon state-of-the-art methods [9, 16, 75], with a small model complexity overhead. Extensive experiments validate our effectiveness on large-scale benchmarks, including ScanNetv2 [13], nuScenes [4], and Waymo [57]. For object detection, LargeKernel3D achieves $72.8\%$ NDS on nuScenes, ranking $\mathbf{1}^{st}$ on the nuScenes LIDAR leaderboard. Without bells and whistles, it further improves to $74.2\%$ NDS in a simple voxel-wise multi-modal fusion manner. More importantly, it is scalable to $17\times 17\times 17$ kernel sizes on the large-scale Waymo 3D object detection. + +We visualize the Effective Receptive Fields (ERFs) of plain 3D CNNs and our LargeKernel3D in Fig. 2. It shows that deep small-kernel networks are also constrained by limited ERFs, since sparse features are spatially disconnected. Note that our large-kernel networks elegantly resolve this issue. For the first time, we show that large-kernel CNN designs become effective on essential 3D visual tasks. + +# 2. Related Work + +Convolutional Large-kernel Networks Large-kernel setting has been commonly used in 2D convolutional net + +works [18, 43, 68]. ConvNeXt [43] combines various training techniques and large kernel sizes, to compete with Swin Transformer [42]. RepLKNet [18] is a specific work that focuses on large-kernel designs. It reveals that the large kernel sizes are more beneficial to tasks of object detection and semantic segmentation than image classification. GCNs [47] also show improvement from large-kernel designs on semantic segmentation. There are methods approximating large kernel sizes using implicit techniques, including Fourier domain transformation [52], and continuous functions [53]. Other methods change kernel shapes to enlarge receptive fields using dilated convolutions [5, 76], deformable convolutions [14, 81] and active convolutions [31]. These schemes sparsify kernels, and is hard to capture the original sparse features in 3D deep learning. + +3D Feature Extractors A key challenge in 3D tasks [32,38] is to learn effective representation from the sparse and non-uniformed 3D geometric data, e.g., point clouds. In general, there are two kinds of 3D feature extractors. The first is to learn on point cloud directly, using a series of PointNet networks [48, 49]. The sampling and grouping operations in PointNet++ [49] are also time-consuming. Followups [46, 79] use grid-sampling or scene-partition to save computation in each forward and combine results from multiple runs. The second is to process point clouds with voxelization and apply 3D sparse CNNs. Due to its efficiency advantages, this stream of methods has been widely used in various 3D tasks, such as 3D segmentation [9-11, 33] and backbone networks in 3D object detectors [16, 26, 55, 64]. + +The spatial group convolution (SGC) [78] is relevant to the proposed spatial-wise partition convolution. SGC is originally designed for the task of 3D scene completion. They both conduct the partition operation spatially. The difference is also essential and clear. Our method partition kernel weighs while SGC splits input features into groups. In terms of targets, SGC focuses more on efficiency improve + +Table 1. Efficiency comparison between plain 3D sparse convolution and our SW-LK Conv. The baseline is a submanifold sparse convolutional layer with input and output channels 16. The input data is a sparse tensor with 80,000 voxels randomly scattered and batch size 1. We test all latencies on a single 2080Ti GPU by an average of 10 times running, after a warm-up start of additional 10 times. + +
Kernel Size3×3×35×5×57×7×79×9×911×11×1113×13×1315×15×1517×17×17
PlainParams6.9 K32.0 K87.8 K186.6 K340.7 K562.4 K864.0 K1.3 M
Latency2.5 ms4.2 ms8.9 ms17.5 ms31.1 ms55.1 ms81.1 ms106.3 ms
OursParams-8.9 K12.4 K18.6 K28.2 K42.1 K60.9 K85.5 K
Latency-3.4 ms3.9 ms4.8 ms6.2 ms8.4 ms11.4 ms15.8 ms
+ +ment by changing feature sparsity in each spatial group, while our method is to facilitate large kernels in 3D tasks. Further analysis and comparisons are given in experiments. + +Vision Transformer Vision transformers that conduct attention computation in local areas or windows share a similar spirit with large-kernel models [18]. Swin Transformers [42] capture features in shifted windows with sizes from 7 to 12. Its variants [19, 41] show that larger window sizes are beneficial to performance. Focal Transformer [71] captures fine-grained local attention with adaptive patch sizes. SST [21] and Stratified Transformer [34] apply window-based self-attention on 3D detection and segmentation. + +Position Encoding Since the self-attention in transformers is permutation-equivalent, position encoding is well-designed for imbuing the network with the position information. It can be grouped into two streams of absolute and relative position encoding. For the first group, positions are encoded in a precise manner. Specifically, encoding [63] is generated with the sinusoidal functions of different frequencies. They are then added to the input. In contrast, relative position encoding [54] takes the relative relationship into consideration. It can naturally handle longer sequences and is more scalable. Most work [3, 50, 66, 73] computes the relative distance between tokens and applies implicit encoding using learnable transformations. Besides, the literature [12] shows that convolution with padding can provide effective relative position information for relative position encoding. In addition to transformers, the recent work [72] also shows that position embedding is beneficial to the CNNs with fourier transformation. + +Considering that our spatial-wise partition convolution divides the kernel into different portions in pursuit of higher efficiency. The position information may be blurred due to weight sharing in each portion. We thus use relative position encoding as a bias to supplement the lost position information. More details are provided in Sec. 4. + +# 3. Revisiting 3D Sparse CNNs + +Preliminary 3D sparse CNNs consist of 3D sparse convolutions, which are typically regular and submanifold sparse + +convolutions [25]. We formulate 3D sparse convolutions in Eq. (1). Given a set of sparse input features $\{\mathbf{x}_{p\in P}\}$ with a number of $c_{\mathrm{in}}$ channels, the position of each feature $p\in P$ sparsely distributes in 3D space. We process these features by a convolution with kernel weights $\mathbf{w}\in \mathbb{R}^{|K| \times c_{\mathrm{in}} \times c_{\mathrm{out}}}$ . For example, in the 3D coordinate space, $\mathbf{w}$ contains $c_{\mathrm{in}} \times c_{\mathrm{out}}$ spatial kernels with size 3 and $|K| = 27$ . The convolution process at the output position $\bar{p}$ is represented as + +$$ +\mathrm {y} _ {\bar {p}} = \sum_ {k \in K} \mathrm {w} _ {k} \cdot \mathrm {x} _ {\bar {p} + k}, \tag {1} +$$ + +where $k$ is an 3D offset distance from $\bar{p}$ . $\bar{p} + k$ is the location around center $\bar{p}$ . It enumerates all discrete locations in the kernel space $K$ where sparse features $\mathbf{x}_{\bar{p} + k}$ exist. + +Convolution Types Regular sparse convolutions enlarge their output positions by dilating each input position $p \in P$ to the kernel shape $K$ . It dramatically decreases feature density and increases the computational burden. Thus, regular sparse convolutions with stride 2 are only employed at the first layer in each stage for down-sampling. Submanifold sparse convolutions, in contrast, fix their output positions $\bar{p}$ identical to input positions $p \in P$ , which preserves the computation cost at low levels. Please refer to the original paper [25] for more details. + +Due to the efficiency advantage, submanifold sparse convolutions dominate most layers of 3D CNNs, except for the down-sampling layers. However, limited by the small local scope, it misses sufficient information flow for the spatially disconnected features. Increasing kernel sizes becomes a potential solution to relieve this issue. + +Obstacles in 3D Large Kernels Efficiency is the first issue in 3D large-kernel CNNs. When we increase kernel sizes, the amount of parameters and computational burden grows much faster than those of 2D CNNs. For instance, the parameter amount in one 3D convolutional layer increases from $27 \cdot C_{in \cdot out}$ to $343 \cdot c_{in} \cdot c_{out}$ , given its kernel size changing from 3 to 7. It is thus clear that naively enlarging 3D kernels is unreasonable. + +Optimization difficulty is the second obstacle. The booming parameters require sufficient data for learning. How- + +![](images/8f4373936a081c48af3a50c9f77409e663af35690da8ce009898d2a09f2324bf.jpg) +(a) Plain 3D CNN + +![](images/90ca9a1279931199f5c1b34c13b953d2f94afa692ea8e8f87c5fd04ea3b59ca0.jpg) +(b) Plain 3D CNN - 2x + +![](images/9d2afaa194ef9ec7eea68f981ef69034c946b11a49d48e3f2d7d94fd49e98b55.jpg) +(c) LargeKernel3D +Figure 2. Effective Receptive Fields (ERF) of plain 3D CNN, plain 3D CNN - $2 \times$ , and our LargeKernel3D for 3D object detection. The plain 3D CNN backbone has insufficient ERF size, which hardly covers a nearby car. Plain 3D CNN - $2 \times$ is a deeper version with its layers doubled in each stage. More layers help little in ERF, as the disconnection between sparse features. Our LargeKernel3D obtains large ERF at both the object centers (left) and edges (right), capturing context information. More illustrations are provided in the appendix. The figure is best viewed in color and by zoom-in. + +![](images/bc9ae4b31ba796d0c855e673deeb60a0c624ad6ceeb8ab53d47c48cacc87c6ab.jpg) +Feature of interest + +![](images/29e089707ad2b981be90e1ac90c16b08cabc705cb82ee42a70005524220d3b3a.jpg) +Magnitude of ERF + +ever, 3D datasets are commonly not in that large scale as 2D benchmarks. For example, ImageNet [15] contains millions of images, while 3D datasets commonly contain only no more than one thousand scenes. The over-fitting issue gradually deteriorates the performance when increasing kernel sizes from $3 \times 3 \times 3$ to $7 \times 7 \times 7$ in MinkowskiNet-34 [9]. + +Previous 2D knowledge is not helpful in 3D large-kernel CNNs. Recent 2D methods [18, 43] show some helpful components in large-kernel CNNs, including depth-wise convolutions [29], layer normalization [1], GELU [28] activation. We examine these popular components and find that they are either ineffective or even harmful in 3D CNNs. To demonstrate this finding, we use MinkowskiNet-34 [9] to benchmark and train on the 3D semantic segmentation dataset of ScanNetv2 [13]. We change the original activation function from ReLU to GELU, batch normalization to layer normalization, and plain convolution to depth-wise operation, respectively. Directly using these components makes the final system yield performance drop on both small and large kernel networks. It requires us to seek other ways to construct 3D large-kernel CNNs. + +# 4. 3D Large-kernel Convolutional Network + +# 4.1. Spatial-wise Partition Convolution + +A standard convolution kernel can be viewed as a 3D matrix, which consists of input channels $C_{\mathrm{in}}$ , output channels $C_{\mathrm{out}}$ , and the spatial kernel dimension $|K|$ . Taking kernel size as $k$ , the volume of spatial kernel dimension $|K| = k \times k$ for 2D convolutions and $k \times k \times k$ for 3D convolutions. Depth-wise convolutions share weights along channel dimensions, where group numbers equal to input channels. Point-wise convolutions fix kernel size as 1, which is common as a conjunction layer to depth-wise convolutions to adjust output channels. + +Different from 2D methods, which rely on depthwise convolutions for performance boosting [27, 43] and accuracy-FLOPs trade-offs [18], we empirically find that + +![](images/6e602c8795741cc5cc6ecc030aa488440413ecefcbf2e328442422ba2e6a648c.jpg) +Figure 3. Illustration on spatial-wise partition convolution. In the plain large-kernel convolution, due to the sparsity of input features, only a small proportion of weights are involved and updated in each training step. The spatial-wise partition convolution relieves this issue by sharing weights among spatial neighbors. It increases the chance for weights to be optimized. During inference, we reformulate the spatial-wise partition convolutions into small ones, with feature assignment in a large scope. + +![](images/eb332a305d5b6a514cb12c507458607ae072f4338c1daca62578f81b37087a71.jpg) +feature + +![](images/297098d66294db1a446494caf032616047ac976bf79953b61e557dc28900cad8.jpg) +weight + +![](images/e5f5173fb694520f7d92b37a01f8d0d9707b714a396416337803e50819d98c57.jpg) +group +assign + +![](images/0020c31d6aa5fe563383023250eaa512b46318323c5bf1fd3d324024d14aa3be.jpg) + +depth-wise convolutions are not beneficial to 3D tasks, no matter whether point-wise convolutions are included. + +We instead propose spatial-wise partition convolution for 3D large-kernel CNNs. It shares weights among spatial dimension $K$ on convolutional kernels, instead of among channel dimension. It is also different from SGC [78], which partitions spatial groups on input features. Specially, in Eq. (1), $w_{k}$ shares the same values in a local area $k \in K$ . We thus group the original large-kernel convolution from $7 \times 7$ into $3 \times 3$ , by sharing weights among spatial neighbors. Spatial-wise partition convolution is specially designed for 3D tasks and has the following advantages in terms of efficiency and performance. + +Regarding efficiency, when naively enlarging the kernel size from $3 \times 3 \times 3$ to $7 \times 7 \times 7$ on MinkowskiNet-34 [9], both model size and latency have a sharp increase by multiple times. In contrast, our spatial-wise partition convolution avoids increasing parameters and introduces limited latency overhead. The advantage of our method over plain large kernels attributes to the specific implementation of sparse + +![](images/a71e09d5a750e504684d67c2d222f2532206e293c0b72fa47f4ad4548a7f4fcc.jpg) +Input & Weight + +![](images/bba440df8df5086009492dd08de536228cb53b44260915b5a4f79bba292fa875.jpg) + +![](images/f21bf1001bad0c6cfbc2680ad24c2b895eb89c3058b81e4435fc802a93b6a022.jpg) +Position Encodings + +![](images/6d57a0400b83600c0c4d93bf62896aef93de291d47707f20ce88cef87ba8f6b2.jpg) + +![](images/37659452c43261793e96a5d9aed1fd48507de048b76bc2b5d0e060cf63478652.jpg) +Output & Weight + +![](images/aaeaaca078c9d53f1150a74f595190e6f0fa75329a638660ff568122d065a23b.jpg) +Sparse feature + +![](images/e5c02c82c9d8f99cd794fc38494989db12c351fc8407a63fae44dee0c0f438c5.jpg) +Conv weight + +![](images/1b0cba53db37c124ef02e54263dd5b7679f7ac08dad302d7fc74235082b76c5b.jpg) +Position encoding + +![](images/74d9a1316e66b36722b961b932360297b24a07ddb10e61e6235837b96fcfef0a.jpg) +Spatial-wise group +Figure 4. Structure of spatial-wise large-kernel convolution (SW-LK Conv). It consists of a large-kernel spatial-wise partition convolution and a learnable position embedding. The position embedding is used to make up the detail-capturing ability of large kernels. + +convolution. For a spatial-wise partition convolution, we directly use the small-kernel layer during inference, and enlarge its feature-assign areas to the large-kernel scope. As shown in Fig. 3, thanks to the weight-sharing operation, it much saves the multiplication, e.g., from 343 to 27 times. We implement this operation upon the open-sourced spconv library and omit the details here. Tab. 4 shows that our implementation on spatial-wise partition convolution is far more efficient than the plain large-kernel baseline. The optimization difficulty of large-kernel CNNs is relieved with the help of spatial-wise partition convolutions, which constrains model sizes to a limited number. It avoids requiring a large amount of data for training and the over-fitting issue. + +# 4.2. Kernel-wise Position Encoding + +Considering that the spatial-wise partition convolution is designed in a sharing weights manner against the spatial sparsity. Although this design is efficient, there is still an issue: voxels within an area share the same weight, which results in local details blurred. This phenomenon is further amplified with an increase of kernel sizes. To address this problem, we propose the kernel-wise position embedding. We illustrate this design in Fig. 4. + +Particularly, we initialize position weights $\mathrm{e} \in \mathbb{R}^{K \times c_{\mathrm{in}}}$ , which corresponds to the convolution kernel. During the convolution process, we let the input features query the position weights of the equivalent position and add them together. This process modifies Eq. (1) to + +$$ +\mathrm {y} _ {\bar {p}} = \sum_ {k \in K} \mathrm {w} _ {k} \cdot \left(\mathrm {x} _ {\bar {p} + k} + \mathrm {e} _ {k}\right). \tag {2} +$$ + +This simple design essentially adds bias with relative position information to the input features. There is almost no extra calculation and additional parameters. It is a decent solution to the position insensitivity problem caused by sharing weights, especially for the extremely large kernels, e.g., $17 \times 17 \times 17$ . For more experimental results and details, please refer to the Sec. 5. + +# 4.3. Large-kernel Architecture + +Following the above designs and observations, we now describe the architectures of our large-kernel 3D CNNs. We readily replace the plain 3D submanifold sparse convolution [25] layers with our SW-LK Conv in existing 3D backbones for semantic segmentation and object detection. + +3D Semantic Segmentation The architectures of LargeKernel3D for 3D semantic segmentation resemble MinkowskiNet [9], including 1 stem layer and 8 stages. The stem layer is a $5 \times 5 \times 5$ submanifold convolution. The first 4 stages account for down-sampling and the last 4 stages are for up-sampling. As for the U-Net structure, the first 4 features are concatenated into the up-sampling stages. We replace the original layers in MinkowskiNet-34 [9] by SW-LK Convs, where spatial-wise $7 \times 7 \times 7$ convolutions is grouped into $3 \times 3 \times 3$ splits. By default, other hyper-parameters, including channels and block numbers, follow MinkowskiNet-34 [9]. +3D Object Detection The typical backbone networks in 3D object detectors [16, 55, 75] consist of 1 stem layer and 4 stages. A $3 \times 3 \times 3$ submanifold convolution [25] layer serves as the stem. In each stage, except for the first one, there is a sparse convolutional layer with stride 2 for down-sampling. We substitute other plain blocks with SW-LK Convs. For models on nuScenes dataset, we find that $7 \times 7 \times 7$ kernel sizes are enough. They both use the $3 \times 3 \times 3$ spatial-wise groups. For models on Waymo dataset, kernel sizes are scalable to $17 \times 17 \times 17$ . We remain the last stage of backbone network as the original, because receptive fields have already been sufficiently enlarged in the front stages. We keep these hyper-parameters unchanged by the default settings in baseline detectors [16, 75]. We include these detailed numbers in appendix. + +# 5. Experiments + +# 5.1. Experimental Setting + +3D Semantic Segmentation ScanNetv2 [13] is a large-scale benchmark in 3D semantic segmentation. It con + +Table 2. Ablations on various techniques and kernel sizes on MinkowskiNet-34 and ScanNetv2. LN denotes the layer normalization. DW Conv denotes the depth-wise convolution. + +
KernelBaseline+GELU+LN+DW Conv+PWOurs
3×3×371.770.266.870.670.7-
7×7×768.668.465.068.768.773.5
+ +Table 3. Ablations on group convolution on ScanNetv2. + +
KernelBaselineGroup 24816DWOurs
3x3x371.771.571.270.770.670.6-
7x7x768.668.869.268.868.768.773.5
+ +Table 4. Comparisons with relevant convolutional schemes on ScanNetv2. Baseline is a MinkowskiNet-34 network. All models listed are trained in the same training hyper-parameters. + +
MethodParamsFLOPsLatencymIoU
Baseline37.9 M182.8 G108 ms71.7
+ Kernel 5×5×5170.3M537.5 G212 ms70.7
+ Kernel 7×7×7465.0M1089.5 G487 ms68.6
Dilate conv37.9M100.1 G98 ms64.6
Pooling + Dilate37.9M183.2 G115 msnan
Spatial group [78]37.9M127.2 G96 ms70.0
Deformable conv42.5M250.1 G238 ms72.0
LargeKernel3D-T38.4M171.4 G111 ms72.8
LargeKernel3D40.2M240.0 G145 ms73.5
+ +Table 5. Results on other backbone networks andScanNetv2. + +
ModelBaseline+OursΔ
MinkowskiNet-14 [9]67.069.7+2.7
MinkowskiNet-18 [9]69.571.5+2.0
SparseConvNet [24]69.371.2+1.9
+ +tains 1,201 indoor RGB-D scenes for training, 312 scenes for validation, and 100 scenes for testing. Semantic labels in 20 categories are annotated. We train our models with the default settings in MinkowskiNet [9], including training hyper-parameters and data augmentations. We evaluate models in the mean Intersection over Union (mIoU) metric. Detailed experimental settings, including network structures and training details, are listed in the appendix. + +3D Object Detection nuScenes, and Waymo are all popular 3D object detection benchmarks. nuScenes is a large dataset and contains 1,000 driving sequences in total. Among them, there are 700 scenes split for training, 150 scenes for validation, and 150 scenes for testing. It contains LIDAR, camera, and radar sources with a complete $360^{\circ}$ environment. We evaluate our methods on both LIDAR-only and LIDAR- + +Table 6. Effects of the spatial-wise partition manners on SW-LK Conv and ScanNetv2. Center group means the size of central area. Shifting is to translate the center position by 1 in all 3 dimensions. + +
Center group1×1×11×1×13×3×35×5×5
ShiftingX✓XX
mIoU73.566.870.668.2
+ +Table 7. Improvement over various kernel sizes on LargeKernel3D upon CenterPoint, training on 1/5 Waymo training set and evaluate on the validation set. $\Delta$ means the improvement from the kernel 3 baseline. L1 and L2 means LEVEL_1 and LEVEL_2 mAP. + +
KernelVehiclePedestrianCyclist
L1L2L1L2L1L2
Baseline70.962.971.563.569.166.5
7×7×771.963.871.763.770.467.8
11×11×1172.264.271.863.970.268.3
15×15×1572.764.673.865.870.868.2
17×17×1773.265.174.166.071.068.1
Δ2.3↑2.2↑2.6↑2.5↑1.9↑1.6↑
+ +Table 8. Effects of position embedding (PE) in the mAP of vehicle detection on Waymo validation set. + +
KernelPELatencyLEVEL_1LEVEL_2
3×3×3-109 ms70.962.9
7×7×7×120 ms71.663.4
✓122 ms71.963.8
17×17×17×158 ms71.563.3
✓164 ms73.265.1
+ +RGB fusion settings. The main evaluation metrics are mAP and nuScenes detection score (NDS). Waymo [57] dataset also contains 1,000 sequences in total, with 798 for training and 202 for validation. For Waymo dataset, we use 1/5 training data for the ablation study and full training set for main results. Results in Waymo are evaluated on difficulty LEVEL_1 and LEVEL_2 objects. In experiments, we validate our networks on state-of-the-art detection framework of CenterPoint [75] on nuScenes [4] and Waymo [57]. + +# 5.2. Ablation Studies + +Usefulness of 2D CNN Techniques We first validate the techniques that have proven effective on 2D CNNs, including layer normalization [1], depth-wise convolution [29, 43], and GeLU [28]. We conduct experiments on MinkowskiNet-34 [9] on the ScanNet [13] semantic segmentation dataset, as shown in Tab. 2. Kernel $7 \times 7 \times 7$ means modifying kernel sizes in all stages to 7. All these + +Table 9. Comparison with other methods on nuScenes test split. $\ddagger$ means flipping and rotation testing-time augmentations. + +
MethodNDSmAPCarTruckBusTrailerC.V.PedMotBycT.C.Bar
PointPillars [35]45.330.568.423.028.223.44.159.727.41.130.838.9
3DSSD [74]56.442.681.247.261.430.512.670.236.08.631.147.9
CBGS [80]63.352.881.148.554.942.910.580.151.522.370.965.7
CenterPoint [75]65.558.084.651.060.253.217.583.453.728.776.770.9
HotSpotNet [7]66.059.383.150.956.453.323.081.363.536.673.071.6
CVCNET [6]66.658.282.649.559.451.116.283.061.838.869.769.7
UVTR-L [37]69.763.986.352.262.859.733.784.568.841.174.774.9
VISTA [17]69.863.084.455.163.754.225.182.870.045.478.571.4
Focals Conv [8]70.063.886.756.367.759.523.887.564.536.381.474.1
TransFusion-L [2]70.265.586.256.766.358.828.286.168.344.282.078.2
LargeKernel3D70.665.485.553.864.459.529.785.972.746.879.975.5
LargeKernel3D‡72.868.786.758.567.762.731.988.577.154.982.376.6
LargeKernel3D-F‡74.271.287.760.169.366.034.389.481.360.286.777.4
+ +techniques bring no obvious benefit to baseline networks. In contrast, SW-LK Conv introduces clear improvement upon these strong networks. We also show the effects of group convolution with different group numbers in Tab. 3. + +Comparisons with Relevant Schemes We compare both performance and efficiency in Tab. 4 using various existing schemes to enlarge receptive fields. Dilated Conv [5] contains $3 \times 3 \times 3$ kernel parameters. It dilates to $7 \times 7 \times 7$ spatial sizes. Pooling + Dilated Conv inserts a 3D average pooling layer before the dilated convolutions to enlarge receptive fields. Spatial group conv is implemented, following the settings in the original paper [78]. We extend Deformable Conv [14] to 3D offset prediction, following [61]. Latencies are measured on an NVIDIA 2080ti GPU. It shows that none of these related schemes present better performance than the baseline. One reason for the low performance of dilation and deformable convolutions is that they tend to factorize the original dense kernels into sparse ones, which cause more information loss when applied to sparse 3D features than their 2D counterparts. Our LargeKernel3D achieves the best performance among these methods. In addition, we also build a tiny version, LargeKernel3D-T, which has half channel numbers in the last two stages. It introduces almost no additional computation overhead to baseline, but still has notable performance improvement. Except for the MinkowskiNet-34, we also show our effects on other backbone networks in Tab. 5. + +Spatial-wise Group Partition Manner We ablate the effects of different spatial-wise group partition manners in Tab. 6. We study the size of central groups and center shifting. This ablation study is conducted on the LargeKernel3D and the Scannetv2 dataset. We find that both large central + +Table 10. Comparison on ScanNetv2 mIoU on 3D semantic segmentation. † Sliding-window testing. + +
MethodLatencyvaltest
PointCNN [36]--45.8
PointNet++ [49]-53.555.7
RandLA-Net [30]--64.5
PointConv [67]80 ms61.066.6
PointASNL [69]-63.566.6
KPConv [61]-69.268.6
FusionNet [77]--68.8
Point Transformer† [79]1012 ms70.6-
Fast Point Transformer [46]298 ms72.1-
SparseConvNet [24]-69.372.5
Stratified Transformer† [34]1624 ms74.373.7
MinkowskiNet-34108 ms71.7
+ LargeKernel3D14573.573.9
+ +sizes and center shifting hurt the performance. As the center sizes enlarge from $1 \times 1 \times 1$ to $5 \times 5 \times 5$ , the accuracy sharply drops. Because submanifold sparse convolution [25] always aligns each individual voxel feature at its kernel center, we suppose that central features should maintain distinct and clean. Therefore, we keep the center size as $1 \times 1 \times 1$ without shifting, as a default setting. + +Further Enlarging Kernel Sizes We show that LargeKernel3D is scalable to kernel sizes $17 \times 17 \times 17$ on the outdoor dataset Waymo [57] in Tab. 7 with baseline kernel $3 \times 3 \times 3$ . Models in this ablation are trained on $1/5$ training data and evaluated on the full validation set. Results with full training data are compared in Tab. 11. It shows that the mAP on all categories increases by around $2\%$ . This setting demon- + +Table 11. Performance of vehicle detection on the Waymo val split. All models listed take LIDAR-only input and single frames, without any test-time augmentations or model ensemble. + +
MethodLEVEL_13D AP / APHLEVEL_23D AP / APH
VoTr-SSD [45]68.99 / 68.3960.22 / 59.69
PointPillars [75]72.08 / 71.5363.55 / 63.06
SECOND [70]72.27 / 71.6963.85 / 63.33
RangeDet [23]72.85 / 72.3364.03 / 63.57
SST [22]74.22 / 73.7765.47 / 65.07
VoTr-TSD [45]74.95 / 74.2565.91 / 65.29
RSN [59]75.1 / 74.666.0 / 65.5
Voxel RCNN [16]75.59 / ——66.59 / ——
LIDAR-RCNN [39]76.0 / 75.568.3 / 67.9
SST [22]76.22 / 75.7968.04 / 67.64
Pyramid RCNN [44]76.30 / 75.6867.23 / 66.68
Part-A2-Net [56]77.05 / 76.5168.47 / 67.14
PV-RCNN [55]77.51 / 76.8968.98 / 68.41
SWFormer [58]69.2 / 68.880.9 / 72.7
CenterPoint [75]76.59 / 76.0568.85 / 68.35
+ LargeKernel3D78.07 / 77.6169.81 / 69.38
+ +strates that a large-scale dataset is a key to unlocking the potential and capability of large kernel methods. In addition, we also try to extend the kernel size to $19 \times 19 \times 19$ , but obtain no further gains. + +Effects of Position Embedding In LargeKernel3D, position embedding is introduced to relieve the feature-blurring issue caused by weight-sharing. We ablate its effects in Tab. 8, in terms of both latency and performance. Position embedding introduces limited latency overhead on both kernel $7 \times 7 \times 7$ and $17 \times 17 \times 17$ models. In terms of performance, its effects on the $7 \times 7 \times 7$ model are a bit marginal, but essential on the $17 \times 17 \times 17$ model, which has larger kernel sizes and suffers from feature blurring. + +Shrinking Kernels During Inference For the spatial-wise partition convolution, we can shrink kernels into small ones during inference. As shown in Tab. 4, the latency of LargeKernel3D is $145\mathrm{ms}$ on ScanNetv2. It degrades to $514\mathrm{ms}$ with the same $73.5\%$ mIoU, if we disable shrinking. + +# 5.3. Main Results + +3D Semantic Segmentation We make comparisons with other 3D semantic segmentation methods on the ScanNetv2 dataset in Tab. 10. Our method surpasses others on test split. MinkowskiNet [9] is already a state-of-the-art method in ScanNetv2. Our SW-LK Conv further improves its performance. Our method is also superior to transformer-based methods [46,79]. Stratified Transformer [34] uses a sliding- + +window testing technique† and splits integrated scenes into overlapped parts. The method tests each part one by one and then ensembles results together, taking hours on evaluation. Moreover, our results are better on the test split. + +3D Object Detection We compare our LargeKernel3D upon CenterPoint [75] with previous methods on the test split of the nuScenes [4] dataset in Tab. 9. LargeKernel3D improves CenterPoint [75] to $70.6\%$ and $72.8\%$ NDS, with and without test augmentation, both outperforming other LIDAR methods. The multi-modal modal LargeKernel3D-F further improves to $74.2\%$ NDS and $71.2\%$ mAP. The fusion module directly follows a simple painting-based manner [8]. Results on the val split is shown in the appendix. + +We also show the effectiveness of LargeKernel3D model on the vehicle detection of Waymo [57] validation set in Tab. 11. The kernel size of LargeKernel3D is $17 \times 17 \times 17$ . LargeKernel3D improves the vehicle performance of CenterPoint [75] by around $1.5\%$ LEVEL_1 AP / APH. Models listed take single-frame LIDAR data without any test-time augmentations or ensemble. It also performs better than other methods. We use CenterPoint [75] to keep consistency to the nuScenes benchmark. Note that LargeKernel3D has the potential to achieve further performance if equipped with stronger detection heads [55]. + +# 6. Conclusion and Discussion + +We have studied large-kernel designs for 3D convolutional networks, which have essential differences from the solutions in 2D CNNs. We present spatial-wise partition convolution (SW Conv) that is specifically designed for 3D large kernels. It effectively resolves the efficiency and optimization issues in plain 3D large-kernel CNNs. Based on this design, we further propose the SW-LK Conv and the corresponding LargeKernel3D for 3D semantic segmentation and object detection. Our 3D large-kernel networks achieve decent improvement on both semantic segmentation and object detection tasks. For the first time, we show that 3D large kernels can be realized efficiently and effectively. We expect our findings to advance further development of 3D networks. Additional experiments and limitation analysis are provided in the appendix. + +Limitations LargeKernel3D mainly relies on hand-designed spatial kernel sizes in 3D semantic segmentation and object detection benchmarks. These sizes might be suboptimal for other datasets or tasks, depending on the overall scene sizes and data sparsity. Other search-based techniques [60] might be helpful, which we will try latter. + +Acknowledgement. This work is supported by Shenzhen Science and Technology Program (KQTD20210811090149095), Hong Kong Research Grant Council - Early Career Scheme (No. 27209621), and General Research Fund Scheme (No. 17202422). + +# References + +[1] Lei Jimmy Ba, Jamie Ryan Kiros, and Geoffrey E. Hinton. Layer normalization. CoRR, abs/1607.06450, 2016. 4, 6 +[2] Xuyang Bai, Zeyu Hu, Xinge Zhu, Qingqiu Huang, Yilun Chen, Hongbo Fu, and Chiew-Lan Tai. Transfusion: Robust lidar-camera fusion for 3d object detection with transformers. 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However, when directly applying large convolutional kernels in 3D CNNs, severe difficulties are met, where those successful module designs in 2D become surprisingly ineffective on 3D networks, including the popular depth-wise convolution. To address this vital challenge, we instead propose the spatial-wise partition convolution and its large-kernel module. As a result, it avoids the optimization and efficiency issues of naive 3D large kernels. Our large-kernel 3D CNN network, LargeKernel3D, yields notable improvement in 3D tasks of semantic segmentation and object detection. It achieves " + }, + { + "bbox": [ + 46, + 230, + 290, + 482 + ], + "type": "inline_equation", + "content": "73.9\\%" + }, + { + "bbox": [ + 46, + 230, + 290, + 482 + ], + "type": "text", + "content": " mIoU on the ScanNetv2 semantic segmentation and " + }, + { + "bbox": [ + 46, + 230, + 290, + 482 + ], + "type": "inline_equation", + "content": "72.8\\%" + }, + { + "bbox": [ + 46, + 230, + 290, + 482 + ], + "type": "text", + "content": " NDS nuScenes object detection benchmarks, ranking " + }, + { + "bbox": [ + 46, + 230, + 290, + 482 + ], + "type": "inline_equation", + "content": "1^{st}" + }, + { + "bbox": [ + 46, + 230, + 290, + 482 + ], + "type": "text", + "content": " on the nuScenes LIDAR leaderboard. The performance further boosts to " + }, + { + "bbox": [ + 46, + 230, + 290, + 482 + ], + "type": "inline_equation", + "content": "74.2\\%" + }, + { + "bbox": [ + 46, + 230, + 290, + 482 + ], + "type": "text", + "content": " NDS with a simple multi-modal fusion. In addition, LargeKernel3D can be scaled to " + }, + { + "bbox": [ + 46, + 230, + 290, + 482 + ], + "type": "inline_equation", + "content": "17\\times 17\\times 17" + }, + { + "bbox": [ + 46, + 230, + 290, + 482 + ], + "type": "text", + "content": " kernel size on Waymo 3D object detection. For the first time, we show that large kernels are feasible and essential for 3D visual tasks. Our code and models is available at github.com/dvlab-research/LargeKernel3D." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 505, + 128, + 517 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 505, + 128, + 517 + ], + "spans": [ + { + "bbox": [ + 47, + 505, + 128, + 517 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 525, + 288, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 525, + 288, + 694 + ], + "spans": [ + { + "bbox": [ + 46, + 525, + 288, + 694 + ], + "type": "text", + "content": "3D Sparse convolutional neural networks (CNNs) have been widely used as feature extractors in 3D tasks, e.g., semantic segmentation [9,24] and object detection [55,65,75]. The advantages of efficiency and convenient usage ensure its important role in various applications, such as autonomous driving and robotics. However, 3D sparse CNNs are recently challenged by transformer-based methods [45,46,79], mainly from the aspect of building effective receptive fields. Both global and local [21,45] self-attention mechanisms are able to capture context information from a large spatial scope. 2D Vision Transformers (ViTs) also emphasize their advantages in modeling long-range dependencies [20,42,51]. In contrast, common 3D sparse CNNs are limited in this regard. It is because the receptive fields" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 205, + 545, + 242 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 205, + 545, + 242 + ], + "spans": [ + { + "bbox": [ + 306, + 205, + 545, + 242 + ], + "type": "text", + "content": "of default 3D sparse CNN are constrained by small kernel sizes and spatial disconnection of sparse features (due to the property of submanifold sparse convolution [25])." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 243, + 546, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 243, + 546, + 399 + ], + "spans": [ + { + "bbox": [ + 304, + 243, + 546, + 399 + ], + "type": "text", + "content": "Literature about 2D CNNs [18, 43, 62] presents a series of methods, combined with large kernels, to enlarge the receptive fields and model capacity. ConvNeXt [43] employs " + }, + { + "bbox": [ + 304, + 243, + 546, + 399 + ], + "type": "inline_equation", + "content": "7 \\times 7" + }, + { + "bbox": [ + 304, + 243, + 546, + 399 + ], + "type": "text", + "content": " depth-wise convolution as a strong design, combing with other training techniques to challenge its Swin Transformer counterpart [42]. RepLKNet [18] pursues extremely large kernel sizes of " + }, + { + "bbox": [ + 304, + 243, + 546, + 399 + ], + "type": "inline_equation", + "content": "31 \\times 31" + }, + { + "bbox": [ + 304, + 243, + 546, + 399 + ], + "type": "text", + "content": " to boost the performance of different tasks. To ensure the effectiveness of RepLKNet [18], additional factors, including depth-wise convolution, are also required. Other work [27] also emphasizes the importance of depth-wise convolution. Due to differences between 3D and 2D tasks, these methods, however, are found not a good solution for 3D sparse CNNs." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 400, + 547, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 400, + 547, + 544 + ], + "spans": [ + { + "bbox": [ + 304, + 400, + 547, + 544 + ], + "type": "text", + "content": "We first analyze the difficulties of 3D large-kernel CNN design in two aspects. The first challenge is efficiency. It is easy to understand that 3D convolution is with the cubic kernel size and computation increases fast. For example, the model size increases " + }, + { + "bbox": [ + 304, + 400, + 547, + 544 + ], + "type": "inline_equation", + "content": "10+" + }, + { + "bbox": [ + 304, + 400, + 547, + 544 + ], + "type": "text", + "content": " times when kernels change from " + }, + { + "bbox": [ + 304, + 400, + 547, + 544 + ], + "type": "inline_equation", + "content": "3 \\times 3 \\times 3" + }, + { + "bbox": [ + 304, + 400, + 547, + 544 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 400, + 547, + 544 + ], + "type": "inline_equation", + "content": "7 \\times 7 \\times 7" + }, + { + "bbox": [ + 304, + 400, + 547, + 544 + ], + "type": "text", + "content": ". The second difficulty exists in the optimization procedure. 3D datasets may contain only thousands of scenes, which cannot match 2D image benchmarks [15, 40] in terms of scales. In addition, 3D point clouds or voxels are sparse, instead of dense images. Thus, it might be insufficient to optimize the proliferated parameters of large kernels and leads to over-fitting." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 546, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 546, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 546, + 547, + 713 + ], + "type": "text", + "content": "In this paper, we propose spatial-wise partition convolution as the 3D large-kernel design. It is a new family of group convolution by sharing weights among spatially adjacent locations, rather than depth-wise convolution [29] of channel-level groups. As shown in Fig. 1, spatial-wise partition convolution remaps a large kernel " + }, + { + "bbox": [ + 304, + 546, + 547, + 713 + ], + "type": "inline_equation", + "content": "(e.g., 7 \\times 7)" + }, + { + "bbox": [ + 304, + 546, + 547, + 713 + ], + "type": "text", + "content": " as a small one " + }, + { + "bbox": [ + 304, + 546, + 547, + 713 + ], + "type": "inline_equation", + "content": "(e.g., 3 \\times 3)" + }, + { + "bbox": [ + 304, + 546, + 547, + 713 + ], + "type": "text", + "content": " via grouping spatial neighbors, while the absolutely large spatial size remains unchanged. With regard to the efficiency issue, it occupies few model sizes to keep parameters the same as those of small kernels. Moreover, it takes less latency, compared with plain large kernel counterparts. As for the optimization challenge, weight-sharing among spatial dimensions gives parameters more chance to update and overcome the over-fitting issue." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 128, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 128, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 128, + 712 + ], + "type": "text", + "content": "*Equal Contribution." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "13488" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 70, + 202, + 178 + ], + "blocks": [ + { + "bbox": [ + 49, + 70, + 202, + 178 + ], + "lines": [ + { + "bbox": [ + 49, + 70, + 202, + 178 + ], + "spans": [ + { + "bbox": [ + 49, + 70, + 202, + 178 + ], + "type": "image", + "image_path": "7012f8da40b09801a0e5e833a2187f227f43c1f5e91081c6cb18774651966b7d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 80, + 180, + 168, + 191 + ], + "lines": [ + { + "bbox": [ + 80, + 180, + 168, + 191 + ], + "spans": [ + { + "bbox": [ + 80, + 180, + 168, + 191 + ], + "type": "text", + "content": "Small-kernel sparse conv" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 212, + 70, + 373, + 178 + ], + "blocks": [ + { + "bbox": [ + 212, + 70, + 373, + 178 + ], + "lines": [ + { + "bbox": [ + 212, + 70, + 373, + 178 + ], + "spans": [ + { + "bbox": [ + 212, + 70, + 373, + 178 + ], + "type": "image", + "image_path": "cea45d776185dfeb745398c2de74993d87bd89446abaa5826adbbd15361d6f16.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 247, + 180, + 335, + 191 + ], + "lines": [ + { + "bbox": [ + 247, + 180, + 335, + 191 + ], + "spans": [ + { + "bbox": [ + 247, + 180, + 335, + 191 + ], + "type": "text", + "content": "Large-kernel sparse conv" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 201, + 547, + 246 + ], + "lines": [ + { + "bbox": [ + 46, + 201, + 547, + 246 + ], + "spans": [ + { + "bbox": [ + 46, + 201, + 547, + 246 + ], + "type": "text", + "content": "Figure 1. Sparse convolutions with different kernels. Small-kernel sparse convolution gathers features in a local area. It is efficient but discards sufficient information flow due to feature disconnection and the small scope. Large-kernel sparse convolution is capable of capturing long-range information, at the price of a large number of parameters and computation. Our proposed spatial-wise partition convolution uses large kernel sizes, and shares weights among local neighbors for efficiency. We show 2D features for the simplicity sake." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 383, + 70, + 545, + 178 + ], + "blocks": [ + { + "bbox": [ + 383, + 70, + 545, + 178 + ], + "lines": [ + { + "bbox": [ + 383, + 70, + 545, + 178 + ], + "spans": [ + { + "bbox": [ + 383, + 70, + 545, + 178 + ], + "type": "image", + "image_path": "64ace8631b92f635a6d6c2bcd90919523a388b114de5b4a09b66e5602dd7d47b.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 416, + 180, + 511, + 191 + ], + "lines": [ + { + "bbox": [ + 416, + 180, + 511, + 191 + ], + "spans": [ + { + "bbox": [ + 416, + 180, + 511, + 191 + ], + "type": "text", + "content": "Spatial-wise partition conv" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 276, + 287, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 276, + 287, + 384 + ], + "spans": [ + { + "bbox": [ + 46, + 276, + 287, + 384 + ], + "type": "text", + "content": "To increase the detail-capturing ability of large kernels [18], we introduce position embeddings for spatial-wise group convolution. It makes notable effects for large kernel sizes. We name the proposed block as spatial-wise large-kernel convolution (SW-LK Conv). We compare the efficiency between plain 3D submanifold sparse convolution and ours, as shown in Tab. 1. Both parameters and latency of the baseline increases dramatically, as its kernel size becomes larger, while ours is far more efficient." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 384, + 287, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 384, + 287, + 564 + ], + "spans": [ + { + "bbox": [ + 46, + 384, + 287, + 564 + ], + "type": "text", + "content": "SW-LK Conv can readily replace plain convolution layers in existing 3D convolutional networks. We establish large-kernel backbone networks LargeKernel3D on existing 3D semantic segmentation [9] and object detection [16, 75] networks. It achieves notable improvement upon state-of-the-art methods [9, 16, 75], with a small model complexity overhead. Extensive experiments validate our effectiveness on large-scale benchmarks, including ScanNetv2 [13], nuScenes [4], and Waymo [57]. For object detection, LargeKernel3D achieves " + }, + { + "bbox": [ + 46, + 384, + 287, + 564 + ], + "type": "inline_equation", + "content": "72.8\\%" + }, + { + "bbox": [ + 46, + 384, + 287, + 564 + ], + "type": "text", + "content": " NDS on nuScenes, ranking " + }, + { + "bbox": [ + 46, + 384, + 287, + 564 + ], + "type": "inline_equation", + "content": "\\mathbf{1}^{st}" + }, + { + "bbox": [ + 46, + 384, + 287, + 564 + ], + "type": "text", + "content": " on the nuScenes LIDAR leaderboard. Without bells and whistles, it further improves to " + }, + { + "bbox": [ + 46, + 384, + 287, + 564 + ], + "type": "inline_equation", + "content": "74.2\\%" + }, + { + "bbox": [ + 46, + 384, + 287, + 564 + ], + "type": "text", + "content": " NDS in a simple voxel-wise multi-modal fusion manner. More importantly, it is scalable to " + }, + { + "bbox": [ + 46, + 384, + 287, + 564 + ], + "type": "inline_equation", + "content": "17\\times 17\\times 17" + }, + { + "bbox": [ + 46, + 384, + 287, + 564 + ], + "type": "text", + "content": " kernel sizes on the large-scale Waymo 3D object detection." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 565, + 287, + 649 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 565, + 287, + 649 + ], + "spans": [ + { + "bbox": [ + 46, + 565, + 287, + 649 + ], + "type": "text", + "content": "We visualize the Effective Receptive Fields (ERFs) of plain 3D CNNs and our LargeKernel3D in Fig. 2. It shows that deep small-kernel networks are also constrained by limited ERFs, since sparse features are spatially disconnected. Note that our large-kernel networks elegantly resolve this issue. For the first time, we show that large-kernel CNN designs become effective on essential 3D visual tasks." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 663, + 134, + 675 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 663, + 134, + 675 + ], + "spans": [ + { + "bbox": [ + 47, + 663, + 134, + 675 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "content": "Convolutional Large-kernel Networks Large-kernel setting has been commonly used in 2D convolutional net" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 276, + 545, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 276, + 545, + 456 + ], + "spans": [ + { + "bbox": [ + 304, + 276, + 545, + 456 + ], + "type": "text", + "content": "works [18, 43, 68]. ConvNeXt [43] combines various training techniques and large kernel sizes, to compete with Swin Transformer [42]. RepLKNet [18] is a specific work that focuses on large-kernel designs. It reveals that the large kernel sizes are more beneficial to tasks of object detection and semantic segmentation than image classification. GCNs [47] also show improvement from large-kernel designs on semantic segmentation. There are methods approximating large kernel sizes using implicit techniques, including Fourier domain transformation [52], and continuous functions [53]. Other methods change kernel shapes to enlarge receptive fields using dilated convolutions [5, 76], deformable convolutions [14, 81] and active convolutions [31]. These schemes sparsify kernels, and is hard to capture the original sparse features in 3D deep learning." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 461, + 545, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 461, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 461, + 545, + 628 + ], + "type": "text", + "content": "3D Feature Extractors A key challenge in 3D tasks [32,38] is to learn effective representation from the sparse and non-uniformed 3D geometric data, e.g., point clouds. In general, there are two kinds of 3D feature extractors. The first is to learn on point cloud directly, using a series of PointNet networks [48, 49]. The sampling and grouping operations in PointNet++ [49] are also time-consuming. Followups [46, 79] use grid-sampling or scene-partition to save computation in each forward and combine results from multiple runs. The second is to process point clouds with voxelization and apply 3D sparse CNNs. Due to its efficiency advantages, this stream of methods has been widely used in various 3D tasks, such as 3D segmentation [9-11, 33] and backbone networks in 3D object detectors [16, 26, 55, 64]." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": "The spatial group convolution (SGC) [78] is relevant to the proposed spatial-wise partition convolution. SGC is originally designed for the task of 3D scene completion. They both conduct the partition operation spatially. The difference is also essential and clear. Our method partition kernel weighs while SGC splits input features into groups. In terms of targets, SGC focuses more on efficiency improve" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13489" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 55, + 112, + 537, + 178 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 547, + 106 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 547, + 106 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 547, + 106 + ], + "type": "text", + "content": "Table 1. Efficiency comparison between plain 3D sparse convolution and our SW-LK Conv. The baseline is a submanifold sparse convolutional layer with input and output channels 16. The input data is a sparse tensor with 80,000 voxels randomly scattered and batch size 1. We test all latencies on a single 2080Ti GPU by an average of 10 times running, after a warm-up start of additional 10 times." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 55, + 112, + 537, + 178 + ], + "lines": [ + { + "bbox": [ + 55, + 112, + 537, + 178 + ], + "spans": [ + { + "bbox": [ + 55, + 112, + 537, + 178 + ], + "type": "table", + "html": "
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", + "image_path": "39aa5bb89c62206e710d3422070dcf674f6301eeb1e5edfdf2f9053594d98205.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 206, + 288, + 243 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 206, + 288, + 243 + ], + "spans": [ + { + "bbox": [ + 46, + 206, + 288, + 243 + ], + "type": "text", + "content": "ment by changing feature sparsity in each spatial group, while our method is to facilitate large kernels in 3D tasks. Further analysis and comparisons are given in experiments." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 247, + 287, + 357 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 247, + 287, + 357 + ], + "spans": [ + { + "bbox": [ + 46, + 247, + 287, + 357 + ], + "type": "text", + "content": "Vision Transformer Vision transformers that conduct attention computation in local areas or windows share a similar spirit with large-kernel models [18]. Swin Transformers [42] capture features in shifted windows with sizes from 7 to 12. Its variants [19, 41] show that larger window sizes are beneficial to performance. Focal Transformer [71] captures fine-grained local attention with adaptive patch sizes. SST [21] and Stratified Transformer [34] apply window-based self-attention on 3D detection and segmentation." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 361, + 287, + 577 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 361, + 287, + 577 + ], + "spans": [ + { + "bbox": [ + 46, + 361, + 287, + 577 + ], + "type": "text", + "content": "Position Encoding Since the self-attention in transformers is permutation-equivalent, position encoding is well-designed for imbuing the network with the position information. It can be grouped into two streams of absolute and relative position encoding. For the first group, positions are encoded in a precise manner. Specifically, encoding [63] is generated with the sinusoidal functions of different frequencies. They are then added to the input. In contrast, relative position encoding [54] takes the relative relationship into consideration. It can naturally handle longer sequences and is more scalable. Most work [3, 50, 66, 73] computes the relative distance between tokens and applies implicit encoding using learnable transformations. Besides, the literature [12] shows that convolution with padding can provide effective relative position information for relative position encoding. In addition to transformers, the recent work [72] also shows that position embedding is beneficial to the CNNs with fourier transformation." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 578, + 287, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 578, + 287, + 651 + ], + "spans": [ + { + "bbox": [ + 46, + 578, + 287, + 651 + ], + "type": "text", + "content": "Considering that our spatial-wise partition convolution divides the kernel into different portions in pursuit of higher efficiency. The position information may be blurred due to weight sharing in each portion. We thus use relative position encoding as a bias to supplement the lost position information. More details are provided in Sec. 4." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 663, + 204, + 677 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 663, + 204, + 677 + ], + "spans": [ + { + "bbox": [ + 47, + 663, + 204, + 677 + ], + "type": "text", + "content": "3. Revisiting 3D Sparse CNNs" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "type": "text", + "content": "Preliminary 3D sparse CNNs consist of 3D sparse convolutions, which are typically regular and submanifold sparse" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 206, + 547, + 315 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 206, + 547, + 315 + ], + "spans": [ + { + "bbox": [ + 304, + 206, + 547, + 315 + ], + "type": "text", + "content": "convolutions [25]. We formulate 3D sparse convolutions in Eq. (1). Given a set of sparse input features " + }, + { + "bbox": [ + 304, + 206, + 547, + 315 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{x}_{p\\in P}\\}" + }, + { + "bbox": [ + 304, + 206, + 547, + 315 + ], + "type": "text", + "content": " with a number of " + }, + { + "bbox": [ + 304, + 206, + 547, + 315 + ], + "type": "inline_equation", + "content": "c_{\\mathrm{in}}" + }, + { + "bbox": [ + 304, + 206, + 547, + 315 + ], + "type": "text", + "content": " channels, the position of each feature " + }, + { + "bbox": [ + 304, + 206, + 547, + 315 + ], + "type": "inline_equation", + "content": "p\\in P" + }, + { + "bbox": [ + 304, + 206, + 547, + 315 + ], + "type": "text", + "content": " sparsely distributes in 3D space. We process these features by a convolution with kernel weights " + }, + { + "bbox": [ + 304, + 206, + 547, + 315 + ], + "type": "inline_equation", + "content": "\\mathbf{w}\\in \\mathbb{R}^{|K| \\times c_{\\mathrm{in}} \\times c_{\\mathrm{out}}}" + }, + { + "bbox": [ + 304, + 206, + 547, + 315 + ], + "type": "text", + "content": ". For example, in the 3D coordinate space, " + }, + { + "bbox": [ + 304, + 206, + 547, + 315 + ], + "type": "inline_equation", + "content": "\\mathbf{w}" + }, + { + "bbox": [ + 304, + 206, + 547, + 315 + ], + "type": "text", + "content": " contains " + }, + { + "bbox": [ + 304, + 206, + 547, + 315 + ], + "type": "inline_equation", + "content": "c_{\\mathrm{in}} \\times c_{\\mathrm{out}}" + }, + { + "bbox": [ + 304, + 206, + 547, + 315 + ], + "type": "text", + "content": " spatial kernels with size 3 and " + }, + { + "bbox": [ + 304, + 206, + 547, + 315 + ], + "type": "inline_equation", + "content": "|K| = 27" + }, + { + "bbox": [ + 304, + 206, + 547, + 315 + ], + "type": "text", + "content": ". The convolution process at the output position " + }, + { + "bbox": [ + 304, + 206, + 547, + 315 + ], + "type": "inline_equation", + "content": "\\bar{p}" + }, + { + "bbox": [ + 304, + 206, + 547, + 315 + ], + "type": "text", + "content": " is represented as" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 380, + 323, + 545, + 349 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 380, + 323, + 545, + 349 + ], + "spans": [ + { + "bbox": [ + 380, + 323, + 545, + 349 + ], + "type": "interline_equation", + "content": "\\mathrm {y} _ {\\bar {p}} = \\sum_ {k \\in K} \\mathrm {w} _ {k} \\cdot \\mathrm {x} _ {\\bar {p} + k}, \\tag {1}", + "image_path": "0a600fb4ddbffec0430f6c5bab419b656d5f2b486941048874b59d5ade90949a.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 356, + 547, + 394 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 356, + 547, + 394 + ], + "spans": [ + { + "bbox": [ + 304, + 356, + 547, + 394 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 356, + 547, + 394 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 356, + 547, + 394 + ], + "type": "text", + "content": " is an 3D offset distance from " + }, + { + "bbox": [ + 304, + 356, + 547, + 394 + ], + "type": "inline_equation", + "content": "\\bar{p}" + }, + { + "bbox": [ + 304, + 356, + 547, + 394 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 356, + 547, + 394 + ], + "type": "inline_equation", + "content": "\\bar{p} + k" + }, + { + "bbox": [ + 304, + 356, + 547, + 394 + ], + "type": "text", + "content": " is the location around center " + }, + { + "bbox": [ + 304, + 356, + 547, + 394 + ], + "type": "inline_equation", + "content": "\\bar{p}" + }, + { + "bbox": [ + 304, + 356, + 547, + 394 + ], + "type": "text", + "content": ". It enumerates all discrete locations in the kernel space " + }, + { + "bbox": [ + 304, + 356, + 547, + 394 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 356, + 547, + 394 + ], + "type": "text", + "content": " where sparse features " + }, + { + "bbox": [ + 304, + 356, + 547, + 394 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{\\bar{p} + k}" + }, + { + "bbox": [ + 304, + 356, + 547, + 394 + ], + "type": "text", + "content": " exist." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 397, + 547, + 517 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 397, + 547, + 517 + ], + "spans": [ + { + "bbox": [ + 304, + 397, + 547, + 517 + ], + "type": "text", + "content": "Convolution Types Regular sparse convolutions enlarge their output positions by dilating each input position " + }, + { + "bbox": [ + 304, + 397, + 547, + 517 + ], + "type": "inline_equation", + "content": "p \\in P" + }, + { + "bbox": [ + 304, + 397, + 547, + 517 + ], + "type": "text", + "content": " to the kernel shape " + }, + { + "bbox": [ + 304, + 397, + 547, + 517 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 397, + 547, + 517 + ], + "type": "text", + "content": ". It dramatically decreases feature density and increases the computational burden. Thus, regular sparse convolutions with stride 2 are only employed at the first layer in each stage for down-sampling. Submanifold sparse convolutions, in contrast, fix their output positions " + }, + { + "bbox": [ + 304, + 397, + 547, + 517 + ], + "type": "inline_equation", + "content": "\\bar{p}" + }, + { + "bbox": [ + 304, + 397, + 547, + 517 + ], + "type": "text", + "content": " identical to input positions " + }, + { + "bbox": [ + 304, + 397, + 547, + 517 + ], + "type": "inline_equation", + "content": "p \\in P" + }, + { + "bbox": [ + 304, + 397, + 547, + 517 + ], + "type": "text", + "content": ", which preserves the computation cost at low levels. Please refer to the original paper [25] for more details." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 517, + 547, + 589 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 517, + 547, + 589 + ], + "spans": [ + { + "bbox": [ + 304, + 517, + 547, + 589 + ], + "type": "text", + "content": "Due to the efficiency advantage, submanifold sparse convolutions dominate most layers of 3D CNNs, except for the down-sampling layers. However, limited by the small local scope, it misses sufficient information flow for the spatially disconnected features. Increasing kernel sizes becomes a potential solution to relieve this issue." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 594, + 547, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 547, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 547, + 689 + ], + "type": "text", + "content": "Obstacles in 3D Large Kernels Efficiency is the first issue in 3D large-kernel CNNs. When we increase kernel sizes, the amount of parameters and computational burden grows much faster than those of 2D CNNs. For instance, the parameter amount in one 3D convolutional layer increases from " + }, + { + "bbox": [ + 304, + 594, + 547, + 689 + ], + "type": "inline_equation", + "content": "27 \\cdot C_{in \\cdot out}" + }, + { + "bbox": [ + 304, + 594, + 547, + 689 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 594, + 547, + 689 + ], + "type": "inline_equation", + "content": "343 \\cdot c_{in} \\cdot c_{out}" + }, + { + "bbox": [ + 304, + 594, + 547, + 689 + ], + "type": "text", + "content": ", given its kernel size changing from 3 to 7. It is thus clear that naively enlarging 3D kernels is unreasonable." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 689, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 689, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 689, + 547, + 715 + ], + "type": "text", + "content": "Optimization difficulty is the second obstacle. The booming parameters require sufficient data for learning. How-" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "13490" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 71, + 141, + 148 + ], + "blocks": [ + { + "bbox": [ + 49, + 71, + 141, + 148 + ], + "lines": [ + { + "bbox": [ + 49, + 71, + 141, + 148 + ], + "spans": [ + { + "bbox": [ + 49, + 71, + 141, + 148 + ], + "type": "image", + "image_path": "8f4373936a081c48af3a50c9f77409e663af35690da8ce009898d2a09f2324bf.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 65, + 150, + 125, + 159 + ], + "lines": [ + { + "bbox": [ + 65, + 150, + 125, + 159 + ], + "spans": [ + { + "bbox": [ + 65, + 150, + 125, + 159 + ], + "type": "text", + "content": "(a) Plain 3D CNN" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 141, + 72, + 232, + 148 + ], + "blocks": [ + { + "bbox": [ + 141, + 72, + 232, + 148 + ], + "lines": [ + { + "bbox": [ + 141, + 72, + 232, + 148 + ], + "spans": [ + { + "bbox": [ + 141, + 72, + 232, + 148 + ], + "type": "image", + "image_path": "90ca9a1279931199f5c1b34c13b953d2f94afa692ea8e8f87c5fd04ea3b59ca0.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 149, + 150, + 223, + 159 + ], + "lines": [ + { + "bbox": [ + 149, + 150, + 223, + 159 + ], + "spans": [ + { + "bbox": [ + 149, + 150, + 223, + 159 + ], + "type": "text", + "content": "(b) Plain 3D CNN - 2x" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 232, + 72, + 324, + 148 + ], + "blocks": [ + { + "bbox": [ + 232, + 72, + 324, + 148 + ], + "lines": [ + { + "bbox": [ + 232, + 72, + 324, + 148 + ], + "spans": [ + { + "bbox": [ + 232, + 72, + 324, + 148 + ], + "type": "image", + "image_path": "9d2afaa194ef9ec7eea68f981ef69034c946b11a49d48e3f2d7d94fd49e98b55.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 247, + 150, + 309, + 160 + ], + "lines": [ + { + "bbox": [ + 247, + 150, + 309, + 160 + ], + "spans": [ + { + "bbox": [ + 247, + 150, + 309, + 160 + ], + "type": "text", + "content": "(c) LargeKernel3D" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 169, + 547, + 224 + ], + "lines": [ + { + "bbox": [ + 46, + 169, + 547, + 224 + ], + "spans": [ + { + "bbox": [ + 46, + 169, + 547, + 224 + ], + "type": "text", + "content": "Figure 2. Effective Receptive Fields (ERF) of plain 3D CNN, plain 3D CNN - " + }, + { + "bbox": [ + 46, + 169, + 547, + 224 + ], + "type": "inline_equation", + "content": "2 \\times" + }, + { + "bbox": [ + 46, + 169, + 547, + 224 + ], + "type": "text", + "content": ", and our LargeKernel3D for 3D object detection. The plain 3D CNN backbone has insufficient ERF size, which hardly covers a nearby car. Plain 3D CNN - " + }, + { + "bbox": [ + 46, + 169, + 547, + 224 + ], + "type": "inline_equation", + "content": "2 \\times" + }, + { + "bbox": [ + 46, + 169, + 547, + 224 + ], + "type": "text", + "content": " is a deeper version with its layers doubled in each stage. More layers help little in ERF, as the disconnection between sparse features. Our LargeKernel3D obtains large ERF at both the object centers (left) and edges (right), capturing context information. More illustrations are provided in the appendix. The figure is best viewed in color and by zoom-in." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 327, + 72, + 472, + 148 + ], + "blocks": [ + { + "bbox": [ + 327, + 72, + 472, + 148 + ], + "lines": [ + { + "bbox": [ + 327, + 72, + 472, + 148 + ], + "spans": [ + { + "bbox": [ + 327, + 72, + 472, + 148 + ], + "type": "image", + "image_path": "bc9ae4b31ba796d0c855e673deeb60a0c624ad6ceeb8ab53d47c48cacc87c6ab.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 339, + 150, + 406, + 159 + ], + "lines": [ + { + "bbox": [ + 339, + 150, + 406, + 159 + ], + "spans": [ + { + "bbox": [ + 339, + 150, + 406, + 159 + ], + "type": "text", + "content": "Feature of interest" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 472, + 72, + 544, + 148 + ], + "blocks": [ + { + "bbox": [ + 472, + 72, + 544, + 148 + ], + "lines": [ + { + "bbox": [ + 472, + 72, + 544, + 148 + ], + "spans": [ + { + "bbox": [ + 472, + 72, + 544, + 148 + ], + "type": "image", + "image_path": "29e089707ad2b981be90e1ac90c16b08cabc705cb82ee42a70005524220d3b3a.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 479, + 150, + 540, + 159 + ], + "lines": [ + { + "bbox": [ + 479, + 150, + 540, + 159 + ], + "spans": [ + { + "bbox": [ + 479, + 150, + 540, + 159 + ], + "type": "text", + "content": "Magnitude of ERF" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 255, + 286, + 327 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 255, + 286, + 327 + ], + "spans": [ + { + "bbox": [ + 46, + 255, + 286, + 327 + ], + "type": "text", + "content": "ever, 3D datasets are commonly not in that large scale as 2D benchmarks. For example, ImageNet [15] contains millions of images, while 3D datasets commonly contain only no more than one thousand scenes. The over-fitting issue gradually deteriorates the performance when increasing kernel sizes from " + }, + { + "bbox": [ + 46, + 255, + 286, + 327 + ], + "type": "inline_equation", + "content": "3 \\times 3 \\times 3" + }, + { + "bbox": [ + 46, + 255, + 286, + 327 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 255, + 286, + 327 + ], + "type": "inline_equation", + "content": "7 \\times 7 \\times 7" + }, + { + "bbox": [ + 46, + 255, + 286, + 327 + ], + "type": "text", + "content": " in MinkowskiNet-34 [9]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 327, + 286, + 507 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 327, + 286, + 507 + ], + "spans": [ + { + "bbox": [ + 46, + 327, + 286, + 507 + ], + "type": "text", + "content": "Previous 2D knowledge is not helpful in 3D large-kernel CNNs. Recent 2D methods [18, 43] show some helpful components in large-kernel CNNs, including depth-wise convolutions [29], layer normalization [1], GELU [28] activation. We examine these popular components and find that they are either ineffective or even harmful in 3D CNNs. To demonstrate this finding, we use MinkowskiNet-34 [9] to benchmark and train on the 3D semantic segmentation dataset of ScanNetv2 [13]. We change the original activation function from ReLU to GELU, batch normalization to layer normalization, and plain convolution to depth-wise operation, respectively. Directly using these components makes the final system yield performance drop on both small and large kernel networks. It requires us to seek other ways to construct 3D large-kernel CNNs." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 518, + 268, + 532 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 518, + 268, + 532 + ], + "spans": [ + { + "bbox": [ + 47, + 518, + 268, + 532 + ], + "type": "text", + "content": "4. 3D Large-kernel Convolutional Network" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 47, + 539, + 231, + 551 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 539, + 231, + 551 + ], + "spans": [ + { + "bbox": [ + 47, + 539, + 231, + 551 + ], + "type": "text", + "content": "4.1. Spatial-wise Partition Convolution" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 557, + 286, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 557, + 286, + 676 + ], + "spans": [ + { + "bbox": [ + 46, + 557, + 286, + 676 + ], + "type": "text", + "content": "A standard convolution kernel can be viewed as a 3D matrix, which consists of input channels " + }, + { + "bbox": [ + 46, + 557, + 286, + 676 + ], + "type": "inline_equation", + "content": "C_{\\mathrm{in}}" + }, + { + "bbox": [ + 46, + 557, + 286, + 676 + ], + "type": "text", + "content": ", output channels " + }, + { + "bbox": [ + 46, + 557, + 286, + 676 + ], + "type": "inline_equation", + "content": "C_{\\mathrm{out}}" + }, + { + "bbox": [ + 46, + 557, + 286, + 676 + ], + "type": "text", + "content": ", and the spatial kernel dimension " + }, + { + "bbox": [ + 46, + 557, + 286, + 676 + ], + "type": "inline_equation", + "content": "|K|" + }, + { + "bbox": [ + 46, + 557, + 286, + 676 + ], + "type": "text", + "content": ". Taking kernel size as " + }, + { + "bbox": [ + 46, + 557, + 286, + 676 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 557, + 286, + 676 + ], + "type": "text", + "content": ", the volume of spatial kernel dimension " + }, + { + "bbox": [ + 46, + 557, + 286, + 676 + ], + "type": "inline_equation", + "content": "|K| = k \\times k" + }, + { + "bbox": [ + 46, + 557, + 286, + 676 + ], + "type": "text", + "content": " for 2D convolutions and " + }, + { + "bbox": [ + 46, + 557, + 286, + 676 + ], + "type": "inline_equation", + "content": "k \\times k \\times k" + }, + { + "bbox": [ + 46, + 557, + 286, + 676 + ], + "type": "text", + "content": " for 3D convolutions. Depth-wise convolutions share weights along channel dimensions, where group numbers equal to input channels. Point-wise convolutions fix kernel size as 1, which is common as a conjunction layer to depth-wise convolutions to adjust output channels." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "type": "text", + "content": "Different from 2D methods, which rely on depthwise convolutions for performance boosting [27, 43] and accuracy-FLOPs trade-offs [18], we empirically find that" + } + ] + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 308, + 254, + 485, + 335 + ], + "blocks": [ + { + "bbox": [ + 308, + 254, + 485, + 335 + ], + "lines": [ + { + "bbox": [ + 308, + 254, + 485, + 335 + ], + "spans": [ + { + "bbox": [ + 308, + 254, + 485, + 335 + ], + "type": "image", + "image_path": "6e602c8795741cc5cc6ecc030aa488440413ecefcbf2e328442422ba2e6a648c.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 345, + 545, + 433 + ], + "lines": [ + { + "bbox": [ + 305, + 345, + 545, + 433 + ], + "spans": [ + { + "bbox": [ + 305, + 345, + 545, + 433 + ], + "type": "text", + "content": "Figure 3. Illustration on spatial-wise partition convolution. In the plain large-kernel convolution, due to the sparsity of input features, only a small proportion of weights are involved and updated in each training step. The spatial-wise partition convolution relieves this issue by sharing weights among spatial neighbors. It increases the chance for weights to be optimized. During inference, we reformulate the spatial-wise partition convolutions into small ones, with feature assignment in a large scope." + } + ] + } + ], + "index": 26, + "angle": 0, + "type": "image_caption" + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 504, + 258, + 514, + 266 + ], + "blocks": [ + { + "bbox": [ + 504, + 258, + 514, + 266 + ], + "lines": [ + { + "bbox": [ + 504, + 258, + 514, + 266 + ], + "spans": [ + { + "bbox": [ + 504, + 258, + 514, + 266 + ], + "type": "image", + "image_path": "eb332a305d5b6a514cb12c507458607ae072f4338c1daca62578f81b37087a71.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 522, + 258, + 544, + 266 + ], + "lines": [ + { + "bbox": [ + 522, + 258, + 544, + 266 + ], + "spans": [ + { + "bbox": [ + 522, + 258, + 544, + 266 + ], + "type": "text", + "content": "feature" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + } + ], + "index": 18 + }, + { + "type": "image", + "bbox": [ + 504, + 275, + 517, + 287 + ], + "blocks": [ + { + "bbox": [ + 504, + 275, + 517, + 287 + ], + "lines": [ + { + "bbox": [ + 504, + 275, + 517, + 287 + ], + "spans": [ + { + "bbox": [ + 504, + 275, + 517, + 287 + ], + "type": "image", + "image_path": "297098d66294db1a446494caf032616047ac976bf79953b61e557dc28900cad8.jpg" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 522, + 277, + 544, + 285 + ], + "lines": [ + { + "bbox": [ + 522, + 277, + 544, + 285 + ], + "spans": [ + { + "bbox": [ + 522, + 277, + 544, + 285 + ], + "type": "text", + "content": "weight" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_caption" + } + ], + "index": 20 + }, + { + "type": "image", + "bbox": [ + 501, + 295, + 520, + 315 + ], + "blocks": [ + { + "bbox": [ + 501, + 295, + 520, + 315 + ], + "lines": [ + { + "bbox": [ + 501, + 295, + 520, + 315 + ], + "spans": [ + { + "bbox": [ + 501, + 295, + 520, + 315 + ], + "type": "image", + "image_path": "e5f5173fb694520f7d92b37a01f8d0d9707b714a396416337803e50819d98c57.jpg" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 522, + 301, + 541, + 308 + ], + "lines": [ + { + "bbox": [ + 522, + 301, + 541, + 308 + ], + "spans": [ + { + "bbox": [ + 522, + 301, + 541, + 308 + ], + "type": "text", + "content": "group" + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 522, + 323, + 542, + 331 + ], + "lines": [ + { + "bbox": [ + 522, + 323, + 542, + 331 + ], + "spans": [ + { + "bbox": [ + 522, + 323, + 542, + 331 + ], + "type": "text", + "content": "assign" + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "image_caption" + } + ], + "index": 22 + }, + { + "type": "image", + "bbox": [ + 501, + 323, + 512, + 331 + ], + "blocks": [ + { + "bbox": [ + 501, + 323, + 512, + 331 + ], + "lines": [ + { + "bbox": [ + 501, + 323, + 512, + 331 + ], + "spans": [ + { + "bbox": [ + 501, + 323, + 512, + 331 + ], + "type": "image", + "image_path": "0020c31d6aa5fe563383023250eaa512b46318323c5bf1fd3d324024d14aa3be.jpg" + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "image_body" + } + ], + "index": 24 + }, + { + "bbox": [ + 305, + 469, + 544, + 492 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 469, + 544, + 492 + ], + "spans": [ + { + "bbox": [ + 305, + 469, + 544, + 492 + ], + "type": "text", + "content": "depth-wise convolutions are not beneficial to 3D tasks, no matter whether point-wise convolutions are included." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 304, + 495, + 545, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 495, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 495, + 545, + 628 + ], + "type": "text", + "content": "We instead propose spatial-wise partition convolution for 3D large-kernel CNNs. It shares weights among spatial dimension " + }, + { + "bbox": [ + 304, + 495, + 545, + 628 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 495, + 545, + 628 + ], + "type": "text", + "content": " on convolutional kernels, instead of among channel dimension. It is also different from SGC [78], which partitions spatial groups on input features. Specially, in Eq. (1), " + }, + { + "bbox": [ + 304, + 495, + 545, + 628 + ], + "type": "inline_equation", + "content": "w_{k}" + }, + { + "bbox": [ + 304, + 495, + 545, + 628 + ], + "type": "text", + "content": " shares the same values in a local area " + }, + { + "bbox": [ + 304, + 495, + 545, + 628 + ], + "type": "inline_equation", + "content": "k \\in K" + }, + { + "bbox": [ + 304, + 495, + 545, + 628 + ], + "type": "text", + "content": ". We thus group the original large-kernel convolution from " + }, + { + "bbox": [ + 304, + 495, + 545, + 628 + ], + "type": "inline_equation", + "content": "7 \\times 7" + }, + { + "bbox": [ + 304, + 495, + 545, + 628 + ], + "type": "text", + "content": " into " + }, + { + "bbox": [ + 304, + 495, + 545, + 628 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 304, + 495, + 545, + 628 + ], + "type": "text", + "content": ", by sharing weights among spatial neighbors. Spatial-wise partition convolution is specially designed for 3D tasks and has the following advantages in terms of efficiency and performance." + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": "Regarding efficiency, when naively enlarging the kernel size from " + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "3 \\times 3 \\times 3" + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "7 \\times 7 \\times 7" + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": " on MinkowskiNet-34 [9], both model size and latency have a sharp increase by multiple times. In contrast, our spatial-wise partition convolution avoids increasing parameters and introduces limited latency overhead. The advantage of our method over plain large kernels attributes to the specific implementation of sparse" + } + ] + } + ], + "index": 29 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13491" + } + ] + } + ], + "index": 30 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 72, + 72, + 147, + 148 + ], + "blocks": [ + { + "bbox": [ + 72, + 72, + 147, + 148 + ], + "lines": [ + { + "bbox": [ + 72, + 72, + 147, + 148 + ], + "spans": [ + { + "bbox": [ + 72, + 72, + 147, + 148 + ], + "type": "image", + "image_path": "a71e09d5a750e504684d67c2d222f2532206e293c0b72fa47f4ad4548a7f4fcc.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 81, + 150, + 139, + 161 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+ 154 + ], + "blocks": [ + { + "bbox": [ + 416, + 131, + 440, + 154 + ], + "lines": [ + { + "bbox": [ + 416, + 131, + 440, + 154 + ], + "spans": [ + { + "bbox": [ + 416, + 131, + 440, + 154 + ], + "type": "image", + "image_path": "74d9a1316e66b36722b961b932360297b24a07ddb10e61e6235837b96fcfef0a.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 442, + 136, + 511, + 146 + ], + "lines": [ + { + "bbox": [ + 442, + 136, + 511, + 146 + ], + "spans": [ + { + "bbox": [ + 442, + 136, + 511, + 146 + ], + "type": "text", + "content": "Spatial-wise group" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 171, + 545, + 194 + ], + "lines": [ + { + "bbox": [ + 46, + 171, + 545, + 194 + ], + "spans": [ + { + "bbox": [ + 46, + 171, + 545, + 194 + ], + "type": "text", + "content": "Figure 4. Structure of spatial-wise large-kernel convolution (SW-LK Conv). It consists of a large-kernel spatial-wise partition convolution and a learnable position embedding. The position embedding is used to make up the detail-capturing ability of large kernels." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 225, + 289, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 225, + 289, + 380 + ], + "spans": [ + { + "bbox": [ + 46, + 225, + 289, + 380 + ], + "type": "text", + "content": "convolution. For a spatial-wise partition convolution, we directly use the small-kernel layer during inference, and enlarge its feature-assign areas to the large-kernel scope. As shown in Fig. 3, thanks to the weight-sharing operation, it much saves the multiplication, e.g., from 343 to 27 times. We implement this operation upon the open-sourced spconv library and omit the details here. Tab. 4 shows that our implementation on spatial-wise partition convolution is far more efficient than the plain large-kernel baseline. The optimization difficulty of large-kernel CNNs is relieved with the help of spatial-wise partition convolutions, which constrains model sizes to a limited number. It avoids requiring a large amount of data for training and the over-fitting issue." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 47, + 394, + 213, + 407 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 394, + 213, + 407 + ], + "spans": [ + { + "bbox": [ + 47, + 394, + 213, + 407 + ], + "type": "text", + "content": "4.2. Kernel-wise Position Encoding" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 46, + 415, + 287, + 511 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 415, + 287, + 511 + ], + "spans": [ + { + "bbox": [ + 46, + 415, + 287, + 511 + ], + "type": "text", + "content": "Considering that the spatial-wise partition convolution is designed in a sharing weights manner against the spatial sparsity. Although this design is efficient, there is still an issue: voxels within an area share the same weight, which results in local details blurred. This phenomenon is further amplified with an increase of kernel sizes. To address this problem, we propose the kernel-wise position embedding. We illustrate this design in Fig. 4." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 46, + 512, + 287, + 573 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 512, + 287, + 573 + ], + "spans": [ + { + "bbox": [ + 46, + 512, + 287, + 573 + ], + "type": "text", + "content": "Particularly, we initialize position weights " + }, + { + "bbox": [ + 46, + 512, + 287, + 573 + ], + "type": "inline_equation", + "content": "\\mathrm{e} \\in \\mathbb{R}^{K \\times c_{\\mathrm{in}}}" + }, + { + "bbox": [ + 46, + 512, + 287, + 573 + ], + "type": "text", + "content": ", which corresponds to the convolution kernel. During the convolution process, we let the input features query the position weights of the equivalent position and add them together. This process modifies Eq. (1) to" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 590, + 287, + 617 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 590, + 287, + 617 + ], + "spans": [ + { + "bbox": [ + 106, + 590, + 287, + 617 + ], + "type": "interline_equation", + "content": "\\mathrm {y} _ {\\bar {p}} = \\sum_ {k \\in K} \\mathrm {w} _ {k} \\cdot \\left(\\mathrm {x} _ {\\bar {p} + k} + \\mathrm {e} _ {k}\\right). \\tag {2}", + "image_path": "a5bb43c8aaf0e0dd40db269e846eb841327d086bb67126a91e71215c7741667b.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 46, + 629, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 288, + 713 + ], + "type": "text", + "content": "This simple design essentially adds bias with relative position information to the input features. There is almost no extra calculation and additional parameters. It is a decent solution to the position insensitivity problem caused by sharing weights, especially for the extremely large kernels, e.g., " + }, + { + "bbox": [ + 46, + 629, + 288, + 713 + ], + "type": "inline_equation", + "content": "17 \\times 17 \\times 17" + }, + { + "bbox": [ + 46, + 629, + 288, + 713 + ], + "type": "text", + "content": ". For more experimental results and details, please refer to the Sec. 5." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 305, + 224, + 452, + 237 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 224, + 452, + 237 + ], + "spans": [ + { + "bbox": [ + 305, + 224, + 452, + 237 + ], + "type": "text", + "content": "4.3. Large-kernel Architecture" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 243, + 545, + 302 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 243, + 545, + 302 + ], + "spans": [ + { + "bbox": [ + 304, + 243, + 545, + 302 + ], + "type": "text", + "content": "Following the above designs and observations, we now describe the architectures of our large-kernel 3D CNNs. We readily replace the plain 3D submanifold sparse convolution [25] layers with our SW-LK Conv in existing 3D backbones for semantic segmentation and object detection." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 307, + 547, + 635 + ], + "type": "list", + "angle": 0, + "index": 27, + "blocks": [ + { + "bbox": [ + 304, + 307, + 546, + 451 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 307, + 546, + 451 + ], + "spans": [ + { + "bbox": [ + 304, + 307, + 546, + 451 + ], + "type": "text", + "content": "3D Semantic Segmentation The architectures of LargeKernel3D for 3D semantic segmentation resemble MinkowskiNet [9], including 1 stem layer and 8 stages. The stem layer is a " + }, + { + "bbox": [ + 304, + 307, + 546, + 451 + ], + "type": "inline_equation", + "content": "5 \\times 5 \\times 5" + }, + { + "bbox": [ + 304, + 307, + 546, + 451 + ], + "type": "text", + "content": " submanifold convolution. The first 4 stages account for down-sampling and the last 4 stages are for up-sampling. As for the U-Net structure, the first 4 features are concatenated into the up-sampling stages. We replace the original layers in MinkowskiNet-34 [9] by SW-LK Convs, where spatial-wise " + }, + { + "bbox": [ + 304, + 307, + 546, + 451 + ], + "type": "inline_equation", + "content": "7 \\times 7 \\times 7" + }, + { + "bbox": [ + 304, + 307, + 546, + 451 + ], + "type": "text", + "content": " convolutions is grouped into " + }, + { + "bbox": [ + 304, + 307, + 546, + 451 + ], + "type": "inline_equation", + "content": "3 \\times 3 \\times 3" + }, + { + "bbox": [ + 304, + 307, + 546, + 451 + ], + "type": "text", + "content": " splits. By default, other hyper-parameters, including channels and block numbers, follow MinkowskiNet-34 [9]." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 304, + 456, + 547, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 456, + 547, + 635 + ], + "spans": [ + { + "bbox": [ + 304, + 456, + 547, + 635 + ], + "type": "text", + "content": "3D Object Detection The typical backbone networks in 3D object detectors [16, 55, 75] consist of 1 stem layer and 4 stages. A " + }, + { + "bbox": [ + 304, + 456, + 547, + 635 + ], + "type": "inline_equation", + "content": "3 \\times 3 \\times 3" + }, + { + "bbox": [ + 304, + 456, + 547, + 635 + ], + "type": "text", + "content": " submanifold convolution [25] layer serves as the stem. In each stage, except for the first one, there is a sparse convolutional layer with stride 2 for down-sampling. We substitute other plain blocks with SW-LK Convs. For models on nuScenes dataset, we find that " + }, + { + "bbox": [ + 304, + 456, + 547, + 635 + ], + "type": "inline_equation", + "content": "7 \\times 7 \\times 7" + }, + { + "bbox": [ + 304, + 456, + 547, + 635 + ], + "type": "text", + "content": " kernel sizes are enough. They both use the " + }, + { + "bbox": [ + 304, + 456, + 547, + 635 + ], + "type": "inline_equation", + "content": "3 \\times 3 \\times 3" + }, + { + "bbox": [ + 304, + 456, + 547, + 635 + ], + "type": "text", + "content": " spatial-wise groups. For models on Waymo dataset, kernel sizes are scalable to " + }, + { + "bbox": [ + 304, + 456, + 547, + 635 + ], + "type": "inline_equation", + "content": "17 \\times 17 \\times 17" + }, + { + "bbox": [ + 304, + 456, + 547, + 635 + ], + "type": "text", + "content": ". We remain the last stage of backbone network as the original, because receptive fields have already been sufficiently enlarged in the front stages. We keep these hyper-parameters unchanged by the default settings in baseline detectors [16, 75]. We include these detailed numbers in appendix." + } + ] + } + ], + "index": 26 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 647, + 387, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 647, + 387, + 659 + ], + "spans": [ + { + "bbox": [ + 306, + 647, + 387, + 659 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 306, + 666, + 428, + 679 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 666, + 428, + 679 + ], + "spans": [ + { + "bbox": [ + 306, + 666, + 428, + 679 + ], + "type": "text", + "content": "5.1. Experimental Setting" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": "3D Semantic Segmentation ScanNetv2 [13] is a large-scale benchmark in 3D semantic segmentation. It con" + } + ] + } + ], + "index": 30 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13492" + } + ] + } + ], + "index": 31 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 114, + 287, + 147 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 288, + 104 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 288, + 104 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 288, + 104 + ], + "type": "text", + "content": "Table 2. Ablations on various techniques and kernel sizes on MinkowskiNet-34 and ScanNetv2. LN denotes the layer normalization. DW Conv denotes the depth-wise convolution." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 114, + 287, + 147 + ], + "lines": [ + { + "bbox": [ + 50, + 114, + 287, + 147 + ], + "spans": [ + { + "bbox": [ + 50, + 114, + 287, + 147 + ], + "type": "table", + "html": "
KernelBaseline+GELU+LN+DW Conv+PWOurs
3×3×371.770.266.870.670.7-
7×7×768.668.465.068.768.773.5
", + "image_path": "1fac9e476e3e811296d0be5c01abc9e394ff00adcc3db50b72628029bfa9eea5.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 50, + 190, + 287, + 224 + ], + "blocks": [ + { + "bbox": [ + 64, + 168, + 268, + 180 + ], + "lines": [ + { + "bbox": [ + 64, + 168, + 268, + 180 + ], + "spans": [ + { + "bbox": [ + 64, + 168, + 268, + 180 + ], + "type": "text", + "content": "Table 3. Ablations on group convolution on ScanNetv2." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 190, + 287, + 224 + ], + "lines": [ + { + "bbox": [ + 50, + 190, + 287, + 224 + ], + "spans": [ + { + "bbox": [ + 50, + 190, + 287, + 224 + ], + "type": "table", + "html": "
KernelBaselineGroup 24816DWOurs
3x3x371.771.571.270.770.670.6-
7x7x768.668.869.268.868.768.773.5
", + "image_path": "055e648c3037fa0c7eef7984670f3ddc0d196866769e0ede887dc7b05a821719.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 50, + 289, + 287, + 402 + ], + "blocks": [ + { + "bbox": [ + 47, + 247, + 287, + 281 + ], + "lines": [ + { + "bbox": [ + 47, + 247, + 287, + 281 + ], + "spans": [ + { + "bbox": [ + 47, + 247, + 287, + 281 + ], + "type": "text", + "content": "Table 4. Comparisons with relevant convolutional schemes on ScanNetv2. Baseline is a MinkowskiNet-34 network. All models listed are trained in the same training hyper-parameters." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 289, + 287, + 402 + ], + "lines": [ + { + "bbox": [ + 50, + 289, + 287, + 402 + ], + "spans": [ + { + "bbox": [ + 50, + 289, + 287, + 402 + ], + "type": "table", + "html": "
MethodParamsFLOPsLatencymIoU
Baseline37.9 M182.8 G108 ms71.7
+ Kernel 5×5×5170.3M537.5 G212 ms70.7
+ Kernel 7×7×7465.0M1089.5 G487 ms68.6
Dilate conv37.9M100.1 G98 ms64.6
Pooling + Dilate37.9M183.2 G115 msnan
Spatial group [78]37.9M127.2 G96 ms70.0
Deformable conv42.5M250.1 G238 ms72.0
LargeKernel3D-T38.4M171.4 G111 ms72.8
LargeKernel3D40.2M240.0 G145 ms73.5
", + "image_path": "c0e963d82a172d7d1a9eeb033f8afda4868ac32c74e61a1c484ca6a989b5e03a.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 60, + 445, + 275, + 497 + ], + "blocks": [ + { + "bbox": [ + 56, + 425, + 277, + 436 + ], + "lines": [ + { + "bbox": [ + 56, + 425, + 277, + 436 + ], + "spans": [ + { + "bbox": [ + 56, + 425, + 277, + 436 + ], + "type": "text", + "content": "Table 5. Results on other backbone networks andScanNetv2." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 60, + 445, + 275, + 497 + ], + "lines": [ + { + "bbox": [ + 60, + 445, + 275, + 497 + ], + "spans": [ + { + "bbox": [ + 60, + 445, + 275, + 497 + ], + "type": "table", + "html": "
ModelBaseline+OursΔ
MinkowskiNet-14 [9]67.069.7+2.7
MinkowskiNet-18 [9]69.571.5+2.0
SparseConvNet [24]69.371.2+1.9
", + "image_path": "0397193a099f125e35616423be7ad15283e4d8e29999685de29817be9a405248.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 528, + 287, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 528, + 287, + 624 + ], + "spans": [ + { + "bbox": [ + 46, + 528, + 287, + 624 + ], + "type": "text", + "content": "tains 1,201 indoor RGB-D scenes for training, 312 scenes for validation, and 100 scenes for testing. Semantic labels in 20 categories are annotated. We train our models with the default settings in MinkowskiNet [9], including training hyper-parameters and data augmentations. We evaluate models in the mean Intersection over Union (mIoU) metric. Detailed experimental settings, including network structures and training details, are listed in the appendix." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 629, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 288, + 714 + ], + "type": "text", + "content": "3D Object Detection nuScenes, and Waymo are all popular 3D object detection benchmarks. nuScenes is a large dataset and contains 1,000 driving sequences in total. Among them, there are 700 scenes split for training, 150 scenes for validation, and 150 scenes for testing. It contains LIDAR, camera, and radar sources with a complete " + }, + { + "bbox": [ + 46, + 629, + 288, + 714 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 46, + 629, + 288, + 714 + ], + "type": "text", + "content": " environment. We evaluate our methods on both LIDAR-only and LIDAR-" + } + ] + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 307, + 113, + 545, + 156 + ], + "blocks": [ + { + "bbox": [ + 305, + 70, + 545, + 104 + ], + "lines": [ + { + "bbox": [ + 305, + 70, + 545, + 104 + ], + "spans": [ + { + "bbox": [ + 305, + 70, + 545, + 104 + ], + "type": "text", + "content": "Table 6. Effects of the spatial-wise partition manners on SW-LK Conv and ScanNetv2. Center group means the size of central area. Shifting is to translate the center position by 1 in all 3 dimensions." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 113, + 545, + 156 + ], + "lines": [ + { + "bbox": [ + 307, + 113, + 545, + 156 + ], + "spans": [ + { + "bbox": [ + 307, + 113, + 545, + 156 + ], + "type": "table", + "html": "
Center group1×1×11×1×13×3×35×5×5
ShiftingX✓XX
mIoU73.566.870.668.2
", + "image_path": "89d684f59419ed57c39b9181fcbd30157e001b7497cfb61498e834c6b02eaad3.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "type": "table", + "bbox": [ + 309, + 232, + 545, + 330 + ], + "blocks": [ + { + "bbox": [ + 305, + 177, + 545, + 221 + ], + "lines": [ + { + "bbox": [ + 305, + 177, + 545, + 221 + ], + "spans": [ + { + "bbox": [ + 305, + 177, + 545, + 221 + ], + "type": "text", + "content": "Table 7. Improvement over various kernel sizes on LargeKernel3D upon CenterPoint, training on 1/5 Waymo training set and evaluate on the validation set. " + }, + { + "bbox": [ + 305, + 177, + 545, + 221 + ], + "type": "inline_equation", + "content": "\\Delta" + }, + { + "bbox": [ + 305, + 177, + 545, + 221 + ], + "type": "text", + "content": " means the improvement from the kernel 3 baseline. L1 and L2 means LEVEL_1 and LEVEL_2 mAP." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 309, + 232, + 545, + 330 + ], + "lines": [ + { + "bbox": [ + 309, + 232, + 545, + 330 + ], + "spans": [ + { + "bbox": [ + 309, + 232, + 545, + 330 + ], + "type": "table", + "html": "
KernelVehiclePedestrianCyclist
L1L2L1L2L1L2
Baseline70.962.971.563.569.166.5
7×7×771.963.871.763.770.467.8
11×11×1172.264.271.863.970.268.3
15×15×1572.764.673.865.870.868.2
17×17×1773.265.174.166.071.068.1
Δ2.3↑2.2↑2.6↑2.5↑1.9↑1.6↑
", + "image_path": "7fc7c8ef730b291a98ba8f2048a05832f95c04096b8dd4e76c94b2daa3ab9850.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_body" + } + ], + "index": 13 + }, + { + "type": "table", + "bbox": [ + 308, + 383, + 541, + 459 + ], + "blocks": [ + { + "bbox": [ + 305, + 351, + 545, + 373 + ], + "lines": [ + { + "bbox": [ + 305, + 351, + 545, + 373 + ], + "spans": [ + { + "bbox": [ + 305, + 351, + 545, + 373 + ], + "type": "text", + "content": "Table 8. Effects of position embedding (PE) in the mAP of vehicle detection on Waymo validation set." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 383, + 541, + 459 + ], + "lines": [ + { + "bbox": [ + 308, + 383, + 541, + 459 + ], + "spans": [ + { + "bbox": [ + 308, + 383, + 541, + 459 + ], + "type": "table", + "html": "
KernelPELatencyLEVEL_1LEVEL_2
3×3×3-109 ms70.962.9
7×7×7×120 ms71.663.4
✓122 ms71.963.8
17×17×17×158 ms71.563.3
✓164 ms73.265.1
", + "image_path": "d2d23d68d3adc2407a576eb8ecee6069996309380c22e486e6df00cc4f4b2581.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "table_body" + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 489, + 545, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 489, + 545, + 598 + ], + "spans": [ + { + "bbox": [ + 304, + 489, + 545, + 598 + ], + "type": "text", + "content": "RGB fusion settings. The main evaluation metrics are mAP and nuScenes detection score (NDS). Waymo [57] dataset also contains 1,000 sequences in total, with 798 for training and 202 for validation. For Waymo dataset, we use 1/5 training data for the ablation study and full training set for main results. Results in Waymo are evaluated on difficulty LEVEL_1 and LEVEL_2 objects. In experiments, we validate our networks on state-of-the-art detection framework of CenterPoint [75] on nuScenes [4] and Waymo [57]." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 605, + 406, + 618 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 605, + 406, + 618 + ], + "spans": [ + { + "bbox": [ + 306, + 605, + 406, + 618 + ], + "type": "text", + "content": "5.2. Ablation Studies" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 629, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 545, + 715 + ], + "type": "text", + "content": "Usefulness of 2D CNN Techniques We first validate the techniques that have proven effective on 2D CNNs, including layer normalization [1], depth-wise convolution [29, 43], and GeLU [28]. We conduct experiments on MinkowskiNet-34 [9] on the ScanNet [13] semantic segmentation dataset, as shown in Tab. 2. Kernel " + }, + { + "bbox": [ + 304, + 629, + 545, + 715 + ], + "type": "inline_equation", + "content": "7 \\times 7 \\times 7" + }, + { + "bbox": [ + 304, + 629, + 545, + 715 + ], + "type": "text", + "content": " means modifying kernel sizes in all stages to 7. All these" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13493" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 91, + 547, + 281 + ], + "blocks": [ + { + "bbox": [ + 75, + 71, + 516, + 83 + ], + "lines": [ + { + "bbox": [ + 75, + 71, + 516, + 83 + ], + "spans": [ + { + "bbox": [ + 75, + 71, + 516, + 83 + ], + "type": "text", + "content": "Table 9. Comparison with other methods on nuScenes test split. " + }, + { + "bbox": [ + 75, + 71, + 516, + 83 + ], + "type": "inline_equation", + "content": "\\ddagger" + }, + { + "bbox": [ + 75, + 71, + 516, + 83 + ], + "type": "text", + "content": " means flipping and rotation testing-time augmentations." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 91, + 547, + 281 + ], + "lines": [ + { + "bbox": [ + 50, + 91, + 547, + 281 + ], + "spans": [ + { + "bbox": [ + 50, + 91, + 547, + 281 + ], + "type": "table", + "html": "
MethodNDSmAPCarTruckBusTrailerC.V.PedMotBycT.C.Bar
PointPillars [35]45.330.568.423.028.223.44.159.727.41.130.838.9
3DSSD [74]56.442.681.247.261.430.512.670.236.08.631.147.9
CBGS [80]63.352.881.148.554.942.910.580.151.522.370.965.7
CenterPoint [75]65.558.084.651.060.253.217.583.453.728.776.770.9
HotSpotNet [7]66.059.383.150.956.453.323.081.363.536.673.071.6
CVCNET [6]66.658.282.649.559.451.116.283.061.838.869.769.7
UVTR-L [37]69.763.986.352.262.859.733.784.568.841.174.774.9
VISTA [17]69.863.084.455.163.754.225.182.870.045.478.571.4
Focals Conv [8]70.063.886.756.367.759.523.887.564.536.381.474.1
TransFusion-L [2]70.265.586.256.766.358.828.286.168.344.282.078.2
LargeKernel3D70.665.485.553.864.459.529.785.972.746.879.975.5
LargeKernel3D‡72.868.786.758.567.762.731.988.577.154.982.376.6
LargeKernel3D-F‡74.271.287.760.169.366.034.389.481.360.286.777.4
", + "image_path": "4dbdff16721225f4cb43c9228674951291d379eb43d63d67e21c0035bc6ba270.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 311, + 288, + 358 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 311, + 288, + 358 + ], + "spans": [ + { + "bbox": [ + 46, + 311, + 288, + 358 + ], + "type": "text", + "content": "techniques bring no obvious benefit to baseline networks. In contrast, SW-LK Conv introduces clear improvement upon these strong networks. We also show the effects of group convolution with different group numbers in Tab. 3." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 369, + 287, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 369, + 287, + 643 + ], + "spans": [ + { + "bbox": [ + 46, + 369, + 287, + 643 + ], + "type": "text", + "content": "Comparisons with Relevant Schemes We compare both performance and efficiency in Tab. 4 using various existing schemes to enlarge receptive fields. Dilated Conv [5] contains " + }, + { + "bbox": [ + 46, + 369, + 287, + 643 + ], + "type": "inline_equation", + "content": "3 \\times 3 \\times 3" + }, + { + "bbox": [ + 46, + 369, + 287, + 643 + ], + "type": "text", + "content": " kernel parameters. It dilates to " + }, + { + "bbox": [ + 46, + 369, + 287, + 643 + ], + "type": "inline_equation", + "content": "7 \\times 7 \\times 7" + }, + { + "bbox": [ + 46, + 369, + 287, + 643 + ], + "type": "text", + "content": " spatial sizes. Pooling + Dilated Conv inserts a 3D average pooling layer before the dilated convolutions to enlarge receptive fields. Spatial group conv is implemented, following the settings in the original paper [78]. We extend Deformable Conv [14] to 3D offset prediction, following [61]. Latencies are measured on an NVIDIA 2080ti GPU. It shows that none of these related schemes present better performance than the baseline. One reason for the low performance of dilation and deformable convolutions is that they tend to factorize the original dense kernels into sparse ones, which cause more information loss when applied to sparse 3D features than their 2D counterparts. Our LargeKernel3D achieves the best performance among these methods. In addition, we also build a tiny version, LargeKernel3D-T, which has half channel numbers in the last two stages. It introduces almost no additional computation overhead to baseline, but still has notable performance improvement. Except for the MinkowskiNet-34, we also show our effects on other backbone networks in Tab. 5." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "content": "Spatial-wise Group Partition Manner We ablate the effects of different spatial-wise group partition manners in Tab. 6. We study the size of central groups and center shifting. This ablation study is conducted on the LargeKernel3D and the Scannetv2 dataset. We find that both large central" + } + ] + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 308, + 340, + 541, + 515 + ], + "blocks": [ + { + "bbox": [ + 305, + 308, + 545, + 331 + ], + "lines": [ + { + "bbox": [ + 305, + 308, + 545, + 331 + ], + "spans": [ + { + "bbox": [ + 305, + 308, + 545, + 331 + ], + "type": "text", + "content": "Table 10. Comparison on ScanNetv2 mIoU on 3D semantic segmentation. † Sliding-window testing." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 340, + 541, + 515 + ], + "lines": [ + { + "bbox": [ + 308, + 340, + 541, + 515 + ], + "spans": [ + { + "bbox": [ + 308, + 340, + 541, + 515 + ], + "type": "table", + "html": "
MethodLatencyvaltest
PointCNN [36]--45.8
PointNet++ [49]-53.555.7
RandLA-Net [30]--64.5
PointConv [67]80 ms61.066.6
PointASNL [69]-63.566.6
KPConv [61]-69.268.6
FusionNet [77]--68.8
Point Transformer† [79]1012 ms70.6-
Fast Point Transformer [46]298 ms72.1-
SparseConvNet [24]-69.372.5
Stratified Transformer† [34]1624 ms74.373.7
MinkowskiNet-34108 ms71.7
+ LargeKernel3D14573.573.9
", + "image_path": "8a69a9215f18f03f6f49b66477e2d718d9a85d9d5055fad5a28ec97eef435b8b.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 539, + 545, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 539, + 545, + 624 + ], + "spans": [ + { + "bbox": [ + 304, + 539, + 545, + 624 + ], + "type": "text", + "content": "sizes and center shifting hurt the performance. As the center sizes enlarge from " + }, + { + "bbox": [ + 304, + 539, + 545, + 624 + ], + "type": "inline_equation", + "content": "1 \\times 1 \\times 1" + }, + { + "bbox": [ + 304, + 539, + 545, + 624 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 539, + 545, + 624 + ], + "type": "inline_equation", + "content": "5 \\times 5 \\times 5" + }, + { + "bbox": [ + 304, + 539, + 545, + 624 + ], + "type": "text", + "content": ", the accuracy sharply drops. Because submanifold sparse convolution [25] always aligns each individual voxel feature at its kernel center, we suppose that central features should maintain distinct and clean. Therefore, we keep the center size as " + }, + { + "bbox": [ + 304, + 539, + 545, + 624 + ], + "type": "inline_equation", + "content": "1 \\times 1 \\times 1" + }, + { + "bbox": [ + 304, + 539, + 545, + 624 + ], + "type": "text", + "content": " without shifting, as a default setting." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 629, + 546, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 546, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 546, + 715 + ], + "type": "text", + "content": "Further Enlarging Kernel Sizes We show that LargeKernel3D is scalable to kernel sizes " + }, + { + "bbox": [ + 304, + 629, + 546, + 715 + ], + "type": "inline_equation", + "content": "17 \\times 17 \\times 17" + }, + { + "bbox": [ + 304, + 629, + 546, + 715 + ], + "type": "text", + "content": " on the outdoor dataset Waymo [57] in Tab. 7 with baseline kernel " + }, + { + "bbox": [ + 304, + 629, + 546, + 715 + ], + "type": "inline_equation", + "content": "3 \\times 3 \\times 3" + }, + { + "bbox": [ + 304, + 629, + 546, + 715 + ], + "type": "text", + "content": ". Models in this ablation are trained on " + }, + { + "bbox": [ + 304, + 629, + 546, + 715 + ], + "type": "inline_equation", + "content": "1/5" + }, + { + "bbox": [ + 304, + 629, + 546, + 715 + ], + "type": "text", + "content": " training data and evaluated on the full validation set. Results with full training data are compared in Tab. 11. It shows that the mAP on all categories increases by around " + }, + { + "bbox": [ + 304, + 629, + 546, + 715 + ], + "type": "inline_equation", + "content": "2\\%" + }, + { + "bbox": [ + 304, + 629, + 546, + 715 + ], + "type": "text", + "content": ". This setting demon-" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "13494" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 51, + 114, + 284, + 335 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 288, + 104 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 288, + 104 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 288, + 104 + ], + "type": "text", + "content": "Table 11. Performance of vehicle detection on the Waymo val split. All models listed take LIDAR-only input and single frames, without any test-time augmentations or model ensemble." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 51, + 114, + 284, + 335 + ], + "lines": [ + { + "bbox": [ + 51, + 114, + 284, + 335 + ], + "spans": [ + { + "bbox": [ + 51, + 114, + 284, + 335 + ], + "type": "table", + "html": "
MethodLEVEL_13D AP / APHLEVEL_23D AP / APH
VoTr-SSD [45]68.99 / 68.3960.22 / 59.69
PointPillars [75]72.08 / 71.5363.55 / 63.06
SECOND [70]72.27 / 71.6963.85 / 63.33
RangeDet [23]72.85 / 72.3364.03 / 63.57
SST [22]74.22 / 73.7765.47 / 65.07
VoTr-TSD [45]74.95 / 74.2565.91 / 65.29
RSN [59]75.1 / 74.666.0 / 65.5
Voxel RCNN [16]75.59 / ——66.59 / ——
LIDAR-RCNN [39]76.0 / 75.568.3 / 67.9
SST [22]76.22 / 75.7968.04 / 67.64
Pyramid RCNN [44]76.30 / 75.6867.23 / 66.68
Part-A2-Net [56]77.05 / 76.5168.47 / 67.14
PV-RCNN [55]77.51 / 76.8968.98 / 68.41
SWFormer [58]69.2 / 68.880.9 / 72.7
CenterPoint [75]76.59 / 76.0568.85 / 68.35
+ LargeKernel3D78.07 / 77.6169.81 / 69.38
", + "image_path": "21a9c9b0b8471b765b0ea2be022ad6b821bf8c405a97c032ca418046d04f4747.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 369, + 287, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 369, + 287, + 418 + ], + "spans": [ + { + "bbox": [ + 46, + 369, + 287, + 418 + ], + "type": "text", + "content": "strates that a large-scale dataset is a key to unlocking the potential and capability of large kernel methods. In addition, we also try to extend the kernel size to " + }, + { + "bbox": [ + 46, + 369, + 287, + 418 + ], + "type": "inline_equation", + "content": "19 \\times 19 \\times 19" + }, + { + "bbox": [ + 46, + 369, + 287, + 418 + ], + "type": "text", + "content": ", but obtain no further gains." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 422, + 287, + 531 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 422, + 287, + 531 + ], + "spans": [ + { + "bbox": [ + 46, + 422, + 287, + 531 + ], + "type": "text", + "content": "Effects of Position Embedding In LargeKernel3D, position embedding is introduced to relieve the feature-blurring issue caused by weight-sharing. We ablate its effects in Tab. 8, in terms of both latency and performance. Position embedding introduces limited latency overhead on both kernel " + }, + { + "bbox": [ + 46, + 422, + 287, + 531 + ], + "type": "inline_equation", + "content": "7 \\times 7 \\times 7" + }, + { + "bbox": [ + 46, + 422, + 287, + 531 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 422, + 287, + 531 + ], + "type": "inline_equation", + "content": "17 \\times 17 \\times 17" + }, + { + "bbox": [ + 46, + 422, + 287, + 531 + ], + "type": "text", + "content": " models. In terms of performance, its effects on the " + }, + { + "bbox": [ + 46, + 422, + 287, + 531 + ], + "type": "inline_equation", + "content": "7 \\times 7 \\times 7" + }, + { + "bbox": [ + 46, + 422, + 287, + 531 + ], + "type": "text", + "content": " model are a bit marginal, but essential on the " + }, + { + "bbox": [ + 46, + 422, + 287, + 531 + ], + "type": "inline_equation", + "content": "17 \\times 17 \\times 17" + }, + { + "bbox": [ + 46, + 422, + 287, + 531 + ], + "type": "text", + "content": " model, which has larger kernel sizes and suffers from feature blurring." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 536, + 287, + 597 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 536, + 287, + 597 + ], + "spans": [ + { + "bbox": [ + 46, + 536, + 287, + 597 + ], + "type": "text", + "content": "Shrinking Kernels During Inference For the spatial-wise partition convolution, we can shrink kernels into small ones during inference. As shown in Tab. 4, the latency of LargeKernel3D is " + }, + { + "bbox": [ + 46, + 536, + 287, + 597 + ], + "type": "inline_equation", + "content": "145\\mathrm{ms}" + }, + { + "bbox": [ + 46, + 536, + 287, + 597 + ], + "type": "text", + "content": " on ScanNetv2. It degrades to " + }, + { + "bbox": [ + 46, + 536, + 287, + 597 + ], + "type": "inline_equation", + "content": "514\\mathrm{ms}" + }, + { + "bbox": [ + 46, + 536, + 287, + 597 + ], + "type": "text", + "content": " with the same " + }, + { + "bbox": [ + 46, + 536, + 287, + 597 + ], + "type": "inline_equation", + "content": "73.5\\%" + }, + { + "bbox": [ + 46, + 536, + 287, + 597 + ], + "type": "text", + "content": " mIoU, if we disable shrinking." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 605, + 132, + 617 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 605, + 132, + 617 + ], + "spans": [ + { + "bbox": [ + 47, + 605, + 132, + 617 + ], + "type": "text", + "content": "5.3. Main Results" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "content": "3D Semantic Segmentation We make comparisons with other 3D semantic segmentation methods on the ScanNetv2 dataset in Tab. 10. Our method surpasses others on test split. MinkowskiNet [9] is already a state-of-the-art method in ScanNetv2. Our SW-LK Conv further improves its performance. Our method is also superior to transformer-based methods [46,79]. Stratified Transformer [34] uses a sliding-" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 545, + 121 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 121 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 121 + ], + "type": "text", + "content": "window testing technique† and splits integrated scenes into overlapped parts. The method tests each part one by one and then ensembles results together, taking hours on evaluation. Moreover, our results are better on the test split." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 126, + 545, + 236 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 126, + 545, + 236 + ], + "spans": [ + { + "bbox": [ + 304, + 126, + 545, + 236 + ], + "type": "text", + "content": "3D Object Detection We compare our LargeKernel3D upon CenterPoint [75] with previous methods on the test split of the nuScenes [4] dataset in Tab. 9. LargeKernel3D improves CenterPoint [75] to " + }, + { + "bbox": [ + 304, + 126, + 545, + 236 + ], + "type": "inline_equation", + "content": "70.6\\%" + }, + { + "bbox": [ + 304, + 126, + 545, + 236 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 126, + 545, + 236 + ], + "type": "inline_equation", + "content": "72.8\\%" + }, + { + "bbox": [ + 304, + 126, + 545, + 236 + ], + "type": "text", + "content": " NDS, with and without test augmentation, both outperforming other LIDAR methods. The multi-modal modal LargeKernel3D-F further improves to " + }, + { + "bbox": [ + 304, + 126, + 545, + 236 + ], + "type": "inline_equation", + "content": "74.2\\%" + }, + { + "bbox": [ + 304, + 126, + 545, + 236 + ], + "type": "text", + "content": " NDS and " + }, + { + "bbox": [ + 304, + 126, + 545, + 236 + ], + "type": "inline_equation", + "content": "71.2\\%" + }, + { + "bbox": [ + 304, + 126, + 545, + 236 + ], + "type": "text", + "content": " mAP. The fusion module directly follows a simple painting-based manner [8]. Results on the val split is shown in the appendix." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 236, + 547, + 369 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 236, + 547, + 369 + ], + "spans": [ + { + "bbox": [ + 304, + 236, + 547, + 369 + ], + "type": "text", + "content": "We also show the effectiveness of LargeKernel3D model on the vehicle detection of Waymo [57] validation set in Tab. 11. The kernel size of LargeKernel3D is " + }, + { + "bbox": [ + 304, + 236, + 547, + 369 + ], + "type": "inline_equation", + "content": "17 \\times 17 \\times 17" + }, + { + "bbox": [ + 304, + 236, + 547, + 369 + ], + "type": "text", + "content": ". LargeKernel3D improves the vehicle performance of CenterPoint [75] by around " + }, + { + "bbox": [ + 304, + 236, + 547, + 369 + ], + "type": "inline_equation", + "content": "1.5\\%" + }, + { + "bbox": [ + 304, + 236, + 547, + 369 + ], + "type": "text", + "content": " LEVEL_1 AP / APH. Models listed take single-frame LIDAR data without any test-time augmentations or ensemble. It also performs better than other methods. We use CenterPoint [75] to keep consistency to the nuScenes benchmark. Note that LargeKernel3D has the potential to achieve further performance if equipped with stronger detection heads [55]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 385, + 458, + 398 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 385, + 458, + 398 + ], + "spans": [ + { + "bbox": [ + 306, + 385, + 458, + 398 + ], + "type": "text", + "content": "6. Conclusion and Discussion" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 407, + 545, + 587 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 407, + 545, + 587 + ], + "spans": [ + { + "bbox": [ + 304, + 407, + 545, + 587 + ], + "type": "text", + "content": "We have studied large-kernel designs for 3D convolutional networks, which have essential differences from the solutions in 2D CNNs. We present spatial-wise partition convolution (SW Conv) that is specifically designed for 3D large kernels. It effectively resolves the efficiency and optimization issues in plain 3D large-kernel CNNs. Based on this design, we further propose the SW-LK Conv and the corresponding LargeKernel3D for 3D semantic segmentation and object detection. Our 3D large-kernel networks achieve decent improvement on both semantic segmentation and object detection tasks. For the first time, we show that 3D large kernels can be realized efficiently and effectively. We expect our findings to advance further development of 3D networks. Additional experiments and limitation analysis are provided in the appendix." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 592, + 545, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 592, + 545, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 592, + 545, + 665 + ], + "type": "text", + "content": "Limitations LargeKernel3D mainly relies on hand-designed spatial kernel sizes in 3D semantic segmentation and object detection benchmarks. These sizes might be suboptimal for other datasets or tasks, depending on the overall scene sizes and data sparsity. Other search-based techniques [60] might be helpful, which we will try latter." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 669, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 669, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 669, + 545, + 713 + ], + "type": "text", + "content": "Acknowledgement. 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In CVPR, pages 9308-9316, 2019. 2" + } + ] + } + ], + "index": 25 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "13498" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/LaserMix for Semi-Supervised LiDAR Semantic Segmentation/0dfb46c8-457c-4c6b-aa9f-3e7c68a2add5_content_list.json b/2023/LaserMix for Semi-Supervised LiDAR Semantic Segmentation/0dfb46c8-457c-4c6b-aa9f-3e7c68a2add5_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..71f4cfcc1adc50750625252273b456d21260b0a3 --- /dev/null +++ b/2023/LaserMix for Semi-Supervised LiDAR Semantic Segmentation/0dfb46c8-457c-4c6b-aa9f-3e7c68a2add5_content_list.json @@ -0,0 +1,1801 @@ +[ + { + "type": "text", + "text": "LaserMix for Semi-Supervised LiDAR Semantic Segmentation", + "text_level": 1, + "bbox": [ + 168, + 130, + 802, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Lingdong Kong $^{1,2,3,*}$ Jiawei Ren $^{1,*}$ Liang Pan $^{1}$ Ziwei Liu $^{1,\\text{口}}$", + "bbox": [ + 217, + 179, + 756, + 200 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ S-Lab, Nanyang Technological University $^{2}$ National University of Singapore $^{3}$ CNRS@CREATE", + "bbox": [ + 84, + 204, + 887, + 223 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{lingdong001,jiawei011}@e.ntu.edu.sg {liang.pan,ziwei.liu}@ntu.edu.sg", + "bbox": [ + 171, + 224, + 797, + 241 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/e0b7140b13cde9d26d8fbb9cfea928327b9f32ccd9c902894f5bac5964768d2e.jpg", + "image_caption": [ + "Option 1: Range View" + ], + "image_footnote": [], + "bbox": [ + 78, + 263, + 377, + 494 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/81902df7b48ae9eb36aba09b702c2ecb2b53b97fb011c5f1aa625bd02c16b5cd.jpg", + "image_caption": [ + "LiDAR Representation" + ], + "image_footnote": [], + "bbox": [ + 383, + 263, + 593, + 338 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/d2494263c35f7d98774c2fd878006d5bea1810fe63c71a8b55587a1bc2e0f880.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 393, + 401, + 483, + 431 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/fc6d50b221142931e82a822773d01a57801b098c490d533b7268e20c25a41a43.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 413, + 435, + 465, + 465 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/640ed0ae358b9bdfb8c3767d0707693625f955e30144221bca7ed58b44a2b8e7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 395, + 469, + 483, + 492 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/d063b1954baff34f09c72d982b59f274cdea06a99cbfe2bbc2828f09f77919d1.jpg", + "image_caption": [ + "Option 2: Voxel" + ], + "image_footnote": [], + "bbox": [ + 503, + 400, + 591, + 430 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/f77ab86efd1ced814a6f5bd32fb53e8b4d2820a5b44dce2de6acbe4e5fb036e4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 522, + 434, + 571, + 455 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/b2c598d668998b80db82a11b3d1a60c1c82d332e59beae7dbaeddef8249456d5.jpg", + "image_caption": [ + "Figure 1. Left: The LiDAR point cloud contains strong spatial prior. Objects and backgrounds around the ego-vehicle have a patterned distribution on different (lower, middle, upper) laser beams. Middle: Following the scene structure, the proposed LaserMix blends beams from different LiDAR scans, which is compatible with various popular LiDAR representations. Right: We achieve superior results over SoTA methods in both low-data (10%, 20%, and 50% semantic labels) and high-data (full semantic labels) regimes on nuScenes [11]." + ], + "image_footnote": [], + "bbox": [ + 501, + 465, + 589, + 496 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/4d8f2bd6eaf8ca4f96cbc1797b099540f661c6f507dcfb5a77daf3ab29cee36b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 607, + 266, + 890, + 494 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 595, + 313, + 611 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Densely annotating LiDAR point clouds is costly, which often restrains the scalability of fully-supervised learning methods. In this work, we study the underexplored semi-supervised learning (SSL) in LiDAR semantic segmentation. Our core idea is to leverage the strong spatial cues of LiDAR point clouds to better exploit unlabeled data. We propose LaserMix to mix laser beams from different LiDAR scans and then encourage the model to make consistent and confident predictions before and after mixing. Our framework has three appealing properties. 1) Generic: LaserMix is agnostic to LiDAR representations (e.g., range view and voxel), and hence our SSL framework can be universally applied. 2) Statistically grounded: We provide a detailed analysis to theoretically explain the applicability of the proposed framework. 3) Effective: Comprehensive experimental analysis on popular LiDAR segmentation", + "bbox": [ + 75, + 623, + 470, + 864 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "datasets (nuScenes, SemanticKITTI, and ScribbleKITTI) demonstrates our effectiveness and superiority. Notably, we achieve competitive results over fully-supervised counterparts with $2 \\times$ to $5 \\times$ fewer labels and improve the supervised-only baseline significantly by relatively $10.8\\%$ . We hope this concise yet high-performing framework could facilitate future research in semi-supervised LiDAR segmentation. Code is publicly available1.", + "bbox": [ + 496, + 582, + 893, + 704 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 500, + 718, + 632, + 734 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "LiDAR segmentation is one of the fundamental tasks in autonomous driving perception [41]. It enables autonomous vehicles to semantically perceive the dense 3D structure of the surrounding scenes [15, 34, 39]. However, densely annotating LiDAR point clouds is inevitably expensive and labor-intensive [18, 23, 47], which restrains the scalability of fully-supervised LiDAR segmentation methods. Semisupervised learning (SSL) that directly leverages the easy-to-acquire unlabeled data is hence a viable and promising", + "bbox": [ + 496, + 743, + 893, + 878 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 47 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "(*) Lingdong and Jiawei contributed equally to this work. (☑) Ziwei serves as the corresponding author. E-mail: ziwei.liu@ntu.edu.sg.", + "bbox": [ + 76, + 875, + 470, + 901 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "1https://github.com/ldkong1205/LaserMix.", + "bbox": [ + 517, + 887, + 830, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "21705", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "solution to achieve scalable LiDAR segmentation [13, 14].", + "bbox": [ + 76, + 90, + 464, + 107 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Yet, semi-supervised LiDAR segmentation is still under-explored. Modern SSL frameworks are mainly designed for image recognition [2, 3, 42] and semantic segmentation [6, 21, 37] tasks, which only yield sub-par performance on LiDAR data due to the large modality gap between 2D and 3D. Recent research [20] proposed to consider semi-supervised point cloud semantic segmentation as a fresh task and proposed a point contrastive learning framework. However, their solutions do not differentiate indoor and outdoor scenes and therefore overlook the intrinsic and important properties that only exist in LiDAR point clouds.", + "bbox": [ + 75, + 107, + 468, + 273 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, we explore the use of spatial prior for semi-supervised LiDAR segmentation. Unlike the general 2D/3D segmentation tasks, the spatial cues are especially significant in LiDAR data. In fact, LiDAR point clouds serve as a perfect reflection of real-world distributions, which is highly dependent on the spatial areas in the LiDAR-centered 3D coordinates. As shown in Fig. 1 (left), the top laser beams travel outward long distance and perceive mostly vegetation, while the middle and bottom beams tend to detect car and road from the medium and close distances, respectively. To effectively leverage this strong spatial prior, we propose LaserMix to mix laser beams from different LiDAR scans, and then encourage the LiDAR segmentation model to make consistent and confident predictions before and after mixing. Our SSL framework is statistically grounded, which consists of the following components:", + "bbox": [ + 75, + 275, + 470, + 517 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1) Partitioning the LiDAR scan into low-variation areas. We observe a strong distribution pattern on laser beams as shown in Fig. 1 (left) and thus propose the laser partition.", + "2) Efficiently mixing every area in the scan with foreign data and obtaining model predictions. We propose LaserMix to manipulate the laser-grouped areas from two LiDAR scans in an intertwining way as depicted in Fig. 1 (middle) and serves as an efficient LiDAR mixing strategy for SSL.", + "3) Encouraging models to make confident and consistent predictions on the same area in different mixing. We hence propose a mixing-based teacher-student training pipeline." + ], + "bbox": [ + 75, + 518, + 468, + 688 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Despite the simplicity of our overall pipeline, it achieves competitive results over the fully supervised counterpart using $2 \\times$ to $5 \\times$ fewer labels as shown in Fig. 1 (right) and significantly outperforms all prevailing semi-supervised segmentation methods on nuScenes [11] (up to $+5.7\\%$ mIoU) and SemanticKITTI [1] (up to $+3.5\\%$ mIoU). Moreover, LaserMix directly operates on point clouds so as to be agnostic to different LiDAR representations, e.g., range view [32] and voxel [58]. Therefore, our pipeline is highly compatible with existing state-of-the-art (SoTA) LiDAR segmentation methods under various representations [46, 56, 57]. Besides, our pipeline achieves competitive performance using very limited annotations on weak supervision dataset [47]: it achieves $54.4\\%$ mIoU on Se", + "bbox": [ + 75, + 689, + 470, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "manticKITTI [1] using only $0.8\\%$ labels, which is on-par with PolarNet [56] $(54.3\\%)$ , RandLA-Net [19] $(53.9\\%)$ , and RangeNet++ [32] $(52.2\\%)$ using $100\\%$ labels. Spatial prior is proven to play a pivotal role in the success of our framework through comprehensive empirical analysis. To summarize, this work has the following key contributions:", + "bbox": [ + 496, + 90, + 890, + 181 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We present a statistically grounded SSL framework that effectively leverages the spatial cues in LiDAR data to facilitate learning with semi-supervisions.", + "- We propose LaserMix, a novel and representation-agnostic mixing technique that strives to maximize the \"strength\" of the spatial cues in our SSL framework.", + "- Our overall pipeline significantly outperforms previous SoTA methods in both low- and high-data regimes. We hope this work could lay a solid foundation for semi-supervised LiDAR segmentation." + ], + "bbox": [ + 517, + 183, + 890, + 340 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 345, + 640, + 363 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "LiDAR Segmentation. Various approaches from different aspects have been proposed for LiDAR scene segmentation, i.e., range view [8, 32, 49, 57], bird's eye view [56], voxel [44, 58], and multi-view [26, 50] methods. Although appealing results have been achieved, these fully-supervised methods rely on large-scale annotated LiDAR datasets and their performance would degrade severely in the low-data regime [13]. Recent works seek weak [18, 55], scribble [47], and box [28] supervisions or activate learning [27, 31] to ease the annotation cost. We tackle this problem from the perspective of semi-supervised learning (SSL), aiming at directly leveraging the easy-to-acquire unlabeled data to boost the LiDAR semantic segmentation performance.", + "bbox": [ + 496, + 371, + 890, + 568 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "SSL in 2D. Well-known SSL algorithms are prevailing in handling image recognition problems [2, 3, 24, 42, 45]. In the context of semantic segmentation, CutMix-Seg [12] and PseudoSeg [60] apply perturbations on inputs and hope the decision boundary lies in the low-density region. CPS [6] and GCT [21] enforce consistency between two perturbed networks [29]. These perturbations [30, 36, 52], however, are either inapplicable or only yield sub-par results in 3D. Another line of research is entropy minimization. Methods like CBST [59] and $\\mathrm{ST} + +$ [51] generate pseudo-labels [25] offline per round during self-training. The extra storage needed might become costly for large-scale LiDAR datasets [1, 4, 11]. Our framework encourages both consistency regularization and entropy minimization and does not require extra overhead, which better maintains scalability.", + "bbox": [ + 496, + 568, + 890, + 794 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "SSL in 3D. Most works focus on developing SSL for object-centric point clouds [22, 43] or indoor scenes [7, 9, 17, 34], whose scale and diversity are much lower than the outdoor LiDAR point clouds [1, 4]. Some other works [38, 40, 48] try to utilize SSL for 3D object detection on LiDAR data. A recent work [20] tackles semi-supervised point cloud semantic segmentation using contrastive learning, but it still", + "bbox": [ + 496, + 795, + 890, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "21706", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "mainly focused on indoor scenes and does not distinguish between the uniformly distributed indoor point clouds and the spatially structured LiDAR point clouds. We are one of the first works to explore SSL for LiDAR segmentation. Our work also establishes comprehensive SSL benchmarks upon popular autonomous driving databases [1, 11, 47].", + "bbox": [ + 75, + 90, + 472, + 183 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Approach", + "text_level": 1, + "bbox": [ + 76, + 195, + 186, + 212 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we first introduce our SSL framework that leverages the spatial prior of LiDAR data by encouraging confidence and consistency in predictions (Sec. 3.1). We then present LaserMix which strives to maximize the \"strength\" of the spatial prior and mixes LiDAR scans in an efficient manner (Sec. 3.2). Finally, we elaborate on the overall pipeline (Sec. 3.3) and the pseudo-code (Algo. 1).", + "bbox": [ + 75, + 219, + 468, + 327 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Leveraging the Spatial Prior for SSL", + "text_level": 1, + "bbox": [ + 76, + 334, + 395, + 349 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Spatial Prior Formulation. The distribution of real-world objects/backgrounds has a strong correlation to their spatial positions in the LiDAR scan. Objects/backgrounds inside a specified spatial area of a LiDAR point cloud follow similar patterns, e.g., the close-range area is most likely road while the long-range area consists of building, vegetation, etc. In another word, there exists a spatial area $a \\in A$ where LiDAR points and semantic labels inside the area (denoted as $X_{\\mathrm{in}}$ and $Y_{\\mathrm{in}}$ , respectively) will have relatively low variations. Formally, the conditional entropy $H(X_{\\mathrm{in}}, Y_{\\mathrm{in}}|A)$ is smaller. Therefore, when estimating the parameter $\\theta$ of the segmentation network $\\mathcal{G}_{\\theta}$ , we would expect:", + "bbox": [ + 75, + 357, + 472, + 540 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbb {E} _ {\\theta} \\left[ H \\left(X _ {\\text {i n}}, Y _ {\\text {i n}} \\mid A\\right) \\right] = c, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 549, + 468, + 566 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $c$ is a small constant. Similar to the classic entropy minimization [16], the constraint in Eq. (1) can be converted to a prior on the model parameter $\\theta$ using the principle of maximum entropy:", + "bbox": [ + 75, + 575, + 468, + 637 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} P (\\theta) \\propto \\exp (- \\lambda H (X _ {\\text {i n}}, Y _ {\\text {i n}} | A)) \\tag {2} \\\\ \\propto \\exp (- \\lambda H (Y _ {\\mathrm {i n}} | X _ {\\mathrm {i n}}, A)), \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 158, + 646, + 468, + 681 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\lambda > 0$ is the Lagrange multiplier corresponding to constant $c$ ; $H(X_{\\mathrm{in}}|A)$ has been ignored for being independent of the model parameter $\\theta$ . We consider Eq. (2) as the formal formulation of the spatial prior and discuss how to empirically compute it in the following sections.", + "bbox": [ + 75, + 691, + 468, + 766 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Marginalization. To utilize the spatial prior defined in Eq. (2), we empirically compute the entropy $H(Y_{\\mathrm{in}}|X_{\\mathrm{in}},A)$ of the LiDAR points inside area $A$ as follows:", + "bbox": [ + 75, + 766, + 468, + 811 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {H} \\left(Y _ {\\text {i n}} \\mid X _ {\\text {i n}}, A\\right) = \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 119, + 820, + 468, + 845 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathbb {E}} _ {X _ {\\mathrm {i n}}, Y _ {\\mathrm {i n}}, A} \\big [ P (Y _ {\\mathrm {i n}} | X _ {\\mathrm {i n}}, A) \\log P (Y _ {\\mathrm {i n}} | X _ {\\mathrm {i n}}, A) \\big ],\n$$\n", + "text_format": "latex", + "bbox": [ + 119, + 843, + 426, + 862 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\hat{\\cdot}$ denotes the empirical estimation. The end-to-end LiDAR segmentation model $\\mathcal{G}_{\\theta}$ usually takes full-sized", + "bbox": [ + 75, + 869, + 468, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "data as inputs during inference. Therefore, to compute $P(Y_{\\mathrm{in}}|X_{\\mathrm{in}},A)$ in Eq. (3), we first pad the data outside the area to obtain the full-sized data. Here we denote the data outside the area as $X_{\\mathrm{out}}$ ; we then let the model infer $P(Y_{\\mathrm{in}}|X_{\\mathrm{in}},X_{\\mathrm{out}},A)$ , and finally marginalize $X_{\\mathrm{out}}$ as:", + "bbox": [ + 498, + 90, + 890, + 167 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nP \\left(Y _ {\\mathrm {i n}} \\mid X _ {\\mathrm {i n}}, A\\right) = \\hat {\\mathbb {E}} _ {X _ {\\mathrm {o u t}}} \\left[ P \\left(Y _ {\\mathrm {i n}} \\mid X _ {\\mathrm {i n}}, X _ {\\mathrm {o u t}}, A\\right) \\right]. \\quad (4)\n$$\n", + "text_format": "latex", + "bbox": [ + 539, + 174, + 890, + 193 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The generative distribution of the padding $P(X_{\\mathrm{out}})$ can be directly obtained from the dataset.", + "bbox": [ + 496, + 199, + 890, + 229 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Training. Finally, we train the segmentation model $\\mathcal{G}_{\\theta}$ using the standard maximum-a-posteriori (MAP) estimation. We maximize the posterior that can be computed by Eq. (2), Eq. (3) and Eq. (4), which is formulated as follows:", + "bbox": [ + 496, + 229, + 890, + 291 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} C (\\theta) = L (\\theta) - \\lambda \\hat {H} \\left(Y _ {\\mathrm {i n}} \\mid X _ {\\mathrm {i n}}, A\\right) = L (\\theta) \\tag {5} \\\\ - \\lambda \\hat {\\mathbb {E}} _ {X _ {\\text {i n}}, Y _ {\\text {i n}}, A} [ P (Y _ {\\text {i n}} | X _ {\\text {i n}}, A) \\log P (Y _ {\\text {i n}} | X _ {\\text {i n}}, A) ]. \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 517, + 297, + 890, + 335 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Here, $L(\\theta)$ is the likelihood function computed using labeled data, i.e., the conventional supervised learning. Minimizing $\\hat{H}(Y_{\\mathrm{in}}|X_{\\mathrm{in}},A)$ requires the marginal probability $P(Y_{\\mathrm{in}}|X_{\\mathrm{in}},A)$ to be confident, which further requires $P(Y_{\\mathrm{in}}|X_{\\mathrm{in}},X_{\\mathrm{out}},A)$ to be both confident and consistent with respect to different outside data $X_{\\mathrm{out}}$ .", + "bbox": [ + 496, + 343, + 890, + 434 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In summary, our proposed SSL framework in Eq. (5) encourages the segmentation model to make confident and consistent predictions at a predefined area, regardless of the data outside the area. The predefined area set $A$ determines the \"strength\" of the prior. When setting $A$ to the full area (i.e., the whole point cloud), our framework degrades to the classic entropy minimization framework [16].", + "bbox": [ + 496, + 434, + 890, + 540 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Implementation. There are three key steps for implementing our framework:", + "bbox": [ + 496, + 540, + 890, + 570 + ], + "page_idx": 2 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Step 1): Select a proper partition set $A$ which maintains strong spatial prior;", + "- Step 2): Efficiently compute the marginal probability, i.e., $P(Y_{\\mathrm{in}}|X_{\\mathrm{in}},A)$ ;", + "- Step 3): Efficiently minimize the marginal entropy, i.e., $\\hat{H}(Y_{\\mathrm{in}}|X_{\\mathrm{in}},A)$ ." + ], + "bbox": [ + 517, + 573, + 890, + 672 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We propose a simple yet effective implementation following these steps in the next section.", + "bbox": [ + 496, + 674, + 890, + 705 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. LaserMix", + "text_level": 1, + "bbox": [ + 500, + 712, + 611, + 727 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Partition. LiDAR sensors have a fixed number (e.g., 32, 64, and 128) of laser beams which are emitted isotropically around the ego-vehicle with predefined inclination angles as shown in Fig. 2. To obtain a proper set of spatial areas $A$ , we propose to partition the LiDAR point cloud based on laser beams. Specifically, points captured by the same laser beam have a unified inclination angle to the sensor plane. For point $i$ , its inclination $\\phi_i$ is defined as follows:", + "bbox": [ + 496, + 734, + 890, + 857 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\phi_ {i} = \\arctan \\left(\\frac {p _ {i} ^ {z}}{\\sqrt {\\left(p _ {i} ^ {x}\\right) ^ {2} + \\left(p _ {i} ^ {y}\\right) ^ {2}}}\\right), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 584, + 864, + 890, + 898 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "21707", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $(p^x,p^y,p^z)$ is the Cartesian coordinates of the LiDAR points. Given two LiDAR scans $x_{1}$ and $x_{2}$ , we first group all points from each scan by their inclination angles. Concretely, to form $m$ non-overlapping areas, a set of $m + 1$ inclination angles $\\Phi = \\{\\phi_0,\\phi_1,\\phi_2,\\dots,\\phi_m\\}$ will be evenly sampled within the range of the minimum and maximum inclination angles in the dataset (defined by sensor configurations), and the area set $A = \\{a_{1},a_{2},\\ldots,a_{m}\\}$ can be formed by bounding area $a_{i}$ in the inclination range $[\\phi_{i - 1},\\phi_i)$ .", + "bbox": [ + 75, + 90, + 468, + 226 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Role in our framework: Laser partition effectively \"excites\" a strong spatial prior in the LiDAR point cloud, as described by Step 1 in our framework. As shown in Fig. 1 (left), we find an overt pattern in semantic classes detected by each laser beam. More concrete evidence on this aspect has been included in the Appendix. Despite being an empirical choice, we will show in later sections that laser partition significantly outperforms other partition choices, including random points (MixUp-like partition [54]), random areas (CutMix-like partition [53]), and other heuristics like azimuth $\\alpha$ (sensor horizontal direction) or radius $r$ (sensor range direction) partitions.", + "bbox": [ + 75, + 227, + 470, + 407 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Mixing. To this end, we propose LaserMix, a simple yet effective LiDAR mixing strategy that can better control the \"strength\" of the spatial prior. LaserMix mixes the aforementioned laser partitioned areas $A$ from two scans in an intertwining way, i.e., one takes from odd-indexed areas $A_{1} = \\{a_{1},a_{3},\\ldots \\}$ and the other takes from even-indexed areas $A_{2} = \\{a_{2},a_{4},\\ldots \\}$ , so that each area's neighbor will be from the other scan:", + "bbox": [ + 76, + 407, + 468, + 527 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {x} _ {1}, \\tilde {x} _ {2} = \\operatorname {L a s e r M i x} \\left(x _ {1}, x _ {2}\\right),\n$$\n", + "text_format": "latex", + "bbox": [ + 181, + 535, + 370, + 550 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {x} _ {1} = x _ {1} ^ {a _ {1}} \\cup x _ {2} ^ {a _ {2}} \\cup x _ {1} ^ {a _ {3}} \\cup \\dots , \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 176, + 553, + 468, + 570 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {x} _ {2} = x _ {2} ^ {a _ {1}} \\cup x _ {1} ^ {a _ {2}} \\cup x _ {2} ^ {a _ {3}} \\cup \\dots ,\n$$\n", + "text_format": "latex", + "bbox": [ + 176, + 571, + 372, + 589 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $x_{i}^{a_{j}}$ is the data crop of $x_{i}$ in the area $a_{j}$ . The semantic labels are mixed in the same way. LaserMix is directly applied to the point clouds and is thus agnostic to the various LiDAR representations [19, 32, 56, 58]. We show LaserMix's instantiations with the range view and voxel representations as in Fig. 1 (middle), since they are currently the most efficient and the best-performing options, respectively.", + "bbox": [ + 75, + 598, + 468, + 704 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Role in our framework: LaserMix helps to efficiently compute the marginal probability $P(Y_{\\mathrm{in}}|X_{\\mathrm{in}},A)$ , as described by Step 2 in our framework. The cost for directly computing the marginal probability in Eq. (4) on real-world LiDAR data is prohibitive; we need to iterate through all areas in $A$ and all outside data in $X_{\\mathrm{out}}$ , which requires $|A|\\cdot |X_{\\mathrm{out}}|$ predictions in total. To reduce the training overhead, we take advantage of the fact that a prediction in an area will be largely affected by its neighboring areas and let $X_{\\mathrm{out}}$ fill only the neighbors instead of all the remaining areas. LaserMix mixes two scans by intertwining the areas so that the neighbors of each area are filled with data from the other scan. As a result, we obtain the prediction on", + "bbox": [ + 75, + 704, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/c10b229c12476492fd4ae3f300ce19973e52045f873c3b9241bdde5a974f60cf.jpg", + "image_caption": [ + "Figure 2. Laser partition example. We group LiDAR points $(p_i^x, p_i^y, p_i^z)$ whose inclinations $\\phi_i$ are within the same inclination range into the same area, as depicted in the color regions." + ], + "image_footnote": [], + "bbox": [ + 506, + 87, + 888, + 325 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "all areas $A$ of two scans from only two predictions, which on average reduces the cost from $|A|$ to 1. The scan before and after mixing counts as two data fillings, therefore $|X_{\\mathrm{out}}| = 2$ . Overall, the training overhead is reduced from $|A|\\cdot |X_{\\mathrm{out}}|$ to 2: only one prediction on original data and one additional prediction on mixed data are required for each LiDAR scan. During training, the memory consumption for a batch will be $2\\times$ compared to a standard SSL framework, and the training speed will not be affected.", + "bbox": [ + 498, + 396, + 892, + 532 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Overall Pipeline", + "text_level": 1, + "bbox": [ + 500, + 541, + 661, + 558 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We show the overall framework in Fig. 3 and the pseudocode in Algo. 1. There are two branches in our pipeline, one Student net $\\mathcal{G}_{\\theta}^{s}$ and one Teacher net $\\mathcal{G}_{\\theta}^{t}$ . During training, a batch is composed of half labeled data and half unlabeled data. We collect the predictions from both $\\mathcal{G}_{\\theta}^{s}$ and $\\mathcal{G}_{\\theta}^{t}$ , and produce pseudo-labels from Teacher net's prediction with a predefined confidence threshold $T$ . For labeled data, we compute the cross-entropy loss between the Student net's prediction and the ground-truth as $\\mathcal{L}_{\\mathrm{sup}}$ . For unlabeled data, LaserMix blends every scan with a random labeled scan, together with their pseudo-label or ground-truth. Then, we let $\\mathcal{G}_{\\theta}^{s}$ predict on the mixed data and compute the cross-entropy loss $\\mathcal{L}_{\\mathrm{mix}}$ ( $w/$ mixed labels). The point-wise cross-entropy loss for a scan $x$ and its corresponding ground-truth/pseudolabel $y$ on the segmentation net $\\mathcal{G}_{\\theta}$ is defined as:", + "bbox": [ + 498, + 564, + 890, + 790 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {c e}} = \\frac {1}{| x |} \\sum_ {i = 1} ^ {| x |} \\operatorname {C r o s s E n t r o p y} \\left(y ^ {(i)}, \\mathcal {G} _ {\\theta} ^ {(i)} (x)\\right), \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 549, + 801, + 890, + 844 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $(i)$ denotes the $i$ -th point. Moreover, we adopt the mean teacher idea in [45] and use Exponential Moving Average (EMA) to update the weights of $\\mathcal{G}_{\\theta}^{t}$ from $\\mathcal{G}_{\\theta}^{s}$ , and com", + "bbox": [ + 498, + 854, + 890, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "21708", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/4a95c87655788b65571e5a72f6d72de8246008d3a46325feeb809ff83d358976.jpg", + "image_caption": [ + "Figure 3. Framework overview. The labeled scan $x_{l}$ is fed into the Student net to compute the supervised loss $\\mathcal{L}_{\\mathrm{sup}}$ ( $w/$ ground-truth $y_{l}$ ). The unlabeled scan $x_{u}$ and the generated pseudo-label $y_{u}$ are mixed with $(x_{l},y_{l})$ via LaserMix (Sec. 3.2) to produce mixed data sample $(x_{\\mathrm{mix}},y_{\\mathrm{mix}})$ , which is then fed into the Student net to compute the mixing loss $\\mathcal{L}_{\\mathrm{mix}}$ . Additionally, we adopt the EMA update in [45] for the Teacher net and compute the mean teacher loss $\\mathcal{L}_{\\mathrm{mt}}$ over Student net's and Teacher net's predictions." + ], + "image_footnote": [], + "bbox": [ + 84, + 89, + 883, + 311 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "pute the L2 loss between their predictions as $\\mathcal{L}_{\\mathrm{mt}}$", + "bbox": [ + 76, + 398, + 406, + 415 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {m t}} = \\left| \\left| \\mathcal {G} _ {\\theta} ^ {s} (x) - \\mathcal {G} _ {\\theta} ^ {t} (x) \\right| \\right| _ {2} ^ {2}, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 181, + 422, + 468, + 439 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $||\\cdot ||_2^2$ is the L2 norm. The overall loss function is $\\mathcal{L} = \\mathcal{L}_{\\mathrm{sup}} + \\lambda_{\\mathrm{mix}}\\mathcal{L}_{\\mathrm{mix}} + \\lambda_{\\mathrm{mt}}\\mathcal{L}_{\\mathrm{mt}}$ , where $\\lambda_{\\mathrm{mix}}$ and $\\lambda_{\\mathrm{mt}}$ are loss weights. We use the Teacher net during inference as it empirically gives more stable results. There will be no extra inference overhead in our framework.", + "bbox": [ + 76, + 446, + 468, + 521 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Role in our framework: Our overall pipeline minimizes the marginal entropy, as described by Step 3 in our framework. Since the objective for minimizing the entropy has a hard optimization landscape, pseudo-labeling is a common resort in practice [25]. Unlike conventional pseudo-label optimization in SSL which only aims to encourage the predictions to be confident, minimizing the marginal entropy requires all predictions to be both confident and consistent. Therefore, we use the ground-truth and pseudo-label as an anchor and encourage the model's predictions to be confident and consistent with these supervision signals.", + "bbox": [ + 75, + 523, + 468, + 689 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 700, + 209, + 718 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Settings", + "text_level": 1, + "bbox": [ + 76, + 726, + 174, + 742 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Protocol. We follow the Realistic Evaluation Protocol [35] when building the benchmark. Specifically, all experiments share the same backbones and are within the same codebase. All configurations and augmentations are unified to ensure a fair comparison among different SSL algorithms.", + "bbox": [ + 75, + 750, + 468, + 824 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Data. We build three SSL benchmarks upon nuScenes [11], SemanticKITTI [1], and ScribbleKITTI [47]. nuScenes [11] and SemanticKITTI [1] are the two most popular LiDAR segmentation datasets, with 29130 and 19130 training scans and 6019 and 4071 validation scans, respectively.", + "bbox": [ + 75, + 825, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Algorithm 1 Pseudo-code for one training iteration." + ], + "code_body": "1: Input: Shuffled labeled batch $(X_{l},Y_{l}) = \\{(x_{l}^{(b)},y_{l}^{(b)});b\\in$ $(1,\\dots ,B)\\}$ , shuffled unlabeled batch $X_{u} = \\{x_{u}^{(b)};b\\in$ $(1,\\dots ,B)\\}$ , threshold $T$ , loss weights $\\lambda_{\\mathrm{mix}}$ and $\\lambda_{\\mathrm{mt}}$ , Student net and Teacher net. \n2: for $b = 1$ to $B$ do \n3: $x_{\\mathrm{mix}}^{(2b - 1)},x_{\\mathrm{mix}}^{(2b)} = \\mathrm{LaserMix}(x_l^{(b)},x_u^{(b)}) / /$ LaserMix data \n4: end for \n5: $X_{\\mathrm{mix}} = \\{x_{\\mathrm{mix}}^{(i)};i\\in (1,\\dots ,2B)\\}$ \n6: $S_{l},S_{u},S_{\\mathrm{mix}} =$ Student $\\big(\\mathrm{Concat}(X_l,X_u,X_{\\mathrm{mix}})\\big)$ //Student pred \n7: $\\hat{S}_l,\\hat{S}_u =$ Teacher $\\big(\\mathrm{Concat}(X_l,X_u)\\big)$ //Teacher pred \n8: $Y_{u} =$ PseudoLabel $(\\hat{S}_u,T)$ //Pseudo-label generation process \n9: for $b = 1$ to $B$ do \n10: $y_{\\mathrm{mix}}^{(2b - 1)},y_{\\mathrm{mix}}^{(2b)} = \\mathrm{LaserMix}(y_l^{(b)},y_u^{(b)}) / /$ LaserMix label \n11: end for \n12: $Y_{\\mathrm{mix}} = \\{y_{\\mathrm{mix}}^{(i)};i\\in (1,\\dots ,2B)\\}$ \n13: $L_{\\mathrm{sup}} =$ CrossEntropy $(S_l,Y_l)$ // Supervised loss \n14: $L_{\\mathrm{mix}} =$ CrossEntropy $(S_{\\mathrm{mix}},Y_{\\mathrm{mix}})$ // Mixing loss \n15: $L_{\\mathrm{mt}} = L2\\big(\\mathrm{Concat}(S_l,S_u),\\mathrm{Concat}(\\hat{S}_l,\\hat{S}_u)\\big)$ //MeanTeacher loss \n16: $L = L_{\\mathrm{sup}} + \\lambda_{\\mathrm{mix}}L_{\\mathrm{mix}} + \\lambda_{\\mathrm{mt}}L_{\\mathrm{mt}}$ //Overall loss \n17: Backward(L), Update(Student), UpdateEMA(Teacher)", + "bbox": [ + 508, + 417, + 890, + 690 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "ScribbleKITTI [47] is a recent variant of SemanticKITTI [1], which contains the same number of scans but is annotated with line scribbles (approximately $8.06\\%$ valid semantic labels) rather than dense annotations. For all three LiDAR segmentation datasets, we uniformly sample $1\\%$ , $10\\%$ , $20\\%$ , and $50\\%$ labeled training scans and assume the remaining ones as unlabeled. This is in line with the conventional settings from the semi-supervised image segmentation community [6, 21, 37]. We also conduct experiments with sequential splits and show the results in the Appendix. Implementation Details. We adopt FIDNet [57] and Cylinder3D [58] as the segmentation backbones for the range", + "bbox": [ + 496, + 718, + 892, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "21709", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/29f06e6cc8cf944ea14c50117e88fa401b744604ee76964aa89f13556759990d.jpg", + "table_caption": [ + "Table 1. Benchmarking results among different SSL methods with the LiDAR range view (top) and voxel (bottom) representations. All mIoU scores are given in percentage (\\%). The best and second best score for each data split is highlighted in bold and underline." + ], + "table_footnote": [], + "table_body": "
Repr.MethodnuScenes [11]SemanticKITTI [1]ScribbleKITTI [47]
1%10%20%50%1%10%20%50%1%10%20%50%
Range ViewSup.-only38.357.562.767.636.252.255.957.233.147.749.952.5
MeanTeacher [45]42.160.465.469.437.553.156.157.434.249.851.653.3
CBST [59]40.960.564.369.339.953.456.156.935.750.752.754.6
CutMix-Seg [12]43.863.964.869.837.454.356.657.636.750.752.954.3
CPS [6]40.760.864.968.036.552.356.357.433.750.052.854.6
LaserMix (Ours)49.568.270.673.043.458.859.461.438.354.455.658.7
Δ↑+11.2+10.7+7.9+5.4+7.2+6.6+3.5+4.2+5.2+6.7+5.7+6.2
VoxelSup.-only50.965.966.671.245.456.157.858.739.248.052.153.8
MeanTeacher [45]51.666.067.171.745.457.159.260.041.050.152.853.9
CBST [59]53.066.569.671.648.858.359.459.741.550.653.354.5
CPS [6]52.966.370.072.546.758.759.660.541.451.853.954.8
LaserMix (Ours)55.369.971.873.250.660.061.962.344.253.755.156.8
Δ↑+4.4+4.0+5.2+2.0+5.2+3.9+4.1+3.6+5.0+5.7+3.0+3.0
", + "bbox": [ + 161, + 122, + 803, + 343 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/4d848fa5cbd2977e27c798ec2172850f967cc6c5638ae1415ea1353aea8f1c8c.jpg", + "table_caption": [ + "Table 2. Comparison to the state-of-the-art 3D SSL method [20] on the val set of SemanticKITTI [1]. All mIoU scores are given in percentage $(\\%)$ ." + ], + "table_footnote": [], + "table_body": "
Method5%10%20%30%40%
GPC [20]41.849.958.859.459.9
Ours (RV)54.658.859.460.160.8
Δ↑+12.8+8.9+0.6+0.7+0.9
Ours (Voxel)56.760.061.962.162.3
Δ↑+14.9+10.1+3.1+1.7+1.4
", + "bbox": [ + 84, + 402, + 380, + 497 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/e1ff15d6933937c72031dd8cd75e0482f7783d6f9257ebabebdef2ec4a4c57f6.jpg", + "table_caption": [ + "Table 3. Ablation results on the val set of nuScenes [11]. (1) Baseline results [45]; (2) Results with Student net supervision (SS); (3) Results with Teacher net supervision (TS). All mIoU scores are given in percentage $(\\%)$ ." + ], + "table_footnote": [], + "table_body": "
#\\( {\\mathcal{L}}_{\\text{mt }} \\)\\( {\\mathcal{L}}_{\\text{mix }} \\)SSTS1%10%20%50%
(1)✓42.160.465.469.4
(2)✓✓45.6(+3.5)64.3(+3.9)67.8(+2.4)71.6(+2.2)
✓✓✓47.0(+4.9)65.5(+5.1)69.5(+4.1)72.0(+2.6)
(3)✓✓46.0(+3.9)64.1(+3.7)69.5(+4.1)72.3(+2.9)
✓✓✓49.5(+7.4)68.2(+7.8)70.6(+5.2)73.0(+3.6)
", + "bbox": [ + 421, + 402, + 887, + 497 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "view and the voxel options, respectively. The input resolution of range images is set as $64 \\times 2048$ for SemanticKITTI [1] and ScribbleKITTI [47], and $32 \\times 1920$ for nuScenes [11]. The voxel resolution is fixed as [240, 180, 20] for all three sets. The number of spatial areas $m$ in LaserMix is uniformly sampled from 2 to 6 areas. We denote the supervised-only baseline as sup.-only. Due to the lack of Li-DAR SSL works [20], we also compare SoTA consistency regularization [6, 12, 45] and entropy minimization [59] methods from semi-supervised image segmentation. We report the intersection-over-union (IoU) over each semantic class and the mean IoU (mIoU) scores over all classes in our benchmarks. All experiments are implemented using PyTorch on NVIDIA Tesla V100 GPUs with 32GB RAM.", + "bbox": [ + 75, + 521, + 468, + 731 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Comparative Study", + "text_level": 1, + "bbox": [ + 76, + 741, + 264, + 758 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Improvements over Baseline. Tab. 1 benchmarks results on nuScenes [11], SemanticKITTI [1], and ScribbleKITTI [47]. For all three sets under different data splits, we observe significant improvements in our approach over the sup.-only baseline. Such gains are especially evident in range view, which reach up to $11.2\\%$ mIoU. We also observe constant improvements for the voxel option, which provide on average $4.1\\%$ mIoU gains over all splits across all sets. The results verify the effectiveness of our frame-", + "bbox": [ + 75, + 763, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "work and further highlight the importance of leveraging unlabeled data in LiDAR semantic segmentation.", + "bbox": [ + 496, + 521, + 888, + 550 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Compare with SoTA. We compare LaserMix with $\\mathrm{GPC}^2$ [20], the SoTA 3D SSL method tested on SemanticKITTI [1]. The results in Tab. 2 show that our approach exhibits much better results than GPC [20], especially in scenarios where very few annotations are available. We also reimplemented popular SSL algorithms from the image segmentation domain and show their results in Tab. 1. We find that these methods, albeit competitive in 2D, only yield sub-par performance in the LiDAR SSL benchmark, highlighting the importance of exploiting the LiDAR data structure.", + "bbox": [ + 496, + 551, + 890, + 703 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Compare with Full Labels. As shown in Fig. 1 (right), the comparisons between the prevailing LiDAR segmentation methods attests that our approach can achieve more competitive scores over the fully-supervised counterparts [5, 8, 32, 56] while with $2 \\times$ to $5 \\times$ fewer annotations. The strong augmentation and regularization ability of LaserMix have yielded better results in the high-data regime and extreme low-data regime (i.e., $0.8\\%$ labels on [47]), which validates the generalizability of our approach.", + "bbox": [ + 496, + 704, + 890, + 840 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Qualitative Examination. Fig. 5 visualizes the scene segmentation results for different SSL algorithms on the val", + "bbox": [ + 496, + 840, + 890, + 871 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "2Note that GPC uses private backbone / split. See Appendix for details.", + "bbox": [ + 514, + 886, + 888, + 898 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "21710", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/03c3f253dd1454a7e84af6443bb7d33afe021d8eb15a4e17a4b6de39b529dcb6.jpg", + "image_caption": [ + "Figure 4. Ablation studies on: Left: Different mixing-based techniques used in point partition & mixing; Middle: Different EMA decay rates between the Teacher net and the Student net; Right: Different confidence thresholds $T$ used in the pseudo-label generation." + ], + "image_footnote": [], + "bbox": [ + 76, + 87, + 493, + 276 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6877d8b02fbd4dbcf09e2320e04373d0fc8d7583d3cbb6bf69f1e118d062c853.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 503, + 85, + 689, + 275 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ae96b550fc093755d4eb28a4306a89c713c14c0f6e54593b2c1272d24d50341f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 705, + 85, + 893, + 275 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "set of nuScenes [11], where each example covers a driving scene centered by the ego-vehicle. We find that previous arts [6, 45, 59] can only improve predictions in limited regions, while our approach holistically eliminates false predictions in almost every direction around the ego-vehicle. The consistency enlightened by LaserMix has yielded better segmentation accuracy under annotation scarcity.", + "bbox": [ + 75, + 330, + 472, + 439 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 450, + 230, + 467 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Without loss of generalizability, we stick with the $10\\%$ budget setting and range view backbones in our ablations.", + "bbox": [ + 75, + 474, + 468, + 505 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Framework Setups. The component analysis in Tab. 3 shows that $\\mathcal{L}_{\\mathrm{mix}}$ contributes significantly to the overall improvement. Meanwhile, using the Teacher net instead of the Student net to generate pseudo-labels leads to better results, as the formal is temporally ensembled and encourages consistency in-between mixed and original data, which is crucial besides enforcing confident predictions. It is worth noting that all of our model configurations have achieved superior results than the baseline MeanTeacher [45], which further emphasizes the effectiveness of our framework in tackling LiDAR segmentation with semi-supervisions.", + "bbox": [ + 75, + 506, + 470, + 672 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Mixing Strategies. Fig. 4 (left) compares LaserMix with other mixing methods [10, 33, 53, 54]. MixUp and CutMix can be considered as setting $A$ to random points and random areas, respectively. We observe that MixUp has no improvements over the baseline on average since there is no distribution pattern in random points. CutMix has a considerable improvement over the baseline, as there is always a structure prior in scene segmentation, i.e., the same semantic class points tend to cluster, which reduces the entropy in any continuous area. This prior is often used in image semantic segmentation SSL [12]. However, our spatial prior is much stronger, where not only the area structure but also the area's spatial position has been considered. LaserMix outperforms CutMix by a large margin (up to $3.3\\%$ mIoU) on all sets. CutOut can be considered as setting $X_{\\mathrm{out}}$ to", + "bbox": [ + 75, + 672, + 470, + 901 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/dc41c731b882d1afbf2536860404cae6ef15b8b6d49b8e371554831133602fe6.jpg", + "table_caption": [ + "Table 4. Ablation studies on laser beam partitions (horizontal: inclination direction $\\phi$ ; vertical: azimuth direction $\\alpha$ ). $(i - \\alpha, j - \\phi)$ denotes that there are $i$ azimuth and $j$ inclination partitions." + ], + "table_footnote": [], + "table_body": "
Baseline(1α, 2φ)(1α, 3φ)(1α, 4φ)(1α, 5φ)(1α, 6φ)
60.463.5(+3.1)65.2(+4.8)66.5(+6.1)66.2(+5.8)65.4(+5.0)
(2α, 1φ)(2α, 2φ)(2α, 3φ)(2α, 4φ)(2α, 5φ)(2α, 6φ)
61.5(+1.1)63.3(+2.9)65.9(+5.5)66.1(+5.7)66.7(+6.3)65.3(+4.9)
(3α, 1φ)(3α, 2φ)(3α, 3φ)(3α, 4φ)(3α, 5φ)(3α, 6φ)
60.9(+0.6)64.2(+3.8)65.9(+5.5)66.3(+5.9)66.0(+5.6)65.2(+4.8)
(4α, 1φ)(4α, 2φ)(4α, 3φ)(4α, 4φ)(4α, 5φ)(4α, 6φ)
60.9(+0.6)64.7(+4.3)65.3(+4.9)65.6(+5.2)65.7(+5.3)65.2(+4.8)
", + "bbox": [ + 503, + 375, + 890, + 679 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "a dummy filling instead of sampling from datasets, and it leads to a considerable performance drop from CutMix.", + "bbox": [ + 496, + 702, + 890, + 733 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Orderless Mix. We revert the area ordering (i.e., put the topmost laser beam at the bottom, and vice versa) in LaserMix, and the performance drops from $68.2\\%$ to $64.4\\%$ $(-3.8\\% \\mathrm{mIoU})$ . When we shuffle the ordering, the performance drops to $63.8\\%$ $(-4.4\\% \\mathrm{mIoU})$ , which becomes comparable with CutMix. The results once again confirm the superiority of using spatial prior in LiDAR SSL.", + "bbox": [ + 496, + 734, + 890, + 839 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Other Heuristics. Besides our proposed inclination partition, the LiDAR scans can also be split based on azimuth (sensor horizontal direction). Results in Tab. 4 reveal that in contrast to laser partitioning, pure azimuth splitting (the", + "bbox": [ + 496, + 839, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "21711", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e872031056d6d0e643bfc2a43801058638e75dda53d10ce7ddf7066bfee65090.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 80, + 107, + 210, + 239 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ed6705a442c06e557f96d9701f1361d3566a7879302572cbe1873a039c8a7933.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 215, + 107, + 346, + 239 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7b8d957025e533c74e35c0f24ec03c62cc9c54925d5edf7262992d32b3779587.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 351, + 107, + 482, + 239 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a8554b59f6ea7b4a493196fbdf9aff1527814543526bf190bb773e227381d15e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 486, + 107, + 617, + 239 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8e5ec042d1f9591f55168dbde0c396bfb1f3c752f4c512440ff071381d567ffc.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 622, + 107, + 754, + 239 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/47d86b73a62475059b44ae3ca3b04a98e20eb961348c97ddd3977f0168edd425.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 759, + 107, + 890, + 239 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6edcba58f651c94aa5819dc2c805fea3af88b2b01e652eb9b0fa6b64361b00af.jpg", + "image_caption": [ + "Figure 5. Error maps visualized from LiDAR bird's eye view and range view on nuScenes [11]. Each example shows a street scene of size $50\\mathrm{m}$ by $50\\mathrm{m}$ by $8\\mathrm{m}$ . The correct and incorrect predictions are painted in green and red to highlight the differences. Best viewed in color." + ], + "image_footnote": [], + "bbox": [ + 80, + 246, + 210, + 398 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0aea44d0452284df8b3a5b5a2d20801c0f00e95729813c8af041fbc916c2c27f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 215, + 247, + 346, + 398 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/4ad3201649ba28f64d5439285f02f3bad3432dcff9ec0857f8ebbd0bfd52d4a1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 351, + 247, + 482, + 398 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1660fe10ba3d0d9dbc26477b7e4ba3540bafc7a165b3c9cf9de3ccfb87729345.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 486, + 247, + 617, + 398 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ca454577287bd03716d0184d29e5564bdaea904a2bad41dabb93cc56a92e365b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 622, + 247, + 754, + 398 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c0b98a8a14e617ac91471d4e316c7a302288912d8cbe8e493ab26504051f8029.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 759, + 247, + 890, + 398 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "first column) does not improve the performance, which is attributed to the fact that the semantic distribution has a weak correlation in the azimuth direction. We also observe that the results tend to improve as the mixing granularity increases (row direction in Tab. 4). The scores start to drop when the granularity is beyond a certain limit (e.g., the last two columns). We conjecture that over-fine-grained partition and mixing tend to hurt semantic coherence.", + "bbox": [ + 75, + 462, + 468, + 580 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Mix Unlabeled Data Only. To verify that our method is more than trivially augmenting seen data and label pairs, we apply LaserMix only on unlabeled data. Instead of mixing an unlabeled scan with a labeled scan as described in Sec. 3.3, we mix two unlabeled scans with their pseudolabels. The score drops from $68.2\\%$ to $66.9\\%$ $(-1.3\\% \\mathrm{mIoU})$ but still outperforms all existing methods by large margins. This verifies that LaserMix indeed brings a strong consistency regularization effect during SSL.", + "bbox": [ + 75, + 582, + 468, + 717 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "EMA. Fig. 4 (middle) provides results with different EMA decay rates, Typically, a rate between 0.9 and 0.99 yields the best possible results. Large rates like 0.999 tend to hurt the consistency between the two networks. The results also verify that the teacher-student pipeline [45] has good synergy with our proposed SSL framework. Thanks to this simplicity, more modern SSL techniques can be easily incorporated into the current framework in future works.", + "bbox": [ + 75, + 719, + 468, + 837 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Confidence Threshold. As pseudo-labels play an important role in our framework, we further analyze the impact of the threshold parameter $T$ used in pseudo-label generation and show results in Fig. 4 (right). When $T$ is too low,", + "bbox": [ + 75, + 839, + 468, + 898 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "a forced consistency to low-quality pseudo-labels tends to deteriorate the performance. When $T$ is too high, the benefits from mixing might diminish. Generally, $T$ is a dataset-dependent parameter and we find that a value around 0.9 leads to the best possible results on the three tested LiDAR segmentation datasets [1, 11, 47] in our benchmark.", + "bbox": [ + 496, + 462, + 890, + 551 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 565, + 617, + 580 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this work, we exploit the unique spatial prior in LiDAR scenes for semi-supervised LiDAR semantic segmentation. We proposed a statistically-principled and effective SSL pipeline, including LaserMix, a novel LiDAR mixing technique that intertwines laser beams from different scans. Through comprehensive empirical analysis, we show the importance of spatial prior and the superiority of our approach on three popular benchmarks. The effectiveness and simplicity of our framework have shed light on the scalable deployment of the LiDAR semantic mapping system.", + "bbox": [ + 496, + 590, + 890, + 742 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments. This study is supported by the Ministry of Education, Singapore, under its MOE AcRF Tier 2 (MOET2EP20221-0012), the National Research Foundation, Singapore under its AI Singapore Programme (AISG Award No: AISG2-PhD-2021-08-018), NTU NAP, and under the RIE2020 Industry Alignment Fund - Industry Collaboration Projects (IAF-ICP) Funding Initiative, as well as cash and in-kind contribution from the industry partner(s). This research is part of the programme DesCartes and is supported by the National Research Foundation, Prime Minister's Office, Singapore under its Campus for Research Excellence and Technological Enterprise (CREATE) programme.", + "bbox": [ + 496, + 747, + 892, + 900 + ], + "page_idx": 7 + }, + { + "type": "header", + "text": "$\\bullet$ barrier $\\bullet$ bicycle $\\bullet$ bus $\\bullet$ car $\\bullet$ driveable $\\bullet$ flat $\\bullet$ ignored $\\bullet$ manmade $\\bullet$ motor $\\bullet$ pedestrian $\\bullet$ sidewalk $\\bullet$ terrain $\\bullet$ trailer $\\bullet$ truck $\\bullet$ vegetation", + "bbox": [ + 76, + 88, + 890, + 101 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "21712", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Jens Behley, Martin Garbade, Andres Milioto, Jan Quenzel, Sven Behnke, Cyril Stachniss, and Juergen Gall. 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In International Conference on Learning Representations (ICLR), 2020. 2" + ], + "bbox": [ + 78, + 90, + 470, + 780 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "21715", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/LaserMix for Semi-Supervised LiDAR Semantic Segmentation/0dfb46c8-457c-4c6b-aa9f-3e7c68a2add5_model.json b/2023/LaserMix for Semi-Supervised LiDAR Semantic Segmentation/0dfb46c8-457c-4c6b-aa9f-3e7c68a2add5_model.json new file mode 100644 index 0000000000000000000000000000000000000000..49c16deec151a82b07575e9e8eb576e8eaa18795 --- /dev/null +++ b/2023/LaserMix for Semi-Supervised LiDAR Semantic Segmentation/0dfb46c8-457c-4c6b-aa9f-3e7c68a2add5_model.json @@ -0,0 +1,2532 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.048 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.169, + 0.131, + 0.803, + 0.154 + ], + "angle": 0, + "content": "LaserMix for Semi-Supervised LiDAR Semantic Segmentation" + }, + { + "type": "text", + "bbox": [ + 0.218, + 0.18, + 0.757, + 0.201 + ], + "angle": 0, + "content": "Lingdong Kong\\(^{1,2,3,*}\\) Jiawei Ren\\(^{1,*}\\) Liang Pan\\(^{1}\\) Ziwei Liu\\(^{1,\\text{口}}\\)" + }, + { + "type": "text", + "bbox": [ + 0.086, + 0.205, + 0.888, + 0.224 + ], + "angle": 0, + "content": "\\(^{1}\\)S-Lab, Nanyang Technological University \\(^{2}\\)National University of Singapore \\(^{3}\\)CNRS@CREATE" + }, + { + "type": "text", + "bbox": [ + 0.173, + 0.226, + 0.799, + 0.242 + ], + "angle": 0, + "content": "{lingdong001,jiawei011}@e.ntu.edu.sg {liang.pan,ziwei.liu}@ntu.edu.sg" + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.264, + 0.379, + 0.495 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.384, + 0.264, + 0.594, + 0.339 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.433, + 0.348, + 0.553, + 0.36 + ], + "angle": 0, + "content": "LiDAR Representation" + }, + { + "type": "image_caption", + "bbox": [ + 0.382, + 0.385, + 0.497, + 0.396 + ], + "angle": 0, + "content": "Option 1: Range View" + }, + { + "type": "image", + "bbox": [ + 0.395, + 0.402, + 0.484, + 0.432 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.415, + 0.436, + 0.466, + 0.466 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.396, + 0.47, + 0.484, + 0.493 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.506, + 0.385, + 0.588, + 0.396 + ], + "angle": 0, + "content": "Option 2: Voxel" + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.401, + 0.592, + 0.431 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.524, + 0.435, + 0.573, + 0.456 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.467, + 0.591, + 0.497 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.609, + 0.267, + 0.891, + 0.495 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.505, + 0.894, + 0.562 + ], + "angle": 0, + "content": "Figure 1. Left: The LiDAR point cloud contains strong spatial prior. Objects and backgrounds around the ego-vehicle have a patterned distribution on different (lower, middle, upper) laser beams. Middle: Following the scene structure, the proposed LaserMix blends beams from different LiDAR scans, which is compatible with various popular LiDAR representations. Right: We achieve superior results over SoTA methods in both low-data (10%, 20%, and 50% semantic labels) and high-data (full semantic labels) regimes on nuScenes [11]." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.597, + 0.314, + 0.612 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.624, + 0.471, + 0.866 + ], + "angle": 0, + "content": "Densely annotating LiDAR point clouds is costly, which often restrains the scalability of fully-supervised learning methods. In this work, we study the underexplored semi-supervised learning (SSL) in LiDAR semantic segmentation. Our core idea is to leverage the strong spatial cues of LiDAR point clouds to better exploit unlabeled data. We propose LaserMix to mix laser beams from different LiDAR scans and then encourage the model to make consistent and confident predictions before and after mixing. Our framework has three appealing properties. 1) Generic: LaserMix is agnostic to LiDAR representations (e.g., range view and voxel), and hence our SSL framework can be universally applied. 2) Statistically grounded: We provide a detailed analysis to theoretically explain the applicability of the proposed framework. 3) Effective: Comprehensive experimental analysis on popular LiDAR segmentation" + }, + { + "type": "page_footnote", + "bbox": [ + 0.077, + 0.875, + 0.471, + 0.902 + ], + "angle": 0, + "content": "(*) Lingdong and Jiawei contributed equally to this work. (☑) Ziwei serves as the corresponding author. E-mail: ziwei.liu@ntu.edu.sg." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.583, + 0.895, + 0.705 + ], + "angle": 0, + "content": "datasets (nuScenes, SemanticKITTI, and ScribbleKITTI) demonstrates our effectiveness and superiority. Notably, we achieve competitive results over fully-supervised counterparts with \\(2 \\times\\) to \\(5 \\times\\) fewer labels and improve the supervised-only baseline significantly by relatively \\(10.8\\%\\). We hope this concise yet high-performing framework could facilitate future research in semi-supervised LiDAR segmentation. Code is publicly available1." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.719, + 0.633, + 0.735 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.744, + 0.894, + 0.88 + ], + "angle": 0, + "content": "LiDAR segmentation is one of the fundamental tasks in autonomous driving perception [41]. It enables autonomous vehicles to semantically perceive the dense 3D structure of the surrounding scenes [15, 34, 39]. However, densely annotating LiDAR point clouds is inevitably expensive and labor-intensive [18, 23, 47], which restrains the scalability of fully-supervised LiDAR segmentation methods. Semisupervised learning (SSL) that directly leverages the easy-to-acquire unlabeled data is hence a viable and promising" + }, + { + "type": "page_footnote", + "bbox": [ + 0.518, + 0.888, + 0.831, + 0.901 + ], + "angle": 0, + "content": "1https://github.com/ldkong1205/LaserMix." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "21705" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.465, + 0.108 + ], + "angle": 0, + "content": "solution to achieve scalable LiDAR segmentation [13, 14]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.108, + 0.47, + 0.275 + ], + "angle": 0, + "content": "Yet, semi-supervised LiDAR segmentation is still under-explored. Modern SSL frameworks are mainly designed for image recognition [2, 3, 42] and semantic segmentation [6, 21, 37] tasks, which only yield sub-par performance on LiDAR data due to the large modality gap between 2D and 3D. Recent research [20] proposed to consider semi-supervised point cloud semantic segmentation as a fresh task and proposed a point contrastive learning framework. However, their solutions do not differentiate indoor and outdoor scenes and therefore overlook the intrinsic and important properties that only exist in LiDAR point clouds." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.276, + 0.471, + 0.518 + ], + "angle": 0, + "content": "In this work, we explore the use of spatial prior for semi-supervised LiDAR segmentation. Unlike the general 2D/3D segmentation tasks, the spatial cues are especially significant in LiDAR data. In fact, LiDAR point clouds serve as a perfect reflection of real-world distributions, which is highly dependent on the spatial areas in the LiDAR-centered 3D coordinates. As shown in Fig. 1 (left), the top laser beams travel outward long distance and perceive mostly vegetation, while the middle and bottom beams tend to detect car and road from the medium and close distances, respectively. To effectively leverage this strong spatial prior, we propose LaserMix to mix laser beams from different LiDAR scans, and then encourage the LiDAR segmentation model to make consistent and confident predictions before and after mixing. Our SSL framework is statistically grounded, which consists of the following components:" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.519, + 0.47, + 0.564 + ], + "angle": 0, + "content": "1) Partitioning the LiDAR scan into low-variation areas. We observe a strong distribution pattern on laser beams as shown in Fig. 1 (left) and thus propose the laser partition." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.566, + 0.47, + 0.642 + ], + "angle": 0, + "content": "2) Efficiently mixing every area in the scan with foreign data and obtaining model predictions. We propose LaserMix to manipulate the laser-grouped areas from two LiDAR scans in an intertwining way as depicted in Fig. 1 (middle) and serves as an efficient LiDAR mixing strategy for SSL." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.643, + 0.47, + 0.689 + ], + "angle": 0, + "content": "3) Encouraging models to make confident and consistent predictions on the same area in different mixing. We hence propose a mixing-based teacher-student training pipeline." + }, + { + "type": "list", + "bbox": [ + 0.076, + 0.519, + 0.47, + 0.689 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.69, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Despite the simplicity of our overall pipeline, it achieves competitive results over the fully supervised counterpart using \\(2 \\times\\) to \\(5 \\times\\) fewer labels as shown in Fig. 1 (right) and significantly outperforms all prevailing semi-supervised segmentation methods on nuScenes [11] (up to \\(+5.7\\%\\) mIoU) and SemanticKITTI [1] (up to \\(+3.5\\%\\) mIoU). Moreover, LaserMix directly operates on point clouds so as to be agnostic to different LiDAR representations, e.g., range view [32] and voxel [58]. Therefore, our pipeline is highly compatible with existing state-of-the-art (SoTA) LiDAR segmentation methods under various representations [46, 56, 57]. Besides, our pipeline achieves competitive performance using very limited annotations on weak supervision dataset [47]: it achieves \\(54.4\\%\\) mIoU on Se" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.182 + ], + "angle": 0, + "content": "manticKITTI [1] using only \\(0.8\\%\\) labels, which is on-par with PolarNet [56] \\((54.3\\%)\\), RandLA-Net [19] \\((53.9\\%)\\), and RangeNet++ [32] \\((52.2\\%)\\) using \\(100\\%\\) labels. Spatial prior is proven to play a pivotal role in the success of our framework through comprehensive empirical analysis. To summarize, this work has the following key contributions:" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.184, + 0.892, + 0.23 + ], + "angle": 0, + "content": "- We present a statistically grounded SSL framework that effectively leverages the spatial cues in LiDAR data to facilitate learning with semi-supervisions." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.232, + 0.892, + 0.277 + ], + "angle": 0, + "content": "- We propose LaserMix, a novel and representation-agnostic mixing technique that strives to maximize the \"strength\" of the spatial cues in our SSL framework." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.28, + 0.892, + 0.342 + ], + "angle": 0, + "content": "- Our overall pipeline significantly outperforms previous SoTA methods in both low- and high-data regimes. We hope this work could lay a solid foundation for semi-supervised LiDAR segmentation." + }, + { + "type": "list", + "bbox": [ + 0.518, + 0.184, + 0.892, + 0.342 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.347, + 0.642, + 0.364 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.372, + 0.892, + 0.569 + ], + "angle": 0, + "content": "LiDAR Segmentation. Various approaches from different aspects have been proposed for LiDAR scene segmentation, i.e., range view [8, 32, 49, 57], bird's eye view [56], voxel [44, 58], and multi-view [26, 50] methods. Although appealing results have been achieved, these fully-supervised methods rely on large-scale annotated LiDAR datasets and their performance would degrade severely in the low-data regime [13]. Recent works seek weak [18, 55], scribble [47], and box [28] supervisions or activate learning [27, 31] to ease the annotation cost. We tackle this problem from the perspective of semi-supervised learning (SSL), aiming at directly leveraging the easy-to-acquire unlabeled data to boost the LiDAR semantic segmentation performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.569, + 0.892, + 0.795 + ], + "angle": 0, + "content": "SSL in 2D. Well-known SSL algorithms are prevailing in handling image recognition problems [2, 3, 24, 42, 45]. In the context of semantic segmentation, CutMix-Seg [12] and PseudoSeg [60] apply perturbations on inputs and hope the decision boundary lies in the low-density region. CPS [6] and GCT [21] enforce consistency between two perturbed networks [29]. These perturbations [30, 36, 52], however, are either inapplicable or only yield sub-par results in 3D. Another line of research is entropy minimization. Methods like CBST [59] and \\(\\mathrm{ST} + +\\) [51] generate pseudo-labels [25] offline per round during self-training. The extra storage needed might become costly for large-scale LiDAR datasets [1, 4, 11]. Our framework encourages both consistency regularization and entropy minimization and does not require extra overhead, which better maintains scalability." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.892, + 0.902 + ], + "angle": 0, + "content": "SSL in 3D. Most works focus on developing SSL for object-centric point clouds [22, 43] or indoor scenes [7, 9, 17, 34], whose scale and diversity are much lower than the outdoor LiDAR point clouds [1, 4]. Some other works [38, 40, 48] try to utilize SSL for 3D object detection on LiDAR data. A recent work [20] tackles semi-supervised point cloud semantic segmentation using contrastive learning, but it still" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "21706" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.184 + ], + "angle": 0, + "content": "mainly focused on indoor scenes and does not distinguish between the uniformly distributed indoor point clouds and the spatially structured LiDAR point clouds. We are one of the first works to explore SSL for LiDAR segmentation. Our work also establishes comprehensive SSL benchmarks upon popular autonomous driving databases [1, 11, 47]." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.196, + 0.187, + 0.213 + ], + "angle": 0, + "content": "3. Approach" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.22, + 0.47, + 0.328 + ], + "angle": 0, + "content": "In this section, we first introduce our SSL framework that leverages the spatial prior of LiDAR data by encouraging confidence and consistency in predictions (Sec. 3.1). We then present LaserMix which strives to maximize the \"strength\" of the spatial prior and mixes LiDAR scans in an efficient manner (Sec. 3.2). Finally, we elaborate on the overall pipeline (Sec. 3.3) and the pseudo-code (Algo. 1)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.335, + 0.396, + 0.351 + ], + "angle": 0, + "content": "3.1. Leveraging the Spatial Prior for SSL" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.358, + 0.473, + 0.541 + ], + "angle": 0, + "content": "Spatial Prior Formulation. The distribution of real-world objects/backgrounds has a strong correlation to their spatial positions in the LiDAR scan. Objects/backgrounds inside a specified spatial area of a LiDAR point cloud follow similar patterns, e.g., the close-range area is most likely road while the long-range area consists of building, vegetation, etc. In another word, there exists a spatial area \\(a \\in A\\) where LiDAR points and semantic labels inside the area (denoted as \\(X_{\\mathrm{in}}\\) and \\(Y_{\\mathrm{in}}\\), respectively) will have relatively low variations. Formally, the conditional entropy \\(H(X_{\\mathrm{in}}, Y_{\\mathrm{in}}|A)\\) is smaller. Therefore, when estimating the parameter \\(\\theta\\) of the segmentation network \\(\\mathcal{G}_{\\theta}\\), we would expect:" + }, + { + "type": "equation", + "bbox": [ + 0.19, + 0.55, + 0.47, + 0.567 + ], + "angle": 0, + "content": "\\[\n\\mathbb {E} _ {\\theta} \\left[ H \\left(X _ {\\text {i n}}, Y _ {\\text {i n}} \\mid A\\right) \\right] = c, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.576, + 0.47, + 0.638 + ], + "angle": 0, + "content": "where \\( c \\) is a small constant. Similar to the classic entropy minimization [16], the constraint in Eq. (1) can be converted to a prior on the model parameter \\( \\theta \\) using the principle of maximum entropy:" + }, + { + "type": "equation", + "bbox": [ + 0.16, + 0.647, + 0.47, + 0.682 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} P (\\theta) \\propto \\exp (- \\lambda H (X _ {\\text {i n}}, Y _ {\\text {i n}} | A)) \\tag {2} \\\\ \\propto \\exp (- \\lambda H (Y _ {\\mathrm {i n}} | X _ {\\mathrm {i n}}, A)), \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.692, + 0.47, + 0.767 + ], + "angle": 0, + "content": "where \\(\\lambda > 0\\) is the Lagrange multiplier corresponding to constant \\(c\\); \\(H(X_{\\mathrm{in}}|A)\\) has been ignored for being independent of the model parameter \\(\\theta\\). We consider Eq. (2) as the formal formulation of the spatial prior and discuss how to empirically compute it in the following sections." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.767, + 0.469, + 0.813 + ], + "angle": 0, + "content": "Marginalization. To utilize the spatial prior defined in Eq. (2), we empirically compute the entropy \\( H(Y_{\\mathrm{in}}|X_{\\mathrm{in}},A) \\) of the LiDAR points inside area \\( A \\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.12, + 0.821, + 0.469, + 0.847 + ], + "angle": 0, + "content": "\\[\n\\hat {H} \\left(Y _ {\\text {i n}} \\mid X _ {\\text {i n}}, A\\right) = \\tag {3}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.12, + 0.844, + 0.427, + 0.863 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathbb {E}} _ {X _ {\\mathrm {i n}}, Y _ {\\mathrm {i n}}, A} \\big [ P (Y _ {\\mathrm {i n}} | X _ {\\mathrm {i n}}, A) \\log P (Y _ {\\mathrm {i n}} | X _ {\\mathrm {i n}}, A) \\big ],\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.47, + 0.902 + ], + "angle": 0, + "content": "where \\(\\hat{\\cdot}\\) denotes the empirical estimation. The end-to-end LiDAR segmentation model \\(\\mathcal{G}_{\\theta}\\) usually takes full-sized" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.169 + ], + "angle": 0, + "content": "data as inputs during inference. Therefore, to compute \\( P(Y_{\\mathrm{in}}|X_{\\mathrm{in}},A) \\) in Eq. (3), we first pad the data outside the area to obtain the full-sized data. Here we denote the data outside the area as \\( X_{\\mathrm{out}} \\); we then let the model infer \\( P(Y_{\\mathrm{in}}|X_{\\mathrm{in}},X_{\\mathrm{out}},A) \\), and finally marginalize \\( X_{\\mathrm{out}} \\) as:" + }, + { + "type": "equation", + "bbox": [ + 0.54, + 0.175, + 0.892, + 0.194 + ], + "angle": 0, + "content": "\\[\nP \\left(Y _ {\\mathrm {i n}} \\mid X _ {\\mathrm {i n}}, A\\right) = \\hat {\\mathbb {E}} _ {X _ {\\mathrm {o u t}}} \\left[ P \\left(Y _ {\\mathrm {i n}} \\mid X _ {\\mathrm {i n}}, X _ {\\mathrm {o u t}}, A\\right) \\right]. \\quad (4)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.2, + 0.892, + 0.23 + ], + "angle": 0, + "content": "The generative distribution of the padding \\( P(X_{\\mathrm{out}}) \\) can be directly obtained from the dataset." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.231, + 0.892, + 0.292 + ], + "angle": 0, + "content": "Training. Finally, we train the segmentation model \\(\\mathcal{G}_{\\theta}\\) using the standard maximum-a-posteriori (MAP) estimation. We maximize the posterior that can be computed by Eq. (2), Eq. (3) and Eq. (4), which is formulated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.518, + 0.298, + 0.892, + 0.337 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} C (\\theta) = L (\\theta) - \\lambda \\hat {H} \\left(Y _ {\\mathrm {i n}} \\mid X _ {\\mathrm {i n}}, A\\right) = L (\\theta) \\tag {5} \\\\ - \\lambda \\hat {\\mathbb {E}} _ {X _ {\\text {i n}}, Y _ {\\text {i n}}, A} [ P (Y _ {\\text {i n}} | X _ {\\text {i n}}, A) \\log P (Y _ {\\text {i n}} | X _ {\\text {i n}}, A) ]. \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.344, + 0.892, + 0.435 + ], + "angle": 0, + "content": "Here, \\( L(\\theta) \\) is the likelihood function computed using labeled data, i.e., the conventional supervised learning. Minimizing \\( \\hat{H}(Y_{\\mathrm{in}}|X_{\\mathrm{in}},A) \\) requires the marginal probability \\( P(Y_{\\mathrm{in}}|X_{\\mathrm{in}},A) \\) to be confident, which further requires \\( P(Y_{\\mathrm{in}}|X_{\\mathrm{in}},X_{\\mathrm{out}},A) \\) to be both confident and consistent with respect to different outside data \\( X_{\\mathrm{out}} \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.435, + 0.892, + 0.541 + ], + "angle": 0, + "content": "In summary, our proposed SSL framework in Eq. (5) encourages the segmentation model to make confident and consistent predictions at a predefined area, regardless of the data outside the area. The predefined area set \\( A \\) determines the \"strength\" of the prior. When setting \\( A \\) to the full area (i.e., the whole point cloud), our framework degrades to the classic entropy minimization framework [16]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.541, + 0.892, + 0.571 + ], + "angle": 0, + "content": "Implementation. There are three key steps for implementing our framework:" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.574, + 0.891, + 0.604 + ], + "angle": 0, + "content": "- Step 1): Select a proper partition set \\( A \\) which maintains strong spatial prior;" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.608, + 0.891, + 0.639 + ], + "angle": 0, + "content": "- Step 2): Efficiently compute the marginal probability, i.e., \\( P(Y_{\\mathrm{in}}|X_{\\mathrm{in}},A) \\);" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.642, + 0.891, + 0.673 + ], + "angle": 0, + "content": "- Step 3): Efficiently minimize the marginal entropy, i.e., \\(\\hat{H}(Y_{\\mathrm{in}}|X_{\\mathrm{in}},A)\\)." + }, + { + "type": "list", + "bbox": [ + 0.518, + 0.574, + 0.891, + 0.673 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.892, + 0.706 + ], + "angle": 0, + "content": "We propose a simple yet effective implementation following these steps in the next section." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.713, + 0.612, + 0.728 + ], + "angle": 0, + "content": "3.2. LaserMix" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.736, + 0.892, + 0.858 + ], + "angle": 0, + "content": "Partition. LiDAR sensors have a fixed number (e.g., 32, 64, and 128) of laser beams which are emitted isotropically around the ego-vehicle with predefined inclination angles as shown in Fig. 2. To obtain a proper set of spatial areas \\( A \\), we propose to partition the LiDAR point cloud based on laser beams. Specifically, points captured by the same laser beam have a unified inclination angle to the sensor plane. For point \\( i \\), its inclination \\( \\phi_i \\) is defined as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.586, + 0.865, + 0.892, + 0.9 + ], + "angle": 0, + "content": "\\[\n\\phi_ {i} = \\arctan \\left(\\frac {p _ {i} ^ {z}}{\\sqrt {\\left(p _ {i} ^ {x}\\right) ^ {2} + \\left(p _ {i} ^ {y}\\right) ^ {2}}}\\right), \\tag {6}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "21707" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.47, + 0.227 + ], + "angle": 0, + "content": "where \\((p^x,p^y,p^z)\\) is the Cartesian coordinates of the LiDAR points. Given two LiDAR scans \\(x_{1}\\) and \\(x_{2}\\), we first group all points from each scan by their inclination angles. Concretely, to form \\(m\\) non-overlapping areas, a set of \\(m + 1\\) inclination angles \\(\\Phi = \\{\\phi_0,\\phi_1,\\phi_2,\\dots,\\phi_m\\}\\) will be evenly sampled within the range of the minimum and maximum inclination angles in the dataset (defined by sensor configurations), and the area set \\(A = \\{a_{1},a_{2},\\ldots,a_{m}\\}\\) can be formed by bounding area \\(a_{i}\\) in the inclination range \\([\\phi_{i - 1},\\phi_i)\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.228, + 0.471, + 0.408 + ], + "angle": 0, + "content": "Role in our framework: Laser partition effectively \"excites\" a strong spatial prior in the LiDAR point cloud, as described by Step 1 in our framework. As shown in Fig. 1 (left), we find an overt pattern in semantic classes detected by each laser beam. More concrete evidence on this aspect has been included in the Appendix. Despite being an empirical choice, we will show in later sections that laser partition significantly outperforms other partition choices, including random points (MixUp-like partition [54]), random areas (CutMix-like partition [53]), and other heuristics like azimuth \\(\\alpha\\) (sensor horizontal direction) or radius \\(r\\) (sensor range direction) partitions." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.409, + 0.47, + 0.528 + ], + "angle": 0, + "content": "Mixing. To this end, we propose LaserMix, a simple yet effective LiDAR mixing strategy that can better control the \"strength\" of the spatial prior. LaserMix mixes the aforementioned laser partitioned areas \\( A \\) from two scans in an intertwining way, i.e., one takes from odd-indexed areas \\( A_{1} = \\{a_{1},a_{3},\\ldots \\} \\) and the other takes from even-indexed areas \\( A_{2} = \\{a_{2},a_{4},\\ldots \\} \\), so that each area's neighbor will be from the other scan:" + }, + { + "type": "equation", + "bbox": [ + 0.182, + 0.536, + 0.372, + 0.551 + ], + "angle": 0, + "content": "\\[\n\\tilde {x} _ {1}, \\tilde {x} _ {2} = \\operatorname {L a s e r M i x} \\left(x _ {1}, x _ {2}\\right),\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.177, + 0.554, + 0.469, + 0.571 + ], + "angle": 0, + "content": "\\[\n\\tilde {x} _ {1} = x _ {1} ^ {a _ {1}} \\cup x _ {2} ^ {a _ {2}} \\cup x _ {1} ^ {a _ {3}} \\cup \\dots , \\tag {7}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.177, + 0.573, + 0.373, + 0.59 + ], + "angle": 0, + "content": "\\[\n\\tilde {x} _ {2} = x _ {2} ^ {a _ {1}} \\cup x _ {1} ^ {a _ {2}} \\cup x _ {2} ^ {a _ {3}} \\cup \\dots ,\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.599, + 0.469, + 0.705 + ], + "angle": 0, + "content": "where \\( x_{i}^{a_{j}} \\) is the data crop of \\( x_{i} \\) in the area \\( a_{j} \\). The semantic labels are mixed in the same way. LaserMix is directly applied to the point clouds and is thus agnostic to the various LiDAR representations [19, 32, 56, 58]. We show LaserMix's instantiations with the range view and voxel representations as in Fig. 1 (middle), since they are currently the most efficient and the best-performing options, respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Role in our framework: LaserMix helps to efficiently compute the marginal probability \\( P(Y_{\\mathrm{in}}|X_{\\mathrm{in}},A) \\), as described by Step 2 in our framework. The cost for directly computing the marginal probability in Eq. (4) on real-world LiDAR data is prohibitive; we need to iterate through all areas in \\( A \\) and all outside data in \\( X_{\\mathrm{out}} \\), which requires \\( |A|\\cdot |X_{\\mathrm{out}}| \\) predictions in total. To reduce the training overhead, we take advantage of the fact that a prediction in an area will be largely affected by its neighboring areas and let \\( X_{\\mathrm{out}} \\) fill only the neighbors instead of all the remaining areas. LaserMix mixes two scans by intertwining the areas so that the neighbors of each area are filled with data from the other scan. As a result, we obtain the prediction on" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.088, + 0.89, + 0.326 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.332, + 0.892, + 0.375 + ], + "angle": 0, + "content": "Figure 2. Laser partition example. We group LiDAR points \\((p_i^x, p_i^y, p_i^z)\\) whose inclinations \\(\\phi_i\\) are within the same inclination range into the same area, as depicted in the color regions." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.397, + 0.893, + 0.533 + ], + "angle": 0, + "content": "all areas \\( A \\) of two scans from only two predictions, which on average reduces the cost from \\( |A| \\) to 1. The scan before and after mixing counts as two data fillings, therefore \\( |X_{\\mathrm{out}}| = 2 \\). Overall, the training overhead is reduced from \\( |A|\\cdot |X_{\\mathrm{out}}| \\) to 2: only one prediction on original data and one additional prediction on mixed data are required for each LiDAR scan. During training, the memory consumption for a batch will be \\( 2\\times \\) compared to a standard SSL framework, and the training speed will not be affected." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.542, + 0.662, + 0.559 + ], + "angle": 0, + "content": "3.3. Overall Pipeline" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.565, + 0.892, + 0.791 + ], + "angle": 0, + "content": "We show the overall framework in Fig. 3 and the pseudocode in Algo. 1. There are two branches in our pipeline, one Student net \\(\\mathcal{G}_{\\theta}^{s}\\) and one Teacher net \\(\\mathcal{G}_{\\theta}^{t}\\). During training, a batch is composed of half labeled data and half unlabeled data. We collect the predictions from both \\(\\mathcal{G}_{\\theta}^{s}\\) and \\(\\mathcal{G}_{\\theta}^{t}\\), and produce pseudo-labels from Teacher net's prediction with a predefined confidence threshold \\(T\\). For labeled data, we compute the cross-entropy loss between the Student net's prediction and the ground-truth as \\(\\mathcal{L}_{\\mathrm{sup}}\\). For unlabeled data, LaserMix blends every scan with a random labeled scan, together with their pseudo-label or ground-truth. Then, we let \\(\\mathcal{G}_{\\theta}^{s}\\) predict on the mixed data and compute the cross-entropy loss \\(\\mathcal{L}_{\\mathrm{mix}}\\) (\\(w/\\) mixed labels). The point-wise cross-entropy loss for a scan \\(x\\) and its corresponding ground-truth/pseudolabel \\(y\\) on the segmentation net \\(\\mathcal{G}_{\\theta}\\) is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.55, + 0.803, + 0.892, + 0.845 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {c e}} = \\frac {1}{| x |} \\sum_ {i = 1} ^ {| x |} \\operatorname {C r o s s E n t r o p y} \\left(y ^ {(i)}, \\mathcal {G} _ {\\theta} ^ {(i)} (x)\\right), \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.892, + 0.903 + ], + "angle": 0, + "content": "where \\((i)\\) denotes the \\(i\\)-th point. Moreover, we adopt the mean teacher idea in [45] and use Exponential Moving Average (EMA) to update the weights of \\(\\mathcal{G}_{\\theta}^{t}\\) from \\(\\mathcal{G}_{\\theta}^{s}\\), and com" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "21708" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.086, + 0.09, + 0.885, + 0.313 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.321, + 0.893, + 0.378 + ], + "angle": 0, + "content": "Figure 3. Framework overview. The labeled scan \\( x_{l} \\) is fed into the Student net to compute the supervised loss \\( \\mathcal{L}_{\\mathrm{sup}} \\) (\\( w/ \\) ground-truth \\( y_{l} \\)). The unlabeled scan \\( x_{u} \\) and the generated pseudo-label \\( y_{u} \\) are mixed with \\( (x_{l},y_{l}) \\) via LaserMix (Sec. 3.2) to produce mixed data sample \\( (x_{\\mathrm{mix}},y_{\\mathrm{mix}}) \\), which is then fed into the Student net to compute the mixing loss \\( \\mathcal{L}_{\\mathrm{mix}} \\). Additionally, we adopt the EMA update in [45] for the Teacher net and compute the mean teacher loss \\( \\mathcal{L}_{\\mathrm{mt}} \\) over Student net's and Teacher net's predictions." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.4, + 0.407, + 0.416 + ], + "angle": 0, + "content": "pute the L2 loss between their predictions as \\(\\mathcal{L}_{\\mathrm{mt}}\\)" + }, + { + "type": "equation", + "bbox": [ + 0.182, + 0.423, + 0.47, + 0.44 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {m t}} = \\left| \\left| \\mathcal {G} _ {\\theta} ^ {s} (x) - \\mathcal {G} _ {\\theta} ^ {t} (x) \\right| \\right| _ {2} ^ {2}, \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.448, + 0.47, + 0.522 + ], + "angle": 0, + "content": "where \\(||\\cdot ||_2^2\\) is the L2 norm. The overall loss function is \\(\\mathcal{L} = \\mathcal{L}_{\\mathrm{sup}} + \\lambda_{\\mathrm{mix}}\\mathcal{L}_{\\mathrm{mix}} + \\lambda_{\\mathrm{mt}}\\mathcal{L}_{\\mathrm{mt}}\\), where \\(\\lambda_{\\mathrm{mix}}\\) and \\(\\lambda_{\\mathrm{mt}}\\) are loss weights. We use the Teacher net during inference as it empirically gives more stable results. There will be no extra inference overhead in our framework." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.524, + 0.47, + 0.69 + ], + "angle": 0, + "content": "Role in our framework: Our overall pipeline minimizes the marginal entropy, as described by Step 3 in our framework. Since the objective for minimizing the entropy has a hard optimization landscape, pseudo-labeling is a common resort in practice [25]. Unlike conventional pseudo-label optimization in SSL which only aims to encourage the predictions to be confident, minimizing the marginal entropy requires all predictions to be both confident and consistent. Therefore, we use the ground-truth and pseudo-label as an anchor and encourage the model's predictions to be confident and consistent with these supervision signals." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.702, + 0.21, + 0.719 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.727, + 0.176, + 0.743 + ], + "angle": 0, + "content": "4.1. Settings" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.469, + 0.825 + ], + "angle": 0, + "content": "Protocol. We follow the Realistic Evaluation Protocol [35] when building the benchmark. Specifically, all experiments share the same backbones and are within the same codebase. All configurations and augmentations are unified to ensure a fair comparison among different SSL algorithms." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.469, + 0.902 + ], + "angle": 0, + "content": "Data. We build three SSL benchmarks upon nuScenes [11], SemanticKITTI [1], and ScribbleKITTI [47]. nuScenes [11] and SemanticKITTI [1] are the two most popular LiDAR segmentation datasets, with 29130 and 19130 training scans and 6019 and 4071 validation scans, respectively." + }, + { + "type": "code_caption", + "bbox": [ + 0.502, + 0.4, + 0.843, + 0.415 + ], + "angle": 0, + "content": "Algorithm 1 Pseudo-code for one training iteration." + }, + { + "type": "algorithm", + "bbox": [ + 0.509, + 0.419, + 0.892, + 0.691 + ], + "angle": 0, + "content": "1: Input: Shuffled labeled batch \\((X_{l},Y_{l}) = \\{(x_{l}^{(b)},y_{l}^{(b)});b\\in\\) \\((1,\\dots ,B)\\}\\) , shuffled unlabeled batch \\(X_{u} = \\{x_{u}^{(b)};b\\in\\) \\((1,\\dots ,B)\\}\\) , threshold \\(T\\) , loss weights \\(\\lambda_{\\mathrm{mix}}\\) and \\(\\lambda_{\\mathrm{mt}}\\) , Student net and Teacher net. \n2: for \\(b = 1\\) to \\(B\\) do \n3: \\(x_{\\mathrm{mix}}^{(2b - 1)},x_{\\mathrm{mix}}^{(2b)} = \\mathrm{LaserMix}(x_l^{(b)},x_u^{(b)}) / /\\) LaserMix data \n4: end for \n5: \\(X_{\\mathrm{mix}} = \\{x_{\\mathrm{mix}}^{(i)};i\\in (1,\\dots ,2B)\\}\\) \n6: \\(S_{l},S_{u},S_{\\mathrm{mix}} =\\) Student \\(\\big(\\mathrm{Concat}(X_l,X_u,X_{\\mathrm{mix}})\\big)\\) //Student pred \n7: \\(\\hat{S}_l,\\hat{S}_u =\\) Teacher \\(\\big(\\mathrm{Concat}(X_l,X_u)\\big)\\) //Teacher pred \n8: \\(Y_{u} =\\) PseudoLabel \\((\\hat{S}_u,T)\\) //Pseudo-label generation process \n9: for \\(b = 1\\) to \\(B\\) do \n10: \\(y_{\\mathrm{mix}}^{(2b - 1)},y_{\\mathrm{mix}}^{(2b)} = \\mathrm{LaserMix}(y_l^{(b)},y_u^{(b)}) / /\\) LaserMix label \n11: end for \n12: \\(Y_{\\mathrm{mix}} = \\{y_{\\mathrm{mix}}^{(i)};i\\in (1,\\dots ,2B)\\}\\) \n13: \\(L_{\\mathrm{sup}} =\\) CrossEntropy \\((S_l,Y_l)\\) // Supervised loss \n14: \\(L_{\\mathrm{mix}} =\\) CrossEntropy \\((S_{\\mathrm{mix}},Y_{\\mathrm{mix}})\\) // Mixing loss \n15: \\(L_{\\mathrm{mt}} = L2\\big(\\mathrm{Concat}(S_l,S_u),\\mathrm{Concat}(\\hat{S}_l,\\hat{S}_u)\\big)\\) //MeanTeacher loss \n16: \\(L = L_{\\mathrm{sup}} + \\lambda_{\\mathrm{mix}}L_{\\mathrm{mix}} + \\lambda_{\\mathrm{mt}}L_{\\mathrm{mt}}\\) //Overall loss \n17: Backward(L), Update(Student), UpdateEMA(Teacher)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.719, + 0.893, + 0.902 + ], + "angle": 0, + "content": "ScribbleKITTI [47] is a recent variant of SemanticKITTI [1], which contains the same number of scans but is annotated with line scribbles (approximately \\(8.06\\%\\) valid semantic labels) rather than dense annotations. For all three LiDAR segmentation datasets, we uniformly sample \\(1\\%\\), \\(10\\%\\), \\(20\\%\\), and \\(50\\%\\) labeled training scans and assume the remaining ones as unlabeled. This is in line with the conventional settings from the semi-supervised image segmentation community [6, 21, 37]. We also conduct experiments with sequential splits and show the results in the Appendix. Implementation Details. We adopt FIDNet [57] and Cylinder3D [58] as the segmentation backbones for the range" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "21709" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.892, + 0.118 + ], + "angle": 0, + "content": "Table 1. Benchmarking results among different SSL methods with the LiDAR range view (top) and voxel (bottom) representations. All mIoU scores are given in percentage (\\%). The best and second best score for each data split is highlighted in bold and underline." + }, + { + "type": "table", + "bbox": [ + 0.162, + 0.123, + 0.805, + 0.344 + ], + "angle": 0, + "content": "
Repr.MethodnuScenes [11]SemanticKITTI [1]ScribbleKITTI [47]
1%10%20%50%1%10%20%50%1%10%20%50%
Range ViewSup.-only38.357.562.767.636.252.255.957.233.147.749.952.5
MeanTeacher [45]42.160.465.469.437.553.156.157.434.249.851.653.3
CBST [59]40.960.564.369.339.953.456.156.935.750.752.754.6
CutMix-Seg [12]43.863.964.869.837.454.356.657.636.750.752.954.3
CPS [6]40.760.864.968.036.552.356.357.433.750.052.854.6
LaserMix (Ours)49.568.270.673.043.458.859.461.438.354.455.658.7
Δ↑+11.2+10.7+7.9+5.4+7.2+6.6+3.5+4.2+5.2+6.7+5.7+6.2
VoxelSup.-only50.965.966.671.245.456.157.858.739.248.052.153.8
MeanTeacher [45]51.666.067.171.745.457.159.260.041.050.152.853.9
CBST [59]53.066.569.671.648.858.359.459.741.550.653.354.5
CPS [6]52.966.370.072.546.758.759.660.541.451.853.954.8
LaserMix (Ours)55.369.971.873.250.660.061.962.344.253.755.156.8
Δ↑+4.4+4.0+5.2+2.0+5.2+3.9+4.1+3.6+5.0+5.7+3.0+3.0
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.357, + 0.391, + 0.399 + ], + "angle": 0, + "content": "Table 2. Comparison to the state-of-the-art 3D SSL method [20] on the val set of SemanticKITTI [1]. All mIoU scores are given in percentage \\((\\%)\\)." + }, + { + "type": "table", + "bbox": [ + 0.086, + 0.403, + 0.382, + 0.498 + ], + "angle": 0, + "content": "
Method5%10%20%30%40%
GPC [20]41.849.958.859.459.9
Ours (RV)54.658.859.460.160.8
Δ↑+12.8+8.9+0.6+0.7+0.9
Ours (Voxel)56.760.061.962.162.3
Δ↑+14.9+10.1+3.1+1.7+1.4
" + }, + { + "type": "table_caption", + "bbox": [ + 0.416, + 0.357, + 0.892, + 0.399 + ], + "angle": 0, + "content": "Table 3. Ablation results on the val set of nuScenes [11]. (1) Baseline results [45]; (2) Results with Student net supervision (SS); (3) Results with Teacher net supervision (TS). All mIoU scores are given in percentage \\((\\%)\\)." + }, + { + "type": "table", + "bbox": [ + 0.422, + 0.403, + 0.888, + 0.498 + ], + "angle": 0, + "content": "
#\\( {\\mathcal{L}}_{\\text{mt }} \\)\\( {\\mathcal{L}}_{\\text{mix }} \\)SSTS1%10%20%50%
(1)✓42.160.465.469.4
(2)✓✓45.6(+3.5)64.3(+3.9)67.8(+2.4)71.6(+2.2)
✓✓✓47.0(+4.9)65.5(+5.1)69.5(+4.1)72.0(+2.6)
(3)✓✓46.0(+3.9)64.1(+3.7)69.5(+4.1)72.3(+2.9)
✓✓✓49.5(+7.4)68.2(+7.8)70.6(+5.2)73.0(+3.6)
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.522, + 0.47, + 0.732 + ], + "angle": 0, + "content": "view and the voxel options, respectively. The input resolution of range images is set as \\(64 \\times 2048\\) for SemanticKITTI [1] and ScribbleKITTI [47], and \\(32 \\times 1920\\) for nuScenes [11]. The voxel resolution is fixed as [240, 180, 20] for all three sets. The number of spatial areas \\(m\\) in LaserMix is uniformly sampled from 2 to 6 areas. We denote the supervised-only baseline as sup.-only. Due to the lack of Li-DAR SSL works [20], we also compare SoTA consistency regularization [6, 12, 45] and entropy minimization [59] methods from semi-supervised image segmentation. We report the intersection-over-union (IoU) over each semantic class and the mean IoU (mIoU) scores over all classes in our benchmarks. All experiments are implemented using PyTorch on NVIDIA Tesla V100 GPUs with 32GB RAM." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.742, + 0.265, + 0.759 + ], + "angle": 0, + "content": "4.2. Comparative Study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Improvements over Baseline. Tab. 1 benchmarks results on nuScenes [11], SemanticKITTI [1], and ScribbleKITTI [47]. For all three sets under different data splits, we observe significant improvements in our approach over the sup.-only baseline. Such gains are especially evident in range view, which reach up to \\(11.2\\%\\) mIoU. We also observe constant improvements for the voxel option, which provide on average \\(4.1\\%\\) mIoU gains over all splits across all sets. The results verify the effectiveness of our frame-" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.522, + 0.89, + 0.551 + ], + "angle": 0, + "content": "work and further highlight the importance of leveraging unlabeled data in LiDAR semantic segmentation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.552, + 0.892, + 0.704 + ], + "angle": 0, + "content": "Compare with SoTA. We compare LaserMix with \\(\\mathrm{GPC}^2\\) [20], the SoTA 3D SSL method tested on SemanticKITTI [1]. The results in Tab. 2 show that our approach exhibits much better results than GPC [20], especially in scenarios where very few annotations are available. We also reimplemented popular SSL algorithms from the image segmentation domain and show their results in Tab. 1. We find that these methods, albeit competitive in 2D, only yield sub-par performance in the LiDAR SSL benchmark, highlighting the importance of exploiting the LiDAR data structure." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.892, + 0.841 + ], + "angle": 0, + "content": "Compare with Full Labels. As shown in Fig. 1 (right), the comparisons between the prevailing LiDAR segmentation methods attests that our approach can achieve more competitive scores over the fully-supervised counterparts [5, 8, 32, 56] while with \\(2 \\times\\) to \\(5 \\times\\) fewer annotations. The strong augmentation and regularization ability of LaserMix have yielded better results in the high-data regime and extreme low-data regime (i.e., \\(0.8\\%\\) labels on [47]), which validates the generalizability of our approach." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.842, + 0.892, + 0.872 + ], + "angle": 0, + "content": "Qualitative Examination. Fig. 5 visualizes the scene segmentation results for different SSL algorithms on the val" + }, + { + "type": "page_footnote", + "bbox": [ + 0.516, + 0.887, + 0.89, + 0.9 + ], + "angle": 0, + "content": "2Note that GPC uses private backbone / split. See Appendix for details." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "21710" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.088, + 0.495, + 0.277 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.087, + 0.691, + 0.276 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.706, + 0.087, + 0.895, + 0.276 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.281, + 0.893, + 0.31 + ], + "angle": 0, + "content": "Figure 4. Ablation studies on: Left: Different mixing-based techniques used in point partition & mixing; Middle: Different EMA decay rates between the Teacher net and the Student net; Right: Different confidence thresholds \\( T \\) used in the pseudo-label generation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.332, + 0.473, + 0.44 + ], + "angle": 0, + "content": "set of nuScenes [11], where each example covers a driving scene centered by the ego-vehicle. We find that previous arts [6, 45, 59] can only improve predictions in limited regions, while our approach holistically eliminates false predictions in almost every direction around the ego-vehicle. The consistency enlightened by LaserMix has yielded better segmentation accuracy under annotation scarcity." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.451, + 0.232, + 0.468 + ], + "angle": 0, + "content": "4.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.475, + 0.47, + 0.506 + ], + "angle": 0, + "content": "Without loss of generalizability, we stick with the \\(10\\%\\) budget setting and range view backbones in our ablations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.507, + 0.471, + 0.674 + ], + "angle": 0, + "content": "Framework Setups. The component analysis in Tab. 3 shows that \\(\\mathcal{L}_{\\mathrm{mix}}\\) contributes significantly to the overall improvement. Meanwhile, using the Teacher net instead of the Student net to generate pseudo-labels leads to better results, as the formal is temporally ensembled and encourages consistency in-between mixed and original data, which is crucial besides enforcing confident predictions. It is worth noting that all of our model configurations have achieved superior results than the baseline MeanTeacher [45], which further emphasizes the effectiveness of our framework in tackling LiDAR segmentation with semi-supervisions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.674, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Mixing Strategies. Fig. 4 (left) compares LaserMix with other mixing methods [10, 33, 53, 54]. MixUp and CutMix can be considered as setting \\( A \\) to random points and random areas, respectively. We observe that MixUp has no improvements over the baseline on average since there is no distribution pattern in random points. CutMix has a considerable improvement over the baseline, as there is always a structure prior in scene segmentation, i.e., the same semantic class points tend to cluster, which reduces the entropy in any continuous area. This prior is often used in image semantic segmentation SSL [12]. However, our spatial prior is much stronger, where not only the area structure but also the area's spatial position has been considered. LaserMix outperforms CutMix by a large margin (up to \\( 3.3\\% \\) mIoU) on all sets. CutOut can be considered as setting \\( X_{\\mathrm{out}} \\) to" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.33, + 0.895, + 0.373 + ], + "angle": 0, + "content": "Table 4. Ablation studies on laser beam partitions (horizontal: inclination direction \\(\\phi\\); vertical: azimuth direction \\(\\alpha\\)). \\((i - \\alpha, j - \\phi)\\) denotes that there are \\(i\\) azimuth and \\(j\\) inclination partitions." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.376, + 0.892, + 0.68 + ], + "angle": 0, + "content": "
Baseline(1α, 2φ)(1α, 3φ)(1α, 4φ)(1α, 5φ)(1α, 6φ)
60.463.5(+3.1)65.2(+4.8)66.5(+6.1)66.2(+5.8)65.4(+5.0)
(2α, 1φ)(2α, 2φ)(2α, 3φ)(2α, 4φ)(2α, 5φ)(2α, 6φ)
61.5(+1.1)63.3(+2.9)65.9(+5.5)66.1(+5.7)66.7(+6.3)65.3(+4.9)
(3α, 1φ)(3α, 2φ)(3α, 3φ)(3α, 4φ)(3α, 5φ)(3α, 6φ)
60.9(+0.6)64.2(+3.8)65.9(+5.5)66.3(+5.9)66.0(+5.6)65.2(+4.8)
(4α, 1φ)(4α, 2φ)(4α, 3φ)(4α, 4φ)(4α, 5φ)(4α, 6φ)
60.9(+0.6)64.7(+4.3)65.3(+4.9)65.6(+5.2)65.7(+5.3)65.2(+4.8)
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.703, + 0.892, + 0.734 + ], + "angle": 0, + "content": "a dummy filling instead of sampling from datasets, and it leads to a considerable performance drop from CutMix." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.84 + ], + "angle": 0, + "content": "Orderless Mix. We revert the area ordering (i.e., put the topmost laser beam at the bottom, and vice versa) in LaserMix, and the performance drops from \\(68.2\\%\\) to \\(64.4\\%\\) \\((-3.8\\% \\mathrm{mIoU})\\). When we shuffle the ordering, the performance drops to \\(63.8\\%\\) \\((-4.4\\% \\mathrm{mIoU})\\), which becomes comparable with CutMix. The results once again confirm the superiority of using spatial prior in LiDAR SSL." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Other Heuristics. Besides our proposed inclination partition, the LiDAR scans can also be split based on azimuth (sensor horizontal direction). Results in Tab. 4 reveal that in contrast to laser partitioning, pure azimuth splitting (the" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "21711" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.078, + 0.089, + 0.891, + 0.102 + ], + "angle": 0, + "content": "\\(\\bullet\\) barrier \\(\\bullet\\) bicycle \\(\\bullet\\) bus \\(\\bullet\\) car \\(\\bullet\\) driveable \\(\\bullet\\) flat \\(\\bullet\\) ignored \\(\\bullet\\) manmade \\(\\bullet\\) motor \\(\\bullet\\) pedestrian \\(\\bullet\\) sidewalk \\(\\bullet\\) terrain \\(\\bullet\\) trailer \\(\\bullet\\) truck \\(\\bullet\\) vegetation" + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.108, + 0.212, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.217, + 0.108, + 0.348, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.352, + 0.108, + 0.483, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.487, + 0.108, + 0.619, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.623, + 0.108, + 0.755, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.76, + 0.108, + 0.891, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.247, + 0.212, + 0.399 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.217, + 0.248, + 0.348, + 0.399 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.352, + 0.248, + 0.483, + 0.399 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.487, + 0.248, + 0.619, + 0.399 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.623, + 0.248, + 0.755, + 0.399 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.76, + 0.248, + 0.891, + 0.399 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.409, + 0.893, + 0.438 + ], + "angle": 0, + "content": "Figure 5. Error maps visualized from LiDAR bird's eye view and range view on nuScenes [11]. Each example shows a street scene of size \\(50\\mathrm{m}\\) by \\(50\\mathrm{m}\\) by \\(8\\mathrm{m}\\). The correct and incorrect predictions are painted in green and red to highlight the differences. Best viewed in color." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.463, + 0.469, + 0.582 + ], + "angle": 0, + "content": "first column) does not improve the performance, which is attributed to the fact that the semantic distribution has a weak correlation in the azimuth direction. We also observe that the results tend to improve as the mixing granularity increases (row direction in Tab. 4). The scores start to drop when the granularity is beyond a certain limit (e.g., the last two columns). We conjecture that over-fine-grained partition and mixing tend to hurt semantic coherence." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.583, + 0.469, + 0.718 + ], + "angle": 0, + "content": "Mix Unlabeled Data Only. To verify that our method is more than trivially augmenting seen data and label pairs, we apply LaserMix only on unlabeled data. Instead of mixing an unlabeled scan with a labeled scan as described in Sec. 3.3, we mix two unlabeled scans with their pseudolabels. The score drops from \\(68.2\\%\\) to \\(66.9\\%\\) \\((-1.3\\% \\mathrm{mIoU})\\) but still outperforms all existing methods by large margins. This verifies that LaserMix indeed brings a strong consistency regularization effect during SSL." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.469, + 0.838 + ], + "angle": 0, + "content": "EMA. Fig. 4 (middle) provides results with different EMA decay rates, Typically, a rate between 0.9 and 0.99 yields the best possible results. Large rates like 0.999 tend to hurt the consistency between the two networks. The results also verify that the teacher-student pipeline [45] has good synergy with our proposed SSL framework. Thanks to this simplicity, more modern SSL techniques can be easily incorporated into the current framework in future works." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.469, + 0.9 + ], + "angle": 0, + "content": "Confidence Threshold. As pseudo-labels play an important role in our framework, we further analyze the impact of the threshold parameter \\( T \\) used in pseudo-label generation and show results in Fig. 4 (right). When \\( T \\) is too low," + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.463, + 0.892, + 0.553 + ], + "angle": 0, + "content": "a forced consistency to low-quality pseudo-labels tends to deteriorate the performance. When \\( T \\) is too high, the benefits from mixing might diminish. Generally, \\( T \\) is a dataset-dependent parameter and we find that a value around 0.9 leads to the best possible results on the three tested LiDAR segmentation datasets [1, 11, 47] in our benchmark." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.566, + 0.619, + 0.582 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.592, + 0.892, + 0.743 + ], + "angle": 0, + "content": "In this work, we exploit the unique spatial prior in LiDAR scenes for semi-supervised LiDAR semantic segmentation. We proposed a statistically-principled and effective SSL pipeline, including LaserMix, a novel LiDAR mixing technique that intertwines laser beams from different scans. Through comprehensive empirical analysis, we show the importance of spatial prior and the superiority of our approach on three popular benchmarks. The effectiveness and simplicity of our framework have shed light on the scalable deployment of the LiDAR semantic mapping system." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.748, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Acknowledgments. This study is supported by the Ministry of Education, Singapore, under its MOE AcRF Tier 2 (MOET2EP20221-0012), the National Research Foundation, Singapore under its AI Singapore Programme (AISG Award No: AISG2-PhD-2021-08-018), NTU NAP, and under the RIE2020 Industry Alignment Fund - Industry Collaboration Projects (IAF-ICP) Funding Initiative, as well as cash and in-kind contribution from the industry partner(s). This research is part of the programme DesCartes and is supported by the National Research Foundation, Prime Minister's Office, Singapore under its Campus for Research Excellence and Technological Enterprise (CREATE) programme." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "21712" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.197 + ], + "angle": 0, + "content": "[1] Jens Behley, Martin Garbade, Andres Milioto, Jan Quenzel, Sven Behnke, Cyril Stachniss, and Juergen Gall. Semantickitti: A dataset for semantic scene understanding of lidar sequences. 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In International Conference on Learning Representations (ICLR), 2020. 2" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.471, + 0.781 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "21715" + } + ] +] \ No newline at end of file diff --git a/2023/LaserMix for Semi-Supervised LiDAR Semantic Segmentation/0dfb46c8-457c-4c6b-aa9f-3e7c68a2add5_origin.pdf b/2023/LaserMix for Semi-Supervised LiDAR Semantic Segmentation/0dfb46c8-457c-4c6b-aa9f-3e7c68a2add5_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..7d16d8762a4e67608554ea3acb8d96553e8b6617 --- /dev/null +++ b/2023/LaserMix for Semi-Supervised LiDAR Semantic Segmentation/0dfb46c8-457c-4c6b-aa9f-3e7c68a2add5_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:6c00d25ca7198e4ac236ecf59cd66cf593e67b8bea53a5740a16d8abfa3e8fd7 +size 4735505 diff --git a/2023/LaserMix for Semi-Supervised LiDAR Semantic Segmentation/full.md b/2023/LaserMix for Semi-Supervised LiDAR Semantic Segmentation/full.md new file mode 100644 index 0000000000000000000000000000000000000000..b696df2b55e3e5fdf3a4b66da0b10a869d296e14 --- /dev/null +++ b/2023/LaserMix for Semi-Supervised LiDAR Semantic Segmentation/full.md @@ -0,0 +1,374 @@ +# LaserMix for Semi-Supervised LiDAR Semantic Segmentation + +Lingdong Kong $^{1,2,3,*}$ Jiawei Ren $^{1,*}$ Liang Pan $^{1}$ Ziwei Liu $^{1,\text{口}}$ + +$^{1}$ S-Lab, Nanyang Technological University $^{2}$ National University of Singapore $^{3}$ CNRS@CREATE + +{lingdong001,jiawei011}@e.ntu.edu.sg {liang.pan,ziwei.liu}@ntu.edu.sg + +![](images/e0b7140b13cde9d26d8fbb9cfea928327b9f32ccd9c902894f5bac5964768d2e.jpg) +Option 1: Range View + +![](images/81902df7b48ae9eb36aba09b702c2ecb2b53b97fb011c5f1aa625bd02c16b5cd.jpg) +LiDAR Representation + +![](images/d2494263c35f7d98774c2fd878006d5bea1810fe63c71a8b55587a1bc2e0f880.jpg) + +![](images/fc6d50b221142931e82a822773d01a57801b098c490d533b7268e20c25a41a43.jpg) + +![](images/640ed0ae358b9bdfb8c3767d0707693625f955e30144221bca7ed58b44a2b8e7.jpg) + +![](images/d063b1954baff34f09c72d982b59f274cdea06a99cbfe2bbc2828f09f77919d1.jpg) +Option 2: Voxel + +![](images/f77ab86efd1ced814a6f5bd32fb53e8b4d2820a5b44dce2de6acbe4e5fb036e4.jpg) + +![](images/b2c598d668998b80db82a11b3d1a60c1c82d332e59beae7dbaeddef8249456d5.jpg) +Figure 1. Left: The LiDAR point cloud contains strong spatial prior. Objects and backgrounds around the ego-vehicle have a patterned distribution on different (lower, middle, upper) laser beams. Middle: Following the scene structure, the proposed LaserMix blends beams from different LiDAR scans, which is compatible with various popular LiDAR representations. Right: We achieve superior results over SoTA methods in both low-data (10%, 20%, and 50% semantic labels) and high-data (full semantic labels) regimes on nuScenes [11]. + +![](images/4d8f2bd6eaf8ca4f96cbc1797b099540f661c6f507dcfb5a77daf3ab29cee36b.jpg) + +# Abstract + +Densely annotating LiDAR point clouds is costly, which often restrains the scalability of fully-supervised learning methods. In this work, we study the underexplored semi-supervised learning (SSL) in LiDAR semantic segmentation. Our core idea is to leverage the strong spatial cues of LiDAR point clouds to better exploit unlabeled data. We propose LaserMix to mix laser beams from different LiDAR scans and then encourage the model to make consistent and confident predictions before and after mixing. Our framework has three appealing properties. 1) Generic: LaserMix is agnostic to LiDAR representations (e.g., range view and voxel), and hence our SSL framework can be universally applied. 2) Statistically grounded: We provide a detailed analysis to theoretically explain the applicability of the proposed framework. 3) Effective: Comprehensive experimental analysis on popular LiDAR segmentation + +datasets (nuScenes, SemanticKITTI, and ScribbleKITTI) demonstrates our effectiveness and superiority. Notably, we achieve competitive results over fully-supervised counterparts with $2 \times$ to $5 \times$ fewer labels and improve the supervised-only baseline significantly by relatively $10.8\%$ . We hope this concise yet high-performing framework could facilitate future research in semi-supervised LiDAR segmentation. Code is publicly available1. + +# 1. Introduction + +LiDAR segmentation is one of the fundamental tasks in autonomous driving perception [41]. It enables autonomous vehicles to semantically perceive the dense 3D structure of the surrounding scenes [15, 34, 39]. However, densely annotating LiDAR point clouds is inevitably expensive and labor-intensive [18, 23, 47], which restrains the scalability of fully-supervised LiDAR segmentation methods. Semisupervised learning (SSL) that directly leverages the easy-to-acquire unlabeled data is hence a viable and promising + +solution to achieve scalable LiDAR segmentation [13, 14]. + +Yet, semi-supervised LiDAR segmentation is still under-explored. Modern SSL frameworks are mainly designed for image recognition [2, 3, 42] and semantic segmentation [6, 21, 37] tasks, which only yield sub-par performance on LiDAR data due to the large modality gap between 2D and 3D. Recent research [20] proposed to consider semi-supervised point cloud semantic segmentation as a fresh task and proposed a point contrastive learning framework. However, their solutions do not differentiate indoor and outdoor scenes and therefore overlook the intrinsic and important properties that only exist in LiDAR point clouds. + +In this work, we explore the use of spatial prior for semi-supervised LiDAR segmentation. Unlike the general 2D/3D segmentation tasks, the spatial cues are especially significant in LiDAR data. In fact, LiDAR point clouds serve as a perfect reflection of real-world distributions, which is highly dependent on the spatial areas in the LiDAR-centered 3D coordinates. As shown in Fig. 1 (left), the top laser beams travel outward long distance and perceive mostly vegetation, while the middle and bottom beams tend to detect car and road from the medium and close distances, respectively. To effectively leverage this strong spatial prior, we propose LaserMix to mix laser beams from different LiDAR scans, and then encourage the LiDAR segmentation model to make consistent and confident predictions before and after mixing. Our SSL framework is statistically grounded, which consists of the following components: + +1) Partitioning the LiDAR scan into low-variation areas. We observe a strong distribution pattern on laser beams as shown in Fig. 1 (left) and thus propose the laser partition. +2) Efficiently mixing every area in the scan with foreign data and obtaining model predictions. We propose LaserMix to manipulate the laser-grouped areas from two LiDAR scans in an intertwining way as depicted in Fig. 1 (middle) and serves as an efficient LiDAR mixing strategy for SSL. +3) Encouraging models to make confident and consistent predictions on the same area in different mixing. We hence propose a mixing-based teacher-student training pipeline. + +Despite the simplicity of our overall pipeline, it achieves competitive results over the fully supervised counterpart using $2 \times$ to $5 \times$ fewer labels as shown in Fig. 1 (right) and significantly outperforms all prevailing semi-supervised segmentation methods on nuScenes [11] (up to $+5.7\%$ mIoU) and SemanticKITTI [1] (up to $+3.5\%$ mIoU). Moreover, LaserMix directly operates on point clouds so as to be agnostic to different LiDAR representations, e.g., range view [32] and voxel [58]. Therefore, our pipeline is highly compatible with existing state-of-the-art (SoTA) LiDAR segmentation methods under various representations [46, 56, 57]. Besides, our pipeline achieves competitive performance using very limited annotations on weak supervision dataset [47]: it achieves $54.4\%$ mIoU on Se + +manticKITTI [1] using only $0.8\%$ labels, which is on-par with PolarNet [56] $(54.3\%)$ , RandLA-Net [19] $(53.9\%)$ , and RangeNet++ [32] $(52.2\%)$ using $100\%$ labels. Spatial prior is proven to play a pivotal role in the success of our framework through comprehensive empirical analysis. To summarize, this work has the following key contributions: + +- We present a statistically grounded SSL framework that effectively leverages the spatial cues in LiDAR data to facilitate learning with semi-supervisions. +- We propose LaserMix, a novel and representation-agnostic mixing technique that strives to maximize the "strength" of the spatial cues in our SSL framework. +- Our overall pipeline significantly outperforms previous SoTA methods in both low- and high-data regimes. We hope this work could lay a solid foundation for semi-supervised LiDAR segmentation. + +# 2. Related Work + +LiDAR Segmentation. Various approaches from different aspects have been proposed for LiDAR scene segmentation, i.e., range view [8, 32, 49, 57], bird's eye view [56], voxel [44, 58], and multi-view [26, 50] methods. Although appealing results have been achieved, these fully-supervised methods rely on large-scale annotated LiDAR datasets and their performance would degrade severely in the low-data regime [13]. Recent works seek weak [18, 55], scribble [47], and box [28] supervisions or activate learning [27, 31] to ease the annotation cost. We tackle this problem from the perspective of semi-supervised learning (SSL), aiming at directly leveraging the easy-to-acquire unlabeled data to boost the LiDAR semantic segmentation performance. + +SSL in 2D. Well-known SSL algorithms are prevailing in handling image recognition problems [2, 3, 24, 42, 45]. In the context of semantic segmentation, CutMix-Seg [12] and PseudoSeg [60] apply perturbations on inputs and hope the decision boundary lies in the low-density region. CPS [6] and GCT [21] enforce consistency between two perturbed networks [29]. These perturbations [30, 36, 52], however, are either inapplicable or only yield sub-par results in 3D. Another line of research is entropy minimization. Methods like CBST [59] and $\mathrm{ST} + +$ [51] generate pseudo-labels [25] offline per round during self-training. The extra storage needed might become costly for large-scale LiDAR datasets [1, 4, 11]. Our framework encourages both consistency regularization and entropy minimization and does not require extra overhead, which better maintains scalability. + +SSL in 3D. Most works focus on developing SSL for object-centric point clouds [22, 43] or indoor scenes [7, 9, 17, 34], whose scale and diversity are much lower than the outdoor LiDAR point clouds [1, 4]. Some other works [38, 40, 48] try to utilize SSL for 3D object detection on LiDAR data. A recent work [20] tackles semi-supervised point cloud semantic segmentation using contrastive learning, but it still + +mainly focused on indoor scenes and does not distinguish between the uniformly distributed indoor point clouds and the spatially structured LiDAR point clouds. We are one of the first works to explore SSL for LiDAR segmentation. Our work also establishes comprehensive SSL benchmarks upon popular autonomous driving databases [1, 11, 47]. + +# 3. Approach + +In this section, we first introduce our SSL framework that leverages the spatial prior of LiDAR data by encouraging confidence and consistency in predictions (Sec. 3.1). We then present LaserMix which strives to maximize the "strength" of the spatial prior and mixes LiDAR scans in an efficient manner (Sec. 3.2). Finally, we elaborate on the overall pipeline (Sec. 3.3) and the pseudo-code (Algo. 1). + +# 3.1. Leveraging the Spatial Prior for SSL + +Spatial Prior Formulation. The distribution of real-world objects/backgrounds has a strong correlation to their spatial positions in the LiDAR scan. Objects/backgrounds inside a specified spatial area of a LiDAR point cloud follow similar patterns, e.g., the close-range area is most likely road while the long-range area consists of building, vegetation, etc. In another word, there exists a spatial area $a \in A$ where LiDAR points and semantic labels inside the area (denoted as $X_{\mathrm{in}}$ and $Y_{\mathrm{in}}$ , respectively) will have relatively low variations. Formally, the conditional entropy $H(X_{\mathrm{in}}, Y_{\mathrm{in}}|A)$ is smaller. Therefore, when estimating the parameter $\theta$ of the segmentation network $\mathcal{G}_{\theta}$ , we would expect: + +$$ +\mathbb {E} _ {\theta} \left[ H \left(X _ {\text {i n}}, Y _ {\text {i n}} \mid A\right) \right] = c, \tag {1} +$$ + +where $c$ is a small constant. Similar to the classic entropy minimization [16], the constraint in Eq. (1) can be converted to a prior on the model parameter $\theta$ using the principle of maximum entropy: + +$$ +\begin{array}{l} P (\theta) \propto \exp (- \lambda H (X _ {\text {i n}}, Y _ {\text {i n}} | A)) \tag {2} \\ \propto \exp (- \lambda H (Y _ {\mathrm {i n}} | X _ {\mathrm {i n}}, A)), \\ \end{array} +$$ + +where $\lambda > 0$ is the Lagrange multiplier corresponding to constant $c$ ; $H(X_{\mathrm{in}}|A)$ has been ignored for being independent of the model parameter $\theta$ . We consider Eq. (2) as the formal formulation of the spatial prior and discuss how to empirically compute it in the following sections. + +Marginalization. To utilize the spatial prior defined in Eq. (2), we empirically compute the entropy $H(Y_{\mathrm{in}}|X_{\mathrm{in}},A)$ of the LiDAR points inside area $A$ as follows: + +$$ +\hat {H} \left(Y _ {\text {i n}} \mid X _ {\text {i n}}, A\right) = \tag {3} +$$ + +$$ +\hat {\mathbb {E}} _ {X _ {\mathrm {i n}}, Y _ {\mathrm {i n}}, A} \big [ P (Y _ {\mathrm {i n}} | X _ {\mathrm {i n}}, A) \log P (Y _ {\mathrm {i n}} | X _ {\mathrm {i n}}, A) \big ], +$$ + +where $\hat{\cdot}$ denotes the empirical estimation. The end-to-end LiDAR segmentation model $\mathcal{G}_{\theta}$ usually takes full-sized + +data as inputs during inference. Therefore, to compute $P(Y_{\mathrm{in}}|X_{\mathrm{in}},A)$ in Eq. (3), we first pad the data outside the area to obtain the full-sized data. Here we denote the data outside the area as $X_{\mathrm{out}}$ ; we then let the model infer $P(Y_{\mathrm{in}}|X_{\mathrm{in}},X_{\mathrm{out}},A)$ , and finally marginalize $X_{\mathrm{out}}$ as: + +$$ +P \left(Y _ {\mathrm {i n}} \mid X _ {\mathrm {i n}}, A\right) = \hat {\mathbb {E}} _ {X _ {\mathrm {o u t}}} \left[ P \left(Y _ {\mathrm {i n}} \mid X _ {\mathrm {i n}}, X _ {\mathrm {o u t}}, A\right) \right]. \quad (4) +$$ + +The generative distribution of the padding $P(X_{\mathrm{out}})$ can be directly obtained from the dataset. + +Training. Finally, we train the segmentation model $\mathcal{G}_{\theta}$ using the standard maximum-a-posteriori (MAP) estimation. We maximize the posterior that can be computed by Eq. (2), Eq. (3) and Eq. (4), which is formulated as follows: + +$$ +\begin{array}{l} C (\theta) = L (\theta) - \lambda \hat {H} \left(Y _ {\mathrm {i n}} \mid X _ {\mathrm {i n}}, A\right) = L (\theta) \tag {5} \\ - \lambda \hat {\mathbb {E}} _ {X _ {\text {i n}}, Y _ {\text {i n}}, A} [ P (Y _ {\text {i n}} | X _ {\text {i n}}, A) \log P (Y _ {\text {i n}} | X _ {\text {i n}}, A) ]. \\ \end{array} +$$ + +Here, $L(\theta)$ is the likelihood function computed using labeled data, i.e., the conventional supervised learning. Minimizing $\hat{H}(Y_{\mathrm{in}}|X_{\mathrm{in}},A)$ requires the marginal probability $P(Y_{\mathrm{in}}|X_{\mathrm{in}},A)$ to be confident, which further requires $P(Y_{\mathrm{in}}|X_{\mathrm{in}},X_{\mathrm{out}},A)$ to be both confident and consistent with respect to different outside data $X_{\mathrm{out}}$ . + +In summary, our proposed SSL framework in Eq. (5) encourages the segmentation model to make confident and consistent predictions at a predefined area, regardless of the data outside the area. The predefined area set $A$ determines the "strength" of the prior. When setting $A$ to the full area (i.e., the whole point cloud), our framework degrades to the classic entropy minimization framework [16]. + +Implementation. There are three key steps for implementing our framework: + +- Step 1): Select a proper partition set $A$ which maintains strong spatial prior; +- Step 2): Efficiently compute the marginal probability, i.e., $P(Y_{\mathrm{in}}|X_{\mathrm{in}},A)$ ; +- Step 3): Efficiently minimize the marginal entropy, i.e., $\hat{H}(Y_{\mathrm{in}}|X_{\mathrm{in}},A)$ . + +We propose a simple yet effective implementation following these steps in the next section. + +# 3.2. LaserMix + +Partition. LiDAR sensors have a fixed number (e.g., 32, 64, and 128) of laser beams which are emitted isotropically around the ego-vehicle with predefined inclination angles as shown in Fig. 2. To obtain a proper set of spatial areas $A$ , we propose to partition the LiDAR point cloud based on laser beams. Specifically, points captured by the same laser beam have a unified inclination angle to the sensor plane. For point $i$ , its inclination $\phi_i$ is defined as follows: + +$$ +\phi_ {i} = \arctan \left(\frac {p _ {i} ^ {z}}{\sqrt {\left(p _ {i} ^ {x}\right) ^ {2} + \left(p _ {i} ^ {y}\right) ^ {2}}}\right), \tag {6} +$$ + +where $(p^x,p^y,p^z)$ is the Cartesian coordinates of the LiDAR points. Given two LiDAR scans $x_{1}$ and $x_{2}$ , we first group all points from each scan by their inclination angles. Concretely, to form $m$ non-overlapping areas, a set of $m + 1$ inclination angles $\Phi = \{\phi_0,\phi_1,\phi_2,\dots,\phi_m\}$ will be evenly sampled within the range of the minimum and maximum inclination angles in the dataset (defined by sensor configurations), and the area set $A = \{a_{1},a_{2},\ldots,a_{m}\}$ can be formed by bounding area $a_{i}$ in the inclination range $[\phi_{i - 1},\phi_i)$ . + +Role in our framework: Laser partition effectively "excites" a strong spatial prior in the LiDAR point cloud, as described by Step 1 in our framework. As shown in Fig. 1 (left), we find an overt pattern in semantic classes detected by each laser beam. More concrete evidence on this aspect has been included in the Appendix. Despite being an empirical choice, we will show in later sections that laser partition significantly outperforms other partition choices, including random points (MixUp-like partition [54]), random areas (CutMix-like partition [53]), and other heuristics like azimuth $\alpha$ (sensor horizontal direction) or radius $r$ (sensor range direction) partitions. + +Mixing. To this end, we propose LaserMix, a simple yet effective LiDAR mixing strategy that can better control the "strength" of the spatial prior. LaserMix mixes the aforementioned laser partitioned areas $A$ from two scans in an intertwining way, i.e., one takes from odd-indexed areas $A_{1} = \{a_{1},a_{3},\ldots \}$ and the other takes from even-indexed areas $A_{2} = \{a_{2},a_{4},\ldots \}$ , so that each area's neighbor will be from the other scan: + +$$ +\tilde {x} _ {1}, \tilde {x} _ {2} = \operatorname {L a s e r M i x} \left(x _ {1}, x _ {2}\right), +$$ + +$$ +\tilde {x} _ {1} = x _ {1} ^ {a _ {1}} \cup x _ {2} ^ {a _ {2}} \cup x _ {1} ^ {a _ {3}} \cup \dots , \tag {7} +$$ + +$$ +\tilde {x} _ {2} = x _ {2} ^ {a _ {1}} \cup x _ {1} ^ {a _ {2}} \cup x _ {2} ^ {a _ {3}} \cup \dots , +$$ + +where $x_{i}^{a_{j}}$ is the data crop of $x_{i}$ in the area $a_{j}$ . The semantic labels are mixed in the same way. LaserMix is directly applied to the point clouds and is thus agnostic to the various LiDAR representations [19, 32, 56, 58]. We show LaserMix's instantiations with the range view and voxel representations as in Fig. 1 (middle), since they are currently the most efficient and the best-performing options, respectively. + +Role in our framework: LaserMix helps to efficiently compute the marginal probability $P(Y_{\mathrm{in}}|X_{\mathrm{in}},A)$ , as described by Step 2 in our framework. The cost for directly computing the marginal probability in Eq. (4) on real-world LiDAR data is prohibitive; we need to iterate through all areas in $A$ and all outside data in $X_{\mathrm{out}}$ , which requires $|A|\cdot |X_{\mathrm{out}}|$ predictions in total. To reduce the training overhead, we take advantage of the fact that a prediction in an area will be largely affected by its neighboring areas and let $X_{\mathrm{out}}$ fill only the neighbors instead of all the remaining areas. LaserMix mixes two scans by intertwining the areas so that the neighbors of each area are filled with data from the other scan. As a result, we obtain the prediction on + +![](images/c10b229c12476492fd4ae3f300ce19973e52045f873c3b9241bdde5a974f60cf.jpg) +Figure 2. Laser partition example. We group LiDAR points $(p_i^x, p_i^y, p_i^z)$ whose inclinations $\phi_i$ are within the same inclination range into the same area, as depicted in the color regions. + +all areas $A$ of two scans from only two predictions, which on average reduces the cost from $|A|$ to 1. The scan before and after mixing counts as two data fillings, therefore $|X_{\mathrm{out}}| = 2$ . Overall, the training overhead is reduced from $|A|\cdot |X_{\mathrm{out}}|$ to 2: only one prediction on original data and one additional prediction on mixed data are required for each LiDAR scan. During training, the memory consumption for a batch will be $2\times$ compared to a standard SSL framework, and the training speed will not be affected. + +# 3.3. Overall Pipeline + +We show the overall framework in Fig. 3 and the pseudocode in Algo. 1. There are two branches in our pipeline, one Student net $\mathcal{G}_{\theta}^{s}$ and one Teacher net $\mathcal{G}_{\theta}^{t}$ . During training, a batch is composed of half labeled data and half unlabeled data. We collect the predictions from both $\mathcal{G}_{\theta}^{s}$ and $\mathcal{G}_{\theta}^{t}$ , and produce pseudo-labels from Teacher net's prediction with a predefined confidence threshold $T$ . For labeled data, we compute the cross-entropy loss between the Student net's prediction and the ground-truth as $\mathcal{L}_{\mathrm{sup}}$ . For unlabeled data, LaserMix blends every scan with a random labeled scan, together with their pseudo-label or ground-truth. Then, we let $\mathcal{G}_{\theta}^{s}$ predict on the mixed data and compute the cross-entropy loss $\mathcal{L}_{\mathrm{mix}}$ ( $w/$ mixed labels). The point-wise cross-entropy loss for a scan $x$ and its corresponding ground-truth/pseudolabel $y$ on the segmentation net $\mathcal{G}_{\theta}$ is defined as: + +$$ +\mathcal {L} _ {\mathrm {c e}} = \frac {1}{| x |} \sum_ {i = 1} ^ {| x |} \operatorname {C r o s s E n t r o p y} \left(y ^ {(i)}, \mathcal {G} _ {\theta} ^ {(i)} (x)\right), \tag {8} +$$ + +where $(i)$ denotes the $i$ -th point. Moreover, we adopt the mean teacher idea in [45] and use Exponential Moving Average (EMA) to update the weights of $\mathcal{G}_{\theta}^{t}$ from $\mathcal{G}_{\theta}^{s}$ , and com + +![](images/4a95c87655788b65571e5a72f6d72de8246008d3a46325feeb809ff83d358976.jpg) +Figure 3. Framework overview. The labeled scan $x_{l}$ is fed into the Student net to compute the supervised loss $\mathcal{L}_{\mathrm{sup}}$ ( $w/$ ground-truth $y_{l}$ ). The unlabeled scan $x_{u}$ and the generated pseudo-label $y_{u}$ are mixed with $(x_{l},y_{l})$ via LaserMix (Sec. 3.2) to produce mixed data sample $(x_{\mathrm{mix}},y_{\mathrm{mix}})$ , which is then fed into the Student net to compute the mixing loss $\mathcal{L}_{\mathrm{mix}}$ . Additionally, we adopt the EMA update in [45] for the Teacher net and compute the mean teacher loss $\mathcal{L}_{\mathrm{mt}}$ over Student net's and Teacher net's predictions. + +pute the L2 loss between their predictions as $\mathcal{L}_{\mathrm{mt}}$ + +$$ +\mathcal {L} _ {\mathrm {m t}} = \left| \left| \mathcal {G} _ {\theta} ^ {s} (x) - \mathcal {G} _ {\theta} ^ {t} (x) \right| \right| _ {2} ^ {2}, \tag {9} +$$ + +where $||\cdot ||_2^2$ is the L2 norm. The overall loss function is $\mathcal{L} = \mathcal{L}_{\mathrm{sup}} + \lambda_{\mathrm{mix}}\mathcal{L}_{\mathrm{mix}} + \lambda_{\mathrm{mt}}\mathcal{L}_{\mathrm{mt}}$ , where $\lambda_{\mathrm{mix}}$ and $\lambda_{\mathrm{mt}}$ are loss weights. We use the Teacher net during inference as it empirically gives more stable results. There will be no extra inference overhead in our framework. + +Role in our framework: Our overall pipeline minimizes the marginal entropy, as described by Step 3 in our framework. Since the objective for minimizing the entropy has a hard optimization landscape, pseudo-labeling is a common resort in practice [25]. Unlike conventional pseudo-label optimization in SSL which only aims to encourage the predictions to be confident, minimizing the marginal entropy requires all predictions to be both confident and consistent. Therefore, we use the ground-truth and pseudo-label as an anchor and encourage the model's predictions to be confident and consistent with these supervision signals. + +# 4. Experiments + +# 4.1. Settings + +Protocol. We follow the Realistic Evaluation Protocol [35] when building the benchmark. Specifically, all experiments share the same backbones and are within the same codebase. All configurations and augmentations are unified to ensure a fair comparison among different SSL algorithms. + +Data. We build three SSL benchmarks upon nuScenes [11], SemanticKITTI [1], and ScribbleKITTI [47]. nuScenes [11] and SemanticKITTI [1] are the two most popular LiDAR segmentation datasets, with 29130 and 19130 training scans and 6019 and 4071 validation scans, respectively. + +Algorithm 1 Pseudo-code for one training iteration. +1: Input: Shuffled labeled batch $(X_{l},Y_{l}) = \{(x_{l}^{(b)},y_{l}^{(b)});b\in$ $(1,\dots ,B)\}$ , shuffled unlabeled batch $X_{u} = \{x_{u}^{(b)};b\in$ $(1,\dots ,B)\}$ , threshold $T$ , loss weights $\lambda_{\mathrm{mix}}$ and $\lambda_{\mathrm{mt}}$ , Student net and Teacher net. +2: for $b = 1$ to $B$ do +3: $x_{\mathrm{mix}}^{(2b - 1)},x_{\mathrm{mix}}^{(2b)} = \mathrm{LaserMix}(x_l^{(b)},x_u^{(b)}) / /$ LaserMix data +4: end for +5: $X_{\mathrm{mix}} = \{x_{\mathrm{mix}}^{(i)};i\in (1,\dots ,2B)\}$ +6: $S_{l},S_{u},S_{\mathrm{mix}} =$ Student $\big(\mathrm{Concat}(X_l,X_u,X_{\mathrm{mix}})\big)$ //Student pred +7: $\hat{S}_l,\hat{S}_u =$ Teacher $\big(\mathrm{Concat}(X_l,X_u)\big)$ //Teacher pred +8: $Y_{u} =$ PseudoLabel $(\hat{S}_u,T)$ //Pseudo-label generation process +9: for $b = 1$ to $B$ do +10: $y_{\mathrm{mix}}^{(2b - 1)},y_{\mathrm{mix}}^{(2b)} = \mathrm{LaserMix}(y_l^{(b)},y_u^{(b)}) / /$ LaserMix label +11: end for +12: $Y_{\mathrm{mix}} = \{y_{\mathrm{mix}}^{(i)};i\in (1,\dots ,2B)\}$ +13: $L_{\mathrm{sup}} =$ CrossEntropy $(S_l,Y_l)$ // Supervised loss +14: $L_{\mathrm{mix}} =$ CrossEntropy $(S_{\mathrm{mix}},Y_{\mathrm{mix}})$ // Mixing loss +15: $L_{\mathrm{mt}} = L2\big(\mathrm{Concat}(S_l,S_u),\mathrm{Concat}(\hat{S}_l,\hat{S}_u)\big)$ //MeanTeacher loss +16: $L = L_{\mathrm{sup}} + \lambda_{\mathrm{mix}}L_{\mathrm{mix}} + \lambda_{\mathrm{mt}}L_{\mathrm{mt}}$ //Overall loss +17: Backward(L), Update(Student), UpdateEMA(Teacher) + +ScribbleKITTI [47] is a recent variant of SemanticKITTI [1], which contains the same number of scans but is annotated with line scribbles (approximately $8.06\%$ valid semantic labels) rather than dense annotations. For all three LiDAR segmentation datasets, we uniformly sample $1\%$ , $10\%$ , $20\%$ , and $50\%$ labeled training scans and assume the remaining ones as unlabeled. This is in line with the conventional settings from the semi-supervised image segmentation community [6, 21, 37]. We also conduct experiments with sequential splits and show the results in the Appendix. Implementation Details. We adopt FIDNet [57] and Cylinder3D [58] as the segmentation backbones for the range + +Table 1. Benchmarking results among different SSL methods with the LiDAR range view (top) and voxel (bottom) representations. All mIoU scores are given in percentage (\%). The best and second best score for each data split is highlighted in bold and underline. + +
Repr.MethodnuScenes [11]SemanticKITTI [1]ScribbleKITTI [47]
1%10%20%50%1%10%20%50%1%10%20%50%
Range ViewSup.-only38.357.562.767.636.252.255.957.233.147.749.952.5
MeanTeacher [45]42.160.465.469.437.553.156.157.434.249.851.653.3
CBST [59]40.960.564.369.339.953.456.156.935.750.752.754.6
CutMix-Seg [12]43.863.964.869.837.454.356.657.636.750.752.954.3
CPS [6]40.760.864.968.036.552.356.357.433.750.052.854.6
LaserMix (Ours)49.568.270.673.043.458.859.461.438.354.455.658.7
Δ↑+11.2+10.7+7.9+5.4+7.2+6.6+3.5+4.2+5.2+6.7+5.7+6.2
VoxelSup.-only50.965.966.671.245.456.157.858.739.248.052.153.8
MeanTeacher [45]51.666.067.171.745.457.159.260.041.050.152.853.9
CBST [59]53.066.569.671.648.858.359.459.741.550.653.354.5
CPS [6]52.966.370.072.546.758.759.660.541.451.853.954.8
LaserMix (Ours)55.369.971.873.250.660.061.962.344.253.755.156.8
Δ↑+4.4+4.0+5.2+2.0+5.2+3.9+4.1+3.6+5.0+5.7+3.0+3.0
+ +Table 2. Comparison to the state-of-the-art 3D SSL method [20] on the val set of SemanticKITTI [1]. All mIoU scores are given in percentage $(\%)$ . + +
Method5%10%20%30%40%
GPC [20]41.849.958.859.459.9
Ours (RV)54.658.859.460.160.8
Δ↑+12.8+8.9+0.6+0.7+0.9
Ours (Voxel)56.760.061.962.162.3
Δ↑+14.9+10.1+3.1+1.7+1.4
+ +Table 3. Ablation results on the val set of nuScenes [11]. (1) Baseline results [45]; (2) Results with Student net supervision (SS); (3) Results with Teacher net supervision (TS). All mIoU scores are given in percentage $(\%)$ . + +
#\( {\mathcal{L}}_{\text{mt }} \)\( {\mathcal{L}}_{\text{mix }} \)SSTS1%10%20%50%
(1)✓42.160.465.469.4
(2)✓✓45.6(+3.5)64.3(+3.9)67.8(+2.4)71.6(+2.2)
✓✓✓47.0(+4.9)65.5(+5.1)69.5(+4.1)72.0(+2.6)
(3)✓✓46.0(+3.9)64.1(+3.7)69.5(+4.1)72.3(+2.9)
✓✓✓49.5(+7.4)68.2(+7.8)70.6(+5.2)73.0(+3.6)
+ +view and the voxel options, respectively. The input resolution of range images is set as $64 \times 2048$ for SemanticKITTI [1] and ScribbleKITTI [47], and $32 \times 1920$ for nuScenes [11]. The voxel resolution is fixed as [240, 180, 20] for all three sets. The number of spatial areas $m$ in LaserMix is uniformly sampled from 2 to 6 areas. We denote the supervised-only baseline as sup.-only. Due to the lack of Li-DAR SSL works [20], we also compare SoTA consistency regularization [6, 12, 45] and entropy minimization [59] methods from semi-supervised image segmentation. We report the intersection-over-union (IoU) over each semantic class and the mean IoU (mIoU) scores over all classes in our benchmarks. All experiments are implemented using PyTorch on NVIDIA Tesla V100 GPUs with 32GB RAM. + +# 4.2. Comparative Study + +Improvements over Baseline. Tab. 1 benchmarks results on nuScenes [11], SemanticKITTI [1], and ScribbleKITTI [47]. For all three sets under different data splits, we observe significant improvements in our approach over the sup.-only baseline. Such gains are especially evident in range view, which reach up to $11.2\%$ mIoU. We also observe constant improvements for the voxel option, which provide on average $4.1\%$ mIoU gains over all splits across all sets. The results verify the effectiveness of our frame- + +work and further highlight the importance of leveraging unlabeled data in LiDAR semantic segmentation. + +Compare with SoTA. We compare LaserMix with $\mathrm{GPC}^2$ [20], the SoTA 3D SSL method tested on SemanticKITTI [1]. The results in Tab. 2 show that our approach exhibits much better results than GPC [20], especially in scenarios where very few annotations are available. We also reimplemented popular SSL algorithms from the image segmentation domain and show their results in Tab. 1. We find that these methods, albeit competitive in 2D, only yield sub-par performance in the LiDAR SSL benchmark, highlighting the importance of exploiting the LiDAR data structure. + +Compare with Full Labels. As shown in Fig. 1 (right), the comparisons between the prevailing LiDAR segmentation methods attests that our approach can achieve more competitive scores over the fully-supervised counterparts [5, 8, 32, 56] while with $2 \times$ to $5 \times$ fewer annotations. The strong augmentation and regularization ability of LaserMix have yielded better results in the high-data regime and extreme low-data regime (i.e., $0.8\%$ labels on [47]), which validates the generalizability of our approach. + +Qualitative Examination. Fig. 5 visualizes the scene segmentation results for different SSL algorithms on the val + +![](images/03c3f253dd1454a7e84af6443bb7d33afe021d8eb15a4e17a4b6de39b529dcb6.jpg) +Figure 4. Ablation studies on: Left: Different mixing-based techniques used in point partition & mixing; Middle: Different EMA decay rates between the Teacher net and the Student net; Right: Different confidence thresholds $T$ used in the pseudo-label generation. + +![](images/6877d8b02fbd4dbcf09e2320e04373d0fc8d7583d3cbb6bf69f1e118d062c853.jpg) + +![](images/ae96b550fc093755d4eb28a4306a89c713c14c0f6e54593b2c1272d24d50341f.jpg) + +set of nuScenes [11], where each example covers a driving scene centered by the ego-vehicle. We find that previous arts [6, 45, 59] can only improve predictions in limited regions, while our approach holistically eliminates false predictions in almost every direction around the ego-vehicle. The consistency enlightened by LaserMix has yielded better segmentation accuracy under annotation scarcity. + +# 4.3. Ablation Study + +Without loss of generalizability, we stick with the $10\%$ budget setting and range view backbones in our ablations. + +Framework Setups. The component analysis in Tab. 3 shows that $\mathcal{L}_{\mathrm{mix}}$ contributes significantly to the overall improvement. Meanwhile, using the Teacher net instead of the Student net to generate pseudo-labels leads to better results, as the formal is temporally ensembled and encourages consistency in-between mixed and original data, which is crucial besides enforcing confident predictions. It is worth noting that all of our model configurations have achieved superior results than the baseline MeanTeacher [45], which further emphasizes the effectiveness of our framework in tackling LiDAR segmentation with semi-supervisions. + +Mixing Strategies. Fig. 4 (left) compares LaserMix with other mixing methods [10, 33, 53, 54]. MixUp and CutMix can be considered as setting $A$ to random points and random areas, respectively. We observe that MixUp has no improvements over the baseline on average since there is no distribution pattern in random points. CutMix has a considerable improvement over the baseline, as there is always a structure prior in scene segmentation, i.e., the same semantic class points tend to cluster, which reduces the entropy in any continuous area. This prior is often used in image semantic segmentation SSL [12]. However, our spatial prior is much stronger, where not only the area structure but also the area's spatial position has been considered. LaserMix outperforms CutMix by a large margin (up to $3.3\%$ mIoU) on all sets. CutOut can be considered as setting $X_{\mathrm{out}}$ to + +Table 4. Ablation studies on laser beam partitions (horizontal: inclination direction $\phi$ ; vertical: azimuth direction $\alpha$ ). $(i - \alpha, j - \phi)$ denotes that there are $i$ azimuth and $j$ inclination partitions. + +
Baseline(1α, 2φ)(1α, 3φ)(1α, 4φ)(1α, 5φ)(1α, 6φ)
60.463.5(+3.1)65.2(+4.8)66.5(+6.1)66.2(+5.8)65.4(+5.0)
(2α, 1φ)(2α, 2φ)(2α, 3φ)(2α, 4φ)(2α, 5φ)(2α, 6φ)
61.5(+1.1)63.3(+2.9)65.9(+5.5)66.1(+5.7)66.7(+6.3)65.3(+4.9)
(3α, 1φ)(3α, 2φ)(3α, 3φ)(3α, 4φ)(3α, 5φ)(3α, 6φ)
60.9(+0.6)64.2(+3.8)65.9(+5.5)66.3(+5.9)66.0(+5.6)65.2(+4.8)
(4α, 1φ)(4α, 2φ)(4α, 3φ)(4α, 4φ)(4α, 5φ)(4α, 6φ)
60.9(+0.6)64.7(+4.3)65.3(+4.9)65.6(+5.2)65.7(+5.3)65.2(+4.8)
+ +a dummy filling instead of sampling from datasets, and it leads to a considerable performance drop from CutMix. + +Orderless Mix. We revert the area ordering (i.e., put the topmost laser beam at the bottom, and vice versa) in LaserMix, and the performance drops from $68.2\%$ to $64.4\%$ $(-3.8\% \mathrm{mIoU})$ . When we shuffle the ordering, the performance drops to $63.8\%$ $(-4.4\% \mathrm{mIoU})$ , which becomes comparable with CutMix. The results once again confirm the superiority of using spatial prior in LiDAR SSL. + +Other Heuristics. Besides our proposed inclination partition, the LiDAR scans can also be split based on azimuth (sensor horizontal direction). Results in Tab. 4 reveal that in contrast to laser partitioning, pure azimuth splitting (the + +![](images/e872031056d6d0e643bfc2a43801058638e75dda53d10ce7ddf7066bfee65090.jpg) + +![](images/ed6705a442c06e557f96d9701f1361d3566a7879302572cbe1873a039c8a7933.jpg) + +![](images/7b8d957025e533c74e35c0f24ec03c62cc9c54925d5edf7262992d32b3779587.jpg) + +![](images/a8554b59f6ea7b4a493196fbdf9aff1527814543526bf190bb773e227381d15e.jpg) + +![](images/8e5ec042d1f9591f55168dbde0c396bfb1f3c752f4c512440ff071381d567ffc.jpg) + +![](images/47d86b73a62475059b44ae3ca3b04a98e20eb961348c97ddd3977f0168edd425.jpg) + +![](images/6edcba58f651c94aa5819dc2c805fea3af88b2b01e652eb9b0fa6b64361b00af.jpg) +Figure 5. Error maps visualized from LiDAR bird's eye view and range view on nuScenes [11]. Each example shows a street scene of size $50\mathrm{m}$ by $50\mathrm{m}$ by $8\mathrm{m}$ . The correct and incorrect predictions are painted in green and red to highlight the differences. Best viewed in color. + +![](images/0aea44d0452284df8b3a5b5a2d20801c0f00e95729813c8af041fbc916c2c27f.jpg) + +![](images/4ad3201649ba28f64d5439285f02f3bad3432dcff9ec0857f8ebbd0bfd52d4a1.jpg) + +![](images/1660fe10ba3d0d9dbc26477b7e4ba3540bafc7a165b3c9cf9de3ccfb87729345.jpg) + +![](images/ca454577287bd03716d0184d29e5564bdaea904a2bad41dabb93cc56a92e365b.jpg) + +![](images/c0b98a8a14e617ac91471d4e316c7a302288912d8cbe8e493ab26504051f8029.jpg) + +first column) does not improve the performance, which is attributed to the fact that the semantic distribution has a weak correlation in the azimuth direction. We also observe that the results tend to improve as the mixing granularity increases (row direction in Tab. 4). The scores start to drop when the granularity is beyond a certain limit (e.g., the last two columns). We conjecture that over-fine-grained partition and mixing tend to hurt semantic coherence. + +Mix Unlabeled Data Only. To verify that our method is more than trivially augmenting seen data and label pairs, we apply LaserMix only on unlabeled data. Instead of mixing an unlabeled scan with a labeled scan as described in Sec. 3.3, we mix two unlabeled scans with their pseudolabels. The score drops from $68.2\%$ to $66.9\%$ $(-1.3\% \mathrm{mIoU})$ but still outperforms all existing methods by large margins. This verifies that LaserMix indeed brings a strong consistency regularization effect during SSL. + +EMA. Fig. 4 (middle) provides results with different EMA decay rates, Typically, a rate between 0.9 and 0.99 yields the best possible results. Large rates like 0.999 tend to hurt the consistency between the two networks. The results also verify that the teacher-student pipeline [45] has good synergy with our proposed SSL framework. Thanks to this simplicity, more modern SSL techniques can be easily incorporated into the current framework in future works. + +Confidence Threshold. As pseudo-labels play an important role in our framework, we further analyze the impact of the threshold parameter $T$ used in pseudo-label generation and show results in Fig. 4 (right). When $T$ is too low, + +a forced consistency to low-quality pseudo-labels tends to deteriorate the performance. When $T$ is too high, the benefits from mixing might diminish. Generally, $T$ is a dataset-dependent parameter and we find that a value around 0.9 leads to the best possible results on the three tested LiDAR segmentation datasets [1, 11, 47] in our benchmark. + +# 5. Conclusion + +In this work, we exploit the unique spatial prior in LiDAR scenes for semi-supervised LiDAR semantic segmentation. We proposed a statistically-principled and effective SSL pipeline, including LaserMix, a novel LiDAR mixing technique that intertwines laser beams from different scans. Through comprehensive empirical analysis, we show the importance of spatial prior and the superiority of our approach on three popular benchmarks. The effectiveness and simplicity of our framework have shed light on the scalable deployment of the LiDAR semantic mapping system. + +Acknowledgments. This study is supported by the Ministry of Education, Singapore, under its MOE AcRF Tier 2 (MOET2EP20221-0012), the National Research Foundation, Singapore under its AI Singapore Programme (AISG Award No: AISG2-PhD-2021-08-018), NTU NAP, and under the RIE2020 Industry Alignment Fund - Industry Collaboration Projects (IAF-ICP) Funding Initiative, as well as cash and in-kind contribution from the industry partner(s). 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Left: The LiDAR point cloud contains strong spatial prior. Objects and backgrounds around the ego-vehicle have a patterned distribution on different (lower, middle, upper) laser beams. Middle: Following the scene structure, the proposed LaserMix blends beams from different LiDAR scans, which is compatible with various popular LiDAR representations. Right: We achieve superior results over SoTA methods in both low-data (10%, 20%, and 50% semantic labels) and high-data (full semantic labels) regimes on nuScenes [11]." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 372, + 211, + 545, + 392 + ], + "blocks": [ + { + "bbox": [ + 372, + 211, + 545, + 392 + ], + "lines": [ + { + "bbox": [ + 372, + 211, + 545, + 392 + ], + "spans": [ + { + "bbox": [ + 372, + 211, + 545, + 392 + ], + "type": "image", + "image_path": "4d8f2bd6eaf8ca4f96cbc1797b099540f661c6f507dcfb5a77daf3ab29cee36b.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + } + ], + "index": 17 + }, + { + "bbox": [ + 143, + 472, + 192, + 484 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 472, + 192, + 484 + ], + "spans": [ + { + "bbox": [ + 143, + 472, + 192, + 484 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 46, + 494, + 288, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 494, + 288, + 685 + ], + "spans": [ + { + "bbox": [ + 46, + 494, + 288, + 685 + ], + "type": "text", + "content": "Densely annotating LiDAR point clouds is costly, which often restrains the scalability of fully-supervised learning methods. In this work, we study the underexplored semi-supervised learning (SSL) in LiDAR semantic segmentation. Our core idea is to leverage the strong spatial cues of LiDAR point clouds to better exploit unlabeled data. We propose LaserMix to mix laser beams from different LiDAR scans and then encourage the model to make consistent and confident predictions before and after mixing. Our framework has three appealing properties. 1) Generic: LaserMix is agnostic to LiDAR representations (e.g., range view and voxel), and hence our SSL framework can be universally applied. 2) Statistically grounded: We provide a detailed analysis to theoretically explain the applicability of the proposed framework. 3) Effective: Comprehensive experimental analysis on popular LiDAR segmentation" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 461, + 547, + 558 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 461, + 547, + 558 + ], + "spans": [ + { + "bbox": [ + 304, + 461, + 547, + 558 + ], + "type": "text", + "content": "datasets (nuScenes, SemanticKITTI, and ScribbleKITTI) demonstrates our effectiveness and superiority. Notably, we achieve competitive results over fully-supervised counterparts with " + }, + { + "bbox": [ + 304, + 461, + 547, + 558 + ], + "type": "inline_equation", + "content": "2 \\times" + }, + { + "bbox": [ + 304, + 461, + 547, + 558 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 461, + 547, + 558 + ], + "type": "inline_equation", + "content": "5 \\times" + }, + { + "bbox": [ + 304, + 461, + 547, + 558 + ], + "type": "text", + "content": " fewer labels and improve the supervised-only baseline significantly by relatively " + }, + { + "bbox": [ + 304, + 461, + 547, + 558 + ], + "type": "inline_equation", + "content": "10.8\\%" + }, + { + "bbox": [ + 304, + 461, + 547, + 558 + ], + "type": "text", + "content": ". We hope this concise yet high-performing framework could facilitate future research in semi-supervised LiDAR segmentation. Code is publicly available1." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 306, + 569, + 387, + 582 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 569, + 387, + 582 + ], + "spans": [ + { + "bbox": [ + 306, + 569, + 387, + 582 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 589, + 547, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 589, + 547, + 696 + ], + "spans": [ + { + "bbox": [ + 304, + 589, + 547, + 696 + ], + "type": "text", + "content": "LiDAR segmentation is one of the fundamental tasks in autonomous driving perception [41]. It enables autonomous vehicles to semantically perceive the dense 3D structure of the surrounding scenes [15, 34, 39]. However, densely annotating LiDAR point clouds is inevitably expensive and labor-intensive [18, 23, 47], which restrains the scalability of fully-supervised LiDAR segmentation methods. Semisupervised learning (SSL) that directly leverages the easy-to-acquire unlabeled data is hence a viable and promising" + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 38 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 38 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 38 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 693, + 288, + 714 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 693, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 693, + 288, + 714 + ], + "type": "text", + "content": "(*) Lingdong and Jiawei contributed equally to this work. (☑) Ziwei serves as the corresponding author. E-mail: ziwei.liu@ntu.edu.sg." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 317, + 703, + 508, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 703, + 508, + 713 + ], + "spans": [ + { + "bbox": [ + 317, + 703, + 508, + 713 + ], + "type": "text", + "content": "1https://github.com/ldkong1205/LaserMix." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "21705" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 284, + 85 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 284, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 284, + 85 + ], + "type": "text", + "content": "solution to achieve scalable LiDAR segmentation [13, 14]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 85, + 287, + 217 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 85, + 287, + 217 + ], + "spans": [ + { + "bbox": [ + 46, + 85, + 287, + 217 + ], + "type": "text", + "content": "Yet, semi-supervised LiDAR segmentation is still under-explored. Modern SSL frameworks are mainly designed for image recognition [2, 3, 42] and semantic segmentation [6, 21, 37] tasks, which only yield sub-par performance on LiDAR data due to the large modality gap between 2D and 3D. Recent research [20] proposed to consider semi-supervised point cloud semantic segmentation as a fresh task and proposed a point contrastive learning framework. However, their solutions do not differentiate indoor and outdoor scenes and therefore overlook the intrinsic and important properties that only exist in LiDAR point clouds." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 218, + 288, + 410 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 218, + 288, + 410 + ], + "spans": [ + { + "bbox": [ + 46, + 218, + 288, + 410 + ], + "type": "text", + "content": "In this work, we explore the use of spatial prior for semi-supervised LiDAR segmentation. Unlike the general 2D/3D segmentation tasks, the spatial cues are especially significant in LiDAR data. In fact, LiDAR point clouds serve as a perfect reflection of real-world distributions, which is highly dependent on the spatial areas in the LiDAR-centered 3D coordinates. As shown in Fig. 1 (left), the top laser beams travel outward long distance and perceive mostly vegetation, while the middle and bottom beams tend to detect car and road from the medium and close distances, respectively. To effectively leverage this strong spatial prior, we propose LaserMix to mix laser beams from different LiDAR scans, and then encourage the LiDAR segmentation model to make consistent and confident predictions before and after mixing. Our SSL framework is statistically grounded, which consists of the following components:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 411, + 287, + 545 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 47, + 411, + 287, + 446 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 411, + 287, + 446 + ], + "spans": [ + { + "bbox": [ + 47, + 411, + 287, + 446 + ], + "type": "text", + "content": "1) Partitioning the LiDAR scan into low-variation areas. We observe a strong distribution pattern on laser beams as shown in Fig. 1 (left) and thus propose the laser partition." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 448, + 287, + 508 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 448, + 287, + 508 + ], + "spans": [ + { + "bbox": [ + 46, + 448, + 287, + 508 + ], + "type": "text", + "content": "2) Efficiently mixing every area in the scan with foreign data and obtaining model predictions. We propose LaserMix to manipulate the laser-grouped areas from two LiDAR scans in an intertwining way as depicted in Fig. 1 (middle) and serves as an efficient LiDAR mixing strategy for SSL." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 509, + 287, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 509, + 287, + 545 + ], + "spans": [ + { + "bbox": [ + 46, + 509, + 287, + 545 + ], + "type": "text", + "content": "3) Encouraging models to make confident and consistent predictions on the same area in different mixing. We hence propose a mixing-based teacher-student training pipeline." + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 46, + 546, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 546, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 546, + 288, + 714 + ], + "type": "text", + "content": "Despite the simplicity of our overall pipeline, it achieves competitive results over the fully supervised counterpart using " + }, + { + "bbox": [ + 46, + 546, + 288, + 714 + ], + "type": "inline_equation", + "content": "2 \\times" + }, + { + "bbox": [ + 46, + 546, + 288, + 714 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 546, + 288, + 714 + ], + "type": "inline_equation", + "content": "5 \\times" + }, + { + "bbox": [ + 46, + 546, + 288, + 714 + ], + "type": "text", + "content": " fewer labels as shown in Fig. 1 (right) and significantly outperforms all prevailing semi-supervised segmentation methods on nuScenes [11] (up to " + }, + { + "bbox": [ + 46, + 546, + 288, + 714 + ], + "type": "inline_equation", + "content": "+5.7\\%" + }, + { + "bbox": [ + 46, + 546, + 288, + 714 + ], + "type": "text", + "content": " mIoU) and SemanticKITTI [1] (up to " + }, + { + "bbox": [ + 46, + 546, + 288, + 714 + ], + "type": "inline_equation", + "content": "+3.5\\%" + }, + { + "bbox": [ + 46, + 546, + 288, + 714 + ], + "type": "text", + "content": " mIoU). Moreover, LaserMix directly operates on point clouds so as to be agnostic to different LiDAR representations, e.g., range view [32] and voxel [58]. Therefore, our pipeline is highly compatible with existing state-of-the-art (SoTA) LiDAR segmentation methods under various representations [46, 56, 57]. Besides, our pipeline achieves competitive performance using very limited annotations on weak supervision dataset [47]: it achieves " + }, + { + "bbox": [ + 46, + 546, + 288, + 714 + ], + "type": "inline_equation", + "content": "54.4\\%" + }, + { + "bbox": [ + 46, + 546, + 288, + 714 + ], + "type": "text", + "content": " mIoU on Se" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": "manticKITTI [1] using only " + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "inline_equation", + "content": "0.8\\%" + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": " labels, which is on-par with PolarNet [56] " + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "inline_equation", + "content": "(54.3\\%)" + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": ", RandLA-Net [19] " + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "inline_equation", + "content": "(53.9\\%)" + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": ", and RangeNet++ [32] " + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "inline_equation", + "content": "(52.2\\%)" + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": " using " + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": " labels. Spatial prior is proven to play a pivotal role in the success of our framework through comprehensive empirical analysis. To summarize, this work has the following key contributions:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 317, + 145, + 545, + 270 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 317, + 145, + 545, + 182 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 145, + 545, + 182 + ], + "spans": [ + { + "bbox": [ + 317, + 145, + 545, + 182 + ], + "type": "text", + "content": "- We present a statistically grounded SSL framework that effectively leverages the spatial cues in LiDAR data to facilitate learning with semi-supervisions." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 317, + 183, + 545, + 219 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 183, + 545, + 219 + ], + "spans": [ + { + "bbox": [ + 317, + 183, + 545, + 219 + ], + "type": "text", + "content": "- We propose LaserMix, a novel and representation-agnostic mixing technique that strives to maximize the \"strength\" of the spatial cues in our SSL framework." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 317, + 221, + 545, + 270 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 221, + 545, + 270 + ], + "spans": [ + { + "bbox": [ + 317, + 221, + 545, + 270 + ], + "type": "text", + "content": "- Our overall pipeline significantly outperforms previous SoTA methods in both low- and high-data regimes. We hope this work could lay a solid foundation for semi-supervised LiDAR segmentation." + } + ] + } + ], + "index": 11 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 274, + 392, + 288 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 274, + 392, + 288 + ], + "spans": [ + { + "bbox": [ + 306, + 274, + 392, + 288 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 294, + 545, + 450 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 294, + 545, + 450 + ], + "spans": [ + { + "bbox": [ + 304, + 294, + 545, + 450 + ], + "type": "text", + "content": "LiDAR Segmentation. Various approaches from different aspects have been proposed for LiDAR scene segmentation, i.e., range view [8, 32, 49, 57], bird's eye view [56], voxel [44, 58], and multi-view [26, 50] methods. Although appealing results have been achieved, these fully-supervised methods rely on large-scale annotated LiDAR datasets and their performance would degrade severely in the low-data regime [13]. Recent works seek weak [18, 55], scribble [47], and box [28] supervisions or activate learning [27, 31] to ease the annotation cost. We tackle this problem from the perspective of semi-supervised learning (SSL), aiming at directly leveraging the easy-to-acquire unlabeled data to boost the LiDAR semantic segmentation performance." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 450, + 545, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 450, + 545, + 629 + ], + "spans": [ + { + "bbox": [ + 304, + 450, + 545, + 629 + ], + "type": "text", + "content": "SSL in 2D. Well-known SSL algorithms are prevailing in handling image recognition problems [2, 3, 24, 42, 45]. In the context of semantic segmentation, CutMix-Seg [12] and PseudoSeg [60] apply perturbations on inputs and hope the decision boundary lies in the low-density region. CPS [6] and GCT [21] enforce consistency between two perturbed networks [29]. These perturbations [30, 36, 52], however, are either inapplicable or only yield sub-par results in 3D. Another line of research is entropy minimization. Methods like CBST [59] and " + }, + { + "bbox": [ + 304, + 450, + 545, + 629 + ], + "type": "inline_equation", + "content": "\\mathrm{ST} + +" + }, + { + "bbox": [ + 304, + 450, + 545, + 629 + ], + "type": "text", + "content": " [51] generate pseudo-labels [25] offline per round during self-training. The extra storage needed might become costly for large-scale LiDAR datasets [1, 4, 11]. Our framework encourages both consistency regularization and entropy minimization and does not require extra overhead, which better maintains scalability." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 630, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 545, + 714 + ], + "type": "text", + "content": "SSL in 3D. Most works focus on developing SSL for object-centric point clouds [22, 43] or indoor scenes [7, 9, 17, 34], whose scale and diversity are much lower than the outdoor LiDAR point clouds [1, 4]. Some other works [38, 40, 48] try to utilize SSL for 3D object detection on LiDAR data. A recent work [20] tackles semi-supervised point cloud semantic segmentation using contrastive learning, but it still" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "21706" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "type": "text", + "content": "mainly focused on indoor scenes and does not distinguish between the uniformly distributed indoor point clouds and the spatially structured LiDAR point clouds. We are one of the first works to explore SSL for LiDAR segmentation. Our work also establishes comprehensive SSL benchmarks upon popular autonomous driving databases [1, 11, 47]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 155, + 114, + 168 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 155, + 114, + 168 + ], + "spans": [ + { + "bbox": [ + 47, + 155, + 114, + 168 + ], + "type": "text", + "content": "3. Approach" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 174, + 287, + 259 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 174, + 287, + 259 + ], + "spans": [ + { + "bbox": [ + 46, + 174, + 287, + 259 + ], + "type": "text", + "content": "In this section, we first introduce our SSL framework that leverages the spatial prior of LiDAR data by encouraging confidence and consistency in predictions (Sec. 3.1). We then present LaserMix which strives to maximize the \"strength\" of the spatial prior and mixes LiDAR scans in an efficient manner (Sec. 3.2). Finally, we elaborate on the overall pipeline (Sec. 3.3) and the pseudo-code (Algo. 1)." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 265, + 242, + 277 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 265, + 242, + 277 + ], + "spans": [ + { + "bbox": [ + 47, + 265, + 242, + 277 + ], + "type": "text", + "content": "3.1. Leveraging the Spatial Prior for SSL" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 283, + 289, + 428 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 283, + 289, + 428 + ], + "spans": [ + { + "bbox": [ + 46, + 283, + 289, + 428 + ], + "type": "text", + "content": "Spatial Prior Formulation. The distribution of real-world objects/backgrounds has a strong correlation to their spatial positions in the LiDAR scan. Objects/backgrounds inside a specified spatial area of a LiDAR point cloud follow similar patterns, e.g., the close-range area is most likely road while the long-range area consists of building, vegetation, etc. In another word, there exists a spatial area " + }, + { + "bbox": [ + 46, + 283, + 289, + 428 + ], + "type": "inline_equation", + "content": "a \\in A" + }, + { + "bbox": [ + 46, + 283, + 289, + 428 + ], + "type": "text", + "content": " where LiDAR points and semantic labels inside the area (denoted as " + }, + { + "bbox": [ + 46, + 283, + 289, + 428 + ], + "type": "inline_equation", + "content": "X_{\\mathrm{in}}" + }, + { + "bbox": [ + 46, + 283, + 289, + 428 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 283, + 289, + 428 + ], + "type": "inline_equation", + "content": "Y_{\\mathrm{in}}" + }, + { + "bbox": [ + 46, + 283, + 289, + 428 + ], + "type": "text", + "content": ", respectively) will have relatively low variations. Formally, the conditional entropy " + }, + { + "bbox": [ + 46, + 283, + 289, + 428 + ], + "type": "inline_equation", + "content": "H(X_{\\mathrm{in}}, Y_{\\mathrm{in}}|A)" + }, + { + "bbox": [ + 46, + 283, + 289, + 428 + ], + "type": "text", + "content": " is smaller. Therefore, when estimating the parameter " + }, + { + "bbox": [ + 46, + 283, + 289, + 428 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 283, + 289, + 428 + ], + "type": "text", + "content": " of the segmentation network " + }, + { + "bbox": [ + 46, + 283, + 289, + 428 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{\\theta}" + }, + { + "bbox": [ + 46, + 283, + 289, + 428 + ], + "type": "text", + "content": ", we would expect:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 116, + 435, + 287, + 449 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 435, + 287, + 449 + ], + "spans": [ + { + "bbox": [ + 116, + 435, + 287, + 449 + ], + "type": "interline_equation", + "content": "\\mathbb {E} _ {\\theta} \\left[ H \\left(X _ {\\text {i n}}, Y _ {\\text {i n}} \\mid A\\right) \\right] = c, \\tag {1}", + "image_path": "b72a842fc458dea7dc07e9a1f4d91c95d5200b513c789a5fbb441a2b921e47a5.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 456, + 287, + 505 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 456, + 287, + 505 + ], + "spans": [ + { + "bbox": [ + 46, + 456, + 287, + 505 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 456, + 287, + 505 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 456, + 287, + 505 + ], + "type": "text", + "content": " is a small constant. Similar to the classic entropy minimization [16], the constraint in Eq. (1) can be converted to a prior on the model parameter " + }, + { + "bbox": [ + 46, + 456, + 287, + 505 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 456, + 287, + 505 + ], + "type": "text", + "content": " using the principle of maximum entropy:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 97, + 512, + 287, + 540 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 97, + 512, + 287, + 540 + ], + "spans": [ + { + "bbox": [ + 97, + 512, + 287, + 540 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} P (\\theta) \\propto \\exp (- \\lambda H (X _ {\\text {i n}}, Y _ {\\text {i n}} | A)) \\tag {2} \\\\ \\propto \\exp (- \\lambda H (Y _ {\\mathrm {i n}} | X _ {\\mathrm {i n}}, A)), \\\\ \\end{array}", + "image_path": "8f8982c894ce4f8c5236f32b689e31d3798fb9c1f58264c987d2a800c094f287.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 548, + 287, + 607 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 548, + 287, + 607 + ], + "spans": [ + { + "bbox": [ + 46, + 548, + 287, + 607 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 548, + 287, + 607 + ], + "type": "inline_equation", + "content": "\\lambda > 0" + }, + { + "bbox": [ + 46, + 548, + 287, + 607 + ], + "type": "text", + "content": " is the Lagrange multiplier corresponding to constant " + }, + { + "bbox": [ + 46, + 548, + 287, + 607 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 548, + 287, + 607 + ], + "type": "text", + "content": "; " + }, + { + "bbox": [ + 46, + 548, + 287, + 607 + ], + "type": "inline_equation", + "content": "H(X_{\\mathrm{in}}|A)" + }, + { + "bbox": [ + 46, + 548, + 287, + 607 + ], + "type": "text", + "content": " has been ignored for being independent of the model parameter " + }, + { + "bbox": [ + 46, + 548, + 287, + 607 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 548, + 287, + 607 + ], + "type": "text", + "content": ". We consider Eq. (2) as the formal formulation of the spatial prior and discuss how to empirically compute it in the following sections." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 607, + 287, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 607, + 287, + 643 + ], + "spans": [ + { + "bbox": [ + 46, + 607, + 287, + 643 + ], + "type": "text", + "content": "Marginalization. To utilize the spatial prior defined in Eq. (2), we empirically compute the entropy " + }, + { + "bbox": [ + 46, + 607, + 287, + 643 + ], + "type": "inline_equation", + "content": "H(Y_{\\mathrm{in}}|X_{\\mathrm{in}},A)" + }, + { + "bbox": [ + 46, + 607, + 287, + 643 + ], + "type": "text", + "content": " of the LiDAR points inside area " + }, + { + "bbox": [ + 46, + 607, + 287, + 643 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 46, + 607, + 287, + 643 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 73, + 650, + 287, + 670 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 73, + 650, + 287, + 670 + ], + "spans": [ + { + "bbox": [ + 73, + 650, + 287, + 670 + ], + "type": "interline_equation", + "content": "\\hat {H} \\left(Y _ {\\text {i n}} \\mid X _ {\\text {i n}}, A\\right) = \\tag {3}", + "image_path": "6326f6d3ee06fef8367c407db755a90c0ce0a8e8311d7cea8682ef4221fdb013.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 73, + 668, + 261, + 683 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 73, + 668, + 261, + 683 + ], + "spans": [ + { + "bbox": [ + 73, + 668, + 261, + 683 + ], + "type": "interline_equation", + "content": "\\hat {\\mathbb {E}} _ {X _ {\\mathrm {i n}}, Y _ {\\mathrm {i n}}, A} \\big [ P (Y _ {\\mathrm {i n}} | X _ {\\mathrm {i n}}, A) \\log P (Y _ {\\mathrm {i n}} | X _ {\\mathrm {i n}}, A) \\big ],", + "image_path": "9bcd9b5e254bb79bfeecbf5abf3cc85d76278c87256bc44bfc6f23f5aa5fb061.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\hat{\\cdot}" + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "content": " denotes the empirical estimation. The end-to-end LiDAR segmentation model " + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{\\theta}" + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "content": " usually takes full-sized" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 72, + 545, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 133 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 133 + ], + "type": "text", + "content": "data as inputs during inference. Therefore, to compute " + }, + { + "bbox": [ + 305, + 72, + 545, + 133 + ], + "type": "inline_equation", + "content": "P(Y_{\\mathrm{in}}|X_{\\mathrm{in}},A)" + }, + { + "bbox": [ + 305, + 72, + 545, + 133 + ], + "type": "text", + "content": " in Eq. (3), we first pad the data outside the area to obtain the full-sized data. Here we denote the data outside the area as " + }, + { + "bbox": [ + 305, + 72, + 545, + 133 + ], + "type": "inline_equation", + "content": "X_{\\mathrm{out}}" + }, + { + "bbox": [ + 305, + 72, + 545, + 133 + ], + "type": "text", + "content": "; we then let the model infer " + }, + { + "bbox": [ + 305, + 72, + 545, + 133 + ], + "type": "inline_equation", + "content": "P(Y_{\\mathrm{in}}|X_{\\mathrm{in}},X_{\\mathrm{out}},A)" + }, + { + "bbox": [ + 305, + 72, + 545, + 133 + ], + "type": "text", + "content": ", and finally marginalize " + }, + { + "bbox": [ + 305, + 72, + 545, + 133 + ], + "type": "inline_equation", + "content": "X_{\\mathrm{out}}" + }, + { + "bbox": [ + 305, + 72, + 545, + 133 + ], + "type": "text", + "content": " as:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 330, + 138, + 545, + 153 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 330, + 138, + 545, + 153 + ], + "spans": [ + { + "bbox": [ + 330, + 138, + 545, + 153 + ], + "type": "interline_equation", + "content": "P \\left(Y _ {\\mathrm {i n}} \\mid X _ {\\mathrm {i n}}, A\\right) = \\hat {\\mathbb {E}} _ {X _ {\\mathrm {o u t}}} \\left[ P \\left(Y _ {\\mathrm {i n}} \\mid X _ {\\mathrm {i n}}, X _ {\\mathrm {o u t}}, A\\right) \\right]. \\quad (4)", + "image_path": "afbbd2b8c0fa98c640b0bb02c4734eca3d22efdb9b768b9d66e8bae27b35bd0b.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 158, + 545, + 182 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 158, + 545, + 182 + ], + "spans": [ + { + "bbox": [ + 304, + 158, + 545, + 182 + ], + "type": "text", + "content": "The generative distribution of the padding " + }, + { + "bbox": [ + 304, + 158, + 545, + 182 + ], + "type": "inline_equation", + "content": "P(X_{\\mathrm{out}})" + }, + { + "bbox": [ + 304, + 158, + 545, + 182 + ], + "type": "text", + "content": " can be directly obtained from the dataset." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 182, + 545, + 231 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 182, + 545, + 231 + ], + "spans": [ + { + "bbox": [ + 304, + 182, + 545, + 231 + ], + "type": "text", + "content": "Training. Finally, we train the segmentation model " + }, + { + "bbox": [ + 304, + 182, + 545, + 231 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{\\theta}" + }, + { + "bbox": [ + 304, + 182, + 545, + 231 + ], + "type": "text", + "content": " using the standard maximum-a-posteriori (MAP) estimation. We maximize the posterior that can be computed by Eq. (2), Eq. (3) and Eq. (4), which is formulated as follows:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 317, + 236, + 545, + 266 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 236, + 545, + 266 + ], + "spans": [ + { + "bbox": [ + 317, + 236, + 545, + 266 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} C (\\theta) = L (\\theta) - \\lambda \\hat {H} \\left(Y _ {\\mathrm {i n}} \\mid X _ {\\mathrm {i n}}, A\\right) = L (\\theta) \\tag {5} \\\\ - \\lambda \\hat {\\mathbb {E}} _ {X _ {\\text {i n}}, Y _ {\\text {i n}}, A} [ P (Y _ {\\text {i n}} | X _ {\\text {i n}}, A) \\log P (Y _ {\\text {i n}} | X _ {\\text {i n}}, A) ]. \\\\ \\end{array}", + "image_path": "6efe58c99ad258246b76edb6c6baf1d7f73abf703603a1cc53791816fe0ea3c5.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 272, + 545, + 344 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 272, + 545, + 344 + ], + "spans": [ + { + "bbox": [ + 304, + 272, + 545, + 344 + ], + "type": "text", + "content": "Here, " + }, + { + "bbox": [ + 304, + 272, + 545, + 344 + ], + "type": "inline_equation", + "content": "L(\\theta)" + }, + { + "bbox": [ + 304, + 272, + 545, + 344 + ], + "type": "text", + "content": " is the likelihood function computed using labeled data, i.e., the conventional supervised learning. Minimizing " + }, + { + "bbox": [ + 304, + 272, + 545, + 344 + ], + "type": "inline_equation", + "content": "\\hat{H}(Y_{\\mathrm{in}}|X_{\\mathrm{in}},A)" + }, + { + "bbox": [ + 304, + 272, + 545, + 344 + ], + "type": "text", + "content": " requires the marginal probability " + }, + { + "bbox": [ + 304, + 272, + 545, + 344 + ], + "type": "inline_equation", + "content": "P(Y_{\\mathrm{in}}|X_{\\mathrm{in}},A)" + }, + { + "bbox": [ + 304, + 272, + 545, + 344 + ], + "type": "text", + "content": " to be confident, which further requires " + }, + { + "bbox": [ + 304, + 272, + 545, + 344 + ], + "type": "inline_equation", + "content": "P(Y_{\\mathrm{in}}|X_{\\mathrm{in}},X_{\\mathrm{out}},A)" + }, + { + "bbox": [ + 304, + 272, + 545, + 344 + ], + "type": "text", + "content": " to be both confident and consistent with respect to different outside data " + }, + { + "bbox": [ + 304, + 272, + 545, + 344 + ], + "type": "inline_equation", + "content": "X_{\\mathrm{out}}" + }, + { + "bbox": [ + 304, + 272, + 545, + 344 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 344, + 545, + 428 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 344, + 545, + 428 + ], + "spans": [ + { + "bbox": [ + 304, + 344, + 545, + 428 + ], + "type": "text", + "content": "In summary, our proposed SSL framework in Eq. (5) encourages the segmentation model to make confident and consistent predictions at a predefined area, regardless of the data outside the area. The predefined area set " + }, + { + "bbox": [ + 304, + 344, + 545, + 428 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 304, + 344, + 545, + 428 + ], + "type": "text", + "content": " determines the \"strength\" of the prior. When setting " + }, + { + "bbox": [ + 304, + 344, + 545, + 428 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 304, + 344, + 545, + 428 + ], + "type": "text", + "content": " to the full area (i.e., the whole point cloud), our framework degrades to the classic entropy minimization framework [16]." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 428, + 545, + 452 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 428, + 545, + 452 + ], + "spans": [ + { + "bbox": [ + 304, + 428, + 545, + 452 + ], + "type": "text", + "content": "Implementation. There are three key steps for implementing our framework:" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 317, + 454, + 545, + 533 + ], + "type": "list", + "angle": 0, + "index": 24, + "blocks": [ + { + "bbox": [ + 317, + 454, + 545, + 478 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 454, + 545, + 478 + ], + "spans": [ + { + "bbox": [ + 317, + 454, + 545, + 478 + ], + "type": "text", + "content": "- Step 1): Select a proper partition set " + }, + { + "bbox": [ + 317, + 454, + 545, + 478 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 317, + 454, + 545, + 478 + ], + "type": "text", + "content": " which maintains strong spatial prior;" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 317, + 481, + 545, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 481, + 545, + 506 + ], + "spans": [ + { + "bbox": [ + 317, + 481, + 545, + 506 + ], + "type": "text", + "content": "- Step 2): Efficiently compute the marginal probability, i.e., " + }, + { + "bbox": [ + 317, + 481, + 545, + 506 + ], + "type": "inline_equation", + "content": "P(Y_{\\mathrm{in}}|X_{\\mathrm{in}},A)" + }, + { + "bbox": [ + 317, + 481, + 545, + 506 + ], + "type": "text", + "content": ";" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 317, + 508, + 545, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 508, + 545, + 533 + ], + "spans": [ + { + "bbox": [ + 317, + 508, + 545, + 533 + ], + "type": "text", + "content": "- Step 3): Efficiently minimize the marginal entropy, i.e., " + }, + { + "bbox": [ + 317, + 508, + 545, + 533 + ], + "type": "inline_equation", + "content": "\\hat{H}(Y_{\\mathrm{in}}|X_{\\mathrm{in}},A)" + }, + { + "bbox": [ + 317, + 508, + 545, + 533 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 23 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 304, + 534, + 545, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 545, + 559 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 545, + 559 + ], + "type": "text", + "content": "We propose a simple yet effective implementation following these steps in the next section." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 306, + 564, + 374, + 576 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 564, + 374, + 576 + ], + "spans": [ + { + "bbox": [ + 306, + 564, + 374, + 576 + ], + "type": "text", + "content": "3.2. LaserMix" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 304, + 582, + 545, + 679 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 679 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 679 + ], + "type": "text", + "content": "Partition. LiDAR sensors have a fixed number (e.g., 32, 64, and 128) of laser beams which are emitted isotropically around the ego-vehicle with predefined inclination angles as shown in Fig. 2. To obtain a proper set of spatial areas " + }, + { + "bbox": [ + 304, + 582, + 545, + 679 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 304, + 582, + 545, + 679 + ], + "type": "text", + "content": ", we propose to partition the LiDAR point cloud based on laser beams. Specifically, points captured by the same laser beam have a unified inclination angle to the sensor plane. For point " + }, + { + "bbox": [ + 304, + 582, + 545, + 679 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 582, + 545, + 679 + ], + "type": "text", + "content": ", its inclination " + }, + { + "bbox": [ + 304, + 582, + 545, + 679 + ], + "type": "inline_equation", + "content": "\\phi_i" + }, + { + "bbox": [ + 304, + 582, + 545, + 679 + ], + "type": "text", + "content": " is defined as follows:" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 358, + 685, + 545, + 712 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 358, + 685, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 358, + 685, + 545, + 712 + ], + "type": "interline_equation", + "content": "\\phi_ {i} = \\arctan \\left(\\frac {p _ {i} ^ {z}}{\\sqrt {\\left(p _ {i} ^ {x}\\right) ^ {2} + \\left(p _ {i} ^ {y}\\right) ^ {2}}}\\right), \\tag {6}", + "image_path": "2cbd3bde7724c6cb0eaa2b07bde86804da05cabdb60b9ffad4fb1ff451de0693.jpg" + } + ] + } + ], + "index": 28 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21707" + } + ] + } + ], + "index": 29 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "type": "inline_equation", + "content": "(p^x,p^y,p^z)" + }, + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "type": "text", + "content": " is the Cartesian coordinates of the LiDAR points. Given two LiDAR scans " + }, + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "type": "inline_equation", + "content": "x_{1}" + }, + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "type": "inline_equation", + "content": "x_{2}" + }, + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "type": "text", + "content": ", we first group all points from each scan by their inclination angles. Concretely, to form " + }, + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "type": "text", + "content": " non-overlapping areas, a set of " + }, + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "type": "inline_equation", + "content": "m + 1" + }, + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "type": "text", + "content": " inclination angles " + }, + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "type": "inline_equation", + "content": "\\Phi = \\{\\phi_0,\\phi_1,\\phi_2,\\dots,\\phi_m\\}" + }, + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "type": "text", + "content": " will be evenly sampled within the range of the minimum and maximum inclination angles in the dataset (defined by sensor configurations), and the area set " + }, + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "type": "inline_equation", + "content": "A = \\{a_{1},a_{2},\\ldots,a_{m}\\}" + }, + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "type": "text", + "content": " can be formed by bounding area " + }, + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "type": "inline_equation", + "content": "a_{i}" + }, + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "type": "text", + "content": " in the inclination range " + }, + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "type": "inline_equation", + "content": "[\\phi_{i - 1},\\phi_i)" + }, + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 180, + 288, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 180, + 288, + 323 + ], + "spans": [ + { + "bbox": [ + 46, + 180, + 288, + 323 + ], + "type": "text", + "content": "Role in our framework: Laser partition effectively \"excites\" a strong spatial prior in the LiDAR point cloud, as described by Step 1 in our framework. As shown in Fig. 1 (left), we find an overt pattern in semantic classes detected by each laser beam. More concrete evidence on this aspect has been included in the Appendix. Despite being an empirical choice, we will show in later sections that laser partition significantly outperforms other partition choices, including random points (MixUp-like partition [54]), random areas (CutMix-like partition [53]), and other heuristics like azimuth " + }, + { + "bbox": [ + 46, + 180, + 288, + 323 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 180, + 288, + 323 + ], + "type": "text", + "content": " (sensor horizontal direction) or radius " + }, + { + "bbox": [ + 46, + 180, + 288, + 323 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 46, + 180, + 288, + 323 + ], + "type": "text", + "content": " (sensor range direction) partitions." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 323, + 287, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 323, + 287, + 418 + ], + "spans": [ + { + "bbox": [ + 47, + 323, + 287, + 418 + ], + "type": "text", + "content": "Mixing. To this end, we propose LaserMix, a simple yet effective LiDAR mixing strategy that can better control the \"strength\" of the spatial prior. LaserMix mixes the aforementioned laser partitioned areas " + }, + { + "bbox": [ + 47, + 323, + 287, + 418 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 47, + 323, + 287, + 418 + ], + "type": "text", + "content": " from two scans in an intertwining way, i.e., one takes from odd-indexed areas " + }, + { + "bbox": [ + 47, + 323, + 287, + 418 + ], + "type": "inline_equation", + "content": "A_{1} = \\{a_{1},a_{3},\\ldots \\}" + }, + { + "bbox": [ + 47, + 323, + 287, + 418 + ], + "type": "text", + "content": " and the other takes from even-indexed areas " + }, + { + "bbox": [ + 47, + 323, + 287, + 418 + ], + "type": "inline_equation", + "content": "A_{2} = \\{a_{2},a_{4},\\ldots \\}" + }, + { + "bbox": [ + 47, + 323, + 287, + 418 + ], + "type": "text", + "content": ", so that each area's neighbor will be from the other scan:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 111, + 424, + 227, + 436 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 111, + 424, + 227, + 436 + ], + "spans": [ + { + "bbox": [ + 111, + 424, + 227, + 436 + ], + "type": "interline_equation", + "content": "\\tilde {x} _ {1}, \\tilde {x} _ {2} = \\operatorname {L a s e r M i x} \\left(x _ {1}, x _ {2}\\right),", + "image_path": "a9eb458177fe84657bc967c3b3b2e0aff16393043ad2cdbb539ac867c82b8756.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 108, + 438, + 287, + 452 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 438, + 287, + 452 + ], + "spans": [ + { + "bbox": [ + 108, + 438, + 287, + 452 + ], + "type": "interline_equation", + "content": "\\tilde {x} _ {1} = x _ {1} ^ {a _ {1}} \\cup x _ {2} ^ {a _ {2}} \\cup x _ {1} ^ {a _ {3}} \\cup \\dots , \\tag {7}", + "image_path": "80e52153517d5d7153087a8f4206e009f75ed5207684898bc3a173e920056962.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 108, + 453, + 228, + 467 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 453, + 228, + 467 + ], + "spans": [ + { + "bbox": [ + 108, + 453, + 228, + 467 + ], + "type": "interline_equation", + "content": "\\tilde {x} _ {2} = x _ {2} ^ {a _ {1}} \\cup x _ {1} ^ {a _ {2}} \\cup x _ {2} ^ {a _ {3}} \\cup \\dots ,", + "image_path": "67bfc5197ac13504aa9fa426433098200765310ed72c906f08f0f847924b15f5.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 474, + 287, + 558 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 474, + 287, + 558 + ], + "spans": [ + { + "bbox": [ + 46, + 474, + 287, + 558 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 474, + 287, + 558 + ], + "type": "inline_equation", + "content": "x_{i}^{a_{j}}" + }, + { + "bbox": [ + 46, + 474, + 287, + 558 + ], + "type": "text", + "content": " is the data crop of " + }, + { + "bbox": [ + 46, + 474, + 287, + 558 + ], + "type": "inline_equation", + "content": "x_{i}" + }, + { + "bbox": [ + 46, + 474, + 287, + 558 + ], + "type": "text", + "content": " in the area " + }, + { + "bbox": [ + 46, + 474, + 287, + 558 + ], + "type": "inline_equation", + "content": "a_{j}" + }, + { + "bbox": [ + 46, + 474, + 287, + 558 + ], + "type": "text", + "content": ". The semantic labels are mixed in the same way. LaserMix is directly applied to the point clouds and is thus agnostic to the various LiDAR representations [19, 32, 56, 58]. We show LaserMix's instantiations with the range view and voxel representations as in Fig. 1 (middle), since they are currently the most efficient and the best-performing options, respectively." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 558, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 287, + 713 + ], + "type": "text", + "content": "Role in our framework: LaserMix helps to efficiently compute the marginal probability " + }, + { + "bbox": [ + 46, + 558, + 287, + 713 + ], + "type": "inline_equation", + "content": "P(Y_{\\mathrm{in}}|X_{\\mathrm{in}},A)" + }, + { + "bbox": [ + 46, + 558, + 287, + 713 + ], + "type": "text", + "content": ", as described by Step 2 in our framework. The cost for directly computing the marginal probability in Eq. (4) on real-world LiDAR data is prohibitive; we need to iterate through all areas in " + }, + { + "bbox": [ + 46, + 558, + 287, + 713 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 46, + 558, + 287, + 713 + ], + "type": "text", + "content": " and all outside data in " + }, + { + "bbox": [ + 46, + 558, + 287, + 713 + ], + "type": "inline_equation", + "content": "X_{\\mathrm{out}}" + }, + { + "bbox": [ + 46, + 558, + 287, + 713 + ], + "type": "text", + "content": ", which requires " + }, + { + "bbox": [ + 46, + 558, + 287, + 713 + ], + "type": "inline_equation", + "content": "|A|\\cdot |X_{\\mathrm{out}}|" + }, + { + "bbox": [ + 46, + 558, + 287, + 713 + ], + "type": "text", + "content": " predictions in total. To reduce the training overhead, we take advantage of the fact that a prediction in an area will be largely affected by its neighboring areas and let " + }, + { + "bbox": [ + 46, + 558, + 287, + 713 + ], + "type": "inline_equation", + "content": "X_{\\mathrm{out}}" + }, + { + "bbox": [ + 46, + 558, + 287, + 713 + ], + "type": "text", + "content": " fill only the neighbors instead of all the remaining areas. LaserMix mixes two scans by intertwining the areas so that the neighbors of each area are filled with data from the other scan. As a result, we obtain the prediction on" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 310, + 69, + 544, + 258 + ], + "blocks": [ + { + "bbox": [ + 310, + 69, + 544, + 258 + ], + "lines": [ + { + "bbox": [ + 310, + 69, + 544, + 258 + ], + "spans": [ + { + "bbox": [ + 310, + 69, + 544, + 258 + ], + "type": "image", + "image_path": "c10b229c12476492fd4ae3f300ce19973e52045f873c3b9241bdde5a974f60cf.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 262, + 545, + 297 + ], + "lines": [ + { + "bbox": [ + 306, + 262, + 545, + 297 + ], + "spans": [ + { + "bbox": [ + 306, + 262, + 545, + 297 + ], + "type": "text", + "content": "Figure 2. Laser partition example. We group LiDAR points " + }, + { + "bbox": [ + 306, + 262, + 545, + 297 + ], + "type": "inline_equation", + "content": "(p_i^x, p_i^y, p_i^z)" + }, + { + "bbox": [ + 306, + 262, + 545, + 297 + ], + "type": "text", + "content": " whose inclinations " + }, + { + "bbox": [ + 306, + 262, + 545, + 297 + ], + "type": "inline_equation", + "content": "\\phi_i" + }, + { + "bbox": [ + 306, + 262, + 545, + 297 + ], + "type": "text", + "content": " are within the same inclination range into the same area, as depicted in the color regions." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 314, + 546, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 314, + 546, + 422 + ], + "spans": [ + { + "bbox": [ + 305, + 314, + 546, + 422 + ], + "type": "text", + "content": "all areas " + }, + { + "bbox": [ + 305, + 314, + 546, + 422 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 305, + 314, + 546, + 422 + ], + "type": "text", + "content": " of two scans from only two predictions, which on average reduces the cost from " + }, + { + "bbox": [ + 305, + 314, + 546, + 422 + ], + "type": "inline_equation", + "content": "|A|" + }, + { + "bbox": [ + 305, + 314, + 546, + 422 + ], + "type": "text", + "content": " to 1. The scan before and after mixing counts as two data fillings, therefore " + }, + { + "bbox": [ + 305, + 314, + 546, + 422 + ], + "type": "inline_equation", + "content": "|X_{\\mathrm{out}}| = 2" + }, + { + "bbox": [ + 305, + 314, + 546, + 422 + ], + "type": "text", + "content": ". Overall, the training overhead is reduced from " + }, + { + "bbox": [ + 305, + 314, + 546, + 422 + ], + "type": "inline_equation", + "content": "|A|\\cdot |X_{\\mathrm{out}}|" + }, + { + "bbox": [ + 305, + 314, + 546, + 422 + ], + "type": "text", + "content": " to 2: only one prediction on original data and one additional prediction on mixed data are required for each LiDAR scan. During training, the memory consumption for a batch will be " + }, + { + "bbox": [ + 305, + 314, + 546, + 422 + ], + "type": "inline_equation", + "content": "2\\times" + }, + { + "bbox": [ + 305, + 314, + 546, + 422 + ], + "type": "text", + "content": " compared to a standard SSL framework, and the training speed will not be affected." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 429, + 405, + 442 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 429, + 405, + 442 + ], + "spans": [ + { + "bbox": [ + 306, + 429, + 405, + 442 + ], + "type": "text", + "content": "3.3. Overall Pipeline" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 447, + 545, + 626 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 447, + 545, + 626 + ], + "spans": [ + { + "bbox": [ + 305, + 447, + 545, + 626 + ], + "type": "text", + "content": "We show the overall framework in Fig. 3 and the pseudocode in Algo. 1. There are two branches in our pipeline, one Student net " + }, + { + "bbox": [ + 305, + 447, + 545, + 626 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{\\theta}^{s}" + }, + { + "bbox": [ + 305, + 447, + 545, + 626 + ], + "type": "text", + "content": " and one Teacher net " + }, + { + "bbox": [ + 305, + 447, + 545, + 626 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{\\theta}^{t}" + }, + { + "bbox": [ + 305, + 447, + 545, + 626 + ], + "type": "text", + "content": ". During training, a batch is composed of half labeled data and half unlabeled data. We collect the predictions from both " + }, + { + "bbox": [ + 305, + 447, + 545, + 626 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{\\theta}^{s}" + }, + { + "bbox": [ + 305, + 447, + 545, + 626 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 447, + 545, + 626 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{\\theta}^{t}" + }, + { + "bbox": [ + 305, + 447, + 545, + 626 + ], + "type": "text", + "content": ", and produce pseudo-labels from Teacher net's prediction with a predefined confidence threshold " + }, + { + "bbox": [ + 305, + 447, + 545, + 626 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 305, + 447, + 545, + 626 + ], + "type": "text", + "content": ". For labeled data, we compute the cross-entropy loss between the Student net's prediction and the ground-truth as " + }, + { + "bbox": [ + 305, + 447, + 545, + 626 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{sup}}" + }, + { + "bbox": [ + 305, + 447, + 545, + 626 + ], + "type": "text", + "content": ". For unlabeled data, LaserMix blends every scan with a random labeled scan, together with their pseudo-label or ground-truth. Then, we let " + }, + { + "bbox": [ + 305, + 447, + 545, + 626 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{\\theta}^{s}" + }, + { + "bbox": [ + 305, + 447, + 545, + 626 + ], + "type": "text", + "content": " predict on the mixed data and compute the cross-entropy loss " + }, + { + "bbox": [ + 305, + 447, + 545, + 626 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{mix}}" + }, + { + "bbox": [ + 305, + 447, + 545, + 626 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 305, + 447, + 545, + 626 + ], + "type": "inline_equation", + "content": "w/" + }, + { + "bbox": [ + 305, + 447, + 545, + 626 + ], + "type": "text", + "content": " mixed labels). The point-wise cross-entropy loss for a scan " + }, + { + "bbox": [ + 305, + 447, + 545, + 626 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 305, + 447, + 545, + 626 + ], + "type": "text", + "content": " and its corresponding ground-truth/pseudolabel " + }, + { + "bbox": [ + 305, + 447, + 545, + 626 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 305, + 447, + 545, + 626 + ], + "type": "text", + "content": " on the segmentation net " + }, + { + "bbox": [ + 305, + 447, + 545, + 626 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{\\theta}" + }, + { + "bbox": [ + 305, + 447, + 545, + 626 + ], + "type": "text", + "content": " is defined as:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 336, + 635, + 545, + 669 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 336, + 635, + 545, + 669 + ], + "spans": [ + { + "bbox": [ + 336, + 635, + 545, + 669 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {c e}} = \\frac {1}{| x |} \\sum_ {i = 1} ^ {| x |} \\operatorname {C r o s s E n t r o p y} \\left(y ^ {(i)}, \\mathcal {G} _ {\\theta} ^ {(i)} (x)\\right), \\tag {8}", + "image_path": "e12a7b7788ad277148ce849605c9d2371741234534a450e88a50fe5c4ca6c9f5.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 677, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 545, + 715 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 677, + 545, + 715 + ], + "type": "inline_equation", + "content": "(i)" + }, + { + "bbox": [ + 305, + 677, + 545, + 715 + ], + "type": "text", + "content": " denotes the " + }, + { + "bbox": [ + 305, + 677, + 545, + 715 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 305, + 677, + 545, + 715 + ], + "type": "text", + "content": "-th point. Moreover, we adopt the mean teacher idea in [45] and use Exponential Moving Average (EMA) to update the weights of " + }, + { + "bbox": [ + 305, + 677, + 545, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{\\theta}^{t}" + }, + { + "bbox": [ + 305, + 677, + 545, + 715 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 305, + 677, + 545, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{\\theta}^{s}" + }, + { + "bbox": [ + 305, + 677, + 545, + 715 + ], + "type": "text", + "content": ", and com" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21708" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 52, + 71, + 541, + 247 + ], + "blocks": [ + { + "bbox": [ + 52, + 71, + 541, + 247 + ], + "lines": [ + { + "bbox": [ + 52, + 71, + 541, + 247 + ], + "spans": [ + { + "bbox": [ + 52, + 71, + 541, + 247 + ], + "type": "image", + "image_path": "4a95c87655788b65571e5a72f6d72de8246008d3a46325feeb809ff83d358976.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 254, + 546, + 299 + ], + "lines": [ + { + "bbox": [ + 46, + 254, + 546, + 299 + ], + "spans": [ + { + "bbox": [ + 46, + 254, + 546, + 299 + ], + "type": "text", + "content": "Figure 3. Framework overview. The labeled scan " + }, + { + "bbox": [ + 46, + 254, + 546, + 299 + ], + "type": "inline_equation", + "content": "x_{l}" + }, + { + "bbox": [ + 46, + 254, + 546, + 299 + ], + "type": "text", + "content": " is fed into the Student net to compute the supervised loss " + }, + { + "bbox": [ + 46, + 254, + 546, + 299 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{sup}}" + }, + { + "bbox": [ + 46, + 254, + 546, + 299 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 46, + 254, + 546, + 299 + ], + "type": "inline_equation", + "content": "w/" + }, + { + "bbox": [ + 46, + 254, + 546, + 299 + ], + "type": "text", + "content": " ground-truth " + }, + { + "bbox": [ + 46, + 254, + 546, + 299 + ], + "type": "inline_equation", + "content": "y_{l}" + }, + { + "bbox": [ + 46, + 254, + 546, + 299 + ], + "type": "text", + "content": "). The unlabeled scan " + }, + { + "bbox": [ + 46, + 254, + 546, + 299 + ], + "type": "inline_equation", + "content": "x_{u}" + }, + { + "bbox": [ + 46, + 254, + 546, + 299 + ], + "type": "text", + "content": " and the generated pseudo-label " + }, + { + "bbox": [ + 46, + 254, + 546, + 299 + ], + "type": "inline_equation", + "content": "y_{u}" + }, + { + "bbox": [ + 46, + 254, + 546, + 299 + ], + "type": "text", + "content": " are mixed with " + }, + { + "bbox": [ + 46, + 254, + 546, + 299 + ], + "type": "inline_equation", + "content": "(x_{l},y_{l})" + }, + { + "bbox": [ + 46, + 254, + 546, + 299 + ], + "type": "text", + "content": " via LaserMix (Sec. 3.2) to produce mixed data sample " + }, + { + "bbox": [ + 46, + 254, + 546, + 299 + ], + "type": "inline_equation", + "content": "(x_{\\mathrm{mix}},y_{\\mathrm{mix}})" + }, + { + "bbox": [ + 46, + 254, + 546, + 299 + ], + "type": "text", + "content": ", which is then fed into the Student net to compute the mixing loss " + }, + { + "bbox": [ + 46, + 254, + 546, + 299 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{mix}}" + }, + { + "bbox": [ + 46, + 254, + 546, + 299 + ], + "type": "text", + "content": ". Additionally, we adopt the EMA update in [45] for the Teacher net and compute the mean teacher loss " + }, + { + "bbox": [ + 46, + 254, + 546, + 299 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{mt}}" + }, + { + "bbox": [ + 46, + 254, + 546, + 299 + ], + "type": "text", + "content": " over Student net's and Teacher net's predictions." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 316, + 249, + 329 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 316, + 249, + 329 + ], + "spans": [ + { + "bbox": [ + 47, + 316, + 249, + 329 + ], + "type": "text", + "content": "pute the L2 loss between their predictions as " + }, + { + "bbox": [ + 47, + 316, + 249, + 329 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{mt}}" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 111, + 335, + 287, + 348 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 111, + 335, + 287, + 348 + ], + "spans": [ + { + "bbox": [ + 111, + 335, + 287, + 348 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {m t}} = \\left| \\left| \\mathcal {G} _ {\\theta} ^ {s} (x) - \\mathcal {G} _ {\\theta} ^ {t} (x) \\right| \\right| _ {2} ^ {2}, \\tag {9}", + "image_path": "a8bdfe2a3128ff083336b1d81cd3bf68b61f819ccbe6ee813a4025f2990b328a.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 354, + 287, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 354, + 287, + 413 + ], + "spans": [ + { + "bbox": [ + 47, + 354, + 287, + 413 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 354, + 287, + 413 + ], + "type": "inline_equation", + "content": "||\\cdot ||_2^2" + }, + { + "bbox": [ + 47, + 354, + 287, + 413 + ], + "type": "text", + "content": " is the L2 norm. The overall loss function is " + }, + { + "bbox": [ + 47, + 354, + 287, + 413 + ], + "type": "inline_equation", + "content": "\\mathcal{L} = \\mathcal{L}_{\\mathrm{sup}} + \\lambda_{\\mathrm{mix}}\\mathcal{L}_{\\mathrm{mix}} + \\lambda_{\\mathrm{mt}}\\mathcal{L}_{\\mathrm{mt}}" + }, + { + "bbox": [ + 47, + 354, + 287, + 413 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 47, + 354, + 287, + 413 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{mix}}" + }, + { + "bbox": [ + 47, + 354, + 287, + 413 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 354, + 287, + 413 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{mt}}" + }, + { + "bbox": [ + 47, + 354, + 287, + 413 + ], + "type": "text", + "content": " are loss weights. We use the Teacher net during inference as it empirically gives more stable results. There will be no extra inference overhead in our framework." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 415, + 287, + 546 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 415, + 287, + 546 + ], + "spans": [ + { + "bbox": [ + 46, + 415, + 287, + 546 + ], + "type": "text", + "content": "Role in our framework: Our overall pipeline minimizes the marginal entropy, as described by Step 3 in our framework. Since the objective for minimizing the entropy has a hard optimization landscape, pseudo-labeling is a common resort in practice [25]. Unlike conventional pseudo-label optimization in SSL which only aims to encourage the predictions to be confident, minimizing the marginal entropy requires all predictions to be both confident and consistent. Therefore, we use the ground-truth and pseudo-label as an anchor and encourage the model's predictions to be confident and consistent with these supervision signals." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 555, + 128, + 569 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 555, + 128, + 569 + ], + "spans": [ + { + "bbox": [ + 47, + 555, + 128, + 569 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 575, + 107, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 575, + 107, + 588 + ], + "spans": [ + { + "bbox": [ + 47, + 575, + 107, + 588 + ], + "type": "text", + "content": "4.1. Settings" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 594, + 287, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 287, + 653 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 287, + 653 + ], + "type": "text", + "content": "Protocol. We follow the Realistic Evaluation Protocol [35] when building the benchmark. Specifically, all experiments share the same backbones and are within the same codebase. All configurations and augmentations are unified to ensure a fair comparison among different SSL algorithms." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "type": "text", + "content": "Data. We build three SSL benchmarks upon nuScenes [11], SemanticKITTI [1], and ScribbleKITTI [47]. nuScenes [11] and SemanticKITTI [1] are the two most popular LiDAR segmentation datasets, with 29130 and 19130 training scans and 6019 and 4071 validation scans, respectively." + } + ] + } + ], + "index": 9 + }, + { + "type": "code", + "bbox": [ + 311, + 331, + 545, + 547 + ], + "blocks": [ + { + "bbox": [ + 307, + 316, + 515, + 328 + ], + "lines": [ + { + "bbox": [ + 307, + 316, + 515, + 328 + ], + "spans": [ + { + "bbox": [ + 307, + 316, + 515, + 328 + ], + "type": "text", + "content": "Algorithm 1 Pseudo-code for one training iteration." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 311, + 331, + 545, + 547 + ], + "lines": [ + { + "bbox": [ + 311, + 331, + 545, + 547 + ], + "spans": [ + { + "bbox": [ + 311, + 331, + 545, + 547 + ], + "type": "text", + "content": "1: Input: Shuffled labeled batch " + }, + { + "bbox": [ + 311, + 331, + 545, + 547 + ], + "type": "inline_equation", + "content": "(X_{l},Y_{l}) = \\{(x_{l}^{(b)},y_{l}^{(b)});b\\in" + }, + { + "bbox": [ + 311, + 331, + 545, + 547 + ], + "type": "inline_equation", + "content": "(1,\\dots ,B)\\}" + }, + { + "bbox": [ + 311, + 331, + 545, + 547 + ], + "type": "text", + "content": " , shuffled unlabeled batch " + }, + { + "bbox": [ + 311, + 331, + 545, + 547 + ], + "type": "inline_equation", + "content": "X_{u} = \\{x_{u}^{(b)};b\\in" + }, + { + "bbox": [ + 311, + 331, + 545, + 547 + ], + "type": "inline_equation", + "content": "(1,\\dots ,B)\\}" + }, + { + "bbox": [ + 311, + 331, + 545, + 547 + ], + "type": "text", + "content": " , threshold " + }, + { + "bbox": [ + 311, + 331, + 545, + 547 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 311, + 331, + 545, + 547 + ], + "type": "text", + "content": " , loss weights " + }, + { + "bbox": [ + 311, + 331, + 545, + 547 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{mix}}" + }, + { + "bbox": [ + 311, + 331, + 545, + 547 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 311, + 331, + 545, + 547 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{mt}}" + }, + { + "bbox": [ + 311, + 331, + 545, + 547 + ], + "type": "text", + "content": " , Student net and Teacher net. \n2: for " + }, + { + "bbox": [ + 311, + 331, + 545, + 547 + ], + "type": "inline_equation", + "content": "b = 1" + }, + { + "bbox": [ + 311, + 331, + 545, + 547 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 311, + 331, + 545, + 547 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 311, + 331, + 545, + 547 + ], + "type": "text", + "content": " do \n3: " + }, + { + "bbox": [ + 311, + 331, + 545, + 547 + ], + "type": "inline_equation", + "content": "x_{\\mathrm{mix}}^{(2b - 1)},x_{\\mathrm{mix}}^{(2b)} = \\mathrm{LaserMix}(x_l^{(b)},x_u^{(b)}) / /" + }, + { + "bbox": [ + 311, + 331, + 545, + 547 + ], + "type": "text", + "content": " LaserMix data \n4: end for \n5: " + }, + { + "bbox": [ + 311, + 331, + 545, + 547 + ], + "type": "inline_equation", + "content": "X_{\\mathrm{mix}} = \\{x_{\\mathrm{mix}}^{(i)};i\\in (1,\\dots ,2B)\\}" + }, + { + "bbox": [ + 311, + 331, + 545, + 547 + ], + "type": "text", + "content": " \n6: " + }, + { + "bbox": [ + 311, + 331, + 545, + 547 + ], + "type": "inline_equation", + "content": "S_{l},S_{u},S_{\\mathrm{mix}} =" + }, + { + "bbox": [ + 311, + 331, + 545, + 547 + ], + "type": "text", + "content": " Student " + }, + { + "bbox": [ + 311, + 331, + 545, + 547 + ], + "type": "inline_equation", + "content": "\\big(\\mathrm{Concat}(X_l,X_u,X_{\\mathrm{mix}})\\big)" + }, + { + "bbox": [ + 311, + 331, + 545, + 547 + ], + "type": "text", + "content": " //Student pred \n7: " + }, + { + "bbox": [ + 311, + 331, + 545, + 547 + ], + "type": "inline_equation", + "content": "\\hat{S}_l,\\hat{S}_u =" + }, + { + "bbox": [ + 311, + 331, + 545, + 547 + ], + "type": "text", + "content": " Teacher " + }, + { + "bbox": [ + 311, + 331, + 545, + 547 + ], + "type": "inline_equation", + "content": "\\big(\\mathrm{Concat}(X_l,X_u)\\big)" + }, + { + "bbox": [ + 311, + 331, + 545, + 547 + ], + "type": "text", + "content": " //Teacher pred \n8: " + }, + { + "bbox": [ + 311, + 331, + 545, + 547 + ], + "type": "inline_equation", + "content": "Y_{u} =" + }, + { + "bbox": [ + 311, + 331, + 545, + 547 + ], + "type": "text", + "content": " PseudoLabel " + }, + { + "bbox": [ + 311, + 331, + 545, + 547 + ], + "type": "inline_equation", + "content": "(\\hat{S}_u,T)" + }, + { + "bbox": [ + 311, + 331, + 545, + 547 + ], + "type": "text", + "content": " //Pseudo-label generation process \n9: for " + }, + { + "bbox": [ + 311, + 331, + 545, + 547 + ], + "type": "inline_equation", + "content": "b = 1" + }, + { + "bbox": [ + 311, + 331, + 545, + 547 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 311, + 331, + 545, + 547 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 311, + 331, + 545, + 547 + ], + "type": "text", + "content": " do \n10: " + }, + { + "bbox": [ + 311, + 331, + 545, + 547 + ], + "type": "inline_equation", + "content": "y_{\\mathrm{mix}}^{(2b - 1)},y_{\\mathrm{mix}}^{(2b)} = \\mathrm{LaserMix}(y_l^{(b)},y_u^{(b)}) / /" + }, + { + "bbox": [ + 311, + 331, + 545, + 547 + ], + "type": "text", + "content": " LaserMix label \n11: end for \n12: " + }, + { + "bbox": [ + 311, + 331, + 545, + 547 + ], + "type": "inline_equation", + "content": "Y_{\\mathrm{mix}} = \\{y_{\\mathrm{mix}}^{(i)};i\\in (1,\\dots ,2B)\\}" + }, + { + "bbox": [ + 311, + 331, + 545, + 547 + ], + "type": "text", + "content": " \n13: " + }, + { + "bbox": [ + 311, + 331, + 545, + 547 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{sup}} =" + }, + { + "bbox": [ + 311, + 331, + 545, + 547 + ], + "type": "text", + "content": " CrossEntropy " + }, + { + "bbox": [ + 311, + 331, + 545, + 547 + ], + "type": "inline_equation", + "content": "(S_l,Y_l)" + }, + { + "bbox": [ + 311, + 331, + 545, + 547 + ], + "type": "text", + "content": " // Supervised loss \n14: " + }, + { + "bbox": [ + 311, + 331, + 545, + 547 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{mix}} =" + }, + { + "bbox": [ + 311, + 331, + 545, + 547 + ], + "type": "text", + "content": " CrossEntropy " + }, + { + "bbox": [ + 311, + 331, + 545, + 547 + ], + "type": "inline_equation", + "content": "(S_{\\mathrm{mix}},Y_{\\mathrm{mix}})" + }, + { + "bbox": [ + 311, + 331, + 545, + 547 + ], + "type": "text", + "content": " // Mixing loss \n15: " + }, + { + "bbox": [ + 311, + 331, + 545, + 547 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{mt}} = L2\\big(\\mathrm{Concat}(S_l,S_u),\\mathrm{Concat}(\\hat{S}_l,\\hat{S}_u)\\big)" + }, + { + "bbox": [ + 311, + 331, + 545, + 547 + ], + "type": "text", + "content": " //MeanTeacher loss \n16: " + }, + { + "bbox": [ + 311, + 331, + 545, + 547 + ], + "type": "inline_equation", + "content": "L = L_{\\mathrm{sup}} + \\lambda_{\\mathrm{mix}}L_{\\mathrm{mix}} + \\lambda_{\\mathrm{mt}}L_{\\mathrm{mt}}" + }, + { + "bbox": [ + 311, + 331, + 545, + 547 + ], + "type": "text", + "content": " //Overall loss \n17: Backward(L), Update(Student), UpdateEMA(Teacher)" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "code_body" + } + ], + "index": 11, + "sub_type": "algorithm" + }, + { + "bbox": [ + 304, + 569, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 569, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 569, + 546, + 714 + ], + "type": "text", + "content": "ScribbleKITTI [47] is a recent variant of SemanticKITTI [1], which contains the same number of scans but is annotated with line scribbles (approximately " + }, + { + "bbox": [ + 304, + 569, + 546, + 714 + ], + "type": "inline_equation", + "content": "8.06\\%" + }, + { + "bbox": [ + 304, + 569, + 546, + 714 + ], + "type": "text", + "content": " valid semantic labels) rather than dense annotations. For all three LiDAR segmentation datasets, we uniformly sample " + }, + { + "bbox": [ + 304, + 569, + 546, + 714 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 304, + 569, + 546, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 569, + 546, + 714 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 304, + 569, + 546, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 569, + 546, + 714 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 304, + 569, + 546, + 714 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 569, + 546, + 714 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 304, + 569, + 546, + 714 + ], + "type": "text", + "content": " labeled training scans and assume the remaining ones as unlabeled. This is in line with the conventional settings from the semi-supervised image segmentation community [6, 21, 37]. We also conduct experiments with sequential splits and show the results in the Appendix. Implementation Details. We adopt FIDNet [57] and Cylinder3D [58] as the segmentation backbones for the range" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "21709" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 99, + 97, + 492, + 272 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 545, + 93 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 545, + 93 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 545, + 93 + ], + "type": "text", + "content": "Table 1. Benchmarking results among different SSL methods with the LiDAR range view (top) and voxel (bottom) representations. All mIoU scores are given in percentage (\\%). The best and second best score for each data split is highlighted in bold and underline." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 99, + 97, + 492, + 272 + ], + "lines": [ + { + "bbox": [ + 99, + 97, + 492, + 272 + ], + "spans": [ + { + "bbox": [ + 99, + 97, + 492, + 272 + ], + "type": "table", + "html": "
Repr.MethodnuScenes [11]SemanticKITTI [1]ScribbleKITTI [47]
1%10%20%50%1%10%20%50%1%10%20%50%
Range ViewSup.-only38.357.562.767.636.252.255.957.233.147.749.952.5
MeanTeacher [45]42.160.465.469.437.553.156.157.434.249.851.653.3
CBST [59]40.960.564.369.339.953.456.156.935.750.752.754.6
CutMix-Seg [12]43.863.964.869.837.454.356.657.636.750.752.954.3
CPS [6]40.760.864.968.036.552.356.357.433.750.052.854.6
LaserMix (Ours)49.568.270.673.043.458.859.461.438.354.455.658.7
Δ↑+11.2+10.7+7.9+5.4+7.2+6.6+3.5+4.2+5.2+6.7+5.7+6.2
VoxelSup.-only50.965.966.671.245.456.157.858.739.248.052.153.8
MeanTeacher [45]51.666.067.171.745.457.159.260.041.050.152.853.9
CBST [59]53.066.569.671.648.858.359.459.741.550.653.354.5
CPS [6]52.966.370.072.546.758.759.660.541.451.853.954.8
LaserMix (Ours)55.369.971.873.250.660.061.962.344.253.755.156.8
Δ↑+4.4+4.0+5.2+2.0+5.2+3.9+4.1+3.6+5.0+5.7+3.0+3.0
", + "image_path": "29f06e6cc8cf944ea14c50117e88fa401b744604ee76964aa89f13556759990d.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 52, + 319, + 233, + 394 + ], + "blocks": [ + { + "bbox": [ + 46, + 282, + 239, + 316 + ], + "lines": [ + { + "bbox": [ + 46, + 282, + 239, + 316 + ], + "spans": [ + { + "bbox": [ + 46, + 282, + 239, + 316 + ], + "type": "text", + "content": "Table 2. Comparison to the state-of-the-art 3D SSL method [20] on the val set of SemanticKITTI [1]. All mIoU scores are given in percentage " + }, + { + "bbox": [ + 46, + 282, + 239, + 316 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 46, + 282, + 239, + 316 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 52, + 319, + 233, + 394 + ], + "lines": [ + { + "bbox": [ + 52, + 319, + 233, + 394 + ], + "spans": [ + { + "bbox": [ + 52, + 319, + 233, + 394 + ], + "type": "table", + "html": "
Method5%10%20%30%40%
GPC [20]41.849.958.859.459.9
Ours (RV)54.658.859.460.160.8
Δ↑+12.8+8.9+0.6+0.7+0.9
Ours (Voxel)56.760.061.962.162.3
Δ↑+14.9+10.1+3.1+1.7+1.4
", + "image_path": "4d848fa5cbd2977e27c798ec2172850f967cc6c5638ae1415ea1353aea8f1c8c.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 258, + 319, + 543, + 394 + ], + "blocks": [ + { + "bbox": [ + 254, + 282, + 545, + 316 + ], + "lines": [ + { + "bbox": [ + 254, + 282, + 545, + 316 + ], + "spans": [ + { + "bbox": [ + 254, + 282, + 545, + 316 + ], + "type": "text", + "content": "Table 3. Ablation results on the val set of nuScenes [11]. (1) Baseline results [45]; (2) Results with Student net supervision (SS); (3) Results with Teacher net supervision (TS). All mIoU scores are given in percentage " + }, + { + "bbox": [ + 254, + 282, + 545, + 316 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 254, + 282, + 545, + 316 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 258, + 319, + 543, + 394 + ], + "lines": [ + { + "bbox": [ + 258, + 319, + 543, + 394 + ], + "spans": [ + { + "bbox": [ + 258, + 319, + 543, + 394 + ], + "type": "table", + "html": "
#\\( {\\mathcal{L}}_{\\text{mt }} \\)\\( {\\mathcal{L}}_{\\text{mix }} \\)SSTS1%10%20%50%
(1)✓42.160.465.469.4
(2)✓✓45.6(+3.5)64.3(+3.9)67.8(+2.4)71.6(+2.2)
✓✓✓47.0(+4.9)65.5(+5.1)69.5(+4.1)72.0(+2.6)
(3)✓✓46.0(+3.9)64.1(+3.7)69.5(+4.1)72.3(+2.9)
✓✓✓49.5(+7.4)68.2(+7.8)70.6(+5.2)73.0(+3.6)
", + "image_path": "e1ff15d6933937c72031dd8cd75e0482f7783d6f9257ebabebdef2ec4a4c57f6.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 413, + 287, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 413, + 287, + 579 + ], + "spans": [ + { + "bbox": [ + 46, + 413, + 287, + 579 + ], + "type": "text", + "content": "view and the voxel options, respectively. The input resolution of range images is set as " + }, + { + "bbox": [ + 46, + 413, + 287, + 579 + ], + "type": "inline_equation", + "content": "64 \\times 2048" + }, + { + "bbox": [ + 46, + 413, + 287, + 579 + ], + "type": "text", + "content": " for SemanticKITTI [1] and ScribbleKITTI [47], and " + }, + { + "bbox": [ + 46, + 413, + 287, + 579 + ], + "type": "inline_equation", + "content": "32 \\times 1920" + }, + { + "bbox": [ + 46, + 413, + 287, + 579 + ], + "type": "text", + "content": " for nuScenes [11]. The voxel resolution is fixed as [240, 180, 20] for all three sets. The number of spatial areas " + }, + { + "bbox": [ + 46, + 413, + 287, + 579 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 413, + 287, + 579 + ], + "type": "text", + "content": " in LaserMix is uniformly sampled from 2 to 6 areas. We denote the supervised-only baseline as sup.-only. Due to the lack of Li-DAR SSL works [20], we also compare SoTA consistency regularization [6, 12, 45] and entropy minimization [59] methods from semi-supervised image segmentation. We report the intersection-over-union (IoU) over each semantic class and the mean IoU (mIoU) scores over all classes in our benchmarks. All experiments are implemented using PyTorch on NVIDIA Tesla V100 GPUs with 32GB RAM." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 587, + 162, + 601 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 587, + 162, + 601 + ], + "spans": [ + { + "bbox": [ + 47, + 587, + 162, + 601 + ], + "type": "text", + "content": "4.2. Comparative Study" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "content": "Improvements over Baseline. Tab. 1 benchmarks results on nuScenes [11], SemanticKITTI [1], and ScribbleKITTI [47]. For all three sets under different data splits, we observe significant improvements in our approach over the sup.-only baseline. Such gains are especially evident in range view, which reach up to " + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "inline_equation", + "content": "11.2\\%" + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "content": " mIoU. We also observe constant improvements for the voxel option, which provide on average " + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "inline_equation", + "content": "4.1\\%" + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "content": " mIoU gains over all splits across all sets. The results verify the effectiveness of our frame-" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 413, + 544, + 436 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 413, + 544, + 436 + ], + "spans": [ + { + "bbox": [ + 304, + 413, + 544, + 436 + ], + "type": "text", + "content": "work and further highlight the importance of leveraging unlabeled data in LiDAR semantic segmentation." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 437, + 545, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 437, + 545, + 557 + ], + "spans": [ + { + "bbox": [ + 304, + 437, + 545, + 557 + ], + "type": "text", + "content": "Compare with SoTA. We compare LaserMix with " + }, + { + "bbox": [ + 304, + 437, + 545, + 557 + ], + "type": "inline_equation", + "content": "\\mathrm{GPC}^2" + }, + { + "bbox": [ + 304, + 437, + 545, + 557 + ], + "type": "text", + "content": " [20], the SoTA 3D SSL method tested on SemanticKITTI [1]. The results in Tab. 2 show that our approach exhibits much better results than GPC [20], especially in scenarios where very few annotations are available. We also reimplemented popular SSL algorithms from the image segmentation domain and show their results in Tab. 1. We find that these methods, albeit competitive in 2D, only yield sub-par performance in the LiDAR SSL benchmark, highlighting the importance of exploiting the LiDAR data structure." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 558, + 545, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 545, + 666 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 545, + 666 + ], + "type": "text", + "content": "Compare with Full Labels. As shown in Fig. 1 (right), the comparisons between the prevailing LiDAR segmentation methods attests that our approach can achieve more competitive scores over the fully-supervised counterparts [5, 8, 32, 56] while with " + }, + { + "bbox": [ + 304, + 558, + 545, + 666 + ], + "type": "inline_equation", + "content": "2 \\times" + }, + { + "bbox": [ + 304, + 558, + 545, + 666 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 558, + 545, + 666 + ], + "type": "inline_equation", + "content": "5 \\times" + }, + { + "bbox": [ + 304, + 558, + 545, + 666 + ], + "type": "text", + "content": " fewer annotations. The strong augmentation and regularization ability of LaserMix have yielded better results in the high-data regime and extreme low-data regime (i.e., " + }, + { + "bbox": [ + 304, + 558, + 545, + 666 + ], + "type": "inline_equation", + "content": "0.8\\%" + }, + { + "bbox": [ + 304, + 558, + 545, + 666 + ], + "type": "text", + "content": " labels on [47]), which validates the generalizability of our approach." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 666, + 545, + 690 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 666, + 545, + 690 + ], + "spans": [ + { + "bbox": [ + 304, + 666, + 545, + 690 + ], + "type": "text", + "content": "Qualitative Examination. Fig. 5 visualizes the scene segmentation results for different SSL algorithms on the val" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 315, + 702, + 544, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 702, + 544, + 712 + ], + "spans": [ + { + "bbox": [ + 315, + 702, + 544, + 712 + ], + "type": "text", + "content": "2Note that GPC uses private backbone / split. See Appendix for details." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21710" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 69, + 302, + 219 + ], + "blocks": [ + { + "bbox": [ + 47, + 69, + 302, + 219 + ], + "lines": [ + { + "bbox": [ + 47, + 69, + 302, + 219 + ], + "spans": [ + { + "bbox": [ + 47, + 69, + 302, + 219 + ], + "type": "image", + "image_path": "03c3f253dd1454a7e84af6443bb7d33afe021d8eb15a4e17a4b6de39b529dcb6.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 222, + 546, + 245 + ], + "lines": [ + { + "bbox": [ + 46, + 222, + 546, + 245 + ], + "spans": [ + { + "bbox": [ + 46, + 222, + 546, + 245 + ], + "type": "text", + "content": "Figure 4. Ablation studies on: Left: Different mixing-based techniques used in point partition & mixing; Middle: Different EMA decay rates between the Teacher net and the Student net; Right: Different confidence thresholds " + }, + { + "bbox": [ + 46, + 222, + 546, + 245 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 222, + 546, + 245 + ], + "type": "text", + "content": " used in the pseudo-label generation." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 308, + 68, + 422, + 218 + ], + "blocks": [ + { + "bbox": [ + 308, + 68, + 422, + 218 + ], + "lines": [ + { + "bbox": [ + 308, + 68, + 422, + 218 + ], + "spans": [ + { + "bbox": [ + 308, + 68, + 422, + 218 + ], + "type": "image", + "image_path": "6877d8b02fbd4dbcf09e2320e04373d0fc8d7583d3cbb6bf69f1e118d062c853.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 432, + 68, + 547, + 218 + ], + "blocks": [ + { + "bbox": [ + 432, + 68, + 547, + 218 + ], + "lines": [ + { + "bbox": [ + 432, + 68, + 547, + 218 + ], + "spans": [ + { + "bbox": [ + 432, + 68, + 547, + 218 + ], + "type": "image", + "image_path": "ae96b550fc093755d4eb28a4306a89c713c14c0f6e54593b2c1272d24d50341f.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 262, + 289, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 262, + 289, + 348 + ], + "spans": [ + { + "bbox": [ + 46, + 262, + 289, + 348 + ], + "type": "text", + "content": "set of nuScenes [11], where each example covers a driving scene centered by the ego-vehicle. We find that previous arts [6, 45, 59] can only improve predictions in limited regions, while our approach holistically eliminates false predictions in almost every direction around the ego-vehicle. The consistency enlightened by LaserMix has yielded better segmentation accuracy under annotation scarcity." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 357, + 141, + 370 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 357, + 141, + 370 + ], + "spans": [ + { + "bbox": [ + 47, + 357, + 141, + 370 + ], + "type": "text", + "content": "4.3. Ablation Study" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 376, + 287, + 400 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 376, + 287, + 400 + ], + "spans": [ + { + "bbox": [ + 46, + 376, + 287, + 400 + ], + "type": "text", + "content": "Without loss of generalizability, we stick with the " + }, + { + "bbox": [ + 46, + 376, + 287, + 400 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 46, + 376, + 287, + 400 + ], + "type": "text", + "content": " budget setting and range view backbones in our ablations." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 401, + 288, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 401, + 288, + 533 + ], + "spans": [ + { + "bbox": [ + 46, + 401, + 288, + 533 + ], + "type": "text", + "content": "Framework Setups. The component analysis in Tab. 3 shows that " + }, + { + "bbox": [ + 46, + 401, + 288, + 533 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{mix}}" + }, + { + "bbox": [ + 46, + 401, + 288, + 533 + ], + "type": "text", + "content": " contributes significantly to the overall improvement. Meanwhile, using the Teacher net instead of the Student net to generate pseudo-labels leads to better results, as the formal is temporally ensembled and encourages consistency in-between mixed and original data, which is crucial besides enforcing confident predictions. It is worth noting that all of our model configurations have achieved superior results than the baseline MeanTeacher [45], which further emphasizes the effectiveness of our framework in tackling LiDAR segmentation with semi-supervisions." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 533, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 533, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 533, + 288, + 714 + ], + "type": "text", + "content": "Mixing Strategies. Fig. 4 (left) compares LaserMix with other mixing methods [10, 33, 53, 54]. MixUp and CutMix can be considered as setting " + }, + { + "bbox": [ + 46, + 533, + 288, + 714 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 46, + 533, + 288, + 714 + ], + "type": "text", + "content": " to random points and random areas, respectively. We observe that MixUp has no improvements over the baseline on average since there is no distribution pattern in random points. CutMix has a considerable improvement over the baseline, as there is always a structure prior in scene segmentation, i.e., the same semantic class points tend to cluster, which reduces the entropy in any continuous area. This prior is often used in image semantic segmentation SSL [12]. However, our spatial prior is much stronger, where not only the area structure but also the area's spatial position has been considered. LaserMix outperforms CutMix by a large margin (up to " + }, + { + "bbox": [ + 46, + 533, + 288, + 714 + ], + "type": "inline_equation", + "content": "3.3\\%" + }, + { + "bbox": [ + 46, + 533, + 288, + 714 + ], + "type": "text", + "content": " mIoU) on all sets. CutOut can be considered as setting " + }, + { + "bbox": [ + 46, + 533, + 288, + 714 + ], + "type": "inline_equation", + "content": "X_{\\mathrm{out}}" + }, + { + "bbox": [ + 46, + 533, + 288, + 714 + ], + "type": "text", + "content": " to" + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 308, + 297, + 545, + 538 + ], + "blocks": [ + { + "bbox": [ + 305, + 261, + 547, + 295 + ], + "lines": [ + { + "bbox": [ + 305, + 261, + 547, + 295 + ], + "spans": [ + { + "bbox": [ + 305, + 261, + 547, + 295 + ], + "type": "text", + "content": "Table 4. Ablation studies on laser beam partitions (horizontal: inclination direction " + }, + { + "bbox": [ + 305, + 261, + 547, + 295 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 305, + 261, + 547, + 295 + ], + "type": "text", + "content": "; vertical: azimuth direction " + }, + { + "bbox": [ + 305, + 261, + 547, + 295 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 305, + 261, + 547, + 295 + ], + "type": "text", + "content": "). " + }, + { + "bbox": [ + 305, + 261, + 547, + 295 + ], + "type": "inline_equation", + "content": "(i - \\alpha, j - \\phi)" + }, + { + "bbox": [ + 305, + 261, + 547, + 295 + ], + "type": "text", + "content": " denotes that there are " + }, + { + "bbox": [ + 305, + 261, + 547, + 295 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 305, + 261, + 547, + 295 + ], + "type": "text", + "content": " azimuth and " + }, + { + "bbox": [ + 305, + 261, + 547, + 295 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 305, + 261, + 547, + 295 + ], + "type": "text", + "content": " inclination partitions." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 297, + 545, + 538 + ], + "lines": [ + { + "bbox": [ + 308, + 297, + 545, + 538 + ], + "spans": [ + { + "bbox": [ + 308, + 297, + 545, + 538 + ], + "type": "table", + "html": "
Baseline(1α, 2φ)(1α, 3φ)(1α, 4φ)(1α, 5φ)(1α, 6φ)
60.463.5(+3.1)65.2(+4.8)66.5(+6.1)66.2(+5.8)65.4(+5.0)
(2α, 1φ)(2α, 2φ)(2α, 3φ)(2α, 4φ)(2α, 5φ)(2α, 6φ)
61.5(+1.1)63.3(+2.9)65.9(+5.5)66.1(+5.7)66.7(+6.3)65.3(+4.9)
(3α, 1φ)(3α, 2φ)(3α, 3φ)(3α, 4φ)(3α, 5φ)(3α, 6φ)
60.9(+0.6)64.2(+3.8)65.9(+5.5)66.3(+5.9)66.0(+5.6)65.2(+4.8)
(4α, 1φ)(4α, 2φ)(4α, 3φ)(4α, 4φ)(4α, 5φ)(4α, 6φ)
60.9(+0.6)64.7(+4.3)65.3(+4.9)65.6(+5.2)65.7(+5.3)65.2(+4.8)
", + "image_path": "dc41c731b882d1afbf2536860404cae6ef15b8b6d49b8e371554831133602fe6.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 556, + 545, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 556, + 545, + 581 + ], + "spans": [ + { + "bbox": [ + 304, + 556, + 545, + 581 + ], + "type": "text", + "content": "a dummy filling instead of sampling from datasets, and it leads to a considerable performance drop from CutMix." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 582, + 545, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 665 + ], + "type": "text", + "content": "Orderless Mix. We revert the area ordering (i.e., put the topmost laser beam at the bottom, and vice versa) in LaserMix, and the performance drops from " + }, + { + "bbox": [ + 304, + 582, + 545, + 665 + ], + "type": "inline_equation", + "content": "68.2\\%" + }, + { + "bbox": [ + 304, + 582, + 545, + 665 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 582, + 545, + 665 + ], + "type": "inline_equation", + "content": "64.4\\%" + }, + { + "bbox": [ + 304, + 582, + 545, + 665 + ], + "type": "inline_equation", + "content": "(-3.8\\% \\mathrm{mIoU})" + }, + { + "bbox": [ + 304, + 582, + 545, + 665 + ], + "type": "text", + "content": ". When we shuffle the ordering, the performance drops to " + }, + { + "bbox": [ + 304, + 582, + 545, + 665 + ], + "type": "inline_equation", + "content": "63.8\\%" + }, + { + "bbox": [ + 304, + 582, + 545, + 665 + ], + "type": "inline_equation", + "content": "(-4.4\\% \\mathrm{mIoU})" + }, + { + "bbox": [ + 304, + 582, + 545, + 665 + ], + "type": "text", + "content": ", which becomes comparable with CutMix. The results once again confirm the superiority of using spatial prior in LiDAR SSL." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "Other Heuristics. Besides our proposed inclination partition, the LiDAR scans can also be split based on azimuth (sensor horizontal direction). 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Error maps visualized from LiDAR bird's eye view and range view on nuScenes [11]. Each example shows a street scene of size " + }, + { + "bbox": [ + 46, + 323, + 546, + 346 + ], + "type": "inline_equation", + "content": "50\\mathrm{m}" + }, + { + "bbox": [ + 46, + 323, + 546, + 346 + ], + "type": "text", + "content": " by " + }, + { + "bbox": [ + 46, + 323, + 546, + 346 + ], + "type": "inline_equation", + "content": "50\\mathrm{m}" + }, + { + "bbox": [ + 46, + 323, + 546, + 346 + ], + "type": "text", + "content": " by " + }, + { + "bbox": [ + 46, + 323, + 546, + 346 + ], + "type": "inline_equation", + "content": "8\\mathrm{m}" + }, + { + "bbox": [ + 46, + 323, + 546, + 346 + ], + "type": "text", + "content": ". The correct and incorrect predictions are painted in green and red to highlight the differences. Best viewed in color." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 132, + 196, + 212, + 316 + ], + "blocks": [ + { + "bbox": [ + 132, + 196, + 212, + 316 + ], + "lines": [ + { + "bbox": [ + 132, + 196, + 212, + 316 + ], + "spans": [ + { + "bbox": [ + 132, + 196, + 212, + 316 + ], + "type": "image", + "image_path": "0aea44d0452284df8b3a5b5a2d20801c0f00e95729813c8af041fbc916c2c27f.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 215, + 196, + 295, + 316 + ], + "blocks": [ + { + "bbox": [ + 215, + 196, + 295, + 316 + ], + "lines": [ + { + "bbox": [ + 215, + 196, + 295, + 316 + ], + "spans": [ + { + "bbox": [ + 215, + 196, + 295, + 316 + ], + "type": "image", + "image_path": "4ad3201649ba28f64d5439285f02f3bad3432dcff9ec0857f8ebbd0bfd52d4a1.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 298, + 196, + 378, + 316 + ], + "blocks": [ + { + "bbox": [ + 298, + 196, + 378, + 316 + ], + "lines": [ + { + "bbox": [ + 298, + 196, + 378, + 316 + ], + "spans": [ + { + "bbox": [ + 298, + 196, + 378, + 316 + ], + "type": "image", + "image_path": "1660fe10ba3d0d9dbc26477b7e4ba3540bafc7a165b3c9cf9de3ccfb87729345.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 381, + 196, + 462, + 316 + ], + "blocks": [ + { + "bbox": [ + 381, + 196, + 462, + 316 + ], + "lines": [ + { + "bbox": [ + 381, + 196, + 462, + 316 + ], + "spans": [ + { + "bbox": [ + 381, + 196, + 462, + 316 + ], + "type": "image", + "image_path": "ca454577287bd03716d0184d29e5564bdaea904a2bad41dabb93cc56a92e365b.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 465, + 196, + 545, + 316 + ], + "blocks": [ + { + "bbox": [ + 465, + 196, + 545, + 316 + ], + "lines": [ + { + "bbox": [ + 465, + 196, + 545, + 316 + ], + "spans": [ + { + "bbox": [ + 465, + 196, + 545, + 316 + ], + "type": "image", + "image_path": "c0b98a8a14e617ac91471d4e316c7a302288912d8cbe8e493ab26504051f8029.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 366, + 287, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 366, + 287, + 460 + ], + "spans": [ + { + "bbox": [ + 46, + 366, + 287, + 460 + ], + "type": "text", + "content": "first column) does not improve the performance, which is attributed to the fact that the semantic distribution has a weak correlation in the azimuth direction. We also observe that the results tend to improve as the mixing granularity increases (row direction in Tab. 4). The scores start to drop when the granularity is beyond a certain limit (e.g., the last two columns). We conjecture that over-fine-grained partition and mixing tend to hurt semantic coherence." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 461, + 287, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 461, + 287, + 568 + ], + "spans": [ + { + "bbox": [ + 46, + 461, + 287, + 568 + ], + "type": "text", + "content": "Mix Unlabeled Data Only. To verify that our method is more than trivially augmenting seen data and label pairs, we apply LaserMix only on unlabeled data. Instead of mixing an unlabeled scan with a labeled scan as described in Sec. 3.3, we mix two unlabeled scans with their pseudolabels. The score drops from " + }, + { + "bbox": [ + 46, + 461, + 287, + 568 + ], + "type": "inline_equation", + "content": "68.2\\%" + }, + { + "bbox": [ + 46, + 461, + 287, + 568 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 461, + 287, + 568 + ], + "type": "inline_equation", + "content": "66.9\\%" + }, + { + "bbox": [ + 46, + 461, + 287, + 568 + ], + "type": "inline_equation", + "content": "(-1.3\\% \\mathrm{mIoU})" + }, + { + "bbox": [ + 46, + 461, + 287, + 568 + ], + "type": "text", + "content": " but still outperforms all existing methods by large margins. This verifies that LaserMix indeed brings a strong consistency regularization effect during SSL." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 46, + 570, + 287, + 663 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 287, + 663 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 287, + 663 + ], + "type": "text", + "content": "EMA. Fig. 4 (middle) provides results with different EMA decay rates, Typically, a rate between 0.9 and 0.99 yields the best possible results. Large rates like 0.999 tend to hurt the consistency between the two networks. The results also verify that the teacher-student pipeline [45] has good synergy with our proposed SSL framework. Thanks to this simplicity, more modern SSL techniques can be easily incorporated into the current framework in future works." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 46, + 665, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 712 + ], + "type": "text", + "content": "Confidence Threshold. As pseudo-labels play an important role in our framework, we further analyze the impact of the threshold parameter " + }, + { + "bbox": [ + 46, + 665, + 287, + 712 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 665, + 287, + 712 + ], + "type": "text", + "content": " used in pseudo-label generation and show results in Fig. 4 (right). When " + }, + { + "bbox": [ + 46, + 665, + 287, + 712 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 665, + 287, + 712 + ], + "type": "text", + "content": " is too low," + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 366, + 545, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 366, + 545, + 437 + ], + "spans": [ + { + "bbox": [ + 304, + 366, + 545, + 437 + ], + "type": "text", + "content": "a forced consistency to low-quality pseudo-labels tends to deteriorate the performance. When " + }, + { + "bbox": [ + 304, + 366, + 545, + 437 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 366, + 545, + 437 + ], + "type": "text", + "content": " is too high, the benefits from mixing might diminish. Generally, " + }, + { + "bbox": [ + 304, + 366, + 545, + 437 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 366, + 545, + 437 + ], + "type": "text", + "content": " is a dataset-dependent parameter and we find that a value around 0.9 leads to the best possible results on the three tested LiDAR segmentation datasets [1, 11, 47] in our benchmark." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 448, + 378, + 460 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 448, + 378, + 460 + ], + "spans": [ + { + "bbox": [ + 306, + 448, + 378, + 460 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 468, + 545, + 588 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 468, + 545, + 588 + ], + "spans": [ + { + "bbox": [ + 304, + 468, + 545, + 588 + ], + "type": "text", + "content": "In this work, we exploit the unique spatial prior in LiDAR scenes for semi-supervised LiDAR semantic segmentation. We proposed a statistically-principled and effective SSL pipeline, including LaserMix, a novel LiDAR mixing technique that intertwines laser beams from different scans. Through comprehensive empirical analysis, we show the importance of spatial prior and the superiority of our approach on three popular benchmarks. The effectiveness and simplicity of our framework have shed light on the scalable deployment of the LiDAR semantic mapping system." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 592, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 592, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 592, + 546, + 713 + ], + "type": "text", + "content": "Acknowledgments. This study is supported by the Ministry of Education, Singapore, under its MOE AcRF Tier 2 (MOET2EP20221-0012), the National Research Foundation, Singapore under its AI Singapore Programme (AISG Award No: AISG2-PhD-2021-08-018), NTU NAP, and under the RIE2020 Industry Alignment Fund - Industry Collaboration Projects (IAF-ICP) Funding Initiative, as well as cash and in-kind contribution from the industry partner(s). This research is part of the programme DesCartes and is supported by the National Research Foundation, Prime Minister's Office, Singapore under its Campus for Research Excellence and Technological Enterprise (CREATE) programme." + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 47, + 70, + 545, + 80 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 70, + 545, + 80 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 545, + 80 + ], + "type": "inline_equation", + "content": "\\bullet" + }, + { + "bbox": [ + 47, + 70, + 545, + 80 + ], + "type": "text", + "content": " barrier " + }, + { + "bbox": [ + 47, + 70, + 545, + 80 + ], + "type": "inline_equation", + "content": "\\bullet" + }, + { + "bbox": [ + 47, + 70, + 545, + 80 + ], + "type": "text", + "content": " bicycle " + }, + { + "bbox": [ + 47, + 70, + 545, + 80 + ], + "type": "inline_equation", + "content": "\\bullet" + }, + { + "bbox": [ + 47, + 70, + 545, + 80 + ], + "type": "text", + "content": " bus " + }, + { + "bbox": [ + 47, + 70, + 545, + 80 + ], + "type": "inline_equation", + "content": "\\bullet" + }, + { + "bbox": [ + 47, + 70, + 545, + 80 + ], + "type": "text", + "content": " car " + }, + { + "bbox": [ + 47, + 70, + 545, + 80 + ], + "type": "inline_equation", + "content": "\\bullet" + }, + { + "bbox": [ + 47, + 70, + 545, + 80 + ], + "type": "text", + "content": " driveable " + }, + { + "bbox": [ + 47, + 70, + 545, + 80 + ], + "type": "inline_equation", + "content": "\\bullet" + }, + { + "bbox": [ + 47, + 70, + 545, + 80 + ], + "type": "text", + "content": " flat " + }, + { + "bbox": [ + 47, + 70, + 545, + 80 + ], + "type": "inline_equation", + "content": "\\bullet" + }, + { + "bbox": [ + 47, + 70, + 545, + 80 + ], + "type": "text", + "content": " ignored " + }, + { + "bbox": [ + 47, + 70, + 545, + 80 + ], + "type": "inline_equation", + "content": "\\bullet" + }, + { + "bbox": [ + 47, + 70, + 545, + 80 + ], + "type": "text", + "content": " manmade " + }, + { + "bbox": [ + 47, + 70, + 545, + 80 + ], + "type": "inline_equation", + "content": "\\bullet" + }, + { + "bbox": [ + 47, + 70, + 545, + 80 + ], + "type": "text", + "content": " motor " + }, + { + "bbox": [ + 47, + 70, + 545, + 80 + ], + "type": "inline_equation", + "content": "\\bullet" + }, + { + "bbox": [ + 47, + 70, + 545, + 80 + ], + "type": "text", + "content": " pedestrian " + }, + { + "bbox": [ + 47, + 70, + 545, + 80 + ], + "type": "inline_equation", + "content": "\\bullet" + }, + { + "bbox": [ + 47, + 70, + 545, + 80 + ], + "type": "text", + "content": " sidewalk " + }, + { + "bbox": [ + 47, + 70, + 545, + 80 + ], + "type": "inline_equation", + "content": "\\bullet" + }, + { + "bbox": [ + 47, + 70, + 545, + 80 + ], + "type": "text", + "content": " terrain " + }, + { + "bbox": [ + 47, + 70, + 545, + 80 + ], + "type": "inline_equation", + "content": "\\bullet" + }, + { + "bbox": [ + 47, + 70, + 545, + 80 + ], + "type": "text", + "content": " trailer " + }, + { + "bbox": [ + 47, + 70, + 545, + 80 + ], + "type": "inline_equation", + "content": "\\bullet" + }, + { + "bbox": [ + 47, + 70, + 545, + 80 + ], + "type": "text", + "content": " truck " + }, + { + "bbox": [ + 47, + 70, + 545, + 80 + ], + "type": "inline_equation", + "content": "\\bullet" + }, + { + "bbox": [ + 47, + 70, + 545, + 80 + ], + "type": "text", + "content": " vegetation" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21712" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 156 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 156 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 156 + ], + "type": "text", + "content": "[1] Jens Behley, Martin Garbade, Andres Milioto, Jan Quenzel, Sven Behnke, Cyril Stachniss, and Juergen Gall. 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RAFTformer is a two-stage fully transformer based architecture comprising of a video transformer backbone that operates on high resolution, short-range clips, and a head transformer encoder that temporally aggregates information from multiple short-range clips to span a long-term horizon. Additionally, we propose a novel self-supervised shuffled causal masking scheme as a model level augmentation to improve forecasting fidelity. Finally, we also propose a novel real-time evaluation setting for action forecasting that directly couples model inference latency to overall forecasting performance and brings forth a hitherto overlooked trade-off between latency and action forecasting performance. Our parsimonious network design facilitates RAFTformer inference latency to be $9 \\times$ smaller than prior works at the same forecasting accuracy. Owing to its two-staged design, RAFTformer uses $94\\%$ less training compute and $90\\%$ lesser training parameters to outperform prior state-of-the-art baselines by 4.9 points on EGTEA Gaze+ and by 1.4 points on EPIC-Kitchens-100 validation set, as measured by Top-5 recall (T5R) in the offline setting. In the real-time setting, RAFTformer outperforms prior works by an even greater margin of up to 4.4 T5R points on the EPIC-Kitchens-100 dataset. Project Webpage: https://karttikeya.github.io/publication/RAFTformer/.", + "bbox": [ + 76, + 287, + 473, + 694 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 709, + 209, + 724 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Latency matters. It is a crucial system design consideration for countless applications that operate in real-time from hardware design [65], network engineering [63], and satellite communications [30] to capital trading [32], human vision [59] and COVID transmission patterns [54]. However, it has not been a center stage design consideration in modern computer vision systems of the past decade [11,45]. Modern vision system design has largely focused on the", + "bbox": [ + 75, + 733, + 468, + 854 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/8cae1987f001aaa922bf43d041f42357f1946ed8965d3ec9aa471acf10c20730.jpg", + "image_caption": [ + "Figure 1. Action Forecasting is the task of predicting actions that will happen after a pre-determined time span, say $t_f$ seconds, into the future. Prior works consider an offline evaluation setting that ignores the model inference latency. We propose a latency-aware real-time evaluation setting where the model is required to finish forecasting $t_f$ seconds before the target time. We present RAFTformer, a fast action anticipation transformer that outperforms prior works both in offline & real-time setting while forecasting actions in real-time (≥25 FPS)." + ], + "image_footnote": [], + "bbox": [ + 509, + 260, + 888, + 484 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "correctness of systems rather than the latency of the predictions. While vision-based forecasting systems are often meant for embodied real-time deployment on autonomous agents like self-driving cars and robots, they are evaluated in an offline setting where inference latency is neglected (Figure 1). Interestingly, recent neural network architectures have adopted FLOPs as a proxy for latency as a second axis for model design. While a sufficient fidelity metric for offline after-the-fact applications like automatic content recognition, latency often comes second to correctness, even for real-time systems such as forecasting models.", + "bbox": [ + 496, + 625, + 892, + 790 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Forecasting empowers reactive planning [17]. An autonomous system present in rich human environments inevitably needs to understand human actions around it for smooth task planning and execution. Autonomous agent planning critically depends on anticipating the future of the scene in various forms such as trajectory prediction [22, 23, 57, 58], action forecasting [19, 25, 80] or future scene", + "bbox": [ + 496, + 795, + 893, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* Work done during Harshayu's internship at HRI with Chiho Choi's supervision who is now at Samsung Semiconductor US Karttikeya Mangalam is the corresponding author", + "bbox": [ + 75, + 862, + 468, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "18759", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "segmentation [8] and anticipating the future is an activity humans subconsciously do for day-to-day tasks [60]. And while vision-based forecasting systems are often meant for embodied real-time deployment on autonomous agents like autonomous cars and robots, they are evaluated in an offline setting where inference latency is neglected (Figure 1).", + "bbox": [ + 75, + 90, + 470, + 181 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, we propose a real-time evaluation setting (Figure 1) that closely mimics the real-world deployment for a forecasting system. Suppose that in a real-time system, the design specifications require the forecasting system outputs $t_f$ seconds in advance of the event to be able to plan and use the forecasts effectively. In current offline settings, the forecasting system begins the inference $t_f$ seconds in advance of the event ('Present' in Figure 1) and the model latency is ignored (or assumed to be 0) such that the predictions are available instantly. However, in our proposed real-time setting, the model is required to start inference in advance of 'Present' so that the outputs are available with a horizon of $t_f$ seconds, meeting the design specification.", + "bbox": [ + 75, + 184, + 468, + 381 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We observe that in the real-time setting, the prior works fare quite poorly because of their slow model inference latency (Table 3). A large latency implies that the model has to start inference further in the past and has to rely on older video data to make forecasts with the benefit of more expressiveness (Figure 2). A smaller latency means the model can enjoy more recent video data but has limited capacity. Simply said, models that are only evaluated in the offline setting may fare poorly in the real-time deployment setting due to their latency agnostic design (Figure 2).", + "bbox": [ + 75, + 382, + 468, + 532 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We present, RAFTformer, a real-time action forecasting transformer that uses a two-stage transformer encoder-based network for lightning fast forecasts in inference. RAFTformer uses a shuffled casual masking scheme based feature prediction loss for learning strong temporal cues that transfer to feature prediction. Further, RAFTformer uses specialized anticipation tokens for learning to predict action at multiple temporal horizons that improve model reasoning capabilities of short-term action forecasting as well. Finally, the model is explicitly designed for real-time embodied deployments that allows inference up to an order of magnitude faster than prior state-of-the-art methods. In summary, our contributions are three-fold,", + "bbox": [ + 75, + 536, + 468, + 731 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "First, we propose Real-time Action Forecasting Transformer (RAFTformer), a real-time action forecasting transformer with latency at least $9 \\times$ smaller than prior state-of-the-art action forecasting methods. RAFTformer uses specialized anticipation tokens and a novel shuffled casual masking-based self-supervision loss that allows it to outperform prior work while maintaining low latency with a reduction of $94\\%$ in GPU training time and $90\\%$ in the number of trainable parameters compares to prior works. To the best of our knowledge, our work is the first to achieve action anticipation in real-time (i.e. 25 fps).", + "bbox": [ + 75, + 734, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/d8b14c4788415741396220e49009cd343151625e0fb90d85fc005f050ca0c242.jpg", + "image_caption": [ + "Figure 2. Evaluation Performance vs. Latency. Bigger models perform better in latency agnostic offline settings. In the real-time evaluation setting, we observe that, beyond a limit, bigger models with higher latency cause a drop in forecasting performance. In practical deployment, there exists a trade-off between latency and high-fidelity forecasts. See §4.3.1 for details." + ], + "image_footnote": [], + "bbox": [ + 506, + 94, + 885, + 247 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Second, we propose a latency-aware real-time evaluation setting (Figure 1) that better mimics practical deployment settings for embodied forecasting systems. Real-time evaluation demonstrates a clear trade-off between inference latency and model forecasting fidelity, paving the path for the development of latency-aware forecasting models in the future (also see [20]).", + "bbox": [ + 498, + 366, + 890, + 472 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Third, Through extensive experiments, we show that RAFTformer outperforms prior state-of-the-art methods by 4.9 points on the EGTEA Gaze+ dataset, by 1.4 points on the EPIC-Kitchens-100 dataset according to the Top-5 Recall metric and by a relative margin of $5.3\\%$ on the top-1 accuracy metric on EPIC-Kitchens-55 dataset.", + "bbox": [ + 498, + 474, + 890, + 566 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 585, + 640, + 599 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Action Anticipation. Over the last few years, action anticipation has seen significant advances following the promising results in video recognition [2,4,12,15,24,38,40, 49,55,61,80,87] and video segmentation [27,43,48,76,81]. While earlier works [1, 56, 68] use CNN-based methods for video action anticipation, many follow-up works transitioned into using recurrent sequence-based networks [19, 22, 64, 66, 71]. Using multiple spatial and temporal scales was another key idea explored in several anticipation works [15, 70, 70, 77, 80, 86]. Masking-based self-supervision has proven to be a new frontier for both image [5, 14, 33, 35, 62] and video [31, 74] representation learning. This concept has also been explored in the context of video anticipation [25] which differs from prior works that explore temporal consistency [16, 37, 42, 79, 82], inter-frame predictability [28, 29, 36], and cross-modal correspondence [3, 44, 73]. In our work we propose a novel generalized self-supervision scheme which is a crucial part of our model's ability to generalize and outperform SOTA.", + "bbox": [ + 496, + 613, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "18760", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Transformers for Video Anticipation. With the rise of transformers for sequence tasks, recent works have explored various image and video-based transformers [25, 26, 26, 78, 80, 85] for anticipating actions. [25] proposes a ViT-based [11] spatial transformer backbone with a transformer decoder head to anticipate the next action with a $1s$ horizon. [25] predicts actions in the same latent space as their feature decodings causing conflation between feature reconstruction and future prediction. We propose specialized anticipation tokens to address this problem. Furthermore, [25] uses a recurrent decoder and frame-level operation, which is inefficient for both training compute and inference latency. MeMViT [80] proposes another fully transformer model which extends MViT [12] for better long-range modeling using a novel caching mechanism. However, their model is trained to only predict the next action and thus does not explicitly learn to model the future or evolving scene dynamics. Furthermore, their model is less efficient than RAFTformer in terms of both training and inference time due to its larger model and input size and complete end-to-end training. RAFTformer uses a fixed pre-trained video network and only trains the RAFTformer network. Recently [26] propose a transformer-based model for long-term action anticipation. They focus on a sequential prediction rather than next-action prediction and do not focus on inference latency.", + "bbox": [ + 76, + 90, + 472, + 482 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Real-Time Systems. Latency matters, especially for real-time applications. Autonomous agents need to reason about nearby agents and take real-time decisions. This vision has led to great progress in the development of real-time systems in the related fields of semantic segmentation [13], video object segmentation [76], object detection [7, 51, 53, 67], multi-object tracking [41]. While some progress has also been made in activity understanding [72, 84], it is limited to recognition and detection. Keeping this in mind, some recent works in action anticipation have also started focusing on efficiency and memory footprint and report training time, inference time, and trainable parameters [80]. Although a step in the right direction, these works have high inference times in comparison to their desired anticipation horizon. Our proposed method is significantly faster during both training and inference, has fewer trainable parameters and a smaller memory footprint, and still outperforms state-of-the-art methods.", + "bbox": [ + 76, + 481, + 472, + 753 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Real-Time Action Forecasting Transformer", + "text_level": 1, + "bbox": [ + 76, + 768, + 464, + 787 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we first present the problem formulation (§3.1), followed by the architectural details of the video backbone for feature extraction (§3.2) and the RAFTformer model architecture (§3.3) including anticipation tokens (§3.3.1), shuffled causal masking (§3.3.2) and permutation encodings (§3.3.3), finishing with an outline of the loss functions used for training the model (§3.5).", + "bbox": [ + 75, + 795, + 468, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Problem Formulation", + "text_level": 1, + "bbox": [ + 498, + 90, + 705, + 107 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given an observed video starting from time $T = 0$ and of arbitrary length $t$ , $V_{0,t} = [F_0, \\dots, F_t]$ where $F_i$ denotes the frame at time $i$ , the task is to predict the future action $t_f$ seconds in the future, i.e., action $\\mathrm{A}_{t + t_f}$ at time $T = t + t_f$ .", + "bbox": [ + 496, + 114, + 893, + 178 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Pre-trained Video Backbone", + "text_level": 1, + "bbox": [ + 498, + 186, + 756, + 200 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In contrast to state-of-the-art models [25, 80] that train end-to-end, we demonstrate that a two-stage training process is both efficient and produces high-fidelity forecasts. First, we split the full duration of the past video $V_{0,t}$ into sub-clips $V = [C_0,C_1,\\dots,C_N]$ in a sliding window fashion. Each clip, $C_i$ , is independently processed with the short-term video backbone like MViT [12] to extract clip-level features. Previous works, such as [25], have employed image backbones for comparable undertakings, while we contend that video backbones offer richer spatio-temporal features, thus benefiting the downstream task. Further, a video backbone also allows lower latency since the produced clip embeddings already contain fused features for several images at once.", + "bbox": [ + 496, + 209, + 893, + 421 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our two-stage design also allows for hierarchical temporal processing of the long-form past video. The short-term recognition backbone model operates on short, high-resolution clips. These extracted features are then used as input to the head network to process longer-range lower resolution features that capture key information from each clip. This is a crucial design consideration to lower the inference latency in RAFTformer while still capturing longer-range temporal dependencies compared to [19, 25].", + "bbox": [ + 496, + 422, + 893, + 559 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.3.RAFTformer Model Network", + "text_level": 1, + "bbox": [ + 498, + 568, + 764, + 584 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We propose RAFTformer as a transformer encoder model. The transformer encoder has the advantage of being able to effectively learn across clip dependencies by attending over independently extracted clip features without facing memory bottlenecks such as faced in LSTM encoders [34] that have been used in some prior works [19,70]. However, to make the encoder effective for action forecasting on pre-trained features, we propose several changes to the training process to allow two-staged training to work as well as end-to-end training for action forecasting.", + "bbox": [ + 496, + 593, + 893, + 744 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.3.1 Anticipation Tokens", + "text_level": 1, + "bbox": [ + 498, + 753, + 696, + 770 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The extracted clip embeddings $[C_0\\cdots C_{N-1}]$ form the first part of the input to the action anticipation head. For the second part, we propose to train learnable 'anticipation tokens' that can aggregate global context and later can be decoded into future predictions. This design choice stands in contrast to prior works like [25] where the output of the anticipation token is implicitly designed to be in the same latent space as the output of their image-feature tokens. In", + "bbox": [ + 496, + 779, + 893, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "18761", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/6eba557065fa750a29a0c8a2b969291b2572e354663fd503fcbb5e44e3efea74.jpg", + "image_caption": [ + "Figure 3. RAFTformer is a real-time action anticipation transformer architecture comprised of two stages. The first stage is a pretrained short-term backbone that produces individual clip embeddings independently of other clips (§3.2). In the second stage (§3.3), absolute position encodings are added and the resulting sequence is shuffled with a sampled permutation $\\pi^{*} \\sim \\pi$ . The permutation encodings (§3.3.3) are then added to the shuffled sequence and after concatenation with anticipation tokens, the sequence is processed with the RAFTformer encoder. The output tokens are decoded via short & long-term action anticipation heads (§3.4), as well as the feature prediction head trained with self-supervised loss ( $\\mathcal{L}_{\\mathrm{SCM}}$ ), future feature prediction loss ( $\\mathcal{L}_{\\mathrm{future}}$ ) and action forecasting loss ( $\\mathcal{L}_{\\mathrm{focal}}$ ) (§3.5)." + ], + "image_footnote": [], + "bbox": [ + 78, + 85, + 893, + 327 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "contrast to prior works, we find that temporal aggregation such as mean pooling for forecasting leads to subpar performance (see Table 5). Hence, we use the output tokens corresponding to $[C_0\\cdots C_N]$ solely for self-supervised feature loss rather than action anticipation.", + "bbox": [ + 75, + 444, + 468, + 518 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Instead, for action anticipation, we propose to train learnable 'anticipation tokens' to learn useful global context from the clip tokens. The output of the anticipation token is no longer restricted to be in the same latent space as the output of clip-feature tokens like in [25] and can better capture the information needed to anticipate the next action. Further, we propose to use multiple anticipation tokens to generate additional supervision, with each token attending to different past video lengths and producing forecasts for different time horizons in the future.", + "bbox": [ + 75, + 520, + 470, + 672 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3.2 Self-Supervision via Shuffled Feature Prediction", + "text_level": 1, + "bbox": [ + 76, + 679, + 467, + 695 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Prior works explored using the self-supervision task of predicting frame or clip features and using an MSE loss [25]. We propose using a generalized form of masking-based self-supervision [33] based on predicting shuffled future features. Predicting future clip features has a two-fold benefit: (A) It encourages causally learning the observed sequence incentivizing the model to grasp underlying scene dynamics and (B) Prediction in the latent feature space allows reasoning semantically about the future without wasting modeling capacity with low pixel level scene details.", + "bbox": [ + 75, + 703, + 468, + 854 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Different from loss functions proposed in prior works [25], we propose an improved auto-regressive scheme for self-supervised learning by future feature pre", + "bbox": [ + 75, + 854, + 470, + 901 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/7f8a0e24e45395c32584a6047f26e89251412de493d86527456c87e4bada27cb.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Auto-regressive [1,2,3,4]Shuffle π1: [4,1,3,2]Another Shuffle π2: [3,4,2,1]
1 → 24 → 13 → 4
2 → 31 → 34 → 2
3 → 43 → 22 → 1
", + "bbox": [ + 513, + 441, + 877, + 518 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Table 1. Encoding the input permutation $\\pi$ . Shuffling the input sequence arbitrarily changes the successor of each token.", + "bbox": [ + 500, + 523, + 893, + 551 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "diction. Rather than sequentially predicting missing clip features in order to use a causal attention mask, we propose to use a model-level augmentation of the attention masking scheme where some of the attention weights are not used from the original causal mask.", + "bbox": [ + 498, + 563, + 893, + 640 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Random Masking. Construction of a sparse augmented attention mask is non-trivial. Simply generating a random mask such as in MAE [33] fails to isolate information within the intended partitioning due to multi-hop message passing caused by repeated application of the same mask. For example, in Figure 4, the attention mask prohibits token 1 to access token 2 and 3 (shown by 'white'). However, after two layers, token 1 in layer 2 can access information in token 2 in layer 0 (shown by red border), indirectly through token 4 in later 1 because of multi-hop message passing. This temporal information leakage can cause self-supervision to fail. For example, self-supervising token 1 with token 2 feature prediction would collapse in setup of Figure 4. To prevent this, we propose a simple yet effective solution.", + "bbox": [ + 496, + 674, + 893, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "18762", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Shuffled Causal Masking. We know that vanilla causal masks ensure that information available to each token is invariant under repeated applications of the attention mask, i.e., multi-hop message passing. Since multi-hop message passing is token permutation invariant, any permutation of the tokens from the causal mask will preserve the invariance of accessible information under multiple hops. Thus, this allows a general framework for structured randomized mask construction without temporal leakage. We notice that a row-wise permutation of the attention mask is equivalent to the same permutation applied to the sequence itself. Hence, the same effect as properly constructed random masks can simply be achieved by shuffling the input token sequence itself. This allows generalizing vanilla autoregressive prediction order to arbitrary sequence permutations without any multi-hop information leakage through the layers. Thus, rather than predicting clip features sequentially from 0 to $N - 1$ like [25], our proposed scheme allows for exponentially more variations.", + "bbox": [ + 76, + 90, + 472, + 378 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Referring to Figure 3, we first add absolute position embeddings (APE) to each of the clip features before shuffling them. This allows the transformer to leverage the information about the actual temporal order of each clip in the video. Without the absolute position embeddings, the transformer is input permutation equivariant, which is not a desirable property for action forecasting. However, while APE is sufficient for positional information in vanilla autoregressive ordering, it is not enough for prediction under our proposed Shuffled Causal Masking (SCM) scheme. In autoregressive ordering, for any specific token, the next token in the sequence corresponds to a fixed position and hence the self-supervised training process can subtly learn this bias via next-token feature supervision. In contrast, under SCM the temporal position of the next token varies depending on the shuffling permutation. Hence, self-supervised training cannot learn to perform effective feature prediction without information about the shuffling permutation.", + "bbox": [ + 76, + 378, + 472, + 652 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3.3 Permutation Position Encoding", + "text_level": 1, + "bbox": [ + 76, + 661, + 349, + 678 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Naïve Encodings. For an $L$ length sequence, there exist $L!$ possible permutations. Encoding each permutation $(\\pi)$ by itself is clearly intractable. First, we observe that encoding $\\pi^{*}$ as a set of $O(L)$ embeddings which are shared among different $\\pi$ is more efficient. A follow-up solution would be to instead encode each predecessor $\\mapsto$ successor relationship as an encoding and have $L - 1$ of such embeddings together encode $\\pi^{*}$ . This reduces to the total number of required embeddings to $L(L - 1)$ from $L!$ . Each $\\pi^{*}$ now shares every one of its $L$ embeddings with other $\\pi$ , but considered as a set, the $L$ embeddings uniquely encode $\\pi^{*}$ . However, even $L^2$ becomes intractable for large $L$ .", + "bbox": [ + 76, + 686, + 468, + 868 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Permutation Position Encodings $(\\pi \\mathrm{PE})$ provides an elegant solution for encoding $\\pi^{*}$ requiring only $L$ total encod", + "bbox": [ + 76, + 869, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/a789e94b775d299c15f0c0e1b6f1dc172688bd9ddbdc95e1b4d42a0ae9e6c8a9.jpg", + "image_caption": [ + "Figure 4. Random Masking Self-Supervision Illustration of how naive random masking (white denotes masked out) fails for self-supervised feature prediction task. We can see that in Layer 1 the tokens can only access information according to the provided mask. However, if the same mask is used in Layer 2, there is information leakage across tokens which is undesirable." + ], + "image_footnote": [], + "bbox": [ + 517, + 90, + 844, + 237 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "ings to be learned. $\\pi$ PE encodes the predecessor $\\mapsto$ successor relationships but further simplifies by noting that adding the encoding to the token itself makes the predecessor information redundant. The token itself is the predecessor and has the positional information available from APE. Hence, we simply encode the successor positional information, and that in combination with APE uniquely encodes $\\pi^{*}$ . Hence, we design $\\pi$ PE to be the encoding of the original temporal position of the successor in the permuted sequence. So for the $\\pi_{1}$ permutation in Table 1, we would add $\\pi$ PE[1] to token 4, $\\pi$ PE[3] to token 1 and $\\pi$ PE[2] to token 3.", + "bbox": [ + 496, + 344, + 893, + 512 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Overall Mechanism", + "text_level": 1, + "bbox": [ + 500, + 527, + 687, + 542 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The past video is split into clips, and the clip embeddings $[C_0\\cdots C_{N-1}]$ are extracted using a video backbone (Figure 3). Anticipation tokens are concatenated to the extracted sequence ( $\\S 3.3.1$ ), followed by the addition of absolute position encoding to the concatenated sequence. Now, the clip embedding is shuffled according to a randomly chosen permutation $\\pi^*$ to obtain $[C_{\\pi^*[0]}\\cdots C_{\\pi^*[N-1]}\\]$ . The sampled permutation $\\pi^*$ is then encoded by adding the successor's ( $\\S 3.3.3$ ) embedding to each token. In Figure 3, $\\pi^*[1] = 3$ and $\\pi^*[2] = N$ , hence $\\pi \\mathrm{PE}[\\pi^*[1+1]]$ is added to the token $\\pi^*[1]$ i.e., $\\pi \\mathrm{PE}[N]$ is added to $E_3$ , which is used to self-supervise the feature at position 1 in the shuffled sequence, i.e., token 3 ( $\\S 3.3.2$ ). The shuffled input sequence, in addition to the anticipation tokens, is now propagated through the transformer encoder using a causal attention masking scheme and the output is decoded with the head networks.", + "bbox": [ + 496, + 555, + 893, + 797 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Head Networks We propose using three MLP heads on top of the transformer encoder network (Figure 3). Two MLP heads decode the anticipation tokens into the predicted future action distribution. The third MLP head up-samples the encoded tokens to the original representation space of the input tokens to allow self-supervision loss.", + "bbox": [ + 496, + 809, + 893, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "18763", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/aa3b1d6a5b34def38caa9fc070785738f07682129d202c54d2f6993d48f90c13.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
SplitMethodAddl. ModalityInitEpic BoxesTop-5 RecallParameters (×106)GPU HoursInference Latency (ms)
VerbNounAction
ValTempAgg [70]NoneIN1K24.229.813.0---
RULSTM [19]NoneIN1K--13.3---
RULSTM [19]Obj+FlowIN1K✓30.827.814.0---
TempAgg [70]Obj+Flow+ROIIN1K✓23.231.414.7---
AVT [25]NoneIN21K30.231.714.9378-420
AVT+ [25]ObjIN21K✓28.232.015.9---
TSN-AVT+ [25]ObjIN21K✓31.825.514.8---
MeMVit [80]NoneK40032.833.215.159-160
MeMVit [80]NoneK70032.237.017.7212368350
TestRAFTformerNoneK400 + IN1K33.335.517.6262340
RAFTformerNoneK70033.737.118.02627110
RAFTformer-2BNoneK700 + IN1K33.837.919.15250160
RULSTM [19]Obj+FlowIN1K✓25.326.711.2---
TBN [83]Obj+FlowIN1K✓21.526.811.0---
AVT+ [25]Obj+FlowIN21K✓25.628.812.6---
Abstract Goal [69]Obj+FlowIN1K✓31.430.114.3---
AFFT [85]Obj+Flow-✓20.731.814.9---
RAFTformerNoneK400 + IN1K27.332.814.0262340
RAFTformerNoneK70027.434.014.72627110
RAFTformer-2BNoneK700 + IN1K30.134.115.45250160
", + "bbox": [ + 119, + 88, + 848, + 425 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. Offline Evaluation Results on the EK-100 dataset for $t_f = 1$ second horizon. Latency is measured over the entire model including the backbone & head networks on a single 16G Tesla V100 GPU. Methods that use other modalities (+RGB) are deemphasized.", + "bbox": [ + 75, + 428, + 893, + 458 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3.5. Loss Functions", + "text_level": 1, + "bbox": [ + 76, + 464, + 230, + 479 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We observe that the ground truth action distributions are often long-tailed, and propose to use the the focal loss [52], for supervising the future action prediction distributions.", + "bbox": [ + 75, + 487, + 470, + 532 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {f o c a l}} = \\sum_ {A _ {i} \\in A} \\sum_ {i = 0} ^ {n} - (1 - p _ {A _ {i}}) ^ {\\gamma} \\log \\left(p _ {A _ {i}}\\right)\n$$\n", + "text_format": "latex", + "bbox": [ + 137, + 536, + 410, + 575 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $p_i$ is the predicted probability for the correct class for the $i$ th example, $A_i$ represents predictions from a specific anticipation token and $\\gamma$ is the focusing parameter where $\\gamma = 0$ is cross entropy loss. Increasing $\\gamma$ results in an increased penalty for hard, misclassified examples.", + "bbox": [ + 75, + 582, + 468, + 657 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For self-supervision using shuffled causal masking to predict next-token embeddings, we use an expected $\\ell_2$ loss over both past tokens, with the expectation being oversampled permutations $\\pi^{*} \\sim \\pi$ .", + "bbox": [ + 75, + 657, + 468, + 717 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal{L}_{\\mathrm{SCM}} = \\underset {\\pi^{*}\\sim \\pi}{\\mathbb{E}}\\sum_{j = 0}^{N - 1}\\| E_{\\pi^{*}[j]} - \\hat{E}_{\\pi^{*}[j]}\\|_{2}^{2}\n$$\n", + "text_format": "latex", + "bbox": [ + 143, + 720, + 403, + 762 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $E_{\\pi^{*}[j]}$ and $\\hat{E}_{\\pi^{*}[j]}$ denotes the original and the predicted clip embedding at position $j$ after permuting with $\\pi^{*}$ . For future token prediction, we use a simple $\\ell_2$ loss:", + "bbox": [ + 76, + 761, + 468, + 808 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {f u t u r e}} = \\left\\| E _ {\\mathrm {f u t u r e}} - \\hat {E} _ {\\mathrm {f u t u r e}} \\right\\| _ {2} ^ {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 176, + 811, + 369, + 832 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $E_{\\mathrm{future}}$ is the MViT embedding for the next clip (after $t_f$ ). Finally, the overall loss is simply a weighted sum,", + "bbox": [ + 76, + 837, + 470, + 869 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {\\text {f o c a l}} + \\lambda_ {1} \\mathcal {L} _ {\\text {S C M}} + \\lambda_ {2} \\mathcal {L} _ {\\text {f u t u r e}}\n$$\n", + "text_format": "latex", + "bbox": [ + 161, + 875, + 385, + 892 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 498, + 463, + 633, + 479 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets & Metrics. We use the widely benchmarked EPIC-KITCHENS dataset [9], an unscripted set with nearly $20 \\times$ more action classes and $10 - 100 \\times$ more observed sequences than other action datasets like 50 Salads [47] and Breakfast [46], used in prior work [19]. We use both the EPIC-55 & EPIC-100 anticipation splits and the EGTEA+ Gaze dataset [50]. Dataset details in supplementary.", + "bbox": [ + 496, + 486, + 890, + 593 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Since human decision-making is inherently multimodal, we propose an approach to predict multiple reasonable future action forecasts. In addition to top-1 accuracy, we report top-5 recall following prior works [19, 25, 80]. We use the baseline data splits and report metrics on both the validation and test set. In addition, we report the number of trainable model parameters (M), the total compute spent for training the model to convergence on a Tesla V100 GPU (in hours), and the inference latency (in milliseconds).", + "bbox": [ + 496, + 594, + 892, + 731 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Evaluation Setting", + "text_level": 1, + "bbox": [ + 498, + 743, + 679, + 758 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Offline evaluation is the setting where the model inference latency is ignored, or in other words, assumed to be zero. All prior works [19, 25, 80] consider this setting. Referring to Figure 1, prior works assume access to all past video frames up till the present moment $T = t$ . Using this information, the model then predicts that action with a $t_f$ second horizon at $T = t + t_f$ . However, the prediction would actually be produced at time $T = t + t_l$ where $t_l$ is the model inference latency. This is not practically useful", + "bbox": [ + 496, + 763, + 893, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "18764", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/b4956e386c44e4aedd68caae19211c2059b0d68222d25a0b726dc8edd696cfe5.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ModelInitLatency (t1 ms)Inference Start Time StampInference End Time StampTarget Time StampTop-5 Recall
VerbNounAction
AVT [25]IN21Ktavt = 420TT + tavtT + 130.231.714.9
RAFTformerK400 + IN1ktours = 40T + tavt - toursT + tavtT + 134.138.219.3 (+4.4)
MemViT [80]K400tvit = 160TT + tvitT + 132.833.215.1
RAFTformerK400 + IN1ktours = 40T + tvit - toursT + tvitT + 133.837.118.1 (+3.0)
MemViT [80]K700tvit = 350TT + tvitT + 132.237.017.7
RAFTformerK400 + IN1ktours = 40T + tvit - toursT + tvitT + 133.737.919.0 (+1.3)
", + "bbox": [ + 130, + 88, + 836, + 228 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/f0c4e3bf3d7fc9eb964df4b171ac71576e2ef021ca013d95e4376084a8c57512.jpg", + "table_caption": [ + "Table 3. Real-time Evaluation Results for benchmarking action forecasting methods in a practical setting (§4.1). Each comparison is performed between a pair of models where their start time ('Inference Start') times have been adjusted (Figure 1) by their latency so that they produce the forecasting output for the 'Target Time' simultaneously ('Inference End'). For prior works [25,80], start & end times are kept the same as their original offline settings (Table 2) to avoid any training recipe change. Faster models can pragmatically utilize recent frames while slower models must rely on higher fidelity prediction from older frames. Latency measured on a single 16G Tesla V100 GPU." + ], + "table_footnote": [], + "table_body": "
ModelInitTop-1 Acc
RULSTM [19]TSN/IN1k13.1
ActionBanks [70]TSN/IN1k12.3
AVT-h [25]TSN/IN1k13.1
RAFTformerTSN/IN1k13.8
", + "bbox": [ + 138, + 306, + 405, + 402 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "since often, we require time horizon $t_f$ to meaningfully use the predicted future outcomes. Further, this does not account for absurdities where a large model might even have latency $t_l > t_f$ , in which case the model is predicting an action that has already happened by the time it predicts it! A complex model can have great offline performance but its inference time would make it unusable in practice.", + "bbox": [ + 75, + 438, + 468, + 544 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Real-time evaluation. To remedy this impractical situation, we consider the real-time evaluation setting. In this setting, the model is required to finish inference with at least $t_f$ seconds horizon before the target time (Fig. 1). Hence, the model is allowed access to past video data only for $T < t - t_l$ . This setting even allows for large models where $t_l > t_f$ since predictions would still be produced with $t_f$ seconds before the target time. Unlike other recognition scenarios where latency is a mere annoyance, in the case of future forecasting, models are often used in real-time rather than offline. The offline setting subtly oversteps the prediction horizon $t_f$ , by receiving forecasts with a margin much less than the postulated $t_f$ horizon. By coupling model latency to the past video data observed, the real-time setting incentivizes the development of efficient forecasting methods that utilize the recent data better than relying on slow large models that cannot miss the recent frames, which arguably are the most crucial for near future prediction.", + "bbox": [ + 75, + 551, + 468, + 824 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. EPIC-Kitchens-100", + "text_level": 1, + "bbox": [ + 76, + 830, + 264, + 847 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Network Details. For feature extraction, we fix the pretrained 16x4 (K400+IN1K) and 32x3 (K700) MViT-B backbones [12, 49] trained for recognition on the EK100", + "bbox": [ + 75, + 854, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/6afc0d6cedb05397ec81a7d6cedece9d7718e2b926c5a13192cdd29e1ea6272f.jpg", + "table_caption": [ + "Table 4. Offline Evaluation results on the Epic-Kitchens-55." + ], + "table_footnote": [], + "table_body": "
ModelSettingTop-5 Recall
ATFLSCM2×AT
Mean pooling✓15.2
16.1 (+0.9)
RAFTformer✓✓16.8 (+0.7)
✓✓✓17.4 (+0.6)
✓✓✓✓17.6 (+0.2)
", + "bbox": [ + 522, + 308, + 867, + 407 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 5. EK100 Ablation Study. FL is feature loss (no SCM), SCM is Shuffled Causal Masking (\\$3.3.2), AT $\\left( {2 \\times }\\right)$ are single (double) anticipation tokens (§3.3.1).", + "bbox": [ + 498, + 409, + 890, + 453 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "dataset. Each clip is embedded as a 768-dimensional feature vector. Unless mentioned otherwise, the action forecasting experiments use a $t_f = 1$ second horizon. RAFTformer encoder is a lightweight 4 layer, 4 head transformer encoder using post-normalization and ReLU activations. A linear projection from up-projects $768 \\rightarrow 1024$ for the transformer. We only shuffle during training with a probability of 0.3. The output of the encoder is down projected from $1024 \\rightarrow 768$ channels. Both short-term and long-term action prediction heads are fast & lightweight MLPs $(1024 \\rightarrow 2048 \\rightarrow 3806)$ . We set $\\lambda_1 = \\lambda_2 = 14$ . For other details, please see supplementary.", + "bbox": [ + 496, + 482, + 890, + 664 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Offline Evaluation. In Table 2 we first report RAFTformer results against prior works, including previous SOTA MeMViT [80]. Results that use additional modalities like Object (Obj), Flow (Flow), Object Region of Interest (ROI), or Epic Kitchen boxes are de-emphasized. Using only RGB, RAFTformer (K700) outperforms the AVT RGB model in action T5R by 3.1 points and the AVT RGB+Obj model by 2.1 points. RAFTformer slightly outperforms MeMViT action T5R while predicting actions $8.75 \\times$ faster with $8.2 \\times$ lesser trainable parameters and a $16 \\times$ faster training. We also combine two separate RAFTformer models to train a two-backbone model (RAFTformer-2B) that achieves state-of-the-art by with a $1.4\\%$ T5R increase. In the second section, we report our submitted results to the EK100 test server. We observe that RAFTformer general", + "bbox": [ + 496, + 672, + 892, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "18765", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/2d88fa9b0e4d54c2d5fb5bd46025b7d1678d2a39d4dab4f79012bca5eee55107.jpg", + "table_caption": [], + "table_footnote": [ + "Table 6. EGTEA Gaze+. Under same initialization, RAFTformer outperforms prior methods without additional modalities." + ], + "table_body": "
ModelInitModalityTop-5 Recall
DMR [75]-RGB38.1
ATSN [9]TSN/IN1kRGB+Flow31.6
MCE [18]TSN/IN1kRGB+Flow43.8
TCN [6]-RGB47.1
FN [10]VGG-16RGB42.7
ED [21]VGG-16/TSRGB+Flow54.6
RULSTM [19]TSN/IN1kRGB+Obj+Flow58.6
RAFTformerTSN/IN1kRGB63.5
", + "bbox": [ + 99, + 88, + 444, + 217 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "izes well to the test set, improving upon the $\\mathrm{AVT + }$ multimodal ensemble model [25] by 2.8 T5R points.", + "bbox": [ + 76, + 256, + 467, + 286 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3. Additional Datasets", + "text_level": 1, + "bbox": [ + 76, + 294, + 264, + 309 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "EPIC-Kitchens 55. We also compare RAFTformer to prior baselines on the EK55 dataset in Table 4 on top-1 accuracy. We evaluate against other models using the same initialization for a fair comparison. We observe that RAFTformer outperforms prior benchmarks by about $0.7\\%$ using the exact same backbone features. This shows the superiority of our proposed shuffle causal masking (§3.3.2) & anticipation token prediction (§3.3.1) in a controlled setting.", + "bbox": [ + 75, + 314, + 467, + 434 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Real-time Evaluation. In table 3, we fix the target - start time difference to be what the prior models such as, AVT [25] or MeMViT [80] were designed for, to avoid any unintended change in their training recipes. Hence, we shift RAFTformer start time so that the output forecasts are produced simultaneously for the pair.", + "bbox": [ + 75, + 436, + 467, + 526 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We observe that RAFTformer outperforms prior methods by an even larger margin in the real-time evaluation setting than the offline setting. RAFTformer effectively utilizes its compute to produce the maximum forecasting effect at the least latency cost. This allows RAFTformer to exploit more recent information that slower models miss because of higher inference latencies $(t_{\\mathrm{ours}} < \\{t_{\\mathrm{avt}}, t_{\\mathrm{vit}}\\})$ . This also shows the disproportional effect of inference latency on forecasting performance. While RAFTFormer K400 + IN1K has a similar Top-5 Recall as MeMViT K700 in the offline setting, in the practical real-time evaluation (Table 3), RAFTformer outperforms MeMViT by $1.3\\%$ by leveraging its faster inference latency (40 vs. 350 ms).", + "bbox": [ + 75, + 527, + 467, + 723 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3.1 Latency vs. Offline & Real-time Forecasting", + "text_level": 1, + "bbox": [ + 76, + 732, + 434, + 746 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In offline evaluation, latency is ignored and all models have data access parity. As scaling laws [39] would predict, bigger models (with higher latency) have stronger forecasting performance (Blue curve in Fig. 2). In the real-time setting, a higher latency implies access to less recent data (Green curve in Fig. 2) and hence, an interesting trade-off materializes. At first, as latency (and model size) increases, the performance improves. This is because the benefit of having a more expressive model outweighs the cost of access to older video data. However, as the latency increases fur", + "bbox": [ + 75, + 750, + 467, + 898 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ther, the real-time performance starts decreasing. Now the harm of not having access to recent data outweighs the benefit of a more expressive model. For our setting, the optimal RAFTformer model has a latency of $40~\\mathrm{ms}$ with an offline and real-time performance of 19.6 and 19.3 Top-5 recall respectively. A similar trade-off would exist for any combination of dataset, model, and deployment hardware regimes. Plots are for RAFTformer models of varying backbone parameter count for $t_f = 0.58$ second prediction on EK100.", + "bbox": [ + 496, + 90, + 890, + 227 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3.2 Ablations", + "text_level": 1, + "bbox": [ + 500, + 234, + 622, + 247 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We ablate RAFTformer thoroughly in Table 5. In contrast to prior works [25,80] that pool information or use the same embedding for feature supervision and action prediction, we train explicit anticipation tokens (§3.3.1) to perform forecasting, improving T5R by 1.1. Anticipation tokens specialize in predicting the next action instead of using features that multi-task between reconstructing clip features and future action prediction [25]. Self-supervision via feature loss (FL) further improves by 0.7 T5R. Further, our SCM technique effectively regularizes FL that improves 0.6 T5R. Finally, an additional anticipation token $(2\\times \\mathrm{AT})$ for supervision further improves 0.2 T5R. Additional longer-horizon anticipation task helps in learning transferable global video features to the main anticipation task.", + "bbox": [ + 496, + 255, + 890, + 467 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "EGTEA Gaze+. We also evaluate the EGTEA Gaze+ dataset in Table 6 to showcase RAFTformer performance on new settings outside of EPIC-Kitchens. Again, we use the setting of anticipating $1s$ into the future and use the T5R metric. While prior methods use many input modalities including as object, flow, and RGB, we significantly outperform the prior state-of-the-art in this setting [19] by $4.9\\%$ . Note that we use pre-extracted TSN RGB features as provided by [19] for direct comparison. Our very strong performance on another egocentric video dataset with complex human tasks further validates the promise of RAFTformer.", + "bbox": [ + 496, + 469, + 890, + 635 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 640, + 617, + 655 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We propose Real-Time Action Forecasting Transformer (RAFTformer), a parsimonious two-stage fully transformer-based architecture consisting of a short-range video transformer backbone for feature extraction and a long-range head transformer encoder for long-term temporal aggregation across multiple clips. We also introduce a real-time evaluation setting for action forecasting models that directly penalizes high latency and closely mimics the real-world deployment scenario for forecasting models. RAFTformer outperforms prior state-of-the-art methods by significant margins across several action forecasting benchmarks in the offline setting, and by an even larger margin of upto 4.4 T5R, in the real-time setting. RAFTformer achieves $9 \\times$ lower inference latency at the same forecasting fidelity, using $16 \\times$ less training compute and $10 \\times$ lesser trainable parameters than prior baselines.", + "bbox": [ + 496, + 657, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "18766", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Yazan Abu Farha, Alexander Richard, and Juergen Gall. When will you do what?-anticipating temporal occurrences of activities. 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In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 2349-2358, 2017. 2" + ], + "bbox": [ + 503, + 92, + 890, + 488 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "18769", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Latency Matters_ Real-Time Action Forecasting Transformer/12d94c79-6b2e-4488-a967-716930fdb6d3_model.json b/2023/Latency Matters_ Real-Time Action Forecasting Transformer/12d94c79-6b2e-4488-a967-716930fdb6d3_model.json new file mode 100644 index 0000000000000000000000000000000000000000..fc9203e99c071b471d53ff85fd1475cc6229eb87 --- /dev/null +++ b/2023/Latency Matters_ Real-Time Action Forecasting Transformer/12d94c79-6b2e-4488-a967-716930fdb6d3_model.json @@ -0,0 +1,2389 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.175, + 0.131, + 0.797, + 0.154 + ], + "angle": 0, + "content": "Latency Matters: Real-Time Action Forecasting Transformer" + }, + { + "type": "text", + "bbox": [ + 0.135, + 0.18, + 0.298, + 0.2 + ], + "angle": 0, + "content": "Harshayu Girase\\(^{1,2*}\\)" + }, + { + "type": "text", + "bbox": [ + 0.331, + 0.181, + 0.461, + 0.199 + ], + "angle": 0, + "content": "Nakul Agarwal1" + }, + { + "type": "text", + "bbox": [ + 0.503, + 0.181, + 0.603, + 0.199 + ], + "angle": 0, + "content": "Chiho Choi" + }, + { + "type": "text", + "bbox": [ + 0.645, + 0.181, + 0.834, + 0.199 + ], + "angle": 0, + "content": "Karttikeya Mangalam\\(^{2*}\\)" + }, + { + "type": "text", + "bbox": [ + 0.371, + 0.202, + 0.597, + 0.216 + ], + "angle": 0, + "content": "* denotes equal technical contribution" + }, + { + "type": "text", + "bbox": [ + 0.281, + 0.218, + 0.532, + 0.235 + ], + "angle": 0, + "content": "1Honda Research Institute USA" + }, + { + "type": "text", + "bbox": [ + 0.572, + 0.219, + 0.686, + 0.236 + ], + "angle": 0, + "content": "\\(^{2}\\)UC Berkeley" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.256, + 0.314, + 0.272 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.288, + 0.474, + 0.695 + ], + "angle": 0, + "content": "We present RAFTformer, a real-time action forecasting transformer for latency-aware real-world action forecasting. RAFTformer is a two-stage fully transformer based architecture comprising of a video transformer backbone that operates on high resolution, short-range clips, and a head transformer encoder that temporally aggregates information from multiple short-range clips to span a long-term horizon. Additionally, we propose a novel self-supervised shuffled causal masking scheme as a model level augmentation to improve forecasting fidelity. Finally, we also propose a novel real-time evaluation setting for action forecasting that directly couples model inference latency to overall forecasting performance and brings forth a hitherto overlooked trade-off between latency and action forecasting performance. Our parsimonious network design facilitates RAFTformer inference latency to be \\(9 \\times\\) smaller than prior works at the same forecasting accuracy. Owing to its two-staged design, RAFTformer uses \\(94\\%\\) less training compute and \\(90\\%\\) lesser training parameters to outperform prior state-of-the-art baselines by 4.9 points on EGTEA Gaze+ and by 1.4 points on EPIC-Kitchens-100 validation set, as measured by Top-5 recall (T5R) in the offline setting. In the real-time setting, RAFTformer outperforms prior works by an even greater margin of up to 4.4 T5R points on the EPIC-Kitchens-100 dataset. Project Webpage: https://karttikeya.github.io/publication/RAFTformer/." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.71, + 0.21, + 0.725 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.734, + 0.47, + 0.856 + ], + "angle": 0, + "content": "Latency matters. It is a crucial system design consideration for countless applications that operate in real-time from hardware design [65], network engineering [63], and satellite communications [30] to capital trading [32], human vision [59] and COVID transmission patterns [54]. However, it has not been a center stage design consideration in modern computer vision systems of the past decade [11,45]. Modern vision system design has largely focused on the" + }, + { + "type": "page_footnote", + "bbox": [ + 0.076, + 0.863, + 0.469, + 0.901 + ], + "angle": 0, + "content": "* Work done during Harshayu's internship at HRI with Chiho Choi's supervision who is now at Samsung Semiconductor US Karttikeya Mangalam is the corresponding author" + }, + { + "type": "image", + "bbox": [ + 0.511, + 0.261, + 0.889, + 0.486 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.49, + 0.893, + 0.614 + ], + "angle": 0, + "content": "Figure 1. Action Forecasting is the task of predicting actions that will happen after a pre-determined time span, say \\( t_f \\) seconds, into the future. Prior works consider an offline evaluation setting that ignores the model inference latency. We propose a latency-aware real-time evaluation setting where the model is required to finish forecasting \\( t_f \\) seconds before the target time. We present RAFTformer, a fast action anticipation transformer that outperforms prior works both in offline & real-time setting while forecasting actions in real-time (≥25 FPS)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.625, + 0.893, + 0.791 + ], + "angle": 0, + "content": "correctness of systems rather than the latency of the predictions. While vision-based forecasting systems are often meant for embodied real-time deployment on autonomous agents like self-driving cars and robots, they are evaluated in an offline setting where inference latency is neglected (Figure 1). Interestingly, recent neural network architectures have adopted FLOPs as a proxy for latency as a second axis for model design. While a sufficient fidelity metric for offline after-the-fact applications like automatic content recognition, latency often comes second to correctness, even for real-time systems such as forecasting models." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Forecasting empowers reactive planning [17]. An autonomous system present in rich human environments inevitably needs to understand human actions around it for smooth task planning and execution. Autonomous agent planning critically depends on anticipating the future of the scene in various forms such as trajectory prediction [22, 23, 57, 58], action forecasting [19, 25, 80] or future scene" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18759" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.471, + 0.183 + ], + "angle": 0, + "content": "segmentation [8] and anticipating the future is an activity humans subconsciously do for day-to-day tasks [60]. And while vision-based forecasting systems are often meant for embodied real-time deployment on autonomous agents like autonomous cars and robots, they are evaluated in an offline setting where inference latency is neglected (Figure 1)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.185, + 0.47, + 0.382 + ], + "angle": 0, + "content": "In this work, we propose a real-time evaluation setting (Figure 1) that closely mimics the real-world deployment for a forecasting system. Suppose that in a real-time system, the design specifications require the forecasting system outputs \\( t_f \\) seconds in advance of the event to be able to plan and use the forecasts effectively. In current offline settings, the forecasting system begins the inference \\( t_f \\) seconds in advance of the event ('Present' in Figure 1) and the model latency is ignored (or assumed to be 0) such that the predictions are available instantly. However, in our proposed real-time setting, the model is required to start inference in advance of 'Present' so that the outputs are available with a horizon of \\( t_f \\) seconds, meeting the design specification." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.383, + 0.469, + 0.534 + ], + "angle": 0, + "content": "We observe that in the real-time setting, the prior works fare quite poorly because of their slow model inference latency (Table 3). A large latency implies that the model has to start inference further in the past and has to rely on older video data to make forecasts with the benefit of more expressiveness (Figure 2). A smaller latency means the model can enjoy more recent video data but has limited capacity. Simply said, models that are only evaluated in the offline setting may fare poorly in the real-time deployment setting due to their latency agnostic design (Figure 2)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.537, + 0.469, + 0.732 + ], + "angle": 0, + "content": "We present, RAFTformer, a real-time action forecasting transformer that uses a two-stage transformer encoder-based network for lightning fast forecasts in inference. RAFTformer uses a shuffled casual masking scheme based feature prediction loss for learning strong temporal cues that transfer to feature prediction. Further, RAFTformer uses specialized anticipation tokens for learning to predict action at multiple temporal horizons that improve model reasoning capabilities of short-term action forecasting as well. Finally, the model is explicitly designed for real-time embodied deployments that allows inference up to an order of magnitude faster than prior state-of-the-art methods. In summary, our contributions are three-fold," + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.469, + 0.901 + ], + "angle": 0, + "content": "First, we propose Real-time Action Forecasting Transformer (RAFTformer), a real-time action forecasting transformer with latency at least \\(9 \\times\\) smaller than prior state-of-the-art action forecasting methods. RAFTformer uses specialized anticipation tokens and a novel shuffled casual masking-based self-supervision loss that allows it to outperform prior work while maintaining low latency with a reduction of \\(94\\%\\) in GPU training time and \\(90\\%\\) in the number of trainable parameters compares to prior works. To the best of our knowledge, our work is the first to achieve action anticipation in real-time (i.e. 25 fps)." + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.095, + 0.887, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.264, + 0.892, + 0.348 + ], + "angle": 0, + "content": "Figure 2. Evaluation Performance vs. Latency. Bigger models perform better in latency agnostic offline settings. In the real-time evaluation setting, we observe that, beyond a limit, bigger models with higher latency cause a drop in forecasting performance. In practical deployment, there exists a trade-off between latency and high-fidelity forecasts. See §4.3.1 for details." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.367, + 0.892, + 0.473 + ], + "angle": 0, + "content": "Second, we propose a latency-aware real-time evaluation setting (Figure 1) that better mimics practical deployment settings for embodied forecasting systems. Real-time evaluation demonstrates a clear trade-off between inference latency and model forecasting fidelity, paving the path for the development of latency-aware forecasting models in the future (also see [20])." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.476, + 0.892, + 0.567 + ], + "angle": 0, + "content": "Third, Through extensive experiments, we show that RAFTformer outperforms prior state-of-the-art methods by 4.9 points on the EGTEA Gaze+ dataset, by 1.4 points on the EPIC-Kitchens-100 dataset according to the Top-5 Recall metric and by a relative margin of \\(5.3\\%\\) on the top-1 accuracy metric on EPIC-Kitchens-55 dataset." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.586, + 0.642, + 0.601 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Action Anticipation. Over the last few years, action anticipation has seen significant advances following the promising results in video recognition [2,4,12,15,24,38,40, 49,55,61,80,87] and video segmentation [27,43,48,76,81]. While earlier works [1, 56, 68] use CNN-based methods for video action anticipation, many follow-up works transitioned into using recurrent sequence-based networks [19, 22, 64, 66, 71]. Using multiple spatial and temporal scales was another key idea explored in several anticipation works [15, 70, 70, 77, 80, 86]. Masking-based self-supervision has proven to be a new frontier for both image [5, 14, 33, 35, 62] and video [31, 74] representation learning. This concept has also been explored in the context of video anticipation [25] which differs from prior works that explore temporal consistency [16, 37, 42, 79, 82], inter-frame predictability [28, 29, 36], and cross-modal correspondence [3, 44, 73]. In our work we propose a novel generalized self-supervision scheme which is a crucial part of our model's ability to generalize and outperform SOTA." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.956 + ], + "angle": 0, + "content": "18760" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.483 + ], + "angle": 0, + "content": "Transformers for Video Anticipation. With the rise of transformers for sequence tasks, recent works have explored various image and video-based transformers [25, 26, 26, 78, 80, 85] for anticipating actions. [25] proposes a ViT-based [11] spatial transformer backbone with a transformer decoder head to anticipate the next action with a \\(1s\\) horizon. [25] predicts actions in the same latent space as their feature decodings causing conflation between feature reconstruction and future prediction. We propose specialized anticipation tokens to address this problem. Furthermore, [25] uses a recurrent decoder and frame-level operation, which is inefficient for both training compute and inference latency. MeMViT [80] proposes another fully transformer model which extends MViT [12] for better long-range modeling using a novel caching mechanism. However, their model is trained to only predict the next action and thus does not explicitly learn to model the future or evolving scene dynamics. Furthermore, their model is less efficient than RAFTformer in terms of both training and inference time due to its larger model and input size and complete end-to-end training. RAFTformer uses a fixed pre-trained video network and only trains the RAFTformer network. Recently [26] propose a transformer-based model for long-term action anticipation. They focus on a sequential prediction rather than next-action prediction and do not focus on inference latency." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.482, + 0.473, + 0.754 + ], + "angle": 0, + "content": "Real-Time Systems. Latency matters, especially for real-time applications. Autonomous agents need to reason about nearby agents and take real-time decisions. This vision has led to great progress in the development of real-time systems in the related fields of semantic segmentation [13], video object segmentation [76], object detection [7, 51, 53, 67], multi-object tracking [41]. While some progress has also been made in activity understanding [72, 84], it is limited to recognition and detection. Keeping this in mind, some recent works in action anticipation have also started focusing on efficiency and memory footprint and report training time, inference time, and trainable parameters [80]. Although a step in the right direction, these works have high inference times in comparison to their desired anticipation horizon. Our proposed method is significantly faster during both training and inference, has fewer trainable parameters and a smaller memory footprint, and still outperforms state-of-the-art methods." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.769, + 0.465, + 0.788 + ], + "angle": 0, + "content": "3. Real-Time Action Forecasting Transformer" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.47, + 0.903 + ], + "angle": 0, + "content": "In this section, we first present the problem formulation (§3.1), followed by the architectural details of the video backbone for feature extraction (§3.2) and the RAFTformer model architecture (§3.3) including anticipation tokens (§3.3.1), shuffled causal masking (§3.3.2) and permutation encodings (§3.3.3), finishing with an outline of the loss functions used for training the model (§3.5)." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.091, + 0.707, + 0.108 + ], + "angle": 0, + "content": "3.1. Problem Formulation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.115, + 0.895, + 0.179 + ], + "angle": 0, + "content": "Given an observed video starting from time \\( T = 0 \\) and of arbitrary length \\( t \\), \\( V_{0,t} = [F_0, \\dots, F_t] \\) where \\( F_i \\) denotes the frame at time \\( i \\), the task is to predict the future action \\( t_f \\) seconds in the future, i.e., action \\( \\mathrm{A}_{t + t_f} \\) at time \\( T = t + t_f \\)." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.187, + 0.757, + 0.202 + ], + "angle": 0, + "content": "3.2. Pre-trained Video Backbone" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.21, + 0.895, + 0.422 + ], + "angle": 0, + "content": "In contrast to state-of-the-art models [25, 80] that train end-to-end, we demonstrate that a two-stage training process is both efficient and produces high-fidelity forecasts. First, we split the full duration of the past video \\( V_{0,t} \\) into sub-clips \\( V = [C_0,C_1,\\dots,C_N] \\) in a sliding window fashion. Each clip, \\( C_i \\), is independently processed with the short-term video backbone like MViT [12] to extract clip-level features. Previous works, such as [25], have employed image backbones for comparable undertakings, while we contend that video backbones offer richer spatio-temporal features, thus benefiting the downstream task. Further, a video backbone also allows lower latency since the produced clip embeddings already contain fused features for several images at once." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.423, + 0.895, + 0.56 + ], + "angle": 0, + "content": "Our two-stage design also allows for hierarchical temporal processing of the long-form past video. The short-term recognition backbone model operates on short, high-resolution clips. These extracted features are then used as input to the head network to process longer-range lower resolution features that capture key information from each clip. This is a crucial design consideration to lower the inference latency in RAFTformer while still capturing longer-range temporal dependencies compared to [19, 25]." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.569, + 0.766, + 0.585 + ], + "angle": 0, + "content": "3.3.RAFTformer Model Network" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.594, + 0.895, + 0.746 + ], + "angle": 0, + "content": "We propose RAFTformer as a transformer encoder model. The transformer encoder has the advantage of being able to effectively learn across clip dependencies by attending over independently extracted clip features without facing memory bottlenecks such as faced in LSTM encoders [34] that have been used in some prior works [19,70]. However, to make the encoder effective for action forecasting on pre-trained features, we propose several changes to the training process to allow two-staged training to work as well as end-to-end training for action forecasting." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.755, + 0.697, + 0.771 + ], + "angle": 0, + "content": "3.3.1 Anticipation Tokens" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.895, + 0.903 + ], + "angle": 0, + "content": "The extracted clip embeddings \\([C_0\\cdots C_{N-1}]\\) form the first part of the input to the action anticipation head. For the second part, we propose to train learnable 'anticipation tokens' that can aggregate global context and later can be decoded into future predictions. This design choice stands in contrast to prior works like [25] where the output of the anticipation token is implicitly designed to be in the same latent space as the output of their image-feature tokens. In" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18761" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.08, + 0.086, + 0.895, + 0.328 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.335, + 0.895, + 0.42 + ], + "angle": 0, + "content": "Figure 3. RAFTformer is a real-time action anticipation transformer architecture comprised of two stages. The first stage is a pretrained short-term backbone that produces individual clip embeddings independently of other clips (§3.2). In the second stage (§3.3), absolute position encodings are added and the resulting sequence is shuffled with a sampled permutation \\(\\pi^{*} \\sim \\pi\\). The permutation encodings (§3.3.3) are then added to the shuffled sequence and after concatenation with anticipation tokens, the sequence is processed with the RAFTformer encoder. The output tokens are decoded via short & long-term action anticipation heads (§3.4), as well as the feature prediction head trained with self-supervised loss (\\(\\mathcal{L}_{\\mathrm{SCM}}\\)), future feature prediction loss (\\(\\mathcal{L}_{\\mathrm{future}}\\)) and action forecasting loss (\\(\\mathcal{L}_{\\mathrm{focal}}\\)) (§3.5)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.445, + 0.47, + 0.52 + ], + "angle": 0, + "content": "contrast to prior works, we find that temporal aggregation such as mean pooling for forecasting leads to subpar performance (see Table 5). Hence, we use the output tokens corresponding to \\([C_0\\cdots C_N]\\) solely for self-supervised feature loss rather than action anticipation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.521, + 0.471, + 0.673 + ], + "angle": 0, + "content": "Instead, for action anticipation, we propose to train learnable 'anticipation tokens' to learn useful global context from the clip tokens. The output of the anticipation token is no longer restricted to be in the same latent space as the output of clip-feature tokens like in [25] and can better capture the information needed to anticipate the next action. Further, we propose to use multiple anticipation tokens to generate additional supervision, with each token attending to different past video lengths and producing forecasts for different time horizons in the future." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.68, + 0.468, + 0.696 + ], + "angle": 0, + "content": "3.3.2 Self-Supervision via Shuffled Feature Prediction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.704, + 0.47, + 0.856 + ], + "angle": 0, + "content": "Prior works explored using the self-supervision task of predicting frame or clip features and using an MSE loss [25]. We propose using a generalized form of masking-based self-supervision [33] based on predicting shuffled future features. Predicting future clip features has a two-fold benefit: (A) It encourages causally learning the observed sequence incentivizing the model to grasp underlying scene dynamics and (B) Prediction in the latent feature space allows reasoning semantically about the future without wasting modeling capacity with low pixel level scene details." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Different from loss functions proposed in prior works [25], we propose an improved auto-regressive scheme for self-supervised learning by future feature pre" + }, + { + "type": "table", + "bbox": [ + 0.514, + 0.443, + 0.878, + 0.519 + ], + "angle": 0, + "content": "
Auto-regressive [1,2,3,4]Shuffle π1: [4,1,3,2]Another Shuffle π2: [3,4,2,1]
1 → 24 → 13 → 4
2 → 31 → 34 → 2
3 → 43 → 22 → 1
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.524, + 0.894, + 0.553 + ], + "angle": 0, + "content": "Table 1. Encoding the input permutation \\(\\pi\\). Shuffling the input sequence arbitrarily changes the successor of each token." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.564, + 0.894, + 0.641 + ], + "angle": 0, + "content": "diction. Rather than sequentially predicting missing clip features in order to use a causal attention mask, we propose to use a model-level augmentation of the attention masking scheme where some of the attention weights are not used from the original causal mask." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Random Masking. Construction of a sparse augmented attention mask is non-trivial. Simply generating a random mask such as in MAE [33] fails to isolate information within the intended partitioning due to multi-hop message passing caused by repeated application of the same mask. For example, in Figure 4, the attention mask prohibits token 1 to access token 2 and 3 (shown by 'white'). However, after two layers, token 1 in layer 2 can access information in token 2 in layer 0 (shown by red border), indirectly through token 4 in later 1 because of multi-hop message passing. This temporal information leakage can cause self-supervision to fail. For example, self-supervising token 1 with token 2 feature prediction would collapse in setup of Figure 4. To prevent this, we propose a simple yet effective solution." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "18762" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.091, + 0.473, + 0.379 + ], + "angle": 0, + "content": "Shuffled Causal Masking. We know that vanilla causal masks ensure that information available to each token is invariant under repeated applications of the attention mask, i.e., multi-hop message passing. Since multi-hop message passing is token permutation invariant, any permutation of the tokens from the causal mask will preserve the invariance of accessible information under multiple hops. Thus, this allows a general framework for structured randomized mask construction without temporal leakage. We notice that a row-wise permutation of the attention mask is equivalent to the same permutation applied to the sequence itself. Hence, the same effect as properly constructed random masks can simply be achieved by shuffling the input token sequence itself. This allows generalizing vanilla autoregressive prediction order to arbitrary sequence permutations without any multi-hop information leakage through the layers. Thus, rather than predicting clip features sequentially from 0 to \\( N - 1 \\) like [25], our proposed scheme allows for exponentially more variations." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.379, + 0.473, + 0.653 + ], + "angle": 0, + "content": "Referring to Figure 3, we first add absolute position embeddings (APE) to each of the clip features before shuffling them. This allows the transformer to leverage the information about the actual temporal order of each clip in the video. Without the absolute position embeddings, the transformer is input permutation equivariant, which is not a desirable property for action forecasting. However, while APE is sufficient for positional information in vanilla autoregressive ordering, it is not enough for prediction under our proposed Shuffled Causal Masking (SCM) scheme. In autoregressive ordering, for any specific token, the next token in the sequence corresponds to a fixed position and hence the self-supervised training process can subtly learn this bias via next-token feature supervision. In contrast, under SCM the temporal position of the next token varies depending on the shuffling permutation. Hence, self-supervised training cannot learn to perform effective feature prediction without information about the shuffling permutation." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.662, + 0.35, + 0.679 + ], + "angle": 0, + "content": "3.3.3 Permutation Position Encoding" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.688, + 0.47, + 0.869 + ], + "angle": 0, + "content": "Naïve Encodings. For an \\(L\\) length sequence, there exist \\(L!\\) possible permutations. Encoding each permutation \\((\\pi)\\) by itself is clearly intractable. First, we observe that encoding \\(\\pi^{*}\\) as a set of \\(O(L)\\) embeddings which are shared among different \\(\\pi\\) is more efficient. A follow-up solution would be to instead encode each predecessor \\(\\mapsto\\) successor relationship as an encoding and have \\(L - 1\\) of such embeddings together encode \\(\\pi^{*}\\). This reduces to the total number of required embeddings to \\(L(L - 1)\\) from \\(L!\\). Each \\(\\pi^{*}\\) now shares every one of its \\(L\\) embeddings with other \\(\\pi\\), but considered as a set, the \\(L\\) embeddings uniquely encode \\(\\pi^{*}\\). However, even \\(L^2\\) becomes intractable for large \\(L\\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Permutation Position Encodings \\((\\pi \\mathrm{PE})\\) provides an elegant solution for encoding \\(\\pi^{*}\\) requiring only \\(L\\) total encod" + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.091, + 0.845, + 0.238 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.242, + 0.895, + 0.326 + ], + "angle": 0, + "content": "Figure 4. Random Masking Self-Supervision Illustration of how naive random masking (white denotes masked out) fails for self-supervised feature prediction task. We can see that in Layer 1 the tokens can only access information according to the provided mask. However, if the same mask is used in Layer 2, there is information leakage across tokens which is undesirable." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.345, + 0.895, + 0.513 + ], + "angle": 0, + "content": "ings to be learned. \\(\\pi\\)PE encodes the predecessor \\(\\mapsto\\) successor relationships but further simplifies by noting that adding the encoding to the token itself makes the predecessor information redundant. The token itself is the predecessor and has the positional information available from APE. Hence, we simply encode the successor positional information, and that in combination with APE uniquely encodes \\(\\pi^{*}\\). Hence, we design \\(\\pi\\)PE to be the encoding of the original temporal position of the successor in the permuted sequence. So for the \\(\\pi_{1}\\) permutation in Table 1, we would add \\(\\pi\\)PE[1] to token 4, \\(\\pi\\)PE[3] to token 1 and \\(\\pi\\)PE[2] to token 3." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.528, + 0.688, + 0.543 + ], + "angle": 0, + "content": "3.4. Overall Mechanism" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.556, + 0.895, + 0.799 + ], + "angle": 0, + "content": "The past video is split into clips, and the clip embeddings \\([C_0\\cdots C_{N-1}]\\) are extracted using a video backbone (Figure 3). Anticipation tokens are concatenated to the extracted sequence (\\(\\S 3.3.1\\)), followed by the addition of absolute position encoding to the concatenated sequence. Now, the clip embedding is shuffled according to a randomly chosen permutation \\(\\pi^*\\) to obtain \\([C_{\\pi^*[0]}\\cdots C_{\\pi^*[N-1]}\\]\\). The sampled permutation \\(\\pi^*\\) is then encoded by adding the successor's (\\(\\S 3.3.3\\)) embedding to each token. In Figure 3, \\(\\pi^*[1] = 3\\) and \\(\\pi^*[2] = N\\), hence \\(\\pi \\mathrm{PE}[\\pi^*[1+1]]\\) is added to the token \\(\\pi^*[1]\\) i.e., \\(\\pi \\mathrm{PE}[N]\\) is added to \\(E_3\\), which is used to self-supervise the feature at position 1 in the shuffled sequence, i.e., token 3 (\\(\\S 3.3.2\\)). The shuffled input sequence, in addition to the anticipation tokens, is now propagated through the transformer encoder using a causal attention masking scheme and the output is decoded with the head networks." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.894, + 0.903 + ], + "angle": 0, + "content": "Head Networks We propose using three MLP heads on top of the transformer encoder network (Figure 3). Two MLP heads decode the anticipation tokens into the predicted future action distribution. The third MLP head up-samples the encoded tokens to the original representation space of the input tokens to allow self-supervision loss." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18763" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.12, + 0.089, + 0.849, + 0.426 + ], + "angle": 0, + "content": "
SplitMethodAddl. ModalityInitEpic BoxesTop-5 RecallParameters (×106)GPU HoursInference Latency (ms)
VerbNounAction
ValTempAgg [70]NoneIN1K24.229.813.0---
RULSTM [19]NoneIN1K--13.3---
RULSTM [19]Obj+FlowIN1K✓30.827.814.0---
TempAgg [70]Obj+Flow+ROIIN1K✓23.231.414.7---
AVT [25]NoneIN21K30.231.714.9378-420
AVT+ [25]ObjIN21K✓28.232.015.9---
TSN-AVT+ [25]ObjIN21K✓31.825.514.8---
MeMVit [80]NoneK40032.833.215.159-160
MeMVit [80]NoneK70032.237.017.7212368350
TestRAFTformerNoneK400 + IN1K33.335.517.6262340
RAFTformerNoneK70033.737.118.02627110
RAFTformer-2BNoneK700 + IN1K33.837.919.15250160
RULSTM [19]Obj+FlowIN1K✓25.326.711.2---
TBN [83]Obj+FlowIN1K✓21.526.811.0---
AVT+ [25]Obj+FlowIN21K✓25.628.812.6---
Abstract Goal [69]Obj+FlowIN1K✓31.430.114.3---
AFFT [85]Obj+Flow-✓20.731.814.9---
RAFTformerNoneK400 + IN1K27.332.814.0262340
RAFTformerNoneK70027.434.014.72627110
RAFTformer-2BNoneK700 + IN1K30.134.115.45250160
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.429, + 0.895, + 0.459 + ], + "angle": 0, + "content": "Table 2. Offline Evaluation Results on the EK-100 dataset for \\( t_f = 1 \\) second horizon. Latency is measured over the entire model including the backbone & head networks on a single 16G Tesla V100 GPU. Methods that use other modalities (+RGB) are deemphasized." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.465, + 0.232, + 0.48 + ], + "angle": 0, + "content": "3.5. Loss Functions" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.488, + 0.471, + 0.534 + ], + "angle": 0, + "content": "We observe that the ground truth action distributions are often long-tailed, and propose to use the the focal loss [52], for supervising the future action prediction distributions." + }, + { + "type": "equation", + "bbox": [ + 0.138, + 0.537, + 0.411, + 0.577 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {f o c a l}} = \\sum_ {A _ {i} \\in A} \\sum_ {i = 0} ^ {n} - (1 - p _ {A _ {i}}) ^ {\\gamma} \\log \\left(p _ {A _ {i}}\\right)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.583, + 0.47, + 0.658 + ], + "angle": 0, + "content": "where \\( p_i \\) is the predicted probability for the correct class for the \\( i \\)th example, \\( A_i \\) represents predictions from a specific anticipation token and \\( \\gamma \\) is the focusing parameter where \\( \\gamma = 0 \\) is cross entropy loss. Increasing \\( \\gamma \\) results in an increased penalty for hard, misclassified examples." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.659, + 0.47, + 0.718 + ], + "angle": 0, + "content": "For self-supervision using shuffled causal masking to predict next-token embeddings, we use an expected \\(\\ell_2\\) loss over both past tokens, with the expectation being oversampled permutations \\(\\pi^{*} \\sim \\pi\\)." + }, + { + "type": "equation", + "bbox": [ + 0.145, + 0.721, + 0.405, + 0.763 + ], + "angle": 0, + "content": "\\[\n\\mathcal{L}_{\\mathrm{SCM}} = \\underset {\\pi^{*}\\sim \\pi}{\\mathbb{E}}\\sum_{j = 0}^{N - 1}\\| E_{\\pi^{*}[j]} - \\hat{E}_{\\pi^{*}[j]}\\|_{2}^{2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.762, + 0.47, + 0.809 + ], + "angle": 0, + "content": "where \\( E_{\\pi^{*}[j]} \\) and \\( \\hat{E}_{\\pi^{*}[j]} \\) denotes the original and the predicted clip embedding at position \\( j \\) after permuting with \\( \\pi^{*} \\). For future token prediction, we use a simple \\( \\ell_2 \\) loss:" + }, + { + "type": "equation", + "bbox": [ + 0.178, + 0.813, + 0.37, + 0.833 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {f u t u r e}} = \\left\\| E _ {\\mathrm {f u t u r e}} - \\hat {E} _ {\\mathrm {f u t u r e}} \\right\\| _ {2} ^ {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.838, + 0.471, + 0.87 + ], + "angle": 0, + "content": "where \\( E_{\\mathrm{future}} \\) is the MViT embedding for the next clip (after \\( t_f \\)). Finally, the overall loss is simply a weighted sum," + }, + { + "type": "equation", + "bbox": [ + 0.162, + 0.876, + 0.386, + 0.893 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {\\text {f o c a l}} + \\lambda_ {1} \\mathcal {L} _ {\\text {S C M}} + \\lambda_ {2} \\mathcal {L} _ {\\text {f u t u r e}}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.464, + 0.634, + 0.481 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.487, + 0.892, + 0.594 + ], + "angle": 0, + "content": "Datasets & Metrics. We use the widely benchmarked EPIC-KITCHENS dataset [9], an unscripted set with nearly \\(20 \\times\\) more action classes and \\(10 - 100 \\times\\) more observed sequences than other action datasets like 50 Salads [47] and Breakfast [46], used in prior work [19]. We use both the EPIC-55 & EPIC-100 anticipation splits and the EGTEA+ Gaze dataset [50]. Dataset details in supplementary." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.595, + 0.893, + 0.732 + ], + "angle": 0, + "content": "Since human decision-making is inherently multimodal, we propose an approach to predict multiple reasonable future action forecasts. In addition to top-1 accuracy, we report top-5 recall following prior works [19, 25, 80]. We use the baseline data splits and report metrics on both the validation and test set. In addition, we report the number of trainable model parameters (M), the total compute spent for training the model to convergence on a Tesla V100 GPU (in hours), and the inference latency (in milliseconds)." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.744, + 0.681, + 0.76 + ], + "angle": 0, + "content": "4.1. Evaluation Setting" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.894, + 0.903 + ], + "angle": 0, + "content": "Offline evaluation is the setting where the model inference latency is ignored, or in other words, assumed to be zero. All prior works [19, 25, 80] consider this setting. Referring to Figure 1, prior works assume access to all past video frames up till the present moment \\( T = t \\). Using this information, the model then predicts that action with a \\( t_f \\) second horizon at \\( T = t + t_f \\). However, the prediction would actually be produced at time \\( T = t + t_l \\) where \\( t_l \\) is the model inference latency. This is not practically useful" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "18764" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.132, + 0.089, + 0.837, + 0.229 + ], + "angle": 0, + "content": "
ModelInitLatency (t1 ms)Inference Start Time StampInference End Time StampTarget Time StampTop-5 Recall
VerbNounAction
AVT [25]IN21Ktavt = 420TT + tavtT + 130.231.714.9
RAFTformerK400 + IN1ktours = 40T + tavt - toursT + tavtT + 134.138.219.3 (+4.4)
MemViT [80]K400tvit = 160TT + tvitT + 132.833.215.1
RAFTformerK400 + IN1ktours = 40T + tvit - toursT + tvitT + 133.837.118.1 (+3.0)
MemViT [80]K700tvit = 350TT + tvitT + 132.237.017.7
RAFTformerK400 + IN1ktours = 40T + tvit - toursT + tvitT + 133.737.919.0 (+1.3)
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.232, + 0.892, + 0.304 + ], + "angle": 0, + "content": "Table 3. Real-time Evaluation Results for benchmarking action forecasting methods in a practical setting (§4.1). Each comparison is performed between a pair of models where their start time ('Inference Start') times have been adjusted (Figure 1) by their latency so that they produce the forecasting output for the 'Target Time' simultaneously ('Inference End'). For prior works [25,80], start & end times are kept the same as their original offline settings (Table 2) to avoid any training recipe change. Faster models can pragmatically utilize recent frames while slower models must rely on higher fidelity prediction from older frames. Latency measured on a single 16G Tesla V100 GPU." + }, + { + "type": "table", + "bbox": [ + 0.14, + 0.308, + 0.406, + 0.404 + ], + "angle": 0, + "content": "
ModelInitTop-1 Acc
RULSTM [19]TSN/IN1k13.1
ActionBanks [70]TSN/IN1k12.3
AVT-h [25]TSN/IN1k13.1
RAFTformerTSN/IN1k13.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.091, + 0.407, + 0.455, + 0.421 + ], + "angle": 0, + "content": "Table 4. Offline Evaluation results on the Epic-Kitchens-55." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.439, + 0.47, + 0.545 + ], + "angle": 0, + "content": "since often, we require time horizon \\( t_f \\) to meaningfully use the predicted future outcomes. Further, this does not account for absurdities where a large model might even have latency \\( t_l > t_f \\), in which case the model is predicting an action that has already happened by the time it predicts it! A complex model can have great offline performance but its inference time would make it unusable in practice." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.552, + 0.47, + 0.825 + ], + "angle": 0, + "content": "Real-time evaluation. To remedy this impractical situation, we consider the real-time evaluation setting. In this setting, the model is required to finish inference with at least \\( t_f \\) seconds horizon before the target time (Fig. 1). Hence, the model is allowed access to past video data only for \\( T < t - t_l \\). This setting even allows for large models where \\( t_l > t_f \\) since predictions would still be produced with \\( t_f \\) seconds before the target time. Unlike other recognition scenarios where latency is a mere annoyance, in the case of future forecasting, models are often used in real-time rather than offline. The offline setting subtly oversteps the prediction horizon \\( t_f \\), by receiving forecasts with a margin much less than the postulated \\( t_f \\) horizon. By coupling model latency to the past video data observed, the real-time setting incentivizes the development of efficient forecasting methods that utilize the recent data better than relying on slow large models that cannot miss the recent frames, which arguably are the most crucial for near future prediction." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.832, + 0.265, + 0.848 + ], + "angle": 0, + "content": "4.2. EPIC-Kitchens-100" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Network Details. For feature extraction, we fix the pretrained 16x4 (K400+IN1K) and 32x3 (K700) MViT-B backbones [12, 49] trained for recognition on the EK100" + }, + { + "type": "table", + "bbox": [ + 0.523, + 0.309, + 0.868, + 0.408 + ], + "angle": 0, + "content": "
ModelSettingTop-5 Recall
ATFLSCM2×AT
Mean pooling✓15.2
16.1 (+0.9)
RAFTformer✓✓16.8 (+0.7)
✓✓✓17.4 (+0.6)
✓✓✓✓17.6 (+0.2)
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.41, + 0.892, + 0.454 + ], + "angle": 0, + "content": "Table 5. EK100 Ablation Study. FL is feature loss (no SCM), SCM is Shuffled Causal Masking (\\$3.3.2), AT \\( \\left( {2 \\times }\\right) \\) are single (double) anticipation tokens (§3.3.1)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.483, + 0.892, + 0.665 + ], + "angle": 0, + "content": "dataset. Each clip is embedded as a 768-dimensional feature vector. Unless mentioned otherwise, the action forecasting experiments use a \\( t_f = 1 \\) second horizon. RAFTformer encoder is a lightweight 4 layer, 4 head transformer encoder using post-normalization and ReLU activations. A linear projection from up-projects \\( 768 \\rightarrow 1024 \\) for the transformer. We only shuffle during training with a probability of 0.3. The output of the encoder is down projected from \\( 1024 \\rightarrow 768 \\) channels. Both short-term and long-term action prediction heads are fast & lightweight MLPs \\( (1024 \\rightarrow 2048 \\rightarrow 3806) \\). We set \\( \\lambda_1 = \\lambda_2 = 14 \\). For other details, please see supplementary." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.674, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Offline Evaluation. In Table 2 we first report RAFTformer results against prior works, including previous SOTA MeMViT [80]. Results that use additional modalities like Object (Obj), Flow (Flow), Object Region of Interest (ROI), or Epic Kitchen boxes are de-emphasized. Using only RGB, RAFTformer (K700) outperforms the AVT RGB model in action T5R by 3.1 points and the AVT RGB+Obj model by 2.1 points. RAFTformer slightly outperforms MeMViT action T5R while predicting actions \\(8.75 \\times\\) faster with \\(8.2 \\times\\) lesser trainable parameters and a \\(16 \\times\\) faster training. We also combine two separate RAFTformer models to train a two-backbone model (RAFTformer-2B) that achieves state-of-the-art by with a \\(1.4\\%\\) T5R increase. In the second section, we report our submitted results to the EK100 test server. We observe that RAFTformer general" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18765" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.101, + 0.089, + 0.445, + 0.218 + ], + "angle": 0, + "content": "
ModelInitModalityTop-5 Recall
DMR [75]-RGB38.1
ATSN [9]TSN/IN1kRGB+Flow31.6
MCE [18]TSN/IN1kRGB+Flow43.8
TCN [6]-RGB47.1
FN [10]VGG-16RGB42.7
ED [21]VGG-16/TSRGB+Flow54.6
RULSTM [19]TSN/IN1kRGB+Obj+Flow58.6
RAFTformerTSN/IN1kRGB63.5
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.077, + 0.222, + 0.47, + 0.25 + ], + "angle": 0, + "content": "Table 6. EGTEA Gaze+. Under same initialization, RAFTformer outperforms prior methods without additional modalities." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.257, + 0.468, + 0.287 + ], + "angle": 0, + "content": "izes well to the test set, improving upon the \\(\\mathrm{AVT + }\\) multimodal ensemble model [25] by 2.8 T5R points." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.295, + 0.266, + 0.31 + ], + "angle": 0, + "content": "4.3. Additional Datasets" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.315, + 0.468, + 0.435 + ], + "angle": 0, + "content": "EPIC-Kitchens 55. We also compare RAFTformer to prior baselines on the EK55 dataset in Table 4 on top-1 accuracy. We evaluate against other models using the same initialization for a fair comparison. We observe that RAFTformer outperforms prior benchmarks by about \\(0.7\\%\\) using the exact same backbone features. This shows the superiority of our proposed shuffle causal masking (§3.3.2) & anticipation token prediction (§3.3.1) in a controlled setting." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.437, + 0.468, + 0.527 + ], + "angle": 0, + "content": "Real-time Evaluation. In table 3, we fix the target - start time difference to be what the prior models such as, AVT [25] or MeMViT [80] were designed for, to avoid any unintended change in their training recipes. Hence, we shift RAFTformer start time so that the output forecasts are produced simultaneously for the pair." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.528, + 0.468, + 0.724 + ], + "angle": 0, + "content": "We observe that RAFTformer outperforms prior methods by an even larger margin in the real-time evaluation setting than the offline setting. RAFTformer effectively utilizes its compute to produce the maximum forecasting effect at the least latency cost. This allows RAFTformer to exploit more recent information that slower models miss because of higher inference latencies \\((t_{\\mathrm{ours}} < \\{t_{\\mathrm{avt}}, t_{\\mathrm{vit}}\\})\\). This also shows the disproportional effect of inference latency on forecasting performance. While RAFTFormer K400 + IN1K has a similar Top-5 Recall as MeMViT K700 in the offline setting, in the practical real-time evaluation (Table 3), RAFTformer outperforms MeMViT by \\(1.3\\%\\) by leveraging its faster inference latency (40 vs. 350 ms)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.733, + 0.436, + 0.747 + ], + "angle": 0, + "content": "4.3.1 Latency vs. Offline & Real-time Forecasting" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.468, + 0.9 + ], + "angle": 0, + "content": "In offline evaluation, latency is ignored and all models have data access parity. As scaling laws [39] would predict, bigger models (with higher latency) have stronger forecasting performance (Blue curve in Fig. 2). In the real-time setting, a higher latency implies access to less recent data (Green curve in Fig. 2) and hence, an interesting trade-off materializes. At first, as latency (and model size) increases, the performance improves. This is because the benefit of having a more expressive model outweighs the cost of access to older video data. However, as the latency increases fur" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.228 + ], + "angle": 0, + "content": "ther, the real-time performance starts decreasing. Now the harm of not having access to recent data outweighs the benefit of a more expressive model. For our setting, the optimal RAFTformer model has a latency of \\(40~\\mathrm{ms}\\) with an offline and real-time performance of 19.6 and 19.3 Top-5 recall respectively. A similar trade-off would exist for any combination of dataset, model, and deployment hardware regimes. Plots are for RAFTformer models of varying backbone parameter count for \\(t_f = 0.58\\) second prediction on EK100." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.235, + 0.623, + 0.248 + ], + "angle": 0, + "content": "4.3.2 Ablations" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.256, + 0.892, + 0.468 + ], + "angle": 0, + "content": "We ablate RAFTformer thoroughly in Table 5. In contrast to prior works [25,80] that pool information or use the same embedding for feature supervision and action prediction, we train explicit anticipation tokens (§3.3.1) to perform forecasting, improving T5R by 1.1. Anticipation tokens specialize in predicting the next action instead of using features that multi-task between reconstructing clip features and future action prediction [25]. Self-supervision via feature loss (FL) further improves by 0.7 T5R. Further, our SCM technique effectively regularizes FL that improves 0.6 T5R. Finally, an additional anticipation token \\((2\\times \\mathrm{AT})\\) for supervision further improves 0.2 T5R. Additional longer-horizon anticipation task helps in learning transferable global video features to the main anticipation task." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.47, + 0.892, + 0.636 + ], + "angle": 0, + "content": "EGTEA Gaze+. We also evaluate the EGTEA Gaze+ dataset in Table 6 to showcase RAFTformer performance on new settings outside of EPIC-Kitchens. Again, we use the setting of anticipating \\(1s\\) into the future and use the T5R metric. While prior methods use many input modalities including as object, flow, and RGB, we significantly outperform the prior state-of-the-art in this setting [19] by \\(4.9\\%\\). Note that we use pre-extracted TSN RGB features as provided by [19] for direct comparison. Our very strong performance on another egocentric video dataset with complex human tasks further validates the promise of RAFTformer." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.641, + 0.619, + 0.656 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.659, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We propose Real-Time Action Forecasting Transformer (RAFTformer), a parsimonious two-stage fully transformer-based architecture consisting of a short-range video transformer backbone for feature extraction and a long-range head transformer encoder for long-term temporal aggregation across multiple clips. We also introduce a real-time evaluation setting for action forecasting models that directly penalizes high latency and closely mimics the real-world deployment scenario for forecasting models. RAFTformer outperforms prior state-of-the-art methods by significant margins across several action forecasting benchmarks in the offline setting, and by an even larger margin of upto 4.4 T5R, in the real-time setting. RAFTformer achieves \\(9 \\times\\) lower inference latency at the same forecasting fidelity, using \\(16 \\times\\) less training compute and \\(10 \\times\\) lesser trainable parameters than prior baselines." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18766" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.117, + 0.469, + 0.158 + ], + "angle": 0, + "content": "[1] Yazan Abu Farha, Alexander Richard, and Juergen Gall. When will you do what?-anticipating temporal occurrences of activities. 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RAFTformer is a two-stage fully transformer based architecture comprising of a video transformer backbone that operates on high resolution, short-range clips, and a head transformer encoder that temporally aggregates information from multiple short-range clips to span a long-term horizon. Additionally, we propose a novel self-supervised shuffled causal masking scheme as a model level augmentation to improve forecasting fidelity. Finally, we also propose a novel real-time evaluation setting for action forecasting that directly couples model inference latency to overall forecasting performance and brings forth a hitherto overlooked trade-off between latency and action forecasting performance. Our parsimonious network design facilitates RAFTformer inference latency to be $9 \times$ smaller than prior works at the same forecasting accuracy. Owing to its two-staged design, RAFTformer uses $94\%$ less training compute and $90\%$ lesser training parameters to outperform prior state-of-the-art baselines by 4.9 points on EGTEA Gaze+ and by 1.4 points on EPIC-Kitchens-100 validation set, as measured by Top-5 recall (T5R) in the offline setting. In the real-time setting, RAFTformer outperforms prior works by an even greater margin of up to 4.4 T5R points on the EPIC-Kitchens-100 dataset. Project Webpage: https://karttikeya.github.io/publication/RAFTformer/. + +# 1. Introduction + +Latency matters. It is a crucial system design consideration for countless applications that operate in real-time from hardware design [65], network engineering [63], and satellite communications [30] to capital trading [32], human vision [59] and COVID transmission patterns [54]. However, it has not been a center stage design consideration in modern computer vision systems of the past decade [11,45]. Modern vision system design has largely focused on the + +![](images/8cae1987f001aaa922bf43d041f42357f1946ed8965d3ec9aa471acf10c20730.jpg) +Figure 1. Action Forecasting is the task of predicting actions that will happen after a pre-determined time span, say $t_f$ seconds, into the future. Prior works consider an offline evaluation setting that ignores the model inference latency. We propose a latency-aware real-time evaluation setting where the model is required to finish forecasting $t_f$ seconds before the target time. We present RAFTformer, a fast action anticipation transformer that outperforms prior works both in offline & real-time setting while forecasting actions in real-time (≥25 FPS). + +correctness of systems rather than the latency of the predictions. While vision-based forecasting systems are often meant for embodied real-time deployment on autonomous agents like self-driving cars and robots, they are evaluated in an offline setting where inference latency is neglected (Figure 1). Interestingly, recent neural network architectures have adopted FLOPs as a proxy for latency as a second axis for model design. While a sufficient fidelity metric for offline after-the-fact applications like automatic content recognition, latency often comes second to correctness, even for real-time systems such as forecasting models. + +Forecasting empowers reactive planning [17]. An autonomous system present in rich human environments inevitably needs to understand human actions around it for smooth task planning and execution. Autonomous agent planning critically depends on anticipating the future of the scene in various forms such as trajectory prediction [22, 23, 57, 58], action forecasting [19, 25, 80] or future scene + +segmentation [8] and anticipating the future is an activity humans subconsciously do for day-to-day tasks [60]. And while vision-based forecasting systems are often meant for embodied real-time deployment on autonomous agents like autonomous cars and robots, they are evaluated in an offline setting where inference latency is neglected (Figure 1). + +In this work, we propose a real-time evaluation setting (Figure 1) that closely mimics the real-world deployment for a forecasting system. Suppose that in a real-time system, the design specifications require the forecasting system outputs $t_f$ seconds in advance of the event to be able to plan and use the forecasts effectively. In current offline settings, the forecasting system begins the inference $t_f$ seconds in advance of the event ('Present' in Figure 1) and the model latency is ignored (or assumed to be 0) such that the predictions are available instantly. However, in our proposed real-time setting, the model is required to start inference in advance of 'Present' so that the outputs are available with a horizon of $t_f$ seconds, meeting the design specification. + +We observe that in the real-time setting, the prior works fare quite poorly because of their slow model inference latency (Table 3). A large latency implies that the model has to start inference further in the past and has to rely on older video data to make forecasts with the benefit of more expressiveness (Figure 2). A smaller latency means the model can enjoy more recent video data but has limited capacity. Simply said, models that are only evaluated in the offline setting may fare poorly in the real-time deployment setting due to their latency agnostic design (Figure 2). + +We present, RAFTformer, a real-time action forecasting transformer that uses a two-stage transformer encoder-based network for lightning fast forecasts in inference. RAFTformer uses a shuffled casual masking scheme based feature prediction loss for learning strong temporal cues that transfer to feature prediction. Further, RAFTformer uses specialized anticipation tokens for learning to predict action at multiple temporal horizons that improve model reasoning capabilities of short-term action forecasting as well. Finally, the model is explicitly designed for real-time embodied deployments that allows inference up to an order of magnitude faster than prior state-of-the-art methods. In summary, our contributions are three-fold, + +First, we propose Real-time Action Forecasting Transformer (RAFTformer), a real-time action forecasting transformer with latency at least $9 \times$ smaller than prior state-of-the-art action forecasting methods. RAFTformer uses specialized anticipation tokens and a novel shuffled casual masking-based self-supervision loss that allows it to outperform prior work while maintaining low latency with a reduction of $94\%$ in GPU training time and $90\%$ in the number of trainable parameters compares to prior works. To the best of our knowledge, our work is the first to achieve action anticipation in real-time (i.e. 25 fps). + +![](images/d8b14c4788415741396220e49009cd343151625e0fb90d85fc005f050ca0c242.jpg) +Figure 2. Evaluation Performance vs. Latency. Bigger models perform better in latency agnostic offline settings. In the real-time evaluation setting, we observe that, beyond a limit, bigger models with higher latency cause a drop in forecasting performance. In practical deployment, there exists a trade-off between latency and high-fidelity forecasts. See §4.3.1 for details. + +Second, we propose a latency-aware real-time evaluation setting (Figure 1) that better mimics practical deployment settings for embodied forecasting systems. Real-time evaluation demonstrates a clear trade-off between inference latency and model forecasting fidelity, paving the path for the development of latency-aware forecasting models in the future (also see [20]). + +Third, Through extensive experiments, we show that RAFTformer outperforms prior state-of-the-art methods by 4.9 points on the EGTEA Gaze+ dataset, by 1.4 points on the EPIC-Kitchens-100 dataset according to the Top-5 Recall metric and by a relative margin of $5.3\%$ on the top-1 accuracy metric on EPIC-Kitchens-55 dataset. + +# 2. Related Work + +Action Anticipation. Over the last few years, action anticipation has seen significant advances following the promising results in video recognition [2,4,12,15,24,38,40, 49,55,61,80,87] and video segmentation [27,43,48,76,81]. While earlier works [1, 56, 68] use CNN-based methods for video action anticipation, many follow-up works transitioned into using recurrent sequence-based networks [19, 22, 64, 66, 71]. Using multiple spatial and temporal scales was another key idea explored in several anticipation works [15, 70, 70, 77, 80, 86]. Masking-based self-supervision has proven to be a new frontier for both image [5, 14, 33, 35, 62] and video [31, 74] representation learning. This concept has also been explored in the context of video anticipation [25] which differs from prior works that explore temporal consistency [16, 37, 42, 79, 82], inter-frame predictability [28, 29, 36], and cross-modal correspondence [3, 44, 73]. In our work we propose a novel generalized self-supervision scheme which is a crucial part of our model's ability to generalize and outperform SOTA. + +Transformers for Video Anticipation. With the rise of transformers for sequence tasks, recent works have explored various image and video-based transformers [25, 26, 26, 78, 80, 85] for anticipating actions. [25] proposes a ViT-based [11] spatial transformer backbone with a transformer decoder head to anticipate the next action with a $1s$ horizon. [25] predicts actions in the same latent space as their feature decodings causing conflation between feature reconstruction and future prediction. We propose specialized anticipation tokens to address this problem. Furthermore, [25] uses a recurrent decoder and frame-level operation, which is inefficient for both training compute and inference latency. MeMViT [80] proposes another fully transformer model which extends MViT [12] for better long-range modeling using a novel caching mechanism. However, their model is trained to only predict the next action and thus does not explicitly learn to model the future or evolving scene dynamics. Furthermore, their model is less efficient than RAFTformer in terms of both training and inference time due to its larger model and input size and complete end-to-end training. RAFTformer uses a fixed pre-trained video network and only trains the RAFTformer network. Recently [26] propose a transformer-based model for long-term action anticipation. They focus on a sequential prediction rather than next-action prediction and do not focus on inference latency. + +Real-Time Systems. Latency matters, especially for real-time applications. Autonomous agents need to reason about nearby agents and take real-time decisions. This vision has led to great progress in the development of real-time systems in the related fields of semantic segmentation [13], video object segmentation [76], object detection [7, 51, 53, 67], multi-object tracking [41]. While some progress has also been made in activity understanding [72, 84], it is limited to recognition and detection. Keeping this in mind, some recent works in action anticipation have also started focusing on efficiency and memory footprint and report training time, inference time, and trainable parameters [80]. Although a step in the right direction, these works have high inference times in comparison to their desired anticipation horizon. Our proposed method is significantly faster during both training and inference, has fewer trainable parameters and a smaller memory footprint, and still outperforms state-of-the-art methods. + +# 3. Real-Time Action Forecasting Transformer + +In this section, we first present the problem formulation (§3.1), followed by the architectural details of the video backbone for feature extraction (§3.2) and the RAFTformer model architecture (§3.3) including anticipation tokens (§3.3.1), shuffled causal masking (§3.3.2) and permutation encodings (§3.3.3), finishing with an outline of the loss functions used for training the model (§3.5). + +# 3.1. Problem Formulation + +Given an observed video starting from time $T = 0$ and of arbitrary length $t$ , $V_{0,t} = [F_0, \dots, F_t]$ where $F_i$ denotes the frame at time $i$ , the task is to predict the future action $t_f$ seconds in the future, i.e., action $\mathrm{A}_{t + t_f}$ at time $T = t + t_f$ . + +# 3.2. Pre-trained Video Backbone + +In contrast to state-of-the-art models [25, 80] that train end-to-end, we demonstrate that a two-stage training process is both efficient and produces high-fidelity forecasts. First, we split the full duration of the past video $V_{0,t}$ into sub-clips $V = [C_0,C_1,\dots,C_N]$ in a sliding window fashion. Each clip, $C_i$ , is independently processed with the short-term video backbone like MViT [12] to extract clip-level features. Previous works, such as [25], have employed image backbones for comparable undertakings, while we contend that video backbones offer richer spatio-temporal features, thus benefiting the downstream task. Further, a video backbone also allows lower latency since the produced clip embeddings already contain fused features for several images at once. + +Our two-stage design also allows for hierarchical temporal processing of the long-form past video. The short-term recognition backbone model operates on short, high-resolution clips. These extracted features are then used as input to the head network to process longer-range lower resolution features that capture key information from each clip. This is a crucial design consideration to lower the inference latency in RAFTformer while still capturing longer-range temporal dependencies compared to [19, 25]. + +# 3.3.RAFTformer Model Network + +We propose RAFTformer as a transformer encoder model. The transformer encoder has the advantage of being able to effectively learn across clip dependencies by attending over independently extracted clip features without facing memory bottlenecks such as faced in LSTM encoders [34] that have been used in some prior works [19,70]. However, to make the encoder effective for action forecasting on pre-trained features, we propose several changes to the training process to allow two-staged training to work as well as end-to-end training for action forecasting. + +# 3.3.1 Anticipation Tokens + +The extracted clip embeddings $[C_0\cdots C_{N-1}]$ form the first part of the input to the action anticipation head. For the second part, we propose to train learnable 'anticipation tokens' that can aggregate global context and later can be decoded into future predictions. This design choice stands in contrast to prior works like [25] where the output of the anticipation token is implicitly designed to be in the same latent space as the output of their image-feature tokens. In + +![](images/6eba557065fa750a29a0c8a2b969291b2572e354663fd503fcbb5e44e3efea74.jpg) +Figure 3. RAFTformer is a real-time action anticipation transformer architecture comprised of two stages. The first stage is a pretrained short-term backbone that produces individual clip embeddings independently of other clips (§3.2). In the second stage (§3.3), absolute position encodings are added and the resulting sequence is shuffled with a sampled permutation $\pi^{*} \sim \pi$ . The permutation encodings (§3.3.3) are then added to the shuffled sequence and after concatenation with anticipation tokens, the sequence is processed with the RAFTformer encoder. The output tokens are decoded via short & long-term action anticipation heads (§3.4), as well as the feature prediction head trained with self-supervised loss ( $\mathcal{L}_{\mathrm{SCM}}$ ), future feature prediction loss ( $\mathcal{L}_{\mathrm{future}}$ ) and action forecasting loss ( $\mathcal{L}_{\mathrm{focal}}$ ) (§3.5). + +contrast to prior works, we find that temporal aggregation such as mean pooling for forecasting leads to subpar performance (see Table 5). Hence, we use the output tokens corresponding to $[C_0\cdots C_N]$ solely for self-supervised feature loss rather than action anticipation. + +Instead, for action anticipation, we propose to train learnable 'anticipation tokens' to learn useful global context from the clip tokens. The output of the anticipation token is no longer restricted to be in the same latent space as the output of clip-feature tokens like in [25] and can better capture the information needed to anticipate the next action. Further, we propose to use multiple anticipation tokens to generate additional supervision, with each token attending to different past video lengths and producing forecasts for different time horizons in the future. + +# 3.3.2 Self-Supervision via Shuffled Feature Prediction + +Prior works explored using the self-supervision task of predicting frame or clip features and using an MSE loss [25]. We propose using a generalized form of masking-based self-supervision [33] based on predicting shuffled future features. Predicting future clip features has a two-fold benefit: (A) It encourages causally learning the observed sequence incentivizing the model to grasp underlying scene dynamics and (B) Prediction in the latent feature space allows reasoning semantically about the future without wasting modeling capacity with low pixel level scene details. + +Different from loss functions proposed in prior works [25], we propose an improved auto-regressive scheme for self-supervised learning by future feature pre + +
Auto-regressive [1,2,3,4]Shuffle π1: [4,1,3,2]Another Shuffle π2: [3,4,2,1]
1 → 24 → 13 → 4
2 → 31 → 34 → 2
3 → 43 → 22 → 1
+ +Table 1. Encoding the input permutation $\pi$ . Shuffling the input sequence arbitrarily changes the successor of each token. + +diction. Rather than sequentially predicting missing clip features in order to use a causal attention mask, we propose to use a model-level augmentation of the attention masking scheme where some of the attention weights are not used from the original causal mask. + +Random Masking. Construction of a sparse augmented attention mask is non-trivial. Simply generating a random mask such as in MAE [33] fails to isolate information within the intended partitioning due to multi-hop message passing caused by repeated application of the same mask. For example, in Figure 4, the attention mask prohibits token 1 to access token 2 and 3 (shown by 'white'). However, after two layers, token 1 in layer 2 can access information in token 2 in layer 0 (shown by red border), indirectly through token 4 in later 1 because of multi-hop message passing. This temporal information leakage can cause self-supervision to fail. For example, self-supervising token 1 with token 2 feature prediction would collapse in setup of Figure 4. To prevent this, we propose a simple yet effective solution. + +Shuffled Causal Masking. We know that vanilla causal masks ensure that information available to each token is invariant under repeated applications of the attention mask, i.e., multi-hop message passing. Since multi-hop message passing is token permutation invariant, any permutation of the tokens from the causal mask will preserve the invariance of accessible information under multiple hops. Thus, this allows a general framework for structured randomized mask construction without temporal leakage. We notice that a row-wise permutation of the attention mask is equivalent to the same permutation applied to the sequence itself. Hence, the same effect as properly constructed random masks can simply be achieved by shuffling the input token sequence itself. This allows generalizing vanilla autoregressive prediction order to arbitrary sequence permutations without any multi-hop information leakage through the layers. Thus, rather than predicting clip features sequentially from 0 to $N - 1$ like [25], our proposed scheme allows for exponentially more variations. + +Referring to Figure 3, we first add absolute position embeddings (APE) to each of the clip features before shuffling them. This allows the transformer to leverage the information about the actual temporal order of each clip in the video. Without the absolute position embeddings, the transformer is input permutation equivariant, which is not a desirable property for action forecasting. However, while APE is sufficient for positional information in vanilla autoregressive ordering, it is not enough for prediction under our proposed Shuffled Causal Masking (SCM) scheme. In autoregressive ordering, for any specific token, the next token in the sequence corresponds to a fixed position and hence the self-supervised training process can subtly learn this bias via next-token feature supervision. In contrast, under SCM the temporal position of the next token varies depending on the shuffling permutation. Hence, self-supervised training cannot learn to perform effective feature prediction without information about the shuffling permutation. + +# 3.3.3 Permutation Position Encoding + +Naïve Encodings. For an $L$ length sequence, there exist $L!$ possible permutations. Encoding each permutation $(\pi)$ by itself is clearly intractable. First, we observe that encoding $\pi^{*}$ as a set of $O(L)$ embeddings which are shared among different $\pi$ is more efficient. A follow-up solution would be to instead encode each predecessor $\mapsto$ successor relationship as an encoding and have $L - 1$ of such embeddings together encode $\pi^{*}$ . This reduces to the total number of required embeddings to $L(L - 1)$ from $L!$ . Each $\pi^{*}$ now shares every one of its $L$ embeddings with other $\pi$ , but considered as a set, the $L$ embeddings uniquely encode $\pi^{*}$ . However, even $L^2$ becomes intractable for large $L$ . + +Permutation Position Encodings $(\pi \mathrm{PE})$ provides an elegant solution for encoding $\pi^{*}$ requiring only $L$ total encod + +![](images/a789e94b775d299c15f0c0e1b6f1dc172688bd9ddbdc95e1b4d42a0ae9e6c8a9.jpg) +Figure 4. Random Masking Self-Supervision Illustration of how naive random masking (white denotes masked out) fails for self-supervised feature prediction task. We can see that in Layer 1 the tokens can only access information according to the provided mask. However, if the same mask is used in Layer 2, there is information leakage across tokens which is undesirable. + +ings to be learned. $\pi$ PE encodes the predecessor $\mapsto$ successor relationships but further simplifies by noting that adding the encoding to the token itself makes the predecessor information redundant. The token itself is the predecessor and has the positional information available from APE. Hence, we simply encode the successor positional information, and that in combination with APE uniquely encodes $\pi^{*}$ . Hence, we design $\pi$ PE to be the encoding of the original temporal position of the successor in the permuted sequence. So for the $\pi_{1}$ permutation in Table 1, we would add $\pi$ PE[1] to token 4, $\pi$ PE[3] to token 1 and $\pi$ PE[2] to token 3. + +# 3.4. Overall Mechanism + +The past video is split into clips, and the clip embeddings $[C_0\cdots C_{N-1}]$ are extracted using a video backbone (Figure 3). Anticipation tokens are concatenated to the extracted sequence ( $\S 3.3.1$ ), followed by the addition of absolute position encoding to the concatenated sequence. Now, the clip embedding is shuffled according to a randomly chosen permutation $\pi^*$ to obtain $[C_{\pi^*[0]}\cdots C_{\pi^*[N-1]}\]$ . The sampled permutation $\pi^*$ is then encoded by adding the successor's ( $\S 3.3.3$ ) embedding to each token. In Figure 3, $\pi^*[1] = 3$ and $\pi^*[2] = N$ , hence $\pi \mathrm{PE}[\pi^*[1+1]]$ is added to the token $\pi^*[1]$ i.e., $\pi \mathrm{PE}[N]$ is added to $E_3$ , which is used to self-supervise the feature at position 1 in the shuffled sequence, i.e., token 3 ( $\S 3.3.2$ ). The shuffled input sequence, in addition to the anticipation tokens, is now propagated through the transformer encoder using a causal attention masking scheme and the output is decoded with the head networks. + +Head Networks We propose using three MLP heads on top of the transformer encoder network (Figure 3). Two MLP heads decode the anticipation tokens into the predicted future action distribution. The third MLP head up-samples the encoded tokens to the original representation space of the input tokens to allow self-supervision loss. + +
SplitMethodAddl. ModalityInitEpic BoxesTop-5 RecallParameters (×106)GPU HoursInference Latency (ms)
VerbNounAction
ValTempAgg [70]NoneIN1K24.229.813.0---
RULSTM [19]NoneIN1K--13.3---
RULSTM [19]Obj+FlowIN1K✓30.827.814.0---
TempAgg [70]Obj+Flow+ROIIN1K✓23.231.414.7---
AVT [25]NoneIN21K30.231.714.9378-420
AVT+ [25]ObjIN21K✓28.232.015.9---
TSN-AVT+ [25]ObjIN21K✓31.825.514.8---
MeMVit [80]NoneK40032.833.215.159-160
MeMVit [80]NoneK70032.237.017.7212368350
TestRAFTformerNoneK400 + IN1K33.335.517.6262340
RAFTformerNoneK70033.737.118.02627110
RAFTformer-2BNoneK700 + IN1K33.837.919.15250160
RULSTM [19]Obj+FlowIN1K✓25.326.711.2---
TBN [83]Obj+FlowIN1K✓21.526.811.0---
AVT+ [25]Obj+FlowIN21K✓25.628.812.6---
Abstract Goal [69]Obj+FlowIN1K✓31.430.114.3---
AFFT [85]Obj+Flow-✓20.731.814.9---
RAFTformerNoneK400 + IN1K27.332.814.0262340
RAFTformerNoneK70027.434.014.72627110
RAFTformer-2BNoneK700 + IN1K30.134.115.45250160
+ +Table 2. Offline Evaluation Results on the EK-100 dataset for $t_f = 1$ second horizon. Latency is measured over the entire model including the backbone & head networks on a single 16G Tesla V100 GPU. Methods that use other modalities (+RGB) are deemphasized. + +# 3.5. Loss Functions + +We observe that the ground truth action distributions are often long-tailed, and propose to use the the focal loss [52], for supervising the future action prediction distributions. + +$$ +\mathcal {L} _ {\text {f o c a l}} = \sum_ {A _ {i} \in A} \sum_ {i = 0} ^ {n} - (1 - p _ {A _ {i}}) ^ {\gamma} \log \left(p _ {A _ {i}}\right) +$$ + +where $p_i$ is the predicted probability for the correct class for the $i$ th example, $A_i$ represents predictions from a specific anticipation token and $\gamma$ is the focusing parameter where $\gamma = 0$ is cross entropy loss. Increasing $\gamma$ results in an increased penalty for hard, misclassified examples. + +For self-supervision using shuffled causal masking to predict next-token embeddings, we use an expected $\ell_2$ loss over both past tokens, with the expectation being oversampled permutations $\pi^{*} \sim \pi$ . + +$$ +\mathcal{L}_{\mathrm{SCM}} = \underset {\pi^{*}\sim \pi}{\mathbb{E}}\sum_{j = 0}^{N - 1}\| E_{\pi^{*}[j]} - \hat{E}_{\pi^{*}[j]}\|_{2}^{2} +$$ + +where $E_{\pi^{*}[j]}$ and $\hat{E}_{\pi^{*}[j]}$ denotes the original and the predicted clip embedding at position $j$ after permuting with $\pi^{*}$ . For future token prediction, we use a simple $\ell_2$ loss: + +$$ +\mathcal {L} _ {\mathrm {f u t u r e}} = \left\| E _ {\mathrm {f u t u r e}} - \hat {E} _ {\mathrm {f u t u r e}} \right\| _ {2} ^ {2} +$$ + +where $E_{\mathrm{future}}$ is the MViT embedding for the next clip (after $t_f$ ). Finally, the overall loss is simply a weighted sum, + +$$ +\mathcal {L} = \mathcal {L} _ {\text {f o c a l}} + \lambda_ {1} \mathcal {L} _ {\text {S C M}} + \lambda_ {2} \mathcal {L} _ {\text {f u t u r e}} +$$ + +# 4. Experiments + +Datasets & Metrics. We use the widely benchmarked EPIC-KITCHENS dataset [9], an unscripted set with nearly $20 \times$ more action classes and $10 - 100 \times$ more observed sequences than other action datasets like 50 Salads [47] and Breakfast [46], used in prior work [19]. We use both the EPIC-55 & EPIC-100 anticipation splits and the EGTEA+ Gaze dataset [50]. Dataset details in supplementary. + +Since human decision-making is inherently multimodal, we propose an approach to predict multiple reasonable future action forecasts. In addition to top-1 accuracy, we report top-5 recall following prior works [19, 25, 80]. We use the baseline data splits and report metrics on both the validation and test set. In addition, we report the number of trainable model parameters (M), the total compute spent for training the model to convergence on a Tesla V100 GPU (in hours), and the inference latency (in milliseconds). + +# 4.1. Evaluation Setting + +Offline evaluation is the setting where the model inference latency is ignored, or in other words, assumed to be zero. All prior works [19, 25, 80] consider this setting. Referring to Figure 1, prior works assume access to all past video frames up till the present moment $T = t$ . Using this information, the model then predicts that action with a $t_f$ second horizon at $T = t + t_f$ . However, the prediction would actually be produced at time $T = t + t_l$ where $t_l$ is the model inference latency. This is not practically useful + +
ModelInitLatency (t1 ms)Inference Start Time StampInference End Time StampTarget Time StampTop-5 Recall
VerbNounAction
AVT [25]IN21Ktavt = 420TT + tavtT + 130.231.714.9
RAFTformerK400 + IN1ktours = 40T + tavt - toursT + tavtT + 134.138.219.3 (+4.4)
MemViT [80]K400tvit = 160TT + tvitT + 132.833.215.1
RAFTformerK400 + IN1ktours = 40T + tvit - toursT + tvitT + 133.837.118.1 (+3.0)
MemViT [80]K700tvit = 350TT + tvitT + 132.237.017.7
RAFTformerK400 + IN1ktours = 40T + tvit - toursT + tvitT + 133.737.919.0 (+1.3)
+ +Table 3. Real-time Evaluation Results for benchmarking action forecasting methods in a practical setting (§4.1). Each comparison is performed between a pair of models where their start time ('Inference Start') times have been adjusted (Figure 1) by their latency so that they produce the forecasting output for the 'Target Time' simultaneously ('Inference End'). For prior works [25,80], start & end times are kept the same as their original offline settings (Table 2) to avoid any training recipe change. Faster models can pragmatically utilize recent frames while slower models must rely on higher fidelity prediction from older frames. Latency measured on a single 16G Tesla V100 GPU. + +
ModelInitTop-1 Acc
RULSTM [19]TSN/IN1k13.1
ActionBanks [70]TSN/IN1k12.3
AVT-h [25]TSN/IN1k13.1
RAFTformerTSN/IN1k13.8
+ +since often, we require time horizon $t_f$ to meaningfully use the predicted future outcomes. Further, this does not account for absurdities where a large model might even have latency $t_l > t_f$ , in which case the model is predicting an action that has already happened by the time it predicts it! A complex model can have great offline performance but its inference time would make it unusable in practice. + +Real-time evaluation. To remedy this impractical situation, we consider the real-time evaluation setting. In this setting, the model is required to finish inference with at least $t_f$ seconds horizon before the target time (Fig. 1). Hence, the model is allowed access to past video data only for $T < t - t_l$ . This setting even allows for large models where $t_l > t_f$ since predictions would still be produced with $t_f$ seconds before the target time. Unlike other recognition scenarios where latency is a mere annoyance, in the case of future forecasting, models are often used in real-time rather than offline. The offline setting subtly oversteps the prediction horizon $t_f$ , by receiving forecasts with a margin much less than the postulated $t_f$ horizon. By coupling model latency to the past video data observed, the real-time setting incentivizes the development of efficient forecasting methods that utilize the recent data better than relying on slow large models that cannot miss the recent frames, which arguably are the most crucial for near future prediction. + +# 4.2. EPIC-Kitchens-100 + +Network Details. For feature extraction, we fix the pretrained 16x4 (K400+IN1K) and 32x3 (K700) MViT-B backbones [12, 49] trained for recognition on the EK100 + +Table 4. Offline Evaluation results on the Epic-Kitchens-55. + +
ModelSettingTop-5 Recall
ATFLSCM2×AT
Mean pooling✓15.2
16.1 (+0.9)
RAFTformer✓✓16.8 (+0.7)
✓✓✓17.4 (+0.6)
✓✓✓✓17.6 (+0.2)
+ +Table 5. EK100 Ablation Study. FL is feature loss (no SCM), SCM is Shuffled Causal Masking (\$3.3.2), AT $\left( {2 \times }\right)$ are single (double) anticipation tokens (§3.3.1). + +dataset. Each clip is embedded as a 768-dimensional feature vector. Unless mentioned otherwise, the action forecasting experiments use a $t_f = 1$ second horizon. RAFTformer encoder is a lightweight 4 layer, 4 head transformer encoder using post-normalization and ReLU activations. A linear projection from up-projects $768 \rightarrow 1024$ for the transformer. We only shuffle during training with a probability of 0.3. The output of the encoder is down projected from $1024 \rightarrow 768$ channels. Both short-term and long-term action prediction heads are fast & lightweight MLPs $(1024 \rightarrow 2048 \rightarrow 3806)$ . We set $\lambda_1 = \lambda_2 = 14$ . For other details, please see supplementary. + +Offline Evaluation. In Table 2 we first report RAFTformer results against prior works, including previous SOTA MeMViT [80]. Results that use additional modalities like Object (Obj), Flow (Flow), Object Region of Interest (ROI), or Epic Kitchen boxes are de-emphasized. Using only RGB, RAFTformer (K700) outperforms the AVT RGB model in action T5R by 3.1 points and the AVT RGB+Obj model by 2.1 points. RAFTformer slightly outperforms MeMViT action T5R while predicting actions $8.75 \times$ faster with $8.2 \times$ lesser trainable parameters and a $16 \times$ faster training. We also combine two separate RAFTformer models to train a two-backbone model (RAFTformer-2B) that achieves state-of-the-art by with a $1.4\%$ T5R increase. In the second section, we report our submitted results to the EK100 test server. We observe that RAFTformer general + +
ModelInitModalityTop-5 Recall
DMR [75]-RGB38.1
ATSN [9]TSN/IN1kRGB+Flow31.6
MCE [18]TSN/IN1kRGB+Flow43.8
TCN [6]-RGB47.1
FN [10]VGG-16RGB42.7
ED [21]VGG-16/TSRGB+Flow54.6
RULSTM [19]TSN/IN1kRGB+Obj+Flow58.6
RAFTformerTSN/IN1kRGB63.5
+ +Table 6. EGTEA Gaze+. Under same initialization, RAFTformer outperforms prior methods without additional modalities. + +izes well to the test set, improving upon the $\mathrm{AVT + }$ multimodal ensemble model [25] by 2.8 T5R points. + +# 4.3. Additional Datasets + +EPIC-Kitchens 55. We also compare RAFTformer to prior baselines on the EK55 dataset in Table 4 on top-1 accuracy. We evaluate against other models using the same initialization for a fair comparison. We observe that RAFTformer outperforms prior benchmarks by about $0.7\%$ using the exact same backbone features. This shows the superiority of our proposed shuffle causal masking (§3.3.2) & anticipation token prediction (§3.3.1) in a controlled setting. + +Real-time Evaluation. In table 3, we fix the target - start time difference to be what the prior models such as, AVT [25] or MeMViT [80] were designed for, to avoid any unintended change in their training recipes. Hence, we shift RAFTformer start time so that the output forecasts are produced simultaneously for the pair. + +We observe that RAFTformer outperforms prior methods by an even larger margin in the real-time evaluation setting than the offline setting. RAFTformer effectively utilizes its compute to produce the maximum forecasting effect at the least latency cost. This allows RAFTformer to exploit more recent information that slower models miss because of higher inference latencies $(t_{\mathrm{ours}} < \{t_{\mathrm{avt}}, t_{\mathrm{vit}}\})$ . This also shows the disproportional effect of inference latency on forecasting performance. While RAFTFormer K400 + IN1K has a similar Top-5 Recall as MeMViT K700 in the offline setting, in the practical real-time evaluation (Table 3), RAFTformer outperforms MeMViT by $1.3\%$ by leveraging its faster inference latency (40 vs. 350 ms). + +# 4.3.1 Latency vs. Offline & Real-time Forecasting + +In offline evaluation, latency is ignored and all models have data access parity. As scaling laws [39] would predict, bigger models (with higher latency) have stronger forecasting performance (Blue curve in Fig. 2). In the real-time setting, a higher latency implies access to less recent data (Green curve in Fig. 2) and hence, an interesting trade-off materializes. At first, as latency (and model size) increases, the performance improves. This is because the benefit of having a more expressive model outweighs the cost of access to older video data. However, as the latency increases fur + +ther, the real-time performance starts decreasing. Now the harm of not having access to recent data outweighs the benefit of a more expressive model. For our setting, the optimal RAFTformer model has a latency of $40~\mathrm{ms}$ with an offline and real-time performance of 19.6 and 19.3 Top-5 recall respectively. A similar trade-off would exist for any combination of dataset, model, and deployment hardware regimes. Plots are for RAFTformer models of varying backbone parameter count for $t_f = 0.58$ second prediction on EK100. + +# 4.3.2 Ablations + +We ablate RAFTformer thoroughly in Table 5. In contrast to prior works [25,80] that pool information or use the same embedding for feature supervision and action prediction, we train explicit anticipation tokens (§3.3.1) to perform forecasting, improving T5R by 1.1. Anticipation tokens specialize in predicting the next action instead of using features that multi-task between reconstructing clip features and future action prediction [25]. Self-supervision via feature loss (FL) further improves by 0.7 T5R. Further, our SCM technique effectively regularizes FL that improves 0.6 T5R. Finally, an additional anticipation token $(2\times \mathrm{AT})$ for supervision further improves 0.2 T5R. Additional longer-horizon anticipation task helps in learning transferable global video features to the main anticipation task. + +EGTEA Gaze+. We also evaluate the EGTEA Gaze+ dataset in Table 6 to showcase RAFTformer performance on new settings outside of EPIC-Kitchens. Again, we use the setting of anticipating $1s$ into the future and use the T5R metric. While prior methods use many input modalities including as object, flow, and RGB, we significantly outperform the prior state-of-the-art in this setting [19] by $4.9\%$ . Note that we use pre-extracted TSN RGB features as provided by [19] for direct comparison. Our very strong performance on another egocentric video dataset with complex human tasks further validates the promise of RAFTformer. + +# 5. Conclusion + +We propose Real-Time Action Forecasting Transformer (RAFTformer), a parsimonious two-stage fully transformer-based architecture consisting of a short-range video transformer backbone for feature extraction and a long-range head transformer encoder for long-term temporal aggregation across multiple clips. We also introduce a real-time evaluation setting for action forecasting models that directly penalizes high latency and closely mimics the real-world deployment scenario for forecasting models. RAFTformer outperforms prior state-of-the-art methods by significant margins across several action forecasting benchmarks in the offline setting, and by an even larger margin of upto 4.4 T5R, in the real-time setting. 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Our parsimonious network design facilitates RAFTformer inference latency to be " + }, + { + "bbox": [ + 47, + 228, + 290, + 550 + ], + "type": "inline_equation", + "content": "9 \\times" + }, + { + "bbox": [ + 47, + 228, + 290, + 550 + ], + "type": "text", + "content": " smaller than prior works at the same forecasting accuracy. Owing to its two-staged design, RAFTformer uses " + }, + { + "bbox": [ + 47, + 228, + 290, + 550 + ], + "type": "inline_equation", + "content": "94\\%" + }, + { + "bbox": [ + 47, + 228, + 290, + 550 + ], + "type": "text", + "content": " less training compute and " + }, + { + "bbox": [ + 47, + 228, + 290, + 550 + ], + "type": "inline_equation", + "content": "90\\%" + }, + { + "bbox": [ + 47, + 228, + 290, + 550 + ], + "type": "text", + "content": " lesser training parameters to outperform prior state-of-the-art baselines by 4.9 points on EGTEA Gaze+ and by 1.4 points on EPIC-Kitchens-100 validation set, as measured by Top-5 recall (T5R) in the offline setting. In the real-time setting, RAFTformer outperforms prior works by an even greater margin of up to 4.4 T5R points on the EPIC-Kitchens-100 dataset. Project Webpage: https://karttikeya.github.io/publication/RAFTformer/." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 562, + 128, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 562, + 128, + 574 + ], + "spans": [ + { + "bbox": [ + 47, + 562, + 128, + 574 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 581, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 581, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 581, + 287, + 677 + ], + "type": "text", + "content": "Latency matters. It is a crucial system design consideration for countless applications that operate in real-time from hardware design [65], network engineering [63], and satellite communications [30] to capital trading [32], human vision [59] and COVID transmission patterns [54]. However, it has not been a center stage design consideration in modern computer vision systems of the past decade [11,45]. Modern vision system design has largely focused on the" + } + ] + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 312, + 206, + 544, + 384 + ], + "blocks": [ + { + "bbox": [ + 312, + 206, + 544, + 384 + ], + "lines": [ + { + "bbox": [ + 312, + 206, + 544, + 384 + ], + "spans": [ + { + "bbox": [ + 312, + 206, + 544, + 384 + ], + "type": "image", + "image_path": "8cae1987f001aaa922bf43d041f42357f1946ed8965d3ec9aa471acf10c20730.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 388, + 546, + 486 + ], + "lines": [ + { + "bbox": [ + 304, + 388, + 546, + 486 + ], + "spans": [ + { + "bbox": [ + 304, + 388, + 546, + 486 + ], + "type": "text", + "content": "Figure 1. Action Forecasting is the task of predicting actions that will happen after a pre-determined time span, say " + }, + { + "bbox": [ + 304, + 388, + 546, + 486 + ], + "type": "inline_equation", + "content": "t_f" + }, + { + "bbox": [ + 304, + 388, + 546, + 486 + ], + "type": "text", + "content": " seconds, into the future. Prior works consider an offline evaluation setting that ignores the model inference latency. We propose a latency-aware real-time evaluation setting where the model is required to finish forecasting " + }, + { + "bbox": [ + 304, + 388, + 546, + 486 + ], + "type": "inline_equation", + "content": "t_f" + }, + { + "bbox": [ + 304, + 388, + 546, + 486 + ], + "type": "text", + "content": " seconds before the target time. We present RAFTformer, a fast action anticipation transformer that outperforms prior works both in offline & real-time setting while forecasting actions in real-time (≥25 FPS)." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 495, + 546, + 626 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 495, + 546, + 626 + ], + "spans": [ + { + "bbox": [ + 304, + 495, + 546, + 626 + ], + "type": "text", + "content": "correctness of systems rather than the latency of the predictions. While vision-based forecasting systems are often meant for embodied real-time deployment on autonomous agents like self-driving cars and robots, they are evaluated in an offline setting where inference latency is neglected (Figure 1). Interestingly, recent neural network architectures have adopted FLOPs as a proxy for latency as a second axis for model design. While a sufficient fidelity metric for offline after-the-fact applications like automatic content recognition, latency often comes second to correctness, even for real-time systems such as forecasting models." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 630, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 547, + 713 + ], + "type": "text", + "content": "Forecasting empowers reactive planning [17]. An autonomous system present in rich human environments inevitably needs to understand human actions around it for smooth task planning and execution. Autonomous agent planning critically depends on anticipating the future of the scene in various forms such as trajectory prediction [22, 23, 57, 58], action forecasting [19, 25, 80] or future scene" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 683, + 287, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 683, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 683, + 287, + 713 + ], + "type": "text", + "content": "* Work done during Harshayu's internship at HRI with Chiho Choi's supervision who is now at Samsung Semiconductor US Karttikeya Mangalam is the corresponding author" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18759" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 144 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 144 + ], + "type": "text", + "content": "segmentation [8] and anticipating the future is an activity humans subconsciously do for day-to-day tasks [60]. And while vision-based forecasting systems are often meant for embodied real-time deployment on autonomous agents like autonomous cars and robots, they are evaluated in an offline setting where inference latency is neglected (Figure 1)." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 146, + 287, + 302 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 146, + 287, + 302 + ], + "spans": [ + { + "bbox": [ + 46, + 146, + 287, + 302 + ], + "type": "text", + "content": "In this work, we propose a real-time evaluation setting (Figure 1) that closely mimics the real-world deployment for a forecasting system. Suppose that in a real-time system, the design specifications require the forecasting system outputs " + }, + { + "bbox": [ + 46, + 146, + 287, + 302 + ], + "type": "inline_equation", + "content": "t_f" + }, + { + "bbox": [ + 46, + 146, + 287, + 302 + ], + "type": "text", + "content": " seconds in advance of the event to be able to plan and use the forecasts effectively. In current offline settings, the forecasting system begins the inference " + }, + { + "bbox": [ + 46, + 146, + 287, + 302 + ], + "type": "inline_equation", + "content": "t_f" + }, + { + "bbox": [ + 46, + 146, + 287, + 302 + ], + "type": "text", + "content": " seconds in advance of the event ('Present' in Figure 1) and the model latency is ignored (or assumed to be 0) such that the predictions are available instantly. However, in our proposed real-time setting, the model is required to start inference in advance of 'Present' so that the outputs are available with a horizon of " + }, + { + "bbox": [ + 46, + 146, + 287, + 302 + ], + "type": "inline_equation", + "content": "t_f" + }, + { + "bbox": [ + 46, + 146, + 287, + 302 + ], + "type": "text", + "content": " seconds, meeting the design specification." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 303, + 287, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 303, + 287, + 422 + ], + "spans": [ + { + "bbox": [ + 46, + 303, + 287, + 422 + ], + "type": "text", + "content": "We observe that in the real-time setting, the prior works fare quite poorly because of their slow model inference latency (Table 3). A large latency implies that the model has to start inference further in the past and has to rely on older video data to make forecasts with the benefit of more expressiveness (Figure 2). A smaller latency means the model can enjoy more recent video data but has limited capacity. Simply said, models that are only evaluated in the offline setting may fare poorly in the real-time deployment setting due to their latency agnostic design (Figure 2)." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 425, + 287, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 425, + 287, + 579 + ], + "spans": [ + { + "bbox": [ + 46, + 425, + 287, + 579 + ], + "type": "text", + "content": "We present, RAFTformer, a real-time action forecasting transformer that uses a two-stage transformer encoder-based network for lightning fast forecasts in inference. RAFTformer uses a shuffled casual masking scheme based feature prediction loss for learning strong temporal cues that transfer to feature prediction. Further, RAFTformer uses specialized anticipation tokens for learning to predict action at multiple temporal horizons that improve model reasoning capabilities of short-term action forecasting as well. Finally, the model is explicitly designed for real-time embodied deployments that allows inference up to an order of magnitude faster than prior state-of-the-art methods. In summary, our contributions are three-fold," + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "text", + "content": "First, we propose Real-time Action Forecasting Transformer (RAFTformer), a real-time action forecasting transformer with latency at least " + }, + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "inline_equation", + "content": "9 \\times" + }, + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "text", + "content": " smaller than prior state-of-the-art action forecasting methods. RAFTformer uses specialized anticipation tokens and a novel shuffled casual masking-based self-supervision loss that allows it to outperform prior work while maintaining low latency with a reduction of " + }, + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "inline_equation", + "content": "94\\%" + }, + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "text", + "content": " in GPU training time and " + }, + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "inline_equation", + "content": "90\\%" + }, + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "text", + "content": " in the number of trainable parameters compares to prior works. To the best of our knowledge, our work is the first to achieve action anticipation in real-time (i.e. 25 fps)." + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 310, + 75, + 542, + 196 + ], + "blocks": [ + { + "bbox": [ + 310, + 75, + 542, + 196 + ], + "lines": [ + { + "bbox": [ + 310, + 75, + 542, + 196 + ], + "spans": [ + { + "bbox": [ + 310, + 75, + 542, + 196 + ], + "type": "image", + "image_path": "d8b14c4788415741396220e49009cd343151625e0fb90d85fc005f050ca0c242.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 209, + 545, + 275 + ], + "lines": [ + { + "bbox": [ + 305, + 209, + 545, + 275 + ], + "spans": [ + { + "bbox": [ + 305, + 209, + 545, + 275 + ], + "type": "text", + "content": "Figure 2. Evaluation Performance vs. Latency. Bigger models perform better in latency agnostic offline settings. In the real-time evaluation setting, we observe that, beyond a limit, bigger models with higher latency cause a drop in forecasting performance. In practical deployment, there exists a trade-off between latency and high-fidelity forecasts. See §4.3.1 for details." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 290, + 545, + 374 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 290, + 545, + 374 + ], + "spans": [ + { + "bbox": [ + 305, + 290, + 545, + 374 + ], + "type": "text", + "content": "Second, we propose a latency-aware real-time evaluation setting (Figure 1) that better mimics practical deployment settings for embodied forecasting systems. Real-time evaluation demonstrates a clear trade-off between inference latency and model forecasting fidelity, paving the path for the development of latency-aware forecasting models in the future (also see [20])." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 376, + 545, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 376, + 545, + 449 + ], + "spans": [ + { + "bbox": [ + 305, + 376, + 545, + 449 + ], + "type": "text", + "content": "Third, Through extensive experiments, we show that RAFTformer outperforms prior state-of-the-art methods by 4.9 points on the EGTEA Gaze+ dataset, by 1.4 points on the EPIC-Kitchens-100 dataset according to the Top-5 Recall metric and by a relative margin of " + }, + { + "bbox": [ + 305, + 376, + 545, + 449 + ], + "type": "inline_equation", + "content": "5.3\\%" + }, + { + "bbox": [ + 305, + 376, + 545, + 449 + ], + "type": "text", + "content": " on the top-1 accuracy metric on EPIC-Kitchens-55 dataset." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 464, + 392, + 475 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 464, + 392, + 475 + ], + "spans": [ + { + "bbox": [ + 306, + 464, + 392, + 475 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 486, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 486, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 545, + 713 + ], + "type": "text", + "content": "Action Anticipation. Over the last few years, action anticipation has seen significant advances following the promising results in video recognition [2,4,12,15,24,38,40, 49,55,61,80,87] and video segmentation [27,43,48,76,81]. While earlier works [1, 56, 68] use CNN-based methods for video action anticipation, many follow-up works transitioned into using recurrent sequence-based networks [19, 22, 64, 66, 71]. Using multiple spatial and temporal scales was another key idea explored in several anticipation works [15, 70, 70, 77, 80, 86]. Masking-based self-supervision has proven to be a new frontier for both image [5, 14, 33, 35, 62] and video [31, 74] representation learning. This concept has also been explored in the context of video anticipation [25] which differs from prior works that explore temporal consistency [16, 37, 42, 79, 82], inter-frame predictability [28, 29, 36], and cross-modal correspondence [3, 44, 73]. In our work we propose a novel generalized self-supervision scheme which is a crucial part of our model's ability to generalize and outperform SOTA." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18760" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 382 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 382 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 382 + ], + "type": "text", + "content": "Transformers for Video Anticipation. With the rise of transformers for sequence tasks, recent works have explored various image and video-based transformers [25, 26, 26, 78, 80, 85] for anticipating actions. [25] proposes a ViT-based [11] spatial transformer backbone with a transformer decoder head to anticipate the next action with a " + }, + { + "bbox": [ + 47, + 72, + 289, + 382 + ], + "type": "inline_equation", + "content": "1s" + }, + { + "bbox": [ + 47, + 72, + 289, + 382 + ], + "type": "text", + "content": " horizon. [25] predicts actions in the same latent space as their feature decodings causing conflation between feature reconstruction and future prediction. We propose specialized anticipation tokens to address this problem. Furthermore, [25] uses a recurrent decoder and frame-level operation, which is inefficient for both training compute and inference latency. MeMViT [80] proposes another fully transformer model which extends MViT [12] for better long-range modeling using a novel caching mechanism. However, their model is trained to only predict the next action and thus does not explicitly learn to model the future or evolving scene dynamics. Furthermore, their model is less efficient than RAFTformer in terms of both training and inference time due to its larger model and input size and complete end-to-end training. RAFTformer uses a fixed pre-trained video network and only trains the RAFTformer network. Recently [26] propose a transformer-based model for long-term action anticipation. They focus on a sequential prediction rather than next-action prediction and do not focus on inference latency." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 381, + 289, + 597 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 381, + 289, + 597 + ], + "spans": [ + { + "bbox": [ + 47, + 381, + 289, + 597 + ], + "type": "text", + "content": "Real-Time Systems. Latency matters, especially for real-time applications. Autonomous agents need to reason about nearby agents and take real-time decisions. This vision has led to great progress in the development of real-time systems in the related fields of semantic segmentation [13], video object segmentation [76], object detection [7, 51, 53, 67], multi-object tracking [41]. While some progress has also been made in activity understanding [72, 84], it is limited to recognition and detection. Keeping this in mind, some recent works in action anticipation have also started focusing on efficiency and memory footprint and report training time, inference time, and trainable parameters [80]. Although a step in the right direction, these works have high inference times in comparison to their desired anticipation horizon. Our proposed method is significantly faster during both training and inference, has fewer trainable parameters and a smaller memory footprint, and still outperforms state-of-the-art methods." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 609, + 284, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 609, + 284, + 624 + ], + "spans": [ + { + "bbox": [ + 47, + 609, + 284, + 624 + ], + "type": "text", + "content": "3. Real-Time Action Forecasting Transformer" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 630, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 287, + 715 + ], + "type": "text", + "content": "In this section, we first present the problem formulation (§3.1), followed by the architectural details of the video backbone for feature extraction (§3.2) and the RAFTformer model architecture (§3.3) including anticipation tokens (§3.3.1), shuffled causal masking (§3.3.2) and permutation encodings (§3.3.3), finishing with an outline of the loss functions used for training the model (§3.5)." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 305, + 72, + 432, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 432, + 85 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 432, + 85 + ], + "type": "text", + "content": "3.1. Problem Formulation" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 91, + 547, + 141 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 91, + 547, + 141 + ], + "spans": [ + { + "bbox": [ + 304, + 91, + 547, + 141 + ], + "type": "text", + "content": "Given an observed video starting from time " + }, + { + "bbox": [ + 304, + 91, + 547, + 141 + ], + "type": "inline_equation", + "content": "T = 0" + }, + { + "bbox": [ + 304, + 91, + 547, + 141 + ], + "type": "text", + "content": " and of arbitrary length " + }, + { + "bbox": [ + 304, + 91, + 547, + 141 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 91, + 547, + 141 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 91, + 547, + 141 + ], + "type": "inline_equation", + "content": "V_{0,t} = [F_0, \\dots, F_t]" + }, + { + "bbox": [ + 304, + 91, + 547, + 141 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 91, + 547, + 141 + ], + "type": "inline_equation", + "content": "F_i" + }, + { + "bbox": [ + 304, + 91, + 547, + 141 + ], + "type": "text", + "content": " denotes the frame at time " + }, + { + "bbox": [ + 304, + 91, + 547, + 141 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 91, + 547, + 141 + ], + "type": "text", + "content": ", the task is to predict the future action " + }, + { + "bbox": [ + 304, + 91, + 547, + 141 + ], + "type": "inline_equation", + "content": "t_f" + }, + { + "bbox": [ + 304, + 91, + 547, + 141 + ], + "type": "text", + "content": " seconds in the future, i.e., action " + }, + { + "bbox": [ + 304, + 91, + 547, + 141 + ], + "type": "inline_equation", + "content": "\\mathrm{A}_{t + t_f}" + }, + { + "bbox": [ + 304, + 91, + 547, + 141 + ], + "type": "text", + "content": " at time " + }, + { + "bbox": [ + 304, + 91, + 547, + 141 + ], + "type": "inline_equation", + "content": "T = t + t_f" + }, + { + "bbox": [ + 304, + 91, + 547, + 141 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 148, + 463, + 159 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 148, + 463, + 159 + ], + "spans": [ + { + "bbox": [ + 305, + 148, + 463, + 159 + ], + "type": "text", + "content": "3.2. Pre-trained Video Backbone" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 166, + 547, + 334 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 166, + 547, + 334 + ], + "spans": [ + { + "bbox": [ + 304, + 166, + 547, + 334 + ], + "type": "text", + "content": "In contrast to state-of-the-art models [25, 80] that train end-to-end, we demonstrate that a two-stage training process is both efficient and produces high-fidelity forecasts. First, we split the full duration of the past video " + }, + { + "bbox": [ + 304, + 166, + 547, + 334 + ], + "type": "inline_equation", + "content": "V_{0,t}" + }, + { + "bbox": [ + 304, + 166, + 547, + 334 + ], + "type": "text", + "content": " into sub-clips " + }, + { + "bbox": [ + 304, + 166, + 547, + 334 + ], + "type": "inline_equation", + "content": "V = [C_0,C_1,\\dots,C_N]" + }, + { + "bbox": [ + 304, + 166, + 547, + 334 + ], + "type": "text", + "content": " in a sliding window fashion. Each clip, " + }, + { + "bbox": [ + 304, + 166, + 547, + 334 + ], + "type": "inline_equation", + "content": "C_i" + }, + { + "bbox": [ + 304, + 166, + 547, + 334 + ], + "type": "text", + "content": ", is independently processed with the short-term video backbone like MViT [12] to extract clip-level features. Previous works, such as [25], have employed image backbones for comparable undertakings, while we contend that video backbones offer richer spatio-temporal features, thus benefiting the downstream task. Further, a video backbone also allows lower latency since the produced clip embeddings already contain fused features for several images at once." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 335, + 547, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 335, + 547, + 443 + ], + "spans": [ + { + "bbox": [ + 304, + 335, + 547, + 443 + ], + "type": "text", + "content": "Our two-stage design also allows for hierarchical temporal processing of the long-form past video. The short-term recognition backbone model operates on short, high-resolution clips. These extracted features are then used as input to the head network to process longer-range lower resolution features that capture key information from each clip. This is a crucial design consideration to lower the inference latency in RAFTformer while still capturing longer-range temporal dependencies compared to [19, 25]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 450, + 468, + 463 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 450, + 468, + 463 + ], + "spans": [ + { + "bbox": [ + 305, + 450, + 468, + 463 + ], + "type": "text", + "content": "3.3.RAFTformer Model Network" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 470, + 547, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 470, + 547, + 590 + ], + "spans": [ + { + "bbox": [ + 304, + 470, + 547, + 590 + ], + "type": "text", + "content": "We propose RAFTformer as a transformer encoder model. The transformer encoder has the advantage of being able to effectively learn across clip dependencies by attending over independently extracted clip features without facing memory bottlenecks such as faced in LSTM encoders [34] that have been used in some prior works [19,70]. However, to make the encoder effective for action forecasting on pre-trained features, we propose several changes to the training process to allow two-staged training to work as well as end-to-end training for action forecasting." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 597, + 426, + 610 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 597, + 426, + 610 + ], + "spans": [ + { + "bbox": [ + 305, + 597, + 426, + 610 + ], + "type": "text", + "content": "3.3.1 Anticipation Tokens" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 617, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 547, + 715 + ], + "type": "text", + "content": "The extracted clip embeddings " + }, + { + "bbox": [ + 304, + 617, + 547, + 715 + ], + "type": "inline_equation", + "content": "[C_0\\cdots C_{N-1}]" + }, + { + "bbox": [ + 304, + 617, + 547, + 715 + ], + "type": "text", + "content": " form the first part of the input to the action anticipation head. For the second part, we propose to train learnable 'anticipation tokens' that can aggregate global context and later can be decoded into future predictions. This design choice stands in contrast to prior works like [25] where the output of the anticipation token is implicitly designed to be in the same latent space as the output of their image-feature tokens. In" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18761" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 68, + 547, + 259 + ], + "blocks": [ + { + "bbox": [ + 48, + 68, + 547, + 259 + ], + "lines": [ + { + "bbox": [ + 48, + 68, + 547, + 259 + ], + "spans": [ + { + "bbox": [ + 48, + 68, + 547, + 259 + ], + "type": "image", + "image_path": "6eba557065fa750a29a0c8a2b969291b2572e354663fd503fcbb5e44e3efea74.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 265, + 547, + 332 + ], + "lines": [ + { + "bbox": [ + 46, + 265, + 547, + 332 + ], + "spans": [ + { + "bbox": [ + 46, + 265, + 547, + 332 + ], + "type": "text", + "content": "Figure 3. RAFTformer is a real-time action anticipation transformer architecture comprised of two stages. The first stage is a pretrained short-term backbone that produces individual clip embeddings independently of other clips (§3.2). In the second stage (§3.3), absolute position encodings are added and the resulting sequence is shuffled with a sampled permutation " + }, + { + "bbox": [ + 46, + 265, + 547, + 332 + ], + "type": "inline_equation", + "content": "\\pi^{*} \\sim \\pi" + }, + { + "bbox": [ + 46, + 265, + 547, + 332 + ], + "type": "text", + "content": ". The permutation encodings (§3.3.3) are then added to the shuffled sequence and after concatenation with anticipation tokens, the sequence is processed with the RAFTformer encoder. The output tokens are decoded via short & long-term action anticipation heads (§3.4), as well as the feature prediction head trained with self-supervised loss (" + }, + { + "bbox": [ + 46, + 265, + 547, + 332 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{SCM}}" + }, + { + "bbox": [ + 46, + 265, + 547, + 332 + ], + "type": "text", + "content": "), future feature prediction loss (" + }, + { + "bbox": [ + 46, + 265, + 547, + 332 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{future}}" + }, + { + "bbox": [ + 46, + 265, + 547, + 332 + ], + "type": "text", + "content": ") and action forecasting loss (" + }, + { + "bbox": [ + 46, + 265, + 547, + 332 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{focal}}" + }, + { + "bbox": [ + 46, + 265, + 547, + 332 + ], + "type": "text", + "content": ") (§3.5)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 352, + 287, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 352, + 287, + 411 + ], + "spans": [ + { + "bbox": [ + 46, + 352, + 287, + 411 + ], + "type": "text", + "content": "contrast to prior works, we find that temporal aggregation such as mean pooling for forecasting leads to subpar performance (see Table 5). Hence, we use the output tokens corresponding to " + }, + { + "bbox": [ + 46, + 352, + 287, + 411 + ], + "type": "inline_equation", + "content": "[C_0\\cdots C_N]" + }, + { + "bbox": [ + 46, + 352, + 287, + 411 + ], + "type": "text", + "content": " solely for self-supervised feature loss rather than action anticipation." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 412, + 288, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 412, + 288, + 533 + ], + "spans": [ + { + "bbox": [ + 46, + 412, + 288, + 533 + ], + "type": "text", + "content": "Instead, for action anticipation, we propose to train learnable 'anticipation tokens' to learn useful global context from the clip tokens. The output of the anticipation token is no longer restricted to be in the same latent space as the output of clip-feature tokens like in [25] and can better capture the information needed to anticipate the next action. Further, we propose to use multiple anticipation tokens to generate additional supervision, with each token attending to different past video lengths and producing forecasts for different time horizons in the future." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 538, + 286, + 551 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 538, + 286, + 551 + ], + "spans": [ + { + "bbox": [ + 47, + 538, + 286, + 551 + ], + "type": "text", + "content": "3.3.2 Self-Supervision via Shuffled Feature Prediction" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 557, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 557, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 557, + 287, + 677 + ], + "type": "text", + "content": "Prior works explored using the self-supervision task of predicting frame or clip features and using an MSE loss [25]. We propose using a generalized form of masking-based self-supervision [33] based on predicting shuffled future features. Predicting future clip features has a two-fold benefit: (A) It encourages causally learning the observed sequence incentivizing the model to grasp underlying scene dynamics and (B) Prediction in the latent feature space allows reasoning semantically about the future without wasting modeling capacity with low pixel level scene details." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 677, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 288, + 714 + ], + "type": "text", + "content": "Different from loss functions proposed in prior works [25], we propose an improved auto-regressive scheme for self-supervised learning by future feature pre" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 314, + 350, + 537, + 411 + ], + "blocks": [ + { + "bbox": [ + 314, + 350, + 537, + 411 + ], + "lines": [ + { + "bbox": [ + 314, + 350, + 537, + 411 + ], + "spans": [ + { + "bbox": [ + 314, + 350, + 537, + 411 + ], + "type": "table", + "html": "
Auto-regressive [1,2,3,4]Shuffle π1: [4,1,3,2]Another Shuffle π2: [3,4,2,1]
1 → 24 → 13 → 4
2 → 31 → 34 → 2
3 → 43 → 22 → 1
", + "image_path": "7f8a0e24e45395c32584a6047f26e89251412de493d86527456c87e4bada27cb.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 415, + 547, + 437 + ], + "lines": [ + { + "bbox": [ + 306, + 415, + 547, + 437 + ], + "spans": [ + { + "bbox": [ + 306, + 415, + 547, + 437 + ], + "type": "text", + "content": "Table 1. Encoding the input permutation " + }, + { + "bbox": [ + 306, + 415, + 547, + 437 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 306, + 415, + 547, + 437 + ], + "type": "text", + "content": ". Shuffling the input sequence arbitrarily changes the successor of each token." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 446, + 547, + 507 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 446, + 547, + 507 + ], + "spans": [ + { + "bbox": [ + 305, + 446, + 547, + 507 + ], + "type": "text", + "content": "diction. Rather than sequentially predicting missing clip features in order to use a causal attention mask, we propose to use a model-level augmentation of the attention masking scheme where some of the attention weights are not used from the original causal mask." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 534, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 547, + 713 + ], + "type": "text", + "content": "Random Masking. Construction of a sparse augmented attention mask is non-trivial. Simply generating a random mask such as in MAE [33] fails to isolate information within the intended partitioning due to multi-hop message passing caused by repeated application of the same mask. For example, in Figure 4, the attention mask prohibits token 1 to access token 2 and 3 (shown by 'white'). However, after two layers, token 1 in layer 2 can access information in token 2 in layer 0 (shown by red border), indirectly through token 4 in later 1 because of multi-hop message passing. This temporal information leakage can cause self-supervision to fail. For example, self-supervising token 1 with token 2 feature prediction would collapse in setup of Figure 4. To prevent this, we propose a simple yet effective solution." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "18762" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 300 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 300 + ], + "type": "text", + "content": "Shuffled Causal Masking. We know that vanilla causal masks ensure that information available to each token is invariant under repeated applications of the attention mask, i.e., multi-hop message passing. Since multi-hop message passing is token permutation invariant, any permutation of the tokens from the causal mask will preserve the invariance of accessible information under multiple hops. Thus, this allows a general framework for structured randomized mask construction without temporal leakage. We notice that a row-wise permutation of the attention mask is equivalent to the same permutation applied to the sequence itself. Hence, the same effect as properly constructed random masks can simply be achieved by shuffling the input token sequence itself. This allows generalizing vanilla autoregressive prediction order to arbitrary sequence permutations without any multi-hop information leakage through the layers. Thus, rather than predicting clip features sequentially from 0 to " + }, + { + "bbox": [ + 47, + 72, + 289, + 300 + ], + "type": "inline_equation", + "content": "N - 1" + }, + { + "bbox": [ + 47, + 72, + 289, + 300 + ], + "type": "text", + "content": " like [25], our proposed scheme allows for exponentially more variations." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 300, + 289, + 517 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 300, + 289, + 517 + ], + "spans": [ + { + "bbox": [ + 47, + 300, + 289, + 517 + ], + "type": "text", + "content": "Referring to Figure 3, we first add absolute position embeddings (APE) to each of the clip features before shuffling them. This allows the transformer to leverage the information about the actual temporal order of each clip in the video. Without the absolute position embeddings, the transformer is input permutation equivariant, which is not a desirable property for action forecasting. However, while APE is sufficient for positional information in vanilla autoregressive ordering, it is not enough for prediction under our proposed Shuffled Causal Masking (SCM) scheme. In autoregressive ordering, for any specific token, the next token in the sequence corresponds to a fixed position and hence the self-supervised training process can subtly learn this bias via next-token feature supervision. In contrast, under SCM the temporal position of the next token varies depending on the shuffling permutation. Hence, self-supervised training cannot learn to perform effective feature prediction without information about the shuffling permutation." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 524, + 214, + 537 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 524, + 214, + 537 + ], + "spans": [ + { + "bbox": [ + 47, + 524, + 214, + 537 + ], + "type": "text", + "content": "3.3.3 Permutation Position Encoding" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 544, + 287, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 544, + 287, + 688 + ], + "spans": [ + { + "bbox": [ + 47, + 544, + 287, + 688 + ], + "type": "text", + "content": "Naïve Encodings. For an " + }, + { + "bbox": [ + 47, + 544, + 287, + 688 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 47, + 544, + 287, + 688 + ], + "type": "text", + "content": " length sequence, there exist " + }, + { + "bbox": [ + 47, + 544, + 287, + 688 + ], + "type": "inline_equation", + "content": "L!" + }, + { + "bbox": [ + 47, + 544, + 287, + 688 + ], + "type": "text", + "content": " possible permutations. Encoding each permutation " + }, + { + "bbox": [ + 47, + 544, + 287, + 688 + ], + "type": "inline_equation", + "content": "(\\pi)" + }, + { + "bbox": [ + 47, + 544, + 287, + 688 + ], + "type": "text", + "content": " by itself is clearly intractable. First, we observe that encoding " + }, + { + "bbox": [ + 47, + 544, + 287, + 688 + ], + "type": "inline_equation", + "content": "\\pi^{*}" + }, + { + "bbox": [ + 47, + 544, + 287, + 688 + ], + "type": "text", + "content": " as a set of " + }, + { + "bbox": [ + 47, + 544, + 287, + 688 + ], + "type": "inline_equation", + "content": "O(L)" + }, + { + "bbox": [ + 47, + 544, + 287, + 688 + ], + "type": "text", + "content": " embeddings which are shared among different " + }, + { + "bbox": [ + 47, + 544, + 287, + 688 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 47, + 544, + 287, + 688 + ], + "type": "text", + "content": " is more efficient. A follow-up solution would be to instead encode each predecessor " + }, + { + "bbox": [ + 47, + 544, + 287, + 688 + ], + "type": "inline_equation", + "content": "\\mapsto" + }, + { + "bbox": [ + 47, + 544, + 287, + 688 + ], + "type": "text", + "content": " successor relationship as an encoding and have " + }, + { + "bbox": [ + 47, + 544, + 287, + 688 + ], + "type": "inline_equation", + "content": "L - 1" + }, + { + "bbox": [ + 47, + 544, + 287, + 688 + ], + "type": "text", + "content": " of such embeddings together encode " + }, + { + "bbox": [ + 47, + 544, + 287, + 688 + ], + "type": "inline_equation", + "content": "\\pi^{*}" + }, + { + "bbox": [ + 47, + 544, + 287, + 688 + ], + "type": "text", + "content": ". This reduces to the total number of required embeddings to " + }, + { + "bbox": [ + 47, + 544, + 287, + 688 + ], + "type": "inline_equation", + "content": "L(L - 1)" + }, + { + "bbox": [ + 47, + 544, + 287, + 688 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 47, + 544, + 287, + 688 + ], + "type": "inline_equation", + "content": "L!" + }, + { + "bbox": [ + 47, + 544, + 287, + 688 + ], + "type": "text", + "content": ". Each " + }, + { + "bbox": [ + 47, + 544, + 287, + 688 + ], + "type": "inline_equation", + "content": "\\pi^{*}" + }, + { + "bbox": [ + 47, + 544, + 287, + 688 + ], + "type": "text", + "content": " now shares every one of its " + }, + { + "bbox": [ + 47, + 544, + 287, + 688 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 47, + 544, + 287, + 688 + ], + "type": "text", + "content": " embeddings with other " + }, + { + "bbox": [ + 47, + 544, + 287, + 688 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 47, + 544, + 287, + 688 + ], + "type": "text", + "content": ", but considered as a set, the " + }, + { + "bbox": [ + 47, + 544, + 287, + 688 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 47, + 544, + 287, + 688 + ], + "type": "text", + "content": " embeddings uniquely encode " + }, + { + "bbox": [ + 47, + 544, + 287, + 688 + ], + "type": "inline_equation", + "content": "\\pi^{*}" + }, + { + "bbox": [ + 47, + 544, + 287, + 688 + ], + "type": "text", + "content": ". However, even " + }, + { + "bbox": [ + 47, + 544, + 287, + 688 + ], + "type": "inline_equation", + "content": "L^2" + }, + { + "bbox": [ + 47, + 544, + 287, + 688 + ], + "type": "text", + "content": " becomes intractable for large " + }, + { + "bbox": [ + 47, + 544, + 287, + 688 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 47, + 544, + 287, + 688 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": "Permutation Position Encodings " + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "(\\pi \\mathrm{PE})" + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": " provides an elegant solution for encoding " + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\pi^{*}" + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": " requiring only " + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": " total encod" + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 317, + 72, + 517, + 188 + ], + "blocks": [ + { + "bbox": [ + 317, + 72, + 517, + 188 + ], + "lines": [ + { + "bbox": [ + 317, + 72, + 517, + 188 + ], + "spans": [ + { + "bbox": [ + 317, + 72, + 517, + 188 + ], + "type": "image", + "image_path": "a789e94b775d299c15f0c0e1b6f1dc172688bd9ddbdc95e1b4d42a0ae9e6c8a9.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 191, + 547, + 258 + ], + "lines": [ + { + "bbox": [ + 304, + 191, + 547, + 258 + ], + "spans": [ + { + "bbox": [ + 304, + 191, + 547, + 258 + ], + "type": "text", + "content": "Figure 4. Random Masking Self-Supervision Illustration of how naive random masking (white denotes masked out) fails for self-supervised feature prediction task. We can see that in Layer 1 the tokens can only access information according to the provided mask. However, if the same mask is used in Layer 2, there is information leakage across tokens which is undesirable." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 273, + 547, + 406 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 273, + 547, + 406 + ], + "spans": [ + { + "bbox": [ + 304, + 273, + 547, + 406 + ], + "type": "text", + "content": "ings to be learned. " + }, + { + "bbox": [ + 304, + 273, + 547, + 406 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 304, + 273, + 547, + 406 + ], + "type": "text", + "content": "PE encodes the predecessor " + }, + { + "bbox": [ + 304, + 273, + 547, + 406 + ], + "type": "inline_equation", + "content": "\\mapsto" + }, + { + "bbox": [ + 304, + 273, + 547, + 406 + ], + "type": "text", + "content": " successor relationships but further simplifies by noting that adding the encoding to the token itself makes the predecessor information redundant. The token itself is the predecessor and has the positional information available from APE. Hence, we simply encode the successor positional information, and that in combination with APE uniquely encodes " + }, + { + "bbox": [ + 304, + 273, + 547, + 406 + ], + "type": "inline_equation", + "content": "\\pi^{*}" + }, + { + "bbox": [ + 304, + 273, + 547, + 406 + ], + "type": "text", + "content": ". Hence, we design " + }, + { + "bbox": [ + 304, + 273, + 547, + 406 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 304, + 273, + 547, + 406 + ], + "type": "text", + "content": "PE to be the encoding of the original temporal position of the successor in the permuted sequence. So for the " + }, + { + "bbox": [ + 304, + 273, + 547, + 406 + ], + "type": "inline_equation", + "content": "\\pi_{1}" + }, + { + "bbox": [ + 304, + 273, + 547, + 406 + ], + "type": "text", + "content": " permutation in Table 1, we would add " + }, + { + "bbox": [ + 304, + 273, + 547, + 406 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 304, + 273, + 547, + 406 + ], + "type": "text", + "content": "PE[1] to token 4, " + }, + { + "bbox": [ + 304, + 273, + 547, + 406 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 304, + 273, + 547, + 406 + ], + "type": "text", + "content": "PE[3] to token 1 and " + }, + { + "bbox": [ + 304, + 273, + 547, + 406 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 304, + 273, + 547, + 406 + ], + "type": "text", + "content": "PE[2] to token 3." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 418, + 421, + 430 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 418, + 421, + 430 + ], + "spans": [ + { + "bbox": [ + 306, + 418, + 421, + 430 + ], + "type": "text", + "content": "3.4. Overall Mechanism" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 440, + 547, + 632 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 440, + 547, + 632 + ], + "spans": [ + { + "bbox": [ + 304, + 440, + 547, + 632 + ], + "type": "text", + "content": "The past video is split into clips, and the clip embeddings " + }, + { + "bbox": [ + 304, + 440, + 547, + 632 + ], + "type": "inline_equation", + "content": "[C_0\\cdots C_{N-1}]" + }, + { + "bbox": [ + 304, + 440, + 547, + 632 + ], + "type": "text", + "content": " are extracted using a video backbone (Figure 3). Anticipation tokens are concatenated to the extracted sequence (" + }, + { + "bbox": [ + 304, + 440, + 547, + 632 + ], + "type": "inline_equation", + "content": "\\S 3.3.1" + }, + { + "bbox": [ + 304, + 440, + 547, + 632 + ], + "type": "text", + "content": "), followed by the addition of absolute position encoding to the concatenated sequence. Now, the clip embedding is shuffled according to a randomly chosen permutation " + }, + { + "bbox": [ + 304, + 440, + 547, + 632 + ], + "type": "inline_equation", + "content": "\\pi^*" + }, + { + "bbox": [ + 304, + 440, + 547, + 632 + ], + "type": "text", + "content": " to obtain " + }, + { + "bbox": [ + 304, + 440, + 547, + 632 + ], + "type": "inline_equation", + "content": "[C_{\\pi^*[0]}\\cdots C_{\\pi^*[N-1]}\\]" + }, + { + "bbox": [ + 304, + 440, + 547, + 632 + ], + "type": "text", + "content": ". The sampled permutation " + }, + { + "bbox": [ + 304, + 440, + 547, + 632 + ], + "type": "inline_equation", + "content": "\\pi^*" + }, + { + "bbox": [ + 304, + 440, + 547, + 632 + ], + "type": "text", + "content": " is then encoded by adding the successor's (" + }, + { + "bbox": [ + 304, + 440, + 547, + 632 + ], + "type": "inline_equation", + "content": "\\S 3.3.3" + }, + { + "bbox": [ + 304, + 440, + 547, + 632 + ], + "type": "text", + "content": ") embedding to each token. In Figure 3, " + }, + { + "bbox": [ + 304, + 440, + 547, + 632 + ], + "type": "inline_equation", + "content": "\\pi^*[1] = 3" + }, + { + "bbox": [ + 304, + 440, + 547, + 632 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 440, + 547, + 632 + ], + "type": "inline_equation", + "content": "\\pi^*[2] = N" + }, + { + "bbox": [ + 304, + 440, + 547, + 632 + ], + "type": "text", + "content": ", hence " + }, + { + "bbox": [ + 304, + 440, + 547, + 632 + ], + "type": "inline_equation", + "content": "\\pi \\mathrm{PE}[\\pi^*[1+1]]" + }, + { + "bbox": [ + 304, + 440, + 547, + 632 + ], + "type": "text", + "content": " is added to the token " + }, + { + "bbox": [ + 304, + 440, + 547, + 632 + ], + "type": "inline_equation", + "content": "\\pi^*[1]" + }, + { + "bbox": [ + 304, + 440, + 547, + 632 + ], + "type": "text", + "content": " i.e., " + }, + { + "bbox": [ + 304, + 440, + 547, + 632 + ], + "type": "inline_equation", + "content": "\\pi \\mathrm{PE}[N]" + }, + { + "bbox": [ + 304, + 440, + 547, + 632 + ], + "type": "text", + "content": " is added to " + }, + { + "bbox": [ + 304, + 440, + 547, + 632 + ], + "type": "inline_equation", + "content": "E_3" + }, + { + "bbox": [ + 304, + 440, + 547, + 632 + ], + "type": "text", + "content": ", which is used to self-supervise the feature at position 1 in the shuffled sequence, i.e., token 3 (" + }, + { + "bbox": [ + 304, + 440, + 547, + 632 + ], + "type": "inline_equation", + "content": "\\S 3.3.2" + }, + { + "bbox": [ + 304, + 440, + 547, + 632 + ], + "type": "text", + "content": "). The shuffled input sequence, in addition to the anticipation tokens, is now propagated through the transformer encoder using a causal attention masking scheme and the output is decoded with the head networks." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "content": "Head Networks We propose using three MLP heads on top of the transformer encoder network (Figure 3). Two MLP heads decode the anticipation tokens into the predicted future action distribution. The third MLP head up-samples the encoded tokens to the original representation space of the input tokens to allow self-supervision loss." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18763" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 73, + 70, + 519, + 337 + ], + "blocks": [ + { + "bbox": [ + 73, + 70, + 519, + 337 + ], + "lines": [ + { + "bbox": [ + 73, + 70, + 519, + 337 + ], + "spans": [ + { + "bbox": [ + 73, + 70, + 519, + 337 + ], + "type": "table", + "html": "
SplitMethodAddl. ModalityInitEpic BoxesTop-5 RecallParameters (×106)GPU HoursInference Latency (ms)
VerbNounAction
ValTempAgg [70]NoneIN1K24.229.813.0---
RULSTM [19]NoneIN1K--13.3---
RULSTM [19]Obj+FlowIN1K✓30.827.814.0---
TempAgg [70]Obj+Flow+ROIIN1K✓23.231.414.7---
AVT [25]NoneIN21K30.231.714.9378-420
AVT+ [25]ObjIN21K✓28.232.015.9---
TSN-AVT+ [25]ObjIN21K✓31.825.514.8---
MeMVit [80]NoneK40032.833.215.159-160
MeMVit [80]NoneK70032.237.017.7212368350
TestRAFTformerNoneK400 + IN1K33.335.517.6262340
RAFTformerNoneK70033.737.118.02627110
RAFTformer-2BNoneK700 + IN1K33.837.919.15250160
RULSTM [19]Obj+FlowIN1K✓25.326.711.2---
TBN [83]Obj+FlowIN1K✓21.526.811.0---
AVT+ [25]Obj+FlowIN21K✓25.628.812.6---
Abstract Goal [69]Obj+FlowIN1K✓31.430.114.3---
AFFT [85]Obj+Flow-✓20.731.814.9---
RAFTformerNoneK400 + IN1K27.332.814.0262340
RAFTformerNoneK70027.434.014.72627110
RAFTformer-2BNoneK700 + IN1K30.134.115.45250160
", + "image_path": "aa3b1d6a5b34def38caa9fc070785738f07682129d202c54d2f6993d48f90c13.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 339, + 547, + 363 + ], + "lines": [ + { + "bbox": [ + 46, + 339, + 547, + 363 + ], + "spans": [ + { + "bbox": [ + 46, + 339, + 547, + 363 + ], + "type": "text", + "content": "Table 2. Offline Evaluation Results on the EK-100 dataset for " + }, + { + "bbox": [ + 46, + 339, + 547, + 363 + ], + "type": "inline_equation", + "content": "t_f = 1" + }, + { + "bbox": [ + 46, + 339, + 547, + 363 + ], + "type": "text", + "content": " second horizon. Latency is measured over the entire model including the backbone & head networks on a single 16G Tesla V100 GPU. Methods that use other modalities (+RGB) are deemphasized." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 47, + 368, + 141, + 380 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 368, + 141, + 380 + ], + "spans": [ + { + "bbox": [ + 47, + 368, + 141, + 380 + ], + "type": "text", + "content": "3.5. Loss Functions" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 386, + 288, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 386, + 288, + 422 + ], + "spans": [ + { + "bbox": [ + 46, + 386, + 288, + 422 + ], + "type": "text", + "content": "We observe that the ground truth action distributions are often long-tailed, and propose to use the the focal loss [52], for supervising the future action prediction distributions." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 84, + 425, + 251, + 456 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 84, + 425, + 251, + 456 + ], + "spans": [ + { + "bbox": [ + 84, + 425, + 251, + 456 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {f o c a l}} = \\sum_ {A _ {i} \\in A} \\sum_ {i = 0} ^ {n} - (1 - p _ {A _ {i}}) ^ {\\gamma} \\log \\left(p _ {A _ {i}}\\right)", + "image_path": "11075b2f70fa889f80eaccbf3aa6d2392dbec5e533752c1ec2f92daa29069f73.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 461, + 287, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 461, + 287, + 521 + ], + "spans": [ + { + "bbox": [ + 46, + 461, + 287, + 521 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 461, + 287, + 521 + ], + "type": "inline_equation", + "content": "p_i" + }, + { + "bbox": [ + 46, + 461, + 287, + 521 + ], + "type": "text", + "content": " is the predicted probability for the correct class for the " + }, + { + "bbox": [ + 46, + 461, + 287, + 521 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 461, + 287, + 521 + ], + "type": "text", + "content": "th example, " + }, + { + "bbox": [ + 46, + 461, + 287, + 521 + ], + "type": "inline_equation", + "content": "A_i" + }, + { + "bbox": [ + 46, + 461, + 287, + 521 + ], + "type": "text", + "content": " represents predictions from a specific anticipation token and " + }, + { + "bbox": [ + 46, + 461, + 287, + 521 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 46, + 461, + 287, + 521 + ], + "type": "text", + "content": " is the focusing parameter where " + }, + { + "bbox": [ + 46, + 461, + 287, + 521 + ], + "type": "inline_equation", + "content": "\\gamma = 0" + }, + { + "bbox": [ + 46, + 461, + 287, + 521 + ], + "type": "text", + "content": " is cross entropy loss. Increasing " + }, + { + "bbox": [ + 46, + 461, + 287, + 521 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 46, + 461, + 287, + 521 + ], + "type": "text", + "content": " results in an increased penalty for hard, misclassified examples." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 521, + 287, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 287, + 568 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 287, + 568 + ], + "type": "text", + "content": "For self-supervision using shuffled causal masking to predict next-token embeddings, we use an expected " + }, + { + "bbox": [ + 46, + 521, + 287, + 568 + ], + "type": "inline_equation", + "content": "\\ell_2" + }, + { + "bbox": [ + 46, + 521, + 287, + 568 + ], + "type": "text", + "content": " loss over both past tokens, with the expectation being oversampled permutations " + }, + { + "bbox": [ + 46, + 521, + 287, + 568 + ], + "type": "inline_equation", + "content": "\\pi^{*} \\sim \\pi" + }, + { + "bbox": [ + 46, + 521, + 287, + 568 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 88, + 571, + 247, + 604 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 88, + 571, + 247, + 604 + ], + "spans": [ + { + "bbox": [ + 88, + 571, + 247, + 604 + ], + "type": "interline_equation", + "content": "\\mathcal{L}_{\\mathrm{SCM}} = \\underset {\\pi^{*}\\sim \\pi}{\\mathbb{E}}\\sum_{j = 0}^{N - 1}\\| E_{\\pi^{*}[j]} - \\hat{E}_{\\pi^{*}[j]}\\|_{2}^{2}", + "image_path": "2d6c3fb417dd1e5c1fb34fa8a7489574e1a89bb7d908132ee184b102098090fb.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 603, + 287, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 603, + 287, + 640 + ], + "spans": [ + { + "bbox": [ + 47, + 603, + 287, + 640 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 603, + 287, + 640 + ], + "type": "inline_equation", + "content": "E_{\\pi^{*}[j]}" + }, + { + "bbox": [ + 47, + 603, + 287, + 640 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 603, + 287, + 640 + ], + "type": "inline_equation", + "content": "\\hat{E}_{\\pi^{*}[j]}" + }, + { + "bbox": [ + 47, + 603, + 287, + 640 + ], + "type": "text", + "content": " denotes the original and the predicted clip embedding at position " + }, + { + "bbox": [ + 47, + 603, + 287, + 640 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 47, + 603, + 287, + 640 + ], + "type": "text", + "content": " after permuting with " + }, + { + "bbox": [ + 47, + 603, + 287, + 640 + ], + "type": "inline_equation", + "content": "\\pi^{*}" + }, + { + "bbox": [ + 47, + 603, + 287, + 640 + ], + "type": "text", + "content": ". For future token prediction, we use a simple " + }, + { + "bbox": [ + 47, + 603, + 287, + 640 + ], + "type": "inline_equation", + "content": "\\ell_2" + }, + { + "bbox": [ + 47, + 603, + 287, + 640 + ], + "type": "text", + "content": " loss:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 108, + 643, + 226, + 659 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 643, + 226, + 659 + ], + "spans": [ + { + "bbox": [ + 108, + 643, + 226, + 659 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {f u t u r e}} = \\left\\| E _ {\\mathrm {f u t u r e}} - \\hat {E} _ {\\mathrm {f u t u r e}} \\right\\| _ {2} ^ {2}", + "image_path": "1eb3a8f73e3770f59169892a62e2ec055172c07ee11636ce16f00b771555bf2c.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 663, + 288, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 663, + 288, + 689 + ], + "spans": [ + { + "bbox": [ + 47, + 663, + 288, + 689 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 663, + 288, + 689 + ], + "type": "inline_equation", + "content": "E_{\\mathrm{future}}" + }, + { + "bbox": [ + 47, + 663, + 288, + 689 + ], + "type": "text", + "content": " is the MViT embedding for the next clip (after " + }, + { + "bbox": [ + 47, + 663, + 288, + 689 + ], + "type": "inline_equation", + "content": "t_f" + }, + { + "bbox": [ + 47, + 663, + 288, + 689 + ], + "type": "text", + "content": "). Finally, the overall loss is simply a weighted sum," + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 99, + 693, + 236, + 707 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 99, + 693, + 236, + 707 + ], + "spans": [ + { + "bbox": [ + 99, + 693, + 236, + 707 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\mathcal {L} _ {\\text {f o c a l}} + \\lambda_ {1} \\mathcal {L} _ {\\text {S C M}} + \\lambda_ {2} \\mathcal {L} _ {\\text {f u t u r e}}", + "image_path": "7b2f8c6ad0e91dcff86d20aefa8703c9529a46b1f418654698eb2823d88d6565.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 367, + 388, + 380 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 367, + 388, + 380 + ], + "spans": [ + { + "bbox": [ + 305, + 367, + 388, + 380 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 385, + 545, + 470 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 385, + 545, + 470 + ], + "spans": [ + { + "bbox": [ + 304, + 385, + 545, + 470 + ], + "type": "text", + "content": "Datasets & Metrics. We use the widely benchmarked EPIC-KITCHENS dataset [9], an unscripted set with nearly " + }, + { + "bbox": [ + 304, + 385, + 545, + 470 + ], + "type": "inline_equation", + "content": "20 \\times" + }, + { + "bbox": [ + 304, + 385, + 545, + 470 + ], + "type": "text", + "content": " more action classes and " + }, + { + "bbox": [ + 304, + 385, + 545, + 470 + ], + "type": "inline_equation", + "content": "10 - 100 \\times" + }, + { + "bbox": [ + 304, + 385, + 545, + 470 + ], + "type": "text", + "content": " more observed sequences than other action datasets like 50 Salads [47] and Breakfast [46], used in prior work [19]. We use both the EPIC-55 & EPIC-100 anticipation splits and the EGTEA+ Gaze dataset [50]. Dataset details in supplementary." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 471, + 546, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 471, + 546, + 579 + ], + "spans": [ + { + "bbox": [ + 304, + 471, + 546, + 579 + ], + "type": "text", + "content": "Since human decision-making is inherently multimodal, we propose an approach to predict multiple reasonable future action forecasts. In addition to top-1 accuracy, we report top-5 recall following prior works [19, 25, 80]. We use the baseline data splits and report metrics on both the validation and test set. In addition, we report the number of trainable model parameters (M), the total compute spent for training the model to convergence on a Tesla V100 GPU (in hours), and the inference latency (in milliseconds)." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 589, + 416, + 601 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 589, + 416, + 601 + ], + "spans": [ + { + "bbox": [ + 305, + 589, + 416, + 601 + ], + "type": "text", + "content": "4.1. Evaluation Setting" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": "Offline evaluation is the setting where the model inference latency is ignored, or in other words, assumed to be zero. All prior works [19, 25, 80] consider this setting. Referring to Figure 1, prior works assume access to all past video frames up till the present moment " + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "inline_equation", + "content": "T = t" + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": ". Using this information, the model then predicts that action with a " + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "inline_equation", + "content": "t_f" + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": " second horizon at " + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "inline_equation", + "content": "T = t + t_f" + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": ". However, the prediction would actually be produced at time " + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "inline_equation", + "content": "T = t + t_l" + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "inline_equation", + "content": "t_l" + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": " is the model inference latency. This is not practically useful" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "18764" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 80, + 70, + 512, + 181 + ], + "blocks": [ + { + "bbox": [ + 80, + 70, + 512, + 181 + ], + "lines": [ + { + "bbox": [ + 80, + 70, + 512, + 181 + ], + "spans": [ + { + "bbox": [ + 80, + 70, + 512, + 181 + ], + "type": "table", + "html": "
ModelInitLatency (t1 ms)Inference Start Time StampInference End Time StampTarget Time StampTop-5 Recall
VerbNounAction
AVT [25]IN21Ktavt = 420TT + tavtT + 130.231.714.9
RAFTformerK400 + IN1ktours = 40T + tavt - toursT + tavtT + 134.138.219.3 (+4.4)
MemViT [80]K400tvit = 160TT + tvitT + 132.833.215.1
RAFTformerK400 + IN1ktours = 40T + tvit - toursT + tvitT + 133.837.118.1 (+3.0)
MemViT [80]K700tvit = 350TT + tvitT + 132.237.017.7
RAFTformerK400 + IN1ktours = 40T + tvit - toursT + tvitT + 133.737.919.0 (+1.3)
", + "image_path": "b4956e386c44e4aedd68caae19211c2059b0d68222d25a0b726dc8edd696cfe5.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 85, + 243, + 248, + 319 + ], + "blocks": [ + { + "bbox": [ + 46, + 183, + 545, + 240 + ], + "lines": [ + { + "bbox": [ + 46, + 183, + 545, + 240 + ], + "spans": [ + { + "bbox": [ + 46, + 183, + 545, + 240 + ], + "type": "text", + "content": "Table 3. Real-time Evaluation Results for benchmarking action forecasting methods in a practical setting (§4.1). Each comparison is performed between a pair of models where their start time ('Inference Start') times have been adjusted (Figure 1) by their latency so that they produce the forecasting output for the 'Target Time' simultaneously ('Inference End'). For prior works [25,80], start & end times are kept the same as their original offline settings (Table 2) to avoid any training recipe change. Faster models can pragmatically utilize recent frames while slower models must rely on higher fidelity prediction from older frames. Latency measured on a single 16G Tesla V100 GPU." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 85, + 243, + 248, + 319 + ], + "lines": [ + { + "bbox": [ + 85, + 243, + 248, + 319 + ], + "spans": [ + { + "bbox": [ + 85, + 243, + 248, + 319 + ], + "type": "table", + "html": "
ModelInitTop-1 Acc
RULSTM [19]TSN/IN1k13.1
ActionBanks [70]TSN/IN1k12.3
AVT-h [25]TSN/IN1k13.1
RAFTformerTSN/IN1k13.8
", + "image_path": "f0c4e3bf3d7fc9eb964df4b171ac71576e2ef021ca013d95e4376084a8c57512.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 347, + 287, + 431 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 347, + 287, + 431 + ], + "spans": [ + { + "bbox": [ + 46, + 347, + 287, + 431 + ], + "type": "text", + "content": "since often, we require time horizon " + }, + { + "bbox": [ + 46, + 347, + 287, + 431 + ], + "type": "inline_equation", + "content": "t_f" + }, + { + "bbox": [ + 46, + 347, + 287, + 431 + ], + "type": "text", + "content": " to meaningfully use the predicted future outcomes. Further, this does not account for absurdities where a large model might even have latency " + }, + { + "bbox": [ + 46, + 347, + 287, + 431 + ], + "type": "inline_equation", + "content": "t_l > t_f" + }, + { + "bbox": [ + 46, + 347, + 287, + 431 + ], + "type": "text", + "content": ", in which case the model is predicting an action that has already happened by the time it predicts it! A complex model can have great offline performance but its inference time would make it unusable in practice." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 437, + 287, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 437, + 287, + 653 + ], + "spans": [ + { + "bbox": [ + 46, + 437, + 287, + 653 + ], + "type": "text", + "content": "Real-time evaluation. To remedy this impractical situation, we consider the real-time evaluation setting. In this setting, the model is required to finish inference with at least " + }, + { + "bbox": [ + 46, + 437, + 287, + 653 + ], + "type": "inline_equation", + "content": "t_f" + }, + { + "bbox": [ + 46, + 437, + 287, + 653 + ], + "type": "text", + "content": " seconds horizon before the target time (Fig. 1). Hence, the model is allowed access to past video data only for " + }, + { + "bbox": [ + 46, + 437, + 287, + 653 + ], + "type": "inline_equation", + "content": "T < t - t_l" + }, + { + "bbox": [ + 46, + 437, + 287, + 653 + ], + "type": "text", + "content": ". This setting even allows for large models where " + }, + { + "bbox": [ + 46, + 437, + 287, + 653 + ], + "type": "inline_equation", + "content": "t_l > t_f" + }, + { + "bbox": [ + 46, + 437, + 287, + 653 + ], + "type": "text", + "content": " since predictions would still be produced with " + }, + { + "bbox": [ + 46, + 437, + 287, + 653 + ], + "type": "inline_equation", + "content": "t_f" + }, + { + "bbox": [ + 46, + 437, + 287, + 653 + ], + "type": "text", + "content": " seconds before the target time. Unlike other recognition scenarios where latency is a mere annoyance, in the case of future forecasting, models are often used in real-time rather than offline. The offline setting subtly oversteps the prediction horizon " + }, + { + "bbox": [ + 46, + 437, + 287, + 653 + ], + "type": "inline_equation", + "content": "t_f" + }, + { + "bbox": [ + 46, + 437, + 287, + 653 + ], + "type": "text", + "content": ", by receiving forecasts with a margin much less than the postulated " + }, + { + "bbox": [ + 46, + 437, + 287, + 653 + ], + "type": "inline_equation", + "content": "t_f" + }, + { + "bbox": [ + 46, + 437, + 287, + 653 + ], + "type": "text", + "content": " horizon. By coupling model latency to the past video data observed, the real-time setting incentivizes the development of efficient forecasting methods that utilize the recent data better than relying on slow large models that cannot miss the recent frames, which arguably are the most crucial for near future prediction." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 658, + 162, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 658, + 162, + 671 + ], + "spans": [ + { + "bbox": [ + 47, + 658, + 162, + 671 + ], + "type": "text", + "content": "4.2. EPIC-Kitchens-100" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": "Network Details. For feature extraction, we fix the pretrained 16x4 (K400+IN1K) and 32x3 (K700) MViT-B backbones [12, 49] trained for recognition on the EK100" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 320, + 244, + 531, + 323 + ], + "blocks": [ + { + "bbox": [ + 55, + 322, + 278, + 333 + ], + "lines": [ + { + "bbox": [ + 55, + 322, + 278, + 333 + ], + "spans": [ + { + "bbox": [ + 55, + 322, + 278, + 333 + ], + "type": "text", + "content": "Table 4. Offline Evaluation results on the Epic-Kitchens-55." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 320, + 244, + 531, + 323 + ], + "lines": [ + { + "bbox": [ + 320, + 244, + 531, + 323 + ], + "spans": [ + { + "bbox": [ + 320, + 244, + 531, + 323 + ], + "type": "table", + "html": "
ModelSettingTop-5 Recall
ATFLSCM2×AT
Mean pooling✓15.2
16.1 (+0.9)
RAFTformer✓✓16.8 (+0.7)
✓✓✓17.4 (+0.6)
✓✓✓✓17.6 (+0.2)
", + "image_path": "6afc0d6cedb05397ec81a7d6cedece9d7718e2b926c5a13192cdd29e1ea6272f.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 324, + 545, + 359 + ], + "lines": [ + { + "bbox": [ + 305, + 324, + 545, + 359 + ], + "spans": [ + { + "bbox": [ + 305, + 324, + 545, + 359 + ], + "type": "text", + "content": "Table 5. EK100 Ablation Study. FL is feature loss (no SCM), SCM is Shuffled Causal Masking (\\$3.3.2), AT " + }, + { + "bbox": [ + 305, + 324, + 545, + 359 + ], + "type": "inline_equation", + "content": "\\left( {2 \\times }\\right)" + }, + { + "bbox": [ + 305, + 324, + 545, + 359 + ], + "type": "text", + "content": " are single (double) anticipation tokens (§3.3.1)." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 382, + 545, + 526 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 382, + 545, + 526 + ], + "spans": [ + { + "bbox": [ + 304, + 382, + 545, + 526 + ], + "type": "text", + "content": "dataset. Each clip is embedded as a 768-dimensional feature vector. Unless mentioned otherwise, the action forecasting experiments use a " + }, + { + "bbox": [ + 304, + 382, + 545, + 526 + ], + "type": "inline_equation", + "content": "t_f = 1" + }, + { + "bbox": [ + 304, + 382, + 545, + 526 + ], + "type": "text", + "content": " second horizon. RAFTformer encoder is a lightweight 4 layer, 4 head transformer encoder using post-normalization and ReLU activations. A linear projection from up-projects " + }, + { + "bbox": [ + 304, + 382, + 545, + 526 + ], + "type": "inline_equation", + "content": "768 \\rightarrow 1024" + }, + { + "bbox": [ + 304, + 382, + 545, + 526 + ], + "type": "text", + "content": " for the transformer. We only shuffle during training with a probability of 0.3. The output of the encoder is down projected from " + }, + { + "bbox": [ + 304, + 382, + 545, + 526 + ], + "type": "inline_equation", + "content": "1024 \\rightarrow 768" + }, + { + "bbox": [ + 304, + 382, + 545, + 526 + ], + "type": "text", + "content": " channels. Both short-term and long-term action prediction heads are fast & lightweight MLPs " + }, + { + "bbox": [ + 304, + 382, + 545, + 526 + ], + "type": "inline_equation", + "content": "(1024 \\rightarrow 2048 \\rightarrow 3806)" + }, + { + "bbox": [ + 304, + 382, + 545, + 526 + ], + "type": "text", + "content": ". We set " + }, + { + "bbox": [ + 304, + 382, + 545, + 526 + ], + "type": "inline_equation", + "content": "\\lambda_1 = \\lambda_2 = 14" + }, + { + "bbox": [ + 304, + 382, + 545, + 526 + ], + "type": "text", + "content": ". For other details, please see supplementary." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 533, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 546, + 713 + ], + "type": "text", + "content": "Offline Evaluation. In Table 2 we first report RAFTformer results against prior works, including previous SOTA MeMViT [80]. Results that use additional modalities like Object (Obj), Flow (Flow), Object Region of Interest (ROI), or Epic Kitchen boxes are de-emphasized. Using only RGB, RAFTformer (K700) outperforms the AVT RGB model in action T5R by 3.1 points and the AVT RGB+Obj model by 2.1 points. RAFTformer slightly outperforms MeMViT action T5R while predicting actions " + }, + { + "bbox": [ + 304, + 533, + 546, + 713 + ], + "type": "inline_equation", + "content": "8.75 \\times" + }, + { + "bbox": [ + 304, + 533, + 546, + 713 + ], + "type": "text", + "content": " faster with " + }, + { + "bbox": [ + 304, + 533, + 546, + 713 + ], + "type": "inline_equation", + "content": "8.2 \\times" + }, + { + "bbox": [ + 304, + 533, + 546, + 713 + ], + "type": "text", + "content": " lesser trainable parameters and a " + }, + { + "bbox": [ + 304, + 533, + 546, + 713 + ], + "type": "inline_equation", + "content": "16 \\times" + }, + { + "bbox": [ + 304, + 533, + 546, + 713 + ], + "type": "text", + "content": " faster training. We also combine two separate RAFTformer models to train a two-backbone model (RAFTformer-2B) that achieves state-of-the-art by with a " + }, + { + "bbox": [ + 304, + 533, + 546, + 713 + ], + "type": "inline_equation", + "content": "1.4\\%" + }, + { + "bbox": [ + 304, + 533, + 546, + 713 + ], + "type": "text", + "content": " T5R increase. In the second section, we report our submitted results to the EK100 test server. We observe that RAFTformer general" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18765" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 61, + 70, + 272, + 172 + ], + "blocks": [ + { + "bbox": [ + 61, + 70, + 272, + 172 + ], + "lines": [ + { + "bbox": [ + 61, + 70, + 272, + 172 + ], + "spans": [ + { + "bbox": [ + 61, + 70, + 272, + 172 + ], + "type": "table", + "html": "
ModelInitModalityTop-5 Recall
DMR [75]-RGB38.1
ATSN [9]TSN/IN1kRGB+Flow31.6
MCE [18]TSN/IN1kRGB+Flow43.8
TCN [6]-RGB47.1
FN [10]VGG-16RGB42.7
ED [21]VGG-16/TSRGB+Flow54.6
RULSTM [19]TSN/IN1kRGB+Obj+Flow58.6
RAFTformerTSN/IN1kRGB63.5
", + "image_path": "2d88fa9b0e4d54c2d5fb5bd46025b7d1678d2a39d4dab4f79012bca5eee55107.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 47, + 175, + 287, + 198 + ], + "lines": [ + { + "bbox": [ + 47, + 175, + 287, + 198 + ], + "spans": [ + { + "bbox": [ + 47, + 175, + 287, + 198 + ], + "type": "text", + "content": "Table 6. EGTEA Gaze+. Under same initialization, RAFTformer outperforms prior methods without additional modalities." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 203, + 286, + 227 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 203, + 286, + 227 + ], + "spans": [ + { + "bbox": [ + 47, + 203, + 286, + 227 + ], + "type": "text", + "content": "izes well to the test set, improving upon the " + }, + { + "bbox": [ + 47, + 203, + 286, + 227 + ], + "type": "inline_equation", + "content": "\\mathrm{AVT + }" + }, + { + "bbox": [ + 47, + 203, + 286, + 227 + ], + "type": "text", + "content": " multimodal ensemble model [25] by 2.8 T5R points." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 233, + 162, + 245 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 233, + 162, + 245 + ], + "spans": [ + { + "bbox": [ + 47, + 233, + 162, + 245 + ], + "type": "text", + "content": "4.3. Additional Datasets" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 249, + 286, + 344 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 249, + 286, + 344 + ], + "spans": [ + { + "bbox": [ + 46, + 249, + 286, + 344 + ], + "type": "text", + "content": "EPIC-Kitchens 55. We also compare RAFTformer to prior baselines on the EK55 dataset in Table 4 on top-1 accuracy. We evaluate against other models using the same initialization for a fair comparison. We observe that RAFTformer outperforms prior benchmarks by about " + }, + { + "bbox": [ + 46, + 249, + 286, + 344 + ], + "type": "inline_equation", + "content": "0.7\\%" + }, + { + "bbox": [ + 46, + 249, + 286, + 344 + ], + "type": "text", + "content": " using the exact same backbone features. This shows the superiority of our proposed shuffle causal masking (§3.3.2) & anticipation token prediction (§3.3.1) in a controlled setting." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 346, + 286, + 417 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 346, + 286, + 417 + ], + "spans": [ + { + "bbox": [ + 46, + 346, + 286, + 417 + ], + "type": "text", + "content": "Real-time Evaluation. In table 3, we fix the target - start time difference to be what the prior models such as, AVT [25] or MeMViT [80] were designed for, to avoid any unintended change in their training recipes. Hence, we shift RAFTformer start time so that the output forecasts are produced simultaneously for the pair." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 418, + 286, + 573 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 418, + 286, + 573 + ], + "spans": [ + { + "bbox": [ + 46, + 418, + 286, + 573 + ], + "type": "text", + "content": "We observe that RAFTformer outperforms prior methods by an even larger margin in the real-time evaluation setting than the offline setting. RAFTformer effectively utilizes its compute to produce the maximum forecasting effect at the least latency cost. This allows RAFTformer to exploit more recent information that slower models miss because of higher inference latencies " + }, + { + "bbox": [ + 46, + 418, + 286, + 573 + ], + "type": "inline_equation", + "content": "(t_{\\mathrm{ours}} < \\{t_{\\mathrm{avt}}, t_{\\mathrm{vit}}\\})" + }, + { + "bbox": [ + 46, + 418, + 286, + 573 + ], + "type": "text", + "content": ". This also shows the disproportional effect of inference latency on forecasting performance. While RAFTFormer K400 + IN1K has a similar Top-5 Recall as MeMViT K700 in the offline setting, in the practical real-time evaluation (Table 3), RAFTformer outperforms MeMViT by " + }, + { + "bbox": [ + 46, + 418, + 286, + 573 + ], + "type": "inline_equation", + "content": "1.3\\%" + }, + { + "bbox": [ + 46, + 418, + 286, + 573 + ], + "type": "text", + "content": " by leveraging its faster inference latency (40 vs. 350 ms)." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 580, + 266, + 591 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 580, + 266, + 591 + ], + "spans": [ + { + "bbox": [ + 47, + 580, + 266, + 591 + ], + "type": "text", + "content": "4.3.1 Latency vs. Offline & Real-time Forecasting" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 594, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 286, + 712 + ], + "type": "text", + "content": "In offline evaluation, latency is ignored and all models have data access parity. As scaling laws [39] would predict, bigger models (with higher latency) have stronger forecasting performance (Blue curve in Fig. 2). In the real-time setting, a higher latency implies access to less recent data (Green curve in Fig. 2) and hence, an interesting trade-off materializes. At first, as latency (and model size) increases, the performance improves. This is because the benefit of having a more expressive model outweighs the cost of access to older video data. However, as the latency increases fur" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "text", + "content": "ther, the real-time performance starts decreasing. Now the harm of not having access to recent data outweighs the benefit of a more expressive model. For our setting, the optimal RAFTformer model has a latency of " + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "inline_equation", + "content": "40~\\mathrm{ms}" + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "text", + "content": " with an offline and real-time performance of 19.6 and 19.3 Top-5 recall respectively. A similar trade-off would exist for any combination of dataset, model, and deployment hardware regimes. Plots are for RAFTformer models of varying backbone parameter count for " + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "inline_equation", + "content": "t_f = 0.58" + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "text", + "content": " second prediction on EK100." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 186, + 381, + 196 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 186, + 381, + 196 + ], + "spans": [ + { + "bbox": [ + 306, + 186, + 381, + 196 + ], + "type": "text", + "content": "4.3.2 Ablations" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 202, + 545, + 370 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 202, + 545, + 370 + ], + "spans": [ + { + "bbox": [ + 304, + 202, + 545, + 370 + ], + "type": "text", + "content": "We ablate RAFTformer thoroughly in Table 5. In contrast to prior works [25,80] that pool information or use the same embedding for feature supervision and action prediction, we train explicit anticipation tokens (§3.3.1) to perform forecasting, improving T5R by 1.1. Anticipation tokens specialize in predicting the next action instead of using features that multi-task between reconstructing clip features and future action prediction [25]. Self-supervision via feature loss (FL) further improves by 0.7 T5R. Further, our SCM technique effectively regularizes FL that improves 0.6 T5R. Finally, an additional anticipation token " + }, + { + "bbox": [ + 304, + 202, + 545, + 370 + ], + "type": "inline_equation", + "content": "(2\\times \\mathrm{AT})" + }, + { + "bbox": [ + 304, + 202, + 545, + 370 + ], + "type": "text", + "content": " for supervision further improves 0.2 T5R. Additional longer-horizon anticipation task helps in learning transferable global video features to the main anticipation task." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 372, + 545, + 503 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 372, + 545, + 503 + ], + "spans": [ + { + "bbox": [ + 304, + 372, + 545, + 503 + ], + "type": "text", + "content": "EGTEA Gaze+. We also evaluate the EGTEA Gaze+ dataset in Table 6 to showcase RAFTformer performance on new settings outside of EPIC-Kitchens. Again, we use the setting of anticipating " + }, + { + "bbox": [ + 304, + 372, + 545, + 503 + ], + "type": "inline_equation", + "content": "1s" + }, + { + "bbox": [ + 304, + 372, + 545, + 503 + ], + "type": "text", + "content": " into the future and use the T5R metric. While prior methods use many input modalities including as object, flow, and RGB, we significantly outperform the prior state-of-the-art in this setting [19] by " + }, + { + "bbox": [ + 304, + 372, + 545, + 503 + ], + "type": "inline_equation", + "content": "4.9\\%" + }, + { + "bbox": [ + 304, + 372, + 545, + 503 + ], + "type": "text", + "content": ". Note that we use pre-extracted TSN RGB features as provided by [19] for direct comparison. Our very strong performance on another egocentric video dataset with complex human tasks further validates the promise of RAFTformer." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 507, + 378, + 519 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 507, + 378, + 519 + ], + "spans": [ + { + "bbox": [ + 306, + 507, + 378, + 519 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "type": "text", + "content": "We propose Real-Time Action Forecasting Transformer (RAFTformer), a parsimonious two-stage fully transformer-based architecture consisting of a short-range video transformer backbone for feature extraction and a long-range head transformer encoder for long-term temporal aggregation across multiple clips. We also introduce a real-time evaluation setting for action forecasting models that directly penalizes high latency and closely mimics the real-world deployment scenario for forecasting models. RAFTformer outperforms prior state-of-the-art methods by significant margins across several action forecasting benchmarks in the offline setting, and by an even larger margin of upto 4.4 T5R, in the real-time setting. RAFTformer achieves " + }, + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "type": "inline_equation", + "content": "9 \\times" + }, + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "type": "text", + "content": " lower inference latency at the same forecasting fidelity, using " + }, + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "type": "inline_equation", + "content": "16 \\times" + }, + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "type": "text", + "content": " less training compute and " + }, + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "type": "inline_equation", + "content": "10 \\times" + }, + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "type": "text", + "content": " lesser trainable parameters than prior baselines." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18766" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 92, + 287, + 713 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 53, + 92, + 287, + 125 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 92, + 287, + 125 + ], + "spans": [ + { + "bbox": [ + 53, + 92, + 287, + 125 + ], + "type": "text", + "content": "[1] Yazan Abu Farha, Alexander Richard, and Juergen Gall. 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In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 2349-2358, 2017. 2" + } + ] + } + ], + "index": 24 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "18769" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Latent-NeRF for Shape-Guided Generation of 3D Shapes and Textures/ca0b263a-3321-4fb3-b039-4fe859baac3c_content_list.json b/2023/Latent-NeRF for Shape-Guided Generation of 3D Shapes and Textures/ca0b263a-3321-4fb3-b039-4fe859baac3c_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..c182cf5fc3756c42692e40b22d2aae97c358dcd0 --- /dev/null +++ b/2023/Latent-NeRF for Shape-Guided Generation of 3D Shapes and Textures/ca0b263a-3321-4fb3-b039-4fe859baac3c_content_list.json @@ -0,0 +1,1975 @@ +[ + { + "type": "text", + "text": "Latent-NeRF for Shape-Guided Generation of 3D Shapes and Textures", + "text_level": 1, + "bbox": [ + 127, + 117, + 841, + 138 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Gal Metzer*", + "bbox": [ + 112, + 166, + 212, + 185 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Elad Richardson*", + "bbox": [ + 253, + 167, + 393, + 185 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Or Patashnik", + "bbox": [ + 434, + 167, + 539, + 185 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Raja Giryes", + "bbox": [ + 578, + 167, + 676, + 186 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Daniel Cohen-Or", + "bbox": [ + 715, + 167, + 856, + 185 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Tel Aviv University", + "text_level": 1, + "bbox": [ + 403, + 203, + 560, + 222 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/90a850f90a046c3205d0bee42578a9d25696c183b516fecfaa89c2095941c7fa.jpg", + "image_caption": [ + "\"A stack of pancakes covered in maple syrup\"", + "Latent-NeRF", + "Figure 1. Our three text-guided models: a purely text-guided Latent-NeRF, Latent-NeRF with Sketch-Shape guidance for more exact control over the generated shape, and Latent-Paint for texture generation for explicit shapes. The top row represents the models' inputs." + ], + "image_footnote": [], + "bbox": [ + 101, + 292, + 222, + 386 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/4ee5ec5387257e297b6608988bd34911e265cbc8efcc3930949cbf1433af89b4.jpg", + "image_caption": [ + "\"A highly detailed sandcastle\"" + ], + "image_footnote": [], + "bbox": [ + 225, + 292, + 344, + 385 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/f201577e4e8eb335b3a878330e2c02e940b18c640083202ecd293e4eb6661442.jpg", + "image_caption": [ + "\"A German Shepherd\"" + ], + "image_footnote": [], + "bbox": [ + 364, + 252, + 467, + 376 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/e86384fee109f93aadc20626162dcb8830cdc3b547b87e2618c0edc2c9288f0a.jpg", + "image_caption": [ + "Sketch-Shape" + ], + "image_footnote": [], + "bbox": [ + 460, + 292, + 581, + 386 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/8b8403b65ae0fa691d2ec5a296751e835367ed85790ab10ee4e41e07306c66a6.jpg", + "image_caption": [ + "\"A fish with leopard spots\"" + ], + "image_footnote": [], + "bbox": [ + 602, + 250, + 730, + 376 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/87f5dd570c242d767f9c2da81c6d4e9d8b4a9005fcd7e0a5fd6567f5302fdc2f.jpg", + "image_caption": [ + "Latent-Paint" + ], + "image_footnote": [], + "bbox": [ + 733, + 295, + 854, + 385 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 465, + 312, + 479 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Text-guided image generation has progressed rapidly in recent years, inspiring major breakthroughs in text-guided shape generation. Recently, it has been shown that using score distillation, one can successfully text-guide a NeRF model to generate a 3D object. We adapt the score distillation to the publicly available, and computationally efficient, Latent Diffusion Models, which apply the entire diffusion process in a compact latent space of a pretrained autoencoder. As NeRFs operate in image space, a naive solution for guiding them with latent score distillation would require encoding to the latent space at each guidance step. Instead, we propose to bring the NeRF to the latent space, resulting in a Latent-NeRF. Analyzing our Latent-NeRF, we show that while Text-to-3D models can generate impressive results, they are inherently unconstrained and may lack the ability to guide or enforce a specific 3D structure. To assist and direct the 3D generation, we propose to guide our Latent-NeRF using a Sketch-Shape: an abstract geometry that defines the coarse structure of the desired object. Then, we present means to integrate such a constraint directly into a Latent-NeRF. This unique combination of text and shape guidance allows for increased control over the generation process. We also show that latent score distillation can be successfully applied directly on 3D meshes. This allows for generating high-quality textures on a given geometry. Our experiments validate the power of our different forms of guidance and the efficiency of using latent rendering.", + "bbox": [ + 73, + 502, + 472, + 910 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 501, + 465, + 630, + 479 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Text-guided image generation has seen tremendous success in recent years, primarily due to the breathtaking development in Language-Image models [25, 28, 36] and diffusion models [14, 21, 37-40]. These breakthroughs have also resulted in fast progression for text-guided shape generation [9, 29, 53]. Most recently, it has been shown [35] that one can directly use score distillation from a 2D diffusion model to guide the generation of a 3D object represented as a Neural Radiance Field (NeRF) [30].", + "bbox": [ + 496, + 491, + 890, + 627 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "While Text-to-3D can generate impressive results, it is inherently unconstrained and may lack the ability to guide or enforce a 3D structure. In this paper, we show how to introduce shape-guidance to the generation process to guide it toward a specific shape, thus allowing increased control over the generation process. Our method builds upon two models, a NeRF model [30], and a Latent Diffusion Model (LDM) [39]. Latent Models, which apply the entire diffusion process in a compact latent space, have recently gained popularity due to their efficiency and publicly available pretrained checkpoints. As score distillation was previously applied only on RGB diffusion models, we first present two key modifications to the NeRF model that are better paired with guidance from a latent model. First, instead of representing our NeRF in the standard RGB space, we propose a Latent-NeRF which operates directly in the latent space of the LDM, thus avoiding the burden of encoding a rendered RGB image to a latent space for each and every guid", + "bbox": [ + 496, + 628, + 892, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "12663", + "bbox": [ + 480, + 949, + 517, + 960 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ing step. Secondly, we show that after training, one can easily transform a Latent-NeRF back into a regular NeRF. This allows further refinement in RGB space, where we can also introduce shading constraints or apply further guidance from RGB diffusion models [40]. This is achieved by introducing a learnable linear layer that can be optionally added to a trained Latent-NeRF, where the linear layer is initialized using an approximate mapping between the latent and RGB values [45].", + "bbox": [ + 75, + 90, + 472, + 227 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our first form of shape-guidance is applied using a coarse 3D model, which we call a Sketch-Shape. Given a Sketch-Shape, we apply soft constraint during the NeRF optimization process to guide its occupancy based on the given shape. Easily combined with Latent-NeRF optimization, the additional constraint can be tuned to meet a desired level of strictness. Using a Sketch-Shape allows users to define their base geometry, where Latent-NeRF then refines the shape and introduces texture based on a guiding prompt.", + "bbox": [ + 75, + 227, + 472, + 364 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We further present Latent-Paint, another form of shape-guidance where the generation process is applied directly on a given 3D mesh, and we have not only the structure but also the exact parameterization of the input mesh. This is achieved by representing a texture map in the latent space and propagating the guidance gradients directly to the texture map through the rendered mesh. By doing so, we allow for the first time to colorize a mesh using guidance from a pretrained diffusion model and enjoy its expressiveness.", + "bbox": [ + 75, + 364, + 472, + 500 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We evaluate our different forms of guidance under a variety of scenarios and show that together with our latent-based guidance, they offer a compelling solution for constrained shape and texture generation.", + "bbox": [ + 75, + 500, + 472, + 560 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 573, + 218, + 588 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3D Shape Generation 3D shape synthesis is a longstanding problem in computer graphics and computer vision. In recent years, with the emergence of neural networks, the research in 3D modeling has immensely advanced. The most conventional supervision type is applied directly with 3D shapes, through different representations such as implicit functions [10, 20, 33], meshes [19, 50] or point clouds [27, 49]. As 3D supervision is often difficult to obtain, other works use images to guide the generative task [6, 7, 32]. In fact, even when 3D data is available, 2D renderings are sometimes chosen as the supervising primitive [5, 8, 18]. For example, in GET3D [18], two generators are trained, one generates a 3D SDF, and the other a texture field. The output textured mesh is then obtained in a differentiable manner by utilizing DMTet [42]. These generators are adversarially trained with a dataset of 2D images. In [47] a diffusion model has been used to generate multiple views of a given input image. Yet, it has been trained in a supervised manner on a multi-view dataset, unlike our work which does not require a dataset.", + "bbox": [ + 75, + 598, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Text-to-3D with 2D Supervision. Recently, the success of text-guided synthesis in numerous domains [1,2,17,34, 44], has motivated a surge of works that use Language-Image models to guide 3D scenes representations. CLIP-Forge [41] consists of two separate components, an implicit autoencoder conditioned on shape codes, and a normalizing flow model that is trained to generate shape codes according to CLIP embeddings. CLIP-Forge exploits the fact that CLIP has a joint text-image embedding space to train on image embeddings and infer on text embeddings, achieving text-to-shape capabilities. Text2Mesh [29] introduced mesh colorization and geometric fine-tuning by optimizing an initial mesh through differential rendering and CLIP [36] guidance. TANGO [9] follows a similar optimization scheme, while improving results by considering an explicit shading model. CLIP-Mesh [26] optimizes an initial spherical mesh according to a target text prompt, using a modified CLIP loss that accounts for the gap and ambiguity between image/text CLIP embeddings. Similarly to our method, they also use UV texture mapping to bake colors into the mesh. DreamFields [24] employs CLIP guidance as well, but uses NeRFs to represent the 3D object instead of an explicit triangular mesh, together with a dedicated sparsity loss. CLIPNeRF [46] pretrains a disentangled NeRF representation network on rendered object datasets, which is then used to constraint a NeRF scene optimization under CLIP loss, between random renderings of the NeRF and target image or text CLIP embedding. DreamFusion [35] introduced, for the first time, the use of largely successful pretrained 2D diffusion models for text-guided 3D object generation. DreamFusion uses a proprietary 2D diffusion model [40] to supervise the generation of 3D objects represented by NeRFs. To guide a NeRF scene using the pretrained diffusion model, the authors derive a Score-Distillation loss, see Section 3.1 for more details.", + "bbox": [ + 496, + 90, + 893, + 621 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Neural Rendering The recent rapid progression of neural networks has immensely advanced the performance of differential renderers. Particularly NeRF [4, 30, 31] have shown astounding performance on novel view generation and relighting, also extending to other applications like 3D reconstruction [51]. Thanks to their differentiable nature, it has been recently shown that one can introduce different neural objectives during training to guide the 3D modeling.", + "bbox": [ + 496, + 637, + 893, + 758 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 500, + 768, + 591, + 784 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Here we present our shape-guidance solution. We describe the Latent-NeRF framework, presented in Figure 2, and then introduce different guidance controls that can be combined with Latent-NeRF for controlling its generation. Yet, before showing our solution, we provide a quick overview of two recently proposed techniques that are highly relevant to our method.", + "bbox": [ + 496, + 795, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "12664", + "bbox": [ + 480, + 949, + 519, + 960 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3.1. Preliminaries", + "text_level": 1, + "bbox": [ + 76, + 90, + 217, + 104 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "A latent diffusion model (LDM) [39] is a specific form of a diffusion model that is trained to denoise latent codes of a pretrained autoencoder, instead of the high-resolution images directly. First, an autoencoder composed of an encoder $\\mathcal{E}$ , and a decoder $\\mathcal{D}$ is trained to reconstruct natural images $x \\sim X$ , where $X$ is the image training dataset, in the following form: $\\tilde{x} = \\mathcal{D}(\\mathcal{E}(x))$ . The autoencoder is trained with a reconstruction loss, perceptual loss [54] and a patch-based adversarial loss [22]. Then, given the trained autoencoder, a denoising diffusion probabilistic model (DDPM) [21] is trained to generate a spatial latent $z$ from noise, according to the distribution $z = \\mathcal{E}(x)$ s.t. $x \\sim X$ . In order to generate a novel image, a latent $\\tilde{z}$ is sampled from this learned distribution, using the trained DDPM, and passed to the decoder to obtain the final image $\\mathcal{D}(\\tilde{z})$ . Operating in the latent space requires less compute, and leads to faster training and sampling, which makes LDM widely popular. In fact, the recent Stable Diffusion model is also an LDM.", + "bbox": [ + 75, + 112, + 472, + 398 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Score Distillation is a method that enables using a diffusion model as a critic, i.e., using it as a loss without explicitly back-propagating through the diffusion process. It has been introduced in DreamFusion [35] for guiding 3D generation using the Imagen model [40]. To perform score distillation, noise is first added to a given image (e.g., one view of the NeRF's output). Then, the diffusion model is used to predict the added noise from the noised image. Finally, the difference between the predicted and added noises is used for calculating per-pixel gradients. For NeRF, the gradients are back-propagated for updating the 3D NeRF model.", + "bbox": [ + 75, + 400, + 472, + 566 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Going into more detail, at each iteration of the score distillation optimization, a rendered image $x$ is noised to a randomly drawn time step $t$ ,", + "bbox": [ + 75, + 566, + 470, + 612 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nx _ {t} = \\sqrt {\\bar {\\alpha} _ {t}} x + \\sqrt {1 - \\bar {\\alpha} _ {t}} \\epsilon , \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 186, + 618, + 468, + 638 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\epsilon \\sim \\mathcal{N}(0,I)$ , and $\\bar{\\alpha}_t$ is a time-dependent constant specified by the diffusion model. Then, the per-pixel score distillation gradients are taken to be", + "bbox": [ + 75, + 642, + 468, + 688 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\nabla_ {x} L _ {S D S} = w (t) \\left(\\epsilon_ {\\phi} \\left(x _ {t}, t, T\\right) - \\epsilon\\right), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 153, + 696, + 468, + 714 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\epsilon_{\\phi}$ is the diffusion model's denoiser (which approximates the noise to be removed), $\\phi$ are the denoiser's parameters, $T$ is an optional guiding text prompt, and $w(t)$ is a constant multiplier that depends on $\\alpha_{t}$ . During training, gradients are propagated from the pixel gradients to the NeRF parameters and gradually change the 3D object. Please refer to [35] for the complete details and derivation of Score Distillation. Note that DreamFusion uses the proprietary Imagen [40] model that is very computationally demanding. We rely on the publicly available Stable Diffusion model and the re-implementation of DreamFusion [43] (it operates in the RGB space and not the latent as we propose).", + "bbox": [ + 75, + 719, + 472, + 901 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/5a25ffcac610385e6ecd95b08abd3d952c559ca9cddad6c023e5e358d2fdfecc.jpg", + "image_caption": [ + "Figure 2. An overview of Latent-NeRF trained with a similar score distillation scheme as proposed by [35]. At each training iteration we render the scene from a random view point to produce a feature map $z$ . Then, $z$ is noised with $\\epsilon$ according to a random diffusion step $t$ . The noised version of $z$ , i.e., $x_{t}$ , is denoised using Stable Diffusion [39], with the input text prompt. Finally, the input noise is subtracted from the predicted noise by Stable Diffusion, to approximate per-pixel gradients that are back propagated to the NeRF representation." + ], + "image_footnote": [], + "bbox": [ + 521, + 87, + 874, + 253 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Latent-NeRF", + "text_level": 1, + "bbox": [ + 500, + 416, + 638, + 430 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We now turn to describe our Latent-NeRF approach. In this method, a NeRF model is optimized to render 2D feature maps in Stable Diffusion's latent space $\\mathcal{Z}$ . Latent-NeRF outputs four pseudo-color channels, $(c_{1}, c_{2}, c_{3}, c_{4})$ , corresponding to the four latent features that stable diffusion operates over, and a volume density $\\sigma$ . Figure 2 illustrates this process. Representing the scene using NeRF implicitly imposes spatial consistency between different views, due to the spatial radiance field and rendering equation. Still, the fact that $\\mathcal{Z}$ can be represented by a NeRF with spatial consistencies is non-trivial. Previous works [1, 45] showed that super-pixels in $\\mathcal{Z}$ depend mainly on individual patches in the output image. This can be attributed to the high resolution $(64 \\times 64)$ and low channel-wise depth (4) of this latent space, which encourages local dependency over the autoencoder's image and latent spaces. Assuming $\\mathcal{Z}$ is a near patch level representation of its corresponding RGB image makes the latents nearly equivariant to spatial transformations of the scene, which justifies the use of NeRFs for representing the 3D scenes.", + "bbox": [ + 496, + 439, + 893, + 743 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Text Guidance The vanilla form of Latent-NeRF is text-guided, with no other constraints for the scene generation. In this setting, we employ the following loss:", + "bbox": [ + 496, + 765, + 893, + 811 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nL = \\lambda_ {S D S} L _ {S D S} + \\lambda_ {s p a r s e} L _ {s p a r s e},\n$$\n", + "text_format": "latex", + "bbox": [ + 573, + 825, + 816, + 842 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $L_{SDS}$ is the Score-Distillation loss depicted in Figure 2. Note, that the exact value of this loss is not accessible. Instead, the gradients implied by it are approximated", + "bbox": [ + 496, + 854, + 893, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "12665", + "bbox": [ + 480, + 949, + 517, + 960 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/4caa0b131ba1db558e4050511f712acacae2d68250365d90fc7c433c52226a9d.jpg", + "image_caption": [ + "Figure 3. To perform fine-tuning in RGB, we take a Latent-NeRF model that was trained in latent space (conventional setting), apply the matrix adapter to the channel output of the model to get an RGB preview, and then continue optimizing the MLP's weights through supervision in RGB to improve the result." + ], + "image_footnote": [], + "bbox": [ + 78, + 87, + 467, + 205 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "by a single forward pass through the denoiser. These gradients are directly passed to the autograd solver. The loss $L_{sparse} = BE(w_{blend})$ suggested in [43] prevents floating \"radiance clouds\" by penalizing the binary entropy of ill-defined background masks $w_{blend}$ . Namely, it encourages a strict blending of the object NeRF and background NeRF.", + "bbox": [ + 75, + 319, + 468, + 411 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "RGB Refinement Using Latent-NeRF, one may successfully learn to represent 3D scenes even when optimizing solely in latent space. Still, in some cases, it could be beneficial to further refine the model by fine-tuning it in pixel space, and have the NeRF model operate directly in RGB. To do so, we must convert the NeRF that was trained in latent space to a NeRF that operates in RGB. This requires converting the MLP's output from the four latent channels to three RGB channels such that the initial rendered RGB image is close to the decoder output, when applied to the rendered latent of the original model. Interestingly, it has been shown [45] that a linear approximation is sufficient to predict plausible RGB colors given a single four-channel latent super pixel, via the following transformation", + "bbox": [ + 75, + 445, + 468, + 657 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left( \\begin{array}{c} \\hat {r} \\\\ \\hat {g} \\\\ \\hat {b} \\end{array} \\right) = \\left( \\begin{array}{c c c c} 0. 2 9 8 & 0. 1 8 7 & - 0. 1 5 8 & - 0. 1 8 4 \\\\ 0. 2 0 7 & 0. 2 8 6 & 0. 1 8 9 & - 0. 2 7 1 \\\\ 0. 2 0 8 & 0. 1 7 3 & 0. 2 6 4 & - 0. 4 7 3 \\end{array} \\right) \\left( \\begin{array}{c} c _ {1} \\\\ c _ {2} \\\\ c _ {3} \\\\ c _ {4} \\end{array} \\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 91, + 672, + 467, + 748 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "which was calculated using pairs of RGB images and their corresponding latent codes over a collection of natural images. As our NeRF model is already composed of a set of fully connected layers, we simply add another linear layer that is initialized using the weights in Equation 3. This converts our Latent-NeRF to operate in pixel space and ensures that our refinement process starts from a valid result. The additional layer is then fine-tuned together with the rest of the model, to create the refined and final output. The overall fine-tuning procedure is illustrated in Figure 3.", + "bbox": [ + 75, + 750, + 470, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Sketch-Shape Guidance", + "text_level": 1, + "bbox": [ + 500, + 90, + 718, + 107 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Next, we introduce a novel technique for guiding the Latent-NeRF generation based on a coarse geometry, which we call a Sketch-Shape.", + "bbox": [ + 498, + 113, + 890, + 157 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "A Sketch-Shape is an abstract coarse alignment of simple 3D primitives like spheres, boxes, cylinders, etc., that together depict an outline of a more complex object. Figures 9, 10, 11 illustrate such simple shapes. Ideally, we would like the output density of our MLP to match that of the Sketch-Shape, such that the output Latent-NeRF result resembles the input shape. Nevertheless, we would also like the new NeRF to have the capacity to create new details and geometries that match the input text prompt and improve the fidelity of the shape. To achieve this lenient constraint, we encourage the NeRF's occupancy to match the winding-number [3, 23] indicator of the Sketch-Shape, but with decaying importance near the surface to allow new geometries. This loss reads as", + "bbox": [ + 496, + 159, + 892, + 369 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\text {S k e t c h - S h a p e}} = C E \\left(\\alpha_ {N e R F} (p), \\alpha_ {G T} (p)\\right) \\cdot \\left(1 - e ^ {- \\frac {d ^ {2}}{2 \\sigma_ {S}}}\\right). \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 371, + 890, + 407 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "This loss implies that the occupancy should be well constrained away from the surface, and free to be set by score distillation near the surface. This loss is applied in addition to the Latent-NeRF loss, over the entire point set $p$ that is used by the NeRF's volumetric rendering. $d$ represents the distance of $p$ from the surface, and $\\sigma_{S}$ is a hyperparameter that controls how lenient the loss is, i.e., lower $\\sigma_{S}$ values imply a tighter constraint to the input Sketch-Shape. Applying the loss only on the sampled point-set $p$ , makes it more efficient as these points are already evaluated as part", + "bbox": [ + 496, + 407, + 892, + 559 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/2533b47fcca42c5ffb10524cd128da90b16a97d859bb15063f6e6f592c75fb6f.jpg", + "image_caption": [ + "Figure 4. An overview of Latent-Paint texture generation, trained with a similar score distillation loss [35]. The object is represented as a textured mesh, with a latent texture image that has four pseudo-color channels. At each iteration, the mesh is rendered with a differential renderer, to create a feature map from a random viewpoint. Score distillation is applied to the rendered feature map, and the gradients back-propagate to the latent texture image through the differential renderer. See Section 3.4." + ], + "image_footnote": [], + "bbox": [ + 516, + 566, + 875, + 773 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "12666", + "bbox": [ + 480, + 949, + 517, + 960 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "of the Latent-NeRF rendering process.", + "bbox": [ + 76, + 90, + 334, + 104 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Latent-Paint of Explicit Shapes", + "text_level": 1, + "bbox": [ + 76, + 116, + 354, + 132 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We now move to a more strict constraint, where the guidance is based on an exact structure of a given shape, e.g., provided in the form of a mesh. We call this approach Latent-Paint, which leads to the generation of novel textures for a given shape. Our method generates texture over a UV texture map, which can either be supplied by the input mesh, or calculated on-the-fly using XAtlas [52]. To color a mesh, we first initialize a random latent texture image of size $H \\times W \\times 4$ , where $H$ and $W$ can be chosen according to the desired texture granularity. We set them both to be 128 in our experiments.", + "bbox": [ + 75, + 138, + 470, + 305 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Figure 4 presents the training process. At each score distillation iteration, we render the mesh with a differentiable renderer [15] to obtain a $64 \\times 64 \\times 4$ feature map that is pseudo-colored by the latent texture image. Then, we apply the score distillation loss from Equation 2 in the same way it is applied for Latent-NeRF. Yet, instead of backpropagating the loss to the NeRF's MLP parameters, we optimize the deep texture image by back-propagating through the differentiable renderer. To get the final RGB texture image, we simply pass the latent texture image through Stable Diffusion's decoder $\\mathcal{D}$ once, to get a larger high-quality RGB texture.", + "bbox": [ + 75, + 306, + 470, + 486 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Evaluation", + "text_level": 1, + "bbox": [ + 76, + 501, + 192, + 516 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We now validate the effectiveness of our different forms of guidance through a variety of experiments.", + "bbox": [ + 76, + 526, + 468, + 556 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implementation Details We use the Stable Diffusion implementation by HuggingFace Diffusers, with the v1-4 checkpoint. For score distillation, we use the code-base provided by [43], with Instant-NGP [31] as our NeRF model.", + "bbox": [ + 75, + 575, + 468, + 638 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/38623be138dfd9d1197e05290df3d245cf020711eeb64585d68f45c7ea30251d.jpg", + "image_caption": [ + "Figure 5. Latent-NeRF results from different viewpoints." + ], + "image_footnote": [], + "bbox": [ + 84, + 657, + 464, + 868 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/e9b384a95deee28996d433a0a3aa5666551af66cb8203e1a709087698fe1a883.jpg", + "image_caption": [ + "Figure 6. Qualitative comparison with other text-to-3D methods." + ], + "image_footnote": [], + "bbox": [ + 509, + 93, + 879, + 521 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Latent-NeRF usually takes less than 15 minutes to converge on a single V100, while using an RGB-NeRF with Stable Diffusion [43] takes about 30 minutes, due to the increased overhead from encoding into the latent space. Note that DreamFusion [35] takes about 1.5 hours on 4 TPUs. This clearly shows the computational advantage of Latent-NeRF.", + "bbox": [ + 496, + 577, + 890, + 667 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Text-Guided Generation", + "text_level": 1, + "bbox": [ + 500, + 679, + 723, + 694 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Qualitative Results We begin by demonstrating the effectiveness of the latent rendering approach with Latent-NeRF. In Figs. 1, 5 and 7, we show several results obtained by our method. In the supplementary material we provide additional results of different objects, including video visualizations. In Figure 5, we show the consistency of our learned shapes from several viewpoints. Next, we use the baseline set by DreamFusion [35] to qualitatively compare our approach (with the proposed RGB refinement) against other methods. As can be seen in Figure 6, Latent-NeRF achieves significantly better results than DreamFields [24] and CLIPMesh [26]. We believe that the better quality of DreamFusion can be attributed to the high quality of Ima", + "bbox": [ + 496, + 703, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "12667", + "bbox": [ + 480, + 949, + 517, + 960 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/13eaf8616d0a3ab9a3d8ca93641c943c80b2c7570197361488646054ee96f869.jpg", + "image_caption": [ + "Figure 7. RGB refinement combined with (i) Latent-NeRF (icecream and temple), and (ii) Sketch-Shape (lego and car). For each shape we also show the normals direction." + ], + "image_footnote": [], + "bbox": [ + 80, + 87, + 468, + 388 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "gen [40], but unfortunately, we cannot validate this as the model is not publicly available to the community.", + "bbox": [ + 75, + 468, + 468, + 500 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "RGB Refinement Figure 7 shows the quality improvement achieved by our RGB refinement method. It reveals that RGB refinement is mostly useful for complex objects or for regions with detailed textures. Refinement iterations in the RGB space are about $\\times 2$ slower than iterations in latent space, thus, increasing the runtime to more than 30 minutes. Thanks to our linear mapping from a Latent-NeRF to an RGB-NeRF, practitioners may apply the refinement method only after the 3D shape has already converged with the more efficient latent training. This allows a fast exploration of 3D shapes, and an optional polishing step with RGB refinement.", + "bbox": [ + 75, + 516, + 472, + 698 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Textual-Inversion As our Latent-NeRF is supervised by Stable-Diffusion, we can also use Textual Inversion [16] tokens as part of the input text prompt. This allows conditioning the object generation on specific objects and styles, defined only by input images. Results using Textual Inversion are presented in Figure 8.", + "bbox": [ + 75, + 715, + 468, + 808 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Sketch-Shape Guidance", + "text_level": 1, + "bbox": [ + 76, + 816, + 297, + 833 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Figure 9 shows different Sketch-Shape results with the same conditioning mesh. The different text prompts are able to guide the shape toward refined geometries that better match the text prompt. The rough Sketch-Shape in this", + "bbox": [ + 75, + 839, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/60ce59e8125f6d1b622168d0b03acacdcb5da433d68054fecd71dd6a539ece5f.jpg", + "image_caption": [ + "Figure 8. Results of Latent-NeRF using a token learned from the images on the left with Textual Inversion [16]." + ], + "image_footnote": [], + "bbox": [ + 506, + 87, + 890, + 258 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/967f6d9baca7295a594032363cc2b94b4d5cea3da9a67e27ec81931181afc618.jpg", + "image_caption": [ + "Figure 9. Sketch-Shape results using different prompts. This examples shows how the same Sketch-Shape can influence different objects according to different text prompts." + ], + "image_footnote": [], + "bbox": [ + 503, + 316, + 888, + 590 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "figure, was quickly designed in Blender [12] and allows us to easily define a coarse shape that guides the Latent-NeRF. Moreover, Figure 17 depicts an ablation over the lenient parameter $\\sigma_{S}$ from Eq. (4). When $\\sigma_{S}$ is set to 0.05, the generated mesh takes the form of the conditioning shape (shown in Figure 9). As $\\sigma_{S}$ grows, more details are added on top of the base shape, until little to no resemblance is observed at $\\sigma_{S} = 1.5$ . Figure 10 contains additional results of different shapes generated with the same conditioning mesh, here a coarse house shape. The normals visualization (bottom row) shows that our method can add fine geometric details.", + "bbox": [ + 496, + 672, + 890, + 839 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Figure 11 demonstrates that our proposed approach can successfully work with a variety of different Sketch-Shapes. Notice that our method handles a variety of different shapes and also works well with shapes extruded from 2D sketches.", + "bbox": [ + 496, + 839, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "12668", + "bbox": [ + 480, + 949, + 517, + 960 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/fde7a84b93c2a3a1942725a86885f653671988f5e221a6277ac40009dc6fd58b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 241, + 90, + 305, + 135 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a5a0f38be39665d7235a9e1578117339ca0f00781a142a4c5ff7888c8542aea5.jpg", + "image_caption": [ + "Input" + ], + "image_footnote": [], + "bbox": [ + 84, + 150, + 274, + 223 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0d36679c28bbfe647820181231e6fa6e684e16907f676f0a8e225abc3f11553d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 274, + 150, + 366, + 222 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ec08daf7d12f1fb4682f8ebeea280fd975e41fbf36a8451c381e48da003137d5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 367, + 150, + 462, + 222 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e8c584bef623d03e63817d87094c5d0a1882fa4caa9809135dc8896d1497dd42.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 84, + 224, + 274, + 297 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/17d8b1ce0269551e37d5eac95ad19c449c9202be69f85ce280acc3a5269f892f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 274, + 224, + 367, + 297 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e066b57a8c77a296dfdde2007e026534120c7dfdbf8d6f4b76b57474a974a77b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 367, + 224, + 462, + 297 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6e6aef0f7e73065e79d37137ce7e30eae41d9fca8afb08564198805db6bf36cd.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 84, + 299, + 274, + 372 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/51c15bf41b347a49ee1f33bcd1c5ea5d31954bbb344616fd243afdd7ddcd3c7a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 274, + 299, + 367, + 372 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/04de86f92ecac34a7ce71900b4bb3a9f9ad67929d6b9186dac94c0c4bc223dcb.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 367, + 299, + 462, + 372 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a4cf16b5ea802a77d760e0f3caa4e3ae0fd6379768ab4a30acd1a9bed1d59623.jpg", + "image_caption": [ + "\"A house made of lego\"" + ], + "image_footnote": [], + "bbox": [ + 106, + 388, + 165, + 438 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/dd65cec776e1fddcd06f68544bbb8b6f7057a09cdb58d255bd281f8e5386fac8.jpg", + "image_caption": [ + "\"A gingerbread house\"" + ], + "image_footnote": [], + "bbox": [ + 197, + 388, + 259, + 438 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/9d2f47dd75e50a7f06fea1e371b2d37096e6840b4902848699be652e77e9925d.jpg", + "image_caption": [ + "\"A gothic house\"" + ], + "image_footnote": [], + "bbox": [ + 294, + 388, + 354, + 438 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b9c2c604f0f26f71cb18ac278a02a219c99c623b7f39432a5dd48a30311d1871.jpg", + "image_caption": [ + "\"A house made of candy\"" + ], + "image_footnote": [], + "bbox": [ + 387, + 388, + 450, + 438 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We also exhibit in Figure 14 the effectiveness of shape-guidance, by showing results of the same prompts with and without the shape loss.", + "bbox": [ + 76, + 536, + 468, + 580 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Latent-Paint Generation", + "text_level": 1, + "bbox": [ + 76, + 590, + 302, + 604 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We tested Latent-Paint on a variety of input shapes shown in Figs. 12 and 13. As all of the shapes in these figures do not contain precomputed UV parameterization, we use XAtlas [52] to compute such parameterization automatically. In contrast, the fish mesh in Figure 15 (obtained from [13]) already contains high quality UV parameterization, which we are also able work with. Figure 13 compares our Latent-Paint approach to two closely related methods, Tango [9] and CLIPMesh [26]. As can be seen, our approach achieves more precise textures thanks to the guidance from the diffusion model.", + "bbox": [ + 75, + 613, + 468, + 779 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Note that Latent-Paint can work without assuming or computing any UV-map by simply optimizing per-face latent attributes. Yet, we found it better to use a UV-map for two main reasons: (i) The UV map makes the texture granularity independent of the geometric resolution, i.e., coarse geometries do not imply course colorization; and (ii) texture maps are easier to use with downstream applications like MeshLab [11] and Blender [12].", + "bbox": [ + 75, + 780, + 468, + 902 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/cdf9480bc1764abdd05a51e7b802e2957232df22fba4a8ec6457de47c6ca6d4d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 532, + 102, + 576, + 148 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7841b82805f329575a70fef47698f0c4363b6adea8ac897f93dc63e42f51c580.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 601, + 89, + 694, + 162 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d0d2cedd2f112c23ed7f01b3daa0f08760b4cb11d858d08249063a8a3fbf6f62.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 694, + 89, + 787, + 162 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/13f93880f39bdb37a290aaf5dd969f5639d46fab308bf19258c971689f1731a7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 789, + 89, + 885, + 162 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/83d87fe07afa76c82a9a92c0182ab36727f8cec5735583a2f07e404624bf2e70.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 529, + 183, + 578, + 233 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/170510934e4187254d8ce5e4401d47b0756afac29b92e7325d3d609625b1e090.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 601, + 164, + 694, + 244 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e001f7abe8de722ceb10868742dd7d1afc693313d3bba67b124ccec5954acacb.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 694, + 164, + 797, + 244 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/895be43ed85df7bced3048326b46a1a45dca9cb6bb809dee5a8cf47c1faab623.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 797, + 164, + 883, + 244 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5196982ceb7c3e82e0775d7b7cde800dd0df1a926312e315c8863b71565ac252.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 529, + 268, + 578, + 319 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/cf8364fe15fc95cbf2106da0b585d4075791d0244b7bd730018f042b3b722179.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 601, + 250, + 694, + 330 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/54e5f28f30a919700710522a2926a9ed37df5fd70c1b8d9158257b0f04da6b12.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 694, + 250, + 787, + 330 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0bd4fd29e8e00fd72221cc63cc7c24971ef2bc3632bfad3bb3051f18c66d369e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 789, + 250, + 885, + 330 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6e3cbbf67eaf4e1623f0eed1daae45fb23634a549cfa0b069774de146ffb98fe.jpg", + "image_caption": [ + "Figure 11. Additional Sketch-Shape-guided results." + ], + "image_footnote": [], + "bbox": [ + 527, + 364, + 580, + 393 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3c8c94628e040f505dcfd84de25b529d241f14c28ed7d5729865db5dd0989ee9.jpg", + "image_caption": [ + "a sports car, highly detailed" + ], + "image_footnote": [], + "bbox": [ + 601, + 343, + 694, + 416 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a4d4c070d0e421b11d5df14b6fff216ce8c9d65839ec8d8f94fef14bb37e7ced.jpg", + "image_caption": [ + "Input" + ], + "image_footnote": [], + "bbox": [ + 694, + 343, + 787, + 416 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8fc4c38edf99e4be4c4edb7c1ee3a1b6c7220ac0d20ddccacac0b68ccbe64301.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 789, + 343, + 885, + 416 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/cb4dce63a42695b7718a77a24eac8f1bcd80e5aef64c8b278f21147da7243a61.jpg", + "image_caption": [ + "Figure 10. Sketch-Shape results, conditioned on a low-poly house shape. Our RGB Refinement was applied to improve detail quality." + ], + "image_footnote": [], + "bbox": [ + 506, + 496, + 596, + 570 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/00b39922a599e34f261a06f2df8d99cdea1bfe5b8c89bd725378813404de228e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 599, + 513, + 733, + 571 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/85f9826b966c8572cb3984ba5878d726003705739205ff3c0d7572b31face365.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 736, + 494, + 831, + 571 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/be3bcf96f06493a88e2606a1cc8598dd1d46ae36cf25f147d5d4134c99af40d8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 841, + 476, + 901, + 571 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/df16f9cdedc2f42068987ee93f546f0b058f2db844fc8e9072f60aa2d0ab168e.jpg", + "image_caption": [ + "\"A wooden brown cabinet\"" + ], + "image_footnote": [], + "bbox": [ + 506, + 594, + 596, + 667 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a6c2daf77014007b940e6e1b4c8a7ae2df5972ec54e2482dad4cb31a85fea6ea.jpg", + "image_caption": [ + "\"A next gen nascar\"" + ], + "image_footnote": [], + "bbox": [ + 599, + 612, + 735, + 667 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f60f1934cc8ed3620fe46aea1f24329fdd66fe55cda02fe2c30eaf4f3c1fcfb0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 736, + 590, + 831, + 667 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/eef58d98d27669247bbe1d644c1468be0df63e437086b8729b5bf2624aed5418.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 841, + 571, + 901, + 669 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2356a540d21d3dc49e38c318e078302232cad551d8087d2538eae7efdbcf87c3.jpg", + "image_caption": [ + "\"A steel cabinet\"" + ], + "image_footnote": [], + "bbox": [ + 506, + 712, + 596, + 785 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6cc83234ce7b36d65c43ba1bb1f1de59484f542997fd397cf76e9ee070d084a2.jpg", + "image_caption": [ + "\"A next gen nascar\"" + ], + "image_footnote": [], + "bbox": [ + 599, + 729, + 735, + 786 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2efa2b2127d505d3edb83b7fb69914aaf172125721c5417cfff74feb2cc549fc.jpg", + "image_caption": [ + "\"A pink grand piano\"", + "\"A garden gnome with a green hat\"" + ], + "image_footnote": [], + "bbox": [ + 736, + 709, + 831, + 786 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/56b2b68649ba006e662614387ad4f73f386530d27a5c770cd6389e4d7a0c3496.jpg", + "image_caption": [ + "\"A garden gnome with a red hat\"", + "Figure 12. Latent-Paint results on shapes from ModelNet40 [48]. UV parameterization was not given for any of the meshes in this figure. For the Nascar shapes, the same text prompt was used with a different initialization." + ], + "image_footnote": [], + "bbox": [ + 841, + 690, + 901, + 786 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "12669", + "bbox": [ + 478, + 949, + 517, + 960 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f90f36bca5547ae78916192fd86c4af8082642d2270c8fcd3e857b3ceee65675.jpg", + "image_caption": [ + "Figure 13. Generating different shoe textures over the same input mesh by only changing the conditioning text prompt. The surface parameterization was computed using XAtlas [52]." + ], + "image_footnote": [], + "bbox": [ + 107, + 88, + 460, + 311 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Shape guidance No shape guidance Shape guidance No shape guidance", + "bbox": [ + 102, + 366, + 437, + 377 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/76183cfc6131694a8d3b750c46c63a888f34794451aafc409e8b912b70db54e4.jpg", + "image_caption": [ + "Figure 14. Results for the same prompts with and without shape-guidance. The guiding shapes are the same as in Figure 11." + ], + "image_footnote": [], + "bbox": [ + 102, + 377, + 433, + 450 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7f80ef3ed24b765b6afb35c1d9b0edcc5c517efc94f436e5ba97669568487ab7.jpg", + "image_caption": [ + "Figure 15. Latent-Paint results for an input mesh containing precomputed UV parameterization. Model courtesy of \"Keenan's 3D Model Repository\" [13]." + ], + "image_footnote": [], + "bbox": [ + 102, + 500, + 444, + 588 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e5cd4e3166b7a7622b6c698a756ebd0dc59a85a6ce8bf22e339bf54ff97b1935.jpg", + "image_caption": [ + "Stable Diffusion with \"A photo of a squirrel, backview\"", + "Figure 16. note that the generated squirrel in the first row contains two faces from some view directions; see the second to the left view. This problem may be attributed to the fact that Stable Diffusion fails to generate back views of a squirrel; see bottom row." + ], + "image_footnote": [], + "bbox": [ + 122, + 652, + 421, + 757 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Limitations", + "text_level": 1, + "bbox": [ + 76, + 853, + 197, + 868 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Our presented technique is yet a preliminary step towards the challenging goal of a comprehensive text-to-", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/93628da91db22f9c849208a7218d97f37a50b94465baab670e881365b12fa542.jpg", + "image_caption": [ + "Figure 17. Sketch-Shape ablation over $\\sigma_S$ values (Eq. (4)) and input shape from Figure 9. As $\\sigma_S$ grows, the constraint becomes more lenient, and enables the shape to evolve into new geometries." + ], + "image_footnote": [], + "bbox": [ + 501, + 79, + 898, + 215 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "shape model that uses no 3D supervision. Still, the proposed latent framework has its limitations. To attain a plausible 3D shape, we use the same \"prompt tweaking\" used by DreamFusion [35], i.e., adding a directional text-prompt (e.g., \"front\", \"side\" with respect to the camera) to the input text prompt. We find that this assistance tends to fail with our approach when applied to certain objects. Moreover, we find that even Stable Diffusion tends to generate unsatisfactory images when specifying the desired direction as shown in Figure 16. Additionally, similar to most works that employ diffusion models, there is a stochastic behavior to the results, such that the quality of the results may significantly vary between different seeds.", + "bbox": [ + 496, + 277, + 892, + 473 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusions", + "text_level": 1, + "bbox": [ + 500, + 488, + 625, + 503 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this work, we introduced a latent framework for generating 3D shapes and textures using different forms of text and shape guidance. We first adapted the score distillation loss for LDMs, enabling the use of recent, powerful and publicly available text-to-image generation models for 3D shape generation. Successfully applying score distillation on LDMs results in a fast and flexible object generation framework. We then introduced shape-guided control on the generated model. We showed two versions of shape-guided generation, Sketch-Shape and Latent-Paint, and demonstrated their effectiveness for providing additional control over the generation process.", + "bbox": [ + 496, + 508, + 890, + 689 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Typically, the notion of rendering refers to generating an image in pixel space. Here, we have presented a method that renders directly into the latent space of a neural model. We believe that our Latent-NeRF approach opens the avenue for more latent space rendering methods, which can gain from a compact and effective latent representation, and advance the use of neural models that operate in latent space rather than pixel space. Furthermore, our novel approach and its ease-of-use nature would encourage further research toward effective text-guided shape generation.", + "bbox": [ + 496, + 691, + 892, + 843 + ], + "page_idx": 7 + }, + { + "type": "aside_text", + "text": "Latent-Paint (Ours) CLIPMesh [26] Tango [9]", + "bbox": [ + 76, + 89, + 94, + 287 + ], + "page_idx": 7 + }, + { + "type": "page_footnote", + "text": "This work was supported by the European research council (ERC-StG 757497 PI Giryes), and the Israel Science Foundation (grants no. 2492/20 and 3441/21).", + "bbox": [ + 500, + 862, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "12670", + "bbox": [ + 480, + 949, + 517, + 960 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Omri Avrahami, Ohad Fried, and Dani Lischinski. 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In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 586-595, 2018. 3", + "bbox": [ + 78, + 90, + 470, + 161 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "12673", + "bbox": [ + 480, + 950, + 517, + 960 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Latent-NeRF for Shape-Guided Generation of 3D Shapes and Textures/ca0b263a-3321-4fb3-b039-4fe859baac3c_model.json b/2023/Latent-NeRF for Shape-Guided Generation of 3D Shapes and Textures/ca0b263a-3321-4fb3-b039-4fe859baac3c_model.json new file mode 100644 index 0000000000000000000000000000000000000000..f2da648f646d6aa4d955b1539d0b78b9df326e58 --- /dev/null +++ b/2023/Latent-NeRF for Shape-Guided Generation of 3D Shapes and Textures/ca0b263a-3321-4fb3-b039-4fe859baac3c_model.json @@ -0,0 +1,2741 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.128, + 0.118, + 0.843, + 0.14 + ], + "angle": 0, + "content": "Latent-NeRF for Shape-Guided Generation of 3D Shapes and Textures" + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.167, + 0.214, + 0.186 + ], + "angle": 0, + "content": "Gal Metzer*" + }, + { + "type": "text", + "bbox": [ + 0.254, + 0.168, + 0.394, + 0.186 + ], + "angle": 0, + "content": "Elad Richardson*" + }, + { + "type": "text", + "bbox": [ + 0.435, + 0.169, + 0.54, + 0.186 + ], + "angle": 0, + "content": "Or Patashnik" + }, + { + "type": "text", + "bbox": [ + 0.58, + 0.169, + 0.678, + 0.187 + ], + "angle": 0, + "content": "Raja Giryes" + }, + { + "type": "text", + "bbox": [ + 0.717, + 0.169, + 0.857, + 0.186 + ], + "angle": 0, + "content": "Daniel Cohen-Or" + }, + { + "type": "title", + "bbox": [ + 0.404, + 0.204, + 0.562, + 0.223 + ], + "angle": 0, + "content": "Tel Aviv University" + }, + { + "type": "image_caption", + "bbox": [ + 0.101, + 0.258, + 0.226, + 0.292 + ], + "angle": 0, + "content": "\"A stack of pancakes covered in maple syrup\"" + }, + { + "type": "image_caption", + "bbox": [ + 0.244, + 0.265, + 0.331, + 0.286 + ], + "angle": 0, + "content": "\"A highly detailed sandcastle\"" + }, + { + "type": "image", + "bbox": [ + 0.102, + 0.294, + 0.223, + 0.387 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.171, + 0.394, + 0.279, + 0.409 + ], + "angle": 0, + "content": "Latent-NeRF" + }, + { + "type": "image", + "bbox": [ + 0.226, + 0.294, + 0.346, + 0.386 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.365, + 0.253, + 0.468, + 0.377 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.479, + 0.265, + 0.534, + 0.285 + ], + "angle": 0, + "content": "\"A German Shepherd\"" + }, + { + "type": "image", + "bbox": [ + 0.461, + 0.294, + 0.582, + 0.387 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.42, + 0.394, + 0.531, + 0.412 + ], + "angle": 0, + "content": "Sketch-Shape" + }, + { + "type": "image", + "bbox": [ + 0.603, + 0.25, + 0.731, + 0.377 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.744, + 0.264, + 0.812, + 0.286 + ], + "angle": 0, + "content": "\"A fish with leopard spots\"" + }, + { + "type": "image", + "bbox": [ + 0.735, + 0.296, + 0.856, + 0.386 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.676, + 0.394, + 0.776, + 0.409 + ], + "angle": 0, + "content": "Latent-Paint" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.425, + 0.895, + 0.454 + ], + "angle": 0, + "content": "Figure 1. Our three text-guided models: a purely text-guided Latent-NeRF, Latent-NeRF with Sketch-Shape guidance for more exact control over the generated shape, and Latent-Paint for texture generation for explicit shapes. The top row represents the models' inputs." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.466, + 0.313, + 0.481 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.503, + 0.473, + 0.911 + ], + "angle": 0, + "content": "Text-guided image generation has progressed rapidly in recent years, inspiring major breakthroughs in text-guided shape generation. Recently, it has been shown that using score distillation, one can successfully text-guide a NeRF model to generate a 3D object. We adapt the score distillation to the publicly available, and computationally efficient, Latent Diffusion Models, which apply the entire diffusion process in a compact latent space of a pretrained autoencoder. As NeRFs operate in image space, a naive solution for guiding them with latent score distillation would require encoding to the latent space at each guidance step. Instead, we propose to bring the NeRF to the latent space, resulting in a Latent-NeRF. Analyzing our Latent-NeRF, we show that while Text-to-3D models can generate impressive results, they are inherently unconstrained and may lack the ability to guide or enforce a specific 3D structure. To assist and direct the 3D generation, we propose to guide our Latent-NeRF using a Sketch-Shape: an abstract geometry that defines the coarse structure of the desired object. Then, we present means to integrate such a constraint directly into a Latent-NeRF. This unique combination of text and shape guidance allows for increased control over the generation process. We also show that latent score distillation can be successfully applied directly on 3D meshes. This allows for generating high-quality textures on a given geometry. Our experiments validate the power of our different forms of guidance and the efficiency of using latent rendering." + }, + { + "type": "title", + "bbox": [ + 0.502, + 0.466, + 0.631, + 0.481 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.492, + 0.892, + 0.628 + ], + "angle": 0, + "content": "Text-guided image generation has seen tremendous success in recent years, primarily due to the breathtaking development in Language-Image models [25, 28, 36] and diffusion models [14, 21, 37-40]. These breakthroughs have also resulted in fast progression for text-guided shape generation [9, 29, 53]. Most recently, it has been shown [35] that one can directly use score distillation from a 2D diffusion model to guide the generation of a 3D object represented as a Neural Radiance Field (NeRF) [30]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.63, + 0.893, + 0.901 + ], + "angle": 0, + "content": "While Text-to-3D can generate impressive results, it is inherently unconstrained and may lack the ability to guide or enforce a 3D structure. In this paper, we show how to introduce shape-guidance to the generation process to guide it toward a specific shape, thus allowing increased control over the generation process. Our method builds upon two models, a NeRF model [30], and a Latent Diffusion Model (LDM) [39]. Latent Models, which apply the entire diffusion process in a compact latent space, have recently gained popularity due to their efficiency and publicly available pretrained checkpoints. As score distillation was previously applied only on RGB diffusion models, we first present two key modifications to the NeRF model that are better paired with guidance from a latent model. First, instead of representing our NeRF in the standard RGB space, we propose a Latent-NeRF which operates directly in the latent space of the LDM, thus avoiding the burden of encoding a rendered RGB image to a latent space for each and every guid" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.95, + 0.519, + 0.962 + ], + "angle": 0, + "content": "12663" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.228 + ], + "angle": 0, + "content": "ing step. Secondly, we show that after training, one can easily transform a Latent-NeRF back into a regular NeRF. This allows further refinement in RGB space, where we can also introduce shading constraints or apply further guidance from RGB diffusion models [40]. This is achieved by introducing a learnable linear layer that can be optionally added to a trained Latent-NeRF, where the linear layer is initialized using an approximate mapping between the latent and RGB values [45]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.228, + 0.473, + 0.365 + ], + "angle": 0, + "content": "Our first form of shape-guidance is applied using a coarse 3D model, which we call a Sketch-Shape. Given a Sketch-Shape, we apply soft constraint during the NeRF optimization process to guide its occupancy based on the given shape. Easily combined with Latent-NeRF optimization, the additional constraint can be tuned to meet a desired level of strictness. Using a Sketch-Shape allows users to define their base geometry, where Latent-NeRF then refines the shape and introduces texture based on a guiding prompt." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.365, + 0.473, + 0.501 + ], + "angle": 0, + "content": "We further present Latent-Paint, another form of shape-guidance where the generation process is applied directly on a given 3D mesh, and we have not only the structure but also the exact parameterization of the input mesh. This is achieved by representing a texture map in the latent space and propagating the guidance gradients directly to the texture map through the rendered mesh. By doing so, we allow for the first time to colorize a mesh using guidance from a pretrained diffusion model and enjoy its expressiveness." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.5, + 0.473, + 0.561 + ], + "angle": 0, + "content": "We evaluate our different forms of guidance under a variety of scenarios and show that together with our latent-based guidance, they offer a compelling solution for constrained shape and texture generation." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.574, + 0.22, + 0.589 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.599, + 0.473, + 0.903 + ], + "angle": 0, + "content": "3D Shape Generation 3D shape synthesis is a longstanding problem in computer graphics and computer vision. In recent years, with the emergence of neural networks, the research in 3D modeling has immensely advanced. The most conventional supervision type is applied directly with 3D shapes, through different representations such as implicit functions [10, 20, 33], meshes [19, 50] or point clouds [27, 49]. As 3D supervision is often difficult to obtain, other works use images to guide the generative task [6, 7, 32]. In fact, even when 3D data is available, 2D renderings are sometimes chosen as the supervising primitive [5, 8, 18]. For example, in GET3D [18], two generators are trained, one generates a 3D SDF, and the other a texture field. The output textured mesh is then obtained in a differentiable manner by utilizing DMTet [42]. These generators are adversarially trained with a dataset of 2D images. In [47] a diffusion model has been used to generate multiple views of a given input image. Yet, it has been trained in a supervised manner on a multi-view dataset, unlike our work which does not require a dataset." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.622 + ], + "angle": 0, + "content": "Text-to-3D with 2D Supervision. Recently, the success of text-guided synthesis in numerous domains [1,2,17,34, 44], has motivated a surge of works that use Language-Image models to guide 3D scenes representations. CLIP-Forge [41] consists of two separate components, an implicit autoencoder conditioned on shape codes, and a normalizing flow model that is trained to generate shape codes according to CLIP embeddings. CLIP-Forge exploits the fact that CLIP has a joint text-image embedding space to train on image embeddings and infer on text embeddings, achieving text-to-shape capabilities. Text2Mesh [29] introduced mesh colorization and geometric fine-tuning by optimizing an initial mesh through differential rendering and CLIP [36] guidance. TANGO [9] follows a similar optimization scheme, while improving results by considering an explicit shading model. CLIP-Mesh [26] optimizes an initial spherical mesh according to a target text prompt, using a modified CLIP loss that accounts for the gap and ambiguity between image/text CLIP embeddings. Similarly to our method, they also use UV texture mapping to bake colors into the mesh. DreamFields [24] employs CLIP guidance as well, but uses NeRFs to represent the 3D object instead of an explicit triangular mesh, together with a dedicated sparsity loss. CLIPNeRF [46] pretrains a disentangled NeRF representation network on rendered object datasets, which is then used to constraint a NeRF scene optimization under CLIP loss, between random renderings of the NeRF and target image or text CLIP embedding. DreamFusion [35] introduced, for the first time, the use of largely successful pretrained 2D diffusion models for text-guided 3D object generation. DreamFusion uses a proprietary 2D diffusion model [40] to supervise the generation of 3D objects represented by NeRFs. To guide a NeRF scene using the pretrained diffusion model, the authors derive a Score-Distillation loss, see Section 3.1 for more details." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.638, + 0.895, + 0.76 + ], + "angle": 0, + "content": "Neural Rendering The recent rapid progression of neural networks has immensely advanced the performance of differential renderers. Particularly NeRF [4, 30, 31] have shown astounding performance on novel view generation and relighting, also extending to other applications like 3D reconstruction [51]. Thanks to their differentiable nature, it has been recently shown that one can introduce different neural objectives during training to guide the 3D modeling." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.77, + 0.593, + 0.785 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Here we present our shape-guidance solution. We describe the Latent-NeRF framework, presented in Figure 2, and then introduce different guidance controls that can be combined with Latent-NeRF for controlling its generation. Yet, before showing our solution, we provide a quick overview of two recently proposed techniques that are highly relevant to our method." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.95, + 0.52, + 0.962 + ], + "angle": 0, + "content": "12664" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.091, + 0.218, + 0.105 + ], + "angle": 0, + "content": "3.1. Preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.113, + 0.473, + 0.4 + ], + "angle": 0, + "content": "A latent diffusion model (LDM) [39] is a specific form of a diffusion model that is trained to denoise latent codes of a pretrained autoencoder, instead of the high-resolution images directly. First, an autoencoder composed of an encoder \\(\\mathcal{E}\\), and a decoder \\(\\mathcal{D}\\) is trained to reconstruct natural images \\(x \\sim X\\), where \\(X\\) is the image training dataset, in the following form: \\(\\tilde{x} = \\mathcal{D}(\\mathcal{E}(x))\\). The autoencoder is trained with a reconstruction loss, perceptual loss [54] and a patch-based adversarial loss [22]. Then, given the trained autoencoder, a denoising diffusion probabilistic model (DDPM) [21] is trained to generate a spatial latent \\(z\\) from noise, according to the distribution \\(z = \\mathcal{E}(x)\\) s.t. \\(x \\sim X\\). In order to generate a novel image, a latent \\(\\tilde{z}\\) is sampled from this learned distribution, using the trained DDPM, and passed to the decoder to obtain the final image \\(\\mathcal{D}(\\tilde{z})\\). Operating in the latent space requires less compute, and leads to faster training and sampling, which makes LDM widely popular. In fact, the recent Stable Diffusion model is also an LDM." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.401, + 0.473, + 0.568 + ], + "angle": 0, + "content": "Score Distillation is a method that enables using a diffusion model as a critic, i.e., using it as a loss without explicitly back-propagating through the diffusion process. It has been introduced in DreamFusion [35] for guiding 3D generation using the Imagen model [40]. To perform score distillation, noise is first added to a given image (e.g., one view of the NeRF's output). Then, the diffusion model is used to predict the added noise from the noised image. Finally, the difference between the predicted and added noises is used for calculating per-pixel gradients. For NeRF, the gradients are back-propagated for updating the 3D NeRF model." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.568, + 0.472, + 0.613 + ], + "angle": 0, + "content": "Going into more detail, at each iteration of the score distillation optimization, a rendered image \\( x \\) is noised to a randomly drawn time step \\( t \\)," + }, + { + "type": "equation", + "bbox": [ + 0.187, + 0.619, + 0.47, + 0.639 + ], + "angle": 0, + "content": "\\[\nx _ {t} = \\sqrt {\\bar {\\alpha} _ {t}} x + \\sqrt {1 - \\bar {\\alpha} _ {t}} \\epsilon , \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.643, + 0.47, + 0.689 + ], + "angle": 0, + "content": "where \\(\\epsilon \\sim \\mathcal{N}(0,I)\\), and \\(\\bar{\\alpha}_t\\) is a time-dependent constant specified by the diffusion model. Then, the per-pixel score distillation gradients are taken to be" + }, + { + "type": "equation", + "bbox": [ + 0.154, + 0.697, + 0.47, + 0.715 + ], + "angle": 0, + "content": "\\[\n\\nabla_ {x} L _ {S D S} = w (t) \\left(\\epsilon_ {\\phi} \\left(x _ {t}, t, T\\right) - \\epsilon\\right), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.473, + 0.902 + ], + "angle": 0, + "content": "where \\(\\epsilon_{\\phi}\\) is the diffusion model's denoiser (which approximates the noise to be removed), \\(\\phi\\) are the denoiser's parameters, \\(T\\) is an optional guiding text prompt, and \\(w(t)\\) is a constant multiplier that depends on \\(\\alpha_{t}\\). During training, gradients are propagated from the pixel gradients to the NeRF parameters and gradually change the 3D object. Please refer to [35] for the complete details and derivation of Score Distillation. Note that DreamFusion uses the proprietary Imagen [40] model that is very computationally demanding. We rely on the publicly available Stable Diffusion model and the re-implementation of DreamFusion [43] (it operates in the RGB space and not the latent as we propose)." + }, + { + "type": "image", + "bbox": [ + 0.522, + 0.088, + 0.875, + 0.254 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.263, + 0.895, + 0.39 + ], + "angle": 0, + "content": "Figure 2. An overview of Latent-NeRF trained with a similar score distillation scheme as proposed by [35]. At each training iteration we render the scene from a random view point to produce a feature map \\( z \\). Then, \\( z \\) is noised with \\( \\epsilon \\) according to a random diffusion step \\( t \\). The noised version of \\( z \\), i.e., \\( x_{t} \\), is denoised using Stable Diffusion [39], with the input text prompt. Finally, the input noise is subtracted from the predicted noise by Stable Diffusion, to approximate per-pixel gradients that are back propagated to the NeRF representation." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.417, + 0.64, + 0.431 + ], + "angle": 0, + "content": "3.2. Latent-NeRF" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.44, + 0.895, + 0.744 + ], + "angle": 0, + "content": "We now turn to describe our Latent-NeRF approach. In this method, a NeRF model is optimized to render 2D feature maps in Stable Diffusion's latent space \\(\\mathcal{Z}\\). Latent-NeRF outputs four pseudo-color channels, \\((c_{1}, c_{2}, c_{3}, c_{4})\\), corresponding to the four latent features that stable diffusion operates over, and a volume density \\(\\sigma\\). Figure 2 illustrates this process. Representing the scene using NeRF implicitly imposes spatial consistency between different views, due to the spatial radiance field and rendering equation. Still, the fact that \\(\\mathcal{Z}\\) can be represented by a NeRF with spatial consistencies is non-trivial. Previous works [1, 45] showed that super-pixels in \\(\\mathcal{Z}\\) depend mainly on individual patches in the output image. This can be attributed to the high resolution \\((64 \\times 64)\\) and low channel-wise depth (4) of this latent space, which encourages local dependency over the autoencoder's image and latent spaces. Assuming \\(\\mathcal{Z}\\) is a near patch level representation of its corresponding RGB image makes the latents nearly equivariant to spatial transformations of the scene, which justifies the use of NeRFs for representing the 3D scenes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.766, + 0.894, + 0.813 + ], + "angle": 0, + "content": "Text Guidance The vanilla form of Latent-NeRF is text-guided, with no other constraints for the scene generation. In this setting, we employ the following loss:" + }, + { + "type": "equation", + "bbox": [ + 0.575, + 0.826, + 0.818, + 0.843 + ], + "angle": 0, + "content": "\\[\nL = \\lambda_ {S D S} L _ {S D S} + \\lambda_ {s p a r s e} L _ {s p a r s e},\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.895, + 0.903 + ], + "angle": 0, + "content": "where \\(L_{SDS}\\) is the Score-Distillation loss depicted in Figure 2. Note, that the exact value of this loss is not accessible. Instead, the gradients implied by it are approximated" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.95, + 0.519, + 0.962 + ], + "angle": 0, + "content": "12665" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.08, + 0.088, + 0.468, + 0.206 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.217, + 0.471, + 0.287 + ], + "angle": 0, + "content": "Figure 3. To perform fine-tuning in RGB, we take a Latent-NeRF model that was trained in latent space (conventional setting), apply the matrix adapter to the channel output of the model to get an RGB preview, and then continue optimizing the MLP's weights through supervision in RGB to improve the result." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.32, + 0.47, + 0.412 + ], + "angle": 0, + "content": "by a single forward pass through the denoiser. These gradients are directly passed to the autograd solver. The loss \\( L_{sparse} = BE(w_{blend}) \\) suggested in [43] prevents floating \"radiance clouds\" by penalizing the binary entropy of ill-defined background masks \\( w_{blend} \\). Namely, it encourages a strict blending of the object NeRF and background NeRF." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.446, + 0.47, + 0.658 + ], + "angle": 0, + "content": "RGB Refinement Using Latent-NeRF, one may successfully learn to represent 3D scenes even when optimizing solely in latent space. Still, in some cases, it could be beneficial to further refine the model by fine-tuning it in pixel space, and have the NeRF model operate directly in RGB. To do so, we must convert the NeRF that was trained in latent space to a NeRF that operates in RGB. This requires converting the MLP's output from the four latent channels to three RGB channels such that the initial rendered RGB image is close to the decoder output, when applied to the rendered latent of the original model. Interestingly, it has been shown [45] that a linear approximation is sufficient to predict plausible RGB colors given a single four-channel latent super pixel, via the following transformation" + }, + { + "type": "equation", + "bbox": [ + 0.092, + 0.674, + 0.468, + 0.749 + ], + "angle": 0, + "content": "\\[\n\\left( \\begin{array}{c} \\hat {r} \\\\ \\hat {g} \\\\ \\hat {b} \\end{array} \\right) = \\left( \\begin{array}{c c c c} 0. 2 9 8 & 0. 1 8 7 & - 0. 1 5 8 & - 0. 1 8 4 \\\\ 0. 2 0 7 & 0. 2 8 6 & 0. 1 8 9 & - 0. 2 7 1 \\\\ 0. 2 0 8 & 0. 1 7 3 & 0. 2 6 4 & - 0. 4 7 3 \\end{array} \\right) \\left( \\begin{array}{c} c _ {1} \\\\ c _ {2} \\\\ c _ {3} \\\\ c _ {4} \\end{array} \\right), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.471, + 0.902 + ], + "angle": 0, + "content": "which was calculated using pairs of RGB images and their corresponding latent codes over a collection of natural images. As our NeRF model is already composed of a set of fully connected layers, we simply add another linear layer that is initialized using the weights in Equation 3. This converts our Latent-NeRF to operate in pixel space and ensures that our refinement process starts from a valid result. The additional layer is then fine-tuned together with the rest of the model, to create the refined and final output. The overall fine-tuning procedure is illustrated in Figure 3." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.091, + 0.72, + 0.108 + ], + "angle": 0, + "content": "3.3. Sketch-Shape Guidance" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.114, + 0.892, + 0.159 + ], + "angle": 0, + "content": "Next, we introduce a novel technique for guiding the Latent-NeRF generation based on a coarse geometry, which we call a Sketch-Shape." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.16, + 0.893, + 0.37 + ], + "angle": 0, + "content": "A Sketch-Shape is an abstract coarse alignment of simple 3D primitives like spheres, boxes, cylinders, etc., that together depict an outline of a more complex object. Figures 9, 10, 11 illustrate such simple shapes. Ideally, we would like the output density of our MLP to match that of the Sketch-Shape, such that the output Latent-NeRF result resembles the input shape. Nevertheless, we would also like the new NeRF to have the capacity to create new details and geometries that match the input text prompt and improve the fidelity of the shape. To achieve this lenient constraint, we encourage the NeRF's occupancy to match the winding-number [3, 23] indicator of the Sketch-Shape, but with decaying importance near the surface to allow new geometries. This loss reads as" + }, + { + "type": "equation", + "bbox": [ + 0.5, + 0.372, + 0.892, + 0.408 + ], + "angle": 0, + "content": "\\[\nL _ {\\text {S k e t c h - S h a p e}} = C E \\left(\\alpha_ {N e R F} (p), \\alpha_ {G T} (p)\\right) \\cdot \\left(1 - e ^ {- \\frac {d ^ {2}}{2 \\sigma_ {S}}}\\right). \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.408, + 0.893, + 0.56 + ], + "angle": 0, + "content": "This loss implies that the occupancy should be well constrained away from the surface, and free to be set by score distillation near the surface. This loss is applied in addition to the Latent-NeRF loss, over the entire point set \\( p \\) that is used by the NeRF's volumetric rendering. \\( d \\) represents the distance of \\( p \\) from the surface, and \\( \\sigma_{S} \\) is a hyperparameter that controls how lenient the loss is, i.e., lower \\( \\sigma_{S} \\) values imply a tighter constraint to the input Sketch-Shape. Applying the loss only on the sampled point-set \\( p \\), makes it more efficient as these points are already evaluated as part" + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.568, + 0.877, + 0.774 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.786, + 0.892, + 0.897 + ], + "angle": 0, + "content": "Figure 4. An overview of Latent-Paint texture generation, trained with a similar score distillation loss [35]. The object is represented as a textured mesh, with a latent texture image that has four pseudo-color channels. At each iteration, the mesh is rendered with a differential renderer, to create a feature map from a random viewpoint. Score distillation is applied to the rendered feature map, and the gradients back-propagate to the latent texture image through the differential renderer. See Section 3.4." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.95, + 0.519, + 0.962 + ], + "angle": 0, + "content": "12666" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.335, + 0.106 + ], + "angle": 0, + "content": "of the Latent-NeRF rendering process." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.117, + 0.355, + 0.133 + ], + "angle": 0, + "content": "3.4. Latent-Paint of Explicit Shapes" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.14, + 0.471, + 0.306 + ], + "angle": 0, + "content": "We now move to a more strict constraint, where the guidance is based on an exact structure of a given shape, e.g., provided in the form of a mesh. We call this approach Latent-Paint, which leads to the generation of novel textures for a given shape. Our method generates texture over a UV texture map, which can either be supplied by the input mesh, or calculated on-the-fly using XAtlas [52]. To color a mesh, we first initialize a random latent texture image of size \\( H \\times W \\times 4 \\), where \\( H \\) and \\( W \\) can be chosen according to the desired texture granularity. We set them both to be 128 in our experiments." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.307, + 0.471, + 0.487 + ], + "angle": 0, + "content": "Figure 4 presents the training process. At each score distillation iteration, we render the mesh with a differentiable renderer [15] to obtain a \\(64 \\times 64 \\times 4\\) feature map that is pseudo-colored by the latent texture image. Then, we apply the score distillation loss from Equation 2 in the same way it is applied for Latent-NeRF. Yet, instead of backpropagating the loss to the NeRF's MLP parameters, we optimize the deep texture image by back-propagating through the differentiable renderer. To get the final RGB texture image, we simply pass the latent texture image through Stable Diffusion's decoder \\(\\mathcal{D}\\) once, to get a larger high-quality RGB texture." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.502, + 0.194, + 0.517 + ], + "angle": 0, + "content": "4. Evaluation" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.527, + 0.47, + 0.558 + ], + "angle": 0, + "content": "We now validate the effectiveness of our different forms of guidance through a variety of experiments." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.577, + 0.47, + 0.639 + ], + "angle": 0, + "content": "Implementation Details We use the Stable Diffusion implementation by HuggingFace Diffusers, with the v1-4 checkpoint. For score distillation, we use the code-base provided by [43], with Instant-NGP [31] as our NeRF model." + }, + { + "type": "image", + "bbox": [ + 0.085, + 0.659, + 0.465, + 0.869 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.104, + 0.883, + 0.442, + 0.897 + ], + "angle": 0, + "content": "Figure 5. Latent-NeRF results from different viewpoints." + }, + { + "type": "image", + "bbox": [ + 0.51, + 0.094, + 0.88, + 0.522 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.503, + 0.535, + 0.888, + 0.55 + ], + "angle": 0, + "content": "Figure 6. Qualitative comparison with other text-to-3D methods." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.578, + 0.892, + 0.669 + ], + "angle": 0, + "content": "Latent-NeRF usually takes less than 15 minutes to converge on a single V100, while using an RGB-NeRF with Stable Diffusion [43] takes about 30 minutes, due to the increased overhead from encoding into the latent space. Note that DreamFusion [35] takes about 1.5 hours on 4 TPUs. This clearly shows the computational advantage of Latent-NeRF." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.68, + 0.724, + 0.695 + ], + "angle": 0, + "content": "4.1. Text-Guided Generation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Qualitative Results We begin by demonstrating the effectiveness of the latent rendering approach with Latent-NeRF. In Figs. 1, 5 and 7, we show several results obtained by our method. In the supplementary material we provide additional results of different objects, including video visualizations. In Figure 5, we show the consistency of our learned shapes from several viewpoints. Next, we use the baseline set by DreamFusion [35] to qualitatively compare our approach (with the proposed RGB refinement) against other methods. As can be seen in Figure 6, Latent-NeRF achieves significantly better results than DreamFields [24] and CLIPMesh [26]. We believe that the better quality of DreamFusion can be attributed to the high quality of Ima" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.95, + 0.519, + 0.962 + ], + "angle": 0, + "content": "12667" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.088, + 0.47, + 0.389 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.4, + 0.471, + 0.444 + ], + "angle": 0, + "content": "Figure 7. RGB refinement combined with (i) Latent-NeRF (icecream and temple), and (ii) Sketch-Shape (lego and car). For each shape we also show the normals direction." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.469, + 0.47, + 0.501 + ], + "angle": 0, + "content": "gen [40], but unfortunately, we cannot validate this as the model is not publicly available to the community." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.517, + 0.473, + 0.699 + ], + "angle": 0, + "content": "RGB Refinement Figure 7 shows the quality improvement achieved by our RGB refinement method. It reveals that RGB refinement is mostly useful for complex objects or for regions with detailed textures. Refinement iterations in the RGB space are about \\(\\times 2\\) slower than iterations in latent space, thus, increasing the runtime to more than 30 minutes. Thanks to our linear mapping from a Latent-NeRF to an RGB-NeRF, practitioners may apply the refinement method only after the 3D shape has already converged with the more efficient latent training. This allows a fast exploration of 3D shapes, and an optional polishing step with RGB refinement." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.717, + 0.47, + 0.809 + ], + "angle": 0, + "content": "Textual-Inversion As our Latent-NeRF is supervised by Stable-Diffusion, we can also use Textual Inversion [16] tokens as part of the input text prompt. This allows conditioning the object generation on specific objects and styles, defined only by input images. Results using Textual Inversion are presented in Figure 8." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.818, + 0.299, + 0.834 + ], + "angle": 0, + "content": "4.2. Sketch-Shape Guidance" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Figure 9 shows different Sketch-Shape results with the same conditioning mesh. The different text prompts are able to guide the shape toward refined geometries that better match the text prompt. The rough Sketch-Shape in this" + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.088, + 0.891, + 0.26 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.272, + 0.893, + 0.302 + ], + "angle": 0, + "content": "Figure 8. Results of Latent-NeRF using a token learned from the images on the left with Textual Inversion [16]." + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.317, + 0.889, + 0.591 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.605, + 0.893, + 0.648 + ], + "angle": 0, + "content": "Figure 9. Sketch-Shape results using different prompts. This examples shows how the same Sketch-Shape can influence different objects according to different text prompts." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.674, + 0.892, + 0.84 + ], + "angle": 0, + "content": "figure, was quickly designed in Blender [12] and allows us to easily define a coarse shape that guides the Latent-NeRF. Moreover, Figure 17 depicts an ablation over the lenient parameter \\(\\sigma_{S}\\) from Eq. (4). When \\(\\sigma_{S}\\) is set to 0.05, the generated mesh takes the form of the conditioning shape (shown in Figure 9). As \\(\\sigma_{S}\\) grows, more details are added on top of the base shape, until little to no resemblance is observed at \\(\\sigma_{S} = 1.5\\). Figure 10 contains additional results of different shapes generated with the same conditioning mesh, here a coarse house shape. The normals visualization (bottom row) shows that our method can add fine geometric details." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Figure 11 demonstrates that our proposed approach can successfully work with a variety of different Sketch-Shapes. Notice that our method handles a variety of different shapes and also works well with shapes extruded from 2D sketches." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.95, + 0.519, + 0.962 + ], + "angle": 0, + "content": "12668" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.242, + 0.092, + 0.307, + 0.136 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.26, + 0.14, + 0.288, + 0.15 + ], + "angle": 0, + "content": "Input" + }, + { + "type": "image", + "bbox": [ + 0.086, + 0.151, + 0.275, + 0.224 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.276, + 0.151, + 0.367, + 0.223 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.368, + 0.151, + 0.464, + 0.223 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.086, + 0.225, + 0.275, + 0.299 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.276, + 0.225, + 0.368, + 0.299 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.369, + 0.225, + 0.463, + 0.299 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.086, + 0.3, + 0.275, + 0.373 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.276, + 0.3, + 0.368, + 0.373 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.369, + 0.3, + 0.463, + 0.373 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.107, + 0.389, + 0.166, + 0.439 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.097, + 0.449, + 0.169, + 0.47 + ], + "angle": 0, + "content": "\"A house made of lego\"" + }, + { + "type": "image", + "bbox": [ + 0.199, + 0.389, + 0.261, + 0.439 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.191, + 0.449, + 0.264, + 0.47 + ], + "angle": 0, + "content": "\"A gingerbread house\"" + }, + { + "type": "image", + "bbox": [ + 0.295, + 0.389, + 0.356, + 0.439 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.298, + 0.449, + 0.345, + 0.47 + ], + "angle": 0, + "content": "\"A gothic house\"" + }, + { + "type": "image", + "bbox": [ + 0.388, + 0.389, + 0.451, + 0.439 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.38, + 0.449, + 0.452, + 0.47 + ], + "angle": 0, + "content": "\"A house made of candy\"" + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.482, + 0.47, + 0.51 + ], + "angle": 0, + "content": "Figure 10. Sketch-Shape results, conditioned on a low-poly house shape. Our RGB Refinement was applied to improve detail quality." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.537, + 0.47, + 0.582 + ], + "angle": 0, + "content": "We also exhibit in Figure 14 the effectiveness of shape-guidance, by showing results of the same prompts with and without the shape loss." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.591, + 0.303, + 0.606 + ], + "angle": 0, + "content": "4.3. Latent-Paint Generation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.614, + 0.469, + 0.78 + ], + "angle": 0, + "content": "We tested Latent-Paint on a variety of input shapes shown in Figs. 12 and 13. As all of the shapes in these figures do not contain precomputed UV parameterization, we use XAtlas [52] to compute such parameterization automatically. In contrast, the fish mesh in Figure 15 (obtained from [13]) already contains high quality UV parameterization, which we are also able work with. Figure 13 compares our Latent-Paint approach to two closely related methods, Tango [9] and CLIPMesh [26]. As can be seen, our approach achieves more precise textures thanks to the guidance from the diffusion model." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Note that Latent-Paint can work without assuming or computing any UV-map by simply optimizing per-face latent attributes. Yet, we found it better to use a UV-map for two main reasons: (i) The UV map makes the texture granularity independent of the geometric resolution, i.e., coarse geometries do not imply course colorization; and (ii) texture maps are easier to use with downstream applications like MeshLab [11] and Blender [12]." + }, + { + "type": "image", + "bbox": [ + 0.533, + 0.103, + 0.578, + 0.15 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.602, + 0.09, + 0.695, + 0.163 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.696, + 0.09, + 0.788, + 0.163 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.79, + 0.09, + 0.887, + 0.163 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.531, + 0.184, + 0.579, + 0.234 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.602, + 0.165, + 0.695, + 0.245 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.696, + 0.165, + 0.799, + 0.246 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.799, + 0.165, + 0.885, + 0.246 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.53, + 0.269, + 0.579, + 0.32 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.602, + 0.25, + 0.695, + 0.332 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.696, + 0.25, + 0.789, + 0.332 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.79, + 0.25, + 0.887, + 0.332 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.529, + 0.366, + 0.581, + 0.394 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.602, + 0.344, + 0.696, + 0.417 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.696, + 0.344, + 0.789, + 0.417 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.79, + 0.344, + 0.887, + 0.417 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.676, + 0.419, + 0.812, + 0.43 + ], + "angle": 0, + "content": "a sports car, highly detailed" + }, + { + "type": "image_caption", + "bbox": [ + 0.542, + 0.441, + 0.849, + 0.456 + ], + "angle": 0, + "content": "Figure 11. Additional Sketch-Shape-guided results." + }, + { + "type": "image_caption", + "bbox": [ + 0.683, + 0.467, + 0.711, + 0.477 + ], + "angle": 0, + "content": "Input" + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.497, + 0.597, + 0.571 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.601, + 0.514, + 0.735, + 0.572 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.738, + 0.496, + 0.832, + 0.572 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.843, + 0.477, + 0.903, + 0.572 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.595, + 0.597, + 0.669 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.601, + 0.613, + 0.736, + 0.668 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.738, + 0.591, + 0.832, + 0.669 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.842, + 0.573, + 0.903, + 0.67 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.832, + 0.671, + 0.914, + 0.691 + ], + "angle": 0, + "content": "\"A garden gnome with a red hat\"" + }, + { + "type": "image_caption", + "bbox": [ + 0.517, + 0.671, + 0.59, + 0.691 + ], + "angle": 0, + "content": "\"A wooden brown cabinet\"" + }, + { + "type": "image_caption", + "bbox": [ + 0.601, + 0.671, + 0.696, + 0.691 + ], + "angle": 0, + "content": "\"A next gen nascar\"" + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.713, + 0.598, + 0.786 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.533, + 0.789, + 0.574, + 0.808 + ], + "angle": 0, + "content": "\"A steel cabinet\"" + }, + { + "type": "image", + "bbox": [ + 0.601, + 0.731, + 0.736, + 0.787 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.641, + 0.789, + 0.698, + 0.808 + ], + "angle": 0, + "content": "\"A next gen nascar\"" + }, + { + "type": "image", + "bbox": [ + 0.738, + 0.71, + 0.832, + 0.787 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.754, + 0.789, + 0.815, + 0.808 + ], + "angle": 0, + "content": "\"A pink grand piano\"" + }, + { + "type": "image", + "bbox": [ + 0.843, + 0.691, + 0.903, + 0.787 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.832, + 0.789, + 0.914, + 0.809 + ], + "angle": 0, + "content": "\"A garden gnome with a green hat\"" + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.814, + 0.892, + 0.868 + ], + "angle": 0, + "content": "Figure 12. Latent-Paint results on shapes from ModelNet40 [48]. UV parameterization was not given for any of the meshes in this figure. For the Nascar shapes, the same text prompt was used with a different initialization." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.95, + 0.519, + 0.962 + ], + "angle": 0, + "content": "12669" + } + ], + [ + { + "type": "aside_text", + "bbox": [ + 0.078, + 0.09, + 0.096, + 0.289 + ], + "angle": 270, + "content": "Latent-Paint (Ours) CLIPMesh [26] Tango [9]" + }, + { + "type": "image", + "bbox": [ + 0.108, + 0.089, + 0.462, + 0.312 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.313, + 0.47, + 0.356 + ], + "angle": 0, + "content": "Figure 13. Generating different shoe textures over the same input mesh by only changing the conditioning text prompt. The surface parameterization was computed using XAtlas [52]." + }, + { + "type": "text", + "bbox": [ + 0.104, + 0.367, + 0.439, + 0.378 + ], + "angle": 0, + "content": "Shape guidance No shape guidance Shape guidance No shape guidance" + }, + { + "type": "image", + "bbox": [ + 0.103, + 0.378, + 0.434, + 0.452 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.457, + 0.469, + 0.485 + ], + "angle": 0, + "content": "Figure 14. Results for the same prompts with and without shape-guidance. The guiding shapes are the same as in Figure 11." + }, + { + "type": "image", + "bbox": [ + 0.104, + 0.5, + 0.446, + 0.589 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.597, + 0.47, + 0.639 + ], + "angle": 0, + "content": "Figure 15. Latent-Paint results for an input mesh containing precomputed UV parameterization. Model courtesy of \"Keenan's 3D Model Repository\" [13]." + }, + { + "type": "image", + "bbox": [ + 0.123, + 0.653, + 0.422, + 0.758 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.142, + 0.759, + 0.402, + 0.77 + ], + "angle": 0, + "content": "Stable Diffusion with \"A photo of a squirrel, backview\"" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.773, + 0.47, + 0.829 + ], + "angle": 0, + "content": "Figure 16. note that the generated squirrel in the first row contains two faces from some view directions; see the second to the left view. This problem may be attributed to the fact that Stable Diffusion fails to generate back views of a squirrel; see bottom row." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.854, + 0.199, + 0.869 + ], + "angle": 0, + "content": "5. Limitations" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Our presented technique is yet a preliminary step towards the challenging goal of a comprehensive text-to-" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.08, + 0.9, + 0.216 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.221, + 0.892, + 0.264 + ], + "angle": 0, + "content": "Figure 17. Sketch-Shape ablation over \\(\\sigma_S\\) values (Eq. (4)) and input shape from Figure 9. As \\(\\sigma_S\\) grows, the constraint becomes more lenient, and enables the shape to evolve into new geometries." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.278, + 0.893, + 0.474 + ], + "angle": 0, + "content": "shape model that uses no 3D supervision. Still, the proposed latent framework has its limitations. To attain a plausible 3D shape, we use the same \"prompt tweaking\" used by DreamFusion [35], i.e., adding a directional text-prompt (e.g., \"front\", \"side\" with respect to the camera) to the input text prompt. We find that this assistance tends to fail with our approach when applied to certain objects. Moreover, we find that even Stable Diffusion tends to generate unsatisfactory images when specifying the desired direction as shown in Figure 16. Additionally, similar to most works that employ diffusion models, there is a stochastic behavior to the results, such that the quality of the results may significantly vary between different seeds." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.489, + 0.627, + 0.505 + ], + "angle": 0, + "content": "6. Conclusions" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.509, + 0.892, + 0.69 + ], + "angle": 0, + "content": "In this work, we introduced a latent framework for generating 3D shapes and textures using different forms of text and shape guidance. We first adapted the score distillation loss for LDMs, enabling the use of recent, powerful and publicly available text-to-image generation models for 3D shape generation. Successfully applying score distillation on LDMs results in a fast and flexible object generation framework. We then introduced shape-guided control on the generated model. We showed two versions of shape-guided generation, Sketch-Shape and Latent-Paint, and demonstrated their effectiveness for providing additional control over the generation process." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.692, + 0.893, + 0.844 + ], + "angle": 0, + "content": "Typically, the notion of rendering refers to generating an image in pixel space. Here, we have presented a method that renders directly into the latent space of a neural model. We believe that our Latent-NeRF approach opens the avenue for more latent space rendering methods, which can gain from a compact and effective latent representation, and advance the use of neural models that operate in latent space rather than pixel space. Furthermore, our novel approach and its ease-of-use nature would encourage further research toward effective text-guided shape generation." + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.863, + 0.892, + 0.9 + ], + "angle": 0, + "content": "This work was supported by the European research council (ERC-StG 757497 PI Giryes), and the Israel Science Foundation (grants no. 2492/20 and 3441/21)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.95, + 0.519, + 0.962 + ], + "angle": 0, + "content": "12670" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.156 + ], + "angle": 0, + "content": "[1] Omri Avrahami, Ohad Fried, and Dani Lischinski. 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Our three text-guided models: a purely text-guided Latent-NeRF, Latent-NeRF with Sketch-Shape guidance for more exact control over the generated shape, and Latent-Paint for texture generation for explicit shapes. The top row represents the models' inputs. + +![](images/4ee5ec5387257e297b6608988bd34911e265cbc8efcc3930949cbf1433af89b4.jpg) +"A highly detailed sandcastle" + +![](images/f201577e4e8eb335b3a878330e2c02e940b18c640083202ecd293e4eb6661442.jpg) +"A German Shepherd" + +![](images/e86384fee109f93aadc20626162dcb8830cdc3b547b87e2618c0edc2c9288f0a.jpg) +Sketch-Shape + +![](images/8b8403b65ae0fa691d2ec5a296751e835367ed85790ab10ee4e41e07306c66a6.jpg) +"A fish with leopard spots" + +![](images/87f5dd570c242d767f9c2da81c6d4e9d8b4a9005fcd7e0a5fd6567f5302fdc2f.jpg) +Latent-Paint + +# Abstract + +Text-guided image generation has progressed rapidly in recent years, inspiring major breakthroughs in text-guided shape generation. Recently, it has been shown that using score distillation, one can successfully text-guide a NeRF model to generate a 3D object. We adapt the score distillation to the publicly available, and computationally efficient, Latent Diffusion Models, which apply the entire diffusion process in a compact latent space of a pretrained autoencoder. As NeRFs operate in image space, a naive solution for guiding them with latent score distillation would require encoding to the latent space at each guidance step. Instead, we propose to bring the NeRF to the latent space, resulting in a Latent-NeRF. Analyzing our Latent-NeRF, we show that while Text-to-3D models can generate impressive results, they are inherently unconstrained and may lack the ability to guide or enforce a specific 3D structure. To assist and direct the 3D generation, we propose to guide our Latent-NeRF using a Sketch-Shape: an abstract geometry that defines the coarse structure of the desired object. Then, we present means to integrate such a constraint directly into a Latent-NeRF. This unique combination of text and shape guidance allows for increased control over the generation process. We also show that latent score distillation can be successfully applied directly on 3D meshes. This allows for generating high-quality textures on a given geometry. Our experiments validate the power of our different forms of guidance and the efficiency of using latent rendering. + +# 1. Introduction + +Text-guided image generation has seen tremendous success in recent years, primarily due to the breathtaking development in Language-Image models [25, 28, 36] and diffusion models [14, 21, 37-40]. These breakthroughs have also resulted in fast progression for text-guided shape generation [9, 29, 53]. Most recently, it has been shown [35] that one can directly use score distillation from a 2D diffusion model to guide the generation of a 3D object represented as a Neural Radiance Field (NeRF) [30]. + +While Text-to-3D can generate impressive results, it is inherently unconstrained and may lack the ability to guide or enforce a 3D structure. In this paper, we show how to introduce shape-guidance to the generation process to guide it toward a specific shape, thus allowing increased control over the generation process. Our method builds upon two models, a NeRF model [30], and a Latent Diffusion Model (LDM) [39]. Latent Models, which apply the entire diffusion process in a compact latent space, have recently gained popularity due to their efficiency and publicly available pretrained checkpoints. As score distillation was previously applied only on RGB diffusion models, we first present two key modifications to the NeRF model that are better paired with guidance from a latent model. First, instead of representing our NeRF in the standard RGB space, we propose a Latent-NeRF which operates directly in the latent space of the LDM, thus avoiding the burden of encoding a rendered RGB image to a latent space for each and every guid + +ing step. Secondly, we show that after training, one can easily transform a Latent-NeRF back into a regular NeRF. This allows further refinement in RGB space, where we can also introduce shading constraints or apply further guidance from RGB diffusion models [40]. This is achieved by introducing a learnable linear layer that can be optionally added to a trained Latent-NeRF, where the linear layer is initialized using an approximate mapping between the latent and RGB values [45]. + +Our first form of shape-guidance is applied using a coarse 3D model, which we call a Sketch-Shape. Given a Sketch-Shape, we apply soft constraint during the NeRF optimization process to guide its occupancy based on the given shape. Easily combined with Latent-NeRF optimization, the additional constraint can be tuned to meet a desired level of strictness. Using a Sketch-Shape allows users to define their base geometry, where Latent-NeRF then refines the shape and introduces texture based on a guiding prompt. + +We further present Latent-Paint, another form of shape-guidance where the generation process is applied directly on a given 3D mesh, and we have not only the structure but also the exact parameterization of the input mesh. This is achieved by representing a texture map in the latent space and propagating the guidance gradients directly to the texture map through the rendered mesh. By doing so, we allow for the first time to colorize a mesh using guidance from a pretrained diffusion model and enjoy its expressiveness. + +We evaluate our different forms of guidance under a variety of scenarios and show that together with our latent-based guidance, they offer a compelling solution for constrained shape and texture generation. + +# 2. Related Work + +3D Shape Generation 3D shape synthesis is a longstanding problem in computer graphics and computer vision. In recent years, with the emergence of neural networks, the research in 3D modeling has immensely advanced. The most conventional supervision type is applied directly with 3D shapes, through different representations such as implicit functions [10, 20, 33], meshes [19, 50] or point clouds [27, 49]. As 3D supervision is often difficult to obtain, other works use images to guide the generative task [6, 7, 32]. In fact, even when 3D data is available, 2D renderings are sometimes chosen as the supervising primitive [5, 8, 18]. For example, in GET3D [18], two generators are trained, one generates a 3D SDF, and the other a texture field. The output textured mesh is then obtained in a differentiable manner by utilizing DMTet [42]. These generators are adversarially trained with a dataset of 2D images. In [47] a diffusion model has been used to generate multiple views of a given input image. Yet, it has been trained in a supervised manner on a multi-view dataset, unlike our work which does not require a dataset. + +Text-to-3D with 2D Supervision. Recently, the success of text-guided synthesis in numerous domains [1,2,17,34, 44], has motivated a surge of works that use Language-Image models to guide 3D scenes representations. CLIP-Forge [41] consists of two separate components, an implicit autoencoder conditioned on shape codes, and a normalizing flow model that is trained to generate shape codes according to CLIP embeddings. CLIP-Forge exploits the fact that CLIP has a joint text-image embedding space to train on image embeddings and infer on text embeddings, achieving text-to-shape capabilities. Text2Mesh [29] introduced mesh colorization and geometric fine-tuning by optimizing an initial mesh through differential rendering and CLIP [36] guidance. TANGO [9] follows a similar optimization scheme, while improving results by considering an explicit shading model. CLIP-Mesh [26] optimizes an initial spherical mesh according to a target text prompt, using a modified CLIP loss that accounts for the gap and ambiguity between image/text CLIP embeddings. Similarly to our method, they also use UV texture mapping to bake colors into the mesh. DreamFields [24] employs CLIP guidance as well, but uses NeRFs to represent the 3D object instead of an explicit triangular mesh, together with a dedicated sparsity loss. CLIPNeRF [46] pretrains a disentangled NeRF representation network on rendered object datasets, which is then used to constraint a NeRF scene optimization under CLIP loss, between random renderings of the NeRF and target image or text CLIP embedding. DreamFusion [35] introduced, for the first time, the use of largely successful pretrained 2D diffusion models for text-guided 3D object generation. DreamFusion uses a proprietary 2D diffusion model [40] to supervise the generation of 3D objects represented by NeRFs. To guide a NeRF scene using the pretrained diffusion model, the authors derive a Score-Distillation loss, see Section 3.1 for more details. + +Neural Rendering The recent rapid progression of neural networks has immensely advanced the performance of differential renderers. Particularly NeRF [4, 30, 31] have shown astounding performance on novel view generation and relighting, also extending to other applications like 3D reconstruction [51]. Thanks to their differentiable nature, it has been recently shown that one can introduce different neural objectives during training to guide the 3D modeling. + +# 3. Method + +Here we present our shape-guidance solution. We describe the Latent-NeRF framework, presented in Figure 2, and then introduce different guidance controls that can be combined with Latent-NeRF for controlling its generation. Yet, before showing our solution, we provide a quick overview of two recently proposed techniques that are highly relevant to our method. + +# 3.1. Preliminaries + +A latent diffusion model (LDM) [39] is a specific form of a diffusion model that is trained to denoise latent codes of a pretrained autoencoder, instead of the high-resolution images directly. First, an autoencoder composed of an encoder $\mathcal{E}$ , and a decoder $\mathcal{D}$ is trained to reconstruct natural images $x \sim X$ , where $X$ is the image training dataset, in the following form: $\tilde{x} = \mathcal{D}(\mathcal{E}(x))$ . The autoencoder is trained with a reconstruction loss, perceptual loss [54] and a patch-based adversarial loss [22]. Then, given the trained autoencoder, a denoising diffusion probabilistic model (DDPM) [21] is trained to generate a spatial latent $z$ from noise, according to the distribution $z = \mathcal{E}(x)$ s.t. $x \sim X$ . In order to generate a novel image, a latent $\tilde{z}$ is sampled from this learned distribution, using the trained DDPM, and passed to the decoder to obtain the final image $\mathcal{D}(\tilde{z})$ . Operating in the latent space requires less compute, and leads to faster training and sampling, which makes LDM widely popular. In fact, the recent Stable Diffusion model is also an LDM. + +Score Distillation is a method that enables using a diffusion model as a critic, i.e., using it as a loss without explicitly back-propagating through the diffusion process. It has been introduced in DreamFusion [35] for guiding 3D generation using the Imagen model [40]. To perform score distillation, noise is first added to a given image (e.g., one view of the NeRF's output). Then, the diffusion model is used to predict the added noise from the noised image. Finally, the difference between the predicted and added noises is used for calculating per-pixel gradients. For NeRF, the gradients are back-propagated for updating the 3D NeRF model. + +Going into more detail, at each iteration of the score distillation optimization, a rendered image $x$ is noised to a randomly drawn time step $t$ , + +$$ +x _ {t} = \sqrt {\bar {\alpha} _ {t}} x + \sqrt {1 - \bar {\alpha} _ {t}} \epsilon , \tag {1} +$$ + +where $\epsilon \sim \mathcal{N}(0,I)$ , and $\bar{\alpha}_t$ is a time-dependent constant specified by the diffusion model. Then, the per-pixel score distillation gradients are taken to be + +$$ +\nabla_ {x} L _ {S D S} = w (t) \left(\epsilon_ {\phi} \left(x _ {t}, t, T\right) - \epsilon\right), \tag {2} +$$ + +where $\epsilon_{\phi}$ is the diffusion model's denoiser (which approximates the noise to be removed), $\phi$ are the denoiser's parameters, $T$ is an optional guiding text prompt, and $w(t)$ is a constant multiplier that depends on $\alpha_{t}$ . During training, gradients are propagated from the pixel gradients to the NeRF parameters and gradually change the 3D object. Please refer to [35] for the complete details and derivation of Score Distillation. Note that DreamFusion uses the proprietary Imagen [40] model that is very computationally demanding. We rely on the publicly available Stable Diffusion model and the re-implementation of DreamFusion [43] (it operates in the RGB space and not the latent as we propose). + +![](images/5a25ffcac610385e6ecd95b08abd3d952c559ca9cddad6c023e5e358d2fdfecc.jpg) +Figure 2. An overview of Latent-NeRF trained with a similar score distillation scheme as proposed by [35]. At each training iteration we render the scene from a random view point to produce a feature map $z$ . Then, $z$ is noised with $\epsilon$ according to a random diffusion step $t$ . The noised version of $z$ , i.e., $x_{t}$ , is denoised using Stable Diffusion [39], with the input text prompt. Finally, the input noise is subtracted from the predicted noise by Stable Diffusion, to approximate per-pixel gradients that are back propagated to the NeRF representation. + +# 3.2. Latent-NeRF + +We now turn to describe our Latent-NeRF approach. In this method, a NeRF model is optimized to render 2D feature maps in Stable Diffusion's latent space $\mathcal{Z}$ . Latent-NeRF outputs four pseudo-color channels, $(c_{1}, c_{2}, c_{3}, c_{4})$ , corresponding to the four latent features that stable diffusion operates over, and a volume density $\sigma$ . Figure 2 illustrates this process. Representing the scene using NeRF implicitly imposes spatial consistency between different views, due to the spatial radiance field and rendering equation. Still, the fact that $\mathcal{Z}$ can be represented by a NeRF with spatial consistencies is non-trivial. Previous works [1, 45] showed that super-pixels in $\mathcal{Z}$ depend mainly on individual patches in the output image. This can be attributed to the high resolution $(64 \times 64)$ and low channel-wise depth (4) of this latent space, which encourages local dependency over the autoencoder's image and latent spaces. Assuming $\mathcal{Z}$ is a near patch level representation of its corresponding RGB image makes the latents nearly equivariant to spatial transformations of the scene, which justifies the use of NeRFs for representing the 3D scenes. + +Text Guidance The vanilla form of Latent-NeRF is text-guided, with no other constraints for the scene generation. In this setting, we employ the following loss: + +$$ +L = \lambda_ {S D S} L _ {S D S} + \lambda_ {s p a r s e} L _ {s p a r s e}, +$$ + +where $L_{SDS}$ is the Score-Distillation loss depicted in Figure 2. Note, that the exact value of this loss is not accessible. Instead, the gradients implied by it are approximated + +![](images/4caa0b131ba1db558e4050511f712acacae2d68250365d90fc7c433c52226a9d.jpg) +Figure 3. To perform fine-tuning in RGB, we take a Latent-NeRF model that was trained in latent space (conventional setting), apply the matrix adapter to the channel output of the model to get an RGB preview, and then continue optimizing the MLP's weights through supervision in RGB to improve the result. + +by a single forward pass through the denoiser. These gradients are directly passed to the autograd solver. The loss $L_{sparse} = BE(w_{blend})$ suggested in [43] prevents floating "radiance clouds" by penalizing the binary entropy of ill-defined background masks $w_{blend}$ . Namely, it encourages a strict blending of the object NeRF and background NeRF. + +RGB Refinement Using Latent-NeRF, one may successfully learn to represent 3D scenes even when optimizing solely in latent space. Still, in some cases, it could be beneficial to further refine the model by fine-tuning it in pixel space, and have the NeRF model operate directly in RGB. To do so, we must convert the NeRF that was trained in latent space to a NeRF that operates in RGB. This requires converting the MLP's output from the four latent channels to three RGB channels such that the initial rendered RGB image is close to the decoder output, when applied to the rendered latent of the original model. Interestingly, it has been shown [45] that a linear approximation is sufficient to predict plausible RGB colors given a single four-channel latent super pixel, via the following transformation + +$$ +\left( \begin{array}{c} \hat {r} \\ \hat {g} \\ \hat {b} \end{array} \right) = \left( \begin{array}{c c c c} 0. 2 9 8 & 0. 1 8 7 & - 0. 1 5 8 & - 0. 1 8 4 \\ 0. 2 0 7 & 0. 2 8 6 & 0. 1 8 9 & - 0. 2 7 1 \\ 0. 2 0 8 & 0. 1 7 3 & 0. 2 6 4 & - 0. 4 7 3 \end{array} \right) \left( \begin{array}{c} c _ {1} \\ c _ {2} \\ c _ {3} \\ c _ {4} \end{array} \right), \tag {3} +$$ + +which was calculated using pairs of RGB images and their corresponding latent codes over a collection of natural images. As our NeRF model is already composed of a set of fully connected layers, we simply add another linear layer that is initialized using the weights in Equation 3. This converts our Latent-NeRF to operate in pixel space and ensures that our refinement process starts from a valid result. The additional layer is then fine-tuned together with the rest of the model, to create the refined and final output. The overall fine-tuning procedure is illustrated in Figure 3. + +# 3.3. Sketch-Shape Guidance + +Next, we introduce a novel technique for guiding the Latent-NeRF generation based on a coarse geometry, which we call a Sketch-Shape. + +A Sketch-Shape is an abstract coarse alignment of simple 3D primitives like spheres, boxes, cylinders, etc., that together depict an outline of a more complex object. Figures 9, 10, 11 illustrate such simple shapes. Ideally, we would like the output density of our MLP to match that of the Sketch-Shape, such that the output Latent-NeRF result resembles the input shape. Nevertheless, we would also like the new NeRF to have the capacity to create new details and geometries that match the input text prompt and improve the fidelity of the shape. To achieve this lenient constraint, we encourage the NeRF's occupancy to match the winding-number [3, 23] indicator of the Sketch-Shape, but with decaying importance near the surface to allow new geometries. This loss reads as + +$$ +L _ {\text {S k e t c h - S h a p e}} = C E \left(\alpha_ {N e R F} (p), \alpha_ {G T} (p)\right) \cdot \left(1 - e ^ {- \frac {d ^ {2}}{2 \sigma_ {S}}}\right). \tag {4} +$$ + +This loss implies that the occupancy should be well constrained away from the surface, and free to be set by score distillation near the surface. This loss is applied in addition to the Latent-NeRF loss, over the entire point set $p$ that is used by the NeRF's volumetric rendering. $d$ represents the distance of $p$ from the surface, and $\sigma_{S}$ is a hyperparameter that controls how lenient the loss is, i.e., lower $\sigma_{S}$ values imply a tighter constraint to the input Sketch-Shape. Applying the loss only on the sampled point-set $p$ , makes it more efficient as these points are already evaluated as part + +![](images/2533b47fcca42c5ffb10524cd128da90b16a97d859bb15063f6e6f592c75fb6f.jpg) +Figure 4. An overview of Latent-Paint texture generation, trained with a similar score distillation loss [35]. The object is represented as a textured mesh, with a latent texture image that has four pseudo-color channels. At each iteration, the mesh is rendered with a differential renderer, to create a feature map from a random viewpoint. Score distillation is applied to the rendered feature map, and the gradients back-propagate to the latent texture image through the differential renderer. See Section 3.4. + +of the Latent-NeRF rendering process. + +# 3.4. Latent-Paint of Explicit Shapes + +We now move to a more strict constraint, where the guidance is based on an exact structure of a given shape, e.g., provided in the form of a mesh. We call this approach Latent-Paint, which leads to the generation of novel textures for a given shape. Our method generates texture over a UV texture map, which can either be supplied by the input mesh, or calculated on-the-fly using XAtlas [52]. To color a mesh, we first initialize a random latent texture image of size $H \times W \times 4$ , where $H$ and $W$ can be chosen according to the desired texture granularity. We set them both to be 128 in our experiments. + +Figure 4 presents the training process. At each score distillation iteration, we render the mesh with a differentiable renderer [15] to obtain a $64 \times 64 \times 4$ feature map that is pseudo-colored by the latent texture image. Then, we apply the score distillation loss from Equation 2 in the same way it is applied for Latent-NeRF. Yet, instead of backpropagating the loss to the NeRF's MLP parameters, we optimize the deep texture image by back-propagating through the differentiable renderer. To get the final RGB texture image, we simply pass the latent texture image through Stable Diffusion's decoder $\mathcal{D}$ once, to get a larger high-quality RGB texture. + +# 4. Evaluation + +We now validate the effectiveness of our different forms of guidance through a variety of experiments. + +Implementation Details We use the Stable Diffusion implementation by HuggingFace Diffusers, with the v1-4 checkpoint. For score distillation, we use the code-base provided by [43], with Instant-NGP [31] as our NeRF model. + +![](images/38623be138dfd9d1197e05290df3d245cf020711eeb64585d68f45c7ea30251d.jpg) +Figure 5. Latent-NeRF results from different viewpoints. + +![](images/e9b384a95deee28996d433a0a3aa5666551af66cb8203e1a709087698fe1a883.jpg) +Figure 6. Qualitative comparison with other text-to-3D methods. + +Latent-NeRF usually takes less than 15 minutes to converge on a single V100, while using an RGB-NeRF with Stable Diffusion [43] takes about 30 minutes, due to the increased overhead from encoding into the latent space. Note that DreamFusion [35] takes about 1.5 hours on 4 TPUs. This clearly shows the computational advantage of Latent-NeRF. + +# 4.1. Text-Guided Generation + +Qualitative Results We begin by demonstrating the effectiveness of the latent rendering approach with Latent-NeRF. In Figs. 1, 5 and 7, we show several results obtained by our method. In the supplementary material we provide additional results of different objects, including video visualizations. In Figure 5, we show the consistency of our learned shapes from several viewpoints. Next, we use the baseline set by DreamFusion [35] to qualitatively compare our approach (with the proposed RGB refinement) against other methods. As can be seen in Figure 6, Latent-NeRF achieves significantly better results than DreamFields [24] and CLIPMesh [26]. We believe that the better quality of DreamFusion can be attributed to the high quality of Ima + +![](images/13eaf8616d0a3ab9a3d8ca93641c943c80b2c7570197361488646054ee96f869.jpg) +Figure 7. RGB refinement combined with (i) Latent-NeRF (icecream and temple), and (ii) Sketch-Shape (lego and car). For each shape we also show the normals direction. + +gen [40], but unfortunately, we cannot validate this as the model is not publicly available to the community. + +RGB Refinement Figure 7 shows the quality improvement achieved by our RGB refinement method. It reveals that RGB refinement is mostly useful for complex objects or for regions with detailed textures. Refinement iterations in the RGB space are about $\times 2$ slower than iterations in latent space, thus, increasing the runtime to more than 30 minutes. Thanks to our linear mapping from a Latent-NeRF to an RGB-NeRF, practitioners may apply the refinement method only after the 3D shape has already converged with the more efficient latent training. This allows a fast exploration of 3D shapes, and an optional polishing step with RGB refinement. + +Textual-Inversion As our Latent-NeRF is supervised by Stable-Diffusion, we can also use Textual Inversion [16] tokens as part of the input text prompt. This allows conditioning the object generation on specific objects and styles, defined only by input images. Results using Textual Inversion are presented in Figure 8. + +# 4.2. Sketch-Shape Guidance + +Figure 9 shows different Sketch-Shape results with the same conditioning mesh. The different text prompts are able to guide the shape toward refined geometries that better match the text prompt. The rough Sketch-Shape in this + +![](images/60ce59e8125f6d1b622168d0b03acacdcb5da433d68054fecd71dd6a539ece5f.jpg) +Figure 8. Results of Latent-NeRF using a token learned from the images on the left with Textual Inversion [16]. + +![](images/967f6d9baca7295a594032363cc2b94b4d5cea3da9a67e27ec81931181afc618.jpg) +Figure 9. Sketch-Shape results using different prompts. This examples shows how the same Sketch-Shape can influence different objects according to different text prompts. + +figure, was quickly designed in Blender [12] and allows us to easily define a coarse shape that guides the Latent-NeRF. Moreover, Figure 17 depicts an ablation over the lenient parameter $\sigma_{S}$ from Eq. (4). When $\sigma_{S}$ is set to 0.05, the generated mesh takes the form of the conditioning shape (shown in Figure 9). As $\sigma_{S}$ grows, more details are added on top of the base shape, until little to no resemblance is observed at $\sigma_{S} = 1.5$ . Figure 10 contains additional results of different shapes generated with the same conditioning mesh, here a coarse house shape. The normals visualization (bottom row) shows that our method can add fine geometric details. + +Figure 11 demonstrates that our proposed approach can successfully work with a variety of different Sketch-Shapes. Notice that our method handles a variety of different shapes and also works well with shapes extruded from 2D sketches. + +![](images/fde7a84b93c2a3a1942725a86885f653671988f5e221a6277ac40009dc6fd58b.jpg) + +![](images/a5a0f38be39665d7235a9e1578117339ca0f00781a142a4c5ff7888c8542aea5.jpg) +Input + +![](images/0d36679c28bbfe647820181231e6fa6e684e16907f676f0a8e225abc3f11553d.jpg) + +![](images/ec08daf7d12f1fb4682f8ebeea280fd975e41fbf36a8451c381e48da003137d5.jpg) + +![](images/e8c584bef623d03e63817d87094c5d0a1882fa4caa9809135dc8896d1497dd42.jpg) + +![](images/17d8b1ce0269551e37d5eac95ad19c449c9202be69f85ce280acc3a5269f892f.jpg) + +![](images/e066b57a8c77a296dfdde2007e026534120c7dfdbf8d6f4b76b57474a974a77b.jpg) + +![](images/6e6aef0f7e73065e79d37137ce7e30eae41d9fca8afb08564198805db6bf36cd.jpg) + +![](images/51c15bf41b347a49ee1f33bcd1c5ea5d31954bbb344616fd243afdd7ddcd3c7a.jpg) + +![](images/04de86f92ecac34a7ce71900b4bb3a9f9ad67929d6b9186dac94c0c4bc223dcb.jpg) + +![](images/a4cf16b5ea802a77d760e0f3caa4e3ae0fd6379768ab4a30acd1a9bed1d59623.jpg) +"A house made of lego" + +![](images/dd65cec776e1fddcd06f68544bbb8b6f7057a09cdb58d255bd281f8e5386fac8.jpg) +"A gingerbread house" + +![](images/9d2f47dd75e50a7f06fea1e371b2d37096e6840b4902848699be652e77e9925d.jpg) +"A gothic house" + +![](images/b9c2c604f0f26f71cb18ac278a02a219c99c623b7f39432a5dd48a30311d1871.jpg) +"A house made of candy" + +We also exhibit in Figure 14 the effectiveness of shape-guidance, by showing results of the same prompts with and without the shape loss. + +# 4.3. Latent-Paint Generation + +We tested Latent-Paint on a variety of input shapes shown in Figs. 12 and 13. As all of the shapes in these figures do not contain precomputed UV parameterization, we use XAtlas [52] to compute such parameterization automatically. In contrast, the fish mesh in Figure 15 (obtained from [13]) already contains high quality UV parameterization, which we are also able work with. Figure 13 compares our Latent-Paint approach to two closely related methods, Tango [9] and CLIPMesh [26]. As can be seen, our approach achieves more precise textures thanks to the guidance from the diffusion model. + +Note that Latent-Paint can work without assuming or computing any UV-map by simply optimizing per-face latent attributes. Yet, we found it better to use a UV-map for two main reasons: (i) The UV map makes the texture granularity independent of the geometric resolution, i.e., coarse geometries do not imply course colorization; and (ii) texture maps are easier to use with downstream applications like MeshLab [11] and Blender [12]. + +![](images/cdf9480bc1764abdd05a51e7b802e2957232df22fba4a8ec6457de47c6ca6d4d.jpg) + +![](images/7841b82805f329575a70fef47698f0c4363b6adea8ac897f93dc63e42f51c580.jpg) + +![](images/d0d2cedd2f112c23ed7f01b3daa0f08760b4cb11d858d08249063a8a3fbf6f62.jpg) + +![](images/13f93880f39bdb37a290aaf5dd969f5639d46fab308bf19258c971689f1731a7.jpg) + +![](images/83d87fe07afa76c82a9a92c0182ab36727f8cec5735583a2f07e404624bf2e70.jpg) + +![](images/170510934e4187254d8ce5e4401d47b0756afac29b92e7325d3d609625b1e090.jpg) + +![](images/e001f7abe8de722ceb10868742dd7d1afc693313d3bba67b124ccec5954acacb.jpg) + +![](images/895be43ed85df7bced3048326b46a1a45dca9cb6bb809dee5a8cf47c1faab623.jpg) + +![](images/5196982ceb7c3e82e0775d7b7cde800dd0df1a926312e315c8863b71565ac252.jpg) + +![](images/cf8364fe15fc95cbf2106da0b585d4075791d0244b7bd730018f042b3b722179.jpg) + +![](images/54e5f28f30a919700710522a2926a9ed37df5fd70c1b8d9158257b0f04da6b12.jpg) + +![](images/0bd4fd29e8e00fd72221cc63cc7c24971ef2bc3632bfad3bb3051f18c66d369e.jpg) + +![](images/6e3cbbf67eaf4e1623f0eed1daae45fb23634a549cfa0b069774de146ffb98fe.jpg) +Figure 11. Additional Sketch-Shape-guided results. + +![](images/3c8c94628e040f505dcfd84de25b529d241f14c28ed7d5729865db5dd0989ee9.jpg) +a sports car, highly detailed + +![](images/a4d4c070d0e421b11d5df14b6fff216ce8c9d65839ec8d8f94fef14bb37e7ced.jpg) +Input + +![](images/8fc4c38edf99e4be4c4edb7c1ee3a1b6c7220ac0d20ddccacac0b68ccbe64301.jpg) + +![](images/cb4dce63a42695b7718a77a24eac8f1bcd80e5aef64c8b278f21147da7243a61.jpg) +Figure 10. Sketch-Shape results, conditioned on a low-poly house shape. Our RGB Refinement was applied to improve detail quality. + +![](images/00b39922a599e34f261a06f2df8d99cdea1bfe5b8c89bd725378813404de228e.jpg) + +![](images/85f9826b966c8572cb3984ba5878d726003705739205ff3c0d7572b31face365.jpg) + +![](images/be3bcf96f06493a88e2606a1cc8598dd1d46ae36cf25f147d5d4134c99af40d8.jpg) + +![](images/df16f9cdedc2f42068987ee93f546f0b058f2db844fc8e9072f60aa2d0ab168e.jpg) +"A wooden brown cabinet" + +![](images/a6c2daf77014007b940e6e1b4c8a7ae2df5972ec54e2482dad4cb31a85fea6ea.jpg) +"A next gen nascar" + +![](images/f60f1934cc8ed3620fe46aea1f24329fdd66fe55cda02fe2c30eaf4f3c1fcfb0.jpg) + +![](images/eef58d98d27669247bbe1d644c1468be0df63e437086b8729b5bf2624aed5418.jpg) + +![](images/2356a540d21d3dc49e38c318e078302232cad551d8087d2538eae7efdbcf87c3.jpg) +"A steel cabinet" + +![](images/6cc83234ce7b36d65c43ba1bb1f1de59484f542997fd397cf76e9ee070d084a2.jpg) +"A next gen nascar" + +![](images/2efa2b2127d505d3edb83b7fb69914aaf172125721c5417cfff74feb2cc549fc.jpg) +"A pink grand piano" +"A garden gnome with a green hat" + +![](images/56b2b68649ba006e662614387ad4f73f386530d27a5c770cd6389e4d7a0c3496.jpg) +"A garden gnome with a red hat" +Figure 12. Latent-Paint results on shapes from ModelNet40 [48]. UV parameterization was not given for any of the meshes in this figure. For the Nascar shapes, the same text prompt was used with a different initialization. + +![](images/f90f36bca5547ae78916192fd86c4af8082642d2270c8fcd3e857b3ceee65675.jpg) +Figure 13. Generating different shoe textures over the same input mesh by only changing the conditioning text prompt. The surface parameterization was computed using XAtlas [52]. + +Shape guidance No shape guidance Shape guidance No shape guidance + +![](images/76183cfc6131694a8d3b750c46c63a888f34794451aafc409e8b912b70db54e4.jpg) +Figure 14. Results for the same prompts with and without shape-guidance. The guiding shapes are the same as in Figure 11. + +![](images/7f80ef3ed24b765b6afb35c1d9b0edcc5c517efc94f436e5ba97669568487ab7.jpg) +Figure 15. Latent-Paint results for an input mesh containing precomputed UV parameterization. Model courtesy of "Keenan's 3D Model Repository" [13]. + +![](images/e5cd4e3166b7a7622b6c698a756ebd0dc59a85a6ce8bf22e339bf54ff97b1935.jpg) +Stable Diffusion with "A photo of a squirrel, backview" +Figure 16. note that the generated squirrel in the first row contains two faces from some view directions; see the second to the left view. This problem may be attributed to the fact that Stable Diffusion fails to generate back views of a squirrel; see bottom row. + +# 5. Limitations + +Our presented technique is yet a preliminary step towards the challenging goal of a comprehensive text-to- + +![](images/93628da91db22f9c849208a7218d97f37a50b94465baab670e881365b12fa542.jpg) +Figure 17. Sketch-Shape ablation over $\sigma_S$ values (Eq. (4)) and input shape from Figure 9. As $\sigma_S$ grows, the constraint becomes more lenient, and enables the shape to evolve into new geometries. + +shape model that uses no 3D supervision. Still, the proposed latent framework has its limitations. To attain a plausible 3D shape, we use the same "prompt tweaking" used by DreamFusion [35], i.e., adding a directional text-prompt (e.g., "front", "side" with respect to the camera) to the input text prompt. We find that this assistance tends to fail with our approach when applied to certain objects. Moreover, we find that even Stable Diffusion tends to generate unsatisfactory images when specifying the desired direction as shown in Figure 16. Additionally, similar to most works that employ diffusion models, there is a stochastic behavior to the results, such that the quality of the results may significantly vary between different seeds. + +# 6. Conclusions + +In this work, we introduced a latent framework for generating 3D shapes and textures using different forms of text and shape guidance. We first adapted the score distillation loss for LDMs, enabling the use of recent, powerful and publicly available text-to-image generation models for 3D shape generation. Successfully applying score distillation on LDMs results in a fast and flexible object generation framework. We then introduced shape-guided control on the generated model. We showed two versions of shape-guided generation, Sketch-Shape and Latent-Paint, and demonstrated their effectiveness for providing additional control over the generation process. + +Typically, the notion of rendering refers to generating an image in pixel space. Here, we have presented a method that renders directly into the latent space of a neural model. We believe that our Latent-NeRF approach opens the avenue for more latent space rendering methods, which can gain from a compact and effective latent representation, and advance the use of neural models that operate in latent space rather than pixel space. Furthermore, our novel approach and its ease-of-use nature would encourage further research toward effective text-guided shape generation. + +# References + +[1] Omri Avrahami, Ohad Fried, and Dani Lischinski. Blended latent diffusion. arXiv preprint arXiv:2206.02779, 2022. 2, 3 +[2] Omer Bar-Tal, Dolev Ofri-Amar, Rafail Fridman, Yoni Kasten, and Tali Dekel. Text2live: Text-driven layered image and video editing. arXiv preprint arXiv:2204.02491, 2022. 2 +[3] Gavin Barill, Neil G Dickson, Ryan Schmidt, David IW Levin, and Alec Jacobson. Fast winding numbers for soups and clouds. ACM Transactions on Graphics (TOG), 37(4):1-12, 2018. 4 +[4] Jonathan T Barron, Ben Mildenhall, Matthew Tancik, Peter Hedman, Ricardo Martin-Brualla, and Pratul P Srinivasan. Mip-nerf: A multiscale representation for anti-aliasing neural radiance fields. 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Hierarchical text-conditional image generation with clip latents. arXiv preprint arXiv:2204.06125, 2022. 1 +[38] Aditya Ramesh, Mikhail Pavlov, Gabriel Goh, Scott Gray, Chelsea Voss, Alec Radford, Mark Chen, and Ilya Sutskever. Zero-shot text-to-image generation. arXiv:2102.12092, 2021. 1 +[39] Robin Rombach, Andreas Blattmann, Dominik Lorenz, Patrick Esser, and Björn Ommer. High-resolution image synthesis with latent diffusion models, 2021. 1, 3 +[40] Chitwan Sahara, William Chan, Saurabh Saxena, Lala Li, Jay Whang, Emily Denton, Seyed Kamyar Seyed Ghasemipour, Burcu Karagol Ayan, S. Sara Mahdavi, + +Rapha Gontijo Lopes, Tim Salimans, Jonathan Ho, David J Fleet, and Mohammad Norouzi. Photorealistic text-to-image diffusion models with deep language understanding, 2022. 1, 2, 3, 6 +[41] Aditya Sanghi, Hang Chu, Joseph G Lambourne, Ye Wang, Chin-Yi Cheng, and Marco Fumero. Clip-forge: Towards zero-shot text-to-shape generation. arXiv preprint arXiv:2110.02624, 2021. 2 +[42] Tianchang Shen, Jun Gao, Kangxue Yin, Ming-Yu Liu, and Sanja Fidler. Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. In Advances in Neural Information Processing Systems (NeurIPS), 2021. 2 +[43] Jiaxiang Tang. A pytorch implementation of the text-to-3d model dreamfusion, powered by the stable diffusion text-to-2d model. https://github.com/ashawkey/stable-dreamfusion, 2022. 3, 4, 5 +[44] Guy Tevet, Brian Gordon, Amir Hertz, Amit H Bermano, and Daniel Cohen-Or. Motionclip: Exposing human motion generation to clip space. arXiv preprint arXiv:2203.08063, 2022. 2 +[45] Kevin Turner. Decoding latents to rgb without upscaling. https://discuss.huggingface.co/t/decoding-latents-t-orgb-without-upscaling/23204, 2022. 2, 3, 4 +[46] Can Wang, Menglei Chai, Mingming He, Dongdong Chen, and Jing Liao. Clip-nerf: Text-and-image driven manipulation of neural radiance fields. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 3835–3844, 2022. 2 +[47] Daniel Watson, William Chan, Ricardo Martin-Brualla, Jonathan Ho, Andrea Tagliasacchi, and Mohammad Norouzi. Novel view synthesis with diffusion models. arXiv:2210.04628, 2022. 2 +[48] Zhirong Wu, Shuran Song, Aditya Khosla, Fisher Yu, Linguuang Zhang, Xiaou Tang, and Jianxiong Xiao. 3d shapenets: A deep representation for volumetric shapes. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 1912-1920, 2015. 7 +[49] Guandao Yang, Xun Huang, Zekun Hao, Ming-Yu Liu, Serge Belongie, and Bharath Hariharan. Pointflow: 3d point cloud generation with continuous normalizing flows. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 4541-4550, 2019. 2 +[50] Jie Yang, Kaichun Mo, Yu-Kun Lai, Leonidas J Guibas, and Lin Gao. Dsg-net: Learning disentangled structure and geometry for 3d shape generation. ACM Transactions on Graphics (TOG), 2022. 2 +[51] Lior Yariv, Jiatao Gu, Yoni Kasten, and Yaron Lipman. Volume rendering of neural implicit surfaces. In Thirty-Fifth Conference on Neural Information Processing Systems, 2021. 2 +[52] Jonathan Young. Xatlas: Mesh parameterization / uv unwrapping library. https://github.com/jpcy/xatlas, 2022. 5, 7, 8 +[53] Xiaohui Zeng, Arash Vahdat, Francis Williams, Zan Gojcic, Or Litany, Sanja Fidler, and Karsten Kreis. Lion: Latent point diffusion models for 3d shape generation. arXiv preprint arXiv:2210.06978, 2022. 1 + +[54] Richard Zhang, Phillip Isola, Alexei A Efros, Eli Shechtman, and Oliver Wang. The unreasonable effectiveness of deep features as a perceptual metric. 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Recently, it has been shown that using score distillation, one can successfully text-guide a NeRF model to generate a 3D object. We adapt the score distillation to the publicly available, and computationally efficient, Latent Diffusion Models, which apply the entire diffusion process in a compact latent space of a pretrained autoencoder. As NeRFs operate in image space, a naive solution for guiding them with latent score distillation would require encoding to the latent space at each guidance step. Instead, we propose to bring the NeRF to the latent space, resulting in a Latent-NeRF. Analyzing our Latent-NeRF, we show that while Text-to-3D models can generate impressive results, they are inherently unconstrained and may lack the ability to guide or enforce a specific 3D structure. To assist and direct the 3D generation, we propose to guide our Latent-NeRF using a Sketch-Shape: an abstract geometry that defines the coarse structure of the desired object. Then, we present means to integrate such a constraint directly into a Latent-NeRF. This unique combination of text and shape guidance allows for increased control over the generation process. We also show that latent score distillation can be successfully applied directly on 3D meshes. This allows for generating high-quality textures on a given geometry. Our experiments validate the power of our different forms of guidance and the efficiency of using latent rendering." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 307, + 369, + 386, + 380 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 369, + 386, + 380 + ], + "spans": [ + { + "bbox": [ + 307, + 369, + 386, + 380 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 304, + 389, + 545, + 497 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 389, + 545, + 497 + ], + "spans": [ + { + "bbox": [ + 304, + 389, + 545, + 497 + ], + "type": "text", + "content": "Text-guided image generation has seen tremendous success in recent years, primarily due to the breathtaking development in Language-Image models [25, 28, 36] and diffusion models [14, 21, 37-40]. These breakthroughs have also resulted in fast progression for text-guided shape generation [9, 29, 53]. Most recently, it has been shown [35] that one can directly use score distillation from a 2D diffusion model to guide the generation of a 3D object represented as a Neural Radiance Field (NeRF) [30]." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 304, + 498, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 546, + 713 + ], + "type": "text", + "content": "While Text-to-3D can generate impressive results, it is inherently unconstrained and may lack the ability to guide or enforce a 3D structure. In this paper, we show how to introduce shape-guidance to the generation process to guide it toward a specific shape, thus allowing increased control over the generation process. Our method builds upon two models, a NeRF model [30], and a Latent Diffusion Model (LDM) [39]. Latent Models, which apply the entire diffusion process in a compact latent space, have recently gained popularity due to their efficiency and publicly available pretrained checkpoints. As score distillation was previously applied only on RGB diffusion models, we first present two key modifications to the NeRF model that are better paired with guidance from a latent model. First, instead of representing our NeRF in the standard RGB space, we propose a Latent-NeRF which operates directly in the latent space of the LDM, thus avoiding the burden of encoding a rendered RGB image to a latent space for each and every guid" + } + ] + } + ], + "index": 27 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 752, + 317, + 761 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 752, + 317, + 761 + ], + "spans": [ + { + "bbox": [ + 294, + 752, + 317, + 761 + ], + "type": "text", + "content": "12663" + } + ] + } + ], + "index": 28 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 180 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 180 + ], + "type": "text", + "content": "ing step. Secondly, we show that after training, one can easily transform a Latent-NeRF back into a regular NeRF. This allows further refinement in RGB space, where we can also introduce shading constraints or apply further guidance from RGB diffusion models [40]. This is achieved by introducing a learnable linear layer that can be optionally added to a trained Latent-NeRF, where the linear layer is initialized using an approximate mapping between the latent and RGB values [45]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 180, + 289, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 180, + 289, + 289 + ], + "spans": [ + { + "bbox": [ + 46, + 180, + 289, + 289 + ], + "type": "text", + "content": "Our first form of shape-guidance is applied using a coarse 3D model, which we call a Sketch-Shape. Given a Sketch-Shape, we apply soft constraint during the NeRF optimization process to guide its occupancy based on the given shape. Easily combined with Latent-NeRF optimization, the additional constraint can be tuned to meet a desired level of strictness. Using a Sketch-Shape allows users to define their base geometry, where Latent-NeRF then refines the shape and introduces texture based on a guiding prompt." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 289, + 289, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 289, + 289, + 396 + ], + "spans": [ + { + "bbox": [ + 46, + 289, + 289, + 396 + ], + "type": "text", + "content": "We further present Latent-Paint, another form of shape-guidance where the generation process is applied directly on a given 3D mesh, and we have not only the structure but also the exact parameterization of the input mesh. This is achieved by representing a texture map in the latent space and propagating the guidance gradients directly to the texture map through the rendered mesh. By doing so, we allow for the first time to colorize a mesh using guidance from a pretrained diffusion model and enjoy its expressiveness." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 396, + 289, + 444 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 396, + 289, + 444 + ], + "spans": [ + { + "bbox": [ + 46, + 396, + 289, + 444 + ], + "type": "text", + "content": "We evaluate our different forms of guidance under a variety of scenarios and show that together with our latent-based guidance, they offer a compelling solution for constrained shape and texture generation." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 454, + 134, + 466 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 454, + 134, + 466 + ], + "spans": [ + { + "bbox": [ + 47, + 454, + 134, + 466 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 474, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 474, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 474, + 289, + 715 + ], + "type": "text", + "content": "3D Shape Generation 3D shape synthesis is a longstanding problem in computer graphics and computer vision. In recent years, with the emergence of neural networks, the research in 3D modeling has immensely advanced. The most conventional supervision type is applied directly with 3D shapes, through different representations such as implicit functions [10, 20, 33], meshes [19, 50] or point clouds [27, 49]. As 3D supervision is often difficult to obtain, other works use images to guide the generative task [6, 7, 32]. In fact, even when 3D data is available, 2D renderings are sometimes chosen as the supervising primitive [5, 8, 18]. For example, in GET3D [18], two generators are trained, one generates a 3D SDF, and the other a texture field. The output textured mesh is then obtained in a differentiable manner by utilizing DMTet [42]. These generators are adversarially trained with a dataset of 2D images. In [47] a diffusion model has been used to generate multiple views of a given input image. Yet, it has been trained in a supervised manner on a multi-view dataset, unlike our work which does not require a dataset." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 547, + 492 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 492 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 492 + ], + "type": "text", + "content": "Text-to-3D with 2D Supervision. Recently, the success of text-guided synthesis in numerous domains [1,2,17,34, 44], has motivated a surge of works that use Language-Image models to guide 3D scenes representations. CLIP-Forge [41] consists of two separate components, an implicit autoencoder conditioned on shape codes, and a normalizing flow model that is trained to generate shape codes according to CLIP embeddings. CLIP-Forge exploits the fact that CLIP has a joint text-image embedding space to train on image embeddings and infer on text embeddings, achieving text-to-shape capabilities. Text2Mesh [29] introduced mesh colorization and geometric fine-tuning by optimizing an initial mesh through differential rendering and CLIP [36] guidance. TANGO [9] follows a similar optimization scheme, while improving results by considering an explicit shading model. CLIP-Mesh [26] optimizes an initial spherical mesh according to a target text prompt, using a modified CLIP loss that accounts for the gap and ambiguity between image/text CLIP embeddings. Similarly to our method, they also use UV texture mapping to bake colors into the mesh. DreamFields [24] employs CLIP guidance as well, but uses NeRFs to represent the 3D object instead of an explicit triangular mesh, together with a dedicated sparsity loss. CLIPNeRF [46] pretrains a disentangled NeRF representation network on rendered object datasets, which is then used to constraint a NeRF scene optimization under CLIP loss, between random renderings of the NeRF and target image or text CLIP embedding. DreamFusion [35] introduced, for the first time, the use of largely successful pretrained 2D diffusion models for text-guided 3D object generation. DreamFusion uses a proprietary 2D diffusion model [40] to supervise the generation of 3D objects represented by NeRFs. To guide a NeRF scene using the pretrained diffusion model, the authors derive a Score-Distillation loss, see Section 3.1 for more details." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 505, + 547, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 505, + 547, + 601 + ], + "spans": [ + { + "bbox": [ + 304, + 505, + 547, + 601 + ], + "type": "text", + "content": "Neural Rendering The recent rapid progression of neural networks has immensely advanced the performance of differential renderers. Particularly NeRF [4, 30, 31] have shown astounding performance on novel view generation and relighting, also extending to other applications like 3D reconstruction [51]. Thanks to their differentiable nature, it has been recently shown that one can introduce different neural objectives during training to guide the 3D modeling." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 609, + 362, + 621 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 609, + 362, + 621 + ], + "spans": [ + { + "bbox": [ + 306, + 609, + 362, + 621 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 630, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 547, + 715 + ], + "type": "text", + "content": "Here we present our shape-guidance solution. We describe the Latent-NeRF framework, presented in Figure 2, and then introduce different guidance controls that can be combined with Latent-NeRF for controlling its generation. Yet, before showing our solution, we provide a quick overview of two recently proposed techniques that are highly relevant to our method." + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 752, + 318, + 761 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 752, + 318, + 761 + ], + "spans": [ + { + "bbox": [ + 294, + 752, + 318, + 761 + ], + "type": "text", + "content": "12664" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 133, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 133, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 133, + 83 + ], + "type": "text", + "content": "3.1. Preliminaries" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 89, + 289, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 89, + 289, + 316 + ], + "spans": [ + { + "bbox": [ + 46, + 89, + 289, + 316 + ], + "type": "text", + "content": "A latent diffusion model (LDM) [39] is a specific form of a diffusion model that is trained to denoise latent codes of a pretrained autoencoder, instead of the high-resolution images directly. First, an autoencoder composed of an encoder " + }, + { + "bbox": [ + 46, + 89, + 289, + 316 + ], + "type": "inline_equation", + "content": "\\mathcal{E}" + }, + { + "bbox": [ + 46, + 89, + 289, + 316 + ], + "type": "text", + "content": ", and a decoder " + }, + { + "bbox": [ + 46, + 89, + 289, + 316 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 46, + 89, + 289, + 316 + ], + "type": "text", + "content": " is trained to reconstruct natural images " + }, + { + "bbox": [ + 46, + 89, + 289, + 316 + ], + "type": "inline_equation", + "content": "x \\sim X" + }, + { + "bbox": [ + 46, + 89, + 289, + 316 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 89, + 289, + 316 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 46, + 89, + 289, + 316 + ], + "type": "text", + "content": " is the image training dataset, in the following form: " + }, + { + "bbox": [ + 46, + 89, + 289, + 316 + ], + "type": "inline_equation", + "content": "\\tilde{x} = \\mathcal{D}(\\mathcal{E}(x))" + }, + { + "bbox": [ + 46, + 89, + 289, + 316 + ], + "type": "text", + "content": ". The autoencoder is trained with a reconstruction loss, perceptual loss [54] and a patch-based adversarial loss [22]. Then, given the trained autoencoder, a denoising diffusion probabilistic model (DDPM) [21] is trained to generate a spatial latent " + }, + { + "bbox": [ + 46, + 89, + 289, + 316 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 89, + 289, + 316 + ], + "type": "text", + "content": " from noise, according to the distribution " + }, + { + "bbox": [ + 46, + 89, + 289, + 316 + ], + "type": "inline_equation", + "content": "z = \\mathcal{E}(x)" + }, + { + "bbox": [ + 46, + 89, + 289, + 316 + ], + "type": "text", + "content": " s.t. " + }, + { + "bbox": [ + 46, + 89, + 289, + 316 + ], + "type": "inline_equation", + "content": "x \\sim X" + }, + { + "bbox": [ + 46, + 89, + 289, + 316 + ], + "type": "text", + "content": ". In order to generate a novel image, a latent " + }, + { + "bbox": [ + 46, + 89, + 289, + 316 + ], + "type": "inline_equation", + "content": "\\tilde{z}" + }, + { + "bbox": [ + 46, + 89, + 289, + 316 + ], + "type": "text", + "content": " is sampled from this learned distribution, using the trained DDPM, and passed to the decoder to obtain the final image " + }, + { + "bbox": [ + 46, + 89, + 289, + 316 + ], + "type": "inline_equation", + "content": "\\mathcal{D}(\\tilde{z})" + }, + { + "bbox": [ + 46, + 89, + 289, + 316 + ], + "type": "text", + "content": ". Operating in the latent space requires less compute, and leads to faster training and sampling, which makes LDM widely popular. In fact, the recent Stable Diffusion model is also an LDM." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 317, + 289, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 317, + 289, + 449 + ], + "spans": [ + { + "bbox": [ + 46, + 317, + 289, + 449 + ], + "type": "text", + "content": "Score Distillation is a method that enables using a diffusion model as a critic, i.e., using it as a loss without explicitly back-propagating through the diffusion process. It has been introduced in DreamFusion [35] for guiding 3D generation using the Imagen model [40]. To perform score distillation, noise is first added to a given image (e.g., one view of the NeRF's output). Then, the diffusion model is used to predict the added noise from the noised image. Finally, the difference between the predicted and added noises is used for calculating per-pixel gradients. For NeRF, the gradients are back-propagated for updating the 3D NeRF model." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 449, + 288, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 449, + 288, + 485 + ], + "spans": [ + { + "bbox": [ + 46, + 449, + 288, + 485 + ], + "type": "text", + "content": "Going into more detail, at each iteration of the score distillation optimization, a rendered image " + }, + { + "bbox": [ + 46, + 449, + 288, + 485 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 449, + 288, + 485 + ], + "type": "text", + "content": " is noised to a randomly drawn time step " + }, + { + "bbox": [ + 46, + 449, + 288, + 485 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 449, + 288, + 485 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 114, + 490, + 287, + 506 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 114, + 490, + 287, + 506 + ], + "spans": [ + { + "bbox": [ + 114, + 490, + 287, + 506 + ], + "type": "interline_equation", + "content": "x _ {t} = \\sqrt {\\bar {\\alpha} _ {t}} x + \\sqrt {1 - \\bar {\\alpha} _ {t}} \\epsilon , \\tag {1}", + "image_path": "3dfefecdef759e8cb57814e53fc2e0a542f603ebbb25e93c88a035269da6fe7d.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 509, + 287, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 509, + 287, + 545 + ], + "spans": [ + { + "bbox": [ + 46, + 509, + 287, + 545 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 509, + 287, + 545 + ], + "type": "inline_equation", + "content": "\\epsilon \\sim \\mathcal{N}(0,I)" + }, + { + "bbox": [ + 46, + 509, + 287, + 545 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 509, + 287, + 545 + ], + "type": "inline_equation", + "content": "\\bar{\\alpha}_t" + }, + { + "bbox": [ + 46, + 509, + 287, + 545 + ], + "type": "text", + "content": " is a time-dependent constant specified by the diffusion model. Then, the per-pixel score distillation gradients are taken to be" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 94, + 552, + 287, + 566 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 94, + 552, + 287, + 566 + ], + "spans": [ + { + "bbox": [ + 94, + 552, + 287, + 566 + ], + "type": "interline_equation", + "content": "\\nabla_ {x} L _ {S D S} = w (t) \\left(\\epsilon_ {\\phi} \\left(x _ {t}, t, T\\right) - \\epsilon\\right), \\tag {2}", + "image_path": "d35903a8aea7a1a0b40d5ea4c03805efc1dbb70dadf5efa240c269722166d265.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 570, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 289, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 570, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\phi}" + }, + { + "bbox": [ + 46, + 570, + 289, + 714 + ], + "type": "text", + "content": " is the diffusion model's denoiser (which approximates the noise to be removed), " + }, + { + "bbox": [ + 46, + 570, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 46, + 570, + 289, + 714 + ], + "type": "text", + "content": " are the denoiser's parameters, " + }, + { + "bbox": [ + 46, + 570, + 289, + 714 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 570, + 289, + 714 + ], + "type": "text", + "content": " is an optional guiding text prompt, and " + }, + { + "bbox": [ + 46, + 570, + 289, + 714 + ], + "type": "inline_equation", + "content": "w(t)" + }, + { + "bbox": [ + 46, + 570, + 289, + 714 + ], + "type": "text", + "content": " is a constant multiplier that depends on " + }, + { + "bbox": [ + 46, + 570, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\alpha_{t}" + }, + { + "bbox": [ + 46, + 570, + 289, + 714 + ], + "type": "text", + "content": ". During training, gradients are propagated from the pixel gradients to the NeRF parameters and gradually change the 3D object. Please refer to [35] for the complete details and derivation of Score Distillation. Note that DreamFusion uses the proprietary Imagen [40] model that is very computationally demanding. We rely on the publicly available Stable Diffusion model and the re-implementation of DreamFusion [43] (it operates in the RGB space and not the latent as we propose)." + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 319, + 69, + 535, + 201 + ], + "blocks": [ + { + "bbox": [ + 319, + 69, + 535, + 201 + ], + "lines": [ + { + "bbox": [ + 319, + 69, + 535, + 201 + ], + "spans": [ + { + "bbox": [ + 319, + 69, + 535, + 201 + ], + "type": "image", + "image_path": "5a25ffcac610385e6ecd95b08abd3d952c559ca9cddad6c023e5e358d2fdfecc.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 208, + 547, + 308 + ], + "lines": [ + { + "bbox": [ + 304, + 208, + 547, + 308 + ], + "spans": [ + { + "bbox": [ + 304, + 208, + 547, + 308 + ], + "type": "text", + "content": "Figure 2. An overview of Latent-NeRF trained with a similar score distillation scheme as proposed by [35]. At each training iteration we render the scene from a random view point to produce a feature map " + }, + { + "bbox": [ + 304, + 208, + 547, + 308 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 304, + 208, + 547, + 308 + ], + "type": "text", + "content": ". Then, " + }, + { + "bbox": [ + 304, + 208, + 547, + 308 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 304, + 208, + 547, + 308 + ], + "type": "text", + "content": " is noised with " + }, + { + "bbox": [ + 304, + 208, + 547, + 308 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 304, + 208, + 547, + 308 + ], + "type": "text", + "content": " according to a random diffusion step " + }, + { + "bbox": [ + 304, + 208, + 547, + 308 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 208, + 547, + 308 + ], + "type": "text", + "content": ". The noised version of " + }, + { + "bbox": [ + 304, + 208, + 547, + 308 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 304, + 208, + 547, + 308 + ], + "type": "text", + "content": ", i.e., " + }, + { + "bbox": [ + 304, + 208, + 547, + 308 + ], + "type": "inline_equation", + "content": "x_{t}" + }, + { + "bbox": [ + 304, + 208, + 547, + 308 + ], + "type": "text", + "content": ", is denoised using Stable Diffusion [39], with the input text prompt. Finally, the input noise is subtracted from the predicted noise by Stable Diffusion, to approximate per-pixel gradients that are back propagated to the NeRF representation." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 330, + 391, + 341 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 330, + 391, + 341 + ], + "spans": [ + { + "bbox": [ + 306, + 330, + 391, + 341 + ], + "type": "text", + "content": "3.2. Latent-NeRF" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 348, + 547, + 589 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 348, + 547, + 589 + ], + "spans": [ + { + "bbox": [ + 304, + 348, + 547, + 589 + ], + "type": "text", + "content": "We now turn to describe our Latent-NeRF approach. In this method, a NeRF model is optimized to render 2D feature maps in Stable Diffusion's latent space " + }, + { + "bbox": [ + 304, + 348, + 547, + 589 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}" + }, + { + "bbox": [ + 304, + 348, + 547, + 589 + ], + "type": "text", + "content": ". Latent-NeRF outputs four pseudo-color channels, " + }, + { + "bbox": [ + 304, + 348, + 547, + 589 + ], + "type": "inline_equation", + "content": "(c_{1}, c_{2}, c_{3}, c_{4})" + }, + { + "bbox": [ + 304, + 348, + 547, + 589 + ], + "type": "text", + "content": ", corresponding to the four latent features that stable diffusion operates over, and a volume density " + }, + { + "bbox": [ + 304, + 348, + 547, + 589 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 304, + 348, + 547, + 589 + ], + "type": "text", + "content": ". Figure 2 illustrates this process. Representing the scene using NeRF implicitly imposes spatial consistency between different views, due to the spatial radiance field and rendering equation. Still, the fact that " + }, + { + "bbox": [ + 304, + 348, + 547, + 589 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}" + }, + { + "bbox": [ + 304, + 348, + 547, + 589 + ], + "type": "text", + "content": " can be represented by a NeRF with spatial consistencies is non-trivial. Previous works [1, 45] showed that super-pixels in " + }, + { + "bbox": [ + 304, + 348, + 547, + 589 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}" + }, + { + "bbox": [ + 304, + 348, + 547, + 589 + ], + "type": "text", + "content": " depend mainly on individual patches in the output image. This can be attributed to the high resolution " + }, + { + "bbox": [ + 304, + 348, + 547, + 589 + ], + "type": "inline_equation", + "content": "(64 \\times 64)" + }, + { + "bbox": [ + 304, + 348, + 547, + 589 + ], + "type": "text", + "content": " and low channel-wise depth (4) of this latent space, which encourages local dependency over the autoencoder's image and latent spaces. Assuming " + }, + { + "bbox": [ + 304, + 348, + 547, + 589 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}" + }, + { + "bbox": [ + 304, + 348, + 547, + 589 + ], + "type": "text", + "content": " is a near patch level representation of its corresponding RGB image makes the latents nearly equivariant to spatial transformations of the scene, which justifies the use of NeRFs for representing the 3D scenes." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 606, + 547, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 606, + 547, + 643 + ], + "spans": [ + { + "bbox": [ + 304, + 606, + 547, + 643 + ], + "type": "text", + "content": "Text Guidance The vanilla form of Latent-NeRF is text-guided, with no other constraints for the scene generation. In this setting, we employ the following loss:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 351, + 654, + 500, + 667 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 351, + 654, + 500, + 667 + ], + "spans": [ + { + "bbox": [ + 351, + 654, + 500, + 667 + ], + "type": "interline_equation", + "content": "L = \\lambda_ {S D S} L _ {S D S} + \\lambda_ {s p a r s e} L _ {s p a r s e},", + "image_path": "d02998d4f24b9cabd1cc69338c5023690a706d3588fcb54aa8d3a5ccd9f8839d.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "type": "inline_equation", + "content": "L_{SDS}" + }, + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "type": "text", + "content": " is the Score-Distillation loss depicted in Figure 2. Note, that the exact value of this loss is not accessible. Instead, the gradients implied by it are approximated" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 752, + 317, + 761 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 752, + 317, + 761 + ], + "spans": [ + { + "bbox": [ + 294, + 752, + 317, + 761 + ], + "type": "text", + "content": "12665" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 69, + 286, + 163 + ], + "blocks": [ + { + "bbox": [ + 48, + 69, + 286, + 163 + ], + "lines": [ + { + "bbox": [ + 48, + 69, + 286, + 163 + ], + "spans": [ + { + "bbox": [ + 48, + 69, + 286, + 163 + ], + "type": "image", + "image_path": "4caa0b131ba1db558e4050511f712acacae2d68250365d90fc7c433c52226a9d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 171, + 288, + 227 + ], + "lines": [ + { + "bbox": [ + 46, + 171, + 288, + 227 + ], + "spans": [ + { + "bbox": [ + 46, + 171, + 288, + 227 + ], + "type": "text", + "content": "Figure 3. To perform fine-tuning in RGB, we take a Latent-NeRF model that was trained in latent space (conventional setting), apply the matrix adapter to the channel output of the model to get an RGB preview, and then continue optimizing the MLP's weights through supervision in RGB to improve the result." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 253, + 287, + 326 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 253, + 287, + 326 + ], + "spans": [ + { + "bbox": [ + 46, + 253, + 287, + 326 + ], + "type": "text", + "content": "by a single forward pass through the denoiser. These gradients are directly passed to the autograd solver. The loss " + }, + { + "bbox": [ + 46, + 253, + 287, + 326 + ], + "type": "inline_equation", + "content": "L_{sparse} = BE(w_{blend})" + }, + { + "bbox": [ + 46, + 253, + 287, + 326 + ], + "type": "text", + "content": " suggested in [43] prevents floating \"radiance clouds\" by penalizing the binary entropy of ill-defined background masks " + }, + { + "bbox": [ + 46, + 253, + 287, + 326 + ], + "type": "inline_equation", + "content": "w_{blend}" + }, + { + "bbox": [ + 46, + 253, + 287, + 326 + ], + "type": "text", + "content": ". Namely, it encourages a strict blending of the object NeRF and background NeRF." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 353, + 287, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 353, + 287, + 521 + ], + "spans": [ + { + "bbox": [ + 46, + 353, + 287, + 521 + ], + "type": "text", + "content": "RGB Refinement Using Latent-NeRF, one may successfully learn to represent 3D scenes even when optimizing solely in latent space. Still, in some cases, it could be beneficial to further refine the model by fine-tuning it in pixel space, and have the NeRF model operate directly in RGB. To do so, we must convert the NeRF that was trained in latent space to a NeRF that operates in RGB. This requires converting the MLP's output from the four latent channels to three RGB channels such that the initial rendered RGB image is close to the decoder output, when applied to the rendered latent of the original model. Interestingly, it has been shown [45] that a linear approximation is sufficient to predict plausible RGB colors given a single four-channel latent super pixel, via the following transformation" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 56, + 533, + 286, + 593 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 533, + 286, + 593 + ], + "spans": [ + { + "bbox": [ + 56, + 533, + 286, + 593 + ], + "type": "interline_equation", + "content": "\\left( \\begin{array}{c} \\hat {r} \\\\ \\hat {g} \\\\ \\hat {b} \\end{array} \\right) = \\left( \\begin{array}{c c c c} 0. 2 9 8 & 0. 1 8 7 & - 0. 1 5 8 & - 0. 1 8 4 \\\\ 0. 2 0 7 & 0. 2 8 6 & 0. 1 8 9 & - 0. 2 7 1 \\\\ 0. 2 0 8 & 0. 1 7 3 & 0. 2 6 4 & - 0. 4 7 3 \\end{array} \\right) \\left( \\begin{array}{c} c _ {1} \\\\ c _ {2} \\\\ c _ {3} \\\\ c _ {4} \\end{array} \\right), \\tag {3}", + "image_path": "980c06e5dfc19fa9663e840c12f7533de1310ae12a97301565dd4918dfb3d248.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": "which was calculated using pairs of RGB images and their corresponding latent codes over a collection of natural images. As our NeRF model is already composed of a set of fully connected layers, we simply add another linear layer that is initialized using the weights in Equation 3. This converts our Latent-NeRF to operate in pixel space and ensures that our refinement process starts from a valid result. The additional layer is then fine-tuned together with the rest of the model, to create the refined and final output. The overall fine-tuning procedure is illustrated in Figure 3." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 72, + 440, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 440, + 85 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 440, + 85 + ], + "type": "text", + "content": "3.3. Sketch-Shape Guidance" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 90, + 545, + 125 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 90, + 545, + 125 + ], + "spans": [ + { + "bbox": [ + 305, + 90, + 545, + 125 + ], + "type": "text", + "content": "Next, we introduce a novel technique for guiding the Latent-NeRF generation based on a coarse geometry, which we call a Sketch-Shape." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 126, + 546, + 293 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 126, + 546, + 293 + ], + "spans": [ + { + "bbox": [ + 304, + 126, + 546, + 293 + ], + "type": "text", + "content": "A Sketch-Shape is an abstract coarse alignment of simple 3D primitives like spheres, boxes, cylinders, etc., that together depict an outline of a more complex object. Figures 9, 10, 11 illustrate such simple shapes. Ideally, we would like the output density of our MLP to match that of the Sketch-Shape, such that the output Latent-NeRF result resembles the input shape. Nevertheless, we would also like the new NeRF to have the capacity to create new details and geometries that match the input text prompt and improve the fidelity of the shape. To achieve this lenient constraint, we encourage the NeRF's occupancy to match the winding-number [3, 23] indicator of the Sketch-Shape, but with decaying importance near the surface to allow new geometries. This loss reads as" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 294, + 545, + 323 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 294, + 545, + 323 + ], + "spans": [ + { + "bbox": [ + 306, + 294, + 545, + 323 + ], + "type": "interline_equation", + "content": "L _ {\\text {S k e t c h - S h a p e}} = C E \\left(\\alpha_ {N e R F} (p), \\alpha_ {G T} (p)\\right) \\cdot \\left(1 - e ^ {- \\frac {d ^ {2}}{2 \\sigma_ {S}}}\\right). \\tag {4}", + "image_path": "6cbd070b3a116ead1b95b129327321b06a0edf3cb2f0b30e8e041295b7371692.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 323, + 546, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 323, + 546, + 443 + ], + "spans": [ + { + "bbox": [ + 304, + 323, + 546, + 443 + ], + "type": "text", + "content": "This loss implies that the occupancy should be well constrained away from the surface, and free to be set by score distillation near the surface. This loss is applied in addition to the Latent-NeRF loss, over the entire point set " + }, + { + "bbox": [ + 304, + 323, + 546, + 443 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 304, + 323, + 546, + 443 + ], + "type": "text", + "content": " that is used by the NeRF's volumetric rendering. " + }, + { + "bbox": [ + 304, + 323, + 546, + 443 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 323, + 546, + 443 + ], + "type": "text", + "content": " represents the distance of " + }, + { + "bbox": [ + 304, + 323, + 546, + 443 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 304, + 323, + 546, + 443 + ], + "type": "text", + "content": " from the surface, and " + }, + { + "bbox": [ + 304, + 323, + 546, + 443 + ], + "type": "inline_equation", + "content": "\\sigma_{S}" + }, + { + "bbox": [ + 304, + 323, + 546, + 443 + ], + "type": "text", + "content": " is a hyperparameter that controls how lenient the loss is, i.e., lower " + }, + { + "bbox": [ + 304, + 323, + 546, + 443 + ], + "type": "inline_equation", + "content": "\\sigma_{S}" + }, + { + "bbox": [ + 304, + 323, + 546, + 443 + ], + "type": "text", + "content": " values imply a tighter constraint to the input Sketch-Shape. Applying the loss only on the sampled point-set " + }, + { + "bbox": [ + 304, + 323, + 546, + 443 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 304, + 323, + 546, + 443 + ], + "type": "text", + "content": ", makes it more efficient as these points are already evaluated as part" + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 316, + 449, + 536, + 613 + ], + "blocks": [ + { + "bbox": [ + 316, + 449, + 536, + 613 + ], + "lines": [ + { + "bbox": [ + 316, + 449, + 536, + 613 + ], + "spans": [ + { + "bbox": [ + 316, + 449, + 536, + 613 + ], + "type": "image", + "image_path": "2533b47fcca42c5ffb10524cd128da90b16a97d859bb15063f6e6f592c75fb6f.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 622, + 545, + 710 + ], + "lines": [ + { + "bbox": [ + 304, + 622, + 545, + 710 + ], + "spans": [ + { + "bbox": [ + 304, + 622, + 545, + 710 + ], + "type": "text", + "content": "Figure 4. An overview of Latent-Paint texture generation, trained with a similar score distillation loss [35]. The object is represented as a textured mesh, with a latent texture image that has four pseudo-color channels. At each iteration, the mesh is rendered with a differential renderer, to create a feature map from a random viewpoint. Score distillation is applied to the rendered feature map, and the gradients back-propagate to the latent texture image through the differential renderer. See Section 3.4." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 752, + 317, + 761 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 752, + 317, + 761 + ], + "spans": [ + { + "bbox": [ + 294, + 752, + 317, + 761 + ], + "type": "text", + "content": "12666" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 205, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 205, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 205, + 83 + ], + "type": "text", + "content": "of the Latent-NeRF rendering process." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 92, + 217, + 105 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 92, + 217, + 105 + ], + "spans": [ + { + "bbox": [ + 47, + 92, + 217, + 105 + ], + "type": "text", + "content": "3.4. Latent-Paint of Explicit Shapes" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 110, + 288, + 242 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 110, + 288, + 242 + ], + "spans": [ + { + "bbox": [ + 46, + 110, + 288, + 242 + ], + "type": "text", + "content": "We now move to a more strict constraint, where the guidance is based on an exact structure of a given shape, e.g., provided in the form of a mesh. We call this approach Latent-Paint, which leads to the generation of novel textures for a given shape. Our method generates texture over a UV texture map, which can either be supplied by the input mesh, or calculated on-the-fly using XAtlas [52]. To color a mesh, we first initialize a random latent texture image of size " + }, + { + "bbox": [ + 46, + 110, + 288, + 242 + ], + "type": "inline_equation", + "content": "H \\times W \\times 4" + }, + { + "bbox": [ + 46, + 110, + 288, + 242 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 110, + 288, + 242 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 46, + 110, + 288, + 242 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 110, + 288, + 242 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 46, + 110, + 288, + 242 + ], + "type": "text", + "content": " can be chosen according to the desired texture granularity. We set them both to be 128 in our experiments." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 243, + 288, + 385 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 243, + 288, + 385 + ], + "spans": [ + { + "bbox": [ + 46, + 243, + 288, + 385 + ], + "type": "text", + "content": "Figure 4 presents the training process. At each score distillation iteration, we render the mesh with a differentiable renderer [15] to obtain a " + }, + { + "bbox": [ + 46, + 243, + 288, + 385 + ], + "type": "inline_equation", + "content": "64 \\times 64 \\times 4" + }, + { + "bbox": [ + 46, + 243, + 288, + 385 + ], + "type": "text", + "content": " feature map that is pseudo-colored by the latent texture image. Then, we apply the score distillation loss from Equation 2 in the same way it is applied for Latent-NeRF. Yet, instead of backpropagating the loss to the NeRF's MLP parameters, we optimize the deep texture image by back-propagating through the differentiable renderer. To get the final RGB texture image, we simply pass the latent texture image through Stable Diffusion's decoder " + }, + { + "bbox": [ + 46, + 243, + 288, + 385 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 46, + 243, + 288, + 385 + ], + "type": "text", + "content": " once, to get a larger high-quality RGB texture." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 397, + 118, + 409 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 397, + 118, + 409 + ], + "spans": [ + { + "bbox": [ + 47, + 397, + 118, + 409 + ], + "type": "text", + "content": "4. Evaluation" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 417, + 287, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 417, + 287, + 441 + ], + "spans": [ + { + "bbox": [ + 47, + 417, + 287, + 441 + ], + "type": "text", + "content": "We now validate the effectiveness of our different forms of guidance through a variety of experiments." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 456, + 287, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 456, + 287, + 506 + ], + "spans": [ + { + "bbox": [ + 46, + 456, + 287, + 506 + ], + "type": "text", + "content": "Implementation Details We use the Stable Diffusion implementation by HuggingFace Diffusers, with the v1-4 checkpoint. For score distillation, we use the code-base provided by [43], with Instant-NGP [31] as our NeRF model." + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 52, + 521, + 284, + 688 + ], + "blocks": [ + { + "bbox": [ + 52, + 521, + 284, + 688 + ], + "lines": [ + { + "bbox": [ + 52, + 521, + 284, + 688 + ], + "spans": [ + { + "bbox": [ + 52, + 521, + 284, + 688 + ], + "type": "image", + "image_path": "38623be138dfd9d1197e05290df3d245cf020711eeb64585d68f45c7ea30251d.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 63, + 699, + 270, + 710 + ], + "lines": [ + { + "bbox": [ + 63, + 699, + 270, + 710 + ], + "spans": [ + { + "bbox": [ + 63, + 699, + 270, + 710 + ], + "type": "text", + "content": "Figure 5. Latent-NeRF results from different viewpoints." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 312, + 74, + 538, + 413 + ], + "blocks": [ + { + "bbox": [ + 312, + 74, + 538, + 413 + ], + "lines": [ + { + "bbox": [ + 312, + 74, + 538, + 413 + ], + "spans": [ + { + "bbox": [ + 312, + 74, + 538, + 413 + ], + "type": "image", + "image_path": "e9b384a95deee28996d433a0a3aa5666551af66cb8203e1a709087698fe1a883.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 307, + 423, + 543, + 435 + ], + "lines": [ + { + "bbox": [ + 307, + 423, + 543, + 435 + ], + "spans": [ + { + "bbox": [ + 307, + 423, + 543, + 435 + ], + "type": "text", + "content": "Figure 6. Qualitative comparison with other text-to-3D methods." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 457, + 545, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 457, + 545, + 529 + ], + "spans": [ + { + "bbox": [ + 304, + 457, + 545, + 529 + ], + "type": "text", + "content": "Latent-NeRF usually takes less than 15 minutes to converge on a single V100, while using an RGB-NeRF with Stable Diffusion [43] takes about 30 minutes, due to the increased overhead from encoding into the latent space. Note that DreamFusion [35] takes about 1.5 hours on 4 TPUs. This clearly shows the computational advantage of Latent-NeRF." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 538, + 443, + 550 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 538, + 443, + 550 + ], + "spans": [ + { + "bbox": [ + 306, + 538, + 443, + 550 + ], + "type": "text", + "content": "4.1. Text-Guided Generation" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 557, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 545, + 713 + ], + "type": "text", + "content": "Qualitative Results We begin by demonstrating the effectiveness of the latent rendering approach with Latent-NeRF. In Figs. 1, 5 and 7, we show several results obtained by our method. In the supplementary material we provide additional results of different objects, including video visualizations. In Figure 5, we show the consistency of our learned shapes from several viewpoints. Next, we use the baseline set by DreamFusion [35] to qualitatively compare our approach (with the proposed RGB refinement) against other methods. As can be seen in Figure 6, Latent-NeRF achieves significantly better results than DreamFields [24] and CLIPMesh [26]. We believe that the better quality of DreamFusion can be attributed to the high quality of Ima" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 752, + 317, + 761 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 752, + 317, + 761 + ], + "spans": [ + { + "bbox": [ + 294, + 752, + 317, + 761 + ], + "type": "text", + "content": "12667" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 69, + 287, + 308 + ], + "blocks": [ + { + "bbox": [ + 49, + 69, + 287, + 308 + ], + "lines": [ + { + "bbox": [ + 49, + 69, + 287, + 308 + ], + "spans": [ + { + "bbox": [ + 49, + 69, + 287, + 308 + ], + "type": "image", + "image_path": "13eaf8616d0a3ab9a3d8ca93641c943c80b2c7570197361488646054ee96f869.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 316, + 288, + 351 + ], + "lines": [ + { + "bbox": [ + 46, + 316, + 288, + 351 + ], + "spans": [ + { + "bbox": [ + 46, + 316, + 288, + 351 + ], + "type": "text", + "content": "Figure 7. RGB refinement combined with (i) Latent-NeRF (icecream and temple), and (ii) Sketch-Shape (lego and car). For each shape we also show the normals direction." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 371, + 287, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 371, + 287, + 396 + ], + "spans": [ + { + "bbox": [ + 46, + 371, + 287, + 396 + ], + "type": "text", + "content": "gen [40], but unfortunately, we cannot validate this as the model is not publicly available to the community." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 409, + 289, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 409, + 289, + 553 + ], + "spans": [ + { + "bbox": [ + 46, + 409, + 289, + 553 + ], + "type": "text", + "content": "RGB Refinement Figure 7 shows the quality improvement achieved by our RGB refinement method. It reveals that RGB refinement is mostly useful for complex objects or for regions with detailed textures. Refinement iterations in the RGB space are about " + }, + { + "bbox": [ + 46, + 409, + 289, + 553 + ], + "type": "inline_equation", + "content": "\\times 2" + }, + { + "bbox": [ + 46, + 409, + 289, + 553 + ], + "type": "text", + "content": " slower than iterations in latent space, thus, increasing the runtime to more than 30 minutes. Thanks to our linear mapping from a Latent-NeRF to an RGB-NeRF, practitioners may apply the refinement method only after the 3D shape has already converged with the more efficient latent training. This allows a fast exploration of 3D shapes, and an optional polishing step with RGB refinement." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 567, + 287, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 567, + 287, + 640 + ], + "spans": [ + { + "bbox": [ + 46, + 567, + 287, + 640 + ], + "type": "text", + "content": "Textual-Inversion As our Latent-NeRF is supervised by Stable-Diffusion, we can also use Textual Inversion [16] tokens as part of the input text prompt. This allows conditioning the object generation on specific objects and styles, defined only by input images. Results using Textual Inversion are presented in Figure 8." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 647, + 182, + 660 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 647, + 182, + 660 + ], + "spans": [ + { + "bbox": [ + 47, + 647, + 182, + 660 + ], + "type": "text", + "content": "4.2. Sketch-Shape Guidance" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": "Figure 9 shows different Sketch-Shape results with the same conditioning mesh. The different text prompts are able to guide the shape toward refined geometries that better match the text prompt. The rough Sketch-Shape in this" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 310, + 69, + 545, + 205 + ], + "blocks": [ + { + "bbox": [ + 310, + 69, + 545, + 205 + ], + "lines": [ + { + "bbox": [ + 310, + 69, + 545, + 205 + ], + "spans": [ + { + "bbox": [ + 310, + 69, + 545, + 205 + ], + "type": "image", + "image_path": "60ce59e8125f6d1b622168d0b03acacdcb5da433d68054fecd71dd6a539ece5f.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 215, + 546, + 239 + ], + "lines": [ + { + "bbox": [ + 305, + 215, + 546, + 239 + ], + "spans": [ + { + "bbox": [ + 305, + 215, + 546, + 239 + ], + "type": "text", + "content": "Figure 8. Results of Latent-NeRF using a token learned from the images on the left with Textual Inversion [16]." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 308, + 251, + 544, + 468 + ], + "blocks": [ + { + "bbox": [ + 308, + 251, + 544, + 468 + ], + "lines": [ + { + "bbox": [ + 308, + 251, + 544, + 468 + ], + "spans": [ + { + "bbox": [ + 308, + 251, + 544, + 468 + ], + "type": "image", + "image_path": "967f6d9baca7295a594032363cc2b94b4d5cea3da9a67e27ec81931181afc618.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 479, + 546, + 513 + ], + "lines": [ + { + "bbox": [ + 305, + 479, + 546, + 513 + ], + "spans": [ + { + "bbox": [ + 305, + 479, + 546, + 513 + ], + "type": "text", + "content": "Figure 9. Sketch-Shape results using different prompts. This examples shows how the same Sketch-Shape can influence different objects according to different text prompts." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 533, + 545, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 545, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 545, + 665 + ], + "type": "text", + "content": "figure, was quickly designed in Blender [12] and allows us to easily define a coarse shape that guides the Latent-NeRF. Moreover, Figure 17 depicts an ablation over the lenient parameter " + }, + { + "bbox": [ + 304, + 533, + 545, + 665 + ], + "type": "inline_equation", + "content": "\\sigma_{S}" + }, + { + "bbox": [ + 304, + 533, + 545, + 665 + ], + "type": "text", + "content": " from Eq. (4). When " + }, + { + "bbox": [ + 304, + 533, + 545, + 665 + ], + "type": "inline_equation", + "content": "\\sigma_{S}" + }, + { + "bbox": [ + 304, + 533, + 545, + 665 + ], + "type": "text", + "content": " is set to 0.05, the generated mesh takes the form of the conditioning shape (shown in Figure 9). As " + }, + { + "bbox": [ + 304, + 533, + 545, + 665 + ], + "type": "inline_equation", + "content": "\\sigma_{S}" + }, + { + "bbox": [ + 304, + 533, + 545, + 665 + ], + "type": "text", + "content": " grows, more details are added on top of the base shape, until little to no resemblance is observed at " + }, + { + "bbox": [ + 304, + 533, + 545, + 665 + ], + "type": "inline_equation", + "content": "\\sigma_{S} = 1.5" + }, + { + "bbox": [ + 304, + 533, + 545, + 665 + ], + "type": "text", + "content": ". Figure 10 contains additional results of different shapes generated with the same conditioning mesh, here a coarse house shape. The normals visualization (bottom row) shows that our method can add fine geometric details." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "Figure 11 demonstrates that our proposed approach can successfully work with a variety of different Sketch-Shapes. 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+ "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 232, + 355, + 276, + 372 + ], + "lines": [ + { + "bbox": [ + 232, + 355, + 276, + 372 + ], + "spans": [ + { + "bbox": [ + 232, + 355, + 276, + 372 + ], + "type": "text", + "content": "\"A house made of candy\"" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 17 + }, + { + "bbox": [ + 47, + 425, + 287, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 425, + 287, + 460 + ], + "spans": [ + { + "bbox": [ + 47, + 425, + 287, + 460 + ], + "type": "text", + "content": "We also exhibit in Figure 14 the effectiveness of shape-guidance, by showing results of the same prompts with and without the shape loss." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 47, + 468, + 185, + 479 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 468, + 185, + 479 + ], + "spans": [ + { + "bbox": [ + 47, + 468, + 185, + 479 + ], + "type": "text", + "content": "4.3. Latent-Paint Generation" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 46, + 486, + 287, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 486, + 287, + 617 + ], + "spans": [ + { + "bbox": [ + 46, + 486, + 287, + 617 + ], + "type": "text", + "content": "We tested Latent-Paint on a variety of input shapes shown in Figs. 12 and 13. As all of the shapes in these figures do not contain precomputed UV parameterization, we use XAtlas [52] to compute such parameterization automatically. In contrast, the fish mesh in Figure 15 (obtained from [13]) already contains high quality UV parameterization, which we are also able work with. Figure 13 compares our Latent-Paint approach to two closely related methods, Tango [9] and CLIPMesh [26]. As can be seen, our approach achieves more precise textures thanks to the guidance from the diffusion model." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 46, + 618, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 618, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 618, + 287, + 715 + ], + "type": "text", + "content": "Note that Latent-Paint can work without assuming or computing any UV-map by simply optimizing per-face latent attributes. Yet, we found it better to use a UV-map for two main reasons: (i) The UV map makes the texture granularity independent of the geometric resolution, i.e., coarse geometries do not imply course colorization; and (ii) texture maps are easier to use with downstream applications like MeshLab [11] and Blender [12]." + } + ] + } + ], + "index": 23 + }, + { + "type": "image", + "bbox": [ + 326, + 81, + 353, + 118 + ], + "blocks": [ + { + "bbox": [ + 326, + 81, + 353, + 118 + ], + "lines": [ + { + "bbox": [ + 326, + 81, + 353, + 118 + ], + "spans": [ + { + "bbox": [ + 326, + 81, + 353, + 118 + ], + "type": "image", + "image_path": "cdf9480bc1764abdd05a51e7b802e2957232df22fba4a8ec6457de47c6ca6d4d.jpg" + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "image_body" + } + ], + "index": 24 + }, + { + "type": "image", + "bbox": [ + 368, + 71, + 425, + 129 + ], + "blocks": [ + { + "bbox": [ + 368, + 71, + 425, + 129 + ], + "lines": [ + { + "bbox": [ + 368, + 71, + 425, + 129 + ], + "spans": [ + 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"spans": [ + { + "bbox": [ + 451, + 562, + 509, + 623 + ], + "type": "image", + "image_path": "2efa2b2127d505d3edb83b7fb69914aaf172125721c5417cfff74feb2cc549fc.jpg" + } + ] + } + ], + "index": 58, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 461, + 624, + 498, + 639 + ], + "lines": [ + { + "bbox": [ + 461, + 624, + 498, + 639 + ], + "spans": [ + { + "bbox": [ + 461, + 624, + 498, + 639 + ], + "type": "text", + "content": "\"A pink grand piano\"" + } + ] + } + ], + "index": 59, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 509, + 624, + 559, + 640 + ], + "lines": [ + { + "bbox": [ + 509, + 624, + 559, + 640 + ], + "spans": [ + { + "bbox": [ + 509, + 624, + 559, + 640 + ], + "type": "text", + "content": "\"A garden gnome with a green hat\"" + } + ] + } + ], + "index": 61, + "angle": 0, + "type": "image_caption" + } + ], + "index": 58 + }, + { + "type": "image", + "bbox": [ + 515, + 547, + 552, + 623 + ], + "blocks": [ + { + "bbox": [ + 509, + 531, + 559, + 547 + ], + "lines": [ + { + "bbox": [ + 509, + 531, + 559, + 547 + ], + "spans": [ + { + "bbox": [ + 509, + 531, + 559, + 547 + ], + "type": "text", + "content": "\"A garden gnome with a red hat\"" + } + ] + } + ], + "index": 51, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 515, + 547, + 552, + 623 + ], + "lines": [ + { + "bbox": [ + 515, + 547, + 552, + 623 + ], + "spans": [ + { + "bbox": [ + 515, + 547, + 552, + 623 + ], + "type": "image", + "image_path": "56b2b68649ba006e662614387ad4f73f386530d27a5c770cd6389e4d7a0c3496.jpg" + } + ] + } + ], + "index": 60, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 644, + 545, + 687 + ], + "lines": [ + { + "bbox": [ + 306, + 644, + 545, + 687 + ], + "spans": [ + { + "bbox": [ + 306, + 644, + 545, + 687 + ], + "type": "text", + "content": "Figure 12. Latent-Paint results on shapes from ModelNet40 [48]. UV parameterization was not given for any of the meshes in this figure. For the Nascar shapes, the same text prompt was used with a different initialization." + } + ] + } + ], + "index": 62, + "angle": 0, + "type": "image_caption" + } + ], + "index": 60 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 752, + 317, + 761 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 752, + 317, + 761 + ], + "spans": [ + { + "bbox": [ + 293, + 752, + 317, + 761 + ], + "type": "text", + "content": "12669" + } + ] + } + ], + "index": 63 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 66, + 70, + 282, + 247 + ], + "blocks": [ + { + "bbox": [ + 66, + 70, + 282, + 247 + ], + "lines": [ + { + "bbox": [ + 66, + 70, + 282, + 247 + ], + "spans": [ + { + "bbox": [ + 66, + 70, + 282, + 247 + ], + "type": "image", + "image_path": "f90f36bca5547ae78916192fd86c4af8082642d2270c8fcd3e857b3ceee65675.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 247, + 287, + 281 + ], + "lines": [ + { + "bbox": [ + 47, + 247, + 287, + 281 + ], + "spans": [ + { + "bbox": [ + 47, + 247, + 287, + 281 + ], + "type": "text", + "content": "Figure 13. Generating different shoe textures over the same input mesh by only changing the conditioning text prompt. The surface parameterization was computed using XAtlas [52]." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "bbox": [ + 63, + 290, + 268, + 299 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 290, + 268, + 299 + ], + "spans": [ + { + "bbox": [ + 63, + 290, + 268, + 299 + ], + "type": "text", + "content": "Shape guidance No shape guidance Shape guidance No shape guidance" + } + ] + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 63, + 299, + 265, + 357 + ], + "blocks": [ + { + "bbox": [ + 63, + 299, + 265, + 357 + ], + "lines": [ + { + "bbox": [ + 63, + 299, + 265, + 357 + ], + "spans": [ + { + "bbox": [ + 63, + 299, + 265, + 357 + ], + "type": "image", + "image_path": "76183cfc6131694a8d3b750c46c63a888f34794451aafc409e8b912b70db54e4.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 361, + 287, + 384 + ], + "lines": [ + { + "bbox": [ + 47, + 361, + 287, + 384 + ], + "spans": [ + { + "bbox": [ + 47, + 361, + 287, + 384 + ], + "type": "text", + "content": "Figure 14. Results for the same prompts with and without shape-guidance. The guiding shapes are the same as in Figure 11." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 63, + 396, + 272, + 466 + ], + "blocks": [ + { + "bbox": [ + 63, + 396, + 272, + 466 + ], + "lines": [ + { + "bbox": [ + 63, + 396, + 272, + 466 + ], + "spans": [ + { + "bbox": [ + 63, + 396, + 272, + 466 + ], + "type": "image", + "image_path": "7f80ef3ed24b765b6afb35c1d9b0edcc5c517efc94f436e5ba97669568487ab7.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 472, + 287, + 506 + ], + "lines": [ + { + "bbox": [ + 46, + 472, + 287, + 506 + ], + "spans": [ + { + "bbox": [ + 46, + 472, + 287, + 506 + ], + "type": "text", + "content": "Figure 15. Latent-Paint results for an input mesh containing precomputed UV parameterization. Model courtesy of \"Keenan's 3D Model Repository\" [13]." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 75, + 517, + 258, + 600 + ], + "blocks": [ + { + "bbox": [ + 75, + 517, + 258, + 600 + ], + "lines": [ + { + "bbox": [ + 75, + 517, + 258, + 600 + ], + "spans": [ + { + "bbox": [ + 75, + 517, + 258, + 600 + ], + "type": "image", + "image_path": "e5cd4e3166b7a7622b6c698a756ebd0dc59a85a6ce8bf22e339bf54ff97b1935.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 86, + 601, + 246, + 609 + ], + "lines": [ + { + "bbox": [ + 86, + 601, + 246, + 609 + ], + "spans": [ + { + "bbox": [ + 86, + 601, + 246, + 609 + ], + "type": "text", + "content": "Stable Diffusion with \"A photo of a squirrel, backview\"" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 612, + 287, + 656 + ], + "lines": [ + { + "bbox": [ + 46, + 612, + 287, + 656 + ], + "spans": [ + { + "bbox": [ + 46, + 612, + 287, + 656 + ], + "type": "text", + "content": "Figure 16. note that the generated squirrel in the first row contains two faces from some view directions; see the second to the left view. This problem may be attributed to the fact that Stable Diffusion fails to generate back views of a squirrel; see bottom row." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 676, + 121, + 688 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 676, + 121, + 688 + ], + "spans": [ + { + "bbox": [ + 47, + 676, + 121, + 688 + ], + "type": "text", + "content": "5. Limitations" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "Our presented technique is yet a preliminary step towards the challenging goal of a comprehensive text-to-" + } + ] + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 307, + 63, + 550, + 171 + ], + "blocks": [ + { + "bbox": [ + 307, + 63, + 550, + 171 + ], + "lines": [ + { + "bbox": [ + 307, + 63, + 550, + 171 + ], + "spans": [ + { + "bbox": [ + 307, + 63, + 550, + 171 + ], + "type": "image", + "image_path": "93628da91db22f9c849208a7218d97f37a50b94465baab670e881365b12fa542.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 175, + 545, + 209 + ], + "lines": [ + { + "bbox": [ + 305, + 175, + 545, + 209 + ], + "spans": [ + { + "bbox": [ + 305, + 175, + 545, + 209 + ], + "type": "text", + "content": "Figure 17. Sketch-Shape ablation over " + }, + { + "bbox": [ + 305, + 175, + 545, + 209 + ], + "type": "inline_equation", + "content": "\\sigma_S" + }, + { + "bbox": [ + 305, + 175, + 545, + 209 + ], + "type": "text", + "content": " values (Eq. (4)) and input shape from Figure 9. As " + }, + { + "bbox": [ + 305, + 175, + 545, + 209 + ], + "type": "inline_equation", + "content": "\\sigma_S" + }, + { + "bbox": [ + 305, + 175, + 545, + 209 + ], + "type": "text", + "content": " grows, the constraint becomes more lenient, and enables the shape to evolve into new geometries." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 220, + 546, + 375 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 220, + 546, + 375 + ], + "spans": [ + { + "bbox": [ + 304, + 220, + 546, + 375 + ], + "type": "text", + "content": "shape model that uses no 3D supervision. Still, the proposed latent framework has its limitations. To attain a plausible 3D shape, we use the same \"prompt tweaking\" used by DreamFusion [35], i.e., adding a directional text-prompt (e.g., \"front\", \"side\" with respect to the camera) to the input text prompt. We find that this assistance tends to fail with our approach when applied to certain objects. Moreover, we find that even Stable Diffusion tends to generate unsatisfactory images when specifying the desired direction as shown in Figure 16. Additionally, similar to most works that employ diffusion models, there is a stochastic behavior to the results, such that the quality of the results may significantly vary between different seeds." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 387, + 383, + 399 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 387, + 383, + 399 + ], + "spans": [ + { + "bbox": [ + 306, + 387, + 383, + 399 + ], + "type": "text", + "content": "6. Conclusions" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 403, + 545, + 546 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 403, + 545, + 546 + ], + "spans": [ + { + "bbox": [ + 304, + 403, + 545, + 546 + ], + "type": "text", + "content": "In this work, we introduced a latent framework for generating 3D shapes and textures using different forms of text and shape guidance. We first adapted the score distillation loss for LDMs, enabling the use of recent, powerful and publicly available text-to-image generation models for 3D shape generation. Successfully applying score distillation on LDMs results in a fast and flexible object generation framework. We then introduced shape-guided control on the generated model. We showed two versions of shape-guided generation, Sketch-Shape and Latent-Paint, and demonstrated their effectiveness for providing additional control over the generation process." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 548, + 546, + 668 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 548, + 546, + 668 + ], + "spans": [ + { + "bbox": [ + 304, + 548, + 546, + 668 + ], + "type": "text", + "content": "Typically, the notion of rendering refers to generating an image in pixel space. Here, we have presented a method that renders directly into the latent space of a neural model. We believe that our Latent-NeRF approach opens the avenue for more latent space rendering methods, which can gain from a compact and effective latent representation, and advance the use of neural models that operate in latent space rather than pixel space. Furthermore, our novel approach and its ease-of-use nature would encourage further research toward effective text-guided shape generation." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 47, + 71, + 58, + 228 + ], + "type": "aside_text", + "angle": 270, + "lines": [ + { + "bbox": [ + 47, + 71, + 58, + 228 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 58, + 228 + ], + "type": "text", + "content": "Latent-Paint (Ours) CLIPMesh [26] Tango [9]" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 306, + 683, + 545, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 683, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 306, + 683, + 545, + 712 + ], + "type": "text", + "content": "This work was supported by the European research council (ERC-StG 757497 PI Giryes), and the Israel Science Foundation (grants no. 2492/20 and 3441/21)." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 294, + 752, + 317, + 761 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 752, + 317, + 761 + ], + "spans": [ + { + "bbox": [ + 294, + 752, + 317, + 761 + ], + "type": "text", + "content": "12670" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "type": "text", + "content": "[1] Omri Avrahami, Ohad Fried, and Dani Lischinski. 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Lion: Latent point diffusion models for 3d shape generation. arXiv preprint arXiv:2210.06978, 2022. 1" + } + ] + } + ], + "index": 28 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 752, + 318, + 761 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 752, + 318, + 761 + ], + "spans": [ + { + "bbox": [ + 294, + 752, + 318, + 761 + ], + "type": "text", + "content": "12672" + } + ] + } + ], + "index": 30 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 72, + 288, + 128 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 72, + 288, + 128 + ], + "spans": [ + { + "bbox": [ + 48, + 72, + 288, + 128 + ], + "type": "text", + "content": "[54] Richard Zhang, Phillip Isola, Alexei A Efros, Eli Shechtman, and Oliver Wang. The unreasonable effectiveness of deep features as a perceptual metric. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 586-595, 2018. 3" + } + ] + } + ], + "index": 0 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 753, + 317, + 761 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 753, + 317, + 761 + ], + "spans": [ + { + "bbox": [ + 294, + 753, + 317, + 761 + ], + "type": "text", + "content": "12673" + } + ] + } + ], + "index": 1 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Layout-Based Causal Inference for Object Navigation/18995e77-a0be-4475-8773-41d7233fd2aa_content_list.json b/2023/Layout-Based Causal Inference for Object Navigation/18995e77-a0be-4475-8773-41d7233fd2aa_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..e2d5820e467e3e52558da5089bb1f82d46c42964 --- /dev/null +++ b/2023/Layout-Based Causal Inference for Object Navigation/18995e77-a0be-4475-8773-41d7233fd2aa_content_list.json @@ -0,0 +1,1438 @@ +[ + { + "type": "text", + "text": "Layout-based Causal Inference for Object Navigation", + "text_level": 1, + "bbox": [ + 214, + 130, + 756, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Sixian Zhang $^{1,2}$ , Xinhang Song $^{1,2}$ , Weijie Li $^{1,2}$ , Yubing Bai $^{1,2}$ , Xinyao Yu $^{1,2}$ , Shuqiang Jiang $^{1,2}$", + "bbox": [ + 109, + 179, + 856, + 200 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1Key Lab of Intelligent Information Processing Laboratory of the Chinese Academy of Sciences (CAS),", + "bbox": [ + 176, + 200, + 792, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Institute of Computing Technology, Beijing $^2$ University of Chinese Academy of Sciences, Beijing", + "bbox": [ + 192, + 218, + 774, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{sixian.zhang, xinhang.song, weijie.li, yubing.bai, xinyao.yu}@vip1.ict.ac.cn", + "bbox": [ + 143, + 236, + 823, + 252 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "sqjiang@ict.ac.cn", + "bbox": [ + 405, + 253, + 558, + 268 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 304, + 313, + 320 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Previous works for ObjectNav task attempt to learn the association (e.g. relation graph) between the visual inputs and the goal during training. Such association contains the prior knowledge of navigating in training environments, which is denoted as the experience. The experience performs a positive effect on helping the agent infer the likely location of the goal when the layout gap between the unseen environments of the test and the prior knowledge obtained in training is minor. However, when the layout gap is significant, the experience exerts a negative effect on navigation. Motivated by keeping the positive effect and removing the negative effect of the experience, we propose the layout-based soft Total Direct Effect (L-sTDE) framework based on the causal inference to adjust the prediction of the navigation policy. In particular, we propose to calculate the layout gap which is defined as the KL divergence between the posterior and the prior distribution of the object layout. Then the sTDE is proposed to appropriately control the effect of the experience based on the layout gap. Experimental results on AI2THOR, RoboTHOR, and Habitat demonstrate the effectiveness of our method. The code is available at https://github.com/sx-zhang/Layout-based-sTDE.git.", + "bbox": [ + 75, + 335, + 473, + 684 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 709, + 209, + 724 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The visual object-oriented navigation task (i.e. Object-Nav) [3] requires the agent to navigate to a user-specified goal (e.g. laptop) based on the egocentric visual observations. A typical challenge is navigating in unseen environments, where the goal is invisible most of the time, i.e. the partial observable problem, which typically results in the agent's meaningless actions (e.g. back-tracking or getting lost at dead-ends). Although encouraging the exploration in the unseen environment (until the goal is visible) is an intuitive solution, the lack of environment layout information still limits the efficiency of goal-oriented navigation.", + "bbox": [ + 75, + 734, + 468, + 902 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/e95d5897987e85443d26760a9d208a4e8932abf190099b677c3bbb08161e5fa6.jpg", + "image_caption": [ + "S: Observation" + ], + "image_footnote": [], + "bbox": [ + 521, + 305, + 643, + 405 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/8c4c4aaa21593b4ad368e0a8680222991bbf762f6e317d87000dbf8d53895688.jpg", + "image_caption": [ + "Intervention", + "(a) The factual prediction", + "Z:Experience A:Action", + "(b) The counterfactual prediction", + "Figure 1. The proposed causal graph. (a) represents the fact prediction $a$ , i.e. the original prediction of the trained model. (b) refers to the counter-fact prediction $\\bar{a}$ , i.e. the prediction is only affected by the experience $Z$ . (b) is realized by applying the intervention and counterfactual operations to the original model." + ], + "image_footnote": [], + "bbox": [ + 669, + 304, + 849, + 406 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, the learning-based methods attempt to model the prior knowledge of the spatial relationships among the objects, so the agent could infer the likely locations of the goal based on the current observation (which objects are observed currently) and the prior knowledge (the spatial relationships between the goal and the observed objects) learned in the training stage. Some works utilize additional modules to construct the objects graph [15, 59, 60], the region graph [63] and the attention mechanism [32], while others [16, 56] employ a network that implicitly learns the spatial relationships end-to-end. All these methods attempt to establish prior knowledge in training environments, so that the agent would utilize the prior knowledge to associate the real-time observations with the goal, and infer the likely locations of the goal during the inference. The underlying assumption of these methods is that all of the object layouts in unseen environments should be exactly consistent with those in training environments. However, the layout consistency assumption is only partially correct due to the limited training data. Thus, those methods typically suffer from poor generalization [31] in unseen environments.", + "bbox": [ + 496, + 551, + 893, + 868 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To reveal the causes of poor generalization, we propose to use the casual graph (i.e. Structural Causal Model, SCM", + "bbox": [ + 498, + 869, + 893, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "10792", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "[38]) to analyze these navigation works. As illustrated in Fig. 1 (a), the navigation model takes the observation $S$ and the goal $G$ as the input, and predicts the action $A$ at each timestamp. The causal links $S \\rightarrow Z$ and $G \\rightarrow Z$ represent that the observation and the goal are embedded by the pre-constructed modules [15, 32, 59, 60, 63] or the pre-trained network [16, 56]. The embedding vector is defined as the experience $Z$ in the causal graph, which introduces the prior knowledge to influence action prediction ( $Z \\rightarrow A$ ). Meanwhile, the real-time observation and the goal also independently affect the prediction without being encoded by the prior knowledge module, which is represented as $S \\rightarrow A$ and $G \\rightarrow A$ , respectively. The causal links $S \\rightarrow A$ and $G \\rightarrow A$ represent the exploration-based effect (only related to the current episode) on the action prediction, which is different from the experience-based effect $Z \\rightarrow A$ . Consider two cases of the layout gap between the current environment and the prior knowledge: 1) the layout gap is minor and 2) the layout gap is significant. In the former case, the object layout is consistent in the current environment and the prior knowledge. Thus, the experience $Z$ exerts a positive effect on the prediction of action $A$ . However, the effect of experience $Z$ in the latter case could be negative. If the agent still relies on the \"negative\" experience to predict actions, it will suffer from poor generalization. Therefore, wisely utilizing the experience is essential to the ObjectNav task.", + "bbox": [ + 76, + 90, + 472, + 484 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Motivated by wisely utilizing the learned experience, we propose the soft Total Direct Effect (sTDE) framework based on the Total Direct Effect analysis in causal inference. Our sTDE improves the generalization of the trained model in inference by eliminating the prediction bias brought by the experience. To decouple the effect of experience, we construct the counter-fact prediction $\\bar{a}$ : the prediction is only affected by the experience $Z$ while ignoring the $S$ and $G$ , as shown in Fig. 1 (b). Then we propose the object layout estimator that calculates whether the effect of the experience is positive, by measuring the layout gap between the current environment and the prior knowledge. Furthermore, our sTDE will remove the counter-fact prediction $\\bar{a}$ from the fact prediction $a$ when the layout gap is large.", + "bbox": [ + 76, + 488, + 472, + 700 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we propose the layout-based soft TDE framework for the ObjectNav task. Specifically, we adopt the Dirichlet-Multinomial distribution [22] to formulate the contextual relationship between objects, which represents the object layout of the environment. Before training, the agent learns prior layout distribution (i.e. the prior parameters of Dirichlet-Multinomial distribution) by randomly exploring the training environments. In the training stage, based on the Bayesian inference, the agent estimates the posterior layout distribution with the prior distribution and newly obtained observations. Then the constantly updated posterior layout is encoded into the navigation model and utilized to learn the environment-adaptive experience. The", + "bbox": [ + 76, + 704, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "entire model is trained with RL by maximizing the reward of reaching the goal. In the test stage, our agent will not directly use the trained policy as most previous works do. The agent first calculates the layout gap and the counter-fact prediction. The layout gap is determined by calculating the KL divergence between the posterior and prior distribution of object layouts and serves as a weight to determine whether to remove the counter-fact prediction (i.e. experience effect) from the original prediction. The experimental results on AI2THOR [27], RoboTHOR [12] and Habitat [48] indicate that our layout-based sTDE (L-sTDE) can be a plug-and-play method to boost existing methods to achieve better navigation performances.", + "bbox": [ + 496, + 90, + 893, + 287 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 301, + 640, + 316 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Visual Object Navigation. Target-oriented visual navigation can be categorized [5] into PointGoal [8, 18, 43, 55], AreaGoal [28, 57], AudioGoal [10, 11], ImageGoal [19, 29, 48], LanguageGoal (vision-and-language navigation) [23, 40, 41] and ObjectGoal. We focus on visual ObjectGoal navigation, which sets the object category as the target. Previous map-based methods usually build a metric map [6-8, 44] or topological map [9, 47] to memorize the environment layout. Besides, a popular deep-learning pipeline is to take an end-to-end network [2, 17, 34] to process the visual embedding and goal embedding, then predict the navigation action. Based on that, recent learning-based methods propose various improvement ideas, such as semantic representation [35], prior knowledge [59], object relation graph [15, 60, 63], attention mechanism [32], meta-learning [56], and transformer structure [16]. These well-trained modules provide prior knowledge to guide the agent in unseen environments. In our work, we denote such knowledge learned from training (with whatever improvement designs) as the experience. We try to find out, under different environment layouts, whether the learned experience takes a positive effect or not, and how to better utilize the experience to improve the navigation.", + "bbox": [ + 496, + 325, + 893, + 674 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Causal Inference. Causal inference [38, 39] provides analysis tools (e.g. intervention, counter-fact) to reveal the causal effect behind the data-based statistical correlation, which is widely adopted in epidemiology, psychology, or politics research [24, 30, 46]. Recently, causal inference is introduced into the computer vision society for scene graph generation [50], vision and language task [1,36], long-tailed classification [49] and few/zero-shot learning [4, 62]. For the visual navigation task, [37] generates counterfactual observations to improve generalization to new environments for VLN (vision-and-language navigation) task. [54] proposes causal CT (continuous-time) models for visual drone navigation tasks. In our work, we focus on the ObjectNav task and utilize the causal inference to wisely control the effect of experience in the inference.", + "bbox": [ + 496, + 674, + 895, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "10793", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Preliminaries of ObjectNav Task", + "text_level": 1, + "bbox": [ + 76, + 89, + 375, + 107 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Task Definition. The ObjectNav task requires the agent to navigate to a user-specified object category from a random starting location in an unseen scene, and the agent is only allowed to utilize the egocentric visual observation (e.g. RGB images) and the semantic embedding of the target object. Formally, at each timestamp $t$ , the agent receives the observation $S = s^t$ and the goal $G = g^t$ and is expected to adopt an action $A = a^t$ , $a^t \\in \\mathcal{A}$ . The discrete action space is defined as: $\\mathcal{A} = \\{MoveAhead, RotateLeft, RotateRight, LookDown, LookUp, Done\\}$ . When the agent outputs the Done action, the episode terminates. An episode is considered successful if, within a certain number of steps, the final location of the agent is close to the goal within a distance threshold (e.g. $1m$ ) and the goal is visible in the egocentric observation.", + "bbox": [ + 75, + 114, + 468, + 340 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Navigation Model. Prevailing ObjectNav works can be summarized as a visual-goal encoder and a policy function, as shown in Fig. 2. The visual-goal encoder is constructed to associate the visual observation $S$ and the goal $G$ . We denote such association as the experience $Z$ since the encoder could learn the prior experience during the training.", + "bbox": [ + 75, + 340, + 468, + 431 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Previous learning-based methods typically implement the visual-goal encoder as an object relation graph [15, 59, 60], region graph [63], attention module [32] and transformer structure [16]. For instance, the ORG [15] builds an object relation graph, where the nodes are defined as the object categories and the edges are defined as the spatial correlations among different categories. The object relation graph takes the observation and the goal as inputs and encodes them with the learned edges to obtain the experience $Z$ . Previous map-based methods [7, 44] typically construct the semantic map based on the observations, and embed the map with the target. Such embedding is also regarded as the experience $Z$ . Based on the observation, target object, and these learned experiences, the policy module will output the prediction. These navigation models are typically trained with the RL (reinforcement learning) [33, 55, 64].", + "bbox": [ + 75, + 431, + 470, + 674 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. The Proposed Solution", + "text_level": 1, + "bbox": [ + 76, + 686, + 290, + 703 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.1. Layout-based Soft Total Direct Effect", + "text_level": 1, + "bbox": [ + 76, + 710, + 398, + 726 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We humans make decisions in a causality-based manner: we have the instinct to assess the effect of the navigation experience [51] and wisely eliminate the cognition bias from the experience. However, the machines are likelihood-based [50] and the predictions depend on the association likelihood between observations, goal, and actions, which is mainly learned from limited training data. Therefore, the predictions are inevitably biased due to the biased experience. Prevailing methods [15, 16, 56, 59, 60, 63] entirely accept the experience learned in the training stage, and rarely consider whether the prior experience is beneficial to the", + "bbox": [ + 75, + 734, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/d068a7e5d2b7515d7dc5320ef9b095cc57ec8bb6bb13dad931fc0532992b75d5.jpg", + "image_caption": [ + "Figure 2. Prevailing navigation framework (top) and our contributions (bottom). Our layout estimator outputs the expectation $w^t$ of posterior layout distribution and the layout gap $D_{\\Delta}^{t}$ . The $w^t$ is proposed to enhance the adaptability of the experience $z^t$ to new environments. The layout gap $D_{\\Delta}^{t}$ serves as a weight to alleviate the experience bias." + ], + "image_footnote": [], + "bbox": [ + 504, + 89, + 890, + 330 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "current environment. However, as previously discussed, the learned experience has both positive and negative effects, especially in the unseen environments, which may have a different layout from the training environments. Therefore, keeping positive effects and removing negative effects of learned experience is essential to the navigation models.", + "bbox": [ + 496, + 452, + 890, + 542 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The causal inference [39,52,53] encourages the machine to discover the causality behind the association likelihood, which has been proven to be an effective analysis method in many computer vision tasks [36, 49, 50, 61]. From the perspective of causal inference, the experience $Z$ serves as the mediator between the input (observation $S$ and target $G$ ) and the output (action $A$ ) as illustrated in Fig. 1 (a). To eliminate the mediation fallacy, the causal inference [38] introduces the Total Direct Effect (TDE) analysis to remove the prediction bias brought by the mediator.", + "bbox": [ + 496, + 542, + 890, + 694 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Total Direct Effect. The fundamental principle behind TDE analysis [36, 49, 50] is to build a bias prediction $\\bar{a}^t$ that is exclusively affected by the mediator, and then remove the bias item from the original prediction $a^t$ . The TDE analysis is formulated as:", + "bbox": [ + 496, + 694, + 890, + 768 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nT D E \\left(a ^ {t}\\right) = a ^ {t} - \\bar {a} ^ {t} \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 622, + 784, + 890, + 801 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $a^t = \\pi (A|S = s^t,G = g^t)$ is the factual prediction of a trained model $\\pi$ , which takes the observation $S = s^t$ and target $G = g^{t}$ as the input, as shown in Fig. 1 (a). The latter is the counterfactual prediction $\\bar{a}^t = \\pi (A|do(S = \\bar{s}^t,G = \\bar{g}^t),Z = Z_{s^t,g^t})$ as shown in Fig. 1 (b). The calculation of $\\bar{a}^t$ includes two operations", + "bbox": [ + 496, + 809, + 890, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "10794", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "in causal inference: intervention and counterfactual operations. The intervention operation is denoted as $do(\\cdot)$ and realized by specifying a certain value for the variable (e.g. $do(S = \\bar{s}^t)$ ). The intervened value (e.g. $\\bar{s}^t$ , $\\bar{g}^t$ ) is set to a random or zero vector. The intervention operation eliminates the effect of observation $S$ and goal $G$ on the action prediction, while it also changes the value of the causal successor (i.e. $Z$ ). However, since our motivation is to model the case only affected by the mediator, which requires the mediator $Z$ to remain the original value. To this end, the counterfactual operation assigns the original value to the variable $Z$ as if $S = s^t$ , $G = g^t$ had existed. The counterfactual operation is symbolized as $Z = Z_{s^t, g^t}$ .", + "bbox": [ + 75, + 90, + 472, + 287 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The TDE analysis is easily realized by manipulating the values of several variables (e.g. $S, G, Z$ ) and is efficient in removing the effect of the mediator (i.e. experience). However, the experience is not always detrimental. It can also be beneficial when the object layout gap is minor. Therefore, we propose the soft TDE to appropriately maintain the positive effect of experience.", + "bbox": [ + 75, + 287, + 472, + 393 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Soft Total Direct Effect. In alternative to previous TDE analysis, our soft TDE modifies the Eq. 1 by adding a trade-off weight, which is formulated as:", + "bbox": [ + 76, + 395, + 472, + 441 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\ns T D E (a ^ {t}) = a ^ {t} - R e L U (D _ {\\Delta} ^ {t} - \\varepsilon) \\cdot \\bar {a} ^ {t} \\qquad (2)\n$$\n", + "text_format": "latex", + "bbox": [ + 137, + 458, + 468, + 477 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $ReLU(\\cdot)$ is the ReLU activation function, and $\\varepsilon$ is a threshold hyperparameter. The $D_{\\Delta}^{t}$ is the object layout gap, which is produced by our layout estimator (Sec. 4.2) as shown in Fig. 2. The $D_{\\Delta}^{t}$ evaluates the effect of the experience $Z$ , and preserves the positive experience when the layout gap between the current environment and prior knowledge is minor (i.e. $D_{\\Delta}^{t}$ is less than the threshold $\\varepsilon$ ).", + "bbox": [ + 75, + 484, + 472, + 594 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. Layout Estimator", + "text_level": 1, + "bbox": [ + 76, + 604, + 250, + 619 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Object Layout. For the ObjectNav task, the main challenge is the partially observable problem, that the agent can only observe the partial area at each time. With continuously observing during the navigation process, more objects will be observed, and the partially known problem can also be alleviated. Considering objects are usually distributed in a reasonable layout, the adjacent relation of objects is essential to help the agent infer the location of the target object based on the observed objects. Therefore, we concentrate on the contextual relationship to represent the object layout. The object layout in a scene is defined as the set $D = \\{\\theta_{i}\\}_{i=1}^{K}$ , where $K$ is the number of object categories. The $\\theta_{i} = (\\theta_{i,j})_{j=1}^{K}$ represents the context distribution of object category $c_{i}$ . Each dimension $\\theta_{i,j}$ represents the probability $p(c_{j}|c_{i})$ that the object category $c_{j}$ can be observed around the category $c_{i}$ in an observation. Specifically, we assume that the context distribution follows the Dirichlet distribution: $\\theta_{i} = (\\theta_{i,j})_{j=1}^{K} \\sim \\text{Dir}(\\alpha_{i})$ , where", + "bbox": [ + 75, + 628, + 472, + 902 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/47cd8672246a84e1dc5892f5085577f3b54d1920e871d61f934af64b4ba08df7.jpg", + "image_caption": [ + "Figure 3. The calculation of the likelihood function $p(s_i^t |\\theta_i)$ ." + ], + "image_footnote": [], + "bbox": [ + 506, + 88, + 890, + 311 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$\\sum_{j}\\theta_{i,j} = 1,\\theta_{i,j}\\geq 0$ , and $\\alpha_{i} = (\\alpha_{i,j})_{j = 1}^{K},\\alpha_{i,j} > 0$ parameterizes the distribution. The Dirichlet distribution is chosen for two reasons: 1) the conjugate prior permits concise calculations; 2) the likelihood-equivalence property [22].", + "bbox": [ + 496, + 359, + 890, + 422 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "At the beginning of every new episode, the parameter $\\alpha_{i}$ is initialized as the prior initial value $\\alpha_{i}^{*}$ ( $\\alpha_{i}^{*}$ will be detailed in Sec. 4.3). At each timestamp $t$ , our method computes the posterior object distribution based on the incoming observations. Specifically, the agent receives the visual observation $s^t$ , and the visual observation is then converted into a count vector $n^t \\in \\mathbb{R}^K$ , where each dimension of $n^t = (n_i^t)_{i=1}^K$ , $n_i^t \\geq 0$ records the number of each object category appearing in the current observation. The count vector $n^t$ is obtained by the object detection or segmentation modules (e.g. Faster R-CNN [45] or Mask R-CNN [20]). As shown in Fig. 3, we define $n_{-i}^t = (n_{-i,j}^t)_{j=1}^K$ , $n_{-i,j}^t \\geq 0$ as the count of other categories (except $c_i$ ) and define $s_i^t$ as the contextual observation of the category $c_i$ . Conditioned on $c_i$ , assume the probability that $s_i^t$ is observed follows the multinomial distribution $s_i^t \\sim Mult(n_{-i}^t, \\theta_i)$ . Then the likelihood function can be calculated as:", + "bbox": [ + 496, + 424, + 892, + 686 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\np \\left(s _ {i} ^ {t} \\mid \\theta_ {i}\\right) = \\prod_ {j = 1} ^ {K} \\theta_ {i, j} ^ {n _ {- i, j} ^ {t}} \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 619, + 700, + 890, + 743 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Meanwhile, according to the previous Dirichlet distribution assumption, the prior distribution of $\\theta_{i}$ at timestamp $t$ is $p\\left(\\theta_i|\\alpha_i^t\\right) = Dir\\left(\\theta_i|\\alpha_i^t\\right)$ . Considering the contextual observation $s_i^t$ , the posterior distribution of $\\theta_{i}$ is further calculated according to the Bayesian inference as the following:", + "bbox": [ + 496, + 753, + 893, + 829 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\np \\left(\\theta_ {i} \\mid s _ {i} ^ {t}, \\alpha_ {i} ^ {t}\\right) = \\frac {p \\left(s _ {i} ^ {t} \\mid \\theta_ {i}\\right) p \\left(\\theta_ {i} \\mid \\alpha_ {i} ^ {t}\\right)}{p \\left(s _ {i} ^ {t} \\mid \\alpha_ {i} ^ {t}\\right)} = D i r \\left(\\theta_ {i} \\mid \\alpha_ {i} ^ {t} + n _ {- i} ^ {t}\\right) \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 508, + 853, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "10795", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The Eq. 4 indicates that the posterior distribution $p(\\theta_i | s_i^t, \\alpha_i^t)$ also satisfies the Dirichlet distribution (the calculation process is detailed in the supplements), which is known as the conjugate prior property. The conjugate prior property guarantees the succinct calculation for the posterior distribution of $\\theta_i$ , i.e., simply combining the count vector $n_{-i}^t$ of context objects around category $c_i$ with the hyperparameter $\\alpha_i^t$ of the prior distribution. Similarly, the posterior distributions of other object categories can also be obtained following the Eq. 4.", + "bbox": [ + 75, + 90, + 468, + 241 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Furthermore, the posterior distributions at time $t$ serves as the prior distributions at time $t + 1$ , thus the value of hyperparameter $\\alpha_{i}$ is updated by $\\alpha_{i}^{t + 1} = \\alpha_{i}^{t} + n_{-i}^{t}$ . This update guarantees the knowledge of object layout is continuously adapted to the current navigation environment.", + "bbox": [ + 75, + 242, + 468, + 316 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Based on the obtained posterior distribution, the layout gap $D_{\\Delta}^{t}$ is defined as the KL divergence between the posterior and prior object layout over all categories. Formally, the object layout gap $D_{\\Delta}^{t}$ is defined as:", + "bbox": [ + 76, + 316, + 468, + 378 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nD _ {\\Delta} ^ {t} = \\tanh \\left( \\right.\\frac {1}{K} \\sum_ {i = 1} ^ {K} K L \\left( \\right.p \\left(\\theta_ {i} \\mid s ^ {t}, \\alpha_ {i} ^ {t}\\right)\\left\\| \\right. p \\left(\\theta_ {i} \\mid \\alpha_ {i} ^ {t}\\right)\\left. \\right)\\left. \\right) \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 91, + 388, + 468, + 429 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\tanh(\\cdot)$ is the tanh activation function. The layout gap $D_{\\Delta}^{t}$ estimates the gap between the posterior object layout at time $t$ and the prior knowledge before time $t$ , which plays a vital role in the Eq. 2.", + "bbox": [ + 75, + 436, + 468, + 497 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Environment-Adaptive Experience. The prevailing methods [15, 16, 59] typically encode the visual observation $s^t$ and the target object $g^t$ into the experience $z^t \\in \\mathbb{R}^{K \\times M}$ during training, where $K$ is the number of object categories and $M$ refers to the feature dimension. The learned experience could be both biased (the layout gap between the training and test environments) and environment-static (without adaptation to the current environment). Therefore, in addition to eliminate the bias in the inference, we also propose to enhance the environmental adaptability of the experience $z^t$ to achieve a better performance. To this end, the dynamically updated knowledge of object layout $D = \\{\\theta_i\\}_{i=1}^K$ is encoded into the navigation framework. Specifically, the expectation of the posterior distribution of the object layout $D$ is formalized as $w^t \\in \\mathbb{R}^{K \\times K}$ , $w_{i,j}^t > 0$ . For $j = i$ , since $p(c_i | c_i)$ always exists, we set $w_{i,j}^t = 1$ . When $j \\neq i$ , $w_{i,j}^t = \\mathbb{E}_{p(\\theta_i | s_i^t, \\alpha_i^t)}(\\theta_{i,j})$ , where $\\mathbb{E}(\\cdot)$ denote the expectation calculation. Based on [22], the expectation of the Dirichlet function $Dir(\\theta_i | \\alpha_i^t + n_{-i}^t)$ is equivalent to the normalization of its parameters. Accordingly, for $j \\neq i$ ,", + "bbox": [ + 75, + 498, + 468, + 801 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nw _ {i, j} ^ {t} = \\mathbb {E} _ {p \\left(\\theta_ {i} \\mid s _ {i} ^ {t}, \\alpha_ {i} ^ {t}\\right)} \\left(\\theta_ {i, j}\\right) = \\frac {\\alpha_ {i , j} ^ {t} + n _ {- i , j} ^ {t}}{\\sum_ {j = 1} ^ {K} \\left(\\alpha_ {i , j} ^ {t} + n _ {- i , j} ^ {t}\\right)} \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 821, + 468, + 861 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Since $w^{t}$ is updated in real-time, we propose to improve the environment-static experience $z^{t}$ to environment-", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "adaptive experience $\\hat{z}^t$ by incorporating the dynamically updated knowledge of object layout, where $\\hat{z}^t$ is given by:", + "bbox": [ + 498, + 90, + 890, + 121 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {z} ^ {t} = z ^ {t} \\odot [ w ^ {t} \\times g ^ {t} ] \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 624, + 133, + 890, + 152 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\odot$ represents the element-wise multiplication, $\\times$ refers to the matrix multiplication, and $g^{t}\\in \\mathbb{R}^{K}$ is a one-hot vector indicating the target category of the goal. The result of $[w^t\\times g^t ]\\in \\mathbb{R}^K$ indicates the probability of the target $g^{t}$ is observed conditioned on each object category, which serves as a weight on the category-specific dimension of $z^t$", + "bbox": [ + 496, + 157, + 890, + 250 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Training and Inference", + "text_level": 1, + "bbox": [ + 498, + 258, + 714, + 273 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As shown in Fig. 2, our layout estimator outputs (1) the expectation $w^t$ of the posterior layout distribution, and (2) the layout gap $D_{\\Delta}^{t}$ . Both $w^t$ and $D_{\\Delta}^{t}$ are calculated mathematically without learnable parameters, thus our method has the plug-and-play property to boost the existing methods. Specifically, our layout-based sTDE is realized as: (1) Before training, to determine the initial value $(\\alpha_i^*)_{i=1}^K$ , we first employ a random agent equipped with our object layout estimator, whose parameters $(\\alpha_i)^K_{i=1}$ are initialized as all one vector. Then the agent randomly explores the training scenes to obtain sufficient observations to update the parameters by Eq. 4. The updated parameters are defined as $(\\alpha_i^*)_{i=1}^K$ . (2) In the training stage, at the beginning of every episode, all parameters $(\\alpha_i)^K_{i=1}$ are initialized as the prior parameters $(\\alpha_i^*)_{i=1}^K$ . The layout estimator calculates the posterior distribution of object layout $D$ (Eq. 4), using the constant observation $s^t$ and the prior distribution. Then the expectation of the posterior distribution $w^t$ is estimated and incorporated in the navigation model $\\pi$ (Eq. 6, 7). The model $\\pi$ is trained with RL. (3) In the causal-inference stage, the agent will not directly use the trained policy $\\pi$ , while it first calculates the layout gap $D_{\\Delta}^{t}$ (Eq. 5) and the counter-fact prediction $\\bar{a}^t$ (the effect of the experience). Then the agent appropriately removes the counter-fact prediction $\\bar{a}^t$ from the fact prediction $a^t$ based on the layout gap $D_{\\Delta}^{t}$ (Eq. 2). For more details and algorithms of training and inference, please refer to the supplements.", + "bbox": [ + 496, + 281, + 890, + 688 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Note that the expectation of the posterior distribution of the object layout $w^{t}$ affects the prediction of the model during both training and inference, while $D_{\\Delta}^{t}$ is utilized for debiasing only in the inference. Furthermore, we want to explain why the debiasing operation only acts in inference. As shown in Fig. 1, the prediction is influenced by two effects: the inputs (the observation $S$ and the goal $G$ ) and their mediator (the experience $E$ ). The mediator (experience) has agnostic effects because it is learned from limited training data. The training data can not cover all room layouts, thus resulting the prediction bias in the inference. Consequently, the debiasing operation (i.e. the sTDE partially removes the effect of experience from prediction) is conducted in inference to decouple the effect from the training data.", + "bbox": [ + 496, + 688, + 892, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "10796", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/7faa6a3b890fed9cfffc6d287260bb9cf9ab192f7cad457e9239037d339a4ec9.jpg", + "image_caption": [ + "Figure 4. The correlation between the navigation performance on success rate (SR) and the layout similarity." + ], + "image_footnote": [], + "bbox": [ + 81, + 88, + 467, + 243 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 76, + 306, + 209, + 323 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 76, + 330, + 266, + 348 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We utilize the AI2THOR [27], RoboTHOR [12] simulators to conduct ablation studies and compare our method with the learning-based methods [15, 16, 32, 56, 59, 63, 64]. The experimental settings on above datasets follow the primary works [15, 16, 63]. Besides, we choose the Gibson [58] dataset in the Habitat simulator [48] to compare our method with the map-based methods and adopt the same settings as [7]. For more details about the settings of the datasets (e.g. the split of training, validation, testing scenes, and the target objects), please refer to the supplements.", + "bbox": [ + 75, + 354, + 468, + 505 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Our method and the related works are both trained to maximize the navigation reward via RL. The reward function penalizes the agent by -0.01 for each step and rewards it by 5 if the episode is successful (the successful episode is defined in Sec. 3). All methods are trained with 6M episodes, where in each episode, the starting position of the agent and the goal are randomly selected. Note that, since our method needs prerequisite exploration to determine the initial parameters $(\\alpha_{i}^{*})_{i = 1}^{K}$ of the layout distribution. To be fair, we employ the agent to randomly explore the training rooms to learn the initial parameters for 2M episodes, then we train our method with 4M episodes.", + "bbox": [ + 75, + 506, + 468, + 686 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For evaluation, we repeatedly run 3 trials and report the results with mean $\\pm$ standard deviation. We choose SR (Success Rate), SPL (Success weighted by Path Length), and DTS (Distance to Goal) metrics for evaluation, which are detailed in the supplements. For all results in the following tables, the $\\uparrow$ means that the larger value is better, while $\\downarrow$ indicates the opposite.", + "bbox": [ + 75, + 686, + 467, + 792 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. The Compared Methods", + "text_level": 1, + "bbox": [ + 76, + 801, + 302, + 816 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We choose the learning-based methods [15, 16, 32, 56, 59, 63, 64] and the map-based method [7] for comparison. Random: the agent adopts random actions. RGB(D) + RL (A3C) [48, 64]: the agent utilizes the simple embeddings of visual input and the goal, and is trained with A3C [34].", + "bbox": [ + 75, + 824, + 467, + 900 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/f7db9292303efec60f8300922b5396aadfaf3268bb1697ecfd9b52312dfa21d7.jpg", + "image_caption": [ + "Figure 5. Category-wise improvement of our method compared to the baseline. The categories are arranged from high to low based on their average layout similarity between training and testing scenes." + ], + "image_footnote": [], + "bbox": [ + 504, + 88, + 887, + 204 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "SP [59]: SP constructs the scene prior knowledge from the external dataset. The prior knowledge encoded with GCN [26] is provided to the agent as the additional information. SAVN [56]: SAVN establishes a sub-network to learn a self-supervised interaction loss. EOTP [32]: EOTP proposes an attention module to encode the semantic information about the observed objects. ORG [15]: ORG proposes to learn an object relation graph, and builds a memory-augmented tentative policy network (TPN) to produce self-supervision. VTNet [16]: VTNet employs the Transformer network to encode the visual information and the goal. HOZ [63]: HOZ attempts to abstract the region relation among the objects and proposes to learn the region relation graph to associate the vision and the goal. SemExp [7]: SemExp builds an episodic semantic map and trains a goal-oriented policy taking the semantic map as the input.", + "bbox": [ + 496, + 301, + 890, + 544 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.3. Evaluation Results", + "text_level": 1, + "bbox": [ + 500, + 556, + 679, + 570 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we adopt the ORG [15] as the baseline and conduct evaluations on the validation set of AI2THOR.", + "bbox": [ + 498, + 580, + 890, + 609 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Correlation between layout and success rate. Our motivation is that the layout gap between training and testing scenes may have an impact on navigation. To verify this, we take the statistic and visualize the results in Fig. 4 (a), where the y-axis represents the success rate of navigating to objects $c_{i}$ in a testing scene $R_{j}$ , the x-axis represents the layout similarity of the object $c_{i}$ between the training scenes and the test scenes, and the scatter points represent all target objects in all test scenes. As shown in Fig. 4 (b), the layout similarity is defined as the cosine similarity of the statistics vectors (the count of cooccurrence objects) obtained in the training scenes and the test scene $R_{j}$ . Fig. 4 (a) indicates that the navigation performance on SR during inference has a generally positive correlation with the layout similarity, which supports our motivation.", + "bbox": [ + 496, + 612, + 890, + 838 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Improvements of our method compared to baseline. The navigation performance of the baseline (green bar) and the improvements brought by our method (blue bar) are shown in Fig. 5. All goals (x-axis) are arranged from high", + "bbox": [ + 498, + 840, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "10797", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/7670fa5f1fbaf1bf1bc8c9d8b1512897b312423c5391489fd9c5ecc0bfe45bb3.jpg", + "image_caption": [ + "Figure 6. The ablation study of the threshold $\\varepsilon$ and the visualization of the object layout gap $D_{\\Delta}^{t}$ over the navigation steps." + ], + "image_footnote": [], + "bbox": [ + 81, + 88, + 267, + 222 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/28df14622981d9ff5fc7eec70b3c389b54638d3e36a69f48552bdbe65ba34c44.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 272, + 88, + 467, + 222 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "to low based on their layout similarity. The results indicate that our method can bring more obvious improvement in the categories with low layout similarity (as illustrated by the red dashed circle). We presume that the goals with a larger layout gap are more susceptible to the effects of the experience, thus benefiting more from our de-biased method. The results once again support our motivation.", + "bbox": [ + 75, + 291, + 467, + 397 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Ablations on the threshold $\\varepsilon$ . The threshold $\\varepsilon$ influences the agent by Eq. 2, which determines whether to remove the prediction bias introduced by the experience. As shown in Fig. 6 (a), the results of different threshold $\\varepsilon$ basically show the same trend on the SR, SPL metrics: as the value of threshold $\\varepsilon$ increases, the performances on these metrics initially increase and then decrease. When the value of threshold $\\varepsilon$ is small, the Eq. 2 tends to consider that the majority of experiences $Z$ are negative and need to be removed. At this point, gradually increasing the threshold $\\varepsilon$ could retain more experiences and improve performance. However, when the threshold $\\varepsilon$ is too large (e.g. $\\varepsilon = 1$ ), the Eq. 2 falls into another extreme which considers all experiences are positive and need to be preserved, resulting in the performance degradation. The results on DTS metric indicate that excessively removing the experience ( $\\varepsilon$ is small) will increase the exploration of the agent, thus resulting in worse performance on DTS. Based on the above results, we choose the threshold as $\\varepsilon = 0.5$ .", + "bbox": [ + 75, + 398, + 467, + 684 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Visualization of the object layout gap $D_{\\Delta}^{t}$ . The object layout gap $D_{\\Delta}^{t}$ represents the KL divergence between the posterior and the prior distribution of the layout. The average value of the $D_{\\Delta}^{t}$ over navigation steps in AI2THOR is illustrated in Fig. 6 (b). The results indicate that the layout gap decreases as the number of steps increases (the purple line). However, without updating by our method (the grey line), the layout gap is maintained at a large value. The trend of $D_{\\Delta}^{t}$ demonstrates that the learned knowledge (posterior distribution of the layout) by our method is gradually approaching the real layout of the current scene. It also reveals that the $w^{t}$ (the expectation of posterior distribution) is environment-adaptive information for guiding the agent.", + "bbox": [ + 75, + 686, + 467, + 883 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Additionally, considering the threshold $\\varepsilon = 0.5$ and", + "bbox": [ + 96, + 885, + 467, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 1. The ablation studies. (I) The ablations of several components. The $w^t$ represents encoding the expectation of the posterior distribution of object layout into the model, and $D_{\\Delta}^{t}$ represents de-biasing the trained model in the inference with our sTDE. (II) The comparison of different de-bias methods.", + "bbox": [ + 498, + 88, + 890, + 157 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/999d0de0ecb8faecdd71e9951be5a8761be0a8331c50194662ac58a3dadee4df.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
IDMethod \nBaseline w t DΔtSR↑ (%)SPL↑ (%)DTS↓ (m)
I1✓66.48±0.2238.42±0.390.54±0.01
2✓71.40±0.3739.11±0.440.49±0.02
3✓74.95±0.3841.68±0.230.47±0.02
II4w/o De-bias71.40±0.3739.11±0.440.49±0.02
5TDE [53]69.24±0.1238.38±0.160.52±0.01
6Ours sTDE (zero)74.95±0.3841.68±0.230.47±0.02
7Ours sTDE (random)75.03±0.6941.48±0.440.46±0.03
", + "bbox": [ + 513, + 161, + 874, + 306 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "looking back at Fig. 6 (b), we can observe how our layout-based sTDE works in the time (i.e. steps) dimension. According to the Eq. 2, the de-bias operation is activated when $(D_{\\Delta}^{t} - \\varepsilon) > 0$ , as shown in the upper purple shadow. At the beginning of an episode, the agent is unfamiliar with the current scene, and the layout gap is large. At this stage, our layout-based sTDE is activated to eliminate the prediction bias caused by the experience. Then with continuous navigating and updating, the prior knowledge of the object layout has been gradually adjusted to fit the current scene. Therefore, at this stage, the updated experience is applicable to the current scene and fully accepted for the navigation.", + "bbox": [ + 496, + 321, + 890, + 503 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Ablations of different components. We evaluate different components of our method. The ablation study in Tab. 1 (I) indicates the efficacy of each component in our method. Specifically, the expectation $w^{t}$ of the posterior distribution of the object layout improves the baseline (ORG) performance by $4.92\\%$ , $0.69\\%$ and $-0.05m$ on SR, SPL and DTS metrics. Moreover, the soft Total Direct Effect (sTDE) further improves the performance and gains $3.55\\%$ , $2.57\\%$ and $-0.02m$ improvement on SR, SPL and DTS metrics. Overall, our method outperforms the baseline by $8.47\\%$ , $3.26\\%$ and $-0.07m$ on SR, SPL and DTS metrics.", + "bbox": [ + 496, + 505, + 890, + 671 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparison with TDE and sTDE. The TDE analysis is effective in removing the mediation fallacy and is applied in many works [36, 49, 50], which regard the mediator (i.e. the experience in our work) as the cause of prediction bias and remove it in the inference by Eq. 1. However, directly applying TDE makes the agent completely ignore the positive effect of the experience. Thus, as shown in Tab. 1 (II), employing TDE (line 5) even degrades the navigation performance (compared with line 4). Compared with TDE, our sTDE (line 6 and 7) adaptively retains the positive effects of the experience and obtains significant improvements. Previous work [50] introduces constructing the counterfactual item (i.e. $\\bar{a}^t$ ), by setting the value of observation $S$ and the goal $G$ to random or zero. We respectively adopt these two ways (line 6 and 7) and find out that their performances", + "bbox": [ + 496, + 674, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "10798", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/07476c4de7c590a48ee74d9dca17057cfd8d112effbfd91d3d72ab947a8659e9.jpg", + "table_caption": [ + "Table 2. The comparisons with the related works (learning-based methods) in AI2THOR and RoboTHOR simulators. The L-sTDE represents our layout-based soft TDE framework based on different baselines. The improvements are shown in blue font." + ], + "table_footnote": [], + "table_body": "
IDMethodAI2THORRoboTHOR
SR↑ (%)SPL↑ (%)DTS↓ (m)SR↑ (%)SPL↑ (%)DTS↓ (m)
1Random4.68 ±1.742.42 ±1.351.36 ±0.012.92 ±0.391.34 ±0.202.40 ±0.02
2RGB+RL (A3C) [64]59.06 ±0.1934.56 ±0.440.68 ±0.0127.48 ±0.4616.45 ±0.122.08 ±0.02
3SP [59]62.19 ±0.6737.60 ±0.350.61 ±0.0226.22 ±0.7816.90 ±0.332.06 ±0.02
4SAVN [56]63.27 ±0.1138.20 ±0.040.56 ±0.0128.53 ±0.7718.27 ±0.351.96 ±0.02
5EOTP [32]65.61 ±0.2538.93 ±0.100.55 ±0.0128.84 ±0.4118.82 ±0.351.95 ±0.02
6ORG [15]66.53 ±0.2939.00 ±0.340.54 ±0.0129.64 ±0.8919.13 ±0.591.95 ±0.03
7ORG+TPN [15]68.60 ±0.2939.40 ±0.170.54 ±0.0130.05 ±0.0619.05 ±0.081.89 ±0.01
8VTNet [16]70.10 ±1.0039.60 ±0.100.52 ±0.0131.62 ±0.7419.63 ±0.421.87 ±0.03
9HOZ [63]70.38 ±0.1439.04 ±0.110.48 ±0.0232.27 ±1.1420.48 ±0.481.85 ±0.01
10Ours L-sTDE (EOTP)69.62 (4.01↑) ±0.7140.02 (1.09↑) ±0.470.52 (0.03↑) ±0.0137.37 (8.53↑) ±0.7522.00 (3.18↑) ±0.421.81 (0.14↑) ±0.02
11Ours L-sTDE (ORG)74.85 (8.32↑) ±0.3341.56 (2.56↑) ±0.110.47 (0.07↑) ±0.0239.27 (9.63↑) ±0.5522.81 (3.68↑) ±0.471.77 (0.18↑) ±0.02
12Ours L-sTDE (VTNet)75.25 (5.15↑) ±0.3941.69 (2.09↑) ±0.130.47 (0.05↑) ±0.0241.53 (9.91↑) ±0.6723.87 (4.24↑) ±0.501.72 (0.15↑) ±0.02
13Ours L-sTDE (HOZ)75.05 (4.67↑) ±0.2941.53 (2.49↑) ±0.210.46 (0.02↑) ±0.0242.13 (9.86↑) ±0.7824.54 (4.06↑) ±0.431.67 (0.18↑) ±0.01
", + "bbox": [ + 76, + 119, + 906, + 309 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "are similar, except that using the random value makes the performance more volatile (i.e. larger standard deviation). Therefore, we set the value of the observation and the goal as zeros to construct the counterfactual item. More ablation studies and visualizations are detailed in the supplements.", + "bbox": [ + 75, + 333, + 468, + 411 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.4. Comparisons with the Related Works", + "text_level": 1, + "bbox": [ + 76, + 421, + 401, + 438 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this section, we evaluate all methods on the test datasets of AI2THOR, RoboTHOR, and Gibson. We compare the learning-based methods [15, 16, 32, 56, 59, 63, 64] in AI2THOR and RoboTHOR as shown in Tab. 2. With the egocentric RGB input, all methods are constructed with the Faster R-CNN backbone, which is pre-trained following [15]. To keep fair comparisons, we present VTNet [16] using their reported results with Faster R-CNN. Since other methods [32, 56, 59, 64] are originally proposed with the ResNet [21] pre-trained in ImageNet [14] as the visual backbone. For fair comparisons, following the recommendation of [15], we additionally encode the detection information provided by Faster R-CNN to these methods [32, 56, 59, 64]. Therefore, the implemented performances are higher than those results reported in the original papers. As shown in Tab. 2, benefiting from the incorporation of our layout-based sTDE (L-sTDE), the performances of existing methods are improved, especially our L-sTDE based on HOZ and VTNet achieve new SOTA performance. Other learning-based methods employ CLIP [42] as the backbone [25], or adopt pre-training on large-scale datasets (e.g. ProcTHOR [13]), and we compare our L-sTDE with these methods in the supplements.", + "bbox": [ + 73, + 446, + 470, + 792 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Since most map-based methods require the RGB-D visual inputs and segmentation information provided by Mask R-CNN [20] to construct the semantic map, we take another comparison with the map-based methods as shown in Tab. 3. The map-based methods employ a parameter-free modular system to build the semantic map, then encode the map into the policy. We regard the encoded map as the ex", + "bbox": [ + 75, + 795, + 468, + 902 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/63120cc5807d80972e1c8e58bd2e8736c607dc4e58393d0526680618305345a0.jpg", + "table_caption": [ + "Table 3. The comparisons with the related works (map-based methods) in Gibson simulators." + ], + "table_footnote": [], + "table_body": "
IDMethodSR↑ (%)SPL↑ (%)DTS↓ (m)
1Random0.040.043.89
2RGBD+RL [48]8.422.873.23
3SemExp [7]65.3533.521.56
4Ours L-sTDE (SemExp)66.96 (1.61↑)34.33 (0.81↑)1.53 (0.03↑)
", + "bbox": [ + 501, + 361, + 913, + 445 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "experience $z^t$ and modify [7] with our L-sTDE. The results indicate that our method still brings some performance improvements, although the gains are limited compared to that of the learning-based methods. We analyze that, compared with the learning-based methods whose parameters are all trained end-to-end, the map-based methods utilize a modular system, and only a small number of parameters (the policy) need to be trained. Therefore, the map-based methods are less affected by the experience learned from training, and thus benefit less from our method.", + "bbox": [ + 496, + 457, + 890, + 609 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 623, + 617, + 638 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We propose the layout-based soft Total Direct Effect framework for ObjectNav task. Our motivation is to keep the positive effect and remove the negative effect of the experience, which is learned as the prior knowledge in training. Specifically, we propose to calculate the layout gap between the current environment and the prior knowledge. Then the layout gap is utilized to assess whether the impact of the learned experience is positive. Furthermore, the soft Total Direct Effect is proposed to appropriately control the effect of the experience on action prediction. The experiment results indicate the effectiveness of our method.", + "bbox": [ + 496, + 647, + 890, + 813 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements: This work was supported by Beijing Natural Science Foundation under Grant JQ22012, Z190020, in part by the National Natural Science Foundation of China under Grant 62125207, 62272443, 62032022 and U1936203, in part by the National Postdoctoral Program for Innovative Talents under Grant BX201700255.", + "bbox": [ + 496, + 816, + 893, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "10799", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 106 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Ehsan Abbasnejad, Damien Teney, Amin Parvaneh, Javen Shi, and Anton van den Hengel. Counterfactual vision and language learning. 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In 2017 IEEE International Conference on Robotics and Automation, ICRA 2017, Singapore, Singapore, May 29 - June 3, 2017, pages 3357-3364, 2017. 3, 6, 8" + ], + "bbox": [ + 501, + 92, + 890, + 890 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "10802", + "bbox": [ + 480, + 945, + 519, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Layout-Based Causal Inference for Object Navigation/18995e77-a0be-4475-8773-41d7233fd2aa_model.json b/2023/Layout-Based Causal Inference for Object Navigation/18995e77-a0be-4475-8773-41d7233fd2aa_model.json new file mode 100644 index 0000000000000000000000000000000000000000..bb3ff0dd1d2dfdb9f5731f89e9f80790a0374196 --- /dev/null +++ b/2023/Layout-Based Causal Inference for Object Navigation/18995e77-a0be-4475-8773-41d7233fd2aa_model.json @@ -0,0 +1,2191 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.215, + 0.131, + 0.757, + 0.154 + ], + "angle": 0, + "content": "Layout-based Causal Inference for Object Navigation" + }, + { + "type": "text", + "bbox": [ + 0.111, + 0.18, + 0.857, + 0.201 + ], + "angle": 0, + "content": "Sixian Zhang\\(^{1,2}\\), Xinhang Song\\(^{1,2}\\), Weijie Li\\(^{1,2}\\), Yubing Bai\\(^{1,2}\\), Xinyao Yu\\(^{1,2}\\), Shuqiang Jiang\\(^{1,2}\\)" + }, + { + "type": "text", + "bbox": [ + 0.178, + 0.201, + 0.794, + 0.217 + ], + "angle": 0, + "content": "1Key Lab of Intelligent Information Processing Laboratory of the Chinese Academy of Sciences (CAS)," + }, + { + "type": "text", + "bbox": [ + 0.194, + 0.219, + 0.776, + 0.234 + ], + "angle": 0, + "content": "Institute of Computing Technology, Beijing \\(^2\\)University of Chinese Academy of Sciences, Beijing" + }, + { + "type": "text", + "bbox": [ + 0.145, + 0.237, + 0.825, + 0.253 + ], + "angle": 0, + "content": "{sixian.zhang, xinhang.song, weijie.li, yubing.bai, xinyao.yu}@vip1.ict.ac.cn" + }, + { + "type": "text", + "bbox": [ + 0.406, + 0.255, + 0.56, + 0.269 + ], + "angle": 0, + "content": "sqjiang@ict.ac.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.305, + 0.314, + 0.321 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.336, + 0.474, + 0.685 + ], + "angle": 0, + "content": "Previous works for ObjectNav task attempt to learn the association (e.g. relation graph) between the visual inputs and the goal during training. Such association contains the prior knowledge of navigating in training environments, which is denoted as the experience. The experience performs a positive effect on helping the agent infer the likely location of the goal when the layout gap between the unseen environments of the test and the prior knowledge obtained in training is minor. However, when the layout gap is significant, the experience exerts a negative effect on navigation. Motivated by keeping the positive effect and removing the negative effect of the experience, we propose the layout-based soft Total Direct Effect (L-sTDE) framework based on the causal inference to adjust the prediction of the navigation policy. In particular, we propose to calculate the layout gap which is defined as the KL divergence between the posterior and the prior distribution of the object layout. Then the sTDE is proposed to appropriately control the effect of the experience based on the layout gap. Experimental results on AI2THOR, RoboTHOR, and Habitat demonstrate the effectiveness of our method. The code is available at https://github.com/sx-zhang/Layout-based-sTDE.git." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.71, + 0.21, + 0.725 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.47, + 0.903 + ], + "angle": 0, + "content": "The visual object-oriented navigation task (i.e. Object-Nav) [3] requires the agent to navigate to a user-specified goal (e.g. laptop) based on the egocentric visual observations. A typical challenge is navigating in unseen environments, where the goal is invisible most of the time, i.e. the partial observable problem, which typically results in the agent's meaningless actions (e.g. back-tracking or getting lost at dead-ends). Although encouraging the exploration in the unseen environment (until the goal is visible) is an intuitive solution, the lack of environment layout information still limits the efficiency of goal-oriented navigation." + }, + { + "type": "image", + "bbox": [ + 0.522, + 0.306, + 0.644, + 0.406 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.538, + 0.419, + 0.616, + 0.431 + ], + "angle": 0, + "content": "S: Observation" + }, + { + "type": "image", + "bbox": [ + 0.671, + 0.305, + 0.85, + 0.407 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.694, + 0.407, + 0.776, + 0.414 + ], + "angle": 0, + "content": "Intervention" + }, + { + "type": "image_caption", + "bbox": [ + 0.519, + 0.44, + 0.66, + 0.452 + ], + "angle": 0, + "content": "(a) The factual prediction" + }, + { + "type": "image_caption", + "bbox": [ + 0.693, + 0.419, + 0.855, + 0.431 + ], + "angle": 0, + "content": "Z:Experience A:Action" + }, + { + "type": "image_caption", + "bbox": [ + 0.692, + 0.44, + 0.874, + 0.453 + ], + "angle": 0, + "content": "(b) The counterfactual prediction" + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.462, + 0.895, + 0.533 + ], + "angle": 0, + "content": "Figure 1. The proposed causal graph. (a) represents the fact prediction \\( a \\), i.e. the original prediction of the trained model. (b) refers to the counter-fact prediction \\( \\bar{a} \\), i.e. the prediction is only affected by the experience \\( Z \\). (b) is realized by applying the intervention and counterfactual operations to the original model." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.552, + 0.895, + 0.869 + ], + "angle": 0, + "content": "Recently, the learning-based methods attempt to model the prior knowledge of the spatial relationships among the objects, so the agent could infer the likely locations of the goal based on the current observation (which objects are observed currently) and the prior knowledge (the spatial relationships between the goal and the observed objects) learned in the training stage. Some works utilize additional modules to construct the objects graph [15, 59, 60], the region graph [63] and the attention mechanism [32], while others [16, 56] employ a network that implicitly learns the spatial relationships end-to-end. All these methods attempt to establish prior knowledge in training environments, so that the agent would utilize the prior knowledge to associate the real-time observations with the goal, and infer the likely locations of the goal during the inference. The underlying assumption of these methods is that all of the object layouts in unseen environments should be exactly consistent with those in training environments. However, the layout consistency assumption is only partially correct due to the limited training data. Thus, those methods typically suffer from poor generalization [31] in unseen environments." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.895, + 0.902 + ], + "angle": 0, + "content": "To reveal the causes of poor generalization, we propose to use the casual graph (i.e. Structural Causal Model, SCM" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "10792" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.485 + ], + "angle": 0, + "content": "[38]) to analyze these navigation works. As illustrated in Fig. 1 (a), the navigation model takes the observation \\( S \\) and the goal \\( G \\) as the input, and predicts the action \\( A \\) at each timestamp. The causal links \\( S \\rightarrow Z \\) and \\( G \\rightarrow Z \\) represent that the observation and the goal are embedded by the pre-constructed modules [15, 32, 59, 60, 63] or the pre-trained network [16, 56]. The embedding vector is defined as the experience \\( Z \\) in the causal graph, which introduces the prior knowledge to influence action prediction (\\( Z \\rightarrow A \\)). Meanwhile, the real-time observation and the goal also independently affect the prediction without being encoded by the prior knowledge module, which is represented as \\( S \\rightarrow A \\) and \\( G \\rightarrow A \\), respectively. The causal links \\( S \\rightarrow A \\) and \\( G \\rightarrow A \\) represent the exploration-based effect (only related to the current episode) on the action prediction, which is different from the experience-based effect \\( Z \\rightarrow A \\). Consider two cases of the layout gap between the current environment and the prior knowledge: 1) the layout gap is minor and 2) the layout gap is significant. In the former case, the object layout is consistent in the current environment and the prior knowledge. Thus, the experience \\( Z \\) exerts a positive effect on the prediction of action \\( A \\). However, the effect of experience \\( Z \\) in the latter case could be negative. If the agent still relies on the \"negative\" experience to predict actions, it will suffer from poor generalization. Therefore, wisely utilizing the experience is essential to the ObjectNav task." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.489, + 0.473, + 0.702 + ], + "angle": 0, + "content": "Motivated by wisely utilizing the learned experience, we propose the soft Total Direct Effect (sTDE) framework based on the Total Direct Effect analysis in causal inference. Our sTDE improves the generalization of the trained model in inference by eliminating the prediction bias brought by the experience. To decouple the effect of experience, we construct the counter-fact prediction \\(\\bar{a}\\): the prediction is only affected by the experience \\(Z\\) while ignoring the \\(S\\) and \\(G\\), as shown in Fig. 1 (b). Then we propose the object layout estimator that calculates whether the effect of the experience is positive, by measuring the layout gap between the current environment and the prior knowledge. Furthermore, our sTDE will remove the counter-fact prediction \\(\\bar{a}\\) from the fact prediction \\(a\\) when the layout gap is large." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.705, + 0.473, + 0.903 + ], + "angle": 0, + "content": "In this paper, we propose the layout-based soft TDE framework for the ObjectNav task. Specifically, we adopt the Dirichlet-Multinomial distribution [22] to formulate the contextual relationship between objects, which represents the object layout of the environment. Before training, the agent learns prior layout distribution (i.e. the prior parameters of Dirichlet-Multinomial distribution) by randomly exploring the training environments. In the training stage, based on the Bayesian inference, the agent estimates the posterior layout distribution with the prior distribution and newly obtained observations. Then the constantly updated posterior layout is encoded into the navigation model and utilized to learn the environment-adaptive experience. The" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.289 + ], + "angle": 0, + "content": "entire model is trained with RL by maximizing the reward of reaching the goal. In the test stage, our agent will not directly use the trained policy as most previous works do. The agent first calculates the layout gap and the counter-fact prediction. The layout gap is determined by calculating the KL divergence between the posterior and prior distribution of object layouts and serves as a weight to determine whether to remove the counter-fact prediction (i.e. experience effect) from the original prediction. The experimental results on AI2THOR [27], RoboTHOR [12] and Habitat [48] indicate that our layout-based sTDE (L-sTDE) can be a plug-and-play method to boost existing methods to achieve better navigation performances." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.302, + 0.642, + 0.318 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.327, + 0.895, + 0.675 + ], + "angle": 0, + "content": "Visual Object Navigation. Target-oriented visual navigation can be categorized [5] into PointGoal [8, 18, 43, 55], AreaGoal [28, 57], AudioGoal [10, 11], ImageGoal [19, 29, 48], LanguageGoal (vision-and-language navigation) [23, 40, 41] and ObjectGoal. We focus on visual ObjectGoal navigation, which sets the object category as the target. Previous map-based methods usually build a metric map [6-8, 44] or topological map [9, 47] to memorize the environment layout. Besides, a popular deep-learning pipeline is to take an end-to-end network [2, 17, 34] to process the visual embedding and goal embedding, then predict the navigation action. Based on that, recent learning-based methods propose various improvement ideas, such as semantic representation [35], prior knowledge [59], object relation graph [15, 60, 63], attention mechanism [32], meta-learning [56], and transformer structure [16]. These well-trained modules provide prior knowledge to guide the agent in unseen environments. In our work, we denote such knowledge learned from training (with whatever improvement designs) as the experience. We try to find out, under different environment layouts, whether the learned experience takes a positive effect or not, and how to better utilize the experience to improve the navigation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.896, + 0.902 + ], + "angle": 0, + "content": "Causal Inference. Causal inference [38, 39] provides analysis tools (e.g. intervention, counter-fact) to reveal the causal effect behind the data-based statistical correlation, which is widely adopted in epidemiology, psychology, or politics research [24, 30, 46]. Recently, causal inference is introduced into the computer vision society for scene graph generation [50], vision and language task [1,36], long-tailed classification [49] and few/zero-shot learning [4, 62]. For the visual navigation task, [37] generates counterfactual observations to improve generalization to new environments for VLN (vision-and-language navigation) task. [54] proposes causal CT (continuous-time) models for visual drone navigation tasks. In our work, we focus on the ObjectNav task and utilize the causal inference to wisely control the effect of experience in the inference." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "10793" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.077, + 0.09, + 0.376, + 0.108 + ], + "angle": 0, + "content": "3. Preliminaries of ObjectNav Task" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.115, + 0.47, + 0.341 + ], + "angle": 0, + "content": "Task Definition. The ObjectNav task requires the agent to navigate to a user-specified object category from a random starting location in an unseen scene, and the agent is only allowed to utilize the egocentric visual observation (e.g. RGB images) and the semantic embedding of the target object. Formally, at each timestamp \\( t \\), the agent receives the observation \\( S = s^t \\) and the goal \\( G = g^t \\) and is expected to adopt an action \\( A = a^t \\), \\( a^t \\in \\mathcal{A} \\). The discrete action space is defined as: \\( \\mathcal{A} = \\{MoveAhead, RotateLeft, RotateRight, LookDown, LookUp, Done\\} \\). When the agent outputs the Done action, the episode terminates. An episode is considered successful if, within a certain number of steps, the final location of the agent is close to the goal within a distance threshold (e.g. \\( 1m \\)) and the goal is visible in the egocentric observation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.342, + 0.47, + 0.432 + ], + "angle": 0, + "content": "Navigation Model. Prevailing ObjectNav works can be summarized as a visual-goal encoder and a policy function, as shown in Fig. 2. The visual-goal encoder is constructed to associate the visual observation \\( S \\) and the goal \\( G \\). We denote such association as the experience \\( Z \\) since the encoder could learn the prior experience during the training." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.433, + 0.471, + 0.675 + ], + "angle": 0, + "content": "Previous learning-based methods typically implement the visual-goal encoder as an object relation graph [15, 59, 60], region graph [63], attention module [32] and transformer structure [16]. For instance, the ORG [15] builds an object relation graph, where the nodes are defined as the object categories and the edges are defined as the spatial correlations among different categories. The object relation graph takes the observation and the goal as inputs and encodes them with the learned edges to obtain the experience \\( Z \\). Previous map-based methods [7, 44] typically construct the semantic map based on the observations, and embed the map with the target. Such embedding is also regarded as the experience \\( Z \\). Based on the observation, target object, and these learned experiences, the policy module will output the prediction. These navigation models are typically trained with the RL (reinforcement learning) [33, 55, 64]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.687, + 0.292, + 0.704 + ], + "angle": 0, + "content": "4. The Proposed Solution" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.712, + 0.4, + 0.727 + ], + "angle": 0, + "content": "4.1. Layout-based Soft Total Direct Effect" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.47, + 0.901 + ], + "angle": 0, + "content": "We humans make decisions in a causality-based manner: we have the instinct to assess the effect of the navigation experience [51] and wisely eliminate the cognition bias from the experience. However, the machines are likelihood-based [50] and the predictions depend on the association likelihood between observations, goal, and actions, which is mainly learned from limited training data. Therefore, the predictions are inevitably biased due to the biased experience. Prevailing methods [15, 16, 56, 59, 60, 63] entirely accept the experience learned in the training stage, and rarely consider whether the prior experience is beneficial to the" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.09, + 0.891, + 0.332 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.342, + 0.894, + 0.426 + ], + "angle": 0, + "content": "Figure 2. Prevailing navigation framework (top) and our contributions (bottom). Our layout estimator outputs the expectation \\( w^t \\) of posterior layout distribution and the layout gap \\( D_{\\Delta}^{t} \\). The \\( w^t \\) is proposed to enhance the adaptability of the experience \\( z^t \\) to new environments. The layout gap \\( D_{\\Delta}^{t} \\) serves as a weight to alleviate the experience bias." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.453, + 0.892, + 0.543 + ], + "angle": 0, + "content": "current environment. However, as previously discussed, the learned experience has both positive and negative effects, especially in the unseen environments, which may have a different layout from the training environments. Therefore, keeping positive effects and removing negative effects of learned experience is essential to the navigation models." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.544, + 0.892, + 0.695 + ], + "angle": 0, + "content": "The causal inference [39,52,53] encourages the machine to discover the causality behind the association likelihood, which has been proven to be an effective analysis method in many computer vision tasks [36, 49, 50, 61]. From the perspective of causal inference, the experience \\( Z \\) serves as the mediator between the input (observation \\( S \\) and target \\( G \\)) and the output (action \\( A \\)) as illustrated in Fig. 1 (a). To eliminate the mediation fallacy, the causal inference [38] introduces the Total Direct Effect (TDE) analysis to remove the prediction bias brought by the mediator." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.695, + 0.892, + 0.77 + ], + "angle": 0, + "content": "Total Direct Effect. The fundamental principle behind TDE analysis [36, 49, 50] is to build a bias prediction \\(\\bar{a}^t\\) that is exclusively affected by the mediator, and then remove the bias item from the original prediction \\(a^t\\). The TDE analysis is formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.624, + 0.785, + 0.891, + 0.803 + ], + "angle": 0, + "content": "\\[\nT D E \\left(a ^ {t}\\right) = a ^ {t} - \\bar {a} ^ {t} \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.892, + 0.902 + ], + "angle": 0, + "content": "where \\(a^t = \\pi (A|S = s^t,G = g^t)\\) is the factual prediction of a trained model \\(\\pi\\), which takes the observation \\(S = s^t\\) and target \\(G = g^{t}\\) as the input, as shown in Fig. 1 (a). The latter is the counterfactual prediction \\(\\bar{a}^t = \\pi (A|do(S = \\bar{s}^t,G = \\bar{g}^t),Z = Z_{s^t,g^t})\\) as shown in Fig. 1 (b). The calculation of \\(\\bar{a}^t\\) includes two operations" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10794" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.289 + ], + "angle": 0, + "content": "in causal inference: intervention and counterfactual operations. The intervention operation is denoted as \\( do(\\cdot) \\) and realized by specifying a certain value for the variable (e.g. \\( do(S = \\bar{s}^t) \\)). The intervened value (e.g. \\( \\bar{s}^t \\), \\( \\bar{g}^t \\)) is set to a random or zero vector. The intervention operation eliminates the effect of observation \\( S \\) and goal \\( G \\) on the action prediction, while it also changes the value of the causal successor (i.e. \\( Z \\)). However, since our motivation is to model the case only affected by the mediator, which requires the mediator \\( Z \\) to remain the original value. To this end, the counterfactual operation assigns the original value to the variable \\( Z \\) as if \\( S = s^t \\), \\( G = g^t \\) had existed. The counterfactual operation is symbolized as \\( Z = Z_{s^t, g^t} \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.289, + 0.473, + 0.395 + ], + "angle": 0, + "content": "The TDE analysis is easily realized by manipulating the values of several variables (e.g. \\( S, G, Z \\)) and is efficient in removing the effect of the mediator (i.e. experience). However, the experience is not always detrimental. It can also be beneficial when the object layout gap is minor. Therefore, we propose the soft TDE to appropriately maintain the positive effect of experience." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.396, + 0.473, + 0.442 + ], + "angle": 0, + "content": "Soft Total Direct Effect. In alternative to previous TDE analysis, our soft TDE modifies the Eq. 1 by adding a trade-off weight, which is formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.138, + 0.459, + 0.47, + 0.478 + ], + "angle": 0, + "content": "\\[\ns T D E (a ^ {t}) = a ^ {t} - R e L U (D _ {\\Delta} ^ {t} - \\varepsilon) \\cdot \\bar {a} ^ {t} \\qquad (2)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.486, + 0.473, + 0.595 + ], + "angle": 0, + "content": "where \\(ReLU(\\cdot)\\) is the ReLU activation function, and \\(\\varepsilon\\) is a threshold hyperparameter. The \\(D_{\\Delta}^{t}\\) is the object layout gap, which is produced by our layout estimator (Sec. 4.2) as shown in Fig. 2. The \\(D_{\\Delta}^{t}\\) evaluates the effect of the experience \\(Z\\), and preserves the positive experience when the layout gap between the current environment and prior knowledge is minor (i.e. \\(D_{\\Delta}^{t}\\) is less than the threshold \\(\\varepsilon\\))." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.605, + 0.251, + 0.621 + ], + "angle": 0, + "content": "4.2. Layout Estimator" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.629, + 0.473, + 0.904 + ], + "angle": 0, + "content": "Object Layout. For the ObjectNav task, the main challenge is the partially observable problem, that the agent can only observe the partial area at each time. With continuously observing during the navigation process, more objects will be observed, and the partially known problem can also be alleviated. Considering objects are usually distributed in a reasonable layout, the adjacent relation of objects is essential to help the agent infer the location of the target object based on the observed objects. Therefore, we concentrate on the contextual relationship to represent the object layout. The object layout in a scene is defined as the set \\( D = \\{\\theta_{i}\\}_{i=1}^{K} \\), where \\( K \\) is the number of object categories. The \\( \\theta_{i} = (\\theta_{i,j})_{j=1}^{K} \\) represents the context distribution of object category \\( c_{i} \\). Each dimension \\( \\theta_{i,j} \\) represents the probability \\( p(c_{j}|c_{i}) \\) that the object category \\( c_{j} \\) can be observed around the category \\( c_{i} \\) in an observation. Specifically, we assume that the context distribution follows the Dirichlet distribution: \\( \\theta_{i} = (\\theta_{i,j})_{j=1}^{K} \\sim \\text{Dir}(\\alpha_{i}) \\), where" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.089, + 0.891, + 0.312 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.515, + 0.319, + 0.878, + 0.335 + ], + "angle": 0, + "content": "Figure 3. The calculation of the likelihood function \\( p(s_i^t |\\theta_i) \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.36, + 0.892, + 0.424 + ], + "angle": 0, + "content": "\\(\\sum_{j}\\theta_{i,j} = 1,\\theta_{i,j}\\geq 0\\) , and \\(\\alpha_{i} = (\\alpha_{i,j})_{j = 1}^{K},\\alpha_{i,j} > 0\\) parameterizes the distribution. The Dirichlet distribution is chosen for two reasons: 1) the conjugate prior permits concise calculations; 2) the likelihood-equivalence property [22]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.425, + 0.893, + 0.687 + ], + "angle": 0, + "content": "At the beginning of every new episode, the parameter \\(\\alpha_{i}\\) is initialized as the prior initial value \\(\\alpha_{i}^{*}\\) (\\(\\alpha_{i}^{*}\\) will be detailed in Sec. 4.3). At each timestamp \\(t\\), our method computes the posterior object distribution based on the incoming observations. Specifically, the agent receives the visual observation \\(s^t\\), and the visual observation is then converted into a count vector \\(n^t \\in \\mathbb{R}^K\\), where each dimension of \\(n^t = (n_i^t)_{i=1}^K\\), \\(n_i^t \\geq 0\\) records the number of each object category appearing in the current observation. The count vector \\(n^t\\) is obtained by the object detection or segmentation modules (e.g. Faster R-CNN [45] or Mask R-CNN [20]). As shown in Fig. 3, we define \\(n_{-i}^t = (n_{-i,j}^t)_{j=1}^K\\), \\(n_{-i,j}^t \\geq 0\\) as the count of other categories (except \\(c_i\\)) and define \\(s_i^t\\) as the contextual observation of the category \\(c_i\\). Conditioned on \\(c_i\\), assume the probability that \\(s_i^t\\) is observed follows the multinomial distribution \\(s_i^t \\sim Mult(n_{-i}^t, \\theta_i)\\). Then the likelihood function can be calculated as:" + }, + { + "type": "equation", + "bbox": [ + 0.62, + 0.702, + 0.892, + 0.744 + ], + "angle": 0, + "content": "\\[\np \\left(s _ {i} ^ {t} \\mid \\theta_ {i}\\right) = \\prod_ {j = 1} ^ {K} \\theta_ {i, j} ^ {n _ {- i, j} ^ {t}} \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.754, + 0.895, + 0.83 + ], + "angle": 0, + "content": "Meanwhile, according to the previous Dirichlet distribution assumption, the prior distribution of \\(\\theta_{i}\\) at timestamp \\(t\\) is \\(p\\left(\\theta_i|\\alpha_i^t\\right) = Dir\\left(\\theta_i|\\alpha_i^t\\right)\\). Considering the contextual observation \\(s_i^t\\), the posterior distribution of \\(\\theta_{i}\\) is further calculated according to the Bayesian inference as the following:" + }, + { + "type": "equation", + "bbox": [ + 0.509, + 0.854, + 0.892, + 0.901 + ], + "angle": 0, + "content": "\\[\np \\left(\\theta_ {i} \\mid s _ {i} ^ {t}, \\alpha_ {i} ^ {t}\\right) = \\frac {p \\left(s _ {i} ^ {t} \\mid \\theta_ {i}\\right) p \\left(\\theta_ {i} \\mid \\alpha_ {i} ^ {t}\\right)}{p \\left(s _ {i} ^ {t} \\mid \\alpha_ {i} ^ {t}\\right)} = D i r \\left(\\theta_ {i} \\mid \\alpha_ {i} ^ {t} + n _ {- i} ^ {t}\\right) \\tag {4}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10795" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.242 + ], + "angle": 0, + "content": "The Eq. 4 indicates that the posterior distribution \\( p(\\theta_i | s_i^t, \\alpha_i^t) \\) also satisfies the Dirichlet distribution (the calculation process is detailed in the supplements), which is known as the conjugate prior property. The conjugate prior property guarantees the succinct calculation for the posterior distribution of \\( \\theta_i \\), i.e., simply combining the count vector \\( n_{-i}^t \\) of context objects around category \\( c_i \\) with the hyperparameter \\( \\alpha_i^t \\) of the prior distribution. Similarly, the posterior distributions of other object categories can also be obtained following the Eq. 4." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.243, + 0.47, + 0.318 + ], + "angle": 0, + "content": "Furthermore, the posterior distributions at time \\( t \\) serves as the prior distributions at time \\( t + 1 \\), thus the value of hyperparameter \\( \\alpha_{i} \\) is updated by \\( \\alpha_{i}^{t + 1} = \\alpha_{i}^{t} + n_{-i}^{t} \\). This update guarantees the knowledge of object layout is continuously adapted to the current navigation environment." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.318, + 0.469, + 0.38 + ], + "angle": 0, + "content": "Based on the obtained posterior distribution, the layout gap \\( D_{\\Delta}^{t} \\) is defined as the KL divergence between the posterior and prior object layout over all categories. Formally, the object layout gap \\( D_{\\Delta}^{t} \\) is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.093, + 0.389, + 0.47, + 0.43 + ], + "angle": 0, + "content": "\\[\nD _ {\\Delta} ^ {t} = \\tanh \\left( \\right.\\frac {1}{K} \\sum_ {i = 1} ^ {K} K L \\left( \\right.p \\left(\\theta_ {i} \\mid s ^ {t}, \\alpha_ {i} ^ {t}\\right)\\left\\| \\right. p \\left(\\theta_ {i} \\mid \\alpha_ {i} ^ {t}\\right)\\left. \\right)\\left. \\right) \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.438, + 0.469, + 0.498 + ], + "angle": 0, + "content": "where \\( \\tanh(\\cdot) \\) is the tanh activation function. The layout gap \\( D_{\\Delta}^{t} \\) estimates the gap between the posterior object layout at time \\( t \\) and the prior knowledge before time \\( t \\), which plays a vital role in the Eq. 2." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.499, + 0.47, + 0.803 + ], + "angle": 0, + "content": "Environment-Adaptive Experience. The prevailing methods [15, 16, 59] typically encode the visual observation \\( s^t \\) and the target object \\( g^t \\) into the experience \\( z^t \\in \\mathbb{R}^{K \\times M} \\) during training, where \\( K \\) is the number of object categories and \\( M \\) refers to the feature dimension. The learned experience could be both biased (the layout gap between the training and test environments) and environment-static (without adaptation to the current environment). Therefore, in addition to eliminate the bias in the inference, we also propose to enhance the environmental adaptability of the experience \\( z^t \\) to achieve a better performance. To this end, the dynamically updated knowledge of object layout \\( D = \\{\\theta_i\\}_{i=1}^K \\) is encoded into the navigation framework. Specifically, the expectation of the posterior distribution of the object layout \\( D \\) is formalized as \\( w^t \\in \\mathbb{R}^{K \\times K} \\), \\( w_{i,j}^t > 0 \\). For \\( j = i \\), since \\( p(c_i | c_i) \\) always exists, we set \\( w_{i,j}^t = 1 \\). When \\( j \\neq i \\), \\( w_{i,j}^t = \\mathbb{E}_{p(\\theta_i | s_i^t, \\alpha_i^t)}(\\theta_{i,j}) \\), where \\( \\mathbb{E}(\\cdot) \\) denote the expectation calculation. Based on [22], the expectation of the Dirichlet function \\( Dir(\\theta_i | \\alpha_i^t + n_{-i}^t) \\) is equivalent to the normalization of its parameters. Accordingly, for \\( j \\neq i \\)," + }, + { + "type": "equation", + "bbox": [ + 0.1, + 0.822, + 0.469, + 0.862 + ], + "angle": 0, + "content": "\\[\nw _ {i, j} ^ {t} = \\mathbb {E} _ {p \\left(\\theta_ {i} \\mid s _ {i} ^ {t}, \\alpha_ {i} ^ {t}\\right)} \\left(\\theta_ {i, j}\\right) = \\frac {\\alpha_ {i , j} ^ {t} + n _ {- i , j} ^ {t}}{\\sum_ {j = 1} ^ {K} \\left(\\alpha_ {i , j} ^ {t} + n _ {- i , j} ^ {t}\\right)} \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Since \\( w^{t} \\) is updated in real-time, we propose to improve the environment-static experience \\( z^{t} \\) to environment-" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.122 + ], + "angle": 0, + "content": "adaptive experience \\(\\hat{z}^t\\) by incorporating the dynamically updated knowledge of object layout, where \\(\\hat{z}^t\\) is given by:" + }, + { + "type": "equation", + "bbox": [ + 0.625, + 0.135, + 0.892, + 0.154 + ], + "angle": 0, + "content": "\\[\n\\hat {z} ^ {t} = z ^ {t} \\odot [ w ^ {t} \\times g ^ {t} ] \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.159, + 0.892, + 0.25 + ], + "angle": 0, + "content": "where \\(\\odot\\) represents the element-wise multiplication, \\(\\times\\) refers to the matrix multiplication, and \\(g^{t}\\in \\mathbb{R}^{K}\\) is a one-hot vector indicating the target category of the goal. The result of \\([w^t\\times g^t ]\\in \\mathbb{R}^K\\) indicates the probability of the target \\(g^{t}\\) is observed conditioned on each object category, which serves as a weight on the category-specific dimension of \\(z^t\\)" + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.259, + 0.715, + 0.275 + ], + "angle": 0, + "content": "4.3. Training and Inference" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.282, + 0.892, + 0.689 + ], + "angle": 0, + "content": "As shown in Fig. 2, our layout estimator outputs (1) the expectation \\( w^t \\) of the posterior layout distribution, and (2) the layout gap \\( D_{\\Delta}^{t} \\). Both \\( w^t \\) and \\( D_{\\Delta}^{t} \\) are calculated mathematically without learnable parameters, thus our method has the plug-and-play property to boost the existing methods. Specifically, our layout-based sTDE is realized as: (1) Before training, to determine the initial value \\( (\\alpha_i^*)_{i=1}^K \\), we first employ a random agent equipped with our object layout estimator, whose parameters \\( (\\alpha_i)^K_{i=1} \\) are initialized as all one vector. Then the agent randomly explores the training scenes to obtain sufficient observations to update the parameters by Eq. 4. The updated parameters are defined as \\( (\\alpha_i^*)_{i=1}^K \\). (2) In the training stage, at the beginning of every episode, all parameters \\( (\\alpha_i)^K_{i=1} \\) are initialized as the prior parameters \\( (\\alpha_i^*)_{i=1}^K \\). The layout estimator calculates the posterior distribution of object layout \\( D \\) (Eq. 4), using the constant observation \\( s^t \\) and the prior distribution. Then the expectation of the posterior distribution \\( w^t \\) is estimated and incorporated in the navigation model \\( \\pi \\) (Eq. 6, 7). The model \\( \\pi \\) is trained with RL. (3) In the causal-inference stage, the agent will not directly use the trained policy \\( \\pi \\), while it first calculates the layout gap \\( D_{\\Delta}^{t} \\) (Eq. 5) and the counter-fact prediction \\( \\bar{a}^t \\) (the effect of the experience). Then the agent appropriately removes the counter-fact prediction \\( \\bar{a}^t \\) from the fact prediction \\( a^t \\) based on the layout gap \\( D_{\\Delta}^{t} \\) (Eq. 2). For more details and algorithms of training and inference, please refer to the supplements." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Note that the expectation of the posterior distribution of the object layout \\( w^{t} \\) affects the prediction of the model during both training and inference, while \\( D_{\\Delta}^{t} \\) is utilized for debiasing only in the inference. Furthermore, we want to explain why the debiasing operation only acts in inference. As shown in Fig. 1, the prediction is influenced by two effects: the inputs (the observation \\( S \\) and the goal \\( G \\)) and their mediator (the experience \\( E \\)). The mediator (experience) has agnostic effects because it is learned from limited training data. The training data can not cover all room layouts, thus resulting the prediction bias in the inference. Consequently, the debiasing operation (i.e. the sTDE partially removes the effect of experience from prediction) is conducted in inference to decouple the effect from the training data." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10796" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.089, + 0.468, + 0.244 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.255, + 0.47, + 0.283 + ], + "angle": 0, + "content": "Figure 4. The correlation between the navigation performance on success rate (SR) and the layout similarity." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.308, + 0.21, + 0.324 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.332, + 0.267, + 0.349 + ], + "angle": 0, + "content": "5.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.355, + 0.47, + 0.506 + ], + "angle": 0, + "content": "We utilize the AI2THOR [27], RoboTHOR [12] simulators to conduct ablation studies and compare our method with the learning-based methods [15, 16, 32, 56, 59, 63, 64]. The experimental settings on above datasets follow the primary works [15, 16, 63]. Besides, we choose the Gibson [58] dataset in the Habitat simulator [48] to compare our method with the map-based methods and adopt the same settings as [7]. For more details about the settings of the datasets (e.g. the split of training, validation, testing scenes, and the target objects), please refer to the supplements." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.507, + 0.47, + 0.687 + ], + "angle": 0, + "content": "Our method and the related works are both trained to maximize the navigation reward via RL. The reward function penalizes the agent by -0.01 for each step and rewards it by 5 if the episode is successful (the successful episode is defined in Sec. 3). All methods are trained with 6M episodes, where in each episode, the starting position of the agent and the goal are randomly selected. Note that, since our method needs prerequisite exploration to determine the initial parameters \\((\\alpha_{i}^{*})_{i = 1}^{K}\\) of the layout distribution. To be fair, we employ the agent to randomly explore the training rooms to learn the initial parameters for 2M episodes, then we train our method with 4M episodes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.688, + 0.468, + 0.793 + ], + "angle": 0, + "content": "For evaluation, we repeatedly run 3 trials and report the results with mean \\(\\pm\\) standard deviation. We choose SR (Success Rate), SPL (Success weighted by Path Length), and DTS (Distance to Goal) metrics for evaluation, which are detailed in the supplements. For all results in the following tables, the \\(\\uparrow\\) means that the larger value is better, while \\(\\downarrow\\) indicates the opposite." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.802, + 0.303, + 0.818 + ], + "angle": 0, + "content": "5.2. The Compared Methods" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.468, + 0.901 + ], + "angle": 0, + "content": "We choose the learning-based methods [15, 16, 32, 56, 59, 63, 64] and the map-based method [7] for comparison. Random: the agent adopts random actions. RGB(D) + RL (A3C) [48, 64]: the agent utilizes the simple embeddings of visual input and the goal, and is trained with A3C [34]." + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.089, + 0.888, + 0.205 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.217, + 0.892, + 0.273 + ], + "angle": 0, + "content": "Figure 5. Category-wise improvement of our method compared to the baseline. The categories are arranged from high to low based on their average layout similarity between training and testing scenes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.302, + 0.892, + 0.545 + ], + "angle": 0, + "content": "SP [59]: SP constructs the scene prior knowledge from the external dataset. The prior knowledge encoded with GCN [26] is provided to the agent as the additional information. SAVN [56]: SAVN establishes a sub-network to learn a self-supervised interaction loss. EOTP [32]: EOTP proposes an attention module to encode the semantic information about the observed objects. ORG [15]: ORG proposes to learn an object relation graph, and builds a memory-augmented tentative policy network (TPN) to produce self-supervision. VTNet [16]: VTNet employs the Transformer network to encode the visual information and the goal. HOZ [63]: HOZ attempts to abstract the region relation among the objects and proposes to learn the region relation graph to associate the vision and the goal. SemExp [7]: SemExp builds an episodic semantic map and trains a goal-oriented policy taking the semantic map as the input." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.557, + 0.681, + 0.571 + ], + "angle": 0, + "content": "5.3. Evaluation Results" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.581, + 0.891, + 0.611 + ], + "angle": 0, + "content": "In this section, we adopt the ORG [15] as the baseline and conduct evaluations on the validation set of AI2THOR." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.613, + 0.892, + 0.839 + ], + "angle": 0, + "content": "Correlation between layout and success rate. Our motivation is that the layout gap between training and testing scenes may have an impact on navigation. To verify this, we take the statistic and visualize the results in Fig. 4 (a), where the y-axis represents the success rate of navigating to objects \\( c_{i} \\) in a testing scene \\( R_{j} \\), the x-axis represents the layout similarity of the object \\( c_{i} \\) between the training scenes and the test scenes, and the scatter points represent all target objects in all test scenes. As shown in Fig. 4 (b), the layout similarity is defined as the cosine similarity of the statistics vectors (the count of cooccurrence objects) obtained in the training scenes and the test scene \\( R_{j} \\). Fig. 4 (a) indicates that the navigation performance on SR during inference has a generally positive correlation with the layout similarity, which supports our motivation." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.841, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Improvements of our method compared to baseline. The navigation performance of the baseline (green bar) and the improvements brought by our method (blue bar) are shown in Fig. 5. All goals (x-axis) are arranged from high" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10797" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.089, + 0.268, + 0.223 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.274, + 0.089, + 0.468, + 0.223 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.234, + 0.47, + 0.263 + ], + "angle": 0, + "content": "Figure 6. The ablation study of the threshold \\(\\varepsilon\\) and the visualization of the object layout gap \\(D_{\\Delta}^{t}\\) over the navigation steps." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.292, + 0.468, + 0.398 + ], + "angle": 0, + "content": "to low based on their layout similarity. The results indicate that our method can bring more obvious improvement in the categories with low layout similarity (as illustrated by the red dashed circle). We presume that the goals with a larger layout gap are more susceptible to the effects of the experience, thus benefiting more from our de-biased method. The results once again support our motivation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.399, + 0.468, + 0.685 + ], + "angle": 0, + "content": "Ablations on the threshold \\(\\varepsilon\\). The threshold \\(\\varepsilon\\) influences the agent by Eq. 2, which determines whether to remove the prediction bias introduced by the experience. As shown in Fig. 6 (a), the results of different threshold \\(\\varepsilon\\) basically show the same trend on the SR, SPL metrics: as the value of threshold \\(\\varepsilon\\) increases, the performances on these metrics initially increase and then decrease. When the value of threshold \\(\\varepsilon\\) is small, the Eq. 2 tends to consider that the majority of experiences \\(Z\\) are negative and need to be removed. At this point, gradually increasing the threshold \\(\\varepsilon\\) could retain more experiences and improve performance. However, when the threshold \\(\\varepsilon\\) is too large (e.g. \\(\\varepsilon = 1\\)), the Eq. 2 falls into another extreme which considers all experiences are positive and need to be preserved, resulting in the performance degradation. The results on DTS metric indicate that excessively removing the experience (\\(\\varepsilon\\) is small) will increase the exploration of the agent, thus resulting in worse performance on DTS. Based on the above results, we choose the threshold as \\(\\varepsilon = 0.5\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.688, + 0.468, + 0.884 + ], + "angle": 0, + "content": "Visualization of the object layout gap \\( D_{\\Delta}^{t} \\). The object layout gap \\( D_{\\Delta}^{t} \\) represents the KL divergence between the posterior and the prior distribution of the layout. The average value of the \\( D_{\\Delta}^{t} \\) over navigation steps in AI2THOR is illustrated in Fig. 6 (b). The results indicate that the layout gap decreases as the number of steps increases (the purple line). However, without updating by our method (the grey line), the layout gap is maintained at a large value. The trend of \\( D_{\\Delta}^{t} \\) demonstrates that the learned knowledge (posterior distribution of the layout) by our method is gradually approaching the real layout of the current scene. It also reveals that the \\( w^{t} \\) (the expectation of posterior distribution) is environment-adaptive information for guiding the agent." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.886, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Additionally, considering the threshold \\(\\varepsilon = 0.5\\) and" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.089, + 0.892, + 0.159 + ], + "angle": 0, + "content": "Table 1. The ablation studies. (I) The ablations of several components. The \\( w^t \\) represents encoding the expectation of the posterior distribution of object layout into the model, and \\( D_{\\Delta}^{t} \\) represents de-biasing the trained model in the inference with our sTDE. (II) The comparison of different de-bias methods." + }, + { + "type": "table", + "bbox": [ + 0.514, + 0.162, + 0.875, + 0.307 + ], + "angle": 0, + "content": "
IDMethod \nBaseline w t DΔtSR↑ (%)SPL↑ (%)DTS↓ (m)
I1✓66.48±0.2238.42±0.390.54±0.01
2✓71.40±0.3739.11±0.440.49±0.02
3✓74.95±0.3841.68±0.230.47±0.02
II4w/o De-bias71.40±0.3739.11±0.440.49±0.02
5TDE [53]69.24±0.1238.38±0.160.52±0.01
6Ours sTDE (zero)74.95±0.3841.68±0.230.47±0.02
7Ours sTDE (random)75.03±0.6941.48±0.440.46±0.03
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.322, + 0.892, + 0.504 + ], + "angle": 0, + "content": "looking back at Fig. 6 (b), we can observe how our layout-based sTDE works in the time (i.e. steps) dimension. According to the Eq. 2, the de-bias operation is activated when \\((D_{\\Delta}^{t} - \\varepsilon) > 0\\), as shown in the upper purple shadow. At the beginning of an episode, the agent is unfamiliar with the current scene, and the layout gap is large. At this stage, our layout-based sTDE is activated to eliminate the prediction bias caused by the experience. Then with continuous navigating and updating, the prior knowledge of the object layout has been gradually adjusted to fit the current scene. Therefore, at this stage, the updated experience is applicable to the current scene and fully accepted for the navigation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.506, + 0.892, + 0.672 + ], + "angle": 0, + "content": "Ablations of different components. We evaluate different components of our method. The ablation study in Tab. 1 (I) indicates the efficacy of each component in our method. Specifically, the expectation \\( w^{t} \\) of the posterior distribution of the object layout improves the baseline (ORG) performance by \\( 4.92\\% \\), \\( 0.69\\% \\) and \\( -0.05m \\) on SR, SPL and DTS metrics. Moreover, the soft Total Direct Effect (sTDE) further improves the performance and gains \\( 3.55\\% \\), \\( 2.57\\% \\) and \\( -0.02m \\) improvement on SR, SPL and DTS metrics. Overall, our method outperforms the baseline by \\( 8.47\\% \\), \\( 3.26\\% \\) and \\( -0.07m \\) on SR, SPL and DTS metrics." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Comparison with TDE and sTDE. The TDE analysis is effective in removing the mediation fallacy and is applied in many works [36, 49, 50], which regard the mediator (i.e. the experience in our work) as the cause of prediction bias and remove it in the inference by Eq. 1. However, directly applying TDE makes the agent completely ignore the positive effect of the experience. Thus, as shown in Tab. 1 (II), employing TDE (line 5) even degrades the navigation performance (compared with line 4). Compared with TDE, our sTDE (line 6 and 7) adaptively retains the positive effects of the experience and obtains significant improvements. Previous work [50] introduces constructing the counterfactual item (i.e. \\(\\bar{a}^t\\)), by setting the value of observation \\(S\\) and the goal \\(G\\) to random or zero. We respectively adopt these two ways (line 6 and 7) and find out that their performances" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10798" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.892, + 0.118 + ], + "angle": 0, + "content": "Table 2. The comparisons with the related works (learning-based methods) in AI2THOR and RoboTHOR simulators. The L-sTDE represents our layout-based soft TDE framework based on different baselines. The improvements are shown in blue font." + }, + { + "type": "table", + "bbox": [ + 0.078, + 0.12, + 0.907, + 0.31 + ], + "angle": 0, + "content": "
IDMethodAI2THORRoboTHOR
SR↑ (%)SPL↑ (%)DTS↓ (m)SR↑ (%)SPL↑ (%)DTS↓ (m)
1Random4.68 ±1.742.42 ±1.351.36 ±0.012.92 ±0.391.34 ±0.202.40 ±0.02
2RGB+RL (A3C) [64]59.06 ±0.1934.56 ±0.440.68 ±0.0127.48 ±0.4616.45 ±0.122.08 ±0.02
3SP [59]62.19 ±0.6737.60 ±0.350.61 ±0.0226.22 ±0.7816.90 ±0.332.06 ±0.02
4SAVN [56]63.27 ±0.1138.20 ±0.040.56 ±0.0128.53 ±0.7718.27 ±0.351.96 ±0.02
5EOTP [32]65.61 ±0.2538.93 ±0.100.55 ±0.0128.84 ±0.4118.82 ±0.351.95 ±0.02
6ORG [15]66.53 ±0.2939.00 ±0.340.54 ±0.0129.64 ±0.8919.13 ±0.591.95 ±0.03
7ORG+TPN [15]68.60 ±0.2939.40 ±0.170.54 ±0.0130.05 ±0.0619.05 ±0.081.89 ±0.01
8VTNet [16]70.10 ±1.0039.60 ±0.100.52 ±0.0131.62 ±0.7419.63 ±0.421.87 ±0.03
9HOZ [63]70.38 ±0.1439.04 ±0.110.48 ±0.0232.27 ±1.1420.48 ±0.481.85 ±0.01
10Ours L-sTDE (EOTP)69.62 (4.01↑) ±0.7140.02 (1.09↑) ±0.470.52 (0.03↑) ±0.0137.37 (8.53↑) ±0.7522.00 (3.18↑) ±0.421.81 (0.14↑) ±0.02
11Ours L-sTDE (ORG)74.85 (8.32↑) ±0.3341.56 (2.56↑) ±0.110.47 (0.07↑) ±0.0239.27 (9.63↑) ±0.5522.81 (3.68↑) ±0.471.77 (0.18↑) ±0.02
12Ours L-sTDE (VTNet)75.25 (5.15↑) ±0.3941.69 (2.09↑) ±0.130.47 (0.05↑) ±0.0241.53 (9.91↑) ±0.6723.87 (4.24↑) ±0.501.72 (0.15↑) ±0.02
13Ours L-sTDE (HOZ)75.05 (4.67↑) ±0.2941.53 (2.49↑) ±0.210.46 (0.02↑) ±0.0242.13 (9.86↑) ±0.7824.54 (4.06↑) ±0.431.67 (0.18↑) ±0.01
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.334, + 0.47, + 0.412 + ], + "angle": 0, + "content": "are similar, except that using the random value makes the performance more volatile (i.e. larger standard deviation). Therefore, we set the value of the observation and the goal as zeros to construct the counterfactual item. More ablation studies and visualizations are detailed in the supplements." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.422, + 0.402, + 0.439 + ], + "angle": 0, + "content": "5.4. Comparisons with the Related Works" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.447, + 0.471, + 0.794 + ], + "angle": 0, + "content": "In this section, we evaluate all methods on the test datasets of AI2THOR, RoboTHOR, and Gibson. We compare the learning-based methods [15, 16, 32, 56, 59, 63, 64] in AI2THOR and RoboTHOR as shown in Tab. 2. With the egocentric RGB input, all methods are constructed with the Faster R-CNN backbone, which is pre-trained following [15]. To keep fair comparisons, we present VTNet [16] using their reported results with Faster R-CNN. Since other methods [32, 56, 59, 64] are originally proposed with the ResNet [21] pre-trained in ImageNet [14] as the visual backbone. For fair comparisons, following the recommendation of [15], we additionally encode the detection information provided by Faster R-CNN to these methods [32, 56, 59, 64]. Therefore, the implemented performances are higher than those results reported in the original papers. As shown in Tab. 2, benefiting from the incorporation of our layout-based sTDE (L-sTDE), the performances of existing methods are improved, especially our L-sTDE based on HOZ and VTNet achieve new SOTA performance. Other learning-based methods employ CLIP [42] as the backbone [25], or adopt pre-training on large-scale datasets (e.g. ProcTHOR [13]), and we compare our L-sTDE with these methods in the supplements." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Since most map-based methods require the RGB-D visual inputs and segmentation information provided by Mask R-CNN [20] to construct the semantic map, we take another comparison with the map-based methods as shown in Tab. 3. The map-based methods employ a parameter-free modular system to build the semantic map, then encode the map into the policy. We regard the encoded map as the ex" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.332, + 0.892, + 0.36 + ], + "angle": 0, + "content": "Table 3. The comparisons with the related works (map-based methods) in Gibson simulators." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.362, + 0.915, + 0.446 + ], + "angle": 0, + "content": "
IDMethodSR↑ (%)SPL↑ (%)DTS↓ (m)
1Random0.040.043.89
2RGBD+RL [48]8.422.873.23
3SemExp [7]65.3533.521.56
4Ours L-sTDE (SemExp)66.96 (1.61↑)34.33 (0.81↑)1.53 (0.03↑)
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.458, + 0.892, + 0.61 + ], + "angle": 0, + "content": "experience \\( z^t \\) and modify [7] with our L-sTDE. The results indicate that our method still brings some performance improvements, although the gains are limited compared to that of the learning-based methods. We analyze that, compared with the learning-based methods whose parameters are all trained end-to-end, the map-based methods utilize a modular system, and only a small number of parameters (the policy) need to be trained. Therefore, the map-based methods are less affected by the experience learned from training, and thus benefit less from our method." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.624, + 0.619, + 0.639 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.648, + 0.892, + 0.814 + ], + "angle": 0, + "content": "We propose the layout-based soft Total Direct Effect framework for ObjectNav task. Our motivation is to keep the positive effect and remove the negative effect of the experience, which is learned as the prior knowledge in training. Specifically, we propose to calculate the layout gap between the current environment and the prior knowledge. Then the layout gap is utilized to assess whether the impact of the learned experience is positive. Furthermore, the soft Total Direct Effect is proposed to appropriately control the effect of the experience on action prediction. The experiment results indicate the effectiveness of our method." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.817, + 0.894, + 0.9 + ], + "angle": 0, + "content": "Acknowledgements: This work was supported by Beijing Natural Science Foundation under Grant JQ22012, Z190020, in part by the National Natural Science Foundation of China under Grant 62125207, 62272443, 62032022 and U1936203, in part by the National Postdoctoral Program for Innovative Talents under Grant BX201700255." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10799" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.079, + 0.09, + 0.176, + 0.107 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.184 + ], + "angle": 0, + "content": "[1] Ehsan Abbasnejad, Damien Teney, Amin Parvaneh, Javen Shi, and Anton van den Hengel. Counterfactual vision and language learning. 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Such association contains the prior knowledge of navigating in training environments, which is denoted as the experience. The experience performs a positive effect on helping the agent infer the likely location of the goal when the layout gap between the unseen environments of the test and the prior knowledge obtained in training is minor. However, when the layout gap is significant, the experience exerts a negative effect on navigation. Motivated by keeping the positive effect and removing the negative effect of the experience, we propose the layout-based soft Total Direct Effect (L-sTDE) framework based on the causal inference to adjust the prediction of the navigation policy. In particular, we propose to calculate the layout gap which is defined as the KL divergence between the posterior and the prior distribution of the object layout. Then the sTDE is proposed to appropriately control the effect of the experience based on the layout gap. Experimental results on AI2THOR, RoboTHOR, and Habitat demonstrate the effectiveness of our method. The code is available at https://github.com/sx-zhang/Layout-based-sTDE.git. + +# 1. Introduction + +The visual object-oriented navigation task (i.e. Object-Nav) [3] requires the agent to navigate to a user-specified goal (e.g. laptop) based on the egocentric visual observations. A typical challenge is navigating in unseen environments, where the goal is invisible most of the time, i.e. the partial observable problem, which typically results in the agent's meaningless actions (e.g. back-tracking or getting lost at dead-ends). Although encouraging the exploration in the unseen environment (until the goal is visible) is an intuitive solution, the lack of environment layout information still limits the efficiency of goal-oriented navigation. + +![](images/e95d5897987e85443d26760a9d208a4e8932abf190099b677c3bbb08161e5fa6.jpg) +S: Observation + +![](images/8c4c4aaa21593b4ad368e0a8680222991bbf762f6e317d87000dbf8d53895688.jpg) +Intervention +(a) The factual prediction +Z:Experience A:Action +(b) The counterfactual prediction +Figure 1. The proposed causal graph. (a) represents the fact prediction $a$ , i.e. the original prediction of the trained model. (b) refers to the counter-fact prediction $\bar{a}$ , i.e. the prediction is only affected by the experience $Z$ . (b) is realized by applying the intervention and counterfactual operations to the original model. + +Recently, the learning-based methods attempt to model the prior knowledge of the spatial relationships among the objects, so the agent could infer the likely locations of the goal based on the current observation (which objects are observed currently) and the prior knowledge (the spatial relationships between the goal and the observed objects) learned in the training stage. Some works utilize additional modules to construct the objects graph [15, 59, 60], the region graph [63] and the attention mechanism [32], while others [16, 56] employ a network that implicitly learns the spatial relationships end-to-end. All these methods attempt to establish prior knowledge in training environments, so that the agent would utilize the prior knowledge to associate the real-time observations with the goal, and infer the likely locations of the goal during the inference. The underlying assumption of these methods is that all of the object layouts in unseen environments should be exactly consistent with those in training environments. However, the layout consistency assumption is only partially correct due to the limited training data. Thus, those methods typically suffer from poor generalization [31] in unseen environments. + +To reveal the causes of poor generalization, we propose to use the casual graph (i.e. Structural Causal Model, SCM + +[38]) to analyze these navigation works. As illustrated in Fig. 1 (a), the navigation model takes the observation $S$ and the goal $G$ as the input, and predicts the action $A$ at each timestamp. The causal links $S \rightarrow Z$ and $G \rightarrow Z$ represent that the observation and the goal are embedded by the pre-constructed modules [15, 32, 59, 60, 63] or the pre-trained network [16, 56]. The embedding vector is defined as the experience $Z$ in the causal graph, which introduces the prior knowledge to influence action prediction ( $Z \rightarrow A$ ). Meanwhile, the real-time observation and the goal also independently affect the prediction without being encoded by the prior knowledge module, which is represented as $S \rightarrow A$ and $G \rightarrow A$ , respectively. The causal links $S \rightarrow A$ and $G \rightarrow A$ represent the exploration-based effect (only related to the current episode) on the action prediction, which is different from the experience-based effect $Z \rightarrow A$ . Consider two cases of the layout gap between the current environment and the prior knowledge: 1) the layout gap is minor and 2) the layout gap is significant. In the former case, the object layout is consistent in the current environment and the prior knowledge. Thus, the experience $Z$ exerts a positive effect on the prediction of action $A$ . However, the effect of experience $Z$ in the latter case could be negative. If the agent still relies on the "negative" experience to predict actions, it will suffer from poor generalization. Therefore, wisely utilizing the experience is essential to the ObjectNav task. + +Motivated by wisely utilizing the learned experience, we propose the soft Total Direct Effect (sTDE) framework based on the Total Direct Effect analysis in causal inference. Our sTDE improves the generalization of the trained model in inference by eliminating the prediction bias brought by the experience. To decouple the effect of experience, we construct the counter-fact prediction $\bar{a}$ : the prediction is only affected by the experience $Z$ while ignoring the $S$ and $G$ , as shown in Fig. 1 (b). Then we propose the object layout estimator that calculates whether the effect of the experience is positive, by measuring the layout gap between the current environment and the prior knowledge. Furthermore, our sTDE will remove the counter-fact prediction $\bar{a}$ from the fact prediction $a$ when the layout gap is large. + +In this paper, we propose the layout-based soft TDE framework for the ObjectNav task. Specifically, we adopt the Dirichlet-Multinomial distribution [22] to formulate the contextual relationship between objects, which represents the object layout of the environment. Before training, the agent learns prior layout distribution (i.e. the prior parameters of Dirichlet-Multinomial distribution) by randomly exploring the training environments. In the training stage, based on the Bayesian inference, the agent estimates the posterior layout distribution with the prior distribution and newly obtained observations. Then the constantly updated posterior layout is encoded into the navigation model and utilized to learn the environment-adaptive experience. The + +entire model is trained with RL by maximizing the reward of reaching the goal. In the test stage, our agent will not directly use the trained policy as most previous works do. The agent first calculates the layout gap and the counter-fact prediction. The layout gap is determined by calculating the KL divergence between the posterior and prior distribution of object layouts and serves as a weight to determine whether to remove the counter-fact prediction (i.e. experience effect) from the original prediction. The experimental results on AI2THOR [27], RoboTHOR [12] and Habitat [48] indicate that our layout-based sTDE (L-sTDE) can be a plug-and-play method to boost existing methods to achieve better navigation performances. + +# 2. Related Work + +Visual Object Navigation. Target-oriented visual navigation can be categorized [5] into PointGoal [8, 18, 43, 55], AreaGoal [28, 57], AudioGoal [10, 11], ImageGoal [19, 29, 48], LanguageGoal (vision-and-language navigation) [23, 40, 41] and ObjectGoal. We focus on visual ObjectGoal navigation, which sets the object category as the target. Previous map-based methods usually build a metric map [6-8, 44] or topological map [9, 47] to memorize the environment layout. Besides, a popular deep-learning pipeline is to take an end-to-end network [2, 17, 34] to process the visual embedding and goal embedding, then predict the navigation action. Based on that, recent learning-based methods propose various improvement ideas, such as semantic representation [35], prior knowledge [59], object relation graph [15, 60, 63], attention mechanism [32], meta-learning [56], and transformer structure [16]. These well-trained modules provide prior knowledge to guide the agent in unseen environments. In our work, we denote such knowledge learned from training (with whatever improvement designs) as the experience. We try to find out, under different environment layouts, whether the learned experience takes a positive effect or not, and how to better utilize the experience to improve the navigation. + +Causal Inference. Causal inference [38, 39] provides analysis tools (e.g. intervention, counter-fact) to reveal the causal effect behind the data-based statistical correlation, which is widely adopted in epidemiology, psychology, or politics research [24, 30, 46]. Recently, causal inference is introduced into the computer vision society for scene graph generation [50], vision and language task [1,36], long-tailed classification [49] and few/zero-shot learning [4, 62]. For the visual navigation task, [37] generates counterfactual observations to improve generalization to new environments for VLN (vision-and-language navigation) task. [54] proposes causal CT (continuous-time) models for visual drone navigation tasks. In our work, we focus on the ObjectNav task and utilize the causal inference to wisely control the effect of experience in the inference. + +# 3. Preliminaries of ObjectNav Task + +Task Definition. The ObjectNav task requires the agent to navigate to a user-specified object category from a random starting location in an unseen scene, and the agent is only allowed to utilize the egocentric visual observation (e.g. RGB images) and the semantic embedding of the target object. Formally, at each timestamp $t$ , the agent receives the observation $S = s^t$ and the goal $G = g^t$ and is expected to adopt an action $A = a^t$ , $a^t \in \mathcal{A}$ . The discrete action space is defined as: $\mathcal{A} = \{MoveAhead, RotateLeft, RotateRight, LookDown, LookUp, Done\}$ . When the agent outputs the Done action, the episode terminates. An episode is considered successful if, within a certain number of steps, the final location of the agent is close to the goal within a distance threshold (e.g. $1m$ ) and the goal is visible in the egocentric observation. + +Navigation Model. Prevailing ObjectNav works can be summarized as a visual-goal encoder and a policy function, as shown in Fig. 2. The visual-goal encoder is constructed to associate the visual observation $S$ and the goal $G$ . We denote such association as the experience $Z$ since the encoder could learn the prior experience during the training. + +Previous learning-based methods typically implement the visual-goal encoder as an object relation graph [15, 59, 60], region graph [63], attention module [32] and transformer structure [16]. For instance, the ORG [15] builds an object relation graph, where the nodes are defined as the object categories and the edges are defined as the spatial correlations among different categories. The object relation graph takes the observation and the goal as inputs and encodes them with the learned edges to obtain the experience $Z$ . Previous map-based methods [7, 44] typically construct the semantic map based on the observations, and embed the map with the target. Such embedding is also regarded as the experience $Z$ . Based on the observation, target object, and these learned experiences, the policy module will output the prediction. These navigation models are typically trained with the RL (reinforcement learning) [33, 55, 64]. + +# 4. The Proposed Solution + +# 4.1. Layout-based Soft Total Direct Effect + +We humans make decisions in a causality-based manner: we have the instinct to assess the effect of the navigation experience [51] and wisely eliminate the cognition bias from the experience. However, the machines are likelihood-based [50] and the predictions depend on the association likelihood between observations, goal, and actions, which is mainly learned from limited training data. Therefore, the predictions are inevitably biased due to the biased experience. Prevailing methods [15, 16, 56, 59, 60, 63] entirely accept the experience learned in the training stage, and rarely consider whether the prior experience is beneficial to the + +![](images/d068a7e5d2b7515d7dc5320ef9b095cc57ec8bb6bb13dad931fc0532992b75d5.jpg) +Figure 2. Prevailing navigation framework (top) and our contributions (bottom). Our layout estimator outputs the expectation $w^t$ of posterior layout distribution and the layout gap $D_{\Delta}^{t}$ . The $w^t$ is proposed to enhance the adaptability of the experience $z^t$ to new environments. The layout gap $D_{\Delta}^{t}$ serves as a weight to alleviate the experience bias. + +current environment. However, as previously discussed, the learned experience has both positive and negative effects, especially in the unseen environments, which may have a different layout from the training environments. Therefore, keeping positive effects and removing negative effects of learned experience is essential to the navigation models. + +The causal inference [39,52,53] encourages the machine to discover the causality behind the association likelihood, which has been proven to be an effective analysis method in many computer vision tasks [36, 49, 50, 61]. From the perspective of causal inference, the experience $Z$ serves as the mediator between the input (observation $S$ and target $G$ ) and the output (action $A$ ) as illustrated in Fig. 1 (a). To eliminate the mediation fallacy, the causal inference [38] introduces the Total Direct Effect (TDE) analysis to remove the prediction bias brought by the mediator. + +Total Direct Effect. The fundamental principle behind TDE analysis [36, 49, 50] is to build a bias prediction $\bar{a}^t$ that is exclusively affected by the mediator, and then remove the bias item from the original prediction $a^t$ . The TDE analysis is formulated as: + +$$ +T D E \left(a ^ {t}\right) = a ^ {t} - \bar {a} ^ {t} \tag {1} +$$ + +where $a^t = \pi (A|S = s^t,G = g^t)$ is the factual prediction of a trained model $\pi$ , which takes the observation $S = s^t$ and target $G = g^{t}$ as the input, as shown in Fig. 1 (a). The latter is the counterfactual prediction $\bar{a}^t = \pi (A|do(S = \bar{s}^t,G = \bar{g}^t),Z = Z_{s^t,g^t})$ as shown in Fig. 1 (b). The calculation of $\bar{a}^t$ includes two operations + +in causal inference: intervention and counterfactual operations. The intervention operation is denoted as $do(\cdot)$ and realized by specifying a certain value for the variable (e.g. $do(S = \bar{s}^t)$ ). The intervened value (e.g. $\bar{s}^t$ , $\bar{g}^t$ ) is set to a random or zero vector. The intervention operation eliminates the effect of observation $S$ and goal $G$ on the action prediction, while it also changes the value of the causal successor (i.e. $Z$ ). However, since our motivation is to model the case only affected by the mediator, which requires the mediator $Z$ to remain the original value. To this end, the counterfactual operation assigns the original value to the variable $Z$ as if $S = s^t$ , $G = g^t$ had existed. The counterfactual operation is symbolized as $Z = Z_{s^t, g^t}$ . + +The TDE analysis is easily realized by manipulating the values of several variables (e.g. $S, G, Z$ ) and is efficient in removing the effect of the mediator (i.e. experience). However, the experience is not always detrimental. It can also be beneficial when the object layout gap is minor. Therefore, we propose the soft TDE to appropriately maintain the positive effect of experience. + +Soft Total Direct Effect. In alternative to previous TDE analysis, our soft TDE modifies the Eq. 1 by adding a trade-off weight, which is formulated as: + +$$ +s T D E (a ^ {t}) = a ^ {t} - R e L U (D _ {\Delta} ^ {t} - \varepsilon) \cdot \bar {a} ^ {t} \qquad (2) +$$ + +where $ReLU(\cdot)$ is the ReLU activation function, and $\varepsilon$ is a threshold hyperparameter. The $D_{\Delta}^{t}$ is the object layout gap, which is produced by our layout estimator (Sec. 4.2) as shown in Fig. 2. The $D_{\Delta}^{t}$ evaluates the effect of the experience $Z$ , and preserves the positive experience when the layout gap between the current environment and prior knowledge is minor (i.e. $D_{\Delta}^{t}$ is less than the threshold $\varepsilon$ ). + +# 4.2. Layout Estimator + +Object Layout. For the ObjectNav task, the main challenge is the partially observable problem, that the agent can only observe the partial area at each time. With continuously observing during the navigation process, more objects will be observed, and the partially known problem can also be alleviated. Considering objects are usually distributed in a reasonable layout, the adjacent relation of objects is essential to help the agent infer the location of the target object based on the observed objects. Therefore, we concentrate on the contextual relationship to represent the object layout. The object layout in a scene is defined as the set $D = \{\theta_{i}\}_{i=1}^{K}$ , where $K$ is the number of object categories. The $\theta_{i} = (\theta_{i,j})_{j=1}^{K}$ represents the context distribution of object category $c_{i}$ . Each dimension $\theta_{i,j}$ represents the probability $p(c_{j}|c_{i})$ that the object category $c_{j}$ can be observed around the category $c_{i}$ in an observation. Specifically, we assume that the context distribution follows the Dirichlet distribution: $\theta_{i} = (\theta_{i,j})_{j=1}^{K} \sim \text{Dir}(\alpha_{i})$ , where + +![](images/47cd8672246a84e1dc5892f5085577f3b54d1920e871d61f934af64b4ba08df7.jpg) +Figure 3. The calculation of the likelihood function $p(s_i^t |\theta_i)$ . + +$\sum_{j}\theta_{i,j} = 1,\theta_{i,j}\geq 0$ , and $\alpha_{i} = (\alpha_{i,j})_{j = 1}^{K},\alpha_{i,j} > 0$ parameterizes the distribution. The Dirichlet distribution is chosen for two reasons: 1) the conjugate prior permits concise calculations; 2) the likelihood-equivalence property [22]. + +At the beginning of every new episode, the parameter $\alpha_{i}$ is initialized as the prior initial value $\alpha_{i}^{*}$ ( $\alpha_{i}^{*}$ will be detailed in Sec. 4.3). At each timestamp $t$ , our method computes the posterior object distribution based on the incoming observations. Specifically, the agent receives the visual observation $s^t$ , and the visual observation is then converted into a count vector $n^t \in \mathbb{R}^K$ , where each dimension of $n^t = (n_i^t)_{i=1}^K$ , $n_i^t \geq 0$ records the number of each object category appearing in the current observation. The count vector $n^t$ is obtained by the object detection or segmentation modules (e.g. Faster R-CNN [45] or Mask R-CNN [20]). As shown in Fig. 3, we define $n_{-i}^t = (n_{-i,j}^t)_{j=1}^K$ , $n_{-i,j}^t \geq 0$ as the count of other categories (except $c_i$ ) and define $s_i^t$ as the contextual observation of the category $c_i$ . Conditioned on $c_i$ , assume the probability that $s_i^t$ is observed follows the multinomial distribution $s_i^t \sim Mult(n_{-i}^t, \theta_i)$ . Then the likelihood function can be calculated as: + +$$ +p \left(s _ {i} ^ {t} \mid \theta_ {i}\right) = \prod_ {j = 1} ^ {K} \theta_ {i, j} ^ {n _ {- i, j} ^ {t}} \tag {3} +$$ + +Meanwhile, according to the previous Dirichlet distribution assumption, the prior distribution of $\theta_{i}$ at timestamp $t$ is $p\left(\theta_i|\alpha_i^t\right) = Dir\left(\theta_i|\alpha_i^t\right)$ . Considering the contextual observation $s_i^t$ , the posterior distribution of $\theta_{i}$ is further calculated according to the Bayesian inference as the following: + +$$ +p \left(\theta_ {i} \mid s _ {i} ^ {t}, \alpha_ {i} ^ {t}\right) = \frac {p \left(s _ {i} ^ {t} \mid \theta_ {i}\right) p \left(\theta_ {i} \mid \alpha_ {i} ^ {t}\right)}{p \left(s _ {i} ^ {t} \mid \alpha_ {i} ^ {t}\right)} = D i r \left(\theta_ {i} \mid \alpha_ {i} ^ {t} + n _ {- i} ^ {t}\right) \tag {4} +$$ + +The Eq. 4 indicates that the posterior distribution $p(\theta_i | s_i^t, \alpha_i^t)$ also satisfies the Dirichlet distribution (the calculation process is detailed in the supplements), which is known as the conjugate prior property. The conjugate prior property guarantees the succinct calculation for the posterior distribution of $\theta_i$ , i.e., simply combining the count vector $n_{-i}^t$ of context objects around category $c_i$ with the hyperparameter $\alpha_i^t$ of the prior distribution. Similarly, the posterior distributions of other object categories can also be obtained following the Eq. 4. + +Furthermore, the posterior distributions at time $t$ serves as the prior distributions at time $t + 1$ , thus the value of hyperparameter $\alpha_{i}$ is updated by $\alpha_{i}^{t + 1} = \alpha_{i}^{t} + n_{-i}^{t}$ . This update guarantees the knowledge of object layout is continuously adapted to the current navigation environment. + +Based on the obtained posterior distribution, the layout gap $D_{\Delta}^{t}$ is defined as the KL divergence between the posterior and prior object layout over all categories. Formally, the object layout gap $D_{\Delta}^{t}$ is defined as: + +$$ +D _ {\Delta} ^ {t} = \tanh \left( \right.\frac {1}{K} \sum_ {i = 1} ^ {K} K L \left( \right.p \left(\theta_ {i} \mid s ^ {t}, \alpha_ {i} ^ {t}\right)\left\| \right. p \left(\theta_ {i} \mid \alpha_ {i} ^ {t}\right)\left. \right)\left. \right) \tag {5} +$$ + +where $\tanh(\cdot)$ is the tanh activation function. The layout gap $D_{\Delta}^{t}$ estimates the gap between the posterior object layout at time $t$ and the prior knowledge before time $t$ , which plays a vital role in the Eq. 2. + +Environment-Adaptive Experience. The prevailing methods [15, 16, 59] typically encode the visual observation $s^t$ and the target object $g^t$ into the experience $z^t \in \mathbb{R}^{K \times M}$ during training, where $K$ is the number of object categories and $M$ refers to the feature dimension. The learned experience could be both biased (the layout gap between the training and test environments) and environment-static (without adaptation to the current environment). Therefore, in addition to eliminate the bias in the inference, we also propose to enhance the environmental adaptability of the experience $z^t$ to achieve a better performance. To this end, the dynamically updated knowledge of object layout $D = \{\theta_i\}_{i=1}^K$ is encoded into the navigation framework. Specifically, the expectation of the posterior distribution of the object layout $D$ is formalized as $w^t \in \mathbb{R}^{K \times K}$ , $w_{i,j}^t > 0$ . For $j = i$ , since $p(c_i | c_i)$ always exists, we set $w_{i,j}^t = 1$ . When $j \neq i$ , $w_{i,j}^t = \mathbb{E}_{p(\theta_i | s_i^t, \alpha_i^t)}(\theta_{i,j})$ , where $\mathbb{E}(\cdot)$ denote the expectation calculation. Based on [22], the expectation of the Dirichlet function $Dir(\theta_i | \alpha_i^t + n_{-i}^t)$ is equivalent to the normalization of its parameters. Accordingly, for $j \neq i$ , + +$$ +w _ {i, j} ^ {t} = \mathbb {E} _ {p \left(\theta_ {i} \mid s _ {i} ^ {t}, \alpha_ {i} ^ {t}\right)} \left(\theta_ {i, j}\right) = \frac {\alpha_ {i , j} ^ {t} + n _ {- i , j} ^ {t}}{\sum_ {j = 1} ^ {K} \left(\alpha_ {i , j} ^ {t} + n _ {- i , j} ^ {t}\right)} \tag {6} +$$ + +Since $w^{t}$ is updated in real-time, we propose to improve the environment-static experience $z^{t}$ to environment- + +adaptive experience $\hat{z}^t$ by incorporating the dynamically updated knowledge of object layout, where $\hat{z}^t$ is given by: + +$$ +\hat {z} ^ {t} = z ^ {t} \odot [ w ^ {t} \times g ^ {t} ] \tag {7} +$$ + +where $\odot$ represents the element-wise multiplication, $\times$ refers to the matrix multiplication, and $g^{t}\in \mathbb{R}^{K}$ is a one-hot vector indicating the target category of the goal. The result of $[w^t\times g^t ]\in \mathbb{R}^K$ indicates the probability of the target $g^{t}$ is observed conditioned on each object category, which serves as a weight on the category-specific dimension of $z^t$ + +# 4.3. Training and Inference + +As shown in Fig. 2, our layout estimator outputs (1) the expectation $w^t$ of the posterior layout distribution, and (2) the layout gap $D_{\Delta}^{t}$ . Both $w^t$ and $D_{\Delta}^{t}$ are calculated mathematically without learnable parameters, thus our method has the plug-and-play property to boost the existing methods. Specifically, our layout-based sTDE is realized as: (1) Before training, to determine the initial value $(\alpha_i^*)_{i=1}^K$ , we first employ a random agent equipped with our object layout estimator, whose parameters $(\alpha_i)^K_{i=1}$ are initialized as all one vector. Then the agent randomly explores the training scenes to obtain sufficient observations to update the parameters by Eq. 4. The updated parameters are defined as $(\alpha_i^*)_{i=1}^K$ . (2) In the training stage, at the beginning of every episode, all parameters $(\alpha_i)^K_{i=1}$ are initialized as the prior parameters $(\alpha_i^*)_{i=1}^K$ . The layout estimator calculates the posterior distribution of object layout $D$ (Eq. 4), using the constant observation $s^t$ and the prior distribution. Then the expectation of the posterior distribution $w^t$ is estimated and incorporated in the navigation model $\pi$ (Eq. 6, 7). The model $\pi$ is trained with RL. (3) In the causal-inference stage, the agent will not directly use the trained policy $\pi$ , while it first calculates the layout gap $D_{\Delta}^{t}$ (Eq. 5) and the counter-fact prediction $\bar{a}^t$ (the effect of the experience). Then the agent appropriately removes the counter-fact prediction $\bar{a}^t$ from the fact prediction $a^t$ based on the layout gap $D_{\Delta}^{t}$ (Eq. 2). For more details and algorithms of training and inference, please refer to the supplements. + +Note that the expectation of the posterior distribution of the object layout $w^{t}$ affects the prediction of the model during both training and inference, while $D_{\Delta}^{t}$ is utilized for debiasing only in the inference. Furthermore, we want to explain why the debiasing operation only acts in inference. As shown in Fig. 1, the prediction is influenced by two effects: the inputs (the observation $S$ and the goal $G$ ) and their mediator (the experience $E$ ). The mediator (experience) has agnostic effects because it is learned from limited training data. The training data can not cover all room layouts, thus resulting the prediction bias in the inference. Consequently, the debiasing operation (i.e. the sTDE partially removes the effect of experience from prediction) is conducted in inference to decouple the effect from the training data. + +![](images/7faa6a3b890fed9cfffc6d287260bb9cf9ab192f7cad457e9239037d339a4ec9.jpg) +Figure 4. The correlation between the navigation performance on success rate (SR) and the layout similarity. + +# 5. Experiments + +# 5.1. Experimental Setup + +We utilize the AI2THOR [27], RoboTHOR [12] simulators to conduct ablation studies and compare our method with the learning-based methods [15, 16, 32, 56, 59, 63, 64]. The experimental settings on above datasets follow the primary works [15, 16, 63]. Besides, we choose the Gibson [58] dataset in the Habitat simulator [48] to compare our method with the map-based methods and adopt the same settings as [7]. For more details about the settings of the datasets (e.g. the split of training, validation, testing scenes, and the target objects), please refer to the supplements. + +Our method and the related works are both trained to maximize the navigation reward via RL. The reward function penalizes the agent by -0.01 for each step and rewards it by 5 if the episode is successful (the successful episode is defined in Sec. 3). All methods are trained with 6M episodes, where in each episode, the starting position of the agent and the goal are randomly selected. Note that, since our method needs prerequisite exploration to determine the initial parameters $(\alpha_{i}^{*})_{i = 1}^{K}$ of the layout distribution. To be fair, we employ the agent to randomly explore the training rooms to learn the initial parameters for 2M episodes, then we train our method with 4M episodes. + +For evaluation, we repeatedly run 3 trials and report the results with mean $\pm$ standard deviation. We choose SR (Success Rate), SPL (Success weighted by Path Length), and DTS (Distance to Goal) metrics for evaluation, which are detailed in the supplements. For all results in the following tables, the $\uparrow$ means that the larger value is better, while $\downarrow$ indicates the opposite. + +# 5.2. The Compared Methods + +We choose the learning-based methods [15, 16, 32, 56, 59, 63, 64] and the map-based method [7] for comparison. Random: the agent adopts random actions. RGB(D) + RL (A3C) [48, 64]: the agent utilizes the simple embeddings of visual input and the goal, and is trained with A3C [34]. + +![](images/f7db9292303efec60f8300922b5396aadfaf3268bb1697ecfd9b52312dfa21d7.jpg) +Figure 5. Category-wise improvement of our method compared to the baseline. The categories are arranged from high to low based on their average layout similarity between training and testing scenes. + +SP [59]: SP constructs the scene prior knowledge from the external dataset. The prior knowledge encoded with GCN [26] is provided to the agent as the additional information. SAVN [56]: SAVN establishes a sub-network to learn a self-supervised interaction loss. EOTP [32]: EOTP proposes an attention module to encode the semantic information about the observed objects. ORG [15]: ORG proposes to learn an object relation graph, and builds a memory-augmented tentative policy network (TPN) to produce self-supervision. VTNet [16]: VTNet employs the Transformer network to encode the visual information and the goal. HOZ [63]: HOZ attempts to abstract the region relation among the objects and proposes to learn the region relation graph to associate the vision and the goal. SemExp [7]: SemExp builds an episodic semantic map and trains a goal-oriented policy taking the semantic map as the input. + +# 5.3. Evaluation Results + +In this section, we adopt the ORG [15] as the baseline and conduct evaluations on the validation set of AI2THOR. + +Correlation between layout and success rate. Our motivation is that the layout gap between training and testing scenes may have an impact on navigation. To verify this, we take the statistic and visualize the results in Fig. 4 (a), where the y-axis represents the success rate of navigating to objects $c_{i}$ in a testing scene $R_{j}$ , the x-axis represents the layout similarity of the object $c_{i}$ between the training scenes and the test scenes, and the scatter points represent all target objects in all test scenes. As shown in Fig. 4 (b), the layout similarity is defined as the cosine similarity of the statistics vectors (the count of cooccurrence objects) obtained in the training scenes and the test scene $R_{j}$ . Fig. 4 (a) indicates that the navigation performance on SR during inference has a generally positive correlation with the layout similarity, which supports our motivation. + +Improvements of our method compared to baseline. The navigation performance of the baseline (green bar) and the improvements brought by our method (blue bar) are shown in Fig. 5. All goals (x-axis) are arranged from high + +![](images/7670fa5f1fbaf1bf1bc8c9d8b1512897b312423c5391489fd9c5ecc0bfe45bb3.jpg) +Figure 6. The ablation study of the threshold $\varepsilon$ and the visualization of the object layout gap $D_{\Delta}^{t}$ over the navigation steps. + +![](images/28df14622981d9ff5fc7eec70b3c389b54638d3e36a69f48552bdbe65ba34c44.jpg) + +to low based on their layout similarity. The results indicate that our method can bring more obvious improvement in the categories with low layout similarity (as illustrated by the red dashed circle). We presume that the goals with a larger layout gap are more susceptible to the effects of the experience, thus benefiting more from our de-biased method. The results once again support our motivation. + +Ablations on the threshold $\varepsilon$ . The threshold $\varepsilon$ influences the agent by Eq. 2, which determines whether to remove the prediction bias introduced by the experience. As shown in Fig. 6 (a), the results of different threshold $\varepsilon$ basically show the same trend on the SR, SPL metrics: as the value of threshold $\varepsilon$ increases, the performances on these metrics initially increase and then decrease. When the value of threshold $\varepsilon$ is small, the Eq. 2 tends to consider that the majority of experiences $Z$ are negative and need to be removed. At this point, gradually increasing the threshold $\varepsilon$ could retain more experiences and improve performance. However, when the threshold $\varepsilon$ is too large (e.g. $\varepsilon = 1$ ), the Eq. 2 falls into another extreme which considers all experiences are positive and need to be preserved, resulting in the performance degradation. The results on DTS metric indicate that excessively removing the experience ( $\varepsilon$ is small) will increase the exploration of the agent, thus resulting in worse performance on DTS. Based on the above results, we choose the threshold as $\varepsilon = 0.5$ . + +Visualization of the object layout gap $D_{\Delta}^{t}$ . The object layout gap $D_{\Delta}^{t}$ represents the KL divergence between the posterior and the prior distribution of the layout. The average value of the $D_{\Delta}^{t}$ over navigation steps in AI2THOR is illustrated in Fig. 6 (b). The results indicate that the layout gap decreases as the number of steps increases (the purple line). However, without updating by our method (the grey line), the layout gap is maintained at a large value. The trend of $D_{\Delta}^{t}$ demonstrates that the learned knowledge (posterior distribution of the layout) by our method is gradually approaching the real layout of the current scene. It also reveals that the $w^{t}$ (the expectation of posterior distribution) is environment-adaptive information for guiding the agent. + +Additionally, considering the threshold $\varepsilon = 0.5$ and + +Table 1. The ablation studies. (I) The ablations of several components. The $w^t$ represents encoding the expectation of the posterior distribution of object layout into the model, and $D_{\Delta}^{t}$ represents de-biasing the trained model in the inference with our sTDE. (II) The comparison of different de-bias methods. + +
IDMethod +Baseline w t DΔtSR↑ (%)SPL↑ (%)DTS↓ (m)
I1✓66.48±0.2238.42±0.390.54±0.01
2✓71.40±0.3739.11±0.440.49±0.02
3✓74.95±0.3841.68±0.230.47±0.02
II4w/o De-bias71.40±0.3739.11±0.440.49±0.02
5TDE [53]69.24±0.1238.38±0.160.52±0.01
6Ours sTDE (zero)74.95±0.3841.68±0.230.47±0.02
7Ours sTDE (random)75.03±0.6941.48±0.440.46±0.03
+ +looking back at Fig. 6 (b), we can observe how our layout-based sTDE works in the time (i.e. steps) dimension. According to the Eq. 2, the de-bias operation is activated when $(D_{\Delta}^{t} - \varepsilon) > 0$ , as shown in the upper purple shadow. At the beginning of an episode, the agent is unfamiliar with the current scene, and the layout gap is large. At this stage, our layout-based sTDE is activated to eliminate the prediction bias caused by the experience. Then with continuous navigating and updating, the prior knowledge of the object layout has been gradually adjusted to fit the current scene. Therefore, at this stage, the updated experience is applicable to the current scene and fully accepted for the navigation. + +Ablations of different components. We evaluate different components of our method. The ablation study in Tab. 1 (I) indicates the efficacy of each component in our method. Specifically, the expectation $w^{t}$ of the posterior distribution of the object layout improves the baseline (ORG) performance by $4.92\%$ , $0.69\%$ and $-0.05m$ on SR, SPL and DTS metrics. Moreover, the soft Total Direct Effect (sTDE) further improves the performance and gains $3.55\%$ , $2.57\%$ and $-0.02m$ improvement on SR, SPL and DTS metrics. Overall, our method outperforms the baseline by $8.47\%$ , $3.26\%$ and $-0.07m$ on SR, SPL and DTS metrics. + +Comparison with TDE and sTDE. The TDE analysis is effective in removing the mediation fallacy and is applied in many works [36, 49, 50], which regard the mediator (i.e. the experience in our work) as the cause of prediction bias and remove it in the inference by Eq. 1. However, directly applying TDE makes the agent completely ignore the positive effect of the experience. Thus, as shown in Tab. 1 (II), employing TDE (line 5) even degrades the navigation performance (compared with line 4). Compared with TDE, our sTDE (line 6 and 7) adaptively retains the positive effects of the experience and obtains significant improvements. Previous work [50] introduces constructing the counterfactual item (i.e. $\bar{a}^t$ ), by setting the value of observation $S$ and the goal $G$ to random or zero. We respectively adopt these two ways (line 6 and 7) and find out that their performances + +Table 2. The comparisons with the related works (learning-based methods) in AI2THOR and RoboTHOR simulators. The L-sTDE represents our layout-based soft TDE framework based on different baselines. The improvements are shown in blue font. + +
IDMethodAI2THORRoboTHOR
SR↑ (%)SPL↑ (%)DTS↓ (m)SR↑ (%)SPL↑ (%)DTS↓ (m)
1Random4.68 ±1.742.42 ±1.351.36 ±0.012.92 ±0.391.34 ±0.202.40 ±0.02
2RGB+RL (A3C) [64]59.06 ±0.1934.56 ±0.440.68 ±0.0127.48 ±0.4616.45 ±0.122.08 ±0.02
3SP [59]62.19 ±0.6737.60 ±0.350.61 ±0.0226.22 ±0.7816.90 ±0.332.06 ±0.02
4SAVN [56]63.27 ±0.1138.20 ±0.040.56 ±0.0128.53 ±0.7718.27 ±0.351.96 ±0.02
5EOTP [32]65.61 ±0.2538.93 ±0.100.55 ±0.0128.84 ±0.4118.82 ±0.351.95 ±0.02
6ORG [15]66.53 ±0.2939.00 ±0.340.54 ±0.0129.64 ±0.8919.13 ±0.591.95 ±0.03
7ORG+TPN [15]68.60 ±0.2939.40 ±0.170.54 ±0.0130.05 ±0.0619.05 ±0.081.89 ±0.01
8VTNet [16]70.10 ±1.0039.60 ±0.100.52 ±0.0131.62 ±0.7419.63 ±0.421.87 ±0.03
9HOZ [63]70.38 ±0.1439.04 ±0.110.48 ±0.0232.27 ±1.1420.48 ±0.481.85 ±0.01
10Ours L-sTDE (EOTP)69.62 (4.01↑) ±0.7140.02 (1.09↑) ±0.470.52 (0.03↑) ±0.0137.37 (8.53↑) ±0.7522.00 (3.18↑) ±0.421.81 (0.14↑) ±0.02
11Ours L-sTDE (ORG)74.85 (8.32↑) ±0.3341.56 (2.56↑) ±0.110.47 (0.07↑) ±0.0239.27 (9.63↑) ±0.5522.81 (3.68↑) ±0.471.77 (0.18↑) ±0.02
12Ours L-sTDE (VTNet)75.25 (5.15↑) ±0.3941.69 (2.09↑) ±0.130.47 (0.05↑) ±0.0241.53 (9.91↑) ±0.6723.87 (4.24↑) ±0.501.72 (0.15↑) ±0.02
13Ours L-sTDE (HOZ)75.05 (4.67↑) ±0.2941.53 (2.49↑) ±0.210.46 (0.02↑) ±0.0242.13 (9.86↑) ±0.7824.54 (4.06↑) ±0.431.67 (0.18↑) ±0.01
+ +are similar, except that using the random value makes the performance more volatile (i.e. larger standard deviation). Therefore, we set the value of the observation and the goal as zeros to construct the counterfactual item. More ablation studies and visualizations are detailed in the supplements. + +# 5.4. Comparisons with the Related Works + +In this section, we evaluate all methods on the test datasets of AI2THOR, RoboTHOR, and Gibson. We compare the learning-based methods [15, 16, 32, 56, 59, 63, 64] in AI2THOR and RoboTHOR as shown in Tab. 2. With the egocentric RGB input, all methods are constructed with the Faster R-CNN backbone, which is pre-trained following [15]. To keep fair comparisons, we present VTNet [16] using their reported results with Faster R-CNN. Since other methods [32, 56, 59, 64] are originally proposed with the ResNet [21] pre-trained in ImageNet [14] as the visual backbone. For fair comparisons, following the recommendation of [15], we additionally encode the detection information provided by Faster R-CNN to these methods [32, 56, 59, 64]. Therefore, the implemented performances are higher than those results reported in the original papers. As shown in Tab. 2, benefiting from the incorporation of our layout-based sTDE (L-sTDE), the performances of existing methods are improved, especially our L-sTDE based on HOZ and VTNet achieve new SOTA performance. Other learning-based methods employ CLIP [42] as the backbone [25], or adopt pre-training on large-scale datasets (e.g. ProcTHOR [13]), and we compare our L-sTDE with these methods in the supplements. + +Since most map-based methods require the RGB-D visual inputs and segmentation information provided by Mask R-CNN [20] to construct the semantic map, we take another comparison with the map-based methods as shown in Tab. 3. The map-based methods employ a parameter-free modular system to build the semantic map, then encode the map into the policy. We regard the encoded map as the ex + +Table 3. The comparisons with the related works (map-based methods) in Gibson simulators. + +
IDMethodSR↑ (%)SPL↑ (%)DTS↓ (m)
1Random0.040.043.89
2RGBD+RL [48]8.422.873.23
3SemExp [7]65.3533.521.56
4Ours L-sTDE (SemExp)66.96 (1.61↑)34.33 (0.81↑)1.53 (0.03↑)
+ +experience $z^t$ and modify [7] with our L-sTDE. The results indicate that our method still brings some performance improvements, although the gains are limited compared to that of the learning-based methods. We analyze that, compared with the learning-based methods whose parameters are all trained end-to-end, the map-based methods utilize a modular system, and only a small number of parameters (the policy) need to be trained. Therefore, the map-based methods are less affected by the experience learned from training, and thus benefit less from our method. + +# 6. Conclusion + +We propose the layout-based soft Total Direct Effect framework for ObjectNav task. Our motivation is to keep the positive effect and remove the negative effect of the experience, which is learned as the prior knowledge in training. Specifically, we propose to calculate the layout gap between the current environment and the prior knowledge. Then the layout gap is utilized to assess whether the impact of the learned experience is positive. Furthermore, the soft Total Direct Effect is proposed to appropriately control the effect of the experience on action prediction. The experiment results indicate the effectiveness of our method. + +Acknowledgements: This work was supported by Beijing Natural Science Foundation under Grant JQ22012, Z190020, in part by the National Natural Science Foundation of China under Grant 62125207, 62272443, 62032022 and U1936203, in part by the National Postdoctoral Program for Innovative Talents under Grant BX201700255. + +# References + +[1] Ehsan Abbasnejad, Damien Teney, Amin Parvaneh, Javen Shi, and Anton van den Hengel. Counterfactual vision and language learning. In 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2020, Seattle, WA, USA, June 13-19, 2020, pages 10041-10051, 2020. 2 +[2] Ziad Al-Halah, Santhosh K. Ramakrishnan, and Kristen Grauman. 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weijie.li, yubing.bai, xinyao.yu}@vip1.ict.ac.cn" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 248, + 201, + 342, + 213 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 248, + 201, + 342, + 213 + ], + "spans": [ + { + "bbox": [ + 248, + 201, + 342, + 213 + ], + "type": "text", + "content": "sqjiang@ict.ac.cn" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 143, + 241, + 192, + 254 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 241, + 192, + 254 + ], + "spans": [ + { + "bbox": [ + 143, + 241, + 192, + 254 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 266, + 290, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 266, + 290, + 542 + ], + "spans": [ + { + "bbox": [ + 46, + 266, + 290, + 542 + ], + "type": "text", + "content": "Previous works for ObjectNav task attempt to learn the association (e.g. relation graph) between the visual inputs 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Such association contains the prior knowledge of navigating in training environments, which is denoted as the experience. The experience performs a positive effect on helping the agent infer the likely location of the goal when the layout gap between the unseen environments of the test and the prior knowledge obtained in training is minor. However, when the layout gap is significant, the experience exerts a negative effect on navigation. Motivated by keeping the positive effect and removing the negative effect of the experience, we propose the layout-based soft Total Direct Effect (L-sTDE) framework based on the causal inference to adjust the prediction of the navigation policy. In particular, we propose to calculate the layout gap which is defined as the KL divergence between the posterior and the prior distribution of the object layout. Then the sTDE is proposed to appropriately control the effect of the experience based on the layout gap. 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The proposed causal graph. (a) represents the fact prediction " + }, + { + "bbox": [ + 304, + 365, + 547, + 422 + ], + "type": "inline_equation", + "content": "a" + }, + { + "bbox": [ + 304, + 365, + 547, + 422 + ], + "type": "text", + "content": ", i.e. the original prediction of the trained model. (b) refers to the counter-fact prediction " + }, + { + "bbox": [ + 304, + 365, + 547, + 422 + ], + "type": "inline_equation", + "content": "\\bar{a}" + }, + { + "bbox": [ + 304, + 365, + 547, + 422 + ], + "type": "text", + "content": ", i.e. the prediction is only affected by the experience " + }, + { + "bbox": [ + 304, + 365, + 547, + 422 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 304, + 365, + 547, + 422 + ], + "type": "text", + "content": ". (b) is realized by applying the intervention and counterfactual operations to the original model." + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 437, + 547, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 437, + 547, + 688 + ], + "spans": [ + { + "bbox": [ + 304, + 437, + 547, + 688 + ], + "type": "text", + "content": "Recently, the learning-based methods attempt to model the prior knowledge of the spatial relationships among the objects, so the agent could infer the likely locations of the goal based on the current observation (which objects are observed currently) and the prior knowledge (the spatial relationships between the goal and the observed objects) learned in the training stage. Some works utilize additional modules to construct the objects graph [15, 59, 60], the region graph [63] and the attention mechanism [32], while others [16, 56] employ a network that implicitly learns the spatial relationships end-to-end. All these methods attempt to establish prior knowledge in training environments, so that the agent would utilize the prior knowledge to associate the real-time observations with the goal, and infer the likely locations of the goal during the inference. The underlying assumption of these methods is that all of the object layouts in unseen environments should be exactly consistent with those in training environments. However, the layout consistency assumption is only partially correct due to the limited training data. Thus, those methods typically suffer from poor generalization [31] in unseen environments." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 689, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 547, + 714 + ], + "type": "text", + "content": "To reveal the causes of poor generalization, we propose to use the casual graph (i.e. Structural Causal Model, SCM" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "10792" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 384 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 384 + ], + "type": "text", + "content": "[38]) to analyze these navigation works. As illustrated in Fig. 1 (a), the navigation model takes the observation " + }, + { + "bbox": [ + 47, + 72, + 289, + 384 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 47, + 72, + 289, + 384 + ], + "type": "text", + "content": " and the goal " + }, + { + "bbox": [ + 47, + 72, + 289, + 384 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 47, + 72, + 289, + 384 + ], + "type": "text", + "content": " as the input, and predicts the action " + }, + { + "bbox": [ + 47, + 72, + 289, + 384 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 47, + 72, + 289, + 384 + ], + "type": "text", + "content": " at each timestamp. The causal links " + }, + { + "bbox": [ + 47, + 72, + 289, + 384 + ], + "type": "inline_equation", + "content": "S \\rightarrow Z" + }, + { + "bbox": [ + 47, + 72, + 289, + 384 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 72, + 289, + 384 + ], + "type": "inline_equation", + "content": "G \\rightarrow Z" + }, + { + "bbox": [ + 47, + 72, + 289, + 384 + ], + "type": "text", + "content": " represent that the observation and the goal are embedded by the pre-constructed modules [15, 32, 59, 60, 63] or the pre-trained network [16, 56]. The embedding vector is defined as the experience " + }, + { + "bbox": [ + 47, + 72, + 289, + 384 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 47, + 72, + 289, + 384 + ], + "type": "text", + "content": " in the causal graph, which introduces the prior knowledge to influence action prediction (" + }, + { + "bbox": [ + 47, + 72, + 289, + 384 + ], + "type": "inline_equation", + "content": "Z \\rightarrow A" + }, + { + "bbox": [ + 47, + 72, + 289, + 384 + ], + "type": "text", + "content": "). Meanwhile, the real-time observation and the goal also independently affect the prediction without being encoded by the prior knowledge module, which is represented as " + }, + { + "bbox": [ + 47, + 72, + 289, + 384 + ], + "type": "inline_equation", + "content": "S \\rightarrow A" + }, + { + "bbox": [ + 47, + 72, + 289, + 384 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 72, + 289, + 384 + ], + "type": "inline_equation", + "content": "G \\rightarrow A" + }, + { + "bbox": [ + 47, + 72, + 289, + 384 + ], + "type": "text", + "content": ", respectively. The causal links " + }, + { + "bbox": [ + 47, + 72, + 289, + 384 + ], + "type": "inline_equation", + "content": "S \\rightarrow A" + }, + { + "bbox": [ + 47, + 72, + 289, + 384 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 72, + 289, + 384 + ], + "type": "inline_equation", + "content": "G \\rightarrow A" + }, + { + "bbox": [ + 47, + 72, + 289, + 384 + ], + "type": "text", + "content": " represent the exploration-based effect (only related to the current episode) on the action prediction, which is different from the experience-based effect " + }, + { + "bbox": [ + 47, + 72, + 289, + 384 + ], + "type": "inline_equation", + "content": "Z \\rightarrow A" + }, + { + "bbox": [ + 47, + 72, + 289, + 384 + ], + "type": "text", + "content": ". Consider two cases of the layout gap between the current environment and the prior knowledge: 1) the layout gap is minor and 2) the layout gap is significant. In the former case, the object layout is consistent in the current environment and the prior knowledge. Thus, the experience " + }, + { + "bbox": [ + 47, + 72, + 289, + 384 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 47, + 72, + 289, + 384 + ], + "type": "text", + "content": " exerts a positive effect on the prediction of action " + }, + { + "bbox": [ + 47, + 72, + 289, + 384 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 47, + 72, + 289, + 384 + ], + "type": "text", + "content": ". However, the effect of experience " + }, + { + "bbox": [ + 47, + 72, + 289, + 384 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 47, + 72, + 289, + 384 + ], + "type": "text", + "content": " in the latter case could be negative. If the agent still relies on the \"negative\" experience to predict actions, it will suffer from poor generalization. Therefore, wisely utilizing the experience is essential to the ObjectNav task." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 387, + 289, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 387, + 289, + 555 + ], + "spans": [ + { + "bbox": [ + 47, + 387, + 289, + 555 + ], + "type": "text", + "content": "Motivated by wisely utilizing the learned experience, we propose the soft Total Direct Effect (sTDE) framework based on the Total Direct Effect analysis in causal inference. Our sTDE improves the generalization of the trained model in inference by eliminating the prediction bias brought by the experience. To decouple the effect of experience, we construct the counter-fact prediction " + }, + { + "bbox": [ + 47, + 387, + 289, + 555 + ], + "type": "inline_equation", + "content": "\\bar{a}" + }, + { + "bbox": [ + 47, + 387, + 289, + 555 + ], + "type": "text", + "content": ": the prediction is only affected by the experience " + }, + { + "bbox": [ + 47, + 387, + 289, + 555 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 47, + 387, + 289, + 555 + ], + "type": "text", + "content": " while ignoring the " + }, + { + "bbox": [ + 47, + 387, + 289, + 555 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 47, + 387, + 289, + 555 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 387, + 289, + 555 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 47, + 387, + 289, + 555 + ], + "type": "text", + "content": ", as shown in Fig. 1 (b). Then we propose the object layout estimator that calculates whether the effect of the experience is positive, by measuring the layout gap between the current environment and the prior knowledge. Furthermore, our sTDE will remove the counter-fact prediction " + }, + { + "bbox": [ + 47, + 387, + 289, + 555 + ], + "type": "inline_equation", + "content": "\\bar{a}" + }, + { + "bbox": [ + 47, + 387, + 289, + 555 + ], + "type": "text", + "content": " from the fact prediction " + }, + { + "bbox": [ + 47, + 387, + 289, + 555 + ], + "type": "inline_equation", + "content": "a" + }, + { + "bbox": [ + 47, + 387, + 289, + 555 + ], + "type": "text", + "content": " when the layout gap is large." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 558, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 558, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 558, + 289, + 715 + ], + "type": "text", + "content": "In this paper, we propose the layout-based soft TDE framework for the ObjectNav task. Specifically, we adopt the Dirichlet-Multinomial distribution [22] to formulate the contextual relationship between objects, which represents the object layout of the environment. Before training, the agent learns prior layout distribution (i.e. the prior parameters of Dirichlet-Multinomial distribution) by randomly exploring the training environments. In the training stage, based on the Bayesian inference, the agent estimates the posterior layout distribution with the prior distribution and newly obtained observations. Then the constantly updated posterior layout is encoded into the navigation model and utilized to learn the environment-adaptive experience. The" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 304, + 72, + 547, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 228 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 228 + ], + "type": "text", + "content": "entire model is trained with RL by maximizing the reward of reaching the goal. In the test stage, our agent will not directly use the trained policy as most previous works do. The agent first calculates the layout gap and the counter-fact prediction. The layout gap is determined by calculating the KL divergence between the posterior and prior distribution of object layouts and serves as a weight to determine whether to remove the counter-fact prediction (i.e. experience effect) from the original prediction. The experimental results on AI2THOR [27], RoboTHOR [12] and Habitat [48] indicate that our layout-based sTDE (L-sTDE) can be a plug-and-play method to boost existing methods to achieve better navigation performances." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 306, + 239, + 392, + 251 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 239, + 392, + 251 + ], + "spans": [ + { + "bbox": [ + 306, + 239, + 392, + 251 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 258, + 547, + 534 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 258, + 547, + 534 + ], + "spans": [ + { + "bbox": [ + 304, + 258, + 547, + 534 + ], + "type": "text", + "content": "Visual Object Navigation. Target-oriented visual navigation can be categorized [5] into PointGoal [8, 18, 43, 55], AreaGoal [28, 57], AudioGoal [10, 11], ImageGoal [19, 29, 48], LanguageGoal (vision-and-language navigation) [23, 40, 41] and ObjectGoal. We focus on visual ObjectGoal navigation, which sets the object category as the target. Previous map-based methods usually build a metric map [6-8, 44] or topological map [9, 47] to memorize the environment layout. Besides, a popular deep-learning pipeline is to take an end-to-end network [2, 17, 34] to process the visual embedding and goal embedding, then predict the navigation action. Based on that, recent learning-based methods propose various improvement ideas, such as semantic representation [35], prior knowledge [59], object relation graph [15, 60, 63], attention mechanism [32], meta-learning [56], and transformer structure [16]. These well-trained modules provide prior knowledge to guide the agent in unseen environments. In our work, we denote such knowledge learned from training (with whatever improvement designs) as the experience. We try to find out, under different environment layouts, whether the learned experience takes a positive effect or not, and how to better utilize the experience to improve the navigation." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 534, + 548, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 548, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 548, + 714 + ], + "type": "text", + "content": "Causal Inference. Causal inference [38, 39] provides analysis tools (e.g. intervention, counter-fact) to reveal the causal effect behind the data-based statistical correlation, which is widely adopted in epidemiology, psychology, or politics research [24, 30, 46]. Recently, causal inference is introduced into the computer vision society for scene graph generation [50], vision and language task [1,36], long-tailed classification [49] and few/zero-shot learning [4, 62]. For the visual navigation task, [37] generates counterfactual observations to improve generalization to new environments for VLN (vision-and-language navigation) task. [54] proposes causal CT (continuous-time) models for visual drone navigation tasks. In our work, we focus on the ObjectNav task and utilize the causal inference to wisely control the effect of experience in the inference." + } + ] + } + ], + "index": 6 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "10793" + } + ] + } + ], + "index": 7 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 71, + 230, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 71, + 230, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 230, + 85 + ], + "type": "text", + "content": "3. Preliminaries of ObjectNav Task" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 91, + 287, + 270 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 91, + 287, + 270 + ], + "spans": [ + { + "bbox": [ + 46, + 91, + 287, + 270 + ], + "type": "text", + "content": "Task Definition. The ObjectNav task requires the agent to navigate to a user-specified object category from a random starting location in an unseen scene, and the agent is only allowed to utilize the egocentric visual observation (e.g. RGB images) and the semantic embedding of the target object. Formally, at each timestamp " + }, + { + "bbox": [ + 46, + 91, + 287, + 270 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 91, + 287, + 270 + ], + "type": "text", + "content": ", the agent receives the observation " + }, + { + "bbox": [ + 46, + 91, + 287, + 270 + ], + "type": "inline_equation", + "content": "S = s^t" + }, + { + "bbox": [ + 46, + 91, + 287, + 270 + ], + "type": "text", + "content": " and the goal " + }, + { + "bbox": [ + 46, + 91, + 287, + 270 + ], + "type": "inline_equation", + "content": "G = g^t" + }, + { + "bbox": [ + 46, + 91, + 287, + 270 + ], + "type": "text", + "content": " and is expected to adopt an action " + }, + { + "bbox": [ + 46, + 91, + 287, + 270 + ], + "type": "inline_equation", + "content": "A = a^t" + }, + { + "bbox": [ + 46, + 91, + 287, + 270 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 91, + 287, + 270 + ], + "type": "inline_equation", + "content": "a^t \\in \\mathcal{A}" + }, + { + "bbox": [ + 46, + 91, + 287, + 270 + ], + "type": "text", + "content": ". The discrete action space is defined as: " + }, + { + "bbox": [ + 46, + 91, + 287, + 270 + ], + "type": "inline_equation", + "content": "\\mathcal{A} = \\{MoveAhead, RotateLeft, RotateRight, LookDown, LookUp, Done\\}" + }, + { + "bbox": [ + 46, + 91, + 287, + 270 + ], + "type": "text", + "content": ". When the agent outputs the Done action, the episode terminates. An episode is considered successful if, within a certain number of steps, the final location of the agent is close to the goal within a distance threshold (e.g. " + }, + { + "bbox": [ + 46, + 91, + 287, + 270 + ], + "type": "inline_equation", + "content": "1m" + }, + { + "bbox": [ + 46, + 91, + 287, + 270 + ], + "type": "text", + "content": ") and the goal is visible in the egocentric observation." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 270, + 287, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 270, + 287, + 342 + ], + "spans": [ + { + "bbox": [ + 46, + 270, + 287, + 342 + ], + "type": "text", + "content": "Navigation Model. Prevailing ObjectNav works can be summarized as a visual-goal encoder and a policy function, as shown in Fig. 2. The visual-goal encoder is constructed to associate the visual observation " + }, + { + "bbox": [ + 46, + 270, + 287, + 342 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 270, + 287, + 342 + ], + "type": "text", + "content": " and the goal " + }, + { + "bbox": [ + 46, + 270, + 287, + 342 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 46, + 270, + 287, + 342 + ], + "type": "text", + "content": ". We denote such association as the experience " + }, + { + "bbox": [ + 46, + 270, + 287, + 342 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 46, + 270, + 287, + 342 + ], + "type": "text", + "content": " since the encoder could learn the prior experience during the training." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 342, + 288, + 534 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 342, + 288, + 534 + ], + "spans": [ + { + "bbox": [ + 46, + 342, + 288, + 534 + ], + "type": "text", + "content": "Previous learning-based methods typically implement the visual-goal encoder as an object relation graph [15, 59, 60], region graph [63], attention module [32] and transformer structure [16]. For instance, the ORG [15] builds an object relation graph, where the nodes are defined as the object categories and the edges are defined as the spatial correlations among different categories. The object relation graph takes the observation and the goal as inputs and encodes them with the learned edges to obtain the experience " + }, + { + "bbox": [ + 46, + 342, + 288, + 534 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 46, + 342, + 288, + 534 + ], + "type": "text", + "content": ". Previous map-based methods [7, 44] typically construct the semantic map based on the observations, and embed the map with the target. Such embedding is also regarded as the experience " + }, + { + "bbox": [ + 46, + 342, + 288, + 534 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 46, + 342, + 288, + 534 + ], + "type": "text", + "content": ". Based on the observation, target object, and these learned experiences, the policy module will output the prediction. These navigation models are typically trained with the RL (reinforcement learning) [33, 55, 64]." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 544, + 178, + 557 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 544, + 178, + 557 + ], + "spans": [ + { + "bbox": [ + 47, + 544, + 178, + 557 + ], + "type": "text", + "content": "4. The Proposed Solution" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 563, + 244, + 575 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 563, + 244, + 575 + ], + "spans": [ + { + "bbox": [ + 47, + 563, + 244, + 575 + ], + "type": "text", + "content": "4.1. Layout-based Soft Total Direct Effect" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "text", + "content": "We humans make decisions in a causality-based manner: we have the instinct to assess the effect of the navigation experience [51] and wisely eliminate the cognition bias from the experience. However, the machines are likelihood-based [50] and the predictions depend on the association likelihood between observations, goal, and actions, which is mainly learned from limited training data. Therefore, the predictions are inevitably biased due to the biased experience. Prevailing methods [15, 16, 56, 59, 60, 63] entirely accept the experience learned in the training stage, and rarely consider whether the prior experience is beneficial to the" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 309, + 71, + 545, + 262 + ], + "blocks": [ + { + "bbox": [ + 309, + 71, + 545, + 262 + ], + "lines": [ + { + "bbox": [ + 309, + 71, + 545, + 262 + ], + "spans": [ + { + "bbox": [ + 309, + 71, + 545, + 262 + ], + "type": "image", + "image_path": "d068a7e5d2b7515d7dc5320ef9b095cc57ec8bb6bb13dad931fc0532992b75d5.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 270, + 547, + 337 + ], + "lines": [ + { + "bbox": [ + 304, + 270, + 547, + 337 + ], + "spans": [ + { + "bbox": [ + 304, + 270, + 547, + 337 + ], + "type": "text", + "content": "Figure 2. Prevailing navigation framework (top) and our contributions (bottom). Our layout estimator outputs the expectation " + }, + { + "bbox": [ + 304, + 270, + 547, + 337 + ], + "type": "inline_equation", + "content": "w^t" + }, + { + "bbox": [ + 304, + 270, + 547, + 337 + ], + "type": "text", + "content": " of posterior layout distribution and the layout gap " + }, + { + "bbox": [ + 304, + 270, + 547, + 337 + ], + "type": "inline_equation", + "content": "D_{\\Delta}^{t}" + }, + { + "bbox": [ + 304, + 270, + 547, + 337 + ], + "type": "text", + "content": ". The " + }, + { + "bbox": [ + 304, + 270, + 547, + 337 + ], + "type": "inline_equation", + "content": "w^t" + }, + { + "bbox": [ + 304, + 270, + 547, + 337 + ], + "type": "text", + "content": " is proposed to enhance the adaptability of the experience " + }, + { + "bbox": [ + 304, + 270, + 547, + 337 + ], + "type": "inline_equation", + "content": "z^t" + }, + { + "bbox": [ + 304, + 270, + 547, + 337 + ], + "type": "text", + "content": " to new environments. The layout gap " + }, + { + "bbox": [ + 304, + 270, + 547, + 337 + ], + "type": "inline_equation", + "content": "D_{\\Delta}^{t}" + }, + { + "bbox": [ + 304, + 270, + 547, + 337 + ], + "type": "text", + "content": " serves as a weight to alleviate the experience bias." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 358, + 545, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 358, + 545, + 430 + ], + "spans": [ + { + "bbox": [ + 304, + 358, + 545, + 430 + ], + "type": "text", + "content": "current environment. However, as previously discussed, the learned experience has both positive and negative effects, especially in the unseen environments, which may have a different layout from the training environments. Therefore, keeping positive effects and removing negative effects of learned experience is essential to the navigation models." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 430, + 545, + 550 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 430, + 545, + 550 + ], + "spans": [ + { + "bbox": [ + 304, + 430, + 545, + 550 + ], + "type": "text", + "content": "The causal inference [39,52,53] encourages the machine to discover the causality behind the association likelihood, which has been proven to be an effective analysis method in many computer vision tasks [36, 49, 50, 61]. From the perspective of causal inference, the experience " + }, + { + "bbox": [ + 304, + 430, + 545, + 550 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 304, + 430, + 545, + 550 + ], + "type": "text", + "content": " serves as the mediator between the input (observation " + }, + { + "bbox": [ + 304, + 430, + 545, + 550 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 430, + 545, + 550 + ], + "type": "text", + "content": " and target " + }, + { + "bbox": [ + 304, + 430, + 545, + 550 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 304, + 430, + 545, + 550 + ], + "type": "text", + "content": ") and the output (action " + }, + { + "bbox": [ + 304, + 430, + 545, + 550 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 304, + 430, + 545, + 550 + ], + "type": "text", + "content": ") as illustrated in Fig. 1 (a). To eliminate the mediation fallacy, the causal inference [38] introduces the Total Direct Effect (TDE) analysis to remove the prediction bias brought by the mediator." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 550, + 545, + 609 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 550, + 545, + 609 + ], + "spans": [ + { + "bbox": [ + 304, + 550, + 545, + 609 + ], + "type": "text", + "content": "Total Direct Effect. The fundamental principle behind TDE analysis [36, 49, 50] is to build a bias prediction " + }, + { + "bbox": [ + 304, + 550, + 545, + 609 + ], + "type": "inline_equation", + "content": "\\bar{a}^t" + }, + { + "bbox": [ + 304, + 550, + 545, + 609 + ], + "type": "text", + "content": " that is exclusively affected by the mediator, and then remove the bias item from the original prediction " + }, + { + "bbox": [ + 304, + 550, + 545, + 609 + ], + "type": "inline_equation", + "content": "a^t" + }, + { + "bbox": [ + 304, + 550, + 545, + 609 + ], + "type": "text", + "content": ". The TDE analysis is formulated as:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 381, + 621, + 545, + 635 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 381, + 621, + 545, + 635 + ], + "spans": [ + { + "bbox": [ + 381, + 621, + 545, + 635 + ], + "type": "interline_equation", + "content": "T D E \\left(a ^ {t}\\right) = a ^ {t} - \\bar {a} ^ {t} \\tag {1}", + "image_path": "a59ac693ed86f35197c8bfdc928e95152104745683724162ff4fc2da2c622ec6.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 641, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 545, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 641, + 545, + 714 + ], + "type": "inline_equation", + "content": "a^t = \\pi (A|S = s^t,G = g^t)" + }, + { + "bbox": [ + 304, + 641, + 545, + 714 + ], + "type": "text", + "content": " is the factual prediction of a trained model " + }, + { + "bbox": [ + 304, + 641, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 304, + 641, + 545, + 714 + ], + "type": "text", + "content": ", which takes the observation " + }, + { + "bbox": [ + 304, + 641, + 545, + 714 + ], + "type": "inline_equation", + "content": "S = s^t" + }, + { + "bbox": [ + 304, + 641, + 545, + 714 + ], + "type": "text", + "content": " and target " + }, + { + "bbox": [ + 304, + 641, + 545, + 714 + ], + "type": "inline_equation", + "content": "G = g^{t}" + }, + { + "bbox": [ + 304, + 641, + 545, + 714 + ], + "type": "text", + "content": " as the input, as shown in Fig. 1 (a). The latter is the counterfactual prediction " + }, + { + "bbox": [ + 304, + 641, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\bar{a}^t = \\pi (A|do(S = \\bar{s}^t,G = \\bar{g}^t),Z = Z_{s^t,g^t})" + }, + { + "bbox": [ + 304, + 641, + 545, + 714 + ], + "type": "text", + "content": " as shown in Fig. 1 (b). The calculation of " + }, + { + "bbox": [ + 304, + 641, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\bar{a}^t" + }, + { + "bbox": [ + 304, + 641, + 545, + 714 + ], + "type": "text", + "content": " includes two operations" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10794" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": "in causal inference: intervention and counterfactual operations. The intervention operation is denoted as " + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "inline_equation", + "content": "do(\\cdot)" + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": " and realized by specifying a certain value for the variable (e.g. " + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "inline_equation", + "content": "do(S = \\bar{s}^t)" + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": "). The intervened value (e.g. " + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "inline_equation", + "content": "\\bar{s}^t" + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "inline_equation", + "content": "\\bar{g}^t" + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": ") is set to a random or zero vector. The intervention operation eliminates the effect of observation " + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": " and goal " + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": " on the action prediction, while it also changes the value of the causal successor (i.e. " + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": "). However, since our motivation is to model the case only affected by the mediator, which requires the mediator " + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": " to remain the original value. To this end, the counterfactual operation assigns the original value to the variable " + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": " as if " + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "inline_equation", + "content": "S = s^t" + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "inline_equation", + "content": "G = g^t" + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": " had existed. The counterfactual operation is symbolized as " + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "inline_equation", + "content": "Z = Z_{s^t, g^t}" + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 228, + 289, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 228, + 289, + 312 + ], + "spans": [ + { + "bbox": [ + 46, + 228, + 289, + 312 + ], + "type": "text", + "content": "The TDE analysis is easily realized by manipulating the values of several variables (e.g. " + }, + { + "bbox": [ + 46, + 228, + 289, + 312 + ], + "type": "inline_equation", + "content": "S, G, Z" + }, + { + "bbox": [ + 46, + 228, + 289, + 312 + ], + "type": "text", + "content": ") and is efficient in removing the effect of the mediator (i.e. experience). However, the experience is not always detrimental. It can also be beneficial when the object layout gap is minor. Therefore, we propose the soft TDE to appropriately maintain the positive effect of experience." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 313, + 289, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 313, + 289, + 350 + ], + "spans": [ + { + "bbox": [ + 47, + 313, + 289, + 350 + ], + "type": "text", + "content": "Soft Total Direct Effect. In alternative to previous TDE analysis, our soft TDE modifies the Eq. 1 by adding a trade-off weight, which is formulated as:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 84, + 363, + 287, + 378 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 84, + 363, + 287, + 378 + ], + "spans": [ + { + "bbox": [ + 84, + 363, + 287, + 378 + ], + "type": "interline_equation", + "content": "s T D E (a ^ {t}) = a ^ {t} - R e L U (D _ {\\Delta} ^ {t} - \\varepsilon) \\cdot \\bar {a} ^ {t} \\qquad (2)", + "image_path": "443cfffce901ed10577a1fdb94f49b97924adcb25b28d608d80e6b8228dc88cb.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 384, + 289, + 471 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 384, + 289, + 471 + ], + "spans": [ + { + "bbox": [ + 46, + 384, + 289, + 471 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 384, + 289, + 471 + ], + "type": "inline_equation", + "content": "ReLU(\\cdot)" + }, + { + "bbox": [ + 46, + 384, + 289, + 471 + ], + "type": "text", + "content": " is the ReLU activation function, and " + }, + { + "bbox": [ + 46, + 384, + 289, + 471 + ], + "type": "inline_equation", + "content": "\\varepsilon" + }, + { + "bbox": [ + 46, + 384, + 289, + 471 + ], + "type": "text", + "content": " is a threshold hyperparameter. The " + }, + { + "bbox": [ + 46, + 384, + 289, + 471 + ], + "type": "inline_equation", + "content": "D_{\\Delta}^{t}" + }, + { + "bbox": [ + 46, + 384, + 289, + 471 + ], + "type": "text", + "content": " is the object layout gap, which is produced by our layout estimator (Sec. 4.2) as shown in Fig. 2. The " + }, + { + "bbox": [ + 46, + 384, + 289, + 471 + ], + "type": "inline_equation", + "content": "D_{\\Delta}^{t}" + }, + { + "bbox": [ + 46, + 384, + 289, + 471 + ], + "type": "text", + "content": " evaluates the effect of the experience " + }, + { + "bbox": [ + 46, + 384, + 289, + 471 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 46, + 384, + 289, + 471 + ], + "type": "text", + "content": ", and preserves the positive experience when the layout gap between the current environment and prior knowledge is minor (i.e. " + }, + { + "bbox": [ + 46, + 384, + 289, + 471 + ], + "type": "inline_equation", + "content": "D_{\\Delta}^{t}" + }, + { + "bbox": [ + 46, + 384, + 289, + 471 + ], + "type": "text", + "content": " is less than the threshold " + }, + { + "bbox": [ + 46, + 384, + 289, + 471 + ], + "type": "inline_equation", + "content": "\\varepsilon" + }, + { + "bbox": [ + 46, + 384, + 289, + 471 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 479, + 153, + 491 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 479, + 153, + 491 + ], + "spans": [ + { + "bbox": [ + 47, + 479, + 153, + 491 + ], + "type": "text", + "content": "4.2. Layout Estimator" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 498, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 289, + 715 + ], + "type": "text", + "content": "Object Layout. For the ObjectNav task, the main challenge is the partially observable problem, that the agent can only observe the partial area at each time. With continuously observing during the navigation process, more objects will be observed, and the partially known problem can also be alleviated. Considering objects are usually distributed in a reasonable layout, the adjacent relation of objects is essential to help the agent infer the location of the target object based on the observed objects. Therefore, we concentrate on the contextual relationship to represent the object layout. The object layout in a scene is defined as the set " + }, + { + "bbox": [ + 46, + 498, + 289, + 715 + ], + "type": "inline_equation", + "content": "D = \\{\\theta_{i}\\}_{i=1}^{K}" + }, + { + "bbox": [ + 46, + 498, + 289, + 715 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 498, + 289, + 715 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 498, + 289, + 715 + ], + "type": "text", + "content": " is the number of object categories. The " + }, + { + "bbox": [ + 46, + 498, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\theta_{i} = (\\theta_{i,j})_{j=1}^{K}" + }, + { + "bbox": [ + 46, + 498, + 289, + 715 + ], + "type": "text", + "content": " represents the context distribution of object category " + }, + { + "bbox": [ + 46, + 498, + 289, + 715 + ], + "type": "inline_equation", + "content": "c_{i}" + }, + { + "bbox": [ + 46, + 498, + 289, + 715 + ], + "type": "text", + "content": ". Each dimension " + }, + { + "bbox": [ + 46, + 498, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\theta_{i,j}" + }, + { + "bbox": [ + 46, + 498, + 289, + 715 + ], + "type": "text", + "content": " represents the probability " + }, + { + "bbox": [ + 46, + 498, + 289, + 715 + ], + "type": "inline_equation", + "content": "p(c_{j}|c_{i})" + }, + { + "bbox": [ + 46, + 498, + 289, + 715 + ], + "type": "text", + "content": " that the object category " + }, + { + "bbox": [ + 46, + 498, + 289, + 715 + ], + "type": "inline_equation", + "content": "c_{j}" + }, + { + "bbox": [ + 46, + 498, + 289, + 715 + ], + "type": "text", + "content": " can be observed around the category " + }, + { + "bbox": [ + 46, + 498, + 289, + 715 + ], + "type": "inline_equation", + "content": "c_{i}" + }, + { + "bbox": [ + 46, + 498, + 289, + 715 + ], + "type": "text", + "content": " in an observation. Specifically, we assume that the context distribution follows the Dirichlet distribution: " + }, + { + "bbox": [ + 46, + 498, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\theta_{i} = (\\theta_{i,j})_{j=1}^{K} \\sim \\text{Dir}(\\alpha_{i})" + }, + { + "bbox": [ + 46, + 498, + 289, + 715 + ], + "type": "text", + "content": ", where" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 310, + 70, + 545, + 247 + ], + "blocks": [ + { + "bbox": [ + 310, + 70, + 545, + 247 + ], + "lines": [ + { + "bbox": [ + 310, + 70, + 545, + 247 + ], + "spans": [ + { + "bbox": [ + 310, + 70, + 545, + 247 + ], + "type": "image", + "image_path": "47cd8672246a84e1dc5892f5085577f3b54d1920e871d61f934af64b4ba08df7.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 315, + 252, + 537, + 265 + ], + "lines": [ + { + "bbox": [ + 315, + 252, + 537, + 265 + ], + "spans": [ + { + "bbox": [ + 315, + 252, + 537, + 265 + ], + "type": "text", + "content": "Figure 3. The calculation of the likelihood function " + }, + { + "bbox": [ + 315, + 252, + 537, + 265 + ], + "type": "inline_equation", + "content": "p(s_i^t |\\theta_i)" + }, + { + "bbox": [ + 315, + 252, + 537, + 265 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 285, + 545, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 285, + 545, + 335 + ], + "spans": [ + { + "bbox": [ + 304, + 285, + 545, + 335 + ], + "type": "inline_equation", + "content": "\\sum_{j}\\theta_{i,j} = 1,\\theta_{i,j}\\geq 0" + }, + { + "bbox": [ + 304, + 285, + 545, + 335 + ], + "type": "text", + "content": " , and " + }, + { + "bbox": [ + 304, + 285, + 545, + 335 + ], + "type": "inline_equation", + "content": "\\alpha_{i} = (\\alpha_{i,j})_{j = 1}^{K},\\alpha_{i,j} > 0" + }, + { + "bbox": [ + 304, + 285, + 545, + 335 + ], + "type": "text", + "content": " parameterizes the distribution. The Dirichlet distribution is chosen for two reasons: 1) the conjugate prior permits concise calculations; 2) the likelihood-equivalence property [22]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 336, + 546, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 336, + 546, + 544 + ], + "spans": [ + { + "bbox": [ + 304, + 336, + 546, + 544 + ], + "type": "text", + "content": "At the beginning of every new episode, the parameter " + }, + { + "bbox": [ + 304, + 336, + 546, + 544 + ], + "type": "inline_equation", + "content": "\\alpha_{i}" + }, + { + "bbox": [ + 304, + 336, + 546, + 544 + ], + "type": "text", + "content": " is initialized as the prior initial value " + }, + { + "bbox": [ + 304, + 336, + 546, + 544 + ], + "type": "inline_equation", + "content": "\\alpha_{i}^{*}" + }, + { + "bbox": [ + 304, + 336, + 546, + 544 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 304, + 336, + 546, + 544 + ], + "type": "inline_equation", + "content": "\\alpha_{i}^{*}" + }, + { + "bbox": [ + 304, + 336, + 546, + 544 + ], + "type": "text", + "content": " will be detailed in Sec. 4.3). At each timestamp " + }, + { + "bbox": [ + 304, + 336, + 546, + 544 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 336, + 546, + 544 + ], + "type": "text", + "content": ", our method computes the posterior object distribution based on the incoming observations. Specifically, the agent receives the visual observation " + }, + { + "bbox": [ + 304, + 336, + 546, + 544 + ], + "type": "inline_equation", + "content": "s^t" + }, + { + "bbox": [ + 304, + 336, + 546, + 544 + ], + "type": "text", + "content": ", and the visual observation is then converted into a count vector " + }, + { + "bbox": [ + 304, + 336, + 546, + 544 + ], + "type": "inline_equation", + "content": "n^t \\in \\mathbb{R}^K" + }, + { + "bbox": [ + 304, + 336, + 546, + 544 + ], + "type": "text", + "content": ", where each dimension of " + }, + { + "bbox": [ + 304, + 336, + 546, + 544 + ], + "type": "inline_equation", + "content": "n^t = (n_i^t)_{i=1}^K" + }, + { + "bbox": [ + 304, + 336, + 546, + 544 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 336, + 546, + 544 + ], + "type": "inline_equation", + "content": "n_i^t \\geq 0" + }, + { + "bbox": [ + 304, + 336, + 546, + 544 + ], + "type": "text", + "content": " records the number of each object category appearing in the current observation. The count vector " + }, + { + "bbox": [ + 304, + 336, + 546, + 544 + ], + "type": "inline_equation", + "content": "n^t" + }, + { + "bbox": [ + 304, + 336, + 546, + 544 + ], + "type": "text", + "content": " is obtained by the object detection or segmentation modules (e.g. Faster R-CNN [45] or Mask R-CNN [20]). As shown in Fig. 3, we define " + }, + { + "bbox": [ + 304, + 336, + 546, + 544 + ], + "type": "inline_equation", + "content": "n_{-i}^t = (n_{-i,j}^t)_{j=1}^K" + }, + { + "bbox": [ + 304, + 336, + 546, + 544 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 336, + 546, + 544 + ], + "type": "inline_equation", + "content": "n_{-i,j}^t \\geq 0" + }, + { + "bbox": [ + 304, + 336, + 546, + 544 + ], + "type": "text", + "content": " as the count of other categories (except " + }, + { + "bbox": [ + 304, + 336, + 546, + 544 + ], + "type": "inline_equation", + "content": "c_i" + }, + { + "bbox": [ + 304, + 336, + 546, + 544 + ], + "type": "text", + "content": ") and define " + }, + { + "bbox": [ + 304, + 336, + 546, + 544 + ], + "type": "inline_equation", + "content": "s_i^t" + }, + { + "bbox": [ + 304, + 336, + 546, + 544 + ], + "type": "text", + "content": " as the contextual observation of the category " + }, + { + "bbox": [ + 304, + 336, + 546, + 544 + ], + "type": "inline_equation", + "content": "c_i" + }, + { + "bbox": [ + 304, + 336, + 546, + 544 + ], + "type": "text", + "content": ". Conditioned on " + }, + { + "bbox": [ + 304, + 336, + 546, + 544 + ], + "type": "inline_equation", + "content": "c_i" + }, + { + "bbox": [ + 304, + 336, + 546, + 544 + ], + "type": "text", + "content": ", assume the probability that " + }, + { + "bbox": [ + 304, + 336, + 546, + 544 + ], + "type": "inline_equation", + "content": "s_i^t" + }, + { + "bbox": [ + 304, + 336, + 546, + 544 + ], + "type": "text", + "content": " is observed follows the multinomial distribution " + }, + { + "bbox": [ + 304, + 336, + 546, + 544 + ], + "type": "inline_equation", + "content": "s_i^t \\sim Mult(n_{-i}^t, \\theta_i)" + }, + { + "bbox": [ + 304, + 336, + 546, + 544 + ], + "type": "text", + "content": ". Then the likelihood function can be calculated as:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 379, + 555, + 545, + 589 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 379, + 555, + 545, + 589 + ], + "spans": [ + { + "bbox": [ + 379, + 555, + 545, + 589 + ], + "type": "interline_equation", + "content": "p \\left(s _ {i} ^ {t} \\mid \\theta_ {i}\\right) = \\prod_ {j = 1} ^ {K} \\theta_ {i, j} ^ {n _ {- i, j} ^ {t}} \\tag {3}", + "image_path": "1a75510c4c7f60c721fd22bebeb8062be95f7e9af0f09eb3c6144b1976ca94d9.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 597, + 547, + 657 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 597, + 547, + 657 + ], + "spans": [ + { + "bbox": [ + 304, + 597, + 547, + 657 + ], + "type": "text", + "content": "Meanwhile, according to the previous Dirichlet distribution assumption, the prior distribution of " + }, + { + "bbox": [ + 304, + 597, + 547, + 657 + ], + "type": "inline_equation", + "content": "\\theta_{i}" + }, + { + "bbox": [ + 304, + 597, + 547, + 657 + ], + "type": "text", + "content": " at timestamp " + }, + { + "bbox": [ + 304, + 597, + 547, + 657 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 597, + 547, + 657 + ], + "type": "text", + "content": " is " + }, + { + "bbox": [ + 304, + 597, + 547, + 657 + ], + "type": "inline_equation", + "content": "p\\left(\\theta_i|\\alpha_i^t\\right) = Dir\\left(\\theta_i|\\alpha_i^t\\right)" + }, + { + "bbox": [ + 304, + 597, + 547, + 657 + ], + "type": "text", + "content": ". Considering the contextual observation " + }, + { + "bbox": [ + 304, + 597, + 547, + 657 + ], + "type": "inline_equation", + "content": "s_i^t" + }, + { + "bbox": [ + 304, + 597, + 547, + 657 + ], + "type": "text", + "content": ", the posterior distribution of " + }, + { + "bbox": [ + 304, + 597, + 547, + 657 + ], + "type": "inline_equation", + "content": "\\theta_{i}" + }, + { + "bbox": [ + 304, + 597, + 547, + 657 + ], + "type": "text", + "content": " is further calculated according to the Bayesian inference as the following:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 311, + 676, + 545, + 713 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 311, + 676, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 311, + 676, + 545, + 713 + ], + "type": "interline_equation", + "content": "p \\left(\\theta_ {i} \\mid s _ {i} ^ {t}, \\alpha_ {i} ^ {t}\\right) = \\frac {p \\left(s _ {i} ^ {t} \\mid \\theta_ {i}\\right) p \\left(\\theta_ {i} \\mid \\alpha_ {i} ^ {t}\\right)}{p \\left(s _ {i} ^ {t} \\mid \\alpha_ {i} ^ {t}\\right)} = D i r \\left(\\theta_ {i} \\mid \\alpha_ {i} ^ {t} + n _ {- i} ^ {t}\\right) \\tag {4}", + "image_path": "905bef3e04e25935dbbcaaeb0ab245b09ed5c6c3f4c167c66fed88f6fdc4df90.jpg" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10795" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 191 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 191 + ], + "type": "text", + "content": "The Eq. 4 indicates that the posterior distribution " + }, + { + "bbox": [ + 46, + 72, + 287, + 191 + ], + "type": "inline_equation", + "content": "p(\\theta_i | s_i^t, \\alpha_i^t)" + }, + { + "bbox": [ + 46, + 72, + 287, + 191 + ], + "type": "text", + "content": " also satisfies the Dirichlet distribution (the calculation process is detailed in the supplements), which is known as the conjugate prior property. The conjugate prior property guarantees the succinct calculation for the posterior distribution of " + }, + { + "bbox": [ + 46, + 72, + 287, + 191 + ], + "type": "inline_equation", + "content": "\\theta_i" + }, + { + "bbox": [ + 46, + 72, + 287, + 191 + ], + "type": "text", + "content": ", i.e., simply combining the count vector " + }, + { + "bbox": [ + 46, + 72, + 287, + 191 + ], + "type": "inline_equation", + "content": "n_{-i}^t" + }, + { + "bbox": [ + 46, + 72, + 287, + 191 + ], + "type": "text", + "content": " of context objects around category " + }, + { + "bbox": [ + 46, + 72, + 287, + 191 + ], + "type": "inline_equation", + "content": "c_i" + }, + { + "bbox": [ + 46, + 72, + 287, + 191 + ], + "type": "text", + "content": " with the hyperparameter " + }, + { + "bbox": [ + 46, + 72, + 287, + 191 + ], + "type": "inline_equation", + "content": "\\alpha_i^t" + }, + { + "bbox": [ + 46, + 72, + 287, + 191 + ], + "type": "text", + "content": " of the prior distribution. Similarly, the posterior distributions of other object categories can also be obtained following the Eq. 4." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 192, + 287, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 192, + 287, + 251 + ], + "spans": [ + { + "bbox": [ + 46, + 192, + 287, + 251 + ], + "type": "text", + "content": "Furthermore, the posterior distributions at time " + }, + { + "bbox": [ + 46, + 192, + 287, + 251 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 192, + 287, + 251 + ], + "type": "text", + "content": " serves as the prior distributions at time " + }, + { + "bbox": [ + 46, + 192, + 287, + 251 + ], + "type": "inline_equation", + "content": "t + 1" + }, + { + "bbox": [ + 46, + 192, + 287, + 251 + ], + "type": "text", + "content": ", thus the value of hyperparameter " + }, + { + "bbox": [ + 46, + 192, + 287, + 251 + ], + "type": "inline_equation", + "content": "\\alpha_{i}" + }, + { + "bbox": [ + 46, + 192, + 287, + 251 + ], + "type": "text", + "content": " is updated by " + }, + { + "bbox": [ + 46, + 192, + 287, + 251 + ], + "type": "inline_equation", + "content": "\\alpha_{i}^{t + 1} = \\alpha_{i}^{t} + n_{-i}^{t}" + }, + { + "bbox": [ + 46, + 192, + 287, + 251 + ], + "type": "text", + "content": ". This update guarantees the knowledge of object layout is continuously adapted to the current navigation environment." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 251, + 287, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 251, + 287, + 300 + ], + "spans": [ + { + "bbox": [ + 47, + 251, + 287, + 300 + ], + "type": "text", + "content": "Based on the obtained posterior distribution, the layout gap " + }, + { + "bbox": [ + 47, + 251, + 287, + 300 + ], + "type": "inline_equation", + "content": "D_{\\Delta}^{t}" + }, + { + "bbox": [ + 47, + 251, + 287, + 300 + ], + "type": "text", + "content": " is defined as the KL divergence between the posterior and prior object layout over all categories. Formally, the object layout gap " + }, + { + "bbox": [ + 47, + 251, + 287, + 300 + ], + "type": "inline_equation", + "content": "D_{\\Delta}^{t}" + }, + { + "bbox": [ + 47, + 251, + 287, + 300 + ], + "type": "text", + "content": " is defined as:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 56, + 308, + 287, + 340 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 308, + 287, + 340 + ], + "spans": [ + { + "bbox": [ + 56, + 308, + 287, + 340 + ], + "type": "interline_equation", + "content": "D _ {\\Delta} ^ {t} = \\tanh \\left( \\right.\\frac {1}{K} \\sum_ {i = 1} ^ {K} K L \\left( \\right.p \\left(\\theta_ {i} \\mid s ^ {t}, \\alpha_ {i} ^ {t}\\right)\\left\\| \\right. p \\left(\\theta_ {i} \\mid \\alpha_ {i} ^ {t}\\right)\\left. \\right)\\left. \\right) \\tag {5}", + "image_path": "23ea9a7f6f84c5d76ca940694a05fcb78a17477dbecac022ce753b3bf2b32fc9.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 346, + 287, + 394 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 346, + 287, + 394 + ], + "spans": [ + { + "bbox": [ + 46, + 346, + 287, + 394 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 346, + 287, + 394 + ], + "type": "inline_equation", + "content": "\\tanh(\\cdot)" + }, + { + "bbox": [ + 46, + 346, + 287, + 394 + ], + "type": "text", + "content": " is the tanh activation function. The layout gap " + }, + { + "bbox": [ + 46, + 346, + 287, + 394 + ], + "type": "inline_equation", + "content": "D_{\\Delta}^{t}" + }, + { + "bbox": [ + 46, + 346, + 287, + 394 + ], + "type": "text", + "content": " estimates the gap between the posterior object layout at time " + }, + { + "bbox": [ + 46, + 346, + 287, + 394 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 346, + 287, + 394 + ], + "type": "text", + "content": " and the prior knowledge before time " + }, + { + "bbox": [ + 46, + 346, + 287, + 394 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 346, + 287, + 394 + ], + "type": "text", + "content": ", which plays a vital role in the Eq. 2." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 395, + 287, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 395, + 287, + 635 + ], + "spans": [ + { + "bbox": [ + 46, + 395, + 287, + 635 + ], + "type": "text", + "content": "Environment-Adaptive Experience. The prevailing methods [15, 16, 59] typically encode the visual observation " + }, + { + "bbox": [ + 46, + 395, + 287, + 635 + ], + "type": "inline_equation", + "content": "s^t" + }, + { + "bbox": [ + 46, + 395, + 287, + 635 + ], + "type": "text", + "content": " and the target object " + }, + { + "bbox": [ + 46, + 395, + 287, + 635 + ], + "type": "inline_equation", + "content": "g^t" + }, + { + "bbox": [ + 46, + 395, + 287, + 635 + ], + "type": "text", + "content": " into the experience " + }, + { + "bbox": [ + 46, + 395, + 287, + 635 + ], + "type": "inline_equation", + "content": "z^t \\in \\mathbb{R}^{K \\times M}" + }, + { + "bbox": [ + 46, + 395, + 287, + 635 + ], + "type": "text", + "content": " during training, where " + }, + { + "bbox": [ + 46, + 395, + 287, + 635 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 395, + 287, + 635 + ], + "type": "text", + "content": " is the number of object categories and " + }, + { + "bbox": [ + 46, + 395, + 287, + 635 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 395, + 287, + 635 + ], + "type": "text", + "content": " refers to the feature dimension. The learned experience could be both biased (the layout gap between the training and test environments) and environment-static (without adaptation to the current environment). Therefore, in addition to eliminate the bias in the inference, we also propose to enhance the environmental adaptability of the experience " + }, + { + "bbox": [ + 46, + 395, + 287, + 635 + ], + "type": "inline_equation", + "content": "z^t" + }, + { + "bbox": [ + 46, + 395, + 287, + 635 + ], + "type": "text", + "content": " to achieve a better performance. To this end, the dynamically updated knowledge of object layout " + }, + { + "bbox": [ + 46, + 395, + 287, + 635 + ], + "type": "inline_equation", + "content": "D = \\{\\theta_i\\}_{i=1}^K" + }, + { + "bbox": [ + 46, + 395, + 287, + 635 + ], + "type": "text", + "content": " is encoded into the navigation framework. Specifically, the expectation of the posterior distribution of the object layout " + }, + { + "bbox": [ + 46, + 395, + 287, + 635 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 46, + 395, + 287, + 635 + ], + "type": "text", + "content": " is formalized as " + }, + { + "bbox": [ + 46, + 395, + 287, + 635 + ], + "type": "inline_equation", + "content": "w^t \\in \\mathbb{R}^{K \\times K}" + }, + { + "bbox": [ + 46, + 395, + 287, + 635 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 395, + 287, + 635 + ], + "type": "inline_equation", + "content": "w_{i,j}^t > 0" + }, + { + "bbox": [ + 46, + 395, + 287, + 635 + ], + "type": "text", + "content": ". For " + }, + { + "bbox": [ + 46, + 395, + 287, + 635 + ], + "type": "inline_equation", + "content": "j = i" + }, + { + "bbox": [ + 46, + 395, + 287, + 635 + ], + "type": "text", + "content": ", since " + }, + { + "bbox": [ + 46, + 395, + 287, + 635 + ], + "type": "inline_equation", + "content": "p(c_i | c_i)" + }, + { + "bbox": [ + 46, + 395, + 287, + 635 + ], + "type": "text", + "content": " always exists, we set " + }, + { + "bbox": [ + 46, + 395, + 287, + 635 + ], + "type": "inline_equation", + "content": "w_{i,j}^t = 1" + }, + { + "bbox": [ + 46, + 395, + 287, + 635 + ], + "type": "text", + "content": ". When " + }, + { + "bbox": [ + 46, + 395, + 287, + 635 + ], + "type": "inline_equation", + "content": "j \\neq i" + }, + { + "bbox": [ + 46, + 395, + 287, + 635 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 395, + 287, + 635 + ], + "type": "inline_equation", + "content": "w_{i,j}^t = \\mathbb{E}_{p(\\theta_i | s_i^t, \\alpha_i^t)}(\\theta_{i,j})" + }, + { + "bbox": [ + 46, + 395, + 287, + 635 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 395, + 287, + 635 + ], + "type": "inline_equation", + "content": "\\mathbb{E}(\\cdot)" + }, + { + "bbox": [ + 46, + 395, + 287, + 635 + ], + "type": "text", + "content": " denote the expectation calculation. Based on [22], the expectation of the Dirichlet function " + }, + { + "bbox": [ + 46, + 395, + 287, + 635 + ], + "type": "inline_equation", + "content": "Dir(\\theta_i | \\alpha_i^t + n_{-i}^t)" + }, + { + "bbox": [ + 46, + 395, + 287, + 635 + ], + "type": "text", + "content": " is equivalent to the normalization of its parameters. Accordingly, for " + }, + { + "bbox": [ + 46, + 395, + 287, + 635 + ], + "type": "inline_equation", + "content": "j \\neq i" + }, + { + "bbox": [ + 46, + 395, + 287, + 635 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 61, + 651, + 287, + 682 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 651, + 287, + 682 + ], + "spans": [ + { + "bbox": [ + 61, + 651, + 287, + 682 + ], + "type": "interline_equation", + "content": "w _ {i, j} ^ {t} = \\mathbb {E} _ {p \\left(\\theta_ {i} \\mid s _ {i} ^ {t}, \\alpha_ {i} ^ {t}\\right)} \\left(\\theta_ {i, j}\\right) = \\frac {\\alpha_ {i , j} ^ {t} + n _ {- i , j} ^ {t}}{\\sum_ {j = 1} ^ {K} \\left(\\alpha_ {i , j} ^ {t} + n _ {- i , j} ^ {t}\\right)} \\tag {6}", + "image_path": "4bf040dc264f1f0655009a91e2c555f7fee80d92b30be4d17f6c7d123f67c20c.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "Since " + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "inline_equation", + "content": "w^{t}" + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": " is updated in real-time, we propose to improve the environment-static experience " + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "inline_equation", + "content": "z^{t}" + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": " to environment-" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "content": "adaptive experience " + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "inline_equation", + "content": "\\hat{z}^t" + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "content": " by incorporating the dynamically updated knowledge of object layout, where " + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "inline_equation", + "content": "\\hat{z}^t" + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "content": " is given by:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 382, + 106, + 545, + 121 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 382, + 106, + 545, + 121 + ], + "spans": [ + { + "bbox": [ + 382, + 106, + 545, + 121 + ], + "type": "interline_equation", + "content": "\\hat {z} ^ {t} = z ^ {t} \\odot [ w ^ {t} \\times g ^ {t} ] \\tag {7}", + "image_path": "6669961d40ce30f5e73999cd57db05b61987ef742cd671e5df57afe0e36c470e.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 125, + 545, + 198 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 125, + 545, + 198 + ], + "spans": [ + { + "bbox": [ + 304, + 125, + 545, + 198 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 125, + 545, + 198 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 304, + 125, + 545, + 198 + ], + "type": "text", + "content": " represents the element-wise multiplication, " + }, + { + "bbox": [ + 304, + 125, + 545, + 198 + ], + "type": "inline_equation", + "content": "\\times" + }, + { + "bbox": [ + 304, + 125, + 545, + 198 + ], + "type": "text", + "content": " refers to the matrix multiplication, and " + }, + { + "bbox": [ + 304, + 125, + 545, + 198 + ], + "type": "inline_equation", + "content": "g^{t}\\in \\mathbb{R}^{K}" + }, + { + "bbox": [ + 304, + 125, + 545, + 198 + ], + "type": "text", + "content": " is a one-hot vector indicating the target category of the goal. The result of " + }, + { + "bbox": [ + 304, + 125, + 545, + 198 + ], + "type": "inline_equation", + "content": "[w^t\\times g^t ]\\in \\mathbb{R}^K" + }, + { + "bbox": [ + 304, + 125, + 545, + 198 + ], + "type": "text", + "content": " indicates the probability of the target " + }, + { + "bbox": [ + 304, + 125, + 545, + 198 + ], + "type": "inline_equation", + "content": "g^{t}" + }, + { + "bbox": [ + 304, + 125, + 545, + 198 + ], + "type": "text", + "content": " is observed conditioned on each object category, which serves as a weight on the category-specific dimension of " + }, + { + "bbox": [ + 304, + 125, + 545, + 198 + ], + "type": "inline_equation", + "content": "z^t" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 205, + 437, + 217 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 205, + 437, + 217 + ], + "spans": [ + { + "bbox": [ + 305, + 205, + 437, + 217 + ], + "type": "text", + "content": "4.3. Training and Inference" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 223, + 545, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 223, + 545, + 545 + ], + "spans": [ + { + "bbox": [ + 304, + 223, + 545, + 545 + ], + "type": "text", + "content": "As shown in Fig. 2, our layout estimator outputs (1) the expectation " + }, + { + "bbox": [ + 304, + 223, + 545, + 545 + ], + "type": "inline_equation", + "content": "w^t" + }, + { + "bbox": [ + 304, + 223, + 545, + 545 + ], + "type": "text", + "content": " of the posterior layout distribution, and (2) the layout gap " + }, + { + "bbox": [ + 304, + 223, + 545, + 545 + ], + "type": "inline_equation", + "content": "D_{\\Delta}^{t}" + }, + { + "bbox": [ + 304, + 223, + 545, + 545 + ], + "type": "text", + "content": ". Both " + }, + { + "bbox": [ + 304, + 223, + 545, + 545 + ], + "type": "inline_equation", + "content": "w^t" + }, + { + "bbox": [ + 304, + 223, + 545, + 545 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 223, + 545, + 545 + ], + "type": "inline_equation", + "content": "D_{\\Delta}^{t}" + }, + { + "bbox": [ + 304, + 223, + 545, + 545 + ], + "type": "text", + "content": " are calculated mathematically without learnable parameters, thus our method has the plug-and-play property to boost the existing methods. Specifically, our layout-based sTDE is realized as: (1) Before training, to determine the initial value " + }, + { + "bbox": [ + 304, + 223, + 545, + 545 + ], + "type": "inline_equation", + "content": "(\\alpha_i^*)_{i=1}^K" + }, + { + "bbox": [ + 304, + 223, + 545, + 545 + ], + "type": "text", + "content": ", we first employ a random agent equipped with our object layout estimator, whose parameters " + }, + { + "bbox": [ + 304, + 223, + 545, + 545 + ], + "type": "inline_equation", + "content": "(\\alpha_i)^K_{i=1}" + }, + { + "bbox": [ + 304, + 223, + 545, + 545 + ], + "type": "text", + "content": " are initialized as all one vector. Then the agent randomly explores the training scenes to obtain sufficient observations to update the parameters by Eq. 4. The updated parameters are defined as " + }, + { + "bbox": [ + 304, + 223, + 545, + 545 + ], + "type": "inline_equation", + "content": "(\\alpha_i^*)_{i=1}^K" + }, + { + "bbox": [ + 304, + 223, + 545, + 545 + ], + "type": "text", + "content": ". (2) In the training stage, at the beginning of every episode, all parameters " + }, + { + "bbox": [ + 304, + 223, + 545, + 545 + ], + "type": "inline_equation", + "content": "(\\alpha_i)^K_{i=1}" + }, + { + "bbox": [ + 304, + 223, + 545, + 545 + ], + "type": "text", + "content": " are initialized as the prior parameters " + }, + { + "bbox": [ + 304, + 223, + 545, + 545 + ], + "type": "inline_equation", + "content": "(\\alpha_i^*)_{i=1}^K" + }, + { + "bbox": [ + 304, + 223, + 545, + 545 + ], + "type": "text", + "content": ". The layout estimator calculates the posterior distribution of object layout " + }, + { + "bbox": [ + 304, + 223, + 545, + 545 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 223, + 545, + 545 + ], + "type": "text", + "content": " (Eq. 4), using the constant observation " + }, + { + "bbox": [ + 304, + 223, + 545, + 545 + ], + "type": "inline_equation", + "content": "s^t" + }, + { + "bbox": [ + 304, + 223, + 545, + 545 + ], + "type": "text", + "content": " and the prior distribution. Then the expectation of the posterior distribution " + }, + { + "bbox": [ + 304, + 223, + 545, + 545 + ], + "type": "inline_equation", + "content": "w^t" + }, + { + "bbox": [ + 304, + 223, + 545, + 545 + ], + "type": "text", + "content": " is estimated and incorporated in the navigation model " + }, + { + "bbox": [ + 304, + 223, + 545, + 545 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 304, + 223, + 545, + 545 + ], + "type": "text", + "content": " (Eq. 6, 7). The model " + }, + { + "bbox": [ + 304, + 223, + 545, + 545 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 304, + 223, + 545, + 545 + ], + "type": "text", + "content": " is trained with RL. (3) In the causal-inference stage, the agent will not directly use the trained policy " + }, + { + "bbox": [ + 304, + 223, + 545, + 545 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 304, + 223, + 545, + 545 + ], + "type": "text", + "content": ", while it first calculates the layout gap " + }, + { + "bbox": [ + 304, + 223, + 545, + 545 + ], + "type": "inline_equation", + "content": "D_{\\Delta}^{t}" + }, + { + "bbox": [ + 304, + 223, + 545, + 545 + ], + "type": "text", + "content": " (Eq. 5) and the counter-fact prediction " + }, + { + "bbox": [ + 304, + 223, + 545, + 545 + ], + "type": "inline_equation", + "content": "\\bar{a}^t" + }, + { + "bbox": [ + 304, + 223, + 545, + 545 + ], + "type": "text", + "content": " (the effect of the experience). Then the agent appropriately removes the counter-fact prediction " + }, + { + "bbox": [ + 304, + 223, + 545, + 545 + ], + "type": "inline_equation", + "content": "\\bar{a}^t" + }, + { + "bbox": [ + 304, + 223, + 545, + 545 + ], + "type": "text", + "content": " from the fact prediction " + }, + { + "bbox": [ + 304, + 223, + 545, + 545 + ], + "type": "inline_equation", + "content": "a^t" + }, + { + "bbox": [ + 304, + 223, + 545, + 545 + ], + "type": "text", + "content": " based on the layout gap " + }, + { + "bbox": [ + 304, + 223, + 545, + 545 + ], + "type": "inline_equation", + "content": "D_{\\Delta}^{t}" + }, + { + "bbox": [ + 304, + 223, + 545, + 545 + ], + "type": "text", + "content": " (Eq. 2). For more details and algorithms of training and inference, please refer to the supplements." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 545, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 546, + 713 + ], + "type": "text", + "content": "Note that the expectation of the posterior distribution of the object layout " + }, + { + "bbox": [ + 304, + 545, + 546, + 713 + ], + "type": "inline_equation", + "content": "w^{t}" + }, + { + "bbox": [ + 304, + 545, + 546, + 713 + ], + "type": "text", + "content": " affects the prediction of the model during both training and inference, while " + }, + { + "bbox": [ + 304, + 545, + 546, + 713 + ], + "type": "inline_equation", + "content": "D_{\\Delta}^{t}" + }, + { + "bbox": [ + 304, + 545, + 546, + 713 + ], + "type": "text", + "content": " is utilized for debiasing only in the inference. Furthermore, we want to explain why the debiasing operation only acts in inference. As shown in Fig. 1, the prediction is influenced by two effects: the inputs (the observation " + }, + { + "bbox": [ + 304, + 545, + 546, + 713 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 545, + 546, + 713 + ], + "type": "text", + "content": " and the goal " + }, + { + "bbox": [ + 304, + 545, + 546, + 713 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 304, + 545, + 546, + 713 + ], + "type": "text", + "content": ") and their mediator (the experience " + }, + { + "bbox": [ + 304, + 545, + 546, + 713 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 304, + 545, + 546, + 713 + ], + "type": "text", + "content": "). The mediator (experience) has agnostic effects because it is learned from limited training data. The training data can not cover all room layouts, thus resulting the prediction bias in the inference. Consequently, the debiasing operation (i.e. the sTDE partially removes the effect of experience from prediction) is conducted in inference to decouple the effect from the training data." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10796" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 70, + 286, + 193 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 286, + 193 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 286, + 193 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 286, + 193 + ], + "type": "image", + "image_path": "7faa6a3b890fed9cfffc6d287260bb9cf9ab192f7cad457e9239037d339a4ec9.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 201, + 287, + 224 + ], + "lines": [ + { + "bbox": [ + 46, + 201, + 287, + 224 + ], + "spans": [ + { + "bbox": [ + 46, + 201, + 287, + 224 + ], + "type": "text", + "content": "Figure 4. The correlation between the navigation performance on success rate (SR) and the layout similarity." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 243, + 128, + 256 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 243, + 128, + 256 + ], + "spans": [ + { + "bbox": [ + 47, + 243, + 128, + 256 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 262, + 163, + 276 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 262, + 163, + 276 + ], + "spans": [ + { + "bbox": [ + 47, + 262, + 163, + 276 + ], + "type": "text", + "content": "5.1. Experimental Setup" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 281, + 287, + 400 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 281, + 287, + 400 + ], + "spans": [ + { + "bbox": [ + 46, + 281, + 287, + 400 + ], + "type": "text", + "content": "We utilize the AI2THOR [27], RoboTHOR [12] simulators to conduct ablation studies and compare our method with the learning-based methods [15, 16, 32, 56, 59, 63, 64]. The experimental settings on above datasets follow the primary works [15, 16, 63]. Besides, we choose the Gibson [58] dataset in the Habitat simulator [48] to compare our method with the map-based methods and adopt the same settings as [7]. For more details about the settings of the datasets (e.g. the split of training, validation, testing scenes, and the target objects), please refer to the supplements." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 401, + 287, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 401, + 287, + 544 + ], + "spans": [ + { + "bbox": [ + 46, + 401, + 287, + 544 + ], + "type": "text", + "content": "Our method and the related works are both trained to maximize the navigation reward via RL. The reward function penalizes the agent by -0.01 for each step and rewards it by 5 if the episode is successful (the successful episode is defined in Sec. 3). All methods are trained with 6M episodes, where in each episode, the starting position of the agent and the goal are randomly selected. Note that, since our method needs prerequisite exploration to determine the initial parameters " + }, + { + "bbox": [ + 46, + 401, + 287, + 544 + ], + "type": "inline_equation", + "content": "(\\alpha_{i}^{*})_{i = 1}^{K}" + }, + { + "bbox": [ + 46, + 401, + 287, + 544 + ], + "type": "text", + "content": " of the layout distribution. To be fair, we employ the agent to randomly explore the training rooms to learn the initial parameters for 2M episodes, then we train our method with 4M episodes." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 544, + 286, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 544, + 286, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 544, + 286, + 628 + ], + "type": "text", + "content": "For evaluation, we repeatedly run 3 trials and report the results with mean " + }, + { + "bbox": [ + 46, + 544, + 286, + 628 + ], + "type": "inline_equation", + "content": "\\pm" + }, + { + "bbox": [ + 46, + 544, + 286, + 628 + ], + "type": "text", + "content": " standard deviation. We choose SR (Success Rate), SPL (Success weighted by Path Length), and DTS (Distance to Goal) metrics for evaluation, which are detailed in the supplements. For all results in the following tables, the " + }, + { + "bbox": [ + 46, + 544, + 286, + 628 + ], + "type": "inline_equation", + "content": "\\uparrow" + }, + { + "bbox": [ + 46, + 544, + 286, + 628 + ], + "type": "text", + "content": " means that the larger value is better, while " + }, + { + "bbox": [ + 46, + 544, + 286, + 628 + ], + "type": "inline_equation", + "content": "\\downarrow" + }, + { + "bbox": [ + 46, + 544, + 286, + 628 + ], + "type": "text", + "content": " indicates the opposite." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 635, + 185, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 635, + 185, + 647 + ], + "spans": [ + { + "bbox": [ + 47, + 635, + 185, + 647 + ], + "type": "text", + "content": "5.2. The Compared Methods" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 653, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 286, + 713 + ], + "type": "text", + "content": "We choose the learning-based methods [15, 16, 32, 56, 59, 63, 64] and the map-based method [7] for comparison. Random: the agent adopts random actions. RGB(D) + RL (A3C) [48, 64]: the agent utilizes the simple embeddings of visual input and the goal, and is trained with A3C [34]." + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 309, + 70, + 543, + 162 + ], + "blocks": [ + { + "bbox": [ + 309, + 70, + 543, + 162 + ], + "lines": [ + { + "bbox": [ + 309, + 70, + 543, + 162 + ], + "spans": [ + { + "bbox": [ + 309, + 70, + 543, + 162 + ], + "type": "image", + "image_path": "f7db9292303efec60f8300922b5396aadfaf3268bb1697ecfd9b52312dfa21d7.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 171, + 545, + 216 + ], + "lines": [ + { + "bbox": [ + 305, + 171, + 545, + 216 + ], + "spans": [ + { + "bbox": [ + 305, + 171, + 545, + 216 + ], + "type": "text", + "content": "Figure 5. Category-wise improvement of our method compared to the baseline. The categories are arranged from high to low based on their average layout similarity between training and testing scenes." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 239, + 545, + 431 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 239, + 545, + 431 + ], + "spans": [ + { + "bbox": [ + 304, + 239, + 545, + 431 + ], + "type": "text", + "content": "SP [59]: SP constructs the scene prior knowledge from the external dataset. The prior knowledge encoded with GCN [26] is provided to the agent as the additional information. SAVN [56]: SAVN establishes a sub-network to learn a self-supervised interaction loss. EOTP [32]: EOTP proposes an attention module to encode the semantic information about the observed objects. ORG [15]: ORG proposes to learn an object relation graph, and builds a memory-augmented tentative policy network (TPN) to produce self-supervision. VTNet [16]: VTNet employs the Transformer network to encode the visual information and the goal. HOZ [63]: HOZ attempts to abstract the region relation among the objects and proposes to learn the region relation graph to associate the vision and the goal. SemExp [7]: SemExp builds an episodic semantic map and trains a goal-oriented policy taking the semantic map as the input." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 441, + 416, + 452 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 441, + 416, + 452 + ], + "spans": [ + { + "bbox": [ + 306, + 441, + 416, + 452 + ], + "type": "text", + "content": "5.3. Evaluation Results" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 460, + 545, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 460, + 545, + 483 + ], + "spans": [ + { + "bbox": [ + 305, + 460, + 545, + 483 + ], + "type": "text", + "content": "In this section, we adopt the ORG [15] as the baseline and conduct evaluations on the validation set of AI2THOR." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 485, + 545, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 485, + 545, + 664 + ], + "spans": [ + { + "bbox": [ + 304, + 485, + 545, + 664 + ], + "type": "text", + "content": "Correlation between layout and success rate. Our motivation is that the layout gap between training and testing scenes may have an impact on navigation. To verify this, we take the statistic and visualize the results in Fig. 4 (a), where the y-axis represents the success rate of navigating to objects " + }, + { + "bbox": [ + 304, + 485, + 545, + 664 + ], + "type": "inline_equation", + "content": "c_{i}" + }, + { + "bbox": [ + 304, + 485, + 545, + 664 + ], + "type": "text", + "content": " in a testing scene " + }, + { + "bbox": [ + 304, + 485, + 545, + 664 + ], + "type": "inline_equation", + "content": "R_{j}" + }, + { + "bbox": [ + 304, + 485, + 545, + 664 + ], + "type": "text", + "content": ", the x-axis represents the layout similarity of the object " + }, + { + "bbox": [ + 304, + 485, + 545, + 664 + ], + "type": "inline_equation", + "content": "c_{i}" + }, + { + "bbox": [ + 304, + 485, + 545, + 664 + ], + "type": "text", + "content": " between the training scenes and the test scenes, and the scatter points represent all target objects in all test scenes. As shown in Fig. 4 (b), the layout similarity is defined as the cosine similarity of the statistics vectors (the count of cooccurrence objects) obtained in the training scenes and the test scene " + }, + { + "bbox": [ + 304, + 485, + 545, + 664 + ], + "type": "inline_equation", + "content": "R_{j}" + }, + { + "bbox": [ + 304, + 485, + 545, + 664 + ], + "type": "text", + "content": ". Fig. 4 (a) indicates that the navigation performance on SR during inference has a generally positive correlation with the layout similarity, which supports our motivation." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 666, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 666, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 666, + 545, + 713 + ], + "type": "text", + "content": "Improvements of our method compared to baseline. The navigation performance of the baseline (green bar) and the improvements brought by our method (blue bar) are shown in Fig. 5. All goals (x-axis) are arranged from high" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10797" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 70, + 164, + 176 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 164, + 176 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 164, + 176 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 164, + 176 + ], + "type": "image", + "image_path": "7670fa5f1fbaf1bf1bc8c9d8b1512897b312423c5391489fd9c5ecc0bfe45bb3.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 185, + 287, + 208 + ], + "lines": [ + { + "bbox": [ + 46, + 185, + 287, + 208 + ], + "spans": [ + { + "bbox": [ + 46, + 185, + 287, + 208 + ], + "type": "text", + "content": "Figure 6. The ablation study of the threshold " + }, + { + "bbox": [ + 46, + 185, + 287, + 208 + ], + "type": "inline_equation", + "content": "\\varepsilon" + }, + { + "bbox": [ + 46, + 185, + 287, + 208 + ], + "type": "text", + "content": " and the visualization of the object layout gap " + }, + { + "bbox": [ + 46, + 185, + 287, + 208 + ], + "type": "inline_equation", + "content": "D_{\\Delta}^{t}" + }, + { + "bbox": [ + 46, + 185, + 287, + 208 + ], + "type": "text", + "content": " over the navigation steps." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 167, + 70, + 286, + 176 + ], + "blocks": [ + { + "bbox": [ + 167, + 70, + 286, + 176 + ], + "lines": [ + { + "bbox": [ + 167, + 70, + 286, + 176 + ], + "spans": [ + { + "bbox": [ + 167, + 70, + 286, + 176 + ], + "type": "image", + "image_path": "28df14622981d9ff5fc7eec70b3c389b54638d3e36a69f48552bdbe65ba34c44.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 231, + 286, + 315 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 231, + 286, + 315 + ], + "spans": [ + { + "bbox": [ + 46, + 231, + 286, + 315 + ], + "type": "text", + "content": "to low based on their layout similarity. The results indicate that our method can bring more obvious improvement in the categories with low layout similarity (as illustrated by the red dashed circle). We presume that the goals with a larger layout gap are more susceptible to the effects of the experience, thus benefiting more from our de-biased method. The results once again support our motivation." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 316, + 286, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 316, + 286, + 542 + ], + "spans": [ + { + "bbox": [ + 46, + 316, + 286, + 542 + ], + "type": "text", + "content": "Ablations on the threshold " + }, + { + "bbox": [ + 46, + 316, + 286, + 542 + ], + "type": "inline_equation", + "content": "\\varepsilon" + }, + { + "bbox": [ + 46, + 316, + 286, + 542 + ], + "type": "text", + "content": ". The threshold " + }, + { + "bbox": [ + 46, + 316, + 286, + 542 + ], + "type": "inline_equation", + "content": "\\varepsilon" + }, + { + "bbox": [ + 46, + 316, + 286, + 542 + ], + "type": "text", + "content": " influences the agent by Eq. 2, which determines whether to remove the prediction bias introduced by the experience. As shown in Fig. 6 (a), the results of different threshold " + }, + { + "bbox": [ + 46, + 316, + 286, + 542 + ], + "type": "inline_equation", + "content": "\\varepsilon" + }, + { + "bbox": [ + 46, + 316, + 286, + 542 + ], + "type": "text", + "content": " basically show the same trend on the SR, SPL metrics: as the value of threshold " + }, + { + "bbox": [ + 46, + 316, + 286, + 542 + ], + "type": "inline_equation", + "content": "\\varepsilon" + }, + { + "bbox": [ + 46, + 316, + 286, + 542 + ], + "type": "text", + "content": " increases, the performances on these metrics initially increase and then decrease. When the value of threshold " + }, + { + "bbox": [ + 46, + 316, + 286, + 542 + ], + "type": "inline_equation", + "content": "\\varepsilon" + }, + { + "bbox": [ + 46, + 316, + 286, + 542 + ], + "type": "text", + "content": " is small, the Eq. 2 tends to consider that the majority of experiences " + }, + { + "bbox": [ + 46, + 316, + 286, + 542 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 46, + 316, + 286, + 542 + ], + "type": "text", + "content": " are negative and need to be removed. At this point, gradually increasing the threshold " + }, + { + "bbox": [ + 46, + 316, + 286, + 542 + ], + "type": "inline_equation", + "content": "\\varepsilon" + }, + { + "bbox": [ + 46, + 316, + 286, + 542 + ], + "type": "text", + "content": " could retain more experiences and improve performance. However, when the threshold " + }, + { + "bbox": [ + 46, + 316, + 286, + 542 + ], + "type": "inline_equation", + "content": "\\varepsilon" + }, + { + "bbox": [ + 46, + 316, + 286, + 542 + ], + "type": "text", + "content": " is too large (e.g. " + }, + { + "bbox": [ + 46, + 316, + 286, + 542 + ], + "type": "inline_equation", + "content": "\\varepsilon = 1" + }, + { + "bbox": [ + 46, + 316, + 286, + 542 + ], + "type": "text", + "content": "), the Eq. 2 falls into another extreme which considers all experiences are positive and need to be preserved, resulting in the performance degradation. The results on DTS metric indicate that excessively removing the experience (" + }, + { + "bbox": [ + 46, + 316, + 286, + 542 + ], + "type": "inline_equation", + "content": "\\varepsilon" + }, + { + "bbox": [ + 46, + 316, + 286, + 542 + ], + "type": "text", + "content": " is small) will increase the exploration of the agent, thus resulting in worse performance on DTS. Based on the above results, we choose the threshold as " + }, + { + "bbox": [ + 46, + 316, + 286, + 542 + ], + "type": "inline_equation", + "content": "\\varepsilon = 0.5" + }, + { + "bbox": [ + 46, + 316, + 286, + 542 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 544, + 286, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 544, + 286, + 700 + ], + "spans": [ + { + "bbox": [ + 46, + 544, + 286, + 700 + ], + "type": "text", + "content": "Visualization of the object layout gap " + }, + { + "bbox": [ + 46, + 544, + 286, + 700 + ], + "type": "inline_equation", + "content": "D_{\\Delta}^{t}" + }, + { + "bbox": [ + 46, + 544, + 286, + 700 + ], + "type": "text", + "content": ". The object layout gap " + }, + { + "bbox": [ + 46, + 544, + 286, + 700 + ], + "type": "inline_equation", + "content": "D_{\\Delta}^{t}" + }, + { + "bbox": [ + 46, + 544, + 286, + 700 + ], + "type": "text", + "content": " represents the KL divergence between the posterior and the prior distribution of the layout. The average value of the " + }, + { + "bbox": [ + 46, + 544, + 286, + 700 + ], + "type": "inline_equation", + "content": "D_{\\Delta}^{t}" + }, + { + "bbox": [ + 46, + 544, + 286, + 700 + ], + "type": "text", + "content": " over navigation steps in AI2THOR is illustrated in Fig. 6 (b). The results indicate that the layout gap decreases as the number of steps increases (the purple line). However, without updating by our method (the grey line), the layout gap is maintained at a large value. The trend of " + }, + { + "bbox": [ + 46, + 544, + 286, + 700 + ], + "type": "inline_equation", + "content": "D_{\\Delta}^{t}" + }, + { + "bbox": [ + 46, + 544, + 286, + 700 + ], + "type": "text", + "content": " demonstrates that the learned knowledge (posterior distribution of the layout) by our method is gradually approaching the real layout of the current scene. It also reveals that the " + }, + { + "bbox": [ + 46, + 544, + 286, + 700 + ], + "type": "inline_equation", + "content": "w^{t}" + }, + { + "bbox": [ + 46, + 544, + 286, + 700 + ], + "type": "text", + "content": " (the expectation of posterior distribution) is environment-adaptive information for guiding the agent." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 59, + 701, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 701, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 59, + 701, + 286, + 713 + ], + "type": "text", + "content": "Additionally, considering the threshold " + }, + { + "bbox": [ + 59, + 701, + 286, + 713 + ], + "type": "inline_equation", + "content": "\\varepsilon = 0.5" + }, + { + "bbox": [ + 59, + 701, + 286, + 713 + ], + "type": "text", + "content": " and" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 70, + 545, + 125 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 70, + 545, + 125 + ], + "spans": [ + { + "bbox": [ + 305, + 70, + 545, + 125 + ], + "type": "text", + "content": "Table 1. The ablation studies. (I) The ablations of several components. The " + }, + { + "bbox": [ + 305, + 70, + 545, + 125 + ], + "type": "inline_equation", + "content": "w^t" + }, + { + "bbox": [ + 305, + 70, + 545, + 125 + ], + "type": "text", + "content": " represents encoding the expectation of the posterior distribution of object layout into the model, and " + }, + { + "bbox": [ + 305, + 70, + 545, + 125 + ], + "type": "inline_equation", + "content": "D_{\\Delta}^{t}" + }, + { + "bbox": [ + 305, + 70, + 545, + 125 + ], + "type": "text", + "content": " represents de-biasing the trained model in the inference with our sTDE. (II) The comparison of different de-bias methods." + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 314, + 128, + 535, + 243 + ], + "blocks": [ + { + "bbox": [ + 314, + 128, + 535, + 243 + ], + "lines": [ + { + "bbox": [ + 314, + 128, + 535, + 243 + ], + "spans": [ + { + "bbox": [ + 314, + 128, + 535, + 243 + ], + "type": "table", + "html": "
IDMethod \nBaseline w t DΔtSR↑ (%)SPL↑ (%)DTS↓ (m)
I1✓66.48±0.2238.42±0.390.54±0.01
2✓71.40±0.3739.11±0.440.49±0.02
3✓74.95±0.3841.68±0.230.47±0.02
II4w/o De-bias71.40±0.3739.11±0.440.49±0.02
5TDE [53]69.24±0.1238.38±0.160.52±0.01
6Ours sTDE (zero)74.95±0.3841.68±0.230.47±0.02
7Ours sTDE (random)75.03±0.6941.48±0.440.46±0.03
", + "image_path": "999d0de0ecb8faecdd71e9951be5a8761be0a8331c50194662ac58a3dadee4df.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 255, + 545, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 255, + 545, + 399 + ], + "spans": [ + { + "bbox": [ + 304, + 255, + 545, + 399 + ], + "type": "text", + "content": "looking back at Fig. 6 (b), we can observe how our layout-based sTDE works in the time (i.e. steps) dimension. According to the Eq. 2, the de-bias operation is activated when " + }, + { + "bbox": [ + 304, + 255, + 545, + 399 + ], + "type": "inline_equation", + "content": "(D_{\\Delta}^{t} - \\varepsilon) > 0" + }, + { + "bbox": [ + 304, + 255, + 545, + 399 + ], + "type": "text", + "content": ", as shown in the upper purple shadow. At the beginning of an episode, the agent is unfamiliar with the current scene, and the layout gap is large. At this stage, our layout-based sTDE is activated to eliminate the prediction bias caused by the experience. Then with continuous navigating and updating, the prior knowledge of the object layout has been gradually adjusted to fit the current scene. Therefore, at this stage, the updated experience is applicable to the current scene and fully accepted for the navigation." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 400, + 545, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 400, + 545, + 532 + ], + "spans": [ + { + "bbox": [ + 304, + 400, + 545, + 532 + ], + "type": "text", + "content": "Ablations of different components. We evaluate different components of our method. The ablation study in Tab. 1 (I) indicates the efficacy of each component in our method. Specifically, the expectation " + }, + { + "bbox": [ + 304, + 400, + 545, + 532 + ], + "type": "inline_equation", + "content": "w^{t}" + }, + { + "bbox": [ + 304, + 400, + 545, + 532 + ], + "type": "text", + "content": " of the posterior distribution of the object layout improves the baseline (ORG) performance by " + }, + { + "bbox": [ + 304, + 400, + 545, + 532 + ], + "type": "inline_equation", + "content": "4.92\\%" + }, + { + "bbox": [ + 304, + 400, + 545, + 532 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 400, + 545, + 532 + ], + "type": "inline_equation", + "content": "0.69\\%" + }, + { + "bbox": [ + 304, + 400, + 545, + 532 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 400, + 545, + 532 + ], + "type": "inline_equation", + "content": "-0.05m" + }, + { + "bbox": [ + 304, + 400, + 545, + 532 + ], + "type": "text", + "content": " on SR, SPL and DTS metrics. Moreover, the soft Total Direct Effect (sTDE) further improves the performance and gains " + }, + { + "bbox": [ + 304, + 400, + 545, + 532 + ], + "type": "inline_equation", + "content": "3.55\\%" + }, + { + "bbox": [ + 304, + 400, + 545, + 532 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 400, + 545, + 532 + ], + "type": "inline_equation", + "content": "2.57\\%" + }, + { + "bbox": [ + 304, + 400, + 545, + 532 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 400, + 545, + 532 + ], + "type": "inline_equation", + "content": "-0.02m" + }, + { + "bbox": [ + 304, + 400, + 545, + 532 + ], + "type": "text", + "content": " improvement on SR, SPL and DTS metrics. Overall, our method outperforms the baseline by " + }, + { + "bbox": [ + 304, + 400, + 545, + 532 + ], + "type": "inline_equation", + "content": "8.47\\%" + }, + { + "bbox": [ + 304, + 400, + 545, + 532 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 400, + 545, + 532 + ], + "type": "inline_equation", + "content": "3.26\\%" + }, + { + "bbox": [ + 304, + 400, + 545, + 532 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 400, + 545, + 532 + ], + "type": "inline_equation", + "content": "-0.07m" + }, + { + "bbox": [ + 304, + 400, + 545, + 532 + ], + "type": "text", + "content": " on SR, SPL and DTS metrics." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": "Comparison with TDE and sTDE. The TDE analysis is effective in removing the mediation fallacy and is applied in many works [36, 49, 50], which regard the mediator (i.e. the experience in our work) as the cause of prediction bias and remove it in the inference by Eq. 1. However, directly applying TDE makes the agent completely ignore the positive effect of the experience. Thus, as shown in Tab. 1 (II), employing TDE (line 5) even degrades the navigation performance (compared with line 4). Compared with TDE, our sTDE (line 6 and 7) adaptively retains the positive effects of the experience and obtains significant improvements. Previous work [50] introduces constructing the counterfactual item (i.e. " + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\bar{a}^t" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": "), by setting the value of observation " + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": " and the goal " + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": " to random or zero. We respectively adopt these two ways (line 6 and 7) and find out that their performances" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10798" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 47, + 95, + 555, + 245 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 545, + 93 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 545, + 93 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 545, + 93 + ], + "type": "text", + "content": "Table 2. The comparisons with the related works (learning-based methods) in AI2THOR and RoboTHOR simulators. The L-sTDE represents our layout-based soft TDE framework based on different baselines. The improvements are shown in blue font." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 47, + 95, + 555, + 245 + ], + "lines": [ + { + "bbox": [ + 47, + 95, + 555, + 245 + ], + "spans": [ + { + "bbox": [ + 47, + 95, + 555, + 245 + ], + "type": "table", + "html": "
IDMethodAI2THORRoboTHOR
SR↑ (%)SPL↑ (%)DTS↓ (m)SR↑ (%)SPL↑ (%)DTS↓ (m)
1Random4.68 ±1.742.42 ±1.351.36 ±0.012.92 ±0.391.34 ±0.202.40 ±0.02
2RGB+RL (A3C) [64]59.06 ±0.1934.56 ±0.440.68 ±0.0127.48 ±0.4616.45 ±0.122.08 ±0.02
3SP [59]62.19 ±0.6737.60 ±0.350.61 ±0.0226.22 ±0.7816.90 ±0.332.06 ±0.02
4SAVN [56]63.27 ±0.1138.20 ±0.040.56 ±0.0128.53 ±0.7718.27 ±0.351.96 ±0.02
5EOTP [32]65.61 ±0.2538.93 ±0.100.55 ±0.0128.84 ±0.4118.82 ±0.351.95 ±0.02
6ORG [15]66.53 ±0.2939.00 ±0.340.54 ±0.0129.64 ±0.8919.13 ±0.591.95 ±0.03
7ORG+TPN [15]68.60 ±0.2939.40 ±0.170.54 ±0.0130.05 ±0.0619.05 ±0.081.89 ±0.01
8VTNet [16]70.10 ±1.0039.60 ±0.100.52 ±0.0131.62 ±0.7419.63 ±0.421.87 ±0.03
9HOZ [63]70.38 ±0.1439.04 ±0.110.48 ±0.0232.27 ±1.1420.48 ±0.481.85 ±0.01
10Ours L-sTDE (EOTP)69.62 (4.01↑) ±0.7140.02 (1.09↑) ±0.470.52 (0.03↑) ±0.0137.37 (8.53↑) ±0.7522.00 (3.18↑) ±0.421.81 (0.14↑) ±0.02
11Ours L-sTDE (ORG)74.85 (8.32↑) ±0.3341.56 (2.56↑) ±0.110.47 (0.07↑) ±0.0239.27 (9.63↑) ±0.5522.81 (3.68↑) ±0.471.77 (0.18↑) ±0.02
12Ours L-sTDE (VTNet)75.25 (5.15↑) ±0.3941.69 (2.09↑) ±0.130.47 (0.05↑) ±0.0241.53 (9.91↑) ±0.6723.87 (4.24↑) ±0.501.72 (0.15↑) ±0.02
13Ours L-sTDE (HOZ)75.05 (4.67↑) ±0.2941.53 (2.49↑) ±0.210.46 (0.02↑) ±0.0242.13 (9.86↑) ±0.7824.54 (4.06↑) ±0.431.67 (0.18↑) ±0.01
", + "image_path": "07476c4de7c590a48ee74d9dca17057cfd8d112effbfd91d3d72ab947a8659e9.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 264, + 287, + 326 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 264, + 287, + 326 + ], + "spans": [ + { + "bbox": [ + 46, + 264, + 287, + 326 + ], + "type": "text", + "content": "are similar, except that using the random value makes the performance more volatile (i.e. larger standard deviation). Therefore, we set the value of the observation and the goal as zeros to construct the counterfactual item. More ablation studies and visualizations are detailed in the supplements." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 334, + 246, + 347 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 334, + 246, + 347 + ], + "spans": [ + { + "bbox": [ + 47, + 334, + 246, + 347 + ], + "type": "text", + "content": "5.4. Comparisons with the Related Works" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 354, + 288, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 354, + 288, + 628 + ], + "spans": [ + { + "bbox": [ + 45, + 354, + 288, + 628 + ], + "type": "text", + "content": "In this section, we evaluate all methods on the test datasets of AI2THOR, RoboTHOR, and Gibson. We compare the learning-based methods [15, 16, 32, 56, 59, 63, 64] in AI2THOR and RoboTHOR as shown in Tab. 2. With the egocentric RGB input, all methods are constructed with the Faster R-CNN backbone, which is pre-trained following [15]. To keep fair comparisons, we present VTNet [16] using their reported results with Faster R-CNN. Since other methods [32, 56, 59, 64] are originally proposed with the ResNet [21] pre-trained in ImageNet [14] as the visual backbone. For fair comparisons, following the recommendation of [15], we additionally encode the detection information provided by Faster R-CNN to these methods [32, 56, 59, 64]. Therefore, the implemented performances are higher than those results reported in the original papers. As shown in Tab. 2, benefiting from the incorporation of our layout-based sTDE (L-sTDE), the performances of existing methods are improved, especially our L-sTDE based on HOZ and VTNet achieve new SOTA performance. Other learning-based methods employ CLIP [42] as the backbone [25], or adopt pre-training on large-scale datasets (e.g. ProcTHOR [13]), and we compare our L-sTDE with these methods in the supplements." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 630, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 287, + 715 + ], + "type": "text", + "content": "Since most map-based methods require the RGB-D visual inputs and segmentation information provided by Mask R-CNN [20] to construct the semantic map, we take another comparison with the map-based methods as shown in Tab. 3. The map-based methods employ a parameter-free modular system to build the semantic map, then encode the map into the policy. We regard the encoded map as the ex" + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 307, + 286, + 559, + 353 + ], + "blocks": [ + { + "bbox": [ + 305, + 262, + 545, + 285 + ], + "lines": [ + { + "bbox": [ + 305, + 262, + 545, + 285 + ], + "spans": [ + { + "bbox": [ + 305, + 262, + 545, + 285 + ], + "type": "text", + "content": "Table 3. The comparisons with the related works (map-based methods) in Gibson simulators." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 286, + 559, + 353 + ], + "lines": [ + { + "bbox": [ + 307, + 286, + 559, + 353 + ], + "spans": [ + { + "bbox": [ + 307, + 286, + 559, + 353 + ], + "type": "table", + "html": "
IDMethodSR↑ (%)SPL↑ (%)DTS↓ (m)
1Random0.040.043.89
2RGBD+RL [48]8.422.873.23
3SemExp [7]65.3533.521.56
4Ours L-sTDE (SemExp)66.96 (1.61↑)34.33 (0.81↑)1.53 (0.03↑)
", + "image_path": "63120cc5807d80972e1c8e58bd2e8736c607dc4e58393d0526680618305345a0.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 362, + 545, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 362, + 545, + 483 + ], + "spans": [ + { + "bbox": [ + 304, + 362, + 545, + 483 + ], + "type": "text", + "content": "experience " + }, + { + "bbox": [ + 304, + 362, + 545, + 483 + ], + "type": "inline_equation", + "content": "z^t" + }, + { + "bbox": [ + 304, + 362, + 545, + 483 + ], + "type": "text", + "content": " and modify [7] with our L-sTDE. The results indicate that our method still brings some performance improvements, although the gains are limited compared to that of the learning-based methods. We analyze that, compared with the learning-based methods whose parameters are all trained end-to-end, the map-based methods utilize a modular system, and only a small number of parameters (the policy) need to be trained. Therefore, the map-based methods are less affected by the experience learned from training, and thus benefit less from our method." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 494, + 378, + 506 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 494, + 378, + 506 + ], + "spans": [ + { + "bbox": [ + 306, + 494, + 378, + 506 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 513, + 545, + 644 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 513, + 545, + 644 + ], + "spans": [ + { + "bbox": [ + 304, + 513, + 545, + 644 + ], + "type": "text", + "content": "We propose the layout-based soft Total Direct Effect framework for ObjectNav task. Our motivation is to keep the positive effect and remove the negative effect of the experience, which is learned as the prior knowledge in training. Specifically, we propose to calculate the layout gap between the current environment and the prior knowledge. Then the layout gap is utilized to assess whether the impact of the learned experience is positive. Furthermore, the soft Total Direct Effect is proposed to appropriately control the effect of the experience on action prediction. The experiment results indicate the effectiveness of our method." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 647, + 547, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 647, + 547, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 647, + 547, + 712 + ], + "type": "text", + "content": "Acknowledgements: This work was supported by Beijing Natural Science Foundation under Grant JQ22012, Z190020, in part by the National Natural Science Foundation of China under Grant 62125207, 62272443, 62032022 and U1936203, in part by the National Postdoctoral Program for Innovative Talents under Grant BX201700255." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10799" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "text", + "content": "[1] Ehsan Abbasnejad, Damien Teney, Amin Parvaneh, Javen Shi, and Anton van den Hengel. 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In this work, we try to solve a broad range of layout generation tasks in a single model that is based on discrete state-space diffusion models. Our model, named LayoutDM, naturally handles the structured layout data in the discrete representation and learns to progressively infer a noiseless layout from the initial input, where we model the layout corruption process by modality-wise discrete diffusion. For conditional generation, we propose to inject layout constraints in the form of masking or logit adjustment during inference. We show in the experiments that our LayoutDM successfully generates high-quality layouts and outperforms both task-specific and task-agnostic baselines on several layout tasks. $^{1}$", + "bbox": [ + 75, + 319, + 470, + 561 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 592, + 207, + 607 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Graphic layouts play a critical role in visual communication. Automatically creating a visually pleasing layout has tremendous application benefits that range from authoring of printed media [45] to designing application user interface [5], and there has been a growing research interest in the community. The task of layout generation considers the arrangement of elements, where each element has a tuple of attributes, such as category, position, or size, and depending on the task setup, there could be optional control inputs that specify part of the elements or attributes. Due to the structured nature of layout data, it is crucial to consider relationships between elements in a generation. For this reason, current generation approaches either build an autoregressive model [2, 11] or develop a dedicated inference strategy to explicitly consider relationships [19-21].", + "bbox": [ + 75, + 618, + 468, + 845 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this paper, we propose to utilize discrete state-space", + "bbox": [ + 94, + 845, + 468, + 861 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/04b2039837f404eef03c4baab9e29886016f32c767486f0f742c41b253b3e685.jpg", + "image_caption": [ + "Figure 1. Overview of LayoutDM. Top: LayoutDM is trained to gradually generate a complete layout from a blank state in discrete state space. Bottom: During sampling, we can steer LayoutDM to perform various conditional generation tasks without additional training or external models." + ], + "image_footnote": [], + "bbox": [ + 506, + 285, + 874, + 537 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "diffusion models [3, 9, 14] for layout generation tasks. Diffusion models have shown promising performance for various generation tasks, including images and texts [13]. We formulate the diffusion process for layout structure by modality-wise discrete diffusion, and train a denoising backbone network to progressively infer the complete layout with or without conditional inputs. To support variable-length layout data, we extend the discrete state-space with a special PAD token instead of the typical end-of-sequence token used in autoregressive models. Our model can incorporate complex layout constraints via logit adjustment, so that we can refine an existing layout or impose relative size constraints between elements without additional training.", + "bbox": [ + 496, + 656, + 890, + 853 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We discuss two key advantages of LayoutDM over existing models for conditional layout generation. Our model avoids the immutable dependency chain issue [20] that hap", + "bbox": [ + 498, + 854, + 890, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "1Please find the code and models at: https://cyberagentailab.github.io/layout-dm.", + "bbox": [ + 76, + 875, + 423, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "10167", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "pens in autoregressive models [11]. Autoregressive models fail to perform conditional generation when the condition disagrees with the pre-defined generation order of elements and attributes. Unlike non-autoregressive models [20], our model can generate variable-length elements. We empirically show in Sec. 4.5 that naively extending non-autoregressive models by padding results in suboptimal variable length generation while padding combined with our diffusion formulation leads to significant improvement.", + "bbox": [ + 75, + 90, + 468, + 226 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We evaluate LayoutDM on various layout generation tasks tackled by previous works [20, 21, 33, 36] using two large-scale datasets, Rico [5] and PubLayNet [45]. LayoutDM outperforms task-agnostic baselines in the majority of cases and shows promising performance compared with task-specific baselines. We further conduct an ablation study to prove the significant impact of our design choices in LayoutDM, including quantization of continuous variables and positional embedding.", + "bbox": [ + 75, + 227, + 467, + 363 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We summarize our contributions as follows:", + "bbox": [ + 96, + 364, + 388, + 378 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We formulate the discrete diffusion process for layout generation and propose a modality-wise diffusion and a padding approach to model highly structured layout data.", + "- We propose to inject complex layout constraints via masking and logit adjustment during the inference, so that our model can solve diverse tasks in a single model.", + "- We empirically show solid performance for various conditional layout generation tasks on public datasets." + ], + "bbox": [ + 76, + 380, + 468, + 500 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 517, + 218, + 532 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Layout Generation", + "text_level": 1, + "bbox": [ + 76, + 542, + 259, + 559 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Studies on automatic layout generation have appeared several times in literature [1, 26, 32, 42]. Layout tasks are commonly observed in design applications, including magazine covers, posters, presentation slides, application user interface, or banner advertising [5, 8, 10, 18, 35, 41, 42, 44]. Recent approaches to layout generation consider both unconditional generation [2, 11, 15, 16] and conditional generation in various setups, such as conditional inputs of category or size [19-21, 23], relational constraints [19, 21], element completion [11], and refinement [36]. Some attempt at solving multiple tasks in a single model [20, 33].", + "bbox": [ + 75, + 566, + 467, + 733 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "BLT [20] points out that the recent autoregressive decoders [2, 11] are not fully capable of considering partial inputs, i.e. known elements or attributes, during generation because they have a fixed generation order. BLT addresses the conditional generation by fill-in-the-blank task formulation using a bidirectional Transformer encoder similar to masked language models [6]. However, BLT cannot solve layout completion demonstrated in the decoder-based models because of the requirement of the known number of elements. Our LayoutDM enjoys the best of both worlds and supports a broader range of conditional generation tasks in", + "bbox": [ + 75, + 734, + 467, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "a single model.", + "bbox": [ + 498, + 90, + 602, + 104 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Another layout-specific consideration is the complex user-specified constraints, such as the positional requirements between two boxes (e.g., a header box should be on top of a paragraph box). Earlier approaches [31, 32, 43] propose hand-crafted cost functions representing the violation degree of aesthetic constraints so that those constraints guide the optimization process of layout inference. CLG-LO [19] proposes an aesthetically constrained optimization framework for pre-trained GANs. Our LayoutDM solves such constrained generation tasks on top of the task-agnostic iterative prediction via logit adjustment.", + "bbox": [ + 496, + 106, + 890, + 272 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Discrete Diffusion Models", + "text_level": 1, + "bbox": [ + 500, + 280, + 733, + 294 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Diffusion models [38] are generative models characterized by a forward and reverse Markov process. The forward process corrupts the data into a sequence of increasingly noisy variables. The reverse process gradually denoises the variables toward the actual data distribution. Diffusion models are stable to train and achieve faster sampling than autoregressive models by parallel iterative refinement. Recently, many approaches have learned the reverse process by a neural network and show strong empirical performance [7, 13, 39] in continuous state spaces, such as images.", + "bbox": [ + 496, + 303, + 890, + 455 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Discrete state spaces are a natural representation of discrete variables, such as text. D3PM [3] extends the pioneering work of Hoogeboom et al. [14] to structured categorical corruption processes for diffusion models in discrete state spaces, while maintaining the advantages of diffusion models for continuous state spaces. VQDiffusion [9] develops a corruption approach called mask-and-replace, so as to avoid accumulated prediction errors that are common in models based on iterative prediction. Following the corruption model of VQDiffusion, we carefully design a modality-wise corruption process for layout tasks that involve tokens from disjoint sets of vocabulary per modality.", + "bbox": [ + 496, + 455, + 890, + 635 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Several studies consider a conditional input to the inference process of diffusion models. Some approaches alter the reverse diffusion iteration to carefully inject given conditions for free-form image inpainting [28] or image editing by strokes or composition [30]. We extend the discrete state-space diffusion models via hard masking or logit adjustment to support the conditional generation of layouts.", + "bbox": [ + 496, + 636, + 890, + 742 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. LayoutDM", + "text_level": 1, + "bbox": [ + 500, + 753, + 616, + 771 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our LayoutDM builds on discrete-state space diffusion models [3, 9]. We first briefly review the fundamental of discrete diffusion models in Sec. 3.1. Sec. 3.2 explains our approach to layout generation within the diffusion framework while discussing features inherent in layout compared with text. Sec. 3.3 discusses how we extend denoising steps to perform various conditional layout generation by imposing conditions in each step of the reverse process.", + "bbox": [ + 496, + 779, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "10168", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3.1. Preliminary: Discrete Diffusion Models", + "text_level": 1, + "bbox": [ + 76, + 90, + 416, + 107 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Diffusion models [38] are generative models characterized by a forward and reverse Markov process. While many diffusion models are defined on continuous space with Gaussian corruption, D3PM [3] introduces a general diffusion framework for categorical variables designed primarily for texts. Let $T \\in \\mathbb{N}$ be a total timestep of the diffusion model, we first explain the forward diffusion process. For a scalar discrete variable with $K$ categories $z_{t} \\in \\{1,2,\\dots,K\\}$ at timestep $t \\in \\mathbb{N}$ , probabilities that $z_{t-1}$ transits to $z_{t}$ are defined by using a transition matrix $Q_{t} \\in [0,1]^{K \\times K}$ , with $[Q_{t}]_{mn} = q(z_{t} = m|z_{t-1} = n)$ ,", + "bbox": [ + 76, + 113, + 473, + 282 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nq \\left(z _ {t} \\mid z _ {t - 1}\\right) = \\boldsymbol {v} \\left(z _ {t}\\right) ^ {\\top} \\mathbf {Q} _ {t} \\boldsymbol {v} \\left(z _ {t - 1}\\right), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 163, + 292, + 468, + 311 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\pmb{v}(z_t) \\in \\{0,1\\}^K$ is a column one-hot vector of $z_{t}$ . The categorical distribution over $z_{t}$ given $z_{t-1}$ is computed by a column vector $\\mathbf{Q}_t \\pmb{v}(z_{t-1}) \\in [0,1]^K$ . Assuming the Markov property, we can derive $q(z_t|z_0) = \\pmb{v}(z_t)^{\\top} \\overline{\\mathbf{Q}}_t \\pmb{v}(z_0)$ where $\\overline{\\mathbf{Q}}_t = \\mathbf{Q}_t \\mathbf{Q}_{t-1} \\cdots \\mathbf{Q}_1$ and:", + "bbox": [ + 76, + 314, + 468, + 391 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} q \\left(z _ {t - 1} \\mid z _ {t}, z _ {0}\\right) = \\frac {q \\left(z _ {t} \\mid z _ {t - 1} , z _ {0}\\right) q \\left(z _ {t - 1} \\mid z _ {0}\\right)}{q \\left(z _ {t} \\mid z _ {0}\\right)} \\\\ = \\frac {\\left(\\boldsymbol {v} \\left(z _ {t}\\right) ^ {\\top} \\mathbf {Q} _ {t} \\boldsymbol {v} \\left(z _ {t - 1}\\right)\\right) \\left(\\boldsymbol {v} \\left(z _ {t - 1}\\right) ^ {\\top} \\overline {{\\mathbf {Q}}} _ {t - 1} \\boldsymbol {v} \\left(z _ {0}\\right)\\right)}{\\boldsymbol {v} \\left(z _ {t}\\right) ^ {\\top} \\overline {{\\mathbf {Q}}} _ {t} \\boldsymbol {v} \\left(z _ {0}\\right)}. \\tag {2} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 96, + 398, + 468, + 479 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Note that due to the Markov property, $q(z_{t}|z_{t - 1},z_{0}) = q(z_{t}|z_{t - 1})$ . When we consider $N$ -dimensional variables $z_{t}\\in \\{1,2,\\dots ,K\\}^{N}$ , the corruption is applied to each variable $z_{t}$ independently. In the following, we explain with $N$ -dimensional variables $z_{t}$ .", + "bbox": [ + 76, + 484, + 468, + 559 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In contrast to the forward process, the reverse denoising process considers a conditional distribution of $\\mathbf{z}_{t-1}$ over $\\mathbf{z}_t$ by a neural network $p_{\\theta}(\\mathbf{z}_{t-1}|\\mathbf{z}_t) \\in [0,1]^{N \\times K}$ . $\\mathbf{z}_{t-1}$ is sampled according to this distribution. Note that the typical implementation is to predict unnormalized log probabilities $\\log p_{\\theta}(\\mathbf{z}_{t-1}|\\mathbf{z}_t)$ by a stack of bidirectional Transformer encoder blocks. D3PM uses a neural network $\\tilde{p}_{\\theta}(\\tilde{\\mathbf{z}}_0|\\mathbf{z}_t)$ , combines it with the posterior $q(\\mathbf{z}_{t-1}|\\mathbf{z}_t,\\mathbf{z}_0)$ , and sums over possible $\\tilde{\\mathbf{z}}_0$ to obtain the following parameterization:", + "bbox": [ + 76, + 561, + 470, + 696 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\np _ {\\theta} \\left(\\boldsymbol {z} _ {t - 1} | \\boldsymbol {z} _ {t}\\right) \\propto \\sum_ {\\tilde {\\boldsymbol {z}} _ {0}} q \\left(\\boldsymbol {z} _ {t - 1} | \\boldsymbol {z} _ {t}, \\tilde {\\boldsymbol {z}} _ {0}\\right) \\tilde {p} _ {\\theta} \\left(\\tilde {\\boldsymbol {z}} _ {0} | \\boldsymbol {z} _ {t}\\right). \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 120, + 704, + 468, + 736 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In addition to the commonly used variational lower bound objective $\\mathcal{L}_{\\mathrm{vb}}$ , D3PM introduces an auxiliary denoising objective. The overall objective is as follows:", + "bbox": [ + 76, + 744, + 468, + 789 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\lambda} = \\mathcal {L} _ {\\mathrm {v b}} + \\lambda \\underset { \\begin{array}{c} \\boldsymbol {z} _ {t} \\sim q (\\boldsymbol {z} _ {t} | \\boldsymbol {z} _ {0}) \\\\ \\boldsymbol {z} _ {0} \\sim q (\\boldsymbol {z} _ {0}) \\end{array} } {\\mathbb {E}} \\left[ - \\log \\tilde {p} _ {\\theta} \\left(\\boldsymbol {z} _ {0} | \\boldsymbol {z} _ {t}\\right) \\right], \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 124, + 797, + 468, + 833 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\lambda$ is a hyper-parameter to balance the two loss terms.", + "bbox": [ + 76, + 840, + 468, + 854 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Although D3PM proposes many variants of $\\mathbf{Q}_t$ , VQD-iffusion [9] offers an improved version of $\\mathbf{Q}_t$ called mask-and-replace strategy. They introduce an additional special", + "bbox": [ + 76, + 854, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/f2eaafce04f7ba63ce81fdf4bf9055acdb8f49135ecc8bf175c6e7ff37b523dd.jpg", + "image_caption": [ + "Figure 2. Overview of the corruption and denoising processes in LayoutDM. For simplicity, we use a toy layout consisting of two elements and the model generates three elements at maximum." + ], + "image_footnote": [], + "bbox": [ + 498, + 87, + 893, + 212 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "token [MASK] and three probabilities $\\gamma_{t}$ of replacing the current token with the [MASK] token, $\\beta_{t}$ of replacing the token with other tokens, and $\\alpha_{t}$ of not changing the token. The [MASK] token never transitions to other states. The transition matrix $\\mathbf{Q}_t\\in [0,1]^{(K + 1)\\times (K + 1)}$ is defined by:", + "bbox": [ + 496, + 290, + 890, + 367 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {Q} _ {t} = \\left[ \\begin{array}{c c c c c} \\alpha_ {t} + \\beta_ {t} & \\beta_ {t} & \\dots & \\beta_ {t} & 0 \\\\ \\beta_ {t} & \\alpha_ {t} + \\beta_ {t} & \\dots & \\beta_ {t} & 0 \\\\ \\vdots & \\vdots & \\ddots & \\beta_ {t} & 0 \\\\ \\beta_ {t} & \\beta_ {t} & \\beta_ {t} & \\alpha_ {t} + \\beta_ {t} & 0 \\\\ \\gamma_ {t} & \\gamma_ {t} & \\gamma_ {t} & \\gamma_ {t} & 1 \\end{array} \\right]. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 522, + 376, + 890, + 465 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "$(\\alpha_{t}, \\beta_{t}, \\gamma_{t})$ is carefully designed so that $z_{t}$ converges to the [MASK] token for sufficiently large $t$ . During testing, we start from $\\mathbf{z}_{T}$ filled with [MASK] tokens and iteratively sample new set of tokens $\\mathbf{z}_{t-1}$ from $p_{\\theta}(\\mathbf{z}_{t-1} | \\mathbf{z}_{t})$ .", + "bbox": [ + 500, + 474, + 890, + 536 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Unconditional Layout Generation", + "text_level": 1, + "bbox": [ + 500, + 544, + 795, + 561 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "A layout $l$ is a set of elements represented by $l = \\{(c_1, b_1), \\ldots, (c_E, b_E)\\}$ . $E \\in \\mathbb{N}$ is the number of elements in the layout. $c_i \\in \\{1, \\ldots, C\\}$ is categorical information of the $i$ -th element in the layout. $b_i \\in [0, 1]^4$ is the bounding box of the $i$ -th element in normalized coordinates, where the first two values indicate the center location, and the last two indicate the width and height. Following previous works [2, 11, 20] that regard layout generation as generating a sequence of tokens, we quantize each value in $b_i$ and obtain $[x_i, y_i, w_i, h_i]^\\top \\in \\{1, \\ldots, B\\}^4$ , where $B$ is a number of the bins. The layout $l$ is now represented by $l = \\{(c_1, x_1, y_1, w_1, h_1), \\ldots\\}$ .", + "bbox": [ + 496, + 568, + 890, + 750 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this work, we corrupt a layout in a modality-wise manner in the forward process, and we denoise the corrupted layout while considering all elements and modalities in the reverse process, as we illustrate in Fig. 2. Similarly to D3PM [3], we parameterize $p_{\\theta}$ by a Transformer encoder [40], which processes an ordered 1D sequence. To process $l$ by $p_{\\theta}$ while avoiding the order dependency issue [20], we randomly shuffle $l$ in element-wise manner and then flatten it to produce $l_{\\mathrm{flat}} = (c_1, x_1, y_1, w_1, h_1, c_2, x_2, \\ldots)$ .", + "bbox": [ + 496, + 750, + 890, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "10169", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Variable length generation Existing diffusion models generate fixed-dimensional data and are not directly applicable to the layout generation because the number of elements in each layout varies. To handle this, we introduce a [PAD] token and define a maximum number of elements in the layout as $M \\in \\mathbb{N}$ . Each layout is fixed-dimensional data composed of $5M$ tokens by appending $5(M - E)$ [PAD] tokens. [PAD] is treated similarly to the ordinary token in VQDiffusion and $\\mathbf{Q}_t$ 's dimension becomes $(K + 2) \\times (K + 2)$ .", + "bbox": [ + 76, + 90, + 472, + 243 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Modality-wise diffusion Discrete state-space models assume that all the standard tokens are switchable by corruption. However, layout tokens comprise a disjoint set of token groups for each attribute in the element. For example, applying the transition rule Eq. (5) may change a token representing an element's category to another token representing the width. To avoid such invalid switching, we propose to apply disjoint corruption matrices $\\mathbf{Q}_t^c,\\mathbf{Q}_t^x,\\mathbf{Q}_t^y,\\mathbf{Q}_t^w,\\mathbf{Q}_t^h$ for tokens representing different attributes $c,x,y,w,h$ , as we show in Fig. 2. The size of each matrix is $(C + 2)\\times$ $(C + 2)$ for $\\mathbf{Q}_t^c$ and otherwise $(B + 2)\\times (B + 2)$ , where $+2$ is for [PAD] and [MASK].", + "bbox": [ + 76, + 263, + 472, + 446 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Adaptive Quantization The distribution of the position and size information in layouts is highly imbalanced; e.g., elements tend to be aligned to either left, center, or right. Applying uniform quantization to those quantities as in existing layout generation models [2, 11, 20] results in the loss of information. As a pre-processing, we propose to apply a classical clustering algorithm, such as KMeans [29] on $x$ , $y$ , $w$ , and $h$ independently to obtain balanced position and size tokens for each dataset. We show in Sec. 4.7 how quantization strategy affects the resulting quality.", + "bbox": [ + 76, + 465, + 472, + 619 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Decoupled Positional Encoding Previous works apply standard positional encoding to a flattened sequence of layout tokens $l_{\\mathrm{flat}}$ [2, 11, 20]. We argue that this flattening approach could lose the structure information of the layout and lead to inferior generation performance. In layout, each token has two types of indices: $i$ -th element and $j$ -th attribute. We empirically find that independently applying positional encoding to those indices improves final generation performance, which we study in Sec. 4.7.", + "bbox": [ + 76, + 638, + 472, + 776 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Conditional Generation", + "text_level": 1, + "bbox": [ + 76, + 786, + 295, + 801 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We elaborate on solving various conditional layout generation tasks using pre-trained frozen LayoutDM. We inject conditional information in both the initial state $\\mathbf{z}_T$ and sampled states $\\{\\mathbf{z}_t\\}_{t=0}^{T-1}$ during inference but do not modify the denoising network $p_\\theta$ . The actual implementation of the injection differs by the type of conditions.", + "bbox": [ + 75, + 809, + 470, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Strong Constraints The most typical condition is partially known layout fields. Let $\\mathbf{z}^{\\mathrm{known}} \\in \\mathbb{Z}^{N}$ contain the known fields and $\\mathbf{m} \\in \\{0,1\\}^{N}$ be a mask vector denoting the known and unknown field as 1 and 0, respectively. In each timestep $t$ , we sample $\\hat{\\mathbf{z}}_{t-1}$ from $p_{\\theta}(\\mathbf{z}_{t-1}|\\mathbf{z}_t)$ in Eq. (3) and then inject the condition by $\\mathbf{z}_{t-1} = \\mathbf{m} \\odot \\mathbf{z}^{\\mathrm{known}} + (\\mathbf{1} - \\mathbf{m}) \\odot \\hat{\\mathbf{z}}_{t-1}$ , where $\\mathbf{1}$ denotes a $N$ -dimensional all-ones vector and $\\odot$ denotes element-wise product.", + "bbox": [ + 496, + 90, + 893, + 213 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Weak Constraints We may impose a weaker constraint during generation, such as an element in the center. We offer a way to impose such constraints in a unified framework without additional training or external neural network models. We propose to adjust the logits to inject weak constraints in log probability space by", + "bbox": [ + 496, + 229, + 893, + 321 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\log \\hat {p} _ {\\theta} \\left(\\boldsymbol {z} _ {t - 1} | \\boldsymbol {z} _ {t}\\right) \\propto \\log p _ {\\theta} \\left(\\boldsymbol {z} _ {t - 1} | \\boldsymbol {z} _ {t}\\right) + \\lambda_ {\\pi} \\pi , \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 549, + 327, + 890, + 343 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\pi \\in \\mathbb{R}^{N\\times K}$ is a prior term that weights the desired outputs, and $\\lambda_{\\pi}\\in \\mathbb{R}$ is a hyper-parameter. The prior term can be defined either hard-coded (Refinement in Sec. 4.5) or through differentiable loss functions (Relationship in Sec. 4.5). Let $\\{\\mathcal{L}_i\\}_{i = 1}^L$ be a set of differentiable loss functions given the prediction, the later prior definition can be written by:", + "bbox": [ + 496, + 349, + 893, + 455 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {\\pi} = - \\nabla_ {p _ {\\theta} \\left(\\boldsymbol {z} _ {t - 1} \\mid \\boldsymbol {z} _ {t}\\right)} \\sum_ {i = 1} ^ {L} \\mathcal {L} _ {i} \\left(p _ {\\theta} \\left(\\boldsymbol {z} _ {t - 1} \\mid \\boldsymbol {z} _ {t}\\right)\\right). \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 553, + 460, + 890, + 503 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Although the formulation of Eq. (7) resembles steering diffusion models by gradients from external models [7, 25], our primal focus is incorporating classical hand-crafted energies for aesthetics principles of layout [32] that do not depend on an external model. In practice, we tune the hyperparameters for imposing weak constraints, such as $\\lambda_{\\pi}$ . Note that these hyper-parameters are only for inference and are easier to tune than the other training hyper-parameters.", + "bbox": [ + 496, + 508, + 893, + 630 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Experiment", + "text_level": 1, + "bbox": [ + 500, + 641, + 624, + 657 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Datasets", + "text_level": 1, + "bbox": [ + 500, + 666, + 602, + 680 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We use two large-scale datasets for comparison, Rico [5] and PubLayNet [45]. As we mention in Sec. 3.2, an element in a layout for each dataset is described by the five attributes. For preprocessing, we set the maximum number of elements per layout $M$ to 25. If a layout contains more elements, we discard the whole layout.", + "bbox": [ + 496, + 688, + 890, + 779 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We provide an overview of each dataset. Rico is a dataset of user interface designs for mobile applications containing 25 element categories such as text button, toolbar, and icon. We divide the dataset into 35,851 / 2,109 / 4,218 samples for train, validation, and test splits. PubLayNet is a dataset of research papers containing five element categories, such as table, image, and text. We divide the dataset into 315,757 / 16,619 / 11,142 samples for train, validation, and test splits.", + "bbox": [ + 496, + 780, + 893, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "10170", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. Evaluation Metrics", + "text_level": 1, + "bbox": [ + 76, + 90, + 261, + 104 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We employ two primary metrics: FID and Maximum IoU (Max.). These metrics take into account both fidelity and diversity [12], which are two mutually complementary properties widely used in evaluating generative models. FID [12] captures the similarity of generated data to real ones in feature space. We employ an improved feature extraction model for layouts [19] instead of a conventional method [21] to compute FID. Maximum IoU [19] measures the conditional similarity between generated and real layouts. The similarity is measured by computing optimal matching that maximizes average IoU between generated and real layouts that have an identical set of categories. For reference, we show the FID and Maximum IoU computed between the validation and test data as Real data.", + "bbox": [ + 75, + 113, + 472, + 325 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Tasks and Baselines", + "text_level": 1, + "bbox": [ + 76, + 334, + 266, + 348 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We test LayoutDM on six tasks for evaluation.", + "bbox": [ + 96, + 357, + 403, + 372 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Unconditional generates layouts without any conditional input or constraint.", + "bbox": [ + 76, + 372, + 468, + 401 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Category $\\rightarrow$ size+position (C $\\rightarrow$ S + P) is a generation task conditioned on the category of each element [20].", + "bbox": [ + 76, + 402, + 468, + 431 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Category $^+$ size $\\rightarrow$ position $(\\mathbf{C} + \\mathbf{S}\\rightarrow \\mathbf{P})$ is conditioned on the category and size of each element.", + "bbox": [ + 76, + 433, + 468, + 462 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Completion is conditioned on a small number of elements whose attributes are all known. Given a complete layout, we randomly sample from $0\\%$ to $20\\%$ of elements.", + "bbox": [ + 76, + 463, + 468, + 508 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Refinement is conditioned on a noisy layout in which only geometric information is perturbed [36]. Following RUITE [36], we synthesize the input layout by adding random noise to the size and position of each element. We sample noise from a standard normal distribution with a mean of 0 and a variance of 0.01.", + "bbox": [ + 76, + 508, + 468, + 598 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Relationship is conditioned on the category of each element and some relationship constraints between the elements [21]. Following CLG-LO [19], we employ the size and location relationships and randomly sample $10\\%$ relationships between elements for the experiment.", + "bbox": [ + 76, + 598, + 468, + 672 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The first four tasks handle basic layout fields. We include a few task-agnostic models for comparison using existing controllable layout generation methods or simple adaptation of generative models in the following:", + "bbox": [ + 76, + 674, + 468, + 734 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "LayoutTrans is a simple autoregressive model [11] trained on a element-level shuffled layout, following [33]. We set a variable generation order to $c \\to w \\to h \\to x \\to y$ .", + "bbox": [ + 76, + 734, + 468, + 780 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "MaskGIT* is originally a non-autoregressive model for unconditional fixed-length data generation [4]. We use [PAD] to enable variable-length generation.", + "bbox": [ + 76, + 780, + 468, + 825 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "BLT is a non-autoregressive model with layout-specific decoding strategy [20].", + "bbox": [ + 76, + 825, + 468, + 854 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "BART is a denoising autoencoder that can solve both comprehension and generation tasks based on Transformer encoder-decoder backbone [22]. We randomly generate a", + "bbox": [ + 76, + 854, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "number of [MASK] tokens from a uniform distribution between one and the sequence length, and perform masking based on the number.", + "bbox": [ + 496, + 90, + 890, + 135 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "VQDiffusion* is a diffusion-based model originally for text-to-image generation [9]. We adapt the model for layout using $K = C + 4B + 2$ tokens, including [PAD].", + "bbox": [ + 496, + 136, + 890, + 181 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.4. Implementation Details", + "text_level": 1, + "bbox": [ + 500, + 195, + 718, + 210 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We re-implement most of the models since there are few official implementations publicly available except [11, 19, 20] $^2$ . We train all the models on the two datasets with three independent trials and report the average of the results.", + "bbox": [ + 496, + 220, + 890, + 280 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "LayoutDM follows VQDiffusion for hyper-parameters unless specified, such as configurations for $p_{\\theta}$ and the transition matrix parameters i.e. $\\alpha_{t}$ and $\\gamma_{t}$ . We set the loss weight $\\lambda = 0.1$ (in Eq. (4)) and the diffusion timesteps $T = 100$ . For optimization, we use AdamW [27] with learning rate of $5.0 \\times 10^{-4}$ , $\\beta_{1} = 0.9$ , and $\\beta_{2} = 0.98$ .", + "bbox": [ + 496, + 281, + 890, + 372 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Many models, including LayoutDM, use Transformer [40] encoder backbone. We define a shared configuration as follows: 4 layers, 8 attention heads, 512 embedding dimensions, 2048 hidden dimensions, and 0.1 dropout rate. For other models with extra modules, we adjust the number of hidden dimensions to roughly match the number of parameters for a fair comparison. We randomly shuffle elements in the layout to avoid fixed-order generation during training. We search best hyper-parameters to obtain the best FID using the validation set.", + "bbox": [ + 496, + 375, + 890, + 525 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.5.Quantitative Evaluation", + "text_level": 1, + "bbox": [ + 500, + 537, + 720, + 554 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$\\mathbf{C} \\rightarrow \\mathbf{S} + \\mathbf{P}$ , $\\mathbf{C} + \\mathbf{S} \\rightarrow \\mathbf{P}$ , Completion In these tasks, we inject conditions by masking. We summarize comparisons in Tab. 1. As task-specific models, we include Layout-VAE [16], NDN-none [21], and LayoutGAN++ [19] for $\\mathbf{C} \\rightarrow \\mathbf{S} + \\mathbf{P}$ . We also adapt these models for $\\mathbf{C} + \\mathbf{S} \\rightarrow \\mathbf{P}$ . LayoutDM outperforms other models except LayoutTrans [11] in completion. The significant performance gap between LayoutDM and VQDiffusion* suggests the contribution of our proposals to go beyond the simple discrete diffusion models discussed in Sec. 3.2. Results in the completion suggest that a combination of padding and diffusion models is the primal key to the generation quality. We find that FID and Maximum IoU are not highly correlated only in the completion task. We conjecture that Maximum IoU may become unstable when categories are also predicted, unlike the $\\mathbf{C} \\rightarrow \\mathbf{S} + \\mathbf{P}$ and $\\mathbf{C} + \\mathbf{S} \\rightarrow \\mathbf{P}$ tasks where categories are given.", + "bbox": [ + 496, + 563, + 890, + 804 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Fig. 3 shows the qualitative results of some models, including LayoutDM. We can see that LayoutDM generates", + "bbox": [ + 496, + 805, + 890, + 837 + ], + "page_idx": 4 + }, + { + "type": "page_footnote", + "text": "2 Unfortunately, most datasets have no official train-val-test splits, and previous approaches work on different splits and pre-processing strategies. Furthermore, models for FID computation also vary. Thus, we cannot directly compare our results with the reported figure in the literature.", + "bbox": [ + 496, + 849, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "10171", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/9510b0f2095ee1530c200932420c0ee6ef7701c86ed982479fe4cd7c1e146789.jpg", + "table_caption": [ + "Table 1. Quantitative comparison in conditional generation given partially known fields. Top two results are highlighted in bold and underline, respectively. $\\dagger$ indicates the results of BLT trained with [PAD] as an additional vocabulary since the original model cannot perform unordered completion in practice." + ], + "table_footnote": [], + "table_body": "
ModelTask DatasetCategory → Size+PositionCategory+Size → PositionCompletion
Rico FID ↓PubLayNet Max. ↑FID ↓Max. ↑Rico FID ↓Max. ↑PubLayNet FID ↓Max. ↑Rico FID ↓Max. ↑PubLayNet FID ↓Max. ↑
Task-specific models
LayoutVAE [16]33.30.24926.00.31630.60.28327.50.315-----
NDN-none [21]28.40.15861.10.16262.80.21969.40.222-----
LayoutGAN++ [19]6.840.26724.00.2636.220.3489.940.342-----
Task-agnostic models
LayoutTrans [11]5.570.22314.10.2723.730.32316.90.3203.710.5378.360.451
MaskGIT* [4]26.10.26217.20.3198.050.3205.860.38033.50.53319.70.484
BLT [20]17.40.20272.10.2154.480.3405.100.387117†0.471†131†0.345†
BART [22]3.970.2539.360.3203.180.3345.880.3758.870.5279.580.446
VQDiffusion* [9]4.340.25210.30.3193.210.3317.130.37411.00.54111.10.373
LayoutDM3.550.2777.950.3102.220.3924.250.3819.000.5767.650.377
Real data1.850.6916.250.4381.850.6916.250.4381.850.6916.250.438
", + "bbox": [ + 84, + 133, + 885, + 392 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/c052df74a74cfd37cb53b40775420b90ea54e35f7bf13c6dd0c79ad7654b3494.jpg", + "image_caption": [ + "Figure 3. Comparison in conditional generation given partially known fields." + ], + "image_footnote": [], + "bbox": [ + 89, + 401, + 488, + 666 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/2523a6d5fc751ca702791f586038145ff1666f3f1d0aab5a97cb4d0b892de453.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 493, + 401, + 870, + 666 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "high-quality layouts with fewer layout aesthetics violations, such as misalignment and overlap, given diverse conditions.", + "bbox": [ + 75, + 719, + 470, + 750 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Unconditional Generation Tab. 2 summarizes the results of unconditional generation. Unconditional layout generation methods often assume fixed order for element generation e.g. top-to-bottom rather than random order for better generation quality by constraining the prediction. For reference, we additionally report the results of LayoutTrans [11] trained on the fixed element order (LayoutTrans-fixed). Although we design LayoutDM's primarily for conditional", + "bbox": [ + 75, + 779, + 472, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "generation, LayoutDM achieves the best FID under random element order setting. We conjecture that BLT's poor performance is due to train-test mask distribution inconsistency caused by their hierarchical masking strategy for training. BLT masks a randomly sampled number of fields from a single semantic group i.e. category, position, or size. However, decoding starts with all masked tokens in inference. The alignment metric of Real data stays at 0.109 in Rico. Too small alignment values of LayoutTrans and MaskGIT can be a signal of producing trivial outputs in Rico.", + "bbox": [ + 496, + 719, + 893, + 872 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "10172", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/c76e919a4a96772a0a504778814150beeb5eab97157f6c858340091beebba9ef.jpg", + "table_caption": [ + "Table 2. Quantitative comparison in unconditional generation. Top two results are highlighted in bold and underline, respectively." + ], + "table_footnote": [], + "table_body": "
ModelDatasetRicoPubLayNet
FID ↓Align. ↓FID ↓Align. ↓
LayoutTrans-fixed [11]6.470.13317.10.084
LayoutTrans [11]7.630.06813.90.127
MaskGIT* [4]52.10.01527.10.101
BLT [20]88.21.0301160.153
BART [22]11.90.09016.60.116
VQDiffusion* [9]7.460.17815.40.193
LayoutDM6.650.16213.90.195
Real data1.850.1096.250.0214
", + "bbox": [ + 78, + 122, + 475, + 296 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/5f430fb0cdbae0563c97c061b03b566d1be2cb4021f8cb093e764a12cf18cb8c.jpg", + "table_caption": [ + "Table 3. Quantitative comparison in the refinement task. Top two results are highlighted in bold and underline, respectively." + ], + "table_footnote": [], + "table_body": "
DatasetRicoPubLayNet
ModelFID ↓ Max. ↑ Sim ↑ FID ↓ Max. ↑ Sim ↑
Task-specific models
RUIT [36]3.230.4210.2216.390.4150.174
Task-agnostic models
Noisy input1340.2130.1771300.2420.147
LayoutDM2.770.3700.2056.750.3520.149
w/o logit adj.3.550.2770.1687.950.3100.127
Real data1.850.6910.2606.250.4380.216
", + "bbox": [ + 84, + 345, + 462, + 506 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6af11653bd84344e7d04e93f7d09d49e0da29777cf7d1c1ce0fd3be9fc5c7cab.jpg", + "image_caption": [ + "Figure 4. Qualitative comparison in the refinement task." + ], + "image_footnote": [], + "bbox": [ + 125, + 529, + 415, + 705 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Refinement Our LayoutDM performs this task with a combination of the strong constraints of element categories, i.e., setting $z^{\\mathrm{known}} = \\{(c_1, [\\mathrm{MASK}], \\dots, [\\mathrm{MASK}]), \\dots\\}$ , and the weak constraints that geometric outputs appear near noisy inputs. As an example of the weak constraint, we describe a constraint that imposes the x-coordinate estimate of $i$ -th element close to the noisy continuous observation $\\hat{x}_i$ . We denote a sliced vector of the prior term $\\pi$ in Eq. (6) that corresponds to the x-coordinate of $i$ -th element as $\\pi_x^i \\in \\mathbb{R}^K$", + "bbox": [ + 75, + 763, + 468, + 902 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5b12d31d160cafd34bd1efc8a436c274d7341b7870cc0d290efc1b9fcf0cc73d.jpg", + "image_caption": [ + "Figure 5. Quality-violation trade-off in the relationship task. Lower scores indicate better performance for both metrics." + ], + "image_footnote": [], + "bbox": [ + 504, + 89, + 875, + 270 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/1b4f46a108163d886a576dbef3e7e1739fa646f25df362e022a25e71c0e63fde.jpg", + "image_caption": [ + "Figure 6. Qualitative comparison in the relationship task." + ], + "image_footnote": [], + "bbox": [ + 503, + 321, + 880, + 491 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "and define by:", + "bbox": [ + 500, + 546, + 596, + 561 + ], + "page_idx": 6 + }, + { + "type": "equation", + "text": "\n$$\n\\left[ \\pi_ {x} ^ {i} \\right] _ {j} = \\left\\{ \\begin{array}{l l} 1 & \\text {i f} | \\operatorname {l o c} (j) - \\hat {x} _ {i} | < m \\text {a n d} j \\in X \\\\ 0 & \\text {o t h e r w i s e ,} \\end{array} \\right. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 539, + 571, + 890, + 613 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "where $m$ is a hyper-parameter indicating a margin, $X$ is a set of indices denoting tokens for $x$ in the vocabularies, and $\\mathrm{loc}(j)$ is a function that returns the centroid value of $j$ -th token in the vocabularies. We define similar constraints for the other geometric variables and elements.", + "bbox": [ + 496, + 625, + 890, + 698 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We summarize the performance in Tab. 3. We additionally report DocSim [34] (Sim) to measure the similarity of a predicted and its corresponding ground truth layout. Imposing noisy geometric fields as a weak prior significantly improves the masking-only model and makes the performance much closer to RUITE [36], which is a denoising model not applicable to other layout tasks. We compare some results in Fig. 4. Both LayoutDM and RUITE successfully recover complete layouts from non-trivially noisy layouts.", + "bbox": [ + 496, + 699, + 892, + 835 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Relationship We use Eq. (7) to incorporate the relational constraints during the sampling step of LayoutDM. We follow [19] to employ the loss functions penalizing size and", + "bbox": [ + 498, + 854, + 892, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "10173", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/748788104512bedf0b7a893cce4765d4207b9f95637a981d495cb79f9d69ce2a.jpg", + "image_caption": [ + "Figure 7. Speed-quality trade-off of different models for $\\mathrm{C + S\\to P}$" + ], + "image_footnote": [], + "bbox": [ + 78, + 88, + 468, + 275 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/c61cf820b752cd05e36d3e317c7a07f209367307c683022618bb3f5e1d51c028.jpg", + "table_caption": [ + "Table 4. Ablation study results on layout-specific modification in unconditional generation of Rico [5] dataset." + ], + "table_footnote": [], + "table_body": "
FID ↓Align. ↓
LayoutDM6.650.162
w/o modality-wise diff.7.320.156
w/o decoupled pos. enc.6.780.227
w/ uniform-quantization7.580.256
w/ percentile-quantization9.790.232
Real Data1.850.109
", + "bbox": [ + 119, + 373, + 419, + 502 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "location relationships between elements that do not match user specifications. We define the loss functions for continuous bounding boxes, and we have to convert the predicted discrete bounding boxes to continuous ones in a differentiable manner. Given estimated probabilities of discrete x-coordinates $p(x)$ , for example, we compute the continuous x-coordinate $\\bar{x}$ by $\\bar{x} = \\sum_{n\\in X}p(x = n)\\log (n)$ . Similar conversion applies to the other attributes. Empirically, we find that applying the logit adjustment multiple times (three times in our experiments) to each diffusion step moderately improves performance.", + "bbox": [ + 75, + 544, + 467, + 710 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We compare LayoutDM with two task-specific approaches: NDN-partial [21] and CLG-LO based on LayoutGAN++ [19]. We show the results in Fig. 5. We additionally report constraint violation error rates [19]. LayoutDM can control the strength of the logit adjustment as in Eq. (6) and produces an FID-violation trade-off curve. LayoutDM is comparable to NDN-partial in Rico and outperforms NDN-partial by a large margin in PubLayNet. Although LayoutDM is inferior to CLG-LO in both datasets, note that the average runtime of CLG-LO is 4.0s, which is much slower than 0.5s in LayoutDM. We show some results of LayoutDM in Fig. 6.", + "bbox": [ + 75, + 719, + 467, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.6. Speed-Quality Trade-off", + "text_level": 1, + "bbox": [ + 500, + 90, + 723, + 107 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Runtime is also essential for a controllable generation. We show a speed-quality trade-off curve for $\\mathrm{C + S\\rightarrow P}$ as shown in Fig. 7. The Transformer encoder-only models, such as LayoutDM and BLT, can achieve fast generation at the sacrifice of quality. We employ fast-sampling strategy employed in discrete diffusion models [3] for LayoutDM by $p_{\\theta}(z_{t - \\Delta}|\\boldsymbol {z}_t)\\propto \\sum_{\\tilde{\\boldsymbol{z}}_0}q(\\boldsymbol{z}_{t - \\Delta},\\boldsymbol {z}_t|\\tilde{\\boldsymbol{z}}_0)\\tilde{p}_{\\theta}(\\tilde{\\boldsymbol{z}}_0|\\boldsymbol {z}_t)$ , where $\\Delta \\in \\mathbb{N}$ indicates a step size for generation in $\\frac{T}{\\Delta}$ steps. Despite being a task-agnostic model, LayoutDM achieves the best quality-speed trade-off except for task-specific LayoutGAN++ [19] that runs under 10ms.", + "bbox": [ + 496, + 114, + 890, + 282 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.7. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 294, + 651, + 310 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We investigate whether techniques in Sec. 3.2 improve the performance. First, we evaluate a choice of quantization methods for the geometric fields of elements. Instead of KMeans, we compute centroids for the quantization by:", + "bbox": [ + 496, + 318, + 890, + 378 + ], + "page_idx": 7 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Uniform: This is dataset-agnostic quantization, which is popular in previous works [2, 11, 20]. Following [11], we choose $\\{0.0, \\frac{1}{B}, \\dots, \\frac{B - 1}{B}\\}$ and $\\{\\frac{1}{B}, \\dots, \\frac{B - 1}{B}, 1.0\\}$ for the position and size, respectively.", + "- Percentile: we sort the data into equally sized groups and obtain average values for each group as the centroids. This is dataset-specific quantization similar to KMeans." + ], + "bbox": [ + 500, + 380, + 890, + 484 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We show the result at the bottom of Tab. 4. We additionally report the Alignment metric (Align.) used in [19] since the choice of the quantization affects the alignment between elements. Compared to Linear and Percentile, KMeans quantization significantly improves both FID and Alignment. We confirm that our modality-wise diffusion and decoupled positional encoding both moderately improve the performance, as we show at the top half of Tab. 4.", + "bbox": [ + 496, + 486, + 890, + 607 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Discussion", + "text_level": 1, + "bbox": [ + 500, + 625, + 612, + 638 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "LayoutDM is based on diffusion models for discrete state-space. Using continuous state-space as in latent diffusion models [37] would be interesting. Extension of LayoutDM to handle various layout properties such as color [17] and image/text [41] is also appealing.", + "bbox": [ + 496, + 650, + 890, + 724 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We believe our proposed logit adjustment can incorporate more attributes. Attribute-conditional LayoutGAN [24] considers area, aspect ratio, and reading order of elements for fine-grained control. Since these attributes can be easily converted to the size and location relationship constraints, incorporating them with our LayoutDM is not very difficult.", + "bbox": [ + 496, + 726, + 890, + 816 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Potential negative impact Our model might be used to automatically generate the basic structure of fake websites or mobile applications, which could lead to scams or the spreading of misinformation.", + "bbox": [ + 496, + 839, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "10174", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 106 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Maneesh Agrawala, Wilmot Li, and Floraine Berthouzoz. Design principles for visual communication. 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In ICDAR, 2019. 1, 2, 4" + ], + "bbox": [ + 78, + 90, + 468, + 643 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "10176", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/LayoutDM_ Discrete Diffusion Model for Controllable Layout Generation/77614c7d-0145-49cc-9bc8-8f5b07a869f4_model.json b/2023/LayoutDM_ Discrete Diffusion Model for Controllable Layout Generation/77614c7d-0145-49cc-9bc8-8f5b07a869f4_model.json new file mode 100644 index 0000000000000000000000000000000000000000..76d72bfb9aaee8a2f35152fa35e34533499db146 --- /dev/null +++ b/2023/LayoutDM_ Discrete Diffusion Model for Controllable Layout Generation/77614c7d-0145-49cc-9bc8-8f5b07a869f4_model.json @@ -0,0 +1,2255 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.114, + 0.131, + 0.856, + 0.152 + ], + "angle": 0, + "content": "LayoutDM: Discrete Diffusion Model for Controllable Layout Generation" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.181, + 0.196, + 0.198 + ], + "angle": 0, + "content": "Naoto Inoue" + }, + { + "type": "text", + "bbox": [ + 0.237, + 0.181, + 0.369, + 0.198 + ], + "angle": 0, + "content": "Kotaro Kikuchi" + }, + { + "type": "text", + "bbox": [ + 0.411, + 0.181, + 0.562, + 0.198 + ], + "angle": 0, + "content": "Edgar Simo-Serra²" + }, + { + "type": "text", + "bbox": [ + 0.604, + 0.182, + 0.706, + 0.199 + ], + "angle": 0, + "content": "Mayu Otani" + }, + { + "type": "text", + "bbox": [ + 0.749, + 0.181, + 0.888, + 0.199 + ], + "angle": 0, + "content": "Kota Yamaguchi1" + }, + { + "type": "text", + "bbox": [ + 0.284, + 0.199, + 0.445, + 0.218 + ], + "angle": 0, + "content": "1CyberAgent, Japan" + }, + { + "type": "text", + "bbox": [ + 0.484, + 0.199, + 0.696, + 0.218 + ], + "angle": 0, + "content": "\\(^{2}\\)Waseda University, Japan" + }, + { + "type": "text", + "bbox": [ + 0.217, + 0.22, + 0.761, + 0.234 + ], + "angle": 0, + "content": "{inoue_naoto, kikuchi_kotaro_xa}@cyberagent.co.jp ess@waseda.jp" + }, + { + "type": "text", + "bbox": [ + 0.294, + 0.237, + 0.681, + 0.252 + ], + "angle": 0, + "content": "{otani_mayu, yamaguchi_kota}@cyberagent.co.jp" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.287, + 0.312, + 0.302 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.32, + 0.471, + 0.562 + ], + "angle": 0, + "content": "Controllable layout generation aims at synthesizing plausible arrangement of element bounding boxes with optional constraints, such as type or position of a specific element. In this work, we try to solve a broad range of layout generation tasks in a single model that is based on discrete state-space diffusion models. Our model, named LayoutDM, naturally handles the structured layout data in the discrete representation and learns to progressively infer a noiseless layout from the initial input, where we model the layout corruption process by modality-wise discrete diffusion. For conditional generation, we propose to inject layout constraints in the form of masking or logit adjustment during inference. We show in the experiments that our LayoutDM successfully generates high-quality layouts and outperforms both task-specific and task-agnostic baselines on several layout tasks.\\(^{1}\\)" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.593, + 0.208, + 0.608 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.619, + 0.47, + 0.846 + ], + "angle": 0, + "content": "Graphic layouts play a critical role in visual communication. Automatically creating a visually pleasing layout has tremendous application benefits that range from authoring of printed media [45] to designing application user interface [5], and there has been a growing research interest in the community. The task of layout generation considers the arrangement of elements, where each element has a tuple of attributes, such as category, position, or size, and depending on the task setup, there could be optional control inputs that specify part of the elements or attributes. Due to the structured nature of layout data, it is crucial to consider relationships between elements in a generation. For this reason, current generation approaches either build an autoregressive model [2, 11] or develop a dedicated inference strategy to explicitly consider relationships [19-21]." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.847, + 0.469, + 0.862 + ], + "angle": 0, + "content": "In this paper, we propose to utilize discrete state-space" + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.286, + 0.875, + 0.539 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.558, + 0.892, + 0.628 + ], + "angle": 0, + "content": "Figure 1. Overview of LayoutDM. Top: LayoutDM is trained to gradually generate a complete layout from a blank state in discrete state space. Bottom: During sampling, we can steer LayoutDM to perform various conditional generation tasks without additional training or external models." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.657, + 0.892, + 0.854 + ], + "angle": 0, + "content": "diffusion models [3, 9, 14] for layout generation tasks. Diffusion models have shown promising performance for various generation tasks, including images and texts [13]. We formulate the diffusion process for layout structure by modality-wise discrete diffusion, and train a denoising backbone network to progressively infer the complete layout with or without conditional inputs. To support variable-length layout data, we extend the discrete state-space with a special PAD token instead of the typical end-of-sequence token used in autoregressive models. Our model can incorporate complex layout constraints via logit adjustment, so that we can refine an existing layout or impose relative size constraints between elements without additional training." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We discuss two key advantages of LayoutDM over existing models for conditional layout generation. Our model avoids the immutable dependency chain issue [20] that hap" + }, + { + "type": "page_footnote", + "bbox": [ + 0.078, + 0.875, + 0.424, + 0.901 + ], + "angle": 0, + "content": "1Please find the code and models at: https://cyberagentailab.github.io/layout-dm." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "10167" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.227 + ], + "angle": 0, + "content": "pens in autoregressive models [11]. Autoregressive models fail to perform conditional generation when the condition disagrees with the pre-defined generation order of elements and attributes. Unlike non-autoregressive models [20], our model can generate variable-length elements. We empirically show in Sec. 4.5 that naively extending non-autoregressive models by padding results in suboptimal variable length generation while padding combined with our diffusion formulation leads to significant improvement." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.228, + 0.468, + 0.364 + ], + "angle": 0, + "content": "We evaluate LayoutDM on various layout generation tasks tackled by previous works [20, 21, 33, 36] using two large-scale datasets, Rico [5] and PubLayNet [45]. LayoutDM outperforms task-agnostic baselines in the majority of cases and shows promising performance compared with task-specific baselines. We further conduct an ablation study to prove the significant impact of our design choices in LayoutDM, including quantization of continuous variables and positional embedding." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.365, + 0.389, + 0.379 + ], + "angle": 0, + "content": "We summarize our contributions as follows:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.381, + 0.469, + 0.426 + ], + "angle": 0, + "content": "- We formulate the discrete diffusion process for layout generation and propose a modality-wise diffusion and a padding approach to model highly structured layout data." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.428, + 0.468, + 0.47 + ], + "angle": 0, + "content": "- We propose to inject complex layout constraints via masking and logit adjustment during the inference, so that our model can solve diverse tasks in a single model." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.472, + 0.468, + 0.501 + ], + "angle": 0, + "content": "- We empirically show solid performance for various conditional layout generation tasks on public datasets." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.381, + 0.469, + 0.501 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.518, + 0.219, + 0.533 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.544, + 0.26, + 0.56 + ], + "angle": 0, + "content": "2.1. Layout Generation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.568, + 0.468, + 0.734 + ], + "angle": 0, + "content": "Studies on automatic layout generation have appeared several times in literature [1, 26, 32, 42]. Layout tasks are commonly observed in design applications, including magazine covers, posters, presentation slides, application user interface, or banner advertising [5, 8, 10, 18, 35, 41, 42, 44]. Recent approaches to layout generation consider both unconditional generation [2, 11, 15, 16] and conditional generation in various setups, such as conditional inputs of category or size [19-21, 23], relational constraints [19, 21], element completion [11], and refinement [36]. Some attempt at solving multiple tasks in a single model [20, 33]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.468, + 0.901 + ], + "angle": 0, + "content": "BLT [20] points out that the recent autoregressive decoders [2, 11] are not fully capable of considering partial inputs, i.e. known elements or attributes, during generation because they have a fixed generation order. BLT addresses the conditional generation by fill-in-the-blank task formulation using a bidirectional Transformer encoder similar to masked language models [6]. However, BLT cannot solve layout completion demonstrated in the decoder-based models because of the requirement of the known number of elements. Our LayoutDM enjoys the best of both worlds and supports a broader range of conditional generation tasks in" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.604, + 0.106 + ], + "angle": 0, + "content": "a single model." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.107, + 0.892, + 0.273 + ], + "angle": 0, + "content": "Another layout-specific consideration is the complex user-specified constraints, such as the positional requirements between two boxes (e.g., a header box should be on top of a paragraph box). Earlier approaches [31, 32, 43] propose hand-crafted cost functions representing the violation degree of aesthetic constraints so that those constraints guide the optimization process of layout inference. CLG-LO [19] proposes an aesthetically constrained optimization framework for pre-trained GANs. Our LayoutDM solves such constrained generation tasks on top of the task-agnostic iterative prediction via logit adjustment." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.281, + 0.734, + 0.295 + ], + "angle": 0, + "content": "2.2. Discrete Diffusion Models" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.304, + 0.892, + 0.456 + ], + "angle": 0, + "content": "Diffusion models [38] are generative models characterized by a forward and reverse Markov process. The forward process corrupts the data into a sequence of increasingly noisy variables. The reverse process gradually denoises the variables toward the actual data distribution. Diffusion models are stable to train and achieve faster sampling than autoregressive models by parallel iterative refinement. Recently, many approaches have learned the reverse process by a neural network and show strong empirical performance [7, 13, 39] in continuous state spaces, such as images." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.456, + 0.892, + 0.636 + ], + "angle": 0, + "content": "Discrete state spaces are a natural representation of discrete variables, such as text. D3PM [3] extends the pioneering work of Hoogeboom et al. [14] to structured categorical corruption processes for diffusion models in discrete state spaces, while maintaining the advantages of diffusion models for continuous state spaces. VQDiffusion [9] develops a corruption approach called mask-and-replace, so as to avoid accumulated prediction errors that are common in models based on iterative prediction. Following the corruption model of VQDiffusion, we carefully design a modality-wise corruption process for layout tasks that involve tokens from disjoint sets of vocabulary per modality." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.637, + 0.892, + 0.743 + ], + "angle": 0, + "content": "Several studies consider a conditional input to the inference process of diffusion models. Some approaches alter the reverse diffusion iteration to carefully inject given conditions for free-form image inpainting [28] or image editing by strokes or composition [30]. We extend the discrete state-space diffusion models via hard masking or logit adjustment to support the conditional generation of layouts." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.755, + 0.617, + 0.772 + ], + "angle": 0, + "content": "3. LayoutDM" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Our LayoutDM builds on discrete-state space diffusion models [3, 9]. We first briefly review the fundamental of discrete diffusion models in Sec. 3.1. Sec. 3.2 explains our approach to layout generation within the diffusion framework while discussing features inherent in layout compared with text. Sec. 3.3 discusses how we extend denoising steps to perform various conditional layout generation by imposing conditions in each step of the reverse process." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10168" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.077, + 0.091, + 0.417, + 0.108 + ], + "angle": 0, + "content": "3.1. Preliminary: Discrete Diffusion Models" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.114, + 0.474, + 0.283 + ], + "angle": 0, + "content": "Diffusion models [38] are generative models characterized by a forward and reverse Markov process. While many diffusion models are defined on continuous space with Gaussian corruption, D3PM [3] introduces a general diffusion framework for categorical variables designed primarily for texts. Let \\( T \\in \\mathbb{N} \\) be a total timestep of the diffusion model, we first explain the forward diffusion process. For a scalar discrete variable with \\( K \\) categories \\( z_{t} \\in \\{1,2,\\dots,K\\} \\) at timestep \\( t \\in \\mathbb{N} \\), probabilities that \\( z_{t-1} \\) transits to \\( z_{t} \\) are defined by using a transition matrix \\( Q_{t} \\in [0,1]^{K \\times K} \\), with \\( [Q_{t}]_{mn} = q(z_{t} = m|z_{t-1} = n) \\)," + }, + { + "type": "equation", + "bbox": [ + 0.165, + 0.294, + 0.47, + 0.312 + ], + "angle": 0, + "content": "\\[\nq \\left(z _ {t} \\mid z _ {t - 1}\\right) = \\boldsymbol {v} \\left(z _ {t}\\right) ^ {\\top} \\mathbf {Q} _ {t} \\boldsymbol {v} \\left(z _ {t - 1}\\right), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.315, + 0.47, + 0.392 + ], + "angle": 0, + "content": "where \\(\\pmb{v}(z_t) \\in \\{0,1\\}^K\\) is a column one-hot vector of \\(z_{t}\\). The categorical distribution over \\(z_{t}\\) given \\(z_{t-1}\\) is computed by a column vector \\(\\mathbf{Q}_t \\pmb{v}(z_{t-1}) \\in [0,1]^K\\). Assuming the Markov property, we can derive \\(q(z_t|z_0) = \\pmb{v}(z_t)^{\\top} \\overline{\\mathbf{Q}}_t \\pmb{v}(z_0)\\) where \\(\\overline{\\mathbf{Q}}_t = \\mathbf{Q}_t \\mathbf{Q}_{t-1} \\cdots \\mathbf{Q}_1\\) and:" + }, + { + "type": "equation", + "bbox": [ + 0.097, + 0.399, + 0.469, + 0.48 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} q \\left(z _ {t - 1} \\mid z _ {t}, z _ {0}\\right) = \\frac {q \\left(z _ {t} \\mid z _ {t - 1} , z _ {0}\\right) q \\left(z _ {t - 1} \\mid z _ {0}\\right)}{q \\left(z _ {t} \\mid z _ {0}\\right)} \\\\ = \\frac {\\left(\\boldsymbol {v} \\left(z _ {t}\\right) ^ {\\top} \\mathbf {Q} _ {t} \\boldsymbol {v} \\left(z _ {t - 1}\\right)\\right) \\left(\\boldsymbol {v} \\left(z _ {t - 1}\\right) ^ {\\top} \\overline {{\\mathbf {Q}}} _ {t - 1} \\boldsymbol {v} \\left(z _ {0}\\right)\\right)}{\\boldsymbol {v} \\left(z _ {t}\\right) ^ {\\top} \\overline {{\\mathbf {Q}}} _ {t} \\boldsymbol {v} \\left(z _ {0}\\right)}. \\tag {2} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.486, + 0.47, + 0.56 + ], + "angle": 0, + "content": "Note that due to the Markov property, \\( q(z_{t}|z_{t - 1},z_{0}) = q(z_{t}|z_{t - 1}) \\). When we consider \\( N \\)-dimensional variables \\( z_{t}\\in \\{1,2,\\dots ,K\\}^{N} \\), the corruption is applied to each variable \\( z_{t} \\) independently. In the following, we explain with \\( N \\)-dimensional variables \\( z_{t} \\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.562, + 0.471, + 0.698 + ], + "angle": 0, + "content": "In contrast to the forward process, the reverse denoising process considers a conditional distribution of \\( \\mathbf{z}_{t-1} \\) over \\( \\mathbf{z}_t \\) by a neural network \\( p_{\\theta}(\\mathbf{z}_{t-1}|\\mathbf{z}_t) \\in [0,1]^{N \\times K} \\). \\( \\mathbf{z}_{t-1} \\) is sampled according to this distribution. Note that the typical implementation is to predict unnormalized log probabilities \\( \\log p_{\\theta}(\\mathbf{z}_{t-1}|\\mathbf{z}_t) \\) by a stack of bidirectional Transformer encoder blocks. D3PM uses a neural network \\( \\tilde{p}_{\\theta}(\\tilde{\\mathbf{z}}_0|\\mathbf{z}_t) \\), combines it with the posterior \\( q(\\mathbf{z}_{t-1}|\\mathbf{z}_t,\\mathbf{z}_0) \\), and sums over possible \\( \\tilde{\\mathbf{z}}_0 \\) to obtain the following parameterization:" + }, + { + "type": "equation", + "bbox": [ + 0.122, + 0.705, + 0.47, + 0.737 + ], + "angle": 0, + "content": "\\[\np _ {\\theta} \\left(\\boldsymbol {z} _ {t - 1} | \\boldsymbol {z} _ {t}\\right) \\propto \\sum_ {\\tilde {\\boldsymbol {z}} _ {0}} q \\left(\\boldsymbol {z} _ {t - 1} | \\boldsymbol {z} _ {t}, \\tilde {\\boldsymbol {z}} _ {0}\\right) \\tilde {p} _ {\\theta} \\left(\\tilde {\\boldsymbol {z}} _ {0} | \\boldsymbol {z} _ {t}\\right). \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.745, + 0.47, + 0.79 + ], + "angle": 0, + "content": "In addition to the commonly used variational lower bound objective \\(\\mathcal{L}_{\\mathrm{vb}}\\), D3PM introduces an auxiliary denoising objective. The overall objective is as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.125, + 0.799, + 0.47, + 0.834 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\lambda} = \\mathcal {L} _ {\\mathrm {v b}} + \\lambda \\underset { \\begin{array}{c} \\boldsymbol {z} _ {t} \\sim q (\\boldsymbol {z} _ {t} | \\boldsymbol {z} _ {0}) \\\\ \\boldsymbol {z} _ {0} \\sim q (\\boldsymbol {z} _ {0}) \\end{array} } {\\mathbb {E}} \\left[ - \\log \\tilde {p} _ {\\theta} \\left(\\boldsymbol {z} _ {0} | \\boldsymbol {z} _ {t}\\right) \\right], \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.841, + 0.469, + 0.855 + ], + "angle": 0, + "content": "where \\(\\lambda\\) is a hyper-parameter to balance the two loss terms." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Although D3PM proposes many variants of \\(\\mathbf{Q}_t\\), VQD-iffusion [9] offers an improved version of \\(\\mathbf{Q}_t\\) called mask-and-replace strategy. They introduce an additional special" + }, + { + "type": "image", + "bbox": [ + 0.499, + 0.088, + 0.895, + 0.213 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.222, + 0.894, + 0.264 + ], + "angle": 0, + "content": "Figure 2. Overview of the corruption and denoising processes in LayoutDM. For simplicity, we use a toy layout consisting of two elements and the model generates three elements at maximum." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.291, + 0.892, + 0.368 + ], + "angle": 0, + "content": "token [MASK] and three probabilities \\(\\gamma_{t}\\) of replacing the current token with the [MASK] token, \\(\\beta_{t}\\) of replacing the token with other tokens, and \\(\\alpha_{t}\\) of not changing the token. The [MASK] token never transitions to other states. The transition matrix \\(\\mathbf{Q}_t\\in [0,1]^{(K + 1)\\times (K + 1)}\\) is defined by:" + }, + { + "type": "equation", + "bbox": [ + 0.524, + 0.377, + 0.892, + 0.466 + ], + "angle": 0, + "content": "\\[\n\\mathbf {Q} _ {t} = \\left[ \\begin{array}{c c c c c} \\alpha_ {t} + \\beta_ {t} & \\beta_ {t} & \\dots & \\beta_ {t} & 0 \\\\ \\beta_ {t} & \\alpha_ {t} + \\beta_ {t} & \\dots & \\beta_ {t} & 0 \\\\ \\vdots & \\vdots & \\ddots & \\beta_ {t} & 0 \\\\ \\beta_ {t} & \\beta_ {t} & \\beta_ {t} & \\alpha_ {t} + \\beta_ {t} & 0 \\\\ \\gamma_ {t} & \\gamma_ {t} & \\gamma_ {t} & \\gamma_ {t} & 1 \\end{array} \\right]. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.475, + 0.892, + 0.537 + ], + "angle": 0, + "content": "\\((\\alpha_{t}, \\beta_{t}, \\gamma_{t})\\) is carefully designed so that \\(z_{t}\\) converges to the [MASK] token for sufficiently large \\(t\\). During testing, we start from \\(\\mathbf{z}_{T}\\) filled with [MASK] tokens and iteratively sample new set of tokens \\(\\mathbf{z}_{t-1}\\) from \\(p_{\\theta}(\\mathbf{z}_{t-1} | \\mathbf{z}_{t})\\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.545, + 0.796, + 0.562 + ], + "angle": 0, + "content": "3.2. Unconditional Layout Generation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.569, + 0.892, + 0.75 + ], + "angle": 0, + "content": "A layout \\( l \\) is a set of elements represented by \\( l = \\{(c_1, b_1), \\ldots, (c_E, b_E)\\} \\). \\( E \\in \\mathbb{N} \\) is the number of elements in the layout. \\( c_i \\in \\{1, \\ldots, C\\} \\) is categorical information of the \\( i \\)-th element in the layout. \\( b_i \\in [0, 1]^4 \\) is the bounding box of the \\( i \\)-th element in normalized coordinates, where the first two values indicate the center location, and the last two indicate the width and height. Following previous works [2, 11, 20] that regard layout generation as generating a sequence of tokens, we quantize each value in \\( b_i \\) and obtain \\( [x_i, y_i, w_i, h_i]^\\top \\in \\{1, \\ldots, B\\}^4 \\), where \\( B \\) is a number of the bins. The layout \\( l \\) is now represented by \\( l = \\{(c_1, x_1, y_1, w_1, h_1), \\ldots\\} \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.751, + 0.892, + 0.902 + ], + "angle": 0, + "content": "In this work, we corrupt a layout in a modality-wise manner in the forward process, and we denoise the corrupted layout while considering all elements and modalities in the reverse process, as we illustrate in Fig. 2. Similarly to D3PM [3], we parameterize \\( p_{\\theta} \\) by a Transformer encoder [40], which processes an ordered 1D sequence. To process \\( l \\) by \\( p_{\\theta} \\) while avoiding the order dependency issue [20], we randomly shuffle \\( l \\) in element-wise manner and then flatten it to produce \\( l_{\\mathrm{flat}} = (c_1, x_1, y_1, w_1, h_1, c_2, x_2, \\ldots) \\)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10169" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.244 + ], + "angle": 0, + "content": "Variable length generation Existing diffusion models generate fixed-dimensional data and are not directly applicable to the layout generation because the number of elements in each layout varies. To handle this, we introduce a [PAD] token and define a maximum number of elements in the layout as \\( M \\in \\mathbb{N} \\). Each layout is fixed-dimensional data composed of \\( 5M \\) tokens by appending \\( 5(M - E) \\) [PAD] tokens. [PAD] is treated similarly to the ordinary token in VQDiffusion and \\( \\mathbf{Q}_t \\)'s dimension becomes \\( (K + 2) \\times (K + 2) \\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.264, + 0.473, + 0.448 + ], + "angle": 0, + "content": "Modality-wise diffusion Discrete state-space models assume that all the standard tokens are switchable by corruption. However, layout tokens comprise a disjoint set of token groups for each attribute in the element. For example, applying the transition rule Eq. (5) may change a token representing an element's category to another token representing the width. To avoid such invalid switching, we propose to apply disjoint corruption matrices \\(\\mathbf{Q}_t^c,\\mathbf{Q}_t^x,\\mathbf{Q}_t^y,\\mathbf{Q}_t^w,\\mathbf{Q}_t^h\\) for tokens representing different attributes \\(c,x,y,w,h\\), as we show in Fig. 2. The size of each matrix is \\((C + 2)\\times\\) \\((C + 2)\\) for \\(\\mathbf{Q}_t^c\\) and otherwise \\((B + 2)\\times (B + 2)\\), where \\(+2\\) is for [PAD] and [MASK]." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.467, + 0.473, + 0.62 + ], + "angle": 0, + "content": "Adaptive Quantization The distribution of the position and size information in layouts is highly imbalanced; e.g., elements tend to be aligned to either left, center, or right. Applying uniform quantization to those quantities as in existing layout generation models [2, 11, 20] results in the loss of information. As a pre-processing, we propose to apply a classical clustering algorithm, such as KMeans [29] on \\( x \\), \\( y \\), \\( w \\), and \\( h \\) independently to obtain balanced position and size tokens for each dataset. We show in Sec. 4.7 how quantization strategy affects the resulting quality." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.64, + 0.473, + 0.777 + ], + "angle": 0, + "content": "Decoupled Positional Encoding Previous works apply standard positional encoding to a flattened sequence of layout tokens \\( l_{\\mathrm{flat}} \\) [2, 11, 20]. We argue that this flattening approach could lose the structure information of the layout and lead to inferior generation performance. In layout, each token has two types of indices: \\( i \\)-th element and \\( j \\)-th attribute. We empirically find that independently applying positional encoding to those indices improves final generation performance, which we study in Sec. 4.7." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.787, + 0.296, + 0.803 + ], + "angle": 0, + "content": "3.3. Conditional Generation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.471, + 0.903 + ], + "angle": 0, + "content": "We elaborate on solving various conditional layout generation tasks using pre-trained frozen LayoutDM. We inject conditional information in both the initial state \\( \\mathbf{z}_T \\) and sampled states \\( \\{\\mathbf{z}_t\\}_{t=0}^{T-1} \\) during inference but do not modify the denoising network \\( p_\\theta \\). The actual implementation of the injection differs by the type of conditions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.214 + ], + "angle": 0, + "content": "Strong Constraints The most typical condition is partially known layout fields. Let \\( \\mathbf{z}^{\\mathrm{known}} \\in \\mathbb{Z}^{N} \\) contain the known fields and \\( \\mathbf{m} \\in \\{0,1\\}^{N} \\) be a mask vector denoting the known and unknown field as 1 and 0, respectively. In each timestep \\( t \\), we sample \\( \\hat{\\mathbf{z}}_{t-1} \\) from \\( p_{\\theta}(\\mathbf{z}_{t-1}|\\mathbf{z}_t) \\) in Eq. (3) and then inject the condition by \\( \\mathbf{z}_{t-1} = \\mathbf{m} \\odot \\mathbf{z}^{\\mathrm{known}} + (\\mathbf{1} - \\mathbf{m}) \\odot \\hat{\\mathbf{z}}_{t-1} \\), where \\( \\mathbf{1} \\) denotes a \\( N \\)-dimensional all-ones vector and \\( \\odot \\) denotes element-wise product." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.23, + 0.895, + 0.322 + ], + "angle": 0, + "content": "Weak Constraints We may impose a weaker constraint during generation, such as an element in the center. We offer a way to impose such constraints in a unified framework without additional training or external neural network models. We propose to adjust the logits to inject weak constraints in log probability space by" + }, + { + "type": "equation", + "bbox": [ + 0.55, + 0.328, + 0.892, + 0.344 + ], + "angle": 0, + "content": "\\[\n\\log \\hat {p} _ {\\theta} \\left(\\boldsymbol {z} _ {t - 1} | \\boldsymbol {z} _ {t}\\right) \\propto \\log p _ {\\theta} \\left(\\boldsymbol {z} _ {t - 1} | \\boldsymbol {z} _ {t}\\right) + \\lambda_ {\\pi} \\pi , \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.35, + 0.895, + 0.457 + ], + "angle": 0, + "content": "where \\(\\pi \\in \\mathbb{R}^{N\\times K}\\) is a prior term that weights the desired outputs, and \\(\\lambda_{\\pi}\\in \\mathbb{R}\\) is a hyper-parameter. The prior term can be defined either hard-coded (Refinement in Sec. 4.5) or through differentiable loss functions (Relationship in Sec. 4.5). Let \\(\\{\\mathcal{L}_i\\}_{i = 1}^L\\) be a set of differentiable loss functions given the prediction, the later prior definition can be written by:" + }, + { + "type": "equation", + "bbox": [ + 0.554, + 0.462, + 0.892, + 0.504 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {\\pi} = - \\nabla_ {p _ {\\theta} \\left(\\boldsymbol {z} _ {t - 1} \\mid \\boldsymbol {z} _ {t}\\right)} \\sum_ {i = 1} ^ {L} \\mathcal {L} _ {i} \\left(p _ {\\theta} \\left(\\boldsymbol {z} _ {t - 1} \\mid \\boldsymbol {z} _ {t}\\right)\\right). \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.509, + 0.895, + 0.631 + ], + "angle": 0, + "content": "Although the formulation of Eq. (7) resembles steering diffusion models by gradients from external models [7, 25], our primal focus is incorporating classical hand-crafted energies for aesthetics principles of layout [32] that do not depend on an external model. In practice, we tune the hyperparameters for imposing weak constraints, such as \\(\\lambda_{\\pi}\\). Note that these hyper-parameters are only for inference and are easier to tune than the other training hyper-parameters." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.642, + 0.625, + 0.659 + ], + "angle": 0, + "content": "4. Experiment" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.667, + 0.603, + 0.681 + ], + "angle": 0, + "content": "4.1. Datasets" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.892, + 0.78 + ], + "angle": 0, + "content": "We use two large-scale datasets for comparison, Rico [5] and PubLayNet [45]. As we mention in Sec. 3.2, an element in a layout for each dataset is described by the five attributes. For preprocessing, we set the maximum number of elements per layout \\( M \\) to 25. If a layout contains more elements, we discard the whole layout." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.781, + 0.895, + 0.902 + ], + "angle": 0, + "content": "We provide an overview of each dataset. Rico is a dataset of user interface designs for mobile applications containing 25 element categories such as text button, toolbar, and icon. We divide the dataset into 35,851 / 2,109 / 4,218 samples for train, validation, and test splits. PubLayNet is a dataset of research papers containing five element categories, such as table, image, and text. We divide the dataset into 315,757 / 16,619 / 11,142 samples for train, validation, and test splits." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "10170" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.077, + 0.091, + 0.262, + 0.106 + ], + "angle": 0, + "content": "4.2. Evaluation Metrics" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.114, + 0.473, + 0.326 + ], + "angle": 0, + "content": "We employ two primary metrics: FID and Maximum IoU (Max.). These metrics take into account both fidelity and diversity [12], which are two mutually complementary properties widely used in evaluating generative models. FID [12] captures the similarity of generated data to real ones in feature space. We employ an improved feature extraction model for layouts [19] instead of a conventional method [21] to compute FID. Maximum IoU [19] measures the conditional similarity between generated and real layouts. The similarity is measured by computing optimal matching that maximizes average IoU between generated and real layouts that have an identical set of categories. For reference, we show the FID and Maximum IoU computed between the validation and test data as Real data." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.335, + 0.267, + 0.349 + ], + "angle": 0, + "content": "4.3. Tasks and Baselines" + }, + { + "type": "text", + "bbox": [ + 0.098, + 0.358, + 0.404, + 0.373 + ], + "angle": 0, + "content": "We test LayoutDM on six tasks for evaluation." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.373, + 0.469, + 0.402 + ], + "angle": 0, + "content": "Unconditional generates layouts without any conditional input or constraint." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.403, + 0.469, + 0.433 + ], + "angle": 0, + "content": "Category \\(\\rightarrow\\) size+position (C \\(\\rightarrow\\) S + P) is a generation task conditioned on the category of each element [20]." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.434, + 0.469, + 0.463 + ], + "angle": 0, + "content": "Category \\(^+\\) size \\(\\rightarrow\\) position \\((\\mathbf{C} + \\mathbf{S}\\rightarrow \\mathbf{P})\\) is conditioned on the category and size of each element." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.464, + 0.469, + 0.509 + ], + "angle": 0, + "content": "Completion is conditioned on a small number of elements whose attributes are all known. Given a complete layout, we randomly sample from \\(0\\%\\) to \\(20\\%\\) of elements." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.509, + 0.469, + 0.599 + ], + "angle": 0, + "content": "Refinement is conditioned on a noisy layout in which only geometric information is perturbed [36]. Following RUITE [36], we synthesize the input layout by adding random noise to the size and position of each element. We sample noise from a standard normal distribution with a mean of 0 and a variance of 0.01." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.599, + 0.469, + 0.674 + ], + "angle": 0, + "content": "Relationship is conditioned on the category of each element and some relationship constraints between the elements [21]. Following CLG-LO [19], we employ the size and location relationships and randomly sample \\(10\\%\\) relationships between elements for the experiment." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.675, + 0.469, + 0.735 + ], + "angle": 0, + "content": "The first four tasks handle basic layout fields. We include a few task-agnostic models for comparison using existing controllable layout generation methods or simple adaptation of generative models in the following:" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.735, + 0.469, + 0.781 + ], + "angle": 0, + "content": "LayoutTrans is a simple autoregressive model [11] trained on a element-level shuffled layout, following [33]. We set a variable generation order to \\( c \\to w \\to h \\to x \\to y \\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.781, + 0.469, + 0.826 + ], + "angle": 0, + "content": "MaskGIT* is originally a non-autoregressive model for unconditional fixed-length data generation [4]. We use [PAD] to enable variable-length generation." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.826, + 0.469, + 0.856 + ], + "angle": 0, + "content": "BLT is a non-autoregressive model with layout-specific decoding strategy [20]." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.469, + 0.901 + ], + "angle": 0, + "content": "BART is a denoising autoencoder that can solve both comprehension and generation tasks based on Transformer encoder-decoder backbone [22]. We randomly generate a" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.136 + ], + "angle": 0, + "content": "number of [MASK] tokens from a uniform distribution between one and the sequence length, and perform masking based on the number." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.137, + 0.892, + 0.183 + ], + "angle": 0, + "content": "VQDiffusion* is a diffusion-based model originally for text-to-image generation [9]. We adapt the model for layout using \\( K = C + 4B + 2 \\) tokens, including [PAD]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.196, + 0.719, + 0.212 + ], + "angle": 0, + "content": "4.4. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.221, + 0.892, + 0.281 + ], + "angle": 0, + "content": "We re-implement most of the models since there are few official implementations publicly available except [11, 19, 20]\\(^2\\). We train all the models on the two datasets with three independent trials and report the average of the results." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.282, + 0.892, + 0.373 + ], + "angle": 0, + "content": "LayoutDM follows VQDiffusion for hyper-parameters unless specified, such as configurations for \\( p_{\\theta} \\) and the transition matrix parameters i.e. \\( \\alpha_{t} \\) and \\( \\gamma_{t} \\). We set the loss weight \\( \\lambda = 0.1 \\) (in Eq. (4)) and the diffusion timesteps \\( T = 100 \\). For optimization, we use AdamW [27] with learning rate of \\( 5.0 \\times 10^{-4} \\), \\( \\beta_{1} = 0.9 \\), and \\( \\beta_{2} = 0.98 \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.375, + 0.892, + 0.526 + ], + "angle": 0, + "content": "Many models, including LayoutDM, use Transformer [40] encoder backbone. We define a shared configuration as follows: 4 layers, 8 attention heads, 512 embedding dimensions, 2048 hidden dimensions, and 0.1 dropout rate. For other models with extra modules, we adjust the number of hidden dimensions to roughly match the number of parameters for a fair comparison. We randomly shuffle elements in the layout to avoid fixed-order generation during training. We search best hyper-parameters to obtain the best FID using the validation set." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.539, + 0.722, + 0.555 + ], + "angle": 0, + "content": "4.5.Quantitative Evaluation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.564, + 0.892, + 0.805 + ], + "angle": 0, + "content": "\\(\\mathbf{C} \\rightarrow \\mathbf{S} + \\mathbf{P}\\), \\(\\mathbf{C} + \\mathbf{S} \\rightarrow \\mathbf{P}\\), Completion In these tasks, we inject conditions by masking. We summarize comparisons in Tab. 1. As task-specific models, we include Layout-VAE [16], NDN-none [21], and LayoutGAN++ [19] for \\(\\mathbf{C} \\rightarrow \\mathbf{S} + \\mathbf{P}\\). We also adapt these models for \\(\\mathbf{C} + \\mathbf{S} \\rightarrow \\mathbf{P}\\). LayoutDM outperforms other models except LayoutTrans [11] in completion. The significant performance gap between LayoutDM and VQDiffusion* suggests the contribution of our proposals to go beyond the simple discrete diffusion models discussed in Sec. 3.2. Results in the completion suggest that a combination of padding and diffusion models is the primal key to the generation quality. We find that FID and Maximum IoU are not highly correlated only in the completion task. We conjecture that Maximum IoU may become unstable when categories are also predicted, unlike the \\(\\mathbf{C} \\rightarrow \\mathbf{S} + \\mathbf{P}\\) and \\(\\mathbf{C} + \\mathbf{S} \\rightarrow \\mathbf{P}\\) tasks where categories are given." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.806, + 0.892, + 0.838 + ], + "angle": 0, + "content": "Fig. 3 shows the qualitative results of some models, including LayoutDM. We can see that LayoutDM generates" + }, + { + "type": "page_footnote", + "bbox": [ + 0.498, + 0.851, + 0.892, + 0.901 + ], + "angle": 0, + "content": "2 Unfortunately, most datasets have no official train-val-test splits, and previous approaches work on different splits and pre-processing strategies. Furthermore, models for FID computation also vary. Thus, we cannot directly compare our results with the reported figure in the literature." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "10171" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.895, + 0.133 + ], + "angle": 0, + "content": "Table 1. Quantitative comparison in conditional generation given partially known fields. Top two results are highlighted in bold and underline, respectively. \\(\\dagger\\) indicates the results of BLT trained with [PAD] as an additional vocabulary since the original model cannot perform unordered completion in practice." + }, + { + "type": "table", + "bbox": [ + 0.085, + 0.135, + 0.887, + 0.393 + ], + "angle": 0, + "content": "
ModelTask DatasetCategory → Size+PositionCategory+Size → PositionCompletion
Rico FID ↓PubLayNet Max. ↑FID ↓Max. ↑Rico FID ↓Max. ↑PubLayNet FID ↓Max. ↑Rico FID ↓Max. ↑PubLayNet FID ↓Max. ↑
Task-specific models
LayoutVAE [16]33.30.24926.00.31630.60.28327.50.315-----
NDN-none [21]28.40.15861.10.16262.80.21969.40.222-----
LayoutGAN++ [19]6.840.26724.00.2636.220.3489.940.342-----
Task-agnostic models
LayoutTrans [11]5.570.22314.10.2723.730.32316.90.3203.710.5378.360.451
MaskGIT* [4]26.10.26217.20.3198.050.3205.860.38033.50.53319.70.484
BLT [20]17.40.20272.10.2154.480.3405.100.387117†0.471†131†0.345†
BART [22]3.970.2539.360.3203.180.3345.880.3758.870.5279.580.446
VQDiffusion* [9]4.340.25210.30.3193.210.3317.130.37411.00.54111.10.373
LayoutDM3.550.2777.950.3102.220.3924.250.3819.000.5767.650.377
Real data1.850.6916.250.4381.850.6916.250.4381.850.6916.250.438
" + }, + { + "type": "image", + "bbox": [ + 0.091, + 0.402, + 0.489, + 0.667 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.494, + 0.402, + 0.871, + 0.667 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.256, + 0.679, + 0.713, + 0.695 + ], + "angle": 0, + "content": "Figure 3. Comparison in conditional generation given partially known fields." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.471, + 0.751 + ], + "angle": 0, + "content": "high-quality layouts with fewer layout aesthetics violations, such as misalignment and overlap, given diverse conditions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Unconditional Generation Tab. 2 summarizes the results of unconditional generation. Unconditional layout generation methods often assume fixed order for element generation e.g. top-to-bottom rather than random order for better generation quality by constraining the prediction. For reference, we additionally report the results of LayoutTrans [11] trained on the fixed element order (LayoutTrans-fixed). Although we design LayoutDM's primarily for conditional" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.895, + 0.873 + ], + "angle": 0, + "content": "generation, LayoutDM achieves the best FID under random element order setting. We conjecture that BLT's poor performance is due to train-test mask distribution inconsistency caused by their hierarchical masking strategy for training. BLT masks a randomly sampled number of fields from a single semantic group i.e. category, position, or size. However, decoding starts with all masked tokens in inference. The alignment metric of Real data stays at 0.109 in Rico. Too small alignment values of LayoutTrans and MaskGIT can be a signal of producing trivial outputs in Rico." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "10172" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.09, + 0.47, + 0.118 + ], + "angle": 0, + "content": "Table 2. Quantitative comparison in unconditional generation. Top two results are highlighted in bold and underline, respectively." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.123, + 0.477, + 0.297 + ], + "angle": 0, + "content": "
ModelDatasetRicoPubLayNet
FID ↓Align. ↓FID ↓Align. ↓
LayoutTrans-fixed [11]6.470.13317.10.084
LayoutTrans [11]7.630.06813.90.127
MaskGIT* [4]52.10.01527.10.101
BLT [20]88.21.0301160.153
BART [22]11.90.09016.60.116
VQDiffusion* [9]7.460.17815.40.193
LayoutDM6.650.16213.90.195
Real data1.850.1096.250.0214
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.315, + 0.468, + 0.344 + ], + "angle": 0, + "content": "Table 3. Quantitative comparison in the refinement task. Top two results are highlighted in bold and underline, respectively." + }, + { + "type": "table", + "bbox": [ + 0.085, + 0.347, + 0.464, + 0.507 + ], + "angle": 0, + "content": "
DatasetRicoPubLayNet
ModelFID ↓ Max. ↑ Sim ↑ FID ↓ Max. ↑ Sim ↑
Task-specific models
RUIT [36]3.230.4210.2216.390.4150.174
Task-agnostic models
Noisy input1340.2130.1771300.2420.147
LayoutDM2.770.3700.2056.750.3520.149
w/o logit adj.3.550.2770.1687.950.3100.127
Real data1.850.6910.2606.250.4380.216
" + }, + { + "type": "image", + "bbox": [ + 0.127, + 0.53, + 0.416, + 0.706 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.106, + 0.718, + 0.438, + 0.733 + ], + "angle": 0, + "content": "Figure 4. Qualitative comparison in the refinement task." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Refinement Our LayoutDM performs this task with a combination of the strong constraints of element categories, i.e., setting \\( z^{\\mathrm{known}} = \\{(c_1, [\\mathrm{MASK}], \\dots, [\\mathrm{MASK}]), \\dots\\} \\), and the weak constraints that geometric outputs appear near noisy inputs. As an example of the weak constraint, we describe a constraint that imposes the x-coordinate estimate of \\( i \\)-th element close to the noisy continuous observation \\( \\hat{x}_i \\). We denote a sliced vector of the prior term \\( \\pi \\) in Eq. (6) that corresponds to the x-coordinate of \\( i \\)-th element as \\( \\pi_x^i \\in \\mathbb{R}^K \\)" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.09, + 0.877, + 0.271 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.281, + 0.89, + 0.309 + ], + "angle": 0, + "content": "Figure 5. Quality-violation trade-off in the relationship task. Lower scores indicate better performance for both metrics." + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.323, + 0.882, + 0.492 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.525, + 0.506, + 0.866, + 0.521 + ], + "angle": 0, + "content": "Figure 6. Qualitative comparison in the relationship task." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.547, + 0.598, + 0.562 + ], + "angle": 0, + "content": "and define by:" + }, + { + "type": "equation", + "bbox": [ + 0.54, + 0.573, + 0.891, + 0.614 + ], + "angle": 0, + "content": "\\[\n\\left[ \\pi_ {x} ^ {i} \\right] _ {j} = \\left\\{ \\begin{array}{l l} 1 & \\text {i f} | \\operatorname {l o c} (j) - \\hat {x} _ {i} | < m \\text {a n d} j \\in X \\\\ 0 & \\text {o t h e r w i s e ,} \\end{array} \\right. \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.625, + 0.892, + 0.699 + ], + "angle": 0, + "content": "where \\( m \\) is a hyper-parameter indicating a margin, \\( X \\) is a set of indices denoting tokens for \\( x \\) in the vocabularies, and \\( \\mathrm{loc}(j) \\) is a function that returns the centroid value of \\( j \\)-th token in the vocabularies. We define similar constraints for the other geometric variables and elements." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.7, + 0.893, + 0.837 + ], + "angle": 0, + "content": "We summarize the performance in Tab. 3. We additionally report DocSim [34] (Sim) to measure the similarity of a predicted and its corresponding ground truth layout. Imposing noisy geometric fields as a weak prior significantly improves the masking-only model and makes the performance much closer to RUITE [36], which is a denoising model not applicable to other layout tasks. We compare some results in Fig. 4. Both LayoutDM and RUITE successfully recover complete layouts from non-trivially noisy layouts." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.893, + 0.902 + ], + "angle": 0, + "content": "Relationship We use Eq. (7) to incorporate the relational constraints during the sampling step of LayoutDM. We follow [19] to employ the loss functions penalizing size and" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10173" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.08, + 0.089, + 0.47, + 0.276 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.078, + 0.289, + 0.468, + 0.304 + ], + "angle": 0, + "content": "Figure 7. Speed-quality trade-off of different models for \\(\\mathrm{C + S\\to P}\\)" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.335, + 0.468, + 0.362 + ], + "angle": 0, + "content": "Table 4. Ablation study results on layout-specific modification in unconditional generation of Rico [5] dataset." + }, + { + "type": "table", + "bbox": [ + 0.12, + 0.374, + 0.421, + 0.503 + ], + "angle": 0, + "content": "
FID ↓Align. ↓
LayoutDM6.650.162
w/o modality-wise diff.7.320.156
w/o decoupled pos. enc.6.780.227
w/ uniform-quantization7.580.256
w/ percentile-quantization9.790.232
Real Data1.850.109
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.545, + 0.468, + 0.711 + ], + "angle": 0, + "content": "location relationships between elements that do not match user specifications. We define the loss functions for continuous bounding boxes, and we have to convert the predicted discrete bounding boxes to continuous ones in a differentiable manner. Given estimated probabilities of discrete x-coordinates \\( p(x) \\), for example, we compute the continuous x-coordinate \\( \\bar{x} \\) by \\( \\bar{x} = \\sum_{n\\in X}p(x = n)\\log (n) \\). Similar conversion applies to the other attributes. Empirically, we find that applying the logit adjustment multiple times (three times in our experiments) to each diffusion step moderately improves performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.468, + 0.901 + ], + "angle": 0, + "content": "We compare LayoutDM with two task-specific approaches: NDN-partial [21] and CLG-LO based on LayoutGAN++ [19]. We show the results in Fig. 5. We additionally report constraint violation error rates [19]. LayoutDM can control the strength of the logit adjustment as in Eq. (6) and produces an FID-violation trade-off curve. LayoutDM is comparable to NDN-partial in Rico and outperforms NDN-partial by a large margin in PubLayNet. Although LayoutDM is inferior to CLG-LO in both datasets, note that the average runtime of CLG-LO is 4.0s, which is much slower than 0.5s in LayoutDM. We show some results of LayoutDM in Fig. 6." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.091, + 0.725, + 0.108 + ], + "angle": 0, + "content": "4.6. Speed-Quality Trade-off" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.115, + 0.892, + 0.283 + ], + "angle": 0, + "content": "Runtime is also essential for a controllable generation. We show a speed-quality trade-off curve for \\(\\mathrm{C + S\\rightarrow P}\\) as shown in Fig. 7. The Transformer encoder-only models, such as LayoutDM and BLT, can achieve fast generation at the sacrifice of quality. We employ fast-sampling strategy employed in discrete diffusion models [3] for LayoutDM by \\(p_{\\theta}(z_{t - \\Delta}|\\boldsymbol {z}_t)\\propto \\sum_{\\tilde{\\boldsymbol{z}}_0}q(\\boldsymbol{z}_{t - \\Delta},\\boldsymbol {z}_t|\\tilde{\\boldsymbol{z}}_0)\\tilde{p}_{\\theta}(\\tilde{\\boldsymbol{z}}_0|\\boldsymbol {z}_t)\\), where \\(\\Delta \\in \\mathbb{N}\\) indicates a step size for generation in \\(\\frac{T}{\\Delta}\\) steps. Despite being a task-agnostic model, LayoutDM achieves the best quality-speed trade-off except for task-specific LayoutGAN++ [19] that runs under 10ms." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.295, + 0.653, + 0.311 + ], + "angle": 0, + "content": "4.7. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.319, + 0.892, + 0.38 + ], + "angle": 0, + "content": "We investigate whether techniques in Sec. 3.2 improve the performance. First, we evaluate a choice of quantization methods for the geometric fields of elements. Instead of KMeans, we compute centroids for the quantization by:" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.381, + 0.892, + 0.44 + ], + "angle": 0, + "content": "- Uniform: This is dataset-agnostic quantization, which is popular in previous works [2, 11, 20]. Following [11], we choose \\(\\{0.0, \\frac{1}{B}, \\dots, \\frac{B - 1}{B}\\}\\) and \\(\\{\\frac{1}{B}, \\dots, \\frac{B - 1}{B}, 1.0\\}\\) for the position and size, respectively." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.442, + 0.892, + 0.485 + ], + "angle": 0, + "content": "- Percentile: we sort the data into equally sized groups and obtain average values for each group as the centroids. This is dataset-specific quantization similar to KMeans." + }, + { + "type": "list", + "bbox": [ + 0.5, + 0.381, + 0.892, + 0.485 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.487, + 0.891, + 0.608 + ], + "angle": 0, + "content": "We show the result at the bottom of Tab. 4. We additionally report the Alignment metric (Align.) used in [19] since the choice of the quantization affects the alignment between elements. Compared to Linear and Percentile, KMeans quantization significantly improves both FID and Alignment. We confirm that our modality-wise diffusion and decoupled positional encoding both moderately improve the performance, as we show at the top half of Tab. 4." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.625, + 0.614, + 0.64 + ], + "angle": 0, + "content": "5. Discussion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.651, + 0.892, + 0.726 + ], + "angle": 0, + "content": "LayoutDM is based on diffusion models for discrete state-space. Using continuous state-space as in latent diffusion models [37] would be interesting. Extension of LayoutDM to handle various layout properties such as color [17] and image/text [41] is also appealing." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.727, + 0.892, + 0.817 + ], + "angle": 0, + "content": "We believe our proposed logit adjustment can incorporate more attributes. Attribute-conditional LayoutGAN [24] considers area, aspect ratio, and reading order of elements for fine-grained control. Since these attributes can be easily converted to the size and location relationship constraints, incorporating them with our LayoutDM is not very difficult." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Potential negative impact Our model might be used to automatically generate the basic structure of fake websites or mobile applications, which could lead to scams or the spreading of misinformation." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10174" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.175, + 0.107 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.156 + ], + "angle": 0, + "content": "[1] Maneesh Agrawala, Wilmot Li, and Floraine Berthouzoz. Design principles for visual communication. 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In ICDAR, 2019. 1, 2, 4" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.47, + 0.645 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "10176" + } + ] +] \ No newline at end of file diff --git a/2023/LayoutDM_ Discrete Diffusion Model for Controllable Layout Generation/77614c7d-0145-49cc-9bc8-8f5b07a869f4_origin.pdf b/2023/LayoutDM_ Discrete Diffusion Model for Controllable Layout Generation/77614c7d-0145-49cc-9bc8-8f5b07a869f4_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..f40291944f9b5794c1fd1f960637b97dbca3eacd --- /dev/null +++ b/2023/LayoutDM_ Discrete Diffusion Model for Controllable Layout Generation/77614c7d-0145-49cc-9bc8-8f5b07a869f4_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:1d7528cdaf1d337513c181a36d9d3ba19537cc31a7308a16d7c6433c2229ae2f +size 613940 diff --git a/2023/LayoutDM_ Discrete Diffusion Model for Controllable Layout Generation/full.md b/2023/LayoutDM_ Discrete Diffusion Model for Controllable Layout Generation/full.md new file mode 100644 index 0000000000000000000000000000000000000000..4a2de914522e948409fb474e0ed7283e53987039 --- /dev/null +++ b/2023/LayoutDM_ Discrete Diffusion Model for Controllable Layout Generation/full.md @@ -0,0 +1,331 @@ +# LayoutDM: Discrete Diffusion Model for Controllable Layout Generation + +Naoto Inoue + +Kotaro Kikuchi + +Edgar Simo-Serra² + +Mayu Otani + +Kota Yamaguchi1 + +1CyberAgent, Japan + +$^{2}$ Waseda University, Japan + +{inoue_naoto, kikuchi_kotaro_xa}@cyberagent.co.jp ess@waseda.jp + +{otani_mayu, yamaguchi_kota}@cyberagent.co.jp + +# Abstract + +Controllable layout generation aims at synthesizing plausible arrangement of element bounding boxes with optional constraints, such as type or position of a specific element. In this work, we try to solve a broad range of layout generation tasks in a single model that is based on discrete state-space diffusion models. Our model, named LayoutDM, naturally handles the structured layout data in the discrete representation and learns to progressively infer a noiseless layout from the initial input, where we model the layout corruption process by modality-wise discrete diffusion. For conditional generation, we propose to inject layout constraints in the form of masking or logit adjustment during inference. We show in the experiments that our LayoutDM successfully generates high-quality layouts and outperforms both task-specific and task-agnostic baselines on several layout tasks. $^{1}$ + +# 1. Introduction + +Graphic layouts play a critical role in visual communication. Automatically creating a visually pleasing layout has tremendous application benefits that range from authoring of printed media [45] to designing application user interface [5], and there has been a growing research interest in the community. The task of layout generation considers the arrangement of elements, where each element has a tuple of attributes, such as category, position, or size, and depending on the task setup, there could be optional control inputs that specify part of the elements or attributes. Due to the structured nature of layout data, it is crucial to consider relationships between elements in a generation. For this reason, current generation approaches either build an autoregressive model [2, 11] or develop a dedicated inference strategy to explicitly consider relationships [19-21]. + +In this paper, we propose to utilize discrete state-space + +![](images/04b2039837f404eef03c4baab9e29886016f32c767486f0f742c41b253b3e685.jpg) +Figure 1. Overview of LayoutDM. Top: LayoutDM is trained to gradually generate a complete layout from a blank state in discrete state space. Bottom: During sampling, we can steer LayoutDM to perform various conditional generation tasks without additional training or external models. + +diffusion models [3, 9, 14] for layout generation tasks. Diffusion models have shown promising performance for various generation tasks, including images and texts [13]. We formulate the diffusion process for layout structure by modality-wise discrete diffusion, and train a denoising backbone network to progressively infer the complete layout with or without conditional inputs. To support variable-length layout data, we extend the discrete state-space with a special PAD token instead of the typical end-of-sequence token used in autoregressive models. Our model can incorporate complex layout constraints via logit adjustment, so that we can refine an existing layout or impose relative size constraints between elements without additional training. + +We discuss two key advantages of LayoutDM over existing models for conditional layout generation. Our model avoids the immutable dependency chain issue [20] that hap + +pens in autoregressive models [11]. Autoregressive models fail to perform conditional generation when the condition disagrees with the pre-defined generation order of elements and attributes. Unlike non-autoregressive models [20], our model can generate variable-length elements. We empirically show in Sec. 4.5 that naively extending non-autoregressive models by padding results in suboptimal variable length generation while padding combined with our diffusion formulation leads to significant improvement. + +We evaluate LayoutDM on various layout generation tasks tackled by previous works [20, 21, 33, 36] using two large-scale datasets, Rico [5] and PubLayNet [45]. LayoutDM outperforms task-agnostic baselines in the majority of cases and shows promising performance compared with task-specific baselines. We further conduct an ablation study to prove the significant impact of our design choices in LayoutDM, including quantization of continuous variables and positional embedding. + +We summarize our contributions as follows: + +- We formulate the discrete diffusion process for layout generation and propose a modality-wise diffusion and a padding approach to model highly structured layout data. +- We propose to inject complex layout constraints via masking and logit adjustment during the inference, so that our model can solve diverse tasks in a single model. +- We empirically show solid performance for various conditional layout generation tasks on public datasets. + +# 2. Related Work + +# 2.1. Layout Generation + +Studies on automatic layout generation have appeared several times in literature [1, 26, 32, 42]. Layout tasks are commonly observed in design applications, including magazine covers, posters, presentation slides, application user interface, or banner advertising [5, 8, 10, 18, 35, 41, 42, 44]. Recent approaches to layout generation consider both unconditional generation [2, 11, 15, 16] and conditional generation in various setups, such as conditional inputs of category or size [19-21, 23], relational constraints [19, 21], element completion [11], and refinement [36]. Some attempt at solving multiple tasks in a single model [20, 33]. + +BLT [20] points out that the recent autoregressive decoders [2, 11] are not fully capable of considering partial inputs, i.e. known elements or attributes, during generation because they have a fixed generation order. BLT addresses the conditional generation by fill-in-the-blank task formulation using a bidirectional Transformer encoder similar to masked language models [6]. However, BLT cannot solve layout completion demonstrated in the decoder-based models because of the requirement of the known number of elements. Our LayoutDM enjoys the best of both worlds and supports a broader range of conditional generation tasks in + +a single model. + +Another layout-specific consideration is the complex user-specified constraints, such as the positional requirements between two boxes (e.g., a header box should be on top of a paragraph box). Earlier approaches [31, 32, 43] propose hand-crafted cost functions representing the violation degree of aesthetic constraints so that those constraints guide the optimization process of layout inference. CLG-LO [19] proposes an aesthetically constrained optimization framework for pre-trained GANs. Our LayoutDM solves such constrained generation tasks on top of the task-agnostic iterative prediction via logit adjustment. + +# 2.2. Discrete Diffusion Models + +Diffusion models [38] are generative models characterized by a forward and reverse Markov process. The forward process corrupts the data into a sequence of increasingly noisy variables. The reverse process gradually denoises the variables toward the actual data distribution. Diffusion models are stable to train and achieve faster sampling than autoregressive models by parallel iterative refinement. Recently, many approaches have learned the reverse process by a neural network and show strong empirical performance [7, 13, 39] in continuous state spaces, such as images. + +Discrete state spaces are a natural representation of discrete variables, such as text. D3PM [3] extends the pioneering work of Hoogeboom et al. [14] to structured categorical corruption processes for diffusion models in discrete state spaces, while maintaining the advantages of diffusion models for continuous state spaces. VQDiffusion [9] develops a corruption approach called mask-and-replace, so as to avoid accumulated prediction errors that are common in models based on iterative prediction. Following the corruption model of VQDiffusion, we carefully design a modality-wise corruption process for layout tasks that involve tokens from disjoint sets of vocabulary per modality. + +Several studies consider a conditional input to the inference process of diffusion models. Some approaches alter the reverse diffusion iteration to carefully inject given conditions for free-form image inpainting [28] or image editing by strokes or composition [30]. We extend the discrete state-space diffusion models via hard masking or logit adjustment to support the conditional generation of layouts. + +# 3. LayoutDM + +Our LayoutDM builds on discrete-state space diffusion models [3, 9]. We first briefly review the fundamental of discrete diffusion models in Sec. 3.1. Sec. 3.2 explains our approach to layout generation within the diffusion framework while discussing features inherent in layout compared with text. Sec. 3.3 discusses how we extend denoising steps to perform various conditional layout generation by imposing conditions in each step of the reverse process. + +# 3.1. Preliminary: Discrete Diffusion Models + +Diffusion models [38] are generative models characterized by a forward and reverse Markov process. While many diffusion models are defined on continuous space with Gaussian corruption, D3PM [3] introduces a general diffusion framework for categorical variables designed primarily for texts. Let $T \in \mathbb{N}$ be a total timestep of the diffusion model, we first explain the forward diffusion process. For a scalar discrete variable with $K$ categories $z_{t} \in \{1,2,\dots,K\}$ at timestep $t \in \mathbb{N}$ , probabilities that $z_{t-1}$ transits to $z_{t}$ are defined by using a transition matrix $Q_{t} \in [0,1]^{K \times K}$ , with $[Q_{t}]_{mn} = q(z_{t} = m|z_{t-1} = n)$ , + +$$ +q \left(z _ {t} \mid z _ {t - 1}\right) = \boldsymbol {v} \left(z _ {t}\right) ^ {\top} \mathbf {Q} _ {t} \boldsymbol {v} \left(z _ {t - 1}\right), \tag {1} +$$ + +where $\pmb{v}(z_t) \in \{0,1\}^K$ is a column one-hot vector of $z_{t}$ . The categorical distribution over $z_{t}$ given $z_{t-1}$ is computed by a column vector $\mathbf{Q}_t \pmb{v}(z_{t-1}) \in [0,1]^K$ . Assuming the Markov property, we can derive $q(z_t|z_0) = \pmb{v}(z_t)^{\top} \overline{\mathbf{Q}}_t \pmb{v}(z_0)$ where $\overline{\mathbf{Q}}_t = \mathbf{Q}_t \mathbf{Q}_{t-1} \cdots \mathbf{Q}_1$ and: + +$$ +\begin{array}{l} q \left(z _ {t - 1} \mid z _ {t}, z _ {0}\right) = \frac {q \left(z _ {t} \mid z _ {t - 1} , z _ {0}\right) q \left(z _ {t - 1} \mid z _ {0}\right)}{q \left(z _ {t} \mid z _ {0}\right)} \\ = \frac {\left(\boldsymbol {v} \left(z _ {t}\right) ^ {\top} \mathbf {Q} _ {t} \boldsymbol {v} \left(z _ {t - 1}\right)\right) \left(\boldsymbol {v} \left(z _ {t - 1}\right) ^ {\top} \overline {{\mathbf {Q}}} _ {t - 1} \boldsymbol {v} \left(z _ {0}\right)\right)}{\boldsymbol {v} \left(z _ {t}\right) ^ {\top} \overline {{\mathbf {Q}}} _ {t} \boldsymbol {v} \left(z _ {0}\right)}. \tag {2} \\ \end{array} +$$ + +Note that due to the Markov property, $q(z_{t}|z_{t - 1},z_{0}) = q(z_{t}|z_{t - 1})$ . When we consider $N$ -dimensional variables $z_{t}\in \{1,2,\dots ,K\}^{N}$ , the corruption is applied to each variable $z_{t}$ independently. In the following, we explain with $N$ -dimensional variables $z_{t}$ . + +In contrast to the forward process, the reverse denoising process considers a conditional distribution of $\mathbf{z}_{t-1}$ over $\mathbf{z}_t$ by a neural network $p_{\theta}(\mathbf{z}_{t-1}|\mathbf{z}_t) \in [0,1]^{N \times K}$ . $\mathbf{z}_{t-1}$ is sampled according to this distribution. Note that the typical implementation is to predict unnormalized log probabilities $\log p_{\theta}(\mathbf{z}_{t-1}|\mathbf{z}_t)$ by a stack of bidirectional Transformer encoder blocks. D3PM uses a neural network $\tilde{p}_{\theta}(\tilde{\mathbf{z}}_0|\mathbf{z}_t)$ , combines it with the posterior $q(\mathbf{z}_{t-1}|\mathbf{z}_t,\mathbf{z}_0)$ , and sums over possible $\tilde{\mathbf{z}}_0$ to obtain the following parameterization: + +$$ +p _ {\theta} \left(\boldsymbol {z} _ {t - 1} | \boldsymbol {z} _ {t}\right) \propto \sum_ {\tilde {\boldsymbol {z}} _ {0}} q \left(\boldsymbol {z} _ {t - 1} | \boldsymbol {z} _ {t}, \tilde {\boldsymbol {z}} _ {0}\right) \tilde {p} _ {\theta} \left(\tilde {\boldsymbol {z}} _ {0} | \boldsymbol {z} _ {t}\right). \tag {3} +$$ + +In addition to the commonly used variational lower bound objective $\mathcal{L}_{\mathrm{vb}}$ , D3PM introduces an auxiliary denoising objective. The overall objective is as follows: + +$$ +\mathcal {L} _ {\lambda} = \mathcal {L} _ {\mathrm {v b}} + \lambda \underset { \begin{array}{c} \boldsymbol {z} _ {t} \sim q (\boldsymbol {z} _ {t} | \boldsymbol {z} _ {0}) \\ \boldsymbol {z} _ {0} \sim q (\boldsymbol {z} _ {0}) \end{array} } {\mathbb {E}} \left[ - \log \tilde {p} _ {\theta} \left(\boldsymbol {z} _ {0} | \boldsymbol {z} _ {t}\right) \right], \tag {4} +$$ + +where $\lambda$ is a hyper-parameter to balance the two loss terms. + +Although D3PM proposes many variants of $\mathbf{Q}_t$ , VQD-iffusion [9] offers an improved version of $\mathbf{Q}_t$ called mask-and-replace strategy. They introduce an additional special + +![](images/f2eaafce04f7ba63ce81fdf4bf9055acdb8f49135ecc8bf175c6e7ff37b523dd.jpg) +Figure 2. Overview of the corruption and denoising processes in LayoutDM. For simplicity, we use a toy layout consisting of two elements and the model generates three elements at maximum. + +token [MASK] and three probabilities $\gamma_{t}$ of replacing the current token with the [MASK] token, $\beta_{t}$ of replacing the token with other tokens, and $\alpha_{t}$ of not changing the token. The [MASK] token never transitions to other states. The transition matrix $\mathbf{Q}_t\in [0,1]^{(K + 1)\times (K + 1)}$ is defined by: + +$$ +\mathbf {Q} _ {t} = \left[ \begin{array}{c c c c c} \alpha_ {t} + \beta_ {t} & \beta_ {t} & \dots & \beta_ {t} & 0 \\ \beta_ {t} & \alpha_ {t} + \beta_ {t} & \dots & \beta_ {t} & 0 \\ \vdots & \vdots & \ddots & \beta_ {t} & 0 \\ \beta_ {t} & \beta_ {t} & \beta_ {t} & \alpha_ {t} + \beta_ {t} & 0 \\ \gamma_ {t} & \gamma_ {t} & \gamma_ {t} & \gamma_ {t} & 1 \end{array} \right]. \tag {5} +$$ + +$(\alpha_{t}, \beta_{t}, \gamma_{t})$ is carefully designed so that $z_{t}$ converges to the [MASK] token for sufficiently large $t$ . During testing, we start from $\mathbf{z}_{T}$ filled with [MASK] tokens and iteratively sample new set of tokens $\mathbf{z}_{t-1}$ from $p_{\theta}(\mathbf{z}_{t-1} | \mathbf{z}_{t})$ . + +# 3.2. Unconditional Layout Generation + +A layout $l$ is a set of elements represented by $l = \{(c_1, b_1), \ldots, (c_E, b_E)\}$ . $E \in \mathbb{N}$ is the number of elements in the layout. $c_i \in \{1, \ldots, C\}$ is categorical information of the $i$ -th element in the layout. $b_i \in [0, 1]^4$ is the bounding box of the $i$ -th element in normalized coordinates, where the first two values indicate the center location, and the last two indicate the width and height. Following previous works [2, 11, 20] that regard layout generation as generating a sequence of tokens, we quantize each value in $b_i$ and obtain $[x_i, y_i, w_i, h_i]^\top \in \{1, \ldots, B\}^4$ , where $B$ is a number of the bins. The layout $l$ is now represented by $l = \{(c_1, x_1, y_1, w_1, h_1), \ldots\}$ . + +In this work, we corrupt a layout in a modality-wise manner in the forward process, and we denoise the corrupted layout while considering all elements and modalities in the reverse process, as we illustrate in Fig. 2. Similarly to D3PM [3], we parameterize $p_{\theta}$ by a Transformer encoder [40], which processes an ordered 1D sequence. To process $l$ by $p_{\theta}$ while avoiding the order dependency issue [20], we randomly shuffle $l$ in element-wise manner and then flatten it to produce $l_{\mathrm{flat}} = (c_1, x_1, y_1, w_1, h_1, c_2, x_2, \ldots)$ . + +Variable length generation Existing diffusion models generate fixed-dimensional data and are not directly applicable to the layout generation because the number of elements in each layout varies. To handle this, we introduce a [PAD] token and define a maximum number of elements in the layout as $M \in \mathbb{N}$ . Each layout is fixed-dimensional data composed of $5M$ tokens by appending $5(M - E)$ [PAD] tokens. [PAD] is treated similarly to the ordinary token in VQDiffusion and $\mathbf{Q}_t$ 's dimension becomes $(K + 2) \times (K + 2)$ . + +Modality-wise diffusion Discrete state-space models assume that all the standard tokens are switchable by corruption. However, layout tokens comprise a disjoint set of token groups for each attribute in the element. For example, applying the transition rule Eq. (5) may change a token representing an element's category to another token representing the width. To avoid such invalid switching, we propose to apply disjoint corruption matrices $\mathbf{Q}_t^c,\mathbf{Q}_t^x,\mathbf{Q}_t^y,\mathbf{Q}_t^w,\mathbf{Q}_t^h$ for tokens representing different attributes $c,x,y,w,h$ , as we show in Fig. 2. The size of each matrix is $(C + 2)\times$ $(C + 2)$ for $\mathbf{Q}_t^c$ and otherwise $(B + 2)\times (B + 2)$ , where $+2$ is for [PAD] and [MASK]. + +Adaptive Quantization The distribution of the position and size information in layouts is highly imbalanced; e.g., elements tend to be aligned to either left, center, or right. Applying uniform quantization to those quantities as in existing layout generation models [2, 11, 20] results in the loss of information. As a pre-processing, we propose to apply a classical clustering algorithm, such as KMeans [29] on $x$ , $y$ , $w$ , and $h$ independently to obtain balanced position and size tokens for each dataset. We show in Sec. 4.7 how quantization strategy affects the resulting quality. + +Decoupled Positional Encoding Previous works apply standard positional encoding to a flattened sequence of layout tokens $l_{\mathrm{flat}}$ [2, 11, 20]. We argue that this flattening approach could lose the structure information of the layout and lead to inferior generation performance. In layout, each token has two types of indices: $i$ -th element and $j$ -th attribute. We empirically find that independently applying positional encoding to those indices improves final generation performance, which we study in Sec. 4.7. + +# 3.3. Conditional Generation + +We elaborate on solving various conditional layout generation tasks using pre-trained frozen LayoutDM. We inject conditional information in both the initial state $\mathbf{z}_T$ and sampled states $\{\mathbf{z}_t\}_{t=0}^{T-1}$ during inference but do not modify the denoising network $p_\theta$ . The actual implementation of the injection differs by the type of conditions. + +Strong Constraints The most typical condition is partially known layout fields. Let $\mathbf{z}^{\mathrm{known}} \in \mathbb{Z}^{N}$ contain the known fields and $\mathbf{m} \in \{0,1\}^{N}$ be a mask vector denoting the known and unknown field as 1 and 0, respectively. In each timestep $t$ , we sample $\hat{\mathbf{z}}_{t-1}$ from $p_{\theta}(\mathbf{z}_{t-1}|\mathbf{z}_t)$ in Eq. (3) and then inject the condition by $\mathbf{z}_{t-1} = \mathbf{m} \odot \mathbf{z}^{\mathrm{known}} + (\mathbf{1} - \mathbf{m}) \odot \hat{\mathbf{z}}_{t-1}$ , where $\mathbf{1}$ denotes a $N$ -dimensional all-ones vector and $\odot$ denotes element-wise product. + +Weak Constraints We may impose a weaker constraint during generation, such as an element in the center. We offer a way to impose such constraints in a unified framework without additional training or external neural network models. We propose to adjust the logits to inject weak constraints in log probability space by + +$$ +\log \hat {p} _ {\theta} \left(\boldsymbol {z} _ {t - 1} | \boldsymbol {z} _ {t}\right) \propto \log p _ {\theta} \left(\boldsymbol {z} _ {t - 1} | \boldsymbol {z} _ {t}\right) + \lambda_ {\pi} \pi , \tag {6} +$$ + +where $\pi \in \mathbb{R}^{N\times K}$ is a prior term that weights the desired outputs, and $\lambda_{\pi}\in \mathbb{R}$ is a hyper-parameter. The prior term can be defined either hard-coded (Refinement in Sec. 4.5) or through differentiable loss functions (Relationship in Sec. 4.5). Let $\{\mathcal{L}_i\}_{i = 1}^L$ be a set of differentiable loss functions given the prediction, the later prior definition can be written by: + +$$ +\boldsymbol {\pi} = - \nabla_ {p _ {\theta} \left(\boldsymbol {z} _ {t - 1} \mid \boldsymbol {z} _ {t}\right)} \sum_ {i = 1} ^ {L} \mathcal {L} _ {i} \left(p _ {\theta} \left(\boldsymbol {z} _ {t - 1} \mid \boldsymbol {z} _ {t}\right)\right). \tag {7} +$$ + +Although the formulation of Eq. (7) resembles steering diffusion models by gradients from external models [7, 25], our primal focus is incorporating classical hand-crafted energies for aesthetics principles of layout [32] that do not depend on an external model. In practice, we tune the hyperparameters for imposing weak constraints, such as $\lambda_{\pi}$ . Note that these hyper-parameters are only for inference and are easier to tune than the other training hyper-parameters. + +# 4. Experiment + +# 4.1. Datasets + +We use two large-scale datasets for comparison, Rico [5] and PubLayNet [45]. As we mention in Sec. 3.2, an element in a layout for each dataset is described by the five attributes. For preprocessing, we set the maximum number of elements per layout $M$ to 25. If a layout contains more elements, we discard the whole layout. + +We provide an overview of each dataset. Rico is a dataset of user interface designs for mobile applications containing 25 element categories such as text button, toolbar, and icon. We divide the dataset into 35,851 / 2,109 / 4,218 samples for train, validation, and test splits. PubLayNet is a dataset of research papers containing five element categories, such as table, image, and text. We divide the dataset into 315,757 / 16,619 / 11,142 samples for train, validation, and test splits. + +# 4.2. Evaluation Metrics + +We employ two primary metrics: FID and Maximum IoU (Max.). These metrics take into account both fidelity and diversity [12], which are two mutually complementary properties widely used in evaluating generative models. FID [12] captures the similarity of generated data to real ones in feature space. We employ an improved feature extraction model for layouts [19] instead of a conventional method [21] to compute FID. Maximum IoU [19] measures the conditional similarity between generated and real layouts. The similarity is measured by computing optimal matching that maximizes average IoU between generated and real layouts that have an identical set of categories. For reference, we show the FID and Maximum IoU computed between the validation and test data as Real data. + +# 4.3. Tasks and Baselines + +We test LayoutDM on six tasks for evaluation. + +Unconditional generates layouts without any conditional input or constraint. + +Category $\rightarrow$ size+position (C $\rightarrow$ S + P) is a generation task conditioned on the category of each element [20]. + +Category $^+$ size $\rightarrow$ position $(\mathbf{C} + \mathbf{S}\rightarrow \mathbf{P})$ is conditioned on the category and size of each element. + +Completion is conditioned on a small number of elements whose attributes are all known. Given a complete layout, we randomly sample from $0\%$ to $20\%$ of elements. + +Refinement is conditioned on a noisy layout in which only geometric information is perturbed [36]. Following RUITE [36], we synthesize the input layout by adding random noise to the size and position of each element. We sample noise from a standard normal distribution with a mean of 0 and a variance of 0.01. + +Relationship is conditioned on the category of each element and some relationship constraints between the elements [21]. Following CLG-LO [19], we employ the size and location relationships and randomly sample $10\%$ relationships between elements for the experiment. + +The first four tasks handle basic layout fields. We include a few task-agnostic models for comparison using existing controllable layout generation methods or simple adaptation of generative models in the following: + +LayoutTrans is a simple autoregressive model [11] trained on a element-level shuffled layout, following [33]. We set a variable generation order to $c \to w \to h \to x \to y$ . + +MaskGIT* is originally a non-autoregressive model for unconditional fixed-length data generation [4]. We use [PAD] to enable variable-length generation. + +BLT is a non-autoregressive model with layout-specific decoding strategy [20]. + +BART is a denoising autoencoder that can solve both comprehension and generation tasks based on Transformer encoder-decoder backbone [22]. We randomly generate a + +number of [MASK] tokens from a uniform distribution between one and the sequence length, and perform masking based on the number. + +VQDiffusion* is a diffusion-based model originally for text-to-image generation [9]. We adapt the model for layout using $K = C + 4B + 2$ tokens, including [PAD]. + +# 4.4. Implementation Details + +We re-implement most of the models since there are few official implementations publicly available except [11, 19, 20] $^2$ . We train all the models on the two datasets with three independent trials and report the average of the results. + +LayoutDM follows VQDiffusion for hyper-parameters unless specified, such as configurations for $p_{\theta}$ and the transition matrix parameters i.e. $\alpha_{t}$ and $\gamma_{t}$ . We set the loss weight $\lambda = 0.1$ (in Eq. (4)) and the diffusion timesteps $T = 100$ . For optimization, we use AdamW [27] with learning rate of $5.0 \times 10^{-4}$ , $\beta_{1} = 0.9$ , and $\beta_{2} = 0.98$ . + +Many models, including LayoutDM, use Transformer [40] encoder backbone. We define a shared configuration as follows: 4 layers, 8 attention heads, 512 embedding dimensions, 2048 hidden dimensions, and 0.1 dropout rate. For other models with extra modules, we adjust the number of hidden dimensions to roughly match the number of parameters for a fair comparison. We randomly shuffle elements in the layout to avoid fixed-order generation during training. We search best hyper-parameters to obtain the best FID using the validation set. + +# 4.5.Quantitative Evaluation + +$\mathbf{C} \rightarrow \mathbf{S} + \mathbf{P}$ , $\mathbf{C} + \mathbf{S} \rightarrow \mathbf{P}$ , Completion In these tasks, we inject conditions by masking. We summarize comparisons in Tab. 1. As task-specific models, we include Layout-VAE [16], NDN-none [21], and LayoutGAN++ [19] for $\mathbf{C} \rightarrow \mathbf{S} + \mathbf{P}$ . We also adapt these models for $\mathbf{C} + \mathbf{S} \rightarrow \mathbf{P}$ . LayoutDM outperforms other models except LayoutTrans [11] in completion. The significant performance gap between LayoutDM and VQDiffusion* suggests the contribution of our proposals to go beyond the simple discrete diffusion models discussed in Sec. 3.2. Results in the completion suggest that a combination of padding and diffusion models is the primal key to the generation quality. We find that FID and Maximum IoU are not highly correlated only in the completion task. We conjecture that Maximum IoU may become unstable when categories are also predicted, unlike the $\mathbf{C} \rightarrow \mathbf{S} + \mathbf{P}$ and $\mathbf{C} + \mathbf{S} \rightarrow \mathbf{P}$ tasks where categories are given. + +Fig. 3 shows the qualitative results of some models, including LayoutDM. We can see that LayoutDM generates + +Table 1. Quantitative comparison in conditional generation given partially known fields. Top two results are highlighted in bold and underline, respectively. $\dagger$ indicates the results of BLT trained with [PAD] as an additional vocabulary since the original model cannot perform unordered completion in practice. + +
ModelTask DatasetCategory → Size+PositionCategory+Size → PositionCompletion
Rico FID ↓PubLayNet Max. ↑FID ↓Max. ↑Rico FID ↓Max. ↑PubLayNet FID ↓Max. ↑Rico FID ↓Max. ↑PubLayNet FID ↓Max. ↑
Task-specific models
LayoutVAE [16]33.30.24926.00.31630.60.28327.50.315-----
NDN-none [21]28.40.15861.10.16262.80.21969.40.222-----
LayoutGAN++ [19]6.840.26724.00.2636.220.3489.940.342-----
Task-agnostic models
LayoutTrans [11]5.570.22314.10.2723.730.32316.90.3203.710.5378.360.451
MaskGIT* [4]26.10.26217.20.3198.050.3205.860.38033.50.53319.70.484
BLT [20]17.40.20272.10.2154.480.3405.100.387117†0.471†131†0.345†
BART [22]3.970.2539.360.3203.180.3345.880.3758.870.5279.580.446
VQDiffusion* [9]4.340.25210.30.3193.210.3317.130.37411.00.54111.10.373
LayoutDM3.550.2777.950.3102.220.3924.250.3819.000.5767.650.377
Real data1.850.6916.250.4381.850.6916.250.4381.850.6916.250.438
+ +![](images/c052df74a74cfd37cb53b40775420b90ea54e35f7bf13c6dd0c79ad7654b3494.jpg) +Figure 3. Comparison in conditional generation given partially known fields. + +![](images/2523a6d5fc751ca702791f586038145ff1666f3f1d0aab5a97cb4d0b892de453.jpg) + +high-quality layouts with fewer layout aesthetics violations, such as misalignment and overlap, given diverse conditions. + +Unconditional Generation Tab. 2 summarizes the results of unconditional generation. Unconditional layout generation methods often assume fixed order for element generation e.g. top-to-bottom rather than random order for better generation quality by constraining the prediction. For reference, we additionally report the results of LayoutTrans [11] trained on the fixed element order (LayoutTrans-fixed). Although we design LayoutDM's primarily for conditional + +generation, LayoutDM achieves the best FID under random element order setting. We conjecture that BLT's poor performance is due to train-test mask distribution inconsistency caused by their hierarchical masking strategy for training. BLT masks a randomly sampled number of fields from a single semantic group i.e. category, position, or size. However, decoding starts with all masked tokens in inference. The alignment metric of Real data stays at 0.109 in Rico. Too small alignment values of LayoutTrans and MaskGIT can be a signal of producing trivial outputs in Rico. + +Table 2. Quantitative comparison in unconditional generation. Top two results are highlighted in bold and underline, respectively. + +
ModelDatasetRicoPubLayNet
FID ↓Align. ↓FID ↓Align. ↓
LayoutTrans-fixed [11]6.470.13317.10.084
LayoutTrans [11]7.630.06813.90.127
MaskGIT* [4]52.10.01527.10.101
BLT [20]88.21.0301160.153
BART [22]11.90.09016.60.116
VQDiffusion* [9]7.460.17815.40.193
LayoutDM6.650.16213.90.195
Real data1.850.1096.250.0214
+ +Table 3. Quantitative comparison in the refinement task. Top two results are highlighted in bold and underline, respectively. + +
DatasetRicoPubLayNet
ModelFID ↓ Max. ↑ Sim ↑ FID ↓ Max. ↑ Sim ↑
Task-specific models
RUIT [36]3.230.4210.2216.390.4150.174
Task-agnostic models
Noisy input1340.2130.1771300.2420.147
LayoutDM2.770.3700.2056.750.3520.149
w/o logit adj.3.550.2770.1687.950.3100.127
Real data1.850.6910.2606.250.4380.216
+ +![](images/6af11653bd84344e7d04e93f7d09d49e0da29777cf7d1c1ce0fd3be9fc5c7cab.jpg) +Figure 4. Qualitative comparison in the refinement task. + +Refinement Our LayoutDM performs this task with a combination of the strong constraints of element categories, i.e., setting $z^{\mathrm{known}} = \{(c_1, [\mathrm{MASK}], \dots, [\mathrm{MASK}]), \dots\}$ , and the weak constraints that geometric outputs appear near noisy inputs. As an example of the weak constraint, we describe a constraint that imposes the x-coordinate estimate of $i$ -th element close to the noisy continuous observation $\hat{x}_i$ . We denote a sliced vector of the prior term $\pi$ in Eq. (6) that corresponds to the x-coordinate of $i$ -th element as $\pi_x^i \in \mathbb{R}^K$ + +![](images/5b12d31d160cafd34bd1efc8a436c274d7341b7870cc0d290efc1b9fcf0cc73d.jpg) +Figure 5. Quality-violation trade-off in the relationship task. Lower scores indicate better performance for both metrics. + +![](images/1b4f46a108163d886a576dbef3e7e1739fa646f25df362e022a25e71c0e63fde.jpg) +Figure 6. Qualitative comparison in the relationship task. + +and define by: + +$$ +\left[ \pi_ {x} ^ {i} \right] _ {j} = \left\{ \begin{array}{l l} 1 & \text {i f} | \operatorname {l o c} (j) - \hat {x} _ {i} | < m \text {a n d} j \in X \\ 0 & \text {o t h e r w i s e ,} \end{array} \right. \tag {8} +$$ + +where $m$ is a hyper-parameter indicating a margin, $X$ is a set of indices denoting tokens for $x$ in the vocabularies, and $\mathrm{loc}(j)$ is a function that returns the centroid value of $j$ -th token in the vocabularies. We define similar constraints for the other geometric variables and elements. + +We summarize the performance in Tab. 3. We additionally report DocSim [34] (Sim) to measure the similarity of a predicted and its corresponding ground truth layout. Imposing noisy geometric fields as a weak prior significantly improves the masking-only model and makes the performance much closer to RUITE [36], which is a denoising model not applicable to other layout tasks. We compare some results in Fig. 4. Both LayoutDM and RUITE successfully recover complete layouts from non-trivially noisy layouts. + +Relationship We use Eq. (7) to incorporate the relational constraints during the sampling step of LayoutDM. We follow [19] to employ the loss functions penalizing size and + +![](images/748788104512bedf0b7a893cce4765d4207b9f95637a981d495cb79f9d69ce2a.jpg) +Figure 7. Speed-quality trade-off of different models for $\mathrm{C + S\to P}$ + +Table 4. Ablation study results on layout-specific modification in unconditional generation of Rico [5] dataset. + +
FID ↓Align. ↓
LayoutDM6.650.162
w/o modality-wise diff.7.320.156
w/o decoupled pos. enc.6.780.227
w/ uniform-quantization7.580.256
w/ percentile-quantization9.790.232
Real Data1.850.109
+ +location relationships between elements that do not match user specifications. We define the loss functions for continuous bounding boxes, and we have to convert the predicted discrete bounding boxes to continuous ones in a differentiable manner. Given estimated probabilities of discrete x-coordinates $p(x)$ , for example, we compute the continuous x-coordinate $\bar{x}$ by $\bar{x} = \sum_{n\in X}p(x = n)\log (n)$ . Similar conversion applies to the other attributes. Empirically, we find that applying the logit adjustment multiple times (three times in our experiments) to each diffusion step moderately improves performance. + +We compare LayoutDM with two task-specific approaches: NDN-partial [21] and CLG-LO based on LayoutGAN++ [19]. We show the results in Fig. 5. We additionally report constraint violation error rates [19]. LayoutDM can control the strength of the logit adjustment as in Eq. (6) and produces an FID-violation trade-off curve. LayoutDM is comparable to NDN-partial in Rico and outperforms NDN-partial by a large margin in PubLayNet. Although LayoutDM is inferior to CLG-LO in both datasets, note that the average runtime of CLG-LO is 4.0s, which is much slower than 0.5s in LayoutDM. We show some results of LayoutDM in Fig. 6. + +# 4.6. Speed-Quality Trade-off + +Runtime is also essential for a controllable generation. We show a speed-quality trade-off curve for $\mathrm{C + S\rightarrow P}$ as shown in Fig. 7. The Transformer encoder-only models, such as LayoutDM and BLT, can achieve fast generation at the sacrifice of quality. We employ fast-sampling strategy employed in discrete diffusion models [3] for LayoutDM by $p_{\theta}(z_{t - \Delta}|\boldsymbol {z}_t)\propto \sum_{\tilde{\boldsymbol{z}}_0}q(\boldsymbol{z}_{t - \Delta},\boldsymbol {z}_t|\tilde{\boldsymbol{z}}_0)\tilde{p}_{\theta}(\tilde{\boldsymbol{z}}_0|\boldsymbol {z}_t)$ , where $\Delta \in \mathbb{N}$ indicates a step size for generation in $\frac{T}{\Delta}$ steps. Despite being a task-agnostic model, LayoutDM achieves the best quality-speed trade-off except for task-specific LayoutGAN++ [19] that runs under 10ms. + +# 4.7. Ablation Study + +We investigate whether techniques in Sec. 3.2 improve the performance. First, we evaluate a choice of quantization methods for the geometric fields of elements. Instead of KMeans, we compute centroids for the quantization by: + +- Uniform: This is dataset-agnostic quantization, which is popular in previous works [2, 11, 20]. Following [11], we choose $\{0.0, \frac{1}{B}, \dots, \frac{B - 1}{B}\}$ and $\{\frac{1}{B}, \dots, \frac{B - 1}{B}, 1.0\}$ for the position and size, respectively. +- Percentile: we sort the data into equally sized groups and obtain average values for each group as the centroids. This is dataset-specific quantization similar to KMeans. + +We show the result at the bottom of Tab. 4. We additionally report the Alignment metric (Align.) used in [19] since the choice of the quantization affects the alignment between elements. Compared to Linear and Percentile, KMeans quantization significantly improves both FID and Alignment. We confirm that our modality-wise diffusion and decoupled positional encoding both moderately improve the performance, as we show at the top half of Tab. 4. + +# 5. Discussion + +LayoutDM is based on diffusion models for discrete state-space. Using continuous state-space as in latent diffusion models [37] would be interesting. 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In ICDAR, 2019. 1, 2, 4 \ No newline at end of file diff --git a/2023/LayoutDM_ Discrete Diffusion Model for Controllable Layout Generation/images.zip b/2023/LayoutDM_ Discrete Diffusion Model for Controllable Layout Generation/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..c82e944b1358594fbdbc6b8e715100943e15e15d --- /dev/null +++ b/2023/LayoutDM_ Discrete Diffusion Model for Controllable Layout Generation/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:66d1914f7dac072c78afefe3785713c4249188f5ba19316af2f7efb5b4b0291e +size 568454 diff --git a/2023/LayoutDM_ Discrete Diffusion Model for Controllable Layout Generation/layout.json b/2023/LayoutDM_ Discrete Diffusion Model for Controllable Layout Generation/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..5ae8a85386fc2be040a4816035e72e9533954987 --- /dev/null +++ b/2023/LayoutDM_ Discrete Diffusion Model for Controllable Layout Generation/layout.json @@ -0,0 +1,9706 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 69, + 103, + 523, + 120 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 103, + 523, + 120 + ], + "spans": [ + { + "bbox": [ + 69, + 103, + 523, + 120 + ], + "type": "text", + "content": "LayoutDM: Discrete Diffusion Model for Controllable Layout Generation" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 53, + 143, + 119, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 143, + 119, + 156 + ], + "spans": [ + { + "bbox": [ + 53, + 143, + 119, + 156 + ], + "type": "text", + "content": "Naoto Inoue" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 145, + 143, + 225, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 143, + 225, + 156 + ], + "spans": [ + { + "bbox": [ + 145, + 143, + 225, + 156 + ], + "type": "text", + "content": "Kotaro Kikuchi" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 251, + 143, + 343, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 251, + 143, + 343, + 156 + ], + "spans": [ + { + "bbox": [ + 251, + 143, + 343, + 156 + ], + "type": "text", + "content": "Edgar Simo-Serra²" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 369, + 144, + 432, + 157 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 369, + 144, + 432, + 157 + ], + "spans": [ + { + "bbox": [ + 369, + 144, + 432, + 157 + ], + "type": "text", + "content": "Mayu Otani" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 458, + 143, + 543, + 157 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 458, + 143, + 543, + 157 + ], + "spans": [ + { + "bbox": [ + 458, + 143, + 543, + 157 + ], + "type": "text", + "content": "Kota Yamaguchi1" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 173, + 157, + 272, + 172 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 173, + 157, + 272, + 172 + ], + "spans": [ + { + "bbox": [ + 173, + 157, + 272, + 172 + ], + "type": "text", + "content": "1CyberAgent, Japan" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 296, + 157, + 425, + 172 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 157, + 425, + 172 + ], + "spans": [ + { + "bbox": [ + 296, + 157, + 425, + 172 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 296, + 157, + 425, + 172 + ], + "type": "text", + "content": "Waseda University, Japan" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 132, + 174, + 465, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 132, + 174, + 465, + 185 + ], + "spans": [ + { + "bbox": [ + 132, + 174, + 465, + 185 + ], + "type": "text", + "content": "{inoue_naoto, kikuchi_kotaro_xa}@cyberagent.co.jp ess@waseda.jp" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 179, + 187, + 416, + 199 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 179, + 187, + 416, + 199 + ], + "spans": [ + { + "bbox": [ + 179, + 187, + 416, + 199 + ], + "type": "text", + "content": "{otani_mayu, yamaguchi_kota}@cyberagent.co.jp" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 143, + 227, + 190, + 239 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 227, + 190, + 239 + ], + "spans": [ + { + "bbox": [ + 143, + 227, + 190, + 239 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 253, + 288, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 253, + 288, + 445 + ], + "spans": [ + { + "bbox": [ + 46, + 253, + 288, + 445 + ], + "type": "text", + "content": "Controllable layout generation aims at synthesizing plausible arrangement of element bounding boxes with optional constraints, such as type or position of a specific element. In this work, we try to solve a broad range of layout generation tasks in a single model that is based on discrete state-space diffusion models. Our model, named LayoutDM, naturally handles the structured layout data in the discrete representation and learns to progressively infer a noiseless layout from the initial input, where we model the layout corruption process by modality-wise discrete diffusion. For conditional generation, we propose to inject layout constraints in the form of masking or logit adjustment during inference. We show in the experiments that our LayoutDM successfully generates high-quality layouts and outperforms both task-specific and task-agnostic baselines on several layout tasks." + }, + { + "bbox": [ + 46, + 253, + 288, + 445 + ], + "type": "inline_equation", + "content": "^{1}" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 47, + 469, + 127, + 481 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 469, + 127, + 481 + ], + "spans": [ + { + "bbox": [ + 47, + 469, + 127, + 481 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 490, + 287, + 670 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 490, + 287, + 670 + ], + "spans": [ + { + "bbox": [ + 46, + 490, + 287, + 670 + ], + "type": "text", + "content": "Graphic layouts play a critical role in visual communication. Automatically creating a visually pleasing layout has tremendous application benefits that range from authoring of printed media [45] to designing application user interface [5], and there has been a growing research interest in the community. The task of layout generation considers the arrangement of elements, where each element has a tuple of attributes, such as category, position, or size, and depending on the task setup, there could be optional control inputs that specify part of the elements or attributes. Due to the structured nature of layout data, it is crucial to consider relationships between elements in a generation. For this reason, current generation approaches either build an autoregressive model [2, 11] or develop a dedicated inference strategy to explicitly consider relationships [19-21]." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 58, + 670, + 287, + 682 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 670, + 287, + 682 + ], + "spans": [ + { + "bbox": [ + 58, + 670, + 287, + 682 + ], + "type": "text", + "content": "In this paper, we propose to utilize discrete state-space" + } + ] + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 310, + 226, + 535, + 426 + ], + "blocks": [ + { + "bbox": [ + 310, + 226, + 535, + 426 + ], + "lines": [ + { + "bbox": [ + 310, + 226, + 535, + 426 + ], + "spans": [ + { + "bbox": [ + 310, + 226, + 535, + 426 + ], + "type": "image", + "image_path": "04b2039837f404eef03c4baab9e29886016f32c767486f0f742c41b253b3e685.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 441, + 545, + 497 + ], + "lines": [ + { + "bbox": [ + 305, + 441, + 545, + 497 + ], + "spans": [ + { + "bbox": [ + 305, + 441, + 545, + 497 + ], + "type": "text", + "content": "Figure 1. Overview of LayoutDM. Top: LayoutDM is trained to gradually generate a complete layout from a blank state in discrete state space. Bottom: During sampling, we can steer LayoutDM to perform various conditional generation tasks without additional training or external models." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 520, + 545, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 520, + 545, + 676 + ], + "spans": [ + { + "bbox": [ + 304, + 520, + 545, + 676 + ], + "type": "text", + "content": "diffusion models [3, 9, 14] for layout generation tasks. Diffusion models have shown promising performance for various generation tasks, including images and texts [13]. We formulate the diffusion process for layout structure by modality-wise discrete diffusion, and train a denoising backbone network to progressively infer the complete layout with or without conditional inputs. To support variable-length layout data, we extend the discrete state-space with a special PAD token instead of the typical end-of-sequence token used in autoregressive models. Our model can incorporate complex layout constraints via logit adjustment, so that we can refine an existing layout or impose relative size constraints between elements without additional training." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "content": "We discuss two key advantages of LayoutDM over existing models for conditional layout generation. Our model avoids the immutable dependency chain issue [20] that hap" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 693, + 259, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 693, + 259, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 693, + 259, + 713 + ], + "type": "text", + "content": "1Please find the code and models at: https://cyberagentailab.github.io/layout-dm." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10167" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "type": "text", + "content": "pens in autoregressive models [11]. Autoregressive models fail to perform conditional generation when the condition disagrees with the pre-defined generation order of elements and attributes. Unlike non-autoregressive models [20], our model can generate variable-length elements. We empirically show in Sec. 4.5 that naively extending non-autoregressive models by padding results in suboptimal variable length generation while padding combined with our diffusion formulation leads to significant improvement." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 180, + 286, + 288 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 180, + 286, + 288 + ], + "spans": [ + { + "bbox": [ + 46, + 180, + 286, + 288 + ], + "type": "text", + "content": "We evaluate LayoutDM on various layout generation tasks tackled by previous works [20, 21, 33, 36] using two large-scale datasets, Rico [5] and PubLayNet [45]. LayoutDM outperforms task-agnostic baselines in the majority of cases and shows promising performance compared with task-specific baselines. We further conduct an ablation study to prove the significant impact of our design choices in LayoutDM, including quantization of continuous variables and positional embedding." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 59, + 289, + 238, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 289, + 238, + 300 + ], + "spans": [ + { + "bbox": [ + 59, + 289, + 238, + 300 + ], + "type": "text", + "content": "We summarize our contributions as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 301, + 287, + 396 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 47, + 301, + 287, + 337 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 301, + 287, + 337 + ], + "spans": [ + { + "bbox": [ + 47, + 301, + 287, + 337 + ], + "type": "text", + "content": "- We formulate the discrete diffusion process for layout generation and propose a modality-wise diffusion and a padding approach to model highly structured layout data." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 338, + 286, + 372 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 338, + 286, + 372 + ], + "spans": [ + { + "bbox": [ + 47, + 338, + 286, + 372 + ], + "type": "text", + "content": "- We propose to inject complex layout constraints via masking and logit adjustment during the inference, so that our model can solve diverse tasks in a single model." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 373, + 286, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 373, + 286, + 396 + ], + "spans": [ + { + "bbox": [ + 47, + 373, + 286, + 396 + ], + "type": "text", + "content": "- We empirically show solid performance for various conditional layout generation tasks on public datasets." + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 410, + 134, + 422 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 410, + 134, + 422 + ], + "spans": [ + { + "bbox": [ + 47, + 410, + 134, + 422 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 430, + 159, + 443 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 430, + 159, + 443 + ], + "spans": [ + { + "bbox": [ + 47, + 430, + 159, + 443 + ], + "type": "text", + "content": "2.1. Layout Generation" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 449, + 286, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 449, + 286, + 581 + ], + "spans": [ + { + "bbox": [ + 46, + 449, + 286, + 581 + ], + "type": "text", + "content": "Studies on automatic layout generation have appeared several times in literature [1, 26, 32, 42]. Layout tasks are commonly observed in design applications, including magazine covers, posters, presentation slides, application user interface, or banner advertising [5, 8, 10, 18, 35, 41, 42, 44]. Recent approaches to layout generation consider both unconditional generation [2, 11, 15, 16] and conditional generation in various setups, such as conditional inputs of category or size [19-21, 23], relational constraints [19, 21], element completion [11], and refinement [36]. Some attempt at solving multiple tasks in a single model [20, 33]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 582, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 286, + 713 + ], + "type": "text", + "content": "BLT [20] points out that the recent autoregressive decoders [2, 11] are not fully capable of considering partial inputs, i.e. known elements or attributes, during generation because they have a fixed generation order. BLT addresses the conditional generation by fill-in-the-blank task formulation using a bidirectional Transformer encoder similar to masked language models [6]. However, BLT cannot solve layout completion demonstrated in the decoder-based models because of the requirement of the known number of elements. Our LayoutDM enjoys the best of both worlds and supports a broader range of conditional generation tasks in" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 72, + 369, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 369, + 83 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 369, + 83 + ], + "type": "text", + "content": "a single model." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 84, + 545, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 84, + 545, + 216 + ], + "spans": [ + { + "bbox": [ + 304, + 84, + 545, + 216 + ], + "type": "text", + "content": "Another layout-specific consideration is the complex user-specified constraints, such as the positional requirements between two boxes (e.g., a header box should be on top of a paragraph box). Earlier approaches [31, 32, 43] propose hand-crafted cost functions representing the violation degree of aesthetic constraints so that those constraints guide the optimization process of layout inference. CLG-LO [19] proposes an aesthetically constrained optimization framework for pre-trained GANs. Our LayoutDM solves such constrained generation tasks on top of the task-agnostic iterative prediction via logit adjustment." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 222, + 449, + 233 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 222, + 449, + 233 + ], + "spans": [ + { + "bbox": [ + 306, + 222, + 449, + 233 + ], + "type": "text", + "content": "2.2. Discrete Diffusion Models" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 240, + 545, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 240, + 545, + 361 + ], + "spans": [ + { + "bbox": [ + 304, + 240, + 545, + 361 + ], + "type": "text", + "content": "Diffusion models [38] are generative models characterized by a forward and reverse Markov process. The forward process corrupts the data into a sequence of increasingly noisy variables. The reverse process gradually denoises the variables toward the actual data distribution. Diffusion models are stable to train and achieve faster sampling than autoregressive models by parallel iterative refinement. Recently, many approaches have learned the reverse process by a neural network and show strong empirical performance [7, 13, 39] in continuous state spaces, such as images." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 361, + 545, + 503 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 361, + 545, + 503 + ], + "spans": [ + { + "bbox": [ + 304, + 361, + 545, + 503 + ], + "type": "text", + "content": "Discrete state spaces are a natural representation of discrete variables, such as text. D3PM [3] extends the pioneering work of Hoogeboom et al. [14] to structured categorical corruption processes for diffusion models in discrete state spaces, while maintaining the advantages of diffusion models for continuous state spaces. VQDiffusion [9] develops a corruption approach called mask-and-replace, so as to avoid accumulated prediction errors that are common in models based on iterative prediction. Following the corruption model of VQDiffusion, we carefully design a modality-wise corruption process for layout tasks that involve tokens from disjoint sets of vocabulary per modality." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 504, + 545, + 588 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 504, + 545, + 588 + ], + "spans": [ + { + "bbox": [ + 304, + 504, + 545, + 588 + ], + "type": "text", + "content": "Several studies consider a conditional input to the inference process of diffusion models. Some approaches alter the reverse diffusion iteration to carefully inject given conditions for free-form image inpainting [28] or image editing by strokes or composition [30]. We extend the discrete state-space diffusion models via hard masking or logit adjustment to support the conditional generation of layouts." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 597, + 377, + 611 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 597, + 377, + 611 + ], + "spans": [ + { + "bbox": [ + 306, + 597, + 377, + 611 + ], + "type": "text", + "content": "3. LayoutDM" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": "Our LayoutDM builds on discrete-state space diffusion models [3, 9]. We first briefly review the fundamental of discrete diffusion models in Sec. 3.1. Sec. 3.2 explains our approach to layout generation within the diffusion framework while discussing features inherent in layout compared with text. Sec. 3.3 discusses how we extend denoising steps to perform various conditional layout generation by imposing conditions in each step of the reverse process." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10168" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 255, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 255, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 255, + 85 + ], + "type": "text", + "content": "3.1. Preliminary: Discrete Diffusion Models" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 90, + 290, + 224 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 90, + 290, + 224 + ], + "spans": [ + { + "bbox": [ + 47, + 90, + 290, + 224 + ], + "type": "text", + "content": "Diffusion models [38] are generative models characterized by a forward and reverse Markov process. While many diffusion models are defined on continuous space with Gaussian corruption, D3PM [3] introduces a general diffusion framework for categorical variables designed primarily for texts. Let " + }, + { + "bbox": [ + 47, + 90, + 290, + 224 + ], + "type": "inline_equation", + "content": "T \\in \\mathbb{N}" + }, + { + "bbox": [ + 47, + 90, + 290, + 224 + ], + "type": "text", + "content": " be a total timestep of the diffusion model, we first explain the forward diffusion process. For a scalar discrete variable with " + }, + { + "bbox": [ + 47, + 90, + 290, + 224 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 47, + 90, + 290, + 224 + ], + "type": "text", + "content": " categories " + }, + { + "bbox": [ + 47, + 90, + 290, + 224 + ], + "type": "inline_equation", + "content": "z_{t} \\in \\{1,2,\\dots,K\\}" + }, + { + "bbox": [ + 47, + 90, + 290, + 224 + ], + "type": "text", + "content": " at timestep " + }, + { + "bbox": [ + 47, + 90, + 290, + 224 + ], + "type": "inline_equation", + "content": "t \\in \\mathbb{N}" + }, + { + "bbox": [ + 47, + 90, + 290, + 224 + ], + "type": "text", + "content": ", probabilities that " + }, + { + "bbox": [ + 47, + 90, + 290, + 224 + ], + "type": "inline_equation", + "content": "z_{t-1}" + }, + { + "bbox": [ + 47, + 90, + 290, + 224 + ], + "type": "text", + "content": " transits to " + }, + { + "bbox": [ + 47, + 90, + 290, + 224 + ], + "type": "inline_equation", + "content": "z_{t}" + }, + { + "bbox": [ + 47, + 90, + 290, + 224 + ], + "type": "text", + "content": " are defined by using a transition matrix " + }, + { + "bbox": [ + 47, + 90, + 290, + 224 + ], + "type": "inline_equation", + "content": "Q_{t} \\in [0,1]^{K \\times K}" + }, + { + "bbox": [ + 47, + 90, + 290, + 224 + ], + "type": "text", + "content": ", with " + }, + { + "bbox": [ + 47, + 90, + 290, + 224 + ], + "type": "inline_equation", + "content": "[Q_{t}]_{mn} = q(z_{t} = m|z_{t-1} = n)" + }, + { + "bbox": [ + 47, + 90, + 290, + 224 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 100, + 232, + 287, + 247 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 100, + 232, + 287, + 247 + ], + "spans": [ + { + "bbox": [ + 100, + 232, + 287, + 247 + ], + "type": "interline_equation", + "content": "q \\left(z _ {t} \\mid z _ {t - 1}\\right) = \\boldsymbol {v} \\left(z _ {t}\\right) ^ {\\top} \\mathbf {Q} _ {t} \\boldsymbol {v} \\left(z _ {t - 1}\\right), \\tag {1}", + "image_path": "edafc5a65d3ebe9edcef46072b42d0d3d7366b158fd3d922bc980677bc26a131.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 249, + 287, + 310 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 249, + 287, + 310 + ], + "spans": [ + { + "bbox": [ + 47, + 249, + 287, + 310 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 249, + 287, + 310 + ], + "type": "inline_equation", + "content": "\\pmb{v}(z_t) \\in \\{0,1\\}^K" + }, + { + "bbox": [ + 47, + 249, + 287, + 310 + ], + "type": "text", + "content": " is a column one-hot vector of " + }, + { + "bbox": [ + 47, + 249, + 287, + 310 + ], + "type": "inline_equation", + "content": "z_{t}" + }, + { + "bbox": [ + 47, + 249, + 287, + 310 + ], + "type": "text", + "content": ". The categorical distribution over " + }, + { + "bbox": [ + 47, + 249, + 287, + 310 + ], + "type": "inline_equation", + "content": "z_{t}" + }, + { + "bbox": [ + 47, + 249, + 287, + 310 + ], + "type": "text", + "content": " given " + }, + { + "bbox": [ + 47, + 249, + 287, + 310 + ], + "type": "inline_equation", + "content": "z_{t-1}" + }, + { + "bbox": [ + 47, + 249, + 287, + 310 + ], + "type": "text", + "content": " is computed by a column vector " + }, + { + "bbox": [ + 47, + 249, + 287, + 310 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}_t \\pmb{v}(z_{t-1}) \\in [0,1]^K" + }, + { + "bbox": [ + 47, + 249, + 287, + 310 + ], + "type": "text", + "content": ". Assuming the Markov property, we can derive " + }, + { + "bbox": [ + 47, + 249, + 287, + 310 + ], + "type": "inline_equation", + "content": "q(z_t|z_0) = \\pmb{v}(z_t)^{\\top} \\overline{\\mathbf{Q}}_t \\pmb{v}(z_0)" + }, + { + "bbox": [ + 47, + 249, + 287, + 310 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 47, + 249, + 287, + 310 + ], + "type": "inline_equation", + "content": "\\overline{\\mathbf{Q}}_t = \\mathbf{Q}_t \\mathbf{Q}_{t-1} \\cdots \\mathbf{Q}_1" + }, + { + "bbox": [ + 47, + 249, + 287, + 310 + ], + "type": "text", + "content": " and:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 59, + 316, + 287, + 380 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 316, + 287, + 380 + ], + "spans": [ + { + "bbox": [ + 59, + 316, + 287, + 380 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} q \\left(z _ {t - 1} \\mid z _ {t}, z _ {0}\\right) = \\frac {q \\left(z _ {t} \\mid z _ {t - 1} , z _ {0}\\right) q \\left(z _ {t - 1} \\mid z _ {0}\\right)}{q \\left(z _ {t} \\mid z _ {0}\\right)} \\\\ = \\frac {\\left(\\boldsymbol {v} \\left(z _ {t}\\right) ^ {\\top} \\mathbf {Q} _ {t} \\boldsymbol {v} \\left(z _ {t - 1}\\right)\\right) \\left(\\boldsymbol {v} \\left(z _ {t - 1}\\right) ^ {\\top} \\overline {{\\mathbf {Q}}} _ {t - 1} \\boldsymbol {v} \\left(z _ {0}\\right)\\right)}{\\boldsymbol {v} \\left(z _ {t}\\right) ^ {\\top} \\overline {{\\mathbf {Q}}} _ {t} \\boldsymbol {v} \\left(z _ {0}\\right)}. \\tag {2} \\\\ \\end{array}", + "image_path": "a06a8d9fe903785f27f1a3dc00252611b17dff8dcf412197ca020d4203b93e9d.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 384, + 287, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 384, + 287, + 443 + ], + "spans": [ + { + "bbox": [ + 47, + 384, + 287, + 443 + ], + "type": "text", + "content": "Note that due to the Markov property, " + }, + { + "bbox": [ + 47, + 384, + 287, + 443 + ], + "type": "inline_equation", + "content": "q(z_{t}|z_{t - 1},z_{0}) = q(z_{t}|z_{t - 1})" + }, + { + "bbox": [ + 47, + 384, + 287, + 443 + ], + "type": "text", + "content": ". When we consider " + }, + { + "bbox": [ + 47, + 384, + 287, + 443 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 47, + 384, + 287, + 443 + ], + "type": "text", + "content": "-dimensional variables " + }, + { + "bbox": [ + 47, + 384, + 287, + 443 + ], + "type": "inline_equation", + "content": "z_{t}\\in \\{1,2,\\dots ,K\\}^{N}" + }, + { + "bbox": [ + 47, + 384, + 287, + 443 + ], + "type": "text", + "content": ", the corruption is applied to each variable " + }, + { + "bbox": [ + 47, + 384, + 287, + 443 + ], + "type": "inline_equation", + "content": "z_{t}" + }, + { + "bbox": [ + 47, + 384, + 287, + 443 + ], + "type": "text", + "content": " independently. In the following, we explain with " + }, + { + "bbox": [ + 47, + 384, + 287, + 443 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 47, + 384, + 287, + 443 + ], + "type": "text", + "content": "-dimensional variables " + }, + { + "bbox": [ + 47, + 384, + 287, + 443 + ], + "type": "inline_equation", + "content": "z_{t}" + }, + { + "bbox": [ + 47, + 384, + 287, + 443 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 445, + 288, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 445, + 288, + 552 + ], + "spans": [ + { + "bbox": [ + 47, + 445, + 288, + 552 + ], + "type": "text", + "content": "In contrast to the forward process, the reverse denoising process considers a conditional distribution of " + }, + { + "bbox": [ + 47, + 445, + 288, + 552 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{t-1}" + }, + { + "bbox": [ + 47, + 445, + 288, + 552 + ], + "type": "text", + "content": " over " + }, + { + "bbox": [ + 47, + 445, + 288, + 552 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_t" + }, + { + "bbox": [ + 47, + 445, + 288, + 552 + ], + "type": "text", + "content": " by a neural network " + }, + { + "bbox": [ + 47, + 445, + 288, + 552 + ], + "type": "inline_equation", + "content": "p_{\\theta}(\\mathbf{z}_{t-1}|\\mathbf{z}_t) \\in [0,1]^{N \\times K}" + }, + { + "bbox": [ + 47, + 445, + 288, + 552 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 47, + 445, + 288, + 552 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{t-1}" + }, + { + "bbox": [ + 47, + 445, + 288, + 552 + ], + "type": "text", + "content": " is sampled according to this distribution. Note that the typical implementation is to predict unnormalized log probabilities " + }, + { + "bbox": [ + 47, + 445, + 288, + 552 + ], + "type": "inline_equation", + "content": "\\log p_{\\theta}(\\mathbf{z}_{t-1}|\\mathbf{z}_t)" + }, + { + "bbox": [ + 47, + 445, + 288, + 552 + ], + "type": "text", + "content": " by a stack of bidirectional Transformer encoder blocks. D3PM uses a neural network " + }, + { + "bbox": [ + 47, + 445, + 288, + 552 + ], + "type": "inline_equation", + "content": "\\tilde{p}_{\\theta}(\\tilde{\\mathbf{z}}_0|\\mathbf{z}_t)" + }, + { + "bbox": [ + 47, + 445, + 288, + 552 + ], + "type": "text", + "content": ", combines it with the posterior " + }, + { + "bbox": [ + 47, + 445, + 288, + 552 + ], + "type": "inline_equation", + "content": "q(\\mathbf{z}_{t-1}|\\mathbf{z}_t,\\mathbf{z}_0)" + }, + { + "bbox": [ + 47, + 445, + 288, + 552 + ], + "type": "text", + "content": ", and sums over possible " + }, + { + "bbox": [ + 47, + 445, + 288, + 552 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{z}}_0" + }, + { + "bbox": [ + 47, + 445, + 288, + 552 + ], + "type": "text", + "content": " to obtain the following parameterization:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 74, + 558, + 287, + 583 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 74, + 558, + 287, + 583 + ], + "spans": [ + { + "bbox": [ + 74, + 558, + 287, + 583 + ], + "type": "interline_equation", + "content": "p _ {\\theta} \\left(\\boldsymbol {z} _ {t - 1} | \\boldsymbol {z} _ {t}\\right) \\propto \\sum_ {\\tilde {\\boldsymbol {z}} _ {0}} q \\left(\\boldsymbol {z} _ {t - 1} | \\boldsymbol {z} _ {t}, \\tilde {\\boldsymbol {z}} _ {0}\\right) \\tilde {p} _ {\\theta} \\left(\\tilde {\\boldsymbol {z}} _ {0} | \\boldsymbol {z} _ {t}\\right). \\tag {3}", + "image_path": "831f8dabee606a1e1935d1a5e877c640911c7ea1ff01500a0398b38f9f1cbbb5.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 590, + 287, + 625 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 590, + 287, + 625 + ], + "spans": [ + { + "bbox": [ + 47, + 590, + 287, + 625 + ], + "type": "text", + "content": "In addition to the commonly used variational lower bound objective " + }, + { + "bbox": [ + 47, + 590, + 287, + 625 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{vb}}" + }, + { + "bbox": [ + 47, + 590, + 287, + 625 + ], + "type": "text", + "content": ", D3PM introduces an auxiliary denoising objective. The overall objective is as follows:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 76, + 632, + 287, + 660 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 76, + 632, + 287, + 660 + ], + "spans": [ + { + "bbox": [ + 76, + 632, + 287, + 660 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\lambda} = \\mathcal {L} _ {\\mathrm {v b}} + \\lambda \\underset { \\begin{array}{c} \\boldsymbol {z} _ {t} \\sim q (\\boldsymbol {z} _ {t} | \\boldsymbol {z} _ {0}) \\\\ \\boldsymbol {z} _ {0} \\sim q (\\boldsymbol {z} _ {0}) \\end{array} } {\\mathbb {E}} \\left[ - \\log \\tilde {p} _ {\\theta} \\left(\\boldsymbol {z} _ {0} | \\boldsymbol {z} _ {t}\\right) \\right], \\tag {4}", + "image_path": "a5a22d7173adfd9a8e8002b8546303800d4a72a4f304278b2955227b09411e68.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 666, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 666, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 47, + 666, + 287, + 677 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 666, + 287, + 677 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 47, + 666, + 287, + 677 + ], + "type": "text", + "content": " is a hyper-parameter to balance the two loss terms." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "content": "Although D3PM proposes many variants of " + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}_t" + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "content": ", VQD-iffusion [9] offers an improved version of " + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}_t" + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "content": " called mask-and-replace strategy. They introduce an additional special" + } + ] + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 305, + 69, + 547, + 168 + ], + "blocks": [ + { + "bbox": [ + 305, + 69, + 547, + 168 + ], + "lines": [ + { + "bbox": [ + 305, + 69, + 547, + 168 + ], + "spans": [ + { + "bbox": [ + 305, + 69, + 547, + 168 + ], + "type": "image", + "image_path": "f2eaafce04f7ba63ce81fdf4bf9055acdb8f49135ecc8bf175c6e7ff37b523dd.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 175, + 547, + 209 + ], + "lines": [ + { + "bbox": [ + 304, + 175, + 547, + 209 + ], + "spans": [ + { + "bbox": [ + 304, + 175, + 547, + 209 + ], + "type": "text", + "content": "Figure 2. Overview of the corruption and denoising processes in LayoutDM. For simplicity, we use a toy layout consisting of two elements and the model generates three elements at maximum." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 230, + 545, + 291 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 230, + 545, + 291 + ], + "spans": [ + { + "bbox": [ + 304, + 230, + 545, + 291 + ], + "type": "text", + "content": "token [MASK] and three probabilities " + }, + { + "bbox": [ + 304, + 230, + 545, + 291 + ], + "type": "inline_equation", + "content": "\\gamma_{t}" + }, + { + "bbox": [ + 304, + 230, + 545, + 291 + ], + "type": "text", + "content": " of replacing the current token with the [MASK] token, " + }, + { + "bbox": [ + 304, + 230, + 545, + 291 + ], + "type": "inline_equation", + "content": "\\beta_{t}" + }, + { + "bbox": [ + 304, + 230, + 545, + 291 + ], + "type": "text", + "content": " of replacing the token with other tokens, and " + }, + { + "bbox": [ + 304, + 230, + 545, + 291 + ], + "type": "inline_equation", + "content": "\\alpha_{t}" + }, + { + "bbox": [ + 304, + 230, + 545, + 291 + ], + "type": "text", + "content": " of not changing the token. The [MASK] token never transitions to other states. The transition matrix " + }, + { + "bbox": [ + 304, + 230, + 545, + 291 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}_t\\in [0,1]^{(K + 1)\\times (K + 1)}" + }, + { + "bbox": [ + 304, + 230, + 545, + 291 + ], + "type": "text", + "content": " is defined by:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 320, + 298, + 545, + 369 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 298, + 545, + 369 + ], + "spans": [ + { + "bbox": [ + 320, + 298, + 545, + 369 + ], + "type": "interline_equation", + "content": "\\mathbf {Q} _ {t} = \\left[ \\begin{array}{c c c c c} \\alpha_ {t} + \\beta_ {t} & \\beta_ {t} & \\dots & \\beta_ {t} & 0 \\\\ \\beta_ {t} & \\alpha_ {t} + \\beta_ {t} & \\dots & \\beta_ {t} & 0 \\\\ \\vdots & \\vdots & \\ddots & \\beta_ {t} & 0 \\\\ \\beta_ {t} & \\beta_ {t} & \\beta_ {t} & \\alpha_ {t} + \\beta_ {t} & 0 \\\\ \\gamma_ {t} & \\gamma_ {t} & \\gamma_ {t} & \\gamma_ {t} & 1 \\end{array} \\right]. \\tag {5}", + "image_path": "e5f23a8f61469a5cf3ed533c42000286e02706039713a4f1f19916f61fe185fb.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 376, + 545, + 425 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 376, + 545, + 425 + ], + "spans": [ + { + "bbox": [ + 306, + 376, + 545, + 425 + ], + "type": "inline_equation", + "content": "(\\alpha_{t}, \\beta_{t}, \\gamma_{t})" + }, + { + "bbox": [ + 306, + 376, + 545, + 425 + ], + "type": "text", + "content": " is carefully designed so that " + }, + { + "bbox": [ + 306, + 376, + 545, + 425 + ], + "type": "inline_equation", + "content": "z_{t}" + }, + { + "bbox": [ + 306, + 376, + 545, + 425 + ], + "type": "text", + "content": " converges to the [MASK] token for sufficiently large " + }, + { + "bbox": [ + 306, + 376, + 545, + 425 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 306, + 376, + 545, + 425 + ], + "type": "text", + "content": ". During testing, we start from " + }, + { + "bbox": [ + 306, + 376, + 545, + 425 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{T}" + }, + { + "bbox": [ + 306, + 376, + 545, + 425 + ], + "type": "text", + "content": " filled with [MASK] tokens and iteratively sample new set of tokens " + }, + { + "bbox": [ + 306, + 376, + 545, + 425 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{t-1}" + }, + { + "bbox": [ + 306, + 376, + 545, + 425 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 306, + 376, + 545, + 425 + ], + "type": "inline_equation", + "content": "p_{\\theta}(\\mathbf{z}_{t-1} | \\mathbf{z}_{t})" + }, + { + "bbox": [ + 306, + 376, + 545, + 425 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 431, + 487, + 445 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 431, + 487, + 445 + ], + "spans": [ + { + "bbox": [ + 306, + 431, + 487, + 445 + ], + "type": "text", + "content": "3.2. Unconditional Layout Generation" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 450, + 545, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 450, + 545, + 594 + ], + "spans": [ + { + "bbox": [ + 304, + 450, + 545, + 594 + ], + "type": "text", + "content": "A layout " + }, + { + "bbox": [ + 304, + 450, + 545, + 594 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 304, + 450, + 545, + 594 + ], + "type": "text", + "content": " is a set of elements represented by " + }, + { + "bbox": [ + 304, + 450, + 545, + 594 + ], + "type": "inline_equation", + "content": "l = \\{(c_1, b_1), \\ldots, (c_E, b_E)\\}" + }, + { + "bbox": [ + 304, + 450, + 545, + 594 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 450, + 545, + 594 + ], + "type": "inline_equation", + "content": "E \\in \\mathbb{N}" + }, + { + "bbox": [ + 304, + 450, + 545, + 594 + ], + "type": "text", + "content": " is the number of elements in the layout. " + }, + { + "bbox": [ + 304, + 450, + 545, + 594 + ], + "type": "inline_equation", + "content": "c_i \\in \\{1, \\ldots, C\\}" + }, + { + "bbox": [ + 304, + 450, + 545, + 594 + ], + "type": "text", + "content": " is categorical information of the " + }, + { + "bbox": [ + 304, + 450, + 545, + 594 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 450, + 545, + 594 + ], + "type": "text", + "content": "-th element in the layout. " + }, + { + "bbox": [ + 304, + 450, + 545, + 594 + ], + "type": "inline_equation", + "content": "b_i \\in [0, 1]^4" + }, + { + "bbox": [ + 304, + 450, + 545, + 594 + ], + "type": "text", + "content": " is the bounding box of the " + }, + { + "bbox": [ + 304, + 450, + 545, + 594 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 450, + 545, + 594 + ], + "type": "text", + "content": "-th element in normalized coordinates, where the first two values indicate the center location, and the last two indicate the width and height. Following previous works [2, 11, 20] that regard layout generation as generating a sequence of tokens, we quantize each value in " + }, + { + "bbox": [ + 304, + 450, + 545, + 594 + ], + "type": "inline_equation", + "content": "b_i" + }, + { + "bbox": [ + 304, + 450, + 545, + 594 + ], + "type": "text", + "content": " and obtain " + }, + { + "bbox": [ + 304, + 450, + 545, + 594 + ], + "type": "inline_equation", + "content": "[x_i, y_i, w_i, h_i]^\\top \\in \\{1, \\ldots, B\\}^4" + }, + { + "bbox": [ + 304, + 450, + 545, + 594 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 450, + 545, + 594 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 304, + 450, + 545, + 594 + ], + "type": "text", + "content": " is a number of the bins. The layout " + }, + { + "bbox": [ + 304, + 450, + 545, + 594 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 304, + 450, + 545, + 594 + ], + "type": "text", + "content": " is now represented by " + }, + { + "bbox": [ + 304, + 450, + 545, + 594 + ], + "type": "inline_equation", + "content": "l = \\{(c_1, x_1, y_1, w_1, h_1), \\ldots\\}" + }, + { + "bbox": [ + 304, + 450, + 545, + 594 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 594, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 714 + ], + "type": "text", + "content": "In this work, we corrupt a layout in a modality-wise manner in the forward process, and we denoise the corrupted layout while considering all elements and modalities in the reverse process, as we illustrate in Fig. 2. Similarly to D3PM [3], we parameterize " + }, + { + "bbox": [ + 304, + 594, + 545, + 714 + ], + "type": "inline_equation", + "content": "p_{\\theta}" + }, + { + "bbox": [ + 304, + 594, + 545, + 714 + ], + "type": "text", + "content": " by a Transformer encoder [40], which processes an ordered 1D sequence. To process " + }, + { + "bbox": [ + 304, + 594, + 545, + 714 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 304, + 594, + 545, + 714 + ], + "type": "text", + "content": " by " + }, + { + "bbox": [ + 304, + 594, + 545, + 714 + ], + "type": "inline_equation", + "content": "p_{\\theta}" + }, + { + "bbox": [ + 304, + 594, + 545, + 714 + ], + "type": "text", + "content": " while avoiding the order dependency issue [20], we randomly shuffle " + }, + { + "bbox": [ + 304, + 594, + 545, + 714 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 304, + 594, + 545, + 714 + ], + "type": "text", + "content": " in element-wise manner and then flatten it to produce " + }, + { + "bbox": [ + 304, + 594, + 545, + 714 + ], + "type": "inline_equation", + "content": "l_{\\mathrm{flat}} = (c_1, x_1, y_1, w_1, h_1, c_2, x_2, \\ldots)" + }, + { + "bbox": [ + 304, + 594, + 545, + 714 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10169" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 193 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 193 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 193 + ], + "type": "text", + "content": "Variable length generation Existing diffusion models generate fixed-dimensional data and are not directly applicable to the layout generation because the number of elements in each layout varies. To handle this, we introduce a [PAD] token and define a maximum number of elements in the layout as " + }, + { + "bbox": [ + 47, + 72, + 289, + 193 + ], + "type": "inline_equation", + "content": "M \\in \\mathbb{N}" + }, + { + "bbox": [ + 47, + 72, + 289, + 193 + ], + "type": "text", + "content": ". Each layout is fixed-dimensional data composed of " + }, + { + "bbox": [ + 47, + 72, + 289, + 193 + ], + "type": "inline_equation", + "content": "5M" + }, + { + "bbox": [ + 47, + 72, + 289, + 193 + ], + "type": "text", + "content": " tokens by appending " + }, + { + "bbox": [ + 47, + 72, + 289, + 193 + ], + "type": "inline_equation", + "content": "5(M - E)" + }, + { + "bbox": [ + 47, + 72, + 289, + 193 + ], + "type": "text", + "content": " [PAD] tokens. [PAD] is treated similarly to the ordinary token in VQDiffusion and " + }, + { + "bbox": [ + 47, + 72, + 289, + 193 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}_t" + }, + { + "bbox": [ + 47, + 72, + 289, + 193 + ], + "type": "text", + "content": "'s dimension becomes " + }, + { + "bbox": [ + 47, + 72, + 289, + 193 + ], + "type": "inline_equation", + "content": "(K + 2) \\times (K + 2)" + }, + { + "bbox": [ + 47, + 72, + 289, + 193 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 209, + 289, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 209, + 289, + 354 + ], + "spans": [ + { + "bbox": [ + 47, + 209, + 289, + 354 + ], + "type": "text", + "content": "Modality-wise diffusion Discrete state-space models assume that all the standard tokens are switchable by corruption. However, layout tokens comprise a disjoint set of token groups for each attribute in the element. For example, applying the transition rule Eq. (5) may change a token representing an element's category to another token representing the width. To avoid such invalid switching, we propose to apply disjoint corruption matrices " + }, + { + "bbox": [ + 47, + 209, + 289, + 354 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}_t^c,\\mathbf{Q}_t^x,\\mathbf{Q}_t^y,\\mathbf{Q}_t^w,\\mathbf{Q}_t^h" + }, + { + "bbox": [ + 47, + 209, + 289, + 354 + ], + "type": "text", + "content": " for tokens representing different attributes " + }, + { + "bbox": [ + 47, + 209, + 289, + 354 + ], + "type": "inline_equation", + "content": "c,x,y,w,h" + }, + { + "bbox": [ + 47, + 209, + 289, + 354 + ], + "type": "text", + "content": ", as we show in Fig. 2. The size of each matrix is " + }, + { + "bbox": [ + 47, + 209, + 289, + 354 + ], + "type": "inline_equation", + "content": "(C + 2)\\times" + }, + { + "bbox": [ + 47, + 209, + 289, + 354 + ], + "type": "inline_equation", + "content": "(C + 2)" + }, + { + "bbox": [ + 47, + 209, + 289, + 354 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 47, + 209, + 289, + 354 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}_t^c" + }, + { + "bbox": [ + 47, + 209, + 289, + 354 + ], + "type": "text", + "content": " and otherwise " + }, + { + "bbox": [ + 47, + 209, + 289, + 354 + ], + "type": "inline_equation", + "content": "(B + 2)\\times (B + 2)" + }, + { + "bbox": [ + 47, + 209, + 289, + 354 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 47, + 209, + 289, + 354 + ], + "type": "inline_equation", + "content": "+2" + }, + { + "bbox": [ + 47, + 209, + 289, + 354 + ], + "type": "text", + "content": " is for [PAD] and [MASK]." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 369, + 289, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 369, + 289, + 491 + ], + "spans": [ + { + "bbox": [ + 47, + 369, + 289, + 491 + ], + "type": "text", + "content": "Adaptive Quantization The distribution of the position and size information in layouts is highly imbalanced; e.g., elements tend to be aligned to either left, center, or right. Applying uniform quantization to those quantities as in existing layout generation models [2, 11, 20] results in the loss of information. As a pre-processing, we propose to apply a classical clustering algorithm, such as KMeans [29] on " + }, + { + "bbox": [ + 47, + 369, + 289, + 491 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 47, + 369, + 289, + 491 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 369, + 289, + 491 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 47, + 369, + 289, + 491 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 369, + 289, + 491 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 47, + 369, + 289, + 491 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 369, + 289, + 491 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 47, + 369, + 289, + 491 + ], + "type": "text", + "content": " independently to obtain balanced position and size tokens for each dataset. We show in Sec. 4.7 how quantization strategy affects the resulting quality." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 506, + 289, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 506, + 289, + 615 + ], + "spans": [ + { + "bbox": [ + 47, + 506, + 289, + 615 + ], + "type": "text", + "content": "Decoupled Positional Encoding Previous works apply standard positional encoding to a flattened sequence of layout tokens " + }, + { + "bbox": [ + 47, + 506, + 289, + 615 + ], + "type": "inline_equation", + "content": "l_{\\mathrm{flat}}" + }, + { + "bbox": [ + 47, + 506, + 289, + 615 + ], + "type": "text", + "content": " [2, 11, 20]. We argue that this flattening approach could lose the structure information of the layout and lead to inferior generation performance. In layout, each token has two types of indices: " + }, + { + "bbox": [ + 47, + 506, + 289, + 615 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 47, + 506, + 289, + 615 + ], + "type": "text", + "content": "-th element and " + }, + { + "bbox": [ + 47, + 506, + 289, + 615 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 47, + 506, + 289, + 615 + ], + "type": "text", + "content": "-th attribute. We empirically find that independently applying positional encoding to those indices improves final generation performance, which we study in Sec. 4.7." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 623, + 181, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 623, + 181, + 635 + ], + "spans": [ + { + "bbox": [ + 47, + 623, + 181, + 635 + ], + "type": "text", + "content": "3.3. Conditional Generation" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "type": "text", + "content": "We elaborate on solving various conditional layout generation tasks using pre-trained frozen LayoutDM. We inject conditional information in both the initial state " + }, + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_T" + }, + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "type": "text", + "content": " and sampled states " + }, + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{z}_t\\}_{t=0}^{T-1}" + }, + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "type": "text", + "content": " during inference but do not modify the denoising network " + }, + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "type": "inline_equation", + "content": "p_\\theta" + }, + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "type": "text", + "content": ". The actual implementation of the injection differs by the type of conditions." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 547, + 169 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 169 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 169 + ], + "type": "text", + "content": "Strong Constraints The most typical condition is partially known layout fields. Let " + }, + { + "bbox": [ + 304, + 72, + 547, + 169 + ], + "type": "inline_equation", + "content": "\\mathbf{z}^{\\mathrm{known}} \\in \\mathbb{Z}^{N}" + }, + { + "bbox": [ + 304, + 72, + 547, + 169 + ], + "type": "text", + "content": " contain the known fields and " + }, + { + "bbox": [ + 304, + 72, + 547, + 169 + ], + "type": "inline_equation", + "content": "\\mathbf{m} \\in \\{0,1\\}^{N}" + }, + { + "bbox": [ + 304, + 72, + 547, + 169 + ], + "type": "text", + "content": " be a mask vector denoting the known and unknown field as 1 and 0, respectively. In each timestep " + }, + { + "bbox": [ + 304, + 72, + 547, + 169 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 72, + 547, + 169 + ], + "type": "text", + "content": ", we sample " + }, + { + "bbox": [ + 304, + 72, + 547, + 169 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{z}}_{t-1}" + }, + { + "bbox": [ + 304, + 72, + 547, + 169 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 304, + 72, + 547, + 169 + ], + "type": "inline_equation", + "content": "p_{\\theta}(\\mathbf{z}_{t-1}|\\mathbf{z}_t)" + }, + { + "bbox": [ + 304, + 72, + 547, + 169 + ], + "type": "text", + "content": " in Eq. (3) and then inject the condition by " + }, + { + "bbox": [ + 304, + 72, + 547, + 169 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{t-1} = \\mathbf{m} \\odot \\mathbf{z}^{\\mathrm{known}} + (\\mathbf{1} - \\mathbf{m}) \\odot \\hat{\\mathbf{z}}_{t-1}" + }, + { + "bbox": [ + 304, + 72, + 547, + 169 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 72, + 547, + 169 + ], + "type": "inline_equation", + "content": "\\mathbf{1}" + }, + { + "bbox": [ + 304, + 72, + 547, + 169 + ], + "type": "text", + "content": " denotes a " + }, + { + "bbox": [ + 304, + 72, + 547, + 169 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 72, + 547, + 169 + ], + "type": "text", + "content": "-dimensional all-ones vector and " + }, + { + "bbox": [ + 304, + 72, + 547, + 169 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 304, + 72, + 547, + 169 + ], + "type": "text", + "content": " denotes element-wise product." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 182, + 547, + 255 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 182, + 547, + 255 + ], + "spans": [ + { + "bbox": [ + 304, + 182, + 547, + 255 + ], + "type": "text", + "content": "Weak Constraints We may impose a weaker constraint during generation, such as an element in the center. We offer a way to impose such constraints in a unified framework without additional training or external neural network models. We propose to adjust the logits to inject weak constraints in log probability space by" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 336, + 259, + 545, + 272 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 336, + 259, + 545, + 272 + ], + "spans": [ + { + "bbox": [ + 336, + 259, + 545, + 272 + ], + "type": "interline_equation", + "content": "\\log \\hat {p} _ {\\theta} \\left(\\boldsymbol {z} _ {t - 1} | \\boldsymbol {z} _ {t}\\right) \\propto \\log p _ {\\theta} \\left(\\boldsymbol {z} _ {t - 1} | \\boldsymbol {z} _ {t}\\right) + \\lambda_ {\\pi} \\pi , \\tag {6}", + "image_path": "482ec4f3178813a58fc8d71ade85df808f5a9f7a091d936bd60738cec420c8dc.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 277, + 547, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 277, + 547, + 361 + ], + "spans": [ + { + "bbox": [ + 304, + 277, + 547, + 361 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 277, + 547, + 361 + ], + "type": "inline_equation", + "content": "\\pi \\in \\mathbb{R}^{N\\times K}" + }, + { + "bbox": [ + 304, + 277, + 547, + 361 + ], + "type": "text", + "content": " is a prior term that weights the desired outputs, and " + }, + { + "bbox": [ + 304, + 277, + 547, + 361 + ], + "type": "inline_equation", + "content": "\\lambda_{\\pi}\\in \\mathbb{R}" + }, + { + "bbox": [ + 304, + 277, + 547, + 361 + ], + "type": "text", + "content": " is a hyper-parameter. The prior term can be defined either hard-coded (Refinement in Sec. 4.5) or through differentiable loss functions (Relationship in Sec. 4.5). Let " + }, + { + "bbox": [ + 304, + 277, + 547, + 361 + ], + "type": "inline_equation", + "content": "\\{\\mathcal{L}_i\\}_{i = 1}^L" + }, + { + "bbox": [ + 304, + 277, + 547, + 361 + ], + "type": "text", + "content": " be a set of differentiable loss functions given the prediction, the later prior definition can be written by:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 339, + 365, + 545, + 399 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 339, + 365, + 545, + 399 + ], + "spans": [ + { + "bbox": [ + 339, + 365, + 545, + 399 + ], + "type": "interline_equation", + "content": "\\boldsymbol {\\pi} = - \\nabla_ {p _ {\\theta} \\left(\\boldsymbol {z} _ {t - 1} \\mid \\boldsymbol {z} _ {t}\\right)} \\sum_ {i = 1} ^ {L} \\mathcal {L} _ {i} \\left(p _ {\\theta} \\left(\\boldsymbol {z} _ {t - 1} \\mid \\boldsymbol {z} _ {t}\\right)\\right). \\tag {7}", + "image_path": "5d8a10b67b4e75feba6674fb353eae470e68e34d2d7f4127805623c0c9b879a4.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 403, + 547, + 499 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 403, + 547, + 499 + ], + "spans": [ + { + "bbox": [ + 304, + 403, + 547, + 499 + ], + "type": "text", + "content": "Although the formulation of Eq. (7) resembles steering diffusion models by gradients from external models [7, 25], our primal focus is incorporating classical hand-crafted energies for aesthetics principles of layout [32] that do not depend on an external model. In practice, we tune the hyperparameters for imposing weak constraints, such as " + }, + { + "bbox": [ + 304, + 403, + 547, + 499 + ], + "type": "inline_equation", + "content": "\\lambda_{\\pi}" + }, + { + "bbox": [ + 304, + 403, + 547, + 499 + ], + "type": "text", + "content": ". Note that these hyper-parameters are only for inference and are easier to tune than the other training hyper-parameters." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 508, + 382, + 521 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 508, + 382, + 521 + ], + "spans": [ + { + "bbox": [ + 306, + 508, + 382, + 521 + ], + "type": "text", + "content": "4. Experiment" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 528, + 369, + 539 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 528, + 369, + 539 + ], + "spans": [ + { + "bbox": [ + 306, + 528, + 369, + 539 + ], + "type": "text", + "content": "4.1. Datasets" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 545, + 545, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 545, + 617 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 545, + 617 + ], + "type": "text", + "content": "We use two large-scale datasets for comparison, Rico [5] and PubLayNet [45]. As we mention in Sec. 3.2, an element in a layout for each dataset is described by the five attributes. For preprocessing, we set the maximum number of elements per layout " + }, + { + "bbox": [ + 304, + 545, + 545, + 617 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 545, + 545, + 617 + ], + "type": "text", + "content": " to 25. If a layout contains more elements, we discard the whole layout." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 618, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 618, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 618, + 547, + 714 + ], + "type": "text", + "content": "We provide an overview of each dataset. Rico is a dataset of user interface designs for mobile applications containing 25 element categories such as text button, toolbar, and icon. We divide the dataset into 35,851 / 2,109 / 4,218 samples for train, validation, and test splits. PubLayNet is a dataset of research papers containing five element categories, such as table, image, and text. We divide the dataset into 315,757 / 16,619 / 11,142 samples for train, validation, and test splits." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "10170" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 160, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 160, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 160, + 83 + ], + "type": "text", + "content": "4.2. Evaluation Metrics" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 90, + 289, + 258 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 90, + 289, + 258 + ], + "spans": [ + { + "bbox": [ + 46, + 90, + 289, + 258 + ], + "type": "text", + "content": "We employ two primary metrics: FID and Maximum IoU (Max.). These metrics take into account both fidelity and diversity [12], which are two mutually complementary properties widely used in evaluating generative models. FID [12] captures the similarity of generated data to real ones in feature space. We employ an improved feature extraction model for layouts [19] instead of a conventional method [21] to compute FID. Maximum IoU [19] measures the conditional similarity between generated and real layouts. The similarity is measured by computing optimal matching that maximizes average IoU between generated and real layouts that have an identical set of categories. For reference, we show the FID and Maximum IoU computed between the validation and test data as Real data." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 265, + 163, + 276 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 265, + 163, + 276 + ], + "spans": [ + { + "bbox": [ + 47, + 265, + 163, + 276 + ], + "type": "text", + "content": "4.3. Tasks and Baselines" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 59, + 283, + 247, + 295 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 283, + 247, + 295 + ], + "spans": [ + { + "bbox": [ + 59, + 283, + 247, + 295 + ], + "type": "text", + "content": "We test LayoutDM on six tasks for evaluation." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 295, + 287, + 318 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 295, + 287, + 318 + ], + "spans": [ + { + "bbox": [ + 47, + 295, + 287, + 318 + ], + "type": "text", + "content": "Unconditional generates layouts without any conditional input or constraint." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 319, + 287, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 319, + 287, + 342 + ], + "spans": [ + { + "bbox": [ + 47, + 319, + 287, + 342 + ], + "type": "text", + "content": "Category " + }, + { + "bbox": [ + 47, + 319, + 287, + 342 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 47, + 319, + 287, + 342 + ], + "type": "text", + "content": " size+position (C " + }, + { + "bbox": [ + 47, + 319, + 287, + 342 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 47, + 319, + 287, + 342 + ], + "type": "text", + "content": " S + P) is a generation task conditioned on the category of each element [20]." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 343, + 287, + 366 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 343, + 287, + 366 + ], + "spans": [ + { + "bbox": [ + 47, + 343, + 287, + 366 + ], + "type": "text", + "content": "Category " + }, + { + "bbox": [ + 47, + 343, + 287, + 366 + ], + "type": "inline_equation", + "content": "^+" + }, + { + "bbox": [ + 47, + 343, + 287, + 366 + ], + "type": "text", + "content": " size " + }, + { + "bbox": [ + 47, + 343, + 287, + 366 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 47, + 343, + 287, + 366 + ], + "type": "text", + "content": " position " + }, + { + "bbox": [ + 47, + 343, + 287, + 366 + ], + "type": "inline_equation", + "content": "(\\mathbf{C} + \\mathbf{S}\\rightarrow \\mathbf{P})" + }, + { + "bbox": [ + 47, + 343, + 287, + 366 + ], + "type": "text", + "content": " is conditioned on the category and size of each element." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 367, + 287, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 367, + 287, + 403 + ], + "spans": [ + { + "bbox": [ + 47, + 367, + 287, + 403 + ], + "type": "text", + "content": "Completion is conditioned on a small number of elements whose attributes are all known. Given a complete layout, we randomly sample from " + }, + { + "bbox": [ + 47, + 367, + 287, + 403 + ], + "type": "inline_equation", + "content": "0\\%" + }, + { + "bbox": [ + 47, + 367, + 287, + 403 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 47, + 367, + 287, + 403 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 47, + 367, + 287, + 403 + ], + "type": "text", + "content": " of elements." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 403, + 287, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 403, + 287, + 474 + ], + "spans": [ + { + "bbox": [ + 47, + 403, + 287, + 474 + ], + "type": "text", + "content": "Refinement is conditioned on a noisy layout in which only geometric information is perturbed [36]. Following RUITE [36], we synthesize the input layout by adding random noise to the size and position of each element. We sample noise from a standard normal distribution with a mean of 0 and a variance of 0.01." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 474, + 287, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 474, + 287, + 533 + ], + "spans": [ + { + "bbox": [ + 47, + 474, + 287, + 533 + ], + "type": "text", + "content": "Relationship is conditioned on the category of each element and some relationship constraints between the elements [21]. Following CLG-LO [19], we employ the size and location relationships and randomly sample " + }, + { + "bbox": [ + 47, + 474, + 287, + 533 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 47, + 474, + 287, + 533 + ], + "type": "text", + "content": " relationships between elements for the experiment." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 534, + 287, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 534, + 287, + 582 + ], + "spans": [ + { + "bbox": [ + 47, + 534, + 287, + 582 + ], + "type": "text", + "content": "The first four tasks handle basic layout fields. We include a few task-agnostic models for comparison using existing controllable layout generation methods or simple adaptation of generative models in the following:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 582, + 287, + 618 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 582, + 287, + 618 + ], + "spans": [ + { + "bbox": [ + 47, + 582, + 287, + 618 + ], + "type": "text", + "content": "LayoutTrans is a simple autoregressive model [11] trained on a element-level shuffled layout, following [33]. We set a variable generation order to " + }, + { + "bbox": [ + 47, + 582, + 287, + 618 + ], + "type": "inline_equation", + "content": "c \\to w \\to h \\to x \\to y" + }, + { + "bbox": [ + 47, + 582, + 287, + 618 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 618, + 287, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 618, + 287, + 654 + ], + "spans": [ + { + "bbox": [ + 47, + 618, + 287, + 654 + ], + "type": "text", + "content": "MaskGIT* is originally a non-autoregressive model for unconditional fixed-length data generation [4]. We use [PAD] to enable variable-length generation." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 654, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 654, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 47, + 654, + 287, + 677 + ], + "type": "text", + "content": "BLT is a non-autoregressive model with layout-specific decoding strategy [20]." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "content": "BART is a denoising autoencoder that can solve both comprehension and generation tasks based on Transformer encoder-decoder backbone [22]. We randomly generate a" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 72, + 545, + 107 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 107 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 107 + ], + "type": "text", + "content": "number of [MASK] tokens from a uniform distribution between one and the sequence length, and perform masking based on the number." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 108, + 545, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 108, + 545, + 144 + ], + "spans": [ + { + "bbox": [ + 304, + 108, + 545, + 144 + ], + "type": "text", + "content": "VQDiffusion* is a diffusion-based model originally for text-to-image generation [9]. We adapt the model for layout using " + }, + { + "bbox": [ + 304, + 108, + 545, + 144 + ], + "type": "inline_equation", + "content": "K = C + 4B + 2" + }, + { + "bbox": [ + 304, + 108, + 545, + 144 + ], + "type": "text", + "content": " tokens, including [PAD]." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 155, + 440, + 167 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 155, + 440, + 167 + ], + "spans": [ + { + "bbox": [ + 306, + 155, + 440, + 167 + ], + "type": "text", + "content": "4.4. Implementation Details" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 175, + 545, + 222 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 175, + 545, + 222 + ], + "spans": [ + { + "bbox": [ + 304, + 175, + 545, + 222 + ], + "type": "text", + "content": "We re-implement most of the models since there are few official implementations publicly available except [11, 19, 20]" + }, + { + "bbox": [ + 304, + 175, + 545, + 222 + ], + "type": "inline_equation", + "content": "^2" + }, + { + "bbox": [ + 304, + 175, + 545, + 222 + ], + "type": "text", + "content": ". We train all the models on the two datasets with three independent trials and report the average of the results." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 223, + 545, + 295 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 223, + 545, + 295 + ], + "spans": [ + { + "bbox": [ + 304, + 223, + 545, + 295 + ], + "type": "text", + "content": "LayoutDM follows VQDiffusion for hyper-parameters unless specified, such as configurations for " + }, + { + "bbox": [ + 304, + 223, + 545, + 295 + ], + "type": "inline_equation", + "content": "p_{\\theta}" + }, + { + "bbox": [ + 304, + 223, + 545, + 295 + ], + "type": "text", + "content": " and the transition matrix parameters i.e. " + }, + { + "bbox": [ + 304, + 223, + 545, + 295 + ], + "type": "inline_equation", + "content": "\\alpha_{t}" + }, + { + "bbox": [ + 304, + 223, + 545, + 295 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 223, + 545, + 295 + ], + "type": "inline_equation", + "content": "\\gamma_{t}" + }, + { + "bbox": [ + 304, + 223, + 545, + 295 + ], + "type": "text", + "content": ". We set the loss weight " + }, + { + "bbox": [ + 304, + 223, + 545, + 295 + ], + "type": "inline_equation", + "content": "\\lambda = 0.1" + }, + { + "bbox": [ + 304, + 223, + 545, + 295 + ], + "type": "text", + "content": " (in Eq. (4)) and the diffusion timesteps " + }, + { + "bbox": [ + 304, + 223, + 545, + 295 + ], + "type": "inline_equation", + "content": "T = 100" + }, + { + "bbox": [ + 304, + 223, + 545, + 295 + ], + "type": "text", + "content": ". For optimization, we use AdamW [27] with learning rate of " + }, + { + "bbox": [ + 304, + 223, + 545, + 295 + ], + "type": "inline_equation", + "content": "5.0 \\times 10^{-4}" + }, + { + "bbox": [ + 304, + 223, + 545, + 295 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 223, + 545, + 295 + ], + "type": "inline_equation", + "content": "\\beta_{1} = 0.9" + }, + { + "bbox": [ + 304, + 223, + 545, + 295 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 223, + 545, + 295 + ], + "type": "inline_equation", + "content": "\\beta_{2} = 0.98" + }, + { + "bbox": [ + 304, + 223, + 545, + 295 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 297, + 545, + 416 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 297, + 545, + 416 + ], + "spans": [ + { + "bbox": [ + 304, + 297, + 545, + 416 + ], + "type": "text", + "content": "Many models, including LayoutDM, use Transformer [40] encoder backbone. We define a shared configuration as follows: 4 layers, 8 attention heads, 512 embedding dimensions, 2048 hidden dimensions, and 0.1 dropout rate. For other models with extra modules, we adjust the number of hidden dimensions to roughly match the number of parameters for a fair comparison. We randomly shuffle elements in the layout to avoid fixed-order generation during training. We search best hyper-parameters to obtain the best FID using the validation set." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 426, + 441, + 439 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 426, + 441, + 439 + ], + "spans": [ + { + "bbox": [ + 306, + 426, + 441, + 439 + ], + "type": "text", + "content": "4.5.Quantitative Evaluation" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 446, + 545, + 637 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 446, + 545, + 637 + ], + "spans": [ + { + "bbox": [ + 304, + 446, + 545, + 637 + ], + "type": "inline_equation", + "content": "\\mathbf{C} \\rightarrow \\mathbf{S} + \\mathbf{P}" + }, + { + "bbox": [ + 304, + 446, + 545, + 637 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 446, + 545, + 637 + ], + "type": "inline_equation", + "content": "\\mathbf{C} + \\mathbf{S} \\rightarrow \\mathbf{P}" + }, + { + "bbox": [ + 304, + 446, + 545, + 637 + ], + "type": "text", + "content": ", Completion In these tasks, we inject conditions by masking. We summarize comparisons in Tab. 1. As task-specific models, we include Layout-VAE [16], NDN-none [21], and LayoutGAN++ [19] for " + }, + { + "bbox": [ + 304, + 446, + 545, + 637 + ], + "type": "inline_equation", + "content": "\\mathbf{C} \\rightarrow \\mathbf{S} + \\mathbf{P}" + }, + { + "bbox": [ + 304, + 446, + 545, + 637 + ], + "type": "text", + "content": ". We also adapt these models for " + }, + { + "bbox": [ + 304, + 446, + 545, + 637 + ], + "type": "inline_equation", + "content": "\\mathbf{C} + \\mathbf{S} \\rightarrow \\mathbf{P}" + }, + { + "bbox": [ + 304, + 446, + 545, + 637 + ], + "type": "text", + "content": ". LayoutDM outperforms other models except LayoutTrans [11] in completion. The significant performance gap between LayoutDM and VQDiffusion* suggests the contribution of our proposals to go beyond the simple discrete diffusion models discussed in Sec. 3.2. Results in the completion suggest that a combination of padding and diffusion models is the primal key to the generation quality. We find that FID and Maximum IoU are not highly correlated only in the completion task. We conjecture that Maximum IoU may become unstable when categories are also predicted, unlike the " + }, + { + "bbox": [ + 304, + 446, + 545, + 637 + ], + "type": "inline_equation", + "content": "\\mathbf{C} \\rightarrow \\mathbf{S} + \\mathbf{P}" + }, + { + "bbox": [ + 304, + 446, + 545, + 637 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 446, + 545, + 637 + ], + "type": "inline_equation", + "content": "\\mathbf{C} + \\mathbf{S} \\rightarrow \\mathbf{P}" + }, + { + "bbox": [ + 304, + 446, + 545, + 637 + ], + "type": "text", + "content": " tasks where categories are given." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 638, + 545, + 663 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 638, + 545, + 663 + ], + "spans": [ + { + "bbox": [ + 304, + 638, + 545, + 663 + ], + "type": "text", + "content": "Fig. 3 shows the qualitative results of some models, including LayoutDM. We can see that LayoutDM generates" + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 304, + 673, + 545, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 673, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 673, + 545, + 713 + ], + "type": "text", + "content": "2 Unfortunately, most datasets have no official train-val-test splits, and previous approaches work on different splits and pre-processing strategies. Furthermore, models for FID computation also vary. Thus, we cannot directly compare our results with the reported figure in the literature." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10171" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 52, + 106, + 542, + 311 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "text", + "content": "Table 1. Quantitative comparison in conditional generation given partially known fields. Top two results are highlighted in bold and underline, respectively. " + }, + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "inline_equation", + "content": "\\dagger" + }, + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "text", + "content": " indicates the results of BLT trained with [PAD] as an additional vocabulary since the original model cannot perform unordered completion in practice." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 52, + 106, + 542, + 311 + ], + "lines": [ + { + "bbox": [ + 52, + 106, + 542, + 311 + ], + "spans": [ + { + "bbox": [ + 52, + 106, + 542, + 311 + ], + "type": "table", + "html": "
ModelTask DatasetCategory → Size+PositionCategory+Size → PositionCompletion
Rico FID ↓PubLayNet Max. ↑FID ↓Max. ↑Rico FID ↓Max. ↑PubLayNet FID ↓Max. ↑Rico FID ↓Max. ↑PubLayNet FID ↓Max. ↑
Task-specific models
LayoutVAE [16]33.30.24926.00.31630.60.28327.50.315-----
NDN-none [21]28.40.15861.10.16262.80.21969.40.222-----
LayoutGAN++ [19]6.840.26724.00.2636.220.3489.940.342-----
Task-agnostic models
LayoutTrans [11]5.570.22314.10.2723.730.32316.90.3203.710.5378.360.451
MaskGIT* [4]26.10.26217.20.3198.050.3205.860.38033.50.53319.70.484
BLT [20]17.40.20272.10.2154.480.3405.100.387117†0.471†131†0.345†
BART [22]3.970.2539.360.3203.180.3345.880.3758.870.5279.580.446
VQDiffusion* [9]4.340.25210.30.3193.210.3317.130.37411.00.54111.10.373
LayoutDM3.550.2777.950.3102.220.3924.250.3819.000.5767.650.377
Real data1.850.6916.250.4381.850.6916.250.4381.850.6916.250.438
", + "image_path": "9510b0f2095ee1530c200932420c0ee6ef7701c86ed982479fe4cd7c1e146789.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 55, + 318, + 299, + 528 + ], + "blocks": [ + { + "bbox": [ + 55, + 318, + 299, + 528 + ], + "lines": [ + { + "bbox": [ + 55, + 318, + 299, + 528 + ], + "spans": [ + { + "bbox": [ + 55, + 318, + 299, + 528 + ], + "type": "image", + "image_path": "c052df74a74cfd37cb53b40775420b90ea54e35f7bf13c6dd0c79ad7654b3494.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 156, + 537, + 436, + 550 + ], + "lines": [ + { + "bbox": [ + 156, + 537, + 436, + 550 + ], + "spans": [ + { + "bbox": [ + 156, + 537, + 436, + 550 + ], + "type": "text", + "content": "Figure 3. Comparison in conditional generation given partially known fields." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 302, + 318, + 533, + 528 + ], + "blocks": [ + { + "bbox": [ + 302, + 318, + 533, + 528 + ], + "lines": [ + { + "bbox": [ + 302, + 318, + 533, + 528 + ], + "spans": [ + { + "bbox": [ + 302, + 318, + 533, + 528 + ], + "type": "image", + "image_path": "2523a6d5fc751ca702791f586038145ff1666f3f1d0aab5a97cb4d0b892de453.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 570, + 288, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 288, + 594 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 288, + 594 + ], + "type": "text", + "content": "high-quality layouts with fewer layout aesthetics violations, such as misalignment and overlap, given diverse conditions." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "text", + "content": "Unconditional Generation Tab. 2 summarizes the results of unconditional generation. Unconditional layout generation methods often assume fixed order for element generation e.g. top-to-bottom rather than random order for better generation quality by constraining the prediction. For reference, we additionally report the results of LayoutTrans [11] trained on the fixed element order (LayoutTrans-fixed). Although we design LayoutDM's primarily for conditional" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 570, + 547, + 691 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 547, + 691 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 547, + 691 + ], + "type": "text", + "content": "generation, LayoutDM achieves the best FID under random element order setting. We conjecture that BLT's poor performance is due to train-test mask distribution inconsistency caused by their hierarchical masking strategy for training. BLT masks a randomly sampled number of fields from a single semantic group i.e. category, position, or size. However, decoding starts with all masked tokens in inference. The alignment metric of Real data stays at 0.109 in Rico. Too small alignment values of LayoutTrans and MaskGIT can be a signal of producing trivial outputs in Rico." + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "10172" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 97, + 291, + 235 + ], + "blocks": [ + { + "bbox": [ + 47, + 71, + 287, + 93 + ], + "lines": [ + { + "bbox": [ + 47, + 71, + 287, + 93 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 287, + 93 + ], + "type": "text", + "content": "Table 2. Quantitative comparison in unconditional generation. Top two results are highlighted in bold and underline, respectively." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 97, + 291, + 235 + ], + "lines": [ + { + "bbox": [ + 48, + 97, + 291, + 235 + ], + "spans": [ + { + "bbox": [ + 48, + 97, + 291, + 235 + ], + "type": "table", + "html": "
ModelDatasetRicoPubLayNet
FID ↓Align. ↓FID ↓Align. ↓
LayoutTrans-fixed [11]6.470.13317.10.084
LayoutTrans [11]7.630.06813.90.127
MaskGIT* [4]52.10.01527.10.101
BLT [20]88.21.0301160.153
BART [22]11.90.09016.60.116
VQDiffusion* [9]7.460.17815.40.193
LayoutDM6.650.16213.90.195
Real data1.850.1096.250.0214
", + "image_path": "c76e919a4a96772a0a504778814150beeb5eab97157f6c858340091beebba9ef.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 52, + 274, + 283, + 401 + ], + "blocks": [ + { + "bbox": [ + 47, + 249, + 286, + 272 + ], + "lines": [ + { + "bbox": [ + 47, + 249, + 286, + 272 + ], + "spans": [ + { + "bbox": [ + 47, + 249, + 286, + 272 + ], + "type": "text", + "content": "Table 3. Quantitative comparison in the refinement task. Top two results are highlighted in bold and underline, respectively." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 52, + 274, + 283, + 401 + ], + "lines": [ + { + "bbox": [ + 52, + 274, + 283, + 401 + ], + "spans": [ + { + "bbox": [ + 52, + 274, + 283, + 401 + ], + "type": "table", + "html": "
DatasetRicoPubLayNet
ModelFID ↓ Max. ↑ Sim ↑ FID ↓ Max. ↑ Sim ↑
Task-specific models
RUIT [36]3.230.4210.2216.390.4150.174
Task-agnostic models
Noisy input1340.2130.1771300.2420.147
LayoutDM2.770.3700.2056.750.3520.149
w/o logit adj.3.550.2770.1687.950.3100.127
Real data1.850.6910.2606.250.4380.216
", + "image_path": "5f430fb0cdbae0563c97c061b03b566d1be2cb4021f8cb093e764a12cf18cb8c.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 77, + 419, + 254, + 559 + ], + "blocks": [ + { + "bbox": [ + 77, + 419, + 254, + 559 + ], + "lines": [ + { + "bbox": [ + 77, + 419, + 254, + 559 + ], + "spans": [ + { + "bbox": [ + 77, + 419, + 254, + 559 + ], + "type": "image", + "image_path": "6af11653bd84344e7d04e93f7d09d49e0da29777cf7d1c1ce0fd3be9fc5c7cab.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 64, + 568, + 268, + 580 + ], + "lines": [ + { + "bbox": [ + 64, + 568, + 268, + 580 + ], + "spans": [ + { + "bbox": [ + 64, + 568, + 268, + 580 + ], + "type": "text", + "content": "Figure 4. Qualitative comparison in the refinement task." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "type": "text", + "content": "Refinement Our LayoutDM performs this task with a combination of the strong constraints of element categories, i.e., setting " + }, + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "type": "inline_equation", + "content": "z^{\\mathrm{known}} = \\{(c_1, [\\mathrm{MASK}], \\dots, [\\mathrm{MASK}]), \\dots\\}" + }, + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "type": "text", + "content": ", and the weak constraints that geometric outputs appear near noisy inputs. As an example of the weak constraint, we describe a constraint that imposes the x-coordinate estimate of " + }, + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "type": "text", + "content": "-th element close to the noisy continuous observation " + }, + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\hat{x}_i" + }, + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "type": "text", + "content": ". We denote a sliced vector of the prior term " + }, + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "type": "text", + "content": " in Eq. (6) that corresponds to the x-coordinate of " + }, + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "type": "text", + "content": "-th element as " + }, + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\pi_x^i \\in \\mathbb{R}^K" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 309, + 71, + 536, + 214 + ], + "blocks": [ + { + "bbox": [ + 309, + 71, + 536, + 214 + ], + "lines": [ + { + "bbox": [ + 309, + 71, + 536, + 214 + ], + "spans": [ + { + "bbox": [ + 309, + 71, + 536, + 214 + ], + "type": "image", + "image_path": "5b12d31d160cafd34bd1efc8a436c274d7341b7870cc0d290efc1b9fcf0cc73d.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 222, + 544, + 244 + ], + "lines": [ + { + "bbox": [ + 305, + 222, + 544, + 244 + ], + "spans": [ + { + "bbox": [ + 305, + 222, + 544, + 244 + ], + "type": "text", + "content": "Figure 5. Quality-violation trade-off in the relationship task. Lower scores indicate better performance for both metrics." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 308, + 255, + 539, + 389 + ], + "blocks": [ + { + "bbox": [ + 308, + 255, + 539, + 389 + ], + "lines": [ + { + "bbox": [ + 308, + 255, + 539, + 389 + ], + "spans": [ + { + "bbox": [ + 308, + 255, + 539, + 389 + ], + "type": "image", + "image_path": "1b4f46a108163d886a576dbef3e7e1739fa646f25df362e022a25e71c0e63fde.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 321, + 400, + 529, + 412 + ], + "lines": [ + { + "bbox": [ + 321, + 400, + 529, + 412 + ], + "spans": [ + { + "bbox": [ + 321, + 400, + 529, + 412 + ], + "type": "text", + "content": "Figure 6. Qualitative comparison in the relationship task." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 433, + 365, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 433, + 365, + 445 + ], + "spans": [ + { + "bbox": [ + 306, + 433, + 365, + 445 + ], + "type": "text", + "content": "and define by:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 330, + 453, + 545, + 486 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 330, + 453, + 545, + 486 + ], + "spans": [ + { + "bbox": [ + 330, + 453, + 545, + 486 + ], + "type": "interline_equation", + "content": "\\left[ \\pi_ {x} ^ {i} \\right] _ {j} = \\left\\{ \\begin{array}{l l} 1 & \\text {i f} | \\operatorname {l o c} (j) - \\hat {x} _ {i} | < m \\text {a n d} j \\in X \\\\ 0 & \\text {o t h e r w i s e ,} \\end{array} \\right. \\tag {8}", + "image_path": "750219d3df08d4d620c209b88292173c93f3dd7be21af24c481fd1b12300280c.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 495, + 545, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 495, + 545, + 553 + ], + "spans": [ + { + "bbox": [ + 304, + 495, + 545, + 553 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 495, + 545, + 553 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 495, + 545, + 553 + ], + "type": "text", + "content": " is a hyper-parameter indicating a margin, " + }, + { + "bbox": [ + 304, + 495, + 545, + 553 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 304, + 495, + 545, + 553 + ], + "type": "text", + "content": " is a set of indices denoting tokens for " + }, + { + "bbox": [ + 304, + 495, + 545, + 553 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 495, + 545, + 553 + ], + "type": "text", + "content": " in the vocabularies, and " + }, + { + "bbox": [ + 304, + 495, + 545, + 553 + ], + "type": "inline_equation", + "content": "\\mathrm{loc}(j)" + }, + { + "bbox": [ + 304, + 495, + 545, + 553 + ], + "type": "text", + "content": " is a function that returns the centroid value of " + }, + { + "bbox": [ + 304, + 495, + 545, + 553 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 304, + 495, + 545, + 553 + ], + "type": "text", + "content": "-th token in the vocabularies. We define similar constraints for the other geometric variables and elements." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 554, + 546, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 554, + 546, + 662 + ], + "spans": [ + { + "bbox": [ + 304, + 554, + 546, + 662 + ], + "type": "text", + "content": "We summarize the performance in Tab. 3. We additionally report DocSim [34] (Sim) to measure the similarity of a predicted and its corresponding ground truth layout. Imposing noisy geometric fields as a weak prior significantly improves the masking-only model and makes the performance much closer to RUITE [36], which is a denoising model not applicable to other layout tasks. We compare some results in Fig. 4. Both LayoutDM and RUITE successfully recover complete layouts from non-trivially noisy layouts." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 677, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 546, + 714 + ], + "type": "text", + "content": "Relationship We use Eq. (7) to incorporate the relational constraints during the sampling step of LayoutDM. We follow [19] to employ the loss functions penalizing size and" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10173" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 70, + 287, + 218 + ], + "blocks": [ + { + "bbox": [ + 48, + 70, + 287, + 218 + ], + "lines": [ + { + "bbox": [ + 48, + 70, + 287, + 218 + ], + "spans": [ + { + "bbox": [ + 48, + 70, + 287, + 218 + ], + "type": "image", + "image_path": "748788104512bedf0b7a893cce4765d4207b9f95637a981d495cb79f9d69ce2a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 228, + 286, + 240 + ], + "lines": [ + { + "bbox": [ + 47, + 228, + 286, + 240 + ], + "spans": [ + { + "bbox": [ + 47, + 228, + 286, + 240 + ], + "type": "text", + "content": "Figure 7. Speed-quality trade-off of different models for " + }, + { + "bbox": [ + 47, + 228, + 286, + 240 + ], + "type": "inline_equation", + "content": "\\mathrm{C + S\\to P}" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 73, + 296, + 257, + 398 + ], + "blocks": [ + { + "bbox": [ + 47, + 265, + 286, + 286 + ], + "lines": [ + { + "bbox": [ + 47, + 265, + 286, + 286 + ], + "spans": [ + { + "bbox": [ + 47, + 265, + 286, + 286 + ], + "type": "text", + "content": "Table 4. Ablation study results on layout-specific modification in unconditional generation of Rico [5] dataset." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 73, + 296, + 257, + 398 + ], + "lines": [ + { + "bbox": [ + 73, + 296, + 257, + 398 + ], + "spans": [ + { + "bbox": [ + 73, + 296, + 257, + 398 + ], + "type": "table", + "html": "
FID ↓Align. ↓
LayoutDM6.650.162
w/o modality-wise diff.7.320.156
w/o decoupled pos. enc.6.780.227
w/ uniform-quantization7.580.256
w/ percentile-quantization9.790.232
Real Data1.850.109
", + "image_path": "c61cf820b752cd05e36d3e317c7a07f209367307c683022618bb3f5e1d51c028.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 431, + 286, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 431, + 286, + 563 + ], + "spans": [ + { + "bbox": [ + 46, + 431, + 286, + 563 + ], + "type": "text", + "content": "location relationships between elements that do not match user specifications. We define the loss functions for continuous bounding boxes, and we have to convert the predicted discrete bounding boxes to continuous ones in a differentiable manner. Given estimated probabilities of discrete x-coordinates " + }, + { + "bbox": [ + 46, + 431, + 286, + 563 + ], + "type": "inline_equation", + "content": "p(x)" + }, + { + "bbox": [ + 46, + 431, + 286, + 563 + ], + "type": "text", + "content": ", for example, we compute the continuous x-coordinate " + }, + { + "bbox": [ + 46, + 431, + 286, + 563 + ], + "type": "inline_equation", + "content": "\\bar{x}" + }, + { + "bbox": [ + 46, + 431, + 286, + 563 + ], + "type": "text", + "content": " by " + }, + { + "bbox": [ + 46, + 431, + 286, + 563 + ], + "type": "inline_equation", + "content": "\\bar{x} = \\sum_{n\\in X}p(x = n)\\log (n)" + }, + { + "bbox": [ + 46, + 431, + 286, + 563 + ], + "type": "text", + "content": ". Similar conversion applies to the other attributes. Empirically, we find that applying the logit adjustment multiple times (three times in our experiments) to each diffusion step moderately improves performance." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 570, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 286, + 713 + ], + "type": "text", + "content": "We compare LayoutDM with two task-specific approaches: NDN-partial [21] and CLG-LO based on LayoutGAN++ [19]. We show the results in Fig. 5. We additionally report constraint violation error rates [19]. LayoutDM can control the strength of the logit adjustment as in Eq. (6) and produces an FID-violation trade-off curve. LayoutDM is comparable to NDN-partial in Rico and outperforms NDN-partial by a large margin in PubLayNet. Although LayoutDM is inferior to CLG-LO in both datasets, note that the average runtime of CLG-LO is 4.0s, which is much slower than 0.5s in LayoutDM. We show some results of LayoutDM in Fig. 6." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 72, + 443, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 443, + 85 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 443, + 85 + ], + "type": "text", + "content": "4.6. Speed-Quality Trade-off" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 91, + 545, + 224 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 91, + 545, + 224 + ], + "spans": [ + { + "bbox": [ + 304, + 91, + 545, + 224 + ], + "type": "text", + "content": "Runtime is also essential for a controllable generation. We show a speed-quality trade-off curve for " + }, + { + "bbox": [ + 304, + 91, + 545, + 224 + ], + "type": "inline_equation", + "content": "\\mathrm{C + S\\rightarrow P}" + }, + { + "bbox": [ + 304, + 91, + 545, + 224 + ], + "type": "text", + "content": " as shown in Fig. 7. The Transformer encoder-only models, such as LayoutDM and BLT, can achieve fast generation at the sacrifice of quality. We employ fast-sampling strategy employed in discrete diffusion models [3] for LayoutDM by " + }, + { + "bbox": [ + 304, + 91, + 545, + 224 + ], + "type": "inline_equation", + "content": "p_{\\theta}(z_{t - \\Delta}|\\boldsymbol {z}_t)\\propto \\sum_{\\tilde{\\boldsymbol{z}}_0}q(\\boldsymbol{z}_{t - \\Delta},\\boldsymbol {z}_t|\\tilde{\\boldsymbol{z}}_0)\\tilde{p}_{\\theta}(\\tilde{\\boldsymbol{z}}_0|\\boldsymbol {z}_t)" + }, + { + "bbox": [ + 304, + 91, + 545, + 224 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 91, + 545, + 224 + ], + "type": "inline_equation", + "content": "\\Delta \\in \\mathbb{N}" + }, + { + "bbox": [ + 304, + 91, + 545, + 224 + ], + "type": "text", + "content": " indicates a step size for generation in " + }, + { + "bbox": [ + 304, + 91, + 545, + 224 + ], + "type": "inline_equation", + "content": "\\frac{T}{\\Delta}" + }, + { + "bbox": [ + 304, + 91, + 545, + 224 + ], + "type": "text", + "content": " steps. Despite being a task-agnostic model, LayoutDM achieves the best quality-speed trade-off except for task-specific LayoutGAN++ [19] that runs under 10ms." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 233, + 399, + 246 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 233, + 399, + 246 + ], + "spans": [ + { + "bbox": [ + 306, + 233, + 399, + 246 + ], + "type": "text", + "content": "4.7. Ablation Study" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 252, + 545, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 252, + 545, + 300 + ], + "spans": [ + { + "bbox": [ + 304, + 252, + 545, + 300 + ], + "type": "text", + "content": "We investigate whether techniques in Sec. 3.2 improve the performance. First, we evaluate a choice of quantization methods for the geometric fields of elements. Instead of KMeans, we compute centroids for the quantization by:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 301, + 545, + 384 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 306, + 301, + 545, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 301, + 545, + 348 + ], + "spans": [ + { + "bbox": [ + 306, + 301, + 545, + 348 + ], + "type": "text", + "content": "- Uniform: This is dataset-agnostic quantization, which is popular in previous works [2, 11, 20]. Following [11], we choose " + }, + { + "bbox": [ + 306, + 301, + 545, + 348 + ], + "type": "inline_equation", + "content": "\\{0.0, \\frac{1}{B}, \\dots, \\frac{B - 1}{B}\\}" + }, + { + "bbox": [ + 306, + 301, + 545, + 348 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 301, + 545, + 348 + ], + "type": "inline_equation", + "content": "\\{\\frac{1}{B}, \\dots, \\frac{B - 1}{B}, 1.0\\}" + }, + { + "bbox": [ + 306, + 301, + 545, + 348 + ], + "type": "text", + "content": " for the position and size, respectively." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 350, + 545, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 350, + 545, + 384 + ], + "spans": [ + { + "bbox": [ + 306, + 350, + 545, + 384 + ], + "type": "text", + "content": "- Percentile: we sort the data into equally sized groups and obtain average values for each group as the centroids. This is dataset-specific quantization similar to KMeans." + } + ] + } + ], + "index": 11 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 304, + 385, + 545, + 481 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 385, + 545, + 481 + ], + "spans": [ + { + "bbox": [ + 304, + 385, + 545, + 481 + ], + "type": "text", + "content": "We show the result at the bottom of Tab. 4. We additionally report the Alignment metric (Align.) used in [19] since the choice of the quantization affects the alignment between elements. Compared to Linear and Percentile, KMeans quantization significantly improves both FID and Alignment. We confirm that our modality-wise diffusion and decoupled positional encoding both moderately improve the performance, as we show at the top half of Tab. 4." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 495, + 375, + 506 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 495, + 375, + 506 + ], + "spans": [ + { + "bbox": [ + 306, + 495, + 375, + 506 + ], + "type": "text", + "content": "5. Discussion" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 515, + 545, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 515, + 545, + 574 + ], + "spans": [ + { + "bbox": [ + 304, + 515, + 545, + 574 + ], + "type": "text", + "content": "LayoutDM is based on diffusion models for discrete state-space. Using continuous state-space as in latent diffusion models [37] would be interesting. Extension of LayoutDM to handle various layout properties such as color [17] and image/text [41] is also appealing." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 575, + 545, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 575, + 545, + 647 + ], + "spans": [ + { + "bbox": [ + 304, + 575, + 545, + 647 + ], + "type": "text", + "content": "We believe our proposed logit adjustment can incorporate more attributes. Attribute-conditional LayoutGAN [24] considers area, aspect ratio, and reading order of elements for fine-grained control. Since these attributes can be easily converted to the size and location relationship constraints, incorporating them with our LayoutDM is not very difficult." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "Potential negative impact Our model might be used to automatically generate the basic structure of fake websites or mobile applications, which could lead to scams or the spreading of misinformation." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10174" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 18, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "type": "text", + "content": "[1] Maneesh Agrawala, Wilmot Li, and Floraine Berthouzoz. 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In ICDAR, 2019. 1, 2, 4" + } + ] + } + ], + "index": 11 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "10176" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/LayoutDM_ Transformer-Based Diffusion Model for Layout Generation/5a042bec-4143-4aa8-b201-8f11f7b47f24_content_list.json b/2023/LayoutDM_ Transformer-Based Diffusion Model for Layout Generation/5a042bec-4143-4aa8-b201-8f11f7b47f24_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..47bee03c6c73706c67f3c02e1968bc302f06471e --- /dev/null +++ b/2023/LayoutDM_ Transformer-Based Diffusion Model for Layout Generation/5a042bec-4143-4aa8-b201-8f11f7b47f24_content_list.json @@ -0,0 +1,1432 @@ +[ + { + "type": "text", + "text": "LayoutDM: Transformer-based Diffusion Model for Layout Generation", + "text_level": 1, + "bbox": [ + 124, + 130, + 844, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Shang Chai, Liansheng Zhuang* \nUniversity of Science and Technology of China \nchaishang@mail.ustc.edu.cn, lszhuang@ustc.edu.cn", + "bbox": [ + 158, + 181, + 586, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Fengying Yan Tianjin University fengying@tju.edu.cn", + "bbox": [ + 633, + 181, + 797, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 268, + 313, + 284 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Automatic layout generation that can synthesize high-quality layouts is an important tool for graphic design in many applications. Though existing methods based on generative models such as Generative Adversarial Networks (GANs) and Variational Auto-Encoders (VAEs) have progressed, they still leave much room for improving the quality and diversity of the results. Inspired by the recent success of diffusion models in generating high-quality images, this paper explores their potential for conditional layout generation and proposes Transformer-based Layout Diffusion Model (LayoutDM) by instantiating the conditional denoising diffusion probabilistic model (DDPM) with a purely transformer-based architecture. Instead of using convolutional neural networks, a transformer-based conditional Layout Denoiser is proposed to learn the reverse diffusion process to generate samples from noised layout data. Benefitting from both transformer and DDPM, our LayoutDM is of desired properties such as high-quality generation, strong sample diversity, faithful distribution coverage, and stationary training in comparison to GANs and VAEs. Quantitative and qualitative experimental results show that our method outperforms state-of-the-art generative models in terms of quality and diversity.", + "bbox": [ + 76, + 301, + 472, + 650 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 680, + 209, + 696 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Layouts, i.e. the arrangement of the elements to be displayed in a design, play a critical role in many applications from magazine pages to advertising posters to application interfaces. A good layout guides viewers' reading order and draws their attention to important information. The semantic relationships of elements, the reading order, canvas space allocation and aesthetic principles must be carefully decided in the layout design process. However, manually arranging design elements to meet aesthetic goals and user-specified constraints is time-consuming. To aid the design of graphic layouts, the task of layout generation aims to", + "bbox": [ + 75, + 707, + 468, + 875 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "generate design layouts given a set of design components with user-specified attributes. Though meaningful attempts are made [1, 10, 11, 15, 18, 21, 23-25, 33, 44-46], it is still challenging to generate realistic and complex layouts, because many factors need to be taken into consideration, such as design elements, their attributes, and their relationships to other elements.", + "bbox": [ + 500, + 268, + 890, + 375 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Over the past few years, generative models such as Generative Adversarial Networks (GANs) [9] and Variational Auto-Encoders (VAEs) [20] have gained much attention in layout generation, as they have shown a great promise in terms of faithfully learning a given data distribution and sampling from it. GANs model the sampling procedure of a complex distribution that is learned in an adversarial manner, while VAEs seek to learn a model that assigns a high likelihood to the observed data samples. Though having shown impressive success in generating high-quality layouts, these models have some limitations of their own. GANs are known for potentially unstable training and less distribution coverage due to their adversarial training nature [4, 5, 27], so they are inferior to state-of-the-art likelihood-based models (such as VAEs) in terms of diversity [28, 29, 34]. VAEs can capture more diversity and are typically easier to scale and train than GANs, but still fall short in terms of visual sample quality and sampling efficiency [22].", + "bbox": [ + 496, + 378, + 892, + 667 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, diffusion models such as denoising diffusion probabilistic model (DDPM) [14] have emerged as a powerful class of generative models, capable of producing high-quality images comparable to those of GANs. Importantly, they additionally offer desirable properties such as strong sample diversity, faithful distribution coverage, a stationary training objective, and easy scalability. This implies that diffusion models are well suited for learning models of complex and diverse data, which also motivates us to explore the potential of diffusion-based generative models for graphic layout generation.", + "bbox": [ + 496, + 670, + 893, + 837 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Though diffusion models have shown splendid performance in high-fidelity image generation [8, 14, 35, 39, 41], it is still a sparsely explored area and provides unique challenges to develop diffusion-based generative models for", + "bbox": [ + 498, + 839, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author.", + "bbox": [ + 94, + 886, + 220, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "18349", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "layout generation. First, diffusion models often use convolutional neural networks such as U-Net [36] to learn the reverse process to construct desired data samples from the noise. However, a layout is a non-sequential data structure consisting of varying length samples with discrete (classes) and continuous (coordinates) elements simultaneously, instead of pixels laid on a regular lattice. Obviously, convolutional neural networks are not suitable for layout denoising, which prevents diffusion models from being directly applied to layout generation. Second, the placement and sizing of a given element depend not only on its attributes (such as category label) but also on its relationship to other elements. How to incorporate the attributes knowledge and model the elements' relationship in diffusion models is still an open problem. Since diffusion models are general frameworks, they leave room for adapting the underlying neural architectures to exploit the properties of the data.", + "bbox": [ + 75, + 90, + 472, + 347 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Inspired by the above insights, by instantiating the conditional denoising diffusion probabilistic model (DDPM) with a transformer architecture, this paper proposes Transformer-based Layout Diffusion Model (i.e., LayoutDM) for conditional layout generation given a set of elements with user-specified attributes. The key idea is to use a purely transformer-based architecture instead of the commonly used convolutional neural networks to learn the reverse diffusion process from noised layout data. Benefiting from the self-attention mechanism in transformer layers, LayoutDM can efficiently capture high-level relationship information between elements, and predict the noise at each time step from the noised layout data. Moreover, the attention mechanism also helps model another aspect of the data - namely a varying and large number of elements. Finally, to generate layouts with desired attributes, LayoutDM designs a conditional Layout Denoiser (cLayoutDenoiser) based on a transformer architecture to learn the reverse diffusion process conditioned on the input attributes. Different from previous transformer models in the context of NLP or video, cLayoutDenoiser omits the positional encoding which indicates the element order in the sequence, as we do not consider the order of designed elements on a canvas in our setting. In comparison with current layout generation approaches (such as GANs and VAEs), our LayoutDM offers several desired properties such as high-quality generation, better diversity, faithful distribution coverage, a stationary training objective, and easy scalability. Extensive experiments on five public datasets show that LayoutDM outperforms state-of-the-art methods in different tasks.", + "bbox": [ + 75, + 347, + 472, + 797 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, our main contributions are as follows:", + "bbox": [ + 96, + 801, + 433, + 815 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- This paper proposes a novel LayoutDM to generate high-quality design layouts for a set of elements with user-specified attributes. Compared with existing methods, LayoutDM is of desired properties such as high-quality generation, better diversity, faithful distribution", + "bbox": [ + 91, + 825, + 468, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "coverage, and stationary training. To our best knowledge, LayoutDM is the first attempt to explore the potential of diffusion model for graphic layout generation.", + "bbox": [ + 526, + 90, + 890, + 137 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- This paper explores a new class of diffusion models by replacing the commonly-used U-Net backbone with a transformer, and designs a novel cLayoutDenoiser to reverse the diffusion process from noised layout data and better capture the relationship of elements.", + "- Extensive experiments demonstrate that our method outperforms state-of-the-art models in terms of visual perceptual quality and diversity on five diverse layout datasets." + ], + "bbox": [ + 514, + 140, + 893, + 280 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 305, + 640, + 321 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Layout Generation", + "text_level": 1, + "bbox": [ + 500, + 330, + 681, + 345 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Automatic layout generation has been widely studied for a long time. Early approaches to layout generation [30, 31] embed design rules into manually-defined energy functions. In recent years, generative model based methods are increasingly progressed. LayoutGAN [24] and LayoutVAE [17] are the first attempts to utilize GAN and VAE to generate graphic and scene layouts. NDN [23] represents the relative positional relationship of elements as a graph and uses a graph neural network based conditional VAE to generate graphic layouts. READ [33] uses heuristics to determine the relationships between elements and trains a Recursive Neural Network (RNN) [37, 38] based VAE to learn the layout distribution. CanvasVAE [45] generates vector graphic documents which contain structured information about canvas and elements. VTN [1] and Coarse2fine [16] deploy self-attention based VAEs to generate graphic layouts, making progress in diversity and perceptual quality. LayoutTransformer [11] and BLT [21] define layouts as discrete sequences and exploit the efficiency of transformer and bidirectional-transformer in structured sequence generation. LayoutNet [46], TextLogo3K [44] and ICVT [6] propose conditional layout generative models which can utilize additional attributes about design elements or entire layouts to aid layout generation in different application scenarios. LayoutGAN++ [18] designs a transformer-based generator and discriminator and generates graphic layouts conditioned on the given element category labels.", + "bbox": [ + 496, + 354, + 890, + 762 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Diffusion Model", + "text_level": 1, + "bbox": [ + 500, + 771, + 661, + 786 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Diffusion models [14, 40] have proved its capability of generating high-quality and diverse samples [8, 14, 35] and have recently achieved state-of-the-art results on several benchmark generation tasks [8]. The diffusion model uses diffusion processes to model the generation and defines the sampling of data as the process of gradually denoising from complete Gaussian noise. The forward process gradually", + "bbox": [ + 496, + 794, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "18350", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/6fda5fb58bedeef15b679c43cbb267d964c5717bdd1200dd0924998a41c5b93b.jpg", + "image_caption": [ + "(a) LayoutDM architecture" + ], + "image_footnote": [], + "bbox": [ + 76, + 89, + 468, + 207 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/0a4247d2420e18416038bfca53d3651553a70139a4d872537d062c168127daaa.jpg", + "image_caption": [ + "(b) Architecture of conditional layout denoiser $\\epsilon_{\\theta}$", + "Figure 1. a) Architecture of LayoutDM. It consists of a forward diffusion process and a reverse process modeled by a conditional layout denoiser $\\epsilon_{\\theta}$ . b) Architecture of our transformer-based conditional layout denoiser, cLayoutDenoiser. cLayoutDenoiser predicts the added noise conditioned on the layout attributes $\\pmb{f}$ and time step $t$ ." + ], + "image_footnote": [], + "bbox": [ + 475, + 95, + 883, + 212 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "adds Gaussian noise to the data from a predefined noise schedule until time step $T$ . The reverse process uses a neural backbone often implemented as a U-Net [8, 14, 36, 42] to parameterize the conditional distribution $p(\\pmb{x}_{t - 1}|\\pmb{x}_t)$ . In this work, we instantiate a conditional diffusion model to achieve conditional layout generation.", + "bbox": [ + 75, + 292, + 468, + 383 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Our Method", + "text_level": 1, + "bbox": [ + 76, + 398, + 207, + 414 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Layout Representation", + "text_level": 1, + "bbox": [ + 76, + 422, + 287, + 439 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In our model, each layout consists of a set of elements, and each element is described by both geometric parameters (i.e. location and size) and its attribute (e.g. category label or textual features). Formally, a layout $l$ is denoted as a flattened sequence of integer indices:", + "bbox": [ + 75, + 446, + 468, + 522 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {l} = \\left(g _ {1}, f _ {1}, g _ {2}, f _ {2}, \\dots , g _ {i}, f _ {i}, \\dots , g _ {N}, f _ {N}\\right),\n$$\n", + "text_format": "latex", + "bbox": [ + 125, + 535, + 418, + 551 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $N$ is the number of elements in the layout. $g_{i} = [x_{i},y_{i},w_{i},h_{i}]$ is a vector that presents the geometric parameters (center coordinates and size) of the $i$ -th element in the layout. $f_{i}$ is the attributes of $i$ -th element which might be category label or textual features. For the sake of convenience, the sequence $\\pmb{g} = (g_1,g_2,\\dots ,g_i\\dots ,g_N)$ is named layout geometric parameters, the sequence $\\pmb {f} = (f_{1},f_{2},\\dots ,f_{i}\\dots ,f_{N})$ is named layout attributes. Note here that, the elements in a layout are unordered, so swapping the items in sequence $\\pmb{g}$ and $\\pmb{f}$ does not affect the meaning of the sequences. We normalize the geometric parameters, i.e., $[x_i,y_i,w_i,h_i]$ , $i = 1,2,\\dots ,N$ , to the interval $[-1,1]$ . In this way, layouts have a uniform structured representation.", + "bbox": [ + 75, + 564, + 468, + 775 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. The LayoutDM Architecture", + "text_level": 1, + "bbox": [ + 76, + 786, + 333, + 801 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Fig. 1a illustrates the architecture of LayoutDM. From a high-level perspective, our LayoutDM is an instance of conditional denoising diffusion probabilistic model (DDPM) with a transformer architecture suitable for layout data. DDPM learns to model the Markov transition from simple distribution to layout data distribution and generates", + "bbox": [ + 75, + 809, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "diverse samples through sequential stochastic transitions. To generate desired layouts, LayoutDM uses the input attributes to guide the generative process in DDPM. We follow the method described in Classifier-Free Diffusion Guidance [13] to realize conditional DDPM, and set the guidance strength $w$ to zero for simplicity.", + "bbox": [ + 496, + 292, + 890, + 383 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Specifically, let $q(\\pmb{g}_0|\\pmb{f})$ be the unknown conditional data distribution, where $\\pmb{g}_0$ is the geometric parameters of real layouts, and $\\pmb{f}$ is the layout attributes. LayoutDM models the conditional distribution $q(\\pmb{g}_0|\\pmb{f})$ by two processes: a forward diffusion process and a reverse denoising diffusion process. First, LayoutDM defines the forward diffusion process $q(\\pmb{g}_t|\\pmb{g}_{t-1})$ which maps layout data to noise by gradually adding Gaussian noise at each time step $t$ :", + "bbox": [ + 496, + 383, + 890, + 505 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nq \\left(\\boldsymbol {g} _ {t} \\mid \\boldsymbol {g} _ {t - 1}\\right) = \\mathcal {N} \\left(\\boldsymbol {g} _ {t}; \\sqrt {1 - \\beta_ {t}} \\boldsymbol {g} _ {t - 1}, \\beta_ {t} \\mathbf {I}\\right) \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 560, + 517, + 890, + 534 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\{\\beta_t\\}_{t=1}^T$ are forward process variances.", + "bbox": [ + 498, + 546, + 803, + 561 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Then, LayoutDM defines the conditional reverse diffusion process $p(\\pmb{g}_{t-1} | \\pmb{g}_t, \\pmb{f})$ which performs iterative denoising from pure Gaussian noise to generate high-quality layouts conditioned on layout attributes $\\pmb{f}$ :", + "bbox": [ + 496, + 561, + 890, + 622 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\np _ {\\theta} \\left(\\boldsymbol {g} _ {t - 1} \\mid \\boldsymbol {g} _ {t}, \\boldsymbol {f}\\right) = \\mathcal {N} \\left(\\boldsymbol {g} _ {t - 1}; \\boldsymbol {\\mu} _ {\\theta} \\left(\\boldsymbol {g} _ {t}, t, \\boldsymbol {f}\\right), \\sigma_ {t} ^ {2} \\mathbf {I}\\right) \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 544, + 633, + 890, + 651 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\sigma_{t}$ is the constant variance following [14], $\\mu_{\\theta}$ is the mean of the Gaussian distribution computed by a neural network, and $\\theta$ is the parameters of the network. As shown in Ho et al. [14], we can reparameterize the mean to make the neural network learn the added noise at time step $t$ instead. In this way, $\\mu_{\\theta}$ can be reparameterized as follows:", + "bbox": [ + 496, + 662, + 890, + 753 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {\\mu} _ {\\theta} \\left(\\boldsymbol {g} _ {t}, t, \\boldsymbol {f}\\right) = \\frac {1}{\\sqrt {\\alpha_ {t}}} \\left(\\boldsymbol {g} _ {t} - \\frac {\\beta_ {t}}{\\sqrt {1 - \\bar {\\alpha} _ {t}}} \\boldsymbol {\\epsilon} _ {\\theta} \\left(\\boldsymbol {g} _ {t}, t, \\boldsymbol {f}\\right)\\right) \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 524, + 763, + 890, + 797 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $t$ is the time step, $\\{\\beta_t\\}_{t=1}^T$ are forward process variances, $\\alpha_t = 1 - \\beta_t$ , and $\\overline{\\alpha}_t = \\prod_{s=1}^t \\alpha_s$ . $\\epsilon_\\theta(\\pmb{g}_t, t, \\pmb{f})$ is the neural network to predict the added noise for layout geometric parameters conditioned on elements' attributes at time step $t$ . We also call the neural network $\\epsilon_\\theta(\\pmb{g}_t, t, \\pmb{f})$ as conditional layout denoiser (cLayoutDenoiser).", + "bbox": [ + 496, + 809, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "18351", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.3. Conditional Layout Denoiser", + "text_level": 1, + "bbox": [ + 76, + 90, + 334, + 107 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The inputs to cLayoutDenoiser are layout geometric parameters $\\pmb{g}_t$ , layout attributes $\\pmb{f}$ and time step $t$ . To deal with sequences data, the conditional layout denoiser $\\epsilon_{\\theta}(\\pmb{g}_t, t, \\pmb{f})$ employs a purely transformer-based architecture instead of convolutional neural networks as its backbone. The architecture of cLayoutDenoiser is illustrated in Fig. 1b. Benefiting from the transformer architecture, cLayoutDenoiser can deal with the sequence with various lengths, and capture the relationships among elements. Moreover, cLayoutDenoiser adds \"attributes embeddings\" to the input \"geometric embeddings\", so as to guide the reverse diffusion process at each time step $t$ . Formally, the architecture of cLayoutDenoiser can be described as follow:", + "bbox": [ + 75, + 113, + 472, + 309 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {h} _ {f} = \\text {A t t r i b u t e s E m b e d d i n g} (\\boldsymbol {f}) \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 125, + 318, + 468, + 334 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {h} _ {g} = \\text {G e o m e t r i c E m b e d d i n g} (\\boldsymbol {g} _ {t}) \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 127, + 337, + 468, + 353 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {E} = \\text {E l e m e n t E m b e d d i n g} \\left(\\boldsymbol {h} _ {f}, \\boldsymbol {h} _ {g}, \\mathrm {T E} (t)\\right) \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 133, + 356, + 468, + 372 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {E} ^ {\\prime} = \\operatorname {T r a n s f o r m e r L a y e r s} (\\mathbf {E}) \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 130, + 375, + 468, + 390 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {\\epsilon} = \\operatorname {F C} \\left(\\mathbf {E} ^ {\\prime}\\right) \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 138, + 393, + 468, + 409 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\pmb{f}$ is the layout attributes, $\\pmb{g}_t$ is the noised layout geometric parameters, $\\pmb{h}_f$ and $\\pmb{h}_g$ are their hidden representations. $\\mathbf{E}$ is the element tokens computed by element embedding module, $\\mathbf{E}'$ is intermediate feature. $\\mathrm{TE}(t)$ denotes the timestep embedding, and $\\epsilon$ is the predicted noise. Note here that, since the element order in the sequence makes no sense in our setting, cLayoutDenoiser omits the positional encoding, which is different from existing transformers in the context of NLP or video.", + "bbox": [ + 75, + 417, + 468, + 551 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Geometric, attributes and timestep embedding. Three embedding modules are used to learn meaningful representations for noised layout geometric parameters $g_{t}$ , layout attributes $f$ and time step $t$ . Geometric embedding projects layout geometric parameters to a specific dimension, aiming to find a more efficient feature space than the original coordinate space. Feature embedding learns the continuous features of discrete element attributes by embedding them into a specific dimension. Following [14], we condition cLayoutTransformer on time step $t$ by adding a sinusoidal time embedding $\\mathrm{TE}(t)$ to make the network aware at which time step it is operating.", + "bbox": [ + 75, + 553, + 468, + 733 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Element embedding. Element embedding module calculates the element tokens used as the input of transformer layers. Element tokens should contain geometric, attributes and time step information, so that transformer can efficiently capture the relationship information between elements conditioned on the time step $t$ and layout attributes $f$ . We concatenate the geometric embedding and attributes embedding, and then use a fully-connected layer to fuse element representation. We further perform an element-wise plus operation with timestep embedding on the results to finally obtain the element tokens.", + "bbox": [ + 75, + 734, + 470, + 901 + ], + "page_idx": 3 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Algorithm 1: Training LayoutDM" + ], + "code_body": "Require: conditional layout denoiser $\\epsilon_{\\theta}$ repeat Sample $(g_0,f)\\sim q_{data};$ $t\\sim$ Uniform( $\\{1,\\dots ,T\\}$ . $\\epsilon \\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I})$ .. $\\pmb {g}_t = \\sqrt{\\alpha}_t\\pmb {g}_0 + \\sqrt{1 - \\overline{\\alpha}_t}\\pmb {\\epsilon};$ Take gradient descent step on $\\nabla_{\\theta}\\| \\boldsymbol {\\epsilon} - \\boldsymbol{\\epsilon}_{\\theta}(\\pmb {g}_t,t,\\pmb {f})\\| ^2;$ \nuntil converged;", + "bbox": [ + 516, + 111, + 787, + 252 + ], + "page_idx": 3 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Algorithm 2: Sampling" + ], + "code_body": "Input: layout attributes $\\pmb{f}$ \nOutput: layout geometric parameters $\\pmb{g_0}$ $g_{T}\\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I})$ \nfor $t = T,\\dots ,1$ do $\\mathbf{z}\\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I})$ if $t > 1$ , else $\\mathbf{z} = \\mathbf{0}$ . $g_{t - 1} = \\frac{1}{\\sqrt{\\alpha_t}} (g_t - \\frac{1 - \\alpha_t}{\\sqrt{1 - \\overline{\\alpha}_t}}\\epsilon_\\theta (g_t,t,\\pmb {f})) + \\sigma_t\\mathbf{z}$ \nend \nreturn $\\pmb{g_0}$", + "bbox": [ + 516, + 286, + 841, + 415 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Transformer layers. Generating an effective layout requires understanding the relationships between layout elements. Self-attention mechanism in Transformer [43] has proven effective in capturing high-level relationships between lots of elements in layout generation [1, 11, 15]. In this paper, we adopt multihead attention mechanism to capture relationship information between elements from element tokens. We stack multiple transformer layers (8 in our model) to enable cLayoutDenoiser to capture relationships between layout elements from the element tokens. Positional encoding is omitted because of the unordered nature of elements.", + "bbox": [ + 496, + 428, + 890, + 609 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathbf {E}} = \\operatorname {L a y e r N o r m} \\left(\\mathbf {E} ^ {l - 1} + \\mathbf {H e a d} \\left(e _ {1} ^ {l - 1}, \\dots , e _ {N} ^ {l - 1}\\right)\\right) \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 517, + 614, + 890, + 633 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {E} ^ {l} = \\operatorname {L a y e r N o r m} (\\hat {\\mathbf {E}} + \\operatorname {F F N} (\\hat {\\mathbf {E}})) \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 636, + 890, + 655 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $l = 1, \\dots, L$ denotes the layer index, Head, LayoutNorm and FFN denote multi-head attention layer, Layer Normalization [3] and fully connected feed-forward network. $\\mathbf{E}^{l-1} = (\\pmb{e}_1^{l-1}, \\dots, \\pmb{e}_N^{l-1})$ are the intermediate element tokens used as the input of $l$ -th transformer layer.", + "bbox": [ + 496, + 660, + 890, + 737 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Training and Inference", + "text_level": 1, + "bbox": [ + 500, + 744, + 714, + 760 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Following denoising diffusion probabilistic model [14], we optimize random terms $L_{t}$ which are the KL divergences between $p_{\\theta}(\\pmb{g}_{t-1}|\\pmb{g}_t, \\pmb{f})$ and forward process posteriors. After simplifying the objective function following the method in [14], the final loss function is as follows:", + "bbox": [ + 496, + 767, + 890, + 843 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} L _ {s i m p l e} (\\theta) = \\left\\| \\boldsymbol {\\epsilon} - \\boldsymbol {\\epsilon} _ {\\theta} \\left(\\boldsymbol {g} _ {t}, t, \\boldsymbol {f}\\right) \\right\\| ^ {2} \\\\ = \\| \\boldsymbol {\\epsilon} - \\boldsymbol {\\epsilon} _ {\\theta} \\left(\\sqrt {\\bar {\\alpha} _ {t}} \\boldsymbol {g} _ {0} + \\sqrt {\\left(1 - \\bar {\\alpha} _ {t}\\right)} \\boldsymbol {\\epsilon}, t, \\boldsymbol {f}\\right) \\| ^ {2} \\tag {11} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 517, + 847, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "18352", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\epsilon \\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I})$ $\\epsilon_{\\theta}$ is our conditional layout denoiser, $g_{t}\\sim \\mathcal{N}(g_{t};\\sqrt{\\overline{\\alpha}_{t}} g_{0},(1 - \\overline{\\alpha}_{t})\\mathbf{I})$ is computed using the property of Gaussian distributions and $\\pmb {g}_0$ is the real layout geometric parameters. $\\{\\beta_t\\}_{t = 1}^T$ are forward process variances, $\\alpha_{t} = 1 - \\beta_{t}$ and $\\overline{\\alpha}_t = \\prod_{s = 1}^t\\alpha_s$", + "bbox": [ + 76, + 90, + 467, + 167 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The training and sampling algorithm of LayoutDM are illustrated in Algorithm 1 and Algorithm 2 respectively.", + "bbox": [ + 76, + 169, + 467, + 200 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 222, + 207, + 238 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Experimental Settings", + "text_level": 1, + "bbox": [ + 76, + 250, + 282, + 266 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets. We evaluate our method on five public datasets of layouts for documents, natural scenes, magazines, text logos and mobile phone UIs. Rico [7] is a dataset of user interface designs for mobile applications, containing 72,219 user interfaces from 9,772 Android apps. PublayNet [47] contains 330K samples of machine-annotated scientific documents crawled from the Internet with five categories (text, title, figure, list, table). Magazine [46] is a magazine layout dataset that covers a wide range of magazine categories. It consists of semantic layout annotations. COCO [26] is a large-scale labeled image dataset that contains images of natural scenes with instance segmentation. TextLogo3K [44] is a recently released dataset of text logos. It consists of 3,470 text logo images with manually annotated bounding boxes and pixel-level masks for each character.", + "bbox": [ + 75, + 276, + 467, + 515 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Evaluation metrics. To validate the effectiveness of LayoutDM, we employ four metrics in the literature to measure the perceptual quality of layouts. To be a fair comparison, we follow the guidance in [18] to evaluate these metrics. Specifically, FID [12] measures the distribution distance between real layouts and generated layouts. We use the pre-trained classifiers in [18] to compute FID. Max IoU [18] measures the similarity between the generated layouts and the reference layouts. It is designed to find the best match for each layout from the generated set to the reference set. Overlap and Alignment measure the perceptual quality of generated layouts. Overlap measures the total overlapping area between any pair of bounding boxes inside the layout. Additionally, we measure the Alignment by computing an alignment loss proposed in [25].", + "bbox": [ + 75, + 520, + 467, + 747 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implementing details. The max time step $T$ in LayoutDM is set to 1000. We set the forward process variances to constants increasing linearly from $\\beta_{1} = 10^{-4}$ to $\\beta_{T} = 0.02$ following Ho's design [14]. We use eight transformer layers which use 8-head attention in our model. Adam optimizer [19] with a learning rate of $1 \\times 10^{-5}$ is used to optimize learnable parameters. The batch size is set to 1024. We implement our model with PyTorch [32] and PyTorch Lightning. All experiments are performed on a single NVIDIA Quadro RTX 6000 GPU device.", + "bbox": [ + 75, + 750, + 467, + 900 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/ef2736e0b31429164c5d62b23f71f5d35bd197e512a12776bc48f81f5dd7cb61.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Dataset\nModelRico
FID↓Max. IoU↑Alignment↓Overlap↓
LayoutGAN-W [24]162.75±0.280.30±0.000.71±0.00174.11±0.22
LayoutGAN-R [24]52.01±0.620.24±0.001.13±0.0469.37±0.66
NDN-none [23]13.76±0.280.35±0.000.56±0.0354.75±0.29
LayoutGAN++ [18]14.43±0.130.36±0.000.60±0.1259.85±0.59
VTN [1]9.31±0.210.36±0.000.88±0.1159.31±0.45
LayoutDM(Ours)3.03±0.060.49±0.000.36±0.0657.55±0.48
Real data4.470.650.2650.58
Dataset\nModelPublayNet
FID↓Max. IoU↑Alignment↓Overlap↓
LayoutGAN-W [24]195.38±0.460.21±0.001.21±0.01138.77±0.21
LayoutGAN-R [24]100.24±0.610.24±0.000.82±0.0145.64±0.32
NDN-none [23]35.67±0.350.31±0.000.35±0.0116.5±0.29
LayoutGAN++ [18]20.48±0.290.36±0.000.19±0.0022.80±0.32
VTN [1]13.07±0.470.37±0.000.30±0.0113.15±0.24
LayoutDM(Ours)4.04±0.080.44±0.000.15±0.003.73±0.08
Real data9.540.530.040.22
Dataset\nModelMagazine
FID↓Max. IoU↑Alignment↓Overlap↓
LayoutGAN-W [24]159.2±0.870.12±0.000.74±0.02188.77±0.93
LayoutGAN-R [24]100.66±0.350.16±0.001.90±0.02111.85±1.44
NDN-none [23]23.27±0.090.22±0.001.05±0.0330.31±0.77
LayoutGAN++ [18]13.35±0.410.26±0.000.80±0.0232.40±0.89
VTN [1]12.34±0.390.25±0.001.07±0.0339.97±0.62
LayoutDM(Ours)9.11±0.150.29±0.000.77±0.0332.53±0.72
Real data12.130.350.4325.64
", + "bbox": [ + 501, + 90, + 890, + 439 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 1. Quantitative comparison conditioned on element category labels. For reference, the FID and Max. IoU computed between the validation and test data, and the Alignment and Overlap computed with the test data are shown as real data. LayoutGAN-W and LayoutGAN-R denote LayoutGAN with wireframe rendering discriminator and with relation-based discriminator.", + "bbox": [ + 498, + 449, + 890, + 532 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2.Quantitative Evaluation", + "text_level": 1, + "bbox": [ + 500, + 542, + 718, + 558 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Comparison with state-of-the-art models. We quantitatively evaluate the quality of conditional layout generation results on benchmark datasets: Rico, PublayNet and Magazine. Since most methods are designed for unconditional layout generation and have no available public implements, we compare our method with conditional LayoutGAN [24], NDN-none [23] and LayoutGAN++ [18] by citing the results in [18]. Moreover, we also implement a conditional VTN [1] as our comparison baseline model, so that we can compare with methods based on both VAEs and GANs. All the metrics are computed on the full test splits of the datasets. We report the mean and standard deviation over five independent evaluations for each experiment.", + "bbox": [ + 496, + 566, + 890, + 763 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The comparison results are reported in Tab. 1. From this table, we can observe that: (1) Our method outperforms SOTA methods on both FID and Max. IoU on all three benchmark datasets, which indicates that the generated layouts by our method are more similar to the real layouts than those by SOTA methods. This verifies that our LayoutDM can produce higher-quality and more diverse layouts than SOTA methods, since FID captures both diversity and fidelity. (2) Layouts generated by our method have a lower", + "bbox": [ + 496, + 763, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "18353", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/50ac107518455ced580118dbe2f1e63bf72e26fad5316a1932004749f3d0eff1.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
IoU↓ [21]Overlap↓ [24]Alignment↓ [23]
L-VAE [17]0.45±1.3%0.15±0.9%0.37±0.7%
NDN [23]0.34±1.8%0.12±0.8%0.39±0.4%
VTN [1]0.21±0.6%0.06±0.2%0.33±0.4%
Trans. [11]0.19±0.3%0.06±0.3%0.33±0.3%
BLT [21]0.19±0.2%0.04±0.1%0.25±0.7%
Ours0.0053±0.5%0.01±0.1%0.22±1.2%
", + "bbox": [ + 88, + 88, + 455, + 188 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "FID score than the real ones in validation splits. This is because the generated layouts have identical attributes to those in the test split, while the real layouts in the validation split have different attributes from those in the test split. We provide more analysis on this point in the supplementary material. (3) With regards to Alignment and Overlap, LayoutDM is slightly weaker on Rico and Magazine. Because our method lacks a discriminator that guides the generator to generate layouts with better alignment and overlap properties as in GANs and does not introduce the layout refine module in NDN. This is likely to cause LayoutDM to be inferior to the state-of-the-art on these two metrics.", + "bbox": [ + 78, + 252, + 467, + 431 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Note here that, we don't compare LayoutDM to other state-of-the-art methods such as LayoutTransformer [11] and Coarse2fine [16], because these methods focus on unconditional layout generation problem which is different to our setting. Recently, Kong et al. [21] reimplement the conditional version of VTN and LayoutTransformer, and compare their proposed BLT model with these models under the settings of conditional layout generation. However, they compute the metrics (IoU [21], Alignment [23], Overlap [24]) in different ways. As an extended comparison, we adopt the metrics used by BLT [21], and compare our LayoutDM with VTN, LayoutTransformer, LayoutVAE, NDN and BLT on PublayNet. The comparison results are reported in Tab. 2. As shown in this table, our model also outperforms SOTA methods on all metrics.", + "bbox": [ + 78, + 448, + 467, + 672 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Effect of transformer layers. We conduct ablation experiments to demonstrate the effectiveness of the transformer layers in LayoutDM. Quantitative results are reported in Tab. 3 and qualitative comparisons are shown in Fig. 3. We have the following observation: After replacing the transformer structure in LayoutDM with a sequence of FC layers, the model can still predict a suitable size for each element, but the positional relationships between elements can not be handled, resulting in significant overlapping and misalignment. This proves that the transformer layers play an essential role and can efficiently capture and utilize the high-level relationships between elements to generate high-quality layouts which follow design rules and aesthetic principles.", + "bbox": [ + 78, + 689, + 467, + 898 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/1eaafdfa10a672b53d7970a273fd13ef7d44a8f800485c041e2dbf2c59b8c0ee.jpg", + "table_caption": [ + "Table 2. Comparison with extended methods on PublayNet. Qualitative results are cited from [21]. \"Trans.\" denotes \"LayoutTransformer\" and \"L-VAE\" denotes \"LayoutVAE\"." + ], + "table_footnote": [], + "table_body": "
ArchitectureRico
FID↓Max.IoU↑Alignment↓Overlap↓
w/o transformer52.640.291.0858.13
Full model3.030.490.3657.55
ArchitecturePublayNet
FID↓Max.IoU↑Alignment↓Overlap↓
w/o transformer99.600.270.8963.87
Full model4.040.440.153.73
", + "bbox": [ + 504, + 89, + 885, + 213 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 3. The quantitative results of ablations on transformer layers. \"Full\" denotes our full model. \"w/o transformer\" denotes model without transformer layers.", + "bbox": [ + 503, + 226, + 888, + 266 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Qualitative Comparisons", + "text_level": 1, + "bbox": [ + 503, + 277, + 725, + 292 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Generation quality comparison. To qualitatively compare the generation performance of different models, we compare with the state-of-the-art method LayoutGAN++ and our implemented conditional VTN. We randomly sample layouts from the test dataset and use the element category labels as conditional inputs. Fig. 2 shows the qualitative comparison results. As one can see, LayoutDM can arrange elements in a reasonable and complicated way, generating higher quality layouts than the other two, with fewer overlapping and better alignment.", + "bbox": [ + 503, + 309, + 888, + 459 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Generation diversity comparison. The diversity of results is also an important factor in evaluating the method. We compare the diversity of layouts generated by conditional VTN, LayoutGAN++, and LayoutDM. Fig. 4 show the comparison results. One can see that conditional VTN and LayoutDM generate more diverse results. The Figure element in the results floats on the page. Compared to the other two models, LayoutGAN++ captures less diversity, which places a large Figure element on the top of the pages in columns 2,4, and 5. LayoutDM performs well in diversity because it breaks the generation into a series of conditional diffusion steps which are relatively easy to model. This alleviates the mode collapse problem in strongly conditional generation task that can lead to the generation of similar modes. We provide more qualitative comparisons on diversity in the supplementary material.", + "bbox": [ + 503, + 468, + 888, + 709 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Rendering results comparison. We render graphic pages for better visualization using the generated layouts. Fig. 5 show the rendering results comparison on PublayNet. We find the layouts generated by LayoutDM follow design rules well and reasonably allocate page space. Compared to the results generated by LayoutGAN++, our results are better in alignment and have no overlapping between elements. Note that we crop the elements from the original document and then render the pages using a simple resize-to-fit method, so the text areas and figures will suffer some distortion. In real design scenarios, this problem can be solved by element customization (e.g., adjust the font size).", + "bbox": [ + 503, + 719, + 888, + 898 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "18354", + "bbox": [ + 480, + 946, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/ac1a71fba8ad3e9328176ecde46122608960c0b57d7e2aec017dad8645449d08.jpg", + "image_caption": [ + "Figure 2. Qualitative comparison on Rico and PublayNet. Element labels indicate the labels of elements used as conditional inputs." + ], + "image_footnote": [], + "bbox": [ + 84, + 85, + 880, + 426 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5dac9dbaa5f24f71858b84ca789eca6aaa8499a0c4922f6bae63b314ec24205b.jpg", + "image_caption": [ + "Figure 3. Ablation study on the effect of transformer layers. \"w/o transformer\" denotes model without transformer layers. \"Full\" denotes our full model." + ], + "image_footnote": [], + "bbox": [ + 84, + 467, + 459, + 657 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Extended Layout Generation Tasks", + "text_level": 1, + "bbox": [ + 76, + 720, + 385, + 738 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Text logo layout generation. TextLogo3K [44] dataset contains character and word embedding of texts in the logos. Although the dataset does not provide any label information, we can still generate logo layouts conditioned on the provided textual features. Positional encoding is added to LayoutDM to make the transformer structure aware of the reading order in textual feature sequences. We compare the logo layout generation results of LayoutDM and those generated by the logo layout generator provided by TextLogo3K [44]. The qualitative results are shown in Fig. 6. As", + "bbox": [ + 75, + 750, + 472, + 902 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d353d36048b59a08c9383ecdc97c90afc274e2003884f7db08b3ab56b7b1c81f.jpg", + "image_caption": [ + "Figure 4. Diversity comparison on PublayNet. We show five samples generated by giving the same category attributes as condition: one Figure and five Texts. The Figure is drawn in purple and the Texts are drawn in red." + ], + "image_footnote": [], + "bbox": [ + 500, + 465, + 890, + 696 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "one can see, our model generates reasonable logo layouts while maintaining the correct reading order and aesthetic principles. Compared to LogoGAN, the style of the logos generated by our model is more flexible, not simply arranging the text from left to right. Our model also performs better when there are large numbers of characters in the layout, where LogoGAN fails to generate reasonable results.", + "bbox": [ + 496, + 773, + 893, + 881 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Scene layout generation. Our model can also generate", + "bbox": [ + 517, + 885, + 890, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "18355", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f2fc7ddb6eed51e61453cdce6710283ea34d077fe079143980095bf17854d5d3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 84, + 87, + 468, + 351 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/9c4770cae20e57c3acfd139b49e9072569849cb7803638212f0407badb2f8c83.jpg", + "image_caption": [ + "Figure 5. Rendering results comparison. Top: Rendered pages using layouts generated by LayoutGAN++. Middle: Rendered pages using layouts generated by LayoutDM. Bottom: Real paper pages in PublayNet.", + "Figure 6. Text logo generation results. \"LogoGAN\" denotes the text logo generation model proposed in [44]. \"Condition\" represents the textual features (including character and word embeddings) used as conditional input in LogoGAN and LayoutDM. \"/\" is the symbol for splitting tokens." + ], + "image_footnote": [], + "bbox": [ + 86, + 425, + 468, + 679 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "natural scene layouts. We illustrate the qualitative results of the scene layout generation on COCO in Fig. 7. Given the labels of scene elements in a scene, our model generates reasonable scene layout proposals. We then use a downstream layout-to-image generation application [2] to finally render natural scene images. The results show that our model learns the principle of scene layouts well and can understand the complex relationships between elements in", + "bbox": [ + 75, + 773, + 470, + 895 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c64a28bccad22f12f6306a45315d7c7e495b90feb80652d1f023851d6f0e10ef.jpg", + "image_caption": [ + "Figure 7. Natural scene layout generation results on COCO. Our model uses scene element labels as conditional input to generate reasonable scene layouts." + ], + "image_footnote": [], + "bbox": [ + 501, + 87, + 890, + 362 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "natural scenes. For example, the boat should be in the river and the cloud should be in the upper part of the scene.", + "bbox": [ + 500, + 425, + 890, + 455 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5. Limitations", + "text_level": 1, + "bbox": [ + 500, + 463, + 625, + 477 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Although our method shows impressive results in the conditional layout generation problem in comparison to existing methods, it still has limitations. For example, like other layout generation methods, our approach treats design elements as being on a single-layer canvas. This can not model a layout with multiple layers occluding each other. Our method also has no advantage over other generative models in generation speed because the generation of the diffusion model requires an iterative denoising process. We leave the solution to the above problems for future work.", + "bbox": [ + 498, + 486, + 890, + 636 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 648, + 617, + 664 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This paper proposes a transformer-based diffusion model LayoutDM to address conditional layout generation. We introduce a purely transformer-based Layout Denoiser to model the diffusion reverse process. Benefitting from both DDPM and transformer, in comparison to existing methods, LayoutDM can generate high-quality generation with desired properties such as better diversity, faithful distribution coverage, and stationary training. Quantitative and qualitative results demonstrate that our model outperforms the state-of-the-art methods in terms of visual perceptual quality and diversity.", + "bbox": [ + 498, + 674, + 890, + 839 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgment. This work was supported in part to Dr. Liansheng Zhuang by NSFC under contract No.U20B2070 and No.61976199, in part to Dr. Fengying Yan by NSFC under contract No.42341207.", + "bbox": [ + 498, + 839, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "18356", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Diego Martín Arroyo, Janis Postels, and Federico Tombari. Variational transformer networks for layout generation. In 2021 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 13637-13647, 2021. 1, 2, 4, 5, 6", + "[2] Oron Ashual and Lior Wolf. Specifying object attributes and relations in interactive scene generation. 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IEEE, Sep. 2019. 5" + ], + "bbox": [ + 501, + 92, + 890, + 752 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "18358", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/LayoutDM_ Transformer-Based Diffusion Model for Layout Generation/5a042bec-4143-4aa8-b201-8f11f7b47f24_model.json b/2023/LayoutDM_ Transformer-Based Diffusion Model for Layout Generation/5a042bec-4143-4aa8-b201-8f11f7b47f24_model.json new file mode 100644 index 0000000000000000000000000000000000000000..28c434b6f2095c67935d85f7a21ba9f64d1bff2a --- /dev/null +++ b/2023/LayoutDM_ Transformer-Based Diffusion Model for Layout Generation/5a042bec-4143-4aa8-b201-8f11f7b47f24_model.json @@ -0,0 +1,2002 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.125, + 0.131, + 0.846, + 0.153 + ], + "angle": 0, + "content": "LayoutDM: Transformer-based Diffusion Model for Layout Generation" + }, + { + "type": "text", + "bbox": [ + 0.16, + 0.182, + 0.588, + 0.234 + ], + "angle": 0, + "content": "Shang Chai, Liansheng Zhuang* \nUniversity of Science and Technology of China \nchaishang@mail.ustc.edu.cn, lszhuang@ustc.edu.cn" + }, + { + "type": "text", + "bbox": [ + 0.634, + 0.182, + 0.799, + 0.234 + ], + "angle": 0, + "content": "Fengying Yan Tianjin University fengying@tju.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.269, + 0.314, + 0.285 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.302, + 0.473, + 0.651 + ], + "angle": 0, + "content": "Automatic layout generation that can synthesize high-quality layouts is an important tool for graphic design in many applications. Though existing methods based on generative models such as Generative Adversarial Networks (GANs) and Variational Auto-Encoders (VAEs) have progressed, they still leave much room for improving the quality and diversity of the results. Inspired by the recent success of diffusion models in generating high-quality images, this paper explores their potential for conditional layout generation and proposes Transformer-based Layout Diffusion Model (LayoutDM) by instantiating the conditional denoising diffusion probabilistic model (DDPM) with a purely transformer-based architecture. Instead of using convolutional neural networks, a transformer-based conditional Layout Denoiser is proposed to learn the reverse diffusion process to generate samples from noised layout data. Benefitting from both transformer and DDPM, our LayoutDM is of desired properties such as high-quality generation, strong sample diversity, faithful distribution coverage, and stationary training in comparison to GANs and VAEs. Quantitative and qualitative experimental results show that our method outperforms state-of-the-art generative models in terms of quality and diversity." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.681, + 0.21, + 0.697 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.708, + 0.47, + 0.875 + ], + "angle": 0, + "content": "Layouts, i.e. the arrangement of the elements to be displayed in a design, play a critical role in many applications from magazine pages to advertising posters to application interfaces. A good layout guides viewers' reading order and draws their attention to important information. The semantic relationships of elements, the reading order, canvas space allocation and aesthetic principles must be carefully decided in the layout design process. However, manually arranging design elements to meet aesthetic goals and user-specified constraints is time-consuming. To aid the design of graphic layouts, the task of layout generation aims to" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.27, + 0.892, + 0.376 + ], + "angle": 0, + "content": "generate design layouts given a set of design components with user-specified attributes. Though meaningful attempts are made [1, 10, 11, 15, 18, 21, 23-25, 33, 44-46], it is still challenging to generate realistic and complex layouts, because many factors need to be taken into consideration, such as design elements, their attributes, and their relationships to other elements." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.38, + 0.893, + 0.668 + ], + "angle": 0, + "content": "Over the past few years, generative models such as Generative Adversarial Networks (GANs) [9] and Variational Auto-Encoders (VAEs) [20] have gained much attention in layout generation, as they have shown a great promise in terms of faithfully learning a given data distribution and sampling from it. GANs model the sampling procedure of a complex distribution that is learned in an adversarial manner, while VAEs seek to learn a model that assigns a high likelihood to the observed data samples. Though having shown impressive success in generating high-quality layouts, these models have some limitations of their own. GANs are known for potentially unstable training and less distribution coverage due to their adversarial training nature [4, 5, 27], so they are inferior to state-of-the-art likelihood-based models (such as VAEs) in terms of diversity [28, 29, 34]. VAEs can capture more diversity and are typically easier to scale and train than GANs, but still fall short in terms of visual sample quality and sampling efficiency [22]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.671, + 0.895, + 0.838 + ], + "angle": 0, + "content": "Recently, diffusion models such as denoising diffusion probabilistic model (DDPM) [14] have emerged as a powerful class of generative models, capable of producing high-quality images comparable to those of GANs. Importantly, they additionally offer desirable properties such as strong sample diversity, faithful distribution coverage, a stationary training objective, and easy scalability. This implies that diffusion models are well suited for learning models of complex and diverse data, which also motivates us to explore the potential of diffusion-based generative models for graphic layout generation." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.84, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Though diffusion models have shown splendid performance in high-fidelity image generation [8, 14, 35, 39, 41], it is still a sparsely explored area and provides unique challenges to develop diffusion-based generative models for" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.222, + 0.9 + ], + "angle": 0, + "content": "*Corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "18349" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.348 + ], + "angle": 0, + "content": "layout generation. First, diffusion models often use convolutional neural networks such as U-Net [36] to learn the reverse process to construct desired data samples from the noise. However, a layout is a non-sequential data structure consisting of varying length samples with discrete (classes) and continuous (coordinates) elements simultaneously, instead of pixels laid on a regular lattice. Obviously, convolutional neural networks are not suitable for layout denoising, which prevents diffusion models from being directly applied to layout generation. Second, the placement and sizing of a given element depend not only on its attributes (such as category label) but also on its relationship to other elements. How to incorporate the attributes knowledge and model the elements' relationship in diffusion models is still an open problem. Since diffusion models are general frameworks, they leave room for adapting the underlying neural architectures to exploit the properties of the data." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.348, + 0.473, + 0.799 + ], + "angle": 0, + "content": "Inspired by the above insights, by instantiating the conditional denoising diffusion probabilistic model (DDPM) with a transformer architecture, this paper proposes Transformer-based Layout Diffusion Model (i.e., LayoutDM) for conditional layout generation given a set of elements with user-specified attributes. The key idea is to use a purely transformer-based architecture instead of the commonly used convolutional neural networks to learn the reverse diffusion process from noised layout data. Benefiting from the self-attention mechanism in transformer layers, LayoutDM can efficiently capture high-level relationship information between elements, and predict the noise at each time step from the noised layout data. Moreover, the attention mechanism also helps model another aspect of the data - namely a varying and large number of elements. Finally, to generate layouts with desired attributes, LayoutDM designs a conditional Layout Denoiser (cLayoutDenoiser) based on a transformer architecture to learn the reverse diffusion process conditioned on the input attributes. Different from previous transformer models in the context of NLP or video, cLayoutDenoiser omits the positional encoding which indicates the element order in the sequence, as we do not consider the order of designed elements on a canvas in our setting. In comparison with current layout generation approaches (such as GANs and VAEs), our LayoutDM offers several desired properties such as high-quality generation, better diversity, faithful distribution coverage, a stationary training objective, and easy scalability. Extensive experiments on five public datasets show that LayoutDM outperforms state-of-the-art methods in different tasks." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.802, + 0.434, + 0.816 + ], + "angle": 0, + "content": "In summary, our main contributions are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.826, + 0.47, + 0.902 + ], + "angle": 0, + "content": "- This paper proposes a novel LayoutDM to generate high-quality design layouts for a set of elements with user-specified attributes. Compared with existing methods, LayoutDM is of desired properties such as high-quality generation, better diversity, faithful distribution" + }, + { + "type": "text", + "bbox": [ + 0.527, + 0.092, + 0.892, + 0.138 + ], + "angle": 0, + "content": "coverage, and stationary training. To our best knowledge, LayoutDM is the first attempt to explore the potential of diffusion model for graphic layout generation." + }, + { + "type": "text", + "bbox": [ + 0.515, + 0.141, + 0.892, + 0.218 + ], + "angle": 0, + "content": "- This paper explores a new class of diffusion models by replacing the commonly-used U-Net backbone with a transformer, and designs a novel cLayoutDenoiser to reverse the diffusion process from noised layout data and better capture the relationship of elements." + }, + { + "type": "text", + "bbox": [ + 0.515, + 0.221, + 0.894, + 0.281 + ], + "angle": 0, + "content": "- Extensive experiments demonstrate that our method outperforms state-of-the-art models in terms of visual perceptual quality and diversity on five diverse layout datasets." + }, + { + "type": "list", + "bbox": [ + 0.515, + 0.141, + 0.894, + 0.281 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.306, + 0.642, + 0.322 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.331, + 0.682, + 0.347 + ], + "angle": 0, + "content": "2.1. Layout Generation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.355, + 0.892, + 0.763 + ], + "angle": 0, + "content": "Automatic layout generation has been widely studied for a long time. Early approaches to layout generation [30, 31] embed design rules into manually-defined energy functions. In recent years, generative model based methods are increasingly progressed. LayoutGAN [24] and LayoutVAE [17] are the first attempts to utilize GAN and VAE to generate graphic and scene layouts. NDN [23] represents the relative positional relationship of elements as a graph and uses a graph neural network based conditional VAE to generate graphic layouts. READ [33] uses heuristics to determine the relationships between elements and trains a Recursive Neural Network (RNN) [37, 38] based VAE to learn the layout distribution. CanvasVAE [45] generates vector graphic documents which contain structured information about canvas and elements. VTN [1] and Coarse2fine [16] deploy self-attention based VAEs to generate graphic layouts, making progress in diversity and perceptual quality. LayoutTransformer [11] and BLT [21] define layouts as discrete sequences and exploit the efficiency of transformer and bidirectional-transformer in structured sequence generation. LayoutNet [46], TextLogo3K [44] and ICVT [6] propose conditional layout generative models which can utilize additional attributes about design elements or entire layouts to aid layout generation in different application scenarios. LayoutGAN++ [18] designs a transformer-based generator and discriminator and generates graphic layouts conditioned on the given element category labels." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.772, + 0.662, + 0.787 + ], + "angle": 0, + "content": "2.2. Diffusion Model" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.894, + 0.903 + ], + "angle": 0, + "content": "Diffusion models [14, 40] have proved its capability of generating high-quality and diverse samples [8, 14, 35] and have recently achieved state-of-the-art results on several benchmark generation tasks [8]. The diffusion model uses diffusion processes to model the generation and defines the sampling of data as the process of gradually denoising from complete Gaussian noise. The forward process gradually" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "18350" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.09, + 0.47, + 0.208 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.204, + 0.215, + 0.347, + 0.227 + ], + "angle": 0, + "content": "(a) LayoutDM architecture" + }, + { + "type": "image", + "bbox": [ + 0.476, + 0.096, + 0.885, + 0.213 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.55, + 0.215, + 0.812, + 0.227 + ], + "angle": 0, + "content": "(b) Architecture of conditional layout denoiser \\(\\epsilon_{\\theta}\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.239, + 0.894, + 0.281 + ], + "angle": 0, + "content": "Figure 1. a) Architecture of LayoutDM. It consists of a forward diffusion process and a reverse process modeled by a conditional layout denoiser \\(\\epsilon_{\\theta}\\). b) Architecture of our transformer-based conditional layout denoiser, cLayoutDenoiser. cLayoutDenoiser predicts the added noise conditioned on the layout attributes \\(\\pmb{f}\\) and time step \\(t\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.294, + 0.469, + 0.384 + ], + "angle": 0, + "content": "adds Gaussian noise to the data from a predefined noise schedule until time step \\( T \\). The reverse process uses a neural backbone often implemented as a U-Net [8, 14, 36, 42] to parameterize the conditional distribution \\( p(\\pmb{x}_{t - 1}|\\pmb{x}_t) \\). In this work, we instantiate a conditional diffusion model to achieve conditional layout generation." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.399, + 0.208, + 0.415 + ], + "angle": 0, + "content": "3. Our Method" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.424, + 0.289, + 0.44 + ], + "angle": 0, + "content": "3.1. Layout Representation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.448, + 0.469, + 0.523 + ], + "angle": 0, + "content": "In our model, each layout consists of a set of elements, and each element is described by both geometric parameters (i.e. location and size) and its attribute (e.g. category label or textual features). Formally, a layout \\( l \\) is denoted as a flattened sequence of integer indices:" + }, + { + "type": "equation", + "bbox": [ + 0.126, + 0.536, + 0.419, + 0.552 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {l} = \\left(g _ {1}, f _ {1}, g _ {2}, f _ {2}, \\dots , g _ {i}, f _ {i}, \\dots , g _ {N}, f _ {N}\\right),\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.565, + 0.469, + 0.776 + ], + "angle": 0, + "content": "where \\(N\\) is the number of elements in the layout. \\(g_{i} = [x_{i},y_{i},w_{i},h_{i}]\\) is a vector that presents the geometric parameters (center coordinates and size) of the \\(i\\)-th element in the layout. \\(f_{i}\\) is the attributes of \\(i\\)-th element which might be category label or textual features. For the sake of convenience, the sequence \\(\\pmb{g} = (g_1,g_2,\\dots ,g_i\\dots ,g_N)\\) is named layout geometric parameters, the sequence \\(\\pmb {f} = (f_{1},f_{2},\\dots ,f_{i}\\dots ,f_{N})\\) is named layout attributes. Note here that, the elements in a layout are unordered, so swapping the items in sequence \\(\\pmb{g}\\) and \\(\\pmb{f}\\) does not affect the meaning of the sequences. We normalize the geometric parameters, i.e., \\([x_i,y_i,w_i,h_i]\\), \\(i = 1,2,\\dots ,N\\), to the interval \\([-1,1]\\). In this way, layouts have a uniform structured representation." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.787, + 0.334, + 0.803 + ], + "angle": 0, + "content": "3.2. The LayoutDM Architecture" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Fig. 1a illustrates the architecture of LayoutDM. From a high-level perspective, our LayoutDM is an instance of conditional denoising diffusion probabilistic model (DDPM) with a transformer architecture suitable for layout data. DDPM learns to model the Markov transition from simple distribution to layout data distribution and generates" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.294, + 0.892, + 0.384 + ], + "angle": 0, + "content": "diverse samples through sequential stochastic transitions. To generate desired layouts, LayoutDM uses the input attributes to guide the generative process in DDPM. We follow the method described in Classifier-Free Diffusion Guidance [13] to realize conditional DDPM, and set the guidance strength \\( w \\) to zero for simplicity." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.384, + 0.892, + 0.506 + ], + "angle": 0, + "content": "Specifically, let \\( q(\\pmb{g}_0|\\pmb{f}) \\) be the unknown conditional data distribution, where \\( \\pmb{g}_0 \\) is the geometric parameters of real layouts, and \\( \\pmb{f} \\) is the layout attributes. LayoutDM models the conditional distribution \\( q(\\pmb{g}_0|\\pmb{f}) \\) by two processes: a forward diffusion process and a reverse denoising diffusion process. First, LayoutDM defines the forward diffusion process \\( q(\\pmb{g}_t|\\pmb{g}_{t-1}) \\) which maps layout data to noise by gradually adding Gaussian noise at each time step \\( t \\):" + }, + { + "type": "equation", + "bbox": [ + 0.561, + 0.518, + 0.891, + 0.535 + ], + "angle": 0, + "content": "\\[\nq \\left(\\boldsymbol {g} _ {t} \\mid \\boldsymbol {g} _ {t - 1}\\right) = \\mathcal {N} \\left(\\boldsymbol {g} _ {t}; \\sqrt {1 - \\beta_ {t}} \\boldsymbol {g} _ {t - 1}, \\beta_ {t} \\mathbf {I}\\right) \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.547, + 0.804, + 0.563 + ], + "angle": 0, + "content": "where \\(\\{\\beta_t\\}_{t=1}^T\\) are forward process variances." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.563, + 0.891, + 0.623 + ], + "angle": 0, + "content": "Then, LayoutDM defines the conditional reverse diffusion process \\( p(\\pmb{g}_{t-1} | \\pmb{g}_t, \\pmb{f}) \\) which performs iterative denoising from pure Gaussian noise to generate high-quality layouts conditioned on layout attributes \\( \\pmb{f} \\):" + }, + { + "type": "equation", + "bbox": [ + 0.545, + 0.634, + 0.891, + 0.652 + ], + "angle": 0, + "content": "\\[\np _ {\\theta} \\left(\\boldsymbol {g} _ {t - 1} \\mid \\boldsymbol {g} _ {t}, \\boldsymbol {f}\\right) = \\mathcal {N} \\left(\\boldsymbol {g} _ {t - 1}; \\boldsymbol {\\mu} _ {\\theta} \\left(\\boldsymbol {g} _ {t}, t, \\boldsymbol {f}\\right), \\sigma_ {t} ^ {2} \\mathbf {I}\\right) \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.664, + 0.892, + 0.754 + ], + "angle": 0, + "content": "where \\(\\sigma_{t}\\) is the constant variance following [14], \\(\\mu_{\\theta}\\) is the mean of the Gaussian distribution computed by a neural network, and \\(\\theta\\) is the parameters of the network. As shown in Ho et al. [14], we can reparameterize the mean to make the neural network learn the added noise at time step \\(t\\) instead. In this way, \\(\\mu_{\\theta}\\) can be reparameterized as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.525, + 0.765, + 0.891, + 0.799 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {\\mu} _ {\\theta} \\left(\\boldsymbol {g} _ {t}, t, \\boldsymbol {f}\\right) = \\frac {1}{\\sqrt {\\alpha_ {t}}} \\left(\\boldsymbol {g} _ {t} - \\frac {\\beta_ {t}}{\\sqrt {1 - \\bar {\\alpha} _ {t}}} \\boldsymbol {\\epsilon} _ {\\theta} \\left(\\boldsymbol {g} _ {t}, t, \\boldsymbol {f}\\right)\\right) \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.892, + 0.901 + ], + "angle": 0, + "content": "where \\(t\\) is the time step, \\(\\{\\beta_t\\}_{t=1}^T\\) are forward process variances, \\(\\alpha_t = 1 - \\beta_t\\), and \\(\\overline{\\alpha}_t = \\prod_{s=1}^t \\alpha_s\\). \\(\\epsilon_\\theta(\\pmb{g}_t, t, \\pmb{f})\\) is the neural network to predict the added noise for layout geometric parameters conditioned on elements' attributes at time step \\(t\\). We also call the neural network \\(\\epsilon_\\theta(\\pmb{g}_t, t, \\pmb{f})\\) as conditional layout denoiser (cLayoutDenoiser)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "18351" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.091, + 0.336, + 0.108 + ], + "angle": 0, + "content": "3.3. Conditional Layout Denoiser" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.114, + 0.473, + 0.31 + ], + "angle": 0, + "content": "The inputs to cLayoutDenoiser are layout geometric parameters \\( \\pmb{g}_t \\), layout attributes \\( \\pmb{f} \\) and time step \\( t \\). To deal with sequences data, the conditional layout denoiser \\( \\epsilon_{\\theta}(\\pmb{g}_t, t, \\pmb{f}) \\) employs a purely transformer-based architecture instead of convolutional neural networks as its backbone. The architecture of cLayoutDenoiser is illustrated in Fig. 1b. Benefiting from the transformer architecture, cLayoutDenoiser can deal with the sequence with various lengths, and capture the relationships among elements. Moreover, cLayoutDenoiser adds \"attributes embeddings\" to the input \"geometric embeddings\", so as to guide the reverse diffusion process at each time step \\( t \\). Formally, the architecture of cLayoutDenoiser can be described as follow:" + }, + { + "type": "equation", + "bbox": [ + 0.127, + 0.319, + 0.47, + 0.335 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {h} _ {f} = \\text {A t t r i b u t e s E m b e d d i n g} (\\boldsymbol {f}) \\tag {4}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.129, + 0.338, + 0.469, + 0.354 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {h} _ {g} = \\text {G e o m e t r i c E m b e d d i n g} (\\boldsymbol {g} _ {t}) \\tag {5}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.135, + 0.357, + 0.469, + 0.373 + ], + "angle": 0, + "content": "\\[\n\\mathbf {E} = \\text {E l e m e n t E m b e d d i n g} \\left(\\boldsymbol {h} _ {f}, \\boldsymbol {h} _ {g}, \\mathrm {T E} (t)\\right) \\tag {6}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.131, + 0.376, + 0.469, + 0.391 + ], + "angle": 0, + "content": "\\[\n\\mathbf {E} ^ {\\prime} = \\operatorname {T r a n s f o r m e r L a y e r s} (\\mathbf {E}) \\tag {7}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.14, + 0.394, + 0.469, + 0.41 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {\\epsilon} = \\operatorname {F C} \\left(\\mathbf {E} ^ {\\prime}\\right) \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.418, + 0.47, + 0.552 + ], + "angle": 0, + "content": "where \\( \\pmb{f} \\) is the layout attributes, \\( \\pmb{g}_t \\) is the noised layout geometric parameters, \\( \\pmb{h}_f \\) and \\( \\pmb{h}_g \\) are their hidden representations. \\( \\mathbf{E} \\) is the element tokens computed by element embedding module, \\( \\mathbf{E}' \\) is intermediate feature. \\( \\mathrm{TE}(t) \\) denotes the timestep embedding, and \\( \\epsilon \\) is the predicted noise. Note here that, since the element order in the sequence makes no sense in our setting, cLayoutDenoiser omits the positional encoding, which is different from existing transformers in the context of NLP or video." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.554, + 0.47, + 0.734 + ], + "angle": 0, + "content": "Geometric, attributes and timestep embedding. Three embedding modules are used to learn meaningful representations for noised layout geometric parameters \\( g_{t} \\), layout attributes \\( f \\) and time step \\( t \\). Geometric embedding projects layout geometric parameters to a specific dimension, aiming to find a more efficient feature space than the original coordinate space. Feature embedding learns the continuous features of discrete element attributes by embedding them into a specific dimension. Following [14], we condition cLayoutTransformer on time step \\( t \\) by adding a sinusoidal time embedding \\( \\mathrm{TE}(t) \\) to make the network aware at which time step it is operating." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Element embedding. Element embedding module calculates the element tokens used as the input of transformer layers. Element tokens should contain geometric, attributes and time step information, so that transformer can efficiently capture the relationship information between elements conditioned on the time step \\( t \\) and layout attributes \\( f \\). We concatenate the geometric embedding and attributes embedding, and then use a fully-connected layer to fuse element representation. We further perform an element-wise plus operation with timestep embedding on the results to finally obtain the element tokens." + }, + { + "type": "code_caption", + "bbox": [ + 0.51, + 0.095, + 0.742, + 0.11 + ], + "angle": 0, + "content": "Algorithm 1: Training LayoutDM" + }, + { + "type": "algorithm", + "bbox": [ + 0.517, + 0.112, + 0.789, + 0.253 + ], + "angle": 0, + "content": "Require: conditional layout denoiser \\(\\epsilon_{\\theta}\\) repeat Sample \\((g_0,f)\\sim q_{data};\\) \\(t\\sim\\) Uniform( \\(\\{1,\\dots ,T\\}\\) . \\(\\epsilon \\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I})\\) .. \\(\\pmb {g}_t = \\sqrt{\\alpha}_t\\pmb {g}_0 + \\sqrt{1 - \\overline{\\alpha}_t}\\pmb {\\epsilon};\\) Take gradient descent step on \\(\\nabla_{\\theta}\\| \\boldsymbol {\\epsilon} - \\boldsymbol{\\epsilon}_{\\theta}(\\pmb {g}_t,t,\\pmb {f})\\| ^2;\\) \nuntil converged;" + }, + { + "type": "code_caption", + "bbox": [ + 0.511, + 0.269, + 0.673, + 0.285 + ], + "angle": 0, + "content": "Algorithm 2: Sampling" + }, + { + "type": "algorithm", + "bbox": [ + 0.517, + 0.287, + 0.842, + 0.416 + ], + "angle": 0, + "content": "Input: layout attributes \\(\\pmb{f}\\) \nOutput: layout geometric parameters \\(\\pmb{g_0}\\) \n\\(g_{T}\\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I})\\) \nfor \\(t = T,\\dots ,1\\) do \\(\\mathbf{z}\\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I})\\) if \\(t > 1\\) , else \\(\\mathbf{z} = \\mathbf{0}\\) . \\(g_{t - 1} = \\frac{1}{\\sqrt{\\alpha_t}} (g_t - \\frac{1 - \\alpha_t}{\\sqrt{1 - \\overline{\\alpha}_t}}\\epsilon_\\theta (g_t,t,\\pmb {f})) + \\sigma_t\\mathbf{z}\\) \nend \nreturn \\(\\pmb{g_0}\\)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.429, + 0.892, + 0.61 + ], + "angle": 0, + "content": "Transformer layers. Generating an effective layout requires understanding the relationships between layout elements. Self-attention mechanism in Transformer [43] has proven effective in capturing high-level relationships between lots of elements in layout generation [1, 11, 15]. In this paper, we adopt multihead attention mechanism to capture relationship information between elements from element tokens. We stack multiple transformer layers (8 in our model) to enable cLayoutDenoiser to capture relationships between layout elements from the element tokens. Positional encoding is omitted because of the unordered nature of elements." + }, + { + "type": "equation", + "bbox": [ + 0.518, + 0.615, + 0.892, + 0.635 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathbf {E}} = \\operatorname {L a y e r N o r m} \\left(\\mathbf {E} ^ {l - 1} + \\mathbf {H e a d} \\left(e _ {1} ^ {l - 1}, \\dots , e _ {N} ^ {l - 1}\\right)\\right) \\tag {9}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.515, + 0.637, + 0.892, + 0.656 + ], + "angle": 0, + "content": "\\[\n\\mathbf {E} ^ {l} = \\operatorname {L a y e r N o r m} (\\hat {\\mathbf {E}} + \\operatorname {F F N} (\\hat {\\mathbf {E}})) \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.661, + 0.892, + 0.738 + ], + "angle": 0, + "content": "where \\(l = 1, \\dots, L\\) denotes the layer index, Head, LayoutNorm and FFN denote multi-head attention layer, Layer Normalization [3] and fully connected feed-forward network. \\(\\mathbf{E}^{l-1} = (\\pmb{e}_1^{l-1}, \\dots, \\pmb{e}_N^{l-1})\\) are the intermediate element tokens used as the input of \\(l\\)-th transformer layer." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.745, + 0.715, + 0.761 + ], + "angle": 0, + "content": "3.4. Training and Inference" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.768, + 0.892, + 0.844 + ], + "angle": 0, + "content": "Following denoising diffusion probabilistic model [14], we optimize random terms \\(L_{t}\\) which are the KL divergences between \\(p_{\\theta}(\\pmb{g}_{t-1}|\\pmb{g}_t, \\pmb{f})\\) and forward process posteriors. After simplifying the objective function following the method in [14], the final loss function is as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.518, + 0.848, + 0.892, + 0.901 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} L _ {s i m p l e} (\\theta) = \\left\\| \\boldsymbol {\\epsilon} - \\boldsymbol {\\epsilon} _ {\\theta} \\left(\\boldsymbol {g} _ {t}, t, \\boldsymbol {f}\\right) \\right\\| ^ {2} \\\\ = \\| \\boldsymbol {\\epsilon} - \\boldsymbol {\\epsilon} _ {\\theta} \\left(\\sqrt {\\bar {\\alpha} _ {t}} \\boldsymbol {g} _ {0} + \\sqrt {\\left(1 - \\bar {\\alpha} _ {t}\\right)} \\boldsymbol {\\epsilon}, t, \\boldsymbol {f}\\right) \\| ^ {2} \\tag {11} \\\\ \\end{array}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18352" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.091, + 0.468, + 0.169 + ], + "angle": 0, + "content": "where \\(\\epsilon \\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I})\\) \\(\\epsilon_{\\theta}\\) is our conditional layout denoiser, \\(g_{t}\\sim \\mathcal{N}(g_{t};\\sqrt{\\overline{\\alpha}_{t}} g_{0},(1 - \\overline{\\alpha}_{t})\\mathbf{I})\\) is computed using the property of Gaussian distributions and \\(\\pmb {g}_0\\) is the real layout geometric parameters. \\(\\{\\beta_t\\}_{t = 1}^T\\) are forward process variances, \\(\\alpha_{t} = 1 - \\beta_{t}\\) and \\(\\overline{\\alpha}_t = \\prod_{s = 1}^t\\alpha_s\\)" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.17, + 0.468, + 0.201 + ], + "angle": 0, + "content": "The training and sampling algorithm of LayoutDM are illustrated in Algorithm 1 and Algorithm 2 respectively." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.223, + 0.208, + 0.239 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.25, + 0.283, + 0.267 + ], + "angle": 0, + "content": "4.1. Experimental Settings" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.277, + 0.468, + 0.516 + ], + "angle": 0, + "content": "Datasets. We evaluate our method on five public datasets of layouts for documents, natural scenes, magazines, text logos and mobile phone UIs. Rico [7] is a dataset of user interface designs for mobile applications, containing 72,219 user interfaces from 9,772 Android apps. PublayNet [47] contains 330K samples of machine-annotated scientific documents crawled from the Internet with five categories (text, title, figure, list, table). Magazine [46] is a magazine layout dataset that covers a wide range of magazine categories. It consists of semantic layout annotations. COCO [26] is a large-scale labeled image dataset that contains images of natural scenes with instance segmentation. TextLogo3K [44] is a recently released dataset of text logos. It consists of 3,470 text logo images with manually annotated bounding boxes and pixel-level masks for each character." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.521, + 0.468, + 0.748 + ], + "angle": 0, + "content": "Evaluation metrics. To validate the effectiveness of LayoutDM, we employ four metrics in the literature to measure the perceptual quality of layouts. To be a fair comparison, we follow the guidance in [18] to evaluate these metrics. Specifically, FID [12] measures the distribution distance between real layouts and generated layouts. We use the pre-trained classifiers in [18] to compute FID. Max IoU [18] measures the similarity between the generated layouts and the reference layouts. It is designed to find the best match for each layout from the generated set to the reference set. Overlap and Alignment measure the perceptual quality of generated layouts. Overlap measures the total overlapping area between any pair of bounding boxes inside the layout. Additionally, we measure the Alignment by computing an alignment loss proposed in [25]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Implementing details. The max time step \\( T \\) in LayoutDM is set to 1000. We set the forward process variances to constants increasing linearly from \\( \\beta_{1} = 10^{-4} \\) to \\( \\beta_{T} = 0.02 \\) following Ho's design [14]. We use eight transformer layers which use 8-head attention in our model. Adam optimizer [19] with a learning rate of \\( 1 \\times 10^{-5} \\) is used to optimize learnable parameters. The batch size is set to 1024. We implement our model with PyTorch [32] and PyTorch Lightning. All experiments are performed on a single NVIDIA Quadro RTX 6000 GPU device." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.091, + 0.892, + 0.44 + ], + "angle": 0, + "content": "
Dataset\nModelRico
FID↓Max. IoU↑Alignment↓Overlap↓
LayoutGAN-W [24]162.75±0.280.30±0.000.71±0.00174.11±0.22
LayoutGAN-R [24]52.01±0.620.24±0.001.13±0.0469.37±0.66
NDN-none [23]13.76±0.280.35±0.000.56±0.0354.75±0.29
LayoutGAN++ [18]14.43±0.130.36±0.000.60±0.1259.85±0.59
VTN [1]9.31±0.210.36±0.000.88±0.1159.31±0.45
LayoutDM(Ours)3.03±0.060.49±0.000.36±0.0657.55±0.48
Real data4.470.650.2650.58
Dataset\nModelPublayNet
FID↓Max. IoU↑Alignment↓Overlap↓
LayoutGAN-W [24]195.38±0.460.21±0.001.21±0.01138.77±0.21
LayoutGAN-R [24]100.24±0.610.24±0.000.82±0.0145.64±0.32
NDN-none [23]35.67±0.350.31±0.000.35±0.0116.5±0.29
LayoutGAN++ [18]20.48±0.290.36±0.000.19±0.0022.80±0.32
VTN [1]13.07±0.470.37±0.000.30±0.0113.15±0.24
LayoutDM(Ours)4.04±0.080.44±0.000.15±0.003.73±0.08
Real data9.540.530.040.22
Dataset\nModelMagazine
FID↓Max. IoU↑Alignment↓Overlap↓
LayoutGAN-W [24]159.2±0.870.12±0.000.74±0.02188.77±0.93
LayoutGAN-R [24]100.66±0.350.16±0.001.90±0.02111.85±1.44
NDN-none [23]23.27±0.090.22±0.001.05±0.0330.31±0.77
LayoutGAN++ [18]13.35±0.410.26±0.000.80±0.0232.40±0.89
VTN [1]12.34±0.390.25±0.001.07±0.0339.97±0.62
LayoutDM(Ours)9.11±0.150.29±0.000.77±0.0332.53±0.72
Real data12.130.350.4325.64
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.45, + 0.892, + 0.533 + ], + "angle": 0, + "content": "Table 1. Quantitative comparison conditioned on element category labels. For reference, the FID and Max. IoU computed between the validation and test data, and the Alignment and Overlap computed with the test data are shown as real data. LayoutGAN-W and LayoutGAN-R denote LayoutGAN with wireframe rendering discriminator and with relation-based discriminator." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.543, + 0.72, + 0.559 + ], + "angle": 0, + "content": "4.2.Quantitative Evaluation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.568, + 0.892, + 0.764 + ], + "angle": 0, + "content": "Comparison with state-of-the-art models. We quantitatively evaluate the quality of conditional layout generation results on benchmark datasets: Rico, PublayNet and Magazine. Since most methods are designed for unconditional layout generation and have no available public implements, we compare our method with conditional LayoutGAN [24], NDN-none [23] and LayoutGAN++ [18] by citing the results in [18]. Moreover, we also implement a conditional VTN [1] as our comparison baseline model, so that we can compare with methods based on both VAEs and GANs. All the metrics are computed on the full test splits of the datasets. We report the mean and standard deviation over five independent evaluations for each experiment." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The comparison results are reported in Tab. 1. From this table, we can observe that: (1) Our method outperforms SOTA methods on both FID and Max. IoU on all three benchmark datasets, which indicates that the generated layouts by our method are more similar to the real layouts than those by SOTA methods. This verifies that our LayoutDM can produce higher-quality and more diverse layouts than SOTA methods, since FID captures both diversity and fidelity. (2) Layouts generated by our method have a lower" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "18353" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.089, + 0.089, + 0.457, + 0.189 + ], + "angle": 0, + "content": "
IoU↓ [21]Overlap↓ [24]Alignment↓ [23]
L-VAE [17]0.45±1.3%0.15±0.9%0.37±0.7%
NDN [23]0.34±1.8%0.12±0.8%0.39±0.4%
VTN [1]0.21±0.6%0.06±0.2%0.33±0.4%
Trans. [11]0.19±0.3%0.06±0.3%0.33±0.3%
BLT [21]0.19±0.2%0.04±0.1%0.25±0.7%
Ours0.0053±0.5%0.01±0.1%0.22±1.2%
" + }, + { + "type": "table_caption", + "bbox": [ + 0.08, + 0.201, + 0.468, + 0.241 + ], + "angle": 0, + "content": "Table 2. Comparison with extended methods on PublayNet. Qualitative results are cited from [21]. \"Trans.\" denotes \"LayoutTransformer\" and \"L-VAE\" denotes \"LayoutVAE\"." + }, + { + "type": "text", + "bbox": [ + 0.08, + 0.253, + 0.468, + 0.432 + ], + "angle": 0, + "content": "FID score than the real ones in validation splits. This is because the generated layouts have identical attributes to those in the test split, while the real layouts in the validation split have different attributes from those in the test split. We provide more analysis on this point in the supplementary material. (3) With regards to Alignment and Overlap, LayoutDM is slightly weaker on Rico and Magazine. Because our method lacks a discriminator that guides the generator to generate layouts with better alignment and overlap properties as in GANs and does not introduce the layout refine module in NDN. This is likely to cause LayoutDM to be inferior to the state-of-the-art on these two metrics." + }, + { + "type": "text", + "bbox": [ + 0.08, + 0.449, + 0.468, + 0.674 + ], + "angle": 0, + "content": "Note here that, we don't compare LayoutDM to other state-of-the-art methods such as LayoutTransformer [11] and Coarse2fine [16], because these methods focus on unconditional layout generation problem which is different to our setting. Recently, Kong et al. [21] reimplement the conditional version of VTN and LayoutTransformer, and compare their proposed BLT model with these models under the settings of conditional layout generation. However, they compute the metrics (IoU [21], Alignment [23], Overlap [24]) in different ways. As an extended comparison, we adopt the metrics used by BLT [21], and compare our LayoutDM with VTN, LayoutTransformer, LayoutVAE, NDN and BLT on PublayNet. The comparison results are reported in Tab. 2. As shown in this table, our model also outperforms SOTA methods on all metrics." + }, + { + "type": "text", + "bbox": [ + 0.08, + 0.69, + 0.468, + 0.9 + ], + "angle": 0, + "content": "Effect of transformer layers. We conduct ablation experiments to demonstrate the effectiveness of the transformer layers in LayoutDM. Quantitative results are reported in Tab. 3 and qualitative comparisons are shown in Fig. 3. We have the following observation: After replacing the transformer structure in LayoutDM with a sequence of FC layers, the model can still predict a suitable size for each element, but the positional relationships between elements can not be handled, resulting in significant overlapping and misalignment. This proves that the transformer layers play an essential role and can efficiently capture and utilize the high-level relationships between elements to generate high-quality layouts which follow design rules and aesthetic principles." + }, + { + "type": "table", + "bbox": [ + 0.506, + 0.09, + 0.887, + 0.214 + ], + "angle": 0, + "content": "
ArchitectureRico
FID↓Max.IoU↑Alignment↓Overlap↓
w/o transformer52.640.291.0858.13
Full model3.030.490.3657.55
ArchitecturePublayNet
FID↓Max.IoU↑Alignment↓Overlap↓
w/o transformer99.600.270.8963.87
Full model4.040.440.153.73
" + }, + { + "type": "table_caption", + "bbox": [ + 0.504, + 0.227, + 0.89, + 0.267 + ], + "angle": 0, + "content": "Table 3. The quantitative results of ablations on transformer layers. \"Full\" denotes our full model. \"w/o transformer\" denotes model without transformer layers." + }, + { + "type": "title", + "bbox": [ + 0.504, + 0.278, + 0.727, + 0.294 + ], + "angle": 0, + "content": "4.3. Qualitative Comparisons" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.31, + 0.89, + 0.46 + ], + "angle": 0, + "content": "Generation quality comparison. To qualitatively compare the generation performance of different models, we compare with the state-of-the-art method LayoutGAN++ and our implemented conditional VTN. We randomly sample layouts from the test dataset and use the element category labels as conditional inputs. Fig. 2 shows the qualitative comparison results. As one can see, LayoutDM can arrange elements in a reasonable and complicated way, generating higher quality layouts than the other two, with fewer overlapping and better alignment." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.469, + 0.89, + 0.71 + ], + "angle": 0, + "content": "Generation diversity comparison. The diversity of results is also an important factor in evaluating the method. We compare the diversity of layouts generated by conditional VTN, LayoutGAN++, and LayoutDM. Fig. 4 show the comparison results. One can see that conditional VTN and LayoutDM generate more diverse results. The Figure element in the results floats on the page. Compared to the other two models, LayoutGAN++ captures less diversity, which places a large Figure element on the top of the pages in columns 2,4, and 5. LayoutDM performs well in diversity because it breaks the generation into a series of conditional diffusion steps which are relatively easy to model. This alleviates the mode collapse problem in strongly conditional generation task that can lead to the generation of similar modes. We provide more qualitative comparisons on diversity in the supplementary material." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.72, + 0.89, + 0.9 + ], + "angle": 0, + "content": "Rendering results comparison. We render graphic pages for better visualization using the generated layouts. Fig. 5 show the rendering results comparison on PublayNet. We find the layouts generated by LayoutDM follow design rules well and reasonably allocate page space. Compared to the results generated by LayoutGAN++, our results are better in alignment and have no overlapping between elements. Note that we crop the elements from the original document and then render the pages using a simple resize-to-fit method, so the text areas and figures will suffer some distortion. In real design scenarios, this problem can be solved by element customization (e.g., adjust the font size)." + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.947, + 0.518, + 0.956 + ], + "angle": 0, + "content": "18354" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.086, + 0.086, + 0.881, + 0.427 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.097, + 0.435, + 0.872, + 0.451 + ], + "angle": 0, + "content": "Figure 2. Qualitative comparison on Rico and PublayNet. Element labels indicate the labels of elements used as conditional inputs." + }, + { + "type": "image", + "bbox": [ + 0.085, + 0.468, + 0.46, + 0.658 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.67, + 0.471, + 0.711 + ], + "angle": 0, + "content": "Figure 3. Ablation study on the effect of transformer layers. \"w/o transformer\" denotes model without transformer layers. \"Full\" denotes our full model." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.722, + 0.387, + 0.739 + ], + "angle": 0, + "content": "4.4. Extended Layout Generation Tasks" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Text logo layout generation. TextLogo3K [44] dataset contains character and word embedding of texts in the logos. Although the dataset does not provide any label information, we can still generate logo layouts conditioned on the provided textual features. Positional encoding is added to LayoutDM to make the transformer structure aware of the reading order in textual feature sequences. We compare the logo layout generation results of LayoutDM and those generated by the logo layout generator provided by TextLogo3K [44]. The qualitative results are shown in Fig. 6. As" + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.466, + 0.892, + 0.697 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.708, + 0.895, + 0.765 + ], + "angle": 0, + "content": "Figure 4. Diversity comparison on PublayNet. We show five samples generated by giving the same category attributes as condition: one Figure and five Texts. The Figure is drawn in purple and the Texts are drawn in red." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.775, + 0.895, + 0.882 + ], + "angle": 0, + "content": "one can see, our model generates reasonable logo layouts while maintaining the correct reading order and aesthetic principles. Compared to LogoGAN, the style of the logos generated by our model is more flexible, not simply arranging the text from left to right. Our model also performs better when there are large numbers of characters in the layout, where LogoGAN fails to generate reasonable results." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.886, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Scene layout generation. Our model can also generate" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18355" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.086, + 0.088, + 0.47, + 0.352 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.366, + 0.47, + 0.422 + ], + "angle": 0, + "content": "Figure 5. Rendering results comparison. Top: Rendered pages using layouts generated by LayoutGAN++. Middle: Rendered pages using layouts generated by LayoutDM. Bottom: Real paper pages in PublayNet." + }, + { + "type": "image", + "bbox": [ + 0.087, + 0.426, + 0.47, + 0.68 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.695, + 0.47, + 0.765 + ], + "angle": 0, + "content": "Figure 6. Text logo generation results. \"LogoGAN\" denotes the text logo generation model proposed in [44]. \"Condition\" represents the textual features (including character and word embeddings) used as conditional input in LogoGAN and LayoutDM. \"/\" is the symbol for splitting tokens." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.775, + 0.471, + 0.896 + ], + "angle": 0, + "content": "natural scene layouts. We illustrate the qualitative results of the scene layout generation on COCO in Fig. 7. Given the labels of scene elements in a scene, our model generates reasonable scene layout proposals. We then use a downstream layout-to-image generation application [2] to finally render natural scene images. The results show that our model learns the principle of scene layouts well and can understand the complex relationships between elements in" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.088, + 0.892, + 0.363 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.373, + 0.892, + 0.416 + ], + "angle": 0, + "content": "Figure 7. Natural scene layout generation results on COCO. Our model uses scene element labels as conditional input to generate reasonable scene layouts." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.426, + 0.892, + 0.457 + ], + "angle": 0, + "content": "natural scenes. For example, the boat should be in the river and the cloud should be in the upper part of the scene." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.464, + 0.627, + 0.478 + ], + "angle": 0, + "content": "4.5. Limitations" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.487, + 0.892, + 0.637 + ], + "angle": 0, + "content": "Although our method shows impressive results in the conditional layout generation problem in comparison to existing methods, it still has limitations. For example, like other layout generation methods, our approach treats design elements as being on a single-layer canvas. This can not model a layout with multiple layers occluding each other. Our method also has no advantage over other generative models in generation speed because the generation of the diffusion model requires an iterative denoising process. We leave the solution to the above problems for future work." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.649, + 0.619, + 0.665 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.675, + 0.892, + 0.84 + ], + "angle": 0, + "content": "This paper proposes a transformer-based diffusion model LayoutDM to address conditional layout generation. We introduce a purely transformer-based Layout Denoiser to model the diffusion reverse process. Benefitting from both DDPM and transformer, in comparison to existing methods, LayoutDM can generate high-quality generation with desired properties such as better diversity, faithful distribution coverage, and stationary training. Quantitative and qualitative results demonstrate that our model outperforms the state-of-the-art methods in terms of visual perceptual quality and diversity." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.84, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Acknowledgment. This work was supported in part to Dr. Liansheng Zhuang by NSFC under contract No.U20B2070 and No.61976199, in part to Dr. Fengying Yan by NSFC under contract No.42341207." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "18356" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.175, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.184 + ], + "angle": 0, + "content": "[1] Diego Martín Arroyo, Janis Postels, and Federico Tombari. Variational transformer networks for layout generation. In 2021 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 13637-13647, 2021. 1, 2, 4, 5, 6" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.185, + 0.472, + 0.24 + ], + "angle": 0, + "content": "[2] Oron Ashual and Lior Wolf. Specifying object attributes and relations in interactive scene generation. 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IEEE, Sep. 2019. 5" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.753 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18358" + } + ] +] \ No newline at end of file diff --git a/2023/LayoutDM_ Transformer-Based Diffusion Model for Layout Generation/5a042bec-4143-4aa8-b201-8f11f7b47f24_origin.pdf b/2023/LayoutDM_ Transformer-Based Diffusion Model for Layout Generation/5a042bec-4143-4aa8-b201-8f11f7b47f24_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..f3d4ee510e1aa0e31de30f5a1ce171ce89de77da --- /dev/null +++ b/2023/LayoutDM_ Transformer-Based Diffusion Model for Layout Generation/5a042bec-4143-4aa8-b201-8f11f7b47f24_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:fa883ddc05275675f419d535117cd9bc2f02e0fd28b5c6ddbd7aa2e87767378b +size 3714009 diff --git a/2023/LayoutDM_ Transformer-Based Diffusion Model for Layout Generation/full.md b/2023/LayoutDM_ Transformer-Based Diffusion Model for Layout Generation/full.md new file mode 100644 index 0000000000000000000000000000000000000000..de8a88a0a1ea2d7acba3126c426460a0b30a1305 --- /dev/null +++ b/2023/LayoutDM_ Transformer-Based Diffusion Model for Layout Generation/full.md @@ -0,0 +1,300 @@ +# LayoutDM: Transformer-based Diffusion Model for Layout Generation + +Shang Chai, Liansheng Zhuang* +University of Science and Technology of China +chaishang@mail.ustc.edu.cn, lszhuang@ustc.edu.cn + +Fengying Yan Tianjin University fengying@tju.edu.cn + +# Abstract + +Automatic layout generation that can synthesize high-quality layouts is an important tool for graphic design in many applications. Though existing methods based on generative models such as Generative Adversarial Networks (GANs) and Variational Auto-Encoders (VAEs) have progressed, they still leave much room for improving the quality and diversity of the results. Inspired by the recent success of diffusion models in generating high-quality images, this paper explores their potential for conditional layout generation and proposes Transformer-based Layout Diffusion Model (LayoutDM) by instantiating the conditional denoising diffusion probabilistic model (DDPM) with a purely transformer-based architecture. Instead of using convolutional neural networks, a transformer-based conditional Layout Denoiser is proposed to learn the reverse diffusion process to generate samples from noised layout data. Benefitting from both transformer and DDPM, our LayoutDM is of desired properties such as high-quality generation, strong sample diversity, faithful distribution coverage, and stationary training in comparison to GANs and VAEs. Quantitative and qualitative experimental results show that our method outperforms state-of-the-art generative models in terms of quality and diversity. + +# 1. Introduction + +Layouts, i.e. the arrangement of the elements to be displayed in a design, play a critical role in many applications from magazine pages to advertising posters to application interfaces. A good layout guides viewers' reading order and draws their attention to important information. The semantic relationships of elements, the reading order, canvas space allocation and aesthetic principles must be carefully decided in the layout design process. However, manually arranging design elements to meet aesthetic goals and user-specified constraints is time-consuming. To aid the design of graphic layouts, the task of layout generation aims to + +generate design layouts given a set of design components with user-specified attributes. Though meaningful attempts are made [1, 10, 11, 15, 18, 21, 23-25, 33, 44-46], it is still challenging to generate realistic and complex layouts, because many factors need to be taken into consideration, such as design elements, their attributes, and their relationships to other elements. + +Over the past few years, generative models such as Generative Adversarial Networks (GANs) [9] and Variational Auto-Encoders (VAEs) [20] have gained much attention in layout generation, as they have shown a great promise in terms of faithfully learning a given data distribution and sampling from it. GANs model the sampling procedure of a complex distribution that is learned in an adversarial manner, while VAEs seek to learn a model that assigns a high likelihood to the observed data samples. Though having shown impressive success in generating high-quality layouts, these models have some limitations of their own. GANs are known for potentially unstable training and less distribution coverage due to their adversarial training nature [4, 5, 27], so they are inferior to state-of-the-art likelihood-based models (such as VAEs) in terms of diversity [28, 29, 34]. VAEs can capture more diversity and are typically easier to scale and train than GANs, but still fall short in terms of visual sample quality and sampling efficiency [22]. + +Recently, diffusion models such as denoising diffusion probabilistic model (DDPM) [14] have emerged as a powerful class of generative models, capable of producing high-quality images comparable to those of GANs. Importantly, they additionally offer desirable properties such as strong sample diversity, faithful distribution coverage, a stationary training objective, and easy scalability. This implies that diffusion models are well suited for learning models of complex and diverse data, which also motivates us to explore the potential of diffusion-based generative models for graphic layout generation. + +Though diffusion models have shown splendid performance in high-fidelity image generation [8, 14, 35, 39, 41], it is still a sparsely explored area and provides unique challenges to develop diffusion-based generative models for + +layout generation. First, diffusion models often use convolutional neural networks such as U-Net [36] to learn the reverse process to construct desired data samples from the noise. However, a layout is a non-sequential data structure consisting of varying length samples with discrete (classes) and continuous (coordinates) elements simultaneously, instead of pixels laid on a regular lattice. Obviously, convolutional neural networks are not suitable for layout denoising, which prevents diffusion models from being directly applied to layout generation. Second, the placement and sizing of a given element depend not only on its attributes (such as category label) but also on its relationship to other elements. How to incorporate the attributes knowledge and model the elements' relationship in diffusion models is still an open problem. Since diffusion models are general frameworks, they leave room for adapting the underlying neural architectures to exploit the properties of the data. + +Inspired by the above insights, by instantiating the conditional denoising diffusion probabilistic model (DDPM) with a transformer architecture, this paper proposes Transformer-based Layout Diffusion Model (i.e., LayoutDM) for conditional layout generation given a set of elements with user-specified attributes. The key idea is to use a purely transformer-based architecture instead of the commonly used convolutional neural networks to learn the reverse diffusion process from noised layout data. Benefiting from the self-attention mechanism in transformer layers, LayoutDM can efficiently capture high-level relationship information between elements, and predict the noise at each time step from the noised layout data. Moreover, the attention mechanism also helps model another aspect of the data - namely a varying and large number of elements. Finally, to generate layouts with desired attributes, LayoutDM designs a conditional Layout Denoiser (cLayoutDenoiser) based on a transformer architecture to learn the reverse diffusion process conditioned on the input attributes. Different from previous transformer models in the context of NLP or video, cLayoutDenoiser omits the positional encoding which indicates the element order in the sequence, as we do not consider the order of designed elements on a canvas in our setting. In comparison with current layout generation approaches (such as GANs and VAEs), our LayoutDM offers several desired properties such as high-quality generation, better diversity, faithful distribution coverage, a stationary training objective, and easy scalability. Extensive experiments on five public datasets show that LayoutDM outperforms state-of-the-art methods in different tasks. + +In summary, our main contributions are as follows: + +- This paper proposes a novel LayoutDM to generate high-quality design layouts for a set of elements with user-specified attributes. Compared with existing methods, LayoutDM is of desired properties such as high-quality generation, better diversity, faithful distribution + +coverage, and stationary training. To our best knowledge, LayoutDM is the first attempt to explore the potential of diffusion model for graphic layout generation. + +- This paper explores a new class of diffusion models by replacing the commonly-used U-Net backbone with a transformer, and designs a novel cLayoutDenoiser to reverse the diffusion process from noised layout data and better capture the relationship of elements. +- Extensive experiments demonstrate that our method outperforms state-of-the-art models in terms of visual perceptual quality and diversity on five diverse layout datasets. + +# 2. Related Work + +# 2.1. Layout Generation + +Automatic layout generation has been widely studied for a long time. Early approaches to layout generation [30, 31] embed design rules into manually-defined energy functions. In recent years, generative model based methods are increasingly progressed. LayoutGAN [24] and LayoutVAE [17] are the first attempts to utilize GAN and VAE to generate graphic and scene layouts. NDN [23] represents the relative positional relationship of elements as a graph and uses a graph neural network based conditional VAE to generate graphic layouts. READ [33] uses heuristics to determine the relationships between elements and trains a Recursive Neural Network (RNN) [37, 38] based VAE to learn the layout distribution. CanvasVAE [45] generates vector graphic documents which contain structured information about canvas and elements. VTN [1] and Coarse2fine [16] deploy self-attention based VAEs to generate graphic layouts, making progress in diversity and perceptual quality. LayoutTransformer [11] and BLT [21] define layouts as discrete sequences and exploit the efficiency of transformer and bidirectional-transformer in structured sequence generation. LayoutNet [46], TextLogo3K [44] and ICVT [6] propose conditional layout generative models which can utilize additional attributes about design elements or entire layouts to aid layout generation in different application scenarios. LayoutGAN++ [18] designs a transformer-based generator and discriminator and generates graphic layouts conditioned on the given element category labels. + +# 2.2. Diffusion Model + +Diffusion models [14, 40] have proved its capability of generating high-quality and diverse samples [8, 14, 35] and have recently achieved state-of-the-art results on several benchmark generation tasks [8]. The diffusion model uses diffusion processes to model the generation and defines the sampling of data as the process of gradually denoising from complete Gaussian noise. The forward process gradually + +![](images/6fda5fb58bedeef15b679c43cbb267d964c5717bdd1200dd0924998a41c5b93b.jpg) +(a) LayoutDM architecture + +![](images/0a4247d2420e18416038bfca53d3651553a70139a4d872537d062c168127daaa.jpg) +(b) Architecture of conditional layout denoiser $\epsilon_{\theta}$ +Figure 1. a) Architecture of LayoutDM. It consists of a forward diffusion process and a reverse process modeled by a conditional layout denoiser $\epsilon_{\theta}$ . b) Architecture of our transformer-based conditional layout denoiser, cLayoutDenoiser. cLayoutDenoiser predicts the added noise conditioned on the layout attributes $\pmb{f}$ and time step $t$ . + +adds Gaussian noise to the data from a predefined noise schedule until time step $T$ . The reverse process uses a neural backbone often implemented as a U-Net [8, 14, 36, 42] to parameterize the conditional distribution $p(\pmb{x}_{t - 1}|\pmb{x}_t)$ . In this work, we instantiate a conditional diffusion model to achieve conditional layout generation. + +# 3. Our Method + +# 3.1. Layout Representation + +In our model, each layout consists of a set of elements, and each element is described by both geometric parameters (i.e. location and size) and its attribute (e.g. category label or textual features). Formally, a layout $l$ is denoted as a flattened sequence of integer indices: + +$$ +\boldsymbol {l} = \left(g _ {1}, f _ {1}, g _ {2}, f _ {2}, \dots , g _ {i}, f _ {i}, \dots , g _ {N}, f _ {N}\right), +$$ + +where $N$ is the number of elements in the layout. $g_{i} = [x_{i},y_{i},w_{i},h_{i}]$ is a vector that presents the geometric parameters (center coordinates and size) of the $i$ -th element in the layout. $f_{i}$ is the attributes of $i$ -th element which might be category label or textual features. For the sake of convenience, the sequence $\pmb{g} = (g_1,g_2,\dots ,g_i\dots ,g_N)$ is named layout geometric parameters, the sequence $\pmb {f} = (f_{1},f_{2},\dots ,f_{i}\dots ,f_{N})$ is named layout attributes. Note here that, the elements in a layout are unordered, so swapping the items in sequence $\pmb{g}$ and $\pmb{f}$ does not affect the meaning of the sequences. We normalize the geometric parameters, i.e., $[x_i,y_i,w_i,h_i]$ , $i = 1,2,\dots ,N$ , to the interval $[-1,1]$ . In this way, layouts have a uniform structured representation. + +# 3.2. The LayoutDM Architecture + +Fig. 1a illustrates the architecture of LayoutDM. From a high-level perspective, our LayoutDM is an instance of conditional denoising diffusion probabilistic model (DDPM) with a transformer architecture suitable for layout data. DDPM learns to model the Markov transition from simple distribution to layout data distribution and generates + +diverse samples through sequential stochastic transitions. To generate desired layouts, LayoutDM uses the input attributes to guide the generative process in DDPM. We follow the method described in Classifier-Free Diffusion Guidance [13] to realize conditional DDPM, and set the guidance strength $w$ to zero for simplicity. + +Specifically, let $q(\pmb{g}_0|\pmb{f})$ be the unknown conditional data distribution, where $\pmb{g}_0$ is the geometric parameters of real layouts, and $\pmb{f}$ is the layout attributes. LayoutDM models the conditional distribution $q(\pmb{g}_0|\pmb{f})$ by two processes: a forward diffusion process and a reverse denoising diffusion process. First, LayoutDM defines the forward diffusion process $q(\pmb{g}_t|\pmb{g}_{t-1})$ which maps layout data to noise by gradually adding Gaussian noise at each time step $t$ : + +$$ +q \left(\boldsymbol {g} _ {t} \mid \boldsymbol {g} _ {t - 1}\right) = \mathcal {N} \left(\boldsymbol {g} _ {t}; \sqrt {1 - \beta_ {t}} \boldsymbol {g} _ {t - 1}, \beta_ {t} \mathbf {I}\right) \tag {1} +$$ + +where $\{\beta_t\}_{t=1}^T$ are forward process variances. + +Then, LayoutDM defines the conditional reverse diffusion process $p(\pmb{g}_{t-1} | \pmb{g}_t, \pmb{f})$ which performs iterative denoising from pure Gaussian noise to generate high-quality layouts conditioned on layout attributes $\pmb{f}$ : + +$$ +p _ {\theta} \left(\boldsymbol {g} _ {t - 1} \mid \boldsymbol {g} _ {t}, \boldsymbol {f}\right) = \mathcal {N} \left(\boldsymbol {g} _ {t - 1}; \boldsymbol {\mu} _ {\theta} \left(\boldsymbol {g} _ {t}, t, \boldsymbol {f}\right), \sigma_ {t} ^ {2} \mathbf {I}\right) \tag {2} +$$ + +where $\sigma_{t}$ is the constant variance following [14], $\mu_{\theta}$ is the mean of the Gaussian distribution computed by a neural network, and $\theta$ is the parameters of the network. As shown in Ho et al. [14], we can reparameterize the mean to make the neural network learn the added noise at time step $t$ instead. In this way, $\mu_{\theta}$ can be reparameterized as follows: + +$$ +\boldsymbol {\mu} _ {\theta} \left(\boldsymbol {g} _ {t}, t, \boldsymbol {f}\right) = \frac {1}{\sqrt {\alpha_ {t}}} \left(\boldsymbol {g} _ {t} - \frac {\beta_ {t}}{\sqrt {1 - \bar {\alpha} _ {t}}} \boldsymbol {\epsilon} _ {\theta} \left(\boldsymbol {g} _ {t}, t, \boldsymbol {f}\right)\right) \tag {3} +$$ + +where $t$ is the time step, $\{\beta_t\}_{t=1}^T$ are forward process variances, $\alpha_t = 1 - \beta_t$ , and $\overline{\alpha}_t = \prod_{s=1}^t \alpha_s$ . $\epsilon_\theta(\pmb{g}_t, t, \pmb{f})$ is the neural network to predict the added noise for layout geometric parameters conditioned on elements' attributes at time step $t$ . We also call the neural network $\epsilon_\theta(\pmb{g}_t, t, \pmb{f})$ as conditional layout denoiser (cLayoutDenoiser). + +# 3.3. Conditional Layout Denoiser + +The inputs to cLayoutDenoiser are layout geometric parameters $\pmb{g}_t$ , layout attributes $\pmb{f}$ and time step $t$ . To deal with sequences data, the conditional layout denoiser $\epsilon_{\theta}(\pmb{g}_t, t, \pmb{f})$ employs a purely transformer-based architecture instead of convolutional neural networks as its backbone. The architecture of cLayoutDenoiser is illustrated in Fig. 1b. Benefiting from the transformer architecture, cLayoutDenoiser can deal with the sequence with various lengths, and capture the relationships among elements. Moreover, cLayoutDenoiser adds "attributes embeddings" to the input "geometric embeddings", so as to guide the reverse diffusion process at each time step $t$ . Formally, the architecture of cLayoutDenoiser can be described as follow: + +$$ +\boldsymbol {h} _ {f} = \text {A t t r i b u t e s E m b e d d i n g} (\boldsymbol {f}) \tag {4} +$$ + +$$ +\boldsymbol {h} _ {g} = \text {G e o m e t r i c E m b e d d i n g} (\boldsymbol {g} _ {t}) \tag {5} +$$ + +$$ +\mathbf {E} = \text {E l e m e n t E m b e d d i n g} \left(\boldsymbol {h} _ {f}, \boldsymbol {h} _ {g}, \mathrm {T E} (t)\right) \tag {6} +$$ + +$$ +\mathbf {E} ^ {\prime} = \operatorname {T r a n s f o r m e r L a y e r s} (\mathbf {E}) \tag {7} +$$ + +$$ +\boldsymbol {\epsilon} = \operatorname {F C} \left(\mathbf {E} ^ {\prime}\right) \tag {8} +$$ + +where $\pmb{f}$ is the layout attributes, $\pmb{g}_t$ is the noised layout geometric parameters, $\pmb{h}_f$ and $\pmb{h}_g$ are their hidden representations. $\mathbf{E}$ is the element tokens computed by element embedding module, $\mathbf{E}'$ is intermediate feature. $\mathrm{TE}(t)$ denotes the timestep embedding, and $\epsilon$ is the predicted noise. Note here that, since the element order in the sequence makes no sense in our setting, cLayoutDenoiser omits the positional encoding, which is different from existing transformers in the context of NLP or video. + +Geometric, attributes and timestep embedding. Three embedding modules are used to learn meaningful representations for noised layout geometric parameters $g_{t}$ , layout attributes $f$ and time step $t$ . Geometric embedding projects layout geometric parameters to a specific dimension, aiming to find a more efficient feature space than the original coordinate space. Feature embedding learns the continuous features of discrete element attributes by embedding them into a specific dimension. Following [14], we condition cLayoutTransformer on time step $t$ by adding a sinusoidal time embedding $\mathrm{TE}(t)$ to make the network aware at which time step it is operating. + +Element embedding. Element embedding module calculates the element tokens used as the input of transformer layers. Element tokens should contain geometric, attributes and time step information, so that transformer can efficiently capture the relationship information between elements conditioned on the time step $t$ and layout attributes $f$ . We concatenate the geometric embedding and attributes embedding, and then use a fully-connected layer to fuse element representation. We further perform an element-wise plus operation with timestep embedding on the results to finally obtain the element tokens. + +Algorithm 1: Training LayoutDM +Require: conditional layout denoiser $\epsilon_{\theta}$ repeat Sample $(g_0,f)\sim q_{data};$ $t\sim$ Uniform( $\{1,\dots ,T\}$ . $\epsilon \sim \mathcal{N}(\mathbf{0},\mathbf{I})$ .. $\pmb {g}_t = \sqrt{\alpha}_t\pmb {g}_0 + \sqrt{1 - \overline{\alpha}_t}\pmb {\epsilon};$ Take gradient descent step on $\nabla_{\theta}\| \boldsymbol {\epsilon} - \boldsymbol{\epsilon}_{\theta}(\pmb {g}_t,t,\pmb {f})\| ^2;$ +until converged; + +Algorithm 2: Sampling +Input: layout attributes $\pmb{f}$ +Output: layout geometric parameters $\pmb{g_0}$ $g_{T}\sim \mathcal{N}(\mathbf{0},\mathbf{I})$ +for $t = T,\dots ,1$ do $\mathbf{z}\sim \mathcal{N}(\mathbf{0},\mathbf{I})$ if $t > 1$ , else $\mathbf{z} = \mathbf{0}$ . $g_{t - 1} = \frac{1}{\sqrt{\alpha_t}} (g_t - \frac{1 - \alpha_t}{\sqrt{1 - \overline{\alpha}_t}}\epsilon_\theta (g_t,t,\pmb {f})) + \sigma_t\mathbf{z}$ +end +return $\pmb{g_0}$ + +Transformer layers. Generating an effective layout requires understanding the relationships between layout elements. Self-attention mechanism in Transformer [43] has proven effective in capturing high-level relationships between lots of elements in layout generation [1, 11, 15]. In this paper, we adopt multihead attention mechanism to capture relationship information between elements from element tokens. We stack multiple transformer layers (8 in our model) to enable cLayoutDenoiser to capture relationships between layout elements from the element tokens. Positional encoding is omitted because of the unordered nature of elements. + +$$ +\hat {\mathbf {E}} = \operatorname {L a y e r N o r m} \left(\mathbf {E} ^ {l - 1} + \mathbf {H e a d} \left(e _ {1} ^ {l - 1}, \dots , e _ {N} ^ {l - 1}\right)\right) \tag {9} +$$ + +$$ +\mathbf {E} ^ {l} = \operatorname {L a y e r N o r m} (\hat {\mathbf {E}} + \operatorname {F F N} (\hat {\mathbf {E}})) \tag {10} +$$ + +where $l = 1, \dots, L$ denotes the layer index, Head, LayoutNorm and FFN denote multi-head attention layer, Layer Normalization [3] and fully connected feed-forward network. $\mathbf{E}^{l-1} = (\pmb{e}_1^{l-1}, \dots, \pmb{e}_N^{l-1})$ are the intermediate element tokens used as the input of $l$ -th transformer layer. + +# 3.4. Training and Inference + +Following denoising diffusion probabilistic model [14], we optimize random terms $L_{t}$ which are the KL divergences between $p_{\theta}(\pmb{g}_{t-1}|\pmb{g}_t, \pmb{f})$ and forward process posteriors. After simplifying the objective function following the method in [14], the final loss function is as follows: + +$$ +\begin{array}{l} L _ {s i m p l e} (\theta) = \left\| \boldsymbol {\epsilon} - \boldsymbol {\epsilon} _ {\theta} \left(\boldsymbol {g} _ {t}, t, \boldsymbol {f}\right) \right\| ^ {2} \\ = \| \boldsymbol {\epsilon} - \boldsymbol {\epsilon} _ {\theta} \left(\sqrt {\bar {\alpha} _ {t}} \boldsymbol {g} _ {0} + \sqrt {\left(1 - \bar {\alpha} _ {t}\right)} \boldsymbol {\epsilon}, t, \boldsymbol {f}\right) \| ^ {2} \tag {11} \\ \end{array} +$$ + +where $\epsilon \sim \mathcal{N}(\mathbf{0},\mathbf{I})$ $\epsilon_{\theta}$ is our conditional layout denoiser, $g_{t}\sim \mathcal{N}(g_{t};\sqrt{\overline{\alpha}_{t}} g_{0},(1 - \overline{\alpha}_{t})\mathbf{I})$ is computed using the property of Gaussian distributions and $\pmb {g}_0$ is the real layout geometric parameters. $\{\beta_t\}_{t = 1}^T$ are forward process variances, $\alpha_{t} = 1 - \beta_{t}$ and $\overline{\alpha}_t = \prod_{s = 1}^t\alpha_s$ + +The training and sampling algorithm of LayoutDM are illustrated in Algorithm 1 and Algorithm 2 respectively. + +# 4. Experiments + +# 4.1. Experimental Settings + +Datasets. We evaluate our method on five public datasets of layouts for documents, natural scenes, magazines, text logos and mobile phone UIs. Rico [7] is a dataset of user interface designs for mobile applications, containing 72,219 user interfaces from 9,772 Android apps. PublayNet [47] contains 330K samples of machine-annotated scientific documents crawled from the Internet with five categories (text, title, figure, list, table). Magazine [46] is a magazine layout dataset that covers a wide range of magazine categories. It consists of semantic layout annotations. COCO [26] is a large-scale labeled image dataset that contains images of natural scenes with instance segmentation. TextLogo3K [44] is a recently released dataset of text logos. It consists of 3,470 text logo images with manually annotated bounding boxes and pixel-level masks for each character. + +Evaluation metrics. To validate the effectiveness of LayoutDM, we employ four metrics in the literature to measure the perceptual quality of layouts. To be a fair comparison, we follow the guidance in [18] to evaluate these metrics. Specifically, FID [12] measures the distribution distance between real layouts and generated layouts. We use the pre-trained classifiers in [18] to compute FID. Max IoU [18] measures the similarity between the generated layouts and the reference layouts. It is designed to find the best match for each layout from the generated set to the reference set. Overlap and Alignment measure the perceptual quality of generated layouts. Overlap measures the total overlapping area between any pair of bounding boxes inside the layout. Additionally, we measure the Alignment by computing an alignment loss proposed in [25]. + +Implementing details. The max time step $T$ in LayoutDM is set to 1000. We set the forward process variances to constants increasing linearly from $\beta_{1} = 10^{-4}$ to $\beta_{T} = 0.02$ following Ho's design [14]. We use eight transformer layers which use 8-head attention in our model. Adam optimizer [19] with a learning rate of $1 \times 10^{-5}$ is used to optimize learnable parameters. The batch size is set to 1024. We implement our model with PyTorch [32] and PyTorch Lightning. All experiments are performed on a single NVIDIA Quadro RTX 6000 GPU device. + +
Dataset +ModelRico
FID↓Max. IoU↑Alignment↓Overlap↓
LayoutGAN-W [24]162.75±0.280.30±0.000.71±0.00174.11±0.22
LayoutGAN-R [24]52.01±0.620.24±0.001.13±0.0469.37±0.66
NDN-none [23]13.76±0.280.35±0.000.56±0.0354.75±0.29
LayoutGAN++ [18]14.43±0.130.36±0.000.60±0.1259.85±0.59
VTN [1]9.31±0.210.36±0.000.88±0.1159.31±0.45
LayoutDM(Ours)3.03±0.060.49±0.000.36±0.0657.55±0.48
Real data4.470.650.2650.58
Dataset +ModelPublayNet
FID↓Max. IoU↑Alignment↓Overlap↓
LayoutGAN-W [24]195.38±0.460.21±0.001.21±0.01138.77±0.21
LayoutGAN-R [24]100.24±0.610.24±0.000.82±0.0145.64±0.32
NDN-none [23]35.67±0.350.31±0.000.35±0.0116.5±0.29
LayoutGAN++ [18]20.48±0.290.36±0.000.19±0.0022.80±0.32
VTN [1]13.07±0.470.37±0.000.30±0.0113.15±0.24
LayoutDM(Ours)4.04±0.080.44±0.000.15±0.003.73±0.08
Real data9.540.530.040.22
Dataset +ModelMagazine
FID↓Max. IoU↑Alignment↓Overlap↓
LayoutGAN-W [24]159.2±0.870.12±0.000.74±0.02188.77±0.93
LayoutGAN-R [24]100.66±0.350.16±0.001.90±0.02111.85±1.44
NDN-none [23]23.27±0.090.22±0.001.05±0.0330.31±0.77
LayoutGAN++ [18]13.35±0.410.26±0.000.80±0.0232.40±0.89
VTN [1]12.34±0.390.25±0.001.07±0.0339.97±0.62
LayoutDM(Ours)9.11±0.150.29±0.000.77±0.0332.53±0.72
Real data12.130.350.4325.64
+ +Table 1. Quantitative comparison conditioned on element category labels. For reference, the FID and Max. IoU computed between the validation and test data, and the Alignment and Overlap computed with the test data are shown as real data. LayoutGAN-W and LayoutGAN-R denote LayoutGAN with wireframe rendering discriminator and with relation-based discriminator. + +# 4.2.Quantitative Evaluation + +Comparison with state-of-the-art models. We quantitatively evaluate the quality of conditional layout generation results on benchmark datasets: Rico, PublayNet and Magazine. Since most methods are designed for unconditional layout generation and have no available public implements, we compare our method with conditional LayoutGAN [24], NDN-none [23] and LayoutGAN++ [18] by citing the results in [18]. Moreover, we also implement a conditional VTN [1] as our comparison baseline model, so that we can compare with methods based on both VAEs and GANs. All the metrics are computed on the full test splits of the datasets. We report the mean and standard deviation over five independent evaluations for each experiment. + +The comparison results are reported in Tab. 1. From this table, we can observe that: (1) Our method outperforms SOTA methods on both FID and Max. IoU on all three benchmark datasets, which indicates that the generated layouts by our method are more similar to the real layouts than those by SOTA methods. This verifies that our LayoutDM can produce higher-quality and more diverse layouts than SOTA methods, since FID captures both diversity and fidelity. (2) Layouts generated by our method have a lower + +
IoU↓ [21]Overlap↓ [24]Alignment↓ [23]
L-VAE [17]0.45±1.3%0.15±0.9%0.37±0.7%
NDN [23]0.34±1.8%0.12±0.8%0.39±0.4%
VTN [1]0.21±0.6%0.06±0.2%0.33±0.4%
Trans. [11]0.19±0.3%0.06±0.3%0.33±0.3%
BLT [21]0.19±0.2%0.04±0.1%0.25±0.7%
Ours0.0053±0.5%0.01±0.1%0.22±1.2%
+ +FID score than the real ones in validation splits. This is because the generated layouts have identical attributes to those in the test split, while the real layouts in the validation split have different attributes from those in the test split. We provide more analysis on this point in the supplementary material. (3) With regards to Alignment and Overlap, LayoutDM is slightly weaker on Rico and Magazine. Because our method lacks a discriminator that guides the generator to generate layouts with better alignment and overlap properties as in GANs and does not introduce the layout refine module in NDN. This is likely to cause LayoutDM to be inferior to the state-of-the-art on these two metrics. + +Note here that, we don't compare LayoutDM to other state-of-the-art methods such as LayoutTransformer [11] and Coarse2fine [16], because these methods focus on unconditional layout generation problem which is different to our setting. Recently, Kong et al. [21] reimplement the conditional version of VTN and LayoutTransformer, and compare their proposed BLT model with these models under the settings of conditional layout generation. However, they compute the metrics (IoU [21], Alignment [23], Overlap [24]) in different ways. As an extended comparison, we adopt the metrics used by BLT [21], and compare our LayoutDM with VTN, LayoutTransformer, LayoutVAE, NDN and BLT on PublayNet. The comparison results are reported in Tab. 2. As shown in this table, our model also outperforms SOTA methods on all metrics. + +Effect of transformer layers. We conduct ablation experiments to demonstrate the effectiveness of the transformer layers in LayoutDM. Quantitative results are reported in Tab. 3 and qualitative comparisons are shown in Fig. 3. We have the following observation: After replacing the transformer structure in LayoutDM with a sequence of FC layers, the model can still predict a suitable size for each element, but the positional relationships between elements can not be handled, resulting in significant overlapping and misalignment. This proves that the transformer layers play an essential role and can efficiently capture and utilize the high-level relationships between elements to generate high-quality layouts which follow design rules and aesthetic principles. + +Table 2. Comparison with extended methods on PublayNet. Qualitative results are cited from [21]. "Trans." denotes "LayoutTransformer" and "L-VAE" denotes "LayoutVAE". + +
ArchitectureRico
FID↓Max.IoU↑Alignment↓Overlap↓
w/o transformer52.640.291.0858.13
Full model3.030.490.3657.55
ArchitecturePublayNet
FID↓Max.IoU↑Alignment↓Overlap↓
w/o transformer99.600.270.8963.87
Full model4.040.440.153.73
+ +Table 3. The quantitative results of ablations on transformer layers. "Full" denotes our full model. "w/o transformer" denotes model without transformer layers. + +# 4.3. Qualitative Comparisons + +Generation quality comparison. To qualitatively compare the generation performance of different models, we compare with the state-of-the-art method LayoutGAN++ and our implemented conditional VTN. We randomly sample layouts from the test dataset and use the element category labels as conditional inputs. Fig. 2 shows the qualitative comparison results. As one can see, LayoutDM can arrange elements in a reasonable and complicated way, generating higher quality layouts than the other two, with fewer overlapping and better alignment. + +Generation diversity comparison. The diversity of results is also an important factor in evaluating the method. We compare the diversity of layouts generated by conditional VTN, LayoutGAN++, and LayoutDM. Fig. 4 show the comparison results. One can see that conditional VTN and LayoutDM generate more diverse results. The Figure element in the results floats on the page. Compared to the other two models, LayoutGAN++ captures less diversity, which places a large Figure element on the top of the pages in columns 2,4, and 5. LayoutDM performs well in diversity because it breaks the generation into a series of conditional diffusion steps which are relatively easy to model. This alleviates the mode collapse problem in strongly conditional generation task that can lead to the generation of similar modes. We provide more qualitative comparisons on diversity in the supplementary material. + +Rendering results comparison. We render graphic pages for better visualization using the generated layouts. Fig. 5 show the rendering results comparison on PublayNet. We find the layouts generated by LayoutDM follow design rules well and reasonably allocate page space. Compared to the results generated by LayoutGAN++, our results are better in alignment and have no overlapping between elements. Note that we crop the elements from the original document and then render the pages using a simple resize-to-fit method, so the text areas and figures will suffer some distortion. In real design scenarios, this problem can be solved by element customization (e.g., adjust the font size). + +![](images/ac1a71fba8ad3e9328176ecde46122608960c0b57d7e2aec017dad8645449d08.jpg) +Figure 2. Qualitative comparison on Rico and PublayNet. Element labels indicate the labels of elements used as conditional inputs. + +![](images/5dac9dbaa5f24f71858b84ca789eca6aaa8499a0c4922f6bae63b314ec24205b.jpg) +Figure 3. Ablation study on the effect of transformer layers. "w/o transformer" denotes model without transformer layers. "Full" denotes our full model. + +# 4.4. Extended Layout Generation Tasks + +Text logo layout generation. TextLogo3K [44] dataset contains character and word embedding of texts in the logos. Although the dataset does not provide any label information, we can still generate logo layouts conditioned on the provided textual features. Positional encoding is added to LayoutDM to make the transformer structure aware of the reading order in textual feature sequences. We compare the logo layout generation results of LayoutDM and those generated by the logo layout generator provided by TextLogo3K [44]. The qualitative results are shown in Fig. 6. As + +![](images/d353d36048b59a08c9383ecdc97c90afc274e2003884f7db08b3ab56b7b1c81f.jpg) +Figure 4. Diversity comparison on PublayNet. We show five samples generated by giving the same category attributes as condition: one Figure and five Texts. The Figure is drawn in purple and the Texts are drawn in red. + +one can see, our model generates reasonable logo layouts while maintaining the correct reading order and aesthetic principles. Compared to LogoGAN, the style of the logos generated by our model is more flexible, not simply arranging the text from left to right. Our model also performs better when there are large numbers of characters in the layout, where LogoGAN fails to generate reasonable results. + +Scene layout generation. Our model can also generate + +![](images/f2fc7ddb6eed51e61453cdce6710283ea34d077fe079143980095bf17854d5d3.jpg) + +![](images/9c4770cae20e57c3acfd139b49e9072569849cb7803638212f0407badb2f8c83.jpg) +Figure 5. Rendering results comparison. Top: Rendered pages using layouts generated by LayoutGAN++. Middle: Rendered pages using layouts generated by LayoutDM. Bottom: Real paper pages in PublayNet. +Figure 6. Text logo generation results. "LogoGAN" denotes the text logo generation model proposed in [44]. "Condition" represents the textual features (including character and word embeddings) used as conditional input in LogoGAN and LayoutDM. "/" is the symbol for splitting tokens. + +natural scene layouts. We illustrate the qualitative results of the scene layout generation on COCO in Fig. 7. Given the labels of scene elements in a scene, our model generates reasonable scene layout proposals. We then use a downstream layout-to-image generation application [2] to finally render natural scene images. The results show that our model learns the principle of scene layouts well and can understand the complex relationships between elements in + +![](images/c64a28bccad22f12f6306a45315d7c7e495b90feb80652d1f023851d6f0e10ef.jpg) +Figure 7. Natural scene layout generation results on COCO. Our model uses scene element labels as conditional input to generate reasonable scene layouts. + +natural scenes. For example, the boat should be in the river and the cloud should be in the upper part of the scene. + +# 4.5. Limitations + +Although our method shows impressive results in the conditional layout generation problem in comparison to existing methods, it still has limitations. For example, like other layout generation methods, our approach treats design elements as being on a single-layer canvas. This can not model a layout with multiple layers occluding each other. Our method also has no advantage over other generative models in generation speed because the generation of the diffusion model requires an iterative denoising process. We leave the solution to the above problems for future work. + +# 5. Conclusion + +This paper proposes a transformer-based diffusion model LayoutDM to address conditional layout generation. We introduce a purely transformer-based Layout Denoiser to model the diffusion reverse process. Benefitting from both DDPM and transformer, in comparison to existing methods, LayoutDM can generate high-quality generation with desired properties such as better diversity, faithful distribution coverage, and stationary training. Quantitative and qualitative results demonstrate that our model outperforms the state-of-the-art methods in terms of visual perceptual quality and diversity. + +Acknowledgment. This work was supported in part to Dr. Liansheng Zhuang by NSFC under contract No.U20B2070 and No.61976199, in part to Dr. Fengying Yan by NSFC under contract No.42341207. + +# References + +[1] Diego Martín Arroyo, Janis Postels, and Federico Tombari. Variational transformer networks for layout generation. In 2021 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 13637-13647, 2021. 1, 2, 4, 5, 6 +[2] Oron Ashual and Lior Wolf. Specifying object attributes and relations in interactive scene generation. 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Though existing methods based on generative models such as Generative Adversarial Networks (GANs) and Variational Auto-Encoders (VAEs) have progressed, they still leave much room for improving the quality and diversity of the results. Inspired by the recent success of diffusion models in generating high-quality images, this paper explores their potential for conditional layout generation and proposes Transformer-based Layout Diffusion Model (LayoutDM) by instantiating the conditional denoising diffusion probabilistic model (DDPM) with a purely transformer-based architecture. Instead of using convolutional neural networks, a transformer-based conditional Layout Denoiser is proposed to learn the reverse diffusion process to generate samples from noised layout data. Benefitting from both transformer and DDPM, our LayoutDM is of desired properties such as high-quality generation, strong sample diversity, faithful distribution coverage, and stationary training in comparison to GANs and VAEs. Quantitative and qualitative experimental results show that our method outperforms state-of-the-art generative models in terms of quality and diversity." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 539, + 128, + 552 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 539, + 128, + 552 + ], + "spans": [ + { + "bbox": [ + 47, + 539, + 128, + 552 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 560, + 287, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 560, + 287, + 693 + ], + "spans": [ + { + "bbox": [ + 46, + 560, + 287, + 693 + ], + "type": "text", + "content": "Layouts, i.e. the arrangement of the elements to be displayed in a design, play a critical role in many applications from magazine pages to advertising posters to application interfaces. A good layout guides viewers' reading order and draws their attention to important information. The semantic relationships of elements, the reading order, canvas space allocation and aesthetic principles must be carefully decided in the layout design process. However, manually arranging design elements to meet aesthetic goals and user-specified constraints is time-consuming. To aid the design of graphic layouts, the task of layout generation aims to" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 213, + 545, + 297 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 213, + 545, + 297 + ], + "spans": [ + { + "bbox": [ + 306, + 213, + 545, + 297 + ], + "type": "text", + "content": "generate design layouts given a set of design components with user-specified attributes. Though meaningful attempts are made [1, 10, 11, 15, 18, 21, 23-25, 33, 44-46], it is still challenging to generate realistic and complex layouts, because many factors need to be taken into consideration, such as design elements, their attributes, and their relationships to other elements." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 300, + 546, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 300, + 546, + 529 + ], + "spans": [ + { + "bbox": [ + 304, + 300, + 546, + 529 + ], + "type": "text", + "content": "Over the past few years, generative models such as Generative Adversarial Networks (GANs) [9] and Variational Auto-Encoders (VAEs) [20] have gained much attention in layout generation, as they have shown a great promise in terms of faithfully learning a given data distribution and sampling from it. GANs model the sampling procedure of a complex distribution that is learned in an adversarial manner, while VAEs seek to learn a model that assigns a high likelihood to the observed data samples. Though having shown impressive success in generating high-quality layouts, these models have some limitations of their own. GANs are known for potentially unstable training and less distribution coverage due to their adversarial training nature [4, 5, 27], so they are inferior to state-of-the-art likelihood-based models (such as VAEs) in terms of diversity [28, 29, 34]. VAEs can capture more diversity and are typically easier to scale and train than GANs, but still fall short in terms of visual sample quality and sampling efficiency [22]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 531, + 547, + 663 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 531, + 547, + 663 + ], + "spans": [ + { + "bbox": [ + 304, + 531, + 547, + 663 + ], + "type": "text", + "content": "Recently, diffusion models such as denoising diffusion probabilistic model (DDPM) [14] have emerged as a powerful class of generative models, capable of producing high-quality images comparable to those of GANs. Importantly, they additionally offer desirable properties such as strong sample diversity, faithful distribution coverage, a stationary training objective, and easy scalability. This implies that diffusion models are well suited for learning models of complex and diverse data, which also motivates us to explore the potential of diffusion-based generative models for graphic layout generation." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 665, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 665, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 665, + 547, + 715 + ], + "type": "text", + "content": "Though diffusion models have shown splendid performance in high-fidelity image generation [8, 14, 35, 39, 41], it is still a sparsely explored area and provides unique challenges to develop diffusion-based generative models for" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 135, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 135, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 135, + 712 + ], + "type": "text", + "content": "*Corresponding author." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "18349" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 275 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 275 + ], + "type": "text", + "content": "layout generation. First, diffusion models often use convolutional neural networks such as U-Net [36] to learn the reverse process to construct desired data samples from the noise. However, a layout is a non-sequential data structure consisting of varying length samples with discrete (classes) and continuous (coordinates) elements simultaneously, instead of pixels laid on a regular lattice. Obviously, convolutional neural networks are not suitable for layout denoising, which prevents diffusion models from being directly applied to layout generation. Second, the placement and sizing of a given element depend not only on its attributes (such as category label) but also on its relationship to other elements. How to incorporate the attributes knowledge and model the elements' relationship in diffusion models is still an open problem. Since diffusion models are general frameworks, they leave room for adapting the underlying neural architectures to exploit the properties of the data." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 275, + 289, + 632 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 275, + 289, + 632 + ], + "spans": [ + { + "bbox": [ + 46, + 275, + 289, + 632 + ], + "type": "text", + "content": "Inspired by the above insights, by instantiating the conditional denoising diffusion probabilistic model (DDPM) with a transformer architecture, this paper proposes Transformer-based Layout Diffusion Model (i.e., LayoutDM) for conditional layout generation given a set of elements with user-specified attributes. The key idea is to use a purely transformer-based architecture instead of the commonly used convolutional neural networks to learn the reverse diffusion process from noised layout data. Benefiting from the self-attention mechanism in transformer layers, LayoutDM can efficiently capture high-level relationship information between elements, and predict the noise at each time step from the noised layout data. Moreover, the attention mechanism also helps model another aspect of the data - namely a varying and large number of elements. Finally, to generate layouts with desired attributes, LayoutDM designs a conditional Layout Denoiser (cLayoutDenoiser) based on a transformer architecture to learn the reverse diffusion process conditioned on the input attributes. Different from previous transformer models in the context of NLP or video, cLayoutDenoiser omits the positional encoding which indicates the element order in the sequence, as we do not consider the order of designed elements on a canvas in our setting. In comparison with current layout generation approaches (such as GANs and VAEs), our LayoutDM offers several desired properties such as high-quality generation, better diversity, faithful distribution coverage, a stationary training objective, and easy scalability. Extensive experiments on five public datasets show that LayoutDM outperforms state-of-the-art methods in different tasks." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 59, + 635, + 265, + 646 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 635, + 265, + 646 + ], + "spans": [ + { + "bbox": [ + 59, + 635, + 265, + 646 + ], + "type": "text", + "content": "In summary, our main contributions are as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 56, + 654, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 654, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 56, + 654, + 287, + 714 + ], + "type": "text", + "content": "- This paper proposes a novel LayoutDM to generate high-quality design layouts for a set of elements with user-specified attributes. Compared with existing methods, LayoutDM is of desired properties such as high-quality generation, better diversity, faithful distribution" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 322, + 72, + 545, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 322, + 72, + 545, + 109 + ], + "spans": [ + { + "bbox": [ + 322, + 72, + 545, + 109 + ], + "type": "text", + "content": "coverage, and stationary training. To our best knowledge, LayoutDM is the first attempt to explore the potential of diffusion model for graphic layout generation." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 315, + 111, + 547, + 222 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 315, + 111, + 545, + 172 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 111, + 545, + 172 + ], + "spans": [ + { + "bbox": [ + 315, + 111, + 545, + 172 + ], + "type": "text", + "content": "- This paper explores a new class of diffusion models by replacing the commonly-used U-Net backbone with a transformer, and designs a novel cLayoutDenoiser to reverse the diffusion process from noised layout data and better capture the relationship of elements." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 315, + 175, + 547, + 222 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 175, + 547, + 222 + ], + "spans": [ + { + "bbox": [ + 315, + 175, + 547, + 222 + ], + "type": "text", + "content": "- Extensive experiments demonstrate that our method outperforms state-of-the-art models in terms of visual perceptual quality and diversity on five diverse layout datasets." + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 242, + 392, + 255 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 242, + 392, + 255 + ], + "spans": [ + { + "bbox": [ + 306, + 242, + 392, + 255 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 262, + 417, + 274 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 262, + 417, + 274 + ], + "spans": [ + { + "bbox": [ + 306, + 262, + 417, + 274 + ], + "type": "text", + "content": "2.1. Layout Generation" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 281, + 545, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 281, + 545, + 604 + ], + "spans": [ + { + "bbox": [ + 304, + 281, + 545, + 604 + ], + "type": "text", + "content": "Automatic layout generation has been widely studied for a long time. Early approaches to layout generation [30, 31] embed design rules into manually-defined energy functions. In recent years, generative model based methods are increasingly progressed. LayoutGAN [24] and LayoutVAE [17] are the first attempts to utilize GAN and VAE to generate graphic and scene layouts. NDN [23] represents the relative positional relationship of elements as a graph and uses a graph neural network based conditional VAE to generate graphic layouts. READ [33] uses heuristics to determine the relationships between elements and trains a Recursive Neural Network (RNN) [37, 38] based VAE to learn the layout distribution. CanvasVAE [45] generates vector graphic documents which contain structured information about canvas and elements. VTN [1] and Coarse2fine [16] deploy self-attention based VAEs to generate graphic layouts, making progress in diversity and perceptual quality. LayoutTransformer [11] and BLT [21] define layouts as discrete sequences and exploit the efficiency of transformer and bidirectional-transformer in structured sequence generation. LayoutNet [46], TextLogo3K [44] and ICVT [6] propose conditional layout generative models which can utilize additional attributes about design elements or entire layouts to aid layout generation in different application scenarios. LayoutGAN++ [18] designs a transformer-based generator and discriminator and generates graphic layouts conditioned on the given element category labels." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 611, + 405, + 623 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 611, + 405, + 623 + ], + "spans": [ + { + "bbox": [ + 306, + 611, + 405, + 623 + ], + "type": "text", + "content": "2.2. Diffusion Model" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "type": "text", + "content": "Diffusion models [14, 40] have proved its capability of generating high-quality and diverse samples [8, 14, 35] and have recently achieved state-of-the-art results on several benchmark generation tasks [8]. The diffusion model uses diffusion processes to model the generation and defines the sampling of data as the process of gradually denoising from complete Gaussian noise. The forward process gradually" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "18350" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 71, + 287, + 164 + ], + "blocks": [ + { + "bbox": [ + 47, + 71, + 287, + 164 + ], + "lines": [ + { + "bbox": [ + 47, + 71, + 287, + 164 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 287, + 164 + ], + "type": "image", + "image_path": "6fda5fb58bedeef15b679c43cbb267d964c5717bdd1200dd0924998a41c5b93b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 124, + 170, + 212, + 179 + ], + "lines": [ + { + "bbox": [ + 124, + 170, + 212, + 179 + ], + "spans": [ + { + "bbox": [ + 124, + 170, + 212, + 179 + ], + "type": "text", + "content": "(a) LayoutDM architecture" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 291, + 76, + 541, + 168 + ], + "blocks": [ + { + "bbox": [ + 291, + 76, + 541, + 168 + ], + "lines": [ + { + "bbox": [ + 291, + 76, + 541, + 168 + ], + "spans": [ + { + "bbox": [ + 291, + 76, + 541, + 168 + ], + "type": "image", + "image_path": "0a4247d2420e18416038bfca53d3651553a70139a4d872537d062c168127daaa.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 336, + 170, + 496, + 179 + ], + "lines": [ + { + "bbox": [ + 336, + 170, + 496, + 179 + ], + "spans": [ + { + "bbox": [ + 336, + 170, + 496, + 179 + ], + "type": "text", + "content": "(b) Architecture of conditional layout denoiser " + }, + { + "bbox": [ + 336, + 170, + 496, + 179 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 189, + 547, + 222 + ], + "lines": [ + { + "bbox": [ + 46, + 189, + 547, + 222 + ], + "spans": [ + { + "bbox": [ + 46, + 189, + 547, + 222 + ], + "type": "text", + "content": "Figure 1. a) Architecture of LayoutDM. It consists of a forward diffusion process and a reverse process modeled by a conditional layout denoiser " + }, + { + "bbox": [ + 46, + 189, + 547, + 222 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 46, + 189, + 547, + 222 + ], + "type": "text", + "content": ". b) Architecture of our transformer-based conditional layout denoiser, cLayoutDenoiser. cLayoutDenoiser predicts the added noise conditioned on the layout attributes " + }, + { + "bbox": [ + 46, + 189, + 547, + 222 + ], + "type": "inline_equation", + "content": "\\pmb{f}" + }, + { + "bbox": [ + 46, + 189, + 547, + 222 + ], + "type": "text", + "content": " and time step " + }, + { + "bbox": [ + 46, + 189, + 547, + 222 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 189, + 547, + 222 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 232, + 287, + 304 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 232, + 287, + 304 + ], + "spans": [ + { + "bbox": [ + 46, + 232, + 287, + 304 + ], + "type": "text", + "content": "adds Gaussian noise to the data from a predefined noise schedule until time step " + }, + { + "bbox": [ + 46, + 232, + 287, + 304 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 232, + 287, + 304 + ], + "type": "text", + "content": ". The reverse process uses a neural backbone often implemented as a U-Net [8, 14, 36, 42] to parameterize the conditional distribution " + }, + { + "bbox": [ + 46, + 232, + 287, + 304 + ], + "type": "inline_equation", + "content": "p(\\pmb{x}_{t - 1}|\\pmb{x}_t)" + }, + { + "bbox": [ + 46, + 232, + 287, + 304 + ], + "type": "text", + "content": ". In this work, we instantiate a conditional diffusion model to achieve conditional layout generation." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 316, + 127, + 328 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 316, + 127, + 328 + ], + "spans": [ + { + "bbox": [ + 47, + 316, + 127, + 328 + ], + "type": "text", + "content": "3. Our Method" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 335, + 176, + 348 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 335, + 176, + 348 + ], + "spans": [ + { + "bbox": [ + 47, + 335, + 176, + 348 + ], + "type": "text", + "content": "3.1. Layout Representation" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 354, + 287, + 414 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 354, + 287, + 414 + ], + "spans": [ + { + "bbox": [ + 46, + 354, + 287, + 414 + ], + "type": "text", + "content": "In our model, each layout consists of a set of elements, and each element is described by both geometric parameters (i.e. location and size) and its attribute (e.g. category label or textual features). Formally, a layout " + }, + { + "bbox": [ + 46, + 354, + 287, + 414 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 46, + 354, + 287, + 414 + ], + "type": "text", + "content": " is denoted as a flattened sequence of integer indices:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 77, + 424, + 256, + 437 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 424, + 256, + 437 + ], + "spans": [ + { + "bbox": [ + 77, + 424, + 256, + 437 + ], + "type": "interline_equation", + "content": "\\boldsymbol {l} = \\left(g _ {1}, f _ {1}, g _ {2}, f _ {2}, \\dots , g _ {i}, f _ {i}, \\dots , g _ {N}, f _ {N}\\right),", + "image_path": "3cdae4d68a1ea5cefffc001a505e1b061142d321e554ef8e2285f2a128389432.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 447, + 287, + 614 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 447, + 287, + 614 + ], + "spans": [ + { + "bbox": [ + 46, + 447, + 287, + 614 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 447, + 287, + 614 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 447, + 287, + 614 + ], + "type": "text", + "content": " is the number of elements in the layout. " + }, + { + "bbox": [ + 46, + 447, + 287, + 614 + ], + "type": "inline_equation", + "content": "g_{i} = [x_{i},y_{i},w_{i},h_{i}]" + }, + { + "bbox": [ + 46, + 447, + 287, + 614 + ], + "type": "text", + "content": " is a vector that presents the geometric parameters (center coordinates and size) of the " + }, + { + "bbox": [ + 46, + 447, + 287, + 614 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 447, + 287, + 614 + ], + "type": "text", + "content": "-th element in the layout. " + }, + { + "bbox": [ + 46, + 447, + 287, + 614 + ], + "type": "inline_equation", + "content": "f_{i}" + }, + { + "bbox": [ + 46, + 447, + 287, + 614 + ], + "type": "text", + "content": " is the attributes of " + }, + { + "bbox": [ + 46, + 447, + 287, + 614 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 447, + 287, + 614 + ], + "type": "text", + "content": "-th element which might be category label or textual features. For the sake of convenience, the sequence " + }, + { + "bbox": [ + 46, + 447, + 287, + 614 + ], + "type": "inline_equation", + "content": "\\pmb{g} = (g_1,g_2,\\dots ,g_i\\dots ,g_N)" + }, + { + "bbox": [ + 46, + 447, + 287, + 614 + ], + "type": "text", + "content": " is named layout geometric parameters, the sequence " + }, + { + "bbox": [ + 46, + 447, + 287, + 614 + ], + "type": "inline_equation", + "content": "\\pmb {f} = (f_{1},f_{2},\\dots ,f_{i}\\dots ,f_{N})" + }, + { + "bbox": [ + 46, + 447, + 287, + 614 + ], + "type": "text", + "content": " is named layout attributes. Note here that, the elements in a layout are unordered, so swapping the items in sequence " + }, + { + "bbox": [ + 46, + 447, + 287, + 614 + ], + "type": "inline_equation", + "content": "\\pmb{g}" + }, + { + "bbox": [ + 46, + 447, + 287, + 614 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 447, + 287, + 614 + ], + "type": "inline_equation", + "content": "\\pmb{f}" + }, + { + "bbox": [ + 46, + 447, + 287, + 614 + ], + "type": "text", + "content": " does not affect the meaning of the sequences. We normalize the geometric parameters, i.e., " + }, + { + "bbox": [ + 46, + 447, + 287, + 614 + ], + "type": "inline_equation", + "content": "[x_i,y_i,w_i,h_i]" + }, + { + "bbox": [ + 46, + 447, + 287, + 614 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 447, + 287, + 614 + ], + "type": "inline_equation", + "content": "i = 1,2,\\dots ,N" + }, + { + "bbox": [ + 46, + 447, + 287, + 614 + ], + "type": "text", + "content": ", to the interval " + }, + { + "bbox": [ + 46, + 447, + 287, + 614 + ], + "type": "inline_equation", + "content": "[-1,1]" + }, + { + "bbox": [ + 46, + 447, + 287, + 614 + ], + "type": "text", + "content": ". In this way, layouts have a uniform structured representation." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 623, + 204, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 623, + 204, + 635 + ], + "spans": [ + { + "bbox": [ + 47, + 623, + 204, + 635 + ], + "type": "text", + "content": "3.2. The LayoutDM Architecture" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "type": "text", + "content": "Fig. 1a illustrates the architecture of LayoutDM. From a high-level perspective, our LayoutDM is an instance of conditional denoising diffusion probabilistic model (DDPM) with a transformer architecture suitable for layout data. DDPM learns to model the Markov transition from simple distribution to layout data distribution and generates" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 232, + 545, + 304 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 232, + 545, + 304 + ], + "spans": [ + { + "bbox": [ + 304, + 232, + 545, + 304 + ], + "type": "text", + "content": "diverse samples through sequential stochastic transitions. To generate desired layouts, LayoutDM uses the input attributes to guide the generative process in DDPM. We follow the method described in Classifier-Free Diffusion Guidance [13] to realize conditional DDPM, and set the guidance strength " + }, + { + "bbox": [ + 304, + 232, + 545, + 304 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 304, + 232, + 545, + 304 + ], + "type": "text", + "content": " to zero for simplicity." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 304, + 545, + 400 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 304, + 545, + 400 + ], + "spans": [ + { + "bbox": [ + 304, + 304, + 545, + 400 + ], + "type": "text", + "content": "Specifically, let " + }, + { + "bbox": [ + 304, + 304, + 545, + 400 + ], + "type": "inline_equation", + "content": "q(\\pmb{g}_0|\\pmb{f})" + }, + { + "bbox": [ + 304, + 304, + 545, + 400 + ], + "type": "text", + "content": " be the unknown conditional data distribution, where " + }, + { + "bbox": [ + 304, + 304, + 545, + 400 + ], + "type": "inline_equation", + "content": "\\pmb{g}_0" + }, + { + "bbox": [ + 304, + 304, + 545, + 400 + ], + "type": "text", + "content": " is the geometric parameters of real layouts, and " + }, + { + "bbox": [ + 304, + 304, + 545, + 400 + ], + "type": "inline_equation", + "content": "\\pmb{f}" + }, + { + "bbox": [ + 304, + 304, + 545, + 400 + ], + "type": "text", + "content": " is the layout attributes. LayoutDM models the conditional distribution " + }, + { + "bbox": [ + 304, + 304, + 545, + 400 + ], + "type": "inline_equation", + "content": "q(\\pmb{g}_0|\\pmb{f})" + }, + { + "bbox": [ + 304, + 304, + 545, + 400 + ], + "type": "text", + "content": " by two processes: a forward diffusion process and a reverse denoising diffusion process. First, LayoutDM defines the forward diffusion process " + }, + { + "bbox": [ + 304, + 304, + 545, + 400 + ], + "type": "inline_equation", + "content": "q(\\pmb{g}_t|\\pmb{g}_{t-1})" + }, + { + "bbox": [ + 304, + 304, + 545, + 400 + ], + "type": "text", + "content": " which maps layout data to noise by gradually adding Gaussian noise at each time step " + }, + { + "bbox": [ + 304, + 304, + 545, + 400 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 304, + 545, + 400 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 343, + 410, + 545, + 423 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 343, + 410, + 545, + 423 + ], + "spans": [ + { + "bbox": [ + 343, + 410, + 545, + 423 + ], + "type": "interline_equation", + "content": "q \\left(\\boldsymbol {g} _ {t} \\mid \\boldsymbol {g} _ {t - 1}\\right) = \\mathcal {N} \\left(\\boldsymbol {g} _ {t}; \\sqrt {1 - \\beta_ {t}} \\boldsymbol {g} _ {t - 1}, \\beta_ {t} \\mathbf {I}\\right) \\tag {1}", + "image_path": "46a0134199b319d1054c9e78171248e10a8beebe68bc1723f4eae68283b767d0.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 433, + 492, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 433, + 492, + 445 + ], + "spans": [ + { + "bbox": [ + 305, + 433, + 492, + 445 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 433, + 492, + 445 + ], + "type": "inline_equation", + "content": "\\{\\beta_t\\}_{t=1}^T" + }, + { + "bbox": [ + 305, + 433, + 492, + 445 + ], + "type": "text", + "content": " are forward process variances." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 445, + 545, + 493 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 445, + 545, + 493 + ], + "spans": [ + { + "bbox": [ + 304, + 445, + 545, + 493 + ], + "type": "text", + "content": "Then, LayoutDM defines the conditional reverse diffusion process " + }, + { + "bbox": [ + 304, + 445, + 545, + 493 + ], + "type": "inline_equation", + "content": "p(\\pmb{g}_{t-1} | \\pmb{g}_t, \\pmb{f})" + }, + { + "bbox": [ + 304, + 445, + 545, + 493 + ], + "type": "text", + "content": " which performs iterative denoising from pure Gaussian noise to generate high-quality layouts conditioned on layout attributes " + }, + { + "bbox": [ + 304, + 445, + 545, + 493 + ], + "type": "inline_equation", + "content": "\\pmb{f}" + }, + { + "bbox": [ + 304, + 445, + 545, + 493 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 333, + 502, + 545, + 516 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 333, + 502, + 545, + 516 + ], + "spans": [ + { + "bbox": [ + 333, + 502, + 545, + 516 + ], + "type": "interline_equation", + "content": "p _ {\\theta} \\left(\\boldsymbol {g} _ {t - 1} \\mid \\boldsymbol {g} _ {t}, \\boldsymbol {f}\\right) = \\mathcal {N} \\left(\\boldsymbol {g} _ {t - 1}; \\boldsymbol {\\mu} _ {\\theta} \\left(\\boldsymbol {g} _ {t}, t, \\boldsymbol {f}\\right), \\sigma_ {t} ^ {2} \\mathbf {I}\\right) \\tag {2}", + "image_path": "e786d77dbcadb9b150ed37d9dd21f57d803bc84203f7f9567f18385666aa6da5.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 525, + 545, + 597 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 525, + 545, + 597 + ], + "spans": [ + { + "bbox": [ + 304, + 525, + 545, + 597 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 525, + 545, + 597 + ], + "type": "inline_equation", + "content": "\\sigma_{t}" + }, + { + "bbox": [ + 304, + 525, + 545, + 597 + ], + "type": "text", + "content": " is the constant variance following [14], " + }, + { + "bbox": [ + 304, + 525, + 545, + 597 + ], + "type": "inline_equation", + "content": "\\mu_{\\theta}" + }, + { + "bbox": [ + 304, + 525, + 545, + 597 + ], + "type": "text", + "content": " is the mean of the Gaussian distribution computed by a neural network, and " + }, + { + "bbox": [ + 304, + 525, + 545, + 597 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 525, + 545, + 597 + ], + "type": "text", + "content": " is the parameters of the network. As shown in Ho et al. [14], we can reparameterize the mean to make the neural network learn the added noise at time step " + }, + { + "bbox": [ + 304, + 525, + 545, + 597 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 525, + 545, + 597 + ], + "type": "text", + "content": " instead. In this way, " + }, + { + "bbox": [ + 304, + 525, + 545, + 597 + ], + "type": "inline_equation", + "content": "\\mu_{\\theta}" + }, + { + "bbox": [ + 304, + 525, + 545, + 597 + ], + "type": "text", + "content": " can be reparameterized as follows:" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 321, + 605, + 545, + 632 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 605, + 545, + 632 + ], + "spans": [ + { + "bbox": [ + 321, + 605, + 545, + 632 + ], + "type": "interline_equation", + "content": "\\boldsymbol {\\mu} _ {\\theta} \\left(\\boldsymbol {g} _ {t}, t, \\boldsymbol {f}\\right) = \\frac {1}{\\sqrt {\\alpha_ {t}}} \\left(\\boldsymbol {g} _ {t} - \\frac {\\beta_ {t}}{\\sqrt {1 - \\bar {\\alpha} _ {t}}} \\boldsymbol {\\epsilon} _ {\\theta} \\left(\\boldsymbol {g} _ {t}, t, \\boldsymbol {f}\\right)\\right) \\tag {3}", + "image_path": "7e3e132e2b9b4e165227cf9738f4686f87b83e051b8e2e000023e97d5b785c40.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "content": " is the time step, " + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\{\\beta_t\\}_{t=1}^T" + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "content": " are forward process variances, " + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\alpha_t = 1 - \\beta_t" + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\overline{\\alpha}_t = \\prod_{s=1}^t \\alpha_s" + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\epsilon_\\theta(\\pmb{g}_t, t, \\pmb{f})" + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "content": " is the neural network to predict the added noise for layout geometric parameters conditioned on elements' attributes at time step " + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "content": ". We also call the neural network " + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\epsilon_\\theta(\\pmb{g}_t, t, \\pmb{f})" + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "content": " as conditional layout denoiser (cLayoutDenoiser)." + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18351" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 205, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 205, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 205, + 85 + ], + "type": "text", + "content": "3.3. Conditional Layout Denoiser" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 90, + 289, + 245 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 90, + 289, + 245 + ], + "spans": [ + { + "bbox": [ + 46, + 90, + 289, + 245 + ], + "type": "text", + "content": "The inputs to cLayoutDenoiser are layout geometric parameters " + }, + { + "bbox": [ + 46, + 90, + 289, + 245 + ], + "type": "inline_equation", + "content": "\\pmb{g}_t" + }, + { + "bbox": [ + 46, + 90, + 289, + 245 + ], + "type": "text", + "content": ", layout attributes " + }, + { + "bbox": [ + 46, + 90, + 289, + 245 + ], + "type": "inline_equation", + "content": "\\pmb{f}" + }, + { + "bbox": [ + 46, + 90, + 289, + 245 + ], + "type": "text", + "content": " and time step " + }, + { + "bbox": [ + 46, + 90, + 289, + 245 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 90, + 289, + 245 + ], + "type": "text", + "content": ". To deal with sequences data, the conditional layout denoiser " + }, + { + "bbox": [ + 46, + 90, + 289, + 245 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(\\pmb{g}_t, t, \\pmb{f})" + }, + { + "bbox": [ + 46, + 90, + 289, + 245 + ], + "type": "text", + "content": " employs a purely transformer-based architecture instead of convolutional neural networks as its backbone. The architecture of cLayoutDenoiser is illustrated in Fig. 1b. Benefiting from the transformer architecture, cLayoutDenoiser can deal with the sequence with various lengths, and capture the relationships among elements. Moreover, cLayoutDenoiser adds \"attributes embeddings\" to the input \"geometric embeddings\", so as to guide the reverse diffusion process at each time step " + }, + { + "bbox": [ + 46, + 90, + 289, + 245 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 90, + 289, + 245 + ], + "type": "text", + "content": ". Formally, the architecture of cLayoutDenoiser can be described as follow:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 77, + 252, + 287, + 265 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 252, + 287, + 265 + ], + "spans": [ + { + "bbox": [ + 77, + 252, + 287, + 265 + ], + "type": "interline_equation", + "content": "\\boldsymbol {h} _ {f} = \\text {A t t r i b u t e s E m b e d d i n g} (\\boldsymbol {f}) \\tag {4}", + "image_path": "a4671e6f11e6aa6fe774d3d1e4a39f1304c914be07033d273f1f7f90d5fc3165.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 78, + 267, + 287, + 280 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 78, + 267, + 287, + 280 + ], + "spans": [ + { + "bbox": [ + 78, + 267, + 287, + 280 + ], + "type": "interline_equation", + "content": "\\boldsymbol {h} _ {g} = \\text {G e o m e t r i c E m b e d d i n g} (\\boldsymbol {g} _ {t}) \\tag {5}", + "image_path": "3482190421173ded13bc89b1f5442f47854d6abc67e92a740aade62f7724d582.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 82, + 282, + 287, + 295 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 82, + 282, + 287, + 295 + ], + "spans": [ + { + "bbox": [ + 82, + 282, + 287, + 295 + ], + "type": "interline_equation", + "content": "\\mathbf {E} = \\text {E l e m e n t E m b e d d i n g} \\left(\\boldsymbol {h} _ {f}, \\boldsymbol {h} _ {g}, \\mathrm {T E} (t)\\right) \\tag {6}", + "image_path": "1b0692c1a94a4aa9160775d5ebe9315f28d5bb493be5712d6873e7d63f9608d3.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 80, + 297, + 287, + 309 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 80, + 297, + 287, + 309 + ], + "spans": [ + { + "bbox": [ + 80, + 297, + 287, + 309 + ], + "type": "interline_equation", + "content": "\\mathbf {E} ^ {\\prime} = \\operatorname {T r a n s f o r m e r L a y e r s} (\\mathbf {E}) \\tag {7}", + "image_path": "bbb0cf24bd0dd7bf0eebb27351152d4f0810f138827f6fc042278ecaabb13ed3.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 85, + 312, + 287, + 324 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 312, + 287, + 324 + ], + "spans": [ + { + "bbox": [ + 85, + 312, + 287, + 324 + ], + "type": "interline_equation", + "content": "\\boldsymbol {\\epsilon} = \\operatorname {F C} \\left(\\mathbf {E} ^ {\\prime}\\right) \\tag {8}", + "image_path": "59a9ee9e1d3b3aff57d0c9d752d007961305daf2273d19cb11aeb700f944f8b6.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 331, + 287, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 331, + 287, + 437 + ], + "spans": [ + { + "bbox": [ + 46, + 331, + 287, + 437 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 331, + 287, + 437 + ], + "type": "inline_equation", + "content": "\\pmb{f}" + }, + { + "bbox": [ + 46, + 331, + 287, + 437 + ], + "type": "text", + "content": " is the layout attributes, " + }, + { + "bbox": [ + 46, + 331, + 287, + 437 + ], + "type": "inline_equation", + "content": "\\pmb{g}_t" + }, + { + "bbox": [ + 46, + 331, + 287, + 437 + ], + "type": "text", + "content": " is the noised layout geometric parameters, " + }, + { + "bbox": [ + 46, + 331, + 287, + 437 + ], + "type": "inline_equation", + "content": "\\pmb{h}_f" + }, + { + "bbox": [ + 46, + 331, + 287, + 437 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 331, + 287, + 437 + ], + "type": "inline_equation", + "content": "\\pmb{h}_g" + }, + { + "bbox": [ + 46, + 331, + 287, + 437 + ], + "type": "text", + "content": " are their hidden representations. " + }, + { + "bbox": [ + 46, + 331, + 287, + 437 + ], + "type": "inline_equation", + "content": "\\mathbf{E}" + }, + { + "bbox": [ + 46, + 331, + 287, + 437 + ], + "type": "text", + "content": " is the element tokens computed by element embedding module, " + }, + { + "bbox": [ + 46, + 331, + 287, + 437 + ], + "type": "inline_equation", + "content": "\\mathbf{E}'" + }, + { + "bbox": [ + 46, + 331, + 287, + 437 + ], + "type": "text", + "content": " is intermediate feature. " + }, + { + "bbox": [ + 46, + 331, + 287, + 437 + ], + "type": "inline_equation", + "content": "\\mathrm{TE}(t)" + }, + { + "bbox": [ + 46, + 331, + 287, + 437 + ], + "type": "text", + "content": " denotes the timestep embedding, and " + }, + { + "bbox": [ + 46, + 331, + 287, + 437 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 46, + 331, + 287, + 437 + ], + "type": "text", + "content": " is the predicted noise. Note here that, since the element order in the sequence makes no sense in our setting, cLayoutDenoiser omits the positional encoding, which is different from existing transformers in the context of NLP or video." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 438, + 287, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 438, + 287, + 581 + ], + "spans": [ + { + "bbox": [ + 46, + 438, + 287, + 581 + ], + "type": "text", + "content": "Geometric, attributes and timestep embedding. Three embedding modules are used to learn meaningful representations for noised layout geometric parameters " + }, + { + "bbox": [ + 46, + 438, + 287, + 581 + ], + "type": "inline_equation", + "content": "g_{t}" + }, + { + "bbox": [ + 46, + 438, + 287, + 581 + ], + "type": "text", + "content": ", layout attributes " + }, + { + "bbox": [ + 46, + 438, + 287, + 581 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 438, + 287, + 581 + ], + "type": "text", + "content": " and time step " + }, + { + "bbox": [ + 46, + 438, + 287, + 581 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 438, + 287, + 581 + ], + "type": "text", + "content": ". Geometric embedding projects layout geometric parameters to a specific dimension, aiming to find a more efficient feature space than the original coordinate space. Feature embedding learns the continuous features of discrete element attributes by embedding them into a specific dimension. Following [14], we condition cLayoutTransformer on time step " + }, + { + "bbox": [ + 46, + 438, + 287, + 581 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 438, + 287, + 581 + ], + "type": "text", + "content": " by adding a sinusoidal time embedding " + }, + { + "bbox": [ + 46, + 438, + 287, + 581 + ], + "type": "inline_equation", + "content": "\\mathrm{TE}(t)" + }, + { + "bbox": [ + 46, + 438, + 287, + 581 + ], + "type": "text", + "content": " to make the network aware at which time step it is operating." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "text", + "content": "Element embedding. Element embedding module calculates the element tokens used as the input of transformer layers. Element tokens should contain geometric, attributes and time step information, so that transformer can efficiently capture the relationship information between elements conditioned on the time step " + }, + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "text", + "content": " and layout attributes " + }, + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "text", + "content": ". We concatenate the geometric embedding and attributes embedding, and then use a fully-connected layer to fuse element representation. We further perform an element-wise plus operation with timestep embedding on the results to finally obtain the element tokens." + } + ] + } + ], + "index": 9 + }, + { + "type": "code", + "bbox": [ + 316, + 88, + 482, + 200 + ], + "blocks": [ + { + "bbox": [ + 312, + 75, + 454, + 87 + ], + "lines": [ + { + "bbox": [ + 312, + 75, + 454, + 87 + ], + "spans": [ + { + "bbox": [ + 312, + 75, + 454, + 87 + ], + "type": "text", + "content": "Algorithm 1: Training LayoutDM" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 316, + 88, + 482, + 200 + ], + "lines": [ + { + "bbox": [ + 316, + 88, + 482, + 200 + ], + "spans": [ + { + "bbox": [ + 316, + 88, + 482, + 200 + ], + "type": "text", + "content": "Require: conditional layout denoiser " + }, + { + "bbox": [ + 316, + 88, + 482, + 200 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 316, + 88, + 482, + 200 + ], + "type": "text", + "content": " repeat Sample " + }, + { + "bbox": [ + 316, + 88, + 482, + 200 + ], + "type": "inline_equation", + "content": "(g_0,f)\\sim q_{data};" + }, + { + "bbox": [ + 316, + 88, + 482, + 200 + ], + "type": "inline_equation", + "content": "t\\sim" + }, + { + "bbox": [ + 316, + 88, + 482, + 200 + ], + "type": "text", + "content": " Uniform( " + }, + { + "bbox": [ + 316, + 88, + 482, + 200 + ], + "type": "inline_equation", + "content": "\\{1,\\dots ,T\\}" + }, + { + "bbox": [ + 316, + 88, + 482, + 200 + ], + "type": "text", + "content": " . " + }, + { + "bbox": [ + 316, + 88, + 482, + 200 + ], + "type": "inline_equation", + "content": "\\epsilon \\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I})" + }, + { + "bbox": [ + 316, + 88, + 482, + 200 + ], + "type": "text", + "content": " .. " + }, + { + "bbox": [ + 316, + 88, + 482, + 200 + ], + "type": "inline_equation", + "content": "\\pmb {g}_t = \\sqrt{\\alpha}_t\\pmb {g}_0 + \\sqrt{1 - \\overline{\\alpha}_t}\\pmb {\\epsilon};" + }, + { + "bbox": [ + 316, + 88, + 482, + 200 + ], + "type": "text", + "content": " Take gradient descent step on " + }, + { + "bbox": [ + 316, + 88, + 482, + 200 + ], + "type": "inline_equation", + "content": "\\nabla_{\\theta}\\| \\boldsymbol {\\epsilon} - \\boldsymbol{\\epsilon}_{\\theta}(\\pmb {g}_t,t,\\pmb {f})\\| ^2;" + }, + { + "bbox": [ + 316, + 88, + 482, + 200 + ], + "type": "text", + "content": " \nuntil converged;" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "code_body" + } + ], + "index": 11, + "sub_type": "algorithm" + }, + { + "type": "code", + "bbox": [ + 316, + 227, + 515, + 329 + ], + "blocks": [ + { + "bbox": [ + 312, + 213, + 411, + 225 + ], + "lines": [ + { + "bbox": [ + 312, + 213, + 411, + 225 + ], + "spans": [ + { + "bbox": [ + 312, + 213, + 411, + 225 + ], + "type": "text", + "content": "Algorithm 2: Sampling" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 316, + 227, + 515, + 329 + ], + "lines": [ + { + "bbox": [ + 316, + 227, + 515, + 329 + ], + "spans": [ + { + "bbox": [ + 316, + 227, + 515, + 329 + ], + "type": "text", + "content": "Input: layout attributes " + }, + { + "bbox": [ + 316, + 227, + 515, + 329 + ], + "type": "inline_equation", + "content": "\\pmb{f}" + }, + { + "bbox": [ + 316, + 227, + 515, + 329 + ], + "type": "text", + "content": " \nOutput: layout geometric parameters " + }, + { + "bbox": [ + 316, + 227, + 515, + 329 + ], + "type": "inline_equation", + "content": "\\pmb{g_0}" + }, + { + "bbox": [ + 316, + 227, + 515, + 329 + ], + "type": "inline_equation", + "content": "g_{T}\\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I})" + }, + { + "bbox": [ + 316, + 227, + 515, + 329 + ], + "type": "text", + "content": " \nfor " + }, + { + "bbox": [ + 316, + 227, + 515, + 329 + ], + "type": "inline_equation", + "content": "t = T,\\dots ,1" + }, + { + "bbox": [ + 316, + 227, + 515, + 329 + ], + "type": "text", + "content": " do " + }, + { + "bbox": [ + 316, + 227, + 515, + 329 + ], + "type": "inline_equation", + "content": "\\mathbf{z}\\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I})" + }, + { + "bbox": [ + 316, + 227, + 515, + 329 + ], + "type": "text", + "content": " if " + }, + { + "bbox": [ + 316, + 227, + 515, + 329 + ], + "type": "inline_equation", + "content": "t > 1" + }, + { + "bbox": [ + 316, + 227, + 515, + 329 + ], + "type": "text", + "content": " , else " + }, + { + "bbox": [ + 316, + 227, + 515, + 329 + ], + "type": "inline_equation", + "content": "\\mathbf{z} = \\mathbf{0}" + }, + { + "bbox": [ + 316, + 227, + 515, + 329 + ], + "type": "text", + "content": " . " + }, + { + "bbox": [ + 316, + 227, + 515, + 329 + ], + "type": "inline_equation", + "content": "g_{t - 1} = \\frac{1}{\\sqrt{\\alpha_t}} (g_t - \\frac{1 - \\alpha_t}{\\sqrt{1 - \\overline{\\alpha}_t}}\\epsilon_\\theta (g_t,t,\\pmb {f})) + \\sigma_t\\mathbf{z}" + }, + { + "bbox": [ + 316, + 227, + 515, + 329 + ], + "type": "text", + "content": " \nend \nreturn " + }, + { + "bbox": [ + 316, + 227, + 515, + 329 + ], + "type": "inline_equation", + "content": "\\pmb{g_0}" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "code_body" + } + ], + "index": 13, + "sub_type": "algorithm" + }, + { + "bbox": [ + 304, + 339, + 545, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 339, + 545, + 483 + ], + "spans": [ + { + "bbox": [ + 304, + 339, + 545, + 483 + ], + "type": "text", + "content": "Transformer layers. Generating an effective layout requires understanding the relationships between layout elements. Self-attention mechanism in Transformer [43] has proven effective in capturing high-level relationships between lots of elements in layout generation [1, 11, 15]. In this paper, we adopt multihead attention mechanism to capture relationship information between elements from element tokens. We stack multiple transformer layers (8 in our model) to enable cLayoutDenoiser to capture relationships between layout elements from the element tokens. Positional encoding is omitted because of the unordered nature of elements." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 317, + 487, + 545, + 502 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 487, + 545, + 502 + ], + "spans": [ + { + "bbox": [ + 317, + 487, + 545, + 502 + ], + "type": "interline_equation", + "content": "\\hat {\\mathbf {E}} = \\operatorname {L a y e r N o r m} \\left(\\mathbf {E} ^ {l - 1} + \\mathbf {H e a d} \\left(e _ {1} ^ {l - 1}, \\dots , e _ {N} ^ {l - 1}\\right)\\right) \\tag {9}", + "image_path": "99eb10a62e3284920222e8a23bd7c54c09c134279af7e680c7fa41eadb07563f.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 315, + 504, + 545, + 519 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 504, + 545, + 519 + ], + "spans": [ + { + "bbox": [ + 315, + 504, + 545, + 519 + ], + "type": "interline_equation", + "content": "\\mathbf {E} ^ {l} = \\operatorname {L a y e r N o r m} (\\hat {\\mathbf {E}} + \\operatorname {F F N} (\\hat {\\mathbf {E}})) \\tag {10}", + "image_path": "c074196bbc7bbe35a9fed93e57bd36906fc93931036f04a820367bd61504c2d1.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 523, + 545, + 584 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 523, + 545, + 584 + ], + "spans": [ + { + "bbox": [ + 304, + 523, + 545, + 584 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 523, + 545, + 584 + ], + "type": "inline_equation", + "content": "l = 1, \\dots, L" + }, + { + "bbox": [ + 304, + 523, + 545, + 584 + ], + "type": "text", + "content": " denotes the layer index, Head, LayoutNorm and FFN denote multi-head attention layer, Layer Normalization [3] and fully connected feed-forward network. " + }, + { + "bbox": [ + 304, + 523, + 545, + 584 + ], + "type": "inline_equation", + "content": "\\mathbf{E}^{l-1} = (\\pmb{e}_1^{l-1}, \\dots, \\pmb{e}_N^{l-1})" + }, + { + "bbox": [ + 304, + 523, + 545, + 584 + ], + "type": "text", + "content": " are the intermediate element tokens used as the input of " + }, + { + "bbox": [ + 304, + 523, + 545, + 584 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 304, + 523, + 545, + 584 + ], + "type": "text", + "content": "-th transformer layer." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 590, + 437, + 602 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 590, + 437, + 602 + ], + "spans": [ + { + "bbox": [ + 306, + 590, + 437, + 602 + ], + "type": "text", + "content": "3.4. Training and Inference" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 608, + 545, + 668 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 608, + 545, + 668 + ], + "spans": [ + { + "bbox": [ + 304, + 608, + 545, + 668 + ], + "type": "text", + "content": "Following denoising diffusion probabilistic model [14], we optimize random terms " + }, + { + "bbox": [ + 304, + 608, + 545, + 668 + ], + "type": "inline_equation", + "content": "L_{t}" + }, + { + "bbox": [ + 304, + 608, + 545, + 668 + ], + "type": "text", + "content": " which are the KL divergences between " + }, + { + "bbox": [ + 304, + 608, + 545, + 668 + ], + "type": "inline_equation", + "content": "p_{\\theta}(\\pmb{g}_{t-1}|\\pmb{g}_t, \\pmb{f})" + }, + { + "bbox": [ + 304, + 608, + 545, + 668 + ], + "type": "text", + "content": " and forward process posteriors. After simplifying the objective function following the method in [14], the final loss function is as follows:" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 317, + 671, + 545, + 713 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 671, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 317, + 671, + 545, + 713 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} L _ {s i m p l e} (\\theta) = \\left\\| \\boldsymbol {\\epsilon} - \\boldsymbol {\\epsilon} _ {\\theta} \\left(\\boldsymbol {g} _ {t}, t, \\boldsymbol {f}\\right) \\right\\| ^ {2} \\\\ = \\| \\boldsymbol {\\epsilon} - \\boldsymbol {\\epsilon} _ {\\theta} \\left(\\sqrt {\\bar {\\alpha} _ {t}} \\boldsymbol {g} _ {0} + \\sqrt {\\left(1 - \\bar {\\alpha} _ {t}\\right)} \\boldsymbol {\\epsilon}, t, \\boldsymbol {f}\\right) \\| ^ {2} \\tag {11} \\\\ \\end{array}", + "image_path": "37057049eab07325f762c6fce8d60e0bc9cc77d9e6c462c0450fba4736344ad3.jpg" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18352" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 286, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 286, + 133 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 286, + 133 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 72, + 286, + 133 + ], + "type": "inline_equation", + "content": "\\epsilon \\sim \\mathcal{N}(\\mathbf{0},\\mathbf{I})" + }, + { + "bbox": [ + 47, + 72, + 286, + 133 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 47, + 72, + 286, + 133 + ], + "type": "text", + "content": " is our conditional layout denoiser, " + }, + { + "bbox": [ + 47, + 72, + 286, + 133 + ], + "type": "inline_equation", + "content": "g_{t}\\sim \\mathcal{N}(g_{t};\\sqrt{\\overline{\\alpha}_{t}} g_{0},(1 - \\overline{\\alpha}_{t})\\mathbf{I})" + }, + { + "bbox": [ + 47, + 72, + 286, + 133 + ], + "type": "text", + "content": " is computed using the property of Gaussian distributions and " + }, + { + "bbox": [ + 47, + 72, + 286, + 133 + ], + "type": "inline_equation", + "content": "\\pmb {g}_0" + }, + { + "bbox": [ + 47, + 72, + 286, + 133 + ], + "type": "text", + "content": " is the real layout geometric parameters. " + }, + { + "bbox": [ + 47, + 72, + 286, + 133 + ], + "type": "inline_equation", + "content": "\\{\\beta_t\\}_{t = 1}^T" + }, + { + "bbox": [ + 47, + 72, + 286, + 133 + ], + "type": "text", + "content": " are forward process variances, " + }, + { + "bbox": [ + 47, + 72, + 286, + 133 + ], + "type": "inline_equation", + "content": "\\alpha_{t} = 1 - \\beta_{t}" + }, + { + "bbox": [ + 47, + 72, + 286, + 133 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 72, + 286, + 133 + ], + "type": "inline_equation", + "content": "\\overline{\\alpha}_t = \\prod_{s = 1}^t\\alpha_s" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 134, + 286, + 159 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 134, + 286, + 159 + ], + "spans": [ + { + "bbox": [ + 47, + 134, + 286, + 159 + ], + "type": "text", + "content": "The training and sampling algorithm of LayoutDM are illustrated in Algorithm 1 and Algorithm 2 respectively." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 176, + 127, + 189 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 176, + 127, + 189 + ], + "spans": [ + { + "bbox": [ + 47, + 176, + 127, + 189 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 198, + 173, + 211 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 198, + 173, + 211 + ], + "spans": [ + { + "bbox": [ + 47, + 198, + 173, + 211 + ], + "type": "text", + "content": "4.1. Experimental Settings" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 219, + 286, + 408 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 219, + 286, + 408 + ], + "spans": [ + { + "bbox": [ + 46, + 219, + 286, + 408 + ], + "type": "text", + "content": "Datasets. We evaluate our method on five public datasets of layouts for documents, natural scenes, magazines, text logos and mobile phone UIs. Rico [7] is a dataset of user interface designs for mobile applications, containing 72,219 user interfaces from 9,772 Android apps. PublayNet [47] contains 330K samples of machine-annotated scientific documents crawled from the Internet with five categories (text, title, figure, list, table). Magazine [46] is a magazine layout dataset that covers a wide range of magazine categories. It consists of semantic layout annotations. COCO [26] is a large-scale labeled image dataset that contains images of natural scenes with instance segmentation. TextLogo3K [44] is a recently released dataset of text logos. It consists of 3,470 text logo images with manually annotated bounding boxes and pixel-level masks for each character." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 412, + 286, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 412, + 286, + 592 + ], + "spans": [ + { + "bbox": [ + 46, + 412, + 286, + 592 + ], + "type": "text", + "content": "Evaluation metrics. To validate the effectiveness of LayoutDM, we employ four metrics in the literature to measure the perceptual quality of layouts. To be a fair comparison, we follow the guidance in [18] to evaluate these metrics. Specifically, FID [12] measures the distribution distance between real layouts and generated layouts. We use the pre-trained classifiers in [18] to compute FID. Max IoU [18] measures the similarity between the generated layouts and the reference layouts. It is designed to find the best match for each layout from the generated set to the reference set. Overlap and Alignment measure the perceptual quality of generated layouts. Overlap measures the total overlapping area between any pair of bounding boxes inside the layout. Additionally, we measure the Alignment by computing an alignment loss proposed in [25]." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 594, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 286, + 713 + ], + "type": "text", + "content": "Implementing details. The max time step " + }, + { + "bbox": [ + 46, + 594, + 286, + 713 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 594, + 286, + 713 + ], + "type": "text", + "content": " in LayoutDM is set to 1000. We set the forward process variances to constants increasing linearly from " + }, + { + "bbox": [ + 46, + 594, + 286, + 713 + ], + "type": "inline_equation", + "content": "\\beta_{1} = 10^{-4}" + }, + { + "bbox": [ + 46, + 594, + 286, + 713 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 594, + 286, + 713 + ], + "type": "inline_equation", + "content": "\\beta_{T} = 0.02" + }, + { + "bbox": [ + 46, + 594, + 286, + 713 + ], + "type": "text", + "content": " following Ho's design [14]. We use eight transformer layers which use 8-head attention in our model. Adam optimizer [19] with a learning rate of " + }, + { + "bbox": [ + 46, + 594, + 286, + 713 + ], + "type": "inline_equation", + "content": "1 \\times 10^{-5}" + }, + { + "bbox": [ + 46, + 594, + 286, + 713 + ], + "type": "text", + "content": " is used to optimize learnable parameters. The batch size is set to 1024. We implement our model with PyTorch [32] and PyTorch Lightning. All experiments are performed on a single NVIDIA Quadro RTX 6000 GPU device." + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 307, + 72, + 545, + 348 + ], + "blocks": [ + { + "bbox": [ + 307, + 72, + 545, + 348 + ], + "lines": [ + { + "bbox": [ + 307, + 72, + 545, + 348 + ], + "spans": [ + { + "bbox": [ + 307, + 72, + 545, + 348 + ], + "type": "table", + "html": "
Dataset\nModelRico
FID↓Max. IoU↑Alignment↓Overlap↓
LayoutGAN-W [24]162.75±0.280.30±0.000.71±0.00174.11±0.22
LayoutGAN-R [24]52.01±0.620.24±0.001.13±0.0469.37±0.66
NDN-none [23]13.76±0.280.35±0.000.56±0.0354.75±0.29
LayoutGAN++ [18]14.43±0.130.36±0.000.60±0.1259.85±0.59
VTN [1]9.31±0.210.36±0.000.88±0.1159.31±0.45
LayoutDM(Ours)3.03±0.060.49±0.000.36±0.0657.55±0.48
Real data4.470.650.2650.58
Dataset\nModelPublayNet
FID↓Max. IoU↑Alignment↓Overlap↓
LayoutGAN-W [24]195.38±0.460.21±0.001.21±0.01138.77±0.21
LayoutGAN-R [24]100.24±0.610.24±0.000.82±0.0145.64±0.32
NDN-none [23]35.67±0.350.31±0.000.35±0.0116.5±0.29
LayoutGAN++ [18]20.48±0.290.36±0.000.19±0.0022.80±0.32
VTN [1]13.07±0.470.37±0.000.30±0.0113.15±0.24
LayoutDM(Ours)4.04±0.080.44±0.000.15±0.003.73±0.08
Real data9.540.530.040.22
Dataset\nModelMagazine
FID↓Max. IoU↑Alignment↓Overlap↓
LayoutGAN-W [24]159.2±0.870.12±0.000.74±0.02188.77±0.93
LayoutGAN-R [24]100.66±0.350.16±0.001.90±0.02111.85±1.44
NDN-none [23]23.27±0.090.22±0.001.05±0.0330.31±0.77
LayoutGAN++ [18]13.35±0.410.26±0.000.80±0.0232.40±0.89
VTN [1]12.34±0.390.25±0.001.07±0.0339.97±0.62
LayoutDM(Ours)9.11±0.150.29±0.000.77±0.0332.53±0.72
Real data12.130.350.4325.64
", + "image_path": "ef2736e0b31429164c5d62b23f71f5d35bd197e512a12776bc48f81f5dd7cb61.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 356, + 545, + 422 + ], + "lines": [ + { + "bbox": [ + 305, + 356, + 545, + 422 + ], + "spans": [ + { + "bbox": [ + 305, + 356, + 545, + 422 + ], + "type": "text", + "content": "Table 1. Quantitative comparison conditioned on element category labels. For reference, the FID and Max. IoU computed between the validation and test data, and the Alignment and Overlap computed with the test data are shown as real data. LayoutGAN-W and LayoutGAN-R denote LayoutGAN with wireframe rendering discriminator and with relation-based discriminator." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 306, + 430, + 440, + 442 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 430, + 440, + 442 + ], + "spans": [ + { + "bbox": [ + 306, + 430, + 440, + 442 + ], + "type": "text", + "content": "4.2.Quantitative Evaluation" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 449, + 545, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 449, + 545, + 605 + ], + "spans": [ + { + "bbox": [ + 304, + 449, + 545, + 605 + ], + "type": "text", + "content": "Comparison with state-of-the-art models. We quantitatively evaluate the quality of conditional layout generation results on benchmark datasets: Rico, PublayNet and Magazine. Since most methods are designed for unconditional layout generation and have no available public implements, we compare our method with conditional LayoutGAN [24], NDN-none [23] and LayoutGAN++ [18] by citing the results in [18]. Moreover, we also implement a conditional VTN [1] as our comparison baseline model, so that we can compare with methods based on both VAEs and GANs. All the metrics are computed on the full test splits of the datasets. We report the mean and standard deviation over five independent evaluations for each experiment." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": "The comparison results are reported in Tab. 1. From this table, we can observe that: (1) Our method outperforms SOTA methods on both FID and Max. IoU on all three benchmark datasets, which indicates that the generated layouts by our method are more similar to the real layouts than those by SOTA methods. This verifies that our LayoutDM can produce higher-quality and more diverse layouts than SOTA methods, since FID captures both diversity and fidelity. (2) Layouts generated by our method have a lower" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18353" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 54, + 70, + 279, + 149 + ], + "blocks": [ + { + "bbox": [ + 54, + 70, + 279, + 149 + ], + "lines": [ + { + "bbox": [ + 54, + 70, + 279, + 149 + ], + "spans": [ + { + "bbox": [ + 54, + 70, + 279, + 149 + ], + "type": "table", + "html": "
IoU↓ [21]Overlap↓ [24]Alignment↓ [23]
L-VAE [17]0.45±1.3%0.15±0.9%0.37±0.7%
NDN [23]0.34±1.8%0.12±0.8%0.39±0.4%
VTN [1]0.21±0.6%0.06±0.2%0.33±0.4%
Trans. [11]0.19±0.3%0.06±0.3%0.33±0.3%
BLT [21]0.19±0.2%0.04±0.1%0.25±0.7%
Ours0.0053±0.5%0.01±0.1%0.22±1.2%
", + "image_path": "50ac107518455ced580118dbe2f1e63bf72e26fad5316a1932004749f3d0eff1.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 200, + 286, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 200, + 286, + 342 + ], + "spans": [ + { + "bbox": [ + 48, + 200, + 286, + 342 + ], + "type": "text", + "content": "FID score than the real ones in validation splits. This is because the generated layouts have identical attributes to those in the test split, while the real layouts in the validation split have different attributes from those in the test split. We provide more analysis on this point in the supplementary material. (3) With regards to Alignment and Overlap, LayoutDM is slightly weaker on Rico and Magazine. Because our method lacks a discriminator that guides the generator to generate layouts with better alignment and overlap properties as in GANs and does not introduce the layout refine module in NDN. This is likely to cause LayoutDM to be inferior to the state-of-the-art on these two metrics." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 48, + 355, + 286, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 355, + 286, + 533 + ], + "spans": [ + { + "bbox": [ + 48, + 355, + 286, + 533 + ], + "type": "text", + "content": "Note here that, we don't compare LayoutDM to other state-of-the-art methods such as LayoutTransformer [11] and Coarse2fine [16], because these methods focus on unconditional layout generation problem which is different to our setting. Recently, Kong et al. [21] reimplement the conditional version of VTN and LayoutTransformer, and compare their proposed BLT model with these models under the settings of conditional layout generation. However, they compute the metrics (IoU [21], Alignment [23], Overlap [24]) in different ways. As an extended comparison, we adopt the metrics used by BLT [21], and compare our LayoutDM with VTN, LayoutTransformer, LayoutVAE, NDN and BLT on PublayNet. The comparison results are reported in Tab. 2. As shown in this table, our model also outperforms SOTA methods on all metrics." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 48, + 546, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 546, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 48, + 546, + 286, + 712 + ], + "type": "text", + "content": "Effect of transformer layers. We conduct ablation experiments to demonstrate the effectiveness of the transformer layers in LayoutDM. Quantitative results are reported in Tab. 3 and qualitative comparisons are shown in Fig. 3. We have the following observation: After replacing the transformer structure in LayoutDM with a sequence of FC layers, the model can still predict a suitable size for each element, but the positional relationships between elements can not be handled, resulting in significant overlapping and misalignment. This proves that the transformer layers play an essential role and can efficiently capture and utilize the high-level relationships between elements to generate high-quality layouts which follow design rules and aesthetic principles." + } + ] + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 309, + 71, + 542, + 169 + ], + "blocks": [ + { + "bbox": [ + 48, + 159, + 286, + 190 + ], + "lines": [ + { + "bbox": [ + 48, + 159, + 286, + 190 + ], + "spans": [ + { + "bbox": [ + 48, + 159, + 286, + 190 + ], + "type": "text", + "content": "Table 2. Comparison with extended methods on PublayNet. Qualitative results are cited from [21]. \"Trans.\" denotes \"LayoutTransformer\" and \"L-VAE\" denotes \"LayoutVAE\"." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 309, + 71, + 542, + 169 + ], + "lines": [ + { + "bbox": [ + 309, + 71, + 542, + 169 + ], + "spans": [ + { + "bbox": [ + 309, + 71, + 542, + 169 + ], + "type": "table", + "html": "
ArchitectureRico
FID↓Max.IoU↑Alignment↓Overlap↓
w/o transformer52.640.291.0858.13
Full model3.030.490.3657.55
ArchitecturePublayNet
FID↓Max.IoU↑Alignment↓Overlap↓
w/o transformer99.600.270.8963.87
Full model4.040.440.153.73
", + "image_path": "1eaafdfa10a672b53d7970a273fd13ef7d44a8f800485c041e2dbf2c59b8c0ee.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 308, + 179, + 544, + 211 + ], + "lines": [ + { + "bbox": [ + 308, + 179, + 544, + 211 + ], + "spans": [ + { + "bbox": [ + 308, + 179, + 544, + 211 + ], + "type": "text", + "content": "Table 3. The quantitative results of ablations on transformer layers. \"Full\" denotes our full model. \"w/o transformer\" denotes model without transformer layers." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 308, + 220, + 444, + 232 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 220, + 444, + 232 + ], + "spans": [ + { + "bbox": [ + 308, + 220, + 444, + 232 + ], + "type": "text", + "content": "4.3. Qualitative Comparisons" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 308, + 245, + 544, + 364 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 245, + 544, + 364 + ], + "spans": [ + { + "bbox": [ + 308, + 245, + 544, + 364 + ], + "type": "text", + "content": "Generation quality comparison. To qualitatively compare the generation performance of different models, we compare with the state-of-the-art method LayoutGAN++ and our implemented conditional VTN. We randomly sample layouts from the test dataset and use the element category labels as conditional inputs. Fig. 2 shows the qualitative comparison results. As one can see, LayoutDM can arrange elements in a reasonable and complicated way, generating higher quality layouts than the other two, with fewer overlapping and better alignment." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 308, + 371, + 544, + 562 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 371, + 544, + 562 + ], + "spans": [ + { + "bbox": [ + 308, + 371, + 544, + 562 + ], + "type": "text", + "content": "Generation diversity comparison. The diversity of results is also an important factor in evaluating the method. We compare the diversity of layouts generated by conditional VTN, LayoutGAN++, and LayoutDM. Fig. 4 show the comparison results. One can see that conditional VTN and LayoutDM generate more diverse results. The Figure element in the results floats on the page. Compared to the other two models, LayoutGAN++ captures less diversity, which places a large Figure element on the top of the pages in columns 2,4, and 5. LayoutDM performs well in diversity because it breaks the generation into a series of conditional diffusion steps which are relatively easy to model. This alleviates the mode collapse problem in strongly conditional generation task that can lead to the generation of similar modes. We provide more qualitative comparisons on diversity in the supplementary material." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 308, + 570, + 544, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 570, + 544, + 712 + ], + "spans": [ + { + "bbox": [ + 308, + 570, + 544, + 712 + ], + "type": "text", + "content": "Rendering results comparison. We render graphic pages for better visualization using the generated layouts. Fig. 5 show the rendering results comparison on PublayNet. We find the layouts generated by LayoutDM follow design rules well and reasonably allocate page space. Compared to the results generated by LayoutGAN++, our results are better in alignment and have no overlapping between elements. Note that we crop the elements from the original document and then render the pages using a simple resize-to-fit method, so the text areas and figures will suffer some distortion. In real design scenarios, this problem can be solved by element customization (e.g., adjust the font size)." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 750, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 750, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 750, + 317, + 757 + ], + "type": "text", + "content": "18354" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 52, + 68, + 539, + 338 + ], + "blocks": [ + { + "bbox": [ + 52, + 68, + 539, + 338 + ], + "lines": [ + { + "bbox": [ + 52, + 68, + 539, + 338 + ], + "spans": [ + { + "bbox": [ + 52, + 68, + 539, + 338 + ], + "type": "image", + "image_path": "ac1a71fba8ad3e9328176ecde46122608960c0b57d7e2aec017dad8645449d08.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 59, + 344, + 533, + 357 + ], + "lines": [ + { + "bbox": [ + 59, + 344, + 533, + 357 + ], + "spans": [ + { + "bbox": [ + 59, + 344, + 533, + 357 + ], + "type": "text", + "content": "Figure 2. Qualitative comparison on Rico and PublayNet. Element labels indicate the labels of elements used as conditional inputs." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 52, + 370, + 281, + 521 + ], + "blocks": [ + { + "bbox": [ + 52, + 370, + 281, + 521 + ], + "lines": [ + { + "bbox": [ + 52, + 370, + 281, + 521 + ], + "spans": [ + { + "bbox": [ + 52, + 370, + 281, + 521 + ], + "type": "image", + "image_path": "5dac9dbaa5f24f71858b84ca789eca6aaa8499a0c4922f6bae63b314ec24205b.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 530, + 288, + 563 + ], + "lines": [ + { + "bbox": [ + 46, + 530, + 288, + 563 + ], + "spans": [ + { + "bbox": [ + 46, + 530, + 288, + 563 + ], + "type": "text", + "content": "Figure 3. Ablation study on the effect of transformer layers. \"w/o transformer\" denotes model without transformer layers. \"Full\" denotes our full model." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 571, + 236, + 585 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 571, + 236, + 585 + ], + "spans": [ + { + "bbox": [ + 47, + 571, + 236, + 585 + ], + "type": "text", + "content": "4.4. Extended Layout Generation Tasks" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": "Text logo layout generation. TextLogo3K [44] dataset contains character and word embedding of texts in the logos. Although the dataset does not provide any label information, we can still generate logo layouts conditioned on the provided textual features. Positional encoding is added to LayoutDM to make the transformer structure aware of the reading order in textual feature sequences. We compare the logo layout generation results of LayoutDM and those generated by the logo layout generator provided by TextLogo3K [44]. The qualitative results are shown in Fig. 6. As" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 306, + 369, + 545, + 552 + ], + "blocks": [ + { + "bbox": [ + 306, + 369, + 545, + 552 + ], + "lines": [ + { + "bbox": [ + 306, + 369, + 545, + 552 + ], + "spans": [ + { + "bbox": [ + 306, + 369, + 545, + 552 + ], + "type": "image", + "image_path": "d353d36048b59a08c9383ecdc97c90afc274e2003884f7db08b3ab56b7b1c81f.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 560, + 547, + 605 + ], + "lines": [ + { + "bbox": [ + 305, + 560, + 547, + 605 + ], + "spans": [ + { + "bbox": [ + 305, + 560, + 547, + 605 + ], + "type": "text", + "content": "Figure 4. Diversity comparison on PublayNet. We show five samples generated by giving the same category attributes as condition: one Figure and five Texts. The Figure is drawn in purple and the Texts are drawn in red." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 613, + 547, + 698 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 613, + 547, + 698 + ], + "spans": [ + { + "bbox": [ + 304, + 613, + 547, + 698 + ], + "type": "text", + "content": "one can see, our model generates reasonable logo layouts while maintaining the correct reading order and aesthetic principles. Compared to LogoGAN, the style of the logos generated by our model is more flexible, not simply arranging the text from left to right. Our model also performs better when there are large numbers of characters in the layout, where LogoGAN fails to generate reasonable results." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "type": "text", + "content": "Scene layout generation. Our model can also generate" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18355" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 52, + 69, + 287, + 278 + ], + "blocks": [ + { + "bbox": [ + 52, + 69, + 287, + 278 + ], + "lines": [ + { + "bbox": [ + 52, + 69, + 287, + 278 + ], + "spans": [ + { + "bbox": [ + 52, + 69, + 287, + 278 + ], + "type": "image", + "image_path": "f2fc7ddb6eed51e61453cdce6710283ea34d077fe079143980095bf17854d5d3.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 53, + 337, + 287, + 538 + ], + "blocks": [ + { + "bbox": [ + 47, + 289, + 287, + 334 + ], + "lines": [ + { + "bbox": [ + 47, + 289, + 287, + 334 + ], + "spans": [ + { + "bbox": [ + 47, + 289, + 287, + 334 + ], + "type": "text", + "content": "Figure 5. Rendering results comparison. Top: Rendered pages using layouts generated by LayoutGAN++. Middle: Rendered pages using layouts generated by LayoutDM. Bottom: Real paper pages in PublayNet." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 53, + 337, + 287, + 538 + ], + "lines": [ + { + "bbox": [ + 53, + 337, + 287, + 538 + ], + "spans": [ + { + "bbox": [ + 53, + 337, + 287, + 538 + ], + "type": "image", + "image_path": "9c4770cae20e57c3acfd139b49e9072569849cb7803638212f0407badb2f8c83.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 550, + 287, + 605 + ], + "lines": [ + { + "bbox": [ + 46, + 550, + 287, + 605 + ], + "spans": [ + { + "bbox": [ + 46, + 550, + 287, + 605 + ], + "type": "text", + "content": "Figure 6. Text logo generation results. \"LogoGAN\" denotes the text logo generation model proposed in [44]. \"Condition\" represents the textual features (including character and word embeddings) used as conditional input in LogoGAN and LayoutDM. \"/\" is the symbol for splitting tokens." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 613, + 288, + 709 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 613, + 288, + 709 + ], + "spans": [ + { + "bbox": [ + 46, + 613, + 288, + 709 + ], + "type": "text", + "content": "natural scene layouts. We illustrate the qualitative results of the scene layout generation on COCO in Fig. 7. Given the labels of scene elements in a scene, our model generates reasonable scene layout proposals. We then use a downstream layout-to-image generation application [2] to finally render natural scene images. The results show that our model learns the principle of scene layouts well and can understand the complex relationships between elements in" + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 307, + 69, + 545, + 287 + ], + "blocks": [ + { + "bbox": [ + 307, + 69, + 545, + 287 + ], + "lines": [ + { + "bbox": [ + 307, + 69, + 545, + 287 + ], + "spans": [ + { + "bbox": [ + 307, + 69, + 545, + 287 + ], + "type": "image", + "image_path": "c64a28bccad22f12f6306a45315d7c7e495b90feb80652d1f023851d6f0e10ef.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 295, + 545, + 329 + ], + "lines": [ + { + "bbox": [ + 306, + 295, + 545, + 329 + ], + "spans": [ + { + "bbox": [ + 306, + 295, + 545, + 329 + ], + "type": "text", + "content": "Figure 7. Natural scene layout generation results on COCO. Our model uses scene element labels as conditional input to generate reasonable scene layouts." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 337, + 545, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 337, + 545, + 361 + ], + "spans": [ + { + "bbox": [ + 306, + 337, + 545, + 361 + ], + "type": "text", + "content": "natural scenes. For example, the boat should be in the river and the cloud should be in the upper part of the scene." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 367, + 383, + 378 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 367, + 383, + 378 + ], + "spans": [ + { + "bbox": [ + 306, + 367, + 383, + 378 + ], + "type": "text", + "content": "4.5. Limitations" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 385, + 545, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 385, + 545, + 504 + ], + "spans": [ + { + "bbox": [ + 305, + 385, + 545, + 504 + ], + "type": "text", + "content": "Although our method shows impressive results in the conditional layout generation problem in comparison to existing methods, it still has limitations. For example, like other layout generation methods, our approach treats design elements as being on a single-layer canvas. This can not model a layout with multiple layers occluding each other. Our method also has no advantage over other generative models in generation speed because the generation of the diffusion model requires an iterative denoising process. We leave the solution to the above problems for future work." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 514, + 378, + 526 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 514, + 378, + 526 + ], + "spans": [ + { + "bbox": [ + 306, + 514, + 378, + 526 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 534, + 545, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 534, + 545, + 665 + ], + "spans": [ + { + "bbox": [ + 305, + 534, + 545, + 665 + ], + "type": "text", + "content": "This paper proposes a transformer-based diffusion model LayoutDM to address conditional layout generation. We introduce a purely transformer-based Layout Denoiser to model the diffusion reverse process. Benefitting from both DDPM and transformer, in comparison to existing methods, LayoutDM can generate high-quality generation with desired properties such as better diversity, faithful distribution coverage, and stationary training. Quantitative and qualitative results demonstrate that our model outperforms the state-of-the-art methods in terms of visual perceptual quality and diversity." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 665, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 665, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 305, + 665, + 545, + 712 + ], + "type": "text", + "content": "Acknowledgment. This work was supported in part to Dr. Liansheng Zhuang by NSFC under contract No.U20B2070 and No.61976199, in part to Dr. Fengying Yan by NSFC under contract No.42341207." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "18356" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 714 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "text", + "content": "[1] Diego Martín Arroyo, Janis Postels, and Federico Tombari. 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IEEE, Sep. 2019. 5" + } + ] + } + ], + "index": 22 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18358" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/LayoutDiffusion_ Controllable Diffusion Model for Layout-to-Image Generation/b7471e7f-ee4c-4b84-b778-22769e778b1d_content_list.json b/2023/LayoutDiffusion_ Controllable Diffusion Model for Layout-to-Image Generation/b7471e7f-ee4c-4b84-b778-22769e778b1d_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..57d6f8634f2ea960ab961c0ec2391ddf14305a49 --- /dev/null +++ b/2023/LayoutDiffusion_ Controllable Diffusion Model for Layout-to-Image Generation/b7471e7f-ee4c-4b84-b778-22769e778b1d_content_list.json @@ -0,0 +1,1733 @@ +[ + { + "type": "text", + "text": "LayoutDiffusion: Controllable Diffusion Model for Layout-to-image Generation", + "text_level": 1, + "bbox": [ + 228, + 130, + 743, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Guangcong Zheng $^{1*}$ , Xianpan Zhou $^{2*}$ , Xuewei Li $^{1\\dagger}$ , Zhongang Qi $^{3}$ , Ying Shan $^{3}$ , Xi Li $^{1,4,5,6\\dagger}$ $^{1}$ College of Computer Science & Technology, Zhejiang University \n $^{2}$ Polytechnic Institute, Zhejiang University ${}^{3}$ ARC Lab, Tencent PCG \n ${}^{4}$ Shanghai Institute for Advanced Study of Zhejiang University \n ${}^{5}$ Shanghai AI Lab ${}^{6}$ Zhejiang - Singapore Innovation and AI Joint Research Lab", + "bbox": [ + 127, + 202, + 849, + 292 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{guangcongzheng, zhouxianpan, xuweili, xilizju}@zju.edu.cn {zhongangqi, yingsshan}@tencent.com", + "bbox": [ + 223, + 294, + 745, + 327 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/a795827e293526b1838ce4f322d156b3029505b02343c57420cb83ce7d4bc7dd.jpg", + "image_caption": [ + "(a) layout-guided vs. text-guided image generation for diffusion model", + "(b) Image-Layout Fusion in a unified space", + "Figure 1. Compared to text, the layout allows diffusion models to obtain more control over the objects while maintaining high quality. Unlike the prevailing methods, we propose a diffusion model named LayoutDiffusion for layout-to-image generation. We transform the difficult multimodal fusion of the image and layout into a unified form by constructing a structural image patch with region information and regarding the patched image as a special layout." + ], + "image_footnote": [], + "bbox": [ + 99, + 359, + 869, + 513 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 592, + 313, + 608 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, diffusion models have achieved great success in image synthesis. However, when it comes to the layout-to-image generation where an image often has a complex scene of multiple objects, how to make strong control over both the global layout map and each detailed object remains a challenging task. In this paper, we propose a diffusion model named LayoutDiffusion that can obtain higher generation quality and greater controllability than the previous works. To overcome the difficult multimodal fusion of image and layout, we propose to construct a structural image patch with region information and transform the patched image into a special layout to fuse with the normal layout in a unified form. Moreover, Layout Fusion Module (LFM) and Object-aware Cross Attention (OaCA) are proposed to model the relationship among multiple objects and designed to be object-aware and position-sensitive, allow", + "bbox": [ + 75, + 625, + 473, + 867 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ing for precisely controlling the spatial related information. Extensive experiments show that our LayoutDiffusion outperforms the previous SOTA methods on FID, CAS by relatively $46.35\\%$ , $26.70\\%$ on COCO-stuff and $44.29\\%$ , $41.82\\%$ on VG. Code is available at https://github.com/ZGCTroy/LayoutDiffusion.", + "bbox": [ + 500, + 594, + 890, + 686 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 500, + 707, + 632, + 722 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, the diffusion model has achieved encouraging progress in conditional image generation, especially in text-to-image generation such as GLIDE [24], Imagen [31], and Stable Diffusion [30]. However, text-guided diffusion models may still fail in the following situations. As shown in Fig. 1 (a), when aiming to generate a complex image with multiple objects, it is hard to design a prompt properly and comprehensively. Even input with well-designed prompts, problems such as missing objects and incorrectly generating objects' positions, shapes, and categories still occur in the state-of-the-art text-guided diffusion model [24, 30, 31].", + "bbox": [ + 496, + 734, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* Equal contribution.", + "bbox": [ + 94, + 875, + 207, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Corresponding author.", + "bbox": [ + 96, + 887, + 220, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "22490", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "This is mainly due to the ambiguity of the text and its weakness in precisely expressing the position of the image space. Fortunately, this is not a problem when using the coarse layout as guidance, which is a set of objects with the annotation of the bounding box (bbox) and object category. With both spatial and high-level semantic information, the diffusion model can obtain more powerful controllability while maintaining the high quality.", + "bbox": [ + 75, + 90, + 472, + 212 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "However, early studies [2, 14, 38, 42] on layout-to-image generation are almost limited to generative adversarial networks (GANs) and often suffer from unstable convergence [1] and mode collapse [27]. Despite the advantages of diffusion models in easy training [10] and significant quality improvement [7], few studies have considered applying diffusion in the layout-to-image generation task. To our knowledge, only LDM [30] supports the condition of layout and has shown encouraging progress in this field.", + "bbox": [ + 75, + 214, + 472, + 351 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, different from LDM that applies the simple multimodal fusion method (e.g., the cross attention) or direct input concatenation for all conditional input, we aim to specifically design the fusion mechanism between layout and image. Moreover, instead of conditioning only in the second stage like LDM, we propose an end-to-end one-stage model that considers the condition for the whole process, which may have the potential to help mitigate loss in the task that requires fine-grained accuracy in pixel space [30]. The fusion between image and layout is a difficult multimodal fusion problem. Compared to the fusion of text and image, the layout has more restrictions on the position, size, and category of objects. This requires a higher controllability of the model and often leads to a decrease in the naturalness and diversity of the generated image. Furthermore, the layout is more sensitive to each token and the loss in token of layout will directly lead to the missing objects.", + "bbox": [ + 75, + 354, + 472, + 626 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address the problems mentioned above, we propose treating the patched image and the input layout in a unified form. Specifically, we construct a structural image patch at multi-resolution by adding the concept of region that contains information of position and size. As a result, each patch of the image is transformed into a special type of object, and the entire patched image will also be regarded as a layout. Finally, the difficult problem of multimodal fusion between image and layout will be transformed into a simple fusion with a unified form in the same spatial space of the image. We name our model LayoutDiffusion, a layout-conditional diffusion model with Layout Fusion Module (LFM), object-aware Cross Attention Mechanism (OaCA), and corresponding classifier-free training and sampling scheme. In detail, LFM fuses the information of each object and models the relationship among multiple objects, providing a latent representation of the entire layout. To make the model pay more attention to the information re", + "bbox": [ + 75, + 628, + 472, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "lated to the object, we propose an object-aware fusion module named OaCA. Cross-attention is made between the image patch feature and layout in a unified coordinate space by representing the positions of both of them as bounding boxes. To further improve the user experience of LayoutDiffusion, we also make several optimizations on the speed of the classifier-free sampling process and could significantly outperform the SOTA models in 25 iterations.", + "bbox": [ + 496, + 90, + 893, + 210 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Experiments are conducted on COCO-stuff [5] and Visual Genome (VG) [19]. Various metrics ranging from quality, diversity, and controllability show that LayoutDiffusion significantly outperforms both state-of-the-art GAN-based and diffusion-based methods.", + "bbox": [ + 496, + 212, + 893, + 286 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our main contribution is listed below.", + "bbox": [ + 517, + 287, + 769, + 301 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Instead of using the dominated GAN-based methods, we propose a diffusion model named LayoutDiffusion for layout-to-image generations, which can generate images with both high-quality and diversity while maintaining precise control over the position and size of multiple objects.", + "- We propose to treat each patch of the image as a special object and accomplish the difficult multimodal fusion of layout and image in a unified form. LFM and OaCA are then proposed to fuse the multi-resolution image patches with user's input layout.", + "- LayoutDiffusion outperforms the SOTA layout-to-image generation method on FID, DS, CAS by relatively around $46.35\\%$ , $9.61\\%$ , $26.70\\%$ on COCO-stuff and $44.29\\%$ , $11.30\\%$ , $41.82\\%$ on VG." + ], + "bbox": [ + 517, + 315, + 890, + 560 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related work", + "text_level": 1, + "bbox": [ + 500, + 575, + 637, + 590 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The related works are mainly from layout-to-image generation and diffusion models.", + "bbox": [ + 500, + 601, + 890, + 631 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Layout-to-Image Generation. Before the layout-to-image generation is formally proposed, the layout is usually used as a complementary feature [15, 29, 40] or an intermediate representation in text-to-image [12], scene-to-image generation [14]. The first image generation directly from the layout appears in Layout2Im [47] and is defined as a set of objects annotated with category and bbox. Models that work well with fine-grained semantic maps at the pixel level can also be easily transformed to this setting [13, 26, 43]. Inspired by StyleGAN [16], LostGAN-v1 [37], LostGAN-v2 [38] used a reconfigurable layout to obtain better control over individual objects. For interactive image synthesis, PLGAN [42] employed panoptic theory [18] by constructing stuff and instance layouts into separate branches and proposed Instance- and Stuff-Aware Normalization to fuse into panoptic layouts. Despite encouraging progress in this field, almost all approaches are limited to the generative", + "bbox": [ + 496, + 643, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "22491", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "adversarial network (GAN) and may suffer from unstable convergence [1] and mode collapse [27]. As a multimodal diffusion model, LDM [30] supports the condition of coarse layout and has shown great potential in layout-guided image generation.", + "bbox": [ + 75, + 90, + 470, + 167 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Diffusion Model. Diffusion models [3, 10, 25, 30, 34-36, 44] are being recognized as a promising family of generative models that have proven to be state-of-the-art sample quality for a variety of image generation benchmarks [6, 41, 45], including class-conditional image generation [7, 48], text-to-image generation [24, 30, 31], and imaged-to-image translation [17, 22, 32]. Classifier guidance was introduced in ADM-G [7] to allow diffusion models to condition the class label. The gradient of the classifier trained on noised images could be added to the image during the sampling process. Then Ho et al. [11] proposed a classifier-free training and sampling strategy by interpolating between predictions of a diffusion model with and without condition input. For the acceleration of training and sampling speed, LDM proposed to first compress the image into smaller resolution and then apply denoising training in the latent space.", + "bbox": [ + 75, + 193, + 472, + 436 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 453, + 166, + 468 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we propose our LayoutDiffusion, as shown in Fig. 2. The whole framework consists mainly of four parts: (a) layout embedding that preprocesses the layout input, (b) layout fusion module that encourages more interaction between objects of layout, (c) image-Layout fusion module that constructs the structural image patch and object-aware cross attention developed with the specific design for layout and image fusion, (d) the layout-conditional diffusion model with training and accelerated sampling methods.", + "bbox": [ + 75, + 479, + 468, + 617 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Layout Embedding", + "text_level": 1, + "bbox": [ + 76, + 630, + 263, + 647 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "A layout $l = \\{o_1, o_2, \\dots, o_n\\}$ is a set of $n$ objects. Each object $o_i$ is represented as $o_i = \\{b_i, c_i\\}$ , where $b_i = (x_0^i, y_0^i, x_1^i, y_1^i) \\in [0, 1]^4$ denotes a bounding box (bbox) and $c_i \\in [0, \\mathcal{C} + 1]$ is its category id.", + "bbox": [ + 76, + 655, + 468, + 715 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To support the input of a variable length sequence, we need to pad $l$ to a fixed length $k$ by adding one $o_l$ in the front and some padding $o_p$ in the end, where $o_l$ represents the entire layout and $o_p$ represents no object. Specifically, $b_l = (0, 0, 1, 1)$ , $c_l = 0$ denotes a object that covers the whole image and $b_p = (0, 0, 0, 0)$ , $c_p = \\mathcal{C} + 1$ denotes a empty object that has no shape or does not appear in the image.", + "bbox": [ + 75, + 717, + 468, + 823 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "After the padding process, we can get a padded $l = \\{o_1, o_2, \\dots, o_k\\}$ consisting of $k$ objects, and each object has its specific position, size, and category. Then, the layout $l$ is transformed into a layout embedding $L = \\{O_1, O_2, \\dots, O_k\\} \\in \\mathbb{R}^{k \\times d_{\\mathcal{L}}}$ by the projection matrix $W_{\\mathcal{B}} \\in$", + "bbox": [ + 76, + 824, + 468, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "$\\mathbb{R}^{4\\times d_{\\mathcal{L}}}$ and $W_{\\mathcal{C}}\\in \\mathbb{R}^{1\\times d_{\\mathcal{L}}}$ using the following equation:", + "bbox": [ + 500, + 90, + 859, + 107 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nL = B _ {\\mathcal {L}} + C _ {\\mathcal {L}} \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 645, + 118, + 890, + 133 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nB _ {\\mathcal {L}} = b W _ {\\mathcal {B}} \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 653, + 137, + 890, + 152 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nC _ {\\mathcal {L}} = c W _ {C} \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 653, + 156, + 890, + 172 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $B_{\\mathcal{L}}, C_{\\mathcal{L}} \\in \\mathbb{R}^{k \\times d_{\\mathcal{L}}}$ are the bounding box embedding and the category embedding of a layout $l$ , respectively. As a result, $L$ is defined as the sum of $B_{\\mathcal{L}}$ and $C_{\\mathcal{L}}$ to include both the content and positional information of a entire layout, and $d_{\\mathcal{L}}$ is the dimension of the layout embedding.", + "bbox": [ + 496, + 185, + 890, + 262 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Layout Fusion Module", + "text_level": 1, + "bbox": [ + 500, + 271, + 710, + 286 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Currently, each object in layout has no relationship with other objects. This leads to a low understanding of the whole scene, especially when multiple objects overlap and block each other. Therefore, to encourage more interaction between multiple objects of the layout to better understand the entire layout before inputting the layout embedding, we propose Layout Fusion Module (LFM), a transformer encoder that uses multiple layers of self-attention to fuse the layout embedding and can be denoted as", + "bbox": [ + 496, + 294, + 890, + 430 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nL ^ {\\prime} = \\operatorname {L F M} (L) \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 643, + 441, + 890, + 458 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": ", where the output is a fused layout embedding $L^{\\prime} = \\{O_{1}^{\\prime},O_{2}^{\\prime},\\dots ,O_{k}^{\\prime}\\} \\in \\mathbb{R}^{k\\times d_{\\mathcal{L}}}$", + "bbox": [ + 500, + 470, + 890, + 503 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.3. Image-Layout Fusion Module", + "text_level": 1, + "bbox": [ + 500, + 511, + 764, + 526 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Structural Image Patch. The fusion of image and layout is a difficult multimodal fusion problem, and one of the most important parts lies in the fusion of position and size. However, the image patch is limited to the semantic information of the whole feature and lacks the spatial information. Therefore, we construct a structural image patch by adding the concept of region that contains the information of position and size.", + "bbox": [ + 496, + 534, + 890, + 654 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Specifically, $I \\in \\mathbb{R}^{h \\times w \\times d_{\\mathcal{I}}}$ denotes the feature map of a entire image with height $h$ , width $w$ , and channel $d_{\\mathcal{I}}$ . We define that $I_{u,v}$ is the $u^{\\mathrm{th}}$ row and $v^{\\mathrm{th}}$ column patch of $I$ and its bounding box, or the ablated region information, is defined as $b_{I_{u,v}}$ by the following equation:", + "bbox": [ + 496, + 654, + 890, + 732 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nb _ {\\mathcal {I} _ {u, v}} = \\left(\\frac {u}{h}, \\frac {v}{w}, \\frac {u + 1}{h}, \\frac {v + 1}{w}\\right) \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 601, + 743, + 890, + 772 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The bounding box sets of a patched image $I$ is defined as $b_{\\mathcal{I}} = \\{b_{\\mathcal{I}_{u,v}}|u\\in [0,h),v\\in [0,w)\\}$ . As a result, the positional information of image patch and layout object is contained in the unified bounding box defined in the same spatial space, leading to better fusion of image and layout.", + "bbox": [ + 496, + 782, + 890, + 858 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Positional Embedding in Unified Space. We define the positional embedding of the image and layout as $P_{\\mathcal{I}}$ and", + "bbox": [ + 496, + 869, + 890, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "22492", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/dea185a46bee7b955fcf0d82c49950d37eafbac5d6b61059d12080c202b026fc.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 76, + 85, + 890, + 239 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/b7672b7661b04c0abe06df22d56484095df0c5f81cea377e0b1e38b5896f34cb.jpg", + "image_caption": [ + "Figure 2. The whole pipeline of LayoutDiffusion. The layout that consisted of bounding box $b$ and objects categories $c$ is transformed into embedding $B_{\\mathcal{L}}, C_{\\mathcal{L}}, L$ . Then Layout Fusion Module fuses layout embedding $L$ to output the fused layout embedding $L'$ . Finally, Image-Layout Fusion Module including direct addition used for global conditioning and Object-aware Cross Attention (OaCA) used for local conditioning, will fuse the layout related $B_{\\mathcal{L}}, C_{\\mathcal{L}}, L'$ and the image feature $I$ at multiple resolutions." + ], + "image_footnote": [], + "bbox": [ + 76, + 241, + 514, + 448 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/036034f21e885159cbef6c3ae1edb619772eb83b1fb1f4469163352238e5725c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 522, + 241, + 888, + 448 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$P_{\\mathcal{L}}$ as follows:", + "bbox": [ + 76, + 539, + 176, + 553 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nB _ {\\mathcal {I}} = b _ {\\mathcal {I}} W _ {\\mathcal {B}} \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 223, + 560, + 468, + 575 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nP _ {\\mathcal {I}} = B _ {\\mathcal {I}} W _ {\\mathcal {P}} \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 227, + 579, + 468, + 594 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nP _ {\\mathcal {L}} = B _ {\\mathcal {L}} W _ {\\mathcal {P}} \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 227, + 598, + 468, + 613 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": ", where $W_{\\mathcal{B}} \\in \\mathbb{R}^{4 \\times d_{\\mathcal{L}}}$ is defined in Eq. 2 and works as a shared projection matrix that transforms the coordinates of bounding box into embedding of $d_{\\mathcal{L}}$ dimension. $W_{\\mathcal{P}} \\in \\mathbb{R}^{d_{\\mathcal{L}} \\times d_{\\mathcal{I}}}$ is the projection matrix that transforms the $B$ to the positional Embedding $P$ .", + "bbox": [ + 75, + 621, + 468, + 698 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Pointwise Addition for Global Conditioning. With the help of LFM in Eq. 4, $O_1'$ can be considered as a global information of the entire layout, and $O_i'(i \\in [2, k])$ is considered as the local information embedding of single object along with the other related objects. One of the easiest ways to condition the layout in the image is to directly add $O_1'$ , the global information of the layout, to the multiple resolution of image features. Specifically, the condition process can be defined as", + "bbox": [ + 75, + 714, + 468, + 848 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nI ^ {\\prime} = I + O _ {1} ^ {\\prime} W \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 218, + 848, + 468, + 867 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": ", where $W \\in \\mathbb{R}^{d_{\\mathcal{L}} \\times d_{\\mathcal{I}}}$ is a projection matrix and $I'$ is the image feature conditioned with global embedding of layout.", + "bbox": [ + 75, + 869, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Object-aware Cross Attention for Local Conditioning.", + "bbox": [ + 498, + 539, + 890, + 553 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Cross attention is successfully applied in [24] to condition text into image feature, where the sequence of the image patch is used as the query and the concatenated sequence of the image patch and text is applied as key and value. The equation of cross-attention is defined as", + "bbox": [ + 498, + 554, + 890, + 628 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {A t t e n t i o n} (Q, K, V) = \\operatorname {s o f t m a x} \\left(\\frac {Q K ^ {T}}{\\sqrt {d _ {k}}}\\right) V \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 529, + 641, + 890, + 676 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": ", where $Q, K, V$ represent the embeddings of query, key, and value, respectively. In the following paper, we will use the subscript image and layout to represent the image patch feature and layout feature, respectively.", + "bbox": [ + 498, + 686, + 890, + 748 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In text-to-image generation, each token in the text sequence is a word. The aggregation of these words constitutes the semantics of a sentence. After the transformer encoder, the first token in text sequence is well-semantic information that generalizes the whole text but may not reverse the semantic meaning of each word. However, the loss in information of one token is relatively serious in layout rather than in text. Each token in the layout sequence is a single object with a specific category, size, and position. The loss of information on a layout token will directly lead", + "bbox": [ + 496, + 750, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "22493", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "to a missing or wrong object in the generated image pixel space.", + "bbox": [ + 75, + 90, + 468, + 119 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Therefore, we take into account the fusion of locations, size, and category of objects and define our object-aware cross-attention (OaCA) as", + "bbox": [ + 75, + 121, + 468, + 165 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nQ = \\Psi_ {1} \\left(Q _ {\\mathcal {I}}, Q _ {\\mathcal {L}}\\right) \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 150, + 178, + 468, + 194 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nK = \\Psi_ {1} \\left(\\Psi_ {2} \\left(K _ {\\mathcal {I}}, K _ {\\mathcal {L}}\\right), \\Psi_ {2} \\left(P _ {\\mathcal {I}}, P _ {\\mathcal {L}}\\right)\\right) \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 196, + 468, + 213 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nV = \\Psi_ {2} \\left(V _ {\\mathcal {I}}, V _ {\\mathcal {L}}\\right) \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 151, + 215, + 468, + 232 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": ", where the query $Q \\in \\mathbb{R}^{hw \\times 2d_{\\mathcal{I}}}$ , $K \\in \\mathbb{R}^{(hw + k) \\times 2d_{\\mathcal{I}}}$ , and $V \\in \\mathbb{R}^{(hw + k) \\times d_{\\mathcal{I}}}$ . $\\Psi_1$ and $\\Psi_2$ denote concatenation on the dimension of the channel and length of the sequence, respectively.", + "bbox": [ + 76, + 244, + 468, + 306 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We first construct the key and value of the layout:", + "bbox": [ + 96, + 306, + 423, + 321 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nK _ {\\mathcal {L}}, V _ {\\mathcal {L}} = \\operatorname {C o n v} \\left(\\frac {1}{2} \\left(\\operatorname {N o r m} \\left(C _ {\\mathcal {L}}\\right) + L ^ {\\prime}\\right)\\right) \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 140, + 332, + 468, + 361 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": ", where $K_{\\mathcal{L}}, V_{\\mathcal{L}} \\in \\mathbb{R}^{k \\times d_{\\mathcal{I}}}$ and Conv is the convolution operation. The embedding of key and value in the layout is related to the category embedding $C_{\\mathcal{L}}$ and the fused layout embedding $L'$ . $C_{\\mathcal{L}}$ focuses on the category information of layout and $L'$ concentrates on the comprehensive information of both the object itself and other objects that may have a relationship with it. By averaging between $L'$ and $C_{\\mathcal{L}}$ , we can obtain both the general information of the object and also emphasize the category information of the object.", + "bbox": [ + 75, + 372, + 468, + 508 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We construct the query, key, and value of the image feature as follows:", + "bbox": [ + 75, + 508, + 468, + 537 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nQ _ {\\mathcal {I}}, K _ {\\mathcal {I}}, V _ {\\mathcal {I}} = \\operatorname {C o n v} (\\operatorname {N o r m} (I)) \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 163, + 550, + 468, + 566 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Layout-conditional Diffusion Model", + "text_level": 1, + "bbox": [ + 76, + 578, + 387, + 593 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Here, we follow the Gaussian diffusion models improved by [10, 35]. Given a data point sampled from a real data distribution $x_0 \\sim q(x_0)$ , a forward diffusion process is defined by adding small amount of Gaussian noise to the $x_0$ in $T$ steps:", + "bbox": [ + 75, + 601, + 468, + 676 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nq \\left(x _ {t} \\mid x _ {t - 1}\\right) := \\mathcal {N} \\left(x _ {t}; \\sqrt {\\alpha_ {t}} x _ {t - 1}, (1 - \\alpha_ {t}) \\mathbf {I}\\right) \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 116, + 689, + 468, + 705 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "If the total noise added throughout the Markov chain is large enough, the $x_{T}$ will be well approximated by $\\mathcal{N}(0,\\mathbf{I})$ . If we add noise at each step with a sufficiently small magnitude $1 - \\alpha_{t}$ , the posterior $q(x_{t - 1}|x_t)$ will be well approximated by a diagonal Gaussian. This nice property ensures that we can reverse the above forward process and sample from $x_{T}\\sim \\mathcal{N}(0,\\mathbf{I})$ , which is a Gaussian noise. However, since the entire dataset is needed, we are unable to easily estimate the posterior. Instead, we have to learn a model $p_{\\theta}(x_{t - 1}|x_t)$ to approximate it:", + "bbox": [ + 75, + 717, + 468, + 868 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\np _ {\\theta} \\left(x _ {t - 1} \\mid x _ {t}\\right) := \\mathcal {N} \\left(\\mu_ {\\theta} \\left(x _ {t}\\right), \\Sigma_ {\\theta} \\left(x _ {t}\\right)\\right) \\tag {17}\n$$\n", + "text_format": "latex", + "bbox": [ + 151, + 880, + 468, + 897 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Instead of using the tractable variational lower bound (VLB) in $\\log p_{\\theta}(x_0)$ , Ho et al. [10] proposed to reweight the terms of the VLB to optimize a surrogate objective. Specifically, we first add $t$ steps of Gaussian noise to a clean sample $x_0$ to generate a noised sample $x_{t} \\sim q(x_{t}|x_{0})$ . Then train a model $\\epsilon_{\\theta}$ to predict the added noise using the following loss:", + "bbox": [ + 498, + 90, + 890, + 196 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} := E _ {t \\sim [ 1, T ], x _ {0} \\sim q (x _ {0}), \\epsilon \\sim \\mathcal {N} (0, \\mathbf {I})} [ \\| \\epsilon - \\epsilon_ {\\theta} (x _ {t}, t) \\| ^ {2} ] \\tag {18}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 208, + 890, + 226 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": ", which is a standard mean-squared error loss.", + "bbox": [ + 500, + 238, + 802, + 252 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To support the layout condition, we apply classifier-free guidance, a technique proposed by Ho et al. [11] for conditional generation that requires no additional training of the classifier. It is accomplished by interpolating between predictions of a diffusion model with and without condition input. For the condition of layout, we first construct a padding layout $l_{\\phi} = \\{o_l,o_p,\\dots ,o_p\\}$ . During training, the condition of layout $l$ of diffusion model will be replaced with $l_{\\phi}$ with a fixed probability. When sampling, the following equation is used to sample a layout-condional image:", + "bbox": [ + 498, + 252, + 890, + 404 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\epsilon} _ {\\theta} \\left(x _ {t}, t | l\\right) = (1 - s) \\cdot \\epsilon_ {\\theta} \\left(x _ {t}, t \\mid l _ {\\phi}\\right) + s \\cdot \\epsilon_ {\\theta} \\left(x _ {t}, t \\mid l\\right) \\tag {19}\n$$\n", + "text_format": "latex", + "bbox": [ + 521, + 415, + 890, + 431 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": ", where the scale $s$ can be used to increase the gap between $\\epsilon_{\\theta}(x_t,t|l_\\phi)$ and $\\epsilon_{\\theta}(x_t,t|l)$ to enhance the strength of conditional guidance.", + "bbox": [ + 498, + 444, + 890, + 488 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To further improve the user experience of LayoutDiffusion, we also make several optimizations on the speed of the classifier-free sampling process and could significantly outperform the SOTA models in 25 iterations. Specifically, we adapt DPM-solver [21] for the conditional classifier-free sampling, a fast dedicated high-order solver for diffusion ODEs [36] with the convergence order guarantee, to accelerate the conditional sampling speed.", + "bbox": [ + 498, + 489, + 890, + 609 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 625, + 630, + 641 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we evaluate our LayoutDiffusion on different benchmarks in terms of various metrics. First, we introduce the datasets and evaluation metrics. Second, we show the qualitative and quantitative results compared with other strategies. Finally, some ablation studies and analysis are also mentioned. More details can be found in Appendix, including model architecture, training hyperparameters, reproduction results, more experimental results and visualizations.", + "bbox": [ + 498, + 648, + 890, + 784 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Datasets", + "text_level": 1, + "bbox": [ + 500, + 795, + 601, + 809 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We conduct our experiments on two popular datasets, COCO-Stuff [5] and Visual Genome [19].", + "bbox": [ + 500, + 818, + 888, + 848 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "COCO-Stuff has 164K images from COCO 2017, of which the images contain bounding boxes and pixel-level segmentation masks for 80 categories of thing and 91 categories", + "bbox": [ + 498, + 854, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "22494", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/dfcd2b773a3a396f58a965a3817b0c914207b2b37bb8f34e5c441bfc3c632eda.jpg", + "image_caption": [ + "Figure 3. Visualization of comparison with SOTA methods on COCO-stuff $256 \\times 256$ . LayoutDiffusion has better generation quality and stronger controllability compared to the other methods." + ], + "image_footnote": [], + "bbox": [ + 81, + 90, + 885, + 542 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/ee84d8e76a0f07374c2a1d0ef500ddfe06fc918764afaba67ad8520ac7ede8d2.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodsCOCO-stuffVG
FID ↓IS ↑DS ↑CAS ↑YOLOScore ↑FID ↓DS ↑CAS ↑
128×128
Grid2Im [2]59.5012.50±0.300.28±0.114.056.80---
LostGAN-v2 [38]24.7614.21±0.400.45±0.0939.9113.6029.000.42±0.0929.74
PLGAN [42]22.7015.60±0.300.16±0.7238.7013.4020.62--
LayoutDiffusion16.5720.17±0.560.47±0.0943.6027.0016.350.49±0.0936.45
256×256
Grid2Im [2]65.2016.40±0.700.34±0.134.819.70---
LostGAN-v2 [38]31.1818.01±0.500.56±0.1040.0017.5032.080.53±0.1034.48
PLGAN [42]29.1018.90±0.300.52±0.1037.6514.4028.06--
LayoutDiffusion15.6128.36±0.750.57±0.1047.7432.0015.630.59±0.1048.90
", + "bbox": [ + 81, + 597, + 885, + 815 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Quantitative results on COCO-stuff [5] and VG [19]. The proposed diffusion method has made great progress in all evaluation metrics, showing better quality, controllability, diversity, and accuracy than previous works. For COCO-stuff, we evaluate on 3097 layout and sample 5 images for each layout. For VG, we evaluate on 5096 layout and sample 1 image for each layout. We also report reproduction scores of previous works in Appendix.", + "bbox": [ + 75, + 827, + 892, + 883 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "22495", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/eba1a7b455c4549d664c21d4965b340640b0413fc9ded5ccff8eeba74da5c425.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
LFMOaCACAFID ↓IS ↑DS ↑CAS ↑YOLOScore ↑
29.94 (+13.37)13.59±0.29 (-6.58)0.70±0.08 (+0.23)3.83 (-39.77)0.00 (-27.00)
✓17.06 (+0.49)19.21±0.53 (-0.96)0.52±0.09 (+0.05)30.86 (-12.74)6.90 (-20.10)
✓16.76 (+0.19)19.57±0.40 (-0.60)0.48±0.09 (+0.01)40.67 (-2.93)18.80 (-8.20)
✓✓16.46 (-0.11)19.79±0.40 (-0.38)0.48±0.10 (+0.01)42.47 (-1.13)23.60 (-3.40)
✓✓16.5720.17±0.560.47±0.0943.6027.00
", + "bbox": [ + 119, + 82, + 846, + 181 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "of stuff, respectively. Following the settings of LostGANv2 [38], we use the COCO 2017 Stuff Segmentation Challenge subset that contains $40\\mathrm{K} / 5\\mathrm{k} / 5\\mathrm{k}$ images for train / val / test-dev set, respectively. We use images in the train and val set with 3 to 8 objects that cover more than $2\\%$ of the image and not belong to crowd. Finally, there are 25,210 train and 3,097 val images.", + "bbox": [ + 75, + 237, + 470, + 343 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Visual Genome collects 108,077 images with dense annotations of objects, attributes, and relationships. Following the setting of SG2Im [14], we divide the data into $80\\%$ , $10\\%$ , $10\\%$ for the train, val, test set, respectively. We select the object and relationship categories occurring at least 2000 and 500 times in the train set, respectively, and select the images with 3 to 30 bounding boxes and ignoring all small objects. Finally, the training / validation / test set will have 62565 / 5062 / 5096 images, respectively.", + "bbox": [ + 75, + 349, + 468, + 486 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Evaluation Metrics & Protocols", + "text_level": 1, + "bbox": [ + 76, + 496, + 356, + 511 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We use five metrics to evaluate the quality, diversity, and controllability of generation.", + "bbox": [ + 75, + 518, + 468, + 550 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Fr'echet Inception Distance (FID) [9] shows the overall visual quality of the generated image by measuring the difference in the distribution of features between the real images and the generated images on an ImageNet-pretrained Inception-V3 [39] network.", + "bbox": [ + 75, + 550, + 468, + 626 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Inception Score (IS) [33] uses an Inception-V3 [39] pretrained on ImageNet network to compute the statistical score of the output of the generated images.", + "bbox": [ + 75, + 626, + 468, + 672 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Diversity Score (DS) calculates the diversity between two generated images of the same layout by comparing the LPIPS [46] metric in a DNN feature space between them.", + "bbox": [ + 75, + 672, + 468, + 717 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Classification Score (CAS) [28] first crops the ground truth box area of images and resizing them at a resolution of $32 \\times 32$ with their class. A ResNet-101 [8] classifier is trained with generated images and tested on real images.", + "bbox": [ + 75, + 717, + 468, + 779 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "YOLOScore [20] evaluates 80 thing categories bbox mAP on generated images using a pretrained YOLOv4 [4] model, and shows the precision of control in one generated model.", + "bbox": [ + 75, + 779, + 468, + 824 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In summary, FID and IS show the generation quality, DS shows the diversity, CAS and YOLOScore represent the controllability. We follow the architecture of ADM [7], which is mainly a UNet. All experiments are conducted on 32 NVIDIA 3090s with mixed precision training [23]. We", + "bbox": [ + 75, + 824, + 468, + 901 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "set batch size 24, learning rate 1e-5. We adopt the fixed linear variance schedule. More details can be found in the Appendix.", + "bbox": [ + 496, + 237, + 890, + 282 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Qualitative results", + "text_level": 1, + "bbox": [ + 500, + 291, + 678, + 308 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparison of generated $256 \\times 256$ images on the COCO-Stuff [5] with our method and previous works [2, 38, 42] is shown in Fig. 3.", + "bbox": [ + 496, + 315, + 890, + 359 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/57d14e26dec80537031b9feaa6085d103b7686532c405b59db1a5133575bdf8c.jpg", + "table_caption": [ + "Table 2. Ablation study of Layout Fusion Module (LFM), Object-aware Cross Attention (OaCA), Cross Attention (CA). We use the model trained for 300,000 iterations on COCO-stuff $128\\times 128$ . The value in brackets denotes the discrepancy to our proposed method(+LFM+OaCA), where red denotes better and green denotes worse." + ], + "table_footnote": [], + "table_body": "
methodFID ↓NparamsThroughout images / sFirst stage V100 daysCond stage V100 days
LDM-8 (100 steps)42.06345M0.457663.69
LDM-4 (200 steps)40.91306M0.2672995.49
ours-small (25 steps)36.16142M0.608-75.83
ours (25 steps)31.68569M0.308-216.55
", + "bbox": [ + 501, + 362, + 890, + 438 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3. Comparison with SOTA diffusion-based methods LDM on COCO-stuff $256 \\times 256$ . We generate the same 2048 images of LDM for a fair comparison.", + "bbox": [ + 496, + 443, + 890, + 486 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "LayoutDiffusion generates more accurate high quality images, which has more recognizable and accurate objects corresponding to their layouts. Grid2Im [2], LostGANv2 [38] and PLGAN [42] generate images with distorted and unreal objects.", + "bbox": [ + 496, + 487, + 890, + 561 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Especially when input a set of multiple objects with complex relationships, previous work can hardly generate recognizable objects in the position corresponding to layouts. For example, in Fig. 3 (a), (c), and (e), the main objects (e.g. train, zebra, bus) in images are poorly generated in previous work, while our LayoutDiffusion generates well. In Fig. 3 (b), only our LayoutDiffusion generates the laptop in the right place. The images generated by our LayoutDiffusion are more sensorially similar to the real ones.", + "bbox": [ + 496, + 561, + 890, + 698 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We show the diversity of LayoutDiffusion in Fig. 4. Images from the same layouts have high quality and diversity (different lighting, textures, colors, and details).", + "bbox": [ + 496, + 699, + 890, + 743 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We continuously add an additional layout from the initial layout, the one in the upper left corner, as shown in Fig. 5. In each step, LayoutDiffusion adds the new object in very precise locations with consistent image quality, showing user-friendly interactivity.", + "bbox": [ + 496, + 744, + 890, + 819 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Quantitative results", + "text_level": 1, + "bbox": [ + 500, + 823, + 687, + 837 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Tab. 1 provides the comparison among previous works and our method in FID, IS, DS, CAS and YOLOScore. Compared to the SOTA method, the proposed method achieves the best performance in comparison.", + "bbox": [ + 496, + 839, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "22496", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b4b1801920248ead66f3763840650c2b58a990e1e28a82e0d2f7b6c3b8abff1b.jpg", + "image_caption": [ + "Figure 4. The diversity of LayoutDiffusion. Each row of images are from the same layout and have great difference." + ], + "image_footnote": [], + "bbox": [ + 99, + 88, + 444, + 237 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In overall generation quality, our LayoutDiffusion outperforms the SOTA model by $46.35\\%$ and $29.29\\%$ at most in FID and IS, respectively. While maintaining high overall image quality, we also show precise and accurate controllability, LayoutDiffusion outperforms the SOTA model by $122.22\\%$ and $41.82\\%$ at most onYOLOScore and CAS, respectively. As for diversity, our LayoutDiffusion still achieves $11.30\\%$ imporvement at most accroding to the DS. Experiments on these metrics show that our methods can successfully generate the higher-quality images with better location and quantity control.", + "bbox": [ + 75, + 273, + 467, + 436 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In particular, we conduct experiments compared to LDM [30] in Tab. 3. \"Ours-small\" uses comparable GPU resources to have better FID performance with much fewer parameters and better throughout compared to LDM-8 when \"Ours-small\" outperforms LDM-4 in all respects. The results of \"Ours\" indicate that LayoutDiffusion can have better FID performance, 31.6, at a higher cost. From these results, LayoutDiffusion always achieves better performance at different cost levels compared with LDM [30].", + "bbox": [ + 75, + 439, + 467, + 574 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5. Ablation studies", + "text_level": 1, + "bbox": [ + 76, + 577, + 236, + 590 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We validate the effectiveness of LFM and OaCA in Tab. 2, using the evaluation metrics in Sec. 4.2. The significant improvement on FID, IS, CAS, and YOLOScore proves that the application of LFM and OaCA allows for higher generation quality and diversity, along with more controllability. Furthermore, when applying both, considerable performance, $13.37 / 6.58 / 39.77 / 27.0$ on FID / IS / CAS / YOLOScore, is gained.", + "bbox": [ + 75, + 594, + 467, + 715 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "An interesting phenomenon is that the change of the Diversity Score (DS) is in the opposite direction of other metrics. This is because DS, which stands for diversity, is physically the opposite of the controllability represented by other metrics such as CAS and YOLOScore. The precise control offered on generated image leads to more constraints on diversity. As a result, the Diversity Score (DS) has a slight drop compared to the baseline.", + "bbox": [ + 75, + 715, + 467, + 835 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Limitations & Societal Impacts", + "text_level": 1, + "bbox": [ + 76, + 849, + 362, + 866 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitations. Despite the significant improvements in various metrics, it is still difficult to generate a realistic im", + "bbox": [ + 75, + 869, + 467, + 900 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3ad8222c1e0d0c03bccec40d64451255e71ac22e4c2a3fe35045ddb412012c51.jpg", + "image_caption": [ + "Figure 5. The interactivity of LayoutDiffusion. We add extra layout continuously, and the new objects are also with high quality." + ], + "image_footnote": [], + "bbox": [ + 504, + 92, + 883, + 233 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "age with no distortion and overlap, especially for a complex multi-object layout. Moreover, the model is trained from scratch in the specific dataset that requires detection labels. How to combine text-guided diffusion models and inherit parameters pre-trained on massive text-image datasets remains a future research.", + "bbox": [ + 498, + 287, + 890, + 377 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Societal Impacts. Trained on the real-world datasets such as COCO [5] and VG [19], LayoutDiffusion has the powerful ability to learn the distribution of data and we should pay attention to some potential copyright infringement issues.", + "bbox": [ + 498, + 378, + 890, + 439 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 446, + 617, + 460 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we have proposed a one-stage end-to-end diffusion model named LayoutDiffusion, which is novel for the task of layout-to-image generation. With the guidance of layout, the diffusion model allows more control over the individual objects while maintaining higher quality than the prevailing GAN-based methods. By constructing a structural image patch with region information, we regrad each patch as a special object and accomplish the difficult multimodal image layout fusion in a unified form. Specifically, Layout Fusion Module and Object-aware Cross Attention are proposed to model the relationship among multiple objects and fuse the patched image feature with layout at multiple resolutions, respectively. Experiments in challenging COCO-stuff and Visual Genome (VG) show that our proposed method significantly outperforms both state-of-the-art GAN-based and diffusion-based methods in various evaluation metrics.", + "bbox": [ + 496, + 465, + 890, + 720 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements. This work is supported in part by National Natural Science Foundation of China under Grant U20A20222, National Science Foundation for Distinguished Young Scholars under Grant 62225605, National Key Research and Development Program of China under Grant 2020AAA0107400, Research Fund of ARC Lab, Tencent PCG, Zhejiang - Singapore Innovation and AI Joint Research Lab, Ant Group through CCF-Ant Research Fund, and sponsored by CCF-AFSG Research Fund, CAAI-HUAWEI MindSpore Open Fund as well as CCF-Zhipu AI Large Model Fund (CCF-Zhipu202302).", + "bbox": [ + 496, + 734, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "22497", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Martin Arjovsky and Léon Bottou. 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Springer, 2022. 3" + ], + "bbox": [ + 501, + 92, + 890, + 261 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "22499", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/LayoutDiffusion_ Controllable Diffusion Model for Layout-to-Image Generation/b7471e7f-ee4c-4b84-b778-22769e778b1d_model.json b/2023/LayoutDiffusion_ Controllable Diffusion Model for Layout-to-Image Generation/b7471e7f-ee4c-4b84-b778-22769e778b1d_model.json new file mode 100644 index 0000000000000000000000000000000000000000..e09e72c04d064e77c5d9e24ac467369ca10d8d4e --- /dev/null +++ b/2023/LayoutDiffusion_ Controllable Diffusion Model for Layout-to-Image Generation/b7471e7f-ee4c-4b84-b778-22769e778b1d_model.json @@ -0,0 +1,2288 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.229, + 0.131, + 0.744, + 0.177 + ], + "angle": 0, + "content": "LayoutDiffusion: Controllable Diffusion Model for Layout-to-image Generation" + }, + { + "type": "text", + "bbox": [ + 0.128, + 0.203, + 0.851, + 0.293 + ], + "angle": 0, + "content": "Guangcong Zheng\\(^{1*}\\), Xianpan Zhou\\(^{2*}\\), Xuewei Li\\(^{1\\dagger}\\), Zhongang Qi\\(^{3}\\), Ying Shan\\(^{3}\\), Xi Li\\(^{1,4,5,6\\dagger}\\) \n\\(^{1}\\)College of Computer Science & Technology, Zhejiang University \n\\(^{2}\\)Polytechnic Institute, Zhejiang University \\({}^{3}\\)ARC Lab, Tencent PCG \n\\({}^{4}\\)Shanghai Institute for Advanced Study of Zhejiang University \n\\({}^{5}\\)Shanghai AI Lab \\({}^{6}\\)Zhejiang - Singapore Innovation and AI Joint Research Lab" + }, + { + "type": "text", + "bbox": [ + 0.225, + 0.295, + 0.746, + 0.328 + ], + "angle": 0, + "content": "{guangcongzheng, zhouxianpan, xuweili, xilizju}@zju.edu.cn {zhongangqi, yingsshan}@tencent.com" + }, + { + "type": "image_caption", + "bbox": [ + 0.101, + 0.344, + 0.52, + 0.358 + ], + "angle": 0, + "content": "(a) layout-guided vs. text-guided image generation for diffusion model" + }, + { + "type": "image", + "bbox": [ + 0.1, + 0.361, + 0.87, + 0.515 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.571, + 0.345, + 0.83, + 0.359 + ], + "angle": 0, + "content": "(b) Image-Layout Fusion in a unified space" + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.525, + 0.895, + 0.582 + ], + "angle": 0, + "content": "Figure 1. Compared to text, the layout allows diffusion models to obtain more control over the objects while maintaining high quality. Unlike the prevailing methods, we propose a diffusion model named LayoutDiffusion for layout-to-image generation. We transform the difficult multimodal fusion of the image and layout into a unified form by constructing a structural image patch with region information and regarding the patched image as a special layout." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.593, + 0.314, + 0.609 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.625, + 0.474, + 0.868 + ], + "angle": 0, + "content": "Recently, diffusion models have achieved great success in image synthesis. However, when it comes to the layout-to-image generation where an image often has a complex scene of multiple objects, how to make strong control over both the global layout map and each detailed object remains a challenging task. In this paper, we propose a diffusion model named LayoutDiffusion that can obtain higher generation quality and greater controllability than the previous works. To overcome the difficult multimodal fusion of image and layout, we propose to construct a structural image patch with region information and transform the patched image into a special layout to fuse with the normal layout in a unified form. Moreover, Layout Fusion Module (LFM) and Object-aware Cross Attention (OaCA) are proposed to model the relationship among multiple objects and designed to be object-aware and position-sensitive, allow" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.595, + 0.892, + 0.687 + ], + "angle": 0, + "content": "ing for precisely controlling the spatial related information. Extensive experiments show that our LayoutDiffusion outperforms the previous SOTA methods on FID, CAS by relatively \\(46.35\\%\\), \\(26.70\\%\\) on COCO-stuff and \\(44.29\\%\\), \\(41.82\\%\\) on VG. Code is available at https://github.com/ZGCTroy/LayoutDiffusion." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.708, + 0.633, + 0.723 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Recently, the diffusion model has achieved encouraging progress in conditional image generation, especially in text-to-image generation such as GLIDE [24], Imagen [31], and Stable Diffusion [30]. However, text-guided diffusion models may still fail in the following situations. As shown in Fig. 1 (a), when aiming to generate a complex image with multiple objects, it is hard to design a prompt properly and comprehensively. Even input with well-designed prompts, problems such as missing objects and incorrectly generating objects' positions, shapes, and categories still occur in the state-of-the-art text-guided diffusion model [24, 30, 31]." + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.875, + 0.208, + 0.888 + ], + "angle": 0, + "content": "* Equal contribution." + }, + { + "type": "page_footnote", + "bbox": [ + 0.097, + 0.888, + 0.222, + 0.9 + ], + "angle": 0, + "content": "† Corresponding author." + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.875, + 0.222, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "22490" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.213 + ], + "angle": 0, + "content": "This is mainly due to the ambiguity of the text and its weakness in precisely expressing the position of the image space. Fortunately, this is not a problem when using the coarse layout as guidance, which is a set of objects with the annotation of the bounding box (bbox) and object category. With both spatial and high-level semantic information, the diffusion model can obtain more powerful controllability while maintaining the high quality." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.215, + 0.473, + 0.352 + ], + "angle": 0, + "content": "However, early studies [2, 14, 38, 42] on layout-to-image generation are almost limited to generative adversarial networks (GANs) and often suffer from unstable convergence [1] and mode collapse [27]. Despite the advantages of diffusion models in easy training [10] and significant quality improvement [7], few studies have considered applying diffusion in the layout-to-image generation task. To our knowledge, only LDM [30] supports the condition of layout and has shown encouraging progress in this field." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.355, + 0.473, + 0.627 + ], + "angle": 0, + "content": "In this paper, different from LDM that applies the simple multimodal fusion method (e.g., the cross attention) or direct input concatenation for all conditional input, we aim to specifically design the fusion mechanism between layout and image. Moreover, instead of conditioning only in the second stage like LDM, we propose an end-to-end one-stage model that considers the condition for the whole process, which may have the potential to help mitigate loss in the task that requires fine-grained accuracy in pixel space [30]. The fusion between image and layout is a difficult multimodal fusion problem. Compared to the fusion of text and image, the layout has more restrictions on the position, size, and category of objects. This requires a higher controllability of the model and often leads to a decrease in the naturalness and diversity of the generated image. Furthermore, the layout is more sensitive to each token and the loss in token of layout will directly lead to the missing objects." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.629, + 0.473, + 0.902 + ], + "angle": 0, + "content": "To address the problems mentioned above, we propose treating the patched image and the input layout in a unified form. Specifically, we construct a structural image patch at multi-resolution by adding the concept of region that contains information of position and size. As a result, each patch of the image is transformed into a special type of object, and the entire patched image will also be regarded as a layout. Finally, the difficult problem of multimodal fusion between image and layout will be transformed into a simple fusion with a unified form in the same spatial space of the image. We name our model LayoutDiffusion, a layout-conditional diffusion model with Layout Fusion Module (LFM), object-aware Cross Attention Mechanism (OaCA), and corresponding classifier-free training and sampling scheme. In detail, LFM fuses the information of each object and models the relationship among multiple objects, providing a latent representation of the entire layout. To make the model pay more attention to the information re" + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.092, + 0.895, + 0.212 + ], + "angle": 0, + "content": "lated to the object, we propose an object-aware fusion module named OaCA. Cross-attention is made between the image patch feature and layout in a unified coordinate space by representing the positions of both of them as bounding boxes. To further improve the user experience of LayoutDiffusion, we also make several optimizations on the speed of the classifier-free sampling process and could significantly outperform the SOTA models in 25 iterations." + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.213, + 0.895, + 0.287 + ], + "angle": 0, + "content": "Experiments are conducted on COCO-stuff [5] and Visual Genome (VG) [19]. Various metrics ranging from quality, diversity, and controllability show that LayoutDiffusion significantly outperforms both state-of-the-art GAN-based and diffusion-based methods." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.289, + 0.771, + 0.302 + ], + "angle": 0, + "content": "Our main contribution is listed below." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.316, + 0.892, + 0.406 + ], + "angle": 0, + "content": "- Instead of using the dominated GAN-based methods, we propose a diffusion model named LayoutDiffusion for layout-to-image generations, which can generate images with both high-quality and diversity while maintaining precise control over the position and size of multiple objects." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.417, + 0.892, + 0.492 + ], + "angle": 0, + "content": "- We propose to treat each patch of the image as a special object and accomplish the difficult multimodal fusion of layout and image in a unified form. LFM and OaCA are then proposed to fuse the multi-resolution image patches with user's input layout." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.502, + 0.892, + 0.561 + ], + "angle": 0, + "content": "- LayoutDiffusion outperforms the SOTA layout-to-image generation method on FID, DS, CAS by relatively around \\(46.35\\%\\), \\(9.61\\%\\), \\(26.70\\%\\) on COCO-stuff and \\(44.29\\%\\), \\(11.30\\%\\), \\(41.82\\%\\) on VG." + }, + { + "type": "list", + "bbox": [ + 0.519, + 0.316, + 0.892, + 0.561 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.576, + 0.638, + 0.592 + ], + "angle": 0, + "content": "2. Related work" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.602, + 0.892, + 0.632 + ], + "angle": 0, + "content": "The related works are mainly from layout-to-image generation and diffusion models." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Layout-to-Image Generation. Before the layout-to-image generation is formally proposed, the layout is usually used as a complementary feature [15, 29, 40] or an intermediate representation in text-to-image [12], scene-to-image generation [14]. The first image generation directly from the layout appears in Layout2Im [47] and is defined as a set of objects annotated with category and bbox. Models that work well with fine-grained semantic maps at the pixel level can also be easily transformed to this setting [13, 26, 43]. Inspired by StyleGAN [16], LostGAN-v1 [37], LostGAN-v2 [38] used a reconfigurable layout to obtain better control over individual objects. For interactive image synthesis, PLGAN [42] employed panoptic theory [18] by constructing stuff and instance layouts into separate branches and proposed Instance- and Stuff-Aware Normalization to fuse into panoptic layouts. Despite encouraging progress in this field, almost all approaches are limited to the generative" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "22491" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.471, + 0.168 + ], + "angle": 0, + "content": "adversarial network (GAN) and may suffer from unstable convergence [1] and mode collapse [27]. As a multimodal diffusion model, LDM [30] supports the condition of coarse layout and has shown great potential in layout-guided image generation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.194, + 0.473, + 0.438 + ], + "angle": 0, + "content": "Diffusion Model. Diffusion models [3, 10, 25, 30, 34-36, 44] are being recognized as a promising family of generative models that have proven to be state-of-the-art sample quality for a variety of image generation benchmarks [6, 41, 45], including class-conditional image generation [7, 48], text-to-image generation [24, 30, 31], and imaged-to-image translation [17, 22, 32]. Classifier guidance was introduced in ADM-G [7] to allow diffusion models to condition the class label. The gradient of the classifier trained on noised images could be added to the image during the sampling process. Then Ho et al. [11] proposed a classifier-free training and sampling strategy by interpolating between predictions of a diffusion model with and without condition input. For the acceleration of training and sampling speed, LDM proposed to first compress the image into smaller resolution and then apply denoising training in the latent space." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.454, + 0.168, + 0.469 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.481, + 0.47, + 0.618 + ], + "angle": 0, + "content": "In this section, we propose our LayoutDiffusion, as shown in Fig. 2. The whole framework consists mainly of four parts: (a) layout embedding that preprocesses the layout input, (b) layout fusion module that encourages more interaction between objects of layout, (c) image-Layout fusion module that constructs the structural image patch and object-aware cross attention developed with the specific design for layout and image fusion, (d) the layout-conditional diffusion model with training and accelerated sampling methods." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.631, + 0.264, + 0.648 + ], + "angle": 0, + "content": "3.1. Layout Embedding" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.656, + 0.469, + 0.717 + ], + "angle": 0, + "content": "A layout \\( l = \\{o_1, o_2, \\dots, o_n\\} \\) is a set of \\( n \\) objects. Each object \\( o_i \\) is represented as \\( o_i = \\{b_i, c_i\\} \\), where \\( b_i = (x_0^i, y_0^i, x_1^i, y_1^i) \\in [0, 1]^4 \\) denotes a bounding box (bbox) and \\( c_i \\in [0, \\mathcal{C} + 1] \\) is its category id." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.718, + 0.469, + 0.824 + ], + "angle": 0, + "content": "To support the input of a variable length sequence, we need to pad \\( l \\) to a fixed length \\( k \\) by adding one \\( o_l \\) in the front and some padding \\( o_p \\) in the end, where \\( o_l \\) represents the entire layout and \\( o_p \\) represents no object. Specifically, \\( b_l = (0, 0, 1, 1) \\), \\( c_l = 0 \\) denotes a object that covers the whole image and \\( b_p = (0, 0, 0, 0) \\), \\( c_p = \\mathcal{C} + 1 \\) denotes a empty object that has no shape or does not appear in the image." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.825, + 0.47, + 0.902 + ], + "angle": 0, + "content": "After the padding process, we can get a padded \\( l = \\{o_1, o_2, \\dots, o_k\\} \\) consisting of \\( k \\) objects, and each object has its specific position, size, and category. Then, the layout \\( l \\) is transformed into a layout embedding \\( L = \\{O_1, O_2, \\dots, O_k\\} \\in \\mathbb{R}^{k \\times d_{\\mathcal{L}}} \\) by the projection matrix \\( W_{\\mathcal{B}} \\in \\)" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.091, + 0.86, + 0.108 + ], + "angle": 0, + "content": "\\(\\mathbb{R}^{4\\times d_{\\mathcal{L}}}\\) and \\(W_{\\mathcal{C}}\\in \\mathbb{R}^{1\\times d_{\\mathcal{L}}}\\) using the following equation:" + }, + { + "type": "equation", + "bbox": [ + 0.647, + 0.119, + 0.892, + 0.135 + ], + "angle": 0, + "content": "\\[\nL = B _ {\\mathcal {L}} + C _ {\\mathcal {L}} \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.654, + 0.138, + 0.891, + 0.154 + ], + "angle": 0, + "content": "\\[\nB _ {\\mathcal {L}} = b W _ {\\mathcal {B}} \\tag {2}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.654, + 0.157, + 0.891, + 0.173 + ], + "angle": 0, + "content": "\\[\nC _ {\\mathcal {L}} = c W _ {C} \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.186, + 0.892, + 0.263 + ], + "angle": 0, + "content": "where \\(B_{\\mathcal{L}}, C_{\\mathcal{L}} \\in \\mathbb{R}^{k \\times d_{\\mathcal{L}}}\\) are the bounding box embedding and the category embedding of a layout \\(l\\), respectively. As a result, \\(L\\) is defined as the sum of \\(B_{\\mathcal{L}}\\) and \\(C_{\\mathcal{L}}\\) to include both the content and positional information of a entire layout, and \\(d_{\\mathcal{L}}\\) is the dimension of the layout embedding." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.272, + 0.712, + 0.287 + ], + "angle": 0, + "content": "3.2. Layout Fusion Module" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.295, + 0.892, + 0.431 + ], + "angle": 0, + "content": "Currently, each object in layout has no relationship with other objects. This leads to a low understanding of the whole scene, especially when multiple objects overlap and block each other. Therefore, to encourage more interaction between multiple objects of the layout to better understand the entire layout before inputting the layout embedding, we propose Layout Fusion Module (LFM), a transformer encoder that uses multiple layers of self-attention to fuse the layout embedding and can be denoted as" + }, + { + "type": "equation", + "bbox": [ + 0.645, + 0.443, + 0.891, + 0.459 + ], + "angle": 0, + "content": "\\[\nL ^ {\\prime} = \\operatorname {L F M} (L) \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.472, + 0.891, + 0.504 + ], + "angle": 0, + "content": ", where the output is a fused layout embedding \\(L^{\\prime} = \\{O_{1}^{\\prime},O_{2}^{\\prime},\\dots ,O_{k}^{\\prime}\\} \\in \\mathbb{R}^{k\\times d_{\\mathcal{L}}}\\)" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.512, + 0.766, + 0.527 + ], + "angle": 0, + "content": "3.3. Image-Layout Fusion Module" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.535, + 0.892, + 0.655 + ], + "angle": 0, + "content": "Structural Image Patch. The fusion of image and layout is a difficult multimodal fusion problem, and one of the most important parts lies in the fusion of position and size. However, the image patch is limited to the semantic information of the whole feature and lacks the spatial information. Therefore, we construct a structural image patch by adding the concept of region that contains the information of position and size." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.655, + 0.892, + 0.733 + ], + "angle": 0, + "content": "Specifically, \\(I \\in \\mathbb{R}^{h \\times w \\times d_{\\mathcal{I}}}\\) denotes the feature map of a entire image with height \\(h\\), width \\(w\\), and channel \\(d_{\\mathcal{I}}\\). We define that \\(I_{u,v}\\) is the \\(u^{\\mathrm{th}}\\) row and \\(v^{\\mathrm{th}}\\) column patch of \\(I\\) and its bounding box, or the ablated region information, is defined as \\(b_{I_{u,v}}\\) by the following equation:" + }, + { + "type": "equation", + "bbox": [ + 0.602, + 0.744, + 0.891, + 0.773 + ], + "angle": 0, + "content": "\\[\nb _ {\\mathcal {I} _ {u, v}} = \\left(\\frac {u}{h}, \\frac {v}{w}, \\frac {u + 1}{h}, \\frac {v + 1}{w}\\right) \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.783, + 0.892, + 0.859 + ], + "angle": 0, + "content": "The bounding box sets of a patched image \\(I\\) is defined as \\(b_{\\mathcal{I}} = \\{b_{\\mathcal{I}_{u,v}}|u\\in [0,h),v\\in [0,w)\\}\\). As a result, the positional information of image patch and layout object is contained in the unified bounding box defined in the same spatial space, leading to better fusion of image and layout." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Positional Embedding in Unified Space. We define the positional embedding of the image and layout as \\( P_{\\mathcal{I}} \\) and" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "22492" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.087, + 0.891, + 0.241 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.078, + 0.242, + 0.516, + 0.449 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.524, + 0.242, + 0.89, + 0.449 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.456, + 0.893, + 0.514 + ], + "angle": 0, + "content": "Figure 2. The whole pipeline of LayoutDiffusion. The layout that consisted of bounding box \\( b \\) and objects categories \\( c \\) is transformed into embedding \\( B_{\\mathcal{L}}, C_{\\mathcal{L}}, L \\). Then Layout Fusion Module fuses layout embedding \\( L \\) to output the fused layout embedding \\( L' \\). Finally, Image-Layout Fusion Module including direct addition used for global conditioning and Object-aware Cross Attention (OaCA) used for local conditioning, will fuse the layout related \\( B_{\\mathcal{L}}, C_{\\mathcal{L}}, L' \\) and the image feature \\( I \\) at multiple resolutions." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.54, + 0.177, + 0.554 + ], + "angle": 0, + "content": "\\(P_{\\mathcal{L}}\\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.225, + 0.561, + 0.469, + 0.577 + ], + "angle": 0, + "content": "\\[\nB _ {\\mathcal {I}} = b _ {\\mathcal {I}} W _ {\\mathcal {B}} \\tag {6}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.228, + 0.58, + 0.469, + 0.595 + ], + "angle": 0, + "content": "\\[\nP _ {\\mathcal {I}} = B _ {\\mathcal {I}} W _ {\\mathcal {P}} \\tag {7}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.228, + 0.599, + 0.469, + 0.614 + ], + "angle": 0, + "content": "\\[\nP _ {\\mathcal {L}} = B _ {\\mathcal {L}} W _ {\\mathcal {P}} \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.622, + 0.47, + 0.699 + ], + "angle": 0, + "content": ", where \\( W_{\\mathcal{B}} \\in \\mathbb{R}^{4 \\times d_{\\mathcal{L}}} \\) is defined in Eq. 2 and works as a shared projection matrix that transforms the coordinates of bounding box into embedding of \\( d_{\\mathcal{L}} \\) dimension. \\( W_{\\mathcal{P}} \\in \\mathbb{R}^{d_{\\mathcal{L}} \\times d_{\\mathcal{I}}} \\) is the projection matrix that transforms the \\( B \\) to the positional Embedding \\( P \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.715, + 0.469, + 0.849 + ], + "angle": 0, + "content": "Pointwise Addition for Global Conditioning. With the help of LFM in Eq. 4, \\(O_1'\\) can be considered as a global information of the entire layout, and \\(O_i'(i \\in [2, k])\\) is considered as the local information embedding of single object along with the other related objects. One of the easiest ways to condition the layout in the image is to directly add \\(O_1'\\), the global information of the layout, to the multiple resolution of image features. Specifically, the condition process can be defined as" + }, + { + "type": "equation", + "bbox": [ + 0.219, + 0.849, + 0.469, + 0.868 + ], + "angle": 0, + "content": "\\[\nI ^ {\\prime} = I + O _ {1} ^ {\\prime} W \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.87, + 0.47, + 0.902 + ], + "angle": 0, + "content": ", where \\(W \\in \\mathbb{R}^{d_{\\mathcal{L}} \\times d_{\\mathcal{I}}}\\) is a projection matrix and \\(I'\\) is the image feature conditioned with global embedding of layout." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.54, + 0.892, + 0.554 + ], + "angle": 0, + "content": "Object-aware Cross Attention for Local Conditioning." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.555, + 0.892, + 0.63 + ], + "angle": 0, + "content": "Cross attention is successfully applied in [24] to condition text into image feature, where the sequence of the image patch is used as the query and the concatenated sequence of the image patch and text is applied as key and value. The equation of cross-attention is defined as" + }, + { + "type": "equation", + "bbox": [ + 0.531, + 0.642, + 0.892, + 0.678 + ], + "angle": 0, + "content": "\\[\n\\operatorname {A t t e n t i o n} (Q, K, V) = \\operatorname {s o f t m a x} \\left(\\frac {Q K ^ {T}}{\\sqrt {d _ {k}}}\\right) V \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.688, + 0.891, + 0.749 + ], + "angle": 0, + "content": ", where \\( Q, K, V \\) represent the embeddings of query, key, and value, respectively. In the following paper, we will use the subscript image and layout to represent the image patch feature and layout feature, respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In text-to-image generation, each token in the text sequence is a word. The aggregation of these words constitutes the semantics of a sentence. After the transformer encoder, the first token in text sequence is well-semantic information that generalizes the whole text but may not reverse the semantic meaning of each word. However, the loss in information of one token is relatively serious in layout rather than in text. Each token in the layout sequence is a single object with a specific category, size, and position. The loss of information on a layout token will directly lead" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "22493" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.12 + ], + "angle": 0, + "content": "to a missing or wrong object in the generated image pixel space." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.122, + 0.469, + 0.166 + ], + "angle": 0, + "content": "Therefore, we take into account the fusion of locations, size, and category of objects and define our object-aware cross-attention (OaCA) as" + }, + { + "type": "equation", + "bbox": [ + 0.151, + 0.179, + 0.469, + 0.195 + ], + "angle": 0, + "content": "\\[\nQ = \\Psi_ {1} \\left(Q _ {\\mathcal {I}}, Q _ {\\mathcal {L}}\\right) \\tag {11}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.15, + 0.198, + 0.469, + 0.214 + ], + "angle": 0, + "content": "\\[\nK = \\Psi_ {1} \\left(\\Psi_ {2} \\left(K _ {\\mathcal {I}}, K _ {\\mathcal {L}}\\right), \\Psi_ {2} \\left(P _ {\\mathcal {I}}, P _ {\\mathcal {L}}\\right)\\right) \\tag {12}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.152, + 0.217, + 0.469, + 0.233 + ], + "angle": 0, + "content": "\\[\nV = \\Psi_ {2} \\left(V _ {\\mathcal {I}}, V _ {\\mathcal {L}}\\right) \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.245, + 0.469, + 0.307 + ], + "angle": 0, + "content": ", where the query \\(Q \\in \\mathbb{R}^{hw \\times 2d_{\\mathcal{I}}}\\), \\(K \\in \\mathbb{R}^{(hw + k) \\times 2d_{\\mathcal{I}}}\\), and \\(V \\in \\mathbb{R}^{(hw + k) \\times d_{\\mathcal{I}}}\\). \\(\\Psi_1\\) and \\(\\Psi_2\\) denote concatenation on the dimension of the channel and length of the sequence, respectively." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.308, + 0.424, + 0.322 + ], + "angle": 0, + "content": "We first construct the key and value of the layout:" + }, + { + "type": "equation", + "bbox": [ + 0.142, + 0.333, + 0.469, + 0.362 + ], + "angle": 0, + "content": "\\[\nK _ {\\mathcal {L}}, V _ {\\mathcal {L}} = \\operatorname {C o n v} \\left(\\frac {1}{2} \\left(\\operatorname {N o r m} \\left(C _ {\\mathcal {L}}\\right) + L ^ {\\prime}\\right)\\right) \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.373, + 0.469, + 0.509 + ], + "angle": 0, + "content": ", where \\( K_{\\mathcal{L}}, V_{\\mathcal{L}} \\in \\mathbb{R}^{k \\times d_{\\mathcal{I}}} \\) and Conv is the convolution operation. The embedding of key and value in the layout is related to the category embedding \\( C_{\\mathcal{L}} \\) and the fused layout embedding \\( L' \\). \\( C_{\\mathcal{L}} \\) focuses on the category information of layout and \\( L' \\) concentrates on the comprehensive information of both the object itself and other objects that may have a relationship with it. By averaging between \\( L' \\) and \\( C_{\\mathcal{L}} \\), we can obtain both the general information of the object and also emphasize the category information of the object." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.51, + 0.469, + 0.539 + ], + "angle": 0, + "content": "We construct the query, key, and value of the image feature as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.165, + 0.551, + 0.469, + 0.568 + ], + "angle": 0, + "content": "\\[\nQ _ {\\mathcal {I}}, K _ {\\mathcal {I}}, V _ {\\mathcal {I}} = \\operatorname {C o n v} (\\operatorname {N o r m} (I)) \\tag {15}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.579, + 0.388, + 0.594 + ], + "angle": 0, + "content": "3.4. Layout-conditional Diffusion Model" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.602, + 0.469, + 0.678 + ], + "angle": 0, + "content": "Here, we follow the Gaussian diffusion models improved by [10, 35]. Given a data point sampled from a real data distribution \\( x_0 \\sim q(x_0) \\), a forward diffusion process is defined by adding small amount of Gaussian noise to the \\( x_0 \\) in \\( T \\) steps:" + }, + { + "type": "equation", + "bbox": [ + 0.117, + 0.69, + 0.469, + 0.707 + ], + "angle": 0, + "content": "\\[\nq \\left(x _ {t} \\mid x _ {t - 1}\\right) := \\mathcal {N} \\left(x _ {t}; \\sqrt {\\alpha_ {t}} x _ {t - 1}, (1 - \\alpha_ {t}) \\mathbf {I}\\right) \\tag {16}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.718, + 0.469, + 0.869 + ], + "angle": 0, + "content": "If the total noise added throughout the Markov chain is large enough, the \\( x_{T} \\) will be well approximated by \\( \\mathcal{N}(0,\\mathbf{I}) \\). If we add noise at each step with a sufficiently small magnitude \\( 1 - \\alpha_{t} \\), the posterior \\( q(x_{t - 1}|x_t) \\) will be well approximated by a diagonal Gaussian. This nice property ensures that we can reverse the above forward process and sample from \\( x_{T}\\sim \\mathcal{N}(0,\\mathbf{I}) \\), which is a Gaussian noise. However, since the entire dataset is needed, we are unable to easily estimate the posterior. Instead, we have to learn a model \\( p_{\\theta}(x_{t - 1}|x_t) \\) to approximate it:" + }, + { + "type": "equation", + "bbox": [ + 0.153, + 0.881, + 0.469, + 0.898 + ], + "angle": 0, + "content": "\\[\np _ {\\theta} \\left(x _ {t - 1} \\mid x _ {t}\\right) := \\mathcal {N} \\left(\\mu_ {\\theta} \\left(x _ {t}\\right), \\Sigma_ {\\theta} \\left(x _ {t}\\right)\\right) \\tag {17}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.198 + ], + "angle": 0, + "content": "Instead of using the tractable variational lower bound (VLB) in \\(\\log p_{\\theta}(x_0)\\), Ho et al. [10] proposed to reweight the terms of the VLB to optimize a surrogate objective. Specifically, we first add \\(t\\) steps of Gaussian noise to a clean sample \\(x_0\\) to generate a noised sample \\(x_{t} \\sim q(x_{t}|x_{0})\\). Then train a model \\(\\epsilon_{\\theta}\\) to predict the added noise using the following loss:" + }, + { + "type": "equation", + "bbox": [ + 0.521, + 0.209, + 0.892, + 0.227 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} := E _ {t \\sim [ 1, T ], x _ {0} \\sim q (x _ {0}), \\epsilon \\sim \\mathcal {N} (0, \\mathbf {I})} [ \\| \\epsilon - \\epsilon_ {\\theta} (x _ {t}, t) \\| ^ {2} ] \\tag {18}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.239, + 0.803, + 0.253 + ], + "angle": 0, + "content": ", which is a standard mean-squared error loss." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.253, + 0.892, + 0.405 + ], + "angle": 0, + "content": "To support the layout condition, we apply classifier-free guidance, a technique proposed by Ho et al. [11] for conditional generation that requires no additional training of the classifier. It is accomplished by interpolating between predictions of a diffusion model with and without condition input. For the condition of layout, we first construct a padding layout \\( l_{\\phi} = \\{o_l,o_p,\\dots ,o_p\\} \\). During training, the condition of layout \\( l \\) of diffusion model will be replaced with \\( l_{\\phi} \\) with a fixed probability. When sampling, the following equation is used to sample a layout-condional image:" + }, + { + "type": "equation", + "bbox": [ + 0.522, + 0.416, + 0.892, + 0.433 + ], + "angle": 0, + "content": "\\[\n\\hat {\\epsilon} _ {\\theta} \\left(x _ {t}, t | l\\right) = (1 - s) \\cdot \\epsilon_ {\\theta} \\left(x _ {t}, t \\mid l _ {\\phi}\\right) + s \\cdot \\epsilon_ {\\theta} \\left(x _ {t}, t \\mid l\\right) \\tag {19}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.445, + 0.891, + 0.489 + ], + "angle": 0, + "content": ", where the scale \\(s\\) can be used to increase the gap between \\(\\epsilon_{\\theta}(x_t,t|l_\\phi)\\) and \\(\\epsilon_{\\theta}(x_t,t|l)\\) to enhance the strength of conditional guidance." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.49, + 0.892, + 0.611 + ], + "angle": 0, + "content": "To further improve the user experience of LayoutDiffusion, we also make several optimizations on the speed of the classifier-free sampling process and could significantly outperform the SOTA models in 25 iterations. Specifically, we adapt DPM-solver [21] for the conditional classifier-free sampling, a fast dedicated high-order solver for diffusion ODEs [36] with the convergence order guarantee, to accelerate the conditional sampling speed." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.625, + 0.632, + 0.642 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.65, + 0.892, + 0.785 + ], + "angle": 0, + "content": "In this section, we evaluate our LayoutDiffusion on different benchmarks in terms of various metrics. First, we introduce the datasets and evaluation metrics. Second, we show the qualitative and quantitative results compared with other strategies. Finally, some ablation studies and analysis are also mentioned. More details can be found in Appendix, including model architecture, training hyperparameters, reproduction results, more experimental results and visualizations." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.796, + 0.602, + 0.81 + ], + "angle": 0, + "content": "4.1. Datasets" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.819, + 0.89, + 0.849 + ], + "angle": 0, + "content": "We conduct our experiments on two popular datasets, COCO-Stuff [5] and Visual Genome [19]." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "COCO-Stuff has 164K images from COCO 2017, of which the images contain bounding boxes and pixel-level segmentation masks for 80 categories of thing and 91 categories" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "22494" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.092, + 0.887, + 0.543 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.559, + 0.893, + 0.587 + ], + "angle": 0, + "content": "Figure 3. Visualization of comparison with SOTA methods on COCO-stuff \\(256 \\times 256\\). LayoutDiffusion has better generation quality and stronger controllability compared to the other methods." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.598, + 0.887, + 0.816 + ], + "angle": 0, + "content": "
MethodsCOCO-stuffVG
FID ↓IS ↑DS ↑CAS ↑YOLOScore ↑FID ↓DS ↑CAS ↑
128×128
Grid2Im [2]59.5012.50±0.300.28±0.114.056.80---
LostGAN-v2 [38]24.7614.21±0.400.45±0.0939.9113.6029.000.42±0.0929.74
PLGAN [42]22.7015.60±0.300.16±0.7238.7013.4020.62--
LayoutDiffusion16.5720.17±0.560.47±0.0943.6027.0016.350.49±0.0936.45
256×256
Grid2Im [2]65.2016.40±0.700.34±0.134.819.70---
LostGAN-v2 [38]31.1818.01±0.500.56±0.1040.0017.5032.080.53±0.1034.48
PLGAN [42]29.1018.90±0.300.52±0.1037.6514.4028.06--
LayoutDiffusion15.6128.36±0.750.57±0.1047.7432.0015.630.59±0.1048.90
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.828, + 0.893, + 0.884 + ], + "angle": 0, + "content": "Table 1. Quantitative results on COCO-stuff [5] and VG [19]. The proposed diffusion method has made great progress in all evaluation metrics, showing better quality, controllability, diversity, and accuracy than previous works. For COCO-stuff, we evaluate on 3097 layout and sample 5 images for each layout. For VG, we evaluate on 5096 layout and sample 1 image for each layout. We also report reproduction scores of previous works in Appendix." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "22495" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.12, + 0.083, + 0.847, + 0.182 + ], + "angle": 0, + "content": "
LFMOaCACAFID ↓IS ↑DS ↑CAS ↑YOLOScore ↑
29.94 (+13.37)13.59±0.29 (-6.58)0.70±0.08 (+0.23)3.83 (-39.77)0.00 (-27.00)
✓17.06 (+0.49)19.21±0.53 (-0.96)0.52±0.09 (+0.05)30.86 (-12.74)6.90 (-20.10)
✓16.76 (+0.19)19.57±0.40 (-0.60)0.48±0.09 (+0.01)40.67 (-2.93)18.80 (-8.20)
✓✓16.46 (-0.11)19.79±0.40 (-0.38)0.48±0.10 (+0.01)42.47 (-1.13)23.60 (-3.40)
✓✓16.5720.17±0.560.47±0.0943.6027.00
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.187, + 0.895, + 0.23 + ], + "angle": 0, + "content": "Table 2. Ablation study of Layout Fusion Module (LFM), Object-aware Cross Attention (OaCA), Cross Attention (CA). We use the model trained for 300,000 iterations on COCO-stuff \\(128\\times 128\\) . The value in brackets denotes the discrepancy to our proposed method(+LFM+OaCA), where red denotes better and green denotes worse." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.238, + 0.471, + 0.344 + ], + "angle": 0, + "content": "of stuff, respectively. Following the settings of LostGANv2 [38], we use the COCO 2017 Stuff Segmentation Challenge subset that contains \\(40\\mathrm{K} / 5\\mathrm{k} / 5\\mathrm{k}\\) images for train / val / test-dev set, respectively. We use images in the train and val set with 3 to 8 objects that cover more than \\(2\\%\\) of the image and not belong to crowd. Finally, there are 25,210 train and 3,097 val images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.35, + 0.47, + 0.487 + ], + "angle": 0, + "content": "Visual Genome collects 108,077 images with dense annotations of objects, attributes, and relationships. Following the setting of SG2Im [14], we divide the data into \\(80\\%\\), \\(10\\%\\), \\(10\\%\\) for the train, val, test set, respectively. We select the object and relationship categories occurring at least 2000 and 500 times in the train set, respectively, and select the images with 3 to 30 bounding boxes and ignoring all small objects. Finally, the training / validation / test set will have 62565 / 5062 / 5096 images, respectively." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.497, + 0.357, + 0.512 + ], + "angle": 0, + "content": "4.2. Evaluation Metrics & Protocols" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.52, + 0.47, + 0.551 + ], + "angle": 0, + "content": "We use five metrics to evaluate the quality, diversity, and controllability of generation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.551, + 0.47, + 0.627 + ], + "angle": 0, + "content": "Fr'echet Inception Distance (FID) [9] shows the overall visual quality of the generated image by measuring the difference in the distribution of features between the real images and the generated images on an ImageNet-pretrained Inception-V3 [39] network." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.627, + 0.47, + 0.673 + ], + "angle": 0, + "content": "Inception Score (IS) [33] uses an Inception-V3 [39] pretrained on ImageNet network to compute the statistical score of the output of the generated images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.673, + 0.47, + 0.718 + ], + "angle": 0, + "content": "Diversity Score (DS) calculates the diversity between two generated images of the same layout by comparing the LPIPS [46] metric in a DNN feature space between them." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.718, + 0.47, + 0.78 + ], + "angle": 0, + "content": "Classification Score (CAS) [28] first crops the ground truth box area of images and resizing them at a resolution of \\(32 \\times 32\\) with their class. A ResNet-101 [8] classifier is trained with generated images and tested on real images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.47, + 0.825 + ], + "angle": 0, + "content": "YOLOScore [20] evaluates 80 thing categories bbox mAP on generated images using a pretrained YOLOv4 [4] model, and shows the precision of control in one generated model." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.47, + 0.902 + ], + "angle": 0, + "content": "In summary, FID and IS show the generation quality, DS shows the diversity, CAS and YOLOScore represent the controllability. We follow the architecture of ADM [7], which is mainly a UNet. All experiments are conducted on 32 NVIDIA 3090s with mixed precision training [23]. We" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.238, + 0.892, + 0.283 + ], + "angle": 0, + "content": "set batch size 24, learning rate 1e-5. We adopt the fixed linear variance schedule. More details can be found in the Appendix." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.292, + 0.679, + 0.309 + ], + "angle": 0, + "content": "4.3. Qualitative results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.316, + 0.892, + 0.361 + ], + "angle": 0, + "content": "Comparison of generated \\(256 \\times 256\\) images on the COCO-Stuff [5] with our method and previous works [2, 38, 42] is shown in Fig. 3." + }, + { + "type": "table", + "bbox": [ + 0.503, + 0.363, + 0.892, + 0.439 + ], + "angle": 0, + "content": "
methodFID ↓NparamsThroughout images / sFirst stage V100 daysCond stage V100 days
LDM-8 (100 steps)42.06345M0.457663.69
LDM-4 (200 steps)40.91306M0.2672995.49
ours-small (25 steps)36.16142M0.608-75.83
ours (25 steps)31.68569M0.308-216.55
" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.444, + 0.892, + 0.487 + ], + "angle": 0, + "content": "Table 3. Comparison with SOTA diffusion-based methods LDM on COCO-stuff \\(256 \\times 256\\). We generate the same 2048 images of LDM for a fair comparison." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.488, + 0.892, + 0.563 + ], + "angle": 0, + "content": "LayoutDiffusion generates more accurate high quality images, which has more recognizable and accurate objects corresponding to their layouts. Grid2Im [2], LostGANv2 [38] and PLGAN [42] generate images with distorted and unreal objects." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.563, + 0.892, + 0.699 + ], + "angle": 0, + "content": "Especially when input a set of multiple objects with complex relationships, previous work can hardly generate recognizable objects in the position corresponding to layouts. For example, in Fig. 3 (a), (c), and (e), the main objects (e.g. train, zebra, bus) in images are poorly generated in previous work, while our LayoutDiffusion generates well. In Fig. 3 (b), only our LayoutDiffusion generates the laptop in the right place. The images generated by our LayoutDiffusion are more sensorially similar to the real ones." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.7, + 0.892, + 0.744 + ], + "angle": 0, + "content": "We show the diversity of LayoutDiffusion in Fig. 4. Images from the same layouts have high quality and diversity (different lighting, textures, colors, and details)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.745, + 0.892, + 0.82 + ], + "angle": 0, + "content": "We continuously add an additional layout from the initial layout, the one in the upper left corner, as shown in Fig. 5. In each step, LayoutDiffusion adds the new object in very precise locations with consistent image quality, showing user-friendly interactivity." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.824, + 0.689, + 0.838 + ], + "angle": 0, + "content": "4.4. Quantitative results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Tab. 1 provides the comparison among previous works and our method in FID, IS, DS, CAS and YOLOScore. Compared to the SOTA method, the proposed method achieves the best performance in comparison." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "22496" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.1, + 0.089, + 0.445, + 0.238 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.245, + 0.468, + 0.273 + ], + "angle": 0, + "content": "Figure 4. The diversity of LayoutDiffusion. Each row of images are from the same layout and have great difference." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.274, + 0.468, + 0.438 + ], + "angle": 0, + "content": "In overall generation quality, our LayoutDiffusion outperforms the SOTA model by \\(46.35\\%\\) and \\(29.29\\%\\) at most in FID and IS, respectively. While maintaining high overall image quality, we also show precise and accurate controllability, LayoutDiffusion outperforms the SOTA model by \\(122.22\\%\\) and \\(41.82\\%\\) at most onYOLOScore and CAS, respectively. As for diversity, our LayoutDiffusion still achieves \\(11.30\\%\\) imporvement at most accroding to the DS. Experiments on these metrics show that our methods can successfully generate the higher-quality images with better location and quantity control." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.44, + 0.468, + 0.575 + ], + "angle": 0, + "content": "In particular, we conduct experiments compared to LDM [30] in Tab. 3. \"Ours-small\" uses comparable GPU resources to have better FID performance with much fewer parameters and better throughout compared to LDM-8 when \"Ours-small\" outperforms LDM-4 in all respects. The results of \"Ours\" indicate that LayoutDiffusion can have better FID performance, 31.6, at a higher cost. From these results, LayoutDiffusion always achieves better performance at different cost levels compared with LDM [30]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.578, + 0.238, + 0.592 + ], + "angle": 0, + "content": "4.5. Ablation studies" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.595, + 0.468, + 0.716 + ], + "angle": 0, + "content": "We validate the effectiveness of LFM and OaCA in Tab. 2, using the evaluation metrics in Sec. 4.2. The significant improvement on FID, IS, CAS, and YOLOScore proves that the application of LFM and OaCA allows for higher generation quality and diversity, along with more controllability. Furthermore, when applying both, considerable performance, \\(13.37 / 6.58 / 39.77 / 27.0\\) on FID / IS / CAS / YOLOScore, is gained." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.716, + 0.468, + 0.837 + ], + "angle": 0, + "content": "An interesting phenomenon is that the change of the Diversity Score (DS) is in the opposite direction of other metrics. This is because DS, which stands for diversity, is physically the opposite of the controllability represented by other metrics such as CAS and YOLOScore. The precise control offered on generated image leads to more constraints on diversity. As a result, the Diversity Score (DS) has a slight drop compared to the baseline." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.85, + 0.363, + 0.867 + ], + "angle": 0, + "content": "5. Limitations & Societal Impacts" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Limitations. Despite the significant improvements in various metrics, it is still difficult to generate a realistic im" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.093, + 0.885, + 0.234 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.253, + 0.892, + 0.281 + ], + "angle": 0, + "content": "Figure 5. The interactivity of LayoutDiffusion. We add extra layout continuously, and the new objects are also with high quality." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.289, + 0.892, + 0.378 + ], + "angle": 0, + "content": "age with no distortion and overlap, especially for a complex multi-object layout. Moreover, the model is trained from scratch in the specific dataset that requires detection labels. How to combine text-guided diffusion models and inherit parameters pre-trained on massive text-image datasets remains a future research." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.379, + 0.892, + 0.44 + ], + "angle": 0, + "content": "Societal Impacts. Trained on the real-world datasets such as COCO [5] and VG [19], LayoutDiffusion has the powerful ability to learn the distribution of data and we should pay attention to some potential copyright infringement issues." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.447, + 0.619, + 0.462 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.466, + 0.892, + 0.721 + ], + "angle": 0, + "content": "In this paper, we have proposed a one-stage end-to-end diffusion model named LayoutDiffusion, which is novel for the task of layout-to-image generation. With the guidance of layout, the diffusion model allows more control over the individual objects while maintaining higher quality than the prevailing GAN-based methods. By constructing a structural image patch with region information, we regrad each patch as a special object and accomplish the difficult multimodal image layout fusion in a unified form. Specifically, Layout Fusion Module and Object-aware Cross Attention are proposed to model the relationship among multiple objects and fuse the patched image feature with layout at multiple resolutions, respectively. Experiments in challenging COCO-stuff and Visual Genome (VG) show that our proposed method significantly outperforms both state-of-the-art GAN-based and diffusion-based methods in various evaluation metrics." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Acknowledgements. This work is supported in part by National Natural Science Foundation of China under Grant U20A20222, National Science Foundation for Distinguished Young Scholars under Grant 62225605, National Key Research and Development Program of China under Grant 2020AAA0107400, Research Fund of ARC Lab, Tencent PCG, Zhejiang - Singapore Innovation and AI Joint Research Lab, Ant Group through CCF-Ant Research Fund, and sponsored by CCF-AFSG Research Fund, CAAI-HUAWEI MindSpore Open Fund as well as CCF-Zhipu AI Large Model Fund (CCF-Zhipu202302)." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "22497" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.157 + ], + "angle": 0, + "content": "[1] Martin Arjovsky and Léon Bottou. 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Springer, 2022. 3" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.262 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "22499" + } + ] +] \ No newline at end of file diff --git a/2023/LayoutDiffusion_ Controllable Diffusion Model for Layout-to-Image Generation/b7471e7f-ee4c-4b84-b778-22769e778b1d_origin.pdf b/2023/LayoutDiffusion_ Controllable Diffusion Model for Layout-to-Image Generation/b7471e7f-ee4c-4b84-b778-22769e778b1d_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..61ce2ecd70c712940d0d6cd677fcd5da02fceb8f --- /dev/null +++ b/2023/LayoutDiffusion_ Controllable Diffusion Model for Layout-to-Image Generation/b7471e7f-ee4c-4b84-b778-22769e778b1d_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:b16a44b30b18a8fdb6112d4c89eddc472edc506ce62a9bd560d9b6bc97295c0a +size 4564719 diff --git a/2023/LayoutDiffusion_ Controllable Diffusion Model for Layout-to-Image Generation/full.md b/2023/LayoutDiffusion_ Controllable Diffusion Model for Layout-to-Image Generation/full.md new file mode 100644 index 0000000000000000000000000000000000000000..e9d309eec2f79ca130136b457a39b38bc104a609 --- /dev/null +++ b/2023/LayoutDiffusion_ Controllable Diffusion Model for Layout-to-Image Generation/full.md @@ -0,0 +1,358 @@ +# LayoutDiffusion: Controllable Diffusion Model for Layout-to-image Generation + +Guangcong Zheng $^{1*}$ , Xianpan Zhou $^{2*}$ , Xuewei Li $^{1\dagger}$ , Zhongang Qi $^{3}$ , Ying Shan $^{3}$ , Xi Li $^{1,4,5,6\dagger}$ $^{1}$ College of Computer Science & Technology, Zhejiang University + $^{2}$ Polytechnic Institute, Zhejiang University ${}^{3}$ ARC Lab, Tencent PCG + ${}^{4}$ Shanghai Institute for Advanced Study of Zhejiang University + ${}^{5}$ Shanghai AI Lab ${}^{6}$ Zhejiang - Singapore Innovation and AI Joint Research Lab + +{guangcongzheng, zhouxianpan, xuweili, xilizju}@zju.edu.cn {zhongangqi, yingsshan}@tencent.com + +![](images/a795827e293526b1838ce4f322d156b3029505b02343c57420cb83ce7d4bc7dd.jpg) +(a) layout-guided vs. text-guided image generation for diffusion model +(b) Image-Layout Fusion in a unified space +Figure 1. Compared to text, the layout allows diffusion models to obtain more control over the objects while maintaining high quality. Unlike the prevailing methods, we propose a diffusion model named LayoutDiffusion for layout-to-image generation. We transform the difficult multimodal fusion of the image and layout into a unified form by constructing a structural image patch with region information and regarding the patched image as a special layout. + +# Abstract + +Recently, diffusion models have achieved great success in image synthesis. However, when it comes to the layout-to-image generation where an image often has a complex scene of multiple objects, how to make strong control over both the global layout map and each detailed object remains a challenging task. In this paper, we propose a diffusion model named LayoutDiffusion that can obtain higher generation quality and greater controllability than the previous works. To overcome the difficult multimodal fusion of image and layout, we propose to construct a structural image patch with region information and transform the patched image into a special layout to fuse with the normal layout in a unified form. Moreover, Layout Fusion Module (LFM) and Object-aware Cross Attention (OaCA) are proposed to model the relationship among multiple objects and designed to be object-aware and position-sensitive, allow + +ing for precisely controlling the spatial related information. Extensive experiments show that our LayoutDiffusion outperforms the previous SOTA methods on FID, CAS by relatively $46.35\%$ , $26.70\%$ on COCO-stuff and $44.29\%$ , $41.82\%$ on VG. Code is available at https://github.com/ZGCTroy/LayoutDiffusion. + +# 1. Introduction + +Recently, the diffusion model has achieved encouraging progress in conditional image generation, especially in text-to-image generation such as GLIDE [24], Imagen [31], and Stable Diffusion [30]. However, text-guided diffusion models may still fail in the following situations. As shown in Fig. 1 (a), when aiming to generate a complex image with multiple objects, it is hard to design a prompt properly and comprehensively. Even input with well-designed prompts, problems such as missing objects and incorrectly generating objects' positions, shapes, and categories still occur in the state-of-the-art text-guided diffusion model [24, 30, 31]. + +This is mainly due to the ambiguity of the text and its weakness in precisely expressing the position of the image space. Fortunately, this is not a problem when using the coarse layout as guidance, which is a set of objects with the annotation of the bounding box (bbox) and object category. With both spatial and high-level semantic information, the diffusion model can obtain more powerful controllability while maintaining the high quality. + +However, early studies [2, 14, 38, 42] on layout-to-image generation are almost limited to generative adversarial networks (GANs) and often suffer from unstable convergence [1] and mode collapse [27]. Despite the advantages of diffusion models in easy training [10] and significant quality improvement [7], few studies have considered applying diffusion in the layout-to-image generation task. To our knowledge, only LDM [30] supports the condition of layout and has shown encouraging progress in this field. + +In this paper, different from LDM that applies the simple multimodal fusion method (e.g., the cross attention) or direct input concatenation for all conditional input, we aim to specifically design the fusion mechanism between layout and image. Moreover, instead of conditioning only in the second stage like LDM, we propose an end-to-end one-stage model that considers the condition for the whole process, which may have the potential to help mitigate loss in the task that requires fine-grained accuracy in pixel space [30]. The fusion between image and layout is a difficult multimodal fusion problem. Compared to the fusion of text and image, the layout has more restrictions on the position, size, and category of objects. This requires a higher controllability of the model and often leads to a decrease in the naturalness and diversity of the generated image. Furthermore, the layout is more sensitive to each token and the loss in token of layout will directly lead to the missing objects. + +To address the problems mentioned above, we propose treating the patched image and the input layout in a unified form. Specifically, we construct a structural image patch at multi-resolution by adding the concept of region that contains information of position and size. As a result, each patch of the image is transformed into a special type of object, and the entire patched image will also be regarded as a layout. Finally, the difficult problem of multimodal fusion between image and layout will be transformed into a simple fusion with a unified form in the same spatial space of the image. We name our model LayoutDiffusion, a layout-conditional diffusion model with Layout Fusion Module (LFM), object-aware Cross Attention Mechanism (OaCA), and corresponding classifier-free training and sampling scheme. In detail, LFM fuses the information of each object and models the relationship among multiple objects, providing a latent representation of the entire layout. To make the model pay more attention to the information re + +lated to the object, we propose an object-aware fusion module named OaCA. Cross-attention is made between the image patch feature and layout in a unified coordinate space by representing the positions of both of them as bounding boxes. To further improve the user experience of LayoutDiffusion, we also make several optimizations on the speed of the classifier-free sampling process and could significantly outperform the SOTA models in 25 iterations. + +Experiments are conducted on COCO-stuff [5] and Visual Genome (VG) [19]. Various metrics ranging from quality, diversity, and controllability show that LayoutDiffusion significantly outperforms both state-of-the-art GAN-based and diffusion-based methods. + +Our main contribution is listed below. + +- Instead of using the dominated GAN-based methods, we propose a diffusion model named LayoutDiffusion for layout-to-image generations, which can generate images with both high-quality and diversity while maintaining precise control over the position and size of multiple objects. +- We propose to treat each patch of the image as a special object and accomplish the difficult multimodal fusion of layout and image in a unified form. LFM and OaCA are then proposed to fuse the multi-resolution image patches with user's input layout. +- LayoutDiffusion outperforms the SOTA layout-to-image generation method on FID, DS, CAS by relatively around $46.35\%$ , $9.61\%$ , $26.70\%$ on COCO-stuff and $44.29\%$ , $11.30\%$ , $41.82\%$ on VG. + +# 2. Related work + +The related works are mainly from layout-to-image generation and diffusion models. + +Layout-to-Image Generation. Before the layout-to-image generation is formally proposed, the layout is usually used as a complementary feature [15, 29, 40] or an intermediate representation in text-to-image [12], scene-to-image generation [14]. The first image generation directly from the layout appears in Layout2Im [47] and is defined as a set of objects annotated with category and bbox. Models that work well with fine-grained semantic maps at the pixel level can also be easily transformed to this setting [13, 26, 43]. Inspired by StyleGAN [16], LostGAN-v1 [37], LostGAN-v2 [38] used a reconfigurable layout to obtain better control over individual objects. For interactive image synthesis, PLGAN [42] employed panoptic theory [18] by constructing stuff and instance layouts into separate branches and proposed Instance- and Stuff-Aware Normalization to fuse into panoptic layouts. Despite encouraging progress in this field, almost all approaches are limited to the generative + +adversarial network (GAN) and may suffer from unstable convergence [1] and mode collapse [27]. As a multimodal diffusion model, LDM [30] supports the condition of coarse layout and has shown great potential in layout-guided image generation. + +Diffusion Model. Diffusion models [3, 10, 25, 30, 34-36, 44] are being recognized as a promising family of generative models that have proven to be state-of-the-art sample quality for a variety of image generation benchmarks [6, 41, 45], including class-conditional image generation [7, 48], text-to-image generation [24, 30, 31], and imaged-to-image translation [17, 22, 32]. Classifier guidance was introduced in ADM-G [7] to allow diffusion models to condition the class label. The gradient of the classifier trained on noised images could be added to the image during the sampling process. Then Ho et al. [11] proposed a classifier-free training and sampling strategy by interpolating between predictions of a diffusion model with and without condition input. For the acceleration of training and sampling speed, LDM proposed to first compress the image into smaller resolution and then apply denoising training in the latent space. + +# 3. Method + +In this section, we propose our LayoutDiffusion, as shown in Fig. 2. The whole framework consists mainly of four parts: (a) layout embedding that preprocesses the layout input, (b) layout fusion module that encourages more interaction between objects of layout, (c) image-Layout fusion module that constructs the structural image patch and object-aware cross attention developed with the specific design for layout and image fusion, (d) the layout-conditional diffusion model with training and accelerated sampling methods. + +# 3.1. Layout Embedding + +A layout $l = \{o_1, o_2, \dots, o_n\}$ is a set of $n$ objects. Each object $o_i$ is represented as $o_i = \{b_i, c_i\}$ , where $b_i = (x_0^i, y_0^i, x_1^i, y_1^i) \in [0, 1]^4$ denotes a bounding box (bbox) and $c_i \in [0, \mathcal{C} + 1]$ is its category id. + +To support the input of a variable length sequence, we need to pad $l$ to a fixed length $k$ by adding one $o_l$ in the front and some padding $o_p$ in the end, where $o_l$ represents the entire layout and $o_p$ represents no object. Specifically, $b_l = (0, 0, 1, 1)$ , $c_l = 0$ denotes a object that covers the whole image and $b_p = (0, 0, 0, 0)$ , $c_p = \mathcal{C} + 1$ denotes a empty object that has no shape or does not appear in the image. + +After the padding process, we can get a padded $l = \{o_1, o_2, \dots, o_k\}$ consisting of $k$ objects, and each object has its specific position, size, and category. Then, the layout $l$ is transformed into a layout embedding $L = \{O_1, O_2, \dots, O_k\} \in \mathbb{R}^{k \times d_{\mathcal{L}}}$ by the projection matrix $W_{\mathcal{B}} \in$ + +$\mathbb{R}^{4\times d_{\mathcal{L}}}$ and $W_{\mathcal{C}}\in \mathbb{R}^{1\times d_{\mathcal{L}}}$ using the following equation: + +$$ +L = B _ {\mathcal {L}} + C _ {\mathcal {L}} \tag {1} +$$ + +$$ +B _ {\mathcal {L}} = b W _ {\mathcal {B}} \tag {2} +$$ + +$$ +C _ {\mathcal {L}} = c W _ {C} \tag {3} +$$ + +where $B_{\mathcal{L}}, C_{\mathcal{L}} \in \mathbb{R}^{k \times d_{\mathcal{L}}}$ are the bounding box embedding and the category embedding of a layout $l$ , respectively. As a result, $L$ is defined as the sum of $B_{\mathcal{L}}$ and $C_{\mathcal{L}}$ to include both the content and positional information of a entire layout, and $d_{\mathcal{L}}$ is the dimension of the layout embedding. + +# 3.2. Layout Fusion Module + +Currently, each object in layout has no relationship with other objects. This leads to a low understanding of the whole scene, especially when multiple objects overlap and block each other. Therefore, to encourage more interaction between multiple objects of the layout to better understand the entire layout before inputting the layout embedding, we propose Layout Fusion Module (LFM), a transformer encoder that uses multiple layers of self-attention to fuse the layout embedding and can be denoted as + +$$ +L ^ {\prime} = \operatorname {L F M} (L) \tag {4} +$$ + +, where the output is a fused layout embedding $L^{\prime} = \{O_{1}^{\prime},O_{2}^{\prime},\dots ,O_{k}^{\prime}\} \in \mathbb{R}^{k\times d_{\mathcal{L}}}$ + +# 3.3. Image-Layout Fusion Module + +Structural Image Patch. The fusion of image and layout is a difficult multimodal fusion problem, and one of the most important parts lies in the fusion of position and size. However, the image patch is limited to the semantic information of the whole feature and lacks the spatial information. Therefore, we construct a structural image patch by adding the concept of region that contains the information of position and size. + +Specifically, $I \in \mathbb{R}^{h \times w \times d_{\mathcal{I}}}$ denotes the feature map of a entire image with height $h$ , width $w$ , and channel $d_{\mathcal{I}}$ . We define that $I_{u,v}$ is the $u^{\mathrm{th}}$ row and $v^{\mathrm{th}}$ column patch of $I$ and its bounding box, or the ablated region information, is defined as $b_{I_{u,v}}$ by the following equation: + +$$ +b _ {\mathcal {I} _ {u, v}} = \left(\frac {u}{h}, \frac {v}{w}, \frac {u + 1}{h}, \frac {v + 1}{w}\right) \tag {5} +$$ + +The bounding box sets of a patched image $I$ is defined as $b_{\mathcal{I}} = \{b_{\mathcal{I}_{u,v}}|u\in [0,h),v\in [0,w)\}$ . As a result, the positional information of image patch and layout object is contained in the unified bounding box defined in the same spatial space, leading to better fusion of image and layout. + +Positional Embedding in Unified Space. We define the positional embedding of the image and layout as $P_{\mathcal{I}}$ and + +![](images/dea185a46bee7b955fcf0d82c49950d37eafbac5d6b61059d12080c202b026fc.jpg) + +![](images/b7672b7661b04c0abe06df22d56484095df0c5f81cea377e0b1e38b5896f34cb.jpg) +Figure 2. The whole pipeline of LayoutDiffusion. The layout that consisted of bounding box $b$ and objects categories $c$ is transformed into embedding $B_{\mathcal{L}}, C_{\mathcal{L}}, L$ . Then Layout Fusion Module fuses layout embedding $L$ to output the fused layout embedding $L'$ . Finally, Image-Layout Fusion Module including direct addition used for global conditioning and Object-aware Cross Attention (OaCA) used for local conditioning, will fuse the layout related $B_{\mathcal{L}}, C_{\mathcal{L}}, L'$ and the image feature $I$ at multiple resolutions. + +![](images/036034f21e885159cbef6c3ae1edb619772eb83b1fb1f4469163352238e5725c.jpg) + +$P_{\mathcal{L}}$ as follows: + +$$ +B _ {\mathcal {I}} = b _ {\mathcal {I}} W _ {\mathcal {B}} \tag {6} +$$ + +$$ +P _ {\mathcal {I}} = B _ {\mathcal {I}} W _ {\mathcal {P}} \tag {7} +$$ + +$$ +P _ {\mathcal {L}} = B _ {\mathcal {L}} W _ {\mathcal {P}} \tag {8} +$$ + +, where $W_{\mathcal{B}} \in \mathbb{R}^{4 \times d_{\mathcal{L}}}$ is defined in Eq. 2 and works as a shared projection matrix that transforms the coordinates of bounding box into embedding of $d_{\mathcal{L}}$ dimension. $W_{\mathcal{P}} \in \mathbb{R}^{d_{\mathcal{L}} \times d_{\mathcal{I}}}$ is the projection matrix that transforms the $B$ to the positional Embedding $P$ . + +Pointwise Addition for Global Conditioning. With the help of LFM in Eq. 4, $O_1'$ can be considered as a global information of the entire layout, and $O_i'(i \in [2, k])$ is considered as the local information embedding of single object along with the other related objects. One of the easiest ways to condition the layout in the image is to directly add $O_1'$ , the global information of the layout, to the multiple resolution of image features. Specifically, the condition process can be defined as + +$$ +I ^ {\prime} = I + O _ {1} ^ {\prime} W \tag {9} +$$ + +, where $W \in \mathbb{R}^{d_{\mathcal{L}} \times d_{\mathcal{I}}}$ is a projection matrix and $I'$ is the image feature conditioned with global embedding of layout. + +Object-aware Cross Attention for Local Conditioning. + +Cross attention is successfully applied in [24] to condition text into image feature, where the sequence of the image patch is used as the query and the concatenated sequence of the image patch and text is applied as key and value. The equation of cross-attention is defined as + +$$ +\operatorname {A t t e n t i o n} (Q, K, V) = \operatorname {s o f t m a x} \left(\frac {Q K ^ {T}}{\sqrt {d _ {k}}}\right) V \tag {10} +$$ + +, where $Q, K, V$ represent the embeddings of query, key, and value, respectively. In the following paper, we will use the subscript image and layout to represent the image patch feature and layout feature, respectively. + +In text-to-image generation, each token in the text sequence is a word. The aggregation of these words constitutes the semantics of a sentence. After the transformer encoder, the first token in text sequence is well-semantic information that generalizes the whole text but may not reverse the semantic meaning of each word. However, the loss in information of one token is relatively serious in layout rather than in text. Each token in the layout sequence is a single object with a specific category, size, and position. The loss of information on a layout token will directly lead + +to a missing or wrong object in the generated image pixel space. + +Therefore, we take into account the fusion of locations, size, and category of objects and define our object-aware cross-attention (OaCA) as + +$$ +Q = \Psi_ {1} \left(Q _ {\mathcal {I}}, Q _ {\mathcal {L}}\right) \tag {11} +$$ + +$$ +K = \Psi_ {1} \left(\Psi_ {2} \left(K _ {\mathcal {I}}, K _ {\mathcal {L}}\right), \Psi_ {2} \left(P _ {\mathcal {I}}, P _ {\mathcal {L}}\right)\right) \tag {12} +$$ + +$$ +V = \Psi_ {2} \left(V _ {\mathcal {I}}, V _ {\mathcal {L}}\right) \tag {13} +$$ + +, where the query $Q \in \mathbb{R}^{hw \times 2d_{\mathcal{I}}}$ , $K \in \mathbb{R}^{(hw + k) \times 2d_{\mathcal{I}}}$ , and $V \in \mathbb{R}^{(hw + k) \times d_{\mathcal{I}}}$ . $\Psi_1$ and $\Psi_2$ denote concatenation on the dimension of the channel and length of the sequence, respectively. + +We first construct the key and value of the layout: + +$$ +K _ {\mathcal {L}}, V _ {\mathcal {L}} = \operatorname {C o n v} \left(\frac {1}{2} \left(\operatorname {N o r m} \left(C _ {\mathcal {L}}\right) + L ^ {\prime}\right)\right) \tag {14} +$$ + +, where $K_{\mathcal{L}}, V_{\mathcal{L}} \in \mathbb{R}^{k \times d_{\mathcal{I}}}$ and Conv is the convolution operation. The embedding of key and value in the layout is related to the category embedding $C_{\mathcal{L}}$ and the fused layout embedding $L'$ . $C_{\mathcal{L}}$ focuses on the category information of layout and $L'$ concentrates on the comprehensive information of both the object itself and other objects that may have a relationship with it. By averaging between $L'$ and $C_{\mathcal{L}}$ , we can obtain both the general information of the object and also emphasize the category information of the object. + +We construct the query, key, and value of the image feature as follows: + +$$ +Q _ {\mathcal {I}}, K _ {\mathcal {I}}, V _ {\mathcal {I}} = \operatorname {C o n v} (\operatorname {N o r m} (I)) \tag {15} +$$ + +# 3.4. Layout-conditional Diffusion Model + +Here, we follow the Gaussian diffusion models improved by [10, 35]. Given a data point sampled from a real data distribution $x_0 \sim q(x_0)$ , a forward diffusion process is defined by adding small amount of Gaussian noise to the $x_0$ in $T$ steps: + +$$ +q \left(x _ {t} \mid x _ {t - 1}\right) := \mathcal {N} \left(x _ {t}; \sqrt {\alpha_ {t}} x _ {t - 1}, (1 - \alpha_ {t}) \mathbf {I}\right) \tag {16} +$$ + +If the total noise added throughout the Markov chain is large enough, the $x_{T}$ will be well approximated by $\mathcal{N}(0,\mathbf{I})$ . If we add noise at each step with a sufficiently small magnitude $1 - \alpha_{t}$ , the posterior $q(x_{t - 1}|x_t)$ will be well approximated by a diagonal Gaussian. This nice property ensures that we can reverse the above forward process and sample from $x_{T}\sim \mathcal{N}(0,\mathbf{I})$ , which is a Gaussian noise. However, since the entire dataset is needed, we are unable to easily estimate the posterior. Instead, we have to learn a model $p_{\theta}(x_{t - 1}|x_t)$ to approximate it: + +$$ +p _ {\theta} \left(x _ {t - 1} \mid x _ {t}\right) := \mathcal {N} \left(\mu_ {\theta} \left(x _ {t}\right), \Sigma_ {\theta} \left(x _ {t}\right)\right) \tag {17} +$$ + +Instead of using the tractable variational lower bound (VLB) in $\log p_{\theta}(x_0)$ , Ho et al. [10] proposed to reweight the terms of the VLB to optimize a surrogate objective. Specifically, we first add $t$ steps of Gaussian noise to a clean sample $x_0$ to generate a noised sample $x_{t} \sim q(x_{t}|x_{0})$ . Then train a model $\epsilon_{\theta}$ to predict the added noise using the following loss: + +$$ +\mathcal {L} := E _ {t \sim [ 1, T ], x _ {0} \sim q (x _ {0}), \epsilon \sim \mathcal {N} (0, \mathbf {I})} [ \| \epsilon - \epsilon_ {\theta} (x _ {t}, t) \| ^ {2} ] \tag {18} +$$ + +, which is a standard mean-squared error loss. + +To support the layout condition, we apply classifier-free guidance, a technique proposed by Ho et al. [11] for conditional generation that requires no additional training of the classifier. It is accomplished by interpolating between predictions of a diffusion model with and without condition input. For the condition of layout, we first construct a padding layout $l_{\phi} = \{o_l,o_p,\dots ,o_p\}$ . During training, the condition of layout $l$ of diffusion model will be replaced with $l_{\phi}$ with a fixed probability. When sampling, the following equation is used to sample a layout-condional image: + +$$ +\hat {\epsilon} _ {\theta} \left(x _ {t}, t | l\right) = (1 - s) \cdot \epsilon_ {\theta} \left(x _ {t}, t \mid l _ {\phi}\right) + s \cdot \epsilon_ {\theta} \left(x _ {t}, t \mid l\right) \tag {19} +$$ + +, where the scale $s$ can be used to increase the gap between $\epsilon_{\theta}(x_t,t|l_\phi)$ and $\epsilon_{\theta}(x_t,t|l)$ to enhance the strength of conditional guidance. + +To further improve the user experience of LayoutDiffusion, we also make several optimizations on the speed of the classifier-free sampling process and could significantly outperform the SOTA models in 25 iterations. Specifically, we adapt DPM-solver [21] for the conditional classifier-free sampling, a fast dedicated high-order solver for diffusion ODEs [36] with the convergence order guarantee, to accelerate the conditional sampling speed. + +# 4. Experiments + +In this section, we evaluate our LayoutDiffusion on different benchmarks in terms of various metrics. First, we introduce the datasets and evaluation metrics. Second, we show the qualitative and quantitative results compared with other strategies. Finally, some ablation studies and analysis are also mentioned. More details can be found in Appendix, including model architecture, training hyperparameters, reproduction results, more experimental results and visualizations. + +# 4.1. Datasets + +We conduct our experiments on two popular datasets, COCO-Stuff [5] and Visual Genome [19]. + +COCO-Stuff has 164K images from COCO 2017, of which the images contain bounding boxes and pixel-level segmentation masks for 80 categories of thing and 91 categories + +![](images/dfcd2b773a3a396f58a965a3817b0c914207b2b37bb8f34e5c441bfc3c632eda.jpg) +Figure 3. Visualization of comparison with SOTA methods on COCO-stuff $256 \times 256$ . LayoutDiffusion has better generation quality and stronger controllability compared to the other methods. + +
MethodsCOCO-stuffVG
FID ↓IS ↑DS ↑CAS ↑YOLOScore ↑FID ↓DS ↑CAS ↑
128×128
Grid2Im [2]59.5012.50±0.300.28±0.114.056.80---
LostGAN-v2 [38]24.7614.21±0.400.45±0.0939.9113.6029.000.42±0.0929.74
PLGAN [42]22.7015.60±0.300.16±0.7238.7013.4020.62--
LayoutDiffusion16.5720.17±0.560.47±0.0943.6027.0016.350.49±0.0936.45
256×256
Grid2Im [2]65.2016.40±0.700.34±0.134.819.70---
LostGAN-v2 [38]31.1818.01±0.500.56±0.1040.0017.5032.080.53±0.1034.48
PLGAN [42]29.1018.90±0.300.52±0.1037.6514.4028.06--
LayoutDiffusion15.6128.36±0.750.57±0.1047.7432.0015.630.59±0.1048.90
+ +Table 1. Quantitative results on COCO-stuff [5] and VG [19]. The proposed diffusion method has made great progress in all evaluation metrics, showing better quality, controllability, diversity, and accuracy than previous works. For COCO-stuff, we evaluate on 3097 layout and sample 5 images for each layout. For VG, we evaluate on 5096 layout and sample 1 image for each layout. We also report reproduction scores of previous works in Appendix. + +
LFMOaCACAFID ↓IS ↑DS ↑CAS ↑YOLOScore ↑
29.94 (+13.37)13.59±0.29 (-6.58)0.70±0.08 (+0.23)3.83 (-39.77)0.00 (-27.00)
✓17.06 (+0.49)19.21±0.53 (-0.96)0.52±0.09 (+0.05)30.86 (-12.74)6.90 (-20.10)
✓16.76 (+0.19)19.57±0.40 (-0.60)0.48±0.09 (+0.01)40.67 (-2.93)18.80 (-8.20)
✓✓16.46 (-0.11)19.79±0.40 (-0.38)0.48±0.10 (+0.01)42.47 (-1.13)23.60 (-3.40)
✓✓16.5720.17±0.560.47±0.0943.6027.00
+ +of stuff, respectively. Following the settings of LostGANv2 [38], we use the COCO 2017 Stuff Segmentation Challenge subset that contains $40\mathrm{K} / 5\mathrm{k} / 5\mathrm{k}$ images for train / val / test-dev set, respectively. We use images in the train and val set with 3 to 8 objects that cover more than $2\%$ of the image and not belong to crowd. Finally, there are 25,210 train and 3,097 val images. + +Visual Genome collects 108,077 images with dense annotations of objects, attributes, and relationships. Following the setting of SG2Im [14], we divide the data into $80\%$ , $10\%$ , $10\%$ for the train, val, test set, respectively. We select the object and relationship categories occurring at least 2000 and 500 times in the train set, respectively, and select the images with 3 to 30 bounding boxes and ignoring all small objects. Finally, the training / validation / test set will have 62565 / 5062 / 5096 images, respectively. + +# 4.2. Evaluation Metrics & Protocols + +We use five metrics to evaluate the quality, diversity, and controllability of generation. + +Fr'echet Inception Distance (FID) [9] shows the overall visual quality of the generated image by measuring the difference in the distribution of features between the real images and the generated images on an ImageNet-pretrained Inception-V3 [39] network. + +Inception Score (IS) [33] uses an Inception-V3 [39] pretrained on ImageNet network to compute the statistical score of the output of the generated images. + +Diversity Score (DS) calculates the diversity between two generated images of the same layout by comparing the LPIPS [46] metric in a DNN feature space between them. + +Classification Score (CAS) [28] first crops the ground truth box area of images and resizing them at a resolution of $32 \times 32$ with their class. A ResNet-101 [8] classifier is trained with generated images and tested on real images. + +YOLOScore [20] evaluates 80 thing categories bbox mAP on generated images using a pretrained YOLOv4 [4] model, and shows the precision of control in one generated model. + +In summary, FID and IS show the generation quality, DS shows the diversity, CAS and YOLOScore represent the controllability. We follow the architecture of ADM [7], which is mainly a UNet. All experiments are conducted on 32 NVIDIA 3090s with mixed precision training [23]. We + +set batch size 24, learning rate 1e-5. We adopt the fixed linear variance schedule. More details can be found in the Appendix. + +# 4.3. Qualitative results + +Comparison of generated $256 \times 256$ images on the COCO-Stuff [5] with our method and previous works [2, 38, 42] is shown in Fig. 3. + +Table 2. Ablation study of Layout Fusion Module (LFM), Object-aware Cross Attention (OaCA), Cross Attention (CA). We use the model trained for 300,000 iterations on COCO-stuff $128\times 128$ . The value in brackets denotes the discrepancy to our proposed method(+LFM+OaCA), where red denotes better and green denotes worse. + +
methodFID ↓NparamsThroughout images / sFirst stage V100 daysCond stage V100 days
LDM-8 (100 steps)42.06345M0.457663.69
LDM-4 (200 steps)40.91306M0.2672995.49
ours-small (25 steps)36.16142M0.608-75.83
ours (25 steps)31.68569M0.308-216.55
+ +Table 3. Comparison with SOTA diffusion-based methods LDM on COCO-stuff $256 \times 256$ . We generate the same 2048 images of LDM for a fair comparison. + +LayoutDiffusion generates more accurate high quality images, which has more recognizable and accurate objects corresponding to their layouts. Grid2Im [2], LostGANv2 [38] and PLGAN [42] generate images with distorted and unreal objects. + +Especially when input a set of multiple objects with complex relationships, previous work can hardly generate recognizable objects in the position corresponding to layouts. For example, in Fig. 3 (a), (c), and (e), the main objects (e.g. train, zebra, bus) in images are poorly generated in previous work, while our LayoutDiffusion generates well. In Fig. 3 (b), only our LayoutDiffusion generates the laptop in the right place. The images generated by our LayoutDiffusion are more sensorially similar to the real ones. + +We show the diversity of LayoutDiffusion in Fig. 4. Images from the same layouts have high quality and diversity (different lighting, textures, colors, and details). + +We continuously add an additional layout from the initial layout, the one in the upper left corner, as shown in Fig. 5. In each step, LayoutDiffusion adds the new object in very precise locations with consistent image quality, showing user-friendly interactivity. + +# 4.4. Quantitative results + +Tab. 1 provides the comparison among previous works and our method in FID, IS, DS, CAS and YOLOScore. Compared to the SOTA method, the proposed method achieves the best performance in comparison. + +![](images/b4b1801920248ead66f3763840650c2b58a990e1e28a82e0d2f7b6c3b8abff1b.jpg) +Figure 4. The diversity of LayoutDiffusion. Each row of images are from the same layout and have great difference. + +In overall generation quality, our LayoutDiffusion outperforms the SOTA model by $46.35\%$ and $29.29\%$ at most in FID and IS, respectively. While maintaining high overall image quality, we also show precise and accurate controllability, LayoutDiffusion outperforms the SOTA model by $122.22\%$ and $41.82\%$ at most onYOLOScore and CAS, respectively. As for diversity, our LayoutDiffusion still achieves $11.30\%$ imporvement at most accroding to the DS. Experiments on these metrics show that our methods can successfully generate the higher-quality images with better location and quantity control. + +In particular, we conduct experiments compared to LDM [30] in Tab. 3. "Ours-small" uses comparable GPU resources to have better FID performance with much fewer parameters and better throughout compared to LDM-8 when "Ours-small" outperforms LDM-4 in all respects. The results of "Ours" indicate that LayoutDiffusion can have better FID performance, 31.6, at a higher cost. From these results, LayoutDiffusion always achieves better performance at different cost levels compared with LDM [30]. + +# 4.5. Ablation studies + +We validate the effectiveness of LFM and OaCA in Tab. 2, using the evaluation metrics in Sec. 4.2. The significant improvement on FID, IS, CAS, and YOLOScore proves that the application of LFM and OaCA allows for higher generation quality and diversity, along with more controllability. Furthermore, when applying both, considerable performance, $13.37 / 6.58 / 39.77 / 27.0$ on FID / IS / CAS / YOLOScore, is gained. + +An interesting phenomenon is that the change of the Diversity Score (DS) is in the opposite direction of other metrics. This is because DS, which stands for diversity, is physically the opposite of the controllability represented by other metrics such as CAS and YOLOScore. The precise control offered on generated image leads to more constraints on diversity. As a result, the Diversity Score (DS) has a slight drop compared to the baseline. + +# 5. Limitations & Societal Impacts + +Limitations. Despite the significant improvements in various metrics, it is still difficult to generate a realistic im + +![](images/3ad8222c1e0d0c03bccec40d64451255e71ac22e4c2a3fe35045ddb412012c51.jpg) +Figure 5. The interactivity of LayoutDiffusion. We add extra layout continuously, and the new objects are also with high quality. + +age with no distortion and overlap, especially for a complex multi-object layout. Moreover, the model is trained from scratch in the specific dataset that requires detection labels. How to combine text-guided diffusion models and inherit parameters pre-trained on massive text-image datasets remains a future research. + +Societal Impacts. Trained on the real-world datasets such as COCO [5] and VG [19], LayoutDiffusion has the powerful ability to learn the distribution of data and we should pay attention to some potential copyright infringement issues. + +# 6. Conclusion + +In this paper, we have proposed a one-stage end-to-end diffusion model named LayoutDiffusion, which is novel for the task of layout-to-image generation. With the guidance of layout, the diffusion model allows more control over the individual objects while maintaining higher quality than the prevailing GAN-based methods. By constructing a structural image patch with region information, we regrad each patch as a special object and accomplish the difficult multimodal image layout fusion in a unified form. Specifically, Layout Fusion Module and Object-aware Cross Attention are proposed to model the relationship among multiple objects and fuse the patched image feature with layout at multiple resolutions, respectively. Experiments in challenging COCO-stuff and Visual Genome (VG) show that our proposed method significantly outperforms both state-of-the-art GAN-based and diffusion-based methods in various evaluation metrics. + +Acknowledgements. This work is supported in part by National Natural Science Foundation of China under Grant U20A20222, National Science Foundation for Distinguished Young Scholars under Grant 62225605, National Key Research and Development Program of China under Grant 2020AAA0107400, Research Fund of ARC Lab, Tencent PCG, Zhejiang - Singapore Innovation and AI Joint Research Lab, Ant Group through CCF-Ant Research Fund, and sponsored by CCF-AFSG Research Fund, CAAI-HUAWEI MindSpore Open Fund as well as CCF-Zhipu AI Large Model Fund (CCF-Zhipu202302). + +# References + +[1] Martin Arjovsky and Léon Bottou. Towards principled methods for training generative adversarial networks. arXiv preprint arXiv:1701.04862, 2017. 2, 3 +[2] Oron Ashual and Lior Wolf. Specifying object attributes and relations in interactive scene generation. In The IEEE International Conference on Computer Vision (ICCV), October 2019. 2, 6, 7 +[3] Fan Bao, Chongxuan Li, Jun Zhu, and Bo Zhang. 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Compared to text, the layout allows diffusion models to obtain more control over the objects while maintaining high quality. Unlike the prevailing methods, we propose a diffusion model named LayoutDiffusion for layout-to-image generation. We transform the difficult multimodal fusion of the image and layout into a unified form by constructing a structural image patch with region information and regarding the patched image as a special layout." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 143, + 469, + 192, + 482 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 469, + 192, + 482 + ], + "spans": [ + { + "bbox": [ + 143, + 469, + 192, + 482 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 495, + 290, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 495, + 290, + 687 + ], + "spans": [ + { + "bbox": [ + 46, + 495, + 290, + 687 + ], + "type": "text", + "content": "Recently, diffusion models have achieved great success in image synthesis. However, when it comes to the layout-to-image generation where an image often has a complex scene of multiple objects, how to make strong control over both the global layout map and each detailed object remains a challenging task. In this paper, we propose a diffusion model named LayoutDiffusion that can obtain higher generation quality and greater controllability than the previous works. To overcome the difficult multimodal fusion of image and layout, we propose to construct a structural image patch with region information and transform the patched image into a special layout to fuse with the normal layout in a unified form. Moreover, Layout Fusion Module (LFM) and Object-aware Cross Attention (OaCA) are proposed to model the relationship among multiple objects and designed to be object-aware and position-sensitive, allow" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 471, + 545, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 471, + 545, + 544 + ], + "spans": [ + { + "bbox": [ + 306, + 471, + 545, + 544 + ], + "type": "text", + "content": "ing for precisely controlling the spatial related information. Extensive experiments show that our LayoutDiffusion outperforms the previous SOTA methods on FID, CAS by relatively " + }, + { + "bbox": [ + 306, + 471, + 545, + 544 + ], + "type": "inline_equation", + "content": "46.35\\%" + }, + { + "bbox": [ + 306, + 471, + 545, + 544 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 306, + 471, + 545, + 544 + ], + "type": "inline_equation", + "content": "26.70\\%" + }, + { + "bbox": [ + 306, + 471, + 545, + 544 + ], + "type": "text", + "content": " on COCO-stuff and " + }, + { + "bbox": [ + 306, + 471, + 545, + 544 + ], + "type": "inline_equation", + "content": "44.29\\%" + }, + { + "bbox": [ + 306, + 471, + 545, + 544 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 306, + 471, + 545, + 544 + ], + "type": "inline_equation", + "content": "41.82\\%" + }, + { + "bbox": [ + 306, + 471, + 545, + 544 + ], + "type": "text", + "content": " on VG. Code is available at https://github.com/ZGCTroy/LayoutDiffusion." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 560, + 387, + 572 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 560, + 387, + 572 + ], + "spans": [ + { + "bbox": [ + 306, + 560, + 387, + 572 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "content": "Recently, the diffusion model has achieved encouraging progress in conditional image generation, especially in text-to-image generation such as GLIDE [24], Imagen [31], and Stable Diffusion [30]. However, text-guided diffusion models may still fail in the following situations. As shown in Fig. 1 (a), when aiming to generate a complex image with multiple objects, it is hard to design a prompt properly and comprehensively. Even input with well-designed prompts, problems such as missing objects and incorrectly generating objects' positions, shapes, and categories still occur in the state-of-the-art text-guided diffusion model [24, 30, 31]." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 693, + 127, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 693, + 127, + 703 + ], + "spans": [ + { + "bbox": [ + 58, + 693, + 127, + 703 + ], + "type": "text", + "content": "* Equal contribution." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 59, + 703, + 135, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 703, + 135, + 712 + ], + "spans": [ + { + "bbox": [ + 59, + 703, + 135, + 712 + ], + "type": "text", + "content": "† Corresponding author." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "22490" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "content": "This is mainly due to the ambiguity of the text and its weakness in precisely expressing the position of the image space. Fortunately, this is not a problem when using the coarse layout as guidance, which is a set of objects with the annotation of the bounding box (bbox) and object category. With both spatial and high-level semantic information, the diffusion model can obtain more powerful controllability while maintaining the high quality." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 170, + 289, + 278 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 170, + 289, + 278 + ], + "spans": [ + { + "bbox": [ + 46, + 170, + 289, + 278 + ], + "type": "text", + "content": "However, early studies [2, 14, 38, 42] on layout-to-image generation are almost limited to generative adversarial networks (GANs) and often suffer from unstable convergence [1] and mode collapse [27]. Despite the advantages of diffusion models in easy training [10] and significant quality improvement [7], few studies have considered applying diffusion in the layout-to-image generation task. To our knowledge, only LDM [30] supports the condition of layout and has shown encouraging progress in this field." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 281, + 289, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 281, + 289, + 496 + ], + "spans": [ + { + "bbox": [ + 46, + 281, + 289, + 496 + ], + "type": "text", + "content": "In this paper, different from LDM that applies the simple multimodal fusion method (e.g., the cross attention) or direct input concatenation for all conditional input, we aim to specifically design the fusion mechanism between layout and image. Moreover, instead of conditioning only in the second stage like LDM, we propose an end-to-end one-stage model that considers the condition for the whole process, which may have the potential to help mitigate loss in the task that requires fine-grained accuracy in pixel space [30]. The fusion between image and layout is a difficult multimodal fusion problem. Compared to the fusion of text and image, the layout has more restrictions on the position, size, and category of objects. This requires a higher controllability of the model and often leads to a decrease in the naturalness and diversity of the generated image. Furthermore, the layout is more sensitive to each token and the loss in token of layout will directly lead to the missing objects." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 498, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 289, + 714 + ], + "type": "text", + "content": "To address the problems mentioned above, we propose treating the patched image and the input layout in a unified form. Specifically, we construct a structural image patch at multi-resolution by adding the concept of region that contains information of position and size. As a result, each patch of the image is transformed into a special type of object, and the entire patched image will also be regarded as a layout. Finally, the difficult problem of multimodal fusion between image and layout will be transformed into a simple fusion with a unified form in the same spatial space of the image. We name our model LayoutDiffusion, a layout-conditional diffusion model with Layout Fusion Module (LFM), object-aware Cross Attention Mechanism (OaCA), and corresponding classifier-free training and sampling scheme. In detail, LFM fuses the information of each object and models the relationship among multiple objects, providing a latent representation of the entire layout. To make the model pay more attention to the information re" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 72, + 547, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 167 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 167 + ], + "type": "text", + "content": "lated to the object, we propose an object-aware fusion module named OaCA. Cross-attention is made between the image patch feature and layout in a unified coordinate space by representing the positions of both of them as bounding boxes. To further improve the user experience of LayoutDiffusion, we also make several optimizations on the speed of the classifier-free sampling process and could significantly outperform the SOTA models in 25 iterations." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 168, + 547, + 227 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 168, + 547, + 227 + ], + "spans": [ + { + "bbox": [ + 304, + 168, + 547, + 227 + ], + "type": "text", + "content": "Experiments are conducted on COCO-stuff [5] and Visual Genome (VG) [19]. Various metrics ranging from quality, diversity, and controllability show that LayoutDiffusion significantly outperforms both state-of-the-art GAN-based and diffusion-based methods." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 317, + 228, + 471, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 228, + 471, + 239 + ], + "spans": [ + { + "bbox": [ + 317, + 228, + 471, + 239 + ], + "type": "text", + "content": "Our main contribution is listed below." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 317, + 250, + 545, + 444 + ], + "type": "list", + "angle": 0, + "index": 10, + "blocks": [ + { + "bbox": [ + 317, + 250, + 545, + 321 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 250, + 545, + 321 + ], + "spans": [ + { + "bbox": [ + 317, + 250, + 545, + 321 + ], + "type": "text", + "content": "- Instead of using the dominated GAN-based methods, we propose a diffusion model named LayoutDiffusion for layout-to-image generations, which can generate images with both high-quality and diversity while maintaining precise control over the position and size of multiple objects." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 317, + 330, + 545, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 330, + 545, + 389 + ], + "spans": [ + { + "bbox": [ + 317, + 330, + 545, + 389 + ], + "type": "text", + "content": "- We propose to treat each patch of the image as a special object and accomplish the difficult multimodal fusion of layout and image in a unified form. LFM and OaCA are then proposed to fuse the multi-resolution image patches with user's input layout." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 317, + 397, + 545, + 444 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 397, + 545, + 444 + ], + "spans": [ + { + "bbox": [ + 317, + 397, + 545, + 444 + ], + "type": "text", + "content": "- LayoutDiffusion outperforms the SOTA layout-to-image generation method on FID, DS, CAS by relatively around " + }, + { + "bbox": [ + 317, + 397, + 545, + 444 + ], + "type": "inline_equation", + "content": "46.35\\%" + }, + { + "bbox": [ + 317, + 397, + 545, + 444 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 317, + 397, + 545, + 444 + ], + "type": "inline_equation", + "content": "9.61\\%" + }, + { + "bbox": [ + 317, + 397, + 545, + 444 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 317, + 397, + 545, + 444 + ], + "type": "inline_equation", + "content": "26.70\\%" + }, + { + "bbox": [ + 317, + 397, + 545, + 444 + ], + "type": "text", + "content": " on COCO-stuff and " + }, + { + "bbox": [ + 317, + 397, + 545, + 444 + ], + "type": "inline_equation", + "content": "44.29\\%" + }, + { + "bbox": [ + 317, + 397, + 545, + 444 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 317, + 397, + 545, + 444 + ], + "type": "inline_equation", + "content": "11.30\\%" + }, + { + "bbox": [ + 317, + 397, + 545, + 444 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 317, + 397, + 545, + 444 + ], + "type": "inline_equation", + "content": "41.82\\%" + }, + { + "bbox": [ + 317, + 397, + 545, + 444 + ], + "type": "text", + "content": " on VG." + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 456, + 390, + 468 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 456, + 390, + 468 + ], + "spans": [ + { + "bbox": [ + 306, + 456, + 390, + 468 + ], + "type": "text", + "content": "2. Related work" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 476, + 545, + 500 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 476, + 545, + 500 + ], + "spans": [ + { + "bbox": [ + 306, + 476, + 545, + 500 + ], + "type": "text", + "content": "The related works are mainly from layout-to-image generation and diffusion models." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 510, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 547, + 715 + ], + "type": "text", + "content": "Layout-to-Image Generation. Before the layout-to-image generation is formally proposed, the layout is usually used as a complementary feature [15, 29, 40] or an intermediate representation in text-to-image [12], scene-to-image generation [14]. The first image generation directly from the layout appears in Layout2Im [47] and is defined as a set of objects annotated with category and bbox. Models that work well with fine-grained semantic maps at the pixel level can also be easily transformed to this setting [13, 26, 43]. Inspired by StyleGAN [16], LostGAN-v1 [37], LostGAN-v2 [38] used a reconfigurable layout to obtain better control over individual objects. For interactive image synthesis, PLGAN [42] employed panoptic theory [18] by constructing stuff and instance layouts into separate branches and proposed Instance- and Stuff-Aware Normalization to fuse into panoptic layouts. Despite encouraging progress in this field, almost all approaches are limited to the generative" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22491" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 133 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 133 + ], + "type": "text", + "content": "adversarial network (GAN) and may suffer from unstable convergence [1] and mode collapse [27]. As a multimodal diffusion model, LDM [30] supports the condition of coarse layout and has shown great potential in layout-guided image generation." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 153, + 289, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 153, + 289, + 346 + ], + "spans": [ + { + "bbox": [ + 46, + 153, + 289, + 346 + ], + "type": "text", + "content": "Diffusion Model. Diffusion models [3, 10, 25, 30, 34-36, 44] are being recognized as a promising family of generative models that have proven to be state-of-the-art sample quality for a variety of image generation benchmarks [6, 41, 45], including class-conditional image generation [7, 48], text-to-image generation [24, 30, 31], and imaged-to-image translation [17, 22, 32]. Classifier guidance was introduced in ADM-G [7] to allow diffusion models to condition the class label. The gradient of the classifier trained on noised images could be added to the image during the sampling process. Then Ho et al. [11] proposed a classifier-free training and sampling strategy by interpolating between predictions of a diffusion model with and without condition input. For the acceleration of training and sampling speed, LDM proposed to first compress the image into smaller resolution and then apply denoising training in the latent space." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 359, + 102, + 371 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 359, + 102, + 371 + ], + "spans": [ + { + "bbox": [ + 47, + 359, + 102, + 371 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 380, + 287, + 489 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 380, + 287, + 489 + ], + "spans": [ + { + "bbox": [ + 46, + 380, + 287, + 489 + ], + "type": "text", + "content": "In this section, we propose our LayoutDiffusion, as shown in Fig. 2. The whole framework consists mainly of four parts: (a) layout embedding that preprocesses the layout input, (b) layout fusion module that encourages more interaction between objects of layout, (c) image-Layout fusion module that constructs the structural image patch and object-aware cross attention developed with the specific design for layout and image fusion, (d) the layout-conditional diffusion model with training and accelerated sampling methods." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 499, + 161, + 513 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 499, + 161, + 513 + ], + "spans": [ + { + "bbox": [ + 47, + 499, + 161, + 513 + ], + "type": "text", + "content": "3.1. Layout Embedding" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 519, + 287, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 519, + 287, + 567 + ], + "spans": [ + { + "bbox": [ + 47, + 519, + 287, + 567 + ], + "type": "text", + "content": "A layout " + }, + { + "bbox": [ + 47, + 519, + 287, + 567 + ], + "type": "inline_equation", + "content": "l = \\{o_1, o_2, \\dots, o_n\\}" + }, + { + "bbox": [ + 47, + 519, + 287, + 567 + ], + "type": "text", + "content": " is a set of " + }, + { + "bbox": [ + 47, + 519, + 287, + 567 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 47, + 519, + 287, + 567 + ], + "type": "text", + "content": " objects. Each object " + }, + { + "bbox": [ + 47, + 519, + 287, + 567 + ], + "type": "inline_equation", + "content": "o_i" + }, + { + "bbox": [ + 47, + 519, + 287, + 567 + ], + "type": "text", + "content": " is represented as " + }, + { + "bbox": [ + 47, + 519, + 287, + 567 + ], + "type": "inline_equation", + "content": "o_i = \\{b_i, c_i\\}" + }, + { + "bbox": [ + 47, + 519, + 287, + 567 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 47, + 519, + 287, + 567 + ], + "type": "inline_equation", + "content": "b_i = (x_0^i, y_0^i, x_1^i, y_1^i) \\in [0, 1]^4" + }, + { + "bbox": [ + 47, + 519, + 287, + 567 + ], + "type": "text", + "content": " denotes a bounding box (bbox) and " + }, + { + "bbox": [ + 47, + 519, + 287, + 567 + ], + "type": "inline_equation", + "content": "c_i \\in [0, \\mathcal{C} + 1]" + }, + { + "bbox": [ + 47, + 519, + 287, + 567 + ], + "type": "text", + "content": " is its category id." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 568, + 287, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 568, + 287, + 652 + ], + "spans": [ + { + "bbox": [ + 46, + 568, + 287, + 652 + ], + "type": "text", + "content": "To support the input of a variable length sequence, we need to pad " + }, + { + "bbox": [ + 46, + 568, + 287, + 652 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 46, + 568, + 287, + 652 + ], + "type": "text", + "content": " to a fixed length " + }, + { + "bbox": [ + 46, + 568, + 287, + 652 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 568, + 287, + 652 + ], + "type": "text", + "content": " by adding one " + }, + { + "bbox": [ + 46, + 568, + 287, + 652 + ], + "type": "inline_equation", + "content": "o_l" + }, + { + "bbox": [ + 46, + 568, + 287, + 652 + ], + "type": "text", + "content": " in the front and some padding " + }, + { + "bbox": [ + 46, + 568, + 287, + 652 + ], + "type": "inline_equation", + "content": "o_p" + }, + { + "bbox": [ + 46, + 568, + 287, + 652 + ], + "type": "text", + "content": " in the end, where " + }, + { + "bbox": [ + 46, + 568, + 287, + 652 + ], + "type": "inline_equation", + "content": "o_l" + }, + { + "bbox": [ + 46, + 568, + 287, + 652 + ], + "type": "text", + "content": " represents the entire layout and " + }, + { + "bbox": [ + 46, + 568, + 287, + 652 + ], + "type": "inline_equation", + "content": "o_p" + }, + { + "bbox": [ + 46, + 568, + 287, + 652 + ], + "type": "text", + "content": " represents no object. Specifically, " + }, + { + "bbox": [ + 46, + 568, + 287, + 652 + ], + "type": "inline_equation", + "content": "b_l = (0, 0, 1, 1)" + }, + { + "bbox": [ + 46, + 568, + 287, + 652 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 568, + 287, + 652 + ], + "type": "inline_equation", + "content": "c_l = 0" + }, + { + "bbox": [ + 46, + 568, + 287, + 652 + ], + "type": "text", + "content": " denotes a object that covers the whole image and " + }, + { + "bbox": [ + 46, + 568, + 287, + 652 + ], + "type": "inline_equation", + "content": "b_p = (0, 0, 0, 0)" + }, + { + "bbox": [ + 46, + 568, + 287, + 652 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 568, + 287, + 652 + ], + "type": "inline_equation", + "content": "c_p = \\mathcal{C} + 1" + }, + { + "bbox": [ + 46, + 568, + 287, + 652 + ], + "type": "text", + "content": " denotes a empty object that has no shape or does not appear in the image." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 653, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 653, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 653, + 287, + 714 + ], + "type": "text", + "content": "After the padding process, we can get a padded " + }, + { + "bbox": [ + 47, + 653, + 287, + 714 + ], + "type": "inline_equation", + "content": "l = \\{o_1, o_2, \\dots, o_k\\}" + }, + { + "bbox": [ + 47, + 653, + 287, + 714 + ], + "type": "text", + "content": " consisting of " + }, + { + "bbox": [ + 47, + 653, + 287, + 714 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 47, + 653, + 287, + 714 + ], + "type": "text", + "content": " objects, and each object has its specific position, size, and category. Then, the layout " + }, + { + "bbox": [ + 47, + 653, + 287, + 714 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 47, + 653, + 287, + 714 + ], + "type": "text", + "content": " is transformed into a layout embedding " + }, + { + "bbox": [ + 47, + 653, + 287, + 714 + ], + "type": "inline_equation", + "content": "L = \\{O_1, O_2, \\dots, O_k\\} \\in \\mathbb{R}^{k \\times d_{\\mathcal{L}}}" + }, + { + "bbox": [ + 47, + 653, + 287, + 714 + ], + "type": "text", + "content": " by the projection matrix " + }, + { + "bbox": [ + 47, + 653, + 287, + 714 + ], + "type": "inline_equation", + "content": "W_{\\mathcal{B}} \\in" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 72, + 526, + 85 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 526, + 85 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 526, + 85 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{4\\times d_{\\mathcal{L}}}" + }, + { + "bbox": [ + 306, + 72, + 526, + 85 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 72, + 526, + 85 + ], + "type": "inline_equation", + "content": "W_{\\mathcal{C}}\\in \\mathbb{R}^{1\\times d_{\\mathcal{L}}}" + }, + { + "bbox": [ + 306, + 72, + 526, + 85 + ], + "type": "text", + "content": " using the following equation:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 395, + 94, + 545, + 106 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 395, + 94, + 545, + 106 + ], + "spans": [ + { + "bbox": [ + 395, + 94, + 545, + 106 + ], + "type": "interline_equation", + "content": "L = B _ {\\mathcal {L}} + C _ {\\mathcal {L}} \\tag {1}", + "image_path": "8178f7b1e76a8b26f3cbcce317b3ad131db88e9dcd7bd02ac9947763a3d8d721.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 400, + 109, + 545, + 121 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 400, + 109, + 545, + 121 + ], + "spans": [ + { + "bbox": [ + 400, + 109, + 545, + 121 + ], + "type": "interline_equation", + "content": "B _ {\\mathcal {L}} = b W _ {\\mathcal {B}} \\tag {2}", + "image_path": "33be3c6250f908d5e1934081c0e5ce5d85e37f6dec3cd8aa7c7dce89aa42782d.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 400, + 124, + 545, + 137 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 400, + 124, + 545, + 137 + ], + "spans": [ + { + "bbox": [ + 400, + 124, + 545, + 137 + ], + "type": "interline_equation", + "content": "C _ {\\mathcal {L}} = c W _ {C} \\tag {3}", + "image_path": "ba5818776eea9624c127f9a513bee99a54a29cd23c7ffead4c1935c7bd036941.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 147, + 545, + 208 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 147, + 545, + 208 + ], + "spans": [ + { + "bbox": [ + 304, + 147, + 545, + 208 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 147, + 545, + 208 + ], + "type": "inline_equation", + "content": "B_{\\mathcal{L}}, C_{\\mathcal{L}} \\in \\mathbb{R}^{k \\times d_{\\mathcal{L}}}" + }, + { + "bbox": [ + 304, + 147, + 545, + 208 + ], + "type": "text", + "content": " are the bounding box embedding and the category embedding of a layout " + }, + { + "bbox": [ + 304, + 147, + 545, + 208 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 304, + 147, + 545, + 208 + ], + "type": "text", + "content": ", respectively. As a result, " + }, + { + "bbox": [ + 304, + 147, + 545, + 208 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 304, + 147, + 545, + 208 + ], + "type": "text", + "content": " is defined as the sum of " + }, + { + "bbox": [ + 304, + 147, + 545, + 208 + ], + "type": "inline_equation", + "content": "B_{\\mathcal{L}}" + }, + { + "bbox": [ + 304, + 147, + 545, + 208 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 147, + 545, + 208 + ], + "type": "inline_equation", + "content": "C_{\\mathcal{L}}" + }, + { + "bbox": [ + 304, + 147, + 545, + 208 + ], + "type": "text", + "content": " to include both the content and positional information of a entire layout, and " + }, + { + "bbox": [ + 304, + 147, + 545, + 208 + ], + "type": "inline_equation", + "content": "d_{\\mathcal{L}}" + }, + { + "bbox": [ + 304, + 147, + 545, + 208 + ], + "type": "text", + "content": " is the dimension of the layout embedding." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 215, + 435, + 227 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 215, + 435, + 227 + ], + "spans": [ + { + "bbox": [ + 306, + 215, + 435, + 227 + ], + "type": "text", + "content": "3.2. Layout Fusion Module" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 233, + 545, + 341 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 233, + 545, + 341 + ], + "spans": [ + { + "bbox": [ + 304, + 233, + 545, + 341 + ], + "type": "text", + "content": "Currently, each object in layout has no relationship with other objects. This leads to a low understanding of the whole scene, especially when multiple objects overlap and block each other. Therefore, to encourage more interaction between multiple objects of the layout to better understand the entire layout before inputting the layout embedding, we propose Layout Fusion Module (LFM), a transformer encoder that uses multiple layers of self-attention to fuse the layout embedding and can be denoted as" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 394, + 350, + 545, + 363 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 394, + 350, + 545, + 363 + ], + "spans": [ + { + "bbox": [ + 394, + 350, + 545, + 363 + ], + "type": "interline_equation", + "content": "L ^ {\\prime} = \\operatorname {L F M} (L) \\tag {4}", + "image_path": "ae1b54f1a848f8d7c526a91656ba3b4db42ac74c82e1cdb256c6a08ea29c302e.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 373, + 545, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 373, + 545, + 399 + ], + "spans": [ + { + "bbox": [ + 306, + 373, + 545, + 399 + ], + "type": "text", + "content": ", where the output is a fused layout embedding " + }, + { + "bbox": [ + 306, + 373, + 545, + 399 + ], + "type": "inline_equation", + "content": "L^{\\prime} = \\{O_{1}^{\\prime},O_{2}^{\\prime},\\dots ,O_{k}^{\\prime}\\} \\in \\mathbb{R}^{k\\times d_{\\mathcal{L}}}" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 405, + 468, + 417 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 405, + 468, + 417 + ], + "spans": [ + { + "bbox": [ + 306, + 405, + 468, + 417 + ], + "type": "text", + "content": "3.3. Image-Layout Fusion Module" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 423, + 545, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 423, + 545, + 518 + ], + "spans": [ + { + "bbox": [ + 304, + 423, + 545, + 518 + ], + "type": "text", + "content": "Structural Image Patch. The fusion of image and layout is a difficult multimodal fusion problem, and one of the most important parts lies in the fusion of position and size. However, the image patch is limited to the semantic information of the whole feature and lacks the spatial information. Therefore, we construct a structural image patch by adding the concept of region that contains the information of position and size." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 518, + 545, + 580 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 518, + 545, + 580 + ], + "spans": [ + { + "bbox": [ + 304, + 518, + 545, + 580 + ], + "type": "text", + "content": "Specifically, " + }, + { + "bbox": [ + 304, + 518, + 545, + 580 + ], + "type": "inline_equation", + "content": "I \\in \\mathbb{R}^{h \\times w \\times d_{\\mathcal{I}}}" + }, + { + "bbox": [ + 304, + 518, + 545, + 580 + ], + "type": "text", + "content": " denotes the feature map of a entire image with height " + }, + { + "bbox": [ + 304, + 518, + 545, + 580 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 304, + 518, + 545, + 580 + ], + "type": "text", + "content": ", width " + }, + { + "bbox": [ + 304, + 518, + 545, + 580 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 304, + 518, + 545, + 580 + ], + "type": "text", + "content": ", and channel " + }, + { + "bbox": [ + 304, + 518, + 545, + 580 + ], + "type": "inline_equation", + "content": "d_{\\mathcal{I}}" + }, + { + "bbox": [ + 304, + 518, + 545, + 580 + ], + "type": "text", + "content": ". We define that " + }, + { + "bbox": [ + 304, + 518, + 545, + 580 + ], + "type": "inline_equation", + "content": "I_{u,v}" + }, + { + "bbox": [ + 304, + 518, + 545, + 580 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 304, + 518, + 545, + 580 + ], + "type": "inline_equation", + "content": "u^{\\mathrm{th}}" + }, + { + "bbox": [ + 304, + 518, + 545, + 580 + ], + "type": "text", + "content": " row and " + }, + { + "bbox": [ + 304, + 518, + 545, + 580 + ], + "type": "inline_equation", + "content": "v^{\\mathrm{th}}" + }, + { + "bbox": [ + 304, + 518, + 545, + 580 + ], + "type": "text", + "content": " column patch of " + }, + { + "bbox": [ + 304, + 518, + 545, + 580 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 304, + 518, + 545, + 580 + ], + "type": "text", + "content": " and its bounding box, or the ablated region information, is defined as " + }, + { + "bbox": [ + 304, + 518, + 545, + 580 + ], + "type": "inline_equation", + "content": "b_{I_{u,v}}" + }, + { + "bbox": [ + 304, + 518, + 545, + 580 + ], + "type": "text", + "content": " by the following equation:" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 368, + 589, + 545, + 612 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 368, + 589, + 545, + 612 + ], + "spans": [ + { + "bbox": [ + 368, + 589, + 545, + 612 + ], + "type": "interline_equation", + "content": "b _ {\\mathcal {I} _ {u, v}} = \\left(\\frac {u}{h}, \\frac {v}{w}, \\frac {u + 1}{h}, \\frac {v + 1}{w}\\right) \\tag {5}", + "image_path": "08289efaf6dbe51a5af1be86fcb9b9e63e24db07e5cb37982c6bd66c7f44555f.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 620, + 545, + 680 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 620, + 545, + 680 + ], + "spans": [ + { + "bbox": [ + 304, + 620, + 545, + 680 + ], + "type": "text", + "content": "The bounding box sets of a patched image " + }, + { + "bbox": [ + 304, + 620, + 545, + 680 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 304, + 620, + 545, + 680 + ], + "type": "text", + "content": " is defined as " + }, + { + "bbox": [ + 304, + 620, + 545, + 680 + ], + "type": "inline_equation", + "content": "b_{\\mathcal{I}} = \\{b_{\\mathcal{I}_{u,v}}|u\\in [0,h),v\\in [0,w)\\}" + }, + { + "bbox": [ + 304, + 620, + 545, + 680 + ], + "type": "text", + "content": ". As a result, the positional information of image patch and layout object is contained in the unified bounding box defined in the same spatial space, leading to better fusion of image and layout." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "text", + "content": "Positional Embedding in Unified Space. We define the positional embedding of the image and layout as " + }, + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "P_{\\mathcal{I}}" + }, + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "text", + "content": " and" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "22492" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 68, + 545, + 190 + ], + "blocks": [ + { + "bbox": [ + 47, + 68, + 545, + 190 + ], + "lines": [ + { + "bbox": [ + 47, + 68, + 545, + 190 + ], + "spans": [ + { + "bbox": [ + 47, + 68, + 545, + 190 + ], + "type": "image", + "image_path": "dea185a46bee7b955fcf0d82c49950d37eafbac5d6b61059d12080c202b026fc.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 47, + 191, + 315, + 355 + ], + "blocks": [ + { + "bbox": [ + 47, + 191, + 315, + 355 + ], + "lines": [ + { + "bbox": [ + 47, + 191, + 315, + 355 + ], + "spans": [ + { + "bbox": [ + 47, + 191, + 315, + 355 + ], + "type": "image", + "image_path": "b7672b7661b04c0abe06df22d56484095df0c5f81cea377e0b1e38b5896f34cb.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 361, + 546, + 407 + ], + "lines": [ + { + "bbox": [ + 46, + 361, + 546, + 407 + ], + "spans": [ + { + "bbox": [ + 46, + 361, + 546, + 407 + ], + "type": "text", + "content": "Figure 2. The whole pipeline of LayoutDiffusion. The layout that consisted of bounding box " + }, + { + "bbox": [ + 46, + 361, + 546, + 407 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 46, + 361, + 546, + 407 + ], + "type": "text", + "content": " and objects categories " + }, + { + "bbox": [ + 46, + 361, + 546, + 407 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 361, + 546, + 407 + ], + "type": "text", + "content": " is transformed into embedding " + }, + { + "bbox": [ + 46, + 361, + 546, + 407 + ], + "type": "inline_equation", + "content": "B_{\\mathcal{L}}, C_{\\mathcal{L}}, L" + }, + { + "bbox": [ + 46, + 361, + 546, + 407 + ], + "type": "text", + "content": ". Then Layout Fusion Module fuses layout embedding " + }, + { + "bbox": [ + 46, + 361, + 546, + 407 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 361, + 546, + 407 + ], + "type": "text", + "content": " to output the fused layout embedding " + }, + { + "bbox": [ + 46, + 361, + 546, + 407 + ], + "type": "inline_equation", + "content": "L'" + }, + { + "bbox": [ + 46, + 361, + 546, + 407 + ], + "type": "text", + "content": ". Finally, Image-Layout Fusion Module including direct addition used for global conditioning and Object-aware Cross Attention (OaCA) used for local conditioning, will fuse the layout related " + }, + { + "bbox": [ + 46, + 361, + 546, + 407 + ], + "type": "inline_equation", + "content": "B_{\\mathcal{L}}, C_{\\mathcal{L}}, L'" + }, + { + "bbox": [ + 46, + 361, + 546, + 407 + ], + "type": "text", + "content": " and the image feature " + }, + { + "bbox": [ + 46, + 361, + 546, + 407 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 46, + 361, + 546, + 407 + ], + "type": "text", + "content": " at multiple resolutions." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 320, + 191, + 544, + 355 + ], + "blocks": [ + { + "bbox": [ + 320, + 191, + 544, + 355 + ], + "lines": [ + { + "bbox": [ + 320, + 191, + 544, + 355 + ], + "spans": [ + { + "bbox": [ + 320, + 191, + 544, + 355 + ], + "type": "image", + "image_path": "036034f21e885159cbef6c3ae1edb619772eb83b1fb1f4469163352238e5725c.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 427, + 108, + 438 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 427, + 108, + 438 + ], + "spans": [ + { + "bbox": [ + 47, + 427, + 108, + 438 + ], + "type": "inline_equation", + "content": "P_{\\mathcal{L}}" + }, + { + "bbox": [ + 47, + 427, + 108, + 438 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 137, + 444, + 287, + 456 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 137, + 444, + 287, + 456 + ], + "spans": [ + { + "bbox": [ + 137, + 444, + 287, + 456 + ], + "type": "interline_equation", + "content": "B _ {\\mathcal {I}} = b _ {\\mathcal {I}} W _ {\\mathcal {B}} \\tag {6}", + "image_path": "135a81d10b446f234561f270fe48b3b4b7671300bbd57f0671b894504778d595.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 139, + 459, + 287, + 471 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 139, + 459, + 287, + 471 + ], + "spans": [ + { + "bbox": [ + 139, + 459, + 287, + 471 + ], + "type": "interline_equation", + "content": "P _ {\\mathcal {I}} = B _ {\\mathcal {I}} W _ {\\mathcal {P}} \\tag {7}", + "image_path": "af762b5df275f8dbcb556f3247c1fee62224bcddec86e92845d0b27b200fd662.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 139, + 474, + 287, + 486 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 139, + 474, + 287, + 486 + ], + "spans": [ + { + "bbox": [ + 139, + 474, + 287, + 486 + ], + "type": "interline_equation", + "content": "P _ {\\mathcal {L}} = B _ {\\mathcal {L}} W _ {\\mathcal {P}} \\tag {8}", + "image_path": "c6f441d937254e7264b14d8ff1d37aa2c544291f7e631a385839136cbbd61f0a.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 492, + 287, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 492, + 287, + 553 + ], + "spans": [ + { + "bbox": [ + 46, + 492, + 287, + 553 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 492, + 287, + 553 + ], + "type": "inline_equation", + "content": "W_{\\mathcal{B}} \\in \\mathbb{R}^{4 \\times d_{\\mathcal{L}}}" + }, + { + "bbox": [ + 46, + 492, + 287, + 553 + ], + "type": "text", + "content": " is defined in Eq. 2 and works as a shared projection matrix that transforms the coordinates of bounding box into embedding of " + }, + { + "bbox": [ + 46, + 492, + 287, + 553 + ], + "type": "inline_equation", + "content": "d_{\\mathcal{L}}" + }, + { + "bbox": [ + 46, + 492, + 287, + 553 + ], + "type": "text", + "content": " dimension. " + }, + { + "bbox": [ + 46, + 492, + 287, + 553 + ], + "type": "inline_equation", + "content": "W_{\\mathcal{P}} \\in \\mathbb{R}^{d_{\\mathcal{L}} \\times d_{\\mathcal{I}}}" + }, + { + "bbox": [ + 46, + 492, + 287, + 553 + ], + "type": "text", + "content": " is the projection matrix that transforms the " + }, + { + "bbox": [ + 46, + 492, + 287, + 553 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 46, + 492, + 287, + 553 + ], + "type": "text", + "content": " to the positional Embedding " + }, + { + "bbox": [ + 46, + 492, + 287, + 553 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 492, + 287, + 553 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 566, + 287, + 672 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 566, + 287, + 672 + ], + "spans": [ + { + "bbox": [ + 46, + 566, + 287, + 672 + ], + "type": "text", + "content": "Pointwise Addition for Global Conditioning. With the help of LFM in Eq. 4, " + }, + { + "bbox": [ + 46, + 566, + 287, + 672 + ], + "type": "inline_equation", + "content": "O_1'" + }, + { + "bbox": [ + 46, + 566, + 287, + 672 + ], + "type": "text", + "content": " can be considered as a global information of the entire layout, and " + }, + { + "bbox": [ + 46, + 566, + 287, + 672 + ], + "type": "inline_equation", + "content": "O_i'(i \\in [2, k])" + }, + { + "bbox": [ + 46, + 566, + 287, + 672 + ], + "type": "text", + "content": " is considered as the local information embedding of single object along with the other related objects. One of the easiest ways to condition the layout in the image is to directly add " + }, + { + "bbox": [ + 46, + 566, + 287, + 672 + ], + "type": "inline_equation", + "content": "O_1'" + }, + { + "bbox": [ + 46, + 566, + 287, + 672 + ], + "type": "text", + "content": ", the global information of the layout, to the multiple resolution of image features. Specifically, the condition process can be defined as" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 134, + 672, + 287, + 687 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 134, + 672, + 287, + 687 + ], + "spans": [ + { + "bbox": [ + 134, + 672, + 287, + 687 + ], + "type": "interline_equation", + "content": "I ^ {\\prime} = I + O _ {1} ^ {\\prime} W \\tag {9}", + "image_path": "f5cdf432092a2419ec3918b86d80f61102d9d0be7a70cc66b180d2b850e94dcc.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "W \\in \\mathbb{R}^{d_{\\mathcal{L}} \\times d_{\\mathcal{I}}}" + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "content": " is a projection matrix and " + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "I'" + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "content": " is the image feature conditioned with global embedding of layout." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 427, + 545, + 438 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 427, + 545, + 438 + ], + "spans": [ + { + "bbox": [ + 305, + 427, + 545, + 438 + ], + "type": "text", + "content": "Object-aware Cross Attention for Local Conditioning." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 439, + 545, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 439, + 545, + 498 + ], + "spans": [ + { + "bbox": [ + 305, + 439, + 545, + 498 + ], + "type": "text", + "content": "Cross attention is successfully applied in [24] to condition text into image feature, where the sequence of the image patch is used as the query and the concatenated sequence of the image patch and text is applied as key and value. The equation of cross-attention is defined as" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 324, + 508, + 545, + 536 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 324, + 508, + 545, + 536 + ], + "spans": [ + { + "bbox": [ + 324, + 508, + 545, + 536 + ], + "type": "interline_equation", + "content": "\\operatorname {A t t e n t i o n} (Q, K, V) = \\operatorname {s o f t m a x} \\left(\\frac {Q K ^ {T}}{\\sqrt {d _ {k}}}\\right) V \\tag {10}", + "image_path": "31419804c3e05e8a0d72a3ec8cb5cebecc59df2f256546101e8a4a14674e531f.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 544, + 545, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 544, + 545, + 593 + ], + "spans": [ + { + "bbox": [ + 305, + 544, + 545, + 593 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 305, + 544, + 545, + 593 + ], + "type": "inline_equation", + "content": "Q, K, V" + }, + { + "bbox": [ + 305, + 544, + 545, + 593 + ], + "type": "text", + "content": " represent the embeddings of query, key, and value, respectively. In the following paper, we will use the subscript image and layout to represent the image patch feature and layout feature, respectively." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": "In text-to-image generation, each token in the text sequence is a word. The aggregation of these words constitutes the semantics of a sentence. After the transformer encoder, the first token in text sequence is well-semantic information that generalizes the whole text but may not reverse the semantic meaning of each word. However, the loss in information of one token is relatively serious in layout rather than in text. Each token in the layout sequence is a single object with a specific category, size, and position. The loss of information on a layout token will directly lead" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22493" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "content": "to a missing or wrong object in the generated image pixel space." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 96, + 287, + 131 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 96, + 287, + 131 + ], + "spans": [ + { + "bbox": [ + 46, + 96, + 287, + 131 + ], + "type": "text", + "content": "Therefore, we take into account the fusion of locations, size, and category of objects and define our object-aware cross-attention (OaCA) as" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 92, + 141, + 287, + 154 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 92, + 141, + 287, + 154 + ], + "spans": [ + { + "bbox": [ + 92, + 141, + 287, + 154 + ], + "type": "interline_equation", + "content": "Q = \\Psi_ {1} \\left(Q _ {\\mathcal {I}}, Q _ {\\mathcal {L}}\\right) \\tag {11}", + "image_path": "49a11d32dc7c478c20d4709c48d50bb68a586ac1ce3d90581e15e09a6a318ef2.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 91, + 156, + 287, + 169 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 156, + 287, + 169 + ], + "spans": [ + { + "bbox": [ + 91, + 156, + 287, + 169 + ], + "type": "interline_equation", + "content": "K = \\Psi_ {1} \\left(\\Psi_ {2} \\left(K _ {\\mathcal {I}}, K _ {\\mathcal {L}}\\right), \\Psi_ {2} \\left(P _ {\\mathcal {I}}, P _ {\\mathcal {L}}\\right)\\right) \\tag {12}", + "image_path": "fb3d51c7e211b64e6d596003ac84839476ebd38072e8cccc5325a0b55e148dc8.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 93, + 171, + 287, + 184 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 93, + 171, + 287, + 184 + ], + "spans": [ + { + "bbox": [ + 93, + 171, + 287, + 184 + ], + "type": "interline_equation", + "content": "V = \\Psi_ {2} \\left(V _ {\\mathcal {I}}, V _ {\\mathcal {L}}\\right) \\tag {13}", + "image_path": "3eb0239a165ad966ab1cb34f9a499c0daed710c7bf7d010d135f5a5295ce0ecd.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 194, + 287, + 243 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 194, + 287, + 243 + ], + "spans": [ + { + "bbox": [ + 47, + 194, + 287, + 243 + ], + "type": "text", + "content": ", where the query " + }, + { + "bbox": [ + 47, + 194, + 287, + 243 + ], + "type": "inline_equation", + "content": "Q \\in \\mathbb{R}^{hw \\times 2d_{\\mathcal{I}}}" + }, + { + "bbox": [ + 47, + 194, + 287, + 243 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 194, + 287, + 243 + ], + "type": "inline_equation", + "content": "K \\in \\mathbb{R}^{(hw + k) \\times 2d_{\\mathcal{I}}}" + }, + { + "bbox": [ + 47, + 194, + 287, + 243 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 194, + 287, + 243 + ], + "type": "inline_equation", + "content": "V \\in \\mathbb{R}^{(hw + k) \\times d_{\\mathcal{I}}}" + }, + { + "bbox": [ + 47, + 194, + 287, + 243 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 47, + 194, + 287, + 243 + ], + "type": "inline_equation", + "content": "\\Psi_1" + }, + { + "bbox": [ + 47, + 194, + 287, + 243 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 194, + 287, + 243 + ], + "type": "inline_equation", + "content": "\\Psi_2" + }, + { + "bbox": [ + 47, + 194, + 287, + 243 + ], + "type": "text", + "content": " denote concatenation on the dimension of the channel and length of the sequence, respectively." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 59, + 243, + 259, + 255 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 243, + 259, + 255 + ], + "spans": [ + { + "bbox": [ + 59, + 243, + 259, + 255 + ], + "type": "text", + "content": "We first construct the key and value of the layout:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 86, + 263, + 287, + 286 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 263, + 287, + 286 + ], + "spans": [ + { + "bbox": [ + 86, + 263, + 287, + 286 + ], + "type": "interline_equation", + "content": "K _ {\\mathcal {L}}, V _ {\\mathcal {L}} = \\operatorname {C o n v} \\left(\\frac {1}{2} \\left(\\operatorname {N o r m} \\left(C _ {\\mathcal {L}}\\right) + L ^ {\\prime}\\right)\\right) \\tag {14}", + "image_path": "3b001257728d1394a6083115012c486ec967e8027e0a1a7f11634b21a7ce8b13.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 295, + 287, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 295, + 287, + 403 + ], + "spans": [ + { + "bbox": [ + 46, + 295, + 287, + 403 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 295, + 287, + 403 + ], + "type": "inline_equation", + "content": "K_{\\mathcal{L}}, V_{\\mathcal{L}} \\in \\mathbb{R}^{k \\times d_{\\mathcal{I}}}" + }, + { + "bbox": [ + 46, + 295, + 287, + 403 + ], + "type": "text", + "content": " and Conv is the convolution operation. The embedding of key and value in the layout is related to the category embedding " + }, + { + "bbox": [ + 46, + 295, + 287, + 403 + ], + "type": "inline_equation", + "content": "C_{\\mathcal{L}}" + }, + { + "bbox": [ + 46, + 295, + 287, + 403 + ], + "type": "text", + "content": " and the fused layout embedding " + }, + { + "bbox": [ + 46, + 295, + 287, + 403 + ], + "type": "inline_equation", + "content": "L'" + }, + { + "bbox": [ + 46, + 295, + 287, + 403 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 46, + 295, + 287, + 403 + ], + "type": "inline_equation", + "content": "C_{\\mathcal{L}}" + }, + { + "bbox": [ + 46, + 295, + 287, + 403 + ], + "type": "text", + "content": " focuses on the category information of layout and " + }, + { + "bbox": [ + 46, + 295, + 287, + 403 + ], + "type": "inline_equation", + "content": "L'" + }, + { + "bbox": [ + 46, + 295, + 287, + 403 + ], + "type": "text", + "content": " concentrates on the comprehensive information of both the object itself and other objects that may have a relationship with it. By averaging between " + }, + { + "bbox": [ + 46, + 295, + 287, + 403 + ], + "type": "inline_equation", + "content": "L'" + }, + { + "bbox": [ + 46, + 295, + 287, + 403 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 295, + 287, + 403 + ], + "type": "inline_equation", + "content": "C_{\\mathcal{L}}" + }, + { + "bbox": [ + 46, + 295, + 287, + 403 + ], + "type": "text", + "content": ", we can obtain both the general information of the object and also emphasize the category information of the object." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 403, + 287, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 403, + 287, + 426 + ], + "spans": [ + { + "bbox": [ + 46, + 403, + 287, + 426 + ], + "type": "text", + "content": "We construct the query, key, and value of the image feature as follows:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 100, + 436, + 287, + 449 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 100, + 436, + 287, + 449 + ], + "spans": [ + { + "bbox": [ + 100, + 436, + 287, + 449 + ], + "type": "interline_equation", + "content": "Q _ {\\mathcal {I}}, K _ {\\mathcal {I}}, V _ {\\mathcal {I}} = \\operatorname {C o n v} (\\operatorname {N o r m} (I)) \\tag {15}", + "image_path": "ff2d67a636375543c719f50d2f874697a32f7519870daf5143f906d2cd186234.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 458, + 237, + 470 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 458, + 237, + 470 + ], + "spans": [ + { + "bbox": [ + 47, + 458, + 237, + 470 + ], + "type": "text", + "content": "3.4. Layout-conditional Diffusion Model" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 476, + 287, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 476, + 287, + 536 + ], + "spans": [ + { + "bbox": [ + 46, + 476, + 287, + 536 + ], + "type": "text", + "content": "Here, we follow the Gaussian diffusion models improved by [10, 35]. Given a data point sampled from a real data distribution " + }, + { + "bbox": [ + 46, + 476, + 287, + 536 + ], + "type": "inline_equation", + "content": "x_0 \\sim q(x_0)" + }, + { + "bbox": [ + 46, + 476, + 287, + 536 + ], + "type": "text", + "content": ", a forward diffusion process is defined by adding small amount of Gaussian noise to the " + }, + { + "bbox": [ + 46, + 476, + 287, + 536 + ], + "type": "inline_equation", + "content": "x_0" + }, + { + "bbox": [ + 46, + 476, + 287, + 536 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 46, + 476, + 287, + 536 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 476, + 287, + 536 + ], + "type": "text", + "content": " steps:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 71, + 546, + 287, + 559 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 71, + 546, + 287, + 559 + ], + "spans": [ + { + "bbox": [ + 71, + 546, + 287, + 559 + ], + "type": "interline_equation", + "content": "q \\left(x _ {t} \\mid x _ {t - 1}\\right) := \\mathcal {N} \\left(x _ {t}; \\sqrt {\\alpha_ {t}} x _ {t - 1}, (1 - \\alpha_ {t}) \\mathbf {I}\\right) \\tag {16}", + "image_path": "fe509faecdf09ca3c16548e6fc47d0be9a70e219818bb8f0669def322505c8fc.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 568, + 287, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 568, + 287, + 688 + ], + "spans": [ + { + "bbox": [ + 46, + 568, + 287, + 688 + ], + "type": "text", + "content": "If the total noise added throughout the Markov chain is large enough, the " + }, + { + "bbox": [ + 46, + 568, + 287, + 688 + ], + "type": "inline_equation", + "content": "x_{T}" + }, + { + "bbox": [ + 46, + 568, + 287, + 688 + ], + "type": "text", + "content": " will be well approximated by " + }, + { + "bbox": [ + 46, + 568, + 287, + 688 + ], + "type": "inline_equation", + "content": "\\mathcal{N}(0,\\mathbf{I})" + }, + { + "bbox": [ + 46, + 568, + 287, + 688 + ], + "type": "text", + "content": ". If we add noise at each step with a sufficiently small magnitude " + }, + { + "bbox": [ + 46, + 568, + 287, + 688 + ], + "type": "inline_equation", + "content": "1 - \\alpha_{t}" + }, + { + "bbox": [ + 46, + 568, + 287, + 688 + ], + "type": "text", + "content": ", the posterior " + }, + { + "bbox": [ + 46, + 568, + 287, + 688 + ], + "type": "inline_equation", + "content": "q(x_{t - 1}|x_t)" + }, + { + "bbox": [ + 46, + 568, + 287, + 688 + ], + "type": "text", + "content": " will be well approximated by a diagonal Gaussian. This nice property ensures that we can reverse the above forward process and sample from " + }, + { + "bbox": [ + 46, + 568, + 287, + 688 + ], + "type": "inline_equation", + "content": "x_{T}\\sim \\mathcal{N}(0,\\mathbf{I})" + }, + { + "bbox": [ + 46, + 568, + 287, + 688 + ], + "type": "text", + "content": ", which is a Gaussian noise. However, since the entire dataset is needed, we are unable to easily estimate the posterior. Instead, we have to learn a model " + }, + { + "bbox": [ + 46, + 568, + 287, + 688 + ], + "type": "inline_equation", + "content": "p_{\\theta}(x_{t - 1}|x_t)" + }, + { + "bbox": [ + 46, + 568, + 287, + 688 + ], + "type": "text", + "content": " to approximate it:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 93, + 697, + 287, + 711 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 93, + 697, + 287, + 711 + ], + "spans": [ + { + "bbox": [ + 93, + 697, + 287, + 711 + ], + "type": "interline_equation", + "content": "p _ {\\theta} \\left(x _ {t - 1} \\mid x _ {t}\\right) := \\mathcal {N} \\left(\\mu_ {\\theta} \\left(x _ {t}\\right), \\Sigma_ {\\theta} \\left(x _ {t}\\right)\\right) \\tag {17}", + "image_path": "59db590864bbc60cce3bf8d50db94ab6c778669f5a4cac90ce5cda5c53664282.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 72, + 545, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 156 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 156 + ], + "type": "text", + "content": "Instead of using the tractable variational lower bound (VLB) in " + }, + { + "bbox": [ + 305, + 72, + 545, + 156 + ], + "type": "inline_equation", + "content": "\\log p_{\\theta}(x_0)" + }, + { + "bbox": [ + 305, + 72, + 545, + 156 + ], + "type": "text", + "content": ", Ho et al. [10] proposed to reweight the terms of the VLB to optimize a surrogate objective. Specifically, we first add " + }, + { + "bbox": [ + 305, + 72, + 545, + 156 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 305, + 72, + 545, + 156 + ], + "type": "text", + "content": " steps of Gaussian noise to a clean sample " + }, + { + "bbox": [ + 305, + 72, + 545, + 156 + ], + "type": "inline_equation", + "content": "x_0" + }, + { + "bbox": [ + 305, + 72, + 545, + 156 + ], + "type": "text", + "content": " to generate a noised sample " + }, + { + "bbox": [ + 305, + 72, + 545, + 156 + ], + "type": "inline_equation", + "content": "x_{t} \\sim q(x_{t}|x_{0})" + }, + { + "bbox": [ + 305, + 72, + 545, + 156 + ], + "type": "text", + "content": ". Then train a model " + }, + { + "bbox": [ + 305, + 72, + 545, + 156 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 305, + 72, + 545, + 156 + ], + "type": "text", + "content": " to predict the added noise using the following loss:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 318, + 165, + 545, + 179 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 165, + 545, + 179 + ], + "spans": [ + { + "bbox": [ + 318, + 165, + 545, + 179 + ], + "type": "interline_equation", + "content": "\\mathcal {L} := E _ {t \\sim [ 1, T ], x _ {0} \\sim q (x _ {0}), \\epsilon \\sim \\mathcal {N} (0, \\mathbf {I})} [ \\| \\epsilon - \\epsilon_ {\\theta} (x _ {t}, t) \\| ^ {2} ] \\tag {18}", + "image_path": "8b49ddc891744c58e367be9f65960242eba06eee65c5549f7fa7547c0da1ece9.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 189, + 491, + 200 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 189, + 491, + 200 + ], + "spans": [ + { + "bbox": [ + 306, + 189, + 491, + 200 + ], + "type": "text", + "content": ", which is a standard mean-squared error loss." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 200, + 545, + 320 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 200, + 545, + 320 + ], + "spans": [ + { + "bbox": [ + 305, + 200, + 545, + 320 + ], + "type": "text", + "content": "To support the layout condition, we apply classifier-free guidance, a technique proposed by Ho et al. [11] for conditional generation that requires no additional training of the classifier. It is accomplished by interpolating between predictions of a diffusion model with and without condition input. For the condition of layout, we first construct a padding layout " + }, + { + "bbox": [ + 305, + 200, + 545, + 320 + ], + "type": "inline_equation", + "content": "l_{\\phi} = \\{o_l,o_p,\\dots ,o_p\\}" + }, + { + "bbox": [ + 305, + 200, + 545, + 320 + ], + "type": "text", + "content": ". During training, the condition of layout " + }, + { + "bbox": [ + 305, + 200, + 545, + 320 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 305, + 200, + 545, + 320 + ], + "type": "text", + "content": " of diffusion model will be replaced with " + }, + { + "bbox": [ + 305, + 200, + 545, + 320 + ], + "type": "inline_equation", + "content": "l_{\\phi}" + }, + { + "bbox": [ + 305, + 200, + 545, + 320 + ], + "type": "text", + "content": " with a fixed probability. When sampling, the following equation is used to sample a layout-condional image:" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 319, + 329, + 545, + 342 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 319, + 329, + 545, + 342 + ], + "spans": [ + { + "bbox": [ + 319, + 329, + 545, + 342 + ], + "type": "interline_equation", + "content": "\\hat {\\epsilon} _ {\\theta} \\left(x _ {t}, t | l\\right) = (1 - s) \\cdot \\epsilon_ {\\theta} \\left(x _ {t}, t \\mid l _ {\\phi}\\right) + s \\cdot \\epsilon_ {\\theta} \\left(x _ {t}, t \\mid l\\right) \\tag {19}", + "image_path": "19ee07b52b9bad0cf4c842e27944df31d5b039d0a374949a5c0c41546a6ffc49.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 352, + 545, + 387 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 352, + 545, + 387 + ], + "spans": [ + { + "bbox": [ + 305, + 352, + 545, + 387 + ], + "type": "text", + "content": ", where the scale " + }, + { + "bbox": [ + 305, + 352, + 545, + 387 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 305, + 352, + 545, + 387 + ], + "type": "text", + "content": " can be used to increase the gap between " + }, + { + "bbox": [ + 305, + 352, + 545, + 387 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(x_t,t|l_\\phi)" + }, + { + "bbox": [ + 305, + 352, + 545, + 387 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 352, + 545, + 387 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(x_t,t|l)" + }, + { + "bbox": [ + 305, + 352, + 545, + 387 + ], + "type": "text", + "content": " to enhance the strength of conditional guidance." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 305, + 388, + 545, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 388, + 545, + 483 + ], + "spans": [ + { + "bbox": [ + 305, + 388, + 545, + 483 + ], + "type": "text", + "content": "To further improve the user experience of LayoutDiffusion, we also make several optimizations on the speed of the classifier-free sampling process and could significantly outperform the SOTA models in 25 iterations. Specifically, we adapt DPM-solver [21] for the conditional classifier-free sampling, a fast dedicated high-order solver for diffusion ODEs [36] with the convergence order guarantee, to accelerate the conditional sampling speed." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 306, + 495, + 386, + 508 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 495, + 386, + 508 + ], + "spans": [ + { + "bbox": [ + 306, + 495, + 386, + 508 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 305, + 514, + 545, + 621 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 514, + 545, + 621 + ], + "spans": [ + { + "bbox": [ + 305, + 514, + 545, + 621 + ], + "type": "text", + "content": "In this section, we evaluate our LayoutDiffusion on different benchmarks in terms of various metrics. First, we introduce the datasets and evaluation metrics. Second, we show the qualitative and quantitative results compared with other strategies. Finally, some ablation studies and analysis are also mentioned. More details can be found in Appendix, including model architecture, training hyperparameters, reproduction results, more experimental results and visualizations." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 306, + 630, + 368, + 641 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 630, + 368, + 641 + ], + "spans": [ + { + "bbox": [ + 306, + 630, + 368, + 641 + ], + "type": "text", + "content": "4.1. Datasets" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 306, + 648, + 544, + 672 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 648, + 544, + 672 + ], + "spans": [ + { + "bbox": [ + 306, + 648, + 544, + 672 + ], + "type": "text", + "content": "We conduct our experiments on two popular datasets, COCO-Stuff [5] and Visual Genome [19]." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "content": "COCO-Stuff has 164K images from COCO 2017, of which the images contain bounding boxes and pixel-level segmentation masks for 80 categories of thing and 91 categories" + } + ] + } + ], + "index": 27 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22494" + } + ] + } + ], + "index": 28 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 72, + 542, + 430 + ], + "blocks": [ + { + "bbox": [ + 50, + 72, + 542, + 430 + ], + "lines": [ + { + "bbox": [ + 50, + 72, + 542, + 430 + ], + "spans": [ + { + "bbox": [ + 50, + 72, + 542, + 430 + ], + "type": "image", + "image_path": "dfcd2b773a3a396f58a965a3817b0c914207b2b37bb8f34e5c441bfc3c632eda.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 442, + 546, + 464 + ], + "lines": [ + { + "bbox": [ + 47, + 442, + 546, + 464 + ], + "spans": [ + { + "bbox": [ + 47, + 442, + 546, + 464 + ], + "type": "text", + "content": "Figure 3. Visualization of comparison with SOTA methods on COCO-stuff " + }, + { + "bbox": [ + 47, + 442, + 546, + 464 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 47, + 442, + 546, + 464 + ], + "type": "text", + "content": ". LayoutDiffusion has better generation quality and stronger controllability compared to the other methods." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 50, + 473, + 542, + 646 + ], + "blocks": [ + { + "bbox": [ + 50, + 473, + 542, + 646 + ], + "lines": [ + { + "bbox": [ + 50, + 473, + 542, + 646 + ], + "spans": [ + { + "bbox": [ + 50, + 473, + 542, + 646 + ], + "type": "table", + "html": "
MethodsCOCO-stuffVG
FID ↓IS ↑DS ↑CAS ↑YOLOScore ↑FID ↓DS ↑CAS ↑
128×128
Grid2Im [2]59.5012.50±0.300.28±0.114.056.80---
LostGAN-v2 [38]24.7614.21±0.400.45±0.0939.9113.6029.000.42±0.0929.74
PLGAN [42]22.7015.60±0.300.16±0.7238.7013.4020.62--
LayoutDiffusion16.5720.17±0.560.47±0.0943.6027.0016.350.49±0.0936.45
256×256
Grid2Im [2]65.2016.40±0.700.34±0.134.819.70---
LostGAN-v2 [38]31.1818.01±0.500.56±0.1040.0017.5032.080.53±0.1034.48
PLGAN [42]29.1018.90±0.300.52±0.1037.6514.4028.06--
LayoutDiffusion15.6128.36±0.750.57±0.1047.7432.0015.630.59±0.1048.90
", + "image_path": "ee84d8e76a0f07374c2a1d0ef500ddfe06fc918764afaba67ad8520ac7ede8d2.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 655, + 546, + 700 + ], + "lines": [ + { + "bbox": [ + 46, + 655, + 546, + 700 + ], + "spans": [ + { + "bbox": [ + 46, + 655, + 546, + 700 + ], + "type": "text", + "content": "Table 1. Quantitative results on COCO-stuff [5] and VG [19]. The proposed diffusion method has made great progress in all evaluation metrics, showing better quality, controllability, diversity, and accuracy than previous works. For COCO-stuff, we evaluate on 3097 layout and sample 5 images for each layout. For VG, we evaluate on 5096 layout and sample 1 image for each layout. We also report reproduction scores of previous works in Appendix." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "22495" + } + ] + } + ], + "index": 4 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 73, + 65, + 518, + 144 + ], + "blocks": [ + { + "bbox": [ + 73, + 65, + 518, + 144 + ], + "lines": [ + { + "bbox": [ + 73, + 65, + 518, + 144 + ], + "spans": [ + { + "bbox": [ + 73, + 65, + 518, + 144 + ], + "type": "table", + "html": "
LFMOaCACAFID ↓IS ↑DS ↑CAS ↑YOLOScore ↑
29.94 (+13.37)13.59±0.29 (-6.58)0.70±0.08 (+0.23)3.83 (-39.77)0.00 (-27.00)
✓17.06 (+0.49)19.21±0.53 (-0.96)0.52±0.09 (+0.05)30.86 (-12.74)6.90 (-20.10)
✓16.76 (+0.19)19.57±0.40 (-0.60)0.48±0.09 (+0.01)40.67 (-2.93)18.80 (-8.20)
✓✓16.46 (-0.11)19.79±0.40 (-0.38)0.48±0.10 (+0.01)42.47 (-1.13)23.60 (-3.40)
✓✓16.5720.17±0.560.47±0.0943.6027.00
", + "image_path": "eba1a7b455c4549d664c21d4965b340640b0413fc9ded5ccff8eeba74da5c425.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 188, + 288, + 272 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 188, + 288, + 272 + ], + "spans": [ + { + "bbox": [ + 46, + 188, + 288, + 272 + ], + "type": "text", + "content": "of stuff, respectively. Following the settings of LostGANv2 [38], we use the COCO 2017 Stuff Segmentation Challenge subset that contains " + }, + { + "bbox": [ + 46, + 188, + 288, + 272 + ], + "type": "inline_equation", + "content": "40\\mathrm{K} / 5\\mathrm{k} / 5\\mathrm{k}" + }, + { + "bbox": [ + 46, + 188, + 288, + 272 + ], + "type": "text", + "content": " images for train / val / test-dev set, respectively. We use images in the train and val set with 3 to 8 objects that cover more than " + }, + { + "bbox": [ + 46, + 188, + 288, + 272 + ], + "type": "inline_equation", + "content": "2\\%" + }, + { + "bbox": [ + 46, + 188, + 288, + 272 + ], + "type": "text", + "content": " of the image and not belong to crowd. Finally, there are 25,210 train and 3,097 val images." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 277, + 287, + 385 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 277, + 287, + 385 + ], + "spans": [ + { + "bbox": [ + 46, + 277, + 287, + 385 + ], + "type": "text", + "content": "Visual Genome collects 108,077 images with dense annotations of objects, attributes, and relationships. Following the setting of SG2Im [14], we divide the data into " + }, + { + "bbox": [ + 46, + 277, + 287, + 385 + ], + "type": "inline_equation", + "content": "80\\%" + }, + { + "bbox": [ + 46, + 277, + 287, + 385 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 277, + 287, + 385 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 46, + 277, + 287, + 385 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 277, + 287, + 385 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 46, + 277, + 287, + 385 + ], + "type": "text", + "content": " for the train, val, test set, respectively. We select the object and relationship categories occurring at least 2000 and 500 times in the train set, respectively, and select the images with 3 to 30 bounding boxes and ignoring all small objects. Finally, the training / validation / test set will have 62565 / 5062 / 5096 images, respectively." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 393, + 218, + 405 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 393, + 218, + 405 + ], + "spans": [ + { + "bbox": [ + 47, + 393, + 218, + 405 + ], + "type": "text", + "content": "4.2. Evaluation Metrics & Protocols" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 411, + 287, + 436 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 411, + 287, + 436 + ], + "spans": [ + { + "bbox": [ + 46, + 411, + 287, + 436 + ], + "type": "text", + "content": "We use five metrics to evaluate the quality, diversity, and controllability of generation." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 436, + 287, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 436, + 287, + 496 + ], + "spans": [ + { + "bbox": [ + 46, + 436, + 287, + 496 + ], + "type": "text", + "content": "Fr'echet Inception Distance (FID) [9] shows the overall visual quality of the generated image by measuring the difference in the distribution of features between the real images and the generated images on an ImageNet-pretrained Inception-V3 [39] network." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 496, + 287, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 496, + 287, + 533 + ], + "spans": [ + { + "bbox": [ + 46, + 496, + 287, + 533 + ], + "type": "text", + "content": "Inception Score (IS) [33] uses an Inception-V3 [39] pretrained on ImageNet network to compute the statistical score of the output of the generated images." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 533, + 287, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 533, + 287, + 568 + ], + "spans": [ + { + "bbox": [ + 46, + 533, + 287, + 568 + ], + "type": "text", + "content": "Diversity Score (DS) calculates the diversity between two generated images of the same layout by comparing the LPIPS [46] metric in a DNN feature space between them." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 568, + 287, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 568, + 287, + 617 + ], + "spans": [ + { + "bbox": [ + 46, + 568, + 287, + 617 + ], + "type": "text", + "content": "Classification Score (CAS) [28] first crops the ground truth box area of images and resizing them at a resolution of " + }, + { + "bbox": [ + 46, + 568, + 287, + 617 + ], + "type": "inline_equation", + "content": "32 \\times 32" + }, + { + "bbox": [ + 46, + 568, + 287, + 617 + ], + "type": "text", + "content": " with their class. A ResNet-101 [8] classifier is trained with generated images and tested on real images." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 617, + 287, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 287, + 653 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 287, + 653 + ], + "type": "text", + "content": "YOLOScore [20] evaluates 80 thing categories bbox mAP on generated images using a pretrained YOLOv4 [4] model, and shows the precision of control in one generated model." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "text", + "content": "In summary, FID and IS show the generation quality, DS shows the diversity, CAS and YOLOScore represent the controllability. We follow the architecture of ADM [7], which is mainly a UNet. All experiments are conducted on 32 NVIDIA 3090s with mixed precision training [23]. We" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 188, + 545, + 224 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 188, + 545, + 224 + ], + "spans": [ + { + "bbox": [ + 304, + 188, + 545, + 224 + ], + "type": "text", + "content": "set batch size 24, learning rate 1e-5. We adopt the fixed linear variance schedule. More details can be found in the Appendix." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 231, + 415, + 244 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 231, + 415, + 244 + ], + "spans": [ + { + "bbox": [ + 306, + 231, + 415, + 244 + ], + "type": "text", + "content": "4.3. Qualitative results" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 250, + 545, + 285 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 250, + 545, + 285 + ], + "spans": [ + { + "bbox": [ + 304, + 250, + 545, + 285 + ], + "type": "text", + "content": "Comparison of generated " + }, + { + "bbox": [ + 304, + 250, + 545, + 285 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 304, + 250, + 545, + 285 + ], + "type": "text", + "content": " images on the COCO-Stuff [5] with our method and previous works [2, 38, 42] is shown in Fig. 3." + } + ] + } + ], + "index": 14 + }, + { + "type": "table", + "bbox": [ + 307, + 287, + 545, + 347 + ], + "blocks": [ + { + "bbox": [ + 46, + 148, + 547, + 182 + ], + "lines": [ + { + "bbox": [ + 46, + 148, + 547, + 182 + ], + "spans": [ + { + "bbox": [ + 46, + 148, + 547, + 182 + ], + "type": "text", + "content": "Table 2. Ablation study of Layout Fusion Module (LFM), Object-aware Cross Attention (OaCA), Cross Attention (CA). We use the model trained for 300,000 iterations on COCO-stuff " + }, + { + "bbox": [ + 46, + 148, + 547, + 182 + ], + "type": "inline_equation", + "content": "128\\times 128" + }, + { + "bbox": [ + 46, + 148, + 547, + 182 + ], + "type": "text", + "content": " . The value in brackets denotes the discrepancy to our proposed method(+LFM+OaCA), where red denotes better and green denotes worse." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 287, + 545, + 347 + ], + "lines": [ + { + "bbox": [ + 307, + 287, + 545, + 347 + ], + "spans": [ + { + "bbox": [ + 307, + 287, + 545, + 347 + ], + "type": "table", + "html": "
methodFID ↓NparamsThroughout images / sFirst stage V100 daysCond stage V100 days
LDM-8 (100 steps)42.06345M0.457663.69
LDM-4 (200 steps)40.91306M0.2672995.49
ours-small (25 steps)36.16142M0.608-75.83
ours (25 steps)31.68569M0.308-216.55
", + "image_path": "57d14e26dec80537031b9feaa6085d103b7686532c405b59db1a5133575bdf8c.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "table_body" + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 351, + 545, + 385 + ], + "lines": [ + { + "bbox": [ + 304, + 351, + 545, + 385 + ], + "spans": [ + { + "bbox": [ + 304, + 351, + 545, + 385 + ], + "type": "text", + "content": "Table 3. Comparison with SOTA diffusion-based methods LDM on COCO-stuff " + }, + { + "bbox": [ + 304, + 351, + 545, + 385 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 304, + 351, + 545, + 385 + ], + "type": "text", + "content": ". We generate the same 2048 images of LDM for a fair comparison." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 386, + 545, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 386, + 545, + 445 + ], + "spans": [ + { + "bbox": [ + 304, + 386, + 545, + 445 + ], + "type": "text", + "content": "LayoutDiffusion generates more accurate high quality images, which has more recognizable and accurate objects corresponding to their layouts. Grid2Im [2], LostGANv2 [38] and PLGAN [42] generate images with distorted and unreal objects." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 445, + 545, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 445, + 545, + 553 + ], + "spans": [ + { + "bbox": [ + 304, + 445, + 545, + 553 + ], + "type": "text", + "content": "Especially when input a set of multiple objects with complex relationships, previous work can hardly generate recognizable objects in the position corresponding to layouts. For example, in Fig. 3 (a), (c), and (e), the main objects (e.g. train, zebra, bus) in images are poorly generated in previous work, while our LayoutDiffusion generates well. In Fig. 3 (b), only our LayoutDiffusion generates the laptop in the right place. The images generated by our LayoutDiffusion are more sensorially similar to the real ones." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 554, + 545, + 589 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 554, + 545, + 589 + ], + "spans": [ + { + "bbox": [ + 304, + 554, + 545, + 589 + ], + "type": "text", + "content": "We show the diversity of LayoutDiffusion in Fig. 4. Images from the same layouts have high quality and diversity (different lighting, textures, colors, and details)." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 590, + 545, + 649 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 590, + 545, + 649 + ], + "spans": [ + { + "bbox": [ + 304, + 590, + 545, + 649 + ], + "type": "text", + "content": "We continuously add an additional layout from the initial layout, the one in the upper left corner, as shown in Fig. 5. In each step, LayoutDiffusion adds the new object in very precise locations with consistent image quality, showing user-friendly interactivity." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 652, + 421, + 663 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 652, + 421, + 663 + ], + "spans": [ + { + "bbox": [ + 306, + 652, + 421, + 663 + ], + "type": "text", + "content": "4.4. Quantitative results" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "Tab. 1 provides the comparison among previous works and our method in FID, IS, DS, CAS and YOLOScore. Compared to the SOTA method, the proposed method achieves the best performance in comparison." + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "22496" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 70, + 272, + 188 + ], + "blocks": [ + { + "bbox": [ + 61, + 70, + 272, + 188 + ], + "lines": [ + { + "bbox": [ + 61, + 70, + 272, + 188 + ], + "spans": [ + { + "bbox": [ + 61, + 70, + 272, + 188 + ], + "type": "image", + "image_path": "b4b1801920248ead66f3763840650c2b58a990e1e28a82e0d2f7b6c3b8abff1b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 194, + 286, + 216 + ], + "lines": [ + { + "bbox": [ + 46, + 194, + 286, + 216 + ], + "spans": [ + { + "bbox": [ + 46, + 194, + 286, + 216 + ], + "type": "text", + "content": "Figure 4. The diversity of LayoutDiffusion. Each row of images are from the same layout and have great difference." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 217, + 286, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 217, + 286, + 346 + ], + "spans": [ + { + "bbox": [ + 46, + 217, + 286, + 346 + ], + "type": "text", + "content": "In overall generation quality, our LayoutDiffusion outperforms the SOTA model by " + }, + { + "bbox": [ + 46, + 217, + 286, + 346 + ], + "type": "inline_equation", + "content": "46.35\\%" + }, + { + "bbox": [ + 46, + 217, + 286, + 346 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 217, + 286, + 346 + ], + "type": "inline_equation", + "content": "29.29\\%" + }, + { + "bbox": [ + 46, + 217, + 286, + 346 + ], + "type": "text", + "content": " at most in FID and IS, respectively. While maintaining high overall image quality, we also show precise and accurate controllability, LayoutDiffusion outperforms the SOTA model by " + }, + { + "bbox": [ + 46, + 217, + 286, + 346 + ], + "type": "inline_equation", + "content": "122.22\\%" + }, + { + "bbox": [ + 46, + 217, + 286, + 346 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 217, + 286, + 346 + ], + "type": "inline_equation", + "content": "41.82\\%" + }, + { + "bbox": [ + 46, + 217, + 286, + 346 + ], + "type": "text", + "content": " at most onYOLOScore and CAS, respectively. As for diversity, our LayoutDiffusion still achieves " + }, + { + "bbox": [ + 46, + 217, + 286, + 346 + ], + "type": "inline_equation", + "content": "11.30\\%" + }, + { + "bbox": [ + 46, + 217, + 286, + 346 + ], + "type": "text", + "content": " imporvement at most accroding to the DS. Experiments on these metrics show that our methods can successfully generate the higher-quality images with better location and quantity control." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 348, + 286, + 455 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 348, + 286, + 455 + ], + "spans": [ + { + "bbox": [ + 46, + 348, + 286, + 455 + ], + "type": "text", + "content": "In particular, we conduct experiments compared to LDM [30] in Tab. 3. \"Ours-small\" uses comparable GPU resources to have better FID performance with much fewer parameters and better throughout compared to LDM-8 when \"Ours-small\" outperforms LDM-4 in all respects. The results of \"Ours\" indicate that LayoutDiffusion can have better FID performance, 31.6, at a higher cost. From these results, LayoutDiffusion always achieves better performance at different cost levels compared with LDM [30]." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 457, + 145, + 468 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 457, + 145, + 468 + ], + "spans": [ + { + "bbox": [ + 47, + 457, + 145, + 468 + ], + "type": "text", + "content": "4.5. Ablation studies" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 471, + 286, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 471, + 286, + 567 + ], + "spans": [ + { + "bbox": [ + 46, + 471, + 286, + 567 + ], + "type": "text", + "content": "We validate the effectiveness of LFM and OaCA in Tab. 2, using the evaluation metrics in Sec. 4.2. The significant improvement on FID, IS, CAS, and YOLOScore proves that the application of LFM and OaCA allows for higher generation quality and diversity, along with more controllability. Furthermore, when applying both, considerable performance, " + }, + { + "bbox": [ + 46, + 471, + 286, + 567 + ], + "type": "inline_equation", + "content": "13.37 / 6.58 / 39.77 / 27.0" + }, + { + "bbox": [ + 46, + 471, + 286, + 567 + ], + "type": "text", + "content": " on FID / IS / CAS / YOLOScore, is gained." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 567, + 286, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 567, + 286, + 662 + ], + "spans": [ + { + "bbox": [ + 46, + 567, + 286, + 662 + ], + "type": "text", + "content": "An interesting phenomenon is that the change of the Diversity Score (DS) is in the opposite direction of other metrics. This is because DS, which stands for diversity, is physically the opposite of the controllability represented by other metrics such as CAS and YOLOScore. The precise control offered on generated image leads to more constraints on diversity. As a result, the Diversity Score (DS) has a slight drop compared to the baseline." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 673, + 222, + 686 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 673, + 222, + 686 + ], + "spans": [ + { + "bbox": [ + 47, + 673, + 222, + 686 + ], + "type": "text", + "content": "5. Limitations & Societal Impacts" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 689, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 286, + 713 + ], + "type": "text", + "content": "Limitations. Despite the significant improvements in various metrics, it is still difficult to generate a realistic im" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 309, + 73, + 541, + 185 + ], + "blocks": [ + { + "bbox": [ + 309, + 73, + 541, + 185 + ], + "lines": [ + { + "bbox": [ + 309, + 73, + 541, + 185 + ], + "spans": [ + { + "bbox": [ + 309, + 73, + 541, + 185 + ], + "type": "image", + "image_path": "3ad8222c1e0d0c03bccec40d64451255e71ac22e4c2a3fe35045ddb412012c51.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 200, + 545, + 222 + ], + "lines": [ + { + "bbox": [ + 305, + 200, + 545, + 222 + ], + "spans": [ + { + "bbox": [ + 305, + 200, + 545, + 222 + ], + "type": "text", + "content": "Figure 5. The interactivity of LayoutDiffusion. We add extra layout continuously, and the new objects are also with high quality." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 228, + 545, + 299 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 228, + 545, + 299 + ], + "spans": [ + { + "bbox": [ + 305, + 228, + 545, + 299 + ], + "type": "text", + "content": "age with no distortion and overlap, especially for a complex multi-object layout. Moreover, the model is trained from scratch in the specific dataset that requires detection labels. How to combine text-guided diffusion models and inherit parameters pre-trained on massive text-image datasets remains a future research." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 300, + 545, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 300, + 545, + 348 + ], + "spans": [ + { + "bbox": [ + 305, + 300, + 545, + 348 + ], + "type": "text", + "content": "Societal Impacts. Trained on the real-world datasets such as COCO [5] and VG [19], LayoutDiffusion has the powerful ability to learn the distribution of data and we should pay attention to some potential copyright infringement issues." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 354, + 378, + 365 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 354, + 378, + 365 + ], + "spans": [ + { + "bbox": [ + 306, + 354, + 378, + 365 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 369, + 545, + 571 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 369, + 545, + 571 + ], + "spans": [ + { + "bbox": [ + 304, + 369, + 545, + 571 + ], + "type": "text", + "content": "In this paper, we have proposed a one-stage end-to-end diffusion model named LayoutDiffusion, which is novel for the task of layout-to-image generation. With the guidance of layout, the diffusion model allows more control over the individual objects while maintaining higher quality than the prevailing GAN-based methods. By constructing a structural image patch with region information, we regrad each patch as a special object and accomplish the difficult multimodal image layout fusion in a unified form. Specifically, Layout Fusion Module and Object-aware Cross Attention are proposed to model the relationship among multiple objects and fuse the patched image feature with layout at multiple resolutions, respectively. Experiments in challenging COCO-stuff and Visual Genome (VG) show that our proposed method significantly outperforms both state-of-the-art GAN-based and diffusion-based methods in various evaluation metrics." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": "Acknowledgements. This work is supported in part by National Natural Science Foundation of China under Grant U20A20222, National Science Foundation for Distinguished Young Scholars under Grant 62225605, National Key Research and Development Program of China under Grant 2020AAA0107400, Research Fund of ARC Lab, Tencent PCG, Zhejiang - Singapore Innovation and AI Joint Research Lab, Ant Group through CCF-Ant Research Fund, and sponsored by CCF-AFSG Research Fund, CAAI-HUAWEI MindSpore Open Fund as well as CCF-Zhipu AI Large Model Fund (CCF-Zhipu202302)." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22497" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 18, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "type": "text", + "content": "[1] Martin Arjovsky and Léon Bottou. 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Springer, 2022. 3" + } + ] + } + ], + "index": 18 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "22499" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/LayoutFormer++_ Conditional Graphic Layout Generation via Constraint Serialization and Decoding Space Restriction/b766a11c-0ea4-4e2b-868e-229f60bdc47b_content_list.json b/2023/LayoutFormer++_ Conditional Graphic Layout Generation via Constraint Serialization and Decoding Space Restriction/b766a11c-0ea4-4e2b-868e-229f60bdc47b_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..eee7e73c78d745373f665f281efbe7459902e80c --- /dev/null +++ b/2023/LayoutFormer++_ Conditional Graphic Layout Generation via Constraint Serialization and Decoding Space Restriction/b766a11c-0ea4-4e2b-868e-229f60bdc47b_content_list.json @@ -0,0 +1,1313 @@ +[ + { + "type": "text", + "text": "LayoutFormer++: Conditional Graphic Layout Generation via Constraint Serialization and Decoding Space Restriction", + "text_level": 1, + "bbox": [ + 109, + 128, + 859, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Zhaoyun Jiang $^{1*}$ , Jiaqi Guo $^{2}$ , Shizhao Sun $^{2}$ , Huayu Deng $^{3*}$ , Zhongkai Wu $^{4*}$ , Vuksan Mijovic $^{5}$ , Zijiang James Yang $^{1}$ , Jian-Guang Lou $^{2}$ , Dongmei Zhang $^{2}$ , Xi'an Jiaotong University, Microsoft Research Asia, Shanghai Jiaotong University, Beihang University, Microsoft,", + "bbox": [ + 183, + 202, + 784, + 273 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "jzyl24@stu.xjtu.edu.cn, deng.hy99@sjtu.edu.cn, 17376487@buaa.edu.cn, zijiang@xjtu.edu.cn, {jiaqiguo, shizsu, vmijovic, jlou, dongmeiz}@microsoft.com", + "bbox": [ + 132, + 277, + 831, + 309 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 344, + 313, + 359 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Conditional graphic layout generation, which generates realistic layouts according to user constraints, is a challenging task that has not been well-studied yet. First, there is limited discussion about how to handle diverse user constraints flexibly and uniformly. Second, to make the layouts conform to user constraints, existing work often sacrifices generation quality significantly. In this work, we propose LayoutFormer++ to tackle the above problems. First, to flexibly handle diverse constraints, we propose a constraint serialization scheme, which represents different user constraints as sequences of tokens with a predefined format. Then, we formulate conditional layout generation as a sequence-to-sequence transformation, and leverage encoder-decoder framework with Transformer as the basic architecture. Furthermore, to make the layout better meet user requirements without harming quality, we propose a decoding space restriction strategy. Specifically, we prune the predicted distribution by ignoring the options that definitely violate user constraints and likely result in low-quality layouts, and make the model samples from the restricted distribution. Experiments demonstrate that LayoutFormer++ outperforms existing approaches on all the tasks in terms of both better generation quality and less constraint violation.", + "bbox": [ + 75, + 377, + 473, + 738 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 771, + 209, + 787 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Graphic designs greatly facilitate information communication in our daily life. During its creation, the layout, i.e., positions and sizes of elements, plays a critical role. To assist layout design, conditional layout generation, which takes user constraints as input and generates layouts as out", + "bbox": [ + 75, + 797, + 468, + 875 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/27d933d5397c7b9803916255e07d1034106de342f1d02cccce0b6bf403e1e941.jpg", + "image_caption": [ + "Figure 1. Comparing with previous conditional layout generation approaches, LayoutFormer++ performs better on sufficient flexibility and good controllability." + ], + "image_footnote": [], + "bbox": [ + 506, + 344, + 888, + 554 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "put, attracts great attention (see Figure 1). It is different from unconditional layout generation, which generates layouts freely without constraints, from at least two aspects. First, the model should be able to handle diverse user constraints, called sufficient flexibility. Figure 2 shows 6 typical tasks of layout generation in real-world applications including layout completion, layout refinement, layout generation conditioned on element types, element types with sizes, element relationships, or any of their combinations. Second, the model should generate layouts conforming to user requirements (i.e., constraints) as many as possible without harming quality, called good controllability (see Figure 1).", + "bbox": [ + 496, + 625, + 892, + 806 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "However, existing work cannot meet the above two requirements. First, there is no existing work can support all the layout generation tasks with different user constraints. Most existing approaches simply focus on tackling a single conditional layout generation task without considering whether they can be applied to other tasks. For example,", + "bbox": [ + 496, + 810, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Work done during an internship at Microsoft Research Asia.", + "bbox": [ + 94, + 886, + 419, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "18403", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "LayoutTransformer [3] can only perform completion task and BLT [10] cannot handle element relationships. Such task-specific approaches hinder the development of solutions for the new task. Second, there are no satisfactory methods to ensure good controllability. Some approaches directly replace the values in the predicted layout with the ones specified in the user constraints [3, 10]. Another work defines a set of heuristic rules and leverages latent optimization [8]. To make the generated layouts meet user requirements, they often degrade the generation quality significantly.", + "bbox": [ + 75, + 90, + 472, + 257 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, we propose a unified model called LayoutFormer++ to support the different scenarios of conditional layout generation. In LayoutFormer++, a set of constraints is represented as a sequence. Specifically, we use a constraint serialization scheme to serialize different user constraints into a sequence of tokens with a predefined format (see Figure 1). The intuition behind this design choice is as follows. First, the sequence format is widely used and effective. Its effectiveness in layout generation has also been demonstrated in recent works [3, 10]. Second, a sequence is very flexible to accommodate different constraints for layout generation. We can serialize any structured information in the user constraints as a sequence. We found although user needs are diverse, they are all about element types and five attributes including type, top coordinate, left coordinate, width and height. Thus, we can simply define a set of vocabularies to describe the attributes respectively and concatenate descriptions of different attributes and elements to construct a sequence.", + "bbox": [ + 75, + 260, + 472, + 547 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Therefore, the conditional layout generation problem can be formulated as a sequence-to-sequence transformation problem. This enables us to leverage a simple yet effective encoder-decoder framework with Transformer [26] as a basic model architecture. The encoder processes the user constraints in a bidirectional way. The decoder predicts the layout sequence autoregressively, where there are multiple decoding steps and the model samples one token from the predicted distribution at each decoding step.", + "bbox": [ + 75, + 550, + 468, + 686 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Furthermore, to achieve good controllability, we introduce a decoding space restriction strategy in the inference stage. Our key idea is to prune the infeasible options in the predicted distribution and make the model sample from the restricted distribution at each decoding step. Specifically, we leverage two kinds of information to prune the options. First, the options that definitely violate the user constraints are pruned. For example, if a user wants one image and two buttons, the option for putting one text box will not be acceptable. Second, the options with low probabilities in the predicted distribution, which will very likely result in low-quality layouts, are also pruned. As the feasible option set may be empty after pruning, we further introduce a backtracking mechanism, in which the model goes back", + "bbox": [ + 75, + 689, + 470, + 900 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/f6e4737ac94ef6dd4b88e71e65d84c91e0e33d669d34b54b4ef2a93ec87548c1.jpg", + "image_caption": [ + "Figure 2. Typical tasks for conditional layout generation." + ], + "image_footnote": [], + "bbox": [ + 514, + 90, + 880, + 218 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "to a certain decoding step and find a better solution. Note that the whole generation process of the proposed strategy still relies on the distribution learned from the training data. Thus, it is less likely to disturb a layout when making it better conform to user constraints.", + "bbox": [ + 496, + 257, + 890, + 332 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We conduct extensive experiments on two public datasets [15, 30] and six layout generation tasks with different user constraints, to evaluate LayoutFormer++ and compare it with state-of-the-art approaches. Experimental results show that LayoutFormer++ can successfully tackle all six layout generation tasks that are handled separately by previous work, demonstrating that it is able to provide sufficient flexibility. Furthermore, LayoutFormer++ significantly outperforms previous approaches in terms of both better generation quality and less constraint violation, indicating that it achieves good controllability.", + "bbox": [ + 496, + 333, + 892, + 500 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 512, + 640, + 527 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Graphic Layout Generation. Graphic layout generation aims at generating aesthetic layouts to tackle users' needs. As users' needs are diverse in real-world applications, various tasks of layout generation are explored (see Figure 2), such as generation condition on element types [8, 10, 12], generation condition on types and sizes [10], generation condition on element relationships [8, 12], refinement [23] and completion [3]. Some other approaches focus on unconstrained generation [2, 7, 13, 27].", + "bbox": [ + 496, + 537, + 890, + 672 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "However, none of existing approaches can achieve sufficient flexibility to handle diverse layout generation tasks, due to the limitations in constraint modeling. Some works represent the constraints in the same format of the target layout, thus can not handle other complex constraints [3, 10, 23]. For example, LayoutTransformer [3] can only handle completion task but cannot deal with relationships between elements. Other works design the modeling formats specific to the constraint, which are hard to adapt to other tasks. For example, [12] leverages graph format to represent the relationships among the elements, which is inconvenient for the size constraints. In this work, we propose LayoutFormer++ with constraint serialization scheme, modeling different constraints into same format of the sequence, eliminating the isolation between layout generation tasks.", + "bbox": [ + 496, + 674, + 892, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "18404", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Existing approaches also consider different methods for constraint satisfaction. Some approaches directly reset the predicted attributes by the values specified in the constraints [3, 10]. Other approaches define the heuristic rules and cost functions to control the generation [8, 12]. For example, [8] designs cost functions for each constraint and takes the constrained generation as an optimization problem. However, these methods often decrease the generation quality significantly. For [3, 10], directly resetting the sequence will make the generated layout deviate from the distribution learned by model. For [8, 12], it is hard to define the rules and cost functions to handle the trade-off between constraint satisfaction and generation quality. Different from existing approaches, we introduce decoding space restriction strategy to prune the infeasible values during decoding process, which does not rely on sophisticated rules or cost functions, and also fits the learned distribution.", + "bbox": [ + 75, + 90, + 472, + 347 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Decoding Methods. Decoding method plays an important role in autoregressive generation. The most prominent decoding methods include Greedy Search, Beam Search, Top-K sampling and Top-P sampling [5], etc. To enable the control over the output sequence, constrained decoding is first proposed in controllable text generation. [1,4,6,16,17,21] propose constrained decoding methods for hard lexical constraints where a set of tokens are required to occur in target output. [22,28] present decoding methods for soft constraints which assign a value between 0 and 1 to indicate how constraints are satisfied. [11, 24, 25] introduce decoding methods for structural constraints which impose a rigorous structures on the output sequence. Inspired by these methods, we propose a new constrained decoding method tailored for conditional layout generation. We carefully design two pruning modules and a backtracking mechanism to improve the satisfaction of constraints while maintaining high layout quality.", + "bbox": [ + 75, + 349, + 472, + 621 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Approach", + "text_level": 1, + "bbox": [ + 76, + 637, + 187, + 656 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Overview", + "text_level": 1, + "bbox": [ + 76, + 662, + 187, + 679 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "A layout is made up of a set of elements, where each element can be described by its type $c$ , left and top coordinate $x$ and $y$ , as well as width $w$ and height $h$ . The continuous attributes $x$ , $y$ , $w$ and $h$ are quantized, which is proven to be helpful for graphic layouts [2, 3, 23]. Thus, an element can be represented by five tokens. Following the state-of-the-art approaches, we represent a layout by concatenating all the elements' tokens, i.e., $L = \\{\\langle \\mathrm{so}\\rangle c_1 x_1 y_1 w_1 h_1 \\dots c_N x_N y_N w_N h_N \\langle \\mathrm{eos}\\rangle\\}$ . Here, $N$ denotes the total number of elements, $\\langle \\mathrm{so}\\rangle$ and $\\langle \\mathrm{eos}\\rangle$ are special tokens indicating the start and end of a sequence.", + "bbox": [ + 75, + 686, + 468, + 854 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this work, we propose a new approach named LayoutFormer++ for conditional layout generation. The overall model architecture is illustrated in Figure 3a.", + "bbox": [ + 75, + 854, + 468, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To achieve sufficient flexibility, different constraints are formatted uniformly into sequence through constraint serialization. The details of the constraint serialization scheme will be introduced in Section 3.2.", + "bbox": [ + 496, + 90, + 890, + 150 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We leverage a Transformer encoder-decoder architecture for LayoutFormer++ based on the experience of previous works. The bidirectional encoder takes the constraint sequence as input and outputs their contextualized representations. The autoregressive decoder iteratively predicts the probabilities of future tokens. The model is trained to minimize the negative log-likelihood of layout tokens, i.e.,", + "bbox": [ + 496, + 150, + 893, + 250 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\text {m i n i m i z e} \\sum_ {t = 1} ^ {N} - \\log P _ {\\boldsymbol {\\theta}} \\left(L _ {t} \\mid L _ {< t}, S\\right), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 584, + 256, + 890, + 292 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $S$ is the input constraint sequence, $L$ is the output layout sequence, $\\theta$ refers to the model parameters and $N$ denotes the length of the layout sequence.", + "bbox": [ + 496, + 301, + 890, + 345 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Finally, we introduce the decoding space restriction strategy with a backtracking mechanism into inference process to achieve good controllability. The details of the decoding space restriction strategy are given in Section 3.3.", + "bbox": [ + 496, + 347, + 890, + 407 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Serializing Constraints", + "text_level": 1, + "bbox": [ + 500, + 415, + 714, + 431 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2.1 Principles", + "text_level": 1, + "bbox": [ + 500, + 439, + 625, + 455 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Instead of directly presenting concrete sequences for the constraints considered in previous work, we first introduce the principles for serializing constraints. These principles not only summarize how the existing constraints are serialized but also provide a general guidance for formulating other constraints. There are two critical questions in serializing constraints. First, how to represent each constraint in a sequence format. Second, how to combine different constraints into a complete sequence.", + "bbox": [ + 496, + 462, + 890, + 598 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Constraint Representation. To present a constraint as a sequence, the basic idea is to first define a set of vocabularies and then concatenate the tokens from these vocabularies. Specifically, the constraints often fall into two categories.", + "bbox": [ + 496, + 599, + 890, + 657 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "First, some constraints are only related to a single element. For example, put an image on the page or the element should be 10 pixel wide. The serialization for such constraint is quite straightforward: we just define a vocabulary and then represent the constraint by a single token from the vocabulary. For example, for the constraints about element type, the vocabulary could be {image, toolbar,..., button}, and the constraint 'an image' can be represented as image.", + "bbox": [ + 496, + 659, + 890, + 794 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Second, other constraints are related to multiple elements. For example, put an image on top of a button. To distinguish the elements referred in the constraint, we first build a vocabulary representing unique IDs for the elements. Then, we define a vocabulary for the relationships between elements. At last, we concatenate the tokens of element IDs and relationships.", + "bbox": [ + 496, + 795, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "18405", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/959513a4efc1d8268a14525d5ab7ffe242e70b7cc22966d6d210d5359eb732d8.jpg", + "image_caption": [ + "(a) Model Architecture" + ], + "image_footnote": [], + "bbox": [ + 112, + 88, + 509, + 224 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/4fb778f68a209b526aadc643e33f1c16f9c19dd935dce5577d36cde54024c635.jpg", + "image_caption": [ + "(b) Input and Output Sequences", + "Figure 3. a The overall model architecture of LayoutFormer++, illustrated by taking the task Gen-R as an example. b The examples of input and output sequences for different conditional layout generation tasks through constraint serialization." + ], + "image_footnote": [], + "bbox": [ + 553, + 97, + 851, + 220 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For example, the vocabulary for element IDs could be $\\{\\mathrm{image}_1,\\dots ,\\mathrm{image}_{K_1},\\dots ,\\mathrm{button}_1,\\dots ,\\mathrm{button}_{K_t}\\}$ , and the vocabulary for relationships could be $\\{\\mathrm{top},\\dots ,\\mathrm{small}\\}$ . Then, the constraint 'an image on top of a button' is represented as $\\mathrm{image}_1$ top $\\mathrm{button}_1$ .", + "bbox": [ + 75, + 295, + 473, + 369 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Constraint Combination. To combine different constraints, we concatenate their sequences. To ease the learning of neural network, we use a fixed order instead of a random order when concatenating different constraints. First, for the constraints only related to a single element, we first concatenate those for the same element and then concatenate those from different elements. Second, for the constraints related to multiple elements, we put them after all the constraints for the single elements.", + "bbox": [ + 75, + 369, + 472, + 507 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2.2 Examples for Typical Tasks", + "text_level": 1, + "bbox": [ + 76, + 525, + 323, + 540 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this work, we consider six typical layout generation tasks which has been explored in previous work. We demonstrate how we formulate the constraint sequences for these tasks according to Section 3.2.1 as followed.", + "bbox": [ + 75, + 549, + 468, + 609 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Generation conditioned on types (Gen-T) is to generate layouts from the element types specified by user constraints. We formulate the input constraint sequence by concatenating the single-element constraints of element type, i.e., $S_{\\mathrm{Gen - T}} = \\{\\langle \\mathrm{sos}\\rangle c_1|c_2|\\dots |c_N\\langle \\mathrm{eos}\\rangle \\} .^1$", + "bbox": [ + 75, + 609, + 468, + 686 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Generation conditioned on types and sizes (Gen-TS) is to generate layouts when user constraints specify the element types and sizes. We formulate the input sequence by concatenating the type, the width and the height constraints as $S_{\\mathrm{Gen - TS}} = \\{\\langle \\mathrm{sos}\\rangle c_1w_1h_1|c_2w_2h_2|\\dots |c_Nw_Nh_N\\langle \\mathrm{eos}\\rangle \\}$ .", + "bbox": [ + 75, + 686, + 468, + 762 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Generation conditioned on relationships (Gen-R) generates layouts conditioned on element relationships. For example, a user could expect to put a large image at the top of a small text box. We formulate a relationship between two elements as $\\{c_{k_{2m-1}} k_{2m-1} r_{k_{2m-1}, k_{2m}} c_{k_{2m}} k_{2m}\\}$ , where $c_{k_{2m-1}}$ and $c_{k_{2m}}$ are the element types, $k_{2m-1}$ and", + "bbox": [ + 75, + 762, + 470, + 853 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$k_{2m}$ are the indexes for the elements, and $r_{k_{2m - 1},k_{2m}}$ is an extra token introduced to denote one kind of relationships. We concatenate the sequences of type constraints and relationship constraints as $S_{\\mathrm{Gen - R}} = \\{\\langle \\mathrm{sos}\\rangle c_1|c_2|\\ldots |c_N||c_{k_1}k_1r_{k_1,k_2}c_{k_2}k_2|\\ldots |c_{k_{2M - 1}}k_{2M - 1}$ $r_{k_{2M - 1},k_{2M}}c_{k_{2M}}k_{2M}\\langle \\mathrm{eos}\\rangle \\}$ , where $M$ is the number of relationships.", + "bbox": [ + 500, + 295, + 893, + 400 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Refinement applies local changes to the elements that need improvements while maintaining the original layout design. We formulate the input as $S_{\\text{Refinement}} = \\{\\langle \\text{sos} \\rangle c_1 x_1 y_1 w_1 h_1 | \\ldots | c_N x_N y_N w_N h_N \\langle \\text{eos} \\rangle \\}$ .", + "bbox": [ + 498, + 401, + 893, + 462 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Completion aims to complete layout from a set of specified elements. We formulate the input as $S_{\\text{Completion}} = \\{\\langle \\mathrm{sos} \\rangle c_1 x_1 y_1 w_1 h_1 | \\ldots | c_P x_P y_P w_P h_P \\langle \\mathrm{eos} \\rangle \\}$ , where $P$ is the number of known elements.", + "bbox": [ + 500, + 462, + 893, + 520 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Unconstrained generation (UGen) aims to generate layouts without any user requirements. We formulate the input as an empty sequence with necessary special tokens, i.e., $S_{\\mathrm{UGen}} = \\{\\langle \\mathrm{sos} \\rangle \\langle \\mathrm{eos} \\rangle \\}$ .", + "bbox": [ + 498, + 521, + 893, + 582 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Decoding Space Restriction", + "text_level": 1, + "bbox": [ + 500, + 590, + 748, + 606 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "During the inference, we introduce the decoding space restriction strategy to the decoding process. Algorithm 1 presents the pseudo-code for the decoding space restriction.", + "bbox": [ + 498, + 613, + 890, + 659 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In each decoding step $t$ , the decoder predicts the probabilities $P$ of the possible values for current attribute. Then, $P$ will be pruned by two modules. The ConstraintPruning prunes the infeasible values which may violate the user given constraints $S$ . The ProbabilityPruning prunes the values which the probabilities are lower than the threshold $\\theta$ .", + "bbox": [ + 498, + 660, + 890, + 748 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "If all the probabilities in $P'$ are pruned, it means there is no feasible value for current attribute. We propose a backtracking mechanism to solve this problem. When $P'$ is empty and the back time $B[t]$ is less than the max back time maxBack, the backtracking mechanism will roll back the decoding process to a previous step $t'$ and restart the prediction. Otherwise, the value $o$ will be sampled from $P'$ and the generation $O$ will be updated. The decoding process will move to the next step by increasing $t$ by 1.", + "bbox": [ + 496, + 750, + 893, + 885 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "While the end-of-sequence token EOS is predicted, or", + "bbox": [ + 519, + 885, + 890, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_footnote", + "text": "1According to the practical experience, we add the special tokens $\\langle \\mathrm{so}s\\rangle$ and $\\langle \\mathrm{eos}\\rangle$ at the start and the end of the sequence, and use a separator token | to distinguish the single constraints.", + "bbox": [ + 76, + 862, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "18406", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "the length of $O$ reaches maxLen, the generation finishes. In the following, we will give more details about the two pruning modules and the backtracking mechanism.", + "bbox": [ + 75, + 90, + 468, + 136 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Constraint Pruning Module. The constraint pruning module prunes the value in $P$ which may violate the related constraints. Take the relationship constraint as example, suppose at step $t$ the decoder predicts possibilities $P$ for the value of the attribute $w_{i}$ of the $i$ -th element, there is a relation constraint $s = \\{w_{i} \\leq w_{j}\\}$ , which specifies the relative size relationships between element $i$ and $j$ . If $w_{j}$ has not been predicted at step $t$ , $w_{i}$ will not be influenced by $w_{j}$ in current step and the $P$ will not be pruned. Otherwise, if $w_{j}$ has been predicted at previous step, the feasible values of $w_{i}$ will be restricted to $(0, w_{j}]$ according to $s$ , and the infeasible values' probabilities in $P$ will be set as 0.", + "bbox": [ + 75, + 137, + 468, + 318 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Probability Pruning Module. The probability pruning module checks each value's probability in $P'$ . The probabilities that are lower than the predetermined threshold $\\theta$ will be pruned by setting as 0. The threshold $\\theta$ is tuned to achieve the best performance by task.", + "bbox": [ + 75, + 319, + 468, + 395 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Backtracking Mechanism. When the probabilities in $P'$ are all set as 0, the backtracking mechanism works to roll back the decoding process to a previous step and restart the prediction. The function Backtracking will check why the $P'$ is pruned as empty, and decide which step $t'$ to backtrack to. One situation is that the current token is restricted by previous token through the constraint. For example, the relation constraint $s = \\{w_i \\leq w_j\\}$ restricts the feasible values of $w_i$ by $w_j$ . In this case, we choose the step of $w_j$ as the backtracking step. Otherwise, since all the previous predictions collectively lead to current circumstance, we randomly pick one previous step to back to.", + "bbox": [ + 75, + 396, + 470, + 577 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 592, + 209, + 609 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Setups", + "text_level": 1, + "bbox": [ + 76, + 618, + 163, + 633 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets. We compare LayoutFormer++ to existing approaches on two public datasets. RICO [15] is a dataset of mobile app UI that contains $66\\mathrm{K}+$ UI layouts with 25 element types. PubLayNet [30] contains $360\\mathrm{K}+$ document layouts with 5 element types. On both datasets, there are a few layouts with quite a lot of elements, which easily leads to an out-of-memory problem. Existing studies use multifarious rules to filter out these layouts. In our experiments, we simply filter out the layouts with more than 20 elements. For RICO, we use $90\\%$ , $5\\%$ and $5\\%$ of data for training, validation and testing. For PubLayNet, we use $95\\%$ and $5\\%$ of official training split for training and validation, and the official validation split for testing.", + "bbox": [ + 75, + 643, + 468, + 838 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Baselines. We try our best to reproduce all the existing approaches. Even so, we regret to not include some approaches for the following reasons. First, due to the missing implementation details and hyperparameter settings, we", + "bbox": [ + 75, + 839, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Algorithm 1: Decoding Space Restriction" + ], + "code_body": "Input: Encoder hidden state $M$ ;User constraints $S$ Output: Layout sequence $O$ 1 Initialize step index $t$ , the back time for each step $B$ and the predicted sequence $O$ 2 while $(O[-1]\\neq \\mathrm{EOS})$ and $(t < maxLen)$ do 3 $P\\gets \\mathrm{Decoder}(O,M)[t]$ . 4 $P^{\\prime}\\gets$ ConstraintPruning $(P,S)$ . 5 $P^{\\prime}\\gets$ ProbabilityPruning $(P^{\\prime},\\theta)$ . 6 if $(P^{\\prime}$ is $\\varnothing$ )and $(B[t] < maxBack)$ then 7 $t^\\prime \\gets$ Backtracking $(P,S,t)$ . 8 $B[t]\\gets B[t] + 1$ . 9 $O\\gets O[:t]$ . 10 t t; 11 else 12 o $\\leftarrow$ Sampling $(P^{\\prime})$ . 13 $O\\gets O\\cup o$ . 14 t t+1; 15 end 16 end", + "bbox": [ + 500, + 109, + 890, + 385 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "fail to reproduce some approaches [13, 14, 18, 20]. Second, a few approaches consider data-specific attributes and are difficult to be applied to arbitrary datasets about graphic layouts [27, 29]. Ultimately, we compare LayoutFormer++ against 1) NDN-none [12], LayoutGAN++ [8] and BLT [10] on Gen-T, 2) BLT [10] on Gen-TS, 3) NDN [12] and CLG-LO [8] on Gen-R, 4) RUAGE [23] on refinement, 5) LayoutTransformer [3] on completion, and 6) VTN [2], Coarse2Fine [7] and LayoutTransformer [3] on UGen.", + "bbox": [ + 496, + 421, + 890, + 558 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Evaluation Metrics. We adopt the metrics proposed by existing works for comprehensive evaluation.", + "bbox": [ + 498, + 559, + 890, + 589 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Maximum Intersection over Union (mIoU) measures the similarity between the generated layouts and the real layouts, which is based on the averaged IoU of bounding boxes. We use the same implementation as [8].", + "bbox": [ + 496, + 590, + 890, + 651 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Alignment (Align.) measures whether the elements are well-aligned. We modify the metric from [14] by normalizing it by the number of elements.", + "bbox": [ + 496, + 652, + 890, + 698 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Overlap measures the abnormal overlap area between elements. We improve the metric from [14] by ignoring the elements that serve as a background or padding, e.g., card, background and modal on RICO.", + "bbox": [ + 496, + 700, + 890, + 760 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Frechet Inception Distance (FID) describes the distribution difference between real and generated layouts. Following [8], we train a neural network to convert the layouts into representative features and then calculate the distribution difference based on learned features.", + "bbox": [ + 496, + 762, + 890, + 837 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Constraint Violation Rate (Vio.%) measures the rate of the violated constraints. We follow the implementation of [8] for Gen-R. For other tasks, we calculate Vio.% by dividing the number of the violated constraints by the total", + "bbox": [ + 496, + 839, + 893, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "18407", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/8f63b549387f56acb5ccbf199f8f9730f387b360477f3b7b216954e511d97159.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
TasksMethodsRICOPubLayNet
mIoU ↑FID ↓Align. ↓Overlap ↓mIoU ↑FID ↓Align. ↓Overlap ↓
Gen-TNDN-none0.3513.760.560.550.3135.670.350.17
LayoutGAN++0.2985.9540.2610.6200.29714.8750.1240.148
BLT0.21625.6330.1500.9830.14038.6840.0360.196
LayoutFormer++0.4321.0960.2300.5300.3488.4110.0200.008
Gen-TSBLT0.6040.9510.1810.6600.4287.9140.0210.419
LayoutFormer++0.6200.7570.2020.5420.4710.7200.0240.037
Gen-RNDN0.36-0.56-0.31-0.36-
CLG-LO0.2868.8980.3110.6150.27719.7380.1230.200
LayoutFormer++0.4245.9720.3320.5370.3534.9540.0250.076
RefinementRUITE0.8110.1070.1330.4830.7810.0610.0290.020.
LayoutFormer++0.8160.0320.1230.4890.7850.0860.0240.006
CompletionLayoutTransformer0.3636.6790.1940.4780.07714.7690.0190.0013
LayoutFormer++0.7324.5740.0770.4870.47110.2510.0200.0022
UGenLayoutTransformer0.43922.8840.0520.4710.06236.3040.0310.0009
VTN0.68676.0640.4610.6940.210103.3730.2050.211
Coarse2Fine0.36046.4830.1280.6760.36150.8540.2210.142
LayoutFormer++0.74219.6880.0470.5470.41746.5220.0290.0009
", + "bbox": [ + 99, + 88, + 870, + 393 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Quantitative comparisons with existing approaches on six layout generation tasks.", + "bbox": [ + 215, + 404, + 754, + 419 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "number of constraints for all the evaluated layouts.", + "bbox": [ + 76, + 431, + 413, + 446 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Among the above metrics, mIoU, Align., Overlap and FID evaluate the generation quality, and Vio.% evaluate the constraint satisfaction. A larger value for mIoU indicates better performance, while smaller values for other metrics indicate better performance.", + "bbox": [ + 75, + 446, + 470, + 522 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation Details. We implement Layout-Former++ by PyTorch [19]. The model is trained using the Adam optimizer [9] with NVIDIA V100 GPUs. For Transformer blocks, we use 8 layers, 8 heads for multi-attention, 512 embedding dimensions and 2048 feed-forward dimensions. Other hyper-parameters, e.g., the batch size, the learning rate, and the threshold $\\theta$ in decoding space restriction, are tuned to achieve the best performance on the validation set2. For Gen-R, following CLG-LO [8], we randomly sample $10\\%$ element relationships as the input. For refinement, following RUTFE [23], we synthesize the input by adding random noise to the position and size of each element, which is sampled from a normal distribution with the mean 0 and the standard variance 0.01.", + "bbox": [ + 75, + 523, + 468, + 734 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Evaluations on Sufficient Flexibility", + "text_level": 1, + "bbox": [ + 76, + 743, + 387, + 758 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To demonstrate the sufficient flexibility of LayoutFormer++, we compare LayoutFormer++ with existing approaches on all six layout generation tasks.", + "bbox": [ + 75, + 766, + 470, + 811 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1 shows the quantitative comparisons to existing works3. It should be noted that the existing approaches can", + "bbox": [ + 76, + 811, + 470, + 842 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "only handle up to two tasks, while LayoutFormer++ can handle all the six tasks. We highlight the results of LayoutFormer++ by bold when it achieves the best performance among all the existing approaches in Table 1. According to the results, LayoutFormer++ achieves significantly better performance than the baselines on most metrics. This demonstrates that LayoutFormer++ not only can flexibly handle diverse user constraints, but also has advantages in the generation ability over existing approaches.", + "bbox": [ + 500, + 431, + 890, + 568 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Figure 4 and 5 show qualitative comparisons on RICO and PubLayNet. Compared to baselines, LayoutFormer++ generates layouts with better spacing, less misalignment, and fewer unreasonable overlaps.", + "bbox": [ + 498, + 568, + 890, + 628 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Evaluations on Good Controllability", + "text_level": 1, + "bbox": [ + 500, + 635, + 815, + 652 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we compare LayoutFormer++ with LayoutGAN++ [13], BLT [10] and CLG-LO [8], which pay attention to the constraint satisfaction. These approaches handle Gen-T, Gen-TS and Gen-R respectively.", + "bbox": [ + 498, + 659, + 890, + 718 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We bold the results of LayoutFormer++ in Table 2 when it outperforms the baselines. For Gen-T and Gen-TS, since all approaches have no constraint violation, we focus on the performance of quality. As the results, LayoutFormer++ outperforms the baselines on both two datasets. For Gen-R, LayoutFormer++ achieves better performance on both quality metrics and Vio.% except a worse Vio.% than CLG-LO on RICO. However, CLG-LO does not make a good tradeoff: the quality of layouts generated by CLG-LO is significantly worse than that of LayoutFormer++. This demonstrates that LayoutFormer++ achieves the best controllability among existing approaches.", + "bbox": [ + 496, + 719, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "2Details of the hyper-parameters can be find in supplemental material.", + "bbox": [ + 94, + 849, + 467, + 862 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "3As we fail to reproduce NDN by ourselves, we directly use the results from [8] in Table 1. It is evaluated on simple datasets that only consider layouts with less than 10 elements.", + "bbox": [ + 76, + 862, + 468, + 898 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "18408", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/f5e8bc0145bb4209fc6d0d1cc5da8b016dbc9453fa146c0fd3666903db033bfb.jpg", + "image_caption": [ + "Figure 4. Qualitative results on RICO." + ], + "image_footnote": [], + "bbox": [ + 102, + 92, + 869, + 597 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/8b69718ad2959c997bd740d6525ff63b89d4030b1a9bd4d28f6d31f6ab61eb9c.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
TasksMethodRICOPubLayNet
mIoU↑FID↓Align.↓Overlap↓Vio. %↓mIoU↑FID↓Align.↓Overlap↓Vio. %↓
Gen-TLayoutGAN++0.2985.9540.2610.6200.0.29714.8750.1240.1480.
LayoutFormer++ Full0.4321.0960.2300.5300.0.3488.4110.0200.0080.
0.4311.3200.2720.5500.0.3459.3670.0200.0090.
0.4391.3920.2060.5455.50.3459.3730.0200.0090.05
Gen-TSBLT0.6040.9510.1810.6600.0.4287.9140.0210.4190.
LayoutFormer++ Full0.6200.7570.2020.5420.0.4710.7200.0240.0370.
0.6130.7820.2060.5430.0.4640.9030.0260.0440.
0.6130.8010.2060.545≈0.0.4640.9030.0260.044≈0.
Gen-RCLG-LO0.2868.8980.3110.6153.660.27719.7380.1230.2006.66
LayoutFormer++ Full0.4245.9720.3320.53711.840.3534.9540.0250.0763.9
0.4198.6040.2840.54412.750.3525.1520.0230.0755.70
0.4585.1260.2210.54633.040.3584.6200.0220.03016.09
", + "bbox": [ + 109, + 631, + 864, + 832 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2. Comparisons with baselines and the model variants to evaluate the controllability.", + "bbox": [ + 215, + 843, + 751, + 857 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "18409", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ce8a9611470b1cfe98c66efd2d2dfd3d95ef483ce6e44a97878c75e9c3136c12.jpg", + "image_caption": [ + "Figure 5. Qualitative results on PubLayNet." + ], + "image_footnote": [], + "bbox": [ + 101, + 90, + 869, + 597 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Besides, we compare LayoutFormer++ framework with two variants. The first denoted as -Back indicates LayoutFormer++ without backtracking mechanism. The second denoted as -Back&Prune. is LayoutFormer++ without both pruning modules and the backtracking mechanism. For each task in Table 2, the last three lines show the comparison between the variants. Comparing -Full with -Back, we find that after disabling the backtracking mechanism, the generation quality decreases. And on Gen-R, the Vio.% also gets worse. Comparing -Full with -Back&Prune, we find that the Vio.% significantly decreases. It shows that the full model consistently decreases the violation while having little impact on quality, which demonstrates that both the pruning modules and the backtracking mechanism play important roles in helping LayoutFormer++ achieve good controllability.", + "bbox": [ + 75, + 647, + 472, + 888 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 645, + 617, + 662 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this work, we propose LayoutFormer++ for conditional layout generation. To achieve the sufficient flexibility, we propose constraint serialization to represent different user constraints by the same sequence format. To achieve the good controllability, we propose decoding space restriction to prune the predicted distribution by disabling the options that violate the constraints or lead to bad quality. Experiments show that LayoutFormer++ can flexibly handle different layout generation tasks with better generation quality and less constraint violation compared to the existing task-specific approaches. In the future, we plan to investigate more practical user requirements for layout design. Besides, as LayoutFormer++ enables a unified way to handle different layout generation tasks, it is possible to develop a powerful pretrained model for layout generation in the future.", + "bbox": [ + 496, + 676, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "18410", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 106 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Peter Anderson, Basura Fernando, Mark Johnson, and Stephen Gould. Guided open vocabulary image captioning with constrained beam search. In Proceedings of the 2017 Conference on Empirical Methods in Natural Language Processing, pages 936-945, Copenhagen, Denmark, Sept. 2017. Association for Computational Linguistics. 3", + "[2] Diego Martin Arroyo, Janis Postels, and Federico Tombari. 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Publaynet: largest dataset ever for document layout analysis. arXiv preprint arXiv:1908.07836, 2019. 2, 5" + ], + "bbox": [ + 78, + 90, + 468, + 896 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "18412", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/LayoutFormer++_ Conditional Graphic Layout Generation via Constraint Serialization and Decoding Space Restriction/b766a11c-0ea4-4e2b-868e-229f60bdc47b_model.json b/2023/LayoutFormer++_ Conditional Graphic Layout Generation via Constraint Serialization and Decoding Space Restriction/b766a11c-0ea4-4e2b-868e-229f60bdc47b_model.json new file mode 100644 index 0000000000000000000000000000000000000000..031131e77598f1c8f9348365b804f3cf896c79a4 --- /dev/null +++ b/2023/LayoutFormer++_ Conditional Graphic Layout Generation via Constraint Serialization and Decoding Space Restriction/b766a11c-0ea4-4e2b-868e-229f60bdc47b_model.json @@ -0,0 +1,1694 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.111, + 0.13, + 0.861, + 0.177 + ], + "angle": 0, + "content": "LayoutFormer++: Conditional Graphic Layout Generation via Constraint Serialization and Decoding Space Restriction" + }, + { + "type": "text", + "bbox": [ + 0.184, + 0.203, + 0.785, + 0.275 + ], + "angle": 0, + "content": "Zhaoyun Jiang\\(^{1*}\\), Jiaqi Guo\\(^{2}\\), Shizhao Sun\\(^{2}\\), Huayu Deng\\(^{3*}\\), Zhongkai Wu\\(^{4*}\\), Vuksan Mijovic\\(^{5}\\), Zijiang James Yang\\(^{1}\\), Jian-Guang Lou\\(^{2}\\), Dongmei Zhang\\(^{2}\\), Xi'an Jiaotong University, Microsoft Research Asia, Shanghai Jiaotong University, Beihang University, Microsoft," + }, + { + "type": "text", + "bbox": [ + 0.133, + 0.278, + 0.832, + 0.31 + ], + "angle": 0, + "content": "jzyl24@stu.xjtu.edu.cn, deng.hy99@sjtu.edu.cn, 17376487@buaa.edu.cn, zijiang@xjtu.edu.cn, {jiaqiguo, shizsu, vmijovic, jlou, dongmeiz}@microsoft.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.345, + 0.314, + 0.361 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.378, + 0.474, + 0.739 + ], + "angle": 0, + "content": "Conditional graphic layout generation, which generates realistic layouts according to user constraints, is a challenging task that has not been well-studied yet. First, there is limited discussion about how to handle diverse user constraints flexibly and uniformly. Second, to make the layouts conform to user constraints, existing work often sacrifices generation quality significantly. In this work, we propose LayoutFormer++ to tackle the above problems. First, to flexibly handle diverse constraints, we propose a constraint serialization scheme, which represents different user constraints as sequences of tokens with a predefined format. Then, we formulate conditional layout generation as a sequence-to-sequence transformation, and leverage encoder-decoder framework with Transformer as the basic architecture. Furthermore, to make the layout better meet user requirements without harming quality, we propose a decoding space restriction strategy. Specifically, we prune the predicted distribution by ignoring the options that definitely violate user constraints and likely result in low-quality layouts, and make the model samples from the restricted distribution. Experiments demonstrate that LayoutFormer++ outperforms existing approaches on all the tasks in terms of both better generation quality and less constraint violation." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.772, + 0.21, + 0.788 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.799, + 0.47, + 0.875 + ], + "angle": 0, + "content": "Graphic designs greatly facilitate information communication in our daily life. During its creation, the layout, i.e., positions and sizes of elements, plays a critical role. To assist layout design, conditional layout generation, which takes user constraints as input and generates layouts as out" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.345, + 0.889, + 0.555 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.563, + 0.892, + 0.606 + ], + "angle": 0, + "content": "Figure 1. Comparing with previous conditional layout generation approaches, LayoutFormer++ performs better on sufficient flexibility and good controllability." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.625, + 0.893, + 0.807 + ], + "angle": 0, + "content": "put, attracts great attention (see Figure 1). It is different from unconditional layout generation, which generates layouts freely without constraints, from at least two aspects. First, the model should be able to handle diverse user constraints, called sufficient flexibility. Figure 2 shows 6 typical tasks of layout generation in real-world applications including layout completion, layout refinement, layout generation conditioned on element types, element types with sizes, element relationships, or any of their combinations. Second, the model should generate layouts conforming to user requirements (i.e., constraints) as many as possible without harming quality, called good controllability (see Figure 1)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.895, + 0.903 + ], + "angle": 0, + "content": "However, existing work cannot meet the above two requirements. First, there is no existing work can support all the layout generation tasks with different user constraints. Most existing approaches simply focus on tackling a single conditional layout generation task without considering whether they can be applied to other tasks. For example," + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.42, + 0.9 + ], + "angle": 0, + "content": "*Work done during an internship at Microsoft Research Asia." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18403" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.258 + ], + "angle": 0, + "content": "LayoutTransformer [3] can only perform completion task and BLT [10] cannot handle element relationships. Such task-specific approaches hinder the development of solutions for the new task. Second, there are no satisfactory methods to ensure good controllability. Some approaches directly replace the values in the predicted layout with the ones specified in the user constraints [3, 10]. Another work defines a set of heuristic rules and leverages latent optimization [8]. To make the generated layouts meet user requirements, they often degrade the generation quality significantly." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.261, + 0.473, + 0.548 + ], + "angle": 0, + "content": "In this work, we propose a unified model called LayoutFormer++ to support the different scenarios of conditional layout generation. In LayoutFormer++, a set of constraints is represented as a sequence. Specifically, we use a constraint serialization scheme to serialize different user constraints into a sequence of tokens with a predefined format (see Figure 1). The intuition behind this design choice is as follows. First, the sequence format is widely used and effective. Its effectiveness in layout generation has also been demonstrated in recent works [3, 10]. Second, a sequence is very flexible to accommodate different constraints for layout generation. We can serialize any structured information in the user constraints as a sequence. We found although user needs are diverse, they are all about element types and five attributes including type, top coordinate, left coordinate, width and height. Thus, we can simply define a set of vocabularies to describe the attributes respectively and concatenate descriptions of different attributes and elements to construct a sequence." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.551, + 0.47, + 0.688 + ], + "angle": 0, + "content": "Therefore, the conditional layout generation problem can be formulated as a sequence-to-sequence transformation problem. This enables us to leverage a simple yet effective encoder-decoder framework with Transformer [26] as a basic model architecture. The encoder processes the user constraints in a bidirectional way. The decoder predicts the layout sequence autoregressively, where there are multiple decoding steps and the model samples one token from the predicted distribution at each decoding step." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.69, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Furthermore, to achieve good controllability, we introduce a decoding space restriction strategy in the inference stage. Our key idea is to prune the infeasible options in the predicted distribution and make the model sample from the restricted distribution at each decoding step. Specifically, we leverage two kinds of information to prune the options. First, the options that definitely violate the user constraints are pruned. For example, if a user wants one image and two buttons, the option for putting one text box will not be acceptable. Second, the options with low probabilities in the predicted distribution, which will very likely result in low-quality layouts, are also pruned. As the feasible option set may be empty after pruning, we further introduce a backtracking mechanism, in which the model goes back" + }, + { + "type": "image", + "bbox": [ + 0.515, + 0.091, + 0.882, + 0.219 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.526, + 0.228, + 0.866, + 0.242 + ], + "angle": 0, + "content": "Figure 2. Typical tasks for conditional layout generation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.258, + 0.892, + 0.333 + ], + "angle": 0, + "content": "to a certain decoding step and find a better solution. Note that the whole generation process of the proposed strategy still relies on the distribution learned from the training data. Thus, it is less likely to disturb a layout when making it better conform to user constraints." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.334, + 0.893, + 0.501 + ], + "angle": 0, + "content": "We conduct extensive experiments on two public datasets [15, 30] and six layout generation tasks with different user constraints, to evaluate LayoutFormer++ and compare it with state-of-the-art approaches. Experimental results show that LayoutFormer++ can successfully tackle all six layout generation tasks that are handled separately by previous work, demonstrating that it is able to provide sufficient flexibility. Furthermore, LayoutFormer++ significantly outperforms previous approaches in terms of both better generation quality and less constraint violation, indicating that it achieves good controllability." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.513, + 0.642, + 0.529 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.539, + 0.892, + 0.674 + ], + "angle": 0, + "content": "Graphic Layout Generation. Graphic layout generation aims at generating aesthetic layouts to tackle users' needs. As users' needs are diverse in real-world applications, various tasks of layout generation are explored (see Figure 2), such as generation condition on element types [8, 10, 12], generation condition on types and sizes [10], generation condition on element relationships [8, 12], refinement [23] and completion [3]. Some other approaches focus on unconstrained generation [2, 7, 13, 27]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.893, + 0.901 + ], + "angle": 0, + "content": "However, none of existing approaches can achieve sufficient flexibility to handle diverse layout generation tasks, due to the limitations in constraint modeling. Some works represent the constraints in the same format of the target layout, thus can not handle other complex constraints [3, 10, 23]. For example, LayoutTransformer [3] can only handle completion task but cannot deal with relationships between elements. Other works design the modeling formats specific to the constraint, which are hard to adapt to other tasks. For example, [12] leverages graph format to represent the relationships among the elements, which is inconvenient for the size constraints. In this work, we propose LayoutFormer++ with constraint serialization scheme, modeling different constraints into same format of the sequence, eliminating the isolation between layout generation tasks." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "18404" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.348 + ], + "angle": 0, + "content": "Existing approaches also consider different methods for constraint satisfaction. Some approaches directly reset the predicted attributes by the values specified in the constraints [3, 10]. Other approaches define the heuristic rules and cost functions to control the generation [8, 12]. For example, [8] designs cost functions for each constraint and takes the constrained generation as an optimization problem. However, these methods often decrease the generation quality significantly. For [3, 10], directly resetting the sequence will make the generated layout deviate from the distribution learned by model. For [8, 12], it is hard to define the rules and cost functions to handle the trade-off between constraint satisfaction and generation quality. Different from existing approaches, we introduce decoding space restriction strategy to prune the infeasible values during decoding process, which does not rely on sophisticated rules or cost functions, and also fits the learned distribution." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.35, + 0.473, + 0.622 + ], + "angle": 0, + "content": "Decoding Methods. Decoding method plays an important role in autoregressive generation. The most prominent decoding methods include Greedy Search, Beam Search, Top-K sampling and Top-P sampling [5], etc. To enable the control over the output sequence, constrained decoding is first proposed in controllable text generation. [1,4,6,16,17,21] propose constrained decoding methods for hard lexical constraints where a set of tokens are required to occur in target output. [22,28] present decoding methods for soft constraints which assign a value between 0 and 1 to indicate how constraints are satisfied. [11, 24, 25] introduce decoding methods for structural constraints which impose a rigorous structures on the output sequence. Inspired by these methods, we propose a new constrained decoding method tailored for conditional layout generation. We carefully design two pruning modules and a backtracking mechanism to improve the satisfaction of constraints while maintaining high layout quality." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.638, + 0.188, + 0.657 + ], + "angle": 0, + "content": "3. Approach" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.664, + 0.189, + 0.68 + ], + "angle": 0, + "content": "3.1. Overview" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.688, + 0.47, + 0.856 + ], + "angle": 0, + "content": "A layout is made up of a set of elements, where each element can be described by its type \\(c\\), left and top coordinate \\(x\\) and \\(y\\), as well as width \\(w\\) and height \\(h\\). The continuous attributes \\(x\\), \\(y\\), \\(w\\) and \\(h\\) are quantized, which is proven to be helpful for graphic layouts [2, 3, 23]. Thus, an element can be represented by five tokens. Following the state-of-the-art approaches, we represent a layout by concatenating all the elements' tokens, i.e., \\(L = \\{\\langle \\mathrm{so}\\rangle c_1 x_1 y_1 w_1 h_1 \\dots c_N x_N y_N w_N h_N \\langle \\mathrm{eos}\\rangle\\}\\). Here, \\(N\\) denotes the total number of elements, \\(\\langle \\mathrm{so}\\rangle\\) and \\(\\langle \\mathrm{eos}\\rangle\\) are special tokens indicating the start and end of a sequence." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.47, + 0.902 + ], + "angle": 0, + "content": "In this work, we propose a new approach named LayoutFormer++ for conditional layout generation. The overall model architecture is illustrated in Figure 3a." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.151 + ], + "angle": 0, + "content": "To achieve sufficient flexibility, different constraints are formatted uniformly into sequence through constraint serialization. The details of the constraint serialization scheme will be introduced in Section 3.2." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.151, + 0.894, + 0.25 + ], + "angle": 0, + "content": "We leverage a Transformer encoder-decoder architecture for LayoutFormer++ based on the experience of previous works. The bidirectional encoder takes the constraint sequence as input and outputs their contextualized representations. The autoregressive decoder iteratively predicts the probabilities of future tokens. The model is trained to minimize the negative log-likelihood of layout tokens, i.e.," + }, + { + "type": "equation", + "bbox": [ + 0.586, + 0.257, + 0.892, + 0.294 + ], + "angle": 0, + "content": "\\[\n\\text {m i n i m i z e} \\sum_ {t = 1} ^ {N} - \\log P _ {\\boldsymbol {\\theta}} \\left(L _ {t} \\mid L _ {< t}, S\\right), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.302, + 0.892, + 0.347 + ], + "angle": 0, + "content": "where \\(S\\) is the input constraint sequence, \\(L\\) is the output layout sequence, \\(\\theta\\) refers to the model parameters and \\(N\\) denotes the length of the layout sequence." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.348, + 0.892, + 0.408 + ], + "angle": 0, + "content": "Finally, we introduce the decoding space restriction strategy with a backtracking mechanism into inference process to achieve good controllability. The details of the decoding space restriction strategy are given in Section 3.3." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.416, + 0.715, + 0.433 + ], + "angle": 0, + "content": "3.2. Serializing Constraints" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.44, + 0.627, + 0.456 + ], + "angle": 0, + "content": "3.2.1 Principles" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.463, + 0.892, + 0.599 + ], + "angle": 0, + "content": "Instead of directly presenting concrete sequences for the constraints considered in previous work, we first introduce the principles for serializing constraints. These principles not only summarize how the existing constraints are serialized but also provide a general guidance for formulating other constraints. There are two critical questions in serializing constraints. First, how to represent each constraint in a sequence format. Second, how to combine different constraints into a complete sequence." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.6, + 0.892, + 0.659 + ], + "angle": 0, + "content": "Constraint Representation. To present a constraint as a sequence, the basic idea is to first define a set of vocabularies and then concatenate the tokens from these vocabularies. Specifically, the constraints often fall into two categories." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.66, + 0.892, + 0.795 + ], + "angle": 0, + "content": "First, some constraints are only related to a single element. For example, put an image on the page or the element should be 10 pixel wide. The serialization for such constraint is quite straightforward: we just define a vocabulary and then represent the constraint by a single token from the vocabulary. For example, for the constraints about element type, the vocabulary could be {image, toolbar,..., button}, and the constraint 'an image' can be represented as image." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Second, other constraints are related to multiple elements. For example, put an image on top of a button. To distinguish the elements referred in the constraint, we first build a vocabulary representing unique IDs for the elements. Then, we define a vocabulary for the relationships between elements. At last, we concatenate the tokens of element IDs and relationships." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "18405" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.113, + 0.089, + 0.511, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.246, + 0.233, + 0.373, + 0.246 + ], + "angle": 0, + "content": "(a) Model Architecture" + }, + { + "type": "image", + "bbox": [ + 0.554, + 0.098, + 0.852, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.617, + 0.225, + 0.786, + 0.238 + ], + "angle": 0, + "content": "(b) Input and Output Sequences" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.25, + 0.895, + 0.278 + ], + "angle": 0, + "content": "Figure 3. a The overall model architecture of LayoutFormer++, illustrated by taking the task Gen-R as an example. b The examples of input and output sequences for different conditional layout generation tasks through constraint serialization." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.296, + 0.475, + 0.37 + ], + "angle": 0, + "content": "For example, the vocabulary for element IDs could be \\(\\{\\mathrm{image}_1,\\dots ,\\mathrm{image}_{K_1},\\dots ,\\mathrm{button}_1,\\dots ,\\mathrm{button}_{K_t}\\}\\), and the vocabulary for relationships could be \\(\\{\\mathrm{top},\\dots ,\\mathrm{small}\\}\\). Then, the constraint 'an image on top of a button' is represented as \\(\\mathrm{image}_1\\) top \\(\\mathrm{button}_1\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.371, + 0.473, + 0.508 + ], + "angle": 0, + "content": "Constraint Combination. To combine different constraints, we concatenate their sequences. To ease the learning of neural network, we use a fixed order instead of a random order when concatenating different constraints. First, for the constraints only related to a single element, we first concatenate those for the same element and then concatenate those from different elements. Second, for the constraints related to multiple elements, we put them after all the constraints for the single elements." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.526, + 0.325, + 0.541 + ], + "angle": 0, + "content": "3.2.2 Examples for Typical Tasks" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.55, + 0.47, + 0.61 + ], + "angle": 0, + "content": "In this work, we consider six typical layout generation tasks which has been explored in previous work. We demonstrate how we formulate the constraint sequences for these tasks according to Section 3.2.1 as followed." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.611, + 0.47, + 0.687 + ], + "angle": 0, + "content": "Generation conditioned on types (Gen-T) is to generate layouts from the element types specified by user constraints. We formulate the input constraint sequence by concatenating the single-element constraints of element type, i.e., \\( S_{\\mathrm{Gen - T}} = \\{\\langle \\mathrm{sos}\\rangle c_1|c_2|\\dots |c_N\\langle \\mathrm{eos}\\rangle \\} .^1 \\)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.687, + 0.47, + 0.763 + ], + "angle": 0, + "content": "Generation conditioned on types and sizes (Gen-TS) is to generate layouts when user constraints specify the element types and sizes. We formulate the input sequence by concatenating the type, the width and the height constraints as \\( S_{\\mathrm{Gen - TS}} = \\{\\langle \\mathrm{sos}\\rangle c_1w_1h_1|c_2w_2h_2|\\dots |c_Nw_Nh_N\\langle \\mathrm{eos}\\rangle \\} \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.763, + 0.471, + 0.854 + ], + "angle": 0, + "content": "Generation conditioned on relationships (Gen-R) generates layouts conditioned on element relationships. For example, a user could expect to put a large image at the top of a small text box. We formulate a relationship between two elements as \\(\\{c_{k_{2m-1}} k_{2m-1} r_{k_{2m-1}, k_{2m}} c_{k_{2m}} k_{2m}\\}\\), where \\(c_{k_{2m-1}}\\) and \\(c_{k_{2m}}\\) are the element types, \\(k_{2m-1}\\) and" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.296, + 0.895, + 0.401 + ], + "angle": 0, + "content": "\\(k_{2m}\\) are the indexes for the elements, and \\(r_{k_{2m - 1},k_{2m}}\\) is an extra token introduced to denote one kind of relationships. We concatenate the sequences of type constraints and relationship constraints as \\(S_{\\mathrm{Gen - R}} = \\{\\langle \\mathrm{sos}\\rangle c_1|c_2|\\ldots |c_N||c_{k_1}k_1r_{k_1,k_2}c_{k_2}k_2|\\ldots |c_{k_{2M - 1}}k_{2M - 1}\\) \\(r_{k_{2M - 1},k_{2M}}c_{k_{2M}}k_{2M}\\langle \\mathrm{eos}\\rangle \\}\\), where \\(M\\) is the number of relationships." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.402, + 0.894, + 0.463 + ], + "angle": 0, + "content": "Refinement applies local changes to the elements that need improvements while maintaining the original layout design. We formulate the input as \\( S_{\\text{Refinement}} = \\{\\langle \\text{sos} \\rangle c_1 x_1 y_1 w_1 h_1 | \\ldots | c_N x_N y_N w_N h_N \\langle \\text{eos} \\rangle \\} \\)." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.463, + 0.894, + 0.521 + ], + "angle": 0, + "content": "Completion aims to complete layout from a set of specified elements. We formulate the input as \\( S_{\\text{Completion}} = \\{\\langle \\mathrm{sos} \\rangle c_1 x_1 y_1 w_1 h_1 | \\ldots | c_P x_P y_P w_P h_P \\langle \\mathrm{eos} \\rangle \\} \\), where \\( P \\) is the number of known elements." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.522, + 0.894, + 0.583 + ], + "angle": 0, + "content": "Unconstrained generation (UGen) aims to generate layouts without any user requirements. We formulate the input as an empty sequence with necessary special tokens, i.e., \\( S_{\\mathrm{UGen}} = \\{\\langle \\mathrm{sos} \\rangle \\langle \\mathrm{eos} \\rangle \\} \\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.591, + 0.749, + 0.607 + ], + "angle": 0, + "content": "3.3. Decoding Space Restriction" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.614, + 0.892, + 0.66 + ], + "angle": 0, + "content": "During the inference, we introduce the decoding space restriction strategy to the decoding process. Algorithm 1 presents the pseudo-code for the decoding space restriction." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.661, + 0.892, + 0.749 + ], + "angle": 0, + "content": "In each decoding step \\( t \\), the decoder predicts the probabilities \\( P \\) of the possible values for current attribute. Then, \\( P \\) will be pruned by two modules. The ConstraintPruning prunes the infeasible values which may violate the user given constraints \\( S \\). The ProbabilityPruning prunes the values which the probabilities are lower than the threshold \\( \\theta \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.895, + 0.886 + ], + "angle": 0, + "content": "If all the probabilities in \\( P' \\) are pruned, it means there is no feasible value for current attribute. We propose a backtracking mechanism to solve this problem. When \\( P' \\) is empty and the back time \\( B[t] \\) is less than the max back time maxBack, the backtracking mechanism will roll back the decoding process to a previous step \\( t' \\) and restart the prediction. Otherwise, the value \\( o \\) will be sampled from \\( P' \\) and the generation \\( O \\) will be updated. The decoding process will move to the next step by increasing \\( t \\) by 1." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.886, + 0.892, + 0.902 + ], + "angle": 0, + "content": "While the end-of-sequence token EOS is predicted, or" + }, + { + "type": "page_footnote", + "bbox": [ + 0.077, + 0.863, + 0.47, + 0.901 + ], + "angle": 0, + "content": "1According to the practical experience, we add the special tokens \\(\\langle \\mathrm{so}s\\rangle\\) and \\(\\langle \\mathrm{eos}\\rangle\\) at the start and the end of the sequence, and use a separator token | to distinguish the single constraints." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "18406" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.137 + ], + "angle": 0, + "content": "the length of \\( O \\) reaches maxLen, the generation finishes. In the following, we will give more details about the two pruning modules and the backtracking mechanism." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.138, + 0.47, + 0.319 + ], + "angle": 0, + "content": "Constraint Pruning Module. The constraint pruning module prunes the value in \\( P \\) which may violate the related constraints. Take the relationship constraint as example, suppose at step \\( t \\) the decoder predicts possibilities \\( P \\) for the value of the attribute \\( w_{i} \\) of the \\( i \\)-th element, there is a relation constraint \\( s = \\{w_{i} \\leq w_{j}\\} \\), which specifies the relative size relationships between element \\( i \\) and \\( j \\). If \\( w_{j} \\) has not been predicted at step \\( t \\), \\( w_{i} \\) will not be influenced by \\( w_{j} \\) in current step and the \\( P \\) will not be pruned. Otherwise, if \\( w_{j} \\) has been predicted at previous step, the feasible values of \\( w_{i} \\) will be restricted to \\( (0, w_{j}] \\) according to \\( s \\), and the infeasible values' probabilities in \\( P \\) will be set as 0." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.32, + 0.47, + 0.396 + ], + "angle": 0, + "content": "Probability Pruning Module. The probability pruning module checks each value's probability in \\( P' \\). The probabilities that are lower than the predetermined threshold \\( \\theta \\) will be pruned by setting as 0. The threshold \\( \\theta \\) is tuned to achieve the best performance by task." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.397, + 0.471, + 0.578 + ], + "angle": 0, + "content": "Backtracking Mechanism. When the probabilities in \\( P' \\) are all set as 0, the backtracking mechanism works to roll back the decoding process to a previous step and restart the prediction. The function Backtracking will check why the \\( P' \\) is pruned as empty, and decide which step \\( t' \\) to backtrack to. One situation is that the current token is restricted by previous token through the constraint. For example, the relation constraint \\( s = \\{w_i \\leq w_j\\} \\) restricts the feasible values of \\( w_i \\) by \\( w_j \\). In this case, we choose the step of \\( w_j \\) as the backtracking step. Otherwise, since all the previous predictions collectively lead to current circumstance, we randomly pick one previous step to back to." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.593, + 0.21, + 0.611 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.619, + 0.165, + 0.635 + ], + "angle": 0, + "content": "4.1. Setups" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.644, + 0.47, + 0.839 + ], + "angle": 0, + "content": "Datasets. We compare LayoutFormer++ to existing approaches on two public datasets. RICO [15] is a dataset of mobile app UI that contains \\(66\\mathrm{K}+\\) UI layouts with 25 element types. PubLayNet [30] contains \\(360\\mathrm{K}+\\) document layouts with 5 element types. On both datasets, there are a few layouts with quite a lot of elements, which easily leads to an out-of-memory problem. Existing studies use multifarious rules to filter out these layouts. In our experiments, we simply filter out the layouts with more than 20 elements. For RICO, we use \\(90\\%\\), \\(5\\%\\) and \\(5\\%\\) of data for training, validation and testing. For PubLayNet, we use \\(95\\%\\) and \\(5\\%\\) of official training split for training and validation, and the official validation split for testing." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Baselines. We try our best to reproduce all the existing approaches. Even so, we regret to not include some approaches for the following reasons. First, due to the missing implementation details and hyperparameter settings, we" + }, + { + "type": "code_caption", + "bbox": [ + 0.51, + 0.095, + 0.792, + 0.11 + ], + "angle": 0, + "content": "Algorithm 1: Decoding Space Restriction" + }, + { + "type": "algorithm", + "bbox": [ + 0.501, + 0.111, + 0.892, + 0.386 + ], + "angle": 0, + "content": "Input: Encoder hidden state \\(M\\) ;User constraints \\(S\\) Output: Layout sequence \\(O\\) 1 Initialize step index \\(t\\) , the back time for each step \\(B\\) and the predicted sequence \\(O\\) 2 while \\((O[-1]\\neq \\mathrm{EOS})\\) and \\((t < maxLen)\\) do 3 \\(P\\gets \\mathrm{Decoder}(O,M)[t]\\) . 4 \\(P^{\\prime}\\gets\\) ConstraintPruning \\((P,S)\\) . 5 \\(P^{\\prime}\\gets\\) ProbabilityPruning \\((P^{\\prime},\\theta)\\) . 6 if \\((P^{\\prime}\\) is \\(\\varnothing\\) )and \\((B[t] < maxBack)\\) then 7 \\(t^\\prime \\gets\\) Backtracking \\((P,S,t)\\) . 8 \\(B[t]\\gets B[t] + 1\\) . 9 \\(O\\gets O[:t]\\) . 10 t t; 11 else 12 o \\(\\leftarrow\\) Sampling \\((P^{\\prime})\\) . 13 \\(O\\gets O\\cup o\\) . 14 t t+1; 15 end 16 end" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.422, + 0.892, + 0.559 + ], + "angle": 0, + "content": "fail to reproduce some approaches [13, 14, 18, 20]. Second, a few approaches consider data-specific attributes and are difficult to be applied to arbitrary datasets about graphic layouts [27, 29]. Ultimately, we compare LayoutFormer++ against 1) NDN-none [12], LayoutGAN++ [8] and BLT [10] on Gen-T, 2) BLT [10] on Gen-TS, 3) NDN [12] and CLG-LO [8] on Gen-R, 4) RUAGE [23] on refinement, 5) LayoutTransformer [3] on completion, and 6) VTN [2], Coarse2Fine [7] and LayoutTransformer [3] on UGen." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.56, + 0.892, + 0.59 + ], + "angle": 0, + "content": "Evaluation Metrics. We adopt the metrics proposed by existing works for comprehensive evaluation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.592, + 0.892, + 0.652 + ], + "angle": 0, + "content": "Maximum Intersection over Union (mIoU) measures the similarity between the generated layouts and the real layouts, which is based on the averaged IoU of bounding boxes. We use the same implementation as [8]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.654, + 0.892, + 0.699 + ], + "angle": 0, + "content": "Alignment (Align.) measures whether the elements are well-aligned. We modify the metric from [14] by normalizing it by the number of elements." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.701, + 0.892, + 0.761 + ], + "angle": 0, + "content": "Overlap measures the abnormal overlap area between elements. We improve the metric from [14] by ignoring the elements that serve as a background or padding, e.g., card, background and modal on RICO." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.763, + 0.892, + 0.838 + ], + "angle": 0, + "content": "Frechet Inception Distance (FID) describes the distribution difference between real and generated layouts. Following [8], we train a neural network to convert the layouts into representative features and then calculate the distribution difference based on learned features." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Constraint Violation Rate (Vio.%) measures the rate of the violated constraints. We follow the implementation of [8] for Gen-R. For other tasks, we calculate Vio.% by dividing the number of the violated constraints by the total" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18407" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.1, + 0.089, + 0.872, + 0.394 + ], + "angle": 0, + "content": "
TasksMethodsRICOPubLayNet
mIoU ↑FID ↓Align. ↓Overlap ↓mIoU ↑FID ↓Align. ↓Overlap ↓
Gen-TNDN-none0.3513.760.560.550.3135.670.350.17
LayoutGAN++0.2985.9540.2610.6200.29714.8750.1240.148
BLT0.21625.6330.1500.9830.14038.6840.0360.196
LayoutFormer++0.4321.0960.2300.5300.3488.4110.0200.008
Gen-TSBLT0.6040.9510.1810.6600.4287.9140.0210.419
LayoutFormer++0.6200.7570.2020.5420.4710.7200.0240.037
Gen-RNDN0.36-0.56-0.31-0.36-
CLG-LO0.2868.8980.3110.6150.27719.7380.1230.200
LayoutFormer++0.4245.9720.3320.5370.3534.9540.0250.076
RefinementRUITE0.8110.1070.1330.4830.7810.0610.0290.020.
LayoutFormer++0.8160.0320.1230.4890.7850.0860.0240.006
CompletionLayoutTransformer0.3636.6790.1940.4780.07714.7690.0190.0013
LayoutFormer++0.7324.5740.0770.4870.47110.2510.0200.0022
UGenLayoutTransformer0.43922.8840.0520.4710.06236.3040.0310.0009
VTN0.68676.0640.4610.6940.210103.3730.2050.211
Coarse2Fine0.36046.4830.1280.6760.36150.8540.2210.142
LayoutFormer++0.74219.6880.0470.5470.41746.5220.0290.0009
" + }, + { + "type": "table_caption", + "bbox": [ + 0.216, + 0.405, + 0.755, + 0.42 + ], + "angle": 0, + "content": "Table 1. Quantitative comparisons with existing approaches on six layout generation tasks." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.433, + 0.414, + 0.447 + ], + "angle": 0, + "content": "number of constraints for all the evaluated layouts." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.448, + 0.471, + 0.523 + ], + "angle": 0, + "content": "Among the above metrics, mIoU, Align., Overlap and FID evaluate the generation quality, and Vio.% evaluate the constraint satisfaction. A larger value for mIoU indicates better performance, while smaller values for other metrics indicate better performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.524, + 0.47, + 0.735 + ], + "angle": 0, + "content": "Implementation Details. We implement Layout-Former++ by PyTorch [19]. The model is trained using the Adam optimizer [9] with NVIDIA V100 GPUs. For Transformer blocks, we use 8 layers, 8 heads for multi-attention, 512 embedding dimensions and 2048 feed-forward dimensions. Other hyper-parameters, e.g., the batch size, the learning rate, and the threshold \\(\\theta\\) in decoding space restriction, are tuned to achieve the best performance on the validation set2. For Gen-R, following CLG-LO [8], we randomly sample \\(10\\%\\) element relationships as the input. For refinement, following RUTFE [23], we synthesize the input by adding random noise to the position and size of each element, which is sampled from a normal distribution with the mean 0 and the standard variance 0.01." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.744, + 0.388, + 0.76 + ], + "angle": 0, + "content": "4.2. Evaluations on Sufficient Flexibility" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.767, + 0.471, + 0.812 + ], + "angle": 0, + "content": "To demonstrate the sufficient flexibility of LayoutFormer++, we compare LayoutFormer++ with existing approaches on all six layout generation tasks." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.812, + 0.471, + 0.843 + ], + "angle": 0, + "content": "Table 1 shows the quantitative comparisons to existing works3. It should be noted that the existing approaches can" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.433, + 0.892, + 0.569 + ], + "angle": 0, + "content": "only handle up to two tasks, while LayoutFormer++ can handle all the six tasks. We highlight the results of LayoutFormer++ by bold when it achieves the best performance among all the existing approaches in Table 1. According to the results, LayoutFormer++ achieves significantly better performance than the baselines on most metrics. This demonstrates that LayoutFormer++ not only can flexibly handle diverse user constraints, but also has advantages in the generation ability over existing approaches." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.569, + 0.892, + 0.63 + ], + "angle": 0, + "content": "Figure 4 and 5 show qualitative comparisons on RICO and PubLayNet. Compared to baselines, LayoutFormer++ generates layouts with better spacing, less misalignment, and fewer unreasonable overlaps." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.636, + 0.816, + 0.653 + ], + "angle": 0, + "content": "4.3. Evaluations on Good Controllability" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.66, + 0.892, + 0.719 + ], + "angle": 0, + "content": "In this section, we compare LayoutFormer++ with LayoutGAN++ [13], BLT [10] and CLG-LO [8], which pay attention to the constraint satisfaction. These approaches handle Gen-T, Gen-TS and Gen-R respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We bold the results of LayoutFormer++ in Table 2 when it outperforms the baselines. For Gen-T and Gen-TS, since all approaches have no constraint violation, we focus on the performance of quality. As the results, LayoutFormer++ outperforms the baselines on both two datasets. For Gen-R, LayoutFormer++ achieves better performance on both quality metrics and Vio.% except a worse Vio.% than CLG-LO on RICO. However, CLG-LO does not make a good tradeoff: the quality of layouts generated by CLG-LO is significantly worse than that of LayoutFormer++. This demonstrates that LayoutFormer++ achieves the best controllability among existing approaches." + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.85, + 0.468, + 0.863 + ], + "angle": 0, + "content": "2Details of the hyper-parameters can be find in supplemental material." + }, + { + "type": "page_footnote", + "bbox": [ + 0.078, + 0.863, + 0.47, + 0.9 + ], + "angle": 0, + "content": "3As we fail to reproduce NDN by ourselves, we directly use the results from [8] in Table 1. It is evaluated on simple datasets that only consider layouts with less than 10 elements." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.85, + 0.47, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "18408" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.104, + 0.093, + 0.87, + 0.598 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.37, + 0.604, + 0.599, + 0.618 + ], + "angle": 0, + "content": "Figure 4. Qualitative results on RICO." + }, + { + "type": "table", + "bbox": [ + 0.11, + 0.632, + 0.865, + 0.833 + ], + "angle": 0, + "content": "
TasksMethodRICOPubLayNet
mIoU↑FID↓Align.↓Overlap↓Vio. %↓mIoU↑FID↓Align.↓Overlap↓Vio. %↓
Gen-TLayoutGAN++0.2985.9540.2610.6200.0.29714.8750.1240.1480.
LayoutFormer++ Full0.4321.0960.2300.5300.0.3488.4110.0200.0080.
0.4311.3200.2720.5500.0.3459.3670.0200.0090.
0.4391.3920.2060.5455.50.3459.3730.0200.0090.05
Gen-TSBLT0.6040.9510.1810.6600.0.4287.9140.0210.4190.
LayoutFormer++ Full0.6200.7570.2020.5420.0.4710.7200.0240.0370.
0.6130.7820.2060.5430.0.4640.9030.0260.0440.
0.6130.8010.2060.545≈0.0.4640.9030.0260.044≈0.
Gen-RCLG-LO0.2868.8980.3110.6153.660.27719.7380.1230.2006.66
LayoutFormer++ Full0.4245.9720.3320.53711.840.3534.9540.0250.0763.9
0.4198.6040.2840.54412.750.3525.1520.0230.0755.70
0.4585.1260.2210.54633.040.3584.6200.0220.03016.09
" + }, + { + "type": "table_caption", + "bbox": [ + 0.217, + 0.844, + 0.752, + 0.858 + ], + "angle": 0, + "content": "Table 2. Comparisons with baselines and the model variants to evaluate the controllability." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18409" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.102, + 0.092, + 0.87, + 0.598 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.353, + 0.607, + 0.615, + 0.622 + ], + "angle": 0, + "content": "Figure 5. Qualitative results on PubLayNet." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.648, + 0.473, + 0.89 + ], + "angle": 0, + "content": "Besides, we compare LayoutFormer++ framework with two variants. The first denoted as -Back indicates LayoutFormer++ without backtracking mechanism. The second denoted as -Back&Prune. is LayoutFormer++ without both pruning modules and the backtracking mechanism. For each task in Table 2, the last three lines show the comparison between the variants. Comparing -Full with -Back, we find that after disabling the backtracking mechanism, the generation quality decreases. And on Gen-R, the Vio.% also gets worse. Comparing -Full with -Back&Prune, we find that the Vio.% significantly decreases. It shows that the full model consistently decreases the violation while having little impact on quality, which demonstrates that both the pruning modules and the backtracking mechanism play important roles in helping LayoutFormer++ achieve good controllability." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.646, + 0.619, + 0.663 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.678, + 0.892, + 0.9 + ], + "angle": 0, + "content": "In this work, we propose LayoutFormer++ for conditional layout generation. To achieve the sufficient flexibility, we propose constraint serialization to represent different user constraints by the same sequence format. To achieve the good controllability, we propose decoding space restriction to prune the predicted distribution by disabling the options that violate the constraints or lead to bad quality. Experiments show that LayoutFormer++ can flexibly handle different layout generation tasks with better generation quality and less constraint violation compared to the existing task-specific approaches. In the future, we plan to investigate more practical user requirements for layout design. Besides, as LayoutFormer++ enables a unified way to handle different layout generation tasks, it is possible to develop a powerful pretrained model for layout generation in the future." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18410" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.079, + 0.09, + 0.176, + 0.107 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.117, + 0.47, + 0.2 + ], + "angle": 0, + "content": "[1] Peter Anderson, Basura Fernando, Mark Johnson, and Stephen Gould. Guided open vocabulary image captioning with constrained beam search. In Proceedings of the 2017 Conference on Empirical Methods in Natural Language Processing, pages 936-945, Copenhagen, Denmark, Sept. 2017. 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Publaynet: largest dataset ever for document layout analysis. arXiv preprint arXiv:1908.07836, 2019. 2, 5" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.469, + 0.897 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.519, + 0.956 + ], + "angle": 0, + "content": "18412" + } + ] +] \ No newline at end of file diff --git a/2023/LayoutFormer++_ Conditional Graphic Layout Generation via Constraint Serialization and Decoding Space Restriction/b766a11c-0ea4-4e2b-868e-229f60bdc47b_origin.pdf b/2023/LayoutFormer++_ Conditional Graphic Layout Generation via Constraint Serialization and Decoding Space Restriction/b766a11c-0ea4-4e2b-868e-229f60bdc47b_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..97995cdc8a114b43932c2d45e06e9db357ccec28 --- /dev/null +++ b/2023/LayoutFormer++_ Conditional Graphic Layout Generation via Constraint Serialization and Decoding Space Restriction/b766a11c-0ea4-4e2b-868e-229f60bdc47b_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:69ed825ed3880df3c09f0fb01f85448873262eb79835a02ea3cdcaeac717fda7 +size 1290270 diff --git a/2023/LayoutFormer++_ Conditional Graphic Layout Generation via Constraint Serialization and Decoding Space Restriction/full.md b/2023/LayoutFormer++_ Conditional Graphic Layout Generation via Constraint Serialization and Decoding Space Restriction/full.md new file mode 100644 index 0000000000000000000000000000000000000000..b7cd767569d5b930362b343a59f2c20aebd0eb1f --- /dev/null +++ b/2023/LayoutFormer++_ Conditional Graphic Layout Generation via Constraint Serialization and Decoding Space Restriction/full.md @@ -0,0 +1,228 @@ +# LayoutFormer++: Conditional Graphic Layout Generation via Constraint Serialization and Decoding Space Restriction + +Zhaoyun Jiang $^{1*}$ , Jiaqi Guo $^{2}$ , Shizhao Sun $^{2}$ , Huayu Deng $^{3*}$ , Zhongkai Wu $^{4*}$ , Vuksan Mijovic $^{5}$ , Zijiang James Yang $^{1}$ , Jian-Guang Lou $^{2}$ , Dongmei Zhang $^{2}$ , Xi'an Jiaotong University, Microsoft Research Asia, Shanghai Jiaotong University, Beihang University, Microsoft, + +jzyl24@stu.xjtu.edu.cn, deng.hy99@sjtu.edu.cn, 17376487@buaa.edu.cn, zijiang@xjtu.edu.cn, {jiaqiguo, shizsu, vmijovic, jlou, dongmeiz}@microsoft.com + +# Abstract + +Conditional graphic layout generation, which generates realistic layouts according to user constraints, is a challenging task that has not been well-studied yet. First, there is limited discussion about how to handle diverse user constraints flexibly and uniformly. Second, to make the layouts conform to user constraints, existing work often sacrifices generation quality significantly. In this work, we propose LayoutFormer++ to tackle the above problems. First, to flexibly handle diverse constraints, we propose a constraint serialization scheme, which represents different user constraints as sequences of tokens with a predefined format. Then, we formulate conditional layout generation as a sequence-to-sequence transformation, and leverage encoder-decoder framework with Transformer as the basic architecture. Furthermore, to make the layout better meet user requirements without harming quality, we propose a decoding space restriction strategy. Specifically, we prune the predicted distribution by ignoring the options that definitely violate user constraints and likely result in low-quality layouts, and make the model samples from the restricted distribution. Experiments demonstrate that LayoutFormer++ outperforms existing approaches on all the tasks in terms of both better generation quality and less constraint violation. + +# 1. Introduction + +Graphic designs greatly facilitate information communication in our daily life. During its creation, the layout, i.e., positions and sizes of elements, plays a critical role. To assist layout design, conditional layout generation, which takes user constraints as input and generates layouts as out + +![](images/27d933d5397c7b9803916255e07d1034106de342f1d02cccce0b6bf403e1e941.jpg) +Figure 1. Comparing with previous conditional layout generation approaches, LayoutFormer++ performs better on sufficient flexibility and good controllability. + +put, attracts great attention (see Figure 1). It is different from unconditional layout generation, which generates layouts freely without constraints, from at least two aspects. First, the model should be able to handle diverse user constraints, called sufficient flexibility. Figure 2 shows 6 typical tasks of layout generation in real-world applications including layout completion, layout refinement, layout generation conditioned on element types, element types with sizes, element relationships, or any of their combinations. Second, the model should generate layouts conforming to user requirements (i.e., constraints) as many as possible without harming quality, called good controllability (see Figure 1). + +However, existing work cannot meet the above two requirements. First, there is no existing work can support all the layout generation tasks with different user constraints. Most existing approaches simply focus on tackling a single conditional layout generation task without considering whether they can be applied to other tasks. For example, + +LayoutTransformer [3] can only perform completion task and BLT [10] cannot handle element relationships. Such task-specific approaches hinder the development of solutions for the new task. Second, there are no satisfactory methods to ensure good controllability. Some approaches directly replace the values in the predicted layout with the ones specified in the user constraints [3, 10]. Another work defines a set of heuristic rules and leverages latent optimization [8]. To make the generated layouts meet user requirements, they often degrade the generation quality significantly. + +In this work, we propose a unified model called LayoutFormer++ to support the different scenarios of conditional layout generation. In LayoutFormer++, a set of constraints is represented as a sequence. Specifically, we use a constraint serialization scheme to serialize different user constraints into a sequence of tokens with a predefined format (see Figure 1). The intuition behind this design choice is as follows. First, the sequence format is widely used and effective. Its effectiveness in layout generation has also been demonstrated in recent works [3, 10]. Second, a sequence is very flexible to accommodate different constraints for layout generation. We can serialize any structured information in the user constraints as a sequence. We found although user needs are diverse, they are all about element types and five attributes including type, top coordinate, left coordinate, width and height. Thus, we can simply define a set of vocabularies to describe the attributes respectively and concatenate descriptions of different attributes and elements to construct a sequence. + +Therefore, the conditional layout generation problem can be formulated as a sequence-to-sequence transformation problem. This enables us to leverage a simple yet effective encoder-decoder framework with Transformer [26] as a basic model architecture. The encoder processes the user constraints in a bidirectional way. The decoder predicts the layout sequence autoregressively, where there are multiple decoding steps and the model samples one token from the predicted distribution at each decoding step. + +Furthermore, to achieve good controllability, we introduce a decoding space restriction strategy in the inference stage. Our key idea is to prune the infeasible options in the predicted distribution and make the model sample from the restricted distribution at each decoding step. Specifically, we leverage two kinds of information to prune the options. First, the options that definitely violate the user constraints are pruned. For example, if a user wants one image and two buttons, the option for putting one text box will not be acceptable. Second, the options with low probabilities in the predicted distribution, which will very likely result in low-quality layouts, are also pruned. As the feasible option set may be empty after pruning, we further introduce a backtracking mechanism, in which the model goes back + +![](images/f6e4737ac94ef6dd4b88e71e65d84c91e0e33d669d34b54b4ef2a93ec87548c1.jpg) +Figure 2. Typical tasks for conditional layout generation. + +to a certain decoding step and find a better solution. Note that the whole generation process of the proposed strategy still relies on the distribution learned from the training data. Thus, it is less likely to disturb a layout when making it better conform to user constraints. + +We conduct extensive experiments on two public datasets [15, 30] and six layout generation tasks with different user constraints, to evaluate LayoutFormer++ and compare it with state-of-the-art approaches. Experimental results show that LayoutFormer++ can successfully tackle all six layout generation tasks that are handled separately by previous work, demonstrating that it is able to provide sufficient flexibility. Furthermore, LayoutFormer++ significantly outperforms previous approaches in terms of both better generation quality and less constraint violation, indicating that it achieves good controllability. + +# 2. Related Work + +Graphic Layout Generation. Graphic layout generation aims at generating aesthetic layouts to tackle users' needs. As users' needs are diverse in real-world applications, various tasks of layout generation are explored (see Figure 2), such as generation condition on element types [8, 10, 12], generation condition on types and sizes [10], generation condition on element relationships [8, 12], refinement [23] and completion [3]. Some other approaches focus on unconstrained generation [2, 7, 13, 27]. + +However, none of existing approaches can achieve sufficient flexibility to handle diverse layout generation tasks, due to the limitations in constraint modeling. Some works represent the constraints in the same format of the target layout, thus can not handle other complex constraints [3, 10, 23]. For example, LayoutTransformer [3] can only handle completion task but cannot deal with relationships between elements. Other works design the modeling formats specific to the constraint, which are hard to adapt to other tasks. For example, [12] leverages graph format to represent the relationships among the elements, which is inconvenient for the size constraints. In this work, we propose LayoutFormer++ with constraint serialization scheme, modeling different constraints into same format of the sequence, eliminating the isolation between layout generation tasks. + +Existing approaches also consider different methods for constraint satisfaction. Some approaches directly reset the predicted attributes by the values specified in the constraints [3, 10]. Other approaches define the heuristic rules and cost functions to control the generation [8, 12]. For example, [8] designs cost functions for each constraint and takes the constrained generation as an optimization problem. However, these methods often decrease the generation quality significantly. For [3, 10], directly resetting the sequence will make the generated layout deviate from the distribution learned by model. For [8, 12], it is hard to define the rules and cost functions to handle the trade-off between constraint satisfaction and generation quality. Different from existing approaches, we introduce decoding space restriction strategy to prune the infeasible values during decoding process, which does not rely on sophisticated rules or cost functions, and also fits the learned distribution. + +Decoding Methods. Decoding method plays an important role in autoregressive generation. The most prominent decoding methods include Greedy Search, Beam Search, Top-K sampling and Top-P sampling [5], etc. To enable the control over the output sequence, constrained decoding is first proposed in controllable text generation. [1,4,6,16,17,21] propose constrained decoding methods for hard lexical constraints where a set of tokens are required to occur in target output. [22,28] present decoding methods for soft constraints which assign a value between 0 and 1 to indicate how constraints are satisfied. [11, 24, 25] introduce decoding methods for structural constraints which impose a rigorous structures on the output sequence. Inspired by these methods, we propose a new constrained decoding method tailored for conditional layout generation. We carefully design two pruning modules and a backtracking mechanism to improve the satisfaction of constraints while maintaining high layout quality. + +# 3. Approach + +# 3.1. Overview + +A layout is made up of a set of elements, where each element can be described by its type $c$ , left and top coordinate $x$ and $y$ , as well as width $w$ and height $h$ . The continuous attributes $x$ , $y$ , $w$ and $h$ are quantized, which is proven to be helpful for graphic layouts [2, 3, 23]. Thus, an element can be represented by five tokens. Following the state-of-the-art approaches, we represent a layout by concatenating all the elements' tokens, i.e., $L = \{\langle \mathrm{so}\rangle c_1 x_1 y_1 w_1 h_1 \dots c_N x_N y_N w_N h_N \langle \mathrm{eos}\rangle\}$ . Here, $N$ denotes the total number of elements, $\langle \mathrm{so}\rangle$ and $\langle \mathrm{eos}\rangle$ are special tokens indicating the start and end of a sequence. + +In this work, we propose a new approach named LayoutFormer++ for conditional layout generation. The overall model architecture is illustrated in Figure 3a. + +To achieve sufficient flexibility, different constraints are formatted uniformly into sequence through constraint serialization. The details of the constraint serialization scheme will be introduced in Section 3.2. + +We leverage a Transformer encoder-decoder architecture for LayoutFormer++ based on the experience of previous works. The bidirectional encoder takes the constraint sequence as input and outputs their contextualized representations. The autoregressive decoder iteratively predicts the probabilities of future tokens. The model is trained to minimize the negative log-likelihood of layout tokens, i.e., + +$$ +\text {m i n i m i z e} \sum_ {t = 1} ^ {N} - \log P _ {\boldsymbol {\theta}} \left(L _ {t} \mid L _ {< t}, S\right), \tag {1} +$$ + +where $S$ is the input constraint sequence, $L$ is the output layout sequence, $\theta$ refers to the model parameters and $N$ denotes the length of the layout sequence. + +Finally, we introduce the decoding space restriction strategy with a backtracking mechanism into inference process to achieve good controllability. The details of the decoding space restriction strategy are given in Section 3.3. + +# 3.2. Serializing Constraints + +# 3.2.1 Principles + +Instead of directly presenting concrete sequences for the constraints considered in previous work, we first introduce the principles for serializing constraints. These principles not only summarize how the existing constraints are serialized but also provide a general guidance for formulating other constraints. There are two critical questions in serializing constraints. First, how to represent each constraint in a sequence format. Second, how to combine different constraints into a complete sequence. + +Constraint Representation. To present a constraint as a sequence, the basic idea is to first define a set of vocabularies and then concatenate the tokens from these vocabularies. Specifically, the constraints often fall into two categories. + +First, some constraints are only related to a single element. For example, put an image on the page or the element should be 10 pixel wide. The serialization for such constraint is quite straightforward: we just define a vocabulary and then represent the constraint by a single token from the vocabulary. For example, for the constraints about element type, the vocabulary could be {image, toolbar,..., button}, and the constraint 'an image' can be represented as image. + +Second, other constraints are related to multiple elements. For example, put an image on top of a button. To distinguish the elements referred in the constraint, we first build a vocabulary representing unique IDs for the elements. Then, we define a vocabulary for the relationships between elements. At last, we concatenate the tokens of element IDs and relationships. + +![](images/959513a4efc1d8268a14525d5ab7ffe242e70b7cc22966d6d210d5359eb732d8.jpg) +(a) Model Architecture + +![](images/4fb778f68a209b526aadc643e33f1c16f9c19dd935dce5577d36cde54024c635.jpg) +(b) Input and Output Sequences +Figure 3. a The overall model architecture of LayoutFormer++, illustrated by taking the task Gen-R as an example. b The examples of input and output sequences for different conditional layout generation tasks through constraint serialization. + +For example, the vocabulary for element IDs could be $\{\mathrm{image}_1,\dots ,\mathrm{image}_{K_1},\dots ,\mathrm{button}_1,\dots ,\mathrm{button}_{K_t}\}$ , and the vocabulary for relationships could be $\{\mathrm{top},\dots ,\mathrm{small}\}$ . Then, the constraint 'an image on top of a button' is represented as $\mathrm{image}_1$ top $\mathrm{button}_1$ . + +Constraint Combination. To combine different constraints, we concatenate their sequences. To ease the learning of neural network, we use a fixed order instead of a random order when concatenating different constraints. First, for the constraints only related to a single element, we first concatenate those for the same element and then concatenate those from different elements. Second, for the constraints related to multiple elements, we put them after all the constraints for the single elements. + +# 3.2.2 Examples for Typical Tasks + +In this work, we consider six typical layout generation tasks which has been explored in previous work. We demonstrate how we formulate the constraint sequences for these tasks according to Section 3.2.1 as followed. + +Generation conditioned on types (Gen-T) is to generate layouts from the element types specified by user constraints. We formulate the input constraint sequence by concatenating the single-element constraints of element type, i.e., $S_{\mathrm{Gen - T}} = \{\langle \mathrm{sos}\rangle c_1|c_2|\dots |c_N\langle \mathrm{eos}\rangle \} .^1$ + +Generation conditioned on types and sizes (Gen-TS) is to generate layouts when user constraints specify the element types and sizes. We formulate the input sequence by concatenating the type, the width and the height constraints as $S_{\mathrm{Gen - TS}} = \{\langle \mathrm{sos}\rangle c_1w_1h_1|c_2w_2h_2|\dots |c_Nw_Nh_N\langle \mathrm{eos}\rangle \}$ . + +Generation conditioned on relationships (Gen-R) generates layouts conditioned on element relationships. For example, a user could expect to put a large image at the top of a small text box. We formulate a relationship between two elements as $\{c_{k_{2m-1}} k_{2m-1} r_{k_{2m-1}, k_{2m}} c_{k_{2m}} k_{2m}\}$ , where $c_{k_{2m-1}}$ and $c_{k_{2m}}$ are the element types, $k_{2m-1}$ and + +$k_{2m}$ are the indexes for the elements, and $r_{k_{2m - 1},k_{2m}}$ is an extra token introduced to denote one kind of relationships. We concatenate the sequences of type constraints and relationship constraints as $S_{\mathrm{Gen - R}} = \{\langle \mathrm{sos}\rangle c_1|c_2|\ldots |c_N||c_{k_1}k_1r_{k_1,k_2}c_{k_2}k_2|\ldots |c_{k_{2M - 1}}k_{2M - 1}$ $r_{k_{2M - 1},k_{2M}}c_{k_{2M}}k_{2M}\langle \mathrm{eos}\rangle \}$ , where $M$ is the number of relationships. + +Refinement applies local changes to the elements that need improvements while maintaining the original layout design. We formulate the input as $S_{\text{Refinement}} = \{\langle \text{sos} \rangle c_1 x_1 y_1 w_1 h_1 | \ldots | c_N x_N y_N w_N h_N \langle \text{eos} \rangle \}$ . + +Completion aims to complete layout from a set of specified elements. We formulate the input as $S_{\text{Completion}} = \{\langle \mathrm{sos} \rangle c_1 x_1 y_1 w_1 h_1 | \ldots | c_P x_P y_P w_P h_P \langle \mathrm{eos} \rangle \}$ , where $P$ is the number of known elements. + +Unconstrained generation (UGen) aims to generate layouts without any user requirements. We formulate the input as an empty sequence with necessary special tokens, i.e., $S_{\mathrm{UGen}} = \{\langle \mathrm{sos} \rangle \langle \mathrm{eos} \rangle \}$ . + +# 3.3. Decoding Space Restriction + +During the inference, we introduce the decoding space restriction strategy to the decoding process. Algorithm 1 presents the pseudo-code for the decoding space restriction. + +In each decoding step $t$ , the decoder predicts the probabilities $P$ of the possible values for current attribute. Then, $P$ will be pruned by two modules. The ConstraintPruning prunes the infeasible values which may violate the user given constraints $S$ . The ProbabilityPruning prunes the values which the probabilities are lower than the threshold $\theta$ . + +If all the probabilities in $P'$ are pruned, it means there is no feasible value for current attribute. We propose a backtracking mechanism to solve this problem. When $P'$ is empty and the back time $B[t]$ is less than the max back time maxBack, the backtracking mechanism will roll back the decoding process to a previous step $t'$ and restart the prediction. Otherwise, the value $o$ will be sampled from $P'$ and the generation $O$ will be updated. The decoding process will move to the next step by increasing $t$ by 1. + +While the end-of-sequence token EOS is predicted, or + +the length of $O$ reaches maxLen, the generation finishes. In the following, we will give more details about the two pruning modules and the backtracking mechanism. + +Constraint Pruning Module. The constraint pruning module prunes the value in $P$ which may violate the related constraints. Take the relationship constraint as example, suppose at step $t$ the decoder predicts possibilities $P$ for the value of the attribute $w_{i}$ of the $i$ -th element, there is a relation constraint $s = \{w_{i} \leq w_{j}\}$ , which specifies the relative size relationships between element $i$ and $j$ . If $w_{j}$ has not been predicted at step $t$ , $w_{i}$ will not be influenced by $w_{j}$ in current step and the $P$ will not be pruned. Otherwise, if $w_{j}$ has been predicted at previous step, the feasible values of $w_{i}$ will be restricted to $(0, w_{j}]$ according to $s$ , and the infeasible values' probabilities in $P$ will be set as 0. + +Probability Pruning Module. The probability pruning module checks each value's probability in $P'$ . The probabilities that are lower than the predetermined threshold $\theta$ will be pruned by setting as 0. The threshold $\theta$ is tuned to achieve the best performance by task. + +Backtracking Mechanism. When the probabilities in $P'$ are all set as 0, the backtracking mechanism works to roll back the decoding process to a previous step and restart the prediction. The function Backtracking will check why the $P'$ is pruned as empty, and decide which step $t'$ to backtrack to. One situation is that the current token is restricted by previous token through the constraint. For example, the relation constraint $s = \{w_i \leq w_j\}$ restricts the feasible values of $w_i$ by $w_j$ . In this case, we choose the step of $w_j$ as the backtracking step. Otherwise, since all the previous predictions collectively lead to current circumstance, we randomly pick one previous step to back to. + +# 4. Experiments + +# 4.1. Setups + +Datasets. We compare LayoutFormer++ to existing approaches on two public datasets. RICO [15] is a dataset of mobile app UI that contains $66\mathrm{K}+$ UI layouts with 25 element types. PubLayNet [30] contains $360\mathrm{K}+$ document layouts with 5 element types. On both datasets, there are a few layouts with quite a lot of elements, which easily leads to an out-of-memory problem. Existing studies use multifarious rules to filter out these layouts. In our experiments, we simply filter out the layouts with more than 20 elements. For RICO, we use $90\%$ , $5\%$ and $5\%$ of data for training, validation and testing. For PubLayNet, we use $95\%$ and $5\%$ of official training split for training and validation, and the official validation split for testing. + +Baselines. We try our best to reproduce all the existing approaches. Even so, we regret to not include some approaches for the following reasons. First, due to the missing implementation details and hyperparameter settings, we + +Algorithm 1: Decoding Space Restriction +Input: Encoder hidden state $M$ ;User constraints $S$ Output: Layout sequence $O$ 1 Initialize step index $t$ , the back time for each step $B$ and the predicted sequence $O$ 2 while $(O[-1]\neq \mathrm{EOS})$ and $(t < maxLen)$ do 3 $P\gets \mathrm{Decoder}(O,M)[t]$ . 4 $P^{\prime}\gets$ ConstraintPruning $(P,S)$ . 5 $P^{\prime}\gets$ ProbabilityPruning $(P^{\prime},\theta)$ . 6 if $(P^{\prime}$ is $\varnothing$ )and $(B[t] < maxBack)$ then 7 $t^\prime \gets$ Backtracking $(P,S,t)$ . 8 $B[t]\gets B[t] + 1$ . 9 $O\gets O[:t]$ . 10 t t; 11 else 12 o $\leftarrow$ Sampling $(P^{\prime})$ . 13 $O\gets O\cup o$ . 14 t t+1; 15 end 16 end + +fail to reproduce some approaches [13, 14, 18, 20]. Second, a few approaches consider data-specific attributes and are difficult to be applied to arbitrary datasets about graphic layouts [27, 29]. Ultimately, we compare LayoutFormer++ against 1) NDN-none [12], LayoutGAN++ [8] and BLT [10] on Gen-T, 2) BLT [10] on Gen-TS, 3) NDN [12] and CLG-LO [8] on Gen-R, 4) RUAGE [23] on refinement, 5) LayoutTransformer [3] on completion, and 6) VTN [2], Coarse2Fine [7] and LayoutTransformer [3] on UGen. + +Evaluation Metrics. We adopt the metrics proposed by existing works for comprehensive evaluation. + +Maximum Intersection over Union (mIoU) measures the similarity between the generated layouts and the real layouts, which is based on the averaged IoU of bounding boxes. We use the same implementation as [8]. + +Alignment (Align.) measures whether the elements are well-aligned. We modify the metric from [14] by normalizing it by the number of elements. + +Overlap measures the abnormal overlap area between elements. We improve the metric from [14] by ignoring the elements that serve as a background or padding, e.g., card, background and modal on RICO. + +Frechet Inception Distance (FID) describes the distribution difference between real and generated layouts. Following [8], we train a neural network to convert the layouts into representative features and then calculate the distribution difference based on learned features. + +Constraint Violation Rate (Vio.%) measures the rate of the violated constraints. We follow the implementation of [8] for Gen-R. For other tasks, we calculate Vio.% by dividing the number of the violated constraints by the total + +
TasksMethodsRICOPubLayNet
mIoU ↑FID ↓Align. ↓Overlap ↓mIoU ↑FID ↓Align. ↓Overlap ↓
Gen-TNDN-none0.3513.760.560.550.3135.670.350.17
LayoutGAN++0.2985.9540.2610.6200.29714.8750.1240.148
BLT0.21625.6330.1500.9830.14038.6840.0360.196
LayoutFormer++0.4321.0960.2300.5300.3488.4110.0200.008
Gen-TSBLT0.6040.9510.1810.6600.4287.9140.0210.419
LayoutFormer++0.6200.7570.2020.5420.4710.7200.0240.037
Gen-RNDN0.36-0.56-0.31-0.36-
CLG-LO0.2868.8980.3110.6150.27719.7380.1230.200
LayoutFormer++0.4245.9720.3320.5370.3534.9540.0250.076
RefinementRUITE0.8110.1070.1330.4830.7810.0610.0290.020.
LayoutFormer++0.8160.0320.1230.4890.7850.0860.0240.006
CompletionLayoutTransformer0.3636.6790.1940.4780.07714.7690.0190.0013
LayoutFormer++0.7324.5740.0770.4870.47110.2510.0200.0022
UGenLayoutTransformer0.43922.8840.0520.4710.06236.3040.0310.0009
VTN0.68676.0640.4610.6940.210103.3730.2050.211
Coarse2Fine0.36046.4830.1280.6760.36150.8540.2210.142
LayoutFormer++0.74219.6880.0470.5470.41746.5220.0290.0009
+ +Table 1. Quantitative comparisons with existing approaches on six layout generation tasks. + +number of constraints for all the evaluated layouts. + +Among the above metrics, mIoU, Align., Overlap and FID evaluate the generation quality, and Vio.% evaluate the constraint satisfaction. A larger value for mIoU indicates better performance, while smaller values for other metrics indicate better performance. + +Implementation Details. We implement Layout-Former++ by PyTorch [19]. The model is trained using the Adam optimizer [9] with NVIDIA V100 GPUs. For Transformer blocks, we use 8 layers, 8 heads for multi-attention, 512 embedding dimensions and 2048 feed-forward dimensions. Other hyper-parameters, e.g., the batch size, the learning rate, and the threshold $\theta$ in decoding space restriction, are tuned to achieve the best performance on the validation set2. For Gen-R, following CLG-LO [8], we randomly sample $10\%$ element relationships as the input. For refinement, following RUTFE [23], we synthesize the input by adding random noise to the position and size of each element, which is sampled from a normal distribution with the mean 0 and the standard variance 0.01. + +# 4.2. Evaluations on Sufficient Flexibility + +To demonstrate the sufficient flexibility of LayoutFormer++, we compare LayoutFormer++ with existing approaches on all six layout generation tasks. + +Table 1 shows the quantitative comparisons to existing works3. It should be noted that the existing approaches can + +only handle up to two tasks, while LayoutFormer++ can handle all the six tasks. We highlight the results of LayoutFormer++ by bold when it achieves the best performance among all the existing approaches in Table 1. According to the results, LayoutFormer++ achieves significantly better performance than the baselines on most metrics. This demonstrates that LayoutFormer++ not only can flexibly handle diverse user constraints, but also has advantages in the generation ability over existing approaches. + +Figure 4 and 5 show qualitative comparisons on RICO and PubLayNet. Compared to baselines, LayoutFormer++ generates layouts with better spacing, less misalignment, and fewer unreasonable overlaps. + +# 4.3. Evaluations on Good Controllability + +In this section, we compare LayoutFormer++ with LayoutGAN++ [13], BLT [10] and CLG-LO [8], which pay attention to the constraint satisfaction. These approaches handle Gen-T, Gen-TS and Gen-R respectively. + +We bold the results of LayoutFormer++ in Table 2 when it outperforms the baselines. For Gen-T and Gen-TS, since all approaches have no constraint violation, we focus on the performance of quality. As the results, LayoutFormer++ outperforms the baselines on both two datasets. For Gen-R, LayoutFormer++ achieves better performance on both quality metrics and Vio.% except a worse Vio.% than CLG-LO on RICO. However, CLG-LO does not make a good tradeoff: the quality of layouts generated by CLG-LO is significantly worse than that of LayoutFormer++. This demonstrates that LayoutFormer++ achieves the best controllability among existing approaches. + +![](images/f5e8bc0145bb4209fc6d0d1cc5da8b016dbc9453fa146c0fd3666903db033bfb.jpg) +Figure 4. Qualitative results on RICO. + +
TasksMethodRICOPubLayNet
mIoU↑FID↓Align.↓Overlap↓Vio. %↓mIoU↑FID↓Align.↓Overlap↓Vio. %↓
Gen-TLayoutGAN++0.2985.9540.2610.6200.0.29714.8750.1240.1480.
LayoutFormer++ Full0.4321.0960.2300.5300.0.3488.4110.0200.0080.
0.4311.3200.2720.5500.0.3459.3670.0200.0090.
0.4391.3920.2060.5455.50.3459.3730.0200.0090.05
Gen-TSBLT0.6040.9510.1810.6600.0.4287.9140.0210.4190.
LayoutFormer++ Full0.6200.7570.2020.5420.0.4710.7200.0240.0370.
0.6130.7820.2060.5430.0.4640.9030.0260.0440.
0.6130.8010.2060.545≈0.0.4640.9030.0260.044≈0.
Gen-RCLG-LO0.2868.8980.3110.6153.660.27719.7380.1230.2006.66
LayoutFormer++ Full0.4245.9720.3320.53711.840.3534.9540.0250.0763.9
0.4198.6040.2840.54412.750.3525.1520.0230.0755.70
0.4585.1260.2210.54633.040.3584.6200.0220.03016.09
+ +Table 2. Comparisons with baselines and the model variants to evaluate the controllability. + +![](images/ce8a9611470b1cfe98c66efd2d2dfd3d95ef483ce6e44a97878c75e9c3136c12.jpg) +Figure 5. Qualitative results on PubLayNet. + +Besides, we compare LayoutFormer++ framework with two variants. The first denoted as -Back indicates LayoutFormer++ without backtracking mechanism. The second denoted as -Back&Prune. is LayoutFormer++ without both pruning modules and the backtracking mechanism. For each task in Table 2, the last three lines show the comparison between the variants. Comparing -Full with -Back, we find that after disabling the backtracking mechanism, the generation quality decreases. And on Gen-R, the Vio.% also gets worse. Comparing -Full with -Back&Prune, we find that the Vio.% significantly decreases. It shows that the full model consistently decreases the violation while having little impact on quality, which demonstrates that both the pruning modules and the backtracking mechanism play important roles in helping LayoutFormer++ achieve good controllability. + +# 5. Conclusion + +In this work, we propose LayoutFormer++ for conditional layout generation. To achieve the sufficient flexibility, we propose constraint serialization to represent different user constraints by the same sequence format. To achieve the good controllability, we propose decoding space restriction to prune the predicted distribution by disabling the options that violate the constraints or lead to bad quality. Experiments show that LayoutFormer++ can flexibly handle different layout generation tasks with better generation quality and less constraint violation compared to the existing task-specific approaches. In the future, we plan to investigate more practical user requirements for layout design. 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Vishwanathan, and R. Garnett, editors, Advances in Neural Information Processing Systems, volume 30. Curran Associates, Inc., 2017. 2 +[27] Kota Yamaguchi. Canvasvae: Learning to generate vector graphic documents. In Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), pages 5481-5489, October 2021. 2, 5 +[28] Maosen Zhang, Nan Jiang, Lei Li, and Yexiang Xue. Language generation via combinatorial constraint satisfaction: A tree search enhanced Monte-Carlo approach. In Findings of the Association for Computational Linguistics: EMNLP 2020, pages 1286-1298, Online, Nov. 2020. Association for Computational Linguistics. 3 +[29] Xinru Zheng, Xiaotian Qiao, Ying Cao, and Rynson W. H. Lau. Content-aware generative modeling of graphic design layouts. ACM Trans. Graph., 38(4), jul 2019. 5 +[30] Xu Zhong, Jianbin Tang, and Antonio Jimeno Yepes. Publaynet: largest dataset ever for document layout analysis. arXiv preprint arXiv:1908.07836, 2019. 2, 5 \ No newline at end of file diff --git a/2023/LayoutFormer++_ Conditional Graphic Layout Generation via Constraint Serialization and Decoding Space Restriction/images.zip b/2023/LayoutFormer++_ Conditional Graphic Layout Generation via Constraint Serialization and Decoding Space Restriction/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..c06e5dcf30720a0b31f87154753684f34cf6f449 --- /dev/null +++ b/2023/LayoutFormer++_ Conditional Graphic Layout Generation via Constraint Serialization and Decoding Space Restriction/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:f2d0ddc31b5cffb781f49434ea77a41e4c6e26c5ca1809269add0b1578fcf466 +size 777155 diff --git a/2023/LayoutFormer++_ Conditional Graphic Layout Generation via Constraint Serialization and Decoding Space Restriction/layout.json b/2023/LayoutFormer++_ Conditional 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], + "index": 3 + }, + { + "bbox": [ + 81, + 220, + 509, + 245 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 81, + 220, + 509, + 245 + ], + "spans": [ + { + "bbox": [ + 81, + 220, + 509, + 245 + ], + "type": "text", + "content": "jzyl24@stu.xjtu.edu.cn, deng.hy99@sjtu.edu.cn, 17376487@buaa.edu.cn, zijiang@xjtu.edu.cn, {jiaqiguo, shizsu, vmijovic, jlou, dongmeiz}@microsoft.com" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 273, + 192, + 285 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 273, + 192, + 285 + ], + "spans": [ + { + "bbox": [ + 143, + 273, + 192, + 285 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 299, + 290, + 585 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 299, + 290, + 585 + ], + "spans": [ + { + "bbox": [ + 46, + 299, + 290, + 585 + ], + "type": "text", + "content": "Conditional graphic layout generation, which generates realistic layouts according to user constraints, is a challenging task that has not been well-studied yet. First, there is limited discussion about how to handle diverse user constraints flexibly and uniformly. Second, to make the layouts conform to user constraints, existing work often sacrifices generation quality significantly. In this work, we propose LayoutFormer++ to tackle the above problems. First, to flexibly handle diverse constraints, we propose a constraint serialization scheme, which represents different user constraints as sequences of tokens with a predefined format. Then, we formulate conditional layout generation as a sequence-to-sequence transformation, and leverage encoder-decoder framework with Transformer as the basic architecture. Furthermore, to make the layout better meet user requirements without harming quality, we propose a decoding space restriction strategy. Specifically, we prune the predicted distribution by ignoring the options that definitely violate user constraints and likely result in low-quality layouts, and make the model samples from the restricted distribution. Experiments demonstrate that LayoutFormer++ outperforms existing approaches on all the tasks in terms of both better generation quality and less constraint violation." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 611, + 128, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 611, + 128, + 624 + ], + "spans": [ + { + "bbox": [ + 47, + 611, + 128, + 624 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 632, + 287, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 632, + 287, + 693 + ], + "spans": [ + { + "bbox": [ + 46, + 632, + 287, + 693 + ], + "type": "text", + "content": "Graphic designs greatly facilitate information communication in our daily life. During its creation, the layout, i.e., positions and sizes of elements, plays a critical role. To assist layout design, conditional layout generation, which takes user constraints as input and generates layouts as out" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 310, + 273, + 544, + 439 + ], + "blocks": [ + { + "bbox": [ + 310, + 273, + 544, + 439 + ], + "lines": [ + { + "bbox": [ + 310, + 273, + 544, + 439 + ], + "spans": [ + { + "bbox": [ + 310, + 273, + 544, + 439 + ], + "type": "image", + "image_path": "27d933d5397c7b9803916255e07d1034106de342f1d02cccce0b6bf403e1e941.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 445, + 545, + 479 + ], + "lines": [ + { + "bbox": [ + 305, + 445, + 545, + 479 + ], + "spans": [ + { + "bbox": [ + 305, + 445, + 545, + 479 + ], + "type": "text", + "content": "Figure 1. Comparing with previous conditional layout generation approaches, LayoutFormer++ performs better on sufficient flexibility and good controllability." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 495, + 546, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 495, + 546, + 639 + ], + "spans": [ + { + "bbox": [ + 304, + 495, + 546, + 639 + ], + "type": "text", + "content": "put, attracts great attention (see Figure 1). It is different from unconditional layout generation, which generates layouts freely without constraints, from at least two aspects. First, the model should be able to handle diverse user constraints, called sufficient flexibility. Figure 2 shows 6 typical tasks of layout generation in real-world applications including layout completion, layout refinement, layout generation conditioned on element types, element types with sizes, element relationships, or any of their combinations. Second, the model should generate layouts conforming to user requirements (i.e., constraints) as many as possible without harming quality, called good controllability (see Figure 1)." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "type": "text", + "content": "However, existing work cannot meet the above two requirements. First, there is no existing work can support all the layout generation tasks with different user constraints. Most existing approaches simply focus on tackling a single conditional layout generation task without considering whether they can be applied to other tasks. For example," + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 257, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 257, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 257, + 712 + ], + "type": "text", + "content": "*Work done during an internship at Microsoft Research Asia." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18403" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": "LayoutTransformer [3] can only perform completion task and BLT [10] cannot handle element relationships. Such task-specific approaches hinder the development of solutions for the new task. Second, there are no satisfactory methods to ensure good controllability. Some approaches directly replace the values in the predicted layout with the ones specified in the user constraints [3, 10]. Another work defines a set of heuristic rules and leverages latent optimization [8]. To make the generated layouts meet user requirements, they often degrade the generation quality significantly." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 206, + 289, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 206, + 289, + 434 + ], + "spans": [ + { + "bbox": [ + 46, + 206, + 289, + 434 + ], + "type": "text", + "content": "In this work, we propose a unified model called LayoutFormer++ to support the different scenarios of conditional layout generation. In LayoutFormer++, a set of constraints is represented as a sequence. Specifically, we use a constraint serialization scheme to serialize different user constraints into a sequence of tokens with a predefined format (see Figure 1). The intuition behind this design choice is as follows. First, the sequence format is widely used and effective. Its effectiveness in layout generation has also been demonstrated in recent works [3, 10]. Second, a sequence is very flexible to accommodate different constraints for layout generation. We can serialize any structured information in the user constraints as a sequence. We found although user needs are diverse, they are all about element types and five attributes including type, top coordinate, left coordinate, width and height. Thus, we can simply define a set of vocabularies to describe the attributes respectively and concatenate descriptions of different attributes and elements to construct a sequence." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 436, + 287, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 436, + 287, + 544 + ], + "spans": [ + { + "bbox": [ + 46, + 436, + 287, + 544 + ], + "type": "text", + "content": "Therefore, the conditional layout generation problem can be formulated as a sequence-to-sequence transformation problem. This enables us to leverage a simple yet effective encoder-decoder framework with Transformer [26] as a basic model architecture. The encoder processes the user constraints in a bidirectional way. The decoder predicts the layout sequence autoregressively, where there are multiple decoding steps and the model samples one token from the predicted distribution at each decoding step." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 546, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 546, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 546, + 288, + 713 + ], + "type": "text", + "content": "Furthermore, to achieve good controllability, we introduce a decoding space restriction strategy in the inference stage. Our key idea is to prune the infeasible options in the predicted distribution and make the model sample from the restricted distribution at each decoding step. Specifically, we leverage two kinds of information to prune the options. First, the options that definitely violate the user constraints are pruned. For example, if a user wants one image and two buttons, the option for putting one text box will not be acceptable. Second, the options with low probabilities in the predicted distribution, which will very likely result in low-quality layouts, are also pruned. As the feasible option set may be empty after pruning, we further introduce a backtracking mechanism, in which the model goes back" + } + ] + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 315, + 72, + 539, + 173 + ], + "blocks": [ + { + "bbox": [ + 315, + 72, + 539, + 173 + ], + "lines": [ + { + "bbox": [ + 315, + 72, + 539, + 173 + ], + "spans": [ + { + "bbox": [ + 315, + 72, + 539, + 173 + ], + "type": "image", + "image_path": "f6e4737ac94ef6dd4b88e71e65d84c91e0e33d669d34b54b4ef2a93ec87548c1.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 321, + 180, + 529, + 191 + ], + "lines": [ + { + "bbox": [ + 321, + 180, + 529, + 191 + ], + "spans": [ + { + "bbox": [ + 321, + 180, + 529, + 191 + ], + "type": "text", + "content": "Figure 2. Typical tasks for conditional layout generation." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 204, + 545, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 204, + 545, + 263 + ], + "spans": [ + { + "bbox": [ + 304, + 204, + 545, + 263 + ], + "type": "text", + "content": "to a certain decoding step and find a better solution. Note that the whole generation process of the proposed strategy still relies on the distribution learned from the training data. Thus, it is less likely to disturb a layout when making it better conform to user constraints." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 264, + 546, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 264, + 546, + 396 + ], + "spans": [ + { + "bbox": [ + 304, + 264, + 546, + 396 + ], + "type": "text", + "content": "We conduct extensive experiments on two public datasets [15, 30] and six layout generation tasks with different user constraints, to evaluate LayoutFormer++ and compare it with state-of-the-art approaches. Experimental results show that LayoutFormer++ can successfully tackle all six layout generation tasks that are handled separately by previous work, demonstrating that it is able to provide sufficient flexibility. Furthermore, LayoutFormer++ significantly outperforms previous approaches in terms of both better generation quality and less constraint violation, indicating that it achieves good controllability." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 406, + 392, + 418 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 406, + 392, + 418 + ], + "spans": [ + { + "bbox": [ + 306, + 406, + 392, + 418 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 426, + 545, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 426, + 545, + 533 + ], + "spans": [ + { + "bbox": [ + 304, + 426, + 545, + 533 + ], + "type": "text", + "content": "Graphic Layout Generation. Graphic layout generation aims at generating aesthetic layouts to tackle users' needs. As users' needs are diverse in real-world applications, various tasks of layout generation are explored (see Figure 2), such as generation condition on element types [8, 10, 12], generation condition on types and sizes [10], generation condition on element relationships [8, 12], refinement [23] and completion [3]. Some other approaches focus on unconstrained generation [2, 7, 13, 27]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 534, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 546, + 713 + ], + "type": "text", + "content": "However, none of existing approaches can achieve sufficient flexibility to handle diverse layout generation tasks, due to the limitations in constraint modeling. Some works represent the constraints in the same format of the target layout, thus can not handle other complex constraints [3, 10, 23]. For example, LayoutTransformer [3] can only handle completion task but cannot deal with relationships between elements. Other works design the modeling formats specific to the constraint, which are hard to adapt to other tasks. For example, [12] leverages graph format to represent the relationships among the elements, which is inconvenient for the size constraints. In this work, we propose LayoutFormer++ with constraint serialization scheme, modeling different constraints into same format of the sequence, eliminating the isolation between layout generation tasks." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "18404" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 275 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 275 + ], + "type": "text", + "content": "Existing approaches also consider different methods for constraint satisfaction. Some approaches directly reset the predicted attributes by the values specified in the constraints [3, 10]. Other approaches define the heuristic rules and cost functions to control the generation [8, 12]. For example, [8] designs cost functions for each constraint and takes the constrained generation as an optimization problem. However, these methods often decrease the generation quality significantly. For [3, 10], directly resetting the sequence will make the generated layout deviate from the distribution learned by model. For [8, 12], it is hard to define the rules and cost functions to handle the trade-off between constraint satisfaction and generation quality. Different from existing approaches, we introduce decoding space restriction strategy to prune the infeasible values during decoding process, which does not rely on sophisticated rules or cost functions, and also fits the learned distribution." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 277, + 289, + 492 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 277, + 289, + 492 + ], + "spans": [ + { + "bbox": [ + 46, + 277, + 289, + 492 + ], + "type": "text", + "content": "Decoding Methods. Decoding method plays an important role in autoregressive generation. The most prominent decoding methods include Greedy Search, Beam Search, Top-K sampling and Top-P sampling [5], etc. To enable the control over the output sequence, constrained decoding is first proposed in controllable text generation. [1,4,6,16,17,21] propose constrained decoding methods for hard lexical constraints where a set of tokens are required to occur in target output. [22,28] present decoding methods for soft constraints which assign a value between 0 and 1 to indicate how constraints are satisfied. [11, 24, 25] introduce decoding methods for structural constraints which impose a rigorous structures on the output sequence. Inspired by these methods, we propose a new constrained decoding method tailored for conditional layout generation. We carefully design two pruning modules and a backtracking mechanism to improve the satisfaction of constraints while maintaining high layout quality." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 505, + 115, + 520 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 505, + 115, + 520 + ], + "spans": [ + { + "bbox": [ + 47, + 505, + 115, + 520 + ], + "type": "text", + "content": "3. Approach" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 525, + 115, + 538 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 525, + 115, + 538 + ], + "spans": [ + { + "bbox": [ + 47, + 525, + 115, + 538 + ], + "type": "text", + "content": "3.1. Overview" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 544, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 544, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 544, + 287, + 677 + ], + "type": "text", + "content": "A layout is made up of a set of elements, where each element can be described by its type " + }, + { + "bbox": [ + 46, + 544, + 287, + 677 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 544, + 287, + 677 + ], + "type": "text", + "content": ", left and top coordinate " + }, + { + "bbox": [ + 46, + 544, + 287, + 677 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 544, + 287, + 677 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 544, + 287, + 677 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 544, + 287, + 677 + ], + "type": "text", + "content": ", as well as width " + }, + { + "bbox": [ + 46, + 544, + 287, + 677 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 46, + 544, + 287, + 677 + ], + "type": "text", + "content": " and height " + }, + { + "bbox": [ + 46, + 544, + 287, + 677 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 46, + 544, + 287, + 677 + ], + "type": "text", + "content": ". The continuous attributes " + }, + { + "bbox": [ + 46, + 544, + 287, + 677 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 544, + 287, + 677 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 544, + 287, + 677 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 544, + 287, + 677 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 544, + 287, + 677 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 46, + 544, + 287, + 677 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 544, + 287, + 677 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 46, + 544, + 287, + 677 + ], + "type": "text", + "content": " are quantized, which is proven to be helpful for graphic layouts [2, 3, 23]. Thus, an element can be represented by five tokens. Following the state-of-the-art approaches, we represent a layout by concatenating all the elements' tokens, i.e., " + }, + { + "bbox": [ + 46, + 544, + 287, + 677 + ], + "type": "inline_equation", + "content": "L = \\{\\langle \\mathrm{so}\\rangle c_1 x_1 y_1 w_1 h_1 \\dots c_N x_N y_N w_N h_N \\langle \\mathrm{eos}\\rangle\\}" + }, + { + "bbox": [ + 46, + 544, + 287, + 677 + ], + "type": "text", + "content": ". Here, " + }, + { + "bbox": [ + 46, + 544, + 287, + 677 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 544, + 287, + 677 + ], + "type": "text", + "content": " denotes the total number of elements, " + }, + { + "bbox": [ + 46, + 544, + 287, + 677 + ], + "type": "inline_equation", + "content": "\\langle \\mathrm{so}\\rangle" + }, + { + "bbox": [ + 46, + 544, + 287, + 677 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 544, + 287, + 677 + ], + "type": "inline_equation", + "content": "\\langle \\mathrm{eos}\\rangle" + }, + { + "bbox": [ + 46, + 544, + 287, + 677 + ], + "type": "text", + "content": " are special tokens indicating the start and end of a sequence." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "text", + "content": "In this work, we propose a new approach named LayoutFormer++ for conditional layout generation. The overall model architecture is illustrated in Figure 3a." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 545, + 119 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 119 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 119 + ], + "type": "text", + "content": "To achieve sufficient flexibility, different constraints are formatted uniformly into sequence through constraint serialization. The details of the constraint serialization scheme will be introduced in Section 3.2." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 119, + 547, + 198 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 119, + 547, + 198 + ], + "spans": [ + { + "bbox": [ + 304, + 119, + 547, + 198 + ], + "type": "text", + "content": "We leverage a Transformer encoder-decoder architecture for LayoutFormer++ based on the experience of previous works. The bidirectional encoder takes the constraint sequence as input and outputs their contextualized representations. The autoregressive decoder iteratively predicts the probabilities of future tokens. The model is trained to minimize the negative log-likelihood of layout tokens, i.e.," + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 358, + 203, + 545, + 232 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 358, + 203, + 545, + 232 + ], + "spans": [ + { + "bbox": [ + 358, + 203, + 545, + 232 + ], + "type": "interline_equation", + "content": "\\text {m i n i m i z e} \\sum_ {t = 1} ^ {N} - \\log P _ {\\boldsymbol {\\theta}} \\left(L _ {t} \\mid L _ {< t}, S\\right), \\tag {1}", + "image_path": "166606665f8ebbca6dff589563ba4ee66cd649277d7d6e0ce8f9430d25ef273d.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 239, + 545, + 274 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 239, + 545, + 274 + ], + "spans": [ + { + "bbox": [ + 304, + 239, + 545, + 274 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 239, + 545, + 274 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 239, + 545, + 274 + ], + "type": "text", + "content": " is the input constraint sequence, " + }, + { + "bbox": [ + 304, + 239, + 545, + 274 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 304, + 239, + 545, + 274 + ], + "type": "text", + "content": " is the output layout sequence, " + }, + { + "bbox": [ + 304, + 239, + 545, + 274 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 239, + 545, + 274 + ], + "type": "text", + "content": " refers to the model parameters and " + }, + { + "bbox": [ + 304, + 239, + 545, + 274 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 239, + 545, + 274 + ], + "type": "text", + "content": " denotes the length of the layout sequence." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 275, + 545, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 275, + 545, + 323 + ], + "spans": [ + { + "bbox": [ + 304, + 275, + 545, + 323 + ], + "type": "text", + "content": "Finally, we introduce the decoding space restriction strategy with a backtracking mechanism into inference process to achieve good controllability. The details of the decoding space restriction strategy are given in Section 3.3." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 329, + 437, + 342 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 329, + 437, + 342 + ], + "spans": [ + { + "bbox": [ + 306, + 329, + 437, + 342 + ], + "type": "text", + "content": "3.2. Serializing Constraints" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 348, + 383, + 361 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 348, + 383, + 361 + ], + "spans": [ + { + "bbox": [ + 306, + 348, + 383, + 361 + ], + "type": "text", + "content": "3.2.1 Principles" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 366, + 545, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 366, + 545, + 474 + ], + "spans": [ + { + "bbox": [ + 304, + 366, + 545, + 474 + ], + "type": "text", + "content": "Instead of directly presenting concrete sequences for the constraints considered in previous work, we first introduce the principles for serializing constraints. These principles not only summarize how the existing constraints are serialized but also provide a general guidance for formulating other constraints. There are two critical questions in serializing constraints. First, how to represent each constraint in a sequence format. Second, how to combine different constraints into a complete sequence." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 475, + 545, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 475, + 545, + 521 + ], + "spans": [ + { + "bbox": [ + 304, + 475, + 545, + 521 + ], + "type": "text", + "content": "Constraint Representation. To present a constraint as a sequence, the basic idea is to first define a set of vocabularies and then concatenate the tokens from these vocabularies. Specifically, the constraints often fall into two categories." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 522, + 545, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 522, + 545, + 629 + ], + "spans": [ + { + "bbox": [ + 304, + 522, + 545, + 629 + ], + "type": "text", + "content": "First, some constraints are only related to a single element. For example, put an image on the page or the element should be 10 pixel wide. The serialization for such constraint is quite straightforward: we just define a vocabulary and then represent the constraint by a single token from the vocabulary. For example, for the constraints about element type, the vocabulary could be {image, toolbar,..., button}, and the constraint 'an image' can be represented as image." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": "Second, other constraints are related to multiple elements. For example, put an image on top of a button. To distinguish the elements referred in the constraint, we first build a vocabulary representing unique IDs for the elements. Then, we define a vocabulary for the relationships between elements. At last, we concatenate the tokens of element IDs and relationships." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "18405" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 69, + 70, + 312, + 178 + ], + "blocks": [ + { + "bbox": [ + 69, + 70, + 312, + 178 + ], + "lines": [ + { + "bbox": [ + 69, + 70, + 312, + 178 + ], + "spans": [ + { + "bbox": [ + 69, + 70, + 312, + 178 + ], + "type": "image", + "image_path": "959513a4efc1d8268a14525d5ab7ffe242e70b7cc22966d6d210d5359eb732d8.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 150, + 184, + 228, + 194 + ], + "lines": [ + { + "bbox": [ + 150, + 184, + 228, + 194 + ], + "spans": [ + { + "bbox": [ + 150, + 184, + 228, + 194 + ], + "type": "text", + "content": "(a) Model Architecture" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 339, + 77, + 521, + 175 + ], + "blocks": [ + { + "bbox": [ + 339, + 77, + 521, + 175 + ], + "lines": [ + { + "bbox": [ + 339, + 77, + 521, + 175 + ], + "spans": [ + { + "bbox": [ + 339, + 77, + 521, + 175 + ], + "type": "image", + "image_path": "4fb778f68a209b526aadc643e33f1c16f9c19dd935dce5577d36cde54024c635.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 377, + 178, + 481, + 188 + ], + "lines": [ + { + "bbox": [ + 377, + 178, + 481, + 188 + ], + "spans": [ + { + "bbox": [ + 377, + 178, + 481, + 188 + ], + "type": "text", + "content": "(b) Input and Output Sequences" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 198, + 547, + 220 + ], + "lines": [ + { + "bbox": [ + 46, + 198, + 547, + 220 + ], + "spans": [ + { + "bbox": [ + 46, + 198, + 547, + 220 + ], + "type": "text", + "content": "Figure 3. a The overall model architecture of LayoutFormer++, illustrated by taking the task Gen-R as an example. b The examples of input and output sequences for different conditional layout generation tasks through constraint serialization." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 234, + 290, + 293 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 234, + 290, + 293 + ], + "spans": [ + { + "bbox": [ + 46, + 234, + 290, + 293 + ], + "type": "text", + "content": "For example, the vocabulary for element IDs could be " + }, + { + "bbox": [ + 46, + 234, + 290, + 293 + ], + "type": "inline_equation", + "content": "\\{\\mathrm{image}_1,\\dots ,\\mathrm{image}_{K_1},\\dots ,\\mathrm{button}_1,\\dots ,\\mathrm{button}_{K_t}\\}" + }, + { + "bbox": [ + 46, + 234, + 290, + 293 + ], + "type": "text", + "content": ", and the vocabulary for relationships could be " + }, + { + "bbox": [ + 46, + 234, + 290, + 293 + ], + "type": "inline_equation", + "content": "\\{\\mathrm{top},\\dots ,\\mathrm{small}\\}" + }, + { + "bbox": [ + 46, + 234, + 290, + 293 + ], + "type": "text", + "content": ". Then, the constraint 'an image on top of a button' is represented as " + }, + { + "bbox": [ + 46, + 234, + 290, + 293 + ], + "type": "inline_equation", + "content": "\\mathrm{image}_1" + }, + { + "bbox": [ + 46, + 234, + 290, + 293 + ], + "type": "text", + "content": " top " + }, + { + "bbox": [ + 46, + 234, + 290, + 293 + ], + "type": "inline_equation", + "content": "\\mathrm{button}_1" + }, + { + "bbox": [ + 46, + 234, + 290, + 293 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 293, + 289, + 402 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 293, + 289, + 402 + ], + "spans": [ + { + "bbox": [ + 46, + 293, + 289, + 402 + ], + "type": "text", + "content": "Constraint Combination. To combine different constraints, we concatenate their sequences. To ease the learning of neural network, we use a fixed order instead of a random order when concatenating different constraints. First, for the constraints only related to a single element, we first concatenate those for the same element and then concatenate those from different elements. Second, for the constraints related to multiple elements, we put them after all the constraints for the single elements." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 416, + 198, + 428 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 416, + 198, + 428 + ], + "spans": [ + { + "bbox": [ + 47, + 416, + 198, + 428 + ], + "type": "text", + "content": "3.2.2 Examples for Typical Tasks" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 435, + 287, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 435, + 287, + 483 + ], + "spans": [ + { + "bbox": [ + 46, + 435, + 287, + 483 + ], + "type": "text", + "content": "In this work, we consider six typical layout generation tasks which has been explored in previous work. We demonstrate how we formulate the constraint sequences for these tasks according to Section 3.2.1 as followed." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 483, + 287, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 483, + 287, + 544 + ], + "spans": [ + { + "bbox": [ + 46, + 483, + 287, + 544 + ], + "type": "text", + "content": "Generation conditioned on types (Gen-T) is to generate layouts from the element types specified by user constraints. We formulate the input constraint sequence by concatenating the single-element constraints of element type, i.e., " + }, + { + "bbox": [ + 46, + 483, + 287, + 544 + ], + "type": "inline_equation", + "content": "S_{\\mathrm{Gen - T}} = \\{\\langle \\mathrm{sos}\\rangle c_1|c_2|\\dots |c_N\\langle \\mathrm{eos}\\rangle \\} .^1" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 544, + 287, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 544, + 287, + 604 + ], + "spans": [ + { + "bbox": [ + 46, + 544, + 287, + 604 + ], + "type": "text", + "content": "Generation conditioned on types and sizes (Gen-TS) is to generate layouts when user constraints specify the element types and sizes. We formulate the input sequence by concatenating the type, the width and the height constraints as " + }, + { + "bbox": [ + 46, + 544, + 287, + 604 + ], + "type": "inline_equation", + "content": "S_{\\mathrm{Gen - TS}} = \\{\\langle \\mathrm{sos}\\rangle c_1w_1h_1|c_2w_2h_2|\\dots |c_Nw_Nh_N\\langle \\mathrm{eos}\\rangle \\}" + }, + { + "bbox": [ + 46, + 544, + 287, + 604 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 604, + 288, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 604, + 288, + 676 + ], + "spans": [ + { + "bbox": [ + 46, + 604, + 288, + 676 + ], + "type": "text", + "content": "Generation conditioned on relationships (Gen-R) generates layouts conditioned on element relationships. For example, a user could expect to put a large image at the top of a small text box. We formulate a relationship between two elements as " + }, + { + "bbox": [ + 46, + 604, + 288, + 676 + ], + "type": "inline_equation", + "content": "\\{c_{k_{2m-1}} k_{2m-1} r_{k_{2m-1}, k_{2m}} c_{k_{2m}} k_{2m}\\}" + }, + { + "bbox": [ + 46, + 604, + 288, + 676 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 604, + 288, + 676 + ], + "type": "inline_equation", + "content": "c_{k_{2m-1}}" + }, + { + "bbox": [ + 46, + 604, + 288, + 676 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 604, + 288, + 676 + ], + "type": "inline_equation", + "content": "c_{k_{2m}}" + }, + { + "bbox": [ + 46, + 604, + 288, + 676 + ], + "type": "text", + "content": " are the element types, " + }, + { + "bbox": [ + 46, + 604, + 288, + 676 + ], + "type": "inline_equation", + "content": "k_{2m-1}" + }, + { + "bbox": [ + 46, + 604, + 288, + 676 + ], + "type": "text", + "content": " and" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 234, + 547, + 317 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 234, + 547, + 317 + ], + "spans": [ + { + "bbox": [ + 306, + 234, + 547, + 317 + ], + "type": "inline_equation", + "content": "k_{2m}" + }, + { + "bbox": [ + 306, + 234, + 547, + 317 + ], + "type": "text", + "content": " are the indexes for the elements, and " + }, + { + "bbox": [ + 306, + 234, + 547, + 317 + ], + "type": "inline_equation", + "content": "r_{k_{2m - 1},k_{2m}}" + }, + { + "bbox": [ + 306, + 234, + 547, + 317 + ], + "type": "text", + "content": " is an extra token introduced to denote one kind of relationships. We concatenate the sequences of type constraints and relationship constraints as " + }, + { + "bbox": [ + 306, + 234, + 547, + 317 + ], + "type": "inline_equation", + "content": "S_{\\mathrm{Gen - R}} = \\{\\langle \\mathrm{sos}\\rangle c_1|c_2|\\ldots |c_N||c_{k_1}k_1r_{k_1,k_2}c_{k_2}k_2|\\ldots |c_{k_{2M - 1}}k_{2M - 1}" + }, + { + "bbox": [ + 306, + 234, + 547, + 317 + ], + "type": "inline_equation", + "content": "r_{k_{2M - 1},k_{2M}}c_{k_{2M}}k_{2M}\\langle \\mathrm{eos}\\rangle \\}" + }, + { + "bbox": [ + 306, + 234, + 547, + 317 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 306, + 234, + 547, + 317 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 306, + 234, + 547, + 317 + ], + "type": "text", + "content": " is the number of relationships." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 318, + 547, + 366 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 318, + 547, + 366 + ], + "spans": [ + { + "bbox": [ + 305, + 318, + 547, + 366 + ], + "type": "text", + "content": "Refinement applies local changes to the elements that need improvements while maintaining the original layout design. We formulate the input as " + }, + { + "bbox": [ + 305, + 318, + 547, + 366 + ], + "type": "inline_equation", + "content": "S_{\\text{Refinement}} = \\{\\langle \\text{sos} \\rangle c_1 x_1 y_1 w_1 h_1 | \\ldots | c_N x_N y_N w_N h_N \\langle \\text{eos} \\rangle \\}" + }, + { + "bbox": [ + 305, + 318, + 547, + 366 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 366, + 547, + 412 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 366, + 547, + 412 + ], + "spans": [ + { + "bbox": [ + 306, + 366, + 547, + 412 + ], + "type": "text", + "content": "Completion aims to complete layout from a set of specified elements. We formulate the input as " + }, + { + "bbox": [ + 306, + 366, + 547, + 412 + ], + "type": "inline_equation", + "content": "S_{\\text{Completion}} = \\{\\langle \\mathrm{sos} \\rangle c_1 x_1 y_1 w_1 h_1 | \\ldots | c_P x_P y_P w_P h_P \\langle \\mathrm{eos} \\rangle \\}" + }, + { + "bbox": [ + 306, + 366, + 547, + 412 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 306, + 366, + 547, + 412 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 306, + 366, + 547, + 412 + ], + "type": "text", + "content": " is the number of known elements." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 413, + 547, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 413, + 547, + 461 + ], + "spans": [ + { + "bbox": [ + 305, + 413, + 547, + 461 + ], + "type": "text", + "content": "Unconstrained generation (UGen) aims to generate layouts without any user requirements. We formulate the input as an empty sequence with necessary special tokens, i.e., " + }, + { + "bbox": [ + 305, + 413, + 547, + 461 + ], + "type": "inline_equation", + "content": "S_{\\mathrm{UGen}} = \\{\\langle \\mathrm{sos} \\rangle \\langle \\mathrm{eos} \\rangle \\}" + }, + { + "bbox": [ + 305, + 413, + 547, + 461 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 468, + 458, + 480 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 468, + 458, + 480 + ], + "spans": [ + { + "bbox": [ + 306, + 468, + 458, + 480 + ], + "type": "text", + "content": "3.3. Decoding Space Restriction" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 486, + 545, + 522 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 486, + 545, + 522 + ], + "spans": [ + { + "bbox": [ + 305, + 486, + 545, + 522 + ], + "type": "text", + "content": "During the inference, we introduce the decoding space restriction strategy to the decoding process. Algorithm 1 presents the pseudo-code for the decoding space restriction." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 523, + 545, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 523, + 545, + 593 + ], + "spans": [ + { + "bbox": [ + 305, + 523, + 545, + 593 + ], + "type": "text", + "content": "In each decoding step " + }, + { + "bbox": [ + 305, + 523, + 545, + 593 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 305, + 523, + 545, + 593 + ], + "type": "text", + "content": ", the decoder predicts the probabilities " + }, + { + "bbox": [ + 305, + 523, + 545, + 593 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 305, + 523, + 545, + 593 + ], + "type": "text", + "content": " of the possible values for current attribute. Then, " + }, + { + "bbox": [ + 305, + 523, + 545, + 593 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 305, + 523, + 545, + 593 + ], + "type": "text", + "content": " will be pruned by two modules. The ConstraintPruning prunes the infeasible values which may violate the user given constraints " + }, + { + "bbox": [ + 305, + 523, + 545, + 593 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 305, + 523, + 545, + 593 + ], + "type": "text", + "content": ". The ProbabilityPruning prunes the values which the probabilities are lower than the threshold " + }, + { + "bbox": [ + 305, + 523, + 545, + 593 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 305, + 523, + 545, + 593 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 594, + 547, + 701 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 547, + 701 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 547, + 701 + ], + "type": "text", + "content": "If all the probabilities in " + }, + { + "bbox": [ + 304, + 594, + 547, + 701 + ], + "type": "inline_equation", + "content": "P'" + }, + { + "bbox": [ + 304, + 594, + 547, + 701 + ], + "type": "text", + "content": " are pruned, it means there is no feasible value for current attribute. We propose a backtracking mechanism to solve this problem. When " + }, + { + "bbox": [ + 304, + 594, + 547, + 701 + ], + "type": "inline_equation", + "content": "P'" + }, + { + "bbox": [ + 304, + 594, + 547, + 701 + ], + "type": "text", + "content": " is empty and the back time " + }, + { + "bbox": [ + 304, + 594, + 547, + 701 + ], + "type": "inline_equation", + "content": "B[t]" + }, + { + "bbox": [ + 304, + 594, + 547, + 701 + ], + "type": "text", + "content": " is less than the max back time maxBack, the backtracking mechanism will roll back the decoding process to a previous step " + }, + { + "bbox": [ + 304, + 594, + 547, + 701 + ], + "type": "inline_equation", + "content": "t'" + }, + { + "bbox": [ + 304, + 594, + 547, + 701 + ], + "type": "text", + "content": " and restart the prediction. Otherwise, the value " + }, + { + "bbox": [ + 304, + 594, + 547, + 701 + ], + "type": "inline_equation", + "content": "o" + }, + { + "bbox": [ + 304, + 594, + 547, + 701 + ], + "type": "text", + "content": " will be sampled from " + }, + { + "bbox": [ + 304, + 594, + 547, + 701 + ], + "type": "inline_equation", + "content": "P'" + }, + { + "bbox": [ + 304, + 594, + 547, + 701 + ], + "type": "text", + "content": " and the generation " + }, + { + "bbox": [ + 304, + 594, + 547, + 701 + ], + "type": "inline_equation", + "content": "O" + }, + { + "bbox": [ + 304, + 594, + 547, + 701 + ], + "type": "text", + "content": " will be updated. The decoding process will move to the next step by increasing " + }, + { + "bbox": [ + 304, + 594, + 547, + 701 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 594, + 547, + 701 + ], + "type": "text", + "content": " by 1." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 318, + 701, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 701, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 318, + 701, + 545, + 714 + ], + "type": "text", + "content": "While the end-of-sequence token EOS is predicted, or" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 47, + 683, + 287, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 683, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 683, + 287, + 713 + ], + "type": "text", + "content": "1According to the practical experience, we add the special tokens " + }, + { + "bbox": [ + 47, + 683, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\langle \\mathrm{so}s\\rangle" + }, + { + "bbox": [ + 47, + 683, + 287, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 683, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\langle \\mathrm{eos}\\rangle" + }, + { + "bbox": [ + 47, + 683, + 287, + 713 + ], + "type": "text", + "content": " at the start and the end of the sequence, and use a separator token | to distinguish the single constraints." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "18406" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "content": "the length of " + }, + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "inline_equation", + "content": "O" + }, + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "content": " reaches maxLen, the generation finishes. In the following, we will give more details about the two pruning modules and the backtracking mechanism." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 109, + 287, + 252 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 109, + 287, + 252 + ], + "spans": [ + { + "bbox": [ + 46, + 109, + 287, + 252 + ], + "type": "text", + "content": "Constraint Pruning Module. The constraint pruning module prunes the value in " + }, + { + "bbox": [ + 46, + 109, + 287, + 252 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 109, + 287, + 252 + ], + "type": "text", + "content": " which may violate the related constraints. Take the relationship constraint as example, suppose at step " + }, + { + "bbox": [ + 46, + 109, + 287, + 252 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 109, + 287, + 252 + ], + "type": "text", + "content": " the decoder predicts possibilities " + }, + { + "bbox": [ + 46, + 109, + 287, + 252 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 109, + 287, + 252 + ], + "type": "text", + "content": " for the value of the attribute " + }, + { + "bbox": [ + 46, + 109, + 287, + 252 + ], + "type": "inline_equation", + "content": "w_{i}" + }, + { + "bbox": [ + 46, + 109, + 287, + 252 + ], + "type": "text", + "content": " of the " + }, + { + "bbox": [ + 46, + 109, + 287, + 252 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 109, + 287, + 252 + ], + "type": "text", + "content": "-th element, there is a relation constraint " + }, + { + "bbox": [ + 46, + 109, + 287, + 252 + ], + "type": "inline_equation", + "content": "s = \\{w_{i} \\leq w_{j}\\}" + }, + { + "bbox": [ + 46, + 109, + 287, + 252 + ], + "type": "text", + "content": ", which specifies the relative size relationships between element " + }, + { + "bbox": [ + 46, + 109, + 287, + 252 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 109, + 287, + 252 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 109, + 287, + 252 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 109, + 287, + 252 + ], + "type": "text", + "content": ". If " + }, + { + "bbox": [ + 46, + 109, + 287, + 252 + ], + "type": "inline_equation", + "content": "w_{j}" + }, + { + "bbox": [ + 46, + 109, + 287, + 252 + ], + "type": "text", + "content": " has not been predicted at step " + }, + { + "bbox": [ + 46, + 109, + 287, + 252 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 109, + 287, + 252 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 109, + 287, + 252 + ], + "type": "inline_equation", + "content": "w_{i}" + }, + { + "bbox": [ + 46, + 109, + 287, + 252 + ], + "type": "text", + "content": " will not be influenced by " + }, + { + "bbox": [ + 46, + 109, + 287, + 252 + ], + "type": "inline_equation", + "content": "w_{j}" + }, + { + "bbox": [ + 46, + 109, + 287, + 252 + ], + "type": "text", + "content": " in current step and the " + }, + { + "bbox": [ + 46, + 109, + 287, + 252 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 109, + 287, + 252 + ], + "type": "text", + "content": " will not be pruned. Otherwise, if " + }, + { + "bbox": [ + 46, + 109, + 287, + 252 + ], + "type": "inline_equation", + "content": "w_{j}" + }, + { + "bbox": [ + 46, + 109, + 287, + 252 + ], + "type": "text", + "content": " has been predicted at previous step, the feasible values of " + }, + { + "bbox": [ + 46, + 109, + 287, + 252 + ], + "type": "inline_equation", + "content": "w_{i}" + }, + { + "bbox": [ + 46, + 109, + 287, + 252 + ], + "type": "text", + "content": " will be restricted to " + }, + { + "bbox": [ + 46, + 109, + 287, + 252 + ], + "type": "inline_equation", + "content": "(0, w_{j}]" + }, + { + "bbox": [ + 46, + 109, + 287, + 252 + ], + "type": "text", + "content": " according to " + }, + { + "bbox": [ + 46, + 109, + 287, + 252 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 46, + 109, + 287, + 252 + ], + "type": "text", + "content": ", and the infeasible values' probabilities in " + }, + { + "bbox": [ + 46, + 109, + 287, + 252 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 109, + 287, + 252 + ], + "type": "text", + "content": " will be set as 0." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 253, + 287, + 313 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 253, + 287, + 313 + ], + "spans": [ + { + "bbox": [ + 46, + 253, + 287, + 313 + ], + "type": "text", + "content": "Probability Pruning Module. The probability pruning module checks each value's probability in " + }, + { + "bbox": [ + 46, + 253, + 287, + 313 + ], + "type": "inline_equation", + "content": "P'" + }, + { + "bbox": [ + 46, + 253, + 287, + 313 + ], + "type": "text", + "content": ". The probabilities that are lower than the predetermined threshold " + }, + { + "bbox": [ + 46, + 253, + 287, + 313 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 253, + 287, + 313 + ], + "type": "text", + "content": " will be pruned by setting as 0. The threshold " + }, + { + "bbox": [ + 46, + 253, + 287, + 313 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 253, + 287, + 313 + ], + "type": "text", + "content": " is tuned to achieve the best performance by task." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 314, + 288, + 457 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 314, + 288, + 457 + ], + "spans": [ + { + "bbox": [ + 46, + 314, + 288, + 457 + ], + "type": "text", + "content": "Backtracking Mechanism. When the probabilities in " + }, + { + "bbox": [ + 46, + 314, + 288, + 457 + ], + "type": "inline_equation", + "content": "P'" + }, + { + "bbox": [ + 46, + 314, + 288, + 457 + ], + "type": "text", + "content": " are all set as 0, the backtracking mechanism works to roll back the decoding process to a previous step and restart the prediction. The function Backtracking will check why the " + }, + { + "bbox": [ + 46, + 314, + 288, + 457 + ], + "type": "inline_equation", + "content": "P'" + }, + { + "bbox": [ + 46, + 314, + 288, + 457 + ], + "type": "text", + "content": " is pruned as empty, and decide which step " + }, + { + "bbox": [ + 46, + 314, + 288, + 457 + ], + "type": "inline_equation", + "content": "t'" + }, + { + "bbox": [ + 46, + 314, + 288, + 457 + ], + "type": "text", + "content": " to backtrack to. One situation is that the current token is restricted by previous token through the constraint. For example, the relation constraint " + }, + { + "bbox": [ + 46, + 314, + 288, + 457 + ], + "type": "inline_equation", + "content": "s = \\{w_i \\leq w_j\\}" + }, + { + "bbox": [ + 46, + 314, + 288, + 457 + ], + "type": "text", + "content": " restricts the feasible values of " + }, + { + "bbox": [ + 46, + 314, + 288, + 457 + ], + "type": "inline_equation", + "content": "w_i" + }, + { + "bbox": [ + 46, + 314, + 288, + 457 + ], + "type": "text", + "content": " by " + }, + { + "bbox": [ + 46, + 314, + 288, + 457 + ], + "type": "inline_equation", + "content": "w_j" + }, + { + "bbox": [ + 46, + 314, + 288, + 457 + ], + "type": "text", + "content": ". In this case, we choose the step of " + }, + { + "bbox": [ + 46, + 314, + 288, + 457 + ], + "type": "inline_equation", + "content": "w_j" + }, + { + "bbox": [ + 46, + 314, + 288, + 457 + ], + "type": "text", + "content": " as the backtracking step. Otherwise, since all the previous predictions collectively lead to current circumstance, we randomly pick one previous step to back to." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 469, + 128, + 483 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 469, + 128, + 483 + ], + "spans": [ + { + "bbox": [ + 47, + 469, + 128, + 483 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 490, + 100, + 502 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 490, + 100, + 502 + ], + "spans": [ + { + "bbox": [ + 47, + 490, + 100, + 502 + ], + "type": "text", + "content": "4.1. Setups" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 510, + 287, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 287, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 287, + 664 + ], + "type": "text", + "content": "Datasets. We compare LayoutFormer++ to existing approaches on two public datasets. RICO [15] is a dataset of mobile app UI that contains " + }, + { + "bbox": [ + 46, + 510, + 287, + 664 + ], + "type": "inline_equation", + "content": "66\\mathrm{K}+" + }, + { + "bbox": [ + 46, + 510, + 287, + 664 + ], + "type": "text", + "content": " UI layouts with 25 element types. PubLayNet [30] contains " + }, + { + "bbox": [ + 46, + 510, + 287, + 664 + ], + "type": "inline_equation", + "content": "360\\mathrm{K}+" + }, + { + "bbox": [ + 46, + 510, + 287, + 664 + ], + "type": "text", + "content": " document layouts with 5 element types. On both datasets, there are a few layouts with quite a lot of elements, which easily leads to an out-of-memory problem. Existing studies use multifarious rules to filter out these layouts. In our experiments, we simply filter out the layouts with more than 20 elements. For RICO, we use " + }, + { + "bbox": [ + 46, + 510, + 287, + 664 + ], + "type": "inline_equation", + "content": "90\\%" + }, + { + "bbox": [ + 46, + 510, + 287, + 664 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 510, + 287, + 664 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 46, + 510, + 287, + 664 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 510, + 287, + 664 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 46, + 510, + 287, + 664 + ], + "type": "text", + "content": " of data for training, validation and testing. For PubLayNet, we use " + }, + { + "bbox": [ + 46, + 510, + 287, + 664 + ], + "type": "inline_equation", + "content": "95\\%" + }, + { + "bbox": [ + 46, + 510, + 287, + 664 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 510, + 287, + 664 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 46, + 510, + 287, + 664 + ], + "type": "text", + "content": " of official training split for training and validation, and the official validation split for testing." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "content": "Baselines. We try our best to reproduce all the existing approaches. Even so, we regret to not include some approaches for the following reasons. First, due to the missing implementation details and hyperparameter settings, we" + } + ] + } + ], + "index": 7 + }, + { + "type": "code", + "bbox": [ + 306, + 87, + 545, + 305 + ], + "blocks": [ + { + "bbox": [ + 312, + 75, + 484, + 87 + ], + "lines": [ + { + "bbox": [ + 312, + 75, + 484, + 87 + ], + "spans": [ + { + "bbox": [ + 312, + 75, + 484, + 87 + ], + "type": "text", + "content": "Algorithm 1: Decoding Space Restriction" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 306, + 87, + 545, + 305 + ], + "lines": [ + { + "bbox": [ + 306, + 87, + 545, + 305 + ], + "spans": [ + { + "bbox": [ + 306, + 87, + 545, + 305 + ], + "type": "text", + "content": "Input: Encoder hidden state " + }, + { + "bbox": [ + 306, + 87, + 545, + 305 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 306, + 87, + 545, + 305 + ], + "type": "text", + "content": " ;User constraints " + }, + { + "bbox": [ + 306, + 87, + 545, + 305 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 306, + 87, + 545, + 305 + ], + "type": "text", + "content": " Output: Layout sequence " + }, + { + "bbox": [ + 306, + 87, + 545, + 305 + ], + "type": "inline_equation", + "content": "O" + }, + { + "bbox": [ + 306, + 87, + 545, + 305 + ], + "type": "text", + "content": " 1 Initialize step index " + }, + { + "bbox": [ + 306, + 87, + 545, + 305 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 306, + 87, + 545, + 305 + ], + "type": "text", + "content": " , the back time for each step " + }, + { + "bbox": [ + 306, + 87, + 545, + 305 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 306, + 87, + 545, + 305 + ], + "type": "text", + "content": " and the predicted sequence " + }, + { + "bbox": [ + 306, + 87, + 545, + 305 + ], + "type": "inline_equation", + "content": "O" + }, + { + "bbox": [ + 306, + 87, + 545, + 305 + ], + "type": "text", + "content": " 2 while " + }, + { + "bbox": [ + 306, + 87, + 545, + 305 + ], + "type": "inline_equation", + "content": "(O[-1]\\neq \\mathrm{EOS})" + }, + { + "bbox": [ + 306, + 87, + 545, + 305 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 87, + 545, + 305 + ], + "type": "inline_equation", + "content": "(t < maxLen)" + }, + { + "bbox": [ + 306, + 87, + 545, + 305 + ], + "type": "text", + "content": " do 3 " + }, + { + "bbox": [ + 306, + 87, + 545, + 305 + ], + "type": "inline_equation", + "content": "P\\gets \\mathrm{Decoder}(O,M)[t]" + }, + { + "bbox": [ + 306, + 87, + 545, + 305 + ], + "type": "text", + "content": " . 4 " + }, + { + "bbox": [ + 306, + 87, + 545, + 305 + ], + "type": "inline_equation", + "content": "P^{\\prime}\\gets" + }, + { + "bbox": [ + 306, + 87, + 545, + 305 + ], + "type": "text", + "content": " ConstraintPruning " + }, + { + "bbox": [ + 306, + 87, + 545, + 305 + ], + "type": "inline_equation", + "content": "(P,S)" + }, + { + "bbox": [ + 306, + 87, + 545, + 305 + ], + "type": "text", + "content": " . 5 " + }, + { + "bbox": [ + 306, + 87, + 545, + 305 + ], + "type": "inline_equation", + "content": "P^{\\prime}\\gets" + }, + { + "bbox": [ + 306, + 87, + 545, + 305 + ], + "type": "text", + "content": " ProbabilityPruning " + }, + { + "bbox": [ + 306, + 87, + 545, + 305 + ], + "type": "inline_equation", + "content": "(P^{\\prime},\\theta)" + }, + { + "bbox": [ + 306, + 87, + 545, + 305 + ], + "type": "text", + "content": " . 6 if " + }, + { + "bbox": [ + 306, + 87, + 545, + 305 + ], + "type": "inline_equation", + "content": "(P^{\\prime}" + }, + { + "bbox": [ + 306, + 87, + 545, + 305 + ], + "type": "text", + "content": " is " + }, + { + "bbox": [ + 306, + 87, + 545, + 305 + ], + "type": "inline_equation", + "content": "\\varnothing" + }, + { + "bbox": [ + 306, + 87, + 545, + 305 + ], + "type": "text", + "content": " )and " + }, + { + "bbox": [ + 306, + 87, + 545, + 305 + ], + "type": "inline_equation", + "content": "(B[t] < maxBack)" + }, + { + "bbox": [ + 306, + 87, + 545, + 305 + ], + "type": "text", + "content": " then 7 " + }, + { + "bbox": [ + 306, + 87, + 545, + 305 + ], + "type": "inline_equation", + "content": "t^\\prime \\gets" + }, + { + "bbox": [ + 306, + 87, + 545, + 305 + ], + "type": "text", + "content": " Backtracking " + }, + { + "bbox": [ + 306, + 87, + 545, + 305 + ], + "type": "inline_equation", + "content": "(P,S,t)" + }, + { + "bbox": [ + 306, + 87, + 545, + 305 + ], + "type": "text", + "content": " . 8 " + }, + { + "bbox": [ + 306, + 87, + 545, + 305 + ], + "type": "inline_equation", + "content": "B[t]\\gets B[t] + 1" + }, + { + "bbox": [ + 306, + 87, + 545, + 305 + ], + "type": "text", + "content": " . 9 " + }, + { + "bbox": [ + 306, + 87, + 545, + 305 + ], + "type": "inline_equation", + "content": "O\\gets O[:t]" + }, + { + "bbox": [ + 306, + 87, + 545, + 305 + ], + "type": "text", + "content": " . 10 t t; 11 else 12 o " + }, + { + "bbox": [ + 306, + 87, + 545, + 305 + ], + "type": "inline_equation", + "content": "\\leftarrow" + }, + { + "bbox": [ + 306, + 87, + 545, + 305 + ], + "type": "text", + "content": " Sampling " + }, + { + "bbox": [ + 306, + 87, + 545, + 305 + ], + "type": "inline_equation", + "content": "(P^{\\prime})" + }, + { + "bbox": [ + 306, + 87, + 545, + 305 + ], + "type": "text", + "content": " . 13 " + }, + { + "bbox": [ + 306, + 87, + 545, + 305 + ], + "type": "inline_equation", + "content": "O\\gets O\\cup o" + }, + { + "bbox": [ + 306, + 87, + 545, + 305 + ], + "type": "text", + "content": " . 14 t t+1; 15 end 16 end" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "code_body" + } + ], + "index": 9, + "sub_type": "algorithm" + }, + { + "bbox": [ + 304, + 334, + 545, + 442 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 334, + 545, + 442 + ], + "spans": [ + { + "bbox": [ + 304, + 334, + 545, + 442 + ], + "type": "text", + "content": "fail to reproduce some approaches [13, 14, 18, 20]. Second, a few approaches consider data-specific attributes and are difficult to be applied to arbitrary datasets about graphic layouts [27, 29]. Ultimately, we compare LayoutFormer++ against 1) NDN-none [12], LayoutGAN++ [8] and BLT [10] on Gen-T, 2) BLT [10] on Gen-TS, 3) NDN [12] and CLG-LO [8] on Gen-R, 4) RUAGE [23] on refinement, 5) LayoutTransformer [3] on completion, and 6) VTN [2], Coarse2Fine [7] and LayoutTransformer [3] on UGen." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 443, + 545, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 443, + 545, + 467 + ], + "spans": [ + { + "bbox": [ + 305, + 443, + 545, + 467 + ], + "type": "text", + "content": "Evaluation Metrics. We adopt the metrics proposed by existing works for comprehensive evaluation." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 468, + 545, + 516 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 468, + 545, + 516 + ], + "spans": [ + { + "bbox": [ + 304, + 468, + 545, + 516 + ], + "type": "text", + "content": "Maximum Intersection over Union (mIoU) measures the similarity between the generated layouts and the real layouts, which is based on the averaged IoU of bounding boxes. We use the same implementation as [8]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 517, + 545, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 517, + 545, + 553 + ], + "spans": [ + { + "bbox": [ + 304, + 517, + 545, + 553 + ], + "type": "text", + "content": "Alignment (Align.) measures whether the elements are well-aligned. We modify the metric from [14] by normalizing it by the number of elements." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 555, + 545, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 555, + 545, + 602 + ], + "spans": [ + { + "bbox": [ + 304, + 555, + 545, + 602 + ], + "type": "text", + "content": "Overlap measures the abnormal overlap area between elements. We improve the metric from [14] by ignoring the elements that serve as a background or padding, e.g., card, background and modal on RICO." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 604, + 545, + 663 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 604, + 545, + 663 + ], + "spans": [ + { + "bbox": [ + 304, + 604, + 545, + 663 + ], + "type": "text", + "content": "Frechet Inception Distance (FID) describes the distribution difference between real and generated layouts. Following [8], we train a neural network to convert the layouts into representative features and then calculate the distribution difference based on learned features." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "content": "Constraint Violation Rate (Vio.%) measures the rate of the violated constraints. We follow the implementation of [8] for Gen-R. For other tasks, we calculate Vio.% by dividing the number of the violated constraints by the total" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18407" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 61, + 70, + 533, + 312 + ], + "blocks": [ + { + "bbox": [ + 61, + 70, + 533, + 312 + ], + "lines": [ + { + "bbox": [ + 61, + 70, + 533, + 312 + ], + "spans": [ + { + "bbox": [ + 61, + 70, + 533, + 312 + ], + "type": "table", + "html": "
TasksMethodsRICOPubLayNet
mIoU ↑FID ↓Align. ↓Overlap ↓mIoU ↑FID ↓Align. ↓Overlap ↓
Gen-TNDN-none0.3513.760.560.550.3135.670.350.17
LayoutGAN++0.2985.9540.2610.6200.29714.8750.1240.148
BLT0.21625.6330.1500.9830.14038.6840.0360.196
LayoutFormer++0.4321.0960.2300.5300.3488.4110.0200.008
Gen-TSBLT0.6040.9510.1810.6600.4287.9140.0210.419
LayoutFormer++0.6200.7570.2020.5420.4710.7200.0240.037
Gen-RNDN0.36-0.56-0.31-0.36-
CLG-LO0.2868.8980.3110.6150.27719.7380.1230.200
LayoutFormer++0.4245.9720.3320.5370.3534.9540.0250.076
RefinementRUITE0.8110.1070.1330.4830.7810.0610.0290.020.
LayoutFormer++0.8160.0320.1230.4890.7850.0860.0240.006
CompletionLayoutTransformer0.3636.6790.1940.4780.07714.7690.0190.0013
LayoutFormer++0.7324.5740.0770.4870.47110.2510.0200.0022
UGenLayoutTransformer0.43922.8840.0520.4710.06236.3040.0310.0009
VTN0.68676.0640.4610.6940.210103.3730.2050.211
Coarse2Fine0.36046.4830.1280.6760.36150.8540.2210.142
LayoutFormer++0.74219.6880.0470.5470.41746.5220.0290.0009
", + "image_path": "8f63b549387f56acb5ccbf199f8f9730f387b360477f3b7b216954e511d97159.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 132, + 320, + 462, + 332 + ], + "lines": [ + { + "bbox": [ + 132, + 320, + 462, + 332 + ], + "spans": [ + { + "bbox": [ + 132, + 320, + 462, + 332 + ], + "type": "text", + "content": "Table 1. Quantitative comparisons with existing approaches on six layout generation tasks." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 47, + 342, + 253, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 342, + 253, + 354 + ], + "spans": [ + { + "bbox": [ + 47, + 342, + 253, + 354 + ], + "type": "text", + "content": "number of constraints for all the evaluated layouts." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 354, + 288, + 414 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 354, + 288, + 414 + ], + "spans": [ + { + "bbox": [ + 46, + 354, + 288, + 414 + ], + "type": "text", + "content": "Among the above metrics, mIoU, Align., Overlap and FID evaluate the generation quality, and Vio.% evaluate the constraint satisfaction. A larger value for mIoU indicates better performance, while smaller values for other metrics indicate better performance." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 415, + 287, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 415, + 287, + 582 + ], + "spans": [ + { + "bbox": [ + 46, + 415, + 287, + 582 + ], + "type": "text", + "content": "Implementation Details. We implement Layout-Former++ by PyTorch [19]. The model is trained using the Adam optimizer [9] with NVIDIA V100 GPUs. For Transformer blocks, we use 8 layers, 8 heads for multi-attention, 512 embedding dimensions and 2048 feed-forward dimensions. Other hyper-parameters, e.g., the batch size, the learning rate, and the threshold " + }, + { + "bbox": [ + 46, + 415, + 287, + 582 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 415, + 287, + 582 + ], + "type": "text", + "content": " in decoding space restriction, are tuned to achieve the best performance on the validation set2. For Gen-R, following CLG-LO [8], we randomly sample " + }, + { + "bbox": [ + 46, + 415, + 287, + 582 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 46, + 415, + 287, + 582 + ], + "type": "text", + "content": " element relationships as the input. For refinement, following RUTFE [23], we synthesize the input by adding random noise to the position and size of each element, which is sampled from a normal distribution with the mean 0 and the standard variance 0.01." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 589, + 237, + 601 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 589, + 237, + 601 + ], + "spans": [ + { + "bbox": [ + 47, + 589, + 237, + 601 + ], + "type": "text", + "content": "4.2. Evaluations on Sufficient Flexibility" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 607, + 288, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 607, + 288, + 643 + ], + "spans": [ + { + "bbox": [ + 46, + 607, + 288, + 643 + ], + "type": "text", + "content": "To demonstrate the sufficient flexibility of LayoutFormer++, we compare LayoutFormer++ with existing approaches on all six layout generation tasks." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 643, + 288, + 667 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 643, + 288, + 667 + ], + "spans": [ + { + "bbox": [ + 47, + 643, + 288, + 667 + ], + "type": "text", + "content": "Table 1 shows the quantitative comparisons to existing works3. It should be noted that the existing approaches can" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 342, + 545, + 450 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 342, + 545, + 450 + ], + "spans": [ + { + "bbox": [ + 306, + 342, + 545, + 450 + ], + "type": "text", + "content": "only handle up to two tasks, while LayoutFormer++ can handle all the six tasks. We highlight the results of LayoutFormer++ by bold when it achieves the best performance among all the existing approaches in Table 1. According to the results, LayoutFormer++ achieves significantly better performance than the baselines on most metrics. This demonstrates that LayoutFormer++ not only can flexibly handle diverse user constraints, but also has advantages in the generation ability over existing approaches." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 450, + 545, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 450, + 545, + 498 + ], + "spans": [ + { + "bbox": [ + 305, + 450, + 545, + 498 + ], + "type": "text", + "content": "Figure 4 and 5 show qualitative comparisons on RICO and PubLayNet. Compared to baselines, LayoutFormer++ generates layouts with better spacing, less misalignment, and fewer unreasonable overlaps." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 503, + 499, + 517 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 503, + 499, + 517 + ], + "spans": [ + { + "bbox": [ + 306, + 503, + 499, + 517 + ], + "type": "text", + "content": "4.3. Evaluations on Good Controllability" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 522, + 545, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 522, + 545, + 569 + ], + "spans": [ + { + "bbox": [ + 305, + 522, + 545, + 569 + ], + "type": "text", + "content": "In this section, we compare LayoutFormer++ with LayoutGAN++ [13], BLT [10] and CLG-LO [8], which pay attention to the constraint satisfaction. These approaches handle Gen-T, Gen-TS and Gen-R respectively." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": "We bold the results of LayoutFormer++ in Table 2 when it outperforms the baselines. For Gen-T and Gen-TS, since all approaches have no constraint violation, we focus on the performance of quality. As the results, LayoutFormer++ outperforms the baselines on both two datasets. For Gen-R, LayoutFormer++ achieves better performance on both quality metrics and Vio.% except a worse Vio.% than CLG-LO on RICO. However, CLG-LO does not make a good tradeoff: the quality of layouts generated by CLG-LO is significantly worse than that of LayoutFormer++. This demonstrates that LayoutFormer++ achieves the best controllability among existing approaches." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 58, + 673, + 286, + 683 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 673, + 286, + 683 + ], + "spans": [ + { + "bbox": [ + 58, + 673, + 286, + 683 + ], + "type": "text", + "content": "2Details of the hyper-parameters can be find in supplemental material." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 47, + 683, + 287, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 683, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 47, + 683, + 287, + 712 + ], + "type": "text", + "content": "3As we fail to reproduce NDN by ourselves, we directly use the results from [8] in Table 1. It is evaluated on simple datasets that only consider layouts with less than 10 elements." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "18408" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 63, + 73, + 532, + 473 + ], + "blocks": [ + { + "bbox": [ + 63, + 73, + 532, + 473 + ], + "lines": [ + { + "bbox": [ + 63, + 73, + 532, + 473 + ], + "spans": [ + { + "bbox": [ + 63, + 73, + 532, + 473 + ], + "type": "image", + "image_path": "f5e8bc0145bb4209fc6d0d1cc5da8b016dbc9453fa146c0fd3666903db033bfb.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 226, + 478, + 366, + 489 + ], + "lines": [ + { + "bbox": [ + 226, + 478, + 366, + 489 + ], + "spans": [ + { + "bbox": [ + 226, + 478, + 366, + 489 + ], + "type": "text", + "content": "Figure 4. Qualitative results on RICO." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 67, + 500, + 529, + 659 + ], + "blocks": [ + { + "bbox": [ + 67, + 500, + 529, + 659 + ], + "lines": [ + { + "bbox": [ + 67, + 500, + 529, + 659 + ], + "spans": [ + { + "bbox": [ + 67, + 500, + 529, + 659 + ], + "type": "table", + "html": "
TasksMethodRICOPubLayNet
mIoU↑FID↓Align.↓Overlap↓Vio. %↓mIoU↑FID↓Align.↓Overlap↓Vio. %↓
Gen-TLayoutGAN++0.2985.9540.2610.6200.0.29714.8750.1240.1480.
LayoutFormer++ Full0.4321.0960.2300.5300.0.3488.4110.0200.0080.
0.4311.3200.2720.5500.0.3459.3670.0200.0090.
0.4391.3920.2060.5455.50.3459.3730.0200.0090.05
Gen-TSBLT0.6040.9510.1810.6600.0.4287.9140.0210.4190.
LayoutFormer++ Full0.6200.7570.2020.5420.0.4710.7200.0240.0370.
0.6130.7820.2060.5430.0.4640.9030.0260.0440.
0.6130.8010.2060.545≈0.0.4640.9030.0260.044≈0.
Gen-RCLG-LO0.2868.8980.3110.6153.660.27719.7380.1230.2006.66
LayoutFormer++ Full0.4245.9720.3320.53711.840.3534.9540.0250.0763.9
0.4198.6040.2840.54412.750.3525.1520.0230.0755.70
0.4585.1260.2210.54633.040.3584.6200.0220.03016.09
", + "image_path": "8b69718ad2959c997bd740d6525ff63b89d4030b1a9bd4d28f6d31f6ab61eb9c.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 132, + 668, + 460, + 679 + ], + "lines": [ + { + "bbox": [ + 132, + 668, + 460, + 679 + ], + "spans": [ + { + "bbox": [ + 132, + 668, + 460, + 679 + ], + "type": "text", + "content": "Table 2. Comparisons with baselines and the model variants to evaluate the controllability." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "18409" + } + ] + } + ], + "index": 4 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 62, + 72, + 532, + 473 + ], + "blocks": [ + { + "bbox": [ + 62, + 72, + 532, + 473 + ], + "lines": [ + { + "bbox": [ + 62, + 72, + 532, + 473 + ], + "spans": [ + { + "bbox": [ + 62, + 72, + 532, + 473 + ], + "type": "image", + "image_path": "ce8a9611470b1cfe98c66efd2d2dfd3d95ef483ce6e44a97878c75e9c3136c12.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 216, + 480, + 376, + 492 + ], + "lines": [ + { + "bbox": [ + 216, + 480, + 376, + 492 + ], + "spans": [ + { + "bbox": [ + 216, + 480, + 376, + 492 + ], + "type": "text", + "content": "Figure 5. Qualitative results on PubLayNet." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 513, + 289, + 704 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 513, + 289, + 704 + ], + "spans": [ + { + "bbox": [ + 46, + 513, + 289, + 704 + ], + "type": "text", + "content": "Besides, we compare LayoutFormer++ framework with two variants. The first denoted as -Back indicates LayoutFormer++ without backtracking mechanism. The second denoted as -Back&Prune. is LayoutFormer++ without both pruning modules and the backtracking mechanism. For each task in Table 2, the last three lines show the comparison between the variants. Comparing -Full with -Back, we find that after disabling the backtracking mechanism, the generation quality decreases. And on Gen-R, the Vio.% also gets worse. Comparing -Full with -Back&Prune, we find that the Vio.% significantly decreases. It shows that the full model consistently decreases the violation while having little impact on quality, which demonstrates that both the pruning modules and the backtracking mechanism play important roles in helping LayoutFormer++ achieve good controllability." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 306, + 511, + 378, + 525 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 511, + 378, + 525 + ], + "spans": [ + { + "bbox": [ + 306, + 511, + 378, + 525 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 536, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 536, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 536, + 545, + 712 + ], + "type": "text", + "content": "In this work, we propose LayoutFormer++ for conditional layout generation. To achieve the sufficient flexibility, we propose constraint serialization to represent different user constraints by the same sequence format. To achieve the good controllability, we propose decoding space restriction to prune the predicted distribution by disabling the options that violate the constraints or lead to bad quality. Experiments show that LayoutFormer++ can flexibly handle different layout generation tasks with better generation quality and less constraint violation compared to the existing task-specific approaches. In the future, we plan to investigate more practical user requirements for layout design. Besides, as LayoutFormer++ enables a unified way to handle different layout generation tasks, it is possible to develop a powerful pretrained model for layout generation in the future." + } + ] + } + ], + "index": 4 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18410" + } + ] + } + ], + "index": 5 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 92, + 288, + 714 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 53, + 92, + 287, + 158 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 92, + 287, + 158 + ], + "spans": [ + { + "bbox": [ + 53, + 92, + 287, + 158 + ], + "type": "text", + "content": "[1] Peter Anderson, Basura Fernando, Mark Johnson, and Stephen Gould. 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Publaynet: largest dataset ever for document layout analysis. arXiv preprint arXiv:1908.07836, 2019. 2, 5" + } + ] + } + ], + "index": 10 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "18412" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Leapfrog Diffusion Model for Stochastic Trajectory Prediction/0cea661d-f5ad-40d3-86cc-3b1fbed56fa4_content_list.json b/2023/Leapfrog Diffusion Model for Stochastic Trajectory Prediction/0cea661d-f5ad-40d3-86cc-3b1fbed56fa4_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..e231a2849ed04177ee30f6e7459a3634fcdd8e0f --- /dev/null +++ b/2023/Leapfrog Diffusion Model for Stochastic Trajectory Prediction/0cea661d-f5ad-40d3-86cc-3b1fbed56fa4_content_list.json @@ -0,0 +1,1846 @@ +[ + { + "type": "text", + "text": "Leapfrog Diffusion Model for Stochastic Trajectory Prediction", + "text_level": 1, + "bbox": [ + 169, + 130, + 799, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Weibo Mao $^{1}$ , Chenxin Xu $^{1}$ , Qi Zhu $^{1}$ , Siheng Chen $^{1,2*}$ , Yanfeng Wang $^{2,1}$ , Shanghai Jiao Tong University, Shanghai AI Laboratory", + "bbox": [ + 199, + 179, + 767, + 217 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{kirino.mao,xcxwakaka,georgezhu,sihengc,wangyanfeng}@sjtu.edu.cn", + "bbox": [ + 200, + 219, + 764, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 268, + 313, + 284 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To model the indeterminacy of human behaviors, stochastic trajectory prediction requires a sophisticated multi-modal distribution of future trajectories. Emerging diffusion models have revealed their tremendous representation capacities in numerous generation tasks, showing potential for stochastic trajectory prediction. However, expensive time consumption prevents diffusion models from real-time prediction, since a large number of denoising steps are required to assure sufficient representation ability. To resolve the dilemma, we present LEapfrog Diffusion model (LED), a novel diffusion-based trajectory prediction model, which provides real-time, precise, and diverse predictions. The core of the proposed LED is to leverage a trainable leapfrog initializer to directly learn an expressive multi-modal distribution of future trajectories, which skips a large number of denoising steps, significantly accelerating inference speed. Moreover, the leapfrog initializer is trained to appropriately allocate correlated samples to provide a diversity of predicted future trajectories, significantly improving prediction performances. Extensive experiments on four real-world datasets, including NBA/NFL/SDD/ETH-UCY, show that LED consistently improves performance and achieves $23.7\\% / 21.9\\%$ ADE/FDE improvement on NFL. The proposed LED also speeds up the inference 19.3/30.8/24.3/25.1 times compared to the standard diffusion model on NBA/NFL/SDD/ETH-UCY, satisfying real-time inference needs. Code is available at https://github.com/MediaBrain-SJTU/LED.", + "bbox": [ + 75, + 301, + 473, + 709 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 741, + 209, + 757 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Trajectory prediction aims to predict the future trajectories for one or multiple interacting agents conditioned on their past movements. This task plays a significant role in numerous applications, such as autonomous driving [24], drones [10], surveillance systems [45], human-robot interaction systems [5], and interactive robotics [20]. Recently, lots of fascinating research progresses have been made from", + "bbox": [ + 75, + 767, + 470, + 875 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/2a86b5ca34fffa6acc3d705145f1b8e75feccea00ca362b1be8e708d1beb865a.jpg", + "image_caption": [ + "Figure 1. Leapfrog diffusion model uses the leapfrog initializer to estimate the denoised distribution and substitute a long sequence of traditional denoising steps, accelerating inference and maintaining representation capacity." + ], + "image_footnote": [], + "bbox": [ + 501, + 265, + 893, + 398 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "many aspects, including temporal encoding [6, 13, 46, 53], interaction modeling [1, 15, 18, 43, 49], and rasterized prediction [11, 12, 26, 48]. In practice, to capture multiple possibilities of future trajectories, a real-world prediction system needs to produce multiple future trajectories. This leads to the emergence of stochastic trajectory prediction, aiming to precisely model the distribution of future trajectories.", + "bbox": [ + 496, + 474, + 893, + 580 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Previous works have proposed a series of deep generative models for stochastic trajectory prediction. For example, [15, 18] exploit the generator adversarial networks (GANs) to model the future trajectory distribution; [27, 38, 49] consider the conditional variational autoencoders (CVAEs) structure; and [3] uses the conditional normalizing flow to relax the Gaussian prior in CVAEs and learn more representative priors. Recently, with the great success in image generation [17, 33] and audio synthesis [4, 21], denoising diffusion probabilistic models have been applied to time-series analysis and trajectory prediction, and show promising prediction performances [14, 44]. Compared to many other generative models, diffusion models have advantages in stable training and modeling sophisticated distributions through sufficient denoising steps [8].", + "bbox": [ + 496, + 582, + 895, + 808 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "However, there are two critical problems in diffusion models for stochastic trajectory prediction. First, the real-time inference is time-consuming [14]. To ensure the representation ability and generate high-quality samples, an adequate number of denoising steps are required in standard diffusion models, which costs more computational time. For", + "bbox": [ + 496, + 810, + 895, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author.", + "bbox": [ + 94, + 886, + 220, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "5517", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "example, experiments show that on the NBA dataset, diffusion models need about 100 denoising steps to achieve decent prediction performances, which would take $\\sim 886\\mathrm{ms}$ to predict; while the next frame comes every $200\\mathrm{ms}$ . Second, as mentioned in [2], a limited number of independent and identically distributed samples might not be able to capture sufficient modalities in the underlying distribution of a generative model. Empirically, a few independent sampled trajectories could miss some important future possibilities due to the lack of appropriate sample allocation, significantly deteriorating prediction performances.", + "bbox": [ + 75, + 90, + 472, + 257 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, we propose leapfrog diffusion model (LED), a novel diffusion-based trajectory prediction model, which significantly accelerates the inference speed and enables adaptive and appropriate allocations of multiple correlated predictions, providing sufficient diversity in predictions. The core idea of the proposed LED is to learn a rough, yet sufficiently expressive distribution to initialize denoised future trajectories; instead of using a plain Gaussian distribution as in standard diffusion models. Specifically, our forward diffusion process is the same as standard diffusion models, which assures that the ultimate representation ability is pristine; while in the reverse denoising process, we leverage a powerful initializer to produce correlated diverse samples and leapfrog or skip a large number of denoising steps; and then, use only a few denoising steps to refine the distribution.", + "bbox": [ + 75, + 258, + 472, + 484 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To implement such a leapfrog initializer, we consider a reparameterization to alleviate the learning burden. We disassemble a denoised distribution into three parts: mean trajectory, variance, and sample positions under the normalized distribution. To estimate these three, we design three corresponding trainable modules, each of which leverages both a social encoder and a temporal encoder to learn the social-temporal features and produce accurate estimation. Furthermore, all the sample positions are simultaneously generated based on the same social-temporal features, enabling appropriate sample allocations to provide diversity.", + "bbox": [ + 75, + 486, + 472, + 652 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To evaluate the effectiveness of the proposed method, we conduct experiments on four trajectory prediction datasets: NBA, NFL Football Dataset, Standford Drones Dataset, and ETH-UCY. The quantitative results show we outperform the previous methods and achieve state-of-the-art performance. Specifically, compared to MID [14], the proposed leapfrog diffusion model reduces the average prediction time from $\\sim 886\\mathrm{ms}$ to $\\sim 46\\mathrm{ms}$ on the NBA dataset, while achieving a $15.6\\% / 13.4\\%$ ADE/FDE improvement.", + "bbox": [ + 75, + 654, + 472, + 789 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The main contributions are concluded as follows,", + "bbox": [ + 96, + 792, + 423, + 806 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a novel LEapfrog Diffusion model (LED), which is a denoising-diffusion-based stochastic trajectory prediction model. It achieves precise and diverse predictions with fast inference speed.", + "- We propose a novel trainable leapfrog initializer to directly model sophisticated denoised distributions, accelerator" + ], + "bbox": [ + 75, + 808, + 472, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ating inference speed, and adaptively allocating the sample diversity, improving prediction performance.", + "bbox": [ + 496, + 90, + 890, + 119 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- We conduct extensive experiments on four datasets including NBA, NFL, SDD, and ETH-UCY. Results show that i) our approach consistently achieves state-of-the-art performance on all datasets; and ii) our method speeds up the inference by around 20 times compared to the standard diffusion model, satisfying real-time prediction needs.", + "bbox": [ + 496, + 121, + 893, + 212 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 498, + 224, + 640, + 242 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Trajectory prediction. Early works on trajectory prediction focus on a deterministic approach by exploring force models [16, 30], RNNs [1, 32, 47], and frequency analysis [28, 29]. For example, [16] models an agent's behavior with attractive and repulsive forces and builds the force equations for prediction. To capture the multi-modalities and model future distribution, recent works start to focus on stochastic trajectory prediction and have proposed a series of deep generative models. Generative Adversarial Network (GAN) structures [7, 9, 15, 18, 22, 36, 42] are proposed to generate multiple future trajectory distribution. [23, 27, 38, 49, 51] use the Variational Auto-Encoder (VAE) structure and learn the distribution through variational inference. [3] relaxes the Gaussian prior and proposes to use the normalizing flow. Heatmap [11, 12, 26] is used for modeling future trajectories' distribution on rasterized images. In this work, we propose a new diffusion-based model for trajectory prediction. Compared to previous generative models, our method has a large representation capacity and can model sophisticated trajectory distributions by using a number of diffusion steps. We also enable the correlation between samples to adaptively adjust sample diversity, improving prediction performance.", + "bbox": [ + 496, + 251, + 893, + 583 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Denoising diffusion probabilistic models. Denoising diffusion probabilistic models (diffusion models) [17, 39, 41] have recently achieved significant results in image generation [8, 33] and audio synthesis [4, 21]. The idea of diffusion models is first proposed by DPM [39], which imitates the diffusion process in non-equilibrium statistical physics and reconstructs the data distribution using the denoising model. Later, [35, 44] propose diffusion models, combining with the seq-to-seq models, for probabilistic time series forecasting. MID [14] is the first to build diffusion models for trajectory prediction in modeling the indeterminacy variation process.", + "bbox": [ + 496, + 584, + 893, + 750 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The standard diffusion models use hundreds of denoising steps, preventing these models from real-time applications. To accelerate the sampling process, DDIM [40] first predicts the original data and then estimates the direction to the next expected timestamp based on the non-Markov process. PD [37] applies the knowledge distillation on the denoising steps with a deterministic diffusion sampler, which will be repeated for times to accelerate the sampling. All these fast sampling methods start denoising from noise inputs, which are randomly and independently initialized. In this work, we", + "bbox": [ + 496, + 750, + 895, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "5518", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "use a trainable leapfrog initializer to initialize a sufficiently expressive distribution, which replaces a large number of former denoising steps for much faster inference speed.", + "bbox": [ + 76, + 90, + 472, + 137 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Background", + "text_level": 1, + "bbox": [ + 76, + 152, + 205, + 167 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Problem Formulation", + "text_level": 1, + "bbox": [ + 76, + 176, + 279, + 191 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Trajectory prediction aims to predict an agent's future trajectory based on the past trajectories of itself and surrounding agents. For a to-be-predicted agent, let $\\mathbf{X} = [\\mathbf{x}^{-T_{\\mathrm{p}} + 1},\\mathbf{x}^{-T_{\\mathrm{p}} + 2},\\dots ,\\mathbf{x}^{0}] \\in \\mathbb{R}^{T_{\\mathrm{p}} \\times 2}$ be the observed past trajectory over $T_{\\mathrm{p}}$ timestamps where $\\mathbf{x}^t \\in \\mathbb{R}^2$ records the 2D spatial coordinate at timestamp $t$ . Let $\\mathcal{N}$ be the neighbouring agent set and $\\mathbb{X}_{\\mathcal{N}} = [\\mathbf{X}_{\\mathcal{N}_1},\\mathbf{X}_{\\mathcal{N}_2},\\dots ,\\mathbf{X}_{\\mathcal{N}_L}] \\in \\mathbb{R}^{L \\times T_{\\mathrm{p}} \\times 2}$ be the past trajectories of neighbours, where $\\mathbf{X}_{\\mathcal{N}_\\ell} \\in \\mathbb{R}^{T_{\\mathrm{p}} \\times 2}$ is the trajectory of the $\\ell$ th neighbour. The corresponding ground-truth future trajectory for the to-be-predicted agent is $\\mathbf{Y} = [\\mathbf{y}^1,\\mathbf{y}^2,\\dots,\\mathbf{y}^{T_{\\mathrm{f}}}] \\in \\mathbb{R}^{T_{\\mathrm{f}} \\times 2}$ over $T_{\\mathrm{f}}$ timestamps, where $\\mathbf{y}^t \\in \\mathbb{R}^2$ is the 2D coordinate at future timestamp $t$ .", + "bbox": [ + 76, + 200, + 468, + 381 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Because of the indeterminacy of future trajectories, it is usually more reliable to predict more than one trajectory to capture multiple possibilities. Here we consider stochastic trajectory prediction, which predicts the distribution of a future trajectory, instead of a single future trajectory. The goal of stochastic trajectory prediction is to train a prediction model $g_{\\theta}(\\cdot)$ with parameters $\\theta$ to generate a distribution $\\mathcal{P}_{\\theta} = g_{\\theta}(\\mathbf{X},\\mathbb{X}_{\\mathcal{N}})$ . Based on this distribution $\\mathcal{P}_{\\theta}$ , we can draw $K$ samples, $\\widehat{\\mathcal{Y}} = \\{\\widehat{\\mathbf{Y}}_1,\\widehat{\\mathbf{Y}}_2,\\dots ,\\widehat{\\mathbf{Y}}_K\\}$ , so that at least one sample is close to the ground-truth future trajectory. The overall learning problem is", + "bbox": [ + 76, + 383, + 468, + 549 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\theta^ {*} = \\min _ {\\theta} \\min _ {\\widehat {\\mathbf {Y}} _ {i} \\in \\widehat {\\mathcal {Y}}} D (\\widehat {\\mathbf {Y}} _ {i}, \\mathbf {Y}), \\quad \\text {s . t .} \\quad \\widehat {\\mathcal {Y}} \\sim \\mathcal {P} _ {\\theta}. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 127, + 551, + 468, + 580 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Diffusion Model for Trajectory Prediction", + "text_level": 1, + "bbox": [ + 76, + 590, + 433, + 607 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Here we present a standard diffusion model for trajectory prediction, which lays a foundation for the proposed method. The core idea is to learn and refine a sophisticated underlying distribution of trajectories through cascading a series of simple denoising steps. To implement this, a diffusion model performs a forward diffusion process to intentionally add a series of noises to a ground-truth future trajectory; and then, it uses a conditional denoising process to recover the future trajectory from noise inputs conditioned on past trajectories.", + "bbox": [ + 76, + 614, + 468, + 750 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Mathematically, let $\\mathbf{X}$ and $\\mathbb{X}_{\\mathcal{N}}$ be the past trajectories of the ego agent and the neighboring agents, respectively, and $\\mathbf{Y}$ be the future trajectory of the ego agent. The diffusion model for trajectory prediction works as follows,", + "bbox": [ + 76, + 751, + 468, + 811 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {Y} ^ {0} = \\mathbf {Y}, \\tag {2a}\n$$\n", + "text_format": "latex", + "bbox": [ + 94, + 813, + 468, + 829 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {Y} ^ {\\gamma} = f _ {\\text {d i f f u s e}} \\left(\\mathbf {Y} ^ {\\gamma - 1}\\right), \\gamma = 1, \\dots , \\Gamma , \\tag {2b}\n$$\n", + "text_format": "latex", + "bbox": [ + 94, + 835, + 468, + 849 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\widehat {\\mathbf {Y}} _ {k} ^ {\\Gamma} \\stackrel {i. i. d} {\\sim} \\mathcal {P} (\\widehat {\\mathbf {Y}} ^ {\\Gamma}) = \\mathcal {N} (\\widehat {\\mathbf {Y}} ^ {\\Gamma}; \\mathbf {0}, \\mathbf {I}), \\text {s a m p l e} K \\text {t i m e s}, \\tag {2c}\n$$\n", + "text_format": "latex", + "bbox": [ + 94, + 856, + 468, + 875 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathbf {Y}} _ {k} ^ {\\gamma} = f _ {\\text {d e n o i s e}} \\left(\\hat {\\mathbf {Y}} _ {k} ^ {\\gamma + 1}, \\mathbf {X}, \\mathbb {X} _ {\\mathcal {N}}\\right), \\gamma = \\Gamma - 1, \\dots , 0, \\tag {2d}\n$$\n", + "text_format": "latex", + "bbox": [ + 94, + 878, + 468, + 897 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathbf{Y}^{\\gamma}$ is the noisy trajectory at the $\\gamma$ th diffusion step and $\\widehat{\\mathbf{Y}}_k^\\gamma$ is the $k$ th sample of denoised trajectory at the $\\gamma$ th denoising step. The final $K$ predicted trajectories are $\\widehat{\\mathcal{V}} = \\{\\widehat{\\mathbf{Y}}_1^0, \\widehat{\\mathbf{Y}}_2^0, \\ldots, \\widehat{\\mathbf{Y}}_K^0\\}$ .", + "bbox": [ + 500, + 90, + 890, + 152 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Step (2a) initializes the diffused trajectory; Step (2b) uses a forward diffusion operation $f_{\\mathrm{diffuse}}(\\cdot)$ to successively add noises to $\\mathbf{Y}^{\\gamma - 1}$ and obtain the diffused trajectory $\\mathbf{Y}^{\\gamma}$ ; Step (2c) draws $K$ independent and identically distributed samples to initialize denoised trajectories $\\widehat{\\mathbf{Y}}_k^\\Gamma$ from a normal distribution; and Step (2d) iteratively applies a denoising operation $f_{\\mathrm{denoise}}(\\cdot)$ to obtain the denoised trajectory $\\widehat{\\mathbf{Y}}_k^\\gamma$ conditioned on past trajectories $\\mathbf{X}, \\mathbb{X}_{\\mathcal{N}}$ . Note that i) Steps (2a) and (2b) correspond to the forward diffusion process and are not used in inference; ii) During training, $\\mathbf{Y}^{\\gamma}$ is naturally the supervision for $\\widehat{\\mathbf{Y}}_k^\\gamma$ at the $\\gamma$ th step. Conceptually, each denoising step is the reverse of the diffusion step, and each pair of $\\mathbf{Y}^{\\gamma}$ and $\\widehat{\\mathbf{Y}}_k^\\gamma$ shares the same underlying distribution.", + "bbox": [ + 496, + 154, + 893, + 349 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The standard diffusion model is expressively powerful in learning sophisticated distributions and has achieved great success in many generation tasks. However, the task of motion prediction requires real-time inference but the running time of a diffusion model is constrained by the large number of denoising steps. Meanwhile, less denoising steps usually cause a weaker representation ability of future distributions. To achieve higher efficiency while preserving a promising representation ability, we propose leapfrog diffusion model, which uses a trainable initializer to capture sophisticated distributions and substitute a large number of denoising steps.", + "bbox": [ + 496, + 351, + 893, + 517 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Leapfrog Diffusion Model", + "text_level": 1, + "bbox": [ + 500, + 532, + 741, + 549 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.1. System Architecture", + "text_level": 1, + "bbox": [ + 500, + 556, + 692, + 571 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we propose the leapfrog diffusion model. Here leapfrog means that a large number of small denoising steps can be replaced by a single, yet powerful leapfrog initializer, which can significantly accelerate the inference speed without losing representation ability. Let $\\mathbf{X}$ and $\\mathbb{X}_{\\mathcal{N}}$ be the past trajectories of the ego agent and its neighboring agents, and $\\mathbf{Y}$ be the future trajectory of the ego agent. Denote $\\tau$ as the leapfrog step. The overall procedure of the proposed leapfrog diffusion model is formulated as follows,", + "bbox": [ + 496, + 580, + 893, + 715 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {Y} ^ {0} = \\mathbf {Y}, \\tag {3a}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 724, + 890, + 739 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {Y} ^ {\\gamma} = f _ {\\text {d i f f u s e}} \\left(\\mathbf {Y} ^ {\\gamma - 1}\\right), \\gamma = 1, \\dots , \\Gamma , \\tag {3b}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 746, + 890, + 761 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathcal {Y}} ^ {\\tau} \\stackrel {K} {\\sim} \\mathcal {P} \\left(\\hat {\\mathbf {Y}} ^ {\\tau}\\right) = f _ {\\text {L S G}} \\left(\\mathbf {X}, \\mathbb {X} _ {\\mathcal {N}}\\right), \\tag {3c}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 767, + 890, + 785 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\widehat {\\mathbf {Y}} _ {k} ^ {\\gamma} = f _ {\\text {d e n o i s e}} \\left(\\widehat {\\mathbf {Y}} _ {k} ^ {\\gamma + 1}, \\mathbf {X}, \\mathbb {X} _ {\\mathcal {N}}\\right), \\gamma = \\tau - 1, \\dots , 0. \\tag {3d}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 789, + 890, + 808 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Compared to the standard diffusion model (2), the main difference lies in Step (3c). The standard diffusion initializes the $\\Gamma$ th denoised distribution $\\mathcal{P}(\\widehat{\\mathbf{Y}}^{\\Gamma})$ by a plain normal distribution (2c) and requires a lot of denoising steps to enrich the expressiveness of the denoised distribution; while in Step (3c), we propose a novel leapfrog initial", + "bbox": [ + 500, + 810, + 893, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "5519", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/178473828a87aff0634fb6c2aa6758e32a1861f4a571c6723c204224a01568c7.jpg", + "image_caption": [ + "Figure 2. Proposed leapfrog diffusion model (LED) in inference phase. The red agent is the to-be-predicted agent. LED first predicts $K$ initialized trajectories at $\\tau$ th denoised step through a trainable leapfrog initializer. Then, followed by a few denoising steps, LED obtains the final predictions. In leapfrog initializer, LED learns statistics and generates correlated samples with the reparameterization." + ], + "image_footnote": [], + "bbox": [ + 112, + 54, + 867, + 204 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "izer $f_{\\mathrm{LSG}}(\\cdot)$ to directly model the $\\tau$ th denoised distribution $\\mathcal{P}(\\widehat{\\mathbf{Y}}^{\\tau})$ , which is hypothetically equivalent to the output of executing $(\\Gamma - \\tau)$ denoising steps (2d). We then draw samples from the distribution $\\mathcal{P}(\\widehat{\\mathbf{Y}}^{\\tau})$ and obtain $K$ future trajectories $\\widehat{\\mathcal{Y}}^{\\tau} = \\{\\widehat{\\mathbf{Y}}_1^{\\tau}, \\widehat{\\mathbf{Y}}_2^{\\tau}, \\dots, \\widehat{\\mathbf{Y}}_K^{\\tau}\\}$ , where $\\stackrel{K}{\\sim}$ in (3d) means $K$ samples are dependent to intentionally allocate appropriate sample diversity. Then, in Step (3d), we only need to apply the remaining $\\tau$ denoising steps for each trajectory $\\widehat{\\mathbf{Y}}_k^\\gamma$ to obtain the final prediction $\\widehat{\\mathcal{Y}} = \\{\\widehat{\\mathbf{Y}}_1^0, \\widehat{\\mathbf{Y}}_2^0, \\dots, \\widehat{\\mathbf{Y}}_K^0\\}$ .", + "bbox": [ + 75, + 260, + 472, + 405 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Note that i) the proposed leapfrog diffusion model reduces the denoising steps from $\\Gamma$ to $\\tau (\\ll \\Gamma)$ in Step (3d) as the leapfrog initializer directly provides the trajectories at denoising step $\\tau$ , accelerating the inference; ii) instead of taking independent and identically distributed samples in Step (2c), the proposed leapfrog initializer generates $K$ trajectories $\\widehat{\\mathcal{Y}}^{\\tau}$ simultaneously in Step (3c), allowing $K$ samples to be aware of each other; and iii) the standard diffusion model and the proposed leapfrog diffusion model share the same forward diffusion process, assuring that the representation capacity is not reduced.", + "bbox": [ + 75, + 406, + 473, + 571 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. Leapfrog Initializer", + "text_level": 1, + "bbox": [ + 76, + 587, + 264, + 603 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We now dive into the design details of the proposed leapfrog initializer, which leapfrogs $(\\Gamma - \\tau)$ denoising steps. In leapfrog initializer, we model the $\\tau$ th denoised distribution $\\mathcal{P}(\\widehat{\\mathbf{Y}}^{\\tau})$ through learning models. However, it is nontrivial for a learning model to directly capture the sophisticated distribution, which usually causes unstable training. To ease the learning burden of the model, we disassemble the distribution $\\mathcal{P}(\\widehat{\\mathbf{Y}}^{\\tau})$ into three representative parts: the mean, global variance and sample prediction. For each part, we design trainable modules correspondingly. Mathematically, let $\\mathbf{X}$ and $\\mathbb{X}_{\\mathcal{N}}$ be the past trajectories of the ego agent and the neighboring agents, respectively. The proposed leapfrog initializer generates $K$ samples as follows,", + "bbox": [ + 75, + 612, + 470, + 809 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mu_ {\\theta} = f _ {\\mu} (\\mathbf {X}, \\mathbb {X} _ {\\mathcal {N}}) \\in \\mathbb {R} ^ {T _ {t} \\times 2}, \\\\ \\sigma_ {\\theta} = f _ {\\sigma} (\\mathbf {X}, \\mathbb {X} _ {\\mathcal {N}}) \\in \\mathbb {R}, \\\\ \\widehat {\\mathbb {S}} _ {\\theta} = \\left[ \\widehat {\\mathbf {S}} _ {\\theta , 1}, \\dots , \\widehat {\\mathbf {S}} _ {\\theta , K} \\right] = f _ {\\widehat {\\mathbb {S}}} (\\mathbf {X}, \\mathbb {X} _ {\\mathcal {N}}, \\sigma_ {\\theta}) \\in \\mathbb {R} ^ {T _ {\\mathrm {f}} \\times 2 \\times K}, \\\\ \\widehat {\\mathbf {Y}} _ {k} ^ {\\tau} = \\mu_ {\\theta} + \\sigma_ {\\theta} \\cdot \\widehat {\\mathbf {S}} _ {\\theta , k} \\in \\mathbb {R} ^ {T _ {\\mathrm {f}} \\times 2}, \\tag {4} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 112, + 823, + 473, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $f_{\\mu}(\\cdot), f_{\\sigma}(\\cdot), f_{\\widehat{\\mathbb{S}}}(\\cdot)$ are three trainable modules, $\\mu_{\\theta}, \\sigma_{\\theta}$ are the mean and standard deviation of $\\mathcal{P}(\\widehat{\\mathbf{Y}}^{\\tau})$ , respectively, and $\\widehat{\\mathbf{S}}_{\\theta,k}$ is the normalized positions for the $k$ th sample.", + "bbox": [ + 496, + 260, + 893, + 309 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To be specific, the mean estimate module $f_{\\mu}(\\cdot)$ infers the mean trajectory of the $\\tau$ th denoised distribution $\\widehat{\\mathcal{P}}(\\widehat{\\mathbf{Y}}^{\\tau})$ with past trajectories $(\\mathbf{X}, \\mathbb{X}_{\\mathcal{N}})$ . The mean trajectory $\\mu_{\\theta}$ is shared across all the $K$ samples. The variance estimate module $f_{\\sigma}(\\cdot)$ infers the standard deviation of the $\\tau$ th denoised distribution $\\widehat{\\mathcal{P}}(\\widehat{\\mathbf{Y}}^{\\tau})$ , reflecting the overall uncertainty of the trajectory, which is also shared across all the $K$ samples. The sample prediction module $f_{\\widehat{\\mathbb{S}}}(\\cdot)$ takes the past trajectories $(\\mathbf{X}, \\mathbb{X}_{\\mathcal{N}})$ and the predicted uncertainty $\\sigma_{\\theta}$ as the input and predicts $K$ normalized positions where each $\\widehat{\\mathbf{S}}_{\\theta,k} \\in \\mathbb{R}^{T_{\\mathrm{f}} \\times 2}$ .", + "bbox": [ + 496, + 310, + 892, + 465 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Note that i) the reparameterization in Eq. (4) allows us to avoid learning a raw sophisticated distribution, making the training much easier; and ii) $K$ normalized predictions are generated simultaneously from the same underlying feature, assuring appropriately allocated trajectories with variance estimation and better capturing the multi-modalities.", + "bbox": [ + 496, + 465, + 893, + 556 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To implement the three trainable modules: $f_{\\mu}(\\cdot), f_{\\sigma}(\\cdot), f_{\\widehat{\\mathbb{S}}}(\\cdot)$ , we consider a similar network design: a social encoder to capture social influence, a temporal encoder to learn temporal embedding, and an aggregation layer to fuse both social and temporal information; see Figure 2. Here we take the mean estimation module $f_{\\mu}(\\cdot)$ as an example. The mean trajectory is obtained as follows,", + "bbox": [ + 496, + 556, + 893, + 662 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathbf {e} _ {\\mu_ {\\theta}} ^ {\\text {s o c i a l}} = \\operatorname {s o f t m a x} \\left(\\frac {f _ {\\mathrm {q}} (\\mathbf {X}) f _ {\\mathrm {k}} (\\mathbb {X} _ {\\mathcal {N}}) ^ {\\top}}{\\sqrt {d}}\\right) f _ {\\mathrm {v}} (\\mathbb {X} _ {\\mathcal {N}}), (5a) \\\\ \\mathbf {e} _ {\\mu_ {\\theta}} ^ {\\text {t e m p}} = f _ {\\mathrm {G R U}} \\left(f _ {\\operatorname {c o n v 1 D}} (\\mathbf {X})\\right), (5b) \\\\ \\mu_ {\\theta} = f _ {\\text {f u s i o n}} \\left(\\left[ \\mathbf {e} _ {\\mu_ {\\theta}} ^ {\\text {s o c i a l}}: \\mathbf {e} _ {\\mu_ {\\theta}} ^ {\\text {t e m p}} \\right]\\right). (5c) \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 526, + 667, + 890, + 743 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Step (5a) obtains the social embedding $\\mathbf{e}_{\\mu_{\\theta}}^{\\mathrm{social}}$ based on the multi-head attention with $d$ the embedding dimension and $f_{\\mathrm{q}}(\\cdot), f_{\\mathrm{k}}(\\cdot), f_{\\mathrm{v}}(\\cdot)$ the query/key/value embedding functions. Step (5b) obtains the temporal embedding through the feature encoder $f_{\\mathrm{conv1D}}(\\cdot)$ , mapping the raw coordinates into the high-dimensional feature, followed by the gated recurrent units $f_{\\mathrm{GRU}}(\\cdot)$ , capturing the temporal dependence in the high dimensional sequence. Step (5c) concatenates both social and temporal embeddings and uses a multi-layer perceptron $f_{\\mathrm{fusion}}(\\cdot)$ to obtain the final mean estimation. Note", + "bbox": [ + 496, + 748, + 893, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "5520", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "that the sample prediction module $f_{\\widehat{\\mathbb{S}}}(\\cdot)$ also takes the estimated standard deviation as the input, working as", + "bbox": [ + 76, + 90, + 472, + 122 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {e} _ {\\hat {\\mathfrak {S}} _ {\\theta}} ^ {\\sigma} = f _ {\\mathrm {e n c o d e}} (\\sigma_ {\\theta}),\n$$\n", + "text_format": "latex", + "bbox": [ + 150, + 131, + 282, + 151 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\widehat {\\mathbb {S}} _ {\\theta} = f _ {\\mathrm {f u s i o n}} ([ \\mathbf {e} _ {\\widehat {\\mathbb {S}} _ {\\theta}} ^ {\\mathrm {s o c i a l}}: \\mathbf {e} _ {\\widehat {\\mathbb {S}} _ {\\theta}} ^ {\\mathrm {t e m p}}: \\mathbf {e} _ {\\widehat {\\mathbb {S}} _ {\\theta}} ^ {\\sigma} ]),\n$$\n", + "text_format": "latex", + "bbox": [ + 153, + 154, + 393, + 176 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where an encoder $f_{\\mathrm{encode}}(\\cdot)$ operates on the estimated variance $\\sigma_{\\theta}$ and generates high dimensional embedding $\\mathbf{e}_{\\hat{\\mathbb{S}}_{\\theta}}^{\\sigma}$ . By this, the variance estimation also involves in the sample prediction process, instead of just scaling these prediction.", + "bbox": [ + 76, + 186, + 468, + 247 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "After obtaining $K$ samples $\\widehat{y}^{\\tau} = \\{\\widehat{\\mathbf{Y}}_1^\\tau ,\\widehat{\\mathbf{Y}}_2^\\tau ,\\dots ,\\widehat{\\mathbf{Y}}_K^\\tau \\}$ from leapfrog initializer, we execute the remaining $\\tau$ denoising steps to iteratively refine those predicted trajectories (3d).", + "bbox": [ + 76, + 248, + 470, + 295 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Denoising Module", + "text_level": 1, + "bbox": [ + 76, + 303, + 253, + 319 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Here we elaborate the design of a denoising module $f_{\\mathrm{denoise}}(\\cdot)$ , which denoises the trajectory $\\widehat{\\mathbf{Y}}_k^{\\gamma +1}$ conditioned on past trajectories $(\\mathbf{X},\\mathbb{X}_{\\mathcal{N}})$ . In a denoising module, two parts are trainable: a transformer-based context encoder $f_{\\mathrm{context}}(\\cdot)$ to learn a social-temporal embedding and a noise estimation module $f_{\\epsilon}(\\cdot)$ to estimate the noise to reduce. Mathematically, the $\\gamma$ th denoising step works as follows,", + "bbox": [ + 76, + 325, + 472, + 434 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {C} = f _ {\\text {c o n t e x t}} (\\mathbf {X}, \\mathbb {X} _ {\\mathcal {N}}), \\tag {6a}\n$$\n", + "text_format": "latex", + "bbox": [ + 102, + 446, + 468, + 463 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\epsilon_ {\\theta} ^ {\\gamma} = f _ {\\epsilon} \\left(\\widehat {\\mathbf {Y}} _ {k} ^ {\\gamma + 1}, \\mathbf {C}, \\gamma + 1\\right), \\tag {6b}\n$$\n", + "text_format": "latex", + "bbox": [ + 104, + 465, + 468, + 486 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathbf {Y}} _ {k} ^ {\\gamma} = \\frac {1}{\\sqrt {\\alpha_ {\\gamma}}} \\left(\\hat {\\mathbf {Y}} _ {k} ^ {\\gamma + 1} - \\frac {1 - \\alpha_ {\\gamma}}{\\sqrt {1 - \\bar {\\alpha} _ {\\gamma}}} \\boldsymbol {\\epsilon} _ {\\theta} ^ {\\gamma}\\right) + \\sqrt {1 - \\alpha_ {\\gamma}} \\mathbf {z}, \\quad (6 c)\n$$\n", + "text_format": "latex", + "bbox": [ + 104, + 488, + 468, + 522 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\alpha_{\\gamma}$ and $\\bar{\\alpha}_{\\gamma} = \\prod_{i=1}^{\\gamma} \\alpha_{i}$ are parameters in the diffusion process and $\\mathbf{z} \\sim \\mathcal{N}(\\mathbf{z}; \\mathbf{0}, \\mathbf{I})$ is a noise. Step (6a) uses a context encoder $f_{\\mathrm{context}}(\\cdot)$ on past trajectories $(\\mathbf{X}, \\mathbb{X}_{\\mathcal{N}})$ to obtain the context condition $\\mathbf{C}$ , which shares a similar structure to mean estimation module $f_{\\mu}(\\cdot)$ ; Step (6b) estimates the noise $\\epsilon_{\\theta}^{\\gamma}$ in the noisy trajectory $\\widehat{\\mathbf{Y}}_k^{\\gamma+1}$ through noise estimation $f_{\\epsilon}(\\cdot)$ implemented by multi-layer perceptions with the context $\\mathbf{C}$ ; Step (6c) provides a standard denoising step [17]; see more details in the supplementary material.", + "bbox": [ + 75, + 525, + 470, + 664 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.4. Training Objective", + "text_level": 1, + "bbox": [ + 76, + 672, + 259, + 689 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To train a leapfrog diffusion model, we consider a two-stage training strategy, where the first stage trains a denoising module and the second stage focuses on a leapfrog initializer. The reason to use two stages is because the training of leapfrog initializer is more stable given fixed distribution $\\mathcal{P}(\\widehat{\\mathbf{Y}}^{\\tau})$ , avoiding non-convergent training.", + "bbox": [ + 76, + 696, + 468, + 787 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Concretely, the first stage trains a denoising module $f_{\\mathrm{denoise}}(\\cdot)$ in Step (3d) based on a standard training schedule of a diffusion model [14, 17] through noise estimation loss:", + "bbox": [ + 76, + 787, + 468, + 832 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {N E}} = \\| \\boldsymbol {\\epsilon} - f _ {\\boldsymbol {\\epsilon}} (\\mathbf {Y} ^ {\\gamma + 1}, f _ {\\text {c o n t e x t}} (\\mathbf {X}, \\mathbb {X} _ {\\mathcal {N}}), \\gamma + 1) \\| _ {2},\n$$\n", + "text_format": "latex", + "bbox": [ + 84, + 842, + 426, + 859 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\gamma \\sim \\mathrm{U}\\{1,2,\\dots ,\\Gamma \\}$ $\\epsilon \\sim \\mathcal{N}(\\epsilon ;\\mathbf{0},\\mathbf{I})$ and the diffused trajectory $\\mathbf{Y}^{\\gamma +1} = \\sqrt{\\bar{\\alpha}_{\\gamma}}\\mathbf{Y}^{0} + \\sqrt{1 - \\bar{\\alpha}_{\\gamma}}\\pmb {\\epsilon}$ . We then back", + "bbox": [ + 75, + 869, + 472, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Algorithm 1 Leapfrog Diffusion Model in Inference", + "text_level": 1, + "bbox": [ + 500, + 90, + 849, + 106 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Input: Observed trajectories $\\mathbf{X}$ , $\\mathbb{X}_{\\mathcal{N}}$ , Leapfrog step $\\tau$", + "bbox": [ + 500, + 109, + 857, + 125 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Output: Predicted trajectories $\\hat{\\mathcal{V}}$", + "bbox": [ + 500, + 126, + 723, + 142 + ], + "page_idx": 4 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1: $\\mu_{\\theta} = f_{\\mu}(\\mathbf{X},\\mathbb{X}_{\\mathcal{N}})$ Mean estimation", + "2: $\\sigma_{\\theta} = f_{\\sigma}(\\mathbf{X},\\mathbb{X}_{\\mathcal{N}})$ $\\triangleright$ Variance estimation", + "3: $\\widehat{\\mathbb{S}}_{\\theta} = f_{\\widehat{\\mathbb{S}}}(\\mathbf{X},\\mathbb{X}_{\\mathcal{N}},\\sigma_{\\theta})$ ▷ Sample prediction", + "4: $\\widehat{\\mathbf{Y}}_k^\\tau = \\mu_\\theta +\\sigma_\\theta \\cdot \\widehat{\\mathbf{S}}_{\\theta ,k},k = 1,\\dots ,K\\ntriangleright$ Reparameterization", + "5: for $\\gamma = \\tau - 1, \\dots, 0$ do", + "6: $\\widehat{\\mathbf{Y}}_k^\\gamma = f_{\\mathrm{denoise}}(\\widehat{\\mathbf{Y}}_k^{\\gamma +1},\\mathbf{X},\\mathbb{X}_{\\mathcal{N}})$ Denoising step", + "7: end for", + "8: $\\widehat{\\mathcal{Y}} = \\widehat{\\mathcal{Y}}^0 = \\{\\widehat{\\mathbf{Y}}_1^0,\\dots ,\\widehat{\\mathbf{Y}}_K^0\\}$", + "9: return $\\hat{y}$" + ], + "bbox": [ + 509, + 143, + 890, + 297 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "propagate this loss and train the parameters in the context encoder $f_{\\mathrm{context}}(\\cdot)$ and the noise estimation module $f_{\\epsilon}(\\cdot)$ .", + "bbox": [ + 498, + 328, + 890, + 359 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In the second stage, we optimize a leapfrog diffusion model with a trainable leapfrog initializer and frozen denoising modules. For each sample, the loss function is", + "bbox": [ + 498, + 359, + 893, + 404 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} = \\mathcal {L} _ {\\text {d i s t a n c e}} + \\mathcal {L} _ {\\text {u n c e r t a i n t y}} \\\\ { = } { w \\cdot \\operatorname* { m i n } _ { k } \\| \\mathbf { Y } - \\widehat { \\mathbf { Y } } _ { k } \\| _ { 2 } + \\Big ( \\frac { \\sum _ { k } \\| \\mathbf { Y } - \\widehat { \\mathbf { Y } } _ { k } \\| _ { 2 } } { \\sigma _ { \\theta } ^ { 2 } K } + \\log \\sigma _ { \\theta } ^ { 2 } \\Big ) , } \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 416, + 890, + 470 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $w \\in \\mathbb{R}$ is a hyperparameter weight. The first term constrains the minimum distance in $K$ predictions. Intuitively, if a leapfrog initializer generates high-quality estimations for distribution $\\mathcal{P}(\\widehat{\\mathbf{Y}}^{\\tau})$ , then one of the $K$ predictions in $\\widehat{\\mathcal{V}}$ should be close to the ground-truth trajectory $\\mathbf{Y}$ . The second term normalizes the variance estimation $\\sigma_{\\theta}$ in reparameterization (4) through an uncertainty loss, balancing the prediction diversity and mean accuracy. Note that the variance estimation controls the dispersion of the predictions, bridging scenery complexity and prediction diversity. The first part $\\frac{\\sum_k\\|\\mathbf{Y}\\widehat{\\mathbf{Y}}_k\\|_2}{\\sigma_\\theta^2K}$ makes the value of $\\sigma_{\\theta}$ proportional to the complexity of the scenario. The second part $\\log \\sigma_{\\theta}^{2}$ is a regulariser used to avoid a trivial solution for $\\sigma_{\\theta}$ , i.e., generating high variance for all predictions.", + "bbox": [ + 498, + 481, + 893, + 700 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Technically, we can also explicitly supervise the estimation of leapfrog initializer in stage two, since the distribution $\\mathcal{P}(\\widehat{\\mathbf{Y}}^{\\tau})$ can be denoised from a normal distribution. For the explicit supervision, we draw $M\\gg K$ samples from $\\mathcal{P}(\\widehat{\\mathbf{Y}}^{\\Gamma})$ under the normal distribution and iteratively denoise these samples through Step (2d) until we get expected denoised trajectories $\\widehat{\\mathbf{Y}}^{\\tau}$ . And then, we calculate the statistics of the denoised distribution $\\mathcal{P}(\\widehat{\\mathbf{Y}}^{\\tau})$ using these $M$ samples, serving as explicit supervisions for mean estimation $f_{\\mu}(\\cdot)$ and variance estimation $f_{\\sigma}(\\cdot)$ . However, since $\\tau \\ll \\Gamma$ , we need to run $(\\Gamma -\\tau)\\approx \\Gamma$ -steps denoising for $M\\gg K$ samples to get statistics, resulting in unacceptable time and storage consumption for training (e.g. $\\sim 6$ days per epoch on NBA", + "bbox": [ + 498, + 703, + 893, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "5521", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/fc60a3d39e328e053c8a2fcae13f3229bd2bc3520286c89965bc3be56ebd6570.jpg", + "table_caption": [ + "Table 1. Comparison with baseline models on NBA dataset. minADE20 /minFDE20 (meters) are reported. Bold/underlined fonts represent the best/second-best result. Compared to the previous SOTA method, MID, our method achieves a $15.6\\% /13.4\\%$ ADE/FDE improvement." + ], + "table_footnote": [], + "table_body": "
TimeSocial-GAN [15] CVPR'18STGAT [19] ICCV'19Social-STGCNN [31] CVPR'20PECNet [27] ECCV'20STAR [52] ECCV'20Trajectory++[38] ECCV'20MemoNet [50] CVPR'22NPSN [2] CVPR'22GroupNet [49] CVPR'22MID [14] CVPR'22Ours
1.0s0.41/0.620.35/0.510.34/0.480.40/0.710.43/0.660.30/0.380.38/0.560.35/0.580.26/0.340.28/0.370.18/0.27
2.0s0.81/1.320.73/1.100.71/0.940.83/1.610.75/1.240.59/0.820.71/1.140.68/1.230.49/0.700.51/0.720.37/0.56
3.0s1.19/1.941.04/1.751.09/1.771.27/2.441.03/1.510.85/1.241.00/1.571.01/1.760.73/1.020.71/0.980.58/0.84
Total(4.0s)1.59/2.411.40/2.181.53/2.261.69/2.951.13/2.011.15/1.571.25/1.471.31/1.790.96/1.300.96/1.270.81/1.10
", + "bbox": [ + 78, + 101, + 885, + 193 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/984669d7f99d092975bde11e55917d1fc5e974cc8cd42842c71284bac51380fb.jpg", + "table_caption": [ + "Table 2. Comparison with baseline models on NFL dataset. $\\mathrm{{minADE}}_{20}/\\mathrm{{minFDE}}_{20}$ (meters) are reported. Bold/underlined fonts represent the best/second-best result. Compared to the previous SOTA method, MID, our method achieves a 23.7%/21.9% improvement." + ], + "table_footnote": [], + "table_body": "
TimeSocial-GAN [15] CVPR'18STGAT [19] ICCV'19Social-STGCNN [31] CVPR'20PECNet [27] ECCV'20STAR [52] ECCV'20Trajectron++[38] ECCV'20LB-EBM[34] CVPR'21NPSN [2] CVPR'22GroupNet[49] CVPR'22MID [14] CVPR'22Ours
1.0s0.37/0.680.35/0.640.45/0.640.52/0.970.49/0.840.41/0.650.75/1.050.43/0.640.32/0.570.30/0.580.21/0.34
2.0s0.83/1.530.82/1.601.06/1.871.19/2.471.02/1.840.93/1.651.26/2.280.83/1.520.73/1.390.71/1.310.49/0.91
Total(3.2s)1.44/2.511.39/2.481.82/3.181.99/3.841.51/2.971.54/2.581.90/3.251.32/2.271.21/2.151.14/1.920.87/1.50
", + "bbox": [ + 80, + 224, + 883, + 305 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "dataset). We thus do not use explicit supervision.", + "bbox": [ + 76, + 318, + 403, + 333 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.5. Inference Phase", + "text_level": 1, + "bbox": [ + 76, + 343, + 236, + 358 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "During the inference, instead of the $\\Gamma$ -steps' denoising, leapfrog diffusion model only takes $\\tau$ -steps, accelerating the inference. To be specific, we first generate $K$ correlated samples to model the distribution $\\mathcal{P}(\\widetilde{\\mathbf{Y}}^{\\tau})$ using the trained leapfrog initializer. Then, these samples will be fed into the denoising process and iteratively fine-tuned to produce the final predictions; see Algorithm 1.", + "bbox": [ + 75, + 367, + 470, + 473 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 76, + 488, + 209, + 503 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Datasets", + "text_level": 1, + "bbox": [ + 76, + 513, + 181, + 527 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We evaluate our method on four trajectory prediction datasets, including two sports datasets (NBA SportVU Dataset, NFL Football Dataset) and two pedestrian datasets (Stanford Drone Dataset, ETH-UCY).", + "bbox": [ + 75, + 536, + 468, + 595 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "NBA SportVU Dataset (NBA): NBA trajectory dataset is collected by NBA using the SportVU tracking system, which records the trajectories of the 10 players and the ball in real basketball games. In this task, we predict the future 4.0s (20 frames) using the 2.0s (10 frames) past trajectory.", + "bbox": [ + 75, + 598, + 468, + 672 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "NFL Football Dataset (NFL): NFL Football Dataset records the position of every player on the field during each play in the 2017 year. We predict the 22 players' (11 players per team) and the ball's future 3.2s (16 frames) trajectory using the historical 1.6s (8 frames) trajectory.", + "bbox": [ + 75, + 672, + 468, + 748 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Stanford Drone Dataset (SDD): SDD is a large-scale pedestrian dataset collected from a university campus in bird's eye view. Following previous works [27, 50], we use the standard train-test split and predict the future 4.8s (12 frames) using 3.2s (8 frames) past.", + "bbox": [ + 75, + 750, + 468, + 824 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "ETH-UCY: ETH-UCY dataset contains 5 subsets: ETH, HOTEL, UNIV, ZARA1, and ZARA2, containing various motion scenes. We use same segment length of 8s as SDD following previous works [18, 27] and use the leave-one-out approach with four sets for training and a left set for testing.", + "bbox": [ + 75, + 824, + 470, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Implementation Details", + "text_level": 1, + "bbox": [ + 500, + 316, + 718, + 333 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In the leapfrog diffusion model, we set the diffusion step $\\Gamma = 100$ for all four datasets and the leapfrog step $\\tau = 5$ on the NBA dataset. In the leapfrog initializer, we build a transformer-based social encoder where the feed-forward dimension is set to 256, the number of heads is 2, and 2 encoder layers are applied; we apply the temporal encoder with 1D convolution kernel being 3, and output channel setting to 32, and we also build a GRU with the hidden size of 256. In the denoising module, we apply the same parameters transformer to extract the context information, and we build the core denoising module with a hidden size of 256. To train the leapfrog diffusion model, we train the denoising module for 100 epochs with an initial learning rate of $10^{-2}$ and decay to half every 16 epochs. With a frozen denoising module, we then train the leapfrog initializer for 200 epochs with an initial learning rate of $10^{-4}$ , decaying by 0.9 every 32 epochs. We set weight parameter $w_{1} = 50$ to emphasize the distance loss. The entire framework is trained with the Adam optimizer on one GTX-3090 GPU. All models are implemented with PyTorch 1.7.1. See more details in the supplementary material.", + "bbox": [ + 496, + 340, + 893, + 657 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.3. Comparison with SOTA Methods", + "text_level": 1, + "bbox": [ + 498, + 665, + 794, + 681 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We measure the performance of different trajectory prediction methods using two metrics: $\\min\\mathrm{ADE}_K$ and $\\min\\mathrm{FDE}_K$ , following previous work [27, 49]. 1) $\\min\\mathrm{ADE}_K$ calculates the minimum time-averaged distance among $K$ predictions and the ground-truth future trajectory; 2) $\\min\\mathrm{FDE}_K$ measures the minimum distance among the $K$ predicted endpoints and the ground-truth endpoints. We calculate these two metrics at different timestamps on sports datasets to better evaluate the performance.", + "bbox": [ + 496, + 688, + 893, + 824 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "NBA dataset. We compare our method with the current 10 state-of-the-art prediction methods at different timestamps; see Table 1. We see that i) our method significantly outperforms all baselines in ADE and FDE at all timestamps. Our method reduces the ADE/FDE at 4.0s from 0.96/1.27", + "bbox": [ + 496, + 825, + 895, + 898 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "5522", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/44d4d4c3d16c859eab620920ce57b4383bd26a5228aad9324d4287d4d4b21bfe.jpg", + "table_caption": [ + "Table 3. Comparison with baseline models on SDD dataset. minADE20/minFDE20 (meters) are reported. Bold/underlined fonts represent the best/second-best result. Our method achieves the best performance in ADE/FDE. * represents the reproduced results from open source." + ], + "table_footnote": [], + "table_body": "
TimeSocial-GAN [15] CVPR'18SOPHIE [36] CVPR'19Trajectory++ [38] ECCV'20NMMP [18] CVPR'20Evolve- Graph [25] NIPS'20PECNet [27] ECCV'20MemoNet [50] CVPR'22NPSN [2] CVPR'22GroupNet [49] CVPR'22MID* [14] CVPR'22Ours
4.8s27.23/41.4416.27/29.3819.30/32.7014.67/26.7213.90/22.909.96/15.888.56/12.668.56/11.859.31/16.119.73/15.328.48/11.66
", + "bbox": [ + 80, + 102, + 883, + 157 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/4435e0f6ccc1ece1eba7d63e1d69c3ab043703881c178d2667a1e875c9b4ccad.jpg", + "table_caption": [ + "Table 4. Comparison with baseline models on ETH-UCY dataset. minADE20/minFDE20 (meters) are reported. Bold/underlined fonts represent the best/second-best result. In most subsets, our method achieves the best or second-best performance in ADE/FDE." + ], + "table_footnote": [], + "table_body": "
SubsetSocial-GAN [15]CVPR'18NMMP [18]CVPR'20STAR [52]ECCV'20PECNet [27]ECCV'20Trajectory++[38]ECCV'20Agentformer[53]ICCV'21MemoNet[50]CVPR'22NPSN [2]CVPR'22GroupNet[49]CVPR'22MID [14]CVPR'22
ETH0.87/1.620.61/1.080.36/0.650.54/0.870.61/1.020.45/0.750.40/0.610.40/0.760.46/0.730.39/0.66
Hotel0.67/1.370.33/0.630.17/0.360.18/0.240.19/0.280.14/0.220.11/0.170.12/0.180.15/0.250.13/0.22
Univ0.76/1.520.52/1.110.31/0.620.35/0.600.30/0.540.25/0.450.24/0.430.22/0.410.26/0.490.22/0.45
Zara10.35/0.680.32/0.660.29/0.520.22/0.390.24/0.420.18/0.300.18/0.320.17/0.310.21/0.390.17/0.30
Zara20.42/0.840.43/0.850.22/0.460.17/0.300.18/0.320.14/0.240.14/0.240.12/0.240.17/0.330.13/0.27
AVG0.61/1.210.41/0.820.26/0.530.29/0.480.30/0.510.23/0.390.21/0.350.21/0.380.25/0.440.21/0.38
", + "bbox": [ + 89, + 188, + 874, + 305 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/0df9007f9362c754f2413467ea97d25ad003db4c35a57d3ab432e837baaab0ab.jpg", + "table_caption": [ + "Table 5. Ablation of leapfrog initializer in the leapfrog diffusion model on NFL with various prediction numbers $K$ . Each module in the leapfrog initializer is beneficial." + ], + "table_footnote": [], + "table_body": "
Mean μθVariance σθSample ΜθK=2K=4
✓correlated2.04±0.18/4.08±0.481.63±0.13/3.05±0.16
✓correlated1.95±0.08/3.90±0.221.49±0.01/2.86±0.02
✓✓i.i.d2.36±0.13/4.31±0.221.90±0.07/3.31±0.05
✓✓correlated1.84±0.05/3.61±0.111.47±0.01/2.83±0.02
Mean μθVariance σθSample ΜθK=8K=20
✓correlated1.25±0.02/2.31±0.040.99±0.03/1.68±0.04
✓correlated1.23±0.01/2.20±0.010.95±0.01/1.54±0.02
✓✓i.i.d1.51±0.04/2.67±0.071.18±0.02/1.90±0.03
✓✓correlated1.18±0.01/2.19±0.010.89±0.01/1.51±0.02
", + "bbox": [ + 84, + 356, + 455, + 511 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "to 0.81/1.10 compared to the current state-of-the-art methods, MID, achieving $15.6\\% / 13.4\\%$ improvement; and ii) performance improvement over previous methods increases with timestamps, reflecting the proposed method can capture more sophisticated distributions at further timestamps.", + "bbox": [ + 75, + 532, + 468, + 608 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "NFL dataset. We compare our method with the current 10 state-of-the-art prediction methods at different timestamps; see Table 2. We see that our model significantly outperforms all baselines in ADE and FDE at all timestamps. Our method reduces the ADE/FDE at 3.2s from 1.14/1.92 to 0.87/1.50 compared to the current state-of-the-art methods, MID, achieving $23.7\\% / 21.9\\%$ improvement.", + "bbox": [ + 75, + 609, + 470, + 715 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "SDD dataset. We compare our method with the current 10 state-of-the-art prediction methods; see Table 3. We see that our method reduces FDE from 11.85 to 11.66 compared to the current state-of-the-art method, NPSN. Notably, the original MID [14] uses a different protocol from all the other methods, we update its code for a fair comparison.", + "bbox": [ + 75, + 717, + 468, + 808 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ETH-UCY dataset. We compare our method with 10 state-of-the-art prediction methods; see Table 4. We see that i) our method reduces FDE from 0.35 to 0.33 compared to the current state-of-the-art method, MemoNet, achieving a $5.7\\%$ improvement; and ii) our method achieves the best or second best to the best performance on most of the subsets.", + "bbox": [ + 75, + 809, + 470, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/1f3d490500339bdb65ba908a95fb32fda7f65e230f844ef21a49ca8ab9ad511b.jpg", + "table_caption": [ + "Table 6. Different steps $\\Gamma /\\tau$ in the standard/leapfrog diffusion model on NBA. $\\tau = 5$ provides the best performance." + ], + "table_footnote": [], + "table_body": "
MethodSteps1.0s2.0s3.0sTotal(4.0s)Inference (ms)
Standard100.45/0.510.98/1.551.62/2.562.21/2.77~87
500.26/0.360.56/0.910.89/1.421.21/1.73~446
Diffusion (Γ)1000.21/0.280.44/0.640.69/0.950.94/1.21~886
2000.21/0.290.44/0.650.69/0.970.94/1.21>1s
5000.21/0.300.45/0.680.70/0.990.95/1.23>1s
Leapfrog30.20/0.310.40/0.620.62/0.880.84/1.10~30
Diffusion (τ)50.18/0.270.37/0.560.58/0.840.81/1.10~46
100.17/0.270.37/0.580.59/0.850.82/1.08~89
", + "bbox": [ + 501, + 343, + 903, + 470 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.4. Ablation Studies", + "text_level": 1, + "bbox": [ + 500, + 493, + 663, + 508 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effect of components in leapfrog initializer. We explore the effect of three key components in leapfrog initializer, including mean estimation, variance estimation, and sample prediction. Table 5 presents the results with mean and variance based on 5 experimental trials. We see that i) the leapfrog initializer achieves stable results with better performance even when prediction number $K$ is small; and ii) the proposed mean estimation, variance estimation, and sample prediction all contribute to promoting prediction accuracy.", + "bbox": [ + 496, + 523, + 893, + 661 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effect of leapfrog step $\\tau$ . Table 6 reports the influence of different leapfrog steps in LED. We see that i) under similar inference time, our method significantly outperforms the standard diffusion model with better representation ability; ii) when $\\tau$ is too small, leapfrog initializer targets to learn more sophisticated distribution, causing worse prediction performance; and iii) when $\\tau$ is too large, leapfrog initializer has already captured the denoised distribution, encountering performance bottleneck and wasting inference time.", + "bbox": [ + 496, + 667, + 893, + 803 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparison to other fast sampling methods. Table 7 compares the performance of our method and the other two fast sampling methods: PD [37] and DDIM [40]. We see that our method significantly outperforms two fast sampling methods under similar inference time since the proposed LED promotes the correlation between predictions.", + "bbox": [ + 496, + 810, + 893, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "5523", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/205b50b00688d86aa6a4485b8a55bc1b25cdf9b05973197595d0231ff01cf1fb.jpg", + "image_caption": [ + "(a) PECNet" + ], + "image_footnote": [], + "bbox": [ + 89, + 75, + 285, + 241 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/07360ce275d43da0a8a45ae2eac66de93110fae6c14398a326da717225b616bf.jpg", + "image_caption": [ + "(b) GroupNet" + ], + "image_footnote": [], + "bbox": [ + 285, + 75, + 482, + 242 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e108ce9f295a15ab4637716be9aa7df76f358f0788e4b3494a19425a98e37cc8.jpg", + "image_caption": [ + "(c) Ours" + ], + "image_footnote": [], + "bbox": [ + 483, + 75, + 679, + 242 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/11552ded243966ff228ef61699a4b61e9651ae39eec663cd2c7eebc365166483.jpg", + "image_caption": [ + "(d) GT" + ], + "image_footnote": [], + "bbox": [ + 681, + 75, + 879, + 242 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/ef0cb2d0e4e720e1cfe5da395925fcbf8da013b862d0c49119f483581b564301.jpg", + "table_caption": [ + "Table 7. Comparison to other fast sampling methods on NBA. $\\eta = 1$ in DDIM. Our method achieves the best performance." + ], + "table_footnote": [], + "table_body": "
Method1.0s2.0s3.0sTotal(4.0s)Inference (ms)
PD (K=1)0.20/0.330.45/0.750.72/1.130.98/1.39~452
PD (K=2)0.21/0.340.46/0.780.73/1.150.98/1.41~230
PD (K=3)0.23/0.370.48/0.790.73/1.150.98/1.43~121
PD (K=4)0.25/0.380.50/0.800.75/1.160.99/1.44~64
DDIM (S=2)0.20/0.290.42/0.650.66/0.960.91/1.21~530
DDIM (S=10)0.22/0.320.44/0.710.69/1.040.93/1.31~107
DDIM (S=20)0.24/0.350.49/0.810.76/1.211.02/1.51~54
Ours0.18/0.270.37/0.560.58/0.840.81/1.10~46
", + "bbox": [ + 78, + 318, + 468, + 445 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3baa9c7e93eb4aff7f1387b3943a818abf6829c32fa114f4ed9497ab54a9fe03.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 83, + 450, + 271, + 527 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/75993486e983ce54ac2d7009da7636aadd6e6a8b8f791700788ea8a83591efc0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 272, + 450, + 455, + 527 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/06487121e2a1b537d6e3839355f2dbd9cb648ee2262dcab14309b4565486a57f.jpg", + "image_caption": [ + "Figure 4. Mean and variance estimation in leapfrog initializer on NBA with $K = 20$ . The estimated variance can reflect the scene complexity of the current agent and produce diverse predictions." + ], + "image_footnote": [ + "Past trajectory Mean estimation Our prediction Ground-truth" + ], + "bbox": [ + 83, + 529, + 269, + 604 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ecc2166b8756bb0923dd67a5a40a359f3b4610e7c45b938f5f8eb1994e1c9a27.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 272, + 529, + 455, + 604 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.5. Qualitative Results", + "text_level": 1, + "bbox": [ + 76, + 667, + 259, + 684 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Visualization of predicted trajectory. Figure 3 compares the predicted trajectories of two baselines PECNet and GroupNet, our LED (Ours), and the ground-truth (GT) trajectories on the NBA dataset. We see that our method produces more accurate predictions than the previous methods.", + "bbox": [ + 75, + 689, + 468, + 763 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Visualization of estimated mean and variance. Figure 4 illustrates the mean and variance estimation in the leapfrog initializer under four scenes on the NBA dataset. We see that the variance estimation can well describe the scene complexity for the current agent by the learned variance, showing the rationality of our variance estimation.", + "bbox": [ + 75, + 763, + 468, + 854 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Visualization of different sampling mechanisms. Figure 5 compares two sampling mechanisms: I.I.D sampling and correlated sampling in the leapfrog initializer. We see", + "bbox": [ + 75, + 854, + 470, + 900 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/4b8a05611797c478dc3fba96f4b933d92cda2f6d2d1f2d5d89de5878d7fd01f5.jpg", + "image_caption": [ + "Figure 3. Visualization comparison on NBA. We compare the best-of-20 predictions by our method and two previous methods. Our method generates a more precise trajectory prediction. (Light color: past trajectory; blue/red/green color: two teams and the basketball.)", + "Figure 5. Comparison between I.I.D and correlated sampling mechanisms in NFL with $K = 4$ . Correlated samples appropriately capture multi-modalities, significantly improving prediction performances. that the proposed correlated sampling can appropriately allocate sample diversity and capture more modalities when the number of trials $K$ is small." + ], + "image_footnote": [], + "bbox": [ + 504, + 290, + 880, + 443 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 546, + 617, + 560 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This paper proposes the leapfrog diffusion model (LED), a diffusion-based trajectory prediction model, which significantly accelerates the overall inference speed and enables appropriate allocations of multiple correlated predictions. During the inference, LED directly models and samples from the denoised distribution through a novel leapfrog initializer with reparameterization. Extensive experiments show that our method achieves state-of-the-art performance on four real-world datasets and satisfies real-time inference needs.", + "bbox": [ + 496, + 566, + 893, + 702 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitation and future work. This work achieves inference acceleration for trajectory prediction tasks partially because the dimension of trajectory data is relatively small and the corresponding distribution is much easier to learn compared with those of image/video data. A possible future work is to explore diffusion models and fast sampling methods for higher-dimensional tasks.", + "bbox": [ + 496, + 703, + 893, + 808 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements", + "text_level": 1, + "bbox": [ + 500, + 821, + 666, + 838 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This research is partially supported by National Natural Science Foundation of China under Grant 62171276 and the Science and Technology Commission of Shanghai Municipal under Grant 21511100900 and 22DZ2229005.", + "bbox": [ + 496, + 839, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "5524", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Alexandre Alahi, Kratarth Goel, Vignesh Ramanathan, Alexandre Robicquet, Li Fei-Fei, and Silvio Savarese. 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In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 9813-9823, 2021. 1, 7" + ], + "bbox": [ + 501, + 92, + 893, + 895 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "5526", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Leapfrog Diffusion Model for Stochastic Trajectory Prediction/0cea661d-f5ad-40d3-86cc-3b1fbed56fa4_model.json b/2023/Leapfrog Diffusion Model for Stochastic Trajectory Prediction/0cea661d-f5ad-40d3-86cc-3b1fbed56fa4_model.json new file mode 100644 index 0000000000000000000000000000000000000000..5543210c54a29df1f0eb856a7c13ad11bdcc281e --- /dev/null +++ b/2023/Leapfrog Diffusion Model for Stochastic Trajectory Prediction/0cea661d-f5ad-40d3-86cc-3b1fbed56fa4_model.json @@ -0,0 +1,2574 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.17, + 0.131, + 0.8, + 0.154 + ], + "angle": 0, + "content": "Leapfrog Diffusion Model for Stochastic Trajectory Prediction" + }, + { + "type": "text", + "bbox": [ + 0.2, + 0.18, + 0.768, + 0.218 + ], + "angle": 0, + "content": "Weibo Mao\\(^{1}\\), Chenxin Xu\\(^{1}\\), Qi Zhu\\(^{1}\\), Siheng Chen\\(^{1,2*}\\), Yanfeng Wang\\(^{2,1}\\), Shanghai Jiao Tong University, Shanghai AI Laboratory" + }, + { + "type": "text", + "bbox": [ + 0.201, + 0.22, + 0.766, + 0.234 + ], + "angle": 0, + "content": "{kirino.mao,xcxwakaka,georgezhu,sihengc,wangyanfeng}@sjtu.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.269, + 0.314, + 0.285 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.302, + 0.474, + 0.71 + ], + "angle": 0, + "content": "To model the indeterminacy of human behaviors, stochastic trajectory prediction requires a sophisticated multi-modal distribution of future trajectories. Emerging diffusion models have revealed their tremendous representation capacities in numerous generation tasks, showing potential for stochastic trajectory prediction. However, expensive time consumption prevents diffusion models from real-time prediction, since a large number of denoising steps are required to assure sufficient representation ability. To resolve the dilemma, we present LEapfrog Diffusion model (LED), a novel diffusion-based trajectory prediction model, which provides real-time, precise, and diverse predictions. The core of the proposed LED is to leverage a trainable leapfrog initializer to directly learn an expressive multi-modal distribution of future trajectories, which skips a large number of denoising steps, significantly accelerating inference speed. Moreover, the leapfrog initializer is trained to appropriately allocate correlated samples to provide a diversity of predicted future trajectories, significantly improving prediction performances. Extensive experiments on four real-world datasets, including NBA/NFL/SDD/ETH-UCY, show that LED consistently improves performance and achieves \\(23.7\\% / 21.9\\%\\) ADE/FDE improvement on NFL. The proposed LED also speeds up the inference 19.3/30.8/24.3/25.1 times compared to the standard diffusion model on NBA/NFL/SDD/ETH-UCY, satisfying real-time inference needs. Code is available at https://github.com/MediaBrain-SJTU/LED." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.742, + 0.21, + 0.758 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.768, + 0.471, + 0.875 + ], + "angle": 0, + "content": "Trajectory prediction aims to predict the future trajectories for one or multiple interacting agents conditioned on their past movements. This task plays a significant role in numerous applications, such as autonomous driving [24], drones [10], surveillance systems [45], human-robot interaction systems [5], and interactive robotics [20]. Recently, lots of fascinating research progresses have been made from" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.266, + 0.895, + 0.4 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.405, + 0.895, + 0.462 + ], + "angle": 0, + "content": "Figure 1. Leapfrog diffusion model uses the leapfrog initializer to estimate the denoised distribution and substitute a long sequence of traditional denoising steps, accelerating inference and maintaining representation capacity." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.475, + 0.895, + 0.581 + ], + "angle": 0, + "content": "many aspects, including temporal encoding [6, 13, 46, 53], interaction modeling [1, 15, 18, 43, 49], and rasterized prediction [11, 12, 26, 48]. In practice, to capture multiple possibilities of future trajectories, a real-world prediction system needs to produce multiple future trajectories. This leads to the emergence of stochastic trajectory prediction, aiming to precisely model the distribution of future trajectories." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.583, + 0.896, + 0.809 + ], + "angle": 0, + "content": "Previous works have proposed a series of deep generative models for stochastic trajectory prediction. For example, [15, 18] exploit the generator adversarial networks (GANs) to model the future trajectory distribution; [27, 38, 49] consider the conditional variational autoencoders (CVAEs) structure; and [3] uses the conditional normalizing flow to relax the Gaussian prior in CVAEs and learn more representative priors. Recently, with the great success in image generation [17, 33] and audio synthesis [4, 21], denoising diffusion probabilistic models have been applied to time-series analysis and trajectory prediction, and show promising prediction performances [14, 44]. Compared to many other generative models, diffusion models have advantages in stable training and modeling sophisticated distributions through sufficient denoising steps [8]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.897, + 0.901 + ], + "angle": 0, + "content": "However, there are two critical problems in diffusion models for stochastic trajectory prediction. First, the real-time inference is time-consuming [14]. To ensure the representation ability and generate high-quality samples, an adequate number of denoising steps are required in standard diffusion models, which costs more computational time. For" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.222, + 0.9 + ], + "angle": 0, + "content": "*Corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5517" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.258 + ], + "angle": 0, + "content": "example, experiments show that on the NBA dataset, diffusion models need about 100 denoising steps to achieve decent prediction performances, which would take \\(\\sim 886\\mathrm{ms}\\) to predict; while the next frame comes every \\(200\\mathrm{ms}\\). Second, as mentioned in [2], a limited number of independent and identically distributed samples might not be able to capture sufficient modalities in the underlying distribution of a generative model. Empirically, a few independent sampled trajectories could miss some important future possibilities due to the lack of appropriate sample allocation, significantly deteriorating prediction performances." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.259, + 0.473, + 0.486 + ], + "angle": 0, + "content": "In this work, we propose leapfrog diffusion model (LED), a novel diffusion-based trajectory prediction model, which significantly accelerates the inference speed and enables adaptive and appropriate allocations of multiple correlated predictions, providing sufficient diversity in predictions. The core idea of the proposed LED is to learn a rough, yet sufficiently expressive distribution to initialize denoised future trajectories; instead of using a plain Gaussian distribution as in standard diffusion models. Specifically, our forward diffusion process is the same as standard diffusion models, which assures that the ultimate representation ability is pristine; while in the reverse denoising process, we leverage a powerful initializer to produce correlated diverse samples and leapfrog or skip a large number of denoising steps; and then, use only a few denoising steps to refine the distribution." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.487, + 0.473, + 0.653 + ], + "angle": 0, + "content": "To implement such a leapfrog initializer, we consider a reparameterization to alleviate the learning burden. We disassemble a denoised distribution into three parts: mean trajectory, variance, and sample positions under the normalized distribution. To estimate these three, we design three corresponding trainable modules, each of which leverages both a social encoder and a temporal encoder to learn the social-temporal features and produce accurate estimation. Furthermore, all the sample positions are simultaneously generated based on the same social-temporal features, enabling appropriate sample allocations to provide diversity." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.655, + 0.473, + 0.79 + ], + "angle": 0, + "content": "To evaluate the effectiveness of the proposed method, we conduct experiments on four trajectory prediction datasets: NBA, NFL Football Dataset, Standford Drones Dataset, and ETH-UCY. The quantitative results show we outperform the previous methods and achieve state-of-the-art performance. Specifically, compared to MID [14], the proposed leapfrog diffusion model reduces the average prediction time from \\(\\sim 886\\mathrm{ms}\\) to \\(\\sim 46\\mathrm{ms}\\) on the NBA dataset, while achieving a \\(15.6\\% / 13.4\\%\\) ADE/FDE improvement." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.793, + 0.424, + 0.807 + ], + "angle": 0, + "content": "The main contributions are concluded as follows," + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.809, + 0.47, + 0.869 + ], + "angle": 0, + "content": "- We propose a novel LEapfrog Diffusion model (LED), which is a denoising-diffusion-based stochastic trajectory prediction model. It achieves precise and diverse predictions with fast inference speed." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.473, + 0.902 + ], + "angle": 0, + "content": "- We propose a novel trainable leapfrog initializer to directly model sophisticated denoised distributions, accelerator" + }, + { + "type": "list", + "bbox": [ + 0.076, + 0.809, + 0.473, + 0.902 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.121 + ], + "angle": 0, + "content": "ating inference speed, and adaptively allocating the sample diversity, improving prediction performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.122, + 0.894, + 0.213 + ], + "angle": 0, + "content": "- We conduct extensive experiments on four datasets including NBA, NFL, SDD, and ETH-UCY. Results show that i) our approach consistently achieves state-of-the-art performance on all datasets; and ii) our method speeds up the inference by around 20 times compared to the standard diffusion model, satisfying real-time prediction needs." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.226, + 0.642, + 0.243 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.252, + 0.895, + 0.584 + ], + "angle": 0, + "content": "Trajectory prediction. Early works on trajectory prediction focus on a deterministic approach by exploring force models [16, 30], RNNs [1, 32, 47], and frequency analysis [28, 29]. For example, [16] models an agent's behavior with attractive and repulsive forces and builds the force equations for prediction. To capture the multi-modalities and model future distribution, recent works start to focus on stochastic trajectory prediction and have proposed a series of deep generative models. Generative Adversarial Network (GAN) structures [7, 9, 15, 18, 22, 36, 42] are proposed to generate multiple future trajectory distribution. [23, 27, 38, 49, 51] use the Variational Auto-Encoder (VAE) structure and learn the distribution through variational inference. [3] relaxes the Gaussian prior and proposes to use the normalizing flow. Heatmap [11, 12, 26] is used for modeling future trajectories' distribution on rasterized images. In this work, we propose a new diffusion-based model for trajectory prediction. Compared to previous generative models, our method has a large representation capacity and can model sophisticated trajectory distributions by using a number of diffusion steps. We also enable the correlation between samples to adaptively adjust sample diversity, improving prediction performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.585, + 0.895, + 0.75 + ], + "angle": 0, + "content": "Denoising diffusion probabilistic models. Denoising diffusion probabilistic models (diffusion models) [17, 39, 41] have recently achieved significant results in image generation [8, 33] and audio synthesis [4, 21]. The idea of diffusion models is first proposed by DPM [39], which imitates the diffusion process in non-equilibrium statistical physics and reconstructs the data distribution using the denoising model. Later, [35, 44] propose diffusion models, combining with the seq-to-seq models, for probabilistic time series forecasting. MID [14] is the first to build diffusion models for trajectory prediction in modeling the indeterminacy variation process." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.897, + 0.901 + ], + "angle": 0, + "content": "The standard diffusion models use hundreds of denoising steps, preventing these models from real-time applications. To accelerate the sampling process, DDIM [40] first predicts the original data and then estimates the direction to the next expected timestamp based on the non-Markov process. PD [37] applies the knowledge distillation on the denoising steps with a deterministic diffusion sampler, which will be repeated for times to accelerate the sampling. All these fast sampling methods start denoising from noise inputs, which are randomly and independently initialized. In this work, we" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5518" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.138 + ], + "angle": 0, + "content": "use a trainable leapfrog initializer to initialize a sufficiently expressive distribution, which replaces a large number of former denoising steps for much faster inference speed." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.153, + 0.206, + 0.169 + ], + "angle": 0, + "content": "3. Background" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.178, + 0.28, + 0.193 + ], + "angle": 0, + "content": "3.1. Problem Formulation" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.202, + 0.47, + 0.382 + ], + "angle": 0, + "content": "Trajectory prediction aims to predict an agent's future trajectory based on the past trajectories of itself and surrounding agents. For a to-be-predicted agent, let \\(\\mathbf{X} = [\\mathbf{x}^{-T_{\\mathrm{p}} + 1},\\mathbf{x}^{-T_{\\mathrm{p}} + 2},\\dots ,\\mathbf{x}^{0}] \\in \\mathbb{R}^{T_{\\mathrm{p}} \\times 2}\\) be the observed past trajectory over \\(T_{\\mathrm{p}}\\) timestamps where \\(\\mathbf{x}^t \\in \\mathbb{R}^2\\) records the 2D spatial coordinate at timestamp \\(t\\). Let \\(\\mathcal{N}\\) be the neighbouring agent set and \\(\\mathbb{X}_{\\mathcal{N}} = [\\mathbf{X}_{\\mathcal{N}_1},\\mathbf{X}_{\\mathcal{N}_2},\\dots ,\\mathbf{X}_{\\mathcal{N}_L}] \\in \\mathbb{R}^{L \\times T_{\\mathrm{p}} \\times 2}\\) be the past trajectories of neighbours, where \\(\\mathbf{X}_{\\mathcal{N}_\\ell} \\in \\mathbb{R}^{T_{\\mathrm{p}} \\times 2}\\) is the trajectory of the \\(\\ell\\)th neighbour. The corresponding ground-truth future trajectory for the to-be-predicted agent is \\(\\mathbf{Y} = [\\mathbf{y}^1,\\mathbf{y}^2,\\dots,\\mathbf{y}^{T_{\\mathrm{f}}}] \\in \\mathbb{R}^{T_{\\mathrm{f}} \\times 2}\\) over \\(T_{\\mathrm{f}}\\) timestamps, where \\(\\mathbf{y}^t \\in \\mathbb{R}^2\\) is the 2D coordinate at future timestamp \\(t\\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.384, + 0.47, + 0.55 + ], + "angle": 0, + "content": "Because of the indeterminacy of future trajectories, it is usually more reliable to predict more than one trajectory to capture multiple possibilities. Here we consider stochastic trajectory prediction, which predicts the distribution of a future trajectory, instead of a single future trajectory. The goal of stochastic trajectory prediction is to train a prediction model \\(g_{\\theta}(\\cdot)\\) with parameters \\(\\theta\\) to generate a distribution \\(\\mathcal{P}_{\\theta} = g_{\\theta}(\\mathbf{X},\\mathbb{X}_{\\mathcal{N}})\\). Based on this distribution \\(\\mathcal{P}_{\\theta}\\), we can draw \\(K\\) samples, \\(\\widehat{\\mathcal{Y}} = \\{\\widehat{\\mathbf{Y}}_1,\\widehat{\\mathbf{Y}}_2,\\dots ,\\widehat{\\mathbf{Y}}_K\\}\\), so that at least one sample is close to the ground-truth future trajectory. The overall learning problem is" + }, + { + "type": "equation", + "bbox": [ + 0.128, + 0.553, + 0.47, + 0.582 + ], + "angle": 0, + "content": "\\[\n\\theta^ {*} = \\min _ {\\theta} \\min _ {\\widehat {\\mathbf {Y}} _ {i} \\in \\widehat {\\mathcal {Y}}} D (\\widehat {\\mathbf {Y}} _ {i}, \\mathbf {Y}), \\quad \\text {s . t .} \\quad \\widehat {\\mathcal {Y}} \\sim \\mathcal {P} _ {\\theta}. \\tag {1}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.592, + 0.434, + 0.608 + ], + "angle": 0, + "content": "3.2. Diffusion Model for Trajectory Prediction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.615, + 0.47, + 0.751 + ], + "angle": 0, + "content": "Here we present a standard diffusion model for trajectory prediction, which lays a foundation for the proposed method. The core idea is to learn and refine a sophisticated underlying distribution of trajectories through cascading a series of simple denoising steps. To implement this, a diffusion model performs a forward diffusion process to intentionally add a series of noises to a ground-truth future trajectory; and then, it uses a conditional denoising process to recover the future trajectory from noise inputs conditioned on past trajectories." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.752, + 0.47, + 0.812 + ], + "angle": 0, + "content": "Mathematically, let \\(\\mathbf{X}\\) and \\(\\mathbb{X}_{\\mathcal{N}}\\) be the past trajectories of the ego agent and the neighboring agents, respectively, and \\(\\mathbf{Y}\\) be the future trajectory of the ego agent. The diffusion model for trajectory prediction works as follows," + }, + { + "type": "equation", + "bbox": [ + 0.095, + 0.814, + 0.47, + 0.83 + ], + "angle": 0, + "content": "\\[\n\\mathbf {Y} ^ {0} = \\mathbf {Y}, \\tag {2a}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.095, + 0.836, + 0.469, + 0.851 + ], + "angle": 0, + "content": "\\[\n\\mathbf {Y} ^ {\\gamma} = f _ {\\text {d i f f u s e}} \\left(\\mathbf {Y} ^ {\\gamma - 1}\\right), \\gamma = 1, \\dots , \\Gamma , \\tag {2b}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.095, + 0.857, + 0.469, + 0.875 + ], + "angle": 0, + "content": "\\[\n\\widehat {\\mathbf {Y}} _ {k} ^ {\\Gamma} \\stackrel {i. i. d} {\\sim} \\mathcal {P} (\\widehat {\\mathbf {Y}} ^ {\\Gamma}) = \\mathcal {N} (\\widehat {\\mathbf {Y}} ^ {\\Gamma}; \\mathbf {0}, \\mathbf {I}), \\text {s a m p l e} K \\text {t i m e s}, \\tag {2c}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.095, + 0.88, + 0.469, + 0.898 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathbf {Y}} _ {k} ^ {\\gamma} = f _ {\\text {d e n o i s e}} \\left(\\hat {\\mathbf {Y}} _ {k} ^ {\\gamma + 1}, \\mathbf {X}, \\mathbb {X} _ {\\mathcal {N}}\\right), \\gamma = \\Gamma - 1, \\dots , 0, \\tag {2d}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.892, + 0.154 + ], + "angle": 0, + "content": "where \\(\\mathbf{Y}^{\\gamma}\\) is the noisy trajectory at the \\(\\gamma\\)th diffusion step and \\(\\widehat{\\mathbf{Y}}_k^\\gamma\\) is the \\(k\\)th sample of denoised trajectory at the \\(\\gamma\\)th denoising step. The final \\(K\\) predicted trajectories are \\(\\widehat{\\mathcal{V}} = \\{\\widehat{\\mathbf{Y}}_1^0, \\widehat{\\mathbf{Y}}_2^0, \\ldots, \\widehat{\\mathbf{Y}}_K^0\\}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.155, + 0.894, + 0.351 + ], + "angle": 0, + "content": "Step (2a) initializes the diffused trajectory; Step (2b) uses a forward diffusion operation \\( f_{\\mathrm{diffuse}}(\\cdot) \\) to successively add noises to \\( \\mathbf{Y}^{\\gamma - 1} \\) and obtain the diffused trajectory \\( \\mathbf{Y}^{\\gamma} \\); Step (2c) draws \\( K \\) independent and identically distributed samples to initialize denoised trajectories \\( \\widehat{\\mathbf{Y}}_k^\\Gamma \\) from a normal distribution; and Step (2d) iteratively applies a denoising operation \\( f_{\\mathrm{denoise}}(\\cdot) \\) to obtain the denoised trajectory \\( \\widehat{\\mathbf{Y}}_k^\\gamma \\) conditioned on past trajectories \\( \\mathbf{X}, \\mathbb{X}_{\\mathcal{N}} \\). Note that i) Steps (2a) and (2b) correspond to the forward diffusion process and are not used in inference; ii) During training, \\( \\mathbf{Y}^{\\gamma} \\) is naturally the supervision for \\( \\widehat{\\mathbf{Y}}_k^\\gamma \\) at the \\( \\gamma \\)th step. Conceptually, each denoising step is the reverse of the diffusion step, and each pair of \\( \\mathbf{Y}^{\\gamma} \\) and \\( \\widehat{\\mathbf{Y}}_k^\\gamma \\) shares the same underlying distribution." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.352, + 0.894, + 0.518 + ], + "angle": 0, + "content": "The standard diffusion model is expressively powerful in learning sophisticated distributions and has achieved great success in many generation tasks. However, the task of motion prediction requires real-time inference but the running time of a diffusion model is constrained by the large number of denoising steps. Meanwhile, less denoising steps usually cause a weaker representation ability of future distributions. To achieve higher efficiency while preserving a promising representation ability, we propose leapfrog diffusion model, which uses a trainable initializer to capture sophisticated distributions and substitute a large number of denoising steps." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.533, + 0.742, + 0.55 + ], + "angle": 0, + "content": "4. Leapfrog Diffusion Model" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.558, + 0.694, + 0.573 + ], + "angle": 0, + "content": "4.1. System Architecture" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.581, + 0.894, + 0.717 + ], + "angle": 0, + "content": "In this section, we propose the leapfrog diffusion model. Here leapfrog means that a large number of small denoising steps can be replaced by a single, yet powerful leapfrog initializer, which can significantly accelerate the inference speed without losing representation ability. Let \\(\\mathbf{X}\\) and \\(\\mathbb{X}_{\\mathcal{N}}\\) be the past trajectories of the ego agent and its neighboring agents, and \\(\\mathbf{Y}\\) be the future trajectory of the ego agent. Denote \\(\\tau\\) as the leapfrog step. The overall procedure of the proposed leapfrog diffusion model is formulated as follows," + }, + { + "type": "equation", + "bbox": [ + 0.521, + 0.726, + 0.892, + 0.741 + ], + "angle": 0, + "content": "\\[\n\\mathbf {Y} ^ {0} = \\mathbf {Y}, \\tag {3a}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.521, + 0.747, + 0.892, + 0.762 + ], + "angle": 0, + "content": "\\[\n\\mathbf {Y} ^ {\\gamma} = f _ {\\text {d i f f u s e}} \\left(\\mathbf {Y} ^ {\\gamma - 1}\\right), \\gamma = 1, \\dots , \\Gamma , \\tag {3b}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.521, + 0.768, + 0.892, + 0.786 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathcal {Y}} ^ {\\tau} \\stackrel {K} {\\sim} \\mathcal {P} \\left(\\hat {\\mathbf {Y}} ^ {\\tau}\\right) = f _ {\\text {L S G}} \\left(\\mathbf {X}, \\mathbb {X} _ {\\mathcal {N}}\\right), \\tag {3c}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.521, + 0.79, + 0.892, + 0.809 + ], + "angle": 0, + "content": "\\[\n\\widehat {\\mathbf {Y}} _ {k} ^ {\\gamma} = f _ {\\text {d e n o i s e}} \\left(\\widehat {\\mathbf {Y}} _ {k} ^ {\\gamma + 1}, \\mathbf {X}, \\mathbb {X} _ {\\mathcal {N}}\\right), \\gamma = \\tau - 1, \\dots , 0. \\tag {3d}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.811, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Compared to the standard diffusion model (2), the main difference lies in Step (3c). The standard diffusion initializes the \\(\\Gamma\\)th denoised distribution \\(\\mathcal{P}(\\widehat{\\mathbf{Y}}^{\\Gamma})\\) by a plain normal distribution (2c) and requires a lot of denoising steps to enrich the expressiveness of the denoised distribution; while in Step (3c), we propose a novel leapfrog initial" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5519" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.113, + 0.055, + 0.868, + 0.205 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.208, + 0.895, + 0.252 + ], + "angle": 0, + "content": "Figure 2. Proposed leapfrog diffusion model (LED) in inference phase. The red agent is the to-be-predicted agent. LED first predicts \\( K \\) initialized trajectories at \\( \\tau \\)th denoised step through a trainable leapfrog initializer. Then, followed by a few denoising steps, LED obtains the final predictions. In leapfrog initializer, LED learns statistics and generates correlated samples with the reparameterization." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.261, + 0.473, + 0.406 + ], + "angle": 0, + "content": "izer \\(f_{\\mathrm{LSG}}(\\cdot)\\) to directly model the \\(\\tau\\)th denoised distribution \\(\\mathcal{P}(\\widehat{\\mathbf{Y}}^{\\tau})\\), which is hypothetically equivalent to the output of executing \\((\\Gamma - \\tau)\\) denoising steps (2d). We then draw samples from the distribution \\(\\mathcal{P}(\\widehat{\\mathbf{Y}}^{\\tau})\\) and obtain \\(K\\) future trajectories \\(\\widehat{\\mathcal{Y}}^{\\tau} = \\{\\widehat{\\mathbf{Y}}_1^{\\tau}, \\widehat{\\mathbf{Y}}_2^{\\tau}, \\dots, \\widehat{\\mathbf{Y}}_K^{\\tau}\\}\\), where \\(\\stackrel{K}{\\sim}\\) in (3d) means \\(K\\) samples are dependent to intentionally allocate appropriate sample diversity. Then, in Step (3d), we only need to apply the remaining \\(\\tau\\) denoising steps for each trajectory \\(\\widehat{\\mathbf{Y}}_k^\\gamma\\) to obtain the final prediction \\(\\widehat{\\mathcal{Y}} = \\{\\widehat{\\mathbf{Y}}_1^0, \\widehat{\\mathbf{Y}}_2^0, \\dots, \\widehat{\\mathbf{Y}}_K^0\\}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.407, + 0.474, + 0.573 + ], + "angle": 0, + "content": "Note that i) the proposed leapfrog diffusion model reduces the denoising steps from \\(\\Gamma\\) to \\(\\tau (\\ll \\Gamma)\\) in Step (3d) as the leapfrog initializer directly provides the trajectories at denoising step \\(\\tau\\), accelerating the inference; ii) instead of taking independent and identically distributed samples in Step (2c), the proposed leapfrog initializer generates \\(K\\) trajectories \\(\\widehat{\\mathcal{Y}}^{\\tau}\\) simultaneously in Step (3c), allowing \\(K\\) samples to be aware of each other; and iii) the standard diffusion model and the proposed leapfrog diffusion model share the same forward diffusion process, assuring that the representation capacity is not reduced." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.588, + 0.266, + 0.604 + ], + "angle": 0, + "content": "4.2. Leapfrog Initializer" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.613, + 0.472, + 0.81 + ], + "angle": 0, + "content": "We now dive into the design details of the proposed leapfrog initializer, which leapfrogs \\((\\Gamma - \\tau)\\) denoising steps. In leapfrog initializer, we model the \\(\\tau\\)th denoised distribution \\(\\mathcal{P}(\\widehat{\\mathbf{Y}}^{\\tau})\\) through learning models. However, it is nontrivial for a learning model to directly capture the sophisticated distribution, which usually causes unstable training. To ease the learning burden of the model, we disassemble the distribution \\(\\mathcal{P}(\\widehat{\\mathbf{Y}}^{\\tau})\\) into three representative parts: the mean, global variance and sample prediction. For each part, we design trainable modules correspondingly. Mathematically, let \\(\\mathbf{X}\\) and \\(\\mathbb{X}_{\\mathcal{N}}\\) be the past trajectories of the ego agent and the neighboring agents, respectively. The proposed leapfrog initializer generates \\(K\\) samples as follows," + }, + { + "type": "equation", + "bbox": [ + 0.113, + 0.824, + 0.474, + 0.902 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mu_ {\\theta} = f _ {\\mu} (\\mathbf {X}, \\mathbb {X} _ {\\mathcal {N}}) \\in \\mathbb {R} ^ {T _ {t} \\times 2}, \\\\ \\sigma_ {\\theta} = f _ {\\sigma} (\\mathbf {X}, \\mathbb {X} _ {\\mathcal {N}}) \\in \\mathbb {R}, \\\\ \\widehat {\\mathbb {S}} _ {\\theta} = \\left[ \\widehat {\\mathbf {S}} _ {\\theta , 1}, \\dots , \\widehat {\\mathbf {S}} _ {\\theta , K} \\right] = f _ {\\widehat {\\mathbb {S}}} (\\mathbf {X}, \\mathbb {X} _ {\\mathcal {N}}, \\sigma_ {\\theta}) \\in \\mathbb {R} ^ {T _ {\\mathrm {f}} \\times 2 \\times K}, \\\\ \\widehat {\\mathbf {Y}} _ {k} ^ {\\tau} = \\mu_ {\\theta} + \\sigma_ {\\theta} \\cdot \\widehat {\\mathbf {S}} _ {\\theta , k} \\in \\mathbb {R} ^ {T _ {\\mathrm {f}} \\times 2}, \\tag {4} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.261, + 0.894, + 0.31 + ], + "angle": 0, + "content": "where \\(f_{\\mu}(\\cdot), f_{\\sigma}(\\cdot), f_{\\widehat{\\mathbb{S}}}(\\cdot)\\) are three trainable modules, \\(\\mu_{\\theta}, \\sigma_{\\theta}\\) are the mean and standard deviation of \\(\\mathcal{P}(\\widehat{\\mathbf{Y}}^{\\tau})\\), respectively, and \\(\\widehat{\\mathbf{S}}_{\\theta,k}\\) is the normalized positions for the \\(k\\)th sample." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.311, + 0.893, + 0.467 + ], + "angle": 0, + "content": "To be specific, the mean estimate module \\(f_{\\mu}(\\cdot)\\) infers the mean trajectory of the \\(\\tau\\)th denoised distribution \\(\\widehat{\\mathcal{P}}(\\widehat{\\mathbf{Y}}^{\\tau})\\) with past trajectories \\((\\mathbf{X}, \\mathbb{X}_{\\mathcal{N}})\\). The mean trajectory \\(\\mu_{\\theta}\\) is shared across all the \\(K\\) samples. The variance estimate module \\(f_{\\sigma}(\\cdot)\\) infers the standard deviation of the \\(\\tau\\)th denoised distribution \\(\\widehat{\\mathcal{P}}(\\widehat{\\mathbf{Y}}^{\\tau})\\), reflecting the overall uncertainty of the trajectory, which is also shared across all the \\(K\\) samples. The sample prediction module \\(f_{\\widehat{\\mathbb{S}}}(\\cdot)\\) takes the past trajectories \\((\\mathbf{X}, \\mathbb{X}_{\\mathcal{N}})\\) and the predicted uncertainty \\(\\sigma_{\\theta}\\) as the input and predicts \\(K\\) normalized positions where each \\(\\widehat{\\mathbf{S}}_{\\theta,k} \\in \\mathbb{R}^{T_{\\mathrm{f}} \\times 2}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.467, + 0.894, + 0.557 + ], + "angle": 0, + "content": "Note that i) the reparameterization in Eq. (4) allows us to avoid learning a raw sophisticated distribution, making the training much easier; and ii) \\(K\\) normalized predictions are generated simultaneously from the same underlying feature, assuring appropriately allocated trajectories with variance estimation and better capturing the multi-modalities." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.557, + 0.894, + 0.663 + ], + "angle": 0, + "content": "To implement the three trainable modules: \\( f_{\\mu}(\\cdot), f_{\\sigma}(\\cdot), f_{\\widehat{\\mathbb{S}}}(\\cdot) \\), we consider a similar network design: a social encoder to capture social influence, a temporal encoder to learn temporal embedding, and an aggregation layer to fuse both social and temporal information; see Figure 2. Here we take the mean estimation module \\( f_{\\mu}(\\cdot) \\) as an example. The mean trajectory is obtained as follows," + }, + { + "type": "equation", + "bbox": [ + 0.527, + 0.668, + 0.892, + 0.744 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathbf {e} _ {\\mu_ {\\theta}} ^ {\\text {s o c i a l}} = \\operatorname {s o f t m a x} \\left(\\frac {f _ {\\mathrm {q}} (\\mathbf {X}) f _ {\\mathrm {k}} (\\mathbb {X} _ {\\mathcal {N}}) ^ {\\top}}{\\sqrt {d}}\\right) f _ {\\mathrm {v}} (\\mathbb {X} _ {\\mathcal {N}}), (5a) \\\\ \\mathbf {e} _ {\\mu_ {\\theta}} ^ {\\text {t e m p}} = f _ {\\mathrm {G R U}} \\left(f _ {\\operatorname {c o n v 1 D}} (\\mathbf {X})\\right), (5b) \\\\ \\mu_ {\\theta} = f _ {\\text {f u s i o n}} \\left(\\left[ \\mathbf {e} _ {\\mu_ {\\theta}} ^ {\\text {s o c i a l}}: \\mathbf {e} _ {\\mu_ {\\theta}} ^ {\\text {t e m p}} \\right]\\right). (5c) \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.749, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Step (5a) obtains the social embedding \\(\\mathbf{e}_{\\mu_{\\theta}}^{\\mathrm{social}}\\) based on the multi-head attention with \\(d\\) the embedding dimension and \\(f_{\\mathrm{q}}(\\cdot), f_{\\mathrm{k}}(\\cdot), f_{\\mathrm{v}}(\\cdot)\\) the query/key/value embedding functions. Step (5b) obtains the temporal embedding through the feature encoder \\(f_{\\mathrm{conv1D}}(\\cdot)\\), mapping the raw coordinates into the high-dimensional feature, followed by the gated recurrent units \\(f_{\\mathrm{GRU}}(\\cdot)\\), capturing the temporal dependence in the high dimensional sequence. Step (5c) concatenates both social and temporal embeddings and uses a multi-layer perceptron \\(f_{\\mathrm{fusion}}(\\cdot)\\) to obtain the final mean estimation. Note" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5520" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.123 + ], + "angle": 0, + "content": "that the sample prediction module \\( f_{\\widehat{\\mathbb{S}}}(\\cdot) \\) also takes the estimated standard deviation as the input, working as" + }, + { + "type": "equation", + "bbox": [ + 0.151, + 0.132, + 0.284, + 0.152 + ], + "angle": 0, + "content": "\\[\n\\mathbf {e} _ {\\hat {\\mathfrak {S}} _ {\\theta}} ^ {\\sigma} = f _ {\\mathrm {e n c o d e}} (\\sigma_ {\\theta}),\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.154, + 0.155, + 0.394, + 0.177 + ], + "angle": 0, + "content": "\\[\n\\widehat {\\mathbb {S}} _ {\\theta} = f _ {\\mathrm {f u s i o n}} ([ \\mathbf {e} _ {\\widehat {\\mathbb {S}} _ {\\theta}} ^ {\\mathrm {s o c i a l}}: \\mathbf {e} _ {\\widehat {\\mathbb {S}} _ {\\theta}} ^ {\\mathrm {t e m p}}: \\mathbf {e} _ {\\widehat {\\mathbb {S}} _ {\\theta}} ^ {\\sigma} ]),\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.187, + 0.47, + 0.248 + ], + "angle": 0, + "content": "where an encoder \\(f_{\\mathrm{encode}}(\\cdot)\\) operates on the estimated variance \\(\\sigma_{\\theta}\\) and generates high dimensional embedding \\(\\mathbf{e}_{\\hat{\\mathbb{S}}_{\\theta}}^{\\sigma}\\). By this, the variance estimation also involves in the sample prediction process, instead of just scaling these prediction." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.249, + 0.472, + 0.296 + ], + "angle": 0, + "content": "After obtaining \\(K\\) samples \\(\\widehat{y}^{\\tau} = \\{\\widehat{\\mathbf{Y}}_1^\\tau ,\\widehat{\\mathbf{Y}}_2^\\tau ,\\dots ,\\widehat{\\mathbf{Y}}_K^\\tau \\}\\) from leapfrog initializer, we execute the remaining \\(\\tau\\) denoising steps to iteratively refine those predicted trajectories (3d)." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.304, + 0.254, + 0.32 + ], + "angle": 0, + "content": "4.3. Denoising Module" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.327, + 0.473, + 0.435 + ], + "angle": 0, + "content": "Here we elaborate the design of a denoising module \\(f_{\\mathrm{denoise}}(\\cdot)\\), which denoises the trajectory \\(\\widehat{\\mathbf{Y}}_k^{\\gamma +1}\\) conditioned on past trajectories \\((\\mathbf{X},\\mathbb{X}_{\\mathcal{N}})\\). In a denoising module, two parts are trainable: a transformer-based context encoder \\(f_{\\mathrm{context}}(\\cdot)\\) to learn a social-temporal embedding and a noise estimation module \\(f_{\\epsilon}(\\cdot)\\) to estimate the noise to reduce. Mathematically, the \\(\\gamma\\)th denoising step works as follows," + }, + { + "type": "equation", + "bbox": [ + 0.104, + 0.447, + 0.47, + 0.464 + ], + "angle": 0, + "content": "\\[\n\\mathbf {C} = f _ {\\text {c o n t e x t}} (\\mathbf {X}, \\mathbb {X} _ {\\mathcal {N}}), \\tag {6a}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.105, + 0.467, + 0.47, + 0.487 + ], + "angle": 0, + "content": "\\[\n\\epsilon_ {\\theta} ^ {\\gamma} = f _ {\\epsilon} \\left(\\widehat {\\mathbf {Y}} _ {k} ^ {\\gamma + 1}, \\mathbf {C}, \\gamma + 1\\right), \\tag {6b}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.105, + 0.489, + 0.47, + 0.523 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathbf {Y}} _ {k} ^ {\\gamma} = \\frac {1}{\\sqrt {\\alpha_ {\\gamma}}} \\left(\\hat {\\mathbf {Y}} _ {k} ^ {\\gamma + 1} - \\frac {1 - \\alpha_ {\\gamma}}{\\sqrt {1 - \\bar {\\alpha} _ {\\gamma}}} \\boldsymbol {\\epsilon} _ {\\theta} ^ {\\gamma}\\right) + \\sqrt {1 - \\alpha_ {\\gamma}} \\mathbf {z}, \\quad (6 c)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.526, + 0.472, + 0.665 + ], + "angle": 0, + "content": "where \\(\\alpha_{\\gamma}\\) and \\(\\bar{\\alpha}_{\\gamma} = \\prod_{i=1}^{\\gamma} \\alpha_{i}\\) are parameters in the diffusion process and \\(\\mathbf{z} \\sim \\mathcal{N}(\\mathbf{z}; \\mathbf{0}, \\mathbf{I})\\) is a noise. Step (6a) uses a context encoder \\(f_{\\mathrm{context}}(\\cdot)\\) on past trajectories \\((\\mathbf{X}, \\mathbb{X}_{\\mathcal{N}})\\) to obtain the context condition \\(\\mathbf{C}\\), which shares a similar structure to mean estimation module \\(f_{\\mu}(\\cdot)\\); Step (6b) estimates the noise \\(\\epsilon_{\\theta}^{\\gamma}\\) in the noisy trajectory \\(\\widehat{\\mathbf{Y}}_k^{\\gamma+1}\\) through noise estimation \\(f_{\\epsilon}(\\cdot)\\) implemented by multi-layer perceptions with the context \\(\\mathbf{C}\\); Step (6c) provides a standard denoising step [17]; see more details in the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.673, + 0.26, + 0.69 + ], + "angle": 0, + "content": "4.4. Training Objective" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.697, + 0.47, + 0.788 + ], + "angle": 0, + "content": "To train a leapfrog diffusion model, we consider a two-stage training strategy, where the first stage trains a denoising module and the second stage focuses on a leapfrog initializer. The reason to use two stages is because the training of leapfrog initializer is more stable given fixed distribution \\(\\mathcal{P}(\\widehat{\\mathbf{Y}}^{\\tau})\\), avoiding non-convergent training." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.788, + 0.47, + 0.833 + ], + "angle": 0, + "content": "Concretely, the first stage trains a denoising module \\( f_{\\mathrm{denoise}}(\\cdot) \\) in Step (3d) based on a standard training schedule of a diffusion model [14, 17] through noise estimation loss:" + }, + { + "type": "equation", + "bbox": [ + 0.085, + 0.843, + 0.428, + 0.861 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {N E}} = \\| \\boldsymbol {\\epsilon} - f _ {\\boldsymbol {\\epsilon}} (\\mathbf {Y} ^ {\\gamma + 1}, f _ {\\text {c o n t e x t}} (\\mathbf {X}, \\mathbb {X} _ {\\mathcal {N}}), \\gamma + 1) \\| _ {2},\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.87, + 0.473, + 0.903 + ], + "angle": 0, + "content": "where \\(\\gamma \\sim \\mathrm{U}\\{1,2,\\dots ,\\Gamma \\}\\) \\(\\epsilon \\sim \\mathcal{N}(\\epsilon ;\\mathbf{0},\\mathbf{I})\\) and the diffused trajectory \\(\\mathbf{Y}^{\\gamma +1} = \\sqrt{\\bar{\\alpha}_{\\gamma}}\\mathbf{Y}^{0} + \\sqrt{1 - \\bar{\\alpha}_{\\gamma}}\\pmb {\\epsilon}\\) . We then back" + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.091, + 0.85, + 0.107 + ], + "angle": 0, + "content": "Algorithm 1 Leapfrog Diffusion Model in Inference" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.111, + 0.858, + 0.126 + ], + "angle": 0, + "content": "Input: Observed trajectories \\(\\mathbf{X}\\), \\(\\mathbb{X}_{\\mathcal{N}}\\), Leapfrog step \\(\\tau\\)" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.127, + 0.725, + 0.143 + ], + "angle": 0, + "content": "Output: Predicted trajectories \\(\\hat{\\mathcal{V}}\\)" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.145, + 0.892, + 0.161 + ], + "angle": 0, + "content": "1: \\(\\mu_{\\theta} = f_{\\mu}(\\mathbf{X},\\mathbb{X}_{\\mathcal{N}})\\) Mean estimation" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.163, + 0.892, + 0.178 + ], + "angle": 0, + "content": "2: \\(\\sigma_{\\theta} = f_{\\sigma}(\\mathbf{X},\\mathbb{X}_{\\mathcal{N}})\\) \\(\\triangleright\\) Variance estimation" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.179, + 0.892, + 0.196 + ], + "angle": 0, + "content": "3: \\(\\widehat{\\mathbb{S}}_{\\theta} = f_{\\widehat{\\mathbb{S}}}(\\mathbf{X},\\mathbb{X}_{\\mathcal{N}},\\sigma_{\\theta})\\) ▷ Sample prediction" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.197, + 0.892, + 0.213 + ], + "angle": 0, + "content": "4: \\(\\widehat{\\mathbf{Y}}_k^\\tau = \\mu_\\theta +\\sigma_\\theta \\cdot \\widehat{\\mathbf{S}}_{\\theta ,k},k = 1,\\dots ,K\\ntriangleright\\) Reparameterization" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.215, + 0.684, + 0.23 + ], + "angle": 0, + "content": "5: for \\(\\gamma = \\tau - 1, \\dots, 0\\) do" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.23, + 0.892, + 0.248 + ], + "angle": 0, + "content": "6: \\(\\widehat{\\mathbf{Y}}_k^\\gamma = f_{\\mathrm{denoise}}(\\widehat{\\mathbf{Y}}_k^{\\gamma +1},\\mathbf{X},\\mathbb{X}_{\\mathcal{N}})\\) Denoising step" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.25, + 0.585, + 0.263 + ], + "angle": 0, + "content": "7: end for" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.264, + 0.712, + 0.283 + ], + "angle": 0, + "content": "8: \\(\\widehat{\\mathcal{Y}} = \\widehat{\\mathcal{Y}}^0 = \\{\\widehat{\\mathbf{Y}}_1^0,\\dots ,\\widehat{\\mathbf{Y}}_K^0\\}\\)" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.284, + 0.594, + 0.299 + ], + "angle": 0, + "content": "9: return \\(\\hat{y}\\)" + }, + { + "type": "list", + "bbox": [ + 0.511, + 0.145, + 0.892, + 0.299 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.329, + 0.892, + 0.36 + ], + "angle": 0, + "content": "propagate this loss and train the parameters in the context encoder \\( f_{\\mathrm{context}}(\\cdot) \\) and the noise estimation module \\( f_{\\epsilon}(\\cdot) \\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.36, + 0.894, + 0.405 + ], + "angle": 0, + "content": "In the second stage, we optimize a leapfrog diffusion model with a trainable leapfrog initializer and frozen denoising modules. For each sample, the loss function is" + }, + { + "type": "equation", + "bbox": [ + 0.5, + 0.417, + 0.892, + 0.472 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} = \\mathcal {L} _ {\\text {d i s t a n c e}} + \\mathcal {L} _ {\\text {u n c e r t a i n t y}} \\\\ { = } { w \\cdot \\operatorname* { m i n } _ { k } \\| \\mathbf { Y } - \\widehat { \\mathbf { Y } } _ { k } \\| _ { 2 } + \\Big ( \\frac { \\sum _ { k } \\| \\mathbf { Y } - \\widehat { \\mathbf { Y } } _ { k } \\| _ { 2 } } { \\sigma _ { \\theta } ^ { 2 } K } + \\log \\sigma _ { \\theta } ^ { 2 } \\Big ) , } \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.482, + 0.894, + 0.702 + ], + "angle": 0, + "content": "where \\( w \\in \\mathbb{R} \\) is a hyperparameter weight. The first term constrains the minimum distance in \\( K \\) predictions. Intuitively, if a leapfrog initializer generates high-quality estimations for distribution \\( \\mathcal{P}(\\widehat{\\mathbf{Y}}^{\\tau}) \\), then one of the \\( K \\) predictions in \\( \\widehat{\\mathcal{V}} \\) should be close to the ground-truth trajectory \\( \\mathbf{Y} \\). The second term normalizes the variance estimation \\( \\sigma_{\\theta} \\) in reparameterization (4) through an uncertainty loss, balancing the prediction diversity and mean accuracy. Note that the variance estimation controls the dispersion of the predictions, bridging scenery complexity and prediction diversity. The first part \\( \\frac{\\sum_k\\|\\mathbf{Y}\\widehat{\\mathbf{Y}}_k\\|_2}{\\sigma_\\theta^2K} \\) makes the value of \\( \\sigma_{\\theta} \\) proportional to the complexity of the scenario. The second part \\( \\log \\sigma_{\\theta}^{2} \\) is a regulariser used to avoid a trivial solution for \\( \\sigma_{\\theta} \\), i.e., generating high variance for all predictions." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.704, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Technically, we can also explicitly supervise the estimation of leapfrog initializer in stage two, since the distribution \\(\\mathcal{P}(\\widehat{\\mathbf{Y}}^{\\tau})\\) can be denoised from a normal distribution. For the explicit supervision, we draw \\(M\\gg K\\) samples from \\(\\mathcal{P}(\\widehat{\\mathbf{Y}}^{\\Gamma})\\) under the normal distribution and iteratively denoise these samples through Step (2d) until we get expected denoised trajectories \\(\\widehat{\\mathbf{Y}}^{\\tau}\\). And then, we calculate the statistics of the denoised distribution \\(\\mathcal{P}(\\widehat{\\mathbf{Y}}^{\\tau})\\) using these \\(M\\) samples, serving as explicit supervisions for mean estimation \\(f_{\\mu}(\\cdot)\\) and variance estimation \\(f_{\\sigma}(\\cdot)\\). However, since \\(\\tau \\ll \\Gamma\\), we need to run \\((\\Gamma -\\tau)\\approx \\Gamma\\)-steps denoising for \\(M\\gg K\\) samples to get statistics, resulting in unacceptable time and storage consumption for training (e.g. \\(\\sim 6\\) days per epoch on NBA" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "5521" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.073, + 0.894, + 0.101 + ], + "angle": 0, + "content": "Table 1. Comparison with baseline models on NBA dataset. minADE20 /minFDE20 (meters) are reported. Bold/underlined fonts represent the best/second-best result. Compared to the previous SOTA method, MID, our method achieves a \\(15.6\\% /13.4\\%\\) ADE/FDE improvement." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.102, + 0.887, + 0.194 + ], + "angle": 0, + "content": "
TimeSocial-GAN [15] CVPR'18STGAT [19] ICCV'19Social-STGCNN [31] CVPR'20PECNet [27] ECCV'20STAR [52] ECCV'20Trajectory++[38] ECCV'20MemoNet [50] CVPR'22NPSN [2] CVPR'22GroupNet [49] CVPR'22MID [14] CVPR'22Ours
1.0s0.41/0.620.35/0.510.34/0.480.40/0.710.43/0.660.30/0.380.38/0.560.35/0.580.26/0.340.28/0.370.18/0.27
2.0s0.81/1.320.73/1.100.71/0.940.83/1.610.75/1.240.59/0.820.71/1.140.68/1.230.49/0.700.51/0.720.37/0.56
3.0s1.19/1.941.04/1.751.09/1.771.27/2.441.03/1.510.85/1.241.00/1.571.01/1.760.73/1.020.71/0.980.58/0.84
Total(4.0s)1.59/2.411.40/2.181.53/2.261.69/2.951.13/2.011.15/1.571.25/1.471.31/1.790.96/1.300.96/1.270.81/1.10
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.197, + 0.893, + 0.224 + ], + "angle": 0, + "content": "Table 2. Comparison with baseline models on NFL dataset. \\( \\mathrm{{minADE}}_{20}/\\mathrm{{minFDE}}_{20} \\) (meters) are reported. Bold/underlined fonts represent the best/second-best result. Compared to the previous SOTA method, MID, our method achieves a 23.7%/21.9% improvement." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.225, + 0.885, + 0.306 + ], + "angle": 0, + "content": "
TimeSocial-GAN [15] CVPR'18STGAT [19] ICCV'19Social-STGCNN [31] CVPR'20PECNet [27] ECCV'20STAR [52] ECCV'20Trajectron++[38] ECCV'20LB-EBM[34] CVPR'21NPSN [2] CVPR'22GroupNet[49] CVPR'22MID [14] CVPR'22Ours
1.0s0.37/0.680.35/0.640.45/0.640.52/0.970.49/0.840.41/0.650.75/1.050.43/0.640.32/0.570.30/0.580.21/0.34
2.0s0.83/1.530.82/1.601.06/1.871.19/2.471.02/1.840.93/1.651.26/2.280.83/1.520.73/1.390.71/1.310.49/0.91
Total(3.2s)1.44/2.511.39/2.481.82/3.181.99/3.841.51/2.971.54/2.581.90/3.251.32/2.271.21/2.151.14/1.920.87/1.50
" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.319, + 0.405, + 0.334 + ], + "angle": 0, + "content": "dataset). We thus do not use explicit supervision." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.344, + 0.238, + 0.359 + ], + "angle": 0, + "content": "4.5. Inference Phase" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.368, + 0.471, + 0.474 + ], + "angle": 0, + "content": "During the inference, instead of the \\(\\Gamma\\)-steps' denoising, leapfrog diffusion model only takes \\(\\tau\\)-steps, accelerating the inference. To be specific, we first generate \\(K\\) correlated samples to model the distribution \\(\\mathcal{P}(\\widetilde{\\mathbf{Y}}^{\\tau})\\) using the trained leapfrog initializer. Then, these samples will be fed into the denoising process and iteratively fine-tuned to produce the final predictions; see Algorithm 1." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.489, + 0.21, + 0.505 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.514, + 0.182, + 0.529 + ], + "angle": 0, + "content": "5.1. Datasets" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.537, + 0.47, + 0.597 + ], + "angle": 0, + "content": "We evaluate our method on four trajectory prediction datasets, including two sports datasets (NBA SportVU Dataset, NFL Football Dataset) and two pedestrian datasets (Stanford Drone Dataset, ETH-UCY)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.599, + 0.47, + 0.674 + ], + "angle": 0, + "content": "NBA SportVU Dataset (NBA): NBA trajectory dataset is collected by NBA using the SportVU tracking system, which records the trajectories of the 10 players and the ball in real basketball games. In this task, we predict the future 4.0s (20 frames) using the 2.0s (10 frames) past trajectory." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.674, + 0.47, + 0.749 + ], + "angle": 0, + "content": "NFL Football Dataset (NFL): NFL Football Dataset records the position of every player on the field during each play in the 2017 year. We predict the 22 players' (11 players per team) and the ball's future 3.2s (16 frames) trajectory using the historical 1.6s (8 frames) trajectory." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.47, + 0.825 + ], + "angle": 0, + "content": "Stanford Drone Dataset (SDD): SDD is a large-scale pedestrian dataset collected from a university campus in bird's eye view. Following previous works [27, 50], we use the standard train-test split and predict the future 4.8s (12 frames) using 3.2s (8 frames) past." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.471, + 0.902 + ], + "angle": 0, + "content": "ETH-UCY: ETH-UCY dataset contains 5 subsets: ETH, HOTEL, UNIV, ZARA1, and ZARA2, containing various motion scenes. We use same segment length of 8s as SDD following previous works [18, 27] and use the leave-one-out approach with four sets for training and a left set for testing." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.318, + 0.719, + 0.334 + ], + "angle": 0, + "content": "5.2. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.341, + 0.895, + 0.659 + ], + "angle": 0, + "content": "In the leapfrog diffusion model, we set the diffusion step \\(\\Gamma = 100\\) for all four datasets and the leapfrog step \\(\\tau = 5\\) on the NBA dataset. In the leapfrog initializer, we build a transformer-based social encoder where the feed-forward dimension is set to 256, the number of heads is 2, and 2 encoder layers are applied; we apply the temporal encoder with 1D convolution kernel being 3, and output channel setting to 32, and we also build a GRU with the hidden size of 256. In the denoising module, we apply the same parameters transformer to extract the context information, and we build the core denoising module with a hidden size of 256. To train the leapfrog diffusion model, we train the denoising module for 100 epochs with an initial learning rate of \\(10^{-2}\\) and decay to half every 16 epochs. With a frozen denoising module, we then train the leapfrog initializer for 200 epochs with an initial learning rate of \\(10^{-4}\\), decaying by 0.9 every 32 epochs. We set weight parameter \\(w_{1} = 50\\) to emphasize the distance loss. The entire framework is trained with the Adam optimizer on one GTX-3090 GPU. All models are implemented with PyTorch 1.7.1. See more details in the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.666, + 0.795, + 0.683 + ], + "angle": 0, + "content": "5.3. Comparison with SOTA Methods" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.895, + 0.825 + ], + "angle": 0, + "content": "We measure the performance of different trajectory prediction methods using two metrics: \\(\\min\\mathrm{ADE}_K\\) and \\(\\min\\mathrm{FDE}_K\\), following previous work [27, 49]. 1) \\(\\min\\mathrm{ADE}_K\\) calculates the minimum time-averaged distance among \\(K\\) predictions and the ground-truth future trajectory; 2) \\(\\min\\mathrm{FDE}_K\\) measures the minimum distance among the \\(K\\) predicted endpoints and the ground-truth endpoints. We calculate these two metrics at different timestamps on sports datasets to better evaluate the performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.897, + 0.9 + ], + "angle": 0, + "content": "NBA dataset. We compare our method with the current 10 state-of-the-art prediction methods at different timestamps; see Table 1. We see that i) our method significantly outperforms all baselines in ADE and FDE at all timestamps. Our method reduces the ADE/FDE at 4.0s from 0.96/1.27" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5522" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.073, + 0.892, + 0.102 + ], + "angle": 0, + "content": "Table 3. Comparison with baseline models on SDD dataset. minADE20/minFDE20 (meters) are reported. Bold/underlined fonts represent the best/second-best result. Our method achieves the best performance in ADE/FDE. * represents the reproduced results from open source." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.103, + 0.885, + 0.158 + ], + "angle": 0, + "content": "
TimeSocial-GAN [15] CVPR'18SOPHIE [36] CVPR'19Trajectory++ [38] ECCV'20NMMP [18] CVPR'20Evolve- Graph [25] NIPS'20PECNet [27] ECCV'20MemoNet [50] CVPR'22NPSN [2] CVPR'22GroupNet [49] CVPR'22MID* [14] CVPR'22Ours
4.8s27.23/41.4416.27/29.3819.30/32.7014.67/26.7213.90/22.909.96/15.888.56/12.668.56/11.859.31/16.119.73/15.328.48/11.66
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.16, + 0.891, + 0.188 + ], + "angle": 0, + "content": "Table 4. Comparison with baseline models on ETH-UCY dataset. minADE20/minFDE20 (meters) are reported. Bold/underlined fonts represent the best/second-best result. In most subsets, our method achieves the best or second-best performance in ADE/FDE." + }, + { + "type": "table", + "bbox": [ + 0.091, + 0.189, + 0.875, + 0.306 + ], + "angle": 0, + "content": "
SubsetSocial-GAN [15]CVPR'18NMMP [18]CVPR'20STAR [52]ECCV'20PECNet [27]ECCV'20Trajectory++[38]ECCV'20Agentformer[53]ICCV'21MemoNet[50]CVPR'22NPSN [2]CVPR'22GroupNet[49]CVPR'22MID [14]CVPR'22
ETH0.87/1.620.61/1.080.36/0.650.54/0.870.61/1.020.45/0.750.40/0.610.40/0.760.46/0.730.39/0.66
Hotel0.67/1.370.33/0.630.17/0.360.18/0.240.19/0.280.14/0.220.11/0.170.12/0.180.15/0.250.13/0.22
Univ0.76/1.520.52/1.110.31/0.620.35/0.600.30/0.540.25/0.450.24/0.430.22/0.410.26/0.490.22/0.45
Zara10.35/0.680.32/0.660.29/0.520.22/0.390.24/0.420.18/0.300.18/0.320.17/0.310.21/0.390.17/0.30
Zara20.42/0.840.43/0.850.22/0.460.17/0.300.18/0.320.14/0.240.14/0.240.12/0.240.17/0.330.13/0.27
AVG0.61/1.210.41/0.820.26/0.530.29/0.480.30/0.510.23/0.390.21/0.350.21/0.380.25/0.440.21/0.38
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.314, + 0.47, + 0.356 + ], + "angle": 0, + "content": "Table 5. Ablation of leapfrog initializer in the leapfrog diffusion model on NFL with various prediction numbers \\( K \\). Each module in the leapfrog initializer is beneficial." + }, + { + "type": "table", + "bbox": [ + 0.086, + 0.357, + 0.456, + 0.512 + ], + "angle": 0, + "content": "
Mean μθVariance σθSample ΜθK=2K=4
✓correlated2.04±0.18/4.08±0.481.63±0.13/3.05±0.16
✓correlated1.95±0.08/3.90±0.221.49±0.01/2.86±0.02
✓✓i.i.d2.36±0.13/4.31±0.221.90±0.07/3.31±0.05
✓✓correlated1.84±0.05/3.61±0.111.47±0.01/2.83±0.02
Mean μθVariance σθSample ΜθK=8K=20
✓correlated1.25±0.02/2.31±0.040.99±0.03/1.68±0.04
✓correlated1.23±0.01/2.20±0.010.95±0.01/1.54±0.02
✓✓i.i.d1.51±0.04/2.67±0.071.18±0.02/1.90±0.03
✓✓correlated1.18±0.01/2.19±0.010.89±0.01/1.51±0.02
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.533, + 0.47, + 0.609 + ], + "angle": 0, + "content": "to 0.81/1.10 compared to the current state-of-the-art methods, MID, achieving \\(15.6\\% / 13.4\\%\\) improvement; and ii) performance improvement over previous methods increases with timestamps, reflecting the proposed method can capture more sophisticated distributions at further timestamps." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.61, + 0.471, + 0.716 + ], + "angle": 0, + "content": "NFL dataset. We compare our method with the current 10 state-of-the-art prediction methods at different timestamps; see Table 2. We see that our model significantly outperforms all baselines in ADE and FDE at all timestamps. Our method reduces the ADE/FDE at 3.2s from 1.14/1.92 to 0.87/1.50 compared to the current state-of-the-art methods, MID, achieving \\(23.7\\% / 21.9\\%\\) improvement." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.718, + 0.47, + 0.809 + ], + "angle": 0, + "content": "SDD dataset. We compare our method with the current 10 state-of-the-art prediction methods; see Table 3. We see that our method reduces FDE from 11.85 to 11.66 compared to the current state-of-the-art method, NPSN. Notably, the original MID [14] uses a different protocol from all the other methods, we update its code for a fair comparison." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.471, + 0.901 + ], + "angle": 0, + "content": "ETH-UCY dataset. We compare our method with 10 state-of-the-art prediction methods; see Table 4. We see that i) our method reduces FDE from 0.35 to 0.33 compared to the current state-of-the-art method, MemoNet, achieving a \\(5.7\\%\\) improvement; and ii) our method achieves the best or second best to the best performance on most of the subsets." + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.314, + 0.892, + 0.343 + ], + "angle": 0, + "content": "Table 6. Different steps \\( \\Gamma /\\tau \\) in the standard/leapfrog diffusion model on NBA. \\( \\tau = 5 \\) provides the best performance." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.344, + 0.905, + 0.471 + ], + "angle": 0, + "content": "
MethodSteps1.0s2.0s3.0sTotal(4.0s)Inference (ms)
Standard100.45/0.510.98/1.551.62/2.562.21/2.77~87
500.26/0.360.56/0.910.89/1.421.21/1.73~446
Diffusion (Γ)1000.21/0.280.44/0.640.69/0.950.94/1.21~886
2000.21/0.290.44/0.650.69/0.970.94/1.21>1s
5000.21/0.300.45/0.680.70/0.990.95/1.23>1s
Leapfrog30.20/0.310.40/0.620.62/0.880.84/1.10~30
Diffusion (τ)50.18/0.270.37/0.560.58/0.840.81/1.10~46
100.17/0.270.37/0.580.59/0.850.82/1.08~89
" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.494, + 0.665, + 0.51 + ], + "angle": 0, + "content": "5.4. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.525, + 0.895, + 0.662 + ], + "angle": 0, + "content": "Effect of components in leapfrog initializer. We explore the effect of three key components in leapfrog initializer, including mean estimation, variance estimation, and sample prediction. Table 5 presents the results with mean and variance based on 5 experimental trials. We see that i) the leapfrog initializer achieves stable results with better performance even when prediction number \\( K \\) is small; and ii) the proposed mean estimation, variance estimation, and sample prediction all contribute to promoting prediction accuracy." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.668, + 0.895, + 0.804 + ], + "angle": 0, + "content": "Effect of leapfrog step \\(\\tau\\). Table 6 reports the influence of different leapfrog steps in LED. We see that i) under similar inference time, our method significantly outperforms the standard diffusion model with better representation ability; ii) when \\(\\tau\\) is too small, leapfrog initializer targets to learn more sophisticated distribution, causing worse prediction performance; and iii) when \\(\\tau\\) is too large, leapfrog initializer has already captured the denoised distribution, encountering performance bottleneck and wasting inference time." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.894, + 0.903 + ], + "angle": 0, + "content": "Comparison to other fast sampling methods. Table 7 compares the performance of our method and the other two fast sampling methods: PD [37] and DDIM [40]. We see that our method significantly outperforms two fast sampling methods under similar inference time since the proposed LED promotes the correlation between predictions." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5523" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.09, + 0.077, + 0.287, + 0.242 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.151, + 0.244, + 0.215, + 0.256 + ], + "angle": 0, + "content": "(a) PECNet" + }, + { + "type": "image", + "bbox": [ + 0.287, + 0.077, + 0.483, + 0.243 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.342, + 0.244, + 0.419, + 0.256 + ], + "angle": 0, + "content": "(b) GroupNet" + }, + { + "type": "image", + "bbox": [ + 0.484, + 0.077, + 0.681, + 0.243 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.554, + 0.244, + 0.602, + 0.256 + ], + "angle": 0, + "content": "(c) Ours" + }, + { + "type": "image", + "bbox": [ + 0.682, + 0.077, + 0.88, + 0.243 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.758, + 0.244, + 0.797, + 0.256 + ], + "angle": 0, + "content": "(d) GT" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.258, + 0.892, + 0.286 + ], + "angle": 0, + "content": "Figure 3. Visualization comparison on NBA. We compare the best-of-20 predictions by our method and two previous methods. Our method generates a more precise trajectory prediction. (Light color: past trajectory; blue/red/green color: two teams and the basketball.)" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.291, + 0.471, + 0.318 + ], + "angle": 0, + "content": "Table 7. Comparison to other fast sampling methods on NBA. \\(\\eta = 1\\) in DDIM. Our method achieves the best performance." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.319, + 0.469, + 0.446 + ], + "angle": 0, + "content": "
Method1.0s2.0s3.0sTotal(4.0s)Inference (ms)
PD (K=1)0.20/0.330.45/0.750.72/1.130.98/1.39~452
PD (K=2)0.21/0.340.46/0.780.73/1.150.98/1.41~230
PD (K=3)0.23/0.370.48/0.790.73/1.150.98/1.43~121
PD (K=4)0.25/0.380.50/0.800.75/1.160.99/1.44~64
DDIM (S=2)0.20/0.290.42/0.650.66/0.960.91/1.21~530
DDIM (S=10)0.22/0.320.44/0.710.69/1.040.93/1.31~107
DDIM (S=20)0.24/0.350.49/0.810.76/1.211.02/1.51~54
Ours0.18/0.270.37/0.560.58/0.840.81/1.10~46
" + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.452, + 0.272, + 0.529 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.274, + 0.452, + 0.457, + 0.529 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.53, + 0.271, + 0.606 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.274, + 0.53, + 0.457, + 0.606 + ], + "angle": 0, + "content": null + }, + { + "type": "image_footnote", + "bbox": [ + 0.084, + 0.608, + 0.457, + 0.619 + ], + "angle": 0, + "content": "Past trajectory Mean estimation Our prediction Ground-truth" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.623, + 0.468, + 0.665 + ], + "angle": 0, + "content": "Figure 4. Mean and variance estimation in leapfrog initializer on NBA with \\( K = 20 \\). The estimated variance can reflect the scene complexity of the current agent and produce diverse predictions." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.669, + 0.26, + 0.685 + ], + "angle": 0, + "content": "5.5. Qualitative Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.69, + 0.47, + 0.764 + ], + "angle": 0, + "content": "Visualization of predicted trajectory. Figure 3 compares the predicted trajectories of two baselines PECNet and GroupNet, our LED (Ours), and the ground-truth (GT) trajectories on the NBA dataset. We see that our method produces more accurate predictions than the previous methods." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.47, + 0.855 + ], + "angle": 0, + "content": "Visualization of estimated mean and variance. Figure 4 illustrates the mean and variance estimation in the leapfrog initializer under four scenes on the NBA dataset. We see that the variance estimation can well describe the scene complexity for the current agent by the learned variance, showing the rationality of our variance estimation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Visualization of different sampling mechanisms. Figure 5 compares two sampling mechanisms: I.I.D sampling and correlated sampling in the leapfrog initializer. We see" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.291, + 0.881, + 0.444 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.447, + 0.895, + 0.536 + ], + "angle": 0, + "content": "Figure 5. Comparison between I.I.D and correlated sampling mechanisms in NFL with \\( K = 4 \\). Correlated samples appropriately capture multi-modalities, significantly improving prediction performances. that the proposed correlated sampling can appropriately allocate sample diversity and capture more modalities when the number of trials \\( K \\) is small." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.547, + 0.619, + 0.561 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.568, + 0.894, + 0.703 + ], + "angle": 0, + "content": "This paper proposes the leapfrog diffusion model (LED), a diffusion-based trajectory prediction model, which significantly accelerates the overall inference speed and enables appropriate allocations of multiple correlated predictions. During the inference, LED directly models and samples from the denoised distribution through a novel leapfrog initializer with reparameterization. Extensive experiments show that our method achieves state-of-the-art performance on four real-world datasets and satisfies real-time inference needs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.894, + 0.809 + ], + "angle": 0, + "content": "Limitation and future work. This work achieves inference acceleration for trajectory prediction tasks partially because the dimension of trajectory data is relatively small and the corresponding distribution is much easier to learn compared with those of image/video data. A possible future work is to explore diffusion models and fast sampling methods for higher-dimensional tasks." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.823, + 0.668, + 0.839 + ], + "angle": 0, + "content": "Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.9 + ], + "angle": 0, + "content": "This research is partially supported by National Natural Science Foundation of China under Grant 62171276 and the Science and Technology Commission of Shanghai Municipal under Grant 21511100900 and 22DZ2229005." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5524" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.175, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.186 + ], + "angle": 0, + "content": "[1] Alexandre Alahi, Kratarth Goel, Vignesh Ramanathan, Alexandre Robicquet, Li Fei-Fei, and Silvio Savarese. 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Emerging diffusion models have revealed their tremendous representation capacities in numerous generation tasks, showing potential for stochastic trajectory prediction. However, expensive time consumption prevents diffusion models from real-time prediction, since a large number of denoising steps are required to assure sufficient representation ability. To resolve the dilemma, we present LEapfrog Diffusion model (LED), a novel diffusion-based trajectory prediction model, which provides real-time, precise, and diverse predictions. The core of the proposed LED is to leverage a trainable leapfrog initializer to directly learn an expressive multi-modal distribution of future trajectories, which skips a large number of denoising steps, significantly accelerating inference speed. Moreover, the leapfrog initializer is trained to appropriately allocate correlated samples to provide a diversity of predicted future trajectories, significantly improving prediction performances. Extensive experiments on four real-world datasets, including NBA/NFL/SDD/ETH-UCY, show that LED consistently improves performance and achieves $23.7\% / 21.9\%$ ADE/FDE improvement on NFL. The proposed LED also speeds up the inference 19.3/30.8/24.3/25.1 times compared to the standard diffusion model on NBA/NFL/SDD/ETH-UCY, satisfying real-time inference needs. Code is available at https://github.com/MediaBrain-SJTU/LED. + +# 1. Introduction + +Trajectory prediction aims to predict the future trajectories for one or multiple interacting agents conditioned on their past movements. This task plays a significant role in numerous applications, such as autonomous driving [24], drones [10], surveillance systems [45], human-robot interaction systems [5], and interactive robotics [20]. Recently, lots of fascinating research progresses have been made from + +![](images/2a86b5ca34fffa6acc3d705145f1b8e75feccea00ca362b1be8e708d1beb865a.jpg) +Figure 1. Leapfrog diffusion model uses the leapfrog initializer to estimate the denoised distribution and substitute a long sequence of traditional denoising steps, accelerating inference and maintaining representation capacity. + +many aspects, including temporal encoding [6, 13, 46, 53], interaction modeling [1, 15, 18, 43, 49], and rasterized prediction [11, 12, 26, 48]. In practice, to capture multiple possibilities of future trajectories, a real-world prediction system needs to produce multiple future trajectories. This leads to the emergence of stochastic trajectory prediction, aiming to precisely model the distribution of future trajectories. + +Previous works have proposed a series of deep generative models for stochastic trajectory prediction. For example, [15, 18] exploit the generator adversarial networks (GANs) to model the future trajectory distribution; [27, 38, 49] consider the conditional variational autoencoders (CVAEs) structure; and [3] uses the conditional normalizing flow to relax the Gaussian prior in CVAEs and learn more representative priors. Recently, with the great success in image generation [17, 33] and audio synthesis [4, 21], denoising diffusion probabilistic models have been applied to time-series analysis and trajectory prediction, and show promising prediction performances [14, 44]. Compared to many other generative models, diffusion models have advantages in stable training and modeling sophisticated distributions through sufficient denoising steps [8]. + +However, there are two critical problems in diffusion models for stochastic trajectory prediction. First, the real-time inference is time-consuming [14]. To ensure the representation ability and generate high-quality samples, an adequate number of denoising steps are required in standard diffusion models, which costs more computational time. For + +example, experiments show that on the NBA dataset, diffusion models need about 100 denoising steps to achieve decent prediction performances, which would take $\sim 886\mathrm{ms}$ to predict; while the next frame comes every $200\mathrm{ms}$ . Second, as mentioned in [2], a limited number of independent and identically distributed samples might not be able to capture sufficient modalities in the underlying distribution of a generative model. Empirically, a few independent sampled trajectories could miss some important future possibilities due to the lack of appropriate sample allocation, significantly deteriorating prediction performances. + +In this work, we propose leapfrog diffusion model (LED), a novel diffusion-based trajectory prediction model, which significantly accelerates the inference speed and enables adaptive and appropriate allocations of multiple correlated predictions, providing sufficient diversity in predictions. The core idea of the proposed LED is to learn a rough, yet sufficiently expressive distribution to initialize denoised future trajectories; instead of using a plain Gaussian distribution as in standard diffusion models. Specifically, our forward diffusion process is the same as standard diffusion models, which assures that the ultimate representation ability is pristine; while in the reverse denoising process, we leverage a powerful initializer to produce correlated diverse samples and leapfrog or skip a large number of denoising steps; and then, use only a few denoising steps to refine the distribution. + +To implement such a leapfrog initializer, we consider a reparameterization to alleviate the learning burden. We disassemble a denoised distribution into three parts: mean trajectory, variance, and sample positions under the normalized distribution. To estimate these three, we design three corresponding trainable modules, each of which leverages both a social encoder and a temporal encoder to learn the social-temporal features and produce accurate estimation. Furthermore, all the sample positions are simultaneously generated based on the same social-temporal features, enabling appropriate sample allocations to provide diversity. + +To evaluate the effectiveness of the proposed method, we conduct experiments on four trajectory prediction datasets: NBA, NFL Football Dataset, Standford Drones Dataset, and ETH-UCY. The quantitative results show we outperform the previous methods and achieve state-of-the-art performance. Specifically, compared to MID [14], the proposed leapfrog diffusion model reduces the average prediction time from $\sim 886\mathrm{ms}$ to $\sim 46\mathrm{ms}$ on the NBA dataset, while achieving a $15.6\% / 13.4\%$ ADE/FDE improvement. + +The main contributions are concluded as follows, + +- We propose a novel LEapfrog Diffusion model (LED), which is a denoising-diffusion-based stochastic trajectory prediction model. It achieves precise and diverse predictions with fast inference speed. +- We propose a novel trainable leapfrog initializer to directly model sophisticated denoised distributions, accelerator + +ating inference speed, and adaptively allocating the sample diversity, improving prediction performance. + +- We conduct extensive experiments on four datasets including NBA, NFL, SDD, and ETH-UCY. Results show that i) our approach consistently achieves state-of-the-art performance on all datasets; and ii) our method speeds up the inference by around 20 times compared to the standard diffusion model, satisfying real-time prediction needs. + +# 2. Related Work + +Trajectory prediction. Early works on trajectory prediction focus on a deterministic approach by exploring force models [16, 30], RNNs [1, 32, 47], and frequency analysis [28, 29]. For example, [16] models an agent's behavior with attractive and repulsive forces and builds the force equations for prediction. To capture the multi-modalities and model future distribution, recent works start to focus on stochastic trajectory prediction and have proposed a series of deep generative models. Generative Adversarial Network (GAN) structures [7, 9, 15, 18, 22, 36, 42] are proposed to generate multiple future trajectory distribution. [23, 27, 38, 49, 51] use the Variational Auto-Encoder (VAE) structure and learn the distribution through variational inference. [3] relaxes the Gaussian prior and proposes to use the normalizing flow. Heatmap [11, 12, 26] is used for modeling future trajectories' distribution on rasterized images. In this work, we propose a new diffusion-based model for trajectory prediction. Compared to previous generative models, our method has a large representation capacity and can model sophisticated trajectory distributions by using a number of diffusion steps. We also enable the correlation between samples to adaptively adjust sample diversity, improving prediction performance. + +Denoising diffusion probabilistic models. Denoising diffusion probabilistic models (diffusion models) [17, 39, 41] have recently achieved significant results in image generation [8, 33] and audio synthesis [4, 21]. The idea of diffusion models is first proposed by DPM [39], which imitates the diffusion process in non-equilibrium statistical physics and reconstructs the data distribution using the denoising model. Later, [35, 44] propose diffusion models, combining with the seq-to-seq models, for probabilistic time series forecasting. MID [14] is the first to build diffusion models for trajectory prediction in modeling the indeterminacy variation process. + +The standard diffusion models use hundreds of denoising steps, preventing these models from real-time applications. To accelerate the sampling process, DDIM [40] first predicts the original data and then estimates the direction to the next expected timestamp based on the non-Markov process. PD [37] applies the knowledge distillation on the denoising steps with a deterministic diffusion sampler, which will be repeated for times to accelerate the sampling. All these fast sampling methods start denoising from noise inputs, which are randomly and independently initialized. In this work, we + +use a trainable leapfrog initializer to initialize a sufficiently expressive distribution, which replaces a large number of former denoising steps for much faster inference speed. + +# 3. Background + +# 3.1. Problem Formulation + +Trajectory prediction aims to predict an agent's future trajectory based on the past trajectories of itself and surrounding agents. For a to-be-predicted agent, let $\mathbf{X} = [\mathbf{x}^{-T_{\mathrm{p}} + 1},\mathbf{x}^{-T_{\mathrm{p}} + 2},\dots ,\mathbf{x}^{0}] \in \mathbb{R}^{T_{\mathrm{p}} \times 2}$ be the observed past trajectory over $T_{\mathrm{p}}$ timestamps where $\mathbf{x}^t \in \mathbb{R}^2$ records the 2D spatial coordinate at timestamp $t$ . Let $\mathcal{N}$ be the neighbouring agent set and $\mathbb{X}_{\mathcal{N}} = [\mathbf{X}_{\mathcal{N}_1},\mathbf{X}_{\mathcal{N}_2},\dots ,\mathbf{X}_{\mathcal{N}_L}] \in \mathbb{R}^{L \times T_{\mathrm{p}} \times 2}$ be the past trajectories of neighbours, where $\mathbf{X}_{\mathcal{N}_\ell} \in \mathbb{R}^{T_{\mathrm{p}} \times 2}$ is the trajectory of the $\ell$ th neighbour. The corresponding ground-truth future trajectory for the to-be-predicted agent is $\mathbf{Y} = [\mathbf{y}^1,\mathbf{y}^2,\dots,\mathbf{y}^{T_{\mathrm{f}}}] \in \mathbb{R}^{T_{\mathrm{f}} \times 2}$ over $T_{\mathrm{f}}$ timestamps, where $\mathbf{y}^t \in \mathbb{R}^2$ is the 2D coordinate at future timestamp $t$ . + +Because of the indeterminacy of future trajectories, it is usually more reliable to predict more than one trajectory to capture multiple possibilities. Here we consider stochastic trajectory prediction, which predicts the distribution of a future trajectory, instead of a single future trajectory. The goal of stochastic trajectory prediction is to train a prediction model $g_{\theta}(\cdot)$ with parameters $\theta$ to generate a distribution $\mathcal{P}_{\theta} = g_{\theta}(\mathbf{X},\mathbb{X}_{\mathcal{N}})$ . Based on this distribution $\mathcal{P}_{\theta}$ , we can draw $K$ samples, $\widehat{\mathcal{Y}} = \{\widehat{\mathbf{Y}}_1,\widehat{\mathbf{Y}}_2,\dots ,\widehat{\mathbf{Y}}_K\}$ , so that at least one sample is close to the ground-truth future trajectory. The overall learning problem is + +$$ +\theta^ {*} = \min _ {\theta} \min _ {\widehat {\mathbf {Y}} _ {i} \in \widehat {\mathcal {Y}}} D (\widehat {\mathbf {Y}} _ {i}, \mathbf {Y}), \quad \text {s . t .} \quad \widehat {\mathcal {Y}} \sim \mathcal {P} _ {\theta}. \tag {1} +$$ + +# 3.2. Diffusion Model for Trajectory Prediction + +Here we present a standard diffusion model for trajectory prediction, which lays a foundation for the proposed method. The core idea is to learn and refine a sophisticated underlying distribution of trajectories through cascading a series of simple denoising steps. To implement this, a diffusion model performs a forward diffusion process to intentionally add a series of noises to a ground-truth future trajectory; and then, it uses a conditional denoising process to recover the future trajectory from noise inputs conditioned on past trajectories. + +Mathematically, let $\mathbf{X}$ and $\mathbb{X}_{\mathcal{N}}$ be the past trajectories of the ego agent and the neighboring agents, respectively, and $\mathbf{Y}$ be the future trajectory of the ego agent. The diffusion model for trajectory prediction works as follows, + +$$ +\mathbf {Y} ^ {0} = \mathbf {Y}, \tag {2a} +$$ + +$$ +\mathbf {Y} ^ {\gamma} = f _ {\text {d i f f u s e}} \left(\mathbf {Y} ^ {\gamma - 1}\right), \gamma = 1, \dots , \Gamma , \tag {2b} +$$ + +$$ +\widehat {\mathbf {Y}} _ {k} ^ {\Gamma} \stackrel {i. i. d} {\sim} \mathcal {P} (\widehat {\mathbf {Y}} ^ {\Gamma}) = \mathcal {N} (\widehat {\mathbf {Y}} ^ {\Gamma}; \mathbf {0}, \mathbf {I}), \text {s a m p l e} K \text {t i m e s}, \tag {2c} +$$ + +$$ +\hat {\mathbf {Y}} _ {k} ^ {\gamma} = f _ {\text {d e n o i s e}} \left(\hat {\mathbf {Y}} _ {k} ^ {\gamma + 1}, \mathbf {X}, \mathbb {X} _ {\mathcal {N}}\right), \gamma = \Gamma - 1, \dots , 0, \tag {2d} +$$ + +where $\mathbf{Y}^{\gamma}$ is the noisy trajectory at the $\gamma$ th diffusion step and $\widehat{\mathbf{Y}}_k^\gamma$ is the $k$ th sample of denoised trajectory at the $\gamma$ th denoising step. The final $K$ predicted trajectories are $\widehat{\mathcal{V}} = \{\widehat{\mathbf{Y}}_1^0, \widehat{\mathbf{Y}}_2^0, \ldots, \widehat{\mathbf{Y}}_K^0\}$ . + +Step (2a) initializes the diffused trajectory; Step (2b) uses a forward diffusion operation $f_{\mathrm{diffuse}}(\cdot)$ to successively add noises to $\mathbf{Y}^{\gamma - 1}$ and obtain the diffused trajectory $\mathbf{Y}^{\gamma}$ ; Step (2c) draws $K$ independent and identically distributed samples to initialize denoised trajectories $\widehat{\mathbf{Y}}_k^\Gamma$ from a normal distribution; and Step (2d) iteratively applies a denoising operation $f_{\mathrm{denoise}}(\cdot)$ to obtain the denoised trajectory $\widehat{\mathbf{Y}}_k^\gamma$ conditioned on past trajectories $\mathbf{X}, \mathbb{X}_{\mathcal{N}}$ . Note that i) Steps (2a) and (2b) correspond to the forward diffusion process and are not used in inference; ii) During training, $\mathbf{Y}^{\gamma}$ is naturally the supervision for $\widehat{\mathbf{Y}}_k^\gamma$ at the $\gamma$ th step. Conceptually, each denoising step is the reverse of the diffusion step, and each pair of $\mathbf{Y}^{\gamma}$ and $\widehat{\mathbf{Y}}_k^\gamma$ shares the same underlying distribution. + +The standard diffusion model is expressively powerful in learning sophisticated distributions and has achieved great success in many generation tasks. However, the task of motion prediction requires real-time inference but the running time of a diffusion model is constrained by the large number of denoising steps. Meanwhile, less denoising steps usually cause a weaker representation ability of future distributions. To achieve higher efficiency while preserving a promising representation ability, we propose leapfrog diffusion model, which uses a trainable initializer to capture sophisticated distributions and substitute a large number of denoising steps. + +# 4. Leapfrog Diffusion Model + +# 4.1. System Architecture + +In this section, we propose the leapfrog diffusion model. Here leapfrog means that a large number of small denoising steps can be replaced by a single, yet powerful leapfrog initializer, which can significantly accelerate the inference speed without losing representation ability. Let $\mathbf{X}$ and $\mathbb{X}_{\mathcal{N}}$ be the past trajectories of the ego agent and its neighboring agents, and $\mathbf{Y}$ be the future trajectory of the ego agent. Denote $\tau$ as the leapfrog step. The overall procedure of the proposed leapfrog diffusion model is formulated as follows, + +$$ +\mathbf {Y} ^ {0} = \mathbf {Y}, \tag {3a} +$$ + +$$ +\mathbf {Y} ^ {\gamma} = f _ {\text {d i f f u s e}} \left(\mathbf {Y} ^ {\gamma - 1}\right), \gamma = 1, \dots , \Gamma , \tag {3b} +$$ + +$$ +\hat {\mathcal {Y}} ^ {\tau} \stackrel {K} {\sim} \mathcal {P} \left(\hat {\mathbf {Y}} ^ {\tau}\right) = f _ {\text {L S G}} \left(\mathbf {X}, \mathbb {X} _ {\mathcal {N}}\right), \tag {3c} +$$ + +$$ +\widehat {\mathbf {Y}} _ {k} ^ {\gamma} = f _ {\text {d e n o i s e}} \left(\widehat {\mathbf {Y}} _ {k} ^ {\gamma + 1}, \mathbf {X}, \mathbb {X} _ {\mathcal {N}}\right), \gamma = \tau - 1, \dots , 0. \tag {3d} +$$ + +Compared to the standard diffusion model (2), the main difference lies in Step (3c). The standard diffusion initializes the $\Gamma$ th denoised distribution $\mathcal{P}(\widehat{\mathbf{Y}}^{\Gamma})$ by a plain normal distribution (2c) and requires a lot of denoising steps to enrich the expressiveness of the denoised distribution; while in Step (3c), we propose a novel leapfrog initial + +![](images/178473828a87aff0634fb6c2aa6758e32a1861f4a571c6723c204224a01568c7.jpg) +Figure 2. Proposed leapfrog diffusion model (LED) in inference phase. The red agent is the to-be-predicted agent. LED first predicts $K$ initialized trajectories at $\tau$ th denoised step through a trainable leapfrog initializer. Then, followed by a few denoising steps, LED obtains the final predictions. In leapfrog initializer, LED learns statistics and generates correlated samples with the reparameterization. + +izer $f_{\mathrm{LSG}}(\cdot)$ to directly model the $\tau$ th denoised distribution $\mathcal{P}(\widehat{\mathbf{Y}}^{\tau})$ , which is hypothetically equivalent to the output of executing $(\Gamma - \tau)$ denoising steps (2d). We then draw samples from the distribution $\mathcal{P}(\widehat{\mathbf{Y}}^{\tau})$ and obtain $K$ future trajectories $\widehat{\mathcal{Y}}^{\tau} = \{\widehat{\mathbf{Y}}_1^{\tau}, \widehat{\mathbf{Y}}_2^{\tau}, \dots, \widehat{\mathbf{Y}}_K^{\tau}\}$ , where $\stackrel{K}{\sim}$ in (3d) means $K$ samples are dependent to intentionally allocate appropriate sample diversity. Then, in Step (3d), we only need to apply the remaining $\tau$ denoising steps for each trajectory $\widehat{\mathbf{Y}}_k^\gamma$ to obtain the final prediction $\widehat{\mathcal{Y}} = \{\widehat{\mathbf{Y}}_1^0, \widehat{\mathbf{Y}}_2^0, \dots, \widehat{\mathbf{Y}}_K^0\}$ . + +Note that i) the proposed leapfrog diffusion model reduces the denoising steps from $\Gamma$ to $\tau (\ll \Gamma)$ in Step (3d) as the leapfrog initializer directly provides the trajectories at denoising step $\tau$ , accelerating the inference; ii) instead of taking independent and identically distributed samples in Step (2c), the proposed leapfrog initializer generates $K$ trajectories $\widehat{\mathcal{Y}}^{\tau}$ simultaneously in Step (3c), allowing $K$ samples to be aware of each other; and iii) the standard diffusion model and the proposed leapfrog diffusion model share the same forward diffusion process, assuring that the representation capacity is not reduced. + +# 4.2. Leapfrog Initializer + +We now dive into the design details of the proposed leapfrog initializer, which leapfrogs $(\Gamma - \tau)$ denoising steps. In leapfrog initializer, we model the $\tau$ th denoised distribution $\mathcal{P}(\widehat{\mathbf{Y}}^{\tau})$ through learning models. However, it is nontrivial for a learning model to directly capture the sophisticated distribution, which usually causes unstable training. To ease the learning burden of the model, we disassemble the distribution $\mathcal{P}(\widehat{\mathbf{Y}}^{\tau})$ into three representative parts: the mean, global variance and sample prediction. For each part, we design trainable modules correspondingly. Mathematically, let $\mathbf{X}$ and $\mathbb{X}_{\mathcal{N}}$ be the past trajectories of the ego agent and the neighboring agents, respectively. The proposed leapfrog initializer generates $K$ samples as follows, + +$$ +\begin{array}{l} \mu_ {\theta} = f _ {\mu} (\mathbf {X}, \mathbb {X} _ {\mathcal {N}}) \in \mathbb {R} ^ {T _ {t} \times 2}, \\ \sigma_ {\theta} = f _ {\sigma} (\mathbf {X}, \mathbb {X} _ {\mathcal {N}}) \in \mathbb {R}, \\ \widehat {\mathbb {S}} _ {\theta} = \left[ \widehat {\mathbf {S}} _ {\theta , 1}, \dots , \widehat {\mathbf {S}} _ {\theta , K} \right] = f _ {\widehat {\mathbb {S}}} (\mathbf {X}, \mathbb {X} _ {\mathcal {N}}, \sigma_ {\theta}) \in \mathbb {R} ^ {T _ {\mathrm {f}} \times 2 \times K}, \\ \widehat {\mathbf {Y}} _ {k} ^ {\tau} = \mu_ {\theta} + \sigma_ {\theta} \cdot \widehat {\mathbf {S}} _ {\theta , k} \in \mathbb {R} ^ {T _ {\mathrm {f}} \times 2}, \tag {4} \\ \end{array} +$$ + +where $f_{\mu}(\cdot), f_{\sigma}(\cdot), f_{\widehat{\mathbb{S}}}(\cdot)$ are three trainable modules, $\mu_{\theta}, \sigma_{\theta}$ are the mean and standard deviation of $\mathcal{P}(\widehat{\mathbf{Y}}^{\tau})$ , respectively, and $\widehat{\mathbf{S}}_{\theta,k}$ is the normalized positions for the $k$ th sample. + +To be specific, the mean estimate module $f_{\mu}(\cdot)$ infers the mean trajectory of the $\tau$ th denoised distribution $\widehat{\mathcal{P}}(\widehat{\mathbf{Y}}^{\tau})$ with past trajectories $(\mathbf{X}, \mathbb{X}_{\mathcal{N}})$ . The mean trajectory $\mu_{\theta}$ is shared across all the $K$ samples. The variance estimate module $f_{\sigma}(\cdot)$ infers the standard deviation of the $\tau$ th denoised distribution $\widehat{\mathcal{P}}(\widehat{\mathbf{Y}}^{\tau})$ , reflecting the overall uncertainty of the trajectory, which is also shared across all the $K$ samples. The sample prediction module $f_{\widehat{\mathbb{S}}}(\cdot)$ takes the past trajectories $(\mathbf{X}, \mathbb{X}_{\mathcal{N}})$ and the predicted uncertainty $\sigma_{\theta}$ as the input and predicts $K$ normalized positions where each $\widehat{\mathbf{S}}_{\theta,k} \in \mathbb{R}^{T_{\mathrm{f}} \times 2}$ . + +Note that i) the reparameterization in Eq. (4) allows us to avoid learning a raw sophisticated distribution, making the training much easier; and ii) $K$ normalized predictions are generated simultaneously from the same underlying feature, assuring appropriately allocated trajectories with variance estimation and better capturing the multi-modalities. + +To implement the three trainable modules: $f_{\mu}(\cdot), f_{\sigma}(\cdot), f_{\widehat{\mathbb{S}}}(\cdot)$ , we consider a similar network design: a social encoder to capture social influence, a temporal encoder to learn temporal embedding, and an aggregation layer to fuse both social and temporal information; see Figure 2. Here we take the mean estimation module $f_{\mu}(\cdot)$ as an example. The mean trajectory is obtained as follows, + +$$ +\begin{array}{l} \mathbf {e} _ {\mu_ {\theta}} ^ {\text {s o c i a l}} = \operatorname {s o f t m a x} \left(\frac {f _ {\mathrm {q}} (\mathbf {X}) f _ {\mathrm {k}} (\mathbb {X} _ {\mathcal {N}}) ^ {\top}}{\sqrt {d}}\right) f _ {\mathrm {v}} (\mathbb {X} _ {\mathcal {N}}), (5a) \\ \mathbf {e} _ {\mu_ {\theta}} ^ {\text {t e m p}} = f _ {\mathrm {G R U}} \left(f _ {\operatorname {c o n v 1 D}} (\mathbf {X})\right), (5b) \\ \mu_ {\theta} = f _ {\text {f u s i o n}} \left(\left[ \mathbf {e} _ {\mu_ {\theta}} ^ {\text {s o c i a l}}: \mathbf {e} _ {\mu_ {\theta}} ^ {\text {t e m p}} \right]\right). (5c) \\ \end{array} +$$ + +Step (5a) obtains the social embedding $\mathbf{e}_{\mu_{\theta}}^{\mathrm{social}}$ based on the multi-head attention with $d$ the embedding dimension and $f_{\mathrm{q}}(\cdot), f_{\mathrm{k}}(\cdot), f_{\mathrm{v}}(\cdot)$ the query/key/value embedding functions. Step (5b) obtains the temporal embedding through the feature encoder $f_{\mathrm{conv1D}}(\cdot)$ , mapping the raw coordinates into the high-dimensional feature, followed by the gated recurrent units $f_{\mathrm{GRU}}(\cdot)$ , capturing the temporal dependence in the high dimensional sequence. Step (5c) concatenates both social and temporal embeddings and uses a multi-layer perceptron $f_{\mathrm{fusion}}(\cdot)$ to obtain the final mean estimation. Note + +that the sample prediction module $f_{\widehat{\mathbb{S}}}(\cdot)$ also takes the estimated standard deviation as the input, working as + +$$ +\mathbf {e} _ {\hat {\mathfrak {S}} _ {\theta}} ^ {\sigma} = f _ {\mathrm {e n c o d e}} (\sigma_ {\theta}), +$$ + +$$ +\widehat {\mathbb {S}} _ {\theta} = f _ {\mathrm {f u s i o n}} ([ \mathbf {e} _ {\widehat {\mathbb {S}} _ {\theta}} ^ {\mathrm {s o c i a l}}: \mathbf {e} _ {\widehat {\mathbb {S}} _ {\theta}} ^ {\mathrm {t e m p}}: \mathbf {e} _ {\widehat {\mathbb {S}} _ {\theta}} ^ {\sigma} ]), +$$ + +where an encoder $f_{\mathrm{encode}}(\cdot)$ operates on the estimated variance $\sigma_{\theta}$ and generates high dimensional embedding $\mathbf{e}_{\hat{\mathbb{S}}_{\theta}}^{\sigma}$ . By this, the variance estimation also involves in the sample prediction process, instead of just scaling these prediction. + +After obtaining $K$ samples $\widehat{y}^{\tau} = \{\widehat{\mathbf{Y}}_1^\tau ,\widehat{\mathbf{Y}}_2^\tau ,\dots ,\widehat{\mathbf{Y}}_K^\tau \}$ from leapfrog initializer, we execute the remaining $\tau$ denoising steps to iteratively refine those predicted trajectories (3d). + +# 4.3. Denoising Module + +Here we elaborate the design of a denoising module $f_{\mathrm{denoise}}(\cdot)$ , which denoises the trajectory $\widehat{\mathbf{Y}}_k^{\gamma +1}$ conditioned on past trajectories $(\mathbf{X},\mathbb{X}_{\mathcal{N}})$ . In a denoising module, two parts are trainable: a transformer-based context encoder $f_{\mathrm{context}}(\cdot)$ to learn a social-temporal embedding and a noise estimation module $f_{\epsilon}(\cdot)$ to estimate the noise to reduce. Mathematically, the $\gamma$ th denoising step works as follows, + +$$ +\mathbf {C} = f _ {\text {c o n t e x t}} (\mathbf {X}, \mathbb {X} _ {\mathcal {N}}), \tag {6a} +$$ + +$$ +\epsilon_ {\theta} ^ {\gamma} = f _ {\epsilon} \left(\widehat {\mathbf {Y}} _ {k} ^ {\gamma + 1}, \mathbf {C}, \gamma + 1\right), \tag {6b} +$$ + +$$ +\hat {\mathbf {Y}} _ {k} ^ {\gamma} = \frac {1}{\sqrt {\alpha_ {\gamma}}} \left(\hat {\mathbf {Y}} _ {k} ^ {\gamma + 1} - \frac {1 - \alpha_ {\gamma}}{\sqrt {1 - \bar {\alpha} _ {\gamma}}} \boldsymbol {\epsilon} _ {\theta} ^ {\gamma}\right) + \sqrt {1 - \alpha_ {\gamma}} \mathbf {z}, \quad (6 c) +$$ + +where $\alpha_{\gamma}$ and $\bar{\alpha}_{\gamma} = \prod_{i=1}^{\gamma} \alpha_{i}$ are parameters in the diffusion process and $\mathbf{z} \sim \mathcal{N}(\mathbf{z}; \mathbf{0}, \mathbf{I})$ is a noise. Step (6a) uses a context encoder $f_{\mathrm{context}}(\cdot)$ on past trajectories $(\mathbf{X}, \mathbb{X}_{\mathcal{N}})$ to obtain the context condition $\mathbf{C}$ , which shares a similar structure to mean estimation module $f_{\mu}(\cdot)$ ; Step (6b) estimates the noise $\epsilon_{\theta}^{\gamma}$ in the noisy trajectory $\widehat{\mathbf{Y}}_k^{\gamma+1}$ through noise estimation $f_{\epsilon}(\cdot)$ implemented by multi-layer perceptions with the context $\mathbf{C}$ ; Step (6c) provides a standard denoising step [17]; see more details in the supplementary material. + +# 4.4. Training Objective + +To train a leapfrog diffusion model, we consider a two-stage training strategy, where the first stage trains a denoising module and the second stage focuses on a leapfrog initializer. The reason to use two stages is because the training of leapfrog initializer is more stable given fixed distribution $\mathcal{P}(\widehat{\mathbf{Y}}^{\tau})$ , avoiding non-convergent training. + +Concretely, the first stage trains a denoising module $f_{\mathrm{denoise}}(\cdot)$ in Step (3d) based on a standard training schedule of a diffusion model [14, 17] through noise estimation loss: + +$$ +\mathcal {L} _ {\mathrm {N E}} = \| \boldsymbol {\epsilon} - f _ {\boldsymbol {\epsilon}} (\mathbf {Y} ^ {\gamma + 1}, f _ {\text {c o n t e x t}} (\mathbf {X}, \mathbb {X} _ {\mathcal {N}}), \gamma + 1) \| _ {2}, +$$ + +where $\gamma \sim \mathrm{U}\{1,2,\dots ,\Gamma \}$ $\epsilon \sim \mathcal{N}(\epsilon ;\mathbf{0},\mathbf{I})$ and the diffused trajectory $\mathbf{Y}^{\gamma +1} = \sqrt{\bar{\alpha}_{\gamma}}\mathbf{Y}^{0} + \sqrt{1 - \bar{\alpha}_{\gamma}}\pmb {\epsilon}$ . We then back + +# Algorithm 1 Leapfrog Diffusion Model in Inference + +Input: Observed trajectories $\mathbf{X}$ , $\mathbb{X}_{\mathcal{N}}$ , Leapfrog step $\tau$ + +Output: Predicted trajectories $\hat{\mathcal{V}}$ + +1: $\mu_{\theta} = f_{\mu}(\mathbf{X},\mathbb{X}_{\mathcal{N}})$ Mean estimation +2: $\sigma_{\theta} = f_{\sigma}(\mathbf{X},\mathbb{X}_{\mathcal{N}})$ $\triangleright$ Variance estimation +3: $\widehat{\mathbb{S}}_{\theta} = f_{\widehat{\mathbb{S}}}(\mathbf{X},\mathbb{X}_{\mathcal{N}},\sigma_{\theta})$ ▷ Sample prediction +4: $\widehat{\mathbf{Y}}_k^\tau = \mu_\theta +\sigma_\theta \cdot \widehat{\mathbf{S}}_{\theta ,k},k = 1,\dots ,K\ntriangleright$ Reparameterization +5: for $\gamma = \tau - 1, \dots, 0$ do +6: $\widehat{\mathbf{Y}}_k^\gamma = f_{\mathrm{denoise}}(\widehat{\mathbf{Y}}_k^{\gamma +1},\mathbf{X},\mathbb{X}_{\mathcal{N}})$ Denoising step +7: end for +8: $\widehat{\mathcal{Y}} = \widehat{\mathcal{Y}}^0 = \{\widehat{\mathbf{Y}}_1^0,\dots ,\widehat{\mathbf{Y}}_K^0\}$ +9: return $\hat{y}$ + +propagate this loss and train the parameters in the context encoder $f_{\mathrm{context}}(\cdot)$ and the noise estimation module $f_{\epsilon}(\cdot)$ . + +In the second stage, we optimize a leapfrog diffusion model with a trainable leapfrog initializer and frozen denoising modules. For each sample, the loss function is + +$$ +\begin{array}{l} \mathcal {L} = \mathcal {L} _ {\text {d i s t a n c e}} + \mathcal {L} _ {\text {u n c e r t a i n t y}} \\ { = } { w \cdot \operatorname* { m i n } _ { k } \| \mathbf { Y } - \widehat { \mathbf { Y } } _ { k } \| _ { 2 } + \Big ( \frac { \sum _ { k } \| \mathbf { Y } - \widehat { \mathbf { Y } } _ { k } \| _ { 2 } } { \sigma _ { \theta } ^ { 2 } K } + \log \sigma _ { \theta } ^ { 2 } \Big ) , } \\ \end{array} +$$ + +where $w \in \mathbb{R}$ is a hyperparameter weight. The first term constrains the minimum distance in $K$ predictions. Intuitively, if a leapfrog initializer generates high-quality estimations for distribution $\mathcal{P}(\widehat{\mathbf{Y}}^{\tau})$ , then one of the $K$ predictions in $\widehat{\mathcal{V}}$ should be close to the ground-truth trajectory $\mathbf{Y}$ . The second term normalizes the variance estimation $\sigma_{\theta}$ in reparameterization (4) through an uncertainty loss, balancing the prediction diversity and mean accuracy. Note that the variance estimation controls the dispersion of the predictions, bridging scenery complexity and prediction diversity. The first part $\frac{\sum_k\|\mathbf{Y}\widehat{\mathbf{Y}}_k\|_2}{\sigma_\theta^2K}$ makes the value of $\sigma_{\theta}$ proportional to the complexity of the scenario. The second part $\log \sigma_{\theta}^{2}$ is a regulariser used to avoid a trivial solution for $\sigma_{\theta}$ , i.e., generating high variance for all predictions. + +Technically, we can also explicitly supervise the estimation of leapfrog initializer in stage two, since the distribution $\mathcal{P}(\widehat{\mathbf{Y}}^{\tau})$ can be denoised from a normal distribution. For the explicit supervision, we draw $M\gg K$ samples from $\mathcal{P}(\widehat{\mathbf{Y}}^{\Gamma})$ under the normal distribution and iteratively denoise these samples through Step (2d) until we get expected denoised trajectories $\widehat{\mathbf{Y}}^{\tau}$ . And then, we calculate the statistics of the denoised distribution $\mathcal{P}(\widehat{\mathbf{Y}}^{\tau})$ using these $M$ samples, serving as explicit supervisions for mean estimation $f_{\mu}(\cdot)$ and variance estimation $f_{\sigma}(\cdot)$ . However, since $\tau \ll \Gamma$ , we need to run $(\Gamma -\tau)\approx \Gamma$ -steps denoising for $M\gg K$ samples to get statistics, resulting in unacceptable time and storage consumption for training (e.g. $\sim 6$ days per epoch on NBA + +Table 1. Comparison with baseline models on NBA dataset. minADE20 /minFDE20 (meters) are reported. Bold/underlined fonts represent the best/second-best result. Compared to the previous SOTA method, MID, our method achieves a $15.6\% /13.4\%$ ADE/FDE improvement. + +
TimeSocial-GAN [15] CVPR'18STGAT [19] ICCV'19Social-STGCNN [31] CVPR'20PECNet [27] ECCV'20STAR [52] ECCV'20Trajectory++[38] ECCV'20MemoNet [50] CVPR'22NPSN [2] CVPR'22GroupNet [49] CVPR'22MID [14] CVPR'22Ours
1.0s0.41/0.620.35/0.510.34/0.480.40/0.710.43/0.660.30/0.380.38/0.560.35/0.580.26/0.340.28/0.370.18/0.27
2.0s0.81/1.320.73/1.100.71/0.940.83/1.610.75/1.240.59/0.820.71/1.140.68/1.230.49/0.700.51/0.720.37/0.56
3.0s1.19/1.941.04/1.751.09/1.771.27/2.441.03/1.510.85/1.241.00/1.571.01/1.760.73/1.020.71/0.980.58/0.84
Total(4.0s)1.59/2.411.40/2.181.53/2.261.69/2.951.13/2.011.15/1.571.25/1.471.31/1.790.96/1.300.96/1.270.81/1.10
+ +Table 2. Comparison with baseline models on NFL dataset. $\mathrm{{minADE}}_{20}/\mathrm{{minFDE}}_{20}$ (meters) are reported. Bold/underlined fonts represent the best/second-best result. Compared to the previous SOTA method, MID, our method achieves a 23.7%/21.9% improvement. + +
TimeSocial-GAN [15] CVPR'18STGAT [19] ICCV'19Social-STGCNN [31] CVPR'20PECNet [27] ECCV'20STAR [52] ECCV'20Trajectron++[38] ECCV'20LB-EBM[34] CVPR'21NPSN [2] CVPR'22GroupNet[49] CVPR'22MID [14] CVPR'22Ours
1.0s0.37/0.680.35/0.640.45/0.640.52/0.970.49/0.840.41/0.650.75/1.050.43/0.640.32/0.570.30/0.580.21/0.34
2.0s0.83/1.530.82/1.601.06/1.871.19/2.471.02/1.840.93/1.651.26/2.280.83/1.520.73/1.390.71/1.310.49/0.91
Total(3.2s)1.44/2.511.39/2.481.82/3.181.99/3.841.51/2.971.54/2.581.90/3.251.32/2.271.21/2.151.14/1.920.87/1.50
+ +dataset). We thus do not use explicit supervision. + +# 4.5. Inference Phase + +During the inference, instead of the $\Gamma$ -steps' denoising, leapfrog diffusion model only takes $\tau$ -steps, accelerating the inference. To be specific, we first generate $K$ correlated samples to model the distribution $\mathcal{P}(\widetilde{\mathbf{Y}}^{\tau})$ using the trained leapfrog initializer. Then, these samples will be fed into the denoising process and iteratively fine-tuned to produce the final predictions; see Algorithm 1. + +# 5. Experiments + +# 5.1. Datasets + +We evaluate our method on four trajectory prediction datasets, including two sports datasets (NBA SportVU Dataset, NFL Football Dataset) and two pedestrian datasets (Stanford Drone Dataset, ETH-UCY). + +NBA SportVU Dataset (NBA): NBA trajectory dataset is collected by NBA using the SportVU tracking system, which records the trajectories of the 10 players and the ball in real basketball games. In this task, we predict the future 4.0s (20 frames) using the 2.0s (10 frames) past trajectory. + +NFL Football Dataset (NFL): NFL Football Dataset records the position of every player on the field during each play in the 2017 year. We predict the 22 players' (11 players per team) and the ball's future 3.2s (16 frames) trajectory using the historical 1.6s (8 frames) trajectory. + +Stanford Drone Dataset (SDD): SDD is a large-scale pedestrian dataset collected from a university campus in bird's eye view. Following previous works [27, 50], we use the standard train-test split and predict the future 4.8s (12 frames) using 3.2s (8 frames) past. + +ETH-UCY: ETH-UCY dataset contains 5 subsets: ETH, HOTEL, UNIV, ZARA1, and ZARA2, containing various motion scenes. We use same segment length of 8s as SDD following previous works [18, 27] and use the leave-one-out approach with four sets for training and a left set for testing. + +# 5.2. Implementation Details + +In the leapfrog diffusion model, we set the diffusion step $\Gamma = 100$ for all four datasets and the leapfrog step $\tau = 5$ on the NBA dataset. In the leapfrog initializer, we build a transformer-based social encoder where the feed-forward dimension is set to 256, the number of heads is 2, and 2 encoder layers are applied; we apply the temporal encoder with 1D convolution kernel being 3, and output channel setting to 32, and we also build a GRU with the hidden size of 256. In the denoising module, we apply the same parameters transformer to extract the context information, and we build the core denoising module with a hidden size of 256. To train the leapfrog diffusion model, we train the denoising module for 100 epochs with an initial learning rate of $10^{-2}$ and decay to half every 16 epochs. With a frozen denoising module, we then train the leapfrog initializer for 200 epochs with an initial learning rate of $10^{-4}$ , decaying by 0.9 every 32 epochs. We set weight parameter $w_{1} = 50$ to emphasize the distance loss. The entire framework is trained with the Adam optimizer on one GTX-3090 GPU. All models are implemented with PyTorch 1.7.1. See more details in the supplementary material. + +# 5.3. Comparison with SOTA Methods + +We measure the performance of different trajectory prediction methods using two metrics: $\min\mathrm{ADE}_K$ and $\min\mathrm{FDE}_K$ , following previous work [27, 49]. 1) $\min\mathrm{ADE}_K$ calculates the minimum time-averaged distance among $K$ predictions and the ground-truth future trajectory; 2) $\min\mathrm{FDE}_K$ measures the minimum distance among the $K$ predicted endpoints and the ground-truth endpoints. We calculate these two metrics at different timestamps on sports datasets to better evaluate the performance. + +NBA dataset. We compare our method with the current 10 state-of-the-art prediction methods at different timestamps; see Table 1. We see that i) our method significantly outperforms all baselines in ADE and FDE at all timestamps. Our method reduces the ADE/FDE at 4.0s from 0.96/1.27 + +Table 3. Comparison with baseline models on SDD dataset. minADE20/minFDE20 (meters) are reported. Bold/underlined fonts represent the best/second-best result. Our method achieves the best performance in ADE/FDE. * represents the reproduced results from open source. + +
TimeSocial-GAN [15] CVPR'18SOPHIE [36] CVPR'19Trajectory++ [38] ECCV'20NMMP [18] CVPR'20Evolve- Graph [25] NIPS'20PECNet [27] ECCV'20MemoNet [50] CVPR'22NPSN [2] CVPR'22GroupNet [49] CVPR'22MID* [14] CVPR'22Ours
4.8s27.23/41.4416.27/29.3819.30/32.7014.67/26.7213.90/22.909.96/15.888.56/12.668.56/11.859.31/16.119.73/15.328.48/11.66
+ +Table 4. Comparison with baseline models on ETH-UCY dataset. minADE20/minFDE20 (meters) are reported. Bold/underlined fonts represent the best/second-best result. In most subsets, our method achieves the best or second-best performance in ADE/FDE. + +
SubsetSocial-GAN [15]CVPR'18NMMP [18]CVPR'20STAR [52]ECCV'20PECNet [27]ECCV'20Trajectory++[38]ECCV'20Agentformer[53]ICCV'21MemoNet[50]CVPR'22NPSN [2]CVPR'22GroupNet[49]CVPR'22MID [14]CVPR'22
ETH0.87/1.620.61/1.080.36/0.650.54/0.870.61/1.020.45/0.750.40/0.610.40/0.760.46/0.730.39/0.66
Hotel0.67/1.370.33/0.630.17/0.360.18/0.240.19/0.280.14/0.220.11/0.170.12/0.180.15/0.250.13/0.22
Univ0.76/1.520.52/1.110.31/0.620.35/0.600.30/0.540.25/0.450.24/0.430.22/0.410.26/0.490.22/0.45
Zara10.35/0.680.32/0.660.29/0.520.22/0.390.24/0.420.18/0.300.18/0.320.17/0.310.21/0.390.17/0.30
Zara20.42/0.840.43/0.850.22/0.460.17/0.300.18/0.320.14/0.240.14/0.240.12/0.240.17/0.330.13/0.27
AVG0.61/1.210.41/0.820.26/0.530.29/0.480.30/0.510.23/0.390.21/0.350.21/0.380.25/0.440.21/0.38
+ +Table 5. Ablation of leapfrog initializer in the leapfrog diffusion model on NFL with various prediction numbers $K$ . Each module in the leapfrog initializer is beneficial. + +
Mean μθVariance σθSample ΜθK=2K=4
✓correlated2.04±0.18/4.08±0.481.63±0.13/3.05±0.16
✓correlated1.95±0.08/3.90±0.221.49±0.01/2.86±0.02
✓✓i.i.d2.36±0.13/4.31±0.221.90±0.07/3.31±0.05
✓✓correlated1.84±0.05/3.61±0.111.47±0.01/2.83±0.02
Mean μθVariance σθSample ΜθK=8K=20
✓correlated1.25±0.02/2.31±0.040.99±0.03/1.68±0.04
✓correlated1.23±0.01/2.20±0.010.95±0.01/1.54±0.02
✓✓i.i.d1.51±0.04/2.67±0.071.18±0.02/1.90±0.03
✓✓correlated1.18±0.01/2.19±0.010.89±0.01/1.51±0.02
+ +to 0.81/1.10 compared to the current state-of-the-art methods, MID, achieving $15.6\% / 13.4\%$ improvement; and ii) performance improvement over previous methods increases with timestamps, reflecting the proposed method can capture more sophisticated distributions at further timestamps. + +NFL dataset. We compare our method with the current 10 state-of-the-art prediction methods at different timestamps; see Table 2. We see that our model significantly outperforms all baselines in ADE and FDE at all timestamps. Our method reduces the ADE/FDE at 3.2s from 1.14/1.92 to 0.87/1.50 compared to the current state-of-the-art methods, MID, achieving $23.7\% / 21.9\%$ improvement. + +SDD dataset. We compare our method with the current 10 state-of-the-art prediction methods; see Table 3. We see that our method reduces FDE from 11.85 to 11.66 compared to the current state-of-the-art method, NPSN. Notably, the original MID [14] uses a different protocol from all the other methods, we update its code for a fair comparison. + +ETH-UCY dataset. We compare our method with 10 state-of-the-art prediction methods; see Table 4. We see that i) our method reduces FDE from 0.35 to 0.33 compared to the current state-of-the-art method, MemoNet, achieving a $5.7\%$ improvement; and ii) our method achieves the best or second best to the best performance on most of the subsets. + +Table 6. Different steps $\Gamma /\tau$ in the standard/leapfrog diffusion model on NBA. $\tau = 5$ provides the best performance. + +
MethodSteps1.0s2.0s3.0sTotal(4.0s)Inference (ms)
Standard100.45/0.510.98/1.551.62/2.562.21/2.77~87
500.26/0.360.56/0.910.89/1.421.21/1.73~446
Diffusion (Γ)1000.21/0.280.44/0.640.69/0.950.94/1.21~886
2000.21/0.290.44/0.650.69/0.970.94/1.21>1s
5000.21/0.300.45/0.680.70/0.990.95/1.23>1s
Leapfrog30.20/0.310.40/0.620.62/0.880.84/1.10~30
Diffusion (τ)50.18/0.270.37/0.560.58/0.840.81/1.10~46
100.17/0.270.37/0.580.59/0.850.82/1.08~89
+ +# 5.4. Ablation Studies + +Effect of components in leapfrog initializer. We explore the effect of three key components in leapfrog initializer, including mean estimation, variance estimation, and sample prediction. Table 5 presents the results with mean and variance based on 5 experimental trials. We see that i) the leapfrog initializer achieves stable results with better performance even when prediction number $K$ is small; and ii) the proposed mean estimation, variance estimation, and sample prediction all contribute to promoting prediction accuracy. + +Effect of leapfrog step $\tau$ . Table 6 reports the influence of different leapfrog steps in LED. We see that i) under similar inference time, our method significantly outperforms the standard diffusion model with better representation ability; ii) when $\tau$ is too small, leapfrog initializer targets to learn more sophisticated distribution, causing worse prediction performance; and iii) when $\tau$ is too large, leapfrog initializer has already captured the denoised distribution, encountering performance bottleneck and wasting inference time. + +Comparison to other fast sampling methods. Table 7 compares the performance of our method and the other two fast sampling methods: PD [37] and DDIM [40]. We see that our method significantly outperforms two fast sampling methods under similar inference time since the proposed LED promotes the correlation between predictions. + +![](images/205b50b00688d86aa6a4485b8a55bc1b25cdf9b05973197595d0231ff01cf1fb.jpg) +(a) PECNet + +![](images/07360ce275d43da0a8a45ae2eac66de93110fae6c14398a326da717225b616bf.jpg) +(b) GroupNet + +![](images/e108ce9f295a15ab4637716be9aa7df76f358f0788e4b3494a19425a98e37cc8.jpg) +(c) Ours + +![](images/11552ded243966ff228ef61699a4b61e9651ae39eec663cd2c7eebc365166483.jpg) +(d) GT + +Table 7. Comparison to other fast sampling methods on NBA. $\eta = 1$ in DDIM. Our method achieves the best performance. + +
Method1.0s2.0s3.0sTotal(4.0s)Inference (ms)
PD (K=1)0.20/0.330.45/0.750.72/1.130.98/1.39~452
PD (K=2)0.21/0.340.46/0.780.73/1.150.98/1.41~230
PD (K=3)0.23/0.370.48/0.790.73/1.150.98/1.43~121
PD (K=4)0.25/0.380.50/0.800.75/1.160.99/1.44~64
DDIM (S=2)0.20/0.290.42/0.650.66/0.960.91/1.21~530
DDIM (S=10)0.22/0.320.44/0.710.69/1.040.93/1.31~107
DDIM (S=20)0.24/0.350.49/0.810.76/1.211.02/1.51~54
Ours0.18/0.270.37/0.560.58/0.840.81/1.10~46
+ +![](images/3baa9c7e93eb4aff7f1387b3943a818abf6829c32fa114f4ed9497ab54a9fe03.jpg) + +![](images/75993486e983ce54ac2d7009da7636aadd6e6a8b8f791700788ea8a83591efc0.jpg) + +Figure 4. Mean and variance estimation in leapfrog initializer on NBA with $K = 20$ . The estimated variance can reflect the scene complexity of the current agent and produce diverse predictions. +![](images/06487121e2a1b537d6e3839355f2dbd9cb648ee2262dcab14309b4565486a57f.jpg) +Past trajectory Mean estimation Our prediction Ground-truth + +![](images/ecc2166b8756bb0923dd67a5a40a359f3b4610e7c45b938f5f8eb1994e1c9a27.jpg) + +# 5.5. Qualitative Results + +Visualization of predicted trajectory. Figure 3 compares the predicted trajectories of two baselines PECNet and GroupNet, our LED (Ours), and the ground-truth (GT) trajectories on the NBA dataset. We see that our method produces more accurate predictions than the previous methods. + +Visualization of estimated mean and variance. Figure 4 illustrates the mean and variance estimation in the leapfrog initializer under four scenes on the NBA dataset. We see that the variance estimation can well describe the scene complexity for the current agent by the learned variance, showing the rationality of our variance estimation. + +Visualization of different sampling mechanisms. Figure 5 compares two sampling mechanisms: I.I.D sampling and correlated sampling in the leapfrog initializer. We see + +![](images/4b8a05611797c478dc3fba96f4b933d92cda2f6d2d1f2d5d89de5878d7fd01f5.jpg) +Figure 3. Visualization comparison on NBA. We compare the best-of-20 predictions by our method and two previous methods. Our method generates a more precise trajectory prediction. (Light color: past trajectory; blue/red/green color: two teams and the basketball.) +Figure 5. Comparison between I.I.D and correlated sampling mechanisms in NFL with $K = 4$ . Correlated samples appropriately capture multi-modalities, significantly improving prediction performances. that the proposed correlated sampling can appropriately allocate sample diversity and capture more modalities when the number of trials $K$ is small. + +# 6. Conclusion + +This paper proposes the leapfrog diffusion model (LED), a diffusion-based trajectory prediction model, which significantly accelerates the overall inference speed and enables appropriate allocations of multiple correlated predictions. During the inference, LED directly models and samples from the denoised distribution through a novel leapfrog initializer with reparameterization. Extensive experiments show that our method achieves state-of-the-art performance on four real-world datasets and satisfies real-time inference needs. + +Limitation and future work. This work achieves inference acceleration for trajectory prediction tasks partially because the dimension of trajectory data is relatively small and the corresponding distribution is much easier to learn compared with those of image/video data. A possible future work is to explore diffusion models and fast sampling methods for higher-dimensional tasks. + +# Acknowledgements + +This research is partially supported by National Natural Science Foundation of China under Grant 62171276 and the Science and Technology Commission of Shanghai Municipal under Grant 21511100900 and 22DZ2229005. + +# References + +[1] Alexandre Alahi, Kratarth Goel, Vignesh Ramanathan, Alexandre Robicquet, Li Fei-Fei, and Silvio Savarese. Social lstm: Human trajectory prediction in crowded spaces. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 961–971, 2016. 1, 2 +[2] Inhwan Bae, Jin-Hwi Park, and Hae-Gon Jeon. 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In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 9813-9823, 2021. 1, 7 \ No newline at end of file diff --git a/2023/Leapfrog Diffusion Model for Stochastic Trajectory Prediction/images.zip b/2023/Leapfrog Diffusion Model for Stochastic Trajectory Prediction/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..cf8f701b78ce92db834868599737c9978e872af9 --- /dev/null +++ b/2023/Leapfrog Diffusion Model for Stochastic Trajectory Prediction/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:c16f30e6fb0c1107e9d6d4a13561bd244047c09c4dc3e381a511e5693b2eccef +size 690342 diff --git a/2023/Leapfrog Diffusion Model for Stochastic Trajectory Prediction/layout.json b/2023/Leapfrog Diffusion Model for Stochastic Trajectory Prediction/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..b6f47aca98fa7bf1ba01e412eb06211cd1843ce3 --- /dev/null +++ b/2023/Leapfrog Diffusion Model for Stochastic Trajectory Prediction/layout.json @@ -0,0 +1,12079 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 104, + 103, + 489, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 103, + 489, + 121 + ], + "spans": [ + { + "bbox": [ + 104, + 103, + 489, + 121 + ], + "type": "text", + "content": "Leapfrog Diffusion Model for Stochastic Trajectory Prediction" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 122, + 142, + 470, + 172 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 122, + 142, + 470, + 172 + ], + "spans": [ + { + "bbox": [ + 122, + 142, + 470, + 172 + ], + "type": "text", + "content": "Weibo Mao" + }, + { + "bbox": [ + 122, + 142, + 470, + 172 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 122, + 142, + 470, + 172 + ], + "type": "text", + "content": ", Chenxin Xu" + }, + { + "bbox": [ + 122, + 142, + 470, + 172 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 122, + 142, + 470, + 172 + ], + "type": "text", + "content": ", Qi Zhu" + }, + { + "bbox": [ + 122, + 142, + 470, + 172 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 122, + 142, + 470, + 172 + ], + "type": "text", + "content": ", Siheng Chen" + }, + { + "bbox": [ + 122, + 142, + 470, + 172 + ], + "type": "inline_equation", + "content": "^{1,2*}" + }, + { + "bbox": [ + 122, + 142, + 470, + 172 + ], + "type": "text", + "content": ", Yanfeng Wang" + }, + { + "bbox": [ + 122, + 142, + 470, + 172 + ], + "type": "inline_equation", + "content": "^{2,1}" + }, + { + "bbox": [ + 122, + 142, + 470, + 172 + ], + "type": "text", + "content": ", Shanghai Jiao Tong University, Shanghai AI Laboratory" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 123, + 174, + 468, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 123, + 174, + 468, + 185 + ], + "spans": [ + { + "bbox": [ + 123, + 174, + 468, + 185 + ], + "type": "text", + "content": "{kirino.mao,xcxwakaka,georgezhu,sihengc,wangyanfeng}@sjtu.edu.cn" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "spans": [ + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 239, + 290, + 562 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 239, + 290, + 562 + ], + "spans": [ + { + "bbox": [ + 46, + 239, + 290, + 562 + ], + "type": "text", + "content": "To model the indeterminacy of human behaviors, stochastic trajectory prediction requires a sophisticated multi-modal distribution of future trajectories. Emerging diffusion models have revealed their tremendous representation capacities in numerous generation tasks, showing potential for stochastic trajectory prediction. However, expensive time consumption prevents diffusion models from real-time prediction, since a large number of denoising steps are required to assure sufficient representation ability. To resolve the dilemma, we present LEapfrog Diffusion model (LED), a novel diffusion-based trajectory prediction model, which provides real-time, precise, and diverse predictions. The core of the proposed LED is to leverage a trainable leapfrog initializer to directly learn an expressive multi-modal distribution of future trajectories, which skips a large number of denoising steps, significantly accelerating inference speed. Moreover, the leapfrog initializer is trained to appropriately allocate correlated samples to provide a diversity of predicted future trajectories, significantly improving prediction performances. Extensive experiments on four real-world datasets, including NBA/NFL/SDD/ETH-UCY, show that LED consistently improves performance and achieves " + }, + { + "bbox": [ + 46, + 239, + 290, + 562 + ], + "type": "inline_equation", + "content": "23.7\\% / 21.9\\%" + }, + { + "bbox": [ + 46, + 239, + 290, + 562 + ], + "type": "text", + "content": " ADE/FDE improvement on NFL. The proposed LED also speeds up the inference 19.3/30.8/24.3/25.1 times compared to the standard diffusion model on NBA/NFL/SDD/ETH-UCY, satisfying real-time inference needs. Code is available at https://github.com/MediaBrain-SJTU/LED." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 587, + 128, + 600 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 587, + 128, + 600 + ], + "spans": [ + { + "bbox": [ + 47, + 587, + 128, + 600 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 608, + 288, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 608, + 288, + 693 + ], + "spans": [ + { + "bbox": [ + 46, + 608, + 288, + 693 + ], + "type": "text", + "content": "Trajectory prediction aims to predict the future trajectories for one or multiple interacting agents conditioned on their past movements. This task plays a significant role in numerous applications, such as autonomous driving [24], drones [10], surveillance systems [45], human-robot interaction systems [5], and interactive robotics [20]. Recently, lots of fascinating research progresses have been made from" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 307, + 210, + 547, + 316 + ], + "blocks": [ + { + "bbox": [ + 307, + 210, + 547, + 316 + ], + "lines": [ + { + "bbox": [ + 307, + 210, + 547, + 316 + ], + "spans": [ + { + "bbox": [ + 307, + 210, + 547, + 316 + ], + "type": "image", + "image_path": "2a86b5ca34fffa6acc3d705145f1b8e75feccea00ca362b1be8e708d1beb865a.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 320, + 547, + 365 + ], + "lines": [ + { + "bbox": [ + 305, + 320, + 547, + 365 + ], + "spans": [ + { + "bbox": [ + 305, + 320, + 547, + 365 + ], + "type": "text", + "content": "Figure 1. Leapfrog diffusion model uses the leapfrog initializer to estimate the denoised distribution and substitute a long sequence of traditional denoising steps, accelerating inference and maintaining representation capacity." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 376, + 547, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 376, + 547, + 460 + ], + "spans": [ + { + "bbox": [ + 304, + 376, + 547, + 460 + ], + "type": "text", + "content": "many aspects, including temporal encoding [6, 13, 46, 53], interaction modeling [1, 15, 18, 43, 49], and rasterized prediction [11, 12, 26, 48]. In practice, to capture multiple possibilities of future trajectories, a real-world prediction system needs to produce multiple future trajectories. This leads to the emergence of stochastic trajectory prediction, aiming to precisely model the distribution of future trajectories." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 461, + 548, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 461, + 548, + 640 + ], + "spans": [ + { + "bbox": [ + 304, + 461, + 548, + 640 + ], + "type": "text", + "content": "Previous works have proposed a series of deep generative models for stochastic trajectory prediction. For example, [15, 18] exploit the generator adversarial networks (GANs) to model the future trajectory distribution; [27, 38, 49] consider the conditional variational autoencoders (CVAEs) structure; and [3] uses the conditional normalizing flow to relax the Gaussian prior in CVAEs and learn more representative priors. Recently, with the great success in image generation [17, 33] and audio synthesis [4, 21], denoising diffusion probabilistic models have been applied to time-series analysis and trajectory prediction, and show promising prediction performances [14, 44]. Compared to many other generative models, diffusion models have advantages in stable training and modeling sophisticated distributions through sufficient denoising steps [8]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 642, + 548, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 548, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 548, + 713 + ], + "type": "text", + "content": "However, there are two critical problems in diffusion models for stochastic trajectory prediction. First, the real-time inference is time-consuming [14]. To ensure the representation ability and generate high-quality samples, an adequate number of denoising steps are required in standard diffusion models, which costs more computational time. For" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 135, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 135, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 135, + 712 + ], + "type": "text", + "content": "*Corresponding author." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5517" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": "example, experiments show that on the NBA dataset, diffusion models need about 100 denoising steps to achieve decent prediction performances, which would take " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "\\sim 886\\mathrm{ms}" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": " to predict; while the next frame comes every " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "200\\mathrm{ms}" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": ". Second, as mentioned in [2], a limited number of independent and identically distributed samples might not be able to capture sufficient modalities in the underlying distribution of a generative model. Empirically, a few independent sampled trajectories could miss some important future possibilities due to the lack of appropriate sample allocation, significantly deteriorating prediction performances." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 205, + 289, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 205, + 289, + 384 + ], + "spans": [ + { + "bbox": [ + 46, + 205, + 289, + 384 + ], + "type": "text", + "content": "In this work, we propose leapfrog diffusion model (LED), a novel diffusion-based trajectory prediction model, which significantly accelerates the inference speed and enables adaptive and appropriate allocations of multiple correlated predictions, providing sufficient diversity in predictions. The core idea of the proposed LED is to learn a rough, yet sufficiently expressive distribution to initialize denoised future trajectories; instead of using a plain Gaussian distribution as in standard diffusion models. Specifically, our forward diffusion process is the same as standard diffusion models, which assures that the ultimate representation ability is pristine; while in the reverse denoising process, we leverage a powerful initializer to produce correlated diverse samples and leapfrog or skip a large number of denoising steps; and then, use only a few denoising steps to refine the distribution." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 385, + 289, + 517 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 385, + 289, + 517 + ], + "spans": [ + { + "bbox": [ + 46, + 385, + 289, + 517 + ], + "type": "text", + "content": "To implement such a leapfrog initializer, we consider a reparameterization to alleviate the learning burden. We disassemble a denoised distribution into three parts: mean trajectory, variance, and sample positions under the normalized distribution. To estimate these three, we design three corresponding trainable modules, each of which leverages both a social encoder and a temporal encoder to learn the social-temporal features and produce accurate estimation. Furthermore, all the sample positions are simultaneously generated based on the same social-temporal features, enabling appropriate sample allocations to provide diversity." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 518, + 289, + 625 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 518, + 289, + 625 + ], + "spans": [ + { + "bbox": [ + 46, + 518, + 289, + 625 + ], + "type": "text", + "content": "To evaluate the effectiveness of the proposed method, we conduct experiments on four trajectory prediction datasets: NBA, NFL Football Dataset, Standford Drones Dataset, and ETH-UCY. The quantitative results show we outperform the previous methods and achieve state-of-the-art performance. Specifically, compared to MID [14], the proposed leapfrog diffusion model reduces the average prediction time from " + }, + { + "bbox": [ + 46, + 518, + 289, + 625 + ], + "type": "inline_equation", + "content": "\\sim 886\\mathrm{ms}" + }, + { + "bbox": [ + 46, + 518, + 289, + 625 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 518, + 289, + 625 + ], + "type": "inline_equation", + "content": "\\sim 46\\mathrm{ms}" + }, + { + "bbox": [ + 46, + 518, + 289, + 625 + ], + "type": "text", + "content": " on the NBA dataset, while achieving a " + }, + { + "bbox": [ + 46, + 518, + 289, + 625 + ], + "type": "inline_equation", + "content": "15.6\\% / 13.4\\%" + }, + { + "bbox": [ + 46, + 518, + 289, + 625 + ], + "type": "text", + "content": " ADE/FDE improvement." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 59, + 628, + 259, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 628, + 259, + 639 + ], + "spans": [ + { + "bbox": [ + 59, + 628, + 259, + 639 + ], + "type": "text", + "content": "The main contributions are concluded as follows," + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 640, + 289, + 714 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 46, + 640, + 287, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 640, + 287, + 688 + ], + "spans": [ + { + "bbox": [ + 46, + 640, + 287, + 688 + ], + "type": "text", + "content": "- We propose a novel LEapfrog Diffusion model (LED), which is a denoising-diffusion-based stochastic trajectory prediction model. It achieves precise and diverse predictions with fast inference speed." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 689, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 289, + 714 + ], + "type": "text", + "content": "- We propose a novel trainable leapfrog initializer to directly model sophisticated denoised distributions, accelerator" + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 304, + 72, + 545, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 95 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 95 + ], + "type": "text", + "content": "ating inference speed, and adaptively allocating the sample diversity, improving prediction performance." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 96, + 547, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 96, + 547, + 168 + ], + "spans": [ + { + "bbox": [ + 304, + 96, + 547, + 168 + ], + "type": "text", + "content": "- We conduct extensive experiments on four datasets including NBA, NFL, SDD, and ETH-UCY. Results show that i) our approach consistently achieves state-of-the-art performance on all datasets; and ii) our method speeds up the inference by around 20 times compared to the standard diffusion model, satisfying real-time prediction needs." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 178, + 392, + 192 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 178, + 392, + 192 + ], + "spans": [ + { + "bbox": [ + 305, + 178, + 392, + 192 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 199, + 547, + 462 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 199, + 547, + 462 + ], + "spans": [ + { + "bbox": [ + 304, + 199, + 547, + 462 + ], + "type": "text", + "content": "Trajectory prediction. Early works on trajectory prediction focus on a deterministic approach by exploring force models [16, 30], RNNs [1, 32, 47], and frequency analysis [28, 29]. For example, [16] models an agent's behavior with attractive and repulsive forces and builds the force equations for prediction. To capture the multi-modalities and model future distribution, recent works start to focus on stochastic trajectory prediction and have proposed a series of deep generative models. Generative Adversarial Network (GAN) structures [7, 9, 15, 18, 22, 36, 42] are proposed to generate multiple future trajectory distribution. [23, 27, 38, 49, 51] use the Variational Auto-Encoder (VAE) structure and learn the distribution through variational inference. [3] relaxes the Gaussian prior and proposes to use the normalizing flow. Heatmap [11, 12, 26] is used for modeling future trajectories' distribution on rasterized images. In this work, we propose a new diffusion-based model for trajectory prediction. Compared to previous generative models, our method has a large representation capacity and can model sophisticated trajectory distributions by using a number of diffusion steps. We also enable the correlation between samples to adaptively adjust sample diversity, improving prediction performance." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 463, + 547, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 463, + 547, + 594 + ], + "spans": [ + { + "bbox": [ + 304, + 463, + 547, + 594 + ], + "type": "text", + "content": "Denoising diffusion probabilistic models. Denoising diffusion probabilistic models (diffusion models) [17, 39, 41] have recently achieved significant results in image generation [8, 33] and audio synthesis [4, 21]. The idea of diffusion models is first proposed by DPM [39], which imitates the diffusion process in non-equilibrium statistical physics and reconstructs the data distribution using the denoising model. Later, [35, 44] propose diffusion models, combining with the seq-to-seq models, for probabilistic time series forecasting. MID [14] is the first to build diffusion models for trajectory prediction in modeling the indeterminacy variation process." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 594, + 548, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 548, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 548, + 713 + ], + "type": "text", + "content": "The standard diffusion models use hundreds of denoising steps, preventing these models from real-time applications. To accelerate the sampling process, DDIM [40] first predicts the original data and then estimates the direction to the next expected timestamp based on the non-Markov process. PD [37] applies the knowledge distillation on the denoising steps with a deterministic diffusion sampler, which will be repeated for times to accelerate the sampling. All these fast sampling methods start denoising from noise inputs, which are randomly and independently initialized. In this work, we" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5518" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 109 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 109 + ], + "type": "text", + "content": "use a trainable leapfrog initializer to initialize a sufficiently expressive distribution, which replaces a large number of former denoising steps for much faster inference speed." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 121, + 126, + 133 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 121, + 126, + 133 + ], + "spans": [ + { + "bbox": [ + 47, + 121, + 126, + 133 + ], + "type": "text", + "content": "3. Background" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 140, + 171, + 152 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 140, + 171, + 152 + ], + "spans": [ + { + "bbox": [ + 47, + 140, + 171, + 152 + ], + "type": "text", + "content": "3.1. Problem Formulation" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 159, + 287, + 302 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 159, + 287, + 302 + ], + "spans": [ + { + "bbox": [ + 47, + 159, + 287, + 302 + ], + "type": "text", + "content": "Trajectory prediction aims to predict an agent's future trajectory based on the past trajectories of itself and surrounding agents. For a to-be-predicted agent, let " + }, + { + "bbox": [ + 47, + 159, + 287, + 302 + ], + "type": "inline_equation", + "content": "\\mathbf{X} = [\\mathbf{x}^{-T_{\\mathrm{p}} + 1},\\mathbf{x}^{-T_{\\mathrm{p}} + 2},\\dots ,\\mathbf{x}^{0}] \\in \\mathbb{R}^{T_{\\mathrm{p}} \\times 2}" + }, + { + "bbox": [ + 47, + 159, + 287, + 302 + ], + "type": "text", + "content": " be the observed past trajectory over " + }, + { + "bbox": [ + 47, + 159, + 287, + 302 + ], + "type": "inline_equation", + "content": "T_{\\mathrm{p}}" + }, + { + "bbox": [ + 47, + 159, + 287, + 302 + ], + "type": "text", + "content": " timestamps where " + }, + { + "bbox": [ + 47, + 159, + 287, + 302 + ], + "type": "inline_equation", + "content": "\\mathbf{x}^t \\in \\mathbb{R}^2" + }, + { + "bbox": [ + 47, + 159, + 287, + 302 + ], + "type": "text", + "content": " records the 2D spatial coordinate at timestamp " + }, + { + "bbox": [ + 47, + 159, + 287, + 302 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 47, + 159, + 287, + 302 + ], + "type": "text", + "content": ". Let " + }, + { + "bbox": [ + 47, + 159, + 287, + 302 + ], + "type": "inline_equation", + "content": "\\mathcal{N}" + }, + { + "bbox": [ + 47, + 159, + 287, + 302 + ], + "type": "text", + "content": " be the neighbouring agent set and " + }, + { + "bbox": [ + 47, + 159, + 287, + 302 + ], + "type": "inline_equation", + "content": "\\mathbb{X}_{\\mathcal{N}} = [\\mathbf{X}_{\\mathcal{N}_1},\\mathbf{X}_{\\mathcal{N}_2},\\dots ,\\mathbf{X}_{\\mathcal{N}_L}] \\in \\mathbb{R}^{L \\times T_{\\mathrm{p}} \\times 2}" + }, + { + "bbox": [ + 47, + 159, + 287, + 302 + ], + "type": "text", + "content": " be the past trajectories of neighbours, where " + }, + { + "bbox": [ + 47, + 159, + 287, + 302 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_{\\mathcal{N}_\\ell} \\in \\mathbb{R}^{T_{\\mathrm{p}} \\times 2}" + }, + { + "bbox": [ + 47, + 159, + 287, + 302 + ], + "type": "text", + "content": " is the trajectory of the " + }, + { + "bbox": [ + 47, + 159, + 287, + 302 + ], + "type": "inline_equation", + "content": "\\ell" + }, + { + "bbox": [ + 47, + 159, + 287, + 302 + ], + "type": "text", + "content": "th neighbour. The corresponding ground-truth future trajectory for the to-be-predicted agent is " + }, + { + "bbox": [ + 47, + 159, + 287, + 302 + ], + "type": "inline_equation", + "content": "\\mathbf{Y} = [\\mathbf{y}^1,\\mathbf{y}^2,\\dots,\\mathbf{y}^{T_{\\mathrm{f}}}] \\in \\mathbb{R}^{T_{\\mathrm{f}} \\times 2}" + }, + { + "bbox": [ + 47, + 159, + 287, + 302 + ], + "type": "text", + "content": " over " + }, + { + "bbox": [ + 47, + 159, + 287, + 302 + ], + "type": "inline_equation", + "content": "T_{\\mathrm{f}}" + }, + { + "bbox": [ + 47, + 159, + 287, + 302 + ], + "type": "text", + "content": " timestamps, where " + }, + { + "bbox": [ + 47, + 159, + 287, + 302 + ], + "type": "inline_equation", + "content": "\\mathbf{y}^t \\in \\mathbb{R}^2" + }, + { + "bbox": [ + 47, + 159, + 287, + 302 + ], + "type": "text", + "content": " is the 2D coordinate at future timestamp " + }, + { + "bbox": [ + 47, + 159, + 287, + 302 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 47, + 159, + 287, + 302 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 304, + 287, + 435 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 304, + 287, + 435 + ], + "spans": [ + { + "bbox": [ + 47, + 304, + 287, + 435 + ], + "type": "text", + "content": "Because of the indeterminacy of future trajectories, it is usually more reliable to predict more than one trajectory to capture multiple possibilities. Here we consider stochastic trajectory prediction, which predicts the distribution of a future trajectory, instead of a single future trajectory. The goal of stochastic trajectory prediction is to train a prediction model " + }, + { + "bbox": [ + 47, + 304, + 287, + 435 + ], + "type": "inline_equation", + "content": "g_{\\theta}(\\cdot)" + }, + { + "bbox": [ + 47, + 304, + 287, + 435 + ], + "type": "text", + "content": " with parameters " + }, + { + "bbox": [ + 47, + 304, + 287, + 435 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 47, + 304, + 287, + 435 + ], + "type": "text", + "content": " to generate a distribution " + }, + { + "bbox": [ + 47, + 304, + 287, + 435 + ], + "type": "inline_equation", + "content": "\\mathcal{P}_{\\theta} = g_{\\theta}(\\mathbf{X},\\mathbb{X}_{\\mathcal{N}})" + }, + { + "bbox": [ + 47, + 304, + 287, + 435 + ], + "type": "text", + "content": ". Based on this distribution " + }, + { + "bbox": [ + 47, + 304, + 287, + 435 + ], + "type": "inline_equation", + "content": "\\mathcal{P}_{\\theta}" + }, + { + "bbox": [ + 47, + 304, + 287, + 435 + ], + "type": "text", + "content": ", we can draw " + }, + { + "bbox": [ + 47, + 304, + 287, + 435 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 47, + 304, + 287, + 435 + ], + "type": "text", + "content": " samples, " + }, + { + "bbox": [ + 47, + 304, + 287, + 435 + ], + "type": "inline_equation", + "content": "\\widehat{\\mathcal{Y}} = \\{\\widehat{\\mathbf{Y}}_1,\\widehat{\\mathbf{Y}}_2,\\dots ,\\widehat{\\mathbf{Y}}_K\\}" + }, + { + "bbox": [ + 47, + 304, + 287, + 435 + ], + "type": "text", + "content": ", so that at least one sample is close to the ground-truth future trajectory. The overall learning problem is" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 78, + 437, + 287, + 460 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 78, + 437, + 287, + 460 + ], + "spans": [ + { + "bbox": [ + 78, + 437, + 287, + 460 + ], + "type": "interline_equation", + "content": "\\theta^ {*} = \\min _ {\\theta} \\min _ {\\widehat {\\mathbf {Y}} _ {i} \\in \\widehat {\\mathcal {Y}}} D (\\widehat {\\mathbf {Y}} _ {i}, \\mathbf {Y}), \\quad \\text {s . t .} \\quad \\widehat {\\mathcal {Y}} \\sim \\mathcal {P} _ {\\theta}. \\tag {1}", + "image_path": "940db56a16c8c2552bead58da4b0fd97716c5fb04ecd5510f312b3c7be916036.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 468, + 265, + 481 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 468, + 265, + 481 + ], + "spans": [ + { + "bbox": [ + 47, + 468, + 265, + 481 + ], + "type": "text", + "content": "3.2. Diffusion Model for Trajectory Prediction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 487, + 287, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 487, + 287, + 594 + ], + "spans": [ + { + "bbox": [ + 47, + 487, + 287, + 594 + ], + "type": "text", + "content": "Here we present a standard diffusion model for trajectory prediction, which lays a foundation for the proposed method. The core idea is to learn and refine a sophisticated underlying distribution of trajectories through cascading a series of simple denoising steps. To implement this, a diffusion model performs a forward diffusion process to intentionally add a series of noises to a ground-truth future trajectory; and then, it uses a conditional denoising process to recover the future trajectory from noise inputs conditioned on past trajectories." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 595, + 287, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 595, + 287, + 643 + ], + "spans": [ + { + "bbox": [ + 47, + 595, + 287, + 643 + ], + "type": "text", + "content": "Mathematically, let " + }, + { + "bbox": [ + 47, + 595, + 287, + 643 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 47, + 595, + 287, + 643 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 595, + 287, + 643 + ], + "type": "inline_equation", + "content": "\\mathbb{X}_{\\mathcal{N}}" + }, + { + "bbox": [ + 47, + 595, + 287, + 643 + ], + "type": "text", + "content": " be the past trajectories of the ego agent and the neighboring agents, respectively, and " + }, + { + "bbox": [ + 47, + 595, + 287, + 643 + ], + "type": "inline_equation", + "content": "\\mathbf{Y}" + }, + { + "bbox": [ + 47, + 595, + 287, + 643 + ], + "type": "text", + "content": " be the future trajectory of the ego agent. The diffusion model for trajectory prediction works as follows," + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 58, + 644, + 287, + 657 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 644, + 287, + 657 + ], + "spans": [ + { + "bbox": [ + 58, + 644, + 287, + 657 + ], + "type": "interline_equation", + "content": "\\mathbf {Y} ^ {0} = \\mathbf {Y}, \\tag {2a}", + "image_path": "fc44d444aa8c5d73fd1da85564d681c0ecf10cea11606abdde48d3bc12afacf6.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 58, + 662, + 287, + 673 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 662, + 287, + 673 + ], + "spans": [ + { + "bbox": [ + 58, + 662, + 287, + 673 + ], + "type": "interline_equation", + "content": "\\mathbf {Y} ^ {\\gamma} = f _ {\\text {d i f f u s e}} \\left(\\mathbf {Y} ^ {\\gamma - 1}\\right), \\gamma = 1, \\dots , \\Gamma , \\tag {2b}", + "image_path": "2d4051a2f0a14ca8b20d77878e7b5803325f362374719565b7e03e3b54591142.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 58, + 678, + 287, + 693 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 678, + 287, + 693 + ], + "spans": [ + { + "bbox": [ + 58, + 678, + 287, + 693 + ], + "type": "interline_equation", + "content": "\\widehat {\\mathbf {Y}} _ {k} ^ {\\Gamma} \\stackrel {i. i. d} {\\sim} \\mathcal {P} (\\widehat {\\mathbf {Y}} ^ {\\Gamma}) = \\mathcal {N} (\\widehat {\\mathbf {Y}} ^ {\\Gamma}; \\mathbf {0}, \\mathbf {I}), \\text {s a m p l e} K \\text {t i m e s}, \\tag {2c}", + "image_path": "5594aec7165a347ee03b893c7306e58559e8cce754d7bac7977600c974968777.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 58, + 696, + 287, + 711 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 696, + 287, + 711 + ], + "spans": [ + { + "bbox": [ + 58, + 696, + 287, + 711 + ], + "type": "interline_equation", + "content": "\\hat {\\mathbf {Y}} _ {k} ^ {\\gamma} = f _ {\\text {d e n o i s e}} \\left(\\hat {\\mathbf {Y}} _ {k} ^ {\\gamma + 1}, \\mathbf {X}, \\mathbb {X} _ {\\mathcal {N}}\\right), \\gamma = \\Gamma - 1, \\dots , 0, \\tag {2d}", + "image_path": "c5509d0d9c54bf9cbfaac0ff56b45d6ff89f5b492a308724a308ac6dd7228c57.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 72, + 545, + 121 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 545, + 121 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 545, + 121 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 72, + 545, + 121 + ], + "type": "inline_equation", + "content": "\\mathbf{Y}^{\\gamma}" + }, + { + "bbox": [ + 306, + 72, + 545, + 121 + ], + "type": "text", + "content": " is the noisy trajectory at the " + }, + { + "bbox": [ + 306, + 72, + 545, + 121 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 306, + 72, + 545, + 121 + ], + "type": "text", + "content": "th diffusion step and " + }, + { + "bbox": [ + 306, + 72, + 545, + 121 + ], + "type": "inline_equation", + "content": "\\widehat{\\mathbf{Y}}_k^\\gamma" + }, + { + "bbox": [ + 306, + 72, + 545, + 121 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 306, + 72, + 545, + 121 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 306, + 72, + 545, + 121 + ], + "type": "text", + "content": "th sample of denoised trajectory at the " + }, + { + "bbox": [ + 306, + 72, + 545, + 121 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 306, + 72, + 545, + 121 + ], + "type": "text", + "content": "th denoising step. The final " + }, + { + "bbox": [ + 306, + 72, + 545, + 121 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 306, + 72, + 545, + 121 + ], + "type": "text", + "content": " predicted trajectories are " + }, + { + "bbox": [ + 306, + 72, + 545, + 121 + ], + "type": "inline_equation", + "content": "\\widehat{\\mathcal{V}} = \\{\\widehat{\\mathbf{Y}}_1^0, \\widehat{\\mathbf{Y}}_2^0, \\ldots, \\widehat{\\mathbf{Y}}_K^0\\}" + }, + { + "bbox": [ + 306, + 72, + 545, + 121 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 122, + 547, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 122, + 547, + 277 + ], + "spans": [ + { + "bbox": [ + 304, + 122, + 547, + 277 + ], + "type": "text", + "content": "Step (2a) initializes the diffused trajectory; Step (2b) uses a forward diffusion operation " + }, + { + "bbox": [ + 304, + 122, + 547, + 277 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{diffuse}}(\\cdot)" + }, + { + "bbox": [ + 304, + 122, + 547, + 277 + ], + "type": "text", + "content": " to successively add noises to " + }, + { + "bbox": [ + 304, + 122, + 547, + 277 + ], + "type": "inline_equation", + "content": "\\mathbf{Y}^{\\gamma - 1}" + }, + { + "bbox": [ + 304, + 122, + 547, + 277 + ], + "type": "text", + "content": " and obtain the diffused trajectory " + }, + { + "bbox": [ + 304, + 122, + 547, + 277 + ], + "type": "inline_equation", + "content": "\\mathbf{Y}^{\\gamma}" + }, + { + "bbox": [ + 304, + 122, + 547, + 277 + ], + "type": "text", + "content": "; Step (2c) draws " + }, + { + "bbox": [ + 304, + 122, + 547, + 277 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 122, + 547, + 277 + ], + "type": "text", + "content": " independent and identically distributed samples to initialize denoised trajectories " + }, + { + "bbox": [ + 304, + 122, + 547, + 277 + ], + "type": "inline_equation", + "content": "\\widehat{\\mathbf{Y}}_k^\\Gamma" + }, + { + "bbox": [ + 304, + 122, + 547, + 277 + ], + "type": "text", + "content": " from a normal distribution; and Step (2d) iteratively applies a denoising operation " + }, + { + "bbox": [ + 304, + 122, + 547, + 277 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{denoise}}(\\cdot)" + }, + { + "bbox": [ + 304, + 122, + 547, + 277 + ], + "type": "text", + "content": " to obtain the denoised trajectory " + }, + { + "bbox": [ + 304, + 122, + 547, + 277 + ], + "type": "inline_equation", + "content": "\\widehat{\\mathbf{Y}}_k^\\gamma" + }, + { + "bbox": [ + 304, + 122, + 547, + 277 + ], + "type": "text", + "content": " conditioned on past trajectories " + }, + { + "bbox": [ + 304, + 122, + 547, + 277 + ], + "type": "inline_equation", + "content": "\\mathbf{X}, \\mathbb{X}_{\\mathcal{N}}" + }, + { + "bbox": [ + 304, + 122, + 547, + 277 + ], + "type": "text", + "content": ". Note that i) Steps (2a) and (2b) correspond to the forward diffusion process and are not used in inference; ii) During training, " + }, + { + "bbox": [ + 304, + 122, + 547, + 277 + ], + "type": "inline_equation", + "content": "\\mathbf{Y}^{\\gamma}" + }, + { + "bbox": [ + 304, + 122, + 547, + 277 + ], + "type": "text", + "content": " is naturally the supervision for " + }, + { + "bbox": [ + 304, + 122, + 547, + 277 + ], + "type": "inline_equation", + "content": "\\widehat{\\mathbf{Y}}_k^\\gamma" + }, + { + "bbox": [ + 304, + 122, + 547, + 277 + ], + "type": "text", + "content": " at the " + }, + { + "bbox": [ + 304, + 122, + 547, + 277 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 304, + 122, + 547, + 277 + ], + "type": "text", + "content": "th step. Conceptually, each denoising step is the reverse of the diffusion step, and each pair of " + }, + { + "bbox": [ + 304, + 122, + 547, + 277 + ], + "type": "inline_equation", + "content": "\\mathbf{Y}^{\\gamma}" + }, + { + "bbox": [ + 304, + 122, + 547, + 277 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 122, + 547, + 277 + ], + "type": "inline_equation", + "content": "\\widehat{\\mathbf{Y}}_k^\\gamma" + }, + { + "bbox": [ + 304, + 122, + 547, + 277 + ], + "type": "text", + "content": " shares the same underlying distribution." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 278, + 547, + 410 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 278, + 547, + 410 + ], + "spans": [ + { + "bbox": [ + 304, + 278, + 547, + 410 + ], + "type": "text", + "content": "The standard diffusion model is expressively powerful in learning sophisticated distributions and has achieved great success in many generation tasks. However, the task of motion prediction requires real-time inference but the running time of a diffusion model is constrained by the large number of denoising steps. Meanwhile, less denoising steps usually cause a weaker representation ability of future distributions. To achieve higher efficiency while preserving a promising representation ability, we propose leapfrog diffusion model, which uses a trainable initializer to capture sophisticated distributions and substitute a large number of denoising steps." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 422, + 454, + 435 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 422, + 454, + 435 + ], + "spans": [ + { + "bbox": [ + 306, + 422, + 454, + 435 + ], + "type": "text", + "content": "4. Leapfrog Diffusion Model" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 441, + 424, + 453 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 441, + 424, + 453 + ], + "spans": [ + { + "bbox": [ + 306, + 441, + 424, + 453 + ], + "type": "text", + "content": "4.1. System Architecture" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 460, + 547, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 460, + 547, + 567 + ], + "spans": [ + { + "bbox": [ + 304, + 460, + 547, + 567 + ], + "type": "text", + "content": "In this section, we propose the leapfrog diffusion model. Here leapfrog means that a large number of small denoising steps can be replaced by a single, yet powerful leapfrog initializer, which can significantly accelerate the inference speed without losing representation ability. Let " + }, + { + "bbox": [ + 304, + 460, + 547, + 567 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 304, + 460, + 547, + 567 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 460, + 547, + 567 + ], + "type": "inline_equation", + "content": "\\mathbb{X}_{\\mathcal{N}}" + }, + { + "bbox": [ + 304, + 460, + 547, + 567 + ], + "type": "text", + "content": " be the past trajectories of the ego agent and its neighboring agents, and " + }, + { + "bbox": [ + 304, + 460, + 547, + 567 + ], + "type": "inline_equation", + "content": "\\mathbf{Y}" + }, + { + "bbox": [ + 304, + 460, + 547, + 567 + ], + "type": "text", + "content": " be the future trajectory of the ego agent. Denote " + }, + { + "bbox": [ + 304, + 460, + 547, + 567 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 460, + 547, + 567 + ], + "type": "text", + "content": " as the leapfrog step. The overall procedure of the proposed leapfrog diffusion model is formulated as follows," + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 318, + 574, + 545, + 586 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 574, + 545, + 586 + ], + "spans": [ + { + "bbox": [ + 318, + 574, + 545, + 586 + ], + "type": "interline_equation", + "content": "\\mathbf {Y} ^ {0} = \\mathbf {Y}, \\tag {3a}", + "image_path": "5fffa185d0f03f5d4495e998fa31a2f0ca45fdb4cb12ac8f1ee74537d6f4da8d.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 318, + 591, + 545, + 603 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 591, + 545, + 603 + ], + "spans": [ + { + "bbox": [ + 318, + 591, + 545, + 603 + ], + "type": "interline_equation", + "content": "\\mathbf {Y} ^ {\\gamma} = f _ {\\text {d i f f u s e}} \\left(\\mathbf {Y} ^ {\\gamma - 1}\\right), \\gamma = 1, \\dots , \\Gamma , \\tag {3b}", + "image_path": "917b55a350ffec6b2c314ad33b5e1d8e09891ab3818fe84d686b7a0630c04bb9.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 318, + 608, + 545, + 622 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 608, + 545, + 622 + ], + "spans": [ + { + "bbox": [ + 318, + 608, + 545, + 622 + ], + "type": "interline_equation", + "content": "\\hat {\\mathcal {Y}} ^ {\\tau} \\stackrel {K} {\\sim} \\mathcal {P} \\left(\\hat {\\mathbf {Y}} ^ {\\tau}\\right) = f _ {\\text {L S G}} \\left(\\mathbf {X}, \\mathbb {X} _ {\\mathcal {N}}\\right), \\tag {3c}", + "image_path": "d15a4ec0e36172c3fd75f639c3d2998d59136333ddefd758d902a3db6413c2f9.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 318, + 625, + 545, + 640 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 625, + 545, + 640 + ], + "spans": [ + { + "bbox": [ + 318, + 625, + 545, + 640 + ], + "type": "interline_equation", + "content": "\\widehat {\\mathbf {Y}} _ {k} ^ {\\gamma} = f _ {\\text {d e n o i s e}} \\left(\\widehat {\\mathbf {Y}} _ {k} ^ {\\gamma + 1}, \\mathbf {X}, \\mathbb {X} _ {\\mathcal {N}}\\right), \\gamma = \\tau - 1, \\dots , 0. \\tag {3d}", + "image_path": "e7db430df0c61d09ca484062f2482c3cf7d1477db52db3709ae8d243d1d54d39.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 306, + 642, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 642, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 642, + 547, + 713 + ], + "type": "text", + "content": "Compared to the standard diffusion model (2), the main difference lies in Step (3c). The standard diffusion initializes the " + }, + { + "bbox": [ + 306, + 642, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\Gamma" + }, + { + "bbox": [ + 306, + 642, + 547, + 713 + ], + "type": "text", + "content": "th denoised distribution " + }, + { + "bbox": [ + 306, + 642, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{P}(\\widehat{\\mathbf{Y}}^{\\Gamma})" + }, + { + "bbox": [ + 306, + 642, + 547, + 713 + ], + "type": "text", + "content": " by a plain normal distribution (2c) and requires a lot of denoising steps to enrich the expressiveness of the denoised distribution; while in Step (3c), we propose a novel leapfrog initial" + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "5519" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 69, + 43, + 531, + 162 + ], + "blocks": [ + { + "bbox": [ + 69, + 43, + 531, + 162 + ], + "lines": [ + { + "bbox": [ + 69, + 43, + 531, + 162 + ], + "spans": [ + { + "bbox": [ + 69, + 43, + 531, + 162 + ], + "type": "image", + "image_path": "178473828a87aff0634fb6c2aa6758e32a1861f4a571c6723c204224a01568c7.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 164, + 547, + 199 + ], + "lines": [ + { + "bbox": [ + 46, + 164, + 547, + 199 + ], + "spans": [ + { + "bbox": [ + 46, + 164, + 547, + 199 + ], + "type": "text", + "content": "Figure 2. Proposed leapfrog diffusion model (LED) in inference phase. The red agent is the to-be-predicted agent. LED first predicts " + }, + { + "bbox": [ + 46, + 164, + 547, + 199 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 164, + 547, + 199 + ], + "type": "text", + "content": " initialized trajectories at " + }, + { + "bbox": [ + 46, + 164, + 547, + 199 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 46, + 164, + 547, + 199 + ], + "type": "text", + "content": "th denoised step through a trainable leapfrog initializer. Then, followed by a few denoising steps, LED obtains the final predictions. In leapfrog initializer, LED learns statistics and generates correlated samples with the reparameterization." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 206, + 289, + 321 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 206, + 289, + 321 + ], + "spans": [ + { + "bbox": [ + 46, + 206, + 289, + 321 + ], + "type": "text", + "content": "izer " + }, + { + "bbox": [ + 46, + 206, + 289, + 321 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{LSG}}(\\cdot)" + }, + { + "bbox": [ + 46, + 206, + 289, + 321 + ], + "type": "text", + "content": " to directly model the " + }, + { + "bbox": [ + 46, + 206, + 289, + 321 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 46, + 206, + 289, + 321 + ], + "type": "text", + "content": "th denoised distribution " + }, + { + "bbox": [ + 46, + 206, + 289, + 321 + ], + "type": "inline_equation", + "content": "\\mathcal{P}(\\widehat{\\mathbf{Y}}^{\\tau})" + }, + { + "bbox": [ + 46, + 206, + 289, + 321 + ], + "type": "text", + "content": ", which is hypothetically equivalent to the output of executing " + }, + { + "bbox": [ + 46, + 206, + 289, + 321 + ], + "type": "inline_equation", + "content": "(\\Gamma - \\tau)" + }, + { + "bbox": [ + 46, + 206, + 289, + 321 + ], + "type": "text", + "content": " denoising steps (2d). We then draw samples from the distribution " + }, + { + "bbox": [ + 46, + 206, + 289, + 321 + ], + "type": "inline_equation", + "content": "\\mathcal{P}(\\widehat{\\mathbf{Y}}^{\\tau})" + }, + { + "bbox": [ + 46, + 206, + 289, + 321 + ], + "type": "text", + "content": " and obtain " + }, + { + "bbox": [ + 46, + 206, + 289, + 321 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 206, + 289, + 321 + ], + "type": "text", + "content": " future trajectories " + }, + { + "bbox": [ + 46, + 206, + 289, + 321 + ], + "type": "inline_equation", + "content": "\\widehat{\\mathcal{Y}}^{\\tau} = \\{\\widehat{\\mathbf{Y}}_1^{\\tau}, \\widehat{\\mathbf{Y}}_2^{\\tau}, \\dots, \\widehat{\\mathbf{Y}}_K^{\\tau}\\}" + }, + { + "bbox": [ + 46, + 206, + 289, + 321 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 206, + 289, + 321 + ], + "type": "inline_equation", + "content": "\\stackrel{K}{\\sim}" + }, + { + "bbox": [ + 46, + 206, + 289, + 321 + ], + "type": "text", + "content": " in (3d) means " + }, + { + "bbox": [ + 46, + 206, + 289, + 321 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 206, + 289, + 321 + ], + "type": "text", + "content": " samples are dependent to intentionally allocate appropriate sample diversity. Then, in Step (3d), we only need to apply the remaining " + }, + { + "bbox": [ + 46, + 206, + 289, + 321 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 46, + 206, + 289, + 321 + ], + "type": "text", + "content": " denoising steps for each trajectory " + }, + { + "bbox": [ + 46, + 206, + 289, + 321 + ], + "type": "inline_equation", + "content": "\\widehat{\\mathbf{Y}}_k^\\gamma" + }, + { + "bbox": [ + 46, + 206, + 289, + 321 + ], + "type": "text", + "content": " to obtain the final prediction " + }, + { + "bbox": [ + 46, + 206, + 289, + 321 + ], + "type": "inline_equation", + "content": "\\widehat{\\mathcal{Y}} = \\{\\widehat{\\mathbf{Y}}_1^0, \\widehat{\\mathbf{Y}}_2^0, \\dots, \\widehat{\\mathbf{Y}}_K^0\\}" + }, + { + "bbox": [ + 46, + 206, + 289, + 321 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 322, + 290, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 322, + 290, + 453 + ], + "spans": [ + { + "bbox": [ + 46, + 322, + 290, + 453 + ], + "type": "text", + "content": "Note that i) the proposed leapfrog diffusion model reduces the denoising steps from " + }, + { + "bbox": [ + 46, + 322, + 290, + 453 + ], + "type": "inline_equation", + "content": "\\Gamma" + }, + { + "bbox": [ + 46, + 322, + 290, + 453 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 322, + 290, + 453 + ], + "type": "inline_equation", + "content": "\\tau (\\ll \\Gamma)" + }, + { + "bbox": [ + 46, + 322, + 290, + 453 + ], + "type": "text", + "content": " in Step (3d) as the leapfrog initializer directly provides the trajectories at denoising step " + }, + { + "bbox": [ + 46, + 322, + 290, + 453 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 46, + 322, + 290, + 453 + ], + "type": "text", + "content": ", accelerating the inference; ii) instead of taking independent and identically distributed samples in Step (2c), the proposed leapfrog initializer generates " + }, + { + "bbox": [ + 46, + 322, + 290, + 453 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 322, + 290, + 453 + ], + "type": "text", + "content": " trajectories " + }, + { + "bbox": [ + 46, + 322, + 290, + 453 + ], + "type": "inline_equation", + "content": "\\widehat{\\mathcal{Y}}^{\\tau}" + }, + { + "bbox": [ + 46, + 322, + 290, + 453 + ], + "type": "text", + "content": " simultaneously in Step (3c), allowing " + }, + { + "bbox": [ + 46, + 322, + 290, + 453 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 322, + 290, + 453 + ], + "type": "text", + "content": " samples to be aware of each other; and iii) the standard diffusion model and the proposed leapfrog diffusion model share the same forward diffusion process, assuring that the representation capacity is not reduced." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 465, + 162, + 478 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 465, + 162, + 478 + ], + "spans": [ + { + "bbox": [ + 47, + 465, + 162, + 478 + ], + "type": "text", + "content": "4.2. Leapfrog Initializer" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 485, + 288, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 485, + 288, + 641 + ], + "spans": [ + { + "bbox": [ + 46, + 485, + 288, + 641 + ], + "type": "text", + "content": "We now dive into the design details of the proposed leapfrog initializer, which leapfrogs " + }, + { + "bbox": [ + 46, + 485, + 288, + 641 + ], + "type": "inline_equation", + "content": "(\\Gamma - \\tau)" + }, + { + "bbox": [ + 46, + 485, + 288, + 641 + ], + "type": "text", + "content": " denoising steps. In leapfrog initializer, we model the " + }, + { + "bbox": [ + 46, + 485, + 288, + 641 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 46, + 485, + 288, + 641 + ], + "type": "text", + "content": "th denoised distribution " + }, + { + "bbox": [ + 46, + 485, + 288, + 641 + ], + "type": "inline_equation", + "content": "\\mathcal{P}(\\widehat{\\mathbf{Y}}^{\\tau})" + }, + { + "bbox": [ + 46, + 485, + 288, + 641 + ], + "type": "text", + "content": " through learning models. However, it is nontrivial for a learning model to directly capture the sophisticated distribution, which usually causes unstable training. To ease the learning burden of the model, we disassemble the distribution " + }, + { + "bbox": [ + 46, + 485, + 288, + 641 + ], + "type": "inline_equation", + "content": "\\mathcal{P}(\\widehat{\\mathbf{Y}}^{\\tau})" + }, + { + "bbox": [ + 46, + 485, + 288, + 641 + ], + "type": "text", + "content": " into three representative parts: the mean, global variance and sample prediction. For each part, we design trainable modules correspondingly. Mathematically, let " + }, + { + "bbox": [ + 46, + 485, + 288, + 641 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 46, + 485, + 288, + 641 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 485, + 288, + 641 + ], + "type": "inline_equation", + "content": "\\mathbb{X}_{\\mathcal{N}}" + }, + { + "bbox": [ + 46, + 485, + 288, + 641 + ], + "type": "text", + "content": " be the past trajectories of the ego agent and the neighboring agents, respectively. The proposed leapfrog initializer generates " + }, + { + "bbox": [ + 46, + 485, + 288, + 641 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 485, + 288, + 641 + ], + "type": "text", + "content": " samples as follows," + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 69, + 652, + 290, + 714 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 652, + 290, + 714 + ], + "spans": [ + { + "bbox": [ + 69, + 652, + 290, + 714 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mu_ {\\theta} = f _ {\\mu} (\\mathbf {X}, \\mathbb {X} _ {\\mathcal {N}}) \\in \\mathbb {R} ^ {T _ {t} \\times 2}, \\\\ \\sigma_ {\\theta} = f _ {\\sigma} (\\mathbf {X}, \\mathbb {X} _ {\\mathcal {N}}) \\in \\mathbb {R}, \\\\ \\widehat {\\mathbb {S}} _ {\\theta} = \\left[ \\widehat {\\mathbf {S}} _ {\\theta , 1}, \\dots , \\widehat {\\mathbf {S}} _ {\\theta , K} \\right] = f _ {\\widehat {\\mathbb {S}}} (\\mathbf {X}, \\mathbb {X} _ {\\mathcal {N}}, \\sigma_ {\\theta}) \\in \\mathbb {R} ^ {T _ {\\mathrm {f}} \\times 2 \\times K}, \\\\ \\widehat {\\mathbf {Y}} _ {k} ^ {\\tau} = \\mu_ {\\theta} + \\sigma_ {\\theta} \\cdot \\widehat {\\mathbf {S}} _ {\\theta , k} \\in \\mathbb {R} ^ {T _ {\\mathrm {f}} \\times 2}, \\tag {4} \\\\ \\end{array}", + "image_path": "5fc1b7202cd941b4d5b4f6b9d1fc6a58fd14aa265e46a8c467f5bb66a5144c03.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 206, + 547, + 245 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 206, + 547, + 245 + ], + "spans": [ + { + "bbox": [ + 304, + 206, + 547, + 245 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 206, + 547, + 245 + ], + "type": "inline_equation", + "content": "f_{\\mu}(\\cdot), f_{\\sigma}(\\cdot), f_{\\widehat{\\mathbb{S}}}(\\cdot)" + }, + { + "bbox": [ + 304, + 206, + 547, + 245 + ], + "type": "text", + "content": " are three trainable modules, " + }, + { + "bbox": [ + 304, + 206, + 547, + 245 + ], + "type": "inline_equation", + "content": "\\mu_{\\theta}, \\sigma_{\\theta}" + }, + { + "bbox": [ + 304, + 206, + 547, + 245 + ], + "type": "text", + "content": " are the mean and standard deviation of " + }, + { + "bbox": [ + 304, + 206, + 547, + 245 + ], + "type": "inline_equation", + "content": "\\mathcal{P}(\\widehat{\\mathbf{Y}}^{\\tau})" + }, + { + "bbox": [ + 304, + 206, + 547, + 245 + ], + "type": "text", + "content": ", respectively, and " + }, + { + "bbox": [ + 304, + 206, + 547, + 245 + ], + "type": "inline_equation", + "content": "\\widehat{\\mathbf{S}}_{\\theta,k}" + }, + { + "bbox": [ + 304, + 206, + 547, + 245 + ], + "type": "text", + "content": " is the normalized positions for the " + }, + { + "bbox": [ + 304, + 206, + 547, + 245 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 206, + 547, + 245 + ], + "type": "text", + "content": "th sample." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 246, + 546, + 369 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 246, + 546, + 369 + ], + "spans": [ + { + "bbox": [ + 304, + 246, + 546, + 369 + ], + "type": "text", + "content": "To be specific, the mean estimate module " + }, + { + "bbox": [ + 304, + 246, + 546, + 369 + ], + "type": "inline_equation", + "content": "f_{\\mu}(\\cdot)" + }, + { + "bbox": [ + 304, + 246, + 546, + 369 + ], + "type": "text", + "content": " infers the mean trajectory of the " + }, + { + "bbox": [ + 304, + 246, + 546, + 369 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 246, + 546, + 369 + ], + "type": "text", + "content": "th denoised distribution " + }, + { + "bbox": [ + 304, + 246, + 546, + 369 + ], + "type": "inline_equation", + "content": "\\widehat{\\mathcal{P}}(\\widehat{\\mathbf{Y}}^{\\tau})" + }, + { + "bbox": [ + 304, + 246, + 546, + 369 + ], + "type": "text", + "content": " with past trajectories " + }, + { + "bbox": [ + 304, + 246, + 546, + 369 + ], + "type": "inline_equation", + "content": "(\\mathbf{X}, \\mathbb{X}_{\\mathcal{N}})" + }, + { + "bbox": [ + 304, + 246, + 546, + 369 + ], + "type": "text", + "content": ". The mean trajectory " + }, + { + "bbox": [ + 304, + 246, + 546, + 369 + ], + "type": "inline_equation", + "content": "\\mu_{\\theta}" + }, + { + "bbox": [ + 304, + 246, + 546, + 369 + ], + "type": "text", + "content": " is shared across all the " + }, + { + "bbox": [ + 304, + 246, + 546, + 369 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 246, + 546, + 369 + ], + "type": "text", + "content": " samples. The variance estimate module " + }, + { + "bbox": [ + 304, + 246, + 546, + 369 + ], + "type": "inline_equation", + "content": "f_{\\sigma}(\\cdot)" + }, + { + "bbox": [ + 304, + 246, + 546, + 369 + ], + "type": "text", + "content": " infers the standard deviation of the " + }, + { + "bbox": [ + 304, + 246, + 546, + 369 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 246, + 546, + 369 + ], + "type": "text", + "content": "th denoised distribution " + }, + { + "bbox": [ + 304, + 246, + 546, + 369 + ], + "type": "inline_equation", + "content": "\\widehat{\\mathcal{P}}(\\widehat{\\mathbf{Y}}^{\\tau})" + }, + { + "bbox": [ + 304, + 246, + 546, + 369 + ], + "type": "text", + "content": ", reflecting the overall uncertainty of the trajectory, which is also shared across all the " + }, + { + "bbox": [ + 304, + 246, + 546, + 369 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 246, + 546, + 369 + ], + "type": "text", + "content": " samples. The sample prediction module " + }, + { + "bbox": [ + 304, + 246, + 546, + 369 + ], + "type": "inline_equation", + "content": "f_{\\widehat{\\mathbb{S}}}(\\cdot)" + }, + { + "bbox": [ + 304, + 246, + 546, + 369 + ], + "type": "text", + "content": " takes the past trajectories " + }, + { + "bbox": [ + 304, + 246, + 546, + 369 + ], + "type": "inline_equation", + "content": "(\\mathbf{X}, \\mathbb{X}_{\\mathcal{N}})" + }, + { + "bbox": [ + 304, + 246, + 546, + 369 + ], + "type": "text", + "content": " and the predicted uncertainty " + }, + { + "bbox": [ + 304, + 246, + 546, + 369 + ], + "type": "inline_equation", + "content": "\\sigma_{\\theta}" + }, + { + "bbox": [ + 304, + 246, + 546, + 369 + ], + "type": "text", + "content": " as the input and predicts " + }, + { + "bbox": [ + 304, + 246, + 546, + 369 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 246, + 546, + 369 + ], + "type": "text", + "content": " normalized positions where each " + }, + { + "bbox": [ + 304, + 246, + 546, + 369 + ], + "type": "inline_equation", + "content": "\\widehat{\\mathbf{S}}_{\\theta,k} \\in \\mathbb{R}^{T_{\\mathrm{f}} \\times 2}" + }, + { + "bbox": [ + 304, + 246, + 546, + 369 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 369, + 547, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 369, + 547, + 441 + ], + "spans": [ + { + "bbox": [ + 304, + 369, + 547, + 441 + ], + "type": "text", + "content": "Note that i) the reparameterization in Eq. (4) allows us to avoid learning a raw sophisticated distribution, making the training much easier; and ii) " + }, + { + "bbox": [ + 304, + 369, + 547, + 441 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 369, + 547, + 441 + ], + "type": "text", + "content": " normalized predictions are generated simultaneously from the same underlying feature, assuring appropriately allocated trajectories with variance estimation and better capturing the multi-modalities." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 441, + 547, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 441, + 547, + 525 + ], + "spans": [ + { + "bbox": [ + 304, + 441, + 547, + 525 + ], + "type": "text", + "content": "To implement the three trainable modules: " + }, + { + "bbox": [ + 304, + 441, + 547, + 525 + ], + "type": "inline_equation", + "content": "f_{\\mu}(\\cdot), f_{\\sigma}(\\cdot), f_{\\widehat{\\mathbb{S}}}(\\cdot)" + }, + { + "bbox": [ + 304, + 441, + 547, + 525 + ], + "type": "text", + "content": ", we consider a similar network design: a social encoder to capture social influence, a temporal encoder to learn temporal embedding, and an aggregation layer to fuse both social and temporal information; see Figure 2. Here we take the mean estimation module " + }, + { + "bbox": [ + 304, + 441, + 547, + 525 + ], + "type": "inline_equation", + "content": "f_{\\mu}(\\cdot)" + }, + { + "bbox": [ + 304, + 441, + 547, + 525 + ], + "type": "text", + "content": " as an example. The mean trajectory is obtained as follows," + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 322, + 529, + 545, + 589 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 322, + 529, + 545, + 589 + ], + "spans": [ + { + "bbox": [ + 322, + 529, + 545, + 589 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathbf {e} _ {\\mu_ {\\theta}} ^ {\\text {s o c i a l}} = \\operatorname {s o f t m a x} \\left(\\frac {f _ {\\mathrm {q}} (\\mathbf {X}) f _ {\\mathrm {k}} (\\mathbb {X} _ {\\mathcal {N}}) ^ {\\top}}{\\sqrt {d}}\\right) f _ {\\mathrm {v}} (\\mathbb {X} _ {\\mathcal {N}}), (5a) \\\\ \\mathbf {e} _ {\\mu_ {\\theta}} ^ {\\text {t e m p}} = f _ {\\mathrm {G R U}} \\left(f _ {\\operatorname {c o n v 1 D}} (\\mathbf {X})\\right), (5b) \\\\ \\mu_ {\\theta} = f _ {\\text {f u s i o n}} \\left(\\left[ \\mathbf {e} _ {\\mu_ {\\theta}} ^ {\\text {s o c i a l}}: \\mathbf {e} _ {\\mu_ {\\theta}} ^ {\\text {t e m p}} \\right]\\right). (5c) \\\\ \\end{array}", + "image_path": "d89b191cf57e88307283d48037912da946a5918dc587e40d8d12ee404ddd450e.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 593, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 593, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 593, + 547, + 714 + ], + "type": "text", + "content": "Step (5a) obtains the social embedding " + }, + { + "bbox": [ + 304, + 593, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{e}_{\\mu_{\\theta}}^{\\mathrm{social}}" + }, + { + "bbox": [ + 304, + 593, + 547, + 714 + ], + "type": "text", + "content": " based on the multi-head attention with " + }, + { + "bbox": [ + 304, + 593, + 547, + 714 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 593, + 547, + 714 + ], + "type": "text", + "content": " the embedding dimension and " + }, + { + "bbox": [ + 304, + 593, + 547, + 714 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{q}}(\\cdot), f_{\\mathrm{k}}(\\cdot), f_{\\mathrm{v}}(\\cdot)" + }, + { + "bbox": [ + 304, + 593, + 547, + 714 + ], + "type": "text", + "content": " the query/key/value embedding functions. Step (5b) obtains the temporal embedding through the feature encoder " + }, + { + "bbox": [ + 304, + 593, + 547, + 714 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{conv1D}}(\\cdot)" + }, + { + "bbox": [ + 304, + 593, + 547, + 714 + ], + "type": "text", + "content": ", mapping the raw coordinates into the high-dimensional feature, followed by the gated recurrent units " + }, + { + "bbox": [ + 304, + 593, + 547, + 714 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{GRU}}(\\cdot)" + }, + { + "bbox": [ + 304, + 593, + 547, + 714 + ], + "type": "text", + "content": ", capturing the temporal dependence in the high dimensional sequence. Step (5c) concatenates both social and temporal embeddings and uses a multi-layer perceptron " + }, + { + "bbox": [ + 304, + 593, + 547, + 714 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{fusion}}(\\cdot)" + }, + { + "bbox": [ + 304, + 593, + 547, + 714 + ], + "type": "text", + "content": " to obtain the final mean estimation. Note" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5520" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 97 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 97 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 97 + ], + "type": "text", + "content": "that the sample prediction module " + }, + { + "bbox": [ + 47, + 72, + 289, + 97 + ], + "type": "inline_equation", + "content": "f_{\\widehat{\\mathbb{S}}}(\\cdot)" + }, + { + "bbox": [ + 47, + 72, + 289, + 97 + ], + "type": "text", + "content": " also takes the estimated standard deviation as the input, working as" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 92, + 104, + 173, + 120 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 92, + 104, + 173, + 120 + ], + "spans": [ + { + "bbox": [ + 92, + 104, + 173, + 120 + ], + "type": "interline_equation", + "content": "\\mathbf {e} _ {\\hat {\\mathfrak {S}} _ {\\theta}} ^ {\\sigma} = f _ {\\mathrm {e n c o d e}} (\\sigma_ {\\theta}),", + "image_path": "f2a5939eb5fafe58bad7dcbeb3fdc02d84e19516beb68427a36fa0182f111487.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 94, + 122, + 241, + 140 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 94, + 122, + 241, + 140 + ], + "spans": [ + { + "bbox": [ + 94, + 122, + 241, + 140 + ], + "type": "interline_equation", + "content": "\\widehat {\\mathbb {S}} _ {\\theta} = f _ {\\mathrm {f u s i o n}} ([ \\mathbf {e} _ {\\widehat {\\mathbb {S}} _ {\\theta}} ^ {\\mathrm {s o c i a l}}: \\mathbf {e} _ {\\widehat {\\mathbb {S}} _ {\\theta}} ^ {\\mathrm {t e m p}}: \\mathbf {e} _ {\\widehat {\\mathbb {S}} _ {\\theta}} ^ {\\sigma} ]),", + "image_path": "fb6a4b1539ab238b6373138fb8762af1d0571efedc1f481570fcf45c47052d53.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 148, + 287, + 196 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 148, + 287, + 196 + ], + "spans": [ + { + "bbox": [ + 47, + 148, + 287, + 196 + ], + "type": "text", + "content": "where an encoder " + }, + { + "bbox": [ + 47, + 148, + 287, + 196 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{encode}}(\\cdot)" + }, + { + "bbox": [ + 47, + 148, + 287, + 196 + ], + "type": "text", + "content": " operates on the estimated variance " + }, + { + "bbox": [ + 47, + 148, + 287, + 196 + ], + "type": "inline_equation", + "content": "\\sigma_{\\theta}" + }, + { + "bbox": [ + 47, + 148, + 287, + 196 + ], + "type": "text", + "content": " and generates high dimensional embedding " + }, + { + "bbox": [ + 47, + 148, + 287, + 196 + ], + "type": "inline_equation", + "content": "\\mathbf{e}_{\\hat{\\mathbb{S}}_{\\theta}}^{\\sigma}" + }, + { + "bbox": [ + 47, + 148, + 287, + 196 + ], + "type": "text", + "content": ". By this, the variance estimation also involves in the sample prediction process, instead of just scaling these prediction." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 197, + 288, + 234 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 197, + 288, + 234 + ], + "spans": [ + { + "bbox": [ + 47, + 197, + 288, + 234 + ], + "type": "text", + "content": "After obtaining " + }, + { + "bbox": [ + 47, + 197, + 288, + 234 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 47, + 197, + 288, + 234 + ], + "type": "text", + "content": " samples " + }, + { + "bbox": [ + 47, + 197, + 288, + 234 + ], + "type": "inline_equation", + "content": "\\widehat{y}^{\\tau} = \\{\\widehat{\\mathbf{Y}}_1^\\tau ,\\widehat{\\mathbf{Y}}_2^\\tau ,\\dots ,\\widehat{\\mathbf{Y}}_K^\\tau \\}" + }, + { + "bbox": [ + 47, + 197, + 288, + 234 + ], + "type": "text", + "content": " from leapfrog initializer, we execute the remaining " + }, + { + "bbox": [ + 47, + 197, + 288, + 234 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 47, + 197, + 288, + 234 + ], + "type": "text", + "content": " denoising steps to iteratively refine those predicted trajectories (3d)." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 240, + 155, + 253 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 240, + 155, + 253 + ], + "spans": [ + { + "bbox": [ + 47, + 240, + 155, + 253 + ], + "type": "text", + "content": "4.3. Denoising Module" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 258, + 289, + 344 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 258, + 289, + 344 + ], + "spans": [ + { + "bbox": [ + 47, + 258, + 289, + 344 + ], + "type": "text", + "content": "Here we elaborate the design of a denoising module " + }, + { + "bbox": [ + 47, + 258, + 289, + 344 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{denoise}}(\\cdot)" + }, + { + "bbox": [ + 47, + 258, + 289, + 344 + ], + "type": "text", + "content": ", which denoises the trajectory " + }, + { + "bbox": [ + 47, + 258, + 289, + 344 + ], + "type": "inline_equation", + "content": "\\widehat{\\mathbf{Y}}_k^{\\gamma +1}" + }, + { + "bbox": [ + 47, + 258, + 289, + 344 + ], + "type": "text", + "content": " conditioned on past trajectories " + }, + { + "bbox": [ + 47, + 258, + 289, + 344 + ], + "type": "inline_equation", + "content": "(\\mathbf{X},\\mathbb{X}_{\\mathcal{N}})" + }, + { + "bbox": [ + 47, + 258, + 289, + 344 + ], + "type": "text", + "content": ". In a denoising module, two parts are trainable: a transformer-based context encoder " + }, + { + "bbox": [ + 47, + 258, + 289, + 344 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{context}}(\\cdot)" + }, + { + "bbox": [ + 47, + 258, + 289, + 344 + ], + "type": "text", + "content": " to learn a social-temporal embedding and a noise estimation module " + }, + { + "bbox": [ + 47, + 258, + 289, + 344 + ], + "type": "inline_equation", + "content": "f_{\\epsilon}(\\cdot)" + }, + { + "bbox": [ + 47, + 258, + 289, + 344 + ], + "type": "text", + "content": " to estimate the noise to reduce. Mathematically, the " + }, + { + "bbox": [ + 47, + 258, + 289, + 344 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 47, + 258, + 289, + 344 + ], + "type": "text", + "content": "th denoising step works as follows," + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 63, + 354, + 287, + 367 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 354, + 287, + 367 + ], + "spans": [ + { + "bbox": [ + 63, + 354, + 287, + 367 + ], + "type": "interline_equation", + "content": "\\mathbf {C} = f _ {\\text {c o n t e x t}} (\\mathbf {X}, \\mathbb {X} _ {\\mathcal {N}}), \\tag {6a}", + "image_path": "c8f0c368b0e1875cca9b89c34f8672899f097d994848a04c8dbe2d650193a7fd.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 64, + 369, + 287, + 385 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 64, + 369, + 287, + 385 + ], + "spans": [ + { + "bbox": [ + 64, + 369, + 287, + 385 + ], + "type": "interline_equation", + "content": "\\epsilon_ {\\theta} ^ {\\gamma} = f _ {\\epsilon} \\left(\\widehat {\\mathbf {Y}} _ {k} ^ {\\gamma + 1}, \\mathbf {C}, \\gamma + 1\\right), \\tag {6b}", + "image_path": "b0bca69c7f497c4bb9d453dfaeff6dee70d858c0fe18da28f1f5fb00f5da16a2.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 64, + 387, + 287, + 414 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 64, + 387, + 287, + 414 + ], + "spans": [ + { + "bbox": [ + 64, + 387, + 287, + 414 + ], + "type": "interline_equation", + "content": "\\hat {\\mathbf {Y}} _ {k} ^ {\\gamma} = \\frac {1}{\\sqrt {\\alpha_ {\\gamma}}} \\left(\\hat {\\mathbf {Y}} _ {k} ^ {\\gamma + 1} - \\frac {1 - \\alpha_ {\\gamma}}{\\sqrt {1 - \\bar {\\alpha} _ {\\gamma}}} \\boldsymbol {\\epsilon} _ {\\theta} ^ {\\gamma}\\right) + \\sqrt {1 - \\alpha_ {\\gamma}} \\mathbf {z}, \\quad (6 c)", + "image_path": "f792930664422a204023842a616fa7f1654558d95ea16109c4ec928993eba96c.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 416, + 288, + 526 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 416, + 288, + 526 + ], + "spans": [ + { + "bbox": [ + 46, + 416, + 288, + 526 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 416, + 288, + 526 + ], + "type": "inline_equation", + "content": "\\alpha_{\\gamma}" + }, + { + "bbox": [ + 46, + 416, + 288, + 526 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 416, + 288, + 526 + ], + "type": "inline_equation", + "content": "\\bar{\\alpha}_{\\gamma} = \\prod_{i=1}^{\\gamma} \\alpha_{i}" + }, + { + "bbox": [ + 46, + 416, + 288, + 526 + ], + "type": "text", + "content": " are parameters in the diffusion process and " + }, + { + "bbox": [ + 46, + 416, + 288, + 526 + ], + "type": "inline_equation", + "content": "\\mathbf{z} \\sim \\mathcal{N}(\\mathbf{z}; \\mathbf{0}, \\mathbf{I})" + }, + { + "bbox": [ + 46, + 416, + 288, + 526 + ], + "type": "text", + "content": " is a noise. Step (6a) uses a context encoder " + }, + { + "bbox": [ + 46, + 416, + 288, + 526 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{context}}(\\cdot)" + }, + { + "bbox": [ + 46, + 416, + 288, + 526 + ], + "type": "text", + "content": " on past trajectories " + }, + { + "bbox": [ + 46, + 416, + 288, + 526 + ], + "type": "inline_equation", + "content": "(\\mathbf{X}, \\mathbb{X}_{\\mathcal{N}})" + }, + { + "bbox": [ + 46, + 416, + 288, + 526 + ], + "type": "text", + "content": " to obtain the context condition " + }, + { + "bbox": [ + 46, + 416, + 288, + 526 + ], + "type": "inline_equation", + "content": "\\mathbf{C}" + }, + { + "bbox": [ + 46, + 416, + 288, + 526 + ], + "type": "text", + "content": ", which shares a similar structure to mean estimation module " + }, + { + "bbox": [ + 46, + 416, + 288, + 526 + ], + "type": "inline_equation", + "content": "f_{\\mu}(\\cdot)" + }, + { + "bbox": [ + 46, + 416, + 288, + 526 + ], + "type": "text", + "content": "; Step (6b) estimates the noise " + }, + { + "bbox": [ + 46, + 416, + 288, + 526 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}^{\\gamma}" + }, + { + "bbox": [ + 46, + 416, + 288, + 526 + ], + "type": "text", + "content": " in the noisy trajectory " + }, + { + "bbox": [ + 46, + 416, + 288, + 526 + ], + "type": "inline_equation", + "content": "\\widehat{\\mathbf{Y}}_k^{\\gamma+1}" + }, + { + "bbox": [ + 46, + 416, + 288, + 526 + ], + "type": "text", + "content": " through noise estimation " + }, + { + "bbox": [ + 46, + 416, + 288, + 526 + ], + "type": "inline_equation", + "content": "f_{\\epsilon}(\\cdot)" + }, + { + "bbox": [ + 46, + 416, + 288, + 526 + ], + "type": "text", + "content": " implemented by multi-layer perceptions with the context " + }, + { + "bbox": [ + 46, + 416, + 288, + 526 + ], + "type": "inline_equation", + "content": "\\mathbf{C}" + }, + { + "bbox": [ + 46, + 416, + 288, + 526 + ], + "type": "text", + "content": "; Step (6c) provides a standard denoising step [17]; see more details in the supplementary material." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 533, + 159, + 546 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 533, + 159, + 546 + ], + "spans": [ + { + "bbox": [ + 47, + 533, + 159, + 546 + ], + "type": "text", + "content": "4.4. Training Objective" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 552, + 287, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 552, + 287, + 624 + ], + "spans": [ + { + "bbox": [ + 47, + 552, + 287, + 624 + ], + "type": "text", + "content": "To train a leapfrog diffusion model, we consider a two-stage training strategy, where the first stage trains a denoising module and the second stage focuses on a leapfrog initializer. The reason to use two stages is because the training of leapfrog initializer is more stable given fixed distribution " + }, + { + "bbox": [ + 47, + 552, + 287, + 624 + ], + "type": "inline_equation", + "content": "\\mathcal{P}(\\widehat{\\mathbf{Y}}^{\\tau})" + }, + { + "bbox": [ + 47, + 552, + 287, + 624 + ], + "type": "text", + "content": ", avoiding non-convergent training." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 624, + 287, + 659 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 624, + 287, + 659 + ], + "spans": [ + { + "bbox": [ + 47, + 624, + 287, + 659 + ], + "type": "text", + "content": "Concretely, the first stage trains a denoising module " + }, + { + "bbox": [ + 47, + 624, + 287, + 659 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{denoise}}(\\cdot)" + }, + { + "bbox": [ + 47, + 624, + 287, + 659 + ], + "type": "text", + "content": " in Step (3d) based on a standard training schedule of a diffusion model [14, 17] through noise estimation loss:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 52, + 667, + 261, + 681 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 667, + 261, + 681 + ], + "spans": [ + { + "bbox": [ + 52, + 667, + 261, + 681 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {N E}} = \\| \\boldsymbol {\\epsilon} - f _ {\\boldsymbol {\\epsilon}} (\\mathbf {Y} ^ {\\gamma + 1}, f _ {\\text {c o n t e x t}} (\\mathbf {X}, \\mathbb {X} _ {\\mathcal {N}}), \\gamma + 1) \\| _ {2},", + "image_path": "38b5930cd329eeb728139e25481ef7f849362db2b512b4c395c88c0688806544.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 689, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 289, + 715 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 689, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\gamma \\sim \\mathrm{U}\\{1,2,\\dots ,\\Gamma \\}" + }, + { + "bbox": [ + 46, + 689, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\epsilon \\sim \\mathcal{N}(\\epsilon ;\\mathbf{0},\\mathbf{I})" + }, + { + "bbox": [ + 46, + 689, + 289, + 715 + ], + "type": "text", + "content": " and the diffused trajectory " + }, + { + "bbox": [ + 46, + 689, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{Y}^{\\gamma +1} = \\sqrt{\\bar{\\alpha}_{\\gamma}}\\mathbf{Y}^{0} + \\sqrt{1 - \\bar{\\alpha}_{\\gamma}}\\pmb {\\epsilon}" + }, + { + "bbox": [ + 46, + 689, + 289, + 715 + ], + "type": "text", + "content": " . We then back" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 72, + 520, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 520, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 520, + 84 + ], + "type": "text", + "content": "Algorithm 1 Leapfrog Diffusion Model in Inference" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 87, + 525, + 99 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 87, + 525, + 99 + ], + "spans": [ + { + "bbox": [ + 306, + 87, + 525, + 99 + ], + "type": "text", + "content": "Input: Observed trajectories " + }, + { + "bbox": [ + 306, + 87, + 525, + 99 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 306, + 87, + 525, + 99 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 306, + 87, + 525, + 99 + ], + "type": "inline_equation", + "content": "\\mathbb{X}_{\\mathcal{N}}" + }, + { + "bbox": [ + 306, + 87, + 525, + 99 + ], + "type": "text", + "content": ", Leapfrog step " + }, + { + "bbox": [ + 306, + 87, + 525, + 99 + ], + "type": "inline_equation", + "content": "\\tau" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 100, + 443, + 113 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 100, + 443, + 113 + ], + "spans": [ + { + "bbox": [ + 306, + 100, + 443, + 113 + ], + "type": "text", + "content": "Output: Predicted trajectories " + }, + { + "bbox": [ + 306, + 100, + 443, + 113 + ], + "type": "inline_equation", + "content": "\\hat{\\mathcal{V}}" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 312, + 114, + 545, + 236 + ], + "type": "list", + "angle": 0, + "index": 28, + "blocks": [ + { + "bbox": [ + 312, + 114, + 545, + 127 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 114, + 545, + 127 + ], + "spans": [ + { + "bbox": [ + 312, + 114, + 545, + 127 + ], + "type": "text", + "content": "1: " + }, + { + "bbox": [ + 312, + 114, + 545, + 127 + ], + "type": "inline_equation", + "content": "\\mu_{\\theta} = f_{\\mu}(\\mathbf{X},\\mathbb{X}_{\\mathcal{N}})" + }, + { + "bbox": [ + 312, + 114, + 545, + 127 + ], + "type": "text", + "content": " Mean estimation" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 312, + 129, + 545, + 140 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 129, + 545, + 140 + ], + "spans": [ + { + "bbox": [ + 312, + 129, + 545, + 140 + ], + "type": "text", + "content": "2: " + }, + { + "bbox": [ + 312, + 129, + 545, + 140 + ], + "type": "inline_equation", + "content": "\\sigma_{\\theta} = f_{\\sigma}(\\mathbf{X},\\mathbb{X}_{\\mathcal{N}})" + }, + { + "bbox": [ + 312, + 129, + 545, + 140 + ], + "type": "inline_equation", + "content": "\\triangleright" + }, + { + "bbox": [ + 312, + 129, + 545, + 140 + ], + "type": "text", + "content": " Variance estimation" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 312, + 141, + 545, + 155 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 141, + 545, + 155 + ], + "spans": [ + { + "bbox": [ + 312, + 141, + 545, + 155 + ], + "type": "text", + "content": "3: " + }, + { + "bbox": [ + 312, + 141, + 545, + 155 + ], + "type": "inline_equation", + "content": "\\widehat{\\mathbb{S}}_{\\theta} = f_{\\widehat{\\mathbb{S}}}(\\mathbf{X},\\mathbb{X}_{\\mathcal{N}},\\sigma_{\\theta})" + }, + { + "bbox": [ + 312, + 141, + 545, + 155 + ], + "type": "text", + "content": " ▷ Sample prediction" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 312, + 156, + 545, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 156, + 545, + 168 + ], + "spans": [ + { + "bbox": [ + 312, + 156, + 545, + 168 + ], + "type": "text", + "content": "4: " + }, + { + "bbox": [ + 312, + 156, + 545, + 168 + ], + "type": "inline_equation", + "content": "\\widehat{\\mathbf{Y}}_k^\\tau = \\mu_\\theta +\\sigma_\\theta \\cdot \\widehat{\\mathbf{S}}_{\\theta ,k},k = 1,\\dots ,K\\ntriangleright" + }, + { + "bbox": [ + 312, + 156, + 545, + 168 + ], + "type": "text", + "content": " Reparameterization" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 312, + 170, + 418, + 182 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 170, + 418, + 182 + ], + "spans": [ + { + "bbox": [ + 312, + 170, + 418, + 182 + ], + "type": "text", + "content": "5: for " + }, + { + "bbox": [ + 312, + 170, + 418, + 182 + ], + "type": "inline_equation", + "content": "\\gamma = \\tau - 1, \\dots, 0" + }, + { + "bbox": [ + 312, + 170, + 418, + 182 + ], + "type": "text", + "content": " do" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 312, + 182, + 545, + 196 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 182, + 545, + 196 + ], + "spans": [ + { + "bbox": [ + 312, + 182, + 545, + 196 + ], + "type": "text", + "content": "6: " + }, + { + "bbox": [ + 312, + 182, + 545, + 196 + ], + "type": "inline_equation", + "content": "\\widehat{\\mathbf{Y}}_k^\\gamma = f_{\\mathrm{denoise}}(\\widehat{\\mathbf{Y}}_k^{\\gamma +1},\\mathbf{X},\\mathbb{X}_{\\mathcal{N}})" + }, + { + "bbox": [ + 312, + 182, + 545, + 196 + ], + "type": "text", + "content": " Denoising step" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 312, + 198, + 358, + 208 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 198, + 358, + 208 + ], + "spans": [ + { + "bbox": [ + 312, + 198, + 358, + 208 + ], + "type": "text", + "content": "7: end for" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 312, + 209, + 435, + 224 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 209, + 435, + 224 + ], + "spans": [ + { + "bbox": [ + 312, + 209, + 435, + 224 + ], + "type": "text", + "content": "8: " + }, + { + "bbox": [ + 312, + 209, + 435, + 224 + ], + "type": "inline_equation", + "content": "\\widehat{\\mathcal{Y}} = \\widehat{\\mathcal{Y}}^0 = \\{\\widehat{\\mathbf{Y}}_1^0,\\dots ,\\widehat{\\mathbf{Y}}_K^0\\}" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 312, + 224, + 363, + 236 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 224, + 363, + 236 + ], + "spans": [ + { + "bbox": [ + 312, + 224, + 363, + 236 + ], + "type": "text", + "content": "9: return " + }, + { + "bbox": [ + 312, + 224, + 363, + 236 + ], + "type": "inline_equation", + "content": "\\hat{y}" + } + ] + } + ], + "index": 27 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 305, + 260, + 545, + 285 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 260, + 545, + 285 + ], + "spans": [ + { + "bbox": [ + 305, + 260, + 545, + 285 + ], + "type": "text", + "content": "propagate this loss and train the parameters in the context encoder " + }, + { + "bbox": [ + 305, + 260, + 545, + 285 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{context}}(\\cdot)" + }, + { + "bbox": [ + 305, + 260, + 545, + 285 + ], + "type": "text", + "content": " and the noise estimation module " + }, + { + "bbox": [ + 305, + 260, + 545, + 285 + ], + "type": "inline_equation", + "content": "f_{\\epsilon}(\\cdot)" + }, + { + "bbox": [ + 305, + 260, + 545, + 285 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 305, + 285, + 547, + 320 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 285, + 547, + 320 + ], + "spans": [ + { + "bbox": [ + 305, + 285, + 547, + 320 + ], + "type": "text", + "content": "In the second stage, we optimize a leapfrog diffusion model with a trainable leapfrog initializer and frozen denoising modules. For each sample, the loss function is" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 306, + 330, + 545, + 373 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 330, + 545, + 373 + ], + "spans": [ + { + "bbox": [ + 306, + 330, + 545, + 373 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} = \\mathcal {L} _ {\\text {d i s t a n c e}} + \\mathcal {L} _ {\\text {u n c e r t a i n t y}} \\\\ { = } { w \\cdot \\operatorname* { m i n } _ { k } \\| \\mathbf { Y } - \\widehat { \\mathbf { Y } } _ { k } \\| _ { 2 } + \\Big ( \\frac { \\sum _ { k } \\| \\mathbf { Y } - \\widehat { \\mathbf { Y } } _ { k } \\| _ { 2 } } { \\sigma _ { \\theta } ^ { 2 } K } + \\log \\sigma _ { \\theta } ^ { 2 } \\Big ) , } \\\\ \\end{array}", + "image_path": "a904a65220d41f48d4920e5aa820c17732eb6c50781683c068e0984db2e02c38.jpg" + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 305, + 381, + 547, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 381, + 547, + 555 + ], + "spans": [ + { + "bbox": [ + 305, + 381, + 547, + 555 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 381, + 547, + 555 + ], + "type": "inline_equation", + "content": "w \\in \\mathbb{R}" + }, + { + "bbox": [ + 305, + 381, + 547, + 555 + ], + "type": "text", + "content": " is a hyperparameter weight. The first term constrains the minimum distance in " + }, + { + "bbox": [ + 305, + 381, + 547, + 555 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 305, + 381, + 547, + 555 + ], + "type": "text", + "content": " predictions. Intuitively, if a leapfrog initializer generates high-quality estimations for distribution " + }, + { + "bbox": [ + 305, + 381, + 547, + 555 + ], + "type": "inline_equation", + "content": "\\mathcal{P}(\\widehat{\\mathbf{Y}}^{\\tau})" + }, + { + "bbox": [ + 305, + 381, + 547, + 555 + ], + "type": "text", + "content": ", then one of the " + }, + { + "bbox": [ + 305, + 381, + 547, + 555 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 305, + 381, + 547, + 555 + ], + "type": "text", + "content": " predictions in " + }, + { + "bbox": [ + 305, + 381, + 547, + 555 + ], + "type": "inline_equation", + "content": "\\widehat{\\mathcal{V}}" + }, + { + "bbox": [ + 305, + 381, + 547, + 555 + ], + "type": "text", + "content": " should be close to the ground-truth trajectory " + }, + { + "bbox": [ + 305, + 381, + 547, + 555 + ], + "type": "inline_equation", + "content": "\\mathbf{Y}" + }, + { + "bbox": [ + 305, + 381, + 547, + 555 + ], + "type": "text", + "content": ". The second term normalizes the variance estimation " + }, + { + "bbox": [ + 305, + 381, + 547, + 555 + ], + "type": "inline_equation", + "content": "\\sigma_{\\theta}" + }, + { + "bbox": [ + 305, + 381, + 547, + 555 + ], + "type": "text", + "content": " in reparameterization (4) through an uncertainty loss, balancing the prediction diversity and mean accuracy. Note that the variance estimation controls the dispersion of the predictions, bridging scenery complexity and prediction diversity. The first part " + }, + { + "bbox": [ + 305, + 381, + 547, + 555 + ], + "type": "inline_equation", + "content": "\\frac{\\sum_k\\|\\mathbf{Y}\\widehat{\\mathbf{Y}}_k\\|_2}{\\sigma_\\theta^2K}" + }, + { + "bbox": [ + 305, + 381, + 547, + 555 + ], + "type": "text", + "content": " makes the value of " + }, + { + "bbox": [ + 305, + 381, + 547, + 555 + ], + "type": "inline_equation", + "content": "\\sigma_{\\theta}" + }, + { + "bbox": [ + 305, + 381, + 547, + 555 + ], + "type": "text", + "content": " proportional to the complexity of the scenario. The second part " + }, + { + "bbox": [ + 305, + 381, + 547, + 555 + ], + "type": "inline_equation", + "content": "\\log \\sigma_{\\theta}^{2}" + }, + { + "bbox": [ + 305, + 381, + 547, + 555 + ], + "type": "text", + "content": " is a regulariser used to avoid a trivial solution for " + }, + { + "bbox": [ + 305, + 381, + 547, + 555 + ], + "type": "inline_equation", + "content": "\\sigma_{\\theta}" + }, + { + "bbox": [ + 305, + 381, + 547, + 555 + ], + "type": "text", + "content": ", i.e., generating high variance for all predictions." + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 305, + 557, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 557, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 557, + 547, + 714 + ], + "type": "text", + "content": "Technically, we can also explicitly supervise the estimation of leapfrog initializer in stage two, since the distribution " + }, + { + "bbox": [ + 305, + 557, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{P}(\\widehat{\\mathbf{Y}}^{\\tau})" + }, + { + "bbox": [ + 305, + 557, + 547, + 714 + ], + "type": "text", + "content": " can be denoised from a normal distribution. For the explicit supervision, we draw " + }, + { + "bbox": [ + 305, + 557, + 547, + 714 + ], + "type": "inline_equation", + "content": "M\\gg K" + }, + { + "bbox": [ + 305, + 557, + 547, + 714 + ], + "type": "text", + "content": " samples from " + }, + { + "bbox": [ + 305, + 557, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{P}(\\widehat{\\mathbf{Y}}^{\\Gamma})" + }, + { + "bbox": [ + 305, + 557, + 547, + 714 + ], + "type": "text", + "content": " under the normal distribution and iteratively denoise these samples through Step (2d) until we get expected denoised trajectories " + }, + { + "bbox": [ + 305, + 557, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\widehat{\\mathbf{Y}}^{\\tau}" + }, + { + "bbox": [ + 305, + 557, + 547, + 714 + ], + "type": "text", + "content": ". And then, we calculate the statistics of the denoised distribution " + }, + { + "bbox": [ + 305, + 557, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{P}(\\widehat{\\mathbf{Y}}^{\\tau})" + }, + { + "bbox": [ + 305, + 557, + 547, + 714 + ], + "type": "text", + "content": " using these " + }, + { + "bbox": [ + 305, + 557, + 547, + 714 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 305, + 557, + 547, + 714 + ], + "type": "text", + "content": " samples, serving as explicit supervisions for mean estimation " + }, + { + "bbox": [ + 305, + 557, + 547, + 714 + ], + "type": "inline_equation", + "content": "f_{\\mu}(\\cdot)" + }, + { + "bbox": [ + 305, + 557, + 547, + 714 + ], + "type": "text", + "content": " and variance estimation " + }, + { + "bbox": [ + 305, + 557, + 547, + 714 + ], + "type": "inline_equation", + "content": "f_{\\sigma}(\\cdot)" + }, + { + "bbox": [ + 305, + 557, + 547, + 714 + ], + "type": "text", + "content": ". However, since " + }, + { + "bbox": [ + 305, + 557, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\tau \\ll \\Gamma" + }, + { + "bbox": [ + 305, + 557, + 547, + 714 + ], + "type": "text", + "content": ", we need to run " + }, + { + "bbox": [ + 305, + 557, + 547, + 714 + ], + "type": "inline_equation", + "content": "(\\Gamma -\\tau)\\approx \\Gamma" + }, + { + "bbox": [ + 305, + 557, + 547, + 714 + ], + "type": "text", + "content": "-steps denoising for " + }, + { + "bbox": [ + 305, + 557, + 547, + 714 + ], + "type": "inline_equation", + "content": "M\\gg K" + }, + { + "bbox": [ + 305, + 557, + 547, + 714 + ], + "type": "text", + "content": " samples to get statistics, resulting in unacceptable time and storage consumption for training (e.g. " + }, + { + "bbox": [ + 305, + 557, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\sim 6" + }, + { + "bbox": [ + 305, + 557, + 547, + 714 + ], + "type": "text", + "content": " days per epoch on NBA" + } + ] + } + ], + "index": 33 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "5521" + } + ] + } + ], + "index": 34 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 80, + 542, + 153 + ], + "blocks": [ + { + "bbox": [ + 47, + 57, + 547, + 79 + ], + "lines": [ + { + "bbox": [ + 47, + 57, + 547, + 79 + ], + "spans": [ + { + "bbox": [ + 47, + 57, + 547, + 79 + ], + "type": "text", + "content": "Table 1. Comparison with baseline models on NBA dataset. minADE20 /minFDE20 (meters) are reported. Bold/underlined fonts represent the best/second-best result. Compared to the previous SOTA method, MID, our method achieves a " + }, + { + "bbox": [ + 47, + 57, + 547, + 79 + ], + "type": "inline_equation", + "content": "15.6\\% /13.4\\%" + }, + { + "bbox": [ + 47, + 57, + 547, + 79 + ], + "type": "text", + "content": " ADE/FDE improvement." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 80, + 542, + 153 + ], + "lines": [ + { + "bbox": [ + 48, + 80, + 542, + 153 + ], + "spans": [ + { + "bbox": [ + 48, + 80, + 542, + 153 + ], + "type": "table", + "html": "
TimeSocial-GAN [15] CVPR'18STGAT [19] ICCV'19Social-STGCNN [31] CVPR'20PECNet [27] ECCV'20STAR [52] ECCV'20Trajectory++[38] ECCV'20MemoNet [50] CVPR'22NPSN [2] CVPR'22GroupNet [49] CVPR'22MID [14] CVPR'22Ours
1.0s0.41/0.620.35/0.510.34/0.480.40/0.710.43/0.660.30/0.380.38/0.560.35/0.580.26/0.340.28/0.370.18/0.27
2.0s0.81/1.320.73/1.100.71/0.940.83/1.610.75/1.240.59/0.820.71/1.140.68/1.230.49/0.700.51/0.720.37/0.56
3.0s1.19/1.941.04/1.751.09/1.771.27/2.441.03/1.510.85/1.241.00/1.571.01/1.760.73/1.020.71/0.980.58/0.84
Total(4.0s)1.59/2.411.40/2.181.53/2.261.69/2.951.13/2.011.15/1.571.25/1.471.31/1.790.96/1.300.96/1.270.81/1.10
", + "image_path": "fc60a3d39e328e053c8a2fcae13f3229bd2bc3520286c89965bc3be56ebd6570.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 49, + 178, + 541, + 242 + ], + "blocks": [ + { + "bbox": [ + 47, + 156, + 546, + 177 + ], + "lines": [ + { + "bbox": [ + 47, + 156, + 546, + 177 + ], + "spans": [ + { + "bbox": [ + 47, + 156, + 546, + 177 + ], + "type": "text", + "content": "Table 2. Comparison with baseline models on NFL dataset. " + }, + { + "bbox": [ + 47, + 156, + 546, + 177 + ], + "type": "inline_equation", + "content": "\\mathrm{{minADE}}_{20}/\\mathrm{{minFDE}}_{20}" + }, + { + "bbox": [ + 47, + 156, + 546, + 177 + ], + "type": "text", + "content": " (meters) are reported. Bold/underlined fonts represent the best/second-best result. Compared to the previous SOTA method, MID, our method achieves a 23.7%/21.9% improvement." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 49, + 178, + 541, + 242 + ], + "lines": [ + { + "bbox": [ + 49, + 178, + 541, + 242 + ], + "spans": [ + { + "bbox": [ + 49, + 178, + 541, + 242 + ], + "type": "table", + "html": "
TimeSocial-GAN [15] CVPR'18STGAT [19] ICCV'19Social-STGCNN [31] CVPR'20PECNet [27] ECCV'20STAR [52] ECCV'20Trajectron++[38] ECCV'20LB-EBM[34] CVPR'21NPSN [2] CVPR'22GroupNet[49] CVPR'22MID [14] CVPR'22Ours
1.0s0.37/0.680.35/0.640.45/0.640.52/0.970.49/0.840.41/0.650.75/1.050.43/0.640.32/0.570.30/0.580.21/0.34
2.0s0.83/1.530.82/1.601.06/1.871.19/2.471.02/1.840.93/1.651.26/2.280.83/1.520.73/1.390.71/1.310.49/0.91
Total(3.2s)1.44/2.511.39/2.481.82/3.181.99/3.841.51/2.971.54/2.581.90/3.251.32/2.271.21/2.151.14/1.920.87/1.50
", + "image_path": "984669d7f99d092975bde11e55917d1fc5e974cc8cd42842c71284bac51380fb.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 252, + 247, + 264 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 252, + 247, + 264 + ], + "spans": [ + { + "bbox": [ + 47, + 252, + 247, + 264 + ], + "type": "text", + "content": "dataset). We thus do not use explicit supervision." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 272, + 145, + 284 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 272, + 145, + 284 + ], + "spans": [ + { + "bbox": [ + 47, + 272, + 145, + 284 + ], + "type": "text", + "content": "4.5. Inference Phase" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 291, + 288, + 375 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 291, + 288, + 375 + ], + "spans": [ + { + "bbox": [ + 46, + 291, + 288, + 375 + ], + "type": "text", + "content": "During the inference, instead of the " + }, + { + "bbox": [ + 46, + 291, + 288, + 375 + ], + "type": "inline_equation", + "content": "\\Gamma" + }, + { + "bbox": [ + 46, + 291, + 288, + 375 + ], + "type": "text", + "content": "-steps' denoising, leapfrog diffusion model only takes " + }, + { + "bbox": [ + 46, + 291, + 288, + 375 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 46, + 291, + 288, + 375 + ], + "type": "text", + "content": "-steps, accelerating the inference. To be specific, we first generate " + }, + { + "bbox": [ + 46, + 291, + 288, + 375 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 291, + 288, + 375 + ], + "type": "text", + "content": " correlated samples to model the distribution " + }, + { + "bbox": [ + 46, + 291, + 288, + 375 + ], + "type": "inline_equation", + "content": "\\mathcal{P}(\\widetilde{\\mathbf{Y}}^{\\tau})" + }, + { + "bbox": [ + 46, + 291, + 288, + 375 + ], + "type": "text", + "content": " using the trained leapfrog initializer. Then, these samples will be fed into the denoising process and iteratively fine-tuned to produce the final predictions; see Algorithm 1." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 387, + 128, + 399 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 387, + 128, + 399 + ], + "spans": [ + { + "bbox": [ + 47, + 387, + 128, + 399 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 407, + 111, + 418 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 407, + 111, + 418 + ], + "spans": [ + { + "bbox": [ + 47, + 407, + 111, + 418 + ], + "type": "text", + "content": "5.1. Datasets" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 425, + 287, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 425, + 287, + 472 + ], + "spans": [ + { + "bbox": [ + 46, + 425, + 287, + 472 + ], + "type": "text", + "content": "We evaluate our method on four trajectory prediction datasets, including two sports datasets (NBA SportVU Dataset, NFL Football Dataset) and two pedestrian datasets (Stanford Drone Dataset, ETH-UCY)." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 474, + 287, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 474, + 287, + 533 + ], + "spans": [ + { + "bbox": [ + 46, + 474, + 287, + 533 + ], + "type": "text", + "content": "NBA SportVU Dataset (NBA): NBA trajectory dataset is collected by NBA using the SportVU tracking system, which records the trajectories of the 10 players and the ball in real basketball games. In this task, we predict the future 4.0s (20 frames) using the 2.0s (10 frames) past trajectory." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 533, + 287, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 533, + 287, + 593 + ], + "spans": [ + { + "bbox": [ + 46, + 533, + 287, + 593 + ], + "type": "text", + "content": "NFL Football Dataset (NFL): NFL Football Dataset records the position of every player on the field during each play in the 2017 year. We predict the 22 players' (11 players per team) and the ball's future 3.2s (16 frames) trajectory using the historical 1.6s (8 frames) trajectory." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 594, + 287, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 287, + 653 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 287, + 653 + ], + "type": "text", + "content": "Stanford Drone Dataset (SDD): SDD is a large-scale pedestrian dataset collected from a university campus in bird's eye view. Following previous works [27, 50], we use the standard train-test split and predict the future 4.8s (12 frames) using 3.2s (8 frames) past." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 653, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 288, + 714 + ], + "type": "text", + "content": "ETH-UCY: ETH-UCY dataset contains 5 subsets: ETH, HOTEL, UNIV, ZARA1, and ZARA2, containing various motion scenes. We use same segment length of 8s as SDD following previous works [18, 27] and use the leave-one-out approach with four sets for training and a left set for testing." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 251, + 440, + 264 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 251, + 440, + 264 + ], + "spans": [ + { + "bbox": [ + 306, + 251, + 440, + 264 + ], + "type": "text", + "content": "5.2. Implementation Details" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 270, + 547, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 270, + 547, + 521 + ], + "spans": [ + { + "bbox": [ + 304, + 270, + 547, + 521 + ], + "type": "text", + "content": "In the leapfrog diffusion model, we set the diffusion step " + }, + { + "bbox": [ + 304, + 270, + 547, + 521 + ], + "type": "inline_equation", + "content": "\\Gamma = 100" + }, + { + "bbox": [ + 304, + 270, + 547, + 521 + ], + "type": "text", + "content": " for all four datasets and the leapfrog step " + }, + { + "bbox": [ + 304, + 270, + 547, + 521 + ], + "type": "inline_equation", + "content": "\\tau = 5" + }, + { + "bbox": [ + 304, + 270, + 547, + 521 + ], + "type": "text", + "content": " on the NBA dataset. In the leapfrog initializer, we build a transformer-based social encoder where the feed-forward dimension is set to 256, the number of heads is 2, and 2 encoder layers are applied; we apply the temporal encoder with 1D convolution kernel being 3, and output channel setting to 32, and we also build a GRU with the hidden size of 256. In the denoising module, we apply the same parameters transformer to extract the context information, and we build the core denoising module with a hidden size of 256. To train the leapfrog diffusion model, we train the denoising module for 100 epochs with an initial learning rate of " + }, + { + "bbox": [ + 304, + 270, + 547, + 521 + ], + "type": "inline_equation", + "content": "10^{-2}" + }, + { + "bbox": [ + 304, + 270, + 547, + 521 + ], + "type": "text", + "content": " and decay to half every 16 epochs. With a frozen denoising module, we then train the leapfrog initializer for 200 epochs with an initial learning rate of " + }, + { + "bbox": [ + 304, + 270, + 547, + 521 + ], + "type": "inline_equation", + "content": "10^{-4}" + }, + { + "bbox": [ + 304, + 270, + 547, + 521 + ], + "type": "text", + "content": ", decaying by 0.9 every 32 epochs. We set weight parameter " + }, + { + "bbox": [ + 304, + 270, + 547, + 521 + ], + "type": "inline_equation", + "content": "w_{1} = 50" + }, + { + "bbox": [ + 304, + 270, + 547, + 521 + ], + "type": "text", + "content": " to emphasize the distance loss. The entire framework is trained with the Adam optimizer on one GTX-3090 GPU. All models are implemented with PyTorch 1.7.1. See more details in the supplementary material." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 527, + 486, + 540 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 527, + 486, + 540 + ], + "spans": [ + { + "bbox": [ + 305, + 527, + 486, + 540 + ], + "type": "text", + "content": "5.3. Comparison with SOTA Methods" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 545, + 547, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 547, + 653 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 547, + 653 + ], + "type": "text", + "content": "We measure the performance of different trajectory prediction methods using two metrics: " + }, + { + "bbox": [ + 304, + 545, + 547, + 653 + ], + "type": "inline_equation", + "content": "\\min\\mathrm{ADE}_K" + }, + { + "bbox": [ + 304, + 545, + 547, + 653 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 545, + 547, + 653 + ], + "type": "inline_equation", + "content": "\\min\\mathrm{FDE}_K" + }, + { + "bbox": [ + 304, + 545, + 547, + 653 + ], + "type": "text", + "content": ", following previous work [27, 49]. 1) " + }, + { + "bbox": [ + 304, + 545, + 547, + 653 + ], + "type": "inline_equation", + "content": "\\min\\mathrm{ADE}_K" + }, + { + "bbox": [ + 304, + 545, + 547, + 653 + ], + "type": "text", + "content": " calculates the minimum time-averaged distance among " + }, + { + "bbox": [ + 304, + 545, + 547, + 653 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 545, + 547, + 653 + ], + "type": "text", + "content": " predictions and the ground-truth future trajectory; 2) " + }, + { + "bbox": [ + 304, + 545, + 547, + 653 + ], + "type": "inline_equation", + "content": "\\min\\mathrm{FDE}_K" + }, + { + "bbox": [ + 304, + 545, + 547, + 653 + ], + "type": "text", + "content": " measures the minimum distance among the " + }, + { + "bbox": [ + 304, + 545, + 547, + 653 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 545, + 547, + 653 + ], + "type": "text", + "content": " predicted endpoints and the ground-truth endpoints. We calculate these two metrics at different timestamps on sports datasets to better evaluate the performance." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 654, + 548, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 548, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 548, + 712 + ], + "type": "text", + "content": "NBA dataset. We compare our method with the current 10 state-of-the-art prediction methods at different timestamps; see Table 1. We see that i) our method significantly outperforms all baselines in ADE and FDE at all timestamps. Our method reduces the ADE/FDE at 4.0s from 0.96/1.27" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5522" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 49, + 81, + 541, + 125 + ], + "blocks": [ + { + "bbox": [ + 47, + 57, + 545, + 80 + ], + "lines": [ + { + "bbox": [ + 47, + 57, + 545, + 80 + ], + "spans": [ + { + "bbox": [ + 47, + 57, + 545, + 80 + ], + "type": "text", + "content": "Table 3. Comparison with baseline models on SDD dataset. minADE20/minFDE20 (meters) are reported. Bold/underlined fonts represent the best/second-best result. Our method achieves the best performance in ADE/FDE. * represents the reproduced results from open source." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 49, + 81, + 541, + 125 + ], + "lines": [ + { + "bbox": [ + 49, + 81, + 541, + 125 + ], + "spans": [ + { + "bbox": [ + 49, + 81, + 541, + 125 + ], + "type": "table", + "html": "
TimeSocial-GAN [15] CVPR'18SOPHIE [36] CVPR'19Trajectory++ [38] ECCV'20NMMP [18] CVPR'20Evolve- Graph [25] NIPS'20PECNet [27] ECCV'20MemoNet [50] CVPR'22NPSN [2] CVPR'22GroupNet [49] CVPR'22MID* [14] CVPR'22Ours
4.8s27.23/41.4416.27/29.3819.30/32.7014.67/26.7213.90/22.909.96/15.888.56/12.668.56/11.859.31/16.119.73/15.328.48/11.66
", + "image_path": "44d4d4c3d16c859eab620920ce57b4383bd26a5228aad9324d4287d4d4b21bfe.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 55, + 149, + 535, + 242 + ], + "blocks": [ + { + "bbox": [ + 47, + 126, + 545, + 148 + ], + "lines": [ + { + "bbox": [ + 47, + 126, + 545, + 148 + ], + "spans": [ + { + "bbox": [ + 47, + 126, + 545, + 148 + ], + "type": "text", + "content": "Table 4. Comparison with baseline models on ETH-UCY dataset. minADE20/minFDE20 (meters) are reported. Bold/underlined fonts represent the best/second-best result. In most subsets, our method achieves the best or second-best performance in ADE/FDE." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 55, + 149, + 535, + 242 + ], + "lines": [ + { + "bbox": [ + 55, + 149, + 535, + 242 + ], + "spans": [ + { + "bbox": [ + 55, + 149, + 535, + 242 + ], + "type": "table", + "html": "
SubsetSocial-GAN [15]CVPR'18NMMP [18]CVPR'20STAR [52]ECCV'20PECNet [27]ECCV'20Trajectory++[38]ECCV'20Agentformer[53]ICCV'21MemoNet[50]CVPR'22NPSN [2]CVPR'22GroupNet[49]CVPR'22MID [14]CVPR'22
ETH0.87/1.620.61/1.080.36/0.650.54/0.870.61/1.020.45/0.750.40/0.610.40/0.760.46/0.730.39/0.66
Hotel0.67/1.370.33/0.630.17/0.360.18/0.240.19/0.280.14/0.220.11/0.170.12/0.180.15/0.250.13/0.22
Univ0.76/1.520.52/1.110.31/0.620.35/0.600.30/0.540.25/0.450.24/0.430.22/0.410.26/0.490.22/0.45
Zara10.35/0.680.32/0.660.29/0.520.22/0.390.24/0.420.18/0.300.18/0.320.17/0.310.21/0.390.17/0.30
Zara20.42/0.840.43/0.850.22/0.460.17/0.300.18/0.320.14/0.240.14/0.240.12/0.240.17/0.330.13/0.27
AVG0.61/1.210.41/0.820.26/0.530.29/0.480.30/0.510.23/0.390.21/0.350.21/0.380.25/0.440.21/0.38
", + "image_path": "4435e0f6ccc1ece1eba7d63e1d69c3ab043703881c178d2667a1e875c9b4ccad.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 52, + 282, + 279, + 405 + ], + "blocks": [ + { + "bbox": [ + 47, + 248, + 287, + 281 + ], + "lines": [ + { + "bbox": [ + 47, + 248, + 287, + 281 + ], + "spans": [ + { + "bbox": [ + 47, + 248, + 287, + 281 + ], + "type": "text", + "content": "Table 5. Ablation of leapfrog initializer in the leapfrog diffusion model on NFL with various prediction numbers " + }, + { + "bbox": [ + 47, + 248, + 287, + 281 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 47, + 248, + 287, + 281 + ], + "type": "text", + "content": ". Each module in the leapfrog initializer is beneficial." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 52, + 282, + 279, + 405 + ], + "lines": [ + { + "bbox": [ + 52, + 282, + 279, + 405 + ], + "spans": [ + { + "bbox": [ + 52, + 282, + 279, + 405 + ], + "type": "table", + "html": "
Mean μθVariance σθSample ΜθK=2K=4
✓correlated2.04±0.18/4.08±0.481.63±0.13/3.05±0.16
✓correlated1.95±0.08/3.90±0.221.49±0.01/2.86±0.02
✓✓i.i.d2.36±0.13/4.31±0.221.90±0.07/3.31±0.05
✓✓correlated1.84±0.05/3.61±0.111.47±0.01/2.83±0.02
Mean μθVariance σθSample ΜθK=8K=20
✓correlated1.25±0.02/2.31±0.040.99±0.03/1.68±0.04
✓correlated1.23±0.01/2.20±0.010.95±0.01/1.54±0.02
✓✓i.i.d1.51±0.04/2.67±0.071.18±0.02/1.90±0.03
✓✓correlated1.18±0.01/2.19±0.010.89±0.01/1.51±0.02
", + "image_path": "0df9007f9362c754f2413467ea97d25ad003db4c35a57d3ab432e837baaab0ab.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 422, + 287, + 482 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 422, + 287, + 482 + ], + "spans": [ + { + "bbox": [ + 46, + 422, + 287, + 482 + ], + "type": "text", + "content": "to 0.81/1.10 compared to the current state-of-the-art methods, MID, achieving " + }, + { + "bbox": [ + 46, + 422, + 287, + 482 + ], + "type": "inline_equation", + "content": "15.6\\% / 13.4\\%" + }, + { + "bbox": [ + 46, + 422, + 287, + 482 + ], + "type": "text", + "content": " improvement; and ii) performance improvement over previous methods increases with timestamps, reflecting the proposed method can capture more sophisticated distributions at further timestamps." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 483, + 288, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 483, + 288, + 567 + ], + "spans": [ + { + "bbox": [ + 46, + 483, + 288, + 567 + ], + "type": "text", + "content": "NFL dataset. We compare our method with the current 10 state-of-the-art prediction methods at different timestamps; see Table 2. We see that our model significantly outperforms all baselines in ADE and FDE at all timestamps. Our method reduces the ADE/FDE at 3.2s from 1.14/1.92 to 0.87/1.50 compared to the current state-of-the-art methods, MID, achieving " + }, + { + "bbox": [ + 46, + 483, + 288, + 567 + ], + "type": "inline_equation", + "content": "23.7\\% / 21.9\\%" + }, + { + "bbox": [ + 46, + 483, + 288, + 567 + ], + "type": "text", + "content": " improvement." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 568, + 287, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 568, + 287, + 640 + ], + "spans": [ + { + "bbox": [ + 46, + 568, + 287, + 640 + ], + "type": "text", + "content": "SDD dataset. We compare our method with the current 10 state-of-the-art prediction methods; see Table 3. We see that our method reduces FDE from 11.85 to 11.66 compared to the current state-of-the-art method, NPSN. Notably, the original MID [14] uses a different protocol from all the other methods, we update its code for a fair comparison." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 641, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 288, + 713 + ], + "type": "text", + "content": "ETH-UCY dataset. We compare our method with 10 state-of-the-art prediction methods; see Table 4. We see that i) our method reduces FDE from 0.35 to 0.33 compared to the current state-of-the-art method, MemoNet, achieving a " + }, + { + "bbox": [ + 46, + 641, + 288, + 713 + ], + "type": "inline_equation", + "content": "5.7\\%" + }, + { + "bbox": [ + 46, + 641, + 288, + 713 + ], + "type": "text", + "content": " improvement; and ii) our method achieves the best or second best to the best performance on most of the subsets." + } + ] + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 307, + 272, + 553, + 373 + ], + "blocks": [ + { + "bbox": [ + 305, + 248, + 545, + 271 + ], + "lines": [ + { + "bbox": [ + 305, + 248, + 545, + 271 + ], + "spans": [ + { + "bbox": [ + 305, + 248, + 545, + 271 + ], + "type": "text", + "content": "Table 6. Different steps " + }, + { + "bbox": [ + 305, + 248, + 545, + 271 + ], + "type": "inline_equation", + "content": "\\Gamma /\\tau" + }, + { + "bbox": [ + 305, + 248, + 545, + 271 + ], + "type": "text", + "content": " in the standard/leapfrog diffusion model on NBA. " + }, + { + "bbox": [ + 305, + 248, + 545, + 271 + ], + "type": "inline_equation", + "content": "\\tau = 5" + }, + { + "bbox": [ + 305, + 248, + 545, + 271 + ], + "type": "text", + "content": " provides the best performance." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 272, + 553, + 373 + ], + "lines": [ + { + "bbox": [ + 307, + 272, + 553, + 373 + ], + "spans": [ + { + "bbox": [ + 307, + 272, + 553, + 373 + ], + "type": "table", + "html": "
MethodSteps1.0s2.0s3.0sTotal(4.0s)Inference (ms)
Standard100.45/0.510.98/1.551.62/2.562.21/2.77~87
500.26/0.360.56/0.910.89/1.421.21/1.73~446
Diffusion (Γ)1000.21/0.280.44/0.640.69/0.950.94/1.21~886
2000.21/0.290.44/0.650.69/0.970.94/1.21>1s
5000.21/0.300.45/0.680.70/0.990.95/1.23>1s
Leapfrog30.20/0.310.40/0.620.62/0.880.84/1.10~30
Diffusion (τ)50.18/0.270.37/0.560.58/0.840.81/1.10~46
100.17/0.270.37/0.580.59/0.850.82/1.08~89
", + "image_path": "1f3d490500339bdb65ba908a95fb32fda7f65e230f844ef21a49ca8ab9ad511b.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 391, + 406, + 403 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 391, + 406, + 403 + ], + "spans": [ + { + "bbox": [ + 306, + 391, + 406, + 403 + ], + "type": "text", + "content": "5.4. Ablation Studies" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 415, + 547, + 524 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 415, + 547, + 524 + ], + "spans": [ + { + "bbox": [ + 304, + 415, + 547, + 524 + ], + "type": "text", + "content": "Effect of components in leapfrog initializer. We explore the effect of three key components in leapfrog initializer, including mean estimation, variance estimation, and sample prediction. Table 5 presents the results with mean and variance based on 5 experimental trials. We see that i) the leapfrog initializer achieves stable results with better performance even when prediction number " + }, + { + "bbox": [ + 304, + 415, + 547, + 524 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 415, + 547, + 524 + ], + "type": "text", + "content": " is small; and ii) the proposed mean estimation, variance estimation, and sample prediction all contribute to promoting prediction accuracy." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 529, + 547, + 636 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 529, + 547, + 636 + ], + "spans": [ + { + "bbox": [ + 304, + 529, + 547, + 636 + ], + "type": "text", + "content": "Effect of leapfrog step " + }, + { + "bbox": [ + 304, + 529, + 547, + 636 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 529, + 547, + 636 + ], + "type": "text", + "content": ". Table 6 reports the influence of different leapfrog steps in LED. We see that i) under similar inference time, our method significantly outperforms the standard diffusion model with better representation ability; ii) when " + }, + { + "bbox": [ + 304, + 529, + 547, + 636 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 529, + 547, + 636 + ], + "type": "text", + "content": " is too small, leapfrog initializer targets to learn more sophisticated distribution, causing worse prediction performance; and iii) when " + }, + { + "bbox": [ + 304, + 529, + 547, + 636 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 529, + 547, + 636 + ], + "type": "text", + "content": " is too large, leapfrog initializer has already captured the denoised distribution, encountering performance bottleneck and wasting inference time." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "type": "text", + "content": "Comparison to other fast sampling methods. Table 7 compares the performance of our method and the other two fast sampling methods: PD [37] and DDIM [40]. We see that our method significantly outperforms two fast sampling methods under similar inference time since the proposed LED promotes the correlation between predictions." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5523" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 55, + 60, + 175, + 191 + ], + "blocks": [ + { + "bbox": [ + 55, + 60, + 175, + 191 + ], + "lines": [ + { + "bbox": [ + 55, + 60, + 175, + 191 + ], + "spans": [ + { + "bbox": [ + 55, + 60, + 175, + 191 + ], + "type": "image", + "image_path": "205b50b00688d86aa6a4485b8a55bc1b25cdf9b05973197595d0231ff01cf1fb.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 92, + 193, + 131, + 202 + ], + "lines": [ + { + "bbox": [ + 92, + 193, + 131, + 202 + ], + "spans": [ + { + "bbox": [ + 92, + 193, + 131, + 202 + ], + "type": "text", + "content": "(a) PECNet" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 175, + 60, + 295, + 192 + ], + "blocks": [ + { + "bbox": [ + 175, + 60, + 295, + 192 + ], + "lines": [ + { + "bbox": [ + 175, + 60, + 295, + 192 + ], + "spans": [ + { + "bbox": [ + 175, + 60, + 295, + 192 + ], + "type": "image", + "image_path": "07360ce275d43da0a8a45ae2eac66de93110fae6c14398a326da717225b616bf.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 209, + 193, + 256, + 202 + ], + "lines": [ + { + "bbox": [ + 209, + 193, + 256, + 202 + ], + "spans": [ + { + "bbox": [ + 209, + 193, + 256, + 202 + ], + "type": "text", + "content": "(b) GroupNet" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 296, + 60, + 416, + 192 + ], + "blocks": [ + { + "bbox": [ + 296, + 60, + 416, + 192 + ], + "lines": [ + { + "bbox": [ + 296, + 60, + 416, + 192 + ], + "spans": [ + { + "bbox": [ + 296, + 60, + 416, + 192 + ], + "type": "image", + "image_path": "e108ce9f295a15ab4637716be9aa7df76f358f0788e4b3494a19425a98e37cc8.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 339, + 193, + 368, + 202 + ], + "lines": [ + { + "bbox": [ + 339, + 193, + 368, + 202 + ], + "spans": [ + { + "bbox": [ + 339, + 193, + 368, + 202 + ], + "type": "text", + "content": "(c) Ours" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 417, + 60, + 538, + 192 + ], + "blocks": [ + { + "bbox": [ + 417, + 60, + 538, + 192 + ], + "lines": [ + { + "bbox": [ + 417, + 60, + 538, + 192 + ], + "spans": [ + { + "bbox": [ + 417, + 60, + 538, + 192 + ], + "type": "image", + "image_path": "11552ded243966ff228ef61699a4b61e9651ae39eec663cd2c7eebc365166483.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 463, + 193, + 487, + 202 + ], + "lines": [ + { + "bbox": [ + 463, + 193, + 487, + 202 + ], + "spans": [ + { + "bbox": [ + 463, + 193, + 487, + 202 + ], + "type": "text", + "content": "(d) GT" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 48, + 252, + 287, + 353 + ], + "blocks": [ + { + "bbox": [ + 47, + 230, + 288, + 251 + ], + "lines": [ + { + "bbox": [ + 47, + 230, + 288, + 251 + ], + "spans": [ + { + "bbox": [ + 47, + 230, + 288, + 251 + ], + "type": "text", + "content": "Table 7. Comparison to other fast sampling methods on NBA. " + }, + { + "bbox": [ + 47, + 230, + 288, + 251 + ], + "type": "inline_equation", + "content": "\\eta = 1" + }, + { + "bbox": [ + 47, + 230, + 288, + 251 + ], + "type": "text", + "content": " in DDIM. Our method achieves the best performance." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 252, + 287, + 353 + ], + "lines": [ + { + "bbox": [ + 48, + 252, + 287, + 353 + ], + "spans": [ + { + "bbox": [ + 48, + 252, + 287, + 353 + ], + "type": "table", + "html": "
Method1.0s2.0s3.0sTotal(4.0s)Inference (ms)
PD (K=1)0.20/0.330.45/0.750.72/1.130.98/1.39~452
PD (K=2)0.21/0.340.46/0.780.73/1.150.98/1.41~230
PD (K=3)0.23/0.370.48/0.790.73/1.150.98/1.43~121
PD (K=4)0.25/0.380.50/0.800.75/1.160.99/1.44~64
DDIM (S=2)0.20/0.290.42/0.650.66/0.960.91/1.21~530
DDIM (S=10)0.22/0.320.44/0.710.69/1.040.93/1.31~107
DDIM (S=20)0.24/0.350.49/0.810.76/1.211.02/1.51~54
Ours0.18/0.270.37/0.560.58/0.840.81/1.10~46
", + "image_path": "ef0cb2d0e4e720e1cfe5da395925fcbf8da013b862d0c49119f483581b564301.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 51, + 357, + 166, + 418 + ], + "blocks": [ + { + "bbox": [ + 51, + 357, + 166, + 418 + ], + "lines": [ + { + "bbox": [ + 51, + 357, + 166, + 418 + ], + "spans": [ + { + "bbox": [ + 51, + 357, + 166, + 418 + ], + "type": "image", + "image_path": "3baa9c7e93eb4aff7f1387b3943a818abf6829c32fa114f4ed9497ab54a9fe03.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 167, + 357, + 279, + 418 + ], + "blocks": [ + { + "bbox": [ + 167, + 357, + 279, + 418 + ], + "lines": [ + { + "bbox": [ + 167, + 357, + 279, + 418 + ], + "spans": [ + { + "bbox": [ + 167, + 357, + 279, + 418 + ], + "type": "image", + "image_path": "75993486e983ce54ac2d7009da7636aadd6e6a8b8f791700788ea8a83591efc0.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 51, + 419, + 165, + 479 + ], + "blocks": [ + { + "bbox": [ + 51, + 419, + 165, + 479 + ], + "lines": [ + { + "bbox": [ + 51, + 419, + 165, + 479 + ], + "spans": [ + { + "bbox": [ + 51, + 419, + 165, + 479 + ], + "type": "image", + "image_path": "06487121e2a1b537d6e3839355f2dbd9cb648ee2262dcab14309b4565486a57f.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 51, + 481, + 279, + 490 + ], + "lines": [ + { + "bbox": [ + 51, + 481, + 279, + 490 + ], + "spans": [ + { + "bbox": [ + 51, + 481, + 279, + 490 + ], + "type": "text", + "content": "Past trajectory Mean estimation Our prediction Ground-truth" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_footnote" + }, + { + "bbox": [ + 46, + 493, + 286, + 526 + ], + "lines": [ + { + "bbox": [ + 46, + 493, + 286, + 526 + ], + "spans": [ + { + "bbox": [ + 46, + 493, + 286, + 526 + ], + "type": "text", + "content": "Figure 4. Mean and variance estimation in leapfrog initializer on NBA with " + }, + { + "bbox": [ + 46, + 493, + 286, + 526 + ], + "type": "inline_equation", + "content": "K = 20" + }, + { + "bbox": [ + 46, + 493, + 286, + 526 + ], + "type": "text", + "content": ". The estimated variance can reflect the scene complexity of the current agent and produce diverse predictions." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 167, + 419, + 279, + 479 + ], + "blocks": [ + { + "bbox": [ + 167, + 419, + 279, + 479 + ], + "lines": [ + { + "bbox": [ + 167, + 419, + 279, + 479 + ], + "spans": [ + { + "bbox": [ + 167, + 419, + 279, + 479 + ], + "type": "image", + "image_path": "ecc2166b8756bb0923dd67a5a40a359f3b4610e7c45b938f5f8eb1994e1c9a27.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + } + ], + "index": 14 + }, + { + "bbox": [ + 47, + 529, + 159, + 542 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 529, + 159, + 542 + ], + "spans": [ + { + "bbox": [ + 47, + 529, + 159, + 542 + ], + "type": "text", + "content": "5.5. Qualitative Results" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 46, + 546, + 287, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 546, + 287, + 605 + ], + "spans": [ + { + "bbox": [ + 46, + 546, + 287, + 605 + ], + "type": "text", + "content": "Visualization of predicted trajectory. Figure 3 compares the predicted trajectories of two baselines PECNet and GroupNet, our LED (Ours), and the ground-truth (GT) trajectories on the NBA dataset. We see that our method produces more accurate predictions than the previous methods." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 46, + 605, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 677 + ], + "type": "text", + "content": "Visualization of estimated mean and variance. Figure 4 illustrates the mean and variance estimation in the leapfrog initializer under four scenes on the NBA dataset. We see that the variance estimation can well describe the scene complexity for the current agent by the learned variance, showing the rationality of our variance estimation." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 46, + 677, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 288, + 713 + ], + "type": "text", + "content": "Visualization of different sampling mechanisms. Figure 5 compares two sampling mechanisms: I.I.D sampling and correlated sampling in the leapfrog initializer. We see" + } + ] + } + ], + "index": 20 + }, + { + "type": "image", + "bbox": [ + 309, + 230, + 539, + 351 + ], + "blocks": [ + { + "bbox": [ + 46, + 204, + 545, + 226 + ], + "lines": [ + { + "bbox": [ + 46, + 204, + 545, + 226 + ], + "spans": [ + { + "bbox": [ + 46, + 204, + 545, + 226 + ], + "type": "text", + "content": "Figure 3. Visualization comparison on NBA. We compare the best-of-20 predictions by our method and two previous methods. Our method generates a more precise trajectory prediction. (Light color: past trajectory; blue/red/green color: two teams and the basketball.)" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 309, + 230, + 539, + 351 + ], + "lines": [ + { + "bbox": [ + 309, + 230, + 539, + 351 + ], + "spans": [ + { + "bbox": [ + 309, + 230, + 539, + 351 + ], + "type": "image", + "image_path": "4b8a05611797c478dc3fba96f4b933d92cda2f6d2d1f2d5d89de5878d7fd01f5.jpg" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 354, + 547, + 424 + ], + "lines": [ + { + "bbox": [ + 305, + 354, + 547, + 424 + ], + "spans": [ + { + "bbox": [ + 305, + 354, + 547, + 424 + ], + "type": "text", + "content": "Figure 5. Comparison between I.I.D and correlated sampling mechanisms in NFL with " + }, + { + "bbox": [ + 305, + 354, + 547, + 424 + ], + "type": "inline_equation", + "content": "K = 4" + }, + { + "bbox": [ + 305, + 354, + 547, + 424 + ], + "type": "text", + "content": ". Correlated samples appropriately capture multi-modalities, significantly improving prediction performances. that the proposed correlated sampling can appropriately allocate sample diversity and capture more modalities when the number of trials " + }, + { + "bbox": [ + 305, + 354, + 547, + 424 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 305, + 354, + 547, + 424 + ], + "type": "text", + "content": " is small." + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_caption" + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 433, + 378, + 444 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 433, + 378, + 444 + ], + "spans": [ + { + "bbox": [ + 306, + 433, + 378, + 444 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 449, + 547, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 449, + 547, + 556 + ], + "spans": [ + { + "bbox": [ + 304, + 449, + 547, + 556 + ], + "type": "text", + "content": "This paper proposes the leapfrog diffusion model (LED), a diffusion-based trajectory prediction model, which significantly accelerates the overall inference speed and enables appropriate allocations of multiple correlated predictions. During the inference, LED directly models and samples from the denoised distribution through a novel leapfrog initializer with reparameterization. Extensive experiments show that our method achieves state-of-the-art performance on four real-world datasets and satisfies real-time inference needs." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 557, + 547, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 547, + 640 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 547, + 640 + ], + "type": "text", + "content": "Limitation and future work. This work achieves inference acceleration for trajectory prediction tasks partially because the dimension of trajectory data is relatively small and the corresponding distribution is much easier to learn compared with those of image/video data. A possible future work is to explore diffusion models and fast sampling methods for higher-dimensional tasks." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 306, + 651, + 408, + 664 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 651, + 408, + 664 + ], + "spans": [ + { + "bbox": [ + 306, + 651, + 408, + 664 + ], + "type": "text", + "content": "Acknowledgements" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 304, + 665, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 712 + ], + "type": "text", + "content": "This research is partially supported by National Natural Science Foundation of China under Grant 62171276 and the Science and Technology Commission of Shanghai Municipal under Grant 21511100900 and 22DZ2229005." + } + ] + } + ], + "index": 27 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5524" + } + ] + } + ], + "index": 28 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 712 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 147 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 147 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 147 + ], + "type": "text", + "content": "[1] Alexandre Alahi, Kratarth Goel, Vignesh Ramanathan, Alexandre Robicquet, Li Fei-Fei, and Silvio Savarese. 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However, the above-mentioned task-specific sampling methods usually fail to explore the geometries of objects in an explicit manner. In this paper, we introduce a new skeleton-aware learning-to-sample method by learning object skeletons as the prior knowledge to preserve the object geometry and topology information during sampling. Specifically, without labor-intensive annotations per object category, we first learn category-agnostic object skeletons via the medial axis transform definition in an unsupervised manner. With object skeleton, we then evaluate the histogram of the local feature size as the prior knowledge to formulate skeleton-aware sampling from a probabilistic perspective. Additionally, the proposed skeleton-aware sampling pipeline with the task network is thus end-to-end trainable by exploring the reparameterization trick. Extensive experiments on three popular downstream tasks, point cloud classification, retrieval, and reconstruction, demonstrate the effectiveness of the proposed method for efficient point cloud analysis.", + "bbox": [ + 75, + 301, + 473, + 633 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 665, + 209, + 681 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "With the development of 3D sensing technologies, acquiring 3D data becomes more accessible than before, and there are a growing number of data repositories available online, such as ModelNet [62], ShapeNet [6], ScanNet [11], and KITTI [18]. Among popular 3D shape representations such as point cloud [41], voxel [72], mesh [55], and multi-view images [51], the point cloud is becoming increasingly popular as the first-hand data captured by Li-DAR or depth camera (e.g., Kinect), which has been widely applied in various applications such as scene reconstruction [19, 26], autonomous driving navigation [35], and virtual reality (VR) [59]. Though a high-resolution point cloud", + "bbox": [ + 75, + 691, + 468, + 875 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/895d585f6fd7aac6dcbe51d30024c8d1478384c5659d1694b2431d1eb18bb82e.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 517, + 270, + 594, + 345 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/f36ebfe5abce0810ac80f7ca02051df41ac0bec458c08b4e6001e02c3794b8ba.jpg", + "image_caption": [ + "(b)" + ], + "image_footnote": [], + "bbox": [ + 611, + 271, + 687, + 344 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/4bad947b4d6e32c290b638baa1394c011442e70aa21bab74bdd10d9a34023f60.jpg", + "image_caption": [ + "(c)" + ], + "image_footnote": [], + "bbox": [ + 702, + 270, + 781, + 343 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/636c7e488f09fc116293fa0ff3c36ac66472ff5427256460081f067e461e5779.jpg", + "image_caption": [ + "(d)", + "Figure 1. (a) Point cloud; (b) Object skeleton; (c) Random sampling; (d) Skeleton-aware sampling. Compared with random sampling, skeleton-aware sampling tends to preserve the object geometry and topology information." + ], + "image_footnote": [], + "bbox": [ + 797, + 270, + 874, + 344 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "can accurately capture the geometry and topology details of complex objects, it remains challenging for those devices with limited computation and storage resources. Therefore, point cloud sampling, aiming to find a small set of points to represent the object shape and topology effectively, is usually indispensable for efficient large-scale point cloud analysis [24, 29, 32, 33, 41, 42, 57, 61, 71].", + "bbox": [ + 496, + 458, + 892, + 565 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Traditional point cloud sampling methods such as random sampling (RS) and farthest point sampling (FPS) [15, 42] usually select a subset of points directly using the raw data information [7, 42, 43, 47, 68]. Specifically, RS is very efficient but may miss sparse regions, while FPS has better coverage on the entire point set but suffers from the latency bottleneck in parallel computation. To improve the performances on downstream tasks, learn-to-sample methods have been recently proposed to jointly optimize the sampling algorithm and each specific downstream task [10, 14, 20,27,56]. Though considerable progress has been achieved in downstream tasks such as point cloud classification and reconstruction, one critical issue remains poorly investigated: as objects usually have complex topology structures and irregular surface morphology, it is challenging to preserve the object's geometrical information during the point cloud sampling process.", + "bbox": [ + 496, + 566, + 892, + 823 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Skeleton is an efficient representation to capture the underlying object shape structures, which has been widely used as the structural abstraction in many visual understanding tasks [31, 37, 53]. Inspired by this, we build our point cloud sampling strategy on top of the object skeleton to", + "bbox": [ + 496, + 824, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Equal contribution", + "bbox": [ + 94, + 886, + 202, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "17671", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "preserve different objects' intrinsic geometrical and topological natures. Here we illustrate a comparison between random sampling and skeleton-aware sampling in Fig. 1. However, the skeleton extraction is usually non-trivial due to the following reasons [30, 52]: 1) given the diversity of object topological structures, it is difficult to have a consistent category-agnostic skeleton definition at the semantic level, where existing datasets usually consider only single or a few known object categories, such as human skeleton; 2) topological methods are usually category-agnostic by emphasizing geometrical and topological properties of the shape, such as its connectivity, topology, length, direction, and width. Nevertheless, they usually require a substantial amount of time for geometrical processing and are also notoriously sensitive to surface noise. Therefore, we resort to the medial axis transform (MAT) definition of object skeleton and deep neural networks to learn effective skeletal representations in an unsupervised manner.", + "bbox": [ + 75, + 90, + 472, + 362 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "With the learned object skeleton, we then formulate the skeleton-aware point cloud sampling pipeline from a probabilistic perspective. Specifically, we first calculate the local feature size (LFS) [2] for each point to measure the object's size near a particular point. We then explore the LFS distribution as the prior sampling probability on each point and use the LFS histogram in practice since per-point LFS is usually sensitive to point cloud noise. By learning object skeletons with deep neural networks, we have the skeleton-aware prior probability for sampling each point. To adapt skeleton-aware sampling for downstream tasks, we jointly optimize the posterior sampling probability on each point in an end-to-end manner. Notably, by exploring the categorical reparameterization with Gumbel-softmax [22], the categorical sampling based on LFS histogram is differentiable. Therefore, both sampling and task networks are end-to-end learnable for task-specific point cloud sampling. In this paper, our main contributions can be summarized as follows:", + "bbox": [ + 75, + 363, + 472, + 636 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. We propose a new skeleton-aware point cloud sampling method to preserve the object geometry and topology information during sampling.", + "2. We introduce the category-agnostic skeleton learning in an unsupervised manner to provide the prior knowledge for skeleton-aware point cloud sampling.", + "3. We conduct extensive experiments on three important downstream tasks, point cloud classification, retrieval, and reconstruction, to evaluate the proposed approach." + ], + "bbox": [ + 89, + 646, + 468, + 804 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 829, + 218, + 844 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Deep Learning on Point Clouds. Deep neural networks have been widely used in point cloud analysis, including point cloud classification/segmentation [29, 33, 41, 42, 57,", + "bbox": [ + 75, + 854, + 468, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "[63], object detection/tracking [9, 48, 49, 72], point cloud autoencoders [1, 39, 65, 67], point cloud generation [1, 50, 58, 64], completion [5, 8, 21, 69] and registration [17, 38, 45]. A point cloud is usually not placed on a regular grid, and each point is independent of others. Meanwhile, the distances to neighboring points are not always fixed. Therefore, it is non-trivial to apply deep learning techniques to 3D point clouds. Specifically, PointNet [41] is the pioneering work in applying deep neural networks to point sets, which embeds the input into high dimensional space pointwisely and then uses a symmetric function to aggregate all point features in a permutation-invariant manner as the global features. The MLP block used in PointNet has become a fundamental component in many point cloud networks to learn pointwise representations. Recently, convolutional architectures have been further explored to aggregate local neighborhood hierarchical information and achieved superior performance on point cloud analysis [29, 54, 61].", + "bbox": [ + 496, + 90, + 890, + 364 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Skeleton-Guided Learning. Object skeleton jointly describes an object's geometry, topology, and symmetry properties in a compact and intuitive way [52], which has benefited various tasks such as shape recognition [3], reconstruction [23, 53], segmentation [31] and point cloud completion [37, 70]. For example, [53] proposes a skeleton-aware deep learning approach to generate the mesh reconstruction of object surface a from single RGB image. [37] presents a learning method for point cloud completion via the shape skeleton. Existing methods directly use the ground truth skeletons as the supervision, which can be calculated by off-line algorithms like DPC [60], Q-MAT [28] or Coverage Axis [13]. However, as mentioned before, the skeleton computation is an ill-posed problem, meaning the computation is not steady and unique. Therefore, deep learning-based skeletal representations have been recently proposed [30, 44]. For example, [30] proposes to learn skeletal meshes from point clouds. Similarly, we also learn the skeleton in an unsupervised manner to facilitate our skeleton-aware sampling strategy.", + "bbox": [ + 496, + 367, + 890, + 671 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Point Cloud Sampling. Point cloud sampling or simplification is essential, since it is always non-trivial to process high-resolution dense point clouds. Therefore, various methods have been explored to simplify dense point clouds [4, 7, 25, 34, 40, 43, 47]. For example, [47] first uses the K-means clustering to select representative points and the remove redundant points. [4] combines clustering and coarse-to-fine approaches for fast point cloud simplification. [34] presents an intrinsic point cloud simplification algorithm with density guarantee, which supports efficient uniform and feature-sensitive resampling. The above-mentioned point cloud simplification algorithms aim to find a subset of points in terms of geometry or topology, but fails to consider the downstream tasks during sampling. Several recent methods have proposed to learn to sample from", + "bbox": [ + 496, + 674, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "17672", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/c8bc9dcebea3bc9064c70d0d292c2e093c4d47682ee98635132e0f3cea91f91e.jpg", + "image_caption": [ + "Figure 2. The main skeleton-aware point cloud sampling framework. Specifically, the whole pipeline consists of two main stages: 1) we first learn object skeleton in an unsupervised manner; 2) with the estimated skeleton, we evaluate the LFS distribution as the initial sampling weight to formulate the sampling process from a probabilistic perspective." + ], + "image_footnote": [], + "bbox": [ + 89, + 97, + 888, + 378 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "dense points [10, 14, 20, 27, 36, 56, 66]. Specifically, [14] and [27] have recently introduced learning-based task-oriented sampling strategies for the downstream tasks such as point cloud classification, retrieval, and reconstruction. [10] further proposes a learnable sampling and joint-training strategy to avoid overfitting on a specific task. [36] introduces a critical point layer to pass on points with the most functional features to the next layer and adaptively sample points. Differently, we not only consider the downstream tasks but also try to preserve the underlying geometrical and topological information in point clouds.", + "bbox": [ + 75, + 463, + 472, + 630 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 643, + 169, + 659 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we first provide an overview of skeleton-aware point cloud sampling. We then describe skeleton estimation and skeleton-aware probabilistic sampling.", + "bbox": [ + 75, + 670, + 468, + 717 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Overview", + "text_level": 1, + "bbox": [ + 76, + 726, + 187, + 739 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The main skeleton-aware point cloud sampling framework is shown in Fig. 2. Given a point cloud $\\mathcal{P}$ , point cloud sampling aims to find a subset of points $\\mathcal{P}_{sub} \\subset \\mathcal{P}$ , where a good sampling strategy is expected that: 1) the selection is consistent regardless of any permutation of input points and outliers; 2) the selected points preserve the geometrical and topological information of the original point cloud; 3) the sampling process can be integrated and optimized jointly with downstream tasks to avoid significant performance degradation. Recently, learning-to-sample methods", + "bbox": [ + 75, + 750, + 472, + 902 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/2325981ac2263ee9143168f69f764934fa9c8fd6cc638c2d18edfb59f960913c.jpg", + "image_caption": [ + "Figure 3. An illustration of the object with its medial axis in 2D space. Specifically, the medial axis is defined as the set of points with more than one closest point on the boundary surface, i.e., the centers of balls maximal inscribed in the object. $\\mathrm{LFS}(p)$ indicates the Euclidean distance from the point $p$ to the medial axis." + ], + "image_footnote": [], + "bbox": [ + 598, + 460, + 795, + 613 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "have achieved remarkable success by selecting task-specific points with end-to-end learning [10, 14, 20, 27, 36]. However, these methods neglect the complex object geometrical and topological structures during learning to sample. Therefore, we introduce object skeleton to explore the structure and topology information for point cloud sampling.", + "bbox": [ + 496, + 717, + 893, + 808 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Object skeleton can be defined as a thin-centered structure that jointly describes the geometry and topology. Following the popular medial axis transform (MAT) definition [52], the object skeleton is characterized by a set of ball centers with the corresponding radii, where each ball is maximal inscribed in the object as shown in Fig. 3.", + "bbox": [ + 496, + 810, + 895, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "17673", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/8d61c3219bd6ed363b1ae7875a747490a1733a9cb110ddbe9f151a7b755f6976.jpg", + "image_caption": [ + "(a) Airplane" + ], + "image_footnote": [], + "bbox": [ + 80, + 87, + 176, + 200 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/e6cdec659bc7c5003df7c20f391787a3570350231090c3a96ab950c70bc38760.jpg", + "image_caption": [ + "Figure 4. An illustration of the LFS distribution of different objects: airplane, lamp, car, and chair. Specifically, the object skeletons are computed using DPC [60] and the LFS values are normalized for a better comparison across different object categories." + ], + "image_footnote": [], + "bbox": [ + 176, + 88, + 271, + 215 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/d1cd73864960f54ec9a71c236db737b9e2d08cc697df26b052d4895fc40283ee.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 274, + 88, + 370, + 215 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/eaa10c3587741f3b23fec1adcf480c285d17d348bfcbd4ca6708d8387bca76a6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 372, + 88, + 467, + 215 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Specifically, the skeleton is a compact shape representation with geometrical clues such as thickness, angles and branches aggregating. The structural and geometrical information significantly benefits complex 3D object analysis [31, 46]. To equip point cloud sampling with the skeleton-aware structural prior, we introduce the local feature size or LFS [2] to measure the size of the object near a particular point, e.g., the dashed line in Fig. 3. Notably, given a smooth manifold $\\mathcal{M}$ and the point $p\\in \\mathcal{M}$ , $\\mathrm{LFS}(p)$ is defined as the Euclidean distance between $p$ and the medial axis of $\\mathcal{M}$ via the nearest point. Intuitively, LFS captures the surface property and how complicated $\\mathcal{M}$ is locally distributed [12].", + "bbox": [ + 75, + 308, + 468, + 503 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "With the object skeleton, we then calculate the LFS histogram to form a robust skeleton-aware prior probability for sampling. Notably, LFS tends to distinguish the object parts with different geometrical structures, e.g., in Fig. 4, each LFS bin is closely related to a specific part of the object. Another important observation is that points with small LFS values are usually located at the delicate parts of the object, such as the areas of sharp edges or corners and these parts are usually informative and critical for geometrical analysis. For example, given the 2D object in Fig. 5, we sample points along the boundary with three different sampling strategies, random sampling, high sampling probability at large LFS area and high sampling probability at small LFS area. If we try to reconstruct the object using sampled points, the last strategy will have the smallest reconstruction error, i.e., points located on delicate parts are more important and the small LFS thus indicates importance. Consequently, we use this LFS histogram as the prior sampling probability. In the following subsection, we introduce the unsupervised skeleton estimation for efficient skeleton-aware point cloud sampling.", + "bbox": [ + 75, + 505, + 470, + 824 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Unsupervised Skeleton Estimation", + "text_level": 1, + "bbox": [ + 76, + 832, + 377, + 848 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "With the medial axis transform or MAT definition, we then have the category-agnostic object skeleton for point cloud sampling. However, it is non-trivial to efficiently ap", + "bbox": [ + 75, + 854, + 468, + 902 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/174a718894dae22f4029262d6c9fce265d989ef7fc4953c5d7e2dbcc6869b5b1.jpg", + "image_caption": [ + "Figure 5. The cyan line is the object's medial axis, and points (red) are sampled on the boundary. (a) Random sampling; (b) High sampling probability at large LFS area; and (c) High sampling probability at small LFS area. Top: LFS histogram and sampling weighting; Middle: 50 points; Bottom: 25 points." + ], + "image_footnote": [], + "bbox": [ + 509, + 88, + 629, + 248 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/b8050b197b8c95b3a5c9e9328d9f9fdf4cc74f1ddd285a4b93e41097b7197c37.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 635, + 88, + 756, + 252 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/986d99fc86eea164fdca2e572818abb9c7a0742567729fc10e6817cacc54452d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 763, + 88, + 883, + 251 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "ply the vanilla MAT algorithm due to its instability and algebraic complexity. Therefore, we introduce an unsupervised skeleton estimation method for point cloud sampling as follows. Given the input point cloud, it then aims to predict a set of $K$ skeletal spheres, where each skeletal sphere is defined by the center (i.e., the skeleton point) $c_{i} \\in \\mathbb{R}^{3}$ and the radius $r_{c_i} \\in \\mathbb{R}$ . That is, the skeletal spheres consist of two components, the coordinates of the sphere centers $\\mathcal{C} \\in \\mathbb{R}^{K \\times 3}$ and their radii $\\mathcal{R} \\in \\mathbb{R}^{K}$ . Generally, the 3D object skeleton contains both 1D curve segments and 2D surface sheets, which can represent underlying structures of various shapes. The rationale for representing the skeleton with sparse skeletal spheres lies in that the final goal of skeleton estimation is to calculate the LFS of each point. Additionally, as mentioned before, we will use the averaged LFS value in each bin instead of each individual LFS value. Therefore, dense LFS is not always necessary, which avoid introducing extra computation and storage cost for predicting dense skeletal points.", + "bbox": [ + 496, + 359, + 892, + 647 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Following [30], we introduce our skeleton estimation algorithm as follows. Specifically, [30] uses PointNet++ [42] as the backbone, and the output of the last set abstraction layer is a set of points $\\mathcal{P}_*$ and the corresponding contextual features $\\mathcal{F}_*$ . A skeletal point can always be considered the local center of a set of surface points. Consequently, the skeletal points can be generated by the convex combination of $\\mathcal{P}_*$ , i.e., $\\mathcal{C} = \\mathcal{W}_*^\\top \\mathcal{P}_*$ , where $\\mathcal{W}_*$ is the predicted weight matrix. The closest distances from $\\mathcal{P}_*$ to the skeletal points $\\mathcal{C}$ can be calculated and denoted as $\\mathcal{D}_*$ , and then the radii of all skeletal spheres are derived by $\\mathcal{R} = \\mathcal{W}_*^\\top \\mathcal{D}_*$ . Similar to [30], we use the same loss function, which consists of three parts: a sampling loss $\\mathcal{L}_s$ , a point-to-sphere loss $\\mathcal{L}_p$ , and a radius regularizer $\\mathcal{L}_r$ , as follows:", + "bbox": [ + 496, + 647, + 893, + 859 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {s} = \\sum_ {p \\in \\mathcal {P} _ {*}} \\min _ {t \\in \\mathcal {T} _ {*}} \\| p - t \\| _ {2} + \\sum_ {t \\in \\mathcal {T} _ {*}} \\min _ {p \\in \\mathcal {P} _ {*}} \\| t - p \\| _ {2}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 527, + 869, + 890, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "17674", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/a3f2b87adb805f602de0fcda787771f01384ae6bb6518906e1f7bbd7df365ca5.jpg", + "image_caption": [ + "(a) KNN neighbors" + ], + "image_footnote": [], + "bbox": [ + 84, + 90, + 269, + 183 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/cec1e3e0b5798e6ba098394e0391f22620b792ebbda368269a9ba7b126fced27.jpg", + "image_caption": [ + "(b) Delaunay neighbors", + "Figure 6. KNN neighbors and Delaunay neighbors. KNN always find the nearest neighbors while the Delaunay neighbors are these connected by Delaunay edges. Cyan line: object skeleton; Black points: surface points; Blue points: centroids. Local neighboring points are connected by blue line segments." + ], + "image_footnote": [], + "bbox": [ + 277, + 90, + 464, + 184 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {p} = \\sum_ {p \\in \\mathcal {P} _ {*}} \\left[ \\min _ {c \\in \\mathcal {C}} \\| p - c \\| _ {2} - r _ {c _ {p} ^ {m i n}} \\right] \\\\ + \\sum_ {c \\in \\mathcal {C}} \\left[ \\min _ {p \\in \\mathcal {P} _ {*}} \\| c - p \\| _ {2} - r _ {c} \\right], \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 155, + 301, + 388, + 369 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {r} = - \\sum_ {c \\in \\mathcal {C}} r _ {c}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 220, + 378, + 468, + 411 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{T}_{*}$ is a set of points sampled on the surface of each skeletal sphere and $c_{p}^{min}$ is the closest skeletal point to $p$ .", + "bbox": [ + 76, + 417, + 468, + 448 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Though the above-mentioned method can generate skeleton, each skeletal point is weighted by all points in $\\mathcal{P}_{*}$ . However, the skeleton prediction is always based on the local region, which means surface points far away from the skeletal point have no contribution to skeleton estimation. What's more, the convex combination requirement in [30] also poses a challenge to neural network learning since the network has to predict a large weight matrix. Therefore, we further propose a local weighting scheme concentrating on neighboring points to predict the skeleton. As shown in Fig. 2, our skeleton estimation network adopts the DGCNN [57] as the backbone to obtain the point-wise contextual features. Then we select K points as the centroids to group local points $\\mathcal{P}_{local} \\in \\mathbb{R}^{K \\times L \\times 3}$ and features $\\mathcal{F}_{local} \\in \\mathbb{R}^{K \\times L \\times D}$ , where $L$ is the number of neighbors of each centroid and $D$ is the dimension of the features. Based on the grouped features, we will predict the weight matrix $\\mathcal{W}_{local} \\in \\mathbb{R}^{K \\times L \\times 1}$ to derive the skeletal points, that is $\\mathcal{C} = \\mathcal{W}_{local}^{\\top} \\mathcal{P}_{local}$ . Here, matrix transposition and multiplication are conducted on the last two dimensions.", + "bbox": [ + 75, + 448, + 468, + 750 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "A critical insight here is how to select neighboring points of each centroid. As presented in [12], the skeletal points can be estimated by Delaunay edge filtering. Inspired by this, we use the Delaunay neighbors instead of the KNN ones to predict the skeletal points. We illustrate the difference between KNN and Delaunay neighbors in Fig. 6. As shown, KNN always finds the nearest $L$ neighbors in Euclidean space. However, if we aim to predict the skeletal points that are always centrally located in the object, it is beneficial to consider the antipodal surface points. That is", + "bbox": [ + 75, + 750, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "the intuition to use the Delaunay neighbors. To select the Delaunay neighbors, we first apply the Delaunay triangulation and pick out these local points connected by Delaunay edges. With the estimated skeleton, we can calculate the LFS of each point. As LFS is sensitive to point cloud noise, the best practice in our work is to use the \"smoothed\" LFS, i.e., the LFS histogram. Given the LSF histogram, we can then have the midpoint of each bin $\\bar{h}_1,\\bar{h}_2,\\dots,\\bar{h}_n$ , where $n$ is the number of bins. If the LFS of one point is in $i$ -th bin, the initial sampling weight for the point is $e^{-\\bar{h}_i} / \\sum_i e^{-\\bar{h}_i}$ .", + "bbox": [ + 496, + 90, + 890, + 243 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Skeleton-Aware Probabilistic Sampling", + "text_level": 1, + "bbox": [ + 500, + 250, + 834, + 266 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As mentioned before, we aim to find a subset of points that not only take care of the downstream tasks but also encode the geometrical structure information of 3D objects. To derive the sampling formulation, we treat the point sampling operation as drawing samples from the probability distribution with replacement. Specifically, given the input point cloud $\\mathcal{P} = \\{p_1,p_2,\\dots ,p_N\\}$ , we already have the prior per-point sampling weight from the first stage, and this initial weight encapsulates the structural information that should be considered. After the point cloud goes through the neural network, we get the point-wise features. Therefore, the posterior sampling probability over point-wise features can be formulated as:", + "bbox": [ + 496, + 273, + 890, + 468 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {P} _ {\\theta} \\left(p _ {1}, \\dots , p _ {N}\\right) = \\prod_ {i = 1} ^ {N} \\sum_ {j} \\mathcal {P} _ {\\theta} \\left(p _ {i} \\mid b _ {i j}\\right) \\mathcal {P} _ {L F S} \\left(b _ {i j}\\right), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 474, + 890, + 516 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $b_{ij}$ denotes the event that $p_i$ locates in the $j$ -th bin of the LFS histogram and the corresponding probability is $\\mathcal{P}_{LFS}(b_{ij})$ . The subscript $\\theta$ indicates trainable parameters of the neural network. During training, we maximize the posterior over all training point clouds with respect to the individual point cloud feature and the network parameters.", + "bbox": [ + 496, + 523, + 890, + 613 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Consequently, with the input point cloud $\\mathcal{P}$ , it is straightforward to consider points as different categories, and the task that samples a representative subset $\\mathcal{P}_{sub} \\subset \\mathcal{P}$ then becomes to learn to draw samples from a discrete distribution, e.g. the categorical distribution. However, the sampling operation is usually non-differentiable. Though [14] and [27] are trainable, the sampled point is less interpretable from the probabilistic perspective, especially when sampling multiple points.", + "bbox": [ + 496, + 613, + 890, + 750 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Categorical Reparameterization. Fortunately, Jang et al. [22] introduce an elegant reparameterization trick called Gumbel-softmax to enable discrete stochastic variables to back-propagate in neural network computation graphs. Therefore, we utilize the Gumbel-softmax trick to facilitate our sampling process. For a categorical distribution $Cat(c_{1},\\dots,c_{k})$ where $k$ denotes the number of categories and $c_{i}$ means the probability of category $i$ , the Gumbel-softmax is designed as a discrete reparameterization trick", + "bbox": [ + 496, + 763, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "17675", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "to estimate smooth gradient with a continuous relaxation for the categorical variable. Given the Gumbel noise $\\pmb{g} = (g_1, \\dots, g_k)$ where $g_i \\sim Gumbel(0, 1)$ is independent identically distributed, a soft categorical sample can be drawn by", + "bbox": [ + 76, + 90, + 468, + 165 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {y} = \\operatorname {s o f t m a x} \\left(\\left(\\log (\\boldsymbol {c}) + \\boldsymbol {g}\\right) / \\tau\\right), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 168, + 167, + 468, + 183 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\pmb{c} = (c_{1},\\dots,c_{k})$ and $\\tau >0$ is the annealing temperature. The equation above is referred as Gumbel-softmax, and as $\\tau \\rightarrow 0$ , $\\pmb{y}$ will degenerate into the Gumbel-max form gradually,", + "bbox": [ + 75, + 186, + 468, + 248 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {y} = \\operatorname {o n e h o t} (\\operatorname {a r g m a x} ((\\log (\\boldsymbol {c}) + \\boldsymbol {g}))), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 258, + 468, + 273 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "which is an unbiased sample from $Cat(c_{1},\\ldots ,c_{k})$ . In this way, we are able to draw differentiable samples from the distribution $Cat(c_{1},\\ldots ,c_{k})$ in the training phase. In practice, $\\tau$ starts at a high value (e.g., 1.0) and anneals to a small value (e.g., 0.1). In the testing phase, discrete samples can be drawn with the Gumbel-max trick.", + "bbox": [ + 75, + 282, + 468, + 372 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Therefore, we use a hard and discrete selection by exploring the trainable categorical reparameterization Gumbel-softmax as follows:", + "bbox": [ + 75, + 373, + 468, + 417 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {P} _ {s u b} = \\left[ G s _ {\\tau} \\left(L p \\left(\\mathcal {W} _ {L F S} \\odot \\mathcal {W} _ {\\theta}\\right) \\right] ^ {\\top} \\mathcal {P}, \\right. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 145, + 426, + 468, + 445 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\mathcal{P} \\in \\mathbb{R}^{N \\times 3}$ is the input point cloud, $\\mathcal{P}_{sub} \\in \\mathbb{R}^{M \\times 3}$ is the sampled point cloud, and $G s_{\\tau}(\\cdot)$ operation is the Gumbel-softmax trick with the annealing temperature $\\tau$ . Additionally, $\\mathcal{W}_{LFS} \\in \\mathbb{R}^{N \\times 1}$ is calculated from the first stage and $\\mathcal{W}_{\\theta} \\in \\mathbb{R}^{N \\times D_{sp}}$ is feature matrix from the sampling network, where $D_{sp}$ indicates the dimension of the features. $Lp(\\cdot): \\mathbb{R}^{N \\times D_{sp}} \\to \\mathbb{R}^{N \\times M}$ is the linear mapping layer. $\\odot$ indicates the element-wise Hadamard product operation. In practice, we start with a large $\\tau$ such as $\\tau = 1.0$ and gradually decrease it. In the training phase, it provides smooth gradients using the discrete reparameterization trick. With annealing, it degenerates to a hard selection in the testing phase.", + "bbox": [ + 75, + 452, + 468, + 650 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 662, + 209, + 679 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we evaluate the proposed skeleton-aware sampling method by applying it to three downstream tasks: point cloud classification, retrieval, and reconstruction. All experiments are conducted on the widely used ModelNet40 [62] dataset, and we use the official split of 9,843 training and 2,468 testing samples.", + "bbox": [ + 75, + 686, + 468, + 777 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Implementation Details", + "text_level": 1, + "bbox": [ + 76, + 786, + 294, + 801 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We implement the proposed method using PyTorch, and we will give the detailed network architecture in our supplementary materials. Our network training consists of two stages. We train the skeleton estimation network in the first stage to get the point cloud skeleton. The number of predicted skeletal spheres is 128, and the number of bins for", + "bbox": [ + 75, + 809, + 468, + 898 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/586d1851a5b96b58ccbbe7e9099cc831152875e6db9c154a6b4dcd015b572836.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Sampling RatioClassification Acc(%)
FPS [42]S-NET [14]SN [27]MS [10]Ours
870.477.583.788.089.1
1646.370.482.285.588.8
3226.360.680.181.587.4
6413.536.154.161.682.9
", + "bbox": [ + 504, + 88, + 890, + 175 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Point cloud classification results on ModelNet40. The task network is trained on complete data with 1024 points.", + "bbox": [ + 498, + 184, + 890, + 213 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "the LFS histogram is 6. In the second stage, we train the sampling network using task losses. In both stages, we use the Adam optimizer with a learning rate of 0.001.", + "bbox": [ + 498, + 242, + 890, + 287 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Point Cloud Classification", + "text_level": 1, + "bbox": [ + 498, + 301, + 735, + 315 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To evaluate the proposed method for point cloud classification, we employ the full version of PointNet [41] as the task network. The classification accuracy of PointNet is trained on the complete data (1024 points per point cloud without normals) and tested on sampled points of different sizes. The evaluation metric is overall accuracy (OA), and for a fair comparison, the upper bound accuracy trained on 1024 points is $89.5\\%$ (the same as MetaSampler [10]). We compare with four methods, FPS [42], S-NET [14], SampleNet [27] and MetaSampler [10]. We report the classification results of four different sampling ratios in Table 1, where the proposed method outperforms recent state-of-the-art methods. Specifically, the classification accuracy achieved by the proposed approach at the sampling ratio of 8 is very close to the upper bound accuracy $(89.1\\%$ vs. $89.5\\%)$ , which shows the effectiveness of our skeleton-aware strategy. We also notice that the performance gap between the proposed method and others is becoming large when increasing the sampling rate (e.g., at the sampling ratio of 64 with 16 points left). This further demonstrates the superiority of the proposed method in preserving task-significant features.", + "bbox": [ + 496, + 325, + 890, + 657 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Ablation Study on Skeleton-Aware Prior. We show how the prior sampling weight operates by comparing with two other commonly used non-learned sampling methods, random sampling (RS) and farthest point sampling (FPS). In Fig. 7, for visualization purposes, we use 10,000 points as input, and the number of sampled points is 1,024. Generally, RS randomly picks 1024 points from the original data, and FPS selects a subset of points far from each other. Since both two methods do not consider any geometrical information, these two sampling methods do not change the LFS distribution. Differently, we propose the skeleton-aware sampling in this work, which is able to use the LFS histogram as the initial sampling weight and also learn to sample for downstream tasks. That is, we will pay more attention to those points with small LFS values. As shown", + "bbox": [ + 496, + 672, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "17676", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/3c84a7512432bdd2294fbc3235dd33f701085b3d2be6ca0d702cacc96508ab88.jpg", + "image_caption": [ + "Figure 7. Visualization of different sampling strategies. RS and FPS do not encode geometrical information to change the LFS distribution after sampling, while the proposed considers the LFS histogram to obtain informative skeleton-aware sampling." + ], + "image_footnote": [], + "bbox": [ + 76, + 88, + 433, + 344 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "in Fig. 7, the RS and FPS keep nearly the same LFS distribution with the original point cloud after sampling, but our method encodes the geometrical information and gives out the different LFS distribution. The final results can also prove this by our sampled points concentrated on small LFS areas. In addition, we report the classification results without the LFS weight in Table 2. Here, \"GT\" means we use the ground truth skeletons computed by DPC [60] instead of the estimated ones from the first stage. As shown, using the skeleton-aware strategy as the initial sampling weight can always benefit the following learning task. Moreover, our method achieves comparable results with that using ground truth skeletons.", + "bbox": [ + 75, + 435, + 468, + 632 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/7475ce6df22eda81942ff65d2809eacc9cc19d4c95aaea299cb814d71ffdb4b2.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Sampling RatioClassification Acc(%)
GTOurs(w/o)Ours
889.188.289.1
1688.887.488.8
3287.585.987.4
6482.880.382.9
", + "bbox": [ + 109, + 640, + 436, + 753 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Ablation Study on LFS Histogram. The number of bins reveals the LFS distribution at different levels. Using wider bins reduces the LFS noise, while using narrower bins gives better precision to the LFS density estimation. Thus, varying the bin number within the LFS histogram can be", + "bbox": [ + 75, + 824, + 468, + 902 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/8cb299f472db4159a4610458040a7ca1bd04e8e70f7db0c79de4643475cae492.jpg", + "table_caption": [ + "Table 2. Point cloud classification results without the initial LFS weight. GT indicates using the ground truth skeletons generated by DPC [60]." + ], + "table_footnote": [], + "table_body": "
Sampling RatioBins
1361218
888.288.489.189.189.0
1687.488.088.888.588.8
3285.986.687.487.287.4
6480.381.282.982.882.7
", + "bbox": [ + 514, + 88, + 880, + 200 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "beneficial. We report the classification results with different bins in Table 3. The aggressive setting is to use only one bin, and this case is equivalent to no initial LSF weight applied. Generally, we find that six bins are suitable for most cases.", + "bbox": [ + 496, + 266, + 890, + 340 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Ablation Study on Skeletal Spheres. As mentioned before, the object's skeleton is represented with a set of skeletal spheres. Generally, increasing the number of predicted skeletal spheres will lead to detailed structures. Thus, it is beneficial to disclose how this hyper-parameter influences the following tasks. We show the classification results in Table 4 with different numbers of skeletal spheres predicted. As shown, our method is not sensitive to the parameter and achieves steady performance.", + "bbox": [ + 496, + 357, + 890, + 493 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/5c2e3e55f02d59e53d67b0ada66ce7a64bb4f9671ca1ea3ffc6e5a47bcb422f9.jpg", + "table_caption": [ + "Table 3. Point cloud classification results with different bins. Generally, we find that six bins already work well in most cases." + ], + "table_footnote": [], + "table_body": "
Sampling RatioSkeletal Spheres
3264128256
887.288.489.189.1
1685.887.188.888.5
3284.085.187.487.2
6479.380.582.982.8
", + "bbox": [ + 537, + 505, + 856, + 619 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 4. Point cloud classification results when using different numbers of skeletal spheres.", + "bbox": [ + 498, + 628, + 890, + 657 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Ablation Study on Annealing Strategy. As we apply the Gumbel-softmax operation in our method, we gradually anneal the temperature $\\tau$ to facilitate our network training in the second stage. Thus, it is beneficial to evaluate the classification performance when adopting different annealing strategies. During training, we let $\\tau = 1.0$ to allow gradients past the samples and then gradually anneal the temperature until $\\tau = 0.5$ (but not completely to 0, as the gradients would blow up). In the test phase, as $\\tau \\to 0.0$ , the softmax becomes an argmax and the Gumbel-softmax distribution becomes the categorical distribution. We report the classification results in Table 5 with four different annealing strategies, including constant, step, linear and exponential. Here, the \"constant\" means $\\tau$ keeps being 1.0 without annealing during training.", + "bbox": [ + 496, + 674, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "17677", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/3b5f67b58e3bf1a19e99350f6a266e62f5cf279d02ccf272bdb069f040a38a45.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Temperature (τ)Sampling Ratio
8163264
Constant87.786.485.181.1
Step88.887.286.682.1
Linear rectified89.087.987.682.3
Exponential89.188.887.482.9
", + "bbox": [ + 112, + 88, + 433, + 200 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Model Complexity. In Table 6, we report the model complexity of the proposed method. Specifically, the FLOPs increase with a large number of predicted skeletal spheres. The number of parameters for the probabilistic sampling network is 1.24M, and the number of FLOPs is 2.93G at the sampling ratio of 8.", + "bbox": [ + 75, + 280, + 468, + 371 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/1cf936c9f7217b0de758f326c6b4a4932fe09ac8d5448bc3ec074d16680731ff.jpg", + "table_caption": [ + "Table 5. Point cloud classification results for using different annealing strategies. Here, the \"Constant\" row means we do not anneal the $\\tau$ and keep $\\tau = 1.0$ during training." + ], + "table_footnote": [], + "table_body": "
Model ComplexityParams (M)FLOPs (G)
Skeletal Spheres321.543.43
641.543.86
1281.544.71
2561.546.41
Sampling Ratio81.242.93
161.232.90
321.222.88
641.212.86
", + "bbox": [ + 112, + 383, + 439, + 539 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3. Point Cloud Retrieval", + "text_level": 1, + "bbox": [ + 76, + 603, + 281, + 618 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this subsection, we perform point cloud retrieval experiments to further demonstrate the effectiveness of the proposed method for downstream tasks. We follow the same evaluation setting in [10, 14, 27] to report the performance on the point cloud retrieval. Specifically, we take our method trained with PointNet [41] for classification as the task network without re-training it. We sample points of different sizes fed into PointNet and use its penultimate layer as the shape descriptor. Retrieval is done based on the L2 distance on the shape descriptor, and the evaluation metric is the mean Average Precision (mAP). In Table. 7, we summarize the performances of different methods and observe that our method consistently outperforms others by a large margin at different sampling ratios.", + "bbox": [ + 75, + 626, + 468, + 838 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Point Cloud Reconstruction", + "text_level": 1, + "bbox": [ + 76, + 847, + 326, + 862 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this subsection, we perform point cloud reconstruction experiments to further demonstrate the effectiveness of the", + "bbox": [ + 75, + 869, + 467, + 900 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/5445f44afcd083df056bc3ee2ebd450d324b7a8eadb0d82470e2e9f65840696b.jpg", + "table_caption": [ + "Table 6. The model complexity of the proposed skeleton estimation network." + ], + "table_footnote": [], + "table_body": "
Sampling RatioRetrieval Performance (mAP)
FPS [42]S-NET [14]SN [27]Ours
858.360.468.872.2
1649.459.065.270.9
3237.759.062.567.1
6427.454.559.562.6
", + "bbox": [ + 504, + 88, + 890, + 188 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "proposed method for downstream tasks. We use an autoencoder as the task network on the ModelNet40 [62] dataset. Following [10], we employ the Point Completion Network (PCN) [69] to minimize the Chamfer distance (CD) [16] between the input and output points. As demonstrated in Table 8, our method outperforms others and the improvement is consistent across all sampling ratios, further exhibiting the effectiveness of our method.", + "bbox": [ + 496, + 270, + 890, + 391 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/8beed66d9354799b43ce86114051005681d9f39dd2f55ae8a4d0180dd883f7c7.jpg", + "table_caption": [ + "Table 7. Point cloud retrieval results on the ModelNet40 dataset. Specifically, the proposed method achieves superior performance across different sampling ratios." + ], + "table_footnote": [], + "table_body": "
Sampling RatioReconstruction Performance (CD)
FPS [42]SN [27]MS [10]Ours
83.783.293.052.97
164.033.323.153.01
324.253.613.373.24
644.784.434.313.78
", + "bbox": [ + 504, + 404, + 890, + 510 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 8. Point cloud reconstruction results on the ModelNet40 dataset. Specifically, the original size of data is 1024 points.", + "bbox": [ + 498, + 520, + 890, + 550 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 587, + 617, + 603 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we propose a skeleton-aware learning-to-sample method for point cloud sampling. The skeletal representation of the point cloud is learned in an unsupervised manner to avoid label-intensive annotations. Given the learned skeleton, the skeleton-aware point cloud sampling process is conducted in a probabilistic way according to the LFS distribution. The proposed skeleton-aware sampling method is end-to-end trainable. To evaluate the proposed method, we perform experiments on several downstream point cloud analysis tasks such as classification, retrieval, and reconstruction, and the proposed method consistently outperforms traditional and recent learning-to-sample methods by a large margin.", + "bbox": [ + 496, + 614, + 890, + 811 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement", + "text_level": 1, + "bbox": [ + 500, + 828, + 660, + 845 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Mr Cheng Wen and Dr Baosheng Yu were supported by Australian Research Council Projects in part by IH180100002 and FL170100117.", + "bbox": [ + 498, + 854, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "17678", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Panos Achlioptas, Olga Diamanti, Ioannis Mitliagkas, and Leonidas Guibas. 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In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 4490-4499, 2018. 1, 2" + ], + "bbox": [ + 501, + 92, + 890, + 571 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "17681", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Learnable Skeleton-Aware 3D Point Cloud Sampling/8f02b705-b134-4074-ba5a-caacbe000bbf_model.json b/2023/Learnable Skeleton-Aware 3D Point Cloud Sampling/8f02b705-b134-4074-ba5a-caacbe000bbf_model.json new file mode 100644 index 0000000000000000000000000000000000000000..aaca1979cccea3dc847f3328ca2647aba5d46d55 --- /dev/null +++ b/2023/Learnable Skeleton-Aware 3D Point Cloud Sampling/8f02b705-b134-4074-ba5a-caacbe000bbf_model.json @@ -0,0 +1,2444 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.219, + 0.131, + 0.753, + 0.154 + ], + "angle": 0, + "content": "Learnable Skeleton-Aware 3D Point Cloud Sampling" + }, + { + "type": "text", + "bbox": [ + 0.289, + 0.182, + 0.68, + 0.199 + ], + "angle": 0, + "content": "Cheng Wen* Baosheng Yu* Dacheng Tao" + }, + { + "type": "text", + "bbox": [ + 0.175, + 0.2, + 0.793, + 0.217 + ], + "angle": 0, + "content": "School of Computer Science, The University of Sydney, NSW 2008, Australia" + }, + { + "type": "text", + "bbox": [ + 0.146, + 0.22, + 0.819, + 0.234 + ], + "angle": 0, + "content": "cwen6671@uni.sydney.edu.au; baosheng.yu@sydney.edu.au; dacheng.tao@gmail.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.269, + 0.314, + 0.285 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.302, + 0.474, + 0.635 + ], + "angle": 0, + "content": "Point cloud sampling is crucial for efficient large-scale point cloud analysis, where learning-to-sample methods have recently received increasing attention from the community for jointly training with downstream tasks. However, the above-mentioned task-specific sampling methods usually fail to explore the geometries of objects in an explicit manner. In this paper, we introduce a new skeleton-aware learning-to-sample method by learning object skeletons as the prior knowledge to preserve the object geometry and topology information during sampling. Specifically, without labor-intensive annotations per object category, we first learn category-agnostic object skeletons via the medial axis transform definition in an unsupervised manner. With object skeleton, we then evaluate the histogram of the local feature size as the prior knowledge to formulate skeleton-aware sampling from a probabilistic perspective. Additionally, the proposed skeleton-aware sampling pipeline with the task network is thus end-to-end trainable by exploring the reparameterization trick. Extensive experiments on three popular downstream tasks, point cloud classification, retrieval, and reconstruction, demonstrate the effectiveness of the proposed method for efficient point cloud analysis." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.666, + 0.21, + 0.682 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.692, + 0.47, + 0.875 + ], + "angle": 0, + "content": "With the development of 3D sensing technologies, acquiring 3D data becomes more accessible than before, and there are a growing number of data repositories available online, such as ModelNet [62], ShapeNet [6], ScanNet [11], and KITTI [18]. Among popular 3D shape representations such as point cloud [41], voxel [72], mesh [55], and multi-view images [51], the point cloud is becoming increasingly popular as the first-hand data captured by Li-DAR or depth camera (e.g., Kinect), which has been widely applied in various applications such as scene reconstruction [19, 26], autonomous driving navigation [35], and virtual reality (VR) [59]. Though a high-resolution point cloud" + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.271, + 0.596, + 0.346 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.549, + 0.349, + 0.566, + 0.361 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.612, + 0.272, + 0.688, + 0.345 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.642, + 0.349, + 0.66, + 0.36 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image", + "bbox": [ + 0.704, + 0.271, + 0.782, + 0.344 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.735, + 0.349, + 0.752, + 0.36 + ], + "angle": 0, + "content": "(c)" + }, + { + "type": "image", + "bbox": [ + 0.798, + 0.271, + 0.875, + 0.345 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.828, + 0.349, + 0.845, + 0.36 + ], + "angle": 0, + "content": "(d)" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.373, + 0.892, + 0.43 + ], + "angle": 0, + "content": "Figure 1. (a) Point cloud; (b) Object skeleton; (c) Random sampling; (d) Skeleton-aware sampling. Compared with random sampling, skeleton-aware sampling tends to preserve the object geometry and topology information." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.459, + 0.893, + 0.566 + ], + "angle": 0, + "content": "can accurately capture the geometry and topology details of complex objects, it remains challenging for those devices with limited computation and storage resources. Therefore, point cloud sampling, aiming to find a small set of points to represent the object shape and topology effectively, is usually indispensable for efficient large-scale point cloud analysis [24, 29, 32, 33, 41, 42, 57, 61, 71]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.567, + 0.893, + 0.824 + ], + "angle": 0, + "content": "Traditional point cloud sampling methods such as random sampling (RS) and farthest point sampling (FPS) [15, 42] usually select a subset of points directly using the raw data information [7, 42, 43, 47, 68]. Specifically, RS is very efficient but may miss sparse regions, while FPS has better coverage on the entire point set but suffers from the latency bottleneck in parallel computation. To improve the performances on downstream tasks, learn-to-sample methods have been recently proposed to jointly optimize the sampling algorithm and each specific downstream task [10, 14, 20,27,56]. Though considerable progress has been achieved in downstream tasks such as point cloud classification and reconstruction, one critical issue remains poorly investigated: as objects usually have complex topology structures and irregular surface morphology, it is challenging to preserve the object's geometrical information during the point cloud sampling process." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.894, + 0.903 + ], + "angle": 0, + "content": "Skeleton is an efficient representation to capture the underlying object shape structures, which has been widely used as the structural abstraction in many visual understanding tasks [31, 37, 53]. Inspired by this, we build our point cloud sampling strategy on top of the object skeleton to" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.204, + 0.9 + ], + "angle": 0, + "content": "*Equal contribution" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "17671" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.363 + ], + "angle": 0, + "content": "preserve different objects' intrinsic geometrical and topological natures. Here we illustrate a comparison between random sampling and skeleton-aware sampling in Fig. 1. However, the skeleton extraction is usually non-trivial due to the following reasons [30, 52]: 1) given the diversity of object topological structures, it is difficult to have a consistent category-agnostic skeleton definition at the semantic level, where existing datasets usually consider only single or a few known object categories, such as human skeleton; 2) topological methods are usually category-agnostic by emphasizing geometrical and topological properties of the shape, such as its connectivity, topology, length, direction, and width. Nevertheless, they usually require a substantial amount of time for geometrical processing and are also notoriously sensitive to surface noise. Therefore, we resort to the medial axis transform (MAT) definition of object skeleton and deep neural networks to learn effective skeletal representations in an unsupervised manner." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.364, + 0.473, + 0.637 + ], + "angle": 0, + "content": "With the learned object skeleton, we then formulate the skeleton-aware point cloud sampling pipeline from a probabilistic perspective. Specifically, we first calculate the local feature size (LFS) [2] for each point to measure the object's size near a particular point. We then explore the LFS distribution as the prior sampling probability on each point and use the LFS histogram in practice since per-point LFS is usually sensitive to point cloud noise. By learning object skeletons with deep neural networks, we have the skeleton-aware prior probability for sampling each point. To adapt skeleton-aware sampling for downstream tasks, we jointly optimize the posterior sampling probability on each point in an end-to-end manner. Notably, by exploring the categorical reparameterization with Gumbel-softmax [22], the categorical sampling based on LFS histogram is differentiable. Therefore, both sampling and task networks are end-to-end learnable for task-specific point cloud sampling. In this paper, our main contributions can be summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.647, + 0.47, + 0.692 + ], + "angle": 0, + "content": "1. We propose a new skeleton-aware point cloud sampling method to preserve the object geometry and topology information during sampling." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.703, + 0.47, + 0.748 + ], + "angle": 0, + "content": "2. We introduce the category-agnostic skeleton learning in an unsupervised manner to provide the prior knowledge for skeleton-aware point cloud sampling." + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.759, + 0.469, + 0.805 + ], + "angle": 0, + "content": "3. We conduct extensive experiments on three important downstream tasks, point cloud classification, retrieval, and reconstruction, to evaluate the proposed approach." + }, + { + "type": "list", + "bbox": [ + 0.09, + 0.647, + 0.47, + 0.805 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.83, + 0.22, + 0.845 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Deep Learning on Point Clouds. Deep neural networks have been widely used in point cloud analysis, including point cloud classification/segmentation [29, 33, 41, 42, 57," + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.365 + ], + "angle": 0, + "content": "[63], object detection/tracking [9, 48, 49, 72], point cloud autoencoders [1, 39, 65, 67], point cloud generation [1, 50, 58, 64], completion [5, 8, 21, 69] and registration [17, 38, 45]. A point cloud is usually not placed on a regular grid, and each point is independent of others. Meanwhile, the distances to neighboring points are not always fixed. Therefore, it is non-trivial to apply deep learning techniques to 3D point clouds. Specifically, PointNet [41] is the pioneering work in applying deep neural networks to point sets, which embeds the input into high dimensional space pointwisely and then uses a symmetric function to aggregate all point features in a permutation-invariant manner as the global features. The MLP block used in PointNet has become a fundamental component in many point cloud networks to learn pointwise representations. Recently, convolutional architectures have been further explored to aggregate local neighborhood hierarchical information and achieved superior performance on point cloud analysis [29, 54, 61]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.368, + 0.892, + 0.672 + ], + "angle": 0, + "content": "Skeleton-Guided Learning. Object skeleton jointly describes an object's geometry, topology, and symmetry properties in a compact and intuitive way [52], which has benefited various tasks such as shape recognition [3], reconstruction [23, 53], segmentation [31] and point cloud completion [37, 70]. For example, [53] proposes a skeleton-aware deep learning approach to generate the mesh reconstruction of object surface a from single RGB image. [37] presents a learning method for point cloud completion via the shape skeleton. Existing methods directly use the ground truth skeletons as the supervision, which can be calculated by off-line algorithms like DPC [60], Q-MAT [28] or Coverage Axis [13]. However, as mentioned before, the skeleton computation is an ill-posed problem, meaning the computation is not steady and unique. Therefore, deep learning-based skeletal representations have been recently proposed [30, 44]. For example, [30] proposes to learn skeletal meshes from point clouds. Similarly, we also learn the skeleton in an unsupervised manner to facilitate our skeleton-aware sampling strategy." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Point Cloud Sampling. Point cloud sampling or simplification is essential, since it is always non-trivial to process high-resolution dense point clouds. Therefore, various methods have been explored to simplify dense point clouds [4, 7, 25, 34, 40, 43, 47]. For example, [47] first uses the K-means clustering to select representative points and the remove redundant points. [4] combines clustering and coarse-to-fine approaches for fast point cloud simplification. [34] presents an intrinsic point cloud simplification algorithm with density guarantee, which supports efficient uniform and feature-sensitive resampling. The above-mentioned point cloud simplification algorithms aim to find a subset of points in terms of geometry or topology, but fails to consider the downstream tasks during sampling. Several recent methods have proposed to learn to sample from" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "17672" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.091, + 0.098, + 0.889, + 0.379 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.395, + 0.896, + 0.44 + ], + "angle": 0, + "content": "Figure 2. The main skeleton-aware point cloud sampling framework. Specifically, the whole pipeline consists of two main stages: 1) we first learn object skeleton in an unsupervised manner; 2) with the estimated skeleton, we evaluate the LFS distribution as the initial sampling weight to formulate the sampling process from a probabilistic perspective." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.464, + 0.473, + 0.631 + ], + "angle": 0, + "content": "dense points [10, 14, 20, 27, 36, 56, 66]. Specifically, [14] and [27] have recently introduced learning-based task-oriented sampling strategies for the downstream tasks such as point cloud classification, retrieval, and reconstruction. [10] further proposes a learnable sampling and joint-training strategy to avoid overfitting on a specific task. [36] introduces a critical point layer to pass on points with the most functional features to the next layer and adaptively sample points. Differently, we not only consider the downstream tasks but also try to preserve the underlying geometrical and topological information in point clouds." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.645, + 0.17, + 0.66 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.671, + 0.47, + 0.718 + ], + "angle": 0, + "content": "In this section, we first provide an overview of skeleton-aware point cloud sampling. We then describe skeleton estimation and skeleton-aware probabilistic sampling." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.727, + 0.188, + 0.74 + ], + "angle": 0, + "content": "3.1. Overview" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.473, + 0.903 + ], + "angle": 0, + "content": "The main skeleton-aware point cloud sampling framework is shown in Fig. 2. Given a point cloud \\(\\mathcal{P}\\), point cloud sampling aims to find a subset of points \\(\\mathcal{P}_{sub} \\subset \\mathcal{P}\\), where a good sampling strategy is expected that: 1) the selection is consistent regardless of any permutation of input points and outliers; 2) the selected points preserve the geometrical and topological information of the original point cloud; 3) the sampling process can be integrated and optimized jointly with downstream tasks to avoid significant performance degradation. Recently, learning-to-sample methods" + }, + { + "type": "image", + "bbox": [ + 0.599, + 0.462, + 0.797, + 0.614 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.625, + 0.895, + 0.696 + ], + "angle": 0, + "content": "Figure 3. An illustration of the object with its medial axis in 2D space. Specifically, the medial axis is defined as the set of points with more than one closest point on the boundary surface, i.e., the centers of balls maximal inscribed in the object. \\(\\mathrm{LFS}(p)\\) indicates the Euclidean distance from the point \\(p\\) to the medial axis." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.718, + 0.895, + 0.809 + ], + "angle": 0, + "content": "have achieved remarkable success by selecting task-specific points with end-to-end learning [10, 14, 20, 27, 36]. However, these methods neglect the complex object geometrical and topological structures during learning to sample. Therefore, we introduce object skeleton to explore the structure and topology information for point cloud sampling." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.896, + 0.903 + ], + "angle": 0, + "content": "Object skeleton can be defined as a thin-centered structure that jointly describes the geometry and topology. Following the popular medial axis transform (MAT) definition [52], the object skeleton is characterized by a set of ball centers with the corresponding radii, where each ball is maximal inscribed in the object as shown in Fig. 3." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "17673" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.088, + 0.177, + 0.201 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.096, + 0.203, + 0.162, + 0.215 + ], + "angle": 0, + "content": "(a) Airplane" + }, + { + "type": "image", + "bbox": [ + 0.178, + 0.089, + 0.272, + 0.216 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.275, + 0.089, + 0.371, + 0.216 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.373, + 0.089, + 0.468, + 0.216 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.227, + 0.47, + 0.283 + ], + "angle": 0, + "content": "Figure 4. An illustration of the LFS distribution of different objects: airplane, lamp, car, and chair. Specifically, the object skeletons are computed using DPC [60] and the LFS values are normalized for a better comparison across different object categories." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.309, + 0.47, + 0.505 + ], + "angle": 0, + "content": "Specifically, the skeleton is a compact shape representation with geometrical clues such as thickness, angles and branches aggregating. The structural and geometrical information significantly benefits complex 3D object analysis [31, 46]. To equip point cloud sampling with the skeleton-aware structural prior, we introduce the local feature size or LFS [2] to measure the size of the object near a particular point, e.g., the dashed line in Fig. 3. Notably, given a smooth manifold \\(\\mathcal{M}\\) and the point \\(p\\in \\mathcal{M}\\), \\(\\mathrm{LFS}(p)\\) is defined as the Euclidean distance between \\(p\\) and the medial axis of \\(\\mathcal{M}\\) via the nearest point. Intuitively, LFS captures the surface property and how complicated \\(\\mathcal{M}\\) is locally distributed [12]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.506, + 0.471, + 0.825 + ], + "angle": 0, + "content": "With the object skeleton, we then calculate the LFS histogram to form a robust skeleton-aware prior probability for sampling. Notably, LFS tends to distinguish the object parts with different geometrical structures, e.g., in Fig. 4, each LFS bin is closely related to a specific part of the object. Another important observation is that points with small LFS values are usually located at the delicate parts of the object, such as the areas of sharp edges or corners and these parts are usually informative and critical for geometrical analysis. For example, given the 2D object in Fig. 5, we sample points along the boundary with three different sampling strategies, random sampling, high sampling probability at large LFS area and high sampling probability at small LFS area. If we try to reconstruct the object using sampled points, the last strategy will have the smallest reconstruction error, i.e., points located on delicate parts are more important and the small LFS thus indicates importance. Consequently, we use this LFS histogram as the prior sampling probability. In the following subsection, we introduce the unsupervised skeleton estimation for efficient skeleton-aware point cloud sampling." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.833, + 0.379, + 0.849 + ], + "angle": 0, + "content": "3.2. Unsupervised Skeleton Estimation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.47, + 0.903 + ], + "angle": 0, + "content": "With the medial axis transform or MAT definition, we then have the category-agnostic object skeleton for point cloud sampling. However, it is non-trivial to efficiently ap" + }, + { + "type": "image", + "bbox": [ + 0.51, + 0.089, + 0.63, + 0.249 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.637, + 0.089, + 0.757, + 0.253 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.764, + 0.089, + 0.885, + 0.252 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.264, + 0.892, + 0.334 + ], + "angle": 0, + "content": "Figure 5. The cyan line is the object's medial axis, and points (red) are sampled on the boundary. (a) Random sampling; (b) High sampling probability at large LFS area; and (c) High sampling probability at small LFS area. Top: LFS histogram and sampling weighting; Middle: 50 points; Bottom: 25 points." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.36, + 0.893, + 0.648 + ], + "angle": 0, + "content": "ply the vanilla MAT algorithm due to its instability and algebraic complexity. Therefore, we introduce an unsupervised skeleton estimation method for point cloud sampling as follows. Given the input point cloud, it then aims to predict a set of \\( K \\) skeletal spheres, where each skeletal sphere is defined by the center (i.e., the skeleton point) \\( c_{i} \\in \\mathbb{R}^{3} \\) and the radius \\( r_{c_i} \\in \\mathbb{R} \\). That is, the skeletal spheres consist of two components, the coordinates of the sphere centers \\( \\mathcal{C} \\in \\mathbb{R}^{K \\times 3} \\) and their radii \\( \\mathcal{R} \\in \\mathbb{R}^{K} \\). Generally, the 3D object skeleton contains both 1D curve segments and 2D surface sheets, which can represent underlying structures of various shapes. The rationale for representing the skeleton with sparse skeletal spheres lies in that the final goal of skeleton estimation is to calculate the LFS of each point. Additionally, as mentioned before, we will use the averaged LFS value in each bin instead of each individual LFS value. Therefore, dense LFS is not always necessary, which avoid introducing extra computation and storage cost for predicting dense skeletal points." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.648, + 0.895, + 0.86 + ], + "angle": 0, + "content": "Following [30], we introduce our skeleton estimation algorithm as follows. Specifically, [30] uses PointNet++ [42] as the backbone, and the output of the last set abstraction layer is a set of points \\(\\mathcal{P}_*\\) and the corresponding contextual features \\(\\mathcal{F}_*\\). A skeletal point can always be considered the local center of a set of surface points. Consequently, the skeletal points can be generated by the convex combination of \\(\\mathcal{P}_*\\), i.e., \\(\\mathcal{C} = \\mathcal{W}_*^\\top \\mathcal{P}_*\\), where \\(\\mathcal{W}_*\\) is the predicted weight matrix. The closest distances from \\(\\mathcal{P}_*\\) to the skeletal points \\(\\mathcal{C}\\) can be calculated and denoted as \\(\\mathcal{D}_*\\), and then the radii of all skeletal spheres are derived by \\(\\mathcal{R} = \\mathcal{W}_*^\\top \\mathcal{D}_*\\). Similar to [30], we use the same loss function, which consists of three parts: a sampling loss \\(\\mathcal{L}_s\\), a point-to-sphere loss \\(\\mathcal{L}_p\\), and a radius regularizer \\(\\mathcal{L}_r\\), as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.528, + 0.871, + 0.892, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {s} = \\sum_ {p \\in \\mathcal {P} _ {*}} \\min _ {t \\in \\mathcal {T} _ {*}} \\| p - t \\| _ {2} + \\sum_ {t \\in \\mathcal {T} _ {*}} \\min _ {p \\in \\mathcal {P} _ {*}} \\| t - p \\| _ {2}, \\tag {1}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17674" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.086, + 0.091, + 0.27, + 0.184 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.126, + 0.19, + 0.229, + 0.203 + ], + "angle": 0, + "content": "(a) KNN neighbors" + }, + { + "type": "image", + "bbox": [ + 0.279, + 0.091, + 0.465, + 0.185 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.308, + 0.191, + 0.434, + 0.203 + ], + "angle": 0, + "content": "(b) Delaunay neighbors" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.215, + 0.47, + 0.284 + ], + "angle": 0, + "content": "Figure 6. KNN neighbors and Delaunay neighbors. KNN always find the nearest neighbors while the Delaunay neighbors are these connected by Delaunay edges. Cyan line: object skeleton; Black points: surface points; Blue points: centroids. Local neighboring points are connected by blue line segments." + }, + { + "type": "equation", + "bbox": [ + 0.156, + 0.302, + 0.389, + 0.37 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {p} = \\sum_ {p \\in \\mathcal {P} _ {*}} \\left[ \\min _ {c \\in \\mathcal {C}} \\| p - c \\| _ {2} - r _ {c _ {p} ^ {m i n}} \\right] \\\\ + \\sum_ {c \\in \\mathcal {C}} \\left[ \\min _ {p \\in \\mathcal {P} _ {*}} \\| c - p \\| _ {2} - r _ {c} \\right], \\\\ \\end{array}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.221, + 0.38, + 0.469, + 0.412 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {r} = - \\sum_ {c \\in \\mathcal {C}} r _ {c}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.418, + 0.469, + 0.449 + ], + "angle": 0, + "content": "where \\(\\mathcal{T}_{*}\\) is a set of points sampled on the surface of each skeletal sphere and \\(c_{p}^{min}\\) is the closest skeletal point to \\(p\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.449, + 0.47, + 0.75 + ], + "angle": 0, + "content": "Though the above-mentioned method can generate skeleton, each skeletal point is weighted by all points in \\(\\mathcal{P}_{*}\\). However, the skeleton prediction is always based on the local region, which means surface points far away from the skeletal point have no contribution to skeleton estimation. What's more, the convex combination requirement in [30] also poses a challenge to neural network learning since the network has to predict a large weight matrix. Therefore, we further propose a local weighting scheme concentrating on neighboring points to predict the skeleton. As shown in Fig. 2, our skeleton estimation network adopts the DGCNN [57] as the backbone to obtain the point-wise contextual features. Then we select K points as the centroids to group local points \\(\\mathcal{P}_{local} \\in \\mathbb{R}^{K \\times L \\times 3}\\) and features \\(\\mathcal{F}_{local} \\in \\mathbb{R}^{K \\times L \\times D}\\), where \\(L\\) is the number of neighbors of each centroid and \\(D\\) is the dimension of the features. Based on the grouped features, we will predict the weight matrix \\(\\mathcal{W}_{local} \\in \\mathbb{R}^{K \\times L \\times 1}\\) to derive the skeletal points, that is \\(\\mathcal{C} = \\mathcal{W}_{local}^{\\top} \\mathcal{P}_{local}\\). Here, matrix transposition and multiplication are conducted on the last two dimensions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.469, + 0.901 + ], + "angle": 0, + "content": "A critical insight here is how to select neighboring points of each centroid. As presented in [12], the skeletal points can be estimated by Delaunay edge filtering. Inspired by this, we use the Delaunay neighbors instead of the KNN ones to predict the skeletal points. We illustrate the difference between KNN and Delaunay neighbors in Fig. 6. As shown, KNN always finds the nearest \\( L \\) neighbors in Euclidean space. However, if we aim to predict the skeletal points that are always centrally located in the object, it is beneficial to consider the antipodal surface points. That is" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.244 + ], + "angle": 0, + "content": "the intuition to use the Delaunay neighbors. To select the Delaunay neighbors, we first apply the Delaunay triangulation and pick out these local points connected by Delaunay edges. With the estimated skeleton, we can calculate the LFS of each point. As LFS is sensitive to point cloud noise, the best practice in our work is to use the \"smoothed\" LFS, i.e., the LFS histogram. Given the LSF histogram, we can then have the midpoint of each bin \\(\\bar{h}_1,\\bar{h}_2,\\dots,\\bar{h}_n\\), where \\(n\\) is the number of bins. If the LFS of one point is in \\(i\\)-th bin, the initial sampling weight for the point is \\(e^{-\\bar{h}_i} / \\sum_i e^{-\\bar{h}_i}\\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.25, + 0.836, + 0.267 + ], + "angle": 0, + "content": "3.3. Skeleton-Aware Probabilistic Sampling" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.274, + 0.892, + 0.469 + ], + "angle": 0, + "content": "As mentioned before, we aim to find a subset of points that not only take care of the downstream tasks but also encode the geometrical structure information of 3D objects. To derive the sampling formulation, we treat the point sampling operation as drawing samples from the probability distribution with replacement. Specifically, given the input point cloud \\(\\mathcal{P} = \\{p_1,p_2,\\dots ,p_N\\}\\), we already have the prior per-point sampling weight from the first stage, and this initial weight encapsulates the structural information that should be considered. After the point cloud goes through the neural network, we get the point-wise features. Therefore, the posterior sampling probability over point-wise features can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.521, + 0.475, + 0.892, + 0.517 + ], + "angle": 0, + "content": "\\[\n\\mathcal {P} _ {\\theta} \\left(p _ {1}, \\dots , p _ {N}\\right) = \\prod_ {i = 1} ^ {N} \\sum_ {j} \\mathcal {P} _ {\\theta} \\left(p _ {i} \\mid b _ {i j}\\right) \\mathcal {P} _ {L F S} \\left(b _ {i j}\\right), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.524, + 0.892, + 0.614 + ], + "angle": 0, + "content": "where \\( b_{ij} \\) denotes the event that \\( p_i \\) locates in the \\( j \\)-th bin of the LFS histogram and the corresponding probability is \\( \\mathcal{P}_{LFS}(b_{ij}) \\). The subscript \\( \\theta \\) indicates trainable parameters of the neural network. During training, we maximize the posterior over all training point clouds with respect to the individual point cloud feature and the network parameters." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.892, + 0.751 + ], + "angle": 0, + "content": "Consequently, with the input point cloud \\(\\mathcal{P}\\), it is straightforward to consider points as different categories, and the task that samples a representative subset \\(\\mathcal{P}_{sub} \\subset \\mathcal{P}\\) then becomes to learn to draw samples from a discrete distribution, e.g. the categorical distribution. However, the sampling operation is usually non-differentiable. Though [14] and [27] are trainable, the sampled point is less interpretable from the probabilistic perspective, especially when sampling multiple points." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Categorical Reparameterization. Fortunately, Jang et al. [22] introduce an elegant reparameterization trick called Gumbel-softmax to enable discrete stochastic variables to back-propagate in neural network computation graphs. Therefore, we utilize the Gumbel-softmax trick to facilitate our sampling process. For a categorical distribution \\(Cat(c_{1},\\dots,c_{k})\\) where \\(k\\) denotes the number of categories and \\(c_{i}\\) means the probability of category \\(i\\), the Gumbel-softmax is designed as a discrete reparameterization trick" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17675" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.166 + ], + "angle": 0, + "content": "to estimate smooth gradient with a continuous relaxation for the categorical variable. Given the Gumbel noise \\( \\pmb{g} = (g_1, \\dots, g_k) \\) where \\( g_i \\sim Gumbel(0, 1) \\) is independent identically distributed, a soft categorical sample can be drawn by" + }, + { + "type": "equation", + "bbox": [ + 0.169, + 0.168, + 0.469, + 0.184 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {y} = \\operatorname {s o f t m a x} \\left(\\left(\\log (\\boldsymbol {c}) + \\boldsymbol {g}\\right) / \\tau\\right), \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.188, + 0.47, + 0.249 + ], + "angle": 0, + "content": "where \\(\\pmb{c} = (c_{1},\\dots,c_{k})\\) and \\(\\tau >0\\) is the annealing temperature. The equation above is referred as Gumbel-softmax, and as \\(\\tau \\rightarrow 0\\), \\(\\pmb{y}\\) will degenerate into the Gumbel-max form gradually," + }, + { + "type": "equation", + "bbox": [ + 0.15, + 0.259, + 0.469, + 0.275 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {y} = \\operatorname {o n e h o t} (\\operatorname {a r g m a x} ((\\log (\\boldsymbol {c}) + \\boldsymbol {g}))), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.283, + 0.469, + 0.373 + ], + "angle": 0, + "content": "which is an unbiased sample from \\(Cat(c_{1},\\ldots ,c_{k})\\). In this way, we are able to draw differentiable samples from the distribution \\(Cat(c_{1},\\ldots ,c_{k})\\) in the training phase. In practice, \\(\\tau\\) starts at a high value (e.g., 1.0) and anneals to a small value (e.g., 0.1). In the testing phase, discrete samples can be drawn with the Gumbel-max trick." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.374, + 0.469, + 0.418 + ], + "angle": 0, + "content": "Therefore, we use a hard and discrete selection by exploring the trainable categorical reparameterization Gumbel-softmax as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.147, + 0.428, + 0.469, + 0.446 + ], + "angle": 0, + "content": "\\[\n\\mathcal {P} _ {s u b} = \\left[ G s _ {\\tau} \\left(L p \\left(\\mathcal {W} _ {L F S} \\odot \\mathcal {W} _ {\\theta}\\right) \\right] ^ {\\top} \\mathcal {P}, \\right. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.453, + 0.47, + 0.651 + ], + "angle": 0, + "content": "where \\(\\mathcal{P} \\in \\mathbb{R}^{N \\times 3}\\) is the input point cloud, \\(\\mathcal{P}_{sub} \\in \\mathbb{R}^{M \\times 3}\\) is the sampled point cloud, and \\(G s_{\\tau}(\\cdot)\\) operation is the Gumbel-softmax trick with the annealing temperature \\(\\tau\\). Additionally, \\(\\mathcal{W}_{LFS} \\in \\mathbb{R}^{N \\times 1}\\) is calculated from the first stage and \\(\\mathcal{W}_{\\theta} \\in \\mathbb{R}^{N \\times D_{sp}}\\) is feature matrix from the sampling network, where \\(D_{sp}\\) indicates the dimension of the features. \\(Lp(\\cdot): \\mathbb{R}^{N \\times D_{sp}} \\to \\mathbb{R}^{N \\times M}\\) is the linear mapping layer. \\(\\odot\\) indicates the element-wise Hadamard product operation. In practice, we start with a large \\(\\tau\\) such as \\(\\tau = 1.0\\) and gradually decrease it. In the training phase, it provides smooth gradients using the discrete reparameterization trick. With annealing, it degenerates to a hard selection in the testing phase." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.663, + 0.21, + 0.68 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.688, + 0.469, + 0.779 + ], + "angle": 0, + "content": "In this section, we evaluate the proposed skeleton-aware sampling method by applying it to three downstream tasks: point cloud classification, retrieval, and reconstruction. All experiments are conducted on the widely used ModelNet40 [62] dataset, and we use the official split of 9,843 training and 2,468 testing samples." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.787, + 0.295, + 0.803 + ], + "angle": 0, + "content": "4.1. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.469, + 0.9 + ], + "angle": 0, + "content": "We implement the proposed method using PyTorch, and we will give the detailed network architecture in our supplementary materials. Our network training consists of two stages. We train the skeleton estimation network in the first stage to get the point cloud skeleton. The number of predicted skeletal spheres is 128, and the number of bins for" + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.089, + 0.892, + 0.176 + ], + "angle": 0, + "content": "
Sampling RatioClassification Acc(%)
FPS [42]S-NET [14]SN [27]MS [10]Ours
870.477.583.788.089.1
1646.370.482.285.588.8
3226.360.680.181.587.4
6413.536.154.161.682.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.185, + 0.892, + 0.214 + ], + "angle": 0, + "content": "Table 1. Point cloud classification results on ModelNet40. The task network is trained on complete data with 1024 points." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.243, + 0.892, + 0.289 + ], + "angle": 0, + "content": "the LFS histogram is 6. In the second stage, we train the sampling network using task losses. In both stages, we use the Adam optimizer with a learning rate of 0.001." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.302, + 0.736, + 0.316 + ], + "angle": 0, + "content": "4.2. Point Cloud Classification" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.326, + 0.892, + 0.658 + ], + "angle": 0, + "content": "To evaluate the proposed method for point cloud classification, we employ the full version of PointNet [41] as the task network. The classification accuracy of PointNet is trained on the complete data (1024 points per point cloud without normals) and tested on sampled points of different sizes. The evaluation metric is overall accuracy (OA), and for a fair comparison, the upper bound accuracy trained on 1024 points is \\(89.5\\%\\) (the same as MetaSampler [10]). We compare with four methods, FPS [42], S-NET [14], SampleNet [27] and MetaSampler [10]. We report the classification results of four different sampling ratios in Table 1, where the proposed method outperforms recent state-of-the-art methods. Specifically, the classification accuracy achieved by the proposed approach at the sampling ratio of 8 is very close to the upper bound accuracy \\((89.1\\%\\) vs. \\(89.5\\%)\\), which shows the effectiveness of our skeleton-aware strategy. We also notice that the performance gap between the proposed method and others is becoming large when increasing the sampling rate (e.g., at the sampling ratio of 64 with 16 points left). This further demonstrates the superiority of the proposed method in preserving task-significant features." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.674, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Ablation Study on Skeleton-Aware Prior. We show how the prior sampling weight operates by comparing with two other commonly used non-learned sampling methods, random sampling (RS) and farthest point sampling (FPS). In Fig. 7, for visualization purposes, we use 10,000 points as input, and the number of sampled points is 1,024. Generally, RS randomly picks 1024 points from the original data, and FPS selects a subset of points far from each other. Since both two methods do not consider any geometrical information, these two sampling methods do not change the LFS distribution. Differently, we propose the skeleton-aware sampling in this work, which is able to use the LFS histogram as the initial sampling weight and also learn to sample for downstream tasks. That is, we will pay more attention to those points with small LFS values. As shown" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17676" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.089, + 0.434, + 0.345 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.357, + 0.47, + 0.412 + ], + "angle": 0, + "content": "Figure 7. Visualization of different sampling strategies. RS and FPS do not encode geometrical information to change the LFS distribution after sampling, while the proposed considers the LFS histogram to obtain informative skeleton-aware sampling." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.436, + 0.47, + 0.633 + ], + "angle": 0, + "content": "in Fig. 7, the RS and FPS keep nearly the same LFS distribution with the original point cloud after sampling, but our method encodes the geometrical information and gives out the different LFS distribution. The final results can also prove this by our sampled points concentrated on small LFS areas. In addition, we report the classification results without the LFS weight in Table 2. Here, \"GT\" means we use the ground truth skeletons computed by DPC [60] instead of the estimated ones from the first stage. As shown, using the skeleton-aware strategy as the initial sampling weight can always benefit the following learning task. Moreover, our method achieves comparable results with that using ground truth skeletons." + }, + { + "type": "table", + "bbox": [ + 0.111, + 0.641, + 0.437, + 0.755 + ], + "angle": 0, + "content": "
Sampling RatioClassification Acc(%)
GTOurs(w/o)Ours
889.188.289.1
1688.887.488.8
3287.585.987.4
6482.880.382.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.766, + 0.47, + 0.809 + ], + "angle": 0, + "content": "Table 2. Point cloud classification results without the initial LFS weight. GT indicates using the ground truth skeletons generated by DPC [60]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Ablation Study on LFS Histogram. The number of bins reveals the LFS distribution at different levels. Using wider bins reduces the LFS noise, while using narrower bins gives better precision to the LFS density estimation. Thus, varying the bin number within the LFS histogram can be" + }, + { + "type": "table", + "bbox": [ + 0.515, + 0.089, + 0.882, + 0.202 + ], + "angle": 0, + "content": "
Sampling RatioBins
1361218
888.288.489.189.189.0
1687.488.088.888.588.8
3285.986.687.487.287.4
6480.381.282.982.882.7
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.213, + 0.892, + 0.241 + ], + "angle": 0, + "content": "Table 3. Point cloud classification results with different bins. Generally, we find that six bins already work well in most cases." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.267, + 0.892, + 0.342 + ], + "angle": 0, + "content": "beneficial. We report the classification results with different bins in Table 3. The aggressive setting is to use only one bin, and this case is equivalent to no initial LSF weight applied. Generally, we find that six bins are suitable for most cases." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.358, + 0.892, + 0.494 + ], + "angle": 0, + "content": "Ablation Study on Skeletal Spheres. As mentioned before, the object's skeleton is represented with a set of skeletal spheres. Generally, increasing the number of predicted skeletal spheres will lead to detailed structures. Thus, it is beneficial to disclose how this hyper-parameter influences the following tasks. We show the classification results in Table 4 with different numbers of skeletal spheres predicted. As shown, our method is not sensitive to the parameter and achieves steady performance." + }, + { + "type": "table", + "bbox": [ + 0.538, + 0.506, + 0.857, + 0.62 + ], + "angle": 0, + "content": "
Sampling RatioSkeletal Spheres
3264128256
887.288.489.189.1
1685.887.188.888.5
3284.085.187.487.2
6479.380.582.982.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.63, + 0.892, + 0.658 + ], + "angle": 0, + "content": "Table 4. Point cloud classification results when using different numbers of skeletal spheres." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Ablation Study on Annealing Strategy. As we apply the Gumbel-softmax operation in our method, we gradually anneal the temperature \\(\\tau\\) to facilitate our network training in the second stage. Thus, it is beneficial to evaluate the classification performance when adopting different annealing strategies. During training, we let \\(\\tau = 1.0\\) to allow gradients past the samples and then gradually anneal the temperature until \\(\\tau = 0.5\\) (but not completely to 0, as the gradients would blow up). In the test phase, as \\(\\tau \\to 0.0\\), the softmax becomes an argmax and the Gumbel-softmax distribution becomes the categorical distribution. We report the classification results in Table 5 with four different annealing strategies, including constant, step, linear and exponential. Here, the \"constant\" means \\(\\tau\\) keeps being 1.0 without annealing during training." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17677" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.114, + 0.089, + 0.434, + 0.202 + ], + "angle": 0, + "content": "
Temperature (τ)Sampling Ratio
8163264
Constant87.786.485.181.1
Step88.887.286.682.1
Linear rectified89.087.987.682.3
Exponential89.188.887.482.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.212, + 0.47, + 0.256 + ], + "angle": 0, + "content": "Table 5. Point cloud classification results for using different annealing strategies. Here, the \"Constant\" row means we do not anneal the \\(\\tau\\) and keep \\(\\tau = 1.0\\) during training." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.281, + 0.47, + 0.372 + ], + "angle": 0, + "content": "Model Complexity. In Table 6, we report the model complexity of the proposed method. Specifically, the FLOPs increase with a large number of predicted skeletal spheres. The number of parameters for the probabilistic sampling network is 1.24M, and the number of FLOPs is 2.93G at the sampling ratio of 8." + }, + { + "type": "table", + "bbox": [ + 0.113, + 0.384, + 0.44, + 0.54 + ], + "angle": 0, + "content": "
Model ComplexityParams (M)FLOPs (G)
Skeletal Spheres321.543.43
641.543.86
1281.544.71
2561.546.41
Sampling Ratio81.242.93
161.232.90
321.222.88
641.212.86
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.55, + 0.468, + 0.579 + ], + "angle": 0, + "content": "Table 6. The model complexity of the proposed skeleton estimation network." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.604, + 0.282, + 0.619 + ], + "angle": 0, + "content": "4.3. Point Cloud Retrieval" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.627, + 0.47, + 0.839 + ], + "angle": 0, + "content": "In this subsection, we perform point cloud retrieval experiments to further demonstrate the effectiveness of the proposed method for downstream tasks. We follow the same evaluation setting in [10, 14, 27] to report the performance on the point cloud retrieval. Specifically, we take our method trained with PointNet [41] for classification as the task network without re-training it. We sample points of different sizes fed into PointNet and use its penultimate layer as the shape descriptor. Retrieval is done based on the L2 distance on the shape descriptor, and the evaluation metric is the mean Average Precision (mAP). In Table. 7, we summarize the performances of different methods and observe that our method consistently outperforms others by a large margin at different sampling ratios." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.848, + 0.327, + 0.863 + ], + "angle": 0, + "content": "4.4. Point Cloud Reconstruction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.468, + 0.901 + ], + "angle": 0, + "content": "In this subsection, we perform point cloud reconstruction experiments to further demonstrate the effectiveness of the" + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.089, + 0.892, + 0.189 + ], + "angle": 0, + "content": "
Sampling RatioRetrieval Performance (mAP)
FPS [42]S-NET [14]SN [27]Ours
858.360.468.872.2
1649.459.065.270.9
3237.759.062.567.1
6427.454.559.562.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.2, + 0.892, + 0.242 + ], + "angle": 0, + "content": "Table 7. Point cloud retrieval results on the ModelNet40 dataset. Specifically, the proposed method achieves superior performance across different sampling ratios." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.271, + 0.892, + 0.392 + ], + "angle": 0, + "content": "proposed method for downstream tasks. We use an autoencoder as the task network on the ModelNet40 [62] dataset. Following [10], we employ the Point Completion Network (PCN) [69] to minimize the Chamfer distance (CD) [16] between the input and output points. As demonstrated in Table 8, our method outperforms others and the improvement is consistent across all sampling ratios, further exhibiting the effectiveness of our method." + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.405, + 0.892, + 0.511 + ], + "angle": 0, + "content": "
Sampling RatioReconstruction Performance (CD)
FPS [42]SN [27]MS [10]Ours
83.783.293.052.97
164.033.323.153.01
324.253.613.373.24
644.784.434.313.78
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.521, + 0.892, + 0.551 + ], + "angle": 0, + "content": "Table 8. Point cloud reconstruction results on the ModelNet40 dataset. Specifically, the original size of data is 1024 points." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.588, + 0.618, + 0.604 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.615, + 0.892, + 0.812 + ], + "angle": 0, + "content": "In this paper, we propose a skeleton-aware learning-to-sample method for point cloud sampling. The skeletal representation of the point cloud is learned in an unsupervised manner to avoid label-intensive annotations. Given the learned skeleton, the skeleton-aware point cloud sampling process is conducted in a probabilistic way according to the LFS distribution. The proposed skeleton-aware sampling method is end-to-end trainable. To evaluate the proposed method, we perform experiments on several downstream point cloud analysis tasks such as classification, retrieval, and reconstruction, and the proposed method consistently outperforms traditional and recent learning-to-sample methods by a large margin." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.829, + 0.661, + 0.846 + ], + "angle": 0, + "content": "Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Mr Cheng Wen and Dr Baosheng Yu were supported by Australian Research Council Projects in part by IH180100002 and FL170100117." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17678" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.171 + ], + "angle": 0, + "content": "[1] Panos Achlioptas, Olga Diamanti, Ioannis Mitliagkas, and Leonidas Guibas. 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However, the above-mentioned task-specific sampling methods usually fail to explore the geometries of objects in an explicit manner. In this paper, we introduce a new skeleton-aware learning-to-sample method by learning object skeletons as the prior knowledge to preserve the object geometry and topology information during sampling. Specifically, without labor-intensive annotations per object category, we first learn category-agnostic object skeletons via the medial axis transform definition in an unsupervised manner. With object skeleton, we then evaluate the histogram of the local feature size as the prior knowledge to formulate skeleton-aware sampling from a probabilistic perspective. Additionally, the proposed skeleton-aware sampling pipeline with the task network is thus end-to-end trainable by exploring the reparameterization trick. Extensive experiments on three popular downstream tasks, point cloud classification, retrieval, and reconstruction, demonstrate the effectiveness of the proposed method for efficient point cloud analysis. + +# 1. Introduction + +With the development of 3D sensing technologies, acquiring 3D data becomes more accessible than before, and there are a growing number of data repositories available online, such as ModelNet [62], ShapeNet [6], ScanNet [11], and KITTI [18]. Among popular 3D shape representations such as point cloud [41], voxel [72], mesh [55], and multi-view images [51], the point cloud is becoming increasingly popular as the first-hand data captured by Li-DAR or depth camera (e.g., Kinect), which has been widely applied in various applications such as scene reconstruction [19, 26], autonomous driving navigation [35], and virtual reality (VR) [59]. Though a high-resolution point cloud + +![](images/895d585f6fd7aac6dcbe51d30024c8d1478384c5659d1694b2431d1eb18bb82e.jpg) +(a) + +![](images/f36ebfe5abce0810ac80f7ca02051df41ac0bec458c08b4e6001e02c3794b8ba.jpg) +(b) + +![](images/4bad947b4d6e32c290b638baa1394c011442e70aa21bab74bdd10d9a34023f60.jpg) +(c) + +![](images/636c7e488f09fc116293fa0ff3c36ac66472ff5427256460081f067e461e5779.jpg) +(d) +Figure 1. (a) Point cloud; (b) Object skeleton; (c) Random sampling; (d) Skeleton-aware sampling. Compared with random sampling, skeleton-aware sampling tends to preserve the object geometry and topology information. + +can accurately capture the geometry and topology details of complex objects, it remains challenging for those devices with limited computation and storage resources. Therefore, point cloud sampling, aiming to find a small set of points to represent the object shape and topology effectively, is usually indispensable for efficient large-scale point cloud analysis [24, 29, 32, 33, 41, 42, 57, 61, 71]. + +Traditional point cloud sampling methods such as random sampling (RS) and farthest point sampling (FPS) [15, 42] usually select a subset of points directly using the raw data information [7, 42, 43, 47, 68]. Specifically, RS is very efficient but may miss sparse regions, while FPS has better coverage on the entire point set but suffers from the latency bottleneck in parallel computation. To improve the performances on downstream tasks, learn-to-sample methods have been recently proposed to jointly optimize the sampling algorithm and each specific downstream task [10, 14, 20,27,56]. Though considerable progress has been achieved in downstream tasks such as point cloud classification and reconstruction, one critical issue remains poorly investigated: as objects usually have complex topology structures and irregular surface morphology, it is challenging to preserve the object's geometrical information during the point cloud sampling process. + +Skeleton is an efficient representation to capture the underlying object shape structures, which has been widely used as the structural abstraction in many visual understanding tasks [31, 37, 53]. Inspired by this, we build our point cloud sampling strategy on top of the object skeleton to + +preserve different objects' intrinsic geometrical and topological natures. Here we illustrate a comparison between random sampling and skeleton-aware sampling in Fig. 1. However, the skeleton extraction is usually non-trivial due to the following reasons [30, 52]: 1) given the diversity of object topological structures, it is difficult to have a consistent category-agnostic skeleton definition at the semantic level, where existing datasets usually consider only single or a few known object categories, such as human skeleton; 2) topological methods are usually category-agnostic by emphasizing geometrical and topological properties of the shape, such as its connectivity, topology, length, direction, and width. Nevertheless, they usually require a substantial amount of time for geometrical processing and are also notoriously sensitive to surface noise. Therefore, we resort to the medial axis transform (MAT) definition of object skeleton and deep neural networks to learn effective skeletal representations in an unsupervised manner. + +With the learned object skeleton, we then formulate the skeleton-aware point cloud sampling pipeline from a probabilistic perspective. Specifically, we first calculate the local feature size (LFS) [2] for each point to measure the object's size near a particular point. We then explore the LFS distribution as the prior sampling probability on each point and use the LFS histogram in practice since per-point LFS is usually sensitive to point cloud noise. By learning object skeletons with deep neural networks, we have the skeleton-aware prior probability for sampling each point. To adapt skeleton-aware sampling for downstream tasks, we jointly optimize the posterior sampling probability on each point in an end-to-end manner. Notably, by exploring the categorical reparameterization with Gumbel-softmax [22], the categorical sampling based on LFS histogram is differentiable. Therefore, both sampling and task networks are end-to-end learnable for task-specific point cloud sampling. In this paper, our main contributions can be summarized as follows: + +1. We propose a new skeleton-aware point cloud sampling method to preserve the object geometry and topology information during sampling. +2. We introduce the category-agnostic skeleton learning in an unsupervised manner to provide the prior knowledge for skeleton-aware point cloud sampling. +3. We conduct extensive experiments on three important downstream tasks, point cloud classification, retrieval, and reconstruction, to evaluate the proposed approach. + +# 2. Related Work + +Deep Learning on Point Clouds. Deep neural networks have been widely used in point cloud analysis, including point cloud classification/segmentation [29, 33, 41, 42, 57, + +[63], object detection/tracking [9, 48, 49, 72], point cloud autoencoders [1, 39, 65, 67], point cloud generation [1, 50, 58, 64], completion [5, 8, 21, 69] and registration [17, 38, 45]. A point cloud is usually not placed on a regular grid, and each point is independent of others. Meanwhile, the distances to neighboring points are not always fixed. Therefore, it is non-trivial to apply deep learning techniques to 3D point clouds. Specifically, PointNet [41] is the pioneering work in applying deep neural networks to point sets, which embeds the input into high dimensional space pointwisely and then uses a symmetric function to aggregate all point features in a permutation-invariant manner as the global features. The MLP block used in PointNet has become a fundamental component in many point cloud networks to learn pointwise representations. Recently, convolutional architectures have been further explored to aggregate local neighborhood hierarchical information and achieved superior performance on point cloud analysis [29, 54, 61]. + +Skeleton-Guided Learning. Object skeleton jointly describes an object's geometry, topology, and symmetry properties in a compact and intuitive way [52], which has benefited various tasks such as shape recognition [3], reconstruction [23, 53], segmentation [31] and point cloud completion [37, 70]. For example, [53] proposes a skeleton-aware deep learning approach to generate the mesh reconstruction of object surface a from single RGB image. [37] presents a learning method for point cloud completion via the shape skeleton. Existing methods directly use the ground truth skeletons as the supervision, which can be calculated by off-line algorithms like DPC [60], Q-MAT [28] or Coverage Axis [13]. However, as mentioned before, the skeleton computation is an ill-posed problem, meaning the computation is not steady and unique. Therefore, deep learning-based skeletal representations have been recently proposed [30, 44]. For example, [30] proposes to learn skeletal meshes from point clouds. Similarly, we also learn the skeleton in an unsupervised manner to facilitate our skeleton-aware sampling strategy. + +Point Cloud Sampling. Point cloud sampling or simplification is essential, since it is always non-trivial to process high-resolution dense point clouds. Therefore, various methods have been explored to simplify dense point clouds [4, 7, 25, 34, 40, 43, 47]. For example, [47] first uses the K-means clustering to select representative points and the remove redundant points. [4] combines clustering and coarse-to-fine approaches for fast point cloud simplification. [34] presents an intrinsic point cloud simplification algorithm with density guarantee, which supports efficient uniform and feature-sensitive resampling. The above-mentioned point cloud simplification algorithms aim to find a subset of points in terms of geometry or topology, but fails to consider the downstream tasks during sampling. Several recent methods have proposed to learn to sample from + +![](images/c8bc9dcebea3bc9064c70d0d292c2e093c4d47682ee98635132e0f3cea91f91e.jpg) +Figure 2. The main skeleton-aware point cloud sampling framework. Specifically, the whole pipeline consists of two main stages: 1) we first learn object skeleton in an unsupervised manner; 2) with the estimated skeleton, we evaluate the LFS distribution as the initial sampling weight to formulate the sampling process from a probabilistic perspective. + +dense points [10, 14, 20, 27, 36, 56, 66]. Specifically, [14] and [27] have recently introduced learning-based task-oriented sampling strategies for the downstream tasks such as point cloud classification, retrieval, and reconstruction. [10] further proposes a learnable sampling and joint-training strategy to avoid overfitting on a specific task. [36] introduces a critical point layer to pass on points with the most functional features to the next layer and adaptively sample points. Differently, we not only consider the downstream tasks but also try to preserve the underlying geometrical and topological information in point clouds. + +# 3. Method + +In this section, we first provide an overview of skeleton-aware point cloud sampling. We then describe skeleton estimation and skeleton-aware probabilistic sampling. + +# 3.1. Overview + +The main skeleton-aware point cloud sampling framework is shown in Fig. 2. Given a point cloud $\mathcal{P}$ , point cloud sampling aims to find a subset of points $\mathcal{P}_{sub} \subset \mathcal{P}$ , where a good sampling strategy is expected that: 1) the selection is consistent regardless of any permutation of input points and outliers; 2) the selected points preserve the geometrical and topological information of the original point cloud; 3) the sampling process can be integrated and optimized jointly with downstream tasks to avoid significant performance degradation. Recently, learning-to-sample methods + +![](images/2325981ac2263ee9143168f69f764934fa9c8fd6cc638c2d18edfb59f960913c.jpg) +Figure 3. An illustration of the object with its medial axis in 2D space. Specifically, the medial axis is defined as the set of points with more than one closest point on the boundary surface, i.e., the centers of balls maximal inscribed in the object. $\mathrm{LFS}(p)$ indicates the Euclidean distance from the point $p$ to the medial axis. + +have achieved remarkable success by selecting task-specific points with end-to-end learning [10, 14, 20, 27, 36]. However, these methods neglect the complex object geometrical and topological structures during learning to sample. Therefore, we introduce object skeleton to explore the structure and topology information for point cloud sampling. + +Object skeleton can be defined as a thin-centered structure that jointly describes the geometry and topology. Following the popular medial axis transform (MAT) definition [52], the object skeleton is characterized by a set of ball centers with the corresponding radii, where each ball is maximal inscribed in the object as shown in Fig. 3. + +![](images/8d61c3219bd6ed363b1ae7875a747490a1733a9cb110ddbe9f151a7b755f6976.jpg) +(a) Airplane + +![](images/e6cdec659bc7c5003df7c20f391787a3570350231090c3a96ab950c70bc38760.jpg) +Figure 4. An illustration of the LFS distribution of different objects: airplane, lamp, car, and chair. Specifically, the object skeletons are computed using DPC [60] and the LFS values are normalized for a better comparison across different object categories. + +![](images/d1cd73864960f54ec9a71c236db737b9e2d08cc697df26b052d4895fc40283ee.jpg) + +![](images/eaa10c3587741f3b23fec1adcf480c285d17d348bfcbd4ca6708d8387bca76a6.jpg) + +Specifically, the skeleton is a compact shape representation with geometrical clues such as thickness, angles and branches aggregating. The structural and geometrical information significantly benefits complex 3D object analysis [31, 46]. To equip point cloud sampling with the skeleton-aware structural prior, we introduce the local feature size or LFS [2] to measure the size of the object near a particular point, e.g., the dashed line in Fig. 3. Notably, given a smooth manifold $\mathcal{M}$ and the point $p\in \mathcal{M}$ , $\mathrm{LFS}(p)$ is defined as the Euclidean distance between $p$ and the medial axis of $\mathcal{M}$ via the nearest point. Intuitively, LFS captures the surface property and how complicated $\mathcal{M}$ is locally distributed [12]. + +With the object skeleton, we then calculate the LFS histogram to form a robust skeleton-aware prior probability for sampling. Notably, LFS tends to distinguish the object parts with different geometrical structures, e.g., in Fig. 4, each LFS bin is closely related to a specific part of the object. Another important observation is that points with small LFS values are usually located at the delicate parts of the object, such as the areas of sharp edges or corners and these parts are usually informative and critical for geometrical analysis. For example, given the 2D object in Fig. 5, we sample points along the boundary with three different sampling strategies, random sampling, high sampling probability at large LFS area and high sampling probability at small LFS area. If we try to reconstruct the object using sampled points, the last strategy will have the smallest reconstruction error, i.e., points located on delicate parts are more important and the small LFS thus indicates importance. Consequently, we use this LFS histogram as the prior sampling probability. In the following subsection, we introduce the unsupervised skeleton estimation for efficient skeleton-aware point cloud sampling. + +# 3.2. Unsupervised Skeleton Estimation + +With the medial axis transform or MAT definition, we then have the category-agnostic object skeleton for point cloud sampling. However, it is non-trivial to efficiently ap + +![](images/174a718894dae22f4029262d6c9fce265d989ef7fc4953c5d7e2dbcc6869b5b1.jpg) +Figure 5. The cyan line is the object's medial axis, and points (red) are sampled on the boundary. (a) Random sampling; (b) High sampling probability at large LFS area; and (c) High sampling probability at small LFS area. Top: LFS histogram and sampling weighting; Middle: 50 points; Bottom: 25 points. + +![](images/b8050b197b8c95b3a5c9e9328d9f9fdf4cc74f1ddd285a4b93e41097b7197c37.jpg) + +![](images/986d99fc86eea164fdca2e572818abb9c7a0742567729fc10e6817cacc54452d.jpg) + +ply the vanilla MAT algorithm due to its instability and algebraic complexity. Therefore, we introduce an unsupervised skeleton estimation method for point cloud sampling as follows. Given the input point cloud, it then aims to predict a set of $K$ skeletal spheres, where each skeletal sphere is defined by the center (i.e., the skeleton point) $c_{i} \in \mathbb{R}^{3}$ and the radius $r_{c_i} \in \mathbb{R}$ . That is, the skeletal spheres consist of two components, the coordinates of the sphere centers $\mathcal{C} \in \mathbb{R}^{K \times 3}$ and their radii $\mathcal{R} \in \mathbb{R}^{K}$ . Generally, the 3D object skeleton contains both 1D curve segments and 2D surface sheets, which can represent underlying structures of various shapes. The rationale for representing the skeleton with sparse skeletal spheres lies in that the final goal of skeleton estimation is to calculate the LFS of each point. Additionally, as mentioned before, we will use the averaged LFS value in each bin instead of each individual LFS value. Therefore, dense LFS is not always necessary, which avoid introducing extra computation and storage cost for predicting dense skeletal points. + +Following [30], we introduce our skeleton estimation algorithm as follows. Specifically, [30] uses PointNet++ [42] as the backbone, and the output of the last set abstraction layer is a set of points $\mathcal{P}_*$ and the corresponding contextual features $\mathcal{F}_*$ . A skeletal point can always be considered the local center of a set of surface points. Consequently, the skeletal points can be generated by the convex combination of $\mathcal{P}_*$ , i.e., $\mathcal{C} = \mathcal{W}_*^\top \mathcal{P}_*$ , where $\mathcal{W}_*$ is the predicted weight matrix. The closest distances from $\mathcal{P}_*$ to the skeletal points $\mathcal{C}$ can be calculated and denoted as $\mathcal{D}_*$ , and then the radii of all skeletal spheres are derived by $\mathcal{R} = \mathcal{W}_*^\top \mathcal{D}_*$ . Similar to [30], we use the same loss function, which consists of three parts: a sampling loss $\mathcal{L}_s$ , a point-to-sphere loss $\mathcal{L}_p$ , and a radius regularizer $\mathcal{L}_r$ , as follows: + +$$ +\mathcal {L} _ {s} = \sum_ {p \in \mathcal {P} _ {*}} \min _ {t \in \mathcal {T} _ {*}} \| p - t \| _ {2} + \sum_ {t \in \mathcal {T} _ {*}} \min _ {p \in \mathcal {P} _ {*}} \| t - p \| _ {2}, \tag {1} +$$ + +![](images/a3f2b87adb805f602de0fcda787771f01384ae6bb6518906e1f7bbd7df365ca5.jpg) +(a) KNN neighbors + +![](images/cec1e3e0b5798e6ba098394e0391f22620b792ebbda368269a9ba7b126fced27.jpg) +(b) Delaunay neighbors +Figure 6. KNN neighbors and Delaunay neighbors. KNN always find the nearest neighbors while the Delaunay neighbors are these connected by Delaunay edges. Cyan line: object skeleton; Black points: surface points; Blue points: centroids. Local neighboring points are connected by blue line segments. + +$$ +\begin{array}{l} \mathcal {L} _ {p} = \sum_ {p \in \mathcal {P} _ {*}} \left[ \min _ {c \in \mathcal {C}} \| p - c \| _ {2} - r _ {c _ {p} ^ {m i n}} \right] \\ + \sum_ {c \in \mathcal {C}} \left[ \min _ {p \in \mathcal {P} _ {*}} \| c - p \| _ {2} - r _ {c} \right], \\ \end{array} +$$ + +$$ +\mathcal {L} _ {r} = - \sum_ {c \in \mathcal {C}} r _ {c}, \tag {3} +$$ + +where $\mathcal{T}_{*}$ is a set of points sampled on the surface of each skeletal sphere and $c_{p}^{min}$ is the closest skeletal point to $p$ . + +Though the above-mentioned method can generate skeleton, each skeletal point is weighted by all points in $\mathcal{P}_{*}$ . However, the skeleton prediction is always based on the local region, which means surface points far away from the skeletal point have no contribution to skeleton estimation. What's more, the convex combination requirement in [30] also poses a challenge to neural network learning since the network has to predict a large weight matrix. Therefore, we further propose a local weighting scheme concentrating on neighboring points to predict the skeleton. As shown in Fig. 2, our skeleton estimation network adopts the DGCNN [57] as the backbone to obtain the point-wise contextual features. Then we select K points as the centroids to group local points $\mathcal{P}_{local} \in \mathbb{R}^{K \times L \times 3}$ and features $\mathcal{F}_{local} \in \mathbb{R}^{K \times L \times D}$ , where $L$ is the number of neighbors of each centroid and $D$ is the dimension of the features. Based on the grouped features, we will predict the weight matrix $\mathcal{W}_{local} \in \mathbb{R}^{K \times L \times 1}$ to derive the skeletal points, that is $\mathcal{C} = \mathcal{W}_{local}^{\top} \mathcal{P}_{local}$ . Here, matrix transposition and multiplication are conducted on the last two dimensions. + +A critical insight here is how to select neighboring points of each centroid. As presented in [12], the skeletal points can be estimated by Delaunay edge filtering. Inspired by this, we use the Delaunay neighbors instead of the KNN ones to predict the skeletal points. We illustrate the difference between KNN and Delaunay neighbors in Fig. 6. As shown, KNN always finds the nearest $L$ neighbors in Euclidean space. However, if we aim to predict the skeletal points that are always centrally located in the object, it is beneficial to consider the antipodal surface points. That is + +the intuition to use the Delaunay neighbors. To select the Delaunay neighbors, we first apply the Delaunay triangulation and pick out these local points connected by Delaunay edges. With the estimated skeleton, we can calculate the LFS of each point. As LFS is sensitive to point cloud noise, the best practice in our work is to use the "smoothed" LFS, i.e., the LFS histogram. Given the LSF histogram, we can then have the midpoint of each bin $\bar{h}_1,\bar{h}_2,\dots,\bar{h}_n$ , where $n$ is the number of bins. If the LFS of one point is in $i$ -th bin, the initial sampling weight for the point is $e^{-\bar{h}_i} / \sum_i e^{-\bar{h}_i}$ . + +# 3.3. Skeleton-Aware Probabilistic Sampling + +As mentioned before, we aim to find a subset of points that not only take care of the downstream tasks but also encode the geometrical structure information of 3D objects. To derive the sampling formulation, we treat the point sampling operation as drawing samples from the probability distribution with replacement. Specifically, given the input point cloud $\mathcal{P} = \{p_1,p_2,\dots ,p_N\}$ , we already have the prior per-point sampling weight from the first stage, and this initial weight encapsulates the structural information that should be considered. After the point cloud goes through the neural network, we get the point-wise features. Therefore, the posterior sampling probability over point-wise features can be formulated as: + +$$ +\mathcal {P} _ {\theta} \left(p _ {1}, \dots , p _ {N}\right) = \prod_ {i = 1} ^ {N} \sum_ {j} \mathcal {P} _ {\theta} \left(p _ {i} \mid b _ {i j}\right) \mathcal {P} _ {L F S} \left(b _ {i j}\right), \tag {4} +$$ + +where $b_{ij}$ denotes the event that $p_i$ locates in the $j$ -th bin of the LFS histogram and the corresponding probability is $\mathcal{P}_{LFS}(b_{ij})$ . The subscript $\theta$ indicates trainable parameters of the neural network. During training, we maximize the posterior over all training point clouds with respect to the individual point cloud feature and the network parameters. + +Consequently, with the input point cloud $\mathcal{P}$ , it is straightforward to consider points as different categories, and the task that samples a representative subset $\mathcal{P}_{sub} \subset \mathcal{P}$ then becomes to learn to draw samples from a discrete distribution, e.g. the categorical distribution. However, the sampling operation is usually non-differentiable. Though [14] and [27] are trainable, the sampled point is less interpretable from the probabilistic perspective, especially when sampling multiple points. + +Categorical Reparameterization. Fortunately, Jang et al. [22] introduce an elegant reparameterization trick called Gumbel-softmax to enable discrete stochastic variables to back-propagate in neural network computation graphs. Therefore, we utilize the Gumbel-softmax trick to facilitate our sampling process. For a categorical distribution $Cat(c_{1},\dots,c_{k})$ where $k$ denotes the number of categories and $c_{i}$ means the probability of category $i$ , the Gumbel-softmax is designed as a discrete reparameterization trick + +to estimate smooth gradient with a continuous relaxation for the categorical variable. Given the Gumbel noise $\pmb{g} = (g_1, \dots, g_k)$ where $g_i \sim Gumbel(0, 1)$ is independent identically distributed, a soft categorical sample can be drawn by + +$$ +\boldsymbol {y} = \operatorname {s o f t m a x} \left(\left(\log (\boldsymbol {c}) + \boldsymbol {g}\right) / \tau\right), \tag {5} +$$ + +where $\pmb{c} = (c_{1},\dots,c_{k})$ and $\tau >0$ is the annealing temperature. The equation above is referred as Gumbel-softmax, and as $\tau \rightarrow 0$ , $\pmb{y}$ will degenerate into the Gumbel-max form gradually, + +$$ +\boldsymbol {y} = \operatorname {o n e h o t} (\operatorname {a r g m a x} ((\log (\boldsymbol {c}) + \boldsymbol {g}))), \tag {6} +$$ + +which is an unbiased sample from $Cat(c_{1},\ldots ,c_{k})$ . In this way, we are able to draw differentiable samples from the distribution $Cat(c_{1},\ldots ,c_{k})$ in the training phase. In practice, $\tau$ starts at a high value (e.g., 1.0) and anneals to a small value (e.g., 0.1). In the testing phase, discrete samples can be drawn with the Gumbel-max trick. + +Therefore, we use a hard and discrete selection by exploring the trainable categorical reparameterization Gumbel-softmax as follows: + +$$ +\mathcal {P} _ {s u b} = \left[ G s _ {\tau} \left(L p \left(\mathcal {W} _ {L F S} \odot \mathcal {W} _ {\theta}\right) \right] ^ {\top} \mathcal {P}, \right. \tag {7} +$$ + +where $\mathcal{P} \in \mathbb{R}^{N \times 3}$ is the input point cloud, $\mathcal{P}_{sub} \in \mathbb{R}^{M \times 3}$ is the sampled point cloud, and $G s_{\tau}(\cdot)$ operation is the Gumbel-softmax trick with the annealing temperature $\tau$ . Additionally, $\mathcal{W}_{LFS} \in \mathbb{R}^{N \times 1}$ is calculated from the first stage and $\mathcal{W}_{\theta} \in \mathbb{R}^{N \times D_{sp}}$ is feature matrix from the sampling network, where $D_{sp}$ indicates the dimension of the features. $Lp(\cdot): \mathbb{R}^{N \times D_{sp}} \to \mathbb{R}^{N \times M}$ is the linear mapping layer. $\odot$ indicates the element-wise Hadamard product operation. In practice, we start with a large $\tau$ such as $\tau = 1.0$ and gradually decrease it. In the training phase, it provides smooth gradients using the discrete reparameterization trick. With annealing, it degenerates to a hard selection in the testing phase. + +# 4. Experiments + +In this section, we evaluate the proposed skeleton-aware sampling method by applying it to three downstream tasks: point cloud classification, retrieval, and reconstruction. All experiments are conducted on the widely used ModelNet40 [62] dataset, and we use the official split of 9,843 training and 2,468 testing samples. + +# 4.1. Implementation Details + +We implement the proposed method using PyTorch, and we will give the detailed network architecture in our supplementary materials. Our network training consists of two stages. We train the skeleton estimation network in the first stage to get the point cloud skeleton. The number of predicted skeletal spheres is 128, and the number of bins for + +
Sampling RatioClassification Acc(%)
FPS [42]S-NET [14]SN [27]MS [10]Ours
870.477.583.788.089.1
1646.370.482.285.588.8
3226.360.680.181.587.4
6413.536.154.161.682.9
+ +Table 1. Point cloud classification results on ModelNet40. The task network is trained on complete data with 1024 points. + +the LFS histogram is 6. In the second stage, we train the sampling network using task losses. In both stages, we use the Adam optimizer with a learning rate of 0.001. + +# 4.2. Point Cloud Classification + +To evaluate the proposed method for point cloud classification, we employ the full version of PointNet [41] as the task network. The classification accuracy of PointNet is trained on the complete data (1024 points per point cloud without normals) and tested on sampled points of different sizes. The evaluation metric is overall accuracy (OA), and for a fair comparison, the upper bound accuracy trained on 1024 points is $89.5\%$ (the same as MetaSampler [10]). We compare with four methods, FPS [42], S-NET [14], SampleNet [27] and MetaSampler [10]. We report the classification results of four different sampling ratios in Table 1, where the proposed method outperforms recent state-of-the-art methods. Specifically, the classification accuracy achieved by the proposed approach at the sampling ratio of 8 is very close to the upper bound accuracy $(89.1\%$ vs. $89.5\%)$ , which shows the effectiveness of our skeleton-aware strategy. We also notice that the performance gap between the proposed method and others is becoming large when increasing the sampling rate (e.g., at the sampling ratio of 64 with 16 points left). This further demonstrates the superiority of the proposed method in preserving task-significant features. + +Ablation Study on Skeleton-Aware Prior. We show how the prior sampling weight operates by comparing with two other commonly used non-learned sampling methods, random sampling (RS) and farthest point sampling (FPS). In Fig. 7, for visualization purposes, we use 10,000 points as input, and the number of sampled points is 1,024. Generally, RS randomly picks 1024 points from the original data, and FPS selects a subset of points far from each other. Since both two methods do not consider any geometrical information, these two sampling methods do not change the LFS distribution. Differently, we propose the skeleton-aware sampling in this work, which is able to use the LFS histogram as the initial sampling weight and also learn to sample for downstream tasks. That is, we will pay more attention to those points with small LFS values. As shown + +![](images/3c84a7512432bdd2294fbc3235dd33f701085b3d2be6ca0d702cacc96508ab88.jpg) +Figure 7. Visualization of different sampling strategies. RS and FPS do not encode geometrical information to change the LFS distribution after sampling, while the proposed considers the LFS histogram to obtain informative skeleton-aware sampling. + +in Fig. 7, the RS and FPS keep nearly the same LFS distribution with the original point cloud after sampling, but our method encodes the geometrical information and gives out the different LFS distribution. The final results can also prove this by our sampled points concentrated on small LFS areas. In addition, we report the classification results without the LFS weight in Table 2. Here, "GT" means we use the ground truth skeletons computed by DPC [60] instead of the estimated ones from the first stage. As shown, using the skeleton-aware strategy as the initial sampling weight can always benefit the following learning task. Moreover, our method achieves comparable results with that using ground truth skeletons. + +
Sampling RatioClassification Acc(%)
GTOurs(w/o)Ours
889.188.289.1
1688.887.488.8
3287.585.987.4
6482.880.382.9
+ +Ablation Study on LFS Histogram. The number of bins reveals the LFS distribution at different levels. Using wider bins reduces the LFS noise, while using narrower bins gives better precision to the LFS density estimation. Thus, varying the bin number within the LFS histogram can be + +Table 2. Point cloud classification results without the initial LFS weight. GT indicates using the ground truth skeletons generated by DPC [60]. + +
Sampling RatioBins
1361218
888.288.489.189.189.0
1687.488.088.888.588.8
3285.986.687.487.287.4
6480.381.282.982.882.7
+ +beneficial. We report the classification results with different bins in Table 3. The aggressive setting is to use only one bin, and this case is equivalent to no initial LSF weight applied. Generally, we find that six bins are suitable for most cases. + +Ablation Study on Skeletal Spheres. As mentioned before, the object's skeleton is represented with a set of skeletal spheres. Generally, increasing the number of predicted skeletal spheres will lead to detailed structures. Thus, it is beneficial to disclose how this hyper-parameter influences the following tasks. We show the classification results in Table 4 with different numbers of skeletal spheres predicted. As shown, our method is not sensitive to the parameter and achieves steady performance. + +Table 3. Point cloud classification results with different bins. Generally, we find that six bins already work well in most cases. + +
Sampling RatioSkeletal Spheres
3264128256
887.288.489.189.1
1685.887.188.888.5
3284.085.187.487.2
6479.380.582.982.8
+ +Table 4. Point cloud classification results when using different numbers of skeletal spheres. + +Ablation Study on Annealing Strategy. As we apply the Gumbel-softmax operation in our method, we gradually anneal the temperature $\tau$ to facilitate our network training in the second stage. Thus, it is beneficial to evaluate the classification performance when adopting different annealing strategies. During training, we let $\tau = 1.0$ to allow gradients past the samples and then gradually anneal the temperature until $\tau = 0.5$ (but not completely to 0, as the gradients would blow up). In the test phase, as $\tau \to 0.0$ , the softmax becomes an argmax and the Gumbel-softmax distribution becomes the categorical distribution. We report the classification results in Table 5 with four different annealing strategies, including constant, step, linear and exponential. Here, the "constant" means $\tau$ keeps being 1.0 without annealing during training. + +
Temperature (τ)Sampling Ratio
8163264
Constant87.786.485.181.1
Step88.887.286.682.1
Linear rectified89.087.987.682.3
Exponential89.188.887.482.9
+ +Model Complexity. In Table 6, we report the model complexity of the proposed method. Specifically, the FLOPs increase with a large number of predicted skeletal spheres. The number of parameters for the probabilistic sampling network is 1.24M, and the number of FLOPs is 2.93G at the sampling ratio of 8. + +Table 5. Point cloud classification results for using different annealing strategies. Here, the "Constant" row means we do not anneal the $\tau$ and keep $\tau = 1.0$ during training. + +
Model ComplexityParams (M)FLOPs (G)
Skeletal Spheres321.543.43
641.543.86
1281.544.71
2561.546.41
Sampling Ratio81.242.93
161.232.90
321.222.88
641.212.86
+ +# 4.3. Point Cloud Retrieval + +In this subsection, we perform point cloud retrieval experiments to further demonstrate the effectiveness of the proposed method for downstream tasks. We follow the same evaluation setting in [10, 14, 27] to report the performance on the point cloud retrieval. Specifically, we take our method trained with PointNet [41] for classification as the task network without re-training it. We sample points of different sizes fed into PointNet and use its penultimate layer as the shape descriptor. Retrieval is done based on the L2 distance on the shape descriptor, and the evaluation metric is the mean Average Precision (mAP). In Table. 7, we summarize the performances of different methods and observe that our method consistently outperforms others by a large margin at different sampling ratios. + +# 4.4. Point Cloud Reconstruction + +In this subsection, we perform point cloud reconstruction experiments to further demonstrate the effectiveness of the + +Table 6. The model complexity of the proposed skeleton estimation network. + +
Sampling RatioRetrieval Performance (mAP)
FPS [42]S-NET [14]SN [27]Ours
858.360.468.872.2
1649.459.065.270.9
3237.759.062.567.1
6427.454.559.562.6
+ +proposed method for downstream tasks. We use an autoencoder as the task network on the ModelNet40 [62] dataset. Following [10], we employ the Point Completion Network (PCN) [69] to minimize the Chamfer distance (CD) [16] between the input and output points. As demonstrated in Table 8, our method outperforms others and the improvement is consistent across all sampling ratios, further exhibiting the effectiveness of our method. + +Table 7. Point cloud retrieval results on the ModelNet40 dataset. Specifically, the proposed method achieves superior performance across different sampling ratios. + +
Sampling RatioReconstruction Performance (CD)
FPS [42]SN [27]MS [10]Ours
83.783.293.052.97
164.033.323.153.01
324.253.613.373.24
644.784.434.313.78
+ +Table 8. Point cloud reconstruction results on the ModelNet40 dataset. Specifically, the original size of data is 1024 points. + +# 5. Conclusion + +In this paper, we propose a skeleton-aware learning-to-sample method for point cloud sampling. The skeletal representation of the point cloud is learned in an unsupervised manner to avoid label-intensive annotations. Given the learned skeleton, the skeleton-aware point cloud sampling process is conducted in a probabilistic way according to the LFS distribution. The proposed skeleton-aware sampling method is end-to-end trainable. To evaluate the proposed method, we perform experiments on several downstream point cloud analysis tasks such as classification, retrieval, and reconstruction, and the proposed method consistently outperforms traditional and recent learning-to-sample methods by a large margin. + +# Acknowledgement + +Mr Cheng Wen and Dr Baosheng Yu were supported by Australian Research Council Projects in part by IH180100002 and FL170100117. + +# References + +[1] Panos Achlioptas, Olga Diamanti, Ioannis Mitliagkas, and Leonidas Guibas. Learning representations and generative models for 3d point clouds. In International Conference on Machine Learning (ICML), pages 40-49. PMLR, 2018. 2 +[2] Nina Amenta and Marshall Bern. Surface reconstruction by voronoi filtering. In Proceedings of the 14th Annual Symposium on Computational Geometry, pages 39-48, 1998. 2, 4 +[3] Xiang Bai, Xinggang Wang, Longin Jan Latecki, Wenyu Liu, and Zhuowen Tu. Active skeleton for non-rigid object detection. 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(a) Point cloud; (b) Object skeleton; (c) Random sampling; (d) Skeleton-aware sampling. Compared with random sampling, skeleton-aware sampling tends to preserve the object geometry and topology information." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 363, + 546, + 448 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 363, + 546, + 448 + ], + "spans": [ + { + "bbox": [ + 304, + 363, + 546, + 448 + ], + "type": "text", + "content": "can accurately capture the geometry and topology details of complex objects, it remains challenging for those devices with limited computation and storage resources. Therefore, point cloud sampling, aiming to find a small set of points to represent the object shape and topology effectively, is usually indispensable for efficient large-scale point cloud analysis [24, 29, 32, 33, 41, 42, 57, 61, 71]." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 449, + 546, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 449, + 546, + 652 + ], + "spans": [ + { + "bbox": [ + 304, + 449, + 546, + 652 + ], + "type": "text", + "content": "Traditional point cloud sampling methods such as random sampling (RS) and farthest point sampling (FPS) [15, 42] usually select a subset of points directly using the raw data information [7, 42, 43, 47, 68]. Specifically, RS is very efficient but may miss sparse regions, while FPS has better coverage on the entire point set but suffers from the latency bottleneck in parallel computation. To improve the performances on downstream tasks, learn-to-sample methods have been recently proposed to jointly optimize the sampling algorithm and each specific downstream task [10, 14, 20,27,56]. Though considerable progress has been achieved in downstream tasks such as point cloud classification and reconstruction, one critical issue remains poorly investigated: as objects usually have complex topology structures and irregular surface morphology, it is challenging to preserve the object's geometrical information during the point cloud sampling process." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "text", + "content": "Skeleton is an efficient representation to capture the underlying object shape structures, which has been widely used as the structural abstraction in many visual understanding tasks [31, 37, 53]. Inspired by this, we build our point cloud sampling strategy on top of the object skeleton to" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 124, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 124, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 124, + 712 + ], + "type": "text", + "content": "*Equal contribution" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17671" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 287 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 287 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 287 + ], + "type": "text", + "content": "preserve different objects' intrinsic geometrical and topological natures. Here we illustrate a comparison between random sampling and skeleton-aware sampling in Fig. 1. However, the skeleton extraction is usually non-trivial due to the following reasons [30, 52]: 1) given the diversity of object topological structures, it is difficult to have a consistent category-agnostic skeleton definition at the semantic level, where existing datasets usually consider only single or a few known object categories, such as human skeleton; 2) topological methods are usually category-agnostic by emphasizing geometrical and topological properties of the shape, such as its connectivity, topology, length, direction, and width. Nevertheless, they usually require a substantial amount of time for geometrical processing and are also notoriously sensitive to surface noise. Therefore, we resort to the medial axis transform (MAT) definition of object skeleton and deep neural networks to learn effective skeletal representations in an unsupervised manner." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 288, + 289, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 288, + 289, + 504 + ], + "spans": [ + { + "bbox": [ + 46, + 288, + 289, + 504 + ], + "type": "text", + "content": "With the learned object skeleton, we then formulate the skeleton-aware point cloud sampling pipeline from a probabilistic perspective. Specifically, we first calculate the local feature size (LFS) [2] for each point to measure the object's size near a particular point. We then explore the LFS distribution as the prior sampling probability on each point and use the LFS histogram in practice since per-point LFS is usually sensitive to point cloud noise. By learning object skeletons with deep neural networks, we have the skeleton-aware prior probability for sampling each point. To adapt skeleton-aware sampling for downstream tasks, we jointly optimize the posterior sampling probability on each point in an end-to-end manner. Notably, by exploring the categorical reparameterization with Gumbel-softmax [22], the categorical sampling based on LFS histogram is differentiable. Therefore, both sampling and task networks are end-to-end learnable for task-specific point cloud sampling. In this paper, our main contributions can be summarized as follows:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 512, + 287, + 637 + ], + "type": "list", + "angle": 0, + "index": 5, + "blocks": [ + { + "bbox": [ + 55, + 512, + 287, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 512, + 287, + 548 + ], + "spans": [ + { + "bbox": [ + 55, + 512, + 287, + 548 + ], + "type": "text", + "content": "1. We propose a new skeleton-aware point cloud sampling method to preserve the object geometry and topology information during sampling." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 556, + 287, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 556, + 287, + 592 + ], + "spans": [ + { + "bbox": [ + 55, + 556, + 287, + 592 + ], + "type": "text", + "content": "2. We introduce the category-agnostic skeleton learning in an unsupervised manner to provide the prior knowledge for skeleton-aware point cloud sampling." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 601, + 287, + 637 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 601, + 287, + 637 + ], + "spans": [ + { + "bbox": [ + 55, + 601, + 287, + 637 + ], + "type": "text", + "content": "3. We conduct extensive experiments on three important downstream tasks, point cloud classification, retrieval, and reconstruction, to evaluate the proposed approach." + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 657, + 134, + 669 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 657, + 134, + 669 + ], + "spans": [ + { + "bbox": [ + 47, + 657, + 134, + 669 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "type": "text", + "content": "Deep Learning on Point Clouds. Deep neural networks have been widely used in point cloud analysis, including point cloud classification/segmentation [29, 33, 41, 42, 57," + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 72, + 545, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 289 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 289 + ], + "type": "text", + "content": "[63], object detection/tracking [9, 48, 49, 72], point cloud autoencoders [1, 39, 65, 67], point cloud generation [1, 50, 58, 64], completion [5, 8, 21, 69] and registration [17, 38, 45]. A point cloud is usually not placed on a regular grid, and each point is independent of others. Meanwhile, the distances to neighboring points are not always fixed. Therefore, it is non-trivial to apply deep learning techniques to 3D point clouds. Specifically, PointNet [41] is the pioneering work in applying deep neural networks to point sets, which embeds the input into high dimensional space pointwisely and then uses a symmetric function to aggregate all point features in a permutation-invariant manner as the global features. The MLP block used in PointNet has become a fundamental component in many point cloud networks to learn pointwise representations. Recently, convolutional architectures have been further explored to aggregate local neighborhood hierarchical information and achieved superior performance on point cloud analysis [29, 54, 61]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 291, + 545, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 291, + 545, + 532 + ], + "spans": [ + { + "bbox": [ + 304, + 291, + 545, + 532 + ], + "type": "text", + "content": "Skeleton-Guided Learning. Object skeleton jointly describes an object's geometry, topology, and symmetry properties in a compact and intuitive way [52], which has benefited various tasks such as shape recognition [3], reconstruction [23, 53], segmentation [31] and point cloud completion [37, 70]. For example, [53] proposes a skeleton-aware deep learning approach to generate the mesh reconstruction of object surface a from single RGB image. [37] presents a learning method for point cloud completion via the shape skeleton. Existing methods directly use the ground truth skeletons as the supervision, which can be calculated by off-line algorithms like DPC [60], Q-MAT [28] or Coverage Axis [13]. However, as mentioned before, the skeleton computation is an ill-posed problem, meaning the computation is not steady and unique. Therefore, deep learning-based skeletal representations have been recently proposed [30, 44]. For example, [30] proposes to learn skeletal meshes from point clouds. Similarly, we also learn the skeleton in an unsupervised manner to facilitate our skeleton-aware sampling strategy." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": "Point Cloud Sampling. Point cloud sampling or simplification is essential, since it is always non-trivial to process high-resolution dense point clouds. Therefore, various methods have been explored to simplify dense point clouds [4, 7, 25, 34, 40, 43, 47]. For example, [47] first uses the K-means clustering to select representative points and the remove redundant points. [4] combines clustering and coarse-to-fine approaches for fast point cloud simplification. [34] presents an intrinsic point cloud simplification algorithm with density guarantee, which supports efficient uniform and feature-sensitive resampling. The above-mentioned point cloud simplification algorithms aim to find a subset of points in terms of geometry or topology, but fails to consider the downstream tasks during sampling. Several recent methods have proposed to learn to sample from" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "17672" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 55, + 77, + 544, + 300 + ], + "blocks": [ + { + "bbox": [ + 55, + 77, + 544, + 300 + ], + "lines": [ + { + "bbox": [ + 55, + 77, + 544, + 300 + ], + "spans": [ + { + "bbox": [ + 55, + 77, + 544, + 300 + ], + "type": "image", + "image_path": "c8bc9dcebea3bc9064c70d0d292c2e093c4d47682ee98635132e0f3cea91f91e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 312, + 548, + 348 + ], + "lines": [ + { + "bbox": [ + 46, + 312, + 548, + 348 + ], + "spans": [ + { + "bbox": [ + 46, + 312, + 548, + 348 + ], + "type": "text", + "content": "Figure 2. The main skeleton-aware point cloud sampling framework. Specifically, the whole pipeline consists of two main stages: 1) we first learn object skeleton in an unsupervised manner; 2) with the estimated skeleton, we evaluate the LFS distribution as the initial sampling weight to formulate the sampling process from a probabilistic perspective." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 367, + 289, + 499 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 367, + 289, + 499 + ], + "spans": [ + { + "bbox": [ + 46, + 367, + 289, + 499 + ], + "type": "text", + "content": "dense points [10, 14, 20, 27, 36, 56, 66]. Specifically, [14] and [27] have recently introduced learning-based task-oriented sampling strategies for the downstream tasks such as point cloud classification, retrieval, and reconstruction. [10] further proposes a learnable sampling and joint-training strategy to avoid overfitting on a specific task. [36] introduces a critical point layer to pass on points with the most functional features to the next layer and adaptively sample points. Differently, we not only consider the downstream tasks but also try to preserve the underlying geometrical and topological information in point clouds." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 510, + 104, + 522 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 510, + 104, + 522 + ], + "spans": [ + { + "bbox": [ + 47, + 510, + 104, + 522 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 531, + 287, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 531, + 287, + 568 + ], + "spans": [ + { + "bbox": [ + 46, + 531, + 287, + 568 + ], + "type": "text", + "content": "In this section, we first provide an overview of skeleton-aware point cloud sampling. We then describe skeleton estimation and skeleton-aware probabilistic sampling." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 575, + 115, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 575, + 115, + 586 + ], + "spans": [ + { + "bbox": [ + 47, + 575, + 115, + 586 + ], + "type": "text", + "content": "3.1. Overview" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": "The main skeleton-aware point cloud sampling framework is shown in Fig. 2. Given a point cloud " + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": ", point cloud sampling aims to find a subset of points " + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{P}_{sub} \\subset \\mathcal{P}" + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": ", where a good sampling strategy is expected that: 1) the selection is consistent regardless of any permutation of input points and outliers; 2) the selected points preserve the geometrical and topological information of the original point cloud; 3) the sampling process can be integrated and optimized jointly with downstream tasks to avoid significant performance degradation. Recently, learning-to-sample methods" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 366, + 365, + 487, + 486 + ], + "blocks": [ + { + "bbox": [ + 366, + 365, + 487, + 486 + ], + "lines": [ + { + "bbox": [ + 366, + 365, + 487, + 486 + ], + "spans": [ + { + "bbox": [ + 366, + 365, + 487, + 486 + ], + "type": "image", + "image_path": "2325981ac2263ee9143168f69f764934fa9c8fd6cc638c2d18edfb59f960913c.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 495, + 547, + 551 + ], + "lines": [ + { + "bbox": [ + 304, + 495, + 547, + 551 + ], + "spans": [ + { + "bbox": [ + 304, + 495, + 547, + 551 + ], + "type": "text", + "content": "Figure 3. An illustration of the object with its medial axis in 2D space. Specifically, the medial axis is defined as the set of points with more than one closest point on the boundary surface, i.e., the centers of balls maximal inscribed in the object. " + }, + { + "bbox": [ + 304, + 495, + 547, + 551 + ], + "type": "inline_equation", + "content": "\\mathrm{LFS}(p)" + }, + { + "bbox": [ + 304, + 495, + 547, + 551 + ], + "type": "text", + "content": " indicates the Euclidean distance from the point " + }, + { + "bbox": [ + 304, + 495, + 547, + 551 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 304, + 495, + 547, + 551 + ], + "type": "text", + "content": " to the medial axis." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 568, + 547, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 568, + 547, + 640 + ], + "spans": [ + { + "bbox": [ + 304, + 568, + 547, + 640 + ], + "type": "text", + "content": "have achieved remarkable success by selecting task-specific points with end-to-end learning [10, 14, 20, 27, 36]. However, these methods neglect the complex object geometrical and topological structures during learning to sample. Therefore, we introduce object skeleton to explore the structure and topology information for point cloud sampling." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 642, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 548, + 715 + ], + "type": "text", + "content": "Object skeleton can be defined as a thin-centered structure that jointly describes the geometry and topology. Following the popular medial axis transform (MAT) definition [52], the object skeleton is characterized by a set of ball centers with the corresponding radii, where each ball is maximal inscribed in the object as shown in Fig. 3." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "17673" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 69, + 108, + 159 + ], + "blocks": [ + { + "bbox": [ + 49, + 69, + 108, + 159 + ], + "lines": [ + { + "bbox": [ + 49, + 69, + 108, + 159 + ], + "spans": [ + { + "bbox": [ + 49, + 69, + 108, + 159 + ], + "type": "image", + "image_path": "8d61c3219bd6ed363b1ae7875a747490a1733a9cb110ddbe9f151a7b755f6976.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 58, + 160, + 99, + 170 + ], + "lines": [ + { + "bbox": [ + 58, + 160, + 99, + 170 + ], + "spans": [ + { + "bbox": [ + 58, + 160, + 99, + 170 + ], + "type": "text", + "content": "(a) Airplane" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 108, + 70, + 166, + 171 + ], + "blocks": [ + { + "bbox": [ + 108, + 70, + 166, + 171 + ], + "lines": [ + { + "bbox": [ + 108, + 70, + 166, + 171 + ], + "spans": [ + { + "bbox": [ + 108, + 70, + 166, + 171 + ], + "type": "image", + "image_path": "e6cdec659bc7c5003df7c20f391787a3570350231090c3a96ab950c70bc38760.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 179, + 287, + 224 + ], + "lines": [ + { + "bbox": [ + 46, + 179, + 287, + 224 + ], + "spans": [ + { + "bbox": [ + 46, + 179, + 287, + 224 + ], + "type": "text", + "content": "Figure 4. An illustration of the LFS distribution of different objects: airplane, lamp, car, and chair. Specifically, the object skeletons are computed using DPC [60] and the LFS values are normalized for a better comparison across different object categories." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 168, + 70, + 227, + 171 + ], + "blocks": [ + { + "bbox": [ + 168, + 70, + 227, + 171 + ], + "lines": [ + { + "bbox": [ + 168, + 70, + 227, + 171 + ], + "spans": [ + { + "bbox": [ + 168, + 70, + 227, + 171 + ], + "type": "image", + "image_path": "d1cd73864960f54ec9a71c236db737b9e2d08cc697df26b052d4895fc40283ee.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 228, + 70, + 286, + 171 + ], + "blocks": [ + { + "bbox": [ + 228, + 70, + 286, + 171 + ], + "lines": [ + { + "bbox": [ + 228, + 70, + 286, + 171 + ], + "spans": [ + { + "bbox": [ + 228, + 70, + 286, + 171 + ], + "type": "image", + "image_path": "eaa10c3587741f3b23fec1adcf480c285d17d348bfcbd4ca6708d8387bca76a6.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 244, + 287, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 244, + 287, + 399 + ], + "spans": [ + { + "bbox": [ + 46, + 244, + 287, + 399 + ], + "type": "text", + "content": "Specifically, the skeleton is a compact shape representation with geometrical clues such as thickness, angles and branches aggregating. The structural and geometrical information significantly benefits complex 3D object analysis [31, 46]. To equip point cloud sampling with the skeleton-aware structural prior, we introduce the local feature size or LFS [2] to measure the size of the object near a particular point, e.g., the dashed line in Fig. 3. Notably, given a smooth manifold " + }, + { + "bbox": [ + 46, + 244, + 287, + 399 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 46, + 244, + 287, + 399 + ], + "type": "text", + "content": " and the point " + }, + { + "bbox": [ + 46, + 244, + 287, + 399 + ], + "type": "inline_equation", + "content": "p\\in \\mathcal{M}" + }, + { + "bbox": [ + 46, + 244, + 287, + 399 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 244, + 287, + 399 + ], + "type": "inline_equation", + "content": "\\mathrm{LFS}(p)" + }, + { + "bbox": [ + 46, + 244, + 287, + 399 + ], + "type": "text", + "content": " is defined as the Euclidean distance between " + }, + { + "bbox": [ + 46, + 244, + 287, + 399 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 46, + 244, + 287, + 399 + ], + "type": "text", + "content": " and the medial axis of " + }, + { + "bbox": [ + 46, + 244, + 287, + 399 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 46, + 244, + 287, + 399 + ], + "type": "text", + "content": " via the nearest point. Intuitively, LFS captures the surface property and how complicated " + }, + { + "bbox": [ + 46, + 244, + 287, + 399 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 46, + 244, + 287, + 399 + ], + "type": "text", + "content": " is locally distributed [12]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 400, + 288, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 400, + 288, + 653 + ], + "spans": [ + { + "bbox": [ + 46, + 400, + 288, + 653 + ], + "type": "text", + "content": "With the object skeleton, we then calculate the LFS histogram to form a robust skeleton-aware prior probability for sampling. Notably, LFS tends to distinguish the object parts with different geometrical structures, e.g., in Fig. 4, each LFS bin is closely related to a specific part of the object. Another important observation is that points with small LFS values are usually located at the delicate parts of the object, such as the areas of sharp edges or corners and these parts are usually informative and critical for geometrical analysis. For example, given the 2D object in Fig. 5, we sample points along the boundary with three different sampling strategies, random sampling, high sampling probability at large LFS area and high sampling probability at small LFS area. If we try to reconstruct the object using sampled points, the last strategy will have the smallest reconstruction error, i.e., points located on delicate parts are more important and the small LFS thus indicates importance. Consequently, we use this LFS histogram as the prior sampling probability. In the following subsection, we introduce the unsupervised skeleton estimation for efficient skeleton-aware point cloud sampling." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 659, + 231, + 672 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 659, + 231, + 672 + ], + "spans": [ + { + "bbox": [ + 47, + 659, + 231, + 672 + ], + "type": "text", + "content": "3.2. Unsupervised Skeleton Estimation" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "type": "text", + "content": "With the medial axis transform or MAT definition, we then have the category-agnostic object skeleton for point cloud sampling. However, it is non-trivial to efficiently ap" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 312, + 70, + 385, + 197 + ], + "blocks": [ + { + "bbox": [ + 312, + 70, + 385, + 197 + ], + "lines": [ + { + "bbox": [ + 312, + 70, + 385, + 197 + ], + "spans": [ + { + "bbox": [ + 312, + 70, + 385, + 197 + ], + "type": "image", + "image_path": "174a718894dae22f4029262d6c9fce265d989ef7fc4953c5d7e2dbcc6869b5b1.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 209, + 545, + 264 + ], + "lines": [ + { + "bbox": [ + 305, + 209, + 545, + 264 + ], + "spans": [ + { + "bbox": [ + 305, + 209, + 545, + 264 + ], + "type": "text", + "content": "Figure 5. The cyan line is the object's medial axis, and points (red) are sampled on the boundary. (a) Random sampling; (b) High sampling probability at large LFS area; and (c) High sampling probability at small LFS area. Top: LFS histogram and sampling weighting; Middle: 50 points; Bottom: 25 points." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 389, + 70, + 463, + 200 + ], + "blocks": [ + { + "bbox": [ + 389, + 70, + 463, + 200 + ], + "lines": [ + { + "bbox": [ + 389, + 70, + 463, + 200 + ], + "spans": [ + { + "bbox": [ + 389, + 70, + 463, + 200 + ], + "type": "image", + "image_path": "b8050b197b8c95b3a5c9e9328d9f9fdf4cc74f1ddd285a4b93e41097b7197c37.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 467, + 70, + 541, + 199 + ], + "blocks": [ + { + "bbox": [ + 467, + 70, + 541, + 199 + ], + "lines": [ + { + "bbox": [ + 467, + 70, + 541, + 199 + ], + "spans": [ + { + "bbox": [ + 467, + 70, + 541, + 199 + ], + "type": "image", + "image_path": "986d99fc86eea164fdca2e572818abb9c7a0742567729fc10e6817cacc54452d.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 285, + 546, + 513 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 285, + 546, + 513 + ], + "spans": [ + { + "bbox": [ + 304, + 285, + 546, + 513 + ], + "type": "text", + "content": "ply the vanilla MAT algorithm due to its instability and algebraic complexity. Therefore, we introduce an unsupervised skeleton estimation method for point cloud sampling as follows. Given the input point cloud, it then aims to predict a set of " + }, + { + "bbox": [ + 304, + 285, + 546, + 513 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 285, + 546, + 513 + ], + "type": "text", + "content": " skeletal spheres, where each skeletal sphere is defined by the center (i.e., the skeleton point) " + }, + { + "bbox": [ + 304, + 285, + 546, + 513 + ], + "type": "inline_equation", + "content": "c_{i} \\in \\mathbb{R}^{3}" + }, + { + "bbox": [ + 304, + 285, + 546, + 513 + ], + "type": "text", + "content": " and the radius " + }, + { + "bbox": [ + 304, + 285, + 546, + 513 + ], + "type": "inline_equation", + "content": "r_{c_i} \\in \\mathbb{R}" + }, + { + "bbox": [ + 304, + 285, + 546, + 513 + ], + "type": "text", + "content": ". That is, the skeletal spheres consist of two components, the coordinates of the sphere centers " + }, + { + "bbox": [ + 304, + 285, + 546, + 513 + ], + "type": "inline_equation", + "content": "\\mathcal{C} \\in \\mathbb{R}^{K \\times 3}" + }, + { + "bbox": [ + 304, + 285, + 546, + 513 + ], + "type": "text", + "content": " and their radii " + }, + { + "bbox": [ + 304, + 285, + 546, + 513 + ], + "type": "inline_equation", + "content": "\\mathcal{R} \\in \\mathbb{R}^{K}" + }, + { + "bbox": [ + 304, + 285, + 546, + 513 + ], + "type": "text", + "content": ". Generally, the 3D object skeleton contains both 1D curve segments and 2D surface sheets, which can represent underlying structures of various shapes. The rationale for representing the skeleton with sparse skeletal spheres lies in that the final goal of skeleton estimation is to calculate the LFS of each point. Additionally, as mentioned before, we will use the averaged LFS value in each bin instead of each individual LFS value. Therefore, dense LFS is not always necessary, which avoid introducing extra computation and storage cost for predicting dense skeletal points." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 513, + 547, + 681 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 513, + 547, + 681 + ], + "spans": [ + { + "bbox": [ + 304, + 513, + 547, + 681 + ], + "type": "text", + "content": "Following [30], we introduce our skeleton estimation algorithm as follows. Specifically, [30] uses PointNet++ [42] as the backbone, and the output of the last set abstraction layer is a set of points " + }, + { + "bbox": [ + 304, + 513, + 547, + 681 + ], + "type": "inline_equation", + "content": "\\mathcal{P}_*" + }, + { + "bbox": [ + 304, + 513, + 547, + 681 + ], + "type": "text", + "content": " and the corresponding contextual features " + }, + { + "bbox": [ + 304, + 513, + 547, + 681 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_*" + }, + { + "bbox": [ + 304, + 513, + 547, + 681 + ], + "type": "text", + "content": ". A skeletal point can always be considered the local center of a set of surface points. Consequently, the skeletal points can be generated by the convex combination of " + }, + { + "bbox": [ + 304, + 513, + 547, + 681 + ], + "type": "inline_equation", + "content": "\\mathcal{P}_*" + }, + { + "bbox": [ + 304, + 513, + 547, + 681 + ], + "type": "text", + "content": ", i.e., " + }, + { + "bbox": [ + 304, + 513, + 547, + 681 + ], + "type": "inline_equation", + "content": "\\mathcal{C} = \\mathcal{W}_*^\\top \\mathcal{P}_*" + }, + { + "bbox": [ + 304, + 513, + 547, + 681 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 513, + 547, + 681 + ], + "type": "inline_equation", + "content": "\\mathcal{W}_*" + }, + { + "bbox": [ + 304, + 513, + 547, + 681 + ], + "type": "text", + "content": " is the predicted weight matrix. The closest distances from " + }, + { + "bbox": [ + 304, + 513, + 547, + 681 + ], + "type": "inline_equation", + "content": "\\mathcal{P}_*" + }, + { + "bbox": [ + 304, + 513, + 547, + 681 + ], + "type": "text", + "content": " to the skeletal points " + }, + { + "bbox": [ + 304, + 513, + 547, + 681 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 304, + 513, + 547, + 681 + ], + "type": "text", + "content": " can be calculated and denoted as " + }, + { + "bbox": [ + 304, + 513, + 547, + 681 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_*" + }, + { + "bbox": [ + 304, + 513, + 547, + 681 + ], + "type": "text", + "content": ", and then the radii of all skeletal spheres are derived by " + }, + { + "bbox": [ + 304, + 513, + 547, + 681 + ], + "type": "inline_equation", + "content": "\\mathcal{R} = \\mathcal{W}_*^\\top \\mathcal{D}_*" + }, + { + "bbox": [ + 304, + 513, + 547, + 681 + ], + "type": "text", + "content": ". Similar to [30], we use the same loss function, which consists of three parts: a sampling loss " + }, + { + "bbox": [ + 304, + 513, + 547, + 681 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_s" + }, + { + "bbox": [ + 304, + 513, + 547, + 681 + ], + "type": "text", + "content": ", a point-to-sphere loss " + }, + { + "bbox": [ + 304, + 513, + 547, + 681 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_p" + }, + { + "bbox": [ + 304, + 513, + 547, + 681 + ], + "type": "text", + "content": ", and a radius regularizer " + }, + { + "bbox": [ + 304, + 513, + 547, + 681 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_r" + }, + { + "bbox": [ + 304, + 513, + 547, + 681 + ], + "type": "text", + "content": ", as follows:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 323, + 689, + 545, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 323, + 689, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 323, + 689, + 545, + 715 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {s} = \\sum_ {p \\in \\mathcal {P} _ {*}} \\min _ {t \\in \\mathcal {T} _ {*}} \\| p - t \\| _ {2} + \\sum_ {t \\in \\mathcal {T} _ {*}} \\min _ {p \\in \\mathcal {P} _ {*}} \\| t - p \\| _ {2}, \\tag {1}", + "image_path": "8cfb167f1921414d73ae2faf8a2c9e69e7ec110da4e5ba77167c58a697666afb.jpg" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17674" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 52, + 72, + 165, + 145 + ], + "blocks": [ + { + "bbox": [ + 52, + 72, + 165, + 145 + ], + "lines": [ + { + "bbox": [ + 52, + 72, + 165, + 145 + ], + "spans": [ + { + "bbox": [ + 52, + 72, + 165, + 145 + ], + "type": "image", + "image_path": "a3f2b87adb805f602de0fcda787771f01384ae6bb6518906e1f7bbd7df365ca5.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 77, + 150, + 140, + 160 + ], + "lines": [ + { + "bbox": [ + 77, + 150, + 140, + 160 + ], + "spans": [ + { + "bbox": [ + 77, + 150, + 140, + 160 + ], + "type": "text", + "content": "(a) KNN neighbors" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 170, + 72, + 284, + 146 + ], + "blocks": [ + { + "bbox": [ + 170, + 72, + 284, + 146 + ], + "lines": [ + { + "bbox": [ + 170, + 72, + 284, + 146 + ], + "spans": [ + { + "bbox": [ + 170, + 72, + 284, + 146 + ], + "type": "image", + "image_path": "cec1e3e0b5798e6ba098394e0391f22620b792ebbda368269a9ba7b126fced27.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 188, + 151, + 265, + 160 + ], + "lines": [ + { + "bbox": [ + 188, + 151, + 265, + 160 + ], + "spans": [ + { + "bbox": [ + 188, + 151, + 265, + 160 + ], + "type": "text", + "content": "(b) Delaunay neighbors" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 170, + 287, + 224 + ], + "lines": [ + { + "bbox": [ + 46, + 170, + 287, + 224 + ], + "spans": [ + { + "bbox": [ + 46, + 170, + 287, + 224 + ], + "type": "text", + "content": "Figure 6. KNN neighbors and Delaunay neighbors. KNN always find the nearest neighbors while the Delaunay neighbors are these connected by Delaunay edges. Cyan line: object skeleton; Black points: surface points; Blue points: centroids. Local neighboring points are connected by blue line segments." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 95, + 239, + 238, + 293 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 95, + 239, + 238, + 293 + ], + "spans": [ + { + "bbox": [ + 95, + 239, + 238, + 293 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {p} = \\sum_ {p \\in \\mathcal {P} _ {*}} \\left[ \\min _ {c \\in \\mathcal {C}} \\| p - c \\| _ {2} - r _ {c _ {p} ^ {m i n}} \\right] \\\\ + \\sum_ {c \\in \\mathcal {C}} \\left[ \\min _ {p \\in \\mathcal {P} _ {*}} \\| c - p \\| _ {2} - r _ {c} \\right], \\\\ \\end{array}", + "image_path": "16cc045eed88f43d85c3b20755c6e273d5e7cadb3a3a8a43a902fd4df6cb8c56.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 135, + 300, + 287, + 326 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 135, + 300, + 287, + 326 + ], + "spans": [ + { + "bbox": [ + 135, + 300, + 287, + 326 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {r} = - \\sum_ {c \\in \\mathcal {C}} r _ {c}, \\tag {3}", + "image_path": "cc7734ebdccc7a21485acdad5f60aaa60abd5f174c81a5856096770acdce6b42.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 331, + 287, + 355 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 331, + 287, + 355 + ], + "spans": [ + { + "bbox": [ + 47, + 331, + 287, + 355 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 331, + 287, + 355 + ], + "type": "inline_equation", + "content": "\\mathcal{T}_{*}" + }, + { + "bbox": [ + 47, + 331, + 287, + 355 + ], + "type": "text", + "content": " is a set of points sampled on the surface of each skeletal sphere and " + }, + { + "bbox": [ + 47, + 331, + 287, + 355 + ], + "type": "inline_equation", + "content": "c_{p}^{min}" + }, + { + "bbox": [ + 47, + 331, + 287, + 355 + ], + "type": "text", + "content": " is the closest skeletal point to " + }, + { + "bbox": [ + 47, + 331, + 287, + 355 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 47, + 331, + 287, + 355 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 355, + 287, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 355, + 287, + 594 + ], + "spans": [ + { + "bbox": [ + 46, + 355, + 287, + 594 + ], + "type": "text", + "content": "Though the above-mentioned method can generate skeleton, each skeletal point is weighted by all points in " + }, + { + "bbox": [ + 46, + 355, + 287, + 594 + ], + "type": "inline_equation", + "content": "\\mathcal{P}_{*}" + }, + { + "bbox": [ + 46, + 355, + 287, + 594 + ], + "type": "text", + "content": ". However, the skeleton prediction is always based on the local region, which means surface points far away from the skeletal point have no contribution to skeleton estimation. What's more, the convex combination requirement in [30] also poses a challenge to neural network learning since the network has to predict a large weight matrix. Therefore, we further propose a local weighting scheme concentrating on neighboring points to predict the skeleton. As shown in Fig. 2, our skeleton estimation network adopts the DGCNN [57] as the backbone to obtain the point-wise contextual features. Then we select K points as the centroids to group local points " + }, + { + "bbox": [ + 46, + 355, + 287, + 594 + ], + "type": "inline_equation", + "content": "\\mathcal{P}_{local} \\in \\mathbb{R}^{K \\times L \\times 3}" + }, + { + "bbox": [ + 46, + 355, + 287, + 594 + ], + "type": "text", + "content": " and features " + }, + { + "bbox": [ + 46, + 355, + 287, + 594 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{local} \\in \\mathbb{R}^{K \\times L \\times D}" + }, + { + "bbox": [ + 46, + 355, + 287, + 594 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 355, + 287, + 594 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 355, + 287, + 594 + ], + "type": "text", + "content": " is the number of neighbors of each centroid and " + }, + { + "bbox": [ + 46, + 355, + 287, + 594 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 46, + 355, + 287, + 594 + ], + "type": "text", + "content": " is the dimension of the features. Based on the grouped features, we will predict the weight matrix " + }, + { + "bbox": [ + 46, + 355, + 287, + 594 + ], + "type": "inline_equation", + "content": "\\mathcal{W}_{local} \\in \\mathbb{R}^{K \\times L \\times 1}" + }, + { + "bbox": [ + 46, + 355, + 287, + 594 + ], + "type": "text", + "content": " to derive the skeletal points, that is " + }, + { + "bbox": [ + 46, + 355, + 287, + 594 + ], + "type": "inline_equation", + "content": "\\mathcal{C} = \\mathcal{W}_{local}^{\\top} \\mathcal{P}_{local}" + }, + { + "bbox": [ + 46, + 355, + 287, + 594 + ], + "type": "text", + "content": ". Here, matrix transposition and multiplication are conducted on the last two dimensions." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "type": "text", + "content": "A critical insight here is how to select neighboring points of each centroid. As presented in [12], the skeletal points can be estimated by Delaunay edge filtering. Inspired by this, we use the Delaunay neighbors instead of the KNN ones to predict the skeletal points. We illustrate the difference between KNN and Delaunay neighbors in Fig. 6. As shown, KNN always finds the nearest " + }, + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "type": "text", + "content": " neighbors in Euclidean space. However, if we aim to predict the skeletal points that are always centrally located in the object, it is beneficial to consider the antipodal surface points. That is" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 72, + 545, + 193 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 193 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 193 + ], + "type": "text", + "content": "the intuition to use the Delaunay neighbors. To select the Delaunay neighbors, we first apply the Delaunay triangulation and pick out these local points connected by Delaunay edges. With the estimated skeleton, we can calculate the LFS of each point. As LFS is sensitive to point cloud noise, the best practice in our work is to use the \"smoothed\" LFS, i.e., the LFS histogram. Given the LSF histogram, we can then have the midpoint of each bin " + }, + { + "bbox": [ + 304, + 72, + 545, + 193 + ], + "type": "inline_equation", + "content": "\\bar{h}_1,\\bar{h}_2,\\dots,\\bar{h}_n" + }, + { + "bbox": [ + 304, + 72, + 545, + 193 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 72, + 545, + 193 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 72, + 545, + 193 + ], + "type": "text", + "content": " is the number of bins. If the LFS of one point is in " + }, + { + "bbox": [ + 304, + 72, + 545, + 193 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 72, + 545, + 193 + ], + "type": "text", + "content": "-th bin, the initial sampling weight for the point is " + }, + { + "bbox": [ + 304, + 72, + 545, + 193 + ], + "type": "inline_equation", + "content": "e^{-\\bar{h}_i} / \\sum_i e^{-\\bar{h}_i}" + }, + { + "bbox": [ + 304, + 72, + 545, + 193 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 198, + 511, + 211 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 198, + 511, + 211 + ], + "spans": [ + { + "bbox": [ + 306, + 198, + 511, + 211 + ], + "type": "text", + "content": "3.3. Skeleton-Aware Probabilistic Sampling" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 217, + 545, + 371 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 217, + 545, + 371 + ], + "spans": [ + { + "bbox": [ + 304, + 217, + 545, + 371 + ], + "type": "text", + "content": "As mentioned before, we aim to find a subset of points that not only take care of the downstream tasks but also encode the geometrical structure information of 3D objects. To derive the sampling formulation, we treat the point sampling operation as drawing samples from the probability distribution with replacement. Specifically, given the input point cloud " + }, + { + "bbox": [ + 304, + 217, + 545, + 371 + ], + "type": "inline_equation", + "content": "\\mathcal{P} = \\{p_1,p_2,\\dots ,p_N\\}" + }, + { + "bbox": [ + 304, + 217, + 545, + 371 + ], + "type": "text", + "content": ", we already have the prior per-point sampling weight from the first stage, and this initial weight encapsulates the structural information that should be considered. After the point cloud goes through the neural network, we get the point-wise features. Therefore, the posterior sampling probability over point-wise features can be formulated as:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 318, + 376, + 545, + 409 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 376, + 545, + 409 + ], + "spans": [ + { + "bbox": [ + 318, + 376, + 545, + 409 + ], + "type": "interline_equation", + "content": "\\mathcal {P} _ {\\theta} \\left(p _ {1}, \\dots , p _ {N}\\right) = \\prod_ {i = 1} ^ {N} \\sum_ {j} \\mathcal {P} _ {\\theta} \\left(p _ {i} \\mid b _ {i j}\\right) \\mathcal {P} _ {L F S} \\left(b _ {i j}\\right), \\tag {4}", + "image_path": "037066ed48c32e74133ae50c9c957d63a829a87aad17b86b44178467f41e14a7.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 415, + 545, + 486 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 415, + 545, + 486 + ], + "spans": [ + { + "bbox": [ + 304, + 415, + 545, + 486 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 415, + 545, + 486 + ], + "type": "inline_equation", + "content": "b_{ij}" + }, + { + "bbox": [ + 304, + 415, + 545, + 486 + ], + "type": "text", + "content": " denotes the event that " + }, + { + "bbox": [ + 304, + 415, + 545, + 486 + ], + "type": "inline_equation", + "content": "p_i" + }, + { + "bbox": [ + 304, + 415, + 545, + 486 + ], + "type": "text", + "content": " locates in the " + }, + { + "bbox": [ + 304, + 415, + 545, + 486 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 304, + 415, + 545, + 486 + ], + "type": "text", + "content": "-th bin of the LFS histogram and the corresponding probability is " + }, + { + "bbox": [ + 304, + 415, + 545, + 486 + ], + "type": "inline_equation", + "content": "\\mathcal{P}_{LFS}(b_{ij})" + }, + { + "bbox": [ + 304, + 415, + 545, + 486 + ], + "type": "text", + "content": ". The subscript " + }, + { + "bbox": [ + 304, + 415, + 545, + 486 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 415, + 545, + 486 + ], + "type": "text", + "content": " indicates trainable parameters of the neural network. During training, we maximize the posterior over all training point clouds with respect to the individual point cloud feature and the network parameters." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 486, + 545, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 486, + 545, + 594 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 545, + 594 + ], + "type": "text", + "content": "Consequently, with the input point cloud " + }, + { + "bbox": [ + 304, + 486, + 545, + 594 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 304, + 486, + 545, + 594 + ], + "type": "text", + "content": ", it is straightforward to consider points as different categories, and the task that samples a representative subset " + }, + { + "bbox": [ + 304, + 486, + 545, + 594 + ], + "type": "inline_equation", + "content": "\\mathcal{P}_{sub} \\subset \\mathcal{P}" + }, + { + "bbox": [ + 304, + 486, + 545, + 594 + ], + "type": "text", + "content": " then becomes to learn to draw samples from a discrete distribution, e.g. the categorical distribution. However, the sampling operation is usually non-differentiable. Though [14] and [27] are trainable, the sampled point is less interpretable from the probabilistic perspective, especially when sampling multiple points." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": "Categorical Reparameterization. Fortunately, Jang et al. [22] introduce an elegant reparameterization trick called Gumbel-softmax to enable discrete stochastic variables to back-propagate in neural network computation graphs. Therefore, we utilize the Gumbel-softmax trick to facilitate our sampling process. For a categorical distribution " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "Cat(c_{1},\\dots,c_{k})" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": " denotes the number of categories and " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "c_{i}" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": " means the probability of category " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": ", the Gumbel-softmax is designed as a discrete reparameterization trick" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17675" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 131 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 131 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 131 + ], + "type": "text", + "content": "to estimate smooth gradient with a continuous relaxation for the categorical variable. Given the Gumbel noise " + }, + { + "bbox": [ + 47, + 72, + 287, + 131 + ], + "type": "inline_equation", + "content": "\\pmb{g} = (g_1, \\dots, g_k)" + }, + { + "bbox": [ + 47, + 72, + 287, + 131 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 47, + 72, + 287, + 131 + ], + "type": "inline_equation", + "content": "g_i \\sim Gumbel(0, 1)" + }, + { + "bbox": [ + 47, + 72, + 287, + 131 + ], + "type": "text", + "content": " is independent identically distributed, a soft categorical sample can be drawn by" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 103, + 133, + 287, + 145 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 103, + 133, + 287, + 145 + ], + "spans": [ + { + "bbox": [ + 103, + 133, + 287, + 145 + ], + "type": "interline_equation", + "content": "\\boldsymbol {y} = \\operatorname {s o f t m a x} \\left(\\left(\\log (\\boldsymbol {c}) + \\boldsymbol {g}\\right) / \\tau\\right), \\tag {5}", + "image_path": "fd34fd9f4a8f73d2657d9ce4d65d7736328724b57264371e241cb627b390c2f1.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 148, + 287, + 197 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 148, + 287, + 197 + ], + "spans": [ + { + "bbox": [ + 46, + 148, + 287, + 197 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 148, + 287, + 197 + ], + "type": "inline_equation", + "content": "\\pmb{c} = (c_{1},\\dots,c_{k})" + }, + { + "bbox": [ + 46, + 148, + 287, + 197 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 148, + 287, + 197 + ], + "type": "inline_equation", + "content": "\\tau >0" + }, + { + "bbox": [ + 46, + 148, + 287, + 197 + ], + "type": "text", + "content": " is the annealing temperature. The equation above is referred as Gumbel-softmax, and as " + }, + { + "bbox": [ + 46, + 148, + 287, + 197 + ], + "type": "inline_equation", + "content": "\\tau \\rightarrow 0" + }, + { + "bbox": [ + 46, + 148, + 287, + 197 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 148, + 287, + 197 + ], + "type": "inline_equation", + "content": "\\pmb{y}" + }, + { + "bbox": [ + 46, + 148, + 287, + 197 + ], + "type": "text", + "content": " will degenerate into the Gumbel-max form gradually," + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 91, + 205, + 287, + 217 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 205, + 287, + 217 + ], + "spans": [ + { + "bbox": [ + 91, + 205, + 287, + 217 + ], + "type": "interline_equation", + "content": "\\boldsymbol {y} = \\operatorname {o n e h o t} (\\operatorname {a r g m a x} ((\\log (\\boldsymbol {c}) + \\boldsymbol {g}))), \\tag {6}", + "image_path": "ca51279c9e2a898bb09bca00f2993356314a19610c090e8a8658cbb4c988260f.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 224, + 287, + 295 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 224, + 287, + 295 + ], + "spans": [ + { + "bbox": [ + 46, + 224, + 287, + 295 + ], + "type": "text", + "content": "which is an unbiased sample from " + }, + { + "bbox": [ + 46, + 224, + 287, + 295 + ], + "type": "inline_equation", + "content": "Cat(c_{1},\\ldots ,c_{k})" + }, + { + "bbox": [ + 46, + 224, + 287, + 295 + ], + "type": "text", + "content": ". In this way, we are able to draw differentiable samples from the distribution " + }, + { + "bbox": [ + 46, + 224, + 287, + 295 + ], + "type": "inline_equation", + "content": "Cat(c_{1},\\ldots ,c_{k})" + }, + { + "bbox": [ + 46, + 224, + 287, + 295 + ], + "type": "text", + "content": " in the training phase. In practice, " + }, + { + "bbox": [ + 46, + 224, + 287, + 295 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 46, + 224, + 287, + 295 + ], + "type": "text", + "content": " starts at a high value (e.g., 1.0) and anneals to a small value (e.g., 0.1). In the testing phase, discrete samples can be drawn with the Gumbel-max trick." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 296, + 287, + 331 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 296, + 287, + 331 + ], + "spans": [ + { + "bbox": [ + 46, + 296, + 287, + 331 + ], + "type": "text", + "content": "Therefore, we use a hard and discrete selection by exploring the trainable categorical reparameterization Gumbel-softmax as follows:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 89, + 338, + 287, + 353 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 89, + 338, + 287, + 353 + ], + "spans": [ + { + "bbox": [ + 89, + 338, + 287, + 353 + ], + "type": "interline_equation", + "content": "\\mathcal {P} _ {s u b} = \\left[ G s _ {\\tau} \\left(L p \\left(\\mathcal {W} _ {L F S} \\odot \\mathcal {W} _ {\\theta}\\right) \\right] ^ {\\top} \\mathcal {P}, \\right. \\tag {7}", + "image_path": "43e504f849baf4f777867eedc7a8d908378dd4d1f865d758a0e6a53d2daefbb8.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 358, + 287, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 358, + 287, + 515 + ], + "spans": [ + { + "bbox": [ + 46, + 358, + 287, + 515 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 358, + 287, + 515 + ], + "type": "inline_equation", + "content": "\\mathcal{P} \\in \\mathbb{R}^{N \\times 3}" + }, + { + "bbox": [ + 46, + 358, + 287, + 515 + ], + "type": "text", + "content": " is the input point cloud, " + }, + { + "bbox": [ + 46, + 358, + 287, + 515 + ], + "type": "inline_equation", + "content": "\\mathcal{P}_{sub} \\in \\mathbb{R}^{M \\times 3}" + }, + { + "bbox": [ + 46, + 358, + 287, + 515 + ], + "type": "text", + "content": " is the sampled point cloud, and " + }, + { + "bbox": [ + 46, + 358, + 287, + 515 + ], + "type": "inline_equation", + "content": "G s_{\\tau}(\\cdot)" + }, + { + "bbox": [ + 46, + 358, + 287, + 515 + ], + "type": "text", + "content": " operation is the Gumbel-softmax trick with the annealing temperature " + }, + { + "bbox": [ + 46, + 358, + 287, + 515 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 46, + 358, + 287, + 515 + ], + "type": "text", + "content": ". Additionally, " + }, + { + "bbox": [ + 46, + 358, + 287, + 515 + ], + "type": "inline_equation", + "content": "\\mathcal{W}_{LFS} \\in \\mathbb{R}^{N \\times 1}" + }, + { + "bbox": [ + 46, + 358, + 287, + 515 + ], + "type": "text", + "content": " is calculated from the first stage and " + }, + { + "bbox": [ + 46, + 358, + 287, + 515 + ], + "type": "inline_equation", + "content": "\\mathcal{W}_{\\theta} \\in \\mathbb{R}^{N \\times D_{sp}}" + }, + { + "bbox": [ + 46, + 358, + 287, + 515 + ], + "type": "text", + "content": " is feature matrix from the sampling network, where " + }, + { + "bbox": [ + 46, + 358, + 287, + 515 + ], + "type": "inline_equation", + "content": "D_{sp}" + }, + { + "bbox": [ + 46, + 358, + 287, + 515 + ], + "type": "text", + "content": " indicates the dimension of the features. " + }, + { + "bbox": [ + 46, + 358, + 287, + 515 + ], + "type": "inline_equation", + "content": "Lp(\\cdot): \\mathbb{R}^{N \\times D_{sp}} \\to \\mathbb{R}^{N \\times M}" + }, + { + "bbox": [ + 46, + 358, + 287, + 515 + ], + "type": "text", + "content": " is the linear mapping layer. " + }, + { + "bbox": [ + 46, + 358, + 287, + 515 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 46, + 358, + 287, + 515 + ], + "type": "text", + "content": " indicates the element-wise Hadamard product operation. In practice, we start with a large " + }, + { + "bbox": [ + 46, + 358, + 287, + 515 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 46, + 358, + 287, + 515 + ], + "type": "text", + "content": " such as " + }, + { + "bbox": [ + 46, + 358, + 287, + 515 + ], + "type": "inline_equation", + "content": "\\tau = 1.0" + }, + { + "bbox": [ + 46, + 358, + 287, + 515 + ], + "type": "text", + "content": " and gradually decrease it. In the training phase, it provides smooth gradients using the discrete reparameterization trick. With annealing, it degenerates to a hard selection in the testing phase." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 525, + 128, + 538 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 525, + 128, + 538 + ], + "spans": [ + { + "bbox": [ + 47, + 525, + 128, + 538 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 544, + 287, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 544, + 287, + 616 + ], + "spans": [ + { + "bbox": [ + 46, + 544, + 287, + 616 + ], + "type": "text", + "content": "In this section, we evaluate the proposed skeleton-aware sampling method by applying it to three downstream tasks: point cloud classification, retrieval, and reconstruction. All experiments are conducted on the widely used ModelNet40 [62] dataset, and we use the official split of 9,843 training and 2,468 testing samples." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 623, + 180, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 623, + 180, + 635 + ], + "spans": [ + { + "bbox": [ + 47, + 623, + 180, + 635 + ], + "type": "text", + "content": "4.1. Implementation Details" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 641, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 287, + 712 + ], + "type": "text", + "content": "We implement the proposed method using PyTorch, and we will give the detailed network architecture in our supplementary materials. Our network training consists of two stages. We train the skeleton estimation network in the first stage to get the point cloud skeleton. The number of predicted skeletal spheres is 128, and the number of bins for" + } + ] + } + ], + "index": 11 + }, + { + "type": "table", + "bbox": [ + 309, + 70, + 545, + 139 + ], + "blocks": [ + { + "bbox": [ + 309, + 70, + 545, + 139 + ], + "lines": [ + { + "bbox": [ + 309, + 70, + 545, + 139 + ], + "spans": [ + { + "bbox": [ + 309, + 70, + 545, + 139 + ], + "type": "table", + "html": "
Sampling RatioClassification Acc(%)
FPS [42]S-NET [14]SN [27]MS [10]Ours
870.477.583.788.089.1
1646.370.482.285.588.8
3226.360.680.181.587.4
6413.536.154.161.682.9
", + "image_path": "586d1851a5b96b58ccbbe7e9099cc831152875e6db9c154a6b4dcd015b572836.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 146, + 545, + 169 + ], + "lines": [ + { + "bbox": [ + 305, + 146, + 545, + 169 + ], + "spans": [ + { + "bbox": [ + 305, + 146, + 545, + 169 + ], + "type": "text", + "content": "Table 1. Point cloud classification results on ModelNet40. The task network is trained on complete data with 1024 points." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 192, + 545, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 192, + 545, + 228 + ], + "spans": [ + { + "bbox": [ + 305, + 192, + 545, + 228 + ], + "type": "text", + "content": "the LFS histogram is 6. In the second stage, we train the sampling network using task losses. In both stages, we use the Adam optimizer with a learning rate of 0.001." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 239, + 450, + 250 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 239, + 450, + 250 + ], + "spans": [ + { + "bbox": [ + 305, + 239, + 450, + 250 + ], + "type": "text", + "content": "4.2. Point Cloud Classification" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 258, + 545, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 258, + 545, + 521 + ], + "spans": [ + { + "bbox": [ + 304, + 258, + 545, + 521 + ], + "type": "text", + "content": "To evaluate the proposed method for point cloud classification, we employ the full version of PointNet [41] as the task network. The classification accuracy of PointNet is trained on the complete data (1024 points per point cloud without normals) and tested on sampled points of different sizes. The evaluation metric is overall accuracy (OA), and for a fair comparison, the upper bound accuracy trained on 1024 points is " + }, + { + "bbox": [ + 304, + 258, + 545, + 521 + ], + "type": "inline_equation", + "content": "89.5\\%" + }, + { + "bbox": [ + 304, + 258, + 545, + 521 + ], + "type": "text", + "content": " (the same as MetaSampler [10]). We compare with four methods, FPS [42], S-NET [14], SampleNet [27] and MetaSampler [10]. We report the classification results of four different sampling ratios in Table 1, where the proposed method outperforms recent state-of-the-art methods. Specifically, the classification accuracy achieved by the proposed approach at the sampling ratio of 8 is very close to the upper bound accuracy " + }, + { + "bbox": [ + 304, + 258, + 545, + 521 + ], + "type": "inline_equation", + "content": "(89.1\\%" + }, + { + "bbox": [ + 304, + 258, + 545, + 521 + ], + "type": "text", + "content": " vs. " + }, + { + "bbox": [ + 304, + 258, + 545, + 521 + ], + "type": "inline_equation", + "content": "89.5\\%)" + }, + { + "bbox": [ + 304, + 258, + 545, + 521 + ], + "type": "text", + "content": ", which shows the effectiveness of our skeleton-aware strategy. We also notice that the performance gap between the proposed method and others is becoming large when increasing the sampling rate (e.g., at the sampling ratio of 64 with 16 points left). This further demonstrates the superiority of the proposed method in preserving task-significant features." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 533, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 545, + 713 + ], + "type": "text", + "content": "Ablation Study on Skeleton-Aware Prior. We show how the prior sampling weight operates by comparing with two other commonly used non-learned sampling methods, random sampling (RS) and farthest point sampling (FPS). In Fig. 7, for visualization purposes, we use 10,000 points as input, and the number of sampled points is 1,024. Generally, RS randomly picks 1024 points from the original data, and FPS selects a subset of points far from each other. Since both two methods do not consider any geometrical information, these two sampling methods do not change the LFS distribution. Differently, we propose the skeleton-aware sampling in this work, which is able to use the LFS histogram as the initial sampling weight and also learn to sample for downstream tasks. That is, we will pay more attention to those points with small LFS values. As shown" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17676" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 70, + 265, + 273 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 265, + 273 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 265, + 273 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 265, + 273 + ], + "type": "image", + "image_path": "3c84a7512432bdd2294fbc3235dd33f701085b3d2be6ca0d702cacc96508ab88.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 282, + 287, + 326 + ], + "lines": [ + { + "bbox": [ + 46, + 282, + 287, + 326 + ], + "spans": [ + { + "bbox": [ + 46, + 282, + 287, + 326 + ], + "type": "text", + "content": "Figure 7. Visualization of different sampling strategies. RS and FPS do not encode geometrical information to change the LFS distribution after sampling, while the proposed considers the LFS histogram to obtain informative skeleton-aware sampling." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 345, + 287, + 501 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 345, + 287, + 501 + ], + "spans": [ + { + "bbox": [ + 46, + 345, + 287, + 501 + ], + "type": "text", + "content": "in Fig. 7, the RS and FPS keep nearly the same LFS distribution with the original point cloud after sampling, but our method encodes the geometrical information and gives out the different LFS distribution. The final results can also prove this by our sampled points concentrated on small LFS areas. In addition, we report the classification results without the LFS weight in Table 2. Here, \"GT\" means we use the ground truth skeletons computed by DPC [60] instead of the estimated ones from the first stage. As shown, using the skeleton-aware strategy as the initial sampling weight can always benefit the following learning task. Moreover, our method achieves comparable results with that using ground truth skeletons." + } + ] + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 67, + 507, + 267, + 597 + ], + "blocks": [ + { + "bbox": [ + 67, + 507, + 267, + 597 + ], + "lines": [ + { + "bbox": [ + 67, + 507, + 267, + 597 + ], + "spans": [ + { + "bbox": [ + 67, + 507, + 267, + 597 + ], + "type": "table", + "html": "
Sampling RatioClassification Acc(%)
GTOurs(w/o)Ours
889.188.289.1
1688.887.488.8
3287.585.987.4
6482.880.382.9
", + "image_path": "7475ce6df22eda81942ff65d2809eacc9cc19d4c95aaea299cb814d71ffdb4b2.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "content": "Ablation Study on LFS Histogram. The number of bins reveals the LFS distribution at different levels. Using wider bins reduces the LFS noise, while using narrower bins gives better precision to the LFS density estimation. Thus, varying the bin number within the LFS histogram can be" + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 315, + 70, + 539, + 159 + ], + "blocks": [ + { + "bbox": [ + 46, + 606, + 287, + 640 + ], + "lines": [ + { + "bbox": [ + 46, + 606, + 287, + 640 + ], + "spans": [ + { + "bbox": [ + 46, + 606, + 287, + 640 + ], + "type": "text", + "content": "Table 2. Point cloud classification results without the initial LFS weight. GT indicates using the ground truth skeletons generated by DPC [60]." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 315, + 70, + 539, + 159 + ], + "lines": [ + { + "bbox": [ + 315, + 70, + 539, + 159 + ], + "spans": [ + { + "bbox": [ + 315, + 70, + 539, + 159 + ], + "type": "table", + "html": "
Sampling RatioBins
1361218
888.288.489.189.189.0
1687.488.088.888.588.8
3285.986.687.487.287.4
6480.381.282.982.882.7
", + "image_path": "8cb299f472db4159a4610458040a7ca1bd04e8e70f7db0c79de4643475cae492.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 211, + 545, + 270 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 211, + 545, + 270 + ], + "spans": [ + { + "bbox": [ + 304, + 211, + 545, + 270 + ], + "type": "text", + "content": "beneficial. We report the classification results with different bins in Table 3. The aggressive setting is to use only one bin, and this case is equivalent to no initial LSF weight applied. Generally, we find that six bins are suitable for most cases." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 283, + 545, + 391 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 283, + 545, + 391 + ], + "spans": [ + { + "bbox": [ + 304, + 283, + 545, + 391 + ], + "type": "text", + "content": "Ablation Study on Skeletal Spheres. As mentioned before, the object's skeleton is represented with a set of skeletal spheres. Generally, increasing the number of predicted skeletal spheres will lead to detailed structures. Thus, it is beneficial to disclose how this hyper-parameter influences the following tasks. We show the classification results in Table 4 with different numbers of skeletal spheres predicted. As shown, our method is not sensitive to the parameter and achieves steady performance." + } + ] + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 329, + 400, + 524, + 491 + ], + "blocks": [ + { + "bbox": [ + 305, + 168, + 545, + 190 + ], + "lines": [ + { + "bbox": [ + 305, + 168, + 545, + 190 + ], + "spans": [ + { + "bbox": [ + 305, + 168, + 545, + 190 + ], + "type": "text", + "content": "Table 3. Point cloud classification results with different bins. Generally, we find that six bins already work well in most cases." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 329, + 400, + 524, + 491 + ], + "lines": [ + { + "bbox": [ + 329, + 400, + 524, + 491 + ], + "spans": [ + { + "bbox": [ + 329, + 400, + 524, + 491 + ], + "type": "table", + "html": "
Sampling RatioSkeletal Spheres
3264128256
887.288.489.189.1
1685.887.188.888.5
3284.085.187.487.2
6479.380.582.982.8
", + "image_path": "5c2e3e55f02d59e53d67b0ada66ce7a64bb4f9671ca1ea3ffc6e5a47bcb422f9.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 498, + 545, + 521 + ], + "lines": [ + { + "bbox": [ + 305, + 498, + 545, + 521 + ], + "spans": [ + { + "bbox": [ + 305, + 498, + 545, + 521 + ], + "type": "text", + "content": "Table 4. Point cloud classification results when using different numbers of skeletal spheres." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": "Ablation Study on Annealing Strategy. As we apply the Gumbel-softmax operation in our method, we gradually anneal the temperature " + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": " to facilitate our network training in the second stage. Thus, it is beneficial to evaluate the classification performance when adopting different annealing strategies. During training, we let " + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\tau = 1.0" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": " to allow gradients past the samples and then gradually anneal the temperature until " + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\tau = 0.5" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": " (but not completely to 0, as the gradients would blow up). In the test phase, as " + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\tau \\to 0.0" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": ", the softmax becomes an argmax and the Gumbel-softmax distribution becomes the categorical distribution. We report the classification results in Table 5 with four different annealing strategies, including constant, step, linear and exponential. Here, the \"constant\" means " + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": " keeps being 1.0 without annealing during training." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17677" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 69, + 70, + 265, + 159 + ], + "blocks": [ + { + "bbox": [ + 69, + 70, + 265, + 159 + ], + "lines": [ + { + "bbox": [ + 69, + 70, + 265, + 159 + ], + "spans": [ + { + "bbox": [ + 69, + 70, + 265, + 159 + ], + "type": "table", + "html": "
Temperature (τ)Sampling Ratio
8163264
Constant87.786.485.181.1
Step88.887.286.682.1
Linear rectified89.087.987.682.3
Exponential89.188.887.482.9
", + "image_path": "3b5f67b58e3bf1a19e99350f6a266e62f5cf279d02ccf272bdb069f040a38a45.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 222, + 287, + 294 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 222, + 287, + 294 + ], + "spans": [ + { + "bbox": [ + 46, + 222, + 287, + 294 + ], + "type": "text", + "content": "Model Complexity. In Table 6, we report the model complexity of the proposed method. Specifically, the FLOPs increase with a large number of predicted skeletal spheres. The number of parameters for the probabilistic sampling network is 1.24M, and the number of FLOPs is 2.93G at the sampling ratio of 8." + } + ] + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 69, + 304, + 269, + 427 + ], + "blocks": [ + { + "bbox": [ + 46, + 167, + 287, + 202 + ], + "lines": [ + { + "bbox": [ + 46, + 167, + 287, + 202 + ], + "spans": [ + { + "bbox": [ + 46, + 167, + 287, + 202 + ], + "type": "text", + "content": "Table 5. Point cloud classification results for using different annealing strategies. Here, the \"Constant\" row means we do not anneal the " + }, + { + "bbox": [ + 46, + 167, + 287, + 202 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 46, + 167, + 287, + 202 + ], + "type": "text", + "content": " and keep " + }, + { + "bbox": [ + 46, + 167, + 287, + 202 + ], + "type": "inline_equation", + "content": "\\tau = 1.0" + }, + { + "bbox": [ + 46, + 167, + 287, + 202 + ], + "type": "text", + "content": " during training." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 69, + 304, + 269, + 427 + ], + "lines": [ + { + "bbox": [ + 69, + 304, + 269, + 427 + ], + "spans": [ + { + "bbox": [ + 69, + 304, + 269, + 427 + ], + "type": "table", + "html": "
Model ComplexityParams (M)FLOPs (G)
Skeletal Spheres321.543.43
641.543.86
1281.544.71
2561.546.41
Sampling Ratio81.242.93
161.232.90
321.222.88
641.212.86
", + "image_path": "1cf936c9f7217b0de758f326c6b4a4932fe09ac8d5448bc3ec074d16680731ff.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 478, + 172, + 490 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 478, + 172, + 490 + ], + "spans": [ + { + "bbox": [ + 47, + 478, + 172, + 490 + ], + "type": "text", + "content": "4.3. Point Cloud Retrieval" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 496, + 287, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 496, + 287, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 496, + 287, + 664 + ], + "type": "text", + "content": "In this subsection, we perform point cloud retrieval experiments to further demonstrate the effectiveness of the proposed method for downstream tasks. We follow the same evaluation setting in [10, 14, 27] to report the performance on the point cloud retrieval. Specifically, we take our method trained with PointNet [41] for classification as the task network without re-training it. We sample points of different sizes fed into PointNet and use its penultimate layer as the shape descriptor. Retrieval is done based on the L2 distance on the shape descriptor, and the evaluation metric is the mean Average Precision (mAP). In Table. 7, we summarize the performances of different methods and observe that our method consistently outperforms others by a large margin at different sampling ratios." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 671, + 200, + 683 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 671, + 200, + 683 + ], + "spans": [ + { + "bbox": [ + 47, + 671, + 200, + 683 + ], + "type": "text", + "content": "4.4. Point Cloud Reconstruction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 689, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 286, + 713 + ], + "type": "text", + "content": "In this subsection, we perform point cloud reconstruction experiments to further demonstrate the effectiveness of the" + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 309, + 70, + 545, + 149 + ], + "blocks": [ + { + "bbox": [ + 46, + 435, + 286, + 458 + ], + "lines": [ + { + "bbox": [ + 46, + 435, + 286, + 458 + ], + "spans": [ + { + "bbox": [ + 46, + 435, + 286, + 458 + ], + "type": "text", + "content": "Table 6. The model complexity of the proposed skeleton estimation network." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 309, + 70, + 545, + 149 + ], + "lines": [ + { + "bbox": [ + 309, + 70, + 545, + 149 + ], + "spans": [ + { + "bbox": [ + 309, + 70, + 545, + 149 + ], + "type": "table", + "html": "
Sampling RatioRetrieval Performance (mAP)
FPS [42]S-NET [14]SN [27]Ours
858.360.468.872.2
1649.459.065.270.9
3237.759.062.567.1
6427.454.559.562.6
", + "image_path": "5445f44afcd083df056bc3ee2ebd450d324b7a8eadb0d82470e2e9f65840696b.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 214, + 545, + 310 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 214, + 545, + 310 + ], + "spans": [ + { + "bbox": [ + 304, + 214, + 545, + 310 + ], + "type": "text", + "content": "proposed method for downstream tasks. We use an autoencoder as the task network on the ModelNet40 [62] dataset. Following [10], we employ the Point Completion Network (PCN) [69] to minimize the Chamfer distance (CD) [16] between the input and output points. As demonstrated in Table 8, our method outperforms others and the improvement is consistent across all sampling ratios, further exhibiting the effectiveness of our method." + } + ] + } + ], + "index": 11 + }, + { + "type": "table", + "bbox": [ + 309, + 320, + 545, + 404 + ], + "blocks": [ + { + "bbox": [ + 305, + 158, + 545, + 191 + ], + "lines": [ + { + "bbox": [ + 305, + 158, + 545, + 191 + ], + "spans": [ + { + "bbox": [ + 305, + 158, + 545, + 191 + ], + "type": "text", + "content": "Table 7. Point cloud retrieval results on the ModelNet40 dataset. Specifically, the proposed method achieves superior performance across different sampling ratios." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 309, + 320, + 545, + 404 + ], + "lines": [ + { + "bbox": [ + 309, + 320, + 545, + 404 + ], + "spans": [ + { + "bbox": [ + 309, + 320, + 545, + 404 + ], + "type": "table", + "html": "
Sampling RatioReconstruction Performance (CD)
FPS [42]SN [27]MS [10]Ours
83.783.293.052.97
164.033.323.153.01
324.253.613.373.24
644.784.434.313.78
", + "image_path": "8beed66d9354799b43ce86114051005681d9f39dd2f55ae8a4d0180dd883f7c7.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 412, + 545, + 436 + ], + "lines": [ + { + "bbox": [ + 305, + 412, + 545, + 436 + ], + "spans": [ + { + "bbox": [ + 305, + 412, + 545, + 436 + ], + "type": "text", + "content": "Table 8. Point cloud reconstruction results on the ModelNet40 dataset. Specifically, the original size of data is 1024 points." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 306, + 465, + 378, + 478 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 465, + 378, + 478 + ], + "spans": [ + { + "bbox": [ + 306, + 465, + 378, + 478 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 487, + 545, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 487, + 545, + 643 + ], + "spans": [ + { + "bbox": [ + 304, + 487, + 545, + 643 + ], + "type": "text", + "content": "In this paper, we propose a skeleton-aware learning-to-sample method for point cloud sampling. The skeletal representation of the point cloud is learned in an unsupervised manner to avoid label-intensive annotations. Given the learned skeleton, the skeleton-aware point cloud sampling process is conducted in a probabilistic way according to the LFS distribution. The proposed skeleton-aware sampling method is end-to-end trainable. To evaluate the proposed method, we perform experiments on several downstream point cloud analysis tasks such as classification, retrieval, and reconstruction, and the proposed method consistently outperforms traditional and recent learning-to-sample methods by a large margin." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 656, + 404, + 670 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 656, + 404, + 670 + ], + "spans": [ + { + "bbox": [ + 306, + 656, + 404, + 670 + ], + "type": "text", + "content": "Acknowledgement" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 677, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 545, + 712 + ], + "type": "text", + "content": "Mr Cheng Wen and Dr Baosheng Yu were supported by Australian Research Council Projects in part by IH180100002 and FL170100117." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17678" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "text", + "content": "[1] Panos Achlioptas, Olga Diamanti, Ioannis Mitliagkas, and Leonidas Guibas. 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Most existing LIC methods are Convolutional Neural Networks-based (CNN-based) or Transformer-based, which have different advantages. Exploiting both advantages is a point worth exploring, which has two challenges: 1) how to effectively fuse the two methods? 2) how to achieve higher performance with a suitable complexity? In this paper, we propose an efficient parallel Transformer-CNN Mixture (TCM) block with a controllable complexity to incorporate the local modeling ability of CNN and the non-local modeling ability of transformers to improve the overall architecture of image compression models. Besides, inspired by the recent progress of entropy estimation models and attention modules, we propose a channel-wise entropy model with parameter-efficient swin-transformer-based attention (SWAtten) modules by using channel squeezing. Experimental results demonstrate our proposed method achieves state-of-the-art rate-distortion performances on three different resolution datasets (i.e., Kodak, Tecnick, CLIC Professional Validation) compared to existing LIC methods. The code is at https://github.com/jmliu206/LIC_TCM.", + "bbox": [ + 75, + 335, + 473, + 698 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 718, + 209, + 734 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Image compression is a crucial topic in the field of image processing. With the rapidly increasing image data, lossy image compression plays an important role in storing and transmitting efficiently. In the passing decades, there were many classical standards, including JPEG [31], WebP [11], and VVC [29], which contain three steps: transform, quantization, and entropy coding, have achieved impressive Rate-Distortion (RD) performance. On the other hand, different from the classical standards, end-to-end learned", + "bbox": [ + 75, + 743, + 468, + 878 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/cb53080d4fdc672dc93e7ddd1bd441deda417378d7afe8625d050edc51edcc7f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 522, + 304, + 751, + 412 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/cc5c8f9aca837ecbd50da36c042bfa9ed35a2d14a52dbcfc8e9bf58474a747dc.jpg", + "image_caption": [ + "VVC (VTM-12.1)", + "0.131bpp|34.69dB|15.04dB", + "Figure 1. Visualization of decompressed images of $\\text{kodim}23$ from Kodak dataset based on different methods (The subfigure is titled as \"Method|Bit rate|PSNR|MS-SSIM\")." + ], + "image_footnote": [], + "bbox": [ + 519, + 412, + 635, + 455 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/abb58a60eb080962196bd55bb276aaef7b744785ac2478c4780d38a5130e1a21.jpg", + "image_caption": [ + "WebP", + "0.180bpp|30.77dB|12.47dB" + ], + "image_footnote": [], + "bbox": [ + 638, + 412, + 753, + 455 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/289a2381fd340c491775ec5cae69c470aab79b690be24e496cb887788f2253fc.jpg", + "image_caption": [ + "Ground Truth" + ], + "image_footnote": [], + "bbox": [ + 756, + 306, + 870, + 347 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/928aed40cc6b770b8b3c0aa78d60923d90ae2b4e39105c9cfa04f99798504bcf.jpg", + "image_caption": [ + "Ours [MSE]" + ], + "image_footnote": [], + "bbox": [ + 758, + 356, + 870, + 397 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/55f7dfecea3d37d84d7c90cf59020daed73ca25ed7605f6ad56d44b4d6a93a01.jpg", + "image_caption": [ + "0.127bpp|35.78dB|16.25dB", + "Ours [MS-SSIM]", + "0.114bpp|30.81dB|17.07dB" + ], + "image_footnote": [], + "bbox": [ + 758, + 412, + 870, + 454 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "image compression (LIC) is optimized as a whole. Some very recent LIC works [5, 13, 32, 34, 36, 37] have outperformed VVC which is the best classical image and video coding standards at present, on both Peak signal-to-noise ratio (PSNR) and Multi-Scale Structural Similarity (MS-SSIM). This suggests that LIC has great potential for next-generation image compression techniques.", + "bbox": [ + 496, + 537, + 890, + 643 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Most LIC methods are CNN-based methods [6, 10, 20, 21, 33] using the variational auto-encoder (VAE) which is proposed by Balle et al. [3]. With the development of vision transformers [9,22] recently, some vision transformer-based LIC methods [23, 36, 37] are also investigated. For CNN-based example, Cheng et al. [6] proposed a residual block-based image compression model. For transformer-based example, Zou et al. [37] tried a swin-transformer-based image compression model. These two kinds of methods have different advantages. CNN has the ability of local modeling, while transformers have the ability to model non-local information. It is still worth exploring whether the advantages of these two methods can be effectively combined with a suitable complexity. In our method, we try to efficiently incorporate both advantages of CNN and transformers by proposing an efficient parallel Transformer-CNN Mixture (TCM) block under a controllable complexity to improve", + "bbox": [ + 496, + 643, + 892, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Heming Sun is the corresponding author.", + "bbox": [ + 94, + 886, + 318, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "14388", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "the RD performance of LIC.", + "bbox": [ + 76, + 90, + 267, + 104 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In addition to the type of the neural network, the design of entropy model is also an important technique in LIC. The most common way is to introduce extra latent variables as hyper-prior to convert the probability model of compact coding-symbols to a joint model [3]. On that basis, many methods spring up. Minnen et al. [26] utilized the masked convolutional layer to capture the context information. Furthermore, they [27] proposed a parallel channel-wise autoregressive entropy model by splitting the latent to 10 slices. The results of encoded slices can assist in the encoding of remaining slices in a pipeline manner.", + "bbox": [ + 75, + 106, + 468, + 271 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recently, many different attention modules [6, 21, 37] were designed and proposed to improve image compression. Attention modules can help the learned model pay more attention to complex regions. However, many of them are time-consuming, or can only capture local information [37]. At the same time, these attention modules are usually placed in both the main and the hyper-prior path of image compression network, which will further introduce large complexity because of a large input size for the main path. To overcome that problem, we try to move attention modules to the channel-wise entropy model which has $1/16$ input size compared with that of main path to reduce complexity. Nevertheless, if the above attention modules are directly added to the entropy model, a large number of parameters will be introduced. Therefore, we propose a parameter-efficient swim-transformer-based attention module (SWAtten) with channel squeezing for the channel-wise entropy model. At the same time, to avoid the latency caused by too many slices, we reduce the number of slices from 10 to 5 to achieve the balance between running speed and RD-performance. As Fig. 1 shows, our method can get pleasant results compared with other methods.", + "bbox": [ + 75, + 272, + 470, + 603 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The contributions of this paper can be summarized as follows:", + "bbox": [ + 76, + 604, + 468, + 633 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a LIC framework with parallel transformer-CNN mixture (TCM) blocks that efficiently incorporate the local modeling ability of CNN and the non-local modeling ability of transformers, while maintaining controllable complexity.", + "- We design a channel-wise auto-regressive entropy model by proposing a parameter-efficient swin-transformer-based attention (SWAtten) module with channel squeezing.", + "- Extensive experiments demonstrate that our approach achieves state-of-the-art (SOTA) performance on three datasets (i.e., Kodak, Tecnick, and CLIC datasets) with different resolutions. The method outperforms VVC (VTM-12.1) by $12.30\\%$ , $13.71\\%$ , $11.85\\%$ in Bjøntegaard-delta-rate (BD-rate) [4] on Kodak, Tecnick, and CLIC datasets, respectively." + ], + "bbox": [ + 94, + 641, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 89, + 640, + 104 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Learned end-to-end Image Compression", + "text_level": 1, + "bbox": [ + 500, + 113, + 844, + 130 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1.1 CNN-based Models", + "text_level": 1, + "bbox": [ + 500, + 137, + 689, + 151 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In the past decade, learned image compression has made significant progress and demonstrated impressive performance. Balle et al. [2] firstly proposed an end-to-end learned CNN-based image compression model. Then they proposed a VAE architecture and introduced a hyper-prior to improve image compression in [3]. Furthermore, a local context model was utilized to improve the entropy model of image compression in [26]. In addition to that, a causal context was proposed by using global context information in [12]. Since the context model is time-consuming, He et al. [14] designed a checkerboard context model to achieve parallel computing, while Minnen et al. [27] used channelwise context to accelerate the computing. Apart from improving the entropy model, some works attempt to adopt different types of convolutional neural networks to enhance image compression, such as Cheng et al. [6] who developed a residual network. Chen et al. [5] introduced octave residual networks into image compression models, and Xie et al. [34] used invertible neural networks (INNs) to improve performance.", + "bbox": [ + 496, + 161, + 890, + 462 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1.2 Transformer-based Models", + "text_level": 1, + "bbox": [ + 500, + 481, + 741, + 494 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "With the rapid development of vision transformers, transformers show impressive performance on not only high-level vision tasks, such as, image classification [22, 30], but also some low-level vision tasks, such as, image restoration [19], and image denoising [35]. Motivated by those works, some transformer-based LIC models are also proposed recently. Some works [36, 37] tried to construct a swim-transformer-based LIC model. Qian et al. [28] used a ViT [9] to help the entropy model capture global context information. Koyuncu et al. [18] utilized a sliding window to reduce the complexity of ViT in entropy models. Kim et al. [15] proposed an Information Transformer to get both global and local dependencies.", + "bbox": [ + 496, + 505, + 890, + 702 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Attention Modules", + "text_level": 1, + "bbox": [ + 500, + 710, + 679, + 724 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Attention modules try to help the learned models focus on important regions to obtain more details. Many attention modules designed for image compression significantly improve the RD-performance. Liu et al. [21] firstly introduced a non-local attention module into image compression. Because of the non-local block, this attention module is time-consuming. Therefore, Cheng et al. [6] removed this nonlocal block and proposed a local attention module to accelerate the computing. Furthermore, Zou et al. [37] adopted a window-based attention module to improve image compression.", + "bbox": [ + 496, + 734, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "14389", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/959cc91f386162a422030cc77380c6a49b58590cdc2267f64b580a8d768fad81.jpg", + "image_caption": [ + "Figure 2. The overall framework of our method (left) and the proposed TCM block (right), enc and dec contain the processes of quantizing and range coding. $\\uparrow 2$ or $\\downarrow 2$ means that the feature size is enlarged/reduced by two times compared to the previous layer." + ], + "image_footnote": [], + "bbox": [ + 89, + 93, + 854, + 247 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Proposed Method", + "text_level": 1, + "bbox": [ + 76, + 311, + 250, + 329 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Problem Formulation", + "text_level": 1, + "bbox": [ + 76, + 337, + 279, + 352 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As Fig.2 shows, the LIC models with a channel-wise entropy model [27] can be formulated by:", + "bbox": [ + 75, + 361, + 468, + 391 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {y} = g _ {a} (\\boldsymbol {x}; \\phi)\n$$\n", + "text_format": "latex", + "bbox": [ + 202, + 404, + 300, + 420 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\boldsymbol {y}} = Q (\\boldsymbol {y} - \\boldsymbol {\\mu}) + \\boldsymbol {\\mu} \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 204, + 422, + 468, + 439 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\boldsymbol {x}} = g _ {s} (\\hat {\\boldsymbol {y}}; \\boldsymbol {\\theta})\n$$\n", + "text_format": "latex", + "bbox": [ + 204, + 441, + 295, + 458 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\pmb{x}$ and $\\hat{\\pmb{x}}$ represent the raw images and decompressed images. By inputting $\\pmb{x}$ to the encoder $g_{a}$ with learned parameters $\\phi$ , we can get the latent representation $\\pmb{y}$ which is estimated to have a mean $\\pmb{\\mu}$ . To encode it, $\\pmb{y}$ is quantized to $\\hat{\\pmb{y}}$ by quantization operator $Q$ . According to previous works [13, 26] and discussion1, we round and encode each $\\lceil \\pmb{y} - \\pmb{\\mu} \\rceil$ to the bitstream instead of $\\lceil \\pmb{y} \\rceil$ and restore the coding-symbol $\\hat{\\pmb{y}}$ as $\\lceil \\pmb{y} - \\pmb{\\mu} \\rceil + \\pmb{\\mu}$ , which can further benefit entropy models. Then, we use range coder to encode losslessly $\\lceil \\pmb{y} - \\pmb{\\mu} \\rceil$ which is modeled as a single Gaussian distribution with the variance $\\sigma$ to bitstreams, and transmit it to decoder $g_{s}$ . In this overall pipeline, $\\Phi = (\\pmb{\\mu},\\pmb{\\sigma})$ in this paper is derived by a channel-wise entropy model as Equation 2, Fig. 2 and Fig. 4 show. The entropy model of [27] divides $\\pmb{y}$ to $s$ even slices $\\{\\pmb{y}_0,\\pmb{y}_1,\\dots,\\pmb{y}_{s-1}\\}$ so that the encoded slices can help improve the encoding of subsequent slices, we formulate it as:", + "bbox": [ + 75, + 469, + 468, + 724 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {z} = h _ {a} \\left(\\boldsymbol {y}; \\phi_ {h}\\right), \\quad \\hat {\\boldsymbol {z}} = Q (\\boldsymbol {z})\n$$\n", + "text_format": "latex", + "bbox": [ + 119, + 734, + 318, + 750 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {F} _ {\\text {m e a n}}, \\mathcal {F} _ {\\text {s c a l e}} = h _ {s} (\\hat {z}; \\boldsymbol {\\theta} _ {h})\n$$\n", + "text_format": "latex", + "bbox": [ + 129, + 753, + 320, + 768 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {r} _ {i}, \\Phi_ {i} = e _ {i} \\left(\\boldsymbol {\\mathcal {F}} _ {\\text {m e a n}}, \\boldsymbol {\\mathcal {F}} _ {\\text {s c a l e}}, \\bar {\\boldsymbol {y}} _ {< i}, \\boldsymbol {y} _ {i}\\right), 0 < = i < s \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 94, + 771, + 468, + 787 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\overline {{\\boldsymbol {y}}} _ {i} = \\boldsymbol {r} _ {i} + \\hat {\\boldsymbol {y}} _ {i}\n$$\n", + "text_format": "latex", + "bbox": [ + 215, + 791, + 305, + 806 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $h_a$ denotes the hyper-prior encoder with parameters $\\phi_h$ . It is used to get side information $z$ to capture spatial dependencies among the elements of $y$ . A factorized density", + "bbox": [ + 76, + 819, + 468, + 864 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "model $\\psi$ is used to encode quantized $\\hat{z}$ as $p_{\\hat{z}|\\psi}(\\hat{z} \\mid \\psi) = \\prod_{j} (p_{z_j|\\psi}(\\psi) * \\mathcal{U}(-\\frac{1}{2}, \\frac{1}{2})) (\\hat{z}_j)$ where $j$ specifies the position of each element or each signal. $\\hat{z}$ is then fed to the hyper-prior decoder $h_s$ with parameters $\\theta_h$ for decoding to obtain two latent features $\\mathcal{F}_{mean}$ , $\\mathcal{F}_{scale}$ which are used to be input to the following each slice network $e_i$ . After that, each slice $y_i$ is sequentially processed to get $\\overline{y}_i$ . During this process, encoded slices $\\overline{y}_{MethodsEncoding Time(/ms)Decoding Time(/ms)Para-meters(/M)FLOPs (/G)BD-rateXie et al. [34]2346521247.55408.21-1.65SwinT_ChARM [36]1328460.55230.37-4.02Ours (Large, w/o squeeze)151141160.45830.90-12.54Ours(Large)15014075.89700.96-12.30Ours(Medium)13012258.72415.20-9.65Ours(Small)10910244.96211.54-7.39", + "bbox": [ + 501, + 220, + 908, + 369 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.6. Visualization", + "text_level": 1, + "bbox": [ + 500, + 392, + 635, + 406 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Fig. 1 shows the visualization example of decompressed images (kodim23) from Kodak dataset by our methods and the classical compression standards WebP, VVC (VTM 12.1) [29]. In some complex texture parts, our methods can keep more details (clearer feather outline).", + "bbox": [ + 498, + 417, + 890, + 492 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 511, + 617, + 526 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we incorporate transformers and CNN to propose an efficient parallel transformer-CNN mixture block that utilizes the local modeling ability of CNN and the non-local modeling ability of transformers. Then, a new image compression architecture is designed based on the TCM block. Besides, we present a swin-transformer-based attention module to improve channel-wise entropy models. The results of experiments show that the image compression model with TCM blocks outperforms the CNN-only/Transformer-only based models under a suitable complexity. Furthermore, the performance of SWAtten surpasses previous attention modules designed for image compression. At last, our method achieves state-of-the-art on three different resolution datasets (i.e., Kodak, Tecnick, CLIC Professional Validation) and is superior to existing image compression methods.", + "bbox": [ + 496, + 537, + 890, + 779 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Acknowledgment", + "text_level": 1, + "bbox": [ + 500, + 797, + 669, + 815 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This paper is supported by Japan Science and Technology Agency (JST), under Grant JPMJPR19M5; Japan Society for the Promotion of Science (JSPS), under Grant 21K17770; Kenjiro Takayanagi Foundation; the Foundation of Ando Laboratory; NICT, Grant Number 03801, Japan.", + "bbox": [ + 496, + 825, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "14395", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Nicola Asuni and Andrea Giachetti. Testimages: a largescale archive for testing visual devices and basic image processing algorithms. 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Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, 2022. 1, 2, 4, 7, 8" + ], + "bbox": [ + 78, + 90, + 467, + 515 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "14397", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Learned Image Compression With Mixed Transformer-CNN Architectures/7db49ad4-b6a9-4b40-bd7f-3899bfab9dd5_model.json b/2023/Learned Image Compression With Mixed Transformer-CNN Architectures/7db49ad4-b6a9-4b40-bd7f-3899bfab9dd5_model.json new file mode 100644 index 0000000000000000000000000000000000000000..fac030bca29cd9b9216c4ffcaef3f3f9d661b67b --- /dev/null +++ b/2023/Learned Image Compression With Mixed Transformer-CNN Architectures/7db49ad4-b6a9-4b40-bd7f-3899bfab9dd5_model.json @@ -0,0 +1,2321 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.111, + 0.131, + 0.861, + 0.154 + ], + "angle": 0, + "content": "Learned Image Compression with Mixed Transformer-CNN Architectures" + }, + { + "type": "text", + "bbox": [ + 0.278, + 0.18, + 0.692, + 0.2 + ], + "angle": 0, + "content": "Jinming Liu14 Heming Sun23* Jiro Katto12" + }, + { + "type": "text", + "bbox": [ + 0.148, + 0.201, + 0.823, + 0.234 + ], + "angle": 0, + "content": "\\(^{1}\\)Department of Computer Science and Communication Engineering, Waseda University, Tokyo, Japan \n\\(^{2}\\)Waseda Research Institute for Science and Engineering, Waseda University, Tokyo, Japan" + }, + { + "type": "text", + "bbox": [ + 0.109, + 0.235, + 0.862, + 0.253 + ], + "angle": 0, + "content": "\\(^{3}\\)JST PRESTO, 4-1-8 Honcho, Kawaguchi, Saitama, Japan \\(^{4}\\) Shanghai Jiao Tong University, Shanghai, China" + }, + { + "type": "text", + "bbox": [ + 0.328, + 0.254, + 0.642, + 0.27 + ], + "angle": 0, + "content": "{jmliu@toki., hemingsun@aoni., katto@}waseda.jp" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.305, + 0.314, + 0.321 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.336, + 0.474, + 0.699 + ], + "angle": 0, + "content": "Learned image compression (LIC) methods have exhibited promising progress and superior rate-distortion performance compared with classical image compression standards. Most existing LIC methods are Convolutional Neural Networks-based (CNN-based) or Transformer-based, which have different advantages. Exploiting both advantages is a point worth exploring, which has two challenges: 1) how to effectively fuse the two methods? 2) how to achieve higher performance with a suitable complexity? In this paper, we propose an efficient parallel Transformer-CNN Mixture (TCM) block with a controllable complexity to incorporate the local modeling ability of CNN and the non-local modeling ability of transformers to improve the overall architecture of image compression models. Besides, inspired by the recent progress of entropy estimation models and attention modules, we propose a channel-wise entropy model with parameter-efficient swin-transformer-based attention (SWAtten) modules by using channel squeezing. Experimental results demonstrate our proposed method achieves state-of-the-art rate-distortion performances on three different resolution datasets (i.e., Kodak, Tecnick, CLIC Professional Validation) compared to existing LIC methods. The code is at https://github.com/jmliu206/LIC_TCM." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.719, + 0.21, + 0.735 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.744, + 0.47, + 0.88 + ], + "angle": 0, + "content": "Image compression is a crucial topic in the field of image processing. With the rapidly increasing image data, lossy image compression plays an important role in storing and transmitting efficiently. In the passing decades, there were many classical standards, including JPEG [31], WebP [11], and VVC [29], which contain three steps: transform, quantization, and entropy coding, have achieved impressive Rate-Distortion (RD) performance. On the other hand, different from the classical standards, end-to-end learned" + }, + { + "type": "image", + "bbox": [ + 0.523, + 0.305, + 0.753, + 0.414 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.521, + 0.414, + 0.637, + 0.456 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.545, + 0.456, + 0.603, + 0.463 + ], + "angle": 0, + "content": "VVC (VTM-12.1)" + }, + { + "type": "image_caption", + "bbox": [ + 0.522, + 0.463, + 0.625, + 0.471 + ], + "angle": 0, + "content": "0.131bpp|34.69dB|15.04dB" + }, + { + "type": "image", + "bbox": [ + 0.64, + 0.414, + 0.754, + 0.456 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.659, + 0.456, + 0.71, + 0.463 + ], + "angle": 0, + "content": "WebP" + }, + { + "type": "image_caption", + "bbox": [ + 0.646, + 0.463, + 0.75, + 0.471 + ], + "angle": 0, + "content": "0.180bpp|30.77dB|12.47dB" + }, + { + "type": "image", + "bbox": [ + 0.758, + 0.307, + 0.872, + 0.348 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.791, + 0.348, + 0.842, + 0.356 + ], + "angle": 0, + "content": "Ground Truth" + }, + { + "type": "image", + "bbox": [ + 0.759, + 0.357, + 0.872, + 0.398 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.799, + 0.398, + 0.842, + 0.405 + ], + "angle": 0, + "content": "Ours [MSE]" + }, + { + "type": "image_caption", + "bbox": [ + 0.768, + 0.406, + 0.871, + 0.413 + ], + "angle": 0, + "content": "0.127bpp|35.78dB|16.25dB" + }, + { + "type": "image", + "bbox": [ + 0.759, + 0.414, + 0.872, + 0.455 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.792, + 0.456, + 0.849, + 0.462 + ], + "angle": 0, + "content": "Ours [MS-SSIM]" + }, + { + "type": "image_caption", + "bbox": [ + 0.768, + 0.463, + 0.871, + 0.471 + ], + "angle": 0, + "content": "0.114bpp|30.81dB|17.07dB" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.481, + 0.895, + 0.524 + ], + "angle": 0, + "content": "Figure 1. Visualization of decompressed images of \\( \\text{kodim}23 \\) from Kodak dataset based on different methods (The subfigure is titled as \"Method|Bit rate|PSNR|MS-SSIM\")." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.538, + 0.892, + 0.644 + ], + "angle": 0, + "content": "image compression (LIC) is optimized as a whole. Some very recent LIC works [5, 13, 32, 34, 36, 37] have outperformed VVC which is the best classical image and video coding standards at present, on both Peak signal-to-noise ratio (PSNR) and Multi-Scale Structural Similarity (MS-SSIM). This suggests that LIC has great potential for next-generation image compression techniques." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.645, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Most LIC methods are CNN-based methods [6, 10, 20, 21, 33] using the variational auto-encoder (VAE) which is proposed by Balle et al. [3]. With the development of vision transformers [9,22] recently, some vision transformer-based LIC methods [23, 36, 37] are also investigated. For CNN-based example, Cheng et al. [6] proposed a residual block-based image compression model. For transformer-based example, Zou et al. [37] tried a swin-transformer-based image compression model. These two kinds of methods have different advantages. CNN has the ability of local modeling, while transformers have the ability to model non-local information. It is still worth exploring whether the advantages of these two methods can be effectively combined with a suitable complexity. In our method, we try to efficiently incorporate both advantages of CNN and transformers by proposing an efficient parallel Transformer-CNN Mixture (TCM) block under a controllable complexity to improve" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.32, + 0.9 + ], + "angle": 0, + "content": "*Heming Sun is the corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "14388" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.269, + 0.106 + ], + "angle": 0, + "content": "the RD performance of LIC." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.107, + 0.47, + 0.272 + ], + "angle": 0, + "content": "In addition to the type of the neural network, the design of entropy model is also an important technique in LIC. The most common way is to introduce extra latent variables as hyper-prior to convert the probability model of compact coding-symbols to a joint model [3]. On that basis, many methods spring up. Minnen et al. [26] utilized the masked convolutional layer to capture the context information. Furthermore, they [27] proposed a parallel channel-wise autoregressive entropy model by splitting the latent to 10 slices. The results of encoded slices can assist in the encoding of remaining slices in a pipeline manner." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.273, + 0.471, + 0.604 + ], + "angle": 0, + "content": "Recently, many different attention modules [6, 21, 37] were designed and proposed to improve image compression. Attention modules can help the learned model pay more attention to complex regions. However, many of them are time-consuming, or can only capture local information [37]. At the same time, these attention modules are usually placed in both the main and the hyper-prior path of image compression network, which will further introduce large complexity because of a large input size for the main path. To overcome that problem, we try to move attention modules to the channel-wise entropy model which has \\(1/16\\) input size compared with that of main path to reduce complexity. Nevertheless, if the above attention modules are directly added to the entropy model, a large number of parameters will be introduced. Therefore, we propose a parameter-efficient swim-transformer-based attention module (SWAtten) with channel squeezing for the channel-wise entropy model. At the same time, to avoid the latency caused by too many slices, we reduce the number of slices from 10 to 5 to achieve the balance between running speed and RD-performance. As Fig. 1 shows, our method can get pleasant results compared with other methods." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.605, + 0.47, + 0.634 + ], + "angle": 0, + "content": "The contributions of this paper can be summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.642, + 0.47, + 0.718 + ], + "angle": 0, + "content": "- We propose a LIC framework with parallel transformer-CNN mixture (TCM) blocks that efficiently incorporate the local modeling ability of CNN and the non-local modeling ability of transformers, while maintaining controllable complexity." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.727, + 0.469, + 0.787 + ], + "angle": 0, + "content": "- We design a channel-wise auto-regressive entropy model by proposing a parameter-efficient swin-transformer-based attention (SWAtten) module with channel squeezing." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.795, + 0.469, + 0.901 + ], + "angle": 0, + "content": "- Extensive experiments demonstrate that our approach achieves state-of-the-art (SOTA) performance on three datasets (i.e., Kodak, Tecnick, and CLIC datasets) with different resolutions. The method outperforms VVC (VTM-12.1) by \\(12.30\\%\\), \\(13.71\\%\\), \\(11.85\\%\\) in Bjøntegaard-delta-rate (BD-rate) [4] on Kodak, Tecnick, and CLIC datasets, respectively." + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.642, + 0.47, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.09, + 0.642, + 0.106 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.114, + 0.845, + 0.131 + ], + "angle": 0, + "content": "2.1. Learned end-to-end Image Compression" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.138, + 0.691, + 0.152 + ], + "angle": 0, + "content": "2.1.1 CNN-based Models" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.162, + 0.892, + 0.463 + ], + "angle": 0, + "content": "In the past decade, learned image compression has made significant progress and demonstrated impressive performance. Balle et al. [2] firstly proposed an end-to-end learned CNN-based image compression model. Then they proposed a VAE architecture and introduced a hyper-prior to improve image compression in [3]. Furthermore, a local context model was utilized to improve the entropy model of image compression in [26]. In addition to that, a causal context was proposed by using global context information in [12]. Since the context model is time-consuming, He et al. [14] designed a checkerboard context model to achieve parallel computing, while Minnen et al. [27] used channelwise context to accelerate the computing. Apart from improving the entropy model, some works attempt to adopt different types of convolutional neural networks to enhance image compression, such as Cheng et al. [6] who developed a residual network. Chen et al. [5] introduced octave residual networks into image compression models, and Xie et al. [34] used invertible neural networks (INNs) to improve performance." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.482, + 0.743, + 0.496 + ], + "angle": 0, + "content": "2.1.2 Transformer-based Models" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.506, + 0.892, + 0.703 + ], + "angle": 0, + "content": "With the rapid development of vision transformers, transformers show impressive performance on not only high-level vision tasks, such as, image classification [22, 30], but also some low-level vision tasks, such as, image restoration [19], and image denoising [35]. Motivated by those works, some transformer-based LIC models are also proposed recently. Some works [36, 37] tried to construct a swim-transformer-based LIC model. Qian et al. [28] used a ViT [9] to help the entropy model capture global context information. Koyuncu et al. [18] utilized a sliding window to reduce the complexity of ViT in entropy models. Kim et al. [15] proposed an Information Transformer to get both global and local dependencies." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.712, + 0.681, + 0.726 + ], + "angle": 0, + "content": "2.2. Attention Modules" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Attention modules try to help the learned models focus on important regions to obtain more details. Many attention modules designed for image compression significantly improve the RD-performance. Liu et al. [21] firstly introduced a non-local attention module into image compression. Because of the non-local block, this attention module is time-consuming. Therefore, Cheng et al. [6] removed this nonlocal block and proposed a local attention module to accelerate the computing. Furthermore, Zou et al. [37] adopted a window-based attention module to improve image compression." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "14389" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.091, + 0.094, + 0.856, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.266, + 0.895, + 0.297 + ], + "angle": 0, + "content": "Figure 2. The overall framework of our method (left) and the proposed TCM block (right), enc and dec contain the processes of quantizing and range coding. \\(\\uparrow 2\\) or \\(\\downarrow 2\\) means that the feature size is enlarged/reduced by two times compared to the previous layer." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.313, + 0.251, + 0.33 + ], + "angle": 0, + "content": "3. Proposed Method" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.338, + 0.281, + 0.353 + ], + "angle": 0, + "content": "3.1. Problem Formulation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.362, + 0.47, + 0.392 + ], + "angle": 0, + "content": "As Fig.2 shows, the LIC models with a channel-wise entropy model [27] can be formulated by:" + }, + { + "type": "equation", + "bbox": [ + 0.204, + 0.405, + 0.301, + 0.421 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {y} = g _ {a} (\\boldsymbol {x}; \\phi)\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.205, + 0.424, + 0.47, + 0.44 + ], + "angle": 0, + "content": "\\[\n\\hat {\\boldsymbol {y}} = Q (\\boldsymbol {y} - \\boldsymbol {\\mu}) + \\boldsymbol {\\mu} \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.205, + 0.442, + 0.297, + 0.459 + ], + "angle": 0, + "content": "\\[\n\\hat {\\boldsymbol {x}} = g _ {s} (\\hat {\\boldsymbol {y}}; \\boldsymbol {\\theta})\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.47, + 0.47, + 0.726 + ], + "angle": 0, + "content": "where \\( \\pmb{x} \\) and \\( \\hat{\\pmb{x}} \\) represent the raw images and decompressed images. By inputting \\( \\pmb{x} \\) to the encoder \\( g_{a} \\) with learned parameters \\( \\phi \\), we can get the latent representation \\( \\pmb{y} \\) which is estimated to have a mean \\( \\pmb{\\mu} \\). To encode it, \\( \\pmb{y} \\) is quantized to \\( \\hat{\\pmb{y}} \\) by quantization operator \\( Q \\). According to previous works [13, 26] and discussion1, we round and encode each \\( \\lceil \\pmb{y} - \\pmb{\\mu} \\rceil \\) to the bitstream instead of \\( \\lceil \\pmb{y} \\rceil \\) and restore the coding-symbol \\( \\hat{\\pmb{y}} \\) as \\( \\lceil \\pmb{y} - \\pmb{\\mu} \\rceil + \\pmb{\\mu} \\), which can further benefit entropy models. Then, we use range coder to encode losslessly \\( \\lceil \\pmb{y} - \\pmb{\\mu} \\rceil \\) which is modeled as a single Gaussian distribution with the variance \\( \\sigma \\) to bitstreams, and transmit it to decoder \\( g_{s} \\). In this overall pipeline, \\( \\Phi = (\\pmb{\\mu},\\pmb{\\sigma}) \\) in this paper is derived by a channel-wise entropy model as Equation 2, Fig. 2 and Fig. 4 show. The entropy model of [27] divides \\( \\pmb{y} \\) to \\( s \\) even slices \\( \\{\\pmb{y}_0,\\pmb{y}_1,\\dots,\\pmb{y}_{s-1}\\} \\) so that the encoded slices can help improve the encoding of subsequent slices, we formulate it as:" + }, + { + "type": "equation", + "bbox": [ + 0.12, + 0.735, + 0.319, + 0.751 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {z} = h _ {a} \\left(\\boldsymbol {y}; \\phi_ {h}\\right), \\quad \\hat {\\boldsymbol {z}} = Q (\\boldsymbol {z})\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.13, + 0.754, + 0.321, + 0.77 + ], + "angle": 0, + "content": "\\[\n\\mathcal {F} _ {\\text {m e a n}}, \\mathcal {F} _ {\\text {s c a l e}} = h _ {s} (\\hat {z}; \\boldsymbol {\\theta} _ {h})\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.096, + 0.772, + 0.47, + 0.789 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {r} _ {i}, \\Phi_ {i} = e _ {i} \\left(\\boldsymbol {\\mathcal {F}} _ {\\text {m e a n}}, \\boldsymbol {\\mathcal {F}} _ {\\text {s c a l e}}, \\bar {\\boldsymbol {y}} _ {< i}, \\boldsymbol {y} _ {i}\\right), 0 < = i < s \\tag {2}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.216, + 0.792, + 0.307, + 0.807 + ], + "angle": 0, + "content": "\\[\n\\overline {{\\boldsymbol {y}}} _ {i} = \\boldsymbol {r} _ {i} + \\hat {\\boldsymbol {y}} _ {i}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.82, + 0.469, + 0.866 + ], + "angle": 0, + "content": "where \\( h_a \\) denotes the hyper-prior encoder with parameters \\( \\phi_h \\). It is used to get side information \\( z \\) to capture spatial dependencies among the elements of \\( y \\). A factorized density" + }, + { + "type": "page_footnote", + "bbox": [ + 0.078, + 0.875, + 0.469, + 0.9 + ], + "angle": 0, + "content": "1https://groups.google.com/g/tensorflow-compression/c/LQtTAo6l26U/m/mxP-VWpDAgAJ" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.313, + 0.892, + 0.587 + ], + "angle": 0, + "content": "model \\(\\psi\\) is used to encode quantized \\(\\hat{z}\\) as \\(p_{\\hat{z}|\\psi}(\\hat{z} \\mid \\psi) = \\prod_{j} (p_{z_j|\\psi}(\\psi) * \\mathcal{U}(-\\frac{1}{2}, \\frac{1}{2})) (\\hat{z}_j)\\) where \\(j\\) specifies the position of each element or each signal. \\(\\hat{z}\\) is then fed to the hyper-prior decoder \\(h_s\\) with parameters \\(\\theta_h\\) for decoding to obtain two latent features \\(\\mathcal{F}_{mean}\\), \\(\\mathcal{F}_{scale}\\) which are used to be input to the following each slice network \\(e_i\\). After that, each slice \\(y_i\\) is sequentially processed to get \\(\\overline{y}_i\\). During this process, encoded slices \\(\\overline{y}_{MethodsEncoding Time(/ms)Decoding Time(/ms)Para-meters(/M)FLOPs (/G)BD-rateXie et al. [34]2346521247.55408.21-1.65SwinT_ChARM [36]1328460.55230.37-4.02Ours (Large, w/o squeeze)151141160.45830.90-12.54Ours(Large)15014075.89700.96-12.30Ours(Medium)13012258.72415.20-9.65Ours(Small)10910244.96211.54-7.39" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.393, + 0.637, + 0.407 + ], + "angle": 0, + "content": "4.6. Visualization" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.418, + 0.892, + 0.493 + ], + "angle": 0, + "content": "Fig. 1 shows the visualization example of decompressed images (kodim23) from Kodak dataset by our methods and the classical compression standards WebP, VVC (VTM 12.1) [29]. In some complex texture parts, our methods can keep more details (clearer feather outline)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.512, + 0.619, + 0.527 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.539, + 0.892, + 0.78 + ], + "angle": 0, + "content": "In this paper, we incorporate transformers and CNN to propose an efficient parallel transformer-CNN mixture block that utilizes the local modeling ability of CNN and the non-local modeling ability of transformers. Then, a new image compression architecture is designed based on the TCM block. Besides, we present a swin-transformer-based attention module to improve channel-wise entropy models. The results of experiments show that the image compression model with TCM blocks outperforms the CNN-only/Transformer-only based models under a suitable complexity. Furthermore, the performance of SWAtten surpasses previous attention modules designed for image compression. At last, our method achieves state-of-the-art on three different resolution datasets (i.e., Kodak, Tecnick, CLIC Professional Validation) and is superior to existing image compression methods." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.799, + 0.671, + 0.816 + ], + "angle": 0, + "content": "6. Acknowledgment" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.901 + ], + "angle": 0, + "content": "This paper is supported by Japan Science and Technology Agency (JST), under Grant JPMJPR19M5; Japan Society for the Promotion of Science (JSPS), under Grant 21K17770; Kenjiro Takayanagi Foundation; the Foundation of Ando Laboratory; NICT, Grant Number 03801, Japan." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14395" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.469, + 0.157 + ], + "angle": 0, + "content": "[1] Nicola Asuni and Andrea Giachetti. Testimages: a largescale archive for testing visual devices and basic image processing algorithms. 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Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, 2022. 1, 2, 4, 7, 8" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.468, + 0.516 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.956 + ], + "angle": 0, + "content": "14397" + } + ] +] \ No newline at end of file diff --git a/2023/Learned Image Compression With Mixed Transformer-CNN Architectures/7db49ad4-b6a9-4b40-bd7f-3899bfab9dd5_origin.pdf b/2023/Learned Image Compression With Mixed Transformer-CNN Architectures/7db49ad4-b6a9-4b40-bd7f-3899bfab9dd5_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..b33a4390936eb34c3c29044cbf20f9eb799a8366 --- /dev/null +++ b/2023/Learned Image Compression With Mixed Transformer-CNN Architectures/7db49ad4-b6a9-4b40-bd7f-3899bfab9dd5_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:4f2819b04430ee279f1a3cb49829fd99921ed392469c4703214e9dc0d22c39eb +size 1474257 diff --git a/2023/Learned Image Compression With Mixed Transformer-CNN Architectures/full.md b/2023/Learned Image Compression With Mixed Transformer-CNN Architectures/full.md new file mode 100644 index 0000000000000000000000000000000000000000..685204a8680d57e19821aa68dbd192b04732eb7c --- /dev/null +++ b/2023/Learned Image Compression With Mixed Transformer-CNN Architectures/full.md @@ -0,0 +1,341 @@ +# Learned Image Compression with Mixed Transformer-CNN Architectures + +Jinming Liu14 Heming Sun23* Jiro Katto12 + +$^{1}$ Department of Computer Science and Communication Engineering, Waseda University, Tokyo, Japan + $^{2}$ Waseda Research Institute for Science and Engineering, Waseda University, Tokyo, Japan + +$^{3}$ JST PRESTO, 4-1-8 Honcho, Kawaguchi, Saitama, Japan $^{4}$ Shanghai Jiao Tong University, Shanghai, China + +{jmliu@toki., hemingsun@aoni., katto@}waseda.jp + +# Abstract + +Learned image compression (LIC) methods have exhibited promising progress and superior rate-distortion performance compared with classical image compression standards. Most existing LIC methods are Convolutional Neural Networks-based (CNN-based) or Transformer-based, which have different advantages. Exploiting both advantages is a point worth exploring, which has two challenges: 1) how to effectively fuse the two methods? 2) how to achieve higher performance with a suitable complexity? In this paper, we propose an efficient parallel Transformer-CNN Mixture (TCM) block with a controllable complexity to incorporate the local modeling ability of CNN and the non-local modeling ability of transformers to improve the overall architecture of image compression models. Besides, inspired by the recent progress of entropy estimation models and attention modules, we propose a channel-wise entropy model with parameter-efficient swin-transformer-based attention (SWAtten) modules by using channel squeezing. Experimental results demonstrate our proposed method achieves state-of-the-art rate-distortion performances on three different resolution datasets (i.e., Kodak, Tecnick, CLIC Professional Validation) compared to existing LIC methods. The code is at https://github.com/jmliu206/LIC_TCM. + +# 1. Introduction + +Image compression is a crucial topic in the field of image processing. With the rapidly increasing image data, lossy image compression plays an important role in storing and transmitting efficiently. In the passing decades, there were many classical standards, including JPEG [31], WebP [11], and VVC [29], which contain three steps: transform, quantization, and entropy coding, have achieved impressive Rate-Distortion (RD) performance. On the other hand, different from the classical standards, end-to-end learned + +![](images/cb53080d4fdc672dc93e7ddd1bd441deda417378d7afe8625d050edc51edcc7f.jpg) + +![](images/cc5c8f9aca837ecbd50da36c042bfa9ed35a2d14a52dbcfc8e9bf58474a747dc.jpg) +VVC (VTM-12.1) +0.131bpp|34.69dB|15.04dB +Figure 1. Visualization of decompressed images of $\text{kodim}23$ from Kodak dataset based on different methods (The subfigure is titled as "Method|Bit rate|PSNR|MS-SSIM"). + +![](images/abb58a60eb080962196bd55bb276aaef7b744785ac2478c4780d38a5130e1a21.jpg) +WebP +0.180bpp|30.77dB|12.47dB + +![](images/289a2381fd340c491775ec5cae69c470aab79b690be24e496cb887788f2253fc.jpg) +Ground Truth + +![](images/928aed40cc6b770b8b3c0aa78d60923d90ae2b4e39105c9cfa04f99798504bcf.jpg) +Ours [MSE] + +![](images/55f7dfecea3d37d84d7c90cf59020daed73ca25ed7605f6ad56d44b4d6a93a01.jpg) +0.127bpp|35.78dB|16.25dB +Ours [MS-SSIM] +0.114bpp|30.81dB|17.07dB + +image compression (LIC) is optimized as a whole. Some very recent LIC works [5, 13, 32, 34, 36, 37] have outperformed VVC which is the best classical image and video coding standards at present, on both Peak signal-to-noise ratio (PSNR) and Multi-Scale Structural Similarity (MS-SSIM). This suggests that LIC has great potential for next-generation image compression techniques. + +Most LIC methods are CNN-based methods [6, 10, 20, 21, 33] using the variational auto-encoder (VAE) which is proposed by Balle et al. [3]. With the development of vision transformers [9,22] recently, some vision transformer-based LIC methods [23, 36, 37] are also investigated. For CNN-based example, Cheng et al. [6] proposed a residual block-based image compression model. For transformer-based example, Zou et al. [37] tried a swin-transformer-based image compression model. These two kinds of methods have different advantages. CNN has the ability of local modeling, while transformers have the ability to model non-local information. It is still worth exploring whether the advantages of these two methods can be effectively combined with a suitable complexity. In our method, we try to efficiently incorporate both advantages of CNN and transformers by proposing an efficient parallel Transformer-CNN Mixture (TCM) block under a controllable complexity to improve + +the RD performance of LIC. + +In addition to the type of the neural network, the design of entropy model is also an important technique in LIC. The most common way is to introduce extra latent variables as hyper-prior to convert the probability model of compact coding-symbols to a joint model [3]. On that basis, many methods spring up. Minnen et al. [26] utilized the masked convolutional layer to capture the context information. Furthermore, they [27] proposed a parallel channel-wise autoregressive entropy model by splitting the latent to 10 slices. The results of encoded slices can assist in the encoding of remaining slices in a pipeline manner. + +Recently, many different attention modules [6, 21, 37] were designed and proposed to improve image compression. Attention modules can help the learned model pay more attention to complex regions. However, many of them are time-consuming, or can only capture local information [37]. At the same time, these attention modules are usually placed in both the main and the hyper-prior path of image compression network, which will further introduce large complexity because of a large input size for the main path. To overcome that problem, we try to move attention modules to the channel-wise entropy model which has $1/16$ input size compared with that of main path to reduce complexity. Nevertheless, if the above attention modules are directly added to the entropy model, a large number of parameters will be introduced. Therefore, we propose a parameter-efficient swim-transformer-based attention module (SWAtten) with channel squeezing for the channel-wise entropy model. At the same time, to avoid the latency caused by too many slices, we reduce the number of slices from 10 to 5 to achieve the balance between running speed and RD-performance. As Fig. 1 shows, our method can get pleasant results compared with other methods. + +The contributions of this paper can be summarized as follows: + +- We propose a LIC framework with parallel transformer-CNN mixture (TCM) blocks that efficiently incorporate the local modeling ability of CNN and the non-local modeling ability of transformers, while maintaining controllable complexity. +- We design a channel-wise auto-regressive entropy model by proposing a parameter-efficient swin-transformer-based attention (SWAtten) module with channel squeezing. +- Extensive experiments demonstrate that our approach achieves state-of-the-art (SOTA) performance on three datasets (i.e., Kodak, Tecnick, and CLIC datasets) with different resolutions. The method outperforms VVC (VTM-12.1) by $12.30\%$ , $13.71\%$ , $11.85\%$ in Bjøntegaard-delta-rate (BD-rate) [4] on Kodak, Tecnick, and CLIC datasets, respectively. + +# 2. Related Work + +# 2.1. Learned end-to-end Image Compression + +# 2.1.1 CNN-based Models + +In the past decade, learned image compression has made significant progress and demonstrated impressive performance. Balle et al. [2] firstly proposed an end-to-end learned CNN-based image compression model. Then they proposed a VAE architecture and introduced a hyper-prior to improve image compression in [3]. Furthermore, a local context model was utilized to improve the entropy model of image compression in [26]. In addition to that, a causal context was proposed by using global context information in [12]. Since the context model is time-consuming, He et al. [14] designed a checkerboard context model to achieve parallel computing, while Minnen et al. [27] used channelwise context to accelerate the computing. Apart from improving the entropy model, some works attempt to adopt different types of convolutional neural networks to enhance image compression, such as Cheng et al. [6] who developed a residual network. Chen et al. [5] introduced octave residual networks into image compression models, and Xie et al. [34] used invertible neural networks (INNs) to improve performance. + +# 2.1.2 Transformer-based Models + +With the rapid development of vision transformers, transformers show impressive performance on not only high-level vision tasks, such as, image classification [22, 30], but also some low-level vision tasks, such as, image restoration [19], and image denoising [35]. Motivated by those works, some transformer-based LIC models are also proposed recently. Some works [36, 37] tried to construct a swim-transformer-based LIC model. Qian et al. [28] used a ViT [9] to help the entropy model capture global context information. Koyuncu et al. [18] utilized a sliding window to reduce the complexity of ViT in entropy models. Kim et al. [15] proposed an Information Transformer to get both global and local dependencies. + +# 2.2. Attention Modules + +Attention modules try to help the learned models focus on important regions to obtain more details. Many attention modules designed for image compression significantly improve the RD-performance. Liu et al. [21] firstly introduced a non-local attention module into image compression. Because of the non-local block, this attention module is time-consuming. Therefore, Cheng et al. [6] removed this nonlocal block and proposed a local attention module to accelerate the computing. Furthermore, Zou et al. [37] adopted a window-based attention module to improve image compression. + +![](images/959cc91f386162a422030cc77380c6a49b58590cdc2267f64b580a8d768fad81.jpg) +Figure 2. The overall framework of our method (left) and the proposed TCM block (right), enc and dec contain the processes of quantizing and range coding. $\uparrow 2$ or $\downarrow 2$ means that the feature size is enlarged/reduced by two times compared to the previous layer. + +# 3. Proposed Method + +# 3.1. Problem Formulation + +As Fig.2 shows, the LIC models with a channel-wise entropy model [27] can be formulated by: + +$$ +\boldsymbol {y} = g _ {a} (\boldsymbol {x}; \phi) +$$ + +$$ +\hat {\boldsymbol {y}} = Q (\boldsymbol {y} - \boldsymbol {\mu}) + \boldsymbol {\mu} \tag {1} +$$ + +$$ +\hat {\boldsymbol {x}} = g _ {s} (\hat {\boldsymbol {y}}; \boldsymbol {\theta}) +$$ + +where $\pmb{x}$ and $\hat{\pmb{x}}$ represent the raw images and decompressed images. By inputting $\pmb{x}$ to the encoder $g_{a}$ with learned parameters $\phi$ , we can get the latent representation $\pmb{y}$ which is estimated to have a mean $\pmb{\mu}$ . To encode it, $\pmb{y}$ is quantized to $\hat{\pmb{y}}$ by quantization operator $Q$ . According to previous works [13, 26] and discussion1, we round and encode each $\lceil \pmb{y} - \pmb{\mu} \rceil$ to the bitstream instead of $\lceil \pmb{y} \rceil$ and restore the coding-symbol $\hat{\pmb{y}}$ as $\lceil \pmb{y} - \pmb{\mu} \rceil + \pmb{\mu}$ , which can further benefit entropy models. Then, we use range coder to encode losslessly $\lceil \pmb{y} - \pmb{\mu} \rceil$ which is modeled as a single Gaussian distribution with the variance $\sigma$ to bitstreams, and transmit it to decoder $g_{s}$ . In this overall pipeline, $\Phi = (\pmb{\mu},\pmb{\sigma})$ in this paper is derived by a channel-wise entropy model as Equation 2, Fig. 2 and Fig. 4 show. The entropy model of [27] divides $\pmb{y}$ to $s$ even slices $\{\pmb{y}_0,\pmb{y}_1,\dots,\pmb{y}_{s-1}\}$ so that the encoded slices can help improve the encoding of subsequent slices, we formulate it as: + +$$ +\boldsymbol {z} = h _ {a} \left(\boldsymbol {y}; \phi_ {h}\right), \quad \hat {\boldsymbol {z}} = Q (\boldsymbol {z}) +$$ + +$$ +\mathcal {F} _ {\text {m e a n}}, \mathcal {F} _ {\text {s c a l e}} = h _ {s} (\hat {z}; \boldsymbol {\theta} _ {h}) +$$ + +$$ +\boldsymbol {r} _ {i}, \Phi_ {i} = e _ {i} \left(\boldsymbol {\mathcal {F}} _ {\text {m e a n}}, \boldsymbol {\mathcal {F}} _ {\text {s c a l e}}, \bar {\boldsymbol {y}} _ {< i}, \boldsymbol {y} _ {i}\right), 0 < = i < s \tag {2} +$$ + +$$ +\overline {{\boldsymbol {y}}} _ {i} = \boldsymbol {r} _ {i} + \hat {\boldsymbol {y}} _ {i} +$$ + +where $h_a$ denotes the hyper-prior encoder with parameters $\phi_h$ . It is used to get side information $z$ to capture spatial dependencies among the elements of $y$ . A factorized density + +model $\psi$ is used to encode quantized $\hat{z}$ as $p_{\hat{z}|\psi}(\hat{z} \mid \psi) = \prod_{j} (p_{z_j|\psi}(\psi) * \mathcal{U}(-\frac{1}{2}, \frac{1}{2})) (\hat{z}_j)$ where $j$ specifies the position of each element or each signal. $\hat{z}$ is then fed to the hyper-prior decoder $h_s$ with parameters $\theta_h$ for decoding to obtain two latent features $\mathcal{F}_{mean}$ , $\mathcal{F}_{scale}$ which are used to be input to the following each slice network $e_i$ . After that, each slice $y_i$ is sequentially processed to get $\overline{y}_i$ . During this process, encoded slices $\overline{y}_{MethodsEncoding Time(/ms)Decoding Time(/ms)Para-meters(/M)FLOPs (/G)BD-rateXie et al. [34]2346521247.55408.21-1.65SwinT_ChARM [36]1328460.55230.37-4.02Ours (Large, w/o squeeze)151141160.45830.90-12.54Ours(Large)15014075.89700.96-12.30Ours(Medium)13012258.72415.20-9.65Ours(Small)10910244.96211.54-7.39 + +# 4.6. Visualization + +Fig. 1 shows the visualization example of decompressed images (kodim23) from Kodak dataset by our methods and the classical compression standards WebP, VVC (VTM 12.1) [29]. In some complex texture parts, our methods can keep more details (clearer feather outline). + +# 5. Conclusion + +In this paper, we incorporate transformers and CNN to propose an efficient parallel transformer-CNN mixture block that utilizes the local modeling ability of CNN and the non-local modeling ability of transformers. Then, a new image compression architecture is designed based on the TCM block. Besides, we present a swin-transformer-based attention module to improve channel-wise entropy models. The results of experiments show that the image compression model with TCM blocks outperforms the CNN-only/Transformer-only based models under a suitable complexity. Furthermore, the performance of SWAtten surpasses previous attention modules designed for image compression. At last, our method achieves state-of-the-art on three different resolution datasets (i.e., Kodak, Tecnick, CLIC Professional Validation) and is superior to existing image compression methods. + +# 6. Acknowledgment + +This paper is supported by Japan Science and Technology Agency (JST), under Grant JPMJPR19M5; Japan Society for the Promotion of Science (JSPS), under Grant 21K17770; Kenjiro Takayanagi Foundation; the Foundation of Ando Laboratory; NICT, Grant Number 03801, Japan. + +# References + +[1] Nicola Asuni and Andrea Giachetti. Testimages: a largescale archive for testing visual devices and basic image processing algorithms. In STAG, pages 63-70, 2014. 6 +[2] Johannes Balle, Valero Laparra, and Eero P Simoncelli. End-to-end optimized image compression. In International Conference on Learning Representations, 2016. 2 +[3] Johannes Ballé, David Minnen, Saurabh Singh, Sung Jin Hwang, and Nick Johnston. Variational image compression with a scale hyperprior. 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Practical blind denoising via swin-conv-unet and data synthesis. arXiv preprint arXiv:2203.13278, 2022. 2 +[36] Yinhao Zhu, Yang Yang, and Taco Cohen. Transformer-based transform coding. In International Conference on Learning Representations, 2022. 1, 2, 3, 7, 8 +[37] Renjie Zou, Chunfeng Song, and Zhaoxiang Zhang. The devil is in the details: Window-based attention for image compression. 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Some very recent LIC works [5, 13, 32, 34, 36, 37] have outperformed VVC which is the best classical image and video coding standards at present, on both Peak signal-to-noise ratio (PSNR) and Multi-Scale Structural Similarity (MS-SSIM). This suggests that LIC has great potential for next-generation image compression techniques." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 304, + 510, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 546, + 713 + ], + "type": "text", + "content": "Most LIC methods are CNN-based methods [6, 10, 20, 21, 33] using the variational auto-encoder (VAE) which is proposed by Balle et al. [3]. With the development of vision transformers [9,22] recently, some vision transformer-based LIC methods [23, 36, 37] are also investigated. For CNN-based example, Cheng et al. [6] proposed a residual block-based image compression model. For transformer-based example, Zou et al. [37] tried a swin-transformer-based image compression model. These two kinds of methods have different advantages. CNN has the ability of local modeling, while transformers have the ability to model non-local information. It is still worth exploring whether the advantages of these two methods can be effectively combined with a suitable complexity. In our method, we try to efficiently incorporate both advantages of CNN and transformers by proposing an efficient parallel Transformer-CNN Mixture (TCM) block under a controllable complexity to improve" + } + ] + } + ], + "index": 28 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 195, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 195, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 195, + 712 + ], + "type": "text", + "content": "*Heming Sun is the corresponding author." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "14388" + } + ] + } + ], + "index": 30 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 164, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 164, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 164, + 83 + ], + "type": "text", + "content": "the RD performance of LIC." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 84, + 287, + 215 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 84, + 287, + 215 + ], + "spans": [ + { + "bbox": [ + 46, + 84, + 287, + 215 + ], + "type": "text", + "content": "In addition to the type of the neural network, the design of entropy model is also an important technique in LIC. The most common way is to introduce extra latent variables as hyper-prior to convert the probability model of compact coding-symbols to a joint model [3]. On that basis, many methods spring up. Minnen et al. [26] utilized the masked convolutional layer to capture the context information. Furthermore, they [27] proposed a parallel channel-wise autoregressive entropy model by splitting the latent to 10 slices. The results of encoded slices can assist in the encoding of remaining slices in a pipeline manner." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 216, + 288, + 478 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 216, + 288, + 478 + ], + "spans": [ + { + "bbox": [ + 46, + 216, + 288, + 478 + ], + "type": "text", + "content": "Recently, many different attention modules [6, 21, 37] were designed and proposed to improve image compression. Attention modules can help the learned model pay more attention to complex regions. However, many of them are time-consuming, or can only capture local information [37]. At the same time, these attention modules are usually placed in both the main and the hyper-prior path of image compression network, which will further introduce large complexity because of a large input size for the main path. To overcome that problem, we try to move attention modules to the channel-wise entropy model which has " + }, + { + "bbox": [ + 46, + 216, + 288, + 478 + ], + "type": "inline_equation", + "content": "1/16" + }, + { + "bbox": [ + 46, + 216, + 288, + 478 + ], + "type": "text", + "content": " input size compared with that of main path to reduce complexity. Nevertheless, if the above attention modules are directly added to the entropy model, a large number of parameters will be introduced. Therefore, we propose a parameter-efficient swim-transformer-based attention module (SWAtten) with channel squeezing for the channel-wise entropy model. At the same time, to avoid the latency caused by too many slices, we reduce the number of slices from 10 to 5 to achieve the balance between running speed and RD-performance. As Fig. 1 shows, our method can get pleasant results compared with other methods." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 479, + 287, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 479, + 287, + 502 + ], + "spans": [ + { + "bbox": [ + 47, + 479, + 287, + 502 + ], + "type": "text", + "content": "The contributions of this paper can be summarized as follows:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 58, + 508, + 287, + 713 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 58, + 508, + 287, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 508, + 287, + 568 + ], + "spans": [ + { + "bbox": [ + 58, + 508, + 287, + 568 + ], + "type": "text", + "content": "- We propose a LIC framework with parallel transformer-CNN mixture (TCM) blocks that efficiently incorporate the local modeling ability of CNN and the non-local modeling ability of transformers, while maintaining controllable complexity." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 58, + 575, + 287, + 623 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 575, + 287, + 623 + ], + "spans": [ + { + "bbox": [ + 58, + 575, + 287, + 623 + ], + "type": "text", + "content": "- We design a channel-wise auto-regressive entropy model by proposing a parameter-efficient swin-transformer-based attention (SWAtten) module with channel squeezing." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 58, + 629, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 629, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 629, + 287, + 713 + ], + "type": "text", + "content": "- Extensive experiments demonstrate that our approach achieves state-of-the-art (SOTA) performance on three datasets (i.e., Kodak, Tecnick, and CLIC datasets) with different resolutions. The method outperforms VVC (VTM-12.1) by " + }, + { + "bbox": [ + 58, + 629, + 287, + 713 + ], + "type": "inline_equation", + "content": "12.30\\%" + }, + { + "bbox": [ + 58, + 629, + 287, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 58, + 629, + 287, + 713 + ], + "type": "inline_equation", + "content": "13.71\\%" + }, + { + "bbox": [ + 58, + 629, + 287, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 58, + 629, + 287, + 713 + ], + "type": "inline_equation", + "content": "11.85\\%" + }, + { + "bbox": [ + 58, + 629, + 287, + 713 + ], + "type": "text", + "content": " in Bjøntegaard-delta-rate (BD-rate) [4] on Kodak, Tecnick, and CLIC datasets, respectively." + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 71, + 392, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 71, + 392, + 83 + ], + "spans": [ + { + "bbox": [ + 306, + 71, + 392, + 83 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 90, + 517, + 103 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 90, + 517, + 103 + ], + "spans": [ + { + "bbox": [ + 306, + 90, + 517, + 103 + ], + "type": "text", + "content": "2.1. Learned end-to-end Image Compression" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 109, + 422, + 120 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 109, + 422, + 120 + ], + "spans": [ + { + "bbox": [ + 306, + 109, + 422, + 120 + ], + "type": "text", + "content": "2.1.1 CNN-based Models" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 128, + 545, + 366 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 128, + 545, + 366 + ], + "spans": [ + { + "bbox": [ + 304, + 128, + 545, + 366 + ], + "type": "text", + "content": "In the past decade, learned image compression has made significant progress and demonstrated impressive performance. Balle et al. [2] firstly proposed an end-to-end learned CNN-based image compression model. Then they proposed a VAE architecture and introduced a hyper-prior to improve image compression in [3]. Furthermore, a local context model was utilized to improve the entropy model of image compression in [26]. In addition to that, a causal context was proposed by using global context information in [12]. Since the context model is time-consuming, He et al. [14] designed a checkerboard context model to achieve parallel computing, while Minnen et al. [27] used channelwise context to accelerate the computing. Apart from improving the entropy model, some works attempt to adopt different types of convolutional neural networks to enhance image compression, such as Cheng et al. [6] who developed a residual network. Chen et al. [5] introduced octave residual networks into image compression models, and Xie et al. [34] used invertible neural networks (INNs) to improve performance." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 381, + 454, + 392 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 381, + 454, + 392 + ], + "spans": [ + { + "bbox": [ + 306, + 381, + 454, + 392 + ], + "type": "text", + "content": "2.1.2 Transformer-based Models" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 400, + 545, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 400, + 545, + 556 + ], + "spans": [ + { + "bbox": [ + 304, + 400, + 545, + 556 + ], + "type": "text", + "content": "With the rapid development of vision transformers, transformers show impressive performance on not only high-level vision tasks, such as, image classification [22, 30], but also some low-level vision tasks, such as, image restoration [19], and image denoising [35]. Motivated by those works, some transformer-based LIC models are also proposed recently. Some works [36, 37] tried to construct a swim-transformer-based LIC model. Qian et al. [28] used a ViT [9] to help the entropy model capture global context information. Koyuncu et al. [18] utilized a sliding window to reduce the complexity of ViT in entropy models. Kim et al. [15] proposed an Information Transformer to get both global and local dependencies." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 563, + 416, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 563, + 416, + 574 + ], + "spans": [ + { + "bbox": [ + 306, + 563, + 416, + 574 + ], + "type": "text", + "content": "2.2. Attention Modules" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": "Attention modules try to help the learned models focus on important regions to obtain more details. Many attention modules designed for image compression significantly improve the RD-performance. Liu et al. [21] firstly introduced a non-local attention module into image compression. Because of the non-local block, this attention module is time-consuming. Therefore, Cheng et al. [6] removed this nonlocal block and proposed a local attention module to accelerate the computing. Furthermore, Zou et al. [37] adopted a window-based attention module to improve image compression." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "14389" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 55, + 74, + 523, + 196 + ], + "blocks": [ + { + "bbox": [ + 55, + 74, + 523, + 196 + ], + "lines": [ + { + "bbox": [ + 55, + 74, + 523, + 196 + ], + "spans": [ + { + "bbox": [ + 55, + 74, + 523, + 196 + ], + "type": "image", + "image_path": "959cc91f386162a422030cc77380c6a49b58590cdc2267f64b580a8d768fad81.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 210, + 547, + 235 + ], + "lines": [ + { + "bbox": [ + 46, + 210, + 547, + 235 + ], + "spans": [ + { + "bbox": [ + 46, + 210, + 547, + 235 + ], + "type": "text", + "content": "Figure 2. The overall framework of our method (left) and the proposed TCM block (right), enc and dec contain the processes of quantizing and range coding. " + }, + { + "bbox": [ + 46, + 210, + 547, + 235 + ], + "type": "inline_equation", + "content": "\\uparrow 2" + }, + { + "bbox": [ + 46, + 210, + 547, + 235 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 46, + 210, + 547, + 235 + ], + "type": "inline_equation", + "content": "\\downarrow 2" + }, + { + "bbox": [ + 46, + 210, + 547, + 235 + ], + "type": "text", + "content": " means that the feature size is enlarged/reduced by two times compared to the previous layer." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 247, + 153, + 261 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 247, + 153, + 261 + ], + "spans": [ + { + "bbox": [ + 47, + 247, + 153, + 261 + ], + "type": "text", + "content": "3. 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Problem Formulation" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 286, + 287, + 310 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 286, + 287, + 310 + ], + "spans": [ + { + "bbox": [ + 46, + 286, + 287, + 310 + ], + "type": "text", + "content": "As Fig.2 shows, the LIC models with a channel-wise entropy model [27] can be formulated by:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 124, + 320, + 184, + 333 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 124, + 320, + 184, + 333 + ], + "spans": [ + { + "bbox": [ + 124, + 320, + 184, + 333 + ], + "type": "interline_equation", + "content": "\\boldsymbol {y} = g _ {a} (\\boldsymbol {x}; \\phi)", + "image_path": "28a772857fd3b395a4c6540fa3c2cc223c80fc5eeda047ccb692e79c71f6563e.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 125, + 335, + 287, + 348 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 125, + 335, + 287, + 348 + ], + "spans": [ + { + "bbox": [ + 125, + 335, + 287, + 348 + ], + "type": "interline_equation", + "content": "\\hat {\\boldsymbol {y}} = Q (\\boldsymbol {y} - \\boldsymbol {\\mu}) + \\boldsymbol {\\mu} \\tag {1}", + "image_path": "b41c829f3d9f7c7edb866b4048d13921c9381e89e20eb9444a4c780711c8077c.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 125, + 350, + 181, + 363 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 125, + 350, + 181, + 363 + ], + "spans": [ + { + "bbox": [ + 125, + 350, + 181, + 363 + ], + "type": "interline_equation", + "content": "\\hat {\\boldsymbol {x}} = g _ {s} (\\hat {\\boldsymbol {y}}; \\boldsymbol {\\theta})", + "image_path": "57213b8955c36c46ec7ceaf1ad95225c0af591de39fb4b1fc405a91b41aade7f.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 372, + 287, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 372, + 287, + 574 + ], + "spans": [ + { + "bbox": [ + 46, + 372, + 287, + 574 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 372, + 287, + 574 + ], + "type": "inline_equation", + "content": "\\pmb{x}" + }, + { + "bbox": [ + 46, + 372, + 287, + 574 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 372, + 287, + 574 + ], + "type": "inline_equation", + "content": "\\hat{\\pmb{x}}" + }, + { + "bbox": [ + 46, + 372, + 287, + 574 + ], + "type": "text", + "content": " represent the raw images and decompressed images. By inputting " + }, + { + "bbox": [ + 46, + 372, + 287, + 574 + ], + "type": "inline_equation", + "content": "\\pmb{x}" + }, + { + "bbox": [ + 46, + 372, + 287, + 574 + ], + "type": "text", + "content": " to the encoder " + }, + { + "bbox": [ + 46, + 372, + 287, + 574 + ], + "type": "inline_equation", + "content": "g_{a}" + }, + { + "bbox": [ + 46, + 372, + 287, + 574 + ], + "type": "text", + "content": " with learned parameters " + }, + { + "bbox": [ + 46, + 372, + 287, + 574 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 46, + 372, + 287, + 574 + ], + "type": "text", + "content": ", we can get the latent representation " + }, + { + "bbox": [ + 46, + 372, + 287, + 574 + ], + "type": "inline_equation", + "content": "\\pmb{y}" + }, + { + "bbox": [ + 46, + 372, + 287, + 574 + ], + "type": "text", + "content": " which is estimated to have a mean " + }, + { + "bbox": [ + 46, + 372, + 287, + 574 + ], + "type": "inline_equation", + "content": "\\pmb{\\mu}" + }, + { + "bbox": [ + 46, + 372, + 287, + 574 + ], + "type": "text", + "content": ". To encode it, " + }, + { + "bbox": [ + 46, + 372, + 287, + 574 + ], + "type": "inline_equation", + "content": "\\pmb{y}" + }, + { + "bbox": [ + 46, + 372, + 287, + 574 + ], + "type": "text", + "content": " is quantized to " + }, + { + "bbox": [ + 46, + 372, + 287, + 574 + ], + "type": "inline_equation", + "content": "\\hat{\\pmb{y}}" + }, + { + "bbox": [ + 46, + 372, + 287, + 574 + ], + "type": "text", + "content": " by quantization operator " + }, + { + "bbox": [ + 46, + 372, + 287, + 574 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 46, + 372, + 287, + 574 + ], + "type": "text", + "content": ". According to previous works [13, 26] and discussion1, we round and encode each " + }, + { + "bbox": [ + 46, + 372, + 287, + 574 + ], + "type": "inline_equation", + "content": "\\lceil \\pmb{y} - \\pmb{\\mu} \\rceil" + }, + { + "bbox": [ + 46, + 372, + 287, + 574 + ], + "type": "text", + "content": " to the bitstream instead of " + }, + { + "bbox": [ + 46, + 372, + 287, + 574 + ], + "type": "inline_equation", + "content": "\\lceil \\pmb{y} \\rceil" + }, + { + "bbox": [ + 46, + 372, + 287, + 574 + ], + "type": "text", + "content": " and restore the coding-symbol " + }, + { + "bbox": [ + 46, + 372, + 287, + 574 + ], + "type": "inline_equation", + "content": "\\hat{\\pmb{y}}" + }, + { + "bbox": [ + 46, + 372, + 287, + 574 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 46, + 372, + 287, + 574 + ], + "type": "inline_equation", + "content": "\\lceil \\pmb{y} - \\pmb{\\mu} \\rceil + \\pmb{\\mu}" + }, + { + "bbox": [ + 46, + 372, + 287, + 574 + ], + "type": "text", + "content": ", which can further benefit entropy models. Then, we use range coder to encode losslessly " + }, + { + "bbox": [ + 46, + 372, + 287, + 574 + ], + "type": "inline_equation", + "content": "\\lceil \\pmb{y} - \\pmb{\\mu} \\rceil" + }, + { + "bbox": [ + 46, + 372, + 287, + 574 + ], + "type": "text", + "content": " which is modeled as a single Gaussian distribution with the variance " + }, + { + "bbox": [ + 46, + 372, + 287, + 574 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 46, + 372, + 287, + 574 + ], + "type": "text", + "content": " to bitstreams, and transmit it to decoder " + }, + { + "bbox": [ + 46, + 372, + 287, + 574 + ], + "type": "inline_equation", + "content": "g_{s}" + }, + { + "bbox": [ + 46, + 372, + 287, + 574 + ], + "type": "text", + "content": ". In this overall pipeline, " + }, + { + "bbox": [ + 46, + 372, + 287, + 574 + ], + "type": "inline_equation", + "content": "\\Phi = (\\pmb{\\mu},\\pmb{\\sigma})" + }, + { + "bbox": [ + 46, + 372, + 287, + 574 + ], + "type": "text", + "content": " in this paper is derived by a channel-wise entropy model as Equation 2, Fig. 2 and Fig. 4 show. The entropy model of [27] divides " + }, + { + "bbox": [ + 46, + 372, + 287, + 574 + ], + "type": "inline_equation", + "content": "\\pmb{y}" + }, + { + "bbox": [ + 46, + 372, + 287, + 574 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 372, + 287, + 574 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 46, + 372, + 287, + 574 + ], + "type": "text", + "content": " even slices " + }, + { + "bbox": [ + 46, + 372, + 287, + 574 + ], + "type": "inline_equation", + "content": "\\{\\pmb{y}_0,\\pmb{y}_1,\\dots,\\pmb{y}_{s-1}\\}" + }, + { + "bbox": [ + 46, + 372, + 287, + 574 + ], + "type": "text", + "content": " so that the encoded slices can help improve the encoding of subsequent slices, we formulate it as:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 73, + 582, + 195, + 594 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 73, + 582, + 195, + 594 + ], + "spans": [ + { + "bbox": [ + 73, + 582, + 195, + 594 + ], + "type": "interline_equation", + "content": "\\boldsymbol {z} = h _ {a} \\left(\\boldsymbol {y}; \\phi_ {h}\\right), \\quad \\hat {\\boldsymbol {z}} = Q (\\boldsymbol {z})", + "image_path": "a267bb16a974b77dfdb206bdb0d1546e6d0285306d4b12fdc2454ad3e8377a33.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 79, + 597, + 196, + 609 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 79, + 597, + 196, + 609 + ], + "spans": [ + { + "bbox": [ + 79, + 597, + 196, + 609 + ], + "type": "interline_equation", + "content": "\\mathcal {F} _ {\\text {m e a n}}, \\mathcal {F} _ {\\text {s c a l e}} = h _ {s} (\\hat {z}; \\boldsymbol {\\theta} _ {h})", + "image_path": "1e2b310316b5d37b099e9e24f0791186597051b831ab8154bf838fefcf2b1838.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 58, + 611, + 287, + 624 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 611, + 287, + 624 + ], + "spans": [ + { + "bbox": [ + 58, + 611, + 287, + 624 + ], + "type": "interline_equation", + "content": "\\boldsymbol {r} _ {i}, \\Phi_ {i} = e _ {i} \\left(\\boldsymbol {\\mathcal {F}} _ {\\text {m e a n}}, \\boldsymbol {\\mathcal {F}} _ {\\text {s c a l e}}, \\bar {\\boldsymbol {y}} _ {< i}, \\boldsymbol {y} _ {i}\\right), 0 < = i < s \\tag {2}", + "image_path": "711cddc541b952cafeb616ccc8743b89ebf98cf7dcb0301dc64a24ca8fd6b6bf.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 132, + 627, + 187, + 639 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 132, + 627, + 187, + 639 + ], + "spans": [ + { + "bbox": [ + 132, + 627, + 187, + 639 + ], + "type": "interline_equation", + "content": "\\overline {{\\boldsymbol {y}}} _ {i} = \\boldsymbol {r} _ {i} + \\hat {\\boldsymbol {y}} _ {i}", + "image_path": "0c3391cf0d770fd71feac65d18e844163ee4c20a047ad2145bfb898b200afaf4.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 649, + 287, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 649, + 287, + 685 + ], + "spans": [ + { + "bbox": [ + 47, + 649, + 287, + 685 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 649, + 287, + 685 + ], + "type": "inline_equation", + "content": "h_a" + }, + { + "bbox": [ + 47, + 649, + 287, + 685 + ], + "type": "text", + "content": " denotes the hyper-prior encoder with parameters " + }, + { + "bbox": [ + 47, + 649, + 287, + 685 + ], + "type": "inline_equation", + "content": "\\phi_h" + }, + { + "bbox": [ + 47, + 649, + 287, + 685 + ], + "type": "text", + "content": ". It is used to get side information " + }, + { + "bbox": [ + 47, + 649, + 287, + 685 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 47, + 649, + 287, + 685 + ], + "type": "text", + "content": " to capture spatial dependencies among the elements of " + }, + { + "bbox": [ + 47, + 649, + 287, + 685 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 47, + 649, + 287, + 685 + ], + "type": "text", + "content": ". A factorized density" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 247, + 545, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 247, + 545, + 464 + ], + "spans": [ + { + "bbox": [ + 304, + 247, + 545, + 464 + ], + "type": "text", + "content": "model " + }, + { + "bbox": [ + 304, + 247, + 545, + 464 + ], + "type": "inline_equation", + "content": "\\psi" + }, + { + "bbox": [ + 304, + 247, + 545, + 464 + ], + "type": "text", + "content": " is used to encode quantized " + }, + { + "bbox": [ + 304, + 247, + 545, + 464 + ], + "type": "inline_equation", + "content": "\\hat{z}" + }, + { + "bbox": [ + 304, + 247, + 545, + 464 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 304, + 247, + 545, + 464 + ], + "type": "inline_equation", + "content": "p_{\\hat{z}|\\psi}(\\hat{z} \\mid \\psi) = \\prod_{j} (p_{z_j|\\psi}(\\psi) * \\mathcal{U}(-\\frac{1}{2}, \\frac{1}{2})) (\\hat{z}_j)" + }, + { + "bbox": [ + 304, + 247, + 545, + 464 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 247, + 545, + 464 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 304, + 247, + 545, + 464 + ], + "type": "text", + "content": " specifies the position of each element or each signal. " + }, + { + "bbox": [ + 304, + 247, + 545, + 464 + ], + "type": "inline_equation", + "content": "\\hat{z}" + }, + { + "bbox": [ + 304, + 247, + 545, + 464 + ], + "type": "text", + "content": " is then fed to the hyper-prior decoder " + }, + { + "bbox": [ + 304, + 247, + 545, + 464 + ], + "type": "inline_equation", + "content": "h_s" + }, + { + "bbox": [ + 304, + 247, + 545, + 464 + ], + "type": "text", + "content": " with parameters " + }, + { + "bbox": [ + 304, + 247, + 545, + 464 + ], + "type": "inline_equation", + "content": "\\theta_h" + }, + { + "bbox": [ + 304, + 247, + 545, + 464 + ], + "type": "text", + "content": " for decoding to obtain two latent features " + }, + { + "bbox": [ + 304, + 247, + 545, + 464 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{mean}" + }, + { + "bbox": [ + 304, + 247, + 545, + 464 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 247, + 545, + 464 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{scale}" + }, + { + "bbox": [ + 304, + 247, + 545, + 464 + ], + "type": "text", + "content": " which are used to be input to the following each slice network " + }, + { + "bbox": [ + 304, + 247, + 545, + 464 + ], + "type": "inline_equation", + "content": "e_i" + }, + { + "bbox": [ + 304, + 247, + 545, + 464 + ], + "type": "text", + "content": ". After that, each slice " + }, + { + "bbox": [ + 304, + 247, + 545, + 464 + ], + "type": "inline_equation", + "content": "y_i" + }, + { + "bbox": [ + 304, + 247, + 545, + 464 + ], + "type": "text", + "content": " is sequentially processed to get " + }, + { + "bbox": [ + 304, + 247, + 545, + 464 + ], + "type": "inline_equation", + "content": "\\overline{y}_i" + }, + { + "bbox": [ + 304, + 247, + 545, + 464 + ], + "type": "text", + "content": ". During this process, encoded slices " + }, + { + "bbox": [ + 304, + 247, + 545, + 464 + ], + "type": "inline_equation", + "content": "\\overline{y}_{MethodsEncoding Time(/ms)Decoding Time(/ms)Para-meters(/M)FLOPs (/G)BD-rateXie et al. [34]2346521247.55408.21-1.65SwinT_ChARM [36]1328460.55230.37-4.02Ours (Large, w/o squeeze)151141160.45830.90-12.54Ours(Large)15014075.89700.96-12.30Ours(Medium)13012258.72415.20-9.65Ours(Small)10910244.96211.54-7.39", + "image_path": "51e5efdec63447c018e746466d08896e7c14ca3d7b8808fa17f1c4629a48347f.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "table_body" + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 311, + 389, + 322 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 311, + 389, + 322 + ], + "spans": [ + { + "bbox": [ + 306, + 311, + 389, + 322 + ], + "type": "text", + "content": "4.6. Visualization" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 331, + 545, + 390 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 331, + 545, + 390 + ], + "spans": [ + { + "bbox": [ + 305, + 331, + 545, + 390 + ], + "type": "text", + "content": "Fig. 1 shows the visualization example of decompressed images (kodim23) from Kodak dataset by our methods and the classical compression standards WebP, VVC (VTM 12.1) [29]. In some complex texture parts, our methods can keep more details (clearer feather outline)." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 405, + 378, + 417 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 405, + 378, + 417 + ], + "spans": [ + { + "bbox": [ + 306, + 405, + 378, + 417 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 426, + 545, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 426, + 545, + 617 + ], + "spans": [ + { + "bbox": [ + 304, + 426, + 545, + 617 + ], + "type": "text", + "content": "In this paper, we incorporate transformers and CNN to propose an efficient parallel transformer-CNN mixture block that utilizes the local modeling ability of CNN and the non-local modeling ability of transformers. Then, a new image compression architecture is designed based on the TCM block. Besides, we present a swin-transformer-based attention module to improve channel-wise entropy models. The results of experiments show that the image compression model with TCM blocks outperforms the CNN-only/Transformer-only based models under a suitable complexity. Furthermore, the performance of SWAtten surpasses previous attention modules designed for image compression. At last, our method achieves state-of-the-art on three different resolution datasets (i.e., Kodak, Tecnick, CLIC Professional Validation) and is superior to existing image compression methods." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 632, + 410, + 646 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 632, + 410, + 646 + ], + "spans": [ + { + "bbox": [ + 306, + 632, + 410, + 646 + ], + "type": "text", + "content": "6. Acknowledgment" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": "This paper is supported by Japan Science and Technology Agency (JST), under Grant JPMJPR19M5; Japan Society for the Promotion of Science (JSPS), under Grant 21K17770; Kenjiro Takayanagi Foundation; the Foundation of Ando Laboratory; NICT, Grant Number 03801, Japan." + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14395" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 91, + 287, + 714 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "type": "text", + "content": "[1] Nicola Asuni and Andrea Giachetti. 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Dinesh Reddy", + "bbox": [ + 287, + 203, + 426, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Christoph Mertz", + "bbox": [ + 467, + 203, + 601, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Carnegie Mellon University", + "bbox": [ + 372, + 222, + 594, + 239 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Srinivasa G. Narasimhan", + "bbox": [ + 640, + 203, + 839, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{anuraggh, dnarapur, cmertz, srinivas}@cs.cmu.edu", + "bbox": [ + 267, + 241, + 700, + 256 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 291, + 313, + 306 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Real-time efficient perception is critical for autonomous navigation and city scale sensing. Orthogonal to architectural improvements, streaming perception approaches have exploited adaptive sampling improving real-time detection performance. In this work, we propose a learnable geometry-guided prior that incorporates rough geometry of the 3D scene (a ground plane and a plane above) to resample images for efficient object detection. This significantly improves small and far-away object detection performance while also being more efficient both in terms of latency and memory. For autonomous navigation, using the same detector and scale, our approach improves detection rate by $+4.1\\mathrm{AP}_S$ or $+39\\%$ and in real-time performance by $+5.3\\mathrm{sAP}_S$ or $+63\\%$ for small objects over state-of-the-art (SOTA). For fixed traffic cameras, our approach detects small objects at image scales other methods cannot. At the same scale, our approach improves detection of small objects by $195\\%$ $(+12.5\\mathrm{AP}_S)$ over naive-downsampling and $63\\%$ $(+4.2\\mathrm{AP}_S)$ over SOTA.", + "bbox": [ + 75, + 324, + 473, + 612 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 645, + 209, + 660 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Visual perception is important for autonomous driving and decision-making for smarter and sustainable cities. Real-time efficient perception is critical to accelerate these advances. For instance, a single traffic camera captures half a million frames every day or a commuter bus acting as a city sensor captures one million frames every day to monitor road conditions [10] or to inform public services [22]. There are thousands of traffic cameras [24] and nearly a million commuter buses [53] in the United States. It is infeasible to transmit and process visual data on the cloud, leading to the rise of edge architectures [43]. However, edge devices are severely resource constrained and real-time inference requires down-sampling images to fit both latency and memory constraints severely impacting accuracy.", + "bbox": [ + 75, + 672, + 468, + 883 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "On the other hand, humans take visual shortcuts [19] to", + "bbox": [ + 76, + 885, + 468, + 900 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Trrrnnnne", + "text_level": 1, + "bbox": [ + 509, + 306, + 527, + 388 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/886afeb3f2b2469e3841960b9e007d475e67d50a0edc8612c3c41b405903c353.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 532, + 292, + 697, + 400 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/cf71d620299bdbc3e8db0af5be49141cf15a287acadb1f40578c77f10257eaec.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 702, + 292, + 880, + 400 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "e e e", + "text_level": 1, + "bbox": [ + 511, + 438, + 529, + 500 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/4f9855606219b6f6fb11abd82a7c0ab8e114d7bc63829a7c7fe85532e048b671.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 532, + 407, + 782, + 532 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/a2980e16f42b3027978eda26dac78a148b174ef72723066ce6c575a94806f39d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 785, + 406, + 880, + 472 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Saaee", + "text_level": 1, + "bbox": [ + 509, + 547, + 529, + 613 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c740d404f39bf6d6499d9409992ff64f161ba9ce287734f9c371f180be8dc69e.jpg", + "image_caption": [ + "Figure 1. Geometric cues (black dashed lines) are implicitly present in scenes. Our Perspective based prior exploits this geometry. Our method (a) takes an image and (b) warps them, and performs detection on warped images. Small objects which are (d) not detected when naively downsampled but (e) are detected when enlarged with our geometric prior. Our method (f) uses a geometric model to construct a saliency prior to focus on relevant areas and (g) enables sensing on resource-constrained edge devices." + ], + "image_footnote": [], + "bbox": [ + 532, + 542, + 705, + 619 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/e29c1f634f3a41f658beb9db95e50c037a5b27136c49b8e14219b6633bc29fa0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 709, + 542, + 880, + 619 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "recognize objects efficiently and employ high-level semantics [19, 52] rooted in scene geometry to focus on relevant parts. Consider the scene in Figure 1 (c), humans can recognize the distant car despite its small appearance (Figure 1 (d)). We are able to contextualize the car in the 3D scene, namely (1) it's on the road and (2) is of the right size we'd expect at that distance. Inspired by these observations, can we incorporate semantic priors about scene geometry in our neural networks to improve detection?", + "bbox": [ + 496, + 763, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "13364", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this work, we develop an approach that enables object detectors to \"zoom\" into relevant image regions (Figure 1 (d) and (e)) guided by the geometry of the scene. Our approach considers that most objects of interests are present within two planar regions, either on the ground plane or within another plane above the ground, and their size in the image follow a geometric relationship. Instead of uniformly downsampling, we sample the image to enlarge far away regions more and detect those smaller objects.", + "bbox": [ + 75, + 90, + 472, + 226 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "While methods like quantization [17], pruning [18], distillation [6] and runtime-optimization [16] improve model efficiency (and are complementary), approaches exploiting spatial and temporal sampling are key for enabling efficient real-time perception [21, 27]. Neural warping mechanisms [23, 36] have been employed for image classification and regression, and recently, detection for self-driving [50]. Prior work [50] observes that end-to-end trained saliency networks fail for object detection. They instead turn to heuristics such as dataset-wide priors and object locations from previous frames, which are suboptimal. We show that formulation of learnable geometric priors is critical for learning end-to-end trained saliency networks for detection. We validate our approach in a variety of scenarios to showcase the generalizability of geometric priors for detection in self-driving on Argoverse-HD [27] and BDD100K [57] datasets, and for traffic-c cameras on WALT [37] dataset.", + "bbox": [ + 75, + 227, + 472, + 484 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- On Argoverse-HD, our learned geometric prior improves performance over naive downsampling by $+6.6$ AP and $+2.7$ AP over SOTA using the same detection architecture. Gains from our approach are achieved by detecting small far-away objects, improving by 9.6 $AP_{S}$ (or $195\\%$ ) over naive down-sampling and 4.2 $AP_{S}$ (or $63\\%$ ) over SOTA.", + "- On WALT, our method detects small objects at image scales where other methods perform poorly. Further, it significantly improves detection rates by 10.7 $AP_{S}$ over naive down-sampling and 3 $AP_{S}$ over SOTA.", + "- Our approach improves object tracking $(+4.8\\%)$ MOTA compared to baseline. It also improves tracking quality, showing increase of $+7.6\\%$ $MT\\%$ and reduction of $-6.7\\%$ $ML\\%$ .", + "- Our approach can be deployed in resource constrained edge devices like Jetson AGX to detect $42\\%$ more rare instances while being 2.2X faster to enable real-time sensing from buses." + ], + "bbox": [ + 94, + 493, + 468, + 785 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 800, + 218, + 814 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We contextualize our work with respect to prior works modelling geometry and also among works that aim to make object detection more accurate and efficient.", + "bbox": [ + 75, + 825, + 468, + 869 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Vision Meets Geometry: Geometry has played a crucial role in multiple vision tasks like detection [8, 20, 48, 55],", + "bbox": [ + 75, + 869, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "segmentation [28, 46], recognition [14, 47] and reconstruction [25, 35, 44]. Perspective Geometric constraints have been used to remove distortion [58], improve depth prediction and semantic segmentation [26] and feature matching [51]. However, in most previous works [25, 44, 55] exploiting these geometric constraints have mainly been concentrated around improving 3D understanding. This can be attributed to a direct correlation between the constraints and the accuracy of reconstruction. Another advantage is the availability of large RGB-D and 3D datasets [5, 15, 39] to learn and exploit 3D constraints. Such constraints have been under-explored for learning based vision tasks like detection and segmentation. A new line of work interpreting classical geometric constraints and algorithms as neural layers [7, 42] have shown considerable promise in merging geometry with deep learning.", + "bbox": [ + 496, + 90, + 890, + 333 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Learning Based Detection: Object detection has mostly been addressed as an learning problem. Even classical-vision based approaches [12, 54] extract image features and learn to classify them into detection scores. With deep learning, learnable architectures have been proposed following this paradigm [4, 34, 38, 40], occasionally incorporating classical-vision ideas such as feature pyramids for improving scale invariance [29]. While learning has shown large improvements in accuracy over the years they still perform poorly while detecting small objects due to lack of geometric scene understanding. To alleviate this problem, we guide the input image with geometry constraints, and our approach complements these architectural improvements.", + "bbox": [ + 496, + 338, + 890, + 535 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Efficient Detection with Priors: Employing priors with learning paradigms achieves improvements with little additional human labelling effort. Object detection has traditionally been tackled as a learning problem and geometric constraints were sparsely used for such tasks, constraints like ground plane [20, 48] were used.", + "bbox": [ + 496, + 541, + 890, + 632 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Temporality [13, 50, 56] has been exploited for improving detection efficiently. Some of these methods [13, 50] deform the input image using approach that exploit temporality to obtain saliency. This approach handles cases where object size decreases with time (object moving away from the camera in scene), but cannot handle new incoming objects. None of these methods explicitly utilize geometry to guide detection, which handles both these cases. Our two-plane prior deforms the image while taking perspective into account without biasing towards previous detections.", + "bbox": [ + 496, + 637, + 890, + 787 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Another complementary line of works automatically learn metaparameters (like image scale) [9, 16, 45] from image features. However, as they do not employ adaptive sampling accounting for image-specific considerations, performance improvements are limited. Methods not optimized for online perception like AdaScale [9] for video object detection do not perform well in real-time situations.", + "bbox": [ + 496, + 795, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "13365", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Approach", + "text_level": 1, + "bbox": [ + 76, + 90, + 187, + 107 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We describe how a geometric model rooted in the interpretation of a 3D scene can be derived from the image. We then describe how to employ this rough 3D model to construct saliency for warping images and improving detection.", + "bbox": [ + 76, + 114, + 468, + 176 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Overview", + "text_level": 1, + "bbox": [ + 76, + 186, + 187, + 202 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Object sizes in the image are determined by the 3D geometry of the world. Let us devise a geometric inductive prior considering a camera mounted on a vehicle. Without loss of generality, assume the vehicle is moving in direction of the dominant vanishing point.", + "bbox": [ + 76, + 210, + 468, + 286 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We are interested in objects that are present in a planar region (See Figure 2) of width $P_{1}P_{2}$ corresponding to the camera view, of length $P_{1}P_{3}$ defined in the direction of the vanishing point. This is the planar region on the ground on which most of the objects of interest are placed (vehicles, pedestrians, etc) and another planar region $Q_{1}\\ldots Q_{4}$ parallel to this ground plane above horizon line, such that all the objects are within this region (e.g., traffic lights).", + "bbox": [ + 75, + 286, + 468, + 407 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "From this simple geometry model, we shall incorporate relationships derived from perspective geometry about objects, i.e., the scale of objects on ground plane is inversely proportional to their depth w.r.t camera [20].", + "bbox": [ + 75, + 407, + 468, + 468 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. 3D Plane parameterization from 2D images", + "text_level": 1, + "bbox": [ + 76, + 479, + 446, + 494 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We parameterize the planes of our inductive geometric prior. We represent 2D pixel projections $u_{1} \\ldots u_{4}$ of 3D points $P_{1} \\ldots P_{4}$ . Assume that the dominant vanishing point in the image is $v = (v_{x}, v_{y})$ and let the image size be $(w, h)$ . Consider $u_{1}$ (Figure 2 (b)). We can define a point on the edge of the image plane,", + "bbox": [ + 76, + 502, + 468, + 593 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nu _ {L} = \\left(0, v _ {y} + v _ {x} \\tan \\theta_ {1}\\right) \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 187, + 601, + 468, + 618 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "$u_{1}$ can be expressed as a linear combination of $v$ and $u_{L}$ ,", + "bbox": [ + 76, + 626, + 434, + 641 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nu _ {1} = \\alpha_ {1} u _ {L} + (1 - \\alpha_ {1}) v \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 648, + 468, + 664 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Similarly, for $u_{2}$ , we can define $u_{R}$ in terms of $v$ and $\\theta_{2}$ and $\\alpha_{2}$ while $u_{3}$ and $u_{4}$ are defined like Equation 1 to represent any arbitrary plane in this viewing direction. However, for simplicity, for ground plane we fix them as $(0,h)$ and $(w,h)$ respectively. Consider the planar region $Q_{1}\\ldots Q_{4}$ at height $H$ above the horizon line. We can similarly define $\\theta_{3}$ and $\\theta_{4}$ to represent the angles from the horizon in the opposite direction and define $q_{1}$ and $q_{2}$ . Again, we set $q_{3}$ as $(0,0)$ and $q_{4}$ as $(w,0)$ . We now have 4 points to calculate homographies $H_{plane}$ for both planes.", + "bbox": [ + 76, + 672, + 468, + 824 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For now, assume $v$ is known. However, we still do not know the values for $\\theta$ 's and $\\alpha$ , and we shall learn these parameters end-to-end from task loss. These parameters are learned and fixed for a given scenario in our learning paradigm. Our reparameterization aims to ease learning of these parameters", + "bbox": [ + 75, + 825, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/de4ef595046c1783ba8dc7fe3ce750c8cc7fa49db14756a3427e9aa9eddc7eab.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 568, + 92, + 826, + 208 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/781c66513e9af13aa5ceaf61f5032d6110e6fefc16680ab0e4865191fd645d6b.jpg", + "image_caption": [ + "Figure 2. Geometry Of The Two Plane Perspective Prior: (a) describes the single view geometry of the proposed two plane prior. Region on the ground plane defined by $P_{1}, \\ldots, P_{4}$ , and rays emanating from camera $C$ to $P_{i}$ intersect at $u_{1} \\ldots u_{4}$ on the image plane. The vanishing point $v$ maps to $P_{\\infty}$ . This planar region accounts for small objects on the ground plane. To account for objects that are tall or do not lie on the ground plane, we consider another plane $Q_{1} \\ldots Q_{4}$ above the horizon line. These two planes encapsulate all the relevant objects in the scene. (b) depicts the re-parameterization of the two planes in the 2D image. Instead of representing the planar points $u_{1} \\ldots u_{4}$ as pixel coordinates, we instead parameterize them in terms of the vanishing point $v$ , $\\theta$ 's and $\\alpha$ to ease learning." + ], + "image_footnote": [], + "bbox": [ + 568, + 208, + 821, + 345 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "as we clamp the values of $\\alpha$ 's to $[0,1]$ and $\\theta$ 's to $[- \\frac{\\pi}{2}, \\frac{\\pi}{2}]$ . It should be noted that all the operations are differentiable.", + "bbox": [ + 498, + 571, + 890, + 602 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.3. From Planes to Saliency", + "text_level": 1, + "bbox": [ + 500, + 614, + 720, + 630 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We leverage geometry to focus on relevant image regions through saliency guided warping [23, 36], and create a saliency map from a parameterized homography using $u_{1} \\ldots u_{4}$ defined earlier. Looking at ground plane from two viewpoints (Figure 3 (a) and (b)), object size decreases by their distance from the camera [20]. We shall establish a relationship to counter this effect and \"sample\" far-away objects on the ground plane more than nearby objects.", + "bbox": [ + 496, + 638, + 890, + 758 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The saliency guided warping proposed by [36] operates using an inverse transformation $\\mathcal{T}_S^{-1}$ parameterized by a saliency map $S$ as follows,", + "bbox": [ + 496, + 758, + 890, + 804 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nI ^ {\\prime} (x, y) = W _ {\\mathcal {T}} (I) = I \\left(\\mathcal {T} _ {S} ^ {- 1} (x, y)\\right) \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 576, + 811, + 890, + 830 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where the warp $W_{\\mathcal{T}}$ implies iterating over output pixel coordinates, using $\\mathcal{T}_S^{-1}$ to find corresponding input coordinates (non-integral), and bilinearly interpolating output color from neighbouring input pixel grid points. For each", + "bbox": [ + 496, + 839, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "13366", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/b0b847b8e7b27272bc9b4120126ecf560e36344085187e6f7544044c3314f3b2.jpg", + "image_caption": [ + "(a) Camera View" + ], + "image_footnote": [], + "bbox": [ + 80, + 89, + 284, + 189 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/aadeee20fd3e8dbd2d7bf0459223ad71e0251893f4845475c3b4905d9467b4f5.jpg", + "image_caption": [ + "(c) Mapping Saliency" + ], + "image_footnote": [], + "bbox": [ + 282, + 90, + 483, + 188 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/5f66e79e5a8b1e53370af0a4c857187cc1902d322f7a2b15529e0973c5d7b05c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 486, + 90, + 684, + 188 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/fa890e5d308d30be676c8feada3e24743cc81f4b279541a9a588d0fe5b3f57d1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 687, + 90, + 887, + 188 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/6381bfc7df66e410bbb07f80a54ce668fbd62761834528c1497e6ac65c0a4307.jpg", + "image_caption": [ + "(b) Bird's Eye View", + "Figure 3. Two-Plane Perspective Prior based Image Resampling: Consider the scene of car, bus and traffic light from (a) camera view and (b) (simplified) bird's eye view. (c) Saliency function that captures the inverse relationship between object size (in camera view) and depth (bird's eye view is looking at $XZ$ plane from above) can be transferred to the camera view (d), by mapping row $z$ using $H$ (marked by blue arrows). (e) and (f) shows that ground plane severely distorts nearby tall objects while squishing traffic light. (g) and (h) shows that additional plane reduces distortion for both tall objects and objects not on ground plane." + ], + "image_footnote": [], + "bbox": [ + 80, + 205, + 281, + 304 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/aa3229e80a2710d5f1ab7860607951b4027478908b09af7acb5d4d1e859eccd9.jpg", + "image_caption": [ + "(d) Saliency On Scene" + ], + "image_footnote": [], + "bbox": [ + 282, + 205, + 483, + 304 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/e35c2ff4b89acd7ec67a0fab4e81ff53246f9440c04ca44f5d034519e1ceb650.jpg", + "image_caption": [ + "(e) Ground Plane Saliency", + "(f) Ground Plane Warp" + ], + "image_footnote": [], + "bbox": [ + 483, + 205, + 684, + 304 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/a692c7d5ffcf061d85890299d00d9b6f304762fffd7088bedb451420483bc9f6.jpg", + "image_caption": [ + "(g) Two Plane Saliency", + "(h) Two Plane Warp" + ], + "image_footnote": [], + "bbox": [ + 687, + 205, + 885, + 304 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "input pixel $(x,y)$ , pixel coordinates with higher $S(x,y)$ values (i.e. salient regions) would be sampled more.", + "bbox": [ + 75, + 436, + 467, + 467 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We construct a saliency $S$ respecting the geometric properties that we desire. Let $H_{plane}$ be the homography between the camera view (using coordinates $u_{1}\\ldots u_{4}$ ) and a bird's eye view of the ground plane assuming plane size to be the original image size $(w,h)$ . In bird's eye view, we propose saliency function for a row of pixels $z$ (assuming bottom-left of this rectangle as $(0,0)$ ) as,", + "bbox": [ + 75, + 469, + 467, + 573 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nS _ {b e v} (z) = e ^ {\\nu \\left(\\frac {z}{h} - 1\\right)} \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 207, + 579, + 468, + 598 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "with a learnable parameter $\\nu (>1)$ . $\\nu$ defines the extent of sampling with respect to depth.", + "bbox": [ + 75, + 607, + 468, + 636 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To map this saliency to camera view, we warp $S_{bev}$ via perspective transform $W_{p}$ and $H_{plane}$ (Figure 3 (c)),", + "bbox": [ + 75, + 637, + 467, + 667 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nS _ {p l a n e} = W _ {p} \\left(H _ {p l a n e} ^ {- 1}, S _ {b e v}\\right) \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 176, + 672, + 468, + 693 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We have defined saliency $S_{plane}$ given $H_{plane}$ in a differentiable manner. Our saliency ensures that objects on the ground plane separated by depth $Z$ are sampled by the factor $e^{\\nu \\frac{Z}{h}}$ in the image.", + "bbox": [ + 75, + 700, + 468, + 760 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Two-Plane Perspective Prior", + "text_level": 1, + "bbox": [ + 76, + 770, + 331, + 787 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Ground Plane saliency focuses on objects that are geometrically constrained to be on this plane and reasonably models objects far away on the plane. However, nearby and tall objects, and small objects far above the ground plane are not modelled well. In Fig 3 (f), nearby objects above ground plane (traffic lights), they are highly distorted. Critically, these same objects when further away are rendered", + "bbox": [ + 75, + 795, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "small in size and appear close to ground (and thus modelled well). Objects we should focus more on are thus the former compared to the latter. Thus, another plane is needed, and direction of the saliency function is reversed to $\\hat{S}_{bev}(z) = e^{\\hat{\\nu}((h - z) / h) - 1}$ to account for these objects that would otherwise be severely distorted.", + "bbox": [ + 496, + 436, + 890, + 527 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To represent the Two-Plane Prior, we represented the planar regions as saliencies. The overall saliency is,", + "bbox": [ + 496, + 527, + 890, + 558 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nS = S _ {\\text {g r o u n d - p l a n e}} + \\lambda S _ {\\text {t o p - p l a n e}} \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 584, + 564, + 890, + 580 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\lambda$ is a learned parameter.", + "bbox": [ + 500, + 585, + 707, + 599 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.5. Additional Considerations", + "text_level": 1, + "bbox": [ + 500, + 609, + 736, + 623 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Warping via a piecewise saliency function imposes additional considerations. The choice of deformation method is critical, saliency sampler [36] implicitly avoids drastic transformations common in other approaches. For e.g., Thin-plate spline performs worse [36], produces extreme transformations and requires regularization [13].", + "bbox": [ + 496, + 632, + 890, + 722 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Fovea [50] observes that restricting the space of allowable warps such that axis alignment is preserved improves accuracy, we adopt the separable formulation of $\\mathcal{T}^{-1}$", + "bbox": [ + 496, + 723, + 890, + 768 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {T} _ {x} ^ {- 1} (x) = \\frac {\\int_ {x ^ {\\prime}} S _ {x} \\left(x ^ {\\prime}\\right) k \\left(x ^ {\\prime} , x\\right) x ^ {\\prime}}{\\int_ {x ^ {\\prime}} S _ {x} \\left(x ^ {\\prime}\\right) k \\left(x , x ^ {\\prime}\\right)} \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 586, + 770, + 890, + 806 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {T} _ {y} ^ {- 1} (y) = \\frac {\\int_ {y ^ {\\prime}} S _ {y} \\left(y ^ {\\prime}\\right) k \\left(y ^ {\\prime} , y\\right) y ^ {\\prime}}{\\int_ {y ^ {\\prime}} S _ {y} \\left(y ^ {\\prime}\\right) k \\left(y , y ^ {\\prime}\\right)} \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 589, + 811, + 890, + 849 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $k$ is a Gaussian kernel. To convert a saliency map $S$ to $S_{x}$ and $S_{y}$ we marginalize it along the two axes. Thus entire rows or columns are \"stretched\" or \"compressed\".", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "13367", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Two-plane prior is learnt end to end as a learnable image warp. For object detection, labels need to be warped too, and [36]'s warp is invertible. Like [50], We employ the loss $\\mathcal{L}(\\mathcal{T}^{-1}(f_{\\phi}(W_{\\mathcal{T}}(I)),L)$ where $(I,L)$ is the image-label pair and omit the use of delta encoding for training RPN [40] (which requires the existence of a closed form $\\mathcal{T}$ ), instead adopting GIoU loss [41]. This ensures $W_{\\mathcal{T}}$ is learnable, as $\\mathcal{T}^{-1}$ is differentiable.", + "bbox": [ + 75, + 90, + 472, + 210 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We did not assume that the vanishing point is within the field of view of our image, and our approach places no restrictions on the vanishing point. Thus far, we explained our formulation while considering a single dominant vanishing point, however, multiple vanishing points can be also considered. Please see supplementary for more details.", + "bbox": [ + 75, + 212, + 472, + 305 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.6. Obtaining the Vanishing Point", + "text_level": 1, + "bbox": [ + 76, + 313, + 346, + 329 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We now describe how we obtain the vanishing point. Many methods exist with trade-offs in accuracy, latency and memory which inform our design to perform warping efficiently with minimal overheads.", + "bbox": [ + 75, + 335, + 468, + 397 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Fixed Cameras: In settings like traffic cameras, the camera is fixed. Thus, the vanishing point is fixed, and we can cache the corresponding saliency $S$ , as all the parameters, once learnt, are fixed. We can define the vanishing point for a camera manually by annotating two parallel lines or any accurate automated approach. Saliency caching renders our approach extremely efficient.", + "bbox": [ + 75, + 398, + 468, + 503 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Autonomous Navigation: Multiple assumptions simplify the problem. We assume that there is one dominant vanishing point and a navigating car is often moving in the viewing direction. Thus, we assume that this vanishing point lies inside the image, and directly regress $v$ from image features using a modified coordinate regression module akin to YOLO [33, 38]. This approach appears to be memory and latency efficient. Other approaches, say, using parallel lane lines [1] or inertial measurements [3] might also be very efficient. An even simpler assumption is to employ the average vanishing point, as vanishing points are highly local, we observe this is a good approximation.", + "bbox": [ + 75, + 503, + 468, + 685 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Temporal Redundancies: In videos, we exploit temporal redundancies, the vanishing point is computed every $n_v$ frames and saliency is cached to amortize latency cost.", + "bbox": [ + 75, + 685, + 468, + 729 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "General Case: This is the most difficult case, and many approaches have been explored in literature to find all vanishing points. Classical approaches [49] while fast are not robust, while deep-learned approaches [31,32,59] are accurate yet expensive (either in latency or memory).", + "bbox": [ + 75, + 729, + 468, + 806 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.7. Learning Geometric Prior from Pseudo-Labels", + "text_level": 1, + "bbox": [ + 76, + 816, + 468, + 832 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Prior work [50] have shown improvements in performance on pre-trained models via heuristics, which didn't require any training. However, their method still employs domain-specific labels (say, from Argoverse-HD) to generate the", + "bbox": [ + 75, + 839, + 468, + 902 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/0162ca8a534119829c44c49c0acab601fa315f12eb7266ccda73d43cebec0619.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 501, + 88, + 694, + 172 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/f370ef3da817e18bca66779a4f188b77377c2142946643016539eebf92fe2fa6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 697, + 88, + 890, + 172 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/b3d035b91cf500d6c2ecc97b3ce5f5c49db5b92bc62665f6b43ccf2aba9cd2f4.jpg", + "image_caption": [ + "Figure 4. Commuter Bus Dataset: The captured data has a unique viewpoint, the average size of objects is small and captured under a wide variety of lighting conditions. Top-left and bottom-right images depict the same bus-stop and trashcan at different time of day and season." + ], + "image_footnote": [], + "bbox": [ + 501, + 174, + 694, + 258 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/2c055f3997cdb04c719b7c912e08a5e29aae4f210031402b4edc7c79ee719f4a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 697, + 174, + 890, + 258 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "prior. Our method can't be used directly with pre-trained models as it learns geometrically inspired parameters end-to-end. However, domain-specific images without labels can be exploited to learn the parameters.", + "bbox": [ + 496, + 368, + 890, + 429 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We propose a simple alternative to learn the proposed prior using pre-trained model without requiring additional domain-specific labels. We generate pseudo-labels from our pre-trained model inferred at 1x scale. We fine-tune and learn our warp function (to $0.5\\mathrm{x}$ scale) end-to-end using these \"free\" labels. Our geometric prior shows improvements without access to ground truth labels.", + "bbox": [ + 496, + 429, + 892, + 535 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Dataset And Evaluation Details", + "text_level": 1, + "bbox": [ + 500, + 549, + 785, + 564 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Datasets", + "text_level": 1, + "bbox": [ + 500, + 574, + 601, + 589 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Argoverse-HD [27]: We employ Argoverse-HD dataset for evaluation in the autonomous navigation scenario. This dataset consists of 30fps video sequences from a car collected at $1920 \\times 1200$ resolution, and dense box annotations are provided for common objects of interest such as vehicles, pedestrians, signboards and traffic lights.", + "bbox": [ + 496, + 598, + 890, + 688 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "WALT [37]: We employ images from 8.4K cameras that overlook public urban settings to analyze the flow of traffic vehicles. The data is captured for 3-second bursts every few minutes and only images with notable changes are stored. We annotated a set of 4738 images with vehicles collected over the time period of a year covering a variety of day/night/dawn settings, seasonal changes and camera viewpoints. We show our results on two splits (approximately $80\\%$ training and $20\\%$ testing). The first, All-Viewpoints, images from all the cameras are equally represented in the train and test sets. Alternatively, we split by camera, Split-by-Camera, images from 6 cameras are part of the training set and 2 cameras are held out for testing.", + "bbox": [ + 496, + 688, + 892, + 885 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Commuter Bus Dataset: We curated this dataset from a", + "bbox": [ + 500, + 885, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "13368", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/6f7abf9e85a0f71fabb52bd8a2c79aa6cae4da45e4c97de23f70ac12c7427c9f.jpg", + "image_caption": [ + "Figure 5. Two-Plane Prior as a Neural Layer: We implemented our approach as a global prior that is learned end-to-end from labelled data. Our prior is dependent on a vanishing point estimate to specify the viewing direction of the camera." + ], + "image_footnote": [], + "bbox": [ + 81, + 88, + 467, + 251 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "commuter bus running on an urban route. The 720p camera of interest has a unique viewpoint and scene geometry (See Figure 4). Annotated categories are trashcans and garbage bags (to help inform public services) and people with special needs (using wheelchairs or strollers), which are a rare occurrence. The dataset size is small with only 750 annotated images (split into $70\\%$ training and $30\\%$ testing). This is an extremely challenging dataset due to its unique viewpoint, small object size, rare categories, along with variations in lighting and seasons.", + "bbox": [ + 75, + 347, + 472, + 500 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Evaluation Details", + "text_level": 1, + "bbox": [ + 76, + 510, + 256, + 526 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We perform apples-to-apples comparisons on the same detector trained using the datasets with identical training schedule and hardware.", + "bbox": [ + 75, + 535, + 468, + 579 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Data: We compare to methods that were trained on fixed training data. In contrast, sAP leaderboards [27] don't restrict data and evaluate on different hardware. We compare with [16, 27] from leaderboard, which follow the same protocols. Other methods on the leaderboard use additional training data to train off-the-self detectors. Our detectors would see similar improvements with additional data.", + "bbox": [ + 75, + 580, + 468, + 686 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Real-Time Evaluation: We evaluate using Streaming AP (sAP) metric proposed by [27], which integrates latency and accuracy into a single metric. Instead of considering models via accuracy-latency tradeoffs [21], real-time performance can be evaluated by applying real-time constraints on the predictions [27]. Frames of the video are observed every 33 milliseconds (30 fps) and predictions for every frame must be emitted before the frame is observed (forecasting is necessary). For a fair comparison, sAP requires evaluation on the same hardware. Streaming results are not directly comparable with other work [27, 50, 56] as they use other hardware (say, V100 or 2080Ti), thus we run the evaluation on our hardware (Titan X).", + "bbox": [ + 75, + 686, + 470, + 883 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Additional details are in the Supplementary.", + "bbox": [ + 76, + 885, + 370, + 901 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/f3a06b12d8ab128a199dd78a6bfff684020edc96a0e9c93a8193efa731d4d6f0.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodScaleAPAPSAPMAPLLatency (ms)
Faster R-CNN0.5x24.24.929.050.978.4 ± 1.8
Fovea (SD) [50]0.5x26.78.229.754.183 ± 2.5
Fovea (SI) [50]0.5x28.010.431.054.585 ± 2.7
Fovea (L:SI) [50]0.5x28.110.330.954.185.4 ± 2.7
Two-Plane Pr. (Pseudo.)0.5x27.19.828.950.2104.5 ± 8.5
Two-Plane Prior0.5x30.814.531.652.9105 ± 8.5
Baseline at higher scales
Faster R-CNN0.75x29.211.632.153.3142 ± 2.5
Faster R-CNN1.0x33.316.834.853.6220 ± 1.7
", + "bbox": [ + 500, + 88, + 903, + 250 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Evaluation on Argoverse-HD: Two-Plane Prior outperforms both SOTA's dataset-wide and temporal priors in overall accuracy. Our method improves small object detection by $+4.1AP_{S}$ or $39\\%$ over SOTA.", + "bbox": [ + 496, + 260, + 893, + 316 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Results and Discussions", + "text_level": 1, + "bbox": [ + 500, + 335, + 723, + 353 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Accuracy-Latency Comparisons: On Argoverse-HD, we compare with Faster R-CNN with naive downsampling (Baseline) and Faster R-CNN paired with adaptive sampling from Fovea [50] which proposed two priors, a dataset-wide prior $(S_{D})$ and frame-specific temporal priors ( $S_{I}$ & $L: S_{I}$ ; from previous frame detections).", + "bbox": [ + 496, + 364, + 893, + 455 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Two-Plane Prior improves (Table 1) upon baseline at the same scale by $+6.6$ AP and over SOTA by $+2.7$ AP. For small objects, the improvements are even more dramatic, our method improves accuracy by $+9.6$ $AP_{S}$ or $195\\%$ over baseline and $+4.2$ $AP_{S}$ or $45\\%$ over SOTA respectively. Surprisingly, our method at $0.5\\mathrm{x}$ scale improves upon Faster R-CNN at $0.75\\mathrm{x}$ scale by $+1.6$ AP having latency improvement of $35\\%$ . Our Two-Plane prior trained via pseudolabels comes very close to SOTA which employ ground truth labels, the gap is only $-1$ AP and improves upon Faster R-CNN model trained on ground truth by $+2.9$ AP inferred at the same scale.", + "bbox": [ + 496, + 455, + 895, + 636 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "WALT dataset [37] comprises images (only images with notable changes are saved) and not videos, we compare with Fovea [50] paired with the dataset-wide prior. We observe similar trends on both splits (Table 3 and Fig 6) and note large improvements over baseline and a consistent improvement over Fovea [50], specially for small objects.", + "bbox": [ + 496, + 638, + 893, + 731 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Real-time/Streaming Comparisons: We use Argoverse-HD dataset, and compare using the sAP metric (Described in Section 4.2). Algorithms may choose any scale and frames as long as real-time latency constraint is satisfied.", + "bbox": [ + 496, + 732, + 893, + 792 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "All compared methods use Faster R-CNN, and we adopt their reported scales (and other parameters). Streamer [27] converts any single frame detector for streaming by scheduling which frames to process and interpolating predictions between processed frames. AdaScale [9] regresses optimal scale from image features to minimize single-frame latency while Adaptive Streamer [16] learns scale choice in", + "bbox": [ + 496, + 795, + 893, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "13369", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/29a3760fd412096490ed6c682ec6efbd41f189f6784148f3aaa8ee00e9c6c2b6.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
IDMethodScale(s)sAPsAPSsAPMsAPL
1Streamer [27]0.5x18.33.115.040.9
21 + Adascale [9]0.2x-0.6x13.40.28.637.4
3Adaptive Streamer [16]0.2x-0.6x21.34.218.847.0
41 + FOVEA (SI) [50]0.5x24.18.424.748.7
51 + Ours (Avg VP)0.5x29.913.731.352.2
61 + Ours0.5x30.013.731.552.2
71 + Ours (VP Oracle)0.5x30.714.531.652.9
", + "bbox": [ + 81, + 88, + 467, + 223 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4e72d6afbd1f8ca09373a66b77b979df0ad2f8947c44116e9649e4d6fb59b4c1.jpg", + "image_caption": [ + "Figure 6. WALT All-Viewpoints Split: Our approach (Two-Plane Prior) shows improved overall performance over naive downsampling and state-of-the-art adaptive sampling technique, specially for small objects at all scales (starting from $0.5\\mathrm{x}$ ). Horizontal line (orange) indicates performance at maximum possible scale $(0.6\\mathrm{x})$ the base detector was trained at (memory constraints)." + ], + "image_footnote": [], + "bbox": [ + 78, + 345, + 274, + 458 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/faabbc2521bf1ed6c8c876b5aebeb5a234d17b5274b9b4c1c4698467117ca42c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 274, + 345, + 467, + 458 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "the streaming setting. Both these methods employ naive-downsampling. State-of-the-art, Fovea [50] employs the temporal prior $(S_I)$ . From Table 2, Two-Plane prior outperforms the above approaches by $+16.5$ sAP, $+8.6$ sAP and $+5.9$ sAP respectively. Comparison with [9, 16, 27] shows the limitations of naive downsampling, even when \"optimal\" scale is chosen. Our geometric prior greatly improves small object detection performance by $63\\%$ or $+5.3$ sAPs over SOTA. To consider dependence on accurate Vanishing Point detection (and its overheads), we use NeurVPS [59] as oracle (we simulate accurate prediction with zero delay) to obtain an upper bound, we observe even average vanishing point location's performance is within $0.8$ sAP.", + "bbox": [ + 75, + 580, + 468, + 777 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Accuracy-Scale Tradeoffs: We experiment with WALT All-Viewpoints split to observe accuracy-scale trade-offs. The native resolution $(4K)$ of the dataset is extremely large and the gradients don't fit within 12 GB memory of our Titan X GPU, thus we cropped the skies and other static regions to reduce input scale (1x) to $1500 \\times 2000$ . Still, the highest scale we were able to train our baseline Faster R-CNN model is 0.6x. So, we use aggressive downsam", + "bbox": [ + 75, + 779, + 470, + 901 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/edd10b4304c60f09b476705aa34b7cbc97348e53e5bcee91845d690dddb30c0d.jpg", + "table_caption": [ + "Table 2. Streaming Evaluation on Argoverse-HD: Ours denotes Two-Plane Prior. Every frame's prediction (streamed at 30FPS) must be emitted before frame is observed [27] (via forecasting). All methods evaluated on Titan X GPU. Underlying detector (Faster R-CNN) is constant across approaches, improvements are solely from spatial sampling mechanisms. Notice improved detection of small objects by $+5.3sAP_{S}$ or $63\\%$ over SOTA." + ], + "table_footnote": [], + "table_body": "
MethodScaleAPAPSAPMAPL
Faster R-CNN0.25x16.707.242.3
FOVEA (SD) [50]0.25x23.2013.954.1
Two-Plane Prior0.25x25.21.018.254.5
Faster R-CNN0.5x29.24.924.755.5
FOVEA (SD) [50]0.5x34.48.730.559.4
Two-Plane Prior0.5x36.411.632.359.0
Baseline at higher scales
Faster R-CNN0.6x33.29.328.656.7
Faster R-CNN*1.0x34.312.630.754.3
", + "bbox": [ + 535, + 88, + 857, + 258 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3. WALT Camera-Split: The viewpoints on the test set were not seen, and Two-Plane Prior shows better performance over both naive downsampling and state-of-the-art adaptive sampling as it generalizes better to unseen scenes and viewpoints. *Not trained at that scale due to memory constraints on Titan X.", + "bbox": [ + 496, + 268, + 893, + 339 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "pling scales $\\{0.5, 0.4375, 0.375, 0.3125, 0.25, 0.125\\}$ . The results are presented in Figure 6. We observe a large and consistent improvement over baseline and Fovea [50], specially for small objects. For instance, considering performance at $0.375x$ scale, our approach is better than baseline by $+13.1AP$ and Fovea by $+1.4AP$ for all objects.", + "bbox": [ + 496, + 351, + 890, + 441 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "For small objects, we observe dramatic improvement, at scales smaller than $0.375\\mathrm{x}$ , other approaches are unable to detect any small objects while our approach does so until $0.125\\mathrm{x}$ scale, showing that our approach degrades more gracefully. At $0.375\\mathrm{x}$ scale, our approach improves upon Faster R-CNN by $+10.7AP_{S}$ and Fovea by $+3.0AP_{S}$ .", + "bbox": [ + 496, + 444, + 892, + 534 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Generalization to new viewpoints: We use WALT Camera-Split, the test scenes and viewpoint are unseen in training. E.g., the vanishing point of one of the held-out cameras is beyond the image's field of view. We operate on the same scale factors in the earlier experiments, and results are presented in Table 3. We note lower overall performance levels due to scene/viewpoint novelty in the test sets. Our approach generalizes better due to the explicit modelling of the viewpoint via the vanishing point (See Section 3.2). We note trends similar to previous experiment, we demonstrate improvements of $+8.5$ AP over naive-downsampling and $+2.0$ AP over Fovea [50] at $0.25\\mathrm{x}$ scale.", + "bbox": [ + 496, + 536, + 893, + 717 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Tracking Improvements: We follow tracking-by-detection and pair IOUTracker [2] with detectors on Argoverse-HD dataset. MOTA and MOTP evaluate overall tracking performance. From Table 4, Our method improves over baseline by $+4.8\\%$ and $+0.7\\%$ . We also focus on tracking quality metrics, Mostly Tracked $\\%$ (MT%) evaluates the percentage of objects tracked for at least $80\\%$ of their lifespan while Mostly Lost $\\%$ (ML%) evaluates percentage of objects for less than $20\\%$ of their lifespan. In both these cases, our approach improves upon the baseline by $+7.6\\%$ and $-6.7\\%$ respectively. To autonomous navigation, we define two relevant metrics, namely, average lifespan extension (ALE)", + "bbox": [ + 496, + 719, + 893, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "13370", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/e4dc7df63800071fe38cc4698a50c97fd6cca6c45d863a460a30605387ad7a32.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodMOTA ↑MOTP ↑MT% ↑ML% ↓MOS ↓ALE% ↑
Faster RCNN39.882.330.735.637.159.3 %
Fovea (SD) [50]43.981.934.131.934.8+5.4 %
Fovea (SI) [50]44.381.836.728.433.8+8.4 %
Two-Plane Prior44.683.038.328.931.6+9.9 %
", + "bbox": [ + 78, + 88, + 486, + 171 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "and minimum object size tracked (MOS), whose motivation and definitions can be viewed in supplementary. We observe that our improvements are better than both Fovea $(S_{D})$ and $(S_{I})$ . As we observe, our method improves tracking lifespan and also helps track smaller objects.", + "bbox": [ + 75, + 277, + 468, + 353 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Efficient City-Scale Sensing: We detect objects on Commuter Bus equipped with a Jetson AGX. Identifying (Recall) relevant frames is key on the edge. Recall of Faster R-CNN with at 1x scale is $43.3AR$ ( $16.9AR_{S}$ ) (Latency: 350ms; infeasible for real-time execution) but drops to $31.7AR$ ( $0.5AR_{S}$ ) at 0.5x scale when naively downsampled (Latency: 154ms). Whereas our approach at 0.5x scale improves recall by $42\\%$ over full resolution execution to 61.7 AR (16.4 ARS) with latency of 158 ms (+4 ms).", + "bbox": [ + 75, + 354, + 468, + 489 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In supplementary, we perform additional comparisons, provide details on handling multiple vanishing points, more tracking results and edge sensing results. We also present some qualitative results and comparisons.", + "bbox": [ + 75, + 489, + 468, + 551 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.1. Ablation Studies", + "text_level": 1, + "bbox": [ + 76, + 559, + 241, + 574 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We discuss some of the considerations of our approach through experiments on the Argoverse-HD dataset.", + "bbox": [ + 75, + 582, + 468, + 613 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Ground Plane vs Two-Plane Prior: We discussed the rationale of employing multiple planes in Fig 3, and our results are consistent. From Table 5, Two-Plane Prior outperforms Ground Plane prior considerably $(+1.8AP)$ . Ground Plane Prior outperforms Two-Plane Prior on small objects by $+1AP_{S}$ but is heavily penalized on medium $(-4.1AP_{M})$ and large objects $(-4.6AP_{L})$ . This is attributed to heavy distortion of tall and nearby objects, and objects that are not on the plane (Figure 3). Lastly, this prior was difficult to learn, the parameter space severely distorted the images (we tuned initialization and learning rate). Thus we did not consider this prior further. The second plane acts as a counterbalance and that warping space is learnable.", + "bbox": [ + 75, + 613, + 468, + 809 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Vanishing Point Estimate Dependence: From Table 5, dominant vanishing point in autonomous navigation is highly local in nature, and estimating VP improves the result by +1.2 AP. Estimating the vanishing point is a design choice, it's important for safety critical applications like autonomous navigation (performance while navigating turns)", + "bbox": [ + 75, + 810, + 468, + 901 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/bce3d3c381ea6e6b76013eb67633eafb8f6c17da31f167789986c2402c8bc84a.jpg", + "table_caption": [ + "Table 4. Tracking Improvements: We setup a tracking by detection pipeline and replace the underlying detection method and observe improvements if any. All the detectors employ the Faster R-CNN architecture and are executed at $0.5\\mathrm{x}$ scale. We observe improvements in tracking metrics due to Two-Plane Prior." + ], + "table_footnote": [], + "table_body": "
MethodScaleAPAPSAPMAPL
Ground Plane Prior0.5x29.115.527.548.3
Two-Plane Prior (Psuedo.)0.5x27.19.828.950.2
Two-Plane Prior (Avg VP)0.5x29.612.730.752.7
Two-Plane Prior0.5x30.814.531.652.9
", + "bbox": [ + 516, + 88, + 877, + 165 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 5. Ablation Study on Argoverse-HD to justify our design choice of using two planes, dependence on accurate vanishing point detection and choice of pseudo labels vs ground truth.", + "bbox": [ + 496, + 174, + 890, + 217 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "however might be omitted for sensing applications.", + "bbox": [ + 496, + 229, + 836, + 244 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Using Pseudo Labels vs Ground Truth: Table 5 shows there is still considerable gap (-3.7 AP) between the Two-Plane Prior trained from pseudo labels and ground truth. We observe that the model under-performs on stopsign, bike and truck classes, which are under-represented in the COCO dataset [30] compared to person and car classes. Performance of the pre-trained model on these classes is low even at 1x scale. Hence, we believe that the performance difference is an artifact of this domain gap.", + "bbox": [ + 496, + 246, + 890, + 382 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusions", + "text_level": 1, + "bbox": [ + 500, + 401, + 625, + 417 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this work, we proposed a learned two-plane perspective prior which incorporates rough geometric constraints from 3D scene interpretations of 2D images to improve object detection. We demonstrated that (a) Geometrically defined spatial sampling prior significantly improves detection performance over multiple axes (accuracy, latency and memory) in terms of both single-frame accuracy and accuracy with real-time constraints over other methods. (b) Not only is our approach is more accurate when adaptively down-sampling at all scales, it degrades much more gracefully for small objects, resulting in latency and memory savings. (c) As our prior is learned end-to-end, we can improve a detector's performance at lower scales for \"free\". (d) Our approach generalizes better to new camera viewpoints and enables efficient city-scale sensing applications. Vanishing point estimation is the bottleneck of our approach [11, 31, 32, 59] for general scenes, and increasing efficiency of its computation we will see substantial improvements. Investigating geometric constraints to improve other aspects of real-time perception systems as future work, like object tracking and trajectory understanding and forecasting, is promising.", + "bbox": [ + 496, + 429, + 890, + 760 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Societal Impact Our approach has strong implications for autonomous-driving and city-scale sensing for smart city applications, wherein efficient data processing would lead to more data-driven decision-making and public policies. However, privacy is a concern, and we shall release the datasets after anonymizing people and license plates.", + "bbox": [ + 496, + 762, + 890, + 853 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements: This work was supported in part by an NSF CPS Grant CNS-2038612, a DOT RITA Mobility-21 Grant 69A3551747111 and by General Motors Israel.", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "13371", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Hala Abualsaud, Sean Liu, David B Lu, Kenny Situ, Akshay Rangesh, and Mohan M Trivedi. Laneaf: Robust multi-lane detection with affinity fields. Robotics and Automation Letters, 2021. 5", + "[2] Erik Bochinski, Volker Eiselein, and Thomas Sikora. 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NeurIPS, 2019. 5, 7, 8" + ], + "bbox": [ + 501, + 90, + 890, + 404 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "13373", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Learned Two-Plane Perspective Prior Based Image Resampling for Efficient Object Detection/875b7e38-656d-435c-a262-1765e6ab04d2_model.json b/2023/Learned Two-Plane Perspective Prior Based Image Resampling for Efficient Object Detection/875b7e38-656d-435c-a262-1765e6ab04d2_model.json new file mode 100644 index 0000000000000000000000000000000000000000..c977795e9e14f38973ae18f79abc96178125b205 --- /dev/null +++ b/2023/Learned Two-Plane Perspective Prior Based Image Resampling for Efficient Object Detection/875b7e38-656d-435c-a262-1765e6ab04d2_model.json @@ -0,0 +1,2662 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.15, + 0.131, + 0.823, + 0.177 + ], + "angle": 0, + "content": "Learned Two-Plane Perspective Prior based Image Resampling for Efficient Object Detection" + }, + { + "type": "text", + "bbox": [ + 0.13, + 0.204, + 0.25, + 0.222 + ], + "angle": 0, + "content": "Anurag Ghosh" + }, + { + "type": "text", + "bbox": [ + 0.289, + 0.204, + 0.428, + 0.222 + ], + "angle": 0, + "content": "N. Dinesh Reddy" + }, + { + "type": "text", + "bbox": [ + 0.468, + 0.204, + 0.602, + 0.222 + ], + "angle": 0, + "content": "Christoph Mertz" + }, + { + "type": "text", + "bbox": [ + 0.374, + 0.223, + 0.596, + 0.24 + ], + "angle": 0, + "content": "Carnegie Mellon University" + }, + { + "type": "text", + "bbox": [ + 0.641, + 0.204, + 0.84, + 0.221 + ], + "angle": 0, + "content": "Srinivasa G. Narasimhan" + }, + { + "type": "text", + "bbox": [ + 0.269, + 0.242, + 0.702, + 0.257 + ], + "angle": 0, + "content": "{anuraggh, dnarapur, cmertz, srinivas}@cs.cmu.edu" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.292, + 0.314, + 0.308 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.325, + 0.474, + 0.613 + ], + "angle": 0, + "content": "Real-time efficient perception is critical for autonomous navigation and city scale sensing. Orthogonal to architectural improvements, streaming perception approaches have exploited adaptive sampling improving real-time detection performance. In this work, we propose a learnable geometry-guided prior that incorporates rough geometry of the 3D scene (a ground plane and a plane above) to resample images for efficient object detection. This significantly improves small and far-away object detection performance while also being more efficient both in terms of latency and memory. For autonomous navigation, using the same detector and scale, our approach improves detection rate by \\(+4.1\\mathrm{AP}_S\\) or \\(+39\\%\\) and in real-time performance by \\(+5.3\\mathrm{sAP}_S\\) or \\(+63\\%\\) for small objects over state-of-the-art (SOTA). For fixed traffic cameras, our approach detects small objects at image scales other methods cannot. At the same scale, our approach improves detection of small objects by \\(195\\%\\) \\((+12.5\\mathrm{AP}_S)\\) over naive-downsampling and \\(63\\%\\) \\((+4.2\\mathrm{AP}_S)\\) over SOTA." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.646, + 0.21, + 0.661 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.673, + 0.47, + 0.884 + ], + "angle": 0, + "content": "Visual perception is important for autonomous driving and decision-making for smarter and sustainable cities. Real-time efficient perception is critical to accelerate these advances. For instance, a single traffic camera captures half a million frames every day or a commuter bus acting as a city sensor captures one million frames every day to monitor road conditions [10] or to inform public services [22]. There are thousands of traffic cameras [24] and nearly a million commuter buses [53] in the United States. It is infeasible to transmit and process visual data on the cloud, leading to the rise of edge architectures [43]. However, edge devices are severely resource constrained and real-time inference requires down-sampling images to fit both latency and memory constraints severely impacting accuracy." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.886, + 0.469, + 0.901 + ], + "angle": 0, + "content": "On the other hand, humans take visual shortcuts [19] to" + }, + { + "type": "title", + "bbox": [ + 0.51, + 0.307, + 0.528, + 0.39 + ], + "angle": 0, + "content": "Trrrnnnne" + }, + { + "type": "image", + "bbox": [ + 0.534, + 0.293, + 0.698, + 0.401 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.703, + 0.293, + 0.881, + 0.401 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.512, + 0.439, + 0.531, + 0.5 + ], + "angle": 0, + "content": "e e e" + }, + { + "type": "image", + "bbox": [ + 0.533, + 0.408, + 0.784, + 0.534 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.787, + 0.407, + 0.881, + 0.473 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.511, + 0.548, + 0.53, + 0.614 + ], + "angle": 0, + "content": "Saaee" + }, + { + "type": "image", + "bbox": [ + 0.534, + 0.544, + 0.706, + 0.62 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.71, + 0.544, + 0.881, + 0.62 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.638, + 0.894, + 0.751 + ], + "angle": 0, + "content": "Figure 1. Geometric cues (black dashed lines) are implicitly present in scenes. Our Perspective based prior exploits this geometry. Our method (a) takes an image and (b) warps them, and performs detection on warped images. Small objects which are (d) not detected when naively downsampled but (e) are detected when enlarged with our geometric prior. Our method (f) uses a geometric model to construct a saliency prior to focus on relevant areas and (g) enables sensing on resource-constrained edge devices." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.895, + 0.903 + ], + "angle": 0, + "content": "recognize objects efficiently and employ high-level semantics [19, 52] rooted in scene geometry to focus on relevant parts. Consider the scene in Figure 1 (c), humans can recognize the distant car despite its small appearance (Figure 1 (d)). We are able to contextualize the car in the 3D scene, namely (1) it's on the road and (2) is of the right size we'd expect at that distance. Inspired by these observations, can we incorporate semantic priors about scene geometry in our neural networks to improve detection?" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "13364" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.227 + ], + "angle": 0, + "content": "In this work, we develop an approach that enables object detectors to \"zoom\" into relevant image regions (Figure 1 (d) and (e)) guided by the geometry of the scene. Our approach considers that most objects of interests are present within two planar regions, either on the ground plane or within another plane above the ground, and their size in the image follow a geometric relationship. Instead of uniformly downsampling, we sample the image to enlarge far away regions more and detect those smaller objects." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.228, + 0.473, + 0.485 + ], + "angle": 0, + "content": "While methods like quantization [17], pruning [18], distillation [6] and runtime-optimization [16] improve model efficiency (and are complementary), approaches exploiting spatial and temporal sampling are key for enabling efficient real-time perception [21, 27]. Neural warping mechanisms [23, 36] have been employed for image classification and regression, and recently, detection for self-driving [50]. Prior work [50] observes that end-to-end trained saliency networks fail for object detection. They instead turn to heuristics such as dataset-wide priors and object locations from previous frames, which are suboptimal. We show that formulation of learnable geometric priors is critical for learning end-to-end trained saliency networks for detection. We validate our approach in a variety of scenarios to showcase the generalizability of geometric priors for detection in self-driving on Argoverse-HD [27] and BDD100K [57] datasets, and for traffic-c cameras on WALT [37] dataset." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.494, + 0.47, + 0.6 + ], + "angle": 0, + "content": "- On Argoverse-HD, our learned geometric prior improves performance over naive downsampling by \\(+6.6\\) AP and \\(+2.7\\) AP over SOTA using the same detection architecture. Gains from our approach are achieved by detecting small far-away objects, improving by 9.6 \\(AP_{S}\\) (or \\(195\\%\\) ) over naive down-sampling and 4.2 \\(AP_{S}\\) (or \\(63\\%\\) ) over SOTA." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.602, + 0.47, + 0.661 + ], + "angle": 0, + "content": "- On WALT, our method detects small objects at image scales where other methods perform poorly. Further, it significantly improves detection rates by 10.7 \\(AP_{S}\\) over naive down-sampling and 3 \\(AP_{S}\\) over SOTA." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.664, + 0.47, + 0.723 + ], + "angle": 0, + "content": "- Our approach improves object tracking \\((+4.8\\%)\\) MOTA compared to baseline. It also improves tracking quality, showing increase of \\(+7.6\\%\\) \\(MT\\%\\) and reduction of \\(-6.7\\%\\) \\(ML\\%\\)." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.727, + 0.47, + 0.786 + ], + "angle": 0, + "content": "- Our approach can be deployed in resource constrained edge devices like Jetson AGX to detect \\(42\\%\\) more rare instances while being 2.2X faster to enable real-time sensing from buses." + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.494, + 0.47, + 0.786 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.801, + 0.22, + 0.815 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.469, + 0.87 + ], + "angle": 0, + "content": "We contextualize our work with respect to prior works modelling geometry and also among works that aim to make object detection more accurate and efficient." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Vision Meets Geometry: Geometry has played a crucial role in multiple vision tasks like detection [8, 20, 48, 55]," + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.334 + ], + "angle": 0, + "content": "segmentation [28, 46], recognition [14, 47] and reconstruction [25, 35, 44]. Perspective Geometric constraints have been used to remove distortion [58], improve depth prediction and semantic segmentation [26] and feature matching [51]. However, in most previous works [25, 44, 55] exploiting these geometric constraints have mainly been concentrated around improving 3D understanding. This can be attributed to a direct correlation between the constraints and the accuracy of reconstruction. Another advantage is the availability of large RGB-D and 3D datasets [5, 15, 39] to learn and exploit 3D constraints. Such constraints have been under-explored for learning based vision tasks like detection and segmentation. A new line of work interpreting classical geometric constraints and algorithms as neural layers [7, 42] have shown considerable promise in merging geometry with deep learning." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.339, + 0.892, + 0.536 + ], + "angle": 0, + "content": "Learning Based Detection: Object detection has mostly been addressed as an learning problem. Even classical-vision based approaches [12, 54] extract image features and learn to classify them into detection scores. With deep learning, learnable architectures have been proposed following this paradigm [4, 34, 38, 40], occasionally incorporating classical-vision ideas such as feature pyramids for improving scale invariance [29]. While learning has shown large improvements in accuracy over the years they still perform poorly while detecting small objects due to lack of geometric scene understanding. To alleviate this problem, we guide the input image with geometry constraints, and our approach complements these architectural improvements." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.542, + 0.892, + 0.633 + ], + "angle": 0, + "content": "Efficient Detection with Priors: Employing priors with learning paradigms achieves improvements with little additional human labelling effort. Object detection has traditionally been tackled as a learning problem and geometric constraints were sparsely used for such tasks, constraints like ground plane [20, 48] were used." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.638, + 0.892, + 0.789 + ], + "angle": 0, + "content": "Temporality [13, 50, 56] has been exploited for improving detection efficiently. Some of these methods [13, 50] deform the input image using approach that exploit temporality to obtain saliency. This approach handles cases where object size decreases with time (object moving away from the camera in scene), but cannot handle new incoming objects. None of these methods explicitly utilize geometry to guide detection, which handles both these cases. Our two-plane prior deforms the image while taking perspective into account without biasing towards previous detections." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Another complementary line of works automatically learn metaparameters (like image scale) [9, 16, 45] from image features. However, as they do not employ adaptive sampling accounting for image-specific considerations, performance improvements are limited. Methods not optimized for online perception like AdaScale [9] for video object detection do not perform well in real-time situations." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13365" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.091, + 0.188, + 0.108 + ], + "angle": 0, + "content": "3. Approach" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.115, + 0.47, + 0.178 + ], + "angle": 0, + "content": "We describe how a geometric model rooted in the interpretation of a 3D scene can be derived from the image. We then describe how to employ this rough 3D model to construct saliency for warping images and improving detection." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.187, + 0.189, + 0.203 + ], + "angle": 0, + "content": "3.1. Overview" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.211, + 0.47, + 0.287 + ], + "angle": 0, + "content": "Object sizes in the image are determined by the 3D geometry of the world. Let us devise a geometric inductive prior considering a camera mounted on a vehicle. Without loss of generality, assume the vehicle is moving in direction of the dominant vanishing point." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.287, + 0.469, + 0.408 + ], + "angle": 0, + "content": "We are interested in objects that are present in a planar region (See Figure 2) of width \\( P_{1}P_{2} \\) corresponding to the camera view, of length \\( P_{1}P_{3} \\) defined in the direction of the vanishing point. This is the planar region on the ground on which most of the objects of interest are placed (vehicles, pedestrians, etc) and another planar region \\( Q_{1}\\ldots Q_{4} \\) parallel to this ground plane above horizon line, such that all the objects are within this region (e.g., traffic lights)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.408, + 0.469, + 0.469 + ], + "angle": 0, + "content": "From this simple geometry model, we shall incorporate relationships derived from perspective geometry about objects, i.e., the scale of objects on ground plane is inversely proportional to their depth w.r.t camera [20]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.48, + 0.447, + 0.496 + ], + "angle": 0, + "content": "3.2. 3D Plane parameterization from 2D images" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.503, + 0.469, + 0.594 + ], + "angle": 0, + "content": "We parameterize the planes of our inductive geometric prior. We represent 2D pixel projections \\( u_{1} \\ldots u_{4} \\) of 3D points \\( P_{1} \\ldots P_{4} \\). Assume that the dominant vanishing point in the image is \\( v = (v_{x}, v_{y}) \\) and let the image size be \\( (w, h) \\). Consider \\( u_{1} \\) (Figure 2 (b)). We can define a point on the edge of the image plane," + }, + { + "type": "equation", + "bbox": [ + 0.188, + 0.602, + 0.469, + 0.619 + ], + "angle": 0, + "content": "\\[\nu _ {L} = \\left(0, v _ {y} + v _ {x} \\tan \\theta_ {1}\\right) \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.627, + 0.435, + 0.642 + ], + "angle": 0, + "content": "\\(u_{1}\\) can be expressed as a linear combination of \\(v\\) and \\(u_{L}\\)," + }, + { + "type": "equation", + "bbox": [ + 0.19, + 0.65, + 0.469, + 0.665 + ], + "angle": 0, + "content": "\\[\nu _ {1} = \\alpha_ {1} u _ {L} + (1 - \\alpha_ {1}) v \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.674, + 0.469, + 0.825 + ], + "angle": 0, + "content": "Similarly, for \\( u_{2} \\), we can define \\( u_{R} \\) in terms of \\( v \\) and \\( \\theta_{2} \\) and \\( \\alpha_{2} \\) while \\( u_{3} \\) and \\( u_{4} \\) are defined like Equation 1 to represent any arbitrary plane in this viewing direction. However, for simplicity, for ground plane we fix them as \\( (0,h) \\) and \\( (w,h) \\) respectively. Consider the planar region \\( Q_{1}\\ldots Q_{4} \\) at height \\( H \\) above the horizon line. We can similarly define \\( \\theta_{3} \\) and \\( \\theta_{4} \\) to represent the angles from the horizon in the opposite direction and define \\( q_{1} \\) and \\( q_{2} \\). Again, we set \\( q_{3} \\) as \\( (0,0) \\) and \\( q_{4} \\) as \\( (w,0) \\). We now have 4 points to calculate homographies \\( H_{plane} \\) for both planes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.469, + 0.901 + ], + "angle": 0, + "content": "For now, assume \\( v \\) is known. However, we still do not know the values for \\( \\theta \\)'s and \\( \\alpha \\), and we shall learn these parameters end-to-end from task loss. These parameters are learned and fixed for a given scenario in our learning paradigm. Our reparameterization aims to ease learning of these parameters" + }, + { + "type": "image", + "bbox": [ + 0.57, + 0.093, + 0.827, + 0.209 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.569, + 0.209, + 0.822, + 0.346 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.363, + 0.892, + 0.543 + ], + "angle": 0, + "content": "Figure 2. Geometry Of The Two Plane Perspective Prior: (a) describes the single view geometry of the proposed two plane prior. Region on the ground plane defined by \\( P_{1}, \\ldots, P_{4} \\), and rays emanating from camera \\( C \\) to \\( P_{i} \\) intersect at \\( u_{1} \\ldots u_{4} \\) on the image plane. The vanishing point \\( v \\) maps to \\( P_{\\infty} \\). This planar region accounts for small objects on the ground plane. To account for objects that are tall or do not lie on the ground plane, we consider another plane \\( Q_{1} \\ldots Q_{4} \\) above the horizon line. These two planes encapsulate all the relevant objects in the scene. (b) depicts the re-parameterization of the two planes in the 2D image. Instead of representing the planar points \\( u_{1} \\ldots u_{4} \\) as pixel coordinates, we instead parameterize them in terms of the vanishing point \\( v \\), \\( \\theta \\)'s and \\( \\alpha \\) to ease learning." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.572, + 0.892, + 0.603 + ], + "angle": 0, + "content": "as we clamp the values of \\(\\alpha\\)'s to \\([0,1]\\) and \\(\\theta\\)'s to \\([- \\frac{\\pi}{2}, \\frac{\\pi}{2}]\\). It should be noted that all the operations are differentiable." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.615, + 0.722, + 0.631 + ], + "angle": 0, + "content": "3.3. From Planes to Saliency" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.639, + 0.892, + 0.759 + ], + "angle": 0, + "content": "We leverage geometry to focus on relevant image regions through saliency guided warping [23, 36], and create a saliency map from a parameterized homography using \\( u_{1} \\ldots u_{4} \\) defined earlier. Looking at ground plane from two viewpoints (Figure 3 (a) and (b)), object size decreases by their distance from the camera [20]. We shall establish a relationship to counter this effect and \"sample\" far-away objects on the ground plane more than nearby objects." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.76, + 0.892, + 0.805 + ], + "angle": 0, + "content": "The saliency guided warping proposed by [36] operates using an inverse transformation \\(\\mathcal{T}_S^{-1}\\) parameterized by a saliency map \\(S\\) as follows," + }, + { + "type": "equation", + "bbox": [ + 0.577, + 0.813, + 0.891, + 0.831 + ], + "angle": 0, + "content": "\\[\nI ^ {\\prime} (x, y) = W _ {\\mathcal {T}} (I) = I \\left(\\mathcal {T} _ {S} ^ {- 1} (x, y)\\right) \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "where the warp \\(W_{\\mathcal{T}}\\) implies iterating over output pixel coordinates, using \\(\\mathcal{T}_S^{-1}\\) to find corresponding input coordinates (non-integral), and bilinearly interpolating output color from neighbouring input pixel grid points. For each" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "13366" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.09, + 0.285, + 0.19 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.113, + 0.19, + 0.235, + 0.202 + ], + "angle": 0, + "content": "(a) Camera View" + }, + { + "type": "image", + "bbox": [ + 0.284, + 0.091, + 0.484, + 0.189 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.301, + 0.19, + 0.462, + 0.204 + ], + "angle": 0, + "content": "(c) Mapping Saliency" + }, + { + "type": "image", + "bbox": [ + 0.487, + 0.091, + 0.686, + 0.189 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.487, + 0.191, + 0.687, + 0.205 + ], + "angle": 0, + "content": "(e) Ground Plane Saliency" + }, + { + "type": "image", + "bbox": [ + 0.688, + 0.091, + 0.888, + 0.189 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.698, + 0.191, + 0.875, + 0.205 + ], + "angle": 0, + "content": "(g) Two Plane Saliency" + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.206, + 0.282, + 0.305 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.105, + 0.308, + 0.258, + 0.322 + ], + "angle": 0, + "content": "(b) Bird's Eye View" + }, + { + "type": "image", + "bbox": [ + 0.284, + 0.206, + 0.485, + 0.305 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.306, + 0.308, + 0.475, + 0.322 + ], + "angle": 0, + "content": "(d) Saliency On Scene" + }, + { + "type": "image", + "bbox": [ + 0.485, + 0.206, + 0.686, + 0.305 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.308, + 0.668, + 0.323 + ], + "angle": 0, + "content": "(f) Ground Plane Warp" + }, + { + "type": "image", + "bbox": [ + 0.688, + 0.206, + 0.887, + 0.305 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.706, + 0.309, + 0.852, + 0.323 + ], + "angle": 0, + "content": "(h) Two Plane Warp" + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.342, + 0.894, + 0.412 + ], + "angle": 0, + "content": "Figure 3. Two-Plane Perspective Prior based Image Resampling: Consider the scene of car, bus and traffic light from (a) camera view and (b) (simplified) bird's eye view. (c) Saliency function that captures the inverse relationship between object size (in camera view) and depth (bird's eye view is looking at \\( XZ \\) plane from above) can be transferred to the camera view (d), by mapping row \\( z \\) using \\( H \\) (marked by blue arrows). (e) and (f) shows that ground plane severely distorts nearby tall objects while squishing traffic light. (g) and (h) shows that additional plane reduces distortion for both tall objects and objects not on ground plane." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.438, + 0.468, + 0.468 + ], + "angle": 0, + "content": "input pixel \\((x,y)\\), pixel coordinates with higher \\(S(x,y)\\) values (i.e. salient regions) would be sampled more." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.47, + 0.468, + 0.574 + ], + "angle": 0, + "content": "We construct a saliency \\(S\\) respecting the geometric properties that we desire. Let \\(H_{plane}\\) be the homography between the camera view (using coordinates \\(u_{1}\\ldots u_{4}\\)) and a bird's eye view of the ground plane assuming plane size to be the original image size \\((w,h)\\). In bird's eye view, we propose saliency function for a row of pixels \\(z\\) (assuming bottom-left of this rectangle as \\((0,0)\\)) as," + }, + { + "type": "equation", + "bbox": [ + 0.208, + 0.58, + 0.469, + 0.599 + ], + "angle": 0, + "content": "\\[\nS _ {b e v} (z) = e ^ {\\nu \\left(\\frac {z}{h} - 1\\right)} \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.608, + 0.469, + 0.637 + ], + "angle": 0, + "content": "with a learnable parameter \\(\\nu (>1)\\). \\(\\nu\\) defines the extent of sampling with respect to depth." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.638, + 0.468, + 0.669 + ], + "angle": 0, + "content": "To map this saliency to camera view, we warp \\( S_{bev} \\) via perspective transform \\( W_{p} \\) and \\( H_{plane} \\) (Figure 3 (c))," + }, + { + "type": "equation", + "bbox": [ + 0.178, + 0.674, + 0.469, + 0.694 + ], + "angle": 0, + "content": "\\[\nS _ {p l a n e} = W _ {p} \\left(H _ {p l a n e} ^ {- 1}, S _ {b e v}\\right) \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.701, + 0.469, + 0.761 + ], + "angle": 0, + "content": "We have defined saliency \\( S_{plane} \\) given \\( H_{plane} \\) in a differentiable manner. Our saliency ensures that objects on the ground plane separated by depth \\( Z \\) are sampled by the factor \\( e^{\\nu \\frac{Z}{h}} \\) in the image." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.771, + 0.332, + 0.788 + ], + "angle": 0, + "content": "3.4. Two-Plane Perspective Prior" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Ground Plane saliency focuses on objects that are geometrically constrained to be on this plane and reasonably models objects far away on the plane. However, nearby and tall objects, and small objects far above the ground plane are not modelled well. In Fig 3 (f), nearby objects above ground plane (traffic lights), they are highly distorted. Critically, these same objects when further away are rendered" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.438, + 0.892, + 0.528 + ], + "angle": 0, + "content": "small in size and appear close to ground (and thus modelled well). Objects we should focus more on are thus the former compared to the latter. Thus, another plane is needed, and direction of the saliency function is reversed to \\(\\hat{S}_{bev}(z) = e^{\\hat{\\nu}((h - z) / h) - 1}\\) to account for these objects that would otherwise be severely distorted." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.529, + 0.892, + 0.559 + ], + "angle": 0, + "content": "To represent the Two-Plane Prior, we represented the planar regions as saliencies. The overall saliency is," + }, + { + "type": "equation", + "bbox": [ + 0.585, + 0.565, + 0.891, + 0.582 + ], + "angle": 0, + "content": "\\[\nS = S _ {\\text {g r o u n d - p l a n e}} + \\lambda S _ {\\text {t o p - p l a n e}} \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.587, + 0.708, + 0.601 + ], + "angle": 0, + "content": "where \\(\\lambda\\) is a learned parameter." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.61, + 0.738, + 0.624 + ], + "angle": 0, + "content": "3.5. Additional Considerations" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.633, + 0.892, + 0.723 + ], + "angle": 0, + "content": "Warping via a piecewise saliency function imposes additional considerations. The choice of deformation method is critical, saliency sampler [36] implicitly avoids drastic transformations common in other approaches. For e.g., Thin-plate spline performs worse [36], produces extreme transformations and requires regularization [13]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.724, + 0.892, + 0.769 + ], + "angle": 0, + "content": "Fovea [50] observes that restricting the space of allowable warps such that axis alignment is preserved improves accuracy, we adopt the separable formulation of \\(\\mathcal{T}^{-1}\\)" + }, + { + "type": "equation", + "bbox": [ + 0.587, + 0.771, + 0.891, + 0.807 + ], + "angle": 0, + "content": "\\[\n\\mathcal {T} _ {x} ^ {- 1} (x) = \\frac {\\int_ {x ^ {\\prime}} S _ {x} \\left(x ^ {\\prime}\\right) k \\left(x ^ {\\prime} , x\\right) x ^ {\\prime}}{\\int_ {x ^ {\\prime}} S _ {x} \\left(x ^ {\\prime}\\right) k \\left(x , x ^ {\\prime}\\right)} \\tag {7}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.59, + 0.813, + 0.891, + 0.851 + ], + "angle": 0, + "content": "\\[\n\\mathcal {T} _ {y} ^ {- 1} (y) = \\frac {\\int_ {y ^ {\\prime}} S _ {y} \\left(y ^ {\\prime}\\right) k \\left(y ^ {\\prime} , y\\right) y ^ {\\prime}}{\\int_ {y ^ {\\prime}} S _ {y} \\left(y ^ {\\prime}\\right) k \\left(y , y ^ {\\prime}\\right)} \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "where \\( k \\) is a Gaussian kernel. To convert a saliency map \\( S \\) to \\( S_{x} \\) and \\( S_{y} \\) we marginalize it along the two axes. Thus entire rows or columns are \"stretched\" or \"compressed\"." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13367" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.212 + ], + "angle": 0, + "content": "Two-plane prior is learnt end to end as a learnable image warp. For object detection, labels need to be warped too, and [36]'s warp is invertible. Like [50], We employ the loss \\(\\mathcal{L}(\\mathcal{T}^{-1}(f_{\\phi}(W_{\\mathcal{T}}(I)),L)\\) where \\((I,L)\\) is the image-label pair and omit the use of delta encoding for training RPN [40] (which requires the existence of a closed form \\(\\mathcal{T}\\)), instead adopting GIoU loss [41]. This ensures \\(W_{\\mathcal{T}}\\) is learnable, as \\(\\mathcal{T}^{-1}\\) is differentiable." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.213, + 0.473, + 0.306 + ], + "angle": 0, + "content": "We did not assume that the vanishing point is within the field of view of our image, and our approach places no restrictions on the vanishing point. Thus far, we explained our formulation while considering a single dominant vanishing point, however, multiple vanishing points can be also considered. Please see supplementary for more details." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.314, + 0.347, + 0.33 + ], + "angle": 0, + "content": "3.6. Obtaining the Vanishing Point" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.337, + 0.47, + 0.398 + ], + "angle": 0, + "content": "We now describe how we obtain the vanishing point. Many methods exist with trade-offs in accuracy, latency and memory which inform our design to perform warping efficiently with minimal overheads." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.399, + 0.47, + 0.504 + ], + "angle": 0, + "content": "Fixed Cameras: In settings like traffic cameras, the camera is fixed. Thus, the vanishing point is fixed, and we can cache the corresponding saliency \\( S \\), as all the parameters, once learnt, are fixed. We can define the vanishing point for a camera manually by annotating two parallel lines or any accurate automated approach. Saliency caching renders our approach extremely efficient." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.505, + 0.47, + 0.686 + ], + "angle": 0, + "content": "Autonomous Navigation: Multiple assumptions simplify the problem. We assume that there is one dominant vanishing point and a navigating car is often moving in the viewing direction. Thus, we assume that this vanishing point lies inside the image, and directly regress \\( v \\) from image features using a modified coordinate regression module akin to YOLO [33, 38]. This approach appears to be memory and latency efficient. Other approaches, say, using parallel lane lines [1] or inertial measurements [3] might also be very efficient. An even simpler assumption is to employ the average vanishing point, as vanishing points are highly local, we observe this is a good approximation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.686, + 0.469, + 0.731 + ], + "angle": 0, + "content": "Temporal Redundancies: In videos, we exploit temporal redundancies, the vanishing point is computed every \\( n_v \\) frames and saliency is cached to amortize latency cost." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.731, + 0.469, + 0.807 + ], + "angle": 0, + "content": "General Case: This is the most difficult case, and many approaches have been explored in literature to find all vanishing points. Classical approaches [49] while fast are not robust, while deep-learned approaches [31,32,59] are accurate yet expensive (either in latency or memory)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.817, + 0.47, + 0.833 + ], + "angle": 0, + "content": "3.7. Learning Geometric Prior from Pseudo-Labels" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Prior work [50] have shown improvements in performance on pre-trained models via heuristics, which didn't require any training. However, their method still employs domain-specific labels (say, from Argoverse-HD) to generate the" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.089, + 0.696, + 0.174 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.698, + 0.089, + 0.892, + 0.174 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.175, + 0.696, + 0.26 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.698, + 0.175, + 0.891, + 0.26 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.272, + 0.894, + 0.342 + ], + "angle": 0, + "content": "Figure 4. Commuter Bus Dataset: The captured data has a unique viewpoint, the average size of objects is small and captured under a wide variety of lighting conditions. Top-left and bottom-right images depict the same bus-stop and trashcan at different time of day and season." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.369, + 0.892, + 0.43 + ], + "angle": 0, + "content": "prior. Our method can't be used directly with pre-trained models as it learns geometrically inspired parameters end-to-end. However, domain-specific images without labels can be exploited to learn the parameters." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.43, + 0.893, + 0.536 + ], + "angle": 0, + "content": "We propose a simple alternative to learn the proposed prior using pre-trained model without requiring additional domain-specific labels. We generate pseudo-labels from our pre-trained model inferred at 1x scale. We fine-tune and learn our warp function (to \\(0.5\\mathrm{x}\\) scale) end-to-end using these \"free\" labels. Our geometric prior shows improvements without access to ground truth labels." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.55, + 0.787, + 0.565 + ], + "angle": 0, + "content": "4. Dataset And Evaluation Details" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.575, + 0.602, + 0.59 + ], + "angle": 0, + "content": "4.1. Datasets" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.892, + 0.689 + ], + "angle": 0, + "content": "Argoverse-HD [27]: We employ Argoverse-HD dataset for evaluation in the autonomous navigation scenario. This dataset consists of 30fps video sequences from a car collected at \\(1920 \\times 1200\\) resolution, and dense box annotations are provided for common objects of interest such as vehicles, pedestrians, signboards and traffic lights." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.893, + 0.886 + ], + "angle": 0, + "content": "WALT [37]: We employ images from 8.4K cameras that overlook public urban settings to analyze the flow of traffic vehicles. The data is captured for 3-second bursts every few minutes and only images with notable changes are stored. We annotated a set of 4738 images with vehicles collected over the time period of a year covering a variety of day/night/dawn settings, seasonal changes and camera viewpoints. We show our results on two splits (approximately \\(80\\%\\) training and \\(20\\%\\) testing). The first, All-Viewpoints, images from all the cameras are equally represented in the train and test sets. Alternatively, we split by camera, Split-by-Camera, images from 6 cameras are part of the training set and 2 cameras are held out for testing." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.886, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Commuter Bus Dataset: We curated this dataset from a" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13368" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.089, + 0.468, + 0.252 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.263, + 0.472, + 0.32 + ], + "angle": 0, + "content": "Figure 5. Two-Plane Prior as a Neural Layer: We implemented our approach as a global prior that is learned end-to-end from labelled data. Our prior is dependent on a vanishing point estimate to specify the viewing direction of the camera." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.348, + 0.473, + 0.501 + ], + "angle": 0, + "content": "commuter bus running on an urban route. The 720p camera of interest has a unique viewpoint and scene geometry (See Figure 4). Annotated categories are trashcans and garbage bags (to help inform public services) and people with special needs (using wheelchairs or strollers), which are a rare occurrence. The dataset size is small with only 750 annotated images (split into \\(70\\%\\) training and \\(30\\%\\) testing). This is an extremely challenging dataset due to its unique viewpoint, small object size, rare categories, along with variations in lighting and seasons." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.511, + 0.258, + 0.527 + ], + "angle": 0, + "content": "4.2. Evaluation Details" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.536, + 0.47, + 0.58 + ], + "angle": 0, + "content": "We perform apples-to-apples comparisons on the same detector trained using the datasets with identical training schedule and hardware." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.582, + 0.47, + 0.687 + ], + "angle": 0, + "content": "Data: We compare to methods that were trained on fixed training data. In contrast, sAP leaderboards [27] don't restrict data and evaluate on different hardware. We compare with [16, 27] from leaderboard, which follow the same protocols. Other methods on the leaderboard use additional training data to train off-the-self detectors. Our detectors would see similar improvements with additional data." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.688, + 0.472, + 0.884 + ], + "angle": 0, + "content": "Real-Time Evaluation: We evaluate using Streaming AP (sAP) metric proposed by [27], which integrates latency and accuracy into a single metric. Instead of considering models via accuracy-latency tradeoffs [21], real-time performance can be evaluated by applying real-time constraints on the predictions [27]. Frames of the video are observed every 33 milliseconds (30 fps) and predictions for every frame must be emitted before the frame is observed (forecasting is necessary). For a fair comparison, sAP requires evaluation on the same hardware. Streaming results are not directly comparable with other work [27, 50, 56] as they use other hardware (say, V100 or 2080Ti), thus we run the evaluation on our hardware (Titan X)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.886, + 0.371, + 0.902 + ], + "angle": 0, + "content": "Additional details are in the Supplementary." + }, + { + "type": "table", + "bbox": [ + 0.501, + 0.089, + 0.905, + 0.251 + ], + "angle": 0, + "content": "
MethodScaleAPAPSAPMAPLLatency (ms)
Faster R-CNN0.5x24.24.929.050.978.4 ± 1.8
Fovea (SD) [50]0.5x26.78.229.754.183 ± 2.5
Fovea (SI) [50]0.5x28.010.431.054.585 ± 2.7
Fovea (L:SI) [50]0.5x28.110.330.954.185.4 ± 2.7
Two-Plane Pr. (Pseudo.)0.5x27.19.828.950.2104.5 ± 8.5
Two-Plane Prior0.5x30.814.531.652.9105 ± 8.5
Baseline at higher scales
Faster R-CNN0.75x29.211.632.153.3142 ± 2.5
Faster R-CNN1.0x33.316.834.853.6220 ± 1.7
" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.261, + 0.895, + 0.318 + ], + "angle": 0, + "content": "Table 1. Evaluation on Argoverse-HD: Two-Plane Prior outperforms both SOTA's dataset-wide and temporal priors in overall accuracy. Our method improves small object detection by \\(+4.1AP_{S}\\) or \\(39\\%\\) over SOTA." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.337, + 0.725, + 0.354 + ], + "angle": 0, + "content": "5. Results and Discussions" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.365, + 0.895, + 0.456 + ], + "angle": 0, + "content": "Accuracy-Latency Comparisons: On Argoverse-HD, we compare with Faster R-CNN with naive downsampling (Baseline) and Faster R-CNN paired with adaptive sampling from Fovea [50] which proposed two priors, a dataset-wide prior \\((S_{D})\\) and frame-specific temporal priors (\\(S_{I}\\) & \\(L: S_{I}\\); from previous frame detections)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.457, + 0.896, + 0.637 + ], + "angle": 0, + "content": "Two-Plane Prior improves (Table 1) upon baseline at the same scale by \\(+6.6\\) AP and over SOTA by \\(+2.7\\) AP. For small objects, the improvements are even more dramatic, our method improves accuracy by \\(+9.6\\) \\(AP_{S}\\) or \\(195\\%\\) over baseline and \\(+4.2\\) \\(AP_{S}\\) or \\(45\\%\\) over SOTA respectively. Surprisingly, our method at \\(0.5\\mathrm{x}\\) scale improves upon Faster R-CNN at \\(0.75\\mathrm{x}\\) scale by \\(+1.6\\) AP having latency improvement of \\(35\\%\\). Our Two-Plane prior trained via pseudolabels comes very close to SOTA which employ ground truth labels, the gap is only \\(-1\\) AP and improves upon Faster R-CNN model trained on ground truth by \\(+2.9\\) AP inferred at the same scale." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.64, + 0.895, + 0.732 + ], + "angle": 0, + "content": "WALT dataset [37] comprises images (only images with notable changes are saved) and not videos, we compare with Fovea [50] paired with the dataset-wide prior. We observe similar trends on both splits (Table 3 and Fig 6) and note large improvements over baseline and a consistent improvement over Fovea [50], specially for small objects." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.733, + 0.895, + 0.794 + ], + "angle": 0, + "content": "Real-time/Streaming Comparisons: We use Argoverse-HD dataset, and compare using the sAP metric (Described in Section 4.2). Algorithms may choose any scale and frames as long as real-time latency constraint is satisfied." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.895, + 0.903 + ], + "angle": 0, + "content": "All compared methods use Faster R-CNN, and we adopt their reported scales (and other parameters). Streamer [27] converts any single frame detector for streaming by scheduling which frames to process and interpolating predictions between processed frames. AdaScale [9] regresses optimal scale from image features to minimize single-frame latency while Adaptive Streamer [16] learns scale choice in" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "13369" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.089, + 0.468, + 0.224 + ], + "angle": 0, + "content": "
IDMethodScale(s)sAPsAPSsAPMsAPL
1Streamer [27]0.5x18.33.115.040.9
21 + Adascale [9]0.2x-0.6x13.40.28.637.4
3Adaptive Streamer [16]0.2x-0.6x21.34.218.847.0
41 + FOVEA (SI) [50]0.5x24.18.424.748.7
51 + Ours (Avg VP)0.5x29.913.731.352.2
61 + Ours0.5x30.013.731.552.2
71 + Ours (VP Oracle)0.5x30.714.531.652.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.234, + 0.47, + 0.332 + ], + "angle": 0, + "content": "Table 2. Streaming Evaluation on Argoverse-HD: Ours denotes Two-Plane Prior. Every frame's prediction (streamed at 30FPS) must be emitted before frame is observed [27] (via forecasting). All methods evaluated on Titan X GPU. Underlying detector (Faster R-CNN) is constant across approaches, improvements are solely from spatial sampling mechanisms. Notice improved detection of small objects by \\(+5.3sAP_{S}\\) or \\(63\\%\\) over SOTA." + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.347, + 0.275, + 0.459 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.275, + 0.347, + 0.468, + 0.459 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.468, + 0.47, + 0.553 + ], + "angle": 0, + "content": "Figure 6. WALT All-Viewpoints Split: Our approach (Two-Plane Prior) shows improved overall performance over naive downsampling and state-of-the-art adaptive sampling technique, specially for small objects at all scales (starting from \\(0.5\\mathrm{x}\\)). Horizontal line (orange) indicates performance at maximum possible scale \\((0.6\\mathrm{x})\\) the base detector was trained at (memory constraints)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.582, + 0.47, + 0.779 + ], + "angle": 0, + "content": "the streaming setting. Both these methods employ naive-downsampling. State-of-the-art, Fovea [50] employs the temporal prior \\((S_I)\\). From Table 2, Two-Plane prior outperforms the above approaches by \\(+16.5\\) sAP, \\(+8.6\\) sAP and \\(+5.9\\) sAP respectively. Comparison with [9, 16, 27] shows the limitations of naive downsampling, even when \"optimal\" scale is chosen. Our geometric prior greatly improves small object detection performance by \\(63\\%\\) or \\(+5.3\\) sAPs over SOTA. To consider dependence on accurate Vanishing Point detection (and its overheads), we use NeurVPS [59] as oracle (we simulate accurate prediction with zero delay) to obtain an upper bound, we observe even average vanishing point location's performance is within \\(0.8\\) sAP." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Accuracy-Scale Tradeoffs: We experiment with WALT All-Viewpoints split to observe accuracy-scale trade-offs. The native resolution \\((4K)\\) of the dataset is extremely large and the gradients don't fit within 12 GB memory of our Titan X GPU, thus we cropped the skies and other static regions to reduce input scale (1x) to \\(1500 \\times 2000\\). Still, the highest scale we were able to train our baseline Faster R-CNN model is 0.6x. So, we use aggressive downsam" + }, + { + "type": "table", + "bbox": [ + 0.536, + 0.089, + 0.859, + 0.26 + ], + "angle": 0, + "content": "
MethodScaleAPAPSAPMAPL
Faster R-CNN0.25x16.707.242.3
FOVEA (SD) [50]0.25x23.2013.954.1
Two-Plane Prior0.25x25.21.018.254.5
Faster R-CNN0.5x29.24.924.755.5
FOVEA (SD) [50]0.5x34.48.730.559.4
Two-Plane Prior0.5x36.411.632.359.0
Baseline at higher scales
Faster R-CNN0.6x33.29.328.656.7
Faster R-CNN*1.0x34.312.630.754.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.27, + 0.894, + 0.34 + ], + "angle": 0, + "content": "Table 3. WALT Camera-Split: The viewpoints on the test set were not seen, and Two-Plane Prior shows better performance over both naive downsampling and state-of-the-art adaptive sampling as it generalizes better to unseen scenes and viewpoints. *Not trained at that scale due to memory constraints on Titan X." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.352, + 0.892, + 0.442 + ], + "angle": 0, + "content": "pling scales \\(\\{0.5, 0.4375, 0.375, 0.3125, 0.25, 0.125\\}\\). The results are presented in Figure 6. We observe a large and consistent improvement over baseline and Fovea [50], specially for small objects. For instance, considering performance at \\(0.375x\\) scale, our approach is better than baseline by \\(+13.1AP\\) and Fovea by \\(+1.4AP\\) for all objects." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.445, + 0.893, + 0.535 + ], + "angle": 0, + "content": "For small objects, we observe dramatic improvement, at scales smaller than \\(0.375\\mathrm{x}\\), other approaches are unable to detect any small objects while our approach does so until \\(0.125\\mathrm{x}\\) scale, showing that our approach degrades more gracefully. At \\(0.375\\mathrm{x}\\) scale, our approach improves upon Faster R-CNN by \\(+10.7AP_{S}\\) and Fovea by \\(+3.0AP_{S}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.537, + 0.894, + 0.718 + ], + "angle": 0, + "content": "Generalization to new viewpoints: We use WALT Camera-Split, the test scenes and viewpoint are unseen in training. E.g., the vanishing point of one of the held-out cameras is beyond the image's field of view. We operate on the same scale factors in the earlier experiments, and results are presented in Table 3. We note lower overall performance levels due to scene/viewpoint novelty in the test sets. Our approach generalizes better due to the explicit modelling of the viewpoint via the vanishing point (See Section 3.2). We note trends similar to previous experiment, we demonstrate improvements of \\(+8.5\\) AP over naive-downsampling and \\(+2.0\\) AP over Fovea [50] at \\(0.25\\mathrm{x}\\) scale." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Tracking Improvements: We follow tracking-by-detection and pair IOUTracker [2] with detectors on Argoverse-HD dataset. MOTA and MOTP evaluate overall tracking performance. From Table 4, Our method improves over baseline by \\(+4.8\\%\\) and \\(+0.7\\%\\). We also focus on tracking quality metrics, Mostly Tracked \\(\\%\\) (MT%) evaluates the percentage of objects tracked for at least \\(80\\%\\) of their lifespan while Mostly Lost \\(\\%\\) (ML%) evaluates percentage of objects for less than \\(20\\%\\) of their lifespan. In both these cases, our approach improves upon the baseline by \\(+7.6\\%\\) and \\(-6.7\\%\\) respectively. To autonomous navigation, we define two relevant metrics, namely, average lifespan extension (ALE)" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "13370" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.079, + 0.089, + 0.487, + 0.172 + ], + "angle": 0, + "content": "
MethodMOTA ↑MOTP ↑MT% ↑ML% ↓MOS ↓ALE% ↑
Faster RCNN39.882.330.735.637.159.3 %
Fovea (SD) [50]43.981.934.131.934.8+5.4 %
Fovea (SI) [50]44.381.836.728.433.8+8.4 %
Two-Plane Prior44.683.038.328.931.6+9.9 %
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.182, + 0.472, + 0.252 + ], + "angle": 0, + "content": "Table 4. Tracking Improvements: We setup a tracking by detection pipeline and replace the underlying detection method and observe improvements if any. All the detectors employ the Faster R-CNN architecture and are executed at \\(0.5\\mathrm{x}\\) scale. We observe improvements in tracking metrics due to Two-Plane Prior." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.278, + 0.469, + 0.354 + ], + "angle": 0, + "content": "and minimum object size tracked (MOS), whose motivation and definitions can be viewed in supplementary. We observe that our improvements are better than both Fovea \\((S_{D})\\) and \\((S_{I})\\). As we observe, our method improves tracking lifespan and also helps track smaller objects." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.355, + 0.47, + 0.49 + ], + "angle": 0, + "content": "Efficient City-Scale Sensing: We detect objects on Commuter Bus equipped with a Jetson AGX. Identifying (Recall) relevant frames is key on the edge. Recall of Faster R-CNN with at 1x scale is \\(43.3AR\\) (\\(16.9AR_{S}\\)) (Latency: 350ms; infeasible for real-time execution) but drops to \\(31.7AR\\) (\\(0.5AR_{S}\\)) at 0.5x scale when naively downsampled (Latency: 154ms). Whereas our approach at 0.5x scale improves recall by \\(42\\%\\) over full resolution execution to 61.7 AR (16.4 ARS) with latency of 158 ms (+4 ms)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.491, + 0.47, + 0.552 + ], + "angle": 0, + "content": "In supplementary, we perform additional comparisons, provide details on handling multiple vanishing points, more tracking results and edge sensing results. We also present some qualitative results and comparisons." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.56, + 0.242, + 0.575 + ], + "angle": 0, + "content": "5.1. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.583, + 0.469, + 0.614 + ], + "angle": 0, + "content": "We discuss some of the considerations of our approach through experiments on the Argoverse-HD dataset." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.614, + 0.469, + 0.81 + ], + "angle": 0, + "content": "Ground Plane vs Two-Plane Prior: We discussed the rationale of employing multiple planes in Fig 3, and our results are consistent. From Table 5, Two-Plane Prior outperforms Ground Plane prior considerably \\((+1.8AP)\\). Ground Plane Prior outperforms Two-Plane Prior on small objects by \\(+1AP_{S}\\) but is heavily penalized on medium \\((-4.1AP_{M})\\) and large objects \\((-4.6AP_{L})\\). This is attributed to heavy distortion of tall and nearby objects, and objects that are not on the plane (Figure 3). Lastly, this prior was difficult to learn, the parameter space severely distorted the images (we tuned initialization and learning rate). Thus we did not consider this prior further. The second plane acts as a counterbalance and that warping space is learnable." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.469, + 0.902 + ], + "angle": 0, + "content": "Vanishing Point Estimate Dependence: From Table 5, dominant vanishing point in autonomous navigation is highly local in nature, and estimating VP improves the result by +1.2 AP. Estimating the vanishing point is a design choice, it's important for safety critical applications like autonomous navigation (performance while navigating turns)" + }, + { + "type": "table", + "bbox": [ + 0.517, + 0.089, + 0.878, + 0.166 + ], + "angle": 0, + "content": "
MethodScaleAPAPSAPMAPL
Ground Plane Prior0.5x29.115.527.548.3
Two-Plane Prior (Psuedo.)0.5x27.19.828.950.2
Two-Plane Prior (Avg VP)0.5x29.612.730.752.7
Two-Plane Prior0.5x30.814.531.652.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.175, + 0.892, + 0.218 + ], + "angle": 0, + "content": "Table 5. Ablation Study on Argoverse-HD to justify our design choice of using two planes, dependence on accurate vanishing point detection and choice of pseudo labels vs ground truth." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.23, + 0.838, + 0.246 + ], + "angle": 0, + "content": "however might be omitted for sensing applications." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.247, + 0.892, + 0.383 + ], + "angle": 0, + "content": "Using Pseudo Labels vs Ground Truth: Table 5 shows there is still considerable gap (-3.7 AP) between the Two-Plane Prior trained from pseudo labels and ground truth. We observe that the model under-performs on stopsign, bike and truck classes, which are under-represented in the COCO dataset [30] compared to person and car classes. Performance of the pre-trained model on these classes is low even at 1x scale. Hence, we believe that the performance difference is an artifact of this domain gap." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.402, + 0.627, + 0.418 + ], + "angle": 0, + "content": "6. Conclusions" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.43, + 0.892, + 0.761 + ], + "angle": 0, + "content": "In this work, we proposed a learned two-plane perspective prior which incorporates rough geometric constraints from 3D scene interpretations of 2D images to improve object detection. We demonstrated that (a) Geometrically defined spatial sampling prior significantly improves detection performance over multiple axes (accuracy, latency and memory) in terms of both single-frame accuracy and accuracy with real-time constraints over other methods. (b) Not only is our approach is more accurate when adaptively down-sampling at all scales, it degrades much more gracefully for small objects, resulting in latency and memory savings. (c) As our prior is learned end-to-end, we can improve a detector's performance at lower scales for \"free\". (d) Our approach generalizes better to new camera viewpoints and enables efficient city-scale sensing applications. Vanishing point estimation is the bottleneck of our approach [11, 31, 32, 59] for general scenes, and increasing efficiency of its computation we will see substantial improvements. Investigating geometric constraints to improve other aspects of real-time perception systems as future work, like object tracking and trajectory understanding and forecasting, is promising." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.763, + 0.892, + 0.854 + ], + "angle": 0, + "content": "Societal Impact Our approach has strong implications for autonomous-driving and city-scale sensing for smart city applications, wherein efficient data processing would lead to more data-driven decision-making and public policies. However, privacy is a concern, and we shall release the datasets after anonymizing people and license plates." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Acknowledgements: This work was supported in part by an NSF CPS Grant CNS-2038612, a DOT RITA Mobility-21 Grant 69A3551747111 and by General Motors Israel." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "13371" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.175, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.117, + 0.47, + 0.171 + ], + "angle": 0, + "content": "[1] Hala Abualsaud, Sean Liu, David B Lu, Kenny Situ, Akshay Rangesh, and Mohan M Trivedi. Laneaf: Robust multi-lane detection with affinity fields. 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Dinesh Reddy + +Christoph Mertz + +Carnegie Mellon University + +Srinivasa G. Narasimhan + +{anuraggh, dnarapur, cmertz, srinivas}@cs.cmu.edu + +# Abstract + +Real-time efficient perception is critical for autonomous navigation and city scale sensing. Orthogonal to architectural improvements, streaming perception approaches have exploited adaptive sampling improving real-time detection performance. In this work, we propose a learnable geometry-guided prior that incorporates rough geometry of the 3D scene (a ground plane and a plane above) to resample images for efficient object detection. This significantly improves small and far-away object detection performance while also being more efficient both in terms of latency and memory. For autonomous navigation, using the same detector and scale, our approach improves detection rate by $+4.1\mathrm{AP}_S$ or $+39\%$ and in real-time performance by $+5.3\mathrm{sAP}_S$ or $+63\%$ for small objects over state-of-the-art (SOTA). For fixed traffic cameras, our approach detects small objects at image scales other methods cannot. At the same scale, our approach improves detection of small objects by $195\%$ $(+12.5\mathrm{AP}_S)$ over naive-downsampling and $63\%$ $(+4.2\mathrm{AP}_S)$ over SOTA. + +# 1. Introduction + +Visual perception is important for autonomous driving and decision-making for smarter and sustainable cities. Real-time efficient perception is critical to accelerate these advances. For instance, a single traffic camera captures half a million frames every day or a commuter bus acting as a city sensor captures one million frames every day to monitor road conditions [10] or to inform public services [22]. There are thousands of traffic cameras [24] and nearly a million commuter buses [53] in the United States. It is infeasible to transmit and process visual data on the cloud, leading to the rise of edge architectures [43]. However, edge devices are severely resource constrained and real-time inference requires down-sampling images to fit both latency and memory constraints severely impacting accuracy. + +On the other hand, humans take visual shortcuts [19] to + +# Trrrnnnne + +![](images/886afeb3f2b2469e3841960b9e007d475e67d50a0edc8612c3c41b405903c353.jpg) + +![](images/cf71d620299bdbc3e8db0af5be49141cf15a287acadb1f40578c77f10257eaec.jpg) + +# e e e + +![](images/4f9855606219b6f6fb11abd82a7c0ab8e114d7bc63829a7c7fe85532e048b671.jpg) + +![](images/a2980e16f42b3027978eda26dac78a148b174ef72723066ce6c575a94806f39d.jpg) + +# Saaee + +![](images/c740d404f39bf6d6499d9409992ff64f161ba9ce287734f9c371f180be8dc69e.jpg) +Figure 1. Geometric cues (black dashed lines) are implicitly present in scenes. Our Perspective based prior exploits this geometry. Our method (a) takes an image and (b) warps them, and performs detection on warped images. Small objects which are (d) not detected when naively downsampled but (e) are detected when enlarged with our geometric prior. Our method (f) uses a geometric model to construct a saliency prior to focus on relevant areas and (g) enables sensing on resource-constrained edge devices. + +![](images/e29c1f634f3a41f658beb9db95e50c037a5b27136c49b8e14219b6633bc29fa0.jpg) + +recognize objects efficiently and employ high-level semantics [19, 52] rooted in scene geometry to focus on relevant parts. Consider the scene in Figure 1 (c), humans can recognize the distant car despite its small appearance (Figure 1 (d)). We are able to contextualize the car in the 3D scene, namely (1) it's on the road and (2) is of the right size we'd expect at that distance. Inspired by these observations, can we incorporate semantic priors about scene geometry in our neural networks to improve detection? + +In this work, we develop an approach that enables object detectors to "zoom" into relevant image regions (Figure 1 (d) and (e)) guided by the geometry of the scene. Our approach considers that most objects of interests are present within two planar regions, either on the ground plane or within another plane above the ground, and their size in the image follow a geometric relationship. Instead of uniformly downsampling, we sample the image to enlarge far away regions more and detect those smaller objects. + +While methods like quantization [17], pruning [18], distillation [6] and runtime-optimization [16] improve model efficiency (and are complementary), approaches exploiting spatial and temporal sampling are key for enabling efficient real-time perception [21, 27]. Neural warping mechanisms [23, 36] have been employed for image classification and regression, and recently, detection for self-driving [50]. Prior work [50] observes that end-to-end trained saliency networks fail for object detection. They instead turn to heuristics such as dataset-wide priors and object locations from previous frames, which are suboptimal. We show that formulation of learnable geometric priors is critical for learning end-to-end trained saliency networks for detection. We validate our approach in a variety of scenarios to showcase the generalizability of geometric priors for detection in self-driving on Argoverse-HD [27] and BDD100K [57] datasets, and for traffic-c cameras on WALT [37] dataset. + +- On Argoverse-HD, our learned geometric prior improves performance over naive downsampling by $+6.6$ AP and $+2.7$ AP over SOTA using the same detection architecture. Gains from our approach are achieved by detecting small far-away objects, improving by 9.6 $AP_{S}$ (or $195\%$ ) over naive down-sampling and 4.2 $AP_{S}$ (or $63\%$ ) over SOTA. +- On WALT, our method detects small objects at image scales where other methods perform poorly. Further, it significantly improves detection rates by 10.7 $AP_{S}$ over naive down-sampling and 3 $AP_{S}$ over SOTA. +- Our approach improves object tracking $(+4.8\%)$ MOTA compared to baseline. It also improves tracking quality, showing increase of $+7.6\%$ $MT\%$ and reduction of $-6.7\%$ $ML\%$ . +- Our approach can be deployed in resource constrained edge devices like Jetson AGX to detect $42\%$ more rare instances while being 2.2X faster to enable real-time sensing from buses. + +# 2. Related Work + +We contextualize our work with respect to prior works modelling geometry and also among works that aim to make object detection more accurate and efficient. + +Vision Meets Geometry: Geometry has played a crucial role in multiple vision tasks like detection [8, 20, 48, 55], + +segmentation [28, 46], recognition [14, 47] and reconstruction [25, 35, 44]. Perspective Geometric constraints have been used to remove distortion [58], improve depth prediction and semantic segmentation [26] and feature matching [51]. However, in most previous works [25, 44, 55] exploiting these geometric constraints have mainly been concentrated around improving 3D understanding. This can be attributed to a direct correlation between the constraints and the accuracy of reconstruction. Another advantage is the availability of large RGB-D and 3D datasets [5, 15, 39] to learn and exploit 3D constraints. Such constraints have been under-explored for learning based vision tasks like detection and segmentation. A new line of work interpreting classical geometric constraints and algorithms as neural layers [7, 42] have shown considerable promise in merging geometry with deep learning. + +Learning Based Detection: Object detection has mostly been addressed as an learning problem. Even classical-vision based approaches [12, 54] extract image features and learn to classify them into detection scores. With deep learning, learnable architectures have been proposed following this paradigm [4, 34, 38, 40], occasionally incorporating classical-vision ideas such as feature pyramids for improving scale invariance [29]. While learning has shown large improvements in accuracy over the years they still perform poorly while detecting small objects due to lack of geometric scene understanding. To alleviate this problem, we guide the input image with geometry constraints, and our approach complements these architectural improvements. + +Efficient Detection with Priors: Employing priors with learning paradigms achieves improvements with little additional human labelling effort. Object detection has traditionally been tackled as a learning problem and geometric constraints were sparsely used for such tasks, constraints like ground plane [20, 48] were used. + +Temporality [13, 50, 56] has been exploited for improving detection efficiently. Some of these methods [13, 50] deform the input image using approach that exploit temporality to obtain saliency. This approach handles cases where object size decreases with time (object moving away from the camera in scene), but cannot handle new incoming objects. None of these methods explicitly utilize geometry to guide detection, which handles both these cases. Our two-plane prior deforms the image while taking perspective into account without biasing towards previous detections. + +Another complementary line of works automatically learn metaparameters (like image scale) [9, 16, 45] from image features. However, as they do not employ adaptive sampling accounting for image-specific considerations, performance improvements are limited. Methods not optimized for online perception like AdaScale [9] for video object detection do not perform well in real-time situations. + +# 3. Approach + +We describe how a geometric model rooted in the interpretation of a 3D scene can be derived from the image. We then describe how to employ this rough 3D model to construct saliency for warping images and improving detection. + +# 3.1. Overview + +Object sizes in the image are determined by the 3D geometry of the world. Let us devise a geometric inductive prior considering a camera mounted on a vehicle. Without loss of generality, assume the vehicle is moving in direction of the dominant vanishing point. + +We are interested in objects that are present in a planar region (See Figure 2) of width $P_{1}P_{2}$ corresponding to the camera view, of length $P_{1}P_{3}$ defined in the direction of the vanishing point. This is the planar region on the ground on which most of the objects of interest are placed (vehicles, pedestrians, etc) and another planar region $Q_{1}\ldots Q_{4}$ parallel to this ground plane above horizon line, such that all the objects are within this region (e.g., traffic lights). + +From this simple geometry model, we shall incorporate relationships derived from perspective geometry about objects, i.e., the scale of objects on ground plane is inversely proportional to their depth w.r.t camera [20]. + +# 3.2. 3D Plane parameterization from 2D images + +We parameterize the planes of our inductive geometric prior. We represent 2D pixel projections $u_{1} \ldots u_{4}$ of 3D points $P_{1} \ldots P_{4}$ . Assume that the dominant vanishing point in the image is $v = (v_{x}, v_{y})$ and let the image size be $(w, h)$ . Consider $u_{1}$ (Figure 2 (b)). We can define a point on the edge of the image plane, + +$$ +u _ {L} = \left(0, v _ {y} + v _ {x} \tan \theta_ {1}\right) \tag {1} +$$ + +$u_{1}$ can be expressed as a linear combination of $v$ and $u_{L}$ , + +$$ +u _ {1} = \alpha_ {1} u _ {L} + (1 - \alpha_ {1}) v \tag {2} +$$ + +Similarly, for $u_{2}$ , we can define $u_{R}$ in terms of $v$ and $\theta_{2}$ and $\alpha_{2}$ while $u_{3}$ and $u_{4}$ are defined like Equation 1 to represent any arbitrary plane in this viewing direction. However, for simplicity, for ground plane we fix them as $(0,h)$ and $(w,h)$ respectively. Consider the planar region $Q_{1}\ldots Q_{4}$ at height $H$ above the horizon line. We can similarly define $\theta_{3}$ and $\theta_{4}$ to represent the angles from the horizon in the opposite direction and define $q_{1}$ and $q_{2}$ . Again, we set $q_{3}$ as $(0,0)$ and $q_{4}$ as $(w,0)$ . We now have 4 points to calculate homographies $H_{plane}$ for both planes. + +For now, assume $v$ is known. However, we still do not know the values for $\theta$ 's and $\alpha$ , and we shall learn these parameters end-to-end from task loss. These parameters are learned and fixed for a given scenario in our learning paradigm. Our reparameterization aims to ease learning of these parameters + +![](images/de4ef595046c1783ba8dc7fe3ce750c8cc7fa49db14756a3427e9aa9eddc7eab.jpg) + +![](images/781c66513e9af13aa5ceaf61f5032d6110e6fefc16680ab0e4865191fd645d6b.jpg) +Figure 2. Geometry Of The Two Plane Perspective Prior: (a) describes the single view geometry of the proposed two plane prior. Region on the ground plane defined by $P_{1}, \ldots, P_{4}$ , and rays emanating from camera $C$ to $P_{i}$ intersect at $u_{1} \ldots u_{4}$ on the image plane. The vanishing point $v$ maps to $P_{\infty}$ . This planar region accounts for small objects on the ground plane. To account for objects that are tall or do not lie on the ground plane, we consider another plane $Q_{1} \ldots Q_{4}$ above the horizon line. These two planes encapsulate all the relevant objects in the scene. (b) depicts the re-parameterization of the two planes in the 2D image. Instead of representing the planar points $u_{1} \ldots u_{4}$ as pixel coordinates, we instead parameterize them in terms of the vanishing point $v$ , $\theta$ 's and $\alpha$ to ease learning. + +as we clamp the values of $\alpha$ 's to $[0,1]$ and $\theta$ 's to $[- \frac{\pi}{2}, \frac{\pi}{2}]$ . It should be noted that all the operations are differentiable. + +# 3.3. From Planes to Saliency + +We leverage geometry to focus on relevant image regions through saliency guided warping [23, 36], and create a saliency map from a parameterized homography using $u_{1} \ldots u_{4}$ defined earlier. Looking at ground plane from two viewpoints (Figure 3 (a) and (b)), object size decreases by their distance from the camera [20]. We shall establish a relationship to counter this effect and "sample" far-away objects on the ground plane more than nearby objects. + +The saliency guided warping proposed by [36] operates using an inverse transformation $\mathcal{T}_S^{-1}$ parameterized by a saliency map $S$ as follows, + +$$ +I ^ {\prime} (x, y) = W _ {\mathcal {T}} (I) = I \left(\mathcal {T} _ {S} ^ {- 1} (x, y)\right) \tag {3} +$$ + +where the warp $W_{\mathcal{T}}$ implies iterating over output pixel coordinates, using $\mathcal{T}_S^{-1}$ to find corresponding input coordinates (non-integral), and bilinearly interpolating output color from neighbouring input pixel grid points. For each + +![](images/b0b847b8e7b27272bc9b4120126ecf560e36344085187e6f7544044c3314f3b2.jpg) +(a) Camera View + +![](images/aadeee20fd3e8dbd2d7bf0459223ad71e0251893f4845475c3b4905d9467b4f5.jpg) +(c) Mapping Saliency + +![](images/5f66e79e5a8b1e53370af0a4c857187cc1902d322f7a2b15529e0973c5d7b05c.jpg) + +![](images/fa890e5d308d30be676c8feada3e24743cc81f4b279541a9a588d0fe5b3f57d1.jpg) + +![](images/6381bfc7df66e410bbb07f80a54ce668fbd62761834528c1497e6ac65c0a4307.jpg) +(b) Bird's Eye View +Figure 3. Two-Plane Perspective Prior based Image Resampling: Consider the scene of car, bus and traffic light from (a) camera view and (b) (simplified) bird's eye view. (c) Saliency function that captures the inverse relationship between object size (in camera view) and depth (bird's eye view is looking at $XZ$ plane from above) can be transferred to the camera view (d), by mapping row $z$ using $H$ (marked by blue arrows). (e) and (f) shows that ground plane severely distorts nearby tall objects while squishing traffic light. (g) and (h) shows that additional plane reduces distortion for both tall objects and objects not on ground plane. + +![](images/aa3229e80a2710d5f1ab7860607951b4027478908b09af7acb5d4d1e859eccd9.jpg) +(d) Saliency On Scene + +![](images/e35c2ff4b89acd7ec67a0fab4e81ff53246f9440c04ca44f5d034519e1ceb650.jpg) +(e) Ground Plane Saliency +(f) Ground Plane Warp + +![](images/a692c7d5ffcf061d85890299d00d9b6f304762fffd7088bedb451420483bc9f6.jpg) +(g) Two Plane Saliency +(h) Two Plane Warp + +input pixel $(x,y)$ , pixel coordinates with higher $S(x,y)$ values (i.e. salient regions) would be sampled more. + +We construct a saliency $S$ respecting the geometric properties that we desire. Let $H_{plane}$ be the homography between the camera view (using coordinates $u_{1}\ldots u_{4}$ ) and a bird's eye view of the ground plane assuming plane size to be the original image size $(w,h)$ . In bird's eye view, we propose saliency function for a row of pixels $z$ (assuming bottom-left of this rectangle as $(0,0)$ ) as, + +$$ +S _ {b e v} (z) = e ^ {\nu \left(\frac {z}{h} - 1\right)} \tag {4} +$$ + +with a learnable parameter $\nu (>1)$ . $\nu$ defines the extent of sampling with respect to depth. + +To map this saliency to camera view, we warp $S_{bev}$ via perspective transform $W_{p}$ and $H_{plane}$ (Figure 3 (c)), + +$$ +S _ {p l a n e} = W _ {p} \left(H _ {p l a n e} ^ {- 1}, S _ {b e v}\right) \tag {5} +$$ + +We have defined saliency $S_{plane}$ given $H_{plane}$ in a differentiable manner. Our saliency ensures that objects on the ground plane separated by depth $Z$ are sampled by the factor $e^{\nu \frac{Z}{h}}$ in the image. + +# 3.4. Two-Plane Perspective Prior + +Ground Plane saliency focuses on objects that are geometrically constrained to be on this plane and reasonably models objects far away on the plane. However, nearby and tall objects, and small objects far above the ground plane are not modelled well. In Fig 3 (f), nearby objects above ground plane (traffic lights), they are highly distorted. Critically, these same objects when further away are rendered + +small in size and appear close to ground (and thus modelled well). Objects we should focus more on are thus the former compared to the latter. Thus, another plane is needed, and direction of the saliency function is reversed to $\hat{S}_{bev}(z) = e^{\hat{\nu}((h - z) / h) - 1}$ to account for these objects that would otherwise be severely distorted. + +To represent the Two-Plane Prior, we represented the planar regions as saliencies. The overall saliency is, + +$$ +S = S _ {\text {g r o u n d - p l a n e}} + \lambda S _ {\text {t o p - p l a n e}} \tag {6} +$$ + +where $\lambda$ is a learned parameter. + +# 3.5. Additional Considerations + +Warping via a piecewise saliency function imposes additional considerations. The choice of deformation method is critical, saliency sampler [36] implicitly avoids drastic transformations common in other approaches. For e.g., Thin-plate spline performs worse [36], produces extreme transformations and requires regularization [13]. + +Fovea [50] observes that restricting the space of allowable warps such that axis alignment is preserved improves accuracy, we adopt the separable formulation of $\mathcal{T}^{-1}$ + +$$ +\mathcal {T} _ {x} ^ {- 1} (x) = \frac {\int_ {x ^ {\prime}} S _ {x} \left(x ^ {\prime}\right) k \left(x ^ {\prime} , x\right) x ^ {\prime}}{\int_ {x ^ {\prime}} S _ {x} \left(x ^ {\prime}\right) k \left(x , x ^ {\prime}\right)} \tag {7} +$$ + +$$ +\mathcal {T} _ {y} ^ {- 1} (y) = \frac {\int_ {y ^ {\prime}} S _ {y} \left(y ^ {\prime}\right) k \left(y ^ {\prime} , y\right) y ^ {\prime}}{\int_ {y ^ {\prime}} S _ {y} \left(y ^ {\prime}\right) k \left(y , y ^ {\prime}\right)} \tag {8} +$$ + +where $k$ is a Gaussian kernel. To convert a saliency map $S$ to $S_{x}$ and $S_{y}$ we marginalize it along the two axes. Thus entire rows or columns are "stretched" or "compressed". + +Two-plane prior is learnt end to end as a learnable image warp. For object detection, labels need to be warped too, and [36]'s warp is invertible. Like [50], We employ the loss $\mathcal{L}(\mathcal{T}^{-1}(f_{\phi}(W_{\mathcal{T}}(I)),L)$ where $(I,L)$ is the image-label pair and omit the use of delta encoding for training RPN [40] (which requires the existence of a closed form $\mathcal{T}$ ), instead adopting GIoU loss [41]. This ensures $W_{\mathcal{T}}$ is learnable, as $\mathcal{T}^{-1}$ is differentiable. + +We did not assume that the vanishing point is within the field of view of our image, and our approach places no restrictions on the vanishing point. Thus far, we explained our formulation while considering a single dominant vanishing point, however, multiple vanishing points can be also considered. Please see supplementary for more details. + +# 3.6. Obtaining the Vanishing Point + +We now describe how we obtain the vanishing point. Many methods exist with trade-offs in accuracy, latency and memory which inform our design to perform warping efficiently with minimal overheads. + +Fixed Cameras: In settings like traffic cameras, the camera is fixed. Thus, the vanishing point is fixed, and we can cache the corresponding saliency $S$ , as all the parameters, once learnt, are fixed. We can define the vanishing point for a camera manually by annotating two parallel lines or any accurate automated approach. Saliency caching renders our approach extremely efficient. + +Autonomous Navigation: Multiple assumptions simplify the problem. We assume that there is one dominant vanishing point and a navigating car is often moving in the viewing direction. Thus, we assume that this vanishing point lies inside the image, and directly regress $v$ from image features using a modified coordinate regression module akin to YOLO [33, 38]. This approach appears to be memory and latency efficient. Other approaches, say, using parallel lane lines [1] or inertial measurements [3] might also be very efficient. An even simpler assumption is to employ the average vanishing point, as vanishing points are highly local, we observe this is a good approximation. + +Temporal Redundancies: In videos, we exploit temporal redundancies, the vanishing point is computed every $n_v$ frames and saliency is cached to amortize latency cost. + +General Case: This is the most difficult case, and many approaches have been explored in literature to find all vanishing points. Classical approaches [49] while fast are not robust, while deep-learned approaches [31,32,59] are accurate yet expensive (either in latency or memory). + +# 3.7. Learning Geometric Prior from Pseudo-Labels + +Prior work [50] have shown improvements in performance on pre-trained models via heuristics, which didn't require any training. However, their method still employs domain-specific labels (say, from Argoverse-HD) to generate the + +![](images/0162ca8a534119829c44c49c0acab601fa315f12eb7266ccda73d43cebec0619.jpg) + +![](images/f370ef3da817e18bca66779a4f188b77377c2142946643016539eebf92fe2fa6.jpg) + +![](images/b3d035b91cf500d6c2ecc97b3ce5f5c49db5b92bc62665f6b43ccf2aba9cd2f4.jpg) +Figure 4. Commuter Bus Dataset: The captured data has a unique viewpoint, the average size of objects is small and captured under a wide variety of lighting conditions. Top-left and bottom-right images depict the same bus-stop and trashcan at different time of day and season. + +![](images/2c055f3997cdb04c719b7c912e08a5e29aae4f210031402b4edc7c79ee719f4a.jpg) + +prior. Our method can't be used directly with pre-trained models as it learns geometrically inspired parameters end-to-end. However, domain-specific images without labels can be exploited to learn the parameters. + +We propose a simple alternative to learn the proposed prior using pre-trained model without requiring additional domain-specific labels. We generate pseudo-labels from our pre-trained model inferred at 1x scale. We fine-tune and learn our warp function (to $0.5\mathrm{x}$ scale) end-to-end using these "free" labels. Our geometric prior shows improvements without access to ground truth labels. + +# 4. Dataset And Evaluation Details + +# 4.1. Datasets + +Argoverse-HD [27]: We employ Argoverse-HD dataset for evaluation in the autonomous navigation scenario. This dataset consists of 30fps video sequences from a car collected at $1920 \times 1200$ resolution, and dense box annotations are provided for common objects of interest such as vehicles, pedestrians, signboards and traffic lights. + +WALT [37]: We employ images from 8.4K cameras that overlook public urban settings to analyze the flow of traffic vehicles. The data is captured for 3-second bursts every few minutes and only images with notable changes are stored. We annotated a set of 4738 images with vehicles collected over the time period of a year covering a variety of day/night/dawn settings, seasonal changes and camera viewpoints. We show our results on two splits (approximately $80\%$ training and $20\%$ testing). The first, All-Viewpoints, images from all the cameras are equally represented in the train and test sets. Alternatively, we split by camera, Split-by-Camera, images from 6 cameras are part of the training set and 2 cameras are held out for testing. + +Commuter Bus Dataset: We curated this dataset from a + +![](images/6f7abf9e85a0f71fabb52bd8a2c79aa6cae4da45e4c97de23f70ac12c7427c9f.jpg) +Figure 5. Two-Plane Prior as a Neural Layer: We implemented our approach as a global prior that is learned end-to-end from labelled data. Our prior is dependent on a vanishing point estimate to specify the viewing direction of the camera. + +commuter bus running on an urban route. The 720p camera of interest has a unique viewpoint and scene geometry (See Figure 4). Annotated categories are trashcans and garbage bags (to help inform public services) and people with special needs (using wheelchairs or strollers), which are a rare occurrence. The dataset size is small with only 750 annotated images (split into $70\%$ training and $30\%$ testing). This is an extremely challenging dataset due to its unique viewpoint, small object size, rare categories, along with variations in lighting and seasons. + +# 4.2. Evaluation Details + +We perform apples-to-apples comparisons on the same detector trained using the datasets with identical training schedule and hardware. + +Data: We compare to methods that were trained on fixed training data. In contrast, sAP leaderboards [27] don't restrict data and evaluate on different hardware. We compare with [16, 27] from leaderboard, which follow the same protocols. Other methods on the leaderboard use additional training data to train off-the-self detectors. Our detectors would see similar improvements with additional data. + +Real-Time Evaluation: We evaluate using Streaming AP (sAP) metric proposed by [27], which integrates latency and accuracy into a single metric. Instead of considering models via accuracy-latency tradeoffs [21], real-time performance can be evaluated by applying real-time constraints on the predictions [27]. Frames of the video are observed every 33 milliseconds (30 fps) and predictions for every frame must be emitted before the frame is observed (forecasting is necessary). For a fair comparison, sAP requires evaluation on the same hardware. Streaming results are not directly comparable with other work [27, 50, 56] as they use other hardware (say, V100 or 2080Ti), thus we run the evaluation on our hardware (Titan X). + +Additional details are in the Supplementary. + +
MethodScaleAPAPSAPMAPLLatency (ms)
Faster R-CNN0.5x24.24.929.050.978.4 ± 1.8
Fovea (SD) [50]0.5x26.78.229.754.183 ± 2.5
Fovea (SI) [50]0.5x28.010.431.054.585 ± 2.7
Fovea (L:SI) [50]0.5x28.110.330.954.185.4 ± 2.7
Two-Plane Pr. (Pseudo.)0.5x27.19.828.950.2104.5 ± 8.5
Two-Plane Prior0.5x30.814.531.652.9105 ± 8.5
Baseline at higher scales
Faster R-CNN0.75x29.211.632.153.3142 ± 2.5
Faster R-CNN1.0x33.316.834.853.6220 ± 1.7
+ +Table 1. Evaluation on Argoverse-HD: Two-Plane Prior outperforms both SOTA's dataset-wide and temporal priors in overall accuracy. Our method improves small object detection by $+4.1AP_{S}$ or $39\%$ over SOTA. + +# 5. Results and Discussions + +Accuracy-Latency Comparisons: On Argoverse-HD, we compare with Faster R-CNN with naive downsampling (Baseline) and Faster R-CNN paired with adaptive sampling from Fovea [50] which proposed two priors, a dataset-wide prior $(S_{D})$ and frame-specific temporal priors ( $S_{I}$ & $L: S_{I}$ ; from previous frame detections). + +Two-Plane Prior improves (Table 1) upon baseline at the same scale by $+6.6$ AP and over SOTA by $+2.7$ AP. For small objects, the improvements are even more dramatic, our method improves accuracy by $+9.6$ $AP_{S}$ or $195\%$ over baseline and $+4.2$ $AP_{S}$ or $45\%$ over SOTA respectively. Surprisingly, our method at $0.5\mathrm{x}$ scale improves upon Faster R-CNN at $0.75\mathrm{x}$ scale by $+1.6$ AP having latency improvement of $35\%$ . Our Two-Plane prior trained via pseudolabels comes very close to SOTA which employ ground truth labels, the gap is only $-1$ AP and improves upon Faster R-CNN model trained on ground truth by $+2.9$ AP inferred at the same scale. + +WALT dataset [37] comprises images (only images with notable changes are saved) and not videos, we compare with Fovea [50] paired with the dataset-wide prior. We observe similar trends on both splits (Table 3 and Fig 6) and note large improvements over baseline and a consistent improvement over Fovea [50], specially for small objects. + +Real-time/Streaming Comparisons: We use Argoverse-HD dataset, and compare using the sAP metric (Described in Section 4.2). Algorithms may choose any scale and frames as long as real-time latency constraint is satisfied. + +All compared methods use Faster R-CNN, and we adopt their reported scales (and other parameters). Streamer [27] converts any single frame detector for streaming by scheduling which frames to process and interpolating predictions between processed frames. AdaScale [9] regresses optimal scale from image features to minimize single-frame latency while Adaptive Streamer [16] learns scale choice in + +
IDMethodScale(s)sAPsAPSsAPMsAPL
1Streamer [27]0.5x18.33.115.040.9
21 + Adascale [9]0.2x-0.6x13.40.28.637.4
3Adaptive Streamer [16]0.2x-0.6x21.34.218.847.0
41 + FOVEA (SI) [50]0.5x24.18.424.748.7
51 + Ours (Avg VP)0.5x29.913.731.352.2
61 + Ours0.5x30.013.731.552.2
71 + Ours (VP Oracle)0.5x30.714.531.652.9
+ +![](images/4e72d6afbd1f8ca09373a66b77b979df0ad2f8947c44116e9649e4d6fb59b4c1.jpg) +Figure 6. WALT All-Viewpoints Split: Our approach (Two-Plane Prior) shows improved overall performance over naive downsampling and state-of-the-art adaptive sampling technique, specially for small objects at all scales (starting from $0.5\mathrm{x}$ ). Horizontal line (orange) indicates performance at maximum possible scale $(0.6\mathrm{x})$ the base detector was trained at (memory constraints). + +![](images/faabbc2521bf1ed6c8c876b5aebeb5a234d17b5274b9b4c1c4698467117ca42c.jpg) + +the streaming setting. Both these methods employ naive-downsampling. State-of-the-art, Fovea [50] employs the temporal prior $(S_I)$ . From Table 2, Two-Plane prior outperforms the above approaches by $+16.5$ sAP, $+8.6$ sAP and $+5.9$ sAP respectively. Comparison with [9, 16, 27] shows the limitations of naive downsampling, even when "optimal" scale is chosen. Our geometric prior greatly improves small object detection performance by $63\%$ or $+5.3$ sAPs over SOTA. To consider dependence on accurate Vanishing Point detection (and its overheads), we use NeurVPS [59] as oracle (we simulate accurate prediction with zero delay) to obtain an upper bound, we observe even average vanishing point location's performance is within $0.8$ sAP. + +Accuracy-Scale Tradeoffs: We experiment with WALT All-Viewpoints split to observe accuracy-scale trade-offs. The native resolution $(4K)$ of the dataset is extremely large and the gradients don't fit within 12 GB memory of our Titan X GPU, thus we cropped the skies and other static regions to reduce input scale (1x) to $1500 \times 2000$ . Still, the highest scale we were able to train our baseline Faster R-CNN model is 0.6x. So, we use aggressive downsam + +Table 2. Streaming Evaluation on Argoverse-HD: Ours denotes Two-Plane Prior. Every frame's prediction (streamed at 30FPS) must be emitted before frame is observed [27] (via forecasting). All methods evaluated on Titan X GPU. Underlying detector (Faster R-CNN) is constant across approaches, improvements are solely from spatial sampling mechanisms. Notice improved detection of small objects by $+5.3sAP_{S}$ or $63\%$ over SOTA. + +
MethodScaleAPAPSAPMAPL
Faster R-CNN0.25x16.707.242.3
FOVEA (SD) [50]0.25x23.2013.954.1
Two-Plane Prior0.25x25.21.018.254.5
Faster R-CNN0.5x29.24.924.755.5
FOVEA (SD) [50]0.5x34.48.730.559.4
Two-Plane Prior0.5x36.411.632.359.0
Baseline at higher scales
Faster R-CNN0.6x33.29.328.656.7
Faster R-CNN*1.0x34.312.630.754.3
+ +Table 3. WALT Camera-Split: The viewpoints on the test set were not seen, and Two-Plane Prior shows better performance over both naive downsampling and state-of-the-art adaptive sampling as it generalizes better to unseen scenes and viewpoints. *Not trained at that scale due to memory constraints on Titan X. + +pling scales $\{0.5, 0.4375, 0.375, 0.3125, 0.25, 0.125\}$ . The results are presented in Figure 6. We observe a large and consistent improvement over baseline and Fovea [50], specially for small objects. For instance, considering performance at $0.375x$ scale, our approach is better than baseline by $+13.1AP$ and Fovea by $+1.4AP$ for all objects. + +For small objects, we observe dramatic improvement, at scales smaller than $0.375\mathrm{x}$ , other approaches are unable to detect any small objects while our approach does so until $0.125\mathrm{x}$ scale, showing that our approach degrades more gracefully. At $0.375\mathrm{x}$ scale, our approach improves upon Faster R-CNN by $+10.7AP_{S}$ and Fovea by $+3.0AP_{S}$ . + +Generalization to new viewpoints: We use WALT Camera-Split, the test scenes and viewpoint are unseen in training. E.g., the vanishing point of one of the held-out cameras is beyond the image's field of view. We operate on the same scale factors in the earlier experiments, and results are presented in Table 3. We note lower overall performance levels due to scene/viewpoint novelty in the test sets. Our approach generalizes better due to the explicit modelling of the viewpoint via the vanishing point (See Section 3.2). We note trends similar to previous experiment, we demonstrate improvements of $+8.5$ AP over naive-downsampling and $+2.0$ AP over Fovea [50] at $0.25\mathrm{x}$ scale. + +Tracking Improvements: We follow tracking-by-detection and pair IOUTracker [2] with detectors on Argoverse-HD dataset. MOTA and MOTP evaluate overall tracking performance. From Table 4, Our method improves over baseline by $+4.8\%$ and $+0.7\%$ . We also focus on tracking quality metrics, Mostly Tracked $\%$ (MT%) evaluates the percentage of objects tracked for at least $80\%$ of their lifespan while Mostly Lost $\%$ (ML%) evaluates percentage of objects for less than $20\%$ of their lifespan. In both these cases, our approach improves upon the baseline by $+7.6\%$ and $-6.7\%$ respectively. To autonomous navigation, we define two relevant metrics, namely, average lifespan extension (ALE) + +
MethodMOTA ↑MOTP ↑MT% ↑ML% ↓MOS ↓ALE% ↑
Faster RCNN39.882.330.735.637.159.3 %
Fovea (SD) [50]43.981.934.131.934.8+5.4 %
Fovea (SI) [50]44.381.836.728.433.8+8.4 %
Two-Plane Prior44.683.038.328.931.6+9.9 %
+ +and minimum object size tracked (MOS), whose motivation and definitions can be viewed in supplementary. We observe that our improvements are better than both Fovea $(S_{D})$ and $(S_{I})$ . As we observe, our method improves tracking lifespan and also helps track smaller objects. + +Efficient City-Scale Sensing: We detect objects on Commuter Bus equipped with a Jetson AGX. Identifying (Recall) relevant frames is key on the edge. Recall of Faster R-CNN with at 1x scale is $43.3AR$ ( $16.9AR_{S}$ ) (Latency: 350ms; infeasible for real-time execution) but drops to $31.7AR$ ( $0.5AR_{S}$ ) at 0.5x scale when naively downsampled (Latency: 154ms). Whereas our approach at 0.5x scale improves recall by $42\%$ over full resolution execution to 61.7 AR (16.4 ARS) with latency of 158 ms (+4 ms). + +In supplementary, we perform additional comparisons, provide details on handling multiple vanishing points, more tracking results and edge sensing results. We also present some qualitative results and comparisons. + +# 5.1. Ablation Studies + +We discuss some of the considerations of our approach through experiments on the Argoverse-HD dataset. + +Ground Plane vs Two-Plane Prior: We discussed the rationale of employing multiple planes in Fig 3, and our results are consistent. From Table 5, Two-Plane Prior outperforms Ground Plane prior considerably $(+1.8AP)$ . Ground Plane Prior outperforms Two-Plane Prior on small objects by $+1AP_{S}$ but is heavily penalized on medium $(-4.1AP_{M})$ and large objects $(-4.6AP_{L})$ . This is attributed to heavy distortion of tall and nearby objects, and objects that are not on the plane (Figure 3). Lastly, this prior was difficult to learn, the parameter space severely distorted the images (we tuned initialization and learning rate). Thus we did not consider this prior further. The second plane acts as a counterbalance and that warping space is learnable. + +Vanishing Point Estimate Dependence: From Table 5, dominant vanishing point in autonomous navigation is highly local in nature, and estimating VP improves the result by +1.2 AP. Estimating the vanishing point is a design choice, it's important for safety critical applications like autonomous navigation (performance while navigating turns) + +Table 4. Tracking Improvements: We setup a tracking by detection pipeline and replace the underlying detection method and observe improvements if any. All the detectors employ the Faster R-CNN architecture and are executed at $0.5\mathrm{x}$ scale. We observe improvements in tracking metrics due to Two-Plane Prior. + +
MethodScaleAPAPSAPMAPL
Ground Plane Prior0.5x29.115.527.548.3
Two-Plane Prior (Psuedo.)0.5x27.19.828.950.2
Two-Plane Prior (Avg VP)0.5x29.612.730.752.7
Two-Plane Prior0.5x30.814.531.652.9
+ +Table 5. Ablation Study on Argoverse-HD to justify our design choice of using two planes, dependence on accurate vanishing point detection and choice of pseudo labels vs ground truth. + +however might be omitted for sensing applications. + +Using Pseudo Labels vs Ground Truth: Table 5 shows there is still considerable gap (-3.7 AP) between the Two-Plane Prior trained from pseudo labels and ground truth. We observe that the model under-performs on stopsign, bike and truck classes, which are under-represented in the COCO dataset [30] compared to person and car classes. Performance of the pre-trained model on these classes is low even at 1x scale. Hence, we believe that the performance difference is an artifact of this domain gap. + +# 6. Conclusions + +In this work, we proposed a learned two-plane perspective prior which incorporates rough geometric constraints from 3D scene interpretations of 2D images to improve object detection. We demonstrated that (a) Geometrically defined spatial sampling prior significantly improves detection performance over multiple axes (accuracy, latency and memory) in terms of both single-frame accuracy and accuracy with real-time constraints over other methods. (b) Not only is our approach is more accurate when adaptively down-sampling at all scales, it degrades much more gracefully for small objects, resulting in latency and memory savings. (c) As our prior is learned end-to-end, we can improve a detector's performance at lower scales for "free". (d) Our approach generalizes better to new camera viewpoints and enables efficient city-scale sensing applications. Vanishing point estimation is the bottleneck of our approach [11, 31, 32, 59] for general scenes, and increasing efficiency of its computation we will see substantial improvements. Investigating geometric constraints to improve other aspects of real-time perception systems as future work, like object tracking and trajectory understanding and forecasting, is promising. + +Societal Impact Our approach has strong implications for autonomous-driving and city-scale sensing for smart city applications, wherein efficient data processing would lead to more data-driven decision-making and public policies. However, privacy is a concern, and we shall release the datasets after anonymizing people and license plates. + +Acknowledgements: This work was supported in part by an NSF CPS Grant CNS-2038612, a DOT RITA Mobility-21 Grant 69A3551747111 and by General Motors Israel. + +# References + +[1] Hala Abualsaud, Sean Liu, David B Lu, Kenny Situ, Akshay Rangesh, and Mohan M Trivedi. Laneaf: Robust multi-lane detection with affinity fields. Robotics and Automation Letters, 2021. 5 +[2] Erik Bochinski, Volker Eiselein, and Thomas Sikora. 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Introduction" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 533, + 287, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 533, + 287, + 700 + ], + "spans": [ + { + "bbox": [ + 46, + 533, + 287, + 700 + ], + "type": "text", + "content": "Visual perception is important for autonomous driving and decision-making for smarter and sustainable cities. Real-time efficient perception is critical to accelerate these advances. For instance, a single traffic camera captures half a million frames every day or a commuter bus acting as a city sensor captures one million frames every day to monitor road conditions [10] or to inform public services [22]. There are thousands of traffic cameras [24] and nearly a million commuter buses [53] in the United States. It is infeasible to transmit and process visual data on the cloud, leading to the rise of edge architectures [43]. However, edge devices are severely resource constrained and real-time inference requires down-sampling images to fit both latency and memory constraints severely impacting accuracy." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 701, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 701, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 701, + 287, + 713 + ], + "type": "text", + "content": "On the other hand, humans take visual shortcuts [19] to" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 312, + 243, + 323, + 308 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 243, + 323, + 308 + ], + "spans": [ + { + "bbox": [ + 312, + 243, + 323, + 308 + ], + "type": "text", + "content": "Trrrnnnne" + } + ] + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 326, + 232, + 427, + 317 + ], + "blocks": [ + { + "bbox": [ + 326, + 232, + 427, + 317 + ], + "lines": [ + { + "bbox": [ + 326, + 232, + 427, + 317 + ], + "spans": [ + { + "bbox": [ + 326, + 232, + 427, + 317 + ], + "type": "image", + "image_path": "886afeb3f2b2469e3841960b9e007d475e67d50a0edc8612c3c41b405903c353.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 430, + 232, + 539, + 317 + ], + "blocks": [ + { + "bbox": [ + 430, + 232, + 539, + 317 + ], + "lines": [ + { + "bbox": [ + 430, + 232, + 539, + 317 + ], + "spans": [ + { + "bbox": [ + 430, + 232, + 539, + 317 + ], + "type": "image", + "image_path": "cf71d620299bdbc3e8db0af5be49141cf15a287acadb1f40578c77f10257eaec.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 347, + 324, + 396 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 347, + 324, + 396 + ], + "spans": [ + { + "bbox": [ + 313, + 347, + 324, + 396 + ], + "type": "text", + "content": "e e e" + } + ] + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 326, + 323, + 479, + 422 + ], + "blocks": [ + { + "bbox": [ + 326, + 323, + 479, + 422 + ], + "lines": [ + { + "bbox": [ + 326, + 323, + 479, + 422 + ], + "spans": [ + { + "bbox": [ + 326, + 323, + 479, + 422 + ], + "type": "image", + "image_path": "4f9855606219b6f6fb11abd82a7c0ab8e114d7bc63829a7c7fe85532e048b671.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_body" + } + ], + "index": 18 + }, + { + "type": "image", + "bbox": [ + 481, + 322, + 539, + 374 + ], + "blocks": [ + { + "bbox": [ + 481, + 322, + 539, + 374 + ], + "lines": [ + { + "bbox": [ + 481, + 322, + 539, + 374 + ], + "spans": [ + { + "bbox": [ + 481, + 322, + 539, + 374 + ], + "type": "image", + "image_path": "a2980e16f42b3027978eda26dac78a148b174ef72723066ce6c575a94806f39d.jpg" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_body" + } + ], + "index": 19 + }, + { + "bbox": [ + 312, + 434, + 324, + 486 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 434, + 324, + 486 + ], + "spans": [ + { + "bbox": [ + 312, + 434, + 324, + 486 + ], + "type": "text", + "content": "Saaee" + } + ] + } + ], + "index": 20 + }, + { + "type": "image", + "bbox": [ + 326, + 430, + 432, + 491 + ], + "blocks": [ + { + "bbox": [ + 326, + 430, + 432, + 491 + ], + "lines": [ + { + "bbox": [ + 326, + 430, + 432, + 491 + ], + "spans": [ + { + "bbox": [ + 326, + 430, + 432, + 491 + ], + "type": "image", + "image_path": "c740d404f39bf6d6499d9409992ff64f161ba9ce287734f9c371f180be8dc69e.jpg" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 505, + 547, + 594 + ], + "lines": [ + { + "bbox": [ + 304, + 505, + 547, + 594 + ], + "spans": [ + { + "bbox": [ + 304, + 505, + 547, + 594 + ], + "type": "text", + "content": "Figure 1. Geometric cues (black dashed lines) are implicitly present in scenes. Our Perspective based prior exploits this geometry. Our method (a) takes an image and (b) warps them, and performs detection on warped images. Small objects which are (d) not detected when naively downsampled but (e) are detected when enlarged with our geometric prior. Our method (f) uses a geometric model to construct a saliency prior to focus on relevant areas and (g) enables sensing on resource-constrained edge devices." + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_caption" + } + ], + "index": 21 + }, + { + "type": "image", + "bbox": [ + 434, + 430, + 539, + 491 + ], + "blocks": [ + { + "bbox": [ + 434, + 430, + 539, + 491 + ], + "lines": [ + { + "bbox": [ + 434, + 430, + 539, + 491 + ], + "spans": [ + { + "bbox": [ + 434, + 430, + 539, + 491 + ], + "type": "image", + "image_path": "e29c1f634f3a41f658beb9db95e50c037a5b27136c49b8e14219b6633bc29fa0.jpg" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_body" + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": "recognize objects efficiently and employ high-level semantics [19, 52] rooted in scene geometry to focus on relevant parts. Consider the scene in Figure 1 (c), humans can recognize the distant car despite its small appearance (Figure 1 (d)). We are able to contextualize the car in the 3D scene, namely (1) it's on the road and (2) is of the right size we'd expect at that distance. Inspired by these observations, can we incorporate semantic priors about scene geometry in our neural networks to improve detection?" + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "13364" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 179 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 179 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 179 + ], + "type": "text", + "content": "In this work, we develop an approach that enables object detectors to \"zoom\" into relevant image regions (Figure 1 (d) and (e)) guided by the geometry of the scene. Our approach considers that most objects of interests are present within two planar regions, either on the ground plane or within another plane above the ground, and their size in the image follow a geometric relationship. Instead of uniformly downsampling, we sample the image to enlarge far away regions more and detect those smaller objects." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 180, + 289, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 180, + 289, + 384 + ], + "spans": [ + { + "bbox": [ + 46, + 180, + 289, + 384 + ], + "type": "text", + "content": "While methods like quantization [17], pruning [18], distillation [6] and runtime-optimization [16] improve model efficiency (and are complementary), approaches exploiting spatial and temporal sampling are key for enabling efficient real-time perception [21, 27]. Neural warping mechanisms [23, 36] have been employed for image classification and regression, and recently, detection for self-driving [50]. Prior work [50] observes that end-to-end trained saliency networks fail for object detection. They instead turn to heuristics such as dataset-wide priors and object locations from previous frames, which are suboptimal. We show that formulation of learnable geometric priors is critical for learning end-to-end trained saliency networks for detection. We validate our approach in a variety of scenarios to showcase the generalizability of geometric priors for detection in self-driving on Argoverse-HD [27] and BDD100K [57] datasets, and for traffic-c cameras on WALT [37] dataset." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 391, + 287, + 622 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 58, + 391, + 287, + 475 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 391, + 287, + 475 + ], + "spans": [ + { + "bbox": [ + 58, + 391, + 287, + 475 + ], + "type": "text", + "content": "- On Argoverse-HD, our learned geometric prior improves performance over naive downsampling by " + }, + { + "bbox": [ + 58, + 391, + 287, + 475 + ], + "type": "inline_equation", + "content": "+6.6" + }, + { + "bbox": [ + 58, + 391, + 287, + 475 + ], + "type": "text", + "content": " AP and " + }, + { + "bbox": [ + 58, + 391, + 287, + 475 + ], + "type": "inline_equation", + "content": "+2.7" + }, + { + "bbox": [ + 58, + 391, + 287, + 475 + ], + "type": "text", + "content": " AP over SOTA using the same detection architecture. Gains from our approach are achieved by detecting small far-away objects, improving by 9.6 " + }, + { + "bbox": [ + 58, + 391, + 287, + 475 + ], + "type": "inline_equation", + "content": "AP_{S}" + }, + { + "bbox": [ + 58, + 391, + 287, + 475 + ], + "type": "text", + "content": " (or " + }, + { + "bbox": [ + 58, + 391, + 287, + 475 + ], + "type": "inline_equation", + "content": "195\\%" + }, + { + "bbox": [ + 58, + 391, + 287, + 475 + ], + "type": "text", + "content": " ) over naive down-sampling and 4.2 " + }, + { + "bbox": [ + 58, + 391, + 287, + 475 + ], + "type": "inline_equation", + "content": "AP_{S}" + }, + { + "bbox": [ + 58, + 391, + 287, + 475 + ], + "type": "text", + "content": " (or " + }, + { + "bbox": [ + 58, + 391, + 287, + 475 + ], + "type": "inline_equation", + "content": "63\\%" + }, + { + "bbox": [ + 58, + 391, + 287, + 475 + ], + "type": "text", + "content": " ) over SOTA." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 58, + 476, + 287, + 523 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 476, + 287, + 523 + ], + "spans": [ + { + "bbox": [ + 58, + 476, + 287, + 523 + ], + "type": "text", + "content": "- On WALT, our method detects small objects at image scales where other methods perform poorly. Further, it significantly improves detection rates by 10.7 " + }, + { + "bbox": [ + 58, + 476, + 287, + 523 + ], + "type": "inline_equation", + "content": "AP_{S}" + }, + { + "bbox": [ + 58, + 476, + 287, + 523 + ], + "type": "text", + "content": " over naive down-sampling and 3 " + }, + { + "bbox": [ + 58, + 476, + 287, + 523 + ], + "type": "inline_equation", + "content": "AP_{S}" + }, + { + "bbox": [ + 58, + 476, + 287, + 523 + ], + "type": "text", + "content": " over SOTA." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 58, + 525, + 287, + 572 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 525, + 287, + 572 + ], + "spans": [ + { + "bbox": [ + 58, + 525, + 287, + 572 + ], + "type": "text", + "content": "- Our approach improves object tracking " + }, + { + "bbox": [ + 58, + 525, + 287, + 572 + ], + "type": "inline_equation", + "content": "(+4.8\\%)" + }, + { + "bbox": [ + 58, + 525, + 287, + 572 + ], + "type": "text", + "content": " MOTA compared to baseline. It also improves tracking quality, showing increase of " + }, + { + "bbox": [ + 58, + 525, + 287, + 572 + ], + "type": "inline_equation", + "content": "+7.6\\%" + }, + { + "bbox": [ + 58, + 525, + 287, + 572 + ], + "type": "inline_equation", + "content": "MT\\%" + }, + { + "bbox": [ + 58, + 525, + 287, + 572 + ], + "type": "text", + "content": " and reduction of " + }, + { + "bbox": [ + 58, + 525, + 287, + 572 + ], + "type": "inline_equation", + "content": "-6.7\\%" + }, + { + "bbox": [ + 58, + 525, + 287, + 572 + ], + "type": "inline_equation", + "content": "ML\\%" + }, + { + "bbox": [ + 58, + 525, + 287, + 572 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 58, + 575, + 287, + 622 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 575, + 287, + 622 + ], + "spans": [ + { + "bbox": [ + 58, + 575, + 287, + 622 + ], + "type": "text", + "content": "- Our approach can be deployed in resource constrained edge devices like Jetson AGX to detect " + }, + { + "bbox": [ + 58, + 575, + 287, + 622 + ], + "type": "inline_equation", + "content": "42\\%" + }, + { + "bbox": [ + 58, + 575, + 287, + 622 + ], + "type": "text", + "content": " more rare instances while being 2.2X faster to enable real-time sensing from buses." + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 634, + 134, + 645 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 634, + 134, + 645 + ], + "spans": [ + { + "bbox": [ + 47, + 634, + 134, + 645 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 654, + 287, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 287, + 689 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 287, + 689 + ], + "type": "text", + "content": "We contextualize our work with respect to prior works modelling geometry and also among works that aim to make object detection more accurate and efficient." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "content": "Vision Meets Geometry: Geometry has played a crucial role in multiple vision tasks like detection [8, 20, 48, 55]," + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 72, + 545, + 264 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 264 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 264 + ], + "type": "text", + "content": "segmentation [28, 46], recognition [14, 47] and reconstruction [25, 35, 44]. Perspective Geometric constraints have been used to remove distortion [58], improve depth prediction and semantic segmentation [26] and feature matching [51]. However, in most previous works [25, 44, 55] exploiting these geometric constraints have mainly been concentrated around improving 3D understanding. This can be attributed to a direct correlation between the constraints and the accuracy of reconstruction. Another advantage is the availability of large RGB-D and 3D datasets [5, 15, 39] to learn and exploit 3D constraints. Such constraints have been under-explored for learning based vision tasks like detection and segmentation. A new line of work interpreting classical geometric constraints and algorithms as neural layers [7, 42] have shown considerable promise in merging geometry with deep learning." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 268, + 545, + 424 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 268, + 545, + 424 + ], + "spans": [ + { + "bbox": [ + 304, + 268, + 545, + 424 + ], + "type": "text", + "content": "Learning Based Detection: Object detection has mostly been addressed as an learning problem. Even classical-vision based approaches [12, 54] extract image features and learn to classify them into detection scores. With deep learning, learnable architectures have been proposed following this paradigm [4, 34, 38, 40], occasionally incorporating classical-vision ideas such as feature pyramids for improving scale invariance [29]. While learning has shown large improvements in accuracy over the years they still perform poorly while detecting small objects due to lack of geometric scene understanding. To alleviate this problem, we guide the input image with geometry constraints, and our approach complements these architectural improvements." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 429, + 545, + 501 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 429, + 545, + 501 + ], + "spans": [ + { + "bbox": [ + 304, + 429, + 545, + 501 + ], + "type": "text", + "content": "Efficient Detection with Priors: Employing priors with learning paradigms achieves improvements with little additional human labelling effort. Object detection has traditionally been tackled as a learning problem and geometric constraints were sparsely used for such tasks, constraints like ground plane [20, 48] were used." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 505, + 545, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 505, + 545, + 624 + ], + "spans": [ + { + "bbox": [ + 304, + 505, + 545, + 624 + ], + "type": "text", + "content": "Temporality [13, 50, 56] has been exploited for improving detection efficiently. Some of these methods [13, 50] deform the input image using approach that exploit temporality to obtain saliency. This approach handles cases where object size decreases with time (object moving away from the camera in scene), but cannot handle new incoming objects. None of these methods explicitly utilize geometry to guide detection, which handles both these cases. Our two-plane prior deforms the image while taking perspective into account without biasing towards previous detections." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": "Another complementary line of works automatically learn metaparameters (like image scale) [9, 16, 45] from image features. However, as they do not employ adaptive sampling accounting for image-specific considerations, performance improvements are limited. Methods not optimized for online perception like AdaScale [9] for video object detection do not perform well in real-time situations." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13365" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 115, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 115, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 115, + 85 + ], + "type": "text", + "content": "3. Approach" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 91, + 287, + 140 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 91, + 287, + 140 + ], + "spans": [ + { + "bbox": [ + 47, + 91, + 287, + 140 + ], + "type": "text", + "content": "We describe how a geometric model rooted in the interpretation of a 3D scene can be derived from the image. We then describe how to employ this rough 3D model to construct saliency for warping images and improving detection." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 148, + 115, + 160 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 148, + 115, + 160 + ], + "spans": [ + { + "bbox": [ + 47, + 148, + 115, + 160 + ], + "type": "text", + "content": "3.1. Overview" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 167, + 287, + 227 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 167, + 287, + 227 + ], + "spans": [ + { + "bbox": [ + 47, + 167, + 287, + 227 + ], + "type": "text", + "content": "Object sizes in the image are determined by the 3D geometry of the world. Let us devise a geometric inductive prior considering a camera mounted on a vehicle. Without loss of generality, assume the vehicle is moving in direction of the dominant vanishing point." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 227, + 287, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 227, + 287, + 323 + ], + "spans": [ + { + "bbox": [ + 46, + 227, + 287, + 323 + ], + "type": "text", + "content": "We are interested in objects that are present in a planar region (See Figure 2) of width " + }, + { + "bbox": [ + 46, + 227, + 287, + 323 + ], + "type": "inline_equation", + "content": "P_{1}P_{2}" + }, + { + "bbox": [ + 46, + 227, + 287, + 323 + ], + "type": "text", + "content": " corresponding to the camera view, of length " + }, + { + "bbox": [ + 46, + 227, + 287, + 323 + ], + "type": "inline_equation", + "content": "P_{1}P_{3}" + }, + { + "bbox": [ + 46, + 227, + 287, + 323 + ], + "type": "text", + "content": " defined in the direction of the vanishing point. This is the planar region on the ground on which most of the objects of interest are placed (vehicles, pedestrians, etc) and another planar region " + }, + { + "bbox": [ + 46, + 227, + 287, + 323 + ], + "type": "inline_equation", + "content": "Q_{1}\\ldots Q_{4}" + }, + { + "bbox": [ + 46, + 227, + 287, + 323 + ], + "type": "text", + "content": " parallel to this ground plane above horizon line, such that all the objects are within this region (e.g., traffic lights)." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 323, + 287, + 371 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 323, + 287, + 371 + ], + "spans": [ + { + "bbox": [ + 46, + 323, + 287, + 371 + ], + "type": "text", + "content": "From this simple geometry model, we shall incorporate relationships derived from perspective geometry about objects, i.e., the scale of objects on ground plane is inversely proportional to their depth w.r.t camera [20]." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 380, + 273, + 392 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 380, + 273, + 392 + ], + "spans": [ + { + "bbox": [ + 47, + 380, + 273, + 392 + ], + "type": "text", + "content": "3.2. 3D Plane parameterization from 2D images" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 398, + 287, + 470 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 398, + 287, + 470 + ], + "spans": [ + { + "bbox": [ + 47, + 398, + 287, + 470 + ], + "type": "text", + "content": "We parameterize the planes of our inductive geometric prior. We represent 2D pixel projections " + }, + { + "bbox": [ + 47, + 398, + 287, + 470 + ], + "type": "inline_equation", + "content": "u_{1} \\ldots u_{4}" + }, + { + "bbox": [ + 47, + 398, + 287, + 470 + ], + "type": "text", + "content": " of 3D points " + }, + { + "bbox": [ + 47, + 398, + 287, + 470 + ], + "type": "inline_equation", + "content": "P_{1} \\ldots P_{4}" + }, + { + "bbox": [ + 47, + 398, + 287, + 470 + ], + "type": "text", + "content": ". Assume that the dominant vanishing point in the image is " + }, + { + "bbox": [ + 47, + 398, + 287, + 470 + ], + "type": "inline_equation", + "content": "v = (v_{x}, v_{y})" + }, + { + "bbox": [ + 47, + 398, + 287, + 470 + ], + "type": "text", + "content": " and let the image size be " + }, + { + "bbox": [ + 47, + 398, + 287, + 470 + ], + "type": "inline_equation", + "content": "(w, h)" + }, + { + "bbox": [ + 47, + 398, + 287, + 470 + ], + "type": "text", + "content": ". Consider " + }, + { + "bbox": [ + 47, + 398, + 287, + 470 + ], + "type": "inline_equation", + "content": "u_{1}" + }, + { + "bbox": [ + 47, + 398, + 287, + 470 + ], + "type": "text", + "content": " (Figure 2 (b)). We can define a point on the edge of the image plane," + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 115, + 476, + 287, + 490 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 115, + 476, + 287, + 490 + ], + "spans": [ + { + "bbox": [ + 115, + 476, + 287, + 490 + ], + "type": "interline_equation", + "content": "u _ {L} = \\left(0, v _ {y} + v _ {x} \\tan \\theta_ {1}\\right) \\tag {1}", + "image_path": "1fbc2ede5b3c1aff08990144ade2153ffe61928c16e8ce45d17618f06e4c6b93.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 496, + 266, + 508 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 496, + 266, + 508 + ], + "spans": [ + { + "bbox": [ + 47, + 496, + 266, + 508 + ], + "type": "inline_equation", + "content": "u_{1}" + }, + { + "bbox": [ + 47, + 496, + 266, + 508 + ], + "type": "text", + "content": " can be expressed as a linear combination of " + }, + { + "bbox": [ + 47, + 496, + 266, + 508 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 47, + 496, + 266, + 508 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 496, + 266, + 508 + ], + "type": "inline_equation", + "content": "u_{L}" + }, + { + "bbox": [ + 47, + 496, + 266, + 508 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 116, + 514, + 287, + 526 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 514, + 287, + 526 + ], + "spans": [ + { + "bbox": [ + 116, + 514, + 287, + 526 + ], + "type": "interline_equation", + "content": "u _ {1} = \\alpha_ {1} u _ {L} + (1 - \\alpha_ {1}) v \\tag {2}", + "image_path": "7d3889124ea30542525458e500de6f74ffed08b4fc692741c0c51ad1bd2ea7ea.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 533, + 287, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 533, + 287, + 653 + ], + "spans": [ + { + "bbox": [ + 47, + 533, + 287, + 653 + ], + "type": "text", + "content": "Similarly, for " + }, + { + "bbox": [ + 47, + 533, + 287, + 653 + ], + "type": "inline_equation", + "content": "u_{2}" + }, + { + "bbox": [ + 47, + 533, + 287, + 653 + ], + "type": "text", + "content": ", we can define " + }, + { + "bbox": [ + 47, + 533, + 287, + 653 + ], + "type": "inline_equation", + "content": "u_{R}" + }, + { + "bbox": [ + 47, + 533, + 287, + 653 + ], + "type": "text", + "content": " in terms of " + }, + { + "bbox": [ + 47, + 533, + 287, + 653 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 47, + 533, + 287, + 653 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 533, + 287, + 653 + ], + "type": "inline_equation", + "content": "\\theta_{2}" + }, + { + "bbox": [ + 47, + 533, + 287, + 653 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 533, + 287, + 653 + ], + "type": "inline_equation", + "content": "\\alpha_{2}" + }, + { + "bbox": [ + 47, + 533, + 287, + 653 + ], + "type": "text", + "content": " while " + }, + { + "bbox": [ + 47, + 533, + 287, + 653 + ], + "type": "inline_equation", + "content": "u_{3}" + }, + { + "bbox": [ + 47, + 533, + 287, + 653 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 533, + 287, + 653 + ], + "type": "inline_equation", + "content": "u_{4}" + }, + { + "bbox": [ + 47, + 533, + 287, + 653 + ], + "type": "text", + "content": " are defined like Equation 1 to represent any arbitrary plane in this viewing direction. However, for simplicity, for ground plane we fix them as " + }, + { + "bbox": [ + 47, + 533, + 287, + 653 + ], + "type": "inline_equation", + "content": "(0,h)" + }, + { + "bbox": [ + 47, + 533, + 287, + 653 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 533, + 287, + 653 + ], + "type": "inline_equation", + "content": "(w,h)" + }, + { + "bbox": [ + 47, + 533, + 287, + 653 + ], + "type": "text", + "content": " respectively. Consider the planar region " + }, + { + "bbox": [ + 47, + 533, + 287, + 653 + ], + "type": "inline_equation", + "content": "Q_{1}\\ldots Q_{4}" + }, + { + "bbox": [ + 47, + 533, + 287, + 653 + ], + "type": "text", + "content": " at height " + }, + { + "bbox": [ + 47, + 533, + 287, + 653 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 47, + 533, + 287, + 653 + ], + "type": "text", + "content": " above the horizon line. We can similarly define " + }, + { + "bbox": [ + 47, + 533, + 287, + 653 + ], + "type": "inline_equation", + "content": "\\theta_{3}" + }, + { + "bbox": [ + 47, + 533, + 287, + 653 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 533, + 287, + 653 + ], + "type": "inline_equation", + "content": "\\theta_{4}" + }, + { + "bbox": [ + 47, + 533, + 287, + 653 + ], + "type": "text", + "content": " to represent the angles from the horizon in the opposite direction and define " + }, + { + "bbox": [ + 47, + 533, + 287, + 653 + ], + "type": "inline_equation", + "content": "q_{1}" + }, + { + "bbox": [ + 47, + 533, + 287, + 653 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 533, + 287, + 653 + ], + "type": "inline_equation", + "content": "q_{2}" + }, + { + "bbox": [ + 47, + 533, + 287, + 653 + ], + "type": "text", + "content": ". Again, we set " + }, + { + "bbox": [ + 47, + 533, + 287, + 653 + ], + "type": "inline_equation", + "content": "q_{3}" + }, + { + "bbox": [ + 47, + 533, + 287, + 653 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 47, + 533, + 287, + 653 + ], + "type": "inline_equation", + "content": "(0,0)" + }, + { + "bbox": [ + 47, + 533, + 287, + 653 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 533, + 287, + 653 + ], + "type": "inline_equation", + "content": "q_{4}" + }, + { + "bbox": [ + 47, + 533, + 287, + 653 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 47, + 533, + 287, + 653 + ], + "type": "inline_equation", + "content": "(w,0)" + }, + { + "bbox": [ + 47, + 533, + 287, + 653 + ], + "type": "text", + "content": ". We now have 4 points to calculate homographies " + }, + { + "bbox": [ + 47, + 533, + 287, + 653 + ], + "type": "inline_equation", + "content": "H_{plane}" + }, + { + "bbox": [ + 47, + 533, + 287, + 653 + ], + "type": "text", + "content": " for both planes." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "text", + "content": "For now, assume " + }, + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "text", + "content": " is known. However, we still do not know the values for " + }, + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "text", + "content": "'s and " + }, + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "text", + "content": ", and we shall learn these parameters end-to-end from task loss. These parameters are learned and fixed for a given scenario in our learning paradigm. Our reparameterization aims to ease learning of these parameters" + } + ] + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 348, + 73, + 506, + 165 + ], + "blocks": [ + { + "bbox": [ + 348, + 73, + 506, + 165 + ], + "lines": [ + { + "bbox": [ + 348, + 73, + 506, + 165 + ], + "spans": [ + { + "bbox": [ + 348, + 73, + 506, + 165 + ], + "type": "image", + "image_path": "de4ef595046c1783ba8dc7fe3ce750c8cc7fa49db14756a3427e9aa9eddc7eab.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 348, + 165, + 503, + 274 + ], + "blocks": [ + { + "bbox": [ + 348, + 165, + 503, + 274 + ], + "lines": [ + { + "bbox": [ + 348, + 165, + 503, + 274 + ], + "spans": [ + { + "bbox": [ + 348, + 165, + 503, + 274 + ], + "type": "image", + "image_path": "781c66513e9af13aa5ceaf61f5032d6110e6fefc16680ab0e4865191fd645d6b.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 287, + 545, + 430 + ], + "lines": [ + { + "bbox": [ + 304, + 287, + 545, + 430 + ], + "spans": [ + { + "bbox": [ + 304, + 287, + 545, + 430 + ], + "type": "text", + "content": "Figure 2. Geometry Of The Two Plane Perspective Prior: (a) describes the single view geometry of the proposed two plane prior. Region on the ground plane defined by " + }, + { + "bbox": [ + 304, + 287, + 545, + 430 + ], + "type": "inline_equation", + "content": "P_{1}, \\ldots, P_{4}" + }, + { + "bbox": [ + 304, + 287, + 545, + 430 + ], + "type": "text", + "content": ", and rays emanating from camera " + }, + { + "bbox": [ + 304, + 287, + 545, + 430 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 304, + 287, + 545, + 430 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 287, + 545, + 430 + ], + "type": "inline_equation", + "content": "P_{i}" + }, + { + "bbox": [ + 304, + 287, + 545, + 430 + ], + "type": "text", + "content": " intersect at " + }, + { + "bbox": [ + 304, + 287, + 545, + 430 + ], + "type": "inline_equation", + "content": "u_{1} \\ldots u_{4}" + }, + { + "bbox": [ + 304, + 287, + 545, + 430 + ], + "type": "text", + "content": " on the image plane. The vanishing point " + }, + { + "bbox": [ + 304, + 287, + 545, + 430 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 304, + 287, + 545, + 430 + ], + "type": "text", + "content": " maps to " + }, + { + "bbox": [ + 304, + 287, + 545, + 430 + ], + "type": "inline_equation", + "content": "P_{\\infty}" + }, + { + "bbox": [ + 304, + 287, + 545, + 430 + ], + "type": "text", + "content": ". This planar region accounts for small objects on the ground plane. To account for objects that are tall or do not lie on the ground plane, we consider another plane " + }, + { + "bbox": [ + 304, + 287, + 545, + 430 + ], + "type": "inline_equation", + "content": "Q_{1} \\ldots Q_{4}" + }, + { + "bbox": [ + 304, + 287, + 545, + 430 + ], + "type": "text", + "content": " above the horizon line. These two planes encapsulate all the relevant objects in the scene. (b) depicts the re-parameterization of the two planes in the 2D image. Instead of representing the planar points " + }, + { + "bbox": [ + 304, + 287, + 545, + 430 + ], + "type": "inline_equation", + "content": "u_{1} \\ldots u_{4}" + }, + { + "bbox": [ + 304, + 287, + 545, + 430 + ], + "type": "text", + "content": " as pixel coordinates, we instead parameterize them in terms of the vanishing point " + }, + { + "bbox": [ + 304, + 287, + 545, + 430 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 304, + 287, + 545, + 430 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 287, + 545, + 430 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 287, + 545, + 430 + ], + "type": "text", + "content": "'s and " + }, + { + "bbox": [ + 304, + 287, + 545, + 430 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 287, + 545, + 430 + ], + "type": "text", + "content": " to ease learning." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 453, + 545, + 477 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 453, + 545, + 477 + ], + "spans": [ + { + "bbox": [ + 305, + 453, + 545, + 477 + ], + "type": "text", + "content": "as we clamp the values of " + }, + { + "bbox": [ + 305, + 453, + 545, + 477 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 305, + 453, + 545, + 477 + ], + "type": "text", + "content": "'s to " + }, + { + "bbox": [ + 305, + 453, + 545, + 477 + ], + "type": "inline_equation", + "content": "[0,1]" + }, + { + "bbox": [ + 305, + 453, + 545, + 477 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 453, + 545, + 477 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 305, + 453, + 545, + 477 + ], + "type": "text", + "content": "'s to " + }, + { + "bbox": [ + 305, + 453, + 545, + 477 + ], + "type": "inline_equation", + "content": "[- \\frac{\\pi}{2}, \\frac{\\pi}{2}]" + }, + { + "bbox": [ + 305, + 453, + 545, + 477 + ], + "type": "text", + "content": ". It should be noted that all the operations are differentiable." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 487, + 441, + 499 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 487, + 441, + 499 + ], + "spans": [ + { + "bbox": [ + 306, + 487, + 441, + 499 + ], + "type": "text", + "content": "3.3. From Planes to Saliency" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 506, + 545, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 506, + 545, + 601 + ], + "spans": [ + { + "bbox": [ + 304, + 506, + 545, + 601 + ], + "type": "text", + "content": "We leverage geometry to focus on relevant image regions through saliency guided warping [23, 36], and create a saliency map from a parameterized homography using " + }, + { + "bbox": [ + 304, + 506, + 545, + 601 + ], + "type": "inline_equation", + "content": "u_{1} \\ldots u_{4}" + }, + { + "bbox": [ + 304, + 506, + 545, + 601 + ], + "type": "text", + "content": " defined earlier. Looking at ground plane from two viewpoints (Figure 3 (a) and (b)), object size decreases by their distance from the camera [20]. We shall establish a relationship to counter this effect and \"sample\" far-away objects on the ground plane more than nearby objects." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 601, + 545, + 637 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 601, + 545, + 637 + ], + "spans": [ + { + "bbox": [ + 304, + 601, + 545, + 637 + ], + "type": "text", + "content": "The saliency guided warping proposed by [36] operates using an inverse transformation " + }, + { + "bbox": [ + 304, + 601, + 545, + 637 + ], + "type": "inline_equation", + "content": "\\mathcal{T}_S^{-1}" + }, + { + "bbox": [ + 304, + 601, + 545, + 637 + ], + "type": "text", + "content": " parameterized by a saliency map " + }, + { + "bbox": [ + 304, + 601, + 545, + 637 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 601, + 545, + 637 + ], + "type": "text", + "content": " as follows," + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 353, + 643, + 545, + 658 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 353, + 643, + 545, + 658 + ], + "spans": [ + { + "bbox": [ + 353, + 643, + 545, + 658 + ], + "type": "interline_equation", + "content": "I ^ {\\prime} (x, y) = W _ {\\mathcal {T}} (I) = I \\left(\\mathcal {T} _ {S} ^ {- 1} (x, y)\\right) \\tag {3}", + "image_path": "11fab7eb3f4dfdd28c6c0976055e5cda111ed2f07b7865ee0016e371f90af2b5.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "where the warp " + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "inline_equation", + "content": "W_{\\mathcal{T}}" + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": " implies iterating over output pixel coordinates, using " + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{T}_S^{-1}" + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": " to find corresponding input coordinates (non-integral), and bilinearly interpolating output color from neighbouring input pixel grid points. For each" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "13366" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 71, + 174, + 150 + ], + "blocks": [ + { + "bbox": [ + 49, + 71, + 174, + 150 + ], + "lines": [ + { + "bbox": [ + 49, + 71, + 174, + 150 + ], + "spans": [ + { + "bbox": [ + 49, + 71, + 174, + 150 + ], + "type": "image", + "image_path": "b0b847b8e7b27272bc9b4120126ecf560e36344085187e6f7544044c3314f3b2.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 69, + 150, + 143, + 159 + ], + "lines": [ + { + "bbox": [ + 69, + 150, + 143, + 159 + ], + "spans": [ + { + "bbox": [ + 69, + 150, + 143, + 159 + ], + "type": "text", + "content": "(a) Camera View" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 173, + 72, + 296, + 149 + ], + "blocks": [ + { + "bbox": [ + 173, + 72, + 296, + 149 + ], + "lines": [ + { + "bbox": [ + 173, + 72, + 296, + 149 + ], + "spans": [ + { + "bbox": [ + 173, + 72, + 296, + 149 + ], + "type": "image", + "image_path": "aadeee20fd3e8dbd2d7bf0459223ad71e0251893f4845475c3b4905d9467b4f5.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 184, + 150, + 282, + 161 + ], + "lines": [ + { + "bbox": [ + 184, + 150, + 282, + 161 + ], + "spans": [ + { + "bbox": [ + 184, + 150, + 282, + 161 + ], + "type": "text", + "content": "(c) Mapping Saliency" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 298, + 72, + 419, + 149 + ], + "blocks": [ + { + "bbox": [ + 298, + 72, + 419, + 149 + ], + "lines": [ + { + "bbox": [ + 298, + 72, + 419, + 149 + ], + "spans": [ + { + "bbox": [ + 298, + 72, + 419, + 149 + ], + "type": "image", + "image_path": "5f66e79e5a8b1e53370af0a4c857187cc1902d322f7a2b15529e0973c5d7b05c.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 421, + 72, + 543, + 149 + ], + "blocks": [ + { + "bbox": [ + 421, + 72, + 543, + 149 + ], + "lines": [ + { + "bbox": [ + 421, + 72, + 543, + 149 + ], + "spans": [ + { + "bbox": [ + 421, + 72, + 543, + 149 + ], + "type": "image", + "image_path": "fa890e5d308d30be676c8feada3e24743cc81f4b279541a9a588d0fe5b3f57d1.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 49, + 163, + 172, + 241 + ], + "blocks": [ + { + "bbox": [ + 49, + 163, + 172, + 241 + ], + "lines": [ + { + "bbox": [ + 49, + 163, + 172, + 241 + ], + "spans": [ + { + "bbox": [ + 49, + 163, + 172, + 241 + ], + "type": "image", + "image_path": "6381bfc7df66e410bbb07f80a54ce668fbd62761834528c1497e6ac65c0a4307.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 64, + 243, + 157, + 255 + ], + "lines": [ + { + "bbox": [ + 64, + 243, + 157, + 255 + ], + "spans": [ + { + "bbox": [ + 64, + 243, + 157, + 255 + ], + "type": "text", + "content": "(b) Bird's Eye View" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 45, + 270, + 547, + 326 + ], + "lines": [ + { + "bbox": [ + 45, + 270, + 547, + 326 + ], + "spans": [ + { + "bbox": [ + 45, + 270, + 547, + 326 + ], + "type": "text", + "content": "Figure 3. Two-Plane Perspective Prior based Image Resampling: Consider the scene of car, bus and traffic light from (a) camera view and (b) (simplified) bird's eye view. (c) Saliency function that captures the inverse relationship between object size (in camera view) and depth (bird's eye view is looking at " + }, + { + "bbox": [ + 45, + 270, + 547, + 326 + ], + "type": "inline_equation", + "content": "XZ" + }, + { + "bbox": [ + 45, + 270, + 547, + 326 + ], + "type": "text", + "content": " plane from above) can be transferred to the camera view (d), by mapping row " + }, + { + "bbox": [ + 45, + 270, + 547, + 326 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 45, + 270, + 547, + 326 + ], + "type": "text", + "content": " using " + }, + { + "bbox": [ + 45, + 270, + 547, + 326 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 45, + 270, + 547, + 326 + ], + "type": "text", + "content": " (marked by blue arrows). (e) and (f) shows that ground plane severely distorts nearby tall objects while squishing traffic light. (g) and (h) shows that additional plane reduces distortion for both tall objects and objects not on ground plane." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 173, + 163, + 296, + 241 + ], + "blocks": [ + { + "bbox": [ + 173, + 163, + 296, + 241 + ], + "lines": [ + { + "bbox": [ + 173, + 163, + 296, + 241 + ], + "spans": [ + { + "bbox": [ + 173, + 163, + 296, + 241 + ], + "type": "image", + "image_path": "aa3229e80a2710d5f1ab7860607951b4027478908b09af7acb5d4d1e859eccd9.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 187, + 243, + 290, + 255 + ], + "lines": [ + { + "bbox": [ + 187, + 243, + 290, + 255 + ], + "spans": [ + { + "bbox": [ + 187, + 243, + 290, + 255 + ], + "type": "text", + "content": "(d) Saliency On Scene" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 296, + 163, + 419, + 241 + ], + "blocks": [ + { + "bbox": [ + 298, + 151, + 420, + 162 + ], + "lines": [ + { + "bbox": [ + 298, + 151, + 420, + 162 + ], + "spans": [ + { + "bbox": [ + 298, + 151, + 420, + 162 + ], + "type": "text", + "content": "(e) Ground Plane Saliency" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 296, + 163, + 419, + 241 + ], + "lines": [ + { + "bbox": [ + 296, + 163, + 419, + 241 + ], + "spans": [ + { + "bbox": [ + 296, + 163, + 419, + 241 + ], + "type": "image", + "image_path": "e35c2ff4b89acd7ec67a0fab4e81ff53246f9440c04ca44f5d034519e1ceb650.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 243, + 408, + 255 + ], + "lines": [ + { + "bbox": [ + 304, + 243, + 408, + 255 + ], + "spans": [ + { + "bbox": [ + 304, + 243, + 408, + 255 + ], + "type": "text", + "content": "(f) Ground Plane Warp" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 421, + 163, + 542, + 241 + ], + "blocks": [ + { + "bbox": [ + 427, + 151, + 535, + 162 + ], + "lines": [ + { + "bbox": [ + 427, + 151, + 535, + 162 + ], + "spans": [ + { + "bbox": [ + 427, + 151, + 535, + 162 + ], + "type": "text", + "content": "(g) Two Plane Saliency" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 421, + 163, + 542, + 241 + ], + "lines": [ + { + "bbox": [ + 421, + 163, + 542, + 241 + ], + "spans": [ + { + "bbox": [ + 421, + 163, + 542, + 241 + ], + "type": "image", + "image_path": "a692c7d5ffcf061d85890299d00d9b6f304762fffd7088bedb451420483bc9f6.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 432, + 244, + 521, + 255 + ], + "lines": [ + { + "bbox": [ + 432, + 244, + 521, + 255 + ], + "spans": [ + { + "bbox": [ + 432, + 244, + 521, + 255 + ], + "type": "text", + "content": "(h) Two Plane Warp" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 346, + 286, + 370 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 346, + 286, + 370 + ], + "spans": [ + { + "bbox": [ + 46, + 346, + 286, + 370 + ], + "type": "text", + "content": "input pixel " + }, + { + "bbox": [ + 46, + 346, + 286, + 370 + ], + "type": "inline_equation", + "content": "(x,y)" + }, + { + "bbox": [ + 46, + 346, + 286, + 370 + ], + "type": "text", + "content": ", pixel coordinates with higher " + }, + { + "bbox": [ + 46, + 346, + 286, + 370 + ], + "type": "inline_equation", + "content": "S(x,y)" + }, + { + "bbox": [ + 46, + 346, + 286, + 370 + ], + "type": "text", + "content": " values (i.e. salient regions) would be sampled more." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 46, + 372, + 286, + 454 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 372, + 286, + 454 + ], + "spans": [ + { + "bbox": [ + 46, + 372, + 286, + 454 + ], + "type": "text", + "content": "We construct a saliency " + }, + { + "bbox": [ + 46, + 372, + 286, + 454 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 372, + 286, + 454 + ], + "type": "text", + "content": " respecting the geometric properties that we desire. Let " + }, + { + "bbox": [ + 46, + 372, + 286, + 454 + ], + "type": "inline_equation", + "content": "H_{plane}" + }, + { + "bbox": [ + 46, + 372, + 286, + 454 + ], + "type": "text", + "content": " be the homography between the camera view (using coordinates " + }, + { + "bbox": [ + 46, + 372, + 286, + 454 + ], + "type": "inline_equation", + "content": "u_{1}\\ldots u_{4}" + }, + { + "bbox": [ + 46, + 372, + 286, + 454 + ], + "type": "text", + "content": ") and a bird's eye view of the ground plane assuming plane size to be the original image size " + }, + { + "bbox": [ + 46, + 372, + 286, + 454 + ], + "type": "inline_equation", + "content": "(w,h)" + }, + { + "bbox": [ + 46, + 372, + 286, + 454 + ], + "type": "text", + "content": ". In bird's eye view, we propose saliency function for a row of pixels " + }, + { + "bbox": [ + 46, + 372, + 286, + 454 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 372, + 286, + 454 + ], + "type": "text", + "content": " (assuming bottom-left of this rectangle as " + }, + { + "bbox": [ + 46, + 372, + 286, + 454 + ], + "type": "inline_equation", + "content": "(0,0)" + }, + { + "bbox": [ + 46, + 372, + 286, + 454 + ], + "type": "text", + "content": ") as," + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 127, + 459, + 287, + 474 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 127, + 459, + 287, + 474 + ], + "spans": [ + { + "bbox": [ + 127, + 459, + 287, + 474 + ], + "type": "interline_equation", + "content": "S _ {b e v} (z) = e ^ {\\nu \\left(\\frac {z}{h} - 1\\right)} \\tag {4}", + "image_path": "3845ff54c73a5697cb86eae7f0c48de51d45e5cf322e0c83fa85342fa386bcc1.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 46, + 481, + 287, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 481, + 287, + 504 + ], + "spans": [ + { + "bbox": [ + 46, + 481, + 287, + 504 + ], + "type": "text", + "content": "with a learnable parameter " + }, + { + "bbox": [ + 46, + 481, + 287, + 504 + ], + "type": "inline_equation", + "content": "\\nu (>1)" + }, + { + "bbox": [ + 46, + 481, + 287, + 504 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 46, + 481, + 287, + 504 + ], + "type": "inline_equation", + "content": "\\nu" + }, + { + "bbox": [ + 46, + 481, + 287, + 504 + ], + "type": "text", + "content": " defines the extent of sampling with respect to depth." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 46, + 505, + 286, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 505, + 286, + 529 + ], + "spans": [ + { + "bbox": [ + 46, + 505, + 286, + 529 + ], + "type": "text", + "content": "To map this saliency to camera view, we warp " + }, + { + "bbox": [ + 46, + 505, + 286, + 529 + ], + "type": "inline_equation", + "content": "S_{bev}" + }, + { + "bbox": [ + 46, + 505, + 286, + 529 + ], + "type": "text", + "content": " via perspective transform " + }, + { + "bbox": [ + 46, + 505, + 286, + 529 + ], + "type": "inline_equation", + "content": "W_{p}" + }, + { + "bbox": [ + 46, + 505, + 286, + 529 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 505, + 286, + 529 + ], + "type": "inline_equation", + "content": "H_{plane}" + }, + { + "bbox": [ + 46, + 505, + 286, + 529 + ], + "type": "text", + "content": " (Figure 3 (c))," + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 108, + 533, + 287, + 549 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 533, + 287, + 549 + ], + "spans": [ + { + "bbox": [ + 108, + 533, + 287, + 549 + ], + "type": "interline_equation", + "content": "S _ {p l a n e} = W _ {p} \\left(H _ {p l a n e} ^ {- 1}, S _ {b e v}\\right) \\tag {5}", + "image_path": "dae25002109e8c669c923ae36c743633b4cb3eb178f58818d824e4a8a9ff08c2.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 46, + 555, + 287, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 555, + 287, + 602 + ], + "spans": [ + { + "bbox": [ + 46, + 555, + 287, + 602 + ], + "type": "text", + "content": "We have defined saliency " + }, + { + "bbox": [ + 46, + 555, + 287, + 602 + ], + "type": "inline_equation", + "content": "S_{plane}" + }, + { + "bbox": [ + 46, + 555, + 287, + 602 + ], + "type": "text", + "content": " given " + }, + { + "bbox": [ + 46, + 555, + 287, + 602 + ], + "type": "inline_equation", + "content": "H_{plane}" + }, + { + "bbox": [ + 46, + 555, + 287, + 602 + ], + "type": "text", + "content": " in a differentiable manner. Our saliency ensures that objects on the ground plane separated by depth " + }, + { + "bbox": [ + 46, + 555, + 287, + 602 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 46, + 555, + 287, + 602 + ], + "type": "text", + "content": " are sampled by the factor " + }, + { + "bbox": [ + 46, + 555, + 287, + 602 + ], + "type": "inline_equation", + "content": "e^{\\nu \\frac{Z}{h}}" + }, + { + "bbox": [ + 46, + 555, + 287, + 602 + ], + "type": "text", + "content": " in the image." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 47, + 610, + 203, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 610, + 203, + 624 + ], + "spans": [ + { + "bbox": [ + 47, + 610, + 203, + 624 + ], + "type": "text", + "content": "3.4. Two-Plane Perspective Prior" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "text", + "content": "Ground Plane saliency focuses on objects that are geometrically constrained to be on this plane and reasonably models objects far away on the plane. However, nearby and tall objects, and small objects far above the ground plane are not modelled well. In Fig 3 (f), nearby objects above ground plane (traffic lights), they are highly distorted. Critically, these same objects when further away are rendered" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 304, + 346, + 545, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 346, + 545, + 418 + ], + "spans": [ + { + "bbox": [ + 304, + 346, + 545, + 418 + ], + "type": "text", + "content": "small in size and appear close to ground (and thus modelled well). Objects we should focus more on are thus the former compared to the latter. Thus, another plane is needed, and direction of the saliency function is reversed to " + }, + { + "bbox": [ + 304, + 346, + 545, + 418 + ], + "type": "inline_equation", + "content": "\\hat{S}_{bev}(z) = e^{\\hat{\\nu}((h - z) / h) - 1}" + }, + { + "bbox": [ + 304, + 346, + 545, + 418 + ], + "type": "text", + "content": " to account for these objects that would otherwise be severely distorted." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 304, + 418, + 545, + 442 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 418, + 545, + 442 + ], + "spans": [ + { + "bbox": [ + 304, + 418, + 545, + 442 + ], + "type": "text", + "content": "To represent the Two-Plane Prior, we represented the planar regions as saliencies. The overall saliency is," + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 358, + 447, + 545, + 460 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 358, + 447, + 545, + 460 + ], + "spans": [ + { + "bbox": [ + 358, + 447, + 545, + 460 + ], + "type": "interline_equation", + "content": "S = S _ {\\text {g r o u n d - p l a n e}} + \\lambda S _ {\\text {t o p - p l a n e}} \\tag {6}", + "image_path": "c1a560c1f31cbd1839b3ab657e96425bfe9a6d36c5b109c36189c9f879fde0d8.jpg" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 306, + 464, + 433, + 475 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 464, + 433, + 475 + ], + "spans": [ + { + "bbox": [ + 306, + 464, + 433, + 475 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 464, + 433, + 475 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 306, + 464, + 433, + 475 + ], + "type": "text", + "content": " is a learned parameter." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 306, + 483, + 451, + 494 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 483, + 451, + 494 + ], + "spans": [ + { + "bbox": [ + 306, + 483, + 451, + 494 + ], + "type": "text", + "content": "3.5. Additional Considerations" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 304, + 501, + 545, + 572 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 501, + 545, + 572 + ], + "spans": [ + { + "bbox": [ + 304, + 501, + 545, + 572 + ], + "type": "text", + "content": "Warping via a piecewise saliency function imposes additional considerations. The choice of deformation method is critical, saliency sampler [36] implicitly avoids drastic transformations common in other approaches. For e.g., Thin-plate spline performs worse [36], produces extreme transformations and requires regularization [13]." + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 304, + 573, + 545, + 609 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 573, + 545, + 609 + ], + "spans": [ + { + "bbox": [ + 304, + 573, + 545, + 609 + ], + "type": "text", + "content": "Fovea [50] observes that restricting the space of allowable warps such that axis alignment is preserved improves accuracy, we adopt the separable formulation of " + }, + { + "bbox": [ + 304, + 573, + 545, + 609 + ], + "type": "inline_equation", + "content": "\\mathcal{T}^{-1}" + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 359, + 610, + 545, + 639 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 359, + 610, + 545, + 639 + ], + "spans": [ + { + "bbox": [ + 359, + 610, + 545, + 639 + ], + "type": "interline_equation", + "content": "\\mathcal {T} _ {x} ^ {- 1} (x) = \\frac {\\int_ {x ^ {\\prime}} S _ {x} \\left(x ^ {\\prime}\\right) k \\left(x ^ {\\prime} , x\\right) x ^ {\\prime}}{\\int_ {x ^ {\\prime}} S _ {x} \\left(x ^ {\\prime}\\right) k \\left(x , x ^ {\\prime}\\right)} \\tag {7}", + "image_path": "f937ecbc594aee8f228ea63839be4a4f978d9bef484ea22020d6cc237fe3776b.jpg" + } + ] + } + ], + "index": 33 + }, + { + "bbox": [ + 361, + 643, + 545, + 673 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 361, + 643, + 545, + 673 + ], + "spans": [ + { + "bbox": [ + 361, + 643, + 545, + 673 + ], + "type": "interline_equation", + "content": "\\mathcal {T} _ {y} ^ {- 1} (y) = \\frac {\\int_ {y ^ {\\prime}} S _ {y} \\left(y ^ {\\prime}\\right) k \\left(y ^ {\\prime} , y\\right) y ^ {\\prime}}{\\int_ {y ^ {\\prime}} S _ {y} \\left(y ^ {\\prime}\\right) k \\left(y , y ^ {\\prime}\\right)} \\tag {8}", + "image_path": "14f2ba82ba8a01c54f751999cbdf9859e5a7333e97a1f224b0cc46d58c172f1c.jpg" + } + ] + } + ], + "index": 34 + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": " is a Gaussian kernel. To convert a saliency map " + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "inline_equation", + "content": "S_{x}" + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "inline_equation", + "content": "S_{y}" + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": " we marginalize it along the two axes. Thus entire rows or columns are \"stretched\" or \"compressed\"." + } + ] + } + ], + "index": 35 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13367" + } + ] + } + ], + "index": 36 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "text", + "content": "Two-plane prior is learnt end to end as a learnable image warp. For object detection, labels need to be warped too, and [36]'s warp is invertible. Like [50], We employ the loss " + }, + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "inline_equation", + "content": "\\mathcal{L}(\\mathcal{T}^{-1}(f_{\\phi}(W_{\\mathcal{T}}(I)),L)" + }, + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "inline_equation", + "content": "(I,L)" + }, + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "text", + "content": " is the image-label pair and omit the use of delta encoding for training RPN [40] (which requires the existence of a closed form " + }, + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "text", + "content": "), instead adopting GIoU loss [41]. This ensures " + }, + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "inline_equation", + "content": "W_{\\mathcal{T}}" + }, + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "text", + "content": " is learnable, as " + }, + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "inline_equation", + "content": "\\mathcal{T}^{-1}" + }, + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "text", + "content": " is differentiable." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 168, + 289, + 242 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 168, + 289, + 242 + ], + "spans": [ + { + "bbox": [ + 46, + 168, + 289, + 242 + ], + "type": "text", + "content": "We did not assume that the vanishing point is within the field of view of our image, and our approach places no restrictions on the vanishing point. Thus far, we explained our formulation while considering a single dominant vanishing point, however, multiple vanishing points can be also considered. Please see supplementary for more details." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 248, + 212, + 261 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 248, + 212, + 261 + ], + "spans": [ + { + "bbox": [ + 47, + 248, + 212, + 261 + ], + "type": "text", + "content": "3.6. Obtaining the Vanishing Point" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 266, + 287, + 315 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 266, + 287, + 315 + ], + "spans": [ + { + "bbox": [ + 46, + 266, + 287, + 315 + ], + "type": "text", + "content": "We now describe how we obtain the vanishing point. Many methods exist with trade-offs in accuracy, latency and memory which inform our design to perform warping efficiently with minimal overheads." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 316, + 287, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 316, + 287, + 399 + ], + "spans": [ + { + "bbox": [ + 46, + 316, + 287, + 399 + ], + "type": "text", + "content": "Fixed Cameras: In settings like traffic cameras, the camera is fixed. Thus, the vanishing point is fixed, and we can cache the corresponding saliency " + }, + { + "bbox": [ + 46, + 316, + 287, + 399 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 316, + 287, + 399 + ], + "type": "text", + "content": ", as all the parameters, once learnt, are fixed. We can define the vanishing point for a camera manually by annotating two parallel lines or any accurate automated approach. Saliency caching renders our approach extremely efficient." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 399, + 287, + 543 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 399, + 287, + 543 + ], + "spans": [ + { + "bbox": [ + 46, + 399, + 287, + 543 + ], + "type": "text", + "content": "Autonomous Navigation: Multiple assumptions simplify the problem. We assume that there is one dominant vanishing point and a navigating car is often moving in the viewing direction. Thus, we assume that this vanishing point lies inside the image, and directly regress " + }, + { + "bbox": [ + 46, + 399, + 287, + 543 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 46, + 399, + 287, + 543 + ], + "type": "text", + "content": " from image features using a modified coordinate regression module akin to YOLO [33, 38]. This approach appears to be memory and latency efficient. Other approaches, say, using parallel lane lines [1] or inertial measurements [3] might also be very efficient. An even simpler assumption is to employ the average vanishing point, as vanishing points are highly local, we observe this is a good approximation." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 543, + 287, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 543, + 287, + 578 + ], + "spans": [ + { + "bbox": [ + 46, + 543, + 287, + 578 + ], + "type": "text", + "content": "Temporal Redundancies: In videos, we exploit temporal redundancies, the vanishing point is computed every " + }, + { + "bbox": [ + 46, + 543, + 287, + 578 + ], + "type": "inline_equation", + "content": "n_v" + }, + { + "bbox": [ + 46, + 543, + 287, + 578 + ], + "type": "text", + "content": " frames and saliency is cached to amortize latency cost." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 578, + 287, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 578, + 287, + 639 + ], + "spans": [ + { + "bbox": [ + 46, + 578, + 287, + 639 + ], + "type": "text", + "content": "General Case: This is the most difficult case, and many approaches have been explored in literature to find all vanishing points. Classical approaches [49] while fast are not robust, while deep-learned approaches [31,32,59] are accurate yet expensive (either in latency or memory)." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 647, + 287, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 647, + 287, + 659 + ], + "spans": [ + { + "bbox": [ + 47, + 647, + 287, + 659 + ], + "type": "text", + "content": "3.7. Learning Geometric Prior from Pseudo-Labels" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 665, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 715 + ], + "type": "text", + "content": "Prior work [50] have shown improvements in performance on pre-trained models via heuristics, which didn't require any training. However, their method still employs domain-specific labels (say, from Argoverse-HD) to generate the" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 307, + 70, + 425, + 137 + ], + "blocks": [ + { + "bbox": [ + 307, + 70, + 425, + 137 + ], + "lines": [ + { + "bbox": [ + 307, + 70, + 425, + 137 + ], + "spans": [ + { + "bbox": [ + 307, + 70, + 425, + 137 + ], + "type": "image", + "image_path": "0162ca8a534119829c44c49c0acab601fa315f12eb7266ccda73d43cebec0619.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 427, + 70, + 545, + 137 + ], + "blocks": [ + { + "bbox": [ + 427, + 70, + 545, + 137 + ], + "lines": [ + { + "bbox": [ + 427, + 70, + 545, + 137 + ], + "spans": [ + { + "bbox": [ + 427, + 70, + 545, + 137 + ], + "type": "image", + "image_path": "f370ef3da817e18bca66779a4f188b77377c2142946643016539eebf92fe2fa6.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 307, + 138, + 425, + 205 + ], + "blocks": [ + { + "bbox": [ + 307, + 138, + 425, + 205 + ], + "lines": [ + { + "bbox": [ + 307, + 138, + 425, + 205 + ], + "spans": [ + { + "bbox": [ + 307, + 138, + 425, + 205 + ], + "type": "image", + "image_path": "b3d035b91cf500d6c2ecc97b3ce5f5c49db5b92bc62665f6b43ccf2aba9cd2f4.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 215, + 547, + 270 + ], + "lines": [ + { + "bbox": [ + 304, + 215, + 547, + 270 + ], + "spans": [ + { + "bbox": [ + 304, + 215, + 547, + 270 + ], + "type": "text", + "content": "Figure 4. Commuter Bus Dataset: The captured data has a unique viewpoint, the average size of objects is small and captured under a wide variety of lighting conditions. Top-left and bottom-right images depict the same bus-stop and trashcan at different time of day and season." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 427, + 138, + 545, + 205 + ], + "blocks": [ + { + "bbox": [ + 427, + 138, + 545, + 205 + ], + "lines": [ + { + "bbox": [ + 427, + 138, + 545, + 205 + ], + "spans": [ + { + "bbox": [ + 427, + 138, + 545, + 205 + ], + "type": "image", + "image_path": "2c055f3997cdb04c719b7c912e08a5e29aae4f210031402b4edc7c79ee719f4a.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 292, + 545, + 340 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 292, + 545, + 340 + ], + "spans": [ + { + "bbox": [ + 304, + 292, + 545, + 340 + ], + "type": "text", + "content": "prior. Our method can't be used directly with pre-trained models as it learns geometrically inspired parameters end-to-end. However, domain-specific images without labels can be exploited to learn the parameters." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 340, + 546, + 424 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 340, + 546, + 424 + ], + "spans": [ + { + "bbox": [ + 304, + 340, + 546, + 424 + ], + "type": "text", + "content": "We propose a simple alternative to learn the proposed prior using pre-trained model without requiring additional domain-specific labels. We generate pseudo-labels from our pre-trained model inferred at 1x scale. We fine-tune and learn our warp function (to " + }, + { + "bbox": [ + 304, + 340, + 546, + 424 + ], + "type": "inline_equation", + "content": "0.5\\mathrm{x}" + }, + { + "bbox": [ + 304, + 340, + 546, + 424 + ], + "type": "text", + "content": " scale) end-to-end using these \"free\" labels. Our geometric prior shows improvements without access to ground truth labels." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 435, + 481, + 447 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 435, + 481, + 447 + ], + "spans": [ + { + "bbox": [ + 306, + 435, + 481, + 447 + ], + "type": "text", + "content": "4. Dataset And Evaluation Details" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 455, + 368, + 467 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 455, + 368, + 467 + ], + "spans": [ + { + "bbox": [ + 306, + 455, + 368, + 467 + ], + "type": "text", + "content": "4.1. Datasets" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 474, + 545, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 545, + 545 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 545, + 545 + ], + "type": "text", + "content": "Argoverse-HD [27]: We employ Argoverse-HD dataset for evaluation in the autonomous navigation scenario. This dataset consists of 30fps video sequences from a car collected at " + }, + { + "bbox": [ + 304, + 474, + 545, + 545 + ], + "type": "inline_equation", + "content": "1920 \\times 1200" + }, + { + "bbox": [ + 304, + 474, + 545, + 545 + ], + "type": "text", + "content": " resolution, and dense box annotations are provided for common objects of interest such as vehicles, pedestrians, signboards and traffic lights." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 545, + 546, + 701 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 546, + 701 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 546, + 701 + ], + "type": "text", + "content": "WALT [37]: We employ images from 8.4K cameras that overlook public urban settings to analyze the flow of traffic vehicles. The data is captured for 3-second bursts every few minutes and only images with notable changes are stored. We annotated a set of 4738 images with vehicles collected over the time period of a year covering a variety of day/night/dawn settings, seasonal changes and camera viewpoints. We show our results on two splits (approximately " + }, + { + "bbox": [ + 304, + 545, + 546, + 701 + ], + "type": "inline_equation", + "content": "80\\%" + }, + { + "bbox": [ + 304, + 545, + 546, + 701 + ], + "type": "text", + "content": " training and " + }, + { + "bbox": [ + 304, + 545, + 546, + 701 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 304, + 545, + 546, + 701 + ], + "type": "text", + "content": " testing). The first, All-Viewpoints, images from all the cameras are equally represented in the train and test sets. Alternatively, we split by camera, Split-by-Camera, images from 6 cameras are part of the training set and 2 cameras are held out for testing." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 701, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 701, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 701, + 545, + 713 + ], + "type": "text", + "content": "Commuter Bus Dataset: We curated this dataset from a" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13368" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 70, + 286, + 199 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 286, + 199 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 286, + 199 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 286, + 199 + ], + "type": "image", + "image_path": "6f7abf9e85a0f71fabb52bd8a2c79aa6cae4da45e4c97de23f70ac12c7427c9f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 208, + 288, + 253 + ], + "lines": [ + { + "bbox": [ + 46, + 208, + 288, + 253 + ], + "spans": [ + { + "bbox": [ + 46, + 208, + 288, + 253 + ], + "type": "text", + "content": "Figure 5. Two-Plane Prior as a Neural Layer: We implemented our approach as a global prior that is learned end-to-end from labelled data. Our prior is dependent on a vanishing point estimate to specify the viewing direction of the camera." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 275, + 289, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 275, + 289, + 396 + ], + "spans": [ + { + "bbox": [ + 46, + 275, + 289, + 396 + ], + "type": "text", + "content": "commuter bus running on an urban route. The 720p camera of interest has a unique viewpoint and scene geometry (See Figure 4). Annotated categories are trashcans and garbage bags (to help inform public services) and people with special needs (using wheelchairs or strollers), which are a rare occurrence. The dataset size is small with only 750 annotated images (split into " + }, + { + "bbox": [ + 46, + 275, + 289, + 396 + ], + "type": "inline_equation", + "content": "70\\%" + }, + { + "bbox": [ + 46, + 275, + 289, + 396 + ], + "type": "text", + "content": " training and " + }, + { + "bbox": [ + 46, + 275, + 289, + 396 + ], + "type": "inline_equation", + "content": "30\\%" + }, + { + "bbox": [ + 46, + 275, + 289, + 396 + ], + "type": "text", + "content": " testing). This is an extremely challenging dataset due to its unique viewpoint, small object size, rare categories, along with variations in lighting and seasons." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 404, + 157, + 417 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 404, + 157, + 417 + ], + "spans": [ + { + "bbox": [ + 47, + 404, + 157, + 417 + ], + "type": "text", + "content": "4.2. Evaluation Details" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 424, + 287, + 459 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 424, + 287, + 459 + ], + "spans": [ + { + "bbox": [ + 46, + 424, + 287, + 459 + ], + "type": "text", + "content": "We perform apples-to-apples comparisons on the same detector trained using the datasets with identical training schedule and hardware." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 460, + 287, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 460, + 287, + 544 + ], + "spans": [ + { + "bbox": [ + 46, + 460, + 287, + 544 + ], + "type": "text", + "content": "Data: We compare to methods that were trained on fixed training data. In contrast, sAP leaderboards [27] don't restrict data and evaluate on different hardware. We compare with [16, 27] from leaderboard, which follow the same protocols. Other methods on the leaderboard use additional training data to train off-the-self detectors. Our detectors would see similar improvements with additional data." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 544, + 288, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 544, + 288, + 700 + ], + "spans": [ + { + "bbox": [ + 46, + 544, + 288, + 700 + ], + "type": "text", + "content": "Real-Time Evaluation: We evaluate using Streaming AP (sAP) metric proposed by [27], which integrates latency and accuracy into a single metric. Instead of considering models via accuracy-latency tradeoffs [21], real-time performance can be evaluated by applying real-time constraints on the predictions [27]. Frames of the video are observed every 33 milliseconds (30 fps) and predictions for every frame must be emitted before the frame is observed (forecasting is necessary). For a fair comparison, sAP requires evaluation on the same hardware. Streaming results are not directly comparable with other work [27, 50, 56] as they use other hardware (say, V100 or 2080Ti), thus we run the evaluation on our hardware (Titan X)." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 701, + 227, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 701, + 227, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 701, + 227, + 714 + ], + "type": "text", + "content": "Additional details are in the Supplementary." + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 306, + 70, + 553, + 198 + ], + "blocks": [ + { + "bbox": [ + 306, + 70, + 553, + 198 + ], + "lines": [ + { + "bbox": [ + 306, + 70, + 553, + 198 + ], + "spans": [ + { + "bbox": [ + 306, + 70, + 553, + 198 + ], + "type": "table", + "html": "
MethodScaleAPAPSAPMAPLLatency (ms)
Faster R-CNN0.5x24.24.929.050.978.4 ± 1.8
Fovea (SD) [50]0.5x26.78.229.754.183 ± 2.5
Fovea (SI) [50]0.5x28.010.431.054.585 ± 2.7
Fovea (L:SI) [50]0.5x28.110.330.954.185.4 ± 2.7
Two-Plane Pr. (Pseudo.)0.5x27.19.828.950.2104.5 ± 8.5
Two-Plane Prior0.5x30.814.531.652.9105 ± 8.5
Baseline at higher scales
Faster R-CNN0.75x29.211.632.153.3142 ± 2.5
Faster R-CNN1.0x33.316.834.853.6220 ± 1.7
", + "image_path": "f3a06b12d8ab128a199dd78a6bfff684020edc96a0e9c93a8193efa731d4d6f0.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 206, + 547, + 251 + ], + "lines": [ + { + "bbox": [ + 304, + 206, + 547, + 251 + ], + "spans": [ + { + "bbox": [ + 304, + 206, + 547, + 251 + ], + "type": "text", + "content": "Table 1. Evaluation on Argoverse-HD: Two-Plane Prior outperforms both SOTA's dataset-wide and temporal priors in overall accuracy. Our method improves small object detection by " + }, + { + "bbox": [ + 304, + 206, + 547, + 251 + ], + "type": "inline_equation", + "content": "+4.1AP_{S}" + }, + { + "bbox": [ + 304, + 206, + 547, + 251 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 304, + 206, + 547, + 251 + ], + "type": "inline_equation", + "content": "39\\%" + }, + { + "bbox": [ + 304, + 206, + 547, + 251 + ], + "type": "text", + "content": " over SOTA." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 306, + 266, + 443, + 280 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 266, + 443, + 280 + ], + "spans": [ + { + "bbox": [ + 306, + 266, + 443, + 280 + ], + "type": "text", + "content": "5. Results and Discussions" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 289, + 547, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 289, + 547, + 361 + ], + "spans": [ + { + "bbox": [ + 304, + 289, + 547, + 361 + ], + "type": "text", + "content": "Accuracy-Latency Comparisons: On Argoverse-HD, we compare with Faster R-CNN with naive downsampling (Baseline) and Faster R-CNN paired with adaptive sampling from Fovea [50] which proposed two priors, a dataset-wide prior " + }, + { + "bbox": [ + 304, + 289, + 547, + 361 + ], + "type": "inline_equation", + "content": "(S_{D})" + }, + { + "bbox": [ + 304, + 289, + 547, + 361 + ], + "type": "text", + "content": " and frame-specific temporal priors (" + }, + { + "bbox": [ + 304, + 289, + 547, + 361 + ], + "type": "inline_equation", + "content": "S_{I}" + }, + { + "bbox": [ + 304, + 289, + 547, + 361 + ], + "type": "text", + "content": " & " + }, + { + "bbox": [ + 304, + 289, + 547, + 361 + ], + "type": "inline_equation", + "content": "L: S_{I}" + }, + { + "bbox": [ + 304, + 289, + 547, + 361 + ], + "type": "text", + "content": "; from previous frame detections)." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 361, + 548, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 361, + 548, + 504 + ], + "spans": [ + { + "bbox": [ + 304, + 361, + 548, + 504 + ], + "type": "text", + "content": "Two-Plane Prior improves (Table 1) upon baseline at the same scale by " + }, + { + "bbox": [ + 304, + 361, + 548, + 504 + ], + "type": "inline_equation", + "content": "+6.6" + }, + { + "bbox": [ + 304, + 361, + 548, + 504 + ], + "type": "text", + "content": " AP and over SOTA by " + }, + { + "bbox": [ + 304, + 361, + 548, + 504 + ], + "type": "inline_equation", + "content": "+2.7" + }, + { + "bbox": [ + 304, + 361, + 548, + 504 + ], + "type": "text", + "content": " AP. For small objects, the improvements are even more dramatic, our method improves accuracy by " + }, + { + "bbox": [ + 304, + 361, + 548, + 504 + ], + "type": "inline_equation", + "content": "+9.6" + }, + { + "bbox": [ + 304, + 361, + 548, + 504 + ], + "type": "inline_equation", + "content": "AP_{S}" + }, + { + "bbox": [ + 304, + 361, + 548, + 504 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 304, + 361, + 548, + 504 + ], + "type": "inline_equation", + "content": "195\\%" + }, + { + "bbox": [ + 304, + 361, + 548, + 504 + ], + "type": "text", + "content": " over baseline and " + }, + { + "bbox": [ + 304, + 361, + 548, + 504 + ], + "type": "inline_equation", + "content": "+4.2" + }, + { + "bbox": [ + 304, + 361, + 548, + 504 + ], + "type": "inline_equation", + "content": "AP_{S}" + }, + { + "bbox": [ + 304, + 361, + 548, + 504 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 304, + 361, + 548, + 504 + ], + "type": "inline_equation", + "content": "45\\%" + }, + { + "bbox": [ + 304, + 361, + 548, + 504 + ], + "type": "text", + "content": " over SOTA respectively. Surprisingly, our method at " + }, + { + "bbox": [ + 304, + 361, + 548, + 504 + ], + "type": "inline_equation", + "content": "0.5\\mathrm{x}" + }, + { + "bbox": [ + 304, + 361, + 548, + 504 + ], + "type": "text", + "content": " scale improves upon Faster R-CNN at " + }, + { + "bbox": [ + 304, + 361, + 548, + 504 + ], + "type": "inline_equation", + "content": "0.75\\mathrm{x}" + }, + { + "bbox": [ + 304, + 361, + 548, + 504 + ], + "type": "text", + "content": " scale by " + }, + { + "bbox": [ + 304, + 361, + 548, + 504 + ], + "type": "inline_equation", + "content": "+1.6" + }, + { + "bbox": [ + 304, + 361, + 548, + 504 + ], + "type": "text", + "content": " AP having latency improvement of " + }, + { + "bbox": [ + 304, + 361, + 548, + 504 + ], + "type": "inline_equation", + "content": "35\\%" + }, + { + "bbox": [ + 304, + 361, + 548, + 504 + ], + "type": "text", + "content": ". Our Two-Plane prior trained via pseudolabels comes very close to SOTA which employ ground truth labels, the gap is only " + }, + { + "bbox": [ + 304, + 361, + 548, + 504 + ], + "type": "inline_equation", + "content": "-1" + }, + { + "bbox": [ + 304, + 361, + 548, + 504 + ], + "type": "text", + "content": " AP and improves upon Faster R-CNN model trained on ground truth by " + }, + { + "bbox": [ + 304, + 361, + 548, + 504 + ], + "type": "inline_equation", + "content": "+2.9" + }, + { + "bbox": [ + 304, + 361, + 548, + 504 + ], + "type": "text", + "content": " AP inferred at the same scale." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 506, + 547, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 506, + 547, + 579 + ], + "spans": [ + { + "bbox": [ + 304, + 506, + 547, + 579 + ], + "type": "text", + "content": "WALT dataset [37] comprises images (only images with notable changes are saved) and not videos, we compare with Fovea [50] paired with the dataset-wide prior. We observe similar trends on both splits (Table 3 and Fig 6) and note large improvements over baseline and a consistent improvement over Fovea [50], specially for small objects." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 580, + 547, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 580, + 547, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 580, + 547, + 628 + ], + "type": "text", + "content": "Real-time/Streaming Comparisons: We use Argoverse-HD dataset, and compare using the sAP metric (Described in Section 4.2). Algorithms may choose any scale and frames as long as real-time latency constraint is satisfied." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 630, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 547, + 715 + ], + "type": "text", + "content": "All compared methods use Faster R-CNN, and we adopt their reported scales (and other parameters). Streamer [27] converts any single frame detector for streaming by scheduling which frames to process and interpolating predictions between processed frames. AdaScale [9] regresses optimal scale from image features to minimize single-frame latency while Adaptive Streamer [16] learns scale choice in" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "13369" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 70, + 286, + 177 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 286, + 177 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 286, + 177 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 286, + 177 + ], + "type": "table", + "html": "
IDMethodScale(s)sAPsAPSsAPMsAPL
1Streamer [27]0.5x18.33.115.040.9
21 + Adascale [9]0.2x-0.6x13.40.28.637.4
3Adaptive Streamer [16]0.2x-0.6x21.34.218.847.0
41 + FOVEA (SI) [50]0.5x24.18.424.748.7
51 + Ours (Avg VP)0.5x29.913.731.352.2
61 + Ours0.5x30.013.731.552.2
71 + Ours (VP Oracle)0.5x30.714.531.652.9
", + "image_path": "29a3760fd412096490ed6c682ec6efbd41f189f6784148f3aaa8ee00e9c6c2b6.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 48, + 274, + 168, + 363 + ], + "blocks": [ + { + "bbox": [ + 48, + 274, + 168, + 363 + ], + "lines": [ + { + "bbox": [ + 48, + 274, + 168, + 363 + ], + "spans": [ + { + "bbox": [ + 48, + 274, + 168, + 363 + ], + "type": "image", + "image_path": "4e72d6afbd1f8ca09373a66b77b979df0ad2f8947c44116e9649e4d6fb59b4c1.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 370, + 287, + 437 + ], + "lines": [ + { + "bbox": [ + 46, + 370, + 287, + 437 + ], + "spans": [ + { + "bbox": [ + 46, + 370, + 287, + 437 + ], + "type": "text", + "content": "Figure 6. WALT All-Viewpoints Split: Our approach (Two-Plane Prior) shows improved overall performance over naive downsampling and state-of-the-art adaptive sampling technique, specially for small objects at all scales (starting from " + }, + { + "bbox": [ + 46, + 370, + 287, + 437 + ], + "type": "inline_equation", + "content": "0.5\\mathrm{x}" + }, + { + "bbox": [ + 46, + 370, + 287, + 437 + ], + "type": "text", + "content": "). Horizontal line (orange) indicates performance at maximum possible scale " + }, + { + "bbox": [ + 46, + 370, + 287, + 437 + ], + "type": "inline_equation", + "content": "(0.6\\mathrm{x})" + }, + { + "bbox": [ + 46, + 370, + 287, + 437 + ], + "type": "text", + "content": " the base detector was trained at (memory constraints)." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 168, + 274, + 286, + 363 + ], + "blocks": [ + { + "bbox": [ + 168, + 274, + 286, + 363 + ], + "lines": [ + { + "bbox": [ + 168, + 274, + 286, + 363 + ], + "spans": [ + { + "bbox": [ + 168, + 274, + 286, + 363 + ], + "type": "image", + "image_path": "faabbc2521bf1ed6c8c876b5aebeb5a234d17b5274b9b4c1c4698467117ca42c.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 460, + 287, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 460, + 287, + 616 + ], + "spans": [ + { + "bbox": [ + 46, + 460, + 287, + 616 + ], + "type": "text", + "content": "the streaming setting. Both these methods employ naive-downsampling. State-of-the-art, Fovea [50] employs the temporal prior " + }, + { + "bbox": [ + 46, + 460, + 287, + 616 + ], + "type": "inline_equation", + "content": "(S_I)" + }, + { + "bbox": [ + 46, + 460, + 287, + 616 + ], + "type": "text", + "content": ". From Table 2, Two-Plane prior outperforms the above approaches by " + }, + { + "bbox": [ + 46, + 460, + 287, + 616 + ], + "type": "inline_equation", + "content": "+16.5" + }, + { + "bbox": [ + 46, + 460, + 287, + 616 + ], + "type": "text", + "content": " sAP, " + }, + { + "bbox": [ + 46, + 460, + 287, + 616 + ], + "type": "inline_equation", + "content": "+8.6" + }, + { + "bbox": [ + 46, + 460, + 287, + 616 + ], + "type": "text", + "content": " sAP and " + }, + { + "bbox": [ + 46, + 460, + 287, + 616 + ], + "type": "inline_equation", + "content": "+5.9" + }, + { + "bbox": [ + 46, + 460, + 287, + 616 + ], + "type": "text", + "content": " sAP respectively. Comparison with [9, 16, 27] shows the limitations of naive downsampling, even when \"optimal\" scale is chosen. Our geometric prior greatly improves small object detection performance by " + }, + { + "bbox": [ + 46, + 460, + 287, + 616 + ], + "type": "inline_equation", + "content": "63\\%" + }, + { + "bbox": [ + 46, + 460, + 287, + 616 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 46, + 460, + 287, + 616 + ], + "type": "inline_equation", + "content": "+5.3" + }, + { + "bbox": [ + 46, + 460, + 287, + 616 + ], + "type": "text", + "content": " sAPs over SOTA. To consider dependence on accurate Vanishing Point detection (and its overheads), we use NeurVPS [59] as oracle (we simulate accurate prediction with zero delay) to obtain an upper bound, we observe even average vanishing point location's performance is within " + }, + { + "bbox": [ + 46, + 460, + 287, + 616 + ], + "type": "inline_equation", + "content": "0.8" + }, + { + "bbox": [ + 46, + 460, + 287, + 616 + ], + "type": "text", + "content": " sAP." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "text", + "content": "Accuracy-Scale Tradeoffs: We experiment with WALT All-Viewpoints split to observe accuracy-scale trade-offs. The native resolution " + }, + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "inline_equation", + "content": "(4K)" + }, + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "text", + "content": " of the dataset is extremely large and the gradients don't fit within 12 GB memory of our Titan X GPU, thus we cropped the skies and other static regions to reduce input scale (1x) to " + }, + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "inline_equation", + "content": "1500 \\times 2000" + }, + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "text", + "content": ". Still, the highest scale we were able to train our baseline Faster R-CNN model is 0.6x. So, we use aggressive downsam" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 328, + 70, + 525, + 205 + ], + "blocks": [ + { + "bbox": [ + 46, + 185, + 287, + 262 + ], + "lines": [ + { + "bbox": [ + 46, + 185, + 287, + 262 + ], + "spans": [ + { + "bbox": [ + 46, + 185, + 287, + 262 + ], + "type": "text", + "content": "Table 2. Streaming Evaluation on Argoverse-HD: Ours denotes Two-Plane Prior. Every frame's prediction (streamed at 30FPS) must be emitted before frame is observed [27] (via forecasting). All methods evaluated on Titan X GPU. Underlying detector (Faster R-CNN) is constant across approaches, improvements are solely from spatial sampling mechanisms. Notice improved detection of small objects by " + }, + { + "bbox": [ + 46, + 185, + 287, + 262 + ], + "type": "inline_equation", + "content": "+5.3sAP_{S}" + }, + { + "bbox": [ + 46, + 185, + 287, + 262 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 46, + 185, + 287, + 262 + ], + "type": "inline_equation", + "content": "63\\%" + }, + { + "bbox": [ + 46, + 185, + 287, + 262 + ], + "type": "text", + "content": " over SOTA." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 328, + 70, + 525, + 205 + ], + "lines": [ + { + "bbox": [ + 328, + 70, + 525, + 205 + ], + "spans": [ + { + "bbox": [ + 328, + 70, + 525, + 205 + ], + "type": "table", + "html": "
MethodScaleAPAPSAPMAPL
Faster R-CNN0.25x16.707.242.3
FOVEA (SD) [50]0.25x23.2013.954.1
Two-Plane Prior0.25x25.21.018.254.5
Faster R-CNN0.5x29.24.924.755.5
FOVEA (SD) [50]0.5x34.48.730.559.4
Two-Plane Prior0.5x36.411.632.359.0
Baseline at higher scales
Faster R-CNN0.6x33.29.328.656.7
Faster R-CNN*1.0x34.312.630.754.3
", + "image_path": "edd10b4304c60f09b476705aa34b7cbc97348e53e5bcee91845d690dddb30c0d.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 213, + 547, + 269 + ], + "lines": [ + { + "bbox": [ + 304, + 213, + 547, + 269 + ], + "spans": [ + { + "bbox": [ + 304, + 213, + 547, + 269 + ], + "type": "text", + "content": "Table 3. WALT Camera-Split: The viewpoints on the test set were not seen, and Two-Plane Prior shows better performance over both naive downsampling and state-of-the-art adaptive sampling as it generalizes better to unseen scenes and viewpoints. *Not trained at that scale due to memory constraints on Titan X." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 278, + 545, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 278, + 545, + 350 + ], + "spans": [ + { + "bbox": [ + 304, + 278, + 545, + 350 + ], + "type": "text", + "content": "pling scales " + }, + { + "bbox": [ + 304, + 278, + 545, + 350 + ], + "type": "inline_equation", + "content": "\\{0.5, 0.4375, 0.375, 0.3125, 0.25, 0.125\\}" + }, + { + "bbox": [ + 304, + 278, + 545, + 350 + ], + "type": "text", + "content": ". The results are presented in Figure 6. We observe a large and consistent improvement over baseline and Fovea [50], specially for small objects. For instance, considering performance at " + }, + { + "bbox": [ + 304, + 278, + 545, + 350 + ], + "type": "inline_equation", + "content": "0.375x" + }, + { + "bbox": [ + 304, + 278, + 545, + 350 + ], + "type": "text", + "content": " scale, our approach is better than baseline by " + }, + { + "bbox": [ + 304, + 278, + 545, + 350 + ], + "type": "inline_equation", + "content": "+13.1AP" + }, + { + "bbox": [ + 304, + 278, + 545, + 350 + ], + "type": "text", + "content": " and Fovea by " + }, + { + "bbox": [ + 304, + 278, + 545, + 350 + ], + "type": "inline_equation", + "content": "+1.4AP" + }, + { + "bbox": [ + 304, + 278, + 545, + 350 + ], + "type": "text", + "content": " for all objects." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 352, + 546, + 423 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 352, + 546, + 423 + ], + "spans": [ + { + "bbox": [ + 304, + 352, + 546, + 423 + ], + "type": "text", + "content": "For small objects, we observe dramatic improvement, at scales smaller than " + }, + { + "bbox": [ + 304, + 352, + 546, + 423 + ], + "type": "inline_equation", + "content": "0.375\\mathrm{x}" + }, + { + "bbox": [ + 304, + 352, + 546, + 423 + ], + "type": "text", + "content": ", other approaches are unable to detect any small objects while our approach does so until " + }, + { + "bbox": [ + 304, + 352, + 546, + 423 + ], + "type": "inline_equation", + "content": "0.125\\mathrm{x}" + }, + { + "bbox": [ + 304, + 352, + 546, + 423 + ], + "type": "text", + "content": " scale, showing that our approach degrades more gracefully. At " + }, + { + "bbox": [ + 304, + 352, + 546, + 423 + ], + "type": "inline_equation", + "content": "0.375\\mathrm{x}" + }, + { + "bbox": [ + 304, + 352, + 546, + 423 + ], + "type": "text", + "content": " scale, our approach improves upon Faster R-CNN by " + }, + { + "bbox": [ + 304, + 352, + 546, + 423 + ], + "type": "inline_equation", + "content": "+10.7AP_{S}" + }, + { + "bbox": [ + 304, + 352, + 546, + 423 + ], + "type": "text", + "content": " and Fovea by " + }, + { + "bbox": [ + 304, + 352, + 546, + 423 + ], + "type": "inline_equation", + "content": "+3.0AP_{S}" + }, + { + "bbox": [ + 304, + 352, + 546, + 423 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 425, + 547, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 425, + 547, + 568 + ], + "spans": [ + { + "bbox": [ + 304, + 425, + 547, + 568 + ], + "type": "text", + "content": "Generalization to new viewpoints: We use WALT Camera-Split, the test scenes and viewpoint are unseen in training. E.g., the vanishing point of one of the held-out cameras is beyond the image's field of view. We operate on the same scale factors in the earlier experiments, and results are presented in Table 3. We note lower overall performance levels due to scene/viewpoint novelty in the test sets. Our approach generalizes better due to the explicit modelling of the viewpoint via the vanishing point (See Section 3.2). We note trends similar to previous experiment, we demonstrate improvements of " + }, + { + "bbox": [ + 304, + 425, + 547, + 568 + ], + "type": "inline_equation", + "content": "+8.5" + }, + { + "bbox": [ + 304, + 425, + 547, + 568 + ], + "type": "text", + "content": " AP over naive-downsampling and " + }, + { + "bbox": [ + 304, + 425, + 547, + 568 + ], + "type": "inline_equation", + "content": "+2.0" + }, + { + "bbox": [ + 304, + 425, + 547, + 568 + ], + "type": "text", + "content": " AP over Fovea [50] at " + }, + { + "bbox": [ + 304, + 425, + 547, + 568 + ], + "type": "inline_equation", + "content": "0.25\\mathrm{x}" + }, + { + "bbox": [ + 304, + 425, + 547, + 568 + ], + "type": "text", + "content": " scale." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "content": "Tracking Improvements: We follow tracking-by-detection and pair IOUTracker [2] with detectors on Argoverse-HD dataset. MOTA and MOTP evaluate overall tracking performance. From Table 4, Our method improves over baseline by " + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "inline_equation", + "content": "+4.8\\%" + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "inline_equation", + "content": "+0.7\\%" + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "content": ". We also focus on tracking quality metrics, Mostly Tracked " + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\%" + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "content": " (MT%) evaluates the percentage of objects tracked for at least " + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "inline_equation", + "content": "80\\%" + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "content": " of their lifespan while Mostly Lost " + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\%" + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "content": " (ML%) evaluates percentage of objects for less than " + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "content": " of their lifespan. In both these cases, our approach improves upon the baseline by " + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "inline_equation", + "content": "+7.6\\%" + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "inline_equation", + "content": "-6.7\\%" + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "content": " respectively. To autonomous navigation, we define two relevant metrics, namely, average lifespan extension (ALE)" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "13370" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 70, + 298, + 136 + ], + "blocks": [ + { + "bbox": [ + 48, + 70, + 298, + 136 + ], + "lines": [ + { + "bbox": [ + 48, + 70, + 298, + 136 + ], + "spans": [ + { + "bbox": [ + 48, + 70, + 298, + 136 + ], + "type": "table", + "html": "
MethodMOTA ↑MOTP ↑MT% ↑ML% ↓MOS ↓ALE% ↑
Faster RCNN39.882.330.735.637.159.3 %
Fovea (SD) [50]43.981.934.131.934.8+5.4 %
Fovea (SI) [50]44.381.836.728.433.8+8.4 %
Two-Plane Prior44.683.038.328.931.6+9.9 %
", + "image_path": "e4dc7df63800071fe38cc4698a50c97fd6cca6c45d863a460a30605387ad7a32.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 220, + 287, + 280 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 220, + 287, + 280 + ], + "spans": [ + { + "bbox": [ + 46, + 220, + 287, + 280 + ], + "type": "text", + "content": "and minimum object size tracked (MOS), whose motivation and definitions can be viewed in supplementary. We observe that our improvements are better than both Fovea " + }, + { + "bbox": [ + 46, + 220, + 287, + 280 + ], + "type": "inline_equation", + "content": "(S_{D})" + }, + { + "bbox": [ + 46, + 220, + 287, + 280 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 220, + 287, + 280 + ], + "type": "inline_equation", + "content": "(S_{I})" + }, + { + "bbox": [ + 46, + 220, + 287, + 280 + ], + "type": "text", + "content": ". As we observe, our method improves tracking lifespan and also helps track smaller objects." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 281, + 287, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 281, + 287, + 388 + ], + "spans": [ + { + "bbox": [ + 46, + 281, + 287, + 388 + ], + "type": "text", + "content": "Efficient City-Scale Sensing: We detect objects on Commuter Bus equipped with a Jetson AGX. Identifying (Recall) relevant frames is key on the edge. Recall of Faster R-CNN with at 1x scale is " + }, + { + "bbox": [ + 46, + 281, + 287, + 388 + ], + "type": "inline_equation", + "content": "43.3AR" + }, + { + "bbox": [ + 46, + 281, + 287, + 388 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 46, + 281, + 287, + 388 + ], + "type": "inline_equation", + "content": "16.9AR_{S}" + }, + { + "bbox": [ + 46, + 281, + 287, + 388 + ], + "type": "text", + "content": ") (Latency: 350ms; infeasible for real-time execution) but drops to " + }, + { + "bbox": [ + 46, + 281, + 287, + 388 + ], + "type": "inline_equation", + "content": "31.7AR" + }, + { + "bbox": [ + 46, + 281, + 287, + 388 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 46, + 281, + 287, + 388 + ], + "type": "inline_equation", + "content": "0.5AR_{S}" + }, + { + "bbox": [ + 46, + 281, + 287, + 388 + ], + "type": "text", + "content": ") at 0.5x scale when naively downsampled (Latency: 154ms). Whereas our approach at 0.5x scale improves recall by " + }, + { + "bbox": [ + 46, + 281, + 287, + 388 + ], + "type": "inline_equation", + "content": "42\\%" + }, + { + "bbox": [ + 46, + 281, + 287, + 388 + ], + "type": "text", + "content": " over full resolution execution to 61.7 AR (16.4 ARS) with latency of 158 ms (+4 ms)." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 388, + 287, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 388, + 287, + 437 + ], + "spans": [ + { + "bbox": [ + 46, + 388, + 287, + 437 + ], + "type": "text", + "content": "In supplementary, we perform additional comparisons, provide details on handling multiple vanishing points, more tracking results and edge sensing results. We also present some qualitative results and comparisons." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 443, + 148, + 455 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 443, + 148, + 455 + ], + "spans": [ + { + "bbox": [ + 47, + 443, + 148, + 455 + ], + "type": "text", + "content": "5.1. Ablation Studies" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 461, + 287, + 486 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 461, + 287, + 486 + ], + "spans": [ + { + "bbox": [ + 46, + 461, + 287, + 486 + ], + "type": "text", + "content": "We discuss some of the considerations of our approach through experiments on the Argoverse-HD dataset." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 486, + 287, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 486, + 287, + 641 + ], + "spans": [ + { + "bbox": [ + 46, + 486, + 287, + 641 + ], + "type": "text", + "content": "Ground Plane vs Two-Plane Prior: We discussed the rationale of employing multiple planes in Fig 3, and our results are consistent. From Table 5, Two-Plane Prior outperforms Ground Plane prior considerably " + }, + { + "bbox": [ + 46, + 486, + 287, + 641 + ], + "type": "inline_equation", + "content": "(+1.8AP)" + }, + { + "bbox": [ + 46, + 486, + 287, + 641 + ], + "type": "text", + "content": ". Ground Plane Prior outperforms Two-Plane Prior on small objects by " + }, + { + "bbox": [ + 46, + 486, + 287, + 641 + ], + "type": "inline_equation", + "content": "+1AP_{S}" + }, + { + "bbox": [ + 46, + 486, + 287, + 641 + ], + "type": "text", + "content": " but is heavily penalized on medium " + }, + { + "bbox": [ + 46, + 486, + 287, + 641 + ], + "type": "inline_equation", + "content": "(-4.1AP_{M})" + }, + { + "bbox": [ + 46, + 486, + 287, + 641 + ], + "type": "text", + "content": " and large objects " + }, + { + "bbox": [ + 46, + 486, + 287, + 641 + ], + "type": "inline_equation", + "content": "(-4.6AP_{L})" + }, + { + "bbox": [ + 46, + 486, + 287, + 641 + ], + "type": "text", + "content": ". This is attributed to heavy distortion of tall and nearby objects, and objects that are not on the plane (Figure 3). Lastly, this prior was difficult to learn, the parameter space severely distorted the images (we tuned initialization and learning rate). Thus we did not consider this prior further. The second plane acts as a counterbalance and that warping space is learnable." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 642, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 287, + 714 + ], + "type": "text", + "content": "Vanishing Point Estimate Dependence: From Table 5, dominant vanishing point in autonomous navigation is highly local in nature, and estimating VP improves the result by +1.2 AP. Estimating the vanishing point is a design choice, it's important for safety critical applications like autonomous navigation (performance while navigating turns)" + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 316, + 70, + 537, + 131 + ], + "blocks": [ + { + "bbox": [ + 46, + 144, + 288, + 199 + ], + "lines": [ + { + "bbox": [ + 46, + 144, + 288, + 199 + ], + "spans": [ + { + "bbox": [ + 46, + 144, + 288, + 199 + ], + "type": "text", + "content": "Table 4. Tracking Improvements: We setup a tracking by detection pipeline and replace the underlying detection method and observe improvements if any. All the detectors employ the Faster R-CNN architecture and are executed at " + }, + { + "bbox": [ + 46, + 144, + 288, + 199 + ], + "type": "inline_equation", + "content": "0.5\\mathrm{x}" + }, + { + "bbox": [ + 46, + 144, + 288, + 199 + ], + "type": "text", + "content": " scale. We observe improvements in tracking metrics due to Two-Plane Prior." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 316, + 70, + 537, + 131 + ], + "lines": [ + { + "bbox": [ + 316, + 70, + 537, + 131 + ], + "spans": [ + { + "bbox": [ + 316, + 70, + 537, + 131 + ], + "type": "table", + "html": "
MethodScaleAPAPSAPMAPL
Ground Plane Prior0.5x29.115.527.548.3
Two-Plane Prior (Psuedo.)0.5x27.19.828.950.2
Two-Plane Prior (Avg VP)0.5x29.612.730.752.7
Two-Plane Prior0.5x30.814.531.652.9
", + "image_path": "bce3d3c381ea6e6b76013eb67633eafb8f6c17da31f167789986c2402c8bc84a.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 138, + 545, + 172 + ], + "lines": [ + { + "bbox": [ + 304, + 138, + 545, + 172 + ], + "spans": [ + { + "bbox": [ + 304, + 138, + 545, + 172 + ], + "type": "text", + "content": "Table 5. Ablation Study on Argoverse-HD to justify our design choice of using two planes, dependence on accurate vanishing point detection and choice of pseudo labels vs ground truth." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 182, + 512, + 194 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 182, + 512, + 194 + ], + "spans": [ + { + "bbox": [ + 304, + 182, + 512, + 194 + ], + "type": "text", + "content": "however might be omitted for sensing applications." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 195, + 545, + 303 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 195, + 545, + 303 + ], + "spans": [ + { + "bbox": [ + 304, + 195, + 545, + 303 + ], + "type": "text", + "content": "Using Pseudo Labels vs Ground Truth: Table 5 shows there is still considerable gap (-3.7 AP) between the Two-Plane Prior trained from pseudo labels and ground truth. We observe that the model under-performs on stopsign, bike and truck classes, which are under-represented in the COCO dataset [30] compared to person and car classes. Performance of the pre-trained model on these classes is low even at 1x scale. Hence, we believe that the performance difference is an artifact of this domain gap." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 318, + 383, + 331 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 318, + 383, + 331 + ], + "spans": [ + { + "bbox": [ + 306, + 318, + 383, + 331 + ], + "type": "text", + "content": "6. Conclusions" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 340, + 545, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 340, + 545, + 602 + ], + "spans": [ + { + "bbox": [ + 304, + 340, + 545, + 602 + ], + "type": "text", + "content": "In this work, we proposed a learned two-plane perspective prior which incorporates rough geometric constraints from 3D scene interpretations of 2D images to improve object detection. We demonstrated that (a) Geometrically defined spatial sampling prior significantly improves detection performance over multiple axes (accuracy, latency and memory) in terms of both single-frame accuracy and accuracy with real-time constraints over other methods. (b) Not only is our approach is more accurate when adaptively down-sampling at all scales, it degrades much more gracefully for small objects, resulting in latency and memory savings. (c) As our prior is learned end-to-end, we can improve a detector's performance at lower scales for \"free\". (d) Our approach generalizes better to new camera viewpoints and enables efficient city-scale sensing applications. Vanishing point estimation is the bottleneck of our approach [11, 31, 32, 59] for general scenes, and increasing efficiency of its computation we will see substantial improvements. Investigating geometric constraints to improve other aspects of real-time perception systems as future work, like object tracking and trajectory understanding and forecasting, is promising." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 604, + 545, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 604, + 545, + 676 + ], + "spans": [ + { + "bbox": [ + 304, + 604, + 545, + 676 + ], + "type": "text", + "content": "Societal Impact Our approach has strong implications for autonomous-driving and city-scale sensing for smart city applications, wherein efficient data processing would lead to more data-driven decision-making and public policies. However, privacy is a concern, and we shall release the datasets after anonymizing people and license plates." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": "Acknowledgements: This work was supported in part by an NSF CPS Grant CNS-2038612, a DOT RITA Mobility-21 Grant 69A3551747111 and by General Motors Israel." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13371" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 92, + 287, + 712 + ], + "type": "list", + "angle": 0, + "index": 17, + "blocks": [ + { + "bbox": [ + 53, + 92, + 287, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 92, + 287, + 135 + ], + "spans": [ + { + "bbox": [ + 53, + 92, + 287, + 135 + ], + "type": "text", + "content": "[1] Hala Abualsaud, Sean Liu, David B Lu, Kenny Situ, Akshay Rangesh, and Mohan M Trivedi. 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NeurIPS, 2019. 5, 7, 8" + } + ] + } + ], + "index": 25 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13373" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Learning 3D Representations From 2D Pre-Trained Models via Image-to-Point Masked Autoencoders/89a76a16-b222-401c-8388-b5d09eb2345e_content_list.json b/2023/Learning 3D Representations From 2D Pre-Trained Models via Image-to-Point Masked Autoencoders/89a76a16-b222-401c-8388-b5d09eb2345e_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..8007abdd7e5a7621728f827373398aa6e8e5a910 --- /dev/null +++ b/2023/Learning 3D Representations From 2D Pre-Trained Models via Image-to-Point Masked Autoencoders/89a76a16-b222-401c-8388-b5d09eb2345e_content_list.json @@ -0,0 +1,1415 @@ +[ + { + "type": "text", + "text": "Learning 3D Representations from 2D Pre-trained Models via Image-to-Point Masked Autoencoders", + "text_level": 1, + "bbox": [ + 173, + 130, + 797, + 174 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Renrui Zhang $^{1,2}$ , Liuhui Wang $^{3}$ , Yu Qiao $^{1}$ , Peng Gao $^{\\dagger 1}$ , Hongsheng Li $^{2,4}$", + "bbox": [ + 197, + 194, + 772, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ Shanghai Artificial Intelligence Laboratory", + "bbox": [ + 308, + 223, + 658, + 241 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{2}$ CUHK MMLab $^{3}$ Peking University $^{4}$ CPII under InnoHK", + "bbox": [ + 233, + 241, + 735, + 258 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{zhangrenrui, gaopeng}@pjlab.org.cn, hsli@ee.cuhk.edu.cn", + "bbox": [ + 153, + 261, + 810, + 279 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 323, + 313, + 339 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Pre-training by numerous image data has become a facto for robust 2D representations. In contrast, due to the expensive data processing, a paucity of 3D datasets severely hinders the learning for high-quality 3D features. In this paper, we propose an alternative to obtain superior 3D representations from 2D pre-trained models via Image-to-Point Masked Autoencoders, named as I2P-MAE. By self-supervised pre-training, we leverage the well learned 2D knowledge to guide 3D masked autoencoding, which reconstructs the masked point tokens with an encoder-decoder architecture. Specifically, we first utilize off-the-shelf 2D models to extract the multi-view visual features of the input point cloud, and then conduct two types of image-to-point learning schemes. For one, we introduce a 2D-guided masking strategy that maintains semantically important point tokens to be visible. Compared to random masking, the network can better concentrate on significant 3D structures with key spatial cues. For another, we enforce these visible tokens to reconstruct multi-view 2D features after the decoder. This enables the network to effectively inherit high-level 2D semantics for discriminative 3D modeling. Aided by our image-to-point pre-training, the frozen I2P-MAE, without any fine-tuning, achieves $93.4\\%$ accuracy for linear SVM on ModelNet40, competitive to existing fully trained methods. By further fine-tuning on on ScanObjectNN's hardest split, I2P-MAE attains the state-of-the-art $90.11\\%$ accuracy, $+3.68\\%$ to the second-best, demonstrating superior transferable capacity. Code is available at https://github.com/ZrrSkywalker/I2P-MAE.", + "bbox": [ + 76, + 353, + 473, + 792 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 78, + 820, + 209, + 835 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Driven by huge volumes of image data [11, 40, 56, 61], pre-training for better visual representations has gained", + "bbox": [ + 76, + 845, + 468, + 878 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/207059056250d47aaabecdf9ef65e3a78f5923ac46dfb4ee7626a4eab659e041.jpg", + "image_caption": [ + "Figure 1. Image-to-Point Masked Autoencoders. We leverage the 2D pre-trained models to guide the MAE pre-training in 3D, which alleviates the need of large-scale 3D datasets and learns from 2D knowledge for superior 3D representations." + ], + "image_footnote": [], + "bbox": [ + 503, + 325, + 888, + 554 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "much attention in computer vision, which benefits a variety of downstream tasks [8, 29, 39, 55, 62]. Besides supervised pre-training with labels, many researches develop advanced self-supervised approaches to fully utilize raw image data via pre-text tasks, e.g., image-image contrast [5, 9, 10, 21, 28], language-image contrast [12, 53], and masked image modeling [3, 4, 18, 19, 27, 31, 42, 70]. Given the popularity of 2D pre-trained models, it is still absent for large-scale 3D datasets in the community, attributed to the expensive data acquisition and labor-intensive annotation. The widely adopted ShapeNet [6] only contains $50\\mathrm{k}$ point clouds of 55 object categories, far less than the 14 million ImageNet [11] and 400 million image-text pairs [53] in 2D vision. Though there have been attempts to extract self-supervisory signals for 3D pre-training [33, 41, 47, 64, 69, 76, 78, 83], raw point clouds with sparse structural patterns cannot provide suf", + "bbox": [ + 496, + 659, + 892, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Corresponding author", + "bbox": [ + 101, + 887, + 228, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "21769", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/3afe659521215fa9ad7bcd3257ee8a83c220e396192398ebe31ba7ae3caf96ec.jpg", + "image_caption": [ + "Figure 2. Comparison of (Left) Existing Methods [47, 78] and (Right) our I2P-MAE. On top of the general 3D MAE architecture, I2P-MAE introduces two schemes of image-to-point learning: 2D-guided masking and 2D-semantic reconstruction." + ], + "image_footnote": [], + "bbox": [ + 89, + 88, + 228, + 281 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/d854ae3aef966742b261f2bae65e2fcf679e2604a0105b0cf9b95393b9ff3e85.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 251, + 87, + 454, + 280 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ficient and diversified semantics compared to colorful images, which constrain the generalization capacity of pretraining. Considering the homology of images and point clouds, both of which depict certain visual characteristics of objects and are related by 2D-3D geometric mapping, we ask the question: can off-the-shelf 2D pre-trained models help 3D representation learning by transferring robust 2D knowledge into 3D domains?", + "bbox": [ + 75, + 380, + 468, + 501 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To tackle this challenge, we propose I2P-MAE, a Masked Autoencoding framework that conducts Image-to-Point knowledge transfer for self-supervised 3D point cloud pre-training. As shown in Figure 1, aided by 2D semantics learned from abundant image data, our I2P-MAE produces high-quality 3D representations and exerts strong transferable capacity to downstream 3D tasks. Specifically, referring to 3D MAE models [47, 78] in Figure 2 (Left), we first adopt an asymmetric encoder-decoder transformer [14] as our fundamental architecture for 3D pre-training, which takes as input a randomly masked point cloud and reconstructs the masked points from the visible ones. Then, to acquire 2D semantics for the 3D shape, we bridge the modal gap by efficiently projecting the point cloud into multi-view depth maps. This requires no time-consuming offline rendering and largely preserves 3D geometries from different perspectives. On top of that, we utilize off-the-shelf 2D models to obtain the multi-view 2D features along with 2D attention maps of the point cloud, and respectively guide the pre-training from two aspects, as shown in Figure 2 (Right).", + "bbox": [ + 75, + 505, + 468, + 808 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Firstly, different from existing methods [47, 78] to randomly sample visible tokens, we introduce a 2D-guided masking strategy that reserves point tokens with more spatial semantics to be visible for the MAE encoder. In detail, we back-project the multi-view attention maps into 3D space as a spatial attention cloud. Each element in the", + "bbox": [ + 75, + 810, + 470, + 902 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/c919ddf9cf0f44dc90cd561001b674234216d70377cee04db16132b28b25f2d6.jpg", + "image_caption": [ + "Figure 3. Pre-training Epochs vs. Linear SVM Accuracy on ModelNet40 [67]. With the image-to-point learning schemes, I2P-MAE exerts superior transferable capability with much faster convergence speed than Point-MAE [47] and Point-M2AE [78]." + ], + "image_footnote": [], + "bbox": [ + 526, + 85, + 867, + 284 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "cloud indicates the semantic significance of the corresponding point token. Guided by this, the 3D network can better focus on the visible critical structures to understand the global 3D shape, and also reconstruct the masked tokens from important spatial cues.", + "bbox": [ + 496, + 380, + 890, + 455 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Secondly, in addition to the recovering of masked point tokens, we propose to concurrently reconstruct 2D semantics from the visible point tokens after the MAE decoder. For each visible token, we respectively fetch its projected 2D representations from different views, and integrate them as the 2D-semantic learning target. By simultaneously reconstructing the masked 3D coordinates and visible 2D concepts, I2P-MAE is able to learn both low-level spatial patterns and high-level semantics pre-trained in 2D domains, contributing to superior 3D representations.", + "bbox": [ + 496, + 458, + 892, + 609 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "With the aforementioned image-to-point guidance, our I2P-MAE significantly accelerates the convergence speed of pre-training and exhibits state-of-the-art performance on 3D downstream tasks, as shown in Figure 3. Learning from 2D ViT [14] pre-trained by CLIP [53], I2P-MAE, without any fine-tuning, achieves $93.4\\%$ classification accuracy by linear SVM on ModelNet40 [67], which has surpassed the fully fine-tuned results of Point-BERT [76] and Point-MAE [33]. After fine-tuning, I2P-MAE further achieves $90.11\\%$ classification accuracy on the hardest split of ScanObjectNN [63], significantly exceeding the second-best Point-M2AE [78] by $+3.68\\%$ . The experiments fully demonstrate the effectiveness of learning from pre-trained 2D models for superior 3D representations.", + "bbox": [ + 496, + 611, + 893, + 823 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our contributions are summarized as follows:", + "bbox": [ + 517, + 824, + 821, + 839 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- We propose Image-to-Point Masked Autoencoders (I2P-MAE), a pre-training framework to leverage 2D pre-trained models for learning 3D representations.", + "bbox": [ + 517, + 854, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "21770", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We introduce two strategies, 2D-guided masking and 2D-semantic reconstruction, to effectively transfer the well learned 2D knowledge into 3D domains.", + "- Extensive experiments have been conducted to indicate the significance of our image-to-point pre-training." + ], + "bbox": [ + 96, + 90, + 467, + 176 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 191, + 217, + 207 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3D Point Cloud Pre-training. Supervised learning for point clouds has attained remarkable progress by delicately designed architectures [22, 50, 51, 80, 81] and local operators [2, 37, 65, 68, 72, 82]. However, such methods learned from closed-set datasets [63, 67] are limited to produce general 3D representations. Instead, self-supervised pre-training via unlabelled point clouds [6] have revealed promising transferable ability, which provides a good network initialization for downstream fine-tuning. Mainstream 3D self-supervised approaches adopt encoder-decoder architectures to recover the input point clouds from the transformed representations, including point rearrangement [57], part occlusion [64], rotation [49], downsampling [36], and codeword encoding [74]. Concurrent works also adopt contrastive pre-text tasks between 3D data pairs, such as local-global relation [17, 54], temporal frames [32], and augmented viewpoints [69]. More recent works adopt pretrained CLIP [53] for zero-shot 3D recognition [24, 79, 86], or introduce masked point modeling [13, 16, 33, 41] as strong 3D self-supervised learners. Therein, Point-BERT [76] utilizes pre-trained tokenizers to indicate discrete point tokens, while Point-MAE [47], Point-M2AE [78], and PiMAE [7] apply Masked Autoencoders (MAE) to directly reconstruct masked 3D coordinates. Our I2P-MAE also adopts MAE as the basic pre-training framework, but is guided by 2D pretrained models via image-to-point learning schemes, which benefits 3D pre-training with diverse 2D semantics.", + "bbox": [ + 76, + 217, + 472, + 625 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2D-to-3D Learning. Except for jointly training 2D-3D networks [1, 23, 38, 46, 73], only a few existing researches focus on 2D-to-3D learning, and can be categorized into two groups. To eliminate the modal gap, the first group either upgrades 2D pre-trained networks into 3D variants for processing point clouds (convolutional kernels inflation [71, 77], modality-agnostic transformer [52]), or projects 3D point clouds into 2D images with parameter-efficient tuning (multi-view adapter [79], point-to-pixel prompting [66]). Different from them, our I2P-MAE benefits from three properties. 1) Pre-training: We learn from 2D models during the pre-training stage, and then can be flexibly adapted to various 3D scenarios by fine-tuning. However, prior works are required to utilize 2D models on every different downstream task. 2) Self-supervision: I2P-MAE is pre-trained by raw point clouds in a self-supervised manner and learns more general 3D representations. In con", + "bbox": [ + 76, + 643, + 472, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "trast, prior works are supervised by labelled downstream 3D data, which might constrain the diverse 2D semantics into specific 3D domains. 3) Independence: Prior works directly inherit 2D network architectures for 3D training, which is memory-consuming and not 3D extensible, while we train an independent 3D network and regard 2D models as semantic teachers. Another group of 2D-to-3D methods utilize paired real-world 2D-3D data of indoor [44] or outdoor [59] scenes, and conduct contrastive learning for knowledge transfer. Our approach also differs from them in two ways. 4) Masked Autoencoding. I2P-MAE learns 2D semantics via the MAE-style pre-training without any contrastive loss between point-pixel pairs. 5) 3D Data Only. We require no real-world image dataset during the pre-training and efficiently project the 3D shape into depth maps for 2D features extraction.", + "bbox": [ + 496, + 90, + 893, + 332 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 500, + 349, + 591, + 364 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The overall pipeline of I2P-MAE is shown in Figure 4. In Section 3.1, we first introduce I2P-MAE's basic 3D architecture for point cloud masked autoencoding without 2D guidance. Then in Section 3.2, we show the details of utilizing 2D pre-trained models to obtain visual representations from 3D point clouds. Finally in Section 3.3, we present how to conduct image-to-point knowledge transfer for 3D representation learning.", + "bbox": [ + 496, + 376, + 893, + 498 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Basic 3D Architecture", + "text_level": 1, + "bbox": [ + 500, + 508, + 705, + 523 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As our basic framework for image-to-point learning, I2P-MAE refers to existing works [47, 78] to conduct 3D point cloud masked autoencoding, which consists of a token embedding module, an encoder-decoder transformer, and a head for reconstructing masked 3D coordinates.", + "bbox": [ + 496, + 534, + 893, + 609 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Token Embedding. Given a raw point cloud $P \\in \\mathbb{R}^{N \\times 3}$ , we first adopt Furthest Point Sampling (FPS) to downsample the point number from $N$ to $M$ , denoted as $P^T \\in \\mathbb{R}^{M \\times 3}$ . Then, we utilize $k$ Nearest-Neighbour ( $k$ -NN) to search the $k$ neighbors for each downsampled point, and aggregate their features via a mini-PointNet [50] to obtain $M$ point tokens. In this way, each token can represent a local spatial region and interact long-range features with others in the follow-up transformer. We formulate them as $T \\in \\mathbb{R}^{M \\times C}$ , where $C$ denotes the feature dimension.", + "bbox": [ + 496, + 633, + 893, + 785 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Encoder-Decoder Transformer. To build the pre-text learning targets, we mask the point tokens with a high ratio, e.g., $80\\%$ , and only feed the visible ones, $T_{\\mathrm{vis}} \\in \\mathbb{R}^{M_{\\mathrm{vis}} \\times C}$ , into the transformer encoder, where $M_{\\mathrm{vis}}$ denotes the visible token number. Each encoder block contains a self-attention layer and is pre-trained to understand the global", + "bbox": [ + 496, + 809, + 893, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "21771", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/fe6ba77c67b3b8b16b95eb510ca621d0cf94c1f802e41afab29e6f9f1570a845.jpg", + "image_caption": [ + "Figure 4. The Pipeline of I2P-MAE. Given an input point cloud, we leverage the 2D pre-trained models to generate two guidance signals from the projected depth maps: 2D attention maps and 2D visual features. We respectively conduct 2D-guided masking and 2D-semantic reconstruction to transfer the encoded 2D knowledge for 3D point cloud pre-training." + ], + "image_footnote": [], + "bbox": [ + 83, + 85, + 890, + 424 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3D shape from the remaining visible parts. After encoding, we concatenate the encoded $T_{\\mathrm{vis}}^e$ with a set of shared learnable masked tokens $T_{\\mathrm{mask}} \\in \\mathbb{R}^{M_{\\mathrm{mask}} \\times C}$ , and input them into a lightweight decoder, where $M_{\\mathrm{mask}}$ denotes the masked token number and $M = M_{\\mathrm{mask}} + M_{\\mathrm{vis}}$ . In the transformer decoder, the masked tokens learn to capture informative spatial cues from visible ones and reconstruct the masked 3D coordinates. Importantly, we follow Point-M2AE [78] to modify our transformer to be a hierarchical architecture for encoding the multi-scale representations.", + "bbox": [ + 75, + 503, + 472, + 656 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3D-coordinate Reconstruction. On top of the decoded point tokens $\\{T_{\\mathrm{vis}}^d, T_{\\mathrm{mask}}^d\\}$ , we utilize $T_{\\mathrm{mask}}^d$ to reconstruct 3D coordinates of the masked tokens along with their $k$ neighboring points. A reconstruction head of a single linear projection layer is adopted to predict $P_{\\mathrm{mask}} \\in \\mathbb{R}^{M_{\\mathrm{mask}} \\times k \\times 3}$ , the ground-truth 3D coordinates of the masked points. Then, we compute the loss by Chamfer Distance [15] and formulate it as", + "bbox": [ + 76, + 684, + 472, + 806 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {3 D}} = \\frac {1}{M _ {\\mathrm {m a s k}} k} \\mathrm {C h a m f e r} \\left(\\mathrm {H} _ {\\mathrm {3 D}} \\left(T _ {\\mathrm {m a s k}} ^ {d}\\right), P _ {\\mathrm {m a s k}}\\right), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 821, + 468, + 854 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathrm{H}_{3\\mathrm{D}}(\\cdot)$ denotes the head to reconstruct the masked 3D coordinates.", + "bbox": [ + 76, + 869, + 470, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. 2D Pre-trained Representations", + "text_level": 1, + "bbox": [ + 500, + 503, + 779, + 520 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We can leverage 2D models of different architectures (ResNet [30], ViT [14]) and various pre-training approaches (supervised [30, 45] and self-supervised [5, 53] ones) to assist the 3D representation learning. To align the input modality for 2D models, we project the input point cloud onto multiple image planes to create depth maps, and then encode them into multi-view 2D representations.", + "bbox": [ + 496, + 527, + 890, + 633 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Efficient Projection. To ensure the efficiency of pretraining, we simply project the input point cloud $P$ from three orthogonal views respectively along the $x, y, z$ axes. For every point, we directly omit each of its three coordinates and round down the other two to obtain the 2D location on the corresponding map. The projected pixel value is set as the omitted coordinate to reflect relative depth relations of points, which is then repeated by three times to imitate the three-channel RGB. The projection of I2PMAE is highly time-efficient and involves no offline rendering [48, 60], projective transformation [20, 79], or learnble prompting [66]. We denote the projected multi-view depth maps of $P$ as $\\{I_i\\}_{i=1}^3$ .", + "bbox": [ + 496, + 652, + 890, + 851 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "2D Visual Features. We then utilize a 2D pre-trained model, e.g., a pre-trained ResNet or ViT, to extract multi-", + "bbox": [ + 498, + 869, + 890, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "21772", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "view features of the point cloud with $C$ channels, formulated as $\\{F_i^{2\\mathrm{D}}\\}_{i = 1}^3$ , where $F_{i}\\in \\mathbb{R}^{H\\times W\\times C}$ and $H,W$ denote the feature map size. Such 2D features contain sufficient high-level semantics learned from large-scale image data. The geometric information loss during projection can also be alleviated by encoding from different views.", + "bbox": [ + 75, + 90, + 472, + 183 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "2D Attention Maps. In addition to 2D features, we also acquire a semantic attention map for each view via the 2D pre-trained model. The one-channel maps indicate the semantic importance of different image regions, which we denote as $\\{S_i^{2\\mathrm{D}}\\}_{i = 1}^3$ , where $S_{i}\\in \\mathbb{R}^{H\\times W\\times 1}$ . For ResNet, we adopt pixel-wise max pooling on $\\{F_i^{2\\mathrm{D}}\\}_{i = 1}^3$ to reduce the feature dimension to one. For ViT, we adopt attention maps of the class token at the last transformer layer, since the attention weights to the class token reveal how much the features contribute to the final classification.", + "bbox": [ + 75, + 199, + 470, + 349 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Image-to-Point Learning Schemes", + "text_level": 1, + "bbox": [ + 76, + 359, + 375, + 376 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "On top of the 2D pre-trained representations for the point cloud, I2P-MAE's pre-training is guided by two image-top-point learning designs: 2D-guided masking before the encoder, and 2D-semantic reconstruction after the decoder.", + "bbox": [ + 75, + 383, + 468, + 444 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "2D-guided Masking. The conventional masking strategy samples masked tokens randomly following a uniform distribution, which might prevent the encoder from 'seeing' important spatial characteristics and disturb the decoder by nonsignificant structures. Therefore, we leverage the 2D attention maps to guide the masking of point tokens, which samples more semantically significant 3D parts for encoding. Specifically, indexed by the coordinates of point tokens $P^T \\in \\mathbb{R}^{M \\times 3}$ , we back-project the multi-view attention maps $\\{S_i^{2\\mathrm{D}}\\}_{i=1}^3$ into 3D space and aggregate them as a 3D attention cloud $S^{3\\mathrm{D}} \\in \\mathbb{R}^{M \\times 1}$ . For each point in $S^{3\\mathrm{D}}$ , we assign the semantic score by averaging the corresponding 2D values from multi-view attention maps as", + "bbox": [ + 75, + 460, + 472, + 657 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nS ^ {\\mathrm {3 D}} = \\operatorname {S o f t m a x} \\left(\\frac {1}{3} \\sum_ {i = 1} ^ {3} \\operatorname {I 2 P} \\left(S _ {i} ^ {\\mathrm {2 D}}, P ^ {T}\\right)\\right), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 133, + 667, + 468, + 709 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathrm{I2P}(\\cdot)$ denotes the 2D-to-3D back-projection operation in Figure 5. We apply a softmax function to normalize the $M$ points within $S^{3\\mathrm{D}}$ , and regard each element's magnitude as the visible probability for the corresponding point token. With this 2D semantic prior, the random masking becomes a nonuniform sampling with different probabilities for different tokens, where the tokens covering more critical 3D structures are more likely to be preserved. This boosts the representation learning of the encoder by focusing more on significant 3D geometries, and provides the masked tokens with more informative cues at the decoder for better reconstruction.", + "bbox": [ + 75, + 719, + 472, + 900 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/46bef7c4e00cd3fd629790df351752c5e51eaafda49030003859674be2e7e772.jpg", + "image_caption": [ + "Figure 5. Image-to-Point Operation (I2P). Indexed by 3D point coordinates, the corresponding multi-view 2D representations are back-projected into 3D space for aggregation." + ], + "image_footnote": [], + "bbox": [ + 532, + 89, + 859, + 311 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "2D-semantic Reconstruction. The 3D-coordinate reconstruction of masked point tokens enables the network to explore low-level 3D patterns. On top of that, we further enforce the visible point tokens, $T_{\\mathrm{vis}}^d$ , to reconstruct the extracted 2D semantics from different views, which effectively transfers the 2D pre-trained knowledge into 3D pre-training. To obtain the 2D-semantic targets, we utilize the coordinates of visible point tokens $P_{\\mathrm{vis}}^T \\in \\mathbb{R}^{M_{\\mathrm{vis}} \\times 3}$ as indices to aggregate corresponding 2D features from $\\{F_i^{2\\mathrm{D}}\\}_{i=1}^3$ by channel-wise concatenation, formulated as", + "bbox": [ + 498, + 393, + 893, + 547 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nF _ {\\text {v i s}} ^ {\\mathrm {3 D}} = \\operatorname {C o n c a t} \\left\\{\\mathrm {I 2 P} \\left(F _ {i} ^ {\\mathrm {2 D}}, P _ {\\text {v i s}} ^ {T}\\right) \\right\\} _ {i = 1} ^ {3}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 563, + 563, + 890, + 594 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $F_{\\mathrm{vis}}^{3\\mathrm{D}} \\in \\mathbb{R}^{M_{\\mathrm{vis}} \\times 3C}$ . As the multi-view depth maps depict a 3D shape from different perspectives, the concatenation between multi-view 2D features can better integrate the rich semantics inherited from 2D pre-trained models. Then, we also adopt a reconstruction head of a single linear projection layer for $T_{\\mathrm{vis}}^d$ , and compute the $l_2$ loss as", + "bbox": [ + 498, + 598, + 893, + 691 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {2 D}} = \\frac {1}{M _ {\\mathrm {v i s}}} \\left(\\mathrm {H} _ {\\mathrm {2 D}} \\left(T _ {\\mathrm {v i s}} ^ {d}\\right) - F _ {\\mathrm {v i s}} ^ {\\mathrm {3 D}}\\right) ^ {2}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 573, + 696, + 890, + 729 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathrm{H}_{2\\mathrm{D}}(\\cdot)$ denotes the head to reconstruct visible 2D semantics, parallel to $\\mathrm{H}_{3\\mathrm{D}}(\\cdot)$ for masked 3D coordinates. The final pre-training loss of our I2P-MAE is then formulated as $\\mathcal{L}_{\\mathrm{I2P}} = \\mathcal{L}_{\\mathrm{3D}} + \\mathcal{L}_{\\mathrm{2D}}$ . With such image-to-point feature learning, I2P-MAE not only encodes low-level spatial variations from 3D coordinates, but also explores high-level semantic knowledge from 2D representations. As the 2D-guided masking has preserved visible tokens with more spatial significance, the 2D-semantic reconstruction upon them further benefits I2P-MAE to learn more discriminative 3D representations.", + "bbox": [ + 498, + 734, + 893, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "21773", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/a48f9eddb48007c93ac587a769b39f1a1138a82483a442d46330ff6cf3e61c37.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodModelNet40OBJ-BG
SO-Net [35]87.3-
FoldingNet [74]88.4-
VIP-GAN [26]90.2-
DGCNN + Jigsaw [58]90.659.5
DGCNN + OcCo [64]90.778.3
DGCNN + CrossPoint [1]91.281.7
Transformer + OcCo [76]89.6-
Point-BERT [76]87.4-
Point-MAE [47]91.077.7
3D-OAE [85]92.3-
Point-M2AE [78]92.984.1
I2P-MAE93.487.1
Improvement+0.5+3.0
", + "bbox": [ + 93, + 88, + 455, + 327 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 420, + 209, + 436 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In Section 4.1, we first introduce our pre-training settings and the linear SVM classification performance without fine-tuning. Then in Section 4.2, we present the results by fully fine-tuning I2P-MAE on various 3D downstream tasks. Finally in Section 4.3, we conduct ablation studies to investigate the characteristics of I2P-MAE.", + "bbox": [ + 75, + 445, + 468, + 536 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Image-to-Point Pre-training", + "text_level": 1, + "bbox": [ + 76, + 547, + 328, + 561 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Settings. We adopt the popular ShapeNet [6] for self-supervised 3D pre-training, which contains 57,448 synthetic point clouds with 55 object categories. For fair comparison, we follow the same MAE transformer architecture as Point-M2AE [78]: a 3-stage encoder with 5 blocks per stage, a 2-stage decoder with 1 block per stage, 2,048 input point number $(N)$ , 512 downsampled number $(M)$ , 16 nearest neighbors $(k)$ , 384 feature channels $(C)$ , and the mask ratio of $80\\%$ . For off-the-shelf 2D models, we utilize ViT-Base [14] pre-trained by CLIP [53] as default and keep its weights frozen during 3D pre-training. We project the point cloud into three $224 \\times 224$ depth maps, and obtain the 2D feature size $H \\times W$ of $14 \\times 14$ . I2P-MAE is pre-trained for 300 epochs with a batch size 64 and learning rate $10^{-3}$ . We adopt AdamW [34] optimizer with a weight decay $5 \\times 10^{-2}$ and the cosine scheduler with 10-epoch warm-up.", + "bbox": [ + 75, + 570, + 468, + 813 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Linear SVM. To evaluate the transfer capacity, we directly utilize the features extracted by I2P-MAE's encoder for linear SVM on the synthetic ModelNet40 [67] and real-world ScanObjectNN [63] without any fine-tuning or voting. As shown in Table 1, for 3D shape classification in", + "bbox": [ + 75, + 824, + 468, + 902 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/8478797c74d17c203caf2849ec41cc116696c69141002d4bc0d40bae45a16adb.jpg", + "table_caption": [ + "Table 1. Linear SVM Classification on ModelNet40 [67] and ScanObjectNN [63]. We compare the accuracy (\\%) of existing self-supervised methods, and the second-best one is underlined. We adopt the OBJ-BG split for ScanObjectNN following [1]." + ], + "table_footnote": [], + "table_body": "
MethodOBJ-BGOBJ-ONLYPB-T50-RS
PointNet [50]73.379.268.0
PointNet++ [51]82.384.377.9
PointCNN [37]86.185.578.5
MVTN [25]--82.8
PointMLP [2]--85.2
Transformer [76]79.8680.5577.24
[P] Point-BERT [76]87.4388.1283.07
[P] 3D-OAE [85]89.1688.6483.17
[P] MaskPoint [41]89.3088.1084.30
[P] Point-MAE [47]90.0288.2985.18
[P] MAE3D [33]--86.20
[P] Point-M2AE [78]91.2288.8186.43
[P] I2P-MAE94.1591.5790.11
Improvement+2.93+2.76+3.68
", + "bbox": [ + 503, + 88, + 890, + 327 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. Real-world 3D Classification on ScanObjectNN [63]. We report the accuracy $(\\%)$ on the official three splits of ScanObjectNN. [P] denotes to fine-tune the models after self-supervised pre-training.", + "bbox": [ + 496, + 338, + 890, + 395 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "both domains, I2P-MAE shows superior performance and exceeds the second-best respectively by $+0.5\\%$ and $+3.0\\%$ accuracy. Our SVM results $(93.4\\%, 87.1\\%)$ can even surpass some existing methods after full downstream training in Table 2 and 3, e.g., PointCNN [37] $(92.2\\%, 86.1\\%)$ , Transformer [76] $(91.4\\%, 79.86\\%)$ , and Point-BERT [76] $(92.7\\%, 87.43\\%)$ . In addition, guided by the 2D pre-trained models, I2P-MAE exhibits much faster pre-training convergence than Point-MAE [47] and Point-M2AE in Figure 3. Therefore, the SVM performance of I2P-MAE demonstrates its learned high-quality 3D representations and the significance of our image-to-point learning schemes.", + "bbox": [ + 496, + 422, + 890, + 604 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Downstream Tasks", + "text_level": 1, + "bbox": [ + 500, + 614, + 681, + 630 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "After pre-training, I2P-MAE is fine-tuned for real-world and synthetic 3D classification, and part segmentation. Except ModelNet40 [67], we do not use the voting strategy [43] for evaluation.", + "bbox": [ + 496, + 638, + 890, + 700 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Real-world 3D Classification. The challenging ScanObjectNN [63] consists of 11,416 training and 2,882 test 3D shapes, which are scanned from the real-world scenes and thus include backgrounds with noises. As shown in Table 2, our I2P-MAE exerts great advantages over other self-supervised methods, surpassing the second-best by $+2.93\\%$ , $+2.76\\%$ , and $+3.68\\%$ respectively for the three splits. This is also the first model reaching $90\\%$ accuracy on the hardest PB-T50-RS spilt. As the pre-training point clouds [6] are synthetic 3D shapes with a large domain gap with the real-world ScanobjectNN, the results well indicate the universality of I2P-MAE inherited from the 2D pre-trained models.", + "bbox": [ + 496, + 719, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "21774", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/6ce940832ac4598ef4652115ce6b9f3d32b84bc516d92fe951cb09c7177a88cf.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodPointsNo VotingVoting
PointNet [50]1k89.2-
PointNet++ [51]1k90.7-
PointCNN [37]1k92.2-
Point Transformer [84]-93.7
Transformer [76]1k91.4-
[P] Point-BERT [76]1k92.793.2
[P] 3D-OAE [85]1k-93.4
[P] Point-MAE [47]1k93.293.8
Point-MAE8k-94.0
[P] Point-M2AE [78]1k93.494.0
[P] I2P-MAE-SVM1k93.4-
I2P-MAE1k93.794.1
", + "bbox": [ + 96, + 88, + 450, + 305 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Synthetic 3D Classification. The widely adopted ModelNet40 [67] contains 9,843 training and 2,468 test 3D point clouds, which are sampled from the synthetic CAD models of 40 categories. We report the classification accuracy of existing methods before and after the voting in Table 3. As shown, our I2P-MAE achieves leading performance for both settings with only 1k input point number. For linear SVM without any fine-tuning, I2P-MAE-SVM can already attain $93.4\\%$ accuracy and exceed most previous works, indicating the powerful transfer ability. By fine-tuning the entire network, the accuracy can be further boosted by $+0.3\\%$ accuracy, and achieve $94.1\\%$ after the offline voting.", + "bbox": [ + 75, + 386, + 468, + 568 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Part Segmentation. The synthetic ShapeNetPart [75] is selected from ShapeNet [6] with 16 object categories and 50 part categories, which contains 14,007 and 2,874 samples for training and validation. We utilize the same segmentation head after the pre-trained encoder as previous works [47, 78] for fair comparison. The head only conducts simple upsampling for point tokens at different stages and concatenates them alone the feature dimension as the output. Two types of mean IoU scores, $\\mathrm{mIoU}_C$ and $\\mathrm{mIoU}_I$ are reported in Table 4. For such highly saturated benchmark, I2P-MAE can still exert leading performance guided by the well learned 2D knowledge, e.g., $+0.29\\%$ and $+0.25\\%$ higher than Point-M2AE concerning the two metrics. This demonstrates that the 2D guidance also benefits the understanding for fine-grained point-wise 3D patterns.", + "bbox": [ + 75, + 588, + 467, + 815 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 830, + 230, + 847 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, we explore the effectiveness of different characteristics in I2P-MAE. We utilize our final solution as the baseline and report the linear SVM accuracy $(\\%)$ .", + "bbox": [ + 75, + 854, + 467, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/75f89691ee49242645e548af0151500fcb2bf48ae0da82f50306fb02588669b6.jpg", + "table_caption": [ + "Table 3. Synthetic 3D Classification on ModelNet40 [67]. We report the accuracy $(\\%)$ before and after the voting [43]. [P] denotes to fine-tune the models after self-supervised pre-training." + ], + "table_footnote": [], + "table_body": "
MethodmIoUCmIoUI
PointNet [50]80.3983.70
PointNet++ [51]81.8585.10
DGCNN [65]82.3385.20
PointMLP [2]84.6086.10
Transformer [76]83.4285.10
[P] Transformer + OcCo [76]83.4285.10
[P] Point-BERT [76]84.1185.60
[P] 3D-OAE [85]-85.70
[P] MaskPoint [41]84.4086.00
[P] Point-MAE [47]-86.10
[P] Point-M2AE [78]84.8686.51
[P] I2P-MAE85.1586.76
", + "bbox": [ + 519, + 88, + 874, + 305 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/9dff2ee06dbcdd1c547b677e91957e8efac79fe61bf69adbb0e5507e1ab22c5a.jpg", + "table_caption": [ + "Table 4. Part Segmentation on ShapeNetPart [75]. We report the average IoU scores $(\\%)$ for part categories and instances, respectively denoted as $\\mathrm{mIoU}_C$ and $\\mathrm{mIoU}_I$ ." + ], + "table_footnote": [], + "table_body": "
Method20%40%60%80%100%
Point-MAE [47]89.490.290.390.591.0
Point-M2AE [78]90.892.092.192.492.9
I2P-MAE92.192.793.193.193.4
Improvement+1.3+0.7+1.0+0.7+0.5
", + "bbox": [ + 501, + 383, + 890, + 482 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 5. Pre-training with Limited 3D Data. We utilize randomly sampled 3D data from ShapeNet [6] for pre-training.", + "bbox": [ + 498, + 493, + 890, + 522 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Pre-training with Limited 3D Data. In Table 5, we randomly sample the pre-training dataset, ShapeNet [6], with different ratios, and evaluate the performance of I2P-MAE when 3D data is further deficient. Aided by 2D pre-trained models, I2P-MAE still achieves competitive downstream accuracy in low-data regimes, especially for $20\\%$ and $60\\%$ , which outperforms Point-M2AE [78] by $+1.3\\%$ and $+1.0$ , respectively. Importantly, with only $60\\%$ of the pre-training, I2P-MAE $(93.1\\%)$ outperforms Point-MAE $(91.0\\%)$ and Point-M2AE $(92.9\\%)$ with full training data. This indicates that our image-to-point learning scheme effectively can alleviate the need for large-scale 3D training datasets.", + "bbox": [ + 496, + 547, + 890, + 731 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "2D-guided Masking. In Table 6, we experiment different masking strategies for I2P-MAE. The first row represents 2D-guided masking, which preserves more semantically important tokens to be visible for the encoder. Compared to the second-row random masking, the guidance of 2D attention maps contributes to $+0.4\\%$ and $+0.9\\%$ accuracy on two datasets. Then, we reverse the token scores in the spatial attention cloud, and instead mask the most important tokens. As shown in the third row, the results are largely harmed, demonstrating the significance of encoding", + "bbox": [ + 496, + 750, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "21775", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/6d1994d6a30fe2221b1a4d028426bdab177e987f9b85a9bc60abaa8918325d5d.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
2D-guidedVisibleRatioModelNet40OBJ-BG
✓Important0.893.487.1
-Random0.893.086.2
✓Unimportant0.892.884.5
✓Important0.792.583.8
✓Important0.992.885.6
", + "bbox": [ + 80, + 89, + 468, + 195 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/3f70a4818a8ad749bd5b0aae3d6c73c9d37d558cfdca2a7536fff2191245fecd.jpg", + "table_caption": [ + "Table 6. 2D-guided Masking. 'Visible' denotes whether the preserved visible point tokens are more semantically important than the masked ones. 'Ratio' denotes the masking ratio." + ], + "table_footnote": [], + "table_body": "
TokensTargetsModelNet40OBJ-BG
MaskedVisible3D2D
✓✓MV93.487.1
✓-M-92.984.7
-✓-V91.980.2
✓--M91.277.8
✓-MM92.684.9
", + "bbox": [ + 78, + 262, + 468, + 381 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 7. 2D-semantic Reconstruction. We utilize 'M' and 'V' to denote the reconstruction targets of masked and visible tokens. '3D' and '2D' denote 3D coordinates and 2D semantics.", + "bbox": [ + 76, + 391, + 468, + 433 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "critical 3D structures. Finally, we modify the masking ratio by $\\pm 0.1$ , which controls the proportion between visible and masked tokens. The performance decay indicates that, the 2D-semantic and 3D-coordinate reconstruction are required to be well balanced for a properly challenging pre-text task.", + "bbox": [ + 75, + 449, + 468, + 526 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "2D-semantic Reconstruction. In Table 7, we investigate which groups of tokens are the best for learning 2D semantic targets. The comparison of the first two rows reveals the effectiveness of reconstructing 2D semantics from visible tokens, i.e., $+0.5\\%$ and $+2.4\\%$ classification accuracy. By only using 2D targets for either the visible or masked tokens (the $3^{\\mathrm{rd}}$ and $4^{\\mathrm{th}}$ rows), we verify that the 3D-coordinate reconstruction still plays an important role in I2P-MAE, which learns low-level geometric 3D patterns and provides complementary knowledge to the high-level 2D semantics. However, if the 3D and 2D targets are both reconstructed from the masked tokens (the last row), the network is restricted to learn 2D knowledge from the masked nonsignificant 3D geometries, other than the more discriminative parts. Also, assigning two targets on the same tokens might cause 2D-3D semantic conflicts. Therefore, the two targets are best to be reconstructed separately.", + "bbox": [ + 75, + 542, + 468, + 801 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Visualization", + "text_level": 1, + "bbox": [ + 76, + 814, + 210, + 830 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We visualize the input point cloud, random masking, spatial attention cloud, 2D-guided masking, and the reconstructed 3D coordinates in Figure 6. Guided by the semantic scores from 2D pre-trained models (darker points indicate", + "bbox": [ + 75, + 839, + 470, + 901 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f57a1df68264115a3bd36467fd1894872eeb4d82779256ba9ff5acde56dfe166.jpg", + "image_caption": [ + "Figure 6. Visualization of I2P-MAE. Guided by the spatial attention cloud, I2P-MAE's masking (the $4^{th}$ column) preserves more semantically important 3D structures than random masking." + ], + "image_footnote": [], + "bbox": [ + 509, + 93, + 877, + 340 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "higher scores), the masked point cloud largely preserves significant parts of the 3D shape, e.g., the main body of an airplane, the grip of a guitar, the frame of a chair and telephone. By this, the 3D network can learn more discriminative features by reconstructing these visible 2D semantics.", + "bbox": [ + 498, + 425, + 890, + 501 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 518, + 617, + 535 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we propose I2P-MAE, a masked point modeling framework with effective image-to-point learning schemes. We introduce two approaches to transfer the well learned 2D knowledge into 3D domains: 2D-guided masking and 2D-semantic reconstruction. Aided by the 2D guidance, I2P-MAE learns superior 3D representations and alleviates the demand for large-scale 3D data. For future work, not limited to masking and reconstruction, we will explore more sufficient image-to-point learning approaches, e.g., point token sampling and 2D-3D class-token contrast. Also, we expect our pre-trained models to benefit wider ranges of 3D tasks, e.g., 3D object detection and visual grounding.", + "bbox": [ + 496, + 547, + 890, + 729 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement. This project is funded in part by National Key R&D Program of China Project 2022ZD0161100, by the Centre for Perceptual and Interactive Intelligence (CPII) Ltd under the Innovation and Technology Commission (ITC)'s InnoHK, by General Research Fund of Hong Kong RGC Project 14204021, by the National Natural Science Foundation of China (Grant No. 62206272), and by Shanghai Committee of Science and Technology (Grant No. 21DZ1100100). Hongsheng Li is a PI of CPII under the InnoHK.", + "bbox": [ + 496, + 750, + 892, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "21776", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Mohamed Afham, Isuru Dissanayake, Dinithi Dissanayake, Amaya Dharmasiri, Kanchana Thilakarathna, and Ranga Rodrigo. 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Pointclip v2: Adapting clip for powerful 3d open-world learning. arXiv preprint arXiv:2211.11682, 2022. 3" + ], + "bbox": [ + 78, + 90, + 468, + 513 + ], + "page_idx": 11 + }, + { + "type": "page_number", + "text": "21780", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 11 + } +] \ No newline at end of file diff --git a/2023/Learning 3D Representations From 2D Pre-Trained Models via Image-to-Point Masked Autoencoders/89a76a16-b222-401c-8388-b5d09eb2345e_model.json b/2023/Learning 3D Representations From 2D Pre-Trained Models via Image-to-Point Masked Autoencoders/89a76a16-b222-401c-8388-b5d09eb2345e_model.json new file mode 100644 index 0000000000000000000000000000000000000000..0b2a5639fa001cc0f39e3c64ea44ebf26fe44e40 --- /dev/null +++ b/2023/Learning 3D Representations From 2D Pre-Trained Models via Image-to-Point Masked Autoencoders/89a76a16-b222-401c-8388-b5d09eb2345e_model.json @@ -0,0 +1,2369 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.174, + 0.131, + 0.798, + 0.175 + ], + "angle": 0, + "content": "Learning 3D Representations from 2D Pre-trained Models via Image-to-Point Masked Autoencoders" + }, + { + "type": "text", + "bbox": [ + 0.198, + 0.195, + 0.773, + 0.216 + ], + "angle": 0, + "content": "Renrui Zhang\\(^{1,2}\\), Liuhui Wang\\(^{3}\\), Yu Qiao\\(^{1}\\), Peng Gao\\(^{\\dagger 1}\\), Hongsheng Li\\(^{2,4}\\)" + }, + { + "type": "text", + "bbox": [ + 0.31, + 0.224, + 0.66, + 0.242 + ], + "angle": 0, + "content": "\\(^{1}\\)Shanghai Artificial Intelligence Laboratory" + }, + { + "type": "text", + "bbox": [ + 0.235, + 0.242, + 0.736, + 0.26 + ], + "angle": 0, + "content": "\\(^{2}\\)CUHK MMLab \\(^{3}\\)Peking University \\(^{4}\\)CPII under InnoHK" + }, + { + "type": "text", + "bbox": [ + 0.155, + 0.262, + 0.812, + 0.28 + ], + "angle": 0, + "content": "{zhangrenrui, gaopeng}@pjlab.org.cn, hsli@ee.cuhk.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.324, + 0.314, + 0.34 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.354, + 0.474, + 0.794 + ], + "angle": 0, + "content": "Pre-training by numerous image data has become a facto for robust 2D representations. In contrast, due to the expensive data processing, a paucity of 3D datasets severely hinders the learning for high-quality 3D features. In this paper, we propose an alternative to obtain superior 3D representations from 2D pre-trained models via Image-to-Point Masked Autoencoders, named as I2P-MAE. By self-supervised pre-training, we leverage the well learned 2D knowledge to guide 3D masked autoencoding, which reconstructs the masked point tokens with an encoder-decoder architecture. Specifically, we first utilize off-the-shelf 2D models to extract the multi-view visual features of the input point cloud, and then conduct two types of image-to-point learning schemes. For one, we introduce a 2D-guided masking strategy that maintains semantically important point tokens to be visible. Compared to random masking, the network can better concentrate on significant 3D structures with key spatial cues. For another, we enforce these visible tokens to reconstruct multi-view 2D features after the decoder. This enables the network to effectively inherit high-level 2D semantics for discriminative 3D modeling. Aided by our image-to-point pre-training, the frozen I2P-MAE, without any fine-tuning, achieves \\(93.4\\%\\) accuracy for linear SVM on ModelNet40, competitive to existing fully trained methods. By further fine-tuning on on ScanObjectNN's hardest split, I2P-MAE attains the state-of-the-art \\(90.11\\%\\) accuracy, \\(+3.68\\%\\) to the second-best, demonstrating superior transferable capacity. Code is available at https://github.com/ZrrSkywalker/I2P-MAE." + }, + { + "type": "title", + "bbox": [ + 0.079, + 0.821, + 0.21, + 0.836 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.847, + 0.47, + 0.879 + ], + "angle": 0, + "content": "Driven by huge volumes of image data [11, 40, 56, 61], pre-training for better visual representations has gained" + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.326, + 0.889, + 0.555 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.571, + 0.892, + 0.627 + ], + "angle": 0, + "content": "Figure 1. Image-to-Point Masked Autoencoders. We leverage the 2D pre-trained models to guide the MAE pre-training in 3D, which alleviates the need of large-scale 3D datasets and learns from 2D knowledge for superior 3D representations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.66, + 0.893, + 0.903 + ], + "angle": 0, + "content": "much attention in computer vision, which benefits a variety of downstream tasks [8, 29, 39, 55, 62]. Besides supervised pre-training with labels, many researches develop advanced self-supervised approaches to fully utilize raw image data via pre-text tasks, e.g., image-image contrast [5, 9, 10, 21, 28], language-image contrast [12, 53], and masked image modeling [3, 4, 18, 19, 27, 31, 42, 70]. Given the popularity of 2D pre-trained models, it is still absent for large-scale 3D datasets in the community, attributed to the expensive data acquisition and labor-intensive annotation. The widely adopted ShapeNet [6] only contains \\(50\\mathrm{k}\\) point clouds of 55 object categories, far less than the 14 million ImageNet [11] and 400 million image-text pairs [53] in 2D vision. Though there have been attempts to extract self-supervisory signals for 3D pre-training [33, 41, 47, 64, 69, 76, 78, 83], raw point clouds with sparse structural patterns cannot provide suf" + }, + { + "type": "page_footnote", + "bbox": [ + 0.102, + 0.888, + 0.23, + 0.901 + ], + "angle": 0, + "content": "† Corresponding author" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "21769" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.09, + 0.089, + 0.23, + 0.282 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.252, + 0.088, + 0.455, + 0.281 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.292, + 0.471, + 0.351 + ], + "angle": 0, + "content": "Figure 2. Comparison of (Left) Existing Methods [47, 78] and (Right) our I2P-MAE. On top of the general 3D MAE architecture, I2P-MAE introduces two schemes of image-to-point learning: 2D-guided masking and 2D-semantic reconstruction." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.381, + 0.47, + 0.502 + ], + "angle": 0, + "content": "ficient and diversified semantics compared to colorful images, which constrain the generalization capacity of pretraining. Considering the homology of images and point clouds, both of which depict certain visual characteristics of objects and are related by 2D-3D geometric mapping, we ask the question: can off-the-shelf 2D pre-trained models help 3D representation learning by transferring robust 2D knowledge into 3D domains?" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.506, + 0.47, + 0.809 + ], + "angle": 0, + "content": "To tackle this challenge, we propose I2P-MAE, a Masked Autoencoding framework that conducts Image-to-Point knowledge transfer for self-supervised 3D point cloud pre-training. As shown in Figure 1, aided by 2D semantics learned from abundant image data, our I2P-MAE produces high-quality 3D representations and exerts strong transferable capacity to downstream 3D tasks. Specifically, referring to 3D MAE models [47, 78] in Figure 2 (Left), we first adopt an asymmetric encoder-decoder transformer [14] as our fundamental architecture for 3D pre-training, which takes as input a randomly masked point cloud and reconstructs the masked points from the visible ones. Then, to acquire 2D semantics for the 3D shape, we bridge the modal gap by efficiently projecting the point cloud into multi-view depth maps. This requires no time-consuming offline rendering and largely preserves 3D geometries from different perspectives. On top of that, we utilize off-the-shelf 2D models to obtain the multi-view 2D features along with 2D attention maps of the point cloud, and respectively guide the pre-training from two aspects, as shown in Figure 2 (Right)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.471, + 0.904 + ], + "angle": 0, + "content": "Firstly, different from existing methods [47, 78] to randomly sample visible tokens, we introduce a 2D-guided masking strategy that reserves point tokens with more spatial semantics to be visible for the MAE encoder. In detail, we back-project the multi-view attention maps into 3D space as a spatial attention cloud. Each element in the" + }, + { + "type": "image", + "bbox": [ + 0.527, + 0.087, + 0.868, + 0.285 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.292, + 0.892, + 0.351 + ], + "angle": 0, + "content": "Figure 3. Pre-training Epochs vs. Linear SVM Accuracy on ModelNet40 [67]. With the image-to-point learning schemes, I2P-MAE exerts superior transferable capability with much faster convergence speed than Point-MAE [47] and Point-M2AE [78]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.381, + 0.892, + 0.457 + ], + "angle": 0, + "content": "cloud indicates the semantic significance of the corresponding point token. Guided by this, the 3D network can better focus on the visible critical structures to understand the global 3D shape, and also reconstruct the masked tokens from important spatial cues." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.459, + 0.893, + 0.61 + ], + "angle": 0, + "content": "Secondly, in addition to the recovering of masked point tokens, we propose to concurrently reconstruct 2D semantics from the visible point tokens after the MAE decoder. For each visible token, we respectively fetch its projected 2D representations from different views, and integrate them as the 2D-semantic learning target. By simultaneously reconstructing the masked 3D coordinates and visible 2D concepts, I2P-MAE is able to learn both low-level spatial patterns and high-level semantics pre-trained in 2D domains, contributing to superior 3D representations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.612, + 0.894, + 0.824 + ], + "angle": 0, + "content": "With the aforementioned image-to-point guidance, our I2P-MAE significantly accelerates the convergence speed of pre-training and exhibits state-of-the-art performance on 3D downstream tasks, as shown in Figure 3. Learning from 2D ViT [14] pre-trained by CLIP [53], I2P-MAE, without any fine-tuning, achieves \\(93.4\\%\\) classification accuracy by linear SVM on ModelNet40 [67], which has surpassed the fully fine-tuned results of Point-BERT [76] and Point-MAE [33]. After fine-tuning, I2P-MAE further achieves \\(90.11\\%\\) classification accuracy on the hardest split of ScanObjectNN [63], significantly exceeding the second-best Point-M2AE [78] by \\(+3.68\\%\\). The experiments fully demonstrate the effectiveness of learning from pre-trained 2D models for superior 3D representations." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.825, + 0.822, + 0.84 + ], + "angle": 0, + "content": "Our contributions are summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.856, + 0.894, + 0.903 + ], + "angle": 0, + "content": "- We propose Image-to-Point Masked Autoencoders (I2P-MAE), a pre-training framework to leverage 2D pre-trained models for learning 3D representations." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "21770" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.097, + 0.092, + 0.468, + 0.136 + ], + "angle": 0, + "content": "- We introduce two strategies, 2D-guided masking and 2D-semantic reconstruction, to effectively transfer the well learned 2D knowledge into 3D domains." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.148, + 0.468, + 0.177 + ], + "angle": 0, + "content": "- Extensive experiments have been conducted to indicate the significance of our image-to-point pre-training." + }, + { + "type": "list", + "bbox": [ + 0.097, + 0.092, + 0.468, + 0.177 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.192, + 0.218, + 0.208 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.218, + 0.473, + 0.626 + ], + "angle": 0, + "content": "3D Point Cloud Pre-training. Supervised learning for point clouds has attained remarkable progress by delicately designed architectures [22, 50, 51, 80, 81] and local operators [2, 37, 65, 68, 72, 82]. However, such methods learned from closed-set datasets [63, 67] are limited to produce general 3D representations. Instead, self-supervised pre-training via unlabelled point clouds [6] have revealed promising transferable ability, which provides a good network initialization for downstream fine-tuning. Mainstream 3D self-supervised approaches adopt encoder-decoder architectures to recover the input point clouds from the transformed representations, including point rearrangement [57], part occlusion [64], rotation [49], downsampling [36], and codeword encoding [74]. Concurrent works also adopt contrastive pre-text tasks between 3D data pairs, such as local-global relation [17, 54], temporal frames [32], and augmented viewpoints [69]. More recent works adopt pretrained CLIP [53] for zero-shot 3D recognition [24, 79, 86], or introduce masked point modeling [13, 16, 33, 41] as strong 3D self-supervised learners. Therein, Point-BERT [76] utilizes pre-trained tokenizers to indicate discrete point tokens, while Point-MAE [47], Point-M2AE [78], and PiMAE [7] apply Masked Autoencoders (MAE) to directly reconstruct masked 3D coordinates. Our I2P-MAE also adopts MAE as the basic pre-training framework, but is guided by 2D pretrained models via image-to-point learning schemes, which benefits 3D pre-training with diverse 2D semantics." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.644, + 0.473, + 0.902 + ], + "angle": 0, + "content": "2D-to-3D Learning. Except for jointly training 2D-3D networks [1, 23, 38, 46, 73], only a few existing researches focus on 2D-to-3D learning, and can be categorized into two groups. To eliminate the modal gap, the first group either upgrades 2D pre-trained networks into 3D variants for processing point clouds (convolutional kernels inflation [71, 77], modality-agnostic transformer [52]), or projects 3D point clouds into 2D images with parameter-efficient tuning (multi-view adapter [79], point-to-pixel prompting [66]). Different from them, our I2P-MAE benefits from three properties. 1) Pre-training: We learn from 2D models during the pre-training stage, and then can be flexibly adapted to various 3D scenarios by fine-tuning. However, prior works are required to utilize 2D models on every different downstream task. 2) Self-supervision: I2P-MAE is pre-trained by raw point clouds in a self-supervised manner and learns more general 3D representations. In con" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.333 + ], + "angle": 0, + "content": "trast, prior works are supervised by labelled downstream 3D data, which might constrain the diverse 2D semantics into specific 3D domains. 3) Independence: Prior works directly inherit 2D network architectures for 3D training, which is memory-consuming and not 3D extensible, while we train an independent 3D network and regard 2D models as semantic teachers. Another group of 2D-to-3D methods utilize paired real-world 2D-3D data of indoor [44] or outdoor [59] scenes, and conduct contrastive learning for knowledge transfer. Our approach also differs from them in two ways. 4) Masked Autoencoding. I2P-MAE learns 2D semantics via the MAE-style pre-training without any contrastive loss between point-pixel pairs. 5) 3D Data Only. We require no real-world image dataset during the pre-training and efficiently project the 3D shape into depth maps for 2D features extraction." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.35, + 0.593, + 0.366 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.377, + 0.895, + 0.499 + ], + "angle": 0, + "content": "The overall pipeline of I2P-MAE is shown in Figure 4. In Section 3.1, we first introduce I2P-MAE's basic 3D architecture for point cloud masked autoencoding without 2D guidance. Then in Section 3.2, we show the details of utilizing 2D pre-trained models to obtain visual representations from 3D point clouds. Finally in Section 3.3, we present how to conduct image-to-point knowledge transfer for 3D representation learning." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.51, + 0.707, + 0.525 + ], + "angle": 0, + "content": "3.1. Basic 3D Architecture" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.535, + 0.894, + 0.61 + ], + "angle": 0, + "content": "As our basic framework for image-to-point learning, I2P-MAE refers to existing works [47, 78] to conduct 3D point cloud masked autoencoding, which consists of a token embedding module, an encoder-decoder transformer, and a head for reconstructing masked 3D coordinates." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.634, + 0.895, + 0.786 + ], + "angle": 0, + "content": "Token Embedding. Given a raw point cloud \\( P \\in \\mathbb{R}^{N \\times 3} \\), we first adopt Furthest Point Sampling (FPS) to downsample the point number from \\( N \\) to \\( M \\), denoted as \\( P^T \\in \\mathbb{R}^{M \\times 3} \\). Then, we utilize \\( k \\) Nearest-Neighbour (\\( k \\)-NN) to search the \\( k \\) neighbors for each downsampled point, and aggregate their features via a mini-PointNet [50] to obtain \\( M \\) point tokens. In this way, each token can represent a local spatial region and interact long-range features with others in the follow-up transformer. We formulate them as \\( T \\in \\mathbb{R}^{M \\times C} \\), where \\( C \\) denotes the feature dimension." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Encoder-Decoder Transformer. To build the pre-text learning targets, we mask the point tokens with a high ratio, e.g., \\(80\\%\\), and only feed the visible ones, \\(T_{\\mathrm{vis}} \\in \\mathbb{R}^{M_{\\mathrm{vis}} \\times C}\\), into the transformer encoder, where \\(M_{\\mathrm{vis}}\\) denotes the visible token number. Each encoder block contains a self-attention layer and is pre-trained to understand the global" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "21771" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.086, + 0.891, + 0.425 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.436, + 0.895, + 0.482 + ], + "angle": 0, + "content": "Figure 4. The Pipeline of I2P-MAE. Given an input point cloud, we leverage the 2D pre-trained models to generate two guidance signals from the projected depth maps: 2D attention maps and 2D visual features. We respectively conduct 2D-guided masking and 2D-semantic reconstruction to transfer the encoded 2D knowledge for 3D point cloud pre-training." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.505, + 0.473, + 0.657 + ], + "angle": 0, + "content": "3D shape from the remaining visible parts. After encoding, we concatenate the encoded \\( T_{\\mathrm{vis}}^e \\) with a set of shared learnable masked tokens \\( T_{\\mathrm{mask}} \\in \\mathbb{R}^{M_{\\mathrm{mask}} \\times C} \\), and input them into a lightweight decoder, where \\( M_{\\mathrm{mask}} \\) denotes the masked token number and \\( M = M_{\\mathrm{mask}} + M_{\\mathrm{vis}} \\). In the transformer decoder, the masked tokens learn to capture informative spatial cues from visible ones and reconstruct the masked 3D coordinates. Importantly, we follow Point-M2AE [78] to modify our transformer to be a hierarchical architecture for encoding the multi-scale representations." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.685, + 0.473, + 0.807 + ], + "angle": 0, + "content": "3D-coordinate Reconstruction. On top of the decoded point tokens \\(\\{T_{\\mathrm{vis}}^d, T_{\\mathrm{mask}}^d\\}\\), we utilize \\(T_{\\mathrm{mask}}^d\\) to reconstruct 3D coordinates of the masked tokens along with their \\(k\\) neighboring points. A reconstruction head of a single linear projection layer is adopted to predict \\(P_{\\mathrm{mask}} \\in \\mathbb{R}^{M_{\\mathrm{mask}} \\times k \\times 3}\\), the ground-truth 3D coordinates of the masked points. Then, we compute the loss by Chamfer Distance [15] and formulate it as" + }, + { + "type": "equation", + "bbox": [ + 0.1, + 0.823, + 0.47, + 0.855 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {3 D}} = \\frac {1}{M _ {\\mathrm {m a s k}} k} \\mathrm {C h a m f e r} \\left(\\mathrm {H} _ {\\mathrm {3 D}} \\left(T _ {\\mathrm {m a s k}} ^ {d}\\right), P _ {\\mathrm {m a s k}}\\right), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.471, + 0.902 + ], + "angle": 0, + "content": "where \\(\\mathrm{H}_{3\\mathrm{D}}(\\cdot)\\) denotes the head to reconstruct the masked 3D coordinates." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.504, + 0.78, + 0.521 + ], + "angle": 0, + "content": "3.2. 2D Pre-trained Representations" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.528, + 0.892, + 0.634 + ], + "angle": 0, + "content": "We can leverage 2D models of different architectures (ResNet [30], ViT [14]) and various pre-training approaches (supervised [30, 45] and self-supervised [5, 53] ones) to assist the 3D representation learning. To align the input modality for 2D models, we project the input point cloud onto multiple image planes to create depth maps, and then encode them into multi-view 2D representations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.654, + 0.892, + 0.852 + ], + "angle": 0, + "content": "Efficient Projection. To ensure the efficiency of pretraining, we simply project the input point cloud \\( P \\) from three orthogonal views respectively along the \\( x, y, z \\) axes. For every point, we directly omit each of its three coordinates and round down the other two to obtain the 2D location on the corresponding map. The projected pixel value is set as the omitted coordinate to reflect relative depth relations of points, which is then repeated by three times to imitate the three-channel RGB. The projection of I2PMAE is highly time-efficient and involves no offline rendering [48, 60], projective transformation [20, 79], or learnble prompting [66]. We denote the projected multi-view depth maps of \\( P \\) as \\( \\{I_i\\}_{i=1}^3 \\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "2D Visual Features. We then utilize a 2D pre-trained model, e.g., a pre-trained ResNet or ViT, to extract multi-" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "21772" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.184 + ], + "angle": 0, + "content": "view features of the point cloud with \\( C \\) channels, formulated as \\( \\{F_i^{2\\mathrm{D}}\\}_{i = 1}^3 \\), where \\( F_{i}\\in \\mathbb{R}^{H\\times W\\times C} \\) and \\( H,W \\) denote the feature map size. Such 2D features contain sufficient high-level semantics learned from large-scale image data. The geometric information loss during projection can also be alleviated by encoding from different views." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.2, + 0.472, + 0.351 + ], + "angle": 0, + "content": "2D Attention Maps. In addition to 2D features, we also acquire a semantic attention map for each view via the 2D pre-trained model. The one-channel maps indicate the semantic importance of different image regions, which we denote as \\(\\{S_i^{2\\mathrm{D}}\\}_{i = 1}^3\\), where \\(S_{i}\\in \\mathbb{R}^{H\\times W\\times 1}\\). For ResNet, we adopt pixel-wise max pooling on \\(\\{F_i^{2\\mathrm{D}}\\}_{i = 1}^3\\) to reduce the feature dimension to one. For ViT, we adopt attention maps of the class token at the last transformer layer, since the attention weights to the class token reveal how much the features contribute to the final classification." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.36, + 0.377, + 0.377 + ], + "angle": 0, + "content": "3.3. Image-to-Point Learning Schemes" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.384, + 0.47, + 0.445 + ], + "angle": 0, + "content": "On top of the 2D pre-trained representations for the point cloud, I2P-MAE's pre-training is guided by two image-top-point learning designs: 2D-guided masking before the encoder, and 2D-semantic reconstruction after the decoder." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.462, + 0.473, + 0.659 + ], + "angle": 0, + "content": "2D-guided Masking. The conventional masking strategy samples masked tokens randomly following a uniform distribution, which might prevent the encoder from 'seeing' important spatial characteristics and disturb the decoder by nonsignificant structures. Therefore, we leverage the 2D attention maps to guide the masking of point tokens, which samples more semantically significant 3D parts for encoding. Specifically, indexed by the coordinates of point tokens \\( P^T \\in \\mathbb{R}^{M \\times 3} \\), we back-project the multi-view attention maps \\( \\{S_i^{2\\mathrm{D}}\\}_{i=1}^3 \\) into 3D space and aggregate them as a 3D attention cloud \\( S^{3\\mathrm{D}} \\in \\mathbb{R}^{M \\times 1} \\). For each point in \\( S^{3\\mathrm{D}} \\), we assign the semantic score by averaging the corresponding 2D values from multi-view attention maps as" + }, + { + "type": "equation", + "bbox": [ + 0.134, + 0.669, + 0.47, + 0.71 + ], + "angle": 0, + "content": "\\[\nS ^ {\\mathrm {3 D}} = \\operatorname {S o f t m a x} \\left(\\frac {1}{3} \\sum_ {i = 1} ^ {3} \\operatorname {I 2 P} \\left(S _ {i} ^ {\\mathrm {2 D}}, P ^ {T}\\right)\\right), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.473, + 0.901 + ], + "angle": 0, + "content": "where \\(\\mathrm{I2P}(\\cdot)\\) denotes the 2D-to-3D back-projection operation in Figure 5. We apply a softmax function to normalize the \\(M\\) points within \\(S^{3\\mathrm{D}}\\), and regard each element's magnitude as the visible probability for the corresponding point token. With this 2D semantic prior, the random masking becomes a nonuniform sampling with different probabilities for different tokens, where the tokens covering more critical 3D structures are more likely to be preserved. This boosts the representation learning of the encoder by focusing more on significant 3D geometries, and provides the masked tokens with more informative cues at the decoder for better reconstruction." + }, + { + "type": "image", + "bbox": [ + 0.534, + 0.09, + 0.861, + 0.313 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.329, + 0.895, + 0.373 + ], + "angle": 0, + "content": "Figure 5. Image-to-Point Operation (I2P). Indexed by 3D point coordinates, the corresponding multi-view 2D representations are back-projected into 3D space for aggregation." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.394, + 0.895, + 0.548 + ], + "angle": 0, + "content": "2D-semantic Reconstruction. The 3D-coordinate reconstruction of masked point tokens enables the network to explore low-level 3D patterns. On top of that, we further enforce the visible point tokens, \\( T_{\\mathrm{vis}}^d \\), to reconstruct the extracted 2D semantics from different views, which effectively transfers the 2D pre-trained knowledge into 3D pre-training. To obtain the 2D-semantic targets, we utilize the coordinates of visible point tokens \\( P_{\\mathrm{vis}}^T \\in \\mathbb{R}^{M_{\\mathrm{vis}} \\times 3} \\) as indices to aggregate corresponding 2D features from \\( \\{F_i^{2\\mathrm{D}}\\}_{i=1}^3 \\) by channel-wise concatenation, formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.564, + 0.564, + 0.892, + 0.595 + ], + "angle": 0, + "content": "\\[\nF _ {\\text {v i s}} ^ {\\mathrm {3 D}} = \\operatorname {C o n c a t} \\left\\{\\mathrm {I 2 P} \\left(F _ {i} ^ {\\mathrm {2 D}}, P _ {\\text {v i s}} ^ {T}\\right) \\right\\} _ {i = 1} ^ {3}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.599, + 0.895, + 0.693 + ], + "angle": 0, + "content": "where \\(F_{\\mathrm{vis}}^{3\\mathrm{D}} \\in \\mathbb{R}^{M_{\\mathrm{vis}} \\times 3C}\\). As the multi-view depth maps depict a 3D shape from different perspectives, the concatenation between multi-view 2D features can better integrate the rich semantics inherited from 2D pre-trained models. Then, we also adopt a reconstruction head of a single linear projection layer for \\(T_{\\mathrm{vis}}^d\\), and compute the \\(l_2\\) loss as" + }, + { + "type": "equation", + "bbox": [ + 0.574, + 0.697, + 0.892, + 0.73 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {2 D}} = \\frac {1}{M _ {\\mathrm {v i s}}} \\left(\\mathrm {H} _ {\\mathrm {2 D}} \\left(T _ {\\mathrm {v i s}} ^ {d}\\right) - F _ {\\mathrm {v i s}} ^ {\\mathrm {3 D}}\\right) ^ {2}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.735, + 0.895, + 0.902 + ], + "angle": 0, + "content": "where \\(\\mathrm{H}_{2\\mathrm{D}}(\\cdot)\\) denotes the head to reconstruct visible 2D semantics, parallel to \\(\\mathrm{H}_{3\\mathrm{D}}(\\cdot)\\) for masked 3D coordinates. The final pre-training loss of our I2P-MAE is then formulated as \\(\\mathcal{L}_{\\mathrm{I2P}} = \\mathcal{L}_{\\mathrm{3D}} + \\mathcal{L}_{\\mathrm{2D}}\\). With such image-to-point feature learning, I2P-MAE not only encodes low-level spatial variations from 3D coordinates, but also explores high-level semantic knowledge from 2D representations. As the 2D-guided masking has preserved visible tokens with more spatial significance, the 2D-semantic reconstruction upon them further benefits I2P-MAE to learn more discriminative 3D representations." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "21773" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.094, + 0.089, + 0.457, + 0.328 + ], + "angle": 0, + "content": "
MethodModelNet40OBJ-BG
SO-Net [35]87.3-
FoldingNet [74]88.4-
VIP-GAN [26]90.2-
DGCNN + Jigsaw [58]90.659.5
DGCNN + OcCo [64]90.778.3
DGCNN + CrossPoint [1]91.281.7
Transformer + OcCo [76]89.6-
Point-BERT [76]87.4-
Point-MAE [47]91.077.7
3D-OAE [85]92.3-
Point-M2AE [78]92.984.1
I2P-MAE93.487.1
Improvement+0.5+3.0
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.339, + 0.472, + 0.396 + ], + "angle": 0, + "content": "Table 1. Linear SVM Classification on ModelNet40 [67] and ScanObjectNN [63]. We compare the accuracy (\\%) of existing self-supervised methods, and the second-best one is underlined. We adopt the OBJ-BG split for ScanObjectNN following [1]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.421, + 0.21, + 0.438 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.446, + 0.47, + 0.537 + ], + "angle": 0, + "content": "In Section 4.1, we first introduce our pre-training settings and the linear SVM classification performance without fine-tuning. Then in Section 4.2, we present the results by fully fine-tuning I2P-MAE on various 3D downstream tasks. Finally in Section 4.3, we conduct ablation studies to investigate the characteristics of I2P-MAE." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.548, + 0.33, + 0.563 + ], + "angle": 0, + "content": "4.1. Image-to-Point Pre-training" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.571, + 0.47, + 0.814 + ], + "angle": 0, + "content": "Settings. We adopt the popular ShapeNet [6] for self-supervised 3D pre-training, which contains 57,448 synthetic point clouds with 55 object categories. For fair comparison, we follow the same MAE transformer architecture as Point-M2AE [78]: a 3-stage encoder with 5 blocks per stage, a 2-stage decoder with 1 block per stage, 2,048 input point number \\((N)\\), 512 downsampled number \\((M)\\), 16 nearest neighbors \\((k)\\), 384 feature channels \\((C)\\), and the mask ratio of \\(80\\%\\). For off-the-shelf 2D models, we utilize ViT-Base [14] pre-trained by CLIP [53] as default and keep its weights frozen during 3D pre-training. We project the point cloud into three \\(224 \\times 224\\) depth maps, and obtain the 2D feature size \\(H \\times W\\) of \\(14 \\times 14\\). I2P-MAE is pre-trained for 300 epochs with a batch size 64 and learning rate \\(10^{-3}\\). We adopt AdamW [34] optimizer with a weight decay \\(5 \\times 10^{-2}\\) and the cosine scheduler with 10-epoch warm-up." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Linear SVM. To evaluate the transfer capacity, we directly utilize the features extracted by I2P-MAE's encoder for linear SVM on the synthetic ModelNet40 [67] and real-world ScanObjectNN [63] without any fine-tuning or voting. As shown in Table 1, for 3D shape classification in" + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.089, + 0.892, + 0.328 + ], + "angle": 0, + "content": "
MethodOBJ-BGOBJ-ONLYPB-T50-RS
PointNet [50]73.379.268.0
PointNet++ [51]82.384.377.9
PointCNN [37]86.185.578.5
MVTN [25]--82.8
PointMLP [2]--85.2
Transformer [76]79.8680.5577.24
[P] Point-BERT [76]87.4388.1283.07
[P] 3D-OAE [85]89.1688.6483.17
[P] MaskPoint [41]89.3088.1084.30
[P] Point-MAE [47]90.0288.2985.18
[P] MAE3D [33]--86.20
[P] Point-M2AE [78]91.2288.8186.43
[P] I2P-MAE94.1591.5790.11
Improvement+2.93+2.76+3.68
" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.339, + 0.892, + 0.396 + ], + "angle": 0, + "content": "Table 2. Real-world 3D Classification on ScanObjectNN [63]. We report the accuracy \\((\\%)\\) on the official three splits of ScanObjectNN. [P] denotes to fine-tune the models after self-supervised pre-training." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.423, + 0.892, + 0.606 + ], + "angle": 0, + "content": "both domains, I2P-MAE shows superior performance and exceeds the second-best respectively by \\(+0.5\\%\\) and \\(+3.0\\%\\) accuracy. Our SVM results \\((93.4\\%, 87.1\\%)\\) can even surpass some existing methods after full downstream training in Table 2 and 3, e.g., PointCNN [37] \\((92.2\\%, 86.1\\%)\\), Transformer [76] \\((91.4\\%, 79.86\\%)\\), and Point-BERT [76] \\((92.7\\%, 87.43\\%)\\). In addition, guided by the 2D pre-trained models, I2P-MAE exhibits much faster pre-training convergence than Point-MAE [47] and Point-M2AE in Figure 3. Therefore, the SVM performance of I2P-MAE demonstrates its learned high-quality 3D representations and the significance of our image-to-point learning schemes." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.616, + 0.683, + 0.631 + ], + "angle": 0, + "content": "4.2. Downstream Tasks" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.64, + 0.892, + 0.702 + ], + "angle": 0, + "content": "After pre-training, I2P-MAE is fine-tuned for real-world and synthetic 3D classification, and part segmentation. Except ModelNet40 [67], we do not use the voting strategy [43] for evaluation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Real-world 3D Classification. The challenging ScanObjectNN [63] consists of 11,416 training and 2,882 test 3D shapes, which are scanned from the real-world scenes and thus include backgrounds with noises. As shown in Table 2, our I2P-MAE exerts great advantages over other self-supervised methods, surpassing the second-best by \\(+2.93\\%\\), \\(+2.76\\%\\), and \\(+3.68\\%\\) respectively for the three splits. This is also the first model reaching \\(90\\%\\) accuracy on the hardest PB-T50-RS spilt. As the pre-training point clouds [6] are synthetic 3D shapes with a large domain gap with the real-world ScanobjectNN, the results well indicate the universality of I2P-MAE inherited from the 2D pre-trained models." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "21774" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.097, + 0.089, + 0.451, + 0.306 + ], + "angle": 0, + "content": "
MethodPointsNo VotingVoting
PointNet [50]1k89.2-
PointNet++ [51]1k90.7-
PointCNN [37]1k92.2-
Point Transformer [84]-93.7
Transformer [76]1k91.4-
[P] Point-BERT [76]1k92.793.2
[P] 3D-OAE [85]1k-93.4
[P] Point-MAE [47]1k93.293.8
Point-MAE8k-94.0
[P] Point-M2AE [78]1k93.494.0
[P] I2P-MAE-SVM1k93.4-
I2P-MAE1k93.794.1
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.317, + 0.47, + 0.361 + ], + "angle": 0, + "content": "Table 3. Synthetic 3D Classification on ModelNet40 [67]. We report the accuracy \\((\\%)\\) before and after the voting [43]. [P] denotes to fine-tune the models after self-supervised pre-training." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.387, + 0.47, + 0.569 + ], + "angle": 0, + "content": "Synthetic 3D Classification. The widely adopted ModelNet40 [67] contains 9,843 training and 2,468 test 3D point clouds, which are sampled from the synthetic CAD models of 40 categories. We report the classification accuracy of existing methods before and after the voting in Table 3. As shown, our I2P-MAE achieves leading performance for both settings with only 1k input point number. For linear SVM without any fine-tuning, I2P-MAE-SVM can already attain \\(93.4\\%\\) accuracy and exceed most previous works, indicating the powerful transfer ability. By fine-tuning the entire network, the accuracy can be further boosted by \\(+0.3\\%\\) accuracy, and achieve \\(94.1\\%\\) after the offline voting." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.589, + 0.468, + 0.816 + ], + "angle": 0, + "content": "Part Segmentation. The synthetic ShapeNetPart [75] is selected from ShapeNet [6] with 16 object categories and 50 part categories, which contains 14,007 and 2,874 samples for training and validation. We utilize the same segmentation head after the pre-trained encoder as previous works [47, 78] for fair comparison. The head only conducts simple upsampling for point tokens at different stages and concatenates them alone the feature dimension as the output. Two types of mean IoU scores, \\(\\mathrm{mIoU}_C\\) and \\(\\mathrm{mIoU}_I\\) are reported in Table 4. For such highly saturated benchmark, I2P-MAE can still exert leading performance guided by the well learned 2D knowledge, e.g., \\(+0.29\\%\\) and \\(+0.25\\%\\) higher than Point-M2AE concerning the two metrics. This demonstrates that the 2D guidance also benefits the understanding for fine-grained point-wise 3D patterns." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.831, + 0.231, + 0.848 + ], + "angle": 0, + "content": "4.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.468, + 0.901 + ], + "angle": 0, + "content": "In this section, we explore the effectiveness of different characteristics in I2P-MAE. We utilize our final solution as the baseline and report the linear SVM accuracy \\((\\%)\\)." + }, + { + "type": "table", + "bbox": [ + 0.52, + 0.089, + 0.875, + 0.306 + ], + "angle": 0, + "content": "
MethodmIoUCmIoUI
PointNet [50]80.3983.70
PointNet++ [51]81.8585.10
DGCNN [65]82.3385.20
PointMLP [2]84.6086.10
Transformer [76]83.4285.10
[P] Transformer + OcCo [76]83.4285.10
[P] Point-BERT [76]84.1185.60
[P] 3D-OAE [85]-85.70
[P] MaskPoint [41]84.4086.00
[P] Point-MAE [47]-86.10
[P] Point-M2AE [78]84.8686.51
[P] I2P-MAE85.1586.76
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.318, + 0.892, + 0.361 + ], + "angle": 0, + "content": "Table 4. Part Segmentation on ShapeNetPart [75]. We report the average IoU scores \\((\\%)\\) for part categories and instances, respectively denoted as \\(\\mathrm{mIoU}_C\\) and \\(\\mathrm{mIoU}_I\\)." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.385, + 0.891, + 0.483 + ], + "angle": 0, + "content": "
Method20%40%60%80%100%
Point-MAE [47]89.490.290.390.591.0
Point-M2AE [78]90.892.092.192.492.9
I2P-MAE92.192.793.193.193.4
Improvement+1.3+0.7+1.0+0.7+0.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.494, + 0.891, + 0.523 + ], + "angle": 0, + "content": "Table 5. Pre-training with Limited 3D Data. We utilize randomly sampled 3D data from ShapeNet [6] for pre-training." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.549, + 0.892, + 0.732 + ], + "angle": 0, + "content": "Pre-training with Limited 3D Data. In Table 5, we randomly sample the pre-training dataset, ShapeNet [6], with different ratios, and evaluate the performance of I2P-MAE when 3D data is further deficient. Aided by 2D pre-trained models, I2P-MAE still achieves competitive downstream accuracy in low-data regimes, especially for \\(20\\%\\) and \\(60\\%\\), which outperforms Point-M2AE [78] by \\(+1.3\\%\\) and \\(+1.0\\), respectively. Importantly, with only \\(60\\%\\) of the pre-training, I2P-MAE \\((93.1\\%)\\) outperforms Point-MAE \\((91.0\\%)\\) and Point-M2AE \\((92.9\\%)\\) with full training data. This indicates that our image-to-point learning scheme effectively can alleviate the need for large-scale 3D training datasets." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.901 + ], + "angle": 0, + "content": "2D-guided Masking. In Table 6, we experiment different masking strategies for I2P-MAE. The first row represents 2D-guided masking, which preserves more semantically important tokens to be visible for the encoder. Compared to the second-row random masking, the guidance of 2D attention maps contributes to \\(+0.4\\%\\) and \\(+0.9\\%\\) accuracy on two datasets. Then, we reverse the token scores in the spatial attention cloud, and instead mask the most important tokens. As shown in the third row, the results are largely harmed, demonstrating the significance of encoding" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "21775" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.081, + 0.09, + 0.47, + 0.196 + ], + "angle": 0, + "content": "
2D-guidedVisibleRatioModelNet40OBJ-BG
✓Important0.893.487.1
-Random0.893.086.2
✓Unimportant0.892.884.5
✓Important0.792.583.8
✓Important0.992.885.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.206, + 0.471, + 0.25 + ], + "angle": 0, + "content": "Table 6. 2D-guided Masking. 'Visible' denotes whether the preserved visible point tokens are more semantically important than the masked ones. 'Ratio' denotes the masking ratio." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.263, + 0.47, + 0.382 + ], + "angle": 0, + "content": "
TokensTargetsModelNet40OBJ-BG
MaskedVisible3D2D
✓✓MV93.487.1
✓-M-92.984.7
-✓-V91.980.2
✓--M91.277.8
✓-MM92.684.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.392, + 0.469, + 0.434 + ], + "angle": 0, + "content": "Table 7. 2D-semantic Reconstruction. We utilize 'M' and 'V' to denote the reconstruction targets of masked and visible tokens. '3D' and '2D' denote 3D coordinates and 2D semantics." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.45, + 0.47, + 0.527 + ], + "angle": 0, + "content": "critical 3D structures. Finally, we modify the masking ratio by \\(\\pm 0.1\\), which controls the proportion between visible and masked tokens. The performance decay indicates that, the 2D-semantic and 3D-coordinate reconstruction are required to be well balanced for a properly challenging pre-text task." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.544, + 0.47, + 0.803 + ], + "angle": 0, + "content": "2D-semantic Reconstruction. In Table 7, we investigate which groups of tokens are the best for learning 2D semantic targets. The comparison of the first two rows reveals the effectiveness of reconstructing 2D semantics from visible tokens, i.e., \\(+0.5\\%\\) and \\(+2.4\\%\\) classification accuracy. By only using 2D targets for either the visible or masked tokens (the \\(3^{\\mathrm{rd}}\\) and \\(4^{\\mathrm{th}}\\) rows), we verify that the 3D-coordinate reconstruction still plays an important role in I2P-MAE, which learns low-level geometric 3D patterns and provides complementary knowledge to the high-level 2D semantics. However, if the 3D and 2D targets are both reconstructed from the masked tokens (the last row), the network is restricted to learn 2D knowledge from the masked nonsignificant 3D geometries, other than the more discriminative parts. Also, assigning two targets on the same tokens might cause 2D-3D semantic conflicts. Therefore, the two targets are best to be reconstructed separately." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.815, + 0.212, + 0.831 + ], + "angle": 0, + "content": "5. Visualization" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.902 + ], + "angle": 0, + "content": "We visualize the input point cloud, random masking, spatial attention cloud, 2D-guided masking, and the reconstructed 3D coordinates in Figure 6. Guided by the semantic scores from 2D pre-trained models (darker points indicate" + }, + { + "type": "image", + "bbox": [ + 0.511, + 0.094, + 0.878, + 0.341 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.357, + 0.892, + 0.4 + ], + "angle": 0, + "content": "Figure 6. Visualization of I2P-MAE. Guided by the spatial attention cloud, I2P-MAE's masking (the \\(4^{th}\\) column) preserves more semantically important 3D structures than random masking." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.426, + 0.892, + 0.502 + ], + "angle": 0, + "content": "higher scores), the masked point cloud largely preserves significant parts of the 3D shape, e.g., the main body of an airplane, the grip of a guitar, the frame of a chair and telephone. By this, the 3D network can learn more discriminative features by reconstructing these visible 2D semantics." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.52, + 0.619, + 0.536 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.548, + 0.892, + 0.73 + ], + "angle": 0, + "content": "In this paper, we propose I2P-MAE, a masked point modeling framework with effective image-to-point learning schemes. We introduce two approaches to transfer the well learned 2D knowledge into 3D domains: 2D-guided masking and 2D-semantic reconstruction. Aided by the 2D guidance, I2P-MAE learns superior 3D representations and alleviates the demand for large-scale 3D data. For future work, not limited to masking and reconstruction, we will explore more sufficient image-to-point learning approaches, e.g., point token sampling and 2D-3D class-token contrast. Also, we expect our pre-trained models to benefit wider ranges of 3D tasks, e.g., 3D object detection and visual grounding." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Acknowledgement. This project is funded in part by National Key R&D Program of China Project 2022ZD0161100, by the Centre for Perceptual and Interactive Intelligence (CPII) Ltd under the Innovation and Technology Commission (ITC)'s InnoHK, by General Research Fund of Hong Kong RGC Project 14204021, by the National Natural Science Foundation of China (Grant No. 62206272), and by Shanghai Committee of Science and Technology (Grant No. 21DZ1100100). Hongsheng Li is a PI of CPII under the InnoHK." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "21776" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.185 + ], + "angle": 0, + "content": "[1] Mohamed Afham, Isuru Dissanayake, Dinithi Dissanayake, Amaya Dharmasiri, Kanchana Thilakarathna, and Ranga Rodrigo. 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In contrast, due to the expensive data processing, a paucity of 3D datasets severely hinders the learning for high-quality 3D features. In this paper, we propose an alternative to obtain superior 3D representations from 2D pre-trained models via Image-to-Point Masked Autoencoders, named as I2P-MAE. By self-supervised pre-training, we leverage the well learned 2D knowledge to guide 3D masked autoencoding, which reconstructs the masked point tokens with an encoder-decoder architecture. Specifically, we first utilize off-the-shelf 2D models to extract the multi-view visual features of the input point cloud, and then conduct two types of image-to-point learning schemes. For one, we introduce a 2D-guided masking strategy that maintains semantically important point tokens to be visible. Compared to random masking, the network can better concentrate on significant 3D structures with key spatial cues. For another, we enforce these visible tokens to reconstruct multi-view 2D features after the decoder. This enables the network to effectively inherit high-level 2D semantics for discriminative 3D modeling. Aided by our image-to-point pre-training, the frozen I2P-MAE, without any fine-tuning, achieves $93.4\%$ accuracy for linear SVM on ModelNet40, competitive to existing fully trained methods. By further fine-tuning on on ScanObjectNN's hardest split, I2P-MAE attains the state-of-the-art $90.11\%$ accuracy, $+3.68\%$ to the second-best, demonstrating superior transferable capacity. Code is available at https://github.com/ZrrSkywalker/I2P-MAE. + +# 1. Introduction + +Driven by huge volumes of image data [11, 40, 56, 61], pre-training for better visual representations has gained + +![](images/207059056250d47aaabecdf9ef65e3a78f5923ac46dfb4ee7626a4eab659e041.jpg) +Figure 1. Image-to-Point Masked Autoencoders. We leverage the 2D pre-trained models to guide the MAE pre-training in 3D, which alleviates the need of large-scale 3D datasets and learns from 2D knowledge for superior 3D representations. + +much attention in computer vision, which benefits a variety of downstream tasks [8, 29, 39, 55, 62]. Besides supervised pre-training with labels, many researches develop advanced self-supervised approaches to fully utilize raw image data via pre-text tasks, e.g., image-image contrast [5, 9, 10, 21, 28], language-image contrast [12, 53], and masked image modeling [3, 4, 18, 19, 27, 31, 42, 70]. Given the popularity of 2D pre-trained models, it is still absent for large-scale 3D datasets in the community, attributed to the expensive data acquisition and labor-intensive annotation. The widely adopted ShapeNet [6] only contains $50\mathrm{k}$ point clouds of 55 object categories, far less than the 14 million ImageNet [11] and 400 million image-text pairs [53] in 2D vision. Though there have been attempts to extract self-supervisory signals for 3D pre-training [33, 41, 47, 64, 69, 76, 78, 83], raw point clouds with sparse structural patterns cannot provide suf + +![](images/3afe659521215fa9ad7bcd3257ee8a83c220e396192398ebe31ba7ae3caf96ec.jpg) +Figure 2. Comparison of (Left) Existing Methods [47, 78] and (Right) our I2P-MAE. On top of the general 3D MAE architecture, I2P-MAE introduces two schemes of image-to-point learning: 2D-guided masking and 2D-semantic reconstruction. + +![](images/d854ae3aef966742b261f2bae65e2fcf679e2604a0105b0cf9b95393b9ff3e85.jpg) + +ficient and diversified semantics compared to colorful images, which constrain the generalization capacity of pretraining. Considering the homology of images and point clouds, both of which depict certain visual characteristics of objects and are related by 2D-3D geometric mapping, we ask the question: can off-the-shelf 2D pre-trained models help 3D representation learning by transferring robust 2D knowledge into 3D domains? + +To tackle this challenge, we propose I2P-MAE, a Masked Autoencoding framework that conducts Image-to-Point knowledge transfer for self-supervised 3D point cloud pre-training. As shown in Figure 1, aided by 2D semantics learned from abundant image data, our I2P-MAE produces high-quality 3D representations and exerts strong transferable capacity to downstream 3D tasks. Specifically, referring to 3D MAE models [47, 78] in Figure 2 (Left), we first adopt an asymmetric encoder-decoder transformer [14] as our fundamental architecture for 3D pre-training, which takes as input a randomly masked point cloud and reconstructs the masked points from the visible ones. Then, to acquire 2D semantics for the 3D shape, we bridge the modal gap by efficiently projecting the point cloud into multi-view depth maps. This requires no time-consuming offline rendering and largely preserves 3D geometries from different perspectives. On top of that, we utilize off-the-shelf 2D models to obtain the multi-view 2D features along with 2D attention maps of the point cloud, and respectively guide the pre-training from two aspects, as shown in Figure 2 (Right). + +Firstly, different from existing methods [47, 78] to randomly sample visible tokens, we introduce a 2D-guided masking strategy that reserves point tokens with more spatial semantics to be visible for the MAE encoder. In detail, we back-project the multi-view attention maps into 3D space as a spatial attention cloud. Each element in the + +![](images/c919ddf9cf0f44dc90cd561001b674234216d70377cee04db16132b28b25f2d6.jpg) +Figure 3. Pre-training Epochs vs. Linear SVM Accuracy on ModelNet40 [67]. With the image-to-point learning schemes, I2P-MAE exerts superior transferable capability with much faster convergence speed than Point-MAE [47] and Point-M2AE [78]. + +cloud indicates the semantic significance of the corresponding point token. Guided by this, the 3D network can better focus on the visible critical structures to understand the global 3D shape, and also reconstruct the masked tokens from important spatial cues. + +Secondly, in addition to the recovering of masked point tokens, we propose to concurrently reconstruct 2D semantics from the visible point tokens after the MAE decoder. For each visible token, we respectively fetch its projected 2D representations from different views, and integrate them as the 2D-semantic learning target. By simultaneously reconstructing the masked 3D coordinates and visible 2D concepts, I2P-MAE is able to learn both low-level spatial patterns and high-level semantics pre-trained in 2D domains, contributing to superior 3D representations. + +With the aforementioned image-to-point guidance, our I2P-MAE significantly accelerates the convergence speed of pre-training and exhibits state-of-the-art performance on 3D downstream tasks, as shown in Figure 3. Learning from 2D ViT [14] pre-trained by CLIP [53], I2P-MAE, without any fine-tuning, achieves $93.4\%$ classification accuracy by linear SVM on ModelNet40 [67], which has surpassed the fully fine-tuned results of Point-BERT [76] and Point-MAE [33]. After fine-tuning, I2P-MAE further achieves $90.11\%$ classification accuracy on the hardest split of ScanObjectNN [63], significantly exceeding the second-best Point-M2AE [78] by $+3.68\%$ . The experiments fully demonstrate the effectiveness of learning from pre-trained 2D models for superior 3D representations. + +Our contributions are summarized as follows: + +- We propose Image-to-Point Masked Autoencoders (I2P-MAE), a pre-training framework to leverage 2D pre-trained models for learning 3D representations. + +- We introduce two strategies, 2D-guided masking and 2D-semantic reconstruction, to effectively transfer the well learned 2D knowledge into 3D domains. +- Extensive experiments have been conducted to indicate the significance of our image-to-point pre-training. + +# 2. Related Work + +3D Point Cloud Pre-training. Supervised learning for point clouds has attained remarkable progress by delicately designed architectures [22, 50, 51, 80, 81] and local operators [2, 37, 65, 68, 72, 82]. However, such methods learned from closed-set datasets [63, 67] are limited to produce general 3D representations. Instead, self-supervised pre-training via unlabelled point clouds [6] have revealed promising transferable ability, which provides a good network initialization for downstream fine-tuning. Mainstream 3D self-supervised approaches adopt encoder-decoder architectures to recover the input point clouds from the transformed representations, including point rearrangement [57], part occlusion [64], rotation [49], downsampling [36], and codeword encoding [74]. Concurrent works also adopt contrastive pre-text tasks between 3D data pairs, such as local-global relation [17, 54], temporal frames [32], and augmented viewpoints [69]. More recent works adopt pretrained CLIP [53] for zero-shot 3D recognition [24, 79, 86], or introduce masked point modeling [13, 16, 33, 41] as strong 3D self-supervised learners. Therein, Point-BERT [76] utilizes pre-trained tokenizers to indicate discrete point tokens, while Point-MAE [47], Point-M2AE [78], and PiMAE [7] apply Masked Autoencoders (MAE) to directly reconstruct masked 3D coordinates. Our I2P-MAE also adopts MAE as the basic pre-training framework, but is guided by 2D pretrained models via image-to-point learning schemes, which benefits 3D pre-training with diverse 2D semantics. + +2D-to-3D Learning. Except for jointly training 2D-3D networks [1, 23, 38, 46, 73], only a few existing researches focus on 2D-to-3D learning, and can be categorized into two groups. To eliminate the modal gap, the first group either upgrades 2D pre-trained networks into 3D variants for processing point clouds (convolutional kernels inflation [71, 77], modality-agnostic transformer [52]), or projects 3D point clouds into 2D images with parameter-efficient tuning (multi-view adapter [79], point-to-pixel prompting [66]). Different from them, our I2P-MAE benefits from three properties. 1) Pre-training: We learn from 2D models during the pre-training stage, and then can be flexibly adapted to various 3D scenarios by fine-tuning. However, prior works are required to utilize 2D models on every different downstream task. 2) Self-supervision: I2P-MAE is pre-trained by raw point clouds in a self-supervised manner and learns more general 3D representations. In con + +trast, prior works are supervised by labelled downstream 3D data, which might constrain the diverse 2D semantics into specific 3D domains. 3) Independence: Prior works directly inherit 2D network architectures for 3D training, which is memory-consuming and not 3D extensible, while we train an independent 3D network and regard 2D models as semantic teachers. Another group of 2D-to-3D methods utilize paired real-world 2D-3D data of indoor [44] or outdoor [59] scenes, and conduct contrastive learning for knowledge transfer. Our approach also differs from them in two ways. 4) Masked Autoencoding. I2P-MAE learns 2D semantics via the MAE-style pre-training without any contrastive loss between point-pixel pairs. 5) 3D Data Only. We require no real-world image dataset during the pre-training and efficiently project the 3D shape into depth maps for 2D features extraction. + +# 3. Method + +The overall pipeline of I2P-MAE is shown in Figure 4. In Section 3.1, we first introduce I2P-MAE's basic 3D architecture for point cloud masked autoencoding without 2D guidance. Then in Section 3.2, we show the details of utilizing 2D pre-trained models to obtain visual representations from 3D point clouds. Finally in Section 3.3, we present how to conduct image-to-point knowledge transfer for 3D representation learning. + +# 3.1. Basic 3D Architecture + +As our basic framework for image-to-point learning, I2P-MAE refers to existing works [47, 78] to conduct 3D point cloud masked autoencoding, which consists of a token embedding module, an encoder-decoder transformer, and a head for reconstructing masked 3D coordinates. + +Token Embedding. Given a raw point cloud $P \in \mathbb{R}^{N \times 3}$ , we first adopt Furthest Point Sampling (FPS) to downsample the point number from $N$ to $M$ , denoted as $P^T \in \mathbb{R}^{M \times 3}$ . Then, we utilize $k$ Nearest-Neighbour ( $k$ -NN) to search the $k$ neighbors for each downsampled point, and aggregate their features via a mini-PointNet [50] to obtain $M$ point tokens. In this way, each token can represent a local spatial region and interact long-range features with others in the follow-up transformer. We formulate them as $T \in \mathbb{R}^{M \times C}$ , where $C$ denotes the feature dimension. + +Encoder-Decoder Transformer. To build the pre-text learning targets, we mask the point tokens with a high ratio, e.g., $80\%$ , and only feed the visible ones, $T_{\mathrm{vis}} \in \mathbb{R}^{M_{\mathrm{vis}} \times C}$ , into the transformer encoder, where $M_{\mathrm{vis}}$ denotes the visible token number. Each encoder block contains a self-attention layer and is pre-trained to understand the global + +![](images/fe6ba77c67b3b8b16b95eb510ca621d0cf94c1f802e41afab29e6f9f1570a845.jpg) +Figure 4. The Pipeline of I2P-MAE. Given an input point cloud, we leverage the 2D pre-trained models to generate two guidance signals from the projected depth maps: 2D attention maps and 2D visual features. We respectively conduct 2D-guided masking and 2D-semantic reconstruction to transfer the encoded 2D knowledge for 3D point cloud pre-training. + +3D shape from the remaining visible parts. After encoding, we concatenate the encoded $T_{\mathrm{vis}}^e$ with a set of shared learnable masked tokens $T_{\mathrm{mask}} \in \mathbb{R}^{M_{\mathrm{mask}} \times C}$ , and input them into a lightweight decoder, where $M_{\mathrm{mask}}$ denotes the masked token number and $M = M_{\mathrm{mask}} + M_{\mathrm{vis}}$ . In the transformer decoder, the masked tokens learn to capture informative spatial cues from visible ones and reconstruct the masked 3D coordinates. Importantly, we follow Point-M2AE [78] to modify our transformer to be a hierarchical architecture for encoding the multi-scale representations. + +3D-coordinate Reconstruction. On top of the decoded point tokens $\{T_{\mathrm{vis}}^d, T_{\mathrm{mask}}^d\}$ , we utilize $T_{\mathrm{mask}}^d$ to reconstruct 3D coordinates of the masked tokens along with their $k$ neighboring points. A reconstruction head of a single linear projection layer is adopted to predict $P_{\mathrm{mask}} \in \mathbb{R}^{M_{\mathrm{mask}} \times k \times 3}$ , the ground-truth 3D coordinates of the masked points. Then, we compute the loss by Chamfer Distance [15] and formulate it as + +$$ +\mathcal {L} _ {\mathrm {3 D}} = \frac {1}{M _ {\mathrm {m a s k}} k} \mathrm {C h a m f e r} \left(\mathrm {H} _ {\mathrm {3 D}} \left(T _ {\mathrm {m a s k}} ^ {d}\right), P _ {\mathrm {m a s k}}\right), \tag {1} +$$ + +where $\mathrm{H}_{3\mathrm{D}}(\cdot)$ denotes the head to reconstruct the masked 3D coordinates. + +# 3.2. 2D Pre-trained Representations + +We can leverage 2D models of different architectures (ResNet [30], ViT [14]) and various pre-training approaches (supervised [30, 45] and self-supervised [5, 53] ones) to assist the 3D representation learning. To align the input modality for 2D models, we project the input point cloud onto multiple image planes to create depth maps, and then encode them into multi-view 2D representations. + +Efficient Projection. To ensure the efficiency of pretraining, we simply project the input point cloud $P$ from three orthogonal views respectively along the $x, y, z$ axes. For every point, we directly omit each of its three coordinates and round down the other two to obtain the 2D location on the corresponding map. The projected pixel value is set as the omitted coordinate to reflect relative depth relations of points, which is then repeated by three times to imitate the three-channel RGB. The projection of I2PMAE is highly time-efficient and involves no offline rendering [48, 60], projective transformation [20, 79], or learnble prompting [66]. We denote the projected multi-view depth maps of $P$ as $\{I_i\}_{i=1}^3$ . + +2D Visual Features. We then utilize a 2D pre-trained model, e.g., a pre-trained ResNet or ViT, to extract multi- + +view features of the point cloud with $C$ channels, formulated as $\{F_i^{2\mathrm{D}}\}_{i = 1}^3$ , where $F_{i}\in \mathbb{R}^{H\times W\times C}$ and $H,W$ denote the feature map size. Such 2D features contain sufficient high-level semantics learned from large-scale image data. The geometric information loss during projection can also be alleviated by encoding from different views. + +2D Attention Maps. In addition to 2D features, we also acquire a semantic attention map for each view via the 2D pre-trained model. The one-channel maps indicate the semantic importance of different image regions, which we denote as $\{S_i^{2\mathrm{D}}\}_{i = 1}^3$ , where $S_{i}\in \mathbb{R}^{H\times W\times 1}$ . For ResNet, we adopt pixel-wise max pooling on $\{F_i^{2\mathrm{D}}\}_{i = 1}^3$ to reduce the feature dimension to one. For ViT, we adopt attention maps of the class token at the last transformer layer, since the attention weights to the class token reveal how much the features contribute to the final classification. + +# 3.3. Image-to-Point Learning Schemes + +On top of the 2D pre-trained representations for the point cloud, I2P-MAE's pre-training is guided by two image-top-point learning designs: 2D-guided masking before the encoder, and 2D-semantic reconstruction after the decoder. + +2D-guided Masking. The conventional masking strategy samples masked tokens randomly following a uniform distribution, which might prevent the encoder from 'seeing' important spatial characteristics and disturb the decoder by nonsignificant structures. Therefore, we leverage the 2D attention maps to guide the masking of point tokens, which samples more semantically significant 3D parts for encoding. Specifically, indexed by the coordinates of point tokens $P^T \in \mathbb{R}^{M \times 3}$ , we back-project the multi-view attention maps $\{S_i^{2\mathrm{D}}\}_{i=1}^3$ into 3D space and aggregate them as a 3D attention cloud $S^{3\mathrm{D}} \in \mathbb{R}^{M \times 1}$ . For each point in $S^{3\mathrm{D}}$ , we assign the semantic score by averaging the corresponding 2D values from multi-view attention maps as + +$$ +S ^ {\mathrm {3 D}} = \operatorname {S o f t m a x} \left(\frac {1}{3} \sum_ {i = 1} ^ {3} \operatorname {I 2 P} \left(S _ {i} ^ {\mathrm {2 D}}, P ^ {T}\right)\right), \tag {2} +$$ + +where $\mathrm{I2P}(\cdot)$ denotes the 2D-to-3D back-projection operation in Figure 5. We apply a softmax function to normalize the $M$ points within $S^{3\mathrm{D}}$ , and regard each element's magnitude as the visible probability for the corresponding point token. With this 2D semantic prior, the random masking becomes a nonuniform sampling with different probabilities for different tokens, where the tokens covering more critical 3D structures are more likely to be preserved. This boosts the representation learning of the encoder by focusing more on significant 3D geometries, and provides the masked tokens with more informative cues at the decoder for better reconstruction. + +![](images/46bef7c4e00cd3fd629790df351752c5e51eaafda49030003859674be2e7e772.jpg) +Figure 5. Image-to-Point Operation (I2P). Indexed by 3D point coordinates, the corresponding multi-view 2D representations are back-projected into 3D space for aggregation. + +2D-semantic Reconstruction. The 3D-coordinate reconstruction of masked point tokens enables the network to explore low-level 3D patterns. On top of that, we further enforce the visible point tokens, $T_{\mathrm{vis}}^d$ , to reconstruct the extracted 2D semantics from different views, which effectively transfers the 2D pre-trained knowledge into 3D pre-training. To obtain the 2D-semantic targets, we utilize the coordinates of visible point tokens $P_{\mathrm{vis}}^T \in \mathbb{R}^{M_{\mathrm{vis}} \times 3}$ as indices to aggregate corresponding 2D features from $\{F_i^{2\mathrm{D}}\}_{i=1}^3$ by channel-wise concatenation, formulated as + +$$ +F _ {\text {v i s}} ^ {\mathrm {3 D}} = \operatorname {C o n c a t} \left\{\mathrm {I 2 P} \left(F _ {i} ^ {\mathrm {2 D}}, P _ {\text {v i s}} ^ {T}\right) \right\} _ {i = 1} ^ {3}, \tag {3} +$$ + +where $F_{\mathrm{vis}}^{3\mathrm{D}} \in \mathbb{R}^{M_{\mathrm{vis}} \times 3C}$ . As the multi-view depth maps depict a 3D shape from different perspectives, the concatenation between multi-view 2D features can better integrate the rich semantics inherited from 2D pre-trained models. Then, we also adopt a reconstruction head of a single linear projection layer for $T_{\mathrm{vis}}^d$ , and compute the $l_2$ loss as + +$$ +\mathcal {L} _ {\mathrm {2 D}} = \frac {1}{M _ {\mathrm {v i s}}} \left(\mathrm {H} _ {\mathrm {2 D}} \left(T _ {\mathrm {v i s}} ^ {d}\right) - F _ {\mathrm {v i s}} ^ {\mathrm {3 D}}\right) ^ {2}, \tag {4} +$$ + +where $\mathrm{H}_{2\mathrm{D}}(\cdot)$ denotes the head to reconstruct visible 2D semantics, parallel to $\mathrm{H}_{3\mathrm{D}}(\cdot)$ for masked 3D coordinates. The final pre-training loss of our I2P-MAE is then formulated as $\mathcal{L}_{\mathrm{I2P}} = \mathcal{L}_{\mathrm{3D}} + \mathcal{L}_{\mathrm{2D}}$ . With such image-to-point feature learning, I2P-MAE not only encodes low-level spatial variations from 3D coordinates, but also explores high-level semantic knowledge from 2D representations. As the 2D-guided masking has preserved visible tokens with more spatial significance, the 2D-semantic reconstruction upon them further benefits I2P-MAE to learn more discriminative 3D representations. + +
MethodModelNet40OBJ-BG
SO-Net [35]87.3-
FoldingNet [74]88.4-
VIP-GAN [26]90.2-
DGCNN + Jigsaw [58]90.659.5
DGCNN + OcCo [64]90.778.3
DGCNN + CrossPoint [1]91.281.7
Transformer + OcCo [76]89.6-
Point-BERT [76]87.4-
Point-MAE [47]91.077.7
3D-OAE [85]92.3-
Point-M2AE [78]92.984.1
I2P-MAE93.487.1
Improvement+0.5+3.0
+ +# 4. Experiments + +In Section 4.1, we first introduce our pre-training settings and the linear SVM classification performance without fine-tuning. Then in Section 4.2, we present the results by fully fine-tuning I2P-MAE on various 3D downstream tasks. Finally in Section 4.3, we conduct ablation studies to investigate the characteristics of I2P-MAE. + +# 4.1. Image-to-Point Pre-training + +Settings. We adopt the popular ShapeNet [6] for self-supervised 3D pre-training, which contains 57,448 synthetic point clouds with 55 object categories. For fair comparison, we follow the same MAE transformer architecture as Point-M2AE [78]: a 3-stage encoder with 5 blocks per stage, a 2-stage decoder with 1 block per stage, 2,048 input point number $(N)$ , 512 downsampled number $(M)$ , 16 nearest neighbors $(k)$ , 384 feature channels $(C)$ , and the mask ratio of $80\%$ . For off-the-shelf 2D models, we utilize ViT-Base [14] pre-trained by CLIP [53] as default and keep its weights frozen during 3D pre-training. We project the point cloud into three $224 \times 224$ depth maps, and obtain the 2D feature size $H \times W$ of $14 \times 14$ . I2P-MAE is pre-trained for 300 epochs with a batch size 64 and learning rate $10^{-3}$ . We adopt AdamW [34] optimizer with a weight decay $5 \times 10^{-2}$ and the cosine scheduler with 10-epoch warm-up. + +Linear SVM. To evaluate the transfer capacity, we directly utilize the features extracted by I2P-MAE's encoder for linear SVM on the synthetic ModelNet40 [67] and real-world ScanObjectNN [63] without any fine-tuning or voting. As shown in Table 1, for 3D shape classification in + +Table 1. Linear SVM Classification on ModelNet40 [67] and ScanObjectNN [63]. We compare the accuracy (\%) of existing self-supervised methods, and the second-best one is underlined. We adopt the OBJ-BG split for ScanObjectNN following [1]. + +
MethodOBJ-BGOBJ-ONLYPB-T50-RS
PointNet [50]73.379.268.0
PointNet++ [51]82.384.377.9
PointCNN [37]86.185.578.5
MVTN [25]--82.8
PointMLP [2]--85.2
Transformer [76]79.8680.5577.24
[P] Point-BERT [76]87.4388.1283.07
[P] 3D-OAE [85]89.1688.6483.17
[P] MaskPoint [41]89.3088.1084.30
[P] Point-MAE [47]90.0288.2985.18
[P] MAE3D [33]--86.20
[P] Point-M2AE [78]91.2288.8186.43
[P] I2P-MAE94.1591.5790.11
Improvement+2.93+2.76+3.68
+ +Table 2. Real-world 3D Classification on ScanObjectNN [63]. We report the accuracy $(\%)$ on the official three splits of ScanObjectNN. [P] denotes to fine-tune the models after self-supervised pre-training. + +both domains, I2P-MAE shows superior performance and exceeds the second-best respectively by $+0.5\%$ and $+3.0\%$ accuracy. Our SVM results $(93.4\%, 87.1\%)$ can even surpass some existing methods after full downstream training in Table 2 and 3, e.g., PointCNN [37] $(92.2\%, 86.1\%)$ , Transformer [76] $(91.4\%, 79.86\%)$ , and Point-BERT [76] $(92.7\%, 87.43\%)$ . In addition, guided by the 2D pre-trained models, I2P-MAE exhibits much faster pre-training convergence than Point-MAE [47] and Point-M2AE in Figure 3. Therefore, the SVM performance of I2P-MAE demonstrates its learned high-quality 3D representations and the significance of our image-to-point learning schemes. + +# 4.2. Downstream Tasks + +After pre-training, I2P-MAE is fine-tuned for real-world and synthetic 3D classification, and part segmentation. Except ModelNet40 [67], we do not use the voting strategy [43] for evaluation. + +Real-world 3D Classification. The challenging ScanObjectNN [63] consists of 11,416 training and 2,882 test 3D shapes, which are scanned from the real-world scenes and thus include backgrounds with noises. As shown in Table 2, our I2P-MAE exerts great advantages over other self-supervised methods, surpassing the second-best by $+2.93\%$ , $+2.76\%$ , and $+3.68\%$ respectively for the three splits. This is also the first model reaching $90\%$ accuracy on the hardest PB-T50-RS spilt. As the pre-training point clouds [6] are synthetic 3D shapes with a large domain gap with the real-world ScanobjectNN, the results well indicate the universality of I2P-MAE inherited from the 2D pre-trained models. + +
MethodPointsNo VotingVoting
PointNet [50]1k89.2-
PointNet++ [51]1k90.7-
PointCNN [37]1k92.2-
Point Transformer [84]-93.7
Transformer [76]1k91.4-
[P] Point-BERT [76]1k92.793.2
[P] 3D-OAE [85]1k-93.4
[P] Point-MAE [47]1k93.293.8
Point-MAE8k-94.0
[P] Point-M2AE [78]1k93.494.0
[P] I2P-MAE-SVM1k93.4-
I2P-MAE1k93.794.1
+ +Synthetic 3D Classification. The widely adopted ModelNet40 [67] contains 9,843 training and 2,468 test 3D point clouds, which are sampled from the synthetic CAD models of 40 categories. We report the classification accuracy of existing methods before and after the voting in Table 3. As shown, our I2P-MAE achieves leading performance for both settings with only 1k input point number. For linear SVM without any fine-tuning, I2P-MAE-SVM can already attain $93.4\%$ accuracy and exceed most previous works, indicating the powerful transfer ability. By fine-tuning the entire network, the accuracy can be further boosted by $+0.3\%$ accuracy, and achieve $94.1\%$ after the offline voting. + +Part Segmentation. The synthetic ShapeNetPart [75] is selected from ShapeNet [6] with 16 object categories and 50 part categories, which contains 14,007 and 2,874 samples for training and validation. We utilize the same segmentation head after the pre-trained encoder as previous works [47, 78] for fair comparison. The head only conducts simple upsampling for point tokens at different stages and concatenates them alone the feature dimension as the output. Two types of mean IoU scores, $\mathrm{mIoU}_C$ and $\mathrm{mIoU}_I$ are reported in Table 4. For such highly saturated benchmark, I2P-MAE can still exert leading performance guided by the well learned 2D knowledge, e.g., $+0.29\%$ and $+0.25\%$ higher than Point-M2AE concerning the two metrics. This demonstrates that the 2D guidance also benefits the understanding for fine-grained point-wise 3D patterns. + +# 4.3. Ablation Study + +In this section, we explore the effectiveness of different characteristics in I2P-MAE. We utilize our final solution as the baseline and report the linear SVM accuracy $(\%)$ . + +Table 3. Synthetic 3D Classification on ModelNet40 [67]. We report the accuracy $(\%)$ before and after the voting [43]. [P] denotes to fine-tune the models after self-supervised pre-training. + +
MethodmIoUCmIoUI
PointNet [50]80.3983.70
PointNet++ [51]81.8585.10
DGCNN [65]82.3385.20
PointMLP [2]84.6086.10
Transformer [76]83.4285.10
[P] Transformer + OcCo [76]83.4285.10
[P] Point-BERT [76]84.1185.60
[P] 3D-OAE [85]-85.70
[P] MaskPoint [41]84.4086.00
[P] Point-MAE [47]-86.10
[P] Point-M2AE [78]84.8686.51
[P] I2P-MAE85.1586.76
+ +Table 4. Part Segmentation on ShapeNetPart [75]. We report the average IoU scores $(\%)$ for part categories and instances, respectively denoted as $\mathrm{mIoU}_C$ and $\mathrm{mIoU}_I$ . + +
Method20%40%60%80%100%
Point-MAE [47]89.490.290.390.591.0
Point-M2AE [78]90.892.092.192.492.9
I2P-MAE92.192.793.193.193.4
Improvement+1.3+0.7+1.0+0.7+0.5
+ +Table 5. Pre-training with Limited 3D Data. We utilize randomly sampled 3D data from ShapeNet [6] for pre-training. + +Pre-training with Limited 3D Data. In Table 5, we randomly sample the pre-training dataset, ShapeNet [6], with different ratios, and evaluate the performance of I2P-MAE when 3D data is further deficient. Aided by 2D pre-trained models, I2P-MAE still achieves competitive downstream accuracy in low-data regimes, especially for $20\%$ and $60\%$ , which outperforms Point-M2AE [78] by $+1.3\%$ and $+1.0$ , respectively. Importantly, with only $60\%$ of the pre-training, I2P-MAE $(93.1\%)$ outperforms Point-MAE $(91.0\%)$ and Point-M2AE $(92.9\%)$ with full training data. This indicates that our image-to-point learning scheme effectively can alleviate the need for large-scale 3D training datasets. + +2D-guided Masking. In Table 6, we experiment different masking strategies for I2P-MAE. The first row represents 2D-guided masking, which preserves more semantically important tokens to be visible for the encoder. Compared to the second-row random masking, the guidance of 2D attention maps contributes to $+0.4\%$ and $+0.9\%$ accuracy on two datasets. Then, we reverse the token scores in the spatial attention cloud, and instead mask the most important tokens. As shown in the third row, the results are largely harmed, demonstrating the significance of encoding + +
2D-guidedVisibleRatioModelNet40OBJ-BG
✓Important0.893.487.1
-Random0.893.086.2
✓Unimportant0.892.884.5
✓Important0.792.583.8
✓Important0.992.885.6
+ +Table 6. 2D-guided Masking. 'Visible' denotes whether the preserved visible point tokens are more semantically important than the masked ones. 'Ratio' denotes the masking ratio. + +
TokensTargetsModelNet40OBJ-BG
MaskedVisible3D2D
✓✓MV93.487.1
✓-M-92.984.7
-✓-V91.980.2
✓--M91.277.8
✓-MM92.684.9
+ +Table 7. 2D-semantic Reconstruction. We utilize 'M' and 'V' to denote the reconstruction targets of masked and visible tokens. '3D' and '2D' denote 3D coordinates and 2D semantics. + +critical 3D structures. Finally, we modify the masking ratio by $\pm 0.1$ , which controls the proportion between visible and masked tokens. The performance decay indicates that, the 2D-semantic and 3D-coordinate reconstruction are required to be well balanced for a properly challenging pre-text task. + +2D-semantic Reconstruction. In Table 7, we investigate which groups of tokens are the best for learning 2D semantic targets. The comparison of the first two rows reveals the effectiveness of reconstructing 2D semantics from visible tokens, i.e., $+0.5\%$ and $+2.4\%$ classification accuracy. By only using 2D targets for either the visible or masked tokens (the $3^{\mathrm{rd}}$ and $4^{\mathrm{th}}$ rows), we verify that the 3D-coordinate reconstruction still plays an important role in I2P-MAE, which learns low-level geometric 3D patterns and provides complementary knowledge to the high-level 2D semantics. However, if the 3D and 2D targets are both reconstructed from the masked tokens (the last row), the network is restricted to learn 2D knowledge from the masked nonsignificant 3D geometries, other than the more discriminative parts. Also, assigning two targets on the same tokens might cause 2D-3D semantic conflicts. Therefore, the two targets are best to be reconstructed separately. + +# 5. Visualization + +We visualize the input point cloud, random masking, spatial attention cloud, 2D-guided masking, and the reconstructed 3D coordinates in Figure 6. Guided by the semantic scores from 2D pre-trained models (darker points indicate + +![](images/f57a1df68264115a3bd36467fd1894872eeb4d82779256ba9ff5acde56dfe166.jpg) +Figure 6. Visualization of I2P-MAE. Guided by the spatial attention cloud, I2P-MAE's masking (the $4^{th}$ column) preserves more semantically important 3D structures than random masking. + +higher scores), the masked point cloud largely preserves significant parts of the 3D shape, e.g., the main body of an airplane, the grip of a guitar, the frame of a chair and telephone. By this, the 3D network can learn more discriminative features by reconstructing these visible 2D semantics. + +# 6. Conclusion + +In this paper, we propose I2P-MAE, a masked point modeling framework with effective image-to-point learning schemes. We introduce two approaches to transfer the well learned 2D knowledge into 3D domains: 2D-guided masking and 2D-semantic reconstruction. Aided by the 2D guidance, I2P-MAE learns superior 3D representations and alleviates the demand for large-scale 3D data. For future work, not limited to masking and reconstruction, we will explore more sufficient image-to-point learning approaches, e.g., point token sampling and 2D-3D class-token contrast. Also, we expect our pre-trained models to benefit wider ranges of 3D tasks, e.g., 3D object detection and visual grounding. + +Acknowledgement. This project is funded in part by National Key R&D Program of China Project 2022ZD0161100, by the Centre for Perceptual and Interactive Intelligence (CPII) Ltd under the Innovation and Technology Commission (ITC)'s InnoHK, by General Research Fund of Hong Kong RGC Project 14204021, by the National Natural Science Foundation of China (Grant No. 62206272), and by Shanghai Committee of Science and Technology (Grant No. 21DZ1100100). 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Pointclip v2: Adapting clip for powerful 3d open-world learning. arXiv preprint arXiv:2211.11682, 2022. 3 \ No newline at end of file diff --git a/2023/Learning 3D Representations From 2D Pre-Trained Models via Image-to-Point Masked Autoencoders/images.zip b/2023/Learning 3D Representations From 2D Pre-Trained Models via Image-to-Point Masked Autoencoders/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..95f9ee1ac109134f957c97e78b4f6d83c9abd667 --- /dev/null +++ b/2023/Learning 3D Representations From 2D Pre-Trained Models via Image-to-Point Masked Autoencoders/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:28ab6d87640e3d6130700affe21ed65861fdf9e1b015f710cf3ac6f7ddfa4930 +size 474678 diff --git a/2023/Learning 3D Representations From 2D Pre-Trained Models via Image-to-Point Masked Autoencoders/layout.json b/2023/Learning 3D Representations From 2D Pre-Trained Models via Image-to-Point Masked Autoencoders/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..385bec69ba3b5d3f56eb34b48bc5fcc9bebc597f --- /dev/null +++ b/2023/Learning 3D Representations From 2D Pre-Trained Models via Image-to-Point Masked Autoencoders/layout.json @@ -0,0 +1,9444 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 106, + 103, + 488, + 138 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 103, + 488, + 138 + ], + "spans": [ + { + "bbox": [ + 106, + 103, + 488, + 138 + ], + "type": "text", + "content": "Learning 3D Representations from 2D Pre-trained Models via Image-to-Point Masked Autoencoders" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 121, + 154, + 473, + 171 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 121, + 154, + 473, + 171 + ], + "spans": [ + { + "bbox": [ + 121, + 154, + 473, + 171 + ], + "type": "text", + "content": "Renrui Zhang" + }, + { + "bbox": [ + 121, + 154, + 473, + 171 + ], + "type": "inline_equation", + "content": "^{1,2}" + }, + { + "bbox": [ + 121, + 154, + 473, + 171 + ], + "type": "text", + "content": ", Liuhui Wang" + }, + { + "bbox": [ + 121, + 154, + 473, + 171 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 121, + 154, + 473, + 171 + ], + "type": "text", + "content": ", Yu Qiao" + }, + { + "bbox": [ + 121, + 154, + 473, + 171 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 121, + 154, + 473, + 171 + ], + "type": "text", + "content": ", Peng Gao" + }, + { + "bbox": [ + 121, + 154, + 473, + 171 + ], + "type": "inline_equation", + "content": "^{\\dagger 1}" + }, + { + "bbox": [ + 121, + 154, + 473, + 171 + ], + "type": "text", + "content": ", Hongsheng Li" + }, + { + "bbox": [ + 121, + 154, + 473, + 171 + ], + "type": "inline_equation", + "content": "^{2,4}" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 189, + 177, + 403, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 189, + 177, + 403, + 191 + ], + "spans": [ + { + "bbox": [ + 189, + 177, + 403, + 191 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 189, + 177, + 403, + 191 + ], + "type": "text", + "content": "Shanghai Artificial Intelligence Laboratory" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 191, + 450, + 205 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 191, + 450, + 205 + ], + "spans": [ + { + "bbox": [ + 143, + 191, + 450, + 205 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 143, + 191, + 450, + 205 + ], + "type": "text", + "content": "CUHK MMLab " + }, + { + "bbox": [ + 143, + 191, + 450, + 205 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 143, + 191, + 450, + 205 + ], + "type": "text", + "content": "Peking University " + }, + { + "bbox": [ + 143, + 191, + 450, + 205 + ], + "type": "inline_equation", + "content": "^{4}" + }, + { + "bbox": [ + 143, + 191, + 450, + 205 + ], + "type": "text", + "content": "CPII under InnoHK" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 94, + 207, + 496, + 221 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 94, + 207, + 496, + 221 + ], + "spans": [ + { + "bbox": [ + 94, + 207, + 496, + 221 + ], + "type": "text", + "content": "{zhangrenrui, gaopeng}@pjlab.org.cn, hsli@ee.cuhk.edu.cn" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 143, + 256, + 192, + 269 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 256, + 192, + 269 + ], + "spans": [ + { + "bbox": [ + 143, + 256, + 192, + 269 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 280, + 290, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 280, + 290, + 628 + ], + "spans": [ + { + "bbox": [ + 47, + 280, + 290, + 628 + ], + "type": "text", + "content": "Pre-training by numerous image data has become a facto for robust 2D representations. In contrast, due to the expensive data processing, a paucity of 3D datasets severely hinders the learning for high-quality 3D features. In this paper, we propose an alternative to obtain superior 3D representations from 2D pre-trained models via Image-to-Point Masked Autoencoders, named as I2P-MAE. By self-supervised pre-training, we leverage the well learned 2D knowledge to guide 3D masked autoencoding, which reconstructs the masked point tokens with an encoder-decoder architecture. Specifically, we first utilize off-the-shelf 2D models to extract the multi-view visual features of the input point cloud, and then conduct two types of image-to-point learning schemes. For one, we introduce a 2D-guided masking strategy that maintains semantically important point tokens to be visible. Compared to random masking, the network can better concentrate on significant 3D structures with key spatial cues. For another, we enforce these visible tokens to reconstruct multi-view 2D features after the decoder. This enables the network to effectively inherit high-level 2D semantics for discriminative 3D modeling. Aided by our image-to-point pre-training, the frozen I2P-MAE, without any fine-tuning, achieves " + }, + { + "bbox": [ + 47, + 280, + 290, + 628 + ], + "type": "inline_equation", + "content": "93.4\\%" + }, + { + "bbox": [ + 47, + 280, + 290, + 628 + ], + "type": "text", + "content": " accuracy for linear SVM on ModelNet40, competitive to existing fully trained methods. By further fine-tuning on on ScanObjectNN's hardest split, I2P-MAE attains the state-of-the-art " + }, + { + "bbox": [ + 47, + 280, + 290, + 628 + ], + "type": "inline_equation", + "content": "90.11\\%" + }, + { + "bbox": [ + 47, + 280, + 290, + 628 + ], + "type": "text", + "content": " accuracy, " + }, + { + "bbox": [ + 47, + 280, + 290, + 628 + ], + "type": "inline_equation", + "content": "+3.68\\%" + }, + { + "bbox": [ + 47, + 280, + 290, + 628 + ], + "type": "text", + "content": " to the second-best, demonstrating superior transferable capacity. Code is available at https://github.com/ZrrSkywalker/I2P-MAE." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 48, + 650, + 128, + 662 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 650, + 128, + 662 + ], + "spans": [ + { + "bbox": [ + 48, + 650, + 128, + 662 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 670, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 670, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 47, + 670, + 287, + 696 + ], + "type": "text", + "content": "Driven by huge volumes of image data [11, 40, 56, 61], pre-training for better visual representations has gained" + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 308, + 258, + 544, + 439 + ], + "blocks": [ + { + "bbox": [ + 308, + 258, + 544, + 439 + ], + "lines": [ + { + "bbox": [ + 308, + 258, + 544, + 439 + ], + "spans": [ + { + "bbox": [ + 308, + 258, + 544, + 439 + ], + "type": "image", + "image_path": "207059056250d47aaabecdf9ef65e3a78f5923ac46dfb4ee7626a4eab659e041.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 452, + 545, + 496 + ], + "lines": [ + { + "bbox": [ + 305, + 452, + 545, + 496 + ], + "spans": [ + { + "bbox": [ + 305, + 452, + 545, + 496 + ], + "type": "text", + "content": "Figure 1. Image-to-Point Masked Autoencoders. We leverage the 2D pre-trained models to guide the MAE pre-training in 3D, which alleviates the need of large-scale 3D datasets and learns from 2D knowledge for superior 3D representations." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 522, + 546, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 522, + 546, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 522, + 546, + 715 + ], + "type": "text", + "content": "much attention in computer vision, which benefits a variety of downstream tasks [8, 29, 39, 55, 62]. Besides supervised pre-training with labels, many researches develop advanced self-supervised approaches to fully utilize raw image data via pre-text tasks, e.g., image-image contrast [5, 9, 10, 21, 28], language-image contrast [12, 53], and masked image modeling [3, 4, 18, 19, 27, 31, 42, 70]. Given the popularity of 2D pre-trained models, it is still absent for large-scale 3D datasets in the community, attributed to the expensive data acquisition and labor-intensive annotation. The widely adopted ShapeNet [6] only contains " + }, + { + "bbox": [ + 304, + 522, + 546, + 715 + ], + "type": "inline_equation", + "content": "50\\mathrm{k}" + }, + { + "bbox": [ + 304, + 522, + 546, + 715 + ], + "type": "text", + "content": " point clouds of 55 object categories, far less than the 14 million ImageNet [11] and 400 million image-text pairs [53] in 2D vision. Though there have been attempts to extract self-supervisory signals for 3D pre-training [33, 41, 47, 64, 69, 76, 78, 83], raw point clouds with sparse structural patterns cannot provide suf" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 62, + 703, + 140, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 703, + 140, + 713 + ], + "spans": [ + { + "bbox": [ + 62, + 703, + 140, + 713 + ], + "type": "text", + "content": "† Corresponding author" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "21769" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 55, + 70, + 140, + 223 + ], + "blocks": [ + { + "bbox": [ + 55, + 70, + 140, + 223 + ], + "lines": [ + { + "bbox": [ + 55, + 70, + 140, + 223 + ], + "spans": [ + { + "bbox": [ + 55, + 70, + 140, + 223 + ], + "type": "image", + "image_path": "3afe659521215fa9ad7bcd3257ee8a83c220e396192398ebe31ba7ae3caf96ec.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 231, + 288, + 277 + ], + "lines": [ + { + "bbox": [ + 46, + 231, + 288, + 277 + ], + "spans": [ + { + "bbox": [ + 46, + 231, + 288, + 277 + ], + "type": "text", + "content": "Figure 2. Comparison of (Left) Existing Methods [47, 78] and (Right) our I2P-MAE. On top of the general 3D MAE architecture, I2P-MAE introduces two schemes of image-to-point learning: 2D-guided masking and 2D-semantic reconstruction." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 154, + 69, + 278, + 222 + ], + "blocks": [ + { + "bbox": [ + 154, + 69, + 278, + 222 + ], + "lines": [ + { + "bbox": [ + 154, + 69, + 278, + 222 + ], + "spans": [ + { + "bbox": [ + 154, + 69, + 278, + 222 + ], + "type": "image", + "image_path": "d854ae3aef966742b261f2bae65e2fcf679e2604a0105b0cf9b95393b9ff3e85.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 301, + 287, + 397 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 301, + 287, + 397 + ], + "spans": [ + { + "bbox": [ + 46, + 301, + 287, + 397 + ], + "type": "text", + "content": "ficient and diversified semantics compared to colorful images, which constrain the generalization capacity of pretraining. Considering the homology of images and point clouds, both of which depict certain visual characteristics of objects and are related by 2D-3D geometric mapping, we ask the question: can off-the-shelf 2D pre-trained models help 3D representation learning by transferring robust 2D knowledge into 3D domains?" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 400, + 287, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 400, + 287, + 640 + ], + "spans": [ + { + "bbox": [ + 46, + 400, + 287, + 640 + ], + "type": "text", + "content": "To tackle this challenge, we propose I2P-MAE, a Masked Autoencoding framework that conducts Image-to-Point knowledge transfer for self-supervised 3D point cloud pre-training. As shown in Figure 1, aided by 2D semantics learned from abundant image data, our I2P-MAE produces high-quality 3D representations and exerts strong transferable capacity to downstream 3D tasks. Specifically, referring to 3D MAE models [47, 78] in Figure 2 (Left), we first adopt an asymmetric encoder-decoder transformer [14] as our fundamental architecture for 3D pre-training, which takes as input a randomly masked point cloud and reconstructs the masked points from the visible ones. Then, to acquire 2D semantics for the 3D shape, we bridge the modal gap by efficiently projecting the point cloud into multi-view depth maps. This requires no time-consuming offline rendering and largely preserves 3D geometries from different perspectives. On top of that, we utilize off-the-shelf 2D models to obtain the multi-view 2D features along with 2D attention maps of the point cloud, and respectively guide the pre-training from two aspects, as shown in Figure 2 (Right)." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 642, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 288, + 715 + ], + "type": "text", + "content": "Firstly, different from existing methods [47, 78] to randomly sample visible tokens, we introduce a 2D-guided masking strategy that reserves point tokens with more spatial semantics to be visible for the MAE encoder. In detail, we back-project the multi-view attention maps into 3D space as a spatial attention cloud. Each element in the" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 322, + 68, + 531, + 225 + ], + "blocks": [ + { + "bbox": [ + 322, + 68, + 531, + 225 + ], + "lines": [ + { + "bbox": [ + 322, + 68, + 531, + 225 + ], + "spans": [ + { + "bbox": [ + 322, + 68, + 531, + 225 + ], + "type": "image", + "image_path": "c919ddf9cf0f44dc90cd561001b674234216d70377cee04db16132b28b25f2d6.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 231, + 545, + 277 + ], + "lines": [ + { + "bbox": [ + 305, + 231, + 545, + 277 + ], + "spans": [ + { + "bbox": [ + 305, + 231, + 545, + 277 + ], + "type": "text", + "content": "Figure 3. Pre-training Epochs vs. Linear SVM Accuracy on ModelNet40 [67]. With the image-to-point learning schemes, I2P-MAE exerts superior transferable capability with much faster convergence speed than Point-MAE [47] and Point-M2AE [78]." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 301, + 545, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 301, + 545, + 361 + ], + "spans": [ + { + "bbox": [ + 304, + 301, + 545, + 361 + ], + "type": "text", + "content": "cloud indicates the semantic significance of the corresponding point token. Guided by this, the 3D network can better focus on the visible critical structures to understand the global 3D shape, and also reconstruct the masked tokens from important spatial cues." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 363, + 546, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 363, + 546, + 483 + ], + "spans": [ + { + "bbox": [ + 304, + 363, + 546, + 483 + ], + "type": "text", + "content": "Secondly, in addition to the recovering of masked point tokens, we propose to concurrently reconstruct 2D semantics from the visible point tokens after the MAE decoder. For each visible token, we respectively fetch its projected 2D representations from different views, and integrate them as the 2D-semantic learning target. By simultaneously reconstructing the masked 3D coordinates and visible 2D concepts, I2P-MAE is able to learn both low-level spatial patterns and high-level semantics pre-trained in 2D domains, contributing to superior 3D representations." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 484, + 547, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 484, + 547, + 652 + ], + "spans": [ + { + "bbox": [ + 304, + 484, + 547, + 652 + ], + "type": "text", + "content": "With the aforementioned image-to-point guidance, our I2P-MAE significantly accelerates the convergence speed of pre-training and exhibits state-of-the-art performance on 3D downstream tasks, as shown in Figure 3. Learning from 2D ViT [14] pre-trained by CLIP [53], I2P-MAE, without any fine-tuning, achieves " + }, + { + "bbox": [ + 304, + 484, + 547, + 652 + ], + "type": "inline_equation", + "content": "93.4\\%" + }, + { + "bbox": [ + 304, + 484, + 547, + 652 + ], + "type": "text", + "content": " classification accuracy by linear SVM on ModelNet40 [67], which has surpassed the fully fine-tuned results of Point-BERT [76] and Point-MAE [33]. After fine-tuning, I2P-MAE further achieves " + }, + { + "bbox": [ + 304, + 484, + 547, + 652 + ], + "type": "inline_equation", + "content": "90.11\\%" + }, + { + "bbox": [ + 304, + 484, + 547, + 652 + ], + "type": "text", + "content": " classification accuracy on the hardest split of ScanObjectNN [63], significantly exceeding the second-best Point-M2AE [78] by " + }, + { + "bbox": [ + 304, + 484, + 547, + 652 + ], + "type": "inline_equation", + "content": "+3.68\\%" + }, + { + "bbox": [ + 304, + 484, + 547, + 652 + ], + "type": "text", + "content": ". The experiments fully demonstrate the effectiveness of learning from pre-trained 2D models for superior 3D representations." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 317, + 653, + 503, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 653, + 503, + 665 + ], + "spans": [ + { + "bbox": [ + 317, + 653, + 503, + 665 + ], + "type": "text", + "content": "Our contributions are summarized as follows:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 317, + 677, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 677, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 317, + 677, + 547, + 715 + ], + "type": "text", + "content": "- We propose Image-to-Point Masked Autoencoders (I2P-MAE), a pre-training framework to leverage 2D pre-trained models for learning 3D representations." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "21770" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 59, + 72, + 286, + 140 + ], + "type": "list", + "angle": 0, + "index": 2, + "blocks": [ + { + "bbox": [ + 59, + 72, + 286, + 107 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 72, + 286, + 107 + ], + "spans": [ + { + "bbox": [ + 59, + 72, + 286, + 107 + ], + "type": "text", + "content": "- We introduce two strategies, 2D-guided masking and 2D-semantic reconstruction, to effectively transfer the well learned 2D knowledge into 3D domains." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 59, + 117, + 286, + 140 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 117, + 286, + 140 + ], + "spans": [ + { + "bbox": [ + 59, + 117, + 286, + 140 + ], + "type": "text", + "content": "- Extensive experiments have been conducted to indicate the significance of our image-to-point pre-training." + } + ] + } + ], + "index": 1 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 152, + 133, + 164 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 152, + 133, + 164 + ], + "spans": [ + { + "bbox": [ + 47, + 152, + 133, + 164 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 172, + 289, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 172, + 289, + 495 + ], + "spans": [ + { + "bbox": [ + 47, + 172, + 289, + 495 + ], + "type": "text", + "content": "3D Point Cloud Pre-training. Supervised learning for point clouds has attained remarkable progress by delicately designed architectures [22, 50, 51, 80, 81] and local operators [2, 37, 65, 68, 72, 82]. However, such methods learned from closed-set datasets [63, 67] are limited to produce general 3D representations. Instead, self-supervised pre-training via unlabelled point clouds [6] have revealed promising transferable ability, which provides a good network initialization for downstream fine-tuning. Mainstream 3D self-supervised approaches adopt encoder-decoder architectures to recover the input point clouds from the transformed representations, including point rearrangement [57], part occlusion [64], rotation [49], downsampling [36], and codeword encoding [74]. Concurrent works also adopt contrastive pre-text tasks between 3D data pairs, such as local-global relation [17, 54], temporal frames [32], and augmented viewpoints [69]. More recent works adopt pretrained CLIP [53] for zero-shot 3D recognition [24, 79, 86], or introduce masked point modeling [13, 16, 33, 41] as strong 3D self-supervised learners. Therein, Point-BERT [76] utilizes pre-trained tokenizers to indicate discrete point tokens, while Point-MAE [47], Point-M2AE [78], and PiMAE [7] apply Masked Autoencoders (MAE) to directly reconstruct masked 3D coordinates. Our I2P-MAE also adopts MAE as the basic pre-training framework, but is guided by 2D pretrained models via image-to-point learning schemes, which benefits 3D pre-training with diverse 2D semantics." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 510, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 510, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 510, + 289, + 714 + ], + "type": "text", + "content": "2D-to-3D Learning. Except for jointly training 2D-3D networks [1, 23, 38, 46, 73], only a few existing researches focus on 2D-to-3D learning, and can be categorized into two groups. To eliminate the modal gap, the first group either upgrades 2D pre-trained networks into 3D variants for processing point clouds (convolutional kernels inflation [71, 77], modality-agnostic transformer [52]), or projects 3D point clouds into 2D images with parameter-efficient tuning (multi-view adapter [79], point-to-pixel prompting [66]). Different from them, our I2P-MAE benefits from three properties. 1) Pre-training: We learn from 2D models during the pre-training stage, and then can be flexibly adapted to various 3D scenarios by fine-tuning. However, prior works are required to utilize 2D models on every different downstream task. 2) Self-supervision: I2P-MAE is pre-trained by raw point clouds in a self-supervised manner and learns more general 3D representations. In con" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 547, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 263 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 263 + ], + "type": "text", + "content": "trast, prior works are supervised by labelled downstream 3D data, which might constrain the diverse 2D semantics into specific 3D domains. 3) Independence: Prior works directly inherit 2D network architectures for 3D training, which is memory-consuming and not 3D extensible, while we train an independent 3D network and regard 2D models as semantic teachers. Another group of 2D-to-3D methods utilize paired real-world 2D-3D data of indoor [44] or outdoor [59] scenes, and conduct contrastive learning for knowledge transfer. Our approach also differs from them in two ways. 4) Masked Autoencoding. I2P-MAE learns 2D semantics via the MAE-style pre-training without any contrastive loss between point-pixel pairs. 5) 3D Data Only. We require no real-world image dataset during the pre-training and efficiently project the 3D shape into depth maps for 2D features extraction." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 277, + 362, + 289 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 277, + 362, + 289 + ], + "spans": [ + { + "bbox": [ + 306, + 277, + 362, + 289 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 298, + 547, + 395 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 298, + 547, + 395 + ], + "spans": [ + { + "bbox": [ + 304, + 298, + 547, + 395 + ], + "type": "text", + "content": "The overall pipeline of I2P-MAE is shown in Figure 4. In Section 3.1, we first introduce I2P-MAE's basic 3D architecture for point cloud masked autoencoding without 2D guidance. Then in Section 3.2, we show the details of utilizing 2D pre-trained models to obtain visual representations from 3D point clouds. Finally in Section 3.3, we present how to conduct image-to-point knowledge transfer for 3D representation learning." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 403, + 432, + 415 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 403, + 432, + 415 + ], + "spans": [ + { + "bbox": [ + 306, + 403, + 432, + 415 + ], + "type": "text", + "content": "3.1. Basic 3D Architecture" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 423, + 547, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 423, + 547, + 483 + ], + "spans": [ + { + "bbox": [ + 304, + 423, + 547, + 483 + ], + "type": "text", + "content": "As our basic framework for image-to-point learning, I2P-MAE refers to existing works [47, 78] to conduct 3D point cloud masked autoencoding, which consists of a token embedding module, an encoder-decoder transformer, and a head for reconstructing masked 3D coordinates." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 502, + 547, + 622 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 502, + 547, + 622 + ], + "spans": [ + { + "bbox": [ + 304, + 502, + 547, + 622 + ], + "type": "text", + "content": "Token Embedding. Given a raw point cloud " + }, + { + "bbox": [ + 304, + 502, + 547, + 622 + ], + "type": "inline_equation", + "content": "P \\in \\mathbb{R}^{N \\times 3}" + }, + { + "bbox": [ + 304, + 502, + 547, + 622 + ], + "type": "text", + "content": ", we first adopt Furthest Point Sampling (FPS) to downsample the point number from " + }, + { + "bbox": [ + 304, + 502, + 547, + 622 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 502, + 547, + 622 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 502, + 547, + 622 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 502, + 547, + 622 + ], + "type": "text", + "content": ", denoted as " + }, + { + "bbox": [ + 304, + 502, + 547, + 622 + ], + "type": "inline_equation", + "content": "P^T \\in \\mathbb{R}^{M \\times 3}" + }, + { + "bbox": [ + 304, + 502, + 547, + 622 + ], + "type": "text", + "content": ". Then, we utilize " + }, + { + "bbox": [ + 304, + 502, + 547, + 622 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 502, + 547, + 622 + ], + "type": "text", + "content": " Nearest-Neighbour (" + }, + { + "bbox": [ + 304, + 502, + 547, + 622 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 502, + 547, + 622 + ], + "type": "text", + "content": "-NN) to search the " + }, + { + "bbox": [ + 304, + 502, + 547, + 622 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 502, + 547, + 622 + ], + "type": "text", + "content": " neighbors for each downsampled point, and aggregate their features via a mini-PointNet [50] to obtain " + }, + { + "bbox": [ + 304, + 502, + 547, + 622 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 502, + 547, + 622 + ], + "type": "text", + "content": " point tokens. In this way, each token can represent a local spatial region and interact long-range features with others in the follow-up transformer. We formulate them as " + }, + { + "bbox": [ + 304, + 502, + 547, + 622 + ], + "type": "inline_equation", + "content": "T \\in \\mathbb{R}^{M \\times C}" + }, + { + "bbox": [ + 304, + 502, + 547, + 622 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 502, + 547, + 622 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 304, + 502, + 547, + 622 + ], + "type": "text", + "content": " denotes the feature dimension." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "content": "Encoder-Decoder Transformer. To build the pre-text learning targets, we mask the point tokens with a high ratio, e.g., " + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "inline_equation", + "content": "80\\%" + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "content": ", and only feed the visible ones, " + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "inline_equation", + "content": "T_{\\mathrm{vis}} \\in \\mathbb{R}^{M_{\\mathrm{vis}} \\times C}" + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "content": ", into the transformer encoder, where " + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "inline_equation", + "content": "M_{\\mathrm{vis}}" + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "content": " denotes the visible token number. Each encoder block contains a self-attention layer and is pre-trained to understand the global" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21771" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 68, + 545, + 336 + ], + "blocks": [ + { + "bbox": [ + 51, + 68, + 545, + 336 + ], + "lines": [ + { + "bbox": [ + 51, + 68, + 545, + 336 + ], + "spans": [ + { + "bbox": [ + 51, + 68, + 545, + 336 + ], + "type": "image", + "image_path": "fe6ba77c67b3b8b16b95eb510ca621d0cf94c1f802e41afab29e6f9f1570a845.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 345, + 547, + 381 + ], + "lines": [ + { + "bbox": [ + 46, + 345, + 547, + 381 + ], + "spans": [ + { + "bbox": [ + 46, + 345, + 547, + 381 + ], + "type": "text", + "content": "Figure 4. The Pipeline of I2P-MAE. Given an input point cloud, we leverage the 2D pre-trained models to generate two guidance signals from the projected depth maps: 2D attention maps and 2D visual features. We respectively conduct 2D-guided masking and 2D-semantic reconstruction to transfer the encoded 2D knowledge for 3D point cloud pre-training." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 399, + 289, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 399, + 289, + 520 + ], + "spans": [ + { + "bbox": [ + 46, + 399, + 289, + 520 + ], + "type": "text", + "content": "3D shape from the remaining visible parts. After encoding, we concatenate the encoded " + }, + { + "bbox": [ + 46, + 399, + 289, + 520 + ], + "type": "inline_equation", + "content": "T_{\\mathrm{vis}}^e" + }, + { + "bbox": [ + 46, + 399, + 289, + 520 + ], + "type": "text", + "content": " with a set of shared learnable masked tokens " + }, + { + "bbox": [ + 46, + 399, + 289, + 520 + ], + "type": "inline_equation", + "content": "T_{\\mathrm{mask}} \\in \\mathbb{R}^{M_{\\mathrm{mask}} \\times C}" + }, + { + "bbox": [ + 46, + 399, + 289, + 520 + ], + "type": "text", + "content": ", and input them into a lightweight decoder, where " + }, + { + "bbox": [ + 46, + 399, + 289, + 520 + ], + "type": "inline_equation", + "content": "M_{\\mathrm{mask}}" + }, + { + "bbox": [ + 46, + 399, + 289, + 520 + ], + "type": "text", + "content": " denotes the masked token number and " + }, + { + "bbox": [ + 46, + 399, + 289, + 520 + ], + "type": "inline_equation", + "content": "M = M_{\\mathrm{mask}} + M_{\\mathrm{vis}}" + }, + { + "bbox": [ + 46, + 399, + 289, + 520 + ], + "type": "text", + "content": ". In the transformer decoder, the masked tokens learn to capture informative spatial cues from visible ones and reconstruct the masked 3D coordinates. Importantly, we follow Point-M2AE [78] to modify our transformer to be a hierarchical architecture for encoding the multi-scale representations." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 542, + 289, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 542, + 289, + 639 + ], + "spans": [ + { + "bbox": [ + 47, + 542, + 289, + 639 + ], + "type": "text", + "content": "3D-coordinate Reconstruction. On top of the decoded point tokens " + }, + { + "bbox": [ + 47, + 542, + 289, + 639 + ], + "type": "inline_equation", + "content": "\\{T_{\\mathrm{vis}}^d, T_{\\mathrm{mask}}^d\\}" + }, + { + "bbox": [ + 47, + 542, + 289, + 639 + ], + "type": "text", + "content": ", we utilize " + }, + { + "bbox": [ + 47, + 542, + 289, + 639 + ], + "type": "inline_equation", + "content": "T_{\\mathrm{mask}}^d" + }, + { + "bbox": [ + 47, + 542, + 289, + 639 + ], + "type": "text", + "content": " to reconstruct 3D coordinates of the masked tokens along with their " + }, + { + "bbox": [ + 47, + 542, + 289, + 639 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 47, + 542, + 289, + 639 + ], + "type": "text", + "content": " neighboring points. A reconstruction head of a single linear projection layer is adopted to predict " + }, + { + "bbox": [ + 47, + 542, + 289, + 639 + ], + "type": "inline_equation", + "content": "P_{\\mathrm{mask}} \\in \\mathbb{R}^{M_{\\mathrm{mask}} \\times k \\times 3}" + }, + { + "bbox": [ + 47, + 542, + 289, + 639 + ], + "type": "text", + "content": ", the ground-truth 3D coordinates of the masked points. Then, we compute the loss by Chamfer Distance [15] and formulate it as" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 61, + 651, + 287, + 677 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 651, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 61, + 651, + 287, + 677 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {3 D}} = \\frac {1}{M _ {\\mathrm {m a s k}} k} \\mathrm {C h a m f e r} \\left(\\mathrm {H} _ {\\mathrm {3 D}} \\left(T _ {\\mathrm {m a s k}} ^ {d}\\right), P _ {\\mathrm {m a s k}}\\right), \\tag {1}", + "image_path": "91f70e0941a75c3b8ed5dfda1ec8ce559ee569ff0f068d480fe52480b3187b6a.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathrm{H}_{3\\mathrm{D}}(\\cdot)" + }, + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "type": "text", + "content": " denotes the head to reconstruct the masked 3D coordinates." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 399, + 477, + 412 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 399, + 477, + 412 + ], + "spans": [ + { + "bbox": [ + 306, + 399, + 477, + 412 + ], + "type": "text", + "content": "3.2. 2D Pre-trained Representations" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 418, + 545, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 418, + 545, + 502 + ], + "spans": [ + { + "bbox": [ + 304, + 418, + 545, + 502 + ], + "type": "text", + "content": "We can leverage 2D models of different architectures (ResNet [30], ViT [14]) and various pre-training approaches (supervised [30, 45] and self-supervised [5, 53] ones) to assist the 3D representation learning. To align the input modality for 2D models, we project the input point cloud onto multiple image planes to create depth maps, and then encode them into multi-view 2D representations." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 517, + 545, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 517, + 545, + 674 + ], + "spans": [ + { + "bbox": [ + 304, + 517, + 545, + 674 + ], + "type": "text", + "content": "Efficient Projection. To ensure the efficiency of pretraining, we simply project the input point cloud " + }, + { + "bbox": [ + 304, + 517, + 545, + 674 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 304, + 517, + 545, + 674 + ], + "type": "text", + "content": " from three orthogonal views respectively along the " + }, + { + "bbox": [ + 304, + 517, + 545, + 674 + ], + "type": "inline_equation", + "content": "x, y, z" + }, + { + "bbox": [ + 304, + 517, + 545, + 674 + ], + "type": "text", + "content": " axes. For every point, we directly omit each of its three coordinates and round down the other two to obtain the 2D location on the corresponding map. The projected pixel value is set as the omitted coordinate to reflect relative depth relations of points, which is then repeated by three times to imitate the three-channel RGB. The projection of I2PMAE is highly time-efficient and involves no offline rendering [48, 60], projective transformation [20, 79], or learnble prompting [66]. We denote the projected multi-view depth maps of " + }, + { + "bbox": [ + 304, + 517, + 545, + 674 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 304, + 517, + 545, + 674 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 304, + 517, + 545, + 674 + ], + "type": "inline_equation", + "content": "\\{I_i\\}_{i=1}^3" + }, + { + "bbox": [ + 304, + 517, + 545, + 674 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "content": "2D Visual Features. We then utilize a 2D pre-trained model, e.g., a pre-trained ResNet or ViT, to extract multi-" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "21772" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "type": "text", + "content": "view features of the point cloud with " + }, + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "type": "text", + "content": " channels, formulated as " + }, + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "type": "inline_equation", + "content": "\\{F_i^{2\\mathrm{D}}\\}_{i = 1}^3" + }, + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "type": "inline_equation", + "content": "F_{i}\\in \\mathbb{R}^{H\\times W\\times C}" + }, + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "type": "inline_equation", + "content": "H,W" + }, + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "type": "text", + "content": " denote the feature map size. Such 2D features contain sufficient high-level semantics learned from large-scale image data. The geometric information loss during projection can also be alleviated by encoding from different views." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 158, + 288, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 158, + 288, + 277 + ], + "spans": [ + { + "bbox": [ + 46, + 158, + 288, + 277 + ], + "type": "text", + "content": "2D Attention Maps. In addition to 2D features, we also acquire a semantic attention map for each view via the 2D pre-trained model. The one-channel maps indicate the semantic importance of different image regions, which we denote as " + }, + { + "bbox": [ + 46, + 158, + 288, + 277 + ], + "type": "inline_equation", + "content": "\\{S_i^{2\\mathrm{D}}\\}_{i = 1}^3" + }, + { + "bbox": [ + 46, + 158, + 288, + 277 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 158, + 288, + 277 + ], + "type": "inline_equation", + "content": "S_{i}\\in \\mathbb{R}^{H\\times W\\times 1}" + }, + { + "bbox": [ + 46, + 158, + 288, + 277 + ], + "type": "text", + "content": ". For ResNet, we adopt pixel-wise max pooling on " + }, + { + "bbox": [ + 46, + 158, + 288, + 277 + ], + "type": "inline_equation", + "content": "\\{F_i^{2\\mathrm{D}}\\}_{i = 1}^3" + }, + { + "bbox": [ + 46, + 158, + 288, + 277 + ], + "type": "text", + "content": " to reduce the feature dimension to one. For ViT, we adopt attention maps of the class token at the last transformer layer, since the attention weights to the class token reveal how much the features contribute to the final classification." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 285, + 230, + 298 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 285, + 230, + 298 + ], + "spans": [ + { + "bbox": [ + 47, + 285, + 230, + 298 + ], + "type": "text", + "content": "3.3. Image-to-Point Learning Schemes" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 304, + 287, + 352 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 304, + 287, + 352 + ], + "spans": [ + { + "bbox": [ + 46, + 304, + 287, + 352 + ], + "type": "text", + "content": "On top of the 2D pre-trained representations for the point cloud, I2P-MAE's pre-training is guided by two image-top-point learning designs: 2D-guided masking before the encoder, and 2D-semantic reconstruction after the decoder." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 365, + 289, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 365, + 289, + 521 + ], + "spans": [ + { + "bbox": [ + 46, + 365, + 289, + 521 + ], + "type": "text", + "content": "2D-guided Masking. The conventional masking strategy samples masked tokens randomly following a uniform distribution, which might prevent the encoder from 'seeing' important spatial characteristics and disturb the decoder by nonsignificant structures. Therefore, we leverage the 2D attention maps to guide the masking of point tokens, which samples more semantically significant 3D parts for encoding. Specifically, indexed by the coordinates of point tokens " + }, + { + "bbox": [ + 46, + 365, + 289, + 521 + ], + "type": "inline_equation", + "content": "P^T \\in \\mathbb{R}^{M \\times 3}" + }, + { + "bbox": [ + 46, + 365, + 289, + 521 + ], + "type": "text", + "content": ", we back-project the multi-view attention maps " + }, + { + "bbox": [ + 46, + 365, + 289, + 521 + ], + "type": "inline_equation", + "content": "\\{S_i^{2\\mathrm{D}}\\}_{i=1}^3" + }, + { + "bbox": [ + 46, + 365, + 289, + 521 + ], + "type": "text", + "content": " into 3D space and aggregate them as a 3D attention cloud " + }, + { + "bbox": [ + 46, + 365, + 289, + 521 + ], + "type": "inline_equation", + "content": "S^{3\\mathrm{D}} \\in \\mathbb{R}^{M \\times 1}" + }, + { + "bbox": [ + 46, + 365, + 289, + 521 + ], + "type": "text", + "content": ". For each point in " + }, + { + "bbox": [ + 46, + 365, + 289, + 521 + ], + "type": "inline_equation", + "content": "S^{3\\mathrm{D}}" + }, + { + "bbox": [ + 46, + 365, + 289, + 521 + ], + "type": "text", + "content": ", we assign the semantic score by averaging the corresponding 2D values from multi-view attention maps as" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 82, + 529, + 287, + 562 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 82, + 529, + 287, + 562 + ], + "spans": [ + { + "bbox": [ + 82, + 529, + 287, + 562 + ], + "type": "interline_equation", + "content": "S ^ {\\mathrm {3 D}} = \\operatorname {S o f t m a x} \\left(\\frac {1}{3} \\sum_ {i = 1} ^ {3} \\operatorname {I 2 P} \\left(S _ {i} ^ {\\mathrm {2 D}}, P ^ {T}\\right)\\right), \\tag {2}", + "image_path": "34f8619e7563311ac61afe5beb1af7f8c1fb086c0c33cef25bfe1f7720829d2d.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 570, + 289, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 289, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 289, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 570, + 289, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{I2P}(\\cdot)" + }, + { + "bbox": [ + 46, + 570, + 289, + 713 + ], + "type": "text", + "content": " denotes the 2D-to-3D back-projection operation in Figure 5. We apply a softmax function to normalize the " + }, + { + "bbox": [ + 46, + 570, + 289, + 713 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 570, + 289, + 713 + ], + "type": "text", + "content": " points within " + }, + { + "bbox": [ + 46, + 570, + 289, + 713 + ], + "type": "inline_equation", + "content": "S^{3\\mathrm{D}}" + }, + { + "bbox": [ + 46, + 570, + 289, + 713 + ], + "type": "text", + "content": ", and regard each element's magnitude as the visible probability for the corresponding point token. With this 2D semantic prior, the random masking becomes a nonuniform sampling with different probabilities for different tokens, where the tokens covering more critical 3D structures are more likely to be preserved. This boosts the representation learning of the encoder by focusing more on significant 3D geometries, and provides the masked tokens with more informative cues at the decoder for better reconstruction." + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 326, + 71, + 526, + 247 + ], + "blocks": [ + { + "bbox": [ + 326, + 71, + 526, + 247 + ], + "lines": [ + { + "bbox": [ + 326, + 71, + 526, + 247 + ], + "spans": [ + { + "bbox": [ + 326, + 71, + 526, + 247 + ], + "type": "image", + "image_path": "46bef7c4e00cd3fd629790df351752c5e51eaafda49030003859674be2e7e772.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 260, + 547, + 295 + ], + "lines": [ + { + "bbox": [ + 305, + 260, + 547, + 295 + ], + "spans": [ + { + "bbox": [ + 305, + 260, + 547, + 295 + ], + "type": "text", + "content": "Figure 5. Image-to-Point Operation (I2P). Indexed by 3D point coordinates, the corresponding multi-view 2D representations are back-projected into 3D space for aggregation." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 312, + 547, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 312, + 547, + 434 + ], + "spans": [ + { + "bbox": [ + 305, + 312, + 547, + 434 + ], + "type": "text", + "content": "2D-semantic Reconstruction. The 3D-coordinate reconstruction of masked point tokens enables the network to explore low-level 3D patterns. On top of that, we further enforce the visible point tokens, " + }, + { + "bbox": [ + 305, + 312, + 547, + 434 + ], + "type": "inline_equation", + "content": "T_{\\mathrm{vis}}^d" + }, + { + "bbox": [ + 305, + 312, + 547, + 434 + ], + "type": "text", + "content": ", to reconstruct the extracted 2D semantics from different views, which effectively transfers the 2D pre-trained knowledge into 3D pre-training. To obtain the 2D-semantic targets, we utilize the coordinates of visible point tokens " + }, + { + "bbox": [ + 305, + 312, + 547, + 434 + ], + "type": "inline_equation", + "content": "P_{\\mathrm{vis}}^T \\in \\mathbb{R}^{M_{\\mathrm{vis}} \\times 3}" + }, + { + "bbox": [ + 305, + 312, + 547, + 434 + ], + "type": "text", + "content": " as indices to aggregate corresponding 2D features from " + }, + { + "bbox": [ + 305, + 312, + 547, + 434 + ], + "type": "inline_equation", + "content": "\\{F_i^{2\\mathrm{D}}\\}_{i=1}^3" + }, + { + "bbox": [ + 305, + 312, + 547, + 434 + ], + "type": "text", + "content": " by channel-wise concatenation, formulated as" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 345, + 446, + 545, + 471 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 345, + 446, + 545, + 471 + ], + "spans": [ + { + "bbox": [ + 345, + 446, + 545, + 471 + ], + "type": "interline_equation", + "content": "F _ {\\text {v i s}} ^ {\\mathrm {3 D}} = \\operatorname {C o n c a t} \\left\\{\\mathrm {I 2 P} \\left(F _ {i} ^ {\\mathrm {2 D}}, P _ {\\text {v i s}} ^ {T}\\right) \\right\\} _ {i = 1} ^ {3}, \\tag {3}", + "image_path": "d45c575dc07b025f40b8776221f0e8d177331110e627e403a621a0472b1c5382.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 474, + 547, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 474, + 547, + 548 + ], + "spans": [ + { + "bbox": [ + 305, + 474, + 547, + 548 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 474, + 547, + 548 + ], + "type": "inline_equation", + "content": "F_{\\mathrm{vis}}^{3\\mathrm{D}} \\in \\mathbb{R}^{M_{\\mathrm{vis}} \\times 3C}" + }, + { + "bbox": [ + 305, + 474, + 547, + 548 + ], + "type": "text", + "content": ". As the multi-view depth maps depict a 3D shape from different perspectives, the concatenation between multi-view 2D features can better integrate the rich semantics inherited from 2D pre-trained models. Then, we also adopt a reconstruction head of a single linear projection layer for " + }, + { + "bbox": [ + 305, + 474, + 547, + 548 + ], + "type": "inline_equation", + "content": "T_{\\mathrm{vis}}^d" + }, + { + "bbox": [ + 305, + 474, + 547, + 548 + ], + "type": "text", + "content": ", and compute the " + }, + { + "bbox": [ + 305, + 474, + 547, + 548 + ], + "type": "inline_equation", + "content": "l_2" + }, + { + "bbox": [ + 305, + 474, + 547, + 548 + ], + "type": "text", + "content": " loss as" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 351, + 552, + 545, + 578 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 351, + 552, + 545, + 578 + ], + "spans": [ + { + "bbox": [ + 351, + 552, + 545, + 578 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {2 D}} = \\frac {1}{M _ {\\mathrm {v i s}}} \\left(\\mathrm {H} _ {\\mathrm {2 D}} \\left(T _ {\\mathrm {v i s}} ^ {d}\\right) - F _ {\\mathrm {v i s}} ^ {\\mathrm {3 D}}\\right) ^ {2}, \\tag {4}", + "image_path": "02b890b935503939fcde20e1a045331349db51216b8ae3456b0f2a6441a5f1ab.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 582, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 582, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 582, + 547, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 582, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\mathrm{H}_{2\\mathrm{D}}(\\cdot)" + }, + { + "bbox": [ + 305, + 582, + 547, + 714 + ], + "type": "text", + "content": " denotes the head to reconstruct visible 2D semantics, parallel to " + }, + { + "bbox": [ + 305, + 582, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\mathrm{H}_{3\\mathrm{D}}(\\cdot)" + }, + { + "bbox": [ + 305, + 582, + 547, + 714 + ], + "type": "text", + "content": " for masked 3D coordinates. The final pre-training loss of our I2P-MAE is then formulated as " + }, + { + "bbox": [ + 305, + 582, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{I2P}} = \\mathcal{L}_{\\mathrm{3D}} + \\mathcal{L}_{\\mathrm{2D}}" + }, + { + "bbox": [ + 305, + 582, + 547, + 714 + ], + "type": "text", + "content": ". With such image-to-point feature learning, I2P-MAE not only encodes low-level spatial variations from 3D coordinates, but also explores high-level semantic knowledge from 2D representations. As the 2D-guided masking has preserved visible tokens with more spatial significance, the 2D-semantic reconstruction upon them further benefits I2P-MAE to learn more discriminative 3D representations." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "21773" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 57, + 70, + 279, + 259 + ], + "blocks": [ + { + "bbox": [ + 57, + 70, + 279, + 259 + ], + "lines": [ + { + "bbox": [ + 57, + 70, + 279, + 259 + ], + "spans": [ + { + "bbox": [ + 57, + 70, + 279, + 259 + ], + "type": "table", + "html": "
MethodModelNet40OBJ-BG
SO-Net [35]87.3-
FoldingNet [74]88.4-
VIP-GAN [26]90.2-
DGCNN + Jigsaw [58]90.659.5
DGCNN + OcCo [64]90.778.3
DGCNN + CrossPoint [1]91.281.7
Transformer + OcCo [76]89.6-
Point-BERT [76]87.4-
Point-MAE [47]91.077.7
3D-OAE [85]92.3-
Point-M2AE [78]92.984.1
I2P-MAE93.487.1
Improvement+0.5+3.0
", + "image_path": "a48f9eddb48007c93ac587a769b39f1a1138a82483a442d46330ff6cf3e61c37.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 333, + 128, + 346 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 333, + 128, + 346 + ], + "spans": [ + { + "bbox": [ + 47, + 333, + 128, + 346 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 353, + 287, + 425 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 353, + 287, + 425 + ], + "spans": [ + { + "bbox": [ + 46, + 353, + 287, + 425 + ], + "type": "text", + "content": "In Section 4.1, we first introduce our pre-training settings and the linear SVM classification performance without fine-tuning. Then in Section 4.2, we present the results by fully fine-tuning I2P-MAE on various 3D downstream tasks. Finally in Section 4.3, we conduct ablation studies to investigate the characteristics of I2P-MAE." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 434, + 201, + 445 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 434, + 201, + 445 + ], + "spans": [ + { + "bbox": [ + 47, + 434, + 201, + 445 + ], + "type": "text", + "content": "4.1. Image-to-Point Pre-training" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 452, + 287, + 644 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 452, + 287, + 644 + ], + "spans": [ + { + "bbox": [ + 46, + 452, + 287, + 644 + ], + "type": "text", + "content": "Settings. We adopt the popular ShapeNet [6] for self-supervised 3D pre-training, which contains 57,448 synthetic point clouds with 55 object categories. For fair comparison, we follow the same MAE transformer architecture as Point-M2AE [78]: a 3-stage encoder with 5 blocks per stage, a 2-stage decoder with 1 block per stage, 2,048 input point number " + }, + { + "bbox": [ + 46, + 452, + 287, + 644 + ], + "type": "inline_equation", + "content": "(N)" + }, + { + "bbox": [ + 46, + 452, + 287, + 644 + ], + "type": "text", + "content": ", 512 downsampled number " + }, + { + "bbox": [ + 46, + 452, + 287, + 644 + ], + "type": "inline_equation", + "content": "(M)" + }, + { + "bbox": [ + 46, + 452, + 287, + 644 + ], + "type": "text", + "content": ", 16 nearest neighbors " + }, + { + "bbox": [ + 46, + 452, + 287, + 644 + ], + "type": "inline_equation", + "content": "(k)" + }, + { + "bbox": [ + 46, + 452, + 287, + 644 + ], + "type": "text", + "content": ", 384 feature channels " + }, + { + "bbox": [ + 46, + 452, + 287, + 644 + ], + "type": "inline_equation", + "content": "(C)" + }, + { + "bbox": [ + 46, + 452, + 287, + 644 + ], + "type": "text", + "content": ", and the mask ratio of " + }, + { + "bbox": [ + 46, + 452, + 287, + 644 + ], + "type": "inline_equation", + "content": "80\\%" + }, + { + "bbox": [ + 46, + 452, + 287, + 644 + ], + "type": "text", + "content": ". For off-the-shelf 2D models, we utilize ViT-Base [14] pre-trained by CLIP [53] as default and keep its weights frozen during 3D pre-training. We project the point cloud into three " + }, + { + "bbox": [ + 46, + 452, + 287, + 644 + ], + "type": "inline_equation", + "content": "224 \\times 224" + }, + { + "bbox": [ + 46, + 452, + 287, + 644 + ], + "type": "text", + "content": " depth maps, and obtain the 2D feature size " + }, + { + "bbox": [ + 46, + 452, + 287, + 644 + ], + "type": "inline_equation", + "content": "H \\times W" + }, + { + "bbox": [ + 46, + 452, + 287, + 644 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 46, + 452, + 287, + 644 + ], + "type": "inline_equation", + "content": "14 \\times 14" + }, + { + "bbox": [ + 46, + 452, + 287, + 644 + ], + "type": "text", + "content": ". I2P-MAE is pre-trained for 300 epochs with a batch size 64 and learning rate " + }, + { + "bbox": [ + 46, + 452, + 287, + 644 + ], + "type": "inline_equation", + "content": "10^{-3}" + }, + { + "bbox": [ + 46, + 452, + 287, + 644 + ], + "type": "text", + "content": ". We adopt AdamW [34] optimizer with a weight decay " + }, + { + "bbox": [ + 46, + 452, + 287, + 644 + ], + "type": "inline_equation", + "content": "5 \\times 10^{-2}" + }, + { + "bbox": [ + 46, + 452, + 287, + 644 + ], + "type": "text", + "content": " and the cosine scheduler with 10-epoch warm-up." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "content": "Linear SVM. To evaluate the transfer capacity, we directly utilize the features extracted by I2P-MAE's encoder for linear SVM on the synthetic ModelNet40 [67] and real-world ScanObjectNN [63] without any fine-tuning or voting. As shown in Table 1, for 3D shape classification in" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 308, + 70, + 545, + 259 + ], + "blocks": [ + { + "bbox": [ + 46, + 268, + 288, + 313 + ], + "lines": [ + { + "bbox": [ + 46, + 268, + 288, + 313 + ], + "spans": [ + { + "bbox": [ + 46, + 268, + 288, + 313 + ], + "type": "text", + "content": "Table 1. Linear SVM Classification on ModelNet40 [67] and ScanObjectNN [63]. We compare the accuracy (\\%) of existing self-supervised methods, and the second-best one is underlined. We adopt the OBJ-BG split for ScanObjectNN following [1]." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 70, + 545, + 259 + ], + "lines": [ + { + "bbox": [ + 308, + 70, + 545, + 259 + ], + "spans": [ + { + "bbox": [ + 308, + 70, + 545, + 259 + ], + "type": "table", + "html": "
MethodOBJ-BGOBJ-ONLYPB-T50-RS
PointNet [50]73.379.268.0
PointNet++ [51]82.384.377.9
PointCNN [37]86.185.578.5
MVTN [25]--82.8
PointMLP [2]--85.2
Transformer [76]79.8680.5577.24
[P] Point-BERT [76]87.4388.1283.07
[P] 3D-OAE [85]89.1688.6483.17
[P] MaskPoint [41]89.3088.1084.30
[P] Point-MAE [47]90.0288.2985.18
[P] MAE3D [33]--86.20
[P] Point-M2AE [78]91.2288.8186.43
[P] I2P-MAE94.1591.5790.11
Improvement+2.93+2.76+3.68
", + "image_path": "8478797c74d17c203caf2849ec41cc116696c69141002d4bc0d40bae45a16adb.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 268, + 545, + 313 + ], + "lines": [ + { + "bbox": [ + 304, + 268, + 545, + 313 + ], + "spans": [ + { + "bbox": [ + 304, + 268, + 545, + 313 + ], + "type": "text", + "content": "Table 2. Real-world 3D Classification on ScanObjectNN [63]. We report the accuracy " + }, + { + "bbox": [ + 304, + 268, + 545, + 313 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 304, + 268, + 545, + 313 + ], + "type": "text", + "content": " on the official three splits of ScanObjectNN. [P] denotes to fine-tune the models after self-supervised pre-training." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 335, + 545, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 335, + 545, + 479 + ], + "spans": [ + { + "bbox": [ + 304, + 335, + 545, + 479 + ], + "type": "text", + "content": "both domains, I2P-MAE shows superior performance and exceeds the second-best respectively by " + }, + { + "bbox": [ + 304, + 335, + 545, + 479 + ], + "type": "inline_equation", + "content": "+0.5\\%" + }, + { + "bbox": [ + 304, + 335, + 545, + 479 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 335, + 545, + 479 + ], + "type": "inline_equation", + "content": "+3.0\\%" + }, + { + "bbox": [ + 304, + 335, + 545, + 479 + ], + "type": "text", + "content": " accuracy. Our SVM results " + }, + { + "bbox": [ + 304, + 335, + 545, + 479 + ], + "type": "inline_equation", + "content": "(93.4\\%, 87.1\\%)" + }, + { + "bbox": [ + 304, + 335, + 545, + 479 + ], + "type": "text", + "content": " can even surpass some existing methods after full downstream training in Table 2 and 3, e.g., PointCNN [37] " + }, + { + "bbox": [ + 304, + 335, + 545, + 479 + ], + "type": "inline_equation", + "content": "(92.2\\%, 86.1\\%)" + }, + { + "bbox": [ + 304, + 335, + 545, + 479 + ], + "type": "text", + "content": ", Transformer [76] " + }, + { + "bbox": [ + 304, + 335, + 545, + 479 + ], + "type": "inline_equation", + "content": "(91.4\\%, 79.86\\%)" + }, + { + "bbox": [ + 304, + 335, + 545, + 479 + ], + "type": "text", + "content": ", and Point-BERT [76] " + }, + { + "bbox": [ + 304, + 335, + 545, + 479 + ], + "type": "inline_equation", + "content": "(92.7\\%, 87.43\\%)" + }, + { + "bbox": [ + 304, + 335, + 545, + 479 + ], + "type": "text", + "content": ". In addition, guided by the 2D pre-trained models, I2P-MAE exhibits much faster pre-training convergence than Point-MAE [47] and Point-M2AE in Figure 3. Therefore, the SVM performance of I2P-MAE demonstrates its learned high-quality 3D representations and the significance of our image-to-point learning schemes." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 487, + 417, + 499 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 487, + 417, + 499 + ], + "spans": [ + { + "bbox": [ + 306, + 487, + 417, + 499 + ], + "type": "text", + "content": "4.2. Downstream Tasks" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 506, + 545, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 506, + 545, + 555 + ], + "spans": [ + { + "bbox": [ + 304, + 506, + 545, + 555 + ], + "type": "text", + "content": "After pre-training, I2P-MAE is fine-tuned for real-world and synthetic 3D classification, and part segmentation. Except ModelNet40 [67], we do not use the voting strategy [43] for evaluation." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": "Real-world 3D Classification. The challenging ScanObjectNN [63] consists of 11,416 training and 2,882 test 3D shapes, which are scanned from the real-world scenes and thus include backgrounds with noises. As shown in Table 2, our I2P-MAE exerts great advantages over other self-supervised methods, surpassing the second-best by " + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "inline_equation", + "content": "+2.93\\%" + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "inline_equation", + "content": "+2.76\\%" + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "inline_equation", + "content": "+3.68\\%" + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": " respectively for the three splits. This is also the first model reaching " + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "inline_equation", + "content": "90\\%" + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": " accuracy on the hardest PB-T50-RS spilt. As the pre-training point clouds [6] are synthetic 3D shapes with a large domain gap with the real-world ScanobjectNN, the results well indicate the universality of I2P-MAE inherited from the 2D pre-trained models." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "21774" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 59, + 70, + 276, + 242 + ], + "blocks": [ + { + "bbox": [ + 59, + 70, + 276, + 242 + ], + "lines": [ + { + "bbox": [ + 59, + 70, + 276, + 242 + ], + "spans": [ + { + "bbox": [ + 59, + 70, + 276, + 242 + ], + "type": "table", + "html": "
MethodPointsNo VotingVoting
PointNet [50]1k89.2-
PointNet++ [51]1k90.7-
PointCNN [37]1k92.2-
Point Transformer [84]-93.7
Transformer [76]1k91.4-
[P] Point-BERT [76]1k92.793.2
[P] 3D-OAE [85]1k-93.4
[P] Point-MAE [47]1k93.293.8
Point-MAE8k-94.0
[P] Point-M2AE [78]1k93.494.0
[P] I2P-MAE-SVM1k93.4-
I2P-MAE1k93.794.1
", + "image_path": "6ce940832ac4598ef4652115ce6b9f3d32b84bc516d92fe951cb09c7177a88cf.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 306, + 287, + 450 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 306, + 287, + 450 + ], + "spans": [ + { + "bbox": [ + 46, + 306, + 287, + 450 + ], + "type": "text", + "content": "Synthetic 3D Classification. The widely adopted ModelNet40 [67] contains 9,843 training and 2,468 test 3D point clouds, which are sampled from the synthetic CAD models of 40 categories. We report the classification accuracy of existing methods before and after the voting in Table 3. As shown, our I2P-MAE achieves leading performance for both settings with only 1k input point number. For linear SVM without any fine-tuning, I2P-MAE-SVM can already attain " + }, + { + "bbox": [ + 46, + 306, + 287, + 450 + ], + "type": "inline_equation", + "content": "93.4\\%" + }, + { + "bbox": [ + 46, + 306, + 287, + 450 + ], + "type": "text", + "content": " accuracy and exceed most previous works, indicating the powerful transfer ability. By fine-tuning the entire network, the accuracy can be further boosted by " + }, + { + "bbox": [ + 46, + 306, + 287, + 450 + ], + "type": "inline_equation", + "content": "+0.3\\%" + }, + { + "bbox": [ + 46, + 306, + 287, + 450 + ], + "type": "text", + "content": " accuracy, and achieve " + }, + { + "bbox": [ + 46, + 306, + 287, + 450 + ], + "type": "inline_equation", + "content": "94.1\\%" + }, + { + "bbox": [ + 46, + 306, + 287, + 450 + ], + "type": "text", + "content": " after the offline voting." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 466, + 286, + 646 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 466, + 286, + 646 + ], + "spans": [ + { + "bbox": [ + 46, + 466, + 286, + 646 + ], + "type": "text", + "content": "Part Segmentation. The synthetic ShapeNetPart [75] is selected from ShapeNet [6] with 16 object categories and 50 part categories, which contains 14,007 and 2,874 samples for training and validation. We utilize the same segmentation head after the pre-trained encoder as previous works [47, 78] for fair comparison. The head only conducts simple upsampling for point tokens at different stages and concatenates them alone the feature dimension as the output. Two types of mean IoU scores, " + }, + { + "bbox": [ + 46, + 466, + 286, + 646 + ], + "type": "inline_equation", + "content": "\\mathrm{mIoU}_C" + }, + { + "bbox": [ + 46, + 466, + 286, + 646 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 466, + 286, + 646 + ], + "type": "inline_equation", + "content": "\\mathrm{mIoU}_I" + }, + { + "bbox": [ + 46, + 466, + 286, + 646 + ], + "type": "text", + "content": " are reported in Table 4. For such highly saturated benchmark, I2P-MAE can still exert leading performance guided by the well learned 2D knowledge, e.g., " + }, + { + "bbox": [ + 46, + 466, + 286, + 646 + ], + "type": "inline_equation", + "content": "+0.29\\%" + }, + { + "bbox": [ + 46, + 466, + 286, + 646 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 466, + 286, + 646 + ], + "type": "inline_equation", + "content": "+0.25\\%" + }, + { + "bbox": [ + 46, + 466, + 286, + 646 + ], + "type": "text", + "content": " higher than Point-M2AE concerning the two metrics. This demonstrates that the 2D guidance also benefits the understanding for fine-grained point-wise 3D patterns." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 658, + 141, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 658, + 141, + 671 + ], + "spans": [ + { + "bbox": [ + 47, + 658, + 141, + 671 + ], + "type": "text", + "content": "4.3. Ablation Study" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "type": "text", + "content": "In this section, we explore the effectiveness of different characteristics in I2P-MAE. We utilize our final solution as the baseline and report the linear SVM accuracy " + }, + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 318, + 70, + 535, + 242 + ], + "blocks": [ + { + "bbox": [ + 46, + 251, + 287, + 285 + ], + "lines": [ + { + "bbox": [ + 46, + 251, + 287, + 285 + ], + "spans": [ + { + "bbox": [ + 46, + 251, + 287, + 285 + ], + "type": "text", + "content": "Table 3. Synthetic 3D Classification on ModelNet40 [67]. We report the accuracy " + }, + { + "bbox": [ + 46, + 251, + 287, + 285 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 46, + 251, + 287, + 285 + ], + "type": "text", + "content": " before and after the voting [43]. [P] denotes to fine-tune the models after self-supervised pre-training." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 318, + 70, + 535, + 242 + ], + "lines": [ + { + "bbox": [ + 318, + 70, + 535, + 242 + ], + "spans": [ + { + "bbox": [ + 318, + 70, + 535, + 242 + ], + "type": "table", + "html": "
MethodmIoUCmIoUI
PointNet [50]80.3983.70
PointNet++ [51]81.8585.10
DGCNN [65]82.3385.20
PointMLP [2]84.6086.10
Transformer [76]83.4285.10
[P] Transformer + OcCo [76]83.4285.10
[P] Point-BERT [76]84.1185.60
[P] 3D-OAE [85]-85.70
[P] MaskPoint [41]84.4086.00
[P] Point-MAE [47]-86.10
[P] Point-M2AE [78]84.8686.51
[P] I2P-MAE85.1586.76
", + "image_path": "75f89691ee49242645e548af0151500fcb2bf48ae0da82f50306fb02588669b6.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 307, + 304, + 545, + 382 + ], + "blocks": [ + { + "bbox": [ + 305, + 251, + 545, + 285 + ], + "lines": [ + { + "bbox": [ + 305, + 251, + 545, + 285 + ], + "spans": [ + { + "bbox": [ + 305, + 251, + 545, + 285 + ], + "type": "text", + "content": "Table 4. Part Segmentation on ShapeNetPart [75]. We report the average IoU scores " + }, + { + "bbox": [ + 305, + 251, + 545, + 285 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 305, + 251, + 545, + 285 + ], + "type": "text", + "content": " for part categories and instances, respectively denoted as " + }, + { + "bbox": [ + 305, + 251, + 545, + 285 + ], + "type": "inline_equation", + "content": "\\mathrm{mIoU}_C" + }, + { + "bbox": [ + 305, + 251, + 545, + 285 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 251, + 545, + 285 + ], + "type": "inline_equation", + "content": "\\mathrm{mIoU}_I" + }, + { + "bbox": [ + 305, + 251, + 545, + 285 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 304, + 545, + 382 + ], + "lines": [ + { + "bbox": [ + 307, + 304, + 545, + 382 + ], + "spans": [ + { + "bbox": [ + 307, + 304, + 545, + 382 + ], + "type": "table", + "html": "
Method20%40%60%80%100%
Point-MAE [47]89.490.290.390.591.0
Point-M2AE [78]90.892.092.192.492.9
I2P-MAE92.192.793.193.193.4
Improvement+1.3+0.7+1.0+0.7+0.5
", + "image_path": "9dff2ee06dbcdd1c547b677e91957e8efac79fe61bf69adbb0e5507e1ab22c5a.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 391, + 545, + 414 + ], + "lines": [ + { + "bbox": [ + 305, + 391, + 545, + 414 + ], + "spans": [ + { + "bbox": [ + 305, + 391, + 545, + 414 + ], + "type": "text", + "content": "Table 5. Pre-training with Limited 3D Data. We utilize randomly sampled 3D data from ShapeNet [6] for pre-training." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 434, + 545, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 434, + 545, + 579 + ], + "spans": [ + { + "bbox": [ + 304, + 434, + 545, + 579 + ], + "type": "text", + "content": "Pre-training with Limited 3D Data. In Table 5, we randomly sample the pre-training dataset, ShapeNet [6], with different ratios, and evaluate the performance of I2P-MAE when 3D data is further deficient. Aided by 2D pre-trained models, I2P-MAE still achieves competitive downstream accuracy in low-data regimes, especially for " + }, + { + "bbox": [ + 304, + 434, + 545, + 579 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 304, + 434, + 545, + 579 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 434, + 545, + 579 + ], + "type": "inline_equation", + "content": "60\\%" + }, + { + "bbox": [ + 304, + 434, + 545, + 579 + ], + "type": "text", + "content": ", which outperforms Point-M2AE [78] by " + }, + { + "bbox": [ + 304, + 434, + 545, + 579 + ], + "type": "inline_equation", + "content": "+1.3\\%" + }, + { + "bbox": [ + 304, + 434, + 545, + 579 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 434, + 545, + 579 + ], + "type": "inline_equation", + "content": "+1.0" + }, + { + "bbox": [ + 304, + 434, + 545, + 579 + ], + "type": "text", + "content": ", respectively. Importantly, with only " + }, + { + "bbox": [ + 304, + 434, + 545, + 579 + ], + "type": "inline_equation", + "content": "60\\%" + }, + { + "bbox": [ + 304, + 434, + 545, + 579 + ], + "type": "text", + "content": " of the pre-training, I2P-MAE " + }, + { + "bbox": [ + 304, + 434, + 545, + 579 + ], + "type": "inline_equation", + "content": "(93.1\\%)" + }, + { + "bbox": [ + 304, + 434, + 545, + 579 + ], + "type": "text", + "content": " outperforms Point-MAE " + }, + { + "bbox": [ + 304, + 434, + 545, + 579 + ], + "type": "inline_equation", + "content": "(91.0\\%)" + }, + { + "bbox": [ + 304, + 434, + 545, + 579 + ], + "type": "text", + "content": " and Point-M2AE " + }, + { + "bbox": [ + 304, + 434, + 545, + 579 + ], + "type": "inline_equation", + "content": "(92.9\\%)" + }, + { + "bbox": [ + 304, + 434, + 545, + 579 + ], + "type": "text", + "content": " with full training data. This indicates that our image-to-point learning scheme effectively can alleviate the need for large-scale 3D training datasets." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": "2D-guided Masking. In Table 6, we experiment different masking strategies for I2P-MAE. The first row represents 2D-guided masking, which preserves more semantically important tokens to be visible for the encoder. Compared to the second-row random masking, the guidance of 2D attention maps contributes to " + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "+0.4\\%" + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "+0.9\\%" + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": " accuracy on two datasets. Then, we reverse the token scores in the spatial attention cloud, and instead mask the most important tokens. As shown in the third row, the results are largely harmed, demonstrating the significance of encoding" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21775" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 49, + 71, + 287, + 155 + ], + "blocks": [ + { + "bbox": [ + 49, + 71, + 287, + 155 + ], + "lines": [ + { + "bbox": [ + 49, + 71, + 287, + 155 + ], + "spans": [ + { + "bbox": [ + 49, + 71, + 287, + 155 + ], + "type": "table", + "html": "
2D-guidedVisibleRatioModelNet40OBJ-BG
✓Important0.893.487.1
-Random0.893.086.2
✓Unimportant0.892.884.5
✓Important0.792.583.8
✓Important0.992.885.6
", + "image_path": "6d1994d6a30fe2221b1a4d028426bdab177e987f9b85a9bc60abaa8918325d5d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 48, + 208, + 287, + 302 + ], + "blocks": [ + { + "bbox": [ + 47, + 163, + 288, + 198 + ], + "lines": [ + { + "bbox": [ + 47, + 163, + 288, + 198 + ], + "spans": [ + { + "bbox": [ + 47, + 163, + 288, + 198 + ], + "type": "text", + "content": "Table 6. 2D-guided Masking. 'Visible' denotes whether the preserved visible point tokens are more semantically important than the masked ones. 'Ratio' denotes the masking ratio." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 208, + 287, + 302 + ], + "lines": [ + { + "bbox": [ + 48, + 208, + 287, + 302 + ], + "spans": [ + { + "bbox": [ + 48, + 208, + 287, + 302 + ], + "type": "table", + "html": "
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Finally, we modify the masking ratio by " + }, + { + "bbox": [ + 46, + 356, + 287, + 417 + ], + "type": "inline_equation", + "content": "\\pm 0.1" + }, + { + "bbox": [ + 46, + 356, + 287, + 417 + ], + "type": "text", + "content": ", which controls the proportion between visible and masked tokens. The performance decay indicates that, the 2D-semantic and 3D-coordinate reconstruction are required to be well balanced for a properly challenging pre-text task." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 430, + 287, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 430, + 287, + 635 + ], + "spans": [ + { + "bbox": [ + 46, + 430, + 287, + 635 + ], + "type": "text", + "content": "2D-semantic Reconstruction. In Table 7, we investigate which groups of tokens are the best for learning 2D semantic targets. The comparison of the first two rows reveals the effectiveness of reconstructing 2D semantics from visible tokens, i.e., " + }, + { + "bbox": [ + 46, + 430, + 287, + 635 + ], + "type": "inline_equation", + "content": "+0.5\\%" + }, + { + "bbox": [ + 46, + 430, + 287, + 635 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 430, + 287, + 635 + ], + "type": "inline_equation", + "content": "+2.4\\%" + }, + { + "bbox": [ + 46, + 430, + 287, + 635 + ], + "type": "text", + "content": " classification accuracy. By only using 2D targets for either the visible or masked tokens (the " + }, + { + "bbox": [ + 46, + 430, + 287, + 635 + ], + "type": "inline_equation", + "content": "3^{\\mathrm{rd}}" + }, + { + "bbox": [ + 46, + 430, + 287, + 635 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 430, + 287, + 635 + ], + "type": "inline_equation", + "content": "4^{\\mathrm{th}}" + }, + { + "bbox": [ + 46, + 430, + 287, + 635 + ], + "type": "text", + "content": " rows), we verify that the 3D-coordinate reconstruction still plays an important role in I2P-MAE, which learns low-level geometric 3D patterns and provides complementary knowledge to the high-level 2D semantics. However, if the 3D and 2D targets are both reconstructed from the masked tokens (the last row), the network is restricted to learn 2D knowledge from the masked nonsignificant 3D geometries, other than the more discriminative parts. Also, assigning two targets on the same tokens might cause 2D-3D semantic conflicts. Therefore, the two targets are best to be reconstructed separately." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 645, + 129, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 645, + 129, + 658 + ], + "spans": [ + { + "bbox": [ + 47, + 645, + 129, + 658 + ], + "type": "text", + "content": "5. Visualization" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "content": "We visualize the input point cloud, random masking, spatial attention cloud, 2D-guided masking, and the reconstructed 3D coordinates in Figure 6. Guided by the semantic scores from 2D pre-trained models (darker points indicate" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 312, + 74, + 537, + 270 + ], + "blocks": [ + { + "bbox": [ + 312, + 74, + 537, + 270 + ], + "lines": [ + { + "bbox": [ + 312, + 74, + 537, + 270 + ], + "spans": [ + { + "bbox": [ + 312, + 74, + 537, + 270 + ], + "type": "image", + "image_path": "f57a1df68264115a3bd36467fd1894872eeb4d82779256ba9ff5acde56dfe166.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 282, + 545, + 316 + ], + "lines": [ + { + "bbox": [ + 305, + 282, + 545, + 316 + ], + "spans": [ + { + "bbox": [ + 305, + 282, + 545, + 316 + ], + "type": "text", + "content": "Figure 6. Visualization of I2P-MAE. Guided by the spatial attention cloud, I2P-MAE's masking (the " + }, + { + "bbox": [ + 305, + 282, + 545, + 316 + ], + "type": "inline_equation", + "content": "4^{th}" + }, + { + "bbox": [ + 305, + 282, + 545, + 316 + ], + "type": "text", + "content": " column) preserves more semantically important 3D structures than random masking." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 337, + 545, + 397 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 337, + 545, + 397 + ], + "spans": [ + { + "bbox": [ + 305, + 337, + 545, + 397 + ], + "type": "text", + "content": "higher scores), the masked point cloud largely preserves significant parts of the 3D shape, e.g., the main body of an airplane, the grip of a guitar, the frame of a chair and telephone. By this, the 3D network can learn more discriminative features by reconstructing these visible 2D semantics." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 411, + 378, + 424 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 411, + 378, + 424 + ], + "spans": [ + { + "bbox": [ + 306, + 411, + 378, + 424 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 434, + 545, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 434, + 545, + 578 + ], + "spans": [ + { + "bbox": [ + 304, + 434, + 545, + 578 + ], + "type": "text", + "content": "In this paper, we propose I2P-MAE, a masked point modeling framework with effective image-to-point learning schemes. We introduce two approaches to transfer the well learned 2D knowledge into 3D domains: 2D-guided masking and 2D-semantic reconstruction. Aided by the 2D guidance, I2P-MAE learns superior 3D representations and alleviates the demand for large-scale 3D data. For future work, not limited to masking and reconstruction, we will explore more sufficient image-to-point learning approaches, e.g., point token sampling and 2D-3D class-token contrast. Also, we expect our pre-trained models to benefit wider ranges of 3D tasks, e.g., 3D object detection and visual grounding." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "text", + "content": "Acknowledgement. This project is funded in part by National Key R&D Program of China Project 2022ZD0161100, by the Centre for Perceptual and Interactive Intelligence (CPII) Ltd under the Innovation and Technology Commission (ITC)'s InnoHK, by General Research Fund of Hong Kong RGC Project 14204021, by the National Natural Science Foundation of China (Grant No. 62206272), and by Shanghai Committee of Science and Technology (Grant No. 21DZ1100100). Hongsheng Li is a PI of CPII under the InnoHK." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "21776" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 146 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 146 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 146 + ], + "type": "text", + "content": "[1] Mohamed Afham, Isuru Dissanayake, Dinithi Dissanayake, Amaya Dharmasiri, Kanchana Thilakarathna, and Ranga Rodrigo. 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Recent works have shown advances in 3D scene estimation from various input modalities (e.g., images, 3D scans), by leveraging 3D supervision (e.g., 3D bounding boxes or CAD models), for which collection at scale is expensive and often intractable. To address this shortcoming, we propose a new method to learn 3D scene priors of layout and shape without requiring any 3D ground truth. Instead, we rely on 2D supervision from multi-view RGB images. Our method represents a 3D scene as a latent vector, from which we can progressively decode to a sequence of objects characterized by their class categories, 3D bounding boxes, and meshes. With our trained autoregressive decoder representing the scene prior, our method facilitates many downstream applications, including scene synthesis, interpolation, and single-view reconstruction. Experiments on 3DFRONT and ScanNet show that our method outperforms state of the art in single-view reconstruction, and achieves state-of-the-art results in scene synthesis against baselines which require for 3D supervision. Project page: https://yinyunie.github.io/scenegprior-page/", + "bbox": [ + 76, + 282, + 472, + 616 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 647, + 209, + 662 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Understanding the geometric structures in real world scenes takes significant meaning in 3D computer vision. In recent years, many prominent approaches have been proposed to understand 3D scenes for different applications, e.g., scene synthesis [24,28,36,48,49,52] and semantic reconstruction [6,15,16,18-21,26,30,34,35,56]. These methods have shown initial promise in estimating object layouts and shapes in 3D scenes, from RGB or RGB-D input data.", + "bbox": [ + 75, + 672, + 468, + 794 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "However, such methods have focused on leveraging full 3D supervision for layout and shape learning, in task-specific fashion. Such ground truth 3D scene geometry with semantic decomposition to objects and structures is difficult and expensive to acquire, requiring significant artist modeling efforts [13] or expert annotations [1] of CAD modeling. In contrast, 2D image and video acquisition is significantly", + "bbox": [ + 75, + 795, + 468, + 901 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/2b0a187f95ac48cfbbaa3a6c5333e4d183427f04e59bd10d71691b85ffefbfe7.jpg", + "image_caption": [ + "Figure 1. We learn 3D scene priors with 2D supervision. We model a latent hypersphere surface to represent a manifold of 3D scenes, characterizing the semantic and geometric distribution of objects in 3D scenes. This supports many downstream applications, including scene synthesis, interpolation and single-view reconstruction." + ], + "image_footnote": [], + "bbox": [ + 501, + 250, + 893, + 407 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "more accessible. We thus propose to instead learn a general 3D scene prior from only multi-view 2D information. This approach takes a unified perspective to 3D scene understanding: our 3D scene prior is learned in a generalizable fashion from only multi-view 2D information, enabling application to multiple downstream tasks, including scene synthesis and single-view reconstruction.", + "bbox": [ + 496, + 518, + 893, + 625 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In order to understand geometric 3D scene structure from only multi-view RGB images, we must bridge the domain gap between 3D geometry and RGB colors. To this end, we propose to leverage the 2D semantic domain: we learn our 3D scene prior by ensuring that our learned 3D scene structures and objects, when differentiably rendered, match the 2D semantic distribution of estimated 2D instance segmentations from the RGB images. This enables supervision of 3D object and layout structures guided by 2D information.", + "bbox": [ + 496, + 627, + 893, + 777 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Our 3D scene prior is learned by optimizing for a mapping from a latent space (parameterized as a hypersphere surface) to a manifold of 3D scenes, as shown in Fig. 1. Each random vector sampled from the latent space is decoded into a sequence of objects autoregressively using our permutation-invariant transformer. Each output object is characterized by their class category, 3D bounding box and mesh. By training this decoder, we encode the scene prior", + "bbox": [ + 496, + 779, + 893, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "792", + "bbox": [ + 485, + 945, + 511, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "into a latent space, sampling on which enables us to synthesize plausible 3D scenes. With such formulation, our method supports many other downstream tasks on different conditions, e.g., scene synthesis, interpolation and single-view reconstruction.", + "bbox": [ + 75, + 90, + 468, + 165 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, we present our contributions as follows:", + "bbox": [ + 96, + 167, + 446, + 181 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We present a new perspective on general 3D scene prior learning with only 2D supervision. We learn the prior distribution of both semantic object instance layouts and shapes via mapping from a latent space to the 3D scene space, by training from 2D multi-view data.", + "- We formulate scene prior learning as an autoregressive sequence decoding problem, and propose a novel permutation-invariant transformer corresponding with a 2D view loss to map a latent vector from a hypersphere surface to a sequence of semantic instances characterized by their class categories, 3D bounding boxes and meshes.", + "- Our learned 3D scene prior supports many downstream tasks: single-view scene reconstruction, scene synthesis and interpolation. Experiments on 3D-FRONT and ScanNet show that our method matches state-of-the-art performance in scene synthesis against methods requiring 3D supervision, and outperforms state of the art in single-view reconstruction." + ], + "bbox": [ + 94, + 188, + 467, + 472 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 496, + 218, + 511 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3D Semantic Scene Synthesis 3D semantic scene synthesis has received extensive exploration in recent decades, particularly following the popularity of 3D indoor scene datasets and 3D deep learning. Given a collection of synthesized or real 3D scenes, many methods have been proposed to learn the distribution of object layouts to synthesize unseen but plausible 3D scene arrangements.", + "bbox": [ + 75, + 522, + 467, + 626 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Traditional methods for scene synthesis usually formulate the task as data-driven object placement [57], where a scene with object instances is represented as a graph [3, 4, 39, 59], or is connected to human activities to build a human-centric representation [12, 14, 31, 39]. Scene priors are explicitly hard-coded based on design guidelines [32, 54], represented by frequency statistics (e.g., objects co-occurrence map) [3, 4, 10], inferred by affordance map from human activities [12, 14, 22], or learned from arrangement examples in 3D scenes [11, 14]. Given an initial scene [14, 32, 54], a 2D sketch [51] or a text [3, 4], several methods synthesize object placements under the guidance of scene priors with different optimization strategies, e.g., manual interactions [4, 32, 42], iterative methods [12, 14, 29, 50] or non-linear optimization [3, 4, 11, 39, 51, 54, 55], to maximize a plausibility score or a joint probability.", + "bbox": [ + 75, + 628, + 467, + 868 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "With deep learning techniques, many methods instead learn scene priors with neural networks. They keep the", + "bbox": [ + 76, + 869, + 467, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "problem formulation and use recurrent networks [29, 36, 41, 47-49], feed-forward models [33, 58], GANs [53], or VAEs [38, 52] to synthesize object poses recursively or in one stage from an initial scene or random noise, and usually require 3D information for training. In contrast, our method directly learns the joint semantic and geometric distribution of instances in scenes with 2D supervision, which enables a general scene priors that supports semantic scene synthesis from a latent random vector.", + "bbox": [ + 496, + 90, + 890, + 226 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Single-view Scene Reconstruction Single image reconstruction methods have also been designed around various task-specific, data-driven scene priors [6, 15, 16, 18, 20, 21, 25-27, 30, 34, 37, 45, 56]. Izadinia et al. [21] propose a deep learning-based method to retrieve and align CAD models to an input image. Further methods were developed with a similar top-down approach to reconstruct a scene by detection and retrieval, in which [20, 21, 25] use a render-and-compare strategy. [18, 26, 27] improve the offline shape retrieval with an end-to-end 2D-3D shape matching with pose alignment. Other works focus on shape reconstruction instead of retrieval, where object shapes are learned as meshes [15, 16, 34], volume grids [37, 45], or implicit functions [30, 30, 56] with the supervision of paired 3D object shapes or multi-view images. However, modeling scenes with a top-down manner usually focuses on per-object perception without any global scene reasoning. In contrast, we focus on learning prior distribution of 3D scenes, to generate plausible object layouts conditioned on an input image.", + "bbox": [ + 496, + 232, + 890, + 518 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 500, + 532, + 633, + 550 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our work aims to learn the prior distribution of 3D semantic scenes. We formulate this problem by learning a mapping $f$ from a parameterized latent space $\\mathcal{Z}$ to the scene space $S$ , and hope each sample $z \\in \\mathcal{Z}$ corresponds to a reasonable 3D scene $s \\in S$ as in", + "bbox": [ + 496, + 558, + 890, + 632 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\ns = f (z); z \\in \\mathcal {Z}, s \\in \\mathcal {S}. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 606, + 646, + 890, + 662 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In Eq. 1, there are four key components: the parameterization of latent space $\\mathcal{Z}$ and scene space $S$ , the architecture of $f$ , and the losses to train $f$ . We illustrate our approach in Fig. 2, the latent space $\\mathcal{Z}$ is represented as a unit hypersphere surface, each latent vector $\\mathbf{z}$ sampled from which conditions the generation of an object sequence with our permutation-invariant transformer. We formulate a 3D scene $s \\in S$ as a set of objects with their class categories, positions and shapes, thus each object from the transformer is decoded into a category label, a 3D bounding box and a mesh with a completeness score indicating whether the generated scene is complete or not. Training our network only needs 2D supervision. We design a 2D view loss between the renderings of generated scenes and the ground-truth instance masks under respective camera views.", + "bbox": [ + 496, + 674, + 890, + 898 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "793", + "bbox": [ + 485, + 945, + 509, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/e0f9d4b9bd2f0698f40e49926f175187e8277a859aa02ace5ad02c9b9c2f1813.jpg", + "image_caption": [ + "Figure 2. Overview of our approach. Our method represents each scene as a learnable latent vector $\\mathbf{z}$ on a hypersphere. To build mapping from the latent surface to the semantic scene space, we propose a permutation-invariant transformer to generate objects $\\{\\pmb{x}_k\\}$ autoregressively conditioned on previous objects and $\\mathbf{z}$ . For each object feature, we regress its object class label, 3D bounding box, shape feature and completeness score, which respectively represent the object layout, geometry, and the completeness of the output scene. We do not require 3D supervision, and instead leverage differentiable rendering with multi-view 2D instance masks supervision." + ], + "image_footnote": [], + "bbox": [ + 81, + 89, + 893, + 281 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Latent Space Parameterization", + "text_level": 1, + "bbox": [ + 76, + 380, + 352, + 396 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We parameterize the latent space $\\mathcal{Z}$ as a unit hypersphere surface. We choose a spherical surface as the latent representation because it does not have strict boundaries (e.g., uniform distribution), and sampling on it will not produce outliers (e.g., gaussian distribution) [8], which guarantees the continuity when moving from one latent vector to another. We formulate the sampling process from $\\mathcal{Z}$ as", + "bbox": [ + 75, + 402, + 470, + 508 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {z} = \\frac {\\sum_ {i = 1} ^ {M} w _ {i} \\cdot \\phi_ {i}}{| | \\sum_ {i = 1} ^ {M} w _ {i} \\cdot \\phi_ {i} | | _ {2}}; \\sum_ {i = 1} ^ {M} w _ {i} = 1, w _ {i} > 0 \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 117, + 518, + 468, + 558 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\{\\phi_i|\\phi_i\\in \\mathbb{R}^{D_z},||\\phi_i||_2 = 1\\}$ is a set of $M$ fixed vectors with unit length, which uniformly spreads on the sphere surface. $D_{z}$ is the dimension of the hypersphere. Therefore, by sampling a set of weights $\\{w_{i}\\}$ , we can obtain a latent vector $\\pmb {z}\\in \\mathbb{R}^{D_z}$ for scene generation. Note that both $\\{w_{i}\\}$ and our network $f$ are learnable during training.", + "bbox": [ + 75, + 568, + 468, + 660 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Permutation-invariant Transformer", + "text_level": 1, + "bbox": [ + 76, + 667, + 390, + 684 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We generate a sequence of objects in a scene, conditioned on the latent vector $\\mathbf{z}$ , in an autoregressive fashion. New objects are generated conditioned on the previous ones, which can be formulated as to estimate the distribution of", + "bbox": [ + 75, + 691, + 468, + 767 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nP _ {\\theta} \\left(\\boldsymbol {x} _ {1}, \\dots , \\boldsymbol {x} _ {N} \\mid \\boldsymbol {z}\\right) = P _ {\\theta} \\left(\\boldsymbol {x} _ {1} \\mid \\boldsymbol {z}\\right) \\prod_ {k = 2} ^ {N} P _ {\\theta} \\left(\\boldsymbol {x} _ {k} \\mid \\boldsymbol {x} _ {1}, \\dots , \\boldsymbol {x} _ {k - 1}; \\boldsymbol {z}\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 777, + 491, + 809 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\pmb{x}_k$ denotes the $k$ -th object feature. $N$ is the maximal number of objects to be generated. $\\theta$ is the trainable network. Every new object $\\pmb{x}_k$ is generated conditioning on $\\pmb{x}_1, \\dots, \\pmb{x}_{k-1}$ and $\\pmb{z}$ .", + "bbox": [ + 75, + 810, + 468, + 869 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We observe that objects in a scene are an unordered set, where each permutation of an object sequence should be", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "equivalent to each other, e.g., [chair, table, lamp] should be equivalent to [lamp, chair, table] given the three objects. Thus, the generation of the next object $\\pmb{x}_k$ should be independent to the order of previous objects $\\{x_1, \\dots, x_{k-1}\\}$ , which can be formulated as", + "bbox": [ + 496, + 380, + 892, + 455 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nP _ {\\theta} \\left(\\boldsymbol {x} _ {k} \\mid \\boldsymbol {x} _ {p _ {1}}, \\dots , \\boldsymbol {x} _ {p _ {k - 1}}; \\boldsymbol {z}\\right) = P _ {\\theta} \\left(\\boldsymbol {x} _ {k} \\mid \\boldsymbol {x} _ {q _ {1}}, \\dots , \\boldsymbol {x} _ {q _ {k - 1}}; \\boldsymbol {z}\\right)\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 479, + 874, + 497 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n1 \\leq p _ {i}, q _ {i} \\leq k - 1 \\text {a n d} p _ {i} \\neq p _ {j}, q _ {i} \\neq q _ {j}, \\forall i \\neq j. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 516, + 500, + 890, + 527 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "This requires our generation network to be permutation-invariant to the input objects. We model this step using a transformer backbone [23], which is illustrated in Fig. 3. Inspired by [36, 46] where removing the positional encoding in a transformer encoder makes the network agnostic to the object order, we consider this design and encode permutation-invariant scene context $\\pmb{F}_k \\in \\mathbb{R}^{k \\times D_z}$ from previous objects $\\{\\pmb{x}_1, \\dots, \\pmb{x}_{k-1}\\}$ . Note that $\\pmb{x}_0$ in Fig. 2 and 3 is a learnable start token which indicates an empty room.", + "bbox": [ + 496, + 529, + 890, + 664 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "$F_{k}$ contains attention signals between object pairs and the scene context feature. We use $F_{k}$ as the keys and values, and the latent vector $\\mathcal{Z}$ as the query to infer the next object based on the scene context. We adopt a transformer decoder for object inference, where we also do not use positional encoding. Afterwards, it outputs the next possible object $\\pmb{x}_k\\in \\mathbb{R}^{D_z}$ . We forward this step autoregressively to obtain an object feature sequence $\\{\\pmb {x}_1,\\dots,\\pmb {x}_N\\}$ .", + "bbox": [ + 496, + 665, + 890, + 787 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.3. Layout and Shape Decoder", + "text_level": 1, + "bbox": [ + 498, + 795, + 743, + 811 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we decode object features $\\{\\pmb{x}_k\\}$ into a set of object categories, 3D bounding boxes and shapes.", + "bbox": [ + 496, + 818, + 890, + 849 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Scene Parameterization We focus on indoor scenarios, and represent a 3D scene in a world coordinate system with the floor center located at the origin. Each object inside", + "bbox": [ + 496, + 854, + 892, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "794", + "bbox": [ + 485, + 945, + 509, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/8f816f149ecd90c1b41fda70ad1d4992b79cb8138a11196a46cf34d937893ab8.jpg", + "image_caption": [ + "Figure 3. Transformer for autoregressive object generation. From the start token $\\pmb{x}_0$ , we design a permutation-invariant transformer to autoregressively generate a new object feature $\\pmb{x}_k$ by querying the encoded scene context $\\pmb{F}_k$ with the latent vector $\\pmb{z}$ ." + ], + "image_footnote": [], + "bbox": [ + 81, + 89, + 482, + 196 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "is characterized by its class label $l \\in \\mathbb{L}$ , axis-aligned 3D bounding box with size $s \\in \\mathbb{R}^3$ and center $c \\in \\mathbb{R}^3$ , and 3D mesh $M \\in \\mathbb{M}$ in the canonical system, where $\\mathbb{L}$ denotes all class categories and $\\mathbb{M}$ is the shape space.", + "bbox": [ + 75, + 273, + 468, + 335 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Layout Decoder We adopt a layout decoder to estimate the class category $l_{k}$ , box center $c_{k}$ , size $s_{k}$ and completeness score $p_{k}$ from each object feature $x_{k}$ , which is implemented by two MLPs respectively:", + "bbox": [ + 75, + 340, + 468, + 402 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\{\\boldsymbol {l} _ {k}, \\boldsymbol {c} _ {k}, \\boldsymbol {s} _ {k}, \\boldsymbol {p} _ {k} \\right\\} = \\operatorname {M L P} _ {2} \\left(\\operatorname {M L P} _ {1} \\left(\\boldsymbol {x} _ {k}\\right)\\right), k = 1, \\dots , N. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 86, + 412, + 468, + 429 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The completeness $\\pmb{p}_k$ is a binary score of whether $\\pmb{x}_k$ is the last object or not, indicating whether we should continue object generation.", + "bbox": [ + 75, + 440, + 468, + 484 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Shape Decoder We estimate object shapes by deforming a template sphere from $\\pmb{x}_k$ . Inspired by [17], we use MLPs to learn the offsets from vertices $V \\in \\mathbb{R}^{|\\mathbf{V}| \\times 3}$ on the template sphere to the target surface by", + "bbox": [ + 75, + 491, + 468, + 551 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\Delta \\boldsymbol {v} _ {k} = \\operatorname {M L P} _ {3} (\\operatorname {C o n c a t} [ \\operatorname {M L P} _ {1} (\\boldsymbol {x} _ {k}), \\boldsymbol {v} ]), \\boldsymbol {v} \\in \\boldsymbol {V}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 116, + 563, + 468, + 579 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $V$ denotes the set of vertices on the template; $\\mathrm{MLP}_3$ is an point-wise MLP, and we share $\\mathrm{MLP}_1$ with Eq. 5. Afterwards, the vertices of the $k$ -th object mesh $M_k$ is predicted as $S_k = \\{\\pmb{v} + \\Delta \\pmb{v}_k\\}$ . Note that $M_k$ is in a canonical system, which is transformed to the world system with the bounding boxes in Eq. 5 by $\\pmb{o}_k = \\pmb{s}_k \\cdot \\pmb{M}_i + \\pmb{c}_k$ . Finally, we obtain $\\{\\pmb{o}_k\\}$ as the set of output objects in a scene.", + "bbox": [ + 75, + 590, + 468, + 696 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. View Loss", + "text_level": 1, + "bbox": [ + 76, + 705, + 191, + 720 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Instead of using 3D data, our method leverages multiviewed instance masks with tracks to supervise layout and shape generation. We consider $T$ views in a 3D scene with $n$ tracked objects $\\{o_j^{gt}\\}$ , $j = 1,\\dots,n$ . Each object $o_j^{gt}$ is observable in $T_{j}$ views, where $T_{j} \\subseteq T$ . We denote $\\pmb{m}_{j}^{p}$ as the mask of object $o_j^{gt}$ observed in the view $p \\in T_{j}$ . For each mask $\\pmb{m}_{j}^{p}$ , there are a class label $l_{j}^{gt}$ and camera parameters $\\mathrm{cam}^p$ .", + "bbox": [ + 75, + 728, + 468, + 853 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We train our model with a set of view losses between the ground-truth masks and the renderings of generated objects. We illustrate our training strategy in Fig. 4, which", + "bbox": [ + 75, + 854, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/0bad6c7a15676b406c7b37f0a321b45c9e33b28791df8d809a4746dcf173d6d8.jpg", + "image_caption": [ + "Figure 4. Optimization strategy for layout and shape training. We train layout learning and mesh deformation end-to-end with two stages to guarantee that objects are deformed after alignment." + ], + "image_footnote": [], + "bbox": [ + 506, + 89, + 903, + 237 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "is trained end-to-end with two stages: 1) layout pretraining and 2) layout+shape joint learning. We pretrain the layout first because 1) shape deformation from 2D requires an ideal alignment between its renderings and ground-truth masks; 2) differentiable rendering is not required in the first stage thus the efficiency is largely improved.", + "bbox": [ + 496, + 304, + 890, + 396 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Layout Loss Our network is initialized with all objects $\\{o_k\\}$ at the floor center. In the first stage, we learn the object layout without shape decoding (i.e., $\\Delta v_{k} = 0$ in Eq. 6). Only object categories, centers, sizes and completeness scores are optimized ( $\\{l_k, c_k, s_k, p_k\\}$ ). Therefore, we define the layout loss $\\mathcal{L}_{layout}$ as the combination of 1) classification loss $\\mathcal{L}_l$ ; 2) 2D bounding box loss $\\mathcal{L}_{box}$ ; 3) completeness loss $\\mathcal{L}_p$ , and 4) frustum loss $\\mathcal{L}_f$ .", + "bbox": [ + 496, + 400, + 890, + 521 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For an object prediction $\\pmb{o}_k$ , we project the vertices on its mesh to all views in $T$ and calculate the 2D bounding boxes $B_k = \\{b^1, \\dots, b^T\\}_k$ . For each ground-truth object $o_j^{gt}$ , we also have its 2D bounding boxes $B_j^{gt} = \\{b^1, \\dots, b^{T_j}\\}_j^{gt}$ in $T_j$ views. We let $l_k$ as the predicted class label of $o_k$ , and $l_j^{gt}$ as the ground-truth label of $o_j^{gt}$ respectively. For each prediction pair $(B_k, l_k)$ , we adopt the Hungarian algorithm [2, 43] to find its optimal bipartite matching $(B_{\\sigma(k)}^{gt}, l_{\\sigma(k)}^{gt})$ from the ground truth. Therefore we can obtain the matches from each prediction $o_k$ to a ground-truth $o_{\\sigma(k)}^{gt}$ , which is the basis of our loss functions. For details of Hungarian matching, we refer to the supplemental.", + "bbox": [ + 496, + 522, + 890, + 705 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Based on Hungarian matching, our layout loss can be formulated as", + "bbox": [ + 498, + 705, + 890, + 734 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {L} = \\lambda_ {l} \\mathcal {L} _ {l} + \\lambda_ {b o x} \\mathcal {L} _ {b o x} + \\lambda_ {p} \\mathcal {L} _ {p} + \\lambda_ {f} \\mathcal {L} _ {f}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 555, + 747, + 890, + 763 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_l$ is the cross-entropy loss between $l_{k}$ and $l_{\\sigma (k)}^{gt}$ for object classification; $\\mathcal{L}_{box}$ is the average $L_{1}$ distance between 2D bounding boxes in $B_{k}$ and $B_{\\sigma (k)}^{gt}$ on each view of $T_{\\sigma (k)}$ ; $\\mathcal{L}_p$ is the binary cross entropy loss to judge whether $\\boldsymbol{o}_k$ is the last object or not. For objects whose initial position is not located in a view frustum of their matched groundtruth, we design a frustum loss $\\mathcal{L}_f$ to enforce their 3D center $\\pmb{c}$ moving into the target frustum. Further details can be found in the supplemental.", + "bbox": [ + 496, + 773, + 890, + 910 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "795", + "bbox": [ + 485, + 945, + 509, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Shape Loss After the layout loss converges, we switch on the shape decoder in Eq. 6 and use 2D instance masks $\\{\\pmb{m}_j^p\\}$ for mesh deformation. In addition to 2D bounding boxes, we also render the soft silhouettes of each $\\pmb{o}_k$ on all views $T$ , by a soft silhouette Shader from [40]. The shape loss of $\\pmb{o}_k$ is defined as a multi-view mask loss as", + "bbox": [ + 76, + 90, + 472, + 181 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {S} = \\sum_ {p \\in T _ {\\sigma (k)}} \\operatorname {B C E} \\left(\\boldsymbol {r} _ {k} ^ {p}, \\boldsymbol {m} _ {\\sigma (k)} ^ {p}\\right) \\mathbb {1} [ \\operatorname {I o U} \\left(\\boldsymbol {r} _ {k} ^ {p}, \\boldsymbol {m} _ {\\sigma (k)} ^ {p}\\right) > 0. 5 ], \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 186, + 472, + 219 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\pmb{r}_k^p$ is the rendering of $\\pmb{o}_k$ in view $p\\in T_{\\sigma (k)};m_{\\sigma (k)}^p$ is the corresponding mask of $\\pmb{o}_{\\sigma (k)}^{gt}$ . For pairs whose IoU larger than 0.5, we use binary cross entropy to calculate the mask loss, which is inspired by [16] that we only use those well-aligned masks for supervision. We optimize $\\mathcal{L}_S$ to improve object mesh deformation.", + "bbox": [ + 75, + 220, + 468, + 314 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Finally, we train the our network end-to-end with $\\mathcal{L} = \\mathcal{L}_L + \\lambda_S\\mathcal{L}_S$ . All losses above are averaged across all objects. $\\{\\lambda \\}$ are weights that balance the losses.", + "bbox": [ + 76, + 315, + 468, + 361 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiment Setup", + "text_level": 1, + "bbox": [ + 76, + 372, + 253, + 388 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets and Tasks We train and test our method on two downstream tasks: 3D scene synthesis and single-view scene reconstruction.", + "bbox": [ + 75, + 397, + 468, + 441 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For scene synthesis, we use the 3D-FRONT [13] dataset for training and evaluation as in [36, 52]. 3D-FRONT is a synthetic indoor scene dataset with 18,968 rooms populated with 3D furniture objects, wherein we choose bedrooms and living rooms for our training and testing. We use [9] to sample virtual camera poses in each room and render the 2D instance masks for objects under different views, which produces 102,268 views in 3,922 bedrooms ( $\\approx$ 5.53 objects in each room), and 80,997 views in 1,496 living rooms ( $\\approx$ 9.82 objects in each room). For each room type, the train/test split ratio is 9:1 over rooms. We provide additional rendering details in the supplemental.", + "bbox": [ + 75, + 441, + 468, + 623 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For single-view scene reconstruction, we use the ScanNet dataset [7] for benchmarking. ScanNet is a real indoor scene dataset with 1,513 rooms in 21 room types. It provides 3D scans with semantic instance labels, as well as 2D scanning data where each room is captured into an RGB video sequence, and each frame contains a calibrated camera pose and 2D instance masks with tracking IDs. We uniformly sample up to 100 frames on each video and obtains 108,059 valid frames from all scenes. We use the official train/val split for our training and evaluation.", + "bbox": [ + 75, + 625, + 468, + 773 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implementation For each task, we train our network on 4 NVIDIA 2080 Ti GPUs with batch size at 16. Each sample in a batch contains a scene with 20 randomly sampled views. We augment each scene in 3D-FRONT and ScanNet with axis-aligned rotations by 90, 180, 270 degrees. As in Sec. 3.4, we train our network end-to-end with two stages. We first train the layout learning in first 800 epochs, followed by the shape learning with 500 epochs. We use Adam", + "bbox": [ + 75, + 780, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "as the optimizer with initial learning rate 1e-4, which is decayed by $0.1 \\times$ after 300 epochs, in both of the two stages. The losses are weighted by $\\lambda_{l} = \\lambda_{p} = \\lambda_{f} = 1$ , $\\lambda_{box} = 5$ , $\\lambda_{S} = 2$ to balance loss values. For layer and differentiable rendering specifications, we refer to the supplemental.", + "bbox": [ + 496, + 90, + 890, + 167 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For scene synthesis, we randomly sample latent vectors by Eq. 2 to synthesize diverse scenes. For single-view reconstruction, we freeze the generation network and take the single-view instance masks as the ground-truth to optimize the latent vector with our loss function. After it converges, we generate the 3D scene with the learned latent vector. We provide additional details about this optimization step in the supplemental.", + "bbox": [ + 496, + 167, + 890, + 287 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Evaluation Metrics We evaluate our method on the tasks of scene synthesis and single-view scene reconstruction using 3D-FRONT and ScanNet respectively. For scene synthesis, we generate 1000 scenes for each method and use FID score (FID), scene classification accuracy (SCA) and category KL divergence (KL) from [36] to measure the generation plausibility against the ground-truth in the test set. We refer readers to [36] for their definitions. For FID and SCA calculation, we render the generated and the ground-truth scenes into $512^2$ images with a top-down orthographic projection, where each object is textured with a unique category-specific color. We unify this setting among all baselines for a fair comparison.", + "bbox": [ + 496, + 296, + 892, + 492 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For single-view reconstruction, we use the metrics of 3D box IoU and chamfer distance between generated objects and the ground-truth. 3D box IoU measures the layout accuracy by comparing the 3D object bounding box between each ground-truth object and the prediction. Chamfer distance measures the accuracy of both layout and shape prediction. It calculates the point-wise $L_{2}$ distance between generated object surface points and the ground-truth.", + "bbox": [ + 496, + 493, + 890, + 613 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Results and Analysis", + "text_level": 1, + "bbox": [ + 500, + 628, + 696, + 645 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We evaluate our method qualitatively and quantitatively on the tasks of scene synthesis and single-view reconstruction in comparisons with state-of-the-art baselines, as well as scene interpolation and an ablation analysis on different network configurations.", + "bbox": [ + 496, + 654, + 890, + 729 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.1. Scene Synthesis", + "text_level": 1, + "bbox": [ + 500, + 739, + 656, + 756 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Baselines Since there are no previous works that synthesize 3D semantic instance scenes by learning from only 2D supervision, for a fair comparison, we use several state-of-the-art baselines while train them under 2D supervision. Additionally, we also compare with the state-of-the-art methods which use 3D training data, to explore the boundary of scene synthesis by learning with only 2D supervision. We consider the following baselines: 1) ATISS [36], a transformer encoder-based method that learns the distri", + "bbox": [ + 496, + 763, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "796", + "bbox": [ + 486, + 945, + 509, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/e5718e1ae9d37197196045640795ff22c2576a5176881effad9922bbf5c3199c.jpg", + "image_caption": [ + "Figure 5. Qualitative comparisons with the state-of-the-art on scene synthesis. Note that both ATISS [36] and Sync2Gen [52] use 3D data for training while our method learns with only 2D supervision." + ], + "image_footnote": [], + "bbox": [ + 89, + 87, + 282, + 443 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/6d8a773edf8258b443450aeee00d1028a74b75970eec878b0c961d6d50eb4174.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 287, + 87, + 480, + 443 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/52048f689036febfc750041ea29c954adfe57ba977ea86171c3dbb8bc54536bb.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 486, + 87, + 681, + 443 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/7657c0d80cb7f64d41890ca71e3a2aa31522a7d0441db735f82f865ef8869db4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 684, + 88, + 879, + 443 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "bution of 3D object bounding box properties. By progressively sampling from each property distribution, it generates a sequence of object boxes as the output. 2) Sync2Gen [52], a VAE-based method that maps a scene arrangement (parameterized with a sequence of 3D object attributes) to itself. After training, a 3D scene can be generated by sampling from the bottleneck latent distribution. 3) ATISS-2D. We use the transformer in ATISS [36] as the backbone and adapt it to be trainable under 2D supervision with our view loss. 4) GAN. We customize the generative adversary network for semantic scene synthesis from [53] to make it trainable with only 2D supervision. 5) LSTM. We replace our transformer with an LSTM network, while keeping other modules unchanged. Detailed architecture specifications are given in the supplemental. We train/test all methods on the same split for fair comparisons.", + "bbox": [ + 75, + 489, + 472, + 731 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Qualitative Comparisons Fig. 5 visualizes the qualitative comparisons with ATISS [36] and Sync2Gen [52], which are the state-of-the-art scene synthesis methods using 3D object data for training. While our method learns with only 2D supervision. Both the two methods add a shape retrieval post-processing to obtain object CAD models for evaluation. For fair comparison, we adopt shape retrieval by using Chamfer distance to measure the similarity between our reconstructed shape and CAD models in 3D-FRONT. We provide the details in the supplemental. From", + "bbox": [ + 75, + 750, + 472, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Fig. 5, we observe that ATISS is vulnerable to the penetration issues between object bounding boxes (row 2,3,4,6). Sync2Gen addresses this by involving a Bayesian optimization post-processing to refine object placement based on a 3D object arrangement prior, but it is still vulnerable to penetration issues (row 1,2,6). Our method learns object layout and shape from only 2D data, where we learn each object conditioned on the existence of previous generated objects under the multi-view constraint, which helps to avoid object intersections and produces plausible scene arrangements.", + "bbox": [ + 496, + 489, + 893, + 642 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Quantitative Comparisons Tab. 1 presents the quantitative comparisons between methods under different supervision sources. We observe that our method achieves better FID, SCA and KL scores against these methods using the same 2D supervision, which indicates that we produce better generation plausibility and more realistic object category distribution. To explore the boundary of our method, we also compare with prior arts which use 3D supervision. The results show that our method still presents better visual plausibility (FID and SCA scores) than ATISS, and shows comparable performance against Sync2Gen.", + "bbox": [ + 496, + 652, + 893, + 819 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Single-view Reconstruction", + "text_level": 1, + "bbox": [ + 500, + 830, + 745, + 847 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Baselines We evaluate our method on single-view instance reconstruction from real images, and compare with the prior arts which use 3D supervision: Total3D [34] and", + "bbox": [ + 496, + 854, + 893, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "797", + "bbox": [ + 486, + 945, + 509, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/d6e109e7c1dcf096987a89706bfbaeaac671be07d4455ccac118043840d8ee05.jpg", + "image_caption": [ + "(a) Input" + ], + "image_footnote": [], + "bbox": [ + 117, + 88, + 209, + 441 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/511afd759c4a3f994792a018e9115b0d5d349769419c89dfb3eaac763d6234b6.jpg", + "image_caption": [ + "(b) Total3D [34]" + ], + "image_footnote": [], + "bbox": [ + 215, + 89, + 395, + 441 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4945315c00eaca8b1408cb554688c337170721f9c92423a7f29a380911c3f01d.jpg", + "image_caption": [ + "(c) Im3D [56]" + ], + "image_footnote": [], + "bbox": [ + 400, + 90, + 578, + 441 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b5bc65336f849fe6693b2f114461bd11084a5c354b054955798cc13c6ba2ac95.jpg", + "image_caption": [ + "(d) Ours", + "Figure 6. Qualitative comparisons with the state-of-the-art on single view reconstruction. Note that both Total3D [36] and Im3D [52] use 3D data for training while our method learns from only 2D supervisions. For each method we present the reconstruction result from both the image view and a global view. For our method, we also provide the reconstruction result without shape retrieval on the left." + ], + "image_footnote": [], + "bbox": [ + 586, + 88, + 852, + 440 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/80ec695182bd57b987579beb0386d856a9fc96d8e7483eab6d1e8b1b389fcbd4.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
SupervisionBedroomLiving room
FID (↓)SCAKL (↓)FID (↓)SCAKL (↓)
ATISS [36]3D26.820.970.0150.020.970.02
Sync2Gen* [52]3D25.240.800.0335.340.880.02
Sync2Gen [52]3D23.860.830.0235.600.860.08
ATISS-2D [36]2D38.130.960.1065.070.980.36
GAN [53]2D24.420.970.0544.760.990.08
LSTM2D67.971.000.3086.771.000.26
Ours2D21.590.850.0340.470.960.02
", + "bbox": [ + 81, + 515, + 468, + 609 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 1. Quantitative comparisons on scene synthesis. Note that SCA score closer to 0.5 is better. Sync2Gen* is the version of [52] without Bayesian optimization. ATISS-2D is customized from ATISS [36] while using our 2D view loss. GAN is customized from [53] with using only 2D supervision.", + "bbox": [ + 76, + 621, + 468, + 691 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Im3D [56]. Both of them learn 3D scenes with a fully supervised manner, i.e., they require ground-truth object meshes, 2D detections, 3D posed object bounding boxes, and camera poses for training, while our method learns from multi-view 2D instance masks with camera poses. We also compare with USL [16] which is an unsupervised method without using 3D supervision. Similar with ours, they require multi-view tracked instance masks for learning. We train and test all methods using the official split on ScanNet. For Total3D [34] and Im3D [56], we use their pretrained model and finetune their 3D detector on ScanNet. For finetuning, we uniformly sample up to 20 views to cover each scene,", + "bbox": [ + 76, + 719, + 472, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "with each view contains at least three objects, which produces 11,395 valid views. For USL [16], we reproduce their network due to the unavailability of an official implementation, and train it on the same data with ours. For fair comparison, we use ground-truth 2D object detections and camera poses as the input for training and testing all baselines.", + "bbox": [ + 496, + 518, + 890, + 609 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Qualitative Comparisons Fig. 6 presents the qualitative comparisons with Total3D [34] and Im3D [56], which are the state-of-the-art single-view scene reconstruction methods. Both Total3D [34] and Im3D [56] pretrain their shape generator on a 3D shape dataset [44]. To produce better object geometry, our method keeps the shape retrieval in Sec. 5.1 while using the ShapeNet [5] dataset to retrieve CAD models given object positions and meshes. We observe that Total3D presents better mesh quality than Im3D. However, since objects in ScanNet images are usually occluded due to the high scene complexity, it struggles to estimate 3D object poses from 2D detections and results in erroneous object placement (row 1,3,5,6). Im3D addresses this by involving a refinement stage to improve object layout. However, for those severely occluded or partially visible objects, it is vulnerable to object penetration issues (row 1,3,7). Instead of detecting 3D objects from 2D detections (as in Total3D and Im3D), our method focuses on the prior learning of object arrangements, i.e., to understand what a", + "bbox": [ + 496, + 613, + 892, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "798", + "bbox": [ + 486, + 945, + 511, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/b914484c89b5b7b7fb219ba872a0be5cfd594e108f16484005af6c5dc0ac230e.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Supervision3D Box IoU (↑)CD (↓)
Total3D [34]3D0.151.36
Im3D [56]3D0.230.84
USL* [16]2D0.101.73
Ours (w/o retrieval)2D0.251.01
Ours2D0.270.79
", + "bbox": [ + 81, + 88, + 470, + 176 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "reasonable object layout looks like in multiple views, which helps to produce better scene configurations.", + "bbox": [ + 76, + 244, + 468, + 275 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Quantitative Comparisons Tab. 2 presents the quantitative comparisons, where we observe that Total3D [34] and USL [16] struggles to detect 3D object bounding boxes from 2D detections (lower 3D Box IoU) because both of them predict object centers by depth estimation, which is still a challenging problem due to the ambiguity. Our method attempts to reconstruct a plausible scene from the learned scene prior conditioned on the input instance masks, which presents more reasonable 3D object bounding boxes. Since training and testing our method requires instance masks for supervision, the mask quality has a direct influence to our reconstruction results. However, mask artifacts are inevitable in real images (row 1-5 in Fig. 6 (a)). By learning shapes from multi-view observations with a naive shape retrieval post-processing, our method presents convincing object layouts and geometries.", + "bbox": [ + 75, + 282, + 472, + 525 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.3. Discussion", + "text_level": 1, + "bbox": [ + 76, + 536, + 194, + 550 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Scene Interpolation Fig. 7 presents the interpolation results between two scenes. Given the latent vectors of two scenes, we interpolate intermediate vectors by sampling from the geodesic curve between them on the hypersphere surface (see Fig. 1). By decoding them, we can obtain the interpolated scenes. The transition between intermediates results show that our method interpolate not only the object pose and geometry but also the semantics and scene context, where the interpolated scenes are constrained with a reasonable scene layout.", + "bbox": [ + 75, + 559, + 468, + 710 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Ablations In Tab. 3 we investigate the effects of each submodule in scene synthesis, i.e., hyper-spherical latent space, permutation-invariant transformer, and stage-wise layout and shape learning, by replacing them with uniform latent space parameterization $(\\mathbf{c}_1)$ , LSTM $(\\mathbf{c}_2)$ , and one-stage layout and shape training $(\\mathbf{c}_3)$ , respectively. From the results, we observe that our transformer plays the most important role. LSTM encodes object order information. However, objects in a scene is an unordered set, and our transformer learns the permutation-invariant context to predict the next object recursively, which largely improves our performance. The hypersphere parameterization and stage-", + "bbox": [ + 75, + 719, + 470, + 901 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/c9b7d15d538d4650e255da6e89c9dccc863f6e5c2c815c1cce24bd89da9edc40.jpg", + "table_caption": [ + "Table 2. Quantitative comparisons on single-view reconstruction. Note that USL* is reproduced from [16] due to the unavailability of the official implementation." + ], + "table_footnote": [], + "table_body": "
BedroomLiving room
FID (↓)SCAKL (↓)FID (↓)SCAKL (↓)
c130.610.960.2495.511.000.38
c267.971.000.3086.771.000.26
c324.240.900.0443.430.980.03
Ours21.590.850.0340.470.960.02
", + "bbox": [ + 524, + 88, + 872, + 169 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 3. Ablation analysis on different configurations.", + "bbox": [ + 534, + 179, + 856, + 193 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/cf693cec7a010803257a5f00e63da3018f51fbc5ffeecae0418d046b10a79f8a.jpg", + "image_caption": [ + "Figure 7. Scene interpolation between two samples (the leftmost and the rightmost)." + ], + "image_footnote": [], + "bbox": [ + 503, + 202, + 888, + 282 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "wise training further increases the output plausibility and stabilizes the learning process, and combining them delivers the best performance.", + "bbox": [ + 498, + 335, + 890, + 381 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitations Since training our network requires 2D posed images with instance masks, erroneous camera poses or mask labels would mislead the learning process. We believe an interesting direction for future work is to incorporate an uncertainty model to learn stable scene priors from noisy masks and camera poses.", + "bbox": [ + 498, + 387, + 890, + 478 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 491, + 617, + 506 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We have presented a novel approach to learn the prior distribution of object layouts and shapes in 3D scenes with only 2D supervision. Our proposed method represents a 3D scene as a latent vector. By decoding it autoregressively using a permutation-invariant transformer, we recover a sequence of object instances characterized by their class categories, 3D bounding boxes and meshes. Since collecting 3D data at scale is expensive and intractable, we design a 2D view loss to train object generation using only 2D supervision. We demonstrate that such prior learning approach enables various downstream tasks, i.e., scene synthesis, interpolation and single-view reconstruction, and produces convincing scene arrangements. We hope that this establishes a step towards a universal self-supervised scene estimator that mimics human vision to understand, emulate and create 3D surroundings from only image observations.", + "bbox": [ + 496, + 516, + 890, + 758 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments This work was supported by the ERC Starting Grant Scan2CAD (804724), the German Research Foundation (DFG) Grant \"Making Machine Learning on Static and Dynamic 3D Data Practical\", the German Research Foundation (DFG) Research Unit \"Learning and Simulation in Visual Computing\", NSFC-62172348, and the Bavarian State Ministry of Science and the Arts coordinated by the Bavarian Research Institute for Digital Transformation (bidt).", + "bbox": [ + 496, + 763, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "799", + "bbox": [ + 486, + 945, + 509, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Armen Avetisyan, Manuel Dahnert, Angela Dai, Manolis Savva, Angel X Chang, and Matthias Nießner. 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Journal of Computer Science and Technology, 33(2):323-334, 2018. 2" + ], + "bbox": [ + 78, + 90, + 468, + 598 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "802", + "bbox": [ + 486, + 945, + 509, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Learning 3D Scene Priors With 2D Supervision/f5053186-7d13-4536-aa34-2cf3b485f9c7_model.json b/2023/Learning 3D Scene Priors With 2D Supervision/f5053186-7d13-4536-aa34-2cf3b485f9c7_model.json new file mode 100644 index 0000000000000000000000000000000000000000..7612611fcd4a95e814ac3ae8cbbf679fe7f76909 --- /dev/null +++ b/2023/Learning 3D Scene Priors With 2D Supervision/f5053186-7d13-4536-aa34-2cf3b485f9c7_model.json @@ -0,0 +1,2290 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.249, + 0.131, + 0.723, + 0.154 + ], + "angle": 0, + "content": "Learning 3D Scene Priors with 2D Supervision" + }, + { + "type": "text", + "bbox": [ + 0.141, + 0.18, + 0.825, + 0.218 + ], + "angle": 0, + "content": "Yinyu Nie1 Angela Dai1 Xiaoguang Han2 Matthias Nießner1 \n1Technical University of Munich 2The Chinese University of Hong Kong (Shenzhen)" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.252, + 0.314, + 0.267 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.284, + 0.473, + 0.617 + ], + "angle": 0, + "content": "Holistic 3D scene understanding entails estimation of both layout configuration and object geometry in a 3D environment. Recent works have shown advances in 3D scene estimation from various input modalities (e.g., images, 3D scans), by leveraging 3D supervision (e.g., 3D bounding boxes or CAD models), for which collection at scale is expensive and often intractable. To address this shortcoming, we propose a new method to learn 3D scene priors of layout and shape without requiring any 3D ground truth. Instead, we rely on 2D supervision from multi-view RGB images. Our method represents a 3D scene as a latent vector, from which we can progressively decode to a sequence of objects characterized by their class categories, 3D bounding boxes, and meshes. With our trained autoregressive decoder representing the scene prior, our method facilitates many downstream applications, including scene synthesis, interpolation, and single-view reconstruction. Experiments on 3DFRONT and ScanNet show that our method outperforms state of the art in single-view reconstruction, and achieves state-of-the-art results in scene synthesis against baselines which require for 3D supervision. Project page: https://yinyunie.github.io/scenegprior-page/" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.648, + 0.21, + 0.663 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.674, + 0.47, + 0.795 + ], + "angle": 0, + "content": "Understanding the geometric structures in real world scenes takes significant meaning in 3D computer vision. In recent years, many prominent approaches have been proposed to understand 3D scenes for different applications, e.g., scene synthesis [24,28,36,48,49,52] and semantic reconstruction [6,15,16,18-21,26,30,34,35,56]. These methods have shown initial promise in estimating object layouts and shapes in 3D scenes, from RGB or RGB-D input data." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.47, + 0.902 + ], + "angle": 0, + "content": "However, such methods have focused on leveraging full 3D supervision for layout and shape learning, in task-specific fashion. Such ground truth 3D scene geometry with semantic decomposition to objects and structures is difficult and expensive to acquire, requiring significant artist modeling efforts [13] or expert annotations [1] of CAD modeling. In contrast, 2D image and video acquisition is significantly" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.25, + 0.895, + 0.409 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.418, + 0.895, + 0.501 + ], + "angle": 0, + "content": "Figure 1. We learn 3D scene priors with 2D supervision. We model a latent hypersphere surface to represent a manifold of 3D scenes, characterizing the semantic and geometric distribution of objects in 3D scenes. This supports many downstream applications, including scene synthesis, interpolation and single-view reconstruction." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.52, + 0.894, + 0.626 + ], + "angle": 0, + "content": "more accessible. We thus propose to instead learn a general 3D scene prior from only multi-view 2D information. This approach takes a unified perspective to 3D scene understanding: our 3D scene prior is learned in a generalizable fashion from only multi-view 2D information, enabling application to multiple downstream tasks, including scene synthesis and single-view reconstruction." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.628, + 0.895, + 0.778 + ], + "angle": 0, + "content": "In order to understand geometric 3D scene structure from only multi-view RGB images, we must bridge the domain gap between 3D geometry and RGB colors. To this end, we propose to leverage the 2D semantic domain: we learn our 3D scene prior by ensuring that our learned 3D scene structures and objects, when differentiably rendered, match the 2D semantic distribution of estimated 2D instance segmentations from the RGB images. This enables supervision of 3D object and layout structures guided by 2D information." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Our 3D scene prior is learned by optimizing for a mapping from a latent space (parameterized as a hypersphere surface) to a manifold of 3D scenes, as shown in Fig. 1. Each random vector sampled from the latent space is decoded into a sequence of objects autoregressively using our permutation-invariant transformer. Each output object is characterized by their class category, 3D bounding box and mesh. By training this decoder, we encode the scene prior" + }, + { + "type": "page_number", + "bbox": [ + 0.486, + 0.946, + 0.512, + 0.957 + ], + "angle": 0, + "content": "792" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.166 + ], + "angle": 0, + "content": "into a latent space, sampling on which enables us to synthesize plausible 3D scenes. With such formulation, our method supports many other downstream tasks on different conditions, e.g., scene synthesis, interpolation and single-view reconstruction." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.168, + 0.447, + 0.182 + ], + "angle": 0, + "content": "In summary, we present our contributions as follows:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.189, + 0.468, + 0.263 + ], + "angle": 0, + "content": "- We present a new perspective on general 3D scene prior learning with only 2D supervision. We learn the prior distribution of both semantic object instance layouts and shapes via mapping from a latent space to the 3D scene space, by training from 2D multi-view data." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.266, + 0.468, + 0.368 + ], + "angle": 0, + "content": "- We formulate scene prior learning as an autoregressive sequence decoding problem, and propose a novel permutation-invariant transformer corresponding with a 2D view loss to map a latent vector from a hypersphere surface to a sequence of semantic instances characterized by their class categories, 3D bounding boxes and meshes." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.371, + 0.468, + 0.473 + ], + "angle": 0, + "content": "- Our learned 3D scene prior supports many downstream tasks: single-view scene reconstruction, scene synthesis and interpolation. Experiments on 3D-FRONT and ScanNet show that our method matches state-of-the-art performance in scene synthesis against methods requiring 3D supervision, and outperforms state of the art in single-view reconstruction." + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.189, + 0.468, + 0.473 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.497, + 0.219, + 0.512 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.523, + 0.468, + 0.627 + ], + "angle": 0, + "content": "3D Semantic Scene Synthesis 3D semantic scene synthesis has received extensive exploration in recent decades, particularly following the popularity of 3D indoor scene datasets and 3D deep learning. Given a collection of synthesized or real 3D scenes, many methods have been proposed to learn the distribution of object layouts to synthesize unseen but plausible 3D scene arrangements." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.63, + 0.468, + 0.869 + ], + "angle": 0, + "content": "Traditional methods for scene synthesis usually formulate the task as data-driven object placement [57], where a scene with object instances is represented as a graph [3, 4, 39, 59], or is connected to human activities to build a human-centric representation [12, 14, 31, 39]. Scene priors are explicitly hard-coded based on design guidelines [32, 54], represented by frequency statistics (e.g., objects co-occurrence map) [3, 4, 10], inferred by affordance map from human activities [12, 14, 22], or learned from arrangement examples in 3D scenes [11, 14]. Given an initial scene [14, 32, 54], a 2D sketch [51] or a text [3, 4], several methods synthesize object placements under the guidance of scene priors with different optimization strategies, e.g., manual interactions [4, 32, 42], iterative methods [12, 14, 29, 50] or non-linear optimization [3, 4, 11, 39, 51, 54, 55], to maximize a plausibility score or a joint probability." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.468, + 0.901 + ], + "angle": 0, + "content": "With deep learning techniques, many methods instead learn scene priors with neural networks. They keep the" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.227 + ], + "angle": 0, + "content": "problem formulation and use recurrent networks [29, 36, 41, 47-49], feed-forward models [33, 58], GANs [53], or VAEs [38, 52] to synthesize object poses recursively or in one stage from an initial scene or random noise, and usually require 3D information for training. In contrast, our method directly learns the joint semantic and geometric distribution of instances in scenes with 2D supervision, which enables a general scene priors that supports semantic scene synthesis from a latent random vector." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.233, + 0.892, + 0.52 + ], + "angle": 0, + "content": "Single-view Scene Reconstruction Single image reconstruction methods have also been designed around various task-specific, data-driven scene priors [6, 15, 16, 18, 20, 21, 25-27, 30, 34, 37, 45, 56]. Izadinia et al. [21] propose a deep learning-based method to retrieve and align CAD models to an input image. Further methods were developed with a similar top-down approach to reconstruct a scene by detection and retrieval, in which [20, 21, 25] use a render-and-compare strategy. [18, 26, 27] improve the offline shape retrieval with an end-to-end 2D-3D shape matching with pose alignment. Other works focus on shape reconstruction instead of retrieval, where object shapes are learned as meshes [15, 16, 34], volume grids [37, 45], or implicit functions [30, 30, 56] with the supervision of paired 3D object shapes or multi-view images. However, modeling scenes with a top-down manner usually focuses on per-object perception without any global scene reasoning. In contrast, we focus on learning prior distribution of 3D scenes, to generate plausible object layouts conditioned on an input image." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.534, + 0.634, + 0.551 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.559, + 0.892, + 0.633 + ], + "angle": 0, + "content": "Our work aims to learn the prior distribution of 3D semantic scenes. We formulate this problem by learning a mapping \\( f \\) from a parameterized latent space \\( \\mathcal{Z} \\) to the scene space \\( S \\), and hope each sample \\( z \\in \\mathcal{Z} \\) corresponds to a reasonable 3D scene \\( s \\in S \\) as in" + }, + { + "type": "equation", + "bbox": [ + 0.607, + 0.647, + 0.891, + 0.663 + ], + "angle": 0, + "content": "\\[\ns = f (z); z \\in \\mathcal {Z}, s \\in \\mathcal {S}. \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.892, + 0.9 + ], + "angle": 0, + "content": "In Eq. 1, there are four key components: the parameterization of latent space \\(\\mathcal{Z}\\) and scene space \\(S\\), the architecture of \\(f\\), and the losses to train \\(f\\). We illustrate our approach in Fig. 2, the latent space \\(\\mathcal{Z}\\) is represented as a unit hypersphere surface, each latent vector \\(\\mathbf{z}\\) sampled from which conditions the generation of an object sequence with our permutation-invariant transformer. We formulate a 3D scene \\(s \\in S\\) as a set of objects with their class categories, positions and shapes, thus each object from the transformer is decoded into a category label, a 3D bounding box and a mesh with a completeness score indicating whether the generated scene is complete or not. Training our network only needs 2D supervision. We design a 2D view loss between the renderings of generated scenes and the ground-truth instance masks under respective camera views." + }, + { + "type": "page_number", + "bbox": [ + 0.486, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "793" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.09, + 0.895, + 0.282 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.297, + 0.893, + 0.368 + ], + "angle": 0, + "content": "Figure 2. Overview of our approach. Our method represents each scene as a learnable latent vector \\( \\mathbf{z} \\) on a hypersphere. To build mapping from the latent surface to the semantic scene space, we propose a permutation-invariant transformer to generate objects \\( \\{\\pmb{x}_k\\} \\) autoregressively conditioned on previous objects and \\( \\mathbf{z} \\). For each object feature, we regress its object class label, 3D bounding box, shape feature and completeness score, which respectively represent the object layout, geometry, and the completeness of the output scene. We do not require 3D supervision, and instead leverage differentiable rendering with multi-view 2D instance masks supervision." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.381, + 0.353, + 0.397 + ], + "angle": 0, + "content": "3.1. Latent Space Parameterization" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.403, + 0.471, + 0.51 + ], + "angle": 0, + "content": "We parameterize the latent space \\(\\mathcal{Z}\\) as a unit hypersphere surface. We choose a spherical surface as the latent representation because it does not have strict boundaries (e.g., uniform distribution), and sampling on it will not produce outliers (e.g., gaussian distribution) [8], which guarantees the continuity when moving from one latent vector to another. We formulate the sampling process from \\(\\mathcal{Z}\\) as" + }, + { + "type": "equation", + "bbox": [ + 0.118, + 0.52, + 0.47, + 0.559 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {z} = \\frac {\\sum_ {i = 1} ^ {M} w _ {i} \\cdot \\phi_ {i}}{| | \\sum_ {i = 1} ^ {M} w _ {i} \\cdot \\phi_ {i} | | _ {2}}; \\sum_ {i = 1} ^ {M} w _ {i} = 1, w _ {i} > 0 \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.569, + 0.47, + 0.661 + ], + "angle": 0, + "content": "where \\(\\{\\phi_i|\\phi_i\\in \\mathbb{R}^{D_z},||\\phi_i||_2 = 1\\}\\) is a set of \\(M\\) fixed vectors with unit length, which uniformly spreads on the sphere surface. \\(D_{z}\\) is the dimension of the hypersphere. Therefore, by sampling a set of weights \\(\\{w_{i}\\}\\), we can obtain a latent vector \\(\\pmb {z}\\in \\mathbb{R}^{D_z}\\) for scene generation. Note that both \\(\\{w_{i}\\}\\) and our network \\(f\\) are learnable during training." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.669, + 0.391, + 0.685 + ], + "angle": 0, + "content": "3.2. Permutation-invariant Transformer" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.693, + 0.469, + 0.768 + ], + "angle": 0, + "content": "We generate a sequence of objects in a scene, conditioned on the latent vector \\( \\mathbf{z} \\), in an autoregressive fashion. New objects are generated conditioned on the previous ones, which can be formulated as to estimate the distribution of" + }, + { + "type": "equation", + "bbox": [ + 0.077, + 0.778, + 0.493, + 0.81 + ], + "angle": 0, + "content": "\\[\nP _ {\\theta} \\left(\\boldsymbol {x} _ {1}, \\dots , \\boldsymbol {x} _ {N} \\mid \\boldsymbol {z}\\right) = P _ {\\theta} \\left(\\boldsymbol {x} _ {1} \\mid \\boldsymbol {z}\\right) \\prod_ {k = 2} ^ {N} P _ {\\theta} \\left(\\boldsymbol {x} _ {k} \\mid \\boldsymbol {x} _ {1}, \\dots , \\boldsymbol {x} _ {k - 1}; \\boldsymbol {z}\\right), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.469, + 0.87 + ], + "angle": 0, + "content": "where \\( \\pmb{x}_k \\) denotes the \\( k \\)-th object feature. \\( N \\) is the maximal number of objects to be generated. \\( \\theta \\) is the trainable network. Every new object \\( \\pmb{x}_k \\) is generated conditioning on \\( \\pmb{x}_1, \\dots, \\pmb{x}_{k-1} \\) and \\( \\pmb{z} \\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "We observe that objects in a scene are an unordered set, where each permutation of an object sequence should be" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.381, + 0.893, + 0.456 + ], + "angle": 0, + "content": "equivalent to each other, e.g., [chair, table, lamp] should be equivalent to [lamp, chair, table] given the three objects. Thus, the generation of the next object \\( \\pmb{x}_k \\) should be independent to the order of previous objects \\( \\{x_1, \\dots, x_{k-1}\\} \\), which can be formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.515, + 0.48, + 0.875, + 0.498 + ], + "angle": 0, + "content": "\\[\nP _ {\\theta} \\left(\\boldsymbol {x} _ {k} \\mid \\boldsymbol {x} _ {p _ {1}}, \\dots , \\boldsymbol {x} _ {p _ {k - 1}}; \\boldsymbol {z}\\right) = P _ {\\theta} \\left(\\boldsymbol {x} _ {k} \\mid \\boldsymbol {x} _ {q _ {1}}, \\dots , \\boldsymbol {x} _ {q _ {k - 1}}; \\boldsymbol {z}\\right)\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.517, + 0.5, + 0.891, + 0.529 + ], + "angle": 0, + "content": "\\[\n1 \\leq p _ {i}, q _ {i} \\leq k - 1 \\text {a n d} p _ {i} \\neq p _ {j}, q _ {i} \\neq q _ {j}, \\forall i \\neq j. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.53, + 0.892, + 0.665 + ], + "angle": 0, + "content": "This requires our generation network to be permutation-invariant to the input objects. We model this step using a transformer backbone [23], which is illustrated in Fig. 3. Inspired by [36, 46] where removing the positional encoding in a transformer encoder makes the network agnostic to the object order, we consider this design and encode permutation-invariant scene context \\( \\pmb{F}_k \\in \\mathbb{R}^{k \\times D_z} \\) from previous objects \\( \\{\\pmb{x}_1, \\dots, \\pmb{x}_{k-1}\\} \\). Note that \\( \\pmb{x}_0 \\) in Fig. 2 and 3 is a learnable start token which indicates an empty room." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.666, + 0.892, + 0.788 + ], + "angle": 0, + "content": "\\(F_{k}\\) contains attention signals between object pairs and the scene context feature. We use \\(F_{k}\\) as the keys and values, and the latent vector \\(\\mathcal{Z}\\) as the query to infer the next object based on the scene context. We adopt a transformer decoder for object inference, where we also do not use positional encoding. Afterwards, it outputs the next possible object \\(\\pmb{x}_k\\in \\mathbb{R}^{D_z}\\). We forward this step autoregressively to obtain an object feature sequence \\(\\{\\pmb {x}_1,\\dots,\\pmb {x}_N\\}\\)." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.796, + 0.745, + 0.813 + ], + "angle": 0, + "content": "3.3. Layout and Shape Decoder" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.819, + 0.892, + 0.85 + ], + "angle": 0, + "content": "In this section, we decode object features \\(\\{\\pmb{x}_k\\}\\) into a set of object categories, 3D bounding boxes and shapes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Scene Parameterization We focus on indoor scenarios, and represent a 3D scene in a world coordinate system with the floor center located at the origin. Each object inside" + }, + { + "type": "page_number", + "bbox": [ + 0.486, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "794" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.09, + 0.483, + 0.198 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.206, + 0.471, + 0.262 + ], + "angle": 0, + "content": "Figure 3. Transformer for autoregressive object generation. From the start token \\( \\pmb{x}_0 \\), we design a permutation-invariant transformer to autoregressively generate a new object feature \\( \\pmb{x}_k \\) by querying the encoded scene context \\( \\pmb{F}_k \\) with the latent vector \\( \\pmb{z} \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.275, + 0.47, + 0.337 + ], + "angle": 0, + "content": "is characterized by its class label \\( l \\in \\mathbb{L} \\), axis-aligned 3D bounding box with size \\( s \\in \\mathbb{R}^3 \\) and center \\( c \\in \\mathbb{R}^3 \\), and 3D mesh \\( M \\in \\mathbb{M} \\) in the canonical system, where \\( \\mathbb{L} \\) denotes all class categories and \\( \\mathbb{M} \\) is the shape space." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.342, + 0.469, + 0.403 + ], + "angle": 0, + "content": "Layout Decoder We adopt a layout decoder to estimate the class category \\( l_{k} \\), box center \\( c_{k} \\), size \\( s_{k} \\) and completeness score \\( p_{k} \\) from each object feature \\( x_{k} \\), which is implemented by two MLPs respectively:" + }, + { + "type": "equation", + "bbox": [ + 0.088, + 0.413, + 0.469, + 0.43 + ], + "angle": 0, + "content": "\\[\n\\left\\{\\boldsymbol {l} _ {k}, \\boldsymbol {c} _ {k}, \\boldsymbol {s} _ {k}, \\boldsymbol {p} _ {k} \\right\\} = \\operatorname {M L P} _ {2} \\left(\\operatorname {M L P} _ {1} \\left(\\boldsymbol {x} _ {k}\\right)\\right), k = 1, \\dots , N. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.441, + 0.469, + 0.486 + ], + "angle": 0, + "content": "The completeness \\( \\pmb{p}_k \\) is a binary score of whether \\( \\pmb{x}_k \\) is the last object or not, indicating whether we should continue object generation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.492, + 0.469, + 0.553 + ], + "angle": 0, + "content": "Shape Decoder We estimate object shapes by deforming a template sphere from \\( \\pmb{x}_k \\). Inspired by [17], we use MLPs to learn the offsets from vertices \\( V \\in \\mathbb{R}^{|\\mathbf{V}| \\times 3} \\) on the template sphere to the target surface by" + }, + { + "type": "equation", + "bbox": [ + 0.117, + 0.564, + 0.469, + 0.58 + ], + "angle": 0, + "content": "\\[\n\\Delta \\boldsymbol {v} _ {k} = \\operatorname {M L P} _ {3} (\\operatorname {C o n c a t} [ \\operatorname {M L P} _ {1} (\\boldsymbol {x} _ {k}), \\boldsymbol {v} ]), \\boldsymbol {v} \\in \\boldsymbol {V}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.591, + 0.469, + 0.698 + ], + "angle": 0, + "content": "where \\(V\\) denotes the set of vertices on the template; \\(\\mathrm{MLP}_3\\) is an point-wise MLP, and we share \\(\\mathrm{MLP}_1\\) with Eq. 5. Afterwards, the vertices of the \\(k\\)-th object mesh \\(M_k\\) is predicted as \\(S_k = \\{\\pmb{v} + \\Delta \\pmb{v}_k\\}\\). Note that \\(M_k\\) is in a canonical system, which is transformed to the world system with the bounding boxes in Eq. 5 by \\(\\pmb{o}_k = \\pmb{s}_k \\cdot \\pmb{M}_i + \\pmb{c}_k\\). Finally, we obtain \\(\\{\\pmb{o}_k\\}\\) as the set of output objects in a scene." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.706, + 0.192, + 0.721 + ], + "angle": 0, + "content": "3.4. View Loss" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.729, + 0.469, + 0.854 + ], + "angle": 0, + "content": "Instead of using 3D data, our method leverages multiviewed instance masks with tracks to supervise layout and shape generation. We consider \\(T\\) views in a 3D scene with \\(n\\) tracked objects \\(\\{o_j^{gt}\\}\\), \\(j = 1,\\dots,n\\). Each object \\(o_j^{gt}\\) is observable in \\(T_{j}\\) views, where \\(T_{j} \\subseteq T\\). We denote \\(\\pmb{m}_{j}^{p}\\) as the mask of object \\(o_j^{gt}\\) observed in the view \\(p \\in T_{j}\\). For each mask \\(\\pmb{m}_{j}^{p}\\), there are a class label \\(l_{j}^{gt}\\) and camera parameters \\(\\mathrm{cam}^p\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.469, + 0.902 + ], + "angle": 0, + "content": "We train our model with a set of view losses between the ground-truth masks and the renderings of generated objects. We illustrate our training strategy in Fig. 4, which" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.09, + 0.905, + 0.238 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.25, + 0.892, + 0.293 + ], + "angle": 0, + "content": "Figure 4. Optimization strategy for layout and shape training. We train layout learning and mesh deformation end-to-end with two stages to guarantee that objects are deformed after alignment." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.305, + 0.892, + 0.397 + ], + "angle": 0, + "content": "is trained end-to-end with two stages: 1) layout pretraining and 2) layout+shape joint learning. We pretrain the layout first because 1) shape deformation from 2D requires an ideal alignment between its renderings and ground-truth masks; 2) differentiable rendering is not required in the first stage thus the efficiency is largely improved." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.401, + 0.892, + 0.522 + ], + "angle": 0, + "content": "Layout Loss Our network is initialized with all objects \\(\\{o_k\\}\\) at the floor center. In the first stage, we learn the object layout without shape decoding (i.e., \\(\\Delta v_{k} = 0\\) in Eq. 6). Only object categories, centers, sizes and completeness scores are optimized (\\(\\{l_k, c_k, s_k, p_k\\}\\)). Therefore, we define the layout loss \\(\\mathcal{L}_{layout}\\) as the combination of 1) classification loss \\(\\mathcal{L}_l\\); 2) 2D bounding box loss \\(\\mathcal{L}_{box}\\); 3) completeness loss \\(\\mathcal{L}_p\\), and 4) frustum loss \\(\\mathcal{L}_f\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.523, + 0.892, + 0.706 + ], + "angle": 0, + "content": "For an object prediction \\( \\pmb{o}_k \\), we project the vertices on its mesh to all views in \\( T \\) and calculate the 2D bounding boxes \\( B_k = \\{b^1, \\dots, b^T\\}_k \\). For each ground-truth object \\( o_j^{gt} \\), we also have its 2D bounding boxes \\( B_j^{gt} = \\{b^1, \\dots, b^{T_j}\\}_j^{gt} \\) in \\( T_j \\) views. We let \\( l_k \\) as the predicted class label of \\( o_k \\), and \\( l_j^{gt} \\) as the ground-truth label of \\( o_j^{gt} \\) respectively. For each prediction pair \\( (B_k, l_k) \\), we adopt the Hungarian algorithm [2, 43] to find its optimal bipartite matching \\( (B_{\\sigma(k)}^{gt}, l_{\\sigma(k)}^{gt}) \\) from the ground truth. Therefore we can obtain the matches from each prediction \\( o_k \\) to a ground-truth \\( o_{\\sigma(k)}^{gt} \\), which is the basis of our loss functions. For details of Hungarian matching, we refer to the supplemental." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.707, + 0.891, + 0.736 + ], + "angle": 0, + "content": "Based on Hungarian matching, our layout loss can be formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.557, + 0.748, + 0.891, + 0.765 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {L} = \\lambda_ {l} \\mathcal {L} _ {l} + \\lambda_ {b o x} \\mathcal {L} _ {b o x} + \\lambda_ {p} \\mathcal {L} _ {p} + \\lambda_ {f} \\mathcal {L} _ {f}, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.775, + 0.892, + 0.911 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_l\\) is the cross-entropy loss between \\(l_{k}\\) and \\(l_{\\sigma (k)}^{gt}\\) for object classification; \\(\\mathcal{L}_{box}\\) is the average \\(L_{1}\\) distance between 2D bounding boxes in \\(B_{k}\\) and \\(B_{\\sigma (k)}^{gt}\\) on each view of \\(T_{\\sigma (k)}\\); \\(\\mathcal{L}_p\\) is the binary cross entropy loss to judge whether \\(\\boldsymbol{o}_k\\) is the last object or not. For objects whose initial position is not located in a view frustum of their matched groundtruth, we design a frustum loss \\(\\mathcal{L}_f\\) to enforce their 3D center \\(\\pmb{c}\\) moving into the target frustum. Further details can be found in the supplemental." + }, + { + "type": "page_number", + "bbox": [ + 0.486, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "795" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.182 + ], + "angle": 0, + "content": "Shape Loss After the layout loss converges, we switch on the shape decoder in Eq. 6 and use 2D instance masks \\(\\{\\pmb{m}_j^p\\}\\) for mesh deformation. In addition to 2D bounding boxes, we also render the soft silhouettes of each \\(\\pmb{o}_k\\) on all views \\(T\\), by a soft silhouette Shader from [40]. The shape loss of \\(\\pmb{o}_k\\) is defined as a multi-view mask loss as" + }, + { + "type": "equation", + "bbox": [ + 0.078, + 0.188, + 0.473, + 0.22 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {S} = \\sum_ {p \\in T _ {\\sigma (k)}} \\operatorname {B C E} \\left(\\boldsymbol {r} _ {k} ^ {p}, \\boldsymbol {m} _ {\\sigma (k)} ^ {p}\\right) \\mathbb {1} [ \\operatorname {I o U} \\left(\\boldsymbol {r} _ {k} ^ {p}, \\boldsymbol {m} _ {\\sigma (k)} ^ {p}\\right) > 0. 5 ], \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.221, + 0.469, + 0.315 + ], + "angle": 0, + "content": "where \\(\\pmb{r}_k^p\\) is the rendering of \\(\\pmb{o}_k\\) in view \\(p\\in T_{\\sigma (k)};m_{\\sigma (k)}^p\\) is the corresponding mask of \\(\\pmb{o}_{\\sigma (k)}^{gt}\\). For pairs whose IoU larger than 0.5, we use binary cross entropy to calculate the mask loss, which is inspired by [16] that we only use those well-aligned masks for supervision. We optimize \\(\\mathcal{L}_S\\) to improve object mesh deformation." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.316, + 0.469, + 0.362 + ], + "angle": 0, + "content": "Finally, we train the our network end-to-end with \\(\\mathcal{L} = \\mathcal{L}_L + \\lambda_S\\mathcal{L}_S\\). All losses above are averaged across all objects. \\(\\{\\lambda \\}\\) are weights that balance the losses." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.373, + 0.254, + 0.39 + ], + "angle": 0, + "content": "4. Experiment Setup" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.398, + 0.469, + 0.442 + ], + "angle": 0, + "content": "Datasets and Tasks We train and test our method on two downstream tasks: 3D scene synthesis and single-view scene reconstruction." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.443, + 0.469, + 0.624 + ], + "angle": 0, + "content": "For scene synthesis, we use the 3D-FRONT [13] dataset for training and evaluation as in [36, 52]. 3D-FRONT is a synthetic indoor scene dataset with 18,968 rooms populated with 3D furniture objects, wherein we choose bedrooms and living rooms for our training and testing. We use [9] to sample virtual camera poses in each room and render the 2D instance masks for objects under different views, which produces 102,268 views in 3,922 bedrooms (\\(\\approx\\)5.53 objects in each room), and 80,997 views in 1,496 living rooms (\\(\\approx\\)9.82 objects in each room). For each room type, the train/test split ratio is 9:1 over rooms. We provide additional rendering details in the supplemental." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.625, + 0.469, + 0.775 + ], + "angle": 0, + "content": "For single-view scene reconstruction, we use the ScanNet dataset [7] for benchmarking. ScanNet is a real indoor scene dataset with 1,513 rooms in 21 room types. It provides 3D scans with semantic instance labels, as well as 2D scanning data where each room is captured into an RGB video sequence, and each frame contains a calibrated camera pose and 2D instance masks with tracking IDs. We uniformly sample up to 100 frames on each video and obtains 108,059 valid frames from all scenes. We use the official train/val split for our training and evaluation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Implementation For each task, we train our network on 4 NVIDIA 2080 Ti GPUs with batch size at 16. Each sample in a batch contains a scene with 20 randomly sampled views. We augment each scene in 3D-FRONT and ScanNet with axis-aligned rotations by 90, 180, 270 degrees. As in Sec. 3.4, we train our network end-to-end with two stages. We first train the layout learning in first 800 epochs, followed by the shape learning with 500 epochs. We use Adam" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.168 + ], + "angle": 0, + "content": "as the optimizer with initial learning rate 1e-4, which is decayed by \\(0.1 \\times\\) after 300 epochs, in both of the two stages. The losses are weighted by \\(\\lambda_{l} = \\lambda_{p} = \\lambda_{f} = 1\\), \\(\\lambda_{box} = 5\\), \\(\\lambda_{S} = 2\\) to balance loss values. For layer and differentiable rendering specifications, we refer to the supplemental." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.168, + 0.892, + 0.289 + ], + "angle": 0, + "content": "For scene synthesis, we randomly sample latent vectors by Eq. 2 to synthesize diverse scenes. For single-view reconstruction, we freeze the generation network and take the single-view instance masks as the ground-truth to optimize the latent vector with our loss function. After it converges, we generate the 3D scene with the learned latent vector. We provide additional details about this optimization step in the supplemental." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.297, + 0.893, + 0.493 + ], + "angle": 0, + "content": "Evaluation Metrics We evaluate our method on the tasks of scene synthesis and single-view scene reconstruction using 3D-FRONT and ScanNet respectively. For scene synthesis, we generate 1000 scenes for each method and use FID score (FID), scene classification accuracy (SCA) and category KL divergence (KL) from [36] to measure the generation plausibility against the ground-truth in the test set. We refer readers to [36] for their definitions. For FID and SCA calculation, we render the generated and the ground-truth scenes into \\(512^2\\) images with a top-down orthographic projection, where each object is textured with a unique category-specific color. We unify this setting among all baselines for a fair comparison." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.494, + 0.892, + 0.614 + ], + "angle": 0, + "content": "For single-view reconstruction, we use the metrics of 3D box IoU and chamfer distance between generated objects and the ground-truth. 3D box IoU measures the layout accuracy by comparing the 3D object bounding box between each ground-truth object and the prediction. Chamfer distance measures the accuracy of both layout and shape prediction. It calculates the point-wise \\( L_{2} \\) distance between generated object surface points and the ground-truth." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.63, + 0.697, + 0.646 + ], + "angle": 0, + "content": "5. Results and Analysis" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.655, + 0.892, + 0.731 + ], + "angle": 0, + "content": "We evaluate our method qualitatively and quantitatively on the tasks of scene synthesis and single-view reconstruction in comparisons with state-of-the-art baselines, as well as scene interpolation and an ablation analysis on different network configurations." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.741, + 0.657, + 0.757 + ], + "angle": 0, + "content": "5.1. Scene Synthesis" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Baselines Since there are no previous works that synthesize 3D semantic instance scenes by learning from only 2D supervision, for a fair comparison, we use several state-of-the-art baselines while train them under 2D supervision. Additionally, we also compare with the state-of-the-art methods which use 3D training data, to explore the boundary of scene synthesis by learning with only 2D supervision. We consider the following baselines: 1) ATISS [36], a transformer encoder-based method that learns the distri" + }, + { + "type": "page_number", + "bbox": [ + 0.487, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "796" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.091, + 0.088, + 0.284, + 0.444 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.289, + 0.088, + 0.482, + 0.444 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.487, + 0.088, + 0.682, + 0.444 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.685, + 0.089, + 0.88, + 0.444 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.454, + 0.894, + 0.484 + ], + "angle": 0, + "content": "Figure 5. Qualitative comparisons with the state-of-the-art on scene synthesis. Note that both ATISS [36] and Sync2Gen [52] use 3D data for training while our method learns with only 2D supervision." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.49, + 0.473, + 0.732 + ], + "angle": 0, + "content": "bution of 3D object bounding box properties. By progressively sampling from each property distribution, it generates a sequence of object boxes as the output. 2) Sync2Gen [52], a VAE-based method that maps a scene arrangement (parameterized with a sequence of 3D object attributes) to itself. After training, a 3D scene can be generated by sampling from the bottleneck latent distribution. 3) ATISS-2D. We use the transformer in ATISS [36] as the backbone and adapt it to be trainable under 2D supervision with our view loss. 4) GAN. We customize the generative adversary network for semantic scene synthesis from [53] to make it trainable with only 2D supervision. 5) LSTM. We replace our transformer with an LSTM network, while keeping other modules unchanged. Detailed architecture specifications are given in the supplemental. We train/test all methods on the same split for fair comparisons." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Qualitative Comparisons Fig. 5 visualizes the qualitative comparisons with ATISS [36] and Sync2Gen [52], which are the state-of-the-art scene synthesis methods using 3D object data for training. While our method learns with only 2D supervision. Both the two methods add a shape retrieval post-processing to obtain object CAD models for evaluation. For fair comparison, we adopt shape retrieval by using Chamfer distance to measure the similarity between our reconstructed shape and CAD models in 3D-FRONT. We provide the details in the supplemental. From" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.49, + 0.895, + 0.643 + ], + "angle": 0, + "content": "Fig. 5, we observe that ATISS is vulnerable to the penetration issues between object bounding boxes (row 2,3,4,6). Sync2Gen addresses this by involving a Bayesian optimization post-processing to refine object placement based on a 3D object arrangement prior, but it is still vulnerable to penetration issues (row 1,2,6). Our method learns object layout and shape from only 2D data, where we learn each object conditioned on the existence of previous generated objects under the multi-view constraint, which helps to avoid object intersections and produces plausible scene arrangements." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.653, + 0.895, + 0.82 + ], + "angle": 0, + "content": "Quantitative Comparisons Tab. 1 presents the quantitative comparisons between methods under different supervision sources. We observe that our method achieves better FID, SCA and KL scores against these methods using the same 2D supervision, which indicates that we produce better generation plausibility and more realistic object category distribution. To explore the boundary of our method, we also compare with prior arts which use 3D supervision. The results show that our method still presents better visual plausibility (FID and SCA scores) than ATISS, and shows comparable performance against Sync2Gen." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.831, + 0.746, + 0.848 + ], + "angle": 0, + "content": "5.2. Single-view Reconstruction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Baselines We evaluate our method on single-view instance reconstruction from real images, and compare with the prior arts which use 3D supervision: Total3D [34] and" + }, + { + "type": "page_number", + "bbox": [ + 0.487, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "797" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.119, + 0.089, + 0.21, + 0.442 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.14, + 0.445, + 0.188, + 0.456 + ], + "angle": 0, + "content": "(a) Input" + }, + { + "type": "image", + "bbox": [ + 0.217, + 0.09, + 0.396, + 0.442 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.261, + 0.442, + 0.351, + 0.455 + ], + "angle": 0, + "content": "(b) Total3D [34]" + }, + { + "type": "image", + "bbox": [ + 0.401, + 0.091, + 0.58, + 0.442 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.453, + 0.442, + 0.529, + 0.455 + ], + "angle": 0, + "content": "(c) Im3D [56]" + }, + { + "type": "image", + "bbox": [ + 0.587, + 0.089, + 0.853, + 0.441 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.696, + 0.441, + 0.743, + 0.453 + ], + "angle": 0, + "content": "(d) Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.469, + 0.895, + 0.512 + ], + "angle": 0, + "content": "Figure 6. Qualitative comparisons with the state-of-the-art on single view reconstruction. Note that both Total3D [36] and Im3D [52] use 3D data for training while our method learns from only 2D supervisions. For each method we present the reconstruction result from both the image view and a global view. For our method, we also provide the reconstruction result without shape retrieval on the left." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.516, + 0.469, + 0.611 + ], + "angle": 0, + "content": "
SupervisionBedroomLiving room
FID (↓)SCAKL (↓)FID (↓)SCAKL (↓)
ATISS [36]3D26.820.970.0150.020.970.02
Sync2Gen* [52]3D25.240.800.0335.340.880.02
Sync2Gen [52]3D23.860.830.0235.600.860.08
ATISS-2D [36]2D38.130.960.1065.070.980.36
GAN [53]2D24.420.970.0544.760.990.08
LSTM2D67.971.000.3086.771.000.26
Ours2D21.590.850.0340.470.960.02
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.622, + 0.47, + 0.692 + ], + "angle": 0, + "content": "Table 1. Quantitative comparisons on scene synthesis. Note that SCA score closer to 0.5 is better. Sync2Gen* is the version of [52] without Bayesian optimization. ATISS-2D is customized from ATISS [36] while using our 2D view loss. GAN is customized from [53] with using only 2D supervision." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.72, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Im3D [56]. Both of them learn 3D scenes with a fully supervised manner, i.e., they require ground-truth object meshes, 2D detections, 3D posed object bounding boxes, and camera poses for training, while our method learns from multi-view 2D instance masks with camera poses. We also compare with USL [16] which is an unsupervised method without using 3D supervision. Similar with ours, they require multi-view tracked instance masks for learning. We train and test all methods using the official split on ScanNet. For Total3D [34] and Im3D [56], we use their pretrained model and finetune their 3D detector on ScanNet. For finetuning, we uniformly sample up to 20 views to cover each scene," + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.519, + 0.892, + 0.61 + ], + "angle": 0, + "content": "with each view contains at least three objects, which produces 11,395 valid views. For USL [16], we reproduce their network due to the unavailability of an official implementation, and train it on the same data with ours. For fair comparison, we use ground-truth 2D object detections and camera poses as the input for training and testing all baselines." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Qualitative Comparisons Fig. 6 presents the qualitative comparisons with Total3D [34] and Im3D [56], which are the state-of-the-art single-view scene reconstruction methods. Both Total3D [34] and Im3D [56] pretrain their shape generator on a 3D shape dataset [44]. To produce better object geometry, our method keeps the shape retrieval in Sec. 5.1 while using the ShapeNet [5] dataset to retrieve CAD models given object positions and meshes. We observe that Total3D presents better mesh quality than Im3D. However, since objects in ScanNet images are usually occluded due to the high scene complexity, it struggles to estimate 3D object poses from 2D detections and results in erroneous object placement (row 1,3,5,6). Im3D addresses this by involving a refinement stage to improve object layout. However, for those severely occluded or partially visible objects, it is vulnerable to object penetration issues (row 1,3,7). Instead of detecting 3D objects from 2D detections (as in Total3D and Im3D), our method focuses on the prior learning of object arrangements, i.e., to understand what a" + }, + { + "type": "page_number", + "bbox": [ + 0.487, + 0.946, + 0.512, + 0.957 + ], + "angle": 0, + "content": "798" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.089, + 0.472, + 0.178 + ], + "angle": 0, + "content": "
Supervision3D Box IoU (↑)CD (↓)
Total3D [34]3D0.151.36
Im3D [56]3D0.230.84
USL* [16]2D0.101.73
Ours (w/o retrieval)2D0.251.01
Ours2D0.270.79
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.188, + 0.47, + 0.23 + ], + "angle": 0, + "content": "Table 2. Quantitative comparisons on single-view reconstruction. Note that USL* is reproduced from [16] due to the unavailability of the official implementation." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.245, + 0.47, + 0.276 + ], + "angle": 0, + "content": "reasonable object layout looks like in multiple views, which helps to produce better scene configurations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.284, + 0.473, + 0.526 + ], + "angle": 0, + "content": "Quantitative Comparisons Tab. 2 presents the quantitative comparisons, where we observe that Total3D [34] and USL [16] struggles to detect 3D object bounding boxes from 2D detections (lower 3D Box IoU) because both of them predict object centers by depth estimation, which is still a challenging problem due to the ambiguity. Our method attempts to reconstruct a plausible scene from the learned scene prior conditioned on the input instance masks, which presents more reasonable 3D object bounding boxes. Since training and testing our method requires instance masks for supervision, the mask quality has a direct influence to our reconstruction results. However, mask artifacts are inevitable in real images (row 1-5 in Fig. 6 (a)). By learning shapes from multi-view observations with a naive shape retrieval post-processing, our method presents convincing object layouts and geometries." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.537, + 0.196, + 0.551 + ], + "angle": 0, + "content": "5.3. Discussion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.56, + 0.47, + 0.712 + ], + "angle": 0, + "content": "Scene Interpolation Fig. 7 presents the interpolation results between two scenes. Given the latent vectors of two scenes, we interpolate intermediate vectors by sampling from the geodesic curve between them on the hypersphere surface (see Fig. 1). By decoding them, we can obtain the interpolated scenes. The transition between intermediates results show that our method interpolate not only the object pose and geometry but also the semantics and scene context, where the interpolated scenes are constrained with a reasonable scene layout." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Ablations In Tab. 3 we investigate the effects of each submodule in scene synthesis, i.e., hyper-spherical latent space, permutation-invariant transformer, and stage-wise layout and shape learning, by replacing them with uniform latent space parameterization \\((\\mathbf{c}_1)\\), LSTM \\((\\mathbf{c}_2)\\), and one-stage layout and shape training \\((\\mathbf{c}_3)\\), respectively. From the results, we observe that our transformer plays the most important role. LSTM encodes object order information. However, objects in a scene is an unordered set, and our transformer learns the permutation-invariant context to predict the next object recursively, which largely improves our performance. The hypersphere parameterization and stage-" + }, + { + "type": "table", + "bbox": [ + 0.525, + 0.089, + 0.874, + 0.17 + ], + "angle": 0, + "content": "
BedroomLiving room
FID (↓)SCAKL (↓)FID (↓)SCAKL (↓)
c130.610.960.2495.511.000.38
c267.971.000.3086.771.000.26
c324.240.900.0443.430.980.03
Ours21.590.850.0340.470.960.02
" + }, + { + "type": "table_caption", + "bbox": [ + 0.535, + 0.18, + 0.857, + 0.194 + ], + "angle": 0, + "content": "Table 3. Ablation analysis on different configurations." + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.203, + 0.89, + 0.284 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.294, + 0.892, + 0.323 + ], + "angle": 0, + "content": "Figure 7. Scene interpolation between two samples (the leftmost and the rightmost)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.336, + 0.892, + 0.382 + ], + "angle": 0, + "content": "wise training further increases the output plausibility and stabilizes the learning process, and combining them delivers the best performance." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.388, + 0.892, + 0.479 + ], + "angle": 0, + "content": "Limitations Since training our network requires 2D posed images with instance masks, erroneous camera poses or mask labels would mislead the learning process. We believe an interesting direction for future work is to incorporate an uncertainty model to learn stable scene priors from noisy masks and camera poses." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.492, + 0.619, + 0.507 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.517, + 0.892, + 0.759 + ], + "angle": 0, + "content": "We have presented a novel approach to learn the prior distribution of object layouts and shapes in 3D scenes with only 2D supervision. Our proposed method represents a 3D scene as a latent vector. By decoding it autoregressively using a permutation-invariant transformer, we recover a sequence of object instances characterized by their class categories, 3D bounding boxes and meshes. Since collecting 3D data at scale is expensive and intractable, we design a 2D view loss to train object generation using only 2D supervision. We demonstrate that such prior learning approach enables various downstream tasks, i.e., scene synthesis, interpolation and single-view reconstruction, and produces convincing scene arrangements. We hope that this establishes a step towards a universal self-supervised scene estimator that mimics human vision to understand, emulate and create 3D surroundings from only image observations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Acknowledgments This work was supported by the ERC Starting Grant Scan2CAD (804724), the German Research Foundation (DFG) Grant \"Making Machine Learning on Static and Dynamic 3D Data Practical\", the German Research Foundation (DFG) Research Unit \"Learning and Simulation in Visual Computing\", NSFC-62172348, and the Bavarian State Ministry of Science and the Arts coordinated by the Bavarian Research Institute for Digital Transformation (bidt)." + }, + { + "type": "page_number", + "bbox": [ + 0.487, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "799" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.186 + ], + "angle": 0, + "content": "[1] Armen Avetisyan, Manuel Dahnert, Angela Dai, Manolis Savva, Angel X Chang, and Matthias Nießner. 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Recent works have shown advances in 3D scene estimation from various input modalities (e.g., images, 3D scans), by leveraging 3D supervision (e.g., 3D bounding boxes or CAD models), for which collection at scale is expensive and often intractable. To address this shortcoming, we propose a new method to learn 3D scene priors of layout and shape without requiring any 3D ground truth. Instead, we rely on 2D supervision from multi-view RGB images. Our method represents a 3D scene as a latent vector, from which we can progressively decode to a sequence of objects characterized by their class categories, 3D bounding boxes, and meshes. With our trained autoregressive decoder representing the scene prior, our method facilitates many downstream applications, including scene synthesis, interpolation, and single-view reconstruction. Experiments on 3DFRONT and ScanNet show that our method outperforms state of the art in single-view reconstruction, and achieves state-of-the-art results in scene synthesis against baselines which require for 3D supervision. Project page: https://yinyunie.github.io/scenegprior-page/ + +# 1. Introduction + +Understanding the geometric structures in real world scenes takes significant meaning in 3D computer vision. In recent years, many prominent approaches have been proposed to understand 3D scenes for different applications, e.g., scene synthesis [24,28,36,48,49,52] and semantic reconstruction [6,15,16,18-21,26,30,34,35,56]. These methods have shown initial promise in estimating object layouts and shapes in 3D scenes, from RGB or RGB-D input data. + +However, such methods have focused on leveraging full 3D supervision for layout and shape learning, in task-specific fashion. Such ground truth 3D scene geometry with semantic decomposition to objects and structures is difficult and expensive to acquire, requiring significant artist modeling efforts [13] or expert annotations [1] of CAD modeling. In contrast, 2D image and video acquisition is significantly + +![](images/2b0a187f95ac48cfbbaa3a6c5333e4d183427f04e59bd10d71691b85ffefbfe7.jpg) +Figure 1. We learn 3D scene priors with 2D supervision. We model a latent hypersphere surface to represent a manifold of 3D scenes, characterizing the semantic and geometric distribution of objects in 3D scenes. This supports many downstream applications, including scene synthesis, interpolation and single-view reconstruction. + +more accessible. We thus propose to instead learn a general 3D scene prior from only multi-view 2D information. This approach takes a unified perspective to 3D scene understanding: our 3D scene prior is learned in a generalizable fashion from only multi-view 2D information, enabling application to multiple downstream tasks, including scene synthesis and single-view reconstruction. + +In order to understand geometric 3D scene structure from only multi-view RGB images, we must bridge the domain gap between 3D geometry and RGB colors. To this end, we propose to leverage the 2D semantic domain: we learn our 3D scene prior by ensuring that our learned 3D scene structures and objects, when differentiably rendered, match the 2D semantic distribution of estimated 2D instance segmentations from the RGB images. This enables supervision of 3D object and layout structures guided by 2D information. + +Our 3D scene prior is learned by optimizing for a mapping from a latent space (parameterized as a hypersphere surface) to a manifold of 3D scenes, as shown in Fig. 1. Each random vector sampled from the latent space is decoded into a sequence of objects autoregressively using our permutation-invariant transformer. Each output object is characterized by their class category, 3D bounding box and mesh. By training this decoder, we encode the scene prior + +into a latent space, sampling on which enables us to synthesize plausible 3D scenes. With such formulation, our method supports many other downstream tasks on different conditions, e.g., scene synthesis, interpolation and single-view reconstruction. + +In summary, we present our contributions as follows: + +- We present a new perspective on general 3D scene prior learning with only 2D supervision. We learn the prior distribution of both semantic object instance layouts and shapes via mapping from a latent space to the 3D scene space, by training from 2D multi-view data. +- We formulate scene prior learning as an autoregressive sequence decoding problem, and propose a novel permutation-invariant transformer corresponding with a 2D view loss to map a latent vector from a hypersphere surface to a sequence of semantic instances characterized by their class categories, 3D bounding boxes and meshes. +- Our learned 3D scene prior supports many downstream tasks: single-view scene reconstruction, scene synthesis and interpolation. Experiments on 3D-FRONT and ScanNet show that our method matches state-of-the-art performance in scene synthesis against methods requiring 3D supervision, and outperforms state of the art in single-view reconstruction. + +# 2. Related Work + +3D Semantic Scene Synthesis 3D semantic scene synthesis has received extensive exploration in recent decades, particularly following the popularity of 3D indoor scene datasets and 3D deep learning. Given a collection of synthesized or real 3D scenes, many methods have been proposed to learn the distribution of object layouts to synthesize unseen but plausible 3D scene arrangements. + +Traditional methods for scene synthesis usually formulate the task as data-driven object placement [57], where a scene with object instances is represented as a graph [3, 4, 39, 59], or is connected to human activities to build a human-centric representation [12, 14, 31, 39]. Scene priors are explicitly hard-coded based on design guidelines [32, 54], represented by frequency statistics (e.g., objects co-occurrence map) [3, 4, 10], inferred by affordance map from human activities [12, 14, 22], or learned from arrangement examples in 3D scenes [11, 14]. Given an initial scene [14, 32, 54], a 2D sketch [51] or a text [3, 4], several methods synthesize object placements under the guidance of scene priors with different optimization strategies, e.g., manual interactions [4, 32, 42], iterative methods [12, 14, 29, 50] or non-linear optimization [3, 4, 11, 39, 51, 54, 55], to maximize a plausibility score or a joint probability. + +With deep learning techniques, many methods instead learn scene priors with neural networks. They keep the + +problem formulation and use recurrent networks [29, 36, 41, 47-49], feed-forward models [33, 58], GANs [53], or VAEs [38, 52] to synthesize object poses recursively or in one stage from an initial scene or random noise, and usually require 3D information for training. In contrast, our method directly learns the joint semantic and geometric distribution of instances in scenes with 2D supervision, which enables a general scene priors that supports semantic scene synthesis from a latent random vector. + +Single-view Scene Reconstruction Single image reconstruction methods have also been designed around various task-specific, data-driven scene priors [6, 15, 16, 18, 20, 21, 25-27, 30, 34, 37, 45, 56]. Izadinia et al. [21] propose a deep learning-based method to retrieve and align CAD models to an input image. Further methods were developed with a similar top-down approach to reconstruct a scene by detection and retrieval, in which [20, 21, 25] use a render-and-compare strategy. [18, 26, 27] improve the offline shape retrieval with an end-to-end 2D-3D shape matching with pose alignment. Other works focus on shape reconstruction instead of retrieval, where object shapes are learned as meshes [15, 16, 34], volume grids [37, 45], or implicit functions [30, 30, 56] with the supervision of paired 3D object shapes or multi-view images. However, modeling scenes with a top-down manner usually focuses on per-object perception without any global scene reasoning. In contrast, we focus on learning prior distribution of 3D scenes, to generate plausible object layouts conditioned on an input image. + +# 3. Methodology + +Our work aims to learn the prior distribution of 3D semantic scenes. We formulate this problem by learning a mapping $f$ from a parameterized latent space $\mathcal{Z}$ to the scene space $S$ , and hope each sample $z \in \mathcal{Z}$ corresponds to a reasonable 3D scene $s \in S$ as in + +$$ +s = f (z); z \in \mathcal {Z}, s \in \mathcal {S}. \tag {1} +$$ + +In Eq. 1, there are four key components: the parameterization of latent space $\mathcal{Z}$ and scene space $S$ , the architecture of $f$ , and the losses to train $f$ . We illustrate our approach in Fig. 2, the latent space $\mathcal{Z}$ is represented as a unit hypersphere surface, each latent vector $\mathbf{z}$ sampled from which conditions the generation of an object sequence with our permutation-invariant transformer. We formulate a 3D scene $s \in S$ as a set of objects with their class categories, positions and shapes, thus each object from the transformer is decoded into a category label, a 3D bounding box and a mesh with a completeness score indicating whether the generated scene is complete or not. Training our network only needs 2D supervision. We design a 2D view loss between the renderings of generated scenes and the ground-truth instance masks under respective camera views. + +![](images/e0f9d4b9bd2f0698f40e49926f175187e8277a859aa02ace5ad02c9b9c2f1813.jpg) +Figure 2. Overview of our approach. Our method represents each scene as a learnable latent vector $\mathbf{z}$ on a hypersphere. To build mapping from the latent surface to the semantic scene space, we propose a permutation-invariant transformer to generate objects $\{\pmb{x}_k\}$ autoregressively conditioned on previous objects and $\mathbf{z}$ . For each object feature, we regress its object class label, 3D bounding box, shape feature and completeness score, which respectively represent the object layout, geometry, and the completeness of the output scene. We do not require 3D supervision, and instead leverage differentiable rendering with multi-view 2D instance masks supervision. + +# 3.1. Latent Space Parameterization + +We parameterize the latent space $\mathcal{Z}$ as a unit hypersphere surface. We choose a spherical surface as the latent representation because it does not have strict boundaries (e.g., uniform distribution), and sampling on it will not produce outliers (e.g., gaussian distribution) [8], which guarantees the continuity when moving from one latent vector to another. We formulate the sampling process from $\mathcal{Z}$ as + +$$ +\boldsymbol {z} = \frac {\sum_ {i = 1} ^ {M} w _ {i} \cdot \phi_ {i}}{| | \sum_ {i = 1} ^ {M} w _ {i} \cdot \phi_ {i} | | _ {2}}; \sum_ {i = 1} ^ {M} w _ {i} = 1, w _ {i} > 0 \tag {2} +$$ + +where $\{\phi_i|\phi_i\in \mathbb{R}^{D_z},||\phi_i||_2 = 1\}$ is a set of $M$ fixed vectors with unit length, which uniformly spreads on the sphere surface. $D_{z}$ is the dimension of the hypersphere. Therefore, by sampling a set of weights $\{w_{i}\}$ , we can obtain a latent vector $\pmb {z}\in \mathbb{R}^{D_z}$ for scene generation. Note that both $\{w_{i}\}$ and our network $f$ are learnable during training. + +# 3.2. Permutation-invariant Transformer + +We generate a sequence of objects in a scene, conditioned on the latent vector $\mathbf{z}$ , in an autoregressive fashion. New objects are generated conditioned on the previous ones, which can be formulated as to estimate the distribution of + +$$ +P _ {\theta} \left(\boldsymbol {x} _ {1}, \dots , \boldsymbol {x} _ {N} \mid \boldsymbol {z}\right) = P _ {\theta} \left(\boldsymbol {x} _ {1} \mid \boldsymbol {z}\right) \prod_ {k = 2} ^ {N} P _ {\theta} \left(\boldsymbol {x} _ {k} \mid \boldsymbol {x} _ {1}, \dots , \boldsymbol {x} _ {k - 1}; \boldsymbol {z}\right), \tag {3} +$$ + +where $\pmb{x}_k$ denotes the $k$ -th object feature. $N$ is the maximal number of objects to be generated. $\theta$ is the trainable network. Every new object $\pmb{x}_k$ is generated conditioning on $\pmb{x}_1, \dots, \pmb{x}_{k-1}$ and $\pmb{z}$ . + +We observe that objects in a scene are an unordered set, where each permutation of an object sequence should be + +equivalent to each other, e.g., [chair, table, lamp] should be equivalent to [lamp, chair, table] given the three objects. Thus, the generation of the next object $\pmb{x}_k$ should be independent to the order of previous objects $\{x_1, \dots, x_{k-1}\}$ , which can be formulated as + +$$ +P _ {\theta} \left(\boldsymbol {x} _ {k} \mid \boldsymbol {x} _ {p _ {1}}, \dots , \boldsymbol {x} _ {p _ {k - 1}}; \boldsymbol {z}\right) = P _ {\theta} \left(\boldsymbol {x} _ {k} \mid \boldsymbol {x} _ {q _ {1}}, \dots , \boldsymbol {x} _ {q _ {k - 1}}; \boldsymbol {z}\right) +$$ + +$$ +1 \leq p _ {i}, q _ {i} \leq k - 1 \text {a n d} p _ {i} \neq p _ {j}, q _ {i} \neq q _ {j}, \forall i \neq j. \tag {4} +$$ + +This requires our generation network to be permutation-invariant to the input objects. We model this step using a transformer backbone [23], which is illustrated in Fig. 3. Inspired by [36, 46] where removing the positional encoding in a transformer encoder makes the network agnostic to the object order, we consider this design and encode permutation-invariant scene context $\pmb{F}_k \in \mathbb{R}^{k \times D_z}$ from previous objects $\{\pmb{x}_1, \dots, \pmb{x}_{k-1}\}$ . Note that $\pmb{x}_0$ in Fig. 2 and 3 is a learnable start token which indicates an empty room. + +$F_{k}$ contains attention signals between object pairs and the scene context feature. We use $F_{k}$ as the keys and values, and the latent vector $\mathcal{Z}$ as the query to infer the next object based on the scene context. We adopt a transformer decoder for object inference, where we also do not use positional encoding. Afterwards, it outputs the next possible object $\pmb{x}_k\in \mathbb{R}^{D_z}$ . We forward this step autoregressively to obtain an object feature sequence $\{\pmb {x}_1,\dots,\pmb {x}_N\}$ . + +# 3.3. Layout and Shape Decoder + +In this section, we decode object features $\{\pmb{x}_k\}$ into a set of object categories, 3D bounding boxes and shapes. + +Scene Parameterization We focus on indoor scenarios, and represent a 3D scene in a world coordinate system with the floor center located at the origin. Each object inside + +![](images/8f816f149ecd90c1b41fda70ad1d4992b79cb8138a11196a46cf34d937893ab8.jpg) +Figure 3. Transformer for autoregressive object generation. From the start token $\pmb{x}_0$ , we design a permutation-invariant transformer to autoregressively generate a new object feature $\pmb{x}_k$ by querying the encoded scene context $\pmb{F}_k$ with the latent vector $\pmb{z}$ . + +is characterized by its class label $l \in \mathbb{L}$ , axis-aligned 3D bounding box with size $s \in \mathbb{R}^3$ and center $c \in \mathbb{R}^3$ , and 3D mesh $M \in \mathbb{M}$ in the canonical system, where $\mathbb{L}$ denotes all class categories and $\mathbb{M}$ is the shape space. + +Layout Decoder We adopt a layout decoder to estimate the class category $l_{k}$ , box center $c_{k}$ , size $s_{k}$ and completeness score $p_{k}$ from each object feature $x_{k}$ , which is implemented by two MLPs respectively: + +$$ +\left\{\boldsymbol {l} _ {k}, \boldsymbol {c} _ {k}, \boldsymbol {s} _ {k}, \boldsymbol {p} _ {k} \right\} = \operatorname {M L P} _ {2} \left(\operatorname {M L P} _ {1} \left(\boldsymbol {x} _ {k}\right)\right), k = 1, \dots , N. \tag {5} +$$ + +The completeness $\pmb{p}_k$ is a binary score of whether $\pmb{x}_k$ is the last object or not, indicating whether we should continue object generation. + +Shape Decoder We estimate object shapes by deforming a template sphere from $\pmb{x}_k$ . Inspired by [17], we use MLPs to learn the offsets from vertices $V \in \mathbb{R}^{|\mathbf{V}| \times 3}$ on the template sphere to the target surface by + +$$ +\Delta \boldsymbol {v} _ {k} = \operatorname {M L P} _ {3} (\operatorname {C o n c a t} [ \operatorname {M L P} _ {1} (\boldsymbol {x} _ {k}), \boldsymbol {v} ]), \boldsymbol {v} \in \boldsymbol {V}, \tag {6} +$$ + +where $V$ denotes the set of vertices on the template; $\mathrm{MLP}_3$ is an point-wise MLP, and we share $\mathrm{MLP}_1$ with Eq. 5. Afterwards, the vertices of the $k$ -th object mesh $M_k$ is predicted as $S_k = \{\pmb{v} + \Delta \pmb{v}_k\}$ . Note that $M_k$ is in a canonical system, which is transformed to the world system with the bounding boxes in Eq. 5 by $\pmb{o}_k = \pmb{s}_k \cdot \pmb{M}_i + \pmb{c}_k$ . Finally, we obtain $\{\pmb{o}_k\}$ as the set of output objects in a scene. + +# 3.4. View Loss + +Instead of using 3D data, our method leverages multiviewed instance masks with tracks to supervise layout and shape generation. We consider $T$ views in a 3D scene with $n$ tracked objects $\{o_j^{gt}\}$ , $j = 1,\dots,n$ . Each object $o_j^{gt}$ is observable in $T_{j}$ views, where $T_{j} \subseteq T$ . We denote $\pmb{m}_{j}^{p}$ as the mask of object $o_j^{gt}$ observed in the view $p \in T_{j}$ . For each mask $\pmb{m}_{j}^{p}$ , there are a class label $l_{j}^{gt}$ and camera parameters $\mathrm{cam}^p$ . + +We train our model with a set of view losses between the ground-truth masks and the renderings of generated objects. We illustrate our training strategy in Fig. 4, which + +![](images/0bad6c7a15676b406c7b37f0a321b45c9e33b28791df8d809a4746dcf173d6d8.jpg) +Figure 4. Optimization strategy for layout and shape training. We train layout learning and mesh deformation end-to-end with two stages to guarantee that objects are deformed after alignment. + +is trained end-to-end with two stages: 1) layout pretraining and 2) layout+shape joint learning. We pretrain the layout first because 1) shape deformation from 2D requires an ideal alignment between its renderings and ground-truth masks; 2) differentiable rendering is not required in the first stage thus the efficiency is largely improved. + +Layout Loss Our network is initialized with all objects $\{o_k\}$ at the floor center. In the first stage, we learn the object layout without shape decoding (i.e., $\Delta v_{k} = 0$ in Eq. 6). Only object categories, centers, sizes and completeness scores are optimized ( $\{l_k, c_k, s_k, p_k\}$ ). Therefore, we define the layout loss $\mathcal{L}_{layout}$ as the combination of 1) classification loss $\mathcal{L}_l$ ; 2) 2D bounding box loss $\mathcal{L}_{box}$ ; 3) completeness loss $\mathcal{L}_p$ , and 4) frustum loss $\mathcal{L}_f$ . + +For an object prediction $\pmb{o}_k$ , we project the vertices on its mesh to all views in $T$ and calculate the 2D bounding boxes $B_k = \{b^1, \dots, b^T\}_k$ . For each ground-truth object $o_j^{gt}$ , we also have its 2D bounding boxes $B_j^{gt} = \{b^1, \dots, b^{T_j}\}_j^{gt}$ in $T_j$ views. We let $l_k$ as the predicted class label of $o_k$ , and $l_j^{gt}$ as the ground-truth label of $o_j^{gt}$ respectively. For each prediction pair $(B_k, l_k)$ , we adopt the Hungarian algorithm [2, 43] to find its optimal bipartite matching $(B_{\sigma(k)}^{gt}, l_{\sigma(k)}^{gt})$ from the ground truth. Therefore we can obtain the matches from each prediction $o_k$ to a ground-truth $o_{\sigma(k)}^{gt}$ , which is the basis of our loss functions. For details of Hungarian matching, we refer to the supplemental. + +Based on Hungarian matching, our layout loss can be formulated as + +$$ +\mathcal {L} _ {L} = \lambda_ {l} \mathcal {L} _ {l} + \lambda_ {b o x} \mathcal {L} _ {b o x} + \lambda_ {p} \mathcal {L} _ {p} + \lambda_ {f} \mathcal {L} _ {f}, \tag {7} +$$ + +where $\mathcal{L}_l$ is the cross-entropy loss between $l_{k}$ and $l_{\sigma (k)}^{gt}$ for object classification; $\mathcal{L}_{box}$ is the average $L_{1}$ distance between 2D bounding boxes in $B_{k}$ and $B_{\sigma (k)}^{gt}$ on each view of $T_{\sigma (k)}$ ; $\mathcal{L}_p$ is the binary cross entropy loss to judge whether $\boldsymbol{o}_k$ is the last object or not. For objects whose initial position is not located in a view frustum of their matched groundtruth, we design a frustum loss $\mathcal{L}_f$ to enforce their 3D center $\pmb{c}$ moving into the target frustum. Further details can be found in the supplemental. + +Shape Loss After the layout loss converges, we switch on the shape decoder in Eq. 6 and use 2D instance masks $\{\pmb{m}_j^p\}$ for mesh deformation. In addition to 2D bounding boxes, we also render the soft silhouettes of each $\pmb{o}_k$ on all views $T$ , by a soft silhouette Shader from [40]. The shape loss of $\pmb{o}_k$ is defined as a multi-view mask loss as + +$$ +\mathcal {L} _ {S} = \sum_ {p \in T _ {\sigma (k)}} \operatorname {B C E} \left(\boldsymbol {r} _ {k} ^ {p}, \boldsymbol {m} _ {\sigma (k)} ^ {p}\right) \mathbb {1} [ \operatorname {I o U} \left(\boldsymbol {r} _ {k} ^ {p}, \boldsymbol {m} _ {\sigma (k)} ^ {p}\right) > 0. 5 ], \tag {8} +$$ + +where $\pmb{r}_k^p$ is the rendering of $\pmb{o}_k$ in view $p\in T_{\sigma (k)};m_{\sigma (k)}^p$ is the corresponding mask of $\pmb{o}_{\sigma (k)}^{gt}$ . For pairs whose IoU larger than 0.5, we use binary cross entropy to calculate the mask loss, which is inspired by [16] that we only use those well-aligned masks for supervision. We optimize $\mathcal{L}_S$ to improve object mesh deformation. + +Finally, we train the our network end-to-end with $\mathcal{L} = \mathcal{L}_L + \lambda_S\mathcal{L}_S$ . All losses above are averaged across all objects. $\{\lambda \}$ are weights that balance the losses. + +# 4. Experiment Setup + +Datasets and Tasks We train and test our method on two downstream tasks: 3D scene synthesis and single-view scene reconstruction. + +For scene synthesis, we use the 3D-FRONT [13] dataset for training and evaluation as in [36, 52]. 3D-FRONT is a synthetic indoor scene dataset with 18,968 rooms populated with 3D furniture objects, wherein we choose bedrooms and living rooms for our training and testing. We use [9] to sample virtual camera poses in each room and render the 2D instance masks for objects under different views, which produces 102,268 views in 3,922 bedrooms ( $\approx$ 5.53 objects in each room), and 80,997 views in 1,496 living rooms ( $\approx$ 9.82 objects in each room). For each room type, the train/test split ratio is 9:1 over rooms. We provide additional rendering details in the supplemental. + +For single-view scene reconstruction, we use the ScanNet dataset [7] for benchmarking. ScanNet is a real indoor scene dataset with 1,513 rooms in 21 room types. It provides 3D scans with semantic instance labels, as well as 2D scanning data where each room is captured into an RGB video sequence, and each frame contains a calibrated camera pose and 2D instance masks with tracking IDs. We uniformly sample up to 100 frames on each video and obtains 108,059 valid frames from all scenes. We use the official train/val split for our training and evaluation. + +Implementation For each task, we train our network on 4 NVIDIA 2080 Ti GPUs with batch size at 16. Each sample in a batch contains a scene with 20 randomly sampled views. We augment each scene in 3D-FRONT and ScanNet with axis-aligned rotations by 90, 180, 270 degrees. As in Sec. 3.4, we train our network end-to-end with two stages. We first train the layout learning in first 800 epochs, followed by the shape learning with 500 epochs. We use Adam + +as the optimizer with initial learning rate 1e-4, which is decayed by $0.1 \times$ after 300 epochs, in both of the two stages. The losses are weighted by $\lambda_{l} = \lambda_{p} = \lambda_{f} = 1$ , $\lambda_{box} = 5$ , $\lambda_{S} = 2$ to balance loss values. For layer and differentiable rendering specifications, we refer to the supplemental. + +For scene synthesis, we randomly sample latent vectors by Eq. 2 to synthesize diverse scenes. For single-view reconstruction, we freeze the generation network and take the single-view instance masks as the ground-truth to optimize the latent vector with our loss function. After it converges, we generate the 3D scene with the learned latent vector. We provide additional details about this optimization step in the supplemental. + +Evaluation Metrics We evaluate our method on the tasks of scene synthesis and single-view scene reconstruction using 3D-FRONT and ScanNet respectively. For scene synthesis, we generate 1000 scenes for each method and use FID score (FID), scene classification accuracy (SCA) and category KL divergence (KL) from [36] to measure the generation plausibility against the ground-truth in the test set. We refer readers to [36] for their definitions. For FID and SCA calculation, we render the generated and the ground-truth scenes into $512^2$ images with a top-down orthographic projection, where each object is textured with a unique category-specific color. We unify this setting among all baselines for a fair comparison. + +For single-view reconstruction, we use the metrics of 3D box IoU and chamfer distance between generated objects and the ground-truth. 3D box IoU measures the layout accuracy by comparing the 3D object bounding box between each ground-truth object and the prediction. Chamfer distance measures the accuracy of both layout and shape prediction. It calculates the point-wise $L_{2}$ distance between generated object surface points and the ground-truth. + +# 5. Results and Analysis + +We evaluate our method qualitatively and quantitatively on the tasks of scene synthesis and single-view reconstruction in comparisons with state-of-the-art baselines, as well as scene interpolation and an ablation analysis on different network configurations. + +# 5.1. Scene Synthesis + +Baselines Since there are no previous works that synthesize 3D semantic instance scenes by learning from only 2D supervision, for a fair comparison, we use several state-of-the-art baselines while train them under 2D supervision. Additionally, we also compare with the state-of-the-art methods which use 3D training data, to explore the boundary of scene synthesis by learning with only 2D supervision. We consider the following baselines: 1) ATISS [36], a transformer encoder-based method that learns the distri + +![](images/e5718e1ae9d37197196045640795ff22c2576a5176881effad9922bbf5c3199c.jpg) +Figure 5. Qualitative comparisons with the state-of-the-art on scene synthesis. Note that both ATISS [36] and Sync2Gen [52] use 3D data for training while our method learns with only 2D supervision. + +![](images/6d8a773edf8258b443450aeee00d1028a74b75970eec878b0c961d6d50eb4174.jpg) + +![](images/52048f689036febfc750041ea29c954adfe57ba977ea86171c3dbb8bc54536bb.jpg) + +![](images/7657c0d80cb7f64d41890ca71e3a2aa31522a7d0441db735f82f865ef8869db4.jpg) + +bution of 3D object bounding box properties. By progressively sampling from each property distribution, it generates a sequence of object boxes as the output. 2) Sync2Gen [52], a VAE-based method that maps a scene arrangement (parameterized with a sequence of 3D object attributes) to itself. After training, a 3D scene can be generated by sampling from the bottleneck latent distribution. 3) ATISS-2D. We use the transformer in ATISS [36] as the backbone and adapt it to be trainable under 2D supervision with our view loss. 4) GAN. We customize the generative adversary network for semantic scene synthesis from [53] to make it trainable with only 2D supervision. 5) LSTM. We replace our transformer with an LSTM network, while keeping other modules unchanged. Detailed architecture specifications are given in the supplemental. We train/test all methods on the same split for fair comparisons. + +Qualitative Comparisons Fig. 5 visualizes the qualitative comparisons with ATISS [36] and Sync2Gen [52], which are the state-of-the-art scene synthesis methods using 3D object data for training. While our method learns with only 2D supervision. Both the two methods add a shape retrieval post-processing to obtain object CAD models for evaluation. For fair comparison, we adopt shape retrieval by using Chamfer distance to measure the similarity between our reconstructed shape and CAD models in 3D-FRONT. We provide the details in the supplemental. From + +Fig. 5, we observe that ATISS is vulnerable to the penetration issues between object bounding boxes (row 2,3,4,6). Sync2Gen addresses this by involving a Bayesian optimization post-processing to refine object placement based on a 3D object arrangement prior, but it is still vulnerable to penetration issues (row 1,2,6). Our method learns object layout and shape from only 2D data, where we learn each object conditioned on the existence of previous generated objects under the multi-view constraint, which helps to avoid object intersections and produces plausible scene arrangements. + +Quantitative Comparisons Tab. 1 presents the quantitative comparisons between methods under different supervision sources. We observe that our method achieves better FID, SCA and KL scores against these methods using the same 2D supervision, which indicates that we produce better generation plausibility and more realistic object category distribution. To explore the boundary of our method, we also compare with prior arts which use 3D supervision. The results show that our method still presents better visual plausibility (FID and SCA scores) than ATISS, and shows comparable performance against Sync2Gen. + +# 5.2. Single-view Reconstruction + +Baselines We evaluate our method on single-view instance reconstruction from real images, and compare with the prior arts which use 3D supervision: Total3D [34] and + +![](images/d6e109e7c1dcf096987a89706bfbaeaac671be07d4455ccac118043840d8ee05.jpg) +(a) Input + +![](images/511afd759c4a3f994792a018e9115b0d5d349769419c89dfb3eaac763d6234b6.jpg) +(b) Total3D [34] + +![](images/4945315c00eaca8b1408cb554688c337170721f9c92423a7f29a380911c3f01d.jpg) +(c) Im3D [56] + +![](images/b5bc65336f849fe6693b2f114461bd11084a5c354b054955798cc13c6ba2ac95.jpg) +(d) Ours +Figure 6. Qualitative comparisons with the state-of-the-art on single view reconstruction. Note that both Total3D [36] and Im3D [52] use 3D data for training while our method learns from only 2D supervisions. For each method we present the reconstruction result from both the image view and a global view. For our method, we also provide the reconstruction result without shape retrieval on the left. + +
SupervisionBedroomLiving room
FID (↓)SCAKL (↓)FID (↓)SCAKL (↓)
ATISS [36]3D26.820.970.0150.020.970.02
Sync2Gen* [52]3D25.240.800.0335.340.880.02
Sync2Gen [52]3D23.860.830.0235.600.860.08
ATISS-2D [36]2D38.130.960.1065.070.980.36
GAN [53]2D24.420.970.0544.760.990.08
LSTM2D67.971.000.3086.771.000.26
Ours2D21.590.850.0340.470.960.02
+ +Table 1. Quantitative comparisons on scene synthesis. Note that SCA score closer to 0.5 is better. Sync2Gen* is the version of [52] without Bayesian optimization. ATISS-2D is customized from ATISS [36] while using our 2D view loss. GAN is customized from [53] with using only 2D supervision. + +Im3D [56]. Both of them learn 3D scenes with a fully supervised manner, i.e., they require ground-truth object meshes, 2D detections, 3D posed object bounding boxes, and camera poses for training, while our method learns from multi-view 2D instance masks with camera poses. We also compare with USL [16] which is an unsupervised method without using 3D supervision. Similar with ours, they require multi-view tracked instance masks for learning. We train and test all methods using the official split on ScanNet. For Total3D [34] and Im3D [56], we use their pretrained model and finetune their 3D detector on ScanNet. For finetuning, we uniformly sample up to 20 views to cover each scene, + +with each view contains at least three objects, which produces 11,395 valid views. For USL [16], we reproduce their network due to the unavailability of an official implementation, and train it on the same data with ours. For fair comparison, we use ground-truth 2D object detections and camera poses as the input for training and testing all baselines. + +Qualitative Comparisons Fig. 6 presents the qualitative comparisons with Total3D [34] and Im3D [56], which are the state-of-the-art single-view scene reconstruction methods. Both Total3D [34] and Im3D [56] pretrain their shape generator on a 3D shape dataset [44]. To produce better object geometry, our method keeps the shape retrieval in Sec. 5.1 while using the ShapeNet [5] dataset to retrieve CAD models given object positions and meshes. We observe that Total3D presents better mesh quality than Im3D. However, since objects in ScanNet images are usually occluded due to the high scene complexity, it struggles to estimate 3D object poses from 2D detections and results in erroneous object placement (row 1,3,5,6). Im3D addresses this by involving a refinement stage to improve object layout. However, for those severely occluded or partially visible objects, it is vulnerable to object penetration issues (row 1,3,7). Instead of detecting 3D objects from 2D detections (as in Total3D and Im3D), our method focuses on the prior learning of object arrangements, i.e., to understand what a + +
Supervision3D Box IoU (↑)CD (↓)
Total3D [34]3D0.151.36
Im3D [56]3D0.230.84
USL* [16]2D0.101.73
Ours (w/o retrieval)2D0.251.01
Ours2D0.270.79
+ +reasonable object layout looks like in multiple views, which helps to produce better scene configurations. + +Quantitative Comparisons Tab. 2 presents the quantitative comparisons, where we observe that Total3D [34] and USL [16] struggles to detect 3D object bounding boxes from 2D detections (lower 3D Box IoU) because both of them predict object centers by depth estimation, which is still a challenging problem due to the ambiguity. Our method attempts to reconstruct a plausible scene from the learned scene prior conditioned on the input instance masks, which presents more reasonable 3D object bounding boxes. Since training and testing our method requires instance masks for supervision, the mask quality has a direct influence to our reconstruction results. However, mask artifacts are inevitable in real images (row 1-5 in Fig. 6 (a)). By learning shapes from multi-view observations with a naive shape retrieval post-processing, our method presents convincing object layouts and geometries. + +# 5.3. Discussion + +Scene Interpolation Fig. 7 presents the interpolation results between two scenes. Given the latent vectors of two scenes, we interpolate intermediate vectors by sampling from the geodesic curve between them on the hypersphere surface (see Fig. 1). By decoding them, we can obtain the interpolated scenes. The transition between intermediates results show that our method interpolate not only the object pose and geometry but also the semantics and scene context, where the interpolated scenes are constrained with a reasonable scene layout. + +Ablations In Tab. 3 we investigate the effects of each submodule in scene synthesis, i.e., hyper-spherical latent space, permutation-invariant transformer, and stage-wise layout and shape learning, by replacing them with uniform latent space parameterization $(\mathbf{c}_1)$ , LSTM $(\mathbf{c}_2)$ , and one-stage layout and shape training $(\mathbf{c}_3)$ , respectively. From the results, we observe that our transformer plays the most important role. LSTM encodes object order information. However, objects in a scene is an unordered set, and our transformer learns the permutation-invariant context to predict the next object recursively, which largely improves our performance. The hypersphere parameterization and stage- + +Table 2. Quantitative comparisons on single-view reconstruction. Note that USL* is reproduced from [16] due to the unavailability of the official implementation. + +
BedroomLiving room
FID (↓)SCAKL (↓)FID (↓)SCAKL (↓)
c130.610.960.2495.511.000.38
c267.971.000.3086.771.000.26
c324.240.900.0443.430.980.03
Ours21.590.850.0340.470.960.02
+ +Table 3. Ablation analysis on different configurations. + +![](images/cf693cec7a010803257a5f00e63da3018f51fbc5ffeecae0418d046b10a79f8a.jpg) +Figure 7. Scene interpolation between two samples (the leftmost and the rightmost). + +wise training further increases the output plausibility and stabilizes the learning process, and combining them delivers the best performance. + +Limitations Since training our network requires 2D posed images with instance masks, erroneous camera poses or mask labels would mislead the learning process. We believe an interesting direction for future work is to incorporate an uncertainty model to learn stable scene priors from noisy masks and camera poses. + +# 6. Conclusion + +We have presented a novel approach to learn the prior distribution of object layouts and shapes in 3D scenes with only 2D supervision. Our proposed method represents a 3D scene as a latent vector. By decoding it autoregressively using a permutation-invariant transformer, we recover a sequence of object instances characterized by their class categories, 3D bounding boxes and meshes. Since collecting 3D data at scale is expensive and intractable, we design a 2D view loss to train object generation using only 2D supervision. We demonstrate that such prior learning approach enables various downstream tasks, i.e., scene synthesis, interpolation and single-view reconstruction, and produces convincing scene arrangements. We hope that this establishes a step towards a universal self-supervised scene estimator that mimics human vision to understand, emulate and create 3D surroundings from only image observations. + +Acknowledgments This work was supported by the ERC Starting Grant Scan2CAD (804724), the German Research Foundation (DFG) Grant "Making Machine Learning on Static and Dynamic 3D Data Practical", the German Research Foundation (DFG) Research Unit "Learning and Simulation in Visual Computing", NSFC-62172348, and the Bavarian State Ministry of Science and the Arts coordinated by the Bavarian Research Institute for Digital Transformation (bidt). + +# References + +[1] Armen Avetisyan, Manuel Dahnert, Angela Dai, Manolis Savva, Angel X Chang, and Matthias Nießner. Scan2cad: Learning cad model alignment in rgb-d scans. 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Journal of Computer Science and Technology, 33(2):323-334, 2018. 2 \ No newline at end of file diff --git a/2023/Learning 3D Scene Priors With 2D Supervision/images.zip b/2023/Learning 3D Scene Priors With 2D Supervision/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..3a00a8ba7beda72f3a8b8a5d09dab29cf272b536 --- /dev/null +++ b/2023/Learning 3D Scene Priors With 2D Supervision/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:ac4feff5d1193c2d21085892ca49bbcdf4e0f9a0cf8fc57987ef3dd8df96245d +size 531054 diff --git a/2023/Learning 3D Scene Priors With 2D Supervision/layout.json b/2023/Learning 3D Scene Priors With 2D Supervision/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..f1ff34301cefe26dff07b2fff72e7ea169f40f7e --- /dev/null +++ b/2023/Learning 3D Scene Priors With 2D Supervision/layout.json @@ -0,0 +1,9805 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 152, + 103, + 442, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 152, + 103, + 442, + 121 + ], + "spans": [ + { + "bbox": [ + 152, + 103, + 442, + 121 + ], + "type": "text", + "content": "Learning 3D Scene Priors with 2D Supervision" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 86, + 142, + 504, + 172 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 142, + 504, + 172 + ], + "spans": [ + { + "bbox": [ + 86, + 142, + 504, + 172 + ], + "type": "text", + "content": "Yinyu Nie1 Angela Dai1 Xiaoguang Han2 Matthias Nießner1 \n1Technical University of Munich 2The Chinese University of Hong Kong (Shenzhen)" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 143, + 199, + 192, + 211 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 199, + 192, + 211 + ], + "spans": [ + { + "bbox": [ + 143, + 199, + 192, + 211 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 224, + 289, + 488 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 224, + 289, + 488 + ], + "spans": [ + { + "bbox": [ + 47, + 224, + 289, + 488 + ], + "type": "text", + "content": "Holistic 3D scene understanding entails estimation of both layout configuration and object geometry in a 3D environment. Recent works have shown advances in 3D scene estimation from various input modalities (e.g., images, 3D scans), by leveraging 3D supervision (e.g., 3D bounding boxes or CAD models), for which collection at scale is expensive and often intractable. To address this shortcoming, we propose a new method to learn 3D scene priors of layout and shape without requiring any 3D ground truth. Instead, we rely on 2D supervision from multi-view RGB images. Our method represents a 3D scene as a latent vector, from which we can progressively decode to a sequence of objects characterized by their class categories, 3D bounding boxes, and meshes. With our trained autoregressive decoder representing the scene prior, our method facilitates many downstream applications, including scene synthesis, interpolation, and single-view reconstruction. Experiments on 3DFRONT and ScanNet show that our method outperforms state of the art in single-view reconstruction, and achieves state-of-the-art results in scene synthesis against baselines which require for 3D supervision. Project page: https://yinyunie.github.io/scenegprior-page/" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 513, + 128, + 525 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 513, + 128, + 525 + ], + "spans": [ + { + "bbox": [ + 47, + 513, + 128, + 525 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 533, + 287, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 533, + 287, + 629 + ], + "spans": [ + { + "bbox": [ + 46, + 533, + 287, + 629 + ], + "type": "text", + "content": "Understanding the geometric structures in real world scenes takes significant meaning in 3D computer vision. In recent years, many prominent approaches have been proposed to understand 3D scenes for different applications, e.g., scene synthesis [24,28,36,48,49,52] and semantic reconstruction [6,15,16,18-21,26,30,34,35,56]. These methods have shown initial promise in estimating object layouts and shapes in 3D scenes, from RGB or RGB-D input data." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 630, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 287, + 714 + ], + "type": "text", + "content": "However, such methods have focused on leveraging full 3D supervision for layout and shape learning, in task-specific fashion. Such ground truth 3D scene geometry with semantic decomposition to objects and structures is difficult and expensive to acquire, requiring significant artist modeling efforts [13] or expert annotations [1] of CAD modeling. In contrast, 2D image and video acquisition is significantly" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 307, + 198, + 547, + 323 + ], + "blocks": [ + { + "bbox": [ + 307, + 198, + 547, + 323 + ], + "lines": [ + { + "bbox": [ + 307, + 198, + 547, + 323 + ], + "spans": [ + { + "bbox": [ + 307, + 198, + 547, + 323 + ], + "type": "image", + "image_path": "2b0a187f95ac48cfbbaa3a6c5333e4d183427f04e59bd10d71691b85ffefbfe7.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 331, + 547, + 396 + ], + "lines": [ + { + "bbox": [ + 305, + 331, + 547, + 396 + ], + "spans": [ + { + "bbox": [ + 305, + 331, + 547, + 396 + ], + "type": "text", + "content": "Figure 1. We learn 3D scene priors with 2D supervision. We model a latent hypersphere surface to represent a manifold of 3D scenes, characterizing the semantic and geometric distribution of objects in 3D scenes. This supports many downstream applications, including scene synthesis, interpolation and single-view reconstruction." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 411, + 547, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 411, + 547, + 495 + ], + "spans": [ + { + "bbox": [ + 304, + 411, + 547, + 495 + ], + "type": "text", + "content": "more accessible. We thus propose to instead learn a general 3D scene prior from only multi-view 2D information. This approach takes a unified perspective to 3D scene understanding: our 3D scene prior is learned in a generalizable fashion from only multi-view 2D information, enabling application to multiple downstream tasks, including scene synthesis and single-view reconstruction." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 497, + 547, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 497, + 547, + 616 + ], + "spans": [ + { + "bbox": [ + 304, + 497, + 547, + 616 + ], + "type": "text", + "content": "In order to understand geometric 3D scene structure from only multi-view RGB images, we must bridge the domain gap between 3D geometry and RGB colors. To this end, we propose to leverage the 2D semantic domain: we learn our 3D scene prior by ensuring that our learned 3D scene structures and objects, when differentiably rendered, match the 2D semantic distribution of estimated 2D instance segmentations from the RGB images. This enables supervision of 3D object and layout structures guided by 2D information." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "type": "text", + "content": "Our 3D scene prior is learned by optimizing for a mapping from a latent space (parameterized as a hypersphere surface) to a manifold of 3D scenes, as shown in Fig. 1. Each random vector sampled from the latent space is decoded into a sequence of objects autoregressively using our permutation-invariant transformer. Each output object is characterized by their class category, 3D bounding box and mesh. By training this decoder, we encode the scene prior" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 297, + 749, + 313, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 749, + 313, + 757 + ], + "spans": [ + { + "bbox": [ + 297, + 749, + 313, + 757 + ], + "type": "text", + "content": "792" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 131 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 131 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 131 + ], + "type": "text", + "content": "into a latent space, sampling on which enables us to synthesize plausible 3D scenes. With such formulation, our method supports many other downstream tasks on different conditions, e.g., scene synthesis, interpolation and single-view reconstruction." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 59, + 133, + 273, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 133, + 273, + 144 + ], + "spans": [ + { + "bbox": [ + 59, + 133, + 273, + 144 + ], + "type": "text", + "content": "In summary, we present our contributions as follows:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 149, + 286, + 374 + ], + "type": "list", + "angle": 0, + "index": 5, + "blocks": [ + { + "bbox": [ + 58, + 149, + 286, + 208 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 149, + 286, + 208 + ], + "spans": [ + { + "bbox": [ + 58, + 149, + 286, + 208 + ], + "type": "text", + "content": "- We present a new perspective on general 3D scene prior learning with only 2D supervision. We learn the prior distribution of both semantic object instance layouts and shapes via mapping from a latent space to the 3D scene space, by training from 2D multi-view data." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 58, + 210, + 286, + 291 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 210, + 286, + 291 + ], + "spans": [ + { + "bbox": [ + 58, + 210, + 286, + 291 + ], + "type": "text", + "content": "- We formulate scene prior learning as an autoregressive sequence decoding problem, and propose a novel permutation-invariant transformer corresponding with a 2D view loss to map a latent vector from a hypersphere surface to a sequence of semantic instances characterized by their class categories, 3D bounding boxes and meshes." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 58, + 293, + 286, + 374 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 293, + 286, + 374 + ], + "spans": [ + { + "bbox": [ + 58, + 293, + 286, + 374 + ], + "type": "text", + "content": "- Our learned 3D scene prior supports many downstream tasks: single-view scene reconstruction, scene synthesis and interpolation. Experiments on 3D-FRONT and ScanNet show that our method matches state-of-the-art performance in scene synthesis against methods requiring 3D supervision, and outperforms state of the art in single-view reconstruction." + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 393, + 134, + 405 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 393, + 134, + 405 + ], + "spans": [ + { + "bbox": [ + 47, + 393, + 134, + 405 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 414, + 286, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 414, + 286, + 496 + ], + "spans": [ + { + "bbox": [ + 46, + 414, + 286, + 496 + ], + "type": "text", + "content": "3D Semantic Scene Synthesis 3D semantic scene synthesis has received extensive exploration in recent decades, particularly following the popularity of 3D indoor scene datasets and 3D deep learning. Given a collection of synthesized or real 3D scenes, many methods have been proposed to learn the distribution of object layouts to synthesize unseen but plausible 3D scene arrangements." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 498, + 286, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 286, + 688 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 286, + 688 + ], + "type": "text", + "content": "Traditional methods for scene synthesis usually formulate the task as data-driven object placement [57], where a scene with object instances is represented as a graph [3, 4, 39, 59], or is connected to human activities to build a human-centric representation [12, 14, 31, 39]. Scene priors are explicitly hard-coded based on design guidelines [32, 54], represented by frequency statistics (e.g., objects co-occurrence map) [3, 4, 10], inferred by affordance map from human activities [12, 14, 22], or learned from arrangement examples in 3D scenes [11, 14]. Given an initial scene [14, 32, 54], a 2D sketch [51] or a text [3, 4], several methods synthesize object placements under the guidance of scene priors with different optimization strategies, e.g., manual interactions [4, 32, 42], iterative methods [12, 14, 29, 50] or non-linear optimization [3, 4, 11, 39, 51, 54, 55], to maximize a plausibility score or a joint probability." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 689, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 286, + 713 + ], + "type": "text", + "content": "With deep learning techniques, many methods instead learn scene priors with neural networks. They keep the" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 179 + ], + "type": "text", + "content": "problem formulation and use recurrent networks [29, 36, 41, 47-49], feed-forward models [33, 58], GANs [53], or VAEs [38, 52] to synthesize object poses recursively or in one stage from an initial scene or random noise, and usually require 3D information for training. In contrast, our method directly learns the joint semantic and geometric distribution of instances in scenes with 2D supervision, which enables a general scene priors that supports semantic scene synthesis from a latent random vector." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 184, + 545, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 184, + 545, + 411 + ], + "spans": [ + { + "bbox": [ + 304, + 184, + 545, + 411 + ], + "type": "text", + "content": "Single-view Scene Reconstruction Single image reconstruction methods have also been designed around various task-specific, data-driven scene priors [6, 15, 16, 18, 20, 21, 25-27, 30, 34, 37, 45, 56]. Izadinia et al. [21] propose a deep learning-based method to retrieve and align CAD models to an input image. Further methods were developed with a similar top-down approach to reconstruct a scene by detection and retrieval, in which [20, 21, 25] use a render-and-compare strategy. [18, 26, 27] improve the offline shape retrieval with an end-to-end 2D-3D shape matching with pose alignment. Other works focus on shape reconstruction instead of retrieval, where object shapes are learned as meshes [15, 16, 34], volume grids [37, 45], or implicit functions [30, 30, 56] with the supervision of paired 3D object shapes or multi-view images. However, modeling scenes with a top-down manner usually focuses on per-object perception without any global scene reasoning. In contrast, we focus on learning prior distribution of 3D scenes, to generate plausible object layouts conditioned on an input image." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 422, + 388, + 436 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 422, + 388, + 436 + ], + "spans": [ + { + "bbox": [ + 306, + 422, + 388, + 436 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 442, + 545, + 501 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 442, + 545, + 501 + ], + "spans": [ + { + "bbox": [ + 304, + 442, + 545, + 501 + ], + "type": "text", + "content": "Our work aims to learn the prior distribution of 3D semantic scenes. We formulate this problem by learning a mapping " + }, + { + "bbox": [ + 304, + 442, + 545, + 501 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 442, + 545, + 501 + ], + "type": "text", + "content": " from a parameterized latent space " + }, + { + "bbox": [ + 304, + 442, + 545, + 501 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}" + }, + { + "bbox": [ + 304, + 442, + 545, + 501 + ], + "type": "text", + "content": " to the scene space " + }, + { + "bbox": [ + 304, + 442, + 545, + 501 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 442, + 545, + 501 + ], + "type": "text", + "content": ", and hope each sample " + }, + { + "bbox": [ + 304, + 442, + 545, + 501 + ], + "type": "inline_equation", + "content": "z \\in \\mathcal{Z}" + }, + { + "bbox": [ + 304, + 442, + 545, + 501 + ], + "type": "text", + "content": " corresponds to a reasonable 3D scene " + }, + { + "bbox": [ + 304, + 442, + 545, + 501 + ], + "type": "inline_equation", + "content": "s \\in S" + }, + { + "bbox": [ + 304, + 442, + 545, + 501 + ], + "type": "text", + "content": " as in" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 371, + 512, + 545, + 525 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 371, + 512, + 545, + 525 + ], + "spans": [ + { + "bbox": [ + 371, + 512, + 545, + 525 + ], + "type": "interline_equation", + "content": "s = f (z); z \\in \\mathcal {Z}, s \\in \\mathcal {S}. \\tag {1}", + "image_path": "06588195c461f4edf866e0fb94a3a84198dd5de068dc0d281c028f6ae587a891.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 534, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 545, + 712 + ], + "type": "text", + "content": "In Eq. 1, there are four key components: the parameterization of latent space " + }, + { + "bbox": [ + 304, + 534, + 545, + 712 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}" + }, + { + "bbox": [ + 304, + 534, + 545, + 712 + ], + "type": "text", + "content": " and scene space " + }, + { + "bbox": [ + 304, + 534, + 545, + 712 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 534, + 545, + 712 + ], + "type": "text", + "content": ", the architecture of " + }, + { + "bbox": [ + 304, + 534, + 545, + 712 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 534, + 545, + 712 + ], + "type": "text", + "content": ", and the losses to train " + }, + { + "bbox": [ + 304, + 534, + 545, + 712 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 534, + 545, + 712 + ], + "type": "text", + "content": ". We illustrate our approach in Fig. 2, the latent space " + }, + { + "bbox": [ + 304, + 534, + 545, + 712 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}" + }, + { + "bbox": [ + 304, + 534, + 545, + 712 + ], + "type": "text", + "content": " is represented as a unit hypersphere surface, each latent vector " + }, + { + "bbox": [ + 304, + 534, + 545, + 712 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 304, + 534, + 545, + 712 + ], + "type": "text", + "content": " sampled from which conditions the generation of an object sequence with our permutation-invariant transformer. We formulate a 3D scene " + }, + { + "bbox": [ + 304, + 534, + 545, + 712 + ], + "type": "inline_equation", + "content": "s \\in S" + }, + { + "bbox": [ + 304, + 534, + 545, + 712 + ], + "type": "text", + "content": " as a set of objects with their class categories, positions and shapes, thus each object from the transformer is decoded into a category label, a 3D bounding box and a mesh with a completeness score indicating whether the generated scene is complete or not. Training our network only needs 2D supervision. We design a 2D view loss between the renderings of generated scenes and the ground-truth instance masks under respective camera views." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "type": "text", + "content": "793" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 71, + 547, + 223 + ], + "blocks": [ + { + "bbox": [ + 50, + 71, + 547, + 223 + ], + "lines": [ + { + "bbox": [ + 50, + 71, + 547, + 223 + ], + "spans": [ + { + "bbox": [ + 50, + 71, + 547, + 223 + ], + "type": "image", + "image_path": "e0f9d4b9bd2f0698f40e49926f175187e8277a859aa02ace5ad02c9b9c2f1813.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 235, + 546, + 291 + ], + "lines": [ + { + "bbox": [ + 46, + 235, + 546, + 291 + ], + "spans": [ + { + "bbox": [ + 46, + 235, + 546, + 291 + ], + "type": "text", + "content": "Figure 2. Overview of our approach. Our method represents each scene as a learnable latent vector " + }, + { + "bbox": [ + 46, + 235, + 546, + 291 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 46, + 235, + 546, + 291 + ], + "type": "text", + "content": " on a hypersphere. To build mapping from the latent surface to the semantic scene space, we propose a permutation-invariant transformer to generate objects " + }, + { + "bbox": [ + 46, + 235, + 546, + 291 + ], + "type": "inline_equation", + "content": "\\{\\pmb{x}_k\\}" + }, + { + "bbox": [ + 46, + 235, + 546, + 291 + ], + "type": "text", + "content": " autoregressively conditioned on previous objects and " + }, + { + "bbox": [ + 46, + 235, + 546, + 291 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 46, + 235, + 546, + 291 + ], + "type": "text", + "content": ". For each object feature, we regress its object class label, 3D bounding box, shape feature and completeness score, which respectively represent the object layout, geometry, and the completeness of the output scene. We do not require 3D supervision, and instead leverage differentiable rendering with multi-view 2D instance masks supervision." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 301, + 216, + 314 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 301, + 216, + 314 + ], + "spans": [ + { + "bbox": [ + 47, + 301, + 216, + 314 + ], + "type": "text", + "content": "3.1. Latent Space Parameterization" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 319, + 288, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 319, + 288, + 403 + ], + "spans": [ + { + "bbox": [ + 46, + 319, + 288, + 403 + ], + "type": "text", + "content": "We parameterize the latent space " + }, + { + "bbox": [ + 46, + 319, + 288, + 403 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}" + }, + { + "bbox": [ + 46, + 319, + 288, + 403 + ], + "type": "text", + "content": " as a unit hypersphere surface. We choose a spherical surface as the latent representation because it does not have strict boundaries (e.g., uniform distribution), and sampling on it will not produce outliers (e.g., gaussian distribution) [8], which guarantees the continuity when moving from one latent vector to another. We formulate the sampling process from " + }, + { + "bbox": [ + 46, + 319, + 288, + 403 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}" + }, + { + "bbox": [ + 46, + 319, + 288, + 403 + ], + "type": "text", + "content": " as" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 72, + 411, + 287, + 442 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 72, + 411, + 287, + 442 + ], + "spans": [ + { + "bbox": [ + 72, + 411, + 287, + 442 + ], + "type": "interline_equation", + "content": "\\boldsymbol {z} = \\frac {\\sum_ {i = 1} ^ {M} w _ {i} \\cdot \\phi_ {i}}{| | \\sum_ {i = 1} ^ {M} w _ {i} \\cdot \\phi_ {i} | | _ {2}}; \\sum_ {i = 1} ^ {M} w _ {i} = 1, w _ {i} > 0 \\tag {2}", + "image_path": "d0ce99e8ba73c80245237163f3324f37de56c5a45003819083a9a6348d0d315a.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 450, + 287, + 523 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 450, + 287, + 523 + ], + "spans": [ + { + "bbox": [ + 46, + 450, + 287, + 523 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 450, + 287, + 523 + ], + "type": "inline_equation", + "content": "\\{\\phi_i|\\phi_i\\in \\mathbb{R}^{D_z},||\\phi_i||_2 = 1\\}" + }, + { + "bbox": [ + 46, + 450, + 287, + 523 + ], + "type": "text", + "content": " is a set of " + }, + { + "bbox": [ + 46, + 450, + 287, + 523 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 450, + 287, + 523 + ], + "type": "text", + "content": " fixed vectors with unit length, which uniformly spreads on the sphere surface. " + }, + { + "bbox": [ + 46, + 450, + 287, + 523 + ], + "type": "inline_equation", + "content": "D_{z}" + }, + { + "bbox": [ + 46, + 450, + 287, + 523 + ], + "type": "text", + "content": " is the dimension of the hypersphere. Therefore, by sampling a set of weights " + }, + { + "bbox": [ + 46, + 450, + 287, + 523 + ], + "type": "inline_equation", + "content": "\\{w_{i}\\}" + }, + { + "bbox": [ + 46, + 450, + 287, + 523 + ], + "type": "text", + "content": ", we can obtain a latent vector " + }, + { + "bbox": [ + 46, + 450, + 287, + 523 + ], + "type": "inline_equation", + "content": "\\pmb {z}\\in \\mathbb{R}^{D_z}" + }, + { + "bbox": [ + 46, + 450, + 287, + 523 + ], + "type": "text", + "content": " for scene generation. Note that both " + }, + { + "bbox": [ + 46, + 450, + 287, + 523 + ], + "type": "inline_equation", + "content": "\\{w_{i}\\}" + }, + { + "bbox": [ + 46, + 450, + 287, + 523 + ], + "type": "text", + "content": " and our network " + }, + { + "bbox": [ + 46, + 450, + 287, + 523 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 450, + 287, + 523 + ], + "type": "text", + "content": " are learnable during training." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 529, + 239, + 542 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 529, + 239, + 542 + ], + "spans": [ + { + "bbox": [ + 47, + 529, + 239, + 542 + ], + "type": "text", + "content": "3.2. Permutation-invariant Transformer" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 548, + 287, + 608 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 548, + 287, + 608 + ], + "spans": [ + { + "bbox": [ + 46, + 548, + 287, + 608 + ], + "type": "text", + "content": "We generate a sequence of objects in a scene, conditioned on the latent vector " + }, + { + "bbox": [ + 46, + 548, + 287, + 608 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 46, + 548, + 287, + 608 + ], + "type": "text", + "content": ", in an autoregressive fashion. New objects are generated conditioned on the previous ones, which can be formulated as to estimate the distribution of" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 616, + 301, + 641 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 616, + 301, + 641 + ], + "spans": [ + { + "bbox": [ + 47, + 616, + 301, + 641 + ], + "type": "interline_equation", + "content": "P _ {\\theta} \\left(\\boldsymbol {x} _ {1}, \\dots , \\boldsymbol {x} _ {N} \\mid \\boldsymbol {z}\\right) = P _ {\\theta} \\left(\\boldsymbol {x} _ {1} \\mid \\boldsymbol {z}\\right) \\prod_ {k = 2} ^ {N} P _ {\\theta} \\left(\\boldsymbol {x} _ {k} \\mid \\boldsymbol {x} _ {1}, \\dots , \\boldsymbol {x} _ {k - 1}; \\boldsymbol {z}\\right), \\tag {3}", + "image_path": "29fda0cc4d6c3c7cd95bd1f3324393d9edfc4998bfc9ff87e6c7c8bbdadf6ee3.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 642, + 287, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 287, + 689 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 287, + 689 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 642, + 287, + 689 + ], + "type": "inline_equation", + "content": "\\pmb{x}_k" + }, + { + "bbox": [ + 46, + 642, + 287, + 689 + ], + "type": "text", + "content": " denotes the " + }, + { + "bbox": [ + 46, + 642, + 287, + 689 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 642, + 287, + 689 + ], + "type": "text", + "content": "-th object feature. " + }, + { + "bbox": [ + 46, + 642, + 287, + 689 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 642, + 287, + 689 + ], + "type": "text", + "content": " is the maximal number of objects to be generated. " + }, + { + "bbox": [ + 46, + 642, + 287, + 689 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 642, + 287, + 689 + ], + "type": "text", + "content": " is the trainable network. Every new object " + }, + { + "bbox": [ + 46, + 642, + 287, + 689 + ], + "type": "inline_equation", + "content": "\\pmb{x}_k" + }, + { + "bbox": [ + 46, + 642, + 287, + 689 + ], + "type": "text", + "content": " is generated conditioning on " + }, + { + "bbox": [ + 46, + 642, + 287, + 689 + ], + "type": "inline_equation", + "content": "\\pmb{x}_1, \\dots, \\pmb{x}_{k-1}" + }, + { + "bbox": [ + 46, + 642, + 287, + 689 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 642, + 287, + 689 + ], + "type": "inline_equation", + "content": "\\pmb{z}" + }, + { + "bbox": [ + 46, + 642, + 287, + 689 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "We observe that objects in a scene are an unordered set, where each permutation of an object sequence should be" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 301, + 546, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 301, + 546, + 361 + ], + "spans": [ + { + "bbox": [ + 304, + 301, + 546, + 361 + ], + "type": "text", + "content": "equivalent to each other, e.g., [chair, table, lamp] should be equivalent to [lamp, chair, table] given the three objects. Thus, the generation of the next object " + }, + { + "bbox": [ + 304, + 301, + 546, + 361 + ], + "type": "inline_equation", + "content": "\\pmb{x}_k" + }, + { + "bbox": [ + 304, + 301, + 546, + 361 + ], + "type": "text", + "content": " should be independent to the order of previous objects " + }, + { + "bbox": [ + 304, + 301, + 546, + 361 + ], + "type": "inline_equation", + "content": "\\{x_1, \\dots, x_{k-1}\\}" + }, + { + "bbox": [ + 304, + 301, + 546, + 361 + ], + "type": "text", + "content": ", which can be formulated as" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 315, + 380, + 535, + 394 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 380, + 535, + 394 + ], + "spans": [ + { + "bbox": [ + 315, + 380, + 535, + 394 + ], + "type": "interline_equation", + "content": "P _ {\\theta} \\left(\\boldsymbol {x} _ {k} \\mid \\boldsymbol {x} _ {p _ {1}}, \\dots , \\boldsymbol {x} _ {p _ {k - 1}}; \\boldsymbol {z}\\right) = P _ {\\theta} \\left(\\boldsymbol {x} _ {k} \\mid \\boldsymbol {x} _ {q _ {1}}, \\dots , \\boldsymbol {x} _ {q _ {k - 1}}; \\boldsymbol {z}\\right)", + "image_path": "704cf3268da3043b940f25a85d1b6c90c2d7b21a9e0df1961df87c59243937ec.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 316, + 396, + 545, + 418 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 396, + 545, + 418 + ], + "spans": [ + { + "bbox": [ + 316, + 396, + 545, + 418 + ], + "type": "interline_equation", + "content": "1 \\leq p _ {i}, q _ {i} \\leq k - 1 \\text {a n d} p _ {i} \\neq p _ {j}, q _ {i} \\neq q _ {j}, \\forall i \\neq j. \\tag {4}", + "image_path": "40ab05099f12fb04b4daacfa1884a74f033ad3298dc222174318f69e0492a778.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 419, + 545, + 526 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 419, + 545, + 526 + ], + "spans": [ + { + "bbox": [ + 304, + 419, + 545, + 526 + ], + "type": "text", + "content": "This requires our generation network to be permutation-invariant to the input objects. We model this step using a transformer backbone [23], which is illustrated in Fig. 3. Inspired by [36, 46] where removing the positional encoding in a transformer encoder makes the network agnostic to the object order, we consider this design and encode permutation-invariant scene context " + }, + { + "bbox": [ + 304, + 419, + 545, + 526 + ], + "type": "inline_equation", + "content": "\\pmb{F}_k \\in \\mathbb{R}^{k \\times D_z}" + }, + { + "bbox": [ + 304, + 419, + 545, + 526 + ], + "type": "text", + "content": " from previous objects " + }, + { + "bbox": [ + 304, + 419, + 545, + 526 + ], + "type": "inline_equation", + "content": "\\{\\pmb{x}_1, \\dots, \\pmb{x}_{k-1}\\}" + }, + { + "bbox": [ + 304, + 419, + 545, + 526 + ], + "type": "text", + "content": ". Note that " + }, + { + "bbox": [ + 304, + 419, + 545, + 526 + ], + "type": "inline_equation", + "content": "\\pmb{x}_0" + }, + { + "bbox": [ + 304, + 419, + 545, + 526 + ], + "type": "text", + "content": " in Fig. 2 and 3 is a learnable start token which indicates an empty room." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 527, + 545, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 527, + 545, + 624 + ], + "spans": [ + { + "bbox": [ + 304, + 527, + 545, + 624 + ], + "type": "inline_equation", + "content": "F_{k}" + }, + { + "bbox": [ + 304, + 527, + 545, + 624 + ], + "type": "text", + "content": " contains attention signals between object pairs and the scene context feature. We use " + }, + { + "bbox": [ + 304, + 527, + 545, + 624 + ], + "type": "inline_equation", + "content": "F_{k}" + }, + { + "bbox": [ + 304, + 527, + 545, + 624 + ], + "type": "text", + "content": " as the keys and values, and the latent vector " + }, + { + "bbox": [ + 304, + 527, + 545, + 624 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}" + }, + { + "bbox": [ + 304, + 527, + 545, + 624 + ], + "type": "text", + "content": " as the query to infer the next object based on the scene context. We adopt a transformer decoder for object inference, where we also do not use positional encoding. Afterwards, it outputs the next possible object " + }, + { + "bbox": [ + 304, + 527, + 545, + 624 + ], + "type": "inline_equation", + "content": "\\pmb{x}_k\\in \\mathbb{R}^{D_z}" + }, + { + "bbox": [ + 304, + 527, + 545, + 624 + ], + "type": "text", + "content": ". We forward this step autoregressively to obtain an object feature sequence " + }, + { + "bbox": [ + 304, + 527, + 545, + 624 + ], + "type": "inline_equation", + "content": "\\{\\pmb {x}_1,\\dots,\\pmb {x}_N\\}" + }, + { + "bbox": [ + 304, + 527, + 545, + 624 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 630, + 455, + 643 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 630, + 455, + 643 + ], + "spans": [ + { + "bbox": [ + 305, + 630, + 455, + 643 + ], + "type": "text", + "content": "3.3. Layout and Shape Decoder" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 648, + 545, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 648, + 545, + 673 + ], + "spans": [ + { + "bbox": [ + 304, + 648, + 545, + 673 + ], + "type": "text", + "content": "In this section, we decode object features " + }, + { + "bbox": [ + 304, + 648, + 545, + 673 + ], + "type": "inline_equation", + "content": "\\{\\pmb{x}_k\\}" + }, + { + "bbox": [ + 304, + 648, + 545, + 673 + ], + "type": "text", + "content": " into a set of object categories, 3D bounding boxes and shapes." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 677, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 546, + 713 + ], + "type": "text", + "content": "Scene Parameterization We focus on indoor scenarios, and represent a 3D scene in a world coordinate system with the floor center located at the origin. Each object inside" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "type": "text", + "content": "794" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 71, + 295, + 156 + ], + "blocks": [ + { + "bbox": [ + 50, + 71, + 295, + 156 + ], + "lines": [ + { + "bbox": [ + 50, + 71, + 295, + 156 + ], + "spans": [ + { + "bbox": [ + 50, + 71, + 295, + 156 + ], + "type": "image", + "image_path": "8f816f149ecd90c1b41fda70ad1d4992b79cb8138a11196a46cf34d937893ab8.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 163, + 288, + 207 + ], + "lines": [ + { + "bbox": [ + 46, + 163, + 288, + 207 + ], + "spans": [ + { + "bbox": [ + 46, + 163, + 288, + 207 + ], + "type": "text", + "content": "Figure 3. Transformer for autoregressive object generation. From the start token " + }, + { + "bbox": [ + 46, + 163, + 288, + 207 + ], + "type": "inline_equation", + "content": "\\pmb{x}_0" + }, + { + "bbox": [ + 46, + 163, + 288, + 207 + ], + "type": "text", + "content": ", we design a permutation-invariant transformer to autoregressively generate a new object feature " + }, + { + "bbox": [ + 46, + 163, + 288, + 207 + ], + "type": "inline_equation", + "content": "\\pmb{x}_k" + }, + { + "bbox": [ + 46, + 163, + 288, + 207 + ], + "type": "text", + "content": " by querying the encoded scene context " + }, + { + "bbox": [ + 46, + 163, + 288, + 207 + ], + "type": "inline_equation", + "content": "\\pmb{F}_k" + }, + { + "bbox": [ + 46, + 163, + 288, + 207 + ], + "type": "text", + "content": " with the latent vector " + }, + { + "bbox": [ + 46, + 163, + 288, + 207 + ], + "type": "inline_equation", + "content": "\\pmb{z}" + }, + { + "bbox": [ + 46, + 163, + 288, + 207 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1, + "angle": 0, 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+ { + "bbox": [ + 46, + 217, + 287, + 266 + ], + "type": "inline_equation", + "content": "M \\in \\mathbb{M}" + }, + { + "bbox": [ + 46, + 217, + 287, + 266 + ], + "type": "text", + "content": " in the canonical system, where " + }, + { + "bbox": [ + 46, + 217, + 287, + 266 + ], + "type": "inline_equation", + "content": "\\mathbb{L}" + }, + { + "bbox": [ + 46, + 217, + 287, + 266 + ], + "type": "text", + "content": " denotes all class categories and " + }, + { + "bbox": [ + 46, + 217, + 287, + 266 + ], + "type": "inline_equation", + "content": "\\mathbb{M}" + }, + { + "bbox": [ + 46, + 217, + 287, + 266 + ], + "type": "text", + "content": " is the shape space." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 270, + 287, + 319 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 270, + 287, + 319 + ], + "spans": [ + { + "bbox": [ + 46, + 270, + 287, + 319 + ], + "type": "text", + "content": "Layout Decoder We adopt a layout decoder to estimate the class category " + }, + { + "bbox": [ + 46, + 270, + 287, + 319 + ], + "type": "inline_equation", + "content": "l_{k}" + }, + { + "bbox": [ + 46, + 270, + 287, + 319 + ], + "type": "text", + "content": ", box center " + }, + { + "bbox": [ + 46, + 270, + 287, + 319 + ], + "type": "inline_equation", + "content": "c_{k}" + }, + { + "bbox": [ + 46, + 270, + 287, + 319 + ], + "type": "text", + "content": ", size " + }, + { + "bbox": [ + 46, + 270, + 287, + 319 + ], + "type": "inline_equation", + "content": "s_{k}" + }, + { + "bbox": [ + 46, + 270, + 287, + 319 + ], + "type": "text", + "content": " and completeness score " + }, + { + "bbox": [ + 46, + 270, + 287, + 319 + ], + "type": "inline_equation", + "content": "p_{k}" + }, + { + "bbox": [ + 46, + 270, + 287, + 319 + ], + "type": "text", + "content": " from each object feature " + }, + { + "bbox": [ + 46, + 270, + 287, + 319 + ], + "type": "inline_equation", + "content": "x_{k}" + }, + { + "bbox": [ + 46, + 270, + 287, + 319 + ], + "type": "text", + "content": ", which is implemented by two MLPs respectively:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 53, + 327, + 287, + 340 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 327, + 287, + 340 + ], + "spans": [ + { + "bbox": [ + 53, + 327, + 287, + 340 + ], + "type": "interline_equation", + "content": "\\left\\{\\boldsymbol {l} _ {k}, \\boldsymbol {c} _ {k}, \\boldsymbol {s} _ {k}, \\boldsymbol {p} _ {k} \\right\\} = \\operatorname {M L P} _ {2} \\left(\\operatorname {M L P} _ {1} \\left(\\boldsymbol {x} _ {k}\\right)\\right), k = 1, \\dots , N. \\tag {5}", + "image_path": "77d041afcf3de169094b48db088773860e2771d950170f962bf07f00ff5d75e4.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 349, + 287, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 349, + 287, + 384 + ], + "spans": [ + { + "bbox": [ + 46, + 349, + 287, + 384 + ], + "type": "text", + "content": "The completeness " + }, + { + "bbox": [ + 46, + 349, + 287, + 384 + ], + "type": "inline_equation", + "content": "\\pmb{p}_k" + }, + { + "bbox": [ + 46, + 349, + 287, + 384 + ], + "type": "text", + "content": " is a binary score of whether " + }, + { + "bbox": [ + 46, + 349, + 287, + 384 + ], + "type": "inline_equation", + "content": "\\pmb{x}_k" + }, + { + "bbox": [ + 46, + 349, + 287, + 384 + ], + "type": "text", + "content": " is the last object or not, indicating whether we should continue object generation." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 389, + 287, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 389, + 287, + 437 + ], + "spans": [ + { + "bbox": [ + 46, + 389, + 287, + 437 + ], + "type": "text", + "content": "Shape Decoder We estimate object shapes by deforming a template sphere from " + }, + { + "bbox": [ + 46, + 389, + 287, + 437 + ], + "type": "inline_equation", + "content": "\\pmb{x}_k" + }, + { + "bbox": [ + 46, + 389, + 287, + 437 + ], + "type": "text", + "content": ". Inspired by [17], we use MLPs to learn the offsets from vertices " + }, + { + "bbox": [ + 46, + 389, + 287, + 437 + ], + "type": "inline_equation", + "content": "V \\in \\mathbb{R}^{|\\mathbf{V}| \\times 3}" + }, + { + "bbox": [ + 46, + 389, + 287, + 437 + ], + "type": "text", + "content": " on the template sphere to the target surface by" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 71, + 446, + 287, + 459 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 71, + 446, + 287, + 459 + ], + "spans": [ + { + "bbox": [ + 71, + 446, + 287, + 459 + ], + "type": "interline_equation", + "content": "\\Delta \\boldsymbol {v} _ {k} = \\operatorname {M L P} _ {3} (\\operatorname {C o n c a t} [ \\operatorname {M L P} _ {1} (\\boldsymbol {x} _ {k}), \\boldsymbol {v} ]), \\boldsymbol {v} \\in \\boldsymbol {V}, \\tag {6}", + "image_path": "10581297b61aa65c41984938c3d013f1cdc021e1f1119bafe3987a71c50b79a8.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 468, + 287, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 468, + 287, + 552 + ], + "spans": [ + { + "bbox": [ + 46, + 468, + 287, + 552 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 468, + 287, + 552 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 46, + 468, + 287, + 552 + ], + "type": "text", + "content": " denotes the set of vertices on the template; " + }, + { + "bbox": [ + 46, + 468, + 287, + 552 + ], + "type": "inline_equation", + "content": "\\mathrm{MLP}_3" + }, + { + "bbox": [ + 46, + 468, + 287, + 552 + ], + "type": "text", + "content": " is an point-wise MLP, and we share " + }, + { + "bbox": [ + 46, + 468, + 287, + 552 + ], + "type": "inline_equation", + "content": "\\mathrm{MLP}_1" + }, + { + "bbox": [ + 46, + 468, + 287, + 552 + ], + "type": "text", + "content": " with Eq. 5. Afterwards, the vertices of the " + }, + { + "bbox": [ + 46, + 468, + 287, + 552 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 468, + 287, + 552 + ], + "type": "text", + "content": "-th object mesh " + }, + { + "bbox": [ + 46, + 468, + 287, + 552 + ], + "type": "inline_equation", + "content": "M_k" + }, + { + "bbox": [ + 46, + 468, + 287, + 552 + ], + "type": "text", + "content": " is predicted as " + }, + { + "bbox": [ + 46, + 468, + 287, + 552 + ], + "type": "inline_equation", + "content": "S_k = \\{\\pmb{v} + \\Delta \\pmb{v}_k\\}" + }, + { + "bbox": [ + 46, + 468, + 287, + 552 + ], + "type": "text", + "content": ". Note that " + }, + { + "bbox": [ + 46, + 468, + 287, + 552 + ], + "type": "inline_equation", + "content": "M_k" + }, + { + "bbox": [ + 46, + 468, + 287, + 552 + ], + "type": "text", + "content": " is in a canonical system, which is transformed to the world system with the bounding boxes in Eq. 5 by " + }, + { + "bbox": [ + 46, + 468, + 287, + 552 + ], + "type": "inline_equation", + "content": "\\pmb{o}_k = \\pmb{s}_k \\cdot \\pmb{M}_i + \\pmb{c}_k" + }, + { + "bbox": [ + 46, + 468, + 287, + 552 + ], + "type": "text", + "content": ". Finally, we obtain " + }, + { + "bbox": [ + 46, + 468, + 287, + 552 + ], + "type": "inline_equation", + "content": "\\{\\pmb{o}_k\\}" + }, + { + "bbox": [ + 46, + 468, + 287, + 552 + ], + "type": "text", + "content": " as the set of output objects in a scene." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 559, + 117, + 571 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 559, + 117, + 571 + ], + "spans": [ + { + "bbox": [ + 47, + 559, + 117, + 571 + ], + "type": "text", + "content": "3.4. View Loss" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 577, + 287, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 577, + 287, + 676 + ], + "spans": [ + { + "bbox": [ + 46, + 577, + 287, + 676 + ], + "type": "text", + "content": "Instead of using 3D data, our method leverages multiviewed instance masks with tracks to supervise layout and shape generation. We consider " + }, + { + "bbox": [ + 46, + 577, + 287, + 676 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 577, + 287, + 676 + ], + "type": "text", + "content": " views in a 3D scene with " + }, + { + "bbox": [ + 46, + 577, + 287, + 676 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 577, + 287, + 676 + ], + "type": "text", + "content": " tracked objects " + }, + { + "bbox": [ + 46, + 577, + 287, + 676 + ], + "type": "inline_equation", + "content": "\\{o_j^{gt}\\}" + }, + { + "bbox": [ + 46, + 577, + 287, + 676 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 577, + 287, + 676 + ], + "type": "inline_equation", + "content": "j = 1,\\dots,n" + }, + { + "bbox": [ + 46, + 577, + 287, + 676 + ], + "type": "text", + "content": ". Each object " + }, + { + "bbox": [ + 46, + 577, + 287, + 676 + ], + "type": "inline_equation", + "content": "o_j^{gt}" + }, + { + "bbox": [ + 46, + 577, + 287, + 676 + ], + "type": "text", + "content": " is observable in " + }, + { + "bbox": [ + 46, + 577, + 287, + 676 + ], + "type": "inline_equation", + "content": "T_{j}" + }, + { + "bbox": [ + 46, + 577, + 287, + 676 + ], + "type": "text", + "content": " views, where " + }, + { + "bbox": [ + 46, + 577, + 287, + 676 + ], + "type": "inline_equation", + "content": "T_{j} \\subseteq T" + }, + { + "bbox": [ + 46, + 577, + 287, + 676 + ], + "type": "text", + "content": ". We denote " + }, + { + "bbox": [ + 46, + 577, + 287, + 676 + ], + "type": "inline_equation", + "content": "\\pmb{m}_{j}^{p}" + }, + { + "bbox": [ + 46, + 577, + 287, + 676 + ], + "type": "text", + "content": " as the mask of object " + }, + { + "bbox": [ + 46, + 577, + 287, + 676 + ], + "type": "inline_equation", + "content": "o_j^{gt}" + }, + { + "bbox": [ + 46, + 577, + 287, + 676 + ], + "type": "text", + "content": " observed in the view " + }, + { + "bbox": [ + 46, + 577, + 287, + 676 + ], + "type": "inline_equation", + "content": "p \\in T_{j}" + }, + { + "bbox": [ + 46, + 577, + 287, + 676 + ], + "type": "text", + "content": ". For each mask " + }, + { + "bbox": [ + 46, + 577, + 287, + 676 + ], + "type": "inline_equation", + "content": "\\pmb{m}_{j}^{p}" + }, + { + "bbox": [ + 46, + 577, + 287, + 676 + ], + "type": "text", + "content": ", there are a class label " + }, + { + "bbox": [ + 46, + 577, + 287, + 676 + ], + "type": "inline_equation", + "content": "l_{j}^{gt}" + }, + { + "bbox": [ + 46, + 577, + 287, + 676 + ], + "type": "text", + "content": " and camera parameters " + }, + { + "bbox": [ + 46, + 577, + 287, + 676 + ], + "type": "inline_equation", + "content": "\\mathrm{cam}^p" + }, + { + "bbox": [ + 46, + 577, + 287, + 676 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "text", + "content": "We train our model with a set of view losses between the ground-truth masks and the renderings of generated objects. We illustrate our training strategy in Fig. 4, which" + } + ] + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 310, + 71, + 553, + 188 + ], + "blocks": [ + { + "bbox": [ + 310, + 71, + 553, + 188 + ], + "lines": [ + { + "bbox": [ + 310, + 71, + 553, + 188 + ], + "spans": [ + { + "bbox": [ + 310, + 71, + 553, + 188 + ], + "type": "image", + "image_path": "0bad6c7a15676b406c7b37f0a321b45c9e33b28791df8d809a4746dcf173d6d8.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 198, + 545, + 232 + ], + "lines": [ + { + "bbox": [ + 305, + 198, + 545, + 232 + ], + "spans": [ + { + "bbox": [ + 305, + 198, + 545, + 232 + ], + "type": "text", + "content": "Figure 4. Optimization strategy for layout and shape training. We train layout learning and mesh deformation end-to-end with two stages to guarantee that objects are deformed after alignment." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 241, + 545, + 314 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 241, + 545, + 314 + ], + "spans": [ + { + "bbox": [ + 304, + 241, + 545, + 314 + ], + "type": "text", + "content": "is trained end-to-end with two stages: 1) layout pretraining and 2) layout+shape joint learning. We pretrain the layout first because 1) shape deformation from 2D requires an ideal alignment between its renderings and ground-truth masks; 2) differentiable rendering is not required in the first stage thus the efficiency is largely improved." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 317, + 545, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 317, + 545, + 413 + ], + "spans": [ + { + "bbox": [ + 304, + 317, + 545, + 413 + ], + "type": "text", + "content": "Layout Loss Our network is initialized with all objects " + }, + { + "bbox": [ + 304, + 317, + 545, + 413 + ], + "type": "inline_equation", + "content": "\\{o_k\\}" + }, + { + "bbox": [ + 304, + 317, + 545, + 413 + ], + "type": "text", + "content": " at the floor center. In the first stage, we learn the object layout without shape decoding (i.e., " + }, + { + "bbox": [ + 304, + 317, + 545, + 413 + ], + "type": "inline_equation", + "content": "\\Delta v_{k} = 0" + }, + { + "bbox": [ + 304, + 317, + 545, + 413 + ], + "type": "text", + "content": " in Eq. 6). Only object categories, centers, sizes and completeness scores are optimized (" + }, + { + "bbox": [ + 304, + 317, + 545, + 413 + ], + "type": "inline_equation", + "content": "\\{l_k, c_k, s_k, p_k\\}" + }, + { + "bbox": [ + 304, + 317, + 545, + 413 + ], + "type": "text", + "content": "). Therefore, we define the layout loss " + }, + { + "bbox": [ + 304, + 317, + 545, + 413 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{layout}" + }, + { + "bbox": [ + 304, + 317, + 545, + 413 + ], + "type": "text", + "content": " as the combination of 1) classification loss " + }, + { + "bbox": [ + 304, + 317, + 545, + 413 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_l" + }, + { + "bbox": [ + 304, + 317, + 545, + 413 + ], + "type": "text", + "content": "; 2) 2D bounding box loss " + }, + { + "bbox": [ + 304, + 317, + 545, + 413 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{box}" + }, + { + "bbox": [ + 304, + 317, + 545, + 413 + ], + "type": "text", + "content": "; 3) completeness loss " + }, + { + "bbox": [ + 304, + 317, + 545, + 413 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_p" + }, + { + "bbox": [ + 304, + 317, + 545, + 413 + ], + "type": "text", + "content": ", and 4) frustum loss " + }, + { + "bbox": [ + 304, + 317, + 545, + 413 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_f" + }, + { + "bbox": [ + 304, + 317, + 545, + 413 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 414, + 545, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 414, + 545, + 559 + ], + "spans": [ + { + "bbox": [ + 304, + 414, + 545, + 559 + ], + "type": "text", + "content": "For an object prediction " + }, + { + "bbox": [ + 304, + 414, + 545, + 559 + ], + "type": "inline_equation", + "content": "\\pmb{o}_k" + }, + { + "bbox": [ + 304, + 414, + 545, + 559 + ], + "type": "text", + "content": ", we project the vertices on its mesh to all views in " + }, + { + "bbox": [ + 304, + 414, + 545, + 559 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 414, + 545, + 559 + ], + "type": "text", + "content": " and calculate the 2D bounding boxes " + }, + { + "bbox": [ + 304, + 414, + 545, + 559 + ], + "type": "inline_equation", + "content": "B_k = \\{b^1, \\dots, b^T\\}_k" + }, + { + "bbox": [ + 304, + 414, + 545, + 559 + ], + "type": "text", + "content": ". For each ground-truth object " + }, + { + "bbox": [ + 304, + 414, + 545, + 559 + ], + "type": "inline_equation", + "content": "o_j^{gt}" + }, + { + "bbox": [ + 304, + 414, + 545, + 559 + ], + "type": "text", + "content": ", we also have its 2D bounding boxes " + }, + { + "bbox": [ + 304, + 414, + 545, + 559 + ], + "type": "inline_equation", + "content": "B_j^{gt} = \\{b^1, \\dots, b^{T_j}\\}_j^{gt}" + }, + { + "bbox": [ + 304, + 414, + 545, + 559 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 304, + 414, + 545, + 559 + ], + "type": "inline_equation", + "content": "T_j" + }, + { + "bbox": [ + 304, + 414, + 545, + 559 + ], + "type": "text", + "content": " views. We let " + }, + { + "bbox": [ + 304, + 414, + 545, + 559 + ], + "type": "inline_equation", + "content": "l_k" + }, + { + "bbox": [ + 304, + 414, + 545, + 559 + ], + "type": "text", + "content": " as the predicted class label of " + }, + { + "bbox": [ + 304, + 414, + 545, + 559 + ], + "type": "inline_equation", + "content": "o_k" + }, + { + "bbox": [ + 304, + 414, + 545, + 559 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 414, + 545, + 559 + ], + "type": "inline_equation", + "content": "l_j^{gt}" + }, + { + "bbox": [ + 304, + 414, + 545, + 559 + ], + "type": "text", + "content": " as the ground-truth label of " + }, + { + "bbox": [ + 304, + 414, + 545, + 559 + ], + "type": "inline_equation", + "content": "o_j^{gt}" + }, + { + "bbox": [ + 304, + 414, + 545, + 559 + ], + "type": "text", + "content": " respectively. For each prediction pair " + }, + { + "bbox": [ + 304, + 414, + 545, + 559 + ], + "type": "inline_equation", + "content": "(B_k, l_k)" + }, + { + "bbox": [ + 304, + 414, + 545, + 559 + ], + "type": "text", + "content": ", we adopt the Hungarian algorithm [2, 43] to find its optimal bipartite matching " + }, + { + "bbox": [ + 304, + 414, + 545, + 559 + ], + "type": "inline_equation", + "content": "(B_{\\sigma(k)}^{gt}, l_{\\sigma(k)}^{gt})" + }, + { + "bbox": [ + 304, + 414, + 545, + 559 + ], + "type": "text", + "content": " from the ground truth. Therefore we can obtain the matches from each prediction " + }, + { + "bbox": [ + 304, + 414, + 545, + 559 + ], + "type": "inline_equation", + "content": "o_k" + }, + { + "bbox": [ + 304, + 414, + 545, + 559 + ], + "type": "text", + "content": " to a ground-truth " + }, + { + "bbox": [ + 304, + 414, + 545, + 559 + ], + "type": "inline_equation", + "content": "o_{\\sigma(k)}^{gt}" + }, + { + "bbox": [ + 304, + 414, + 545, + 559 + ], + "type": "text", + "content": ", which is the basis of our loss functions. For details of Hungarian matching, we refer to the supplemental." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 559, + 545, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 559, + 545, + 582 + ], + "spans": [ + { + "bbox": [ + 305, + 559, + 545, + 582 + ], + "type": "text", + "content": "Based on Hungarian matching, our layout loss can be formulated as" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 340, + 592, + 545, + 605 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 340, + 592, + 545, + 605 + ], + "spans": [ + { + "bbox": [ + 340, + 592, + 545, + 605 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {L} = \\lambda_ {l} \\mathcal {L} _ {l} + \\lambda_ {b o x} \\mathcal {L} _ {b o x} + \\lambda_ {p} \\mathcal {L} _ {p} + \\lambda_ {f} \\mathcal {L} _ {f}, \\tag {7}", + "image_path": "a01d030fdc6cdfc2ba1e1bc4f6be223f1b3c150f130f2b3e6f5a4c4c303e76c8.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 613, + 545, + 721 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 613, + 545, + 721 + ], + "spans": [ + { + "bbox": [ + 304, + 613, + 545, + 721 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 613, + 545, + 721 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_l" + }, + { + "bbox": [ + 304, + 613, + 545, + 721 + ], + "type": "text", + "content": " is the cross-entropy loss between " + }, + { + "bbox": [ + 304, + 613, + 545, + 721 + ], + "type": "inline_equation", + "content": "l_{k}" + }, + { + "bbox": [ + 304, + 613, + 545, + 721 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 613, + 545, + 721 + ], + "type": "inline_equation", + "content": "l_{\\sigma (k)}^{gt}" + }, + { + "bbox": [ + 304, + 613, + 545, + 721 + ], + "type": "text", + "content": " for object classification; " + }, + { + "bbox": [ + 304, + 613, + 545, + 721 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{box}" + }, + { + "bbox": [ + 304, + 613, + 545, + 721 + ], + "type": "text", + "content": " is the average " + }, + { + "bbox": [ + 304, + 613, + 545, + 721 + ], + "type": "inline_equation", + "content": "L_{1}" + }, + { + "bbox": [ + 304, + 613, + 545, + 721 + ], + "type": "text", + "content": " distance between 2D bounding boxes in " + }, + { + "bbox": [ + 304, + 613, + 545, + 721 + ], + "type": "inline_equation", + "content": "B_{k}" + }, + { + "bbox": [ + 304, + 613, + 545, + 721 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 613, + 545, + 721 + ], + "type": "inline_equation", + "content": "B_{\\sigma (k)}^{gt}" + }, + { + "bbox": [ + 304, + 613, + 545, + 721 + ], + "type": "text", + "content": " on each view of " + }, + { + "bbox": [ + 304, + 613, + 545, + 721 + ], + "type": "inline_equation", + "content": "T_{\\sigma (k)}" + }, + { + "bbox": [ + 304, + 613, + 545, + 721 + ], + "type": "text", + "content": "; " + }, + { + "bbox": [ + 304, + 613, + 545, + 721 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_p" + }, + { + "bbox": [ + 304, + 613, + 545, + 721 + ], + "type": "text", + "content": " is the binary cross entropy loss to judge whether " + }, + { + "bbox": [ + 304, + 613, + 545, + 721 + ], + "type": "inline_equation", + "content": "\\boldsymbol{o}_k" + }, + { + "bbox": [ + 304, + 613, + 545, + 721 + ], + "type": "text", + "content": " is the last object or not. For objects whose initial position is not located in a view frustum of their matched groundtruth, we design a frustum loss " + }, + { + "bbox": [ + 304, + 613, + 545, + 721 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_f" + }, + { + "bbox": [ + 304, + 613, + 545, + 721 + ], + "type": "text", + "content": " to enforce their 3D center " + }, + { + "bbox": [ + 304, + 613, + 545, + 721 + ], + "type": "inline_equation", + "content": "\\pmb{c}" + }, + { + "bbox": [ + 304, + 613, + 545, + 721 + ], + "type": "text", + "content": " moving into the target frustum. Further details can be found in the supplemental." + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "type": "text", + "content": "795" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 144 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 144 + ], + "type": "text", + "content": "Shape Loss After the layout loss converges, we switch on the shape decoder in Eq. 6 and use 2D instance masks " + }, + { + "bbox": [ + 47, + 72, + 289, + 144 + ], + "type": "inline_equation", + "content": "\\{\\pmb{m}_j^p\\}" + }, + { + "bbox": [ + 47, + 72, + 289, + 144 + ], + "type": "text", + "content": " for mesh deformation. In addition to 2D bounding boxes, we also render the soft silhouettes of each " + }, + { + "bbox": [ + 47, + 72, + 289, + 144 + ], + "type": "inline_equation", + "content": "\\pmb{o}_k" + }, + { + "bbox": [ + 47, + 72, + 289, + 144 + ], + "type": "text", + "content": " on all views " + }, + { + "bbox": [ + 47, + 72, + 289, + 144 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 47, + 72, + 289, + 144 + ], + "type": "text", + "content": ", by a soft silhouette Shader from [40]. The shape loss of " + }, + { + "bbox": [ + 47, + 72, + 289, + 144 + ], + "type": "inline_equation", + "content": "\\pmb{o}_k" + }, + { + "bbox": [ + 47, + 72, + 289, + 144 + ], + "type": "text", + "content": " is defined as a multi-view mask loss as" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 148, + 289, + 174 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 148, + 289, + 174 + ], + "spans": [ + { + "bbox": [ + 47, + 148, + 289, + 174 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {S} = \\sum_ {p \\in T _ {\\sigma (k)}} \\operatorname {B C E} \\left(\\boldsymbol {r} _ {k} ^ {p}, \\boldsymbol {m} _ {\\sigma (k)} ^ {p}\\right) \\mathbb {1} [ \\operatorname {I o U} \\left(\\boldsymbol {r} _ {k} ^ {p}, \\boldsymbol {m} _ {\\sigma (k)} ^ {p}\\right) > 0. 5 ], \\tag {8}", + "image_path": "fe4a30f6b56f4bec325d530a2df77bd75b7cda9acf69aa740e3a4267978b546d.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 175, + 287, + 249 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 175, + 287, + 249 + ], + "spans": [ + { + "bbox": [ + 46, + 175, + 287, + 249 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 175, + 287, + 249 + ], + "type": "inline_equation", + "content": "\\pmb{r}_k^p" + }, + { + "bbox": [ + 46, + 175, + 287, + 249 + ], + "type": "text", + "content": " is the rendering of " + }, + { + "bbox": [ + 46, + 175, + 287, + 249 + ], + "type": "inline_equation", + "content": "\\pmb{o}_k" + }, + { + "bbox": [ + 46, + 175, + 287, + 249 + ], + "type": "text", + "content": " in view " + }, + { + "bbox": [ + 46, + 175, + 287, + 249 + ], + "type": "inline_equation", + "content": "p\\in T_{\\sigma (k)};m_{\\sigma (k)}^p" + }, + { + "bbox": [ + 46, + 175, + 287, + 249 + ], + "type": "text", + "content": " is the corresponding mask of " + }, + { + "bbox": [ + 46, + 175, + 287, + 249 + ], + "type": "inline_equation", + "content": "\\pmb{o}_{\\sigma (k)}^{gt}" + }, + { + "bbox": [ + 46, + 175, + 287, + 249 + ], + "type": "text", + "content": ". For pairs whose IoU larger than 0.5, we use binary cross entropy to calculate the mask loss, which is inspired by [16] that we only use those well-aligned masks for supervision. We optimize " + }, + { + "bbox": [ + 46, + 175, + 287, + 249 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_S" + }, + { + "bbox": [ + 46, + 175, + 287, + 249 + ], + "type": "text", + "content": " to improve object mesh deformation." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 250, + 287, + 286 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 250, + 287, + 286 + ], + "spans": [ + { + "bbox": [ + 47, + 250, + 287, + 286 + ], + "type": "text", + "content": "Finally, we train the our network end-to-end with " + }, + { + "bbox": [ + 47, + 250, + 287, + 286 + ], + "type": "inline_equation", + "content": "\\mathcal{L} = \\mathcal{L}_L + \\lambda_S\\mathcal{L}_S" + }, + { + "bbox": [ + 47, + 250, + 287, + 286 + ], + "type": "text", + "content": ". All losses above are averaged across all objects. " + }, + { + "bbox": [ + 47, + 250, + 287, + 286 + ], + "type": "inline_equation", + "content": "\\{\\lambda \\}" + }, + { + "bbox": [ + 47, + 250, + 287, + 286 + ], + "type": "text", + "content": " are weights that balance the losses." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 295, + 155, + 308 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 295, + 155, + 308 + ], + "spans": [ + { + "bbox": [ + 47, + 295, + 155, + 308 + ], + "type": "text", + "content": "4. Experiment Setup" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 315, + 287, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 315, + 287, + 350 + ], + "spans": [ + { + "bbox": [ + 46, + 315, + 287, + 350 + ], + "type": "text", + "content": "Datasets and Tasks We train and test our method on two downstream tasks: 3D scene synthesis and single-view scene reconstruction." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 350, + 287, + 494 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 350, + 287, + 494 + ], + "spans": [ + { + "bbox": [ + 46, + 350, + 287, + 494 + ], + "type": "text", + "content": "For scene synthesis, we use the 3D-FRONT [13] dataset for training and evaluation as in [36, 52]. 3D-FRONT is a synthetic indoor scene dataset with 18,968 rooms populated with 3D furniture objects, wherein we choose bedrooms and living rooms for our training and testing. We use [9] to sample virtual camera poses in each room and render the 2D instance masks for objects under different views, which produces 102,268 views in 3,922 bedrooms (" + }, + { + "bbox": [ + 46, + 350, + 287, + 494 + ], + "type": "inline_equation", + "content": "\\approx" + }, + { + "bbox": [ + 46, + 350, + 287, + 494 + ], + "type": "text", + "content": "5.53 objects in each room), and 80,997 views in 1,496 living rooms (" + }, + { + "bbox": [ + 46, + 350, + 287, + 494 + ], + "type": "inline_equation", + "content": "\\approx" + }, + { + "bbox": [ + 46, + 350, + 287, + 494 + ], + "type": "text", + "content": "9.82 objects in each room). For each room type, the train/test split ratio is 9:1 over rooms. We provide additional rendering details in the supplemental." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 495, + 287, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 495, + 287, + 613 + ], + "spans": [ + { + "bbox": [ + 46, + 495, + 287, + 613 + ], + "type": "text", + "content": "For single-view scene reconstruction, we use the ScanNet dataset [7] for benchmarking. ScanNet is a real indoor scene dataset with 1,513 rooms in 21 room types. It provides 3D scans with semantic instance labels, as well as 2D scanning data where each room is captured into an RGB video sequence, and each frame contains a calibrated camera pose and 2D instance masks with tracking IDs. We uniformly sample up to 100 frames on each video and obtains 108,059 valid frames from all scenes. We use the official train/val split for our training and evaluation." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 618, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 618, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 618, + 287, + 713 + ], + "type": "text", + "content": "Implementation For each task, we train our network on 4 NVIDIA 2080 Ti GPUs with batch size at 16. Each sample in a batch contains a scene with 20 randomly sampled views. We augment each scene in 3D-FRONT and ScanNet with axis-aligned rotations by 90, 180, 270 degrees. As in Sec. 3.4, we train our network end-to-end with two stages. We first train the layout learning in first 800 epochs, followed by the shape learning with 500 epochs. We use Adam" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": "as the optimizer with initial learning rate 1e-4, which is decayed by " + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "inline_equation", + "content": "0.1 \\times" + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": " after 300 epochs, in both of the two stages. The losses are weighted by " + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "inline_equation", + "content": "\\lambda_{l} = \\lambda_{p} = \\lambda_{f} = 1" + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "inline_equation", + "content": "\\lambda_{box} = 5" + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "inline_equation", + "content": "\\lambda_{S} = 2" + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": " to balance loss values. For layer and differentiable rendering specifications, we refer to the supplemental." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 133, + 545, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 133, + 545, + 228 + ], + "spans": [ + { + "bbox": [ + 304, + 133, + 545, + 228 + ], + "type": "text", + "content": "For scene synthesis, we randomly sample latent vectors by Eq. 2 to synthesize diverse scenes. For single-view reconstruction, we freeze the generation network and take the single-view instance masks as the ground-truth to optimize the latent vector with our loss function. After it converges, we generate the 3D scene with the learned latent vector. We provide additional details about this optimization step in the supplemental." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 235, + 546, + 390 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 235, + 546, + 390 + ], + "spans": [ + { + "bbox": [ + 304, + 235, + 546, + 390 + ], + "type": "text", + "content": "Evaluation Metrics We evaluate our method on the tasks of scene synthesis and single-view scene reconstruction using 3D-FRONT and ScanNet respectively. For scene synthesis, we generate 1000 scenes for each method and use FID score (FID), scene classification accuracy (SCA) and category KL divergence (KL) from [36] to measure the generation plausibility against the ground-truth in the test set. We refer readers to [36] for their definitions. For FID and SCA calculation, we render the generated and the ground-truth scenes into " + }, + { + "bbox": [ + 304, + 235, + 546, + 390 + ], + "type": "inline_equation", + "content": "512^2" + }, + { + "bbox": [ + 304, + 235, + 546, + 390 + ], + "type": "text", + "content": " images with a top-down orthographic projection, where each object is textured with a unique category-specific color. We unify this setting among all baselines for a fair comparison." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 391, + 545, + 486 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 391, + 545, + 486 + ], + "spans": [ + { + "bbox": [ + 304, + 391, + 545, + 486 + ], + "type": "text", + "content": "For single-view reconstruction, we use the metrics of 3D box IoU and chamfer distance between generated objects and the ground-truth. 3D box IoU measures the layout accuracy by comparing the 3D object bounding box between each ground-truth object and the prediction. Chamfer distance measures the accuracy of both layout and shape prediction. It calculates the point-wise " + }, + { + "bbox": [ + 304, + 391, + 545, + 486 + ], + "type": "inline_equation", + "content": "L_{2}" + }, + { + "bbox": [ + 304, + 391, + 545, + 486 + ], + "type": "text", + "content": " distance between generated object surface points and the ground-truth." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 498, + 426, + 511 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 498, + 426, + 511 + ], + "spans": [ + { + "bbox": [ + 306, + 498, + 426, + 511 + ], + "type": "text", + "content": "5. Results and Analysis" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 518, + 545, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 518, + 545, + 578 + ], + "spans": [ + { + "bbox": [ + 304, + 518, + 545, + 578 + ], + "type": "text", + "content": "We evaluate our method qualitatively and quantitatively on the tasks of scene synthesis and single-view reconstruction in comparisons with state-of-the-art baselines, as well as scene interpolation and an ablation analysis on different network configurations." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 586, + 402, + 599 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 586, + 402, + 599 + ], + "spans": [ + { + "bbox": [ + 306, + 586, + 402, + 599 + ], + "type": "text", + "content": "5.1. Scene Synthesis" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": "Baselines Since there are no previous works that synthesize 3D semantic instance scenes by learning from only 2D supervision, for a fair comparison, we use several state-of-the-art baselines while train them under 2D supervision. Additionally, we also compare with the state-of-the-art methods which use 3D training data, to explore the boundary of scene synthesis by learning with only 2D supervision. We consider the following baselines: 1) ATISS [36], a transformer encoder-based method that learns the distri" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "text", + "content": "796" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 55, + 69, + 173, + 351 + ], + "blocks": [ + { + "bbox": [ + 55, + 69, + 173, + 351 + ], + "lines": [ + { + "bbox": [ + 55, + 69, + 173, + 351 + ], + "spans": [ + { + "bbox": [ + 55, + 69, + 173, + 351 + ], + "type": "image", + "image_path": "e5718e1ae9d37197196045640795ff22c2576a5176881effad9922bbf5c3199c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 359, + 547, + 383 + ], + "lines": [ + { + "bbox": [ + 46, + 359, + 547, + 383 + ], + "spans": [ + { + "bbox": [ + 46, + 359, + 547, + 383 + ], + "type": "text", + "content": "Figure 5. Qualitative comparisons with the state-of-the-art on scene synthesis. Note that both ATISS [36] and Sync2Gen [52] use 3D data for training while our method learns with only 2D supervision." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 176, + 69, + 294, + 351 + ], + "blocks": [ + { + "bbox": [ + 176, + 69, + 294, + 351 + ], + "lines": [ + { + "bbox": [ + 176, + 69, + 294, + 351 + ], + "spans": [ + { + "bbox": [ + 176, + 69, + 294, + 351 + ], + "type": "image", + "image_path": "6d8a773edf8258b443450aeee00d1028a74b75970eec878b0c961d6d50eb4174.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 298, + 69, + 417, + 351 + ], + "blocks": [ + { + "bbox": [ + 298, + 69, + 417, + 351 + ], + "lines": [ + { + "bbox": [ + 298, + 69, + 417, + 351 + ], + "spans": [ + { + "bbox": [ + 298, + 69, + 417, + 351 + ], + "type": "image", + "image_path": "52048f689036febfc750041ea29c954adfe57ba977ea86171c3dbb8bc54536bb.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 419, + 70, + 538, + 351 + ], + "blocks": [ + { + "bbox": [ + 419, + 70, + 538, + 351 + ], + "lines": [ + { + "bbox": [ + 419, + 70, + 538, + 351 + ], + "spans": [ + { + "bbox": [ + 419, + 70, + 538, + 351 + ], + "type": "image", + "image_path": "7657c0d80cb7f64d41890ca71e3a2aa31522a7d0441db735f82f865ef8869db4.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 388, + 289, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 388, + 289, + 579 + ], + "spans": [ + { + "bbox": [ + 46, + 388, + 289, + 579 + ], + "type": "text", + "content": "bution of 3D object bounding box properties. By progressively sampling from each property distribution, it generates a sequence of object boxes as the output. 2) Sync2Gen [52], a VAE-based method that maps a scene arrangement (parameterized with a sequence of 3D object attributes) to itself. After training, a 3D scene can be generated by sampling from the bottleneck latent distribution. 3) ATISS-2D. We use the transformer in ATISS [36] as the backbone and adapt it to be trainable under 2D supervision with our view loss. 4) GAN. We customize the generative adversary network for semantic scene synthesis from [53] to make it trainable with only 2D supervision. 5) LSTM. We replace our transformer with an LSTM network, while keeping other modules unchanged. Detailed architecture specifications are given in the supplemental. We train/test all methods on the same split for fair comparisons." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": "Qualitative Comparisons Fig. 5 visualizes the qualitative comparisons with ATISS [36] and Sync2Gen [52], which are the state-of-the-art scene synthesis methods using 3D object data for training. While our method learns with only 2D supervision. Both the two methods add a shape retrieval post-processing to obtain object CAD models for evaluation. For fair comparison, we adopt shape retrieval by using Chamfer distance to measure the similarity between our reconstructed shape and CAD models in 3D-FRONT. We provide the details in the supplemental. From" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 388, + 547, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 388, + 547, + 509 + ], + "spans": [ + { + "bbox": [ + 304, + 388, + 547, + 509 + ], + "type": "text", + "content": "Fig. 5, we observe that ATISS is vulnerable to the penetration issues between object bounding boxes (row 2,3,4,6). Sync2Gen addresses this by involving a Bayesian optimization post-processing to refine object placement based on a 3D object arrangement prior, but it is still vulnerable to penetration issues (row 1,2,6). Our method learns object layout and shape from only 2D data, where we learn each object conditioned on the existence of previous generated objects under the multi-view constraint, which helps to avoid object intersections and produces plausible scene arrangements." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 517, + 547, + 649 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 517, + 547, + 649 + ], + "spans": [ + { + "bbox": [ + 304, + 517, + 547, + 649 + ], + "type": "text", + "content": "Quantitative Comparisons Tab. 1 presents the quantitative comparisons between methods under different supervision sources. We observe that our method achieves better FID, SCA and KL scores against these methods using the same 2D supervision, which indicates that we produce better generation plausibility and more realistic object category distribution. To explore the boundary of our method, we also compare with prior arts which use 3D supervision. The results show that our method still presents better visual plausibility (FID and SCA scores) than ATISS, and shows comparable performance against Sync2Gen." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 658, + 456, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 658, + 456, + 671 + ], + "spans": [ + { + "bbox": [ + 306, + 658, + 456, + 671 + ], + "type": "text", + "content": "5.2. Single-view Reconstruction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "type": "text", + "content": "Baselines We evaluate our method on single-view instance reconstruction from real images, and compare with the prior arts which use 3D supervision: Total3D [34] and" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "text", + "content": "797" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 72, + 70, + 128, + 350 + ], + "blocks": [ + { + "bbox": [ + 72, + 70, + 128, + 350 + ], + "lines": [ + { + "bbox": [ + 72, + 70, + 128, + 350 + ], + "spans": [ + { + "bbox": [ + 72, + 70, + 128, + 350 + ], + "type": "image", + "image_path": "d6e109e7c1dcf096987a89706bfbaeaac671be07d4455ccac118043840d8ee05.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 85, + 352, + 115, + 361 + ], + "lines": [ + { + "bbox": [ + 85, + 352, + 115, + 361 + ], + "spans": [ + { + "bbox": [ + 85, + 352, + 115, + 361 + ], + "type": "text", + "content": "(a) Input" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 132, + 71, + 242, + 350 + ], + "blocks": [ + { + "bbox": [ + 132, + 71, + 242, + 350 + ], + "lines": [ + { + "bbox": [ + 132, + 71, + 242, + 350 + ], + "spans": [ + { + "bbox": [ + 132, + 71, + 242, + 350 + ], + "type": "image", + "image_path": "511afd759c4a3f994792a018e9115b0d5d349769419c89dfb3eaac763d6234b6.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 159, + 350, + 214, + 360 + ], + "lines": [ + { + "bbox": [ + 159, + 350, + 214, + 360 + ], + "spans": [ + { + "bbox": [ + 159, + 350, + 214, + 360 + ], + "type": "text", + "content": "(b) Total3D [34]" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 245, + 72, + 354, + 350 + ], + "blocks": [ + { + "bbox": [ + 245, + 72, + 354, + 350 + ], + "lines": [ + { + "bbox": [ + 245, + 72, + 354, + 350 + ], + "spans": [ + { + "bbox": [ + 245, + 72, + 354, + 350 + ], + "type": "image", + "image_path": "4945315c00eaca8b1408cb554688c337170721f9c92423a7f29a380911c3f01d.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 277, + 350, + 323, + 360 + ], + "lines": [ + { + "bbox": [ + 277, + 350, + 323, + 360 + ], + "spans": [ + { + "bbox": [ + 277, + 350, + 323, + 360 + ], + "type": "text", + "content": "(c) Im3D [56]" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 359, + 70, + 522, + 349 + ], + "blocks": [ + { + "bbox": [ + 359, + 70, + 522, + 349 + ], + "lines": [ + { + "bbox": [ + 359, + 70, + 522, + 349 + ], + "spans": [ + { + "bbox": [ + 359, + 70, + 522, + 349 + ], + "type": "image", + "image_path": "b5bc65336f849fe6693b2f114461bd11084a5c354b054955798cc13c6ba2ac95.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 425, + 349, + 454, + 358 + ], + "lines": [ + { + "bbox": [ + 425, + 349, + 454, + 358 + ], + "spans": [ + { + "bbox": [ + 425, + 349, + 454, + 358 + ], + "type": "text", + "content": "(d) Ours" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 47, + 371, + 547, + 405 + ], + "lines": [ + { + "bbox": [ + 47, + 371, + 547, + 405 + ], + "spans": [ + { + "bbox": [ + 47, + 371, + 547, + 405 + ], + "type": "text", + "content": "Figure 6. Qualitative comparisons with the state-of-the-art on single view reconstruction. Note that both Total3D [36] and Im3D [52] use 3D data for training while our method learns from only 2D supervisions. For each method we present the reconstruction result from both the image view and a global view. For our method, we also provide the reconstruction result without shape retrieval on the left." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 50, + 408, + 287, + 483 + ], + "blocks": [ + { + "bbox": [ + 50, + 408, + 287, + 483 + ], + "lines": [ + { + "bbox": [ + 50, + 408, + 287, + 483 + ], + "spans": [ + { + "bbox": [ + 50, + 408, + 287, + 483 + ], + "type": "table", + "html": "
SupervisionBedroomLiving room
FID (↓)SCAKL (↓)FID (↓)SCAKL (↓)
ATISS [36]3D26.820.970.0150.020.970.02
Sync2Gen* [52]3D25.240.800.0335.340.880.02
Sync2Gen [52]3D23.860.830.0235.600.860.08
ATISS-2D [36]2D38.130.960.1065.070.980.36
GAN [53]2D24.420.970.0544.760.990.08
LSTM2D67.971.000.3086.771.000.26
Ours2D21.590.850.0340.470.960.02
", + "image_path": "80ec695182bd57b987579beb0386d856a9fc96d8e7483eab6d1e8b1b389fcbd4.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 492, + 287, + 548 + ], + "lines": [ + { + "bbox": [ + 47, + 492, + 287, + 548 + ], + "spans": [ + { + "bbox": [ + 47, + 492, + 287, + 548 + ], + "type": "text", + "content": "Table 1. Quantitative comparisons on scene synthesis. Note that SCA score closer to 0.5 is better. Sync2Gen* is the version of [52] without Bayesian optimization. ATISS-2D is customized from ATISS [36] while using our 2D view loss. GAN is customized from [53] with using only 2D supervision." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 47, + 570, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 570, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 570, + 289, + 715 + ], + "type": "text", + "content": "Im3D [56]. Both of them learn 3D scenes with a fully supervised manner, i.e., they require ground-truth object meshes, 2D detections, 3D posed object bounding boxes, and camera poses for training, while our method learns from multi-view 2D instance masks with camera poses. We also compare with USL [16] which is an unsupervised method without using 3D supervision. Similar with ours, they require multi-view tracked instance masks for learning. We train and test all methods using the official split on ScanNet. For Total3D [34] and Im3D [56], we use their pretrained model and finetune their 3D detector on ScanNet. For finetuning, we uniformly sample up to 20 views to cover each scene," + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 411, + 545, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 411, + 545, + 483 + ], + "spans": [ + { + "bbox": [ + 304, + 411, + 545, + 483 + ], + "type": "text", + "content": "with each view contains at least three objects, which produces 11,395 valid views. For USL [16], we reproduce their network due to the unavailability of an official implementation, and train it on the same data with ours. For fair comparison, we use ground-truth 2D object detections and camera poses as the input for training and testing all baselines." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 486, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 486, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 546, + 713 + ], + "type": "text", + "content": "Qualitative Comparisons Fig. 6 presents the qualitative comparisons with Total3D [34] and Im3D [56], which are the state-of-the-art single-view scene reconstruction methods. Both Total3D [34] and Im3D [56] pretrain their shape generator on a 3D shape dataset [44]. To produce better object geometry, our method keeps the shape retrieval in Sec. 5.1 while using the ShapeNet [5] dataset to retrieve CAD models given object positions and meshes. We observe that Total3D presents better mesh quality than Im3D. However, since objects in ScanNet images are usually occluded due to the high scene complexity, it struggles to estimate 3D object poses from 2D detections and results in erroneous object placement (row 1,3,5,6). Im3D addresses this by involving a refinement stage to improve object layout. However, for those severely occluded or partially visible objects, it is vulnerable to object penetration issues (row 1,3,7). Instead of detecting 3D objects from 2D detections (as in Total3D and Im3D), our method focuses on the prior learning of object arrangements, i.e., to understand what a" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 298, + 749, + 313, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 749, + 313, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 749, + 313, + 757 + ], + "type": "text", + "content": "798" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 70, + 288, + 140 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 288, + 140 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 288, + 140 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 288, + 140 + ], + "type": "table", + "html": "
Supervision3D Box IoU (↑)CD (↓)
Total3D [34]3D0.151.36
Im3D [56]3D0.230.84
USL* [16]2D0.101.73
Ours (w/o retrieval)2D0.251.01
Ours2D0.270.79
", + "image_path": "b914484c89b5b7b7fb219ba872a0be5cfd594e108f16484005af6c5dc0ac230e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 194, + 287, + 218 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 194, + 287, + 218 + ], + "spans": [ + { + "bbox": [ + 47, + 194, + 287, + 218 + ], + "type": "text", + "content": "reasonable object layout looks like in multiple views, which helps to produce better scene configurations." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 224, + 289, + 416 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 224, + 289, + 416 + ], + "spans": [ + { + "bbox": [ + 46, + 224, + 289, + 416 + ], + "type": "text", + "content": "Quantitative Comparisons Tab. 2 presents the quantitative comparisons, where we observe that Total3D [34] and USL [16] struggles to detect 3D object bounding boxes from 2D detections (lower 3D Box IoU) because both of them predict object centers by depth estimation, which is still a challenging problem due to the ambiguity. Our method attempts to reconstruct a plausible scene from the learned scene prior conditioned on the input instance masks, which presents more reasonable 3D object bounding boxes. Since training and testing our method requires instance masks for supervision, the mask quality has a direct influence to our reconstruction results. However, mask artifacts are inevitable in real images (row 1-5 in Fig. 6 (a)). By learning shapes from multi-view observations with a naive shape retrieval post-processing, our method presents convincing object layouts and geometries." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 425, + 119, + 436 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 425, + 119, + 436 + ], + "spans": [ + { + "bbox": [ + 47, + 425, + 119, + 436 + ], + "type": "text", + "content": "5.3. Discussion" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 443, + 287, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 443, + 287, + 563 + ], + "spans": [ + { + "bbox": [ + 46, + 443, + 287, + 563 + ], + "type": "text", + "content": "Scene Interpolation Fig. 7 presents the interpolation results between two scenes. Given the latent vectors of two scenes, we interpolate intermediate vectors by sampling from the geodesic curve between them on the hypersphere surface (see Fig. 1). By decoding them, we can obtain the interpolated scenes. The transition between intermediates results show that our method interpolate not only the object pose and geometry but also the semantics and scene context, where the interpolated scenes are constrained with a reasonable scene layout." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": "Ablations In Tab. 3 we investigate the effects of each submodule in scene synthesis, i.e., hyper-spherical latent space, permutation-invariant transformer, and stage-wise layout and shape learning, by replacing them with uniform latent space parameterization " + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "inline_equation", + "content": "(\\mathbf{c}_1)" + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": ", LSTM " + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "inline_equation", + "content": "(\\mathbf{c}_2)" + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": ", and one-stage layout and shape training " + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "inline_equation", + "content": "(\\mathbf{c}_3)" + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": ", respectively. From the results, we observe that our transformer plays the most important role. LSTM encodes object order information. However, objects in a scene is an unordered set, and our transformer learns the permutation-invariant context to predict the next object recursively, which largely improves our performance. The hypersphere parameterization and stage-" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 321, + 70, + 534, + 134 + ], + "blocks": [ + { + "bbox": [ + 47, + 148, + 287, + 182 + ], + "lines": [ + { + "bbox": [ + 47, + 148, + 287, + 182 + ], + "spans": [ + { + "bbox": [ + 47, + 148, + 287, + 182 + ], + "type": "text", + "content": "Table 2. Quantitative comparisons on single-view reconstruction. Note that USL* is reproduced from [16] due to the unavailability of the official implementation." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 321, + 70, + 534, + 134 + ], + "lines": [ + { + "bbox": [ + 321, + 70, + 534, + 134 + ], + "spans": [ + { + "bbox": [ + 321, + 70, + 534, + 134 + ], + "type": "table", + "html": "
BedroomLiving room
FID (↓)SCAKL (↓)FID (↓)SCAKL (↓)
c130.610.960.2495.511.000.38
c267.971.000.3086.771.000.26
c324.240.900.0443.430.980.03
Ours21.590.850.0340.470.960.02
", + "image_path": "c9b7d15d538d4650e255da6e89c9dccc863f6e5c2c815c1cce24bd89da9edc40.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 327, + 142, + 524, + 153 + ], + "lines": [ + { + "bbox": [ + 327, + 142, + 524, + 153 + ], + "spans": [ + { + "bbox": [ + 327, + 142, + 524, + 153 + ], + "type": "text", + "content": "Table 3. Ablation analysis on different configurations." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 308, + 160, + 544, + 224 + ], + "blocks": [ + { + "bbox": [ + 308, + 160, + 544, + 224 + ], + "lines": [ + { + "bbox": [ + 308, + 160, + 544, + 224 + ], + "spans": [ + { + "bbox": [ + 308, + 160, + 544, + 224 + ], + "type": "image", + "image_path": "cf693cec7a010803257a5f00e63da3018f51fbc5ffeecae0418d046b10a79f8a.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 232, + 545, + 255 + ], + "lines": [ + { + "bbox": [ + 306, + 232, + 545, + 255 + ], + "spans": [ + { + "bbox": [ + 306, + 232, + 545, + 255 + ], + "type": "text", + "content": "Figure 7. Scene interpolation between two samples (the leftmost and the rightmost)." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 266, + 545, + 302 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 266, + 545, + 302 + ], + "spans": [ + { + "bbox": [ + 305, + 266, + 545, + 302 + ], + "type": "text", + "content": "wise training further increases the output plausibility and stabilizes the learning process, and combining them delivers the best performance." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 307, + 545, + 379 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 307, + 545, + 379 + ], + "spans": [ + { + "bbox": [ + 305, + 307, + 545, + 379 + ], + "type": "text", + "content": "Limitations Since training our network requires 2D posed images with instance masks, erroneous camera poses or mask labels would mislead the learning process. We believe an interesting direction for future work is to incorporate an uncertainty model to learn stable scene priors from noisy masks and camera poses." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 389, + 378, + 401 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 389, + 378, + 401 + ], + "spans": [ + { + "bbox": [ + 306, + 389, + 378, + 401 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 409, + 545, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 409, + 545, + 601 + ], + "spans": [ + { + "bbox": [ + 304, + 409, + 545, + 601 + ], + "type": "text", + "content": "We have presented a novel approach to learn the prior distribution of object layouts and shapes in 3D scenes with only 2D supervision. Our proposed method represents a 3D scene as a latent vector. By decoding it autoregressively using a permutation-invariant transformer, we recover a sequence of object instances characterized by their class categories, 3D bounding boxes and meshes. Since collecting 3D data at scale is expensive and intractable, we design a 2D view loss to train object generation using only 2D supervision. We demonstrate that such prior learning approach enables various downstream tasks, i.e., scene synthesis, interpolation and single-view reconstruction, and produces convincing scene arrangements. We hope that this establishes a step towards a universal self-supervised scene estimator that mimics human vision to understand, emulate and create 3D surroundings from only image observations." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 605, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 712 + ], + "type": "text", + "content": "Acknowledgments This work was supported by the ERC Starting Grant Scan2CAD (804724), the German Research Foundation (DFG) Grant \"Making Machine Learning on Static and Dynamic 3D Data Practical\", the German Research Foundation (DFG) Research Unit \"Learning and Simulation in Visual Computing\", NSFC-62172348, and the Bavarian State Ministry of Science and the Arts coordinated by the Bavarian Research Institute for Digital Transformation (bidt)." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "text", + "content": "799" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 147 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 147 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 147 + ], + "type": "text", + "content": "[1] Armen Avetisyan, Manuel Dahnert, Angela Dai, Manolis Savva, Angel X Chang, and Matthias Nießner. 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Journal of Computer Science and Technology, 33(2):323-334, 2018. 2" + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "text", + "content": "802" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Learning 3D-Aware Image Synthesis With Unknown Pose Distribution/d83e531d-6687-4f90-82b7-f461cb8780cb_content_list.json b/2023/Learning 3D-Aware Image Synthesis With Unknown Pose Distribution/d83e531d-6687-4f90-82b7-f461cb8780cb_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..91803019c272b4bceff68590a1e91c58c1808e5c --- /dev/null +++ b/2023/Learning 3D-Aware Image Synthesis With Unknown Pose Distribution/d83e531d-6687-4f90-82b7-f461cb8780cb_content_list.json @@ -0,0 +1,1545 @@ +[ + { + "type": "text", + "text": "Learning 3D-aware Image Synthesis with Unknown Pose Distribution", + "text_level": 1, + "bbox": [ + 133, + 130, + 834, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Zifan Shi $^{1*1}$ Yujun Shen $^{12}$ Yinghao Xu $^{3}$ Sida Peng $^{4}$ Yiyi Liao $^{4}$ Sheng Guo $^{2}$ Qifeng Chen $^{1}$ Dit-Yan Yeung $^{1}$ $^{1}$ HKUST $^{2}$ Ant Group $^{3}$ CUHK $^{4}$ Zhejiang University", + "bbox": [ + 135, + 178, + 833, + 243 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 273, + 313, + 290 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Existing methods for 3D-aware image synthesis largely depend on the 3D pose distribution pre-estimated on the training set. An inaccurate estimation may mislead the model into learning faulty geometry. This work proposes PoF3D that frees generative radiance fields from the requirements of 3D pose priors. We first equip the generator with an efficient pose learner, which is able to infer a pose from a latent code, to approximate the underlying true pose distribution automatically. We then assign the discriminator a task to learn pose distribution under the supervision of the generator and to differentiate real and synthesized images with the predicted pose as the condition. The pose-free generator and the pose-aware discriminator are jointly trained in an adversarial manner. Extensive results on a couple of datasets confirm that the performance of our approach, regarding both image quality and geometry quality, is on par with state of the art. To our best knowledge, PoF3D demonstrates the feasibility of learning high-quality 3D-aware image synthesis without using 3D pose priors for the first time. Project page can be found here.", + "bbox": [ + 73, + 306, + 473, + 625 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 638, + 209, + 652 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "3D-aware image generation has recently received growing attention due to its potential applications [3, 4, 9, 21, 30, 34, 47]. Compared with 2D synthesis, 3D-aware image synthesis requires the understanding of the geometry underlying 2D images, which is commonly achieved by incorporating 3D representations, such as neural radiance fields (NeRF) [2, 16, 17, 24, 25, 50], into generative models like generative adversarial networks (GANs) [8]. Such a formulation allows explicit camera control over the synthesized results, which fits better with our 3D world.", + "bbox": [ + 75, + 664, + 468, + 815 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To enable 3D-aware image synthesis from 2D image collections, existing attempts usually rely on adequate camera pose priors [3, 4, 9, 20, 21, 30, 47] for training.", + "bbox": [ + 75, + 816, + 468, + 863 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/2f4c5820444128fbf6d99639f175902945b6b74a9671686cf1b28fd5b4f212fa.jpg", + "image_caption": [ + "(a) $\\pi$ -GAN: good pose distribution" + ], + "image_footnote": [], + "bbox": [ + 504, + 273, + 888, + 372 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/5630cbaae3a25e5c77608e57b63c0b38566ed629ab35fde4abe33dbbf2b7b189.jpg", + "image_caption": [ + "(b) $\\pi$ -GAN: bad pose distribution" + ], + "image_footnote": [], + "bbox": [ + 504, + 383, + 888, + 434 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/82830da9b00a30eeff4b2837c1101997d7df4bbcf28855805972d500286dcf1f.jpg", + "image_caption": [ + "(c) CAMPARI: good pose initialization", + "Figure 1. Sensitivity to pose priors in existing 3D-aware image synthesis approaches. $\\pi$ -GAN [4] works well given an adequate pose distribution in (a), but fails to learn decent geometries given a slightly changed distribution in (b). CAMPARI [20] delivers reasonable results relying on a good initial pose distribution in (c), but suffers from a wrongly estimated initialization in (d)." + ], + "image_footnote": [], + "bbox": [ + 504, + 434, + 694, + 483 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/31e850e25e5db3d4d0a81bc922059dfcc9f0c8e726f79baaf9e3182063c84340.jpg", + "image_caption": [ + "(d) CAMPARI: bad pose initialization" + ], + "image_footnote": [], + "bbox": [ + 696, + 434, + 888, + 483 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The priors are either estimated by conducting multiple pre-experiments [4, 9, 47], or obtained by borrowing external pose predictors or annotations [3]. Besides using a fixed distribution for pose sampling, some studies also propose to tune the pose priors together with the learning of image generation [20], but they are still dependent on the initial pose distribution. Consequently, although previous methods can produce satisfying images and geometry, their performance is highly sensitive to the given pose prior. For example, on the Cats dataset [51], $\\pi$ -GAN [4] works well with a uniform pose distribution [-0.5, 0.5] (Fig. 1a), but fails to generate a decent underlying geometry when changing the distribution to [-0.3, 0.3] (Fig. 1b). Similarly, on the CelebA dataset [15], CAMPARI [20] learns 3D rotation when using Gaussian distribution $\\mathcal{N}(0,0.24)$ as the initial prior (Fig. 1c), but loses the canonical space (e.g., the middle image of Fig. 1d should be under the frontal view) when changing the initialization to $\\mathcal{N}(0,0.12)$ (Fig. 1d). Such a reliance on pose priors causes unexpected instability of 3D-aware image synthesis, which may burden this task with heavy experimental cost.", + "bbox": [ + 496, + 583, + 892, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "$\\dagger$ indicates equal contribution.", + "bbox": [ + 94, + 875, + 256, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* This work was done during an internship at Ant Group.", + "bbox": [ + 94, + 887, + 397, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "13062", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this work, we present a new approach for 3D-aware image synthesis, which removes the requirements for pose priors. Typically, a latent code is bound to the 3D content alone, where the camera pose is independently sampled from a manually designed distribution. Our method, however, maps a latent code to an image, which is implicitly composed of a 3D representation (i.e., neural radiance field) and a camera pose that can render that image. In this way, the camera pose is directly inferred from the latent code and jointly learned with the content, simplifying the input requirement. To facilitate the pose-free generator better capturing the underlying pose distribution, we re-design the discriminator to make it pose-aware. Concretely, we tailor the discriminator with a pose branch which is required to predict a camera pose from a given image. Then, the estimated pose is further treated as the conditional pseudo label when performing real/fake discrimination. The pose branch in the discriminator learns from the synthesized data and its corresponding pose that is encoded in the latent code, and in turn use the discrimination score to update the pose branch in the generator. With such a loop-back optimization process, two pose branches can align the fake data with the distribution of the dataset.", + "bbox": [ + 76, + 90, + 472, + 436 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We evaluate our pose-free method, which we call PoF3D for short, on various datasets, including FFHQ [12], Cats [51], and Shapenet Cars [5]. Both qualitative and quantitative results demonstrate that PoF3D frees 3D-aware image synthesis from hyper-parameter tuning on pose distributions and dataset labeling, and achieves on par performance with state-of-the-art in terms of image quality and geometry quality.", + "bbox": [ + 76, + 439, + 470, + 560 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 573, + 218, + 588 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3D-aware Image Synthesis. 3D-aware image synthesis has achieved remarkable success recently [33, 43] and benefits lots of 3D-aware applications [39, 44, 49, 55] rather than the conventional 2D applications [1, 26, 27, 38, 40, 41, 54]. Different from 2D synthesis [11-13, 48], some works [18, 19, 56] propose to adopt voxels as 3D representation for image rendering but suffer from the poor image quality and consistency due to the voxel resolution restriction. Then a series of works [4, 6, 23, 30, 45] introduce neural implicit function [16, 17, 24] as the underlying 3D representation for image rendering. However, rendering high-resolution images with direct volume rendering is very heavy. Lots of works [3, 9, 21, 22, 31, 37, 46, 47, 52] resort to either 2D convolutional upsamplers [3, 9, 21, 22, 47], multi-plane image rendering [52], sparse-voxel [31] inference, patch-based training [37] for acceleration. Besides, some works [23, 35] focus on the improvement of geometry quality. Although these methods are able to synthesize high-quality 3D-aware images, they are restricted to strong pose prior, i.e., manually tuned pose distribution, or well-annotated camera", + "bbox": [ + 76, + 598, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "poses [3]. Our work instead naturally enables 3D-aware image synthesis without any pose prior via a pose-free generator, which gives a fruitful avenue for future work.", + "bbox": [ + 496, + 90, + 890, + 136 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Camera Learning from 2D Images. Learning neural radiance fields (NeRF) [17] requires accurate pose annotations. To overcome this, some works [14, 42] try to optimize the annotated camera parameters or directly estimate camera poses with a small network, which is conceptually comparable to ours. On the other hand, our work differs from theirs in that our method focuses on learning pose distribution of a real dataset rather than exact camera poses. CAMPARI [20] and 3DGP [36] investigate a similar problem, aiming to estimate the pose distribution of an actual dataset. However, both of them need a manually designed prior, i.e., uniform or Gaussian, and fail to learn appropriate 3D geometry when the prior is very distant from the native distribution. In contrast, our work abandons all the manually designed prior and allows the generator to learn pose distribution automatically via adversarial training.", + "bbox": [ + 496, + 136, + 892, + 378 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 500, + 390, + 589, + 405 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our proposed method for 3D-aware image synthesis can be freed from the requirement of pose priors. To achieve this goal, we propose some new designs in both the generator and the discriminator in conventional 3D-aware GANs [3, 4, 9, 30]. Specifically, the pose-free generator is equipped with a pose learner that infers the camera pose from the latent code. The pose-aware discriminator extracts a pose from the given image and uses it as the conditional label when performing real/fake classification. The framework is shown in Fig. 2. Before going into details, we first briefly introduce the generative neural radiance field, which plays a crucial role in 3D-aware image synthesis.", + "bbox": [ + 496, + 415, + 890, + 612 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3.1. Preliminary", + "text_level": 1, + "bbox": [ + 500, + 619, + 629, + 636 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "A neural radiance field (NeRF) [17], $\\mathrm{F}(\\mathbf{x},\\mathbf{d})\\rightarrow (\\mathbf{c},\\sigma)$ , provides color $\\mathbf{c}\\in \\mathbb{R}^3$ and volume density $\\sigma \\in \\mathbb{R}$ from a coordinate $\\mathbf{x}\\in \\mathbb{R}^3$ and a viewing direction $\\mathbf{d}\\in \\mathbb{S}^2$ , typically parameterized with multi-layer perceptron (MLP) networks. Then, the pixel values are accumulated from the colors and densities of the points on the sampled rays. However, NeRF is highly dependent on multi-view supervision, leading to the inability to learn from a single-view image collection. To enable random sampling from single-view captures, recent attempts propose to condition NeRF with a latent code $\\mathbf{z}$ , resulting in their generative forms [4, 30], $\\mathrm{G}(\\mathbf{x},\\mathbf{d},\\mathbf{z})\\to (\\mathbf{c},\\sigma)$ , to achieve diverse 3D-aware generation.", + "bbox": [ + 496, + 642, + 890, + 839 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3.2. Pose-free Generator", + "text_level": 1, + "bbox": [ + 500, + 847, + 691, + 861 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Different from NeRF, the camera pose $\\xi$ deriving the spatial point $\\mathbf{x}$ and view direction $\\mathbf{d}$ in conventional 3D-aware", + "bbox": [ + 500, + 869, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "13063", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/b910b6c6a9f2c39fcfe0b6aa42c1c2f6a55a0654d990bbf7a2df8f7a5b4ffbe9.jpg", + "image_caption": [ + "Figure 2. Framework of PoF3D, which consists of a pose-free generator and a pose-aware discriminator. The pose-free generator maps a latent code to a neural radiance field as well as a camera pose, followed by a volume renderer (VR) to output the final image. The pose-aware discriminator first predicts a camera pose from the given image and then use it as the pseudo label for conditional real/fake discrimination, indicated by the orange arrow." + ], + "image_footnote": [], + "bbox": [ + 114, + 104, + 472, + 213 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/43b469944475705a0f06f05d956fe188dd710ce9b98e9777e2dfd34be178a887.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 532, + 101, + 831, + 214 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "generators is randomly sampled from a prior distribution $p_{\\xi}$ rather than well annotated by MVS [32] and SfM [29]. Such a prior distribution requires the knowledge of the pose distribution, and it should be tailored for different datasets, which introduces non-trivial hyperparameter tuning for model training. This generation process can be formulated as", + "bbox": [ + 75, + 290, + 468, + 393 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {G} (\\mathbf {z}, \\xi) = \\mathbf {I} _ {f} \\sim p _ {\\theta} \\left(\\mathbf {I} _ {f} | \\mathbf {z}, \\xi\\right), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 178, + 401, + 468, + 419 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where the generator $\\mathrm{G}$ synthesizes the image $\\mathbf{I}_f$ by modeling the conditional probability given the latent code and the camera pose. Since the camera pose is independent of the latent code, we can rewrite Eq. (1) in the following form:", + "bbox": [ + 75, + 424, + 468, + 484 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\np _ {\\theta} \\left(\\mathbf {I} _ {f} | \\mathbf {z}, \\xi\\right) = \\frac {p _ {\\theta} \\left(\\mathbf {I} _ {f} , \\mathbf {z} , \\xi\\right)}{p (\\mathbf {z} , \\xi)} = \\frac {p _ {\\theta} \\left(\\mathbf {I} _ {f} , \\xi | \\mathbf {z}\\right)}{p (\\xi)} = \\frac {p _ {\\theta} \\left(\\mathbf {I} _ {f} , \\xi | \\mathbf {z}\\right)}{p _ {\\xi}}. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 83, + 500, + 468, + 549 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Obviously, if the pose prior does not align well with the real distribution, it is hard to correctly estimate the image distribution $p_{\\theta}(\\mathbf{I}_f|\\mathbf{z},\\xi)$ . As noticed by [9, 47], it always makes the training diverge if the prior does not align well with the real distribution. To free the generator from sampling poses from a prior distribution, we follow the formulation of conventional 2D GANs that synthesizes images from the latent code only:", + "bbox": [ + 75, + 555, + 468, + 676 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {G} (\\mathbf {z}, \\Psi (\\mathbf {z})) = \\mathbf {I} _ {f} \\sim p _ {\\theta} \\left(\\mathbf {I} _ {f} | \\mathbf {z}, \\Psi (\\mathbf {z})\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 151, + 681, + 468, + 699 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where the camera pose $\\xi$ is parameterized with a nonlinear function $\\Psi(\\cdot)$ that takes $\\mathbf{z}$ as input. Concretely, we implement $\\Psi(\\cdot)$ by introducing an additional pose branch on the top of the generator. The estimated camera pose is further fed into a generative radiance field to render a 2D image. Compared with previous solutions, our generator aims at approximating the conditional probability only from the latent observation, which is prone to simulating the native data distribution without taking the pose prior into account.", + "bbox": [ + 75, + 704, + 468, + 840 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.3. Pose-aware Discriminator", + "text_level": 1, + "bbox": [ + 76, + 847, + 313, + 862 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As mentioned above, we remove the pose prior of a 3D-aware generator by parameterizing camera pose $\\xi$", + "bbox": [ + 75, + 869, + 468, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "from a latent code $\\mathbf{z}$ . The 3D representation leveraged in the generator is helpful in disentangling the camera factor. However, the conventional discriminator remains to differentiate real and fake images from 2D space, leading to inadequate supervision to factorize camera poses from latent codes. It easily makes the generator synthesize flat shapes and learn invalid camera distribution. Therefore, we propose to make the discriminator pose-aware.", + "bbox": [ + 496, + 290, + 890, + 410 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Learning Pose-aware Discriminator. To let the discriminator become aware of poses, we assign a pose estimation task on fake images beyond bi-class domain classification, which is to derive the pose information from the given images. We introduce a pose branch $\\Phi(\\cdot)$ on top of the discriminator and optimize it with the following objective:", + "bbox": [ + 496, + 411, + 890, + 501 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\xi} = \\Phi (\\mathbf {I} _ {f}), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 666, + 526, + 890, + 544 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {p o s e}} = l _ {2} (\\hat {\\xi}, \\xi), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 638, + 547, + 890, + 566 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $l_{2}(\\cdot)$ denotes the function measuring $l_{2}$ distance between poses. $\\xi$ is the pose that is inferred from the same latent code as $\\mathbf{I}_f$ by the generator.", + "bbox": [ + 496, + 575, + 890, + 619 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Performing Pose-aware Discrimination. With the help of the pose branch, our discriminator can be adopted to infer camera poses for the given images. Even though the pose branch training is done on fake images, it is also generalizable on real images $\\mathbf{I}_r$ from the dataset. In such cases, we can leverage the pose-aware discriminator to perform discrimination on real or fake images as well as differentiate whether the image is attached with an accurate pose or not. Concretely, we first ask the discriminator to extract a pose from the input image, and then the pose is treated as a pseudo label to perform conditional bi-class classification. Here, we take the real image part of the discriminator loss as an example:", + "bbox": [ + 496, + 621, + 890, + 816 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {D}} ^ {\\mathbf {I} _ {r}} = - \\mathbb {E} \\left[ \\log \\left(\\mathrm {D} \\left(\\mathbf {I} _ {r} \\mid \\Phi (\\mathbf {I} _ {r})\\right)\\right) \\right]. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 594, + 825, + 890, + 845 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this way, we facilitate the discriminator with awareness of pose cues, leading to better pose alignment across various synthesized samples. As a result, this alignment also", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "13064", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "implicitly prevents the generator from degenerate solutions where a flat shape is usually generated with huge artifacts. It is worth noting that the discriminator learns poses from the generator and, in turn, uses the conditional discrimination score to update the pose branch in the generator. Therefore, the poses are learned in a loop-back manner without any annotations.", + "bbox": [ + 75, + 90, + 472, + 196 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Training Objectives", + "text_level": 1, + "bbox": [ + 76, + 205, + 266, + 222 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Adversarial Loss. We use the standard adversarial loss for training following [8],", + "bbox": [ + 75, + 228, + 468, + 260 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {\\mathrm {D}} = - \\mathbb {E} \\left[ \\log \\left(1 - \\mathrm {D} \\left(\\mathbf {I} _ {f} | \\Phi (\\mathbf {I} _ {f})\\right)\\right) \\right] \\\\ - \\mathbb {E} \\left[ \\log \\left(\\mathrm {D} \\left(\\mathbf {I} _ {r} \\mid \\Phi (\\mathbf {I} _ {r})\\right)\\right) \\right] + \\lambda \\mathbb {E} \\left[ \\left| \\left| \\nabla_ {\\mathbf {I} _ {r}} \\mathrm {D} (\\mathbf {I} _ {r}) \\right| \\right| _ {2} ^ {2} \\right], \\tag {7} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 91, + 268, + 468, + 321 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {G}} = - \\mathbb {E} [ \\log (\\mathrm {D} (\\mathbf {I} _ {f} | \\Phi (\\mathbf {I} _ {f}))) ], \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 91, + 325, + 468, + 344 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{I}_r$ and $\\mathbf{I}_f$ are real data and generated data, respectively. The third term in Eq. (7) is the gradient penalty, and $\\lambda$ denotes the weight for this term.", + "bbox": [ + 75, + 353, + 468, + 398 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Symmetry Loss. Planar underlying shapes are easily generated when single-view images are synthesized for training. To avoid the trivial solution, we ask the network to synthesize the second image under another view, which we choose the symmetrical camera view $\\xi^{\\prime}$ regarding the $yz$ -plane,", + "bbox": [ + 75, + 398, + 468, + 489 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {I} _ {f} ^ {\\prime} = \\mathrm {G} (\\mathbf {z}, \\xi^ {\\prime}). \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 220, + 500, + 468, + 518 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The novel view image will be used to calculate the adversarial loss as in Eq. (7) and Eq. (8), and get $\\mathcal{L}_{\\mathrm{D}'}$ and $\\mathcal{L}_{\\mathrm{G}'}$ .", + "bbox": [ + 75, + 527, + 468, + 558 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Pose Loss. As stated in Sec. 3.3, we also attach an auxiliary pose branch $\\Phi(\\cdot)$ in the discriminator to perform pose estimation on the given images. We use Eq. (5) for pose branch training.", + "bbox": [ + 75, + 558, + 468, + 618 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Full Objectives. In summary, the pose-free generator and the pose-aware discriminator are jointly optimized with", + "bbox": [ + 75, + 619, + 468, + 648 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {\\mathrm {G}} + \\mathcal {L} _ {\\mathrm {G} ^ {\\prime}} + \\mathcal {L} _ {\\mathrm {D}} + \\mathcal {L} _ {\\mathrm {D} ^ {\\prime}} + \\gamma \\mathcal {L} _ {\\text {p o s e}}, \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 140, + 660, + 468, + 676 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\gamma$ is the weight of pose loss.", + "bbox": [ + 76, + 686, + 307, + 702 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.5. Implementation Details", + "text_level": 1, + "bbox": [ + 76, + 710, + 294, + 727 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We build our PoF3D on the architecture of EG3D [3]. For the pose-aware generator, we do not use pose-conditioned generation. Instead, we instantiate the pose branch with two linear layers and a leaky ReLU activation in between. This branch takes in latent codes from $w$ space and outputs camera poses. The camera pose consists of an azimuth angle and an elevation angle, which indicates the camera position for rendering. The triplane resolution is $256 \\times 256$ , and the rendering in the neural radiance field is conducted on $64 \\times 64$ resolution. Both the feature map and the image are rendered. A super-resolution module then", + "bbox": [ + 75, + 734, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "transforms the feature map into a high-resolution image. The pose-aware discriminator is inherited from the dual discriminator in EG3D [3]. We add the pose branch on the features before the last two fully-connected layers that output the realness score. The pose branch is composed of two fully-connected layers with a leaky ReLU as the activation function in the middle. The learning rate of the generator is $2.5e-3$ while that of its pose branch is set to $2.5e-5$ . The discriminator's learning rate is $2e-3$ . More details are available in the Supplementary Material.", + "bbox": [ + 496, + 90, + 890, + 242 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 498, + 258, + 633, + 276 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Experimental Settings", + "text_level": 1, + "bbox": [ + 498, + 285, + 705, + 301 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Datasets. We evaluate PoF3D on three datasets, including FFHQ [12], Cats [51], and Shapenet Cars [5]. FFHQ is a real-world dataset that contains unique 70K high-quality images of human faces. We follow [3] to align and crop the data. Cats include 10K real-world cat images of various resolutions. The data is preprocessed following [6]. Shapenet Cars [5] is a synthetic dataset that contains different car models. We use the dataset rendered from [3] that has around 530K images. Unlike the face-forward datasets, the camera poses of it span the entire $360^{\\circ}$ azimuth and $180^{\\circ}$ elevation distributions. In the experiments, we use the resolution of $256 \\times 256$ for FFHQ and Cats, and $128 \\times 128$ for Shapenet Cars.", + "bbox": [ + 496, + 309, + 890, + 503 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Baselines. We compare our approach against two methods: CAMPARI [20], the state-of-the-art pose learning method in 3D-aware image synthesis, and EG3D [3], the state-of-the-art in 3D-aware image synthesis. We also build a baseline method which is a combination of them, where we incorporate the pose learning method in CAMPARI into the framework of EG3D. More details regarding the baselines can be found in Supplementary Material.", + "bbox": [ + 496, + 506, + 890, + 627 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Metrics. We use five metrics to evaluate the performance, including Fréchet Inception Distance (FID) [10], Depth Error [3], Pose Error [47], Reprojection Error (RE) [47], and Jensen-Shannon Divergence (JS). FID is measured between 50K generated images and all real images. Depth Error is used to assess the quality of geometry. We follow [3] and calculate the mean squared error (MSE) against pseudoground-truth depth estimated by [7] on 10K synthesized samples. We evaluate the pose accuracy on 10K generated samples as well. Given the synthesized images, we leverage the head pose estimator [53] and report the L1 distance between the estimated poses and the poses inferred from the generator. Note that we subtract the respective means of estimated and inferred pose distribution to compensate the canonical shift problem (see Fig. 4). Inter-view consistency is measured by the re-projection error following [47]. We render 5 views by sampling azimuth uniformly in the range of $[-23^{\\circ}, 23^{\\circ}]$ and warp two consecutive views to each other", + "bbox": [ + 496, + 628, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "13065", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/80f7389e0db78c3b0cec43d7ec73506de3a40031f38c6e42bbea6e9aeba3732f.jpg", + "image_caption": [ + "Figure 3. Qualitative comparison between our approach and baselines. CAMPARI [20] struggles to generate reasonable results. \"CAMPARI + EG3D\" suffers from mode collapse on the FFHQ and Cats datasets. EG3D [3] achieves impressive rendering and reconstruction results when camera poses of training images are given. In contrast, our approach can generate high-quality rendering and geometry without any pose priors." + ], + "image_footnote": [], + "bbox": [ + 81, + 89, + 883, + 641 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "to report the MSE. The images are normalized in the range of $[-1, 1]$ for evaluation. Since the azimuth range learned by CAMPARI is much smaller, we use the learned range for sampling in the measurement of CAMPARI. To measure the quality of the learned pose distribution, we report Jensen-Shannon Divergence on $50\\mathrm{K}$ synthesized samples and all real images by averaging divergence values over azimuth and elevation.", + "bbox": [ + 75, + 704, + 472, + 825 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Main Results", + "text_level": 1, + "bbox": [ + 76, + 844, + 217, + 858 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Qualitative Comparison. Fig. 3 shows the qualitative comparison against the baselines. CAMPARI learns faulty", + "bbox": [ + 75, + 869, + 470, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "and very sharp shapes that span the entire space along the ray direction (the same phenomenon as observed in Fig. 1d). Therefore, even if the object is rotated with an extremely small angle (e.g., $2.5^{\\circ}$ ), the caused visual effect is equivalent to that of the normal rotation of a decent shape with a much larger angle (e.g., $23^{\\circ}$ ). We visualize CAMPARI in its own valid range of the horizontal angle (around $[-2.5^{\\circ}, 2.5^{\\circ}]$ for FFHQ, $[-5^{\\circ}, 5^{\\circ}]$ for Cats, and $[-30^{\\circ}, 30^{\\circ}]$ for Shapenet Cars). For others, visualizations on FFHQ and Cats are conducted on the angle range $[-23^{\\circ}, 23^{\\circ}]$ . Poses for cars are randomly sampled from the entire $360^{\\circ}$ azimuth and $180^{\\circ}$ elevation distributions. EG3D leverages ground", + "bbox": [ + 496, + 704, + 893, + 887 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "13066", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/8c534a95e3d1472f0f545af35d2ab70c8de1bf9651d5705d95415515842094b2.jpg", + "table_caption": [ + "Table 1. Quantitative comparison on FFHQ [12], Cats [51], and Shapenet Cars [5]. Our approach significantly outperforms CAMPARI [20] and \"CAMPARI + EG3D\" in terms of depth error, pose error, reprojection error, and Jensen-Shannon divergence score. Note that, EG3D [3] uses pose annotations, while our model is trained without any pose priors. * means we report the FID of EG3D on Shapenet Cars using its released model, which is inconsistent with the one reported in the paper." + ], + "table_footnote": [], + "table_body": "
ModelFFHQ [12]Cats [51]Shapenet Cars [5]
FID50k ↓Depth↓Pose↓RE↓JS↓FID50k ↓RE↓JS↓FID50k ↓JS↓
CAMPARI [20]58.591.780.150.1090.6137.400.0500.6068.910.72
CAMPARI+EG3D3.251.130.18-0.734.83-0.744.660.83
EG3D [3]4.800.290.070.039-5.560.042-9.68*-
Ours4.990.290.100.0370.205.460.0460.243.780.51
", + "bbox": [ + 80, + 143, + 887, + 263 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "truth camera poses for training and generates high-quality images and underlying geometry simultaneously. When incorporated with the pose learning method in CAMPARI, EG3D suffers from pose collapse and converges to one pose on FFHQ and Cats. Hence, novel views are not available in such cases, and the 3D-aware image synthesis problem is degraded to 2D image synthesis. On Shapenet Cars, the generated image and its corresponding shape are visually reasonable under a specific view but become completely unnatural when deviating from that view. Our method, without any pose priors, can generate high-fidelity images and shapes on par with EG3D.", + "bbox": [ + 75, + 270, + 472, + 450 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Quantitative Comparison. We report the quantitative evaluation of baselines and our method in Tab. 1. CAMPARI fails to capture the underlying pose distribution and gets high Jensen-Shannon Divergence scores and pose errors. Consequently, the quality of images and shapes is unsatisfying as well, reflected by high FID scores and depth errors. CAMPARI+EG3D generates planar shapes and collapses to one pose or a small range of poses, which simplifies 3D-aware image synthesis to 2D image synthesis, resulting in lower FID scores but higher depth error, pose error and Jensen-Shannon Divergence score. EG3D, the method that uses pose annotations, exhibits good performance in terms of image quality and geometry quality. Our method yields results on par with EG3D and learns much better underlying pose distribution than the baselines. The quality of the geometry affects the multi-view consistency of the learned neural fields. Thus, EG3D and ours, which synthesize better shapes, can get better scores of reprojection errors. Note that our pose error is higher than that of EG3D, one of the reasons is that there exists the canonical view shift. As we do not provide any information on what the canonical view will be like, the model tends to learn a canonical view that leads to the best of its performance, which could be different from the standard. More discussions are in Sec. 4.4.", + "bbox": [ + 75, + 452, + 472, + 815 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 830, + 232, + 847 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We conduct ablation studies on FFHQ $256 \\times 256$ to analyze the effectiveness of PoF3D. Evaluation results are shown in Tab. 2.", + "bbox": [ + 75, + 854, + 470, + 900 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/81fc684b11432f6bf0c8c68ac30dd061682afbf058bcb029d37592a83b7541c8.jpg", + "table_caption": [ + "Table 2. Ablation studies on FFHQ dataset [12]. We analyze the influence of symmetry loss, pose-aware discriminator, and learning rate. See Sec. 4.3 for more details." + ], + "table_footnote": [], + "table_body": "
ModelFFHQ
FID50k ↓Depth↓Pose↓JS↓
w/o symmetry loss4.500.410.120.20
w/o pose-aware D3.431.300.190.21
w/o pose condition in D3.511.480.190.26
lr = 2.5e-4122.070.820.740.56
lr = 2.5e-610.200.700.160.38
Ours4.990.290.100.20
", + "bbox": [ + 506, + 309, + 880, + 458 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Symmetry Loss. We render an image from the symmetrical camera view and leverage it to pose a constraint on the generated neural radiance field from another view. Without this constraint, although the network can synthesize visually pleasing images under the learned pose and capture a rough pose distribution, the underlying geometry has a tendency to flatten, resulting in higher depth error. The constraint from the symmetrical view can detect the flat shapes because the rendered image under the novel view deviates from the real distribution and shall be corrected by the model.", + "bbox": [ + 496, + 462, + 890, + 612 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Pose-aware Discriminator. To verify the capability of the pose-aware discriminator, we compare it against the simple dual discriminator that removes the conditional label and purely performs real or fake discrimination. The simple dual discriminator does not provide any additional pose information to the generator other than the common realizesscore. Thus, the generator learns the pose freely and has difficulty aligning poses of data to share the same canonical view. For example, in the human face generation, one fake pose can correspond to images under different real poses. As a result, the pose error increases, and planar shapes are more frequently generated. We also report the results where only the pose conditioning discrimination is changed to the conventional pose-free discrimination. It drastically harms the geometry quality. With our pose-aware discriminator, the discriminator predicts the pose from both the fake and real data and uses it as the condition, which forces the generator to synthesize images under the same view as the conditional label, leading to better pose", + "bbox": [ + 496, + 613, + 892, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "13067", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/360cf17053de041798d8b1d510de00bae4f587de244f04cbb62f9f59b5557b95.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 133, + 95, + 367, + 218 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/23d07301fe391fe35729fd60d49da6bc849dfcde9242c7a326c4339bf2b8169a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 385, + 95, + 596, + 215 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e1c73b40bc4303f2ec5a74be99fd61a5eace5888d91401023b065758421a4e81.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 617, + 95, + 826, + 215 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/974d4d184579b14d5ee7d732fc7bfb1a15b0fd5fe9556be22ac32cc25fd2b4ed.jpg", + "image_caption": [ + "Figure 4. Pose distribution learned by the pose-free generator. The proposed approach well captures the pose distribution of the dataset. Note that, there is a slight shift of elevation distribution on the FFHQ dataset. The reason is that the model can automatically learn a canonical space for best performance during training." + ], + "image_footnote": [], + "bbox": [ + 133, + 224, + 364, + 362 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d8e66bcc83eb7eef4f6f7038493fe7a17bbea0df5bffd90c19fca9f8bad8ce15.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 385, + 226, + 596, + 361 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/dc0163a303a3c6df8a9d9d406998143d58d4fcfbd7a2124de18f802d76221cc9.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 616, + 227, + 828, + 362 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/1f481f290e1ae8ee97103fffbcf938d6aed76e04f8743423e705c921ebd40ff4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 138, + 412, + 367, + 534 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/47a6eacaff36474d61e949be2f57de6408568ff77cf7367a55ff51578bfd466b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 388, + 412, + 596, + 532 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/14f8f12fa98788827045e56c9fcb260dce4650d65937d090c22c58cb19b58904.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 620, + 412, + 828, + 532 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7a1dd9497e91314e08b9ce414316d249dab9fe1d0e7f172b93aed4c1d7dba1c0.jpg", + "image_caption": [ + "Figure 5. Pose distribution learned by the pose-aware discriminator. Results demonstrate that our discriminator can learn the pose distribution of the dataset. The issue of canonical space shift also exists from the discriminator perspective, same as Fig. 4." + ], + "image_footnote": [], + "bbox": [ + 138, + 544, + 364, + 679 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2c01d66d0ce2770488f5b9e05b9587d313a14ba19d7aa70cb4451cad079b8f99.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 385, + 544, + 591, + 679 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d3fc83027029ca4770268766186ee8ab6bb58502e6a6d4635c96a8d13896d71b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 620, + 544, + 828, + 680 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "alignment.", + "bbox": [ + 76, + 729, + 151, + 742 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Learning Rate of Pose Learner. Learning rate of the pose branch in the generator matters a lot. With a large learning rate (e.g., 2.5e-4 in Tab. 2), the generator always tries with new poses of large variation at the beginning and leaves the content learning behind, resulting in unstable training and higher tendency of mode collapse. As reported in Tab. 2, all the evaluation metrics experience a significant drop. On the contrary, if the learning rate is too small (e.g., 2.5e-6 in Tab. 2), the generator cannot explore the pose distribution enough and easily gets stuck in a small", + "bbox": [ + 75, + 750, + 472, + 901 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "range of pose distribution, putting more focus on the content learning. Consequently, the model fails to capture and understand the pose distribution, leading to worse shapes. A proper learning rate should balance the exploration of pose distribution and the learning of the content.", + "bbox": [ + 496, + 728, + 893, + 804 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Pose Analysis", + "text_level": 1, + "bbox": [ + 500, + 815, + 640, + 830 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, we analyze the pose distributions that are learned by our pose-free generator and pose-aware discriminator.", + "bbox": [ + 496, + 839, + 892, + 883 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Poses in Pose-free Generator. To visualize the pose", + "bbox": [ + 500, + 885, + 890, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "13068", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7fd9005a3de1a3a38ccf609d6e2006f0673ae1b7443c22070f4710b0405ca321.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 80, + 95, + 888, + 178 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/501ea946bb8c41b4295678666c581886e08499065cc8936e597b804c689de948.jpg", + "image_caption": [ + "Figure 6. Results of linear interpolation between two latent codes. The appearance, the geometry, and the pose all change smoothly, indicating the latent space is semantically meaningful." + ], + "image_footnote": [], + "bbox": [ + 80, + 183, + 888, + 265 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "distribution learned in the pose-free generator, we randomly sample 50K latent codes and infer the poses from them. The pose distributions from the dataset and learned in the generator are shown in Fig. 4. Without any pose priors, our method can capture the pose range and distribution of the dataset in general. As observed in the figure for elevation distributions on the FFHQ dataset, there exists a distribution shift. The reason is that we do not release any information about the canonical view to the model, and therefore, the model can interpret the canonical view freely with different angles which might be different from the one defined in the dataset. Generally, the model will choose the one that leads to the best performance as its canonical view.", + "bbox": [ + 75, + 304, + 467, + 500 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Poses in Pose-aware Discriminator. Since our discriminator is equipped with a pose predictor, we hire it to predict the poses for all data in the dataset and draw the distributions accordingly in Fig. 5. For FFHQ and Cats datasets, the distributions are well approximated, and the canonical view shift problem also exists in the discriminator. On Shapenet Cars, the distribution of azimuth is biased to one side. We conjecture the reason is that the model has difficulty distinguishing the front and rear of the car as they look very similar. As a result, the learned distribution shifts towards a hemisphere instead of the entire sphere.", + "bbox": [ + 75, + 501, + 467, + 667 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5. Applications", + "text_level": 1, + "bbox": [ + 76, + 679, + 209, + 695 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Linearity in Latent Space. To demonstrate the latent space learned by PoF3D is semantically meaningful, we randomly sample two latent codes and linearly interpolate between them. The interpolation results are shown in Fig. 6. We can see that both the appearance and the underlying geometry are changing smoothly. Besides, as we infer the pose from the latent code, poses undergo smooth changes as well.", + "bbox": [ + 75, + 703, + 467, + 808 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Real Image Inversion. One of the potential applications of PoF3D is to reconstruct the geometry from a real image and enable novel view synthesis. To achieve this goal, PTI [28], a GAN inversion method, is adopted to perform on our pose-free generator. In the previous methods [3] that demonstrate GAN inversion as an application, an off-the", + "bbox": [ + 75, + 810, + 467, + 898 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/2e8cca48573ad79f4da005ce9cfd331358abd48a8b50fbd209363333881d9f87.jpg", + "image_caption": [ + "Figure 7. Results of GAN inversion. Thanks to the design of pose-free generator, we do not require pose estimation prior to performing inversion like previous works. Instead, we can directly invert the image to get the 3D representation and the corresponding pose. The reconstructed geometry is realistic and enables vivid novel view synthesis." + ], + "image_footnote": [], + "bbox": [ + 504, + 304, + 887, + 372 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "shelf pose predictor is required to obtain the pose of the given image prior to performing GAN inversion. Ours, however, benefits from the changed formulation in which the camera pose is encoded in the latent space. Therefore, we can get not only the inverted neural radiance field but also the camera pose under which the given image is captured, when performing GAN inversion. The result is shown in Fig. 7. Our method can successfully invert the image and synthesize vivid images under novel views.", + "bbox": [ + 498, + 472, + 890, + 608 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 623, + 617, + 638 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work presents PoF3D, which learns 3D-aware image synthesis without using any pose priors. A pose-free generator is designed to infer camera poses directly from the latent space so that the requirement for pose priors in the previous works is removed. Besides, to help the generator better capture the underlying distribution, we make the discriminator pose-aware by asking it to first predict the camera pose and then use it as a condition when performing conditional real/fake discrimination. With such a design, experimental results demonstrate that our approach is able to synthesize high-quality images and high-fidelity shapes that are on par with state-of-the-art 3D synthesis methods without the need for manual pose tuning or dataset labeling. Acknowledgement. This research has been made possible by funding support from the Research Grants Council of Hong Kong under the Research Impact Fund project R6003-21.", + "bbox": [ + 498, + 648, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "13069", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 106 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Qingyan Bai, Yinghao Xu, Jiapeng Zhu, Weihao Xia, Yujiu Yang, and Yujun Shen. High-fidelity gan inversion with padding space. In Eur. Conf. Comput. Vis., 2022. 2", + "[2] Jonathan T Barron, Ben Mildenhall, Matthew Tancik, Peter Hedman, Ricardo Martin-Brualla, and Pratul P Srinivasan. Mip-nerf: A multiscale representation for anti-aliasing neural radiance fields. In Int. Conf. Comput. 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Syst., 2018. 2" + ], + "bbox": [ + 501, + 92, + 890, + 742 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "13071", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Learning 3D-Aware Image Synthesis With Unknown Pose Distribution/d83e531d-6687-4f90-82b7-f461cb8780cb_model.json b/2023/Learning 3D-Aware Image Synthesis With Unknown Pose Distribution/d83e531d-6687-4f90-82b7-f461cb8780cb_model.json new file mode 100644 index 0000000000000000000000000000000000000000..4f716683a4bc93a377f06a8ee70de9238943b2df --- /dev/null +++ b/2023/Learning 3D-Aware Image Synthesis With Unknown Pose Distribution/d83e531d-6687-4f90-82b7-f461cb8780cb_model.json @@ -0,0 +1,2178 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.135, + 0.131, + 0.836, + 0.154 + ], + "angle": 0, + "content": "Learning 3D-aware Image Synthesis with Unknown Pose Distribution" + }, + { + "type": "text", + "bbox": [ + 0.136, + 0.179, + 0.834, + 0.244 + ], + "angle": 0, + "content": "Zifan Shi\\(^{1*1}\\) Yujun Shen\\(^{12}\\) Yinghao Xu\\(^{3}\\) Sida Peng\\(^{4}\\) Yiyi Liao\\(^{4}\\) Sheng Guo\\(^{2}\\) Qifeng Chen\\(^{1}\\) Dit-Yan Yeung\\(^{1}\\) \n\\(^{1}\\)HKUST \\(^{2}\\)Ant Group \\(^{3}\\)CUHK \\(^{4}\\)Zhejiang University" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.275, + 0.314, + 0.291 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.308, + 0.474, + 0.625 + ], + "angle": 0, + "content": "Existing methods for 3D-aware image synthesis largely depend on the 3D pose distribution pre-estimated on the training set. An inaccurate estimation may mislead the model into learning faulty geometry. This work proposes PoF3D that frees generative radiance fields from the requirements of 3D pose priors. We first equip the generator with an efficient pose learner, which is able to infer a pose from a latent code, to approximate the underlying true pose distribution automatically. We then assign the discriminator a task to learn pose distribution under the supervision of the generator and to differentiate real and synthesized images with the predicted pose as the condition. The pose-free generator and the pose-aware discriminator are jointly trained in an adversarial manner. Extensive results on a couple of datasets confirm that the performance of our approach, regarding both image quality and geometry quality, is on par with state of the art. To our best knowledge, PoF3D demonstrates the feasibility of learning high-quality 3D-aware image synthesis without using 3D pose priors for the first time. Project page can be found here." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.639, + 0.21, + 0.654 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.665, + 0.47, + 0.816 + ], + "angle": 0, + "content": "3D-aware image generation has recently received growing attention due to its potential applications [3, 4, 9, 21, 30, 34, 47]. Compared with 2D synthesis, 3D-aware image synthesis requires the understanding of the geometry underlying 2D images, which is commonly achieved by incorporating 3D representations, such as neural radiance fields (NeRF) [2, 16, 17, 24, 25, 50], into generative models like generative adversarial networks (GANs) [8]. Such a formulation allows explicit camera control over the synthesized results, which fits better with our 3D world." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.817, + 0.47, + 0.864 + ], + "angle": 0, + "content": "To enable 3D-aware image synthesis from 2D image collections, existing attempts usually rely on adequate camera pose priors [3, 4, 9, 20, 21, 30, 47] for training." + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.275, + 0.89, + 0.373 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.53, + 0.374, + 0.672, + 0.383 + ], + "angle": 0, + "content": "(a) \\(\\pi\\) -GAN: good pose distribution" + }, + { + "type": "image_caption", + "bbox": [ + 0.724, + 0.374, + 0.862, + 0.383 + ], + "angle": 0, + "content": "(b) \\(\\pi\\) -GAN: bad pose distribution" + }, + { + "type": "image", + "bbox": [ + 0.506, + 0.385, + 0.889, + 0.435 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.506, + 0.435, + 0.695, + 0.484 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.521, + 0.484, + 0.681, + 0.494 + ], + "angle": 0, + "content": "(c) CAMPARI: good pose initialization" + }, + { + "type": "image", + "bbox": [ + 0.697, + 0.435, + 0.889, + 0.484 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.716, + 0.484, + 0.871, + 0.494 + ], + "angle": 0, + "content": "(d) CAMPARI: bad pose initialization" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.494, + 0.893, + 0.576 + ], + "angle": 0, + "content": "Figure 1. Sensitivity to pose priors in existing 3D-aware image synthesis approaches. \\(\\pi\\)-GAN [4] works well given an adequate pose distribution in (a), but fails to learn decent geometries given a slightly changed distribution in (b). CAMPARI [20] delivers reasonable results relying on a good initial pose distribution in (c), but suffers from a wrongly estimated initialization in (d)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.584, + 0.893, + 0.901 + ], + "angle": 0, + "content": "The priors are either estimated by conducting multiple pre-experiments [4, 9, 47], or obtained by borrowing external pose predictors or annotations [3]. Besides using a fixed distribution for pose sampling, some studies also propose to tune the pose priors together with the learning of image generation [20], but they are still dependent on the initial pose distribution. Consequently, although previous methods can produce satisfying images and geometry, their performance is highly sensitive to the given pose prior. For example, on the Cats dataset [51], \\(\\pi\\)-GAN [4] works well with a uniform pose distribution [-0.5, 0.5] (Fig. 1a), but fails to generate a decent underlying geometry when changing the distribution to [-0.3, 0.3] (Fig. 1b). Similarly, on the CelebA dataset [15], CAMPARI [20] learns 3D rotation when using Gaussian distribution \\(\\mathcal{N}(0,0.24)\\) as the initial prior (Fig. 1c), but loses the canonical space (e.g., the middle image of Fig. 1d should be under the frontal view) when changing the initialization to \\(\\mathcal{N}(0,0.12)\\) (Fig. 1d). Such a reliance on pose priors causes unexpected instability of 3D-aware image synthesis, which may burden this task with heavy experimental cost." + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.876, + 0.258, + 0.888 + ], + "angle": 0, + "content": "\\(\\dagger\\) indicates equal contribution." + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.888, + 0.398, + 0.9 + ], + "angle": 0, + "content": "* This work was done during an internship at Ant Group." + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.876, + 0.398, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "13062" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.438 + ], + "angle": 0, + "content": "In this work, we present a new approach for 3D-aware image synthesis, which removes the requirements for pose priors. Typically, a latent code is bound to the 3D content alone, where the camera pose is independently sampled from a manually designed distribution. Our method, however, maps a latent code to an image, which is implicitly composed of a 3D representation (i.e., neural radiance field) and a camera pose that can render that image. In this way, the camera pose is directly inferred from the latent code and jointly learned with the content, simplifying the input requirement. To facilitate the pose-free generator better capturing the underlying pose distribution, we re-design the discriminator to make it pose-aware. Concretely, we tailor the discriminator with a pose branch which is required to predict a camera pose from a given image. Then, the estimated pose is further treated as the conditional pseudo label when performing real/fake discrimination. The pose branch in the discriminator learns from the synthesized data and its corresponding pose that is encoded in the latent code, and in turn use the discrimination score to update the pose branch in the generator. With such a loop-back optimization process, two pose branches can align the fake data with the distribution of the dataset." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.44, + 0.472, + 0.561 + ], + "angle": 0, + "content": "We evaluate our pose-free method, which we call PoF3D for short, on various datasets, including FFHQ [12], Cats [51], and Shapenet Cars [5]. Both qualitative and quantitative results demonstrate that PoF3D frees 3D-aware image synthesis from hyper-parameter tuning on pose distributions and dataset labeling, and achieves on par performance with state-of-the-art in terms of image quality and geometry quality." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.574, + 0.22, + 0.589 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.599, + 0.473, + 0.903 + ], + "angle": 0, + "content": "3D-aware Image Synthesis. 3D-aware image synthesis has achieved remarkable success recently [33, 43] and benefits lots of 3D-aware applications [39, 44, 49, 55] rather than the conventional 2D applications [1, 26, 27, 38, 40, 41, 54]. Different from 2D synthesis [11-13, 48], some works [18, 19, 56] propose to adopt voxels as 3D representation for image rendering but suffer from the poor image quality and consistency due to the voxel resolution restriction. Then a series of works [4, 6, 23, 30, 45] introduce neural implicit function [16, 17, 24] as the underlying 3D representation for image rendering. However, rendering high-resolution images with direct volume rendering is very heavy. Lots of works [3, 9, 21, 22, 31, 37, 46, 47, 52] resort to either 2D convolutional upsamplers [3, 9, 21, 22, 47], multi-plane image rendering [52], sparse-voxel [31] inference, patch-based training [37] for acceleration. Besides, some works [23, 35] focus on the improvement of geometry quality. Although these methods are able to synthesize high-quality 3D-aware images, they are restricted to strong pose prior, i.e., manually tuned pose distribution, or well-annotated camera" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.137 + ], + "angle": 0, + "content": "poses [3]. Our work instead naturally enables 3D-aware image synthesis without any pose prior via a pose-free generator, which gives a fruitful avenue for future work." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.137, + 0.893, + 0.379 + ], + "angle": 0, + "content": "Camera Learning from 2D Images. Learning neural radiance fields (NeRF) [17] requires accurate pose annotations. To overcome this, some works [14, 42] try to optimize the annotated camera parameters or directly estimate camera poses with a small network, which is conceptually comparable to ours. On the other hand, our work differs from theirs in that our method focuses on learning pose distribution of a real dataset rather than exact camera poses. CAMPARI [20] and 3DGP [36] investigate a similar problem, aiming to estimate the pose distribution of an actual dataset. However, both of them need a manually designed prior, i.e., uniform or Gaussian, and fail to learn appropriate 3D geometry when the prior is very distant from the native distribution. In contrast, our work abandons all the manually designed prior and allows the generator to learn pose distribution automatically via adversarial training." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.391, + 0.591, + 0.406 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.416, + 0.892, + 0.613 + ], + "angle": 0, + "content": "Our proposed method for 3D-aware image synthesis can be freed from the requirement of pose priors. To achieve this goal, we propose some new designs in both the generator and the discriminator in conventional 3D-aware GANs [3, 4, 9, 30]. Specifically, the pose-free generator is equipped with a pose learner that infers the camera pose from the latent code. The pose-aware discriminator extracts a pose from the given image and uses it as the conditional label when performing real/fake classification. The framework is shown in Fig. 2. Before going into details, we first briefly introduce the generative neural radiance field, which plays a crucial role in 3D-aware image synthesis." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.621, + 0.63, + 0.637 + ], + "angle": 0, + "content": "3.1. Preliminary" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.643, + 0.892, + 0.84 + ], + "angle": 0, + "content": "A neural radiance field (NeRF) [17], \\( \\mathrm{F}(\\mathbf{x},\\mathbf{d})\\rightarrow (\\mathbf{c},\\sigma) \\), provides color \\( \\mathbf{c}\\in \\mathbb{R}^3 \\) and volume density \\( \\sigma \\in \\mathbb{R} \\) from a coordinate \\( \\mathbf{x}\\in \\mathbb{R}^3 \\) and a viewing direction \\( \\mathbf{d}\\in \\mathbb{S}^2 \\), typically parameterized with multi-layer perceptron (MLP) networks. Then, the pixel values are accumulated from the colors and densities of the points on the sampled rays. However, NeRF is highly dependent on multi-view supervision, leading to the inability to learn from a single-view image collection. To enable random sampling from single-view captures, recent attempts propose to condition NeRF with a latent code \\( \\mathbf{z} \\), resulting in their generative forms [4, 30], \\( \\mathrm{G}(\\mathbf{x},\\mathbf{d},\\mathbf{z})\\to (\\mathbf{c},\\sigma) \\), to achieve diverse 3D-aware generation." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.848, + 0.692, + 0.862 + ], + "angle": 0, + "content": "3.2. Pose-free Generator" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Different from NeRF, the camera pose \\(\\xi\\) deriving the spatial point \\(\\mathbf{x}\\) and view direction \\(\\mathbf{d}\\) in conventional 3D-aware" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13063" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.116, + 0.106, + 0.473, + 0.214 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.534, + 0.102, + 0.832, + 0.215 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.221, + 0.894, + 0.276 + ], + "angle": 0, + "content": "Figure 2. Framework of PoF3D, which consists of a pose-free generator and a pose-aware discriminator. The pose-free generator maps a latent code to a neural radiance field as well as a camera pose, followed by a volume renderer (VR) to output the final image. The pose-aware discriminator first predicts a camera pose from the given image and then use it as the pseudo label for conditional real/fake discrimination, indicated by the orange arrow." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.291, + 0.47, + 0.395 + ], + "angle": 0, + "content": "generators is randomly sampled from a prior distribution \\( p_{\\xi} \\) rather than well annotated by MVS [32] and SfM [29]. Such a prior distribution requires the knowledge of the pose distribution, and it should be tailored for different datasets, which introduces non-trivial hyperparameter tuning for model training. This generation process can be formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.179, + 0.402, + 0.469, + 0.42 + ], + "angle": 0, + "content": "\\[\n\\mathrm {G} (\\mathbf {z}, \\xi) = \\mathbf {I} _ {f} \\sim p _ {\\theta} \\left(\\mathbf {I} _ {f} | \\mathbf {z}, \\xi\\right), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.425, + 0.47, + 0.486 + ], + "angle": 0, + "content": "where the generator \\( \\mathrm{G} \\) synthesizes the image \\( \\mathbf{I}_f \\) by modeling the conditional probability given the latent code and the camera pose. Since the camera pose is independent of the latent code, we can rewrite Eq. (1) in the following form:" + }, + { + "type": "equation", + "bbox": [ + 0.084, + 0.501, + 0.469, + 0.55 + ], + "angle": 0, + "content": "\\[\np _ {\\theta} \\left(\\mathbf {I} _ {f} | \\mathbf {z}, \\xi\\right) = \\frac {p _ {\\theta} \\left(\\mathbf {I} _ {f} , \\mathbf {z} , \\xi\\right)}{p (\\mathbf {z} , \\xi)} = \\frac {p _ {\\theta} \\left(\\mathbf {I} _ {f} , \\xi | \\mathbf {z}\\right)}{p (\\xi)} = \\frac {p _ {\\theta} \\left(\\mathbf {I} _ {f} , \\xi | \\mathbf {z}\\right)}{p _ {\\xi}}. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.556, + 0.47, + 0.678 + ], + "angle": 0, + "content": "Obviously, if the pose prior does not align well with the real distribution, it is hard to correctly estimate the image distribution \\( p_{\\theta}(\\mathbf{I}_f|\\mathbf{z},\\xi) \\). As noticed by [9, 47], it always makes the training diverge if the prior does not align well with the real distribution. To free the generator from sampling poses from a prior distribution, we follow the formulation of conventional 2D GANs that synthesizes images from the latent code only:" + }, + { + "type": "equation", + "bbox": [ + 0.152, + 0.683, + 0.469, + 0.7 + ], + "angle": 0, + "content": "\\[\n\\mathrm {G} (\\mathbf {z}, \\Psi (\\mathbf {z})) = \\mathbf {I} _ {f} \\sim p _ {\\theta} \\left(\\mathbf {I} _ {f} | \\mathbf {z}, \\Psi (\\mathbf {z})\\right), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.47, + 0.841 + ], + "angle": 0, + "content": "where the camera pose \\(\\xi\\) is parameterized with a nonlinear function \\(\\Psi(\\cdot)\\) that takes \\(\\mathbf{z}\\) as input. Concretely, we implement \\(\\Psi(\\cdot)\\) by introducing an additional pose branch on the top of the generator. The estimated camera pose is further fed into a generative radiance field to render a 2D image. Compared with previous solutions, our generator aims at approximating the conditional probability only from the latent observation, which is prone to simulating the native data distribution without taking the pose prior into account." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.848, + 0.314, + 0.863 + ], + "angle": 0, + "content": "3.3. Pose-aware Discriminator" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.47, + 0.902 + ], + "angle": 0, + "content": "As mentioned above, we remove the pose prior of a 3D-aware generator by parameterizing camera pose \\(\\xi\\)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.291, + 0.892, + 0.411 + ], + "angle": 0, + "content": "from a latent code \\(\\mathbf{z}\\). The 3D representation leveraged in the generator is helpful in disentangling the camera factor. However, the conventional discriminator remains to differentiate real and fake images from 2D space, leading to inadequate supervision to factorize camera poses from latent codes. It easily makes the generator synthesize flat shapes and learn invalid camera distribution. Therefore, we propose to make the discriminator pose-aware." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.412, + 0.892, + 0.502 + ], + "angle": 0, + "content": "Learning Pose-aware Discriminator. To let the discriminator become aware of poses, we assign a pose estimation task on fake images beyond bi-class domain classification, which is to derive the pose information from the given images. We introduce a pose branch \\(\\Phi(\\cdot)\\) on top of the discriminator and optimize it with the following objective:" + }, + { + "type": "equation", + "bbox": [ + 0.667, + 0.527, + 0.891, + 0.545 + ], + "angle": 0, + "content": "\\[\n\\hat {\\xi} = \\Phi (\\mathbf {I} _ {f}), \\tag {4}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.639, + 0.549, + 0.891, + 0.567 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {p o s e}} = l _ {2} (\\hat {\\xi}, \\xi), \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.577, + 0.891, + 0.621 + ], + "angle": 0, + "content": "where \\(l_{2}(\\cdot)\\) denotes the function measuring \\(l_{2}\\) distance between poses. \\(\\xi\\) is the pose that is inferred from the same latent code as \\(\\mathbf{I}_f\\) by the generator." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.622, + 0.892, + 0.818 + ], + "angle": 0, + "content": "Performing Pose-aware Discrimination. With the help of the pose branch, our discriminator can be adopted to infer camera poses for the given images. Even though the pose branch training is done on fake images, it is also generalizable on real images \\(\\mathbf{I}_r\\) from the dataset. In such cases, we can leverage the pose-aware discriminator to perform discrimination on real or fake images as well as differentiate whether the image is attached with an accurate pose or not. Concretely, we first ask the discriminator to extract a pose from the input image, and then the pose is treated as a pseudo label to perform conditional bi-class classification. Here, we take the real image part of the discriminator loss as an example:" + }, + { + "type": "equation", + "bbox": [ + 0.595, + 0.827, + 0.891, + 0.846 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {D}} ^ {\\mathbf {I} _ {r}} = - \\mathbb {E} \\left[ \\log \\left(\\mathrm {D} \\left(\\mathbf {I} _ {r} \\mid \\Phi (\\mathbf {I} _ {r})\\right)\\right) \\right]. \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In this way, we facilitate the discriminator with awareness of pose cues, leading to better pose alignment across various synthesized samples. As a result, this alignment also" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13064" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.198 + ], + "angle": 0, + "content": "implicitly prevents the generator from degenerate solutions where a flat shape is usually generated with huge artifacts. It is worth noting that the discriminator learns poses from the generator and, in turn, uses the conditional discrimination score to update the pose branch in the generator. Therefore, the poses are learned in a loop-back manner without any annotations." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.206, + 0.267, + 0.223 + ], + "angle": 0, + "content": "3.4. Training Objectives" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.229, + 0.47, + 0.261 + ], + "angle": 0, + "content": "Adversarial Loss. We use the standard adversarial loss for training following [8]," + }, + { + "type": "equation", + "bbox": [ + 0.092, + 0.269, + 0.47, + 0.323 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {\\mathrm {D}} = - \\mathbb {E} \\left[ \\log \\left(1 - \\mathrm {D} \\left(\\mathbf {I} _ {f} | \\Phi (\\mathbf {I} _ {f})\\right)\\right) \\right] \\\\ - \\mathbb {E} \\left[ \\log \\left(\\mathrm {D} \\left(\\mathbf {I} _ {r} \\mid \\Phi (\\mathbf {I} _ {r})\\right)\\right) \\right] + \\lambda \\mathbb {E} \\left[ \\left| \\left| \\nabla_ {\\mathbf {I} _ {r}} \\mathrm {D} (\\mathbf {I} _ {r}) \\right| \\right| _ {2} ^ {2} \\right], \\tag {7} \\\\ \\end{array}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.093, + 0.327, + 0.47, + 0.345 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {G}} = - \\mathbb {E} [ \\log (\\mathrm {D} (\\mathbf {I} _ {f} | \\Phi (\\mathbf {I} _ {f}))) ], \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.354, + 0.469, + 0.399 + ], + "angle": 0, + "content": "where \\(\\mathbf{I}_r\\) and \\(\\mathbf{I}_f\\) are real data and generated data, respectively. The third term in Eq. (7) is the gradient penalty, and \\(\\lambda\\) denotes the weight for this term." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.4, + 0.469, + 0.49 + ], + "angle": 0, + "content": "Symmetry Loss. Planar underlying shapes are easily generated when single-view images are synthesized for training. To avoid the trivial solution, we ask the network to synthesize the second image under another view, which we choose the symmetrical camera view \\(\\xi^{\\prime}\\) regarding the \\(yz\\)-plane," + }, + { + "type": "equation", + "bbox": [ + 0.222, + 0.501, + 0.469, + 0.519 + ], + "angle": 0, + "content": "\\[\n\\mathbf {I} _ {f} ^ {\\prime} = \\mathrm {G} (\\mathbf {z}, \\xi^ {\\prime}). \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.528, + 0.469, + 0.559 + ], + "angle": 0, + "content": "The novel view image will be used to calculate the adversarial loss as in Eq. (7) and Eq. (8), and get \\(\\mathcal{L}_{\\mathrm{D}'}\\) and \\(\\mathcal{L}_{\\mathrm{G}'}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.559, + 0.469, + 0.619 + ], + "angle": 0, + "content": "Pose Loss. As stated in Sec. 3.3, we also attach an auxiliary pose branch \\(\\Phi(\\cdot)\\) in the discriminator to perform pose estimation on the given images. We use Eq. (5) for pose branch training." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.62, + 0.469, + 0.65 + ], + "angle": 0, + "content": "Full Objectives. In summary, the pose-free generator and the pose-aware discriminator are jointly optimized with" + }, + { + "type": "equation", + "bbox": [ + 0.142, + 0.661, + 0.469, + 0.677 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {\\mathrm {G}} + \\mathcal {L} _ {\\mathrm {G} ^ {\\prime}} + \\mathcal {L} _ {\\mathrm {D}} + \\mathcal {L} _ {\\mathrm {D} ^ {\\prime}} + \\gamma \\mathcal {L} _ {\\text {p o s e}}, \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.688, + 0.308, + 0.703 + ], + "angle": 0, + "content": "where \\(\\gamma\\) is the weight of pose loss." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.712, + 0.295, + 0.728 + ], + "angle": 0, + "content": "3.5. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.47, + 0.901 + ], + "angle": 0, + "content": "We build our PoF3D on the architecture of EG3D [3]. For the pose-aware generator, we do not use pose-conditioned generation. Instead, we instantiate the pose branch with two linear layers and a leaky ReLU activation in between. This branch takes in latent codes from \\( w \\) space and outputs camera poses. The camera pose consists of an azimuth angle and an elevation angle, which indicates the camera position for rendering. The triplane resolution is \\( 256 \\times 256 \\), and the rendering in the neural radiance field is conducted on \\( 64 \\times 64 \\) resolution. Both the feature map and the image are rendered. A super-resolution module then" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.243 + ], + "angle": 0, + "content": "transforms the feature map into a high-resolution image. The pose-aware discriminator is inherited from the dual discriminator in EG3D [3]. We add the pose branch on the features before the last two fully-connected layers that output the realness score. The pose branch is composed of two fully-connected layers with a leaky ReLU as the activation function in the middle. The learning rate of the generator is \\(2.5e-3\\) while that of its pose branch is set to \\(2.5e-5\\). The discriminator's learning rate is \\(2e-3\\). More details are available in the Supplementary Material." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.26, + 0.634, + 0.277 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.286, + 0.707, + 0.302 + ], + "angle": 0, + "content": "4.1. Experimental Settings" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.31, + 0.892, + 0.505 + ], + "angle": 0, + "content": "Datasets. We evaluate PoF3D on three datasets, including FFHQ [12], Cats [51], and Shapenet Cars [5]. FFHQ is a real-world dataset that contains unique 70K high-quality images of human faces. We follow [3] to align and crop the data. Cats include 10K real-world cat images of various resolutions. The data is preprocessed following [6]. Shapenet Cars [5] is a synthetic dataset that contains different car models. We use the dataset rendered from [3] that has around 530K images. Unlike the face-forward datasets, the camera poses of it span the entire \\(360^{\\circ}\\) azimuth and \\(180^{\\circ}\\) elevation distributions. In the experiments, we use the resolution of \\(256 \\times 256\\) for FFHQ and Cats, and \\(128 \\times 128\\) for Shapenet Cars." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.507, + 0.892, + 0.628 + ], + "angle": 0, + "content": "Baselines. We compare our approach against two methods: CAMPARI [20], the state-of-the-art pose learning method in 3D-aware image synthesis, and EG3D [3], the state-of-the-art in 3D-aware image synthesis. We also build a baseline method which is a combination of them, where we incorporate the pose learning method in CAMPARI into the framework of EG3D. More details regarding the baselines can be found in Supplementary Material." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Metrics. We use five metrics to evaluate the performance, including Fréchet Inception Distance (FID) [10], Depth Error [3], Pose Error [47], Reprojection Error (RE) [47], and Jensen-Shannon Divergence (JS). FID is measured between 50K generated images and all real images. Depth Error is used to assess the quality of geometry. We follow [3] and calculate the mean squared error (MSE) against pseudoground-truth depth estimated by [7] on 10K synthesized samples. We evaluate the pose accuracy on 10K generated samples as well. Given the synthesized images, we leverage the head pose estimator [53] and report the L1 distance between the estimated poses and the poses inferred from the generator. Note that we subtract the respective means of estimated and inferred pose distribution to compensate the canonical shift problem (see Fig. 4). Inter-view consistency is measured by the re-projection error following [47]. We render 5 views by sampling azimuth uniformly in the range of \\([-23^{\\circ}, 23^{\\circ}]\\) and warp two consecutive views to each other" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13065" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.09, + 0.885, + 0.642 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.642, + 0.895, + 0.699 + ], + "angle": 0, + "content": "Figure 3. Qualitative comparison between our approach and baselines. CAMPARI [20] struggles to generate reasonable results. \"CAMPARI + EG3D\" suffers from mode collapse on the FFHQ and Cats datasets. EG3D [3] achieves impressive rendering and reconstruction results when camera poses of training images are given. In contrast, our approach can generate high-quality rendering and geometry without any pose priors." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.473, + 0.826 + ], + "angle": 0, + "content": "to report the MSE. The images are normalized in the range of \\([-1, 1]\\) for evaluation. Since the azimuth range learned by CAMPARI is much smaller, we use the learned range for sampling in the measurement of CAMPARI. To measure the quality of the learned pose distribution, we report Jensen-Shannon Divergence on \\(50\\mathrm{K}\\) synthesized samples and all real images by averaging divergence values over azimuth and elevation." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.845, + 0.218, + 0.859 + ], + "angle": 0, + "content": "4.2. Main Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Qualitative Comparison. Fig. 3 shows the qualitative comparison against the baselines. CAMPARI learns faulty" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.895, + 0.888 + ], + "angle": 0, + "content": "and very sharp shapes that span the entire space along the ray direction (the same phenomenon as observed in Fig. 1d). Therefore, even if the object is rotated with an extremely small angle (e.g., \\(2.5^{\\circ}\\)), the caused visual effect is equivalent to that of the normal rotation of a decent shape with a much larger angle (e.g., \\(23^{\\circ}\\)). We visualize CAMPARI in its own valid range of the horizontal angle (around \\([-2.5^{\\circ}, 2.5^{\\circ}]\\) for FFHQ, \\([-5^{\\circ}, 5^{\\circ}]\\) for Cats, and \\([-30^{\\circ}, 30^{\\circ}]\\) for Shapenet Cars). For others, visualizations on FFHQ and Cats are conducted on the angle range \\([-23^{\\circ}, 23^{\\circ}]\\). Poses for cars are randomly sampled from the entire \\(360^{\\circ}\\) azimuth and \\(180^{\\circ}\\) elevation distributions. EG3D leverages ground" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "13066" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.892, + 0.146 + ], + "angle": 0, + "content": "Table 1. Quantitative comparison on FFHQ [12], Cats [51], and Shapenet Cars [5]. Our approach significantly outperforms CAMPARI [20] and \"CAMPARI + EG3D\" in terms of depth error, pose error, reprojection error, and Jensen-Shannon divergence score. Note that, EG3D [3] uses pose annotations, while our model is trained without any pose priors. * means we report the FID of EG3D on Shapenet Cars using its released model, which is inconsistent with the one reported in the paper." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.145, + 0.888, + 0.265 + ], + "angle": 0, + "content": "
ModelFFHQ [12]Cats [51]Shapenet Cars [5]
FID50k ↓Depth↓Pose↓RE↓JS↓FID50k ↓RE↓JS↓FID50k ↓JS↓
CAMPARI [20]58.591.780.150.1090.6137.400.0500.6068.910.72
CAMPARI+EG3D3.251.130.18-0.734.83-0.744.660.83
EG3D [3]4.800.290.070.039-5.560.042-9.68*-
Ours4.990.290.100.0370.205.460.0460.243.780.51
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.271, + 0.473, + 0.451 + ], + "angle": 0, + "content": "truth camera poses for training and generates high-quality images and underlying geometry simultaneously. When incorporated with the pose learning method in CAMPARI, EG3D suffers from pose collapse and converges to one pose on FFHQ and Cats. Hence, novel views are not available in such cases, and the 3D-aware image synthesis problem is degraded to 2D image synthesis. On Shapenet Cars, the generated image and its corresponding shape are visually reasonable under a specific view but become completely unnatural when deviating from that view. Our method, without any pose priors, can generate high-fidelity images and shapes on par with EG3D." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.453, + 0.473, + 0.816 + ], + "angle": 0, + "content": "Quantitative Comparison. We report the quantitative evaluation of baselines and our method in Tab. 1. CAMPARI fails to capture the underlying pose distribution and gets high Jensen-Shannon Divergence scores and pose errors. Consequently, the quality of images and shapes is unsatisfying as well, reflected by high FID scores and depth errors. CAMPARI+EG3D generates planar shapes and collapses to one pose or a small range of poses, which simplifies 3D-aware image synthesis to 2D image synthesis, resulting in lower FID scores but higher depth error, pose error and Jensen-Shannon Divergence score. EG3D, the method that uses pose annotations, exhibits good performance in terms of image quality and geometry quality. Our method yields results on par with EG3D and learns much better underlying pose distribution than the baselines. The quality of the geometry affects the multi-view consistency of the learned neural fields. Thus, EG3D and ours, which synthesize better shapes, can get better scores of reprojection errors. Note that our pose error is higher than that of EG3D, one of the reasons is that there exists the canonical view shift. As we do not provide any information on what the canonical view will be like, the model tends to learn a canonical view that leads to the best of its performance, which could be different from the standard. More discussions are in Sec. 4.4." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.831, + 0.233, + 0.848 + ], + "angle": 0, + "content": "4.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.471, + 0.901 + ], + "angle": 0, + "content": "We conduct ablation studies on FFHQ \\(256 \\times 256\\) to analyze the effectiveness of PoF3D. Evaluation results are shown in Tab. 2." + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.268, + 0.892, + 0.31 + ], + "angle": 0, + "content": "Table 2. Ablation studies on FFHQ dataset [12]. We analyze the influence of symmetry loss, pose-aware discriminator, and learning rate. See Sec. 4.3 for more details." + }, + { + "type": "table", + "bbox": [ + 0.508, + 0.31, + 0.882, + 0.459 + ], + "angle": 0, + "content": "
ModelFFHQ
FID50k ↓Depth↓Pose↓JS↓
w/o symmetry loss4.500.410.120.20
w/o pose-aware D3.431.300.190.21
w/o pose condition in D3.511.480.190.26
lr = 2.5e-4122.070.820.740.56
lr = 2.5e-610.200.700.160.38
Ours4.990.290.100.20
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.463, + 0.892, + 0.613 + ], + "angle": 0, + "content": "Symmetry Loss. We render an image from the symmetrical camera view and leverage it to pose a constraint on the generated neural radiance field from another view. Without this constraint, although the network can synthesize visually pleasing images under the learned pose and capture a rough pose distribution, the underlying geometry has a tendency to flatten, resulting in higher depth error. The constraint from the symmetrical view can detect the flat shapes because the rendered image under the novel view deviates from the real distribution and shall be corrected by the model." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Pose-aware Discriminator. To verify the capability of the pose-aware discriminator, we compare it against the simple dual discriminator that removes the conditional label and purely performs real or fake discrimination. The simple dual discriminator does not provide any additional pose information to the generator other than the common realizesscore. Thus, the generator learns the pose freely and has difficulty aligning poses of data to share the same canonical view. For example, in the human face generation, one fake pose can correspond to images under different real poses. As a result, the pose error increases, and planar shapes are more frequently generated. We also report the results where only the pose conditioning discrimination is changed to the conventional pose-free discrimination. It drastically harms the geometry quality. With our pose-aware discriminator, the discriminator predicts the pose from both the fake and real data and uses it as the condition, which forces the generator to synthesize images under the same view as the conditional label, leading to better pose" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "13067" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.135, + 0.096, + 0.368, + 0.219 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.387, + 0.096, + 0.597, + 0.217 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.618, + 0.097, + 0.828, + 0.216 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.134, + 0.226, + 0.365, + 0.363 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.387, + 0.227, + 0.597, + 0.362 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.617, + 0.228, + 0.829, + 0.363 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.366, + 0.894, + 0.409 + ], + "angle": 0, + "content": "Figure 4. Pose distribution learned by the pose-free generator. The proposed approach well captures the pose distribution of the dataset. Note that, there is a slight shift of elevation distribution on the FFHQ dataset. The reason is that the model can automatically learn a canonical space for best performance during training." + }, + { + "type": "image", + "bbox": [ + 0.139, + 0.414, + 0.368, + 0.535 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.389, + 0.414, + 0.597, + 0.534 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.621, + 0.414, + 0.83, + 0.534 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.139, + 0.545, + 0.365, + 0.68 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.387, + 0.545, + 0.593, + 0.68 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.621, + 0.545, + 0.829, + 0.681 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.686, + 0.893, + 0.716 + ], + "angle": 0, + "content": "Figure 5. Pose distribution learned by the pose-aware discriminator. Results demonstrate that our discriminator can learn the pose distribution of the dataset. The issue of canonical space shift also exists from the discriminator perspective, same as Fig. 4." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.73, + 0.152, + 0.743 + ], + "angle": 0, + "content": "alignment." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.473, + 0.902 + ], + "angle": 0, + "content": "Learning Rate of Pose Learner. Learning rate of the pose branch in the generator matters a lot. With a large learning rate (e.g., 2.5e-4 in Tab. 2), the generator always tries with new poses of large variation at the beginning and leaves the content learning behind, resulting in unstable training and higher tendency of mode collapse. As reported in Tab. 2, all the evaluation metrics experience a significant drop. On the contrary, if the learning rate is too small (e.g., 2.5e-6 in Tab. 2), the generator cannot explore the pose distribution enough and easily gets stuck in a small" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.729, + 0.894, + 0.805 + ], + "angle": 0, + "content": "range of pose distribution, putting more focus on the content learning. Consequently, the model fails to capture and understand the pose distribution, leading to worse shapes. A proper learning rate should balance the exploration of pose distribution and the learning of the content." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.816, + 0.642, + 0.832 + ], + "angle": 0, + "content": "4.4. Pose Analysis" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.893, + 0.884 + ], + "angle": 0, + "content": "In this section, we analyze the pose distributions that are learned by our pose-free generator and pose-aware discriminator." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.886, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Poses in Pose-free Generator. To visualize the pose" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13068" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.097, + 0.89, + 0.179 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.184, + 0.89, + 0.266 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.269, + 0.89, + 0.298 + ], + "angle": 0, + "content": "Figure 6. Results of linear interpolation between two latent codes. The appearance, the geometry, and the pose all change smoothly, indicating the latent space is semantically meaningful." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.305, + 0.468, + 0.501 + ], + "angle": 0, + "content": "distribution learned in the pose-free generator, we randomly sample 50K latent codes and infer the poses from them. The pose distributions from the dataset and learned in the generator are shown in Fig. 4. Without any pose priors, our method can capture the pose range and distribution of the dataset in general. As observed in the figure for elevation distributions on the FFHQ dataset, there exists a distribution shift. The reason is that we do not release any information about the canonical view to the model, and therefore, the model can interpret the canonical view freely with different angles which might be different from the one defined in the dataset. Generally, the model will choose the one that leads to the best performance as its canonical view." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.502, + 0.468, + 0.668 + ], + "angle": 0, + "content": "Poses in Pose-aware Discriminator. Since our discriminator is equipped with a pose predictor, we hire it to predict the poses for all data in the dataset and draw the distributions accordingly in Fig. 5. For FFHQ and Cats datasets, the distributions are well approximated, and the canonical view shift problem also exists in the discriminator. On Shapenet Cars, the distribution of azimuth is biased to one side. We conjecture the reason is that the model has difficulty distinguishing the front and rear of the car as they look very similar. As a result, the learned distribution shifts towards a hemisphere instead of the entire sphere." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.68, + 0.21, + 0.696 + ], + "angle": 0, + "content": "4.5. Applications" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.704, + 0.468, + 0.809 + ], + "angle": 0, + "content": "Linearity in Latent Space. To demonstrate the latent space learned by PoF3D is semantically meaningful, we randomly sample two latent codes and linearly interpolate between them. The interpolation results are shown in Fig. 6. We can see that both the appearance and the underlying geometry are changing smoothly. Besides, as we infer the pose from the latent code, poses undergo smooth changes as well." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.468, + 0.9 + ], + "angle": 0, + "content": "Real Image Inversion. One of the potential applications of PoF3D is to reconstruct the geometry from a real image and enable novel view synthesis. To achieve this goal, PTI [28], a GAN inversion method, is adopted to perform on our pose-free generator. In the previous methods [3] that demonstrate GAN inversion as an application, an off-the" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.305, + 0.888, + 0.373 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.374, + 0.892, + 0.457 + ], + "angle": 0, + "content": "Figure 7. Results of GAN inversion. Thanks to the design of pose-free generator, we do not require pose estimation prior to performing inversion like previous works. Instead, we can directly invert the image to get the 3D representation and the corresponding pose. The reconstructed geometry is realistic and enables vivid novel view synthesis." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.473, + 0.892, + 0.609 + ], + "angle": 0, + "content": "shelf pose predictor is required to obtain the pose of the given image prior to performing GAN inversion. Ours, however, benefits from the changed formulation in which the camera pose is encoded in the latent space. Therefore, we can get not only the inverted neural radiance field but also the camera pose under which the given image is captured, when performing GAN inversion. The result is shown in Fig. 7. Our method can successfully invert the image and synthesize vivid images under novel views." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.624, + 0.618, + 0.639 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.649, + 0.892, + 0.9 + ], + "angle": 0, + "content": "This work presents PoF3D, which learns 3D-aware image synthesis without using any pose priors. A pose-free generator is designed to infer camera poses directly from the latent space so that the requirement for pose priors in the previous works is removed. Besides, to help the generator better capture the underlying distribution, we make the discriminator pose-aware by asking it to first predict the camera pose and then use it as a condition when performing conditional real/fake discrimination. With such a design, experimental results demonstrate that our approach is able to synthesize high-quality images and high-fidelity shapes that are on par with state-of-the-art 3D synthesis methods without the need for manual pose tuning or dataset labeling. Acknowledgement. This research has been made possible by funding support from the Research Grants Council of Hong Kong under the Research Impact Fund project R6003-21." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13069" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.079, + 0.09, + 0.176, + 0.107 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.157 + ], + "angle": 0, + "content": "[1] Qingyan Bai, Yinghao Xu, Jiapeng Zhu, Weihao Xia, Yujiu Yang, and Yujun Shen. High-fidelity gan inversion with padding space. In Eur. Conf. Comput. Vis., 2022. 2" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.159, + 0.472, + 0.226 + ], + "angle": 0, + "content": "[2] Jonathan T Barron, Ben Mildenhall, Matthew Tancik, Peter Hedman, Ricardo Martin-Brualla, and Pratul P Srinivasan. Mip-nerf: A multiscale representation for anti-aliasing neural radiance fields. In Int. Conf. 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An inaccurate estimation may mislead the model into learning faulty geometry. This work proposes PoF3D that frees generative radiance fields from the requirements of 3D pose priors. We first equip the generator with an efficient pose learner, which is able to infer a pose from a latent code, to approximate the underlying true pose distribution automatically. We then assign the discriminator a task to learn pose distribution under the supervision of the generator and to differentiate real and synthesized images with the predicted pose as the condition. The pose-free generator and the pose-aware discriminator are jointly trained in an adversarial manner. Extensive results on a couple of datasets confirm that the performance of our approach, regarding both image quality and geometry quality, is on par with state of the art. To our best knowledge, PoF3D demonstrates the feasibility of learning high-quality 3D-aware image synthesis without using 3D pose priors for the first time. Project page can be found here. + +# 1. Introduction + +3D-aware image generation has recently received growing attention due to its potential applications [3, 4, 9, 21, 30, 34, 47]. Compared with 2D synthesis, 3D-aware image synthesis requires the understanding of the geometry underlying 2D images, which is commonly achieved by incorporating 3D representations, such as neural radiance fields (NeRF) [2, 16, 17, 24, 25, 50], into generative models like generative adversarial networks (GANs) [8]. Such a formulation allows explicit camera control over the synthesized results, which fits better with our 3D world. + +To enable 3D-aware image synthesis from 2D image collections, existing attempts usually rely on adequate camera pose priors [3, 4, 9, 20, 21, 30, 47] for training. + +![](images/2f4c5820444128fbf6d99639f175902945b6b74a9671686cf1b28fd5b4f212fa.jpg) +(a) $\pi$ -GAN: good pose distribution + +![](images/5630cbaae3a25e5c77608e57b63c0b38566ed629ab35fde4abe33dbbf2b7b189.jpg) +(b) $\pi$ -GAN: bad pose distribution + +![](images/82830da9b00a30eeff4b2837c1101997d7df4bbcf28855805972d500286dcf1f.jpg) +(c) CAMPARI: good pose initialization +Figure 1. Sensitivity to pose priors in existing 3D-aware image synthesis approaches. $\pi$ -GAN [4] works well given an adequate pose distribution in (a), but fails to learn decent geometries given a slightly changed distribution in (b). CAMPARI [20] delivers reasonable results relying on a good initial pose distribution in (c), but suffers from a wrongly estimated initialization in (d). + +![](images/31e850e25e5db3d4d0a81bc922059dfcc9f0c8e726f79baaf9e3182063c84340.jpg) +(d) CAMPARI: bad pose initialization + +The priors are either estimated by conducting multiple pre-experiments [4, 9, 47], or obtained by borrowing external pose predictors or annotations [3]. Besides using a fixed distribution for pose sampling, some studies also propose to tune the pose priors together with the learning of image generation [20], but they are still dependent on the initial pose distribution. Consequently, although previous methods can produce satisfying images and geometry, their performance is highly sensitive to the given pose prior. For example, on the Cats dataset [51], $\pi$ -GAN [4] works well with a uniform pose distribution [-0.5, 0.5] (Fig. 1a), but fails to generate a decent underlying geometry when changing the distribution to [-0.3, 0.3] (Fig. 1b). Similarly, on the CelebA dataset [15], CAMPARI [20] learns 3D rotation when using Gaussian distribution $\mathcal{N}(0,0.24)$ as the initial prior (Fig. 1c), but loses the canonical space (e.g., the middle image of Fig. 1d should be under the frontal view) when changing the initialization to $\mathcal{N}(0,0.12)$ (Fig. 1d). Such a reliance on pose priors causes unexpected instability of 3D-aware image synthesis, which may burden this task with heavy experimental cost. + +In this work, we present a new approach for 3D-aware image synthesis, which removes the requirements for pose priors. Typically, a latent code is bound to the 3D content alone, where the camera pose is independently sampled from a manually designed distribution. Our method, however, maps a latent code to an image, which is implicitly composed of a 3D representation (i.e., neural radiance field) and a camera pose that can render that image. In this way, the camera pose is directly inferred from the latent code and jointly learned with the content, simplifying the input requirement. To facilitate the pose-free generator better capturing the underlying pose distribution, we re-design the discriminator to make it pose-aware. Concretely, we tailor the discriminator with a pose branch which is required to predict a camera pose from a given image. Then, the estimated pose is further treated as the conditional pseudo label when performing real/fake discrimination. The pose branch in the discriminator learns from the synthesized data and its corresponding pose that is encoded in the latent code, and in turn use the discrimination score to update the pose branch in the generator. With such a loop-back optimization process, two pose branches can align the fake data with the distribution of the dataset. + +We evaluate our pose-free method, which we call PoF3D for short, on various datasets, including FFHQ [12], Cats [51], and Shapenet Cars [5]. Both qualitative and quantitative results demonstrate that PoF3D frees 3D-aware image synthesis from hyper-parameter tuning on pose distributions and dataset labeling, and achieves on par performance with state-of-the-art in terms of image quality and geometry quality. + +# 2. Related Work + +3D-aware Image Synthesis. 3D-aware image synthesis has achieved remarkable success recently [33, 43] and benefits lots of 3D-aware applications [39, 44, 49, 55] rather than the conventional 2D applications [1, 26, 27, 38, 40, 41, 54]. Different from 2D synthesis [11-13, 48], some works [18, 19, 56] propose to adopt voxels as 3D representation for image rendering but suffer from the poor image quality and consistency due to the voxel resolution restriction. Then a series of works [4, 6, 23, 30, 45] introduce neural implicit function [16, 17, 24] as the underlying 3D representation for image rendering. However, rendering high-resolution images with direct volume rendering is very heavy. Lots of works [3, 9, 21, 22, 31, 37, 46, 47, 52] resort to either 2D convolutional upsamplers [3, 9, 21, 22, 47], multi-plane image rendering [52], sparse-voxel [31] inference, patch-based training [37] for acceleration. Besides, some works [23, 35] focus on the improvement of geometry quality. Although these methods are able to synthesize high-quality 3D-aware images, they are restricted to strong pose prior, i.e., manually tuned pose distribution, or well-annotated camera + +poses [3]. Our work instead naturally enables 3D-aware image synthesis without any pose prior via a pose-free generator, which gives a fruitful avenue for future work. + +Camera Learning from 2D Images. Learning neural radiance fields (NeRF) [17] requires accurate pose annotations. To overcome this, some works [14, 42] try to optimize the annotated camera parameters or directly estimate camera poses with a small network, which is conceptually comparable to ours. On the other hand, our work differs from theirs in that our method focuses on learning pose distribution of a real dataset rather than exact camera poses. CAMPARI [20] and 3DGP [36] investigate a similar problem, aiming to estimate the pose distribution of an actual dataset. However, both of them need a manually designed prior, i.e., uniform or Gaussian, and fail to learn appropriate 3D geometry when the prior is very distant from the native distribution. In contrast, our work abandons all the manually designed prior and allows the generator to learn pose distribution automatically via adversarial training. + +# 3. Method + +Our proposed method for 3D-aware image synthesis can be freed from the requirement of pose priors. To achieve this goal, we propose some new designs in both the generator and the discriminator in conventional 3D-aware GANs [3, 4, 9, 30]. Specifically, the pose-free generator is equipped with a pose learner that infers the camera pose from the latent code. The pose-aware discriminator extracts a pose from the given image and uses it as the conditional label when performing real/fake classification. The framework is shown in Fig. 2. Before going into details, we first briefly introduce the generative neural radiance field, which plays a crucial role in 3D-aware image synthesis. + +# 3.1. Preliminary + +A neural radiance field (NeRF) [17], $\mathrm{F}(\mathbf{x},\mathbf{d})\rightarrow (\mathbf{c},\sigma)$ , provides color $\mathbf{c}\in \mathbb{R}^3$ and volume density $\sigma \in \mathbb{R}$ from a coordinate $\mathbf{x}\in \mathbb{R}^3$ and a viewing direction $\mathbf{d}\in \mathbb{S}^2$ , typically parameterized with multi-layer perceptron (MLP) networks. Then, the pixel values are accumulated from the colors and densities of the points on the sampled rays. However, NeRF is highly dependent on multi-view supervision, leading to the inability to learn from a single-view image collection. To enable random sampling from single-view captures, recent attempts propose to condition NeRF with a latent code $\mathbf{z}$ , resulting in their generative forms [4, 30], $\mathrm{G}(\mathbf{x},\mathbf{d},\mathbf{z})\to (\mathbf{c},\sigma)$ , to achieve diverse 3D-aware generation. + +# 3.2. Pose-free Generator + +Different from NeRF, the camera pose $\xi$ deriving the spatial point $\mathbf{x}$ and view direction $\mathbf{d}$ in conventional 3D-aware + +![](images/b910b6c6a9f2c39fcfe0b6aa42c1c2f6a55a0654d990bbf7a2df8f7a5b4ffbe9.jpg) +Figure 2. Framework of PoF3D, which consists of a pose-free generator and a pose-aware discriminator. The pose-free generator maps a latent code to a neural radiance field as well as a camera pose, followed by a volume renderer (VR) to output the final image. The pose-aware discriminator first predicts a camera pose from the given image and then use it as the pseudo label for conditional real/fake discrimination, indicated by the orange arrow. + +![](images/43b469944475705a0f06f05d956fe188dd710ce9b98e9777e2dfd34be178a887.jpg) + +generators is randomly sampled from a prior distribution $p_{\xi}$ rather than well annotated by MVS [32] and SfM [29]. Such a prior distribution requires the knowledge of the pose distribution, and it should be tailored for different datasets, which introduces non-trivial hyperparameter tuning for model training. This generation process can be formulated as + +$$ +\mathrm {G} (\mathbf {z}, \xi) = \mathbf {I} _ {f} \sim p _ {\theta} \left(\mathbf {I} _ {f} | \mathbf {z}, \xi\right), \tag {1} +$$ + +where the generator $\mathrm{G}$ synthesizes the image $\mathbf{I}_f$ by modeling the conditional probability given the latent code and the camera pose. Since the camera pose is independent of the latent code, we can rewrite Eq. (1) in the following form: + +$$ +p _ {\theta} \left(\mathbf {I} _ {f} | \mathbf {z}, \xi\right) = \frac {p _ {\theta} \left(\mathbf {I} _ {f} , \mathbf {z} , \xi\right)}{p (\mathbf {z} , \xi)} = \frac {p _ {\theta} \left(\mathbf {I} _ {f} , \xi | \mathbf {z}\right)}{p (\xi)} = \frac {p _ {\theta} \left(\mathbf {I} _ {f} , \xi | \mathbf {z}\right)}{p _ {\xi}}. \tag {2} +$$ + +Obviously, if the pose prior does not align well with the real distribution, it is hard to correctly estimate the image distribution $p_{\theta}(\mathbf{I}_f|\mathbf{z},\xi)$ . As noticed by [9, 47], it always makes the training diverge if the prior does not align well with the real distribution. To free the generator from sampling poses from a prior distribution, we follow the formulation of conventional 2D GANs that synthesizes images from the latent code only: + +$$ +\mathrm {G} (\mathbf {z}, \Psi (\mathbf {z})) = \mathbf {I} _ {f} \sim p _ {\theta} \left(\mathbf {I} _ {f} | \mathbf {z}, \Psi (\mathbf {z})\right), \tag {3} +$$ + +where the camera pose $\xi$ is parameterized with a nonlinear function $\Psi(\cdot)$ that takes $\mathbf{z}$ as input. Concretely, we implement $\Psi(\cdot)$ by introducing an additional pose branch on the top of the generator. The estimated camera pose is further fed into a generative radiance field to render a 2D image. Compared with previous solutions, our generator aims at approximating the conditional probability only from the latent observation, which is prone to simulating the native data distribution without taking the pose prior into account. + +# 3.3. Pose-aware Discriminator + +As mentioned above, we remove the pose prior of a 3D-aware generator by parameterizing camera pose $\xi$ + +from a latent code $\mathbf{z}$ . The 3D representation leveraged in the generator is helpful in disentangling the camera factor. However, the conventional discriminator remains to differentiate real and fake images from 2D space, leading to inadequate supervision to factorize camera poses from latent codes. It easily makes the generator synthesize flat shapes and learn invalid camera distribution. Therefore, we propose to make the discriminator pose-aware. + +Learning Pose-aware Discriminator. To let the discriminator become aware of poses, we assign a pose estimation task on fake images beyond bi-class domain classification, which is to derive the pose information from the given images. We introduce a pose branch $\Phi(\cdot)$ on top of the discriminator and optimize it with the following objective: + +$$ +\hat {\xi} = \Phi (\mathbf {I} _ {f}), \tag {4} +$$ + +$$ +\mathcal {L} _ {\text {p o s e}} = l _ {2} (\hat {\xi}, \xi), \tag {5} +$$ + +where $l_{2}(\cdot)$ denotes the function measuring $l_{2}$ distance between poses. $\xi$ is the pose that is inferred from the same latent code as $\mathbf{I}_f$ by the generator. + +Performing Pose-aware Discrimination. With the help of the pose branch, our discriminator can be adopted to infer camera poses for the given images. Even though the pose branch training is done on fake images, it is also generalizable on real images $\mathbf{I}_r$ from the dataset. In such cases, we can leverage the pose-aware discriminator to perform discrimination on real or fake images as well as differentiate whether the image is attached with an accurate pose or not. Concretely, we first ask the discriminator to extract a pose from the input image, and then the pose is treated as a pseudo label to perform conditional bi-class classification. Here, we take the real image part of the discriminator loss as an example: + +$$ +\mathcal {L} _ {\mathrm {D}} ^ {\mathbf {I} _ {r}} = - \mathbb {E} \left[ \log \left(\mathrm {D} \left(\mathbf {I} _ {r} \mid \Phi (\mathbf {I} _ {r})\right)\right) \right]. \tag {6} +$$ + +In this way, we facilitate the discriminator with awareness of pose cues, leading to better pose alignment across various synthesized samples. As a result, this alignment also + +implicitly prevents the generator from degenerate solutions where a flat shape is usually generated with huge artifacts. It is worth noting that the discriminator learns poses from the generator and, in turn, uses the conditional discrimination score to update the pose branch in the generator. Therefore, the poses are learned in a loop-back manner without any annotations. + +# 3.4. Training Objectives + +Adversarial Loss. We use the standard adversarial loss for training following [8], + +$$ +\begin{array}{l} \mathcal {L} _ {\mathrm {D}} = - \mathbb {E} \left[ \log \left(1 - \mathrm {D} \left(\mathbf {I} _ {f} | \Phi (\mathbf {I} _ {f})\right)\right) \right] \\ - \mathbb {E} \left[ \log \left(\mathrm {D} \left(\mathbf {I} _ {r} \mid \Phi (\mathbf {I} _ {r})\right)\right) \right] + \lambda \mathbb {E} \left[ \left| \left| \nabla_ {\mathbf {I} _ {r}} \mathrm {D} (\mathbf {I} _ {r}) \right| \right| _ {2} ^ {2} \right], \tag {7} \\ \end{array} +$$ + +$$ +\mathcal {L} _ {\mathrm {G}} = - \mathbb {E} [ \log (\mathrm {D} (\mathbf {I} _ {f} | \Phi (\mathbf {I} _ {f}))) ], \tag {8} +$$ + +where $\mathbf{I}_r$ and $\mathbf{I}_f$ are real data and generated data, respectively. The third term in Eq. (7) is the gradient penalty, and $\lambda$ denotes the weight for this term. + +Symmetry Loss. Planar underlying shapes are easily generated when single-view images are synthesized for training. To avoid the trivial solution, we ask the network to synthesize the second image under another view, which we choose the symmetrical camera view $\xi^{\prime}$ regarding the $yz$ -plane, + +$$ +\mathbf {I} _ {f} ^ {\prime} = \mathrm {G} (\mathbf {z}, \xi^ {\prime}). \tag {9} +$$ + +The novel view image will be used to calculate the adversarial loss as in Eq. (7) and Eq. (8), and get $\mathcal{L}_{\mathrm{D}'}$ and $\mathcal{L}_{\mathrm{G}'}$ . + +Pose Loss. As stated in Sec. 3.3, we also attach an auxiliary pose branch $\Phi(\cdot)$ in the discriminator to perform pose estimation on the given images. We use Eq. (5) for pose branch training. + +Full Objectives. In summary, the pose-free generator and the pose-aware discriminator are jointly optimized with + +$$ +\mathcal {L} = \mathcal {L} _ {\mathrm {G}} + \mathcal {L} _ {\mathrm {G} ^ {\prime}} + \mathcal {L} _ {\mathrm {D}} + \mathcal {L} _ {\mathrm {D} ^ {\prime}} + \gamma \mathcal {L} _ {\text {p o s e}}, \tag {10} +$$ + +where $\gamma$ is the weight of pose loss. + +# 3.5. Implementation Details + +We build our PoF3D on the architecture of EG3D [3]. For the pose-aware generator, we do not use pose-conditioned generation. Instead, we instantiate the pose branch with two linear layers and a leaky ReLU activation in between. This branch takes in latent codes from $w$ space and outputs camera poses. The camera pose consists of an azimuth angle and an elevation angle, which indicates the camera position for rendering. The triplane resolution is $256 \times 256$ , and the rendering in the neural radiance field is conducted on $64 \times 64$ resolution. Both the feature map and the image are rendered. A super-resolution module then + +transforms the feature map into a high-resolution image. The pose-aware discriminator is inherited from the dual discriminator in EG3D [3]. We add the pose branch on the features before the last two fully-connected layers that output the realness score. The pose branch is composed of two fully-connected layers with a leaky ReLU as the activation function in the middle. The learning rate of the generator is $2.5e-3$ while that of its pose branch is set to $2.5e-5$ . The discriminator's learning rate is $2e-3$ . More details are available in the Supplementary Material. + +# 4. Experiments + +# 4.1. Experimental Settings + +Datasets. We evaluate PoF3D on three datasets, including FFHQ [12], Cats [51], and Shapenet Cars [5]. FFHQ is a real-world dataset that contains unique 70K high-quality images of human faces. We follow [3] to align and crop the data. Cats include 10K real-world cat images of various resolutions. The data is preprocessed following [6]. Shapenet Cars [5] is a synthetic dataset that contains different car models. We use the dataset rendered from [3] that has around 530K images. Unlike the face-forward datasets, the camera poses of it span the entire $360^{\circ}$ azimuth and $180^{\circ}$ elevation distributions. In the experiments, we use the resolution of $256 \times 256$ for FFHQ and Cats, and $128 \times 128$ for Shapenet Cars. + +Baselines. We compare our approach against two methods: CAMPARI [20], the state-of-the-art pose learning method in 3D-aware image synthesis, and EG3D [3], the state-of-the-art in 3D-aware image synthesis. We also build a baseline method which is a combination of them, where we incorporate the pose learning method in CAMPARI into the framework of EG3D. More details regarding the baselines can be found in Supplementary Material. + +Metrics. We use five metrics to evaluate the performance, including Fréchet Inception Distance (FID) [10], Depth Error [3], Pose Error [47], Reprojection Error (RE) [47], and Jensen-Shannon Divergence (JS). FID is measured between 50K generated images and all real images. Depth Error is used to assess the quality of geometry. We follow [3] and calculate the mean squared error (MSE) against pseudoground-truth depth estimated by [7] on 10K synthesized samples. We evaluate the pose accuracy on 10K generated samples as well. Given the synthesized images, we leverage the head pose estimator [53] and report the L1 distance between the estimated poses and the poses inferred from the generator. Note that we subtract the respective means of estimated and inferred pose distribution to compensate the canonical shift problem (see Fig. 4). Inter-view consistency is measured by the re-projection error following [47]. We render 5 views by sampling azimuth uniformly in the range of $[-23^{\circ}, 23^{\circ}]$ and warp two consecutive views to each other + +![](images/80f7389e0db78c3b0cec43d7ec73506de3a40031f38c6e42bbea6e9aeba3732f.jpg) +Figure 3. Qualitative comparison between our approach and baselines. CAMPARI [20] struggles to generate reasonable results. "CAMPARI + EG3D" suffers from mode collapse on the FFHQ and Cats datasets. EG3D [3] achieves impressive rendering and reconstruction results when camera poses of training images are given. In contrast, our approach can generate high-quality rendering and geometry without any pose priors. + +to report the MSE. The images are normalized in the range of $[-1, 1]$ for evaluation. Since the azimuth range learned by CAMPARI is much smaller, we use the learned range for sampling in the measurement of CAMPARI. To measure the quality of the learned pose distribution, we report Jensen-Shannon Divergence on $50\mathrm{K}$ synthesized samples and all real images by averaging divergence values over azimuth and elevation. + +# 4.2. Main Results + +Qualitative Comparison. Fig. 3 shows the qualitative comparison against the baselines. CAMPARI learns faulty + +and very sharp shapes that span the entire space along the ray direction (the same phenomenon as observed in Fig. 1d). Therefore, even if the object is rotated with an extremely small angle (e.g., $2.5^{\circ}$ ), the caused visual effect is equivalent to that of the normal rotation of a decent shape with a much larger angle (e.g., $23^{\circ}$ ). We visualize CAMPARI in its own valid range of the horizontal angle (around $[-2.5^{\circ}, 2.5^{\circ}]$ for FFHQ, $[-5^{\circ}, 5^{\circ}]$ for Cats, and $[-30^{\circ}, 30^{\circ}]$ for Shapenet Cars). For others, visualizations on FFHQ and Cats are conducted on the angle range $[-23^{\circ}, 23^{\circ}]$ . Poses for cars are randomly sampled from the entire $360^{\circ}$ azimuth and $180^{\circ}$ elevation distributions. EG3D leverages ground + +Table 1. Quantitative comparison on FFHQ [12], Cats [51], and Shapenet Cars [5]. Our approach significantly outperforms CAMPARI [20] and "CAMPARI + EG3D" in terms of depth error, pose error, reprojection error, and Jensen-Shannon divergence score. Note that, EG3D [3] uses pose annotations, while our model is trained without any pose priors. * means we report the FID of EG3D on Shapenet Cars using its released model, which is inconsistent with the one reported in the paper. + +
ModelFFHQ [12]Cats [51]Shapenet Cars [5]
FID50k ↓Depth↓Pose↓RE↓JS↓FID50k ↓RE↓JS↓FID50k ↓JS↓
CAMPARI [20]58.591.780.150.1090.6137.400.0500.6068.910.72
CAMPARI+EG3D3.251.130.18-0.734.83-0.744.660.83
EG3D [3]4.800.290.070.039-5.560.042-9.68*-
Ours4.990.290.100.0370.205.460.0460.243.780.51
+ +truth camera poses for training and generates high-quality images and underlying geometry simultaneously. When incorporated with the pose learning method in CAMPARI, EG3D suffers from pose collapse and converges to one pose on FFHQ and Cats. Hence, novel views are not available in such cases, and the 3D-aware image synthesis problem is degraded to 2D image synthesis. On Shapenet Cars, the generated image and its corresponding shape are visually reasonable under a specific view but become completely unnatural when deviating from that view. Our method, without any pose priors, can generate high-fidelity images and shapes on par with EG3D. + +Quantitative Comparison. We report the quantitative evaluation of baselines and our method in Tab. 1. CAMPARI fails to capture the underlying pose distribution and gets high Jensen-Shannon Divergence scores and pose errors. Consequently, the quality of images and shapes is unsatisfying as well, reflected by high FID scores and depth errors. CAMPARI+EG3D generates planar shapes and collapses to one pose or a small range of poses, which simplifies 3D-aware image synthesis to 2D image synthesis, resulting in lower FID scores but higher depth error, pose error and Jensen-Shannon Divergence score. EG3D, the method that uses pose annotations, exhibits good performance in terms of image quality and geometry quality. Our method yields results on par with EG3D and learns much better underlying pose distribution than the baselines. The quality of the geometry affects the multi-view consistency of the learned neural fields. Thus, EG3D and ours, which synthesize better shapes, can get better scores of reprojection errors. Note that our pose error is higher than that of EG3D, one of the reasons is that there exists the canonical view shift. As we do not provide any information on what the canonical view will be like, the model tends to learn a canonical view that leads to the best of its performance, which could be different from the standard. More discussions are in Sec. 4.4. + +# 4.3. Ablation Study + +We conduct ablation studies on FFHQ $256 \times 256$ to analyze the effectiveness of PoF3D. Evaluation results are shown in Tab. 2. + +Table 2. Ablation studies on FFHQ dataset [12]. We analyze the influence of symmetry loss, pose-aware discriminator, and learning rate. See Sec. 4.3 for more details. + +
ModelFFHQ
FID50k ↓Depth↓Pose↓JS↓
w/o symmetry loss4.500.410.120.20
w/o pose-aware D3.431.300.190.21
w/o pose condition in D3.511.480.190.26
lr = 2.5e-4122.070.820.740.56
lr = 2.5e-610.200.700.160.38
Ours4.990.290.100.20
+ +Symmetry Loss. We render an image from the symmetrical camera view and leverage it to pose a constraint on the generated neural radiance field from another view. Without this constraint, although the network can synthesize visually pleasing images under the learned pose and capture a rough pose distribution, the underlying geometry has a tendency to flatten, resulting in higher depth error. The constraint from the symmetrical view can detect the flat shapes because the rendered image under the novel view deviates from the real distribution and shall be corrected by the model. + +Pose-aware Discriminator. To verify the capability of the pose-aware discriminator, we compare it against the simple dual discriminator that removes the conditional label and purely performs real or fake discrimination. The simple dual discriminator does not provide any additional pose information to the generator other than the common realizesscore. Thus, the generator learns the pose freely and has difficulty aligning poses of data to share the same canonical view. For example, in the human face generation, one fake pose can correspond to images under different real poses. As a result, the pose error increases, and planar shapes are more frequently generated. We also report the results where only the pose conditioning discrimination is changed to the conventional pose-free discrimination. It drastically harms the geometry quality. With our pose-aware discriminator, the discriminator predicts the pose from both the fake and real data and uses it as the condition, which forces the generator to synthesize images under the same view as the conditional label, leading to better pose + +![](images/360cf17053de041798d8b1d510de00bae4f587de244f04cbb62f9f59b5557b95.jpg) + +![](images/23d07301fe391fe35729fd60d49da6bc849dfcde9242c7a326c4339bf2b8169a.jpg) + +![](images/e1c73b40bc4303f2ec5a74be99fd61a5eace5888d91401023b065758421a4e81.jpg) + +![](images/974d4d184579b14d5ee7d732fc7bfb1a15b0fd5fe9556be22ac32cc25fd2b4ed.jpg) +Figure 4. Pose distribution learned by the pose-free generator. The proposed approach well captures the pose distribution of the dataset. Note that, there is a slight shift of elevation distribution on the FFHQ dataset. The reason is that the model can automatically learn a canonical space for best performance during training. + +![](images/d8e66bcc83eb7eef4f6f7038493fe7a17bbea0df5bffd90c19fca9f8bad8ce15.jpg) + +![](images/dc0163a303a3c6df8a9d9d406998143d58d4fcfbd7a2124de18f802d76221cc9.jpg) + +![](images/1f481f290e1ae8ee97103fffbcf938d6aed76e04f8743423e705c921ebd40ff4.jpg) + +![](images/47a6eacaff36474d61e949be2f57de6408568ff77cf7367a55ff51578bfd466b.jpg) + +![](images/14f8f12fa98788827045e56c9fcb260dce4650d65937d090c22c58cb19b58904.jpg) + +![](images/7a1dd9497e91314e08b9ce414316d249dab9fe1d0e7f172b93aed4c1d7dba1c0.jpg) +Figure 5. Pose distribution learned by the pose-aware discriminator. Results demonstrate that our discriminator can learn the pose distribution of the dataset. The issue of canonical space shift also exists from the discriminator perspective, same as Fig. 4. + +![](images/2c01d66d0ce2770488f5b9e05b9587d313a14ba19d7aa70cb4451cad079b8f99.jpg) + +![](images/d3fc83027029ca4770268766186ee8ab6bb58502e6a6d4635c96a8d13896d71b.jpg) + +alignment. + +Learning Rate of Pose Learner. Learning rate of the pose branch in the generator matters a lot. With a large learning rate (e.g., 2.5e-4 in Tab. 2), the generator always tries with new poses of large variation at the beginning and leaves the content learning behind, resulting in unstable training and higher tendency of mode collapse. As reported in Tab. 2, all the evaluation metrics experience a significant drop. On the contrary, if the learning rate is too small (e.g., 2.5e-6 in Tab. 2), the generator cannot explore the pose distribution enough and easily gets stuck in a small + +range of pose distribution, putting more focus on the content learning. Consequently, the model fails to capture and understand the pose distribution, leading to worse shapes. A proper learning rate should balance the exploration of pose distribution and the learning of the content. + +# 4.4. Pose Analysis + +In this section, we analyze the pose distributions that are learned by our pose-free generator and pose-aware discriminator. + +Poses in Pose-free Generator. To visualize the pose + +![](images/7fd9005a3de1a3a38ccf609d6e2006f0673ae1b7443c22070f4710b0405ca321.jpg) + +![](images/501ea946bb8c41b4295678666c581886e08499065cc8936e597b804c689de948.jpg) +Figure 6. Results of linear interpolation between two latent codes. The appearance, the geometry, and the pose all change smoothly, indicating the latent space is semantically meaningful. + +distribution learned in the pose-free generator, we randomly sample 50K latent codes and infer the poses from them. The pose distributions from the dataset and learned in the generator are shown in Fig. 4. Without any pose priors, our method can capture the pose range and distribution of the dataset in general. As observed in the figure for elevation distributions on the FFHQ dataset, there exists a distribution shift. The reason is that we do not release any information about the canonical view to the model, and therefore, the model can interpret the canonical view freely with different angles which might be different from the one defined in the dataset. Generally, the model will choose the one that leads to the best performance as its canonical view. + +Poses in Pose-aware Discriminator. Since our discriminator is equipped with a pose predictor, we hire it to predict the poses for all data in the dataset and draw the distributions accordingly in Fig. 5. For FFHQ and Cats datasets, the distributions are well approximated, and the canonical view shift problem also exists in the discriminator. On Shapenet Cars, the distribution of azimuth is biased to one side. We conjecture the reason is that the model has difficulty distinguishing the front and rear of the car as they look very similar. As a result, the learned distribution shifts towards a hemisphere instead of the entire sphere. + +# 4.5. Applications + +Linearity in Latent Space. To demonstrate the latent space learned by PoF3D is semantically meaningful, we randomly sample two latent codes and linearly interpolate between them. The interpolation results are shown in Fig. 6. We can see that both the appearance and the underlying geometry are changing smoothly. Besides, as we infer the pose from the latent code, poses undergo smooth changes as well. + +Real Image Inversion. One of the potential applications of PoF3D is to reconstruct the geometry from a real image and enable novel view synthesis. To achieve this goal, PTI [28], a GAN inversion method, is adopted to perform on our pose-free generator. In the previous methods [3] that demonstrate GAN inversion as an application, an off-the + +![](images/2e8cca48573ad79f4da005ce9cfd331358abd48a8b50fbd209363333881d9f87.jpg) +Figure 7. Results of GAN inversion. Thanks to the design of pose-free generator, we do not require pose estimation prior to performing inversion like previous works. Instead, we can directly invert the image to get the 3D representation and the corresponding pose. The reconstructed geometry is realistic and enables vivid novel view synthesis. + +shelf pose predictor is required to obtain the pose of the given image prior to performing GAN inversion. Ours, however, benefits from the changed formulation in which the camera pose is encoded in the latent space. Therefore, we can get not only the inverted neural radiance field but also the camera pose under which the given image is captured, when performing GAN inversion. The result is shown in Fig. 7. Our method can successfully invert the image and synthesize vivid images under novel views. + +# 5. Conclusion + +This work presents PoF3D, which learns 3D-aware image synthesis without using any pose priors. A pose-free generator is designed to infer camera poses directly from the latent space so that the requirement for pose priors in the previous works is removed. Besides, to help the generator better capture the underlying distribution, we make the discriminator pose-aware by asking it to first predict the camera pose and then use it as a condition when performing conditional real/fake discrimination. With such a design, experimental results demonstrate that our approach is able to synthesize high-quality images and high-fidelity shapes that are on par with state-of-the-art 3D synthesis methods without the need for manual pose tuning or dataset labeling. Acknowledgement. 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An inaccurate estimation may mislead the model into learning faulty geometry. This work proposes PoF3D that frees generative radiance fields from the requirements of 3D pose priors. We first equip the generator with an efficient pose learner, which is able to infer a pose from a latent code, to approximate the underlying true pose distribution automatically. We then assign the discriminator a task to learn pose distribution under the supervision of the generator and to differentiate real and synthesized images with the predicted pose as the condition. The pose-free generator and the pose-aware discriminator are jointly trained in an adversarial manner. Extensive results on a couple of datasets confirm that the performance of our approach, regarding both image quality and geometry quality, is on par with state of the art. To our best knowledge, PoF3D demonstrates the feasibility of learning high-quality 3D-aware image synthesis without using 3D pose priors for the first time. Project page can be found here." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 506, + 128, + 517 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 506, + 128, + 517 + ], + "spans": [ + { + "bbox": [ + 47, + 506, + 128, + 517 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 526, + 287, + 646 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 526, + 287, + 646 + ], + "spans": [ + { + "bbox": [ + 46, + 526, + 287, + 646 + ], + "type": "text", + "content": "3D-aware image generation has recently received growing attention due to its potential applications [3, 4, 9, 21, 30, 34, 47]. 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Such a formulation allows explicit camera control over the synthesized results, which fits better with our 3D world." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 647, + 287, + 684 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 647, + 287, + 684 + ], + "spans": [ + { + "bbox": [ + 46, + 647, + 287, + 684 + ], + "type": "text", + "content": "To enable 3D-aware image synthesis from 2D image collections, existing attempts usually rely on adequate camera pose priors [3, 4, 9, 20, 21, 30, 47] for training." + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 309, + 217, + 544, + 295 + ], + "blocks": [ + { + "bbox": [ + 309, + 217, + 544, + 295 + ], + "lines": [ + { + "bbox": [ + 309, + 217, + 544, + 295 + ], + "spans": [ + { + "bbox": [ + 309, + 217, + 544, + 295 + ], + "type": "image", + "image_path": "2f4c5820444128fbf6d99639f175902945b6b74a9671686cf1b28fd5b4f212fa.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 324, + 296, + 411, + 303 + ], + "lines": [ + { + "bbox": [ + 324, + 296, + 411, + 303 + ], + "spans": [ + { + "bbox": [ + 324, + 296, + 411, + 303 + ], + "type": "text", + "content": "(a) " + }, + { + "bbox": [ + 324, + 296, + 411, + 303 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 324, + 296, + 411, + 303 + ], + "type": "text", + "content": " -GAN: good pose distribution" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 309, + 304, + 544, + 344 + ], + "blocks": [ + { + "bbox": [ + 443, + 296, + 527, + 303 + ], + "lines": [ + { + "bbox": [ + 443, + 296, + 527, + 303 + ], + "spans": [ + { + "bbox": [ + 443, + 296, + 527, + 303 + ], + "type": "text", + "content": "(b) " + }, + { + "bbox": [ + 443, + 296, + 527, + 303 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 443, + 296, + 527, + 303 + ], + "type": "text", + "content": " -GAN: bad pose distribution" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 309, + 304, + 544, + 344 + ], + "lines": [ + { + "bbox": [ + 309, + 304, + 544, + 344 + ], + "spans": [ + { + "bbox": [ + 309, + 304, + 544, + 344 + ], + "type": "image", + "image_path": "5630cbaae3a25e5c77608e57b63c0b38566ed629ab35fde4abe33dbbf2b7b189.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 309, + 344, + 425, + 383 + ], + "blocks": [ + { + "bbox": [ + 309, + 344, + 425, + 383 + ], + "lines": [ + { + "bbox": [ + 309, + 344, + 425, + 383 + ], + "spans": [ + { + "bbox": [ + 309, + 344, + 425, + 383 + ], + "type": "image", + "image_path": "82830da9b00a30eeff4b2837c1101997d7df4bbcf28855805972d500286dcf1f.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 318, + 383, + 416, + 391 + ], + "lines": [ + { + "bbox": [ + 318, + 383, + 416, + 391 + ], + "spans": [ + { + "bbox": [ + 318, + 383, + 416, + 391 + ], + "type": "text", + "content": "(c) CAMPARI: good pose initialization" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 305, + 391, + 546, + 456 + ], + "lines": [ + { + "bbox": [ + 305, + 391, + 546, + 456 + ], + "spans": [ + { + "bbox": [ + 305, + 391, + 546, + 456 + ], + "type": "text", + "content": "Figure 1. Sensitivity to pose priors in existing 3D-aware image synthesis approaches. " + }, + { + "bbox": [ + 305, + 391, + 546, + 456 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 305, + 391, + 546, + 456 + ], + "type": "text", + "content": "-GAN [4] works well given an adequate pose distribution in (a), but fails to learn decent geometries given a slightly changed distribution in (b). CAMPARI [20] delivers reasonable results relying on a good initial pose distribution in (c), but suffers from a wrongly estimated initialization in (d)." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 426, + 344, + 544, + 383 + ], + "blocks": [ + { + "bbox": [ + 426, + 344, + 544, + 383 + ], + "lines": [ + { + "bbox": [ + 426, + 344, + 544, + 383 + ], + "spans": [ + { + "bbox": [ + 426, + 344, + 544, + 383 + ], + "type": "image", + "image_path": "31e850e25e5db3d4d0a81bc922059dfcc9f0c8e726f79baaf9e3182063c84340.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 438, + 383, + 533, + 391 + ], + "lines": [ + { + "bbox": [ + 438, + 383, + 533, + 391 + ], + "spans": [ + { + "bbox": [ + 438, + 383, + 533, + 391 + ], + "type": "text", + "content": "(d) CAMPARI: bad pose initialization" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 462, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 462, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 462, + 546, + 713 + ], + "type": "text", + "content": "The priors are either estimated by conducting multiple pre-experiments [4, 9, 47], or obtained by borrowing external pose predictors or annotations [3]. Besides using a fixed distribution for pose sampling, some studies also propose to tune the pose priors together with the learning of image generation [20], but they are still dependent on the initial pose distribution. Consequently, although previous methods can produce satisfying images and geometry, their performance is highly sensitive to the given pose prior. For example, on the Cats dataset [51], " + }, + { + "bbox": [ + 304, + 462, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 304, + 462, + 546, + 713 + ], + "type": "text", + "content": "-GAN [4] works well with a uniform pose distribution [-0.5, 0.5] (Fig. 1a), but fails to generate a decent underlying geometry when changing the distribution to [-0.3, 0.3] (Fig. 1b). Similarly, on the CelebA dataset [15], CAMPARI [20] learns 3D rotation when using Gaussian distribution " + }, + { + "bbox": [ + 304, + 462, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{N}(0,0.24)" + }, + { + "bbox": [ + 304, + 462, + 546, + 713 + ], + "type": "text", + "content": " as the initial prior (Fig. 1c), but loses the canonical space (e.g., the middle image of Fig. 1d should be under the frontal view) when changing the initialization to " + }, + { + "bbox": [ + 304, + 462, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{N}(0,0.12)" + }, + { + "bbox": [ + 304, + 462, + 546, + 713 + ], + "type": "text", + "content": " (Fig. 1d). Such a reliance on pose priors causes unexpected instability of 3D-aware image synthesis, which may burden this task with heavy experimental cost." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 693, + 157, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 693, + 157, + 703 + ], + "spans": [ + { + "bbox": [ + 58, + 693, + 157, + 703 + ], + "type": "inline_equation", + "content": "\\dagger" + }, + { + "bbox": [ + 58, + 693, + 157, + 703 + ], + "type": "text", + "content": " indicates equal contribution." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 58, + 703, + 243, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 703, + 243, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 703, + 243, + 712 + ], + "type": "text", + "content": "* This work was done during an internship at Ant Group." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "13062" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 346 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 346 + ], + "type": "text", + "content": "In this work, we present a new approach for 3D-aware image synthesis, which removes the requirements for pose priors. Typically, a latent code is bound to the 3D content alone, where the camera pose is independently sampled from a manually designed distribution. Our method, however, maps a latent code to an image, which is implicitly composed of a 3D representation (i.e., neural radiance field) and a camera pose that can render that image. In this way, the camera pose is directly inferred from the latent code and jointly learned with the content, simplifying the input requirement. To facilitate the pose-free generator better capturing the underlying pose distribution, we re-design the discriminator to make it pose-aware. Concretely, we tailor the discriminator with a pose branch which is required to predict a camera pose from a given image. Then, the estimated pose is further treated as the conditional pseudo label when performing real/fake discrimination. The pose branch in the discriminator learns from the synthesized data and its corresponding pose that is encoded in the latent code, and in turn use the discrimination score to update the pose branch in the generator. With such a loop-back optimization process, two pose branches can align the fake data with the distribution of the dataset." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 348, + 288, + 444 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 348, + 288, + 444 + ], + "spans": [ + { + "bbox": [ + 47, + 348, + 288, + 444 + ], + "type": "text", + "content": "We evaluate our pose-free method, which we call PoF3D for short, on various datasets, including FFHQ [12], Cats [51], and Shapenet Cars [5]. Both qualitative and quantitative results demonstrate that PoF3D frees 3D-aware image synthesis from hyper-parameter tuning on pose distributions and dataset labeling, and achieves on par performance with state-of-the-art in terms of image quality and geometry quality." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 454, + 134, + 466 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 454, + 134, + 466 + ], + "spans": [ + { + "bbox": [ + 47, + 454, + 134, + 466 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 474, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 474, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 474, + 289, + 715 + ], + "type": "text", + "content": "3D-aware Image Synthesis. 3D-aware image synthesis has achieved remarkable success recently [33, 43] and benefits lots of 3D-aware applications [39, 44, 49, 55] rather than the conventional 2D applications [1, 26, 27, 38, 40, 41, 54]. Different from 2D synthesis [11-13, 48], some works [18, 19, 56] propose to adopt voxels as 3D representation for image rendering but suffer from the poor image quality and consistency due to the voxel resolution restriction. Then a series of works [4, 6, 23, 30, 45] introduce neural implicit function [16, 17, 24] as the underlying 3D representation for image rendering. However, rendering high-resolution images with direct volume rendering is very heavy. Lots of works [3, 9, 21, 22, 31, 37, 46, 47, 52] resort to either 2D convolutional upsamplers [3, 9, 21, 22, 47], multi-plane image rendering [52], sparse-voxel [31] inference, patch-based training [37] for acceleration. Besides, some works [23, 35] focus on the improvement of geometry quality. Although these methods are able to synthesize high-quality 3D-aware images, they are restricted to strong pose prior, i.e., manually tuned pose distribution, or well-annotated camera" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "type": "text", + "content": "poses [3]. Our work instead naturally enables 3D-aware image synthesis without any pose prior via a pose-free generator, which gives a fruitful avenue for future work." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 108, + 546, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 108, + 546, + 300 + ], + "spans": [ + { + "bbox": [ + 304, + 108, + 546, + 300 + ], + "type": "text", + "content": "Camera Learning from 2D Images. Learning neural radiance fields (NeRF) [17] requires accurate pose annotations. To overcome this, some works [14, 42] try to optimize the annotated camera parameters or directly estimate camera poses with a small network, which is conceptually comparable to ours. On the other hand, our work differs from theirs in that our method focuses on learning pose distribution of a real dataset rather than exact camera poses. CAMPARI [20] and 3DGP [36] investigate a similar problem, aiming to estimate the pose distribution of an actual dataset. However, both of them need a manually designed prior, i.e., uniform or Gaussian, and fail to learn appropriate 3D geometry when the prior is very distant from the native distribution. In contrast, our work abandons all the manually designed prior and allows the generator to learn pose distribution automatically via adversarial training." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 309, + 361, + 321 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 309, + 361, + 321 + ], + "spans": [ + { + "bbox": [ + 306, + 309, + 361, + 321 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 329, + 545, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 329, + 545, + 485 + ], + "spans": [ + { + "bbox": [ + 304, + 329, + 545, + 485 + ], + "type": "text", + "content": "Our proposed method for 3D-aware image synthesis can be freed from the requirement of pose priors. To achieve this goal, we propose some new designs in both the generator and the discriminator in conventional 3D-aware GANs [3, 4, 9, 30]. Specifically, the pose-free generator is equipped with a pose learner that infers the camera pose from the latent code. The pose-aware discriminator extracts a pose from the given image and uses it as the conditional label when performing real/fake classification. The framework is shown in Fig. 2. Before going into details, we first briefly introduce the generative neural radiance field, which plays a crucial role in 3D-aware image synthesis." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 491, + 385, + 504 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 491, + 385, + 504 + ], + "spans": [ + { + "bbox": [ + 306, + 491, + 385, + 504 + ], + "type": "text", + "content": "3.1. Preliminary" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 509, + 545, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 509, + 545, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 509, + 545, + 665 + ], + "type": "text", + "content": "A neural radiance field (NeRF) [17], " + }, + { + "bbox": [ + 304, + 509, + 545, + 665 + ], + "type": "inline_equation", + "content": "\\mathrm{F}(\\mathbf{x},\\mathbf{d})\\rightarrow (\\mathbf{c},\\sigma)" + }, + { + "bbox": [ + 304, + 509, + 545, + 665 + ], + "type": "text", + "content": ", provides color " + }, + { + "bbox": [ + 304, + 509, + 545, + 665 + ], + "type": "inline_equation", + "content": "\\mathbf{c}\\in \\mathbb{R}^3" + }, + { + "bbox": [ + 304, + 509, + 545, + 665 + ], + "type": "text", + "content": " and volume density " + }, + { + "bbox": [ + 304, + 509, + 545, + 665 + ], + "type": "inline_equation", + "content": "\\sigma \\in \\mathbb{R}" + }, + { + "bbox": [ + 304, + 509, + 545, + 665 + ], + "type": "text", + "content": " from a coordinate " + }, + { + "bbox": [ + 304, + 509, + 545, + 665 + ], + "type": "inline_equation", + "content": "\\mathbf{x}\\in \\mathbb{R}^3" + }, + { + "bbox": [ + 304, + 509, + 545, + 665 + ], + "type": "text", + "content": " and a viewing direction " + }, + { + "bbox": [ + 304, + 509, + 545, + 665 + ], + "type": "inline_equation", + "content": "\\mathbf{d}\\in \\mathbb{S}^2" + }, + { + "bbox": [ + 304, + 509, + 545, + 665 + ], + "type": "text", + "content": ", typically parameterized with multi-layer perceptron (MLP) networks. Then, the pixel values are accumulated from the colors and densities of the points on the sampled rays. However, NeRF is highly dependent on multi-view supervision, leading to the inability to learn from a single-view image collection. To enable random sampling from single-view captures, recent attempts propose to condition NeRF with a latent code " + }, + { + "bbox": [ + 304, + 509, + 545, + 665 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 304, + 509, + 545, + 665 + ], + "type": "text", + "content": ", resulting in their generative forms [4, 30], " + }, + { + "bbox": [ + 304, + 509, + 545, + 665 + ], + "type": "inline_equation", + "content": "\\mathrm{G}(\\mathbf{x},\\mathbf{d},\\mathbf{z})\\to (\\mathbf{c},\\sigma)" + }, + { + "bbox": [ + 304, + 509, + 545, + 665 + ], + "type": "text", + "content": ", to achieve diverse 3D-aware generation." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 671, + 423, + 682 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 671, + 423, + 682 + ], + "spans": [ + { + "bbox": [ + 306, + 671, + 423, + 682 + ], + "type": "text", + "content": "3.2. Pose-free Generator" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": "Different from NeRF, the camera pose " + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\xi" + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": " deriving the spatial point " + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": " and view direction " + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{d}" + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": " in conventional 3D-aware" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13063" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 70, + 83, + 289, + 169 + ], + "blocks": [ + { + "bbox": [ + 70, + 83, + 289, + 169 + ], + "lines": [ + { + "bbox": [ + 70, + 83, + 289, + 169 + ], + "spans": [ + { + "bbox": [ + 70, + 83, + 289, + 169 + ], + "type": "image", + "image_path": "b910b6c6a9f2c39fcfe0b6aa42c1c2f6a55a0654d990bbf7a2df8f7a5b4ffbe9.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 175, + 547, + 218 + ], + "lines": [ + { + "bbox": [ + 45, + 175, + 547, + 218 + ], + "spans": [ + { + "bbox": [ + 45, + 175, + 547, + 218 + ], + "type": "text", + "content": "Figure 2. Framework of PoF3D, which consists of a pose-free generator and a pose-aware discriminator. The pose-free generator maps a latent code to a neural radiance field as well as a camera pose, followed by a volume renderer (VR) to output the final image. The pose-aware discriminator first predicts a camera pose from the given image and then use it as the pseudo label for conditional real/fake discrimination, indicated by the orange arrow." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 326, + 80, + 509, + 170 + ], + "blocks": [ + { + "bbox": [ + 326, + 80, + 509, + 170 + ], + "lines": [ + { + "bbox": [ + 326, + 80, + 509, + 170 + ], + "spans": [ + { + "bbox": [ + 326, + 80, + 509, + 170 + ], + "type": "image", + "image_path": "43b469944475705a0f06f05d956fe188dd710ce9b98e9777e2dfd34be178a887.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 230, + 287, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 230, + 287, + 312 + ], + "spans": [ + { + "bbox": [ + 46, + 230, + 287, + 312 + ], + "type": "text", + "content": "generators is randomly sampled from a prior distribution " + }, + { + "bbox": [ + 46, + 230, + 287, + 312 + ], + "type": "inline_equation", + "content": "p_{\\xi}" + }, + { + "bbox": [ + 46, + 230, + 287, + 312 + ], + "type": "text", + "content": " rather than well annotated by MVS [32] and SfM [29]. Such a prior distribution requires the knowledge of the pose distribution, and it should be tailored for different datasets, which introduces non-trivial hyperparameter tuning for model training. This generation process can be formulated as" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 109, + 318, + 287, + 332 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 109, + 318, + 287, + 332 + ], + "spans": [ + { + "bbox": [ + 109, + 318, + 287, + 332 + ], + "type": "interline_equation", + "content": "\\mathrm {G} (\\mathbf {z}, \\xi) = \\mathbf {I} _ {f} \\sim p _ {\\theta} \\left(\\mathbf {I} _ {f} | \\mathbf {z}, \\xi\\right), \\tag {1}", + "image_path": "18d1dc03beef03da76d80440f85d2180a8b947e726ba57d4fad05dd562732e9f.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 336, + 287, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 336, + 287, + 384 + ], + "spans": [ + { + "bbox": [ + 46, + 336, + 287, + 384 + ], + "type": "text", + "content": "where the generator " + }, + { + "bbox": [ + 46, + 336, + 287, + 384 + ], + "type": "inline_equation", + "content": "\\mathrm{G}" + }, + { + "bbox": [ + 46, + 336, + 287, + 384 + ], + "type": "text", + "content": " synthesizes the image " + }, + { + "bbox": [ + 46, + 336, + 287, + 384 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_f" + }, + { + "bbox": [ + 46, + 336, + 287, + 384 + ], + "type": "text", + "content": " by modeling the conditional probability given the latent code and the camera pose. Since the camera pose is independent of the latent code, we can rewrite Eq. (1) in the following form:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 51, + 396, + 287, + 435 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 396, + 287, + 435 + ], + "spans": [ + { + "bbox": [ + 51, + 396, + 287, + 435 + ], + "type": "interline_equation", + "content": "p _ {\\theta} \\left(\\mathbf {I} _ {f} | \\mathbf {z}, \\xi\\right) = \\frac {p _ {\\theta} \\left(\\mathbf {I} _ {f} , \\mathbf {z} , \\xi\\right)}{p (\\mathbf {z} , \\xi)} = \\frac {p _ {\\theta} \\left(\\mathbf {I} _ {f} , \\xi | \\mathbf {z}\\right)}{p (\\xi)} = \\frac {p _ {\\theta} \\left(\\mathbf {I} _ {f} , \\xi | \\mathbf {z}\\right)}{p _ {\\xi}}. \\tag {2}", + "image_path": "c34ea542bff783bb27e627a515a129e7f048d0e4ffc2fd84c491b847a446097a.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 440, + 287, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 440, + 287, + 536 + ], + "spans": [ + { + "bbox": [ + 46, + 440, + 287, + 536 + ], + "type": "text", + "content": "Obviously, if the pose prior does not align well with the real distribution, it is hard to correctly estimate the image distribution " + }, + { + "bbox": [ + 46, + 440, + 287, + 536 + ], + "type": "inline_equation", + "content": "p_{\\theta}(\\mathbf{I}_f|\\mathbf{z},\\xi)" + }, + { + "bbox": [ + 46, + 440, + 287, + 536 + ], + "type": "text", + "content": ". As noticed by [9, 47], it always makes the training diverge if the prior does not align well with the real distribution. To free the generator from sampling poses from a prior distribution, we follow the formulation of conventional 2D GANs that synthesizes images from the latent code only:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 93, + 540, + 287, + 554 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 93, + 540, + 287, + 554 + ], + "spans": [ + { + "bbox": [ + 93, + 540, + 287, + 554 + ], + "type": "interline_equation", + "content": "\\mathrm {G} (\\mathbf {z}, \\Psi (\\mathbf {z})) = \\mathbf {I} _ {f} \\sim p _ {\\theta} \\left(\\mathbf {I} _ {f} | \\mathbf {z}, \\Psi (\\mathbf {z})\\right), \\tag {3}", + "image_path": "2623b06c0dab786df877c33b4eea3673d66ad449234890bb838d6a595546f58f.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 558, + 287, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 287, + 666 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 287, + 666 + ], + "type": "text", + "content": "where the camera pose " + }, + { + "bbox": [ + 46, + 558, + 287, + 666 + ], + "type": "inline_equation", + "content": "\\xi" + }, + { + "bbox": [ + 46, + 558, + 287, + 666 + ], + "type": "text", + "content": " is parameterized with a nonlinear function " + }, + { + "bbox": [ + 46, + 558, + 287, + 666 + ], + "type": "inline_equation", + "content": "\\Psi(\\cdot)" + }, + { + "bbox": [ + 46, + 558, + 287, + 666 + ], + "type": "text", + "content": " that takes " + }, + { + "bbox": [ + 46, + 558, + 287, + 666 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 46, + 558, + 287, + 666 + ], + "type": "text", + "content": " as input. Concretely, we implement " + }, + { + "bbox": [ + 46, + 558, + 287, + 666 + ], + "type": "inline_equation", + "content": "\\Psi(\\cdot)" + }, + { + "bbox": [ + 46, + 558, + 287, + 666 + ], + "type": "text", + "content": " by introducing an additional pose branch on the top of the generator. The estimated camera pose is further fed into a generative radiance field to render a 2D image. Compared with previous solutions, our generator aims at approximating the conditional probability only from the latent observation, which is prone to simulating the native data distribution without taking the pose prior into account." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 671, + 192, + 683 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 671, + 192, + 683 + ], + "spans": [ + { + "bbox": [ + 47, + 671, + 192, + 683 + ], + "type": "text", + "content": "3.3. Pose-aware Discriminator" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "content": "As mentioned above, we remove the pose prior of a 3D-aware generator by parameterizing camera pose " + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\xi" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 230, + 545, + 325 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 230, + 545, + 325 + ], + "spans": [ + { + "bbox": [ + 304, + 230, + 545, + 325 + ], + "type": "text", + "content": "from a latent code " + }, + { + "bbox": [ + 304, + 230, + 545, + 325 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 304, + 230, + 545, + 325 + ], + "type": "text", + "content": ". The 3D representation leveraged in the generator is helpful in disentangling the camera factor. However, the conventional discriminator remains to differentiate real and fake images from 2D space, leading to inadequate supervision to factorize camera poses from latent codes. It easily makes the generator synthesize flat shapes and learn invalid camera distribution. Therefore, we propose to make the discriminator pose-aware." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 326, + 545, + 397 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 326, + 545, + 397 + ], + "spans": [ + { + "bbox": [ + 304, + 326, + 545, + 397 + ], + "type": "text", + "content": "Learning Pose-aware Discriminator. To let the discriminator become aware of poses, we assign a pose estimation task on fake images beyond bi-class domain classification, which is to derive the pose information from the given images. We introduce a pose branch " + }, + { + "bbox": [ + 304, + 326, + 545, + 397 + ], + "type": "inline_equation", + "content": "\\Phi(\\cdot)" + }, + { + "bbox": [ + 304, + 326, + 545, + 397 + ], + "type": "text", + "content": " on top of the discriminator and optimize it with the following objective:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 408, + 417, + 545, + 431 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 408, + 417, + 545, + 431 + ], + "spans": [ + { + "bbox": [ + 408, + 417, + 545, + 431 + ], + "type": "interline_equation", + "content": "\\hat {\\xi} = \\Phi (\\mathbf {I} _ {f}), \\tag {4}", + "image_path": "7ade47842d9cef5d60602e5da2e40395a2cfcb2129778a6f8770844c6ab10f5b.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 391, + 434, + 545, + 449 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 391, + 434, + 545, + 449 + ], + "spans": [ + { + "bbox": [ + 391, + 434, + 545, + 449 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {p o s e}} = l _ {2} (\\hat {\\xi}, \\xi), \\tag {5}", + "image_path": "8116d43a14490216732df10a4187fd0ce6798a79fc4626da42b79bda1116c936.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 456, + 545, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 456, + 545, + 491 + ], + "spans": [ + { + "bbox": [ + 304, + 456, + 545, + 491 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 456, + 545, + 491 + ], + "type": "inline_equation", + "content": "l_{2}(\\cdot)" + }, + { + "bbox": [ + 304, + 456, + 545, + 491 + ], + "type": "text", + "content": " denotes the function measuring " + }, + { + "bbox": [ + 304, + 456, + 545, + 491 + ], + "type": "inline_equation", + "content": "l_{2}" + }, + { + "bbox": [ + 304, + 456, + 545, + 491 + ], + "type": "text", + "content": " distance between poses. " + }, + { + "bbox": [ + 304, + 456, + 545, + 491 + ], + "type": "inline_equation", + "content": "\\xi" + }, + { + "bbox": [ + 304, + 456, + 545, + 491 + ], + "type": "text", + "content": " is the pose that is inferred from the same latent code as " + }, + { + "bbox": [ + 304, + 456, + 545, + 491 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_f" + }, + { + "bbox": [ + 304, + 456, + 545, + 491 + ], + "type": "text", + "content": " by the generator." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 492, + 545, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 492, + 545, + 647 + ], + "spans": [ + { + "bbox": [ + 304, + 492, + 545, + 647 + ], + "type": "text", + "content": "Performing Pose-aware Discrimination. With the help of the pose branch, our discriminator can be adopted to infer camera poses for the given images. Even though the pose branch training is done on fake images, it is also generalizable on real images " + }, + { + "bbox": [ + 304, + 492, + 545, + 647 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_r" + }, + { + "bbox": [ + 304, + 492, + 545, + 647 + ], + "type": "text", + "content": " from the dataset. In such cases, we can leverage the pose-aware discriminator to perform discrimination on real or fake images as well as differentiate whether the image is attached with an accurate pose or not. Concretely, we first ask the discriminator to extract a pose from the input image, and then the pose is treated as a pseudo label to perform conditional bi-class classification. Here, we take the real image part of the discriminator loss as an example:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 364, + 654, + 545, + 670 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 364, + 654, + 545, + 670 + ], + "spans": [ + { + "bbox": [ + 364, + 654, + 545, + 670 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {D}} ^ {\\mathbf {I} _ {r}} = - \\mathbb {E} \\left[ \\log \\left(\\mathrm {D} \\left(\\mathbf {I} _ {r} \\mid \\Phi (\\mathbf {I} _ {r})\\right)\\right) \\right]. \\tag {6}", + "image_path": "a66cb63abc740cc7c53c696413efcaa2c8db50487f19696d145c3cd26d145298.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": "In this way, we facilitate the discriminator with awareness of pose cues, leading to better pose alignment across various synthesized samples. As a result, this alignment also" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13064" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "type": "text", + "content": "implicitly prevents the generator from degenerate solutions where a flat shape is usually generated with huge artifacts. It is worth noting that the discriminator learns poses from the generator and, in turn, uses the conditional discrimination score to update the pose branch in the generator. Therefore, the poses are learned in a loop-back manner without any annotations." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 163, + 163, + 176 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 163, + 163, + 176 + ], + "spans": [ + { + "bbox": [ + 47, + 163, + 163, + 176 + ], + "type": "text", + "content": "3.4. Training Objectives" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 181, + 287, + 206 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 181, + 287, + 206 + ], + "spans": [ + { + "bbox": [ + 46, + 181, + 287, + 206 + ], + "type": "text", + "content": "Adversarial Loss. We use the standard adversarial loss for training following [8]," + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 56, + 213, + 287, + 255 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 213, + 287, + 255 + ], + "spans": [ + { + "bbox": [ + 56, + 213, + 287, + 255 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {\\mathrm {D}} = - \\mathbb {E} \\left[ \\log \\left(1 - \\mathrm {D} \\left(\\mathbf {I} _ {f} | \\Phi (\\mathbf {I} _ {f})\\right)\\right) \\right] \\\\ - \\mathbb {E} \\left[ \\log \\left(\\mathrm {D} \\left(\\mathbf {I} _ {r} \\mid \\Phi (\\mathbf {I} _ {r})\\right)\\right) \\right] + \\lambda \\mathbb {E} \\left[ \\left| \\left| \\nabla_ {\\mathbf {I} _ {r}} \\mathrm {D} (\\mathbf {I} _ {r}) \\right| \\right| _ {2} ^ {2} \\right], \\tag {7} \\\\ \\end{array}", + "image_path": "2c84edd167d0dda5b49bf81686a436f8ecea77326e92f191687d4009ed2d6ac6.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 56, + 258, + 287, + 273 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 258, + 287, + 273 + ], + "spans": [ + { + "bbox": [ + 56, + 258, + 287, + 273 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {G}} = - \\mathbb {E} [ \\log (\\mathrm {D} (\\mathbf {I} _ {f} | \\Phi (\\mathbf {I} _ {f}))) ], \\tag {8}", + "image_path": "2653d0d00d8b75264ff9c40bccfa5f97f1e00c24fa823e3c6390fc42ba8ed4a2.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 280, + 287, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 280, + 287, + 316 + ], + "spans": [ + { + "bbox": [ + 46, + 280, + 287, + 316 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 280, + 287, + 316 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_r" + }, + { + "bbox": [ + 46, + 280, + 287, + 316 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 280, + 287, + 316 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_f" + }, + { + "bbox": [ + 46, + 280, + 287, + 316 + ], + "type": "text", + "content": " are real data and generated data, respectively. The third term in Eq. (7) is the gradient penalty, and " + }, + { + "bbox": [ + 46, + 280, + 287, + 316 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 46, + 280, + 287, + 316 + ], + "type": "text", + "content": " denotes the weight for this term." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 316, + 287, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 316, + 287, + 388 + ], + "spans": [ + { + "bbox": [ + 46, + 316, + 287, + 388 + ], + "type": "text", + "content": "Symmetry Loss. Planar underlying shapes are easily generated when single-view images are synthesized for training. To avoid the trivial solution, we ask the network to synthesize the second image under another view, which we choose the symmetrical camera view " + }, + { + "bbox": [ + 46, + 316, + 287, + 388 + ], + "type": "inline_equation", + "content": "\\xi^{\\prime}" + }, + { + "bbox": [ + 46, + 316, + 287, + 388 + ], + "type": "text", + "content": " regarding the " + }, + { + "bbox": [ + 46, + 316, + 287, + 388 + ], + "type": "inline_equation", + "content": "yz" + }, + { + "bbox": [ + 46, + 316, + 287, + 388 + ], + "type": "text", + "content": "-plane," + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 135, + 396, + 287, + 411 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 135, + 396, + 287, + 411 + ], + "spans": [ + { + "bbox": [ + 135, + 396, + 287, + 411 + ], + "type": "interline_equation", + "content": "\\mathbf {I} _ {f} ^ {\\prime} = \\mathrm {G} (\\mathbf {z}, \\xi^ {\\prime}). \\tag {9}", + "image_path": "df7823c94e0732aca6d8d0a942e13f244921821ee29b58864d6500621a8d8b74.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 418, + 287, + 442 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 418, + 287, + 442 + ], + "spans": [ + { + "bbox": [ + 46, + 418, + 287, + 442 + ], + "type": "text", + "content": "The novel view image will be used to calculate the adversarial loss as in Eq. (7) and Eq. (8), and get " + }, + { + "bbox": [ + 46, + 418, + 287, + 442 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{D}'}" + }, + { + "bbox": [ + 46, + 418, + 287, + 442 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 418, + 287, + 442 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{G}'}" + }, + { + "bbox": [ + 46, + 418, + 287, + 442 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 442, + 287, + 490 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 442, + 287, + 490 + ], + "spans": [ + { + "bbox": [ + 46, + 442, + 287, + 490 + ], + "type": "text", + "content": "Pose Loss. As stated in Sec. 3.3, we also attach an auxiliary pose branch " + }, + { + "bbox": [ + 46, + 442, + 287, + 490 + ], + "type": "inline_equation", + "content": "\\Phi(\\cdot)" + }, + { + "bbox": [ + 46, + 442, + 287, + 490 + ], + "type": "text", + "content": " in the discriminator to perform pose estimation on the given images. We use Eq. (5) for pose branch training." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 491, + 287, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 491, + 287, + 514 + ], + "spans": [ + { + "bbox": [ + 46, + 491, + 287, + 514 + ], + "type": "text", + "content": "Full Objectives. In summary, the pose-free generator and the pose-aware discriminator are jointly optimized with" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 86, + 523, + 287, + 536 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 523, + 287, + 536 + ], + "spans": [ + { + "bbox": [ + 86, + 523, + 287, + 536 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\mathcal {L} _ {\\mathrm {G}} + \\mathcal {L} _ {\\mathrm {G} ^ {\\prime}} + \\mathcal {L} _ {\\mathrm {D}} + \\mathcal {L} _ {\\mathrm {D} ^ {\\prime}} + \\gamma \\mathcal {L} _ {\\text {p o s e}}, \\tag {10}", + "image_path": "b0cbb4d8127b3559bb3ff85f361537e5a200eee518f63c48216b0c1a5cc15056.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 544, + 188, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 544, + 188, + 556 + ], + "spans": [ + { + "bbox": [ + 47, + 544, + 188, + 556 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 544, + 188, + 556 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 47, + 544, + 188, + 556 + ], + "type": "text", + "content": " is the weight of pose loss." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 563, + 180, + 576 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 563, + 180, + 576 + ], + "spans": [ + { + "bbox": [ + 47, + 563, + 180, + 576 + ], + "type": "text", + "content": "3.5. Implementation Details" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "text", + "content": "We build our PoF3D on the architecture of EG3D [3]. For the pose-aware generator, we do not use pose-conditioned generation. Instead, we instantiate the pose branch with two linear layers and a leaky ReLU activation in between. This branch takes in latent codes from " + }, + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "text", + "content": " space and outputs camera poses. The camera pose consists of an azimuth angle and an elevation angle, which indicates the camera position for rendering. The triplane resolution is " + }, + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "text", + "content": ", and the rendering in the neural radiance field is conducted on " + }, + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "inline_equation", + "content": "64 \\times 64" + }, + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "text", + "content": " resolution. Both the feature map and the image are rendered. A super-resolution module then" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 72, + 545, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 192 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 192 + ], + "type": "text", + "content": "transforms the feature map into a high-resolution image. The pose-aware discriminator is inherited from the dual discriminator in EG3D [3]. We add the pose branch on the features before the last two fully-connected layers that output the realness score. The pose branch is composed of two fully-connected layers with a leaky ReLU as the activation function in the middle. The learning rate of the generator is " + }, + { + "bbox": [ + 304, + 72, + 545, + 192 + ], + "type": "inline_equation", + "content": "2.5e-3" + }, + { + "bbox": [ + 304, + 72, + 545, + 192 + ], + "type": "text", + "content": " while that of its pose branch is set to " + }, + { + "bbox": [ + 304, + 72, + 545, + 192 + ], + "type": "inline_equation", + "content": "2.5e-5" + }, + { + "bbox": [ + 304, + 72, + 545, + 192 + ], + "type": "text", + "content": ". The discriminator's learning rate is " + }, + { + "bbox": [ + 304, + 72, + 545, + 192 + ], + "type": "inline_equation", + "content": "2e-3" + }, + { + "bbox": [ + 304, + 72, + 545, + 192 + ], + "type": "text", + "content": ". More details are available in the Supplementary Material." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 205, + 388, + 219 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 205, + 388, + 219 + ], + "spans": [ + { + "bbox": [ + 305, + 205, + 388, + 219 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 226, + 432, + 239 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 226, + 432, + 239 + ], + "spans": [ + { + "bbox": [ + 305, + 226, + 432, + 239 + ], + "type": "text", + "content": "4.1. Experimental Settings" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 245, + 545, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 245, + 545, + 399 + ], + "spans": [ + { + "bbox": [ + 304, + 245, + 545, + 399 + ], + "type": "text", + "content": "Datasets. We evaluate PoF3D on three datasets, including FFHQ [12], Cats [51], and Shapenet Cars [5]. FFHQ is a real-world dataset that contains unique 70K high-quality images of human faces. We follow [3] to align and crop the data. Cats include 10K real-world cat images of various resolutions. The data is preprocessed following [6]. Shapenet Cars [5] is a synthetic dataset that contains different car models. We use the dataset rendered from [3] that has around 530K images. Unlike the face-forward datasets, the camera poses of it span the entire " + }, + { + "bbox": [ + 304, + 245, + 545, + 399 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 304, + 245, + 545, + 399 + ], + "type": "text", + "content": " azimuth and " + }, + { + "bbox": [ + 304, + 245, + 545, + 399 + ], + "type": "inline_equation", + "content": "180^{\\circ}" + }, + { + "bbox": [ + 304, + 245, + 545, + 399 + ], + "type": "text", + "content": " elevation distributions. In the experiments, we use the resolution of " + }, + { + "bbox": [ + 304, + 245, + 545, + 399 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 304, + 245, + 545, + 399 + ], + "type": "text", + "content": " for FFHQ and Cats, and " + }, + { + "bbox": [ + 304, + 245, + 545, + 399 + ], + "type": "inline_equation", + "content": "128 \\times 128" + }, + { + "bbox": [ + 304, + 245, + 545, + 399 + ], + "type": "text", + "content": " for Shapenet Cars." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 401, + 545, + 497 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 401, + 545, + 497 + ], + "spans": [ + { + "bbox": [ + 304, + 401, + 545, + 497 + ], + "type": "text", + "content": "Baselines. We compare our approach against two methods: CAMPARI [20], the state-of-the-art pose learning method in 3D-aware image synthesis, and EG3D [3], the state-of-the-art in 3D-aware image synthesis. We also build a baseline method which is a combination of them, where we incorporate the pose learning method in CAMPARI into the framework of EG3D. More details regarding the baselines can be found in Supplementary Material." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 498, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 545, + 713 + ], + "type": "text", + "content": "Metrics. We use five metrics to evaluate the performance, including Fréchet Inception Distance (FID) [10], Depth Error [3], Pose Error [47], Reprojection Error (RE) [47], and Jensen-Shannon Divergence (JS). FID is measured between 50K generated images and all real images. Depth Error is used to assess the quality of geometry. We follow [3] and calculate the mean squared error (MSE) against pseudoground-truth depth estimated by [7] on 10K synthesized samples. We evaluate the pose accuracy on 10K generated samples as well. Given the synthesized images, we leverage the head pose estimator [53] and report the L1 distance between the estimated poses and the poses inferred from the generator. Note that we subtract the respective means of estimated and inferred pose distribution to compensate the canonical shift problem (see Fig. 4). Inter-view consistency is measured by the re-projection error following [47]. We render 5 views by sampling azimuth uniformly in the range of " + }, + { + "bbox": [ + 304, + 498, + 545, + 713 + ], + "type": "inline_equation", + "content": "[-23^{\\circ}, 23^{\\circ}]" + }, + { + "bbox": [ + 304, + 498, + 545, + 713 + ], + "type": "text", + "content": " and warp two consecutive views to each other" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13065" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 71, + 541, + 508 + ], + "blocks": [ + { + "bbox": [ + 50, + 71, + 541, + 508 + ], + "lines": [ + { + "bbox": [ + 50, + 71, + 541, + 508 + ], + "spans": [ + { + "bbox": [ + 50, + 71, + 541, + 508 + ], + "type": "image", + "image_path": "80f7389e0db78c3b0cec43d7ec73506de3a40031f38c6e42bbea6e9aeba3732f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 508, + 547, + 553 + ], + "lines": [ + { + "bbox": [ + 46, + 508, + 547, + 553 + ], + "spans": [ + { + "bbox": [ + 46, + 508, + 547, + 553 + ], + "type": "text", + "content": "Figure 3. Qualitative comparison between our approach and baselines. CAMPARI [20] struggles to generate reasonable results. \"CAMPARI + EG3D\" suffers from mode collapse on the FFHQ and Cats datasets. EG3D [3] achieves impressive rendering and reconstruction results when camera poses of training images are given. In contrast, our approach can generate high-quality rendering and geometry without any pose priors." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 558, + 289, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 289, + 654 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 289, + 654 + ], + "type": "text", + "content": "to report the MSE. The images are normalized in the range of " + }, + { + "bbox": [ + 46, + 558, + 289, + 654 + ], + "type": "inline_equation", + "content": "[-1, 1]" + }, + { + "bbox": [ + 46, + 558, + 289, + 654 + ], + "type": "text", + "content": " for evaluation. Since the azimuth range learned by CAMPARI is much smaller, we use the learned range for sampling in the measurement of CAMPARI. To measure the quality of the learned pose distribution, we report Jensen-Shannon Divergence on " + }, + { + "bbox": [ + 46, + 558, + 289, + 654 + ], + "type": "inline_equation", + "content": "50\\mathrm{K}" + }, + { + "bbox": [ + 46, + 558, + 289, + 654 + ], + "type": "text", + "content": " synthesized samples and all real images by averaging divergence values over azimuth and elevation." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 669, + 133, + 680 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 669, + 133, + 680 + ], + "spans": [ + { + "bbox": [ + 47, + 669, + 133, + 680 + ], + "type": "text", + "content": "4.2. Main Results" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "type": "text", + "content": "Qualitative Comparison. Fig. 3 shows the qualitative comparison against the baselines. CAMPARI learns faulty" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 558, + 547, + 703 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 547, + 703 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 547, + 703 + ], + "type": "text", + "content": "and very sharp shapes that span the entire space along the ray direction (the same phenomenon as observed in Fig. 1d). Therefore, even if the object is rotated with an extremely small angle (e.g., " + }, + { + "bbox": [ + 304, + 558, + 547, + 703 + ], + "type": "inline_equation", + "content": "2.5^{\\circ}" + }, + { + "bbox": [ + 304, + 558, + 547, + 703 + ], + "type": "text", + "content": "), the caused visual effect is equivalent to that of the normal rotation of a decent shape with a much larger angle (e.g., " + }, + { + "bbox": [ + 304, + 558, + 547, + 703 + ], + "type": "inline_equation", + "content": "23^{\\circ}" + }, + { + "bbox": [ + 304, + 558, + 547, + 703 + ], + "type": "text", + "content": "). We visualize CAMPARI in its own valid range of the horizontal angle (around " + }, + { + "bbox": [ + 304, + 558, + 547, + 703 + ], + "type": "inline_equation", + "content": "[-2.5^{\\circ}, 2.5^{\\circ}]" + }, + { + "bbox": [ + 304, + 558, + 547, + 703 + ], + "type": "text", + "content": " for FFHQ, " + }, + { + "bbox": [ + 304, + 558, + 547, + 703 + ], + "type": "inline_equation", + "content": "[-5^{\\circ}, 5^{\\circ}]" + }, + { + "bbox": [ + 304, + 558, + 547, + 703 + ], + "type": "text", + "content": " for Cats, and " + }, + { + "bbox": [ + 304, + 558, + 547, + 703 + ], + "type": "inline_equation", + "content": "[-30^{\\circ}, 30^{\\circ}]" + }, + { + "bbox": [ + 304, + 558, + 547, + 703 + ], + "type": "text", + "content": " for Shapenet Cars). For others, visualizations on FFHQ and Cats are conducted on the angle range " + }, + { + "bbox": [ + 304, + 558, + 547, + 703 + ], + "type": "inline_equation", + "content": "[-23^{\\circ}, 23^{\\circ}]" + }, + { + "bbox": [ + 304, + 558, + 547, + 703 + ], + "type": "text", + "content": ". Poses for cars are randomly sampled from the entire " + }, + { + "bbox": [ + 304, + 558, + 547, + 703 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 304, + 558, + 547, + 703 + ], + "type": "text", + "content": " azimuth and " + }, + { + "bbox": [ + 304, + 558, + 547, + 703 + ], + "type": "inline_equation", + "content": "180^{\\circ}" + }, + { + "bbox": [ + 304, + 558, + 547, + 703 + ], + "type": "text", + "content": " elevation distributions. EG3D leverages ground" + } + ] + } + ], + "index": 5 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "13066" + } + ] + } + ], + "index": 6 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 49, + 114, + 543, + 209 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 545, + 115 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 545, + 115 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 545, + 115 + ], + "type": "text", + "content": "Table 1. Quantitative comparison on FFHQ [12], Cats [51], and Shapenet Cars [5]. Our approach significantly outperforms CAMPARI [20] and \"CAMPARI + EG3D\" in terms of depth error, pose error, reprojection error, and Jensen-Shannon divergence score. Note that, EG3D [3] uses pose annotations, while our model is trained without any pose priors. * means we report the FID of EG3D on Shapenet Cars using its released model, which is inconsistent with the one reported in the paper." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 49, + 114, + 543, + 209 + ], + "lines": [ + { + "bbox": [ + 49, + 114, + 543, + 209 + ], + "spans": [ + { + "bbox": [ + 49, + 114, + 543, + 209 + ], + "type": "table", + "html": "
ModelFFHQ [12]Cats [51]Shapenet Cars [5]
FID50k ↓Depth↓Pose↓RE↓JS↓FID50k ↓RE↓JS↓FID50k ↓JS↓
CAMPARI [20]58.591.780.150.1090.6137.400.0500.6068.910.72
CAMPARI+EG3D3.251.130.18-0.734.83-0.744.660.83
EG3D [3]4.800.290.070.039-5.560.042-9.68*-
Ours4.990.290.100.0370.205.460.0460.243.780.51
", + "image_path": "8c534a95e3d1472f0f545af35d2ab70c8de1bf9651d5705d95415515842094b2.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 214, + 289, + 357 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 214, + 289, + 357 + ], + "spans": [ + { + "bbox": [ + 46, + 214, + 289, + 357 + ], + "type": "text", + "content": "truth camera poses for training and generates high-quality images and underlying geometry simultaneously. When incorporated with the pose learning method in CAMPARI, EG3D suffers from pose collapse and converges to one pose on FFHQ and Cats. Hence, novel views are not available in such cases, and the 3D-aware image synthesis problem is degraded to 2D image synthesis. On Shapenet Cars, the generated image and its corresponding shape are visually reasonable under a specific view but become completely unnatural when deviating from that view. Our method, without any pose priors, can generate high-fidelity images and shapes on par with EG3D." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 358, + 289, + 646 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 358, + 289, + 646 + ], + "spans": [ + { + "bbox": [ + 46, + 358, + 289, + 646 + ], + "type": "text", + "content": "Quantitative Comparison. We report the quantitative evaluation of baselines and our method in Tab. 1. CAMPARI fails to capture the underlying pose distribution and gets high Jensen-Shannon Divergence scores and pose errors. Consequently, the quality of images and shapes is unsatisfying as well, reflected by high FID scores and depth errors. CAMPARI+EG3D generates planar shapes and collapses to one pose or a small range of poses, which simplifies 3D-aware image synthesis to 2D image synthesis, resulting in lower FID scores but higher depth error, pose error and Jensen-Shannon Divergence score. EG3D, the method that uses pose annotations, exhibits good performance in terms of image quality and geometry quality. Our method yields results on par with EG3D and learns much better underlying pose distribution than the baselines. The quality of the geometry affects the multi-view consistency of the learned neural fields. Thus, EG3D and ours, which synthesize better shapes, can get better scores of reprojection errors. Note that our pose error is higher than that of EG3D, one of the reasons is that there exists the canonical view shift. As we do not provide any information on what the canonical view will be like, the model tends to learn a canonical view that leads to the best of its performance, which could be different from the standard. More discussions are in Sec. 4.4." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 658, + 142, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 658, + 142, + 671 + ], + "spans": [ + { + "bbox": [ + 47, + 658, + 142, + 671 + ], + "type": "text", + "content": "4.3. Ablation Study" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 677, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 288, + 713 + ], + "type": "text", + "content": "We conduct ablation studies on FFHQ " + }, + { + "bbox": [ + 46, + 677, + 288, + 713 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 46, + 677, + 288, + 713 + ], + "type": "text", + "content": " to analyze the effectiveness of PoF3D. Evaluation results are shown in Tab. 2." + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 310, + 245, + 539, + 363 + ], + "blocks": [ + { + "bbox": [ + 305, + 212, + 545, + 245 + ], + "lines": [ + { + "bbox": [ + 305, + 212, + 545, + 245 + ], + "spans": [ + { + "bbox": [ + 305, + 212, + 545, + 245 + ], + "type": "text", + "content": "Table 2. Ablation studies on FFHQ dataset [12]. We analyze the influence of symmetry loss, pose-aware discriminator, and learning rate. See Sec. 4.3 for more details." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 310, + 245, + 539, + 363 + ], + "lines": [ + { + "bbox": [ + 310, + 245, + 539, + 363 + ], + "spans": [ + { + "bbox": [ + 310, + 245, + 539, + 363 + ], + "type": "table", + "html": "
ModelFFHQ
FID50k ↓Depth↓Pose↓JS↓
w/o symmetry loss4.500.410.120.20
w/o pose-aware D3.431.300.190.21
w/o pose condition in D3.511.480.190.26
lr = 2.5e-4122.070.820.740.56
lr = 2.5e-610.200.700.160.38
Ours4.990.290.100.20
", + "image_path": "81fc684b11432f6bf0c8c68ac30dd061682afbf058bcb029d37592a83b7541c8.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 366, + 545, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 366, + 545, + 485 + ], + "spans": [ + { + "bbox": [ + 304, + 366, + 545, + 485 + ], + "type": "text", + "content": "Symmetry Loss. We render an image from the symmetrical camera view and leverage it to pose a constraint on the generated neural radiance field from another view. Without this constraint, although the network can synthesize visually pleasing images under the learned pose and capture a rough pose distribution, the underlying geometry has a tendency to flatten, resulting in higher depth error. The constraint from the symmetrical view can detect the flat shapes because the rendered image under the novel view deviates from the real distribution and shall be corrected by the model." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 486, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 486, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 546, + 713 + ], + "type": "text", + "content": "Pose-aware Discriminator. To verify the capability of the pose-aware discriminator, we compare it against the simple dual discriminator that removes the conditional label and purely performs real or fake discrimination. The simple dual discriminator does not provide any additional pose information to the generator other than the common realizesscore. Thus, the generator learns the pose freely and has difficulty aligning poses of data to share the same canonical view. For example, in the human face generation, one fake pose can correspond to images under different real poses. As a result, the pose error increases, and planar shapes are more frequently generated. We also report the results where only the pose conditioning discrimination is changed to the conventional pose-free discrimination. It drastically harms the geometry quality. With our pose-aware discriminator, the discriminator predicts the pose from both the fake and real data and uses it as the condition, which forces the generator to synthesize images under the same view as the conditional label, leading to better pose" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "13067" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 82, + 76, + 225, + 173 + ], + "blocks": [ + { + "bbox": [ + 82, + 76, + 225, + 173 + ], + "lines": [ + { + "bbox": [ + 82, + 76, + 225, + 173 + ], + "spans": [ + { + "bbox": [ + 82, + 76, + 225, + 173 + ], + "type": "image", + "image_path": "360cf17053de041798d8b1d510de00bae4f587de244f04cbb62f9f59b5557b95.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 236, + 76, + 365, + 171 + ], + "blocks": [ + { + "bbox": [ + 236, + 76, + 365, + 171 + ], + "lines": [ + { + "bbox": [ + 236, + 76, + 365, + 171 + ], + "spans": [ + { + "bbox": [ + 236, + 76, + 365, + 171 + ], + "type": "image", + "image_path": "23d07301fe391fe35729fd60d49da6bc849dfcde9242c7a326c4339bf2b8169a.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 378, + 76, + 506, + 171 + ], + "blocks": [ + { + "bbox": [ + 378, + 76, + 506, + 171 + ], + "lines": [ + { + "bbox": [ + 378, + 76, + 506, + 171 + ], + "spans": [ + { + "bbox": [ + 378, + 76, + 506, + 171 + ], + "type": "image", + "image_path": "e1c73b40bc4303f2ec5a74be99fd61a5eace5888d91401023b065758421a4e81.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 82, + 178, + 223, + 287 + ], + "blocks": [ + { + "bbox": [ + 82, + 178, + 223, + 287 + ], + "lines": [ + { + "bbox": [ + 82, + 178, + 223, + 287 + ], + "spans": [ + { + "bbox": [ + 82, + 178, + 223, + 287 + ], + "type": "image", + "image_path": "974d4d184579b14d5ee7d732fc7bfb1a15b0fd5fe9556be22ac32cc25fd2b4ed.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 289, + 547, + 323 + ], + "lines": [ + { + "bbox": [ + 46, + 289, + 547, + 323 + ], + "spans": [ + { + "bbox": [ + 46, + 289, + 547, + 323 + ], + "type": "text", + "content": "Figure 4. Pose distribution learned by the pose-free generator. The proposed approach well captures the pose distribution of the dataset. Note that, there is a slight shift of elevation distribution on the FFHQ dataset. The reason is that the model can automatically learn a canonical space for best performance during training." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 236, + 179, + 365, + 286 + ], + "blocks": [ + { + "bbox": [ + 236, + 179, + 365, + 286 + ], + "lines": [ + { + "bbox": [ + 236, + 179, + 365, + 286 + ], + "spans": [ + { + "bbox": [ + 236, + 179, + 365, + 286 + ], + "type": "image", + "image_path": "d8e66bcc83eb7eef4f6f7038493fe7a17bbea0df5bffd90c19fca9f8bad8ce15.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 377, + 180, + 507, + 287 + ], + "blocks": [ + { + "bbox": [ + 377, + 180, + 507, + 287 + ], + "lines": [ + { + "bbox": [ + 377, + 180, + 507, + 287 + ], + "spans": [ + { + "bbox": [ + 377, + 180, + 507, + 287 + ], + "type": "image", + "image_path": "dc0163a303a3c6df8a9d9d406998143d58d4fcfbd7a2124de18f802d76221cc9.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 85, + 327, + 225, + 423 + ], + "blocks": [ + { + "bbox": [ + 85, + 327, + 225, + 423 + ], + "lines": [ + { + "bbox": [ + 85, + 327, + 225, + 423 + ], + "spans": [ + { + "bbox": [ + 85, + 327, + 225, + 423 + ], + "type": "image", + "image_path": "1f481f290e1ae8ee97103fffbcf938d6aed76e04f8743423e705c921ebd40ff4.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 238, + 327, + 365, + 422 + ], + "blocks": [ + { + "bbox": [ + 238, + 327, + 365, + 422 + ], + "lines": [ + { + "bbox": [ + 238, + 327, + 365, + 422 + ], + "spans": [ + { + "bbox": [ + 238, + 327, + 365, + 422 + ], + "type": "image", + "image_path": "47a6eacaff36474d61e949be2f57de6408568ff77cf7367a55ff51578bfd466b.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 380, + 327, + 507, + 422 + ], + "blocks": [ + { + "bbox": [ + 380, + 327, + 507, + 422 + ], + "lines": [ + { + "bbox": [ + 380, + 327, + 507, + 422 + ], + "spans": [ + { + "bbox": [ + 380, + 327, + 507, + 422 + ], + "type": "image", + "image_path": "14f8f12fa98788827045e56c9fcb260dce4650d65937d090c22c58cb19b58904.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 85, + 431, + 223, + 538 + ], + "blocks": [ + { + "bbox": [ + 85, + 431, + 223, + 538 + ], + "lines": [ + { + "bbox": [ + 85, + 431, + 223, + 538 + ], + "spans": [ + { + "bbox": [ + 85, + 431, + 223, + 538 + ], + "type": "image", + "image_path": "7a1dd9497e91314e08b9ce414316d249dab9fe1d0e7f172b93aed4c1d7dba1c0.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 543, + 546, + 567 + ], + "lines": [ + { + "bbox": [ + 46, + 543, + 546, + 567 + ], + "spans": [ + { + "bbox": [ + 46, + 543, + 546, + 567 + ], + "type": "text", + "content": "Figure 5. Pose distribution learned by the pose-aware discriminator. Results demonstrate that our discriminator can learn the pose distribution of the dataset. The issue of canonical space shift also exists from the discriminator perspective, same as Fig. 4." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 236, + 431, + 362, + 538 + ], + "blocks": [ + { + "bbox": [ + 236, + 431, + 362, + 538 + ], + "lines": [ + { + "bbox": [ + 236, + 431, + 362, + 538 + ], + "spans": [ + { + "bbox": [ + 236, + 431, + 362, + 538 + ], + "type": "image", + "image_path": "2c01d66d0ce2770488f5b9e05b9587d313a14ba19d7aa70cb4451cad079b8f99.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 380, + 431, + 507, + 539 + ], + "blocks": [ + { + "bbox": [ + 380, + 431, + 507, + 539 + ], + "lines": [ + { + "bbox": [ + 380, + 431, + 507, + 539 + ], + "spans": [ + { + "bbox": [ + 380, + 431, + 507, + 539 + ], + "type": "image", + "image_path": "d3fc83027029ca4770268766186ee8ab6bb58502e6a6d4635c96a8d13896d71b.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 578, + 93, + 588 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 578, + 93, + 588 + ], + "spans": [ + { + "bbox": [ + 47, + 578, + 93, + 588 + ], + "type": "text", + "content": "alignment." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 594, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 289, + 714 + ], + "type": "text", + "content": "Learning Rate of Pose Learner. Learning rate of the pose branch in the generator matters a lot. With a large learning rate (e.g., 2.5e-4 in Tab. 2), the generator always tries with new poses of large variation at the beginning and leaves the content learning behind, resulting in unstable training and higher tendency of mode collapse. As reported in Tab. 2, all the evaluation metrics experience a significant drop. On the contrary, if the learning rate is too small (e.g., 2.5e-6 in Tab. 2), the generator cannot explore the pose distribution enough and easily gets stuck in a small" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 577, + 547, + 637 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 577, + 547, + 637 + ], + "spans": [ + { + "bbox": [ + 304, + 577, + 547, + 637 + ], + "type": "text", + "content": "range of pose distribution, putting more focus on the content learning. Consequently, the model fails to capture and understand the pose distribution, leading to worse shapes. A proper learning rate should balance the exploration of pose distribution and the learning of the content." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 646, + 392, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 646, + 392, + 658 + ], + "spans": [ + { + "bbox": [ + 306, + 646, + 392, + 658 + ], + "type": "text", + "content": "4.4. Pose Analysis" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 665, + 546, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 546, + 700 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 546, + 700 + ], + "type": "text", + "content": "In this section, we analyze the pose distributions that are learned by our pose-free generator and pose-aware discriminator." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 701, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 701, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 701, + 545, + 714 + ], + "type": "text", + "content": "Poses in Pose-free Generator. To visualize the pose" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13068" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 76, + 544, + 141 + ], + "blocks": [ + { + "bbox": [ + 49, + 76, + 544, + 141 + ], + "lines": [ + { + "bbox": [ + 49, + 76, + 544, + 141 + ], + "spans": [ + { + "bbox": [ + 49, + 76, + 544, + 141 + ], + "type": "image", + "image_path": "7fd9005a3de1a3a38ccf609d6e2006f0673ae1b7443c22070f4710b0405ca321.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 49, + 145, + 544, + 210 + ], + "blocks": [ + { + "bbox": [ + 49, + 145, + 544, + 210 + ], + "lines": [ + { + "bbox": [ + 49, + 145, + 544, + 210 + ], + "spans": [ + { + "bbox": [ + 49, + 145, + 544, + 210 + ], + "type": "image", + "image_path": "501ea946bb8c41b4295678666c581886e08499065cc8936e597b804c689de948.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 213, + 544, + 236 + ], + "lines": [ + { + "bbox": [ + 46, + 213, + 544, + 236 + ], + "spans": [ + { + "bbox": [ + 46, + 213, + 544, + 236 + ], + "type": "text", + "content": "Figure 6. Results of linear interpolation between two latent codes. The appearance, the geometry, and the pose all change smoothly, indicating the latent space is semantically meaningful." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 241, + 286, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 241, + 286, + 396 + ], + "spans": [ + { + "bbox": [ + 46, + 241, + 286, + 396 + ], + "type": "text", + "content": "distribution learned in the pose-free generator, we randomly sample 50K latent codes and infer the poses from them. The pose distributions from the dataset and learned in the generator are shown in Fig. 4. Without any pose priors, our method can capture the pose range and distribution of the dataset in general. As observed in the figure for elevation distributions on the FFHQ dataset, there exists a distribution shift. The reason is that we do not release any information about the canonical view to the model, and therefore, the model can interpret the canonical view freely with different angles which might be different from the one defined in the dataset. Generally, the model will choose the one that leads to the best performance as its canonical view." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 397, + 286, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 397, + 286, + 529 + ], + "spans": [ + { + "bbox": [ + 46, + 397, + 286, + 529 + ], + "type": "text", + "content": "Poses in Pose-aware Discriminator. Since our discriminator is equipped with a pose predictor, we hire it to predict the poses for all data in the dataset and draw the distributions accordingly in Fig. 5. For FFHQ and Cats datasets, the distributions are well approximated, and the canonical view shift problem also exists in the discriminator. On Shapenet Cars, the distribution of azimuth is biased to one side. We conjecture the reason is that the model has difficulty distinguishing the front and rear of the car as they look very similar. As a result, the learned distribution shifts towards a hemisphere instead of the entire sphere." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 538, + 128, + 551 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 538, + 128, + 551 + ], + "spans": [ + { + "bbox": [ + 47, + 538, + 128, + 551 + ], + "type": "text", + "content": "4.5. Applications" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 557, + 286, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 557, + 286, + 640 + ], + "spans": [ + { + "bbox": [ + 46, + 557, + 286, + 640 + ], + "type": "text", + "content": "Linearity in Latent Space. To demonstrate the latent space learned by PoF3D is semantically meaningful, we randomly sample two latent codes and linearly interpolate between them. The interpolation results are shown in Fig. 6. We can see that both the appearance and the underlying geometry are changing smoothly. Besides, as we infer the pose from the latent code, poses undergo smooth changes as well." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 642, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 286, + 712 + ], + "type": "text", + "content": "Real Image Inversion. One of the potential applications of PoF3D is to reconstruct the geometry from a real image and enable novel view synthesis. To achieve this goal, PTI [28], a GAN inversion method, is adopted to perform on our pose-free generator. In the previous methods [3] that demonstrate GAN inversion as an application, an off-the" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 309, + 241, + 543, + 295 + ], + "blocks": [ + { + "bbox": [ + 309, + 241, + 543, + 295 + ], + "lines": [ + { + "bbox": [ + 309, + 241, + 543, + 295 + ], + "spans": [ + { + "bbox": [ + 309, + 241, + 543, + 295 + ], + "type": "image", + "image_path": "2e8cca48573ad79f4da005ce9cfd331358abd48a8b50fbd209363333881d9f87.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 296, + 545, + 361 + ], + "lines": [ + { + "bbox": [ + 305, + 296, + 545, + 361 + ], + "spans": [ + { + "bbox": [ + 305, + 296, + 545, + 361 + ], + "type": "text", + "content": "Figure 7. Results of GAN inversion. Thanks to the design of pose-free generator, we do not require pose estimation prior to performing inversion like previous works. Instead, we can directly invert the image to get the 3D representation and the corresponding pose. The reconstructed geometry is realistic and enables vivid novel view synthesis." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 374, + 545, + 482 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 374, + 545, + 482 + ], + "spans": [ + { + "bbox": [ + 305, + 374, + 545, + 482 + ], + "type": "text", + "content": "shelf pose predictor is required to obtain the pose of the given image prior to performing GAN inversion. Ours, however, benefits from the changed formulation in which the camera pose is encoded in the latent space. Therefore, we can get not only the inverted neural radiance field but also the camera pose under which the given image is captured, when performing GAN inversion. The result is shown in Fig. 7. Our method can successfully invert the image and synthesize vivid images under novel views." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 494, + 378, + 506 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 494, + 378, + 506 + ], + "spans": [ + { + "bbox": [ + 306, + 494, + 378, + 506 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 514, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 514, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 305, + 514, + 545, + 712 + ], + "type": "text", + "content": "This work presents PoF3D, which learns 3D-aware image synthesis without using any pose priors. A pose-free generator is designed to infer camera poses directly from the latent space so that the requirement for pose priors in the previous works is removed. Besides, to help the generator better capture the underlying distribution, we make the discriminator pose-aware by asking it to first predict the camera pose and then use it as a condition when performing conditional real/fake discrimination. With such a design, experimental results demonstrate that our approach is able to synthesize high-quality images and high-fidelity shapes that are on par with state-of-the-art 3D synthesis methods without the need for manual pose tuning or dataset labeling. Acknowledgement. This research has been made possible by funding support from the Research Grants Council of Hong Kong under the Research Impact Fund project R6003-21." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13069" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 715 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "type": "text", + "content": "[1] Qingyan Bai, Yinghao Xu, Jiapeng Zhu, Weihao Xia, Yujiu Yang, and Yujun Shen. 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Syst., 2018. 2" + } + ] + } + ], + "index": 28 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13071" + } + ] + } + ], + "index": 30 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Learning Accurate 3D Shape Based on Stereo Polarimetric Imaging/44df70c3-8a85-4f37-a0ff-da1913972e67_content_list.json b/2023/Learning Accurate 3D Shape Based on Stereo Polarimetric Imaging/44df70c3-8a85-4f37-a0ff-da1913972e67_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..ebcb4646dd05fa122126da3e2ad48c46238e8b39 --- /dev/null +++ b/2023/Learning Accurate 3D Shape Based on Stereo Polarimetric Imaging/44df70c3-8a85-4f37-a0ff-da1913972e67_content_list.json @@ -0,0 +1,1513 @@ +[ + { + "type": "text", + "text": "Learning Accurate 3D Shape Based on Stereo Polarimetric Imaging", + "text_level": 1, + "bbox": [ + 143, + 130, + 826, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Tianyu Huang $^{1*}$ Haoang Li $^{1,2*}$ Kejing He $^{1}$ Congying Sui $^{1}$ Bin Li $^{1}$ Yun-Hui Liu $^{1\\dagger}$ $^{1}$ The Chinese University of Hong Kong, Hong Kong, China \n $^{2}$ Technical University of Munich, Germany", + "bbox": [ + 148, + 179, + 825, + 234 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 268, + 313, + 284 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Shape from Polarization (SfP) aims to recover surface normal using the polarization cues of light. The accuracy of existing SfP methods is affected by two main problems. First, the ambiguity of polarization cues partially results in false normal estimation. Second, the widely-used assumption about orthographic projection is too ideal. To solve these problems, we propose the first approach that combines deep learning and stereo polarization information to recover not only normal but also disparity. Specifically, for the ambiguity problem, we design a Shape Consistency-based Mask Prediction (SCMP) module. It exploits the inherent consistency between normal and disparity to identify the areas with false normal estimation. We replace the unreliable features enclosed by these areas with new features extracted by global attention mechanism. As to the orthographic projection problem, we propose a novel Viewing Direction-aided Positional Encoding (VDPE) strategy. This strategy is based on the unique pixel-viewing direction encoding, and thus enables our neural network to handle the non-orthographic projection. In addition, we establish a real-world stereo SfP dataset that contains various object categories and illumination conditions. Experiments showed that compared with existing SfP methods, our approach is more accurate. Moreover, our approach shows higher robustness to light variation.", + "bbox": [ + 73, + 300, + 473, + 680 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 705, + 209, + 722 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "3D shape recovery is a fundamental problem in computer vision and has been extensively studied [15, 26, 31]. However, existing shape recovery methods have some limitations. For example, the geometry-based methods, e.g., structure from motion [33, 37] have difficulty in dealing with texture-less regions and can only recover sparse point cloud. While the photometric stereo methods [15, 18] can recover dense surface, they need cumbersome photometric calibration. By contrast, shape from polarization", + "bbox": [ + 75, + 729, + 468, + 867 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "(SfP) [11, 20, 40] can avoid the above problems by using the polarization cues of light. Specifically, polarization cues can detect rich geometric details even for white wall [11]. Moreover, such cues can be easily obtained in a single shot with the quad-Bayer polarization camera [46].", + "bbox": [ + 500, + 268, + 890, + 345 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Despite the above advantages of SfP, there remain two main problems that affect the recovery accuracy. First, the ambiguous polarization cues are inevitable due to unidirectional measurement [10]. These cues partially result in false normal estimation. To solve this problem, early SfP methods rely on specific assumptions about shape prior [2, 40] and lead to unsatisfactory recovery accuracy. Recently, some approaches use stereo [16] or multi-view [49] polarization information for disambiguation. However, the accuracy of these methods is limited by the low quality of stereo matching for polarization cues. Second, most existing SfP approaches assume orthographic projection for modelling simplification [35, 40]. Such assumption ignores the influence of viewing directions, which affects the accuracy of polarimetric measurements. A representative work for this problem is based on a perspective phase angle constraint [8], but this constraint is still insufficient.", + "bbox": [ + 496, + 349, + 892, + 604 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In addition to the above attempts to solve the ambiguity and orthographic projection problems, some methods are proposed based on deep learning [3, 12, 23, 25]. They improve the shape recovery accuracy to some extent. However, they still partly suffer from the ambiguity problem due to monocular imaging. By contrast, our method is based on stereo polarimetric imaging. To the best of our knowledge, our approach is the first one that combines stereo polarization information and deep learning to estimate both normal and disparity.", + "bbox": [ + 496, + 609, + 893, + 760 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "As shown in Fig. 1, we integrate convolutional neural network (CNN) with Vision Transformer [13, 14] to design the feature extraction module. This module considers both local and global contexts [34] to extract stereo feature maps. For one thing, we use the feature map of the left view to estimate the normal map. For another thing, we exploit the stereo feature maps to generate a polarimetric cost volume. This cost volume aligns stereo features to estimate the disparity map. Our joint estimation of normal and disparity", + "bbox": [ + 496, + 763, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* Tianyu Huang and Haoang Li contributed equally to this work.", + "bbox": [ + 93, + 875, + 433, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Yun-Hui Liu is the corresponding author.", + "bbox": [ + 96, + 887, + 320, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "17287", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/2c68e4beb4a490b78ad2021f327eaf2f27909e3b0ffa604b117ec20843520d55.jpg", + "image_caption": [ + "Figure 1. Overview of the proposed approach. Given a pair of stereo polarization images, our method can simultaneously recover normal map and disparity map with high quality." + ], + "image_footnote": [], + "bbox": [ + 101, + 88, + 867, + 268 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "contributes to solving the above-mentioned problems in SfP, which is introduced in the following.", + "bbox": [ + 75, + 310, + 468, + 340 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "For the ambiguity problem, we design a Shape Consistency-based Mask Prediction (SCMP) module. This module predicts a mask to identify the areas with inaccurate normal estimation caused by unreliable features in the feature map. We use these areas to achieve a coarse-to-fine refinement for the feature map. At each step, we replace the features enclosed by such areas with new features extracted by the global attention mechanism in Transformer. As to the orthographic projection problem, we introduce a novel Viewing Direction-aided Positional Encoding (VDPE) strategy to Transformer. Based on the pixel-viewing direction encoding, this strategy enables our neural network to handle non-orthographic projection. Moreover, we establish a large real-world stereo SfP dataset.", + "bbox": [ + 75, + 340, + 470, + 551 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To summarize, we propose the first approach that combines stereo polarimetric imaging and deep learning to recover accurate normal and disparity maps simultaneously. Our main contributions are as follows:", + "bbox": [ + 75, + 551, + 468, + 612 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We design a mask prediction module to reduce the effect of ambiguous polarization cues based on the consistency between normal and disparity.", + "- We propose a novel positional encoding design that enables our network to handle the non-orthographic projection in polarimetric measurement.", + "- We establish a large real-world dataset for stereo SfP problem. Our dataset contains various object categories and illumination conditions." + ], + "bbox": [ + 94, + 616, + 468, + 760 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Extensive experiments showed that compared with existing methods, our approach is more accurate. Moreover, our approach shows higher robustness to light variation.", + "bbox": [ + 75, + 763, + 468, + 810 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 821, + 218, + 838 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We first review SfP methods that typically use pure polarization cues with monocular setup. We then introduce the", + "bbox": [ + 76, + 848, + 468, + 878 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "approaches combining polarization and the other cues. Finally, we present works adopting stereo or multi-view setup.", + "bbox": [ + 504, + 310, + 890, + 340 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Pure Polarization. Early SfP methods divide the polarization reflection into two cases, i.e., specular reflection [35] and diffuse reflection [2, 19, 29]. These methods model such two cases individually according to object materials. This strategy is impractical since light reflection involves both cases in the real world. Moreover, their assumptions on shape priors lead to over-smooth shape recovery results. Baek et al. [4] introduced a model that can consider two reflection cases simultaneously. However, their model requires the assumption about ideal surface reflection and thus is relatively unreliable. Considering the complexity of light reflection, some methods [3, 12, 23, 25] based on deep learning are proposed. Although these data-driven methods improve the recovery accuracy, they lead to low generalization. The reason is that their networks are trained on relatively small or synthetic datasets.", + "bbox": [ + 496, + 340, + 890, + 582 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Polarization $+\\mathbf{X}$ . The above pure polarization-based methods suffer from the ambiguity problem of polarization cues. To solve this problem, recent works attempt to introduce additional shape-from-X cues (X represents shading, photometry, depth, etc.). With the cues of shading, Smith et al. [39, 40] proposed to generate a large linear system to directly calculate the height of each pixel. However, their assumptions about the known refractive index and orthographic camera projection limit the recovery accuracy. Ngo et al. [32] combined the polarization with shading cues to additionally estimate the refractive index. Nevertheless, their method needs at least two light directions and is time-consuming. In addition, given the cues of photometry, Atkinson et al. [1] used two calibrated photometric systems to reduce the effects of polarization ambiguity. Tozza et al. [41] improved their method by solving the uncalibrated case. Moreover, based on the cues of depth, Kadambi et al. [21] used the geometric constraints of normals to refine the depth map. This method relies on redundant depth alignment, which leads to low efficiency.", + "bbox": [ + 496, + 583, + 892, + 883 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Stereo and Multi-view Polarization. Stereo or multi-view", + "bbox": [ + 500, + 885, + 890, + 898 + ], + "page_idx": 1 + }, + { + "type": "page_footnote", + "text": "1https://tyhuang98.github.io/learn_stereo_sfp/", + "bbox": [ + 94, + 886, + 457, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "17288", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "imaging setup contributes to the disambiguation of polarization cues. For example, Cui et al. [11] proposed an is-depth contour tracing mechanism in their multi-view setup to fuse the estimated depth and normal maps. Chen et al. [9] proposed a theoretical polarimetric transport model to constrain the recovery solutions from three views. Zhu and Smith [50] adopted a pair of polarization and RGB images. They introduced a high-order graphical model to label the diffuse-dominant and specular-dominant pixels separately, followed by shape recovery. Recently, Fukao et al. [16] proposed an approach to recover per-pixel normals using stereo polarimetric images. They treated the Stokes vector as polarization cues and constructed a cost volume to regress normals. Compared with the above methods, our approach is more robust to noise thanks to our proposed modules, as will be shown in the experiments.", + "bbox": [ + 75, + 90, + 472, + 333 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Proposed Method", + "text_level": 1, + "bbox": [ + 76, + 356, + 250, + 373 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In Section 3.1, we introduce the basic knowledge of polarization. In Section 3.2, we give an overview of our pipeline. In Section 3.3, we introduce the SCMP module that enables our method to solve the ambiguity problem. In Section 3.4, we introduce our VDPE design that aims at handling the non-orthographic projection. In Section 3.5, we introduce our loss function.", + "bbox": [ + 75, + 383, + 470, + 489 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Basic Knowledge of Polarization", + "text_level": 1, + "bbox": [ + 76, + 506, + 362, + 523 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Let us consider a partially polarized light that orthographically passes through a linear polarizer with an angle of $\\phi_{\\mathrm{pol}}$ . The measured intensity of this light follows a sinusoidal variation [10] as", + "bbox": [ + 75, + 532, + 468, + 594 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} I _ {\\phi_ {\\mathrm {p o l}}} = \\frac {I _ {\\operatorname* {m a x}} + I _ {\\operatorname* {m i n}}}{2} + \\frac {I _ {\\operatorname* {m a x}} - I _ {\\operatorname* {m i n}}}{2} \\cos (2 \\phi_ {\\mathrm {p o l}} - 2 \\phi) \\tag {1} \\\\ = \\bar {I} + \\rho \\bar {I} \\cos (2 \\phi_ {\\mathrm {p o l}} - 2 \\phi), \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 96, + 607, + 468, + 656 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $I_{\\mathrm{max}}$ and $I_{\\mathrm{min}}$ denote the upper and lower bounds of the detected light intensity, $\\phi$ denotes the angle of linear polarization (AoLP), $\\rho$ denotes the degree of linear polarization (DoLP), $\\bar{I}$ denotes the average intensity. Based on Eq. (1), two polarization angles $\\phi$ and $\\phi'$ with a $\\pi$ -shift $(\\phi' = \\phi \\pm \\pi)$ result in the same observed light intensity, which is called $\\pi$ -ambiguity problem. With the linear quad-Bayer polarization camera [46], we can measure intensities in different angles of polarizer. By combining these intensities, we can solve the above unknown polarization parameters: $\\phi$ with $\\pi$ -ambiguity, $\\rho$ , and $\\bar{I}$ . These parameters have been proved to be highly related to the surface normal [2, 35]. Details are available in the supplementary material.", + "bbox": [ + 75, + 670, + 468, + 867 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In addition, there is another representation to describe the polarization state of light [10], i.e., the Stokes vector:", + "bbox": [ + 76, + 869, + 468, + 901 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {s} = \\left[ \\begin{array}{c} s _ {0} \\\\ s _ {1} \\\\ s _ {2} \\\\ s _ {3} \\end{array} \\right] = \\left[ \\begin{array}{c} I _ {0} + I _ {9 0} \\\\ I _ {0} - I _ {9 0} \\\\ I _ {4 5} - I _ {1 3 5} \\\\ 0 \\end{array} \\right], \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 583, + 87, + 890, + 152 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $s_0$ represents the light intensity; $s_1$ and $s_2$ represent the linear polarization components in $0^\\circ$ and $45^\\circ$ , respectively; $s_3$ represents the right circular polarization component. The Stokes vector $\\mathbf{s}$ in Eq. (2) can be expressed by the measured intensities $I_0, I_{45}, I_{90}$ and $I_{135}$ . In our context, we follow [12] to call the normalized Stokes vector image \"Stokes map\".", + "bbox": [ + 496, + 161, + 893, + 267 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Pipeline Overview", + "text_level": 1, + "bbox": [ + 500, + 277, + 676, + 295 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As shown in Fig. 1, given the measured stereo polarization images, we compute AoLP&DoLP and Stokes maps, and treat them as the physical priors. By taking these priors as inputs, our network uses a weight-shared feature extraction module to extract stereo feature maps. Our feature extraction is based on the combination of CNN and Transformer to consider both local and global contexts. Note that our Transformer is adapted by the proposed VDPE design (see Section 3.4) to handle the non-orthographic projection. Based on the extracted stereo feature maps, our network predicts both normal and disparity maps.", + "bbox": [ + 496, + 303, + 890, + 469 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Disparity Map. Given the stereo feature maps, we generate a polarimetric cost volume. This volume aligns stereo features and encapsulates the disparity information [22]. We process such volume by a series of Conv3d blocks [42] and the Soft ArgMin operation [22] to infer the disparity map.", + "bbox": [ + 496, + 470, + 890, + 546 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Normal Map. The extracted feature map of the left view is associated with the unknown-but-sought normal map. However, due to the ambiguity problem of polarization cues, this feature map needs to be refined. To achieve this goal, we propose a coarse-to-fine feature refinement strategy. This refinement is based on the proposed SCMP module (see Section 3.3) and Transformer. Our SCMP module incorporates the above cost volume since there exists inherent consistency between disparity and normal. After refinement, the feature map is used to infer the normal map.", + "bbox": [ + 496, + 547, + 890, + 699 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.3. Shape Consistency-based Mask Prediction", + "text_level": 1, + "bbox": [ + 500, + 709, + 861, + 727 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Leveraging the shape consistency between normal and disparity can improve the shape recovery accuracy. Let us first intuitively explain the reason. For one thing, the normal map estimated by polarization cues are per-pixel. However, the normals in some areas are false due to the ambiguity problem, and we cannot obtain a mask to exclude such areas a priori. For another thing, given a disparity map, we can compute a normal map that is globally reliable but coarse. The correct normals labelled by the unknown-but-sought mask are relatively consistent with the normals computed by the disparity map. We leverage such consistency", + "bbox": [ + 496, + 734, + 890, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "17289", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/95e5984bb1709244cffabca79e8a3698a369eb2f17e8358ef1ac7cde7244b290.jpg", + "image_caption": [ + "(a) Proposed SCMP module." + ], + "image_footnote": [], + "bbox": [ + 117, + 85, + 433, + 212 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/ad848414b5847526e2d9733999fc173f05f4044b1f9ce895c22011afc011cc22.jpg", + "image_caption": [ + "(b) The mask embedding operation in our network.", + "Figure 2. Illustration of proposed SCMP module and mask embedding operation. (a) Based on shape consistency, the proposed SCMP module predicts a mask. (b) We employ the predicted mask to purify the feature map $F_{1} / F_{2}$ by a mask embedding operation." + ], + "image_footnote": [], + "bbox": [ + 148, + 233, + 400, + 323 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "to identify this mask by introducing the SCMP module. We will introduce our module details in the following.", + "bbox": [ + 75, + 407, + 468, + 438 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As shown in Fig. 1, we embed two SCMP modules into our network. Fig. 2(a) shows how our first and second SCMP modules are used in our coarse-to-fine feature refinement. Specifically, at the \"coarse\" stage, we take the original feature map $F_{1}$ of the left view and the polarimetric cost volume $C_{1}$ as inputs of the first SCMP module. At the \"fine\" stage, we feed the intermediate feature map $F_{2}$ and cost volume $C_{2}$ to the second SCMP module. At each stage, an initial normal map can be inferred from the feature map $F_{1}$ or $F_{2}$ under supervision. Meanwhile, an initial disparity map can be regressed from the cost volume $C_{1}$ or $C_{2}$ under supervision. Based on this disparity map, we compute a rough normal map using an adaptive normal estimation method [27]. We then exploit the consistency between the normal inferred by our network and the normal computed based on disparity to predict a mask. Specifically, the value $v_{i}$ of the $i$ -th pixel in this mask is computed by", + "bbox": [ + 75, + 439, + 470, + 696 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nv _ {i} = \\left\\{ \\begin{array}{l l} 0, & \\text {i f} \\mathbf {n} _ {i} ^ {N} \\cdot \\mathbf {n} _ {i} ^ {D} < \\tau \\\\ 1, & \\text {o t h e r w i s e} \\end{array} , \\right. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 166, + 704, + 468, + 738 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where “.” denotes the dot product, $\\mathbf{n}_i^N$ and $\\mathbf{n}_i^D$ are the normals inferred by our network and computed based on disparity, respectively, $\\tau$ is a threshold. When $\\mathbf{n}_i^N\\cdot \\mathbf{n}_i^D$ is smaller than the threshold $\\tau$ , the consistency is violated. In our paper, $\\tau$ is 0.7 and 0.9 in the first and second SCMP modules, respectively. We adopt such threshold setup to achieve coarse-to-fine feature refinement.", + "bbox": [ + 75, + 750, + 468, + 853 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We then employ the above mask to purify the feature map $F_{1}$ or $F_{2}$ by a mask embedding operation (see Fig. 2(b)). Each unreliable feature in the areas with false", + "bbox": [ + 75, + 854, + 470, + 900 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/339574c947b73e2bffda48bc3af31feff4337a631f888114843e4ed8c928c462.jpg", + "image_caption": [ + "Figure 3. Illustration of proposed VDPE design. For ease of understanding, we only show the self-attention part in the Transformer." + ], + "image_footnote": [], + "bbox": [ + 529, + 87, + 857, + 202 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "normal estimation is set to zero vector. Then the purified feature map is fed to Transformer for global attention. Thanks to the mask embedding, the effect of the unreliable features resulting in false normal estimation is reduced. In addition, the global attention mechanism in Transformer extracts new features for the masked areas by combing global reliable features. Based on such features, the false normals can be re-estimated in an accurate way.", + "bbox": [ + 496, + 250, + 890, + 369 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Viewing Direction-aided Positional Encoding", + "text_level": 1, + "bbox": [ + 500, + 383, + 879, + 401 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Most existing SfP works [35, 39] assume orthographic projection (i.e., viewing directions of all pixels are $[0,0,1]^{\\top}$ ). This assumption affects the accuracy of polarimetric measurement and further the accuracy of shape recovery. Intuitively, additionally using a viewing direction map can alleviate this problem. We generate this map based on the pixel-viewing direction encoding, i.e., each pixel in this map is associated with a unique viewing direction. To introduce such map into neural network, a straightforward strategy is to feed it to CNN [25]. However, it is well-known that the feature extracted by CNN lacks global information. By contrast, we propose to integrate this map into Transformer. This integration is based on the proposed VDPE design (see the next paragraph). As will be shown in the experiments, such design is more effective than the strategy based on CNN.", + "bbox": [ + 496, + 409, + 892, + 650 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As shown in Fig. 3, we integrate the viewing direction map into the self-attention part of Transformer. Specifically, we reshape the viewing direction map and concatenate it with the linearly projected value in the self-attention block. Then the concatenated volume is passed to a Multi-Layer Perception (MLP) layer to embed with the attention calculation. After that, the self-attention computation result can be formulated as:", + "bbox": [ + 496, + 652, + 890, + 772 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {O u t p u t} = \\left(\\operatorname {S o f t M a x} \\left(\\frac {Q K ^ {\\top}}{\\sqrt {D}}\\right) V\\right) \\oplus \\left(\\operatorname {M L P} (V \\oplus v)\\right), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 780, + 890, + 816 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $V, K, Q$ represent the linearly projected value, key and query respectively, $\\nu$ is the viewing direction map, $D$ is the feature dimension, “ $\\oplus$ ” represents the concatenation operation. Based on Eq. (4), our method can handle the non-orthographic projection reliably.", + "bbox": [ + 496, + 824, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "17290", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/d4593619b9fc481dc3ab6df1905921e84077315f25f4f935874a2ef6cdde8b04.jpg", + "table_caption": [ + "Table 1. Comparison among existing SfP datasets. Our dataset is the first stereo SfP dataset at the object level. Meanwhile, our acquisition is under controlled illumination and does not need reprojection." + ], + "table_footnote": [], + "table_body": "
DatasetLevelTypeSetupControlled IlluminationReprojection Operation
DeepSfP [3]ObjectReal-worldMonocularNoYes
Kondo et al. [23]SceneSyntheticMonocularYesNo
Deschaintre et al. [12]ObjectSyntheticMonocularYesNo
SPW [25]SceneReal-worldMonocularNoYes
CroMo [44]SceneReal-worldStereoNoYes
OursObjectReal-worldStereoYesNo
", + "bbox": [ + 125, + 119, + 838, + 210 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/58972f68f46e8e043a17c15e4bc4b94a5112129229f463e598a20ef0c61cb10f.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 86, + 228, + 256, + 359 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/4b421457723c259c6287bf620363912cb7a626098748453099b6f796e24f3c9e.jpg", + "image_caption": [ + "(b)", + "Figure 4. We establish a real-world stereo SfP dataset, which contains rich shapes and material categories. (a) Representative image pairs. (b) Data capture setup." + ], + "image_footnote": [], + "bbox": [ + 269, + 228, + 460, + 357 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5. Loss Function", + "text_level": 1, + "bbox": [ + 76, + 426, + 220, + 440 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For network training, we use the normal loss and the disparity loss. For the normal loss, we adopt the commonly used cosine similarity loss [6, 7]. Our normal loss consists of three sub-losses $\\mathcal{N}_1$ , $\\mathcal{N}_2$ , and $\\mathcal{N}_{\\mathrm{final}}$ . $\\mathcal{N}_1$ and $\\mathcal{N}_2$ correspond to the initial normal maps in the first and second SCMP modules, respectively. $\\mathcal{N}_{\\mathrm{final}}$ is related to the final predicted normal map of our network. As to the disparity loss, we adopt the widely-used smooth $L_{1}$ loss [5, 17]. Our disparity loss consists of three sub-losses $\\mathcal{D}_1$ , $\\mathcal{D}_2$ , and $\\mathcal{D}_{\\mathrm{final}}$ . $\\mathcal{D}_1$ and $\\mathcal{D}_2$ correspond to the initial disparity maps in the first and second SCMP modules, respectively. $\\mathcal{D}_{\\mathrm{final}}$ is related to the final predicted disparity map of our network.", + "bbox": [ + 75, + 449, + 468, + 630 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "By combing the above sub-losses, we define our final loss $\\mathcal{L}$ as:", + "bbox": [ + 75, + 631, + 468, + 660 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} = \\alpha \\cdot \\left(\\mathcal {N} _ {1} + \\mathcal {N} _ {2}\\right) + \\beta \\cdot \\left(\\mathcal {D} _ {1} + \\mathcal {D} _ {2}\\right) \\tag {5} \\\\ + \\alpha^ {\\prime} \\cdot \\mathcal {N} _ {\\text {f i n a l}} + \\beta^ {\\prime} \\cdot \\mathcal {D} _ {\\text {f i n a l}}, \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 145, + 667, + 468, + 703 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\alpha$ , $\\beta$ , $\\alpha'$ , and $\\beta'$ are the trade-off parameters. During training, we set $\\alpha$ and $\\beta$ as 0.1 for weak supervision since they correspond to the intermediate results. We set $\\alpha'$ and $\\beta'$ as 0.3 for major supervision since they correspond to our final predictions. Further implementation details of our method are available in the supplementary material.", + "bbox": [ + 75, + 710, + 468, + 801 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Dataset", + "text_level": 1, + "bbox": [ + 76, + 815, + 163, + 829 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Most existing SfP datasets are either small [3,25] or only provide synthetic images [12, 23]. In addition, their images are obtained by monocular cameras and cannot be used for research on stereo polarimetric imaging. While a recent", + "bbox": [ + 75, + 839, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "dataset contains abundant stereo polarization images, it only provides the ground truth depth and ignores the normal [44]. To solve this problem, we propose a large real-world SfP dataset with stereo images associated with the ground truth normal and disparity. Considering that arbitrary illumination has been proved to limit the quality of polarization signal [12], we use the controlled illumination (i.e., unpolarized illumination) for data collection. Moreover, the ground truth shapes of existing real-world SfP datasets [3, 25] are obtained by an extra 3D scanner, which introduces the reprojection operation. By contrast, we propose a more concise acquisition design that can avoid this operation. Table 1 shows the comparison among existing SfP datasets.", + "bbox": [ + 496, + 229, + 890, + 426 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Data Composition. Our dataset consists of 2450 pairs of polarization images. We collect data from more than 50 different objects with various shapes and material categories. For data diversity, we collect images from different viewpoints and different illumination conditions for most objects. Each image pair is associated with the ground truth disparity and normal. Moreover, our dataset involves different stereo baselines between stereo images. Fig. 4(a) shows representative image pairs.", + "bbox": [ + 496, + 428, + 890, + 565 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "System Setup for Image Collection. When capturing stereo images, we fix a pair of polarization cameras (see Fig. 4(b)) and calibrate them using a standard calibration method [48]. To achieve different illumination conditions, we use an unpolarized light source to illuminate each object from a set of random directions. Moreover, to improve the diversity of illuminations, we use two unpolarized light sources, i.e., the digital projector and a LED lighting.", + "bbox": [ + 496, + 566, + 890, + 686 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Acquisition of Ground Truth Maps. To acquire the ground-truth normal and disparity maps, we use a stereo structured-light system. We replace the original grayscale cameras of this system with our stereo polarization camera rig (the grayscale information can be extracted from the polarization information). Based on this adapted system, we employ a Gray code-based reconstruction algorithm [30] to reconstruct the disparity map and point cloud of the object. Finally, we use the least-squares normal estimation algorithm [36] to calculate the normal map of the reconstructed point cloud. Each step of our acquisition does not need reprojection operation mentioned above. Our design ensures perfect alignment of the input polarization image and the ground truth normal and disparity.", + "bbox": [ + 496, + 688, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "17291", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/ad30351204389398788729be590528b76a9f8a6f40fbefbdb5874b30a70dd075.jpg", + "image_caption": [ + "Figure 5. Representative accuracy comparisons between various SfP methods for normal recovery. A pair of numbers below each estimated normal map represents the mean of angular errors and the percentage of pixels with angular errors smaller than $11.25^{\\circ}$ ." + ], + "image_footnote": [], + "bbox": [ + 99, + 85, + 872, + 470 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 76, + 525, + 209, + 542 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We first compare our approach with state-of-the-art SfP methods that aim at normal recovery in Section 5.1. Considering that our approach can predict both normal and disparity, we also compare our method with two baselines that jointly estimate normal and disparity in Section 5.2. In addition, we conduct ablation studies in Section 5.3. All the experiments are conducted on our dataset introduced above. Additional experimental results are available in the supplementary material.", + "bbox": [ + 75, + 550, + 468, + 685 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In terms of evaluation criteria, we follow [25] to evaluate the normal accuracy by the angular error between the estimated and ground truth normals. In addition, we follow [45] to report the percentage of pixels with angular errors smaller than specific thresholds (i.e., $11.25^{\\circ}$ , $22.5^{\\circ}$ , and $30.0^{\\circ}$ ). To evaluate the accuracy of disparity map, we follow [47] to use the absolute errors between the estimated and ground truth disparities.", + "bbox": [ + 75, + 686, + 470, + 808 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Comparison to SfP Methods", + "text_level": 1, + "bbox": [ + 76, + 816, + 331, + 832 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Methods for Comparison. We compare our approach with four state-of-the-art SfP methods (i.e., Zhu [50], DeepSfP [3], Fukao [16] and Lei [25]) in terms of normal recovery accuracy and robustness to light variation. As", + "bbox": [ + 76, + 839, + 468, + 901 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/8f5dce3437df27a7cd8ece212a1b430f24ed0dbaf1be8b43760ca238d72cc2cf.jpg", + "table_caption": [ + "Table 2. Accuracy comparisons between various SfP methods for normal recovery on all the data of our testing set." + ], + "table_footnote": [], + "table_body": "
MethodAngular Error (deg.)Pixel Percentage (%)
MeanMedianRMSE11.25°22.5°30.0°
Zhu [50]37.6934.2743.0112.431.945.7
DeepSfP [3]24.7121.4330.1823.647.467.8
Fukao [16]31.2827.5237.1517.439.554.3
Lei [25]22.2719.3228.6728.855.972.1
Ours13.2211.1417.2246.277.590.1
", + "bbox": [ + 501, + 556, + 890, + 664 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "introduced in Section 2, Zhu and Fukao use stereo setup and numerical optimization strategies. DeepSfP and Lei are based on monocular setup and deep learning.", + "bbox": [ + 496, + 686, + 890, + 733 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Normal Recovery Accuracy. As shown in Table 2 and Fig. 5, Zhu and Fukao are affected by the stereo matching quality and thus recover noisy normal maps. DeepSfP shows mistakes in many local areas. While Lei partly alleviates the ambiguity problem, it still loses several details. By contrast, our method achieves the highest accuracy on all the evaluation metrics and also leads to rich object details. This result demonstrates that our integration of deep learning and stereo polarization is effective.", + "bbox": [ + 496, + 733, + 890, + 869 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Robustness to Light Variation. To evaluate the robustness to light variation, we use different illumination conditions", + "bbox": [ + 498, + 869, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "17292", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/cfc680a1ebe3dcd97bfee038eeb3cd43cbb1a99e671e81fe6e2859adc4280681.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 169, + 88, + 225, + 130 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/88d201476d91cf7680c7b59684ebc60922a452d911204979933c99ad6523a4da.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 246, + 88, + 302, + 130 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/22dfbc5bad40d0bc9847409601b3ac9a943b25f2e14a3651b2c9ca75d0b37d52.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 320, + 88, + 375, + 130 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/89cbf1f97f8e699fea147982575173a72aa41d11ab4f84f5c46b889e6912bfa9.jpg", + "image_caption": [ + "Figure 6. Representative comparisons regarding robustness to light variation between various SfP methods. (a) Three different illumination conditions. (b) Due to limited space, we only report the results of Fukao, Lei, and our method. Each method corresponds to two columns. The first column shows the recovered normal maps under different illumination conditions. The second column shows the error maps. The number below each column pair represents the mean of variances of angular errors." + ], + "image_footnote": [], + "bbox": [ + 81, + 146, + 467, + 306 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f856e641252a40dc4fcfb072c3ea7118b3174e68caa84cce5dec61e596773d2b.jpg", + "image_caption": [ + "Figure 7. Comparisons regarding robustness to light variation between various SfP methods on our testing set. The horizontal axis represents different objects." + ], + "image_footnote": [], + "bbox": [ + 86, + 429, + 455, + 530 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "while keeping the viewing direction unchanged. Accordingly, each pixel is associated with a set of angular errors. We compute the variance of the error set of each pixel, followed by obtaining the mean of these variances. Figs. 6 and 7 show that under different illumination conditions, existing SfP approaches lead to unstable recovery results (i.e., the variance is large) and are sensitive to light variation. By contrast, the recovery results of our method are stable and the accuracy remains high despite light variation. The reason is that our network leverages redundant stereo information, and also extracts both local and global contexts for stable estimation.", + "bbox": [ + 75, + 594, + 468, + 773 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.2. Joint Estimation of Disparity and Normal", + "text_level": 1, + "bbox": [ + 76, + 786, + 431, + 801 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Methods for Comparison. Recall that our method can recover both normal and disparity maps. To evaluate performance, we compare our method with two well-known baselines, i.e., Long [28] and Kusupati [24] for joint estimation of normal and depth (depth and disparity are basically equivalent). These methods originally take stereo", + "bbox": [ + 75, + 809, + 467, + 900 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/93b0511410f36b7cdb7e59b86962bc3aec5278be6ce5b95c2cbcefe23e340174.jpg", + "image_caption": [ + "Figure 8. Representative comparisons between various methods for joint estimation of normal and disparity. (a) Intensity images of recovered objects. (b) The first and third rows show the normal maps. The second and fourth rows show the disparity maps. The meanings of numbers below each normal map are the same as those in Fig. 5. The number below each disparity map represents the mean of disparity errors. $\\dagger$ : the same network inputs as ours." + ], + "image_footnote": [], + "bbox": [ + 506, + 87, + 883, + 405 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/45a2e733c8918565ddde7e12c4d6ee1bc4590cf3d3a6d9603c44343284fa1408.jpg", + "table_caption": [ + "Table 3. Accuracy comparisons between various methods for joint estimation of normal and disparity on all the data of our testing set. $\\dagger$ : the same network inputs as ours." + ], + "table_footnote": [], + "table_body": "
MethodAngular Error (deg.)Disparity Error (pix.)
MeanMedianMeanMedian
Long [28]†22.3418.593.913.02
Kusupati [24]†19.6916.113.262.79
Ours13.2211.142.111.98
", + "bbox": [ + 501, + 556, + 890, + 638 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "intensity images as inputs. For an unbiased comparison, we replace their inputs with the physical priors we use (see Section 3.2). Accordingly, we adjust and retrain their networks following their original setups.", + "bbox": [ + 496, + 656, + 890, + 717 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Accuracy of Normal and Disparity. As shown in Table 3 and Fig. 8, Long and Kusupati lead to relatively unsatisfactory results. By contrast, our method can achieve the highest accuracy for both normal and disparity estimation. The reason is that our network architecture can leverage the polarization information, and also alleviate the ambiguity and orthographic projection problems in SfP.", + "bbox": [ + 496, + 717, + 890, + 823 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 832, + 651, + 848 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, we conduct ablation studies regarding our network inputs, SCMP module, and VDPE design.", + "bbox": [ + 498, + 854, + 890, + 883 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Network Inputs. Recall that we take AoLP&DoLP and", + "bbox": [ + 500, + 885, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "17293", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/21a62e2038d4516158aefab3ab027fb31d7b14cc511ae8c7f37bc022c7889344.jpg", + "table_caption": [ + "Table 4. Ablation study regarding different network inputs on all the data of our testing set." + ], + "table_footnote": [], + "table_body": "
Network InputsAngular Error (deg.)Disparity Error (pix.)
MeanMedianMeanMedian
Intensity images33.2530.617.236.15
Raw polarization19.6516.945.194.78
AoLP&DoLP16.5112.864.233.97
Stokes maps17.1315.253.693.12
Inputs as DeepSfP [3]16.1214.374.053.68
Original (AoLP&DoLP and Stokes maps)13.2211.142.111.98
", + "bbox": [ + 78, + 125, + 468, + 253 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/d2d0554380de29a254b97373006f74aa520d466454a6dc3bfea0473852d514cf.jpg", + "table_caption": [ + "Table 5. Ablation study regarding SCMP module on all the data of our testing set." + ], + "table_footnote": [], + "table_body": "
Network DesignAngular Error (deg.)Disparity Error (pix.)
MeanMedianMeanMedian
Without any SCMP22.1318.933.623.11
Without first SCMP16.2114.772.912.49
Without second SCMP15.2314.162.582.17
Original (with both SCMPs)13.2211.142.111.98
", + "bbox": [ + 78, + 306, + 468, + 401 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Stokes maps as the network inputs (see Section 3.2). We replace these inputs with 1) intensity images, 2) raw polarization images, 3) AoLP&DoLP, 4) Stokes maps, and 5) inputs as DeepSfP, respectively. Table 4 shows that our network with original inputs leads to the highest recovery accuracy on both normal and disparity. The reason is that AoLP&DoLP and Stokes maps complement each other and facilitate the usage of polarization cues for our network.", + "bbox": [ + 75, + 429, + 468, + 549 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "SCMP Module. Recall that we embed two SCMP modules in our network for coarse-to-fine feature refinement to solve the ambiguity problem (see Section 3.3). In this study, we compare our strategy with the simplified designs: 1) without any SCMP module, 2) without the first SCMP module, 3) without the second SCMP module. Table 5 shows that with only one SCMP module (regardless of the first or second one), the network can still achieve improvement in normal recovery accuracy, which proves the effectiveness of SCMP. In addition, the effect of the first module is more obvious. By contrast, our original design achieves the highest accuracy, demonstrating the effectiveness of our feature refinement strategy.", + "bbox": [ + 75, + 551, + 468, + 748 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "VDPE Design. Recall that we use the VDPE design in our network to handle the non-orthographic projection (see Section 3.4). In this study, we compare our design with the other encoding strategies: 1) classical position encoding methods based on Absolute Positional Embedding (APE) [43] or Relative Positional Embedding (RPE) [38], 2) viewing encoding (VE) of Lei [25]. Table 6 shows that compared with APE and RPE, both VE and our VDPE show improvement since they introduce the viewing directions and enable the networks to handle the non-orthographic", + "bbox": [ + 75, + 750, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/68a29954a7e10fbd221e27c8de3cfac80bdedcaac412d953d30552b5c4d903b1.jpg", + "image_caption": [ + "Figure 9. Representative ablation study regarding VDPE design. The meanings of numbers below each normal map are the same as those in Fig. 5. The second row shows the error maps corresponding to the normal maps." + ], + "image_footnote": [], + "bbox": [ + 501, + 85, + 885, + 244 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/4f79c88e772c49a3569a588929eeeb0f35051992e77f16c1ed9ea814bcd3b8bd.jpg", + "table_caption": [ + "Table 6. Ablation study regarding VDPE design on all the data of our testing set." + ], + "table_footnote": [], + "table_body": "
Encoding StrategyAngular Error (deg.)Disparity Error (pix.)
MeanMedianMeanMedian
APE [43]17.6815.633.152.81
RPE [38]16.4314.793.112.56
VE [25]15.8914.172.932.42
Original (VDPE)13.2211.142.111.98
", + "bbox": [ + 501, + 358, + 890, + 454 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "projection. Moreover, the proposed VDPE design is more accurate than VE. Fig. 9 shows that RPE and VE both suffer from the non-orthographic projection problem and show higher errors on the area far from the image center. By contrast, our VDPE design avoids this problem and achieves better recovery results. The reason is that our design treats the viewing directions as part of the positional encoding in Transformer, which enhances the usage of viewing directions by global attention.", + "bbox": [ + 496, + 474, + 890, + 609 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusions", + "text_level": 1, + "bbox": [ + 500, + 631, + 625, + 646 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we propose the first approach that combines stereo polarimetric imaging and deep learning to recover accurate normal and disparity. We design a mask prediction module to solve the ambiguity problem based on the shape consistency between normal and disparity. In addition, we propose a novel positional encoding method to solve the orthographic projection problem. Moreover, we establish a large real-world dataset for stereo SfP problem. Experiments on the proposed dataset demonstrate that our method outperforms existing SfP methods in terms of accuracy and robustness to light variation.", + "bbox": [ + 496, + 659, + 890, + 825 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement. This work is supported in part by the CUHK T Sone Robotics Institute, and in part by the InnoHK of the Government of Hong Kong via the Hong Kong Centre for Logistics Robotics.", + "bbox": [ + 496, + 839, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "17294", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Gary A Atkinson. Polarisation photometric stereo. Computer Vision and Image Understanding, 160:158-167, 2017. 2", + "[2] Gary A Atkinson and Edwin R Hancock. Recovery of surface orientation from diffuse polarization. IEEE transactions on image processing, 15(6):1653-1664, 2006. 1, 2, 3", + "[3] Yunhao Ba, Alex Gilbert, Franklin Wang, Jinfa Yang, Rui Chen, Yiqin Wang, Lei Yan, Boxin Shi, and Achuta Kadambi. Deep shape from polarization. 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In IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 7586-7595, 2019. 3, 6" + ], + "bbox": [ + 501, + 92, + 892, + 527 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "17296", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Learning Accurate 3D Shape Based on Stereo Polarimetric Imaging/44df70c3-8a85-4f37-a0ff-da1913972e67_model.json b/2023/Learning Accurate 3D Shape Based on Stereo Polarimetric Imaging/44df70c3-8a85-4f37-a0ff-da1913972e67_model.json new file mode 100644 index 0000000000000000000000000000000000000000..849c5db48e409ad208ed44095c66b33a1121ad15 --- /dev/null +++ b/2023/Learning Accurate 3D Shape Based on Stereo Polarimetric Imaging/44df70c3-8a85-4f37-a0ff-da1913972e67_model.json @@ -0,0 +1,2178 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.145, + 0.131, + 0.828, + 0.154 + ], + "angle": 0, + "content": "Learning Accurate 3D Shape Based on Stereo Polarimetric Imaging" + }, + { + "type": "text", + "bbox": [ + 0.15, + 0.18, + 0.826, + 0.235 + ], + "angle": 0, + "content": "Tianyu Huang\\(^{1*}\\) Haoang Li\\(^{1,2*}\\) Kejing He\\(^{1}\\) Congying Sui\\(^{1}\\) Bin Li\\(^{1}\\) Yun-Hui Liu\\(^{1\\dagger}\\) \n\\(^{1}\\)The Chinese University of Hong Kong, Hong Kong, China \n\\(^{2}\\)Technical University of Munich, Germany" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.269, + 0.314, + 0.285 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.301, + 0.474, + 0.681 + ], + "angle": 0, + "content": "Shape from Polarization (SfP) aims to recover surface normal using the polarization cues of light. The accuracy of existing SfP methods is affected by two main problems. First, the ambiguity of polarization cues partially results in false normal estimation. Second, the widely-used assumption about orthographic projection is too ideal. To solve these problems, we propose the first approach that combines deep learning and stereo polarization information to recover not only normal but also disparity. Specifically, for the ambiguity problem, we design a Shape Consistency-based Mask Prediction (SCMP) module. It exploits the inherent consistency between normal and disparity to identify the areas with false normal estimation. We replace the unreliable features enclosed by these areas with new features extracted by global attention mechanism. As to the orthographic projection problem, we propose a novel Viewing Direction-aided Positional Encoding (VDPE) strategy. This strategy is based on the unique pixel-viewing direction encoding, and thus enables our neural network to handle the non-orthographic projection. In addition, we establish a real-world stereo SfP dataset that contains various object categories and illumination conditions. Experiments showed that compared with existing SfP methods, our approach is more accurate. Moreover, our approach shows higher robustness to light variation." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.706, + 0.21, + 0.723 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.731, + 0.47, + 0.868 + ], + "angle": 0, + "content": "3D shape recovery is a fundamental problem in computer vision and has been extensively studied [15, 26, 31]. However, existing shape recovery methods have some limitations. For example, the geometry-based methods, e.g., structure from motion [33, 37] have difficulty in dealing with texture-less regions and can only recover sparse point cloud. While the photometric stereo methods [15, 18] can recover dense surface, they need cumbersome photometric calibration. By contrast, shape from polarization" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.27, + 0.892, + 0.346 + ], + "angle": 0, + "content": "(SfP) [11, 20, 40] can avoid the above problems by using the polarization cues of light. Specifically, polarization cues can detect rich geometric details even for white wall [11]. Moreover, such cues can be easily obtained in a single shot with the quad-Bayer polarization camera [46]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.35, + 0.893, + 0.606 + ], + "angle": 0, + "content": "Despite the above advantages of SfP, there remain two main problems that affect the recovery accuracy. First, the ambiguous polarization cues are inevitable due to unidirectional measurement [10]. These cues partially result in false normal estimation. To solve this problem, early SfP methods rely on specific assumptions about shape prior [2, 40] and lead to unsatisfactory recovery accuracy. Recently, some approaches use stereo [16] or multi-view [49] polarization information for disambiguation. However, the accuracy of these methods is limited by the low quality of stereo matching for polarization cues. Second, most existing SfP approaches assume orthographic projection for modelling simplification [35, 40]. Such assumption ignores the influence of viewing directions, which affects the accuracy of polarimetric measurements. A representative work for this problem is based on a perspective phase angle constraint [8], but this constraint is still insufficient." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.611, + 0.895, + 0.761 + ], + "angle": 0, + "content": "In addition to the above attempts to solve the ambiguity and orthographic projection problems, some methods are proposed based on deep learning [3, 12, 23, 25]. They improve the shape recovery accuracy to some extent. However, they still partly suffer from the ambiguity problem due to monocular imaging. By contrast, our method is based on stereo polarimetric imaging. To the best of our knowledge, our approach is the first one that combines stereo polarization information and deep learning to estimate both normal and disparity." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.895, + 0.903 + ], + "angle": 0, + "content": "As shown in Fig. 1, we integrate convolutional neural network (CNN) with Vision Transformer [13, 14] to design the feature extraction module. This module considers both local and global contexts [34] to extract stereo feature maps. For one thing, we use the feature map of the left view to estimate the normal map. For another thing, we exploit the stereo feature maps to generate a polarimetric cost volume. This cost volume aligns stereo features to estimate the disparity map. Our joint estimation of normal and disparity" + }, + { + "type": "page_footnote", + "bbox": [ + 0.094, + 0.875, + 0.434, + 0.888 + ], + "angle": 0, + "content": "* Tianyu Huang and Haoang Li contributed equally to this work." + }, + { + "type": "page_footnote", + "bbox": [ + 0.097, + 0.888, + 0.321, + 0.9 + ], + "angle": 0, + "content": "† Yun-Hui Liu is the corresponding author." + }, + { + "type": "list", + "bbox": [ + 0.094, + 0.875, + 0.434, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "17287" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.102, + 0.089, + 0.868, + 0.27 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.272, + 0.895, + 0.302 + ], + "angle": 0, + "content": "Figure 1. Overview of the proposed approach. Given a pair of stereo polarization images, our method can simultaneously recover normal map and disparity map with high quality." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.311, + 0.47, + 0.341 + ], + "angle": 0, + "content": "contributes to solving the above-mentioned problems in SfP, which is introduced in the following." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.342, + 0.471, + 0.552 + ], + "angle": 0, + "content": "For the ambiguity problem, we design a Shape Consistency-based Mask Prediction (SCMP) module. This module predicts a mask to identify the areas with inaccurate normal estimation caused by unreliable features in the feature map. We use these areas to achieve a coarse-to-fine refinement for the feature map. At each step, we replace the features enclosed by such areas with new features extracted by the global attention mechanism in Transformer. As to the orthographic projection problem, we introduce a novel Viewing Direction-aided Positional Encoding (VDPE) strategy to Transformer. Based on the pixel-viewing direction encoding, this strategy enables our neural network to handle non-orthographic projection. Moreover, we establish a large real-world stereo SfP dataset." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.553, + 0.47, + 0.613 + ], + "angle": 0, + "content": "To summarize, we propose the first approach that combines stereo polarimetric imaging and deep learning to recover accurate normal and disparity maps simultaneously. Our main contributions are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.617, + 0.47, + 0.663 + ], + "angle": 0, + "content": "- We design a mask prediction module to reduce the effect of ambiguous polarization cues based on the consistency between normal and disparity." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.666, + 0.47, + 0.712 + ], + "angle": 0, + "content": "- We propose a novel positional encoding design that enables our network to handle the non-orthographic projection in polarimetric measurement." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.716, + 0.47, + 0.761 + ], + "angle": 0, + "content": "- We establish a large real-world dataset for stereo SfP problem. Our dataset contains various object categories and illumination conditions." + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.617, + 0.47, + 0.761 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.47, + 0.811 + ], + "angle": 0, + "content": "Extensive experiments showed that compared with existing methods, our approach is more accurate. Moreover, our approach shows higher robustness to light variation." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.823, + 0.22, + 0.839 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.849, + 0.469, + 0.879 + ], + "angle": 0, + "content": "We first review SfP methods that typically use pure polarization cues with monocular setup. We then introduce the" + }, + { + "type": "text", + "bbox": [ + 0.506, + 0.311, + 0.892, + 0.341 + ], + "angle": 0, + "content": "approaches combining polarization and the other cues. Finally, we present works adopting stereo or multi-view setup." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.342, + 0.892, + 0.583 + ], + "angle": 0, + "content": "Pure Polarization. Early SfP methods divide the polarization reflection into two cases, i.e., specular reflection [35] and diffuse reflection [2, 19, 29]. These methods model such two cases individually according to object materials. This strategy is impractical since light reflection involves both cases in the real world. Moreover, their assumptions on shape priors lead to over-smooth shape recovery results. Baek et al. [4] introduced a model that can consider two reflection cases simultaneously. However, their model requires the assumption about ideal surface reflection and thus is relatively unreliable. Considering the complexity of light reflection, some methods [3, 12, 23, 25] based on deep learning are proposed. Although these data-driven methods improve the recovery accuracy, they lead to low generalization. The reason is that their networks are trained on relatively small or synthetic datasets." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.584, + 0.893, + 0.885 + ], + "angle": 0, + "content": "Polarization \\(+\\mathbf{X}\\). The above pure polarization-based methods suffer from the ambiguity problem of polarization cues. To solve this problem, recent works attempt to introduce additional shape-from-X cues (X represents shading, photometry, depth, etc.). With the cues of shading, Smith et al. [39, 40] proposed to generate a large linear system to directly calculate the height of each pixel. However, their assumptions about the known refractive index and orthographic camera projection limit the recovery accuracy. Ngo et al. [32] combined the polarization with shading cues to additionally estimate the refractive index. Nevertheless, their method needs at least two light directions and is time-consuming. In addition, given the cues of photometry, Atkinson et al. [1] used two calibrated photometric systems to reduce the effects of polarization ambiguity. Tozza et al. [41] improved their method by solving the uncalibrated case. Moreover, based on the cues of depth, Kadambi et al. [21] used the geometric constraints of normals to refine the depth map. This method relies on redundant depth alignment, which leads to low efficiency." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.886, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Stereo and Multi-view Polarization. Stereo or multi-view" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.458, + 0.902 + ], + "angle": 0, + "content": "1https://tyhuang98.github.io/learn_stereo_sfp/" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17288" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.334 + ], + "angle": 0, + "content": "imaging setup contributes to the disambiguation of polarization cues. For example, Cui et al. [11] proposed an is-depth contour tracing mechanism in their multi-view setup to fuse the estimated depth and normal maps. Chen et al. [9] proposed a theoretical polarimetric transport model to constrain the recovery solutions from three views. Zhu and Smith [50] adopted a pair of polarization and RGB images. They introduced a high-order graphical model to label the diffuse-dominant and specular-dominant pixels separately, followed by shape recovery. Recently, Fukao et al. [16] proposed an approach to recover per-pixel normals using stereo polarimetric images. They treated the Stokes vector as polarization cues and constructed a cost volume to regress normals. Compared with the above methods, our approach is more robust to noise thanks to our proposed modules, as will be shown in the experiments." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.357, + 0.251, + 0.374 + ], + "angle": 0, + "content": "3. Proposed Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.385, + 0.471, + 0.491 + ], + "angle": 0, + "content": "In Section 3.1, we introduce the basic knowledge of polarization. In Section 3.2, we give an overview of our pipeline. In Section 3.3, we introduce the SCMP module that enables our method to solve the ambiguity problem. In Section 3.4, we introduce our VDPE design that aims at handling the non-orthographic projection. In Section 3.5, we introduce our loss function." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.507, + 0.363, + 0.525 + ], + "angle": 0, + "content": "3.1. Basic Knowledge of Polarization" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.534, + 0.47, + 0.595 + ], + "angle": 0, + "content": "Let us consider a partially polarized light that orthographically passes through a linear polarizer with an angle of \\(\\phi_{\\mathrm{pol}}\\). The measured intensity of this light follows a sinusoidal variation [10] as" + }, + { + "type": "equation", + "bbox": [ + 0.097, + 0.608, + 0.469, + 0.657 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} I _ {\\phi_ {\\mathrm {p o l}}} = \\frac {I _ {\\operatorname* {m a x}} + I _ {\\operatorname* {m i n}}}{2} + \\frac {I _ {\\operatorname* {m a x}} - I _ {\\operatorname* {m i n}}}{2} \\cos (2 \\phi_ {\\mathrm {p o l}} - 2 \\phi) \\tag {1} \\\\ = \\bar {I} + \\rho \\bar {I} \\cos (2 \\phi_ {\\mathrm {p o l}} - 2 \\phi), \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.671, + 0.47, + 0.868 + ], + "angle": 0, + "content": "where \\( I_{\\mathrm{max}} \\) and \\( I_{\\mathrm{min}} \\) denote the upper and lower bounds of the detected light intensity, \\( \\phi \\) denotes the angle of linear polarization (AoLP), \\( \\rho \\) denotes the degree of linear polarization (DoLP), \\( \\bar{I} \\) denotes the average intensity. Based on Eq. (1), two polarization angles \\( \\phi \\) and \\( \\phi' \\) with a \\( \\pi \\)-shift \\( (\\phi' = \\phi \\pm \\pi) \\) result in the same observed light intensity, which is called \\( \\pi \\)-ambiguity problem. With the linear quad-Bayer polarization camera [46], we can measure intensities in different angles of polarizer. By combining these intensities, we can solve the above unknown polarization parameters: \\( \\phi \\) with \\( \\pi \\)-ambiguity, \\( \\rho \\), and \\( \\bar{I} \\). These parameters have been proved to be highly related to the surface normal [2, 35]. Details are available in the supplementary material." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.902 + ], + "angle": 0, + "content": "In addition, there is another representation to describe the polarization state of light [10], i.e., the Stokes vector:" + }, + { + "type": "equation", + "bbox": [ + 0.584, + 0.088, + 0.892, + 0.153 + ], + "angle": 0, + "content": "\\[\n\\mathbf {s} = \\left[ \\begin{array}{c} s _ {0} \\\\ s _ {1} \\\\ s _ {2} \\\\ s _ {3} \\end{array} \\right] = \\left[ \\begin{array}{c} I _ {0} + I _ {9 0} \\\\ I _ {0} - I _ {9 0} \\\\ I _ {4 5} - I _ {1 3 5} \\\\ 0 \\end{array} \\right], \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.162, + 0.894, + 0.268 + ], + "angle": 0, + "content": "where \\( s_0 \\) represents the light intensity; \\( s_1 \\) and \\( s_2 \\) represent the linear polarization components in \\( 0^\\circ \\) and \\( 45^\\circ \\), respectively; \\( s_3 \\) represents the right circular polarization component. The Stokes vector \\( \\mathbf{s} \\) in Eq. (2) can be expressed by the measured intensities \\( I_0, I_{45}, I_{90} \\) and \\( I_{135} \\). In our context, we follow [12] to call the normalized Stokes vector image \"Stokes map\"." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.279, + 0.677, + 0.296 + ], + "angle": 0, + "content": "3.2. Pipeline Overview" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.304, + 0.892, + 0.47 + ], + "angle": 0, + "content": "As shown in Fig. 1, given the measured stereo polarization images, we compute AoLP&DoLP and Stokes maps, and treat them as the physical priors. By taking these priors as inputs, our network uses a weight-shared feature extraction module to extract stereo feature maps. Our feature extraction is based on the combination of CNN and Transformer to consider both local and global contexts. Note that our Transformer is adapted by the proposed VDPE design (see Section 3.4) to handle the non-orthographic projection. Based on the extracted stereo feature maps, our network predicts both normal and disparity maps." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.471, + 0.892, + 0.547 + ], + "angle": 0, + "content": "Disparity Map. Given the stereo feature maps, we generate a polarimetric cost volume. This volume aligns stereo features and encapsulates the disparity information [22]. We process such volume by a series of Conv3d blocks [42] and the Soft ArgMin operation [22] to infer the disparity map." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.548, + 0.892, + 0.7 + ], + "angle": 0, + "content": "Normal Map. The extracted feature map of the left view is associated with the unknown-but-sought normal map. However, due to the ambiguity problem of polarization cues, this feature map needs to be refined. To achieve this goal, we propose a coarse-to-fine feature refinement strategy. This refinement is based on the proposed SCMP module (see Section 3.3) and Transformer. Our SCMP module incorporates the above cost volume since there exists inherent consistency between disparity and normal. After refinement, the feature map is used to infer the normal map." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.71, + 0.862, + 0.728 + ], + "angle": 0, + "content": "3.3. Shape Consistency-based Mask Prediction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.903 + ], + "angle": 0, + "content": "Leveraging the shape consistency between normal and disparity can improve the shape recovery accuracy. Let us first intuitively explain the reason. For one thing, the normal map estimated by polarization cues are per-pixel. However, the normals in some areas are false due to the ambiguity problem, and we cannot obtain a mask to exclude such areas a priori. For another thing, given a disparity map, we can compute a normal map that is globally reliable but coarse. The correct normals labelled by the unknown-but-sought mask are relatively consistent with the normals computed by the disparity map. We leverage such consistency" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17289" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.118, + 0.087, + 0.434, + 0.213 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.198, + 0.215, + 0.351, + 0.227 + ], + "angle": 0, + "content": "(a) Proposed SCMP module." + }, + { + "type": "image", + "bbox": [ + 0.149, + 0.234, + 0.401, + 0.324 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.136, + 0.326, + 0.406, + 0.338 + ], + "angle": 0, + "content": "(b) The mask embedding operation in our network." + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.34, + 0.47, + 0.397 + ], + "angle": 0, + "content": "Figure 2. Illustration of proposed SCMP module and mask embedding operation. (a) Based on shape consistency, the proposed SCMP module predicts a mask. (b) We employ the predicted mask to purify the feature map \\( F_{1} / F_{2} \\) by a mask embedding operation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.409, + 0.47, + 0.439 + ], + "angle": 0, + "content": "to identify this mask by introducing the SCMP module. We will introduce our module details in the following." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.44, + 0.471, + 0.697 + ], + "angle": 0, + "content": "As shown in Fig. 1, we embed two SCMP modules into our network. Fig. 2(a) shows how our first and second SCMP modules are used in our coarse-to-fine feature refinement. Specifically, at the \"coarse\" stage, we take the original feature map \\( F_{1} \\) of the left view and the polarimetric cost volume \\( C_{1} \\) as inputs of the first SCMP module. At the \"fine\" stage, we feed the intermediate feature map \\( F_{2} \\) and cost volume \\( C_{2} \\) to the second SCMP module. At each stage, an initial normal map can be inferred from the feature map \\( F_{1} \\) or \\( F_{2} \\) under supervision. Meanwhile, an initial disparity map can be regressed from the cost volume \\( C_{1} \\) or \\( C_{2} \\) under supervision. Based on this disparity map, we compute a rough normal map using an adaptive normal estimation method [27]. We then exploit the consistency between the normal inferred by our network and the normal computed based on disparity to predict a mask. Specifically, the value \\( v_{i} \\) of the \\( i \\)-th pixel in this mask is computed by" + }, + { + "type": "equation", + "bbox": [ + 0.168, + 0.705, + 0.47, + 0.739 + ], + "angle": 0, + "content": "\\[\nv _ {i} = \\left\\{ \\begin{array}{l l} 0, & \\text {i f} \\mathbf {n} _ {i} ^ {N} \\cdot \\mathbf {n} _ {i} ^ {D} < \\tau \\\\ 1, & \\text {o t h e r w i s e} \\end{array} , \\right. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.47, + 0.854 + ], + "angle": 0, + "content": "where “.” denotes the dot product, \\(\\mathbf{n}_i^N\\) and \\(\\mathbf{n}_i^D\\) are the normals inferred by our network and computed based on disparity, respectively, \\(\\tau\\) is a threshold. When \\(\\mathbf{n}_i^N\\cdot \\mathbf{n}_i^D\\) is smaller than the threshold \\(\\tau\\), the consistency is violated. In our paper, \\(\\tau\\) is 0.7 and 0.9 in the first and second SCMP modules, respectively. We adopt such threshold setup to achieve coarse-to-fine feature refinement." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.471, + 0.901 + ], + "angle": 0, + "content": "We then employ the above mask to purify the feature map \\( F_{1} \\) or \\( F_{2} \\) by a mask embedding operation (see Fig. 2(b)). Each unreliable feature in the areas with false" + }, + { + "type": "image", + "bbox": [ + 0.531, + 0.088, + 0.859, + 0.203 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.205, + 0.892, + 0.233 + ], + "angle": 0, + "content": "Figure 3. Illustration of proposed VDPE design. For ease of understanding, we only show the self-attention part in the Transformer." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.251, + 0.892, + 0.371 + ], + "angle": 0, + "content": "normal estimation is set to zero vector. Then the purified feature map is fed to Transformer for global attention. Thanks to the mask embedding, the effect of the unreliable features resulting in false normal estimation is reduced. In addition, the global attention mechanism in Transformer extracts new features for the masked areas by combing global reliable features. Based on such features, the false normals can be re-estimated in an accurate way." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.385, + 0.88, + 0.402 + ], + "angle": 0, + "content": "3.4. Viewing Direction-aided Positional Encoding" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.41, + 0.893, + 0.651 + ], + "angle": 0, + "content": "Most existing SfP works [35, 39] assume orthographic projection (i.e., viewing directions of all pixels are \\([0,0,1]^{\\top}\\)). This assumption affects the accuracy of polarimetric measurement and further the accuracy of shape recovery. Intuitively, additionally using a viewing direction map can alleviate this problem. We generate this map based on the pixel-viewing direction encoding, i.e., each pixel in this map is associated with a unique viewing direction. To introduce such map into neural network, a straightforward strategy is to feed it to CNN [25]. However, it is well-known that the feature extracted by CNN lacks global information. By contrast, we propose to integrate this map into Transformer. This integration is based on the proposed VDPE design (see the next paragraph). As will be shown in the experiments, such design is more effective than the strategy based on CNN." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.654, + 0.892, + 0.773 + ], + "angle": 0, + "content": "As shown in Fig. 3, we integrate the viewing direction map into the self-attention part of Transformer. Specifically, we reshape the viewing direction map and concatenate it with the linearly projected value in the self-attention block. Then the concatenated volume is passed to a Multi-Layer Perception (MLP) layer to embed with the attention calculation. After that, the self-attention computation result can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.515, + 0.781, + 0.892, + 0.817 + ], + "angle": 0, + "content": "\\[\n\\operatorname {O u t p u t} = \\left(\\operatorname {S o f t M a x} \\left(\\frac {Q K ^ {\\top}}{\\sqrt {D}}\\right) V\\right) \\oplus \\left(\\operatorname {M L P} (V \\oplus v)\\right), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.892, + 0.901 + ], + "angle": 0, + "content": "where \\(V, K, Q\\) represent the linearly projected value, key and query respectively, \\(\\nu\\) is the viewing direction map, \\(D\\) is the feature dimension, “\\(\\oplus\\)” represents the concatenation operation. Based on Eq. (4), our method can handle the non-orthographic projection reliably." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17290" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.892, + 0.118 + ], + "angle": 0, + "content": "Table 1. Comparison among existing SfP datasets. Our dataset is the first stereo SfP dataset at the object level. Meanwhile, our acquisition is under controlled illumination and does not need reprojection." + }, + { + "type": "table", + "bbox": [ + 0.127, + 0.12, + 0.839, + 0.212 + ], + "angle": 0, + "content": "
DatasetLevelTypeSetupControlled IlluminationReprojection Operation
DeepSfP [3]ObjectReal-worldMonocularNoYes
Kondo et al. [23]SceneSyntheticMonocularYesNo
Deschaintre et al. [12]ObjectSyntheticMonocularYesNo
SPW [25]SceneReal-worldMonocularNoYes
CroMo [44]SceneReal-worldStereoNoYes
OursObjectReal-worldStereoYesNo
" + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.229, + 0.258, + 0.36 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.165, + 0.362, + 0.182, + 0.371 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.271, + 0.229, + 0.462, + 0.358 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.338, + 0.362, + 0.356, + 0.372 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.373, + 0.47, + 0.416 + ], + "angle": 0, + "content": "Figure 4. We establish a real-world stereo SfP dataset, which contains rich shapes and material categories. (a) Representative image pairs. (b) Data capture setup." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.427, + 0.222, + 0.441 + ], + "angle": 0, + "content": "3.5. Loss Function" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.45, + 0.47, + 0.631 + ], + "angle": 0, + "content": "For network training, we use the normal loss and the disparity loss. For the normal loss, we adopt the commonly used cosine similarity loss [6, 7]. Our normal loss consists of three sub-losses \\(\\mathcal{N}_1\\), \\(\\mathcal{N}_2\\), and \\(\\mathcal{N}_{\\mathrm{final}}\\). \\(\\mathcal{N}_1\\) and \\(\\mathcal{N}_2\\) correspond to the initial normal maps in the first and second SCMP modules, respectively. \\(\\mathcal{N}_{\\mathrm{final}}\\) is related to the final predicted normal map of our network. As to the disparity loss, we adopt the widely-used smooth \\(L_{1}\\) loss [5, 17]. Our disparity loss consists of three sub-losses \\(\\mathcal{D}_1\\), \\(\\mathcal{D}_2\\), and \\(\\mathcal{D}_{\\mathrm{final}}\\). \\(\\mathcal{D}_1\\) and \\(\\mathcal{D}_2\\) correspond to the initial disparity maps in the first and second SCMP modules, respectively. \\(\\mathcal{D}_{\\mathrm{final}}\\) is related to the final predicted disparity map of our network." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.632, + 0.469, + 0.661 + ], + "angle": 0, + "content": "By combing the above sub-losses, we define our final loss \\(\\mathcal{L}\\) as:" + }, + { + "type": "equation", + "bbox": [ + 0.146, + 0.668, + 0.469, + 0.704 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} = \\alpha \\cdot \\left(\\mathcal {N} _ {1} + \\mathcal {N} _ {2}\\right) + \\beta \\cdot \\left(\\mathcal {D} _ {1} + \\mathcal {D} _ {2}\\right) \\tag {5} \\\\ + \\alpha^ {\\prime} \\cdot \\mathcal {N} _ {\\text {f i n a l}} + \\beta^ {\\prime} \\cdot \\mathcal {D} _ {\\text {f i n a l}}, \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.712, + 0.469, + 0.803 + ], + "angle": 0, + "content": "where \\(\\alpha\\), \\(\\beta\\), \\(\\alpha'\\), and \\(\\beta'\\) are the trade-off parameters. During training, we set \\(\\alpha\\) and \\(\\beta\\) as 0.1 for weak supervision since they correspond to the intermediate results. We set \\(\\alpha'\\) and \\(\\beta'\\) as 0.3 for major supervision since they correspond to our final predictions. Further implementation details of our method are available in the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.816, + 0.165, + 0.83 + ], + "angle": 0, + "content": "4. Dataset" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Most existing SfP datasets are either small [3,25] or only provide synthetic images [12, 23]. In addition, their images are obtained by monocular cameras and cannot be used for research on stereo polarimetric imaging. While a recent" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.231, + 0.892, + 0.427 + ], + "angle": 0, + "content": "dataset contains abundant stereo polarization images, it only provides the ground truth depth and ignores the normal [44]. To solve this problem, we propose a large real-world SfP dataset with stereo images associated with the ground truth normal and disparity. Considering that arbitrary illumination has been proved to limit the quality of polarization signal [12], we use the controlled illumination (i.e., unpolarized illumination) for data collection. Moreover, the ground truth shapes of existing real-world SfP datasets [3, 25] are obtained by an extra 3D scanner, which introduces the reprojection operation. By contrast, we propose a more concise acquisition design that can avoid this operation. Table 1 shows the comparison among existing SfP datasets." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.429, + 0.892, + 0.566 + ], + "angle": 0, + "content": "Data Composition. Our dataset consists of 2450 pairs of polarization images. We collect data from more than 50 different objects with various shapes and material categories. For data diversity, we collect images from different viewpoints and different illumination conditions for most objects. Each image pair is associated with the ground truth disparity and normal. Moreover, our dataset involves different stereo baselines between stereo images. Fig. 4(a) shows representative image pairs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.567, + 0.892, + 0.688 + ], + "angle": 0, + "content": "System Setup for Image Collection. When capturing stereo images, we fix a pair of polarization cameras (see Fig. 4(b)) and calibrate them using a standard calibration method [48]. To achieve different illumination conditions, we use an unpolarized light source to illuminate each object from a set of random directions. Moreover, to improve the diversity of illuminations, we use two unpolarized light sources, i.e., the digital projector and a LED lighting." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Acquisition of Ground Truth Maps. To acquire the ground-truth normal and disparity maps, we use a stereo structured-light system. We replace the original grayscale cameras of this system with our stereo polarization camera rig (the grayscale information can be extracted from the polarization information). Based on this adapted system, we employ a Gray code-based reconstruction algorithm [30] to reconstruct the disparity map and point cloud of the object. Finally, we use the least-squares normal estimation algorithm [36] to calculate the normal map of the reconstructed point cloud. Each step of our acquisition does not need reprojection operation mentioned above. Our design ensures perfect alignment of the input polarization image and the ground truth normal and disparity." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "17291" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.101, + 0.087, + 0.874, + 0.472 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.476, + 0.893, + 0.506 + ], + "angle": 0, + "content": "Figure 5. Representative accuracy comparisons between various SfP methods for normal recovery. A pair of numbers below each estimated normal map represents the mean of angular errors and the percentage of pixels with angular errors smaller than \\(11.25^{\\circ}\\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.526, + 0.21, + 0.543 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.551, + 0.47, + 0.686 + ], + "angle": 0, + "content": "We first compare our approach with state-of-the-art SfP methods that aim at normal recovery in Section 5.1. Considering that our approach can predict both normal and disparity, we also compare our method with two baselines that jointly estimate normal and disparity in Section 5.2. In addition, we conduct ablation studies in Section 5.3. All the experiments are conducted on our dataset introduced above. Additional experimental results are available in the supplementary material." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.687, + 0.471, + 0.809 + ], + "angle": 0, + "content": "In terms of evaluation criteria, we follow [25] to evaluate the normal accuracy by the angular error between the estimated and ground truth normals. In addition, we follow [45] to report the percentage of pixels with angular errors smaller than specific thresholds (i.e., \\(11.25^{\\circ}\\), \\(22.5^{\\circ}\\), and \\(30.0^{\\circ}\\)). To evaluate the accuracy of disparity map, we follow [47] to use the absolute errors between the estimated and ground truth disparities." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.817, + 0.332, + 0.833 + ], + "angle": 0, + "content": "5.1. Comparison to SfP Methods" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.84, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Methods for Comparison. We compare our approach with four state-of-the-art SfP methods (i.e., Zhu [50], DeepSfP [3], Fukao [16] and Lei [25]) in terms of normal recovery accuracy and robustness to light variation. As" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.525, + 0.892, + 0.553 + ], + "angle": 0, + "content": "Table 2. Accuracy comparisons between various SfP methods for normal recovery on all the data of our testing set." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.558, + 0.892, + 0.665 + ], + "angle": 0, + "content": "
MethodAngular Error (deg.)Pixel Percentage (%)
MeanMedianRMSE11.25°22.5°30.0°
Zhu [50]37.6934.2743.0112.431.945.7
DeepSfP [3]24.7121.4330.1823.647.467.8
Fukao [16]31.2827.5237.1517.439.554.3
Lei [25]22.2719.3228.6728.855.972.1
Ours13.2211.1417.2246.277.590.1
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.688, + 0.892, + 0.734 + ], + "angle": 0, + "content": "introduced in Section 2, Zhu and Fukao use stereo setup and numerical optimization strategies. DeepSfP and Lei are based on monocular setup and deep learning." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.734, + 0.892, + 0.87 + ], + "angle": 0, + "content": "Normal Recovery Accuracy. As shown in Table 2 and Fig. 5, Zhu and Fukao are affected by the stereo matching quality and thus recover noisy normal maps. DeepSfP shows mistakes in many local areas. While Lei partly alleviates the ambiguity problem, it still loses several details. By contrast, our method achieves the highest accuracy on all the evaluation metrics and also leads to rich object details. This result demonstrates that our integration of deep learning and stereo polarization is effective." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Robustness to Light Variation. To evaluate the robustness to light variation, we use different illumination conditions" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17292" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.171, + 0.089, + 0.226, + 0.131 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.248, + 0.089, + 0.303, + 0.131 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.321, + 0.089, + 0.376, + 0.131 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.266, + 0.133, + 0.282, + 0.143 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.147, + 0.468, + 0.307 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.309, + 0.47, + 0.419 + ], + "angle": 0, + "content": "Figure 6. Representative comparisons regarding robustness to light variation between various SfP methods. (a) Three different illumination conditions. (b) Due to limited space, we only report the results of Fukao, Lei, and our method. Each method corresponds to two columns. The first column shows the recovered normal maps under different illumination conditions. The second column shows the error maps. The number below each column pair represents the mean of variances of angular errors." + }, + { + "type": "image", + "bbox": [ + 0.087, + 0.43, + 0.456, + 0.531 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.535, + 0.47, + 0.577 + ], + "angle": 0, + "content": "Figure 7. Comparisons regarding robustness to light variation between various SfP methods on our testing set. The horizontal axis represents different objects." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.595, + 0.47, + 0.775 + ], + "angle": 0, + "content": "while keeping the viewing direction unchanged. Accordingly, each pixel is associated with a set of angular errors. We compute the variance of the error set of each pixel, followed by obtaining the mean of these variances. Figs. 6 and 7 show that under different illumination conditions, existing SfP approaches lead to unstable recovery results (i.e., the variance is large) and are sensitive to light variation. By contrast, the recovery results of our method are stable and the accuracy remains high despite light variation. The reason is that our network leverages redundant stereo information, and also extracts both local and global contexts for stable estimation." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.787, + 0.433, + 0.803 + ], + "angle": 0, + "content": "5.2. Joint Estimation of Disparity and Normal" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Methods for Comparison. Recall that our method can recover both normal and disparity maps. To evaluate performance, we compare our method with two well-known baselines, i.e., Long [28] and Kusupati [24] for joint estimation of normal and depth (depth and disparity are basically equivalent). These methods originally take stereo" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.088, + 0.885, + 0.406 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.407, + 0.892, + 0.504 + ], + "angle": 0, + "content": "Figure 8. Representative comparisons between various methods for joint estimation of normal and disparity. (a) Intensity images of recovered objects. (b) The first and third rows show the normal maps. The second and fourth rows show the disparity maps. The meanings of numbers below each normal map are the same as those in Fig. 5. The number below each disparity map represents the mean of disparity errors. \\(\\dagger\\): the same network inputs as ours." + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.513, + 0.892, + 0.555 + ], + "angle": 0, + "content": "Table 3. Accuracy comparisons between various methods for joint estimation of normal and disparity on all the data of our testing set. \\(\\dagger\\): the same network inputs as ours." + }, + { + "type": "table", + "bbox": [ + 0.503, + 0.557, + 0.891, + 0.64 + ], + "angle": 0, + "content": "
MethodAngular Error (deg.)Disparity Error (pix.)
MeanMedianMeanMedian
Long [28]†22.3418.593.913.02
Kusupati [24]†19.6916.113.262.79
Ours13.2211.142.111.98
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.657, + 0.892, + 0.718 + ], + "angle": 0, + "content": "intensity images as inputs. For an unbiased comparison, we replace their inputs with the physical priors we use (see Section 3.2). Accordingly, we adjust and retrain their networks following their original setups." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.718, + 0.892, + 0.824 + ], + "angle": 0, + "content": "Accuracy of Normal and Disparity. As shown in Table 3 and Fig. 8, Long and Kusupati lead to relatively unsatisfactory results. By contrast, our method can achieve the highest accuracy for both normal and disparity estimation. The reason is that our network architecture can leverage the polarization information, and also alleviate the ambiguity and orthographic projection problems in SfP." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.833, + 0.653, + 0.849 + ], + "angle": 0, + "content": "5.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.892, + 0.885 + ], + "angle": 0, + "content": "In this section, we conduct ablation studies regarding our network inputs, SCMP module, and VDPE design." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.886, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Network Inputs. Recall that we take AoLP&DoLP and" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "17293" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.47, + 0.118 + ], + "angle": 0, + "content": "Table 4. Ablation study regarding different network inputs on all the data of our testing set." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.125, + 0.469, + 0.255 + ], + "angle": 0, + "content": "
Network InputsAngular Error (deg.)Disparity Error (pix.)
MeanMedianMeanMedian
Intensity images33.2530.617.236.15
Raw polarization19.6516.945.194.78
AoLP&DoLP16.5112.864.233.97
Stokes maps17.1315.253.693.12
Inputs as DeepSfP [3]16.1214.374.053.68
Original (AoLP&DoLP and Stokes maps)13.2211.142.111.98
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.272, + 0.47, + 0.3 + ], + "angle": 0, + "content": "Table 5. Ablation study regarding SCMP module on all the data of our testing set." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.307, + 0.469, + 0.402 + ], + "angle": 0, + "content": "
Network DesignAngular Error (deg.)Disparity Error (pix.)
MeanMedianMeanMedian
Without any SCMP22.1318.933.623.11
Without first SCMP16.2114.772.912.49
Without second SCMP15.2314.162.582.17
Original (with both SCMPs)13.2211.142.111.98
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.43, + 0.469, + 0.55 + ], + "angle": 0, + "content": "Stokes maps as the network inputs (see Section 3.2). We replace these inputs with 1) intensity images, 2) raw polarization images, 3) AoLP&DoLP, 4) Stokes maps, and 5) inputs as DeepSfP, respectively. Table 4 shows that our network with original inputs leads to the highest recovery accuracy on both normal and disparity. The reason is that AoLP&DoLP and Stokes maps complement each other and facilitate the usage of polarization cues for our network." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.552, + 0.469, + 0.749 + ], + "angle": 0, + "content": "SCMP Module. Recall that we embed two SCMP modules in our network for coarse-to-fine feature refinement to solve the ambiguity problem (see Section 3.3). In this study, we compare our strategy with the simplified designs: 1) without any SCMP module, 2) without the first SCMP module, 3) without the second SCMP module. Table 5 shows that with only one SCMP module (regardless of the first or second one), the network can still achieve improvement in normal recovery accuracy, which proves the effectiveness of SCMP. In addition, the effect of the first module is more obvious. By contrast, our original design achieves the highest accuracy, demonstrating the effectiveness of our feature refinement strategy." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.469, + 0.901 + ], + "angle": 0, + "content": "VDPE Design. Recall that we use the VDPE design in our network to handle the non-orthographic projection (see Section 3.4). In this study, we compare our design with the other encoding strategies: 1) classical position encoding methods based on Absolute Positional Embedding (APE) [43] or Relative Positional Embedding (RPE) [38], 2) viewing encoding (VE) of Lei [25]. Table 6 shows that compared with APE and RPE, both VE and our VDPE show improvement since they introduce the viewing directions and enable the networks to handle the non-orthographic" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.087, + 0.886, + 0.245 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.25, + 0.892, + 0.306 + ], + "angle": 0, + "content": "Figure 9. Representative ablation study regarding VDPE design. The meanings of numbers below each normal map are the same as those in Fig. 5. The second row shows the error maps corresponding to the normal maps." + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.324, + 0.892, + 0.352 + ], + "angle": 0, + "content": "Table 6. Ablation study regarding VDPE design on all the data of our testing set." + }, + { + "type": "table", + "bbox": [ + 0.503, + 0.359, + 0.891, + 0.455 + ], + "angle": 0, + "content": "
Encoding StrategyAngular Error (deg.)Disparity Error (pix.)
MeanMedianMeanMedian
APE [43]17.6815.633.152.81
RPE [38]16.4314.793.112.56
VE [25]15.8914.172.932.42
Original (VDPE)13.2211.142.111.98
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.475, + 0.892, + 0.611 + ], + "angle": 0, + "content": "projection. Moreover, the proposed VDPE design is more accurate than VE. Fig. 9 shows that RPE and VE both suffer from the non-orthographic projection problem and show higher errors on the area far from the image center. By contrast, our VDPE design avoids this problem and achieves better recovery results. The reason is that our design treats the viewing directions as part of the positional encoding in Transformer, which enhances the usage of viewing directions by global attention." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.632, + 0.627, + 0.647 + ], + "angle": 0, + "content": "6. Conclusions" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.66, + 0.892, + 0.826 + ], + "angle": 0, + "content": "In this paper, we propose the first approach that combines stereo polarimetric imaging and deep learning to recover accurate normal and disparity. We design a mask prediction module to solve the ambiguity problem based on the shape consistency between normal and disparity. In addition, we propose a novel positional encoding method to solve the orthographic projection problem. Moreover, we establish a large real-world dataset for stereo SfP problem. Experiments on the proposed dataset demonstrate that our method outperforms existing SfP methods in terms of accuracy and robustness to light variation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Acknowledgement. This work is supported in part by the CUHK T Sone Robotics Institute, and in part by the InnoHK of the Government of Hong Kong via the Hong Kong Centre for Logistics Robotics." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17294" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.117, + 0.47, + 0.144 + ], + "angle": 0, + "content": "[1] Gary A Atkinson. Polarisation photometric stereo. Computer Vision and Image Understanding, 160:158-167, 2017. 2" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.147, + 0.47, + 0.189 + ], + "angle": 0, + "content": "[2] Gary A Atkinson and Edwin R Hancock. Recovery of surface orientation from diffuse polarization. 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The accuracy of existing SfP methods is affected by two main problems. First, the ambiguity of polarization cues partially results in false normal estimation. Second, the widely-used assumption about orthographic projection is too ideal. To solve these problems, we propose the first approach that combines deep learning and stereo polarization information to recover not only normal but also disparity. Specifically, for the ambiguity problem, we design a Shape Consistency-based Mask Prediction (SCMP) module. It exploits the inherent consistency between normal and disparity to identify the areas with false normal estimation. We replace the unreliable features enclosed by these areas with new features extracted by global attention mechanism. As to the orthographic projection problem, we propose a novel Viewing Direction-aided Positional Encoding (VDPE) strategy. This strategy is based on the unique pixel-viewing direction encoding, and thus enables our neural network to handle the non-orthographic projection. In addition, we establish a real-world stereo SfP dataset that contains various object categories and illumination conditions. Experiments showed that compared with existing SfP methods, our approach is more accurate. Moreover, our approach shows higher robustness to light variation. + +# 1. Introduction + +3D shape recovery is a fundamental problem in computer vision and has been extensively studied [15, 26, 31]. However, existing shape recovery methods have some limitations. For example, the geometry-based methods, e.g., structure from motion [33, 37] have difficulty in dealing with texture-less regions and can only recover sparse point cloud. While the photometric stereo methods [15, 18] can recover dense surface, they need cumbersome photometric calibration. By contrast, shape from polarization + +(SfP) [11, 20, 40] can avoid the above problems by using the polarization cues of light. Specifically, polarization cues can detect rich geometric details even for white wall [11]. Moreover, such cues can be easily obtained in a single shot with the quad-Bayer polarization camera [46]. + +Despite the above advantages of SfP, there remain two main problems that affect the recovery accuracy. First, the ambiguous polarization cues are inevitable due to unidirectional measurement [10]. These cues partially result in false normal estimation. To solve this problem, early SfP methods rely on specific assumptions about shape prior [2, 40] and lead to unsatisfactory recovery accuracy. Recently, some approaches use stereo [16] or multi-view [49] polarization information for disambiguation. However, the accuracy of these methods is limited by the low quality of stereo matching for polarization cues. Second, most existing SfP approaches assume orthographic projection for modelling simplification [35, 40]. Such assumption ignores the influence of viewing directions, which affects the accuracy of polarimetric measurements. A representative work for this problem is based on a perspective phase angle constraint [8], but this constraint is still insufficient. + +In addition to the above attempts to solve the ambiguity and orthographic projection problems, some methods are proposed based on deep learning [3, 12, 23, 25]. They improve the shape recovery accuracy to some extent. However, they still partly suffer from the ambiguity problem due to monocular imaging. By contrast, our method is based on stereo polarimetric imaging. To the best of our knowledge, our approach is the first one that combines stereo polarization information and deep learning to estimate both normal and disparity. + +As shown in Fig. 1, we integrate convolutional neural network (CNN) with Vision Transformer [13, 14] to design the feature extraction module. This module considers both local and global contexts [34] to extract stereo feature maps. For one thing, we use the feature map of the left view to estimate the normal map. For another thing, we exploit the stereo feature maps to generate a polarimetric cost volume. This cost volume aligns stereo features to estimate the disparity map. Our joint estimation of normal and disparity + +![](images/2c68e4beb4a490b78ad2021f327eaf2f27909e3b0ffa604b117ec20843520d55.jpg) +Figure 1. Overview of the proposed approach. Given a pair of stereo polarization images, our method can simultaneously recover normal map and disparity map with high quality. + +contributes to solving the above-mentioned problems in SfP, which is introduced in the following. + +For the ambiguity problem, we design a Shape Consistency-based Mask Prediction (SCMP) module. This module predicts a mask to identify the areas with inaccurate normal estimation caused by unreliable features in the feature map. We use these areas to achieve a coarse-to-fine refinement for the feature map. At each step, we replace the features enclosed by such areas with new features extracted by the global attention mechanism in Transformer. As to the orthographic projection problem, we introduce a novel Viewing Direction-aided Positional Encoding (VDPE) strategy to Transformer. Based on the pixel-viewing direction encoding, this strategy enables our neural network to handle non-orthographic projection. Moreover, we establish a large real-world stereo SfP dataset. + +To summarize, we propose the first approach that combines stereo polarimetric imaging and deep learning to recover accurate normal and disparity maps simultaneously. Our main contributions are as follows: + +- We design a mask prediction module to reduce the effect of ambiguous polarization cues based on the consistency between normal and disparity. +- We propose a novel positional encoding design that enables our network to handle the non-orthographic projection in polarimetric measurement. +- We establish a large real-world dataset for stereo SfP problem. Our dataset contains various object categories and illumination conditions. + +Extensive experiments showed that compared with existing methods, our approach is more accurate. Moreover, our approach shows higher robustness to light variation. + +# 2. Related Work + +We first review SfP methods that typically use pure polarization cues with monocular setup. We then introduce the + +approaches combining polarization and the other cues. Finally, we present works adopting stereo or multi-view setup. + +Pure Polarization. Early SfP methods divide the polarization reflection into two cases, i.e., specular reflection [35] and diffuse reflection [2, 19, 29]. These methods model such two cases individually according to object materials. This strategy is impractical since light reflection involves both cases in the real world. Moreover, their assumptions on shape priors lead to over-smooth shape recovery results. Baek et al. [4] introduced a model that can consider two reflection cases simultaneously. However, their model requires the assumption about ideal surface reflection and thus is relatively unreliable. Considering the complexity of light reflection, some methods [3, 12, 23, 25] based on deep learning are proposed. Although these data-driven methods improve the recovery accuracy, they lead to low generalization. The reason is that their networks are trained on relatively small or synthetic datasets. + +Polarization $+\mathbf{X}$ . The above pure polarization-based methods suffer from the ambiguity problem of polarization cues. To solve this problem, recent works attempt to introduce additional shape-from-X cues (X represents shading, photometry, depth, etc.). With the cues of shading, Smith et al. [39, 40] proposed to generate a large linear system to directly calculate the height of each pixel. However, their assumptions about the known refractive index and orthographic camera projection limit the recovery accuracy. Ngo et al. [32] combined the polarization with shading cues to additionally estimate the refractive index. Nevertheless, their method needs at least two light directions and is time-consuming. In addition, given the cues of photometry, Atkinson et al. [1] used two calibrated photometric systems to reduce the effects of polarization ambiguity. Tozza et al. [41] improved their method by solving the uncalibrated case. Moreover, based on the cues of depth, Kadambi et al. [21] used the geometric constraints of normals to refine the depth map. This method relies on redundant depth alignment, which leads to low efficiency. + +Stereo and Multi-view Polarization. Stereo or multi-view + +imaging setup contributes to the disambiguation of polarization cues. For example, Cui et al. [11] proposed an is-depth contour tracing mechanism in their multi-view setup to fuse the estimated depth and normal maps. Chen et al. [9] proposed a theoretical polarimetric transport model to constrain the recovery solutions from three views. Zhu and Smith [50] adopted a pair of polarization and RGB images. They introduced a high-order graphical model to label the diffuse-dominant and specular-dominant pixels separately, followed by shape recovery. Recently, Fukao et al. [16] proposed an approach to recover per-pixel normals using stereo polarimetric images. They treated the Stokes vector as polarization cues and constructed a cost volume to regress normals. Compared with the above methods, our approach is more robust to noise thanks to our proposed modules, as will be shown in the experiments. + +# 3. Proposed Method + +In Section 3.1, we introduce the basic knowledge of polarization. In Section 3.2, we give an overview of our pipeline. In Section 3.3, we introduce the SCMP module that enables our method to solve the ambiguity problem. In Section 3.4, we introduce our VDPE design that aims at handling the non-orthographic projection. In Section 3.5, we introduce our loss function. + +# 3.1. Basic Knowledge of Polarization + +Let us consider a partially polarized light that orthographically passes through a linear polarizer with an angle of $\phi_{\mathrm{pol}}$ . The measured intensity of this light follows a sinusoidal variation [10] as + +$$ +\begin{array}{l} I _ {\phi_ {\mathrm {p o l}}} = \frac {I _ {\operatorname* {m a x}} + I _ {\operatorname* {m i n}}}{2} + \frac {I _ {\operatorname* {m a x}} - I _ {\operatorname* {m i n}}}{2} \cos (2 \phi_ {\mathrm {p o l}} - 2 \phi) \tag {1} \\ = \bar {I} + \rho \bar {I} \cos (2 \phi_ {\mathrm {p o l}} - 2 \phi), \\ \end{array} +$$ + +where $I_{\mathrm{max}}$ and $I_{\mathrm{min}}$ denote the upper and lower bounds of the detected light intensity, $\phi$ denotes the angle of linear polarization (AoLP), $\rho$ denotes the degree of linear polarization (DoLP), $\bar{I}$ denotes the average intensity. Based on Eq. (1), two polarization angles $\phi$ and $\phi'$ with a $\pi$ -shift $(\phi' = \phi \pm \pi)$ result in the same observed light intensity, which is called $\pi$ -ambiguity problem. With the linear quad-Bayer polarization camera [46], we can measure intensities in different angles of polarizer. By combining these intensities, we can solve the above unknown polarization parameters: $\phi$ with $\pi$ -ambiguity, $\rho$ , and $\bar{I}$ . These parameters have been proved to be highly related to the surface normal [2, 35]. Details are available in the supplementary material. + +In addition, there is another representation to describe the polarization state of light [10], i.e., the Stokes vector: + +$$ +\mathbf {s} = \left[ \begin{array}{c} s _ {0} \\ s _ {1} \\ s _ {2} \\ s _ {3} \end{array} \right] = \left[ \begin{array}{c} I _ {0} + I _ {9 0} \\ I _ {0} - I _ {9 0} \\ I _ {4 5} - I _ {1 3 5} \\ 0 \end{array} \right], \tag {2} +$$ + +where $s_0$ represents the light intensity; $s_1$ and $s_2$ represent the linear polarization components in $0^\circ$ and $45^\circ$ , respectively; $s_3$ represents the right circular polarization component. The Stokes vector $\mathbf{s}$ in Eq. (2) can be expressed by the measured intensities $I_0, I_{45}, I_{90}$ and $I_{135}$ . In our context, we follow [12] to call the normalized Stokes vector image "Stokes map". + +# 3.2. Pipeline Overview + +As shown in Fig. 1, given the measured stereo polarization images, we compute AoLP&DoLP and Stokes maps, and treat them as the physical priors. By taking these priors as inputs, our network uses a weight-shared feature extraction module to extract stereo feature maps. Our feature extraction is based on the combination of CNN and Transformer to consider both local and global contexts. Note that our Transformer is adapted by the proposed VDPE design (see Section 3.4) to handle the non-orthographic projection. Based on the extracted stereo feature maps, our network predicts both normal and disparity maps. + +Disparity Map. Given the stereo feature maps, we generate a polarimetric cost volume. This volume aligns stereo features and encapsulates the disparity information [22]. We process such volume by a series of Conv3d blocks [42] and the Soft ArgMin operation [22] to infer the disparity map. + +Normal Map. The extracted feature map of the left view is associated with the unknown-but-sought normal map. However, due to the ambiguity problem of polarization cues, this feature map needs to be refined. To achieve this goal, we propose a coarse-to-fine feature refinement strategy. This refinement is based on the proposed SCMP module (see Section 3.3) and Transformer. Our SCMP module incorporates the above cost volume since there exists inherent consistency between disparity and normal. After refinement, the feature map is used to infer the normal map. + +# 3.3. Shape Consistency-based Mask Prediction + +Leveraging the shape consistency between normal and disparity can improve the shape recovery accuracy. Let us first intuitively explain the reason. For one thing, the normal map estimated by polarization cues are per-pixel. However, the normals in some areas are false due to the ambiguity problem, and we cannot obtain a mask to exclude such areas a priori. For another thing, given a disparity map, we can compute a normal map that is globally reliable but coarse. The correct normals labelled by the unknown-but-sought mask are relatively consistent with the normals computed by the disparity map. We leverage such consistency + +![](images/95e5984bb1709244cffabca79e8a3698a369eb2f17e8358ef1ac7cde7244b290.jpg) +(a) Proposed SCMP module. + +![](images/ad848414b5847526e2d9733999fc173f05f4044b1f9ce895c22011afc011cc22.jpg) +(b) The mask embedding operation in our network. +Figure 2. Illustration of proposed SCMP module and mask embedding operation. (a) Based on shape consistency, the proposed SCMP module predicts a mask. (b) We employ the predicted mask to purify the feature map $F_{1} / F_{2}$ by a mask embedding operation. + +to identify this mask by introducing the SCMP module. We will introduce our module details in the following. + +As shown in Fig. 1, we embed two SCMP modules into our network. Fig. 2(a) shows how our first and second SCMP modules are used in our coarse-to-fine feature refinement. Specifically, at the "coarse" stage, we take the original feature map $F_{1}$ of the left view and the polarimetric cost volume $C_{1}$ as inputs of the first SCMP module. At the "fine" stage, we feed the intermediate feature map $F_{2}$ and cost volume $C_{2}$ to the second SCMP module. At each stage, an initial normal map can be inferred from the feature map $F_{1}$ or $F_{2}$ under supervision. Meanwhile, an initial disparity map can be regressed from the cost volume $C_{1}$ or $C_{2}$ under supervision. Based on this disparity map, we compute a rough normal map using an adaptive normal estimation method [27]. We then exploit the consistency between the normal inferred by our network and the normal computed based on disparity to predict a mask. Specifically, the value $v_{i}$ of the $i$ -th pixel in this mask is computed by + +$$ +v _ {i} = \left\{ \begin{array}{l l} 0, & \text {i f} \mathbf {n} _ {i} ^ {N} \cdot \mathbf {n} _ {i} ^ {D} < \tau \\ 1, & \text {o t h e r w i s e} \end{array} , \right. \tag {3} +$$ + +where “.” denotes the dot product, $\mathbf{n}_i^N$ and $\mathbf{n}_i^D$ are the normals inferred by our network and computed based on disparity, respectively, $\tau$ is a threshold. When $\mathbf{n}_i^N\cdot \mathbf{n}_i^D$ is smaller than the threshold $\tau$ , the consistency is violated. In our paper, $\tau$ is 0.7 and 0.9 in the first and second SCMP modules, respectively. We adopt such threshold setup to achieve coarse-to-fine feature refinement. + +We then employ the above mask to purify the feature map $F_{1}$ or $F_{2}$ by a mask embedding operation (see Fig. 2(b)). Each unreliable feature in the areas with false + +![](images/339574c947b73e2bffda48bc3af31feff4337a631f888114843e4ed8c928c462.jpg) +Figure 3. Illustration of proposed VDPE design. For ease of understanding, we only show the self-attention part in the Transformer. + +normal estimation is set to zero vector. Then the purified feature map is fed to Transformer for global attention. Thanks to the mask embedding, the effect of the unreliable features resulting in false normal estimation is reduced. In addition, the global attention mechanism in Transformer extracts new features for the masked areas by combing global reliable features. Based on such features, the false normals can be re-estimated in an accurate way. + +# 3.4. Viewing Direction-aided Positional Encoding + +Most existing SfP works [35, 39] assume orthographic projection (i.e., viewing directions of all pixels are $[0,0,1]^{\top}$ ). This assumption affects the accuracy of polarimetric measurement and further the accuracy of shape recovery. Intuitively, additionally using a viewing direction map can alleviate this problem. We generate this map based on the pixel-viewing direction encoding, i.e., each pixel in this map is associated with a unique viewing direction. To introduce such map into neural network, a straightforward strategy is to feed it to CNN [25]. However, it is well-known that the feature extracted by CNN lacks global information. By contrast, we propose to integrate this map into Transformer. This integration is based on the proposed VDPE design (see the next paragraph). As will be shown in the experiments, such design is more effective than the strategy based on CNN. + +As shown in Fig. 3, we integrate the viewing direction map into the self-attention part of Transformer. Specifically, we reshape the viewing direction map and concatenate it with the linearly projected value in the self-attention block. Then the concatenated volume is passed to a Multi-Layer Perception (MLP) layer to embed with the attention calculation. After that, the self-attention computation result can be formulated as: + +$$ +\operatorname {O u t p u t} = \left(\operatorname {S o f t M a x} \left(\frac {Q K ^ {\top}}{\sqrt {D}}\right) V\right) \oplus \left(\operatorname {M L P} (V \oplus v)\right), \tag {4} +$$ + +where $V, K, Q$ represent the linearly projected value, key and query respectively, $\nu$ is the viewing direction map, $D$ is the feature dimension, “ $\oplus$ ” represents the concatenation operation. Based on Eq. (4), our method can handle the non-orthographic projection reliably. + +Table 1. Comparison among existing SfP datasets. Our dataset is the first stereo SfP dataset at the object level. Meanwhile, our acquisition is under controlled illumination and does not need reprojection. + +
DatasetLevelTypeSetupControlled IlluminationReprojection Operation
DeepSfP [3]ObjectReal-worldMonocularNoYes
Kondo et al. [23]SceneSyntheticMonocularYesNo
Deschaintre et al. [12]ObjectSyntheticMonocularYesNo
SPW [25]SceneReal-worldMonocularNoYes
CroMo [44]SceneReal-worldStereoNoYes
OursObjectReal-worldStereoYesNo
+ +![](images/58972f68f46e8e043a17c15e4bc4b94a5112129229f463e598a20ef0c61cb10f.jpg) +(a) + +![](images/4b421457723c259c6287bf620363912cb7a626098748453099b6f796e24f3c9e.jpg) +(b) +Figure 4. We establish a real-world stereo SfP dataset, which contains rich shapes and material categories. (a) Representative image pairs. (b) Data capture setup. + +# 3.5. Loss Function + +For network training, we use the normal loss and the disparity loss. For the normal loss, we adopt the commonly used cosine similarity loss [6, 7]. Our normal loss consists of three sub-losses $\mathcal{N}_1$ , $\mathcal{N}_2$ , and $\mathcal{N}_{\mathrm{final}}$ . $\mathcal{N}_1$ and $\mathcal{N}_2$ correspond to the initial normal maps in the first and second SCMP modules, respectively. $\mathcal{N}_{\mathrm{final}}$ is related to the final predicted normal map of our network. As to the disparity loss, we adopt the widely-used smooth $L_{1}$ loss [5, 17]. Our disparity loss consists of three sub-losses $\mathcal{D}_1$ , $\mathcal{D}_2$ , and $\mathcal{D}_{\mathrm{final}}$ . $\mathcal{D}_1$ and $\mathcal{D}_2$ correspond to the initial disparity maps in the first and second SCMP modules, respectively. $\mathcal{D}_{\mathrm{final}}$ is related to the final predicted disparity map of our network. + +By combing the above sub-losses, we define our final loss $\mathcal{L}$ as: + +$$ +\begin{array}{l} \mathcal {L} = \alpha \cdot \left(\mathcal {N} _ {1} + \mathcal {N} _ {2}\right) + \beta \cdot \left(\mathcal {D} _ {1} + \mathcal {D} _ {2}\right) \tag {5} \\ + \alpha^ {\prime} \cdot \mathcal {N} _ {\text {f i n a l}} + \beta^ {\prime} \cdot \mathcal {D} _ {\text {f i n a l}}, \\ \end{array} +$$ + +where $\alpha$ , $\beta$ , $\alpha'$ , and $\beta'$ are the trade-off parameters. During training, we set $\alpha$ and $\beta$ as 0.1 for weak supervision since they correspond to the intermediate results. We set $\alpha'$ and $\beta'$ as 0.3 for major supervision since they correspond to our final predictions. Further implementation details of our method are available in the supplementary material. + +# 4. Dataset + +Most existing SfP datasets are either small [3,25] or only provide synthetic images [12, 23]. In addition, their images are obtained by monocular cameras and cannot be used for research on stereo polarimetric imaging. While a recent + +dataset contains abundant stereo polarization images, it only provides the ground truth depth and ignores the normal [44]. To solve this problem, we propose a large real-world SfP dataset with stereo images associated with the ground truth normal and disparity. Considering that arbitrary illumination has been proved to limit the quality of polarization signal [12], we use the controlled illumination (i.e., unpolarized illumination) for data collection. Moreover, the ground truth shapes of existing real-world SfP datasets [3, 25] are obtained by an extra 3D scanner, which introduces the reprojection operation. By contrast, we propose a more concise acquisition design that can avoid this operation. Table 1 shows the comparison among existing SfP datasets. + +Data Composition. Our dataset consists of 2450 pairs of polarization images. We collect data from more than 50 different objects with various shapes and material categories. For data diversity, we collect images from different viewpoints and different illumination conditions for most objects. Each image pair is associated with the ground truth disparity and normal. Moreover, our dataset involves different stereo baselines between stereo images. Fig. 4(a) shows representative image pairs. + +System Setup for Image Collection. When capturing stereo images, we fix a pair of polarization cameras (see Fig. 4(b)) and calibrate them using a standard calibration method [48]. To achieve different illumination conditions, we use an unpolarized light source to illuminate each object from a set of random directions. Moreover, to improve the diversity of illuminations, we use two unpolarized light sources, i.e., the digital projector and a LED lighting. + +Acquisition of Ground Truth Maps. To acquire the ground-truth normal and disparity maps, we use a stereo structured-light system. We replace the original grayscale cameras of this system with our stereo polarization camera rig (the grayscale information can be extracted from the polarization information). Based on this adapted system, we employ a Gray code-based reconstruction algorithm [30] to reconstruct the disparity map and point cloud of the object. Finally, we use the least-squares normal estimation algorithm [36] to calculate the normal map of the reconstructed point cloud. Each step of our acquisition does not need reprojection operation mentioned above. Our design ensures perfect alignment of the input polarization image and the ground truth normal and disparity. + +![](images/ad30351204389398788729be590528b76a9f8a6f40fbefbdb5874b30a70dd075.jpg) +Figure 5. Representative accuracy comparisons between various SfP methods for normal recovery. A pair of numbers below each estimated normal map represents the mean of angular errors and the percentage of pixels with angular errors smaller than $11.25^{\circ}$ . + +# 5. Experiments + +We first compare our approach with state-of-the-art SfP methods that aim at normal recovery in Section 5.1. Considering that our approach can predict both normal and disparity, we also compare our method with two baselines that jointly estimate normal and disparity in Section 5.2. In addition, we conduct ablation studies in Section 5.3. All the experiments are conducted on our dataset introduced above. Additional experimental results are available in the supplementary material. + +In terms of evaluation criteria, we follow [25] to evaluate the normal accuracy by the angular error between the estimated and ground truth normals. In addition, we follow [45] to report the percentage of pixels with angular errors smaller than specific thresholds (i.e., $11.25^{\circ}$ , $22.5^{\circ}$ , and $30.0^{\circ}$ ). To evaluate the accuracy of disparity map, we follow [47] to use the absolute errors between the estimated and ground truth disparities. + +# 5.1. Comparison to SfP Methods + +Methods for Comparison. We compare our approach with four state-of-the-art SfP methods (i.e., Zhu [50], DeepSfP [3], Fukao [16] and Lei [25]) in terms of normal recovery accuracy and robustness to light variation. As + +Table 2. Accuracy comparisons between various SfP methods for normal recovery on all the data of our testing set. + +
MethodAngular Error (deg.)Pixel Percentage (%)
MeanMedianRMSE11.25°22.5°30.0°
Zhu [50]37.6934.2743.0112.431.945.7
DeepSfP [3]24.7121.4330.1823.647.467.8
Fukao [16]31.2827.5237.1517.439.554.3
Lei [25]22.2719.3228.6728.855.972.1
Ours13.2211.1417.2246.277.590.1
+ +introduced in Section 2, Zhu and Fukao use stereo setup and numerical optimization strategies. DeepSfP and Lei are based on monocular setup and deep learning. + +Normal Recovery Accuracy. As shown in Table 2 and Fig. 5, Zhu and Fukao are affected by the stereo matching quality and thus recover noisy normal maps. DeepSfP shows mistakes in many local areas. While Lei partly alleviates the ambiguity problem, it still loses several details. By contrast, our method achieves the highest accuracy on all the evaluation metrics and also leads to rich object details. This result demonstrates that our integration of deep learning and stereo polarization is effective. + +Robustness to Light Variation. To evaluate the robustness to light variation, we use different illumination conditions + +![](images/cfc680a1ebe3dcd97bfee038eeb3cd43cbb1a99e671e81fe6e2859adc4280681.jpg) + +![](images/88d201476d91cf7680c7b59684ebc60922a452d911204979933c99ad6523a4da.jpg) +(a) + +![](images/22dfbc5bad40d0bc9847409601b3ac9a943b25f2e14a3651b2c9ca75d0b37d52.jpg) + +![](images/89cbf1f97f8e699fea147982575173a72aa41d11ab4f84f5c46b889e6912bfa9.jpg) +Figure 6. Representative comparisons regarding robustness to light variation between various SfP methods. (a) Three different illumination conditions. (b) Due to limited space, we only report the results of Fukao, Lei, and our method. Each method corresponds to two columns. The first column shows the recovered normal maps under different illumination conditions. The second column shows the error maps. The number below each column pair represents the mean of variances of angular errors. + +![](images/f856e641252a40dc4fcfb072c3ea7118b3174e68caa84cce5dec61e596773d2b.jpg) +Figure 7. Comparisons regarding robustness to light variation between various SfP methods on our testing set. The horizontal axis represents different objects. + +while keeping the viewing direction unchanged. Accordingly, each pixel is associated with a set of angular errors. We compute the variance of the error set of each pixel, followed by obtaining the mean of these variances. Figs. 6 and 7 show that under different illumination conditions, existing SfP approaches lead to unstable recovery results (i.e., the variance is large) and are sensitive to light variation. By contrast, the recovery results of our method are stable and the accuracy remains high despite light variation. The reason is that our network leverages redundant stereo information, and also extracts both local and global contexts for stable estimation. + +# 5.2. Joint Estimation of Disparity and Normal + +Methods for Comparison. Recall that our method can recover both normal and disparity maps. To evaluate performance, we compare our method with two well-known baselines, i.e., Long [28] and Kusupati [24] for joint estimation of normal and depth (depth and disparity are basically equivalent). These methods originally take stereo + +![](images/93b0511410f36b7cdb7e59b86962bc3aec5278be6ce5b95c2cbcefe23e340174.jpg) +Figure 8. Representative comparisons between various methods for joint estimation of normal and disparity. (a) Intensity images of recovered objects. (b) The first and third rows show the normal maps. The second and fourth rows show the disparity maps. The meanings of numbers below each normal map are the same as those in Fig. 5. The number below each disparity map represents the mean of disparity errors. $\dagger$ : the same network inputs as ours. + +Table 3. Accuracy comparisons between various methods for joint estimation of normal and disparity on all the data of our testing set. $\dagger$ : the same network inputs as ours. + +
MethodAngular Error (deg.)Disparity Error (pix.)
MeanMedianMeanMedian
Long [28]†22.3418.593.913.02
Kusupati [24]†19.6916.113.262.79
Ours13.2211.142.111.98
+ +intensity images as inputs. For an unbiased comparison, we replace their inputs with the physical priors we use (see Section 3.2). Accordingly, we adjust and retrain their networks following their original setups. + +Accuracy of Normal and Disparity. As shown in Table 3 and Fig. 8, Long and Kusupati lead to relatively unsatisfactory results. By contrast, our method can achieve the highest accuracy for both normal and disparity estimation. The reason is that our network architecture can leverage the polarization information, and also alleviate the ambiguity and orthographic projection problems in SfP. + +# 5.3. Ablation Study + +In this section, we conduct ablation studies regarding our network inputs, SCMP module, and VDPE design. + +Network Inputs. Recall that we take AoLP&DoLP and + +Table 4. Ablation study regarding different network inputs on all the data of our testing set. + +
Network InputsAngular Error (deg.)Disparity Error (pix.)
MeanMedianMeanMedian
Intensity images33.2530.617.236.15
Raw polarization19.6516.945.194.78
AoLP&DoLP16.5112.864.233.97
Stokes maps17.1315.253.693.12
Inputs as DeepSfP [3]16.1214.374.053.68
Original (AoLP&DoLP and Stokes maps)13.2211.142.111.98
+ +Table 5. Ablation study regarding SCMP module on all the data of our testing set. + +
Network DesignAngular Error (deg.)Disparity Error (pix.)
MeanMedianMeanMedian
Without any SCMP22.1318.933.623.11
Without first SCMP16.2114.772.912.49
Without second SCMP15.2314.162.582.17
Original (with both SCMPs)13.2211.142.111.98
+ +Stokes maps as the network inputs (see Section 3.2). We replace these inputs with 1) intensity images, 2) raw polarization images, 3) AoLP&DoLP, 4) Stokes maps, and 5) inputs as DeepSfP, respectively. Table 4 shows that our network with original inputs leads to the highest recovery accuracy on both normal and disparity. The reason is that AoLP&DoLP and Stokes maps complement each other and facilitate the usage of polarization cues for our network. + +SCMP Module. Recall that we embed two SCMP modules in our network for coarse-to-fine feature refinement to solve the ambiguity problem (see Section 3.3). In this study, we compare our strategy with the simplified designs: 1) without any SCMP module, 2) without the first SCMP module, 3) without the second SCMP module. Table 5 shows that with only one SCMP module (regardless of the first or second one), the network can still achieve improvement in normal recovery accuracy, which proves the effectiveness of SCMP. In addition, the effect of the first module is more obvious. By contrast, our original design achieves the highest accuracy, demonstrating the effectiveness of our feature refinement strategy. + +VDPE Design. Recall that we use the VDPE design in our network to handle the non-orthographic projection (see Section 3.4). In this study, we compare our design with the other encoding strategies: 1) classical position encoding methods based on Absolute Positional Embedding (APE) [43] or Relative Positional Embedding (RPE) [38], 2) viewing encoding (VE) of Lei [25]. Table 6 shows that compared with APE and RPE, both VE and our VDPE show improvement since they introduce the viewing directions and enable the networks to handle the non-orthographic + +![](images/68a29954a7e10fbd221e27c8de3cfac80bdedcaac412d953d30552b5c4d903b1.jpg) +Figure 9. Representative ablation study regarding VDPE design. The meanings of numbers below each normal map are the same as those in Fig. 5. The second row shows the error maps corresponding to the normal maps. + +Table 6. Ablation study regarding VDPE design on all the data of our testing set. + +
Encoding StrategyAngular Error (deg.)Disparity Error (pix.)
MeanMedianMeanMedian
APE [43]17.6815.633.152.81
RPE [38]16.4314.793.112.56
VE [25]15.8914.172.932.42
Original (VDPE)13.2211.142.111.98
+ +projection. Moreover, the proposed VDPE design is more accurate than VE. Fig. 9 shows that RPE and VE both suffer from the non-orthographic projection problem and show higher errors on the area far from the image center. By contrast, our VDPE design avoids this problem and achieves better recovery results. The reason is that our design treats the viewing directions as part of the positional encoding in Transformer, which enhances the usage of viewing directions by global attention. + +# 6. Conclusions + +In this paper, we propose the first approach that combines stereo polarimetric imaging and deep learning to recover accurate normal and disparity. We design a mask prediction module to solve the ambiguity problem based on the shape consistency between normal and disparity. In addition, we propose a novel positional encoding method to solve the orthographic projection problem. Moreover, we establish a large real-world dataset for stereo SfP problem. Experiments on the proposed dataset demonstrate that our method outperforms existing SfP methods in terms of accuracy and robustness to light variation. + +Acknowledgement. This work is supported in part by the CUHK T Sone Robotics Institute, and in part by the InnoHK of the Government of Hong Kong via the Hong Kong Centre for Logistics Robotics. + +# References + +[1] Gary A Atkinson. Polarisation photometric stereo. Computer Vision and Image Understanding, 160:158-167, 2017. 2 +[2] Gary A Atkinson and Edwin R Hancock. Recovery of surface orientation from diffuse polarization. IEEE transactions on image processing, 15(6):1653-1664, 2006. 1, 2, 3 +[3] Yunhao Ba, Alex Gilbert, Franklin Wang, Jinfa Yang, Rui Chen, Yiqin Wang, Lei Yan, Boxin Shi, and Achuta Kadambi. Deep shape from polarization. In European Conference on Computer Vision, pages 554-571. Springer, 2020. 1, 2, 5, 6, 8 +[4] Seung-Hwan Baek, Daniel S Jeon, Xin Tong, and Min H Kim. 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Springer, 2016. 2, 4 +[40] William AP Smith, Ravi Ramamoorthi, and Silvia Tozza. Height-from-polarisation with unknown lighting or albedo. IEEE transactions on pattern analysis and machine intelligence, 41(12):2875-2888, 2018. 1, 2 +[41] Silvia Tozza, Dizhong Zhu, William Smith, Ravi Ramamoorthi, and Edwin Hancock. Uncalibrated, two source photopolarimetric stereo. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2021. 2 +[42] Du Tran, Lubomir Bourdev, Rob Fergus, Lorenzo Torresani, and Manohar Paluri. Learning spatiotemporal features with 3d convolutional networks. In IEEE international conference on computer vision, pages 4489-4497, 2015. 3 +[43] Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N. Gomez, Lukasz Kaiser, and Illia Polosukhin. Attention is all you need. 2017. 8 + +[44] Yannick Verdie, Jifei Song, Barnabe Mas, Benjamin Busam, Aleš Leonardis, and Steven McDonagh. Cromo: Cross-modal learning for monocular depth estimation. In 2022 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 3927-3937, 2022. 5 +[45] Xiaolong Wang, David Fouhey, and Abhinav Gupta. Designing deep networks for surface normal estimation. In IEEE conference on computer vision and pattern recognition, pages 539-547, 2015. 6 +[46] Tomohiro Yamazaki, Yasushi Maruyama, Yusuke Uesaka, Motoaki Nakamura, Yoshihisa Matoba, Takashi Terada, Kenta Komori, Yoshiyuki Ohba, Shinichi Arakawa, Yasutaka Hirasawa, et al. Four-directional pixel-wise polarization cmos image sensor using air-gap wire grid on $2.5\text{-}\mu \mathrm{m}$ back-illuminated pixels. In 2016 IEEE International Electron Devices Meeting (IEDM), pages 8-7, 2016. 1, 3 +[47] Gengshan Yang, Joshua Manela, Michael Happold, and Deva Ramanan. Hierarchical deep stereo matching on high-resolution images. In IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 5515-5524, 2019. 6 +[48] Zhengyou Zhang. A flexible new technique for camera calibration. 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In IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 7586-7595, 2019. 3, 6 \ No newline at end of file diff --git a/2023/Learning Accurate 3D Shape Based on Stereo Polarimetric Imaging/images.zip b/2023/Learning Accurate 3D Shape Based on Stereo Polarimetric Imaging/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..4fe31b16da8a1960f6cb21506af67e31b72d96dc --- /dev/null +++ b/2023/Learning Accurate 3D Shape Based on Stereo Polarimetric Imaging/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:3e90eb1da4dcb24e454272e37ae6cc2f9ec347cba6ade6832c00db5f40a2b692 +size 609558 diff --git a/2023/Learning Accurate 3D Shape Based on Stereo Polarimetric Imaging/layout.json b/2023/Learning Accurate 3D Shape Based on Stereo Polarimetric Imaging/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..7101e9299e76f6303a87186d473840e93a47a532 --- /dev/null +++ b/2023/Learning Accurate 3D Shape Based on Stereo Polarimetric Imaging/layout.json @@ -0,0 +1,8417 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 88, + 103, + 506, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 88, + 103, + 506, + 121 + ], + "spans": [ + { + "bbox": [ + 88, + 103, + 506, + 121 + ], + "type": "text", + "content": "Learning Accurate 3D Shape Based on Stereo Polarimetric Imaging" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 91, + 142, + 505, + 186 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 142, + 505, + 186 + ], + "spans": [ + { + "bbox": [ + 91, + 142, + 505, + 186 + ], + "type": "text", + "content": "Tianyu Huang" + }, + { + "bbox": [ + 91, + 142, + 505, + 186 + ], + "type": "inline_equation", + "content": "^{1*}" + }, + { + "bbox": [ + 91, + 142, + 505, + 186 + ], + "type": "text", + "content": " Haoang Li" + }, + { + "bbox": [ + 91, + 142, + 505, + 186 + ], + "type": "inline_equation", + "content": "^{1,2*}" + }, + { + "bbox": [ + 91, + 142, + 505, + 186 + ], + "type": "text", + "content": " Kejing He" + }, + { + "bbox": [ + 91, + 142, + 505, + 186 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 91, + 142, + 505, + 186 + ], + "type": "text", + "content": " Congying Sui" + }, + { + "bbox": [ + 91, + 142, + 505, + 186 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 91, + 142, + 505, + 186 + ], + "type": "text", + "content": " Bin Li" + }, + { + "bbox": [ + 91, + 142, + 505, + 186 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 91, + 142, + 505, + 186 + ], + "type": "text", + "content": " Yun-Hui Liu" + }, + { + "bbox": [ + 91, + 142, + 505, + 186 + ], + "type": "inline_equation", + "content": "^{1\\dagger}" + }, + { + "bbox": [ + 91, + 142, + 505, + 186 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 91, + 142, + 505, + 186 + ], + "type": "text", + "content": "The Chinese University of Hong Kong, Hong Kong, China \n" + }, + { + "bbox": [ + 91, + 142, + 505, + 186 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 91, + 142, + 505, + 186 + ], + "type": "text", + "content": "Technical University of Munich, Germany" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "spans": [ + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 45, + 238, + 290, + 539 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 238, + 290, + 539 + ], + "spans": [ + { + "bbox": [ + 45, + 238, + 290, + 539 + ], + "type": "text", + "content": "Shape from Polarization (SfP) aims to recover surface normal using the polarization cues of light. The accuracy of existing SfP methods is affected by two main problems. First, the ambiguity of polarization cues partially results in false normal estimation. Second, the widely-used assumption about orthographic projection is too ideal. To solve these problems, we propose the first approach that combines deep learning and stereo polarization information to recover not only normal but also disparity. Specifically, for the ambiguity problem, we design a Shape Consistency-based Mask Prediction (SCMP) module. It exploits the inherent consistency between normal and disparity to identify the areas with false normal estimation. We replace the unreliable features enclosed by these areas with new features extracted by global attention mechanism. As to the orthographic projection problem, we propose a novel Viewing Direction-aided Positional Encoding (VDPE) strategy. This strategy is based on the unique pixel-viewing direction encoding, and thus enables our neural network to handle the non-orthographic projection. In addition, we establish a real-world stereo SfP dataset that contains various object categories and illumination conditions. Experiments showed that compared with existing SfP methods, our approach is more accurate. Moreover, our approach shows higher robustness to light variation." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 559, + 128, + 572 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 559, + 128, + 572 + ], + "spans": [ + { + "bbox": [ + 47, + 559, + 128, + 572 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 578, + 287, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 578, + 287, + 687 + ], + "spans": [ + { + "bbox": [ + 46, + 578, + 287, + 687 + ], + "type": "text", + "content": "3D shape recovery is a fundamental problem in computer vision and has been extensively studied [15, 26, 31]. However, existing shape recovery methods have some limitations. For example, the geometry-based methods, e.g., structure from motion [33, 37] have difficulty in dealing with texture-less regions and can only recover sparse point cloud. While the photometric stereo methods [15, 18] can recover dense surface, they need cumbersome photometric calibration. By contrast, shape from polarization" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 213, + 545, + 274 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 213, + 545, + 274 + ], + "spans": [ + { + "bbox": [ + 306, + 213, + 545, + 274 + ], + "type": "text", + "content": "(SfP) [11, 20, 40] can avoid the above problems by using the polarization cues of light. Specifically, polarization cues can detect rich geometric details even for white wall [11]. Moreover, such cues can be easily obtained in a single shot with the quad-Bayer polarization camera [46]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 277, + 546, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 277, + 546, + 479 + ], + "spans": [ + { + "bbox": [ + 304, + 277, + 546, + 479 + ], + "type": "text", + "content": "Despite the above advantages of SfP, there remain two main problems that affect the recovery accuracy. First, the ambiguous polarization cues are inevitable due to unidirectional measurement [10]. These cues partially result in false normal estimation. To solve this problem, early SfP methods rely on specific assumptions about shape prior [2, 40] and lead to unsatisfactory recovery accuracy. Recently, some approaches use stereo [16] or multi-view [49] polarization information for disambiguation. However, the accuracy of these methods is limited by the low quality of stereo matching for polarization cues. Second, most existing SfP approaches assume orthographic projection for modelling simplification [35, 40]. Such assumption ignores the influence of viewing directions, which affects the accuracy of polarimetric measurements. A representative work for this problem is based on a perspective phase angle constraint [8], but this constraint is still insufficient." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 483, + 547, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 483, + 547, + 602 + ], + "spans": [ + { + "bbox": [ + 304, + 483, + 547, + 602 + ], + "type": "text", + "content": "In addition to the above attempts to solve the ambiguity and orthographic projection problems, some methods are proposed based on deep learning [3, 12, 23, 25]. They improve the shape recovery accuracy to some extent. However, they still partly suffer from the ambiguity problem due to monocular imaging. By contrast, our method is based on stereo polarimetric imaging. To the best of our knowledge, our approach is the first one that combines stereo polarization information and deep learning to estimate both normal and disparity." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": "As shown in Fig. 1, we integrate convolutional neural network (CNN) with Vision Transformer [13, 14] to design the feature extraction module. This module considers both local and global contexts [34] to extract stereo feature maps. For one thing, we use the feature map of the left view to estimate the normal map. For another thing, we exploit the stereo feature maps to generate a polarimetric cost volume. This cost volume aligns stereo features to estimate the disparity map. Our joint estimation of normal and disparity" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 57, + 693, + 265, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 693, + 265, + 703 + ], + "spans": [ + { + "bbox": [ + 57, + 693, + 265, + 703 + ], + "type": "text", + "content": "* Tianyu Huang and Haoang Li contributed equally to this work." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 59, + 703, + 196, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 703, + 196, + 712 + ], + "spans": [ + { + "bbox": [ + 59, + 703, + 196, + 712 + ], + "type": "text", + "content": "† Yun-Hui Liu is the corresponding author." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "17287" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 62, + 70, + 531, + 213 + ], + "blocks": [ + { + "bbox": [ + 62, + 70, + 531, + 213 + ], + "lines": [ + { + "bbox": [ + 62, + 70, + 531, + 213 + ], + "spans": [ + { + "bbox": [ + 62, + 70, + 531, + 213 + ], + "type": "image", + "image_path": "2c68e4beb4a490b78ad2021f327eaf2f27909e3b0ffa604b117ec20843520d55.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 215, + 547, + 239 + ], + "lines": [ + { + "bbox": [ + 46, + 215, + 547, + 239 + ], + "spans": [ + { + "bbox": [ + 46, + 215, + 547, + 239 + ], + "type": "text", + "content": "Figure 1. Overview of the proposed approach. Given a pair of stereo polarization images, our method can simultaneously recover normal map and disparity map with high quality." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 246, + 287, + 270 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 246, + 287, + 270 + ], + "spans": [ + { + "bbox": [ + 46, + 246, + 287, + 270 + ], + "type": "text", + "content": "contributes to solving the above-mentioned problems in SfP, which is introduced in the following." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 270, + 288, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 270, + 288, + 437 + ], + "spans": [ + { + "bbox": [ + 46, + 270, + 288, + 437 + ], + "type": "text", + "content": "For the ambiguity problem, we design a Shape Consistency-based Mask Prediction (SCMP) module. This module predicts a mask to identify the areas with inaccurate normal estimation caused by unreliable features in the feature map. We use these areas to achieve a coarse-to-fine refinement for the feature map. At each step, we replace the features enclosed by such areas with new features extracted by the global attention mechanism in Transformer. As to the orthographic projection problem, we introduce a novel Viewing Direction-aided Positional Encoding (VDPE) strategy to Transformer. Based on the pixel-viewing direction encoding, this strategy enables our neural network to handle non-orthographic projection. Moreover, we establish a large real-world stereo SfP dataset." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 437, + 287, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 437, + 287, + 485 + ], + "spans": [ + { + "bbox": [ + 46, + 437, + 287, + 485 + ], + "type": "text", + "content": "To summarize, we propose the first approach that combines stereo polarimetric imaging and deep learning to recover accurate normal and disparity maps simultaneously. Our main contributions are as follows:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 58, + 488, + 287, + 602 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 58, + 488, + 287, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 488, + 287, + 525 + ], + "spans": [ + { + "bbox": [ + 58, + 488, + 287, + 525 + ], + "type": "text", + "content": "- We design a mask prediction module to reduce the effect of ambiguous polarization cues based on the consistency between normal and disparity." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 58, + 527, + 287, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 527, + 287, + 563 + ], + "spans": [ + { + "bbox": [ + 58, + 527, + 287, + 563 + ], + "type": "text", + "content": "- We propose a novel positional encoding design that enables our network to handle the non-orthographic projection in polarimetric measurement." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 58, + 567, + 287, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 567, + 287, + 602 + ], + "spans": [ + { + "bbox": [ + 58, + 567, + 287, + 602 + ], + "type": "text", + "content": "- We establish a large real-world dataset for stereo SfP problem. Our dataset contains various object categories and illumination conditions." + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 46, + 605, + 287, + 642 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 642 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 642 + ], + "type": "text", + "content": "Extensive experiments showed that compared with existing methods, our approach is more accurate. Moreover, our approach shows higher robustness to light variation." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 651, + 134, + 664 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 651, + 134, + 664 + ], + "spans": [ + { + "bbox": [ + 47, + 651, + 134, + 664 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 672, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 672, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 47, + 672, + 287, + 696 + ], + "type": "text", + "content": "We first review SfP methods that typically use pure polarization cues with monocular setup. We then introduce the" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 309, + 246, + 545, + 270 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 246, + 545, + 270 + ], + "spans": [ + { + "bbox": [ + 309, + 246, + 545, + 270 + ], + "type": "text", + "content": "approaches combining polarization and the other cues. Finally, we present works adopting stereo or multi-view setup." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 270, + 545, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 270, + 545, + 461 + ], + "spans": [ + { + "bbox": [ + 304, + 270, + 545, + 461 + ], + "type": "text", + "content": "Pure Polarization. Early SfP methods divide the polarization reflection into two cases, i.e., specular reflection [35] and diffuse reflection [2, 19, 29]. These methods model such two cases individually according to object materials. This strategy is impractical since light reflection involves both cases in the real world. Moreover, their assumptions on shape priors lead to over-smooth shape recovery results. Baek et al. [4] introduced a model that can consider two reflection cases simultaneously. However, their model requires the assumption about ideal surface reflection and thus is relatively unreliable. Considering the complexity of light reflection, some methods [3, 12, 23, 25] based on deep learning are proposed. Although these data-driven methods improve the recovery accuracy, they lead to low generalization. The reason is that their networks are trained on relatively small or synthetic datasets." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 462, + 546, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 462, + 546, + 700 + ], + "spans": [ + { + "bbox": [ + 304, + 462, + 546, + 700 + ], + "type": "text", + "content": "Polarization " + }, + { + "bbox": [ + 304, + 462, + 546, + 700 + ], + "type": "inline_equation", + "content": "+\\mathbf{X}" + }, + { + "bbox": [ + 304, + 462, + 546, + 700 + ], + "type": "text", + "content": ". The above pure polarization-based methods suffer from the ambiguity problem of polarization cues. To solve this problem, recent works attempt to introduce additional shape-from-X cues (X represents shading, photometry, depth, etc.). With the cues of shading, Smith et al. [39, 40] proposed to generate a large linear system to directly calculate the height of each pixel. However, their assumptions about the known refractive index and orthographic camera projection limit the recovery accuracy. Ngo et al. [32] combined the polarization with shading cues to additionally estimate the refractive index. Nevertheless, their method needs at least two light directions and is time-consuming. In addition, given the cues of photometry, Atkinson et al. [1] used two calibrated photometric systems to reduce the effects of polarization ambiguity. Tozza et al. [41] improved their method by solving the uncalibrated case. Moreover, based on the cues of depth, Kadambi et al. [21] used the geometric constraints of normals to refine the depth map. This method relies on redundant depth alignment, which leads to low efficiency." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 701, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 701, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 306, + 701, + 545, + 712 + ], + "type": "text", + "content": "Stereo and Multi-view Polarization. Stereo or multi-view" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 58, + 702, + 280, + 714 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 280, + 714 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 280, + 714 + ], + "type": "text", + "content": "1https://tyhuang98.github.io/learn_stereo_sfp/" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17288" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 264 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 264 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 264 + ], + "type": "text", + "content": "imaging setup contributes to the disambiguation of polarization cues. For example, Cui et al. [11] proposed an is-depth contour tracing mechanism in their multi-view setup to fuse the estimated depth and normal maps. Chen et al. [9] proposed a theoretical polarimetric transport model to constrain the recovery solutions from three views. Zhu and Smith [50] adopted a pair of polarization and RGB images. They introduced a high-order graphical model to label the diffuse-dominant and specular-dominant pixels separately, followed by shape recovery. Recently, Fukao et al. [16] proposed an approach to recover per-pixel normals using stereo polarimetric images. They treated the Stokes vector as polarization cues and constructed a cost volume to regress normals. Compared with the above methods, our approach is more robust to noise thanks to our proposed modules, as will be shown in the experiments." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 282, + 153, + 296 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 282, + 153, + 296 + ], + "spans": [ + { + "bbox": [ + 47, + 282, + 153, + 296 + ], + "type": "text", + "content": "3. Proposed Method" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 304, + 288, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 304, + 288, + 388 + ], + "spans": [ + { + "bbox": [ + 46, + 304, + 288, + 388 + ], + "type": "text", + "content": "In Section 3.1, we introduce the basic knowledge of polarization. In Section 3.2, we give an overview of our pipeline. In Section 3.3, we introduce the SCMP module that enables our method to solve the ambiguity problem. In Section 3.4, we introduce our VDPE design that aims at handling the non-orthographic projection. In Section 3.5, we introduce our loss function." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 401, + 222, + 415 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 401, + 222, + 415 + ], + "spans": [ + { + "bbox": [ + 47, + 401, + 222, + 415 + ], + "type": "text", + "content": "3.1. Basic Knowledge of Polarization" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 422, + 287, + 471 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 422, + 287, + 471 + ], + "spans": [ + { + "bbox": [ + 46, + 422, + 287, + 471 + ], + "type": "text", + "content": "Let us consider a partially polarized light that orthographically passes through a linear polarizer with an angle of " + }, + { + "bbox": [ + 46, + 422, + 287, + 471 + ], + "type": "inline_equation", + "content": "\\phi_{\\mathrm{pol}}" + }, + { + "bbox": [ + 46, + 422, + 287, + 471 + ], + "type": "text", + "content": ". The measured intensity of this light follows a sinusoidal variation [10] as" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 59, + 481, + 287, + 520 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 481, + 287, + 520 + ], + "spans": [ + { + "bbox": [ + 59, + 481, + 287, + 520 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} I _ {\\phi_ {\\mathrm {p o l}}} = \\frac {I _ {\\operatorname* {m a x}} + I _ {\\operatorname* {m i n}}}{2} + \\frac {I _ {\\operatorname* {m a x}} - I _ {\\operatorname* {m i n}}}{2} \\cos (2 \\phi_ {\\mathrm {p o l}} - 2 \\phi) \\tag {1} \\\\ = \\bar {I} + \\rho \\bar {I} \\cos (2 \\phi_ {\\mathrm {p o l}} - 2 \\phi), \\\\ \\end{array}", + "image_path": "080adc98a647f5c91251c1f153f6d756129762a6fc547bee5a5047812a67e8f1.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 531, + 287, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 531, + 287, + 687 + ], + "spans": [ + { + "bbox": [ + 46, + 531, + 287, + 687 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 531, + 287, + 687 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{max}}" + }, + { + "bbox": [ + 46, + 531, + 287, + 687 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 531, + 287, + 687 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{min}}" + }, + { + "bbox": [ + 46, + 531, + 287, + 687 + ], + "type": "text", + "content": " denote the upper and lower bounds of the detected light intensity, " + }, + { + "bbox": [ + 46, + 531, + 287, + 687 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 46, + 531, + 287, + 687 + ], + "type": "text", + "content": " denotes the angle of linear polarization (AoLP), " + }, + { + "bbox": [ + 46, + 531, + 287, + 687 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 46, + 531, + 287, + 687 + ], + "type": "text", + "content": " denotes the degree of linear polarization (DoLP), " + }, + { + "bbox": [ + 46, + 531, + 287, + 687 + ], + "type": "inline_equation", + "content": "\\bar{I}" + }, + { + "bbox": [ + 46, + 531, + 287, + 687 + ], + "type": "text", + "content": " denotes the average intensity. Based on Eq. (1), two polarization angles " + }, + { + "bbox": [ + 46, + 531, + 287, + 687 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 46, + 531, + 287, + 687 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 531, + 287, + 687 + ], + "type": "inline_equation", + "content": "\\phi'" + }, + { + "bbox": [ + 46, + 531, + 287, + 687 + ], + "type": "text", + "content": " with a " + }, + { + "bbox": [ + 46, + 531, + 287, + 687 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 46, + 531, + 287, + 687 + ], + "type": "text", + "content": "-shift " + }, + { + "bbox": [ + 46, + 531, + 287, + 687 + ], + "type": "inline_equation", + "content": "(\\phi' = \\phi \\pm \\pi)" + }, + { + "bbox": [ + 46, + 531, + 287, + 687 + ], + "type": "text", + "content": " result in the same observed light intensity, which is called " + }, + { + "bbox": [ + 46, + 531, + 287, + 687 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 46, + 531, + 287, + 687 + ], + "type": "text", + "content": "-ambiguity problem. With the linear quad-Bayer polarization camera [46], we can measure intensities in different angles of polarizer. By combining these intensities, we can solve the above unknown polarization parameters: " + }, + { + "bbox": [ + 46, + 531, + 287, + 687 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 46, + 531, + 287, + 687 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 46, + 531, + 287, + 687 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 46, + 531, + 287, + 687 + ], + "type": "text", + "content": "-ambiguity, " + }, + { + "bbox": [ + 46, + 531, + 287, + 687 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 46, + 531, + 287, + 687 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 531, + 287, + 687 + ], + "type": "inline_equation", + "content": "\\bar{I}" + }, + { + "bbox": [ + 46, + 531, + 287, + 687 + ], + "type": "text", + "content": ". These parameters have been proved to be highly related to the surface normal [2, 35]. Details are available in the supplementary material." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": "In addition, there is another representation to describe the polarization state of light [10], i.e., the Stokes vector:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 357, + 69, + 545, + 121 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 357, + 69, + 545, + 121 + ], + "spans": [ + { + "bbox": [ + 357, + 69, + 545, + 121 + ], + "type": "interline_equation", + "content": "\\mathbf {s} = \\left[ \\begin{array}{c} s _ {0} \\\\ s _ {1} \\\\ s _ {2} \\\\ s _ {3} \\end{array} \\right] = \\left[ \\begin{array}{c} I _ {0} + I _ {9 0} \\\\ I _ {0} - I _ {9 0} \\\\ I _ {4 5} - I _ {1 3 5} \\\\ 0 \\end{array} \\right], \\tag {2}", + "image_path": "9218f85335b05442e7cb481dbdb9e044a28ffa596fac990df518f5989fcc935e.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 128, + 547, + 212 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 128, + 547, + 212 + ], + "spans": [ + { + "bbox": [ + 304, + 128, + 547, + 212 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 128, + 547, + 212 + ], + "type": "inline_equation", + "content": "s_0" + }, + { + "bbox": [ + 304, + 128, + 547, + 212 + ], + "type": "text", + "content": " represents the light intensity; " + }, + { + "bbox": [ + 304, + 128, + 547, + 212 + ], + "type": "inline_equation", + "content": "s_1" + }, + { + "bbox": [ + 304, + 128, + 547, + 212 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 128, + 547, + 212 + ], + "type": "inline_equation", + "content": "s_2" + }, + { + "bbox": [ + 304, + 128, + 547, + 212 + ], + "type": "text", + "content": " represent the linear polarization components in " + }, + { + "bbox": [ + 304, + 128, + 547, + 212 + ], + "type": "inline_equation", + "content": "0^\\circ" + }, + { + "bbox": [ + 304, + 128, + 547, + 212 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 128, + 547, + 212 + ], + "type": "inline_equation", + "content": "45^\\circ" + }, + { + "bbox": [ + 304, + 128, + 547, + 212 + ], + "type": "text", + "content": ", respectively; " + }, + { + "bbox": [ + 304, + 128, + 547, + 212 + ], + "type": "inline_equation", + "content": "s_3" + }, + { + "bbox": [ + 304, + 128, + 547, + 212 + ], + "type": "text", + "content": " represents the right circular polarization component. The Stokes vector " + }, + { + "bbox": [ + 304, + 128, + 547, + 212 + ], + "type": "inline_equation", + "content": "\\mathbf{s}" + }, + { + "bbox": [ + 304, + 128, + 547, + 212 + ], + "type": "text", + "content": " in Eq. (2) can be expressed by the measured intensities " + }, + { + "bbox": [ + 304, + 128, + 547, + 212 + ], + "type": "inline_equation", + "content": "I_0, I_{45}, I_{90}" + }, + { + "bbox": [ + 304, + 128, + 547, + 212 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 128, + 547, + 212 + ], + "type": "inline_equation", + "content": "I_{135}" + }, + { + "bbox": [ + 304, + 128, + 547, + 212 + ], + "type": "text", + "content": ". In our context, we follow [12] to call the normalized Stokes vector image \"Stokes map\"." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 220, + 414, + 234 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 220, + 414, + 234 + ], + "spans": [ + { + "bbox": [ + 306, + 220, + 414, + 234 + ], + "type": "text", + "content": "3.2. Pipeline Overview" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 240, + 545, + 372 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 240, + 545, + 372 + ], + "spans": [ + { + "bbox": [ + 304, + 240, + 545, + 372 + ], + "type": "text", + "content": "As shown in Fig. 1, given the measured stereo polarization images, we compute AoLP&DoLP and Stokes maps, and treat them as the physical priors. By taking these priors as inputs, our network uses a weight-shared feature extraction module to extract stereo feature maps. Our feature extraction is based on the combination of CNN and Transformer to consider both local and global contexts. Note that our Transformer is adapted by the proposed VDPE design (see Section 3.4) to handle the non-orthographic projection. Based on the extracted stereo feature maps, our network predicts both normal and disparity maps." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 373, + 545, + 433 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 373, + 545, + 433 + ], + "spans": [ + { + "bbox": [ + 304, + 373, + 545, + 433 + ], + "type": "text", + "content": "Disparity Map. Given the stereo feature maps, we generate a polarimetric cost volume. This volume aligns stereo features and encapsulates the disparity information [22]. We process such volume by a series of Conv3d blocks [42] and the Soft ArgMin operation [22] to infer the disparity map." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 434, + 545, + 554 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 434, + 545, + 554 + ], + "spans": [ + { + "bbox": [ + 304, + 434, + 545, + 554 + ], + "type": "text", + "content": "Normal Map. The extracted feature map of the left view is associated with the unknown-but-sought normal map. However, due to the ambiguity problem of polarization cues, this feature map needs to be refined. To achieve this goal, we propose a coarse-to-fine feature refinement strategy. This refinement is based on the proposed SCMP module (see Section 3.3) and Transformer. Our SCMP module incorporates the above cost volume since there exists inherent consistency between disparity and normal. After refinement, the feature map is used to infer the normal map." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 562, + 527, + 576 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 562, + 527, + 576 + ], + "spans": [ + { + "bbox": [ + 306, + 562, + 527, + 576 + ], + "type": "text", + "content": "3.3. Shape Consistency-based Mask Prediction" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 582, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 715 + ], + "type": "text", + "content": "Leveraging the shape consistency between normal and disparity can improve the shape recovery accuracy. Let us first intuitively explain the reason. For one thing, the normal map estimated by polarization cues are per-pixel. However, the normals in some areas are false due to the ambiguity problem, and we cannot obtain a mask to exclude such areas a priori. For another thing, given a disparity map, we can compute a normal map that is globally reliable but coarse. The correct normals labelled by the unknown-but-sought mask are relatively consistent with the normals computed by the disparity map. We leverage such consistency" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17289" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 72, + 68, + 265, + 168 + ], + "blocks": [ + { + "bbox": [ + 72, + 68, + 265, + 168 + ], + "lines": [ + { + "bbox": [ + 72, + 68, + 265, + 168 + ], + "spans": [ + { + "bbox": [ + 72, + 68, + 265, + 168 + ], + "type": "image", + "image_path": "95e5984bb1709244cffabca79e8a3698a369eb2f17e8358ef1ac7cde7244b290.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 121, + 170, + 214, + 179 + ], + "lines": [ + { + "bbox": [ + 121, + 170, + 214, + 179 + ], + "spans": [ + { + "bbox": [ + 121, + 170, + 214, + 179 + ], + "type": "text", + "content": "(a) Proposed SCMP module." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 91, + 185, + 245, + 256 + ], + "blocks": [ + { + "bbox": [ + 91, + 185, + 245, + 256 + ], + "lines": [ + { + "bbox": [ + 91, + 185, + 245, + 256 + ], + "spans": [ + { + "bbox": [ + 91, + 185, + 245, + 256 + ], + "type": "image", + "image_path": "ad848414b5847526e2d9733999fc173f05f4044b1f9ce895c22011afc011cc22.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 83, + 258, + 248, + 267 + ], + "lines": [ + { + "bbox": [ + 83, + 258, + 248, + 267 + ], + "spans": [ + { + "bbox": [ + 83, + 258, + 248, + 267 + ], + "type": "text", + "content": "(b) The mask embedding operation in our network." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 269, + 287, + 314 + ], + "lines": [ + { + "bbox": [ + 46, + 269, + 287, + 314 + ], + "spans": [ + { + "bbox": [ + 46, + 269, + 287, + 314 + ], + "type": "text", + "content": "Figure 2. Illustration of proposed SCMP module and mask embedding operation. (a) Based on shape consistency, the proposed SCMP module predicts a mask. (b) We employ the predicted mask to purify the feature map " + }, + { + "bbox": [ + 46, + 269, + 287, + 314 + ], + "type": "inline_equation", + "content": "F_{1} / F_{2}" + }, + { + "bbox": [ + 46, + 269, + 287, + 314 + ], + "type": "text", + "content": " by a mask embedding operation." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 323, + 287, + 347 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 323, + 287, + 347 + ], + "spans": [ + { + "bbox": [ + 46, + 323, + 287, + 347 + ], + "type": "text", + "content": "to identify this mask by introducing the SCMP module. We will introduce our module details in the following." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 348, + 288, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 348, + 288, + 552 + ], + "spans": [ + { + "bbox": [ + 46, + 348, + 288, + 552 + ], + "type": "text", + "content": "As shown in Fig. 1, we embed two SCMP modules into our network. Fig. 2(a) shows how our first and second SCMP modules are used in our coarse-to-fine feature refinement. Specifically, at the \"coarse\" stage, we take the original feature map " + }, + { + "bbox": [ + 46, + 348, + 288, + 552 + ], + "type": "inline_equation", + "content": "F_{1}" + }, + { + "bbox": [ + 46, + 348, + 288, + 552 + ], + "type": "text", + "content": " of the left view and the polarimetric cost volume " + }, + { + "bbox": [ + 46, + 348, + 288, + 552 + ], + "type": "inline_equation", + "content": "C_{1}" + }, + { + "bbox": [ + 46, + 348, + 288, + 552 + ], + "type": "text", + "content": " as inputs of the first SCMP module. At the \"fine\" stage, we feed the intermediate feature map " + }, + { + "bbox": [ + 46, + 348, + 288, + 552 + ], + "type": "inline_equation", + "content": "F_{2}" + }, + { + "bbox": [ + 46, + 348, + 288, + 552 + ], + "type": "text", + "content": " and cost volume " + }, + { + "bbox": [ + 46, + 348, + 288, + 552 + ], + "type": "inline_equation", + "content": "C_{2}" + }, + { + "bbox": [ + 46, + 348, + 288, + 552 + ], + "type": "text", + "content": " to the second SCMP module. At each stage, an initial normal map can be inferred from the feature map " + }, + { + "bbox": [ + 46, + 348, + 288, + 552 + ], + "type": "inline_equation", + "content": "F_{1}" + }, + { + "bbox": [ + 46, + 348, + 288, + 552 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 46, + 348, + 288, + 552 + ], + "type": "inline_equation", + "content": "F_{2}" + }, + { + "bbox": [ + 46, + 348, + 288, + 552 + ], + "type": "text", + "content": " under supervision. Meanwhile, an initial disparity map can be regressed from the cost volume " + }, + { + "bbox": [ + 46, + 348, + 288, + 552 + ], + "type": "inline_equation", + "content": "C_{1}" + }, + { + "bbox": [ + 46, + 348, + 288, + 552 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 46, + 348, + 288, + 552 + ], + "type": "inline_equation", + "content": "C_{2}" + }, + { + "bbox": [ + 46, + 348, + 288, + 552 + ], + "type": "text", + "content": " under supervision. Based on this disparity map, we compute a rough normal map using an adaptive normal estimation method [27]. We then exploit the consistency between the normal inferred by our network and the normal computed based on disparity to predict a mask. Specifically, the value " + }, + { + "bbox": [ + 46, + 348, + 288, + 552 + ], + "type": "inline_equation", + "content": "v_{i}" + }, + { + "bbox": [ + 46, + 348, + 288, + 552 + ], + "type": "text", + "content": " of the " + }, + { + "bbox": [ + 46, + 348, + 288, + 552 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 348, + 288, + 552 + ], + "type": "text", + "content": "-th pixel in this mask is computed by" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 102, + 558, + 287, + 585 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 102, + 558, + 287, + 585 + ], + "spans": [ + { + "bbox": [ + 102, + 558, + 287, + 585 + ], + "type": "interline_equation", + "content": "v _ {i} = \\left\\{ \\begin{array}{l l} 0, & \\text {i f} \\mathbf {n} _ {i} ^ {N} \\cdot \\mathbf {n} _ {i} ^ {D} < \\tau \\\\ 1, & \\text {o t h e r w i s e} \\end{array} , \\right. \\tag {3}", + "image_path": "fbb64b30fe802c829d675fcd38efaacc017a36320627084a3f56c39a3dfa632e.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 594, + 287, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 287, + 676 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 287, + 676 + ], + "type": "text", + "content": "where “.” denotes the dot product, " + }, + { + "bbox": [ + 46, + 594, + 287, + 676 + ], + "type": "inline_equation", + "content": "\\mathbf{n}_i^N" + }, + { + "bbox": [ + 46, + 594, + 287, + 676 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 594, + 287, + 676 + ], + "type": "inline_equation", + "content": "\\mathbf{n}_i^D" + }, + { + "bbox": [ + 46, + 594, + 287, + 676 + ], + "type": "text", + "content": " are the normals inferred by our network and computed based on disparity, respectively, " + }, + { + "bbox": [ + 46, + 594, + 287, + 676 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 46, + 594, + 287, + 676 + ], + "type": "text", + "content": " is a threshold. When " + }, + { + "bbox": [ + 46, + 594, + 287, + 676 + ], + "type": "inline_equation", + "content": "\\mathbf{n}_i^N\\cdot \\mathbf{n}_i^D" + }, + { + "bbox": [ + 46, + 594, + 287, + 676 + ], + "type": "text", + "content": " is smaller than the threshold " + }, + { + "bbox": [ + 46, + 594, + 287, + 676 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 46, + 594, + 287, + 676 + ], + "type": "text", + "content": ", the consistency is violated. In our paper, " + }, + { + "bbox": [ + 46, + 594, + 287, + 676 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 46, + 594, + 287, + 676 + ], + "type": "text", + "content": " is 0.7 and 0.9 in the first and second SCMP modules, respectively. We adopt such threshold setup to achieve coarse-to-fine feature refinement." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 677, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 288, + 713 + ], + "type": "text", + "content": "We then employ the above mask to purify the feature map " + }, + { + "bbox": [ + 46, + 677, + 288, + 713 + ], + "type": "inline_equation", + "content": "F_{1}" + }, + { + "bbox": [ + 46, + 677, + 288, + 713 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 46, + 677, + 288, + 713 + ], + "type": "inline_equation", + "content": "F_{2}" + }, + { + "bbox": [ + 46, + 677, + 288, + 713 + ], + "type": "text", + "content": " by a mask embedding operation (see Fig. 2(b)). Each unreliable feature in the areas with false" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 324, + 69, + 525, + 160 + ], + "blocks": [ + { + "bbox": [ + 324, + 69, + 525, + 160 + ], + "lines": [ + { + "bbox": [ + 324, + 69, + 525, + 160 + ], + "spans": [ + { + "bbox": [ + 324, + 69, + 525, + 160 + ], + "type": "image", + "image_path": "339574c947b73e2bffda48bc3af31feff4337a631f888114843e4ed8c928c462.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 162, + 545, + 184 + ], + "lines": [ + { + "bbox": [ + 305, + 162, + 545, + 184 + ], + "spans": [ + { + "bbox": [ + 305, + 162, + 545, + 184 + ], + "type": "text", + "content": "Figure 3. Illustration of proposed VDPE design. For ease of understanding, we only show the self-attention part in the Transformer." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 198, + 545, + 293 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 198, + 545, + 293 + ], + "spans": [ + { + "bbox": [ + 304, + 198, + 545, + 293 + ], + "type": "text", + "content": "normal estimation is set to zero vector. Then the purified feature map is fed to Transformer for global attention. Thanks to the mask embedding, the effect of the unreliable features resulting in false normal estimation is reduced. In addition, the global attention mechanism in Transformer extracts new features for the masked areas by combing global reliable features. Based on such features, the false normals can be re-estimated in an accurate way." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 304, + 538, + 318 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 304, + 538, + 318 + ], + "spans": [ + { + "bbox": [ + 306, + 304, + 538, + 318 + ], + "type": "text", + "content": "3.4. Viewing Direction-aided Positional Encoding" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 324, + 546, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 324, + 546, + 515 + ], + "spans": [ + { + "bbox": [ + 304, + 324, + 546, + 515 + ], + "type": "text", + "content": "Most existing SfP works [35, 39] assume orthographic projection (i.e., viewing directions of all pixels are " + }, + { + "bbox": [ + 304, + 324, + 546, + 515 + ], + "type": "inline_equation", + "content": "[0,0,1]^{\\top}" + }, + { + "bbox": [ + 304, + 324, + 546, + 515 + ], + "type": "text", + "content": "). This assumption affects the accuracy of polarimetric measurement and further the accuracy of shape recovery. Intuitively, additionally using a viewing direction map can alleviate this problem. We generate this map based on the pixel-viewing direction encoding, i.e., each pixel in this map is associated with a unique viewing direction. To introduce such map into neural network, a straightforward strategy is to feed it to CNN [25]. However, it is well-known that the feature extracted by CNN lacks global information. By contrast, we propose to integrate this map into Transformer. This integration is based on the proposed VDPE design (see the next paragraph). As will be shown in the experiments, such design is more effective than the strategy based on CNN." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 517, + 545, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 517, + 545, + 612 + ], + "spans": [ + { + "bbox": [ + 304, + 517, + 545, + 612 + ], + "type": "text", + "content": "As shown in Fig. 3, we integrate the viewing direction map into the self-attention part of Transformer. Specifically, we reshape the viewing direction map and concatenate it with the linearly projected value in the self-attention block. Then the concatenated volume is passed to a Multi-Layer Perception (MLP) layer to embed with the attention calculation. After that, the self-attention computation result can be formulated as:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 315, + 618, + 545, + 647 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 618, + 545, + 647 + ], + "spans": [ + { + "bbox": [ + 315, + 618, + 545, + 647 + ], + "type": "interline_equation", + "content": "\\operatorname {O u t p u t} = \\left(\\operatorname {S o f t M a x} \\left(\\frac {Q K ^ {\\top}}{\\sqrt {D}}\\right) V\\right) \\oplus \\left(\\operatorname {M L P} (V \\oplus v)\\right), \\tag {4}", + "image_path": "23d0f3ef6bba502c3766646399ff51db801c10087d22af54357b96e4d55601bf.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "inline_equation", + "content": "V, K, Q" + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "content": " represent the linearly projected value, key and query respectively, " + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\nu" + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "content": " is the viewing direction map, " + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "content": " is the feature dimension, “" + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\oplus" + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "content": "” represents the concatenation operation. Based on Eq. (4), our method can handle the non-orthographic projection reliably." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17290" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 77, + 95, + 513, + 167 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 545, + 93 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 545, + 93 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 545, + 93 + ], + "type": "text", + "content": "Table 1. Comparison among existing SfP datasets. Our dataset is the first stereo SfP dataset at the object level. Meanwhile, our acquisition is under controlled illumination and does not need reprojection." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 77, + 95, + 513, + 167 + ], + "lines": [ + { + "bbox": [ + 77, + 95, + 513, + 167 + ], + "spans": [ + { + "bbox": [ + 77, + 95, + 513, + 167 + ], + "type": "table", + "html": "
DatasetLevelTypeSetupControlled IlluminationReprojection Operation
DeepSfP [3]ObjectReal-worldMonocularNoYes
Kondo et al. [23]SceneSyntheticMonocularYesNo
Deschaintre et al. [12]ObjectSyntheticMonocularYesNo
SPW [25]SceneReal-worldMonocularNoYes
CroMo [44]SceneReal-worldStereoNoYes
OursObjectReal-worldStereoYesNo
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We establish a real-world stereo SfP dataset, which contains rich shapes and material categories. (a) Representative image pairs. (b) Data capture setup." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 338, + 135, + 349 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 338, + 135, + 349 + ], + "spans": [ + { + "bbox": [ + 47, + 338, + 135, + 349 + ], + "type": "text", + "content": "3.5. Loss Function" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 356, + 287, + 499 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 356, + 287, + 499 + ], + "spans": [ + { + "bbox": [ + 46, + 356, + 287, + 499 + ], + "type": "text", + "content": "For network training, we use the normal loss and the disparity loss. For the normal loss, we adopt the commonly used cosine similarity loss [6, 7]. Our normal loss consists of three sub-losses " + }, + { + "bbox": [ + 46, + 356, + 287, + 499 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_1" + }, + { + "bbox": [ + 46, + 356, + 287, + 499 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 356, + 287, + 499 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_2" + }, + { + "bbox": [ + 46, + 356, + 287, + 499 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 356, + 287, + 499 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_{\\mathrm{final}}" + }, + { + "bbox": [ + 46, + 356, + 287, + 499 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 46, + 356, + 287, + 499 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_1" + }, + { + "bbox": [ + 46, + 356, + 287, + 499 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 356, + 287, + 499 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_2" + }, + { + "bbox": [ + 46, + 356, + 287, + 499 + ], + "type": "text", + "content": " correspond to the initial normal maps in the first and second SCMP modules, respectively. " + }, + { + "bbox": [ + 46, + 356, + 287, + 499 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_{\\mathrm{final}}" + }, + { + "bbox": [ + 46, + 356, + 287, + 499 + ], + "type": "text", + "content": " is related to the final predicted normal map of our network. As to the disparity loss, we adopt the widely-used smooth " + }, + { + "bbox": [ + 46, + 356, + 287, + 499 + ], + "type": "inline_equation", + "content": "L_{1}" + }, + { + "bbox": [ + 46, + 356, + 287, + 499 + ], + "type": "text", + "content": " loss [5, 17]. Our disparity loss consists of three sub-losses " + }, + { + "bbox": [ + 46, + 356, + 287, + 499 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_1" + }, + { + "bbox": [ + 46, + 356, + 287, + 499 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 356, + 287, + 499 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_2" + }, + { + "bbox": [ + 46, + 356, + 287, + 499 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 356, + 287, + 499 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{final}}" + }, + { + "bbox": [ + 46, + 356, + 287, + 499 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 46, + 356, + 287, + 499 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_1" + }, + { + "bbox": [ + 46, + 356, + 287, + 499 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 356, + 287, + 499 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_2" + }, + { + "bbox": [ + 46, + 356, + 287, + 499 + ], + "type": "text", + "content": " correspond to the initial disparity maps in the first and second SCMP modules, respectively. " + }, + { + "bbox": [ + 46, + 356, + 287, + 499 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{final}}" + }, + { + "bbox": [ + 46, + 356, + 287, + 499 + ], + "type": "text", + "content": " is related to the final predicted disparity map of our network." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 500, + 287, + 523 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 500, + 287, + 523 + ], + "spans": [ + { + "bbox": [ + 46, + 500, + 287, + 523 + ], + "type": "text", + "content": "By combing the above sub-losses, we define our final loss " + }, + { + "bbox": [ + 46, + 500, + 287, + 523 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 46, + 500, + 287, + 523 + ], + "type": "text", + "content": " as:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 89, + 529, + 287, + 557 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 89, + 529, + 287, + 557 + ], + "spans": [ + { + "bbox": [ + 89, + 529, + 287, + 557 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} = \\alpha \\cdot \\left(\\mathcal {N} _ {1} + \\mathcal {N} _ {2}\\right) + \\beta \\cdot \\left(\\mathcal {D} _ {1} + \\mathcal {D} _ {2}\\right) \\tag {5} \\\\ + \\alpha^ {\\prime} \\cdot \\mathcal {N} _ {\\text {f i n a l}} + \\beta^ {\\prime} \\cdot \\mathcal {D} _ {\\text {f i n a l}}, \\\\ \\end{array}", + "image_path": "1425350b77b50b9749ebd06dadfed6c12e3cfd3b6e3a3d0e9e01582c76921031.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 563, + 287, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 563, + 287, + 635 + ], + "spans": [ + { + "bbox": [ + 46, + 563, + 287, + 635 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 563, + 287, + 635 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 563, + 287, + 635 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 563, + 287, + 635 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 563, + 287, + 635 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 563, + 287, + 635 + ], + "type": "inline_equation", + "content": "\\alpha'" + }, + { + "bbox": [ + 46, + 563, + 287, + 635 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 563, + 287, + 635 + ], + "type": "inline_equation", + "content": "\\beta'" + }, + { + "bbox": [ + 46, + 563, + 287, + 635 + ], + "type": "text", + "content": " are the trade-off parameters. During training, we set " + }, + { + "bbox": [ + 46, + 563, + 287, + 635 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 563, + 287, + 635 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 563, + 287, + 635 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 563, + 287, + 635 + ], + "type": "text", + "content": " as 0.1 for weak supervision since they correspond to the intermediate results. We set " + }, + { + "bbox": [ + 46, + 563, + 287, + 635 + ], + "type": "inline_equation", + "content": "\\alpha'" + }, + { + "bbox": [ + 46, + 563, + 287, + 635 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 563, + 287, + 635 + ], + "type": "inline_equation", + "content": "\\beta'" + }, + { + "bbox": [ + 46, + 563, + 287, + 635 + ], + "type": "text", + "content": " as 0.3 for major supervision since they correspond to our final predictions. Further implementation details of our method are available in the supplementary material." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 646, + 100, + 657 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 646, + 100, + 657 + ], + "spans": [ + { + "bbox": [ + 47, + 646, + 100, + 657 + ], + "type": "text", + "content": "4. Dataset" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "content": "Most existing SfP datasets are either small [3,25] or only provide synthetic images [12, 23]. In addition, their images are obtained by monocular cameras and cannot be used for research on stereo polarimetric imaging. While a recent" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 182, + 545, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 182, + 545, + 338 + ], + "spans": [ + { + "bbox": [ + 304, + 182, + 545, + 338 + ], + "type": "text", + "content": "dataset contains abundant stereo polarization images, it only provides the ground truth depth and ignores the normal [44]. To solve this problem, we propose a large real-world SfP dataset with stereo images associated with the ground truth normal and disparity. Considering that arbitrary illumination has been proved to limit the quality of polarization signal [12], we use the controlled illumination (i.e., unpolarized illumination) for data collection. Moreover, the ground truth shapes of existing real-world SfP datasets [3, 25] are obtained by an extra 3D scanner, which introduces the reprojection operation. By contrast, we propose a more concise acquisition design that can avoid this operation. Table 1 shows the comparison among existing SfP datasets." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 339, + 545, + 448 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 339, + 545, + 448 + ], + "spans": [ + { + "bbox": [ + 304, + 339, + 545, + 448 + ], + "type": "text", + "content": "Data Composition. Our dataset consists of 2450 pairs of polarization images. We collect data from more than 50 different objects with various shapes and material categories. For data diversity, we collect images from different viewpoints and different illumination conditions for most objects. Each image pair is associated with the ground truth disparity and normal. Moreover, our dataset involves different stereo baselines between stereo images. Fig. 4(a) shows representative image pairs." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 449, + 545, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 449, + 545, + 544 + ], + "spans": [ + { + "bbox": [ + 304, + 449, + 545, + 544 + ], + "type": "text", + "content": "System Setup for Image Collection. When capturing stereo images, we fix a pair of polarization cameras (see Fig. 4(b)) and calibrate them using a standard calibration method [48]. To achieve different illumination conditions, we use an unpolarized light source to illuminate each object from a set of random directions. Moreover, to improve the diversity of illuminations, we use two unpolarized light sources, i.e., the digital projector and a LED lighting." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": "Acquisition of Ground Truth Maps. To acquire the ground-truth normal and disparity maps, we use a stereo structured-light system. We replace the original grayscale cameras of this system with our stereo polarization camera rig (the grayscale information can be extracted from the polarization information). Based on this adapted system, we employ a Gray code-based reconstruction algorithm [30] to reconstruct the disparity map and point cloud of the object. Finally, we use the least-squares normal estimation algorithm [36] to calculate the normal map of the reconstructed point cloud. Each step of our acquisition does not need reprojection operation mentioned above. Our design ensures perfect alignment of the input polarization image and the ground truth normal and disparity." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17291" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 68, + 534, + 373 + ], + "blocks": [ + { + "bbox": [ + 61, + 68, + 534, + 373 + ], + "lines": [ + { + "bbox": [ + 61, + 68, + 534, + 373 + ], + "spans": [ + { + "bbox": [ + 61, + 68, + 534, + 373 + ], + "type": "image", + "image_path": "ad30351204389398788729be590528b76a9f8a6f40fbefbdb5874b30a70dd075.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 376, + 546, + 400 + ], + "lines": [ + { + "bbox": [ + 46, + 376, + 546, + 400 + ], + "spans": [ + { + "bbox": [ + 46, + 376, + 546, + 400 + ], + "type": "text", + "content": "Figure 5. Representative accuracy comparisons between various SfP methods for normal recovery. A pair of numbers below each estimated normal map represents the mean of angular errors and the percentage of pixels with angular errors smaller than " + }, + { + "bbox": [ + 46, + 376, + 546, + 400 + ], + "type": "inline_equation", + "content": "11.25^{\\circ}" + }, + { + "bbox": [ + 46, + 376, + 546, + 400 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 416, + 128, + 430 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 416, + 128, + 430 + ], + "spans": [ + { + "bbox": [ + 47, + 416, + 128, + 430 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 436, + 287, + 543 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 436, + 287, + 543 + ], + "spans": [ + { + "bbox": [ + 46, + 436, + 287, + 543 + ], + "type": "text", + "content": "We first compare our approach with state-of-the-art SfP methods that aim at normal recovery in Section 5.1. Considering that our approach can predict both normal and disparity, we also compare our method with two baselines that jointly estimate normal and disparity in Section 5.2. In addition, we conduct ablation studies in Section 5.3. All the experiments are conducted on our dataset introduced above. Additional experimental results are available in the supplementary material." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 544, + 288, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 544, + 288, + 640 + ], + "spans": [ + { + "bbox": [ + 46, + 544, + 288, + 640 + ], + "type": "text", + "content": "In terms of evaluation criteria, we follow [25] to evaluate the normal accuracy by the angular error between the estimated and ground truth normals. In addition, we follow [45] to report the percentage of pixels with angular errors smaller than specific thresholds (i.e., " + }, + { + "bbox": [ + 46, + 544, + 288, + 640 + ], + "type": "inline_equation", + "content": "11.25^{\\circ}" + }, + { + "bbox": [ + 46, + 544, + 288, + 640 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 544, + 288, + 640 + ], + "type": "inline_equation", + "content": "22.5^{\\circ}" + }, + { + "bbox": [ + 46, + 544, + 288, + 640 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 544, + 288, + 640 + ], + "type": "inline_equation", + "content": "30.0^{\\circ}" + }, + { + "bbox": [ + 46, + 544, + 288, + 640 + ], + "type": "text", + "content": "). To evaluate the accuracy of disparity map, we follow [47] to use the absolute errors between the estimated and ground truth disparities." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 647, + 203, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 647, + 203, + 659 + ], + "spans": [ + { + "bbox": [ + 47, + 647, + 203, + 659 + ], + "type": "text", + "content": "5.1. Comparison to SfP Methods" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "text", + "content": "Methods for Comparison. We compare our approach with four state-of-the-art SfP methods (i.e., Zhu [50], DeepSfP [3], Fukao [16] and Lei [25]) in terms of normal recovery accuracy and robustness to light variation. As" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 307, + 441, + 545, + 526 + ], + "blocks": [ + { + "bbox": [ + 305, + 415, + 545, + 437 + ], + "lines": [ + { + "bbox": [ + 305, + 415, + 545, + 437 + ], + "spans": [ + { + "bbox": [ + 305, + 415, + 545, + 437 + ], + "type": "text", + "content": "Table 2. Accuracy comparisons between various SfP methods for normal recovery on all the data of our testing set." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 441, + 545, + 526 + ], + "lines": [ + { + "bbox": [ + 307, + 441, + 545, + 526 + ], + "spans": [ + { + "bbox": [ + 307, + 441, + 545, + 526 + ], + "type": "table", + "html": "
MethodAngular Error (deg.)Pixel Percentage (%)
MeanMedianRMSE11.25°22.5°30.0°
Zhu [50]37.6934.2743.0112.431.945.7
DeepSfP [3]24.7121.4330.1823.647.467.8
Fukao [16]31.2827.5237.1517.439.554.3
Lei [25]22.2719.3228.6728.855.972.1
Ours13.2211.1417.2246.277.590.1
", + "image_path": "8f5dce3437df27a7cd8ece212a1b430f24ed0dbaf1be8b43760ca238d72cc2cf.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 544, + 545, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 544, + 545, + 581 + ], + "spans": [ + { + "bbox": [ + 304, + 544, + 545, + 581 + ], + "type": "text", + "content": "introduced in Section 2, Zhu and Fukao use stereo setup and numerical optimization strategies. DeepSfP and Lei are based on monocular setup and deep learning." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 581, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 581, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 581, + 545, + 689 + ], + "type": "text", + "content": "Normal Recovery Accuracy. As shown in Table 2 and Fig. 5, Zhu and Fukao are affected by the stereo matching quality and thus recover noisy normal maps. DeepSfP shows mistakes in many local areas. While Lei partly alleviates the ambiguity problem, it still loses several details. By contrast, our method achieves the highest accuracy on all the evaluation metrics and also leads to rich object details. This result demonstrates that our integration of deep learning and stereo polarization is effective." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": "Robustness to Light Variation. To evaluate the robustness to light variation, we use different illumination conditions" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17292" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 104, + 70, + 138, + 103 + ], + "blocks": [ + { + "bbox": [ + 104, + 70, + 138, + 103 + ], + "lines": [ + { + "bbox": [ + 104, + 70, + 138, + 103 + ], + "spans": [ + { + "bbox": [ + 104, + 70, + 138, + 103 + ], + "type": "image", + "image_path": "cfc680a1ebe3dcd97bfee038eeb3cd43cbb1a99e671e81fe6e2859adc4280681.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 151, + 70, + 185, + 103 + ], + "blocks": [ + { + "bbox": [ + 151, + 70, + 185, + 103 + ], + "lines": [ + { + "bbox": [ + 151, + 70, + 185, + 103 + ], + "spans": [ + { + "bbox": [ + 151, + 70, + 185, + 103 + ], + "type": "image", + "image_path": "88d201476d91cf7680c7b59684ebc60922a452d911204979933c99ad6523a4da.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 162, + 105, + 172, + 113 + ], + "lines": [ + { + "bbox": [ + 162, + 105, + 172, + 113 + ], + "spans": [ + { + "bbox": [ + 162, + 105, + 172, + 113 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 196, + 70, + 230, + 103 + ], + "blocks": [ + { + "bbox": [ + 196, + 70, + 230, + 103 + ], + "lines": [ + { + "bbox": [ + 196, + 70, + 230, + 103 + ], + "spans": [ + { + "bbox": [ + 196, + 70, + 230, + 103 + ], + "type": "image", + "image_path": "22dfbc5bad40d0bc9847409601b3ac9a943b25f2e14a3651b2c9ca75d0b37d52.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 50, + 116, + 286, + 243 + ], + "blocks": [ + { + "bbox": [ + 50, + 116, + 286, + 243 + ], + "lines": [ + { + "bbox": [ + 50, + 116, + 286, + 243 + ], + "spans": [ + { + "bbox": [ + 50, + 116, + 286, + 243 + ], + "type": "image", + "image_path": "89cbf1f97f8e699fea147982575173a72aa41d11ab4f84f5c46b889e6912bfa9.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 244, + 287, + 331 + ], + "lines": [ + { + "bbox": [ + 46, + 244, + 287, + 331 + ], + "spans": [ + { + "bbox": [ + 46, + 244, + 287, + 331 + ], + "type": "text", + "content": "Figure 6. Representative comparisons regarding robustness to light variation between various SfP methods. (a) Three different illumination conditions. (b) Due to limited space, we only report the results of Fukao, Lei, and our method. Each method corresponds to two columns. The first column shows the recovered normal maps under different illumination conditions. The second column shows the error maps. The number below each column pair represents the mean of variances of angular errors." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 53, + 340, + 279, + 420 + ], + "blocks": [ + { + "bbox": [ + 53, + 340, + 279, + 420 + ], + "lines": [ + { + "bbox": [ + 53, + 340, + 279, + 420 + ], + "spans": [ + { + "bbox": [ + 53, + 340, + 279, + 420 + ], + "type": "image", + "image_path": "f856e641252a40dc4fcfb072c3ea7118b3174e68caa84cce5dec61e596773d2b.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 423, + 287, + 456 + ], + "lines": [ + { + "bbox": [ + 46, + 423, + 287, + 456 + ], + "spans": [ + { + "bbox": [ + 46, + 423, + 287, + 456 + ], + "type": "text", + "content": "Figure 7. Comparisons regarding robustness to light variation between various SfP methods on our testing set. The horizontal axis represents different objects." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 471, + 287, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 471, + 287, + 613 + ], + "spans": [ + { + "bbox": [ + 46, + 471, + 287, + 613 + ], + "type": "text", + "content": "while keeping the viewing direction unchanged. Accordingly, each pixel is associated with a set of angular errors. We compute the variance of the error set of each pixel, followed by obtaining the mean of these variances. Figs. 6 and 7 show that under different illumination conditions, existing SfP approaches lead to unstable recovery results (i.e., the variance is large) and are sensitive to light variation. By contrast, the recovery results of our method are stable and the accuracy remains high despite light variation. The reason is that our network leverages redundant stereo information, and also extracts both local and global contexts for stable estimation." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 623, + 264, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 623, + 264, + 635 + ], + "spans": [ + { + "bbox": [ + 47, + 623, + 264, + 635 + ], + "type": "text", + "content": "5.2. Joint Estimation of Disparity and Normal" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 641, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 286, + 713 + ], + "type": "text", + "content": "Methods for Comparison. Recall that our method can recover both normal and disparity maps. To evaluate performance, we compare our method with two well-known baselines, i.e., Long [28] and Kusupati [24] for joint estimation of normal and depth (depth and disparity are basically equivalent). These methods originally take stereo" + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 310, + 69, + 541, + 321 + ], + "blocks": [ + { + "bbox": [ + 310, + 69, + 541, + 321 + ], + "lines": [ + { + "bbox": [ + 310, + 69, + 541, + 321 + ], + "spans": [ + { + "bbox": [ + 310, + 69, + 541, + 321 + ], + "type": "image", + "image_path": "93b0511410f36b7cdb7e59b86962bc3aec5278be6ce5b95c2cbcefe23e340174.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 322, + 545, + 399 + ], + "lines": [ + { + "bbox": [ + 305, + 322, + 545, + 399 + ], + "spans": [ + { + "bbox": [ + 305, + 322, + 545, + 399 + ], + "type": "text", + "content": "Figure 8. Representative comparisons between various methods for joint estimation of normal and disparity. (a) Intensity images of recovered objects. (b) The first and third rows show the normal maps. The second and fourth rows show the disparity maps. The meanings of numbers below each normal map are the same as those in Fig. 5. The number below each disparity map represents the mean of disparity errors. " + }, + { + "bbox": [ + 305, + 322, + 545, + 399 + ], + "type": "inline_equation", + "content": "\\dagger" + }, + { + "bbox": [ + 305, + 322, + 545, + 399 + ], + "type": "text", + "content": ": the same network inputs as ours." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "table", + "bbox": [ + 307, + 441, + 545, + 506 + ], + "blocks": [ + { + "bbox": [ + 305, + 406, + 545, + 439 + ], + "lines": [ + { + "bbox": [ + 305, + 406, + 545, + 439 + ], + "spans": [ + { + "bbox": [ + 305, + 406, + 545, + 439 + ], + "type": "text", + "content": "Table 3. Accuracy comparisons between various methods for joint estimation of normal and disparity on all the data of our testing set. " + }, + { + "bbox": [ + 305, + 406, + 545, + 439 + ], + "type": "inline_equation", + "content": "\\dagger" + }, + { + "bbox": [ + 305, + 406, + 545, + 439 + ], + "type": "text", + "content": ": the same network inputs as ours." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 441, + 545, + 506 + ], + "lines": [ + { + "bbox": [ + 307, + 441, + 545, + 506 + ], + "spans": [ + { + "bbox": [ + 307, + 441, + 545, + 506 + ], + "type": "table", + "html": "
MethodAngular Error (deg.)Disparity Error (pix.)
MeanMedianMeanMedian
Long [28]†22.3418.593.913.02
Kusupati [24]†19.6916.113.262.79
Ours13.2211.142.111.98
", + "image_path": "45a2e733c8918565ddde7e12c4d6ee1bc4590cf3d3a6d9603c44343284fa1408.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "table_body" + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 520, + 545, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 520, + 545, + 568 + ], + "spans": [ + { + "bbox": [ + 304, + 520, + 545, + 568 + ], + "type": "text", + "content": "intensity images as inputs. For an unbiased comparison, we replace their inputs with the physical priors we use (see Section 3.2). Accordingly, we adjust and retrain their networks following their original setups." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 568, + 545, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 568, + 545, + 652 + ], + "spans": [ + { + "bbox": [ + 304, + 568, + 545, + 652 + ], + "type": "text", + "content": "Accuracy of Normal and Disparity. As shown in Table 3 and Fig. 8, Long and Kusupati lead to relatively unsatisfactory results. By contrast, our method can achieve the highest accuracy for both normal and disparity estimation. The reason is that our network architecture can leverage the polarization information, and also alleviate the ambiguity and orthographic projection problems in SfP." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 659, + 399, + 672 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 659, + 399, + 672 + ], + "spans": [ + { + "bbox": [ + 306, + 659, + 399, + 672 + ], + "type": "text", + "content": "5.3. Ablation Study" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 677, + 545, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 545, + 700 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 545, + 700 + ], + "type": "text", + "content": "In this section, we conduct ablation studies regarding our network inputs, SCMP module, and VDPE design." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 701, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 701, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 701, + 545, + 713 + ], + "type": "text", + "content": "Network Inputs. Recall that we take AoLP&DoLP and" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17293" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 99, + 287, + 201 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 287, + 93 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 287, + 93 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 287, + 93 + ], + "type": "text", + "content": "Table 4. Ablation study regarding different network inputs on all the data of our testing set." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 99, + 287, + 201 + ], + "lines": [ + { + "bbox": [ + 48, + 99, + 287, + 201 + ], + "spans": [ + { + "bbox": [ + 48, + 99, + 287, + 201 + ], + "type": "table", + "html": "
Network InputsAngular Error (deg.)Disparity Error (pix.)
MeanMedianMeanMedian
Intensity images33.2530.617.236.15
Raw polarization19.6516.945.194.78
AoLP&DoLP16.5112.864.233.97
Stokes maps17.1315.253.693.12
Inputs as DeepSfP [3]16.1214.374.053.68
Original (AoLP&DoLP and Stokes maps)13.2211.142.111.98
", + "image_path": "21a62e2038d4516158aefab3ab027fb31d7b14cc511ae8c7f37bc022c7889344.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 48, + 243, + 287, + 318 + ], + "blocks": [ + { + "bbox": [ + 47, + 215, + 287, + 237 + ], + "lines": [ + { + "bbox": [ + 47, + 215, + 287, + 237 + ], + "spans": [ + { + "bbox": [ + 47, + 215, + 287, + 237 + ], + "type": "text", + "content": "Table 5. Ablation study regarding SCMP module on all the data of our testing set." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 243, + 287, + 318 + ], + "lines": [ + { + "bbox": [ + 48, + 243, + 287, + 318 + ], + "spans": [ + { + "bbox": [ + 48, + 243, + 287, + 318 + ], + "type": "table", + "html": "
Network DesignAngular Error (deg.)Disparity Error (pix.)
MeanMedianMeanMedian
Without any SCMP22.1318.933.623.11
Without first SCMP16.2114.772.912.49
Without second SCMP15.2314.162.582.17
Original (with both SCMPs)13.2211.142.111.98
", + "image_path": "d2d0554380de29a254b97373006f74aa520d466454a6dc3bfea0473852d514cf.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 340, + 287, + 435 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 340, + 287, + 435 + ], + "spans": [ + { + "bbox": [ + 46, + 340, + 287, + 435 + ], + "type": "text", + "content": "Stokes maps as the network inputs (see Section 3.2). We replace these inputs with 1) intensity images, 2) raw polarization images, 3) AoLP&DoLP, 4) Stokes maps, and 5) inputs as DeepSfP, respectively. Table 4 shows that our network with original inputs leads to the highest recovery accuracy on both normal and disparity. The reason is that AoLP&DoLP and Stokes maps complement each other and facilitate the usage of polarization cues for our network." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 437, + 287, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 437, + 287, + 593 + ], + "spans": [ + { + "bbox": [ + 46, + 437, + 287, + 593 + ], + "type": "text", + "content": "SCMP Module. Recall that we embed two SCMP modules in our network for coarse-to-fine feature refinement to solve the ambiguity problem (see Section 3.3). In this study, we compare our strategy with the simplified designs: 1) without any SCMP module, 2) without the first SCMP module, 3) without the second SCMP module. Table 5 shows that with only one SCMP module (regardless of the first or second one), the network can still achieve improvement in normal recovery accuracy, which proves the effectiveness of SCMP. In addition, the effect of the first module is more obvious. By contrast, our original design achieves the highest accuracy, demonstrating the effectiveness of our feature refinement strategy." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "type": "text", + "content": "VDPE Design. Recall that we use the VDPE design in our network to handle the non-orthographic projection (see Section 3.4). In this study, we compare our design with the other encoding strategies: 1) classical position encoding methods based on Absolute Positional Embedding (APE) [43] or Relative Positional Embedding (RPE) [38], 2) viewing encoding (VE) of Lei [25]. Table 6 shows that compared with APE and RPE, both VE and our VDPE show improvement since they introduce the viewing directions and enable the networks to handle the non-orthographic" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 307, + 68, + 542, + 194 + ], + "blocks": [ + { + "bbox": [ + 307, + 68, + 542, + 194 + ], + "lines": [ + { + "bbox": [ + 307, + 68, + 542, + 194 + ], + "spans": [ + { + "bbox": [ + 307, + 68, + 542, + 194 + ], + "type": "image", + "image_path": "68a29954a7e10fbd221e27c8de3cfac80bdedcaac412d953d30552b5c4d903b1.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 198, + 545, + 242 + ], + "lines": [ + { + "bbox": [ + 305, + 198, + 545, + 242 + ], + "spans": [ + { + "bbox": [ + 305, + 198, + 545, + 242 + ], + "type": "text", + "content": "Figure 9. Representative ablation study regarding VDPE design. The meanings of numbers below each normal map are the same as those in Fig. 5. The second row shows the error maps corresponding to the normal maps." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 307, + 284, + 545, + 360 + ], + "blocks": [ + { + "bbox": [ + 306, + 256, + 545, + 278 + ], + "lines": [ + { + "bbox": [ + 306, + 256, + 545, + 278 + ], + "spans": [ + { + "bbox": [ + 306, + 256, + 545, + 278 + ], + "type": "text", + "content": "Table 6. Ablation study regarding VDPE design on all the data of our testing set." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 284, + 545, + 360 + ], + "lines": [ + { + "bbox": [ + 307, + 284, + 545, + 360 + ], + "spans": [ + { + "bbox": [ + 307, + 284, + 545, + 360 + ], + "type": "table", + "html": "
Encoding StrategyAngular Error (deg.)Disparity Error (pix.)
MeanMedianMeanMedian
APE [43]17.6815.633.152.81
RPE [38]16.4314.793.112.56
VE [25]15.8914.172.932.42
Original (VDPE)13.2211.142.111.98
", + "image_path": "4f79c88e772c49a3569a588929eeeb0f35051992e77f16c1ed9ea814bcd3b8bd.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 376, + 545, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 376, + 545, + 483 + ], + "spans": [ + { + "bbox": [ + 304, + 376, + 545, + 483 + ], + "type": "text", + "content": "projection. Moreover, the proposed VDPE design is more accurate than VE. Fig. 9 shows that RPE and VE both suffer from the non-orthographic projection problem and show higher errors on the area far from the image center. By contrast, our VDPE design avoids this problem and achieves better recovery results. The reason is that our design treats the viewing directions as part of the positional encoding in Transformer, which enhances the usage of viewing directions by global attention." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 500, + 383, + 512 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 500, + 383, + 512 + ], + "spans": [ + { + "bbox": [ + 306, + 500, + 383, + 512 + ], + "type": "text", + "content": "6. Conclusions" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 522, + 545, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 522, + 545, + 654 + ], + "spans": [ + { + "bbox": [ + 304, + 522, + 545, + 654 + ], + "type": "text", + "content": "In this paper, we propose the first approach that combines stereo polarimetric imaging and deep learning to recover accurate normal and disparity. We design a mask prediction module to solve the ambiguity problem based on the shape consistency between normal and disparity. In addition, we propose a novel positional encoding method to solve the orthographic projection problem. Moreover, we establish a large real-world dataset for stereo SfP problem. Experiments on the proposed dataset demonstrate that our method outperforms existing SfP methods in terms of accuracy and robustness to light variation." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "Acknowledgement. This work is supported in part by the CUHK T Sone Robotics Institute, and in part by the InnoHK of the Government of Hong Kong via the Hong Kong Centre for Logistics Robotics." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17294" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 92, + 287, + 713 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 53, + 92, + 287, + 114 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 92, + 287, + 114 + ], + "spans": [ + { + "bbox": [ + 53, + 92, + 287, + 114 + ], + "type": "text", + "content": "[1] Gary A Atkinson. 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That is, given a video, we aim to predict an adverb indicating a modification applied to the action (e.g. cut \"finely\"). We cast this problem as a regression task. We measure textual relationships between verbs and adverbs to generate a regression target representing the action change we aim to learn. We test our approach on a range of datasets and achieve state-of-the-art results on both adverb prediction and antonym classification. Furthermore, we outperform previous work when we lift two commonly assumed conditions: the availability of action labels during testing and the pairing of adverbs as antonyms.", + "bbox": [ + 75, + 300, + 468, + 479 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Existing datasets for adverb recognition are either noisy, which makes learning difficult, or contain actions whose appearance is not influenced by adverbs, which makes evaluation less reliable. To address this, we collect a new high quality dataset: Adverbs in Recipes (AIR). We focus on instructional recipes videos, curating a set of actions that exhibit meaningful visual changes when performed differently. Videos in AIR are more tightly trimmed and were manually reviewed by multiple annotators to ensure high labelling quality. Results show that models learn better from AIR given its cleaner videos. At the same time, adverb prediction on AIR is challenging, demonstrating that there is considerable room for improvement.", + "bbox": [ + 75, + 481, + 468, + 678 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 694, + 207, + 709 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Learning how an action is performed in a video is an important step towards expanding our video understanding beyond action recognition. This task has been referred to as \"adverb recognition\", and has potential useful applications in robotics and retrieval. Consider a scenario where a robot handles fragile objects. In such case we would like to tell the robot to grasp objects gently to prevent it from breaking things. Similarly, learning how actions are performed enables more sophisticated queries for retrieval. Imagine learning a new recipe where a crucial step is stirring a mixture vigorously. It would be useful to find good examples showing how to whip a mixture in such a manner.", + "bbox": [ + 75, + 719, + 468, + 900 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/5a3782a3da153dcfcf9b464efeeef77b5a5f4caf3f9e5f3c7695d080e45911d0.jpg", + "image_caption": [ + "Figure 1. We aim to predict the way an action is performed in a video (right). Actions and their outcomes change in different ways when modified by adverbs, e.g. grinding coffee slowly does not have the same effect as grinding it coarsely (left). We learn to predict adverbs by recognising action changes in the video. We define action changes measuring verb-adverb textual relationships." + ], + "image_footnote": [], + "bbox": [ + 519, + 265, + 751, + 468 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c2e5c2ba462eca3388337d582bbb96330c083e854b6189c054e03690bd0646ed.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 789, + 266, + 872, + 450 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Adverb recognition is a challenging problem. Firstly, a single adverb can modify multiple actions in different ways. For example, to grind coffee coarsely (see Figure 1) we need to set a certain granularity in a grinder. Conversely, to spray something coarsely we would just use a spraying can more sparingly. Secondly, compared to actions or objects, adverbs are much harder to identify. Though somewhat subjective [1, 16], the temporal boundaries of an action can be easily determined. The spatial extent of an object is also easy to recognise for a human. Adverbs are instead more abstract: we can see their effect, but we struggle to pinpoint the spatio-temporal location where the adverb is appearing. Consider for example the act of spraying something slowly in Figure 1. We could say that slowly \"is located\" on the hand motions. At the same time, spraying something slowly could implicate a more even coating of a surface. That is, the outcome of an action and the end-state of the involved objects can also change according to the adverb. This makes it hard to label adverbs with visual annotations (e.g. bounding boxes), which makes the problem more challenging.", + "bbox": [ + 496, + 598, + 892, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "23110", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In fact, previous approaches [6, 7] learn adverbs as action changes in a weakly supervised manner. The state-of-the-art approach [6] treats adverbs as learnable parameters that modify actions. Specifically, the action change is learnt during training by contrasting antonyms, i.e. opposite adverbs. We show that learning adverbs in such manner can be difficult and can limit the ability of the model to generalise. We thus propose to define action changes by measuring distances in a text embedding space, and aim to learn such change from the video through regression. We show that our approach achieves new state-of-the-art results through extensive experiments. We also lift two major assumptions made in previous work [6, 7]: the availability of action labels during testing and the pairing of opposite adverbs as antonyms. Our method achieves stronger performance especially when the above assumptions are relaxed.", + "bbox": [ + 76, + 90, + 472, + 332 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Besides being challenging, adverb recognition is also an under-explored domain and only few datasets are available. Doughty and Snoek [7] addressed the problem of scarce annotations, proposing a semi-supervised method that assigns pseudo-labels to boost recognition performance. Three datasets sourced from captioning benchmarks were also collected in [7]. These datasets offer a large number of clips, actions and adverbs. However, adverbs in these datasets appear to be descriptive rather than action modifiers, i.e. actions do not display a significant change when modified by the adverb. This is an issue when adverbs are modelled as action changes as in this work. We thus introduce a new dataset focusing on instructional videos where actions change considerably depending on the way they are carried out. We focus on cooking videos since in this domain action changes are prominent. Our Adverbs in Recipes (AIR) dataset was manually labelled and consists of over 7K videos, 10 adverbs and 48 actions.", + "bbox": [ + 76, + 333, + 472, + 604 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To summarise our contributions: i) we propose a more effective approach to learn adverbs in videos. Our method achieves state-of-the-art results on multiple datasets and with fewer assumptions; ii) we introduce the AIR dataset for adverb recognition. Our focus on a domain where action changes are prominent and our careful manual annotation makes AIR more suitable for training and evaluating models for adverb understanding. We publicly release AIR and our code at github.com/dmoltisanti/air-cvpr23.", + "bbox": [ + 76, + 607, + 472, + 744 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 753, + 218, + 768 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Adverb Recognition Doughty et al. [6] introduced the adverb recognition task and proposed Action Modifiers. Adverbs are treated as learnable parameters that guide the optimisation of the video embeddings via a triplet loss. We show that such approach can be difficult to optimise and propose an alternative learning method. Rather than modelling action changes as trainable parameters we define them measuring distances in a text embedding space.", + "bbox": [ + 76, + 780, + 470, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We then learn action modifications via regression. We provide a more technical comparison in Section 3. A follow-up work [7] proposes a pseudo-labelling method where videos are assigned new labels based on the model prediction. Pseudo labels are obtained in an adaptive away, i.e. the threshold determining whether a label should be assigned is adapted for each adverb independently. In [7] the underlying model is also Action Modifiers [6]. Pang et al. [18, 19] introduced the \"Behaviour Adverb\" task. Here actions are not goal-oriented (e.g. \"kiss, smoke\") and adverbs correspond to moods (e.g. \"sadly, solemnly\"). Models use additional modalities such as human pose [18] or explicitly learn human expressions [8, 19]. While related, this task is different from the scope of this work, where we aim to learn action changes in goal-oriented (e.g. cooking) videos.", + "bbox": [ + 496, + 90, + 893, + 318 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Adverb Datasets HowTo100M Adverbs [6] collects data from the instructional dataset HowTo100M [14] finding adverbs in the narration captions. Videos are loosely trimmed around the timestamp associated with the adverb. Due to the video-text misalignment in HowTo100M, and because training videos were not manually reviewed, videos in HowTo100M Adverbs are noisy. Authors estimated that only $44\\%$ of the training videos actually show the action. In total 6 adverbs were annotated. Three other datasets were introduced in [7]: ActivityNet/MSR-VTT/VATEX Adverbs. These are subsets of the namesake captioning datasets [11,23,26]. Videos were also obtained finding adverbs in captions, but annotations here are clean because captions were provided by annotators. We argue that the captioning nature of the original datasets is a reason of concern for learning action modifications. Indeed, adverbs tend to be a complementary description of the video, i.e. actions do not appear particularly influenced by the adverb. Peering into these datasets (see Figure 4), we found for example \"sit inside/outside, talk outdoors/indoors, walk in/out, move down/up\", etc. These adverbs modify the appearance of the video, however the action themselves are not modified. Arguably, the act of sitting is the same whether it takes place inside or outside, as is the act of walking in or out. Lastly, [18, 19] annotated adverbs for non-task-oriented actions, e.g. \"run, kiss\", however adverbs here express moods and manners, e.g. \"politely, reluctantly\".", + "bbox": [ + 496, + 321, + 893, + 729 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The limited availability of datasets specifically designed for adverb understanding motivates us to collect a new dataset better suited for this task. We focus on recipe instructional videos where actions change significantly according to the adverb. We collect Adverbs in Recipes, which contains 7K videos, 10 adverbs and 48 actions. We employ annotators to verify that actions are carried out as indicated by the adverb. We present our dataset in Section 4.", + "bbox": [ + 496, + 729, + 893, + 851 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Video-text Retrieval Understanding adverbs in videos is related to video-text retrieval [2, 5, 9, 11-13, 15, 17, 22, 28, 30]. Theoretically, these methods could be used to retrieve", + "bbox": [ + 496, + 854, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "23111", + "bbox": [ + 478, + 944, + 517, + 957 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/505d8bf455fdbfd51f99f81067f422602ef5e0c3893c885f392e8361ffe80823.jpg", + "image_caption": [ + "Figure 2. Comparison between the unscaled distance $d$ (left) and the scaled distance $\\delta$ (right), which is scaled using the verb-adverb cosine similarity. Plotted values are the Euclidean distances between corresponding positive and negative sentences. Blue/yellow indicate small/large distances, i.e. a small/big change when adverbs are flipped in the positive sentence (see text for more information)." + ], + "image_footnote": [], + "bbox": [ + 81, + 88, + 486, + 175 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/7cf16ab30e16c33428b5c4fd2f7567df3472e268469a5083b0205aeabacf0abe.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 486, + 89, + 890, + 175 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "videos using adverbs as text queries. However, as noted in [7], most approaches encode text embeddings for whole sentences, i.e. it is hard to retrieve videos querying single words. Some works propose fine-grained video-text retrieval where single parts-of-speech can be queried [4, 24, 27, 29], however these works focus on verbs and nouns and were not evaluated for adverbs. As discussed before, adverbs are more abstract compared to verbs and nouns and are difficult to spatio-temporally localise. This entails that a video-text retrieval approach is unlikely to work well to find adverbs in videos. We test a retrieval baseline with an S3D model [13] where video and text embeddings were jointly learnt. Despite the strong performance on a number of tasks, we show that indeed this model struggles to achieve satisfactory performance.", + "bbox": [ + 75, + 250, + 472, + 477 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 484, + 168, + 500 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We are given a video $x$ labelled with a verb $v$ , which annotates the action, and an adverb $a$ , which indicates the way the action is carried out. Our goal is to predict $a$ in $x$ given $v$ . We also have a mapping $h$ between adverbs opposite in meaning, e.g. $h(\\text{quickly}) = \\text{slowly}$ . We use a pre-trained video backbone $f$ to extract video features $f(x)$ . In this work we deal with long videos (10-40s), so we employ transformer-style attention [21] to attend to the relevant parts of the video. To this end, we use a pre-trained text model $g$ to extract a text embedding $g(v)$ , which we use as query for the attention, obtaining the projected video embedding $f'(x, v)$ . To learn more specialised video features we feed $f'(x, v)$ to a shallow MLP and obtain the final output of the model $\\rho(f'(x, v))$ . We propose two methods to optimise the network casting the problem either as a classification or a regression task. In the former case we utilise the standard Cross Entropy (CE) loss using the ground truth adverb label $a$ . The CE pushes up predictions for the positive class and treats all negative classes equally. In some cases, however, it may be desirable to penalise the model more aggressively for incorrect predictions of antonym classes. Action Modifiers [6] uses the triplet loss for this purpose. However, in [6] negative samples are formed by only pairing antonyms. This is effective for distinguishing opposite adverbs, but does not train the model to distinguish an adverb from other negative non-antonym classes.", + "bbox": [ + 75, + 508, + 472, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We thus propose a second approach based on regression. Casting the task as a regression problem we aim to directly learn the change the adverb introduces to the action and the video. However, we do not have a ground truth quantifying such action modifications. We use a text embedding space to estimate action changes. The high level idea is that we first build a minimal sentence $s$ representing the modified action. We similarly build a negative sentence $\\tilde{s}$ representing the action modified in the opposite way. Calculating the difference between $s$ and $\\tilde{s}$ we have a proxy measure for the change the adverb applies to the action. We build $s$ concatenating the verb and the adverb (e.g. coat thinly), then generate $\\tilde{s}$ replacing the adverb with its antonym (e.g. coat thickly). We then extract text embeddings $g(s)$ and $g(\\tilde{s})$ . Note that $g$ receives a variable length sentence and outputs a fixed-dimension embedding. Let $\\langle \\rangle$ denote concatenation, so $s = \\langle v, a \\rangle$ and $\\tilde{s} = \\langle v, h(a) \\rangle$ . We measure the difference between $s$ and $\\tilde{s}$ to capture how $a$ changes $v$ :", + "bbox": [ + 496, + 250, + 893, + 523 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nd (v, a) = \\left\\| g (\\langle v, a \\rangle) - g (\\langle v, h (a) \\rangle) \\right\\| _ {2} \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 563, + 537, + 890, + 566 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Ideally, $d$ could be used as is. However, we observed that for a given adverb $a$ we obtain similar $d(v, a)$ across most verbs $v$ . This defeats the purpose of measuring action changes via $d$ since $d$ itself is not discriminative enough. This happens because $d$ ignores the correlation between the verb and the adverb. Intuitively, if a verb and an adverb are not semantically correlated (e.g. \"run thinly\") then we cannot expect to capture a meaningful change when flipping the adverb in the negative sentence (recall that $g$ receives full sentences). To address this issue we scale $d$ with the cosine similarity between the verb $v$ and the adverb $a$ :", + "bbox": [ + 496, + 573, + 893, + 739 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\delta (v, a) = d (v, a) \\cdot \\frac {g (v) \\cdot g (a)}{\\| g (v) \\| _ {2} \\cdot \\| g (a) \\| _ {2}} \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 568, + 747, + 890, + 782 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Figure 2 compares $d$ (left) to $\\delta$ (right) for a few (verb, adverb) combinations. Note how the unscaled distance $d$ is not discriminative given that adverbs display a similar $d$ across verbs. On the other hand, the scaled $\\delta$ shows a meaningful distance. For example, we observe a large $\\delta$ for adverbs \"finely\" and \"coarsely\" when paired with verbs \"chop, mince, mash, grate\".", + "bbox": [ + 496, + 794, + 893, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "23112", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/394538ec889fb60f06760c1867d2a5ccbd0b33ee72bc40dfedfb48a04b0a3042.jpg", + "image_caption": [ + "Figure 3. Pipeline of our method. Given a long video $x$ labelled with a verb $v$ and an adverb $a$ we learn video embeddings $f'(x, v)$ through attention. We optimise the model with two alternative methods: standard classification (CE: Cross Entropy) or regression (MSE: Mean Squared Error). We build a regression target measuring distances in a text embedding space, which estimates the action change we aim to learn in the video. The video backbone and text model are initialised from pre-trained models and are not fine-tuned during learning." + ], + "image_footnote": [], + "bbox": [ + 166, + 85, + 803, + 244 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Now that we have an estimate to measure action changes we can build a regression target:", + "bbox": [ + 76, + 324, + 470, + 354 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nY ^ {R} (v) = \\left(t _ {i}, \\forall i \\in \\{1, 2, \\dots , A \\}\\right) = \\left\\{ \\begin{array}{c c} \\delta (v, a) & \\text {i f} y _ {i} = a \\\\ - \\delta (v, a) & \\text {i f} y _ {i} = h (a) \\\\ 0 & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 361, + 478, + 429 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $A$ is the number of adverbs in a dataset and $y_{i}$ denotes the $i$ -th adverb. Let $\\hat{y}_i^v$ indicate the output of the model for the $i$ -th adverb obtained for verb $v$ , i.e. querying the attention model with $g(v)$ . The full output of the model is then $\\hat{Y}^{v} = \\rho (f^{\\prime}(x,v)) = (\\hat{y}_{i}^{v},\\forall i\\in \\{1,2,\\ldots ,A\\})$ .", + "bbox": [ + 75, + 430, + 468, + 506 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We use the Mean Squared Error to train the network: $\\mathcal{L}^R = \\| Y^R (v) - \\hat{Y}^v\\| _2$ . The loss pushes opposite adverbs furthest apart (due to the negative sign of $\\delta$ for the antonym). The loss also tells the model that the video is not modified by other unrelated adverbs (target is 0 for classes that are neither ground truth nor antonyms). This discourages the model to predict negative non-antonym adverbs. Figure 3 illustrates our method. Note that the video backbone and text model are not part of the training, i.e. they are initialised from pre-trained models and are not fine-tuned.", + "bbox": [ + 75, + 506, + 470, + 656 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Learning without Antonyms We also consider a setting where adverbs are not paired in antonyms. Instead of replacing the ground truth adverb with its antonym we simply remove the adverb and generate $\\tilde{s} = v$ . In this case $\\delta$ measures the difference between the action modified by the adverb and the unmodified version of the action. $Y^{R}$ is then $\\delta$ for the ground truth adverb and 0 for all other adverbs.", + "bbox": [ + 75, + 662, + 468, + 768 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Inference As in [6] we are given the action label $v$ during testing. We query the attention model with $g(v)$ and use $\\hat{Y}^v$ to predict each adverb. We also test the model without action labels. In such case we obtain $f'(x, v)$ querying all actions and take the maximum prediction for each adverb:", + "bbox": [ + 76, + 772, + 470, + 848 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\np (x) = \\left(\\max _ {v} \\left(\\hat {y} _ {i} ^ {v}, \\forall v \\in \\mathcal {V}\\right), \\forall i \\in \\{1, 2, \\dots , A \\}\\right) \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 96, + 857, + 468, + 878 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\nu$ denotes the set of action labels.", + "bbox": [ + 76, + 885, + 346, + 898 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Comparison to Action Modifiers Our framework shares the same design as Action Modifiers [6] until $f'(x, v)$ . In [6] $f'(x, v)$ is optimised with two triplet losses: an action loss to help the attention model and an adverb loss to learn adverbs. We do not use an additional action loss. In Action Modifiers adverbs are also modelled as action changes utilising text embeddings. However, in [6] such change is treated as an additional parameter to be learnt. Specifically, an adverb is represented as a learnable matrix $W_{a}$ . The linear combination $o_{v}^{a} = W_{a} g(v)$ represents the change the adverb $a$ applies to the verb $v$ , where $g(v)$ is a text embedding as in our model. Importantly, $o_{v}^{a}$ is used in the triplet losses, thus the optimisation of the video embedding $f'(x, v)$ depends on the optimisation of parameters $W_{a}$ . We argue and show that learning adverbs with this approach can be difficult as the action change the model looks for in the video has also to be learnt. In our formulation instead the action change is pre-computed and is not learnt. We also provide explicit penalty for non-antonym classes rather than contrasting only opposite adverbs. Comparing capacity, our model has a smaller number of parameters which scales better with the number of adverbs. Indeed, each adverb in Action Modifiers requires a learnable matrix, whereas in our model only the last layer of the MLP varies with the number of adverbs (see supplementary material).", + "bbox": [ + 496, + 324, + 890, + 702 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Adverbs in Recipes: the AIR Dataset", + "text_level": 1, + "bbox": [ + 498, + 708, + 834, + 726 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In Section 2 we motivated the need for a new dataset for adverb recognition. Here we introduce the Adverbs in Recipes (AIR) dataset. We wish to find a set of videos where actions change significantly according to the adverb. Compared to captioning benchmarks, instructional datasets contain videos where we can expect to find more of such actions. For this reason we source AIR from HowTo100M [14]. We restrict our interest to recipe videos since changes in cooking actions play an important role. For example, a carrot sliced à la juillienne (thinly) looks very different from a carrot chopped in thick dices (coarsely).", + "bbox": [ + 496, + 734, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "23113", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/d60e67ad922558b850afcf83a6c50e23b11865ffdeaf2a39a1ff03be645a64d7.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
DatasetAccuracyDurationAdvActPairsVideos
CAPTActivityNet Adverbs [7]89.0%37.5s201146353,099
MSR-VTT Adverbs [7]91.0%15.7s181064501,824
VATEX Adverbs [7]93.5%10.0s (f)341351,52414,617
INSTHowTo100M Adverbs [6]44.0%20.0s (f)6722575,824
Adverbs in Recipes (ours)95.3%8.4s10481867,003
", + "bbox": [ + 76, + 88, + 470, + 165 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 1. Comparing video datasets for adverb recognition. CAPT: captioning datasets, where adverbs are descriptive. INST: instructional datasets, where adverbs are action-focused. \"Accuracy\" indicates whether the action is visible as indicated by the adverb. \"Duration\" reports the average length, where (f) denotes a fixed duration. \"Pairs\" counts (verb, adverb) appearing in the dataset rather than the Cartesian product of all verbs and adverbs.", + "bbox": [ + 75, + 176, + 468, + 273 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In other words, adverbs are \"easily visible\" in recipe videos and involve interesting visual cues such as speed, temporal/spatial completeness and objects end-states.", + "bbox": [ + 75, + 282, + 468, + 328 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Data Collection We start selecting all recipe videos in HowTo100M. We then parse captions to keep only those containing a verb and an adverb. We filter videos removing verbs that indicate non visual actions (e.g. \"watch, wait\") or very long-term actions (e.g. \"rise, grow\"), since we do not expect these changes to be fully visible in the videos. We manually merge similar verbs, obtaining in total 48 verbs. We also remove infrequent and too generic adverbs (e.g. \"carefully\"). We cluster similar adverbs gathering a total of 10 adverbs, which we pair in antonyms. To trim videos in a tight manner we use the timestamps of the first/last word in a caption as the start/end of the action segment. At this point we have a set of videos of varying duration, each accompanied with a verb and an adverb. We ask annotators on Amazon Mechanical Turk (AMT) to check whether the action in a video is visible and is carried out as indicated by the adverb. For robustness we ask 3 different annotators to check the same video and employ 5 people for edge cases where annotators disagreed. We keep videos where the majority of the annotators confirmed that the action is visible as indicated by the adverb, collecting 7,003 videos. Figure 2 shows the verbs (columns) and adverbs (rows) in AIR. We provide more details in the supplementary material.", + "bbox": [ + 76, + 349, + 472, + 698 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Comparison to Other Datasets Table 1 compares AIR to other adverb $\\text{dattets}^1$ reviewed in Section 2. \"Accuracy\" estimates the percentage of videos where the action and the adverb effect are visible. On the existing datasets this was estimated watching 200 videos in [7]. For AIR multiple annotators reviewed all videos, however, annotations on AMT can be noisy. We review 302 videos (5% of the dataset) and report this check as \"Accuracy\". Compared", + "bbox": [ + 75, + 718, + 468, + 840 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/ca26cd8e2aaf7faa04bf746db6d08b8aa515800f64019570bdecda0217251bab.jpg", + "image_caption": [ + "Figure 4. Samples from existing datasets for adverb recognition and our new AIR dataset. Many adverbs in the captioning datasets appear to be descriptive rather than a key modification of the action (e.g. the act of talking/sitting is the same whether it takes place indoors/outdoors). In contrast, adverbs in the instructional datasets apply a more prominent change in the action and its outcome (e.g. a vegetable peeled coarsely will still have some skin attached)." + ], + "image_footnote": [], + "bbox": [ + 501, + 88, + 630, + 202 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/1f5a9dc36ac16b9366cfa05a780d2a9769c920bceb16dc1f317efea49bb5da67.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 630, + 88, + 761, + 202 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/0ad6f7ddd98748b132507e52a9fdefc21b8189a9168ad627f7d0f51deeb4fb2d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 761, + 88, + 890, + 202 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "to the instructional-based HowTo100M Adverbs, AIR contains over 1,100 additional clips and 4 more adverbs. Importantly, our videos are manually reviewed (AIR accuracy is over $95\\%$ compared to $44\\%$ ) and better trimmed (averaged duration is 8s compared to fixed 20s segments). AIR features 48 actions which is the smallest number among the five datasets (and consequently the smallest number of pairs). This is due to our more restrictive verb filtering based on visual and task-oriented actions. For example, in the captioning datasets there are actions such as \"tell, talk, sing, look\". Actions in HowTo100M Adverbs are task oriented, however there are also verbs entailing long-term actions (e.g. \"brew\"), which are unlikely to be fully visible.", + "bbox": [ + 496, + 335, + 890, + 532 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Figure 4 shows a few samples from AIR as well as the other datasets. Note how adverbs in the instructional datasets apply a key modification in the action, whereas for the captioning datasets adverbs are descriptive. Cap-tions in the captioning datasets are reliable because they were provided by human annotators. However, annotators did not necessarily use adverbs to indicate a modification to the action. Thus, due to the automatic processing of these datasets, there are several cases where adverbs are descriptive and do not influence the action. Naturally, Figure 4 is not meant to be an exhaustive representation of the caption-ing datasets from [7]. These datasets also contain action-focused adverbs, however without extensively reviewing the videos and the associated adverbs it is hard to gauge how many actions are effectively modified by the adverb.", + "bbox": [ + 496, + 536, + 892, + 762 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To summarise the contributions of AIR: i) we employ annotators to verify that actions are performed in the way indicated by the adverb; ii) this allowed us to trim videos more tightly and obtain cleaner clips with less unrelated content; iii) we carefully choose verbs and adverbs to pick videos where action changes are significant. While we restrict our domain to recipes, cooking actions are visually diverse, entail complex object interactions and are particularly affected by the nuanced ways they are carried out.", + "bbox": [ + 496, + 763, + 893, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_footnote", + "text": "1We report the number of videos from [7]. Some videos are missing as they were removed from YouTube. We were able to download: ActivityNet A.: 2,972 - MSR-VTT A.: 1,747 - VATEX A.: 13,947, HowTo100M A.: 5,462. Duration and pairs are reported from the downloaded videos.", + "bbox": [ + 75, + 849, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "23114", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 76, + 89, + 209, + 107 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation Details We use an S3D model [13, 25] jointly pre-trained on video and text on HowTo100M [14] as our video backbone. Specifically, we use the video output mixed_5c to obtain $f(x)$ . Following [6] we split videos in 1-second segments and sample 16 RGB frames from each segment to obtain the video features. Stacking features from the video segments we have $f(x)^{T \\times D}$ , where $T$ varies depending on the dataset and $D$ is 1024. We use 4 heads for the attention model. The dimension $E$ of the query, key and value is 512, thus the projected video embedding $f'(x, v)$ has dimension $1 \\times E$ . The MLP in our model has 3 layers (hidden units of dimension 512) with ReLU activation function for the hidden layers and dropout [20] set to 0.1. We train all models for 1000 epochs with the ADAM optimiser [10], setting learning rate to $1e^{-4}$ , weight decay to $5e^{-5}$ and batch size to 512. We use the text model jointly trained with S3D to extract text embeddings $g(\\cdot)$ . This network, like the visual backbone, is not fine-tuned. We refer to [13] for more details about S3D and the text model. $f(x)$ and $g(\\cdot)$ are the same for all experiments.", + "bbox": [ + 76, + 114, + 472, + 419 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Baselines Priors: here we do not train any model and simply use the prior distributions of the training set to make a prediction. When using the action label during testing, the prediction for an adverb is the number of training samples labelled with the adverb and the given verb, i.e. $p(x,v) = (\\pi (v,a),\\forall a\\in \\mathcal{A})$ , where $\\pi$ denotes the frequency of $(v,a)$ in the training set and $\\mathcal{A}$ is the set of adverbs in a dataset. While this baseline is a simple look-up table, it can achieve strong performance since it exploits the co-occurrence of verbs and adverbs. When the action label is not used during testing the priors baseline predicts the frequency of each adverb in the training set, i.e. $p(x) = (\\pi (a),\\forall a\\in \\mathcal{A})$ .", + "bbox": [ + 76, + 429, + 472, + 611 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "S3D pre-trained: we test the S3D model we use as the video-text backbone for all experiments. Video and text embeddings were jointly learnt in this model, so we use the dot product between $f(x)$ and $g(\\cdot)$ for predictions. When the action label $v$ is given during inference the prediction is $p(x,v) = (f(x)\\cdot g(\\langle v,a\\rangle),\\forall a\\in \\mathcal{A})$ , where $g(\\langle v,a\\rangle)$ is the text embedding obtained concatenating the given $v$ and each adverb $a$ . When the action label is not given, we have $p(x) = (\\max_v f(x)\\cdot g(\\langle v,a\\rangle),\\forall v\\in \\mathcal{V}),\\forall a\\in \\mathcal{A})$ , where $\\mathcal{V}$ is the set of verbs. This S3D instance has shown very strong performance on several tasks [13], thus this baseline helps gauging the difficulty of detecting adverbs following a basic video-text retrieval approach.", + "bbox": [ + 76, + 612, + 472, + 813 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "SOTA Act Mod: we compare against the state-of-the-art for adverb recognition, Action Modifiers [6], both using the original model and a deeper version with an additional MLP $(MLP + ActMod)$ . Here we append an identical MLP as in our model to the output of the transformer attention. This variant allows a better comparison with our method. We use the official code implementation to run our experiments. Note that Action Modifiers results reported here are not directly comparable to those reported in [6,7]. This is because we could not download several videos since they were removed from YouTube. Also, we use S3D features (identical for all experiments) instead of I3D [3] features.", + "bbox": [ + 500, + 90, + 890, + 271 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Our Variants CLS: our model trained with classification. REG - fixed $\\delta$ : our model trained with regression discarding text embeddings altogether, setting $\\delta = 1$ in Equation 3. This is to validate the premise of using textual context to build a regression target. REG: our model trained with regression using the full formulation.", + "bbox": [ + 498, + 273, + 890, + 364 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation Metrics We report mean Average Precision using two types of averaging: i) weighted (mAP W), where class scores are weighted according to the support size (smaller classes have a smaller weight); ii) macro (mAP M), where all classes have equal weight, which corresponds to \"adverb-to-video (all)\" in [6]. All the evaluated datasets exhibit a significant class imbalance, thus mAP M is a stricter metric compared to mAP W. We also report binary antonym accuracy (Acc-A), which corresponds to \"video-to-adverb (antonym)\" in [6]. Here we only look at the prediction of an adverb $a$ versus its antonym $h(a)$ . A prediction $p$ is correct if $p(a) > p(h(a))$ . All metrics are computed for adverb classes. To show the full potential of all methods we report each best metric independently, i.e. results may come from different epochs. This is to provide a robust comparison, however we note that all models reach stable convergence.", + "bbox": [ + 498, + 366, + 892, + 608 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets We present experiments on the two instructional datasets we saw earlier: HowTo100M Adverbs [6] and our Adverbs In Recipes. As discussed before, we argue that instructional videos are more suitable for this task as adverbs are action-focused, i.e. actions change significantly according to the adverb. For completeness, we also evaluate the three adverb datasets sourced from captioning videos in [7]: ActivityNet/MSR-VTT/VATEX Adverbs3. Adverbs here are descriptive, thus these datasets are less reliable for evaluation. Datasets are summarised in Table 1.", + "bbox": [ + 498, + 609, + 890, + 760 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Results", + "text_level": 1, + "bbox": [ + 500, + 767, + 591, + 781 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Overview We begin our discussion looking at results in Table 2 on the instructional datasets (left). Here we achieve new state-of-the-art results on all metrics. The gap between our best variant and Act Mod is more noticeable for the more challenging mAP W/M metrics. In [6] negative samples are", + "bbox": [ + 498, + 789, + 890, + 867 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "3For these datasets there are several partitions for different tasks (e.g. unseen domain). For convenience we create our own train/test split.", + "bbox": [ + 500, + 875, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "There is no official train/test split in HowTo100M, thus S3D in [13] was trained on videos that appear in the test sets of HowTo100M Adverbs and AIR. However, this is not a concern: Tables 2, 3 show that the S3D pre-trained baseline achieves poor performance, as the original S3D training objective (video-text alignment) is substantially different from ours. Importantly, all methods receive the same features for fair comparison.", + "bbox": [ + 75, + 825, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "23115", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/b456420b28b32ea854d4a99e8ff35707c1a4dd2f429f903b05c1af9bd5334f56.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Priors
S3D pre-trained
Act Mod [6]
MLP + Act Mod [6]
CLS
REG - fixed δ
REG
", + "bbox": [ + 76, + 130, + 174, + 204 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/96048aad8627b2f571979338ce9520761ec16eeb71290a8aec9fb3703d69591e.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Instructional datasets. Action-focused adverbs
HowTo100M Adverbs [6]Adverbs in Recipes
mAP WmAP MAcc-AmAP WmAP MAcc-A
0.4460.3540.7860.4910.2630.854
0.3390.2380.5600.3890.1730.735
0.4060.3720.7960.4210.1700.858
0.2790.1930.7930.4580.1880.857
0.5620.4200.7860.6750.3250.847
0.3200.2150.7060.4580.1450.835
0.5550.4230.7990.6690.2970.862
", + "bbox": [ + 200, + 89, + 470, + 205 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/9e502ff1150f6289a8f7e57485005a44ea24446e678eb20ae154b470fada1026.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Captioning datasets. Descriptive adverbs
ActivityNet Adverbs [7]MSR-VTT Adverbs [7]VATEX Adverbs [7]
mAP WmAP MAcc-AmAP WmAP MAcc-AmAP WmAP MAcc-A
0.2170.1590.7450.3080.1520.7230.2160.0860.752
0.1180.0700.5600.1940.0750.6030.1220.0380.586
0.2110.1520.7480.2460.1480.7340.1390.0590.751
0.1540.1080.7530.2150.1110.7310.2090.0960.752
0.1140.0720.7140.1890.0810.7230.2830.1080.754
0.1130.0700.7060.2210.0960.7060.1750.0510.701
0.1830.1030.7090.2920.1180.7740.2610.0860.755
", + "bbox": [ + 496, + 89, + 895, + 205 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2. Results obtained using the action label during inference. mAP W/M: mean Average Precision with weighted (W) and macro (M) averaging. Acc-A: adverb-vs-antonym accuracy. Coloured rows indicate variants of our method. Bold denotes best result per column. In instructional datasets (left) adverbs are action-focused, so these are more reliable benchmarks to learn action changes. In captioning datasets (right) adverbs are more descriptive and do not influence the action significantly. As such, these datasets are less reliable.", + "bbox": [ + 75, + 218, + 893, + 273 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "formed only pairing opposite adverbs, thus the model does not receive enough penalty for other negative adverbs. In contrast, we provide explicit penalty for non-antonym negative adverbs. The poor performance of S3D pre-trained indicates that learning adverbs in videos is not trivial. Adverbs are not well defined visual entities like objects or actions, thus video-text retrieval approaches looking for correlations between text and video embeddings are likely suboptimal, even when such embeddings are jointly learnt on the same dataset with a strong model, as is the case for S3D.", + "bbox": [ + 75, + 287, + 468, + 438 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Still looking at the instructional datasets, on AIR all methods achieve higher mAP W/Acc-A but lower mAP M. Considering that there are more adverbs in AIR than in HowTo100M Adverbs, the higher mAP W/Acc-A is indicative of the quality of AIR: given that videos are tighter and cleaner it is possible to learn adverbs more effectively. The lower mAP M is due to the long-tail class distribution and shows the opportunities AIR offers to improve methods.", + "bbox": [ + 75, + 439, + 468, + 559 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "On the captioning datasets we observe an interesting result: the Priors baseline outperforms or achieves very high performance. This supports our argument that captioning datasets are not particularly suitable for our task. If a simple look-up table surpasses all learning-based methods, then we conclude it is very difficult to learn adverbs as action changes, because actions are not particularly influenced by adverbs here. While these datasets exhibit a skewed verb-adverb distribution, so do the instructional ones. In fact, on VATEX Adverbs (the biggest dataset with 1,524 pairs) our method attains marginally better results. This is to say that the problem does not lie in the imbalanced class distribution, rather in the nature of the videos.", + "bbox": [ + 75, + 561, + 470, + 755 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Importance of Context We now focus on the importance of using textual context for regression comparing REG - fixed $\\delta$ to REG in Table 2. Visual features vary differently when the same action is modified by different adverbs, e.g. chopping something coarsely entails a more prominent change than chopping it slowly. With REG we learn such visual differences with targets that change (sometimes considerably) across adverbs for a given verb. A fixed target for all positive adverbs discards such differences: the model is", + "bbox": [ + 73, + 763, + 470, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "penalised equally for small/big changes. REG - fixed $\\delta$ does this, and its consistent worse performance validates the idea of using text context as a proxy to learn action changes.", + "bbox": [ + 496, + 287, + 890, + 333 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The Key is in the Optimisation We now compare $MLP + ActMod$ to our method. For this $ActMod$ variant we replace the video embedding $f'(x, v)$ with $\\theta(f'(x, v))$ in the two losses in [6], where $\\theta$ is the additional MLP. With this configuration, the only difference between our method and Action Modifiers lies in the optimisation. In Section 3 we hypothesised that the optimisation of Action Modifiers might be difficult. Results in Table 2 support our hypothesis. When adding the MLP to $ActMod$ , Acc-A remains virtually identical across all datasets. However, mAP W/M drop considerably on HowTo100M Adverbs. This dataset is the noisiest among the five datasets, thus in this case increasing the depth of the model makes optimisation more difficult. Overall, comparing $MLP + ActMod$ to our method we achieve better results even when the additional MLP improves the performance of the original $ActMod$ . We conclude that learning adverbs as pre-defined actions changes rather than as trainable parameters is a better strategy.", + "bbox": [ + 496, + 335, + 892, + 608 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Testing without Action Labels In Table 3 we report results obtained without using the action label at test time. We test Action Modifiers in the same way as described for our method in Section 3. Experiments are directly comparable between Tables 2 and 3 since the tested models are the same. We note a remarkable drop in performance for all methods. This is expected since the task is now harder. In fact we need to predict the right adverb from multiple video embeddings obtained querying all verbs. Nevertheless, our method still achieves the best global performance in this more challenging setting. This shows that our method is more robust and is able to better generalise.", + "bbox": [ + 496, + 609, + 893, + 792 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Learning without Antonyms We now study the case where adverbs are not paired in antonyms. This is a desirable setting as it allows more flexibility in data collection. To train Action Modifiers without antonyms we just sample a random negative adverb as opposed to the antonym for the triplet loss. We illustrated in Section 3 how we train our REG variant. We do not evaluate REG - fixed $\\delta$ here since", + "bbox": [ + 496, + 795, + 893, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "23116", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/ef454a053bd54f7cf462b3a13084300186f6f26ce1024829e8ff9445e3059013.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Instructional datasets. Action-focused adverbs
HowTo100M Adverbs [6]Adverbs in Recipes
mAP WmAP MAcc-AmAP WmAP MAcc-A
Priors0.2470.1670.5600.3350.1000.835
S3D pre-trained0.3290.2220.5940.4250.1770.702
Act Mod [6]0.2690.1830.6010.3460.1070.837
MLP + Act Mod [6]0.2680.1840.7060.3680.1130.835
CLS0.4040.3070.7240.4690.1980.835
REG - fixed δ0.3200.2150.7060.4610.1480.835
REG0.3770.2770.7240.4810.1570.857
", + "bbox": [ + 71, + 88, + 470, + 205 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/7ff4c295eba0a3b7b6853a3a33d8bb96d414047528b35225e0050ab75f94062b.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Captioning datasets. Descriptive adverbs
ActivityNet Adverbs [7]MSR-VTT Adverbs [7]VATEX Adverbs [7]
mAP WmAP MAcc-AmAP WmAP MAcc-AmAP WmAP MAcc-A
0.0940.0500.6920.1370.0560.7230.0890.0290.651
0.1130.0650.5980.1990.0880.6030.1170.0370.604
0.1100.0630.7180.1640.0720.7290.1000.0350.686
0.1090.0700.7140.1620.0970.7230.0920.0360.686
0.1140.0720.7140.1890.0780.7230.1610.0530.712
0.1130.0700.7060.2130.0950.7140.1580.0470.703
0.1200.0730.7060.2400.1020.7490.1690.0570.737
", + "bbox": [ + 496, + 88, + 895, + 205 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/5060af9845750ace2f0cd680186566f700128f7b60a20138450194ea6d1b039d.jpg", + "table_caption": [ + "Table 3. Results obtained without action labels during inference. mAP W/M: mean Average Precision with weighted (W) and macro (M) averaging. Acc-A: adverb-vs-antonym accuracy. Coloured rows indicate variants of our method. Bold denotes best result per column." + ], + "table_footnote": [], + "table_body": "
AntonymsInstructional datasets. Action-focused adverbsCaptioning datasets. Descriptive adverbs
HowTo100M Adverbs [6]Adverbs in RecipesActivityNet Adverbs [7]MSR-VTT Adverbs [7]VATEX Adverbs [7]
mAP WmAP MmAP WmAP MmAP WmAP MmAP WmAP MmAP WmAP M
PriorsX0.4460.3540.4910.2630.2170.1590.3080.1520.2160.086
S3D pre-trainedX0.3390.2380.3890.1730.1180.0700.1940.0750.1220.038
Act Mod [6]✓0.4060.3720.4210.1700.2110.1520.2460.1480.1390.059
X0.4080.3520.4280.1800.2170.1600.2540.1540.1440.060
MLP + Act Mod [6]✓0.2790.1930.4580.1880.1540.1080.2150.1110.2090.096
X0.2810.1980.4650.1970.1640.1150.2290.1320.2130.098
CLSX0.5620.4200.6750.3250.1140.0720.1890.0810.2830.108
REG✓0.5550.4230.6690.2970.1830.1030.2920.1180.2610.086
X0.5730.4810.7160.3930.2060.1210.3190.1140.2820.100
", + "bbox": [ + 112, + 260, + 859, + 406 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 4. Results obtained with action labels during inference and without antonyms during training. mAP W/M: mean Average Precision with weighted (W) and macro (M) averaging. Coloured rows indicate variants of our method. Bold denotes best result per column.", + "bbox": [ + 75, + 417, + 892, + 446 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "without antonyms it would be similar to binary classification. $CLS$ by design does not use antonyms. Table 4 compares results obtained with and without antonyms. Since we assume we do not have antonym labels here we only evaluate mAP W/M. Interestingly, Action Modifiers slightly improves when removing antonyms, which shows again that using only opposite adverbs for contrastive learning limits the model. Discarding antonyms for our regression variant has also a strong positive effective. Since we remove the target $-\\delta$ for antonyms and treat opposite adverbs as any other negative class, we are not forcing the model to push antonyms further compared to other negative adverbs. This is beneficial to learn adverbs more generally.", + "bbox": [ + 75, + 460, + 468, + 656 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Regression vs Classification We now compare CLS and REG in Tables 2, 3 and 4. When testing without action labels (Table 3) and learning without antonyms (Table 4) we notice a more consistent improvement of REG over CLS. Rather than maximising the margin between the positive adverb and all other negative adverbs as in classification, with regression we try to learn the extent of the change applied by an adverb. This is evidently a more effective way to learn adverbs since the visual change introduced by an adverb varies considerably according to the action.", + "bbox": [ + 75, + 657, + 468, + 809 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 76, + 816, + 194, + 832 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We proposed to address adverb recognition as a regression task. Our method attains new state-of-the-art performance on multiple datasets. Importantly, we achieve compelling results when removing two major assumptions: the", + "bbox": [ + 75, + 840, + 468, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "availability of action labels during testing and the pairing of opposite adverbs as antonyms. To address the scarcity of datasets for adverb recognition we introduced AIR. The dataset collects instructional recipe videos where actions are particularly influenced by the modification indicated by adverbs. We believe AIR is a valuable resource that can readily foster advance in adverb understanding.", + "bbox": [ + 496, + 460, + 892, + 566 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitations Since we model action changes measuring distances in a text embedding space we rely on a reasonably good text model. If the model does not capture meaningful relationships between verbs and adverbs then we do not have a reliable proxy to learn adverbs. Because we look for action changes directly in the video, actions need to exhibit a sufficient visual change when modified by the adverb.", + "bbox": [ + 496, + 569, + 892, + 675 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Future Work Directions for future work include exploring ways to capture a broader action context via text. For example, the full caption associated with a video can provide additional information (e.g. object nouns) that could be exploited to better learn action modifications. This would require addressing the problem of video-text alignment, as well as the intrinsic noisy nature of long text embeddings.", + "bbox": [ + 496, + 676, + 892, + 782 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Potential Societal Impact We source AIR from HowTo100M dataset, which gathers videos from YouTube. As such, any societal bias introduced in HowTo100M is potentially included in our data and our trained models.", + "bbox": [ + 496, + 786, + 892, + 847 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements Research funded by UKRI through the Edinburgh Laboratory for Integrated Artificial Intelligence (ELIAI) and the Turing Advanced Autonomy project.", + "bbox": [ + 496, + 854, + 892, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "23117", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Humam Alwassel, Fabian Caba Heilbron, Victor Escorcia, and Bernard Ghanem. Diagnosing error in temporal action detectors. In ECCV, 2018. 1", + "[2] Lisa Anne Hendricks, Oliver Wang, Eli Shechtman, Josef Sivic, Trevor Darrell, and Bryan Russell. 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In CVPR, 2020. 2" + ], + "bbox": [ + 501, + 92, + 890, + 688 + ], + "page_idx": 8 + }, + { + "type": "page_number", + "text": "23118", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 8 + } +] \ No newline at end of file diff --git a/2023/Learning Action Changes by Measuring Verb-Adverb Textual Relationships/bf106286-0480-42c9-8e91-7fe0ead5cbe8_model.json b/2023/Learning Action Changes by Measuring Verb-Adverb Textual Relationships/bf106286-0480-42c9-8e91-7fe0ead5cbe8_model.json new file mode 100644 index 0000000000000000000000000000000000000000..3d361321fd1e4b0835ba084160e618ba5fc10101 --- /dev/null +++ b/2023/Learning Action Changes by Measuring Verb-Adverb Textual Relationships/bf106286-0480-42c9-8e91-7fe0ead5cbe8_model.json @@ -0,0 +1,1560 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.102, + 0.131, + 0.868, + 0.154 + ], + "angle": 0, + "content": "Learning Action Changes by Measuring Verb-Adverb Textual Relationships" + }, + { + "type": "text", + "bbox": [ + 0.225, + 0.181, + 0.744, + 0.217 + ], + "angle": 0, + "content": "Davide Moltisanti, Frank Keller, Hakan Bilen, Laura Sevilla-Lara \nThe University of Edinburgh, United Kingdom" + }, + { + "type": "text", + "bbox": [ + 0.21, + 0.22, + 0.756, + 0.234 + ], + "angle": 0, + "content": "{davide.moltisanti, frank.keller, h.bilen, l.sevilla}@ed.ac.uk" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.269, + 0.314, + 0.285 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.301, + 0.47, + 0.481 + ], + "angle": 0, + "content": "The goal of this work is to understand the way actions are performed in videos. That is, given a video, we aim to predict an adverb indicating a modification applied to the action (e.g. cut \"finely\"). We cast this problem as a regression task. We measure textual relationships between verbs and adverbs to generate a regression target representing the action change we aim to learn. We test our approach on a range of datasets and achieve state-of-the-art results on both adverb prediction and antonym classification. Furthermore, we outperform previous work when we lift two commonly assumed conditions: the availability of action labels during testing and the pairing of adverbs as antonyms." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.482, + 0.47, + 0.679 + ], + "angle": 0, + "content": "Existing datasets for adverb recognition are either noisy, which makes learning difficult, or contain actions whose appearance is not influenced by adverbs, which makes evaluation less reliable. To address this, we collect a new high quality dataset: Adverbs in Recipes (AIR). We focus on instructional recipes videos, curating a set of actions that exhibit meaningful visual changes when performed differently. Videos in AIR are more tightly trimmed and were manually reviewed by multiple annotators to ensure high labelling quality. Results show that models learn better from AIR given its cleaner videos. At the same time, adverb prediction on AIR is challenging, demonstrating that there is considerable room for improvement." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.695, + 0.208, + 0.71 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Learning how an action is performed in a video is an important step towards expanding our video understanding beyond action recognition. This task has been referred to as \"adverb recognition\", and has potential useful applications in robotics and retrieval. Consider a scenario where a robot handles fragile objects. In such case we would like to tell the robot to grasp objects gently to prevent it from breaking things. Similarly, learning how actions are performed enables more sophisticated queries for retrieval. Imagine learning a new recipe where a crucial step is stirring a mixture vigorously. It would be useful to find good examples showing how to whip a mixture in such a manner." + }, + { + "type": "image", + "bbox": [ + 0.52, + 0.266, + 0.752, + 0.469 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.79, + 0.267, + 0.874, + 0.452 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.479, + 0.892, + 0.565 + ], + "angle": 0, + "content": "Figure 1. We aim to predict the way an action is performed in a video (right). Actions and their outcomes change in different ways when modified by adverbs, e.g. grinding coffee slowly does not have the same effect as grinding it coarsely (left). We learn to predict adverbs by recognising action changes in the video. We define action changes measuring verb-adverb textual relationships." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.893, + 0.903 + ], + "angle": 0, + "content": "Adverb recognition is a challenging problem. Firstly, a single adverb can modify multiple actions in different ways. For example, to grind coffee coarsely (see Figure 1) we need to set a certain granularity in a grinder. Conversely, to spray something coarsely we would just use a spraying can more sparingly. Secondly, compared to actions or objects, adverbs are much harder to identify. Though somewhat subjective [1, 16], the temporal boundaries of an action can be easily determined. The spatial extent of an object is also easy to recognise for a human. Adverbs are instead more abstract: we can see their effect, but we struggle to pinpoint the spatio-temporal location where the adverb is appearing. Consider for example the act of spraying something slowly in Figure 1. We could say that slowly \"is located\" on the hand motions. At the same time, spraying something slowly could implicate a more even coating of a surface. That is, the outcome of an action and the end-state of the involved objects can also change according to the adverb. This makes it hard to label adverbs with visual annotations (e.g. bounding boxes), which makes the problem more challenging." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "23110" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.333 + ], + "angle": 0, + "content": "In fact, previous approaches [6, 7] learn adverbs as action changes in a weakly supervised manner. The state-of-the-art approach [6] treats adverbs as learnable parameters that modify actions. Specifically, the action change is learnt during training by contrasting antonyms, i.e. opposite adverbs. We show that learning adverbs in such manner can be difficult and can limit the ability of the model to generalise. We thus propose to define action changes by measuring distances in a text embedding space, and aim to learn such change from the video through regression. We show that our approach achieves new state-of-the-art results through extensive experiments. We also lift two major assumptions made in previous work [6, 7]: the availability of action labels during testing and the pairing of opposite adverbs as antonyms. Our method achieves stronger performance especially when the above assumptions are relaxed." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.334, + 0.473, + 0.606 + ], + "angle": 0, + "content": "Besides being challenging, adverb recognition is also an under-explored domain and only few datasets are available. Doughty and Snoek [7] addressed the problem of scarce annotations, proposing a semi-supervised method that assigns pseudo-labels to boost recognition performance. Three datasets sourced from captioning benchmarks were also collected in [7]. These datasets offer a large number of clips, actions and adverbs. However, adverbs in these datasets appear to be descriptive rather than action modifiers, i.e. actions do not display a significant change when modified by the adverb. This is an issue when adverbs are modelled as action changes as in this work. We thus introduce a new dataset focusing on instructional videos where actions change considerably depending on the way they are carried out. We focus on cooking videos since in this domain action changes are prominent. Our Adverbs in Recipes (AIR) dataset was manually labelled and consists of over 7K videos, 10 adverbs and 48 actions." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.608, + 0.473, + 0.745 + ], + "angle": 0, + "content": "To summarise our contributions: i) we propose a more effective approach to learn adverbs in videos. Our method achieves state-of-the-art results on multiple datasets and with fewer assumptions; ii) we introduce the AIR dataset for adverb recognition. Our focus on a domain where action changes are prominent and our careful manual annotation makes AIR more suitable for training and evaluating models for adverb understanding. We publicly release AIR and our code at github.com/dmoltisanti/air-cvpr23." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.754, + 0.22, + 0.769 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.781, + 0.472, + 0.903 + ], + "angle": 0, + "content": "Adverb Recognition Doughty et al. [6] introduced the adverb recognition task and proposed Action Modifiers. Adverbs are treated as learnable parameters that guide the optimisation of the video embeddings via a triplet loss. We show that such approach can be difficult to optimise and propose an alternative learning method. Rather than modelling action changes as trainable parameters we define them measuring distances in a text embedding space." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.319 + ], + "angle": 0, + "content": "We then learn action modifications via regression. We provide a more technical comparison in Section 3. A follow-up work [7] proposes a pseudo-labelling method where videos are assigned new labels based on the model prediction. Pseudo labels are obtained in an adaptive away, i.e. the threshold determining whether a label should be assigned is adapted for each adverb independently. In [7] the underlying model is also Action Modifiers [6]. Pang et al. [18, 19] introduced the \"Behaviour Adverb\" task. Here actions are not goal-oriented (e.g. \"kiss, smoke\") and adverbs correspond to moods (e.g. \"sadly, solemnly\"). Models use additional modalities such as human pose [18] or explicitly learn human expressions [8, 19]. While related, this task is different from the scope of this work, where we aim to learn action changes in goal-oriented (e.g. cooking) videos." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.322, + 0.895, + 0.73 + ], + "angle": 0, + "content": "Adverb Datasets HowTo100M Adverbs [6] collects data from the instructional dataset HowTo100M [14] finding adverbs in the narration captions. Videos are loosely trimmed around the timestamp associated with the adverb. Due to the video-text misalignment in HowTo100M, and because training videos were not manually reviewed, videos in HowTo100M Adverbs are noisy. Authors estimated that only \\(44\\%\\) of the training videos actually show the action. In total 6 adverbs were annotated. Three other datasets were introduced in [7]: ActivityNet/MSR-VTT/VATEX Adverbs. These are subsets of the namesake captioning datasets [11,23,26]. Videos were also obtained finding adverbs in captions, but annotations here are clean because captions were provided by annotators. We argue that the captioning nature of the original datasets is a reason of concern for learning action modifications. Indeed, adverbs tend to be a complementary description of the video, i.e. actions do not appear particularly influenced by the adverb. Peering into these datasets (see Figure 4), we found for example \"sit inside/outside, talk outdoors/indoors, walk in/out, move down/up\", etc. These adverbs modify the appearance of the video, however the action themselves are not modified. Arguably, the act of sitting is the same whether it takes place inside or outside, as is the act of walking in or out. Lastly, [18, 19] annotated adverbs for non-task-oriented actions, e.g. \"run, kiss\", however adverbs here express moods and manners, e.g. \"politely, reluctantly\"." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.731, + 0.895, + 0.852 + ], + "angle": 0, + "content": "The limited availability of datasets specifically designed for adverb understanding motivates us to collect a new dataset better suited for this task. We focus on recipe instructional videos where actions change significantly according to the adverb. We collect Adverbs in Recipes, which contains 7K videos, 10 adverbs and 48 actions. We employ annotators to verify that actions are carried out as indicated by the adverb. We present our dataset in Section 4." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Video-text Retrieval Understanding adverbs in videos is related to video-text retrieval [2, 5, 9, 11-13, 15, 17, 22, 28, 30]. Theoretically, these methods could be used to retrieve" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.958 + ], + "angle": 0, + "content": "23111" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.089, + 0.487, + 0.176 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.488, + 0.09, + 0.892, + 0.176 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.189, + 0.893, + 0.232 + ], + "angle": 0, + "content": "Figure 2. Comparison between the unscaled distance \\( d \\) (left) and the scaled distance \\( \\delta \\) (right), which is scaled using the verb-adverb cosine similarity. Plotted values are the Euclidean distances between corresponding positive and negative sentences. Blue/yellow indicate small/large distances, i.e. a small/big change when adverbs are flipped in the positive sentence (see text for more information)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.251, + 0.473, + 0.478 + ], + "angle": 0, + "content": "videos using adverbs as text queries. However, as noted in [7], most approaches encode text embeddings for whole sentences, i.e. it is hard to retrieve videos querying single words. Some works propose fine-grained video-text retrieval where single parts-of-speech can be queried [4, 24, 27, 29], however these works focus on verbs and nouns and were not evaluated for adverbs. As discussed before, adverbs are more abstract compared to verbs and nouns and are difficult to spatio-temporally localise. This entails that a video-text retrieval approach is unlikely to work well to find adverbs in videos. We test a retrieval baseline with an S3D model [13] where video and text embeddings were jointly learnt. Despite the strong performance on a number of tasks, we show that indeed this model struggles to achieve satisfactory performance." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.485, + 0.169, + 0.501 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.509, + 0.473, + 0.903 + ], + "angle": 0, + "content": "We are given a video \\( x \\) labelled with a verb \\( v \\), which annotates the action, and an adverb \\( a \\), which indicates the way the action is carried out. Our goal is to predict \\( a \\) in \\( x \\) given \\( v \\). We also have a mapping \\( h \\) between adverbs opposite in meaning, e.g. \\( h(\\text{quickly}) = \\text{slowly} \\). We use a pre-trained video backbone \\( f \\) to extract video features \\( f(x) \\). In this work we deal with long videos (10-40s), so we employ transformer-style attention [21] to attend to the relevant parts of the video. To this end, we use a pre-trained text model \\( g \\) to extract a text embedding \\( g(v) \\), which we use as query for the attention, obtaining the projected video embedding \\( f'(x, v) \\). To learn more specialised video features we feed \\( f'(x, v) \\) to a shallow MLP and obtain the final output of the model \\( \\rho(f'(x, v)) \\). We propose two methods to optimise the network casting the problem either as a classification or a regression task. In the former case we utilise the standard Cross Entropy (CE) loss using the ground truth adverb label \\( a \\). The CE pushes up predictions for the positive class and treats all negative classes equally. In some cases, however, it may be desirable to penalise the model more aggressively for incorrect predictions of antonym classes. Action Modifiers [6] uses the triplet loss for this purpose. However, in [6] negative samples are formed by only pairing antonyms. This is effective for distinguishing opposite adverbs, but does not train the model to distinguish an adverb from other negative non-antonym classes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.251, + 0.895, + 0.525 + ], + "angle": 0, + "content": "We thus propose a second approach based on regression. Casting the task as a regression problem we aim to directly learn the change the adverb introduces to the action and the video. However, we do not have a ground truth quantifying such action modifications. We use a text embedding space to estimate action changes. The high level idea is that we first build a minimal sentence \\( s \\) representing the modified action. We similarly build a negative sentence \\( \\tilde{s} \\) representing the action modified in the opposite way. Calculating the difference between \\( s \\) and \\( \\tilde{s} \\) we have a proxy measure for the change the adverb applies to the action. We build \\( s \\) concatenating the verb and the adverb (e.g. coat thinly), then generate \\( \\tilde{s} \\) replacing the adverb with its antonym (e.g. coat thickly). We then extract text embeddings \\( g(s) \\) and \\( g(\\tilde{s}) \\). Note that \\( g \\) receives a variable length sentence and outputs a fixed-dimension embedding. Let \\( \\langle \\rangle \\) denote concatenation, so \\( s = \\langle v, a \\rangle \\) and \\( \\tilde{s} = \\langle v, h(a) \\rangle \\). We measure the difference between \\( s \\) and \\( \\tilde{s} \\) to capture how \\( a \\) changes \\( v \\):" + }, + { + "type": "equation", + "bbox": [ + 0.565, + 0.538, + 0.892, + 0.567 + ], + "angle": 0, + "content": "\\[\nd (v, a) = \\left\\| g (\\langle v, a \\rangle) - g (\\langle v, h (a) \\rangle) \\right\\| _ {2} \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.574, + 0.895, + 0.741 + ], + "angle": 0, + "content": "Ideally, \\( d \\) could be used as is. However, we observed that for a given adverb \\( a \\) we obtain similar \\( d(v, a) \\) across most verbs \\( v \\). This defeats the purpose of measuring action changes via \\( d \\) since \\( d \\) itself is not discriminative enough. This happens because \\( d \\) ignores the correlation between the verb and the adverb. Intuitively, if a verb and an adverb are not semantically correlated (e.g. \"run thinly\") then we cannot expect to capture a meaningful change when flipping the adverb in the negative sentence (recall that \\( g \\) receives full sentences). To address this issue we scale \\( d \\) with the cosine similarity between the verb \\( v \\) and the adverb \\( a \\):" + }, + { + "type": "equation", + "bbox": [ + 0.57, + 0.748, + 0.892, + 0.784 + ], + "angle": 0, + "content": "\\[\n\\delta (v, a) = d (v, a) \\cdot \\frac {g (v) \\cdot g (a)}{\\| g (v) \\| _ {2} \\cdot \\| g (a) \\| _ {2}} \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Figure 2 compares \\( d \\) (left) to \\( \\delta \\) (right) for a few (verb, adverb) combinations. Note how the unscaled distance \\( d \\) is not discriminative given that adverbs display a similar \\( d \\) across verbs. On the other hand, the scaled \\( \\delta \\) shows a meaningful distance. For example, we observe a large \\( \\delta \\) for adverbs \"finely\" and \"coarsely\" when paired with verbs \"chop, mince, mash, grate\"." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "23112" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.167, + 0.087, + 0.805, + 0.245 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.255, + 0.895, + 0.312 + ], + "angle": 0, + "content": "Figure 3. Pipeline of our method. Given a long video \\( x \\) labelled with a verb \\( v \\) and an adverb \\( a \\) we learn video embeddings \\( f'(x, v) \\) through attention. We optimise the model with two alternative methods: standard classification (CE: Cross Entropy) or regression (MSE: Mean Squared Error). We build a regression target measuring distances in a text embedding space, which estimates the action change we aim to learn in the video. The video backbone and text model are initialised from pre-trained models and are not fine-tuned during learning." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.325, + 0.471, + 0.356 + ], + "angle": 0, + "content": "Now that we have an estimate to measure action changes we can build a regression target:" + }, + { + "type": "equation", + "bbox": [ + 0.077, + 0.362, + 0.48, + 0.43 + ], + "angle": 0, + "content": "\\[\nY ^ {R} (v) = \\left(t _ {i}, \\forall i \\in \\{1, 2, \\dots , A \\}\\right) = \\left\\{ \\begin{array}{c c} \\delta (v, a) & \\text {i f} y _ {i} = a \\\\ - \\delta (v, a) & \\text {i f} y _ {i} = h (a) \\\\ 0 & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.431, + 0.47, + 0.507 + ], + "angle": 0, + "content": "where \\(A\\) is the number of adverbs in a dataset and \\(y_{i}\\) denotes the \\(i\\)-th adverb. Let \\(\\hat{y}_i^v\\) indicate the output of the model for the \\(i\\)-th adverb obtained for verb \\(v\\), i.e. querying the attention model with \\(g(v)\\). The full output of the model is then \\(\\hat{Y}^{v} = \\rho (f^{\\prime}(x,v)) = (\\hat{y}_{i}^{v},\\forall i\\in \\{1,2,\\ldots ,A\\})\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.507, + 0.471, + 0.657 + ], + "angle": 0, + "content": "We use the Mean Squared Error to train the network: \\(\\mathcal{L}^R = \\| Y^R (v) - \\hat{Y}^v\\| _2\\). The loss pushes opposite adverbs furthest apart (due to the negative sign of \\(\\delta\\) for the antonym). The loss also tells the model that the video is not modified by other unrelated adverbs (target is 0 for classes that are neither ground truth nor antonyms). This discourages the model to predict negative non-antonym adverbs. Figure 3 illustrates our method. Note that the video backbone and text model are not part of the training, i.e. they are initialised from pre-trained models and are not fine-tuned." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.663, + 0.47, + 0.769 + ], + "angle": 0, + "content": "Learning without Antonyms We also consider a setting where adverbs are not paired in antonyms. Instead of replacing the ground truth adverb with its antonym we simply remove the adverb and generate \\(\\tilde{s} = v\\). In this case \\(\\delta\\) measures the difference between the action modified by the adverb and the unmodified version of the action. \\(Y^{R}\\) is then \\(\\delta\\) for the ground truth adverb and 0 for all other adverbs." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.773, + 0.471, + 0.849 + ], + "angle": 0, + "content": "Inference As in [6] we are given the action label \\( v \\) during testing. We query the attention model with \\( g(v) \\) and use \\( \\hat{Y}^v \\) to predict each adverb. We also test the model without action labels. In such case we obtain \\( f'(x, v) \\) querying all actions and take the maximum prediction for each adverb:" + }, + { + "type": "equation", + "bbox": [ + 0.097, + 0.858, + 0.47, + 0.88 + ], + "angle": 0, + "content": "\\[\np (x) = \\left(\\max _ {v} \\left(\\hat {y} _ {i} ^ {v}, \\forall v \\in \\mathcal {V}\\right), \\forall i \\in \\{1, 2, \\dots , A \\}\\right) \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.886, + 0.347, + 0.9 + ], + "angle": 0, + "content": "where \\(\\nu\\) denotes the set of action labels." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.325, + 0.892, + 0.703 + ], + "angle": 0, + "content": "Comparison to Action Modifiers Our framework shares the same design as Action Modifiers [6] until \\( f'(x, v) \\). In [6] \\( f'(x, v) \\) is optimised with two triplet losses: an action loss to help the attention model and an adverb loss to learn adverbs. We do not use an additional action loss. In Action Modifiers adverbs are also modelled as action changes utilising text embeddings. However, in [6] such change is treated as an additional parameter to be learnt. Specifically, an adverb is represented as a learnable matrix \\( W_{a} \\). The linear combination \\( o_{v}^{a} = W_{a} g(v) \\) represents the change the adverb \\( a \\) applies to the verb \\( v \\), where \\( g(v) \\) is a text embedding as in our model. Importantly, \\( o_{v}^{a} \\) is used in the triplet losses, thus the optimisation of the video embedding \\( f'(x, v) \\) depends on the optimisation of parameters \\( W_{a} \\). We argue and show that learning adverbs with this approach can be difficult as the action change the model looks for in the video has also to be learnt. In our formulation instead the action change is pre-computed and is not learnt. We also provide explicit penalty for non-antonym classes rather than contrasting only opposite adverbs. Comparing capacity, our model has a smaller number of parameters which scales better with the number of adverbs. Indeed, each adverb in Action Modifiers requires a learnable matrix, whereas in our model only the last layer of the MLP varies with the number of adverbs (see supplementary material)." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.709, + 0.836, + 0.727 + ], + "angle": 0, + "content": "4. Adverbs in Recipes: the AIR Dataset" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In Section 2 we motivated the need for a new dataset for adverb recognition. Here we introduce the Adverbs in Recipes (AIR) dataset. We wish to find a set of videos where actions change significantly according to the adverb. Compared to captioning benchmarks, instructional datasets contain videos where we can expect to find more of such actions. For this reason we source AIR from HowTo100M [14]. We restrict our interest to recipe videos since changes in cooking actions play an important role. For example, a carrot sliced à la juillienne (thinly) looks very different from a carrot chopped in thick dices (coarsely)." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "23113" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.078, + 0.089, + 0.472, + 0.166 + ], + "angle": 0, + "content": "
DatasetAccuracyDurationAdvActPairsVideos
CAPTActivityNet Adverbs [7]89.0%37.5s201146353,099
MSR-VTT Adverbs [7]91.0%15.7s181064501,824
VATEX Adverbs [7]93.5%10.0s (f)341351,52414,617
INSTHowTo100M Adverbs [6]44.0%20.0s (f)6722575,824
Adverbs in Recipes (ours)95.3%8.4s10481867,003
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.177, + 0.47, + 0.274 + ], + "angle": 0, + "content": "Table 1. Comparing video datasets for adverb recognition. CAPT: captioning datasets, where adverbs are descriptive. INST: instructional datasets, where adverbs are action-focused. \"Accuracy\" indicates whether the action is visible as indicated by the adverb. \"Duration\" reports the average length, where (f) denotes a fixed duration. \"Pairs\" counts (verb, adverb) appearing in the dataset rather than the Cartesian product of all verbs and adverbs." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.283, + 0.47, + 0.329 + ], + "angle": 0, + "content": "In other words, adverbs are \"easily visible\" in recipe videos and involve interesting visual cues such as speed, temporal/spatial completeness and objects end-states." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.35, + 0.473, + 0.699 + ], + "angle": 0, + "content": "Data Collection We start selecting all recipe videos in HowTo100M. We then parse captions to keep only those containing a verb and an adverb. We filter videos removing verbs that indicate non visual actions (e.g. \"watch, wait\") or very long-term actions (e.g. \"rise, grow\"), since we do not expect these changes to be fully visible in the videos. We manually merge similar verbs, obtaining in total 48 verbs. We also remove infrequent and too generic adverbs (e.g. \"carefully\"). We cluster similar adverbs gathering a total of 10 adverbs, which we pair in antonyms. To trim videos in a tight manner we use the timestamps of the first/last word in a caption as the start/end of the action segment. At this point we have a set of videos of varying duration, each accompanied with a verb and an adverb. We ask annotators on Amazon Mechanical Turk (AMT) to check whether the action in a video is visible and is carried out as indicated by the adverb. For robustness we ask 3 different annotators to check the same video and employ 5 people for edge cases where annotators disagreed. We keep videos where the majority of the annotators confirmed that the action is visible as indicated by the adverb, collecting 7,003 videos. Figure 2 shows the verbs (columns) and adverbs (rows) in AIR. We provide more details in the supplementary material." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.719, + 0.47, + 0.841 + ], + "angle": 0, + "content": "Comparison to Other Datasets Table 1 compares AIR to other adverb \\( \\text{dattets}^1 \\) reviewed in Section 2. \"Accuracy\" estimates the percentage of videos where the action and the adverb effect are visible. On the existing datasets this was estimated watching 200 videos in [7]. For AIR multiple annotators reviewed all videos, however, annotations on AMT can be noisy. We review 302 videos (5% of the dataset) and report this check as \"Accuracy\". Compared" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.089, + 0.631, + 0.203 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.631, + 0.089, + 0.762, + 0.203 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.762, + 0.089, + 0.892, + 0.203 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.215, + 0.894, + 0.314 + ], + "angle": 0, + "content": "Figure 4. Samples from existing datasets for adverb recognition and our new AIR dataset. Many adverbs in the captioning datasets appear to be descriptive rather than a key modification of the action (e.g. the act of talking/sitting is the same whether it takes place indoors/outdoors). In contrast, adverbs in the instructional datasets apply a more prominent change in the action and its outcome (e.g. a vegetable peeled coarsely will still have some skin attached)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.337, + 0.892, + 0.534 + ], + "angle": 0, + "content": "to the instructional-based HowTo100M Adverbs, AIR contains over 1,100 additional clips and 4 more adverbs. Importantly, our videos are manually reviewed (AIR accuracy is over \\(95\\%\\) compared to \\(44\\%\\)) and better trimmed (averaged duration is 8s compared to fixed 20s segments). AIR features 48 actions which is the smallest number among the five datasets (and consequently the smallest number of pairs). This is due to our more restrictive verb filtering based on visual and task-oriented actions. For example, in the captioning datasets there are actions such as \"tell, talk, sing, look\". Actions in HowTo100M Adverbs are task oriented, however there are also verbs entailing long-term actions (e.g. \"brew\"), which are unlikely to be fully visible." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.537, + 0.893, + 0.763 + ], + "angle": 0, + "content": "Figure 4 shows a few samples from AIR as well as the other datasets. Note how adverbs in the instructional datasets apply a key modification in the action, whereas for the captioning datasets adverbs are descriptive. Cap-tions in the captioning datasets are reliable because they were provided by human annotators. However, annotators did not necessarily use adverbs to indicate a modification to the action. Thus, due to the automatic processing of these datasets, there are several cases where adverbs are descriptive and do not influence the action. Naturally, Figure 4 is not meant to be an exhaustive representation of the caption-ing datasets from [7]. These datasets also contain action-focused adverbs, however without extensively reviewing the videos and the associated adverbs it is hard to gauge how many actions are effectively modified by the adverb." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.894, + 0.903 + ], + "angle": 0, + "content": "To summarise the contributions of AIR: i) we employ annotators to verify that actions are performed in the way indicated by the adverb; ii) this allowed us to trim videos more tightly and obtain cleaner clips with less unrelated content; iii) we carefully choose verbs and adverbs to pick videos where action changes are significant. While we restrict our domain to recipes, cooking actions are visually diverse, entail complex object interactions and are particularly affected by the nuanced ways they are carried out." + }, + { + "type": "page_footnote", + "bbox": [ + 0.076, + 0.851, + 0.47, + 0.901 + ], + "angle": 0, + "content": "1We report the number of videos from [7]. Some videos are missing as they were removed from YouTube. We were able to download: ActivityNet A.: 2,972 - MSR-VTT A.: 1,747 - VATEX A.: 13,947, HowTo100M A.: 5,462. Duration and pairs are reported from the downloaded videos." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "23114" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.09, + 0.21, + 0.108 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.116, + 0.473, + 0.42 + ], + "angle": 0, + "content": "Implementation Details We use an S3D model [13, 25] jointly pre-trained on video and text on HowTo100M [14] as our video backbone. Specifically, we use the video output mixed_5c to obtain \\( f(x) \\). Following [6] we split videos in 1-second segments and sample 16 RGB frames from each segment to obtain the video features. Stacking features from the video segments we have \\( f(x)^{T \\times D} \\), where \\( T \\) varies depending on the dataset and \\( D \\) is 1024. We use 4 heads for the attention model. The dimension \\( E \\) of the query, key and value is 512, thus the projected video embedding \\( f'(x, v) \\) has dimension \\( 1 \\times E \\). The MLP in our model has 3 layers (hidden units of dimension 512) with ReLU activation function for the hidden layers and dropout [20] set to 0.1. We train all models for 1000 epochs with the ADAM optimiser [10], setting learning rate to \\( 1e^{-4} \\), weight decay to \\( 5e^{-5} \\) and batch size to 512. We use the text model jointly trained with S3D to extract text embeddings \\( g(\\cdot) \\). This network, like the visual backbone, is not fine-tuned. We refer to [13] for more details about S3D and the text model. \\( f(x) \\) and \\( g(\\cdot) \\) are the same for all experiments." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.43, + 0.473, + 0.612 + ], + "angle": 0, + "content": "Baselines Priors: here we do not train any model and simply use the prior distributions of the training set to make a prediction. When using the action label during testing, the prediction for an adverb is the number of training samples labelled with the adverb and the given verb, i.e. \\( p(x,v) = (\\pi (v,a),\\forall a\\in \\mathcal{A}) \\), where \\( \\pi \\) denotes the frequency of \\( (v,a) \\) in the training set and \\( \\mathcal{A} \\) is the set of adverbs in a dataset. While this baseline is a simple look-up table, it can achieve strong performance since it exploits the co-occurrence of verbs and adverbs. When the action label is not used during testing the priors baseline predicts the frequency of each adverb in the training set, i.e. \\( p(x) = (\\pi (a),\\forall a\\in \\mathcal{A}) \\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.613, + 0.473, + 0.814 + ], + "angle": 0, + "content": "S3D pre-trained: we test the S3D model we use as the video-text backbone for all experiments. Video and text embeddings were jointly learnt in this model, so we use the dot product between \\( f(x) \\) and \\( g(\\cdot) \\) for predictions. When the action label \\( v \\) is given during inference the prediction is \\( p(x,v) = (f(x)\\cdot g(\\langle v,a\\rangle),\\forall a\\in \\mathcal{A}) \\), where \\( g(\\langle v,a\\rangle) \\) is the text embedding obtained concatenating the given \\( v \\) and each adverb \\( a \\). When the action label is not given, we have \\( p(x) = (\\max_v f(x)\\cdot g(\\langle v,a\\rangle),\\forall v\\in \\mathcal{V}),\\forall a\\in \\mathcal{A}) \\), where \\( \\mathcal{V} \\) is the set of verbs. This S3D instance has shown very strong performance on several tasks [13], thus this baseline helps gauging the difficulty of detecting adverbs following a basic video-text retrieval approach." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.892, + 0.272 + ], + "angle": 0, + "content": "SOTA Act Mod: we compare against the state-of-the-art for adverb recognition, Action Modifiers [6], both using the original model and a deeper version with an additional MLP \\((MLP + ActMod)\\). Here we append an identical MLP as in our model to the output of the transformer attention. This variant allows a better comparison with our method. We use the official code implementation to run our experiments. Note that Action Modifiers results reported here are not directly comparable to those reported in [6,7]. This is because we could not download several videos since they were removed from YouTube. Also, we use S3D features (identical for all experiments) instead of I3D [3] features." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.275, + 0.892, + 0.366 + ], + "angle": 0, + "content": "Our Variants CLS: our model trained with classification. REG - fixed \\(\\delta\\): our model trained with regression discarding text embeddings altogether, setting \\(\\delta = 1\\) in Equation 3. This is to validate the premise of using textual context to build a regression target. REG: our model trained with regression using the full formulation." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.367, + 0.893, + 0.609 + ], + "angle": 0, + "content": "Evaluation Metrics We report mean Average Precision using two types of averaging: i) weighted (mAP W), where class scores are weighted according to the support size (smaller classes have a smaller weight); ii) macro (mAP M), where all classes have equal weight, which corresponds to \"adverb-to-video (all)\" in [6]. All the evaluated datasets exhibit a significant class imbalance, thus mAP M is a stricter metric compared to mAP W. We also report binary antonym accuracy (Acc-A), which corresponds to \"video-to-adverb (antonym)\" in [6]. Here we only look at the prediction of an adverb \\(a\\) versus its antonym \\(h(a)\\). A prediction \\(p\\) is correct if \\(p(a) > p(h(a))\\). All metrics are computed for adverb classes. To show the full potential of all methods we report each best metric independently, i.e. results may come from different epochs. This is to provide a robust comparison, however we note that all models reach stable convergence." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.611, + 0.892, + 0.761 + ], + "angle": 0, + "content": "Datasets We present experiments on the two instructional datasets we saw earlier: HowTo100M Adverbs [6] and our Adverbs In Recipes. As discussed before, we argue that instructional videos are more suitable for this task as adverbs are action-focused, i.e. actions change significantly according to the adverb. For completeness, we also evaluate the three adverb datasets sourced from captioning videos in [7]: ActivityNet/MSR-VTT/VATEX Adverbs3. Adverbs here are descriptive, thus these datasets are less reliable for evaluation. Datasets are summarised in Table 1." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.768, + 0.593, + 0.782 + ], + "angle": 0, + "content": "5.1. Results" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.79, + 0.892, + 0.868 + ], + "angle": 0, + "content": "Overview We begin our discussion looking at results in Table 2 on the instructional datasets (left). Here we achieve new state-of-the-art results on all metrics. The gap between our best variant and Act Mod is more noticeable for the more challenging mAP W/M metrics. In [6] negative samples are" + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.875, + 0.892, + 0.901 + ], + "angle": 0, + "content": "3For these datasets there are several partitions for different tasks (e.g. unseen domain). For convenience we create our own train/test split." + }, + { + "type": "page_footnote", + "bbox": [ + 0.076, + 0.827, + 0.47, + 0.901 + ], + "angle": 0, + "content": "There is no official train/test split in HowTo100M, thus S3D in [13] was trained on videos that appear in the test sets of HowTo100M Adverbs and AIR. However, this is not a concern: Tables 2, 3 show that the S3D pre-trained baseline achieves poor performance, as the original S3D training objective (video-text alignment) is substantially different from ours. Importantly, all methods receive the same features for fair comparison." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "23115" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.078, + 0.131, + 0.175, + 0.205 + ], + "angle": 0, + "content": "
Priors
S3D pre-trained
Act Mod [6]
MLP + Act Mod [6]
CLS
REG - fixed δ
REG
" + }, + { + "type": "table", + "bbox": [ + 0.202, + 0.09, + 0.472, + 0.207 + ], + "angle": 0, + "content": "
Instructional datasets. Action-focused adverbs
HowTo100M Adverbs [6]Adverbs in Recipes
mAP WmAP MAcc-AmAP WmAP MAcc-A
0.4460.3540.7860.4910.2630.854
0.3390.2380.5600.3890.1730.735
0.4060.3720.7960.4210.1700.858
0.2790.1930.7930.4580.1880.857
0.5620.4200.7860.6750.3250.847
0.3200.2150.7060.4580.1450.835
0.5550.4230.7990.6690.2970.862
" + }, + { + "type": "table", + "bbox": [ + 0.498, + 0.09, + 0.897, + 0.206 + ], + "angle": 0, + "content": "
Captioning datasets. Descriptive adverbs
ActivityNet Adverbs [7]MSR-VTT Adverbs [7]VATEX Adverbs [7]
mAP WmAP MAcc-AmAP WmAP MAcc-AmAP WmAP MAcc-A
0.2170.1590.7450.3080.1520.7230.2160.0860.752
0.1180.0700.5600.1940.0750.6030.1220.0380.586
0.2110.1520.7480.2460.1480.7340.1390.0590.751
0.1540.1080.7530.2150.1110.7310.2090.0960.752
0.1140.0720.7140.1890.0810.7230.2830.1080.754
0.1130.0700.7060.2210.0960.7060.1750.0510.701
0.1830.1030.7090.2920.1180.7740.2610.0860.755
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.219, + 0.895, + 0.275 + ], + "angle": 0, + "content": "Table 2. Results obtained using the action label during inference. mAP W/M: mean Average Precision with weighted (W) and macro (M) averaging. Acc-A: adverb-vs-antonym accuracy. Coloured rows indicate variants of our method. Bold denotes best result per column. In instructional datasets (left) adverbs are action-focused, so these are more reliable benchmarks to learn action changes. In captioning datasets (right) adverbs are more descriptive and do not influence the action significantly. As such, these datasets are less reliable." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.289, + 0.47, + 0.439 + ], + "angle": 0, + "content": "formed only pairing opposite adverbs, thus the model does not receive enough penalty for other negative adverbs. In contrast, we provide explicit penalty for non-antonym negative adverbs. The poor performance of S3D pre-trained indicates that learning adverbs in videos is not trivial. Adverbs are not well defined visual entities like objects or actions, thus video-text retrieval approaches looking for correlations between text and video embeddings are likely suboptimal, even when such embeddings are jointly learnt on the same dataset with a strong model, as is the case for S3D." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.44, + 0.47, + 0.56 + ], + "angle": 0, + "content": "Still looking at the instructional datasets, on AIR all methods achieve higher mAP W/Acc-A but lower mAP M. Considering that there are more adverbs in AIR than in HowTo100M Adverbs, the higher mAP W/Acc-A is indicative of the quality of AIR: given that videos are tighter and cleaner it is possible to learn adverbs more effectively. The lower mAP M is due to the long-tail class distribution and shows the opportunities AIR offers to improve methods." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.562, + 0.471, + 0.756 + ], + "angle": 0, + "content": "On the captioning datasets we observe an interesting result: the Priors baseline outperforms or achieves very high performance. This supports our argument that captioning datasets are not particularly suitable for our task. If a simple look-up table surpasses all learning-based methods, then we conclude it is very difficult to learn adverbs as action changes, because actions are not particularly influenced by adverbs here. While these datasets exhibit a skewed verb-adverb distribution, so do the instructional ones. In fact, on VATEX Adverbs (the biggest dataset with 1,524 pairs) our method attains marginally better results. This is to say that the problem does not lie in the imbalanced class distribution, rather in the nature of the videos." + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.765, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Importance of Context We now focus on the importance of using textual context for regression comparing REG - fixed \\(\\delta\\) to REG in Table 2. Visual features vary differently when the same action is modified by different adverbs, e.g. chopping something coarsely entails a more prominent change than chopping it slowly. With REG we learn such visual differences with targets that change (sometimes considerably) across adverbs for a given verb. A fixed target for all positive adverbs discards such differences: the model is" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.289, + 0.892, + 0.334 + ], + "angle": 0, + "content": "penalised equally for small/big changes. REG - fixed \\(\\delta\\) does this, and its consistent worse performance validates the idea of using text context as a proxy to learn action changes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.337, + 0.893, + 0.609 + ], + "angle": 0, + "content": "The Key is in the Optimisation We now compare \\( MLP + ActMod \\) to our method. For this \\( ActMod \\) variant we replace the video embedding \\( f'(x, v) \\) with \\( \\theta(f'(x, v)) \\) in the two losses in [6], where \\( \\theta \\) is the additional MLP. With this configuration, the only difference between our method and Action Modifiers lies in the optimisation. In Section 3 we hypothesised that the optimisation of Action Modifiers might be difficult. Results in Table 2 support our hypothesis. When adding the MLP to \\( ActMod \\), Acc-A remains virtually identical across all datasets. However, mAP W/M drop considerably on HowTo100M Adverbs. This dataset is the noisiest among the five datasets, thus in this case increasing the depth of the model makes optimisation more difficult. Overall, comparing \\( MLP + ActMod \\) to our method we achieve better results even when the additional MLP improves the performance of the original \\( ActMod \\). We conclude that learning adverbs as pre-defined actions changes rather than as trainable parameters is a better strategy." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.611, + 0.894, + 0.793 + ], + "angle": 0, + "content": "Testing without Action Labels In Table 3 we report results obtained without using the action label at test time. We test Action Modifiers in the same way as described for our method in Section 3. Experiments are directly comparable between Tables 2 and 3 since the tested models are the same. We note a remarkable drop in performance for all methods. This is expected since the task is now harder. In fact we need to predict the right adverb from multiple video embeddings obtained querying all verbs. Nevertheless, our method still achieves the best global performance in this more challenging setting. This shows that our method is more robust and is able to better generalise." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Learning without Antonyms We now study the case where adverbs are not paired in antonyms. This is a desirable setting as it allows more flexibility in data collection. To train Action Modifiers without antonyms we just sample a random negative adverb as opposed to the antonym for the triplet loss. We illustrated in Section 3 how we train our REG variant. We do not evaluate REG - fixed \\(\\delta\\) here since" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "23116" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.073, + 0.089, + 0.472, + 0.207 + ], + "angle": 0, + "content": "
Instructional datasets. Action-focused adverbs
HowTo100M Adverbs [6]Adverbs in Recipes
mAP WmAP MAcc-AmAP WmAP MAcc-A
Priors0.2470.1670.5600.3350.1000.835
S3D pre-trained0.3290.2220.5940.4250.1770.702
Act Mod [6]0.2690.1830.6010.3460.1070.837
MLP + Act Mod [6]0.2680.1840.7060.3680.1130.835
CLS0.4040.3070.7240.4690.1980.835
REG - fixed δ0.3200.2150.7060.4610.1480.835
REG0.3770.2770.7240.4810.1570.857
" + }, + { + "type": "table", + "bbox": [ + 0.498, + 0.089, + 0.897, + 0.206 + ], + "angle": 0, + "content": "
Captioning datasets. Descriptive adverbs
ActivityNet Adverbs [7]MSR-VTT Adverbs [7]VATEX Adverbs [7]
mAP WmAP MAcc-AmAP WmAP MAcc-AmAP WmAP MAcc-A
0.0940.0500.6920.1370.0560.7230.0890.0290.651
0.1130.0650.5980.1990.0880.6030.1170.0370.604
0.1100.0630.7180.1640.0720.7290.1000.0350.686
0.1090.0700.7140.1620.0970.7230.0920.0360.686
0.1140.0720.7140.1890.0780.7230.1610.0530.712
0.1130.0700.7060.2130.0950.7140.1580.0470.703
0.1200.0730.7060.2400.1020.7490.1690.0570.737
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.219, + 0.893, + 0.247 + ], + "angle": 0, + "content": "Table 3. Results obtained without action labels during inference. mAP W/M: mean Average Precision with weighted (W) and macro (M) averaging. Acc-A: adverb-vs-antonym accuracy. Coloured rows indicate variants of our method. Bold denotes best result per column." + }, + { + "type": "table", + "bbox": [ + 0.114, + 0.261, + 0.86, + 0.407 + ], + "angle": 0, + "content": "
AntonymsInstructional datasets. Action-focused adverbsCaptioning datasets. Descriptive adverbs
HowTo100M Adverbs [6]Adverbs in RecipesActivityNet Adverbs [7]MSR-VTT Adverbs [7]VATEX Adverbs [7]
mAP WmAP MmAP WmAP MmAP WmAP MmAP WmAP MmAP WmAP M
PriorsX0.4460.3540.4910.2630.2170.1590.3080.1520.2160.086
S3D pre-trainedX0.3390.2380.3890.1730.1180.0700.1940.0750.1220.038
Act Mod [6]✓0.4060.3720.4210.1700.2110.1520.2460.1480.1390.059
X0.4080.3520.4280.1800.2170.1600.2540.1540.1440.060
MLP + Act Mod [6]✓0.2790.1930.4580.1880.1540.1080.2150.1110.2090.096
X0.2810.1980.4650.1970.1640.1150.2290.1320.2130.098
CLSX0.5620.4200.6750.3250.1140.0720.1890.0810.2830.108
REG✓0.5550.4230.6690.2970.1830.1030.2920.1180.2610.086
X0.5730.4810.7160.3930.2060.1210.3190.1140.2820.100
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.419, + 0.893, + 0.448 + ], + "angle": 0, + "content": "Table 4. Results obtained with action labels during inference and without antonyms during training. mAP W/M: mean Average Precision with weighted (W) and macro (M) averaging. Coloured rows indicate variants of our method. Bold denotes best result per column." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.462, + 0.47, + 0.657 + ], + "angle": 0, + "content": "without antonyms it would be similar to binary classification. \\(CLS\\) by design does not use antonyms. Table 4 compares results obtained with and without antonyms. Since we assume we do not have antonym labels here we only evaluate mAP W/M. Interestingly, Action Modifiers slightly improves when removing antonyms, which shows again that using only opposite adverbs for contrastive learning limits the model. Discarding antonyms for our regression variant has also a strong positive effective. Since we remove the target \\(-\\delta\\) for antonyms and treat opposite adverbs as any other negative class, we are not forcing the model to push antonyms further compared to other negative adverbs. This is beneficial to learn adverbs more generally." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.659, + 0.47, + 0.81 + ], + "angle": 0, + "content": "Regression vs Classification We now compare CLS and REG in Tables 2, 3 and 4. When testing without action labels (Table 3) and learning without antonyms (Table 4) we notice a more consistent improvement of REG over CLS. Rather than maximising the margin between the positive adverb and all other negative adverbs as in classification, with regression we try to learn the extent of the change applied by an adverb. This is evidently a more effective way to learn adverbs since the visual change introduced by an adverb varies considerably according to the action." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.818, + 0.196, + 0.833 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.841, + 0.47, + 0.903 + ], + "angle": 0, + "content": "We proposed to address adverb recognition as a regression task. Our method attains new state-of-the-art performance on multiple datasets. Importantly, we achieve compelling results when removing two major assumptions: the" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.462, + 0.893, + 0.568 + ], + "angle": 0, + "content": "availability of action labels during testing and the pairing of opposite adverbs as antonyms. To address the scarcity of datasets for adverb recognition we introduced AIR. The dataset collects instructional recipe videos where actions are particularly influenced by the modification indicated by adverbs. We believe AIR is a valuable resource that can readily foster advance in adverb understanding." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.57, + 0.893, + 0.676 + ], + "angle": 0, + "content": "Limitations Since we model action changes measuring distances in a text embedding space we rely on a reasonably good text model. If the model does not capture meaningful relationships between verbs and adverbs then we do not have a reliable proxy to learn adverbs. Because we look for action changes directly in the video, actions need to exhibit a sufficient visual change when modified by the adverb." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.678, + 0.893, + 0.784 + ], + "angle": 0, + "content": "Future Work Directions for future work include exploring ways to capture a broader action context via text. For example, the full caption associated with a video can provide additional information (e.g. object nouns) that could be exploited to better learn action modifications. This would require addressing the problem of video-text alignment, as well as the intrinsic noisy nature of long text embeddings." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.787, + 0.893, + 0.848 + ], + "angle": 0, + "content": "Potential Societal Impact We source AIR from HowTo100M dataset, which gathers videos from YouTube. As such, any societal bias introduced in HowTo100M is potentially included in our data and our trained models." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.893, + 0.903 + ], + "angle": 0, + "content": "Acknowledgements Research funded by UKRI through the Edinburgh Laboratory for Integrated Artificial Intelligence (ELIAI) and the Turing Advanced Autonomy project." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "23117" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.468, + 0.156 + ], + "angle": 0, + "content": "[1] Humam Alwassel, Fabian Caba Heilbron, Victor Escorcia, and Bernard Ghanem. Diagnosing error in temporal action detectors. 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That is, given a video, we aim to predict an adverb indicating a modification applied to the action (e.g. cut "finely"). We cast this problem as a regression task. We measure textual relationships between verbs and adverbs to generate a regression target representing the action change we aim to learn. We test our approach on a range of datasets and achieve state-of-the-art results on both adverb prediction and antonym classification. Furthermore, we outperform previous work when we lift two commonly assumed conditions: the availability of action labels during testing and the pairing of adverbs as antonyms. + +Existing datasets for adverb recognition are either noisy, which makes learning difficult, or contain actions whose appearance is not influenced by adverbs, which makes evaluation less reliable. To address this, we collect a new high quality dataset: Adverbs in Recipes (AIR). We focus on instructional recipes videos, curating a set of actions that exhibit meaningful visual changes when performed differently. Videos in AIR are more tightly trimmed and were manually reviewed by multiple annotators to ensure high labelling quality. Results show that models learn better from AIR given its cleaner videos. At the same time, adverb prediction on AIR is challenging, demonstrating that there is considerable room for improvement. + +# 1. Introduction + +Learning how an action is performed in a video is an important step towards expanding our video understanding beyond action recognition. This task has been referred to as "adverb recognition", and has potential useful applications in robotics and retrieval. Consider a scenario where a robot handles fragile objects. In such case we would like to tell the robot to grasp objects gently to prevent it from breaking things. Similarly, learning how actions are performed enables more sophisticated queries for retrieval. Imagine learning a new recipe where a crucial step is stirring a mixture vigorously. It would be useful to find good examples showing how to whip a mixture in such a manner. + +![](images/5a3782a3da153dcfcf9b464efeeef77b5a5f4caf3f9e5f3c7695d080e45911d0.jpg) +Figure 1. We aim to predict the way an action is performed in a video (right). Actions and their outcomes change in different ways when modified by adverbs, e.g. grinding coffee slowly does not have the same effect as grinding it coarsely (left). We learn to predict adverbs by recognising action changes in the video. We define action changes measuring verb-adverb textual relationships. + +![](images/c2e5c2ba462eca3388337d582bbb96330c083e854b6189c054e03690bd0646ed.jpg) + +Adverb recognition is a challenging problem. Firstly, a single adverb can modify multiple actions in different ways. For example, to grind coffee coarsely (see Figure 1) we need to set a certain granularity in a grinder. Conversely, to spray something coarsely we would just use a spraying can more sparingly. Secondly, compared to actions or objects, adverbs are much harder to identify. Though somewhat subjective [1, 16], the temporal boundaries of an action can be easily determined. The spatial extent of an object is also easy to recognise for a human. Adverbs are instead more abstract: we can see their effect, but we struggle to pinpoint the spatio-temporal location where the adverb is appearing. Consider for example the act of spraying something slowly in Figure 1. We could say that slowly "is located" on the hand motions. At the same time, spraying something slowly could implicate a more even coating of a surface. That is, the outcome of an action and the end-state of the involved objects can also change according to the adverb. This makes it hard to label adverbs with visual annotations (e.g. bounding boxes), which makes the problem more challenging. + +In fact, previous approaches [6, 7] learn adverbs as action changes in a weakly supervised manner. The state-of-the-art approach [6] treats adverbs as learnable parameters that modify actions. Specifically, the action change is learnt during training by contrasting antonyms, i.e. opposite adverbs. We show that learning adverbs in such manner can be difficult and can limit the ability of the model to generalise. We thus propose to define action changes by measuring distances in a text embedding space, and aim to learn such change from the video through regression. We show that our approach achieves new state-of-the-art results through extensive experiments. We also lift two major assumptions made in previous work [6, 7]: the availability of action labels during testing and the pairing of opposite adverbs as antonyms. Our method achieves stronger performance especially when the above assumptions are relaxed. + +Besides being challenging, adverb recognition is also an under-explored domain and only few datasets are available. Doughty and Snoek [7] addressed the problem of scarce annotations, proposing a semi-supervised method that assigns pseudo-labels to boost recognition performance. Three datasets sourced from captioning benchmarks were also collected in [7]. These datasets offer a large number of clips, actions and adverbs. However, adverbs in these datasets appear to be descriptive rather than action modifiers, i.e. actions do not display a significant change when modified by the adverb. This is an issue when adverbs are modelled as action changes as in this work. We thus introduce a new dataset focusing on instructional videos where actions change considerably depending on the way they are carried out. We focus on cooking videos since in this domain action changes are prominent. Our Adverbs in Recipes (AIR) dataset was manually labelled and consists of over 7K videos, 10 adverbs and 48 actions. + +To summarise our contributions: i) we propose a more effective approach to learn adverbs in videos. Our method achieves state-of-the-art results on multiple datasets and with fewer assumptions; ii) we introduce the AIR dataset for adverb recognition. Our focus on a domain where action changes are prominent and our careful manual annotation makes AIR more suitable for training and evaluating models for adverb understanding. We publicly release AIR and our code at github.com/dmoltisanti/air-cvpr23. + +# 2. Related Work + +Adverb Recognition Doughty et al. [6] introduced the adverb recognition task and proposed Action Modifiers. Adverbs are treated as learnable parameters that guide the optimisation of the video embeddings via a triplet loss. We show that such approach can be difficult to optimise and propose an alternative learning method. Rather than modelling action changes as trainable parameters we define them measuring distances in a text embedding space. + +We then learn action modifications via regression. We provide a more technical comparison in Section 3. A follow-up work [7] proposes a pseudo-labelling method where videos are assigned new labels based on the model prediction. Pseudo labels are obtained in an adaptive away, i.e. the threshold determining whether a label should be assigned is adapted for each adverb independently. In [7] the underlying model is also Action Modifiers [6]. Pang et al. [18, 19] introduced the "Behaviour Adverb" task. Here actions are not goal-oriented (e.g. "kiss, smoke") and adverbs correspond to moods (e.g. "sadly, solemnly"). Models use additional modalities such as human pose [18] or explicitly learn human expressions [8, 19]. While related, this task is different from the scope of this work, where we aim to learn action changes in goal-oriented (e.g. cooking) videos. + +Adverb Datasets HowTo100M Adverbs [6] collects data from the instructional dataset HowTo100M [14] finding adverbs in the narration captions. Videos are loosely trimmed around the timestamp associated with the adverb. Due to the video-text misalignment in HowTo100M, and because training videos were not manually reviewed, videos in HowTo100M Adverbs are noisy. Authors estimated that only $44\%$ of the training videos actually show the action. In total 6 adverbs were annotated. Three other datasets were introduced in [7]: ActivityNet/MSR-VTT/VATEX Adverbs. These are subsets of the namesake captioning datasets [11,23,26]. Videos were also obtained finding adverbs in captions, but annotations here are clean because captions were provided by annotators. We argue that the captioning nature of the original datasets is a reason of concern for learning action modifications. Indeed, adverbs tend to be a complementary description of the video, i.e. actions do not appear particularly influenced by the adverb. Peering into these datasets (see Figure 4), we found for example "sit inside/outside, talk outdoors/indoors, walk in/out, move down/up", etc. These adverbs modify the appearance of the video, however the action themselves are not modified. Arguably, the act of sitting is the same whether it takes place inside or outside, as is the act of walking in or out. Lastly, [18, 19] annotated adverbs for non-task-oriented actions, e.g. "run, kiss", however adverbs here express moods and manners, e.g. "politely, reluctantly". + +The limited availability of datasets specifically designed for adverb understanding motivates us to collect a new dataset better suited for this task. We focus on recipe instructional videos where actions change significantly according to the adverb. We collect Adverbs in Recipes, which contains 7K videos, 10 adverbs and 48 actions. We employ annotators to verify that actions are carried out as indicated by the adverb. We present our dataset in Section 4. + +Video-text Retrieval Understanding adverbs in videos is related to video-text retrieval [2, 5, 9, 11-13, 15, 17, 22, 28, 30]. Theoretically, these methods could be used to retrieve + +![](images/505d8bf455fdbfd51f99f81067f422602ef5e0c3893c885f392e8361ffe80823.jpg) +Figure 2. Comparison between the unscaled distance $d$ (left) and the scaled distance $\delta$ (right), which is scaled using the verb-adverb cosine similarity. Plotted values are the Euclidean distances between corresponding positive and negative sentences. Blue/yellow indicate small/large distances, i.e. a small/big change when adverbs are flipped in the positive sentence (see text for more information). + +![](images/7cf16ab30e16c33428b5c4fd2f7567df3472e268469a5083b0205aeabacf0abe.jpg) + +videos using adverbs as text queries. However, as noted in [7], most approaches encode text embeddings for whole sentences, i.e. it is hard to retrieve videos querying single words. Some works propose fine-grained video-text retrieval where single parts-of-speech can be queried [4, 24, 27, 29], however these works focus on verbs and nouns and were not evaluated for adverbs. As discussed before, adverbs are more abstract compared to verbs and nouns and are difficult to spatio-temporally localise. This entails that a video-text retrieval approach is unlikely to work well to find adverbs in videos. We test a retrieval baseline with an S3D model [13] where video and text embeddings were jointly learnt. Despite the strong performance on a number of tasks, we show that indeed this model struggles to achieve satisfactory performance. + +# 3. Method + +We are given a video $x$ labelled with a verb $v$ , which annotates the action, and an adverb $a$ , which indicates the way the action is carried out. Our goal is to predict $a$ in $x$ given $v$ . We also have a mapping $h$ between adverbs opposite in meaning, e.g. $h(\text{quickly}) = \text{slowly}$ . We use a pre-trained video backbone $f$ to extract video features $f(x)$ . In this work we deal with long videos (10-40s), so we employ transformer-style attention [21] to attend to the relevant parts of the video. To this end, we use a pre-trained text model $g$ to extract a text embedding $g(v)$ , which we use as query for the attention, obtaining the projected video embedding $f'(x, v)$ . To learn more specialised video features we feed $f'(x, v)$ to a shallow MLP and obtain the final output of the model $\rho(f'(x, v))$ . We propose two methods to optimise the network casting the problem either as a classification or a regression task. In the former case we utilise the standard Cross Entropy (CE) loss using the ground truth adverb label $a$ . The CE pushes up predictions for the positive class and treats all negative classes equally. In some cases, however, it may be desirable to penalise the model more aggressively for incorrect predictions of antonym classes. Action Modifiers [6] uses the triplet loss for this purpose. However, in [6] negative samples are formed by only pairing antonyms. This is effective for distinguishing opposite adverbs, but does not train the model to distinguish an adverb from other negative non-antonym classes. + +We thus propose a second approach based on regression. Casting the task as a regression problem we aim to directly learn the change the adverb introduces to the action and the video. However, we do not have a ground truth quantifying such action modifications. We use a text embedding space to estimate action changes. The high level idea is that we first build a minimal sentence $s$ representing the modified action. We similarly build a negative sentence $\tilde{s}$ representing the action modified in the opposite way. Calculating the difference between $s$ and $\tilde{s}$ we have a proxy measure for the change the adverb applies to the action. We build $s$ concatenating the verb and the adverb (e.g. coat thinly), then generate $\tilde{s}$ replacing the adverb with its antonym (e.g. coat thickly). We then extract text embeddings $g(s)$ and $g(\tilde{s})$ . Note that $g$ receives a variable length sentence and outputs a fixed-dimension embedding. Let $\langle \rangle$ denote concatenation, so $s = \langle v, a \rangle$ and $\tilde{s} = \langle v, h(a) \rangle$ . We measure the difference between $s$ and $\tilde{s}$ to capture how $a$ changes $v$ : + +$$ +d (v, a) = \left\| g (\langle v, a \rangle) - g (\langle v, h (a) \rangle) \right\| _ {2} \tag {1} +$$ + +Ideally, $d$ could be used as is. However, we observed that for a given adverb $a$ we obtain similar $d(v, a)$ across most verbs $v$ . This defeats the purpose of measuring action changes via $d$ since $d$ itself is not discriminative enough. This happens because $d$ ignores the correlation between the verb and the adverb. Intuitively, if a verb and an adverb are not semantically correlated (e.g. "run thinly") then we cannot expect to capture a meaningful change when flipping the adverb in the negative sentence (recall that $g$ receives full sentences). To address this issue we scale $d$ with the cosine similarity between the verb $v$ and the adverb $a$ : + +$$ +\delta (v, a) = d (v, a) \cdot \frac {g (v) \cdot g (a)}{\| g (v) \| _ {2} \cdot \| g (a) \| _ {2}} \tag {2} +$$ + +Figure 2 compares $d$ (left) to $\delta$ (right) for a few (verb, adverb) combinations. Note how the unscaled distance $d$ is not discriminative given that adverbs display a similar $d$ across verbs. On the other hand, the scaled $\delta$ shows a meaningful distance. For example, we observe a large $\delta$ for adverbs "finely" and "coarsely" when paired with verbs "chop, mince, mash, grate". + +![](images/394538ec889fb60f06760c1867d2a5ccbd0b33ee72bc40dfedfb48a04b0a3042.jpg) +Figure 3. Pipeline of our method. Given a long video $x$ labelled with a verb $v$ and an adverb $a$ we learn video embeddings $f'(x, v)$ through attention. We optimise the model with two alternative methods: standard classification (CE: Cross Entropy) or regression (MSE: Mean Squared Error). We build a regression target measuring distances in a text embedding space, which estimates the action change we aim to learn in the video. The video backbone and text model are initialised from pre-trained models and are not fine-tuned during learning. + +Now that we have an estimate to measure action changes we can build a regression target: + +$$ +Y ^ {R} (v) = \left(t _ {i}, \forall i \in \{1, 2, \dots , A \}\right) = \left\{ \begin{array}{c c} \delta (v, a) & \text {i f} y _ {i} = a \\ - \delta (v, a) & \text {i f} y _ {i} = h (a) \\ 0 & \text {o t h e r w i s e} \end{array} \right. \tag {3} +$$ + +where $A$ is the number of adverbs in a dataset and $y_{i}$ denotes the $i$ -th adverb. Let $\hat{y}_i^v$ indicate the output of the model for the $i$ -th adverb obtained for verb $v$ , i.e. querying the attention model with $g(v)$ . The full output of the model is then $\hat{Y}^{v} = \rho (f^{\prime}(x,v)) = (\hat{y}_{i}^{v},\forall i\in \{1,2,\ldots ,A\})$ . + +We use the Mean Squared Error to train the network: $\mathcal{L}^R = \| Y^R (v) - \hat{Y}^v\| _2$ . The loss pushes opposite adverbs furthest apart (due to the negative sign of $\delta$ for the antonym). The loss also tells the model that the video is not modified by other unrelated adverbs (target is 0 for classes that are neither ground truth nor antonyms). This discourages the model to predict negative non-antonym adverbs. Figure 3 illustrates our method. Note that the video backbone and text model are not part of the training, i.e. they are initialised from pre-trained models and are not fine-tuned. + +Learning without Antonyms We also consider a setting where adverbs are not paired in antonyms. Instead of replacing the ground truth adverb with its antonym we simply remove the adverb and generate $\tilde{s} = v$ . In this case $\delta$ measures the difference between the action modified by the adverb and the unmodified version of the action. $Y^{R}$ is then $\delta$ for the ground truth adverb and 0 for all other adverbs. + +Inference As in [6] we are given the action label $v$ during testing. We query the attention model with $g(v)$ and use $\hat{Y}^v$ to predict each adverb. We also test the model without action labels. In such case we obtain $f'(x, v)$ querying all actions and take the maximum prediction for each adverb: + +$$ +p (x) = \left(\max _ {v} \left(\hat {y} _ {i} ^ {v}, \forall v \in \mathcal {V}\right), \forall i \in \{1, 2, \dots , A \}\right) \tag {4} +$$ + +where $\nu$ denotes the set of action labels. + +Comparison to Action Modifiers Our framework shares the same design as Action Modifiers [6] until $f'(x, v)$ . In [6] $f'(x, v)$ is optimised with two triplet losses: an action loss to help the attention model and an adverb loss to learn adverbs. We do not use an additional action loss. In Action Modifiers adverbs are also modelled as action changes utilising text embeddings. However, in [6] such change is treated as an additional parameter to be learnt. Specifically, an adverb is represented as a learnable matrix $W_{a}$ . The linear combination $o_{v}^{a} = W_{a} g(v)$ represents the change the adverb $a$ applies to the verb $v$ , where $g(v)$ is a text embedding as in our model. Importantly, $o_{v}^{a}$ is used in the triplet losses, thus the optimisation of the video embedding $f'(x, v)$ depends on the optimisation of parameters $W_{a}$ . We argue and show that learning adverbs with this approach can be difficult as the action change the model looks for in the video has also to be learnt. In our formulation instead the action change is pre-computed and is not learnt. We also provide explicit penalty for non-antonym classes rather than contrasting only opposite adverbs. Comparing capacity, our model has a smaller number of parameters which scales better with the number of adverbs. Indeed, each adverb in Action Modifiers requires a learnable matrix, whereas in our model only the last layer of the MLP varies with the number of adverbs (see supplementary material). + +# 4. Adverbs in Recipes: the AIR Dataset + +In Section 2 we motivated the need for a new dataset for adverb recognition. Here we introduce the Adverbs in Recipes (AIR) dataset. We wish to find a set of videos where actions change significantly according to the adverb. Compared to captioning benchmarks, instructional datasets contain videos where we can expect to find more of such actions. For this reason we source AIR from HowTo100M [14]. We restrict our interest to recipe videos since changes in cooking actions play an important role. For example, a carrot sliced à la juillienne (thinly) looks very different from a carrot chopped in thick dices (coarsely). + +
DatasetAccuracyDurationAdvActPairsVideos
CAPTActivityNet Adverbs [7]89.0%37.5s201146353,099
MSR-VTT Adverbs [7]91.0%15.7s181064501,824
VATEX Adverbs [7]93.5%10.0s (f)341351,52414,617
INSTHowTo100M Adverbs [6]44.0%20.0s (f)6722575,824
Adverbs in Recipes (ours)95.3%8.4s10481867,003
+ +Table 1. Comparing video datasets for adverb recognition. CAPT: captioning datasets, where adverbs are descriptive. INST: instructional datasets, where adverbs are action-focused. "Accuracy" indicates whether the action is visible as indicated by the adverb. "Duration" reports the average length, where (f) denotes a fixed duration. "Pairs" counts (verb, adverb) appearing in the dataset rather than the Cartesian product of all verbs and adverbs. + +In other words, adverbs are "easily visible" in recipe videos and involve interesting visual cues such as speed, temporal/spatial completeness and objects end-states. + +Data Collection We start selecting all recipe videos in HowTo100M. We then parse captions to keep only those containing a verb and an adverb. We filter videos removing verbs that indicate non visual actions (e.g. "watch, wait") or very long-term actions (e.g. "rise, grow"), since we do not expect these changes to be fully visible in the videos. We manually merge similar verbs, obtaining in total 48 verbs. We also remove infrequent and too generic adverbs (e.g. "carefully"). We cluster similar adverbs gathering a total of 10 adverbs, which we pair in antonyms. To trim videos in a tight manner we use the timestamps of the first/last word in a caption as the start/end of the action segment. At this point we have a set of videos of varying duration, each accompanied with a verb and an adverb. We ask annotators on Amazon Mechanical Turk (AMT) to check whether the action in a video is visible and is carried out as indicated by the adverb. For robustness we ask 3 different annotators to check the same video and employ 5 people for edge cases where annotators disagreed. We keep videos where the majority of the annotators confirmed that the action is visible as indicated by the adverb, collecting 7,003 videos. Figure 2 shows the verbs (columns) and adverbs (rows) in AIR. We provide more details in the supplementary material. + +Comparison to Other Datasets Table 1 compares AIR to other adverb $\text{dattets}^1$ reviewed in Section 2. "Accuracy" estimates the percentage of videos where the action and the adverb effect are visible. On the existing datasets this was estimated watching 200 videos in [7]. For AIR multiple annotators reviewed all videos, however, annotations on AMT can be noisy. We review 302 videos (5% of the dataset) and report this check as "Accuracy". Compared + +![](images/ca26cd8e2aaf7faa04bf746db6d08b8aa515800f64019570bdecda0217251bab.jpg) +Figure 4. Samples from existing datasets for adverb recognition and our new AIR dataset. Many adverbs in the captioning datasets appear to be descriptive rather than a key modification of the action (e.g. the act of talking/sitting is the same whether it takes place indoors/outdoors). In contrast, adverbs in the instructional datasets apply a more prominent change in the action and its outcome (e.g. a vegetable peeled coarsely will still have some skin attached). + +![](images/1f5a9dc36ac16b9366cfa05a780d2a9769c920bceb16dc1f317efea49bb5da67.jpg) + +![](images/0ad6f7ddd98748b132507e52a9fdefc21b8189a9168ad627f7d0f51deeb4fb2d.jpg) + +to the instructional-based HowTo100M Adverbs, AIR contains over 1,100 additional clips and 4 more adverbs. Importantly, our videos are manually reviewed (AIR accuracy is over $95\%$ compared to $44\%$ ) and better trimmed (averaged duration is 8s compared to fixed 20s segments). AIR features 48 actions which is the smallest number among the five datasets (and consequently the smallest number of pairs). This is due to our more restrictive verb filtering based on visual and task-oriented actions. For example, in the captioning datasets there are actions such as "tell, talk, sing, look". Actions in HowTo100M Adverbs are task oriented, however there are also verbs entailing long-term actions (e.g. "brew"), which are unlikely to be fully visible. + +Figure 4 shows a few samples from AIR as well as the other datasets. Note how adverbs in the instructional datasets apply a key modification in the action, whereas for the captioning datasets adverbs are descriptive. Cap-tions in the captioning datasets are reliable because they were provided by human annotators. However, annotators did not necessarily use adverbs to indicate a modification to the action. Thus, due to the automatic processing of these datasets, there are several cases where adverbs are descriptive and do not influence the action. Naturally, Figure 4 is not meant to be an exhaustive representation of the caption-ing datasets from [7]. These datasets also contain action-focused adverbs, however without extensively reviewing the videos and the associated adverbs it is hard to gauge how many actions are effectively modified by the adverb. + +To summarise the contributions of AIR: i) we employ annotators to verify that actions are performed in the way indicated by the adverb; ii) this allowed us to trim videos more tightly and obtain cleaner clips with less unrelated content; iii) we carefully choose verbs and adverbs to pick videos where action changes are significant. While we restrict our domain to recipes, cooking actions are visually diverse, entail complex object interactions and are particularly affected by the nuanced ways they are carried out. + +# 5. Experiments + +Implementation Details We use an S3D model [13, 25] jointly pre-trained on video and text on HowTo100M [14] as our video backbone. Specifically, we use the video output mixed_5c to obtain $f(x)$ . Following [6] we split videos in 1-second segments and sample 16 RGB frames from each segment to obtain the video features. Stacking features from the video segments we have $f(x)^{T \times D}$ , where $T$ varies depending on the dataset and $D$ is 1024. We use 4 heads for the attention model. The dimension $E$ of the query, key and value is 512, thus the projected video embedding $f'(x, v)$ has dimension $1 \times E$ . The MLP in our model has 3 layers (hidden units of dimension 512) with ReLU activation function for the hidden layers and dropout [20] set to 0.1. We train all models for 1000 epochs with the ADAM optimiser [10], setting learning rate to $1e^{-4}$ , weight decay to $5e^{-5}$ and batch size to 512. We use the text model jointly trained with S3D to extract text embeddings $g(\cdot)$ . This network, like the visual backbone, is not fine-tuned. We refer to [13] for more details about S3D and the text model. $f(x)$ and $g(\cdot)$ are the same for all experiments. + +Baselines Priors: here we do not train any model and simply use the prior distributions of the training set to make a prediction. When using the action label during testing, the prediction for an adverb is the number of training samples labelled with the adverb and the given verb, i.e. $p(x,v) = (\pi (v,a),\forall a\in \mathcal{A})$ , where $\pi$ denotes the frequency of $(v,a)$ in the training set and $\mathcal{A}$ is the set of adverbs in a dataset. While this baseline is a simple look-up table, it can achieve strong performance since it exploits the co-occurrence of verbs and adverbs. When the action label is not used during testing the priors baseline predicts the frequency of each adverb in the training set, i.e. $p(x) = (\pi (a),\forall a\in \mathcal{A})$ . + +S3D pre-trained: we test the S3D model we use as the video-text backbone for all experiments. Video and text embeddings were jointly learnt in this model, so we use the dot product between $f(x)$ and $g(\cdot)$ for predictions. When the action label $v$ is given during inference the prediction is $p(x,v) = (f(x)\cdot g(\langle v,a\rangle),\forall a\in \mathcal{A})$ , where $g(\langle v,a\rangle)$ is the text embedding obtained concatenating the given $v$ and each adverb $a$ . When the action label is not given, we have $p(x) = (\max_v f(x)\cdot g(\langle v,a\rangle),\forall v\in \mathcal{V}),\forall a\in \mathcal{A})$ , where $\mathcal{V}$ is the set of verbs. This S3D instance has shown very strong performance on several tasks [13], thus this baseline helps gauging the difficulty of detecting adverbs following a basic video-text retrieval approach. + +SOTA Act Mod: we compare against the state-of-the-art for adverb recognition, Action Modifiers [6], both using the original model and a deeper version with an additional MLP $(MLP + ActMod)$ . Here we append an identical MLP as in our model to the output of the transformer attention. This variant allows a better comparison with our method. We use the official code implementation to run our experiments. Note that Action Modifiers results reported here are not directly comparable to those reported in [6,7]. This is because we could not download several videos since they were removed from YouTube. Also, we use S3D features (identical for all experiments) instead of I3D [3] features. + +Our Variants CLS: our model trained with classification. REG - fixed $\delta$ : our model trained with regression discarding text embeddings altogether, setting $\delta = 1$ in Equation 3. This is to validate the premise of using textual context to build a regression target. REG: our model trained with regression using the full formulation. + +Evaluation Metrics We report mean Average Precision using two types of averaging: i) weighted (mAP W), where class scores are weighted according to the support size (smaller classes have a smaller weight); ii) macro (mAP M), where all classes have equal weight, which corresponds to "adverb-to-video (all)" in [6]. All the evaluated datasets exhibit a significant class imbalance, thus mAP M is a stricter metric compared to mAP W. We also report binary antonym accuracy (Acc-A), which corresponds to "video-to-adverb (antonym)" in [6]. Here we only look at the prediction of an adverb $a$ versus its antonym $h(a)$ . A prediction $p$ is correct if $p(a) > p(h(a))$ . All metrics are computed for adverb classes. To show the full potential of all methods we report each best metric independently, i.e. results may come from different epochs. This is to provide a robust comparison, however we note that all models reach stable convergence. + +Datasets We present experiments on the two instructional datasets we saw earlier: HowTo100M Adverbs [6] and our Adverbs In Recipes. As discussed before, we argue that instructional videos are more suitable for this task as adverbs are action-focused, i.e. actions change significantly according to the adverb. For completeness, we also evaluate the three adverb datasets sourced from captioning videos in [7]: ActivityNet/MSR-VTT/VATEX Adverbs3. Adverbs here are descriptive, thus these datasets are less reliable for evaluation. Datasets are summarised in Table 1. + +# 5.1. Results + +Overview We begin our discussion looking at results in Table 2 on the instructional datasets (left). Here we achieve new state-of-the-art results on all metrics. The gap between our best variant and Act Mod is more noticeable for the more challenging mAP W/M metrics. In [6] negative samples are + +
Priors
S3D pre-trained
Act Mod [6]
MLP + Act Mod [6]
CLS
REG - fixed δ
REG
+ +
Instructional datasets. Action-focused adverbs
HowTo100M Adverbs [6]Adverbs in Recipes
mAP WmAP MAcc-AmAP WmAP MAcc-A
0.4460.3540.7860.4910.2630.854
0.3390.2380.5600.3890.1730.735
0.4060.3720.7960.4210.1700.858
0.2790.1930.7930.4580.1880.857
0.5620.4200.7860.6750.3250.847
0.3200.2150.7060.4580.1450.835
0.5550.4230.7990.6690.2970.862
+ +
Captioning datasets. Descriptive adverbs
ActivityNet Adverbs [7]MSR-VTT Adverbs [7]VATEX Adverbs [7]
mAP WmAP MAcc-AmAP WmAP MAcc-AmAP WmAP MAcc-A
0.2170.1590.7450.3080.1520.7230.2160.0860.752
0.1180.0700.5600.1940.0750.6030.1220.0380.586
0.2110.1520.7480.2460.1480.7340.1390.0590.751
0.1540.1080.7530.2150.1110.7310.2090.0960.752
0.1140.0720.7140.1890.0810.7230.2830.1080.754
0.1130.0700.7060.2210.0960.7060.1750.0510.701
0.1830.1030.7090.2920.1180.7740.2610.0860.755
+ +Table 2. Results obtained using the action label during inference. mAP W/M: mean Average Precision with weighted (W) and macro (M) averaging. Acc-A: adverb-vs-antonym accuracy. Coloured rows indicate variants of our method. Bold denotes best result per column. In instructional datasets (left) adverbs are action-focused, so these are more reliable benchmarks to learn action changes. In captioning datasets (right) adverbs are more descriptive and do not influence the action significantly. As such, these datasets are less reliable. + +formed only pairing opposite adverbs, thus the model does not receive enough penalty for other negative adverbs. In contrast, we provide explicit penalty for non-antonym negative adverbs. The poor performance of S3D pre-trained indicates that learning adverbs in videos is not trivial. Adverbs are not well defined visual entities like objects or actions, thus video-text retrieval approaches looking for correlations between text and video embeddings are likely suboptimal, even when such embeddings are jointly learnt on the same dataset with a strong model, as is the case for S3D. + +Still looking at the instructional datasets, on AIR all methods achieve higher mAP W/Acc-A but lower mAP M. Considering that there are more adverbs in AIR than in HowTo100M Adverbs, the higher mAP W/Acc-A is indicative of the quality of AIR: given that videos are tighter and cleaner it is possible to learn adverbs more effectively. The lower mAP M is due to the long-tail class distribution and shows the opportunities AIR offers to improve methods. + +On the captioning datasets we observe an interesting result: the Priors baseline outperforms or achieves very high performance. This supports our argument that captioning datasets are not particularly suitable for our task. If a simple look-up table surpasses all learning-based methods, then we conclude it is very difficult to learn adverbs as action changes, because actions are not particularly influenced by adverbs here. While these datasets exhibit a skewed verb-adverb distribution, so do the instructional ones. In fact, on VATEX Adverbs (the biggest dataset with 1,524 pairs) our method attains marginally better results. This is to say that the problem does not lie in the imbalanced class distribution, rather in the nature of the videos. + +Importance of Context We now focus on the importance of using textual context for regression comparing REG - fixed $\delta$ to REG in Table 2. Visual features vary differently when the same action is modified by different adverbs, e.g. chopping something coarsely entails a more prominent change than chopping it slowly. With REG we learn such visual differences with targets that change (sometimes considerably) across adverbs for a given verb. A fixed target for all positive adverbs discards such differences: the model is + +penalised equally for small/big changes. REG - fixed $\delta$ does this, and its consistent worse performance validates the idea of using text context as a proxy to learn action changes. + +The Key is in the Optimisation We now compare $MLP + ActMod$ to our method. For this $ActMod$ variant we replace the video embedding $f'(x, v)$ with $\theta(f'(x, v))$ in the two losses in [6], where $\theta$ is the additional MLP. With this configuration, the only difference between our method and Action Modifiers lies in the optimisation. In Section 3 we hypothesised that the optimisation of Action Modifiers might be difficult. Results in Table 2 support our hypothesis. When adding the MLP to $ActMod$ , Acc-A remains virtually identical across all datasets. However, mAP W/M drop considerably on HowTo100M Adverbs. This dataset is the noisiest among the five datasets, thus in this case increasing the depth of the model makes optimisation more difficult. Overall, comparing $MLP + ActMod$ to our method we achieve better results even when the additional MLP improves the performance of the original $ActMod$ . We conclude that learning adverbs as pre-defined actions changes rather than as trainable parameters is a better strategy. + +Testing without Action Labels In Table 3 we report results obtained without using the action label at test time. We test Action Modifiers in the same way as described for our method in Section 3. Experiments are directly comparable between Tables 2 and 3 since the tested models are the same. We note a remarkable drop in performance for all methods. This is expected since the task is now harder. In fact we need to predict the right adverb from multiple video embeddings obtained querying all verbs. Nevertheless, our method still achieves the best global performance in this more challenging setting. This shows that our method is more robust and is able to better generalise. + +Learning without Antonyms We now study the case where adverbs are not paired in antonyms. This is a desirable setting as it allows more flexibility in data collection. To train Action Modifiers without antonyms we just sample a random negative adverb as opposed to the antonym for the triplet loss. We illustrated in Section 3 how we train our REG variant. We do not evaluate REG - fixed $\delta$ here since + +
Instructional datasets. Action-focused adverbs
HowTo100M Adverbs [6]Adverbs in Recipes
mAP WmAP MAcc-AmAP WmAP MAcc-A
Priors0.2470.1670.5600.3350.1000.835
S3D pre-trained0.3290.2220.5940.4250.1770.702
Act Mod [6]0.2690.1830.6010.3460.1070.837
MLP + Act Mod [6]0.2680.1840.7060.3680.1130.835
CLS0.4040.3070.7240.4690.1980.835
REG - fixed δ0.3200.2150.7060.4610.1480.835
REG0.3770.2770.7240.4810.1570.857
+ +
Captioning datasets. Descriptive adverbs
ActivityNet Adverbs [7]MSR-VTT Adverbs [7]VATEX Adverbs [7]
mAP WmAP MAcc-AmAP WmAP MAcc-AmAP WmAP MAcc-A
0.0940.0500.6920.1370.0560.7230.0890.0290.651
0.1130.0650.5980.1990.0880.6030.1170.0370.604
0.1100.0630.7180.1640.0720.7290.1000.0350.686
0.1090.0700.7140.1620.0970.7230.0920.0360.686
0.1140.0720.7140.1890.0780.7230.1610.0530.712
0.1130.0700.7060.2130.0950.7140.1580.0470.703
0.1200.0730.7060.2400.1020.7490.1690.0570.737
+ +Table 3. Results obtained without action labels during inference. mAP W/M: mean Average Precision with weighted (W) and macro (M) averaging. Acc-A: adverb-vs-antonym accuracy. Coloured rows indicate variants of our method. Bold denotes best result per column. + +
AntonymsInstructional datasets. Action-focused adverbsCaptioning datasets. Descriptive adverbs
HowTo100M Adverbs [6]Adverbs in RecipesActivityNet Adverbs [7]MSR-VTT Adverbs [7]VATEX Adverbs [7]
mAP WmAP MmAP WmAP MmAP WmAP MmAP WmAP MmAP WmAP M
PriorsX0.4460.3540.4910.2630.2170.1590.3080.1520.2160.086
S3D pre-trainedX0.3390.2380.3890.1730.1180.0700.1940.0750.1220.038
Act Mod [6]✓0.4060.3720.4210.1700.2110.1520.2460.1480.1390.059
X0.4080.3520.4280.1800.2170.1600.2540.1540.1440.060
MLP + Act Mod [6]✓0.2790.1930.4580.1880.1540.1080.2150.1110.2090.096
X0.2810.1980.4650.1970.1640.1150.2290.1320.2130.098
CLSX0.5620.4200.6750.3250.1140.0720.1890.0810.2830.108
REG✓0.5550.4230.6690.2970.1830.1030.2920.1180.2610.086
X0.5730.4810.7160.3930.2060.1210.3190.1140.2820.100
+ +Table 4. Results obtained with action labels during inference and without antonyms during training. mAP W/M: mean Average Precision with weighted (W) and macro (M) averaging. Coloured rows indicate variants of our method. Bold denotes best result per column. + +without antonyms it would be similar to binary classification. $CLS$ by design does not use antonyms. Table 4 compares results obtained with and without antonyms. Since we assume we do not have antonym labels here we only evaluate mAP W/M. Interestingly, Action Modifiers slightly improves when removing antonyms, which shows again that using only opposite adverbs for contrastive learning limits the model. Discarding antonyms for our regression variant has also a strong positive effective. Since we remove the target $-\delta$ for antonyms and treat opposite adverbs as any other negative class, we are not forcing the model to push antonyms further compared to other negative adverbs. This is beneficial to learn adverbs more generally. + +Regression vs Classification We now compare CLS and REG in Tables 2, 3 and 4. When testing without action labels (Table 3) and learning without antonyms (Table 4) we notice a more consistent improvement of REG over CLS. Rather than maximising the margin between the positive adverb and all other negative adverbs as in classification, with regression we try to learn the extent of the change applied by an adverb. This is evidently a more effective way to learn adverbs since the visual change introduced by an adverb varies considerably according to the action. + +# 6. Conclusion + +We proposed to address adverb recognition as a regression task. Our method attains new state-of-the-art performance on multiple datasets. Importantly, we achieve compelling results when removing two major assumptions: the + +availability of action labels during testing and the pairing of opposite adverbs as antonyms. To address the scarcity of datasets for adverb recognition we introduced AIR. The dataset collects instructional recipe videos where actions are particularly influenced by the modification indicated by adverbs. We believe AIR is a valuable resource that can readily foster advance in adverb understanding. + +Limitations Since we model action changes measuring distances in a text embedding space we rely on a reasonably good text model. If the model does not capture meaningful relationships between verbs and adverbs then we do not have a reliable proxy to learn adverbs. Because we look for action changes directly in the video, actions need to exhibit a sufficient visual change when modified by the adverb. + +Future Work Directions for future work include exploring ways to capture a broader action context via text. For example, the full caption associated with a video can provide additional information (e.g. object nouns) that could be exploited to better learn action modifications. This would require addressing the problem of video-text alignment, as well as the intrinsic noisy nature of long text embeddings. + +Potential Societal Impact We source AIR from HowTo100M dataset, which gathers videos from YouTube. As such, any societal bias introduced in HowTo100M is potentially included in our data and our trained models. + +Acknowledgements Research funded by UKRI through the Edinburgh Laboratory for Integrated Artificial Intelligence (ELIAI) and the Turing Advanced Autonomy project. + +# References + +[1] Humam Alwassel, Fabian Caba Heilbron, Victor Escorcia, and Bernard Ghanem. Diagnosing error in temporal action detectors. In ECCV, 2018. 1 +[2] Lisa Anne Hendricks, Oliver Wang, Eli Shechtman, Josef Sivic, Trevor Darrell, and Bryan Russell. Localizing moments in video with natural language. In ICCV, 2017. 2 +[3] Joao Carreira and Andrew Zisserman. Quo vadis, action recognition? a new model and the kinetics dataset. 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In ACM - Multimedia Retrieval, 2018. 2 +[16] Davide Moltisanti, Michael Wray, Walterio Mayol-Cuevas, and Dima Damen. Trespassing the boundaries: Labeling temporal bounds for object interactions in egocentric video. In ICCV, 2017. 1 +[17] Jonghwan Mun, Minsu Cho, and Bohyung Han. Local-global video-text interactions for temporal grounding. In CVPR, 2020. 2 + +[18] Bo Pang, Kaiwen Zha, and Cewu Lu. Human action adverb recognition: Adha dataset and a three-stream hybrid model. In CVPR (workshop), 2018. 2 +[19] Bo Pang, Kaiwen Zha, Yifan Zhang, and Cewu Lu. Further understanding videos through adverbs: A new video task. In AAAI, 2020. 2 +[20] Nitish Srivastava, Geoffrey Hinton, Alex Krizhevsky, Ilya Sutskever, and Ruslan Salakhutdinov. Dropout: a simple way to prevent neural networks from overfitting. In JMLR, 2014. 6 +[21] Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Lukasz Kaiser, and Illia Polosukhin. Attention is all you need. 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Jointly modeling deep video and compositional text to bridge vision and language in a unified framework. In AAAI, 2015. 3 +[28] Jianwei Yang, Yonatan Bisk, and Jianfeng Gao. Taco: Token-aware cascade contrastive learning for video-text alignment. In ICCV, 2021. 2 +[29] Youngjae Yu, Hyungjin Ko, Jongwook Choi, and Gunhee Kim. End-to-end concept word detection for video captioning, retrieval, and question answering. In CVPR, 2017. 3 +[30] Runhao Zeng, Haoming Xu, Wenbing Huang, Peihao Chen, Mingkui Tan, and Chuang Gan. Dense regression network for video grounding. In CVPR, 2020. 2 \ No newline at end of file diff --git a/2023/Learning Action Changes by Measuring Verb-Adverb Textual Relationships/images.zip b/2023/Learning Action Changes by Measuring Verb-Adverb Textual Relationships/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..c474e13e46b4da6d1affd91b9fac8b6a3054ae4c --- /dev/null +++ b/2023/Learning Action Changes by Measuring Verb-Adverb Textual Relationships/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:315d243c52b8a06335ef026d0a9a605e5766d272363a8f045c7605864148d628 +size 437273 diff --git a/2023/Learning Action Changes by Measuring Verb-Adverb Textual Relationships/layout.json b/2023/Learning Action Changes by Measuring Verb-Adverb Textual Relationships/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..cff8d47e0d8f030759e16a2ae3f9be78d83a32ba --- /dev/null +++ b/2023/Learning Action Changes by Measuring Verb-Adverb Textual Relationships/layout.json @@ -0,0 +1,7558 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 62, + 103, + 531, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 103, + 531, + 121 + ], + "spans": [ + { + "bbox": [ + 62, + 103, + 531, + 121 + ], + "type": "text", + "content": "Learning Action Changes by Measuring Verb-Adverb Textual Relationships" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 137, + 143, + 455, + 171 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 137, + 143, + 455, + 171 + ], + "spans": [ + { + "bbox": [ + 137, + 143, + 455, + 171 + ], + "type": "text", + "content": "Davide Moltisanti, Frank Keller, Hakan Bilen, Laura Sevilla-Lara \nThe University of Edinburgh, United Kingdom" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 128, + 174, + 462, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 128, + 174, + 462, + 185 + ], + "spans": [ + { + "bbox": [ + 128, + 174, + 462, + 185 + ], + "type": "text", + "content": "{davide.moltisanti, frank.keller, h.bilen, l.sevilla}@ed.ac.uk" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "spans": [ + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 238, + 287, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 238, + 287, + 380 + ], + "spans": [ + { + "bbox": [ + 46, + 238, + 287, + 380 + ], + "type": "text", + "content": "The goal of this work is to understand the way actions are performed in videos. That is, given a video, we aim to predict an adverb indicating a modification applied to the action (e.g. cut \"finely\"). We cast this problem as a regression task. We measure textual relationships between verbs and adverbs to generate a regression target representing the action change we aim to learn. We test our approach on a range of datasets and achieve state-of-the-art results on both adverb prediction and antonym classification. Furthermore, we outperform previous work when we lift two commonly assumed conditions: the availability of action labels during testing and the pairing of adverbs as antonyms." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 381, + 287, + 537 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 381, + 287, + 537 + ], + "spans": [ + { + "bbox": [ + 46, + 381, + 287, + 537 + ], + "type": "text", + "content": "Existing datasets for adverb recognition are either noisy, which makes learning difficult, or contain actions whose appearance is not influenced by adverbs, which makes evaluation less reliable. To address this, we collect a new high quality dataset: Adverbs in Recipes (AIR). We focus on instructional recipes videos, curating a set of actions that exhibit meaningful visual changes when performed differently. Videos in AIR are more tightly trimmed and were manually reviewed by multiple annotators to ensure high labelling quality. Results show that models learn better from AIR given its cleaner videos. At the same time, adverb prediction on AIR is challenging, demonstrating that there is considerable room for improvement." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 550, + 127, + 562 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 550, + 127, + 562 + ], + "spans": [ + { + "bbox": [ + 47, + 550, + 127, + 562 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "text", + "content": "Learning how an action is performed in a video is an important step towards expanding our video understanding beyond action recognition. This task has been referred to as \"adverb recognition\", and has potential useful applications in robotics and retrieval. Consider a scenario where a robot handles fragile objects. In such case we would like to tell the robot to grasp objects gently to prevent it from breaking things. Similarly, learning how actions are performed enables more sophisticated queries for retrieval. Imagine learning a new recipe where a crucial step is stirring a mixture vigorously. It would be useful to find good examples showing how to whip a mixture in such a manner." + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 318, + 210, + 460, + 371 + ], + "blocks": [ + { + "bbox": [ + 318, + 210, + 460, + 371 + ], + "lines": [ + { + "bbox": [ + 318, + 210, + 460, + 371 + ], + "spans": [ + { + "bbox": [ + 318, + 210, + 460, + 371 + ], + "type": "image", + "image_path": "5a3782a3da153dcfcf9b464efeeef77b5a5f4caf3f9e5f3c7695d080e45911d0.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 379, + 545, + 447 + ], + "lines": [ + { + "bbox": [ + 305, + 379, + 545, + 447 + ], + "spans": [ + { + "bbox": [ + 305, + 379, + 545, + 447 + ], + "type": "text", + "content": "Figure 1. We aim to predict the way an action is performed in a video (right). Actions and their outcomes change in different ways when modified by adverbs, e.g. grinding coffee slowly does not have the same effect as grinding it coarsely (left). We learn to predict adverbs by recognising action changes in the video. We define action changes measuring verb-adverb textual relationships." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 483, + 211, + 534, + 357 + ], + "blocks": [ + { + "bbox": [ + 483, + 211, + 534, + 357 + ], + "lines": [ + { + "bbox": [ + 483, + 211, + 534, + 357 + ], + "spans": [ + { + "bbox": [ + 483, + 211, + 534, + 357 + ], + "type": "image", + "image_path": "c2e5c2ba462eca3388337d582bbb96330c083e854b6189c054e03690bd0646ed.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 474, + 546, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 546, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 546, + 715 + ], + "type": "text", + "content": "Adverb recognition is a challenging problem. Firstly, a single adverb can modify multiple actions in different ways. For example, to grind coffee coarsely (see Figure 1) we need to set a certain granularity in a grinder. Conversely, to spray something coarsely we would just use a spraying can more sparingly. Secondly, compared to actions or objects, adverbs are much harder to identify. Though somewhat subjective [1, 16], the temporal boundaries of an action can be easily determined. The spatial extent of an object is also easy to recognise for a human. Adverbs are instead more abstract: we can see their effect, but we struggle to pinpoint the spatio-temporal location where the adverb is appearing. Consider for example the act of spraying something slowly in Figure 1. We could say that slowly \"is located\" on the hand motions. At the same time, spraying something slowly could implicate a more even coating of a surface. That is, the outcome of an action and the end-state of the involved objects can also change according to the adverb. This makes it hard to label adverbs with visual annotations (e.g. bounding boxes), which makes the problem more challenging." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "23110" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 263 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 263 + ], + "type": "text", + "content": "In fact, previous approaches [6, 7] learn adverbs as action changes in a weakly supervised manner. The state-of-the-art approach [6] treats adverbs as learnable parameters that modify actions. Specifically, the action change is learnt during training by contrasting antonyms, i.e. opposite adverbs. We show that learning adverbs in such manner can be difficult and can limit the ability of the model to generalise. We thus propose to define action changes by measuring distances in a text embedding space, and aim to learn such change from the video through regression. We show that our approach achieves new state-of-the-art results through extensive experiments. We also lift two major assumptions made in previous work [6, 7]: the availability of action labels during testing and the pairing of opposite adverbs as antonyms. Our method achieves stronger performance especially when the above assumptions are relaxed." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 264, + 289, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 264, + 289, + 479 + ], + "spans": [ + { + "bbox": [ + 47, + 264, + 289, + 479 + ], + "type": "text", + "content": "Besides being challenging, adverb recognition is also an under-explored domain and only few datasets are available. Doughty and Snoek [7] addressed the problem of scarce annotations, proposing a semi-supervised method that assigns pseudo-labels to boost recognition performance. Three datasets sourced from captioning benchmarks were also collected in [7]. These datasets offer a large number of clips, actions and adverbs. However, adverbs in these datasets appear to be descriptive rather than action modifiers, i.e. actions do not display a significant change when modified by the adverb. This is an issue when adverbs are modelled as action changes as in this work. We thus introduce a new dataset focusing on instructional videos where actions change considerably depending on the way they are carried out. We focus on cooking videos since in this domain action changes are prominent. Our Adverbs in Recipes (AIR) dataset was manually labelled and consists of over 7K videos, 10 adverbs and 48 actions." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 481, + 289, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 481, + 289, + 590 + ], + "spans": [ + { + "bbox": [ + 47, + 481, + 289, + 590 + ], + "type": "text", + "content": "To summarise our contributions: i) we propose a more effective approach to learn adverbs in videos. Our method achieves state-of-the-art results on multiple datasets and with fewer assumptions; ii) we introduce the AIR dataset for adverb recognition. Our focus on a domain where action changes are prominent and our careful manual annotation makes AIR more suitable for training and evaluating models for adverb understanding. We publicly release AIR and our code at github.com/dmoltisanti/air-cvpr23." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 597, + 134, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 597, + 134, + 609 + ], + "spans": [ + { + "bbox": [ + 47, + 597, + 134, + 609 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 618, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 618, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 618, + 288, + 715 + ], + "type": "text", + "content": "Adverb Recognition Doughty et al. [6] introduced the adverb recognition task and proposed Action Modifiers. Adverbs are treated as learnable parameters that guide the optimisation of the video embeddings via a triplet loss. We show that such approach can be difficult to optimise and propose an alternative learning method. Rather than modelling action changes as trainable parameters we define them measuring distances in a text embedding space." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 72, + 547, + 252 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 252 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 252 + ], + "type": "text", + "content": "We then learn action modifications via regression. We provide a more technical comparison in Section 3. A follow-up work [7] proposes a pseudo-labelling method where videos are assigned new labels based on the model prediction. Pseudo labels are obtained in an adaptive away, i.e. the threshold determining whether a label should be assigned is adapted for each adverb independently. In [7] the underlying model is also Action Modifiers [6]. Pang et al. [18, 19] introduced the \"Behaviour Adverb\" task. Here actions are not goal-oriented (e.g. \"kiss, smoke\") and adverbs correspond to moods (e.g. \"sadly, solemnly\"). Models use additional modalities such as human pose [18] or explicitly learn human expressions [8, 19]. While related, this task is different from the scope of this work, where we aim to learn action changes in goal-oriented (e.g. cooking) videos." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 255, + 547, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 255, + 547, + 578 + ], + "spans": [ + { + "bbox": [ + 304, + 255, + 547, + 578 + ], + "type": "text", + "content": "Adverb Datasets HowTo100M Adverbs [6] collects data from the instructional dataset HowTo100M [14] finding adverbs in the narration captions. Videos are loosely trimmed around the timestamp associated with the adverb. Due to the video-text misalignment in HowTo100M, and because training videos were not manually reviewed, videos in HowTo100M Adverbs are noisy. Authors estimated that only " + }, + { + "bbox": [ + 304, + 255, + 547, + 578 + ], + "type": "inline_equation", + "content": "44\\%" + }, + { + "bbox": [ + 304, + 255, + 547, + 578 + ], + "type": "text", + "content": " of the training videos actually show the action. In total 6 adverbs were annotated. Three other datasets were introduced in [7]: ActivityNet/MSR-VTT/VATEX Adverbs. These are subsets of the namesake captioning datasets [11,23,26]. Videos were also obtained finding adverbs in captions, but annotations here are clean because captions were provided by annotators. We argue that the captioning nature of the original datasets is a reason of concern for learning action modifications. Indeed, adverbs tend to be a complementary description of the video, i.e. actions do not appear particularly influenced by the adverb. Peering into these datasets (see Figure 4), we found for example \"sit inside/outside, talk outdoors/indoors, walk in/out, move down/up\", etc. These adverbs modify the appearance of the video, however the action themselves are not modified. Arguably, the act of sitting is the same whether it takes place inside or outside, as is the act of walking in or out. Lastly, [18, 19] annotated adverbs for non-task-oriented actions, e.g. \"run, kiss\", however adverbs here express moods and manners, e.g. \"politely, reluctantly\"." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 578, + 547, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 578, + 547, + 674 + ], + "spans": [ + { + "bbox": [ + 304, + 578, + 547, + 674 + ], + "type": "text", + "content": "The limited availability of datasets specifically designed for adverb understanding motivates us to collect a new dataset better suited for this task. We focus on recipe instructional videos where actions change significantly according to the adverb. We collect Adverbs in Recipes, which contains 7K videos, 10 adverbs and 48 actions. We employ annotators to verify that actions are carried out as indicated by the adverb. We present our dataset in Section 4." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "type": "text", + "content": "Video-text Retrieval Understanding adverbs in videos is related to video-text retrieval [2, 5, 9, 11-13, 15, 17, 22, 28, 30]. Theoretically, these methods could be used to retrieve" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "type": "text", + "content": "23111" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 70, + 298, + 139 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 298, + 139 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 298, + 139 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 298, + 139 + ], + "type": "image", + "image_path": "505d8bf455fdbfd51f99f81067f422602ef5e0c3893c885f392e8361ffe80823.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 149, + 546, + 183 + ], + "lines": [ + { + "bbox": [ + 46, + 149, + 546, + 183 + ], + "spans": [ + { + "bbox": [ + 46, + 149, + 546, + 183 + ], + "type": "text", + "content": "Figure 2. Comparison between the unscaled distance " + }, + { + "bbox": [ + 46, + 149, + 546, + 183 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 149, + 546, + 183 + ], + "type": "text", + "content": " (left) and the scaled distance " + }, + { + "bbox": [ + 46, + 149, + 546, + 183 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 46, + 149, + 546, + 183 + ], + "type": "text", + "content": " (right), which is scaled using the verb-adverb cosine similarity. Plotted values are the Euclidean distances between corresponding positive and negative sentences. Blue/yellow indicate small/large distances, i.e. a small/big change when adverbs are flipped in the positive sentence (see text for more information)." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 298, + 71, + 545, + 139 + ], + "blocks": [ + { + "bbox": [ + 298, + 71, + 545, + 139 + ], + "lines": [ + { + "bbox": [ + 298, + 71, + 545, + 139 + ], + "spans": [ + { + "bbox": [ + 298, + 71, + 545, + 139 + ], + "type": "image", + "image_path": "7cf16ab30e16c33428b5c4fd2f7567df3472e268469a5083b0205aeabacf0abe.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 198, + 289, + 378 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 198, + 289, + 378 + ], + "spans": [ + { + "bbox": [ + 46, + 198, + 289, + 378 + ], + "type": "text", + "content": "videos using adverbs as text queries. However, as noted in [7], most approaches encode text embeddings for whole sentences, i.e. it is hard to retrieve videos querying single words. Some works propose fine-grained video-text retrieval where single parts-of-speech can be queried [4, 24, 27, 29], however these works focus on verbs and nouns and were not evaluated for adverbs. As discussed before, adverbs are more abstract compared to verbs and nouns and are difficult to spatio-temporally localise. This entails that a video-text retrieval approach is unlikely to work well to find adverbs in videos. We test a retrieval baseline with an S3D model [13] where video and text embeddings were jointly learnt. Despite the strong performance on a number of tasks, we show that indeed this model struggles to achieve satisfactory performance." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 384, + 103, + 396 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 384, + 103, + 396 + ], + "spans": [ + { + "bbox": [ + 47, + 384, + 103, + 396 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 403, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 403, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 403, + 289, + 715 + ], + "type": "text", + "content": "We are given a video " + }, + { + "bbox": [ + 46, + 403, + 289, + 715 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 403, + 289, + 715 + ], + "type": "text", + "content": " labelled with a verb " + }, + { + "bbox": [ + 46, + 403, + 289, + 715 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 46, + 403, + 289, + 715 + ], + "type": "text", + "content": ", which annotates the action, and an adverb " + }, + { + "bbox": [ + 46, + 403, + 289, + 715 + ], + "type": "inline_equation", + "content": "a" + }, + { + "bbox": [ + 46, + 403, + 289, + 715 + ], + "type": "text", + "content": ", which indicates the way the action is carried out. Our goal is to predict " + }, + { + "bbox": [ + 46, + 403, + 289, + 715 + ], + "type": "inline_equation", + "content": "a" + }, + { + "bbox": [ + 46, + 403, + 289, + 715 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 46, + 403, + 289, + 715 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 403, + 289, + 715 + ], + "type": "text", + "content": " given " + }, + { + "bbox": [ + 46, + 403, + 289, + 715 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 46, + 403, + 289, + 715 + ], + "type": "text", + "content": ". We also have a mapping " + }, + { + "bbox": [ + 46, + 403, + 289, + 715 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 46, + 403, + 289, + 715 + ], + "type": "text", + "content": " between adverbs opposite in meaning, e.g. " + }, + { + "bbox": [ + 46, + 403, + 289, + 715 + ], + "type": "inline_equation", + "content": "h(\\text{quickly}) = \\text{slowly}" + }, + { + "bbox": [ + 46, + 403, + 289, + 715 + ], + "type": "text", + "content": ". We use a pre-trained video backbone " + }, + { + "bbox": [ + 46, + 403, + 289, + 715 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 403, + 289, + 715 + ], + "type": "text", + "content": " to extract video features " + }, + { + "bbox": [ + 46, + 403, + 289, + 715 + ], + "type": "inline_equation", + "content": "f(x)" + }, + { + "bbox": [ + 46, + 403, + 289, + 715 + ], + "type": "text", + "content": ". In this work we deal with long videos (10-40s), so we employ transformer-style attention [21] to attend to the relevant parts of the video. To this end, we use a pre-trained text model " + }, + { + "bbox": [ + 46, + 403, + 289, + 715 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 46, + 403, + 289, + 715 + ], + "type": "text", + "content": " to extract a text embedding " + }, + { + "bbox": [ + 46, + 403, + 289, + 715 + ], + "type": "inline_equation", + "content": "g(v)" + }, + { + "bbox": [ + 46, + 403, + 289, + 715 + ], + "type": "text", + "content": ", which we use as query for the attention, obtaining the projected video embedding " + }, + { + "bbox": [ + 46, + 403, + 289, + 715 + ], + "type": "inline_equation", + "content": "f'(x, v)" + }, + { + "bbox": [ + 46, + 403, + 289, + 715 + ], + "type": "text", + "content": ". To learn more specialised video features we feed " + }, + { + "bbox": [ + 46, + 403, + 289, + 715 + ], + "type": "inline_equation", + "content": "f'(x, v)" + }, + { + "bbox": [ + 46, + 403, + 289, + 715 + ], + "type": "text", + "content": " to a shallow MLP and obtain the final output of the model " + }, + { + "bbox": [ + 46, + 403, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\rho(f'(x, v))" + }, + { + "bbox": [ + 46, + 403, + 289, + 715 + ], + "type": "text", + "content": ". We propose two methods to optimise the network casting the problem either as a classification or a regression task. In the former case we utilise the standard Cross Entropy (CE) loss using the ground truth adverb label " + }, + { + "bbox": [ + 46, + 403, + 289, + 715 + ], + "type": "inline_equation", + "content": "a" + }, + { + "bbox": [ + 46, + 403, + 289, + 715 + ], + "type": "text", + "content": ". The CE pushes up predictions for the positive class and treats all negative classes equally. In some cases, however, it may be desirable to penalise the model more aggressively for incorrect predictions of antonym classes. Action Modifiers [6] uses the triplet loss for this purpose. However, in [6] negative samples are formed by only pairing antonyms. This is effective for distinguishing opposite adverbs, but does not train the model to distinguish an adverb from other negative non-antonym classes." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 198, + 547, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 198, + 547, + 415 + ], + "spans": [ + { + "bbox": [ + 304, + 198, + 547, + 415 + ], + "type": "text", + "content": "We thus propose a second approach based on regression. Casting the task as a regression problem we aim to directly learn the change the adverb introduces to the action and the video. However, we do not have a ground truth quantifying such action modifications. We use a text embedding space to estimate action changes. The high level idea is that we first build a minimal sentence " + }, + { + "bbox": [ + 304, + 198, + 547, + 415 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 304, + 198, + 547, + 415 + ], + "type": "text", + "content": " representing the modified action. We similarly build a negative sentence " + }, + { + "bbox": [ + 304, + 198, + 547, + 415 + ], + "type": "inline_equation", + "content": "\\tilde{s}" + }, + { + "bbox": [ + 304, + 198, + 547, + 415 + ], + "type": "text", + "content": " representing the action modified in the opposite way. Calculating the difference between " + }, + { + "bbox": [ + 304, + 198, + 547, + 415 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 304, + 198, + 547, + 415 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 198, + 547, + 415 + ], + "type": "inline_equation", + "content": "\\tilde{s}" + }, + { + "bbox": [ + 304, + 198, + 547, + 415 + ], + "type": "text", + "content": " we have a proxy measure for the change the adverb applies to the action. We build " + }, + { + "bbox": [ + 304, + 198, + 547, + 415 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 304, + 198, + 547, + 415 + ], + "type": "text", + "content": " concatenating the verb and the adverb (e.g. coat thinly), then generate " + }, + { + "bbox": [ + 304, + 198, + 547, + 415 + ], + "type": "inline_equation", + "content": "\\tilde{s}" + }, + { + "bbox": [ + 304, + 198, + 547, + 415 + ], + "type": "text", + "content": " replacing the adverb with its antonym (e.g. coat thickly). We then extract text embeddings " + }, + { + "bbox": [ + 304, + 198, + 547, + 415 + ], + "type": "inline_equation", + "content": "g(s)" + }, + { + "bbox": [ + 304, + 198, + 547, + 415 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 198, + 547, + 415 + ], + "type": "inline_equation", + "content": "g(\\tilde{s})" + }, + { + "bbox": [ + 304, + 198, + 547, + 415 + ], + "type": "text", + "content": ". Note that " + }, + { + "bbox": [ + 304, + 198, + 547, + 415 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 304, + 198, + 547, + 415 + ], + "type": "text", + "content": " receives a variable length sentence and outputs a fixed-dimension embedding. Let " + }, + { + "bbox": [ + 304, + 198, + 547, + 415 + ], + "type": "inline_equation", + "content": "\\langle \\rangle" + }, + { + "bbox": [ + 304, + 198, + 547, + 415 + ], + "type": "text", + "content": " denote concatenation, so " + }, + { + "bbox": [ + 304, + 198, + 547, + 415 + ], + "type": "inline_equation", + "content": "s = \\langle v, a \\rangle" + }, + { + "bbox": [ + 304, + 198, + 547, + 415 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 198, + 547, + 415 + ], + "type": "inline_equation", + "content": "\\tilde{s} = \\langle v, h(a) \\rangle" + }, + { + "bbox": [ + 304, + 198, + 547, + 415 + ], + "type": "text", + "content": ". We measure the difference between " + }, + { + "bbox": [ + 304, + 198, + 547, + 415 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 304, + 198, + 547, + 415 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 198, + 547, + 415 + ], + "type": "inline_equation", + "content": "\\tilde{s}" + }, + { + "bbox": [ + 304, + 198, + 547, + 415 + ], + "type": "text", + "content": " to capture how " + }, + { + "bbox": [ + 304, + 198, + 547, + 415 + ], + "type": "inline_equation", + "content": "a" + }, + { + "bbox": [ + 304, + 198, + 547, + 415 + ], + "type": "text", + "content": " changes " + }, + { + "bbox": [ + 304, + 198, + 547, + 415 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 304, + 198, + 547, + 415 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 345, + 426, + 545, + 449 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 345, + 426, + 545, + 449 + ], + "spans": [ + { + "bbox": [ + 345, + 426, + 545, + 449 + ], + "type": "interline_equation", + "content": "d (v, a) = \\left\\| g (\\langle v, a \\rangle) - g (\\langle v, h (a) \\rangle) \\right\\| _ {2} \\tag {1}", + "image_path": "505eb28daaaa89ddd4ae4219bf0f3575ea877c8075c272f7ed0a3ea62d27b56a.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 454, + 547, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 454, + 547, + 586 + ], + "spans": [ + { + "bbox": [ + 304, + 454, + 547, + 586 + ], + "type": "text", + "content": "Ideally, " + }, + { + "bbox": [ + 304, + 454, + 547, + 586 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 454, + 547, + 586 + ], + "type": "text", + "content": " could be used as is. However, we observed that for a given adverb " + }, + { + "bbox": [ + 304, + 454, + 547, + 586 + ], + "type": "inline_equation", + "content": "a" + }, + { + "bbox": [ + 304, + 454, + 547, + 586 + ], + "type": "text", + "content": " we obtain similar " + }, + { + "bbox": [ + 304, + 454, + 547, + 586 + ], + "type": "inline_equation", + "content": "d(v, a)" + }, + { + "bbox": [ + 304, + 454, + 547, + 586 + ], + "type": "text", + "content": " across most verbs " + }, + { + "bbox": [ + 304, + 454, + 547, + 586 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 304, + 454, + 547, + 586 + ], + "type": "text", + "content": ". This defeats the purpose of measuring action changes via " + }, + { + "bbox": [ + 304, + 454, + 547, + 586 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 454, + 547, + 586 + ], + "type": "text", + "content": " since " + }, + { + "bbox": [ + 304, + 454, + 547, + 586 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 454, + 547, + 586 + ], + "type": "text", + "content": " itself is not discriminative enough. This happens because " + }, + { + "bbox": [ + 304, + 454, + 547, + 586 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 454, + 547, + 586 + ], + "type": "text", + "content": " ignores the correlation between the verb and the adverb. Intuitively, if a verb and an adverb are not semantically correlated (e.g. \"run thinly\") then we cannot expect to capture a meaningful change when flipping the adverb in the negative sentence (recall that " + }, + { + "bbox": [ + 304, + 454, + 547, + 586 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 304, + 454, + 547, + 586 + ], + "type": "text", + "content": " receives full sentences). To address this issue we scale " + }, + { + "bbox": [ + 304, + 454, + 547, + 586 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 454, + 547, + 586 + ], + "type": "text", + "content": " with the cosine similarity between the verb " + }, + { + "bbox": [ + 304, + 454, + 547, + 586 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 304, + 454, + 547, + 586 + ], + "type": "text", + "content": " and the adverb " + }, + { + "bbox": [ + 304, + 454, + 547, + 586 + ], + "type": "inline_equation", + "content": "a" + }, + { + "bbox": [ + 304, + 454, + 547, + 586 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 348, + 592, + 545, + 620 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 348, + 592, + 545, + 620 + ], + "spans": [ + { + "bbox": [ + 348, + 592, + 545, + 620 + ], + "type": "interline_equation", + "content": "\\delta (v, a) = d (v, a) \\cdot \\frac {g (v) \\cdot g (a)}{\\| g (v) \\| _ {2} \\cdot \\| g (a) \\| _ {2}} \\tag {2}", + "image_path": "f80eca26149d6db2f49387ab69b1d5b095de89da07e8028a2b9d118e985020d4.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "type": "text", + "content": "Figure 2 compares " + }, + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "type": "text", + "content": " (left) to " + }, + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "type": "text", + "content": " (right) for a few (verb, adverb) combinations. Note how the unscaled distance " + }, + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "type": "text", + "content": " is not discriminative given that adverbs display a similar " + }, + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "type": "text", + "content": " across verbs. On the other hand, the scaled " + }, + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "type": "text", + "content": " shows a meaningful distance. For example, we observe a large " + }, + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "type": "text", + "content": " for adverbs \"finely\" and \"coarsely\" when paired with verbs \"chop, mince, mash, grate\"." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "23112" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 102, + 68, + 492, + 194 + ], + "blocks": [ + { + "bbox": [ + 102, + 68, + 492, + 194 + ], + "lines": [ + { + "bbox": [ + 102, + 68, + 492, + 194 + ], + "spans": [ + { + "bbox": [ + 102, + 68, + 492, + 194 + ], + "type": "image", + "image_path": "394538ec889fb60f06760c1867d2a5ccbd0b33ee72bc40dfedfb48a04b0a3042.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 201, + 547, + 247 + ], + "lines": [ + { + "bbox": [ + 46, + 201, + 547, + 247 + ], + "spans": [ + { + "bbox": [ + 46, + 201, + 547, + 247 + ], + "type": "text", + "content": "Figure 3. Pipeline of our method. Given a long video " + }, + { + "bbox": [ + 46, + 201, + 547, + 247 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 201, + 547, + 247 + ], + "type": "text", + "content": " labelled with a verb " + }, + { + "bbox": [ + 46, + 201, + 547, + 247 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 46, + 201, + 547, + 247 + ], + "type": "text", + "content": " and an adverb " + }, + { + "bbox": [ + 46, + 201, + 547, + 247 + ], + "type": "inline_equation", + "content": "a" + }, + { + "bbox": [ + 46, + 201, + 547, + 247 + ], + "type": "text", + "content": " we learn video embeddings " + }, + { + "bbox": [ + 46, + 201, + 547, + 247 + ], + "type": "inline_equation", + "content": "f'(x, v)" + }, + { + "bbox": [ + 46, + 201, + 547, + 247 + ], + "type": "text", + "content": " through attention. We optimise the model with two alternative methods: standard classification (CE: Cross Entropy) or regression (MSE: Mean Squared Error). We build a regression target measuring distances in a text embedding space, which estimates the action change we aim to learn in the video. The video backbone and text model are initialised from pre-trained models and are not fine-tuned during learning." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 257, + 288, + 281 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 257, + 288, + 281 + ], + "spans": [ + { + "bbox": [ + 47, + 257, + 288, + 281 + ], + "type": "text", + "content": "Now that we have an estimate to measure action changes we can build a regression target:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 286, + 293, + 340 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 286, + 293, + 340 + ], + "spans": [ + { + "bbox": [ + 47, + 286, + 293, + 340 + ], + "type": "interline_equation", + "content": "Y ^ {R} (v) = \\left(t _ {i}, \\forall i \\in \\{1, 2, \\dots , A \\}\\right) = \\left\\{ \\begin{array}{c c} \\delta (v, a) & \\text {i f} y _ {i} = a \\\\ - \\delta (v, a) & \\text {i f} y _ {i} = h (a) \\\\ 0 & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {3}", + "image_path": "28cb3024cf7ba11a1c3ca59bcbba0e8b72847d13e645e2caa63d722ce6e86495.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 341, + 287, + 401 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 341, + 287, + 401 + ], + "spans": [ + { + "bbox": [ + 46, + 341, + 287, + 401 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 341, + 287, + 401 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 46, + 341, + 287, + 401 + ], + "type": "text", + "content": " is the number of adverbs in a dataset and " + }, + { + "bbox": [ + 46, + 341, + 287, + 401 + ], + "type": "inline_equation", + "content": "y_{i}" + }, + { + "bbox": [ + 46, + 341, + 287, + 401 + ], + "type": "text", + "content": " denotes the " + }, + { + "bbox": [ + 46, + 341, + 287, + 401 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 341, + 287, + 401 + ], + "type": "text", + "content": "-th adverb. Let " + }, + { + "bbox": [ + 46, + 341, + 287, + 401 + ], + "type": "inline_equation", + "content": "\\hat{y}_i^v" + }, + { + "bbox": [ + 46, + 341, + 287, + 401 + ], + "type": "text", + "content": " indicate the output of the model for the " + }, + { + "bbox": [ + 46, + 341, + 287, + 401 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 341, + 287, + 401 + ], + "type": "text", + "content": "-th adverb obtained for verb " + }, + { + "bbox": [ + 46, + 341, + 287, + 401 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 46, + 341, + 287, + 401 + ], + "type": "text", + "content": ", i.e. querying the attention model with " + }, + { + "bbox": [ + 46, + 341, + 287, + 401 + ], + "type": "inline_equation", + "content": "g(v)" + }, + { + "bbox": [ + 46, + 341, + 287, + 401 + ], + "type": "text", + "content": ". The full output of the model is then " + }, + { + "bbox": [ + 46, + 341, + 287, + 401 + ], + "type": "inline_equation", + "content": "\\hat{Y}^{v} = \\rho (f^{\\prime}(x,v)) = (\\hat{y}_{i}^{v},\\forall i\\in \\{1,2,\\ldots ,A\\})" + }, + { + "bbox": [ + 46, + 341, + 287, + 401 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 401, + 288, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 401, + 288, + 520 + ], + "spans": [ + { + "bbox": [ + 46, + 401, + 288, + 520 + ], + "type": "text", + "content": "We use the Mean Squared Error to train the network: " + }, + { + "bbox": [ + 46, + 401, + 288, + 520 + ], + "type": "inline_equation", + "content": "\\mathcal{L}^R = \\| Y^R (v) - \\hat{Y}^v\\| _2" + }, + { + "bbox": [ + 46, + 401, + 288, + 520 + ], + "type": "text", + "content": ". The loss pushes opposite adverbs furthest apart (due to the negative sign of " + }, + { + "bbox": [ + 46, + 401, + 288, + 520 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 46, + 401, + 288, + 520 + ], + "type": "text", + "content": " for the antonym). The loss also tells the model that the video is not modified by other unrelated adverbs (target is 0 for classes that are neither ground truth nor antonyms). This discourages the model to predict negative non-antonym adverbs. Figure 3 illustrates our method. Note that the video backbone and text model are not part of the training, i.e. they are initialised from pre-trained models and are not fine-tuned." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 525, + 287, + 609 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 525, + 287, + 609 + ], + "spans": [ + { + "bbox": [ + 46, + 525, + 287, + 609 + ], + "type": "text", + "content": "Learning without Antonyms We also consider a setting where adverbs are not paired in antonyms. Instead of replacing the ground truth adverb with its antonym we simply remove the adverb and generate " + }, + { + "bbox": [ + 46, + 525, + 287, + 609 + ], + "type": "inline_equation", + "content": "\\tilde{s} = v" + }, + { + "bbox": [ + 46, + 525, + 287, + 609 + ], + "type": "text", + "content": ". In this case " + }, + { + "bbox": [ + 46, + 525, + 287, + 609 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 46, + 525, + 287, + 609 + ], + "type": "text", + "content": " measures the difference between the action modified by the adverb and the unmodified version of the action. " + }, + { + "bbox": [ + 46, + 525, + 287, + 609 + ], + "type": "inline_equation", + "content": "Y^{R}" + }, + { + "bbox": [ + 46, + 525, + 287, + 609 + ], + "type": "text", + "content": " is then " + }, + { + "bbox": [ + 46, + 525, + 287, + 609 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 46, + 525, + 287, + 609 + ], + "type": "text", + "content": " for the ground truth adverb and 0 for all other adverbs." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 612, + 288, + 672 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 612, + 288, + 672 + ], + "spans": [ + { + "bbox": [ + 47, + 612, + 288, + 672 + ], + "type": "text", + "content": "Inference As in [6] we are given the action label " + }, + { + "bbox": [ + 47, + 612, + 288, + 672 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 47, + 612, + 288, + 672 + ], + "type": "text", + "content": " during testing. We query the attention model with " + }, + { + "bbox": [ + 47, + 612, + 288, + 672 + ], + "type": "inline_equation", + "content": "g(v)" + }, + { + "bbox": [ + 47, + 612, + 288, + 672 + ], + "type": "text", + "content": " and use " + }, + { + "bbox": [ + 47, + 612, + 288, + 672 + ], + "type": "inline_equation", + "content": "\\hat{Y}^v" + }, + { + "bbox": [ + 47, + 612, + 288, + 672 + ], + "type": "text", + "content": " to predict each adverb. We also test the model without action labels. In such case we obtain " + }, + { + "bbox": [ + 47, + 612, + 288, + 672 + ], + "type": "inline_equation", + "content": "f'(x, v)" + }, + { + "bbox": [ + 47, + 612, + 288, + 672 + ], + "type": "text", + "content": " querying all actions and take the maximum prediction for each adverb:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 59, + 679, + 287, + 696 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 679, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 59, + 679, + 287, + 696 + ], + "type": "interline_equation", + "content": "p (x) = \\left(\\max _ {v} \\left(\\hat {y} _ {i} ^ {v}, \\forall v \\in \\mathcal {V}\\right), \\forall i \\in \\{1, 2, \\dots , A \\}\\right) \\tag {4}", + "image_path": "3f514482d1f895256382bf3dc33488df73a92f145ba8b70821fcb99b3a30fc01.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 701, + 212, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 701, + 212, + 712 + ], + "spans": [ + { + "bbox": [ + 47, + 701, + 212, + 712 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 701, + 212, + 712 + ], + "type": "inline_equation", + "content": "\\nu" + }, + { + "bbox": [ + 47, + 701, + 212, + 712 + ], + "type": "text", + "content": " denotes the set of action labels." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 257, + 545, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 257, + 545, + 556 + ], + "spans": [ + { + "bbox": [ + 304, + 257, + 545, + 556 + ], + "type": "text", + "content": "Comparison to Action Modifiers Our framework shares the same design as Action Modifiers [6] until " + }, + { + "bbox": [ + 304, + 257, + 545, + 556 + ], + "type": "inline_equation", + "content": "f'(x, v)" + }, + { + "bbox": [ + 304, + 257, + 545, + 556 + ], + "type": "text", + "content": ". In [6] " + }, + { + "bbox": [ + 304, + 257, + 545, + 556 + ], + "type": "inline_equation", + "content": "f'(x, v)" + }, + { + "bbox": [ + 304, + 257, + 545, + 556 + ], + "type": "text", + "content": " is optimised with two triplet losses: an action loss to help the attention model and an adverb loss to learn adverbs. We do not use an additional action loss. In Action Modifiers adverbs are also modelled as action changes utilising text embeddings. However, in [6] such change is treated as an additional parameter to be learnt. Specifically, an adverb is represented as a learnable matrix " + }, + { + "bbox": [ + 304, + 257, + 545, + 556 + ], + "type": "inline_equation", + "content": "W_{a}" + }, + { + "bbox": [ + 304, + 257, + 545, + 556 + ], + "type": "text", + "content": ". The linear combination " + }, + { + "bbox": [ + 304, + 257, + 545, + 556 + ], + "type": "inline_equation", + "content": "o_{v}^{a} = W_{a} g(v)" + }, + { + "bbox": [ + 304, + 257, + 545, + 556 + ], + "type": "text", + "content": " represents the change the adverb " + }, + { + "bbox": [ + 304, + 257, + 545, + 556 + ], + "type": "inline_equation", + "content": "a" + }, + { + "bbox": [ + 304, + 257, + 545, + 556 + ], + "type": "text", + "content": " applies to the verb " + }, + { + "bbox": [ + 304, + 257, + 545, + 556 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 304, + 257, + 545, + 556 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 257, + 545, + 556 + ], + "type": "inline_equation", + "content": "g(v)" + }, + { + "bbox": [ + 304, + 257, + 545, + 556 + ], + "type": "text", + "content": " is a text embedding as in our model. Importantly, " + }, + { + "bbox": [ + 304, + 257, + 545, + 556 + ], + "type": "inline_equation", + "content": "o_{v}^{a}" + }, + { + "bbox": [ + 304, + 257, + 545, + 556 + ], + "type": "text", + "content": " is used in the triplet losses, thus the optimisation of the video embedding " + }, + { + "bbox": [ + 304, + 257, + 545, + 556 + ], + "type": "inline_equation", + "content": "f'(x, v)" + }, + { + "bbox": [ + 304, + 257, + 545, + 556 + ], + "type": "text", + "content": " depends on the optimisation of parameters " + }, + { + "bbox": [ + 304, + 257, + 545, + 556 + ], + "type": "inline_equation", + "content": "W_{a}" + }, + { + "bbox": [ + 304, + 257, + 545, + 556 + ], + "type": "text", + "content": ". We argue and show that learning adverbs with this approach can be difficult as the action change the model looks for in the video has also to be learnt. In our formulation instead the action change is pre-computed and is not learnt. We also provide explicit penalty for non-antonym classes rather than contrasting only opposite adverbs. Comparing capacity, our model has a smaller number of parameters which scales better with the number of adverbs. Indeed, each adverb in Action Modifiers requires a learnable matrix, whereas in our model only the last layer of the MLP varies with the number of adverbs (see supplementary material)." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 561, + 511, + 575 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 561, + 511, + 575 + ], + "spans": [ + { + "bbox": [ + 305, + 561, + 511, + 575 + ], + "type": "text", + "content": "4. Adverbs in Recipes: the AIR Dataset" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": "In Section 2 we motivated the need for a new dataset for adverb recognition. Here we introduce the Adverbs in Recipes (AIR) dataset. We wish to find a set of videos where actions change significantly according to the adverb. Compared to captioning benchmarks, instructional datasets contain videos where we can expect to find more of such actions. For this reason we source AIR from HowTo100M [14]. We restrict our interest to recipe videos since changes in cooking actions play an important role. For example, a carrot sliced à la juillienne (thinly) looks very different from a carrot chopped in thick dices (coarsely)." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "23113" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 47, + 70, + 288, + 131 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 288, + 131 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 288, + 131 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 288, + 131 + ], + "type": "table", + "html": "
DatasetAccuracyDurationAdvActPairsVideos
CAPTActivityNet Adverbs [7]89.0%37.5s201146353,099
MSR-VTT Adverbs [7]91.0%15.7s181064501,824
VATEX Adverbs [7]93.5%10.0s (f)341351,52414,617
INSTHowTo100M Adverbs [6]44.0%20.0s (f)6722575,824
Adverbs in Recipes (ours)95.3%8.4s10481867,003
", + "image_path": "d60e67ad922558b850afcf83a6c50e23b11865ffdeaf2a39a1ff03be645a64d7.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 140, + 287, + 217 + ], + "lines": [ + { + "bbox": [ + 46, + 140, + 287, + 217 + ], + "spans": [ + { + "bbox": [ + 46, + 140, + 287, + 217 + ], + "type": "text", + "content": "Table 1. Comparing video datasets for adverb recognition. CAPT: captioning datasets, where adverbs are descriptive. INST: instructional datasets, where adverbs are action-focused. \"Accuracy\" indicates whether the action is visible as indicated by the adverb. \"Duration\" reports the average length, where (f) denotes a fixed duration. \"Pairs\" counts (verb, adverb) appearing in the dataset rather than the Cartesian product of all verbs and adverbs." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 224, + 287, + 260 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 224, + 287, + 260 + ], + "spans": [ + { + "bbox": [ + 46, + 224, + 287, + 260 + ], + "type": "text", + "content": "In other words, adverbs are \"easily visible\" in recipe videos and involve interesting visual cues such as speed, temporal/spatial completeness and objects end-states." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 277, + 289, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 277, + 289, + 553 + ], + "spans": [ + { + "bbox": [ + 47, + 277, + 289, + 553 + ], + "type": "text", + "content": "Data Collection We start selecting all recipe videos in HowTo100M. We then parse captions to keep only those containing a verb and an adverb. We filter videos removing verbs that indicate non visual actions (e.g. \"watch, wait\") or very long-term actions (e.g. \"rise, grow\"), since we do not expect these changes to be fully visible in the videos. We manually merge similar verbs, obtaining in total 48 verbs. We also remove infrequent and too generic adverbs (e.g. \"carefully\"). We cluster similar adverbs gathering a total of 10 adverbs, which we pair in antonyms. To trim videos in a tight manner we use the timestamps of the first/last word in a caption as the start/end of the action segment. At this point we have a set of videos of varying duration, each accompanied with a verb and an adverb. We ask annotators on Amazon Mechanical Turk (AMT) to check whether the action in a video is visible and is carried out as indicated by the adverb. For robustness we ask 3 different annotators to check the same video and employ 5 people for edge cases where annotators disagreed. We keep videos where the majority of the annotators confirmed that the action is visible as indicated by the adverb, collecting 7,003 videos. Figure 2 shows the verbs (columns) and adverbs (rows) in AIR. We provide more details in the supplementary material." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 569, + 287, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 569, + 287, + 666 + ], + "spans": [ + { + "bbox": [ + 46, + 569, + 287, + 666 + ], + "type": "text", + "content": "Comparison to Other Datasets Table 1 compares AIR to other adverb " + }, + { + "bbox": [ + 46, + 569, + 287, + 666 + ], + "type": "inline_equation", + "content": "\\text{dattets}^1" + }, + { + "bbox": [ + 46, + 569, + 287, + 666 + ], + "type": "text", + "content": " reviewed in Section 2. \"Accuracy\" estimates the percentage of videos where the action and the adverb effect are visible. On the existing datasets this was estimated watching 200 videos in [7]. For AIR multiple annotators reviewed all videos, however, annotations on AMT can be noisy. We review 302 videos (5% of the dataset) and report this check as \"Accuracy\". Compared" + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 307, + 70, + 386, + 160 + ], + "blocks": [ + { + "bbox": [ + 307, + 70, + 386, + 160 + ], + "lines": [ + { + "bbox": [ + 307, + 70, + 386, + 160 + ], + "spans": [ + { + "bbox": [ + 307, + 70, + 386, + 160 + ], + "type": "image", + "image_path": "ca26cd8e2aaf7faa04bf746db6d08b8aa515800f64019570bdecda0217251bab.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 170, + 547, + 248 + ], + "lines": [ + { + "bbox": [ + 304, + 170, + 547, + 248 + ], + "spans": [ + { + "bbox": [ + 304, + 170, + 547, + 248 + ], + "type": "text", + "content": "Figure 4. Samples from existing datasets for adverb recognition and our new AIR dataset. Many adverbs in the captioning datasets appear to be descriptive rather than a key modification of the action (e.g. the act of talking/sitting is the same whether it takes place indoors/outdoors). In contrast, adverbs in the instructional datasets apply a more prominent change in the action and its outcome (e.g. a vegetable peeled coarsely will still have some skin attached)." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 386, + 70, + 466, + 160 + ], + "blocks": [ + { + "bbox": [ + 386, + 70, + 466, + 160 + ], + "lines": [ + { + "bbox": [ + 386, + 70, + 466, + 160 + ], + "spans": [ + { + "bbox": [ + 386, + 70, + 466, + 160 + ], + "type": "image", + "image_path": "1f5a9dc36ac16b9366cfa05a780d2a9769c920bceb16dc1f317efea49bb5da67.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 466, + 70, + 545, + 160 + ], + "blocks": [ + { + "bbox": [ + 466, + 70, + 545, + 160 + ], + "lines": [ + { + "bbox": [ + 466, + 70, + 545, + 160 + ], + "spans": [ + { + "bbox": [ + 466, + 70, + 545, + 160 + ], + "type": "image", + "image_path": "0ad6f7ddd98748b132507e52a9fdefc21b8189a9168ad627f7d0f51deeb4fb2d.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 266, + 545, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 266, + 545, + 422 + ], + "spans": [ + { + "bbox": [ + 304, + 266, + 545, + 422 + ], + "type": "text", + "content": "to the instructional-based HowTo100M Adverbs, AIR contains over 1,100 additional clips and 4 more adverbs. Importantly, our videos are manually reviewed (AIR accuracy is over " + }, + { + "bbox": [ + 304, + 266, + 545, + 422 + ], + "type": "inline_equation", + "content": "95\\%" + }, + { + "bbox": [ + 304, + 266, + 545, + 422 + ], + "type": "text", + "content": " compared to " + }, + { + "bbox": [ + 304, + 266, + 545, + 422 + ], + "type": "inline_equation", + "content": "44\\%" + }, + { + "bbox": [ + 304, + 266, + 545, + 422 + ], + "type": "text", + "content": ") and better trimmed (averaged duration is 8s compared to fixed 20s segments). AIR features 48 actions which is the smallest number among the five datasets (and consequently the smallest number of pairs). This is due to our more restrictive verb filtering based on visual and task-oriented actions. For example, in the captioning datasets there are actions such as \"tell, talk, sing, look\". Actions in HowTo100M Adverbs are task oriented, however there are also verbs entailing long-term actions (e.g. \"brew\"), which are unlikely to be fully visible." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 425, + 546, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 425, + 546, + 604 + ], + "spans": [ + { + "bbox": [ + 304, + 425, + 546, + 604 + ], + "type": "text", + "content": "Figure 4 shows a few samples from AIR as well as the other datasets. Note how adverbs in the instructional datasets apply a key modification in the action, whereas for the captioning datasets adverbs are descriptive. Cap-tions in the captioning datasets are reliable because they were provided by human annotators. However, annotators did not necessarily use adverbs to indicate a modification to the action. Thus, due to the automatic processing of these datasets, there are several cases where adverbs are descriptive and do not influence the action. Naturally, Figure 4 is not meant to be an exhaustive representation of the caption-ing datasets from [7]. These datasets also contain action-focused adverbs, however without extensively reviewing the videos and the associated adverbs it is hard to gauge how many actions are effectively modified by the adverb." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": "To summarise the contributions of AIR: i) we employ annotators to verify that actions are performed in the way indicated by the adverb; ii) this allowed us to trim videos more tightly and obtain cleaner clips with less unrelated content; iii) we carefully choose verbs and adverbs to pick videos where action changes are significant. While we restrict our domain to recipes, cooking actions are visually diverse, entail complex object interactions and are particularly affected by the nuanced ways they are carried out." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 46, + 673, + 287, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 673, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 673, + 287, + 713 + ], + "type": "text", + "content": "1We report the number of videos from [7]. Some videos are missing as they were removed from YouTube. We were able to download: ActivityNet A.: 2,972 - MSR-VTT A.: 1,747 - VATEX A.: 13,947, HowTo100M A.: 5,462. Duration and pairs are reported from the downloaded videos." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "23114" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 71, + 128, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 71, + 128, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 128, + 85 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 91, + 289, + 332 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 91, + 289, + 332 + ], + "spans": [ + { + "bbox": [ + 47, + 91, + 289, + 332 + ], + "type": "text", + "content": "Implementation Details We use an S3D model [13, 25] jointly pre-trained on video and text on HowTo100M [14] as our video backbone. Specifically, we use the video output mixed_5c to obtain " + }, + { + "bbox": [ + 47, + 91, + 289, + 332 + ], + "type": "inline_equation", + "content": "f(x)" + }, + { + "bbox": [ + 47, + 91, + 289, + 332 + ], + "type": "text", + "content": ". Following [6] we split videos in 1-second segments and sample 16 RGB frames from each segment to obtain the video features. Stacking features from the video segments we have " + }, + { + "bbox": [ + 47, + 91, + 289, + 332 + ], + "type": "inline_equation", + "content": "f(x)^{T \\times D}" + }, + { + "bbox": [ + 47, + 91, + 289, + 332 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 47, + 91, + 289, + 332 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 47, + 91, + 289, + 332 + ], + "type": "text", + "content": " varies depending on the dataset and " + }, + { + "bbox": [ + 47, + 91, + 289, + 332 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 47, + 91, + 289, + 332 + ], + "type": "text", + "content": " is 1024. We use 4 heads for the attention model. The dimension " + }, + { + "bbox": [ + 47, + 91, + 289, + 332 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 47, + 91, + 289, + 332 + ], + "type": "text", + "content": " of the query, key and value is 512, thus the projected video embedding " + }, + { + "bbox": [ + 47, + 91, + 289, + 332 + ], + "type": "inline_equation", + "content": "f'(x, v)" + }, + { + "bbox": [ + 47, + 91, + 289, + 332 + ], + "type": "text", + "content": " has dimension " + }, + { + "bbox": [ + 47, + 91, + 289, + 332 + ], + "type": "inline_equation", + "content": "1 \\times E" + }, + { + "bbox": [ + 47, + 91, + 289, + 332 + ], + "type": "text", + "content": ". The MLP in our model has 3 layers (hidden units of dimension 512) with ReLU activation function for the hidden layers and dropout [20] set to 0.1. We train all models for 1000 epochs with the ADAM optimiser [10], setting learning rate to " + }, + { + "bbox": [ + 47, + 91, + 289, + 332 + ], + "type": "inline_equation", + "content": "1e^{-4}" + }, + { + "bbox": [ + 47, + 91, + 289, + 332 + ], + "type": "text", + "content": ", weight decay to " + }, + { + "bbox": [ + 47, + 91, + 289, + 332 + ], + "type": "inline_equation", + "content": "5e^{-5}" + }, + { + "bbox": [ + 47, + 91, + 289, + 332 + ], + "type": "text", + "content": " and batch size to 512. We use the text model jointly trained with S3D to extract text embeddings " + }, + { + "bbox": [ + 47, + 91, + 289, + 332 + ], + "type": "inline_equation", + "content": "g(\\cdot)" + }, + { + "bbox": [ + 47, + 91, + 289, + 332 + ], + "type": "text", + "content": ". This network, like the visual backbone, is not fine-tuned. We refer to [13] for more details about S3D and the text model. " + }, + { + "bbox": [ + 47, + 91, + 289, + 332 + ], + "type": "inline_equation", + "content": "f(x)" + }, + { + "bbox": [ + 47, + 91, + 289, + 332 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 91, + 289, + 332 + ], + "type": "inline_equation", + "content": "g(\\cdot)" + }, + { + "bbox": [ + 47, + 91, + 289, + 332 + ], + "type": "text", + "content": " are the same for all experiments." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 340, + 289, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 340, + 289, + 484 + ], + "spans": [ + { + "bbox": [ + 47, + 340, + 289, + 484 + ], + "type": "text", + "content": "Baselines Priors: here we do not train any model and simply use the prior distributions of the training set to make a prediction. When using the action label during testing, the prediction for an adverb is the number of training samples labelled with the adverb and the given verb, i.e. " + }, + { + "bbox": [ + 47, + 340, + 289, + 484 + ], + "type": "inline_equation", + "content": "p(x,v) = (\\pi (v,a),\\forall a\\in \\mathcal{A})" + }, + { + "bbox": [ + 47, + 340, + 289, + 484 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 47, + 340, + 289, + 484 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 47, + 340, + 289, + 484 + ], + "type": "text", + "content": " denotes the frequency of " + }, + { + "bbox": [ + 47, + 340, + 289, + 484 + ], + "type": "inline_equation", + "content": "(v,a)" + }, + { + "bbox": [ + 47, + 340, + 289, + 484 + ], + "type": "text", + "content": " in the training set and " + }, + { + "bbox": [ + 47, + 340, + 289, + 484 + ], + "type": "inline_equation", + "content": "\\mathcal{A}" + }, + { + "bbox": [ + 47, + 340, + 289, + 484 + ], + "type": "text", + "content": " is the set of adverbs in a dataset. While this baseline is a simple look-up table, it can achieve strong performance since it exploits the co-occurrence of verbs and adverbs. When the action label is not used during testing the priors baseline predicts the frequency of each adverb in the training set, i.e. " + }, + { + "bbox": [ + 47, + 340, + 289, + 484 + ], + "type": "inline_equation", + "content": "p(x) = (\\pi (a),\\forall a\\in \\mathcal{A})" + }, + { + "bbox": [ + 47, + 340, + 289, + 484 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 485, + 289, + 644 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 485, + 289, + 644 + ], + "spans": [ + { + "bbox": [ + 47, + 485, + 289, + 644 + ], + "type": "text", + "content": "S3D pre-trained: we test the S3D model we use as the video-text backbone for all experiments. Video and text embeddings were jointly learnt in this model, so we use the dot product between " + }, + { + "bbox": [ + 47, + 485, + 289, + 644 + ], + "type": "inline_equation", + "content": "f(x)" + }, + { + "bbox": [ + 47, + 485, + 289, + 644 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 485, + 289, + 644 + ], + "type": "inline_equation", + "content": "g(\\cdot)" + }, + { + "bbox": [ + 47, + 485, + 289, + 644 + ], + "type": "text", + "content": " for predictions. When the action label " + }, + { + "bbox": [ + 47, + 485, + 289, + 644 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 47, + 485, + 289, + 644 + ], + "type": "text", + "content": " is given during inference the prediction is " + }, + { + "bbox": [ + 47, + 485, + 289, + 644 + ], + "type": "inline_equation", + "content": "p(x,v) = (f(x)\\cdot g(\\langle v,a\\rangle),\\forall a\\in \\mathcal{A})" + }, + { + "bbox": [ + 47, + 485, + 289, + 644 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 47, + 485, + 289, + 644 + ], + "type": "inline_equation", + "content": "g(\\langle v,a\\rangle)" + }, + { + "bbox": [ + 47, + 485, + 289, + 644 + ], + "type": "text", + "content": " is the text embedding obtained concatenating the given " + }, + { + "bbox": [ + 47, + 485, + 289, + 644 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 47, + 485, + 289, + 644 + ], + "type": "text", + "content": " and each adverb " + }, + { + "bbox": [ + 47, + 485, + 289, + 644 + ], + "type": "inline_equation", + "content": "a" + }, + { + "bbox": [ + 47, + 485, + 289, + 644 + ], + "type": "text", + "content": ". When the action label is not given, we have " + }, + { + "bbox": [ + 47, + 485, + 289, + 644 + ], + "type": "inline_equation", + "content": "p(x) = (\\max_v f(x)\\cdot g(\\langle v,a\\rangle),\\forall v\\in \\mathcal{V}),\\forall a\\in \\mathcal{A})" + }, + { + "bbox": [ + 47, + 485, + 289, + 644 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 47, + 485, + 289, + 644 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 47, + 485, + 289, + 644 + ], + "type": "text", + "content": " is the set of verbs. This S3D instance has shown very strong performance on several tasks [13], thus this baseline helps gauging the difficulty of detecting adverbs following a basic video-text retrieval approach." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 306, + 72, + 545, + 215 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 545, + 215 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 545, + 215 + ], + "type": "text", + "content": "SOTA Act Mod: we compare against the state-of-the-art for adverb recognition, Action Modifiers [6], both using the original model and a deeper version with an additional MLP " + }, + { + "bbox": [ + 306, + 72, + 545, + 215 + ], + "type": "inline_equation", + "content": "(MLP + ActMod)" + }, + { + "bbox": [ + 306, + 72, + 545, + 215 + ], + "type": "text", + "content": ". Here we append an identical MLP as in our model to the output of the transformer attention. This variant allows a better comparison with our method. We use the official code implementation to run our experiments. Note that Action Modifiers results reported here are not directly comparable to those reported in [6,7]. This is because we could not download several videos since they were removed from YouTube. Also, we use S3D features (identical for all experiments) instead of I3D [3] features." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 305, + 217, + 545, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 217, + 545, + 289 + ], + "spans": [ + { + "bbox": [ + 305, + 217, + 545, + 289 + ], + "type": "text", + "content": "Our Variants CLS: our model trained with classification. REG - fixed " + }, + { + "bbox": [ + 305, + 217, + 545, + 289 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 305, + 217, + 545, + 289 + ], + "type": "text", + "content": ": our model trained with regression discarding text embeddings altogether, setting " + }, + { + "bbox": [ + 305, + 217, + 545, + 289 + ], + "type": "inline_equation", + "content": "\\delta = 1" + }, + { + "bbox": [ + 305, + 217, + 545, + 289 + ], + "type": "text", + "content": " in Equation 3. This is to validate the premise of using textual context to build a regression target. REG: our model trained with regression using the full formulation." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 290, + 546, + 482 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 290, + 546, + 482 + ], + "spans": [ + { + "bbox": [ + 305, + 290, + 546, + 482 + ], + "type": "text", + "content": "Evaluation Metrics We report mean Average Precision using two types of averaging: i) weighted (mAP W), where class scores are weighted according to the support size (smaller classes have a smaller weight); ii) macro (mAP M), where all classes have equal weight, which corresponds to \"adverb-to-video (all)\" in [6]. All the evaluated datasets exhibit a significant class imbalance, thus mAP M is a stricter metric compared to mAP W. We also report binary antonym accuracy (Acc-A), which corresponds to \"video-to-adverb (antonym)\" in [6]. Here we only look at the prediction of an adverb " + }, + { + "bbox": [ + 305, + 290, + 546, + 482 + ], + "type": "inline_equation", + "content": "a" + }, + { + "bbox": [ + 305, + 290, + 546, + 482 + ], + "type": "text", + "content": " versus its antonym " + }, + { + "bbox": [ + 305, + 290, + 546, + 482 + ], + "type": "inline_equation", + "content": "h(a)" + }, + { + "bbox": [ + 305, + 290, + 546, + 482 + ], + "type": "text", + "content": ". A prediction " + }, + { + "bbox": [ + 305, + 290, + 546, + 482 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 305, + 290, + 546, + 482 + ], + "type": "text", + "content": " is correct if " + }, + { + "bbox": [ + 305, + 290, + 546, + 482 + ], + "type": "inline_equation", + "content": "p(a) > p(h(a))" + }, + { + "bbox": [ + 305, + 290, + 546, + 482 + ], + "type": "text", + "content": ". All metrics are computed for adverb classes. To show the full potential of all methods we report each best metric independently, i.e. results may come from different epochs. This is to provide a robust comparison, however we note that all models reach stable convergence." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 483, + 545, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 483, + 545, + 602 + ], + "spans": [ + { + "bbox": [ + 305, + 483, + 545, + 602 + ], + "type": "text", + "content": "Datasets We present experiments on the two instructional datasets we saw earlier: HowTo100M Adverbs [6] and our Adverbs In Recipes. As discussed before, we argue that instructional videos are more suitable for this task as adverbs are action-focused, i.e. actions change significantly according to the adverb. For completeness, we also evaluate the three adverb datasets sourced from captioning videos in [7]: ActivityNet/MSR-VTT/VATEX Adverbs3. Adverbs here are descriptive, thus these datasets are less reliable for evaluation. Datasets are summarised in Table 1." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 608, + 362, + 619 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 608, + 362, + 619 + ], + "spans": [ + { + "bbox": [ + 306, + 608, + 362, + 619 + ], + "type": "text", + "content": "5.1. Results" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 625, + 545, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 625, + 545, + 687 + ], + "spans": [ + { + "bbox": [ + 305, + 625, + 545, + 687 + ], + "type": "text", + "content": "Overview We begin our discussion looking at results in Table 2 on the instructional datasets (left). Here we achieve new state-of-the-art results on all metrics. The gap between our best variant and Act Mod is more noticeable for the more challenging mAP W/M metrics. In [6] negative samples are" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "text", + "content": "3For these datasets there are several partitions for different tasks (e.g. unseen domain). For convenience we create our own train/test split." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "text", + "content": "There is no official train/test split in HowTo100M, thus S3D in [13] was trained on videos that appear in the test sets of HowTo100M Adverbs and AIR. However, this is not a concern: Tables 2, 3 show that the S3D pre-trained baseline achieves poor performance, as the original S3D training objective (video-text alignment) is substantially different from ours. Importantly, all methods receive the same features for fair comparison." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23115" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 47, + 103, + 107, + 162 + ], + "blocks": [ + { + "bbox": [ + 47, + 103, + 107, + 162 + ], + "lines": [ + { + "bbox": [ + 47, + 103, + 107, + 162 + ], + "spans": [ + { + "bbox": [ + 47, + 103, + 107, + 162 + ], + "type": "table", + "html": "
Priors
S3D pre-trained
Act Mod [6]
MLP + Act Mod [6]
CLS
REG - fixed δ
REG
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Instructional datasets. Action-focused adverbs
HowTo100M Adverbs [6]Adverbs in Recipes
mAP WmAP MAcc-AmAP WmAP MAcc-A
0.4460.3540.7860.4910.2630.854
0.3390.2380.5600.3890.1730.735
0.4060.3720.7960.4210.1700.858
0.2790.1930.7930.4580.1880.857
0.5620.4200.7860.6750.3250.847
0.3200.2150.7060.4580.1450.835
0.5550.4230.7990.6690.2970.862
", + "image_path": "96048aad8627b2f571979338ce9520761ec16eeb71290a8aec9fb3703d69591e.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 304, + 71, + 548, + 163 + ], + "blocks": [ + { + "bbox": [ + 304, + 71, + 548, + 163 + ], + "lines": [ + { + "bbox": [ + 304, + 71, + 548, + 163 + ], + "spans": [ + { + "bbox": [ + 304, + 71, + 548, + 163 + ], + "type": "table", + "html": "
Captioning datasets. Descriptive adverbs
ActivityNet Adverbs [7]MSR-VTT Adverbs [7]VATEX Adverbs [7]
mAP WmAP MAcc-AmAP WmAP MAcc-AmAP WmAP MAcc-A
0.2170.1590.7450.3080.1520.7230.2160.0860.752
0.1180.0700.5600.1940.0750.6030.1220.0380.586
0.2110.1520.7480.2460.1480.7340.1390.0590.751
0.1540.1080.7530.2150.1110.7310.2090.0960.752
0.1140.0720.7140.1890.0810.7230.2830.1080.754
0.1130.0700.7060.2210.0960.7060.1750.0510.701
0.1830.1030.7090.2920.1180.7740.2610.0860.755
", + "image_path": "9e502ff1150f6289a8f7e57485005a44ea24446e678eb20ae154b470fada1026.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 173, + 547, + 217 + ], + "lines": [ + { + "bbox": [ + 46, + 173, + 547, + 217 + ], + "spans": [ + { + "bbox": [ + 46, + 173, + 547, + 217 + ], + "type": "text", + "content": "Table 2. Results obtained using the action label during inference. mAP W/M: mean Average Precision with weighted (W) and macro (M) averaging. Acc-A: adverb-vs-antonym accuracy. Coloured rows indicate variants of our method. Bold denotes best result per column. In instructional datasets (left) adverbs are action-focused, so these are more reliable benchmarks to learn action changes. In captioning datasets (right) adverbs are more descriptive and do not influence the action significantly. As such, these datasets are less reliable." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 228, + 287, + 347 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 228, + 287, + 347 + ], + "spans": [ + { + "bbox": [ + 46, + 228, + 287, + 347 + ], + "type": "text", + "content": "formed only pairing opposite adverbs, thus the model does not receive enough penalty for other negative adverbs. In contrast, we provide explicit penalty for non-antonym negative adverbs. The poor performance of S3D pre-trained indicates that learning adverbs in videos is not trivial. Adverbs are not well defined visual entities like objects or actions, thus video-text retrieval approaches looking for correlations between text and video embeddings are likely suboptimal, even when such embeddings are jointly learnt on the same dataset with a strong model, as is the case for S3D." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 348, + 287, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 348, + 287, + 443 + ], + "spans": [ + { + "bbox": [ + 46, + 348, + 287, + 443 + ], + "type": "text", + "content": "Still looking at the instructional datasets, on AIR all methods achieve higher mAP W/Acc-A but lower mAP M. Considering that there are more adverbs in AIR than in HowTo100M Adverbs, the higher mAP W/Acc-A is indicative of the quality of AIR: given that videos are tighter and cleaner it is possible to learn adverbs more effectively. The lower mAP M is due to the long-tail class distribution and shows the opportunities AIR offers to improve methods." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 445, + 288, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 445, + 288, + 598 + ], + "spans": [ + { + "bbox": [ + 46, + 445, + 288, + 598 + ], + "type": "text", + "content": "On the captioning datasets we observe an interesting result: the Priors baseline outperforms or achieves very high performance. This supports our argument that captioning datasets are not particularly suitable for our task. If a simple look-up table surpasses all learning-based methods, then we conclude it is very difficult to learn adverbs as action changes, because actions are not particularly influenced by adverbs here. While these datasets exhibit a skewed verb-adverb distribution, so do the instructional ones. In fact, on VATEX Adverbs (the biggest dataset with 1,524 pairs) our method attains marginally better results. This is to say that the problem does not lie in the imbalanced class distribution, rather in the nature of the videos." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 45, + 605, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 605, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 45, + 605, + 288, + 713 + ], + "type": "text", + "content": "Importance of Context We now focus on the importance of using textual context for regression comparing REG - fixed " + }, + { + "bbox": [ + 45, + 605, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 45, + 605, + 288, + 713 + ], + "type": "text", + "content": " to REG in Table 2. Visual features vary differently when the same action is modified by different adverbs, e.g. chopping something coarsely entails a more prominent change than chopping it slowly. With REG we learn such visual differences with targets that change (sometimes considerably) across adverbs for a given verb. A fixed target for all positive adverbs discards such differences: the model is" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 228, + 545, + 264 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 228, + 545, + 264 + ], + "spans": [ + { + "bbox": [ + 304, + 228, + 545, + 264 + ], + "type": "text", + "content": "penalised equally for small/big changes. REG - fixed " + }, + { + "bbox": [ + 304, + 228, + 545, + 264 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 304, + 228, + 545, + 264 + ], + "type": "text", + "content": " does this, and its consistent worse performance validates the idea of using text context as a proxy to learn action changes." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 266, + 546, + 482 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 266, + 546, + 482 + ], + "spans": [ + { + "bbox": [ + 304, + 266, + 546, + 482 + ], + "type": "text", + "content": "The Key is in the Optimisation We now compare " + }, + { + "bbox": [ + 304, + 266, + 546, + 482 + ], + "type": "inline_equation", + "content": "MLP + ActMod" + }, + { + "bbox": [ + 304, + 266, + 546, + 482 + ], + "type": "text", + "content": " to our method. For this " + }, + { + "bbox": [ + 304, + 266, + 546, + 482 + ], + "type": "inline_equation", + "content": "ActMod" + }, + { + "bbox": [ + 304, + 266, + 546, + 482 + ], + "type": "text", + "content": " variant we replace the video embedding " + }, + { + "bbox": [ + 304, + 266, + 546, + 482 + ], + "type": "inline_equation", + "content": "f'(x, v)" + }, + { + "bbox": [ + 304, + 266, + 546, + 482 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 304, + 266, + 546, + 482 + ], + "type": "inline_equation", + "content": "\\theta(f'(x, v))" + }, + { + "bbox": [ + 304, + 266, + 546, + 482 + ], + "type": "text", + "content": " in the two losses in [6], where " + }, + { + "bbox": [ + 304, + 266, + 546, + 482 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 266, + 546, + 482 + ], + "type": "text", + "content": " is the additional MLP. With this configuration, the only difference between our method and Action Modifiers lies in the optimisation. In Section 3 we hypothesised that the optimisation of Action Modifiers might be difficult. Results in Table 2 support our hypothesis. When adding the MLP to " + }, + { + "bbox": [ + 304, + 266, + 546, + 482 + ], + "type": "inline_equation", + "content": "ActMod" + }, + { + "bbox": [ + 304, + 266, + 546, + 482 + ], + "type": "text", + "content": ", Acc-A remains virtually identical across all datasets. However, mAP W/M drop considerably on HowTo100M Adverbs. This dataset is the noisiest among the five datasets, thus in this case increasing the depth of the model makes optimisation more difficult. Overall, comparing " + }, + { + "bbox": [ + 304, + 266, + 546, + 482 + ], + "type": "inline_equation", + "content": "MLP + ActMod" + }, + { + "bbox": [ + 304, + 266, + 546, + 482 + ], + "type": "text", + "content": " to our method we achieve better results even when the additional MLP improves the performance of the original " + }, + { + "bbox": [ + 304, + 266, + 546, + 482 + ], + "type": "inline_equation", + "content": "ActMod" + }, + { + "bbox": [ + 304, + 266, + 546, + 482 + ], + "type": "text", + "content": ". We conclude that learning adverbs as pre-defined actions changes rather than as trainable parameters is a better strategy." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 483, + 547, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 483, + 547, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 483, + 547, + 628 + ], + "type": "text", + "content": "Testing without Action Labels In Table 3 we report results obtained without using the action label at test time. We test Action Modifiers in the same way as described for our method in Section 3. Experiments are directly comparable between Tables 2 and 3 since the tested models are the same. We note a remarkable drop in performance for all methods. This is expected since the task is now harder. In fact we need to predict the right adverb from multiple video embeddings obtained querying all verbs. Nevertheless, our method still achieves the best global performance in this more challenging setting. This shows that our method is more robust and is able to better generalise." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 630, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 547, + 713 + ], + "type": "text", + "content": "Learning without Antonyms We now study the case where adverbs are not paired in antonyms. This is a desirable setting as it allows more flexibility in data collection. To train Action Modifiers without antonyms we just sample a random negative adverb as opposed to the antonym for the triplet loss. We illustrated in Section 3 how we train our REG variant. We do not evaluate REG - fixed " + }, + { + "bbox": [ + 304, + 630, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 304, + 630, + 547, + 713 + ], + "type": "text", + "content": " here since" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "23116" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 44, + 70, + 288, + 163 + ], + "blocks": [ + { + "bbox": [ + 44, + 70, + 288, + 163 + ], + "lines": [ + { + "bbox": [ + 44, + 70, + 288, + 163 + ], + "spans": [ + { + "bbox": [ + 44, + 70, + 288, + 163 + ], + "type": "table", + "html": "
Instructional datasets. Action-focused adverbs
HowTo100M Adverbs [6]Adverbs in Recipes
mAP WmAP MAcc-AmAP WmAP MAcc-A
Priors0.2470.1670.5600.3350.1000.835
S3D pre-trained0.3290.2220.5940.4250.1770.702
Act Mod [6]0.2690.1830.6010.3460.1070.837
MLP + Act Mod [6]0.2680.1840.7060.3680.1130.835
CLS0.4040.3070.7240.4690.1980.835
REG - fixed δ0.3200.2150.7060.4610.1480.835
REG0.3770.2770.7240.4810.1570.857
", + "image_path": "ef454a053bd54f7cf462b3a13084300186f6f26ce1024829e8ff9445e3059013.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 304, + 70, + 548, + 163 + ], + "blocks": [ + { + "bbox": [ + 304, + 70, + 548, + 163 + ], + "lines": [ + { + "bbox": [ + 304, + 70, + 548, + 163 + ], + "spans": [ + { + "bbox": [ + 304, + 70, + 548, + 163 + ], + "type": "table", + "html": "
Captioning datasets. Descriptive adverbs
ActivityNet Adverbs [7]MSR-VTT Adverbs [7]VATEX Adverbs [7]
mAP WmAP MAcc-AmAP WmAP MAcc-AmAP WmAP MAcc-A
0.0940.0500.6920.1370.0560.7230.0890.0290.651
0.1130.0650.5980.1990.0880.6030.1170.0370.604
0.1100.0630.7180.1640.0720.7290.1000.0350.686
0.1090.0700.7140.1620.0970.7230.0920.0360.686
0.1140.0720.7140.1890.0780.7230.1610.0530.712
0.1130.0700.7060.2130.0950.7140.1580.0470.703
0.1200.0730.7060.2400.1020.7490.1690.0570.737
", + "image_path": "7ff4c295eba0a3b7b6853a3a33d8bb96d414047528b35225e0050ab75f94062b.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 69, + 206, + 526, + 322 + ], + "blocks": [ + { + "bbox": [ + 46, + 173, + 546, + 195 + ], + "lines": [ + { + "bbox": [ + 46, + 173, + 546, + 195 + ], + "spans": [ + { + "bbox": [ + 46, + 173, + 546, + 195 + ], + "type": "text", + "content": "Table 3. Results obtained without action labels during inference. mAP W/M: mean Average Precision with weighted (W) and macro (M) averaging. Acc-A: adverb-vs-antonym accuracy. Coloured rows indicate variants of our method. Bold denotes best result per column." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 69, + 206, + 526, + 322 + ], + "lines": [ + { + "bbox": [ + 69, + 206, + 526, + 322 + ], + "spans": [ + { + "bbox": [ + 69, + 206, + 526, + 322 + ], + "type": "table", + "html": "
AntonymsInstructional datasets. Action-focused adverbsCaptioning datasets. Descriptive adverbs
HowTo100M Adverbs [6]Adverbs in RecipesActivityNet Adverbs [7]MSR-VTT Adverbs [7]VATEX Adverbs [7]
mAP WmAP MmAP WmAP MmAP WmAP MmAP WmAP MmAP WmAP M
PriorsX0.4460.3540.4910.2630.2170.1590.3080.1520.2160.086
S3D pre-trainedX0.3390.2380.3890.1730.1180.0700.1940.0750.1220.038
Act Mod [6]✓0.4060.3720.4210.1700.2110.1520.2460.1480.1390.059
X0.4080.3520.4280.1800.2170.1600.2540.1540.1440.060
MLP + Act Mod [6]✓0.2790.1930.4580.1880.1540.1080.2150.1110.2090.096
X0.2810.1980.4650.1970.1640.1150.2290.1320.2130.098
CLSX0.5620.4200.6750.3250.1140.0720.1890.0810.2830.108
REG✓0.5550.4230.6690.2970.1830.1030.2920.1180.2610.086
X0.5730.4810.7160.3930.2060.1210.3190.1140.2820.100
", + "image_path": "5060af9845750ace2f0cd680186566f700128f7b60a20138450194ea6d1b039d.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 331, + 546, + 354 + ], + "lines": [ + { + "bbox": [ + 46, + 331, + 546, + 354 + ], + "spans": [ + { + "bbox": [ + 46, + 331, + 546, + 354 + ], + "type": "text", + "content": "Table 4. Results obtained with action labels during inference and without antonyms during training. mAP W/M: mean Average Precision with weighted (W) and macro (M) averaging. Coloured rows indicate variants of our method. Bold denotes best result per column." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 365, + 287, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 365, + 287, + 520 + ], + "spans": [ + { + "bbox": [ + 46, + 365, + 287, + 520 + ], + "type": "text", + "content": "without antonyms it would be similar to binary classification. " + }, + { + "bbox": [ + 46, + 365, + 287, + 520 + ], + "type": "inline_equation", + "content": "CLS" + }, + { + "bbox": [ + 46, + 365, + 287, + 520 + ], + "type": "text", + "content": " by design does not use antonyms. Table 4 compares results obtained with and without antonyms. Since we assume we do not have antonym labels here we only evaluate mAP W/M. Interestingly, Action Modifiers slightly improves when removing antonyms, which shows again that using only opposite adverbs for contrastive learning limits the model. Discarding antonyms for our regression variant has also a strong positive effective. Since we remove the target " + }, + { + "bbox": [ + 46, + 365, + 287, + 520 + ], + "type": "inline_equation", + "content": "-\\delta" + }, + { + "bbox": [ + 46, + 365, + 287, + 520 + ], + "type": "text", + "content": " for antonyms and treat opposite adverbs as any other negative class, we are not forcing the model to push antonyms further compared to other negative adverbs. This is beneficial to learn adverbs more generally." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 521, + 287, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 287, + 641 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 287, + 641 + ], + "type": "text", + "content": "Regression vs Classification We now compare CLS and REG in Tables 2, 3 and 4. When testing without action labels (Table 3) and learning without antonyms (Table 4) we notice a more consistent improvement of REG over CLS. Rather than maximising the margin between the positive adverb and all other negative adverbs as in classification, with regression we try to learn the extent of the change applied by an adverb. This is evidently a more effective way to learn adverbs since the visual change introduced by an adverb varies considerably according to the action." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 647, + 119, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 647, + 119, + 659 + ], + "spans": [ + { + "bbox": [ + 47, + 647, + 119, + 659 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 666, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 666, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 666, + 287, + 715 + ], + "type": "text", + "content": "We proposed to address adverb recognition as a regression task. Our method attains new state-of-the-art performance on multiple datasets. Importantly, we achieve compelling results when removing two major assumptions: the" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 365, + 546, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 365, + 546, + 449 + ], + "spans": [ + { + "bbox": [ + 304, + 365, + 546, + 449 + ], + "type": "text", + "content": "availability of action labels during testing and the pairing of opposite adverbs as antonyms. To address the scarcity of datasets for adverb recognition we introduced AIR. The dataset collects instructional recipe videos where actions are particularly influenced by the modification indicated by adverbs. We believe AIR is a valuable resource that can readily foster advance in adverb understanding." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 451, + 546, + 535 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 451, + 546, + 535 + ], + "spans": [ + { + "bbox": [ + 304, + 451, + 546, + 535 + ], + "type": "text", + "content": "Limitations Since we model action changes measuring distances in a text embedding space we rely on a reasonably good text model. If the model does not capture meaningful relationships between verbs and adverbs then we do not have a reliable proxy to learn adverbs. Because we look for action changes directly in the video, actions need to exhibit a sufficient visual change when modified by the adverb." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 536, + 546, + 620 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 536, + 546, + 620 + ], + "spans": [ + { + "bbox": [ + 304, + 536, + 546, + 620 + ], + "type": "text", + "content": "Future Work Directions for future work include exploring ways to capture a broader action context via text. For example, the full caption associated with a video can provide additional information (e.g. object nouns) that could be exploited to better learn action modifications. This would require addressing the problem of video-text alignment, as well as the intrinsic noisy nature of long text embeddings." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 623, + 546, + 671 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 623, + 546, + 671 + ], + "spans": [ + { + "bbox": [ + 304, + 623, + 546, + 671 + ], + "type": "text", + "content": "Potential Societal Impact We source AIR from HowTo100M dataset, which gathers videos from YouTube. As such, any societal bias introduced in HowTo100M is potentially included in our data and our trained models." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 677, + 546, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 546, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 546, + 715 + ], + "type": "text", + "content": "Acknowledgements Research funded by UKRI through the Edinburgh Laboratory for Integrated Artificial Intelligence (ELIAI) and the Turing Advanced Autonomy project." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "23117" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 712 + ], + "type": "list", + "angle": 0, + "index": 18, + "blocks": [ + { + "bbox": [ + 53, + 91, + 286, + 123 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 286, + 123 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 286, + 123 + ], + "type": "text", + "content": "[1] Humam Alwassel, Fabian Caba Heilbron, Victor Escorcia, and Bernard Ghanem. 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However, existing event-based stereo networks suffer severe performance degradation when domains shift. Unsupervised domain adaptation (UDA) aims at resolving this problem without using the target domain ground-truth. However, traditional UDA still needs the input event data with ground-truth in the source domain, which is more challenging and costly to obtain than image data. To tackle this issue, we propose a novel unsupervised domain Adaptive Dense Event Stereo (ADES), which resolves gaps between the different domains and input modalities. The proposed ADES framework adapts event-based stereo networks from abundant image datasets with ground-truth on the source domain to event datasets without ground-truth on the target domain, which is a more practical setup. First, we propose a self-supervision module that trains the network on the target domain through image reconstruction, while an artifact prediction network trained on the source domain assists in removing intermittent artifacts in the reconstructed image. Secondly, we utilize the feature-level normalization scheme to align the extracted features along the epipolar line. Finally, we present the motion-invariant consistency module to impose the consistent output between the perturbed motion. Our experiments demonstrate that our approach achieves remarkable results in the adaptation ability of event-based stereo matching from the image domain.", + "bbox": [ + 75, + 300, + 473, + 709 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 724, + 209, + 739 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Stereo matching [22, 41] is one of the most widely used methods for obtaining 3D information by establishing correspondences between stereo images. With considerable interest, learning-based stereo methods have achieved state-of-the-art performance in many benchmark datasets. However, some challenges in stereo matching still exist due to the shortcoming of sensors (e.g., low dynamic range, motion blur due to large exposure time). Event cameras [3] are novel sensors that asynchronously report per-pixel changes of intensity by imitating the human eye. Thanks", + "bbox": [ + 75, + 750, + 468, + 901 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/49f92d8a3f5c46925bb5fe98416149495a78917d7d00a05075a11f97d3f3731e.jpg", + "image_caption": [ + "Figure 1. The proposed ADES framework for adaptive dense event stereo network. ADES aims to exploit the existing frame-based stereo dataset for learning the event stereo network." + ], + "image_footnote": [], + "bbox": [ + 522, + 268, + 867, + 503 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "to the high dynamic range and low latency, the event camera can be considered as a promising sensor for depth estimation, especially in driving scenarios. Recent works [2,8,9,28,30,48,59] have attempted to utilize event cameras for stereo matching even under poor light conditions.", + "bbox": [ + 496, + 566, + 892, + 642 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Despite advances in event stereo, most prior works [9, 28, 48] still experience a significant degradation in performance when domains shift. Unsupervised domain adaptation (UDA) can resolve this problem without using the target domain ground-truth. When UDA is applied for event stereo domain adaptation, it still needs the input event data with ground-truth in the source domain. However, as mentioned in [32], accurate synchronization of events with high temporal resolution and other devices (e.g., Li-DAR) requires additional hardware and post-processing, so it is more challenging to obtain accurate ground truth than images. In this paper, we draw attention to large image datasets with ground-truth, which are easily accessible (e.g., DrivingStereo [57], SceneFlow [24] and KITTI [25]). In this setup, abundant image data from diverse environments helps the event stereo network improve generalizability with high performance. To this end, as shown in", + "bbox": [ + 496, + 643, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "17797", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Fig. 1, we propose a novel Adaptive Dense Event Stereo (ADES), which adapts the stereo network from the source domain having image data with ground-truth to the target domain having event data without ground-truth. ADES resolves gaps between the different domains and input modalities.", + "bbox": [ + 75, + 90, + 468, + 180 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The proposed ADES framework consists of three components: smudge-aware self-supervision module, feature normalization, and motion-invariant consistency module. The proposed smudge-aware self-supervision module leverages dense traits of images via image reconstruction on the event target domain. Image reconstruction using only the event is often interrupted by blurry artifacts, what we call a smudge, so the network cannot estimate the sharp and accurate disparity map. To predict the smudge effect in the target domain, we design the self-supervision pipeline on the source image domain to estimate and suppress the artifact area in the reconstructed image on the target domain.", + "bbox": [ + 75, + 181, + 467, + 361 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In addition, we exploit the feature normalization before generating the cost volume. Normalization scheme [29, 43, 49, 58] was generally used in the domain adaptation between the image modalities. However, due to the characteristics of the event, it is not efficient to normalize over the entire pixel area. Since most of the events are triggered around an edge of objects, some regions (e.g., sky) have very sparse events. Therefore, vanilla normalization can mislead the values of features to shift to the values of the regions without events. While reducing the difference in features between the two domains, we apply a normalization along the epipolar line to take into account the characteristics of events and stereo matching.", + "bbox": [ + 75, + 363, + 467, + 556 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Finally, we focus on the different motion of event cameras from the source and target domains, leading to a severe domain gap. Therefore, we present the motion-invariant consistency module to predict consistent disparity even if the camera motion changes to some extent. This module helps the network to adapt the target domain and also reduces the gap from camera motion. To the best of our knowledge, our work is the first attempt to move from unpaired image domain to event domain for stereo matching. Our main contributions are summarized as below:", + "bbox": [ + 75, + 559, + 467, + 708 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Our work is the first that transfers the disparity estimation task from the rich image dataset with ground-truth to the event stream, resolving gaps between the different domains and input modalities.", + "- We propose a novel adaptive event stereo network, ADES, containing the smudge-aware self-supervision module, feature normalization, and motion-invariant consistency module.", + "- Extensive experiments demonstrate that the ADES framework achieves significantly better performance than the prior works in the adaptation ability between the different domains and modalities for event stereo." + ], + "bbox": [ + 94, + 714, + 467, + 898 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 500, + 89, + 648, + 106 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Stereo depth estimation using Events", + "text_level": 1, + "bbox": [ + 500, + 114, + 818, + 131 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recent event-based stereo matching [2,8,9,28,30,48,59] achieved the high accuracy than early works [5,7,20,35-37, 39,60,64,65] by adopting a learning-based approach with various embedding schemes. They propose additional modules that consider the temporal continuity of events, but the overall framework is similar to frame-based stereo: embedding, matching, and regularization modules. Our proposed pipeline of adaptive stereo matching also follows the general stereo matching, then can be easily applied on other event-based stereo networks.", + "bbox": [ + 498, + 137, + 890, + 287 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Domain Adaptation in Stereo Matching", + "text_level": 1, + "bbox": [ + 500, + 299, + 838, + 316 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To overcome the performance degradation from the domain gap, several works have explored unsupervised domain adaptation (UDA) in frame-based stereo matching. Some works utilize the knowledge distillation [14] and CycleGAN [23,62] to narrow the domain gap. After that, compact and efficient domain adaptation studies [33, 43, 47] for stereo have been conducted. On the other hand, the domain adaptation ability of event stereo networks has not been studied, and we tackle it for the first time.", + "bbox": [ + 498, + 321, + 890, + 458 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.3. Adaptation from Images to Events", + "text_level": 1, + "bbox": [ + 500, + 469, + 799, + 484 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Event-to-image reconstruction methods [10, 27, 31, 34, 38, 42, 44, 50, 52, 53] can be considered the proxy task to transfer a labeled image domain (source) to an unlabeled event domain (target). The results of the event-to-image reconstruction have been used as inputs of end-task (e.g., object recognition, semantic segmentation) network pre-trained on image (source) domain. However, they introduce the extra latency in the inference time and still pose a domain gap between source and target domain.", + "bbox": [ + 498, + 492, + 890, + 628 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "One of the attempts to properly do domain adaptation was grafted networks [17] by utilizing the pre-trained image network. They replaced the encoder of pre-trained network with event encoder, then finetuned it on paired event and image datasets. This setup takes advantage of each modalities, but requires pixel-wise aligned events and images. To overcome the limitation of paired setting, EvDistill [51] leveraged the unpaired images to boost the performance of event-based networks. Through the bidirectional modality reconstruction and cross-modal knowledge distillation, they can transfer the knowledge from image network to event network. After that, research on transferring from an unpaired image to event has been of continuous interest. EV-Transfer [26] hallucinate the motion to generate the fake events from still images. ESS [46] achieve the feature-level alignment with the motion-invariant event embeddings.", + "bbox": [ + 498, + 628, + 890, + 869 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Existing works only focus on the tasks from a single camera (e.g., semantic segmentation, object recognition).", + "bbox": [ + 500, + 869, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "17798", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/97eece041d0e691718804bf67a51bb9048c3c4d7242c5688f99716822c767ec9.jpg", + "image_caption": [ + "Figure 2. Overview of the proposed ADES framework. During training, image datasets (e.g., KITTI) are used for the source domain, and event datasets without ground-truth are used for the target domain. We utilize feature normalization (Sec. 3.4) to narrow the gap between features from other domains. The proposed smudge-aware self-supervision module (Sec. 3.3) and motion-invariant consistency module (Sec. 3.5) are only used in training phase." + ], + "image_footnote": [], + "bbox": [ + 101, + 92, + 869, + 316 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Due to the novel characteristics of event cameras, high-quality large stereo datasets have recently appeared, so related research has yet to be studied. In this paper, we propose an employable ADES framework for an event stereo. Unlike the prior works, we consider the characteristics of the event in the specific situation of stereo matching.", + "bbox": [ + 75, + 398, + 473, + 491 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 501, + 171, + 517 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Problem Setting", + "text_level": 1, + "bbox": [ + 76, + 526, + 238, + 542 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given consecutive stereo image pairs $(I_l^{t - 1}, I_r^{t - 1})$ , $(I_l^t, I_r^t)$ with ground-truth disparity map $\\tilde{d}_l^t$ on source domain, our goal is to train the model to predict the disparity map $D_l^{\\hat{t}}$ at time $\\hat{t}$ from stereo event streams $E_l^{\\hat{t}}$ , $E_r^{\\hat{t}}$ on target event domain. To make it clear that the source and the target domains are unpaired, we denote time for the source domain as $t$ and the target domain as $\\hat{t}$ . We represent an event stream as a voxel grid [63], the most commonly used representation, e.g., by converting $E_l^{\\hat{t}}$ to $V_l^{\\hat{t}}$ .", + "bbox": [ + 75, + 547, + 468, + 689 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. System Overview", + "text_level": 1, + "bbox": [ + 76, + 696, + 246, + 710 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As shown in Fig. 2, our proposed Adaptive Dense Event Stereo (ADES) consists of three novel components: smudge-aware self-supervision module, feature normalization, and motion-invariant consistency module.", + "bbox": [ + 75, + 719, + 468, + 779 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For the source domain, we leverage the pre-trained video-to-event reconstruction network to extract the event representations from image data for the event-based stereo network. There are several video-to-event methods [11, 18], but among them, we adopt the network proposed in [61] that is lightweight and describes events well even with only two sequential images. Each left and right sequential image pairs are passed through the video-to-event net", + "bbox": [ + 75, + 780, + 470, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "work $\\mathcal{G}_{I\\to E}$ and transformed into voxel grids as follows: $V_{l}^{t} = \\mathcal{G}_{I\\to E}(I_{l}^{t - 1},I_{l}^{t}),V_{r}^{t} = \\mathcal{G}_{I\\to E}(I_{r}^{t - 1},I_{r}^{t})$ . The generated voxel grid pairs $(V_{l}^{t},V_{r}^{t})$ from the source domain and the voxel grid pairs $(V_{l}^{\\hat{t}},V_{r}^{\\hat{t}})$ from the target domain are simultaneously fed into a weight shared event-based stereo network. In the process, we narrow the gap between the two domains by normalizing the extracted features. The prediction of source domain $d_l^t$ is supervised by ground-truth disparity $\\tilde{d}_l^t$ , while the result of the target domain is adaptively optimized by the proposed smudge-aware self-supervision module and motion-invariant consistency module.", + "bbox": [ + 496, + 398, + 893, + 568 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.3. Smudge-aware Self-supervision Module (SSM)", + "text_level": 1, + "bbox": [ + 498, + 574, + 892, + 590 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Prior works [21,45,56] verified that self-supervised auxiliary tasks are helpful for domain adaptation, especially in stereo matching task [43]. We also utilize the photometric reconstruction as an auxiliary task of domain adaptation for stereo matching. First, as shown in the bottom of Fig. 3, we generate the image from voxel event representation in target domain. To this end, we leverage the widely used pretrained event-to-image reconstruction network [38]. However, the reconstructed image from event has intermittent artifacts near the boundary of an object. Those blurring and distortion effects, what we call a smudge, disturbs predicting sharp disparity. To estimate the irregular smudge in the target domain, we further design a self-supervision pipeline for smudge prediction in the source domain.", + "bbox": [ + 496, + 598, + 892, + 809 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In the source domain, as shown in the top of Fig. 3, we perturb the random region of image with distortion and blur kernel for imitating smudge effects. To depict realistic smudge effects, we do not generate the smudge on the randomly selected rectangle region but on the regions parsed by superpixel algorithm [1]. Since the edges of superpix", + "bbox": [ + 496, + 810, + 893, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "17799", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/fb200b9f52f9c159506a8d4a7c9b7491f12e5628f927c98c67141fbd33f12dcc.jpg", + "image_caption": [ + "Figure 3. Illustration of the Smudge-aware Self-supervision Module (SSM). To estimate the smudge artifact of the reconstructed image on the target domain, we train the smudge prediction network to predict the smudge in the source domain." + ], + "image_footnote": [], + "bbox": [ + 86, + 88, + 455, + 306 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "els are generally placed on the boundary of an object, they can mimic the characteristics of the smudge effect caused at the boundary of the object due to the noisy sensors. Then, domain-shared smudge prediction network, which is a light-designed U-Net [40] with few convolution layers, is supervised from generated smudge mask. In other words, the output $M_{i}^{t}$ of smudge prediction network is supervised from generated artifact mask $\\tilde{M}_{i}^{t}$ by minimizing the binary cross entropy loss: $\\mathcal{L}_{\\text{source}}^{\\text{mask}} = \\sum_{i \\in \\{l,r\\}} BCE(M_{i}^{t}, \\tilde{M}_{i}^{t})$ .", + "bbox": [ + 75, + 378, + 467, + 516 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In the target domain, as shown in the bottom of Fig. 3, we utilize a shared smudge prediction network from source domain for photometric-based self-supervision. The reconstructed left image $\\hat{I}_l^{\\hat{t}}$ and right image $\\hat{I}_r^{\\hat{t}}$ from voxels $V_l^{\\hat{t}}$ and $V_r^{\\hat{t}}$ are fed into the smudge prediction network. Then, smudge prediction network provides the predicted smudge map $M_l^{\\hat{t}}$ and $M_r^{\\hat{t}}$ , which include per-pixel probability of smudge from 0 to 1. Next, from the predicted dense disparity map $D_l^{\\hat{t}}$ , we can reconstruct the warped left image $W_{r\\to l}(\\hat{I}_r^{\\hat{t}})$ from right image $\\hat{I}_r^{\\hat{t}}$ . Considering the smudge mask maps of both left and right sides, we can calculate the pixel-wise photometric reconstruction error as follows:", + "bbox": [ + 75, + 517, + 467, + 700 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {\\text {t a r g e t}} ^ {\\text {r e c o n}} = \\alpha \\frac {1 - \\operatorname {S S I M} \\left(\\hat {I} _ {l} ^ {\\hat {t}} \\odot M ^ {\\hat {t}} , W _ {r \\rightarrow l} \\left(\\hat {I} _ {r} ^ {\\hat {t}}\\right) \\odot M ^ {\\hat {t}}\\right)}{2} \\tag {1} \\\\ + (1 - \\alpha) \\| \\hat {I} _ {l} ^ {\\hat {t}} \\odot M ^ {\\hat {t}} - W _ {r \\rightarrow l} (\\hat {I} _ {r} ^ {\\hat {t}}) \\odot M ^ {\\hat {t}} \\| _ {1}, \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 710, + 467, + 766 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $M^{\\hat{t}} = 1 - (M_{l}^{\\hat{t}} \\odot W_{r \\to l}(M_{r}^{\\hat{t}}))$ , $\\odot$ means elementwise multiplication, SSIM denotes structural similarity proposed in [54] with a $3 \\times 3$ kernel filter, and $\\alpha$ is set to 0.85.", + "bbox": [ + 75, + 777, + 467, + 824 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Our proposed smudge prediction network is shared in the source and target domains with the same weights. Compared to the stereo network, which is a high-level task, the smudge prediction, which pixel-wisely finds regions of noise and smudge, is a low-level task and less affected by", + "bbox": [ + 75, + 825, + 467, + 900 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/8d62f9815e39c9b2b78396cb3024080b24eb449d2beb97d47bd33dfeb6b3e199.jpg", + "image_caption": [ + "(a) Source" + ], + "image_footnote": [], + "bbox": [ + 500, + 88, + 692, + 203 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/9cb4aa4ce719bae44def2b8e28c59211c995e4d4efb1ca5f3fc04716370c2438.jpg", + "image_caption": [ + "(b) Target", + "Figure 4. Visualization of voxel grids and features extracted by the event stereo network from source (e.g., KITTI) and target (e.g., DSEC) domain. In the upper region of features with few events, there are no activated pixels; in contrast, there are many activated pixels in the lower region with a lot of structure for events." + ], + "image_footnote": [], + "bbox": [ + 694, + 88, + 887, + 203 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "the domain gaps. Therefore, in the target domain, artifacts in the boundary are well predicted in the reconstructed image to estimate the sharp disparity through self-supervision.", + "bbox": [ + 498, + 304, + 890, + 349 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Feature Normalization", + "text_level": 1, + "bbox": [ + 500, + 362, + 709, + 376 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We adopt the feature-level normalization to reduce the gap in the cost volume between two distinct domains. To align the distributions between different domains, the feature normalization [29,49,58] is widely used for image data. Similarly, event features can be also normalized to reduce the gap between the two domains; however, as can be seen in our experimental results (see Table 5), due to the sparsity of the event data, an existing normalization technique [43] for images rather hinders learning of event-based network.", + "bbox": [ + 496, + 386, + 890, + 521 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For event feature normalization, we focus on the characteristics of event-based stereo matching. Events are naturally sparse and triggered predominantly to the edges of the objects. For accurate prediction with sparse information, event stereo networks tend to focus intensely on areas with event information, which leads to features of areas without events not being activated. Therefore, normalizing over all pixels provides results with shifted bias on the region without an event for each scene. Instead, we focus on the correlation between the amount of events and spatial positions. For example, events rarely occur in the upper regions (e.g., sky), while more events occur in the lower regions where illuminance easily changes and rich textures exist (e.g., building). This phenomenon can be qualitatively verified by the extracted features of the network, as shown in Fig. 4. The lower region of the feature map is strongly activated in both domains, while the upper region, where no event occurs, is hardly activated. Therefore, applying the normalization over all pixels used in the dense image [43] to event stereo rather hinders reducing the domain gaps. In addition, since the stereo disparity is defined as the position difference in the horizontal direction when the cameras are rectified, normalization over all spatial positions leads to ambiguity in accurate matching. Therefore, we propose a strategy to normalize the feature along the epipolar (hori", + "bbox": [ + 496, + 523, + 892, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "17800", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/d9bb4ec1323323e642b28dd71a643f9efae5e53a934cd5b9aaa0bc4d0a79e773.jpg", + "image_caption": [ + "Figure 5. Illustration of the Motion-invariant Consistency Module (MCM). Normalize over time denotes to converting temporal values into a range between 0 and 1." + ], + "image_footnote": [], + "bbox": [ + 96, + 90, + 450, + 280 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "zontal) line, which does not violate the regularity according to regions. This normalization is also spatial but less dependent on the global distribution of event data.", + "bbox": [ + 75, + 344, + 468, + 388 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We modify the parameter-free normalization scheme proposed in prior works [43]. Given extracted feature $F$ from network with size of $C \\times H \\times W$ ( $C$ : channel, $H$ : height, $W$ : width), let $F(k,i,j)$ denotes kij-th element, where $k$ is the index of channel and $i,j$ are spatial dimensions. Then, we apply the normalization along channel-dimension to both left and right features as follows:", + "bbox": [ + 75, + 388, + 468, + 494 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nF (k, i, j) = \\frac {F (k , i , j)}{\\sqrt {\\sum_ {c = 0} ^ {C - 1} \\| F (c , i , j) \\| ^ {2} + \\varepsilon}}. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 135, + 503, + 468, + 547 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "After that, we apply the normalization along the epipolar line, which is defined as:", + "bbox": [ + 76, + 556, + 468, + 585 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nF (k, i, j) = \\frac {F (k , i , j)}{\\sqrt {\\sum_ {w = 0} ^ {W - 1} \\| F (k , i , w) \\| ^ {2} + \\varepsilon}}. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 130, + 594, + 468, + 637 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5. Motion-invariant Consistency Module (MCM)", + "text_level": 1, + "bbox": [ + 76, + 645, + 468, + 662 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The motivation of the motion-invariant consistency module on the target domain is two-folds. The first is to resolve the domain gap caused by different camera motion. Second, we desire the event stereo network to be robust on perturbation or noise, adapting to the target domain. The perfectly adapted network should be able invariant to the motion of event camera and estimate the prediction stably, even if there is some perturbation in the input.", + "bbox": [ + 75, + 667, + 468, + 789 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this subsection, we denote the voxel grid corresponding to the events $E^{\\hat{t},T}$ accumulated during time $T$ until $\\hat{t}$ as $V^{\\hat{t},T}$ . Specifically, events are converted to a voxel grid pair $V_{l}^{\\hat{t},T}, V_{r}^{\\hat{t},T}$ , and fed to the network to estimate a disparity map $D_{l}^{\\hat{t}}$ . Since the motion in the datasets is already acquired and immutable, we use a trick to augment event streams of fast or slow motions with temporal perturbation $\\tau$ . If events", + "bbox": [ + 76, + 790, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "are stacked for a longer time $T + \\tau$ (i.e., more events) after normalizing temporal value in events (converting temporal values into a range between 0 and 1) and converted for the same bin of voxel grid, it is able to imitate the voxel grid of an event from an actual fast motion. Conversely, if stacked for a shorter time $T - \\tau$ (i.e., fewer events), it is the same as the voxel grid made with events of slow motion. From this, we can generate a motion perturbed event voxel $V^{\\hat{t},\\hat{T}}$ , where $\\hat{T} = T \\pm \\tau$ without additional data acquisition. As shown in Fig. 5, perturbed voxel pairs $V_{l}^{\\hat{t},\\hat{T}}, V_{r}^{\\hat{t},\\hat{T}}$ are fed into the event stereo network to predict the perturbed disparity map $\\tilde{D}_{l}^{\\hat{t}}$ . Then, for pixel-wise consistency between the prediction of motion-perturbed input and the original input, our consistency loss is defined via $L_{1}$ distance:", + "bbox": [ + 496, + 90, + 892, + 308 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {t a r g e t}} ^ {\\text {c o n s i s t e n c y}} = \\| D _ {l} ^ {\\hat {t}} - \\tilde {D} _ {l} ^ {\\hat {t}} \\| _ {1} \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 599, + 318, + 890, + 340 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "More details about the implementation of motion-invariant consistency module can be seen in supple.", + "bbox": [ + 496, + 349, + 890, + 381 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.6. Loss functions", + "text_level": 1, + "bbox": [ + 500, + 391, + 648, + 405 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "On the source domain, we use the two losses for training the network. We adopt the smooth $L_{1}$ loss for disparity estimation: $\\mathcal{L}_{source}^{task} = \\mathrm{smooth}_{L_1}(\\tilde{d}_l^t -d_l^t)$ , and the binary cross entropy loss for artifact prediction: $\\mathcal{L}_{source}^{mask} = \\sum_{i\\in \\{l,r\\}}BCE(M_i^t,\\tilde{M}_i^t)$ .", + "bbox": [ + 496, + 414, + 890, + 491 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "On the target domain, we use the reconstruction loss $\\mathcal{L}_{\\text {target }}^{\\text {recon }}$ (Eq. 1) and consistency loss $\\mathcal{L}_{\\text {target }}^{\\text {consistency }}$ (Eq. 4).", + "bbox": [ + 500, + 489, + 890, + 521 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Finally, the total loss for an end-to-end optimization process is defined as:", + "bbox": [ + 500, + 521, + 890, + 550 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} ^ {\\text {t o t a l}} = \\mathcal {L} _ {\\text {s o u r c e}} ^ {\\text {t a s k}} + \\lambda_ {1} \\mathcal {L} _ {\\text {s o u r c e}} ^ {\\text {m a s k}} + \\lambda_ {2} \\mathcal {L} _ {\\text {t a r g e t}} ^ {\\text {r e c o n}} + \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 542, + 559, + 890, + 585 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\lambda_ {3} \\mathcal {L} _ {\\text {t a r g e t}} ^ {\\text {c o n s i s t e n c y}},\n$$\n", + "text_format": "latex", + "bbox": [ + 740, + 582, + 844, + 599 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\lambda_1, \\lambda_2$ and $\\lambda_3$ are weight for each loss terms.", + "bbox": [ + 500, + 611, + 841, + 626 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 640, + 633, + 657 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Datasets", + "text_level": 1, + "bbox": [ + 500, + 665, + 602, + 680 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For source domain datasets, we utilize the KITTI dataset [25] and the SceneFlow dataset [24]. The KITTI dataset is a real-world dataset with two subsets (i.e. KITTI 2012 [13] and KITTI 2015 [25]), containing 394 stereo images with sparse ground-truth for training. On the other hand, the SceneFlow dataset [24] is a large synthetic dataset containing diverse scenes. The SceneFlow dataset provides 35k stereo images with dense ground-truth disparity maps.", + "bbox": [ + 496, + 688, + 890, + 809 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For target domain, we use the recently published benchmark dataset of DSEC [12], a large-scale high-quality driving dataset with challenging scenes. DSEC provides high-resolution $(640\\times 480)$ stereo event streams captured in outdoor driving scenes. It contains 53 driving scenarios taken in various lighting conditions, and provides 17k stereo pairs", + "bbox": [ + 496, + 810, + 890, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "17801", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/0cf4e8ce11a60bc63f5d93931e78aa85e936e3b8b3f6ec83c6b716e5294b9334.jpg", + "table_caption": [ + "Table 1. Cross-domain comparisons with other traditional / domain generalization / domain adaptation stereo methods from various source domains. The 2-pixel error $(\\%)$ , 3-pixel error $(\\%)$ , end-point-error, and root mean square error are adopted for evaluation. Zu and In denote the Zurich City and Interlaken sequences, respectively." + ], + "table_footnote": [], + "table_body": "
KITTI-to-DSECSceneFlow-to-DSEC
Method2PE3PEEPERMSE2PE3PEEPERMSE
ZuInZuInZuInZuInZuInZuInZuIn
E2VID [38] on target domain
SGM [16]53.755.347.749.79.310.116.117.053.755.347.749.79.310.1
GwcNet [15]38.237.129.122.03.52.98.25.843.345.028.831.23.04.2
PSMNet [6]36.535.525.924.13.42.96.05.136.439.724.329.62.65.4
AANet [55]46.339.335.326.37.43.817.28.642.839.229.227.33.63.1
DSMNet [58]41.141.630.432.13.24.25.68.146.645.331.230.64.13.7
StereoGAN [23]70.968.866.463.111.49.813.312.273.272.268.073.115.413.4
EventGAN [61] on source domain
GwcNet [15]25.527.319.816.84.63.112.29.155.156.337.237.17.47.3
PSMNet [6]18.920.511.913.64.22.714.810.448.850.635.037.86.85.8
AANet [55]50.447.342.538.69.85.421.711.358.855.445.342.45.75.8
DSMNet [58]18.823.610.512.62.12.44.56.751.252.344.643.26.25.9
StereoGAN [23]61.460.352.850.715.313.718.918.975.271.765.566.313.310.6
ADES (Ours)
AANet13.819.97.19.81.41.72.73.422.324.911.113.91.61.9
PSMNet10.910.25.65.51.21.32.53.217.512.89.46.71.41.3
", + "bbox": [ + 107, + 135, + 859, + 380 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "for training. Following the previous image-to-event transfer tasks for segmentation [46], we adopt sequences acquired during the day with monotonous illuminance, called Zurich City. Furthermore, we also conduct experiments on Interlaken sequences containing the high dynamic range and challenging illuminance scenes. More details about a split of datasets are provided in the supple.", + "bbox": [ + 75, + 395, + 472, + 502 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Implementation details", + "text_level": 1, + "bbox": [ + 76, + 510, + 292, + 526 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The weights $\\lambda_{1}, \\lambda_{2}$ and $\\lambda_{3}$ are set as 0.3, 1, and 0.2, respectively. We train our end-to-end framework using the Adam optimizer [19]. We set the learning rate to $1 \\times 10^{-3}$ with a batch size of 8 using $384 \\times 336$ random crops. To generate the artifacts in Sec. 3.3, we utilize the Blur and OpticalDistortion transforms from library [4]. More details are provided in supple.", + "bbox": [ + 75, + 534, + 470, + 642 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Comparisons with Other Methods", + "text_level": 1, + "bbox": [ + 76, + 650, + 375, + 666 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We compare our proposed ADES framework with the other traditional algorithm (SGM [16]), domain generalization (DSMNet [58]), and domain adaptation (StereoGAN [23]). In addition, we evaluate PSMNet [6], GwcNet [15], and AANet [55], which have achieved comparable performance in stereo matching. We train those networks in the source domain and test the network in the target domain. To align the different modalities between the source and target domains, we utilize E2VID [38] or EventGAN [61]. In the case of E2VID, an image-based stereo network is trained using a grayscale image in the source domain, and when testing, events in the target domain are reconstructed into a gray image using E2VID. Conversely, in the case of EventGAN, the event-based stereo network is trained using the events, which are converted by EventGAN from consecu", + "bbox": [ + 75, + 674, + 470, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "tive images in the source domain. We evaluate the proposed framework by applying it to AANet and PSMNet, which can represent networks using 3D and 4D cost volumes. Especially, AANet is efficient, so it is a widely adopted structure in recent event stereo research [28, 30]. When training, the proposed modules are used, but when evaluating, all the proposed modules without normalization are removed, and only the event stereo network is used to predict the disparity. Table 1 shows the results of training on the various source dataset, such as KITTI and SceneFlow datasets.", + "bbox": [ + 496, + 393, + 893, + 546 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "KITTI-to-DSEC. Even if the networks are trained on the source domain, the results of networks using the events from EventGAN can not achieve high performance. Some networks (PSMNet, GwcNet, and AANet) do not have the ability of domain generalization and adaptation. In addition, the distribution gap of disparity and motion between the domains lead to further degradation of performance. Similarly, most of the results using reconstructed images with E2VID do not show comparable performance. The reconstructed image on the target domain has a large gap with the real image on the source domain, which cannot be dealt with generalization (DSMNet), adaptation (StereoGAN) and conventional methods (SGM). Compared with existing works, our network achieves significantly high performance, considering the gap between domains such as motions and disparity. It is noticeable that in case of AANet+ADES, the performance improvement is significant, e.g., 2PE decreases from 50.4 to 13.8, and RMSE decreases from 21.7 to 2.7 in Zurich City sequence.", + "bbox": [ + 496, + 549, + 893, + 837 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "SceneFlow-to-DSEC. The experiment results trained on the synthetic source domain show a more significant domain gap. Due to the effect of the syn-to-real gap, prior works show significantly lower performance than those", + "bbox": [ + 496, + 839, + 893, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "17802", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/216e814972cf116cfed0580bf361a5e7779dd58b388aa9aa5fff0cb6c17f86e6.jpg", + "image_caption": [ + "Figure 6. Qualitative results for the proposed method with other methods. Compared to EventGAN [61] and E2VID [38], our method can predict accurate and sharp disparity maps." + ], + "image_footnote": [], + "bbox": [ + 94, + 88, + 870, + 354 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/2dc0a4c856cc9f7da6982a2b63180d802cba6a9ea025c44fcf75a86cd15a42b9.jpg", + "table_caption": [ + "Table 2. Results on DSEC benchmark testset" + ], + "table_footnote": [], + "table_body": "
MethodSupervisionRMSE ↓MAE ↓1PE ↓2PE ↓
[48]✓1.3860.57610.922.91
[28]✓1.2220.5299.962.65
[30]✓1.2310.5199.582.62
[59]✓1.2640.5279.522.36
Ours (PSM)1.6980.77118.375.36
Ours (AA)1.9820.93624.017.87
", + "bbox": [ + 96, + 412, + 446, + 508 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "trained on KITTI datasets, e.g., 2PE of PSMNet using EventGAN significantly increases from 20.5 to 50.6 in the Interlaken sequence. Although our proposed method cannot avoid the performance degradation, the decreasing amount is relatively acceptable, e.g., 2PE of PSMNet+ADES increases from 10.2 to 12.8 in the Interlaken sequence. Furthermore, the performance increases in some metrics thanks to the various scenes in the synthetic dataset, e.g., RMSE of PSMNet+ADES decreases from 3.2 to 2.8 in the Interlaken sequence. These results show that our method can be used universally and not limited to a specific source dataset, whether synthetic or real-world.", + "bbox": [ + 75, + 518, + 468, + 699 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In Fig. 6, we provide qualitative comparisons of our method with other methods. E2VID or EventGAN can reduce the gap between modality, but it cannot bridge between domains. On the other hand, our ADES framework predicts sharp and accurate disparity on both AANet and PSMNet. These results demonstrate that our training pipeline resolves the gaps from both domain and modality. More qualitative comparisons are provided in supple.", + "bbox": [ + 75, + 700, + 468, + 821 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Results on DSEC test dataset", + "text_level": 1, + "bbox": [ + 76, + 830, + 336, + 845 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To compare with supervised methods, we utilize the KITTI dataset, which contains ground-truth, as the source domain and the full DSEC train dataset, which lacks", + "bbox": [ + 76, + 854, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/a6ebd2775b0af8136666c9de945d55f04d35f1e883a2c2b901564b5d7654a616.jpg", + "table_caption": [ + "Table 3. Ablation studies for sub-modules: Smudge-aware Self-supervision Module (SSM), Feature Normalization (FN), and Motion-invariant Consistency Module (MCM). $D1$ -error $(\\%)$ is adopted." + ], + "table_footnote": [], + "table_body": "
ModelSSMFNMCMZurichInterlaken
AANet35.226.3
✓33.124.5
✓29.622.7
✓13.315.1
✓✓11.214.6
✓✓8.110.2
✓✓✓7.09.7
PSMNet15.617.2
✓13.816.1
✓13.115.5
✓7.38.9
✓✓6.67.1
✓✓6.06.2
✓✓✓5.65.7
", + "bbox": [ + 501, + 455, + 890, + 642 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ground-truth, as the target domain. Table 2 demonstrates that despite not relying on ground-truth data for the target domain, our approach achieves comparable performance to other supervised methods.", + "bbox": [ + 498, + 656, + 890, + 717 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.5. Ablation Studies", + "text_level": 1, + "bbox": [ + 500, + 726, + 663, + 739 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effectiveness of each components. In Table 3, we conduct the ablation studies to validate the effectiveness of each component. We set the KITTI and DSEC dataset as source and target domain, respectively. Based on AANet and PSMNet from which all proposed modules were removed, the performance was measured while adding the proposed module one by one. The SSM achieves the greatest performance gain as a unitary component, e.g., reducing error rates by $21.9\\%$ on Zurich, and $11.2\\%$ on Interlaken from AANet. In addition, using FN stand-alone reduces the", + "bbox": [ + 496, + 750, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "17803", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/4db4a9879e19bd2dce4c476dc11a9d4ba8f67854ae8024ce7d291c553c874691.jpg", + "table_caption": [ + "Table 4. Comparison of results with and without smudge prediction. $D1$ -error $(\\%)$ is adopted." + ], + "table_footnote": [], + "table_body": "
MethodsZurichInterlaken
w/o Smudge Prediction16.112.3
w/ Smudge Prediction7.09.7
", + "bbox": [ + 83, + 123, + 467, + 169 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/9dff02f15fe2610691a3bfcf9dd375712385cf0b18a1496b2aba0d3e15c0c330.jpg", + "image_caption": [ + "Figure 7. Qualitative results of disparity predictions with and without smudge prediction." + ], + "image_footnote": [], + "bbox": [ + 81, + 172, + 467, + 291 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "error by $1.7\\% \\sim 5.6\\%$ depending on the target domain and model, compared to the baseline. Similarly, MCM also reduces the error by $1.1\\% \\sim 2.1\\%$ . These FN and MCM work even if implemented together with SSM, e.g., compared to the case of using only SSM from AANet in Zurich, when FN and MCM are used together, errors are more reduced by $5.2\\%$ and $2.1\\%$ , respectively. Finally, the performance gain is the most significant when all of the proposed modules are used, and these results validate that all modules are effective for domain adaptation.", + "bbox": [ + 75, + 352, + 467, + 503 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effectiveness of smudge predictions. We investigate the effect of the proposed smudge prediction on SSM. Using the KITTI as the source domain, the quantitative and qualitative results with and without smudge prediction from AANet are shown in Table 4 and Fig. 7. Compared with the absence of smudge prediction, our method utilizes the photometric loss of image reconstruction effectively. Therefore, through SSM using smudge prediction, the performance of the disparity estimation is improved e.g., the $D1$ -error decreases from 16.1 to 7.0 in Zurich City sequence. Specifically, as can be seen in Fig. 7, smudge prediction helps the network to robustly infer the boundary of an object, making a sharp disparity map. We visualize the smudge mask in Fig. 8 to show how smudge masks can aid effective learning in SSM. As shown in 1st row of Fig. 8, when an image is reconstructed from an event via E2VID, smudge-like blurry artifacts appear around the boundary of the object due to the noisy nature of the event streams. Our smudge prediction estimates these artifacts regions, helping to sharpen disparity when performing self-supervision and boosting the performance of disparity estimation.", + "bbox": [ + 75, + 505, + 467, + 821 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Comparison of normalization. Table 5 reports the comparison of our feature normalization with the existing learning-free normalization method [43]. We set the KITTI dataset as the source domain and the model to AANet. Although our epipolar norm is a modified module of the ex", + "bbox": [ + 75, + 824, + 467, + 900 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/6693ef2e0063a9e8a8e543b7674b8cc4b7bcae70f5eb88cd97ca2ce70d806e3c.jpg", + "table_caption": [ + "Table 5. Comparison of epipolar norm with existing cost norm [43]. $D1$ -error $(\\%)$ is adopted." + ], + "table_footnote": [], + "table_body": "
MethodsZurichInterlaken
w/o Norm11.214.6
Cost Norm [43]12.311.1
Our Epipolar Norm7.09.7
", + "bbox": [ + 506, + 122, + 879, + 181 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7447909073deebe9c1fa6c0c43fb17cdc1ee7c21882eb81837c7b8e5b03949f0.jpg", + "image_caption": [ + "Figure 8. Generated smudge mask on the target domain. Top: reconstructed images, Bottom: corresponding smudge mask." + ], + "image_footnote": [], + "bbox": [ + 504, + 185, + 883, + 304 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "isting work, the results verify that it is more effective for the domain adaptation ability of event stereo matching. For example, in the case of [43], which performs the normalization along all pixels in spatial manners, the performance is rather reduced due to the specificity of event stereo. For example, especially in Zurich City, the $D1$ -error increases from 11.2 to 12.3 after introducing the cost norm [43]. On the other hand, our epipolar norm shows a performance improvement in both sequences. From these results, we can confirm that the event stereo network requires a different approach than the existing normalization method, and our normalization is suitable for the domain adaptive event stereo matching.", + "bbox": [ + 496, + 348, + 890, + 545 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 558, + 617, + 573 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we propose a novel framework, ADES, for adaptive dense event stereo from the image domain. Our work is the first that transfers the disparity estimation task from the rich image dataset with ground-truth to the event stream to tackle the absence of ground-truth disparities on the target event domain. To this end, we propose the smudge-aware self-supervision module, feature normalization, and motion-invariant consistency module by focusing on the specificity of event stereo. Extensive experiments demonstrate our framework achieves remarkable performance on both 3D and 4D cost volume networks, whether the source domain is synthetic or real-world image dataset. Furthermore, these results demonstrate that our modules can be used universally in existing event stereo networks. We open up the possibility of using event stereo in domains without ground-truth and expect more future work.", + "bbox": [ + 496, + 583, + 890, + 825 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements. This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (NRF-2022R1A2B5B03002636).", + "bbox": [ + 496, + 839, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "17804", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Radhakrishna Achanta, Appu Shaji, Kevin Smith, Aurelien Lucchi, Pascal Fua, and Sabine Süssrunk. Slic superpixels compared to state-of-the-art superpixel methods. IEEE transactions on pattern analysis and machine intelligence, 34(11):2274-2282, 2012. 3", + "[2] Soikat Hasan Ahmed, Hae Woong Jang, SM Nadim Uddin, and Yong Ju Jung. Deep event stereo leveraged by event-to-image translation. 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Conf.(BMVC), volume 1, 2017. 2", + "bbox": [ + 501, + 90, + 892, + 160 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "17807", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Learning Adaptive Dense Event Stereo From the Image Domain/4f451359-7481-4ea3-a57c-f3f3dbdd863e_model.json b/2023/Learning Adaptive Dense Event Stereo From the Image Domain/4f451359-7481-4ea3-a57c-f3f3dbdd863e_model.json new file mode 100644 index 0000000000000000000000000000000000000000..b94d849061031e1447732c6795a4710ee52f67ee --- /dev/null +++ b/2023/Learning Adaptive Dense Event Stereo From the Image Domain/4f451359-7481-4ea3-a57c-f3f3dbdd863e_model.json @@ -0,0 +1,2279 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.166, + 0.131, + 0.804, + 0.154 + ], + "angle": 0, + "content": "Learning Adaptive Dense Event Stereo from the Image Domain" + }, + { + "type": "text", + "bbox": [ + 0.293, + 0.182, + 0.677, + 0.217 + ], + "angle": 0, + "content": "Hoonhee Cho, Jegyeong Cho, and Kuk-Jin Yoon Visual Intelligence Lab., KAIST, Korea" + }, + { + "type": "text", + "bbox": [ + 0.308, + 0.219, + 0.662, + 0.234 + ], + "angle": 0, + "content": "{gnsgnsgml，j2k0618，kjyoon}@kaist.ac.kr" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.269, + 0.314, + 0.285 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.301, + 0.474, + 0.71 + ], + "angle": 0, + "content": "Recently, event-based stereo matching has been studied due to its robustness in poor light conditions. However, existing event-based stereo networks suffer severe performance degradation when domains shift. Unsupervised domain adaptation (UDA) aims at resolving this problem without using the target domain ground-truth. However, traditional UDA still needs the input event data with ground-truth in the source domain, which is more challenging and costly to obtain than image data. To tackle this issue, we propose a novel unsupervised domain Adaptive Dense Event Stereo (ADES), which resolves gaps between the different domains and input modalities. The proposed ADES framework adapts event-based stereo networks from abundant image datasets with ground-truth on the source domain to event datasets without ground-truth on the target domain, which is a more practical setup. First, we propose a self-supervision module that trains the network on the target domain through image reconstruction, while an artifact prediction network trained on the source domain assists in removing intermittent artifacts in the reconstructed image. Secondly, we utilize the feature-level normalization scheme to align the extracted features along the epipolar line. Finally, we present the motion-invariant consistency module to impose the consistent output between the perturbed motion. Our experiments demonstrate that our approach achieves remarkable results in the adaptation ability of event-based stereo matching from the image domain." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.725, + 0.21, + 0.74 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Stereo matching [22, 41] is one of the most widely used methods for obtaining 3D information by establishing correspondences between stereo images. With considerable interest, learning-based stereo methods have achieved state-of-the-art performance in many benchmark datasets. However, some challenges in stereo matching still exist due to the shortcoming of sensors (e.g., low dynamic range, motion blur due to large exposure time). Event cameras [3] are novel sensors that asynchronously report per-pixel changes of intensity by imitating the human eye. Thanks" + }, + { + "type": "image", + "bbox": [ + 0.523, + 0.27, + 0.868, + 0.505 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.51, + 0.895, + 0.553 + ], + "angle": 0, + "content": "Figure 1. The proposed ADES framework for adaptive dense event stereo network. ADES aims to exploit the existing frame-based stereo dataset for learning the event stereo network." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.567, + 0.893, + 0.643 + ], + "angle": 0, + "content": "to the high dynamic range and low latency, the event camera can be considered as a promising sensor for depth estimation, especially in driving scenarios. Recent works [2,8,9,28,30,48,59] have attempted to utilize event cameras for stereo matching even under poor light conditions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Despite advances in event stereo, most prior works [9, 28, 48] still experience a significant degradation in performance when domains shift. Unsupervised domain adaptation (UDA) can resolve this problem without using the target domain ground-truth. When UDA is applied for event stereo domain adaptation, it still needs the input event data with ground-truth in the source domain. However, as mentioned in [32], accurate synchronization of events with high temporal resolution and other devices (e.g., Li-DAR) requires additional hardware and post-processing, so it is more challenging to obtain accurate ground truth than images. In this paper, we draw attention to large image datasets with ground-truth, which are easily accessible (e.g., DrivingStereo [57], SceneFlow [24] and KITTI [25]). In this setup, abundant image data from diverse environments helps the event stereo network improve generalizability with high performance. To this end, as shown in" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17797" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.181 + ], + "angle": 0, + "content": "Fig. 1, we propose a novel Adaptive Dense Event Stereo (ADES), which adapts the stereo network from the source domain having image data with ground-truth to the target domain having event data without ground-truth. ADES resolves gaps between the different domains and input modalities." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.183, + 0.468, + 0.362 + ], + "angle": 0, + "content": "The proposed ADES framework consists of three components: smudge-aware self-supervision module, feature normalization, and motion-invariant consistency module. The proposed smudge-aware self-supervision module leverages dense traits of images via image reconstruction on the event target domain. Image reconstruction using only the event is often interrupted by blurry artifacts, what we call a smudge, so the network cannot estimate the sharp and accurate disparity map. To predict the smudge effect in the target domain, we design the self-supervision pipeline on the source image domain to estimate and suppress the artifact area in the reconstructed image on the target domain." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.364, + 0.468, + 0.558 + ], + "angle": 0, + "content": "In addition, we exploit the feature normalization before generating the cost volume. Normalization scheme [29, 43, 49, 58] was generally used in the domain adaptation between the image modalities. However, due to the characteristics of the event, it is not efficient to normalize over the entire pixel area. Since most of the events are triggered around an edge of objects, some regions (e.g., sky) have very sparse events. Therefore, vanilla normalization can mislead the values of features to shift to the values of the regions without events. While reducing the difference in features between the two domains, we apply a normalization along the epipolar line to take into account the characteristics of events and stereo matching." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.56, + 0.468, + 0.709 + ], + "angle": 0, + "content": "Finally, we focus on the different motion of event cameras from the source and target domains, leading to a severe domain gap. Therefore, we present the motion-invariant consistency module to predict consistent disparity even if the camera motion changes to some extent. This module helps the network to adapt the target domain and also reduces the gap from camera motion. To the best of our knowledge, our work is the first attempt to move from unpaired image domain to event domain for stereo matching. Our main contributions are summarized as below:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.715, + 0.468, + 0.775 + ], + "angle": 0, + "content": "- Our work is the first that transfers the disparity estimation task from the rich image dataset with ground-truth to the event stream, resolving gaps between the different domains and input modalities." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.779, + 0.468, + 0.838 + ], + "angle": 0, + "content": "- We propose a novel adaptive event stereo network, ADES, containing the smudge-aware self-supervision module, feature normalization, and motion-invariant consistency module." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.841, + 0.468, + 0.899 + ], + "angle": 0, + "content": "- Extensive experiments demonstrate that the ADES framework achieves significantly better performance than the prior works in the adaptation ability between the different domains and modalities for event stereo." + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.715, + 0.468, + 0.899 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.09, + 0.65, + 0.107 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.115, + 0.819, + 0.132 + ], + "angle": 0, + "content": "2.1. Stereo depth estimation using Events" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.138, + 0.892, + 0.289 + ], + "angle": 0, + "content": "Recent event-based stereo matching [2,8,9,28,30,48,59] achieved the high accuracy than early works [5,7,20,35-37, 39,60,64,65] by adopting a learning-based approach with various embedding schemes. They propose additional modules that consider the temporal continuity of events, but the overall framework is similar to frame-based stereo: embedding, matching, and regularization modules. Our proposed pipeline of adaptive stereo matching also follows the general stereo matching, then can be easily applied on other event-based stereo networks." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.3, + 0.839, + 0.317 + ], + "angle": 0, + "content": "2.2. Domain Adaptation in Stereo Matching" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.323, + 0.892, + 0.459 + ], + "angle": 0, + "content": "To overcome the performance degradation from the domain gap, several works have explored unsupervised domain adaptation (UDA) in frame-based stereo matching. Some works utilize the knowledge distillation [14] and CycleGAN [23,62] to narrow the domain gap. After that, compact and efficient domain adaptation studies [33, 43, 47] for stereo have been conducted. On the other hand, the domain adaptation ability of event stereo networks has not been studied, and we tackle it for the first time." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.47, + 0.8, + 0.485 + ], + "angle": 0, + "content": "2.3. Adaptation from Images to Events" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.493, + 0.892, + 0.629 + ], + "angle": 0, + "content": "Event-to-image reconstruction methods [10, 27, 31, 34, 38, 42, 44, 50, 52, 53] can be considered the proxy task to transfer a labeled image domain (source) to an unlabeled event domain (target). The results of the event-to-image reconstruction have been used as inputs of end-task (e.g., object recognition, semantic segmentation) network pre-trained on image (source) domain. However, they introduce the extra latency in the inference time and still pose a domain gap between source and target domain." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.63, + 0.892, + 0.87 + ], + "angle": 0, + "content": "One of the attempts to properly do domain adaptation was grafted networks [17] by utilizing the pre-trained image network. They replaced the encoder of pre-trained network with event encoder, then finetuned it on paired event and image datasets. This setup takes advantage of each modalities, but requires pixel-wise aligned events and images. To overcome the limitation of paired setting, EvDistill [51] leveraged the unpaired images to boost the performance of event-based networks. Through the bidirectional modality reconstruction and cross-modal knowledge distillation, they can transfer the knowledge from image network to event network. After that, research on transferring from an unpaired image to event has been of continuous interest. EV-Transfer [26] hallucinate the motion to generate the fake events from still images. ESS [46] achieve the feature-level alignment with the motion-invariant event embeddings." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Existing works only focus on the tasks from a single camera (e.g., semantic segmentation, object recognition)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17798" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.102, + 0.093, + 0.87, + 0.317 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.326, + 0.896, + 0.385 + ], + "angle": 0, + "content": "Figure 2. Overview of the proposed ADES framework. During training, image datasets (e.g., KITTI) are used for the source domain, and event datasets without ground-truth are used for the target domain. We utilize feature normalization (Sec. 3.4) to narrow the gap between features from other domains. The proposed smudge-aware self-supervision module (Sec. 3.3) and motion-invariant consistency module (Sec. 3.5) are only used in training phase." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.399, + 0.475, + 0.492 + ], + "angle": 0, + "content": "Due to the novel characteristics of event cameras, high-quality large stereo datasets have recently appeared, so related research has yet to be studied. In this paper, we propose an employable ADES framework for an event stereo. Unlike the prior works, we consider the characteristics of the event in the specific situation of stereo matching." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.502, + 0.172, + 0.518 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.527, + 0.24, + 0.544 + ], + "angle": 0, + "content": "3.1. Problem Setting" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.549, + 0.47, + 0.69 + ], + "angle": 0, + "content": "Given consecutive stereo image pairs \\((I_l^{t - 1}, I_r^{t - 1})\\), \\((I_l^t, I_r^t)\\) with ground-truth disparity map \\(\\tilde{d}_l^t\\) on source domain, our goal is to train the model to predict the disparity map \\(D_l^{\\hat{t}}\\) at time \\(\\hat{t}\\) from stereo event streams \\(E_l^{\\hat{t}}\\), \\(E_r^{\\hat{t}}\\) on target event domain. To make it clear that the source and the target domains are unpaired, we denote time for the source domain as \\(t\\) and the target domain as \\(\\hat{t}\\). We represent an event stream as a voxel grid [63], the most commonly used representation, e.g., by converting \\(E_l^{\\hat{t}}\\) to \\(V_l^{\\hat{t}}\\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.697, + 0.248, + 0.712 + ], + "angle": 0, + "content": "3.2. System Overview" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.47, + 0.78 + ], + "angle": 0, + "content": "As shown in Fig. 2, our proposed Adaptive Dense Event Stereo (ADES) consists of three novel components: smudge-aware self-supervision module, feature normalization, and motion-invariant consistency module." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.471, + 0.902 + ], + "angle": 0, + "content": "For the source domain, we leverage the pre-trained video-to-event reconstruction network to extract the event representations from image data for the event-based stereo network. There are several video-to-event methods [11, 18], but among them, we adopt the network proposed in [61] that is lightweight and describes events well even with only two sequential images. Each left and right sequential image pairs are passed through the video-to-event net" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.399, + 0.895, + 0.569 + ], + "angle": 0, + "content": "work \\(\\mathcal{G}_{I\\to E}\\) and transformed into voxel grids as follows: \\(V_{l}^{t} = \\mathcal{G}_{I\\to E}(I_{l}^{t - 1},I_{l}^{t}),V_{r}^{t} = \\mathcal{G}_{I\\to E}(I_{r}^{t - 1},I_{r}^{t})\\) . The generated voxel grid pairs \\((V_{l}^{t},V_{r}^{t})\\) from the source domain and the voxel grid pairs \\((V_{l}^{\\hat{t}},V_{r}^{\\hat{t}})\\) from the target domain are simultaneously fed into a weight shared event-based stereo network. In the process, we narrow the gap between the two domains by normalizing the extracted features. The prediction of source domain \\(d_l^t\\) is supervised by ground-truth disparity \\(\\tilde{d}_l^t\\) , while the result of the target domain is adaptively optimized by the proposed smudge-aware self-supervision module and motion-invariant consistency module." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.575, + 0.893, + 0.592 + ], + "angle": 0, + "content": "3.3. Smudge-aware Self-supervision Module (SSM)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.893, + 0.81 + ], + "angle": 0, + "content": "Prior works [21,45,56] verified that self-supervised auxiliary tasks are helpful for domain adaptation, especially in stereo matching task [43]. We also utilize the photometric reconstruction as an auxiliary task of domain adaptation for stereo matching. First, as shown in the bottom of Fig. 3, we generate the image from voxel event representation in target domain. To this end, we leverage the widely used pretrained event-to-image reconstruction network [38]. However, the reconstructed image from event has intermittent artifacts near the boundary of an object. Those blurring and distortion effects, what we call a smudge, disturbs predicting sharp disparity. To estimate the irregular smudge in the target domain, we further design a self-supervision pipeline for smudge prediction in the source domain." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.895, + 0.903 + ], + "angle": 0, + "content": "In the source domain, as shown in the top of Fig. 3, we perturb the random region of image with distortion and blur kernel for imitating smudge effects. To depict realistic smudge effects, we do not generate the smudge on the randomly selected rectangle region but on the regions parsed by superpixel algorithm [1]. Since the edges of superpix" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "17799" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.087, + 0.089, + 0.457, + 0.307 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.31, + 0.47, + 0.368 + ], + "angle": 0, + "content": "Figure 3. Illustration of the Smudge-aware Self-supervision Module (SSM). To estimate the smudge artifact of the reconstructed image on the target domain, we train the smudge prediction network to predict the smudge in the source domain." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.38, + 0.468, + 0.517 + ], + "angle": 0, + "content": "els are generally placed on the boundary of an object, they can mimic the characteristics of the smudge effect caused at the boundary of the object due to the noisy sensors. Then, domain-shared smudge prediction network, which is a light-designed U-Net [40] with few convolution layers, is supervised from generated smudge mask. In other words, the output \\( M_{i}^{t} \\) of smudge prediction network is supervised from generated artifact mask \\( \\tilde{M}_{i}^{t} \\) by minimizing the binary cross entropy loss: \\( \\mathcal{L}_{\\text{source}}^{\\text{mask}} = \\sum_{i \\in \\{l,r\\}} BCE(M_{i}^{t}, \\tilde{M}_{i}^{t}) \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.518, + 0.468, + 0.702 + ], + "angle": 0, + "content": "In the target domain, as shown in the bottom of Fig. 3, we utilize a shared smudge prediction network from source domain for photometric-based self-supervision. The reconstructed left image \\(\\hat{I}_l^{\\hat{t}}\\) and right image \\(\\hat{I}_r^{\\hat{t}}\\) from voxels \\(V_l^{\\hat{t}}\\) and \\(V_r^{\\hat{t}}\\) are fed into the smudge prediction network. Then, smudge prediction network provides the predicted smudge map \\(M_l^{\\hat{t}}\\) and \\(M_r^{\\hat{t}}\\), which include per-pixel probability of smudge from 0 to 1. Next, from the predicted dense disparity map \\(D_l^{\\hat{t}}\\), we can reconstruct the warped left image \\(W_{r\\to l}(\\hat{I}_r^{\\hat{t}})\\) from right image \\(\\hat{I}_r^{\\hat{t}}\\). Considering the smudge mask maps of both left and right sides, we can calculate the pixel-wise photometric reconstruction error as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.091, + 0.712, + 0.468, + 0.767 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {\\text {t a r g e t}} ^ {\\text {r e c o n}} = \\alpha \\frac {1 - \\operatorname {S S I M} \\left(\\hat {I} _ {l} ^ {\\hat {t}} \\odot M ^ {\\hat {t}} , W _ {r \\rightarrow l} \\left(\\hat {I} _ {r} ^ {\\hat {t}}\\right) \\odot M ^ {\\hat {t}}\\right)}{2} \\tag {1} \\\\ + (1 - \\alpha) \\| \\hat {I} _ {l} ^ {\\hat {t}} \\odot M ^ {\\hat {t}} - W _ {r \\rightarrow l} (\\hat {I} _ {r} ^ {\\hat {t}}) \\odot M ^ {\\hat {t}} \\| _ {1}, \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.779, + 0.468, + 0.825 + ], + "angle": 0, + "content": "where \\( M^{\\hat{t}} = 1 - (M_{l}^{\\hat{t}} \\odot W_{r \\to l}(M_{r}^{\\hat{t}})) \\), \\( \\odot \\) means elementwise multiplication, SSIM denotes structural similarity proposed in [54] with a \\( 3 \\times 3 \\) kernel filter, and \\( \\alpha \\) is set to 0.85." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Our proposed smudge prediction network is shared in the source and target domains with the same weights. Compared to the stereo network, which is a high-level task, the smudge prediction, which pixel-wisely finds regions of noise and smudge, is a low-level task and less affected by" + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.089, + 0.693, + 0.204 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.567, + 0.205, + 0.62, + 0.215 + ], + "angle": 0, + "content": "(a) Source" + }, + { + "type": "image", + "bbox": [ + 0.696, + 0.089, + 0.888, + 0.204 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.763, + 0.205, + 0.813, + 0.215 + ], + "angle": 0, + "content": "(b) Target" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.219, + 0.892, + 0.289 + ], + "angle": 0, + "content": "Figure 4. Visualization of voxel grids and features extracted by the event stereo network from source (e.g., KITTI) and target (e.g., DSEC) domain. In the upper region of features with few events, there are no activated pixels; in contrast, there are many activated pixels in the lower region with a lot of structure for events." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.305, + 0.892, + 0.351 + ], + "angle": 0, + "content": "the domain gaps. Therefore, in the target domain, artifacts in the boundary are well predicted in the reconstructed image to estimate the sharp disparity through self-supervision." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.363, + 0.71, + 0.377 + ], + "angle": 0, + "content": "3.4. Feature Normalization" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.387, + 0.892, + 0.522 + ], + "angle": 0, + "content": "We adopt the feature-level normalization to reduce the gap in the cost volume between two distinct domains. To align the distributions between different domains, the feature normalization [29,49,58] is widely used for image data. Similarly, event features can be also normalized to reduce the gap between the two domains; however, as can be seen in our experimental results (see Table 5), due to the sparsity of the event data, an existing normalization technique [43] for images rather hinders learning of event-based network." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.524, + 0.893, + 0.902 + ], + "angle": 0, + "content": "For event feature normalization, we focus on the characteristics of event-based stereo matching. Events are naturally sparse and triggered predominantly to the edges of the objects. For accurate prediction with sparse information, event stereo networks tend to focus intensely on areas with event information, which leads to features of areas without events not being activated. Therefore, normalizing over all pixels provides results with shifted bias on the region without an event for each scene. Instead, we focus on the correlation between the amount of events and spatial positions. For example, events rarely occur in the upper regions (e.g., sky), while more events occur in the lower regions where illuminance easily changes and rich textures exist (e.g., building). This phenomenon can be qualitatively verified by the extracted features of the network, as shown in Fig. 4. The lower region of the feature map is strongly activated in both domains, while the upper region, where no event occurs, is hardly activated. Therefore, applying the normalization over all pixels used in the dense image [43] to event stereo rather hinders reducing the domain gaps. In addition, since the stereo disparity is defined as the position difference in the horizontal direction when the cameras are rectified, normalization over all spatial positions leads to ambiguity in accurate matching. Therefore, we propose a strategy to normalize the feature along the epipolar (hori" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17800" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.097, + 0.092, + 0.452, + 0.281 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.284, + 0.47, + 0.327 + ], + "angle": 0, + "content": "Figure 5. Illustration of the Motion-invariant Consistency Module (MCM). Normalize over time denotes to converting temporal values into a range between 0 and 1." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.345, + 0.469, + 0.39 + ], + "angle": 0, + "content": "zontal) line, which does not violate the regularity according to regions. This normalization is also spatial but less dependent on the global distribution of event data." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.39, + 0.469, + 0.496 + ], + "angle": 0, + "content": "We modify the parameter-free normalization scheme proposed in prior works [43]. Given extracted feature \\(F\\) from network with size of \\(C \\times H \\times W\\) (\\(C\\): channel, \\(H\\): height, \\(W\\): width), let \\(F(k,i,j)\\) denotes kij-th element, where \\(k\\) is the index of channel and \\(i,j\\) are spatial dimensions. Then, we apply the normalization along channel-dimension to both left and right features as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.136, + 0.505, + 0.469, + 0.548 + ], + "angle": 0, + "content": "\\[\nF (k, i, j) = \\frac {F (k , i , j)}{\\sqrt {\\sum_ {c = 0} ^ {C - 1} \\| F (c , i , j) \\| ^ {2} + \\varepsilon}}. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.557, + 0.47, + 0.587 + ], + "angle": 0, + "content": "After that, we apply the normalization along the epipolar line, which is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.132, + 0.595, + 0.469, + 0.638 + ], + "angle": 0, + "content": "\\[\nF (k, i, j) = \\frac {F (k , i , j)}{\\sqrt {\\sum_ {w = 0} ^ {W - 1} \\| F (k , i , w) \\| ^ {2} + \\varepsilon}}. \\tag {3}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.646, + 0.469, + 0.663 + ], + "angle": 0, + "content": "3.5. Motion-invariant Consistency Module (MCM)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.669, + 0.469, + 0.79 + ], + "angle": 0, + "content": "The motivation of the motion-invariant consistency module on the target domain is two-folds. The first is to resolve the domain gap caused by different camera motion. Second, we desire the event stereo network to be robust on perturbation or noise, adapting to the target domain. The perfectly adapted network should be able invariant to the motion of event camera and estimate the prediction stably, even if there is some perturbation in the input." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.791, + 0.47, + 0.902 + ], + "angle": 0, + "content": "In this subsection, we denote the voxel grid corresponding to the events \\( E^{\\hat{t},T} \\) accumulated during time \\( T \\) until \\( \\hat{t} \\) as \\( V^{\\hat{t},T} \\). Specifically, events are converted to a voxel grid pair \\( V_{l}^{\\hat{t},T}, V_{r}^{\\hat{t},T} \\), and fed to the network to estimate a disparity map \\( D_{l}^{\\hat{t}} \\). Since the motion in the datasets is already acquired and immutable, we use a trick to augment event streams of fast or slow motions with temporal perturbation \\( \\tau \\). If events" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.893, + 0.309 + ], + "angle": 0, + "content": "are stacked for a longer time \\( T + \\tau \\) (i.e., more events) after normalizing temporal value in events (converting temporal values into a range between 0 and 1) and converted for the same bin of voxel grid, it is able to imitate the voxel grid of an event from an actual fast motion. Conversely, if stacked for a shorter time \\( T - \\tau \\) (i.e., fewer events), it is the same as the voxel grid made with events of slow motion. From this, we can generate a motion perturbed event voxel \\( V^{\\hat{t},\\hat{T}} \\), where \\( \\hat{T} = T \\pm \\tau \\) without additional data acquisition. As shown in Fig. 5, perturbed voxel pairs \\( V_{l}^{\\hat{t},\\hat{T}}, V_{r}^{\\hat{t},\\hat{T}} \\) are fed into the event stereo network to predict the perturbed disparity map \\( \\tilde{D}_{l}^{\\hat{t}} \\). Then, for pixel-wise consistency between the prediction of motion-perturbed input and the original input, our consistency loss is defined via \\( L_{1} \\) distance:" + }, + { + "type": "equation", + "bbox": [ + 0.6, + 0.319, + 0.892, + 0.342 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {t a r g e t}} ^ {\\text {c o n s i s t e n c y}} = \\| D _ {l} ^ {\\hat {t}} - \\tilde {D} _ {l} ^ {\\hat {t}} \\| _ {1} \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.351, + 0.892, + 0.382 + ], + "angle": 0, + "content": "More details about the implementation of motion-invariant consistency module can be seen in supple." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.392, + 0.649, + 0.406 + ], + "angle": 0, + "content": "3.6. Loss functions" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.415, + 0.892, + 0.492 + ], + "angle": 0, + "content": "On the source domain, we use the two losses for training the network. We adopt the smooth \\(L_{1}\\) loss for disparity estimation: \\(\\mathcal{L}_{source}^{task} = \\mathrm{smooth}_{L_1}(\\tilde{d}_l^t -d_l^t)\\), and the binary cross entropy loss for artifact prediction: \\(\\mathcal{L}_{source}^{mask} = \\sum_{i\\in \\{l,r\\}}BCE(M_i^t,\\tilde{M}_i^t)\\)." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.491, + 0.891, + 0.522 + ], + "angle": 0, + "content": "On the target domain, we use the reconstruction loss \\(\\mathcal{L}_{\\text {target }}^{\\text {recon }}\\) (Eq. 1) and consistency loss \\(\\mathcal{L}_{\\text {target }}^{\\text {consistency }}\\) (Eq. 4)." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.522, + 0.891, + 0.551 + ], + "angle": 0, + "content": "Finally, the total loss for an end-to-end optimization process is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.544, + 0.56, + 0.891, + 0.587 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} ^ {\\text {t o t a l}} = \\mathcal {L} _ {\\text {s o u r c e}} ^ {\\text {t a s k}} + \\lambda_ {1} \\mathcal {L} _ {\\text {s o u r c e}} ^ {\\text {m a s k}} + \\lambda_ {2} \\mathcal {L} _ {\\text {t a r g e t}} ^ {\\text {r e c o n}} + \\tag {5}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.741, + 0.583, + 0.846, + 0.601 + ], + "angle": 0, + "content": "\\[\n\\lambda_ {3} \\mathcal {L} _ {\\text {t a r g e t}} ^ {\\text {c o n s i s t e n c y}},\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.612, + 0.842, + 0.627 + ], + "angle": 0, + "content": "where \\(\\lambda_1, \\lambda_2\\) and \\(\\lambda_3\\) are weight for each loss terms." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.641, + 0.634, + 0.658 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.666, + 0.603, + 0.681 + ], + "angle": 0, + "content": "4.1. Datasets" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.892, + 0.81 + ], + "angle": 0, + "content": "For source domain datasets, we utilize the KITTI dataset [25] and the SceneFlow dataset [24]. The KITTI dataset is a real-world dataset with two subsets (i.e. KITTI 2012 [13] and KITTI 2015 [25]), containing 394 stereo images with sparse ground-truth for training. On the other hand, the SceneFlow dataset [24] is a large synthetic dataset containing diverse scenes. The SceneFlow dataset provides 35k stereo images with dense ground-truth disparity maps." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.902 + ], + "angle": 0, + "content": "For target domain, we use the recently published benchmark dataset of DSEC [12], a large-scale high-quality driving dataset with challenging scenes. DSEC provides high-resolution \\((640\\times 480)\\) stereo event streams captured in outdoor driving scenes. It contains 53 driving scenarios taken in various lighting conditions, and provides 17k stereo pairs" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "17801" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.895, + 0.133 + ], + "angle": 0, + "content": "Table 1. Cross-domain comparisons with other traditional / domain generalization / domain adaptation stereo methods from various source domains. The 2-pixel error \\((\\%)\\), 3-pixel error \\((\\%)\\), end-point-error, and root mean square error are adopted for evaluation. Zu and In denote the Zurich City and Interlaken sequences, respectively." + }, + { + "type": "table", + "bbox": [ + 0.108, + 0.136, + 0.86, + 0.381 + ], + "angle": 0, + "content": "
KITTI-to-DSECSceneFlow-to-DSEC
Method2PE3PEEPERMSE2PE3PEEPERMSE
ZuInZuInZuInZuInZuInZuInZuIn
E2VID [38] on target domain
SGM [16]53.755.347.749.79.310.116.117.053.755.347.749.79.310.1
GwcNet [15]38.237.129.122.03.52.98.25.843.345.028.831.23.04.2
PSMNet [6]36.535.525.924.13.42.96.05.136.439.724.329.62.65.4
AANet [55]46.339.335.326.37.43.817.28.642.839.229.227.33.63.1
DSMNet [58]41.141.630.432.13.24.25.68.146.645.331.230.64.13.7
StereoGAN [23]70.968.866.463.111.49.813.312.273.272.268.073.115.413.4
EventGAN [61] on source domain
GwcNet [15]25.527.319.816.84.63.112.29.155.156.337.237.17.47.3
PSMNet [6]18.920.511.913.64.22.714.810.448.850.635.037.86.85.8
AANet [55]50.447.342.538.69.85.421.711.358.855.445.342.45.75.8
DSMNet [58]18.823.610.512.62.12.44.56.751.252.344.643.26.25.9
StereoGAN [23]61.460.352.850.715.313.718.918.975.271.765.566.313.310.6
ADES (Ours)
AANet13.819.97.19.81.41.72.73.422.324.911.113.91.61.9
PSMNet10.910.25.65.51.21.32.53.217.512.89.46.71.41.3
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.396, + 0.473, + 0.503 + ], + "angle": 0, + "content": "for training. Following the previous image-to-event transfer tasks for segmentation [46], we adopt sequences acquired during the day with monotonous illuminance, called Zurich City. Furthermore, we also conduct experiments on Interlaken sequences containing the high dynamic range and challenging illuminance scenes. More details about a split of datasets are provided in the supple." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.511, + 0.294, + 0.527 + ], + "angle": 0, + "content": "4.2. Implementation details" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.535, + 0.471, + 0.643 + ], + "angle": 0, + "content": "The weights \\(\\lambda_{1}, \\lambda_{2}\\) and \\(\\lambda_{3}\\) are set as 0.3, 1, and 0.2, respectively. We train our end-to-end framework using the Adam optimizer [19]. We set the learning rate to \\(1 \\times 10^{-3}\\) with a batch size of 8 using \\(384 \\times 336\\) random crops. To generate the artifacts in Sec. 3.3, we utilize the Blur and OpticalDistortion transforms from library [4]. More details are provided in supple." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.651, + 0.377, + 0.667 + ], + "angle": 0, + "content": "4.3. Comparisons with Other Methods" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.675, + 0.471, + 0.901 + ], + "angle": 0, + "content": "We compare our proposed ADES framework with the other traditional algorithm (SGM [16]), domain generalization (DSMNet [58]), and domain adaptation (StereoGAN [23]). In addition, we evaluate PSMNet [6], GwcNet [15], and AANet [55], which have achieved comparable performance in stereo matching. We train those networks in the source domain and test the network in the target domain. To align the different modalities between the source and target domains, we utilize E2VID [38] or EventGAN [61]. In the case of E2VID, an image-based stereo network is trained using a grayscale image in the source domain, and when testing, events in the target domain are reconstructed into a gray image using E2VID. Conversely, in the case of EventGAN, the event-based stereo network is trained using the events, which are converted by EventGAN from consecu" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.395, + 0.895, + 0.547 + ], + "angle": 0, + "content": "tive images in the source domain. We evaluate the proposed framework by applying it to AANet and PSMNet, which can represent networks using 3D and 4D cost volumes. Especially, AANet is efficient, so it is a widely adopted structure in recent event stereo research [28, 30]. When training, the proposed modules are used, but when evaluating, all the proposed modules without normalization are removed, and only the event stereo network is used to predict the disparity. Table 1 shows the results of training on the various source dataset, such as KITTI and SceneFlow datasets." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.55, + 0.895, + 0.838 + ], + "angle": 0, + "content": "KITTI-to-DSEC. Even if the networks are trained on the source domain, the results of networks using the events from EventGAN can not achieve high performance. Some networks (PSMNet, GwcNet, and AANet) do not have the ability of domain generalization and adaptation. In addition, the distribution gap of disparity and motion between the domains lead to further degradation of performance. Similarly, most of the results using reconstructed images with E2VID do not show comparable performance. The reconstructed image on the target domain has a large gap with the real image on the source domain, which cannot be dealt with generalization (DSMNet), adaptation (StereoGAN) and conventional methods (SGM). Compared with existing works, our network achieves significantly high performance, considering the gap between domains such as motions and disparity. It is noticeable that in case of AANet+ADES, the performance improvement is significant, e.g., 2PE decreases from 50.4 to 13.8, and RMSE decreases from 21.7 to 2.7 in Zurich City sequence." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.895, + 0.903 + ], + "angle": 0, + "content": "SceneFlow-to-DSEC. The experiment results trained on the synthetic source domain show a more significant domain gap. Due to the effect of the syn-to-real gap, prior works show significantly lower performance than those" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "17802" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.095, + 0.089, + 0.872, + 0.356 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.357, + 0.895, + 0.387 + ], + "angle": 0, + "content": "Figure 6. Qualitative results for the proposed method with other methods. Compared to EventGAN [61] and E2VID [38], our method can predict accurate and sharp disparity maps." + }, + { + "type": "table_caption", + "bbox": [ + 0.14, + 0.398, + 0.408, + 0.41 + ], + "angle": 0, + "content": "Table 2. Results on DSEC benchmark testset" + }, + { + "type": "table", + "bbox": [ + 0.098, + 0.413, + 0.447, + 0.509 + ], + "angle": 0, + "content": "
MethodSupervisionRMSE ↓MAE ↓1PE ↓2PE ↓
[48]✓1.3860.57610.922.91
[28]✓1.2220.5299.962.65
[30]✓1.2310.5199.582.62
[59]✓1.2640.5279.522.36
Ours (PSM)1.6980.77118.375.36
Ours (AA)1.9820.93624.017.87
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.519, + 0.47, + 0.7 + ], + "angle": 0, + "content": "trained on KITTI datasets, e.g., 2PE of PSMNet using EventGAN significantly increases from 20.5 to 50.6 in the Interlaken sequence. Although our proposed method cannot avoid the performance degradation, the decreasing amount is relatively acceptable, e.g., 2PE of PSMNet+ADES increases from 10.2 to 12.8 in the Interlaken sequence. Furthermore, the performance increases in some metrics thanks to the various scenes in the synthetic dataset, e.g., RMSE of PSMNet+ADES decreases from 3.2 to 2.8 in the Interlaken sequence. These results show that our method can be used universally and not limited to a specific source dataset, whether synthetic or real-world." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.701, + 0.47, + 0.822 + ], + "angle": 0, + "content": "In Fig. 6, we provide qualitative comparisons of our method with other methods. E2VID or EventGAN can reduce the gap between modality, but it cannot bridge between domains. On the other hand, our ADES framework predicts sharp and accurate disparity on both AANet and PSMNet. These results demonstrate that our training pipeline resolves the gaps from both domain and modality. More qualitative comparisons are provided in supple." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.832, + 0.337, + 0.847 + ], + "angle": 0, + "content": "4.4. Results on DSEC test dataset" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.47, + 0.901 + ], + "angle": 0, + "content": "To compare with supervised methods, we utilize the KITTI dataset, which contains ground-truth, as the source domain and the full DSEC train dataset, which lacks" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.397, + 0.892, + 0.454 + ], + "angle": 0, + "content": "Table 3. Ablation studies for sub-modules: Smudge-aware Self-supervision Module (SSM), Feature Normalization (FN), and Motion-invariant Consistency Module (MCM). \\(D1\\)-error \\((\\%)\\) is adopted." + }, + { + "type": "table", + "bbox": [ + 0.503, + 0.457, + 0.892, + 0.643 + ], + "angle": 0, + "content": "
ModelSSMFNMCMZurichInterlaken
AANet35.226.3
✓33.124.5
✓29.622.7
✓13.315.1
✓✓11.214.6
✓✓8.110.2
✓✓✓7.09.7
PSMNet15.617.2
✓13.816.1
✓13.115.5
✓7.38.9
✓✓6.67.1
✓✓6.06.2
✓✓✓5.65.7
" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.657, + 0.892, + 0.718 + ], + "angle": 0, + "content": "ground-truth, as the target domain. Table 2 demonstrates that despite not relying on ground-truth data for the target domain, our approach achieves comparable performance to other supervised methods." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.727, + 0.665, + 0.741 + ], + "angle": 0, + "content": "4.5. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Effectiveness of each components. In Table 3, we conduct the ablation studies to validate the effectiveness of each component. We set the KITTI and DSEC dataset as source and target domain, respectively. Based on AANet and PSMNet from which all proposed modules were removed, the performance was measured while adding the proposed module one by one. The SSM achieves the greatest performance gain as a unitary component, e.g., reducing error rates by \\(21.9\\%\\) on Zurich, and \\(11.2\\%\\) on Interlaken from AANet. In addition, using FN stand-alone reduces the" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17803" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.47, + 0.118 + ], + "angle": 0, + "content": "Table 4. Comparison of results with and without smudge prediction. \\(D1\\)-error \\((\\%)\\) is adopted." + }, + { + "type": "table", + "bbox": [ + 0.084, + 0.124, + 0.468, + 0.17 + ], + "angle": 0, + "content": "
MethodsZurichInterlaken
w/o Smudge Prediction16.112.3
w/ Smudge Prediction7.09.7
" + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.173, + 0.468, + 0.292 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.303, + 0.468, + 0.331 + ], + "angle": 0, + "content": "Figure 7. Qualitative results of disparity predictions with and without smudge prediction." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.353, + 0.468, + 0.504 + ], + "angle": 0, + "content": "error by \\(1.7\\% \\sim 5.6\\%\\) depending on the target domain and model, compared to the baseline. Similarly, MCM also reduces the error by \\(1.1\\% \\sim 2.1\\%\\). These FN and MCM work even if implemented together with SSM, e.g., compared to the case of using only SSM from AANet in Zurich, when FN and MCM are used together, errors are more reduced by \\(5.2\\%\\) and \\(2.1\\%\\), respectively. Finally, the performance gain is the most significant when all of the proposed modules are used, and these results validate that all modules are effective for domain adaptation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.506, + 0.468, + 0.822 + ], + "angle": 0, + "content": "Effectiveness of smudge predictions. We investigate the effect of the proposed smudge prediction on SSM. Using the KITTI as the source domain, the quantitative and qualitative results with and without smudge prediction from AANet are shown in Table 4 and Fig. 7. Compared with the absence of smudge prediction, our method utilizes the photometric loss of image reconstruction effectively. Therefore, through SSM using smudge prediction, the performance of the disparity estimation is improved e.g., the \\(D1\\)-error decreases from 16.1 to 7.0 in Zurich City sequence. Specifically, as can be seen in Fig. 7, smudge prediction helps the network to robustly infer the boundary of an object, making a sharp disparity map. We visualize the smudge mask in Fig. 8 to show how smudge masks can aid effective learning in SSM. As shown in 1st row of Fig. 8, when an image is reconstructed from an event via E2VID, smudge-like blurry artifacts appear around the boundary of the object due to the noisy nature of the event streams. Our smudge prediction estimates these artifacts regions, helping to sharpen disparity when performing self-supervision and boosting the performance of disparity estimation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Comparison of normalization. Table 5 reports the comparison of our feature normalization with the existing learning-free normalization method [43]. We set the KITTI dataset as the source domain and the model to AANet. Although our epipolar norm is a modified module of the ex" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.089, + 0.892, + 0.118 + ], + "angle": 0, + "content": "Table 5. Comparison of epipolar norm with existing cost norm [43]. \\(D1\\)-error \\((\\%)\\) is adopted." + }, + { + "type": "table", + "bbox": [ + 0.507, + 0.123, + 0.88, + 0.182 + ], + "angle": 0, + "content": "
MethodsZurichInterlaken
w/o Norm11.214.6
Cost Norm [43]12.311.1
Our Epipolar Norm7.09.7
" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.186, + 0.884, + 0.305 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.308, + 0.892, + 0.337 + ], + "angle": 0, + "content": "Figure 8. Generated smudge mask on the target domain. Top: reconstructed images, Bottom: corresponding smudge mask." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.349, + 0.892, + 0.546 + ], + "angle": 0, + "content": "isting work, the results verify that it is more effective for the domain adaptation ability of event stereo matching. For example, in the case of [43], which performs the normalization along all pixels in spatial manners, the performance is rather reduced due to the specificity of event stereo. For example, especially in Zurich City, the \\(D1\\)-error increases from 11.2 to 12.3 after introducing the cost norm [43]. On the other hand, our epipolar norm shows a performance improvement in both sequences. From these results, we can confirm that the event stereo network requires a different approach than the existing normalization method, and our normalization is suitable for the domain adaptive event stereo matching." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.559, + 0.619, + 0.574 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.584, + 0.892, + 0.826 + ], + "angle": 0, + "content": "In this paper, we propose a novel framework, ADES, for adaptive dense event stereo from the image domain. Our work is the first that transfers the disparity estimation task from the rich image dataset with ground-truth to the event stream to tackle the absence of ground-truth disparities on the target event domain. To this end, we propose the smudge-aware self-supervision module, feature normalization, and motion-invariant consistency module by focusing on the specificity of event stereo. Extensive experiments demonstrate our framework achieves remarkable performance on both 3D and 4D cost volume networks, whether the source domain is synthetic or real-world image dataset. Furthermore, these results demonstrate that our modules can be used universally in existing event stereo networks. We open up the possibility of using event stereo in domains without ground-truth and expect more future work." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Acknowledgements. This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (NRF-2022R1A2B5B03002636)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17804" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.175, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.185 + ], + "angle": 0, + "content": "[1] Radhakrishna Achanta, Appu Shaji, Kevin Smith, Aurelien Lucchi, Pascal Fua, and Sabine Süssrunk. Slic superpixels compared to state-of-the-art superpixel methods. IEEE transactions on pattern analysis and machine intelligence, 34(11):2274-2282, 2012. 3" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.187, + 0.472, + 0.256 + ], + "angle": 0, + "content": "[2] Soikat Hasan Ahmed, Hae Woong Jang, SM Nadim Uddin, and Yong Ju Jung. 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Conf.(BMVC), volume 1, 2017. 2" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17807" + } + ] +] \ No newline at end of file diff --git a/2023/Learning Adaptive Dense Event Stereo From the Image Domain/4f451359-7481-4ea3-a57c-f3f3dbdd863e_origin.pdf b/2023/Learning Adaptive Dense Event Stereo From the Image Domain/4f451359-7481-4ea3-a57c-f3f3dbdd863e_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..be8a04c38414402f405d0660bd5d72cb2cad7f6c --- /dev/null +++ b/2023/Learning Adaptive Dense Event Stereo From the Image Domain/4f451359-7481-4ea3-a57c-f3f3dbdd863e_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:1bb65323bae1fafc0455ac09d451729119a767628b00511ae0d0bc8587ab19c4 +size 2991203 diff --git a/2023/Learning Adaptive Dense Event Stereo From the Image Domain/full.md b/2023/Learning Adaptive Dense Event Stereo From the Image Domain/full.md new file mode 100644 index 0000000000000000000000000000000000000000..8f1f712a84334c6757ee980df4be086cb4431dd4 --- /dev/null +++ b/2023/Learning Adaptive Dense Event Stereo From the Image Domain/full.md @@ -0,0 +1,310 @@ +# Learning Adaptive Dense Event Stereo from the Image Domain + +Hoonhee Cho, Jegyeong Cho, and Kuk-Jin Yoon Visual Intelligence Lab., KAIST, Korea + +{gnsgnsgml，j2k0618，kjyoon}@kaist.ac.kr + +# Abstract + +Recently, event-based stereo matching has been studied due to its robustness in poor light conditions. However, existing event-based stereo networks suffer severe performance degradation when domains shift. Unsupervised domain adaptation (UDA) aims at resolving this problem without using the target domain ground-truth. However, traditional UDA still needs the input event data with ground-truth in the source domain, which is more challenging and costly to obtain than image data. To tackle this issue, we propose a novel unsupervised domain Adaptive Dense Event Stereo (ADES), which resolves gaps between the different domains and input modalities. The proposed ADES framework adapts event-based stereo networks from abundant image datasets with ground-truth on the source domain to event datasets without ground-truth on the target domain, which is a more practical setup. First, we propose a self-supervision module that trains the network on the target domain through image reconstruction, while an artifact prediction network trained on the source domain assists in removing intermittent artifacts in the reconstructed image. Secondly, we utilize the feature-level normalization scheme to align the extracted features along the epipolar line. Finally, we present the motion-invariant consistency module to impose the consistent output between the perturbed motion. Our experiments demonstrate that our approach achieves remarkable results in the adaptation ability of event-based stereo matching from the image domain. + +# 1. Introduction + +Stereo matching [22, 41] is one of the most widely used methods for obtaining 3D information by establishing correspondences between stereo images. With considerable interest, learning-based stereo methods have achieved state-of-the-art performance in many benchmark datasets. However, some challenges in stereo matching still exist due to the shortcoming of sensors (e.g., low dynamic range, motion blur due to large exposure time). Event cameras [3] are novel sensors that asynchronously report per-pixel changes of intensity by imitating the human eye. Thanks + +![](images/49f92d8a3f5c46925bb5fe98416149495a78917d7d00a05075a11f97d3f3731e.jpg) +Figure 1. The proposed ADES framework for adaptive dense event stereo network. ADES aims to exploit the existing frame-based stereo dataset for learning the event stereo network. + +to the high dynamic range and low latency, the event camera can be considered as a promising sensor for depth estimation, especially in driving scenarios. Recent works [2,8,9,28,30,48,59] have attempted to utilize event cameras for stereo matching even under poor light conditions. + +Despite advances in event stereo, most prior works [9, 28, 48] still experience a significant degradation in performance when domains shift. Unsupervised domain adaptation (UDA) can resolve this problem without using the target domain ground-truth. When UDA is applied for event stereo domain adaptation, it still needs the input event data with ground-truth in the source domain. However, as mentioned in [32], accurate synchronization of events with high temporal resolution and other devices (e.g., Li-DAR) requires additional hardware and post-processing, so it is more challenging to obtain accurate ground truth than images. In this paper, we draw attention to large image datasets with ground-truth, which are easily accessible (e.g., DrivingStereo [57], SceneFlow [24] and KITTI [25]). In this setup, abundant image data from diverse environments helps the event stereo network improve generalizability with high performance. To this end, as shown in + +Fig. 1, we propose a novel Adaptive Dense Event Stereo (ADES), which adapts the stereo network from the source domain having image data with ground-truth to the target domain having event data without ground-truth. ADES resolves gaps between the different domains and input modalities. + +The proposed ADES framework consists of three components: smudge-aware self-supervision module, feature normalization, and motion-invariant consistency module. The proposed smudge-aware self-supervision module leverages dense traits of images via image reconstruction on the event target domain. Image reconstruction using only the event is often interrupted by blurry artifacts, what we call a smudge, so the network cannot estimate the sharp and accurate disparity map. To predict the smudge effect in the target domain, we design the self-supervision pipeline on the source image domain to estimate and suppress the artifact area in the reconstructed image on the target domain. + +In addition, we exploit the feature normalization before generating the cost volume. Normalization scheme [29, 43, 49, 58] was generally used in the domain adaptation between the image modalities. However, due to the characteristics of the event, it is not efficient to normalize over the entire pixel area. Since most of the events are triggered around an edge of objects, some regions (e.g., sky) have very sparse events. Therefore, vanilla normalization can mislead the values of features to shift to the values of the regions without events. While reducing the difference in features between the two domains, we apply a normalization along the epipolar line to take into account the characteristics of events and stereo matching. + +Finally, we focus on the different motion of event cameras from the source and target domains, leading to a severe domain gap. Therefore, we present the motion-invariant consistency module to predict consistent disparity even if the camera motion changes to some extent. This module helps the network to adapt the target domain and also reduces the gap from camera motion. To the best of our knowledge, our work is the first attempt to move from unpaired image domain to event domain for stereo matching. Our main contributions are summarized as below: + +- Our work is the first that transfers the disparity estimation task from the rich image dataset with ground-truth to the event stream, resolving gaps between the different domains and input modalities. +- We propose a novel adaptive event stereo network, ADES, containing the smudge-aware self-supervision module, feature normalization, and motion-invariant consistency module. +- Extensive experiments demonstrate that the ADES framework achieves significantly better performance than the prior works in the adaptation ability between the different domains and modalities for event stereo. + +# 2. Related Works + +# 2.1. Stereo depth estimation using Events + +Recent event-based stereo matching [2,8,9,28,30,48,59] achieved the high accuracy than early works [5,7,20,35-37, 39,60,64,65] by adopting a learning-based approach with various embedding schemes. They propose additional modules that consider the temporal continuity of events, but the overall framework is similar to frame-based stereo: embedding, matching, and regularization modules. Our proposed pipeline of adaptive stereo matching also follows the general stereo matching, then can be easily applied on other event-based stereo networks. + +# 2.2. Domain Adaptation in Stereo Matching + +To overcome the performance degradation from the domain gap, several works have explored unsupervised domain adaptation (UDA) in frame-based stereo matching. Some works utilize the knowledge distillation [14] and CycleGAN [23,62] to narrow the domain gap. After that, compact and efficient domain adaptation studies [33, 43, 47] for stereo have been conducted. On the other hand, the domain adaptation ability of event stereo networks has not been studied, and we tackle it for the first time. + +# 2.3. Adaptation from Images to Events + +Event-to-image reconstruction methods [10, 27, 31, 34, 38, 42, 44, 50, 52, 53] can be considered the proxy task to transfer a labeled image domain (source) to an unlabeled event domain (target). The results of the event-to-image reconstruction have been used as inputs of end-task (e.g., object recognition, semantic segmentation) network pre-trained on image (source) domain. However, they introduce the extra latency in the inference time and still pose a domain gap between source and target domain. + +One of the attempts to properly do domain adaptation was grafted networks [17] by utilizing the pre-trained image network. They replaced the encoder of pre-trained network with event encoder, then finetuned it on paired event and image datasets. This setup takes advantage of each modalities, but requires pixel-wise aligned events and images. To overcome the limitation of paired setting, EvDistill [51] leveraged the unpaired images to boost the performance of event-based networks. Through the bidirectional modality reconstruction and cross-modal knowledge distillation, they can transfer the knowledge from image network to event network. After that, research on transferring from an unpaired image to event has been of continuous interest. EV-Transfer [26] hallucinate the motion to generate the fake events from still images. ESS [46] achieve the feature-level alignment with the motion-invariant event embeddings. + +Existing works only focus on the tasks from a single camera (e.g., semantic segmentation, object recognition). + +![](images/97eece041d0e691718804bf67a51bb9048c3c4d7242c5688f99716822c767ec9.jpg) +Figure 2. Overview of the proposed ADES framework. During training, image datasets (e.g., KITTI) are used for the source domain, and event datasets without ground-truth are used for the target domain. We utilize feature normalization (Sec. 3.4) to narrow the gap between features from other domains. The proposed smudge-aware self-supervision module (Sec. 3.3) and motion-invariant consistency module (Sec. 3.5) are only used in training phase. + +Due to the novel characteristics of event cameras, high-quality large stereo datasets have recently appeared, so related research has yet to be studied. In this paper, we propose an employable ADES framework for an event stereo. Unlike the prior works, we consider the characteristics of the event in the specific situation of stereo matching. + +# 3. Method + +# 3.1. Problem Setting + +Given consecutive stereo image pairs $(I_l^{t - 1}, I_r^{t - 1})$ , $(I_l^t, I_r^t)$ with ground-truth disparity map $\tilde{d}_l^t$ on source domain, our goal is to train the model to predict the disparity map $D_l^{\hat{t}}$ at time $\hat{t}$ from stereo event streams $E_l^{\hat{t}}$ , $E_r^{\hat{t}}$ on target event domain. To make it clear that the source and the target domains are unpaired, we denote time for the source domain as $t$ and the target domain as $\hat{t}$ . We represent an event stream as a voxel grid [63], the most commonly used representation, e.g., by converting $E_l^{\hat{t}}$ to $V_l^{\hat{t}}$ . + +# 3.2. System Overview + +As shown in Fig. 2, our proposed Adaptive Dense Event Stereo (ADES) consists of three novel components: smudge-aware self-supervision module, feature normalization, and motion-invariant consistency module. + +For the source domain, we leverage the pre-trained video-to-event reconstruction network to extract the event representations from image data for the event-based stereo network. There are several video-to-event methods [11, 18], but among them, we adopt the network proposed in [61] that is lightweight and describes events well even with only two sequential images. Each left and right sequential image pairs are passed through the video-to-event net + +work $\mathcal{G}_{I\to E}$ and transformed into voxel grids as follows: $V_{l}^{t} = \mathcal{G}_{I\to E}(I_{l}^{t - 1},I_{l}^{t}),V_{r}^{t} = \mathcal{G}_{I\to E}(I_{r}^{t - 1},I_{r}^{t})$ . The generated voxel grid pairs $(V_{l}^{t},V_{r}^{t})$ from the source domain and the voxel grid pairs $(V_{l}^{\hat{t}},V_{r}^{\hat{t}})$ from the target domain are simultaneously fed into a weight shared event-based stereo network. In the process, we narrow the gap between the two domains by normalizing the extracted features. The prediction of source domain $d_l^t$ is supervised by ground-truth disparity $\tilde{d}_l^t$ , while the result of the target domain is adaptively optimized by the proposed smudge-aware self-supervision module and motion-invariant consistency module. + +# 3.3. Smudge-aware Self-supervision Module (SSM) + +Prior works [21,45,56] verified that self-supervised auxiliary tasks are helpful for domain adaptation, especially in stereo matching task [43]. We also utilize the photometric reconstruction as an auxiliary task of domain adaptation for stereo matching. First, as shown in the bottom of Fig. 3, we generate the image from voxel event representation in target domain. To this end, we leverage the widely used pretrained event-to-image reconstruction network [38]. However, the reconstructed image from event has intermittent artifacts near the boundary of an object. Those blurring and distortion effects, what we call a smudge, disturbs predicting sharp disparity. To estimate the irregular smudge in the target domain, we further design a self-supervision pipeline for smudge prediction in the source domain. + +In the source domain, as shown in the top of Fig. 3, we perturb the random region of image with distortion and blur kernel for imitating smudge effects. To depict realistic smudge effects, we do not generate the smudge on the randomly selected rectangle region but on the regions parsed by superpixel algorithm [1]. Since the edges of superpix + +![](images/fb200b9f52f9c159506a8d4a7c9b7491f12e5628f927c98c67141fbd33f12dcc.jpg) +Figure 3. Illustration of the Smudge-aware Self-supervision Module (SSM). To estimate the smudge artifact of the reconstructed image on the target domain, we train the smudge prediction network to predict the smudge in the source domain. + +els are generally placed on the boundary of an object, they can mimic the characteristics of the smudge effect caused at the boundary of the object due to the noisy sensors. Then, domain-shared smudge prediction network, which is a light-designed U-Net [40] with few convolution layers, is supervised from generated smudge mask. In other words, the output $M_{i}^{t}$ of smudge prediction network is supervised from generated artifact mask $\tilde{M}_{i}^{t}$ by minimizing the binary cross entropy loss: $\mathcal{L}_{\text{source}}^{\text{mask}} = \sum_{i \in \{l,r\}} BCE(M_{i}^{t}, \tilde{M}_{i}^{t})$ . + +In the target domain, as shown in the bottom of Fig. 3, we utilize a shared smudge prediction network from source domain for photometric-based self-supervision. The reconstructed left image $\hat{I}_l^{\hat{t}}$ and right image $\hat{I}_r^{\hat{t}}$ from voxels $V_l^{\hat{t}}$ and $V_r^{\hat{t}}$ are fed into the smudge prediction network. Then, smudge prediction network provides the predicted smudge map $M_l^{\hat{t}}$ and $M_r^{\hat{t}}$ , which include per-pixel probability of smudge from 0 to 1. Next, from the predicted dense disparity map $D_l^{\hat{t}}$ , we can reconstruct the warped left image $W_{r\to l}(\hat{I}_r^{\hat{t}})$ from right image $\hat{I}_r^{\hat{t}}$ . Considering the smudge mask maps of both left and right sides, we can calculate the pixel-wise photometric reconstruction error as follows: + +$$ +\begin{array}{l} \mathcal {L} _ {\text {t a r g e t}} ^ {\text {r e c o n}} = \alpha \frac {1 - \operatorname {S S I M} \left(\hat {I} _ {l} ^ {\hat {t}} \odot M ^ {\hat {t}} , W _ {r \rightarrow l} \left(\hat {I} _ {r} ^ {\hat {t}}\right) \odot M ^ {\hat {t}}\right)}{2} \tag {1} \\ + (1 - \alpha) \| \hat {I} _ {l} ^ {\hat {t}} \odot M ^ {\hat {t}} - W _ {r \rightarrow l} (\hat {I} _ {r} ^ {\hat {t}}) \odot M ^ {\hat {t}} \| _ {1}, \\ \end{array} +$$ + +where $M^{\hat{t}} = 1 - (M_{l}^{\hat{t}} \odot W_{r \to l}(M_{r}^{\hat{t}}))$ , $\odot$ means elementwise multiplication, SSIM denotes structural similarity proposed in [54] with a $3 \times 3$ kernel filter, and $\alpha$ is set to 0.85. + +Our proposed smudge prediction network is shared in the source and target domains with the same weights. Compared to the stereo network, which is a high-level task, the smudge prediction, which pixel-wisely finds regions of noise and smudge, is a low-level task and less affected by + +![](images/8d62f9815e39c9b2b78396cb3024080b24eb449d2beb97d47bd33dfeb6b3e199.jpg) +(a) Source + +![](images/9cb4aa4ce719bae44def2b8e28c59211c995e4d4efb1ca5f3fc04716370c2438.jpg) +(b) Target +Figure 4. Visualization of voxel grids and features extracted by the event stereo network from source (e.g., KITTI) and target (e.g., DSEC) domain. In the upper region of features with few events, there are no activated pixels; in contrast, there are many activated pixels in the lower region with a lot of structure for events. + +the domain gaps. Therefore, in the target domain, artifacts in the boundary are well predicted in the reconstructed image to estimate the sharp disparity through self-supervision. + +# 3.4. Feature Normalization + +We adopt the feature-level normalization to reduce the gap in the cost volume between two distinct domains. To align the distributions between different domains, the feature normalization [29,49,58] is widely used for image data. Similarly, event features can be also normalized to reduce the gap between the two domains; however, as can be seen in our experimental results (see Table 5), due to the sparsity of the event data, an existing normalization technique [43] for images rather hinders learning of event-based network. + +For event feature normalization, we focus on the characteristics of event-based stereo matching. Events are naturally sparse and triggered predominantly to the edges of the objects. For accurate prediction with sparse information, event stereo networks tend to focus intensely on areas with event information, which leads to features of areas without events not being activated. Therefore, normalizing over all pixels provides results with shifted bias on the region without an event for each scene. Instead, we focus on the correlation between the amount of events and spatial positions. For example, events rarely occur in the upper regions (e.g., sky), while more events occur in the lower regions where illuminance easily changes and rich textures exist (e.g., building). This phenomenon can be qualitatively verified by the extracted features of the network, as shown in Fig. 4. The lower region of the feature map is strongly activated in both domains, while the upper region, where no event occurs, is hardly activated. Therefore, applying the normalization over all pixels used in the dense image [43] to event stereo rather hinders reducing the domain gaps. In addition, since the stereo disparity is defined as the position difference in the horizontal direction when the cameras are rectified, normalization over all spatial positions leads to ambiguity in accurate matching. Therefore, we propose a strategy to normalize the feature along the epipolar (hori + +![](images/d9bb4ec1323323e642b28dd71a643f9efae5e53a934cd5b9aaa0bc4d0a79e773.jpg) +Figure 5. Illustration of the Motion-invariant Consistency Module (MCM). Normalize over time denotes to converting temporal values into a range between 0 and 1. + +zontal) line, which does not violate the regularity according to regions. This normalization is also spatial but less dependent on the global distribution of event data. + +We modify the parameter-free normalization scheme proposed in prior works [43]. Given extracted feature $F$ from network with size of $C \times H \times W$ ( $C$ : channel, $H$ : height, $W$ : width), let $F(k,i,j)$ denotes kij-th element, where $k$ is the index of channel and $i,j$ are spatial dimensions. Then, we apply the normalization along channel-dimension to both left and right features as follows: + +$$ +F (k, i, j) = \frac {F (k , i , j)}{\sqrt {\sum_ {c = 0} ^ {C - 1} \| F (c , i , j) \| ^ {2} + \varepsilon}}. \tag {2} +$$ + +After that, we apply the normalization along the epipolar line, which is defined as: + +$$ +F (k, i, j) = \frac {F (k , i , j)}{\sqrt {\sum_ {w = 0} ^ {W - 1} \| F (k , i , w) \| ^ {2} + \varepsilon}}. \tag {3} +$$ + +# 3.5. Motion-invariant Consistency Module (MCM) + +The motivation of the motion-invariant consistency module on the target domain is two-folds. The first is to resolve the domain gap caused by different camera motion. Second, we desire the event stereo network to be robust on perturbation or noise, adapting to the target domain. The perfectly adapted network should be able invariant to the motion of event camera and estimate the prediction stably, even if there is some perturbation in the input. + +In this subsection, we denote the voxel grid corresponding to the events $E^{\hat{t},T}$ accumulated during time $T$ until $\hat{t}$ as $V^{\hat{t},T}$ . Specifically, events are converted to a voxel grid pair $V_{l}^{\hat{t},T}, V_{r}^{\hat{t},T}$ , and fed to the network to estimate a disparity map $D_{l}^{\hat{t}}$ . Since the motion in the datasets is already acquired and immutable, we use a trick to augment event streams of fast or slow motions with temporal perturbation $\tau$ . If events + +are stacked for a longer time $T + \tau$ (i.e., more events) after normalizing temporal value in events (converting temporal values into a range between 0 and 1) and converted for the same bin of voxel grid, it is able to imitate the voxel grid of an event from an actual fast motion. Conversely, if stacked for a shorter time $T - \tau$ (i.e., fewer events), it is the same as the voxel grid made with events of slow motion. From this, we can generate a motion perturbed event voxel $V^{\hat{t},\hat{T}}$ , where $\hat{T} = T \pm \tau$ without additional data acquisition. As shown in Fig. 5, perturbed voxel pairs $V_{l}^{\hat{t},\hat{T}}, V_{r}^{\hat{t},\hat{T}}$ are fed into the event stereo network to predict the perturbed disparity map $\tilde{D}_{l}^{\hat{t}}$ . Then, for pixel-wise consistency between the prediction of motion-perturbed input and the original input, our consistency loss is defined via $L_{1}$ distance: + +$$ +\mathcal {L} _ {\text {t a r g e t}} ^ {\text {c o n s i s t e n c y}} = \| D _ {l} ^ {\hat {t}} - \tilde {D} _ {l} ^ {\hat {t}} \| _ {1} \tag {4} +$$ + +More details about the implementation of motion-invariant consistency module can be seen in supple. + +# 3.6. Loss functions + +On the source domain, we use the two losses for training the network. We adopt the smooth $L_{1}$ loss for disparity estimation: $\mathcal{L}_{source}^{task} = \mathrm{smooth}_{L_1}(\tilde{d}_l^t -d_l^t)$ , and the binary cross entropy loss for artifact prediction: $\mathcal{L}_{source}^{mask} = \sum_{i\in \{l,r\}}BCE(M_i^t,\tilde{M}_i^t)$ . + +On the target domain, we use the reconstruction loss $\mathcal{L}_{\text {target }}^{\text {recon }}$ (Eq. 1) and consistency loss $\mathcal{L}_{\text {target }}^{\text {consistency }}$ (Eq. 4). + +Finally, the total loss for an end-to-end optimization process is defined as: + +$$ +\mathcal {L} ^ {\text {t o t a l}} = \mathcal {L} _ {\text {s o u r c e}} ^ {\text {t a s k}} + \lambda_ {1} \mathcal {L} _ {\text {s o u r c e}} ^ {\text {m a s k}} + \lambda_ {2} \mathcal {L} _ {\text {t a r g e t}} ^ {\text {r e c o n}} + \tag {5} +$$ + +$$ +\lambda_ {3} \mathcal {L} _ {\text {t a r g e t}} ^ {\text {c o n s i s t e n c y}}, +$$ + +where $\lambda_1, \lambda_2$ and $\lambda_3$ are weight for each loss terms. + +# 4. Experiments + +# 4.1. Datasets + +For source domain datasets, we utilize the KITTI dataset [25] and the SceneFlow dataset [24]. The KITTI dataset is a real-world dataset with two subsets (i.e. KITTI 2012 [13] and KITTI 2015 [25]), containing 394 stereo images with sparse ground-truth for training. On the other hand, the SceneFlow dataset [24] is a large synthetic dataset containing diverse scenes. The SceneFlow dataset provides 35k stereo images with dense ground-truth disparity maps. + +For target domain, we use the recently published benchmark dataset of DSEC [12], a large-scale high-quality driving dataset with challenging scenes. DSEC provides high-resolution $(640\times 480)$ stereo event streams captured in outdoor driving scenes. It contains 53 driving scenarios taken in various lighting conditions, and provides 17k stereo pairs + +Table 1. Cross-domain comparisons with other traditional / domain generalization / domain adaptation stereo methods from various source domains. The 2-pixel error $(\%)$ , 3-pixel error $(\%)$ , end-point-error, and root mean square error are adopted for evaluation. Zu and In denote the Zurich City and Interlaken sequences, respectively. + +
KITTI-to-DSECSceneFlow-to-DSEC
Method2PE3PEEPERMSE2PE3PEEPERMSE
ZuInZuInZuInZuInZuInZuInZuIn
E2VID [38] on target domain
SGM [16]53.755.347.749.79.310.116.117.053.755.347.749.79.310.1
GwcNet [15]38.237.129.122.03.52.98.25.843.345.028.831.23.04.2
PSMNet [6]36.535.525.924.13.42.96.05.136.439.724.329.62.65.4
AANet [55]46.339.335.326.37.43.817.28.642.839.229.227.33.63.1
DSMNet [58]41.141.630.432.13.24.25.68.146.645.331.230.64.13.7
StereoGAN [23]70.968.866.463.111.49.813.312.273.272.268.073.115.413.4
EventGAN [61] on source domain
GwcNet [15]25.527.319.816.84.63.112.29.155.156.337.237.17.47.3
PSMNet [6]18.920.511.913.64.22.714.810.448.850.635.037.86.85.8
AANet [55]50.447.342.538.69.85.421.711.358.855.445.342.45.75.8
DSMNet [58]18.823.610.512.62.12.44.56.751.252.344.643.26.25.9
StereoGAN [23]61.460.352.850.715.313.718.918.975.271.765.566.313.310.6
ADES (Ours)
AANet13.819.97.19.81.41.72.73.422.324.911.113.91.61.9
PSMNet10.910.25.65.51.21.32.53.217.512.89.46.71.41.3
+ +for training. Following the previous image-to-event transfer tasks for segmentation [46], we adopt sequences acquired during the day with monotonous illuminance, called Zurich City. Furthermore, we also conduct experiments on Interlaken sequences containing the high dynamic range and challenging illuminance scenes. More details about a split of datasets are provided in the supple. + +# 4.2. Implementation details + +The weights $\lambda_{1}, \lambda_{2}$ and $\lambda_{3}$ are set as 0.3, 1, and 0.2, respectively. We train our end-to-end framework using the Adam optimizer [19]. We set the learning rate to $1 \times 10^{-3}$ with a batch size of 8 using $384 \times 336$ random crops. To generate the artifacts in Sec. 3.3, we utilize the Blur and OpticalDistortion transforms from library [4]. More details are provided in supple. + +# 4.3. Comparisons with Other Methods + +We compare our proposed ADES framework with the other traditional algorithm (SGM [16]), domain generalization (DSMNet [58]), and domain adaptation (StereoGAN [23]). In addition, we evaluate PSMNet [6], GwcNet [15], and AANet [55], which have achieved comparable performance in stereo matching. We train those networks in the source domain and test the network in the target domain. To align the different modalities between the source and target domains, we utilize E2VID [38] or EventGAN [61]. In the case of E2VID, an image-based stereo network is trained using a grayscale image in the source domain, and when testing, events in the target domain are reconstructed into a gray image using E2VID. Conversely, in the case of EventGAN, the event-based stereo network is trained using the events, which are converted by EventGAN from consecu + +tive images in the source domain. We evaluate the proposed framework by applying it to AANet and PSMNet, which can represent networks using 3D and 4D cost volumes. Especially, AANet is efficient, so it is a widely adopted structure in recent event stereo research [28, 30]. When training, the proposed modules are used, but when evaluating, all the proposed modules without normalization are removed, and only the event stereo network is used to predict the disparity. Table 1 shows the results of training on the various source dataset, such as KITTI and SceneFlow datasets. + +KITTI-to-DSEC. Even if the networks are trained on the source domain, the results of networks using the events from EventGAN can not achieve high performance. Some networks (PSMNet, GwcNet, and AANet) do not have the ability of domain generalization and adaptation. In addition, the distribution gap of disparity and motion between the domains lead to further degradation of performance. Similarly, most of the results using reconstructed images with E2VID do not show comparable performance. The reconstructed image on the target domain has a large gap with the real image on the source domain, which cannot be dealt with generalization (DSMNet), adaptation (StereoGAN) and conventional methods (SGM). Compared with existing works, our network achieves significantly high performance, considering the gap between domains such as motions and disparity. It is noticeable that in case of AANet+ADES, the performance improvement is significant, e.g., 2PE decreases from 50.4 to 13.8, and RMSE decreases from 21.7 to 2.7 in Zurich City sequence. + +SceneFlow-to-DSEC. The experiment results trained on the synthetic source domain show a more significant domain gap. Due to the effect of the syn-to-real gap, prior works show significantly lower performance than those + +![](images/216e814972cf116cfed0580bf361a5e7779dd58b388aa9aa5fff0cb6c17f86e6.jpg) +Figure 6. Qualitative results for the proposed method with other methods. Compared to EventGAN [61] and E2VID [38], our method can predict accurate and sharp disparity maps. + +Table 2. Results on DSEC benchmark testset + +
MethodSupervisionRMSE ↓MAE ↓1PE ↓2PE ↓
[48]✓1.3860.57610.922.91
[28]✓1.2220.5299.962.65
[30]✓1.2310.5199.582.62
[59]✓1.2640.5279.522.36
Ours (PSM)1.6980.77118.375.36
Ours (AA)1.9820.93624.017.87
+ +trained on KITTI datasets, e.g., 2PE of PSMNet using EventGAN significantly increases from 20.5 to 50.6 in the Interlaken sequence. Although our proposed method cannot avoid the performance degradation, the decreasing amount is relatively acceptable, e.g., 2PE of PSMNet+ADES increases from 10.2 to 12.8 in the Interlaken sequence. Furthermore, the performance increases in some metrics thanks to the various scenes in the synthetic dataset, e.g., RMSE of PSMNet+ADES decreases from 3.2 to 2.8 in the Interlaken sequence. These results show that our method can be used universally and not limited to a specific source dataset, whether synthetic or real-world. + +In Fig. 6, we provide qualitative comparisons of our method with other methods. E2VID or EventGAN can reduce the gap between modality, but it cannot bridge between domains. On the other hand, our ADES framework predicts sharp and accurate disparity on both AANet and PSMNet. These results demonstrate that our training pipeline resolves the gaps from both domain and modality. More qualitative comparisons are provided in supple. + +# 4.4. Results on DSEC test dataset + +To compare with supervised methods, we utilize the KITTI dataset, which contains ground-truth, as the source domain and the full DSEC train dataset, which lacks + +Table 3. Ablation studies for sub-modules: Smudge-aware Self-supervision Module (SSM), Feature Normalization (FN), and Motion-invariant Consistency Module (MCM). $D1$ -error $(\%)$ is adopted. + +
ModelSSMFNMCMZurichInterlaken
AANet35.226.3
✓33.124.5
✓29.622.7
✓13.315.1
✓✓11.214.6
✓✓8.110.2
✓✓✓7.09.7
PSMNet15.617.2
✓13.816.1
✓13.115.5
✓7.38.9
✓✓6.67.1
✓✓6.06.2
✓✓✓5.65.7
+ +ground-truth, as the target domain. Table 2 demonstrates that despite not relying on ground-truth data for the target domain, our approach achieves comparable performance to other supervised methods. + +# 4.5. Ablation Studies + +Effectiveness of each components. In Table 3, we conduct the ablation studies to validate the effectiveness of each component. We set the KITTI and DSEC dataset as source and target domain, respectively. Based on AANet and PSMNet from which all proposed modules were removed, the performance was measured while adding the proposed module one by one. The SSM achieves the greatest performance gain as a unitary component, e.g., reducing error rates by $21.9\%$ on Zurich, and $11.2\%$ on Interlaken from AANet. In addition, using FN stand-alone reduces the + +Table 4. Comparison of results with and without smudge prediction. $D1$ -error $(\%)$ is adopted. + +
MethodsZurichInterlaken
w/o Smudge Prediction16.112.3
w/ Smudge Prediction7.09.7
+ +![](images/9dff02f15fe2610691a3bfcf9dd375712385cf0b18a1496b2aba0d3e15c0c330.jpg) +Figure 7. Qualitative results of disparity predictions with and without smudge prediction. + +error by $1.7\% \sim 5.6\%$ depending on the target domain and model, compared to the baseline. Similarly, MCM also reduces the error by $1.1\% \sim 2.1\%$ . These FN and MCM work even if implemented together with SSM, e.g., compared to the case of using only SSM from AANet in Zurich, when FN and MCM are used together, errors are more reduced by $5.2\%$ and $2.1\%$ , respectively. Finally, the performance gain is the most significant when all of the proposed modules are used, and these results validate that all modules are effective for domain adaptation. + +Effectiveness of smudge predictions. We investigate the effect of the proposed smudge prediction on SSM. Using the KITTI as the source domain, the quantitative and qualitative results with and without smudge prediction from AANet are shown in Table 4 and Fig. 7. Compared with the absence of smudge prediction, our method utilizes the photometric loss of image reconstruction effectively. Therefore, through SSM using smudge prediction, the performance of the disparity estimation is improved e.g., the $D1$ -error decreases from 16.1 to 7.0 in Zurich City sequence. Specifically, as can be seen in Fig. 7, smudge prediction helps the network to robustly infer the boundary of an object, making a sharp disparity map. We visualize the smudge mask in Fig. 8 to show how smudge masks can aid effective learning in SSM. As shown in 1st row of Fig. 8, when an image is reconstructed from an event via E2VID, smudge-like blurry artifacts appear around the boundary of the object due to the noisy nature of the event streams. Our smudge prediction estimates these artifacts regions, helping to sharpen disparity when performing self-supervision and boosting the performance of disparity estimation. + +Comparison of normalization. Table 5 reports the comparison of our feature normalization with the existing learning-free normalization method [43]. We set the KITTI dataset as the source domain and the model to AANet. Although our epipolar norm is a modified module of the ex + +Table 5. Comparison of epipolar norm with existing cost norm [43]. $D1$ -error $(\%)$ is adopted. + +
MethodsZurichInterlaken
w/o Norm11.214.6
Cost Norm [43]12.311.1
Our Epipolar Norm7.09.7
+ +![](images/7447909073deebe9c1fa6c0c43fb17cdc1ee7c21882eb81837c7b8e5b03949f0.jpg) +Figure 8. Generated smudge mask on the target domain. Top: reconstructed images, Bottom: corresponding smudge mask. + +isting work, the results verify that it is more effective for the domain adaptation ability of event stereo matching. For example, in the case of [43], which performs the normalization along all pixels in spatial manners, the performance is rather reduced due to the specificity of event stereo. For example, especially in Zurich City, the $D1$ -error increases from 11.2 to 12.3 after introducing the cost norm [43]. On the other hand, our epipolar norm shows a performance improvement in both sequences. From these results, we can confirm that the event stereo network requires a different approach than the existing normalization method, and our normalization is suitable for the domain adaptive event stereo matching. + +# 5. Conclusion + +In this paper, we propose a novel framework, ADES, for adaptive dense event stereo from the image domain. Our work is the first that transfers the disparity estimation task from the rich image dataset with ground-truth to the event stream to tackle the absence of ground-truth disparities on the target event domain. To this end, we propose the smudge-aware self-supervision module, feature normalization, and motion-invariant consistency module by focusing on the specificity of event stereo. Extensive experiments demonstrate our framework achieves remarkable performance on both 3D and 4D cost volume networks, whether the source domain is synthetic or real-world image dataset. Furthermore, these results demonstrate that our modules can be used universally in existing event stereo networks. We open up the possibility of using event stereo in domains without ground-truth and expect more future work. + +Acknowledgements. 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IEEE Access, 7:156694-156706, 2019. 3 +[57] Guorun Yang, Xiao Song, Chaoqin Huang, Zhidong Deng, Jianping Shi, and Bolei Zhou. Drivingstereo: A large-scale dataset for stereo matching in autonomous driving scenarios. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 899–908, 2019. 1 +[58] Feihu Zhang, Xiaojuan Qi, Ruigang Yang, Victor Prisacariu, Benjamin Wah, and Philip Torr. Domain-invariant stereo matching networks. In European Conference on Computer Vision, pages 420-439. Springer, 2020. 2, 4, 6 +[59] Kaixuan Zhang, Kaiwei Che, Jianguo Zhang, Jie Cheng, Ziyang Zhang, Qinghai Guo, and Luziwei Leng. Discrete time convolution for fast event-based stereo. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 8676-8686, 2022. 1, 2, 7 +[60] Alex Zihao Zhu, Yibo Chen, and Kostas Daniilidis. Real-time time synchronized event-based stereo. In Proceedings of the European Conference on Computer Vision (ECCV), pages 433-447, 2018. 2 +[61] Alex Zihao Zhu, Ziyun Wang, Kaung Khant, and Kostas Daniilidis. Eventgan: Leveraging large scale image datasets for event cameras. In 2021 IEEE International Conference on Computational Photography (ICCP), pages 1-11. IEEE, 2021. 3, 6, 7 +[62] Jun-Yan Zhu, Taesung Park, Phillip Isola, and Alexei A Efros. Unpaired image-to-image translation using cycle-consistent adversarial networks. In Proceedings of the IEEE international conference on computer vision, pages 2223-2232, 2017. 2 +[63] Alex Zihao Zhu, Liangzhe Yuan, Kenneth Chaney, and Kostas Daniilidis. Unsupervised event-based optical flow using motion compensation. In Proceedings of the European Conference on Computer Vision (ECCV) Workshops, pages 0–0, 2018. 3 +[64] Dongqing Zou, Ping Guo, Qiang Wang, Xiaotao Wang, Guangqi Shao, Feng Shi, Jia Li, and Paul-KJ Park. Context-aware event-driven stereo matching. In 2016 IEEE International Conference on Image Processing (ICIP), pages 1076-1080. IEEE, 2016. 2 + +[65] Dongqing Zou, Feng Shi, Weiheng Liu, Jia Li, Qiang Wang, Paul-KJ Park, Chang-Woo Shi, Yohan J Roh, and Hyunsurk Eric Ryu. Robust dense depth map estimation from sparse dvs stereos. In British Mach. Vis. Conf.(BMVC), volume 1, 2017. 2 \ No newline at end of file diff --git a/2023/Learning Adaptive Dense Event Stereo From the Image Domain/images.zip b/2023/Learning Adaptive Dense Event Stereo From the Image Domain/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..c4ed39a1b7b403c7d72047ee167c0d6131f12578 --- /dev/null +++ b/2023/Learning Adaptive Dense Event Stereo From the Image Domain/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:f6dbd6b060d7f3ce43577ad1b456f9a9b561674ec8b86a8bc06645e58161a3f2 +size 708605 diff --git a/2023/Learning Adaptive Dense Event Stereo From the Image Domain/layout.json b/2023/Learning Adaptive Dense Event Stereo From the Image Domain/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..0d5a96196f517833fac3994de7b108be696a00ef --- /dev/null +++ b/2023/Learning Adaptive Dense Event Stereo From the Image Domain/layout.json @@ -0,0 +1,8637 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 101, + 103, + 492, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 101, + 103, + 492, + 121 + ], + "spans": [ + { + "bbox": [ + 101, + 103, + 492, + 121 + ], + "type": "text", + "content": "Learning Adaptive Dense Event Stereo from the Image Domain" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 179, + 144, + 414, + 171 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 179, + 144, + 414, + 171 + ], + "spans": [ + { + "bbox": [ + 179, + 144, + 414, + 171 + ], + "type": "text", + "content": "Hoonhee Cho, Jegyeong Cho, and Kuk-Jin Yoon Visual Intelligence Lab., KAIST, Korea" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 188, + 173, + 405, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 188, + 173, + 405, + 185 + ], + "spans": [ + { + "bbox": [ + 188, + 173, + 405, + 185 + ], + "type": "text", + "content": "{gnsgnsgml，j2k0618，kjyoon}@kaist.ac.kr" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "spans": [ + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 238, + 290, + 562 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 238, + 290, + 562 + ], + "spans": [ + { + "bbox": [ + 46, + 238, + 290, + 562 + ], + "type": "text", + "content": "Recently, event-based stereo matching has been studied due to its robustness in poor light conditions. However, existing event-based stereo networks suffer severe performance degradation when domains shift. Unsupervised domain adaptation (UDA) aims at resolving this problem without using the target domain ground-truth. However, traditional UDA still needs the input event data with ground-truth in the source domain, which is more challenging and costly to obtain than image data. To tackle this issue, we propose a novel unsupervised domain Adaptive Dense Event Stereo (ADES), which resolves gaps between the different domains and input modalities. The proposed ADES framework adapts event-based stereo networks from abundant image datasets with ground-truth on the source domain to event datasets without ground-truth on the target domain, which is a more practical setup. First, we propose a self-supervision module that trains the network on the target domain through image reconstruction, while an artifact prediction network trained on the source domain assists in removing intermittent artifacts in the reconstructed image. Secondly, we utilize the feature-level normalization scheme to align the extracted features along the epipolar line. Finally, we present the motion-invariant consistency module to impose the consistent output between the perturbed motion. Our experiments demonstrate that our approach achieves remarkable results in the adaptation ability of event-based stereo matching from the image domain." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 574, + 128, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 574, + 128, + 586 + ], + "spans": [ + { + "bbox": [ + 47, + 574, + 128, + 586 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 594, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 287, + 714 + ], + "type": "text", + "content": "Stereo matching [22, 41] is one of the most widely used methods for obtaining 3D information by establishing correspondences between stereo images. With considerable interest, learning-based stereo methods have achieved state-of-the-art performance in many benchmark datasets. However, some challenges in stereo matching still exist due to the shortcoming of sensors (e.g., low dynamic range, motion blur due to large exposure time). Event cameras [3] are novel sensors that asynchronously report per-pixel changes of intensity by imitating the human eye. Thanks" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 320, + 213, + 531, + 399 + ], + "blocks": [ + { + "bbox": [ + 320, + 213, + 531, + 399 + ], + "lines": [ + { + "bbox": [ + 320, + 213, + 531, + 399 + ], + "spans": [ + { + "bbox": [ + 320, + 213, + 531, + 399 + ], + "type": "image", + "image_path": "49f92d8a3f5c46925bb5fe98416149495a78917d7d00a05075a11f97d3f3731e.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 403, + 547, + 437 + ], + "lines": [ + { + "bbox": [ + 305, + 403, + 547, + 437 + ], + "spans": [ + { + "bbox": [ + 305, + 403, + 547, + 437 + ], + "type": "text", + "content": "Figure 1. The proposed ADES framework for adaptive dense event stereo network. ADES aims to exploit the existing frame-based stereo dataset for learning the event stereo network." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 449, + 546, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 449, + 546, + 509 + ], + "spans": [ + { + "bbox": [ + 304, + 449, + 546, + 509 + ], + "type": "text", + "content": "to the high dynamic range and low latency, the event camera can be considered as a promising sensor for depth estimation, especially in driving scenarios. Recent works [2,8,9,28,30,48,59] have attempted to utilize event cameras for stereo matching even under poor light conditions." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 510, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 547, + 715 + ], + "type": "text", + "content": "Despite advances in event stereo, most prior works [9, 28, 48] still experience a significant degradation in performance when domains shift. Unsupervised domain adaptation (UDA) can resolve this problem without using the target domain ground-truth. When UDA is applied for event stereo domain adaptation, it still needs the input event data with ground-truth in the source domain. However, as mentioned in [32], accurate synchronization of events with high temporal resolution and other devices (e.g., Li-DAR) requires additional hardware and post-processing, so it is more challenging to obtain accurate ground truth than images. In this paper, we draw attention to large image datasets with ground-truth, which are easily accessible (e.g., DrivingStereo [57], SceneFlow [24] and KITTI [25]). In this setup, abundant image data from diverse environments helps the event stereo network improve generalizability with high performance. To this end, as shown in" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17797" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 143 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 143 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 143 + ], + "type": "text", + "content": "Fig. 1, we propose a novel Adaptive Dense Event Stereo (ADES), which adapts the stereo network from the source domain having image data with ground-truth to the target domain having event data without ground-truth. ADES resolves gaps between the different domains and input modalities." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 144, + 286, + 286 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 144, + 286, + 286 + ], + "spans": [ + { + "bbox": [ + 46, + 144, + 286, + 286 + ], + "type": "text", + "content": "The proposed ADES framework consists of three components: smudge-aware self-supervision module, feature normalization, and motion-invariant consistency module. The proposed smudge-aware self-supervision module leverages dense traits of images via image reconstruction on the event target domain. Image reconstruction using only the event is often interrupted by blurry artifacts, what we call a smudge, so the network cannot estimate the sharp and accurate disparity map. To predict the smudge effect in the target domain, we design the self-supervision pipeline on the source image domain to estimate and suppress the artifact area in the reconstructed image on the target domain." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 288, + 286, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 288, + 286, + 441 + ], + "spans": [ + { + "bbox": [ + 46, + 288, + 286, + 441 + ], + "type": "text", + "content": "In addition, we exploit the feature normalization before generating the cost volume. Normalization scheme [29, 43, 49, 58] was generally used in the domain adaptation between the image modalities. However, due to the characteristics of the event, it is not efficient to normalize over the entire pixel area. Since most of the events are triggered around an edge of objects, some regions (e.g., sky) have very sparse events. Therefore, vanilla normalization can mislead the values of features to shift to the values of the regions without events. While reducing the difference in features between the two domains, we apply a normalization along the epipolar line to take into account the characteristics of events and stereo matching." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 443, + 286, + 561 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 443, + 286, + 561 + ], + "spans": [ + { + "bbox": [ + 46, + 443, + 286, + 561 + ], + "type": "text", + "content": "Finally, we focus on the different motion of event cameras from the source and target domains, leading to a severe domain gap. Therefore, we present the motion-invariant consistency module to predict consistent disparity even if the camera motion changes to some extent. This module helps the network to adapt the target domain and also reduces the gap from camera motion. To the best of our knowledge, our work is the first attempt to move from unpaired image domain to event domain for stereo matching. Our main contributions are summarized as below:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 58, + 566, + 286, + 712 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 58, + 566, + 286, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 566, + 286, + 613 + ], + "spans": [ + { + "bbox": [ + 58, + 566, + 286, + 613 + ], + "type": "text", + "content": "- Our work is the first that transfers the disparity estimation task from the rich image dataset with ground-truth to the event stream, resolving gaps between the different domains and input modalities." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 58, + 616, + 286, + 663 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 616, + 286, + 663 + ], + "spans": [ + { + "bbox": [ + 58, + 616, + 286, + 663 + ], + "type": "text", + "content": "- We propose a novel adaptive event stereo network, ADES, containing the smudge-aware self-supervision module, feature normalization, and motion-invariant consistency module." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 58, + 666, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 666, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 666, + 286, + 712 + ], + "type": "text", + "content": "- Extensive experiments demonstrate that the ADES framework achieves significantly better performance than the prior works in the adaptation ability between the different domains and modalities for event stereo." + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 71, + 397, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 71, + 397, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 71, + 397, + 84 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 91, + 501, + 104 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 91, + 501, + 104 + ], + "spans": [ + { + "bbox": [ + 306, + 91, + 501, + 104 + ], + "type": "text", + "content": "2.1. Stereo depth estimation using Events" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 109, + 545, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 109, + 545, + 228 + ], + "spans": [ + { + "bbox": [ + 305, + 109, + 545, + 228 + ], + "type": "text", + "content": "Recent event-based stereo matching [2,8,9,28,30,48,59] achieved the high accuracy than early works [5,7,20,35-37, 39,60,64,65] by adopting a learning-based approach with various embedding schemes. They propose additional modules that consider the temporal continuity of events, but the overall framework is similar to frame-based stereo: embedding, matching, and regularization modules. Our proposed pipeline of adaptive stereo matching also follows the general stereo matching, then can be easily applied on other event-based stereo networks." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 237, + 513, + 251 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 237, + 513, + 251 + ], + "spans": [ + { + "bbox": [ + 306, + 237, + 513, + 251 + ], + "type": "text", + "content": "2.2. Domain Adaptation in Stereo Matching" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 255, + 545, + 363 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 255, + 545, + 363 + ], + "spans": [ + { + "bbox": [ + 305, + 255, + 545, + 363 + ], + "type": "text", + "content": "To overcome the performance degradation from the domain gap, several works have explored unsupervised domain adaptation (UDA) in frame-based stereo matching. Some works utilize the knowledge distillation [14] and CycleGAN [23,62] to narrow the domain gap. After that, compact and efficient domain adaptation studies [33, 43, 47] for stereo have been conducted. On the other hand, the domain adaptation ability of event stereo networks has not been studied, and we tackle it for the first time." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 372, + 489, + 384 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 372, + 489, + 384 + ], + "spans": [ + { + "bbox": [ + 306, + 372, + 489, + 384 + ], + "type": "text", + "content": "2.3. Adaptation from Images to Events" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 390, + 545, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 390, + 545, + 498 + ], + "spans": [ + { + "bbox": [ + 305, + 390, + 545, + 498 + ], + "type": "text", + "content": "Event-to-image reconstruction methods [10, 27, 31, 34, 38, 42, 44, 50, 52, 53] can be considered the proxy task to transfer a labeled image domain (source) to an unlabeled event domain (target). The results of the event-to-image reconstruction have been used as inputs of end-task (e.g., object recognition, semantic segmentation) network pre-trained on image (source) domain. However, they introduce the extra latency in the inference time and still pose a domain gap between source and target domain." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 498, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 498, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 305, + 498, + 545, + 689 + ], + "type": "text", + "content": "One of the attempts to properly do domain adaptation was grafted networks [17] by utilizing the pre-trained image network. They replaced the encoder of pre-trained network with event encoder, then finetuned it on paired event and image datasets. This setup takes advantage of each modalities, but requires pixel-wise aligned events and images. To overcome the limitation of paired setting, EvDistill [51] leveraged the unpaired images to boost the performance of event-based networks. Through the bidirectional modality reconstruction and cross-modal knowledge distillation, they can transfer the knowledge from image network to event network. After that, research on transferring from an unpaired image to event has been of continuous interest. EV-Transfer [26] hallucinate the motion to generate the fake events from still images. ESS [46] achieve the feature-level alignment with the motion-invariant event embeddings." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": "Existing works only focus on the tasks from a single camera (e.g., semantic segmentation, object recognition)." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17798" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 62, + 73, + 532, + 251 + ], + "blocks": [ + { + "bbox": [ + 62, + 73, + 532, + 251 + ], + "lines": [ + { + "bbox": [ + 62, + 73, + 532, + 251 + ], + "spans": [ + { + "bbox": [ + 62, + 73, + 532, + 251 + ], + "type": "image", + "image_path": "97eece041d0e691718804bf67a51bb9048c3c4d7242c5688f99716822c767ec9.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 258, + 548, + 304 + ], + "lines": [ + { + "bbox": [ + 46, + 258, + 548, + 304 + ], + "spans": [ + { + "bbox": [ + 46, + 258, + 548, + 304 + ], + "type": "text", + "content": "Figure 2. Overview of the proposed ADES framework. During training, image datasets (e.g., KITTI) are used for the source domain, and event datasets without ground-truth are used for the target domain. We utilize feature normalization (Sec. 3.4) to narrow the gap between features from other domains. The proposed smudge-aware self-supervision module (Sec. 3.3) and motion-invariant consistency module (Sec. 3.5) are only used in training phase." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 316, + 290, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 316, + 290, + 389 + ], + "spans": [ + { + "bbox": [ + 46, + 316, + 290, + 389 + ], + "type": "text", + "content": "Due to the novel characteristics of event cameras, high-quality large stereo datasets have recently appeared, so related research has yet to be studied. In this paper, we propose an employable ADES framework for an event stereo. Unlike the prior works, we consider the characteristics of the event in the specific situation of stereo matching." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 397, + 105, + 410 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 397, + 105, + 410 + ], + "spans": [ + { + "bbox": [ + 47, + 397, + 105, + 410 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 417, + 146, + 430 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 417, + 146, + 430 + ], + "spans": [ + { + "bbox": [ + 47, + 417, + 146, + 430 + ], + "type": "text", + "content": "3.1. Problem Setting" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 434, + 287, + 546 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 434, + 287, + 546 + ], + "spans": [ + { + "bbox": [ + 46, + 434, + 287, + 546 + ], + "type": "text", + "content": "Given consecutive stereo image pairs " + }, + { + "bbox": [ + 46, + 434, + 287, + 546 + ], + "type": "inline_equation", + "content": "(I_l^{t - 1}, I_r^{t - 1})" + }, + { + "bbox": [ + 46, + 434, + 287, + 546 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 434, + 287, + 546 + ], + "type": "inline_equation", + "content": "(I_l^t, I_r^t)" + }, + { + "bbox": [ + 46, + 434, + 287, + 546 + ], + "type": "text", + "content": " with ground-truth disparity map " + }, + { + "bbox": [ + 46, + 434, + 287, + 546 + ], + "type": "inline_equation", + "content": "\\tilde{d}_l^t" + }, + { + "bbox": [ + 46, + 434, + 287, + 546 + ], + "type": "text", + "content": " on source domain, our goal is to train the model to predict the disparity map " + }, + { + "bbox": [ + 46, + 434, + 287, + 546 + ], + "type": "inline_equation", + "content": "D_l^{\\hat{t}}" + }, + { + "bbox": [ + 46, + 434, + 287, + 546 + ], + "type": "text", + "content": " at time " + }, + { + "bbox": [ + 46, + 434, + 287, + 546 + ], + "type": "inline_equation", + "content": "\\hat{t}" + }, + { + "bbox": [ + 46, + 434, + 287, + 546 + ], + "type": "text", + "content": " from stereo event streams " + }, + { + "bbox": [ + 46, + 434, + 287, + 546 + ], + "type": "inline_equation", + "content": "E_l^{\\hat{t}}" + }, + { + "bbox": [ + 46, + 434, + 287, + 546 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 434, + 287, + 546 + ], + "type": "inline_equation", + "content": "E_r^{\\hat{t}}" + }, + { + "bbox": [ + 46, + 434, + 287, + 546 + ], + "type": "text", + "content": " on target event domain. To make it clear that the source and the target domains are unpaired, we denote time for the source domain as " + }, + { + "bbox": [ + 46, + 434, + 287, + 546 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 434, + 287, + 546 + ], + "type": "text", + "content": " and the target domain as " + }, + { + "bbox": [ + 46, + 434, + 287, + 546 + ], + "type": "inline_equation", + "content": "\\hat{t}" + }, + { + "bbox": [ + 46, + 434, + 287, + 546 + ], + "type": "text", + "content": ". We represent an event stream as a voxel grid [63], the most commonly used representation, e.g., by converting " + }, + { + "bbox": [ + 46, + 434, + 287, + 546 + ], + "type": "inline_equation", + "content": "E_l^{\\hat{t}}" + }, + { + "bbox": [ + 46, + 434, + 287, + 546 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 434, + 287, + 546 + ], + "type": "inline_equation", + "content": "V_l^{\\hat{t}}" + }, + { + "bbox": [ + 46, + 434, + 287, + 546 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 552, + 151, + 563 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 552, + 151, + 563 + ], + "spans": [ + { + "bbox": [ + 47, + 552, + 151, + 563 + ], + "type": "text", + "content": "3.2. System Overview" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 570, + 287, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 287, + 617 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 287, + 617 + ], + "type": "text", + "content": "As shown in Fig. 2, our proposed Adaptive Dense Event Stereo (ADES) consists of three novel components: smudge-aware self-supervision module, feature normalization, and motion-invariant consistency module." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "type": "text", + "content": "For the source domain, we leverage the pre-trained video-to-event reconstruction network to extract the event representations from image data for the event-based stereo network. There are several video-to-event methods [11, 18], but among them, we adopt the network proposed in [61] that is lightweight and describes events well even with only two sequential images. Each left and right sequential image pairs are passed through the video-to-event net" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 316, + 547, + 450 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 316, + 547, + 450 + ], + "spans": [ + { + "bbox": [ + 304, + 316, + 547, + 450 + ], + "type": "text", + "content": "work " + }, + { + "bbox": [ + 304, + 316, + 547, + 450 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_{I\\to E}" + }, + { + "bbox": [ + 304, + 316, + 547, + 450 + ], + "type": "text", + "content": " and transformed into voxel grids as follows: " + }, + { + "bbox": [ + 304, + 316, + 547, + 450 + ], + "type": "inline_equation", + "content": "V_{l}^{t} = \\mathcal{G}_{I\\to E}(I_{l}^{t - 1},I_{l}^{t}),V_{r}^{t} = \\mathcal{G}_{I\\to E}(I_{r}^{t - 1},I_{r}^{t})" + }, + { + "bbox": [ + 304, + 316, + 547, + 450 + ], + "type": "text", + "content": " . The generated voxel grid pairs " + }, + { + "bbox": [ + 304, + 316, + 547, + 450 + ], + "type": "inline_equation", + "content": "(V_{l}^{t},V_{r}^{t})" + }, + { + "bbox": [ + 304, + 316, + 547, + 450 + ], + "type": "text", + "content": " from the source domain and the voxel grid pairs " + }, + { + "bbox": [ + 304, + 316, + 547, + 450 + ], + "type": "inline_equation", + "content": "(V_{l}^{\\hat{t}},V_{r}^{\\hat{t}})" + }, + { + "bbox": [ + 304, + 316, + 547, + 450 + ], + "type": "text", + "content": " from the target domain are simultaneously fed into a weight shared event-based stereo network. In the process, we narrow the gap between the two domains by normalizing the extracted features. The prediction of source domain " + }, + { + "bbox": [ + 304, + 316, + 547, + 450 + ], + "type": "inline_equation", + "content": "d_l^t" + }, + { + "bbox": [ + 304, + 316, + 547, + 450 + ], + "type": "text", + "content": " is supervised by ground-truth disparity " + }, + { + "bbox": [ + 304, + 316, + 547, + 450 + ], + "type": "inline_equation", + "content": "\\tilde{d}_l^t" + }, + { + "bbox": [ + 304, + 316, + 547, + 450 + ], + "type": "text", + "content": " , while the result of the target domain is adaptively optimized by the proposed smudge-aware self-supervision module and motion-invariant consistency module." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 455, + 546, + 468 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 455, + 546, + 468 + ], + "spans": [ + { + "bbox": [ + 305, + 455, + 546, + 468 + ], + "type": "text", + "content": "3.3. Smudge-aware Self-supervision Module (SSM)" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 474, + 546, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 546, + 641 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 546, + 641 + ], + "type": "text", + "content": "Prior works [21,45,56] verified that self-supervised auxiliary tasks are helpful for domain adaptation, especially in stereo matching task [43]. We also utilize the photometric reconstruction as an auxiliary task of domain adaptation for stereo matching. First, as shown in the bottom of Fig. 3, we generate the image from voxel event representation in target domain. To this end, we leverage the widely used pretrained event-to-image reconstruction network [38]. However, the reconstructed image from event has intermittent artifacts near the boundary of an object. Those blurring and distortion effects, what we call a smudge, disturbs predicting sharp disparity. To estimate the irregular smudge in the target domain, we further design a self-supervision pipeline for smudge prediction in the source domain." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "type": "text", + "content": "In the source domain, as shown in the top of Fig. 3, we perturb the random region of image with distortion and blur kernel for imitating smudge effects. To depict realistic smudge effects, we do not generate the smudge on the randomly selected rectangle region but on the regions parsed by superpixel algorithm [1]. Since the edges of superpix" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "17799" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 70, + 279, + 243 + ], + "blocks": [ + { + "bbox": [ + 53, + 70, + 279, + 243 + ], + "lines": [ + { + "bbox": [ + 53, + 70, + 279, + 243 + ], + "spans": [ + { + "bbox": [ + 53, + 70, + 279, + 243 + ], + "type": "image", + "image_path": "fb200b9f52f9c159506a8d4a7c9b7491f12e5628f927c98c67141fbd33f12dcc.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 245, + 287, + 291 + ], + "lines": [ + { + "bbox": [ + 46, + 245, + 287, + 291 + ], + "spans": [ + { + "bbox": [ + 46, + 245, + 287, + 291 + ], + "type": "text", + "content": "Figure 3. Illustration of the Smudge-aware Self-supervision Module (SSM). To estimate the smudge artifact of the reconstructed image on the target domain, we train the smudge prediction network to predict the smudge in the source domain." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 300, + 286, + 409 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 300, + 286, + 409 + ], + "spans": [ + { + "bbox": [ + 46, + 300, + 286, + 409 + ], + "type": "text", + "content": "els are generally placed on the boundary of an object, they can mimic the characteristics of the smudge effect caused at the boundary of the object due to the noisy sensors. Then, domain-shared smudge prediction network, which is a light-designed U-Net [40] with few convolution layers, is supervised from generated smudge mask. In other words, the output " + }, + { + "bbox": [ + 46, + 300, + 286, + 409 + ], + "type": "inline_equation", + "content": "M_{i}^{t}" + }, + { + "bbox": [ + 46, + 300, + 286, + 409 + ], + "type": "text", + "content": " of smudge prediction network is supervised from generated artifact mask " + }, + { + "bbox": [ + 46, + 300, + 286, + 409 + ], + "type": "inline_equation", + "content": "\\tilde{M}_{i}^{t}" + }, + { + "bbox": [ + 46, + 300, + 286, + 409 + ], + "type": "text", + "content": " by minimizing the binary cross entropy loss: " + }, + { + "bbox": [ + 46, + 300, + 286, + 409 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text{source}}^{\\text{mask}} = \\sum_{i \\in \\{l,r\\}} BCE(M_{i}^{t}, \\tilde{M}_{i}^{t})" + }, + { + "bbox": [ + 46, + 300, + 286, + 409 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 410, + 286, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 410, + 286, + 555 + ], + "spans": [ + { + "bbox": [ + 46, + 410, + 286, + 555 + ], + "type": "text", + "content": "In the target domain, as shown in the bottom of Fig. 3, we utilize a shared smudge prediction network from source domain for photometric-based self-supervision. The reconstructed left image " + }, + { + "bbox": [ + 46, + 410, + 286, + 555 + ], + "type": "inline_equation", + "content": "\\hat{I}_l^{\\hat{t}}" + }, + { + "bbox": [ + 46, + 410, + 286, + 555 + ], + "type": "text", + "content": " and right image " + }, + { + "bbox": [ + 46, + 410, + 286, + 555 + ], + "type": "inline_equation", + "content": "\\hat{I}_r^{\\hat{t}}" + }, + { + "bbox": [ + 46, + 410, + 286, + 555 + ], + "type": "text", + "content": " from voxels " + }, + { + "bbox": [ + 46, + 410, + 286, + 555 + ], + "type": "inline_equation", + "content": "V_l^{\\hat{t}}" + }, + { + "bbox": [ + 46, + 410, + 286, + 555 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 410, + 286, + 555 + ], + "type": "inline_equation", + "content": "V_r^{\\hat{t}}" + }, + { + "bbox": [ + 46, + 410, + 286, + 555 + ], + "type": "text", + "content": " are fed into the smudge prediction network. Then, smudge prediction network provides the predicted smudge map " + }, + { + "bbox": [ + 46, + 410, + 286, + 555 + ], + "type": "inline_equation", + "content": "M_l^{\\hat{t}}" + }, + { + "bbox": [ + 46, + 410, + 286, + 555 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 410, + 286, + 555 + ], + "type": "inline_equation", + "content": "M_r^{\\hat{t}}" + }, + { + "bbox": [ + 46, + 410, + 286, + 555 + ], + "type": "text", + "content": ", which include per-pixel probability of smudge from 0 to 1. Next, from the predicted dense disparity map " + }, + { + "bbox": [ + 46, + 410, + 286, + 555 + ], + "type": "inline_equation", + "content": "D_l^{\\hat{t}}" + }, + { + "bbox": [ + 46, + 410, + 286, + 555 + ], + "type": "text", + "content": ", we can reconstruct the warped left image " + }, + { + "bbox": [ + 46, + 410, + 286, + 555 + ], + "type": "inline_equation", + "content": "W_{r\\to l}(\\hat{I}_r^{\\hat{t}})" + }, + { + "bbox": [ + 46, + 410, + 286, + 555 + ], + "type": "text", + "content": " from right image " + }, + { + "bbox": [ + 46, + 410, + 286, + 555 + ], + "type": "inline_equation", + "content": "\\hat{I}_r^{\\hat{t}}" + }, + { + "bbox": [ + 46, + 410, + 286, + 555 + ], + "type": "text", + "content": ". Considering the smudge mask maps of both left and right sides, we can calculate the pixel-wise photometric reconstruction error as follows:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 563, + 286, + 607 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 563, + 286, + 607 + ], + "spans": [ + { + "bbox": [ + 55, + 563, + 286, + 607 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {\\text {t a r g e t}} ^ {\\text {r e c o n}} = \\alpha \\frac {1 - \\operatorname {S S I M} \\left(\\hat {I} _ {l} ^ {\\hat {t}} \\odot M ^ {\\hat {t}} , W _ {r \\rightarrow l} \\left(\\hat {I} _ {r} ^ {\\hat {t}}\\right) \\odot M ^ {\\hat {t}}\\right)}{2} \\tag {1} \\\\ + (1 - \\alpha) \\| \\hat {I} _ {l} ^ {\\hat {t}} \\odot M ^ {\\hat {t}} - W _ {r \\rightarrow l} (\\hat {I} _ {r} ^ {\\hat {t}}) \\odot M ^ {\\hat {t}} \\| _ {1}, \\\\ \\end{array}", + "image_path": "5069e7660fc669030e3abf2c2cb133b4c5a12dca564ef395c163489d00a0209a.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 616, + 286, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 616, + 286, + 653 + ], + "spans": [ + { + "bbox": [ + 46, + 616, + 286, + 653 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 616, + 286, + 653 + ], + "type": "inline_equation", + "content": "M^{\\hat{t}} = 1 - (M_{l}^{\\hat{t}} \\odot W_{r \\to l}(M_{r}^{\\hat{t}}))" + }, + { + "bbox": [ + 46, + 616, + 286, + 653 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 616, + 286, + 653 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 46, + 616, + 286, + 653 + ], + "type": "text", + "content": " means elementwise multiplication, SSIM denotes structural similarity proposed in [54] with a " + }, + { + "bbox": [ + 46, + 616, + 286, + 653 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 46, + 616, + 286, + 653 + ], + "type": "text", + "content": " kernel filter, and " + }, + { + "bbox": [ + 46, + 616, + 286, + 653 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 616, + 286, + 653 + ], + "type": "text", + "content": " is set to 0.85." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 654, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 286, + 713 + ], + "type": "text", + "content": "Our proposed smudge prediction network is shared in the source and target domains with the same weights. Compared to the stereo network, which is a high-level task, the smudge prediction, which pixel-wisely finds regions of noise and smudge, is a low-level task and less affected by" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 306, + 70, + 424, + 161 + ], + "blocks": [ + { + "bbox": [ + 306, + 70, + 424, + 161 + ], + "lines": [ + { + "bbox": [ + 306, + 70, + 424, + 161 + ], + "spans": [ + { + "bbox": [ + 306, + 70, + 424, + 161 + ], + "type": "image", + "image_path": "8d62f9815e39c9b2b78396cb3024080b24eb449d2beb97d47bd33dfeb6b3e199.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 347, + 162, + 379, + 170 + ], + "lines": [ + { + "bbox": [ + 347, + 162, + 379, + 170 + ], + "spans": [ + { + "bbox": [ + 347, + 162, + 379, + 170 + ], + "type": "text", + "content": "(a) Source" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 425, + 70, + 543, + 161 + ], + "blocks": [ + { + "bbox": [ + 425, + 70, + 543, + 161 + ], + "lines": [ + { + "bbox": [ + 425, + 70, + 543, + 161 + ], + "spans": [ + { + "bbox": [ + 425, + 70, + 543, + 161 + ], + "type": "image", + "image_path": "9cb4aa4ce719bae44def2b8e28c59211c995e4d4efb1ca5f3fc04716370c2438.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 466, + 162, + 497, + 170 + ], + "lines": [ + { + "bbox": [ + 466, + 162, + 497, + 170 + ], + "spans": [ + { + "bbox": [ + 466, + 162, + 497, + 170 + ], + "type": "text", + "content": "(b) Target" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 305, + 173, + 545, + 228 + ], + "lines": [ + { + "bbox": [ + 305, + 173, + 545, + 228 + ], + "spans": [ + { + "bbox": [ + 305, + 173, + 545, + 228 + ], + "type": "text", + "content": "Figure 4. Visualization of voxel grids and features extracted by the event stereo network from source (e.g., KITTI) and target (e.g., DSEC) domain. In the upper region of features with few events, there are no activated pixels; in contrast, there are many activated pixels in the lower region with a lot of structure for events." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 241, + 545, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 241, + 545, + 277 + ], + "spans": [ + { + "bbox": [ + 305, + 241, + 545, + 277 + ], + "type": "text", + "content": "the domain gaps. Therefore, in the target domain, artifacts in the boundary are well predicted in the reconstructed image to estimate the sharp disparity through self-supervision." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 287, + 434, + 298 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 287, + 434, + 298 + ], + "spans": [ + { + "bbox": [ + 306, + 287, + 434, + 298 + ], + "type": "text", + "content": "3.4. Feature Normalization" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 306, + 545, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 306, + 545, + 413 + ], + "spans": [ + { + "bbox": [ + 304, + 306, + 545, + 413 + ], + "type": "text", + "content": "We adopt the feature-level normalization to reduce the gap in the cost volume between two distinct domains. To align the distributions between different domains, the feature normalization [29,49,58] is widely used for image data. Similarly, event features can be also normalized to reduce the gap between the two domains; however, as can be seen in our experimental results (see Table 5), due to the sparsity of the event data, an existing normalization technique [43] for images rather hinders learning of event-based network." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 415, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 415, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 415, + 546, + 714 + ], + "type": "text", + "content": "For event feature normalization, we focus on the characteristics of event-based stereo matching. Events are naturally sparse and triggered predominantly to the edges of the objects. For accurate prediction with sparse information, event stereo networks tend to focus intensely on areas with event information, which leads to features of areas without events not being activated. Therefore, normalizing over all pixels provides results with shifted bias on the region without an event for each scene. Instead, we focus on the correlation between the amount of events and spatial positions. For example, events rarely occur in the upper regions (e.g., sky), while more events occur in the lower regions where illuminance easily changes and rich textures exist (e.g., building). This phenomenon can be qualitatively verified by the extracted features of the network, as shown in Fig. 4. The lower region of the feature map is strongly activated in both domains, while the upper region, where no event occurs, is hardly activated. Therefore, applying the normalization over all pixels used in the dense image [43] to event stereo rather hinders reducing the domain gaps. In addition, since the stereo disparity is defined as the position difference in the horizontal direction when the cameras are rectified, normalization over all spatial positions leads to ambiguity in accurate matching. Therefore, we propose a strategy to normalize the feature along the epipolar (hori" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17800" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 59, + 72, + 276, + 222 + ], + "blocks": [ + { + "bbox": [ + 59, + 72, + 276, + 222 + ], + "lines": [ + { + "bbox": [ + 59, + 72, + 276, + 222 + ], + "spans": [ + { + "bbox": [ + 59, + 72, + 276, + 222 + ], + "type": "image", + "image_path": "d9bb4ec1323323e642b28dd71a643f9efae5e53a934cd5b9aaa0bc4d0a79e773.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 224, + 287, + 258 + ], + "lines": [ + { + "bbox": [ + 46, + 224, + 287, + 258 + ], + "spans": [ + { + "bbox": [ + 46, + 224, + 287, + 258 + ], + "type": "text", + "content": "Figure 5. Illustration of the Motion-invariant Consistency Module (MCM). Normalize over time denotes to converting temporal values into a range between 0 and 1." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 273, + 287, + 308 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 273, + 287, + 308 + ], + "spans": [ + { + "bbox": [ + 46, + 273, + 287, + 308 + ], + "type": "text", + "content": "zontal) line, which does not violate the regularity according to regions. This normalization is also spatial but less dependent on the global distribution of event data." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 308, + 287, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 308, + 287, + 392 + ], + "spans": [ + { + "bbox": [ + 46, + 308, + 287, + 392 + ], + "type": "text", + "content": "We modify the parameter-free normalization scheme proposed in prior works [43]. Given extracted feature " + }, + { + "bbox": [ + 46, + 308, + 287, + 392 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 46, + 308, + 287, + 392 + ], + "type": "text", + "content": " from network with size of " + }, + { + "bbox": [ + 46, + 308, + 287, + 392 + ], + "type": "inline_equation", + "content": "C \\times H \\times W" + }, + { + "bbox": [ + 46, + 308, + 287, + 392 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 46, + 308, + 287, + 392 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 308, + 287, + 392 + ], + "type": "text", + "content": ": channel, " + }, + { + "bbox": [ + 46, + 308, + 287, + 392 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 46, + 308, + 287, + 392 + ], + "type": "text", + "content": ": height, " + }, + { + "bbox": [ + 46, + 308, + 287, + 392 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 46, + 308, + 287, + 392 + ], + "type": "text", + "content": ": width), let " + }, + { + "bbox": [ + 46, + 308, + 287, + 392 + ], + "type": "inline_equation", + "content": "F(k,i,j)" + }, + { + "bbox": [ + 46, + 308, + 287, + 392 + ], + "type": "text", + "content": " denotes kij-th element, where " + }, + { + "bbox": [ + 46, + 308, + 287, + 392 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 308, + 287, + 392 + ], + "type": "text", + "content": " is the index of channel and " + }, + { + "bbox": [ + 46, + 308, + 287, + 392 + ], + "type": "inline_equation", + "content": "i,j" + }, + { + "bbox": [ + 46, + 308, + 287, + 392 + ], + "type": "text", + "content": " are spatial dimensions. Then, we apply the normalization along channel-dimension to both left and right features as follows:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 83, + 399, + 287, + 434 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 399, + 287, + 434 + ], + "spans": [ + { + "bbox": [ + 83, + 399, + 287, + 434 + ], + "type": "interline_equation", + "content": "F (k, i, j) = \\frac {F (k , i , j)}{\\sqrt {\\sum_ {c = 0} ^ {C - 1} \\| F (c , i , j) \\| ^ {2} + \\varepsilon}}. \\tag {2}", + "image_path": "2eea23c37c4e68989f57d8e240a59a86ade8becd88c71f31d1964a33b2935757.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 441, + 287, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 441, + 287, + 464 + ], + "spans": [ + { + "bbox": [ + 47, + 441, + 287, + 464 + ], + "type": "text", + "content": "After that, we apply the normalization along the epipolar line, which is defined as:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 80, + 471, + 287, + 505 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 80, + 471, + 287, + 505 + ], + "spans": [ + { + "bbox": [ + 80, + 471, + 287, + 505 + ], + "type": "interline_equation", + "content": "F (k, i, j) = \\frac {F (k , i , j)}{\\sqrt {\\sum_ {w = 0} ^ {W - 1} \\| F (k , i , w) \\| ^ {2} + \\varepsilon}}. \\tag {3}", + "image_path": "99dd68184d159dc2d0d0c425c122742177d06c1e75ee4859161d367f276d5387.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 511, + 287, + 525 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 511, + 287, + 525 + ], + "spans": [ + { + "bbox": [ + 47, + 511, + 287, + 525 + ], + "type": "text", + "content": "3.5. Motion-invariant Consistency Module (MCM)" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 529, + 287, + 625 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 529, + 287, + 625 + ], + "spans": [ + { + "bbox": [ + 46, + 529, + 287, + 625 + ], + "type": "text", + "content": "The motivation of the motion-invariant consistency module on the target domain is two-folds. The first is to resolve the domain gap caused by different camera motion. Second, we desire the event stereo network to be robust on perturbation or noise, adapting to the target domain. The perfectly adapted network should be able invariant to the motion of event camera and estimate the prediction stably, even if there is some perturbation in the input." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 626, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 626, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 626, + 287, + 714 + ], + "type": "text", + "content": "In this subsection, we denote the voxel grid corresponding to the events " + }, + { + "bbox": [ + 47, + 626, + 287, + 714 + ], + "type": "inline_equation", + "content": "E^{\\hat{t},T}" + }, + { + "bbox": [ + 47, + 626, + 287, + 714 + ], + "type": "text", + "content": " accumulated during time " + }, + { + "bbox": [ + 47, + 626, + 287, + 714 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 47, + 626, + 287, + 714 + ], + "type": "text", + "content": " until " + }, + { + "bbox": [ + 47, + 626, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\hat{t}" + }, + { + "bbox": [ + 47, + 626, + 287, + 714 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 47, + 626, + 287, + 714 + ], + "type": "inline_equation", + "content": "V^{\\hat{t},T}" + }, + { + "bbox": [ + 47, + 626, + 287, + 714 + ], + "type": "text", + "content": ". Specifically, events are converted to a voxel grid pair " + }, + { + "bbox": [ + 47, + 626, + 287, + 714 + ], + "type": "inline_equation", + "content": "V_{l}^{\\hat{t},T}, V_{r}^{\\hat{t},T}" + }, + { + "bbox": [ + 47, + 626, + 287, + 714 + ], + "type": "text", + "content": ", and fed to the network to estimate a disparity map " + }, + { + "bbox": [ + 47, + 626, + 287, + 714 + ], + "type": "inline_equation", + "content": "D_{l}^{\\hat{t}}" + }, + { + "bbox": [ + 47, + 626, + 287, + 714 + ], + "type": "text", + "content": ". Since the motion in the datasets is already acquired and immutable, we use a trick to augment event streams of fast or slow motions with temporal perturbation " + }, + { + "bbox": [ + 47, + 626, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 47, + 626, + 287, + 714 + ], + "type": "text", + "content": ". If events" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 72, + 546, + 244 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 546, + 244 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 546, + 244 + ], + "type": "text", + "content": "are stacked for a longer time " + }, + { + "bbox": [ + 304, + 72, + 546, + 244 + ], + "type": "inline_equation", + "content": "T + \\tau" + }, + { + "bbox": [ + 304, + 72, + 546, + 244 + ], + "type": "text", + "content": " (i.e., more events) after normalizing temporal value in events (converting temporal values into a range between 0 and 1) and converted for the same bin of voxel grid, it is able to imitate the voxel grid of an event from an actual fast motion. Conversely, if stacked for a shorter time " + }, + { + "bbox": [ + 304, + 72, + 546, + 244 + ], + "type": "inline_equation", + "content": "T - \\tau" + }, + { + "bbox": [ + 304, + 72, + 546, + 244 + ], + "type": "text", + "content": " (i.e., fewer events), it is the same as the voxel grid made with events of slow motion. From this, we can generate a motion perturbed event voxel " + }, + { + "bbox": [ + 304, + 72, + 546, + 244 + ], + "type": "inline_equation", + "content": "V^{\\hat{t},\\hat{T}}" + }, + { + "bbox": [ + 304, + 72, + 546, + 244 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 72, + 546, + 244 + ], + "type": "inline_equation", + "content": "\\hat{T} = T \\pm \\tau" + }, + { + "bbox": [ + 304, + 72, + 546, + 244 + ], + "type": "text", + "content": " without additional data acquisition. As shown in Fig. 5, perturbed voxel pairs " + }, + { + "bbox": [ + 304, + 72, + 546, + 244 + ], + "type": "inline_equation", + "content": "V_{l}^{\\hat{t},\\hat{T}}, V_{r}^{\\hat{t},\\hat{T}}" + }, + { + "bbox": [ + 304, + 72, + 546, + 244 + ], + "type": "text", + "content": " are fed into the event stereo network to predict the perturbed disparity map " + }, + { + "bbox": [ + 304, + 72, + 546, + 244 + ], + "type": "inline_equation", + "content": "\\tilde{D}_{l}^{\\hat{t}}" + }, + { + "bbox": [ + 304, + 72, + 546, + 244 + ], + "type": "text", + "content": ". Then, for pixel-wise consistency between the prediction of motion-perturbed input and the original input, our consistency loss is defined via " + }, + { + "bbox": [ + 304, + 72, + 546, + 244 + ], + "type": "inline_equation", + "content": "L_{1}" + }, + { + "bbox": [ + 304, + 72, + 546, + 244 + ], + "type": "text", + "content": " distance:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 367, + 252, + 545, + 270 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 367, + 252, + 545, + 270 + ], + "spans": [ + { + "bbox": [ + 367, + 252, + 545, + 270 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {t a r g e t}} ^ {\\text {c o n s i s t e n c y}} = \\| D _ {l} ^ {\\hat {t}} - \\tilde {D} _ {l} ^ {\\hat {t}} \\| _ {1} \\tag {4}", + "image_path": "1d8dbdc1a4f931a24205eaa1ae40bbf7bc1b48c720014af1c2137af9df744768.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 277, + 545, + 302 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 277, + 545, + 302 + ], + "spans": [ + { + "bbox": [ + 304, + 277, + 545, + 302 + ], + "type": "text", + "content": "More details about the implementation of motion-invariant consistency module can be seen in supple." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 310, + 397, + 321 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 310, + 397, + 321 + ], + "spans": [ + { + "bbox": [ + 306, + 310, + 397, + 321 + ], + "type": "text", + "content": "3.6. Loss functions" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 328, + 545, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 328, + 545, + 389 + ], + "spans": [ + { + "bbox": [ + 304, + 328, + 545, + 389 + ], + "type": "text", + "content": "On the source domain, we use the two losses for training the network. We adopt the smooth " + }, + { + "bbox": [ + 304, + 328, + 545, + 389 + ], + "type": "inline_equation", + "content": "L_{1}" + }, + { + "bbox": [ + 304, + 328, + 545, + 389 + ], + "type": "text", + "content": " loss for disparity estimation: " + }, + { + "bbox": [ + 304, + 328, + 545, + 389 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{source}^{task} = \\mathrm{smooth}_{L_1}(\\tilde{d}_l^t -d_l^t)" + }, + { + "bbox": [ + 304, + 328, + 545, + 389 + ], + "type": "text", + "content": ", and the binary cross entropy loss for artifact prediction: " + }, + { + "bbox": [ + 304, + 328, + 545, + 389 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{source}^{mask} = \\sum_{i\\in \\{l,r\\}}BCE(M_i^t,\\tilde{M}_i^t)" + }, + { + "bbox": [ + 304, + 328, + 545, + 389 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 388, + 545, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 388, + 545, + 413 + ], + "spans": [ + { + "bbox": [ + 306, + 388, + 545, + 413 + ], + "type": "text", + "content": "On the target domain, we use the reconstruction loss " + }, + { + "bbox": [ + 306, + 388, + 545, + 413 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text {target }}^{\\text {recon }}" + }, + { + "bbox": [ + 306, + 388, + 545, + 413 + ], + "type": "text", + "content": " (Eq. 1) and consistency loss " + }, + { + "bbox": [ + 306, + 388, + 545, + 413 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text {target }}^{\\text {consistency }}" + }, + { + "bbox": [ + 306, + 388, + 545, + 413 + ], + "type": "text", + "content": " (Eq. 4)." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 413, + 545, + 436 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 413, + 545, + 436 + ], + "spans": [ + { + "bbox": [ + 306, + 413, + 545, + 436 + ], + "type": "text", + "content": "Finally, the total loss for an end-to-end optimization process is defined as:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 332, + 443, + 545, + 464 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 332, + 443, + 545, + 464 + ], + "spans": [ + { + "bbox": [ + 332, + 443, + 545, + 464 + ], + "type": "interline_equation", + "content": "\\mathcal {L} ^ {\\text {t o t a l}} = \\mathcal {L} _ {\\text {s o u r c e}} ^ {\\text {t a s k}} + \\lambda_ {1} \\mathcal {L} _ {\\text {s o u r c e}} ^ {\\text {m a s k}} + \\lambda_ {2} \\mathcal {L} _ {\\text {t a r g e t}} ^ {\\text {r e c o n}} + \\tag {5}", + "image_path": "b0f6f327bf44422d3ff8c0be6ebc106ee8ec5c76be90f13462e3169ca5d7e976.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 453, + 461, + 517, + 475 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 453, + 461, + 517, + 475 + ], + "spans": [ + { + "bbox": [ + 453, + 461, + 517, + 475 + ], + "type": "interline_equation", + "content": "\\lambda_ {3} \\mathcal {L} _ {\\text {t a r g e t}} ^ {\\text {c o n s i s t e n c y}},", + "image_path": "aa03ed42c6b61a0045c8d520bfdf835557ef426457704b67f92a01e2ab33c1bd.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 484, + 515, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 484, + 515, + 496 + ], + "spans": [ + { + "bbox": [ + 306, + 484, + 515, + 496 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 484, + 515, + 496 + ], + "type": "inline_equation", + "content": "\\lambda_1, \\lambda_2" + }, + { + "bbox": [ + 306, + 484, + 515, + 496 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 484, + 515, + 496 + ], + "type": "inline_equation", + "content": "\\lambda_3" + }, + { + "bbox": [ + 306, + 484, + 515, + 496 + ], + "type": "text", + "content": " are weight for each loss terms." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 507, + 388, + 521 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 507, + 388, + 521 + ], + "spans": [ + { + "bbox": [ + 306, + 507, + 388, + 521 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 527, + 369, + 539 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 527, + 369, + 539 + ], + "spans": [ + { + "bbox": [ + 306, + 527, + 369, + 539 + ], + "type": "text", + "content": "4.1. Datasets" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 545, + 545, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 545, + 641 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 545, + 641 + ], + "type": "text", + "content": "For source domain datasets, we utilize the KITTI dataset [25] and the SceneFlow dataset [24]. The KITTI dataset is a real-world dataset with two subsets (i.e. KITTI 2012 [13] and KITTI 2015 [25]), containing 394 stereo images with sparse ground-truth for training. On the other hand, the SceneFlow dataset [24] is a large synthetic dataset containing diverse scenes. The SceneFlow dataset provides 35k stereo images with dense ground-truth disparity maps." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 642, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 714 + ], + "type": "text", + "content": "For target domain, we use the recently published benchmark dataset of DSEC [12], a large-scale high-quality driving dataset with challenging scenes. DSEC provides high-resolution " + }, + { + "bbox": [ + 304, + 642, + 545, + 714 + ], + "type": "inline_equation", + "content": "(640\\times 480)" + }, + { + "bbox": [ + 304, + 642, + 545, + 714 + ], + "type": "text", + "content": " stereo event streams captured in outdoor driving scenes. It contains 53 driving scenarios taken in various lighting conditions, and provides 17k stereo pairs" + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17801" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 66, + 107, + 526, + 301 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "text", + "content": "Table 1. Cross-domain comparisons with other traditional / domain generalization / domain adaptation stereo methods from various source domains. The 2-pixel error " + }, + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "text", + "content": ", 3-pixel error " + }, + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "text", + "content": ", end-point-error, and root mean square error are adopted for evaluation. Zu and In denote the Zurich City and Interlaken sequences, respectively." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 66, + 107, + 526, + 301 + ], + "lines": [ + { + "bbox": [ + 66, + 107, + 526, + 301 + ], + "spans": [ + { + "bbox": [ + 66, + 107, + 526, + 301 + ], + "type": "table", + "html": "
KITTI-to-DSECSceneFlow-to-DSEC
Method2PE3PEEPERMSE2PE3PEEPERMSE
ZuInZuInZuInZuInZuInZuInZuIn
E2VID [38] on target domain
SGM [16]53.755.347.749.79.310.116.117.053.755.347.749.79.310.1
GwcNet [15]38.237.129.122.03.52.98.25.843.345.028.831.23.04.2
PSMNet [6]36.535.525.924.13.42.96.05.136.439.724.329.62.65.4
AANet [55]46.339.335.326.37.43.817.28.642.839.229.227.33.63.1
DSMNet [58]41.141.630.432.13.24.25.68.146.645.331.230.64.13.7
StereoGAN [23]70.968.866.463.111.49.813.312.273.272.268.073.115.413.4
EventGAN [61] on source domain
GwcNet [15]25.527.319.816.84.63.112.29.155.156.337.237.17.47.3
PSMNet [6]18.920.511.913.64.22.714.810.448.850.635.037.86.85.8
AANet [55]50.447.342.538.69.85.421.711.358.855.445.342.45.75.8
DSMNet [58]18.823.610.512.62.12.44.56.751.252.344.643.26.25.9
StereoGAN [23]61.460.352.850.715.313.718.918.975.271.765.566.313.310.6
ADES (Ours)
AANet13.819.97.19.81.41.72.73.422.324.911.113.91.61.9
PSMNet10.910.25.65.51.21.32.53.217.512.89.46.71.41.3
", + "image_path": "0cf4e8ce11a60bc63f5d93931e78aa85e936e3b8b3f6ec83c6b716e5294b9334.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 313, + 289, + 398 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 313, + 289, + 398 + ], + "spans": [ + { + "bbox": [ + 46, + 313, + 289, + 398 + ], + "type": "text", + "content": "for training. Following the previous image-to-event transfer tasks for segmentation [46], we adopt sequences acquired during the day with monotonous illuminance, called Zurich City. Furthermore, we also conduct experiments on Interlaken sequences containing the high dynamic range and challenging illuminance scenes. More details about a split of datasets are provided in the supple." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 404, + 179, + 417 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 404, + 179, + 417 + ], + "spans": [ + { + "bbox": [ + 47, + 404, + 179, + 417 + ], + "type": "text", + "content": "4.2. Implementation details" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 423, + 288, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 423, + 288, + 509 + ], + "spans": [ + { + "bbox": [ + 46, + 423, + 288, + 509 + ], + "type": "text", + "content": "The weights " + }, + { + "bbox": [ + 46, + 423, + 288, + 509 + ], + "type": "inline_equation", + "content": "\\lambda_{1}, \\lambda_{2}" + }, + { + "bbox": [ + 46, + 423, + 288, + 509 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 423, + 288, + 509 + ], + "type": "inline_equation", + "content": "\\lambda_{3}" + }, + { + "bbox": [ + 46, + 423, + 288, + 509 + ], + "type": "text", + "content": " are set as 0.3, 1, and 0.2, respectively. We train our end-to-end framework using the Adam optimizer [19]. We set the learning rate to " + }, + { + "bbox": [ + 46, + 423, + 288, + 509 + ], + "type": "inline_equation", + "content": "1 \\times 10^{-3}" + }, + { + "bbox": [ + 46, + 423, + 288, + 509 + ], + "type": "text", + "content": " with a batch size of 8 using " + }, + { + "bbox": [ + 46, + 423, + 288, + 509 + ], + "type": "inline_equation", + "content": "384 \\times 336" + }, + { + "bbox": [ + 46, + 423, + 288, + 509 + ], + "type": "text", + "content": " random crops. To generate the artifacts in Sec. 3.3, we utilize the Blur and OpticalDistortion transforms from library [4]. More details are provided in supple." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 515, + 230, + 528 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 515, + 230, + 528 + ], + "spans": [ + { + "bbox": [ + 47, + 515, + 230, + 528 + ], + "type": "text", + "content": "4.3. Comparisons with Other Methods" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 534, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 534, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 534, + 288, + 713 + ], + "type": "text", + "content": "We compare our proposed ADES framework with the other traditional algorithm (SGM [16]), domain generalization (DSMNet [58]), and domain adaptation (StereoGAN [23]). In addition, we evaluate PSMNet [6], GwcNet [15], and AANet [55], which have achieved comparable performance in stereo matching. We train those networks in the source domain and test the network in the target domain. To align the different modalities between the source and target domains, we utilize E2VID [38] or EventGAN [61]. In the case of E2VID, an image-based stereo network is trained using a grayscale image in the source domain, and when testing, events in the target domain are reconstructed into a gray image using E2VID. Conversely, in the case of EventGAN, the event-based stereo network is trained using the events, which are converted by EventGAN from consecu" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 312, + 547, + 433 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 312, + 547, + 433 + ], + "spans": [ + { + "bbox": [ + 304, + 312, + 547, + 433 + ], + "type": "text", + "content": "tive images in the source domain. We evaluate the proposed framework by applying it to AANet and PSMNet, which can represent networks using 3D and 4D cost volumes. Especially, AANet is efficient, so it is a widely adopted structure in recent event stereo research [28, 30]. When training, the proposed modules are used, but when evaluating, all the proposed modules without normalization are removed, and only the event stereo network is used to predict the disparity. Table 1 shows the results of training on the various source dataset, such as KITTI and SceneFlow datasets." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 435, + 547, + 663 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 435, + 547, + 663 + ], + "spans": [ + { + "bbox": [ + 304, + 435, + 547, + 663 + ], + "type": "text", + "content": "KITTI-to-DSEC. Even if the networks are trained on the source domain, the results of networks using the events from EventGAN can not achieve high performance. Some networks (PSMNet, GwcNet, and AANet) do not have the ability of domain generalization and adaptation. In addition, the distribution gap of disparity and motion between the domains lead to further degradation of performance. Similarly, most of the results using reconstructed images with E2VID do not show comparable performance. The reconstructed image on the target domain has a large gap with the real image on the source domain, which cannot be dealt with generalization (DSMNet), adaptation (StereoGAN) and conventional methods (SGM). Compared with existing works, our network achieves significantly high performance, considering the gap between domains such as motions and disparity. It is noticeable that in case of AANet+ADES, the performance improvement is significant, e.g., 2PE decreases from 50.4 to 13.8, and RMSE decreases from 21.7 to 2.7 in Zurich City sequence." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "content": "SceneFlow-to-DSEC. The experiment results trained on the synthetic source domain show a more significant domain gap. Due to the effect of the syn-to-real gap, prior works show significantly lower performance than those" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "17802" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 58, + 70, + 533, + 281 + ], + "blocks": [ + { + "bbox": [ + 58, + 70, + 533, + 281 + ], + "lines": [ + { + "bbox": [ + 58, + 70, + 533, + 281 + ], + "spans": [ + { + "bbox": [ + 58, + 70, + 533, + 281 + ], + "type": "image", + "image_path": "216e814972cf116cfed0580bf361a5e7779dd58b388aa9aa5fff0cb6c17f86e6.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 282, + 547, + 306 + ], + "lines": [ + { + "bbox": [ + 46, + 282, + 547, + 306 + ], + "spans": [ + { + "bbox": [ + 46, + 282, + 547, + 306 + ], + "type": "text", + "content": "Figure 6. Qualitative results for the proposed method with other methods. Compared to EventGAN [61] and E2VID [38], our method can predict accurate and sharp disparity maps." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 59, + 327, + 273, + 403 + ], + "blocks": [ + { + "bbox": [ + 85, + 315, + 249, + 324 + ], + "lines": [ + { + "bbox": [ + 85, + 315, + 249, + 324 + ], + "spans": [ + { + "bbox": [ + 85, + 315, + 249, + 324 + ], + "type": "text", + "content": "Table 2. Results on DSEC benchmark testset" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 59, + 327, + 273, + 403 + ], + "lines": [ + { + "bbox": [ + 59, + 327, + 273, + 403 + ], + "spans": [ + { + "bbox": [ + 59, + 327, + 273, + 403 + ], + "type": "table", + "html": "
MethodSupervisionRMSE ↓MAE ↓1PE ↓2PE ↓
[48]✓1.3860.57610.922.91
[28]✓1.2220.5299.962.65
[30]✓1.2310.5199.582.62
[59]✓1.2640.5279.522.36
Ours (PSM)1.6980.77118.375.36
Ours (AA)1.9820.93624.017.87
", + "image_path": "2dc0a4c856cc9f7da6982a2b63180d802cba6a9ea025c44fcf75a86cd15a42b9.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 411, + 287, + 554 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 411, + 287, + 554 + ], + "spans": [ + { + "bbox": [ + 46, + 411, + 287, + 554 + ], + "type": "text", + "content": "trained on KITTI datasets, e.g., 2PE of PSMNet using EventGAN significantly increases from 20.5 to 50.6 in the Interlaken sequence. Although our proposed method cannot avoid the performance degradation, the decreasing amount is relatively acceptable, e.g., 2PE of PSMNet+ADES increases from 10.2 to 12.8 in the Interlaken sequence. Furthermore, the performance increases in some metrics thanks to the various scenes in the synthetic dataset, e.g., RMSE of PSMNet+ADES decreases from 3.2 to 2.8 in the Interlaken sequence. These results show that our method can be used universally and not limited to a specific source dataset, whether synthetic or real-world." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 555, + 287, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 555, + 287, + 651 + ], + "spans": [ + { + "bbox": [ + 46, + 555, + 287, + 651 + ], + "type": "text", + "content": "In Fig. 6, we provide qualitative comparisons of our method with other methods. E2VID or EventGAN can reduce the gap between modality, but it cannot bridge between domains. On the other hand, our ADES framework predicts sharp and accurate disparity on both AANet and PSMNet. These results demonstrate that our training pipeline resolves the gaps from both domain and modality. More qualitative comparisons are provided in supple." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 658, + 206, + 670 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 658, + 206, + 670 + ], + "spans": [ + { + "bbox": [ + 47, + 658, + 206, + 670 + ], + "type": "text", + "content": "4.4. Results on DSEC test dataset" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "content": "To compare with supervised methods, we utilize the KITTI dataset, which contains ground-truth, as the source domain and the full DSEC train dataset, which lacks" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 307, + 361, + 545, + 509 + ], + "blocks": [ + { + "bbox": [ + 305, + 314, + 545, + 359 + ], + "lines": [ + { + "bbox": [ + 305, + 314, + 545, + 359 + ], + "spans": [ + { + "bbox": [ + 305, + 314, + 545, + 359 + ], + "type": "text", + "content": "Table 3. Ablation studies for sub-modules: Smudge-aware Self-supervision Module (SSM), Feature Normalization (FN), and Motion-invariant Consistency Module (MCM). " + }, + { + "bbox": [ + 305, + 314, + 545, + 359 + ], + "type": "inline_equation", + "content": "D1" + }, + { + "bbox": [ + 305, + 314, + 545, + 359 + ], + "type": "text", + "content": "-error " + }, + { + "bbox": [ + 305, + 314, + 545, + 359 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 305, + 314, + 545, + 359 + ], + "type": "text", + "content": " is adopted." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 361, + 545, + 509 + ], + "lines": [ + { + "bbox": [ + 307, + 361, + 545, + 509 + ], + "spans": [ + { + "bbox": [ + 307, + 361, + 545, + 509 + ], + "type": "table", + "html": "
ModelSSMFNMCMZurichInterlaken
AANet35.226.3
✓33.124.5
✓29.622.7
✓13.315.1
✓✓11.214.6
✓✓8.110.2
✓✓✓7.09.7
PSMNet15.617.2
✓13.816.1
✓13.115.5
✓7.38.9
✓✓6.67.1
✓✓6.06.2
✓✓✓5.65.7
", + "image_path": "a6ebd2775b0af8136666c9de945d55f04d35f1e883a2c2b901564b5d7654a616.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 520, + 545, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 520, + 545, + 568 + ], + "spans": [ + { + "bbox": [ + 305, + 520, + 545, + 568 + ], + "type": "text", + "content": "ground-truth, as the target domain. Table 2 demonstrates that despite not relying on ground-truth data for the target domain, our approach achieves comparable performance to other supervised methods." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 575, + 406, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 575, + 406, + 586 + ], + "spans": [ + { + "bbox": [ + 306, + 575, + 406, + 586 + ], + "type": "text", + "content": "4.5. Ablation Studies" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": "Effectiveness of each components. In Table 3, we conduct the ablation studies to validate the effectiveness of each component. We set the KITTI and DSEC dataset as source and target domain, respectively. Based on AANet and PSMNet from which all proposed modules were removed, the performance was measured while adding the proposed module one by one. The SSM achieves the greatest performance gain as a unitary component, e.g., reducing error rates by " + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "21.9\\%" + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": " on Zurich, and " + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "11.2\\%" + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": " on Interlaken from AANet. In addition, using FN stand-alone reduces the" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17803" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 51, + 98, + 286, + 134 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 287, + 93 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 287, + 93 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 287, + 93 + ], + "type": "text", + "content": "Table 4. Comparison of results with and without smudge prediction. " + }, + { + "bbox": [ + 47, + 70, + 287, + 93 + ], + "type": "inline_equation", + "content": "D1" + }, + { + "bbox": [ + 47, + 70, + 287, + 93 + ], + "type": "text", + "content": "-error " + }, + { + "bbox": [ + 47, + 70, + 287, + 93 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 47, + 70, + 287, + 93 + ], + "type": "text", + "content": " is adopted." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 51, + 98, + 286, + 134 + ], + "lines": [ + { + "bbox": [ + 51, + 98, + 286, + 134 + ], + "spans": [ + { + "bbox": [ + 51, + 98, + 286, + 134 + ], + "type": "table", + "html": "
MethodsZurichInterlaken
w/o Smudge Prediction16.112.3
w/ Smudge Prediction7.09.7
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Qualitative results of disparity predictions with and without smudge prediction." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 279, + 286, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 279, + 286, + 399 + ], + "spans": [ + { + "bbox": [ + 46, + 279, + 286, + 399 + ], + "type": "text", + "content": "error by " + }, + { + "bbox": [ + 46, + 279, + 286, + 399 + ], + "type": "inline_equation", + "content": "1.7\\% \\sim 5.6\\%" + }, + { + "bbox": [ + 46, + 279, + 286, + 399 + ], + "type": "text", + "content": " depending on the target domain and model, compared to the baseline. Similarly, MCM also reduces the error by " + }, + { + "bbox": [ + 46, + 279, + 286, + 399 + ], + "type": "inline_equation", + "content": "1.1\\% \\sim 2.1\\%" + }, + { + "bbox": [ + 46, + 279, + 286, + 399 + ], + "type": "text", + "content": ". These FN and MCM work even if implemented together with SSM, e.g., compared to the case of using only SSM from AANet in Zurich, when FN and MCM are used together, errors are more reduced by " + }, + { + "bbox": [ + 46, + 279, + 286, + 399 + ], + "type": "inline_equation", + "content": "5.2\\%" + }, + { + "bbox": [ + 46, + 279, + 286, + 399 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 279, + 286, + 399 + ], + "type": "inline_equation", + "content": "2.1\\%" + }, + { + "bbox": [ + 46, + 279, + 286, + 399 + ], + "type": "text", + "content": ", respectively. Finally, the performance gain is the most significant when all of the proposed modules are used, and these results validate that all modules are effective for domain adaptation." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 400, + 286, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 400, + 286, + 651 + ], + "spans": [ + { + "bbox": [ + 46, + 400, + 286, + 651 + ], + "type": "text", + "content": "Effectiveness of smudge predictions. We investigate the effect of the proposed smudge prediction on SSM. Using the KITTI as the source domain, the quantitative and qualitative results with and without smudge prediction from AANet are shown in Table 4 and Fig. 7. Compared with the absence of smudge prediction, our method utilizes the photometric loss of image reconstruction effectively. Therefore, through SSM using smudge prediction, the performance of the disparity estimation is improved e.g., the " + }, + { + "bbox": [ + 46, + 400, + 286, + 651 + ], + "type": "inline_equation", + "content": "D1" + }, + { + "bbox": [ + 46, + 400, + 286, + 651 + ], + "type": "text", + "content": "-error decreases from 16.1 to 7.0 in Zurich City sequence. Specifically, as can be seen in Fig. 7, smudge prediction helps the network to robustly infer the boundary of an object, making a sharp disparity map. We visualize the smudge mask in Fig. 8 to show how smudge masks can aid effective learning in SSM. As shown in 1st row of Fig. 8, when an image is reconstructed from an event via E2VID, smudge-like blurry artifacts appear around the boundary of the object due to the noisy nature of the event streams. Our smudge prediction estimates these artifacts regions, helping to sharpen disparity when performing self-supervision and boosting the performance of disparity estimation." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 653, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 286, + 713 + ], + "type": "text", + "content": "Comparison of normalization. Table 5 reports the comparison of our feature normalization with the existing learning-free normalization method [43]. We set the KITTI dataset as the source domain and the model to AANet. Although our epipolar norm is a modified module of the ex" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 310, + 97, + 538, + 144 + ], + "blocks": [ + { + "bbox": [ + 306, + 70, + 545, + 93 + ], + "lines": [ + { + "bbox": [ + 306, + 70, + 545, + 93 + ], + "spans": [ + { + "bbox": [ + 306, + 70, + 545, + 93 + ], + "type": "text", + "content": "Table 5. Comparison of epipolar norm with existing cost norm [43]. " + }, + { + "bbox": [ + 306, + 70, + 545, + 93 + ], + "type": "inline_equation", + "content": "D1" + }, + { + "bbox": [ + 306, + 70, + 545, + 93 + ], + "type": "text", + "content": "-error " + }, + { + "bbox": [ + 306, + 70, + 545, + 93 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 306, + 70, + 545, + 93 + ], + "type": "text", + "content": " is adopted." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 310, + 97, + 538, + 144 + ], + "lines": [ + { + "bbox": [ + 310, + 97, + 538, + 144 + ], + "spans": [ + { + "bbox": [ + 310, + 97, + 538, + 144 + ], + "type": "table", + "html": "
MethodsZurichInterlaken
w/o Norm11.214.6
Cost Norm [43]12.311.1
Our Epipolar Norm7.09.7
", + "image_path": "6693ef2e0063a9e8a8e543b7674b8cc4b7bcae70f5eb88cd97ca2ce70d806e3c.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 309, + 147, + 541, + 241 + ], + "blocks": [ + { + "bbox": [ + 309, + 147, + 541, + 241 + ], + "lines": [ + { + "bbox": [ + 309, + 147, + 541, + 241 + ], + "spans": [ + { + "bbox": [ + 309, + 147, + 541, + 241 + ], + "type": "image", + "image_path": "7447909073deebe9c1fa6c0c43fb17cdc1ee7c21882eb81837c7b8e5b03949f0.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 243, + 545, + 266 + ], + "lines": [ + { + "bbox": [ + 306, + 243, + 545, + 266 + ], + "spans": [ + { + "bbox": [ + 306, + 243, + 545, + 266 + ], + "type": "text", + "content": "Figure 8. Generated smudge mask on the target domain. Top: reconstructed images, Bottom: corresponding smudge mask." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 276, + 545, + 432 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 276, + 545, + 432 + ], + "spans": [ + { + "bbox": [ + 304, + 276, + 545, + 432 + ], + "type": "text", + "content": "isting work, the results verify that it is more effective for the domain adaptation ability of event stereo matching. For example, in the case of [43], which performs the normalization along all pixels in spatial manners, the performance is rather reduced due to the specificity of event stereo. For example, especially in Zurich City, the " + }, + { + "bbox": [ + 304, + 276, + 545, + 432 + ], + "type": "inline_equation", + "content": "D1" + }, + { + "bbox": [ + 304, + 276, + 545, + 432 + ], + "type": "text", + "content": "-error increases from 11.2 to 12.3 after introducing the cost norm [43]. On the other hand, our epipolar norm shows a performance improvement in both sequences. From these results, we can confirm that the event stereo network requires a different approach than the existing normalization method, and our normalization is suitable for the domain adaptive event stereo matching." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 442, + 378, + 454 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 442, + 378, + 454 + ], + "spans": [ + { + "bbox": [ + 306, + 442, + 378, + 454 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 462, + 545, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 462, + 545, + 654 + ], + "spans": [ + { + "bbox": [ + 304, + 462, + 545, + 654 + ], + "type": "text", + "content": "In this paper, we propose a novel framework, ADES, for adaptive dense event stereo from the image domain. Our work is the first that transfers the disparity estimation task from the rich image dataset with ground-truth to the event stream to tackle the absence of ground-truth disparities on the target event domain. To this end, we propose the smudge-aware self-supervision module, feature normalization, and motion-invariant consistency module by focusing on the specificity of event stereo. Extensive experiments demonstrate our framework achieves remarkable performance on both 3D and 4D cost volume networks, whether the source domain is synthetic or real-world image dataset. Furthermore, these results demonstrate that our modules can be used universally in existing event stereo networks. We open up the possibility of using event stereo in domains without ground-truth and expect more future work." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "Acknowledgements. This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (NRF-2022R1A2B5B03002636)." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17804" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 146 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 146 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 146 + ], + "type": "text", + "content": "[1] Radhakrishna Achanta, Appu Shaji, Kevin Smith, Aurelien Lucchi, Pascal Fua, and Sabine Süssrunk. 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Conf.(BMVC), volume 1, 2017. 2" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17807" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Learning Analytical Posterior Probability for Human Mesh Recovery/3ccf2427-6060-4a89-9b0c-48648bd3064c_content_list.json b/2023/Learning Analytical Posterior Probability for Human Mesh Recovery/3ccf2427-6060-4a89-9b0c-48648bd3064c_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..ce5ccc22e622ddf0fe1803b295559fcdd42201f7 --- /dev/null +++ b/2023/Learning Analytical Posterior Probability for Human Mesh Recovery/3ccf2427-6060-4a89-9b0c-48648bd3064c_content_list.json @@ -0,0 +1,2052 @@ +[ + { + "type": "text", + "text": "Learning Analytical Posterior Probability for Human Mesh Recovery", + "text_level": 1, + "bbox": [ + 135, + 130, + 833, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Qi Fang $^{1}$ Kang Chen $^{1}$ Yinghui Fan $^{1}$ Qing Shuai $^{2}$ Jiefeng Li $^{3}$ Weidong Zhang $^{1}$", + "bbox": [ + 135, + 179, + 825, + 200 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ NetEase Games AI Lab $^{2}$ Zhejiang University $^{3}$ Shanghai Jiao Tong University", + "bbox": [ + 156, + 202, + 805, + 222 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 256, + 313, + 272 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Despite various probabilistic methods for modeling the uncertainty and ambiguity in human mesh recovery, their overall precision is limited because existing formulations for joint rotations are either not constrained to $\\mathcal{SO}(3)$ or difficult to learn for neural networks. To address such an issue, we derive a novel analytical formulation for learning posterior probability distributions of human joint rotations conditioned on bone directions in a Bayesian manner, and based on this, we propose a new posterior-guided framework for human mesh recovery. We demonstrate that our framework is not only superior to existing SOTA baselines on multiple benchmarks but also flexible enough to seamlessly incorporate with additional sensors due to its Bayesian nature. The code is available at https://github.com/NetEase-GameAI/ProPose.", + "bbox": [ + 73, + 287, + 473, + 515 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 542, + 209, + 558 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Human mesh recovery is a task of recovering body meshes and 3D joint rotations of human actors from images, which has ubiquitous applications in animation production, sports analysis, etc. To achieve this goal, various approaches have been proposed in the computer vision community. Existing methods can be divided into two categories, i.e., direct and indirect, respectively. Direct methods use neural networks to regress the rotations (e.g., axis angle [22], rotation matrix [34], 6D vector [29,37,74]) of each humanoid joint in an end-to-end way, while indirect methods recover joint rotations based on some intermediately predicted proxies (e.g., 3D human keypoints [19, 36, 42], 2D heatmaps [52] or part segmentation [27]). However, both methods have obvious weaknesses. Generally, the estimated poses from direct solutions are not so well-aligned with the images (Fig. 1(a)), because joint rotations are more difficult to regress compared with keypoints [19,36]. On the contrary, though indirect solutions tend to have better estimation precision, their performance heavily relies on the precision of the intermediate proxies and thus are vulnerable to noise and error in the predicted keypoints or part segmentation (Fig. 1(b)).", + "bbox": [ + 73, + 568, + 472, + 902 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/39291c7c29388c1f7f3e19bea7278e064d7256556bf50bfc8472ed75f2077261.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 509, + 258, + 598, + 339 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/add0980b6d72febee0d3662d34975a527e5e1f8d9b6d7d8d7afc83e4472a7bd1.jpg", + "image_caption": [ + "Input" + ], + "image_footnote": [], + "bbox": [ + 508, + 339, + 598, + 422 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/6277d235b5ab6da425aa2619dde09af81a2e76cdcc3fef968c0929fff91df37d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 602, + 267, + 686, + 337 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/67f0b32f7d4d3e04e567f6d12543af22f6c39b2556d480ae2e458794a9309035.jpg", + "image_caption": [ + "(a) Direct" + ], + "image_footnote": [], + "bbox": [ + 622, + 342, + 684, + 421 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/eca143fb8255e843e4a0bacc682f28ca17e918fbef8e93400aba0bc8b7745e73.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 687, + 268, + 784, + 338 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/67ffb243bdbc9787d91371ae4e3dd870ac95c88216857e293376b934620e05e3.jpg", + "image_caption": [ + "(b) Indirect" + ], + "image_footnote": [], + "bbox": [ + 710, + 342, + 782, + 420 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/b4cdd2fd8476cbe093765ca49d89c3f367923a4fabf24e0e13ad5adf9f923e31.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 802, + 270, + 872, + 337 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/9f9fa5f3cbbfe885d38c6c03e059c2bb4ef9b37415e3a7bb81d16ac726f99819.jpg", + "image_caption": [ + "(c) Ours", + "Figure 1. Comparisons of (a) the direct method [29], (b) the indirect method [36], and (c) our method." + ], + "image_footnote": [], + "bbox": [ + 805, + 342, + 875, + 417 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To simultaneously achieve high precision and high robustness, some probabilistic methods are developed, which, instead of seeking a unique solution, try to explicitly model the uncertainty of human poses by learning some kind of probability distribution. Prevalent ways of modeling the distribution include multivariate Gaussian distributions [48, 56], normalizing flows [31], and neural networks [51, 53]. In practice, these learned probability distributions can notably improve the estimation results in some extreme cases (e.g., under large occlusion), however, only minor differences can be found in terms of the overall performances on large datasets. One reason is that these probability models cannot truly reflect the rotational uncertainty since they are not strictly constrained to $\\mathcal{SO}(3)$ . Recently, [55] proposes to adopt the matrix Fisher distribution over $\\mathcal{SO}(3)$ [8, 25] to model the rotational uncertainty caused by depth ambiguity. However, even with this mathematically-correct formulation, the actual performance does not improve much either, because the parameters of the matrix Fisher distribution are not easy for deep neural networks to learn directly.", + "bbox": [ + 496, + 517, + 893, + 820 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To address this problem, we propose a new learning-friendly and mathematically-correct formulation for learning probability distributions for human mesh recovery. Our formulation is derived based on the facts that, (i) the joint rotations follow the matrix Fisher distribution over $\\mathcal{SO}(3)$ ,", + "bbox": [ + 496, + 824, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "8781", + "bbox": [ + 482, + 945, + 513, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "(ii) the unit directions of bones follow the von Mises-Fisher distribution [44], (iii) the bone direction can be viewed as the observation of joint rotation (i.e., the latent variable). It can be proven that the probability distributions of joint rotations conditioned on bone directions still follow the matrix Fisher distribution, which allows us to regress the posterior probability distribution of the 3D joint rotations in a Bayesian manner, and more importantly, in an analytical form. Moreover, we mathematically prove that the posterior probability of human joint rotations is more concentrated than the prior probability. Our experimental results demonstrate that such a characteristic makes the posterior probability an easier form to learn (for neural networks) than its prior counterpart.", + "bbox": [ + 75, + 90, + 472, + 301 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Apart from the theoretical contributions, we also propose a new human mesh recovery framework that can utilize the learned analytical posterior probability. We demonstrate that this framework successfully achieves high precision and high robustness at the same time, and outperforms existing SOTA baselines. Furthermore, our framework enables seamless integration with additional sensors that can yield directional/rotational observations (e.g., multi-view cameras, optical markers, IMUs) due to its Bayesian nature. Different from naive multi-sensor fusion algorithms (e.g., Kalman filter [21]) that typically perform fusion at the inference stage, our framework allows fusion in the training stage to learn the noise characteristics of sensors, and thus has the potential to produce better precision. We demonstrate that our fusion mechanism can achieve similar effects to fusing the latent features from multiple sensor input branches, but is much more flexible since it does not require modification of the main backbone.", + "bbox": [ + 75, + 301, + 472, + 574 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The key contributions of this paper are thereby:", + "bbox": [ + 96, + 575, + 410, + 590 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We derive a novel analytical formulation for learning probability distributions for human joint rotations, and theoretically prove that such formulation allows the regression of posterior probability distribution in a Bayesian manner.", + "- We propose a new framework for human mesh recovery by leveraging the learned analytical posterior probability and show that this framework outperforms existing SOTA baselines.", + "- We introduce a novel and flexible multi-sensor fusion mechanism that allows fusing different observations in the training stage." + ], + "bbox": [ + 96, + 601, + 468, + 804 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related work", + "text_level": 1, + "bbox": [ + 76, + 829, + 215, + 845 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this section, we discuss related studies on human mesh recovery, which can be achieved by optimization-based and learning-based methods. Leveraging the parametric human", + "bbox": [ + 76, + 854, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "model [41, 54], optimization-based approaches [2, 9, 15, 51] fit the parameters via iteration while learning-based approaches regress the parameters with neural networks. Our work follows the learning paradigm, therefore we here mainly review recent advances in learning-based methods.", + "bbox": [ + 496, + 90, + 890, + 167 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Direct methods: Given images as input, this kind of approach directly regresses the model parameters with neural networks. Different representations of rotation [22, 34, 74], supervision schemes [20, 29, 37] as well as temporal context [5, 13, 23, 26] are explored to improve performance. However, the gap between the image space and the abstract parameter space of statistical models makes it difficult to generate well-aligned estimations.", + "bbox": [ + 496, + 186, + 890, + 309 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Indirect methods: Instead of regressing rotation representations from RGB images directly, plenty of works introduce proper intermediate or proxy representations, such as segmentation [27, 49, 68], IUV maps [64, 69, 70], keypoints [6, 14, 36, 52] or surface landmarks [30, 32, 42], to guide the learning of neural networks efficiently. HybrIK [36] decomposes the 3D rotation into solvable swings from 3D keypoints and extra predicted twists. PARE [27] learns to predict attention masks which are fused with image feature maps to provide body part information. These solutions may achieve higher precision, but generating only deterministic results and ignoring the uncertainty of estimation make them sensitive to noisy or erroneous proxy predictions.", + "bbox": [ + 496, + 329, + 890, + 526 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Probabilistic methods: To deal with the uncertainty from occlusions or depth ambiguities, several works manage to produce multiple hypotheses [1] or a probability distribution [53]. I2L-MeshNet [48] predicts lixel-based 1D heatmaps for each human mesh vertex for uncertainty modeling. Sengupta et al. [56] assume simple multivariate Gaussian distributions over the parameters of the human model. ProHMR [31] learns a distribution of plausible 3D poses represented by normalizing flows, which is more powerful and expressive than Gaussian distributions. Recently Sengupta et al. [55] further represent the essential distribution of human joint rotation over $\\mathcal{SO}(3)$ by adopting the matrix Fisher distribution [25], which can provide quantified uncertainty estimation. Despite a better explanation for ambiguities, the parameters of the above distribution are not easy to learn, limiting their overall performance on complicated scenes.", + "bbox": [ + 496, + 547, + 890, + 803 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Multi-sensor fusion: Recently an increasing number of approaches attempt to integrate extra observations from other sensors, such as IMUs [10,65,66] and multi-view cameras [7, 71, 73], to obtain more reliable estimations. One simple strategy is combining all observations properly with", + "bbox": [ + 496, + 825, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "8782", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/a10ab4db7c11d27351eda3dc631c962554e79c64f44d509f9effbcf423e61883.jpg", + "image_caption": [ + "Figure 2. Overview of our framework. Given an input image, the multi-branch network predicts the prior matrix Fisher parameters $\\mathbf{F}$ , the 3D keypoints $\\mathbf{J}$ , and the SMPL shape parameters $\\beta$ , respectively. The bone direction $\\mathbf{d}$ calculated from $\\mathbf{J}$ serves as the likelihood conditioned on 3D rotation. The posterior probability can be obtained based on Bayesian rules (Fusion), which still follows the matrix Fisher distribution, but with different parameters and larger confidence. Observations from additional sensors can also be fused into the posterior probability in the same manner. The corresponding human mesh can then be recovered using the estimated rotation and shape." + ], + "image_footnote": [], + "bbox": [ + 83, + 88, + 893, + 314 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Kalman filter [21], which can be treated as a baseline. Some works [43,62,63] fit the human model to evidence including images and IMUs through joint optimization. Apart from these test-time fusion schemes, several approaches [10, 61] incorporate the fusing process into training by concatenating the features from images and IMUs directly. GeoFuse [72] reinforces the image features guided by IMUs to infer the occluded joints. Our framework is also flexible to perform multi-sensor fusion and generates competitive results without specific modification to the backbone.", + "bbox": [ + 75, + 419, + 472, + 571 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methods", + "text_level": 1, + "bbox": [ + 76, + 585, + 174, + 599 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we first mathematically introduce the probability distributions for orientations regarding rotations and directions (Sec. 3.1). Then, we model the human joint rotation and bone direction with the corresponding distribution, and derive the analytical formulation of the posterior probability of joint rotation conditioned on the bone direction with crucial conclusions and discussion (Sec. 3.2). Finally, we describe the proposed framework (Sec. 3.3) and learning details (Sec. 3.4).", + "bbox": [ + 75, + 609, + 468, + 747 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Orientation probability distribution", + "text_level": 1, + "bbox": [ + 76, + 756, + 387, + 772 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Before delving into human modeling, we investigate the orientation representation for general rigid entities. Suppose $\\mathbf{X} \\in \\mathbb{R}^{n \\times p}$ is the parametric representation of the entity orientation, each column of which depicts the direction of a basis. $\\mathbf{X}$ is on the Stiefel manifold $\\mathcal{V}(n,p)$ if $\\mathbf{X}^T\\mathbf{X} = \\mathbf{I}_p$ , and when $n = p$ , it further belongs to the orthogonal group $\\mathcal{O}(n)$ . Additionally, the components of $\\mathcal{O}(n)$ with determinant $+1$ are referred to as the special or", + "bbox": [ + 76, + 780, + 470, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "thogonal group $\\mathcal{SO}(n)$ , which is used to represent the rotation of $n$ degrees of freedom. Meanwhile, if $p = 1$ , the normalized $\\pmb{X}$ , i.e., $n$ -dimensional unit vector on the manifold $(n - 1)$ -sphere $\\mathcal{S}^{n - 1}$ , can represent the single direction as well. From a probabilistic perspective, when $\\pmb{X}$ is a random matrix, there are two common cases.", + "bbox": [ + 496, + 419, + 890, + 510 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Rotation $(n = p)$ : For rotation matrix $\\mathbf{R} \\in \\mathcal{SO}(n)$ , the matrix Fisher distribution $\\mathcal{MF}(\\cdot)$ has been proposed to characterize its probabilistic properties on $\\mathcal{SO}(n)$ [8, 25]. The probability density function is as follows:", + "bbox": [ + 496, + 527, + 890, + 589 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\np (\\boldsymbol {R}; \\boldsymbol {F}) = \\frac {1}{c (\\boldsymbol {F})} \\exp (t r (\\boldsymbol {F} ^ {T} \\boldsymbol {R})) \\sim \\mathcal {M F} (\\boldsymbol {F}), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 539, + 599, + 890, + 631 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\pmb{F} \\in \\mathbb{R}^{n \\times n}$ is the distribution parameter, and $c(\\pmb{F})$ is a normalizing constant. Algebraically, $\\pmb{F}$ can be decomposed into a concentration matrix $\\pmb{K}$ and a mean rotation matrix $\\pmb{M}$ via SVD decomposition:", + "bbox": [ + 496, + 642, + 890, + 703 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {F} = \\boldsymbol {U} \\boldsymbol {S} \\boldsymbol {V} ^ {T} = \\underbrace {\\left(\\boldsymbol {U} \\Delta \\boldsymbol {V} ^ {T}\\right)} _ {\\boldsymbol {M} \\in \\mathbb {R} ^ {n \\times p}} \\underbrace {\\left(\\boldsymbol {V} \\Delta \\boldsymbol {S} \\boldsymbol {V} ^ {T}\\right)} _ {\\boldsymbol {K} \\in \\mathbb {R} ^ {p \\times p}}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 560, + 712, + 890, + 750 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\Delta = \\text{diag}(1, 1, |\\mathbf{U} \\mathbf{V}|)$ is a diagonal orthogonal matrix to ensure the determinant of $\\mathbf{M}$ is $+1$ . $\\mathbf{K}$ is symmetric positive definite as long as $\\mathbf{F}$ is full rank. A rotation estimation $\\hat{\\mathbf{R}}$ can be calculated from the mode of distribution:", + "bbox": [ + 496, + 761, + 890, + 821 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\boldsymbol {R}} = \\boldsymbol {M} = \\boldsymbol {U} \\operatorname {d i a g} (1, 1, | \\boldsymbol {U} \\boldsymbol {V} |) \\boldsymbol {V} ^ {T}. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 573, + 834, + 890, + 853 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Direction $(p = 1)$ : The probability density function for a unit vector $d\\in S^{n - 1}$ is similar to Eq. (1) if we set $p = 1$", + "bbox": [ + 496, + 869, + 890, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "8783", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "which corresponds to the classical von Mises-Fisher distribution $\\mathcal{V}\\mathcal{M}\\mathcal{F}(\\cdot)$ [44]:", + "bbox": [ + 76, + 90, + 468, + 121 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\np (\\boldsymbol {d}; \\kappa , \\boldsymbol {m}) = \\frac {1}{c (\\kappa)} \\exp (\\kappa \\boldsymbol {m} ^ {T} \\boldsymbol {d}) \\sim \\mathcal {V M F} (\\boldsymbol {m}, \\kappa), \\quad (4)\n$$\n", + "text_format": "latex", + "bbox": [ + 96, + 128, + 468, + 161 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $c(\\kappa)$ is a normalizing constant. $\\pmb{m}$ denotes the mean direction and $\\kappa$ denotes the concentration parameter, which have a close meaning to $M$ and $\\pmb{K}$ in Eq. (2), respectively, and thus $\\hat{\\pmb{d}} = \\pmb{m}$ becomes a direction estimation.", + "bbox": [ + 76, + 167, + 468, + 227 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Theoretically, if $\\kappa$ is 0, $\\mathcal{V}\\mathcal{M}\\mathcal{F}(\\boldsymbol{m},0)$ is equivalent to the uniform distribution on the sphere, while if $\\kappa$ is large, it is close to the wrapped normal distribution $\\mathcal{W}\\mathcal{N}(\\boldsymbol{m},\\kappa^{-1})$ that adds up the densities of vectors representing the same direction on the sphere due to the periodicity. Thus, $\\kappa$ can be viewed as the inverse of the variance and denotes the concentration of the distributions.", + "bbox": [ + 75, + 228, + 468, + 333 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Human modeling", + "text_level": 1, + "bbox": [ + 76, + 342, + 246, + 358 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The human joint rotation can be represented as rotation matrix $\\mathbf{R} \\in \\mathcal{SO}(3)$ . Inspired by recent advances in object pose estimation [3, 33, 46, 67], we incorporate the probabilistic modeling for human poses. Specifically, we adopt the matrix Fisher distribution over $\\mathcal{SO}(3)$ as the prior distribution for joint rotation. Moreover, as the bone direction can be easily calculated from the joint rotation, we regard the joint rotation $\\mathbf{R}$ as the latent variable and the bone direction $\\mathbf{d}$ as the corresponding observation, which follows the von Mises-Fisher distribution:", + "bbox": [ + 75, + 364, + 468, + 515 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\np (\\boldsymbol {d} | \\boldsymbol {R}) = \\frac {1}{c (\\kappa)} e x p (\\kappa \\boldsymbol {l} ^ {T} \\boldsymbol {R} ^ {T} \\boldsymbol {d}) \\sim \\mathcal {V M F} (\\boldsymbol {R l}, \\kappa), \\quad (5)\n$$\n", + "text_format": "latex", + "bbox": [ + 98, + 535, + 468, + 566 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $l$ is the unit direction of the bone in the reference pose (e.g., T-pose), ideally satisfying $Rl = d$ .", + "bbox": [ + 76, + 574, + 468, + 604 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Leveraging Bayesian inference, given the prior distribution (Eq. (1)) and the likelihood function (Eq. (5)), the posterior probability of joint rotation conditioned on the bone direction can be derived as follows:", + "bbox": [ + 76, + 604, + 468, + 662 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} p (\\boldsymbol {R} | \\boldsymbol {d}) = \\frac {p (\\boldsymbol {R}) \\cdot p (\\boldsymbol {d} | \\boldsymbol {R})}{p (\\boldsymbol {d})} \\propto p (\\boldsymbol {R}) \\cdot p (\\boldsymbol {d} | \\boldsymbol {R}) \\tag {6} \\\\ = \\frac {1}{c} e x p (t r [ (\\boldsymbol {F} + \\kappa \\boldsymbol {d l} ^ {T}) ^ {T} \\boldsymbol {R} ]) \\sim \\mathcal {M F} (\\boldsymbol {F} + \\kappa \\boldsymbol {d l} ^ {T}). \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 684, + 468, + 748 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "It can be concluded from Eq. (6) that the posterior probability $p(\\mathbf{R}|\\mathbf{d})$ also follows the matrix Fisher distribution with an updated parameter $\\mathbf{F}' = \\mathbf{F} + \\kappa \\mathbf{d}\\mathbf{l}^T$ .", + "bbox": [ + 76, + 753, + 468, + 800 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Property: From another perspective, the posterior parameter $F'$ can be viewed as the multiplication of the same mean term $M$ and a new concentration term $K'$ :", + "bbox": [ + 76, + 816, + 468, + 861 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {F} ^ {\\prime} = \\boldsymbol {F} + \\kappa \\boldsymbol {d l} ^ {T} = M (\\underbrace {\\boldsymbol {K} + \\kappa \\boldsymbol {M} ^ {T} \\boldsymbol {d l} ^ {T}} _ {\\boldsymbol {K} ^ {\\prime}}). \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 133, + 869, + 468, + 904 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "It can be proved that $M^T d\\boldsymbol{l}^T = \\boldsymbol{ll}^T$ is a real symmetric matrix with rank 1, and $K$ from Eq. (2) is also real symmetric, thus the posterior concentration term $K'$ is a real symmetric matrix. According to the interlacing theorem for Hermitian matrices from matrix analysis [17], the eigenvalues for a Hermitian matrix with a rank-1 Hermitian perturbation satisfy the following inequality:", + "bbox": [ + 496, + 90, + 890, + 196 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\lambda_ {1} \\leq \\lambda_ {1} ^ {\\prime} \\leq \\lambda_ {2} \\leq \\dots \\leq \\lambda_ {p - 1} ^ {\\prime} \\leq \\lambda_ {p} \\leq \\lambda_ {p} ^ {\\prime}, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 555, + 205, + 890, + 226 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\lambda_{i}$ and $\\lambda_{i}^{\\prime}$ denote the eigenvalues of $\\pmb{K}$ and $\\pmb{K}^{\\prime}$ , respectively. Note that the eigenvalues of the concentration term equal the singular values of the distribution parameter, which reflect the confidence of the distribution. From Eq. (8) we can get the conclusion that the posterior estimation is more concentrated than the prior estimation as long as the likelihood term is non-zero, and is validated to be a more easily learnable formulation in the experiment and the supplementary material.", + "bbox": [ + 496, + 233, + 890, + 369 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "General form: Similarly, if other sensors that yield directional $\\pmb{d}_i$ or rotational $\\pmb{D}_j$ observations are available, the analytical posterior probability is thereby as follows:", + "bbox": [ + 496, + 386, + 890, + 429 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\np (\\boldsymbol {R} | \\left\\{\\boldsymbol {d} _ {i}, \\boldsymbol {D} _ {j} \\right\\}) \\sim \\mathcal {M F} (\\boldsymbol {F} + \\sum_ {i \\in \\mathcal {Z} _ {1}} \\kappa_ {i} g (\\boldsymbol {d} _ {i}) + \\sum_ {j \\in \\mathcal {Z} _ {3}} \\boldsymbol {D} _ {j} \\boldsymbol {K} _ {j} ^ {T}), \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 504, + 436, + 890, + 467 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\kappa_{i}$ and $K_{j}$ are the concentration terms for weighting. $g(\\cdot)$ is a mapping of IK that converts the directional observation to a rotation estimation, which is not limited to a specific IK algorithm as long as it supports gradient backpropagation (e.g., the simple solution $\\boldsymbol{d}\\boldsymbol{l}^T$ in Eq. (6)). $\\mathcal{Z}_1$ denotes the set of sensors providing directional observations such as accelerometers, while $\\mathcal{Z}_3$ denotes the set of rotational sensors like gyroscopes. We simplify the original derivation by assuming the sensors are unbiased. Please refer to the supplementary material for the derivation.", + "bbox": [ + 496, + 474, + 890, + 626 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Discussion: There are several advantages of our approach. First, adopting the matrix representation is more reasonable than other rotation representations. As presented in [34], a continuous 9D unconstrained representation followed by SVD can achieve comparable or even better performance than the widely used 6D vector [74]. Second, the Gaussian distribution is unsuitable for cases with large uncertainty where the assumption of local linearity cannot hold [11, 12], while the matrix Fisher distribution does not have this problem. Third, the posteriors are easier to learn than the priors in that learning the posteriors can converge to the mode preferred by the likelihood function quickly, while learning the priors may face multiple local minima in the initial stage and thus cannot converge well.", + "bbox": [ + 496, + 643, + 890, + 854 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To recognize the proposed scheme intuitively, we show the schematic diagrams of probabilistic modeling in Fig. 3. For a method without probabilistic modeling (e.g., using IK", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "8784", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/4892c4d0335d5a6aad3b9b9b202585aea25c798d19702e4b0b90435c41eaa63d.jpg", + "image_caption": [ + "Figure 3. Schematic diagrams of probabilistic modeling. The opaque coordinate system $\\triangleleft$ is the ground-truth 3D rotation. The transparent rotation represents a deterministic estimation for a method without probabilistic modeling (row 1), while it denotes a sample from the estimated posterior distribution (row 2). The red region on the sphere represents the probability of a certain rotation, and it could cover the ground-truth even for noisy cases." + ], + "image_footnote": [], + "bbox": [ + 81, + 90, + 459, + 258 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "to solve rotations from keypoints), its underlying model is a single direction, thus it may be erroneous when the estimated bone direction deviates from the ground-truth, as shown in the noisy cases. In contrast, the posterior model can be fused with various models, and for noisy keypoints, it has the potential to recover the exact rotations since the negative impact of its partial reliance on the estimated keypoints can be eliminated by the prior or other observations.", + "bbox": [ + 75, + 395, + 472, + 517 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Learning Framework", + "text_level": 1, + "bbox": [ + 76, + 527, + 279, + 544 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our proposed framework that leverages the derived posterior probability for human mesh recovery is demonstrated in Fig. 2. We adopt the parametric model SMPL [41] as our human representation, which can also be replaced by other human models [51,54]. Given an input image, a CNN backbone is used to extract image features, followed by three output branches, including prior distribution parameter $F$ , 3D keypoints $J$ , and shape parameter $\\beta$ . The adopted keypoints branch consists of normalized 2D keypoints and relative depth to the root joint decoded from the feature, as well as the human scale predicted by a small MLP branch, so as to recover absolute 3D keypoints. Note that other strategies for 3D keypoints estimation are also applicable. The bone direction $d$ is calculated from $J$ . Then we utilize Eq. (9) to fuse $F$ , $d$ , or other optional observations analytically in the sense of probability. With the new distribution parameter $F'$ , we can get the rotation estimation according to Eq. (3). As for $\\kappa$ , it is related to the physical properties (measure covariance) of specific sensors that could be set in advance. If there is no prior knowledge of the sensor, it's feasible to tune it manually or learn it from the data. We simply use the scaled scores of estimated keypoints. For multiple sensors, the concentration term $K$ is simplified as a diagonal matrix.", + "bbox": [ + 75, + 553, + 472, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Objective functions: For the following objective functions, symbols with superscript $*$ indicate the groundtruth, and symbols with hat indicate the estimation. The $L_{1}$ loss is used to supervise the 3D keypoints, while the $L_{2}$ loss is applied to other variables:", + "bbox": [ + 496, + 90, + 893, + 167 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {J} = \\left| \\left| \\hat {\\boldsymbol {J}} - \\boldsymbol {J} ^ {*} \\right| \\right| _ {1}, \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 630, + 176, + 890, + 195 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\beta} = \\left\\| \\hat {\\boldsymbol {\\beta}} - \\boldsymbol {\\beta} ^ {*} \\right\\| _ {2} ^ {2}, \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 632, + 220, + 890, + 239 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The mode of the posterior probability distribution $\\hat{R}$ can be solved according to Eq. (6) and (3), and is supervised if the annotations of SMPL pose parameters $\\theta$ are provided as follows:", + "bbox": [ + 496, + 246, + 893, + 304 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\theta} = \\left| \\left| \\hat {\\boldsymbol {R}} - \\exp (\\boldsymbol {\\theta} ^ {*}) \\right| \\right| _ {2} ^ {2}, \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 606, + 306, + 890, + 325 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\text{expm}$ denotes the exponential map implemented with the Rodrigues' formula.", + "bbox": [ + 496, + 330, + 890, + 359 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Apart from the mode, the whole distribution also needs to be supervised. Since the normalizing constant in the distribution is hard to be calculated stably due to the numerical integration, we propose to supervise the distribution by sampling. Specifically, we adopt the rejection sampling technique to sample Bingham distribution of unit quaternions on $S^3$ based on its equivalence to matrix Fisher distribution. The proposal distribution in rejection sampling is angular central Gaussian (ACG) distribution [24, 55]. Thus the sampling loss is as follows:", + "bbox": [ + 496, + 361, + 890, + 512 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {s} = \\sum_ {i = 1} ^ {N _ {s}} \\rho \\left(\\left| \\left| \\hat {\\boldsymbol {R}} _ {i} - \\exp \\left(\\boldsymbol {\\theta} ^ {*}\\right) \\right| \\right| _ {2} ^ {2}\\right), \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 578, + 523, + 890, + 564 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $N_{s}$ is the number of samples. $\\rho$ is an simple activation function for relaxation, which tolerates small deviations.", + "bbox": [ + 496, + 570, + 890, + 613 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The total objective function is as follows:", + "bbox": [ + 519, + 614, + 795, + 630 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = w _ {1} \\mathcal {L} _ {J} + w _ {2} \\mathcal {L} _ {\\beta} + w _ {3} \\mathcal {L} _ {\\theta} + w _ {4} \\mathcal {L} _ {s}, \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 566, + 643, + 890, + 659 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $w_{1}, w_{2}, w_{3}$ , and $w_{4}$ are weight scalars.", + "bbox": [ + 500, + 671, + 800, + 686 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Implementation details", + "text_level": 1, + "bbox": [ + 500, + 696, + 714, + 712 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We adopt ResNet-34 [16] and HRNet-W48 [58] as backbones. The ResNet backbone is followed by three deconvolutional layers to generate 3D heatmaps with the size of $64 \\times 64 \\times 64$ for keypoints and three MLPs for shape parameters $\\beta$ (10), distribution parameter $F$ (216) and human scale (1). The feature from HRNet backbone is upsampled and directly followed by similar output branches with dimensions motioned above. The input image has a resolution of $256 \\times 256$ . The network is trained for 50 epochs with Adam and an initial learning rate of $1 \\times 10^{-3}$ , decayed with a factor of 10. $w_{1}$ and $w_{2}$ are set to 1. $w_{3}$ and $w_{4}$ are set to 0.1 and increased to 1 in the later stage of training.", + "bbox": [ + 496, + 719, + 893, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "8785", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 89, + 209, + 107 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we demonstrate the effectiveness of our framework on human mesh recovery and multi-sensor fusion, evaluate our key designs via an ablation study, and discuss the limitation and future work of our method.", + "bbox": [ + 75, + 114, + 468, + 175 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Datasets and metrics", + "text_level": 1, + "bbox": [ + 76, + 186, + 272, + 200 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To maintain the fairness of comparison, we adopt the same datasets and metrics as previous methods.", + "bbox": [ + 75, + 209, + 468, + 239 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Human3.6M [18] provides 3D keypoints annotations, and the corresponding SMPL annotations are from MoSh [40]. We use (S1, S5, S6, S7, S8) for training and (S9, S11) for evaluation, following standard practice [22, 36].", + "bbox": [ + 75, + 239, + 468, + 301 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3DPW [62] provides SMPL annotations. Following [36, 37], we add its training set only for experiments on it.", + "bbox": [ + 76, + 301, + 467, + 330 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "MS COCO [39] contains in-the-wild images and 2D keypoints annotations. We use its training set to improve the generalization ability of our method.", + "bbox": [ + 75, + 330, + 467, + 377 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "MPI-INF-3DHP [45] is a multi-view dataset that provides 3D keypoints annotations. We only use it for training.", + "bbox": [ + 75, + 377, + 468, + 407 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "AGORA [50] is a synthetic dataset with challenging scenes and SMPL annotations of adults and kids. Only when evaluating our algorithm on it will we add its training set.", + "bbox": [ + 75, + 407, + 468, + 452 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "TotalCapture [61] contains multi-view videos, IMUs and 3D keypoints annotations for the evaluation of sensor fusion algorithms. We follow [61,72] to divide it.", + "bbox": [ + 75, + 452, + 468, + 498 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Metrics include MPJPE, PA-MPJPE, and PVE all in mm. MPJPE measures the 3D keypoints error, while PA-MPJPE is similar to MPJPE except that a rigid alignment is performed at first. PVE measures the human mesh vertex error.", + "bbox": [ + 75, + 498, + 468, + 559 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Human mesh recovery", + "text_level": 1, + "bbox": [ + 76, + 570, + 285, + 585 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1 shows the evaluation results on public benchmarks. With either ResNet or HRNet as the backbone, our approach outperforms SOTA methods. Besides, we surpass the prior counterpart [55] by a large margin, indicating that our posterior estimation is easier to learn than the single prior. Table 2 shows the results on the AGORA test set. Our framework is more accurate than others, especially for kids. Note that for 2D datasets, despite that the pseudo-GT annotator of CLIFF [37] and EFT dataset [20] can be incorporated to further improve our performance, we only use the original keypoints supervision for fair comparisons.", + "bbox": [ + 75, + 593, + 468, + 758 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Posterior effects: We compare different designs to thoroughly validate the posterior effects and the feature choice in our framework, as shown in Table 3, which include: (a) regressing the parameters $\\mathbf{F}$ only without the keypoint branch; (b) solving rotations from keypoints via IK without probabilistic modeling; (c) deactivating the learned prior parameters in testing (i.e., setting $\\mathbf{F}$ to zero); (d) using the feature close to the end of the backbone to regress prior $\\mathbf{F}$", + "bbox": [ + 75, + 779, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/d92933662449f81f2fc2d7834c08e6efbce3b77f714f53033aa784c4b405dac0.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Methods3DPWHuman3.6M
PA ↓MPJPE ↓PVE ↓PA ↓MPJPE ↓
HMR (R-50) [22]81.3130.0-56.888.0
GraphCMR (R-50) [30]70.2--50.1-
SPIN (R-50) [29]59.296.9116.441.162.5
Sengupta. (H-48) [55]*59.284.7*---
HMR-EFT (R-50) [20]52.4--43.9-
I2L-MeshNet (R-50) [48]58.693.2-41.755.7
SPEC (R-50) [28]53.296.5118.5--
BEV (H-32) [60]46.978.592.3--
PARE (H-32) [27]46.574.588.6--
Graphormer (H-64) [38]45.674.787.734.551.2
PyMAF (H-48) [70]45.374.287.037.254.2
HybrIK (R-34) [36]45.074.186.533.655.4
FastMETRO (R-50) [4]48.377.990.637.353.9
FastMETRO (H-64) [4]44.673.584.133.752.2
CLIFF (R-50) [37]45.772.085.335.150.5
CLIFF (H-48) [37]43.069.081.232.747.1
Ours (R-34)44.171.884.931.648.7
Ours (H-48)40.668.379.429.145.7
", + "bbox": [ + 504, + 89, + 888, + 321 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/1faec3451b2dca43164ce084f9d723ae42468a48caf89b66cf668cbf80167c3e.jpg", + "table_caption": [ + "Table 1. Results on standard benchmarks. 'PA' is PA-MPJPE. $R^{\\prime}$ and $H^{\\prime}$ mean ResNet and HRNet. * with scale correction." + ], + "table_footnote": [], + "table_body": "
MethodsAGORA
MPJPE ↓PVE ↓Kid-MPJPE ↓Kid-PVE ↓
HMR [22]180.5173.6219.4209.3
HMR-EFT [20]165.4159.0202.7193.5
SPIN [29]153.4148.9191.7186.7
PARE [27]146.2140.9193.9186.4
SPEC [28]112.3106.5171.0163.2
ROMP [59]108.1103.4159.8156.6
BEV [60]105.3100.7129.1125.9
Hand4Whole [47]89.884.8153.3146.4
CLIFF [37]81.076.094.189.6
HybrIK [36]77.073.990.286.6
Ours74.470.984.580.5
PLIKS [57]71.567.388.384.2
NIKI [35]67.363.983.980.2
", + "bbox": [ + 504, + 376, + 888, + 564 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/c68c256562c7bf2eec05d603b8dbffbbfddcdde5305293151231f1b71a160df9.jpg", + "table_caption": [ + "Table 2. Results on the AGORA test set. The metrics with the prefix 'Kid-' are calculated only for kids, otherwise for all ages. Two concurrent works are shown in gray for completeness." + ], + "table_footnote": [], + "table_body": "
DesignsHuman3.6M
PA-MPJPE ↓MPJPE ↓
(a) W/o 3D keypoints45.876.5
(b) W/o prior F43.263.6
(c) W/o prior F (in testing)42.758.7
(d) Late feature for F and β29.948.6
(e) Early feature for F and β29.346.5
(f) Ours (full model)29.145.7
", + "bbox": [ + 504, + 631, + 888, + 757 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 3. Ablation study of designs on the Human3.6M dataset.", + "bbox": [ + 500, + 765, + 890, + 779 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "and shape $\\beta$ ; (e) using the feature from the initial stage; (f) our full model with all branches and intermediate feature.", + "bbox": [ + 498, + 809, + 890, + 838 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The performance of design (a) is not good since its estimation cannot align precisely with the image, and it is observed that this design exhibits a slower speed of convergence, reflecting the importance of the likelihood function", + "bbox": [ + 498, + 839, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "8786", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/8ef8793fb4117ce0068e0637d3036a9a6c2740ff58b2050070f49afe48176126.jpg", + "image_caption": [ + "Figure 4. Noise simulation. (a) Rotation error v.s. the mixed noises of both prior and keypoint. (b) Rotation/direction error v.s. keypoint noise. The noise level is the ratio of the noise amplitude to the maximum of the variable. The simulation step is $5\\%$ . 'W/o prior $\\pmb{F}$ ' is an indirect strategy without probability. 'Fixed $\\kappa$ ' uses predefined $\\kappa$ . 'Adaptive $\\kappa$ ' means $\\kappa$ varies with the noise variance." + ], + "image_footnote": [], + "bbox": [ + 76, + 88, + 467, + 212 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/8c1c92dba0b23ab7fd3ab717fbccb3af3580120e4ea006dd99f7ab7c11693a6c.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Noise amplitude5mm10mm15mm30mm50mm
W/o prior F61.362.765.071.580.4
Posterior-based48.549.651.454.559.0
(12.8↓)(13.1↓)(13.6↓)(17.0↓)(21.4↓)
", + "bbox": [ + 81, + 315, + 465, + 369 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "from keypoints. The comparison between design (b) and (e) shows that the prior $\\pmb{F}$ is crucial in fusion. Furthermore, design (c) is better than design (b), indicating the prior $\\pmb{F}$ has guided the keypoints learning to some extent. The difference is more significant in MPJPE since the global rotation is supervised for design (c). As for the feature choice, the intermediate feature adopted by our framework shows slightly better performance than the late and early features.", + "bbox": [ + 75, + 436, + 468, + 556 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Noise robustness: We evaluate the robustness of our framework when suffering from noise. Fig. 4 shows the simulation results with two metrics. The rotation error is the angle to be rotated from the estimated rotation $\\hat{\\pmb{R}}$ to the ground-truth. The direction error is the angle between the estimated bone vector and the ground-truth. Fig. 4 (b) reveals that 'w/o prior $F$ has a small direction error but a large rotation error for the unsolved twist, while the posterior strategy has a much smaller error even with a high keypoint noise level and shows a slower error growth rate. Note that the performance of a simple fixed $\\kappa$ is also acceptable. Fig. 4 (a) shows that when the prior noise level is less than $15\\%$ , the keypoint noise has little effect on the posterior result with the adaptive $\\kappa$ , reflecting the tolerance to noises of the posterior scheme. Table 4 shows the noise test on the Human3.6M dataset. From the difference listed in parentheses, when the noise level is higher, the error of the posterior method increases more slowly compared with the baseline without prior $F$ .", + "bbox": [ + 75, + 564, + 468, + 852 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Samples illustration: Fig. 5 illustrates the samples from the posterior distribution. The right hand has a relatively", + "bbox": [ + 75, + 869, + 468, + 902 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/551a24428e3cf58ef213094dfe6143b345957454f84026c874aa78fd2a5e284a.jpg", + "image_caption": [ + "Figure 5. Samples from the distribution. The mode and samples of the relative rotations are shown. The light color indicates the mode, while the dark color indicates an extra sample. The canonical coordinate is at the top right as a reference." + ], + "image_footnote": [], + "bbox": [ + 504, + 90, + 883, + 224 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/93ea13cf12c54c8b59377216843ad10dfd74c59c799830a5a4ca90e28c3381bb.jpg", + "table_caption": [ + "Table 4. Noise test on the Human3.6M dataset. The 3D keypoints suffer from different levels of noises. MPJPE is reported." + ], + "table_footnote": [], + "table_body": "
MethodsSensorsTotalCapture
PA-MPJPE ↓MPJPE ↓
IMUPVH [10]mv + IMUs-42.6
GeoFuse [72]mv + IMUs20.624.6
Oursmv + IMUs19.423.5
VIP [62]sv + IMUs26.0-
Kalman filtersv + IMUs23.134.7
Ourssv29.042.1
Ours (w/o ref, R-50)sv + IMUs25.841.7
Ours (w/o ref, H-48)sv + IMUs22.338.8
Ours (R-50)sv + IMUs25.032.3
Ours (H-48)sv + IMUs21.228.5
", + "bbox": [ + 504, + 309, + 888, + 474 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 5. Results on the TotalCapture dataset. 'mv' and 'sv' denote multi-view and single-view. 'w/o ref' means lacking a reference skeleton (only a statistical one from training set is adopted), which would slightly weaken the performance of our framework.", + "bbox": [ + 498, + 484, + 890, + 540 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "large uncertainty on rotating around the X-axis due to the uncertain twist angle, as shown by the widespread blue and green samples. The left elbow has a vertical uncertainty on the direction of the forearm since the left hand cannot be easily determined. The left ankle has large confidence, except in the depth direction, therefore the green samples spread horizontally.", + "bbox": [ + 496, + 566, + 890, + 671 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Fig. 6 shows the qualitative comparison with the SOTA methods. The indirect methods that use part segmentation [27] or 3D keypoints [36] perform well in most cases, but may suffer from wrong segmentation for distant people or generate unnatural poses. While the direct method CLIFF [37] may not align the image well for complicated scenes.", + "bbox": [ + 496, + 671, + 890, + 762 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Multi-sensor fusion", + "text_level": 1, + "bbox": [ + 500, + 771, + 686, + 786 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We perform experiments on the TotalCapture dataset [61] using the feed-forward network directly without any iterative optimization. As the original dataset does not provide SMPL annotations, we adopt the human skeleton defined by 19 joints and 11 attached IMUs, as shown in Fig. 7. We choose the optimization-based method VIP [62] and the feature-fused method GeoFuse [72] as baselines.", + "bbox": [ + 496, + 794, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "8787", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f8a558669ebb6899c3d4366b2b96191f3d5ac6644e89b0bfcd1c456049e7408f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 81, + 90, + 161, + 194 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/97bef3aa3ad05c5c4187302d0921ab1108abee83d8e96f383a658b86590d312b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 161, + 95, + 243, + 194 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/537f11be175d3c08e65d7d5646ea4f912331d4d4cdb792f934305f53c541ed93.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 250, + 95, + 326, + 194 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6729f757f32c42ad4b4d8e4b10db6fc7e76b9917dafc921762ed954095a8e428.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 343, + 90, + 421, + 194 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/012df255d6d29ba41b6da0d7d000f20e149dc3e2bfb439fa3bc90216136229e3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 421, + 98, + 527, + 194 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b09c7f104e761edade23d6baa3728362b3a8686d0394ac493e35201a7e9cf581.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 529, + 98, + 635, + 194 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/76d25e7592822959ef09daf030b27fd2a96b56709ba125ff73cb6b1ea7f7caf3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 643, + 90, + 723, + 194 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b18ecbf0940149cc4dccc26336b1b88190777680fd91c3dc795d8162d63506ab.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 730, + 102, + 805, + 189 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/fb144614a7e52491647418b2cb7d3ee0e715424490f3930b6f9215fea8dccb6b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 808, + 102, + 888, + 189 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e3b40ff18cdfde0d04248d26bd8dae12894b2a700e0ec4535936ad99313610bd.jpg", + "image_caption": [ + "Input" + ], + "image_footnote": [], + "bbox": [ + 81, + 196, + 161, + 299 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/9fd15cc30ea84ba89f850acb7f2b7c714ce30d06be35141b7210267ec2829e45.jpg", + "image_caption": [ + "HybrIK" + ], + "image_footnote": [], + "bbox": [ + 161, + 200, + 246, + 299 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/977008a88c2065e04983e989a46c6ca18374aa71e979276f673baad0a1ff7165.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 251, + 200, + 328, + 299 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/581cd8faa030dae49a021d5b889c936fe8e6cc69aa8ec35aff1c02a7ac773b3c.jpg", + "image_caption": [ + "Input" + ], + "image_footnote": [], + "bbox": [ + 343, + 196, + 421, + 299 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e4c92c0340adfbb8914e1b55914be0d08e86737c74ef827f296a73b6ba42fbd7.jpg", + "image_caption": [ + "PARE" + ], + "image_footnote": [], + "bbox": [ + 424, + 200, + 527, + 299 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c53e5ebfedf078fbdd47d8aa443aa5627ab7fab1a9204cacafbbe32c2070fa20.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 529, + 200, + 620, + 299 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/36275191f01db9ed8449b025dabb347124ca64892e1f04531b17699f82291708.jpg", + "image_caption": [ + "Input" + ], + "image_footnote": [], + "bbox": [ + 645, + 196, + 723, + 299 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/785477d74d808cd329105a3686cdbbf5c860d919346071c14df89ddc6f37de0a.jpg", + "image_caption": [ + "CLIFF" + ], + "image_footnote": [], + "bbox": [ + 736, + 200, + 792, + 299 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6d078ec3136ca8439e07087f5445bc9af1005fc1152aedf2f7e672653b982c2a.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 808, + 200, + 862, + 299 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/15cccf09e7ecd81b2e76f23fa89d3065e13d7815b7e23ad9e101e735253c1dad.jpg", + "image_caption": [ + "Figure 6. Qualitative comparison. The input images are from 3DPW [62], MS COCO [39], and AGORA [50], respectively. We compare our approach with SOTA methods including HybrIK [36], PARE [27], and CLIFF [37]. For images with multiple people, the person with a solid yellow circle on the face is estimated." + ], + "image_footnote": [], + "bbox": [ + 140, + 386, + 218, + 474 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/37924811c99f9fc8eae307c99353d1f8a4df363d4ee3c90f941b563fd5667fd4.jpg", + "image_caption": [ + "Side View" + ], + "image_footnote": [], + "bbox": [ + 227, + 386, + 310, + 474 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8bfc4d0d5f0a79ecf50c69bceba78929d66e70e22e82e74e1681a5257225d1d1.jpg", + "image_caption": [ + "IMUT-pose" + ], + "image_footnote": [], + "bbox": [ + 326, + 386, + 441, + 474 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/412b33ae1ce14202d9e3ae86f33cfd485cabcbc93e91a4cd2c5d954867d7d311.jpg", + "image_caption": [ + "Front View" + ], + "image_footnote": [], + "bbox": [ + 96, + 489, + 215, + 577 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6ab21ff8a2fcc050ffdab59c47456a2eb6d1b2be64ce8ea3e34ea760a390a3cd.jpg", + "image_caption": [ + "Figure 7. An example of a multi-sensor case. The estimations from the front-view camera, side-view camera, and IMUs are plotted. The normalized confidence score of the left knee is listed." + ], + "image_footnote": [], + "bbox": [ + 227, + 489, + 326, + 582 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/71c9890f4424f2a6d16b35243f44149ae09da929b7543a0cad8aa82f066b1f59.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 328, + 489, + 444, + 582 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 5 shows the experimental results. Our method outperforms baseline methods, indicating the effectiveness of our posterior scheme. In the 'Kalman filter' setup, we apply a weighted sum to the 3D rotations separately obtained from images and IMUs. As the observation variance required for calculating the Kalman gain is unknown, we pick the weight pairs that can yield the best estimation through grid searching, i.e., from (0.7, 0.3) to (0.3, 0.7). Note that unlike Kalman filter which fuses the observations in the testing stage, our method performs fusing in the training stage, and thus has the potential to obtain higher precision. Our framework is also more flexible than feature-level fusing methods since we do not require modifications of the backbone to incorporate new sensors.", + "bbox": [ + 75, + 657, + 468, + 869 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Fig. 7 shows an example of a scene with multiple cameras and IMUs. The confidence from the two cameras are", + "bbox": [ + 75, + 869, + 468, + 898 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "calculated via the normalized differential entropy of the estimated distribution parameters, while the confidence from IMUs is set to a relatively larger value since IMUs can provide accurate measurements. Note that other metrics that represent the uncertainty from the distribution can also be adopted. It can be observed that the front view produces erroneous knee bending due to the depth ambiguity, therefore its confidence is lower than the side view. As a result, the fused result will be less affected by the noisy estimation.", + "bbox": [ + 496, + 388, + 890, + 523 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Limitation and future work", + "text_level": 1, + "bbox": [ + 500, + 534, + 748, + 549 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Our work has several limitations. First, we only consider the uncertainty of poses, not including that of shapes, which can also be modeled as probability distributions. Second, we model the human joint independently, which is only affected by the parent node. Therefore, how to derive the analytical form of joint rotations conditioned on other hierarchical joints to incorporate anatomical constraints explicitly is still unsolved. Besides, with the single-view uncertainty, the temporal extension also deserves further investigation.", + "bbox": [ + 496, + 558, + 890, + 694 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 708, + 617, + 724 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we derive a novel analytical posterior probability for human joint rotations in a Bayesian manner and prove the property that the posteriors are more concentrated than the priors. Based on the derivation, we propose a new framework for human mesh recovery by leveraging the learned posteriors, which has high precision and robustness, outperforming existing SOTA baselines. Furthermore, our framework can be seamlessly incorporated with additional sensors in the training due to its Bayesian nature. 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In CVPR, pages 5745-5753, 2019. 1, 2, 4" + ], + "bbox": [ + 78, + 90, + 467, + 671 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "8791", + "bbox": [ + 482, + 945, + 513, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Learning Analytical Posterior Probability for Human Mesh Recovery/3ccf2427-6060-4a89-9b0c-48648bd3064c_model.json b/2023/Learning Analytical Posterior Probability for Human Mesh Recovery/3ccf2427-6060-4a89-9b0c-48648bd3064c_model.json new file mode 100644 index 0000000000000000000000000000000000000000..fc766003041ff296602550ebd84e4b4866ed919c --- /dev/null +++ b/2023/Learning Analytical Posterior Probability for Human Mesh Recovery/3ccf2427-6060-4a89-9b0c-48648bd3064c_model.json @@ -0,0 +1,2950 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.136, + 0.131, + 0.834, + 0.153 + ], + "angle": 0, + "content": "Learning Analytical Posterior Probability for Human Mesh Recovery" + }, + { + "type": "text", + "bbox": [ + 0.137, + 0.18, + 0.826, + 0.201 + ], + "angle": 0, + "content": "Qi Fang\\(^{1}\\) Kang Chen\\(^{1}\\) Yinghui Fan\\(^{1}\\) Qing Shuai\\(^{2}\\) Jiefeng Li\\(^{3}\\) Weidong Zhang\\(^{1}\\)" + }, + { + "type": "text", + "bbox": [ + 0.158, + 0.203, + 0.807, + 0.223 + ], + "angle": 0, + "content": "\\(^{1}\\)NetEase Games AI Lab \\(^{2}\\)Zhejiang University \\(^{3}\\)Shanghai Jiao Tong University" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.257, + 0.314, + 0.273 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.289, + 0.474, + 0.516 + ], + "angle": 0, + "content": "Despite various probabilistic methods for modeling the uncertainty and ambiguity in human mesh recovery, their overall precision is limited because existing formulations for joint rotations are either not constrained to \\( \\mathcal{SO}(3) \\) or difficult to learn for neural networks. To address such an issue, we derive a novel analytical formulation for learning posterior probability distributions of human joint rotations conditioned on bone directions in a Bayesian manner, and based on this, we propose a new posterior-guided framework for human mesh recovery. We demonstrate that our framework is not only superior to existing SOTA baselines on multiple benchmarks but also flexible enough to seamlessly incorporate with additional sensors due to its Bayesian nature. The code is available at https://github.com/NetEase-GameAI/ProPose." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.543, + 0.21, + 0.559 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.569, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Human mesh recovery is a task of recovering body meshes and 3D joint rotations of human actors from images, which has ubiquitous applications in animation production, sports analysis, etc. To achieve this goal, various approaches have been proposed in the computer vision community. Existing methods can be divided into two categories, i.e., direct and indirect, respectively. Direct methods use neural networks to regress the rotations (e.g., axis angle [22], rotation matrix [34], 6D vector [29,37,74]) of each humanoid joint in an end-to-end way, while indirect methods recover joint rotations based on some intermediately predicted proxies (e.g., 3D human keypoints [19, 36, 42], 2D heatmaps [52] or part segmentation [27]). However, both methods have obvious weaknesses. Generally, the estimated poses from direct solutions are not so well-aligned with the images (Fig. 1(a)), because joint rotations are more difficult to regress compared with keypoints [19,36]. On the contrary, though indirect solutions tend to have better estimation precision, their performance heavily relies on the precision of the intermediate proxies and thus are vulnerable to noise and error in the predicted keypoints or part segmentation (Fig. 1(b))." + }, + { + "type": "image", + "bbox": [ + 0.51, + 0.26, + 0.599, + 0.34 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.509, + 0.34, + 0.599, + 0.424 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.536, + 0.428, + 0.568, + 0.441 + ], + "angle": 0, + "content": "Input" + }, + { + "type": "image", + "bbox": [ + 0.603, + 0.268, + 0.687, + 0.338 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.624, + 0.343, + 0.686, + 0.422 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.628, + 0.428, + 0.683, + 0.441 + ], + "angle": 0, + "content": "(a) Direct" + }, + { + "type": "image", + "bbox": [ + 0.688, + 0.269, + 0.785, + 0.339 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.711, + 0.343, + 0.783, + 0.421 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.718, + 0.428, + 0.781, + 0.441 + ], + "angle": 0, + "content": "(b) Indirect" + }, + { + "type": "image", + "bbox": [ + 0.803, + 0.271, + 0.874, + 0.338 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.807, + 0.343, + 0.876, + 0.419 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.815, + 0.428, + 0.862, + 0.441 + ], + "angle": 0, + "content": "(c) Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.453, + 0.892, + 0.482 + ], + "angle": 0, + "content": "Figure 1. Comparisons of (a) the direct method [29], (b) the indirect method [36], and (c) our method." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.518, + 0.895, + 0.821 + ], + "angle": 0, + "content": "To simultaneously achieve high precision and high robustness, some probabilistic methods are developed, which, instead of seeking a unique solution, try to explicitly model the uncertainty of human poses by learning some kind of probability distribution. Prevalent ways of modeling the distribution include multivariate Gaussian distributions [48, 56], normalizing flows [31], and neural networks [51, 53]. In practice, these learned probability distributions can notably improve the estimation results in some extreme cases (e.g., under large occlusion), however, only minor differences can be found in terms of the overall performances on large datasets. One reason is that these probability models cannot truly reflect the rotational uncertainty since they are not strictly constrained to \\(\\mathcal{SO}(3)\\). Recently, [55] proposes to adopt the matrix Fisher distribution over \\(\\mathcal{SO}(3)\\) [8, 25] to model the rotational uncertainty caused by depth ambiguity. However, even with this mathematically-correct formulation, the actual performance does not improve much either, because the parameters of the matrix Fisher distribution are not easy for deep neural networks to learn directly." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.895, + 0.903 + ], + "angle": 0, + "content": "To address this problem, we propose a new learning-friendly and mathematically-correct formulation for learning probability distributions for human mesh recovery. Our formulation is derived based on the facts that, (i) the joint rotations follow the matrix Fisher distribution over \\(\\mathcal{SO}(3)\\)," + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.514, + 0.957 + ], + "angle": 0, + "content": "8781" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.302 + ], + "angle": 0, + "content": "(ii) the unit directions of bones follow the von Mises-Fisher distribution [44], (iii) the bone direction can be viewed as the observation of joint rotation (i.e., the latent variable). It can be proven that the probability distributions of joint rotations conditioned on bone directions still follow the matrix Fisher distribution, which allows us to regress the posterior probability distribution of the 3D joint rotations in a Bayesian manner, and more importantly, in an analytical form. Moreover, we mathematically prove that the posterior probability of human joint rotations is more concentrated than the prior probability. Our experimental results demonstrate that such a characteristic makes the posterior probability an easier form to learn (for neural networks) than its prior counterpart." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.303, + 0.473, + 0.575 + ], + "angle": 0, + "content": "Apart from the theoretical contributions, we also propose a new human mesh recovery framework that can utilize the learned analytical posterior probability. We demonstrate that this framework successfully achieves high precision and high robustness at the same time, and outperforms existing SOTA baselines. Furthermore, our framework enables seamless integration with additional sensors that can yield directional/rotational observations (e.g., multi-view cameras, optical markers, IMUs) due to its Bayesian nature. Different from naive multi-sensor fusion algorithms (e.g., Kalman filter [21]) that typically perform fusion at the inference stage, our framework allows fusion in the training stage to learn the noise characteristics of sensors, and thus has the potential to produce better precision. We demonstrate that our fusion mechanism can achieve similar effects to fusing the latent features from multiple sensor input branches, but is much more flexible since it does not require modification of the main backbone." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.576, + 0.411, + 0.591 + ], + "angle": 0, + "content": "The key contributions of this paper are thereby:" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.602, + 0.469, + 0.677 + ], + "angle": 0, + "content": "- We derive a novel analytical formulation for learning probability distributions for human joint rotations, and theoretically prove that such formulation allows the regression of posterior probability distribution in a Bayesian manner." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.688, + 0.469, + 0.749 + ], + "angle": 0, + "content": "- We propose a new framework for human mesh recovery by leveraging the learned analytical posterior probability and show that this framework outperforms existing SOTA baselines." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.759, + 0.469, + 0.805 + ], + "angle": 0, + "content": "- We introduce a novel and flexible multi-sensor fusion mechanism that allows fusing different observations in the training stage." + }, + { + "type": "list", + "bbox": [ + 0.097, + 0.602, + 0.469, + 0.805 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.83, + 0.216, + 0.846 + ], + "angle": 0, + "content": "2. Related work" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.47, + 0.901 + ], + "angle": 0, + "content": "In this section, we discuss related studies on human mesh recovery, which can be achieved by optimization-based and learning-based methods. Leveraging the parametric human" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.168 + ], + "angle": 0, + "content": "model [41, 54], optimization-based approaches [2, 9, 15, 51] fit the parameters via iteration while learning-based approaches regress the parameters with neural networks. Our work follows the learning paradigm, therefore we here mainly review recent advances in learning-based methods." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.188, + 0.892, + 0.31 + ], + "angle": 0, + "content": "Direct methods: Given images as input, this kind of approach directly regresses the model parameters with neural networks. Different representations of rotation [22, 34, 74], supervision schemes [20, 29, 37] as well as temporal context [5, 13, 23, 26] are explored to improve performance. However, the gap between the image space and the abstract parameter space of statistical models makes it difficult to generate well-aligned estimations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.33, + 0.892, + 0.527 + ], + "angle": 0, + "content": "Indirect methods: Instead of regressing rotation representations from RGB images directly, plenty of works introduce proper intermediate or proxy representations, such as segmentation [27, 49, 68], IUV maps [64, 69, 70], keypoints [6, 14, 36, 52] or surface landmarks [30, 32, 42], to guide the learning of neural networks efficiently. HybrIK [36] decomposes the 3D rotation into solvable swings from 3D keypoints and extra predicted twists. PARE [27] learns to predict attention masks which are fused with image feature maps to provide body part information. These solutions may achieve higher precision, but generating only deterministic results and ignoring the uncertainty of estimation make them sensitive to noisy or erroneous proxy predictions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.548, + 0.892, + 0.804 + ], + "angle": 0, + "content": "Probabilistic methods: To deal with the uncertainty from occlusions or depth ambiguities, several works manage to produce multiple hypotheses [1] or a probability distribution [53]. I2L-MeshNet [48] predicts lixel-based 1D heatmaps for each human mesh vertex for uncertainty modeling. Sengupta et al. [56] assume simple multivariate Gaussian distributions over the parameters of the human model. ProHMR [31] learns a distribution of plausible 3D poses represented by normalizing flows, which is more powerful and expressive than Gaussian distributions. Recently Sengupta et al. [55] further represent the essential distribution of human joint rotation over \\(\\mathcal{SO}(3)\\) by adopting the matrix Fisher distribution [25], which can provide quantified uncertainty estimation. Despite a better explanation for ambiguities, the parameters of the above distribution are not easy to learn, limiting their overall performance on complicated scenes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Multi-sensor fusion: Recently an increasing number of approaches attempt to integrate extra observations from other sensors, such as IMUs [10,65,66] and multi-view cameras [7, 71, 73], to obtain more reliable estimations. One simple strategy is combining all observations properly with" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8782" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.089, + 0.895, + 0.315 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.324, + 0.895, + 0.396 + ], + "angle": 0, + "content": "Figure 2. Overview of our framework. Given an input image, the multi-branch network predicts the prior matrix Fisher parameters \\( \\mathbf{F} \\), the 3D keypoints \\( \\mathbf{J} \\), and the SMPL shape parameters \\( \\beta \\), respectively. The bone direction \\( \\mathbf{d} \\) calculated from \\( \\mathbf{J} \\) serves as the likelihood conditioned on 3D rotation. The posterior probability can be obtained based on Bayesian rules (Fusion), which still follows the matrix Fisher distribution, but with different parameters and larger confidence. Observations from additional sensors can also be fused into the posterior probability in the same manner. The corresponding human mesh can then be recovered using the estimated rotation and shape." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.42, + 0.473, + 0.572 + ], + "angle": 0, + "content": "Kalman filter [21], which can be treated as a baseline. Some works [43,62,63] fit the human model to evidence including images and IMUs through joint optimization. Apart from these test-time fusion schemes, several approaches [10, 61] incorporate the fusing process into training by concatenating the features from images and IMUs directly. GeoFuse [72] reinforces the image features guided by IMUs to infer the occluded joints. Our framework is also flexible to perform multi-sensor fusion and generates competitive results without specific modification to the backbone." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.586, + 0.176, + 0.601 + ], + "angle": 0, + "content": "3. Methods" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.611, + 0.47, + 0.748 + ], + "angle": 0, + "content": "In this section, we first mathematically introduce the probability distributions for orientations regarding rotations and directions (Sec. 3.1). Then, we model the human joint rotation and bone direction with the corresponding distribution, and derive the analytical formulation of the posterior probability of joint rotation conditioned on the bone direction with crucial conclusions and discussion (Sec. 3.2). Finally, we describe the proposed framework (Sec. 3.3) and learning details (Sec. 3.4)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.757, + 0.388, + 0.773 + ], + "angle": 0, + "content": "3.1. Orientation probability distribution" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.781, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Before delving into human modeling, we investigate the orientation representation for general rigid entities. Suppose \\( \\mathbf{X} \\in \\mathbb{R}^{n \\times p} \\) is the parametric representation of the entity orientation, each column of which depicts the direction of a basis. \\( \\mathbf{X} \\) is on the Stiefel manifold \\( \\mathcal{V}(n,p) \\) if \\( \\mathbf{X}^T\\mathbf{X} = \\mathbf{I}_p \\), and when \\( n = p \\), it further belongs to the orthogonal group \\( \\mathcal{O}(n) \\). Additionally, the components of \\( \\mathcal{O}(n) \\) with determinant \\( +1 \\) are referred to as the special or" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.42, + 0.892, + 0.511 + ], + "angle": 0, + "content": "thogonal group \\(\\mathcal{SO}(n)\\), which is used to represent the rotation of \\(n\\) degrees of freedom. Meanwhile, if \\(p = 1\\), the normalized \\(\\pmb{X}\\), i.e., \\(n\\)-dimensional unit vector on the manifold \\((n - 1)\\)-sphere \\(\\mathcal{S}^{n - 1}\\), can represent the single direction as well. From a probabilistic perspective, when \\(\\pmb{X}\\) is a random matrix, there are two common cases." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.529, + 0.892, + 0.59 + ], + "angle": 0, + "content": "Rotation \\((n = p)\\): For rotation matrix \\(\\mathbf{R} \\in \\mathcal{SO}(n)\\), the matrix Fisher distribution \\(\\mathcal{MF}(\\cdot)\\) has been proposed to characterize its probabilistic properties on \\(\\mathcal{SO}(n)\\) [8, 25]. The probability density function is as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.54, + 0.6, + 0.892, + 0.632 + ], + "angle": 0, + "content": "\\[\np (\\boldsymbol {R}; \\boldsymbol {F}) = \\frac {1}{c (\\boldsymbol {F})} \\exp (t r (\\boldsymbol {F} ^ {T} \\boldsymbol {R})) \\sim \\mathcal {M F} (\\boldsymbol {F}), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.643, + 0.892, + 0.704 + ], + "angle": 0, + "content": "where \\(\\pmb{F} \\in \\mathbb{R}^{n \\times n}\\) is the distribution parameter, and \\(c(\\pmb{F})\\) is a normalizing constant. Algebraically, \\(\\pmb{F}\\) can be decomposed into a concentration matrix \\(\\pmb{K}\\) and a mean rotation matrix \\(\\pmb{M}\\) via SVD decomposition:" + }, + { + "type": "equation", + "bbox": [ + 0.561, + 0.713, + 0.892, + 0.751 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {F} = \\boldsymbol {U} \\boldsymbol {S} \\boldsymbol {V} ^ {T} = \\underbrace {\\left(\\boldsymbol {U} \\Delta \\boldsymbol {V} ^ {T}\\right)} _ {\\boldsymbol {M} \\in \\mathbb {R} ^ {n \\times p}} \\underbrace {\\left(\\boldsymbol {V} \\Delta \\boldsymbol {S} \\boldsymbol {V} ^ {T}\\right)} _ {\\boldsymbol {K} \\in \\mathbb {R} ^ {p \\times p}}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.762, + 0.892, + 0.822 + ], + "angle": 0, + "content": "where \\(\\Delta = \\text{diag}(1, 1, |\\mathbf{U} \\mathbf{V}|)\\) is a diagonal orthogonal matrix to ensure the determinant of \\(\\mathbf{M}\\) is \\(+1\\). \\(\\mathbf{K}\\) is symmetric positive definite as long as \\(\\mathbf{F}\\) is full rank. A rotation estimation \\(\\hat{\\mathbf{R}}\\) can be calculated from the mode of distribution:" + }, + { + "type": "equation", + "bbox": [ + 0.575, + 0.835, + 0.892, + 0.854 + ], + "angle": 0, + "content": "\\[\n\\hat {\\boldsymbol {R}} = \\boldsymbol {M} = \\boldsymbol {U} \\operatorname {d i a g} (1, 1, | \\boldsymbol {U} \\boldsymbol {V} |) \\boldsymbol {V} ^ {T}. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Direction \\((p = 1)\\): The probability density function for a unit vector \\(d\\in S^{n - 1}\\) is similar to Eq. (1) if we set \\(p = 1\\)" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8783" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.122 + ], + "angle": 0, + "content": "which corresponds to the classical von Mises-Fisher distribution \\(\\mathcal{V}\\mathcal{M}\\mathcal{F}(\\cdot)\\) [44]:" + }, + { + "type": "equation", + "bbox": [ + 0.097, + 0.129, + 0.47, + 0.162 + ], + "angle": 0, + "content": "\\[\np (\\boldsymbol {d}; \\kappa , \\boldsymbol {m}) = \\frac {1}{c (\\kappa)} \\exp (\\kappa \\boldsymbol {m} ^ {T} \\boldsymbol {d}) \\sim \\mathcal {V M F} (\\boldsymbol {m}, \\kappa), \\quad (4)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.169, + 0.469, + 0.228 + ], + "angle": 0, + "content": "where \\(c(\\kappa)\\) is a normalizing constant. \\(\\pmb{m}\\) denotes the mean direction and \\(\\kappa\\) denotes the concentration parameter, which have a close meaning to \\(M\\) and \\(\\pmb{K}\\) in Eq. (2), respectively, and thus \\(\\hat{\\pmb{d}} = \\pmb{m}\\) becomes a direction estimation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.229, + 0.47, + 0.334 + ], + "angle": 0, + "content": "Theoretically, if \\(\\kappa\\) is 0, \\(\\mathcal{V}\\mathcal{M}\\mathcal{F}(\\boldsymbol{m},0)\\) is equivalent to the uniform distribution on the sphere, while if \\(\\kappa\\) is large, it is close to the wrapped normal distribution \\(\\mathcal{W}\\mathcal{N}(\\boldsymbol{m},\\kappa^{-1})\\) that adds up the densities of vectors representing the same direction on the sphere due to the periodicity. Thus, \\(\\kappa\\) can be viewed as the inverse of the variance and denotes the concentration of the distributions." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.343, + 0.248, + 0.359 + ], + "angle": 0, + "content": "3.2. Human modeling" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.366, + 0.47, + 0.516 + ], + "angle": 0, + "content": "The human joint rotation can be represented as rotation matrix \\( \\mathbf{R} \\in \\mathcal{SO}(3) \\). Inspired by recent advances in object pose estimation [3, 33, 46, 67], we incorporate the probabilistic modeling for human poses. Specifically, we adopt the matrix Fisher distribution over \\( \\mathcal{SO}(3) \\) as the prior distribution for joint rotation. Moreover, as the bone direction can be easily calculated from the joint rotation, we regard the joint rotation \\( \\mathbf{R} \\) as the latent variable and the bone direction \\( \\mathbf{d} \\) as the corresponding observation, which follows the von Mises-Fisher distribution:" + }, + { + "type": "equation", + "bbox": [ + 0.099, + 0.536, + 0.47, + 0.568 + ], + "angle": 0, + "content": "\\[\np (\\boldsymbol {d} | \\boldsymbol {R}) = \\frac {1}{c (\\kappa)} e x p (\\kappa \\boldsymbol {l} ^ {T} \\boldsymbol {R} ^ {T} \\boldsymbol {d}) \\sim \\mathcal {V M F} (\\boldsymbol {R l}, \\kappa), \\quad (5)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.575, + 0.469, + 0.605 + ], + "angle": 0, + "content": "where \\( l \\) is the unit direction of the bone in the reference pose (e.g., T-pose), ideally satisfying \\( Rl = d \\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.606, + 0.469, + 0.664 + ], + "angle": 0, + "content": "Leveraging Bayesian inference, given the prior distribution (Eq. (1)) and the likelihood function (Eq. (5)), the posterior probability of joint rotation conditioned on the bone direction can be derived as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.091, + 0.685, + 0.47, + 0.749 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} p (\\boldsymbol {R} | \\boldsymbol {d}) = \\frac {p (\\boldsymbol {R}) \\cdot p (\\boldsymbol {d} | \\boldsymbol {R})}{p (\\boldsymbol {d})} \\propto p (\\boldsymbol {R}) \\cdot p (\\boldsymbol {d} | \\boldsymbol {R}) \\tag {6} \\\\ = \\frac {1}{c} e x p (t r [ (\\boldsymbol {F} + \\kappa \\boldsymbol {d l} ^ {T}) ^ {T} \\boldsymbol {R} ]) \\sim \\mathcal {M F} (\\boldsymbol {F} + \\kappa \\boldsymbol {d l} ^ {T}). \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.755, + 0.469, + 0.801 + ], + "angle": 0, + "content": "It can be concluded from Eq. (6) that the posterior probability \\( p(\\mathbf{R}|\\mathbf{d}) \\) also follows the matrix Fisher distribution with an updated parameter \\( \\mathbf{F}' = \\mathbf{F} + \\kappa \\mathbf{d}\\mathbf{l}^T \\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.818, + 0.469, + 0.862 + ], + "angle": 0, + "content": "Property: From another perspective, the posterior parameter \\( F' \\) can be viewed as the multiplication of the same mean term \\( M \\) and a new concentration term \\( K' \\):" + }, + { + "type": "equation", + "bbox": [ + 0.135, + 0.87, + 0.469, + 0.905 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {F} ^ {\\prime} = \\boldsymbol {F} + \\kappa \\boldsymbol {d l} ^ {T} = M (\\underbrace {\\boldsymbol {K} + \\kappa \\boldsymbol {M} ^ {T} \\boldsymbol {d l} ^ {T}} _ {\\boldsymbol {K} ^ {\\prime}}). \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.091, + 0.892, + 0.198 + ], + "angle": 0, + "content": "It can be proved that \\( M^T d\\boldsymbol{l}^T = \\boldsymbol{ll}^T \\) is a real symmetric matrix with rank 1, and \\( K \\) from Eq. (2) is also real symmetric, thus the posterior concentration term \\( K' \\) is a real symmetric matrix. According to the interlacing theorem for Hermitian matrices from matrix analysis [17], the eigenvalues for a Hermitian matrix with a rank-1 Hermitian perturbation satisfy the following inequality:" + }, + { + "type": "equation", + "bbox": [ + 0.557, + 0.207, + 0.892, + 0.227 + ], + "angle": 0, + "content": "\\[\n\\lambda_ {1} \\leq \\lambda_ {1} ^ {\\prime} \\leq \\lambda_ {2} \\leq \\dots \\leq \\lambda_ {p - 1} ^ {\\prime} \\leq \\lambda_ {p} \\leq \\lambda_ {p} ^ {\\prime}, \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.234, + 0.892, + 0.37 + ], + "angle": 0, + "content": "where \\(\\lambda_{i}\\) and \\(\\lambda_{i}^{\\prime}\\) denote the eigenvalues of \\(\\pmb{K}\\) and \\(\\pmb{K}^{\\prime}\\), respectively. Note that the eigenvalues of the concentration term equal the singular values of the distribution parameter, which reflect the confidence of the distribution. From Eq. (8) we can get the conclusion that the posterior estimation is more concentrated than the prior estimation as long as the likelihood term is non-zero, and is validated to be a more easily learnable formulation in the experiment and the supplementary material." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.387, + 0.892, + 0.43 + ], + "angle": 0, + "content": "General form: Similarly, if other sensors that yield directional \\( \\pmb{d}_i \\) or rotational \\( \\pmb{D}_j \\) observations are available, the analytical posterior probability is thereby as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.506, + 0.438, + 0.892, + 0.468 + ], + "angle": 0, + "content": "\\[\np (\\boldsymbol {R} | \\left\\{\\boldsymbol {d} _ {i}, \\boldsymbol {D} _ {j} \\right\\}) \\sim \\mathcal {M F} (\\boldsymbol {F} + \\sum_ {i \\in \\mathcal {Z} _ {1}} \\kappa_ {i} g (\\boldsymbol {d} _ {i}) + \\sum_ {j \\in \\mathcal {Z} _ {3}} \\boldsymbol {D} _ {j} \\boldsymbol {K} _ {j} ^ {T}), \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.475, + 0.892, + 0.627 + ], + "angle": 0, + "content": "where \\(\\kappa_{i}\\) and \\(K_{j}\\) are the concentration terms for weighting. \\(g(\\cdot)\\) is a mapping of IK that converts the directional observation to a rotation estimation, which is not limited to a specific IK algorithm as long as it supports gradient backpropagation (e.g., the simple solution \\(\\boldsymbol{d}\\boldsymbol{l}^T\\) in Eq. (6)). \\(\\mathcal{Z}_1\\) denotes the set of sensors providing directional observations such as accelerometers, while \\(\\mathcal{Z}_3\\) denotes the set of rotational sensors like gyroscopes. We simplify the original derivation by assuming the sensors are unbiased. Please refer to the supplementary material for the derivation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.645, + 0.892, + 0.855 + ], + "angle": 0, + "content": "Discussion: There are several advantages of our approach. First, adopting the matrix representation is more reasonable than other rotation representations. As presented in [34], a continuous 9D unconstrained representation followed by SVD can achieve comparable or even better performance than the widely used 6D vector [74]. Second, the Gaussian distribution is unsuitable for cases with large uncertainty where the assumption of local linearity cannot hold [11, 12], while the matrix Fisher distribution does not have this problem. Third, the posteriors are easier to learn than the priors in that learning the posteriors can converge to the mode preferred by the likelihood function quickly, while learning the priors may face multiple local minima in the initial stage and thus cannot converge well." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "To recognize the proposed scheme intuitively, we show the schematic diagrams of probabilistic modeling in Fig. 3. For a method without probabilistic modeling (e.g., using IK" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8784" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.092, + 0.46, + 0.259 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.269, + 0.473, + 0.368 + ], + "angle": 0, + "content": "Figure 3. Schematic diagrams of probabilistic modeling. The opaque coordinate system \\(\\triangleleft\\) is the ground-truth 3D rotation. The transparent rotation represents a deterministic estimation for a method without probabilistic modeling (row 1), while it denotes a sample from the estimated posterior distribution (row 2). The red region on the sphere represents the probability of a certain rotation, and it could cover the ground-truth even for noisy cases." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.396, + 0.473, + 0.518 + ], + "angle": 0, + "content": "to solve rotations from keypoints), its underlying model is a single direction, thus it may be erroneous when the estimated bone direction deviates from the ground-truth, as shown in the noisy cases. In contrast, the posterior model can be fused with various models, and for noisy keypoints, it has the potential to recover the exact rotations since the negative impact of its partial reliance on the estimated keypoints can be eliminated by the prior or other observations." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.529, + 0.281, + 0.545 + ], + "angle": 0, + "content": "3.3. Learning Framework" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.554, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Our proposed framework that leverages the derived posterior probability for human mesh recovery is demonstrated in Fig. 2. We adopt the parametric model SMPL [41] as our human representation, which can also be replaced by other human models [51,54]. Given an input image, a CNN backbone is used to extract image features, followed by three output branches, including prior distribution parameter \\( F \\), 3D keypoints \\( J \\), and shape parameter \\( \\beta \\). The adopted keypoints branch consists of normalized 2D keypoints and relative depth to the root joint decoded from the feature, as well as the human scale predicted by a small MLP branch, so as to recover absolute 3D keypoints. Note that other strategies for 3D keypoints estimation are also applicable. The bone direction \\( d \\) is calculated from \\( J \\). Then we utilize Eq. (9) to fuse \\( F \\), \\( d \\), or other optional observations analytically in the sense of probability. With the new distribution parameter \\( F' \\), we can get the rotation estimation according to Eq. (3). As for \\( \\kappa \\), it is related to the physical properties (measure covariance) of specific sensors that could be set in advance. If there is no prior knowledge of the sensor, it's feasible to tune it manually or learn it from the data. We simply use the scaled scores of estimated keypoints. For multiple sensors, the concentration term \\( K \\) is simplified as a diagonal matrix." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.168 + ], + "angle": 0, + "content": "Objective functions: For the following objective functions, symbols with superscript \\(*\\) indicate the groundtruth, and symbols with hat indicate the estimation. The \\(L_{1}\\) loss is used to supervise the 3D keypoints, while the \\(L_{2}\\) loss is applied to other variables:" + }, + { + "type": "equation", + "bbox": [ + 0.632, + 0.178, + 0.892, + 0.196 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {J} = \\left| \\left| \\hat {\\boldsymbol {J}} - \\boldsymbol {J} ^ {*} \\right| \\right| _ {1}, \\tag {10}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.633, + 0.221, + 0.892, + 0.24 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\beta} = \\left\\| \\hat {\\boldsymbol {\\beta}} - \\boldsymbol {\\beta} ^ {*} \\right\\| _ {2} ^ {2}, \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.247, + 0.895, + 0.305 + ], + "angle": 0, + "content": "The mode of the posterior probability distribution \\(\\hat{R}\\) can be solved according to Eq. (6) and (3), and is supervised if the annotations of SMPL pose parameters \\(\\theta\\) are provided as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.607, + 0.307, + 0.892, + 0.326 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\theta} = \\left| \\left| \\hat {\\boldsymbol {R}} - \\exp (\\boldsymbol {\\theta} ^ {*}) \\right| \\right| _ {2} ^ {2}, \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.331, + 0.892, + 0.361 + ], + "angle": 0, + "content": "where \\( \\text{expm} \\) denotes the exponential map implemented with the Rodrigues' formula." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.362, + 0.892, + 0.513 + ], + "angle": 0, + "content": "Apart from the mode, the whole distribution also needs to be supervised. Since the normalizing constant in the distribution is hard to be calculated stably due to the numerical integration, we propose to supervise the distribution by sampling. Specifically, we adopt the rejection sampling technique to sample Bingham distribution of unit quaternions on \\( S^3 \\) based on its equivalence to matrix Fisher distribution. The proposal distribution in rejection sampling is angular central Gaussian (ACG) distribution [24, 55]. Thus the sampling loss is as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.58, + 0.524, + 0.892, + 0.565 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {s} = \\sum_ {i = 1} ^ {N _ {s}} \\rho \\left(\\left| \\left| \\hat {\\boldsymbol {R}} _ {i} - \\exp \\left(\\boldsymbol {\\theta} ^ {*}\\right) \\right| \\right| _ {2} ^ {2}\\right), \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.571, + 0.892, + 0.614 + ], + "angle": 0, + "content": "where \\(N_{s}\\) is the number of samples. \\(\\rho\\) is an simple activation function for relaxation, which tolerates small deviations." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.616, + 0.796, + 0.631 + ], + "angle": 0, + "content": "The total objective function is as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.568, + 0.644, + 0.892, + 0.66 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = w _ {1} \\mathcal {L} _ {J} + w _ {2} \\mathcal {L} _ {\\beta} + w _ {3} \\mathcal {L} _ {\\theta} + w _ {4} \\mathcal {L} _ {s}, \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.672, + 0.802, + 0.687 + ], + "angle": 0, + "content": "where \\(w_{1}, w_{2}, w_{3}\\), and \\(w_{4}\\) are weight scalars." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.697, + 0.715, + 0.713 + ], + "angle": 0, + "content": "3.4. Implementation details" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.895, + 0.903 + ], + "angle": 0, + "content": "We adopt ResNet-34 [16] and HRNet-W48 [58] as backbones. The ResNet backbone is followed by three deconvolutional layers to generate 3D heatmaps with the size of \\(64 \\times 64 \\times 64\\) for keypoints and three MLPs for shape parameters \\(\\beta\\) (10), distribution parameter \\(F\\) (216) and human scale (1). The feature from HRNet backbone is upsampled and directly followed by similar output branches with dimensions motioned above. The input image has a resolution of \\(256 \\times 256\\). The network is trained for 50 epochs with Adam and an initial learning rate of \\(1 \\times 10^{-3}\\), decayed with a factor of 10. \\(w_{1}\\) and \\(w_{2}\\) are set to 1. \\(w_{3}\\) and \\(w_{4}\\) are set to 0.1 and increased to 1 in the later stage of training." + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8785" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.077, + 0.09, + 0.21, + 0.108 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.116, + 0.47, + 0.176 + ], + "angle": 0, + "content": "In this section, we demonstrate the effectiveness of our framework on human mesh recovery and multi-sensor fusion, evaluate our key designs via an ablation study, and discuss the limitation and future work of our method." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.187, + 0.274, + 0.202 + ], + "angle": 0, + "content": "4.1. Datasets and metrics" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.21, + 0.469, + 0.24 + ], + "angle": 0, + "content": "To maintain the fairness of comparison, we adopt the same datasets and metrics as previous methods." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.24, + 0.469, + 0.302 + ], + "angle": 0, + "content": "Human3.6M [18] provides 3D keypoints annotations, and the corresponding SMPL annotations are from MoSh [40]. We use (S1, S5, S6, S7, S8) for training and (S9, S11) for evaluation, following standard practice [22, 36]." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.302, + 0.468, + 0.332 + ], + "angle": 0, + "content": "3DPW [62] provides SMPL annotations. Following [36, 37], we add its training set only for experiments on it." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.332, + 0.468, + 0.378 + ], + "angle": 0, + "content": "MS COCO [39] contains in-the-wild images and 2D keypoints annotations. We use its training set to improve the generalization ability of our method." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.378, + 0.469, + 0.408 + ], + "angle": 0, + "content": "MPI-INF-3DHP [45] is a multi-view dataset that provides 3D keypoints annotations. We only use it for training." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.408, + 0.469, + 0.453 + ], + "angle": 0, + "content": "AGORA [50] is a synthetic dataset with challenging scenes and SMPL annotations of adults and kids. Only when evaluating our algorithm on it will we add its training set." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.453, + 0.469, + 0.499 + ], + "angle": 0, + "content": "TotalCapture [61] contains multi-view videos, IMUs and 3D keypoints annotations for the evaluation of sensor fusion algorithms. We follow [61,72] to divide it." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.499, + 0.469, + 0.56 + ], + "angle": 0, + "content": "Metrics include MPJPE, PA-MPJPE, and PVE all in mm. MPJPE measures the 3D keypoints error, while PA-MPJPE is similar to MPJPE except that a rigid alignment is performed at first. PVE measures the human mesh vertex error." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.571, + 0.286, + 0.587 + ], + "angle": 0, + "content": "4.2. Human mesh recovery" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.594, + 0.47, + 0.76 + ], + "angle": 0, + "content": "Table 1 shows the evaluation results on public benchmarks. With either ResNet or HRNet as the backbone, our approach outperforms SOTA methods. Besides, we surpass the prior counterpart [55] by a large margin, indicating that our posterior estimation is easier to learn than the single prior. Table 2 shows the results on the AGORA test set. Our framework is more accurate than others, especially for kids. Note that for 2D datasets, despite that the pseudo-GT annotator of CLIFF [37] and EFT dataset [20] can be incorporated to further improve our performance, we only use the original keypoints supervision for fair comparisons." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Posterior effects: We compare different designs to thoroughly validate the posterior effects and the feature choice in our framework, as shown in Table 3, which include: (a) regressing the parameters \\( \\mathbf{F} \\) only without the keypoint branch; (b) solving rotations from keypoints via IK without probabilistic modeling; (c) deactivating the learned prior parameters in testing (i.e., setting \\( \\mathbf{F} \\) to zero); (d) using the feature close to the end of the backbone to regress prior \\( \\mathbf{F} \\)" + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.09, + 0.89, + 0.323 + ], + "angle": 0, + "content": "
Methods3DPWHuman3.6M
PA ↓MPJPE ↓PVE ↓PA ↓MPJPE ↓
HMR (R-50) [22]81.3130.0-56.888.0
GraphCMR (R-50) [30]70.2--50.1-
SPIN (R-50) [29]59.296.9116.441.162.5
Sengupta. (H-48) [55]*59.284.7*---
HMR-EFT (R-50) [20]52.4--43.9-
I2L-MeshNet (R-50) [48]58.693.2-41.755.7
SPEC (R-50) [28]53.296.5118.5--
BEV (H-32) [60]46.978.592.3--
PARE (H-32) [27]46.574.588.6--
Graphormer (H-64) [38]45.674.787.734.551.2
PyMAF (H-48) [70]45.374.287.037.254.2
HybrIK (R-34) [36]45.074.186.533.655.4
FastMETRO (R-50) [4]48.377.990.637.353.9
FastMETRO (H-64) [4]44.673.584.133.752.2
CLIFF (R-50) [37]45.772.085.335.150.5
CLIFF (H-48) [37]43.069.081.232.747.1
Ours (R-34)44.171.884.931.648.7
Ours (H-48)40.668.379.429.145.7
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.331, + 0.892, + 0.359 + ], + "angle": 0, + "content": "Table 1. Results on standard benchmarks. 'PA' is PA-MPJPE. \\(R^{\\prime}\\) and \\(H^{\\prime}\\) mean ResNet and HRNet. * with scale correction." + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.377, + 0.89, + 0.565 + ], + "angle": 0, + "content": "
MethodsAGORA
MPJPE ↓PVE ↓Kid-MPJPE ↓Kid-PVE ↓
HMR [22]180.5173.6219.4209.3
HMR-EFT [20]165.4159.0202.7193.5
SPIN [29]153.4148.9191.7186.7
PARE [27]146.2140.9193.9186.4
SPEC [28]112.3106.5171.0163.2
ROMP [59]108.1103.4159.8156.6
BEV [60]105.3100.7129.1125.9
Hand4Whole [47]89.884.8153.3146.4
CLIFF [37]81.076.094.189.6
HybrIK [36]77.073.990.286.6
Ours74.470.984.580.5
PLIKS [57]71.567.388.384.2
NIKI [35]67.363.983.980.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.573, + 0.892, + 0.614 + ], + "angle": 0, + "content": "Table 2. Results on the AGORA test set. The metrics with the prefix 'Kid-' are calculated only for kids, otherwise for all ages. Two concurrent works are shown in gray for completeness." + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.632, + 0.89, + 0.758 + ], + "angle": 0, + "content": "
DesignsHuman3.6M
PA-MPJPE ↓MPJPE ↓
(a) W/o 3D keypoints45.876.5
(b) W/o prior F43.263.6
(c) W/o prior F (in testing)42.758.7
(d) Late feature for F and β29.948.6
(e) Early feature for F and β29.346.5
(f) Ours (full model)29.145.7
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.766, + 0.892, + 0.78 + ], + "angle": 0, + "content": "Table 3. Ablation study of designs on the Human3.6M dataset." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.81, + 0.892, + 0.839 + ], + "angle": 0, + "content": "and shape \\(\\beta\\); (e) using the feature from the initial stage; (f) our full model with all branches and intermediate feature." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The performance of design (a) is not good since its estimation cannot align precisely with the image, and it is observed that this design exhibits a slower speed of convergence, reflecting the importance of the likelihood function" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8786" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.089, + 0.468, + 0.213 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.218, + 0.47, + 0.302 + ], + "angle": 0, + "content": "Figure 4. Noise simulation. (a) Rotation error v.s. the mixed noises of both prior and keypoint. (b) Rotation/direction error v.s. keypoint noise. The noise level is the ratio of the noise amplitude to the maximum of the variable. The simulation step is \\(5\\%\\). 'W/o prior \\(\\pmb{F}\\)' is an indirect strategy without probability. 'Fixed \\(\\kappa\\) ' uses predefined \\(\\kappa\\). 'Adaptive \\(\\kappa\\) ' means \\(\\kappa\\) varies with the noise variance." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.316, + 0.466, + 0.37 + ], + "angle": 0, + "content": "
Noise amplitude5mm10mm15mm30mm50mm
W/o prior F61.362.765.071.580.4
Posterior-based48.549.651.454.559.0
(12.8↓)(13.1↓)(13.6↓)(17.0↓)(21.4↓)
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.382, + 0.469, + 0.412 + ], + "angle": 0, + "content": "Table 4. Noise test on the Human3.6M dataset. The 3D keypoints suffer from different levels of noises. MPJPE is reported." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.437, + 0.469, + 0.558 + ], + "angle": 0, + "content": "from keypoints. The comparison between design (b) and (e) shows that the prior \\( \\pmb{F} \\) is crucial in fusion. Furthermore, design (c) is better than design (b), indicating the prior \\( \\pmb{F} \\) has guided the keypoints learning to some extent. The difference is more significant in MPJPE since the global rotation is supervised for design (c). As for the feature choice, the intermediate feature adopted by our framework shows slightly better performance than the late and early features." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.565, + 0.47, + 0.853 + ], + "angle": 0, + "content": "Noise robustness: We evaluate the robustness of our framework when suffering from noise. Fig. 4 shows the simulation results with two metrics. The rotation error is the angle to be rotated from the estimated rotation \\(\\hat{\\pmb{R}}\\) to the ground-truth. The direction error is the angle between the estimated bone vector and the ground-truth. Fig. 4 (b) reveals that 'w/o prior \\(F\\) has a small direction error but a large rotation error for the unsolved twist, while the posterior strategy has a much smaller error even with a high keypoint noise level and shows a slower error growth rate. Note that the performance of a simple fixed \\(\\kappa\\) is also acceptable. Fig. 4 (a) shows that when the prior noise level is less than \\(15\\%\\), the keypoint noise has little effect on the posterior result with the adaptive \\(\\kappa\\), reflecting the tolerance to noises of the posterior scheme. Table 4 shows the noise test on the Human3.6M dataset. From the difference listed in parentheses, when the noise level is higher, the error of the posterior method increases more slowly compared with the baseline without prior \\(F\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.469, + 0.903 + ], + "angle": 0, + "content": "Samples illustration: Fig. 5 illustrates the samples from the posterior distribution. The right hand has a relatively" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.091, + 0.885, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.238, + 0.892, + 0.294 + ], + "angle": 0, + "content": "Figure 5. Samples from the distribution. The mode and samples of the relative rotations are shown. The light color indicates the mode, while the dark color indicates an extra sample. The canonical coordinate is at the top right as a reference." + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.31, + 0.889, + 0.476 + ], + "angle": 0, + "content": "
MethodsSensorsTotalCapture
PA-MPJPE ↓MPJPE ↓
IMUPVH [10]mv + IMUs-42.6
GeoFuse [72]mv + IMUs20.624.6
Oursmv + IMUs19.423.5
VIP [62]sv + IMUs26.0-
Kalman filtersv + IMUs23.134.7
Ourssv29.042.1
Ours (w/o ref, R-50)sv + IMUs25.841.7
Ours (w/o ref, H-48)sv + IMUs22.338.8
Ours (R-50)sv + IMUs25.032.3
Ours (H-48)sv + IMUs21.228.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.485, + 0.892, + 0.541 + ], + "angle": 0, + "content": "Table 5. Results on the TotalCapture dataset. 'mv' and 'sv' denote multi-view and single-view. 'w/o ref' means lacking a reference skeleton (only a statistical one from training set is adopted), which would slightly weaken the performance of our framework." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.567, + 0.892, + 0.672 + ], + "angle": 0, + "content": "large uncertainty on rotating around the X-axis due to the uncertain twist angle, as shown by the widespread blue and green samples. The left elbow has a vertical uncertainty on the direction of the forearm since the left hand cannot be easily determined. The left ankle has large confidence, except in the depth direction, therefore the green samples spread horizontally." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.672, + 0.892, + 0.763 + ], + "angle": 0, + "content": "Fig. 6 shows the qualitative comparison with the SOTA methods. The indirect methods that use part segmentation [27] or 3D keypoints [36] perform well in most cases, but may suffer from wrong segmentation for distant people or generate unnatural poses. While the direct method CLIFF [37] may not align the image well for complicated scenes." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.772, + 0.687, + 0.787 + ], + "angle": 0, + "content": "4.3. Multi-sensor fusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We perform experiments on the TotalCapture dataset [61] using the feed-forward network directly without any iterative optimization. As the original dataset does not provide SMPL annotations, we adopt the human skeleton defined by 19 joints and 11 attached IMUs, as shown in Fig. 7. We choose the optimization-based method VIP [62] and the feature-fused method GeoFuse [72] as baselines." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8787" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.092, + 0.162, + 0.195 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.163, + 0.096, + 0.245, + 0.195 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.251, + 0.096, + 0.328, + 0.195 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.344, + 0.092, + 0.422, + 0.195 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.423, + 0.099, + 0.529, + 0.195 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.53, + 0.099, + 0.637, + 0.195 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.645, + 0.092, + 0.724, + 0.195 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.732, + 0.103, + 0.807, + 0.19 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.809, + 0.103, + 0.889, + 0.19 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.198, + 0.162, + 0.3 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.163, + 0.202, + 0.248, + 0.3 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.252, + 0.202, + 0.329, + 0.3 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.344, + 0.198, + 0.422, + 0.3 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.426, + 0.202, + 0.528, + 0.3 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.53, + 0.201, + 0.621, + 0.3 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.646, + 0.198, + 0.724, + 0.3 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.738, + 0.202, + 0.793, + 0.3 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.81, + 0.202, + 0.864, + 0.3 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.11, + 0.305, + 0.142, + 0.317 + ], + "angle": 0, + "content": "Input" + }, + { + "type": "image_caption", + "bbox": [ + 0.186, + 0.305, + 0.231, + 0.317 + ], + "angle": 0, + "content": "HybrIK" + }, + { + "type": "image_caption", + "bbox": [ + 0.274, + 0.305, + 0.303, + 0.317 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.37, + 0.305, + 0.402, + 0.317 + ], + "angle": 0, + "content": "Input" + }, + { + "type": "image_caption", + "bbox": [ + 0.458, + 0.305, + 0.495, + 0.317 + ], + "angle": 0, + "content": "PARE" + }, + { + "type": "image_caption", + "bbox": [ + 0.55, + 0.305, + 0.58, + 0.316 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.674, + 0.304, + 0.706, + 0.317 + ], + "angle": 0, + "content": "Input" + }, + { + "type": "image_caption", + "bbox": [ + 0.752, + 0.304, + 0.792, + 0.316 + ], + "angle": 0, + "content": "CLIFF" + }, + { + "type": "image_caption", + "bbox": [ + 0.832, + 0.304, + 0.862, + 0.316 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.33, + 0.895, + 0.373 + ], + "angle": 0, + "content": "Figure 6. Qualitative comparison. The input images are from 3DPW [62], MS COCO [39], and AGORA [50], respectively. We compare our approach with SOTA methods including HybrIK [36], PARE [27], and CLIFF [37]. For images with multiple people, the person with a solid yellow circle on the face is estimated." + }, + { + "type": "image", + "bbox": [ + 0.141, + 0.387, + 0.22, + 0.475 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.129, + 0.478, + 0.19, + 0.489 + ], + "angle": 0, + "content": "Front View" + }, + { + "type": "image", + "bbox": [ + 0.228, + 0.387, + 0.311, + 0.475 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.243, + 0.478, + 0.298, + 0.489 + ], + "angle": 0, + "content": "Side View" + }, + { + "type": "image", + "bbox": [ + 0.327, + 0.387, + 0.442, + 0.475 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.355, + 0.478, + 0.421, + 0.489 + ], + "angle": 0, + "content": "IMUT-pose" + }, + { + "type": "image", + "bbox": [ + 0.097, + 0.491, + 0.217, + 0.578 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.228, + 0.491, + 0.328, + 0.583 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.33, + 0.491, + 0.445, + 0.583 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.593, + 0.47, + 0.635 + ], + "angle": 0, + "content": "Figure 7. An example of a multi-sensor case. The estimations from the front-view camera, side-view camera, and IMUs are plotted. The normalized confidence score of the left knee is listed." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.659, + 0.47, + 0.87 + ], + "angle": 0, + "content": "Table 5 shows the experimental results. Our method outperforms baseline methods, indicating the effectiveness of our posterior scheme. In the 'Kalman filter' setup, we apply a weighted sum to the 3D rotations separately obtained from images and IMUs. As the observation variance required for calculating the Kalman gain is unknown, we pick the weight pairs that can yield the best estimation through grid searching, i.e., from (0.7, 0.3) to (0.3, 0.7). Note that unlike Kalman filter which fuses the observations in the testing stage, our method performs fusing in the training stage, and thus has the potential to obtain higher precision. Our framework is also more flexible than feature-level fusing methods since we do not require modifications of the backbone to incorporate new sensors." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.469, + 0.9 + ], + "angle": 0, + "content": "Fig. 7 shows an example of a scene with multiple cameras and IMUs. The confidence from the two cameras are" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.389, + 0.892, + 0.525 + ], + "angle": 0, + "content": "calculated via the normalized differential entropy of the estimated distribution parameters, while the confidence from IMUs is set to a relatively larger value since IMUs can provide accurate measurements. Note that other metrics that represent the uncertainty from the distribution can also be adopted. It can be observed that the front view produces erroneous knee bending due to the depth ambiguity, therefore its confidence is lower than the side view. As a result, the fused result will be less affected by the noisy estimation." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.535, + 0.749, + 0.55 + ], + "angle": 0, + "content": "4.4. Limitation and future work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.559, + 0.892, + 0.695 + ], + "angle": 0, + "content": "Our work has several limitations. First, we only consider the uncertainty of poses, not including that of shapes, which can also be modeled as probability distributions. Second, we model the human joint independently, which is only affected by the parent node. Therefore, how to derive the analytical form of joint rotations conditioned on other hierarchical joints to incorporate anatomical constraints explicitly is still unsolved. Besides, with the single-view uncertainty, the temporal extension also deserves further investigation." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.709, + 0.619, + 0.725 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In this paper, we derive a novel analytical posterior probability for human joint rotations in a Bayesian manner and prove the property that the posteriors are more concentrated than the priors. Based on the derivation, we propose a new framework for human mesh recovery by leveraging the learned posteriors, which has high precision and robustness, outperforming existing SOTA baselines. Furthermore, our framework can be seamlessly incorporated with additional sensors in the training due to its Bayesian nature. 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To address such an issue, we derive a novel analytical formulation for learning posterior probability distributions of human joint rotations conditioned on bone directions in a Bayesian manner, and based on this, we propose a new posterior-guided framework for human mesh recovery. We demonstrate that our framework is not only superior to existing SOTA baselines on multiple benchmarks but also flexible enough to seamlessly incorporate with additional sensors due to its Bayesian nature. The code is available at https://github.com/NetEase-GameAI/ProPose. + +# 1. Introduction + +Human mesh recovery is a task of recovering body meshes and 3D joint rotations of human actors from images, which has ubiquitous applications in animation production, sports analysis, etc. To achieve this goal, various approaches have been proposed in the computer vision community. Existing methods can be divided into two categories, i.e., direct and indirect, respectively. Direct methods use neural networks to regress the rotations (e.g., axis angle [22], rotation matrix [34], 6D vector [29,37,74]) of each humanoid joint in an end-to-end way, while indirect methods recover joint rotations based on some intermediately predicted proxies (e.g., 3D human keypoints [19, 36, 42], 2D heatmaps [52] or part segmentation [27]). However, both methods have obvious weaknesses. Generally, the estimated poses from direct solutions are not so well-aligned with the images (Fig. 1(a)), because joint rotations are more difficult to regress compared with keypoints [19,36]. On the contrary, though indirect solutions tend to have better estimation precision, their performance heavily relies on the precision of the intermediate proxies and thus are vulnerable to noise and error in the predicted keypoints or part segmentation (Fig. 1(b)). + +![](images/39291c7c29388c1f7f3e19bea7278e064d7256556bf50bfc8472ed75f2077261.jpg) + +![](images/add0980b6d72febee0d3662d34975a527e5e1f8d9b6d7d8d7afc83e4472a7bd1.jpg) +Input + +![](images/6277d235b5ab6da425aa2619dde09af81a2e76cdcc3fef968c0929fff91df37d.jpg) + +![](images/67f0b32f7d4d3e04e567f6d12543af22f6c39b2556d480ae2e458794a9309035.jpg) +(a) Direct + +![](images/eca143fb8255e843e4a0bacc682f28ca17e918fbef8e93400aba0bc8b7745e73.jpg) + +![](images/67ffb243bdbc9787d91371ae4e3dd870ac95c88216857e293376b934620e05e3.jpg) +(b) Indirect + +![](images/b4cdd2fd8476cbe093765ca49d89c3f367923a4fabf24e0e13ad5adf9f923e31.jpg) + +![](images/9f9fa5f3cbbfe885d38c6c03e059c2bb4ef9b37415e3a7bb81d16ac726f99819.jpg) +(c) Ours +Figure 1. Comparisons of (a) the direct method [29], (b) the indirect method [36], and (c) our method. + +To simultaneously achieve high precision and high robustness, some probabilistic methods are developed, which, instead of seeking a unique solution, try to explicitly model the uncertainty of human poses by learning some kind of probability distribution. Prevalent ways of modeling the distribution include multivariate Gaussian distributions [48, 56], normalizing flows [31], and neural networks [51, 53]. In practice, these learned probability distributions can notably improve the estimation results in some extreme cases (e.g., under large occlusion), however, only minor differences can be found in terms of the overall performances on large datasets. One reason is that these probability models cannot truly reflect the rotational uncertainty since they are not strictly constrained to $\mathcal{SO}(3)$ . Recently, [55] proposes to adopt the matrix Fisher distribution over $\mathcal{SO}(3)$ [8, 25] to model the rotational uncertainty caused by depth ambiguity. However, even with this mathematically-correct formulation, the actual performance does not improve much either, because the parameters of the matrix Fisher distribution are not easy for deep neural networks to learn directly. + +To address this problem, we propose a new learning-friendly and mathematically-correct formulation for learning probability distributions for human mesh recovery. Our formulation is derived based on the facts that, (i) the joint rotations follow the matrix Fisher distribution over $\mathcal{SO}(3)$ , + +(ii) the unit directions of bones follow the von Mises-Fisher distribution [44], (iii) the bone direction can be viewed as the observation of joint rotation (i.e., the latent variable). It can be proven that the probability distributions of joint rotations conditioned on bone directions still follow the matrix Fisher distribution, which allows us to regress the posterior probability distribution of the 3D joint rotations in a Bayesian manner, and more importantly, in an analytical form. Moreover, we mathematically prove that the posterior probability of human joint rotations is more concentrated than the prior probability. Our experimental results demonstrate that such a characteristic makes the posterior probability an easier form to learn (for neural networks) than its prior counterpart. + +Apart from the theoretical contributions, we also propose a new human mesh recovery framework that can utilize the learned analytical posterior probability. We demonstrate that this framework successfully achieves high precision and high robustness at the same time, and outperforms existing SOTA baselines. Furthermore, our framework enables seamless integration with additional sensors that can yield directional/rotational observations (e.g., multi-view cameras, optical markers, IMUs) due to its Bayesian nature. Different from naive multi-sensor fusion algorithms (e.g., Kalman filter [21]) that typically perform fusion at the inference stage, our framework allows fusion in the training stage to learn the noise characteristics of sensors, and thus has the potential to produce better precision. We demonstrate that our fusion mechanism can achieve similar effects to fusing the latent features from multiple sensor input branches, but is much more flexible since it does not require modification of the main backbone. + +The key contributions of this paper are thereby: + +- We derive a novel analytical formulation for learning probability distributions for human joint rotations, and theoretically prove that such formulation allows the regression of posterior probability distribution in a Bayesian manner. +- We propose a new framework for human mesh recovery by leveraging the learned analytical posterior probability and show that this framework outperforms existing SOTA baselines. +- We introduce a novel and flexible multi-sensor fusion mechanism that allows fusing different observations in the training stage. + +# 2. Related work + +In this section, we discuss related studies on human mesh recovery, which can be achieved by optimization-based and learning-based methods. Leveraging the parametric human + +model [41, 54], optimization-based approaches [2, 9, 15, 51] fit the parameters via iteration while learning-based approaches regress the parameters with neural networks. Our work follows the learning paradigm, therefore we here mainly review recent advances in learning-based methods. + +Direct methods: Given images as input, this kind of approach directly regresses the model parameters with neural networks. Different representations of rotation [22, 34, 74], supervision schemes [20, 29, 37] as well as temporal context [5, 13, 23, 26] are explored to improve performance. However, the gap between the image space and the abstract parameter space of statistical models makes it difficult to generate well-aligned estimations. + +Indirect methods: Instead of regressing rotation representations from RGB images directly, plenty of works introduce proper intermediate or proxy representations, such as segmentation [27, 49, 68], IUV maps [64, 69, 70], keypoints [6, 14, 36, 52] or surface landmarks [30, 32, 42], to guide the learning of neural networks efficiently. HybrIK [36] decomposes the 3D rotation into solvable swings from 3D keypoints and extra predicted twists. PARE [27] learns to predict attention masks which are fused with image feature maps to provide body part information. These solutions may achieve higher precision, but generating only deterministic results and ignoring the uncertainty of estimation make them sensitive to noisy or erroneous proxy predictions. + +Probabilistic methods: To deal with the uncertainty from occlusions or depth ambiguities, several works manage to produce multiple hypotheses [1] or a probability distribution [53]. I2L-MeshNet [48] predicts lixel-based 1D heatmaps for each human mesh vertex for uncertainty modeling. Sengupta et al. [56] assume simple multivariate Gaussian distributions over the parameters of the human model. ProHMR [31] learns a distribution of plausible 3D poses represented by normalizing flows, which is more powerful and expressive than Gaussian distributions. Recently Sengupta et al. [55] further represent the essential distribution of human joint rotation over $\mathcal{SO}(3)$ by adopting the matrix Fisher distribution [25], which can provide quantified uncertainty estimation. Despite a better explanation for ambiguities, the parameters of the above distribution are not easy to learn, limiting their overall performance on complicated scenes. + +Multi-sensor fusion: Recently an increasing number of approaches attempt to integrate extra observations from other sensors, such as IMUs [10,65,66] and multi-view cameras [7, 71, 73], to obtain more reliable estimations. One simple strategy is combining all observations properly with + +![](images/a10ab4db7c11d27351eda3dc631c962554e79c64f44d509f9effbcf423e61883.jpg) +Figure 2. Overview of our framework. Given an input image, the multi-branch network predicts the prior matrix Fisher parameters $\mathbf{F}$ , the 3D keypoints $\mathbf{J}$ , and the SMPL shape parameters $\beta$ , respectively. The bone direction $\mathbf{d}$ calculated from $\mathbf{J}$ serves as the likelihood conditioned on 3D rotation. The posterior probability can be obtained based on Bayesian rules (Fusion), which still follows the matrix Fisher distribution, but with different parameters and larger confidence. Observations from additional sensors can also be fused into the posterior probability in the same manner. The corresponding human mesh can then be recovered using the estimated rotation and shape. + +Kalman filter [21], which can be treated as a baseline. Some works [43,62,63] fit the human model to evidence including images and IMUs through joint optimization. Apart from these test-time fusion schemes, several approaches [10, 61] incorporate the fusing process into training by concatenating the features from images and IMUs directly. GeoFuse [72] reinforces the image features guided by IMUs to infer the occluded joints. Our framework is also flexible to perform multi-sensor fusion and generates competitive results without specific modification to the backbone. + +# 3. Methods + +In this section, we first mathematically introduce the probability distributions for orientations regarding rotations and directions (Sec. 3.1). Then, we model the human joint rotation and bone direction with the corresponding distribution, and derive the analytical formulation of the posterior probability of joint rotation conditioned on the bone direction with crucial conclusions and discussion (Sec. 3.2). Finally, we describe the proposed framework (Sec. 3.3) and learning details (Sec. 3.4). + +# 3.1. Orientation probability distribution + +Before delving into human modeling, we investigate the orientation representation for general rigid entities. Suppose $\mathbf{X} \in \mathbb{R}^{n \times p}$ is the parametric representation of the entity orientation, each column of which depicts the direction of a basis. $\mathbf{X}$ is on the Stiefel manifold $\mathcal{V}(n,p)$ if $\mathbf{X}^T\mathbf{X} = \mathbf{I}_p$ , and when $n = p$ , it further belongs to the orthogonal group $\mathcal{O}(n)$ . Additionally, the components of $\mathcal{O}(n)$ with determinant $+1$ are referred to as the special or + +thogonal group $\mathcal{SO}(n)$ , which is used to represent the rotation of $n$ degrees of freedom. Meanwhile, if $p = 1$ , the normalized $\pmb{X}$ , i.e., $n$ -dimensional unit vector on the manifold $(n - 1)$ -sphere $\mathcal{S}^{n - 1}$ , can represent the single direction as well. From a probabilistic perspective, when $\pmb{X}$ is a random matrix, there are two common cases. + +Rotation $(n = p)$ : For rotation matrix $\mathbf{R} \in \mathcal{SO}(n)$ , the matrix Fisher distribution $\mathcal{MF}(\cdot)$ has been proposed to characterize its probabilistic properties on $\mathcal{SO}(n)$ [8, 25]. The probability density function is as follows: + +$$ +p (\boldsymbol {R}; \boldsymbol {F}) = \frac {1}{c (\boldsymbol {F})} \exp (t r (\boldsymbol {F} ^ {T} \boldsymbol {R})) \sim \mathcal {M F} (\boldsymbol {F}), \tag {1} +$$ + +where $\pmb{F} \in \mathbb{R}^{n \times n}$ is the distribution parameter, and $c(\pmb{F})$ is a normalizing constant. Algebraically, $\pmb{F}$ can be decomposed into a concentration matrix $\pmb{K}$ and a mean rotation matrix $\pmb{M}$ via SVD decomposition: + +$$ +\boldsymbol {F} = \boldsymbol {U} \boldsymbol {S} \boldsymbol {V} ^ {T} = \underbrace {\left(\boldsymbol {U} \Delta \boldsymbol {V} ^ {T}\right)} _ {\boldsymbol {M} \in \mathbb {R} ^ {n \times p}} \underbrace {\left(\boldsymbol {V} \Delta \boldsymbol {S} \boldsymbol {V} ^ {T}\right)} _ {\boldsymbol {K} \in \mathbb {R} ^ {p \times p}}, \tag {2} +$$ + +where $\Delta = \text{diag}(1, 1, |\mathbf{U} \mathbf{V}|)$ is a diagonal orthogonal matrix to ensure the determinant of $\mathbf{M}$ is $+1$ . $\mathbf{K}$ is symmetric positive definite as long as $\mathbf{F}$ is full rank. A rotation estimation $\hat{\mathbf{R}}$ can be calculated from the mode of distribution: + +$$ +\hat {\boldsymbol {R}} = \boldsymbol {M} = \boldsymbol {U} \operatorname {d i a g} (1, 1, | \boldsymbol {U} \boldsymbol {V} |) \boldsymbol {V} ^ {T}. \tag {3} +$$ + +Direction $(p = 1)$ : The probability density function for a unit vector $d\in S^{n - 1}$ is similar to Eq. (1) if we set $p = 1$ + +which corresponds to the classical von Mises-Fisher distribution $\mathcal{V}\mathcal{M}\mathcal{F}(\cdot)$ [44]: + +$$ +p (\boldsymbol {d}; \kappa , \boldsymbol {m}) = \frac {1}{c (\kappa)} \exp (\kappa \boldsymbol {m} ^ {T} \boldsymbol {d}) \sim \mathcal {V M F} (\boldsymbol {m}, \kappa), \quad (4) +$$ + +where $c(\kappa)$ is a normalizing constant. $\pmb{m}$ denotes the mean direction and $\kappa$ denotes the concentration parameter, which have a close meaning to $M$ and $\pmb{K}$ in Eq. (2), respectively, and thus $\hat{\pmb{d}} = \pmb{m}$ becomes a direction estimation. + +Theoretically, if $\kappa$ is 0, $\mathcal{V}\mathcal{M}\mathcal{F}(\boldsymbol{m},0)$ is equivalent to the uniform distribution on the sphere, while if $\kappa$ is large, it is close to the wrapped normal distribution $\mathcal{W}\mathcal{N}(\boldsymbol{m},\kappa^{-1})$ that adds up the densities of vectors representing the same direction on the sphere due to the periodicity. Thus, $\kappa$ can be viewed as the inverse of the variance and denotes the concentration of the distributions. + +# 3.2. Human modeling + +The human joint rotation can be represented as rotation matrix $\mathbf{R} \in \mathcal{SO}(3)$ . Inspired by recent advances in object pose estimation [3, 33, 46, 67], we incorporate the probabilistic modeling for human poses. Specifically, we adopt the matrix Fisher distribution over $\mathcal{SO}(3)$ as the prior distribution for joint rotation. Moreover, as the bone direction can be easily calculated from the joint rotation, we regard the joint rotation $\mathbf{R}$ as the latent variable and the bone direction $\mathbf{d}$ as the corresponding observation, which follows the von Mises-Fisher distribution: + +$$ +p (\boldsymbol {d} | \boldsymbol {R}) = \frac {1}{c (\kappa)} e x p (\kappa \boldsymbol {l} ^ {T} \boldsymbol {R} ^ {T} \boldsymbol {d}) \sim \mathcal {V M F} (\boldsymbol {R l}, \kappa), \quad (5) +$$ + +where $l$ is the unit direction of the bone in the reference pose (e.g., T-pose), ideally satisfying $Rl = d$ . + +Leveraging Bayesian inference, given the prior distribution (Eq. (1)) and the likelihood function (Eq. (5)), the posterior probability of joint rotation conditioned on the bone direction can be derived as follows: + +$$ +\begin{array}{l} p (\boldsymbol {R} | \boldsymbol {d}) = \frac {p (\boldsymbol {R}) \cdot p (\boldsymbol {d} | \boldsymbol {R})}{p (\boldsymbol {d})} \propto p (\boldsymbol {R}) \cdot p (\boldsymbol {d} | \boldsymbol {R}) \tag {6} \\ = \frac {1}{c} e x p (t r [ (\boldsymbol {F} + \kappa \boldsymbol {d l} ^ {T}) ^ {T} \boldsymbol {R} ]) \sim \mathcal {M F} (\boldsymbol {F} + \kappa \boldsymbol {d l} ^ {T}). \\ \end{array} +$$ + +It can be concluded from Eq. (6) that the posterior probability $p(\mathbf{R}|\mathbf{d})$ also follows the matrix Fisher distribution with an updated parameter $\mathbf{F}' = \mathbf{F} + \kappa \mathbf{d}\mathbf{l}^T$ . + +Property: From another perspective, the posterior parameter $F'$ can be viewed as the multiplication of the same mean term $M$ and a new concentration term $K'$ : + +$$ +\boldsymbol {F} ^ {\prime} = \boldsymbol {F} + \kappa \boldsymbol {d l} ^ {T} = M (\underbrace {\boldsymbol {K} + \kappa \boldsymbol {M} ^ {T} \boldsymbol {d l} ^ {T}} _ {\boldsymbol {K} ^ {\prime}}). \tag {7} +$$ + +It can be proved that $M^T d\boldsymbol{l}^T = \boldsymbol{ll}^T$ is a real symmetric matrix with rank 1, and $K$ from Eq. (2) is also real symmetric, thus the posterior concentration term $K'$ is a real symmetric matrix. According to the interlacing theorem for Hermitian matrices from matrix analysis [17], the eigenvalues for a Hermitian matrix with a rank-1 Hermitian perturbation satisfy the following inequality: + +$$ +\lambda_ {1} \leq \lambda_ {1} ^ {\prime} \leq \lambda_ {2} \leq \dots \leq \lambda_ {p - 1} ^ {\prime} \leq \lambda_ {p} \leq \lambda_ {p} ^ {\prime}, \tag {8} +$$ + +where $\lambda_{i}$ and $\lambda_{i}^{\prime}$ denote the eigenvalues of $\pmb{K}$ and $\pmb{K}^{\prime}$ , respectively. Note that the eigenvalues of the concentration term equal the singular values of the distribution parameter, which reflect the confidence of the distribution. From Eq. (8) we can get the conclusion that the posterior estimation is more concentrated than the prior estimation as long as the likelihood term is non-zero, and is validated to be a more easily learnable formulation in the experiment and the supplementary material. + +General form: Similarly, if other sensors that yield directional $\pmb{d}_i$ or rotational $\pmb{D}_j$ observations are available, the analytical posterior probability is thereby as follows: + +$$ +p (\boldsymbol {R} | \left\{\boldsymbol {d} _ {i}, \boldsymbol {D} _ {j} \right\}) \sim \mathcal {M F} (\boldsymbol {F} + \sum_ {i \in \mathcal {Z} _ {1}} \kappa_ {i} g (\boldsymbol {d} _ {i}) + \sum_ {j \in \mathcal {Z} _ {3}} \boldsymbol {D} _ {j} \boldsymbol {K} _ {j} ^ {T}), \tag {9} +$$ + +where $\kappa_{i}$ and $K_{j}$ are the concentration terms for weighting. $g(\cdot)$ is a mapping of IK that converts the directional observation to a rotation estimation, which is not limited to a specific IK algorithm as long as it supports gradient backpropagation (e.g., the simple solution $\boldsymbol{d}\boldsymbol{l}^T$ in Eq. (6)). $\mathcal{Z}_1$ denotes the set of sensors providing directional observations such as accelerometers, while $\mathcal{Z}_3$ denotes the set of rotational sensors like gyroscopes. We simplify the original derivation by assuming the sensors are unbiased. Please refer to the supplementary material for the derivation. + +Discussion: There are several advantages of our approach. First, adopting the matrix representation is more reasonable than other rotation representations. As presented in [34], a continuous 9D unconstrained representation followed by SVD can achieve comparable or even better performance than the widely used 6D vector [74]. Second, the Gaussian distribution is unsuitable for cases with large uncertainty where the assumption of local linearity cannot hold [11, 12], while the matrix Fisher distribution does not have this problem. Third, the posteriors are easier to learn than the priors in that learning the posteriors can converge to the mode preferred by the likelihood function quickly, while learning the priors may face multiple local minima in the initial stage and thus cannot converge well. + +To recognize the proposed scheme intuitively, we show the schematic diagrams of probabilistic modeling in Fig. 3. For a method without probabilistic modeling (e.g., using IK + +![](images/4892c4d0335d5a6aad3b9b9b202585aea25c798d19702e4b0b90435c41eaa63d.jpg) +Figure 3. Schematic diagrams of probabilistic modeling. The opaque coordinate system $\triangleleft$ is the ground-truth 3D rotation. The transparent rotation represents a deterministic estimation for a method without probabilistic modeling (row 1), while it denotes a sample from the estimated posterior distribution (row 2). The red region on the sphere represents the probability of a certain rotation, and it could cover the ground-truth even for noisy cases. + +to solve rotations from keypoints), its underlying model is a single direction, thus it may be erroneous when the estimated bone direction deviates from the ground-truth, as shown in the noisy cases. In contrast, the posterior model can be fused with various models, and for noisy keypoints, it has the potential to recover the exact rotations since the negative impact of its partial reliance on the estimated keypoints can be eliminated by the prior or other observations. + +# 3.3. Learning Framework + +Our proposed framework that leverages the derived posterior probability for human mesh recovery is demonstrated in Fig. 2. We adopt the parametric model SMPL [41] as our human representation, which can also be replaced by other human models [51,54]. Given an input image, a CNN backbone is used to extract image features, followed by three output branches, including prior distribution parameter $F$ , 3D keypoints $J$ , and shape parameter $\beta$ . The adopted keypoints branch consists of normalized 2D keypoints and relative depth to the root joint decoded from the feature, as well as the human scale predicted by a small MLP branch, so as to recover absolute 3D keypoints. Note that other strategies for 3D keypoints estimation are also applicable. The bone direction $d$ is calculated from $J$ . Then we utilize Eq. (9) to fuse $F$ , $d$ , or other optional observations analytically in the sense of probability. With the new distribution parameter $F'$ , we can get the rotation estimation according to Eq. (3). As for $\kappa$ , it is related to the physical properties (measure covariance) of specific sensors that could be set in advance. If there is no prior knowledge of the sensor, it's feasible to tune it manually or learn it from the data. We simply use the scaled scores of estimated keypoints. For multiple sensors, the concentration term $K$ is simplified as a diagonal matrix. + +Objective functions: For the following objective functions, symbols with superscript $*$ indicate the groundtruth, and symbols with hat indicate the estimation. The $L_{1}$ loss is used to supervise the 3D keypoints, while the $L_{2}$ loss is applied to other variables: + +$$ +\mathcal {L} _ {J} = \left| \left| \hat {\boldsymbol {J}} - \boldsymbol {J} ^ {*} \right| \right| _ {1}, \tag {10} +$$ + +$$ +\mathcal {L} _ {\beta} = \left\| \hat {\boldsymbol {\beta}} - \boldsymbol {\beta} ^ {*} \right\| _ {2} ^ {2}, \tag {11} +$$ + +The mode of the posterior probability distribution $\hat{R}$ can be solved according to Eq. (6) and (3), and is supervised if the annotations of SMPL pose parameters $\theta$ are provided as follows: + +$$ +\mathcal {L} _ {\theta} = \left| \left| \hat {\boldsymbol {R}} - \exp (\boldsymbol {\theta} ^ {*}) \right| \right| _ {2} ^ {2}, \tag {12} +$$ + +where $\text{expm}$ denotes the exponential map implemented with the Rodrigues' formula. + +Apart from the mode, the whole distribution also needs to be supervised. Since the normalizing constant in the distribution is hard to be calculated stably due to the numerical integration, we propose to supervise the distribution by sampling. Specifically, we adopt the rejection sampling technique to sample Bingham distribution of unit quaternions on $S^3$ based on its equivalence to matrix Fisher distribution. The proposal distribution in rejection sampling is angular central Gaussian (ACG) distribution [24, 55]. Thus the sampling loss is as follows: + +$$ +\mathcal {L} _ {s} = \sum_ {i = 1} ^ {N _ {s}} \rho \left(\left| \left| \hat {\boldsymbol {R}} _ {i} - \exp \left(\boldsymbol {\theta} ^ {*}\right) \right| \right| _ {2} ^ {2}\right), \tag {13} +$$ + +where $N_{s}$ is the number of samples. $\rho$ is an simple activation function for relaxation, which tolerates small deviations. + +The total objective function is as follows: + +$$ +\mathcal {L} = w _ {1} \mathcal {L} _ {J} + w _ {2} \mathcal {L} _ {\beta} + w _ {3} \mathcal {L} _ {\theta} + w _ {4} \mathcal {L} _ {s}, \tag {14} +$$ + +where $w_{1}, w_{2}, w_{3}$ , and $w_{4}$ are weight scalars. + +# 3.4. Implementation details + +We adopt ResNet-34 [16] and HRNet-W48 [58] as backbones. The ResNet backbone is followed by three deconvolutional layers to generate 3D heatmaps with the size of $64 \times 64 \times 64$ for keypoints and three MLPs for shape parameters $\beta$ (10), distribution parameter $F$ (216) and human scale (1). The feature from HRNet backbone is upsampled and directly followed by similar output branches with dimensions motioned above. The input image has a resolution of $256 \times 256$ . The network is trained for 50 epochs with Adam and an initial learning rate of $1 \times 10^{-3}$ , decayed with a factor of 10. $w_{1}$ and $w_{2}$ are set to 1. $w_{3}$ and $w_{4}$ are set to 0.1 and increased to 1 in the later stage of training. + +# 4. Experiments + +In this section, we demonstrate the effectiveness of our framework on human mesh recovery and multi-sensor fusion, evaluate our key designs via an ablation study, and discuss the limitation and future work of our method. + +# 4.1. Datasets and metrics + +To maintain the fairness of comparison, we adopt the same datasets and metrics as previous methods. + +Human3.6M [18] provides 3D keypoints annotations, and the corresponding SMPL annotations are from MoSh [40]. We use (S1, S5, S6, S7, S8) for training and (S9, S11) for evaluation, following standard practice [22, 36]. + +3DPW [62] provides SMPL annotations. Following [36, 37], we add its training set only for experiments on it. + +MS COCO [39] contains in-the-wild images and 2D keypoints annotations. We use its training set to improve the generalization ability of our method. + +MPI-INF-3DHP [45] is a multi-view dataset that provides 3D keypoints annotations. We only use it for training. + +AGORA [50] is a synthetic dataset with challenging scenes and SMPL annotations of adults and kids. Only when evaluating our algorithm on it will we add its training set. + +TotalCapture [61] contains multi-view videos, IMUs and 3D keypoints annotations for the evaluation of sensor fusion algorithms. We follow [61,72] to divide it. + +Metrics include MPJPE, PA-MPJPE, and PVE all in mm. MPJPE measures the 3D keypoints error, while PA-MPJPE is similar to MPJPE except that a rigid alignment is performed at first. PVE measures the human mesh vertex error. + +# 4.2. Human mesh recovery + +Table 1 shows the evaluation results on public benchmarks. With either ResNet or HRNet as the backbone, our approach outperforms SOTA methods. Besides, we surpass the prior counterpart [55] by a large margin, indicating that our posterior estimation is easier to learn than the single prior. Table 2 shows the results on the AGORA test set. Our framework is more accurate than others, especially for kids. Note that for 2D datasets, despite that the pseudo-GT annotator of CLIFF [37] and EFT dataset [20] can be incorporated to further improve our performance, we only use the original keypoints supervision for fair comparisons. + +Posterior effects: We compare different designs to thoroughly validate the posterior effects and the feature choice in our framework, as shown in Table 3, which include: (a) regressing the parameters $\mathbf{F}$ only without the keypoint branch; (b) solving rotations from keypoints via IK without probabilistic modeling; (c) deactivating the learned prior parameters in testing (i.e., setting $\mathbf{F}$ to zero); (d) using the feature close to the end of the backbone to regress prior $\mathbf{F}$ + +
Methods3DPWHuman3.6M
PA ↓MPJPE ↓PVE ↓PA ↓MPJPE ↓
HMR (R-50) [22]81.3130.0-56.888.0
GraphCMR (R-50) [30]70.2--50.1-
SPIN (R-50) [29]59.296.9116.441.162.5
Sengupta. (H-48) [55]*59.284.7*---
HMR-EFT (R-50) [20]52.4--43.9-
I2L-MeshNet (R-50) [48]58.693.2-41.755.7
SPEC (R-50) [28]53.296.5118.5--
BEV (H-32) [60]46.978.592.3--
PARE (H-32) [27]46.574.588.6--
Graphormer (H-64) [38]45.674.787.734.551.2
PyMAF (H-48) [70]45.374.287.037.254.2
HybrIK (R-34) [36]45.074.186.533.655.4
FastMETRO (R-50) [4]48.377.990.637.353.9
FastMETRO (H-64) [4]44.673.584.133.752.2
CLIFF (R-50) [37]45.772.085.335.150.5
CLIFF (H-48) [37]43.069.081.232.747.1
Ours (R-34)44.171.884.931.648.7
Ours (H-48)40.668.379.429.145.7
+ +Table 1. Results on standard benchmarks. 'PA' is PA-MPJPE. $R^{\prime}$ and $H^{\prime}$ mean ResNet and HRNet. * with scale correction. + +
MethodsAGORA
MPJPE ↓PVE ↓Kid-MPJPE ↓Kid-PVE ↓
HMR [22]180.5173.6219.4209.3
HMR-EFT [20]165.4159.0202.7193.5
SPIN [29]153.4148.9191.7186.7
PARE [27]146.2140.9193.9186.4
SPEC [28]112.3106.5171.0163.2
ROMP [59]108.1103.4159.8156.6
BEV [60]105.3100.7129.1125.9
Hand4Whole [47]89.884.8153.3146.4
CLIFF [37]81.076.094.189.6
HybrIK [36]77.073.990.286.6
Ours74.470.984.580.5
PLIKS [57]71.567.388.384.2
NIKI [35]67.363.983.980.2
+ +Table 2. Results on the AGORA test set. The metrics with the prefix 'Kid-' are calculated only for kids, otherwise for all ages. Two concurrent works are shown in gray for completeness. + +
DesignsHuman3.6M
PA-MPJPE ↓MPJPE ↓
(a) W/o 3D keypoints45.876.5
(b) W/o prior F43.263.6
(c) W/o prior F (in testing)42.758.7
(d) Late feature for F and β29.948.6
(e) Early feature for F and β29.346.5
(f) Ours (full model)29.145.7
+ +Table 3. Ablation study of designs on the Human3.6M dataset. + +and shape $\beta$ ; (e) using the feature from the initial stage; (f) our full model with all branches and intermediate feature. + +The performance of design (a) is not good since its estimation cannot align precisely with the image, and it is observed that this design exhibits a slower speed of convergence, reflecting the importance of the likelihood function + +![](images/8ef8793fb4117ce0068e0637d3036a9a6c2740ff58b2050070f49afe48176126.jpg) +Figure 4. Noise simulation. (a) Rotation error v.s. the mixed noises of both prior and keypoint. (b) Rotation/direction error v.s. keypoint noise. The noise level is the ratio of the noise amplitude to the maximum of the variable. The simulation step is $5\%$ . 'W/o prior $\pmb{F}$ ' is an indirect strategy without probability. 'Fixed $\kappa$ ' uses predefined $\kappa$ . 'Adaptive $\kappa$ ' means $\kappa$ varies with the noise variance. + +
Noise amplitude5mm10mm15mm30mm50mm
W/o prior F61.362.765.071.580.4
Posterior-based48.549.651.454.559.0
(12.8↓)(13.1↓)(13.6↓)(17.0↓)(21.4↓)
+ +from keypoints. The comparison between design (b) and (e) shows that the prior $\pmb{F}$ is crucial in fusion. Furthermore, design (c) is better than design (b), indicating the prior $\pmb{F}$ has guided the keypoints learning to some extent. The difference is more significant in MPJPE since the global rotation is supervised for design (c). As for the feature choice, the intermediate feature adopted by our framework shows slightly better performance than the late and early features. + +Noise robustness: We evaluate the robustness of our framework when suffering from noise. Fig. 4 shows the simulation results with two metrics. The rotation error is the angle to be rotated from the estimated rotation $\hat{\pmb{R}}$ to the ground-truth. The direction error is the angle between the estimated bone vector and the ground-truth. Fig. 4 (b) reveals that 'w/o prior $F$ has a small direction error but a large rotation error for the unsolved twist, while the posterior strategy has a much smaller error even with a high keypoint noise level and shows a slower error growth rate. Note that the performance of a simple fixed $\kappa$ is also acceptable. Fig. 4 (a) shows that when the prior noise level is less than $15\%$ , the keypoint noise has little effect on the posterior result with the adaptive $\kappa$ , reflecting the tolerance to noises of the posterior scheme. Table 4 shows the noise test on the Human3.6M dataset. From the difference listed in parentheses, when the noise level is higher, the error of the posterior method increases more slowly compared with the baseline without prior $F$ . + +Samples illustration: Fig. 5 illustrates the samples from the posterior distribution. The right hand has a relatively + +![](images/551a24428e3cf58ef213094dfe6143b345957454f84026c874aa78fd2a5e284a.jpg) +Figure 5. Samples from the distribution. The mode and samples of the relative rotations are shown. The light color indicates the mode, while the dark color indicates an extra sample. The canonical coordinate is at the top right as a reference. + +Table 4. Noise test on the Human3.6M dataset. The 3D keypoints suffer from different levels of noises. MPJPE is reported. + +
MethodsSensorsTotalCapture
PA-MPJPE ↓MPJPE ↓
IMUPVH [10]mv + IMUs-42.6
GeoFuse [72]mv + IMUs20.624.6
Oursmv + IMUs19.423.5
VIP [62]sv + IMUs26.0-
Kalman filtersv + IMUs23.134.7
Ourssv29.042.1
Ours (w/o ref, R-50)sv + IMUs25.841.7
Ours (w/o ref, H-48)sv + IMUs22.338.8
Ours (R-50)sv + IMUs25.032.3
Ours (H-48)sv + IMUs21.228.5
+ +Table 5. Results on the TotalCapture dataset. 'mv' and 'sv' denote multi-view and single-view. 'w/o ref' means lacking a reference skeleton (only a statistical one from training set is adopted), which would slightly weaken the performance of our framework. + +large uncertainty on rotating around the X-axis due to the uncertain twist angle, as shown by the widespread blue and green samples. The left elbow has a vertical uncertainty on the direction of the forearm since the left hand cannot be easily determined. The left ankle has large confidence, except in the depth direction, therefore the green samples spread horizontally. + +Fig. 6 shows the qualitative comparison with the SOTA methods. The indirect methods that use part segmentation [27] or 3D keypoints [36] perform well in most cases, but may suffer from wrong segmentation for distant people or generate unnatural poses. While the direct method CLIFF [37] may not align the image well for complicated scenes. + +# 4.3. Multi-sensor fusion + +We perform experiments on the TotalCapture dataset [61] using the feed-forward network directly without any iterative optimization. As the original dataset does not provide SMPL annotations, we adopt the human skeleton defined by 19 joints and 11 attached IMUs, as shown in Fig. 7. We choose the optimization-based method VIP [62] and the feature-fused method GeoFuse [72] as baselines. + +![](images/f8a558669ebb6899c3d4366b2b96191f3d5ac6644e89b0bfcd1c456049e7408f.jpg) + +![](images/97bef3aa3ad05c5c4187302d0921ab1108abee83d8e96f383a658b86590d312b.jpg) + +![](images/537f11be175d3c08e65d7d5646ea4f912331d4d4cdb792f934305f53c541ed93.jpg) + +![](images/6729f757f32c42ad4b4d8e4b10db6fc7e76b9917dafc921762ed954095a8e428.jpg) + +![](images/012df255d6d29ba41b6da0d7d000f20e149dc3e2bfb439fa3bc90216136229e3.jpg) + +![](images/b09c7f104e761edade23d6baa3728362b3a8686d0394ac493e35201a7e9cf581.jpg) + +![](images/76d25e7592822959ef09daf030b27fd2a96b56709ba125ff73cb6b1ea7f7caf3.jpg) + +![](images/b18ecbf0940149cc4dccc26336b1b88190777680fd91c3dc795d8162d63506ab.jpg) + +![](images/fb144614a7e52491647418b2cb7d3ee0e715424490f3930b6f9215fea8dccb6b.jpg) + +![](images/e3b40ff18cdfde0d04248d26bd8dae12894b2a700e0ec4535936ad99313610bd.jpg) +Input + +![](images/9fd15cc30ea84ba89f850acb7f2b7c714ce30d06be35141b7210267ec2829e45.jpg) +HybrIK + +![](images/977008a88c2065e04983e989a46c6ca18374aa71e979276f673baad0a1ff7165.jpg) +Ours + +![](images/581cd8faa030dae49a021d5b889c936fe8e6cc69aa8ec35aff1c02a7ac773b3c.jpg) +Input + +![](images/e4c92c0340adfbb8914e1b55914be0d08e86737c74ef827f296a73b6ba42fbd7.jpg) +PARE + +![](images/c53e5ebfedf078fbdd47d8aa443aa5627ab7fab1a9204cacafbbe32c2070fa20.jpg) +Ours + +![](images/36275191f01db9ed8449b025dabb347124ca64892e1f04531b17699f82291708.jpg) +Input + +![](images/785477d74d808cd329105a3686cdbbf5c860d919346071c14df89ddc6f37de0a.jpg) +CLIFF + +![](images/6d078ec3136ca8439e07087f5445bc9af1005fc1152aedf2f7e672653b982c2a.jpg) +Ours + +![](images/15cccf09e7ecd81b2e76f23fa89d3065e13d7815b7e23ad9e101e735253c1dad.jpg) +Figure 6. Qualitative comparison. The input images are from 3DPW [62], MS COCO [39], and AGORA [50], respectively. We compare our approach with SOTA methods including HybrIK [36], PARE [27], and CLIFF [37]. For images with multiple people, the person with a solid yellow circle on the face is estimated. + +![](images/37924811c99f9fc8eae307c99353d1f8a4df363d4ee3c90f941b563fd5667fd4.jpg) +Side View + +![](images/8bfc4d0d5f0a79ecf50c69bceba78929d66e70e22e82e74e1681a5257225d1d1.jpg) +IMUT-pose + +![](images/412b33ae1ce14202d9e3ae86f33cfd485cabcbc93e91a4cd2c5d954867d7d311.jpg) +Front View + +![](images/6ab21ff8a2fcc050ffdab59c47456a2eb6d1b2be64ce8ea3e34ea760a390a3cd.jpg) +Figure 7. An example of a multi-sensor case. The estimations from the front-view camera, side-view camera, and IMUs are plotted. The normalized confidence score of the left knee is listed. + +![](images/71c9890f4424f2a6d16b35243f44149ae09da929b7543a0cad8aa82f066b1f59.jpg) + +Table 5 shows the experimental results. Our method outperforms baseline methods, indicating the effectiveness of our posterior scheme. In the 'Kalman filter' setup, we apply a weighted sum to the 3D rotations separately obtained from images and IMUs. As the observation variance required for calculating the Kalman gain is unknown, we pick the weight pairs that can yield the best estimation through grid searching, i.e., from (0.7, 0.3) to (0.3, 0.7). Note that unlike Kalman filter which fuses the observations in the testing stage, our method performs fusing in the training stage, and thus has the potential to obtain higher precision. Our framework is also more flexible than feature-level fusing methods since we do not require modifications of the backbone to incorporate new sensors. + +Fig. 7 shows an example of a scene with multiple cameras and IMUs. The confidence from the two cameras are + +calculated via the normalized differential entropy of the estimated distribution parameters, while the confidence from IMUs is set to a relatively larger value since IMUs can provide accurate measurements. Note that other metrics that represent the uncertainty from the distribution can also be adopted. It can be observed that the front view produces erroneous knee bending due to the depth ambiguity, therefore its confidence is lower than the side view. As a result, the fused result will be less affected by the noisy estimation. + +# 4.4. Limitation and future work + +Our work has several limitations. First, we only consider the uncertainty of poses, not including that of shapes, which can also be modeled as probability distributions. Second, we model the human joint independently, which is only affected by the parent node. Therefore, how to derive the analytical form of joint rotations conditioned on other hierarchical joints to incorporate anatomical constraints explicitly is still unsolved. Besides, with the single-view uncertainty, the temporal extension also deserves further investigation. + +# 5. Conclusion + +In this paper, we derive a novel analytical posterior probability for human joint rotations in a Bayesian manner and prove the property that the posteriors are more concentrated than the priors. Based on the derivation, we propose a new framework for human mesh recovery by leveraging the learned posteriors, which has high precision and robustness, outperforming existing SOTA baselines. Furthermore, our framework can be seamlessly incorporated with additional sensors in the training due to its Bayesian nature. 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In CVPR, pages 5745-5753, 2019. 1, 2, 4 \ No newline at end of file diff --git a/2023/Learning Analytical Posterior Probability for Human Mesh Recovery/images.zip b/2023/Learning Analytical Posterior Probability for Human Mesh Recovery/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..7cf696b2976264405fa3cabcf714ed860f4a53a8 --- /dev/null +++ b/2023/Learning Analytical Posterior Probability for Human Mesh Recovery/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:d98426380f5cc6eb6e8b8d644b1cc2d268902f742d7df51f897277bf4da925d6 +size 570186 diff --git a/2023/Learning Analytical Posterior Probability for Human Mesh Recovery/layout.json b/2023/Learning Analytical Posterior Probability for Human Mesh Recovery/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..7327d55f3b48832361f1166046c60d3c38031fc5 --- /dev/null +++ b/2023/Learning Analytical Posterior Probability for Human Mesh Recovery/layout.json @@ -0,0 +1,12102 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 83, + 103, + 510, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 103, + 510, + 121 + ], + "spans": [ + { + "bbox": [ + 83, + 103, + 510, + 121 + ], + "type": "text", + "content": "Learning Analytical Posterior Probability for Human Mesh Recovery" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 83, + 142, + 505, + 159 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 142, + 505, + 159 + ], + "spans": [ + { + "bbox": [ + 83, + 142, + 505, + 159 + ], + "type": "text", + "content": "Qi Fang" + }, + { + "bbox": [ + 83, + 142, + 505, + 159 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 83, + 142, + 505, + 159 + ], + "type": "text", + "content": " Kang Chen" + }, + { + "bbox": [ + 83, + 142, + 505, + 159 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 83, + 142, + 505, + 159 + ], + "type": "text", + "content": " Yinghui Fan" + }, + { + "bbox": [ + 83, + 142, + 505, + 159 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 83, + 142, + 505, + 159 + ], + "type": "text", + "content": " Qing Shuai" + }, + { + "bbox": [ + 83, + 142, + 505, + 159 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 83, + 142, + 505, + 159 + ], + "type": "text", + "content": " Jiefeng Li" + }, + { + "bbox": [ + 83, + 142, + 505, + 159 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 83, + 142, + 505, + 159 + ], + "type": "text", + "content": " Weidong Zhang" + }, + { + "bbox": [ + 83, + 142, + 505, + 159 + ], + "type": "inline_equation", + "content": "^{1}" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 96, + 160, + 493, + 176 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 96, + 160, + 493, + 176 + ], + "spans": [ + { + "bbox": [ + 96, + 160, + 493, + 176 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 96, + 160, + 493, + 176 + ], + "type": "text", + "content": "NetEase Games AI Lab " + }, + { + "bbox": [ + 96, + 160, + 493, + 176 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 96, + 160, + 493, + 176 + ], + "type": "text", + "content": "Zhejiang University " + }, + { + "bbox": [ + 96, + 160, + 493, + 176 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 96, + 160, + 493, + 176 + ], + "type": "text", + "content": "Shanghai Jiao Tong University" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 203, + 192, + 216 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 203, + 192, + 216 + ], + "spans": [ + { + "bbox": [ + 143, + 203, + 192, + 216 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 228, + 290, + 408 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 228, + 290, + 408 + ], + "spans": [ + { + "bbox": [ + 45, + 228, + 290, + 408 + ], + "type": "text", + "content": "Despite various probabilistic methods for modeling the uncertainty and ambiguity in human mesh recovery, their overall precision is limited because existing formulations for joint rotations are either not constrained to " + }, + { + "bbox": [ + 45, + 228, + 290, + 408 + ], + "type": "inline_equation", + "content": "\\mathcal{SO}(3)" + }, + { + "bbox": [ + 45, + 228, + 290, + 408 + ], + "type": "text", + "content": " or difficult to learn for neural networks. To address such an issue, we derive a novel analytical formulation for learning posterior probability distributions of human joint rotations conditioned on bone directions in a Bayesian manner, and based on this, we propose a new posterior-guided framework for human mesh recovery. We demonstrate that our framework is not only superior to existing SOTA baselines on multiple benchmarks but also flexible enough to seamlessly incorporate with additional sensors due to its Bayesian nature. The code is available at https://github.com/NetEase-GameAI/ProPose." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 430, + 128, + 442 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 430, + 128, + 442 + ], + "spans": [ + { + "bbox": [ + 47, + 430, + 128, + 442 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 45, + 450, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 450, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 45, + 450, + 289, + 715 + ], + "type": "text", + "content": "Human mesh recovery is a task of recovering body meshes and 3D joint rotations of human actors from images, which has ubiquitous applications in animation production, sports analysis, etc. To achieve this goal, various approaches have been proposed in the computer vision community. Existing methods can be divided into two categories, i.e., direct and indirect, respectively. Direct methods use neural networks to regress the rotations (e.g., axis angle [22], rotation matrix [34], 6D vector [29,37,74]) of each humanoid joint in an end-to-end way, while indirect methods recover joint rotations based on some intermediately predicted proxies (e.g., 3D human keypoints [19, 36, 42], 2D heatmaps [52] or part segmentation [27]). However, both methods have obvious weaknesses. Generally, the estimated poses from direct solutions are not so well-aligned with the images (Fig. 1(a)), because joint rotations are more difficult to regress compared with keypoints [19,36]. 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"(c) Ours" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 306, + 358, + 545, + 381 + ], + "lines": [ + { + "bbox": [ + 306, + 358, + 545, + 381 + ], + "spans": [ + { + "bbox": [ + 306, + 358, + 545, + 381 + ], + "type": "text", + "content": "Figure 1. Comparisons of (a) the direct method [29], (b) the indirect method [36], and (c) our method." + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_caption" + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 410, + 547, + 650 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 410, + 547, + 650 + ], + "spans": [ + { + "bbox": [ + 304, + 410, + 547, + 650 + ], + "type": "text", + "content": "To simultaneously achieve high precision and high robustness, some probabilistic methods are developed, which, instead of seeking a unique solution, try to explicitly model the uncertainty of human poses by learning some kind of probability distribution. Prevalent ways of modeling the distribution include multivariate Gaussian distributions [48, 56], normalizing flows [31], and neural networks [51, 53]. In practice, these learned probability distributions can notably improve the estimation results in some extreme cases (e.g., under large occlusion), however, only minor differences can be found in terms of the overall performances on large datasets. One reason is that these probability models cannot truly reflect the rotational uncertainty since they are not strictly constrained to " + }, + { + "bbox": [ + 304, + 410, + 547, + 650 + ], + "type": "inline_equation", + "content": "\\mathcal{SO}(3)" + }, + { + "bbox": [ + 304, + 410, + 547, + 650 + ], + "type": "text", + "content": ". Recently, [55] proposes to adopt the matrix Fisher distribution over " + }, + { + "bbox": [ + 304, + 410, + 547, + 650 + ], + "type": "inline_equation", + "content": "\\mathcal{SO}(3)" + }, + { + "bbox": [ + 304, + 410, + 547, + 650 + ], + "type": "text", + "content": " [8, 25] to model the rotational uncertainty caused by depth ambiguity. However, even with this mathematically-correct formulation, the actual performance does not improve much either, because the parameters of the matrix Fisher distribution are not easy for deep neural networks to learn directly." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "text", + "content": "To address this problem, we propose a new learning-friendly and mathematically-correct formulation for learning probability distributions for human mesh recovery. Our formulation is derived based on the facts that, (i) the joint rotations follow the matrix Fisher distribution over " + }, + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{SO}(3)" + }, + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 295, + 749, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 314, + 757 + ], + "type": "text", + "content": "8781" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 239 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 239 + ], + "type": "text", + "content": "(ii) the unit directions of bones follow the von Mises-Fisher distribution [44], (iii) the bone direction can be viewed as the observation of joint rotation (i.e., the latent variable). It can be proven that the probability distributions of joint rotations conditioned on bone directions still follow the matrix Fisher distribution, which allows us to regress the posterior probability distribution of the 3D joint rotations in a Bayesian manner, and more importantly, in an analytical form. Moreover, we mathematically prove that the posterior probability of human joint rotations is more concentrated than the prior probability. Our experimental results demonstrate that such a characteristic makes the posterior probability an easier form to learn (for neural networks) than its prior counterpart." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 239, + 289, + 455 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 239, + 289, + 455 + ], + "spans": [ + { + "bbox": [ + 46, + 239, + 289, + 455 + ], + "type": "text", + "content": "Apart from the theoretical contributions, we also propose a new human mesh recovery framework that can utilize the learned analytical posterior probability. We demonstrate that this framework successfully achieves high precision and high robustness at the same time, and outperforms existing SOTA baselines. Furthermore, our framework enables seamless integration with additional sensors that can yield directional/rotational observations (e.g., multi-view cameras, optical markers, IMUs) due to its Bayesian nature. Different from naive multi-sensor fusion algorithms (e.g., Kalman filter [21]) that typically perform fusion at the inference stage, our framework allows fusion in the training stage to learn the noise characteristics of sensors, and thus has the potential to produce better precision. We demonstrate that our fusion mechanism can achieve similar effects to fusing the latent features from multiple sensor input branches, but is much more flexible since it does not require modification of the main backbone." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 59, + 456, + 251, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 456, + 251, + 468 + ], + "spans": [ + { + "bbox": [ + 59, + 456, + 251, + 468 + ], + "type": "text", + "content": "The key contributions of this paper are thereby:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 59, + 476, + 287, + 637 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 59, + 476, + 287, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 476, + 287, + 536 + ], + "spans": [ + { + "bbox": [ + 59, + 476, + 287, + 536 + ], + "type": "text", + "content": "- We derive a novel analytical formulation for learning probability distributions for human joint rotations, and theoretically prove that such formulation allows the regression of posterior probability distribution in a Bayesian manner." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 59, + 544, + 287, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 544, + 287, + 593 + ], + "spans": [ + { + "bbox": [ + 59, + 544, + 287, + 593 + ], + "type": "text", + "content": "- We propose a new framework for human mesh recovery by leveraging the learned analytical posterior probability and show that this framework outperforms existing SOTA baselines." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 59, + 601, + 287, + 637 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 601, + 287, + 637 + ], + "spans": [ + { + "bbox": [ + 59, + 601, + 287, + 637 + ], + "type": "text", + "content": "- We introduce a novel and flexible multi-sensor fusion mechanism that allows fusing different observations in the training stage." + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 657, + 132, + 670 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 657, + 132, + 670 + ], + "spans": [ + { + "bbox": [ + 47, + 657, + 132, + 670 + ], + "type": "text", + "content": "2. Related work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "content": "In this section, we discuss related studies on human mesh recovery, which can be achieved by optimization-based and learning-based methods. Leveraging the parametric human" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": "model [41, 54], optimization-based approaches [2, 9, 15, 51] fit the parameters via iteration while learning-based approaches regress the parameters with neural networks. Our work follows the learning paradigm, therefore we here mainly review recent advances in learning-based methods." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 148, + 545, + 245 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 148, + 545, + 245 + ], + "spans": [ + { + "bbox": [ + 304, + 148, + 545, + 245 + ], + "type": "text", + "content": "Direct methods: Given images as input, this kind of approach directly regresses the model parameters with neural networks. Different representations of rotation [22, 34, 74], supervision schemes [20, 29, 37] as well as temporal context [5, 13, 23, 26] are explored to improve performance. However, the gap between the image space and the abstract parameter space of statistical models makes it difficult to generate well-aligned estimations." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 261, + 545, + 417 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 261, + 545, + 417 + ], + "spans": [ + { + "bbox": [ + 304, + 261, + 545, + 417 + ], + "type": "text", + "content": "Indirect methods: Instead of regressing rotation representations from RGB images directly, plenty of works introduce proper intermediate or proxy representations, such as segmentation [27, 49, 68], IUV maps [64, 69, 70], keypoints [6, 14, 36, 52] or surface landmarks [30, 32, 42], to guide the learning of neural networks efficiently. HybrIK [36] decomposes the 3D rotation into solvable swings from 3D keypoints and extra predicted twists. PARE [27] learns to predict attention masks which are fused with image feature maps to provide body part information. These solutions may achieve higher precision, but generating only deterministic results and ignoring the uncertainty of estimation make them sensitive to noisy or erroneous proxy predictions." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 434, + 545, + 636 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 434, + 545, + 636 + ], + "spans": [ + { + "bbox": [ + 304, + 434, + 545, + 636 + ], + "type": "text", + "content": "Probabilistic methods: To deal with the uncertainty from occlusions or depth ambiguities, several works manage to produce multiple hypotheses [1] or a probability distribution [53]. I2L-MeshNet [48] predicts lixel-based 1D heatmaps for each human mesh vertex for uncertainty modeling. Sengupta et al. [56] assume simple multivariate Gaussian distributions over the parameters of the human model. ProHMR [31] learns a distribution of plausible 3D poses represented by normalizing flows, which is more powerful and expressive than Gaussian distributions. Recently Sengupta et al. [55] further represent the essential distribution of human joint rotation over " + }, + { + "bbox": [ + 304, + 434, + 545, + 636 + ], + "type": "inline_equation", + "content": "\\mathcal{SO}(3)" + }, + { + "bbox": [ + 304, + 434, + 545, + 636 + ], + "type": "text", + "content": " by adopting the matrix Fisher distribution [25], which can provide quantified uncertainty estimation. Despite a better explanation for ambiguities, the parameters of the above distribution are not easy to learn, limiting their overall performance on complicated scenes." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": "Multi-sensor fusion: Recently an increasing number of approaches attempt to integrate extra observations from other sensors, such as IMUs [10,65,66] and multi-view cameras [7, 71, 73], to obtain more reliable estimations. One simple strategy is combining all observations properly with" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "8782" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 70, + 547, + 249 + ], + "blocks": [ + { + "bbox": [ + 51, + 70, + 547, + 249 + ], + "lines": [ + { + "bbox": [ + 51, + 70, + 547, + 249 + ], + "spans": [ + { + "bbox": [ + 51, + 70, + 547, + 249 + ], + "type": "image", + "image_path": "a10ab4db7c11d27351eda3dc631c962554e79c64f44d509f9effbcf423e61883.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 256, + 547, + 313 + ], + "lines": [ + { + "bbox": [ + 46, + 256, + 547, + 313 + ], + "spans": [ + { + "bbox": [ + 46, + 256, + 547, + 313 + ], + "type": "text", + "content": "Figure 2. Overview of our framework. Given an input image, the multi-branch network predicts the prior matrix Fisher parameters " + }, + { + "bbox": [ + 46, + 256, + 547, + 313 + ], + "type": "inline_equation", + "content": "\\mathbf{F}" + }, + { + "bbox": [ + 46, + 256, + 547, + 313 + ], + "type": "text", + "content": ", the 3D keypoints " + }, + { + "bbox": [ + 46, + 256, + 547, + 313 + ], + "type": "inline_equation", + "content": "\\mathbf{J}" + }, + { + "bbox": [ + 46, + 256, + 547, + 313 + ], + "type": "text", + "content": ", and the SMPL shape parameters " + }, + { + "bbox": [ + 46, + 256, + 547, + 313 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 256, + 547, + 313 + ], + "type": "text", + "content": ", respectively. The bone direction " + }, + { + "bbox": [ + 46, + 256, + 547, + 313 + ], + "type": "inline_equation", + "content": "\\mathbf{d}" + }, + { + "bbox": [ + 46, + 256, + 547, + 313 + ], + "type": "text", + "content": " calculated from " + }, + { + "bbox": [ + 46, + 256, + 547, + 313 + ], + "type": "inline_equation", + "content": "\\mathbf{J}" + }, + { + "bbox": [ + 46, + 256, + 547, + 313 + ], + "type": "text", + "content": " serves as the likelihood conditioned on 3D rotation. The posterior probability can be obtained based on Bayesian rules (Fusion), which still follows the matrix Fisher distribution, but with different parameters and larger confidence. Observations from additional sensors can also be fused into the posterior probability in the same manner. The corresponding human mesh can then be recovered using the estimated rotation and shape." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 332, + 289, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 332, + 289, + 453 + ], + "spans": [ + { + "bbox": [ + 46, + 332, + 289, + 453 + ], + "type": "text", + "content": "Kalman filter [21], which can be treated as a baseline. Some works [43,62,63] fit the human model to evidence including images and IMUs through joint optimization. Apart from these test-time fusion schemes, several approaches [10, 61] incorporate the fusing process into training by concatenating the features from images and IMUs directly. GeoFuse [72] reinforces the image features guided by IMUs to infer the occluded joints. Our framework is also flexible to perform multi-sensor fusion and generates competitive results without specific modification to the backbone." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 464, + 107, + 475 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 464, + 107, + 475 + ], + "spans": [ + { + "bbox": [ + 47, + 464, + 107, + 475 + ], + "type": "text", + "content": "3. Methods" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 483, + 287, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 483, + 287, + 592 + ], + "spans": [ + { + "bbox": [ + 46, + 483, + 287, + 592 + ], + "type": "text", + "content": "In this section, we first mathematically introduce the probability distributions for orientations regarding rotations and directions (Sec. 3.1). Then, we model the human joint rotation and bone direction with the corresponding distribution, and derive the analytical formulation of the posterior probability of joint rotation conditioned on the bone direction with crucial conclusions and discussion (Sec. 3.2). Finally, we describe the proposed framework (Sec. 3.3) and learning details (Sec. 3.4)." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 599, + 237, + 612 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 599, + 237, + 612 + ], + "spans": [ + { + "bbox": [ + 47, + 599, + 237, + 612 + ], + "type": "text", + "content": "3.1. Orientation probability distribution" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 618, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 618, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 618, + 288, + 715 + ], + "type": "text", + "content": "Before delving into human modeling, we investigate the orientation representation for general rigid entities. Suppose " + }, + { + "bbox": [ + 47, + 618, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{X} \\in \\mathbb{R}^{n \\times p}" + }, + { + "bbox": [ + 47, + 618, + 288, + 715 + ], + "type": "text", + "content": " is the parametric representation of the entity orientation, each column of which depicts the direction of a basis. " + }, + { + "bbox": [ + 47, + 618, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 47, + 618, + 288, + 715 + ], + "type": "text", + "content": " is on the Stiefel manifold " + }, + { + "bbox": [ + 47, + 618, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{V}(n,p)" + }, + { + "bbox": [ + 47, + 618, + 288, + 715 + ], + "type": "text", + "content": " if " + }, + { + "bbox": [ + 47, + 618, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{X}^T\\mathbf{X} = \\mathbf{I}_p" + }, + { + "bbox": [ + 47, + 618, + 288, + 715 + ], + "type": "text", + "content": ", and when " + }, + { + "bbox": [ + 47, + 618, + 288, + 715 + ], + "type": "inline_equation", + "content": "n = p" + }, + { + "bbox": [ + 47, + 618, + 288, + 715 + ], + "type": "text", + "content": ", it further belongs to the orthogonal group " + }, + { + "bbox": [ + 47, + 618, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(n)" + }, + { + "bbox": [ + 47, + 618, + 288, + 715 + ], + "type": "text", + "content": ". Additionally, the components of " + }, + { + "bbox": [ + 47, + 618, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(n)" + }, + { + "bbox": [ + 47, + 618, + 288, + 715 + ], + "type": "text", + "content": " with determinant " + }, + { + "bbox": [ + 47, + 618, + 288, + 715 + ], + "type": "inline_equation", + "content": "+1" + }, + { + "bbox": [ + 47, + 618, + 288, + 715 + ], + "type": "text", + "content": " are referred to as the special or" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 332, + 545, + 404 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 332, + 545, + 404 + ], + "spans": [ + { + "bbox": [ + 304, + 332, + 545, + 404 + ], + "type": "text", + "content": "thogonal group " + }, + { + "bbox": [ + 304, + 332, + 545, + 404 + ], + "type": "inline_equation", + "content": "\\mathcal{SO}(n)" + }, + { + "bbox": [ + 304, + 332, + 545, + 404 + ], + "type": "text", + "content": ", which is used to represent the rotation of " + }, + { + "bbox": [ + 304, + 332, + 545, + 404 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 332, + 545, + 404 + ], + "type": "text", + "content": " degrees of freedom. Meanwhile, if " + }, + { + "bbox": [ + 304, + 332, + 545, + 404 + ], + "type": "inline_equation", + "content": "p = 1" + }, + { + "bbox": [ + 304, + 332, + 545, + 404 + ], + "type": "text", + "content": ", the normalized " + }, + { + "bbox": [ + 304, + 332, + 545, + 404 + ], + "type": "inline_equation", + "content": "\\pmb{X}" + }, + { + "bbox": [ + 304, + 332, + 545, + 404 + ], + "type": "text", + "content": ", i.e., " + }, + { + "bbox": [ + 304, + 332, + 545, + 404 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 332, + 545, + 404 + ], + "type": "text", + "content": "-dimensional unit vector on the manifold " + }, + { + "bbox": [ + 304, + 332, + 545, + 404 + ], + "type": "inline_equation", + "content": "(n - 1)" + }, + { + "bbox": [ + 304, + 332, + 545, + 404 + ], + "type": "text", + "content": "-sphere " + }, + { + "bbox": [ + 304, + 332, + 545, + 404 + ], + "type": "inline_equation", + "content": "\\mathcal{S}^{n - 1}" + }, + { + "bbox": [ + 304, + 332, + 545, + 404 + ], + "type": "text", + "content": ", can represent the single direction as well. From a probabilistic perspective, when " + }, + { + "bbox": [ + 304, + 332, + 545, + 404 + ], + "type": "inline_equation", + "content": "\\pmb{X}" + }, + { + "bbox": [ + 304, + 332, + 545, + 404 + ], + "type": "text", + "content": " is a random matrix, there are two common cases." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 418, + 545, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 418, + 545, + 467 + ], + "spans": [ + { + "bbox": [ + 304, + 418, + 545, + 467 + ], + "type": "text", + "content": "Rotation " + }, + { + "bbox": [ + 304, + 418, + 545, + 467 + ], + "type": "inline_equation", + "content": "(n = p)" + }, + { + "bbox": [ + 304, + 418, + 545, + 467 + ], + "type": "text", + "content": ": For rotation matrix " + }, + { + "bbox": [ + 304, + 418, + 545, + 467 + ], + "type": "inline_equation", + "content": "\\mathbf{R} \\in \\mathcal{SO}(n)" + }, + { + "bbox": [ + 304, + 418, + 545, + 467 + ], + "type": "text", + "content": ", the matrix Fisher distribution " + }, + { + "bbox": [ + 304, + 418, + 545, + 467 + ], + "type": "inline_equation", + "content": "\\mathcal{MF}(\\cdot)" + }, + { + "bbox": [ + 304, + 418, + 545, + 467 + ], + "type": "text", + "content": " has been proposed to characterize its probabilistic properties on " + }, + { + "bbox": [ + 304, + 418, + 545, + 467 + ], + "type": "inline_equation", + "content": "\\mathcal{SO}(n)" + }, + { + "bbox": [ + 304, + 418, + 545, + 467 + ], + "type": "text", + "content": " [8, 25]. The probability density function is as follows:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 330, + 475, + 545, + 500 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 330, + 475, + 545, + 500 + ], + "spans": [ + { + "bbox": [ + 330, + 475, + 545, + 500 + ], + "type": "interline_equation", + "content": "p (\\boldsymbol {R}; \\boldsymbol {F}) = \\frac {1}{c (\\boldsymbol {F})} \\exp (t r (\\boldsymbol {F} ^ {T} \\boldsymbol {R})) \\sim \\mathcal {M F} (\\boldsymbol {F}), \\tag {1}", + "image_path": "75ce955d1088ee15851c6355b19665d7ba219f42bed5b93df422cab8a02c2e22.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 509, + 545, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 509, + 545, + 557 + ], + "spans": [ + { + "bbox": [ + 304, + 509, + 545, + 557 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 509, + 545, + 557 + ], + "type": "inline_equation", + "content": "\\pmb{F} \\in \\mathbb{R}^{n \\times n}" + }, + { + "bbox": [ + 304, + 509, + 545, + 557 + ], + "type": "text", + "content": " is the distribution parameter, and " + }, + { + "bbox": [ + 304, + 509, + 545, + 557 + ], + "type": "inline_equation", + "content": "c(\\pmb{F})" + }, + { + "bbox": [ + 304, + 509, + 545, + 557 + ], + "type": "text", + "content": " is a normalizing constant. Algebraically, " + }, + { + "bbox": [ + 304, + 509, + 545, + 557 + ], + "type": "inline_equation", + "content": "\\pmb{F}" + }, + { + "bbox": [ + 304, + 509, + 545, + 557 + ], + "type": "text", + "content": " can be decomposed into a concentration matrix " + }, + { + "bbox": [ + 304, + 509, + 545, + 557 + ], + "type": "inline_equation", + "content": "\\pmb{K}" + }, + { + "bbox": [ + 304, + 509, + 545, + 557 + ], + "type": "text", + "content": " and a mean rotation matrix " + }, + { + "bbox": [ + 304, + 509, + 545, + 557 + ], + "type": "inline_equation", + "content": "\\pmb{M}" + }, + { + "bbox": [ + 304, + 509, + 545, + 557 + ], + "type": "text", + "content": " via SVD decomposition:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 343, + 564, + 545, + 594 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 343, + 564, + 545, + 594 + ], + "spans": [ + { + "bbox": [ + 343, + 564, + 545, + 594 + ], + "type": "interline_equation", + "content": "\\boldsymbol {F} = \\boldsymbol {U} \\boldsymbol {S} \\boldsymbol {V} ^ {T} = \\underbrace {\\left(\\boldsymbol {U} \\Delta \\boldsymbol {V} ^ {T}\\right)} _ {\\boldsymbol {M} \\in \\mathbb {R} ^ {n \\times p}} \\underbrace {\\left(\\boldsymbol {V} \\Delta \\boldsymbol {S} \\boldsymbol {V} ^ {T}\\right)} _ {\\boldsymbol {K} \\in \\mathbb {R} ^ {p \\times p}}, \\tag {2}", + "image_path": "ed85a18c205ca0d619f9ee4c72bdb3bf377c23e328cf0d30a41372cec9d36e4c.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 603, + 545, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 603, + 545, + 651 + ], + "spans": [ + { + "bbox": [ + 304, + 603, + 545, + 651 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 603, + 545, + 651 + ], + "type": "inline_equation", + "content": "\\Delta = \\text{diag}(1, 1, |\\mathbf{U} \\mathbf{V}|)" + }, + { + "bbox": [ + 304, + 603, + 545, + 651 + ], + "type": "text", + "content": " is a diagonal orthogonal matrix to ensure the determinant of " + }, + { + "bbox": [ + 304, + 603, + 545, + 651 + ], + "type": "inline_equation", + "content": "\\mathbf{M}" + }, + { + "bbox": [ + 304, + 603, + 545, + 651 + ], + "type": "text", + "content": " is " + }, + { + "bbox": [ + 304, + 603, + 545, + 651 + ], + "type": "inline_equation", + "content": "+1" + }, + { + "bbox": [ + 304, + 603, + 545, + 651 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 603, + 545, + 651 + ], + "type": "inline_equation", + "content": "\\mathbf{K}" + }, + { + "bbox": [ + 304, + 603, + 545, + 651 + ], + "type": "text", + "content": " is symmetric positive definite as long as " + }, + { + "bbox": [ + 304, + 603, + 545, + 651 + ], + "type": "inline_equation", + "content": "\\mathbf{F}" + }, + { + "bbox": [ + 304, + 603, + 545, + 651 + ], + "type": "text", + "content": " is full rank. A rotation estimation " + }, + { + "bbox": [ + 304, + 603, + 545, + 651 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{R}}" + }, + { + "bbox": [ + 304, + 603, + 545, + 651 + ], + "type": "text", + "content": " can be calculated from the mode of distribution:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 351, + 661, + 545, + 676 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 351, + 661, + 545, + 676 + ], + "spans": [ + { + "bbox": [ + 351, + 661, + 545, + 676 + ], + "type": "interline_equation", + "content": "\\hat {\\boldsymbol {R}} = \\boldsymbol {M} = \\boldsymbol {U} \\operatorname {d i a g} (1, 1, | \\boldsymbol {U} \\boldsymbol {V} |) \\boldsymbol {V} ^ {T}. \\tag {3}", + "image_path": "4888b8a1a166965addf36fea22e4678341caeaf12b48dd9e047fc79ba300e9dd.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "text", + "content": "Direction " + }, + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "(p = 1)" + }, + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "text", + "content": ": The probability density function for a unit vector " + }, + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "d\\in S^{n - 1}" + }, + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "text", + "content": " is similar to Eq. (1) if we set " + }, + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "p = 1" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "8783" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "content": "which corresponds to the classical von Mises-Fisher distribution " + }, + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "inline_equation", + "content": "\\mathcal{V}\\mathcal{M}\\mathcal{F}(\\cdot)" + }, + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "content": " [44]:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 59, + 102, + 287, + 128 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 102, + 287, + 128 + ], + "spans": [ + { + "bbox": [ + 59, + 102, + 287, + 128 + ], + "type": "interline_equation", + "content": "p (\\boldsymbol {d}; \\kappa , \\boldsymbol {m}) = \\frac {1}{c (\\kappa)} \\exp (\\kappa \\boldsymbol {m} ^ {T} \\boldsymbol {d}) \\sim \\mathcal {V M F} (\\boldsymbol {m}, \\kappa), \\quad (4)", + "image_path": "d2087b1bb00b8c7937b88f9cac48925e1d9a769bb96da7227c9fc20aca41df7f.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 133, + 287, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 133, + 287, + 180 + ], + "spans": [ + { + "bbox": [ + 47, + 133, + 287, + 180 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 133, + 287, + 180 + ], + "type": "inline_equation", + "content": "c(\\kappa)" + }, + { + "bbox": [ + 47, + 133, + 287, + 180 + ], + "type": "text", + "content": " is a normalizing constant. " + }, + { + "bbox": [ + 47, + 133, + 287, + 180 + ], + "type": "inline_equation", + "content": "\\pmb{m}" + }, + { + "bbox": [ + 47, + 133, + 287, + 180 + ], + "type": "text", + "content": " denotes the mean direction and " + }, + { + "bbox": [ + 47, + 133, + 287, + 180 + ], + "type": "inline_equation", + "content": "\\kappa" + }, + { + "bbox": [ + 47, + 133, + 287, + 180 + ], + "type": "text", + "content": " denotes the concentration parameter, which have a close meaning to " + }, + { + "bbox": [ + 47, + 133, + 287, + 180 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 47, + 133, + 287, + 180 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 133, + 287, + 180 + ], + "type": "inline_equation", + "content": "\\pmb{K}" + }, + { + "bbox": [ + 47, + 133, + 287, + 180 + ], + "type": "text", + "content": " in Eq. (2), respectively, and thus " + }, + { + "bbox": [ + 47, + 133, + 287, + 180 + ], + "type": "inline_equation", + "content": "\\hat{\\pmb{d}} = \\pmb{m}" + }, + { + "bbox": [ + 47, + 133, + 287, + 180 + ], + "type": "text", + "content": " becomes a direction estimation." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 181, + 287, + 264 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 181, + 287, + 264 + ], + "spans": [ + { + "bbox": [ + 46, + 181, + 287, + 264 + ], + "type": "text", + "content": "Theoretically, if " + }, + { + "bbox": [ + 46, + 181, + 287, + 264 + ], + "type": "inline_equation", + "content": "\\kappa" + }, + { + "bbox": [ + 46, + 181, + 287, + 264 + ], + "type": "text", + "content": " is 0, " + }, + { + "bbox": [ + 46, + 181, + 287, + 264 + ], + "type": "inline_equation", + "content": "\\mathcal{V}\\mathcal{M}\\mathcal{F}(\\boldsymbol{m},0)" + }, + { + "bbox": [ + 46, + 181, + 287, + 264 + ], + "type": "text", + "content": " is equivalent to the uniform distribution on the sphere, while if " + }, + { + "bbox": [ + 46, + 181, + 287, + 264 + ], + "type": "inline_equation", + "content": "\\kappa" + }, + { + "bbox": [ + 46, + 181, + 287, + 264 + ], + "type": "text", + "content": " is large, it is close to the wrapped normal distribution " + }, + { + "bbox": [ + 46, + 181, + 287, + 264 + ], + "type": "inline_equation", + "content": "\\mathcal{W}\\mathcal{N}(\\boldsymbol{m},\\kappa^{-1})" + }, + { + "bbox": [ + 46, + 181, + 287, + 264 + ], + "type": "text", + "content": " that adds up the densities of vectors representing the same direction on the sphere due to the periodicity. Thus, " + }, + { + "bbox": [ + 46, + 181, + 287, + 264 + ], + "type": "inline_equation", + "content": "\\kappa" + }, + { + "bbox": [ + 46, + 181, + 287, + 264 + ], + "type": "text", + "content": " can be viewed as the inverse of the variance and denotes the concentration of the distributions." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 271, + 151, + 284 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 271, + 151, + 284 + ], + "spans": [ + { + "bbox": [ + 47, + 271, + 151, + 284 + ], + "type": "text", + "content": "3.2. Human modeling" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 289, + 287, + 408 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 289, + 287, + 408 + ], + "spans": [ + { + "bbox": [ + 46, + 289, + 287, + 408 + ], + "type": "text", + "content": "The human joint rotation can be represented as rotation matrix " + }, + { + "bbox": [ + 46, + 289, + 287, + 408 + ], + "type": "inline_equation", + "content": "\\mathbf{R} \\in \\mathcal{SO}(3)" + }, + { + "bbox": [ + 46, + 289, + 287, + 408 + ], + "type": "text", + "content": ". Inspired by recent advances in object pose estimation [3, 33, 46, 67], we incorporate the probabilistic modeling for human poses. Specifically, we adopt the matrix Fisher distribution over " + }, + { + "bbox": [ + 46, + 289, + 287, + 408 + ], + "type": "inline_equation", + "content": "\\mathcal{SO}(3)" + }, + { + "bbox": [ + 46, + 289, + 287, + 408 + ], + "type": "text", + "content": " as the prior distribution for joint rotation. Moreover, as the bone direction can be easily calculated from the joint rotation, we regard the joint rotation " + }, + { + "bbox": [ + 46, + 289, + 287, + 408 + ], + "type": "inline_equation", + "content": "\\mathbf{R}" + }, + { + "bbox": [ + 46, + 289, + 287, + 408 + ], + "type": "text", + "content": " as the latent variable and the bone direction " + }, + { + "bbox": [ + 46, + 289, + 287, + 408 + ], + "type": "inline_equation", + "content": "\\mathbf{d}" + }, + { + "bbox": [ + 46, + 289, + 287, + 408 + ], + "type": "text", + "content": " as the corresponding observation, which follows the von Mises-Fisher distribution:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 60, + 424, + 287, + 449 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 60, + 424, + 287, + 449 + ], + "spans": [ + { + "bbox": [ + 60, + 424, + 287, + 449 + ], + "type": "interline_equation", + "content": "p (\\boldsymbol {d} | \\boldsymbol {R}) = \\frac {1}{c (\\kappa)} e x p (\\kappa \\boldsymbol {l} ^ {T} \\boldsymbol {R} ^ {T} \\boldsymbol {d}) \\sim \\mathcal {V M F} (\\boldsymbol {R l}, \\kappa), \\quad (5)", + "image_path": "01c0d00c2ffd1261fb88aed9a748f2ba75eb395d363f1220f2490e51d8d2e79d.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 455, + 287, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 455, + 287, + 479 + ], + "spans": [ + { + "bbox": [ + 47, + 455, + 287, + 479 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 455, + 287, + 479 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 47, + 455, + 287, + 479 + ], + "type": "text", + "content": " is the unit direction of the bone in the reference pose (e.g., T-pose), ideally satisfying " + }, + { + "bbox": [ + 47, + 455, + 287, + 479 + ], + "type": "inline_equation", + "content": "Rl = d" + }, + { + "bbox": [ + 47, + 455, + 287, + 479 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 479, + 287, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 479, + 287, + 525 + ], + "spans": [ + { + "bbox": [ + 47, + 479, + 287, + 525 + ], + "type": "text", + "content": "Leveraging Bayesian inference, given the prior distribution (Eq. (1)) and the likelihood function (Eq. (5)), the posterior probability of joint rotation conditioned on the bone direction can be derived as follows:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 542, + 287, + 593 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 542, + 287, + 593 + ], + "spans": [ + { + "bbox": [ + 55, + 542, + 287, + 593 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} p (\\boldsymbol {R} | \\boldsymbol {d}) = \\frac {p (\\boldsymbol {R}) \\cdot p (\\boldsymbol {d} | \\boldsymbol {R})}{p (\\boldsymbol {d})} \\propto p (\\boldsymbol {R}) \\cdot p (\\boldsymbol {d} | \\boldsymbol {R}) \\tag {6} \\\\ = \\frac {1}{c} e x p (t r [ (\\boldsymbol {F} + \\kappa \\boldsymbol {d l} ^ {T}) ^ {T} \\boldsymbol {R} ]) \\sim \\mathcal {M F} (\\boldsymbol {F} + \\kappa \\boldsymbol {d l} ^ {T}). \\\\ \\end{array}", + "image_path": "4a9792ac60ee0a5f1282c2aa4123a36fbdf0198b62233395428b5fa0b16ed6ff.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 597, + 287, + 634 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 597, + 287, + 634 + ], + "spans": [ + { + "bbox": [ + 47, + 597, + 287, + 634 + ], + "type": "text", + "content": "It can be concluded from Eq. (6) that the posterior probability " + }, + { + "bbox": [ + 47, + 597, + 287, + 634 + ], + "type": "inline_equation", + "content": "p(\\mathbf{R}|\\mathbf{d})" + }, + { + "bbox": [ + 47, + 597, + 287, + 634 + ], + "type": "text", + "content": " also follows the matrix Fisher distribution with an updated parameter " + }, + { + "bbox": [ + 47, + 597, + 287, + 634 + ], + "type": "inline_equation", + "content": "\\mathbf{F}' = \\mathbf{F} + \\kappa \\mathbf{d}\\mathbf{l}^T" + }, + { + "bbox": [ + 47, + 597, + 287, + 634 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 647, + 287, + 682 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 647, + 287, + 682 + ], + "spans": [ + { + "bbox": [ + 47, + 647, + 287, + 682 + ], + "type": "text", + "content": "Property: From another perspective, the posterior parameter " + }, + { + "bbox": [ + 47, + 647, + 287, + 682 + ], + "type": "inline_equation", + "content": "F'" + }, + { + "bbox": [ + 47, + 647, + 287, + 682 + ], + "type": "text", + "content": " can be viewed as the multiplication of the same mean term " + }, + { + "bbox": [ + 47, + 647, + 287, + 682 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 47, + 647, + 287, + 682 + ], + "type": "text", + "content": " and a new concentration term " + }, + { + "bbox": [ + 47, + 647, + 287, + 682 + ], + "type": "inline_equation", + "content": "K'" + }, + { + "bbox": [ + 47, + 647, + 287, + 682 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 82, + 689, + 287, + 716 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 82, + 689, + 287, + 716 + ], + "spans": [ + { + "bbox": [ + 82, + 689, + 287, + 716 + ], + "type": "interline_equation", + "content": "\\boldsymbol {F} ^ {\\prime} = \\boldsymbol {F} + \\kappa \\boldsymbol {d l} ^ {T} = M (\\underbrace {\\boldsymbol {K} + \\kappa \\boldsymbol {M} ^ {T} \\boldsymbol {d l} ^ {T}} _ {\\boldsymbol {K} ^ {\\prime}}). \\tag {7}", + "image_path": "e2ff4d19af70c8032d7e5075714f431144eaa2133e8b5113d21bc545584e0f15.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "content": "It can be proved that " + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "inline_equation", + "content": "M^T d\\boldsymbol{l}^T = \\boldsymbol{ll}^T" + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "content": " is a real symmetric matrix with rank 1, and " + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "content": " from Eq. (2) is also real symmetric, thus the posterior concentration term " + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "inline_equation", + "content": "K'" + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "content": " is a real symmetric matrix. According to the interlacing theorem for Hermitian matrices from matrix analysis [17], the eigenvalues for a Hermitian matrix with a rank-1 Hermitian perturbation satisfy the following inequality:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 340, + 163, + 545, + 179 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 340, + 163, + 545, + 179 + ], + "spans": [ + { + "bbox": [ + 340, + 163, + 545, + 179 + ], + "type": "interline_equation", + "content": "\\lambda_ {1} \\leq \\lambda_ {1} ^ {\\prime} \\leq \\lambda_ {2} \\leq \\dots \\leq \\lambda_ {p - 1} ^ {\\prime} \\leq \\lambda_ {p} \\leq \\lambda_ {p} ^ {\\prime}, \\tag {8}", + "image_path": "46d4709f30c2737fb7a8db052e5558ddc99edfa6fbd47b3f42853262dfd0eee1.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 185, + 545, + 293 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 185, + 545, + 293 + ], + "spans": [ + { + "bbox": [ + 304, + 185, + 545, + 293 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 185, + 545, + 293 + ], + "type": "inline_equation", + "content": "\\lambda_{i}" + }, + { + "bbox": [ + 304, + 185, + 545, + 293 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 185, + 545, + 293 + ], + "type": "inline_equation", + "content": "\\lambda_{i}^{\\prime}" + }, + { + "bbox": [ + 304, + 185, + 545, + 293 + ], + "type": "text", + "content": " denote the eigenvalues of " + }, + { + "bbox": [ + 304, + 185, + 545, + 293 + ], + "type": "inline_equation", + "content": "\\pmb{K}" + }, + { + "bbox": [ + 304, + 185, + 545, + 293 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 185, + 545, + 293 + ], + "type": "inline_equation", + "content": "\\pmb{K}^{\\prime}" + }, + { + "bbox": [ + 304, + 185, + 545, + 293 + ], + "type": "text", + "content": ", respectively. Note that the eigenvalues of the concentration term equal the singular values of the distribution parameter, which reflect the confidence of the distribution. From Eq. (8) we can get the conclusion that the posterior estimation is more concentrated than the prior estimation as long as the likelihood term is non-zero, and is validated to be a more easily learnable formulation in the experiment and the supplementary material." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 306, + 545, + 340 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 306, + 545, + 340 + ], + "spans": [ + { + "bbox": [ + 304, + 306, + 545, + 340 + ], + "type": "text", + "content": "General form: Similarly, if other sensors that yield directional " + }, + { + "bbox": [ + 304, + 306, + 545, + 340 + ], + "type": "inline_equation", + "content": "\\pmb{d}_i" + }, + { + "bbox": [ + 304, + 306, + 545, + 340 + ], + "type": "text", + "content": " or rotational " + }, + { + "bbox": [ + 304, + 306, + 545, + 340 + ], + "type": "inline_equation", + "content": "\\pmb{D}_j" + }, + { + "bbox": [ + 304, + 306, + 545, + 340 + ], + "type": "text", + "content": " observations are available, the analytical posterior probability is thereby as follows:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 309, + 346, + 545, + 370 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 346, + 545, + 370 + ], + "spans": [ + { + "bbox": [ + 309, + 346, + 545, + 370 + ], + "type": "interline_equation", + "content": "p (\\boldsymbol {R} | \\left\\{\\boldsymbol {d} _ {i}, \\boldsymbol {D} _ {j} \\right\\}) \\sim \\mathcal {M F} (\\boldsymbol {F} + \\sum_ {i \\in \\mathcal {Z} _ {1}} \\kappa_ {i} g (\\boldsymbol {d} _ {i}) + \\sum_ {j \\in \\mathcal {Z} _ {3}} \\boldsymbol {D} _ {j} \\boldsymbol {K} _ {j} ^ {T}), \\tag {9}", + "image_path": "4bbe2008692631ea4ab7db234636e2659e156a99112a34a3ab3bc08c2f12e80e.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 376, + 545, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 376, + 545, + 496 + ], + "spans": [ + { + "bbox": [ + 304, + 376, + 545, + 496 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 376, + 545, + 496 + ], + "type": "inline_equation", + "content": "\\kappa_{i}" + }, + { + "bbox": [ + 304, + 376, + 545, + 496 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 376, + 545, + 496 + ], + "type": "inline_equation", + "content": "K_{j}" + }, + { + "bbox": [ + 304, + 376, + 545, + 496 + ], + "type": "text", + "content": " are the concentration terms for weighting. " + }, + { + "bbox": [ + 304, + 376, + 545, + 496 + ], + "type": "inline_equation", + "content": "g(\\cdot)" + }, + { + "bbox": [ + 304, + 376, + 545, + 496 + ], + "type": "text", + "content": " is a mapping of IK that converts the directional observation to a rotation estimation, which is not limited to a specific IK algorithm as long as it supports gradient backpropagation (e.g., the simple solution " + }, + { + "bbox": [ + 304, + 376, + 545, + 496 + ], + "type": "inline_equation", + "content": "\\boldsymbol{d}\\boldsymbol{l}^T" + }, + { + "bbox": [ + 304, + 376, + 545, + 496 + ], + "type": "text", + "content": " in Eq. (6)). " + }, + { + "bbox": [ + 304, + 376, + 545, + 496 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}_1" + }, + { + "bbox": [ + 304, + 376, + 545, + 496 + ], + "type": "text", + "content": " denotes the set of sensors providing directional observations such as accelerometers, while " + }, + { + "bbox": [ + 304, + 376, + 545, + 496 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}_3" + }, + { + "bbox": [ + 304, + 376, + 545, + 496 + ], + "type": "text", + "content": " denotes the set of rotational sensors like gyroscopes. We simplify the original derivation by assuming the sensors are unbiased. Please refer to the supplementary material for the derivation." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 510, + 545, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 545, + 677 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 545, + 677 + ], + "type": "text", + "content": "Discussion: There are several advantages of our approach. First, adopting the matrix representation is more reasonable than other rotation representations. As presented in [34], a continuous 9D unconstrained representation followed by SVD can achieve comparable or even better performance than the widely used 6D vector [74]. Second, the Gaussian distribution is unsuitable for cases with large uncertainty where the assumption of local linearity cannot hold [11, 12], while the matrix Fisher distribution does not have this problem. Third, the posteriors are easier to learn than the priors in that learning the posteriors can converge to the mode preferred by the likelihood function quickly, while learning the priors may face multiple local minima in the initial stage and thus cannot converge well." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": "To recognize the proposed scheme intuitively, we show the schematic diagrams of probabilistic modeling in Fig. 3. For a method without probabilistic modeling (e.g., using IK" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "8784" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 72, + 281, + 205 + ], + "blocks": [ + { + "bbox": [ + 50, + 72, + 281, + 205 + ], + "lines": [ + { + "bbox": [ + 50, + 72, + 281, + 205 + ], + "spans": [ + { + "bbox": [ + 50, + 72, + 281, + 205 + ], + "type": "image", + "image_path": "4892c4d0335d5a6aad3b9b9b202585aea25c798d19702e4b0b90435c41eaa63d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 213, + 289, + 291 + ], + "lines": [ + { + "bbox": [ + 46, + 213, + 289, + 291 + ], + "spans": [ + { + "bbox": [ + 46, + 213, + 289, + 291 + ], + "type": "text", + "content": "Figure 3. Schematic diagrams of probabilistic modeling. The opaque coordinate system " + }, + { + "bbox": [ + 46, + 213, + 289, + 291 + ], + "type": "inline_equation", + "content": "\\triangleleft" + }, + { + "bbox": [ + 46, + 213, + 289, + 291 + ], + "type": "text", + "content": " is the ground-truth 3D rotation. The transparent rotation represents a deterministic estimation for a method without probabilistic modeling (row 1), while it denotes a sample from the estimated posterior distribution (row 2). The red region on the sphere represents the probability of a certain rotation, and it could cover the ground-truth even for noisy cases." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 313, + 289, + 410 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 313, + 289, + 410 + ], + "spans": [ + { + "bbox": [ + 46, + 313, + 289, + 410 + ], + "type": "text", + "content": "to solve rotations from keypoints), its underlying model is a single direction, thus it may be erroneous when the estimated bone direction deviates from the ground-truth, as shown in the noisy cases. In contrast, the posterior model can be fused with various models, and for noisy keypoints, it has the potential to recover the exact rotations since the negative impact of its partial reliance on the estimated keypoints can be eliminated by the prior or other observations." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 418, + 171, + 431 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 418, + 171, + 431 + ], + "spans": [ + { + "bbox": [ + 47, + 418, + 171, + 431 + ], + "type": "text", + "content": "3.3. Learning Framework" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 438, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 438, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 438, + 289, + 715 + ], + "type": "text", + "content": "Our proposed framework that leverages the derived posterior probability for human mesh recovery is demonstrated in Fig. 2. We adopt the parametric model SMPL [41] as our human representation, which can also be replaced by other human models [51,54]. Given an input image, a CNN backbone is used to extract image features, followed by three output branches, including prior distribution parameter " + }, + { + "bbox": [ + 46, + 438, + 289, + 715 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 46, + 438, + 289, + 715 + ], + "type": "text", + "content": ", 3D keypoints " + }, + { + "bbox": [ + 46, + 438, + 289, + 715 + ], + "type": "inline_equation", + "content": "J" + }, + { + "bbox": [ + 46, + 438, + 289, + 715 + ], + "type": "text", + "content": ", and shape parameter " + }, + { + "bbox": [ + 46, + 438, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 438, + 289, + 715 + ], + "type": "text", + "content": ". The adopted keypoints branch consists of normalized 2D keypoints and relative depth to the root joint decoded from the feature, as well as the human scale predicted by a small MLP branch, so as to recover absolute 3D keypoints. Note that other strategies for 3D keypoints estimation are also applicable. The bone direction " + }, + { + "bbox": [ + 46, + 438, + 289, + 715 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 438, + 289, + 715 + ], + "type": "text", + "content": " is calculated from " + }, + { + "bbox": [ + 46, + 438, + 289, + 715 + ], + "type": "inline_equation", + "content": "J" + }, + { + "bbox": [ + 46, + 438, + 289, + 715 + ], + "type": "text", + "content": ". Then we utilize Eq. (9) to fuse " + }, + { + "bbox": [ + 46, + 438, + 289, + 715 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 46, + 438, + 289, + 715 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 438, + 289, + 715 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 438, + 289, + 715 + ], + "type": "text", + "content": ", or other optional observations analytically in the sense of probability. With the new distribution parameter " + }, + { + "bbox": [ + 46, + 438, + 289, + 715 + ], + "type": "inline_equation", + "content": "F'" + }, + { + "bbox": [ + 46, + 438, + 289, + 715 + ], + "type": "text", + "content": ", we can get the rotation estimation according to Eq. (3). As for " + }, + { + "bbox": [ + 46, + 438, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\kappa" + }, + { + "bbox": [ + 46, + 438, + 289, + 715 + ], + "type": "text", + "content": ", it is related to the physical properties (measure covariance) of specific sensors that could be set in advance. If there is no prior knowledge of the sensor, it's feasible to tune it manually or learn it from the data. We simply use the scaled scores of estimated keypoints. For multiple sensors, the concentration term " + }, + { + "bbox": [ + 46, + 438, + 289, + 715 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 438, + 289, + 715 + ], + "type": "text", + "content": " is simplified as a diagonal matrix." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "text", + "content": "Objective functions: For the following objective functions, symbols with superscript " + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "inline_equation", + "content": "*" + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "text", + "content": " indicate the groundtruth, and symbols with hat indicate the estimation. The " + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "inline_equation", + "content": "L_{1}" + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "text", + "content": " loss is used to supervise the 3D keypoints, while the " + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "inline_equation", + "content": "L_{2}" + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "text", + "content": " loss is applied to other variables:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 386, + 140, + 545, + 155 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 386, + 140, + 545, + 155 + ], + "spans": [ + { + "bbox": [ + 386, + 140, + 545, + 155 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {J} = \\left| \\left| \\hat {\\boldsymbol {J}} - \\boldsymbol {J} ^ {*} \\right| \\right| _ {1}, \\tag {10}", + "image_path": "df9b06d26dd9b485b13fce1a7da831e6d43b12f97a5383859de7a5b43842e267.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 387, + 175, + 545, + 190 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 387, + 175, + 545, + 190 + ], + "spans": [ + { + "bbox": [ + 387, + 175, + 545, + 190 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\beta} = \\left\\| \\hat {\\boldsymbol {\\beta}} - \\boldsymbol {\\beta} ^ {*} \\right\\| _ {2} ^ {2}, \\tag {11}", + "image_path": "9e6ee6de167b82f95e23aaef551da2fe2455d4029f83761cf6e1e1f7bda3df2d.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 195, + 547, + 241 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 195, + 547, + 241 + ], + "spans": [ + { + "bbox": [ + 304, + 195, + 547, + 241 + ], + "type": "text", + "content": "The mode of the posterior probability distribution " + }, + { + "bbox": [ + 304, + 195, + 547, + 241 + ], + "type": "inline_equation", + "content": "\\hat{R}" + }, + { + "bbox": [ + 304, + 195, + 547, + 241 + ], + "type": "text", + "content": " can be solved according to Eq. (6) and (3), and is supervised if the annotations of SMPL pose parameters " + }, + { + "bbox": [ + 304, + 195, + 547, + 241 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 195, + 547, + 241 + ], + "type": "text", + "content": " are provided as follows:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 371, + 243, + 545, + 258 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 371, + 243, + 545, + 258 + ], + "spans": [ + { + "bbox": [ + 371, + 243, + 545, + 258 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\theta} = \\left| \\left| \\hat {\\boldsymbol {R}} - \\exp (\\boldsymbol {\\theta} ^ {*}) \\right| \\right| _ {2} ^ {2}, \\tag {12}", + "image_path": "eeb7c62dcf10731c8705fd877bf99f6e13289dc5c9f77b63bb838608e1bd99a3.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 262, + 545, + 285 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 262, + 545, + 285 + ], + "spans": [ + { + "bbox": [ + 304, + 262, + 545, + 285 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 262, + 545, + 285 + ], + "type": "inline_equation", + "content": "\\text{expm}" + }, + { + "bbox": [ + 304, + 262, + 545, + 285 + ], + "type": "text", + "content": " denotes the exponential map implemented with the Rodrigues' formula." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 286, + 545, + 406 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 286, + 545, + 406 + ], + "spans": [ + { + "bbox": [ + 304, + 286, + 545, + 406 + ], + "type": "text", + "content": "Apart from the mode, the whole distribution also needs to be supervised. Since the normalizing constant in the distribution is hard to be calculated stably due to the numerical integration, we propose to supervise the distribution by sampling. Specifically, we adopt the rejection sampling technique to sample Bingham distribution of unit quaternions on " + }, + { + "bbox": [ + 304, + 286, + 545, + 406 + ], + "type": "inline_equation", + "content": "S^3" + }, + { + "bbox": [ + 304, + 286, + 545, + 406 + ], + "type": "text", + "content": " based on its equivalence to matrix Fisher distribution. The proposal distribution in rejection sampling is angular central Gaussian (ACG) distribution [24, 55]. Thus the sampling loss is as follows:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 354, + 415, + 545, + 447 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 354, + 415, + 545, + 447 + ], + "spans": [ + { + "bbox": [ + 354, + 415, + 545, + 447 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {s} = \\sum_ {i = 1} ^ {N _ {s}} \\rho \\left(\\left| \\left| \\hat {\\boldsymbol {R}} _ {i} - \\exp \\left(\\boldsymbol {\\theta} ^ {*}\\right) \\right| \\right| _ {2} ^ {2}\\right), \\tag {13}", + "image_path": "98d07639e47705094cab675e54721726cf0eecf0ce7a3c8227fe83417e21b083.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 452, + 545, + 486 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 452, + 545, + 486 + ], + "spans": [ + { + "bbox": [ + 304, + 452, + 545, + 486 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 452, + 545, + 486 + ], + "type": "inline_equation", + "content": "N_{s}" + }, + { + "bbox": [ + 304, + 452, + 545, + 486 + ], + "type": "text", + "content": " is the number of samples. " + }, + { + "bbox": [ + 304, + 452, + 545, + 486 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 304, + 452, + 545, + 486 + ], + "type": "text", + "content": " is an simple activation function for relaxation, which tolerates small deviations." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 318, + 487, + 487, + 499 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 487, + 487, + 499 + ], + "spans": [ + { + "bbox": [ + 318, + 487, + 487, + 499 + ], + "type": "text", + "content": "The total objective function is as follows:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 347, + 510, + 545, + 522 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 347, + 510, + 545, + 522 + ], + "spans": [ + { + "bbox": [ + 347, + 510, + 545, + 522 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = w _ {1} \\mathcal {L} _ {J} + w _ {2} \\mathcal {L} _ {\\beta} + w _ {3} \\mathcal {L} _ {\\theta} + w _ {4} \\mathcal {L} _ {s}, \\tag {14}", + "image_path": "fa4ef19fa043f6ba9224d8621f065a0bc529b8abdf71f9789ee2000f4ae9dafe.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 532, + 490, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 532, + 490, + 544 + ], + "spans": [ + { + "bbox": [ + 306, + 532, + 490, + 544 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 532, + 490, + 544 + ], + "type": "inline_equation", + "content": "w_{1}, w_{2}, w_{3}" + }, + { + "bbox": [ + 306, + 532, + 490, + 544 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 306, + 532, + 490, + 544 + ], + "type": "inline_equation", + "content": "w_{4}" + }, + { + "bbox": [ + 306, + 532, + 490, + 544 + ], + "type": "text", + "content": " are weight scalars." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 552, + 437, + 564 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 552, + 437, + 564 + ], + "spans": [ + { + "bbox": [ + 306, + 552, + 437, + 564 + ], + "type": "text", + "content": "3.4. Implementation details" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "content": "We adopt ResNet-34 [16] and HRNet-W48 [58] as backbones. The ResNet backbone is followed by three deconvolutional layers to generate 3D heatmaps with the size of " + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "inline_equation", + "content": "64 \\times 64 \\times 64" + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "content": " for keypoints and three MLPs for shape parameters " + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "content": " (10), distribution parameter " + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "content": " (216) and human scale (1). The feature from HRNet backbone is upsampled and directly followed by similar output branches with dimensions motioned above. The input image has a resolution of " + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "content": ". The network is trained for 50 epochs with Adam and an initial learning rate of " + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "inline_equation", + "content": "1 \\times 10^{-3}" + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "content": ", decayed with a factor of 10. " + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "inline_equation", + "content": "w_{1}" + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "inline_equation", + "content": "w_{2}" + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "content": " are set to 1. " + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "inline_equation", + "content": "w_{3}" + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "inline_equation", + "content": "w_{4}" + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "content": " are set to 0.1 and increased to 1 in the later stage of training." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "8785" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 71, + 128, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 71, + 128, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 128, + 85 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 91, + 287, + 139 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 91, + 287, + 139 + ], + "spans": [ + { + "bbox": [ + 46, + 91, + 287, + 139 + ], + "type": "text", + "content": "In this section, we demonstrate the effectiveness of our framework on human mesh recovery and multi-sensor fusion, evaluate our key designs via an ablation study, and discuss the limitation and future work of our method." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 148, + 167, + 159 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 148, + 167, + 159 + ], + "spans": [ + { + "bbox": [ + 47, + 148, + 167, + 159 + ], + "type": "text", + "content": "4.1. Datasets and metrics" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 166, + 287, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 166, + 287, + 190 + ], + "spans": [ + { + "bbox": [ + 46, + 166, + 287, + 190 + ], + "type": "text", + "content": "To maintain the fairness of comparison, we adopt the same datasets and metrics as previous methods." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 190, + 287, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 190, + 287, + 239 + ], + "spans": [ + { + "bbox": [ + 46, + 190, + 287, + 239 + ], + "type": "text", + "content": "Human3.6M [18] provides 3D keypoints annotations, and the corresponding SMPL annotations are from MoSh [40]. We use (S1, S5, S6, S7, S8) for training and (S9, S11) for evaluation, following standard practice [22, 36]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 239, + 286, + 262 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 239, + 286, + 262 + ], + "spans": [ + { + "bbox": [ + 47, + 239, + 286, + 262 + ], + "type": "text", + "content": "3DPW [62] provides SMPL annotations. Following [36, 37], we add its training set only for experiments on it." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 262, + 286, + 299 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 262, + 286, + 299 + ], + "spans": [ + { + "bbox": [ + 46, + 262, + 286, + 299 + ], + "type": "text", + "content": "MS COCO [39] contains in-the-wild images and 2D keypoints annotations. We use its training set to improve the generalization ability of our method." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 299, + 287, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 299, + 287, + 323 + ], + "spans": [ + { + "bbox": [ + 46, + 299, + 287, + 323 + ], + "type": "text", + "content": "MPI-INF-3DHP [45] is a multi-view dataset that provides 3D keypoints annotations. We only use it for training." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 323, + 287, + 358 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 323, + 287, + 358 + ], + "spans": [ + { + "bbox": [ + 46, + 323, + 287, + 358 + ], + "type": "text", + "content": "AGORA [50] is a synthetic dataset with challenging scenes and SMPL annotations of adults and kids. Only when evaluating our algorithm on it will we add its training set." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 358, + 287, + 395 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 358, + 287, + 395 + ], + "spans": [ + { + "bbox": [ + 46, + 358, + 287, + 395 + ], + "type": "text", + "content": "TotalCapture [61] contains multi-view videos, IMUs and 3D keypoints annotations for the evaluation of sensor fusion algorithms. We follow [61,72] to divide it." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 395, + 287, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 395, + 287, + 443 + ], + "spans": [ + { + "bbox": [ + 46, + 395, + 287, + 443 + ], + "type": "text", + "content": "Metrics include MPJPE, PA-MPJPE, and PVE all in mm. MPJPE measures the 3D keypoints error, while PA-MPJPE is similar to MPJPE except that a rigid alignment is performed at first. PVE measures the human mesh vertex error." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 452, + 175, + 464 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 452, + 175, + 464 + ], + "spans": [ + { + "bbox": [ + 47, + 452, + 175, + 464 + ], + "type": "text", + "content": "4.2. Human mesh recovery" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 470, + 287, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 470, + 287, + 601 + ], + "spans": [ + { + "bbox": [ + 46, + 470, + 287, + 601 + ], + "type": "text", + "content": "Table 1 shows the evaluation results on public benchmarks. With either ResNet or HRNet as the backbone, our approach outperforms SOTA methods. Besides, we surpass the prior counterpart [55] by a large margin, indicating that our posterior estimation is easier to learn than the single prior. Table 2 shows the results on the AGORA test set. Our framework is more accurate than others, especially for kids. Note that for 2D datasets, despite that the pseudo-GT annotator of CLIFF [37] and EFT dataset [20] can be incorporated to further improve our performance, we only use the original keypoints supervision for fair comparisons." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "content": "Posterior effects: We compare different designs to thoroughly validate the posterior effects and the feature choice in our framework, as shown in Table 3, which include: (a) regressing the parameters " + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{F}" + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "content": " only without the keypoint branch; (b) solving rotations from keypoints via IK without probabilistic modeling; (c) deactivating the learned prior parameters in testing (i.e., setting " + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{F}" + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "content": " to zero); (d) using the feature close to the end of the backbone to regress prior " + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{F}" + } + ] + } + ], + "index": 13 + }, + { + "type": "table", + "bbox": [ + 309, + 71, + 544, + 255 + ], + "blocks": [ + { + "bbox": [ + 309, + 71, + 544, + 255 + ], + "lines": [ + { + "bbox": [ + 309, + 71, + 544, + 255 + ], + "spans": [ + { + "bbox": [ + 309, + 71, + 544, + 255 + ], + "type": "table", + "html": "
Methods3DPWHuman3.6M
PA ↓MPJPE ↓PVE ↓PA ↓MPJPE ↓
HMR (R-50) [22]81.3130.0-56.888.0
GraphCMR (R-50) [30]70.2--50.1-
SPIN (R-50) [29]59.296.9116.441.162.5
Sengupta. (H-48) [55]*59.284.7*---
HMR-EFT (R-50) [20]52.4--43.9-
I2L-MeshNet (R-50) [48]58.693.2-41.755.7
SPEC (R-50) [28]53.296.5118.5--
BEV (H-32) [60]46.978.592.3--
PARE (H-32) [27]46.574.588.6--
Graphormer (H-64) [38]45.674.787.734.551.2
PyMAF (H-48) [70]45.374.287.037.254.2
HybrIK (R-34) [36]45.074.186.533.655.4
FastMETRO (R-50) [4]48.377.990.637.353.9
FastMETRO (H-64) [4]44.673.584.133.752.2
CLIFF (R-50) [37]45.772.085.335.150.5
CLIFF (H-48) [37]43.069.081.232.747.1
Ours (R-34)44.171.884.931.648.7
Ours (H-48)40.668.379.429.145.7
", + "image_path": "d92933662449f81f2fc2d7834c08e6efbce3b77f714f53033aa784c4b405dac0.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "table_body" + } + ], + "index": 14 + }, + { + "type": "table", + "bbox": [ + 309, + 298, + 544, + 447 + ], + "blocks": [ + { + "bbox": [ + 306, + 262, + 545, + 284 + ], + "lines": [ + { + "bbox": [ + 306, + 262, + 545, + 284 + ], + "spans": [ + { + "bbox": [ + 306, + 262, + 545, + 284 + ], + "type": "text", + "content": "Table 1. Results on standard benchmarks. 'PA' is PA-MPJPE. " + }, + { + "bbox": [ + 306, + 262, + 545, + 284 + ], + "type": "inline_equation", + "content": "R^{\\prime}" + }, + { + "bbox": [ + 306, + 262, + 545, + 284 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 262, + 545, + 284 + ], + "type": "inline_equation", + "content": "H^{\\prime}" + }, + { + "bbox": [ + 306, + 262, + 545, + 284 + ], + "type": "text", + "content": " mean ResNet and HRNet. * with scale correction." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 309, + 298, + 544, + 447 + ], + "lines": [ + { + "bbox": [ + 309, + 298, + 544, + 447 + ], + "spans": [ + { + "bbox": [ + 309, + 298, + 544, + 447 + ], + "type": "table", + "html": "
MethodsAGORA
MPJPE ↓PVE ↓Kid-MPJPE ↓Kid-PVE ↓
HMR [22]180.5173.6219.4209.3
HMR-EFT [20]165.4159.0202.7193.5
SPIN [29]153.4148.9191.7186.7
PARE [27]146.2140.9193.9186.4
SPEC [28]112.3106.5171.0163.2
ROMP [59]108.1103.4159.8156.6
BEV [60]105.3100.7129.1125.9
Hand4Whole [47]89.884.8153.3146.4
CLIFF [37]81.076.094.189.6
HybrIK [36]77.073.990.286.6
Ours74.470.984.580.5
PLIKS [57]71.567.388.384.2
NIKI [35]67.363.983.980.2
", + "image_path": "1faec3451b2dca43164ce084f9d723ae42468a48caf89b66cf668cbf80167c3e.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "table_body" + } + ], + "index": 16 + }, + { + "type": "table", + "bbox": [ + 309, + 500, + 544, + 600 + ], + "blocks": [ + { + "bbox": [ + 305, + 453, + 545, + 486 + ], + "lines": [ + { + "bbox": [ + 305, + 453, + 545, + 486 + ], + "spans": [ + { + "bbox": [ + 305, + 453, + 545, + 486 + ], + "type": "text", + "content": "Table 2. Results on the AGORA test set. The metrics with the prefix 'Kid-' are calculated only for kids, otherwise for all ages. Two concurrent works are shown in gray for completeness." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 309, + 500, + 544, + 600 + ], + "lines": [ + { + "bbox": [ + 309, + 500, + 544, + 600 + ], + "spans": [ + { + "bbox": [ + 309, + 500, + 544, + 600 + ], + "type": "table", + "html": "
DesignsHuman3.6M
PA-MPJPE ↓MPJPE ↓
(a) W/o 3D keypoints45.876.5
(b) W/o prior F43.263.6
(c) W/o prior F (in testing)42.758.7
(d) Late feature for F and β29.948.6
(e) Early feature for F and β29.346.5
(f) Ours (full model)29.145.7
", + "image_path": "c68c256562c7bf2eec05d603b8dbffbbfddcdde5305293151231f1b71a160df9.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "table_body" + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 606, + 545, + 617 + ], + "lines": [ + { + "bbox": [ + 306, + 606, + 545, + 617 + ], + "spans": [ + { + "bbox": [ + 306, + 606, + 545, + 617 + ], + "type": "text", + "content": "Table 3. Ablation study of designs on the Human3.6M dataset." + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 641, + 545, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 641, + 545, + 664 + ], + "spans": [ + { + "bbox": [ + 305, + 641, + 545, + 664 + ], + "type": "text", + "content": "and shape " + }, + { + "bbox": [ + 305, + 641, + 545, + 664 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 305, + 641, + 545, + 664 + ], + "type": "text", + "content": "; (e) using the feature from the initial stage; (f) our full model with all branches and intermediate feature." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "type": "text", + "content": "The performance of design (a) is not good since its estimation cannot align precisely with the image, and it is observed that this design exhibits a slower speed of convergence, reflecting the importance of the likelihood function" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "8786" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 70, + 286, + 168 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 286, + 168 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 286, + 168 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 286, + 168 + ], + "type": "image", + "image_path": "8ef8793fb4117ce0068e0637d3036a9a6c2740ff58b2050070f49afe48176126.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 172, + 287, + 239 + ], + "lines": [ + { + "bbox": [ + 46, + 172, + 287, + 239 + ], + "spans": [ + { + "bbox": [ + 46, + 172, + 287, + 239 + ], + "type": "text", + "content": "Figure 4. Noise simulation. (a) Rotation error v.s. the mixed noises of both prior and keypoint. (b) Rotation/direction error v.s. keypoint noise. The noise level is the ratio of the noise amplitude to the maximum of the variable. The simulation step is " + }, + { + "bbox": [ + 46, + 172, + 287, + 239 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 46, + 172, + 287, + 239 + ], + "type": "text", + "content": ". 'W/o prior " + }, + { + "bbox": [ + 46, + 172, + 287, + 239 + ], + "type": "inline_equation", + "content": "\\pmb{F}" + }, + { + "bbox": [ + 46, + 172, + 287, + 239 + ], + "type": "text", + "content": "' is an indirect strategy without probability. 'Fixed " + }, + { + "bbox": [ + 46, + 172, + 287, + 239 + ], + "type": "inline_equation", + "content": "\\kappa" + }, + { + "bbox": [ + 46, + 172, + 287, + 239 + ], + "type": "text", + "content": " ' uses predefined " + }, + { + "bbox": [ + 46, + 172, + 287, + 239 + ], + "type": "inline_equation", + "content": "\\kappa" + }, + { + "bbox": [ + 46, + 172, + 287, + 239 + ], + "type": "text", + "content": ". 'Adaptive " + }, + { + "bbox": [ + 46, + 172, + 287, + 239 + ], + "type": "inline_equation", + "content": "\\kappa" + }, + { + "bbox": [ + 46, + 172, + 287, + 239 + ], + "type": "text", + "content": " ' means " + }, + { + "bbox": [ + 46, + 172, + 287, + 239 + ], + "type": "inline_equation", + "content": "\\kappa" + }, + { + "bbox": [ + 46, + 172, + 287, + 239 + ], + "type": "text", + "content": " varies with the noise variance." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 50, + 250, + 285, + 293 + ], + "blocks": [ + { + "bbox": [ + 50, + 250, + 285, + 293 + ], + "lines": [ + { + "bbox": [ + 50, + 250, + 285, + 293 + ], + "spans": [ + { + "bbox": [ + 50, + 250, + 285, + 293 + ], + "type": "table", + "html": "
Noise amplitude5mm10mm15mm30mm50mm
W/o prior F61.362.765.071.580.4
Posterior-based48.549.651.454.559.0
(12.8↓)(13.1↓)(13.6↓)(17.0↓)(21.4↓)
", + "image_path": "8c1c92dba0b23ab7fd3ab717fbccb3af3580120e4ea006dd99f7ab7c11693a6c.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 346, + 287, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 346, + 287, + 441 + ], + "spans": [ + { + "bbox": [ + 46, + 346, + 287, + 441 + ], + "type": "text", + "content": "from keypoints. The comparison between design (b) and (e) shows that the prior " + }, + { + "bbox": [ + 46, + 346, + 287, + 441 + ], + "type": "inline_equation", + "content": "\\pmb{F}" + }, + { + "bbox": [ + 46, + 346, + 287, + 441 + ], + "type": "text", + "content": " is crucial in fusion. Furthermore, design (c) is better than design (b), indicating the prior " + }, + { + "bbox": [ + 46, + 346, + 287, + 441 + ], + "type": "inline_equation", + "content": "\\pmb{F}" + }, + { + "bbox": [ + 46, + 346, + 287, + 441 + ], + "type": "text", + "content": " has guided the keypoints learning to some extent. The difference is more significant in MPJPE since the global rotation is supervised for design (c). As for the feature choice, the intermediate feature adopted by our framework shows slightly better performance than the late and early features." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 447, + 287, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 447, + 287, + 675 + ], + "spans": [ + { + "bbox": [ + 46, + 447, + 287, + 675 + ], + "type": "text", + "content": "Noise robustness: We evaluate the robustness of our framework when suffering from noise. Fig. 4 shows the simulation results with two metrics. The rotation error is the angle to be rotated from the estimated rotation " + }, + { + "bbox": [ + 46, + 447, + 287, + 675 + ], + "type": "inline_equation", + "content": "\\hat{\\pmb{R}}" + }, + { + "bbox": [ + 46, + 447, + 287, + 675 + ], + "type": "text", + "content": " to the ground-truth. The direction error is the angle between the estimated bone vector and the ground-truth. Fig. 4 (b) reveals that 'w/o prior " + }, + { + "bbox": [ + 46, + 447, + 287, + 675 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 46, + 447, + 287, + 675 + ], + "type": "text", + "content": " has a small direction error but a large rotation error for the unsolved twist, while the posterior strategy has a much smaller error even with a high keypoint noise level and shows a slower error growth rate. Note that the performance of a simple fixed " + }, + { + "bbox": [ + 46, + 447, + 287, + 675 + ], + "type": "inline_equation", + "content": "\\kappa" + }, + { + "bbox": [ + 46, + 447, + 287, + 675 + ], + "type": "text", + "content": " is also acceptable. Fig. 4 (a) shows that when the prior noise level is less than " + }, + { + "bbox": [ + 46, + 447, + 287, + 675 + ], + "type": "inline_equation", + "content": "15\\%" + }, + { + "bbox": [ + 46, + 447, + 287, + 675 + ], + "type": "text", + "content": ", the keypoint noise has little effect on the posterior result with the adaptive " + }, + { + "bbox": [ + 46, + 447, + 287, + 675 + ], + "type": "inline_equation", + "content": "\\kappa" + }, + { + "bbox": [ + 46, + 447, + 287, + 675 + ], + "type": "text", + "content": ", reflecting the tolerance to noises of the posterior scheme. Table 4 shows the noise test on the Human3.6M dataset. From the difference listed in parentheses, when the noise level is higher, the error of the posterior method increases more slowly compared with the baseline without prior " + }, + { + "bbox": [ + 46, + 447, + 287, + 675 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 46, + 447, + 287, + 675 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 689, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 715 + ], + "type": "text", + "content": "Samples illustration: Fig. 5 illustrates the samples from the posterior distribution. The right hand has a relatively" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 309, + 72, + 541, + 178 + ], + "blocks": [ + { + "bbox": [ + 309, + 72, + 541, + 178 + ], + "lines": [ + { + "bbox": [ + 309, + 72, + 541, + 178 + ], + "spans": [ + { + "bbox": [ + 309, + 72, + 541, + 178 + ], + "type": "image", + "image_path": "551a24428e3cf58ef213094dfe6143b345957454f84026c874aa78fd2a5e284a.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 188, + 545, + 232 + ], + "lines": [ + { + "bbox": [ + 305, + 188, + 545, + 232 + ], + "spans": [ + { + "bbox": [ + 305, + 188, + 545, + 232 + ], + "type": "text", + "content": "Figure 5. Samples from the distribution. The mode and samples of the relative rotations are shown. The light color indicates the mode, while the dark color indicates an extra sample. The canonical coordinate is at the top right as a reference." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 309, + 245, + 544, + 376 + ], + "blocks": [ + { + "bbox": [ + 46, + 302, + 287, + 326 + ], + "lines": [ + { + "bbox": [ + 46, + 302, + 287, + 326 + ], + "spans": [ + { + "bbox": [ + 46, + 302, + 287, + 326 + ], + "type": "text", + "content": "Table 4. Noise test on the Human3.6M dataset. The 3D keypoints suffer from different levels of noises. MPJPE is reported." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 309, + 245, + 544, + 376 + ], + "lines": [ + { + "bbox": [ + 309, + 245, + 544, + 376 + ], + "spans": [ + { + "bbox": [ + 309, + 245, + 544, + 376 + ], + "type": "table", + "html": "
MethodsSensorsTotalCapture
PA-MPJPE ↓MPJPE ↓
IMUPVH [10]mv + IMUs-42.6
GeoFuse [72]mv + IMUs20.624.6
Oursmv + IMUs19.423.5
VIP [62]sv + IMUs26.0-
Kalman filtersv + IMUs23.134.7
Ourssv29.042.1
Ours (w/o ref, R-50)sv + IMUs25.841.7
Ours (w/o ref, H-48)sv + IMUs22.338.8
Ours (R-50)sv + IMUs25.032.3
Ours (H-48)sv + IMUs21.228.5
", + "image_path": "93ea13cf12c54c8b59377216843ad10dfd74c59c799830a5a4ca90e28c3381bb.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 384, + 545, + 428 + ], + "lines": [ + { + "bbox": [ + 305, + 384, + 545, + 428 + ], + "spans": [ + { + "bbox": [ + 305, + 384, + 545, + 428 + ], + "type": "text", + "content": "Table 5. Results on the TotalCapture dataset. 'mv' and 'sv' denote multi-view and single-view. 'w/o ref' means lacking a reference skeleton (only a statistical one from training set is adopted), which would slightly weaken the performance of our framework." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 449, + 545, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 449, + 545, + 532 + ], + "spans": [ + { + "bbox": [ + 304, + 449, + 545, + 532 + ], + "type": "text", + "content": "large uncertainty on rotating around the X-axis due to the uncertain twist angle, as shown by the widespread blue and green samples. The left elbow has a vertical uncertainty on the direction of the forearm since the left hand cannot be easily determined. The left ankle has large confidence, except in the depth direction, therefore the green samples spread horizontally." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 532, + 545, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 532, + 545, + 604 + ], + "spans": [ + { + "bbox": [ + 304, + 532, + 545, + 604 + ], + "type": "text", + "content": "Fig. 6 shows the qualitative comparison with the SOTA methods. The indirect methods that use part segmentation [27] or 3D keypoints [36] perform well in most cases, but may suffer from wrong segmentation for distant people or generate unnatural poses. While the direct method CLIFF [37] may not align the image well for complicated scenes." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 611, + 420, + 623 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 611, + 420, + 623 + ], + "spans": [ + { + "bbox": [ + 306, + 611, + 420, + 623 + ], + "type": "text", + "content": "4.3. Multi-sensor fusion" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": "We perform experiments on the TotalCapture dataset [61] using the feed-forward network directly without any iterative optimization. As the original dataset does not provide SMPL annotations, we adopt the human skeleton defined by 19 joints and 11 attached IMUs, as shown in Fig. 7. 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Qualitative comparison. The input images are from 3DPW [62], MS COCO [39], and AGORA [50], respectively. We compare our approach with SOTA methods including HybrIK [36], PARE [27], and CLIFF [37]. 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An example of a multi-sensor case. The estimations from the front-view camera, side-view camera, and IMUs are plotted. The normalized confidence score of the left knee is listed." + } + ] + } + ], + "index": 37, + "angle": 0, + "type": "image_caption" + } + ], + "index": 35 + }, + { + "type": "image", + "bbox": [ + 201, + 388, + 272, + 461 + ], + "blocks": [ + { + "bbox": [ + 201, + 388, + 272, + 461 + ], + "lines": [ + { + "bbox": [ + 201, + 388, + 272, + 461 + ], + "spans": [ + { + "bbox": [ + 201, + 388, + 272, + 461 + ], + "type": "image", + "image_path": "71c9890f4424f2a6d16b35243f44149ae09da929b7543a0cad8aa82f066b1f59.jpg" + } + ] + } + ], + "index": 36, + "angle": 0, + "type": "image_body" + } + ], + "index": 36 + }, + { + "bbox": [ + 46, + 521, + 287, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 287, + 689 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 287, + 689 + ], + "type": "text", + "content": "Table 5 shows the experimental results. Our method outperforms baseline methods, indicating the effectiveness of our posterior scheme. In the 'Kalman filter' setup, we apply a weighted sum to the 3D rotations separately obtained from images and IMUs. As the observation variance required for calculating the Kalman gain is unknown, we pick the weight pairs that can yield the best estimation through grid searching, i.e., from (0.7, 0.3) to (0.3, 0.7). Note that unlike Kalman filter which fuses the observations in the testing stage, our method performs fusing in the training stage, and thus has the potential to obtain higher precision. Our framework is also more flexible than feature-level fusing methods since we do not require modifications of the backbone to incorporate new sensors." + } + ] + } + ], + "index": 38 + }, + { + "bbox": [ + 46, + 689, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 712 + ], + "type": "text", + "content": "Fig. 7 shows an example of a scene with multiple cameras and IMUs. The confidence from the two cameras are" + } + ] + } + ], + "index": 39 + }, + { + "bbox": [ + 304, + 308, + 545, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 308, + 545, + 415 + ], + "spans": [ + { + "bbox": [ + 304, + 308, + 545, + 415 + ], + "type": "text", + "content": "calculated via the normalized differential entropy of the estimated distribution parameters, while the confidence from IMUs is set to a relatively larger value since IMUs can provide accurate measurements. Note that other metrics that represent the uncertainty from the distribution can also be adopted. It can be observed that the front view produces erroneous knee bending due to the depth ambiguity, therefore its confidence is lower than the side view. As a result, the fused result will be less affected by the noisy estimation." + } + ] + } + ], + "index": 40 + }, + { + "bbox": [ + 306, + 423, + 458, + 435 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 423, + 458, + 435 + ], + "spans": [ + { + "bbox": [ + 306, + 423, + 458, + 435 + ], + "type": "text", + "content": "4.4. Limitation and future work" + } + ] + } + ], + "index": 41 + }, + { + "bbox": [ + 304, + 442, + 545, + 550 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 442, + 545, + 550 + ], + "spans": [ + { + "bbox": [ + 304, + 442, + 545, + 550 + ], + "type": "text", + "content": "Our work has several limitations. First, we only consider the uncertainty of poses, not including that of shapes, which can also be modeled as probability distributions. Second, we model the human joint independently, which is only affected by the parent node. Therefore, how to derive the analytical form of joint rotations conditioned on other hierarchical joints to incorporate anatomical constraints explicitly is still unsolved. Besides, with the single-view uncertainty, the temporal extension also deserves further investigation." + } + ] + } + ], + "index": 42 + }, + { + "bbox": [ + 306, + 561, + 378, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 561, + 378, + 574 + ], + "spans": [ + { + "bbox": [ + 306, + 561, + 378, + 574 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 43 + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": "In this paper, we derive a novel analytical posterior probability for human joint rotations in a Bayesian manner and prove the property that the posteriors are more concentrated than the priors. Based on the derivation, we propose a new framework for human mesh recovery by leveraging the learned posteriors, which has high precision and robustness, outperforming existing SOTA baselines. Furthermore, our framework can be seamlessly incorporated with additional sensors in the training due to its Bayesian nature. 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In CVPR, pages 5745-5753, 2019. 1, 2, 4" + } + ] + } + ], + "index": 10 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 314, + 757 + ], + "type": "text", + "content": "8791" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Learning Anchor Transformations for 3D Garment Animation/172fc2a1-00b1-413a-bcb3-423ae7376cbc_content_list.json b/2023/Learning Anchor Transformations for 3D Garment Animation/172fc2a1-00b1-413a-bcb3-423ae7376cbc_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..42f3ccc73c7289679bfe934d4fc9af5226d5709b --- /dev/null +++ b/2023/Learning Anchor Transformations for 3D Garment Animation/172fc2a1-00b1-413a-bcb3-423ae7376cbc_content_list.json @@ -0,0 +1,1437 @@ +[ + { + "type": "text", + "text": "Learning Anchor Transformations for 3D Garment Animation", + "text_level": 1, + "bbox": [ + 168, + 130, + 802, + 151 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Fang Zhao $^{1}$ , Zekun Li $^{1}$ , Shaoli Huang $^{1*}$ , Junwu Weng $^{1}$ , Tianfei Zhou $^{2}$ , Guo-Sen Xie $^{3}$ , Jue Wang $^{1}$ , Ying Shan $^{1}$", + "bbox": [ + 196, + 190, + 772, + 234 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ Tencent AI Lab $^{2}$ ETH Zurich $^{3}$ Nanjing University of Science and Technology", + "bbox": [ + 166, + 239, + 797, + 258 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 295, + 313, + 311 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "This paper proposes an anchor-based deformation model, namely AnchorDEF, to predict 3D garment animation from a body motion sequence. It deforms a garment mesh template by a mixture of rigid transformations with extra nonlinear displacements. A set of anchors around the mesh surface is introduced to guide the learning of rigid transformation matrices. Once the anchor transformations are found, per-vertex nonlinear displacements of the garment template can be regressed in a canonical space, which reduces the complexity of deformation space learning. By explicitly constraining the transformed anchors to satisfy the consistencies of position, normal and direction, the physical meaning of learned anchor transformations in space is guaranteed for better generalization. Furthermore, an adaptive anchor updating is proposed to optimize the anchor position by being aware of local mesh topology for learning representative anchor transformations. Qualitative and quantitative experiments on different types of garments demonstrate that AnchorDEF achieves the state-of-the-art performance on 3D garment deformation prediction in motion, especially for loose-fitting garments.", + "bbox": [ + 76, + 327, + 473, + 645 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 672, + 209, + 688 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Animating 3D garments has a wide range of applications in 3D content generation, digital humans, virtual try-on, video games, and so on. Existing pipelines of 3D garment animation usually rely on physics based simulation (PBS), which requires a large amount of computational resources and time costs, particularly for high-quality PBS methods.", + "bbox": [ + 75, + 696, + 468, + 787 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Some data-driven or learning-based methods have been proposed to quickly produce 3D garment deformation from static poses or motion sequences with low computational complexity [4,5,9,11,12,16,25-28,31,40]. However, many of them attach garment templates to the skeleton of human body for modeling the articulation of garments, which", + "bbox": [ + 75, + 787, + 468, + 878 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/fdaf0e45b9400481a1b074b684941eab8b33b408a9b3a081f5a188ca6389426c.jpg", + "image_caption": [ + "Figure 1. 3D garment deformation predicted by the proposed AnchorDEF with body motions. Leveraging the anchor transformations, AnchorDEF is able to realistically deform the garment mesh, especially for loose-fitting garments, e.g., dresses." + ], + "image_footnote": [], + "bbox": [ + 509, + 296, + 883, + 592 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "only work with tight garments, e.g., T-shirts and pants, and poorly address loose-fitting ones, e.g., dresses and skirts. In this case, the topology of garments is different from the human body. Therefore, using the skinning blend weights of body yields discontinuities on deformed garment mesh. Several methods [26, 34] smooth out the blend weights to alleviate the discontinuities but may lose the shape details for large deformations of loose-fitting garments, which do not closely follow body movements.", + "bbox": [ + 496, + 688, + 892, + 823 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To this end, we propose an anchor-based deformation model, namely AnchorDEF, for predicting 3D garment deformation from a body motion sequence. It leverages a mixture of rigid anchor transformations to represent principle rotations and translations of garments to detach the", + "bbox": [ + 496, + 824, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author.", + "bbox": [ + 94, + 887, + 220, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "491", + "bbox": [ + 485, + 945, + 509, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "garment articulation from the body skeleton while preserving the body movement prior, then nonlinear displacements can be regressed relatively easily in a canonical space. As shown in Fig. 1, our method can exploit anchor transformations to realistically deform the garment mesh, especially for loose-fitting garments, e.g., dresses.", + "bbox": [ + 75, + 90, + 468, + 181 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Specifically, given a sequence of body motions including poses and translations, we first estimate rigid transformations of a set of anchors around the garment mesh. Using the linear blending skinning (LBS), the garment mesh template is deformed by a weighted combination of the anchor transformations meanwhile per-vertex displacements of the mesh template are regressed to correct artifacts of the blended rigid transformations. To learn physically meaningful anchor transformations for better generalization, we enforce the transformed anchors to maintain consistency with the target's position and normal. In addition, a relative direction constraint is employed to reduce garment-body interpenetrations, which is efficient due to the sparseness of anchors. To make the learned anchor transformations effectively represent the garment deformation, an adaptive anchor updating is further introduced to utilize mesh simplification as supervision to optimize the anchor position. It parameterizes the position with a local attention mask on adjacent mesh vertices and pushes the anchors towards folds and boundaries of garment mesh which usually determine the way of deformation.", + "bbox": [ + 75, + 181, + 470, + 496 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The main contributions of our work can be summarized as follows: 1) We propose an anchor-based deformation model which learns a set of anchor transformations and blend weights in a unified framework to represent the deformation of 3D garments, especially for loose-fitting ones. 2) We propose to learn anchor transformations by position and normal consistencies as well as relative direction constraint for better generalization and fewer garment-body interpenetrations. 3) We introduce an adaptive anchor updating with the mesh simplification as supervision to optimize the anchor position for learning representative anchor transformations.", + "bbox": [ + 75, + 500, + 468, + 679 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 694, + 218, + 709 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Most garment animation and deformation works can be categorized into physics-based simulations (PBS) and learning-based models.", + "bbox": [ + 75, + 719, + 468, + 763 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Physics-based simulations. PBS methods have been developed for decades and achieved impressive accuracy, leveraging laws of physics and stable accurate solvers [1, 13, 18], collision detection [23, 29, 35], and dry frictional contact [19, 21]. But the expensive computational costs, i.e., long simulation time and high-performance devices often are unaffordable in our daily lives.", + "bbox": [ + 75, + 763, + 468, + 869 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Learning-based models. In contrast, learning-based models, which utilize garment animation data attained from PBS", + "bbox": [ + 75, + 869, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "or digital scanning to learn the deformation, can often give satisfactory enough animation visual results with less computational costs [26, 31], regardless of no explicit physical guarantee on accuracy. Previously, researchers have proposed many techniques depending on the motions of human bodies with linear conditional models [8, 11] or secondary motion graphs [14, 15], with a constructed database of high-resolution meshes. Recent works [4, 26, 34] assume that the garment is a submesh of the skinned multi-person linear model (SMPL) and use linear blend skinning (LBS) to transfer body shape to cloth shape. Beyond learning static results within a single frame, adopting recurrent neural networks to handle the dynamic wrinkles of clothes is widely used [25, 31, 34]. For example, [31] prepares a database of PBS for dressed characters with some body shapes and motion and uses the database to learn a function of body shape and dynamics for modeling cloth drape and wrinkles. Although learning-based models can be efficient, their performance heavily relies on large amounts of high-quality PBS results or scanning data, which are usually costly [2, 30, 34]. Thus, some works [3, 32] propose self-supervised training methods to constrain the model with some sort of physical laws to alleviate this problem. Additionally, to ensure the generalization of simulation, combining several pretrained pivot motion networks can handle different unseen garment styles [26] and simulation parameters [25].", + "bbox": [ + 496, + 90, + 890, + 484 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "But most learning-based methods are limited to tight garments and not suitable for dresses or clothes with more freedom, due to their assumption that garments are complementary to SMPL, i.e., the deformation is closely related to body shape, not the motion. To tackle the dynamics, some works propose a neural field to retain high-frequency details [39], handle challenging areas [22], tackle multi-layer garments [33], and warp garments from the canonical pose to the deformation shape [6]. Without utilizing body shape parameters to establish a garment-body aligned model, [37] learns an intrinsic cloth shape descriptor embedding space and using different motion parameters to guide garment latent can attain different shape representation. To eliminate the alignment between clothes dynamics and body vertices, VirtualBones [25] extracts a set of rigid bones from the garment animation and uses body motion to predict the bones' transformation to interpolate the garment shape. Instead of learning based on mesh, [38] uses a point transformer to predict point clouds of various outfits, for various human poses and shapes, which attains more topological flexibility and the ability to model clothing separately from the body.", + "bbox": [ + 496, + 488, + 890, + 806 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "VirtualBones [25] is the most related work to our method, which requires garment skeleton extraction with SSDR [17] as data preprocessing. Different from [25], we decompose the garment deformation by a set of adaptive anchors whose rigid transformations and blend weights are learned in a unified framework.", + "bbox": [ + 496, + 809, + 890, + 898 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "492", + "bbox": [ + 485, + 945, + 509, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/edbde95bd831e3fdcf4f2a43bffa84040ad4e4b51cf4c721064f4798e30897f0.jpg", + "image_caption": [ + "Figure 2. Overview of the proposed AnchorDEF. Given a body motion sequence and a garment mesh template, the garment deformation is predicted by a weighted average of rigid anchor transformations with per-vertex displacements in a canonical space. We explicitly constrain the transformed anchors to satisfy the consistencies of position, normal and direction to guarantee the physical meaning of learned anchor transformations in space for better generalization. Starting from the cluster centers of mesh vertices, the anchor position is updated by a local attention map on adjacent mesh vertices with mesh simplification as supervision. All parameters in our model can be jointly optimized in a unified framework." + ], + "image_footnote": [], + "bbox": [ + 91, + 88, + 883, + 380 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Our Method", + "text_level": 1, + "bbox": [ + 76, + 487, + 207, + 502 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We aim to learn an animated model which is able to predict dynamic 3D garment deformations given a body motion sequence. In this section, we introduce AnchorDEF, an anchor-based deformation model, which leverages s set of adaptive anchors around mesh surface to deform a garment mesh template by a mixture of rigid anchor transformations with additional per-vertex displacements in a canonical space, where the anchor transformations are learned by the consistencies of position, normal and direction. The overview of AnchorDEF is illustrated in Fig. 2.", + "bbox": [ + 75, + 512, + 472, + 662 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Deformation with Anchors", + "text_level": 1, + "bbox": [ + 76, + 672, + 318, + 686 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3D animated models of human body, e.g., SMPL [20], usually deform a body mesh template $\\mathbf{T}$ with blendshapes and skinning, which can be defined as", + "bbox": [ + 75, + 695, + 468, + 742 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nV = W (\\mathbf {T} + B (\\theta), \\mathbf {J}, \\theta , \\mathbf {w}), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 174, + 752, + 468, + 768 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $W$ is a skinning function, e.g., linear blend skinning, with a skeleton $\\mathbf{J}$ , pose parameters $\\theta$ and blend weights $\\mathbf{w}$ , $V$ is the posed vertices and $B$ is the blendshape corresponding to the body pose $\\theta$ . Since the garment is a kind of soft body and it is hard to directly predict the coordinates of each vertex from a body motion sequence, here we also consider to decompose the garment deformation into two parts including a weighed average of rigid transformations and", + "bbox": [ + 75, + 779, + 472, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "nonlinear displacements.", + "bbox": [ + 498, + 489, + 666, + 503 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Most data-driven garment models directly associate garments with the skeleton of human body [4,26,31], i.e., they apply the skinning function to animate the garment by directly using the blend weights of body mesh vertices in the neighborhood, where it is assumed that garments closely follow the body movement. However, for loose-fitting garments, the clothing deformation usually contains more complex nonrigid effects compared to human body which can be seen as a rigid body. In this case, garments behave significantly differently from the body. Thus, it is unreasonable to attach the garment to the body skeleton.", + "bbox": [ + 496, + 503, + 890, + 669 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To address this issue, we adopt a set of anchors $\\{p_n\\}$ around the mesh surface to guide the garment deformation, which detaches the garment from the body skeleton while preserving the body movement prior. Given a body motion sequence consisting of poses and translations, rigid anchor transformations including rotations $\\{R_{n}\\}$ and translations $\\{T_{n}\\}$ are estimated firstly by using Gated Recurrent Units (GRU) [7] (see the supplementary material for the network structure). Then, the $m$ -th deformed garment vertex $v_{m}$ can be represented by a weighted average of anchor transformations:", + "bbox": [ + 496, + 670, + 892, + 835 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nv _ {m} = \\sum_ {n = 1} ^ {N} w _ {m n} \\left(R _ {n} v _ {m} ^ {c} + T _ {n}\\right), w _ {m n} \\geq 0 \\text {a n d} \\sum_ {n = 1} ^ {N} w _ {m n} = 1, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 498, + 845, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "493", + "bbox": [ + 485, + 945, + 509, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $v_{m}^{c}$ is the $m$ -th vertex of garment mesh template, $w_{mn}$ is the blend weight of $v_{m}$ regarding to the $n$ -th anchor and $N$ is the number of anchors. To determine the anchor-vertex relationship and maintain the sparsity of $\\{w_{n}\\}$ , we initialize the anchors as the clustering centers of vertices of the mesh template. Then, each vertex is only influenced by the blend weights of its $N'$ ( $N' \\ll N$ ) nearest anchors and the others remain zeros during training. Compared to the direct prediction of deformed mesh vertex coordinates, the rigid anchor transformations provide more generalized representations of complex deformations due to fewer parameters required to be learned for the prediction.", + "bbox": [ + 75, + 90, + 472, + 271 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Two strategies of anchor transformation configuration are designed for loose and tight types of garments. For the loose type, to utilize the prior of the global human body orientation $R_{global}$ , we predict transformations relative to the root joint $J_{root}$ of the body and the anchor transformation can be defined as:", + "bbox": [ + 75, + 272, + 472, + 363 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} R _ {n} ^ {\\text {l o o s e}} = R _ {\\text {g l o b a l}} R _ {n} ([ \\theta , t ]), \\\\ T _ {n} ^ {\\text {l o o s e}} = R _ {\\text {g l o b a l}} \\left(T _ {n} ([ \\theta , t ]) - R _ {n} ([ \\theta , t ]) J _ {\\text {r o o t}}\\right) + J _ {\\text {r o o t}}, \\tag {3} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 373, + 468, + 426 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\theta$ and $t$ are the body pose and translation, respectively. For the tight type, the garment mostly follows the body movement. Thus, we predict an incremental change on the basis of body vertex rotation $R_{body}$ and offset $T_{body}$ :", + "bbox": [ + 75, + 438, + 468, + 501 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} R _ {n} ^ {t i g h t} = R _ {b o d y} R _ {n} ([ \\theta , t ]), \\\\ T _ {n} ^ {\\text {t i g h t}} = R _ {\\text {b o d y}} T _ {n} ([ \\theta , t ]) + T _ {\\text {b o d y}}, \\tag {4} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 156, + 508, + 468, + 549 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $R_{body}$ and $T_{body}$ is the transformation of the body mesh vertex closest to the anchor $p_n$ . Furthermore, we can combine these two strategies for garments with both tight and loose parts, e.g., dresses, by classifying which part the anchor belongs to according to its distance to body joints.", + "bbox": [ + 75, + 559, + 468, + 633 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Once the primary rotations and translations in the garment deformation caused by the articulation are expressed in Eq. (2), the nonlinear residual deformation can be disentangled with the garment articulation and defined as pervertex displacements $D([\\theta, t])$ in an unposed canonical space. Utilizing the skinning function in Eq. (1), the overall garment deformation is given by", + "bbox": [ + 75, + 633, + 468, + 741 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nV _ {p r e d} = W \\left(\\mathbf {T} _ {g} + D ([ \\theta , t ]), G ([ \\theta , t ]), \\mathbf {w} _ {p}\\right), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 129, + 751, + 468, + 770 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{T}_g$ is the garment mesh template, $\\mathbf{w}_p$ is the anchor-vertex blend weights and $G([\\theta ,t])$ is the anchor transformations predicted with the body motion. We argue that such decomposition by anchors extremely reduces the complexity of pose-dependent garment deformation prediction because large deformations have been handled by transformations of sparse anchors and only small displacements need to be regressed in the canonical space.", + "bbox": [ + 75, + 779, + 472, + 902 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/58b9717ad9817a4115433f67110665eb4c3f3569145f524450b694b9f5a83e88.jpg", + "image_caption": [ + "Figure 3. Examples of adaptive anchor updating by using the local attention mask with the mesh simplification as supervision. The blue points are anchors initialized by $k$ -means and the orange ones are the updated anchors." + ], + "image_footnote": [], + "bbox": [ + 514, + 89, + 879, + 154 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Learning Anchor Transformations", + "text_level": 1, + "bbox": [ + 500, + 244, + 802, + 261 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Different from [25] which resorts to the external skinning decomposition algorithm, i.e., SSDR [17], to extract the garment skeleton from smoothed mesh sequences, here we jointly learn rigid transformations, blend weights and positions of anchors in a unified framework.", + "bbox": [ + 496, + 268, + 890, + 343 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We first apply an L2 loss term on the predicted mesh vertices to recover the shape of deformed mesh:", + "bbox": [ + 498, + 344, + 890, + 375 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {r e c} = \\left| \\left| V _ {p r e d} - V _ {g t} \\right| \\right| _ {2} ^ {2}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 612, + 380, + 890, + 400 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "which minimizes the Euclidean distance between the predicted vertices and the ground-truth deformed vertices. Then a loss term is used to keep the similarity of the graph Laplacians between two meshes:", + "bbox": [ + 496, + 406, + 890, + 465 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {l a p} = \\left\\| \\triangle V _ {p r e d} - \\triangle V _ {g t} \\right\\| _ {2} ^ {2}. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 594, + 472, + 890, + 491 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "A collision term [25] is also added to avoid garment-body collisions. Thus, the loss on the vertex can be given by", + "bbox": [ + 496, + 497, + 890, + 527 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {v e r t}} = \\mathcal {L} _ {\\text {r e c}} + \\beta_ {1} \\mathcal {L} _ {\\text {l a p}} + \\beta_ {2} \\mathcal {L} _ {\\text {c o l l i s i o n}}, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 563, + 536, + 890, + 551 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\beta_{1}$ and $\\beta_{2}$ are trade-off coefficients for controlling the degree of smoothing and collision, respectively.", + "bbox": [ + 496, + 559, + 890, + 589 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "However, only optimizing the vertex position cannot guarantee the physical meaning of learned anchor transformations in space, which leads to poor generalization. Thus, we explicitly constrain the transformed anchors to be located around the deformed mesh surface. To this end, the position of anchor $p$ is recalculated by its adjacent mesh vertices:", + "bbox": [ + 496, + 589, + 890, + 691 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\np = \\frac {1}{K} \\sum_ {v _ {k} ^ {c} \\in K (p, \\mathbf {T} _ {g})} v _ {k} ^ {c}, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 617, + 690, + 890, + 729 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $K(p, \\mathbf{T}_g)$ is the $K$ nearest vertices of $p$ on the mesh template. Then, the target point $p_{tgt}$ of transformed anchor $p_G$ can be defined with the same set of vertices $K(p, \\mathbf{T}_g)$ on the deformed mesh and a transformation consistency loss is defined as", + "bbox": [ + 496, + 732, + 890, + 808 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {c o n s i s}} = \\left\\| p _ {G} - p _ {t g t} \\right\\| _ {2} ^ {2} + \\gamma \\left\\| \\mathbf {n} \\left(p _ {G}\\right) - \\mathbf {n} \\left(p _ {t g t}\\right) \\right\\| _ {2} ^ {2}, \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 513, + 815, + 890, + 834 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{n}(.)$ is the unit normal of point and $\\gamma$ is a weight factor. By encouraging the transformed anchor $p_G$ to be similar to $p_{tgt}$ in position and normal, the learned anchor transformation indicates the mean transformation of $K$ nearest", + "bbox": [ + 496, + 839, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "494", + "bbox": [ + 485, + 945, + 511, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/45c590dd395b4e064c51716ae9422a1bc69453eadb6c22daffc9e7bf14c2c950.jpg", + "image_caption": [ + "Figure 4. Qualitative comparison with and without different components of AnchorDEF including (a) anchor transformation consistency $\\mathcal{L}_{consis}$ and (b) adaptive anchor updating $\\mathcal{L}_{anch}$ . Without $\\mathcal{L}_{consis}$ , the model cannot accurately predict the shape of deformed mesh and loses some surface geometry details. Without $\\mathcal{L}_{anch}$ , the model is unable to produce realistic garment deformations due to the under-expressed anchor transformations." + ], + "image_footnote": [], + "bbox": [ + 86, + 89, + 879, + 375 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "vertices of $p$ . It can be viewed as a regularization for the transformation magnitude and direction to discover essential transformations in deformation.", + "bbox": [ + 75, + 460, + 468, + 505 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We further enforce the direction from $p_{tgt}$ to $p_G$ to be consistent with the direction of $\\mathbf{n}(p_{tgt})$ by minimizing the following penalty term:", + "bbox": [ + 75, + 506, + 470, + 551 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {d i r} = 1 - \\cos \\left(p _ {G} - p _ {t g t}, \\mathbf {n} \\left(p _ {t g t}\\right)\\right), \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 150, + 556, + 468, + 574 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\cos (\\cdot ,\\cdot)$ is the cosine similarity. Intuitively, this penalty term makes $p_{G}$ tend to be outside of the plane formed by $p_{tgt}$ to reduce the garment-body interpenetration. Adaptive Anchor Updating. It is still not enough to have a physically meaningful anchor transformation, we also need an expressive transformation in geometry to better represent the garment deformation. We observe that mesh regions with folds and boundaries usually play an important role on showing garment shape characteristics and contain more deformation information compared with smooth regions.", + "bbox": [ + 75, + 579, + 468, + 729 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To make the anchors reflect such intrinsic structure of garment shape, we propose to employ mesh simplification to provide a signal of supervision for finding such representative anchors. Here Quadric Error Metric (QEM) [10] is used to obtain simplified mesh vertices by collapsing edges while preserving the garment topology. Because there is no one-to-one correspondence between the anchors $\\{p_n\\}$ and the simplified vertices $\\{\\tilde{v}_m\\}$ , the Chamfer distance is adopted as the optimization objective:", + "bbox": [ + 75, + 729, + 470, + 866 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {a n c h} = \\sum_ {p} \\min _ {\\tilde {v}} | | p - \\tilde {v} | | _ {2} ^ {2} + \\sum_ {\\tilde {v}} \\min _ {p} | | p - \\tilde {v} | | _ {2} ^ {2}. \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 94, + 869, + 468, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To be able to update the anchor position, we rewrite Eq. (9) using learnable weights $\\alpha$ as", + "bbox": [ + 498, + 460, + 890, + 491 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\np = \\frac {1}{\\sum_ {j = 1} ^ {K} e ^ {\\alpha_ {j}}} \\sum_ {k = 1} ^ {K} e ^ {\\alpha_ {k}} v _ {k} ^ {c}. \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 604, + 500, + 890, + 544 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Actually, this equals to learning a local attention mask for the anchor to determine how the adjacent vertices contribute to its position. Fig. 3 shows that by optimizing the weights $\\alpha$ with supervision of the simplified vertices, the anchors are pushed to inflection points of folds and boundaries of the mesh and thus able to better represent the deformed mesh vertices by interpolating their transformation matrices. Note that we optimize the anchor position on the entire dataset not only on the mesh template because some smooth regions of the template may create new folds after posing.", + "bbox": [ + 496, + 551, + 892, + 703 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "On the other hand, if we reformulate the transformed anchor $p_G$ with Eq. (13) as:", + "bbox": [ + 496, + 703, + 890, + 733 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\np _ {G} = R p + T = \\frac {1}{\\sum_ {j = 1} ^ {K} e ^ {\\alpha_ {j}}} \\sum_ {k = 1} ^ {K} e ^ {\\alpha_ {k}} \\left(R v _ {k} ^ {c} + T\\right), \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 743, + 890, + 786 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "the process of transformation learning for the anchor, i.e., Eq. (10), can be interpreted as a way to find an appropriate transformation for its adjacent mesh vertices by the importance which is reflected in the weights learned from the mesh simplification. The larger the weight, the greater the impact of the vertex transformation on the anchor transformation learning.", + "bbox": [ + 496, + 794, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "495", + "bbox": [ + 485, + 945, + 509, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/d0609ba541d195d74d6eb42afcbd48dca8654b81e18c758beb1ab8bb8dd397db.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 125, + 90, + 259, + 247 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/97d1b9c0206670243f7062f07688ea1dc999f31ed749ddf7d1b5d0b13ff5f175.jpg", + "image_caption": [ + "(b)", + "Figure 5. Visualization of anchors transformed by (a) only optimizing the mesh vertices during training and (b) AnchorDEF." + ], + "image_footnote": [], + "bbox": [ + 334, + 94, + 452, + 242 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Lastly, combining Eq. (8), Eqs. (10) to (12), the overall objective function for our model is given by:", + "bbox": [ + 76, + 316, + 468, + 347 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {\\text {v e r t}} + \\lambda_ {1} \\mathcal {L} _ {\\text {c o n s i s}} + \\lambda_ {2} \\mathcal {L} _ {\\text {d i r}} + \\lambda_ {3} \\mathcal {L} _ {\\text {a n c h}}, \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 104, + 359, + 468, + 376 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\lambda$ s are loss weights.", + "bbox": [ + 76, + 388, + 253, + 402 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 417, + 209, + 435 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We evaluate the proposed AnchorDEF on the VTO [31] dataset containing two types of garments, i.e., dress and T-shirt. Following [25], RMSE (Root Mean Squared Error), Hausdorff distance and STED (Spatio-Temporal Edge Difference) [36] are adopted to assess the quality of deformed meshes. The first two measure the distance between predicted and ground truth meshes and STED reflects the difference between their dynamics. We also compare AnchorDEF against other 3D garment deformation methods [25, 26].", + "bbox": [ + 75, + 443, + 468, + 594 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation Details. To capture the motion dynamics, a network with 2 GRU layers of size 256 is used as the body motion encoder. Two 2-layered MLPs of size 256 are used to regress the anchor transformations and per-vertex displacements, respectively. The number of anchors associated with each mesh vertex is set to 8, which can obtain the desired smooth surface, and the number of neighboring vertices for computing the anchor position is set to 128. For the garment sequences of VTO, 4 clips are randomly selected for testing and the rest is used as the training set, and the length of training sequence is 30. Please refer to the supplemental materials for more details on training and inference.", + "bbox": [ + 75, + 595, + 470, + 790 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 801, + 230, + 816 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We validate the effectiveness of main components in our proposed AnchorDEF. We firstly assess the importance of anchor transformation consistency, i.e., $\\mathcal{L}_{\\text{consis}}$ in Eq. (10). As reported in Table 1, keeping the consistency of learned anchor transformations is able to improve all metrics due", + "bbox": [ + 76, + 824, + 470, + 900 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/de9a9a9212042bdd71da5d439457b49c233cde99e9012f6390c54327dbebcf52.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Methodsw/o Lconsisw/o LanchAnchorDEF
RMSE ↓17.2116.4916.05
Hausdorff ↓75.0174.5374.20
STED ↓0.05950.05260.0493
", + "bbox": [ + 504, + 89, + 890, + 178 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/3dce5a95eb57df17fa5800419f431349ae16cdddc05e43cd412ed3901a4ba16a.jpg", + "image_caption": [ + "Figure 6. Qualitative comparison with and without the penalty $\\mathcal{L}_{dir}$ on the direction from the target anchor to the transformed one." + ], + "image_footnote": [], + "bbox": [ + 504, + 262, + 888, + 354 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/88967a35f02d45471547027bb244a8ee7250577c1bf28182ee82331b5e9c44b9.jpg", + "image_caption": [ + "Figure 7. Qualitative comparison of using different numbers of anchors. Using 160 anchors produces finer and more accurate deformation compared with other anchor numbers." + ], + "image_footnote": [], + "bbox": [ + 504, + 422, + 888, + 534 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/8214b2265b06d12d2e4873bae3cb7b5d73bdb04ec056706a306a10a78e8b4ef2.jpg", + "table_caption": [ + "Table 1. Quantitative results obtained by different components of AnchorDEF, i.e., without anchor transformation consistency (w/o $\\mathcal{L}_{\\text{cosis}}$ ), without adaptive anchor updating (w/o $\\mathcal{L}_{\\text{anch}}$ ) and the full model (AnchorDEF)." + ], + "table_footnote": [], + "table_body": "
Num. Anchor2080160320
RMSE ↓17.7816.8216.0517.52
Hausdorff ↓75.3074.7174.2075.13
STED ↓0.06200.05390.04930.0625
", + "bbox": [ + 503, + 599, + 890, + 691 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. Quantitative results of using different numbers of anchors.", + "bbox": [ + 500, + 700, + 888, + 715 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "to better generalization. Fig. 4 (a) illustrates the qualitative comparison. One can observe that without $\\mathcal{L}_{\\text {consis }}$ the model cannot accurately predict the shape of deformed mesh and loses some surface geometry details.", + "bbox": [ + 498, + 733, + 890, + 794 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To evaluate the influence of adaptive anchor updating, Table 1 also reports the results without using $\\mathcal{L}_{anch}$ in Eq. (12). The performance drops only using the clustering centers of $k$ -means as the anchors. The reason is that compared with the clustering, the supervision with mesh simplification can provide key topology information, e.g., folds and boundaries, which is useful for learning representative", + "bbox": [ + 496, + 795, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "496", + "bbox": [ + 485, + 945, + 511, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/01699bfded4d6dbf0041707f2b3cd930551f23fe4204bb7d88f040f267e00629.jpg", + "image_caption": [ + "Figure 8. Examples of our AnchorDEF for dynamic garment deformation in motion. The first row is the ground truth generated by physics-based simulation [24]. The second row is the results obtained by AnchorDEF. Our method can produce natural and realistic clothing dynamics, e.g., wrinkles from jumping and the swing of the dress caused by running." + ], + "image_footnote": [], + "bbox": [ + 89, + 90, + 880, + 372 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "anchor transformations. The qualitative results are shown in Fig. 4 (b). It can be observed that without $\\mathcal{L}_{anch}$ the model is unable to produce realistic garment deformations due to the under-expressed anchor transformations.", + "bbox": [ + 75, + 446, + 470, + 506 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Fig. 5 (a) and (b) visualize the anchors transformed by only optimizing the mesh vertices during training and AnchorDEF, respectively. For Fig. 5 (a), without the consistency constraint for anchor transformation, many of the transformed anchors are not on the deformed mesh surface, which is lack of clear physical meaning in space and easy to overfit. In contrast, AnchorDEF enforces the anchors to be transformed onto the deformed mesh surface, which prevents overfitting to a certain extent, thus has better generalization when testing. Furthermore, as shown in Fig. 5 (b), the transformed anchors are mainly distributed at the folds and boundaries of the mesh because of our adaptive anchor updating according to simplified mesh vertices, and thus capable of better expressing the deformation of mesh vertices, in particular those vertices far from them. In this way, the complexity of garment deformation space is reduced more effectively and more mesh shape details can be preserved.", + "bbox": [ + 75, + 507, + 468, + 763 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Then we investigate the impact of the penalty $\\mathcal{L}_{dir}$ (Eq. (11)) on the direction from the target anchor to the transformed one. As illustrated in Fig. 6, with $\\mathcal{L}_{dir}$ the model can reduce the garment-body interpenetration. By enforcing the transformed anchors to be on the positive direction of target normals, the garment mesh vertices influenced by these anchors can be effectively pushed to the outside of the body surface while keeping the deformation accuracy due to moving along the direction of target normals.", + "bbox": [ + 75, + 763, + 470, + 901 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We further assess the influence of the anchor number. Table 2 reports the results obtained by using 20, 80, 160 and 320 anchors, respectively. One can see that using more anchors to guide the mesh deformation obtains better results on all three metrics because the decomposition for the mesh deformation by using the rigid anchor transformations makes the nonlinear deformation can be more easily predicted as the small displacements in the canonical space without considering large rotations and translations caused by the body pose which has been handled by the anchor transformations. However, the performance drops as the number of anchors continues to increase because too many transformation parameters lead to unstable forecasts during testing. Fig. 7 shows the qualitative comparison. Using 160 anchors produces finer and more accurate deformation compared with other anchor numbers. Using 20 anchors only recover the contour of the deformed mesh, and using 80 and 320 anchors fail to obtain realistic deformation.", + "bbox": [ + 496, + 446, + 893, + 717 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Fig. 8 shows some examples of our AnchorDEF for dynamic garment deformation in motion. Given a body motion sequence, our method can produce natural and realistic clothing dynamics, e.g., wrinkles from jumping and the swing of the dress caused by running.", + "bbox": [ + 496, + 718, + 893, + 794 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Comparison with Related Methods", + "text_level": 1, + "bbox": [ + 498, + 801, + 805, + 816 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We compare our method against related 3D garment deformation methods, including TailorNet [26] and VirtualBones [25] on different types of garments. As reported in Table 3, our AnchorDEF achieves the best results in all cases. Fig. 9 presents the qualitative comparison. Tailor-", + "bbox": [ + 496, + 825, + 893, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "497", + "bbox": [ + 485, + 945, + 509, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/1b2f662995d3522f4cf8c266afb524ffd5ca6730cea08d6da99a0be212bd7b9e.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodsDressT-shirt
RMSE ↓Hausdorff ↓STED ↓RMSE ↓Hausdorff ↓STED ↓
TailorNet [26]22.9576.800.07579.9027.020.0418
VirtualBones [25]19.9183.390.072210.5231.510.0452
AnchorDEF16.0574.200.04936.2526.310.0262
", + "bbox": [ + 116, + 88, + 849, + 200 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 3. Quantitative results of 3D garment deformation methods for different types of garments.", + "bbox": [ + 196, + 205, + 771, + 220 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c2fc42c9781079f56af953332a1c481fc2dd90bbfb54721f148f675928a73b97.jpg", + "image_caption": [ + "(a)", + "Figure 9. Qualitative comparison of 3D garment deformation methods for different types of garments, including TailorNet [26], VirtualBones [25] and Our AnchorDEF. With the learned anchor transformations, our method not only recovers large deformations of the dress but also produces fine surface details on the T-shirt." + ], + "image_footnote": [], + "bbox": [ + 86, + 234, + 877, + 438 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Net [26] recovers folds on the T-shirt, but it fails to address the deformation of the dress which has different topology from human body. By interpolating the skinning blend weights, it alleviates the discontinuity of blend weights borrowed from the SMPL [20] body. However, this makes TailorNet only produce the outline of shapes with some folds missing and artifacts for large deformations of loose-fitting garments. VirtualBones [25] can estimate large deformations of the dress by using SSDR [17] to extract virtual bones of garments. However, it tends to keep the original folds of the dress template on the deformed mesh and cannot estimate well new folds generated by body motions on the T-shirt. VirtualBones needs SSDR to extract the garment skeleton and gets blend weights of bones in advance and fixes the bone position and blend weights during network training. Moreover, SSDR is performed on the low-frequency mesh sequences processed by Laplacian smoothing because it fails to address high-frequency garment deformations. Thus, the learned virtual bones are not necessarily optimal. In contrast, by jointly learning the rigid transformations, blend weights and positions of anchors, our AnchorDEF not only recovers large deformations of the dress but also produces fine surface details on the T-shirt. More qualitative results can be found in the supplemental materials.", + "bbox": [ + 75, + 522, + 472, + 898 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusions", + "text_level": 1, + "bbox": [ + 500, + 520, + 627, + 536 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We present AnchorDEF, an anchor based deformation model, to predict 3D garment animation given a body motion sequence. With a set of anchors around the mesh surface, the garment deformation can be decomposed into a mixture of rigid anchor transformations and extra per-vertex displacements in a canonical space. The transformation consistency learning is introduced to guarantee the physical meaning of learned anchor transformations in space. Taking mesh simplification as supervision, We further optimize the anchor position for learning representative anchor transformations by making the anchor aware of local mesh topology with an attention mask. Extensive experiments on different types of garments demonstrate that AnchorDEF can effectively predict 3D garment deformation in motion for both tight and loose-fitting garments.", + "bbox": [ + 496, + 553, + 890, + 781 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitations. Compared with the PBS methods, our method still lacks fine-level dynamics. Better exploiting the temporal information for the network architecture and supervision signals is a good direction for future work.", + "bbox": [ + 496, + 787, + 890, + 848 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments. This work was partly supported by the National Natural Science Foundation of China (Nos. 62276134).", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "498", + "bbox": [ + 485, + 945, + 509, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] David Baraff and Andrew Witkin. Large steps in cloth simulation. In Proceedings of the 25th annual conference on Computer graphics and interactive techniques, 1998. 2", + "[2] Hugo Bertiche, Meysam Madadi, and Sergio Escalera. Cloth3d: clothed 3d humans. In Proceedings of the European conference on computer vision (ECCV), 2020. 2", + "[3] Hugo Bertiche, Meysam Madadi, and Sergio Escalera. 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Tailornet: Predicting clothing in 3d as a function of human pose, shape and garment style. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2020. 1, 2, 3, 6, 7, 8", + "[27] Tobias Pfaff, Meire Fortunato, Alvaro Sanchez-Gonzalez, and Peter W. Battaglia. Learning mesh-based simulation with graph networks. In International Conference on Learning Representations, 2021. 1", + "[28] Gerard Pons-Moll, Sergi Pujades, Sonny Hu, and Michael J Black. Clothcap: Seamless 4d clothing capture and retargeting. ACM Transactions on Graphics (ToG), 2017. 1", + "[29] Xavier Provot. Collision and self-collision handling in cloth model dedicated to design garments. In Computer Animation and Simulation'97, pages 177-189. Springer, 1997. 2", + "[30] Albert Pumarola, Jordi Sanchez-Riera, Gary Choi, Alberto Sanfeliu, and Francesc Moreno-Noguer. 3dpeople: Modeling the geometry of dressed humans. In Proceedings of the IEEE/CVF international conference on computer vision, pages 2242-2251, 2019. 2" + ], + "bbox": [ + 501, + 92, + 890, + 898 + ], + "page_idx": 8 + }, + { + "type": "page_number", + "text": "499", + "bbox": [ + 485, + 945, + 509, + 955 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[31] Igor Santesteban, Miguel A. Otaduy, and Dan Casas. Learning-Based Animation of Clothing for Virtual Try-On. Computer Graphics Forum (Proc. Eurographics), 2019. 1, 2, 3, 6", + "[32] Igor Santesteban, Miguel A Otaduy, and Dan Casas. SNUG: Self-Supervised Neural Dynamic Garments. IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2022. 2", + "[33] Igor Santesteban, Miguel A. Otaduy, Nils Thuerey, and Dan Casas. ULNeF: Untangled layered neural fields for mix-and-match virtual try-on. In Advances in Neural Information Processing Systems, (NeurIPS), 2022. 2", + "[34] Igor Santesteban, Nils Thuerey, Miguel A Otaduy, and Dan Casas. Self-supervised collision handling via generative 3d garment models for virtual try-on. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2021. 1, 2", + "[35] Min Tang, Huamin Wang, Le Tang, Ruofeng Tong, and Dinesh Manocha. CAMA: Contact-aware matrix assembly with unified collision handling for GPU-based cloth simulation. Computer Graphics Forum (Proceedings of Eurographics 2016), 35(2):511-521, 2016. 2", + "[36] Libor Vasa and Vaclav Skala. A perception correlated comparison method for dynamic meshes. IEEE transactions on visualization and computer graphics (TVCG), 2010. 6", + "[37] Tuanfeng Y Wang, Tianjia Shao, Kai Fu, and Niloy J Mitra. Learning an intrinsic garment space for interactive authoring of garment animation. ACM Transactions on Graphics (TOG), 2019. 2", + "[38] Ilya Zakharkin, Kirill Mazur, Artur Grigorev, and Victor Lempitsky. Point-based modeling of human clothing. In Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), 2021. 2", + "[39] Meng Zhang, Tuanfeng Y Wang, Duygu Ceylan, and Niloy J Mitra. Dynamic neural garments. ACM Transactions on Graphics (TOG), 2021. 2", + "[40] Fang Zhao, Wenhao Wang, Shengcai Liao, and Ling Shao. Learning anchored unsigned distance functions with gradient direction alignment for single-view garment reconstruction. In Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), 2021. 1" + ], + "bbox": [ + 78, + 90, + 470, + 670 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "500", + "bbox": [ + 486, + 945, + 511, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Learning Anchor Transformations for 3D Garment Animation/172fc2a1-00b1-413a-bcb3-423ae7376cbc_model.json b/2023/Learning Anchor Transformations for 3D Garment Animation/172fc2a1-00b1-413a-bcb3-423ae7376cbc_model.json new file mode 100644 index 0000000000000000000000000000000000000000..391d484fd510b5a507b3962569f63d420c6be99f --- /dev/null +++ b/2023/Learning Anchor Transformations for 3D Garment Animation/172fc2a1-00b1-413a-bcb3-423ae7376cbc_model.json @@ -0,0 +1,1914 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.169, + 0.131, + 0.803, + 0.152 + ], + "angle": 0, + "content": "Learning Anchor Transformations for 3D Garment Animation" + }, + { + "type": "text", + "bbox": [ + 0.197, + 0.191, + 0.773, + 0.235 + ], + "angle": 0, + "content": "Fang Zhao\\(^{1}\\), Zekun Li\\(^{1}\\), Shaoli Huang\\(^{1*}\\), Junwu Weng\\(^{1}\\), Tianfei Zhou\\(^{2}\\), Guo-Sen Xie\\(^{3}\\), Jue Wang\\(^{1}\\), Ying Shan\\(^{1}\\)" + }, + { + "type": "text", + "bbox": [ + 0.167, + 0.241, + 0.798, + 0.26 + ], + "angle": 0, + "content": "\\(^{1}\\)Tencent AI Lab \\(^{2}\\)ETH Zurich \\(^{3}\\)Nanjing University of Science and Technology" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.296, + 0.314, + 0.312 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.328, + 0.474, + 0.646 + ], + "angle": 0, + "content": "This paper proposes an anchor-based deformation model, namely AnchorDEF, to predict 3D garment animation from a body motion sequence. It deforms a garment mesh template by a mixture of rigid transformations with extra nonlinear displacements. A set of anchors around the mesh surface is introduced to guide the learning of rigid transformation matrices. Once the anchor transformations are found, per-vertex nonlinear displacements of the garment template can be regressed in a canonical space, which reduces the complexity of deformation space learning. By explicitly constraining the transformed anchors to satisfy the consistencies of position, normal and direction, the physical meaning of learned anchor transformations in space is guaranteed for better generalization. Furthermore, an adaptive anchor updating is proposed to optimize the anchor position by being aware of local mesh topology for learning representative anchor transformations. Qualitative and quantitative experiments on different types of garments demonstrate that AnchorDEF achieves the state-of-the-art performance on 3D garment deformation prediction in motion, especially for loose-fitting garments." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.673, + 0.21, + 0.689 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.698, + 0.47, + 0.789 + ], + "angle": 0, + "content": "Animating 3D garments has a wide range of applications in 3D content generation, digital humans, virtual try-on, video games, and so on. Existing pipelines of 3D garment animation usually rely on physics based simulation (PBS), which requires a large amount of computational resources and time costs, particularly for high-quality PBS methods." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.789, + 0.47, + 0.88 + ], + "angle": 0, + "content": "Some data-driven or learning-based methods have been proposed to quickly produce 3D garment deformation from static poses or motion sequences with low computational complexity [4,5,9,11,12,16,25-28,31,40]. However, many of them attach garment templates to the skeleton of human body for modeling the articulation of garments, which" + }, + { + "type": "image", + "bbox": [ + 0.511, + 0.297, + 0.885, + 0.593 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.603, + 0.894, + 0.66 + ], + "angle": 0, + "content": "Figure 1. 3D garment deformation predicted by the proposed AnchorDEF with body motions. Leveraging the anchor transformations, AnchorDEF is able to realistically deform the garment mesh, especially for loose-fitting garments, e.g., dresses." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.893, + 0.824 + ], + "angle": 0, + "content": "only work with tight garments, e.g., T-shirts and pants, and poorly address loose-fitting ones, e.g., dresses and skirts. In this case, the topology of garments is different from the human body. Therefore, using the skinning blend weights of body yields discontinuities on deformed garment mesh. Several methods [26, 34] smooth out the blend weights to alleviate the discontinuities but may lose the shape details for large deformations of loose-fitting garments, which do not closely follow body movements." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.894, + 0.903 + ], + "angle": 0, + "content": "To this end, we propose an anchor-based deformation model, namely AnchorDEF, for predicting 3D garment deformation from a body motion sequence. It leverages a mixture of rigid anchor transformations to represent principle rotations and translations of garments to detach the" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.888, + 0.222, + 0.9 + ], + "angle": 0, + "content": "*Corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.486, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "491" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.182 + ], + "angle": 0, + "content": "garment articulation from the body skeleton while preserving the body movement prior, then nonlinear displacements can be regressed relatively easily in a canonical space. As shown in Fig. 1, our method can exploit anchor transformations to realistically deform the garment mesh, especially for loose-fitting garments, e.g., dresses." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.183, + 0.471, + 0.497 + ], + "angle": 0, + "content": "Specifically, given a sequence of body motions including poses and translations, we first estimate rigid transformations of a set of anchors around the garment mesh. Using the linear blending skinning (LBS), the garment mesh template is deformed by a weighted combination of the anchor transformations meanwhile per-vertex displacements of the mesh template are regressed to correct artifacts of the blended rigid transformations. To learn physically meaningful anchor transformations for better generalization, we enforce the transformed anchors to maintain consistency with the target's position and normal. In addition, a relative direction constraint is employed to reduce garment-body interpenetrations, which is efficient due to the sparseness of anchors. To make the learned anchor transformations effectively represent the garment deformation, an adaptive anchor updating is further introduced to utilize mesh simplification as supervision to optimize the anchor position. It parameterizes the position with a local attention mask on adjacent mesh vertices and pushes the anchors towards folds and boundaries of garment mesh which usually determine the way of deformation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.5, + 0.47, + 0.68 + ], + "angle": 0, + "content": "The main contributions of our work can be summarized as follows: 1) We propose an anchor-based deformation model which learns a set of anchor transformations and blend weights in a unified framework to represent the deformation of 3D garments, especially for loose-fitting ones. 2) We propose to learn anchor transformations by position and normal consistencies as well as relative direction constraint for better generalization and fewer garment-body interpenetrations. 3) We introduce an adaptive anchor updating with the mesh simplification as supervision to optimize the anchor position for learning representative anchor transformations." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.695, + 0.219, + 0.71 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.47, + 0.765 + ], + "angle": 0, + "content": "Most garment animation and deformation works can be categorized into physics-based simulations (PBS) and learning-based models." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.469, + 0.87 + ], + "angle": 0, + "content": "Physics-based simulations. PBS methods have been developed for decades and achieved impressive accuracy, leveraging laws of physics and stable accurate solvers [1, 13, 18], collision detection [23, 29, 35], and dry frictional contact [19, 21]. But the expensive computational costs, i.e., long simulation time and high-performance devices often are unaffordable in our daily lives." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Learning-based models. In contrast, learning-based models, which utilize garment animation data attained from PBS" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.485 + ], + "angle": 0, + "content": "or digital scanning to learn the deformation, can often give satisfactory enough animation visual results with less computational costs [26, 31], regardless of no explicit physical guarantee on accuracy. Previously, researchers have proposed many techniques depending on the motions of human bodies with linear conditional models [8, 11] or secondary motion graphs [14, 15], with a constructed database of high-resolution meshes. Recent works [4, 26, 34] assume that the garment is a submesh of the skinned multi-person linear model (SMPL) and use linear blend skinning (LBS) to transfer body shape to cloth shape. Beyond learning static results within a single frame, adopting recurrent neural networks to handle the dynamic wrinkles of clothes is widely used [25, 31, 34]. For example, [31] prepares a database of PBS for dressed characters with some body shapes and motion and uses the database to learn a function of body shape and dynamics for modeling cloth drape and wrinkles. Although learning-based models can be efficient, their performance heavily relies on large amounts of high-quality PBS results or scanning data, which are usually costly [2, 30, 34]. Thus, some works [3, 32] propose self-supervised training methods to constrain the model with some sort of physical laws to alleviate this problem. Additionally, to ensure the generalization of simulation, combining several pretrained pivot motion networks can handle different unseen garment styles [26] and simulation parameters [25]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.489, + 0.892, + 0.807 + ], + "angle": 0, + "content": "But most learning-based methods are limited to tight garments and not suitable for dresses or clothes with more freedom, due to their assumption that garments are complementary to SMPL, i.e., the deformation is closely related to body shape, not the motion. To tackle the dynamics, some works propose a neural field to retain high-frequency details [39], handle challenging areas [22], tackle multi-layer garments [33], and warp garments from the canonical pose to the deformation shape [6]. Without utilizing body shape parameters to establish a garment-body aligned model, [37] learns an intrinsic cloth shape descriptor embedding space and using different motion parameters to guide garment latent can attain different shape representation. To eliminate the alignment between clothes dynamics and body vertices, VirtualBones [25] extracts a set of rigid bones from the garment animation and uses body motion to predict the bones' transformation to interpolate the garment shape. Instead of learning based on mesh, [38] uses a point transformer to predict point clouds of various outfits, for various human poses and shapes, which attains more topological flexibility and the ability to model clothing separately from the body." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.892, + 0.9 + ], + "angle": 0, + "content": "VirtualBones [25] is the most related work to our method, which requires garment skeleton extraction with SSDR [17] as data preprocessing. Different from [25], we decompose the garment deformation by a set of adaptive anchors whose rigid transformations and blend weights are learned in a unified framework." + }, + { + "type": "page_number", + "bbox": [ + 0.486, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "492" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.092, + 0.089, + 0.885, + 0.381 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.389, + 0.896, + 0.475 + ], + "angle": 0, + "content": "Figure 2. Overview of the proposed AnchorDEF. Given a body motion sequence and a garment mesh template, the garment deformation is predicted by a weighted average of rigid anchor transformations with per-vertex displacements in a canonical space. We explicitly constrain the transformed anchors to satisfy the consistencies of position, normal and direction to guarantee the physical meaning of learned anchor transformations in space for better generalization. Starting from the cluster centers of mesh vertices, the anchor position is updated by a local attention map on adjacent mesh vertices with mesh simplification as supervision. All parameters in our model can be jointly optimized in a unified framework." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.488, + 0.208, + 0.503 + ], + "angle": 0, + "content": "3. Our Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.513, + 0.473, + 0.664 + ], + "angle": 0, + "content": "We aim to learn an animated model which is able to predict dynamic 3D garment deformations given a body motion sequence. In this section, we introduce AnchorDEF, an anchor-based deformation model, which leverages s set of adaptive anchors around mesh surface to deform a garment mesh template by a mixture of rigid anchor transformations with additional per-vertex displacements in a canonical space, where the anchor transformations are learned by the consistencies of position, normal and direction. The overview of AnchorDEF is illustrated in Fig. 2." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.673, + 0.32, + 0.687 + ], + "angle": 0, + "content": "3.1. Deformation with Anchors" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.696, + 0.47, + 0.743 + ], + "angle": 0, + "content": "3D animated models of human body, e.g., SMPL [20], usually deform a body mesh template \\(\\mathbf{T}\\) with blendshapes and skinning, which can be defined as" + }, + { + "type": "equation", + "bbox": [ + 0.175, + 0.753, + 0.47, + 0.77 + ], + "angle": 0, + "content": "\\[\nV = W (\\mathbf {T} + B (\\theta), \\mathbf {J}, \\theta , \\mathbf {w}), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.473, + 0.903 + ], + "angle": 0, + "content": "where \\(W\\) is a skinning function, e.g., linear blend skinning, with a skeleton \\(\\mathbf{J}\\), pose parameters \\(\\theta\\) and blend weights \\(\\mathbf{w}\\), \\(V\\) is the posed vertices and \\(B\\) is the blendshape corresponding to the body pose \\(\\theta\\). Since the garment is a kind of soft body and it is hard to directly predict the coordinates of each vertex from a body motion sequence, here we also consider to decompose the garment deformation into two parts including a weighed average of rigid transformations and" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.49, + 0.668, + 0.504 + ], + "angle": 0, + "content": "nonlinear displacements." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.505, + 0.892, + 0.67 + ], + "angle": 0, + "content": "Most data-driven garment models directly associate garments with the skeleton of human body [4,26,31], i.e., they apply the skinning function to animate the garment by directly using the blend weights of body mesh vertices in the neighborhood, where it is assumed that garments closely follow the body movement. However, for loose-fitting garments, the clothing deformation usually contains more complex nonrigid effects compared to human body which can be seen as a rigid body. In this case, garments behave significantly differently from the body. Thus, it is unreasonable to attach the garment to the body skeleton." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.671, + 0.893, + 0.837 + ], + "angle": 0, + "content": "To address this issue, we adopt a set of anchors \\(\\{p_n\\}\\) around the mesh surface to guide the garment deformation, which detaches the garment from the body skeleton while preserving the body movement prior. Given a body motion sequence consisting of poses and translations, rigid anchor transformations including rotations \\(\\{R_{n}\\}\\) and translations \\(\\{T_{n}\\}\\) are estimated firstly by using Gated Recurrent Units (GRU) [7] (see the supplementary material for the network structure). Then, the \\(m\\) -th deformed garment vertex \\(v_{m}\\) can be represented by a weighted average of anchor transformations:" + }, + { + "type": "equation", + "bbox": [ + 0.499, + 0.847, + 0.892, + 0.901 + ], + "angle": 0, + "content": "\\[\nv _ {m} = \\sum_ {n = 1} ^ {N} w _ {m n} \\left(R _ {n} v _ {m} ^ {c} + T _ {n}\\right), w _ {m n} \\geq 0 \\text {a n d} \\sum_ {n = 1} ^ {N} w _ {m n} = 1, \\tag {2}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.486, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "493" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.272 + ], + "angle": 0, + "content": "where \\( v_{m}^{c} \\) is the \\( m \\)-th vertex of garment mesh template, \\( w_{mn} \\) is the blend weight of \\( v_{m} \\) regarding to the \\( n \\)-th anchor and \\( N \\) is the number of anchors. To determine the anchor-vertex relationship and maintain the sparsity of \\( \\{w_{n}\\} \\), we initialize the anchors as the clustering centers of vertices of the mesh template. Then, each vertex is only influenced by the blend weights of its \\( N' \\) (\\( N' \\ll N \\)) nearest anchors and the others remain zeros during training. Compared to the direct prediction of deformed mesh vertex coordinates, the rigid anchor transformations provide more generalized representations of complex deformations due to fewer parameters required to be learned for the prediction." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.273, + 0.473, + 0.364 + ], + "angle": 0, + "content": "Two strategies of anchor transformation configuration are designed for loose and tight types of garments. For the loose type, to utilize the prior of the global human body orientation \\( R_{global} \\), we predict transformations relative to the root joint \\( J_{root} \\) of the body and the anchor transformation can be defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.09, + 0.374, + 0.469, + 0.427 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} R _ {n} ^ {\\text {l o o s e}} = R _ {\\text {g l o b a l}} R _ {n} ([ \\theta , t ]), \\\\ T _ {n} ^ {\\text {l o o s e}} = R _ {\\text {g l o b a l}} \\left(T _ {n} ([ \\theta , t ]) - R _ {n} ([ \\theta , t ]) J _ {\\text {r o o t}}\\right) + J _ {\\text {r o o t}}, \\tag {3} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.439, + 0.47, + 0.502 + ], + "angle": 0, + "content": "where \\(\\theta\\) and \\(t\\) are the body pose and translation, respectively. For the tight type, the garment mostly follows the body movement. Thus, we predict an incremental change on the basis of body vertex rotation \\(R_{body}\\) and offset \\(T_{body}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.158, + 0.509, + 0.47, + 0.55 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} R _ {n} ^ {t i g h t} = R _ {b o d y} R _ {n} ([ \\theta , t ]), \\\\ T _ {n} ^ {\\text {t i g h t}} = R _ {\\text {b o d y}} T _ {n} ([ \\theta , t ]) + T _ {\\text {b o d y}}, \\tag {4} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.56, + 0.47, + 0.635 + ], + "angle": 0, + "content": "where \\( R_{body} \\) and \\( T_{body} \\) is the transformation of the body mesh vertex closest to the anchor \\( p_n \\). Furthermore, we can combine these two strategies for garments with both tight and loose parts, e.g., dresses, by classifying which part the anchor belongs to according to its distance to body joints." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.635, + 0.47, + 0.742 + ], + "angle": 0, + "content": "Once the primary rotations and translations in the garment deformation caused by the articulation are expressed in Eq. (2), the nonlinear residual deformation can be disentangled with the garment articulation and defined as pervertex displacements \\( D([\\theta, t]) \\) in an unposed canonical space. Utilizing the skinning function in Eq. (1), the overall garment deformation is given by" + }, + { + "type": "equation", + "bbox": [ + 0.13, + 0.752, + 0.469, + 0.771 + ], + "angle": 0, + "content": "\\[\nV _ {p r e d} = W \\left(\\mathbf {T} _ {g} + D ([ \\theta , t ]), G ([ \\theta , t ]), \\mathbf {w} _ {p}\\right), \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.473, + 0.903 + ], + "angle": 0, + "content": "where \\(\\mathbf{T}_g\\) is the garment mesh template, \\(\\mathbf{w}_p\\) is the anchor-vertex blend weights and \\(G([\\theta ,t])\\) is the anchor transformations predicted with the body motion. We argue that such decomposition by anchors extremely reduces the complexity of pose-dependent garment deformation prediction because large deformations have been handled by transformations of sparse anchors and only small displacements need to be regressed in the canonical space." + }, + { + "type": "image", + "bbox": [ + 0.515, + 0.09, + 0.88, + 0.155 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.168, + 0.895, + 0.224 + ], + "angle": 0, + "content": "Figure 3. Examples of adaptive anchor updating by using the local attention mask with the mesh simplification as supervision. The blue points are anchors initialized by \\( k \\)-means and the orange ones are the updated anchors." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.246, + 0.803, + 0.262 + ], + "angle": 0, + "content": "3.2. Learning Anchor Transformations" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.269, + 0.892, + 0.344 + ], + "angle": 0, + "content": "Different from [25] which resorts to the external skinning decomposition algorithm, i.e., SSDR [17], to extract the garment skeleton from smoothed mesh sequences, here we jointly learn rigid transformations, blend weights and positions of anchors in a unified framework." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.345, + 0.892, + 0.376 + ], + "angle": 0, + "content": "We first apply an L2 loss term on the predicted mesh vertices to recover the shape of deformed mesh:" + }, + { + "type": "equation", + "bbox": [ + 0.613, + 0.381, + 0.892, + 0.401 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {r e c} = \\left| \\left| V _ {p r e d} - V _ {g t} \\right| \\right| _ {2} ^ {2}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.407, + 0.892, + 0.466 + ], + "angle": 0, + "content": "which minimizes the Euclidean distance between the predicted vertices and the ground-truth deformed vertices. Then a loss term is used to keep the similarity of the graph Laplacians between two meshes:" + }, + { + "type": "equation", + "bbox": [ + 0.596, + 0.473, + 0.892, + 0.492 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {l a p} = \\left\\| \\triangle V _ {p r e d} - \\triangle V _ {g t} \\right\\| _ {2} ^ {2}. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.498, + 0.892, + 0.529 + ], + "angle": 0, + "content": "A collision term [25] is also added to avoid garment-body collisions. Thus, the loss on the vertex can be given by" + }, + { + "type": "equation", + "bbox": [ + 0.564, + 0.537, + 0.892, + 0.553 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {v e r t}} = \\mathcal {L} _ {\\text {r e c}} + \\beta_ {1} \\mathcal {L} _ {\\text {l a p}} + \\beta_ {2} \\mathcal {L} _ {\\text {c o l l i s i o n}}, \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.56, + 0.892, + 0.59 + ], + "angle": 0, + "content": "where \\(\\beta_{1}\\) and \\(\\beta_{2}\\) are trade-off coefficients for controlling the degree of smoothing and collision, respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.59, + 0.892, + 0.692 + ], + "angle": 0, + "content": "However, only optimizing the vertex position cannot guarantee the physical meaning of learned anchor transformations in space, which leads to poor generalization. Thus, we explicitly constrain the transformed anchors to be located around the deformed mesh surface. To this end, the position of anchor \\( p \\) is recalculated by its adjacent mesh vertices:" + }, + { + "type": "equation", + "bbox": [ + 0.618, + 0.691, + 0.892, + 0.73 + ], + "angle": 0, + "content": "\\[\np = \\frac {1}{K} \\sum_ {v _ {k} ^ {c} \\in K (p, \\mathbf {T} _ {g})} v _ {k} ^ {c}, \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.733, + 0.892, + 0.809 + ], + "angle": 0, + "content": "where \\( K(p, \\mathbf{T}_g) \\) is the \\( K \\) nearest vertices of \\( p \\) on the mesh template. Then, the target point \\( p_{tgt} \\) of transformed anchor \\( p_G \\) can be defined with the same set of vertices \\( K(p, \\mathbf{T}_g) \\) on the deformed mesh and a transformation consistency loss is defined as" + }, + { + "type": "equation", + "bbox": [ + 0.514, + 0.816, + 0.892, + 0.835 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {c o n s i s}} = \\left\\| p _ {G} - p _ {t g t} \\right\\| _ {2} ^ {2} + \\gamma \\left\\| \\mathbf {n} \\left(p _ {G}\\right) - \\mathbf {n} \\left(p _ {t g t}\\right) \\right\\| _ {2} ^ {2}, \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "where \\(\\mathbf{n}(.)\\) is the unit normal of point and \\(\\gamma\\) is a weight factor. By encouraging the transformed anchor \\(p_G\\) to be similar to \\(p_{tgt}\\) in position and normal, the learned anchor transformation indicates the mean transformation of \\(K\\) nearest" + }, + { + "type": "page_number", + "bbox": [ + 0.486, + 0.946, + 0.512, + 0.957 + ], + "angle": 0, + "content": "494" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.088, + 0.09, + 0.88, + 0.376 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.379, + 0.893, + 0.435 + ], + "angle": 0, + "content": "Figure 4. Qualitative comparison with and without different components of AnchorDEF including (a) anchor transformation consistency \\(\\mathcal{L}_{consis}\\) and (b) adaptive anchor updating \\(\\mathcal{L}_{anch}\\). Without \\(\\mathcal{L}_{consis}\\), the model cannot accurately predict the shape of deformed mesh and loses some surface geometry details. Without \\(\\mathcal{L}_{anch}\\), the model is unable to produce realistic garment deformations due to the under-expressed anchor transformations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.461, + 0.47, + 0.506 + ], + "angle": 0, + "content": "vertices of \\( p \\). It can be viewed as a regularization for the transformation magnitude and direction to discover essential transformations in deformation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.507, + 0.471, + 0.552 + ], + "angle": 0, + "content": "We further enforce the direction from \\( p_{tgt} \\) to \\( p_G \\) to be consistent with the direction of \\( \\mathbf{n}(p_{tgt}) \\) by minimizing the following penalty term:" + }, + { + "type": "equation", + "bbox": [ + 0.151, + 0.558, + 0.47, + 0.575 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {d i r} = 1 - \\cos \\left(p _ {G} - p _ {t g t}, \\mathbf {n} \\left(p _ {t g t}\\right)\\right), \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.58, + 0.47, + 0.731 + ], + "angle": 0, + "content": "where \\(\\cos (\\cdot ,\\cdot)\\) is the cosine similarity. Intuitively, this penalty term makes \\(p_{G}\\) tend to be outside of the plane formed by \\(p_{tgt}\\) to reduce the garment-body interpenetration. Adaptive Anchor Updating. It is still not enough to have a physically meaningful anchor transformation, we also need an expressive transformation in geometry to better represent the garment deformation. We observe that mesh regions with folds and boundaries usually play an important role on showing garment shape characteristics and contain more deformation information compared with smooth regions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.731, + 0.471, + 0.867 + ], + "angle": 0, + "content": "To make the anchors reflect such intrinsic structure of garment shape, we propose to employ mesh simplification to provide a signal of supervision for finding such representative anchors. Here Quadric Error Metric (QEM) [10] is used to obtain simplified mesh vertices by collapsing edges while preserving the garment topology. Because there is no one-to-one correspondence between the anchors \\(\\{p_n\\}\\) and the simplified vertices \\(\\{\\tilde{v}_m\\}\\), the Chamfer distance is adopted as the optimization objective:" + }, + { + "type": "equation", + "bbox": [ + 0.095, + 0.871, + 0.47, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {a n c h} = \\sum_ {p} \\min _ {\\tilde {v}} | | p - \\tilde {v} | | _ {2} ^ {2} + \\sum_ {\\tilde {v}} \\min _ {p} | | p - \\tilde {v} | | _ {2} ^ {2}. \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.461, + 0.892, + 0.492 + ], + "angle": 0, + "content": "To be able to update the anchor position, we rewrite Eq. (9) using learnable weights \\(\\alpha\\) as" + }, + { + "type": "equation", + "bbox": [ + 0.605, + 0.501, + 0.892, + 0.545 + ], + "angle": 0, + "content": "\\[\np = \\frac {1}{\\sum_ {j = 1} ^ {K} e ^ {\\alpha_ {j}}} \\sum_ {k = 1} ^ {K} e ^ {\\alpha_ {k}} v _ {k} ^ {c}. \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.553, + 0.893, + 0.704 + ], + "angle": 0, + "content": "Actually, this equals to learning a local attention mask for the anchor to determine how the adjacent vertices contribute to its position. Fig. 3 shows that by optimizing the weights \\(\\alpha\\) with supervision of the simplified vertices, the anchors are pushed to inflection points of folds and boundaries of the mesh and thus able to better represent the deformed mesh vertices by interpolating their transformation matrices. Note that we optimize the anchor position on the entire dataset not only on the mesh template because some smooth regions of the template may create new folds after posing." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.892, + 0.734 + ], + "angle": 0, + "content": "On the other hand, if we reformulate the transformed anchor \\( p_G \\) with Eq. (13) as:" + }, + { + "type": "equation", + "bbox": [ + 0.52, + 0.744, + 0.892, + 0.787 + ], + "angle": 0, + "content": "\\[\np _ {G} = R p + T = \\frac {1}{\\sum_ {j = 1} ^ {K} e ^ {\\alpha_ {j}}} \\sum_ {k = 1} ^ {K} e ^ {\\alpha_ {k}} \\left(R v _ {k} ^ {c} + T\\right), \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.892, + 0.901 + ], + "angle": 0, + "content": "the process of transformation learning for the anchor, i.e., Eq. (10), can be interpreted as a way to find an appropriate transformation for its adjacent mesh vertices by the importance which is reflected in the weights learned from the mesh simplification. The larger the weight, the greater the impact of the vertex transformation on the anchor transformation learning." + }, + { + "type": "page_number", + "bbox": [ + 0.486, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "495" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.092, + 0.162, + 0.113, + 0.178 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.126, + 0.091, + 0.26, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.291, + 0.162, + 0.314, + 0.178 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image", + "bbox": [ + 0.335, + 0.095, + 0.453, + 0.243 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.261, + 0.47, + 0.292 + ], + "angle": 0, + "content": "Figure 5. Visualization of anchors transformed by (a) only optimizing the mesh vertices during training and (b) AnchorDEF." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.317, + 0.47, + 0.348 + ], + "angle": 0, + "content": "Lastly, combining Eq. (8), Eqs. (10) to (12), the overall objective function for our model is given by:" + }, + { + "type": "equation", + "bbox": [ + 0.105, + 0.36, + 0.469, + 0.377 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {\\text {v e r t}} + \\lambda_ {1} \\mathcal {L} _ {\\text {c o n s i s}} + \\lambda_ {2} \\mathcal {L} _ {\\text {d i r}} + \\lambda_ {3} \\mathcal {L} _ {\\text {a n c h}}, \\tag {15}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.389, + 0.254, + 0.404 + ], + "angle": 0, + "content": "where \\(\\lambda\\)s are loss weights." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.419, + 0.21, + 0.436 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.444, + 0.47, + 0.595 + ], + "angle": 0, + "content": "We evaluate the proposed AnchorDEF on the VTO [31] dataset containing two types of garments, i.e., dress and T-shirt. Following [25], RMSE (Root Mean Squared Error), Hausdorff distance and STED (Spatio-Temporal Edge Difference) [36] are adopted to assess the quality of deformed meshes. The first two measure the distance between predicted and ground truth meshes and STED reflects the difference between their dynamics. We also compare AnchorDEF against other 3D garment deformation methods [25, 26]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.596, + 0.471, + 0.791 + ], + "angle": 0, + "content": "Implementation Details. To capture the motion dynamics, a network with 2 GRU layers of size 256 is used as the body motion encoder. Two 2-layered MLPs of size 256 are used to regress the anchor transformations and per-vertex displacements, respectively. The number of anchors associated with each mesh vertex is set to 8, which can obtain the desired smooth surface, and the number of neighboring vertices for computing the anchor position is set to 128. For the garment sequences of VTO, 4 clips are randomly selected for testing and the rest is used as the training set, and the length of training sequence is 30. Please refer to the supplemental materials for more details on training and inference." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.802, + 0.231, + 0.818 + ], + "angle": 0, + "content": "4.1. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.825, + 0.471, + 0.901 + ], + "angle": 0, + "content": "We validate the effectiveness of main components in our proposed AnchorDEF. We firstly assess the importance of anchor transformation consistency, i.e., \\(\\mathcal{L}_{\\text{consis}}\\) in Eq. (10). As reported in Table 1, keeping the consistency of learned anchor transformations is able to improve all metrics due" + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.09, + 0.891, + 0.179 + ], + "angle": 0, + "content": "
Methodsw/o Lconsisw/o LanchAnchorDEF
RMSE ↓17.2116.4916.05
Hausdorff ↓75.0174.5374.20
STED ↓0.05950.05260.0493
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.19, + 0.894, + 0.245 + ], + "angle": 0, + "content": "Table 1. Quantitative results obtained by different components of AnchorDEF, i.e., without anchor transformation consistency (w/o \\(\\mathcal{L}_{\\text{cosis}}\\)), without adaptive anchor updating (w/o \\(\\mathcal{L}_{\\text{anch}}\\)) and the full model (AnchorDEF)." + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.263, + 0.89, + 0.356 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.363, + 0.893, + 0.404 + ], + "angle": 0, + "content": "Figure 6. Qualitative comparison with and without the penalty \\(\\mathcal{L}_{dir}\\) on the direction from the target anchor to the transformed one." + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.423, + 0.89, + 0.535 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.543, + 0.894, + 0.586 + ], + "angle": 0, + "content": "Figure 7. Qualitative comparison of using different numbers of anchors. Using 160 anchors produces finer and more accurate deformation compared with other anchor numbers." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.601, + 0.891, + 0.692 + ], + "angle": 0, + "content": "
Num. Anchor2080160320
RMSE ↓17.7816.8216.0517.52
Hausdorff ↓75.3074.7174.2075.13
STED ↓0.06200.05390.04930.0625
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.702, + 0.89, + 0.716 + ], + "angle": 0, + "content": "Table 2. Quantitative results of using different numbers of anchors." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.734, + 0.891, + 0.795 + ], + "angle": 0, + "content": "to better generalization. Fig. 4 (a) illustrates the qualitative comparison. One can observe that without \\(\\mathcal{L}_{\\text {consis }}\\) the model cannot accurately predict the shape of deformed mesh and loses some surface geometry details." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.892, + 0.901 + ], + "angle": 0, + "content": "To evaluate the influence of adaptive anchor updating, Table 1 also reports the results without using \\(\\mathcal{L}_{anch}\\) in Eq. (12). The performance drops only using the clustering centers of \\(k\\)-means as the anchors. The reason is that compared with the clustering, the supervision with mesh simplification can provide key topology information, e.g., folds and boundaries, which is useful for learning representative" + }, + { + "type": "page_number", + "bbox": [ + 0.486, + 0.946, + 0.512, + 0.957 + ], + "angle": 0, + "content": "496" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.091, + 0.091, + 0.881, + 0.373 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.385, + 0.893, + 0.429 + ], + "angle": 0, + "content": "Figure 8. Examples of our AnchorDEF for dynamic garment deformation in motion. The first row is the ground truth generated by physics-based simulation [24]. The second row is the results obtained by AnchorDEF. Our method can produce natural and realistic clothing dynamics, e.g., wrinkles from jumping and the swing of the dress caused by running." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.447, + 0.471, + 0.507 + ], + "angle": 0, + "content": "anchor transformations. The qualitative results are shown in Fig. 4 (b). It can be observed that without \\(\\mathcal{L}_{anch}\\) the model is unable to produce realistic garment deformations due to the under-expressed anchor transformations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.508, + 0.47, + 0.765 + ], + "angle": 0, + "content": "Fig. 5 (a) and (b) visualize the anchors transformed by only optimizing the mesh vertices during training and AnchorDEF, respectively. For Fig. 5 (a), without the consistency constraint for anchor transformation, many of the transformed anchors are not on the deformed mesh surface, which is lack of clear physical meaning in space and easy to overfit. In contrast, AnchorDEF enforces the anchors to be transformed onto the deformed mesh surface, which prevents overfitting to a certain extent, thus has better generalization when testing. Furthermore, as shown in Fig. 5 (b), the transformed anchors are mainly distributed at the folds and boundaries of the mesh because of our adaptive anchor updating according to simplified mesh vertices, and thus capable of better expressing the deformation of mesh vertices, in particular those vertices far from them. In this way, the complexity of garment deformation space is reduced more effectively and more mesh shape details can be preserved." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Then we investigate the impact of the penalty \\(\\mathcal{L}_{dir}\\) (Eq. (11)) on the direction from the target anchor to the transformed one. As illustrated in Fig. 6, with \\(\\mathcal{L}_{dir}\\) the model can reduce the garment-body interpenetration. By enforcing the transformed anchors to be on the positive direction of target normals, the garment mesh vertices influenced by these anchors can be effectively pushed to the outside of the body surface while keeping the deformation accuracy due to moving along the direction of target normals." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.447, + 0.895, + 0.718 + ], + "angle": 0, + "content": "We further assess the influence of the anchor number. Table 2 reports the results obtained by using 20, 80, 160 and 320 anchors, respectively. One can see that using more anchors to guide the mesh deformation obtains better results on all three metrics because the decomposition for the mesh deformation by using the rigid anchor transformations makes the nonlinear deformation can be more easily predicted as the small displacements in the canonical space without considering large rotations and translations caused by the body pose which has been handled by the anchor transformations. However, the performance drops as the number of anchors continues to increase because too many transformation parameters lead to unstable forecasts during testing. Fig. 7 shows the qualitative comparison. Using 160 anchors produces finer and more accurate deformation compared with other anchor numbers. Using 20 anchors only recover the contour of the deformed mesh, and using 80 and 320 anchors fail to obtain realistic deformation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.719, + 0.895, + 0.795 + ], + "angle": 0, + "content": "Fig. 8 shows some examples of our AnchorDEF for dynamic garment deformation in motion. Given a body motion sequence, our method can produce natural and realistic clothing dynamics, e.g., wrinkles from jumping and the swing of the dress caused by running." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.802, + 0.807, + 0.818 + ], + "angle": 0, + "content": "4.2. Comparison with Related Methods" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.894, + 0.903 + ], + "angle": 0, + "content": "We compare our method against related 3D garment deformation methods, including TailorNet [26] and VirtualBones [25] on different types of garments. As reported in Table 3, our AnchorDEF achieves the best results in all cases. Fig. 9 presents the qualitative comparison. Tailor-" + }, + { + "type": "page_number", + "bbox": [ + 0.486, + 0.946, + 0.511, + 0.956 + ], + "angle": 0, + "content": "497" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.117, + 0.089, + 0.85, + 0.201 + ], + "angle": 0, + "content": "
MethodsDressT-shirt
RMSE ↓Hausdorff ↓STED ↓RMSE ↓Hausdorff ↓STED ↓
TailorNet [26]22.9576.800.07579.9027.020.0418
VirtualBones [25]19.9183.390.072210.5231.510.0452
AnchorDEF16.0574.200.04936.2526.310.0262
" + }, + { + "type": "table_caption", + "bbox": [ + 0.197, + 0.207, + 0.772, + 0.222 + ], + "angle": 0, + "content": "Table 3. Quantitative results of 3D garment deformation methods for different types of garments." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.235, + 0.879, + 0.439 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.255, + 0.439, + 0.272, + 0.45 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.453, + 0.893, + 0.496 + ], + "angle": 0, + "content": "Figure 9. Qualitative comparison of 3D garment deformation methods for different types of garments, including TailorNet [26], VirtualBones [25] and Our AnchorDEF. With the learned anchor transformations, our method not only recovers large deformations of the dress but also produces fine surface details on the T-shirt." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.523, + 0.473, + 0.9 + ], + "angle": 0, + "content": "Net [26] recovers folds on the T-shirt, but it fails to address the deformation of the dress which has different topology from human body. By interpolating the skinning blend weights, it alleviates the discontinuity of blend weights borrowed from the SMPL [20] body. However, this makes TailorNet only produce the outline of shapes with some folds missing and artifacts for large deformations of loose-fitting garments. VirtualBones [25] can estimate large deformations of the dress by using SSDR [17] to extract virtual bones of garments. However, it tends to keep the original folds of the dress template on the deformed mesh and cannot estimate well new folds generated by body motions on the T-shirt. VirtualBones needs SSDR to extract the garment skeleton and gets blend weights of bones in advance and fixes the bone position and blend weights during network training. Moreover, SSDR is performed on the low-frequency mesh sequences processed by Laplacian smoothing because it fails to address high-frequency garment deformations. Thus, the learned virtual bones are not necessarily optimal. In contrast, by jointly learning the rigid transformations, blend weights and positions of anchors, our AnchorDEF not only recovers large deformations of the dress but also produces fine surface details on the T-shirt. More qualitative results can be found in the supplemental materials." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.521, + 0.628, + 0.537 + ], + "angle": 0, + "content": "5. Conclusions" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.554, + 0.892, + 0.782 + ], + "angle": 0, + "content": "We present AnchorDEF, an anchor based deformation model, to predict 3D garment animation given a body motion sequence. With a set of anchors around the mesh surface, the garment deformation can be decomposed into a mixture of rigid anchor transformations and extra per-vertex displacements in a canonical space. The transformation consistency learning is introduced to guarantee the physical meaning of learned anchor transformations in space. Taking mesh simplification as supervision, We further optimize the anchor position for learning representative anchor transformations by making the anchor aware of local mesh topology with an attention mask. Extensive experiments on different types of garments demonstrate that AnchorDEF can effectively predict 3D garment deformation in motion for both tight and loose-fitting garments." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.788, + 0.892, + 0.849 + ], + "angle": 0, + "content": "Limitations. Compared with the PBS methods, our method still lacks fine-level dynamics. Better exploiting the temporal information for the network architecture and supervision signals is a good direction for future work." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Acknowledgments. This work was partly supported by the National Natural Science Foundation of China (Nos. 62276134)." + }, + { + "type": "page_number", + "bbox": [ + 0.486, + 0.946, + 0.511, + 0.956 + ], + "angle": 0, + "content": "498" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.469, + 0.156 + ], + "angle": 0, + "content": "[1] David Baraff and Andrew Witkin. Large steps in cloth simulation. In Proceedings of the 25th annual conference on Computer graphics and interactive techniques, 1998. 2" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.157, + 0.469, + 0.199 + ], + "angle": 0, + "content": "[2] Hugo Bertiche, Meysam Madadi, and Sergio Escalera. Cloth3d: clothed 3d humans. 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In Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), 2021. 1" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.471, + 0.671 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.487, + 0.946, + 0.512, + 0.957 + ], + "angle": 0, + "content": "500" + } + ] +] \ No newline at end of file diff --git a/2023/Learning Anchor Transformations for 3D Garment Animation/172fc2a1-00b1-413a-bcb3-423ae7376cbc_origin.pdf b/2023/Learning Anchor Transformations for 3D Garment Animation/172fc2a1-00b1-413a-bcb3-423ae7376cbc_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..014561a6b50eab570b23f622e04c94941e68d69a --- /dev/null +++ b/2023/Learning Anchor Transformations for 3D Garment Animation/172fc2a1-00b1-413a-bcb3-423ae7376cbc_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:a76e3547a0a4f0e50452b55c8f24298385f181ec2c47203b27e831f53b340e5f +size 7749734 diff --git a/2023/Learning Anchor Transformations for 3D Garment Animation/full.md b/2023/Learning Anchor Transformations for 3D Garment Animation/full.md new file mode 100644 index 0000000000000000000000000000000000000000..c8c2ed823b251ace9d2856013292809dbedb7bb6 --- /dev/null +++ b/2023/Learning Anchor Transformations for 3D Garment Animation/full.md @@ -0,0 +1,292 @@ +# Learning Anchor Transformations for 3D Garment Animation + +Fang Zhao $^{1}$ , Zekun Li $^{1}$ , Shaoli Huang $^{1*}$ , Junwu Weng $^{1}$ , Tianfei Zhou $^{2}$ , Guo-Sen Xie $^{3}$ , Jue Wang $^{1}$ , Ying Shan $^{1}$ + +$^{1}$ Tencent AI Lab $^{2}$ ETH Zurich $^{3}$ Nanjing University of Science and Technology + +# Abstract + +This paper proposes an anchor-based deformation model, namely AnchorDEF, to predict 3D garment animation from a body motion sequence. It deforms a garment mesh template by a mixture of rigid transformations with extra nonlinear displacements. A set of anchors around the mesh surface is introduced to guide the learning of rigid transformation matrices. Once the anchor transformations are found, per-vertex nonlinear displacements of the garment template can be regressed in a canonical space, which reduces the complexity of deformation space learning. By explicitly constraining the transformed anchors to satisfy the consistencies of position, normal and direction, the physical meaning of learned anchor transformations in space is guaranteed for better generalization. Furthermore, an adaptive anchor updating is proposed to optimize the anchor position by being aware of local mesh topology for learning representative anchor transformations. Qualitative and quantitative experiments on different types of garments demonstrate that AnchorDEF achieves the state-of-the-art performance on 3D garment deformation prediction in motion, especially for loose-fitting garments. + +# 1. Introduction + +Animating 3D garments has a wide range of applications in 3D content generation, digital humans, virtual try-on, video games, and so on. Existing pipelines of 3D garment animation usually rely on physics based simulation (PBS), which requires a large amount of computational resources and time costs, particularly for high-quality PBS methods. + +Some data-driven or learning-based methods have been proposed to quickly produce 3D garment deformation from static poses or motion sequences with low computational complexity [4,5,9,11,12,16,25-28,31,40]. However, many of them attach garment templates to the skeleton of human body for modeling the articulation of garments, which + +![](images/fdaf0e45b9400481a1b074b684941eab8b33b408a9b3a081f5a188ca6389426c.jpg) +Figure 1. 3D garment deformation predicted by the proposed AnchorDEF with body motions. Leveraging the anchor transformations, AnchorDEF is able to realistically deform the garment mesh, especially for loose-fitting garments, e.g., dresses. + +only work with tight garments, e.g., T-shirts and pants, and poorly address loose-fitting ones, e.g., dresses and skirts. In this case, the topology of garments is different from the human body. Therefore, using the skinning blend weights of body yields discontinuities on deformed garment mesh. Several methods [26, 34] smooth out the blend weights to alleviate the discontinuities but may lose the shape details for large deformations of loose-fitting garments, which do not closely follow body movements. + +To this end, we propose an anchor-based deformation model, namely AnchorDEF, for predicting 3D garment deformation from a body motion sequence. It leverages a mixture of rigid anchor transformations to represent principle rotations and translations of garments to detach the + +garment articulation from the body skeleton while preserving the body movement prior, then nonlinear displacements can be regressed relatively easily in a canonical space. As shown in Fig. 1, our method can exploit anchor transformations to realistically deform the garment mesh, especially for loose-fitting garments, e.g., dresses. + +Specifically, given a sequence of body motions including poses and translations, we first estimate rigid transformations of a set of anchors around the garment mesh. Using the linear blending skinning (LBS), the garment mesh template is deformed by a weighted combination of the anchor transformations meanwhile per-vertex displacements of the mesh template are regressed to correct artifacts of the blended rigid transformations. To learn physically meaningful anchor transformations for better generalization, we enforce the transformed anchors to maintain consistency with the target's position and normal. In addition, a relative direction constraint is employed to reduce garment-body interpenetrations, which is efficient due to the sparseness of anchors. To make the learned anchor transformations effectively represent the garment deformation, an adaptive anchor updating is further introduced to utilize mesh simplification as supervision to optimize the anchor position. It parameterizes the position with a local attention mask on adjacent mesh vertices and pushes the anchors towards folds and boundaries of garment mesh which usually determine the way of deformation. + +The main contributions of our work can be summarized as follows: 1) We propose an anchor-based deformation model which learns a set of anchor transformations and blend weights in a unified framework to represent the deformation of 3D garments, especially for loose-fitting ones. 2) We propose to learn anchor transformations by position and normal consistencies as well as relative direction constraint for better generalization and fewer garment-body interpenetrations. 3) We introduce an adaptive anchor updating with the mesh simplification as supervision to optimize the anchor position for learning representative anchor transformations. + +# 2. Related Work + +Most garment animation and deformation works can be categorized into physics-based simulations (PBS) and learning-based models. + +Physics-based simulations. PBS methods have been developed for decades and achieved impressive accuracy, leveraging laws of physics and stable accurate solvers [1, 13, 18], collision detection [23, 29, 35], and dry frictional contact [19, 21]. But the expensive computational costs, i.e., long simulation time and high-performance devices often are unaffordable in our daily lives. + +Learning-based models. In contrast, learning-based models, which utilize garment animation data attained from PBS + +or digital scanning to learn the deformation, can often give satisfactory enough animation visual results with less computational costs [26, 31], regardless of no explicit physical guarantee on accuracy. Previously, researchers have proposed many techniques depending on the motions of human bodies with linear conditional models [8, 11] or secondary motion graphs [14, 15], with a constructed database of high-resolution meshes. Recent works [4, 26, 34] assume that the garment is a submesh of the skinned multi-person linear model (SMPL) and use linear blend skinning (LBS) to transfer body shape to cloth shape. Beyond learning static results within a single frame, adopting recurrent neural networks to handle the dynamic wrinkles of clothes is widely used [25, 31, 34]. For example, [31] prepares a database of PBS for dressed characters with some body shapes and motion and uses the database to learn a function of body shape and dynamics for modeling cloth drape and wrinkles. Although learning-based models can be efficient, their performance heavily relies on large amounts of high-quality PBS results or scanning data, which are usually costly [2, 30, 34]. Thus, some works [3, 32] propose self-supervised training methods to constrain the model with some sort of physical laws to alleviate this problem. Additionally, to ensure the generalization of simulation, combining several pretrained pivot motion networks can handle different unseen garment styles [26] and simulation parameters [25]. + +But most learning-based methods are limited to tight garments and not suitable for dresses or clothes with more freedom, due to their assumption that garments are complementary to SMPL, i.e., the deformation is closely related to body shape, not the motion. To tackle the dynamics, some works propose a neural field to retain high-frequency details [39], handle challenging areas [22], tackle multi-layer garments [33], and warp garments from the canonical pose to the deformation shape [6]. Without utilizing body shape parameters to establish a garment-body aligned model, [37] learns an intrinsic cloth shape descriptor embedding space and using different motion parameters to guide garment latent can attain different shape representation. To eliminate the alignment between clothes dynamics and body vertices, VirtualBones [25] extracts a set of rigid bones from the garment animation and uses body motion to predict the bones' transformation to interpolate the garment shape. Instead of learning based on mesh, [38] uses a point transformer to predict point clouds of various outfits, for various human poses and shapes, which attains more topological flexibility and the ability to model clothing separately from the body. + +VirtualBones [25] is the most related work to our method, which requires garment skeleton extraction with SSDR [17] as data preprocessing. Different from [25], we decompose the garment deformation by a set of adaptive anchors whose rigid transformations and blend weights are learned in a unified framework. + +![](images/edbde95bd831e3fdcf4f2a43bffa84040ad4e4b51cf4c721064f4798e30897f0.jpg) +Figure 2. Overview of the proposed AnchorDEF. Given a body motion sequence and a garment mesh template, the garment deformation is predicted by a weighted average of rigid anchor transformations with per-vertex displacements in a canonical space. We explicitly constrain the transformed anchors to satisfy the consistencies of position, normal and direction to guarantee the physical meaning of learned anchor transformations in space for better generalization. Starting from the cluster centers of mesh vertices, the anchor position is updated by a local attention map on adjacent mesh vertices with mesh simplification as supervision. All parameters in our model can be jointly optimized in a unified framework. + +# 3. Our Method + +We aim to learn an animated model which is able to predict dynamic 3D garment deformations given a body motion sequence. In this section, we introduce AnchorDEF, an anchor-based deformation model, which leverages s set of adaptive anchors around mesh surface to deform a garment mesh template by a mixture of rigid anchor transformations with additional per-vertex displacements in a canonical space, where the anchor transformations are learned by the consistencies of position, normal and direction. The overview of AnchorDEF is illustrated in Fig. 2. + +# 3.1. Deformation with Anchors + +3D animated models of human body, e.g., SMPL [20], usually deform a body mesh template $\mathbf{T}$ with blendshapes and skinning, which can be defined as + +$$ +V = W (\mathbf {T} + B (\theta), \mathbf {J}, \theta , \mathbf {w}), \tag {1} +$$ + +where $W$ is a skinning function, e.g., linear blend skinning, with a skeleton $\mathbf{J}$ , pose parameters $\theta$ and blend weights $\mathbf{w}$ , $V$ is the posed vertices and $B$ is the blendshape corresponding to the body pose $\theta$ . Since the garment is a kind of soft body and it is hard to directly predict the coordinates of each vertex from a body motion sequence, here we also consider to decompose the garment deformation into two parts including a weighed average of rigid transformations and + +nonlinear displacements. + +Most data-driven garment models directly associate garments with the skeleton of human body [4,26,31], i.e., they apply the skinning function to animate the garment by directly using the blend weights of body mesh vertices in the neighborhood, where it is assumed that garments closely follow the body movement. However, for loose-fitting garments, the clothing deformation usually contains more complex nonrigid effects compared to human body which can be seen as a rigid body. In this case, garments behave significantly differently from the body. Thus, it is unreasonable to attach the garment to the body skeleton. + +To address this issue, we adopt a set of anchors $\{p_n\}$ around the mesh surface to guide the garment deformation, which detaches the garment from the body skeleton while preserving the body movement prior. Given a body motion sequence consisting of poses and translations, rigid anchor transformations including rotations $\{R_{n}\}$ and translations $\{T_{n}\}$ are estimated firstly by using Gated Recurrent Units (GRU) [7] (see the supplementary material for the network structure). Then, the $m$ -th deformed garment vertex $v_{m}$ can be represented by a weighted average of anchor transformations: + +$$ +v _ {m} = \sum_ {n = 1} ^ {N} w _ {m n} \left(R _ {n} v _ {m} ^ {c} + T _ {n}\right), w _ {m n} \geq 0 \text {a n d} \sum_ {n = 1} ^ {N} w _ {m n} = 1, \tag {2} +$$ + +where $v_{m}^{c}$ is the $m$ -th vertex of garment mesh template, $w_{mn}$ is the blend weight of $v_{m}$ regarding to the $n$ -th anchor and $N$ is the number of anchors. To determine the anchor-vertex relationship and maintain the sparsity of $\{w_{n}\}$ , we initialize the anchors as the clustering centers of vertices of the mesh template. Then, each vertex is only influenced by the blend weights of its $N'$ ( $N' \ll N$ ) nearest anchors and the others remain zeros during training. Compared to the direct prediction of deformed mesh vertex coordinates, the rigid anchor transformations provide more generalized representations of complex deformations due to fewer parameters required to be learned for the prediction. + +Two strategies of anchor transformation configuration are designed for loose and tight types of garments. For the loose type, to utilize the prior of the global human body orientation $R_{global}$ , we predict transformations relative to the root joint $J_{root}$ of the body and the anchor transformation can be defined as: + +$$ +\begin{array}{l} R _ {n} ^ {\text {l o o s e}} = R _ {\text {g l o b a l}} R _ {n} ([ \theta , t ]), \\ T _ {n} ^ {\text {l o o s e}} = R _ {\text {g l o b a l}} \left(T _ {n} ([ \theta , t ]) - R _ {n} ([ \theta , t ]) J _ {\text {r o o t}}\right) + J _ {\text {r o o t}}, \tag {3} \\ \end{array} +$$ + +where $\theta$ and $t$ are the body pose and translation, respectively. For the tight type, the garment mostly follows the body movement. Thus, we predict an incremental change on the basis of body vertex rotation $R_{body}$ and offset $T_{body}$ : + +$$ +\begin{array}{l} R _ {n} ^ {t i g h t} = R _ {b o d y} R _ {n} ([ \theta , t ]), \\ T _ {n} ^ {\text {t i g h t}} = R _ {\text {b o d y}} T _ {n} ([ \theta , t ]) + T _ {\text {b o d y}}, \tag {4} \\ \end{array} +$$ + +where $R_{body}$ and $T_{body}$ is the transformation of the body mesh vertex closest to the anchor $p_n$ . Furthermore, we can combine these two strategies for garments with both tight and loose parts, e.g., dresses, by classifying which part the anchor belongs to according to its distance to body joints. + +Once the primary rotations and translations in the garment deformation caused by the articulation are expressed in Eq. (2), the nonlinear residual deformation can be disentangled with the garment articulation and defined as pervertex displacements $D([\theta, t])$ in an unposed canonical space. Utilizing the skinning function in Eq. (1), the overall garment deformation is given by + +$$ +V _ {p r e d} = W \left(\mathbf {T} _ {g} + D ([ \theta , t ]), G ([ \theta , t ]), \mathbf {w} _ {p}\right), \tag {5} +$$ + +where $\mathbf{T}_g$ is the garment mesh template, $\mathbf{w}_p$ is the anchor-vertex blend weights and $G([\theta ,t])$ is the anchor transformations predicted with the body motion. We argue that such decomposition by anchors extremely reduces the complexity of pose-dependent garment deformation prediction because large deformations have been handled by transformations of sparse anchors and only small displacements need to be regressed in the canonical space. + +![](images/58b9717ad9817a4115433f67110665eb4c3f3569145f524450b694b9f5a83e88.jpg) +Figure 3. Examples of adaptive anchor updating by using the local attention mask with the mesh simplification as supervision. The blue points are anchors initialized by $k$ -means and the orange ones are the updated anchors. + +# 3.2. Learning Anchor Transformations + +Different from [25] which resorts to the external skinning decomposition algorithm, i.e., SSDR [17], to extract the garment skeleton from smoothed mesh sequences, here we jointly learn rigid transformations, blend weights and positions of anchors in a unified framework. + +We first apply an L2 loss term on the predicted mesh vertices to recover the shape of deformed mesh: + +$$ +\mathcal {L} _ {r e c} = \left| \left| V _ {p r e d} - V _ {g t} \right| \right| _ {2} ^ {2}, \tag {6} +$$ + +which minimizes the Euclidean distance between the predicted vertices and the ground-truth deformed vertices. Then a loss term is used to keep the similarity of the graph Laplacians between two meshes: + +$$ +\mathcal {L} _ {l a p} = \left\| \triangle V _ {p r e d} - \triangle V _ {g t} \right\| _ {2} ^ {2}. \tag {7} +$$ + +A collision term [25] is also added to avoid garment-body collisions. Thus, the loss on the vertex can be given by + +$$ +\mathcal {L} _ {\text {v e r t}} = \mathcal {L} _ {\text {r e c}} + \beta_ {1} \mathcal {L} _ {\text {l a p}} + \beta_ {2} \mathcal {L} _ {\text {c o l l i s i o n}}, \tag {8} +$$ + +where $\beta_{1}$ and $\beta_{2}$ are trade-off coefficients for controlling the degree of smoothing and collision, respectively. + +However, only optimizing the vertex position cannot guarantee the physical meaning of learned anchor transformations in space, which leads to poor generalization. Thus, we explicitly constrain the transformed anchors to be located around the deformed mesh surface. To this end, the position of anchor $p$ is recalculated by its adjacent mesh vertices: + +$$ +p = \frac {1}{K} \sum_ {v _ {k} ^ {c} \in K (p, \mathbf {T} _ {g})} v _ {k} ^ {c}, \tag {9} +$$ + +where $K(p, \mathbf{T}_g)$ is the $K$ nearest vertices of $p$ on the mesh template. Then, the target point $p_{tgt}$ of transformed anchor $p_G$ can be defined with the same set of vertices $K(p, \mathbf{T}_g)$ on the deformed mesh and a transformation consistency loss is defined as + +$$ +\mathcal {L} _ {\text {c o n s i s}} = \left\| p _ {G} - p _ {t g t} \right\| _ {2} ^ {2} + \gamma \left\| \mathbf {n} \left(p _ {G}\right) - \mathbf {n} \left(p _ {t g t}\right) \right\| _ {2} ^ {2}, \tag {10} +$$ + +where $\mathbf{n}(.)$ is the unit normal of point and $\gamma$ is a weight factor. By encouraging the transformed anchor $p_G$ to be similar to $p_{tgt}$ in position and normal, the learned anchor transformation indicates the mean transformation of $K$ nearest + +![](images/45c590dd395b4e064c51716ae9422a1bc69453eadb6c22daffc9e7bf14c2c950.jpg) +Figure 4. Qualitative comparison with and without different components of AnchorDEF including (a) anchor transformation consistency $\mathcal{L}_{consis}$ and (b) adaptive anchor updating $\mathcal{L}_{anch}$ . Without $\mathcal{L}_{consis}$ , the model cannot accurately predict the shape of deformed mesh and loses some surface geometry details. Without $\mathcal{L}_{anch}$ , the model is unable to produce realistic garment deformations due to the under-expressed anchor transformations. + +vertices of $p$ . It can be viewed as a regularization for the transformation magnitude and direction to discover essential transformations in deformation. + +We further enforce the direction from $p_{tgt}$ to $p_G$ to be consistent with the direction of $\mathbf{n}(p_{tgt})$ by minimizing the following penalty term: + +$$ +\mathcal {L} _ {d i r} = 1 - \cos \left(p _ {G} - p _ {t g t}, \mathbf {n} \left(p _ {t g t}\right)\right), \tag {11} +$$ + +where $\cos (\cdot ,\cdot)$ is the cosine similarity. Intuitively, this penalty term makes $p_{G}$ tend to be outside of the plane formed by $p_{tgt}$ to reduce the garment-body interpenetration. Adaptive Anchor Updating. It is still not enough to have a physically meaningful anchor transformation, we also need an expressive transformation in geometry to better represent the garment deformation. We observe that mesh regions with folds and boundaries usually play an important role on showing garment shape characteristics and contain more deformation information compared with smooth regions. + +To make the anchors reflect such intrinsic structure of garment shape, we propose to employ mesh simplification to provide a signal of supervision for finding such representative anchors. Here Quadric Error Metric (QEM) [10] is used to obtain simplified mesh vertices by collapsing edges while preserving the garment topology. Because there is no one-to-one correspondence between the anchors $\{p_n\}$ and the simplified vertices $\{\tilde{v}_m\}$ , the Chamfer distance is adopted as the optimization objective: + +$$ +\mathcal {L} _ {a n c h} = \sum_ {p} \min _ {\tilde {v}} | | p - \tilde {v} | | _ {2} ^ {2} + \sum_ {\tilde {v}} \min _ {p} | | p - \tilde {v} | | _ {2} ^ {2}. \tag {12} +$$ + +To be able to update the anchor position, we rewrite Eq. (9) using learnable weights $\alpha$ as + +$$ +p = \frac {1}{\sum_ {j = 1} ^ {K} e ^ {\alpha_ {j}}} \sum_ {k = 1} ^ {K} e ^ {\alpha_ {k}} v _ {k} ^ {c}. \tag {13} +$$ + +Actually, this equals to learning a local attention mask for the anchor to determine how the adjacent vertices contribute to its position. Fig. 3 shows that by optimizing the weights $\alpha$ with supervision of the simplified vertices, the anchors are pushed to inflection points of folds and boundaries of the mesh and thus able to better represent the deformed mesh vertices by interpolating their transformation matrices. Note that we optimize the anchor position on the entire dataset not only on the mesh template because some smooth regions of the template may create new folds after posing. + +On the other hand, if we reformulate the transformed anchor $p_G$ with Eq. (13) as: + +$$ +p _ {G} = R p + T = \frac {1}{\sum_ {j = 1} ^ {K} e ^ {\alpha_ {j}}} \sum_ {k = 1} ^ {K} e ^ {\alpha_ {k}} \left(R v _ {k} ^ {c} + T\right), \tag {14} +$$ + +the process of transformation learning for the anchor, i.e., Eq. (10), can be interpreted as a way to find an appropriate transformation for its adjacent mesh vertices by the importance which is reflected in the weights learned from the mesh simplification. The larger the weight, the greater the impact of the vertex transformation on the anchor transformation learning. + +![](images/d0609ba541d195d74d6eb42afcbd48dca8654b81e18c758beb1ab8bb8dd397db.jpg) +(a) + +![](images/97d1b9c0206670243f7062f07688ea1dc999f31ed749ddf7d1b5d0b13ff5f175.jpg) +(b) +Figure 5. Visualization of anchors transformed by (a) only optimizing the mesh vertices during training and (b) AnchorDEF. + +Lastly, combining Eq. (8), Eqs. (10) to (12), the overall objective function for our model is given by: + +$$ +\mathcal {L} = \mathcal {L} _ {\text {v e r t}} + \lambda_ {1} \mathcal {L} _ {\text {c o n s i s}} + \lambda_ {2} \mathcal {L} _ {\text {d i r}} + \lambda_ {3} \mathcal {L} _ {\text {a n c h}}, \tag {15} +$$ + +where $\lambda$ s are loss weights. + +# 4. Experiments + +We evaluate the proposed AnchorDEF on the VTO [31] dataset containing two types of garments, i.e., dress and T-shirt. Following [25], RMSE (Root Mean Squared Error), Hausdorff distance and STED (Spatio-Temporal Edge Difference) [36] are adopted to assess the quality of deformed meshes. The first two measure the distance between predicted and ground truth meshes and STED reflects the difference between their dynamics. We also compare AnchorDEF against other 3D garment deformation methods [25, 26]. + +Implementation Details. To capture the motion dynamics, a network with 2 GRU layers of size 256 is used as the body motion encoder. Two 2-layered MLPs of size 256 are used to regress the anchor transformations and per-vertex displacements, respectively. The number of anchors associated with each mesh vertex is set to 8, which can obtain the desired smooth surface, and the number of neighboring vertices for computing the anchor position is set to 128. For the garment sequences of VTO, 4 clips are randomly selected for testing and the rest is used as the training set, and the length of training sequence is 30. Please refer to the supplemental materials for more details on training and inference. + +# 4.1. Ablation Study + +We validate the effectiveness of main components in our proposed AnchorDEF. We firstly assess the importance of anchor transformation consistency, i.e., $\mathcal{L}_{\text{consis}}$ in Eq. (10). As reported in Table 1, keeping the consistency of learned anchor transformations is able to improve all metrics due + +
Methodsw/o Lconsisw/o LanchAnchorDEF
RMSE ↓17.2116.4916.05
Hausdorff ↓75.0174.5374.20
STED ↓0.05950.05260.0493
+ +![](images/3dce5a95eb57df17fa5800419f431349ae16cdddc05e43cd412ed3901a4ba16a.jpg) +Figure 6. Qualitative comparison with and without the penalty $\mathcal{L}_{dir}$ on the direction from the target anchor to the transformed one. + +![](images/88967a35f02d45471547027bb244a8ee7250577c1bf28182ee82331b5e9c44b9.jpg) +Figure 7. Qualitative comparison of using different numbers of anchors. Using 160 anchors produces finer and more accurate deformation compared with other anchor numbers. + +Table 1. Quantitative results obtained by different components of AnchorDEF, i.e., without anchor transformation consistency (w/o $\mathcal{L}_{\text{cosis}}$ ), without adaptive anchor updating (w/o $\mathcal{L}_{\text{anch}}$ ) and the full model (AnchorDEF). + +
Num. Anchor2080160320
RMSE ↓17.7816.8216.0517.52
Hausdorff ↓75.3074.7174.2075.13
STED ↓0.06200.05390.04930.0625
+ +Table 2. Quantitative results of using different numbers of anchors. + +to better generalization. Fig. 4 (a) illustrates the qualitative comparison. One can observe that without $\mathcal{L}_{\text {consis }}$ the model cannot accurately predict the shape of deformed mesh and loses some surface geometry details. + +To evaluate the influence of adaptive anchor updating, Table 1 also reports the results without using $\mathcal{L}_{anch}$ in Eq. (12). The performance drops only using the clustering centers of $k$ -means as the anchors. The reason is that compared with the clustering, the supervision with mesh simplification can provide key topology information, e.g., folds and boundaries, which is useful for learning representative + +![](images/01699bfded4d6dbf0041707f2b3cd930551f23fe4204bb7d88f040f267e00629.jpg) +Figure 8. Examples of our AnchorDEF for dynamic garment deformation in motion. The first row is the ground truth generated by physics-based simulation [24]. The second row is the results obtained by AnchorDEF. Our method can produce natural and realistic clothing dynamics, e.g., wrinkles from jumping and the swing of the dress caused by running. + +anchor transformations. The qualitative results are shown in Fig. 4 (b). It can be observed that without $\mathcal{L}_{anch}$ the model is unable to produce realistic garment deformations due to the under-expressed anchor transformations. + +Fig. 5 (a) and (b) visualize the anchors transformed by only optimizing the mesh vertices during training and AnchorDEF, respectively. For Fig. 5 (a), without the consistency constraint for anchor transformation, many of the transformed anchors are not on the deformed mesh surface, which is lack of clear physical meaning in space and easy to overfit. In contrast, AnchorDEF enforces the anchors to be transformed onto the deformed mesh surface, which prevents overfitting to a certain extent, thus has better generalization when testing. Furthermore, as shown in Fig. 5 (b), the transformed anchors are mainly distributed at the folds and boundaries of the mesh because of our adaptive anchor updating according to simplified mesh vertices, and thus capable of better expressing the deformation of mesh vertices, in particular those vertices far from them. In this way, the complexity of garment deformation space is reduced more effectively and more mesh shape details can be preserved. + +Then we investigate the impact of the penalty $\mathcal{L}_{dir}$ (Eq. (11)) on the direction from the target anchor to the transformed one. As illustrated in Fig. 6, with $\mathcal{L}_{dir}$ the model can reduce the garment-body interpenetration. By enforcing the transformed anchors to be on the positive direction of target normals, the garment mesh vertices influenced by these anchors can be effectively pushed to the outside of the body surface while keeping the deformation accuracy due to moving along the direction of target normals. + +We further assess the influence of the anchor number. Table 2 reports the results obtained by using 20, 80, 160 and 320 anchors, respectively. One can see that using more anchors to guide the mesh deformation obtains better results on all three metrics because the decomposition for the mesh deformation by using the rigid anchor transformations makes the nonlinear deformation can be more easily predicted as the small displacements in the canonical space without considering large rotations and translations caused by the body pose which has been handled by the anchor transformations. However, the performance drops as the number of anchors continues to increase because too many transformation parameters lead to unstable forecasts during testing. Fig. 7 shows the qualitative comparison. Using 160 anchors produces finer and more accurate deformation compared with other anchor numbers. Using 20 anchors only recover the contour of the deformed mesh, and using 80 and 320 anchors fail to obtain realistic deformation. + +Fig. 8 shows some examples of our AnchorDEF for dynamic garment deformation in motion. Given a body motion sequence, our method can produce natural and realistic clothing dynamics, e.g., wrinkles from jumping and the swing of the dress caused by running. + +# 4.2. Comparison with Related Methods + +We compare our method against related 3D garment deformation methods, including TailorNet [26] and VirtualBones [25] on different types of garments. As reported in Table 3, our AnchorDEF achieves the best results in all cases. Fig. 9 presents the qualitative comparison. Tailor- + +
MethodsDressT-shirt
RMSE ↓Hausdorff ↓STED ↓RMSE ↓Hausdorff ↓STED ↓
TailorNet [26]22.9576.800.07579.9027.020.0418
VirtualBones [25]19.9183.390.072210.5231.510.0452
AnchorDEF16.0574.200.04936.2526.310.0262
+ +Table 3. Quantitative results of 3D garment deformation methods for different types of garments. + +![](images/c2fc42c9781079f56af953332a1c481fc2dd90bbfb54721f148f675928a73b97.jpg) +(a) +Figure 9. Qualitative comparison of 3D garment deformation methods for different types of garments, including TailorNet [26], VirtualBones [25] and Our AnchorDEF. With the learned anchor transformations, our method not only recovers large deformations of the dress but also produces fine surface details on the T-shirt. + +Net [26] recovers folds on the T-shirt, but it fails to address the deformation of the dress which has different topology from human body. By interpolating the skinning blend weights, it alleviates the discontinuity of blend weights borrowed from the SMPL [20] body. However, this makes TailorNet only produce the outline of shapes with some folds missing and artifacts for large deformations of loose-fitting garments. VirtualBones [25] can estimate large deformations of the dress by using SSDR [17] to extract virtual bones of garments. However, it tends to keep the original folds of the dress template on the deformed mesh and cannot estimate well new folds generated by body motions on the T-shirt. VirtualBones needs SSDR to extract the garment skeleton and gets blend weights of bones in advance and fixes the bone position and blend weights during network training. Moreover, SSDR is performed on the low-frequency mesh sequences processed by Laplacian smoothing because it fails to address high-frequency garment deformations. Thus, the learned virtual bones are not necessarily optimal. In contrast, by jointly learning the rigid transformations, blend weights and positions of anchors, our AnchorDEF not only recovers large deformations of the dress but also produces fine surface details on the T-shirt. More qualitative results can be found in the supplemental materials. + +# 5. Conclusions + +We present AnchorDEF, an anchor based deformation model, to predict 3D garment animation given a body motion sequence. With a set of anchors around the mesh surface, the garment deformation can be decomposed into a mixture of rigid anchor transformations and extra per-vertex displacements in a canonical space. The transformation consistency learning is introduced to guarantee the physical meaning of learned anchor transformations in space. Taking mesh simplification as supervision, We further optimize the anchor position for learning representative anchor transformations by making the anchor aware of local mesh topology with an attention mask. Extensive experiments on different types of garments demonstrate that AnchorDEF can effectively predict 3D garment deformation in motion for both tight and loose-fitting garments. + +Limitations. Compared with the PBS methods, our method still lacks fine-level dynamics. 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Collision and self-collision handling in cloth model dedicated to design garments. In Computer Animation and Simulation'97, pages 177-189. Springer, 1997. 2 +[30] Albert Pumarola, Jordi Sanchez-Riera, Gary Choi, Alberto Sanfeliu, and Francesc Moreno-Noguer. 3dpeople: Modeling the geometry of dressed humans. In Proceedings of the IEEE/CVF international conference on computer vision, pages 2242-2251, 2019. 2 + +[31] Igor Santesteban, Miguel A. Otaduy, and Dan Casas. Learning-Based Animation of Clothing for Virtual Try-On. Computer Graphics Forum (Proc. Eurographics), 2019. 1, 2, 3, 6 +[32] Igor Santesteban, Miguel A Otaduy, and Dan Casas. SNUG: Self-Supervised Neural Dynamic Garments. IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2022. 2 +[33] Igor Santesteban, Miguel A. Otaduy, Nils Thuerey, and Dan Casas. ULNeF: Untangled layered neural fields for mix-and-match virtual try-on. In Advances in Neural Information Processing Systems, (NeurIPS), 2022. 2 +[34] Igor Santesteban, Nils Thuerey, Miguel A Otaduy, and Dan Casas. Self-supervised collision handling via generative 3d garment models for virtual try-on. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2021. 1, 2 +[35] Min Tang, Huamin Wang, Le Tang, Ruofeng Tong, and Dinesh Manocha. CAMA: Contact-aware matrix assembly with unified collision handling for GPU-based cloth simulation. Computer Graphics Forum (Proceedings of Eurographics 2016), 35(2):511-521, 2016. 2 +[36] Libor Vasa and Vaclav Skala. A perception correlated comparison method for dynamic meshes. IEEE transactions on visualization and computer graphics (TVCG), 2010. 6 +[37] Tuanfeng Y Wang, Tianjia Shao, Kai Fu, and Niloy J Mitra. Learning an intrinsic garment space for interactive authoring of garment animation. ACM Transactions on Graphics (TOG), 2019. 2 +[38] Ilya Zakharkin, Kirill Mazur, Artur Grigorev, and Victor Lempitsky. Point-based modeling of human clothing. In Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), 2021. 2 +[39] Meng Zhang, Tuanfeng Y Wang, Duygu Ceylan, and Niloy J Mitra. Dynamic neural garments. ACM Transactions on Graphics (TOG), 2021. 2 +[40] Fang Zhao, Wenhao Wang, Shengcai Liao, and Ling Shao. Learning anchored unsigned distance functions with gradient direction alignment for single-view garment reconstruction. In Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), 2021. 1 \ No newline at end of file diff --git a/2023/Learning Anchor Transformations for 3D Garment Animation/images.zip b/2023/Learning Anchor Transformations for 3D Garment Animation/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..8bb2a5ebb979a26bc822601127fa4dd7bc7ade60 --- /dev/null +++ b/2023/Learning Anchor Transformations for 3D Garment Animation/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:8395a76bdad0e3d73932e6ad8062853083b92c35eddb38316de5e78970f1dafa +size 473848 diff --git a/2023/Learning Anchor Transformations for 3D Garment Animation/layout.json b/2023/Learning Anchor Transformations for 3D Garment Animation/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..70c1435a6cfef40aef807904594218109de4b478 --- /dev/null +++ b/2023/Learning Anchor Transformations for 3D Garment Animation/layout.json @@ -0,0 +1,7649 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 103, + 103, + 491, + 120 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 103, + 103, + 491, + 120 + ], + "spans": [ + { + "bbox": [ + 103, + 103, + 491, + 120 + ], + "type": "text", + "content": "Learning Anchor Transformations for 3D Garment Animation" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 120, + 151, + 473, + 186 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 120, + 151, + 473, + 186 + ], + "spans": [ + { + "bbox": [ + 120, + 151, + 473, + 186 + ], + "type": "text", + "content": "Fang Zhao" + }, + { + "bbox": [ + 120, + 151, + 473, + 186 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 120, + 151, + 473, + 186 + ], + "type": "text", + "content": ", Zekun Li" + }, + { + "bbox": [ + 120, + 151, + 473, + 186 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 120, + 151, + 473, + 186 + ], + "type": "text", + "content": ", Shaoli Huang" + }, + { + "bbox": [ + 120, + 151, + 473, + 186 + ], + "type": "inline_equation", + "content": "^{1*}" + }, + { + "bbox": [ + 120, + 151, + 473, + 186 + ], + "type": "text", + "content": ", Junwu Weng" + }, + { + "bbox": [ + 120, + 151, + 473, + 186 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 120, + 151, + 473, + 186 + ], + "type": "text", + "content": ", Tianfei Zhou" + }, + { + "bbox": [ + 120, + 151, + 473, + 186 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 120, + 151, + 473, + 186 + ], + "type": "text", + "content": ", Guo-Sen Xie" + }, + { + "bbox": [ + 120, + 151, + 473, + 186 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 120, + 151, + 473, + 186 + ], + "type": "text", + "content": ", Jue Wang" + }, + { + "bbox": [ + 120, + 151, + 473, + 186 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 120, + 151, + 473, + 186 + ], + "type": "text", + "content": ", Ying Shan" + }, + { + "bbox": [ + 120, + 151, + 473, + 186 + ], + "type": "inline_equation", + "content": "^{1}" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 102, + 190, + 488, + 205 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 102, + 190, + 488, + 205 + ], + "spans": [ + { + "bbox": [ + 102, + 190, + 488, + 205 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 102, + 190, + 488, + 205 + ], + "type": "text", + "content": "Tencent AI Lab " + }, + { + "bbox": [ + 102, + 190, + 488, + 205 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 102, + 190, + 488, + 205 + ], + "type": "text", + "content": "ETH Zurich " + }, + { + "bbox": [ + 102, + 190, + 488, + 205 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 102, + 190, + 488, + 205 + ], + "type": "text", + "content": "Nanjing University of Science and Technology" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 234, + 192, + 247 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 234, + 192, + 247 + ], + "spans": [ + { + "bbox": [ + 143, + 234, + 192, + 247 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 259, + 290, + 511 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 259, + 290, + 511 + ], + "spans": [ + { + "bbox": [ + 47, + 259, + 290, + 511 + ], + "type": "text", + "content": "This paper proposes an anchor-based deformation model, namely AnchorDEF, to predict 3D garment animation from a body motion sequence. It deforms a garment mesh template by a mixture of rigid transformations with extra nonlinear displacements. A set of anchors around the mesh surface is introduced to guide the learning of rigid transformation matrices. Once the anchor transformations are found, per-vertex nonlinear displacements of the garment template can be regressed in a canonical space, which reduces the complexity of deformation space learning. By explicitly constraining the transformed anchors to satisfy the consistencies of position, normal and direction, the physical meaning of learned anchor transformations in space is guaranteed for better generalization. Furthermore, an adaptive anchor updating is proposed to optimize the anchor position by being aware of local mesh topology for learning representative anchor transformations. Qualitative and quantitative experiments on different types of garments demonstrate that AnchorDEF achieves the state-of-the-art performance on 3D garment deformation prediction in motion, especially for loose-fitting garments." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 533, + 128, + 545 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 533, + 128, + 545 + ], + "spans": [ + { + "bbox": [ + 47, + 533, + 128, + 545 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 552, + 287, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 552, + 287, + 624 + ], + "spans": [ + { + "bbox": [ + 46, + 552, + 287, + 624 + ], + "type": "text", + "content": "Animating 3D garments has a wide range of applications in 3D content generation, digital humans, virtual try-on, video games, and so on. Existing pipelines of 3D garment animation usually rely on physics based simulation (PBS), which requires a large amount of computational resources and time costs, particularly for high-quality PBS methods." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 624, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 624, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 624, + 287, + 696 + ], + "type": "text", + "content": "Some data-driven or learning-based methods have been proposed to quickly produce 3D garment deformation from static poses or motion sequences with low computational complexity [4,5,9,11,12,16,25-28,31,40]. However, many of them attach garment templates to the skeleton of human body for modeling the articulation of garments, which" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 312, + 235, + 541, + 469 + ], + "blocks": [ + { + "bbox": [ + 312, + 235, + 541, + 469 + ], + "lines": [ + { + "bbox": [ + 312, + 235, + 541, + 469 + ], + "spans": [ + { + "bbox": [ + 312, + 235, + 541, + 469 + ], + "type": "image", + "image_path": "fdaf0e45b9400481a1b074b684941eab8b33b408a9b3a081f5a188ca6389426c.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 477, + 547, + 522 + ], + "lines": [ + { + "bbox": [ + 305, + 477, + 547, + 522 + ], + "spans": [ + { + "bbox": [ + 305, + 477, + 547, + 522 + ], + "type": "text", + "content": "Figure 1. 3D garment deformation predicted by the proposed AnchorDEF with body motions. Leveraging the anchor transformations, AnchorDEF is able to realistically deform the garment mesh, especially for loose-fitting garments, e.g., dresses." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 545, + 546, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 546, + 652 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 546, + 652 + ], + "type": "text", + "content": "only work with tight garments, e.g., T-shirts and pants, and poorly address loose-fitting ones, e.g., dresses and skirts. In this case, the topology of garments is different from the human body. Therefore, using the skinning blend weights of body yields discontinuities on deformed garment mesh. Several methods [26, 34] smooth out the blend weights to alleviate the discontinuities but may lose the shape details for large deformations of loose-fitting garments, which do not closely follow body movements." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "text", + "content": "To this end, we propose an anchor-based deformation model, namely AnchorDEF, for predicting 3D garment deformation from a body motion sequence. It leverages a mixture of rigid anchor transformations to represent principle rotations and translations of garments to detach the" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 703, + 135, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 703, + 135, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 703, + 135, + 712 + ], + "type": "text", + "content": "*Corresponding author." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "type": "text", + "content": "491" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "type": "text", + "content": "garment articulation from the body skeleton while preserving the body movement prior, then nonlinear displacements can be regressed relatively easily in a canonical space. As shown in Fig. 1, our method can exploit anchor transformations to realistically deform the garment mesh, especially for loose-fitting garments, e.g., dresses." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 144, + 288, + 393 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 144, + 288, + 393 + ], + "spans": [ + { + "bbox": [ + 46, + 144, + 288, + 393 + ], + "type": "text", + "content": "Specifically, given a sequence of body motions including poses and translations, we first estimate rigid transformations of a set of anchors around the garment mesh. Using the linear blending skinning (LBS), the garment mesh template is deformed by a weighted combination of the anchor transformations meanwhile per-vertex displacements of the mesh template are regressed to correct artifacts of the blended rigid transformations. To learn physically meaningful anchor transformations for better generalization, we enforce the transformed anchors to maintain consistency with the target's position and normal. In addition, a relative direction constraint is employed to reduce garment-body interpenetrations, which is efficient due to the sparseness of anchors. To make the learned anchor transformations effectively represent the garment deformation, an adaptive anchor updating is further introduced to utilize mesh simplification as supervision to optimize the anchor position. It parameterizes the position with a local attention mask on adjacent mesh vertices and pushes the anchors towards folds and boundaries of garment mesh which usually determine the way of deformation." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 396, + 287, + 538 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 396, + 287, + 538 + ], + "spans": [ + { + "bbox": [ + 46, + 396, + 287, + 538 + ], + "type": "text", + "content": "The main contributions of our work can be summarized as follows: 1) We propose an anchor-based deformation model which learns a set of anchor transformations and blend weights in a unified framework to represent the deformation of 3D garments, especially for loose-fitting ones. 2) We propose to learn anchor transformations by position and normal consistencies as well as relative direction constraint for better generalization and fewer garment-body interpenetrations. 3) We introduce an adaptive anchor updating with the mesh simplification as supervision to optimize the anchor position for learning representative anchor transformations." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 550, + 134, + 562 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 550, + 134, + 562 + ], + "spans": [ + { + "bbox": [ + 47, + 550, + 134, + 562 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 570, + 287, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 287, + 605 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 287, + 605 + ], + "type": "text", + "content": "Most garment animation and deformation works can be categorized into physics-based simulations (PBS) and learning-based models." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 605, + 287, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 689 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 689 + ], + "type": "text", + "content": "Physics-based simulations. PBS methods have been developed for decades and achieved impressive accuracy, leveraging laws of physics and stable accurate solvers [1, 13, 18], collision detection [23, 29, 35], and dry frictional contact [19, 21]. But the expensive computational costs, i.e., long simulation time and high-performance devices often are unaffordable in our daily lives." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "content": "Learning-based models. In contrast, learning-based models, which utilize garment animation data attained from PBS" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 545, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 384 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 384 + ], + "type": "text", + "content": "or digital scanning to learn the deformation, can often give satisfactory enough animation visual results with less computational costs [26, 31], regardless of no explicit physical guarantee on accuracy. Previously, researchers have proposed many techniques depending on the motions of human bodies with linear conditional models [8, 11] or secondary motion graphs [14, 15], with a constructed database of high-resolution meshes. Recent works [4, 26, 34] assume that the garment is a submesh of the skinned multi-person linear model (SMPL) and use linear blend skinning (LBS) to transfer body shape to cloth shape. Beyond learning static results within a single frame, adopting recurrent neural networks to handle the dynamic wrinkles of clothes is widely used [25, 31, 34]. For example, [31] prepares a database of PBS for dressed characters with some body shapes and motion and uses the database to learn a function of body shape and dynamics for modeling cloth drape and wrinkles. Although learning-based models can be efficient, their performance heavily relies on large amounts of high-quality PBS results or scanning data, which are usually costly [2, 30, 34]. Thus, some works [3, 32] propose self-supervised training methods to constrain the model with some sort of physical laws to alleviate this problem. Additionally, to ensure the generalization of simulation, combining several pretrained pivot motion networks can handle different unseen garment styles [26] and simulation parameters [25]." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 387, + 545, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 387, + 545, + 639 + ], + "spans": [ + { + "bbox": [ + 304, + 387, + 545, + 639 + ], + "type": "text", + "content": "But most learning-based methods are limited to tight garments and not suitable for dresses or clothes with more freedom, due to their assumption that garments are complementary to SMPL, i.e., the deformation is closely related to body shape, not the motion. To tackle the dynamics, some works propose a neural field to retain high-frequency details [39], handle challenging areas [22], tackle multi-layer garments [33], and warp garments from the canonical pose to the deformation shape [6]. Without utilizing body shape parameters to establish a garment-body aligned model, [37] learns an intrinsic cloth shape descriptor embedding space and using different motion parameters to guide garment latent can attain different shape representation. To eliminate the alignment between clothes dynamics and body vertices, VirtualBones [25] extracts a set of rigid bones from the garment animation and uses body motion to predict the bones' transformation to interpolate the garment shape. Instead of learning based on mesh, [38] uses a point transformer to predict point clouds of various outfits, for various human poses and shapes, which attains more topological flexibility and the ability to model clothing separately from the body." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 641, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 545, + 712 + ], + "type": "text", + "content": "VirtualBones [25] is the most related work to our method, which requires garment skeleton extraction with SSDR [17] as data preprocessing. Different from [25], we decompose the garment deformation by a set of adaptive anchors whose rigid transformations and blend weights are learned in a unified framework." + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "type": "text", + "content": "492" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 70, + 541, + 301 + ], + "blocks": [ + { + "bbox": [ + 56, + 70, + 541, + 301 + ], + "lines": [ + { + "bbox": [ + 56, + 70, + 541, + 301 + ], + "spans": [ + { + "bbox": [ + 56, + 70, + 541, + 301 + ], + "type": "image", + "image_path": "edbde95bd831e3fdcf4f2a43bffa84040ad4e4b51cf4c721064f4798e30897f0.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 308, + 548, + 376 + ], + "lines": [ + { + "bbox": [ + 46, + 308, + 548, + 376 + ], + "spans": [ + { + "bbox": [ + 46, + 308, + 548, + 376 + ], + "type": "text", + "content": "Figure 2. Overview of the proposed AnchorDEF. Given a body motion sequence and a garment mesh template, the garment deformation is predicted by a weighted average of rigid anchor transformations with per-vertex displacements in a canonical space. We explicitly constrain the transformed anchors to satisfy the consistencies of position, normal and direction to guarantee the physical meaning of learned anchor transformations in space for better generalization. Starting from the cluster centers of mesh vertices, the anchor position is updated by a local attention map on adjacent mesh vertices with mesh simplification as supervision. All parameters in our model can be jointly optimized in a unified framework." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 386, + 127, + 398 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 386, + 127, + 398 + ], + "spans": [ + { + "bbox": [ + 47, + 386, + 127, + 398 + ], + "type": "text", + "content": "3. Our Method" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 406, + 289, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 406, + 289, + 525 + ], + "spans": [ + { + "bbox": [ + 46, + 406, + 289, + 525 + ], + "type": "text", + "content": "We aim to learn an animated model which is able to predict dynamic 3D garment deformations given a body motion sequence. In this section, we introduce AnchorDEF, an anchor-based deformation model, which leverages s set of adaptive anchors around mesh surface to deform a garment mesh template by a mixture of rigid anchor transformations with additional per-vertex displacements in a canonical space, where the anchor transformations are learned by the consistencies of position, normal and direction. The overview of AnchorDEF is illustrated in Fig. 2." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 533, + 195, + 544 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 533, + 195, + 544 + ], + "spans": [ + { + "bbox": [ + 47, + 533, + 195, + 544 + ], + "type": "text", + "content": "3.1. Deformation with Anchors" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 551, + 287, + 588 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 551, + 287, + 588 + ], + "spans": [ + { + "bbox": [ + 46, + 551, + 287, + 588 + ], + "type": "text", + "content": "3D animated models of human body, e.g., SMPL [20], usually deform a body mesh template " + }, + { + "bbox": [ + 46, + 551, + 287, + 588 + ], + "type": "inline_equation", + "content": "\\mathbf{T}" + }, + { + "bbox": [ + 46, + 551, + 287, + 588 + ], + "type": "text", + "content": " with blendshapes and skinning, which can be defined as" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 107, + 596, + 287, + 609 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 596, + 287, + 609 + ], + "spans": [ + { + "bbox": [ + 107, + 596, + 287, + 609 + ], + "type": "interline_equation", + "content": "V = W (\\mathbf {T} + B (\\theta), \\mathbf {J}, \\theta , \\mathbf {w}), \\tag {1}", + "image_path": "3daccc5198f938b5f5f6a73aaf3d769c6bd92ed3ff4bda628b6a38b9536aa3a0.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "text", + "content": " is a skinning function, e.g., linear blend skinning, with a skeleton " + }, + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{J}" + }, + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "text", + "content": ", pose parameters " + }, + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "text", + "content": " and blend weights " + }, + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{w}" + }, + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "text", + "content": " is the posed vertices and " + }, + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "text", + "content": " is the blendshape corresponding to the body pose " + }, + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "text", + "content": ". Since the garment is a kind of soft body and it is hard to directly predict the coordinates of each vertex from a body motion sequence, here we also consider to decompose the garment deformation into two parts including a weighed average of rigid transformations and" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 388, + 408, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 388, + 408, + 399 + ], + "spans": [ + { + "bbox": [ + 305, + 388, + 408, + 399 + ], + "type": "text", + "content": "nonlinear displacements." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 399, + 545, + 530 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 399, + 545, + 530 + ], + "spans": [ + { + "bbox": [ + 304, + 399, + 545, + 530 + ], + "type": "text", + "content": "Most data-driven garment models directly associate garments with the skeleton of human body [4,26,31], i.e., they apply the skinning function to animate the garment by directly using the blend weights of body mesh vertices in the neighborhood, where it is assumed that garments closely follow the body movement. However, for loose-fitting garments, the clothing deformation usually contains more complex nonrigid effects compared to human body which can be seen as a rigid body. In this case, garments behave significantly differently from the body. Thus, it is unreasonable to attach the garment to the body skeleton." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 531, + 546, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 531, + 546, + 662 + ], + "spans": [ + { + "bbox": [ + 304, + 531, + 546, + 662 + ], + "type": "text", + "content": "To address this issue, we adopt a set of anchors " + }, + { + "bbox": [ + 304, + 531, + 546, + 662 + ], + "type": "inline_equation", + "content": "\\{p_n\\}" + }, + { + "bbox": [ + 304, + 531, + 546, + 662 + ], + "type": "text", + "content": " around the mesh surface to guide the garment deformation, which detaches the garment from the body skeleton while preserving the body movement prior. Given a body motion sequence consisting of poses and translations, rigid anchor transformations including rotations " + }, + { + "bbox": [ + 304, + 531, + 546, + 662 + ], + "type": "inline_equation", + "content": "\\{R_{n}\\}" + }, + { + "bbox": [ + 304, + 531, + 546, + 662 + ], + "type": "text", + "content": " and translations " + }, + { + "bbox": [ + 304, + 531, + 546, + 662 + ], + "type": "inline_equation", + "content": "\\{T_{n}\\}" + }, + { + "bbox": [ + 304, + 531, + 546, + 662 + ], + "type": "text", + "content": " are estimated firstly by using Gated Recurrent Units (GRU) [7] (see the supplementary material for the network structure). Then, the " + }, + { + "bbox": [ + 304, + 531, + 546, + 662 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 531, + 546, + 662 + ], + "type": "text", + "content": " -th deformed garment vertex " + }, + { + "bbox": [ + 304, + 531, + 546, + 662 + ], + "type": "inline_equation", + "content": "v_{m}" + }, + { + "bbox": [ + 304, + 531, + 546, + 662 + ], + "type": "text", + "content": " can be represented by a weighted average of anchor transformations:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 670, + 545, + 713 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 670, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 670, + 545, + 713 + ], + "type": "interline_equation", + "content": "v _ {m} = \\sum_ {n = 1} ^ {N} w _ {m n} \\left(R _ {n} v _ {m} ^ {c} + T _ {n}\\right), w _ {m n} \\geq 0 \\text {a n d} \\sum_ {n = 1} ^ {N} w _ {m n} = 1, \\tag {2}", + "image_path": "36606ec71e6e8ff24708626d27d73259539d34df60903ed8254ec4ab7200c893.jpg" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "type": "text", + "content": "493" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "type": "inline_equation", + "content": "v_{m}^{c}" + }, + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "type": "text", + "content": "-th vertex of garment mesh template, " + }, + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "type": "inline_equation", + "content": "w_{mn}" + }, + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "type": "text", + "content": " is the blend weight of " + }, + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "type": "inline_equation", + "content": "v_{m}" + }, + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "type": "text", + "content": " regarding to the " + }, + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "type": "text", + "content": "-th anchor and " + }, + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "type": "text", + "content": " is the number of anchors. To determine the anchor-vertex relationship and maintain the sparsity of " + }, + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "type": "inline_equation", + "content": "\\{w_{n}\\}" + }, + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "type": "text", + "content": ", we initialize the anchors as the clustering centers of vertices of the mesh template. Then, each vertex is only influenced by the blend weights of its " + }, + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "type": "inline_equation", + "content": "N'" + }, + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "type": "inline_equation", + "content": "N' \\ll N" + }, + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "type": "text", + "content": ") nearest anchors and the others remain zeros during training. Compared to the direct prediction of deformed mesh vertex coordinates, the rigid anchor transformations provide more generalized representations of complex deformations due to fewer parameters required to be learned for the prediction." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 216, + 289, + 288 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 216, + 289, + 288 + ], + "spans": [ + { + "bbox": [ + 46, + 216, + 289, + 288 + ], + "type": "text", + "content": "Two strategies of anchor transformation configuration are designed for loose and tight types of garments. For the loose type, to utilize the prior of the global human body orientation " + }, + { + "bbox": [ + 46, + 216, + 289, + 288 + ], + "type": "inline_equation", + "content": "R_{global}" + }, + { + "bbox": [ + 46, + 216, + 289, + 288 + ], + "type": "text", + "content": ", we predict transformations relative to the root joint " + }, + { + "bbox": [ + 46, + 216, + 289, + 288 + ], + "type": "inline_equation", + "content": "J_{root}" + }, + { + "bbox": [ + 46, + 216, + 289, + 288 + ], + "type": "text", + "content": " of the body and the anchor transformation can be defined as:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 55, + 296, + 287, + 338 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 296, + 287, + 338 + ], + "spans": [ + { + "bbox": [ + 55, + 296, + 287, + 338 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} R _ {n} ^ {\\text {l o o s e}} = R _ {\\text {g l o b a l}} R _ {n} ([ \\theta , t ]), \\\\ T _ {n} ^ {\\text {l o o s e}} = R _ {\\text {g l o b a l}} \\left(T _ {n} ([ \\theta , t ]) - R _ {n} ([ \\theta , t ]) J _ {\\text {r o o t}}\\right) + J _ {\\text {r o o t}}, \\tag {3} \\\\ \\end{array}", + "image_path": "d534c318764b6b7625526066ace6dd6c78b7195f4d4bb71c0a5793a11c6ec8a4.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 347, + 287, + 397 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 347, + 287, + 397 + ], + "spans": [ + { + "bbox": [ + 46, + 347, + 287, + 397 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 347, + 287, + 397 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 347, + 287, + 397 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 347, + 287, + 397 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 347, + 287, + 397 + ], + "type": "text", + "content": " are the body pose and translation, respectively. For the tight type, the garment mostly follows the body movement. Thus, we predict an incremental change on the basis of body vertex rotation " + }, + { + "bbox": [ + 46, + 347, + 287, + 397 + ], + "type": "inline_equation", + "content": "R_{body}" + }, + { + "bbox": [ + 46, + 347, + 287, + 397 + ], + "type": "text", + "content": " and offset " + }, + { + "bbox": [ + 46, + 347, + 287, + 397 + ], + "type": "inline_equation", + "content": "T_{body}" + }, + { + "bbox": [ + 46, + 347, + 287, + 397 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 96, + 403, + 287, + 435 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 96, + 403, + 287, + 435 + ], + "spans": [ + { + "bbox": [ + 96, + 403, + 287, + 435 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} R _ {n} ^ {t i g h t} = R _ {b o d y} R _ {n} ([ \\theta , t ]), \\\\ T _ {n} ^ {\\text {t i g h t}} = R _ {\\text {b o d y}} T _ {n} ([ \\theta , t ]) + T _ {\\text {b o d y}}, \\tag {4} \\\\ \\end{array}", + "image_path": "8741bba00bd2454065ea463c952e1d2f6c4b21b36af91f66411b299a294b3a82.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 443, + 287, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 443, + 287, + 502 + ], + "spans": [ + { + "bbox": [ + 46, + 443, + 287, + 502 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 443, + 287, + 502 + ], + "type": "inline_equation", + "content": "R_{body}" + }, + { + "bbox": [ + 46, + 443, + 287, + 502 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 443, + 287, + 502 + ], + "type": "inline_equation", + "content": "T_{body}" + }, + { + "bbox": [ + 46, + 443, + 287, + 502 + ], + "type": "text", + "content": " is the transformation of the body mesh vertex closest to the anchor " + }, + { + "bbox": [ + 46, + 443, + 287, + 502 + ], + "type": "inline_equation", + "content": "p_n" + }, + { + "bbox": [ + 46, + 443, + 287, + 502 + ], + "type": "text", + "content": ". Furthermore, we can combine these two strategies for garments with both tight and loose parts, e.g., dresses, by classifying which part the anchor belongs to according to its distance to body joints." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 502, + 287, + 587 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 502, + 287, + 587 + ], + "spans": [ + { + "bbox": [ + 46, + 502, + 287, + 587 + ], + "type": "text", + "content": "Once the primary rotations and translations in the garment deformation caused by the articulation are expressed in Eq. (2), the nonlinear residual deformation can be disentangled with the garment articulation and defined as pervertex displacements " + }, + { + "bbox": [ + 46, + 502, + 287, + 587 + ], + "type": "inline_equation", + "content": "D([\\theta, t])" + }, + { + "bbox": [ + 46, + 502, + 287, + 587 + ], + "type": "text", + "content": " in an unposed canonical space. Utilizing the skinning function in Eq. (1), the overall garment deformation is given by" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 79, + 595, + 287, + 610 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 79, + 595, + 287, + 610 + ], + "spans": [ + { + "bbox": [ + 79, + 595, + 287, + 610 + ], + "type": "interline_equation", + "content": "V _ {p r e d} = W \\left(\\mathbf {T} _ {g} + D ([ \\theta , t ]), G ([ \\theta , t ]), \\mathbf {w} _ {p}\\right), \\tag {5}", + "image_path": "aab0828001f1b2738426b2e3f605c28c67373ffcd0b8554abd77c6dccba8bd88.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{T}_g" + }, + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "text", + "content": " is the garment mesh template, " + }, + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{w}_p" + }, + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "text", + "content": " is the anchor-vertex blend weights and " + }, + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "inline_equation", + "content": "G([\\theta ,t])" + }, + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "text", + "content": " is the anchor transformations predicted with the body motion. We argue that such decomposition by anchors extremely reduces the complexity of pose-dependent garment deformation prediction because large deformations have been handled by transformations of sparse anchors and only small displacements need to be regressed in the canonical space." + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 315, + 71, + 538, + 122 + ], + "blocks": [ + { + "bbox": [ + 315, + 71, + 538, + 122 + ], + "lines": [ + { + "bbox": [ + 315, + 71, + 538, + 122 + ], + "spans": [ + { + "bbox": [ + 315, + 71, + 538, + 122 + ], + "type": "image", + "image_path": "58b9717ad9817a4115433f67110665eb4c3f3569145f524450b694b9f5a83e88.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 133, + 547, + 177 + ], + "lines": [ + { + "bbox": [ + 304, + 133, + 547, + 177 + ], + "spans": [ + { + "bbox": [ + 304, + 133, + 547, + 177 + ], + "type": "text", + "content": "Figure 3. Examples of adaptive anchor updating by using the local attention mask with the mesh simplification as supervision. The blue points are anchors initialized by " + }, + { + "bbox": [ + 304, + 133, + 547, + 177 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 133, + 547, + 177 + ], + "type": "text", + "content": "-means and the orange ones are the updated anchors." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 194, + 491, + 207 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 194, + 491, + 207 + ], + "spans": [ + { + "bbox": [ + 306, + 194, + 491, + 207 + ], + "type": "text", + "content": "3.2. Learning Anchor Transformations" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 213, + 545, + 272 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 213, + 545, + 272 + ], + "spans": [ + { + "bbox": [ + 304, + 213, + 545, + 272 + ], + "type": "text", + "content": "Different from [25] which resorts to the external skinning decomposition algorithm, i.e., SSDR [17], to extract the garment skeleton from smoothed mesh sequences, here we jointly learn rigid transformations, blend weights and positions of anchors in a unified framework." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 273, + 545, + 297 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 273, + 545, + 297 + ], + "spans": [ + { + "bbox": [ + 305, + 273, + 545, + 297 + ], + "type": "text", + "content": "We first apply an L2 loss term on the predicted mesh vertices to recover the shape of deformed mesh:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 375, + 301, + 545, + 317 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 375, + 301, + 545, + 317 + ], + "spans": [ + { + "bbox": [ + 375, + 301, + 545, + 317 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {r e c} = \\left| \\left| V _ {p r e d} - V _ {g t} \\right| \\right| _ {2} ^ {2}, \\tag {6}", + "image_path": "3bf11ea842240b697e61835a433f85f5b8b61e19900a87f5828b131cfbbdc049.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 322, + 545, + 369 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 322, + 545, + 369 + ], + "spans": [ + { + "bbox": [ + 304, + 322, + 545, + 369 + ], + "type": "text", + "content": "which minimizes the Euclidean distance between the predicted vertices and the ground-truth deformed vertices. Then a loss term is used to keep the similarity of the graph Laplacians between two meshes:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 364, + 374, + 545, + 389 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 364, + 374, + 545, + 389 + ], + "spans": [ + { + "bbox": [ + 364, + 374, + 545, + 389 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {l a p} = \\left\\| \\triangle V _ {p r e d} - \\triangle V _ {g t} \\right\\| _ {2} ^ {2}. \\tag {7}", + "image_path": "86d392d3269081c663853a9db3596ae503c4f0be2840afc0bb5298f6e24281b2.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 394, + 545, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 394, + 545, + 418 + ], + "spans": [ + { + "bbox": [ + 304, + 394, + 545, + 418 + ], + "type": "text", + "content": "A collision term [25] is also added to avoid garment-body collisions. Thus, the loss on the vertex can be given by" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 345, + 425, + 545, + 437 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 345, + 425, + 545, + 437 + ], + "spans": [ + { + "bbox": [ + 345, + 425, + 545, + 437 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {v e r t}} = \\mathcal {L} _ {\\text {r e c}} + \\beta_ {1} \\mathcal {L} _ {\\text {l a p}} + \\beta_ {2} \\mathcal {L} _ {\\text {c o l l i s i o n}}, \\tag {8}", + "image_path": "27566148e10dbf5472af6248afc7c533251d86ef89b83ee2a7af7bcf4347a6ca.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 443, + 545, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 443, + 545, + 467 + ], + "spans": [ + { + "bbox": [ + 304, + 443, + 545, + 467 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 443, + 545, + 467 + ], + "type": "inline_equation", + "content": "\\beta_{1}" + }, + { + "bbox": [ + 304, + 443, + 545, + 467 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 443, + 545, + 467 + ], + "type": "inline_equation", + "content": "\\beta_{2}" + }, + { + "bbox": [ + 304, + 443, + 545, + 467 + ], + "type": "text", + "content": " are trade-off coefficients for controlling the degree of smoothing and collision, respectively." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 467, + 545, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 467, + 545, + 548 + ], + "spans": [ + { + "bbox": [ + 304, + 467, + 545, + 548 + ], + "type": "text", + "content": "However, only optimizing the vertex position cannot guarantee the physical meaning of learned anchor transformations in space, which leads to poor generalization. Thus, we explicitly constrain the transformed anchors to be located around the deformed mesh surface. To this end, the position of anchor " + }, + { + "bbox": [ + 304, + 467, + 545, + 548 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 304, + 467, + 545, + 548 + ], + "type": "text", + "content": " is recalculated by its adjacent mesh vertices:" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 378, + 547, + 545, + 578 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 378, + 547, + 545, + 578 + ], + "spans": [ + { + "bbox": [ + 378, + 547, + 545, + 578 + ], + "type": "interline_equation", + "content": "p = \\frac {1}{K} \\sum_ {v _ {k} ^ {c} \\in K (p, \\mathbf {T} _ {g})} v _ {k} ^ {c}, \\tag {9}", + "image_path": "aeb57bbb8193ca33a1bfcba0b2a7c067f794e934bbb26f3ed77906b7d34de19f.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 580, + 545, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 580, + 545, + 640 + ], + "spans": [ + { + "bbox": [ + 304, + 580, + 545, + 640 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 580, + 545, + 640 + ], + "type": "inline_equation", + "content": "K(p, \\mathbf{T}_g)" + }, + { + "bbox": [ + 304, + 580, + 545, + 640 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 304, + 580, + 545, + 640 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 580, + 545, + 640 + ], + "type": "text", + "content": " nearest vertices of " + }, + { + "bbox": [ + 304, + 580, + 545, + 640 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 304, + 580, + 545, + 640 + ], + "type": "text", + "content": " on the mesh template. Then, the target point " + }, + { + "bbox": [ + 304, + 580, + 545, + 640 + ], + "type": "inline_equation", + "content": "p_{tgt}" + }, + { + "bbox": [ + 304, + 580, + 545, + 640 + ], + "type": "text", + "content": " of transformed anchor " + }, + { + "bbox": [ + 304, + 580, + 545, + 640 + ], + "type": "inline_equation", + "content": "p_G" + }, + { + "bbox": [ + 304, + 580, + 545, + 640 + ], + "type": "text", + "content": " can be defined with the same set of vertices " + }, + { + "bbox": [ + 304, + 580, + 545, + 640 + ], + "type": "inline_equation", + "content": "K(p, \\mathbf{T}_g)" + }, + { + "bbox": [ + 304, + 580, + 545, + 640 + ], + "type": "text", + "content": " on the deformed mesh and a transformation consistency loss is defined as" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 314, + 646, + 545, + 661 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 646, + 545, + 661 + ], + "spans": [ + { + "bbox": [ + 314, + 646, + 545, + 661 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {c o n s i s}} = \\left\\| p _ {G} - p _ {t g t} \\right\\| _ {2} ^ {2} + \\gamma \\left\\| \\mathbf {n} \\left(p _ {G}\\right) - \\mathbf {n} \\left(p _ {t g t}\\right) \\right\\| _ {2} ^ {2}, \\tag {10}", + "image_path": "1dfb68101d058591cc13ac9d0b4a0256e21f6dd40fbbe603f4032abe8aeed0b3.jpg" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{n}(.)" + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": " is the unit normal of point and " + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": " is a weight factor. By encouraging the transformed anchor " + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "inline_equation", + "content": "p_G" + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": " to be similar to " + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "inline_equation", + "content": "p_{tgt}" + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": " in position and normal, the learned anchor transformation indicates the mean transformation of " + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": " nearest" + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 297, + 749, + 313, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 749, + 313, + 757 + ], + "spans": [ + { + "bbox": [ + 297, + 749, + 313, + 757 + ], + "type": "text", + "content": "494" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 71, + 538, + 297 + ], + "blocks": [ + { + "bbox": [ + 53, + 71, + 538, + 297 + ], + "lines": [ + { + "bbox": [ + 53, + 71, + 538, + 297 + ], + "spans": [ + { + "bbox": [ + 53, + 71, + 538, + 297 + ], + "type": "image", + "image_path": "45c590dd395b4e064c51716ae9422a1bc69453eadb6c22daffc9e7bf14c2c950.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 300, + 546, + 344 + ], + "lines": [ + { + "bbox": [ + 46, + 300, + 546, + 344 + ], + "spans": [ + { + "bbox": [ + 46, + 300, + 546, + 344 + ], + "type": "text", + "content": "Figure 4. Qualitative comparison with and without different components of AnchorDEF including (a) anchor transformation consistency " + }, + { + "bbox": [ + 46, + 300, + 546, + 344 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{consis}" + }, + { + "bbox": [ + 46, + 300, + 546, + 344 + ], + "type": "text", + "content": " and (b) adaptive anchor updating " + }, + { + "bbox": [ + 46, + 300, + 546, + 344 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{anch}" + }, + { + "bbox": [ + 46, + 300, + 546, + 344 + ], + "type": "text", + "content": ". Without " + }, + { + "bbox": [ + 46, + 300, + 546, + 344 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{consis}" + }, + { + "bbox": [ + 46, + 300, + 546, + 344 + ], + "type": "text", + "content": ", the model cannot accurately predict the shape of deformed mesh and loses some surface geometry details. Without " + }, + { + "bbox": [ + 46, + 300, + 546, + 344 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{anch}" + }, + { + "bbox": [ + 46, + 300, + 546, + 344 + ], + "type": "text", + "content": ", the model is unable to produce realistic garment deformations due to the under-expressed anchor transformations." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 365, + 287, + 400 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 365, + 287, + 400 + ], + "spans": [ + { + "bbox": [ + 46, + 365, + 287, + 400 + ], + "type": "text", + "content": "vertices of " + }, + { + "bbox": [ + 46, + 365, + 287, + 400 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 46, + 365, + 287, + 400 + ], + "type": "text", + "content": ". It can be viewed as a regularization for the transformation magnitude and direction to discover essential transformations in deformation." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 401, + 288, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 401, + 288, + 437 + ], + "spans": [ + { + "bbox": [ + 46, + 401, + 288, + 437 + ], + "type": "text", + "content": "We further enforce the direction from " + }, + { + "bbox": [ + 46, + 401, + 288, + 437 + ], + "type": "inline_equation", + "content": "p_{tgt}" + }, + { + "bbox": [ + 46, + 401, + 288, + 437 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 401, + 288, + 437 + ], + "type": "inline_equation", + "content": "p_G" + }, + { + "bbox": [ + 46, + 401, + 288, + 437 + ], + "type": "text", + "content": " to be consistent with the direction of " + }, + { + "bbox": [ + 46, + 401, + 288, + 437 + ], + "type": "inline_equation", + "content": "\\mathbf{n}(p_{tgt})" + }, + { + "bbox": [ + 46, + 401, + 288, + 437 + ], + "type": "text", + "content": " by minimizing the following penalty term:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 92, + 441, + 287, + 455 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 92, + 441, + 287, + 455 + ], + "spans": [ + { + "bbox": [ + 92, + 441, + 287, + 455 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {d i r} = 1 - \\cos \\left(p _ {G} - p _ {t g t}, \\mathbf {n} \\left(p _ {t g t}\\right)\\right), \\tag {11}", + "image_path": "5938f5c3749f798fc38f4cbd96067ff6becd57ba9365d712ab18b3a2d25157c0.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 459, + 287, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 459, + 287, + 578 + ], + "spans": [ + { + "bbox": [ + 46, + 459, + 287, + 578 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 459, + 287, + 578 + ], + "type": "inline_equation", + "content": "\\cos (\\cdot ,\\cdot)" + }, + { + "bbox": [ + 46, + 459, + 287, + 578 + ], + "type": "text", + "content": " is the cosine similarity. Intuitively, this penalty term makes " + }, + { + "bbox": [ + 46, + 459, + 287, + 578 + ], + "type": "inline_equation", + "content": "p_{G}" + }, + { + "bbox": [ + 46, + 459, + 287, + 578 + ], + "type": "text", + "content": " tend to be outside of the plane formed by " + }, + { + "bbox": [ + 46, + 459, + 287, + 578 + ], + "type": "inline_equation", + "content": "p_{tgt}" + }, + { + "bbox": [ + 46, + 459, + 287, + 578 + ], + "type": "text", + "content": " to reduce the garment-body interpenetration. Adaptive Anchor Updating. It is still not enough to have a physically meaningful anchor transformation, we also need an expressive transformation in geometry to better represent the garment deformation. We observe that mesh regions with folds and boundaries usually play an important role on showing garment shape characteristics and contain more deformation information compared with smooth regions." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 578, + 288, + 686 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 578, + 288, + 686 + ], + "spans": [ + { + "bbox": [ + 46, + 578, + 288, + 686 + ], + "type": "text", + "content": "To make the anchors reflect such intrinsic structure of garment shape, we propose to employ mesh simplification to provide a signal of supervision for finding such representative anchors. Here Quadric Error Metric (QEM) [10] is used to obtain simplified mesh vertices by collapsing edges while preserving the garment topology. Because there is no one-to-one correspondence between the anchors " + }, + { + "bbox": [ + 46, + 578, + 288, + 686 + ], + "type": "inline_equation", + "content": "\\{p_n\\}" + }, + { + "bbox": [ + 46, + 578, + 288, + 686 + ], + "type": "text", + "content": " and the simplified vertices " + }, + { + "bbox": [ + 46, + 578, + 288, + 686 + ], + "type": "inline_equation", + "content": "\\{\\tilde{v}_m\\}" + }, + { + "bbox": [ + 46, + 578, + 288, + 686 + ], + "type": "text", + "content": ", the Chamfer distance is adopted as the optimization objective:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 58, + 689, + 287, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 689, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 58, + 689, + 287, + 715 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {a n c h} = \\sum_ {p} \\min _ {\\tilde {v}} | | p - \\tilde {v} | | _ {2} ^ {2} + \\sum_ {\\tilde {v}} \\min _ {p} | | p - \\tilde {v} | | _ {2} ^ {2}. \\tag {12}", + "image_path": "8b6a29f9cc2145b9e667fe3466b56da3323ebbb05cfb2f1bde931e4a4bbe3d61.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 365, + 545, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 365, + 545, + 389 + ], + "spans": [ + { + "bbox": [ + 305, + 365, + 545, + 389 + ], + "type": "text", + "content": "To be able to update the anchor position, we rewrite Eq. (9) using learnable weights " + }, + { + "bbox": [ + 305, + 365, + 545, + 389 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 305, + 365, + 545, + 389 + ], + "type": "text", + "content": " as" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 370, + 396, + 545, + 431 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 370, + 396, + 545, + 431 + ], + "spans": [ + { + "bbox": [ + 370, + 396, + 545, + 431 + ], + "type": "interline_equation", + "content": "p = \\frac {1}{\\sum_ {j = 1} ^ {K} e ^ {\\alpha_ {j}}} \\sum_ {k = 1} ^ {K} e ^ {\\alpha_ {k}} v _ {k} ^ {c}. \\tag {13}", + "image_path": "d2a5db3c2bbcb9a953de88566ec47180696943a467e0573c4776ac9d583d97d8.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 437, + 546, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 437, + 546, + 557 + ], + "spans": [ + { + "bbox": [ + 304, + 437, + 546, + 557 + ], + "type": "text", + "content": "Actually, this equals to learning a local attention mask for the anchor to determine how the adjacent vertices contribute to its position. Fig. 3 shows that by optimizing the weights " + }, + { + "bbox": [ + 304, + 437, + 546, + 557 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 437, + 546, + 557 + ], + "type": "text", + "content": " with supervision of the simplified vertices, the anchors are pushed to inflection points of folds and boundaries of the mesh and thus able to better represent the deformed mesh vertices by interpolating their transformation matrices. Note that we optimize the anchor position on the entire dataset not only on the mesh template because some smooth regions of the template may create new folds after posing." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 557, + 545, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 545, + 581 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 545, + 581 + ], + "type": "text", + "content": "On the other hand, if we reformulate the transformed anchor " + }, + { + "bbox": [ + 304, + 557, + 545, + 581 + ], + "type": "inline_equation", + "content": "p_G" + }, + { + "bbox": [ + 304, + 557, + 545, + 581 + ], + "type": "text", + "content": " with Eq. (13) as:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 318, + 589, + 545, + 623 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 589, + 545, + 623 + ], + "spans": [ + { + "bbox": [ + 318, + 589, + 545, + 623 + ], + "type": "interline_equation", + "content": "p _ {G} = R p + T = \\frac {1}{\\sum_ {j = 1} ^ {K} e ^ {\\alpha_ {j}}} \\sum_ {k = 1} ^ {K} e ^ {\\alpha_ {k}} \\left(R v _ {k} ^ {c} + T\\right), \\tag {14}", + "image_path": "d88808c8ae153f9bdd99a4212cb7da78a750dae251c59eac3b18d6eb4a2d9db8.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": "the process of transformation learning for the anchor, i.e., Eq. (10), can be interpreted as a way to find an appropriate transformation for its adjacent mesh vertices by the importance which is reflected in the weights learned from the mesh simplification. The larger the weight, the greater the impact of the vertex transformation on the anchor transformation learning." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "type": "text", + "content": "495" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 77, + 72, + 159, + 196 + ], + "blocks": [ + { + "bbox": [ + 56, + 128, + 69, + 140 + ], + "lines": [ + { + "bbox": [ + 56, + 128, + 69, + 140 + ], + "spans": [ + { + "bbox": [ + 56, + 128, + 69, + 140 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 77, + 72, + 159, + 196 + ], + "lines": [ + { + "bbox": [ + 77, + 72, + 159, + 196 + ], + "spans": [ + { + "bbox": [ + 77, + 72, + 159, + 196 + ], + "type": "image", + "image_path": "d0609ba541d195d74d6eb42afcbd48dca8654b81e18c758beb1ab8bb8dd397db.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 205, + 75, + 277, + 192 + ], + "blocks": [ + { + "bbox": [ + 178, + 128, + 192, + 140 + ], + "lines": [ + { + "bbox": [ + 178, + 128, + 192, + 140 + ], + "spans": [ + { + "bbox": [ + 178, + 128, + 192, + 140 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 205, + 75, + 277, + 192 + ], + "lines": [ + { + "bbox": [ + 205, + 75, + 277, + 192 + ], + "spans": [ + { + "bbox": [ + 205, + 75, + 277, + 192 + ], + "type": "image", + "image_path": "97d1b9c0206670243f7062f07688ea1dc999f31ed749ddf7d1b5d0b13ff5f175.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 206, + 287, + 231 + ], + "lines": [ + { + "bbox": [ + 47, + 206, + 287, + 231 + ], + "spans": [ + { + "bbox": [ + 47, + 206, + 287, + 231 + ], + "type": "text", + "content": "Figure 5. Visualization of anchors transformed by (a) only optimizing the mesh vertices during training and (b) AnchorDEF." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 251, + 287, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 251, + 287, + 275 + ], + "spans": [ + { + "bbox": [ + 47, + 251, + 287, + 275 + ], + "type": "text", + "content": "Lastly, combining Eq. (8), Eqs. (10) to (12), the overall objective function for our model is given by:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 64, + 285, + 287, + 298 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 64, + 285, + 287, + 298 + ], + "spans": [ + { + "bbox": [ + 64, + 285, + 287, + 298 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\mathcal {L} _ {\\text {v e r t}} + \\lambda_ {1} \\mathcal {L} _ {\\text {c o n s i s}} + \\lambda_ {2} \\mathcal {L} _ {\\text {d i r}} + \\lambda_ {3} \\mathcal {L} _ {\\text {a n c h}}, \\tag {15}", + "image_path": "186b09e428dffff1dbc06d3f34df3634268e7da0ce86fe846c5869245bb82c09.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 308, + 155, + 319 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 308, + 155, + 319 + ], + "spans": [ + { + "bbox": [ + 47, + 308, + 155, + 319 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 308, + 155, + 319 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 47, + 308, + 155, + 319 + ], + "type": "text", + "content": "s are loss weights." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 331, + 128, + 345 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 331, + 128, + 345 + ], + "spans": [ + { + "bbox": [ + 47, + 331, + 128, + 345 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 351, + 287, + 471 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 351, + 287, + 471 + ], + "spans": [ + { + "bbox": [ + 46, + 351, + 287, + 471 + ], + "type": "text", + "content": "We evaluate the proposed AnchorDEF on the VTO [31] dataset containing two types of garments, i.e., dress and T-shirt. Following [25], RMSE (Root Mean Squared Error), Hausdorff distance and STED (Spatio-Temporal Edge Difference) [36] are adopted to assess the quality of deformed meshes. The first two measure the distance between predicted and ground truth meshes and STED reflects the difference between their dynamics. We also compare AnchorDEF against other 3D garment deformation methods [25, 26]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 472, + 288, + 626 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 472, + 288, + 626 + ], + "spans": [ + { + "bbox": [ + 46, + 472, + 288, + 626 + ], + "type": "text", + "content": "Implementation Details. To capture the motion dynamics, a network with 2 GRU layers of size 256 is used as the body motion encoder. Two 2-layered MLPs of size 256 are used to regress the anchor transformations and per-vertex displacements, respectively. The number of anchors associated with each mesh vertex is set to 8, which can obtain the desired smooth surface, and the number of neighboring vertices for computing the anchor position is set to 128. For the garment sequences of VTO, 4 clips are randomly selected for testing and the rest is used as the training set, and the length of training sequence is 30. Please refer to the supplemental materials for more details on training and inference." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 635, + 141, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 635, + 141, + 647 + ], + "spans": [ + { + "bbox": [ + 47, + 635, + 141, + 647 + ], + "type": "text", + "content": "4.1. Ablation Study" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 653, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 653, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 653, + 288, + 713 + ], + "type": "text", + "content": "We validate the effectiveness of main components in our proposed AnchorDEF. We firstly assess the importance of anchor transformation consistency, i.e., " + }, + { + "bbox": [ + 47, + 653, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text{consis}}" + }, + { + "bbox": [ + 47, + 653, + 288, + 713 + ], + "type": "text", + "content": " in Eq. (10). As reported in Table 1, keeping the consistency of learned anchor transformations is able to improve all metrics due" + } + ] + } + ], + "index": 12 + }, + { + "type": "table", + "bbox": [ + 309, + 71, + 545, + 141 + ], + "blocks": [ + { + "bbox": [ + 309, + 71, + 545, + 141 + ], + "lines": [ + { + "bbox": [ + 309, + 71, + 545, + 141 + ], + "spans": [ + { + "bbox": [ + 309, + 71, + 545, + 141 + ], + "type": "table", + "html": "
Methodsw/o Lconsisw/o LanchAnchorDEF
RMSE ↓17.2116.4916.05
Hausdorff ↓75.0174.5374.20
STED ↓0.05950.05260.0493
", + "image_path": "de9a9a9212042bdd71da5d439457b49c233cde99e9012f6390c54327dbebcf52.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_body" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 309, + 208, + 544, + 281 + ], + "blocks": [ + { + "bbox": [ + 309, + 208, + 544, + 281 + ], + "lines": [ + { + "bbox": [ + 309, + 208, + 544, + 281 + ], + "spans": [ + { + "bbox": [ + 309, + 208, + 544, + 281 + ], + "type": "image", + "image_path": "3dce5a95eb57df17fa5800419f431349ae16cdddc05e43cd412ed3901a4ba16a.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 287, + 546, + 319 + ], + "lines": [ + { + "bbox": [ + 305, + 287, + 546, + 319 + ], + "spans": [ + { + "bbox": [ + 305, + 287, + 546, + 319 + ], + "type": "text", + "content": "Figure 6. Qualitative comparison with and without the penalty " + }, + { + "bbox": [ + 305, + 287, + 546, + 319 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{dir}" + }, + { + "bbox": [ + 305, + 287, + 546, + 319 + ], + "type": "text", + "content": " on the direction from the target anchor to the transformed one." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 309, + 335, + 544, + 423 + ], + "blocks": [ + { + "bbox": [ + 309, + 335, + 544, + 423 + ], + "lines": [ + { + "bbox": [ + 309, + 335, + 544, + 423 + ], + "spans": [ + { + "bbox": [ + 309, + 335, + 544, + 423 + ], + "type": "image", + "image_path": "88967a35f02d45471547027bb244a8ee7250577c1bf28182ee82331b5e9c44b9.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 430, + 547, + 464 + ], + "lines": [ + { + "bbox": [ + 305, + 430, + 547, + 464 + ], + "spans": [ + { + "bbox": [ + 305, + 430, + 547, + 464 + ], + "type": "text", + "content": "Figure 7. Qualitative comparison of using different numbers of anchors. Using 160 anchors produces finer and more accurate deformation compared with other anchor numbers." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 17 + }, + { + "type": "table", + "bbox": [ + 308, + 475, + 545, + 548 + ], + "blocks": [ + { + "bbox": [ + 306, + 150, + 547, + 194 + ], + "lines": [ + { + "bbox": [ + 306, + 150, + 547, + 194 + ], + "spans": [ + { + "bbox": [ + 306, + 150, + 547, + 194 + ], + "type": "text", + "content": "Table 1. Quantitative results obtained by different components of AnchorDEF, i.e., without anchor transformation consistency (w/o " + }, + { + "bbox": [ + 306, + 150, + 547, + 194 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text{cosis}}" + }, + { + "bbox": [ + 306, + 150, + 547, + 194 + ], + "type": "text", + "content": "), without adaptive anchor updating (w/o " + }, + { + "bbox": [ + 306, + 150, + 547, + 194 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text{anch}}" + }, + { + "bbox": [ + 306, + 150, + 547, + 194 + ], + "type": "text", + "content": ") and the full model (AnchorDEF)." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 475, + 545, + 548 + ], + "lines": [ + { + "bbox": [ + 308, + 475, + 545, + 548 + ], + "spans": [ + { + "bbox": [ + 308, + 475, + 545, + 548 + ], + "type": "table", + "html": "
Num. Anchor2080160320
RMSE ↓17.7816.8216.0517.52
Hausdorff ↓75.3074.7174.2075.13
STED ↓0.06200.05390.04930.0625
", + "image_path": "8214b2265b06d12d2e4873bae3cb7b5d73bdb04ec056706a306a10a78e8b4ef2.jpg" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "table_body" + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 555, + 544, + 567 + ], + "lines": [ + { + "bbox": [ + 306, + 555, + 544, + 567 + ], + "spans": [ + { + "bbox": [ + 306, + 555, + 544, + 567 + ], + "type": "text", + "content": "Table 2. Quantitative results of using different numbers of anchors." + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 581, + 545, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 581, + 545, + 629 + ], + "spans": [ + { + "bbox": [ + 305, + 581, + 545, + 629 + ], + "type": "text", + "content": "to better generalization. Fig. 4 (a) illustrates the qualitative comparison. One can observe that without " + }, + { + "bbox": [ + 305, + 581, + 545, + 629 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text {consis }}" + }, + { + "bbox": [ + 305, + 581, + 545, + 629 + ], + "type": "text", + "content": " the model cannot accurately predict the shape of deformed mesh and loses some surface geometry details." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": "To evaluate the influence of adaptive anchor updating, Table 1 also reports the results without using " + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{anch}" + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": " in Eq. (12). The performance drops only using the clustering centers of " + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": "-means as the anchors. The reason is that compared with the clustering, the supervision with mesh simplification can provide key topology information, e.g., folds and boundaries, which is useful for learning representative" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 297, + 749, + 313, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 749, + 313, + 757 + ], + "spans": [ + { + "bbox": [ + 297, + 749, + 313, + 757 + ], + "type": "text", + "content": "496" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 55, + 72, + 539, + 295 + ], + "blocks": [ + { + "bbox": [ + 55, + 72, + 539, + 295 + ], + "lines": [ + { + "bbox": [ + 55, + 72, + 539, + 295 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 539, + 295 + ], + "type": "image", + "image_path": "01699bfded4d6dbf0041707f2b3cd930551f23fe4204bb7d88f040f267e00629.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 304, + 546, + 339 + ], + "lines": [ + { + "bbox": [ + 46, + 304, + 546, + 339 + ], + "spans": [ + { + "bbox": [ + 46, + 304, + 546, + 339 + ], + "type": "text", + "content": "Figure 8. Examples of our AnchorDEF for dynamic garment deformation in motion. The first row is the ground truth generated by physics-based simulation [24]. The second row is the results obtained by AnchorDEF. Our method can produce natural and realistic clothing dynamics, e.g., wrinkles from jumping and the swing of the dress caused by running." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 354, + 288, + 401 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 354, + 288, + 401 + ], + "spans": [ + { + "bbox": [ + 46, + 354, + 288, + 401 + ], + "type": "text", + "content": "anchor transformations. The qualitative results are shown in Fig. 4 (b). It can be observed that without " + }, + { + "bbox": [ + 46, + 354, + 288, + 401 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{anch}" + }, + { + "bbox": [ + 46, + 354, + 288, + 401 + ], + "type": "text", + "content": " the model is unable to produce realistic garment deformations due to the under-expressed anchor transformations." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 402, + 287, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 402, + 287, + 605 + ], + "spans": [ + { + "bbox": [ + 46, + 402, + 287, + 605 + ], + "type": "text", + "content": "Fig. 5 (a) and (b) visualize the anchors transformed by only optimizing the mesh vertices during training and AnchorDEF, respectively. For Fig. 5 (a), without the consistency constraint for anchor transformation, many of the transformed anchors are not on the deformed mesh surface, which is lack of clear physical meaning in space and easy to overfit. In contrast, AnchorDEF enforces the anchors to be transformed onto the deformed mesh surface, which prevents overfitting to a certain extent, thus has better generalization when testing. Furthermore, as shown in Fig. 5 (b), the transformed anchors are mainly distributed at the folds and boundaries of the mesh because of our adaptive anchor updating according to simplified mesh vertices, and thus capable of better expressing the deformation of mesh vertices, in particular those vertices far from them. In this way, the complexity of garment deformation space is reduced more effectively and more mesh shape details can be preserved." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "text", + "content": "Then we investigate the impact of the penalty " + }, + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{dir}" + }, + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "text", + "content": " (Eq. (11)) on the direction from the target anchor to the transformed one. As illustrated in Fig. 6, with " + }, + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{dir}" + }, + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "text", + "content": " the model can reduce the garment-body interpenetration. By enforcing the transformed anchors to be on the positive direction of target normals, the garment mesh vertices influenced by these anchors can be effectively pushed to the outside of the body surface while keeping the deformation accuracy due to moving along the direction of target normals." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 354, + 547, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 354, + 547, + 568 + ], + "spans": [ + { + "bbox": [ + 304, + 354, + 547, + 568 + ], + "type": "text", + "content": "We further assess the influence of the anchor number. Table 2 reports the results obtained by using 20, 80, 160 and 320 anchors, respectively. One can see that using more anchors to guide the mesh deformation obtains better results on all three metrics because the decomposition for the mesh deformation by using the rigid anchor transformations makes the nonlinear deformation can be more easily predicted as the small displacements in the canonical space without considering large rotations and translations caused by the body pose which has been handled by the anchor transformations. However, the performance drops as the number of anchors continues to increase because too many transformation parameters lead to unstable forecasts during testing. Fig. 7 shows the qualitative comparison. Using 160 anchors produces finer and more accurate deformation compared with other anchor numbers. Using 20 anchors only recover the contour of the deformed mesh, and using 80 and 320 anchors fail to obtain realistic deformation." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 569, + 547, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 569, + 547, + 629 + ], + "spans": [ + { + "bbox": [ + 304, + 569, + 547, + 629 + ], + "type": "text", + "content": "Fig. 8 shows some examples of our AnchorDEF for dynamic garment deformation in motion. Given a body motion sequence, our method can produce natural and realistic clothing dynamics, e.g., wrinkles from jumping and the swing of the dress caused by running." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 635, + 493, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 635, + 493, + 647 + ], + "spans": [ + { + "bbox": [ + 305, + 635, + 493, + 647 + ], + "type": "text", + "content": "4.2. Comparison with Related Methods" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "content": "We compare our method against related 3D garment deformation methods, including TailorNet [26] and VirtualBones [25] on different types of garments. As reported in Table 3, our AnchorDEF achieves the best results in all cases. Fig. 9 presents the qualitative comparison. Tailor-" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "type": "text", + "content": "497" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 71, + 70, + 520, + 159 + ], + "blocks": [ + { + "bbox": [ + 71, + 70, + 520, + 159 + ], + "lines": [ + { + "bbox": [ + 71, + 70, + 520, + 159 + ], + "spans": [ + { + "bbox": [ + 71, + 70, + 520, + 159 + ], + "type": "table", + "html": "
MethodsDressT-shirt
RMSE ↓Hausdorff ↓STED ↓RMSE ↓Hausdorff ↓STED ↓
TailorNet [26]22.9576.800.07579.9027.020.0418
VirtualBones [25]19.9183.390.072210.5231.510.0452
AnchorDEF16.0574.200.04936.2526.310.0262
", + "image_path": "1b2f662995d3522f4cf8c266afb524ffd5ca6730cea08d6da99a0be212bd7b9e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 120, + 163, + 472, + 175 + ], + "lines": [ + { + "bbox": [ + 120, + 163, + 472, + 175 + ], + "spans": [ + { + "bbox": [ + 120, + 163, + 472, + 175 + ], + "type": "text", + "content": "Table 3. Quantitative results of 3D garment deformation methods for different types of garments." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 53, + 186, + 537, + 347 + ], + "blocks": [ + { + "bbox": [ + 53, + 186, + 537, + 347 + ], + "lines": [ + { + "bbox": [ + 53, + 186, + 537, + 347 + ], + "spans": [ + { + "bbox": [ + 53, + 186, + 537, + 347 + ], + "type": "image", + "image_path": "c2fc42c9781079f56af953332a1c481fc2dd90bbfb54721f148f675928a73b97.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 156, + 347, + 166, + 356 + ], + "lines": [ + { + "bbox": [ + 156, + 347, + 166, + 356 + ], + "spans": [ + { + "bbox": [ + 156, + 347, + 166, + 356 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 358, + 546, + 392 + ], + "lines": [ + { + "bbox": [ + 46, + 358, + 546, + 392 + ], + "spans": [ + { + "bbox": [ + 46, + 358, + 546, + 392 + ], + "type": "text", + "content": "Figure 9. Qualitative comparison of 3D garment deformation methods for different types of garments, including TailorNet [26], VirtualBones [25] and Our AnchorDEF. With the learned anchor transformations, our method not only recovers large deformations of the dress but also produces fine surface details on the T-shirt." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 414, + 289, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 414, + 289, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 414, + 289, + 712 + ], + "type": "text", + "content": "Net [26] recovers folds on the T-shirt, but it fails to address the deformation of the dress which has different topology from human body. By interpolating the skinning blend weights, it alleviates the discontinuity of blend weights borrowed from the SMPL [20] body. However, this makes TailorNet only produce the outline of shapes with some folds missing and artifacts for large deformations of loose-fitting garments. VirtualBones [25] can estimate large deformations of the dress by using SSDR [17] to extract virtual bones of garments. However, it tends to keep the original folds of the dress template on the deformed mesh and cannot estimate well new folds generated by body motions on the T-shirt. VirtualBones needs SSDR to extract the garment skeleton and gets blend weights of bones in advance and fixes the bone position and blend weights during network training. Moreover, SSDR is performed on the low-frequency mesh sequences processed by Laplacian smoothing because it fails to address high-frequency garment deformations. Thus, the learned virtual bones are not necessarily optimal. In contrast, by jointly learning the rigid transformations, blend weights and positions of anchors, our AnchorDEF not only recovers large deformations of the dress but also produces fine surface details on the T-shirt. More qualitative results can be found in the supplemental materials." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 412, + 384, + 425 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 412, + 384, + 425 + ], + "spans": [ + { + "bbox": [ + 306, + 412, + 384, + 425 + ], + "type": "text", + "content": "5. Conclusions" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 438, + 545, + 619 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 438, + 545, + 619 + ], + "spans": [ + { + "bbox": [ + 304, + 438, + 545, + 619 + ], + "type": "text", + "content": "We present AnchorDEF, an anchor based deformation model, to predict 3D garment animation given a body motion sequence. With a set of anchors around the mesh surface, the garment deformation can be decomposed into a mixture of rigid anchor transformations and extra per-vertex displacements in a canonical space. The transformation consistency learning is introduced to guarantee the physical meaning of learned anchor transformations in space. Taking mesh simplification as supervision, We further optimize the anchor position for learning representative anchor transformations by making the anchor aware of local mesh topology with an attention mask. Extensive experiments on different types of garments demonstrate that AnchorDEF can effectively predict 3D garment deformation in motion for both tight and loose-fitting garments." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 624, + 545, + 672 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 624, + 545, + 672 + ], + "spans": [ + { + "bbox": [ + 304, + 624, + 545, + 672 + ], + "type": "text", + "content": "Limitations. Compared with the PBS methods, our method still lacks fine-level dynamics. Better exploiting the temporal information for the network architecture and supervision signals is a good direction for future work." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": "Acknowledgments. 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In Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), 2021. 1" + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 298, + 749, + 313, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 749, + 313, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 749, + 313, + 757 + ], + "type": "text", + "content": "500" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Learning Articulated Shape With Keypoint Pseudo-Labels From Web Images/e9a40181-29f2-4fab-842a-0bf24d5ccd9e_content_list.json b/2023/Learning Articulated Shape With Keypoint Pseudo-Labels From Web Images/e9a40181-29f2-4fab-842a-0bf24d5ccd9e_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..23da8d5c6234eb7a78b32e6128e6b4dc792651be --- /dev/null +++ b/2023/Learning Articulated Shape With Keypoint Pseudo-Labels From Web Images/e9a40181-29f2-4fab-842a-0bf24d5ccd9e_content_list.json @@ -0,0 +1,1466 @@ +[ + { + "type": "text", + "text": "Learning Articulated Shape with Keypoint Pseudo-labels from Web Images", + "text_level": 1, + "bbox": [ + 104, + 130, + 864, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Anastasis Stathopoulos\nRutgers University", + "bbox": [ + 107, + 181, + 292, + 217 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Georgios Pavlakos \nUC Berkeley", + "bbox": [ + 331, + 181, + 480, + 217 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Ligong Han\nRutgers University", + "bbox": [ + 519, + 181, + 671, + 217 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Dimitris Metaxas\nRutgers University", + "bbox": [ + 710, + 181, + 861, + 217 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 268, + 312, + 284 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "This paper shows that it is possible to learn models for monocular 3D reconstruction of articulated objects (e.g. horses, cows, sheep), using as few as 50-150 images labeled with 2D keypoints. Our proposed approach involves training category-specific keypoint estimators, generating 2D keypoint pseudo-labels on unlabeled web images, and using both the labeled and self-labeled sets to train 3D reconstruction models. It is based on two key insights: (1) 2D keypoint estimation networks trained on as few as 50-150 images of a given object category generalize well and generate reliable pseudo-labels; (2) a data selection mechanism can automatically create a \"curated\" subset of the unlabeled web images that can be used for training - we evaluate four data selection methods. Coupling these two insights enables us to train models that effectively utilize web images, resulting in improved 3D reconstruction performance for several articulated object categories beyond the fully-supervised baseline. Our approach can quickly bootstrap a model and requires only a few images labeled with 2D keypoints. This requirement can be easily satisfied for any new object category. To showcase the practicality of our approach for predicting the 3D shape of arbitrary object categories, we annotate 2D keypoints on 250 giraffe and bear images from COCO in just 2.5 hours per category.", + "bbox": [ + 75, + 300, + 473, + 664 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 708, + 207, + 724 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Predicting the 3D shape of an articulated object from a single image is a challenging task due to its underconstrained nature. Various successful approaches [14, 19] have been developed for inferring the 3D shape of humans. These approaches rely on strong supervision from 3D joint locations acquired using motion capture systems. Similar breakthroughs for other categories of articulated objects, such as animals, remain elusive. This is primarily due to the scarcity of appropriate training data. Some works (such as CMR [15]) learn to predict 3D shapes using only 2D labels for supervision. However, for most object categories even", + "bbox": [ + 75, + 734, + 468, + 901 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/0486219bc5557a1df66b3fa36f45399eb789b0edd7aac3024a01711480e5c7d0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 506, + 268, + 663, + 367 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/3b722e1c7b79f7edf5c396342cbcb331d1b58d651e9a1ca9a9e916f1e0d9d3ac.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 673, + 270, + 890, + 367 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/40493618943f602b2713fc0beb9ad8a9c4539ef7e95653a10a0d8978fb46cf54.jpg", + "image_caption": [ + "Figure 1. Overview of the proposed framework. It includes: (a) training a category-specific keypoint estimator with a limited labeled set $S$ , (b) generating keypoints pseudo-labels on web images, (c) automatic curation of web images to create a subset $\\mathcal{U}'$ , and (d) training a model for 3D shape prediction with images from $S$ and $\\mathcal{U}'$ ." + ], + "image_footnote": [], + "bbox": [ + 504, + 373, + 687, + 453 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/1d3afeae6daa67ea6208bf61af64c0927e7635336c2e5873f0f6e1debc177d5e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 699, + 373, + 890, + 455 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "2D labels are limited or non-existent. We ask: how can we learn models that predict the 3D shape of articulated objects in-the-wild when limited or no annotated images are available for a given object category?", + "bbox": [ + 496, + 580, + 890, + 642 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this paper we propose an approach that requires as few as 50-150 images labeled with 2D keypoints. This labeled set can be easily and quickly created for any object category. Our proposed approach is illustrated in Figure 1 and summarized as follows: (a) train a category-specific keypoint estimation network using a small set $S$ of images labeled with 2D keypoints; (b) generate 2D keypoint pseudo-labels on a large unlabeled set $\\mathcal{U}$ consisting of automatically acquired web images; (c) automatically curate $\\mathcal{U}$ by creating a subset of images and pseudo-labels $\\mathcal{U}'$ according to a selection criterion; (d) train a model for 3D shape prediction with data from both $S$ and $\\mathcal{U}'$ .", + "bbox": [ + 496, + 643, + 892, + 823 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "A key insight is that current 2D keypoint estimators [30, 34, 38] are accurate enough to create robust 2D keypoint detections on unlabeled data, even when trained with a limited number of images. Another insight is that images from $\\mathcal{U}$ increase the variability of several factors, such as", + "bbox": [ + 496, + 825, + 893, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "13092", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/f9e0624561aeb82fac2f4fa17af40ebce84de236b049d9b7a51ab29bcac95163.jpg", + "image_caption": [ + "Figure 2. Given a small set $S$ of images labeled with 2D keypoints, we train a 2D keypoint estimation netowrk $h_{\\phi}$ and generate keypoint pseudo-labels on web images (set $\\mathcal{U}$ ). We select a subset of $\\mathcal{U}$ to train a 3D shape predictor $f_{\\theta}$ . Two methods for data selection can be seen here: (a) CF-CM: an auxiliary 2D keypoint estimator $g_{\\psi}$ generates predictions on $\\mathcal{U}$ and images with the smallest discrepancy between the keypoint estimates of $h_{\\phi}$ and $g_{\\psi}$ are selected (criterion (c)); (b) CF-CM²: $f_{\\theta}$ is trained with samples from $S$ and generates predictions on $\\mathcal{U}$ . Images with the smallest discrepancy between the keypoint estimates of $h_{\\phi}$ and $f_{\\theta}$ are selected (criterion (d)) to retrain $f_{\\theta}$ ." + ], + "image_footnote": [], + "bbox": [ + 83, + 90, + 383, + 263 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/54a388f37a3166be3234581623a10c6e6a37d62c426d417d0cdff97b6507ea51.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 398, + 90, + 630, + 262 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/0fb2ce4c964d6ce1df11d318631728ae636f8ab6c036c17a86706f82be0032a2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 638, + 90, + 888, + 262 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "camera viewpoints, articulations and image backgrounds, that are important for training generalizable models for 3D shape prediction. However, the automatically acquired web images contain a high proportion of low-quality images with wrong or heavy truncated objects. Naively using all web images and pseudo-labels during training leads to degraded performance as can be seen in our experiments in Section 4.2. While successful pseudo-label (PL) selection techniques [4, 5, 23, 29, 40] exist for various tasks, they do not address the challenges in our setting. These works investigate PL selection when the unlabeled images come from curated datasets (e.g. CIFAR-10 [20], Cityscapes [6]), while in our setting they come from the web. In addition, they eventually use all unlabeled images during training while in our case most of the web images should be discarded. To effectively utilize images from the web we investigate four criteria to automatically create a \"curated\" subset that includes images with high-quality pseudo-labels. These contain a confidence-based criterion as well as three consistency-based ones (see Figure 2 for two examples).", + "bbox": [ + 75, + 375, + 472, + 676 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Through extensive experiments on five different articulated object categories (horse, cow, sheep, giraffe, bear) and three public datasets, we demonstrate that training with the proposed data selection approaches leads in considerably better 3D reconstructions compared to the fully-supervised baseline. Using all pseudo-labels leads to degraded performance. We analyze the performance of the data selection methods used and conclude that consistency-based selection criteria are more effective in our setting. Finally, we conduct experiments with varying number of images in the labeled set $S$ . We show that even with only 50 annotated instances and images from web, we can train models that lead to better 3D reconstructions than the fully-supervised models trained with more labels.", + "bbox": [ + 75, + 688, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 372, + 640, + 388 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Monocular 3D shape recovery. The task of 3D shape recovery from a single image is solved considerably well for the human category, with many approaches achieving impressive results [14, 17, 19, 31]. Their success can be attributed to the existence of large datasets with 3D [13, 27] and 2D annotations [1, 26]. However for other articulated object categories, such as animals, datasets with 3D annotations do not exist and even 2D labels are scarce and in some cases not available.", + "bbox": [ + 496, + 398, + 890, + 532 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recent works [10, 15, 18, 21, 22, 24] have addressed several aspects of this problem. In CMR [15], the authors train a system for monocular 3D reconstruction using 2D keypoint and mask annotations. Although their approach works well, it relies on a large number of 2D annotations, such as 6K training samples for 3D reconstruction of birds in CUB [36], which limits its direct applicability to other categories. Follow-up works [10, 24] attempt to eliminate this reliance by using part segmentations [24] or mask labels [10], but their performance is still inferior to CMR [15], and they require mask or part segmentation annotations during training, which are not always available. Instead, we propose a novel approach that addresses the scarcity of 2D keypoint annotations by effectively utilizing images from the web.", + "bbox": [ + 496, + 536, + 892, + 762 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In [18], ACFM leverages temporal information for supervision and applies the learned model on a per-frame basis. In [21, 22] the authors generate 3D reconstructions in the form of a rigid [22] or articulated [21] template, training their models with masks and 2D keypoint labels from Pascal VOC [9] and predicted masks (using Mask-RCNN [11]) from ImageNet [7]. Despite using only a small labeled set and mask pseudo-labels, their approach is not fully automatic as they manually select the predicted masks for their", + "bbox": [ + 496, + 763, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "13093", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "training set. Another line of work [2, 33], regresses the parameters of a statistical animal model [41], but their work only reconstructs the 3D shape of dogs, for which large-scale 2D annotations exist [2]. BARC [33] also uses a dataset with 3D annotations during a pre-training stage.", + "bbox": [ + 75, + 90, + 468, + 167 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Learning with keypoint pseudo-labels. The use of keypoint pseudo-labels has been widely investigated in various works related to 2D pose estimation [3,8,23,28,29,32,39]. In [32, 39], the authors investigate learning with keypoint pseudo-labels for human pose estimation, while in [3,23,29] the goal is to estimate the 2D pose of animals. In the case of animal pose estimation, PLs are used for domain adaptation from synthetic data [23, 29] or from human poses [3]. What is common across these works is that they integrate PLs into the training set (in some cases progressively) and that at the end of the process all samples from the unlabeled set are included. This is not an issue as images in the unlabeled set come from curated datasets. While these approaches can potentially enhance the quality of PLs, a data selection mechanism is still necessary in our case because the unlabeled images come from the web, and most of them should be discarded. To this end, we adapt PL selection criteria form previous works, such as keypoint confidence-based filtering from [3] and multi-transform consistency from [23, 29, 32], to automatically curate the acquired web images.", + "bbox": [ + 75, + 167, + 472, + 484 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Approach", + "text_level": 1, + "bbox": [ + 76, + 500, + 187, + 518 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given a labeled set $\\mathcal{S} = \\{(I_i^{(s)},x_i)\\}_{1}^{N_s}$ comprising of $N_{s}$ images with paired 2D keypoint annotations and an unlabeled set $\\mathcal{U} = \\{I_i^{(u)}\\}_{1}^{N_u}$ containing $N_{u}$ unlabeled images, our goal is to learn a 3D shape recovery model by effectively utilizing both labeled and unlabeled data. We use a limited annotated set $N_{s}$ and unlabeled images from the web, thus $N_{u}$ is much larger than $N_{s}$ . We investigate how keypoint pseudo-labeling on unlabeled images can improve existing 3D reconstruction models. CMR [15] and ACSM [21] are chosen as two canonical examples. Next, we present some relevant background on monocular 3D shape recovery, CMR and ACSM, while in Section 3.2 we present our proposed approach.", + "bbox": [ + 75, + 526, + 472, + 729 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Preliminaries", + "text_level": 1, + "bbox": [ + 76, + 739, + 218, + 753 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given an image $I$ of an object, its 3D structure is recovered by predicting a 3D mesh $M$ and camera pose $\\pi$ with a model $f_{\\theta}$ whose parameters $\\theta$ are learned during training.", + "bbox": [ + 75, + 763, + 468, + 808 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "CMR. The shape in CMR [15] is represented as a 3D mesh $M \\equiv (V, F)$ with vertices $V \\in \\mathbb{R}^{|V| \\times 3}$ and faces $F$ , and is homeomorphic to a sphere. Given an input image $I$ , CMR uses ResNet-18 [12] to acquire an image embedding, which is then processed by a 2-layer MLP and fed to two independent linear layers predicting vertex displacements", + "bbox": [ + 75, + 809, + 468, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "$\\Delta_V \\in \\mathbb{R}^{|V| \\times 3}$ from a template shape $T \\in \\mathbb{R}^{|V| \\times 3}$ and the camera pose. The deformed 3D vertex locations are then computed as $V = T + \\Delta_V$ . A weak-perspective camera model $\\pi \\equiv (s, \\mathbf{t}, \\mathbf{q})$ is used, where $s \\in \\mathbb{R}_+$ is the scale, $\\mathbf{t} \\in \\mathbb{R}^2$ the translation and $\\mathbf{q} \\in \\mathbb{R}^4$ the rotation of the camera in unit quaternion parameterization. Thus, CMR learns to predict $f_\\theta(I) \\equiv (\\Delta_V, \\pi)$ . We refer the reader to [15] for more details.", + "bbox": [ + 496, + 89, + 890, + 210 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "ACSM. The shape in ACSM [21] is also represented as a 3D mesh $M \\equiv (V, F)$ . The mesh $M$ is a pre-defined template shape for each object category with fixed topology. Given a template shape $T$ , its vertices are grouped into $P$ parts. As a result, for each vertex $v$ of $T$ an associated membership $a_{p}^{v} \\in [0,1]$ corresponding to each part $p \\in \\{1, \\dots, P\\}$ is produced. The articulation $\\delta$ of this template $T$ is specified as a rigid transformation w.r.t. each parent part, i.e. $\\delta \\equiv \\{(t_{p}, R_{p})\\}$ , where the torso corresponds to the root part in the hierarchy. Given the articulation parameters $\\delta$ , a global transformation $\\mathcal{T}_{p}(\\cdot, \\delta)$ for each part can be computed using forward kinematics. Thus, the position of each vertex $v$ of $T$ after articulation can be computed as $\\sum_{p} a_{p}^{v} \\mathcal{T}_{p}(v, \\delta)$ . Therefore, to recover the 3D structure of an object with ACSM we need to predict the camera pose $\\pi$ and articulation parameters $\\delta$ . ACSM [21] uses the same image encoder with CMR [15]. The camera pose is parameterized and predicted as in CMR, while independent fully-connected heads regress the articulation parameters $\\delta$ . Thus, ACSM learns to predict $f_{\\theta}(I) \\equiv (\\delta, \\pi)$ . For more details, we refer the reader to [21].", + "bbox": [ + 496, + 210, + 892, + 527 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Keypoint and mask supervision. CMR and ACSM are supervised with 2D annotations, by ensuring that the predicted 3D shape matches with the 2D evidence when projected onto the image space using the predicted camera. Let's assume $k$ 2D keypoint locations $x_{i} \\in \\mathbb{R}^{k \\times 2}$ as label for image $I_{i}$ . Each one of these $k$ 2D keypoints has a semantic correspondence with a 3D keypoint. The 3D keypoints can be computed from the mesh vertices. In CMR the location of 3D keypoints is regressed from that of the mesh vertices using a learnable matrix $A$ , while mesh vertices corresponding to 3D keypoints are pre-determined for ACSM. This leads to $k$ 3D keypoints $\\hat{X}_{i} \\in \\mathbb{R}^{k \\times 3}$ that can be projected onto the image using the predicted camera $\\hat{\\pi}$ . In this setting, keypoint supervision is provided using a reprojection loss on the keypoints:", + "bbox": [ + 496, + 529, + 893, + 757 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nL _ {k p} = \\left\\| x _ {i} - \\hat {\\pi} \\left(\\hat {X} _ {i}\\right) \\right\\| _ {2}. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 614, + 766, + 890, + 785 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Similarly, assuming an instance segmentation mask $m_{i}$ is provided as annotation for $I_{i}$ , we can render the 3D mesh $M = (V_{i}, F)$ through the predicted camera $\\hat{\\pi}_{i}$ using a differentiable renderer [16] $\\mathcal{R}(\\cdot)$ and provide mask supervision with the following loss:", + "bbox": [ + 496, + 796, + 890, + 872 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\text {m a s k}} = \\left\\| m _ {i} - \\mathcal {R} \\left(V _ {i}, F, \\hat {\\pi} _ {i}\\right) \\right\\| _ {2}. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 584, + 883, + 890, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "13094", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In ACSM, a second network $f_{\\theta'}'$ is trained to map each pixel in the object's mask to a point on the surface of the template shape. This facilitates computation of several mask losses. In our experiments with ACSM we only train network $f_{\\theta}$ with the keypoint reprojection loss in Eq. (1).", + "bbox": [ + 75, + 90, + 468, + 167 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. 3D Shape Recovery Approach", + "text_level": 1, + "bbox": [ + 76, + 174, + 344, + 191 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Our proposed approach involves the following steps: (1) annotation of 2D keypoints on $N_{s}$ images (when no labels are available for the given category) to create a labeled set $S$ ; (2) training a 2D keypoint estimation network with samples from $S$ and generating 2D keypoint pseudo-labels on an image collection from the web (unlabeled set $\\mathcal{U}$ ); (3) selecting data from $\\mathcal{U}$ to be used for training according to a criterion; (4) training a 3D shape predictor with samples from $S$ and $\\mathcal{U}$ . We explain all the steps in detail below.", + "bbox": [ + 75, + 196, + 468, + 333 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Data annotation. We annotate $N_S$ images with 2D keypoints, following standard keypoint definitions used in existing datasets. For instance, we use 16 keypoints for quadruped animals as defined in Pascal [9]. The only requirement is to annotate images containing objects with the variety of poses and articulations we wish to model.", + "bbox": [ + 75, + 334, + 468, + 422 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Generating keypoint pseudo-labels. In pseudo-labeling an initial model is trained with labels from a labeled set $S$ and is used to produce artificial labels on an unlabeled set $\\mathcal{U}$ . In this work, instead of tasking the 3D shape predictor $f_{\\theta}$ to produce pseudo-labels for itself, we propose to generate 2D keypoint pseudo-labels using the predictions of a 2D keypoint estimation network [38] $h_{\\phi}$ . This is a natural option since 2D keypoint estimators are easier to train with limited data and yield more precise detections compared to reprojected keypoints obtained from a 3D mesh.", + "bbox": [ + 75, + 424, + 468, + 575 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Most current methods for 2D pose estimation [30,34,38] solve the task by estimating $K$ gaussian heatmaps. Each heatmap encodes the probability of a keypoint at a location in the image. The location of each keypoint can be estimated as the location with the maximum value in the corresponding heatmap, while that value can be used as a confidence estimate for that keypoint. We train a 2D keypoint estimation network $h_\\phi$ with labels from $\\mathcal{S}$ and use it to generate keypoint pseudo-labels on $\\mathcal{U}$ . As such, the unlabeled set is now $\\mathcal{U}_{\\phi} = \\{(I_{i}^{(u)},\\tilde{x}_{i}^{(u)},\\tilde{c}_{i}^{(u)})\\}_{1}^{N_{u}}$ , where $\\tilde{x}_i^{(u)}\\in \\mathbb{R}^{k\\times 2}$ are the estimated locations and $\\tilde{c}_i^{(u)}\\in [0,1]^k$ the corresponding confidence estimates for $k$ keypoints of interest in image $I_{i}^{(u)}$ .", + "bbox": [ + 75, + 575, + 468, + 777 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Learning with keypoint pseudo-labels. Given a labeled set $\\mathcal{S} = \\{(I_i^{(s)},x_i)\\}_{1}^{Ns}$ containing images with keypoint labels $x_{i}$ , we train $f_{\\theta}$ using the supervised loss:", + "bbox": [ + 75, + 779, + 468, + 825 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL _ {k p} ^ {\\mathcal {S}} = \\sum_ {i = 1} ^ {N s} | | x _ {i} - \\hat {\\pi} (\\hat {X} _ {i}) | | _ {2}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 179, + 834, + 468, + 875 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\hat{\\pi}$ is the predicted camera pose and $\\hat{X}_i$ the 3D key", + "bbox": [ + 76, + 883, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "points computed from 3D mesh vertices $V_{i}$ . Similarly, given a set $\\mathcal{U}_{\\phi} = \\{(I_i^{(u)},\\hat{x}_i^{(u)},\\hat{c}_i^{(u)})\\}_{1}^{N_u}$ comprising of images with keypoint pseudo-labels $(\\tilde{x}_i,\\tilde{c}_i)$ , we train using the following modification of the keypoint reprojection loss:", + "bbox": [ + 498, + 90, + 890, + 154 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL _ {k p} ^ {\\mathcal {U}} = \\sum_ {i = 1} ^ {N u} \\left\\| \\tilde {c} _ {i} \\left(\\tilde {x} _ {i} - \\hat {\\pi} \\left(\\hat {X} _ {i}\\right)\\right) \\right\\| _ {2}. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 589, + 162, + 890, + 205 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We can train using data from both $S$ and $\\mathcal{U}_{\\phi}$ with the following objective: $L = L_{kp}^{S} + L_{kp}^{U}$ . However, as $Ns \\ll N_u$ , the training process is dominated by samples from $\\mathcal{U}_{\\phi}$ . When the quality of samples in $\\mathcal{U}_{\\phi}$ is low, as it is the case with uncurated data from the web, training with all the samples from the unlabeled set leads to degraded performance. To mitigate this issue, we train using a subset of $\\mathcal{U}_{\\phi}$ containing useful images and high-quality pseudo-labels that are chosen according to a selection criterion.", + "bbox": [ + 496, + 214, + 890, + 349 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2.1 Data Selection", + "text_level": 1, + "bbox": [ + 500, + 368, + 653, + 382 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given a number of images $N$ to be used by $\\mathcal{U}_{\\phi}$ , we select them according to one of the following criteria.", + "bbox": [ + 496, + 392, + 890, + 421 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Keypoint Confidence. This method, referred to as $KP$ -conf, selects samples from $\\mathcal{U}_{\\phi}$ based on the confidence score of the PLs. In particular, it selects $N$ images with the highest per-sample sum of keypoint confidences $\\sum_{k} \\tilde{\\mathbf{c}}_k^{(u)}$ .", + "bbox": [ + 496, + 422, + 890, + 486 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Multi-Transform Consistency. Intuitively, if one scales or rotates one image the prediction of a good 2D keypoint estimator should change accordingly. In other words, it should be equivariant to the those geometric transformations. We can thus use the consistency to multiple equivariant transformations to select the images with high-quality PLs. We denote this consistency-filtering approach as $CF-MT$ .", + "bbox": [ + 496, + 484, + 890, + 590 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Cross-Model Consistency. Using this consistency filtering approach, referred to as $CF-CM$ , we select samples based on the consistency of two 2D keypoint estimators, $h_{\\phi}$ and $g_{\\psi}$ , with different architectures. Our insight is that the two models have different structural biases and can learn different representations from the same image. Thus, we use the discrepancy in their predictions as a proxy for evaluating the quality of the generated pseudo-labels. For each image $I$ from $\\mathcal{U}$ , we generate keypoint pseudo-labels $\\tilde{x}_{\\phi}$ and $\\tilde{x}_{\\psi}$ with $h_{\\phi}$ and $g_{\\psi}$ respectively, and calculate the discrepancy between the PLs with the following term:", + "bbox": [ + 496, + 590, + 890, + 756 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nD _ {\\mathrm {C F - C M}} = \\left\\| \\tilde {x} _ {\\phi} - \\tilde {x} _ {\\psi} \\right\\| _ {2}. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 614, + 767, + 890, + 785 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We select $N$ samples with the minimum discrepancy creating the subset $\\mathcal{U}_{\\phi, \\psi} \\subset \\mathcal{U}_{\\phi}$ .", + "bbox": [ + 496, + 794, + 890, + 825 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Cross-Model Cross-Modality Consistency. With this consistency filtering criterion, which we dub $CF - CM^2$ , we select samples based on their discrepancy between the predictions of the 2D keypoint estimator $h_{\\phi}$ and the reprojected keypoints from the 3D shape predictor $f_{\\theta}$ . Given an image", + "bbox": [ + 496, + 825, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "13095", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/1ea2597210c5f610cd0d4c4b3a3edbd43e597510ede97220fc03fa7357e3ee06.jpg", + "image_caption": [ + "Figure 3. Sample results on CUB. For each sample, we show the predicted shape and texture from the inferred camera view (b, d) and a novel view (c, e) for models trained with and without keypoint pseudo-labels." + ], + "image_footnote": [], + "bbox": [ + 80, + 88, + 459, + 229 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$I$ from $\\mathcal{U}$ , we calculate the locations for 3D keypoints $\\tilde{X}_{\\theta}$ from the predicted 3D mesh vertices (as explained in Section 3.1). The corresponding 2D keypoints $\\tilde{x}_{\\theta}$ are calculated by projecting $\\tilde{X}_{\\theta}$ onto the image with the predicted camera parameters $\\tilde{\\pi}_{\\theta}$ , i.e. $\\tilde{x}_{\\theta} = \\tilde{\\pi}_{\\theta}(\\tilde{X}_{\\theta})$ . As such, we calculate the discrepancy between the keypoints $\\tilde{x}_{\\phi}$ and $\\tilde{x}_{\\theta}$ as follows:", + "bbox": [ + 75, + 316, + 467, + 407 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nD _ {\\mathrm {C F - C M} ^ {2}} = \\left\\| \\tilde {x} _ {\\phi} - \\tilde {\\pi} _ {\\theta} \\left(\\tilde {X} _ {\\theta}\\right) \\right\\| _ {2}. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 171, + 417, + 468, + 435 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our insight for this consistency check comes from the fact that the two models employ different paradigms for estimating 2D keypoints and have distinct failure modes. 2D keypoints detectors use a bottom-up approach to determine the locations of 2D keypoints. While their predictions are more pixel-accurate than the reprojected keypoints from a 3D mesh, they are not constrained in any way and mainly rely on local cues. Conversely, 3D shape predictors, such as $f_{\\theta}$ , estimate keypoints as part of a 3D mesh, which constrains their predictions with a specific mesh topology. This makes their predictions more robust.", + "bbox": [ + 75, + 444, + 468, + 609 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Additional details", + "text_level": 1, + "bbox": [ + 76, + 618, + 250, + 632 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Here, we present some additional details of our approach. We include extensive implementation details in the supplementary material.", + "bbox": [ + 75, + 642, + 468, + 686 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Data acquisition. For each target object category we download images from Flickr using the urls that belong to the public and freely usable YFCC100M [35]. However, some images contain wrong objects or objects with heavy truncation. There are also repeated images.", + "bbox": [ + 75, + 686, + 468, + 762 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Initial filtering. We remove repeated images with dHash [37]. Then, we detect bounding boxes using MaskRCNN [11] with ResNet50-FPN [12,25] backbone from detector2. Only detections with confidence above a threshold $\\tau$ are retained. We use $\\tau = 0.95$ for all object categories.", + "bbox": [ + 75, + 762, + 468, + 838 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Keypoints from 2D pose estimation network. We train the SimpleBaselines [38] pose estimator, with an ImageNet pretrained ResNet-18 [12] backbone, with labels from $\\mathcal{S}$ and use it to generate keypoint PLs $(\\tilde{x}_{\\phi}^{(u)},\\tilde{c}_{\\phi}^{(u)})$ on $\\mathcal{U}$ .", + "bbox": [ + 75, + 838, + 468, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Data Selection. We curate the web images using a selection criterion. We evaluate the effectiveness of the four selection criteria presented previously. We use each criterion to select the best $N$ data samples from the self-labeled web images. We present experiments with $N \\in \\{1K, 3K\\}$ .", + "bbox": [ + 496, + 90, + 890, + 166 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Training. We train a 3D shape predictor $f_{\\theta}$ with keypoint reprojection losses as defined in Eq. (3) & (4).", + "bbox": [ + 496, + 166, + 890, + 196 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 210, + 630, + 228 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Evaluation metrics. While our models are able to reconstruct the 3D shape as a mesh, evaluating their accuracy remains a challenge due to the absence of 3D ground truth data for the current datasets and object categories. Following prior work [15, 18, 21, 22] we evaluate our models quantitatively using the standard \"Percentage of Correct Keypoints\" (PCK) metric. For $PCK(t)$ , the reprojection is \"correct\" when the predicted 2D keypoint location is within $t \\times \\max(w, h)$ distance of the ground-truth location, where $w$ and $h$ are the width and the height of the object's bounding box. We summarize the PCK performance at different thresholds by computing the area under the curve (AUC), $\\mathrm{AUC}_{a_1}^{a_2} = \\int_{a_1}^{a_2} PCK(t) dt$ . We use $a_1 = 0.05$ and $a_2 = 0.1$ and refer to $\\mathrm{AUC}_{a_1}^{a_2}$ as AUC in our evaluation. Following [10], we also evaluate the predicted camera viewpoint obtained by our models. We calculate the rotation error $\\mathrm{err}_R = \\arccos\\left(\\frac{\\mathrm{Tr}(\\hat{R}^T\\hat{R}) - 1}{2}\\right)$ between predicted camera rotation $\\hat{R}$ and pseudo ground-truth camera $\\tilde{R}$ computed using SfM on keypoint labels. Finally, we offer qualitative results to measure the quality of the predicted 3D shapes.", + "bbox": [ + 496, + 237, + 892, + 549 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Simulated Semi-Supervised Setting", + "text_level": 1, + "bbox": [ + 498, + 559, + 805, + 575 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "First, we investigate the effectiveness of keypoint PLs in a controlled setting. For our experiments we use the CUB dataset [36] that consists of 6K images with bounding box, mask and 2D keypoint labels for training and testing. We study the impact of training with various levels of supervision on 3D reconstruction performance. We split CUB's training set into a labeled set $S$ and an unlabeled set $\\mathcal{U}$ by randomly choosing samples from the initial training set to be included in $S$ , while placing the rest in $\\mathcal{U}$ . This is a controlled setting where we expect the performance of the models trained with labels from $S$ and keypoint pseudo-labels from $\\mathcal{U}$ to be lower-bounded by that of models trained using only $S$ and upper-bounded by the fully-supervised baseline that uses the whole training set. We use CMR [15] for the 3D shape prediction network $f_{\\theta}$ .", + "bbox": [ + 496, + 583, + 890, + 809 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Results on CUB. In Figure 4, we compare the performance of models trained with different number of labeled and pseudo-labeled instances. Following CMR, we also report the mIoU metric. We observe that training with 2D keypoint pseudo-labels consistently improves 3D reconstruction performance by a significant margin across all metrics.", + "bbox": [ + 496, + 810, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "13096", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/80f806ac8965d4918d34ab8bf8620f052690922468cc703243b84526e4b0131d.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
HorseCowSheep
AUC (↑)errR(↓)AUC (↑)errR(↓)AUC (↑)errR(↓)
NACSM (Mask) [21]34.9 (↓15.9)44.3 (↑14.1)30.7 (↓16.9)71.0 (↑36.3)28.2 (↓18.6)73.1 (↑39.3)
ACSM (KP+Mask) [21]37.4 (↓13.4)76.4 (↑46.2)----
ACSM-ours50.830.247.634.746.833.8
ACSM-ours + KP-all50.2 (↓0.6)31.9 (↑1.7)43.9 (↓3.9)40.1 (↑5.4)43.5 (↓3.5)40.7 (↑6.9)
ACSM-ours + KP-conf53.9 (↑3.1)30.8 (↑0.6)47.638.3 (↑3.6)48.1 (↑1.3)38.6 (↑4.8)
ACSM-ours + CF-MT55.1 (↑4.3)30.0 (↓0.2)50.7 (↑3.1)38.9 (↑4.2)51.1 (↑4.3)33.3 (↓0.5)
ACSM-ours + CF-CM54.7 (↑3.9)30.0 (↓0.2)50.9 (↑3.3)38.6 (↑3.9)50.6 (↑3.8)32.8 (↓1.0)
ACSM-ours + CF-CM254.2 (↑3.4)30.9 (↑0.7)49.4 (↑1.8)32.7 (↓2.0)48.6 (↑1.8)32.1 (↓1.7)
NACSM-ours + KP-conf54.3 (↑3.5)30.0 (↓0.2)50.2 (↑2.6)40.2 (↑5.5)49.1 (↑2.3)35.7 (↑1.0)
ACSM-ours + CF-MT55.4 (↑4.6)30.0 (↓0.2)49.2 (↑1.6)39.1 (↑4.4)51.0 (↑4.2)33.9 (↑0.1)
ACSM-ours + CF-CM55.9 (↑5.1)29.8 (↓0.4)50.0 (↑2.4)38.8 (↑4.1)48.4 (↑1.6)34.1 (↑0.3)
ACSM-ours + CF-CM255.5 (↑4.7)28.1 (↓2.1)52.6 (↑5.0)36.2 (↑1.5)53.0 (↑6.2)31.3 (↓2.5)
", + "bbox": [ + 120, + 88, + 849, + 316 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Evaluation on Pascal. $N$ is the number of selected images from the web. ACSM-ours + KP-all uses all available web images. Performance change from the fully-supervised baseline ACSM-ours is shown in green/red.", + "bbox": [ + 75, + 327, + 890, + 356 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The improvement is larger when the initial labeled set $S$ is small (e.g. 100 images). This is a very interesting finding. The quality of the generated keypoint pseudo-labels decreases when the 2D keypoint estimator is trained with fewer samples. However, the keypoint pseudo-labels are accurate enough to provide a useful signal for training CMR, largely improving its performance.", + "bbox": [ + 75, + 382, + 468, + 488 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In Figure 3, we show sample 3D reconstruction results comparing CMR trained with: i) 300 labeled instances and ii) the same labeled instances and additional keypoint pseudo-labels (for 5,700 images). We show the predicted shape and texture from the predicted camera view and a side view. From Figure 3 we can see that the model trained with keypoint pseudo-labels can accurately capture challenging deformations (e.g. open wings), while the other model struggles.", + "bbox": [ + 75, + 489, + 468, + 625 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Learning with Web Images", + "text_level": 1, + "bbox": [ + 76, + 633, + 321, + 651 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We go beyond standard semi-supervised approaches that use unlabeled images from curated datasets by effectively utilizing images from the web for training. We use $N_S = 150$ images annotated with 2D keypoints and evaluate our proposed approach.", + "bbox": [ + 75, + 657, + 468, + 733 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets. We train our models with 2D keypoints from Pascal [9] using the same train/test splits as prior work [21,22]. For categories with less than 150 labeled samples, we augment the labeled training set $S$ by manually labeling some images from COCO [26]. We use Pascal's test split and the Animal Pose dataset [3] for evaluation.", + "bbox": [ + 75, + 734, + 468, + 823 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation details. We train the SimpleBaselines [38] 2D pose estimator using 150 images with 2D keypoint labels and generate pseudo-labels on web images. For criterion CF-MT, we use scaling and rotation transformations. For criterion CF-CM, we train Stacked HourGlass [30] as", + "bbox": [ + 75, + 824, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/76ffc4094edd5fa32363101ecc586334cdc284efbaed2c27b8849eca633e4d85.jpg", + "image_caption": [ + "Figure 4. Evaluation on CUB. We show the AUC, mIoU and camera rotation error (in degrees) for models trained with different number of labeled and pseudo-labeled instances. Performance across all metrics is significantly improved with keypoint PLs." + ], + "image_footnote": [], + "bbox": [ + 500, + 378, + 629, + 462 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/4b521b9779c92d449d1d67ca759b40aa1d5a91c3954dcbbc96f4bb1ef121c288.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 630, + 378, + 759, + 462 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/eb4e166314fe3eb305020315124b888dbc7ad4291640c817c25394ec20debe62.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 759, + 378, + 890, + 462 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "the auxiliary 2D pose estimator. We use ACSM [21] for 3D shape prediction. We found that some template meshes provided in the publicly available ACSM codebase contained incorrect keypoint definitions for certain animals' limbs, with inconsistencies between the right and left sides. After rectifying this issue, we trained ACSM exclusively with keypoint labels and achieved better performance than the one reported in [21], establishing a stronger baseline. We denote our implementation of ACSM trained with 150 images labeled with 2D keypoints as ACSM-ours.", + "bbox": [ + 496, + 561, + 890, + 712 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Baselines. We compare the performance of the models trained with selected web images and pseudo-labels with the fully-supervised baseline (ACSM-ours) as well as with the baseline that uses all pseudo-labels during training, denoted as ACSM-ours+KP-all. To put our results into perspective, we also compare with the models from ACSM [21]. The available models are trained using mask labels from Pascal [9] and manually picked mask pseudolabels from ImageNet [7]. For horses, the authors provide a model trained with keypoint labels from Pascal as well.", + "bbox": [ + 496, + 715, + 890, + 866 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Results on Pascal. First, we evaluate the performance of different methods on Pascal's test set. The results are pre", + "bbox": [ + 498, + 869, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "13097", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/15558ca4d28a96c9095b1d46e80f22b5cf8ce33c94fc5176b8d3a90d7439801b.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
HorseCowSheep
AUC (↑)errR(↓)AUC (↑)errR(↓)AUC (↑)errR(↓)
NACSM (Mask) [21]47.4 (↓19.3)38.0 (↑17.3)46.2 (↓13.4)51.8 (↑22.3)31.4 (↓25.8)65.6 (↑50.0)
ACSM (KP+Mask) [21]51.0 (↓15.7)59.9 (↑39.2)----
ACSM-ours66.720.759.629.557.215.6
ACSM-ours + KP-all69.1 (↑2.4)20.9 (↑0.2)61.2 (↑1.6)27.8 (↓1.7)29.1 (↓28.1)19.9 (↑4.3)
ACSM-ours + KP-conf72.9 (↑6.2)19.6 (↓1.1)65.0 (↑5.4)31.9 (↑2.4)58.5 (↑1.3)20.3 (↑4.7)
ACSM-ours + CF-MT74.6 (↑7.9)19.9 (↓0.8)67.0 (↑7.4)26.2 (↓3.3)59.3 (↑2.1)14.6 (↓1.0)
ACSM-ours + CF-CM75.1 (↑8.4)19.6 (↓1.1)67.2 (↑7.6)25.9 (↓3.6)59.3 (↑2.1)14.7 (↓0.9)
ACSM-ours + CF-CM273.0 (↑6.3)19.7 (↓1.0)67.2 (↑7.6)23.5 (↓6.0)58.7 (↑1.5)15.3 (↓0.3)
NACSM-ours + KP-conf74.3 (↑7.6)19.6 (↓1.1)67.8 (↑7.8)28.0 (↓1.5)57.3 (↑0.1)15.3 (↓0.3)
ACSM-ours + CF-MT74.4 (↑7.7)19.6 (↓1.1)66.0 (↑6.4)29.7 (↑0.2)59.6 (↑2.4)15.1 (↓0.5)
ACSM-ours + CF-CM74.1 (↑7.4)19.6 (↓1.1)66.4 (↑6.8)29.3 (↓0.2)59.4 (↑2.2)15.8 (↑0.2)
ACSM-ours + CF-CM273.8 (↑7.1)19.5 (↓1.2)69.6 (↑10.0)25.2 (↓4.3)60.2 (↑3.0)14.9 (↓0.7)
", + "bbox": [ + 120, + 88, + 849, + 316 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b0742dce177254c40f9d89bd4f9af720da3e7bac1524bc91da1a276dcf04d07d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 76, + 391, + 269, + 515 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/233ee441ecdd9f13adba47b34784fd581cdac56afdc97b03ede79ae98bf8224f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 277, + 391, + 468, + 515 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0068148e50fe8ed973e63adac663524a7cbdbd54aa5f4a5dff568bf6f867e7df.jpg", + "image_caption": [ + "Figure 5. Evaluation under varying initial supervision. We show the AUC and camera rotation error (in degrees) on Pascal (top) and Animal Pose (bottom) for the use of our proposed framework under various levels of initial supervision from $S$ . KP-conf, CF-MT, CF-CM, CF-CM $^2$ use PLs from $N = 3K$ images." + ], + "image_footnote": [], + "bbox": [ + 76, + 518, + 269, + 641 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4570a87761413eb8520e77ec6ec8021d94f185be0e045ae8122f61c4c59e0e97.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 277, + 518, + 468, + 641 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "sented in Table 1. From Table 1 we observe that naively including all pseudo-labels during training (ACM-ours+KP-all) leads in degraded performance. Data selection with KP-conf leads to some improvements, but models trained with pseudo-labels selected from consistency-filtering, i.e. CF-MT, CF-CM and $\\mathrm{CF - CM^2}$ , perform consistently better. The improvement over the fully-supervised baseline is quite substantial for those models. For instance, ACSM-ours+CF-CM has a relative improvement (in AUC) of $10.9\\%$ over ACSM-ours and $17.0\\%$ over ACSM-ours+KP", + "bbox": [ + 75, + 750, + 472, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/44fee6c6b8d524b5d32bfcbf58963456a8b6a5531648d46b25d7862e07e6c1e5.jpg", + "table_caption": [ + "Table 2. Evaluation on Animal Pose. $N$ is the number of selected images from the web. ACSM-ours + KP-all uses all available web images. Training with selected web images significantly improves the fully-supervised baseline. We show the performance change from ACSM-ours in green/red." + ], + "table_footnote": [], + "table_body": "
GiraffeBear
AUC (↑)errR(↓)AUC (↑)errR(↓)
NACSM-ours79.134.759.228.9
ACSM-ours + KP-all75.6 (↓3.5)39.5 (↑4.8)58.2 (↓1.0)35.4 (↑6.5)
ACSM-ours + KP-conf83.3 (↑4.2)31.4 (↓3.3)62.7 (↑3.5)31.0 (↑2.1)
ACSM-ours + CF-MT84.4 (↑5.3)32.1 (↓2.6)62.6 (↑3.6)31.9 (↑3.0)
ACSM-ours + CF-CM84.1 (↑5.0)32.5 (↓2.2)62.8 (↑3.6)31.6 (↑2.7)
ACSM-ours + CF-CM286.6 (↑7.5)28.8 (↓5.9)62.2 (↑3.0)30.7 (↑1.8)
NACSM-ours + KP-conf82.8 (↑3.7)35.6 (↑0.9)59.9 (↑0.7)35.0 (↑6.1)
ACSM-ours + CF-MT83.5 (↑4.4)33.1 (↓1.6)63.1 (↑3.9)31.7 (↑2.8)
ACSM-ours + CF-CM83.6 (↑4.5)33.4 (↓1.3)63.4 (↑4.2)31.5 (↑2.6)
ACSM-ours + CF-CM284.5 (↑5.4)32.8 (↓1.9)62.8 (↑3.6)32.3 (↑3.4)
", + "bbox": [ + 501, + 393, + 890, + 547 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3. Evaluation on COCO. $N$ is the number of selected images from the web. ACSM-ours + KP-all uses all available web images. Performance change from the fully-supervised baseline is shown in green/red.", + "bbox": [ + 498, + 556, + 893, + 613 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "all, averaged across all categories shown in Table 1.", + "bbox": [ + 498, + 641, + 841, + 657 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results on Animal Pose. Next, we evaluate our previously trained models on Animal Pose dataset and present results in Table 2. Results are consistent with those in Pascal. Training models with all pseudo-labels results in large performance degradation in some cases (see Sheep in Table 2). KP-conf improves over the supervised baseline, but the improvement is higher for CF-MT, CF-CM and $\\mathrm{CF - CM^2}$ . Results from Tables 1 & 2 suggest that consistency-filtering is more effective than confidence-based filtering in our setting.", + "bbox": [ + 496, + 657, + 890, + 792 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results on COCO. In this part, we demonstrate the practicality of our approach in predicting the 3D shape of object categories even in the absence of initial annotations for those categories. We evaluate our approach on giraffes and bears. We annotate 250 images from COCO with 2D keypoints in a process that takes only $\\approx 2.5$ hours per-category. Given a mesh template, we only need to associate the 2D", + "bbox": [ + 496, + 795, + 893, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "13098", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f734021cc8a9320c07c81e79143ca57c6926ad51294bad9ddd9deb3415b7d884.jpg", + "image_caption": [ + "Figure 6. Sample results on 3D shape recovery of quadrupeds. For each input image, we show the predicted 3D shape from the inferred viewpoint. (b) original ACSM (models for giraffes and bears are not available), (c) our ACSM implementation, (d) ACSM-ours trained with all PLs, (e) ACSM-ours + KP-conf, (f) ACSM-ours + CF-MT, (g) ACSM-ours + CF-CM, (h) ACSM-ours + CF-CM $^2$ ." + ], + "image_footnote": [], + "bbox": [ + 78, + 85, + 890, + 393 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "keypoint labels with vertices from the 3D mesh. This process is done in meshlab in $\\approx 5$ minutes. We train our models with semi-supervised learning as described in Section 3.2. We use 150 images for training, while the remaining images are used for testing. We compare models that utilize pseudo-labels with the fully-supervised baseline trained with 150 images. The results are presented in Table 3. The results are consistent with those on Pascal and Animal Pose. Again, using all pseudo-labels leads in degraded performance. Data selection is essential, and in most cases leads to improved performance compared to the fully-supervised baseline. The performance gains are higher for consistency-based filtering approaches.", + "bbox": [ + 75, + 470, + 472, + 667 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Results with different number of labels. In Figure 5, we present results on 3D reconstruction of horses with different number $N_{s}$ of images labeled with 2D keypoints. For all experiments, we use $N = 3K$ images with pseudolabels from $\\mathcal{U}$ and vary only the number of initial labels $N_{s}$ from $S$ . From Figure 5, we observe that models with keypoint pseudo-labels outperform the fully-supervised baseline even when $N_{s}$ is just 50. More importantly, we notice that models trained with $N_{s} = 50$ and keypoint pseudolabels outperform fully-supervised models with $N_{s} = 150$ . We also observe, that consistency-based filtering methods are more effective than filtering with keypoint confidence scores. Finally, while all consistency-based filtering approaches lead to similar AUC performance, we notice that CF-CM² leads to lower camera rotation errors in all cases.", + "bbox": [ + 75, + 672, + 472, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Qualitative Examples. In Figure 6, we show sample 3D reconstructions for all models. We observe that ACSM-ours recovers more accurate shapes than the original ACSM version. Training with all PLs results in unnatural articulations in the predicted shapes. Additionally, we observe that some articulations are captured only when training with selected samples through consistency-filtering (e.g. horse legs in the first row for CF-CM $^2$ ).", + "bbox": [ + 496, + 470, + 893, + 592 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Summary", + "text_level": 1, + "bbox": [ + 498, + 625, + 609, + 642 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In summary, we investigated the amount of supervision necessary to train models for 3D shape recovery. We showed that it is possible to learn 3D shape predictors with as few as 50-150 images labeled with 2D keypoints. Such annotations are quick and easy to acquire, taking less than 2 hours for each new object category, making our approach highly practical. Additionally, we utilized automatically acquired web images to improve 3D reconstruction performance for several articulated objects, and found that a data selection method was necessary. To this end, we evaluated the performance of four data selection methods and found that training with data selected through consistency-filtering criteria leads to better 3D reconstructions.", + "bbox": [ + 496, + 656, + 893, + 852 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements: This research has been partially funded by research grants to D. Metaxas through NSF IUCRC CARTA1747778, 2235405, 2212301, 1951890, 2003874.", + "bbox": [ + 498, + 858, + 893, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "13099", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Mykhaylo Andriluka, Leonid Pishchulin, Peter Gehler, and Bernt Schiele. 2d human pose estimation: New benchmark and state of the art analysis. 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In CVPR, pages 6365-6373, 2017. 3" + ], + "bbox": [ + 78, + 90, + 468, + 531 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "13101", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Learning Articulated Shape With Keypoint Pseudo-Labels From Web Images/e9a40181-29f2-4fab-842a-0bf24d5ccd9e_model.json b/2023/Learning Articulated Shape With Keypoint Pseudo-Labels From Web Images/e9a40181-29f2-4fab-842a-0bf24d5ccd9e_model.json new file mode 100644 index 0000000000000000000000000000000000000000..4652947aba0f28de5f690e79e8247a1954ea24dd --- /dev/null +++ b/2023/Learning Articulated Shape With Keypoint Pseudo-Labels From Web Images/e9a40181-29f2-4fab-842a-0bf24d5ccd9e_model.json @@ -0,0 +1,1892 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.106, + 0.131, + 0.865, + 0.154 + ], + "angle": 0, + "content": "Learning Articulated Shape with Keypoint Pseudo-labels from Web Images" + }, + { + "type": "text", + "bbox": [ + 0.108, + 0.182, + 0.294, + 0.218 + ], + "angle": 0, + "content": "Anastasis Stathopoulos\nRutgers University" + }, + { + "type": "text", + "bbox": [ + 0.332, + 0.182, + 0.482, + 0.218 + ], + "angle": 0, + "content": "Georgios Pavlakos \nUC Berkeley" + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.182, + 0.672, + 0.218 + ], + "angle": 0, + "content": "Ligong Han\nRutgers University" + }, + { + "type": "text", + "bbox": [ + 0.711, + 0.182, + 0.862, + 0.218 + ], + "angle": 0, + "content": "Dimitris Metaxas\nRutgers University" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.269, + 0.313, + 0.285 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.301, + 0.474, + 0.665 + ], + "angle": 0, + "content": "This paper shows that it is possible to learn models for monocular 3D reconstruction of articulated objects (e.g. horses, cows, sheep), using as few as 50-150 images labeled with 2D keypoints. Our proposed approach involves training category-specific keypoint estimators, generating 2D keypoint pseudo-labels on unlabeled web images, and using both the labeled and self-labeled sets to train 3D reconstruction models. It is based on two key insights: (1) 2D keypoint estimation networks trained on as few as 50-150 images of a given object category generalize well and generate reliable pseudo-labels; (2) a data selection mechanism can automatically create a \"curated\" subset of the unlabeled web images that can be used for training - we evaluate four data selection methods. Coupling these two insights enables us to train models that effectively utilize web images, resulting in improved 3D reconstruction performance for several articulated object categories beyond the fully-supervised baseline. Our approach can quickly bootstrap a model and requires only a few images labeled with 2D keypoints. This requirement can be easily satisfied for any new object category. To showcase the practicality of our approach for predicting the 3D shape of arbitrary object categories, we annotate 2D keypoints on 250 giraffe and bear images from COCO in just 2.5 hours per category." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.709, + 0.208, + 0.725 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Predicting the 3D shape of an articulated object from a single image is a challenging task due to its underconstrained nature. Various successful approaches [14, 19] have been developed for inferring the 3D shape of humans. These approaches rely on strong supervision from 3D joint locations acquired using motion capture systems. Similar breakthroughs for other categories of articulated objects, such as animals, remain elusive. This is primarily due to the scarcity of appropriate training data. Some works (such as CMR [15]) learn to predict 3D shapes using only 2D labels for supervision. However, for most object categories even" + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.269, + 0.665, + 0.368 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.674, + 0.271, + 0.891, + 0.368 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.506, + 0.374, + 0.688, + 0.454 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.7, + 0.374, + 0.891, + 0.457 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.469, + 0.893, + 0.552 + ], + "angle": 0, + "content": "Figure 1. Overview of the proposed framework. It includes: (a) training a category-specific keypoint estimator with a limited labeled set \\( S \\), (b) generating keypoints pseudo-labels on web images, (c) automatic curation of web images to create a subset \\( \\mathcal{U}' \\), and (d) training a model for 3D shape prediction with images from \\( S \\) and \\( \\mathcal{U}' \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.581, + 0.892, + 0.643 + ], + "angle": 0, + "content": "2D labels are limited or non-existent. We ask: how can we learn models that predict the 3D shape of articulated objects in-the-wild when limited or no annotated images are available for a given object category?" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.893, + 0.824 + ], + "angle": 0, + "content": "In this paper we propose an approach that requires as few as 50-150 images labeled with 2D keypoints. This labeled set can be easily and quickly created for any object category. Our proposed approach is illustrated in Figure 1 and summarized as follows: (a) train a category-specific keypoint estimation network using a small set \\( S \\) of images labeled with 2D keypoints; (b) generate 2D keypoint pseudo-labels on a large unlabeled set \\( \\mathcal{U} \\) consisting of automatically acquired web images; (c) automatically curate \\( \\mathcal{U} \\) by creating a subset of images and pseudo-labels \\( \\mathcal{U}' \\) according to a selection criterion; (d) train a model for 3D shape prediction with data from both \\( S \\) and \\( \\mathcal{U}' \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.894, + 0.901 + ], + "angle": 0, + "content": "A key insight is that current 2D keypoint estimators [30, 34, 38] are accurate enough to create robust 2D keypoint detections on unlabeled data, even when trained with a limited number of images. Another insight is that images from \\(\\mathcal{U}\\) increase the variability of several factors, such as" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13092" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.092, + 0.385, + 0.264 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.399, + 0.091, + 0.632, + 0.263 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.64, + 0.091, + 0.889, + 0.263 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.279, + 0.893, + 0.351 + ], + "angle": 0, + "content": "Figure 2. Given a small set \\( S \\) of images labeled with 2D keypoints, we train a 2D keypoint estimation netowrk \\( h_{\\phi} \\) and generate keypoint pseudo-labels on web images (set \\( \\mathcal{U} \\)). We select a subset of \\( \\mathcal{U} \\) to train a 3D shape predictor \\( f_{\\theta} \\). Two methods for data selection can be seen here: (a) CF-CM: an auxiliary 2D keypoint estimator \\( g_{\\psi} \\) generates predictions on \\( \\mathcal{U} \\) and images with the smallest discrepancy between the keypoint estimates of \\( h_{\\phi} \\) and \\( g_{\\psi} \\) are selected (criterion (c)); (b) CF-CM²: \\( f_{\\theta} \\) is trained with samples from \\( S \\) and generates predictions on \\( \\mathcal{U} \\). Images with the smallest discrepancy between the keypoint estimates of \\( h_{\\phi} \\) and \\( f_{\\theta} \\) are selected (criterion (d)) to retrain \\( f_{\\theta} \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.375, + 0.473, + 0.678 + ], + "angle": 0, + "content": "camera viewpoints, articulations and image backgrounds, that are important for training generalizable models for 3D shape prediction. However, the automatically acquired web images contain a high proportion of low-quality images with wrong or heavy truncated objects. Naively using all web images and pseudo-labels during training leads to degraded performance as can be seen in our experiments in Section 4.2. While successful pseudo-label (PL) selection techniques [4, 5, 23, 29, 40] exist for various tasks, they do not address the challenges in our setting. These works investigate PL selection when the unlabeled images come from curated datasets (e.g. CIFAR-10 [20], Cityscapes [6]), while in our setting they come from the web. In addition, they eventually use all unlabeled images during training while in our case most of the web images should be discarded. To effectively utilize images from the web we investigate four criteria to automatically create a \"curated\" subset that includes images with high-quality pseudo-labels. These contain a confidence-based criterion as well as three consistency-based ones (see Figure 2 for two examples)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Through extensive experiments on five different articulated object categories (horse, cow, sheep, giraffe, bear) and three public datasets, we demonstrate that training with the proposed data selection approaches leads in considerably better 3D reconstructions compared to the fully-supervised baseline. Using all pseudo-labels leads to degraded performance. We analyze the performance of the data selection methods used and conclude that consistency-based selection criteria are more effective in our setting. Finally, we conduct experiments with varying number of images in the labeled set \\( S \\). We show that even with only 50 annotated instances and images from web, we can train models that lead to better 3D reconstructions than the fully-supervised models trained with more labels." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.373, + 0.642, + 0.389 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.4, + 0.892, + 0.534 + ], + "angle": 0, + "content": "Monocular 3D shape recovery. The task of 3D shape recovery from a single image is solved considerably well for the human category, with many approaches achieving impressive results [14, 17, 19, 31]. Their success can be attributed to the existence of large datasets with 3D [13, 27] and 2D annotations [1, 26]. However for other articulated object categories, such as animals, datasets with 3D annotations do not exist and even 2D labels are scarce and in some cases not available." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.537, + 0.893, + 0.763 + ], + "angle": 0, + "content": "Recent works [10, 15, 18, 21, 22, 24] have addressed several aspects of this problem. In CMR [15], the authors train a system for monocular 3D reconstruction using 2D keypoint and mask annotations. Although their approach works well, it relies on a large number of 2D annotations, such as 6K training samples for 3D reconstruction of birds in CUB [36], which limits its direct applicability to other categories. Follow-up works [10, 24] attempt to eliminate this reliance by using part segmentations [24] or mask labels [10], but their performance is still inferior to CMR [15], and they require mask or part segmentation annotations during training, which are not always available. Instead, we propose a novel approach that addresses the scarcity of 2D keypoint annotations by effectively utilizing images from the web." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.895, + 0.903 + ], + "angle": 0, + "content": "In [18], ACFM leverages temporal information for supervision and applies the learned model on a per-frame basis. In [21, 22] the authors generate 3D reconstructions in the form of a rigid [22] or articulated [21] template, training their models with masks and 2D keypoint labels from Pascal VOC [9] and predicted masks (using Mask-RCNN [11]) from ImageNet [7]. Despite using only a small labeled set and mask pseudo-labels, their approach is not fully automatic as they manually select the predicted masks for their" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13093" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.168 + ], + "angle": 0, + "content": "training set. Another line of work [2, 33], regresses the parameters of a statistical animal model [41], but their work only reconstructs the 3D shape of dogs, for which large-scale 2D annotations exist [2]. BARC [33] also uses a dataset with 3D annotations during a pre-training stage." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.168, + 0.473, + 0.486 + ], + "angle": 0, + "content": "Learning with keypoint pseudo-labels. The use of keypoint pseudo-labels has been widely investigated in various works related to 2D pose estimation [3,8,23,28,29,32,39]. In [32, 39], the authors investigate learning with keypoint pseudo-labels for human pose estimation, while in [3,23,29] the goal is to estimate the 2D pose of animals. In the case of animal pose estimation, PLs are used for domain adaptation from synthetic data [23, 29] or from human poses [3]. What is common across these works is that they integrate PLs into the training set (in some cases progressively) and that at the end of the process all samples from the unlabeled set are included. This is not an issue as images in the unlabeled set come from curated datasets. While these approaches can potentially enhance the quality of PLs, a data selection mechanism is still necessary in our case because the unlabeled images come from the web, and most of them should be discarded. To this end, we adapt PL selection criteria form previous works, such as keypoint confidence-based filtering from [3] and multi-transform consistency from [23, 29, 32], to automatically curate the acquired web images." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.501, + 0.188, + 0.519 + ], + "angle": 0, + "content": "3. Approach" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.527, + 0.473, + 0.73 + ], + "angle": 0, + "content": "Given a labeled set \\( \\mathcal{S} = \\{(I_i^{(s)},x_i)\\}_{1}^{N_s} \\) comprising of \\( N_{s} \\) images with paired 2D keypoint annotations and an unlabeled set \\( \\mathcal{U} = \\{I_i^{(u)}\\}_{1}^{N_u} \\) containing \\( N_{u} \\) unlabeled images, our goal is to learn a 3D shape recovery model by effectively utilizing both labeled and unlabeled data. We use a limited annotated set \\( N_{s} \\) and unlabeled images from the web, thus \\( N_{u} \\) is much larger than \\( N_{s} \\). We investigate how keypoint pseudo-labeling on unlabeled images can improve existing 3D reconstruction models. CMR [15] and ACSM [21] are chosen as two canonical examples. Next, we present some relevant background on monocular 3D shape recovery, CMR and ACSM, while in Section 3.2 we present our proposed approach." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.74, + 0.219, + 0.755 + ], + "angle": 0, + "content": "3.1. Preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.764, + 0.47, + 0.809 + ], + "angle": 0, + "content": "Given an image \\(I\\) of an object, its 3D structure is recovered by predicting a 3D mesh \\(M\\) and camera pose \\(\\pi\\) with a model \\(f_{\\theta}\\) whose parameters \\(\\theta\\) are learned during training." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.47, + 0.902 + ], + "angle": 0, + "content": "CMR. The shape in CMR [15] is represented as a 3D mesh \\( M \\equiv (V, F) \\) with vertices \\( V \\in \\mathbb{R}^{|V| \\times 3} \\) and faces \\( F \\), and is homeomorphic to a sphere. Given an input image \\( I \\), CMR uses ResNet-18 [12] to acquire an image embedding, which is then processed by a 2-layer MLP and fed to two independent linear layers predicting vertex displacements" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.09, + 0.892, + 0.211 + ], + "angle": 0, + "content": "\\(\\Delta_V \\in \\mathbb{R}^{|V| \\times 3}\\) from a template shape \\(T \\in \\mathbb{R}^{|V| \\times 3}\\) and the camera pose. The deformed 3D vertex locations are then computed as \\(V = T + \\Delta_V\\). A weak-perspective camera model \\(\\pi \\equiv (s, \\mathbf{t}, \\mathbf{q})\\) is used, where \\(s \\in \\mathbb{R}_+\\) is the scale, \\(\\mathbf{t} \\in \\mathbb{R}^2\\) the translation and \\(\\mathbf{q} \\in \\mathbb{R}^4\\) the rotation of the camera in unit quaternion parameterization. Thus, CMR learns to predict \\(f_\\theta(I) \\equiv (\\Delta_V, \\pi)\\). We refer the reader to [15] for more details." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.212, + 0.893, + 0.529 + ], + "angle": 0, + "content": "ACSM. The shape in ACSM [21] is also represented as a 3D mesh \\( M \\equiv (V, F) \\). The mesh \\( M \\) is a pre-defined template shape for each object category with fixed topology. Given a template shape \\( T \\), its vertices are grouped into \\( P \\) parts. As a result, for each vertex \\( v \\) of \\( T \\) an associated membership \\( a_{p}^{v} \\in [0,1] \\) corresponding to each part \\( p \\in \\{1, \\dots, P\\} \\) is produced. The articulation \\( \\delta \\) of this template \\( T \\) is specified as a rigid transformation w.r.t. each parent part, i.e. \\( \\delta \\equiv \\{(t_{p}, R_{p})\\} \\), where the torso corresponds to the root part in the hierarchy. Given the articulation parameters \\( \\delta \\), a global transformation \\( \\mathcal{T}_{p}(\\cdot, \\delta) \\) for each part can be computed using forward kinematics. Thus, the position of each vertex \\( v \\) of \\( T \\) after articulation can be computed as \\( \\sum_{p} a_{p}^{v} \\mathcal{T}_{p}(v, \\delta) \\). Therefore, to recover the 3D structure of an object with ACSM we need to predict the camera pose \\( \\pi \\) and articulation parameters \\( \\delta \\). ACSM [21] uses the same image encoder with CMR [15]. The camera pose is parameterized and predicted as in CMR, while independent fully-connected heads regress the articulation parameters \\( \\delta \\). Thus, ACSM learns to predict \\( f_{\\theta}(I) \\equiv (\\delta, \\pi) \\). For more details, we refer the reader to [21]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.53, + 0.895, + 0.758 + ], + "angle": 0, + "content": "Keypoint and mask supervision. CMR and ACSM are supervised with 2D annotations, by ensuring that the predicted 3D shape matches with the 2D evidence when projected onto the image space using the predicted camera. Let's assume \\( k \\) 2D keypoint locations \\( x_{i} \\in \\mathbb{R}^{k \\times 2} \\) as label for image \\( I_{i} \\). Each one of these \\( k \\) 2D keypoints has a semantic correspondence with a 3D keypoint. The 3D keypoints can be computed from the mesh vertices. In CMR the location of 3D keypoints is regressed from that of the mesh vertices using a learnable matrix \\( A \\), while mesh vertices corresponding to 3D keypoints are pre-determined for ACSM. This leads to \\( k \\) 3D keypoints \\( \\hat{X}_{i} \\in \\mathbb{R}^{k \\times 3} \\) that can be projected onto the image using the predicted camera \\( \\hat{\\pi} \\). In this setting, keypoint supervision is provided using a reprojection loss on the keypoints:" + }, + { + "type": "equation", + "bbox": [ + 0.616, + 0.767, + 0.892, + 0.786 + ], + "angle": 0, + "content": "\\[\nL _ {k p} = \\left\\| x _ {i} - \\hat {\\pi} \\left(\\hat {X} _ {i}\\right) \\right\\| _ {2}. \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.797, + 0.892, + 0.873 + ], + "angle": 0, + "content": "Similarly, assuming an instance segmentation mask \\( m_{i} \\) is provided as annotation for \\( I_{i} \\), we can render the 3D mesh \\( M = (V_{i}, F) \\) through the predicted camera \\( \\hat{\\pi}_{i} \\) using a differentiable renderer [16] \\( \\mathcal{R}(\\cdot) \\) and provide mask supervision with the following loss:" + }, + { + "type": "equation", + "bbox": [ + 0.585, + 0.885, + 0.892, + 0.902 + ], + "angle": 0, + "content": "\\[\nL _ {\\text {m a s k}} = \\left\\| m _ {i} - \\mathcal {R} \\left(V _ {i}, F, \\hat {\\pi} _ {i}\\right) \\right\\| _ {2}. \\tag {2}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "13094" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.47, + 0.168 + ], + "angle": 0, + "content": "In ACSM, a second network \\( f_{\\theta'}' \\) is trained to map each pixel in the object's mask to a point on the surface of the template shape. This facilitates computation of several mask losses. In our experiments with ACSM we only train network \\( f_{\\theta} \\) with the keypoint reprojection loss in Eq. (1)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.175, + 0.345, + 0.192 + ], + "angle": 0, + "content": "3.2. 3D Shape Recovery Approach" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.198, + 0.469, + 0.334 + ], + "angle": 0, + "content": "Our proposed approach involves the following steps: (1) annotation of 2D keypoints on \\( N_{s} \\) images (when no labels are available for the given category) to create a labeled set \\( S \\); (2) training a 2D keypoint estimation network with samples from \\( S \\) and generating 2D keypoint pseudo-labels on an image collection from the web (unlabeled set \\( \\mathcal{U} \\)); (3) selecting data from \\( \\mathcal{U} \\) to be used for training according to a criterion; (4) training a 3D shape predictor with samples from \\( S \\) and \\( \\mathcal{U} \\). We explain all the steps in detail below." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.335, + 0.469, + 0.424 + ], + "angle": 0, + "content": "Data annotation. We annotate \\( N_S \\) images with 2D keypoints, following standard keypoint definitions used in existing datasets. For instance, we use 16 keypoints for quadruped animals as defined in Pascal [9]. The only requirement is to annotate images containing objects with the variety of poses and articulations we wish to model." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.425, + 0.469, + 0.576 + ], + "angle": 0, + "content": "Generating keypoint pseudo-labels. In pseudo-labeling an initial model is trained with labels from a labeled set \\( S \\) and is used to produce artificial labels on an unlabeled set \\( \\mathcal{U} \\). In this work, instead of tasking the 3D shape predictor \\( f_{\\theta} \\) to produce pseudo-labels for itself, we propose to generate 2D keypoint pseudo-labels using the predictions of a 2D keypoint estimation network [38] \\( h_{\\phi} \\). This is a natural option since 2D keypoint estimators are easier to train with limited data and yield more precise detections compared to reprojected keypoints obtained from a 3D mesh." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.577, + 0.469, + 0.779 + ], + "angle": 0, + "content": "Most current methods for 2D pose estimation [30,34,38] solve the task by estimating \\(K\\) gaussian heatmaps. Each heatmap encodes the probability of a keypoint at a location in the image. The location of each keypoint can be estimated as the location with the maximum value in the corresponding heatmap, while that value can be used as a confidence estimate for that keypoint. We train a 2D keypoint estimation network \\(h_\\phi\\) with labels from \\(\\mathcal{S}\\) and use it to generate keypoint pseudo-labels on \\(\\mathcal{U}\\). As such, the unlabeled set is now \\(\\mathcal{U}_{\\phi} = \\{(I_{i}^{(u)},\\tilde{x}_{i}^{(u)},\\tilde{c}_{i}^{(u)})\\}_{1}^{N_{u}}\\), where \\(\\tilde{x}_i^{(u)}\\in \\mathbb{R}^{k\\times 2}\\) are the estimated locations and \\(\\tilde{c}_i^{(u)}\\in [0,1]^k\\) the corresponding confidence estimates for \\(k\\) keypoints of interest in image \\(I_{i}^{(u)}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.469, + 0.827 + ], + "angle": 0, + "content": "Learning with keypoint pseudo-labels. Given a labeled set \\( \\mathcal{S} = \\{(I_i^{(s)},x_i)\\}_{1}^{Ns} \\) containing images with keypoint labels \\( x_{i} \\), we train \\( f_{\\theta} \\) using the supervised loss:" + }, + { + "type": "equation", + "bbox": [ + 0.18, + 0.835, + 0.469, + 0.876 + ], + "angle": 0, + "content": "\\[\nL _ {k p} ^ {\\mathcal {S}} = \\sum_ {i = 1} ^ {N s} | | x _ {i} - \\hat {\\pi} (\\hat {X} _ {i}) | | _ {2}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.885, + 0.469, + 0.902 + ], + "angle": 0, + "content": "where \\(\\hat{\\pi}\\) is the predicted camera pose and \\(\\hat{X}_i\\) the 3D key" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.155 + ], + "angle": 0, + "content": "points computed from 3D mesh vertices \\(V_{i}\\). Similarly, given a set \\(\\mathcal{U}_{\\phi} = \\{(I_i^{(u)},\\hat{x}_i^{(u)},\\hat{c}_i^{(u)})\\}_{1}^{N_u}\\) comprising of images with keypoint pseudo-labels \\((\\tilde{x}_i,\\tilde{c}_i)\\), we train using the following modification of the keypoint reprojection loss:" + }, + { + "type": "equation", + "bbox": [ + 0.591, + 0.164, + 0.892, + 0.206 + ], + "angle": 0, + "content": "\\[\nL _ {k p} ^ {\\mathcal {U}} = \\sum_ {i = 1} ^ {N u} \\left\\| \\tilde {c} _ {i} \\left(\\tilde {x} _ {i} - \\hat {\\pi} \\left(\\hat {X} _ {i}\\right)\\right) \\right\\| _ {2}. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.215, + 0.892, + 0.351 + ], + "angle": 0, + "content": "We can train using data from both \\(S\\) and \\(\\mathcal{U}_{\\phi}\\) with the following objective: \\(L = L_{kp}^{S} + L_{kp}^{U}\\). However, as \\(Ns \\ll N_u\\), the training process is dominated by samples from \\(\\mathcal{U}_{\\phi}\\). When the quality of samples in \\(\\mathcal{U}_{\\phi}\\) is low, as it is the case with uncurated data from the web, training with all the samples from the unlabeled set leads to degraded performance. To mitigate this issue, we train using a subset of \\(\\mathcal{U}_{\\phi}\\) containing useful images and high-quality pseudo-labels that are chosen according to a selection criterion." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.369, + 0.655, + 0.383 + ], + "angle": 0, + "content": "3.2.1 Data Selection" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.393, + 0.892, + 0.422 + ], + "angle": 0, + "content": "Given a number of images \\(N\\) to be used by \\(\\mathcal{U}_{\\phi}\\), we select them according to one of the following criteria." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.423, + 0.892, + 0.487 + ], + "angle": 0, + "content": "Keypoint Confidence. This method, referred to as \\(KP\\)-conf, selects samples from \\(\\mathcal{U}_{\\phi}\\) based on the confidence score of the PLs. In particular, it selects \\(N\\) images with the highest per-sample sum of keypoint confidences \\(\\sum_{k} \\tilde{\\mathbf{c}}_k^{(u)}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.486, + 0.892, + 0.591 + ], + "angle": 0, + "content": "Multi-Transform Consistency. Intuitively, if one scales or rotates one image the prediction of a good 2D keypoint estimator should change accordingly. In other words, it should be equivariant to the those geometric transformations. We can thus use the consistency to multiple equivariant transformations to select the images with high-quality PLs. We denote this consistency-filtering approach as \\( CF-MT \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.591, + 0.892, + 0.757 + ], + "angle": 0, + "content": "Cross-Model Consistency. Using this consistency filtering approach, referred to as \\( CF-CM \\), we select samples based on the consistency of two 2D keypoint estimators, \\( h_{\\phi} \\) and \\( g_{\\psi} \\), with different architectures. Our insight is that the two models have different structural biases and can learn different representations from the same image. Thus, we use the discrepancy in their predictions as a proxy for evaluating the quality of the generated pseudo-labels. For each image \\( I \\) from \\( \\mathcal{U} \\), we generate keypoint pseudo-labels \\( \\tilde{x}_{\\phi} \\) and \\( \\tilde{x}_{\\psi} \\) with \\( h_{\\phi} \\) and \\( g_{\\psi} \\) respectively, and calculate the discrepancy between the PLs with the following term:" + }, + { + "type": "equation", + "bbox": [ + 0.615, + 0.768, + 0.892, + 0.786 + ], + "angle": 0, + "content": "\\[\nD _ {\\mathrm {C F - C M}} = \\left\\| \\tilde {x} _ {\\phi} - \\tilde {x} _ {\\psi} \\right\\| _ {2}. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.891, + 0.826 + ], + "angle": 0, + "content": "We select \\(N\\) samples with the minimum discrepancy creating the subset \\(\\mathcal{U}_{\\phi, \\psi} \\subset \\mathcal{U}_{\\phi}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Cross-Model Cross-Modality Consistency. With this consistency filtering criterion, which we dub \\( CF - CM^2 \\), we select samples based on their discrepancy between the predictions of the 2D keypoint estimator \\( h_{\\phi} \\) and the reprojected keypoints from the 3D shape predictor \\( f_{\\theta} \\). Given an image" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13095" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.089, + 0.46, + 0.23 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.239, + 0.47, + 0.294 + ], + "angle": 0, + "content": "Figure 3. Sample results on CUB. For each sample, we show the predicted shape and texture from the inferred camera view (b, d) and a novel view (c, e) for models trained with and without keypoint pseudo-labels." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.318, + 0.468, + 0.409 + ], + "angle": 0, + "content": "\\(I\\) from \\(\\mathcal{U}\\), we calculate the locations for 3D keypoints \\(\\tilde{X}_{\\theta}\\) from the predicted 3D mesh vertices (as explained in Section 3.1). The corresponding 2D keypoints \\(\\tilde{x}_{\\theta}\\) are calculated by projecting \\(\\tilde{X}_{\\theta}\\) onto the image with the predicted camera parameters \\(\\tilde{\\pi}_{\\theta}\\), i.e. \\(\\tilde{x}_{\\theta} = \\tilde{\\pi}_{\\theta}(\\tilde{X}_{\\theta})\\). As such, we calculate the discrepancy between the keypoints \\(\\tilde{x}_{\\phi}\\) and \\(\\tilde{x}_{\\theta}\\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.172, + 0.419, + 0.469, + 0.436 + ], + "angle": 0, + "content": "\\[\nD _ {\\mathrm {C F - C M} ^ {2}} = \\left\\| \\tilde {x} _ {\\phi} - \\tilde {\\pi} _ {\\theta} \\left(\\tilde {X} _ {\\theta}\\right) \\right\\| _ {2}. \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.445, + 0.469, + 0.611 + ], + "angle": 0, + "content": "Our insight for this consistency check comes from the fact that the two models employ different paradigms for estimating 2D keypoints and have distinct failure modes. 2D keypoints detectors use a bottom-up approach to determine the locations of 2D keypoints. While their predictions are more pixel-accurate than the reprojected keypoints from a 3D mesh, they are not constrained in any way and mainly rely on local cues. Conversely, 3D shape predictors, such as \\( f_{\\theta} \\), estimate keypoints as part of a 3D mesh, which constrains their predictions with a specific mesh topology. This makes their predictions more robust." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.619, + 0.25, + 0.633 + ], + "angle": 0, + "content": "3.3. Additional details" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.643, + 0.469, + 0.687 + ], + "angle": 0, + "content": "Here, we present some additional details of our approach. We include extensive implementation details in the supplementary material." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.688, + 0.469, + 0.763 + ], + "angle": 0, + "content": "Data acquisition. For each target object category we download images from Flickr using the urls that belong to the public and freely usable YFCC100M [35]. However, some images contain wrong objects or objects with heavy truncation. There are also repeated images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.763, + 0.469, + 0.839 + ], + "angle": 0, + "content": "Initial filtering. We remove repeated images with dHash [37]. Then, we detect bounding boxes using MaskRCNN [11] with ResNet50-FPN [12,25] backbone from detector2. Only detections with confidence above a threshold \\(\\tau\\) are retained. We use \\(\\tau = 0.95\\) for all object categories." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.839, + 0.469, + 0.904 + ], + "angle": 0, + "content": "Keypoints from 2D pose estimation network. We train the SimpleBaselines [38] pose estimator, with an ImageNet pretrained ResNet-18 [12] backbone, with labels from \\(\\mathcal{S}\\) and use it to generate keypoint PLs \\((\\tilde{x}_{\\phi}^{(u)},\\tilde{c}_{\\phi}^{(u)})\\) on \\(\\mathcal{U}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.167 + ], + "angle": 0, + "content": "Data Selection. We curate the web images using a selection criterion. We evaluate the effectiveness of the four selection criteria presented previously. We use each criterion to select the best \\(N\\) data samples from the self-labeled web images. We present experiments with \\(N \\in \\{1K, 3K\\}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.167, + 0.892, + 0.198 + ], + "angle": 0, + "content": "Training. We train a 3D shape predictor \\( f_{\\theta} \\) with keypoint reprojection losses as defined in Eq. (3) & (4)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.212, + 0.632, + 0.229 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.238, + 0.893, + 0.55 + ], + "angle": 0, + "content": "Evaluation metrics. While our models are able to reconstruct the 3D shape as a mesh, evaluating their accuracy remains a challenge due to the absence of 3D ground truth data for the current datasets and object categories. Following prior work [15, 18, 21, 22] we evaluate our models quantitatively using the standard \"Percentage of Correct Keypoints\" (PCK) metric. For \\( PCK(t) \\), the reprojection is \"correct\" when the predicted 2D keypoint location is within \\( t \\times \\max(w, h) \\) distance of the ground-truth location, where \\( w \\) and \\( h \\) are the width and the height of the object's bounding box. We summarize the PCK performance at different thresholds by computing the area under the curve (AUC), \\( \\mathrm{AUC}_{a_1}^{a_2} = \\int_{a_1}^{a_2} PCK(t) dt \\). We use \\( a_1 = 0.05 \\) and \\( a_2 = 0.1 \\) and refer to \\( \\mathrm{AUC}_{a_1}^{a_2} \\) as AUC in our evaluation. Following [10], we also evaluate the predicted camera viewpoint obtained by our models. We calculate the rotation error \\( \\mathrm{err}_R = \\arccos\\left(\\frac{\\mathrm{Tr}(\\hat{R}^T\\hat{R}) - 1}{2}\\right) \\) between predicted camera rotation \\( \\hat{R} \\) and pseudo ground-truth camera \\( \\tilde{R} \\) computed using SfM on keypoint labels. Finally, we offer qualitative results to measure the quality of the predicted 3D shapes." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.56, + 0.807, + 0.576 + ], + "angle": 0, + "content": "4.1. Simulated Semi-Supervised Setting" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.584, + 0.892, + 0.81 + ], + "angle": 0, + "content": "First, we investigate the effectiveness of keypoint PLs in a controlled setting. For our experiments we use the CUB dataset [36] that consists of 6K images with bounding box, mask and 2D keypoint labels for training and testing. We study the impact of training with various levels of supervision on 3D reconstruction performance. We split CUB's training set into a labeled set \\( S \\) and an unlabeled set \\( \\mathcal{U} \\) by randomly choosing samples from the initial training set to be included in \\( S \\), while placing the rest in \\( \\mathcal{U} \\). This is a controlled setting where we expect the performance of the models trained with labels from \\( S \\) and keypoint pseudo-labels from \\( \\mathcal{U} \\) to be lower-bounded by that of models trained using only \\( S \\) and upper-bounded by the fully-supervised baseline that uses the whole training set. We use CMR [15] for the 3D shape prediction network \\( f_{\\theta} \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Results on CUB. In Figure 4, we compare the performance of models trained with different number of labeled and pseudo-labeled instances. Following CMR, we also report the mIoU metric. We observe that training with 2D keypoint pseudo-labels consistently improves 3D reconstruction performance by a significant margin across all metrics." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13096" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.122, + 0.089, + 0.85, + 0.318 + ], + "angle": 0, + "content": "
HorseCowSheep
AUC (↑)errR(↓)AUC (↑)errR(↓)AUC (↑)errR(↓)
NACSM (Mask) [21]34.9 (↓15.9)44.3 (↑14.1)30.7 (↓16.9)71.0 (↑36.3)28.2 (↓18.6)73.1 (↑39.3)
ACSM (KP+Mask) [21]37.4 (↓13.4)76.4 (↑46.2)----
ACSM-ours50.830.247.634.746.833.8
ACSM-ours + KP-all50.2 (↓0.6)31.9 (↑1.7)43.9 (↓3.9)40.1 (↑5.4)43.5 (↓3.5)40.7 (↑6.9)
ACSM-ours + KP-conf53.9 (↑3.1)30.8 (↑0.6)47.638.3 (↑3.6)48.1 (↑1.3)38.6 (↑4.8)
ACSM-ours + CF-MT55.1 (↑4.3)30.0 (↓0.2)50.7 (↑3.1)38.9 (↑4.2)51.1 (↑4.3)33.3 (↓0.5)
ACSM-ours + CF-CM54.7 (↑3.9)30.0 (↓0.2)50.9 (↑3.3)38.6 (↑3.9)50.6 (↑3.8)32.8 (↓1.0)
ACSM-ours + CF-CM254.2 (↑3.4)30.9 (↑0.7)49.4 (↑1.8)32.7 (↓2.0)48.6 (↑1.8)32.1 (↓1.7)
NACSM-ours + KP-conf54.3 (↑3.5)30.0 (↓0.2)50.2 (↑2.6)40.2 (↑5.5)49.1 (↑2.3)35.7 (↑1.0)
ACSM-ours + CF-MT55.4 (↑4.6)30.0 (↓0.2)49.2 (↑1.6)39.1 (↑4.4)51.0 (↑4.2)33.9 (↑0.1)
ACSM-ours + CF-CM55.9 (↑5.1)29.8 (↓0.4)50.0 (↑2.4)38.8 (↑4.1)48.4 (↑1.6)34.1 (↑0.3)
ACSM-ours + CF-CM255.5 (↑4.7)28.1 (↓2.1)52.6 (↑5.0)36.2 (↑1.5)53.0 (↑6.2)31.3 (↓2.5)
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.328, + 0.892, + 0.357 + ], + "angle": 0, + "content": "Table 1. Evaluation on Pascal. \\(N\\) is the number of selected images from the web. ACSM-ours + KP-all uses all available web images. Performance change from the fully-supervised baseline ACSM-ours is shown in green/red." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.383, + 0.469, + 0.489 + ], + "angle": 0, + "content": "The improvement is larger when the initial labeled set \\( S \\) is small (e.g. 100 images). This is a very interesting finding. The quality of the generated keypoint pseudo-labels decreases when the 2D keypoint estimator is trained with fewer samples. However, the keypoint pseudo-labels are accurate enough to provide a useful signal for training CMR, largely improving its performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.49, + 0.469, + 0.626 + ], + "angle": 0, + "content": "In Figure 3, we show sample 3D reconstruction results comparing CMR trained with: i) 300 labeled instances and ii) the same labeled instances and additional keypoint pseudo-labels (for 5,700 images). We show the predicted shape and texture from the predicted camera view and a side view. From Figure 3 we can see that the model trained with keypoint pseudo-labels can accurately capture challenging deformations (e.g. open wings), while the other model struggles." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.635, + 0.322, + 0.652 + ], + "angle": 0, + "content": "4.2. Learning with Web Images" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.659, + 0.469, + 0.734 + ], + "angle": 0, + "content": "We go beyond standard semi-supervised approaches that use unlabeled images from curated datasets by effectively utilizing images from the web for training. We use \\( N_S = 150 \\) images annotated with 2D keypoints and evaluate our proposed approach." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.469, + 0.824 + ], + "angle": 0, + "content": "Datasets. We train our models with 2D keypoints from Pascal [9] using the same train/test splits as prior work [21,22]. For categories with less than 150 labeled samples, we augment the labeled training set \\( S \\) by manually labeling some images from COCO [26]. We use Pascal's test split and the Animal Pose dataset [3] for evaluation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Implementation details. We train the SimpleBaselines [38] 2D pose estimator using 150 images with 2D keypoint labels and generate pseudo-labels on web images. For criterion CF-MT, we use scaling and rotation transformations. For criterion CF-CM, we train Stacked HourGlass [30] as" + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.38, + 0.63, + 0.463 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.631, + 0.38, + 0.76, + 0.463 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.761, + 0.38, + 0.892, + 0.463 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.473, + 0.892, + 0.53 + ], + "angle": 0, + "content": "Figure 4. Evaluation on CUB. We show the AUC, mIoU and camera rotation error (in degrees) for models trained with different number of labeled and pseudo-labeled instances. Performance across all metrics is significantly improved with keypoint PLs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.562, + 0.892, + 0.713 + ], + "angle": 0, + "content": "the auxiliary 2D pose estimator. We use ACSM [21] for 3D shape prediction. We found that some template meshes provided in the publicly available ACSM codebase contained incorrect keypoint definitions for certain animals' limbs, with inconsistencies between the right and left sides. After rectifying this issue, we trained ACSM exclusively with keypoint labels and achieved better performance than the one reported in [21], establishing a stronger baseline. We denote our implementation of ACSM trained with 150 images labeled with 2D keypoints as ACSM-ours." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.717, + 0.892, + 0.867 + ], + "angle": 0, + "content": "Baselines. We compare the performance of the models trained with selected web images and pseudo-labels with the fully-supervised baseline (ACSM-ours) as well as with the baseline that uses all pseudo-labels during training, denoted as ACSM-ours+KP-all. To put our results into perspective, we also compare with the models from ACSM [21]. The available models are trained using mask labels from Pascal [9] and manually picked mask pseudolabels from ImageNet [7]. For horses, the authors provide a model trained with keypoint labels from Pascal as well." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Results on Pascal. First, we evaluate the performance of different methods on Pascal's test set. The results are pre" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13097" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.122, + 0.089, + 0.85, + 0.318 + ], + "angle": 0, + "content": "
HorseCowSheep
AUC (↑)errR(↓)AUC (↑)errR(↓)AUC (↑)errR(↓)
NACSM (Mask) [21]47.4 (↓19.3)38.0 (↑17.3)46.2 (↓13.4)51.8 (↑22.3)31.4 (↓25.8)65.6 (↑50.0)
ACSM (KP+Mask) [21]51.0 (↓15.7)59.9 (↑39.2)----
ACSM-ours66.720.759.629.557.215.6
ACSM-ours + KP-all69.1 (↑2.4)20.9 (↑0.2)61.2 (↑1.6)27.8 (↓1.7)29.1 (↓28.1)19.9 (↑4.3)
ACSM-ours + KP-conf72.9 (↑6.2)19.6 (↓1.1)65.0 (↑5.4)31.9 (↑2.4)58.5 (↑1.3)20.3 (↑4.7)
ACSM-ours + CF-MT74.6 (↑7.9)19.9 (↓0.8)67.0 (↑7.4)26.2 (↓3.3)59.3 (↑2.1)14.6 (↓1.0)
ACSM-ours + CF-CM75.1 (↑8.4)19.6 (↓1.1)67.2 (↑7.6)25.9 (↓3.6)59.3 (↑2.1)14.7 (↓0.9)
ACSM-ours + CF-CM273.0 (↑6.3)19.7 (↓1.0)67.2 (↑7.6)23.5 (↓6.0)58.7 (↑1.5)15.3 (↓0.3)
NACSM-ours + KP-conf74.3 (↑7.6)19.6 (↓1.1)67.8 (↑7.8)28.0 (↓1.5)57.3 (↑0.1)15.3 (↓0.3)
ACSM-ours + CF-MT74.4 (↑7.7)19.6 (↓1.1)66.0 (↑6.4)29.7 (↑0.2)59.6 (↑2.4)15.1 (↓0.5)
ACSM-ours + CF-CM74.1 (↑7.4)19.6 (↓1.1)66.4 (↑6.8)29.3 (↓0.2)59.4 (↑2.2)15.8 (↑0.2)
ACSM-ours + CF-CM273.8 (↑7.1)19.5 (↓1.2)69.6 (↑10.0)25.2 (↓4.3)60.2 (↑3.0)14.9 (↓0.7)
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.328, + 0.895, + 0.371 + ], + "angle": 0, + "content": "Table 2. Evaluation on Animal Pose. \\(N\\) is the number of selected images from the web. ACSM-ours + KP-all uses all available web images. Training with selected web images significantly improves the fully-supervised baseline. We show the performance change from ACSM-ours in green/red." + }, + { + "type": "image", + "bbox": [ + 0.078, + 0.392, + 0.271, + 0.516 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.279, + 0.392, + 0.47, + 0.516 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.077, + 0.52, + 0.27, + 0.642 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.279, + 0.52, + 0.47, + 0.642 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.651, + 0.47, + 0.722 + ], + "angle": 0, + "content": "Figure 5. Evaluation under varying initial supervision. We show the AUC and camera rotation error (in degrees) on Pascal (top) and Animal Pose (bottom) for the use of our proposed framework under various levels of initial supervision from \\( S \\). KP-conf, CF-MT, CF-CM, CF-CM\\(^2\\) use PLs from \\( N = 3K \\) images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.473, + 0.901 + ], + "angle": 0, + "content": "sented in Table 1. From Table 1 we observe that naively including all pseudo-labels during training (ACM-ours+KP-all) leads in degraded performance. Data selection with KP-conf leads to some improvements, but models trained with pseudo-labels selected from consistency-filtering, i.e. CF-MT, CF-CM and \\(\\mathrm{CF - CM^2}\\), perform consistently better. The improvement over the fully-supervised baseline is quite substantial for those models. For instance, ACSM-ours+CF-CM has a relative improvement (in AUC) of \\(10.9\\%\\) over ACSM-ours and \\(17.0\\%\\) over ACSM-ours+KP" + }, + { + "type": "table", + "bbox": [ + 0.503, + 0.394, + 0.892, + 0.548 + ], + "angle": 0, + "content": "
GiraffeBear
AUC (↑)errR(↓)AUC (↑)errR(↓)
NACSM-ours79.134.759.228.9
ACSM-ours + KP-all75.6 (↓3.5)39.5 (↑4.8)58.2 (↓1.0)35.4 (↑6.5)
ACSM-ours + KP-conf83.3 (↑4.2)31.4 (↓3.3)62.7 (↑3.5)31.0 (↑2.1)
ACSM-ours + CF-MT84.4 (↑5.3)32.1 (↓2.6)62.6 (↑3.6)31.9 (↑3.0)
ACSM-ours + CF-CM84.1 (↑5.0)32.5 (↓2.2)62.8 (↑3.6)31.6 (↑2.7)
ACSM-ours + CF-CM286.6 (↑7.5)28.8 (↓5.9)62.2 (↑3.0)30.7 (↑1.8)
NACSM-ours + KP-conf82.8 (↑3.7)35.6 (↑0.9)59.9 (↑0.7)35.0 (↑6.1)
ACSM-ours + CF-MT83.5 (↑4.4)33.1 (↓1.6)63.1 (↑3.9)31.7 (↑2.8)
ACSM-ours + CF-CM83.6 (↑4.5)33.4 (↓1.3)63.4 (↑4.2)31.5 (↑2.6)
ACSM-ours + CF-CM284.5 (↑5.4)32.8 (↓1.9)62.8 (↑3.6)32.3 (↑3.4)
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.557, + 0.894, + 0.614 + ], + "angle": 0, + "content": "Table 3. Evaluation on COCO. \\( N \\) is the number of selected images from the web. ACSM-ours + KP-all uses all available web images. Performance change from the fully-supervised baseline is shown in green/red." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.642, + 0.842, + 0.658 + ], + "angle": 0, + "content": "all, averaged across all categories shown in Table 1." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.659, + 0.892, + 0.794 + ], + "angle": 0, + "content": "Results on Animal Pose. Next, we evaluate our previously trained models on Animal Pose dataset and present results in Table 2. Results are consistent with those in Pascal. Training models with all pseudo-labels results in large performance degradation in some cases (see Sheep in Table 2). KP-conf improves over the supervised baseline, but the improvement is higher for CF-MT, CF-CM and \\(\\mathrm{CF - CM^2}\\). Results from Tables 1 & 2 suggest that consistency-filtering is more effective than confidence-based filtering in our setting." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Results on COCO. In this part, we demonstrate the practicality of our approach in predicting the 3D shape of object categories even in the absence of initial annotations for those categories. We evaluate our approach on giraffes and bears. We annotate 250 images from COCO with 2D keypoints in a process that takes only \\(\\approx 2.5\\) hours per-category. Given a mesh template, we only need to associate the 2D" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "13098" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.079, + 0.086, + 0.891, + 0.395 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.403, + 0.897, + 0.446 + ], + "angle": 0, + "content": "Figure 6. Sample results on 3D shape recovery of quadrupeds. For each input image, we show the predicted 3D shape from the inferred viewpoint. (b) original ACSM (models for giraffes and bears are not available), (c) our ACSM implementation, (d) ACSM-ours trained with all PLs, (e) ACSM-ours + KP-conf, (f) ACSM-ours + CF-MT, (g) ACSM-ours + CF-CM, (h) ACSM-ours + CF-CM\\(^2\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.472, + 0.473, + 0.669 + ], + "angle": 0, + "content": "keypoint labels with vertices from the 3D mesh. This process is done in meshlab in \\(\\approx 5\\) minutes. We train our models with semi-supervised learning as described in Section 3.2. We use 150 images for training, while the remaining images are used for testing. We compare models that utilize pseudo-labels with the fully-supervised baseline trained with 150 images. The results are presented in Table 3. The results are consistent with those on Pascal and Animal Pose. Again, using all pseudo-labels leads in degraded performance. Data selection is essential, and in most cases leads to improved performance compared to the fully-supervised baseline. The performance gains are higher for consistency-based filtering approaches." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.674, + 0.473, + 0.901 + ], + "angle": 0, + "content": "Results with different number of labels. In Figure 5, we present results on 3D reconstruction of horses with different number \\( N_{s} \\) of images labeled with 2D keypoints. For all experiments, we use \\( N = 3K \\) images with pseudolabels from \\( \\mathcal{U} \\) and vary only the number of initial labels \\( N_{s} \\) from \\( S \\). From Figure 5, we observe that models with keypoint pseudo-labels outperform the fully-supervised baseline even when \\( N_{s} \\) is just 50. More importantly, we notice that models trained with \\( N_{s} = 50 \\) and keypoint pseudolabels outperform fully-supervised models with \\( N_{s} = 150 \\). We also observe, that consistency-based filtering methods are more effective than filtering with keypoint confidence scores. Finally, while all consistency-based filtering approaches lead to similar AUC performance, we notice that CF-CM² leads to lower camera rotation errors in all cases." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.472, + 0.895, + 0.593 + ], + "angle": 0, + "content": "Qualitative Examples. In Figure 6, we show sample 3D reconstructions for all models. We observe that ACSM-ours recovers more accurate shapes than the original ACSM version. Training with all PLs results in unnatural articulations in the predicted shapes. Additionally, we observe that some articulations are captured only when training with selected samples through consistency-filtering (e.g. horse legs in the first row for CF-CM\\(^2\\))." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.626, + 0.61, + 0.643 + ], + "angle": 0, + "content": "5. Summary" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.657, + 0.895, + 0.853 + ], + "angle": 0, + "content": "In summary, we investigated the amount of supervision necessary to train models for 3D shape recovery. We showed that it is possible to learn 3D shape predictors with as few as 50-150 images labeled with 2D keypoints. Such annotations are quick and easy to acquire, taking less than 2 hours for each new object category, making our approach highly practical. Additionally, we utilized automatically acquired web images to improve 3D reconstruction performance for several articulated objects, and found that a data selection method was necessary. To this end, we evaluated the performance of four data selection methods and found that training with data selected through consistency-filtering criteria leads to better 3D reconstructions." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.859, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Acknowledgements: This research has been partially funded by research grants to D. Metaxas through NSF IUCRC CARTA1747778, 2235405, 2212301, 1951890, 2003874." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "13099" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.175, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.169 + ], + "angle": 0, + "content": "[1] Mykhaylo Andriluka, Leonid Pishchulin, Peter Gehler, and Bernt Schiele. 2d human pose estimation: New benchmark and state of the art analysis. In CVPR, pages 3686-3693, 2014. 2" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.172, + 0.472, + 0.227 + ], + "angle": 0, + "content": "[2] Benjamin Biggs, Oliver Boyne, James Charles, Andrew Fitzgibbon, and Roberto Cipolla. Who left the dogs out? 3d animal reconstruction with expectation maximization in the loop. In ECCV, pages 195-211. 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Our proposed approach involves training category-specific keypoint estimators, generating 2D keypoint pseudo-labels on unlabeled web images, and using both the labeled and self-labeled sets to train 3D reconstruction models. It is based on two key insights: (1) 2D keypoint estimation networks trained on as few as 50-150 images of a given object category generalize well and generate reliable pseudo-labels; (2) a data selection mechanism can automatically create a "curated" subset of the unlabeled web images that can be used for training - we evaluate four data selection methods. Coupling these two insights enables us to train models that effectively utilize web images, resulting in improved 3D reconstruction performance for several articulated object categories beyond the fully-supervised baseline. Our approach can quickly bootstrap a model and requires only a few images labeled with 2D keypoints. This requirement can be easily satisfied for any new object category. To showcase the practicality of our approach for predicting the 3D shape of arbitrary object categories, we annotate 2D keypoints on 250 giraffe and bear images from COCO in just 2.5 hours per category. + +# 1. Introduction + +Predicting the 3D shape of an articulated object from a single image is a challenging task due to its underconstrained nature. Various successful approaches [14, 19] have been developed for inferring the 3D shape of humans. These approaches rely on strong supervision from 3D joint locations acquired using motion capture systems. Similar breakthroughs for other categories of articulated objects, such as animals, remain elusive. This is primarily due to the scarcity of appropriate training data. Some works (such as CMR [15]) learn to predict 3D shapes using only 2D labels for supervision. However, for most object categories even + +![](images/0486219bc5557a1df66b3fa36f45399eb789b0edd7aac3024a01711480e5c7d0.jpg) + +![](images/3b722e1c7b79f7edf5c396342cbcb331d1b58d651e9a1ca9a9e916f1e0d9d3ac.jpg) + +![](images/40493618943f602b2713fc0beb9ad8a9c4539ef7e95653a10a0d8978fb46cf54.jpg) +Figure 1. Overview of the proposed framework. It includes: (a) training a category-specific keypoint estimator with a limited labeled set $S$ , (b) generating keypoints pseudo-labels on web images, (c) automatic curation of web images to create a subset $\mathcal{U}'$ , and (d) training a model for 3D shape prediction with images from $S$ and $\mathcal{U}'$ . + +![](images/1d3afeae6daa67ea6208bf61af64c0927e7635336c2e5873f0f6e1debc177d5e.jpg) + +2D labels are limited or non-existent. We ask: how can we learn models that predict the 3D shape of articulated objects in-the-wild when limited or no annotated images are available for a given object category? + +In this paper we propose an approach that requires as few as 50-150 images labeled with 2D keypoints. This labeled set can be easily and quickly created for any object category. Our proposed approach is illustrated in Figure 1 and summarized as follows: (a) train a category-specific keypoint estimation network using a small set $S$ of images labeled with 2D keypoints; (b) generate 2D keypoint pseudo-labels on a large unlabeled set $\mathcal{U}$ consisting of automatically acquired web images; (c) automatically curate $\mathcal{U}$ by creating a subset of images and pseudo-labels $\mathcal{U}'$ according to a selection criterion; (d) train a model for 3D shape prediction with data from both $S$ and $\mathcal{U}'$ . + +A key insight is that current 2D keypoint estimators [30, 34, 38] are accurate enough to create robust 2D keypoint detections on unlabeled data, even when trained with a limited number of images. Another insight is that images from $\mathcal{U}$ increase the variability of several factors, such as + +![](images/f9e0624561aeb82fac2f4fa17af40ebce84de236b049d9b7a51ab29bcac95163.jpg) +Figure 2. Given a small set $S$ of images labeled with 2D keypoints, we train a 2D keypoint estimation netowrk $h_{\phi}$ and generate keypoint pseudo-labels on web images (set $\mathcal{U}$ ). We select a subset of $\mathcal{U}$ to train a 3D shape predictor $f_{\theta}$ . Two methods for data selection can be seen here: (a) CF-CM: an auxiliary 2D keypoint estimator $g_{\psi}$ generates predictions on $\mathcal{U}$ and images with the smallest discrepancy between the keypoint estimates of $h_{\phi}$ and $g_{\psi}$ are selected (criterion (c)); (b) CF-CM²: $f_{\theta}$ is trained with samples from $S$ and generates predictions on $\mathcal{U}$ . Images with the smallest discrepancy between the keypoint estimates of $h_{\phi}$ and $f_{\theta}$ are selected (criterion (d)) to retrain $f_{\theta}$ . + +![](images/54a388f37a3166be3234581623a10c6e6a37d62c426d417d0cdff97b6507ea51.jpg) + +![](images/0fb2ce4c964d6ce1df11d318631728ae636f8ab6c036c17a86706f82be0032a2.jpg) + +camera viewpoints, articulations and image backgrounds, that are important for training generalizable models for 3D shape prediction. However, the automatically acquired web images contain a high proportion of low-quality images with wrong or heavy truncated objects. Naively using all web images and pseudo-labels during training leads to degraded performance as can be seen in our experiments in Section 4.2. While successful pseudo-label (PL) selection techniques [4, 5, 23, 29, 40] exist for various tasks, they do not address the challenges in our setting. These works investigate PL selection when the unlabeled images come from curated datasets (e.g. CIFAR-10 [20], Cityscapes [6]), while in our setting they come from the web. In addition, they eventually use all unlabeled images during training while in our case most of the web images should be discarded. To effectively utilize images from the web we investigate four criteria to automatically create a "curated" subset that includes images with high-quality pseudo-labels. These contain a confidence-based criterion as well as three consistency-based ones (see Figure 2 for two examples). + +Through extensive experiments on five different articulated object categories (horse, cow, sheep, giraffe, bear) and three public datasets, we demonstrate that training with the proposed data selection approaches leads in considerably better 3D reconstructions compared to the fully-supervised baseline. Using all pseudo-labels leads to degraded performance. We analyze the performance of the data selection methods used and conclude that consistency-based selection criteria are more effective in our setting. Finally, we conduct experiments with varying number of images in the labeled set $S$ . We show that even with only 50 annotated instances and images from web, we can train models that lead to better 3D reconstructions than the fully-supervised models trained with more labels. + +# 2. Related Work + +Monocular 3D shape recovery. The task of 3D shape recovery from a single image is solved considerably well for the human category, with many approaches achieving impressive results [14, 17, 19, 31]. Their success can be attributed to the existence of large datasets with 3D [13, 27] and 2D annotations [1, 26]. However for other articulated object categories, such as animals, datasets with 3D annotations do not exist and even 2D labels are scarce and in some cases not available. + +Recent works [10, 15, 18, 21, 22, 24] have addressed several aspects of this problem. In CMR [15], the authors train a system for monocular 3D reconstruction using 2D keypoint and mask annotations. Although their approach works well, it relies on a large number of 2D annotations, such as 6K training samples for 3D reconstruction of birds in CUB [36], which limits its direct applicability to other categories. Follow-up works [10, 24] attempt to eliminate this reliance by using part segmentations [24] or mask labels [10], but their performance is still inferior to CMR [15], and they require mask or part segmentation annotations during training, which are not always available. Instead, we propose a novel approach that addresses the scarcity of 2D keypoint annotations by effectively utilizing images from the web. + +In [18], ACFM leverages temporal information for supervision and applies the learned model on a per-frame basis. In [21, 22] the authors generate 3D reconstructions in the form of a rigid [22] or articulated [21] template, training their models with masks and 2D keypoint labels from Pascal VOC [9] and predicted masks (using Mask-RCNN [11]) from ImageNet [7]. Despite using only a small labeled set and mask pseudo-labels, their approach is not fully automatic as they manually select the predicted masks for their + +training set. Another line of work [2, 33], regresses the parameters of a statistical animal model [41], but their work only reconstructs the 3D shape of dogs, for which large-scale 2D annotations exist [2]. BARC [33] also uses a dataset with 3D annotations during a pre-training stage. + +Learning with keypoint pseudo-labels. The use of keypoint pseudo-labels has been widely investigated in various works related to 2D pose estimation [3,8,23,28,29,32,39]. In [32, 39], the authors investigate learning with keypoint pseudo-labels for human pose estimation, while in [3,23,29] the goal is to estimate the 2D pose of animals. In the case of animal pose estimation, PLs are used for domain adaptation from synthetic data [23, 29] or from human poses [3]. What is common across these works is that they integrate PLs into the training set (in some cases progressively) and that at the end of the process all samples from the unlabeled set are included. This is not an issue as images in the unlabeled set come from curated datasets. While these approaches can potentially enhance the quality of PLs, a data selection mechanism is still necessary in our case because the unlabeled images come from the web, and most of them should be discarded. To this end, we adapt PL selection criteria form previous works, such as keypoint confidence-based filtering from [3] and multi-transform consistency from [23, 29, 32], to automatically curate the acquired web images. + +# 3. Approach + +Given a labeled set $\mathcal{S} = \{(I_i^{(s)},x_i)\}_{1}^{N_s}$ comprising of $N_{s}$ images with paired 2D keypoint annotations and an unlabeled set $\mathcal{U} = \{I_i^{(u)}\}_{1}^{N_u}$ containing $N_{u}$ unlabeled images, our goal is to learn a 3D shape recovery model by effectively utilizing both labeled and unlabeled data. We use a limited annotated set $N_{s}$ and unlabeled images from the web, thus $N_{u}$ is much larger than $N_{s}$ . We investigate how keypoint pseudo-labeling on unlabeled images can improve existing 3D reconstruction models. CMR [15] and ACSM [21] are chosen as two canonical examples. Next, we present some relevant background on monocular 3D shape recovery, CMR and ACSM, while in Section 3.2 we present our proposed approach. + +# 3.1. Preliminaries + +Given an image $I$ of an object, its 3D structure is recovered by predicting a 3D mesh $M$ and camera pose $\pi$ with a model $f_{\theta}$ whose parameters $\theta$ are learned during training. + +CMR. The shape in CMR [15] is represented as a 3D mesh $M \equiv (V, F)$ with vertices $V \in \mathbb{R}^{|V| \times 3}$ and faces $F$ , and is homeomorphic to a sphere. Given an input image $I$ , CMR uses ResNet-18 [12] to acquire an image embedding, which is then processed by a 2-layer MLP and fed to two independent linear layers predicting vertex displacements + +$\Delta_V \in \mathbb{R}^{|V| \times 3}$ from a template shape $T \in \mathbb{R}^{|V| \times 3}$ and the camera pose. The deformed 3D vertex locations are then computed as $V = T + \Delta_V$ . A weak-perspective camera model $\pi \equiv (s, \mathbf{t}, \mathbf{q})$ is used, where $s \in \mathbb{R}_+$ is the scale, $\mathbf{t} \in \mathbb{R}^2$ the translation and $\mathbf{q} \in \mathbb{R}^4$ the rotation of the camera in unit quaternion parameterization. Thus, CMR learns to predict $f_\theta(I) \equiv (\Delta_V, \pi)$ . We refer the reader to [15] for more details. + +ACSM. The shape in ACSM [21] is also represented as a 3D mesh $M \equiv (V, F)$ . The mesh $M$ is a pre-defined template shape for each object category with fixed topology. Given a template shape $T$ , its vertices are grouped into $P$ parts. As a result, for each vertex $v$ of $T$ an associated membership $a_{p}^{v} \in [0,1]$ corresponding to each part $p \in \{1, \dots, P\}$ is produced. The articulation $\delta$ of this template $T$ is specified as a rigid transformation w.r.t. each parent part, i.e. $\delta \equiv \{(t_{p}, R_{p})\}$ , where the torso corresponds to the root part in the hierarchy. Given the articulation parameters $\delta$ , a global transformation $\mathcal{T}_{p}(\cdot, \delta)$ for each part can be computed using forward kinematics. Thus, the position of each vertex $v$ of $T$ after articulation can be computed as $\sum_{p} a_{p}^{v} \mathcal{T}_{p}(v, \delta)$ . Therefore, to recover the 3D structure of an object with ACSM we need to predict the camera pose $\pi$ and articulation parameters $\delta$ . ACSM [21] uses the same image encoder with CMR [15]. The camera pose is parameterized and predicted as in CMR, while independent fully-connected heads regress the articulation parameters $\delta$ . Thus, ACSM learns to predict $f_{\theta}(I) \equiv (\delta, \pi)$ . For more details, we refer the reader to [21]. + +Keypoint and mask supervision. CMR and ACSM are supervised with 2D annotations, by ensuring that the predicted 3D shape matches with the 2D evidence when projected onto the image space using the predicted camera. Let's assume $k$ 2D keypoint locations $x_{i} \in \mathbb{R}^{k \times 2}$ as label for image $I_{i}$ . Each one of these $k$ 2D keypoints has a semantic correspondence with a 3D keypoint. The 3D keypoints can be computed from the mesh vertices. In CMR the location of 3D keypoints is regressed from that of the mesh vertices using a learnable matrix $A$ , while mesh vertices corresponding to 3D keypoints are pre-determined for ACSM. This leads to $k$ 3D keypoints $\hat{X}_{i} \in \mathbb{R}^{k \times 3}$ that can be projected onto the image using the predicted camera $\hat{\pi}$ . In this setting, keypoint supervision is provided using a reprojection loss on the keypoints: + +$$ +L _ {k p} = \left\| x _ {i} - \hat {\pi} \left(\hat {X} _ {i}\right) \right\| _ {2}. \tag {1} +$$ + +Similarly, assuming an instance segmentation mask $m_{i}$ is provided as annotation for $I_{i}$ , we can render the 3D mesh $M = (V_{i}, F)$ through the predicted camera $\hat{\pi}_{i}$ using a differentiable renderer [16] $\mathcal{R}(\cdot)$ and provide mask supervision with the following loss: + +$$ +L _ {\text {m a s k}} = \left\| m _ {i} - \mathcal {R} \left(V _ {i}, F, \hat {\pi} _ {i}\right) \right\| _ {2}. \tag {2} +$$ + +In ACSM, a second network $f_{\theta'}'$ is trained to map each pixel in the object's mask to a point on the surface of the template shape. This facilitates computation of several mask losses. In our experiments with ACSM we only train network $f_{\theta}$ with the keypoint reprojection loss in Eq. (1). + +# 3.2. 3D Shape Recovery Approach + +Our proposed approach involves the following steps: (1) annotation of 2D keypoints on $N_{s}$ images (when no labels are available for the given category) to create a labeled set $S$ ; (2) training a 2D keypoint estimation network with samples from $S$ and generating 2D keypoint pseudo-labels on an image collection from the web (unlabeled set $\mathcal{U}$ ); (3) selecting data from $\mathcal{U}$ to be used for training according to a criterion; (4) training a 3D shape predictor with samples from $S$ and $\mathcal{U}$ . We explain all the steps in detail below. + +Data annotation. We annotate $N_S$ images with 2D keypoints, following standard keypoint definitions used in existing datasets. For instance, we use 16 keypoints for quadruped animals as defined in Pascal [9]. The only requirement is to annotate images containing objects with the variety of poses and articulations we wish to model. + +Generating keypoint pseudo-labels. In pseudo-labeling an initial model is trained with labels from a labeled set $S$ and is used to produce artificial labels on an unlabeled set $\mathcal{U}$ . In this work, instead of tasking the 3D shape predictor $f_{\theta}$ to produce pseudo-labels for itself, we propose to generate 2D keypoint pseudo-labels using the predictions of a 2D keypoint estimation network [38] $h_{\phi}$ . This is a natural option since 2D keypoint estimators are easier to train with limited data and yield more precise detections compared to reprojected keypoints obtained from a 3D mesh. + +Most current methods for 2D pose estimation [30,34,38] solve the task by estimating $K$ gaussian heatmaps. Each heatmap encodes the probability of a keypoint at a location in the image. The location of each keypoint can be estimated as the location with the maximum value in the corresponding heatmap, while that value can be used as a confidence estimate for that keypoint. We train a 2D keypoint estimation network $h_\phi$ with labels from $\mathcal{S}$ and use it to generate keypoint pseudo-labels on $\mathcal{U}$ . As such, the unlabeled set is now $\mathcal{U}_{\phi} = \{(I_{i}^{(u)},\tilde{x}_{i}^{(u)},\tilde{c}_{i}^{(u)})\}_{1}^{N_{u}}$ , where $\tilde{x}_i^{(u)}\in \mathbb{R}^{k\times 2}$ are the estimated locations and $\tilde{c}_i^{(u)}\in [0,1]^k$ the corresponding confidence estimates for $k$ keypoints of interest in image $I_{i}^{(u)}$ . + +Learning with keypoint pseudo-labels. Given a labeled set $\mathcal{S} = \{(I_i^{(s)},x_i)\}_{1}^{Ns}$ containing images with keypoint labels $x_{i}$ , we train $f_{\theta}$ using the supervised loss: + +$$ +L _ {k p} ^ {\mathcal {S}} = \sum_ {i = 1} ^ {N s} | | x _ {i} - \hat {\pi} (\hat {X} _ {i}) | | _ {2}, \tag {3} +$$ + +where $\hat{\pi}$ is the predicted camera pose and $\hat{X}_i$ the 3D key + +points computed from 3D mesh vertices $V_{i}$ . Similarly, given a set $\mathcal{U}_{\phi} = \{(I_i^{(u)},\hat{x}_i^{(u)},\hat{c}_i^{(u)})\}_{1}^{N_u}$ comprising of images with keypoint pseudo-labels $(\tilde{x}_i,\tilde{c}_i)$ , we train using the following modification of the keypoint reprojection loss: + +$$ +L _ {k p} ^ {\mathcal {U}} = \sum_ {i = 1} ^ {N u} \left\| \tilde {c} _ {i} \left(\tilde {x} _ {i} - \hat {\pi} \left(\hat {X} _ {i}\right)\right) \right\| _ {2}. \tag {4} +$$ + +We can train using data from both $S$ and $\mathcal{U}_{\phi}$ with the following objective: $L = L_{kp}^{S} + L_{kp}^{U}$ . However, as $Ns \ll N_u$ , the training process is dominated by samples from $\mathcal{U}_{\phi}$ . When the quality of samples in $\mathcal{U}_{\phi}$ is low, as it is the case with uncurated data from the web, training with all the samples from the unlabeled set leads to degraded performance. To mitigate this issue, we train using a subset of $\mathcal{U}_{\phi}$ containing useful images and high-quality pseudo-labels that are chosen according to a selection criterion. + +# 3.2.1 Data Selection + +Given a number of images $N$ to be used by $\mathcal{U}_{\phi}$ , we select them according to one of the following criteria. + +Keypoint Confidence. This method, referred to as $KP$ -conf, selects samples from $\mathcal{U}_{\phi}$ based on the confidence score of the PLs. In particular, it selects $N$ images with the highest per-sample sum of keypoint confidences $\sum_{k} \tilde{\mathbf{c}}_k^{(u)}$ . + +Multi-Transform Consistency. Intuitively, if one scales or rotates one image the prediction of a good 2D keypoint estimator should change accordingly. In other words, it should be equivariant to the those geometric transformations. We can thus use the consistency to multiple equivariant transformations to select the images with high-quality PLs. We denote this consistency-filtering approach as $CF-MT$ . + +Cross-Model Consistency. Using this consistency filtering approach, referred to as $CF-CM$ , we select samples based on the consistency of two 2D keypoint estimators, $h_{\phi}$ and $g_{\psi}$ , with different architectures. Our insight is that the two models have different structural biases and can learn different representations from the same image. Thus, we use the discrepancy in their predictions as a proxy for evaluating the quality of the generated pseudo-labels. For each image $I$ from $\mathcal{U}$ , we generate keypoint pseudo-labels $\tilde{x}_{\phi}$ and $\tilde{x}_{\psi}$ with $h_{\phi}$ and $g_{\psi}$ respectively, and calculate the discrepancy between the PLs with the following term: + +$$ +D _ {\mathrm {C F - C M}} = \left\| \tilde {x} _ {\phi} - \tilde {x} _ {\psi} \right\| _ {2}. \tag {5} +$$ + +We select $N$ samples with the minimum discrepancy creating the subset $\mathcal{U}_{\phi, \psi} \subset \mathcal{U}_{\phi}$ . + +Cross-Model Cross-Modality Consistency. With this consistency filtering criterion, which we dub $CF - CM^2$ , we select samples based on their discrepancy between the predictions of the 2D keypoint estimator $h_{\phi}$ and the reprojected keypoints from the 3D shape predictor $f_{\theta}$ . Given an image + +![](images/1ea2597210c5f610cd0d4c4b3a3edbd43e597510ede97220fc03fa7357e3ee06.jpg) +Figure 3. Sample results on CUB. For each sample, we show the predicted shape and texture from the inferred camera view (b, d) and a novel view (c, e) for models trained with and without keypoint pseudo-labels. + +$I$ from $\mathcal{U}$ , we calculate the locations for 3D keypoints $\tilde{X}_{\theta}$ from the predicted 3D mesh vertices (as explained in Section 3.1). The corresponding 2D keypoints $\tilde{x}_{\theta}$ are calculated by projecting $\tilde{X}_{\theta}$ onto the image with the predicted camera parameters $\tilde{\pi}_{\theta}$ , i.e. $\tilde{x}_{\theta} = \tilde{\pi}_{\theta}(\tilde{X}_{\theta})$ . As such, we calculate the discrepancy between the keypoints $\tilde{x}_{\phi}$ and $\tilde{x}_{\theta}$ as follows: + +$$ +D _ {\mathrm {C F - C M} ^ {2}} = \left\| \tilde {x} _ {\phi} - \tilde {\pi} _ {\theta} \left(\tilde {X} _ {\theta}\right) \right\| _ {2}. \tag {6} +$$ + +Our insight for this consistency check comes from the fact that the two models employ different paradigms for estimating 2D keypoints and have distinct failure modes. 2D keypoints detectors use a bottom-up approach to determine the locations of 2D keypoints. While their predictions are more pixel-accurate than the reprojected keypoints from a 3D mesh, they are not constrained in any way and mainly rely on local cues. Conversely, 3D shape predictors, such as $f_{\theta}$ , estimate keypoints as part of a 3D mesh, which constrains their predictions with a specific mesh topology. This makes their predictions more robust. + +# 3.3. Additional details + +Here, we present some additional details of our approach. We include extensive implementation details in the supplementary material. + +Data acquisition. For each target object category we download images from Flickr using the urls that belong to the public and freely usable YFCC100M [35]. However, some images contain wrong objects or objects with heavy truncation. There are also repeated images. + +Initial filtering. We remove repeated images with dHash [37]. Then, we detect bounding boxes using MaskRCNN [11] with ResNet50-FPN [12,25] backbone from detector2. Only detections with confidence above a threshold $\tau$ are retained. We use $\tau = 0.95$ for all object categories. + +Keypoints from 2D pose estimation network. We train the SimpleBaselines [38] pose estimator, with an ImageNet pretrained ResNet-18 [12] backbone, with labels from $\mathcal{S}$ and use it to generate keypoint PLs $(\tilde{x}_{\phi}^{(u)},\tilde{c}_{\phi}^{(u)})$ on $\mathcal{U}$ . + +Data Selection. We curate the web images using a selection criterion. We evaluate the effectiveness of the four selection criteria presented previously. We use each criterion to select the best $N$ data samples from the self-labeled web images. We present experiments with $N \in \{1K, 3K\}$ . + +Training. We train a 3D shape predictor $f_{\theta}$ with keypoint reprojection losses as defined in Eq. (3) & (4). + +# 4. Experiments + +Evaluation metrics. While our models are able to reconstruct the 3D shape as a mesh, evaluating their accuracy remains a challenge due to the absence of 3D ground truth data for the current datasets and object categories. Following prior work [15, 18, 21, 22] we evaluate our models quantitatively using the standard "Percentage of Correct Keypoints" (PCK) metric. For $PCK(t)$ , the reprojection is "correct" when the predicted 2D keypoint location is within $t \times \max(w, h)$ distance of the ground-truth location, where $w$ and $h$ are the width and the height of the object's bounding box. We summarize the PCK performance at different thresholds by computing the area under the curve (AUC), $\mathrm{AUC}_{a_1}^{a_2} = \int_{a_1}^{a_2} PCK(t) dt$ . We use $a_1 = 0.05$ and $a_2 = 0.1$ and refer to $\mathrm{AUC}_{a_1}^{a_2}$ as AUC in our evaluation. Following [10], we also evaluate the predicted camera viewpoint obtained by our models. We calculate the rotation error $\mathrm{err}_R = \arccos\left(\frac{\mathrm{Tr}(\hat{R}^T\hat{R}) - 1}{2}\right)$ between predicted camera rotation $\hat{R}$ and pseudo ground-truth camera $\tilde{R}$ computed using SfM on keypoint labels. Finally, we offer qualitative results to measure the quality of the predicted 3D shapes. + +# 4.1. Simulated Semi-Supervised Setting + +First, we investigate the effectiveness of keypoint PLs in a controlled setting. For our experiments we use the CUB dataset [36] that consists of 6K images with bounding box, mask and 2D keypoint labels for training and testing. We study the impact of training with various levels of supervision on 3D reconstruction performance. We split CUB's training set into a labeled set $S$ and an unlabeled set $\mathcal{U}$ by randomly choosing samples from the initial training set to be included in $S$ , while placing the rest in $\mathcal{U}$ . This is a controlled setting where we expect the performance of the models trained with labels from $S$ and keypoint pseudo-labels from $\mathcal{U}$ to be lower-bounded by that of models trained using only $S$ and upper-bounded by the fully-supervised baseline that uses the whole training set. We use CMR [15] for the 3D shape prediction network $f_{\theta}$ . + +Results on CUB. In Figure 4, we compare the performance of models trained with different number of labeled and pseudo-labeled instances. Following CMR, we also report the mIoU metric. We observe that training with 2D keypoint pseudo-labels consistently improves 3D reconstruction performance by a significant margin across all metrics. + +
HorseCowSheep
AUC (↑)errR(↓)AUC (↑)errR(↓)AUC (↑)errR(↓)
NACSM (Mask) [21]34.9 (↓15.9)44.3 (↑14.1)30.7 (↓16.9)71.0 (↑36.3)28.2 (↓18.6)73.1 (↑39.3)
ACSM (KP+Mask) [21]37.4 (↓13.4)76.4 (↑46.2)----
ACSM-ours50.830.247.634.746.833.8
ACSM-ours + KP-all50.2 (↓0.6)31.9 (↑1.7)43.9 (↓3.9)40.1 (↑5.4)43.5 (↓3.5)40.7 (↑6.9)
ACSM-ours + KP-conf53.9 (↑3.1)30.8 (↑0.6)47.638.3 (↑3.6)48.1 (↑1.3)38.6 (↑4.8)
ACSM-ours + CF-MT55.1 (↑4.3)30.0 (↓0.2)50.7 (↑3.1)38.9 (↑4.2)51.1 (↑4.3)33.3 (↓0.5)
ACSM-ours + CF-CM54.7 (↑3.9)30.0 (↓0.2)50.9 (↑3.3)38.6 (↑3.9)50.6 (↑3.8)32.8 (↓1.0)
ACSM-ours + CF-CM254.2 (↑3.4)30.9 (↑0.7)49.4 (↑1.8)32.7 (↓2.0)48.6 (↑1.8)32.1 (↓1.7)
NACSM-ours + KP-conf54.3 (↑3.5)30.0 (↓0.2)50.2 (↑2.6)40.2 (↑5.5)49.1 (↑2.3)35.7 (↑1.0)
ACSM-ours + CF-MT55.4 (↑4.6)30.0 (↓0.2)49.2 (↑1.6)39.1 (↑4.4)51.0 (↑4.2)33.9 (↑0.1)
ACSM-ours + CF-CM55.9 (↑5.1)29.8 (↓0.4)50.0 (↑2.4)38.8 (↑4.1)48.4 (↑1.6)34.1 (↑0.3)
ACSM-ours + CF-CM255.5 (↑4.7)28.1 (↓2.1)52.6 (↑5.0)36.2 (↑1.5)53.0 (↑6.2)31.3 (↓2.5)
+ +Table 1. Evaluation on Pascal. $N$ is the number of selected images from the web. ACSM-ours + KP-all uses all available web images. Performance change from the fully-supervised baseline ACSM-ours is shown in green/red. + +The improvement is larger when the initial labeled set $S$ is small (e.g. 100 images). This is a very interesting finding. The quality of the generated keypoint pseudo-labels decreases when the 2D keypoint estimator is trained with fewer samples. However, the keypoint pseudo-labels are accurate enough to provide a useful signal for training CMR, largely improving its performance. + +In Figure 3, we show sample 3D reconstruction results comparing CMR trained with: i) 300 labeled instances and ii) the same labeled instances and additional keypoint pseudo-labels (for 5,700 images). We show the predicted shape and texture from the predicted camera view and a side view. From Figure 3 we can see that the model trained with keypoint pseudo-labels can accurately capture challenging deformations (e.g. open wings), while the other model struggles. + +# 4.2. Learning with Web Images + +We go beyond standard semi-supervised approaches that use unlabeled images from curated datasets by effectively utilizing images from the web for training. We use $N_S = 150$ images annotated with 2D keypoints and evaluate our proposed approach. + +Datasets. We train our models with 2D keypoints from Pascal [9] using the same train/test splits as prior work [21,22]. For categories with less than 150 labeled samples, we augment the labeled training set $S$ by manually labeling some images from COCO [26]. We use Pascal's test split and the Animal Pose dataset [3] for evaluation. + +Implementation details. We train the SimpleBaselines [38] 2D pose estimator using 150 images with 2D keypoint labels and generate pseudo-labels on web images. For criterion CF-MT, we use scaling and rotation transformations. For criterion CF-CM, we train Stacked HourGlass [30] as + +![](images/76ffc4094edd5fa32363101ecc586334cdc284efbaed2c27b8849eca633e4d85.jpg) +Figure 4. Evaluation on CUB. We show the AUC, mIoU and camera rotation error (in degrees) for models trained with different number of labeled and pseudo-labeled instances. Performance across all metrics is significantly improved with keypoint PLs. + +![](images/4b521b9779c92d449d1d67ca759b40aa1d5a91c3954dcbbc96f4bb1ef121c288.jpg) + +![](images/eb4e166314fe3eb305020315124b888dbc7ad4291640c817c25394ec20debe62.jpg) + +the auxiliary 2D pose estimator. We use ACSM [21] for 3D shape prediction. We found that some template meshes provided in the publicly available ACSM codebase contained incorrect keypoint definitions for certain animals' limbs, with inconsistencies between the right and left sides. After rectifying this issue, we trained ACSM exclusively with keypoint labels and achieved better performance than the one reported in [21], establishing a stronger baseline. We denote our implementation of ACSM trained with 150 images labeled with 2D keypoints as ACSM-ours. + +Baselines. We compare the performance of the models trained with selected web images and pseudo-labels with the fully-supervised baseline (ACSM-ours) as well as with the baseline that uses all pseudo-labels during training, denoted as ACSM-ours+KP-all. To put our results into perspective, we also compare with the models from ACSM [21]. The available models are trained using mask labels from Pascal [9] and manually picked mask pseudolabels from ImageNet [7]. For horses, the authors provide a model trained with keypoint labels from Pascal as well. + +Results on Pascal. First, we evaluate the performance of different methods on Pascal's test set. The results are pre + +
HorseCowSheep
AUC (↑)errR(↓)AUC (↑)errR(↓)AUC (↑)errR(↓)
NACSM (Mask) [21]47.4 (↓19.3)38.0 (↑17.3)46.2 (↓13.4)51.8 (↑22.3)31.4 (↓25.8)65.6 (↑50.0)
ACSM (KP+Mask) [21]51.0 (↓15.7)59.9 (↑39.2)----
ACSM-ours66.720.759.629.557.215.6
ACSM-ours + KP-all69.1 (↑2.4)20.9 (↑0.2)61.2 (↑1.6)27.8 (↓1.7)29.1 (↓28.1)19.9 (↑4.3)
ACSM-ours + KP-conf72.9 (↑6.2)19.6 (↓1.1)65.0 (↑5.4)31.9 (↑2.4)58.5 (↑1.3)20.3 (↑4.7)
ACSM-ours + CF-MT74.6 (↑7.9)19.9 (↓0.8)67.0 (↑7.4)26.2 (↓3.3)59.3 (↑2.1)14.6 (↓1.0)
ACSM-ours + CF-CM75.1 (↑8.4)19.6 (↓1.1)67.2 (↑7.6)25.9 (↓3.6)59.3 (↑2.1)14.7 (↓0.9)
ACSM-ours + CF-CM273.0 (↑6.3)19.7 (↓1.0)67.2 (↑7.6)23.5 (↓6.0)58.7 (↑1.5)15.3 (↓0.3)
NACSM-ours + KP-conf74.3 (↑7.6)19.6 (↓1.1)67.8 (↑7.8)28.0 (↓1.5)57.3 (↑0.1)15.3 (↓0.3)
ACSM-ours + CF-MT74.4 (↑7.7)19.6 (↓1.1)66.0 (↑6.4)29.7 (↑0.2)59.6 (↑2.4)15.1 (↓0.5)
ACSM-ours + CF-CM74.1 (↑7.4)19.6 (↓1.1)66.4 (↑6.8)29.3 (↓0.2)59.4 (↑2.2)15.8 (↑0.2)
ACSM-ours + CF-CM273.8 (↑7.1)19.5 (↓1.2)69.6 (↑10.0)25.2 (↓4.3)60.2 (↑3.0)14.9 (↓0.7)
+ +![](images/b0742dce177254c40f9d89bd4f9af720da3e7bac1524bc91da1a276dcf04d07d.jpg) + +![](images/233ee441ecdd9f13adba47b34784fd581cdac56afdc97b03ede79ae98bf8224f.jpg) + +![](images/0068148e50fe8ed973e63adac663524a7cbdbd54aa5f4a5dff568bf6f867e7df.jpg) +Figure 5. Evaluation under varying initial supervision. We show the AUC and camera rotation error (in degrees) on Pascal (top) and Animal Pose (bottom) for the use of our proposed framework under various levels of initial supervision from $S$ . KP-conf, CF-MT, CF-CM, CF-CM $^2$ use PLs from $N = 3K$ images. + +![](images/4570a87761413eb8520e77ec6ec8021d94f185be0e045ae8122f61c4c59e0e97.jpg) + +sented in Table 1. From Table 1 we observe that naively including all pseudo-labels during training (ACM-ours+KP-all) leads in degraded performance. Data selection with KP-conf leads to some improvements, but models trained with pseudo-labels selected from consistency-filtering, i.e. CF-MT, CF-CM and $\mathrm{CF - CM^2}$ , perform consistently better. The improvement over the fully-supervised baseline is quite substantial for those models. For instance, ACSM-ours+CF-CM has a relative improvement (in AUC) of $10.9\%$ over ACSM-ours and $17.0\%$ over ACSM-ours+KP + +Table 2. Evaluation on Animal Pose. $N$ is the number of selected images from the web. ACSM-ours + KP-all uses all available web images. Training with selected web images significantly improves the fully-supervised baseline. We show the performance change from ACSM-ours in green/red. + +
GiraffeBear
AUC (↑)errR(↓)AUC (↑)errR(↓)
NACSM-ours79.134.759.228.9
ACSM-ours + KP-all75.6 (↓3.5)39.5 (↑4.8)58.2 (↓1.0)35.4 (↑6.5)
ACSM-ours + KP-conf83.3 (↑4.2)31.4 (↓3.3)62.7 (↑3.5)31.0 (↑2.1)
ACSM-ours + CF-MT84.4 (↑5.3)32.1 (↓2.6)62.6 (↑3.6)31.9 (↑3.0)
ACSM-ours + CF-CM84.1 (↑5.0)32.5 (↓2.2)62.8 (↑3.6)31.6 (↑2.7)
ACSM-ours + CF-CM286.6 (↑7.5)28.8 (↓5.9)62.2 (↑3.0)30.7 (↑1.8)
NACSM-ours + KP-conf82.8 (↑3.7)35.6 (↑0.9)59.9 (↑0.7)35.0 (↑6.1)
ACSM-ours + CF-MT83.5 (↑4.4)33.1 (↓1.6)63.1 (↑3.9)31.7 (↑2.8)
ACSM-ours + CF-CM83.6 (↑4.5)33.4 (↓1.3)63.4 (↑4.2)31.5 (↑2.6)
ACSM-ours + CF-CM284.5 (↑5.4)32.8 (↓1.9)62.8 (↑3.6)32.3 (↑3.4)
+ +Table 3. Evaluation on COCO. $N$ is the number of selected images from the web. ACSM-ours + KP-all uses all available web images. Performance change from the fully-supervised baseline is shown in green/red. + +all, averaged across all categories shown in Table 1. + +Results on Animal Pose. Next, we evaluate our previously trained models on Animal Pose dataset and present results in Table 2. Results are consistent with those in Pascal. Training models with all pseudo-labels results in large performance degradation in some cases (see Sheep in Table 2). KP-conf improves over the supervised baseline, but the improvement is higher for CF-MT, CF-CM and $\mathrm{CF - CM^2}$ . Results from Tables 1 & 2 suggest that consistency-filtering is more effective than confidence-based filtering in our setting. + +Results on COCO. In this part, we demonstrate the practicality of our approach in predicting the 3D shape of object categories even in the absence of initial annotations for those categories. We evaluate our approach on giraffes and bears. We annotate 250 images from COCO with 2D keypoints in a process that takes only $\approx 2.5$ hours per-category. Given a mesh template, we only need to associate the 2D + +![](images/f734021cc8a9320c07c81e79143ca57c6926ad51294bad9ddd9deb3415b7d884.jpg) +Figure 6. Sample results on 3D shape recovery of quadrupeds. For each input image, we show the predicted 3D shape from the inferred viewpoint. (b) original ACSM (models for giraffes and bears are not available), (c) our ACSM implementation, (d) ACSM-ours trained with all PLs, (e) ACSM-ours + KP-conf, (f) ACSM-ours + CF-MT, (g) ACSM-ours + CF-CM, (h) ACSM-ours + CF-CM $^2$ . + +keypoint labels with vertices from the 3D mesh. This process is done in meshlab in $\approx 5$ minutes. We train our models with semi-supervised learning as described in Section 3.2. We use 150 images for training, while the remaining images are used for testing. We compare models that utilize pseudo-labels with the fully-supervised baseline trained with 150 images. The results are presented in Table 3. The results are consistent with those on Pascal and Animal Pose. Again, using all pseudo-labels leads in degraded performance. Data selection is essential, and in most cases leads to improved performance compared to the fully-supervised baseline. The performance gains are higher for consistency-based filtering approaches. + +Results with different number of labels. In Figure 5, we present results on 3D reconstruction of horses with different number $N_{s}$ of images labeled with 2D keypoints. For all experiments, we use $N = 3K$ images with pseudolabels from $\mathcal{U}$ and vary only the number of initial labels $N_{s}$ from $S$ . From Figure 5, we observe that models with keypoint pseudo-labels outperform the fully-supervised baseline even when $N_{s}$ is just 50. More importantly, we notice that models trained with $N_{s} = 50$ and keypoint pseudolabels outperform fully-supervised models with $N_{s} = 150$ . We also observe, that consistency-based filtering methods are more effective than filtering with keypoint confidence scores. Finally, while all consistency-based filtering approaches lead to similar AUC performance, we notice that CF-CM² leads to lower camera rotation errors in all cases. + +Qualitative Examples. In Figure 6, we show sample 3D reconstructions for all models. We observe that ACSM-ours recovers more accurate shapes than the original ACSM version. Training with all PLs results in unnatural articulations in the predicted shapes. Additionally, we observe that some articulations are captured only when training with selected samples through consistency-filtering (e.g. horse legs in the first row for CF-CM $^2$ ). + +# 5. Summary + +In summary, we investigated the amount of supervision necessary to train models for 3D shape recovery. We showed that it is possible to learn 3D shape predictors with as few as 50-150 images labeled with 2D keypoints. Such annotations are quick and easy to acquire, taking less than 2 hours for each new object category, making our approach highly practical. Additionally, we utilized automatically acquired web images to improve 3D reconstruction performance for several articulated objects, and found that a data selection method was necessary. To this end, we evaluated the performance of four data selection methods and found that training with data selected through consistency-filtering criteria leads to better 3D reconstructions. + +Acknowledgements: This research has been partially funded by research grants to D. Metaxas through NSF IUCRC CARTA1747778, 2235405, 2212301, 1951890, 2003874. + +# References + +[1] Mykhaylo Andriluka, Leonid Pishchulin, Peter Gehler, and Bernt Schiele. 2d human pose estimation: New benchmark and state of the art analysis. In CVPR, pages 3686-3693, 2014. 2 +[2] Benjamin Biggs, Oliver Boyne, James Charles, Andrew Fitzgibbon, and Roberto Cipolla. Who left the dogs out? 3d animal reconstruction with expectation maximization in the loop. In ECCV, pages 195-211. Springer, 2020. 3 +[3] Jinkun Cao, Hongyang Tang, Hao-Shu Fang, Xiaoyong Shen, Cewu Lu, and Yu-Wing Tai. Cross-domain adaptation for animal pose estimation. 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Our proposed approach involves training category-specific keypoint estimators, generating 2D keypoint pseudo-labels on unlabeled web images, and using both the labeled and self-labeled sets to train 3D reconstruction models. It is based on two key insights: (1) 2D keypoint estimation networks trained on as few as 50-150 images of a given object category generalize well and generate reliable pseudo-labels; (2) a data selection mechanism can automatically create a \"curated\" subset of the unlabeled web images that can be used for training - we evaluate four data selection methods. Coupling these two insights enables us to train models that effectively utilize web images, resulting in improved 3D reconstruction performance for several articulated object categories beyond the fully-supervised baseline. Our approach can quickly bootstrap a model and requires only a few images labeled with 2D keypoints. This requirement can be easily satisfied for any new object category. To showcase the practicality of our approach for predicting the 3D shape of arbitrary object categories, we annotate 2D keypoints on 250 giraffe and bear images from COCO in just 2.5 hours per category." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 561, + 127, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 561, + 127, + 574 + ], + "spans": [ + { + "bbox": [ + 47, + 561, + 127, + 574 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "type": "text", + "content": "Predicting the 3D shape of an articulated object from a single image is a challenging task due to its underconstrained nature. Various successful approaches [14, 19] have been developed for inferring the 3D shape of humans. These approaches rely on strong supervision from 3D joint locations acquired using motion capture systems. Similar breakthroughs for other categories of articulated objects, such as animals, remain elusive. This is primarily due to the scarcity of appropriate training data. Some works (such as CMR [15]) learn to predict 3D shapes using only 2D labels for supervision. However, for most object categories even" + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 310, + 213, + 406, + 291 + ], + "blocks": [ + { + "bbox": [ + 310, + 213, + 406, + 291 + ], + "lines": [ + { + "bbox": [ + 310, + 213, + 406, + 291 + ], + "spans": [ + { + "bbox": [ + 310, + 213, + 406, + 291 + ], + "type": "image", + "image_path": "0486219bc5557a1df66b3fa36f45399eb789b0edd7aac3024a01711480e5c7d0.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 412, + 214, + 545, + 291 + ], + "blocks": [ + { + "bbox": [ + 412, + 214, + 545, + 291 + ], + "lines": [ + { + "bbox": [ + 412, + 214, + 545, + 291 + ], + "spans": [ + { + "bbox": [ + 412, + 214, + 545, + 291 + ], + "type": "image", + "image_path": "3b722e1c7b79f7edf5c396342cbcb331d1b58d651e9a1ca9a9e916f1e0d9d3ac.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 309, + 296, + 421, + 359 + ], + "blocks": [ + { + "bbox": [ + 309, + 296, + 421, + 359 + ], + "lines": [ + { + "bbox": [ + 309, + 296, + 421, + 359 + ], + "spans": [ + { + "bbox": [ + 309, + 296, + 421, + 359 + ], + "type": "image", + "image_path": "40493618943f602b2713fc0beb9ad8a9c4539ef7e95653a10a0d8978fb46cf54.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 371, + 546, + 437 + ], + "lines": [ + { + "bbox": [ + 304, + 371, + 546, + 437 + ], + "spans": [ + { + "bbox": [ + 304, + 371, + 546, + 437 + ], + "type": "text", + "content": "Figure 1. Overview of the proposed framework. It includes: (a) training a category-specific keypoint estimator with a limited labeled set " + }, + { + "bbox": [ + 304, + 371, + 546, + 437 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 371, + 546, + 437 + ], + "type": "text", + "content": ", (b) generating keypoints pseudo-labels on web images, (c) automatic curation of web images to create a subset " + }, + { + "bbox": [ + 304, + 371, + 546, + 437 + ], + "type": "inline_equation", + "content": "\\mathcal{U}'" + }, + { + "bbox": [ + 304, + 371, + 546, + 437 + ], + "type": "text", + "content": ", and (d) training a model for 3D shape prediction with images from " + }, + { + "bbox": [ + 304, + 371, + 546, + 437 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 371, + 546, + 437 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 371, + 546, + 437 + ], + "type": "inline_equation", + "content": "\\mathcal{U}'" + }, + { + "bbox": [ + 304, + 371, + 546, + 437 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 428, + 296, + 545, + 361 + ], + "blocks": [ + { + "bbox": [ + 428, + 296, + 545, + 361 + ], + "lines": [ + { + "bbox": [ + 428, + 296, + 545, + 361 + ], + "spans": [ + { + "bbox": [ + 428, + 296, + 545, + 361 + ], + "type": "image", + "image_path": "1d3afeae6daa67ea6208bf61af64c0927e7635336c2e5873f0f6e1debc177d5e.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 460, + 545, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 460, + 545, + 509 + ], + "spans": [ + { + "bbox": [ + 304, + 460, + 545, + 509 + ], + "type": "text", + "content": "2D labels are limited or non-existent. We ask: how can we learn models that predict the 3D shape of articulated objects in-the-wild when limited or no annotated images are available for a given object category?" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 510, + 546, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 546, + 652 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 546, + 652 + ], + "type": "text", + "content": "In this paper we propose an approach that requires as few as 50-150 images labeled with 2D keypoints. This labeled set can be easily and quickly created for any object category. Our proposed approach is illustrated in Figure 1 and summarized as follows: (a) train a category-specific keypoint estimation network using a small set " + }, + { + "bbox": [ + 304, + 510, + 546, + 652 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 510, + 546, + 652 + ], + "type": "text", + "content": " of images labeled with 2D keypoints; (b) generate 2D keypoint pseudo-labels on a large unlabeled set " + }, + { + "bbox": [ + 304, + 510, + 546, + 652 + ], + "type": "inline_equation", + "content": "\\mathcal{U}" + }, + { + "bbox": [ + 304, + 510, + 546, + 652 + ], + "type": "text", + "content": " consisting of automatically acquired web images; (c) automatically curate " + }, + { + "bbox": [ + 304, + 510, + 546, + 652 + ], + "type": "inline_equation", + "content": "\\mathcal{U}" + }, + { + "bbox": [ + 304, + 510, + 546, + 652 + ], + "type": "text", + "content": " by creating a subset of images and pseudo-labels " + }, + { + "bbox": [ + 304, + 510, + 546, + 652 + ], + "type": "inline_equation", + "content": "\\mathcal{U}'" + }, + { + "bbox": [ + 304, + 510, + 546, + 652 + ], + "type": "text", + "content": " according to a selection criterion; (d) train a model for 3D shape prediction with data from both " + }, + { + "bbox": [ + 304, + 510, + 546, + 652 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 510, + 546, + 652 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 510, + 546, + 652 + ], + "type": "inline_equation", + "content": "\\mathcal{U}'" + }, + { + "bbox": [ + 304, + 510, + 546, + 652 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 654, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 547, + 713 + ], + "type": "text", + "content": "A key insight is that current 2D keypoint estimators [30, 34, 38] are accurate enough to create robust 2D keypoint detections on unlabeled data, even when trained with a limited number of images. Another insight is that images from " + }, + { + "bbox": [ + 304, + 654, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{U}" + }, + { + "bbox": [ + 304, + 654, + 547, + 713 + ], + "type": "text", + "content": " increase the variability of several factors, such as" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13092" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 72, + 235, + 209 + ], + "blocks": [ + { + "bbox": [ + 51, + 72, + 235, + 209 + ], + "lines": [ + { + "bbox": [ + 51, + 72, + 235, + 209 + ], + "spans": [ + { + "bbox": [ + 51, + 72, + 235, + 209 + ], + "type": "image", + "image_path": "f9e0624561aeb82fac2f4fa17af40ebce84de236b049d9b7a51ab29bcac95163.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 220, + 546, + 277 + ], + "lines": [ + { + "bbox": [ + 46, + 220, + 546, + 277 + ], + "spans": [ + { + "bbox": [ + 46, + 220, + 546, + 277 + ], + "type": "text", + "content": "Figure 2. Given a small set " + }, + { + "bbox": [ + 46, + 220, + 546, + 277 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 220, + 546, + 277 + ], + "type": "text", + "content": " of images labeled with 2D keypoints, we train a 2D keypoint estimation netowrk " + }, + { + "bbox": [ + 46, + 220, + 546, + 277 + ], + "type": "inline_equation", + "content": "h_{\\phi}" + }, + { + "bbox": [ + 46, + 220, + 546, + 277 + ], + "type": "text", + "content": " and generate keypoint pseudo-labels on web images (set " + }, + { + "bbox": [ + 46, + 220, + 546, + 277 + ], + "type": "inline_equation", + "content": "\\mathcal{U}" + }, + { + "bbox": [ + 46, + 220, + 546, + 277 + ], + "type": "text", + "content": "). We select a subset of " + }, + { + "bbox": [ + 46, + 220, + 546, + 277 + ], + "type": "inline_equation", + "content": "\\mathcal{U}" + }, + { + "bbox": [ + 46, + 220, + 546, + 277 + ], + "type": "text", + "content": " to train a 3D shape predictor " + }, + { + "bbox": [ + 46, + 220, + 546, + 277 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 46, + 220, + 546, + 277 + ], + "type": "text", + "content": ". Two methods for data selection can be seen here: (a) CF-CM: an auxiliary 2D keypoint estimator " + }, + { + "bbox": [ + 46, + 220, + 546, + 277 + ], + "type": "inline_equation", + "content": "g_{\\psi}" + }, + { + "bbox": [ + 46, + 220, + 546, + 277 + ], + "type": "text", + "content": " generates predictions on " + }, + { + "bbox": [ + 46, + 220, + 546, + 277 + ], + "type": "inline_equation", + "content": "\\mathcal{U}" + }, + { + "bbox": [ + 46, + 220, + 546, + 277 + ], + "type": "text", + "content": " and images with the smallest discrepancy between the keypoint estimates of " + }, + { + "bbox": [ + 46, + 220, + 546, + 277 + ], + "type": "inline_equation", + "content": "h_{\\phi}" + }, + { + "bbox": [ + 46, + 220, + 546, + 277 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 220, + 546, + 277 + ], + "type": "inline_equation", + "content": "g_{\\psi}" + }, + { + "bbox": [ + 46, + 220, + 546, + 277 + ], + "type": "text", + "content": " are selected (criterion (c)); (b) CF-CM²: " + }, + { + "bbox": [ + 46, + 220, + 546, + 277 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 46, + 220, + 546, + 277 + ], + "type": "text", + "content": " is trained with samples from " + }, + { + "bbox": [ + 46, + 220, + 546, + 277 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 220, + 546, + 277 + ], + "type": "text", + "content": " and generates predictions on " + }, + { + "bbox": [ + 46, + 220, + 546, + 277 + ], + "type": "inline_equation", + "content": "\\mathcal{U}" + }, + { + "bbox": [ + 46, + 220, + 546, + 277 + ], + "type": "text", + "content": ". Images with the smallest discrepancy between the keypoint estimates of " + }, + { + "bbox": [ + 46, + 220, + 546, + 277 + ], + "type": "inline_equation", + "content": "h_{\\phi}" + }, + { + "bbox": [ + 46, + 220, + 546, + 277 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 220, + 546, + 277 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 46, + 220, + 546, + 277 + ], + "type": "text", + "content": " are selected (criterion (d)) to retrain " + }, + { + "bbox": [ + 46, + 220, + 546, + 277 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 46, + 220, + 546, + 277 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 244, + 72, + 386, + 208 + ], + "blocks": [ + { + "bbox": [ + 244, + 72, + 386, + 208 + ], + "lines": [ + { + "bbox": [ + 244, + 72, + 386, + 208 + ], + "spans": [ + { + "bbox": [ + 244, + 72, + 386, + 208 + ], + "type": "image", + "image_path": "54a388f37a3166be3234581623a10c6e6a37d62c426d417d0cdff97b6507ea51.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 391, + 72, + 544, + 208 + ], + "blocks": [ + { + "bbox": [ + 391, + 72, + 544, + 208 + ], + "lines": [ + { + "bbox": [ + 391, + 72, + 544, + 208 + ], + "spans": [ + { + "bbox": [ + 391, + 72, + 544, + 208 + ], + "type": "image", + "image_path": "0fb2ce4c964d6ce1df11d318631728ae636f8ab6c036c17a86706f82be0032a2.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 297, + 289, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 297, + 289, + 536 + ], + "spans": [ + { + "bbox": [ + 46, + 297, + 289, + 536 + ], + "type": "text", + "content": "camera viewpoints, articulations and image backgrounds, that are important for training generalizable models for 3D shape prediction. However, the automatically acquired web images contain a high proportion of low-quality images with wrong or heavy truncated objects. Naively using all web images and pseudo-labels during training leads to degraded performance as can be seen in our experiments in Section 4.2. While successful pseudo-label (PL) selection techniques [4, 5, 23, 29, 40] exist for various tasks, they do not address the challenges in our setting. These works investigate PL selection when the unlabeled images come from curated datasets (e.g. CIFAR-10 [20], Cityscapes [6]), while in our setting they come from the web. In addition, they eventually use all unlabeled images during training while in our case most of the web images should be discarded. To effectively utilize images from the web we investigate four criteria to automatically create a \"curated\" subset that includes images with high-quality pseudo-labels. These contain a confidence-based criterion as well as three consistency-based ones (see Figure 2 for two examples)." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 545, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 287, + 713 + ], + "type": "text", + "content": "Through extensive experiments on five different articulated object categories (horse, cow, sheep, giraffe, bear) and three public datasets, we demonstrate that training with the proposed data selection approaches leads in considerably better 3D reconstructions compared to the fully-supervised baseline. Using all pseudo-labels leads to degraded performance. We analyze the performance of the data selection methods used and conclude that consistency-based selection criteria are more effective in our setting. Finally, we conduct experiments with varying number of images in the labeled set " + }, + { + "bbox": [ + 46, + 545, + 287, + 713 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 545, + 287, + 713 + ], + "type": "text", + "content": ". We show that even with only 50 annotated instances and images from web, we can train models that lead to better 3D reconstructions than the fully-supervised models trained with more labels." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 295, + 392, + 308 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 295, + 392, + 308 + ], + "spans": [ + { + "bbox": [ + 306, + 295, + 392, + 308 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 316, + 545, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 316, + 545, + 422 + ], + "spans": [ + { + "bbox": [ + 304, + 316, + 545, + 422 + ], + "type": "text", + "content": "Monocular 3D shape recovery. The task of 3D shape recovery from a single image is solved considerably well for the human category, with many approaches achieving impressive results [14, 17, 19, 31]. Their success can be attributed to the existence of large datasets with 3D [13, 27] and 2D annotations [1, 26]. However for other articulated object categories, such as animals, datasets with 3D annotations do not exist and even 2D labels are scarce and in some cases not available." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 425, + 546, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 425, + 546, + 604 + ], + "spans": [ + { + "bbox": [ + 304, + 425, + 546, + 604 + ], + "type": "text", + "content": "Recent works [10, 15, 18, 21, 22, 24] have addressed several aspects of this problem. In CMR [15], the authors train a system for monocular 3D reconstruction using 2D keypoint and mask annotations. Although their approach works well, it relies on a large number of 2D annotations, such as 6K training samples for 3D reconstruction of birds in CUB [36], which limits its direct applicability to other categories. Follow-up works [10, 24] attempt to eliminate this reliance by using part segmentations [24] or mask labels [10], but their performance is still inferior to CMR [15], and they require mask or part segmentation annotations during training, which are not always available. Instead, we propose a novel approach that addresses the scarcity of 2D keypoint annotations by effectively utilizing images from the web." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": "In [18], ACFM leverages temporal information for supervision and applies the learned model on a per-frame basis. In [21, 22] the authors generate 3D reconstructions in the form of a rigid [22] or articulated [21] template, training their models with masks and 2D keypoint labels from Pascal VOC [9] and predicted masks (using Mask-RCNN [11]) from ImageNet [7]. Despite using only a small labeled set and mask pseudo-labels, their approach is not fully automatic as they manually select the predicted masks for their" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13093" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "text", + "content": "training set. Another line of work [2, 33], regresses the parameters of a statistical animal model [41], but their work only reconstructs the 3D shape of dogs, for which large-scale 2D annotations exist [2]. BARC [33] also uses a dataset with 3D annotations during a pre-training stage." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 133, + 289, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 133, + 289, + 384 + ], + "spans": [ + { + "bbox": [ + 46, + 133, + 289, + 384 + ], + "type": "text", + "content": "Learning with keypoint pseudo-labels. The use of keypoint pseudo-labels has been widely investigated in various works related to 2D pose estimation [3,8,23,28,29,32,39]. In [32, 39], the authors investigate learning with keypoint pseudo-labels for human pose estimation, while in [3,23,29] the goal is to estimate the 2D pose of animals. In the case of animal pose estimation, PLs are used for domain adaptation from synthetic data [23, 29] or from human poses [3]. What is common across these works is that they integrate PLs into the training set (in some cases progressively) and that at the end of the process all samples from the unlabeled set are included. This is not an issue as images in the unlabeled set come from curated datasets. While these approaches can potentially enhance the quality of PLs, a data selection mechanism is still necessary in our case because the unlabeled images come from the web, and most of them should be discarded. To this end, we adapt PL selection criteria form previous works, such as keypoint confidence-based filtering from [3] and multi-transform consistency from [23, 29, 32], to automatically curate the acquired web images." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 396, + 115, + 411 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 396, + 115, + 411 + ], + "spans": [ + { + "bbox": [ + 47, + 396, + 115, + 411 + ], + "type": "text", + "content": "3. Approach" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 417, + 289, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 417, + 289, + 578 + ], + "spans": [ + { + "bbox": [ + 46, + 417, + 289, + 578 + ], + "type": "text", + "content": "Given a labeled set " + }, + { + "bbox": [ + 46, + 417, + 289, + 578 + ], + "type": "inline_equation", + "content": "\\mathcal{S} = \\{(I_i^{(s)},x_i)\\}_{1}^{N_s}" + }, + { + "bbox": [ + 46, + 417, + 289, + 578 + ], + "type": "text", + "content": " comprising of " + }, + { + "bbox": [ + 46, + 417, + 289, + 578 + ], + "type": "inline_equation", + "content": "N_{s}" + }, + { + "bbox": [ + 46, + 417, + 289, + 578 + ], + "type": "text", + "content": " images with paired 2D keypoint annotations and an unlabeled set " + }, + { + "bbox": [ + 46, + 417, + 289, + 578 + ], + "type": "inline_equation", + "content": "\\mathcal{U} = \\{I_i^{(u)}\\}_{1}^{N_u}" + }, + { + "bbox": [ + 46, + 417, + 289, + 578 + ], + "type": "text", + "content": " containing " + }, + { + "bbox": [ + 46, + 417, + 289, + 578 + ], + "type": "inline_equation", + "content": "N_{u}" + }, + { + "bbox": [ + 46, + 417, + 289, + 578 + ], + "type": "text", + "content": " unlabeled images, our goal is to learn a 3D shape recovery model by effectively utilizing both labeled and unlabeled data. We use a limited annotated set " + }, + { + "bbox": [ + 46, + 417, + 289, + 578 + ], + "type": "inline_equation", + "content": "N_{s}" + }, + { + "bbox": [ + 46, + 417, + 289, + 578 + ], + "type": "text", + "content": " and unlabeled images from the web, thus " + }, + { + "bbox": [ + 46, + 417, + 289, + 578 + ], + "type": "inline_equation", + "content": "N_{u}" + }, + { + "bbox": [ + 46, + 417, + 289, + 578 + ], + "type": "text", + "content": " is much larger than " + }, + { + "bbox": [ + 46, + 417, + 289, + 578 + ], + "type": "inline_equation", + "content": "N_{s}" + }, + { + "bbox": [ + 46, + 417, + 289, + 578 + ], + "type": "text", + "content": ". We investigate how keypoint pseudo-labeling on unlabeled images can improve existing 3D reconstruction models. CMR [15] and ACSM [21] are chosen as two canonical examples. Next, we present some relevant background on monocular 3D shape recovery, CMR and ACSM, while in Section 3.2 we present our proposed approach." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 586, + 134, + 597 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 586, + 134, + 597 + ], + "spans": [ + { + "bbox": [ + 47, + 586, + 134, + 597 + ], + "type": "text", + "content": "3.1. Preliminaries" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 605, + 287, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 640 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 640 + ], + "type": "text", + "content": "Given an image " + }, + { + "bbox": [ + 46, + 605, + 287, + 640 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 46, + 605, + 287, + 640 + ], + "type": "text", + "content": " of an object, its 3D structure is recovered by predicting a 3D mesh " + }, + { + "bbox": [ + 46, + 605, + 287, + 640 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 605, + 287, + 640 + ], + "type": "text", + "content": " and camera pose " + }, + { + "bbox": [ + 46, + 605, + 287, + 640 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 46, + 605, + 287, + 640 + ], + "type": "text", + "content": " with a model " + }, + { + "bbox": [ + 46, + 605, + 287, + 640 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 46, + 605, + 287, + 640 + ], + "type": "text", + "content": " whose parameters " + }, + { + "bbox": [ + 46, + 605, + 287, + 640 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 605, + 287, + 640 + ], + "type": "text", + "content": " are learned during training." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 641, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 287, + 714 + ], + "type": "text", + "content": "CMR. The shape in CMR [15] is represented as a 3D mesh " + }, + { + "bbox": [ + 46, + 641, + 287, + 714 + ], + "type": "inline_equation", + "content": "M \\equiv (V, F)" + }, + { + "bbox": [ + 46, + 641, + 287, + 714 + ], + "type": "text", + "content": " with vertices " + }, + { + "bbox": [ + 46, + 641, + 287, + 714 + ], + "type": "inline_equation", + "content": "V \\in \\mathbb{R}^{|V| \\times 3}" + }, + { + "bbox": [ + 46, + 641, + 287, + 714 + ], + "type": "text", + "content": " and faces " + }, + { + "bbox": [ + 46, + 641, + 287, + 714 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 46, + 641, + 287, + 714 + ], + "type": "text", + "content": ", and is homeomorphic to a sphere. Given an input image " + }, + { + "bbox": [ + 46, + 641, + 287, + 714 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 46, + 641, + 287, + 714 + ], + "type": "text", + "content": ", CMR uses ResNet-18 [12] to acquire an image embedding, which is then processed by a 2-layer MLP and fed to two independent linear layers predicting vertex displacements" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 71, + 545, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 71, + 545, + 167 + ], + "spans": [ + { + "bbox": [ + 304, + 71, + 545, + 167 + ], + "type": "inline_equation", + "content": "\\Delta_V \\in \\mathbb{R}^{|V| \\times 3}" + }, + { + "bbox": [ + 304, + 71, + 545, + 167 + ], + "type": "text", + "content": " from a template shape " + }, + { + "bbox": [ + 304, + 71, + 545, + 167 + ], + "type": "inline_equation", + "content": "T \\in \\mathbb{R}^{|V| \\times 3}" + }, + { + "bbox": [ + 304, + 71, + 545, + 167 + ], + "type": "text", + "content": " and the camera pose. The deformed 3D vertex locations are then computed as " + }, + { + "bbox": [ + 304, + 71, + 545, + 167 + ], + "type": "inline_equation", + "content": "V = T + \\Delta_V" + }, + { + "bbox": [ + 304, + 71, + 545, + 167 + ], + "type": "text", + "content": ". A weak-perspective camera model " + }, + { + "bbox": [ + 304, + 71, + 545, + 167 + ], + "type": "inline_equation", + "content": "\\pi \\equiv (s, \\mathbf{t}, \\mathbf{q})" + }, + { + "bbox": [ + 304, + 71, + 545, + 167 + ], + "type": "text", + "content": " is used, where " + }, + { + "bbox": [ + 304, + 71, + 545, + 167 + ], + "type": "inline_equation", + "content": "s \\in \\mathbb{R}_+" + }, + { + "bbox": [ + 304, + 71, + 545, + 167 + ], + "type": "text", + "content": " is the scale, " + }, + { + "bbox": [ + 304, + 71, + 545, + 167 + ], + "type": "inline_equation", + "content": "\\mathbf{t} \\in \\mathbb{R}^2" + }, + { + "bbox": [ + 304, + 71, + 545, + 167 + ], + "type": "text", + "content": " the translation and " + }, + { + "bbox": [ + 304, + 71, + 545, + 167 + ], + "type": "inline_equation", + "content": "\\mathbf{q} \\in \\mathbb{R}^4" + }, + { + "bbox": [ + 304, + 71, + 545, + 167 + ], + "type": "text", + "content": " the rotation of the camera in unit quaternion parameterization. Thus, CMR learns to predict " + }, + { + "bbox": [ + 304, + 71, + 545, + 167 + ], + "type": "inline_equation", + "content": "f_\\theta(I) \\equiv (\\Delta_V, \\pi)" + }, + { + "bbox": [ + 304, + 71, + 545, + 167 + ], + "type": "text", + "content": ". We refer the reader to [15] for more details." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 167, + 546, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 167, + 546, + 418 + ], + "spans": [ + { + "bbox": [ + 304, + 167, + 546, + 418 + ], + "type": "text", + "content": "ACSM. The shape in ACSM [21] is also represented as a 3D mesh " + }, + { + "bbox": [ + 304, + 167, + 546, + 418 + ], + "type": "inline_equation", + "content": "M \\equiv (V, F)" + }, + { + "bbox": [ + 304, + 167, + 546, + 418 + ], + "type": "text", + "content": ". The mesh " + }, + { + "bbox": [ + 304, + 167, + 546, + 418 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 167, + 546, + 418 + ], + "type": "text", + "content": " is a pre-defined template shape for each object category with fixed topology. Given a template shape " + }, + { + "bbox": [ + 304, + 167, + 546, + 418 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 167, + 546, + 418 + ], + "type": "text", + "content": ", its vertices are grouped into " + }, + { + "bbox": [ + 304, + 167, + 546, + 418 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 304, + 167, + 546, + 418 + ], + "type": "text", + "content": " parts. As a result, for each vertex " + }, + { + "bbox": [ + 304, + 167, + 546, + 418 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 304, + 167, + 546, + 418 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 304, + 167, + 546, + 418 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 167, + 546, + 418 + ], + "type": "text", + "content": " an associated membership " + }, + { + "bbox": [ + 304, + 167, + 546, + 418 + ], + "type": "inline_equation", + "content": "a_{p}^{v} \\in [0,1]" + }, + { + "bbox": [ + 304, + 167, + 546, + 418 + ], + "type": "text", + "content": " corresponding to each part " + }, + { + "bbox": [ + 304, + 167, + 546, + 418 + ], + "type": "inline_equation", + "content": "p \\in \\{1, \\dots, P\\}" + }, + { + "bbox": [ + 304, + 167, + 546, + 418 + ], + "type": "text", + "content": " is produced. The articulation " + }, + { + "bbox": [ + 304, + 167, + 546, + 418 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 304, + 167, + 546, + 418 + ], + "type": "text", + "content": " of this template " + }, + { + "bbox": [ + 304, + 167, + 546, + 418 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 167, + 546, + 418 + ], + "type": "text", + "content": " is specified as a rigid transformation w.r.t. each parent part, i.e. " + }, + { + "bbox": [ + 304, + 167, + 546, + 418 + ], + "type": "inline_equation", + "content": "\\delta \\equiv \\{(t_{p}, R_{p})\\}" + }, + { + "bbox": [ + 304, + 167, + 546, + 418 + ], + "type": "text", + "content": ", where the torso corresponds to the root part in the hierarchy. Given the articulation parameters " + }, + { + "bbox": [ + 304, + 167, + 546, + 418 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 304, + 167, + 546, + 418 + ], + "type": "text", + "content": ", a global transformation " + }, + { + "bbox": [ + 304, + 167, + 546, + 418 + ], + "type": "inline_equation", + "content": "\\mathcal{T}_{p}(\\cdot, \\delta)" + }, + { + "bbox": [ + 304, + 167, + 546, + 418 + ], + "type": "text", + "content": " for each part can be computed using forward kinematics. Thus, the position of each vertex " + }, + { + "bbox": [ + 304, + 167, + 546, + 418 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 304, + 167, + 546, + 418 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 304, + 167, + 546, + 418 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 167, + 546, + 418 + ], + "type": "text", + "content": " after articulation can be computed as " + }, + { + "bbox": [ + 304, + 167, + 546, + 418 + ], + "type": "inline_equation", + "content": "\\sum_{p} a_{p}^{v} \\mathcal{T}_{p}(v, \\delta)" + }, + { + "bbox": [ + 304, + 167, + 546, + 418 + ], + "type": "text", + "content": ". Therefore, to recover the 3D structure of an object with ACSM we need to predict the camera pose " + }, + { + "bbox": [ + 304, + 167, + 546, + 418 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 304, + 167, + 546, + 418 + ], + "type": "text", + "content": " and articulation parameters " + }, + { + "bbox": [ + 304, + 167, + 546, + 418 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 304, + 167, + 546, + 418 + ], + "type": "text", + "content": ". ACSM [21] uses the same image encoder with CMR [15]. The camera pose is parameterized and predicted as in CMR, while independent fully-connected heads regress the articulation parameters " + }, + { + "bbox": [ + 304, + 167, + 546, + 418 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 304, + 167, + 546, + 418 + ], + "type": "text", + "content": ". Thus, ACSM learns to predict " + }, + { + "bbox": [ + 304, + 167, + 546, + 418 + ], + "type": "inline_equation", + "content": "f_{\\theta}(I) \\equiv (\\delta, \\pi)" + }, + { + "bbox": [ + 304, + 167, + 546, + 418 + ], + "type": "text", + "content": ". For more details, we refer the reader to [21]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 419, + 547, + 600 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 419, + 547, + 600 + ], + "spans": [ + { + "bbox": [ + 304, + 419, + 547, + 600 + ], + "type": "text", + "content": "Keypoint and mask supervision. CMR and ACSM are supervised with 2D annotations, by ensuring that the predicted 3D shape matches with the 2D evidence when projected onto the image space using the predicted camera. Let's assume " + }, + { + "bbox": [ + 304, + 419, + 547, + 600 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 419, + 547, + 600 + ], + "type": "text", + "content": " 2D keypoint locations " + }, + { + "bbox": [ + 304, + 419, + 547, + 600 + ], + "type": "inline_equation", + "content": "x_{i} \\in \\mathbb{R}^{k \\times 2}" + }, + { + "bbox": [ + 304, + 419, + 547, + 600 + ], + "type": "text", + "content": " as label for image " + }, + { + "bbox": [ + 304, + 419, + 547, + 600 + ], + "type": "inline_equation", + "content": "I_{i}" + }, + { + "bbox": [ + 304, + 419, + 547, + 600 + ], + "type": "text", + "content": ". Each one of these " + }, + { + "bbox": [ + 304, + 419, + 547, + 600 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 419, + 547, + 600 + ], + "type": "text", + "content": " 2D keypoints has a semantic correspondence with a 3D keypoint. The 3D keypoints can be computed from the mesh vertices. In CMR the location of 3D keypoints is regressed from that of the mesh vertices using a learnable matrix " + }, + { + "bbox": [ + 304, + 419, + 547, + 600 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 304, + 419, + 547, + 600 + ], + "type": "text", + "content": ", while mesh vertices corresponding to 3D keypoints are pre-determined for ACSM. This leads to " + }, + { + "bbox": [ + 304, + 419, + 547, + 600 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 419, + 547, + 600 + ], + "type": "text", + "content": " 3D keypoints " + }, + { + "bbox": [ + 304, + 419, + 547, + 600 + ], + "type": "inline_equation", + "content": "\\hat{X}_{i} \\in \\mathbb{R}^{k \\times 3}" + }, + { + "bbox": [ + 304, + 419, + 547, + 600 + ], + "type": "text", + "content": " that can be projected onto the image using the predicted camera " + }, + { + "bbox": [ + 304, + 419, + 547, + 600 + ], + "type": "inline_equation", + "content": "\\hat{\\pi}" + }, + { + "bbox": [ + 304, + 419, + 547, + 600 + ], + "type": "text", + "content": ". In this setting, keypoint supervision is provided using a reprojection loss on the keypoints:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 376, + 607, + 545, + 622 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 376, + 607, + 545, + 622 + ], + "spans": [ + { + "bbox": [ + 376, + 607, + 545, + 622 + ], + "type": "interline_equation", + "content": "L _ {k p} = \\left\\| x _ {i} - \\hat {\\pi} \\left(\\hat {X} _ {i}\\right) \\right\\| _ {2}. \\tag {1}", + "image_path": "af933a4be5b20bd44e2ea909d8433c7c93abdb4cc726615d9532cae7e0360c45.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 631, + 545, + 691 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 631, + 545, + 691 + ], + "spans": [ + { + "bbox": [ + 304, + 631, + 545, + 691 + ], + "type": "text", + "content": "Similarly, assuming an instance segmentation mask " + }, + { + "bbox": [ + 304, + 631, + 545, + 691 + ], + "type": "inline_equation", + "content": "m_{i}" + }, + { + "bbox": [ + 304, + 631, + 545, + 691 + ], + "type": "text", + "content": " is provided as annotation for " + }, + { + "bbox": [ + 304, + 631, + 545, + 691 + ], + "type": "inline_equation", + "content": "I_{i}" + }, + { + "bbox": [ + 304, + 631, + 545, + 691 + ], + "type": "text", + "content": ", we can render the 3D mesh " + }, + { + "bbox": [ + 304, + 631, + 545, + 691 + ], + "type": "inline_equation", + "content": "M = (V_{i}, F)" + }, + { + "bbox": [ + 304, + 631, + 545, + 691 + ], + "type": "text", + "content": " through the predicted camera " + }, + { + "bbox": [ + 304, + 631, + 545, + 691 + ], + "type": "inline_equation", + "content": "\\hat{\\pi}_{i}" + }, + { + "bbox": [ + 304, + 631, + 545, + 691 + ], + "type": "text", + "content": " using a differentiable renderer [16] " + }, + { + "bbox": [ + 304, + 631, + 545, + 691 + ], + "type": "inline_equation", + "content": "\\mathcal{R}(\\cdot)" + }, + { + "bbox": [ + 304, + 631, + 545, + 691 + ], + "type": "text", + "content": " and provide mask supervision with the following loss:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 358, + 700, + 545, + 714 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 358, + 700, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 358, + 700, + 545, + 714 + ], + "type": "interline_equation", + "content": "L _ {\\text {m a s k}} = \\left\\| m _ {i} - \\mathcal {R} \\left(V _ {i}, F, \\hat {\\pi} _ {i}\\right) \\right\\| _ {2}. \\tag {2}", + "image_path": "823189ec7864cd91d7cf870af9d1afc4d73677eb510e3c1896c1508c9c4c7b40.jpg" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "13094" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "text", + "content": "In ACSM, a second network " + }, + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "inline_equation", + "content": "f_{\\theta'}'" + }, + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "text", + "content": " is trained to map each pixel in the object's mask to a point on the surface of the template shape. This facilitates computation of several mask losses. In our experiments with ACSM we only train network " + }, + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "text", + "content": " with the keypoint reprojection loss in Eq. (1)." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 138, + 211, + 152 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 138, + 211, + 152 + ], + "spans": [ + { + "bbox": [ + 47, + 138, + 211, + 152 + ], + "type": "text", + "content": "3.2. 3D Shape Recovery Approach" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 156, + 287, + 264 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 156, + 287, + 264 + ], + "spans": [ + { + "bbox": [ + 46, + 156, + 287, + 264 + ], + "type": "text", + "content": "Our proposed approach involves the following steps: (1) annotation of 2D keypoints on " + }, + { + "bbox": [ + 46, + 156, + 287, + 264 + ], + "type": "inline_equation", + "content": "N_{s}" + }, + { + "bbox": [ + 46, + 156, + 287, + 264 + ], + "type": "text", + "content": " images (when no labels are available for the given category) to create a labeled set " + }, + { + "bbox": [ + 46, + 156, + 287, + 264 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 156, + 287, + 264 + ], + "type": "text", + "content": "; (2) training a 2D keypoint estimation network with samples from " + }, + { + "bbox": [ + 46, + 156, + 287, + 264 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 156, + 287, + 264 + ], + "type": "text", + "content": " and generating 2D keypoint pseudo-labels on an image collection from the web (unlabeled set " + }, + { + "bbox": [ + 46, + 156, + 287, + 264 + ], + "type": "inline_equation", + "content": "\\mathcal{U}" + }, + { + "bbox": [ + 46, + 156, + 287, + 264 + ], + "type": "text", + "content": "); (3) selecting data from " + }, + { + "bbox": [ + 46, + 156, + 287, + 264 + ], + "type": "inline_equation", + "content": "\\mathcal{U}" + }, + { + "bbox": [ + 46, + 156, + 287, + 264 + ], + "type": "text", + "content": " to be used for training according to a criterion; (4) training a 3D shape predictor with samples from " + }, + { + "bbox": [ + 46, + 156, + 287, + 264 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 156, + 287, + 264 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 156, + 287, + 264 + ], + "type": "inline_equation", + "content": "\\mathcal{U}" + }, + { + "bbox": [ + 46, + 156, + 287, + 264 + ], + "type": "text", + "content": ". We explain all the steps in detail below." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 265, + 287, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 265, + 287, + 335 + ], + "spans": [ + { + "bbox": [ + 46, + 265, + 287, + 335 + ], + "type": "text", + "content": "Data annotation. We annotate " + }, + { + "bbox": [ + 46, + 265, + 287, + 335 + ], + "type": "inline_equation", + "content": "N_S" + }, + { + "bbox": [ + 46, + 265, + 287, + 335 + ], + "type": "text", + "content": " images with 2D keypoints, following standard keypoint definitions used in existing datasets. For instance, we use 16 keypoints for quadruped animals as defined in Pascal [9]. The only requirement is to annotate images containing objects with the variety of poses and articulations we wish to model." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 336, + 287, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 336, + 287, + 456 + ], + "spans": [ + { + "bbox": [ + 46, + 336, + 287, + 456 + ], + "type": "text", + "content": "Generating keypoint pseudo-labels. In pseudo-labeling an initial model is trained with labels from a labeled set " + }, + { + "bbox": [ + 46, + 336, + 287, + 456 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 336, + 287, + 456 + ], + "type": "text", + "content": " and is used to produce artificial labels on an unlabeled set " + }, + { + "bbox": [ + 46, + 336, + 287, + 456 + ], + "type": "inline_equation", + "content": "\\mathcal{U}" + }, + { + "bbox": [ + 46, + 336, + 287, + 456 + ], + "type": "text", + "content": ". In this work, instead of tasking the 3D shape predictor " + }, + { + "bbox": [ + 46, + 336, + 287, + 456 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 46, + 336, + 287, + 456 + ], + "type": "text", + "content": " to produce pseudo-labels for itself, we propose to generate 2D keypoint pseudo-labels using the predictions of a 2D keypoint estimation network [38] " + }, + { + "bbox": [ + 46, + 336, + 287, + 456 + ], + "type": "inline_equation", + "content": "h_{\\phi}" + }, + { + "bbox": [ + 46, + 336, + 287, + 456 + ], + "type": "text", + "content": ". This is a natural option since 2D keypoint estimators are easier to train with limited data and yield more precise detections compared to reprojected keypoints obtained from a 3D mesh." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 456, + 287, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 456, + 287, + 616 + ], + "spans": [ + { + "bbox": [ + 46, + 456, + 287, + 616 + ], + "type": "text", + "content": "Most current methods for 2D pose estimation [30,34,38] solve the task by estimating " + }, + { + "bbox": [ + 46, + 456, + 287, + 616 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 456, + 287, + 616 + ], + "type": "text", + "content": " gaussian heatmaps. Each heatmap encodes the probability of a keypoint at a location in the image. The location of each keypoint can be estimated as the location with the maximum value in the corresponding heatmap, while that value can be used as a confidence estimate for that keypoint. We train a 2D keypoint estimation network " + }, + { + "bbox": [ + 46, + 456, + 287, + 616 + ], + "type": "inline_equation", + "content": "h_\\phi" + }, + { + "bbox": [ + 46, + 456, + 287, + 616 + ], + "type": "text", + "content": " with labels from " + }, + { + "bbox": [ + 46, + 456, + 287, + 616 + ], + "type": "inline_equation", + "content": "\\mathcal{S}" + }, + { + "bbox": [ + 46, + 456, + 287, + 616 + ], + "type": "text", + "content": " and use it to generate keypoint pseudo-labels on " + }, + { + "bbox": [ + 46, + 456, + 287, + 616 + ], + "type": "inline_equation", + "content": "\\mathcal{U}" + }, + { + "bbox": [ + 46, + 456, + 287, + 616 + ], + "type": "text", + "content": ". As such, the unlabeled set is now " + }, + { + "bbox": [ + 46, + 456, + 287, + 616 + ], + "type": "inline_equation", + "content": "\\mathcal{U}_{\\phi} = \\{(I_{i}^{(u)},\\tilde{x}_{i}^{(u)},\\tilde{c}_{i}^{(u)})\\}_{1}^{N_{u}}" + }, + { + "bbox": [ + 46, + 456, + 287, + 616 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 456, + 287, + 616 + ], + "type": "inline_equation", + "content": "\\tilde{x}_i^{(u)}\\in \\mathbb{R}^{k\\times 2}" + }, + { + "bbox": [ + 46, + 456, + 287, + 616 + ], + "type": "text", + "content": " are the estimated locations and " + }, + { + "bbox": [ + 46, + 456, + 287, + 616 + ], + "type": "inline_equation", + "content": "\\tilde{c}_i^{(u)}\\in [0,1]^k" + }, + { + "bbox": [ + 46, + 456, + 287, + 616 + ], + "type": "text", + "content": " the corresponding confidence estimates for " + }, + { + "bbox": [ + 46, + 456, + 287, + 616 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 456, + 287, + 616 + ], + "type": "text", + "content": " keypoints of interest in image " + }, + { + "bbox": [ + 46, + 456, + 287, + 616 + ], + "type": "inline_equation", + "content": "I_{i}^{(u)}" + }, + { + "bbox": [ + 46, + 456, + 287, + 616 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 617, + 287, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 287, + 654 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 287, + 654 + ], + "type": "text", + "content": "Learning with keypoint pseudo-labels. Given a labeled set " + }, + { + "bbox": [ + 46, + 617, + 287, + 654 + ], + "type": "inline_equation", + "content": "\\mathcal{S} = \\{(I_i^{(s)},x_i)\\}_{1}^{Ns}" + }, + { + "bbox": [ + 46, + 617, + 287, + 654 + ], + "type": "text", + "content": " containing images with keypoint labels " + }, + { + "bbox": [ + 46, + 617, + 287, + 654 + ], + "type": "inline_equation", + "content": "x_{i}" + }, + { + "bbox": [ + 46, + 617, + 287, + 654 + ], + "type": "text", + "content": ", we train " + }, + { + "bbox": [ + 46, + 617, + 287, + 654 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 46, + 617, + 287, + 654 + ], + "type": "text", + "content": " using the supervised loss:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 110, + 661, + 287, + 693 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 110, + 661, + 287, + 693 + ], + "spans": [ + { + "bbox": [ + 110, + 661, + 287, + 693 + ], + "type": "interline_equation", + "content": "L _ {k p} ^ {\\mathcal {S}} = \\sum_ {i = 1} ^ {N s} | | x _ {i} - \\hat {\\pi} (\\hat {X} _ {i}) | | _ {2}, \\tag {3}", + "image_path": "75ed553f24a0043601eda1c81bc13b31537b6938796988d25e3856d5c29447a1.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 700, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 700, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 700, + 287, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 700, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\hat{\\pi}" + }, + { + "bbox": [ + 47, + 700, + 287, + 714 + ], + "type": "text", + "content": " is the predicted camera pose and " + }, + { + "bbox": [ + 47, + 700, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\hat{X}_i" + }, + { + "bbox": [ + 47, + 700, + 287, + 714 + ], + "type": "text", + "content": " the 3D key" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 72, + 545, + 122 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 122 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 122 + ], + "type": "text", + "content": "points computed from 3D mesh vertices " + }, + { + "bbox": [ + 305, + 72, + 545, + 122 + ], + "type": "inline_equation", + "content": "V_{i}" + }, + { + "bbox": [ + 305, + 72, + 545, + 122 + ], + "type": "text", + "content": ". Similarly, given a set " + }, + { + "bbox": [ + 305, + 72, + 545, + 122 + ], + "type": "inline_equation", + "content": "\\mathcal{U}_{\\phi} = \\{(I_i^{(u)},\\hat{x}_i^{(u)},\\hat{c}_i^{(u)})\\}_{1}^{N_u}" + }, + { + "bbox": [ + 305, + 72, + 545, + 122 + ], + "type": "text", + "content": " comprising of images with keypoint pseudo-labels " + }, + { + "bbox": [ + 305, + 72, + 545, + 122 + ], + "type": "inline_equation", + "content": "(\\tilde{x}_i,\\tilde{c}_i)" + }, + { + "bbox": [ + 305, + 72, + 545, + 122 + ], + "type": "text", + "content": ", we train using the following modification of the keypoint reprojection loss:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 361, + 129, + 545, + 163 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 361, + 129, + 545, + 163 + ], + "spans": [ + { + "bbox": [ + 361, + 129, + 545, + 163 + ], + "type": "interline_equation", + "content": "L _ {k p} ^ {\\mathcal {U}} = \\sum_ {i = 1} ^ {N u} \\left\\| \\tilde {c} _ {i} \\left(\\tilde {x} _ {i} - \\hat {\\pi} \\left(\\hat {X} _ {i}\\right)\\right) \\right\\| _ {2}. \\tag {4}", + "image_path": "d360fe250ce4e03ba30d80dd13c499769b2719bdbad528cf95a63e81ae5ee035.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 170, + 545, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 170, + 545, + 277 + ], + "spans": [ + { + "bbox": [ + 304, + 170, + 545, + 277 + ], + "type": "text", + "content": "We can train using data from both " + }, + { + "bbox": [ + 304, + 170, + 545, + 277 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 170, + 545, + 277 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 170, + 545, + 277 + ], + "type": "inline_equation", + "content": "\\mathcal{U}_{\\phi}" + }, + { + "bbox": [ + 304, + 170, + 545, + 277 + ], + "type": "text", + "content": " with the following objective: " + }, + { + "bbox": [ + 304, + 170, + 545, + 277 + ], + "type": "inline_equation", + "content": "L = L_{kp}^{S} + L_{kp}^{U}" + }, + { + "bbox": [ + 304, + 170, + 545, + 277 + ], + "type": "text", + "content": ". However, as " + }, + { + "bbox": [ + 304, + 170, + 545, + 277 + ], + "type": "inline_equation", + "content": "Ns \\ll N_u" + }, + { + "bbox": [ + 304, + 170, + 545, + 277 + ], + "type": "text", + "content": ", the training process is dominated by samples from " + }, + { + "bbox": [ + 304, + 170, + 545, + 277 + ], + "type": "inline_equation", + "content": "\\mathcal{U}_{\\phi}" + }, + { + "bbox": [ + 304, + 170, + 545, + 277 + ], + "type": "text", + "content": ". When the quality of samples in " + }, + { + "bbox": [ + 304, + 170, + 545, + 277 + ], + "type": "inline_equation", + "content": "\\mathcal{U}_{\\phi}" + }, + { + "bbox": [ + 304, + 170, + 545, + 277 + ], + "type": "text", + "content": " is low, as it is the case with uncurated data from the web, training with all the samples from the unlabeled set leads to degraded performance. To mitigate this issue, we train using a subset of " + }, + { + "bbox": [ + 304, + 170, + 545, + 277 + ], + "type": "inline_equation", + "content": "\\mathcal{U}_{\\phi}" + }, + { + "bbox": [ + 304, + 170, + 545, + 277 + ], + "type": "text", + "content": " containing useful images and high-quality pseudo-labels that are chosen according to a selection criterion." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 292, + 400, + 303 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 292, + 400, + 303 + ], + "spans": [ + { + "bbox": [ + 306, + 292, + 400, + 303 + ], + "type": "text", + "content": "3.2.1 Data Selection" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 311, + 545, + 334 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 311, + 545, + 334 + ], + "spans": [ + { + "bbox": [ + 304, + 311, + 545, + 334 + ], + "type": "text", + "content": "Given a number of images " + }, + { + "bbox": [ + 304, + 311, + 545, + 334 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 311, + 545, + 334 + ], + "type": "text", + "content": " to be used by " + }, + { + "bbox": [ + 304, + 311, + 545, + 334 + ], + "type": "inline_equation", + "content": "\\mathcal{U}_{\\phi}" + }, + { + "bbox": [ + 304, + 311, + 545, + 334 + ], + "type": "text", + "content": ", we select them according to one of the following criteria." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 335, + 545, + 385 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 335, + 545, + 385 + ], + "spans": [ + { + "bbox": [ + 304, + 335, + 545, + 385 + ], + "type": "text", + "content": "Keypoint Confidence. This method, referred to as " + }, + { + "bbox": [ + 304, + 335, + 545, + 385 + ], + "type": "inline_equation", + "content": "KP" + }, + { + "bbox": [ + 304, + 335, + 545, + 385 + ], + "type": "text", + "content": "-conf, selects samples from " + }, + { + "bbox": [ + 304, + 335, + 545, + 385 + ], + "type": "inline_equation", + "content": "\\mathcal{U}_{\\phi}" + }, + { + "bbox": [ + 304, + 335, + 545, + 385 + ], + "type": "text", + "content": " based on the confidence score of the PLs. In particular, it selects " + }, + { + "bbox": [ + 304, + 335, + 545, + 385 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 335, + 545, + 385 + ], + "type": "text", + "content": " images with the highest per-sample sum of keypoint confidences " + }, + { + "bbox": [ + 304, + 335, + 545, + 385 + ], + "type": "inline_equation", + "content": "\\sum_{k} \\tilde{\\mathbf{c}}_k^{(u)}" + }, + { + "bbox": [ + 304, + 335, + 545, + 385 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 384, + 545, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 384, + 545, + 468 + ], + "spans": [ + { + "bbox": [ + 304, + 384, + 545, + 468 + ], + "type": "text", + "content": "Multi-Transform Consistency. Intuitively, if one scales or rotates one image the prediction of a good 2D keypoint estimator should change accordingly. In other words, it should be equivariant to the those geometric transformations. We can thus use the consistency to multiple equivariant transformations to select the images with high-quality PLs. We denote this consistency-filtering approach as " + }, + { + "bbox": [ + 304, + 384, + 545, + 468 + ], + "type": "inline_equation", + "content": "CF-MT" + }, + { + "bbox": [ + 304, + 384, + 545, + 468 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 468, + 545, + 599 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 468, + 545, + 599 + ], + "spans": [ + { + "bbox": [ + 304, + 468, + 545, + 599 + ], + "type": "text", + "content": "Cross-Model Consistency. Using this consistency filtering approach, referred to as " + }, + { + "bbox": [ + 304, + 468, + 545, + 599 + ], + "type": "inline_equation", + "content": "CF-CM" + }, + { + "bbox": [ + 304, + 468, + 545, + 599 + ], + "type": "text", + "content": ", we select samples based on the consistency of two 2D keypoint estimators, " + }, + { + "bbox": [ + 304, + 468, + 545, + 599 + ], + "type": "inline_equation", + "content": "h_{\\phi}" + }, + { + "bbox": [ + 304, + 468, + 545, + 599 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 468, + 545, + 599 + ], + "type": "inline_equation", + "content": "g_{\\psi}" + }, + { + "bbox": [ + 304, + 468, + 545, + 599 + ], + "type": "text", + "content": ", with different architectures. Our insight is that the two models have different structural biases and can learn different representations from the same image. Thus, we use the discrepancy in their predictions as a proxy for evaluating the quality of the generated pseudo-labels. For each image " + }, + { + "bbox": [ + 304, + 468, + 545, + 599 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 304, + 468, + 545, + 599 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 304, + 468, + 545, + 599 + ], + "type": "inline_equation", + "content": "\\mathcal{U}" + }, + { + "bbox": [ + 304, + 468, + 545, + 599 + ], + "type": "text", + "content": ", we generate keypoint pseudo-labels " + }, + { + "bbox": [ + 304, + 468, + 545, + 599 + ], + "type": "inline_equation", + "content": "\\tilde{x}_{\\phi}" + }, + { + "bbox": [ + 304, + 468, + 545, + 599 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 468, + 545, + 599 + ], + "type": "inline_equation", + "content": "\\tilde{x}_{\\psi}" + }, + { + "bbox": [ + 304, + 468, + 545, + 599 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 304, + 468, + 545, + 599 + ], + "type": "inline_equation", + "content": "h_{\\phi}" + }, + { + "bbox": [ + 304, + 468, + 545, + 599 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 468, + 545, + 599 + ], + "type": "inline_equation", + "content": "g_{\\psi}" + }, + { + "bbox": [ + 304, + 468, + 545, + 599 + ], + "type": "text", + "content": " respectively, and calculate the discrepancy between the PLs with the following term:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 376, + 608, + 545, + 622 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 376, + 608, + 545, + 622 + ], + "spans": [ + { + "bbox": [ + 376, + 608, + 545, + 622 + ], + "type": "interline_equation", + "content": "D _ {\\mathrm {C F - C M}} = \\left\\| \\tilde {x} _ {\\phi} - \\tilde {x} _ {\\psi} \\right\\| _ {2}. \\tag {5}", + "image_path": "5cc6a849b7deac3f275d53dcf482151ebe4175ad2618bf1991a970c3cf15d6ac.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 629, + 545, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 545, + 654 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 545, + 654 + ], + "type": "text", + "content": "We select " + }, + { + "bbox": [ + 304, + 629, + 545, + 654 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 629, + 545, + 654 + ], + "type": "text", + "content": " samples with the minimum discrepancy creating the subset " + }, + { + "bbox": [ + 304, + 629, + 545, + 654 + ], + "type": "inline_equation", + "content": "\\mathcal{U}_{\\phi, \\psi} \\subset \\mathcal{U}_{\\phi}" + }, + { + "bbox": [ + 304, + 629, + 545, + 654 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": "Cross-Model Cross-Modality Consistency. With this consistency filtering criterion, which we dub " + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "inline_equation", + "content": "CF - CM^2" + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": ", we select samples based on their discrepancy between the predictions of the 2D keypoint estimator " + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "inline_equation", + "content": "h_{\\phi}" + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": " and the reprojected keypoints from the 3D shape predictor " + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": ". Given an image" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13095" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 70, + 281, + 182 + ], + "blocks": [ + { + "bbox": [ + 49, + 70, + 281, + 182 + ], + "lines": [ + { + "bbox": [ + 49, + 70, + 281, + 182 + ], + "spans": [ + { + "bbox": [ + 49, + 70, + 281, + 182 + ], + "type": "image", + "image_path": "1ea2597210c5f610cd0d4c4b3a3edbd43e597510ede97220fc03fa7357e3ee06.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 189, + 287, + 232 + ], + "lines": [ + { + "bbox": [ + 46, + 189, + 287, + 232 + ], + "spans": [ + { + "bbox": [ + 46, + 189, + 287, + 232 + ], + "type": "text", + "content": "Figure 3. Sample results on CUB. For each sample, we show the predicted shape and texture from the inferred camera view (b, d) and a novel view (c, e) for models trained with and without keypoint pseudo-labels." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 251, + 286, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 251, + 286, + 323 + ], + "spans": [ + { + "bbox": [ + 46, + 251, + 286, + 323 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 46, + 251, + 286, + 323 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 46, + 251, + 286, + 323 + ], + "type": "inline_equation", + "content": "\\mathcal{U}" + }, + { + "bbox": [ + 46, + 251, + 286, + 323 + ], + "type": "text", + "content": ", we calculate the locations for 3D keypoints " + }, + { + "bbox": [ + 46, + 251, + 286, + 323 + ], + "type": "inline_equation", + "content": "\\tilde{X}_{\\theta}" + }, + { + "bbox": [ + 46, + 251, + 286, + 323 + ], + "type": "text", + "content": " from the predicted 3D mesh vertices (as explained in Section 3.1). The corresponding 2D keypoints " + }, + { + "bbox": [ + 46, + 251, + 286, + 323 + ], + "type": "inline_equation", + "content": "\\tilde{x}_{\\theta}" + }, + { + "bbox": [ + 46, + 251, + 286, + 323 + ], + "type": "text", + "content": " are calculated by projecting " + }, + { + "bbox": [ + 46, + 251, + 286, + 323 + ], + "type": "inline_equation", + "content": "\\tilde{X}_{\\theta}" + }, + { + "bbox": [ + 46, + 251, + 286, + 323 + ], + "type": "text", + "content": " onto the image with the predicted camera parameters " + }, + { + "bbox": [ + 46, + 251, + 286, + 323 + ], + "type": "inline_equation", + "content": "\\tilde{\\pi}_{\\theta}" + }, + { + "bbox": [ + 46, + 251, + 286, + 323 + ], + "type": "text", + "content": ", i.e. " + }, + { + "bbox": [ + 46, + 251, + 286, + 323 + ], + "type": "inline_equation", + "content": "\\tilde{x}_{\\theta} = \\tilde{\\pi}_{\\theta}(\\tilde{X}_{\\theta})" + }, + { + "bbox": [ + 46, + 251, + 286, + 323 + ], + "type": "text", + "content": ". As such, we calculate the discrepancy between the keypoints " + }, + { + "bbox": [ + 46, + 251, + 286, + 323 + ], + "type": "inline_equation", + "content": "\\tilde{x}_{\\phi}" + }, + { + "bbox": [ + 46, + 251, + 286, + 323 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 251, + 286, + 323 + ], + "type": "inline_equation", + "content": "\\tilde{x}_{\\theta}" + }, + { + "bbox": [ + 46, + 251, + 286, + 323 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 331, + 287, + 345 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 331, + 287, + 345 + ], + "spans": [ + { + "bbox": [ + 105, + 331, + 287, + 345 + ], + "type": "interline_equation", + "content": "D _ {\\mathrm {C F - C M} ^ {2}} = \\left\\| \\tilde {x} _ {\\phi} - \\tilde {\\pi} _ {\\theta} \\left(\\tilde {X} _ {\\theta}\\right) \\right\\| _ {2}. \\tag {6}", + "image_path": "0bd21fc5ee2feaaef0ad702fa60154fffe5a065ab58d53ea3f9eeaed4c5141eb.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 352, + 287, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 352, + 287, + 483 + ], + "spans": [ + { + "bbox": [ + 46, + 352, + 287, + 483 + ], + "type": "text", + "content": "Our insight for this consistency check comes from the fact that the two models employ different paradigms for estimating 2D keypoints and have distinct failure modes. 2D keypoints detectors use a bottom-up approach to determine the locations of 2D keypoints. While their predictions are more pixel-accurate than the reprojected keypoints from a 3D mesh, they are not constrained in any way and mainly rely on local cues. Conversely, 3D shape predictors, such as " + }, + { + "bbox": [ + 46, + 352, + 287, + 483 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 46, + 352, + 287, + 483 + ], + "type": "text", + "content": ", estimate keypoints as part of a 3D mesh, which constrains their predictions with a specific mesh topology. This makes their predictions more robust." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 490, + 153, + 501 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 490, + 153, + 501 + ], + "spans": [ + { + "bbox": [ + 47, + 490, + 153, + 501 + ], + "type": "text", + "content": "3.3. Additional details" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 509, + 287, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 509, + 287, + 544 + ], + "spans": [ + { + "bbox": [ + 46, + 509, + 287, + 544 + ], + "type": "text", + "content": "Here, we present some additional details of our approach. We include extensive implementation details in the supplementary material." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 544, + 287, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 544, + 287, + 604 + ], + "spans": [ + { + "bbox": [ + 46, + 544, + 287, + 604 + ], + "type": "text", + "content": "Data acquisition. For each target object category we download images from Flickr using the urls that belong to the public and freely usable YFCC100M [35]. However, some images contain wrong objects or objects with heavy truncation. There are also repeated images." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 604, + 287, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 604, + 287, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 604, + 287, + 664 + ], + "type": "text", + "content": "Initial filtering. We remove repeated images with dHash [37]. Then, we detect bounding boxes using MaskRCNN [11] with ResNet50-FPN [12,25] backbone from detector2. Only detections with confidence above a threshold " + }, + { + "bbox": [ + 46, + 604, + 287, + 664 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 46, + 604, + 287, + 664 + ], + "type": "text", + "content": " are retained. We use " + }, + { + "bbox": [ + 46, + 604, + 287, + 664 + ], + "type": "inline_equation", + "content": "\\tau = 0.95" + }, + { + "bbox": [ + 46, + 604, + 287, + 664 + ], + "type": "text", + "content": " for all object categories." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 664, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 664, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 664, + 287, + 715 + ], + "type": "text", + "content": "Keypoints from 2D pose estimation network. We train the SimpleBaselines [38] pose estimator, with an ImageNet pretrained ResNet-18 [12] backbone, with labels from " + }, + { + "bbox": [ + 46, + 664, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{S}" + }, + { + "bbox": [ + 46, + 664, + 287, + 715 + ], + "type": "text", + "content": " and use it to generate keypoint PLs " + }, + { + "bbox": [ + 46, + 664, + 287, + 715 + ], + "type": "inline_equation", + "content": "(\\tilde{x}_{\\phi}^{(u)},\\tilde{c}_{\\phi}^{(u)})" + }, + { + "bbox": [ + 46, + 664, + 287, + 715 + ], + "type": "text", + "content": " on " + }, + { + "bbox": [ + 46, + 664, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{U}" + }, + { + "bbox": [ + 46, + 664, + 287, + 715 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 72, + 545, + 132 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 132 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 132 + ], + "type": "text", + "content": "Data Selection. We curate the web images using a selection criterion. We evaluate the effectiveness of the four selection criteria presented previously. We use each criterion to select the best " + }, + { + "bbox": [ + 304, + 72, + 545, + 132 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 72, + 545, + 132 + ], + "type": "text", + "content": " data samples from the self-labeled web images. We present experiments with " + }, + { + "bbox": [ + 304, + 72, + 545, + 132 + ], + "type": "inline_equation", + "content": "N \\in \\{1K, 3K\\}" + }, + { + "bbox": [ + 304, + 72, + 545, + 132 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 132, + 545, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 132, + 545, + 156 + ], + "spans": [ + { + "bbox": [ + 304, + 132, + 545, + 156 + ], + "type": "text", + "content": "Training. We train a 3D shape predictor " + }, + { + "bbox": [ + 304, + 132, + 545, + 156 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 304, + 132, + 545, + 156 + ], + "type": "text", + "content": " with keypoint reprojection losses as defined in Eq. (3) & (4)." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 167, + 386, + 181 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 167, + 386, + 181 + ], + "spans": [ + { + "bbox": [ + 306, + 167, + 386, + 181 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 188, + 546, + 435 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 188, + 546, + 435 + ], + "spans": [ + { + "bbox": [ + 304, + 188, + 546, + 435 + ], + "type": "text", + "content": "Evaluation metrics. While our models are able to reconstruct the 3D shape as a mesh, evaluating their accuracy remains a challenge due to the absence of 3D ground truth data for the current datasets and object categories. Following prior work [15, 18, 21, 22] we evaluate our models quantitatively using the standard \"Percentage of Correct Keypoints\" (PCK) metric. For " + }, + { + "bbox": [ + 304, + 188, + 546, + 435 + ], + "type": "inline_equation", + "content": "PCK(t)" + }, + { + "bbox": [ + 304, + 188, + 546, + 435 + ], + "type": "text", + "content": ", the reprojection is \"correct\" when the predicted 2D keypoint location is within " + }, + { + "bbox": [ + 304, + 188, + 546, + 435 + ], + "type": "inline_equation", + "content": "t \\times \\max(w, h)" + }, + { + "bbox": [ + 304, + 188, + 546, + 435 + ], + "type": "text", + "content": " distance of the ground-truth location, where " + }, + { + "bbox": [ + 304, + 188, + 546, + 435 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 304, + 188, + 546, + 435 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 188, + 546, + 435 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 304, + 188, + 546, + 435 + ], + "type": "text", + "content": " are the width and the height of the object's bounding box. We summarize the PCK performance at different thresholds by computing the area under the curve (AUC), " + }, + { + "bbox": [ + 304, + 188, + 546, + 435 + ], + "type": "inline_equation", + "content": "\\mathrm{AUC}_{a_1}^{a_2} = \\int_{a_1}^{a_2} PCK(t) dt" + }, + { + "bbox": [ + 304, + 188, + 546, + 435 + ], + "type": "text", + "content": ". We use " + }, + { + "bbox": [ + 304, + 188, + 546, + 435 + ], + "type": "inline_equation", + "content": "a_1 = 0.05" + }, + { + "bbox": [ + 304, + 188, + 546, + 435 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 188, + 546, + 435 + ], + "type": "inline_equation", + "content": "a_2 = 0.1" + }, + { + "bbox": [ + 304, + 188, + 546, + 435 + ], + "type": "text", + "content": " and refer to " + }, + { + "bbox": [ + 304, + 188, + 546, + 435 + ], + "type": "inline_equation", + "content": "\\mathrm{AUC}_{a_1}^{a_2}" + }, + { + "bbox": [ + 304, + 188, + 546, + 435 + ], + "type": "text", + "content": " as AUC in our evaluation. Following [10], we also evaluate the predicted camera viewpoint obtained by our models. We calculate the rotation error " + }, + { + "bbox": [ + 304, + 188, + 546, + 435 + ], + "type": "inline_equation", + "content": "\\mathrm{err}_R = \\arccos\\left(\\frac{\\mathrm{Tr}(\\hat{R}^T\\hat{R}) - 1}{2}\\right)" + }, + { + "bbox": [ + 304, + 188, + 546, + 435 + ], + "type": "text", + "content": " between predicted camera rotation " + }, + { + "bbox": [ + 304, + 188, + 546, + 435 + ], + "type": "inline_equation", + "content": "\\hat{R}" + }, + { + "bbox": [ + 304, + 188, + 546, + 435 + ], + "type": "text", + "content": " and pseudo ground-truth camera " + }, + { + "bbox": [ + 304, + 188, + 546, + 435 + ], + "type": "inline_equation", + "content": "\\tilde{R}" + }, + { + "bbox": [ + 304, + 188, + 546, + 435 + ], + "type": "text", + "content": " computed using SfM on keypoint labels. Finally, we offer qualitative results to measure the quality of the predicted 3D shapes." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 443, + 493, + 456 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 443, + 493, + 456 + ], + "spans": [ + { + "bbox": [ + 305, + 443, + 493, + 456 + ], + "type": "text", + "content": "4.1. Simulated Semi-Supervised Setting" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 462, + 545, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 462, + 545, + 641 + ], + "spans": [ + { + "bbox": [ + 304, + 462, + 545, + 641 + ], + "type": "text", + "content": "First, we investigate the effectiveness of keypoint PLs in a controlled setting. For our experiments we use the CUB dataset [36] that consists of 6K images with bounding box, mask and 2D keypoint labels for training and testing. We study the impact of training with various levels of supervision on 3D reconstruction performance. We split CUB's training set into a labeled set " + }, + { + "bbox": [ + 304, + 462, + 545, + 641 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 462, + 545, + 641 + ], + "type": "text", + "content": " and an unlabeled set " + }, + { + "bbox": [ + 304, + 462, + 545, + 641 + ], + "type": "inline_equation", + "content": "\\mathcal{U}" + }, + { + "bbox": [ + 304, + 462, + 545, + 641 + ], + "type": "text", + "content": " by randomly choosing samples from the initial training set to be included in " + }, + { + "bbox": [ + 304, + 462, + 545, + 641 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 462, + 545, + 641 + ], + "type": "text", + "content": ", while placing the rest in " + }, + { + "bbox": [ + 304, + 462, + 545, + 641 + ], + "type": "inline_equation", + "content": "\\mathcal{U}" + }, + { + "bbox": [ + 304, + 462, + 545, + 641 + ], + "type": "text", + "content": ". This is a controlled setting where we expect the performance of the models trained with labels from " + }, + { + "bbox": [ + 304, + 462, + 545, + 641 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 462, + 545, + 641 + ], + "type": "text", + "content": " and keypoint pseudo-labels from " + }, + { + "bbox": [ + 304, + 462, + 545, + 641 + ], + "type": "inline_equation", + "content": "\\mathcal{U}" + }, + { + "bbox": [ + 304, + 462, + 545, + 641 + ], + "type": "text", + "content": " to be lower-bounded by that of models trained using only " + }, + { + "bbox": [ + 304, + 462, + 545, + 641 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 462, + 545, + 641 + ], + "type": "text", + "content": " and upper-bounded by the fully-supervised baseline that uses the whole training set. We use CMR [15] for the 3D shape prediction network " + }, + { + "bbox": [ + 304, + 462, + 545, + 641 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 304, + 462, + 545, + 641 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": "Results on CUB. In Figure 4, we compare the performance of models trained with different number of labeled and pseudo-labeled instances. Following CMR, we also report the mIoU metric. We observe that training with 2D keypoint pseudo-labels consistently improves 3D reconstruction performance by a significant margin across all metrics." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13096" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 74, + 70, + 520, + 251 + ], + "blocks": [ + { + "bbox": [ + 74, + 70, + 520, + 251 + ], + "lines": [ + { + "bbox": [ + 74, + 70, + 520, + 251 + ], + "spans": [ + { + "bbox": [ + 74, + 70, + 520, + 251 + ], + "type": "table", + "html": "
HorseCowSheep
AUC (↑)errR(↓)AUC (↑)errR(↓)AUC (↑)errR(↓)
NACSM (Mask) [21]34.9 (↓15.9)44.3 (↑14.1)30.7 (↓16.9)71.0 (↑36.3)28.2 (↓18.6)73.1 (↑39.3)
ACSM (KP+Mask) [21]37.4 (↓13.4)76.4 (↑46.2)----
ACSM-ours50.830.247.634.746.833.8
ACSM-ours + KP-all50.2 (↓0.6)31.9 (↑1.7)43.9 (↓3.9)40.1 (↑5.4)43.5 (↓3.5)40.7 (↑6.9)
ACSM-ours + KP-conf53.9 (↑3.1)30.8 (↑0.6)47.638.3 (↑3.6)48.1 (↑1.3)38.6 (↑4.8)
ACSM-ours + CF-MT55.1 (↑4.3)30.0 (↓0.2)50.7 (↑3.1)38.9 (↑4.2)51.1 (↑4.3)33.3 (↓0.5)
ACSM-ours + CF-CM54.7 (↑3.9)30.0 (↓0.2)50.9 (↑3.3)38.6 (↑3.9)50.6 (↑3.8)32.8 (↓1.0)
ACSM-ours + CF-CM254.2 (↑3.4)30.9 (↑0.7)49.4 (↑1.8)32.7 (↓2.0)48.6 (↑1.8)32.1 (↓1.7)
NACSM-ours + KP-conf54.3 (↑3.5)30.0 (↓0.2)50.2 (↑2.6)40.2 (↑5.5)49.1 (↑2.3)35.7 (↑1.0)
ACSM-ours + CF-MT55.4 (↑4.6)30.0 (↓0.2)49.2 (↑1.6)39.1 (↑4.4)51.0 (↑4.2)33.9 (↑0.1)
ACSM-ours + CF-CM55.9 (↑5.1)29.8 (↓0.4)50.0 (↑2.4)38.8 (↑4.1)48.4 (↑1.6)34.1 (↑0.3)
ACSM-ours + CF-CM255.5 (↑4.7)28.1 (↓2.1)52.6 (↑5.0)36.2 (↑1.5)53.0 (↑6.2)31.3 (↓2.5)
", + "image_path": "80f806ac8965d4918d34ab8bf8620f052690922468cc703243b84526e4b0131d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 259, + 545, + 282 + ], + "lines": [ + { + "bbox": [ + 46, + 259, + 545, + 282 + ], + "spans": [ + { + "bbox": [ + 46, + 259, + 545, + 282 + ], + "type": "text", + "content": "Table 1. Evaluation on Pascal. " + }, + { + "bbox": [ + 46, + 259, + 545, + 282 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 259, + 545, + 282 + ], + "type": "text", + "content": " is the number of selected images from the web. ACSM-ours + KP-all uses all available web images. Performance change from the fully-supervised baseline ACSM-ours is shown in green/red." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 303, + 287, + 387 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 303, + 287, + 387 + ], + "spans": [ + { + "bbox": [ + 46, + 303, + 287, + 387 + ], + "type": "text", + "content": "The improvement is larger when the initial labeled set " + }, + { + "bbox": [ + 46, + 303, + 287, + 387 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 303, + 287, + 387 + ], + "type": "text", + "content": " is small (e.g. 100 images). This is a very interesting finding. The quality of the generated keypoint pseudo-labels decreases when the 2D keypoint estimator is trained with fewer samples. However, the keypoint pseudo-labels are accurate enough to provide a useful signal for training CMR, largely improving its performance." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 388, + 287, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 388, + 287, + 495 + ], + "spans": [ + { + "bbox": [ + 46, + 388, + 287, + 495 + ], + "type": "text", + "content": "In Figure 3, we show sample 3D reconstruction results comparing CMR trained with: i) 300 labeled instances and ii) the same labeled instances and additional keypoint pseudo-labels (for 5,700 images). We show the predicted shape and texture from the predicted camera view and a side view. From Figure 3 we can see that the model trained with keypoint pseudo-labels can accurately capture challenging deformations (e.g. open wings), while the other model struggles." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 502, + 197, + 516 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 502, + 197, + 516 + ], + "spans": [ + { + "bbox": [ + 47, + 502, + 197, + 516 + ], + "type": "text", + "content": "4.2. Learning with Web Images" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 521, + 287, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 287, + 581 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 287, + 581 + ], + "type": "text", + "content": "We go beyond standard semi-supervised approaches that use unlabeled images from curated datasets by effectively utilizing images from the web for training. We use " + }, + { + "bbox": [ + 46, + 521, + 287, + 581 + ], + "type": "inline_equation", + "content": "N_S = 150" + }, + { + "bbox": [ + 46, + 521, + 287, + 581 + ], + "type": "text", + "content": " images annotated with 2D keypoints and evaluate our proposed approach." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 582, + 287, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 287, + 652 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 287, + 652 + ], + "type": "text", + "content": "Datasets. We train our models with 2D keypoints from Pascal [9] using the same train/test splits as prior work [21,22]. For categories with less than 150 labeled samples, we augment the labeled training set " + }, + { + "bbox": [ + 46, + 582, + 287, + 652 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 582, + 287, + 652 + ], + "type": "text", + "content": " by manually labeling some images from COCO [26]. We use Pascal's test split and the Animal Pose dataset [3] for evaluation." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "text", + "content": "Implementation details. We train the SimpleBaselines [38] 2D pose estimator using 150 images with 2D keypoint labels and generate pseudo-labels on web images. For criterion CF-MT, we use scaling and rotation transformations. For criterion CF-CM, we train Stacked HourGlass [30] as" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 306, + 300, + 385, + 366 + ], + "blocks": [ + { + "bbox": [ + 306, + 300, + 385, + 366 + ], + "lines": [ + { + "bbox": [ + 306, + 300, + 385, + 366 + ], + "spans": [ + { + "bbox": [ + 306, + 300, + 385, + 366 + ], + "type": "image", + "image_path": "76ffc4094edd5fa32363101ecc586334cdc284efbaed2c27b8849eca633e4d85.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 374, + 545, + 419 + ], + "lines": [ + { + "bbox": [ + 305, + 374, + 545, + 419 + ], + "spans": [ + { + "bbox": [ + 305, + 374, + 545, + 419 + ], + "type": "text", + "content": "Figure 4. Evaluation on CUB. We show the AUC, mIoU and camera rotation error (in degrees) for models trained with different number of labeled and pseudo-labeled instances. Performance across all metrics is significantly improved with keypoint PLs." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 386, + 300, + 465, + 366 + ], + "blocks": [ + { + "bbox": [ + 386, + 300, + 465, + 366 + ], + "lines": [ + { + "bbox": [ + 386, + 300, + 465, + 366 + ], + "spans": [ + { + "bbox": [ + 386, + 300, + 465, + 366 + ], + "type": "image", + "image_path": "4b521b9779c92d449d1d67ca759b40aa1d5a91c3954dcbbc96f4bb1ef121c288.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 465, + 300, + 545, + 366 + ], + "blocks": [ + { + "bbox": [ + 465, + 300, + 545, + 366 + ], + "lines": [ + { + "bbox": [ + 465, + 300, + 545, + 366 + ], + "spans": [ + { + "bbox": [ + 465, + 300, + 545, + 366 + ], + "type": "image", + "image_path": "eb4e166314fe3eb305020315124b888dbc7ad4291640c817c25394ec20debe62.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 445, + 545, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 445, + 545, + 564 + ], + "spans": [ + { + "bbox": [ + 304, + 445, + 545, + 564 + ], + "type": "text", + "content": "the auxiliary 2D pose estimator. We use ACSM [21] for 3D shape prediction. We found that some template meshes provided in the publicly available ACSM codebase contained incorrect keypoint definitions for certain animals' limbs, with inconsistencies between the right and left sides. After rectifying this issue, we trained ACSM exclusively with keypoint labels and achieved better performance than the one reported in [21], establishing a stronger baseline. We denote our implementation of ACSM trained with 150 images labeled with 2D keypoints as ACSM-ours." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 567, + 545, + 686 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 567, + 545, + 686 + ], + "spans": [ + { + "bbox": [ + 304, + 567, + 545, + 686 + ], + "type": "text", + "content": "Baselines. We compare the performance of the models trained with selected web images and pseudo-labels with the fully-supervised baseline (ACSM-ours) as well as with the baseline that uses all pseudo-labels during training, denoted as ACSM-ours+KP-all. To put our results into perspective, we also compare with the models from ACSM [21]. The available models are trained using mask labels from Pascal [9] and manually picked mask pseudolabels from ImageNet [7]. For horses, the authors provide a model trained with keypoint labels from Pascal as well." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": "Results on Pascal. First, we evaluate the performance of different methods on Pascal's test set. The results are pre" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13097" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 74, + 70, + 520, + 251 + ], + "blocks": [ + { + "bbox": [ + 74, + 70, + 520, + 251 + ], + "lines": [ + { + "bbox": [ + 74, + 70, + 520, + 251 + ], + "spans": [ + { + "bbox": [ + 74, + 70, + 520, + 251 + ], + "type": "table", + "html": "
HorseCowSheep
AUC (↑)errR(↓)AUC (↑)errR(↓)AUC (↑)errR(↓)
NACSM (Mask) [21]47.4 (↓19.3)38.0 (↑17.3)46.2 (↓13.4)51.8 (↑22.3)31.4 (↓25.8)65.6 (↑50.0)
ACSM (KP+Mask) [21]51.0 (↓15.7)59.9 (↑39.2)----
ACSM-ours66.720.759.629.557.215.6
ACSM-ours + KP-all69.1 (↑2.4)20.9 (↑0.2)61.2 (↑1.6)27.8 (↓1.7)29.1 (↓28.1)19.9 (↑4.3)
ACSM-ours + KP-conf72.9 (↑6.2)19.6 (↓1.1)65.0 (↑5.4)31.9 (↑2.4)58.5 (↑1.3)20.3 (↑4.7)
ACSM-ours + CF-MT74.6 (↑7.9)19.9 (↓0.8)67.0 (↑7.4)26.2 (↓3.3)59.3 (↑2.1)14.6 (↓1.0)
ACSM-ours + CF-CM75.1 (↑8.4)19.6 (↓1.1)67.2 (↑7.6)25.9 (↓3.6)59.3 (↑2.1)14.7 (↓0.9)
ACSM-ours + CF-CM273.0 (↑6.3)19.7 (↓1.0)67.2 (↑7.6)23.5 (↓6.0)58.7 (↑1.5)15.3 (↓0.3)
NACSM-ours + KP-conf74.3 (↑7.6)19.6 (↓1.1)67.8 (↑7.8)28.0 (↓1.5)57.3 (↑0.1)15.3 (↓0.3)
ACSM-ours + CF-MT74.4 (↑7.7)19.6 (↓1.1)66.0 (↑6.4)29.7 (↑0.2)59.6 (↑2.4)15.1 (↓0.5)
ACSM-ours + CF-CM74.1 (↑7.4)19.6 (↓1.1)66.4 (↑6.8)29.3 (↓0.2)59.4 (↑2.2)15.8 (↑0.2)
ACSM-ours + CF-CM273.8 (↑7.1)19.5 (↓1.2)69.6 (↑10.0)25.2 (↓4.3)60.2 (↑3.0)14.9 (↓0.7)
", + "image_path": "15558ca4d28a96c9095b1d46e80f22b5cf8ce33c94fc5176b8d3a90d7439801b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 47, + 310, + 165, + 408 + ], + "blocks": [ + { + "bbox": [ + 47, + 310, + 165, + 408 + ], + "lines": [ + { + "bbox": [ + 47, + 310, + 165, + 408 + ], + "spans": [ + { + "bbox": [ + 47, + 310, + 165, + 408 + ], + "type": "image", + "image_path": "b0742dce177254c40f9d89bd4f9af720da3e7bac1524bc91da1a276dcf04d07d.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 170, + 310, + 287, + 408 + ], + "blocks": [ + { + "bbox": [ + 170, + 310, + 287, + 408 + ], + "lines": [ + { + "bbox": [ + 170, + 310, + 287, + 408 + ], + "spans": [ + { + "bbox": [ + 170, + 310, + 287, + 408 + ], + "type": "image", + "image_path": "233ee441ecdd9f13adba47b34784fd581cdac56afdc97b03ede79ae98bf8224f.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 47, + 411, + 165, + 508 + ], + "blocks": [ + { + "bbox": [ + 47, + 411, + 165, + 508 + ], + "lines": [ + { + "bbox": [ + 47, + 411, + 165, + 508 + ], + "spans": [ + { + "bbox": [ + 47, + 411, + 165, + 508 + ], + "type": "image", + "image_path": "0068148e50fe8ed973e63adac663524a7cbdbd54aa5f4a5dff568bf6f867e7df.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 515, + 287, + 571 + ], + "lines": [ + { + "bbox": [ + 46, + 515, + 287, + 571 + ], + "spans": [ + { + "bbox": [ + 46, + 515, + 287, + 571 + ], + "type": "text", + "content": "Figure 5. Evaluation under varying initial supervision. We show the AUC and camera rotation error (in degrees) on Pascal (top) and Animal Pose (bottom) for the use of our proposed framework under various levels of initial supervision from " + }, + { + "bbox": [ + 46, + 515, + 287, + 571 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 515, + 287, + 571 + ], + "type": "text", + "content": ". KP-conf, CF-MT, CF-CM, CF-CM" + }, + { + "bbox": [ + 46, + 515, + 287, + 571 + ], + "type": "inline_equation", + "content": "^2" + }, + { + "bbox": [ + 46, + 515, + 287, + 571 + ], + "type": "text", + "content": " use PLs from " + }, + { + "bbox": [ + 46, + 515, + 287, + 571 + ], + "type": "inline_equation", + "content": "N = 3K" + }, + { + "bbox": [ + 46, + 515, + 287, + 571 + ], + "type": "text", + "content": " images." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 170, + 411, + 287, + 508 + ], + "blocks": [ + { + "bbox": [ + 170, + 411, + 287, + 508 + ], + "lines": [ + { + "bbox": [ + 170, + 411, + 287, + 508 + ], + "spans": [ + { + "bbox": [ + 170, + 411, + 287, + 508 + ], + "type": "image", + "image_path": "4570a87761413eb8520e77ec6ec8021d94f185be0e045ae8122f61c4c59e0e97.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 594, + 289, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 289, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 289, + 713 + ], + "type": "text", + "content": "sented in Table 1. From Table 1 we observe that naively including all pseudo-labels during training (ACM-ours+KP-all) leads in degraded performance. Data selection with KP-conf leads to some improvements, but models trained with pseudo-labels selected from consistency-filtering, i.e. CF-MT, CF-CM and " + }, + { + "bbox": [ + 46, + 594, + 289, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{CF - CM^2}" + }, + { + "bbox": [ + 46, + 594, + 289, + 713 + ], + "type": "text", + "content": ", perform consistently better. The improvement over the fully-supervised baseline is quite substantial for those models. For instance, ACSM-ours+CF-CM has a relative improvement (in AUC) of " + }, + { + "bbox": [ + 46, + 594, + 289, + 713 + ], + "type": "inline_equation", + "content": "10.9\\%" + }, + { + "bbox": [ + 46, + 594, + 289, + 713 + ], + "type": "text", + "content": " over ACSM-ours and " + }, + { + "bbox": [ + 46, + 594, + 289, + 713 + ], + "type": "inline_equation", + "content": "17.0\\%" + }, + { + "bbox": [ + 46, + 594, + 289, + 713 + ], + "type": "text", + "content": " over ACSM-ours+KP" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 307, + 312, + 545, + 434 + ], + "blocks": [ + { + "bbox": [ + 46, + 259, + 547, + 293 + ], + "lines": [ + { + "bbox": [ + 46, + 259, + 547, + 293 + ], + "spans": [ + { + "bbox": [ + 46, + 259, + 547, + 293 + ], + "type": "text", + "content": "Table 2. Evaluation on Animal Pose. " + }, + { + "bbox": [ + 46, + 259, + 547, + 293 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 259, + 547, + 293 + ], + "type": "text", + "content": " is the number of selected images from the web. ACSM-ours + KP-all uses all available web images. Training with selected web images significantly improves the fully-supervised baseline. We show the performance change from ACSM-ours in green/red." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 312, + 545, + 434 + ], + "lines": [ + { + "bbox": [ + 307, + 312, + 545, + 434 + ], + "spans": [ + { + "bbox": [ + 307, + 312, + 545, + 434 + ], + "type": "table", + "html": "
GiraffeBear
AUC (↑)errR(↓)AUC (↑)errR(↓)
NACSM-ours79.134.759.228.9
ACSM-ours + KP-all75.6 (↓3.5)39.5 (↑4.8)58.2 (↓1.0)35.4 (↑6.5)
ACSM-ours + KP-conf83.3 (↑4.2)31.4 (↓3.3)62.7 (↑3.5)31.0 (↑2.1)
ACSM-ours + CF-MT84.4 (↑5.3)32.1 (↓2.6)62.6 (↑3.6)31.9 (↑3.0)
ACSM-ours + CF-CM84.1 (↑5.0)32.5 (↓2.2)62.8 (↑3.6)31.6 (↑2.7)
ACSM-ours + CF-CM286.6 (↑7.5)28.8 (↓5.9)62.2 (↑3.0)30.7 (↑1.8)
NACSM-ours + KP-conf82.8 (↑3.7)35.6 (↑0.9)59.9 (↑0.7)35.0 (↑6.1)
ACSM-ours + CF-MT83.5 (↑4.4)33.1 (↓1.6)63.1 (↑3.9)31.7 (↑2.8)
ACSM-ours + CF-CM83.6 (↑4.5)33.4 (↓1.3)63.4 (↑4.2)31.5 (↑2.6)
ACSM-ours + CF-CM284.5 (↑5.4)32.8 (↓1.9)62.8 (↑3.6)32.3 (↑3.4)
", + "image_path": "44fee6c6b8d524b5d32bfcbf58963456a8b6a5531648d46b25d7862e07e6c1e5.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 441, + 547, + 486 + ], + "lines": [ + { + "bbox": [ + 305, + 441, + 547, + 486 + ], + "spans": [ + { + "bbox": [ + 305, + 441, + 547, + 486 + ], + "type": "text", + "content": "Table 3. Evaluation on COCO. " + }, + { + "bbox": [ + 305, + 441, + 547, + 486 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 305, + 441, + 547, + 486 + ], + "type": "text", + "content": " is the number of selected images from the web. ACSM-ours + KP-all uses all available web images. Performance change from the fully-supervised baseline is shown in green/red." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 508, + 515, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 508, + 515, + 521 + ], + "spans": [ + { + "bbox": [ + 305, + 508, + 515, + 521 + ], + "type": "text", + "content": "all, averaged across all categories shown in Table 1." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 521, + 545, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 545, + 628 + ], + "type": "text", + "content": "Results on Animal Pose. Next, we evaluate our previously trained models on Animal Pose dataset and present results in Table 2. Results are consistent with those in Pascal. Training models with all pseudo-labels results in large performance degradation in some cases (see Sheep in Table 2). KP-conf improves over the supervised baseline, but the improvement is higher for CF-MT, CF-CM and " + }, + { + "bbox": [ + 304, + 521, + 545, + 628 + ], + "type": "inline_equation", + "content": "\\mathrm{CF - CM^2}" + }, + { + "bbox": [ + 304, + 521, + 545, + 628 + ], + "type": "text", + "content": ". Results from Tables 1 & 2 suggest that consistency-filtering is more effective than confidence-based filtering in our setting." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 630, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 547, + 713 + ], + "type": "text", + "content": "Results on COCO. In this part, we demonstrate the practicality of our approach in predicting the 3D shape of object categories even in the absence of initial annotations for those categories. We evaluate our approach on giraffes and bears. We annotate 250 images from COCO with 2D keypoints in a process that takes only " + }, + { + "bbox": [ + 304, + 630, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\approx 2.5" + }, + { + "bbox": [ + 304, + 630, + 547, + 713 + ], + "type": "text", + "content": " hours per-category. Given a mesh template, we only need to associate the 2D" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "13098" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 68, + 545, + 312 + ], + "blocks": [ + { + "bbox": [ + 48, + 68, + 545, + 312 + ], + "lines": [ + { + "bbox": [ + 48, + 68, + 545, + 312 + ], + "spans": [ + { + "bbox": [ + 48, + 68, + 545, + 312 + ], + "type": "image", + "image_path": "f734021cc8a9320c07c81e79143ca57c6926ad51294bad9ddd9deb3415b7d884.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 319, + 548, + 353 + ], + "lines": [ + { + "bbox": [ + 46, + 319, + 548, + 353 + ], + "spans": [ + { + "bbox": [ + 46, + 319, + 548, + 353 + ], + "type": "text", + "content": "Figure 6. Sample results on 3D shape recovery of quadrupeds. For each input image, we show the predicted 3D shape from the inferred viewpoint. (b) original ACSM (models for giraffes and bears are not available), (c) our ACSM implementation, (d) ACSM-ours trained with all PLs, (e) ACSM-ours + KP-conf, (f) ACSM-ours + CF-MT, (g) ACSM-ours + CF-CM, (h) ACSM-ours + CF-CM" + }, + { + "bbox": [ + 46, + 319, + 548, + 353 + ], + "type": "inline_equation", + "content": "^2" + }, + { + "bbox": [ + 46, + 319, + 548, + 353 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 373, + 289, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 373, + 289, + 529 + ], + "spans": [ + { + "bbox": [ + 46, + 373, + 289, + 529 + ], + "type": "text", + "content": "keypoint labels with vertices from the 3D mesh. This process is done in meshlab in " + }, + { + "bbox": [ + 46, + 373, + 289, + 529 + ], + "type": "inline_equation", + "content": "\\approx 5" + }, + { + "bbox": [ + 46, + 373, + 289, + 529 + ], + "type": "text", + "content": " minutes. We train our models with semi-supervised learning as described in Section 3.2. We use 150 images for training, while the remaining images are used for testing. We compare models that utilize pseudo-labels with the fully-supervised baseline trained with 150 images. The results are presented in Table 3. The results are consistent with those on Pascal and Animal Pose. Again, using all pseudo-labels leads in degraded performance. Data selection is essential, and in most cases leads to improved performance compared to the fully-supervised baseline. The performance gains are higher for consistency-based filtering approaches." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 533, + 289, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 533, + 289, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 533, + 289, + 713 + ], + "type": "text", + "content": "Results with different number of labels. In Figure 5, we present results on 3D reconstruction of horses with different number " + }, + { + "bbox": [ + 46, + 533, + 289, + 713 + ], + "type": "inline_equation", + "content": "N_{s}" + }, + { + "bbox": [ + 46, + 533, + 289, + 713 + ], + "type": "text", + "content": " of images labeled with 2D keypoints. For all experiments, we use " + }, + { + "bbox": [ + 46, + 533, + 289, + 713 + ], + "type": "inline_equation", + "content": "N = 3K" + }, + { + "bbox": [ + 46, + 533, + 289, + 713 + ], + "type": "text", + "content": " images with pseudolabels from " + }, + { + "bbox": [ + 46, + 533, + 289, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{U}" + }, + { + "bbox": [ + 46, + 533, + 289, + 713 + ], + "type": "text", + "content": " and vary only the number of initial labels " + }, + { + "bbox": [ + 46, + 533, + 289, + 713 + ], + "type": "inline_equation", + "content": "N_{s}" + }, + { + "bbox": [ + 46, + 533, + 289, + 713 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 46, + 533, + 289, + 713 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 533, + 289, + 713 + ], + "type": "text", + "content": ". From Figure 5, we observe that models with keypoint pseudo-labels outperform the fully-supervised baseline even when " + }, + { + "bbox": [ + 46, + 533, + 289, + 713 + ], + "type": "inline_equation", + "content": "N_{s}" + }, + { + "bbox": [ + 46, + 533, + 289, + 713 + ], + "type": "text", + "content": " is just 50. More importantly, we notice that models trained with " + }, + { + "bbox": [ + 46, + 533, + 289, + 713 + ], + "type": "inline_equation", + "content": "N_{s} = 50" + }, + { + "bbox": [ + 46, + 533, + 289, + 713 + ], + "type": "text", + "content": " and keypoint pseudolabels outperform fully-supervised models with " + }, + { + "bbox": [ + 46, + 533, + 289, + 713 + ], + "type": "inline_equation", + "content": "N_{s} = 150" + }, + { + "bbox": [ + 46, + 533, + 289, + 713 + ], + "type": "text", + "content": ". We also observe, that consistency-based filtering methods are more effective than filtering with keypoint confidence scores. Finally, while all consistency-based filtering approaches lead to similar AUC performance, we notice that CF-CM² leads to lower camera rotation errors in all cases." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 373, + 547, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 373, + 547, + 469 + ], + "spans": [ + { + "bbox": [ + 304, + 373, + 547, + 469 + ], + "type": "text", + "content": "Qualitative Examples. In Figure 6, we show sample 3D reconstructions for all models. We observe that ACSM-ours recovers more accurate shapes than the original ACSM version. Training with all PLs results in unnatural articulations in the predicted shapes. Additionally, we observe that some articulations are captured only when training with selected samples through consistency-filtering (e.g. horse legs in the first row for CF-CM" + }, + { + "bbox": [ + 304, + 373, + 547, + 469 + ], + "type": "inline_equation", + "content": "^2" + }, + { + "bbox": [ + 304, + 373, + 547, + 469 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 305, + 495, + 373, + 509 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 495, + 373, + 509 + ], + "spans": [ + { + "bbox": [ + 305, + 495, + 373, + 509 + ], + "type": "text", + "content": "5. Summary" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 520, + 547, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 520, + 547, + 675 + ], + "spans": [ + { + "bbox": [ + 304, + 520, + 547, + 675 + ], + "type": "text", + "content": "In summary, we investigated the amount of supervision necessary to train models for 3D shape recovery. We showed that it is possible to learn 3D shape predictors with as few as 50-150 images labeled with 2D keypoints. Such annotations are quick and easy to acquire, taking less than 2 hours for each new object category, making our approach highly practical. Additionally, we utilized automatically acquired web images to improve 3D reconstruction performance for several articulated objects, and found that a data selection method was necessary. To this end, we evaluated the performance of four data selection methods and found that training with data selected through consistency-filtering criteria leads to better 3D reconstructions." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 680, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 680, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 680, + 547, + 713 + ], + "type": "text", + "content": "Acknowledgements: This research has been partially funded by research grants to D. Metaxas through NSF IUCRC CARTA1747778, 2235405, 2212301, 1951890, 2003874." + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "13099" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 17, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 133 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 133 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 133 + ], + "type": "text", + "content": "[1] Mykhaylo Andriluka, Leonid Pishchulin, Peter Gehler, and Bernt Schiele. 2d human pose estimation: New benchmark and state of the art analysis. 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Wong \nThe University of Hong Kong", + "bbox": [ + 274, + 180, + 694, + 217 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{szhao, kykwong}@cs.hku.hk kaihanx@hku.hk", + "bbox": [ + 287, + 219, + 676, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 268, + 313, + 284 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Compositional zero-shot learning (CZSL) aims at learning visual concepts (i.e., attributes and objects) from seen compositions and combining concept knowledge into unseen compositions. The key to CZSL is learning the disentanglement of the attribute-object composition. To this end, we propose to exploit cross-attention as compositional disentanglers to learn disentangled concept embeddings. For example, if we want to recognize an unseen composition \"yellow flower\", we can learn the attribute concept \"yellow\" and object concept \"flower\" from different yellow objects and different flowers respectively. To further constrain the disentanglers to learn the concept of interest, we employ a regularization at the attention level. Specifically, we adapt the earth mover's distance (EMD) as a feature similarity metric in the cross-attention module. Moreover, benefiting from concept disentanglement, we improve the inference process and tune the prediction score by combining multiple concept probabilities. Comprehensive experiments on three CZSL benchmark datasets demonstrate that our method significantly outperforms previous works in both closed- and open-world settings, establishing a new state-of-the-art. Project page: https://haoosz.github.io/ade-czsl/", + "bbox": [ + 73, + 301, + 473, + 633 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 665, + 207, + 681 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Suppose we have never seen white bears (i.e., polar bears) before. Can we picture what it would look like? This is not difficult because we have seen many white animals in daily life (e.g., white dogs and white rabbits) and different bears with various visual attributes in the zoo (e.g., brown bears and black bears). Humans have no difficulty in disentangling \"white\" and \"bear\" from seen instances and combining them into the unseen composition. Inspired by this property of human intelligence, researchers attempt to make machines learn compositions of concepts as well. Compositional zero-shot learning (CZSL) is a specific problem studying visual compositionality, aiming to learn visual concepts from seen", + "bbox": [ + 73, + 691, + 470, + 875 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/96a0d7012211e0c75550d61a06ff7e29e7d5473daf047868aa312de345224039.jpg", + "image_caption": [ + "Figure 1. Motivation illustration. Given images from seen attribute-object compositions, human can disentangle the attribute \"yellow\" from \"yellow bird\" and \"yellow pear\", and the object \"flower\" from \"purple flower\" and \"red flower\". After learning visual properties of the concepts \"yellow\" and \"flower\", human can then recognize images from the unseen composition \"yellow flower\"." + ], + "image_footnote": [], + "bbox": [ + 501, + 268, + 890, + 455 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "compositions of attributes and objects and generalize concept knowledge to unseen compositions.", + "bbox": [ + 496, + 551, + 892, + 582 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Learning attribute-object compositions demands prior knowledge about attributes and objects. However, visual concepts of attributes and objects never appear alone in a natural image. To learn exclusive concepts for compositionality learning, we need to disentangle the attribute concept and the object concept. As illustrated in Fig. 1, if we want to recognize the image of \"yellow flower\", it is necessary to learn the \"yellow\" concept and the \"flower\" concept, i.e., disentangle visual concepts, from images of seen compositions. Previous works [22, 24, 25, 28-30, 36, 46] tackle CZSL by composing attribute and object word embeddings, and projecting word and visual embeddings to a joint space. They fail to disentangle visual concepts. Recently, some works [21, 40, 41, 50] consider visual disentanglement but still have limitations despite their good performance. SCEN [21] learns concept-constant samples contrastively without constructing concept embedding prototypes to avoid learning irrelevant concepts shared by positive samples. IVR [50] disentangles visual features into ideal concept-invariant domains. This ideal domain generalization setting requires a small discrepancy of attribute and object sets and would degenerate on vaster and more", + "bbox": [ + 496, + 583, + 893, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author", + "bbox": [ + 94, + 887, + 220, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "15315", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "complex concepts. ProtoProp [40] and OADis [41] learn local attribute and object prototypes from spatial features on convolutional feature maps. However, spatial disentanglement is sometimes infeasible because attribute and object concepts are highly entangled in spatial features. Taking an image of \"yellow flower\" as an example, the spatial positions related to the attribute \"yellow\" and the object \"flower\" completely overlap, which hinders effective attribute-object disentanglement.", + "bbox": [ + 75, + 90, + 472, + 227 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To overcome the above limitations, we propose a simple visual disentangling framework exploiting Attention as DisEntangler (ADE) on top of vision transformers [6]. We notice that vision transformers (ViT) have access to more sub-space global information across multi-head attentions than CNNs [38]. Therefore, with the expressivity of different subspace representations, token attentions of ViT may provide a more effective way for disentangling visual features, compared to using traditional spatial attentions across local positions on convolutional features [40, 41]. Specifically, it is difficult to disentangle the attribute-object composition \"yellow flower\" by spatial positions, but it is possible for ViT multi-head attentions to project attribute concept \"yellow\" and object concept \"flower\" onto different subspaces. Inspired by this property, we propose to learn cross-attention between two inputs that share the same concept, e.g., \"yellow bird\" and \"yellow pear\" share the same attribute concept \"yellow\". In this way, we can derive attribute- and object-exclusive visual representations by cross-attention disentanglement. To ensure that the concept disentangler is exclusive to the specific concept, we also need to constrain the disentanglers to learn the concept of interest instead of the other concept. For example, given attribute-sharing images, the attribute attention should output similar attribute-exclusive features while the object attention should not. To achieve this goal, we apply a regularization term adapted from the earth mover's distance (EMD) [13] at the attention level. This regularization term forces cross-attention to learn the concept of interest by leveraging the feature similarity captured from all tokens. Mancini et al. [24] propose an open-world evaluation setting, which is neglected by most previous works. We consider both closed-world and the open-world settings in our experiments, demonstrating that our method is coherently efficient in both settings. The contributions of this paper are summarized below:", + "bbox": [ + 75, + 227, + 472, + 755 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a new CZSL approach, named ADE, using cross-attentions to disentangle attribute- and object-exclusive features from paired concept-sharing inputs.", + "- We force attention disentanglers to learn the concept of interest with a regularization term adapted from EMD, ensuring valid attribute-object disentanglement.", + "- We comprehensively evaluate our method in both closed-world and open-world settings on three CZSL datasets, achieving consistent state-of-the-art." + ], + "bbox": [ + 86, + 757, + 470, + 897 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related work", + "text_level": 1, + "bbox": [ + 500, + 89, + 637, + 104 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Visual attribute has been widely studied to understand how visual properties can be learned from objects. The pioneering work by Ferrari and Zisserman [10] learned visual attributes using a probabilistic generative model. The successive work by Lampert et al. [20] used visual attributes to detect unseen objects with an attribute-based multi-label classification. Similarly, Patterson et al. [35] proposed Economic Labeling Algorithm (ELA) to discover multi-label attributes for objects. Different from multi-label classification, other works [4,8,15,23] learned attribute-object relationship to generalize attribute feature across all object categories based on probabilistic models. Visual attributes also benefit downstream tasks, e.g., object recognition [7, 16, 31], action recognition [1,9,26], image captioning [19,33], and semi-supervised learning [42].", + "bbox": [ + 496, + 114, + 893, + 340 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Compositional zero-shot learning (CZSL) is a special case of zero-shot learning (ZSL) [34, 39, 43, 47, 48], aims at recognizing unseen attribute-object compositions learning from seen compositions. Misra et al. [28] first termed and studied CZSL by projecting composed primitives and visual features to a joint embedding space. Nagarajan et al. [30] formulated attributes as matrix operators applied on object vectors. Purushwalkam et al. [36] introduced a task-driven modular architecture to learn unseen compositions by re-weighting a set of sub-tasks. Wei et al. [46] generated attribute-object compositions with GAN [11] to match visual features. Li et al. [22] proposed symmetry principle of attribute-object transformation under the supervision of group axioms. Naeem et al. [29] and Mancini et al. [25] used graph convolutional networks to extract attribute-object representations. Recently, some works shift their interest from word composing to visual disentanglement. Atzmon et al. [2] solved CZSL from a causal perspective to learn disentangled representations. Ruis et al. [40] proposed to learn prototypical representations of objects and attributes. Li et al. [21] disentangled visual features into a Siamese contrastive space and entangled them with a generative model. Saini et al. [41] extracted visual similarity from spatial features to disentangle attributes and objects. Zhang et al. [50] treated CZSL as a domain generalization task, learning attribute- and object-invariant domains. A more realistic open-world CZSL setting was studied in [17, 24, 25], which considered all possible compositions in testing. Very recently, an inspiring work by Nayak et al. [32] introduced compositional soft prompts to CLIP [37] to tackle CZSL problem.", + "bbox": [ + 496, + 340, + 895, + 792 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Attention mechanism has been well studied by non-local neural networks [45] in computer vision and transformers [44] in machine translation. Dosovitskiy et al. [6] adapted transformer architecture to computer vision field, proving its comparable efficiency over traditional CNNs. Inspired by the multi-head self-attention implemented by transformers, our work exploits efficient attention as disentangler for CZSL.", + "bbox": [ + 496, + 795, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "15316", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/925cc16c877a72219acffeb63e39e57ca1d8a082e63125eae57429d70ed42ed2.jpg", + "image_caption": [ + "Figure 2. Method overview. Left (our framework ADE): Given one target image of \"red bus\", we sample two auxiliary images of the same attribute \"red wall\" and of the same object \"blue bus\". We feed the three images into a frozen ViT initialized with DINO [3]. We then input all encoded tokens (i.e., [CLS] and patch tokens) to three attention modules: (1) attribute cross-attention taking paired attribute-sharing tokens as inputs; (2) object cross-attention taking paired object-sharing tokens as inputs; (3) composition self-attention taking tokens of single target image as input. We then project the [CLS] tokens of attention outputs with three MLP embeddings $\\pi_{a}$ , $\\pi_{c}$ , and $\\pi_{o}$ . We finally compute cross entropy losses of embedded visual features with three learnable word embeddings: attribute embeddings, object embeddings, and their linear fused composition embeddings. Right: Illustration of five losses in attribute, object, and composition embedding spaces." + ], + "image_footnote": [], + "bbox": [ + 88, + 88, + 697, + 296 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/a9230fe046a161a5fbfffe9bd11e1a36a3fb687d622c98826d42bf7bba39abb3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 714, + 101, + 867, + 291 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Preliminary", + "text_level": 1, + "bbox": [ + 76, + 407, + 202, + 425 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Compositional zero-shot learning aims at learning a model from limited compositions of attributes (e.g., yellow) and objects (e.g., flower) to recognize an image from novel compositions. Given a set of all possible attributes $\\mathcal{A} = \\{a_0, a_1, \\dots, a_n\\}$ and a set of all possible objects $\\mathcal{O} = \\{o_0, o_1, \\dots, o_m\\}$ , a compositional class set $\\mathcal{C} = \\mathcal{A} \\times \\mathcal{O}$ includes all attribute-object compositions. We divide $\\mathcal{C}$ into two disjoint sets, namely the set of seen classes $\\mathcal{C}_s$ and the set of unseen classes $\\mathcal{C}_u$ , where $\\mathcal{C}_s \\cap \\mathcal{C}_u = \\emptyset$ and $\\mathcal{C}_s \\cup \\mathcal{C}_u = \\mathcal{C}$ . Training images are only from classes in $\\mathcal{C}_s$ and testing images are from classes in $\\mathcal{C}_{test} = \\mathcal{C}_s \\cup \\mathcal{C}_u'$ . For closed-world evaluation, $\\mathcal{C}_u'$ is a predefined subset of $\\mathcal{C}_u$ , i.e., $\\mathcal{C}_u' \\subset \\mathcal{C}_u$ . For open-world evaluation, all possible compositions are considered for testing, i.e., $\\mathcal{C}_u' = \\mathcal{C}_u$ . CZSL task aims to learn a model $f: \\mathcal{X} \\to \\mathcal{C}_{test}$ to predict labels in the testing composition set $c \\in \\mathcal{C}_{test}$ for input images $x \\in \\mathcal{X}$ .", + "bbox": [ + 75, + 430, + 473, + 672 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To learn a CZSL model, a common method is to minimize the cosine similarity score between the visually encoded feature and the word embedding of attribute-object compositions. The similarity score can be expressed as", + "bbox": [ + 75, + 672, + 470, + 734 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\ns (x, (a, o)) = \\frac {\\phi (x)}{| | \\phi (x) | |} \\cdot \\frac {\\psi (a , o)}{| | \\psi (a , o) | |} \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 153, + 736, + 468, + 768 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\phi (\\cdot)$ is the visual encoder, and $\\psi (\\cdot ,\\cdot)$ is the composition function. The CZSL model $f$ can be formulated as", + "bbox": [ + 75, + 770, + 472, + 801 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nf (x; \\theta_ {\\phi}, \\theta_ {\\psi}) = \\underset {a _ {i} \\in \\mathcal {A}, o _ {j} \\in \\mathcal {O}} {\\arg \\max } s (x, \\left(a _ {i}, o _ {j}\\right)) \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 140, + 819, + 468, + 845 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The model $f$ is optimized by learning the model parameters $\\theta_{\\phi}$ and $\\theta_{\\psi}$ to match the input $x$ with the most similar attribute-object composition. Visual encoder $\\phi$ and composition func", + "bbox": [ + 76, + 854, + 472, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "tion $\\psi$ , as two core components, take multiple forms in different methods. For visual encoder, works [40, 41, 50] manually design networks on top of a pretrained backbone (e.g., ResNet18 [12]) to disentangle attribute and object embeddings for visual features. For composition functions, the object conditioned network [41], the graph embedding [29, 40], and the linear projector [24, 50] are commonly used. Unlike employing complex composition functions, we adopt the simple linear projector in our method.", + "bbox": [ + 496, + 409, + 895, + 546 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Our approach", + "text_level": 1, + "bbox": [ + 498, + 559, + 643, + 575 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We aim to disentangle attribute and object features for visual representation by learning from image pairs sharing the same attributes or objects. For example, by learning the object \"flower\" from the \"purple flower\" and the \"red flower\" and learning the attribute \"yellow\" from the \"yellow bird\" and the \"yellow pear\", we can infer what a \"yellow flower\" looks like. To this end, we propose ADE to learn cross-attentions as concept disentanglers with the regularization of a novel token earth mover's distance. The whole framework of our method is shown in Fig. 2.", + "bbox": [ + 496, + 584, + 893, + 736 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.1. Disentanglement with cross-attention", + "text_level": 1, + "bbox": [ + 498, + 744, + 821, + 762 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Multi-head self-attention in transformers [44] is powerful for extracting token connections. Attention maps each query token, and key-value token pairs to an output token. Every output token is a weighted sum of the values, where the weights is the similarity of the corresponding query token and the key tokens. The attention is formulated as:", + "bbox": [ + 496, + 768, + 892, + 859 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {A t t e n t i o n} (Q, K, V) = \\operatorname {s o f t m a x} \\left(\\frac {Q K ^ {T}}{\\sqrt {d _ {k}}}\\right) V \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 547, + 869, + 892, + 905 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "15317", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/e2ec8ae55dc8f89a72ef5576d46254e89c78dfad4c90c56be84a6ad613b8b42a.jpg", + "image_caption": [ + "Figure 3. Illustration of three types of attention." + ], + "image_footnote": [], + "bbox": [ + 78, + 88, + 467, + 169 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where three inputs are query tokens $(Q)$ , key tokens $(K)$ , and value tokens $(V)$ and the scaling factor $d_{k}$ is the dimension of the query and key. Self-attention uses the same input for $Q$ , $K$ , $V$ and effectively captures relationships among [CLS] and patch tokens of a single input image. Normally, the [CLS] token is exclusively used as a global representation of the input image for downstream tasks, but exclusive [CLS] token highly entangles attribute and object concepts.", + "bbox": [ + 76, + 199, + 468, + 321 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For CZSL task, we want to disentangle the exclusive concept by exploiting the semantic similarity between tokens from different concept-sharing features. For this purpose, we introduce a cross-attention mechanism to extract attribute-exclusive or object-exclusive features for paired images sharing the same attribute or object concept. The cross-attention has the same structure as the self-attention, but works on different inputs. Self-attention uses the same input $I$ for $Q$ , $K$ , $V$ (i.e., $Q = K = V = I$ ) while cross-attention uses one of the paired inputs $I$ for the query and the other $I'$ for the key and the value (i.e., $Q = I$ , $K = V = I'$ ). In the cross-attention, the query input and the key input play different roles. The cross-attention output is the weighted sum of the value (also the key) input based on the similarity between the query and key inputs. For a pair of input images, we swap the query and key inputs in computing cross-attention to derive two cross-attended outputs for the respective inputs. Cross-attention with query-key swapping (QKS) is illustrated in Fig. 3.", + "bbox": [ + 76, + 321, + 470, + 594 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The cross-attention outputs paired features of the exclusive concept with paired concept-sharing inputs. Taking the object-sharing pair as an example, object cross-attention leverages the shared object features of the key input to enhance the query input, thus making the outputs exclusive to object feature space, i.e., object-exclusive features $v_{o}$ and $v_{o}'$ . The same applies to attribute-exclusive features $v_{a}$ and $v_{a}'$ extracted from paired attribute-sharing images. We also use a standard self-attention to extract composition feature $v_{c}$ .", + "bbox": [ + 75, + 595, + 468, + 731 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To train cross-attentions, we adopt common cross entropy loss after MLP embedders $(\\pi_{a},\\pi_{c},\\pi_{o})$ for attribute-exclusive features $(v_{a},v_{a}^{\\prime})$ , object-exclusive features $(v_{o},v_{o}^{\\prime})$ , and composition feature $(v_{c})$ . We denote any of these visual features as $v$ and the corresponding embedder as $\\pi$ . We denote the word embedding as $w_{z}$ , where the concept $z\\in \\mathcal{Z}$ can be any of the attribute $a\\in \\mathcal{A}$ , the object $o\\in \\mathcal{O}$ , or the composition $c\\in \\mathcal{C}$ . The class probability of L2-normalized $\\pi (v)$ and $w_{z}$ can be computed as:", + "bbox": [ + 75, + 732, + 468, + 867 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\np _ {\\pi} (z \\mid v) = \\frac {\\exp (\\pi (v) \\cdot w _ {z} / \\tau)}{\\sum_ {\\hat {z} \\in \\mathcal {Z}} \\exp (\\pi (v) \\cdot w _ {\\hat {z}} / \\tau)}, z \\in \\mathcal {Z} \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 117, + 869, + 468, + 904 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\tau$ is the temperature. We then compute the cross entropy to classify visual features:", + "bbox": [ + 498, + 90, + 893, + 121 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nH _ {\\pi} (v, z) = - \\log p _ {\\pi} (z \\mid v), z \\in \\mathcal {Z} \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 578, + 125, + 890, + 140 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Considering different classification objectives of attribute, object, and composition, the general Eq. (5) can be applied to five visual features, i.e., $v_{a}, v_{a}^{\\prime}, v_{o}, v_{o}^{\\prime}, v_{c}$ . Therefore, the training objective is composed of five cross entropy losses:", + "bbox": [ + 496, + 143, + 893, + 204 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {c e} = \\underbrace {H _ {\\pi_ {a}} (v _ {a} , a)} _ {\\mathcal {L} _ {a t t r}} + \\underbrace {H _ {\\pi_ {a}} (v _ {a} ^ {\\prime} , a)} _ {\\mathcal {L} _ {a t t r} ^ {\\prime}} + \\underbrace {H _ {\\pi_ {c}} (v _ {c} , c)} _ {\\mathcal {L} _ {c o m}} +\n$$\n", + "text_format": "latex", + "bbox": [ + 535, + 218, + 852, + 255 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\underbrace {H _ {\\pi_ {o}} \\left(v _ {o} , o\\right)} _ {\\mathcal {L} _ {o b j}} + \\underbrace {H _ {\\pi_ {o}} \\left(v _ {o} ^ {\\prime} , o\\right)} _ {\\mathcal {L} _ {o b j} ^ {\\prime}} \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 581, + 258, + 890, + 297 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where the attribute label $a\\in \\mathcal{A}$ , the object label $o\\in \\mathcal{O}$ , and the composition label $c = (a,o)\\in \\mathcal{C}_{test}$", + "bbox": [ + 500, + 310, + 890, + 340 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. Disentangling constraint at the attention level", + "text_level": 1, + "bbox": [ + 500, + 352, + 883, + 368 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "So far, we have enabled cross-attentions to disentangle concepts, but we want to further ensure that the attribute and the object disentanglers learn the corresponding attribute and object concepts instead of the opposite concepts. To this end, we introduce an attention-level earth mover's distance (EMD) to constrain disentanglers to learn the concept of interest. The EMD is formulated as an optimal transportation problem in [13]. Suppose we have supplies of $n_s$ sources $S = \\{s_i\\}_{i=1}^{n_s}$ and demands of $n_d$ destinations $D = \\{d_j\\}_{j=1}^{n_d}$ . Given the moving cost from the $i$ -th source to the $j$ -th destination $c_{ij}$ , an optimal transportation problem aims to find the minimal-cost flow $f_{ij}$ from sources to destinations:", + "bbox": [ + 496, + 376, + 893, + 556 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\underset {f _ {i j}} {\\text {m i n i m i z e}} \\quad \\sum_ {i = 1} ^ {n _ {s}} \\sum_ {j = 1} ^ {n _ {d}} c _ {i j} f _ {i j} \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 535, + 570, + 890, + 599 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\text {s u b j e c t} f _ {i j} \\geqslant 0, i = 1, \\dots , n _ {s}, j = 1, \\dots , n _ {d} \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 535, + 603, + 890, + 619 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\sum_ {j = 1} ^ {n _ {d}} f _ {i j} = s _ {i}, i = 1, \\dots , n _ {s} \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 617, + 622, + 890, + 648 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\sum_ {i = 1} ^ {n _ {s}} f _ {i j} = d _ {j}, j = 1, \\dots , n _ {d} \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 617, + 650, + 890, + 675 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where the optimal flow $\\tilde{f}_{ij}$ is computed by the moving cost $c_{ij}$ , the supplies $s_i$ , and the demands $d_j$ . The EMD can be further formulated as:", + "bbox": [ + 498, + 689, + 890, + 734 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {E M D} \\left(c _ {i j}, s _ {i}, d _ {j}\\right) = \\left(1 - c _ {i j}\\right) \\tilde {f} _ {i j}. \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 584, + 748, + 890, + 766 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "When the EMD is greater, the distributions $S$ and $\\mathcal{D}$ are closer. In Fig. 4, we show how to use the EMD as a feature similarity metric at the attention level in our cross-attention module. We can derive a cross-attention map from Eq. (3) and the counterpart cross-attention map after query-key swapping. We use the logits of [CLS]-to-patch attentions as supplies $s_i$ and demands $d_j$ , which represent how similar the global feature of one image is to the local patches of the", + "bbox": [ + 496, + 779, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "15318", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/2c42b119f70dfa9e38fac9430870a10d35ce499177dca99449bc897e3f48f4a9.jpg", + "image_caption": [ + "Figure 4. Illustration of the adapted EMD at the attention level. Branches 1 and 2 respectively denote using one of the paired inputs as the query $Q$ . We compute the EMD with two attention maps from 1 and 2 branches. We use the [CLS] -to-patch logits as the supplies $s_i$ and the demands $d_j$ , and one minus the mean matrix of patch-to-patch logits as the moving cost $c_{ij}$ . In this way, we adapt the EMD to our cross-attention module." + ], + "image_footnote": [], + "bbox": [ + 80, + 89, + 465, + 280 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "other image. We use one minus the average map of patch-to-patch attentions as the moving cost $c_{ij}$ . In this way, we can compute an adapted EMD $\\lambda$ for the cross-attention:", + "bbox": [ + 75, + 391, + 470, + 438 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\lambda_ {q} ^ {p} = \\operatorname {E M D} \\left(c _ {i j}, s _ {i}, d _ {j}; p, q\\right), p, q \\in \\{a, o \\} \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 133, + 441, + 468, + 460 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $p$ represents the type of the cross-attention, i.e., attribute cross-attention when $p = a$ and object cross-attention when $p = o$ , and $q$ represents the type of the inputs, i.e., attribute-sharing inputs when $q = a$ and object-sharing inputs when $q = o$ .", + "bbox": [ + 75, + 465, + 470, + 539 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For attribute cross-attention, attribute-sharing inputs should have large EMD $\\lambda_{a}^{a}$ while object-sharing inputs should have small EMD $\\lambda_{o}^{a}$ . It is opposite for object cross-attention, i.e., small $\\lambda_{a}^{o}$ of attribute-sharing inputs and large $\\lambda_{o}^{o}$ of object-sharing inputs. Thus, we formulate the regularization term as:", + "bbox": [ + 75, + 541, + 470, + 628 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {r e g}} = \\lambda_ {o} ^ {a} + \\lambda_ {a} ^ {o} - \\lambda_ {a} ^ {a} - \\lambda_ {o} ^ {o} \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 179, + 633, + 468, + 652 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Training and inference", + "text_level": 1, + "bbox": [ + 76, + 659, + 290, + 675 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "At the training phase, we formulate our final loss as a cross entropy with regularization for all inputs:", + "bbox": [ + 75, + 683, + 468, + 713 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {c e} + \\mathcal {L} _ {r e g} \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 215, + 717, + 468, + 733 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "At inference phase, we feed the same test input into three attention branches in a self-attention manner, deriving three class probabilities $p(c), p(a)$ , and $p(o)^1$ , where $c = (a, o)$ . Unlike most methods modeling single $p(c)$ for prediction, we compute our prediction score by synthesizing attribute, object and composition probabilities:", + "bbox": [ + 75, + 736, + 470, + 827 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {c} = \\underset {c \\in \\mathcal {C} _ {\\text {t e s t}}} {\\arg \\max } p (c) + \\beta \\cdot p (a) \\cdot p (o) \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 153, + 839, + 468, + 864 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We first fix $\\beta = 1.0$ during training and then validate $\\beta = 0.0, 0.1, \\dots, 1.0$ to choose the best $\\beta$ on the validation set. Finally, we compute the composition prediction as Eq. (15) with the chosen $\\beta$ , making the best prediction trade-off between generalized composition and independent concept.", + "bbox": [ + 496, + 90, + 893, + 167 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 500, + 179, + 633, + 195 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.1. Experimental details", + "text_level": 1, + "bbox": [ + 500, + 204, + 694, + 219 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets We use three benchmark datasets in CZSL problem, namely Clothing16K [50], UT-Zappos50K [49], and C-GQA [29]. Clothing16K [50] contains different types of clothing (e.g., shirt, pants) with color attributes (e.g., white, black). UT-Zappos50K [49] is a fine-grained dataset consisting of different kinds of shoes (e.g., sneakers, sandals) with texture attributes (e.g., leather, canvas). C-GQA [29] is a split built on top of Stanford GQA dataset [14], composed of extensive common attribute concepts (e.g., old, wet) and object concepts (e.g., dog, bus) in real life. We follow the common data splits of these three datasets (see Table 1).", + "bbox": [ + 496, + 226, + 893, + 393 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/94bae43b3d4ea57d4290bb7527b88dd5cc57f7752da637675869729bf663975c.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
DatasetsCompositionTrainValTest
|A||O||A| × |O||Cs||X||Cs| / |Cu||X||Cs| / |Cu||X|
Clothing16K [50]987218724210 / 1055159 / 83413
UT-Zappos50K [49]1612192832299815 / 15321418 / 182914
C-GQA [29]4136742783625592269201252 / 10407280888 / 9235098
", + "bbox": [ + 501, + 398, + 895, + 454 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 1. Summary of data split statistics.", + "bbox": [ + 573, + 455, + 815, + 468 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Open-world setting In addition to the standard closed-world setting, we also evaluate our model on the open-world setting [24], which is neglected by most previous works. The open-world setting considers all possible compositions, which requires a much larger testing space than the closed-world setting during inference. Taking UT-Zappos50K as an example (see Table 1), the closed world only considers 36 compositions in the testing set while the open world considers total 192 compositions, in which $\\sim 81\\%$ are ignored under the standard closed-world setting.", + "bbox": [ + 496, + 472, + 893, + 625 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Evaluation metrics Since CZSL models have an inherent bias for seen compositions, we follow the generalized CZSL evaluation protocol [36]. To overcome the negative bias for seen compositions, we apply different calibration terms to unseen compositions and compute the corresponding top-1 accuracy of seen and unseen compositions, where a larger bias makes higher unseen accuracy and lower seen accuracy, and vice versa. We treat seen accuracy as $x$ -axis and unseen accuracy as $y$ -axis to derive an unseen-seen accuracy curve. We can then compute the area under curve (AUC), the best harmonic mean, the best seen accuracy, and the best unseen accuracy from the curve. In our experiments, we report these four metrics for evaluation, among which AUC is the most representative and stable metric for measuring CZSL model performance. Note that the attribute accuracy or the object accuracy alone does not reflect CZSL performance, because the individual accuracy on attribute or object does not necessarily decide the accuracy of their composition.", + "bbox": [ + 496, + 628, + 893, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_footnote", + "text": "1Abbreviations for $p_{\\pi_c}(c|v_c),p_{\\pi_a}(a|v_a)$ , and $p_{\\pi_o}(o|v_o)$ , where $v_{c}$ $v_{a}$ , and $v_{o}$ are outputs from three self-attention.", + "bbox": [ + 76, + 875, + 470, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "15319", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/c594b8d84e62928d280c3b42a986bee93bee7b525f7127318fe56ad77c5f2be7.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Closed-world \nModelsClothing16KUT-Zappos50KC-GQA
AUCHMSeenUnseenAttrObjAUCHMSeenUnseenAttrObjAUCHMSeenUnseenAttrObj
SymNet [22]78.879.398.085.175.684.132.645.660.668.648.277.03.113.530.913.311.434.6
CompCos [24]90.387.298.596.890.291.831.848.158.863.845.572.42.912.830.712.210.433.9
GraphEmb [29]89.284.298.097.490.093.134.548.561.670.050.877.13.815.032.314.913.833.2
Co-CGE [25]88.387.998.594.787.491.430.844.660.962.646.073.53.614.731.614.312.634.6
SCEN [21]78.878.598.089.681.285.430.946.765.762.944.074.43.514.631.713.410.731.4
IVR [50]90.686.699.097.089.393.634.349.261.568.148.474.62.210.927.310.010.337.5
OADis [41]88.486.197.794.284.993.132.646.960.768.849.376.93.814.733.414.38.936.3
ADE (ours)92.488.798.297.790.293.635.151.163.064.346.374.05.218.035.017.716.832.3
", + "bbox": [ + 81, + 88, + 893, + 223 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/5412042f095b816a022ad4e4f14d1c5b240bd91e8b9ba8f28d9e0fcfa600d102.jpg", + "table_caption": [ + "Table 2. Closed-world results on three datasets. We report the area under curve (AUC), the best harmonic mean (HM), the best seen accuracy (Seen), the best unseen accuracy (Unseen), the attribute accuracy (Attr), and the object accuracy (Obj) of the unseen-seen accuracy curve under the closed world-setting. AUC is the core CZSL metric. All models use the same DINO ViT-B-16 backbone." + ], + "table_footnote": [], + "table_body": "
Open-world \nModelsClothing16KUT-Zappos50KC-GQA
AUCHMSeenUnseenAttrObjAUCHMSeenUnseenAttrObjAUCHMSeenUnseenAttrObj
SymNet [22]57.468.398.260.757.681.225.040.660.451.038.275.00.774.930.13.218.437.5
CompCos [24]64.170.898.269.871.783.720.736.058.146.036.471.10.724.332.82.815.137.8
GraphEmb [29]62.068.398.569.771.882.423.540.060.647.037.169.30.814.832.73.217.236.7
Co-CGE [25]59.369.298.763.868.576.222.040.357.743.433.967.20.483.331.12.115.535.7
SCEN [21]53.761.596.762.363.679.122.538.064.847.534.973.30.342.529.51.514.832.3
IVR [50]63.672.098.769.070.384.825.342.360.750.038.471.40.945.730.64.016.936.5
OADis [41]53.463.298.058.657.385.425.341.658.753.940.374.70.714.233.02.614.639.7
ADE (ours)68.074.299.073.175.084.527.144.862.450.739.971.41.427.635.14.822.435.6
", + "bbox": [ + 81, + 273, + 890, + 411 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 3. Open-world results on three datasets. Different from Table 2, open-world setting considers all possible compositions in testing.", + "bbox": [ + 83, + 412, + 883, + 426 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation details We use a frozen ViT-B-16 [6] backbone pretrained with DINO [3] on ImageNet [5] in a self-supervised manner as our visual feature extractor. The ViT-B-16 outputs contain 197 tokens (1 [CLS] and 196 patch tokens) of 768 dimensions. For three attention disentangler modules, we implement one-layer multi-head attention framework following [44], changing the single input to paired inputs for cross-attention. The embedders $\\pi_{a},\\pi_{c},\\pi_{o}$ are the two-layer MLPs following the previous works [24,50], projecting the 768-dimension visual features to 300-dimension word embedding space. The word embedding prototypes are initialized with word2vec [27] for all datasets and learnable during training. The composition function $\\psi$ is one linear layer. We train our model using Adam optimizer [18] with a learning rate of $5\\times 10^{-6}$ for UT-Zappos50K and Clothing16K, and $5\\times 10^{-5}$ for C-GQA. All models are trained with 128 batch size for 300 epochs.", + "bbox": [ + 75, + 436, + 472, + 694 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Comparison", + "text_level": 1, + "bbox": [ + 76, + 709, + 209, + 724 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To ensure a fair comparison and demonstrate that our improvement over baseline models is not merely by ViT, we adopt ViT backbone to state-of-the-art CZSL models and re-train all models. We compare our method with them: (1) OADis [41] disentangles attribute and object features from spatial convolutional maps; (2) SymNet [22] introduces the symmetry principle of attribute-object transformation and group theory as training objectives; (3) CompCos [24] extends CZSL to an open-world setting considering all possible compositions during inference, proposing a feasibility score based on data statistics to remove unfeasible compositions;", + "bbox": [ + 75, + 734, + 472, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "(4) GraphEmb [29] and Co-CGE [25] propose to use graph convolutional networks (GCN) to represent attribute-object relationships and compositions; (5) SCEN [21] projects visual features to a Siamese contrastive space to capture concept prototypes, and introduces complex state transition module to produce virtual compositions; (6) IVR [50] proposes to disentangle visual features into concept-invariant domains from a perspective of domain generalization, by masking specific channels of visual features.", + "bbox": [ + 496, + 436, + 893, + 573 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Closed-world evaluation In Table 2, we compare our ADE model with the state-of-the-art methods. ADE consistently outperforms others by a significant margin. ADE increases the core metric AUC by 1.8 on Clothing16K, 0.6 on UT-Zappos50K, and 1.4 on C-GQA ( $\\sim 37\\%$ relatively). Similarly, ADE increases the best harmonic mean (HM) by $0.8\\%$ on Clothing16K, $1.9\\%$ on UT-Zappos50K, and $3.0\\%$ on C-GQA. We notice that SymNet [22] and SCEN [21] perform badly on Clothing16K. The reason might be that not learning concept prototypes harms the word embedding expressivity on small-scale concepts. We also notice that IVR [50] performs very well on curated datasets Clothing16K and UT-Zappos50K but badly on larger-scale real-world dataset C-GQA. We hypothesize ideal concept-invariant domains might be difficult to learn from natural images and large-scale concepts of C-GQA. In contrast, our ADE model achieves state-of-the-art performance on all datasets.", + "bbox": [ + 496, + 578, + 895, + 835 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Open-world evaluation In Table 3, we consider the open-world setting to compare our ADE with other methods. Likewise, ADE also performs the best among all methods under open-world setting. ADE increases AUC by 3.9 on Cloth-", + "bbox": [ + 496, + 839, + 895, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "15320", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/018e52e761bcc7301087bc016150f60778f25bffb6a3ad0f924381b16da78d2c.jpg", + "table_caption": [], + "table_footnote": [ + "Table 4. Ablate the components in ADE on open-world UT-Zappos50K. CA, AA, and OA denote composition, attribute, and object attention. Reg denotes the regularization term. We test self- or cross-attention for AA and OA." + ], + "table_body": "
CAAAOARegAUCHMSeenUnseen
(0)✘✘✘✘23.841.159.048.9
(1)self✘✘✘25.342.361.149.9
(2)selfselfself✘26.744.661.949.8
(3)selfcrosscross✘26.944.563.448.7
(4)selfcrosscross✓27.144.862.450.7
", + "bbox": [ + 94, + 88, + 426, + 164 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ing16K, 1.8 on UT-Zappos50K, and 0.48 on C-GQA ( $\\sim 51\\%$ relatively). ADE also increases the best harmonic mean (HM) by $2.2\\%$ on Clothing16K, $2.5\\%$ on UT-Zappos50K, and $1.9\\%$ on C-GQA ( $\\sim 33\\%$ relatively). From the above results, ADE surpasses others by a larger margin on open-world AUC and HM than closed-world ones, indicating ADE maintains utmost efficiency when turning from the closed world to the open world. It is worth mentioning that ADE does not apply any special operations (e.g., feasibility masking [24]) for the open world and deals with the two settings in exactly the same way. IVR [50] keeps its performance to a great extent but still lags behind our method significantly.", + "bbox": [ + 75, + 233, + 472, + 416 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Ablation study", + "text_level": 1, + "bbox": [ + 76, + 428, + 227, + 444 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "**Backbone:** ResNet vs ViT Our work leverages ViT as the default backbone to excavate more high-level sub-space information, while ResNet18 is the most common backbone in previous works. In Table 6, we compare our ADE to OADis [41] with both backbones. Our ADE performs similarly to OADis with ResNet18, but outperforms it significantly with ViT. Additionally, we present an ablation study on different components of our method with the ResNet18 backbone in the Appendix. These experiments indicate that our model benefits from ViT and all components of our method are effective regardless of the backbone.", + "bbox": [ + 75, + 453, + 470, + 619 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/9db4d4725be8759c192483283da493c4e40648ac463a5bbadbb65612ecc05a52.jpg", + "table_caption": [], + "table_footnote": [ + "Table 6. Compare ADE and OADis [41] with ResNet18 and ViT." + ], + "table_body": "
Closed-worldClothing16KUT-Zappos50KC-GQA
BackboneModelsAUCHMAUCHMAUCHM
ResNet18OADis [41]85.584.730.044.43.113.6
ADE (ours)87.285.129.547.03.113.7
ViT-B-16OADis [41]88.486.132.646.93.814.7
ADE (ours)92.488.735.151.15.218.0
", + "bbox": [ + 81, + 628, + 467, + 719 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Different parts of ADE We evaluate the effectiveness of attention disentanglers (composition, attribute, and object attention) and the regularization term in our model. We report the ablation study results on the open-world UT-Zappos50K in Table 4. Rows (0)-(2) show attention disentanglers can significantly improve the performance. Rows (2)-(3) show that cross-attention learns disentangled concepts better than self-attention for AA and OA. Rows (3)-(4) show the regularization term can further benefit the visual disentanglement, improving the unseen accuracy and overall AUC.", + "bbox": [ + 75, + 750, + 472, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/78c1a9361bb32d441453c48a16c84f617d62aa09813dd71b4099cd219eb22b6a.jpg", + "table_caption": [], + "table_footnote": [ + "Table 5. Results on closed-world Clothing16K and C-GQA using different inference formulations. Rows (0)-(2) respectively represents the cases when $\\beta = 0.0$ , $\\beta = +\\infty$ , and $\\beta = 1.0$ . Row (3) is our inference formulation, which applies an $\\beta$ optimized on the validation set." + ], + "table_body": "
Inference formulationC-GQAClothing16K
AUCHMSeenUnseenAUCHMSeenUnseen
(0)p(c)4.616.835.116.092.488.898.297.7
(1)p(a) · p(o)4.015.831.415.157.366.396.763.1
(2)p(c) + p(a) · p(o)5.218.035.017.790.485.998.297.0
(3)p(c) + β · p(a) · p(o)5.218.035.017.792.488.798.297.7
", + "bbox": [ + 450, + 88, + 893, + 165 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Inference formulation We also investigate the effect of our inference formulation $p(c) + \\beta \\cdot p(a) \\cdot p(o)$ in Table 5. We report the results with extreme values of $\\beta$ , i.e., $\\beta = 0.0$ and $\\beta = 1.0$ . Note that $\\beta = 0.0$ means only using composition probability for prediction. In addition, we also test the performance only using the product of attribute and object probabilities $p(a) \\cdot p(o)$ . We can observe that the best fixed $\\beta$ value is unfixed among datasets. For example, $\\beta = 1.0$ gives the highest AUC for C-GQA in row (2) while $\\beta = 0.0$ for Clothing16K in row (0). In contrast, our validated $\\beta$ consistently gives the best inference results for both datasets. Another observation on C-GQA is that $p(a) \\cdot p(o)$ alone is not a good prediction, but adding it to $p(c)$ can increase the unseen accuracy. This indicates that the disentangled attribute prediction $p(a)$ and object prediction $p(o)$ indeed enhance the unseen generalization for CZSL problem.", + "bbox": [ + 496, + 233, + 893, + 476 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effect of regularization term We propose an EMD-adapted regularization term at the attention level to force attentions to disentangle the concept of interest. We also investigate the effect of applying the regularization term at the feature level. Specifically, we compare our EMD-based distance to the cosine and euclidean feature distances. The results on open-world UT-Zappos50K are shown in Table 7. Our EMD-based regularization outperforms other distance forms, because our attention-level EMD distance considers token-wise similarity capturing the specific concept-related attention responses.", + "bbox": [ + 496, + 481, + 893, + 648 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/74388ef1d9b10e21eb00214d2d75b8ad8fdee2f7a319c8fa1363d88f4b0359b3.jpg", + "table_caption": [], + "table_footnote": [ + "Table 7. Comparison of different regularization terms on openworld UT-Zappos50K." + ], + "table_body": "
RegAUCHMSeenUnseen
Cosine26.844.763.048.6
Euclidean26.244.362.647.5
Ours (EMD)27.144.862.450.7
", + "bbox": [ + 501, + 655, + 893, + 710 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.4. Qualitative analysis", + "text_level": 1, + "bbox": [ + 500, + 756, + 687, + 772 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Visual disentanglement in feature space is hard to visualize [41]. Inspired by previous work attempts [22, 30, 41, 50], we conduct qualitative analysis of image and text retrieval to show how our ADE model correlates the visual image and the concept composition. In addition, to further validate ADE is efficient to disentangle visual concepts, we conduct unseen-to-seen image retrieval based on their visual concept features extracted by attribute and object attentions.", + "bbox": [ + 496, + 779, + 893, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "15321", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4d72df6e1f4a47e99d5df5ac13faaa7c3a585f4b090f6820485cda51e71b8f01.jpg", + "image_caption": [ + "(a) Top-5 text-to-image retrieval." + ], + "image_footnote": [], + "bbox": [ + 89, + 97, + 331, + 212 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/96596a991f61678d701a70e4ccdb6daabee77ef6c03437aaf90739c3629d1c59.jpg", + "image_caption": [ + "(b) Top-5 image-to-text retrieval.", + "Figure 5. Qualitative analysis. (a) In the last row of \"suede sandals\", the wrong image (red box) is \"fake leather sandals\". (b) Each image has the ground-truth label (black text) and 5 retrieval results (colored text), in which the green text is the correct prediction. (c) We retrieve images sharing the same visual concepts by their visual concept features for unseen images of \"yellow skirt\" and \"pink pants\"." + ], + "image_footnote": [], + "bbox": [ + 344, + 98, + 627, + 213 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/43b9d3534ddefb34936bfe0e861b4f47e999213971b126ae3077f7589946977c.jpg", + "image_caption": [ + "(c) Top-5 visual concept retrieval." + ], + "image_footnote": [], + "bbox": [ + 645, + 95, + 875, + 213 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Image and text retrieval We first consider text-to-image retrieval. Given a text composition, e.g., \"leather heels\", we embed it and retrieve the top-5 closest visual features based on the feature distance. We display four text compositions of the different objects sharing the same attributes and vice versa in Fig. 5a. We can observe that the retrieved images are correct in most of the cases. One exception is when retrieving \"suede sandals\", the third closest image is \"fake leather sandals\". Although \"suede sandals\" and \"fake leather sandals\" are not the same composition, they are quite visually similar. We then consider image-to-text retrieval, shown in Fig. 5b. Given an image, e.g., the image of a \"brown zebra\", we extract its visual feature and retrieve the top-5 closest text composition embeddings. It is difficult to retrieve the ground-truth label in the top-1 closest text composition, but all top-5 results are all semantically related to the image. We take the image of \"blond person\" (row 3, col 2) as an example. Although the text composition \"blond person\" is not retrieved in the top-5 matches, the retrieved results \"white shirts\", \"white outfit\", \"white shorts\", \"white pants\", and \"young girl\" are all reasonable and actually present in the image. Image and text retrieval experiments validate that our ADE efficiently projects visual features and word embeddings into a uniform space.", + "bbox": [ + 75, + 277, + 472, + 641 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Visual concept retrieval Because the attribute and the object are visually coupled in an image to a high degree of entanglement, it is challenging to visualize the disentanglement in feature space [41]. Saini et al. [41] retrieve single attribute or object text from test images. However, this process is the same as multi-label classification and insufficient to validate that disentangled visual concepts are learned from images. Based on the disentanglement ability of ADE, we construct a visual concept retrieval experiment to investigate the distances between visual concept features, i.e., the embedded attribute feature $\\pi_{a}(v_{a})$ and the embedded object feature $\\pi_{o}(v_{o})$ , extracted from different images. Prior to our work, no existing models can do so, because none of them extracts concept-exclusive features like ADE. The results are shown in Fig. 5c. We first extract attribute features and object features from all seen images. Given an unseen image, we retrieve the top-5 closest images by measuring the feature", + "bbox": [ + 75, + 643, + 472, + 901 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "distance between the attribute feature of the given image and that of all seen images, and the same goes for the object feature. For the image of \"yellow skirt\", all retrieval results for the visual concept \"yellow\" are all \"yellow [OBJ]\", and all retrieval results for \"skirt\" are \"[ATTR] skirt\". For the \"pink pants\" image, our model also perfectly retrieves the visual concepts, i.e., the attribute \"pink\" and the object \"pants\". Our experimental results demonstrate that our ADE model is effective to disentangle visual concepts from seen compositions and combine learned concept knowledge into unseen compositions.", + "bbox": [ + 496, + 277, + 893, + 445 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 454, + 617, + 469 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we tackle the problem of compositional zero-shot learning (CZSL). To disentangle visual concepts from the attribute-object composition, we propose ADE adopting cross-attentions to learn the individual concept from paired concept-sharing images. To constrain the disentanglers to learn the concept of interest, we employ a regularization term adapted from the earth mover's distance (EMD), which is used as a feature similarity metric in the cross-attention module. Moreover, to exploit the attribute and object prediction ability of ADE, we improve the inference process by combining attribute, object, and composition probabilities into the final prediction score. We empirically demonstrate ADE outperforms the current state-of-the-art methods under both closed- and open-world settings. We also conduct a comprehensive qualitative analysis to validate the disentanglement ability of attention disentanglers in ADE.", + "bbox": [ + 496, + 479, + 893, + 720 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitations Like existing CZSL methods, it is time- and computation-consuming to derive all composition embeddings when the numbers of attributes and objects are large. Moreover, it remains an open challenge to exploit concepts based on the actual semantics rather than solely on text; for instance, the \"open\" attribute in \"open curtain\" and \"open computer\" has completely different meanings.", + "bbox": [ + 496, + 727, + 893, + 834 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements This work is partially supported by Hong Kong Research Grant Council - Early Career Scheme (Grant No. 27208022) and HKU Seed Fund for Basic Research.", + "bbox": [ + 496, + 839, + 893, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "15322", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Jean-Baptiste Alayrac, Ivan Laptev, Josef Sivic, and Simon Lacoste-Julien. 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In ECCV, 2022. 1, 2, 3, 5, 6, 7" + ], + "bbox": [ + 78, + 90, + 470, + 715 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "15324", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Learning Attention As Disentangler for Compositional Zero-Shot Learning/a88cae1a-24ee-4f75-ab78-cc4922b86fa8_model.json b/2023/Learning Attention As Disentangler for Compositional Zero-Shot Learning/a88cae1a-24ee-4f75-ab78-cc4922b86fa8_model.json new file mode 100644 index 0000000000000000000000000000000000000000..09a823a43b18d914b7835fd3e21ddac728a06057 --- /dev/null +++ b/2023/Learning Attention As Disentangler for Compositional Zero-Shot Learning/a88cae1a-24ee-4f75-ab78-cc4922b86fa8_model.json @@ -0,0 +1,2079 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.111, + 0.131, + 0.859, + 0.154 + ], + "angle": 0, + "content": "Learning Attention as Disentangler for Compositional Zero-shot Learning" + }, + { + "type": "text", + "bbox": [ + 0.275, + 0.181, + 0.696, + 0.218 + ], + "angle": 0, + "content": "Shaozhe Hao Kai Han* Kwan-Yee K. Wong \nThe University of Hong Kong" + }, + { + "type": "text", + "bbox": [ + 0.288, + 0.22, + 0.678, + 0.234 + ], + "angle": 0, + "content": "{szhao, kykwong}@cs.hku.hk kaihanx@hku.hk" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.269, + 0.314, + 0.285 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.074, + 0.302, + 0.474, + 0.635 + ], + "angle": 0, + "content": "Compositional zero-shot learning (CZSL) aims at learning visual concepts (i.e., attributes and objects) from seen compositions and combining concept knowledge into unseen compositions. The key to CZSL is learning the disentanglement of the attribute-object composition. To this end, we propose to exploit cross-attention as compositional disentanglers to learn disentangled concept embeddings. For example, if we want to recognize an unseen composition \"yellow flower\", we can learn the attribute concept \"yellow\" and object concept \"flower\" from different yellow objects and different flowers respectively. To further constrain the disentanglers to learn the concept of interest, we employ a regularization at the attention level. Specifically, we adapt the earth mover's distance (EMD) as a feature similarity metric in the cross-attention module. Moreover, benefiting from concept disentanglement, we improve the inference process and tune the prediction score by combining multiple concept probabilities. Comprehensive experiments on three CZSL benchmark datasets demonstrate that our method significantly outperforms previous works in both closed- and open-world settings, establishing a new state-of-the-art. Project page: https://haoosz.github.io/ade-czsl/" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.666, + 0.208, + 0.682 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.693, + 0.471, + 0.875 + ], + "angle": 0, + "content": "Suppose we have never seen white bears (i.e., polar bears) before. Can we picture what it would look like? This is not difficult because we have seen many white animals in daily life (e.g., white dogs and white rabbits) and different bears with various visual attributes in the zoo (e.g., brown bears and black bears). Humans have no difficulty in disentangling \"white\" and \"bear\" from seen instances and combining them into the unseen composition. Inspired by this property of human intelligence, researchers attempt to make machines learn compositions of concepts as well. Compositional zero-shot learning (CZSL) is a specific problem studying visual compositionality, aiming to learn visual concepts from seen" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.269, + 0.891, + 0.457 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.46, + 0.895, + 0.545 + ], + "angle": 0, + "content": "Figure 1. Motivation illustration. Given images from seen attribute-object compositions, human can disentangle the attribute \"yellow\" from \"yellow bird\" and \"yellow pear\", and the object \"flower\" from \"purple flower\" and \"red flower\". After learning visual properties of the concepts \"yellow\" and \"flower\", human can then recognize images from the unseen composition \"yellow flower\"." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.553, + 0.893, + 0.583 + ], + "angle": 0, + "content": "compositions of attributes and objects and generalize concept knowledge to unseen compositions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.584, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Learning attribute-object compositions demands prior knowledge about attributes and objects. However, visual concepts of attributes and objects never appear alone in a natural image. To learn exclusive concepts for compositionality learning, we need to disentangle the attribute concept and the object concept. As illustrated in Fig. 1, if we want to recognize the image of \"yellow flower\", it is necessary to learn the \"yellow\" concept and the \"flower\" concept, i.e., disentangle visual concepts, from images of seen compositions. Previous works [22, 24, 25, 28-30, 36, 46] tackle CZSL by composing attribute and object word embeddings, and projecting word and visual embeddings to a joint space. They fail to disentangle visual concepts. Recently, some works [21, 40, 41, 50] consider visual disentanglement but still have limitations despite their good performance. SCEN [21] learns concept-constant samples contrastively without constructing concept embedding prototypes to avoid learning irrelevant concepts shared by positive samples. IVR [50] disentangles visual features into ideal concept-invariant domains. This ideal domain generalization setting requires a small discrepancy of attribute and object sets and would degenerate on vaster and more" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.888, + 0.221, + 0.9 + ], + "angle": 0, + "content": "*Corresponding author" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15315" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.228 + ], + "angle": 0, + "content": "complex concepts. ProtoProp [40] and OADis [41] learn local attribute and object prototypes from spatial features on convolutional feature maps. However, spatial disentanglement is sometimes infeasible because attribute and object concepts are highly entangled in spatial features. Taking an image of \"yellow flower\" as an example, the spatial positions related to the attribute \"yellow\" and the object \"flower\" completely overlap, which hinders effective attribute-object disentanglement." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.228, + 0.473, + 0.756 + ], + "angle": 0, + "content": "To overcome the above limitations, we propose a simple visual disentangling framework exploiting Attention as DisEntangler (ADE) on top of vision transformers [6]. We notice that vision transformers (ViT) have access to more sub-space global information across multi-head attentions than CNNs [38]. Therefore, with the expressivity of different subspace representations, token attentions of ViT may provide a more effective way for disentangling visual features, compared to using traditional spatial attentions across local positions on convolutional features [40, 41]. Specifically, it is difficult to disentangle the attribute-object composition \"yellow flower\" by spatial positions, but it is possible for ViT multi-head attentions to project attribute concept \"yellow\" and object concept \"flower\" onto different subspaces. Inspired by this property, we propose to learn cross-attention between two inputs that share the same concept, e.g., \"yellow bird\" and \"yellow pear\" share the same attribute concept \"yellow\". In this way, we can derive attribute- and object-exclusive visual representations by cross-attention disentanglement. To ensure that the concept disentangler is exclusive to the specific concept, we also need to constrain the disentanglers to learn the concept of interest instead of the other concept. For example, given attribute-sharing images, the attribute attention should output similar attribute-exclusive features while the object attention should not. To achieve this goal, we apply a regularization term adapted from the earth mover's distance (EMD) [13] at the attention level. This regularization term forces cross-attention to learn the concept of interest by leveraging the feature similarity captured from all tokens. Mancini et al. [24] propose an open-world evaluation setting, which is neglected by most previous works. We consider both closed-world and the open-world settings in our experiments, demonstrating that our method is coherently efficient in both settings. The contributions of this paper are summarized below:" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.758, + 0.472, + 0.803 + ], + "angle": 0, + "content": "- We propose a new CZSL approach, named ADE, using cross-attentions to disentangle attribute- and object-exclusive features from paired concept-sharing inputs." + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.806, + 0.472, + 0.851 + ], + "angle": 0, + "content": "- We force attention disentanglers to learn the concept of interest with a regularization term adapted from EMD, ensuring valid attribute-object disentanglement." + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.853, + 0.472, + 0.898 + ], + "angle": 0, + "content": "- We comprehensively evaluate our method in both closed-world and open-world settings on three CZSL datasets, achieving consistent state-of-the-art." + }, + { + "type": "list", + "bbox": [ + 0.088, + 0.758, + 0.472, + 0.898 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.09, + 0.638, + 0.106 + ], + "angle": 0, + "content": "2. Related work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.116, + 0.895, + 0.342 + ], + "angle": 0, + "content": "Visual attribute has been widely studied to understand how visual properties can be learned from objects. The pioneering work by Ferrari and Zisserman [10] learned visual attributes using a probabilistic generative model. The successive work by Lampert et al. [20] used visual attributes to detect unseen objects with an attribute-based multi-label classification. Similarly, Patterson et al. [35] proposed Economic Labeling Algorithm (ELA) to discover multi-label attributes for objects. Different from multi-label classification, other works [4,8,15,23] learned attribute-object relationship to generalize attribute feature across all object categories based on probabilistic models. Visual attributes also benefit downstream tasks, e.g., object recognition [7, 16, 31], action recognition [1,9,26], image captioning [19,33], and semi-supervised learning [42]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.342, + 0.897, + 0.794 + ], + "angle": 0, + "content": "Compositional zero-shot learning (CZSL) is a special case of zero-shot learning (ZSL) [34, 39, 43, 47, 48], aims at recognizing unseen attribute-object compositions learning from seen compositions. Misra et al. [28] first termed and studied CZSL by projecting composed primitives and visual features to a joint embedding space. Nagarajan et al. [30] formulated attributes as matrix operators applied on object vectors. Purushwalkam et al. [36] introduced a task-driven modular architecture to learn unseen compositions by re-weighting a set of sub-tasks. Wei et al. [46] generated attribute-object compositions with GAN [11] to match visual features. Li et al. [22] proposed symmetry principle of attribute-object transformation under the supervision of group axioms. Naeem et al. [29] and Mancini et al. [25] used graph convolutional networks to extract attribute-object representations. Recently, some works shift their interest from word composing to visual disentanglement. Atzmon et al. [2] solved CZSL from a causal perspective to learn disentangled representations. Ruis et al. [40] proposed to learn prototypical representations of objects and attributes. Li et al. [21] disentangled visual features into a Siamese contrastive space and entangled them with a generative model. Saini et al. [41] extracted visual similarity from spatial features to disentangle attributes and objects. Zhang et al. [50] treated CZSL as a domain generalization task, learning attribute- and object-invariant domains. A more realistic open-world CZSL setting was studied in [17, 24, 25], which considered all possible compositions in testing. Very recently, an inspiring work by Nayak et al. [32] introduced compositional soft prompts to CLIP [37] to tackle CZSL problem." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Attention mechanism has been well studied by non-local neural networks [45] in computer vision and transformers [44] in machine translation. Dosovitskiy et al. [6] adapted transformer architecture to computer vision field, proving its comparable efficiency over traditional CNNs. Inspired by the multi-head self-attention implemented by transformers, our work exploits efficient attention as disentangler for CZSL." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "15316" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.089, + 0.089, + 0.699, + 0.297 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.715, + 0.102, + 0.868, + 0.292 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.301, + 0.895, + 0.4 + ], + "angle": 0, + "content": "Figure 2. Method overview. Left (our framework ADE): Given one target image of \"red bus\", we sample two auxiliary images of the same attribute \"red wall\" and of the same object \"blue bus\". We feed the three images into a frozen ViT initialized with DINO [3]. We then input all encoded tokens (i.e., [CLS] and patch tokens) to three attention modules: (1) attribute cross-attention taking paired attribute-sharing tokens as inputs; (2) object cross-attention taking paired object-sharing tokens as inputs; (3) composition self-attention taking tokens of single target image as input. We then project the [CLS] tokens of attention outputs with three MLP embeddings \\(\\pi_{a}\\), \\(\\pi_{c}\\), and \\(\\pi_{o}\\). We finally compute cross entropy losses of embedded visual features with three learnable word embeddings: attribute embeddings, object embeddings, and their linear fused composition embeddings. Right: Illustration of five losses in attribute, object, and composition embedding spaces." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.409, + 0.204, + 0.426 + ], + "angle": 0, + "content": "3. Preliminary" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.431, + 0.474, + 0.674 + ], + "angle": 0, + "content": "Compositional zero-shot learning aims at learning a model from limited compositions of attributes (e.g., yellow) and objects (e.g., flower) to recognize an image from novel compositions. Given a set of all possible attributes \\(\\mathcal{A} = \\{a_0, a_1, \\dots, a_n\\}\\) and a set of all possible objects \\(\\mathcal{O} = \\{o_0, o_1, \\dots, o_m\\}\\), a compositional class set \\(\\mathcal{C} = \\mathcal{A} \\times \\mathcal{O}\\) includes all attribute-object compositions. We divide \\(\\mathcal{C}\\) into two disjoint sets, namely the set of seen classes \\(\\mathcal{C}_s\\) and the set of unseen classes \\(\\mathcal{C}_u\\), where \\(\\mathcal{C}_s \\cap \\mathcal{C}_u = \\emptyset\\) and \\(\\mathcal{C}_s \\cup \\mathcal{C}_u = \\mathcal{C}\\). Training images are only from classes in \\(\\mathcal{C}_s\\) and testing images are from classes in \\(\\mathcal{C}_{test} = \\mathcal{C}_s \\cup \\mathcal{C}_u'\\). For closed-world evaluation, \\(\\mathcal{C}_u'\\) is a predefined subset of \\(\\mathcal{C}_u\\), i.e., \\(\\mathcal{C}_u' \\subset \\mathcal{C}_u\\). For open-world evaluation, all possible compositions are considered for testing, i.e., \\(\\mathcal{C}_u' = \\mathcal{C}_u\\). CZSL task aims to learn a model \\(f: \\mathcal{X} \\to \\mathcal{C}_{test}\\) to predict labels in the testing composition set \\(c \\in \\mathcal{C}_{test}\\) for input images \\(x \\in \\mathcal{X}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.674, + 0.472, + 0.735 + ], + "angle": 0, + "content": "To learn a CZSL model, a common method is to minimize the cosine similarity score between the visually encoded feature and the word embedding of attribute-object compositions. The similarity score can be expressed as" + }, + { + "type": "equation", + "bbox": [ + 0.155, + 0.737, + 0.47, + 0.77 + ], + "angle": 0, + "content": "\\[\ns (x, (a, o)) = \\frac {\\phi (x)}{| | \\phi (x) | |} \\cdot \\frac {\\psi (a , o)}{| | \\psi (a , o) | |} \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.771, + 0.473, + 0.802 + ], + "angle": 0, + "content": "where \\(\\phi (\\cdot)\\) is the visual encoder, and \\(\\psi (\\cdot ,\\cdot)\\) is the composition function. The CZSL model \\(f\\) can be formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.141, + 0.82, + 0.47, + 0.847 + ], + "angle": 0, + "content": "\\[\nf (x; \\theta_ {\\phi}, \\theta_ {\\psi}) = \\underset {a _ {i} \\in \\mathcal {A}, o _ {j} \\in \\mathcal {O}} {\\arg \\max } s (x, \\left(a _ {i}, o _ {j}\\right)) \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.473, + 0.902 + ], + "angle": 0, + "content": "The model \\(f\\) is optimized by learning the model parameters \\(\\theta_{\\phi}\\) and \\(\\theta_{\\psi}\\) to match the input \\(x\\) with the most similar attribute-object composition. Visual encoder \\(\\phi\\) and composition func" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.41, + 0.896, + 0.547 + ], + "angle": 0, + "content": "tion \\(\\psi\\), as two core components, take multiple forms in different methods. For visual encoder, works [40, 41, 50] manually design networks on top of a pretrained backbone (e.g., ResNet18 [12]) to disentangle attribute and object embeddings for visual features. For composition functions, the object conditioned network [41], the graph embedding [29, 40], and the linear projector [24, 50] are commonly used. Unlike employing complex composition functions, we adopt the simple linear projector in our method." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.56, + 0.644, + 0.577 + ], + "angle": 0, + "content": "4. Our approach" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.585, + 0.895, + 0.737 + ], + "angle": 0, + "content": "We aim to disentangle attribute and object features for visual representation by learning from image pairs sharing the same attributes or objects. For example, by learning the object \"flower\" from the \"purple flower\" and the \"red flower\" and learning the attribute \"yellow\" from the \"yellow bird\" and the \"yellow pear\", we can infer what a \"yellow flower\" looks like. To this end, we propose ADE to learn cross-attentions as concept disentanglers with the regularization of a novel token earth mover's distance. The whole framework of our method is shown in Fig. 2." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.746, + 0.822, + 0.763 + ], + "angle": 0, + "content": "4.1. Disentanglement with cross-attention" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.769, + 0.893, + 0.86 + ], + "angle": 0, + "content": "Multi-head self-attention in transformers [44] is powerful for extracting token connections. Attention maps each query token, and key-value token pairs to an output token. Every output token is a weighted sum of the values, where the weights is the similarity of the corresponding query token and the key tokens. The attention is formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.548, + 0.87, + 0.893, + 0.906 + ], + "angle": 0, + "content": "\\[\n\\operatorname {A t t e n t i o n} (Q, K, V) = \\operatorname {s o f t m a x} \\left(\\frac {Q K ^ {T}}{\\sqrt {d _ {k}}}\\right) V \\tag {3}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15317" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.08, + 0.089, + 0.468, + 0.17 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.131, + 0.173, + 0.414, + 0.186 + ], + "angle": 0, + "content": "Figure 3. Illustration of three types of attention." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.2, + 0.47, + 0.322 + ], + "angle": 0, + "content": "where three inputs are query tokens \\((Q)\\), key tokens \\((K)\\), and value tokens \\((V)\\) and the scaling factor \\(d_{k}\\) is the dimension of the query and key. Self-attention uses the same input for \\(Q\\), \\(K\\), \\(V\\) and effectively captures relationships among [CLS] and patch tokens of a single input image. Normally, the [CLS] token is exclusively used as a global representation of the input image for downstream tasks, but exclusive [CLS] token highly entangles attribute and object concepts." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.322, + 0.471, + 0.595 + ], + "angle": 0, + "content": "For CZSL task, we want to disentangle the exclusive concept by exploiting the semantic similarity between tokens from different concept-sharing features. For this purpose, we introduce a cross-attention mechanism to extract attribute-exclusive or object-exclusive features for paired images sharing the same attribute or object concept. The cross-attention has the same structure as the self-attention, but works on different inputs. Self-attention uses the same input \\( I \\) for \\( Q \\), \\( K \\), \\( V \\) (i.e., \\( Q = K = V = I \\)) while cross-attention uses one of the paired inputs \\( I \\) for the query and the other \\( I' \\) for the key and the value (i.e., \\( Q = I \\), \\( K = V = I' \\)). In the cross-attention, the query input and the key input play different roles. The cross-attention output is the weighted sum of the value (also the key) input based on the similarity between the query and key inputs. For a pair of input images, we swap the query and key inputs in computing cross-attention to derive two cross-attended outputs for the respective inputs. Cross-attention with query-key swapping (QKS) is illustrated in Fig. 3." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.596, + 0.47, + 0.732 + ], + "angle": 0, + "content": "The cross-attention outputs paired features of the exclusive concept with paired concept-sharing inputs. Taking the object-sharing pair as an example, object cross-attention leverages the shared object features of the key input to enhance the query input, thus making the outputs exclusive to object feature space, i.e., object-exclusive features \\( v_{o} \\) and \\( v_{o}' \\). The same applies to attribute-exclusive features \\( v_{a} \\) and \\( v_{a}' \\) extracted from paired attribute-sharing images. We also use a standard self-attention to extract composition feature \\( v_{c} \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.733, + 0.47, + 0.868 + ], + "angle": 0, + "content": "To train cross-attentions, we adopt common cross entropy loss after MLP embedders \\((\\pi_{a},\\pi_{c},\\pi_{o})\\) for attribute-exclusive features \\((v_{a},v_{a}^{\\prime})\\), object-exclusive features \\((v_{o},v_{o}^{\\prime})\\), and composition feature \\((v_{c})\\). We denote any of these visual features as \\(v\\) and the corresponding embedder as \\(\\pi\\). We denote the word embedding as \\(w_{z}\\), where the concept \\(z\\in \\mathcal{Z}\\) can be any of the attribute \\(a\\in \\mathcal{A}\\), the object \\(o\\in \\mathcal{O}\\), or the composition \\(c\\in \\mathcal{C}\\). The class probability of L2-normalized \\(\\pi (v)\\) and \\(w_{z}\\) can be computed as:" + }, + { + "type": "equation", + "bbox": [ + 0.119, + 0.871, + 0.47, + 0.905 + ], + "angle": 0, + "content": "\\[\np _ {\\pi} (z \\mid v) = \\frac {\\exp (\\pi (v) \\cdot w _ {z} / \\tau)}{\\sum_ {\\hat {z} \\in \\mathcal {Z}} \\exp (\\pi (v) \\cdot w _ {\\hat {z}} / \\tau)}, z \\in \\mathcal {Z} \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.894, + 0.122 + ], + "angle": 0, + "content": "where \\(\\tau\\) is the temperature. We then compute the cross entropy to classify visual features:" + }, + { + "type": "equation", + "bbox": [ + 0.58, + 0.125, + 0.892, + 0.141 + ], + "angle": 0, + "content": "\\[\nH _ {\\pi} (v, z) = - \\log p _ {\\pi} (z \\mid v), z \\in \\mathcal {Z} \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.144, + 0.894, + 0.205 + ], + "angle": 0, + "content": "Considering different classification objectives of attribute, object, and composition, the general Eq. (5) can be applied to five visual features, i.e., \\( v_{a}, v_{a}^{\\prime}, v_{o}, v_{o}^{\\prime}, v_{c} \\). Therefore, the training objective is composed of five cross entropy losses:" + }, + { + "type": "equation", + "bbox": [ + 0.536, + 0.219, + 0.854, + 0.256 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {c e} = \\underbrace {H _ {\\pi_ {a}} (v _ {a} , a)} _ {\\mathcal {L} _ {a t t r}} + \\underbrace {H _ {\\pi_ {a}} (v _ {a} ^ {\\prime} , a)} _ {\\mathcal {L} _ {a t t r} ^ {\\prime}} + \\underbrace {H _ {\\pi_ {c}} (v _ {c} , c)} _ {\\mathcal {L} _ {c o m}} +\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.582, + 0.259, + 0.892, + 0.299 + ], + "angle": 0, + "content": "\\[\n\\underbrace {H _ {\\pi_ {o}} \\left(v _ {o} , o\\right)} _ {\\mathcal {L} _ {o b j}} + \\underbrace {H _ {\\pi_ {o}} \\left(v _ {o} ^ {\\prime} , o\\right)} _ {\\mathcal {L} _ {o b j} ^ {\\prime}} \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.311, + 0.892, + 0.342 + ], + "angle": 0, + "content": "where the attribute label \\(a\\in \\mathcal{A}\\) , the object label \\(o\\in \\mathcal{O}\\) , and the composition label \\(c = (a,o)\\in \\mathcal{C}_{test}\\)" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.353, + 0.885, + 0.369 + ], + "angle": 0, + "content": "4.2. Disentangling constraint at the attention level" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.377, + 0.894, + 0.558 + ], + "angle": 0, + "content": "So far, we have enabled cross-attentions to disentangle concepts, but we want to further ensure that the attribute and the object disentanglers learn the corresponding attribute and object concepts instead of the opposite concepts. To this end, we introduce an attention-level earth mover's distance (EMD) to constrain disentanglers to learn the concept of interest. The EMD is formulated as an optimal transportation problem in [13]. Suppose we have supplies of \\( n_s \\) sources \\( S = \\{s_i\\}_{i=1}^{n_s} \\) and demands of \\( n_d \\) destinations \\( D = \\{d_j\\}_{j=1}^{n_d} \\). Given the moving cost from the \\( i \\)-th source to the \\( j \\)-th destination \\( c_{ij} \\), an optimal transportation problem aims to find the minimal-cost flow \\( f_{ij} \\) from sources to destinations:" + }, + { + "type": "equation", + "bbox": [ + 0.537, + 0.571, + 0.892, + 0.6 + ], + "angle": 0, + "content": "\\[\n\\underset {f _ {i j}} {\\text {m i n i m i z e}} \\quad \\sum_ {i = 1} ^ {n _ {s}} \\sum_ {j = 1} ^ {n _ {d}} c _ {i j} f _ {i j} \\tag {7}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.537, + 0.604, + 0.892, + 0.62 + ], + "angle": 0, + "content": "\\[\n\\text {s u b j e c t} f _ {i j} \\geqslant 0, i = 1, \\dots , n _ {s}, j = 1, \\dots , n _ {d} \\tag {8}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.619, + 0.623, + 0.892, + 0.649 + ], + "angle": 0, + "content": "\\[\n\\sum_ {j = 1} ^ {n _ {d}} f _ {i j} = s _ {i}, i = 1, \\dots , n _ {s} \\tag {9}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.619, + 0.651, + 0.892, + 0.676 + ], + "angle": 0, + "content": "\\[\n\\sum_ {i = 1} ^ {n _ {s}} f _ {i j} = d _ {j}, j = 1, \\dots , n _ {d} \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.69, + 0.891, + 0.735 + ], + "angle": 0, + "content": "where the optimal flow \\(\\tilde{f}_{ij}\\) is computed by the moving cost \\(c_{ij}\\), the supplies \\(s_i\\), and the demands \\(d_j\\). The EMD can be further formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.585, + 0.749, + 0.892, + 0.767 + ], + "angle": 0, + "content": "\\[\n\\operatorname {E M D} \\left(c _ {i j}, s _ {i}, d _ {j}\\right) = \\left(1 - c _ {i j}\\right) \\tilde {f} _ {i j}. \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.901 + ], + "angle": 0, + "content": "When the EMD is greater, the distributions \\( S \\) and \\( \\mathcal{D} \\) are closer. In Fig. 4, we show how to use the EMD as a feature similarity metric at the attention level in our cross-attention module. We can derive a cross-attention map from Eq. (3) and the counterpart cross-attention map after query-key swapping. We use the logits of [CLS]-to-patch attentions as supplies \\( s_i \\) and demands \\( d_j \\), which represent how similar the global feature of one image is to the local patches of the" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15318" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.09, + 0.466, + 0.281 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.283, + 0.473, + 0.382 + ], + "angle": 0, + "content": "Figure 4. Illustration of the adapted EMD at the attention level. Branches 1 and 2 respectively denote using one of the paired inputs as the query \\( Q \\). We compute the EMD with two attention maps from 1 and 2 branches. We use the [CLS] -to-patch logits as the supplies \\( s_i \\) and the demands \\( d_j \\), and one minus the mean matrix of patch-to-patch logits as the moving cost \\( c_{ij} \\). In this way, we adapt the EMD to our cross-attention module." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.392, + 0.472, + 0.439 + ], + "angle": 0, + "content": "other image. We use one minus the average map of patch-to-patch attentions as the moving cost \\( c_{ij} \\). In this way, we can compute an adapted EMD \\( \\lambda \\) for the cross-attention:" + }, + { + "type": "equation", + "bbox": [ + 0.135, + 0.443, + 0.47, + 0.462 + ], + "angle": 0, + "content": "\\[\n\\lambda_ {q} ^ {p} = \\operatorname {E M D} \\left(c _ {i j}, s _ {i}, d _ {j}; p, q\\right), p, q \\in \\{a, o \\} \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.466, + 0.472, + 0.54 + ], + "angle": 0, + "content": "where \\( p \\) represents the type of the cross-attention, i.e., attribute cross-attention when \\( p = a \\) and object cross-attention when \\( p = o \\), and \\( q \\) represents the type of the inputs, i.e., attribute-sharing inputs when \\( q = a \\) and object-sharing inputs when \\( q = o \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.542, + 0.472, + 0.63 + ], + "angle": 0, + "content": "For attribute cross-attention, attribute-sharing inputs should have large EMD \\(\\lambda_{a}^{a}\\) while object-sharing inputs should have small EMD \\(\\lambda_{o}^{a}\\). It is opposite for object cross-attention, i.e., small \\(\\lambda_{a}^{o}\\) of attribute-sharing inputs and large \\(\\lambda_{o}^{o}\\) of object-sharing inputs. Thus, we formulate the regularization term as:" + }, + { + "type": "equation", + "bbox": [ + 0.18, + 0.635, + 0.47, + 0.653 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {r e g}} = \\lambda_ {o} ^ {a} + \\lambda_ {a} ^ {o} - \\lambda_ {a} ^ {a} - \\lambda_ {o} ^ {o} \\tag {13}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.66, + 0.291, + 0.676 + ], + "angle": 0, + "content": "4.3. Training and inference" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.684, + 0.47, + 0.714 + ], + "angle": 0, + "content": "At the training phase, we formulate our final loss as a cross entropy with regularization for all inputs:" + }, + { + "type": "equation", + "bbox": [ + 0.217, + 0.718, + 0.47, + 0.734 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {c e} + \\mathcal {L} _ {r e g} \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.737, + 0.471, + 0.828 + ], + "angle": 0, + "content": "At inference phase, we feed the same test input into three attention branches in a self-attention manner, deriving three class probabilities \\( p(c), p(a) \\), and \\( p(o)^1 \\), where \\( c = (a, o) \\). Unlike most methods modeling single \\( p(c) \\) for prediction, we compute our prediction score by synthesizing attribute, object and composition probabilities:" + }, + { + "type": "equation", + "bbox": [ + 0.154, + 0.84, + 0.47, + 0.866 + ], + "angle": 0, + "content": "\\[\n\\hat {c} = \\underset {c \\in \\mathcal {C} _ {\\text {t e s t}}} {\\arg \\max } p (c) + \\beta \\cdot p (a) \\cdot p (o) \\tag {15}\n\\]" + }, + { + "type": "page_footnote", + "bbox": [ + 0.078, + 0.875, + 0.471, + 0.901 + ], + "angle": 0, + "content": "1Abbreviations for \\(p_{\\pi_c}(c|v_c),p_{\\pi_a}(a|v_a)\\) , and \\(p_{\\pi_o}(o|v_o)\\) , where \\(v_{c}\\) \\(v_{a}\\) , and \\(v_{o}\\) are outputs from three self-attention." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.894, + 0.168 + ], + "angle": 0, + "content": "We first fix \\(\\beta = 1.0\\) during training and then validate \\(\\beta = 0.0, 0.1, \\dots, 1.0\\) to choose the best \\(\\beta\\) on the validation set. Finally, we compute the composition prediction as Eq. (15) with the chosen \\(\\beta\\), making the best prediction trade-off between generalized composition and independent concept." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.18, + 0.634, + 0.196 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.205, + 0.696, + 0.22 + ], + "angle": 0, + "content": "5.1. Experimental details" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.227, + 0.895, + 0.395 + ], + "angle": 0, + "content": "Datasets We use three benchmark datasets in CZSL problem, namely Clothing16K [50], UT-Zappos50K [49], and C-GQA [29]. Clothing16K [50] contains different types of clothing (e.g., shirt, pants) with color attributes (e.g., white, black). UT-Zappos50K [49] is a fine-grained dataset consisting of different kinds of shoes (e.g., sneakers, sandals) with texture attributes (e.g., leather, canvas). C-GQA [29] is a split built on top of Stanford GQA dataset [14], composed of extensive common attribute concepts (e.g., old, wet) and object concepts (e.g., dog, bus) in real life. We follow the common data splits of these three datasets (see Table 1)." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.4, + 0.897, + 0.455 + ], + "angle": 0, + "content": "
DatasetsCompositionTrainValTest
|A||O||A| × |O||Cs||X||Cs| / |Cu||X||Cs| / |Cu||X|
Clothing16K [50]987218724210 / 1055159 / 83413
UT-Zappos50K [49]1612192832299815 / 15321418 / 182914
C-GQA [29]4136742783625592269201252 / 10407280888 / 9235098
" + }, + { + "type": "table_caption", + "bbox": [ + 0.574, + 0.456, + 0.816, + 0.469 + ], + "angle": 0, + "content": "Table 1. Summary of data split statistics." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.473, + 0.895, + 0.625 + ], + "angle": 0, + "content": "Open-world setting In addition to the standard closed-world setting, we also evaluate our model on the open-world setting [24], which is neglected by most previous works. The open-world setting considers all possible compositions, which requires a much larger testing space than the closed-world setting during inference. Taking UT-Zappos50K as an example (see Table 1), the closed world only considers 36 compositions in the testing set while the open world considers total 192 compositions, in which \\(\\sim 81\\%\\) are ignored under the standard closed-world setting." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Evaluation metrics Since CZSL models have an inherent bias for seen compositions, we follow the generalized CZSL evaluation protocol [36]. To overcome the negative bias for seen compositions, we apply different calibration terms to unseen compositions and compute the corresponding top-1 accuracy of seen and unseen compositions, where a larger bias makes higher unseen accuracy and lower seen accuracy, and vice versa. We treat seen accuracy as \\( x \\)-axis and unseen accuracy as \\( y \\)-axis to derive an unseen-seen accuracy curve. We can then compute the area under curve (AUC), the best harmonic mean, the best seen accuracy, and the best unseen accuracy from the curve. In our experiments, we report these four metrics for evaluation, among which AUC is the most representative and stable metric for measuring CZSL model performance. Note that the attribute accuracy or the object accuracy alone does not reflect CZSL performance, because the individual accuracy on attribute or object does not necessarily decide the accuracy of their composition." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15319" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.089, + 0.894, + 0.224 + ], + "angle": 0, + "content": "
Closed-world \nModelsClothing16KUT-Zappos50KC-GQA
AUCHMSeenUnseenAttrObjAUCHMSeenUnseenAttrObjAUCHMSeenUnseenAttrObj
SymNet [22]78.879.398.085.175.684.132.645.660.668.648.277.03.113.530.913.311.434.6
CompCos [24]90.387.298.596.890.291.831.848.158.863.845.572.42.912.830.712.210.433.9
GraphEmb [29]89.284.298.097.490.093.134.548.561.670.050.877.13.815.032.314.913.833.2
Co-CGE [25]88.387.998.594.787.491.430.844.660.962.646.073.53.614.731.614.312.634.6
SCEN [21]78.878.598.089.681.285.430.946.765.762.944.074.43.514.631.713.410.731.4
IVR [50]90.686.699.097.089.393.634.349.261.568.148.474.62.210.927.310.010.337.5
OADis [41]88.486.197.794.284.993.132.646.960.768.849.376.93.814.733.414.38.936.3
ADE (ours)92.488.798.297.790.293.635.151.163.064.346.374.05.218.035.017.716.832.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.225, + 0.893, + 0.268 + ], + "angle": 0, + "content": "Table 2. Closed-world results on three datasets. We report the area under curve (AUC), the best harmonic mean (HM), the best seen accuracy (Seen), the best unseen accuracy (Unseen), the attribute accuracy (Attr), and the object accuracy (Obj) of the unseen-seen accuracy curve under the closed world-setting. AUC is the core CZSL metric. All models use the same DINO ViT-B-16 backbone." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.275, + 0.892, + 0.412 + ], + "angle": 0, + "content": "
Open-world \nModelsClothing16KUT-Zappos50KC-GQA
AUCHMSeenUnseenAttrObjAUCHMSeenUnseenAttrObjAUCHMSeenUnseenAttrObj
SymNet [22]57.468.398.260.757.681.225.040.660.451.038.275.00.774.930.13.218.437.5
CompCos [24]64.170.898.269.871.783.720.736.058.146.036.471.10.724.332.82.815.137.8
GraphEmb [29]62.068.398.569.771.882.423.540.060.647.037.169.30.814.832.73.217.236.7
Co-CGE [25]59.369.298.763.868.576.222.040.357.743.433.967.20.483.331.12.115.535.7
SCEN [21]53.761.596.762.363.679.122.538.064.847.534.973.30.342.529.51.514.832.3
IVR [50]63.672.098.769.070.384.825.342.360.750.038.471.40.945.730.64.016.936.5
OADis [41]53.463.298.058.657.385.425.341.658.753.940.374.70.714.233.02.614.639.7
ADE (ours)68.074.299.073.175.084.527.144.862.450.739.971.41.427.635.14.822.435.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.084, + 0.413, + 0.884, + 0.427 + ], + "angle": 0, + "content": "Table 3. Open-world results on three datasets. Different from Table 2, open-world setting considers all possible compositions in testing." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.438, + 0.473, + 0.695 + ], + "angle": 0, + "content": "Implementation details We use a frozen ViT-B-16 [6] backbone pretrained with DINO [3] on ImageNet [5] in a self-supervised manner as our visual feature extractor. The ViT-B-16 outputs contain 197 tokens (1 [CLS] and 196 patch tokens) of 768 dimensions. For three attention disentangler modules, we implement one-layer multi-head attention framework following [44], changing the single input to paired inputs for cross-attention. The embedders \\(\\pi_{a},\\pi_{c},\\pi_{o}\\) are the two-layer MLPs following the previous works [24,50], projecting the 768-dimension visual features to 300-dimension word embedding space. The word embedding prototypes are initialized with word2vec [27] for all datasets and learnable during training. The composition function \\(\\psi\\) is one linear layer. We train our model using Adam optimizer [18] with a learning rate of \\(5\\times 10^{-6}\\) for UT-Zappos50K and Clothing16K, and \\(5\\times 10^{-5}\\) for C-GQA. All models are trained with 128 batch size for 300 epochs." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.71, + 0.21, + 0.726 + ], + "angle": 0, + "content": "5.2. Comparison" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.473, + 0.902 + ], + "angle": 0, + "content": "To ensure a fair comparison and demonstrate that our improvement over baseline models is not merely by ViT, we adopt ViT backbone to state-of-the-art CZSL models and re-train all models. We compare our method with them: (1) OADis [41] disentangles attribute and object features from spatial convolutional maps; (2) SymNet [22] introduces the symmetry principle of attribute-object transformation and group theory as training objectives; (3) CompCos [24] extends CZSL to an open-world setting considering all possible compositions during inference, proposing a feasibility score based on data statistics to remove unfeasible compositions;" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.438, + 0.895, + 0.574 + ], + "angle": 0, + "content": "(4) GraphEmb [29] and Co-CGE [25] propose to use graph convolutional networks (GCN) to represent attribute-object relationships and compositions; (5) SCEN [21] projects visual features to a Siamese contrastive space to capture concept prototypes, and introduces complex state transition module to produce virtual compositions; (6) IVR [50] proposes to disentangle visual features into concept-invariant domains from a perspective of domain generalization, by masking specific channels of visual features." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.579, + 0.896, + 0.837 + ], + "angle": 0, + "content": "Closed-world evaluation In Table 2, we compare our ADE model with the state-of-the-art methods. ADE consistently outperforms others by a significant margin. ADE increases the core metric AUC by 1.8 on Clothing16K, 0.6 on UT-Zappos50K, and 1.4 on C-GQA (\\(\\sim 37\\%\\) relatively). Similarly, ADE increases the best harmonic mean (HM) by \\(0.8\\%\\) on Clothing16K, \\(1.9\\%\\) on UT-Zappos50K, and \\(3.0\\%\\) on C-GQA. We notice that SymNet [22] and SCEN [21] perform badly on Clothing16K. The reason might be that not learning concept prototypes harms the word embedding expressivity on small-scale concepts. We also notice that IVR [50] performs very well on curated datasets Clothing16K and UT-Zappos50K but badly on larger-scale real-world dataset C-GQA. We hypothesize ideal concept-invariant domains might be difficult to learn from natural images and large-scale concepts of C-GQA. In contrast, our ADE model achieves state-of-the-art performance on all datasets." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.897, + 0.903 + ], + "angle": 0, + "content": "Open-world evaluation In Table 3, we consider the open-world setting to compare our ADE with other methods. Likewise, ADE also performs the best among all methods under open-world setting. ADE increases AUC by 3.9 on Cloth-" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "15320" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.095, + 0.089, + 0.427, + 0.165 + ], + "angle": 0, + "content": "
CAAAOARegAUCHMSeenUnseen
(0)✘✘✘✘23.841.159.048.9
(1)self✘✘✘25.342.361.149.9
(2)selfselfself✘26.744.661.949.8
(3)selfcrosscross✘26.944.563.448.7
(4)selfcrosscross✓27.144.862.450.7
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.076, + 0.168, + 0.44, + 0.222 + ], + "angle": 0, + "content": "Table 4. Ablate the components in ADE on open-world UT-Zappos50K. CA, AA, and OA denote composition, attribute, and object attention. Reg denotes the regularization term. We test self- or cross-attention for AA and OA." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.234, + 0.473, + 0.417 + ], + "angle": 0, + "content": "ing16K, 1.8 on UT-Zappos50K, and 0.48 on C-GQA (\\(\\sim 51\\%\\) relatively). ADE also increases the best harmonic mean (HM) by \\(2.2\\%\\) on Clothing16K, \\(2.5\\%\\) on UT-Zappos50K, and \\(1.9\\%\\) on C-GQA (\\(\\sim 33\\%\\) relatively). From the above results, ADE surpasses others by a larger margin on open-world AUC and HM than closed-world ones, indicating ADE maintains utmost efficiency when turning from the closed world to the open world. It is worth mentioning that ADE does not apply any special operations (e.g., feasibility masking [24]) for the open world and deals with the two settings in exactly the same way. IVR [50] keeps its performance to a great extent but still lags behind our method significantly." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.429, + 0.228, + 0.445 + ], + "angle": 0, + "content": "5.3. Ablation study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.454, + 0.472, + 0.621 + ], + "angle": 0, + "content": "**Backbone:** ResNet vs ViT Our work leverages ViT as the default backbone to excavate more high-level sub-space information, while ResNet18 is the most common backbone in previous works. In Table 6, we compare our ADE to OADis [41] with both backbones. Our ADE performs similarly to OADis with ResNet18, but outperforms it significantly with ViT. Additionally, we present an ablation study on different components of our method with the ResNet18 backbone in the Appendix. These experiments indicate that our model benefits from ViT and all components of our method are effective regardless of the backbone." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.63, + 0.468, + 0.72 + ], + "angle": 0, + "content": "
Closed-worldClothing16KUT-Zappos50KC-GQA
BackboneModelsAUCHMAUCHMAUCHM
ResNet18OADis [41]85.584.730.044.43.113.6
ADE (ours)87.285.129.547.03.113.7
ViT-B-16OADis [41]88.486.132.646.93.814.7
ADE (ours)92.488.735.151.15.218.0
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.081, + 0.722, + 0.466, + 0.735 + ], + "angle": 0, + "content": "Table 6. Compare ADE and OADis [41] with ResNet18 and ViT." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.473, + 0.901 + ], + "angle": 0, + "content": "Different parts of ADE We evaluate the effectiveness of attention disentanglers (composition, attribute, and object attention) and the regularization term in our model. We report the ablation study results on the open-world UT-Zappos50K in Table 4. Rows (0)-(2) show attention disentanglers can significantly improve the performance. Rows (2)-(3) show that cross-attention learns disentangled concepts better than self-attention for AA and OA. Rows (3)-(4) show the regularization term can further benefit the visual disentanglement, improving the unseen accuracy and overall AUC." + }, + { + "type": "table", + "bbox": [ + 0.452, + 0.089, + 0.895, + 0.166 + ], + "angle": 0, + "content": "
Inference formulationC-GQAClothing16K
AUCHMSeenUnseenAUCHMSeenUnseen
(0)p(c)4.616.835.116.092.488.898.297.7
(1)p(a) · p(o)4.015.831.415.157.366.396.763.1
(2)p(c) + p(a) · p(o)5.218.035.017.790.485.998.297.0
(3)p(c) + β · p(a) · p(o)5.218.035.017.792.488.798.297.7
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.448, + 0.168, + 0.895, + 0.223 + ], + "angle": 0, + "content": "Table 5. Results on closed-world Clothing16K and C-GQA using different inference formulations. Rows (0)-(2) respectively represents the cases when \\(\\beta = 0.0\\), \\(\\beta = +\\infty\\), and \\(\\beta = 1.0\\). Row (3) is our inference formulation, which applies an \\(\\beta\\) optimized on the validation set." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.234, + 0.895, + 0.477 + ], + "angle": 0, + "content": "Inference formulation We also investigate the effect of our inference formulation \\( p(c) + \\beta \\cdot p(a) \\cdot p(o) \\) in Table 5. We report the results with extreme values of \\( \\beta \\), i.e., \\( \\beta = 0.0 \\) and \\( \\beta = 1.0 \\). Note that \\( \\beta = 0.0 \\) means only using composition probability for prediction. In addition, we also test the performance only using the product of attribute and object probabilities \\( p(a) \\cdot p(o) \\). We can observe that the best fixed \\( \\beta \\) value is unfixed among datasets. For example, \\( \\beta = 1.0 \\) gives the highest AUC for C-GQA in row (2) while \\( \\beta = 0.0 \\) for Clothing16K in row (0). In contrast, our validated \\( \\beta \\) consistently gives the best inference results for both datasets. Another observation on C-GQA is that \\( p(a) \\cdot p(o) \\) alone is not a good prediction, but adding it to \\( p(c) \\) can increase the unseen accuracy. This indicates that the disentangled attribute prediction \\( p(a) \\) and object prediction \\( p(o) \\) indeed enhance the unseen generalization for CZSL problem." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.482, + 0.895, + 0.649 + ], + "angle": 0, + "content": "Effect of regularization term We propose an EMD-adapted regularization term at the attention level to force attentions to disentangle the concept of interest. We also investigate the effect of applying the regularization term at the feature level. Specifically, we compare our EMD-based distance to the cosine and euclidean feature distances. The results on open-world UT-Zappos50K are shown in Table 7. Our EMD-based regularization outperforms other distance forms, because our attention-level EMD distance considers token-wise similarity capturing the specific concept-related attention responses." + }, + { + "type": "table", + "bbox": [ + 0.503, + 0.656, + 0.895, + 0.712 + ], + "angle": 0, + "content": "
RegAUCHMSeenUnseen
Cosine26.844.763.048.6
Euclidean26.244.362.647.5
Ours (EMD)27.144.862.450.7
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.498, + 0.713, + 0.895, + 0.741 + ], + "angle": 0, + "content": "Table 7. Comparison of different regularization terms on openworld UT-Zappos50K." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.757, + 0.688, + 0.773 + ], + "angle": 0, + "content": "5.4. Qualitative analysis" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Visual disentanglement in feature space is hard to visualize [41]. Inspired by previous work attempts [22, 30, 41, 50], we conduct qualitative analysis of image and text retrieval to show how our ADE model correlates the visual image and the concept composition. In addition, to further validate ADE is efficient to disentangle visual concepts, we conduct unseen-to-seen image retrieval based on their visual concept features extracted by attribute and object attentions." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "15321" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.09, + 0.098, + 0.332, + 0.213 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.123, + 0.217, + 0.296, + 0.228 + ], + "angle": 0, + "content": "(a) Top-5 text-to-image retrieval." + }, + { + "type": "image", + "bbox": [ + 0.346, + 0.099, + 0.628, + 0.214 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.398, + 0.217, + 0.573, + 0.228 + ], + "angle": 0, + "content": "(b) Top-5 image-to-text retrieval." + }, + { + "type": "image", + "bbox": [ + 0.647, + 0.097, + 0.877, + 0.214 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.671, + 0.217, + 0.848, + 0.228 + ], + "angle": 0, + "content": "(c) Top-5 visual concept retrieval." + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.231, + 0.894, + 0.273 + ], + "angle": 0, + "content": "Figure 5. Qualitative analysis. (a) In the last row of \"suede sandals\", the wrong image (red box) is \"fake leather sandals\". (b) Each image has the ground-truth label (black text) and 5 retrieval results (colored text), in which the green text is the correct prediction. (c) We retrieve images sharing the same visual concepts by their visual concept features for unseen images of \"yellow skirt\" and \"pink pants\"." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.279, + 0.473, + 0.642 + ], + "angle": 0, + "content": "Image and text retrieval We first consider text-to-image retrieval. Given a text composition, e.g., \"leather heels\", we embed it and retrieve the top-5 closest visual features based on the feature distance. We display four text compositions of the different objects sharing the same attributes and vice versa in Fig. 5a. We can observe that the retrieved images are correct in most of the cases. One exception is when retrieving \"suede sandals\", the third closest image is \"fake leather sandals\". Although \"suede sandals\" and \"fake leather sandals\" are not the same composition, they are quite visually similar. We then consider image-to-text retrieval, shown in Fig. 5b. Given an image, e.g., the image of a \"brown zebra\", we extract its visual feature and retrieve the top-5 closest text composition embeddings. It is difficult to retrieve the ground-truth label in the top-1 closest text composition, but all top-5 results are all semantically related to the image. We take the image of \"blond person\" (row 3, col 2) as an example. Although the text composition \"blond person\" is not retrieved in the top-5 matches, the retrieved results \"white shirts\", \"white outfit\", \"white shorts\", \"white pants\", and \"young girl\" are all reasonable and actually present in the image. Image and text retrieval experiments validate that our ADE efficiently projects visual features and word embeddings into a uniform space." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.645, + 0.473, + 0.902 + ], + "angle": 0, + "content": "Visual concept retrieval Because the attribute and the object are visually coupled in an image to a high degree of entanglement, it is challenging to visualize the disentanglement in feature space [41]. Saini et al. [41] retrieve single attribute or object text from test images. However, this process is the same as multi-label classification and insufficient to validate that disentangled visual concepts are learned from images. Based on the disentanglement ability of ADE, we construct a visual concept retrieval experiment to investigate the distances between visual concept features, i.e., the embedded attribute feature \\(\\pi_{a}(v_{a})\\) and the embedded object feature \\(\\pi_{o}(v_{o})\\), extracted from different images. Prior to our work, no existing models can do so, because none of them extracts concept-exclusive features like ADE. The results are shown in Fig. 5c. We first extract attribute features and object features from all seen images. Given an unseen image, we retrieve the top-5 closest images by measuring the feature" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.279, + 0.895, + 0.446 + ], + "angle": 0, + "content": "distance between the attribute feature of the given image and that of all seen images, and the same goes for the object feature. For the image of \"yellow skirt\", all retrieval results for the visual concept \"yellow\" are all \"yellow [OBJ]\", and all retrieval results for \"skirt\" are \"[ATTR] skirt\". For the \"pink pants\" image, our model also perfectly retrieves the visual concepts, i.e., the attribute \"pink\" and the object \"pants\". Our experimental results demonstrate that our ADE model is effective to disentangle visual concepts from seen compositions and combine learned concept knowledge into unseen compositions." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.455, + 0.619, + 0.47 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.48, + 0.895, + 0.722 + ], + "angle": 0, + "content": "In this paper, we tackle the problem of compositional zero-shot learning (CZSL). To disentangle visual concepts from the attribute-object composition, we propose ADE adopting cross-attentions to learn the individual concept from paired concept-sharing images. To constrain the disentanglers to learn the concept of interest, we employ a regularization term adapted from the earth mover's distance (EMD), which is used as a feature similarity metric in the cross-attention module. Moreover, to exploit the attribute and object prediction ability of ADE, we improve the inference process by combining attribute, object, and composition probabilities into the final prediction score. We empirically demonstrate ADE outperforms the current state-of-the-art methods under both closed- and open-world settings. We also conduct a comprehensive qualitative analysis to validate the disentanglement ability of attention disentanglers in ADE." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.728, + 0.894, + 0.835 + ], + "angle": 0, + "content": "Limitations Like existing CZSL methods, it is time- and computation-consuming to derive all composition embeddings when the numbers of attributes and objects are large. Moreover, it remains an open challenge to exploit concepts based on the actual semantics rather than solely on text; for instance, the \"open\" attribute in \"open curtain\" and \"open computer\" has completely different meanings." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.895, + 0.9 + ], + "angle": 0, + "content": "Acknowledgements This work is partially supported by Hong Kong Research Grant Council - Early Career Scheme (Grant No. 27208022) and HKU Seed Fund for Basic Research." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15322" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.117, + 0.471, + 0.157 + ], + "angle": 0, + "content": "[1] Jean-Baptiste Alayrac, Ivan Laptev, Josef Sivic, and Simon Lacoste-Julien. Joint discovery of object states and manipulation actions. 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Wong +The University of Hong Kong + +{szhao, kykwong}@cs.hku.hk kaihanx@hku.hk + +# Abstract + +Compositional zero-shot learning (CZSL) aims at learning visual concepts (i.e., attributes and objects) from seen compositions and combining concept knowledge into unseen compositions. The key to CZSL is learning the disentanglement of the attribute-object composition. To this end, we propose to exploit cross-attention as compositional disentanglers to learn disentangled concept embeddings. For example, if we want to recognize an unseen composition "yellow flower", we can learn the attribute concept "yellow" and object concept "flower" from different yellow objects and different flowers respectively. To further constrain the disentanglers to learn the concept of interest, we employ a regularization at the attention level. Specifically, we adapt the earth mover's distance (EMD) as a feature similarity metric in the cross-attention module. Moreover, benefiting from concept disentanglement, we improve the inference process and tune the prediction score by combining multiple concept probabilities. Comprehensive experiments on three CZSL benchmark datasets demonstrate that our method significantly outperforms previous works in both closed- and open-world settings, establishing a new state-of-the-art. Project page: https://haoosz.github.io/ade-czsl/ + +# 1. Introduction + +Suppose we have never seen white bears (i.e., polar bears) before. Can we picture what it would look like? This is not difficult because we have seen many white animals in daily life (e.g., white dogs and white rabbits) and different bears with various visual attributes in the zoo (e.g., brown bears and black bears). Humans have no difficulty in disentangling "white" and "bear" from seen instances and combining them into the unseen composition. Inspired by this property of human intelligence, researchers attempt to make machines learn compositions of concepts as well. Compositional zero-shot learning (CZSL) is a specific problem studying visual compositionality, aiming to learn visual concepts from seen + +![](images/96a0d7012211e0c75550d61a06ff7e29e7d5473daf047868aa312de345224039.jpg) +Figure 1. Motivation illustration. Given images from seen attribute-object compositions, human can disentangle the attribute "yellow" from "yellow bird" and "yellow pear", and the object "flower" from "purple flower" and "red flower". After learning visual properties of the concepts "yellow" and "flower", human can then recognize images from the unseen composition "yellow flower". + +compositions of attributes and objects and generalize concept knowledge to unseen compositions. + +Learning attribute-object compositions demands prior knowledge about attributes and objects. However, visual concepts of attributes and objects never appear alone in a natural image. To learn exclusive concepts for compositionality learning, we need to disentangle the attribute concept and the object concept. As illustrated in Fig. 1, if we want to recognize the image of "yellow flower", it is necessary to learn the "yellow" concept and the "flower" concept, i.e., disentangle visual concepts, from images of seen compositions. Previous works [22, 24, 25, 28-30, 36, 46] tackle CZSL by composing attribute and object word embeddings, and projecting word and visual embeddings to a joint space. They fail to disentangle visual concepts. Recently, some works [21, 40, 41, 50] consider visual disentanglement but still have limitations despite their good performance. SCEN [21] learns concept-constant samples contrastively without constructing concept embedding prototypes to avoid learning irrelevant concepts shared by positive samples. IVR [50] disentangles visual features into ideal concept-invariant domains. This ideal domain generalization setting requires a small discrepancy of attribute and object sets and would degenerate on vaster and more + +complex concepts. ProtoProp [40] and OADis [41] learn local attribute and object prototypes from spatial features on convolutional feature maps. However, spatial disentanglement is sometimes infeasible because attribute and object concepts are highly entangled in spatial features. Taking an image of "yellow flower" as an example, the spatial positions related to the attribute "yellow" and the object "flower" completely overlap, which hinders effective attribute-object disentanglement. + +To overcome the above limitations, we propose a simple visual disentangling framework exploiting Attention as DisEntangler (ADE) on top of vision transformers [6]. We notice that vision transformers (ViT) have access to more sub-space global information across multi-head attentions than CNNs [38]. Therefore, with the expressivity of different subspace representations, token attentions of ViT may provide a more effective way for disentangling visual features, compared to using traditional spatial attentions across local positions on convolutional features [40, 41]. Specifically, it is difficult to disentangle the attribute-object composition "yellow flower" by spatial positions, but it is possible for ViT multi-head attentions to project attribute concept "yellow" and object concept "flower" onto different subspaces. Inspired by this property, we propose to learn cross-attention between two inputs that share the same concept, e.g., "yellow bird" and "yellow pear" share the same attribute concept "yellow". In this way, we can derive attribute- and object-exclusive visual representations by cross-attention disentanglement. To ensure that the concept disentangler is exclusive to the specific concept, we also need to constrain the disentanglers to learn the concept of interest instead of the other concept. For example, given attribute-sharing images, the attribute attention should output similar attribute-exclusive features while the object attention should not. To achieve this goal, we apply a regularization term adapted from the earth mover's distance (EMD) [13] at the attention level. This regularization term forces cross-attention to learn the concept of interest by leveraging the feature similarity captured from all tokens. Mancini et al. [24] propose an open-world evaluation setting, which is neglected by most previous works. We consider both closed-world and the open-world settings in our experiments, demonstrating that our method is coherently efficient in both settings. The contributions of this paper are summarized below: + +- We propose a new CZSL approach, named ADE, using cross-attentions to disentangle attribute- and object-exclusive features from paired concept-sharing inputs. +- We force attention disentanglers to learn the concept of interest with a regularization term adapted from EMD, ensuring valid attribute-object disentanglement. +- We comprehensively evaluate our method in both closed-world and open-world settings on three CZSL datasets, achieving consistent state-of-the-art. + +# 2. Related work + +Visual attribute has been widely studied to understand how visual properties can be learned from objects. The pioneering work by Ferrari and Zisserman [10] learned visual attributes using a probabilistic generative model. The successive work by Lampert et al. [20] used visual attributes to detect unseen objects with an attribute-based multi-label classification. Similarly, Patterson et al. [35] proposed Economic Labeling Algorithm (ELA) to discover multi-label attributes for objects. Different from multi-label classification, other works [4,8,15,23] learned attribute-object relationship to generalize attribute feature across all object categories based on probabilistic models. Visual attributes also benefit downstream tasks, e.g., object recognition [7, 16, 31], action recognition [1,9,26], image captioning [19,33], and semi-supervised learning [42]. + +Compositional zero-shot learning (CZSL) is a special case of zero-shot learning (ZSL) [34, 39, 43, 47, 48], aims at recognizing unseen attribute-object compositions learning from seen compositions. Misra et al. [28] first termed and studied CZSL by projecting composed primitives and visual features to a joint embedding space. Nagarajan et al. [30] formulated attributes as matrix operators applied on object vectors. Purushwalkam et al. [36] introduced a task-driven modular architecture to learn unseen compositions by re-weighting a set of sub-tasks. Wei et al. [46] generated attribute-object compositions with GAN [11] to match visual features. Li et al. [22] proposed symmetry principle of attribute-object transformation under the supervision of group axioms. Naeem et al. [29] and Mancini et al. [25] used graph convolutional networks to extract attribute-object representations. Recently, some works shift their interest from word composing to visual disentanglement. Atzmon et al. [2] solved CZSL from a causal perspective to learn disentangled representations. Ruis et al. [40] proposed to learn prototypical representations of objects and attributes. Li et al. [21] disentangled visual features into a Siamese contrastive space and entangled them with a generative model. Saini et al. [41] extracted visual similarity from spatial features to disentangle attributes and objects. Zhang et al. [50] treated CZSL as a domain generalization task, learning attribute- and object-invariant domains. A more realistic open-world CZSL setting was studied in [17, 24, 25], which considered all possible compositions in testing. Very recently, an inspiring work by Nayak et al. [32] introduced compositional soft prompts to CLIP [37] to tackle CZSL problem. + +Attention mechanism has been well studied by non-local neural networks [45] in computer vision and transformers [44] in machine translation. Dosovitskiy et al. [6] adapted transformer architecture to computer vision field, proving its comparable efficiency over traditional CNNs. Inspired by the multi-head self-attention implemented by transformers, our work exploits efficient attention as disentangler for CZSL. + +![](images/925cc16c877a72219acffeb63e39e57ca1d8a082e63125eae57429d70ed42ed2.jpg) +Figure 2. Method overview. Left (our framework ADE): Given one target image of "red bus", we sample two auxiliary images of the same attribute "red wall" and of the same object "blue bus". We feed the three images into a frozen ViT initialized with DINO [3]. We then input all encoded tokens (i.e., [CLS] and patch tokens) to three attention modules: (1) attribute cross-attention taking paired attribute-sharing tokens as inputs; (2) object cross-attention taking paired object-sharing tokens as inputs; (3) composition self-attention taking tokens of single target image as input. We then project the [CLS] tokens of attention outputs with three MLP embeddings $\pi_{a}$ , $\pi_{c}$ , and $\pi_{o}$ . We finally compute cross entropy losses of embedded visual features with three learnable word embeddings: attribute embeddings, object embeddings, and their linear fused composition embeddings. Right: Illustration of five losses in attribute, object, and composition embedding spaces. + +![](images/a9230fe046a161a5fbfffe9bd11e1a36a3fb687d622c98826d42bf7bba39abb3.jpg) + +# 3. Preliminary + +Compositional zero-shot learning aims at learning a model from limited compositions of attributes (e.g., yellow) and objects (e.g., flower) to recognize an image from novel compositions. Given a set of all possible attributes $\mathcal{A} = \{a_0, a_1, \dots, a_n\}$ and a set of all possible objects $\mathcal{O} = \{o_0, o_1, \dots, o_m\}$ , a compositional class set $\mathcal{C} = \mathcal{A} \times \mathcal{O}$ includes all attribute-object compositions. We divide $\mathcal{C}$ into two disjoint sets, namely the set of seen classes $\mathcal{C}_s$ and the set of unseen classes $\mathcal{C}_u$ , where $\mathcal{C}_s \cap \mathcal{C}_u = \emptyset$ and $\mathcal{C}_s \cup \mathcal{C}_u = \mathcal{C}$ . Training images are only from classes in $\mathcal{C}_s$ and testing images are from classes in $\mathcal{C}_{test} = \mathcal{C}_s \cup \mathcal{C}_u'$ . For closed-world evaluation, $\mathcal{C}_u'$ is a predefined subset of $\mathcal{C}_u$ , i.e., $\mathcal{C}_u' \subset \mathcal{C}_u$ . For open-world evaluation, all possible compositions are considered for testing, i.e., $\mathcal{C}_u' = \mathcal{C}_u$ . CZSL task aims to learn a model $f: \mathcal{X} \to \mathcal{C}_{test}$ to predict labels in the testing composition set $c \in \mathcal{C}_{test}$ for input images $x \in \mathcal{X}$ . + +To learn a CZSL model, a common method is to minimize the cosine similarity score between the visually encoded feature and the word embedding of attribute-object compositions. The similarity score can be expressed as + +$$ +s (x, (a, o)) = \frac {\phi (x)}{| | \phi (x) | |} \cdot \frac {\psi (a , o)}{| | \psi (a , o) | |} \tag {1} +$$ + +where $\phi (\cdot)$ is the visual encoder, and $\psi (\cdot ,\cdot)$ is the composition function. The CZSL model $f$ can be formulated as + +$$ +f (x; \theta_ {\phi}, \theta_ {\psi}) = \underset {a _ {i} \in \mathcal {A}, o _ {j} \in \mathcal {O}} {\arg \max } s (x, \left(a _ {i}, o _ {j}\right)) \tag {2} +$$ + +The model $f$ is optimized by learning the model parameters $\theta_{\phi}$ and $\theta_{\psi}$ to match the input $x$ with the most similar attribute-object composition. Visual encoder $\phi$ and composition func + +tion $\psi$ , as two core components, take multiple forms in different methods. For visual encoder, works [40, 41, 50] manually design networks on top of a pretrained backbone (e.g., ResNet18 [12]) to disentangle attribute and object embeddings for visual features. For composition functions, the object conditioned network [41], the graph embedding [29, 40], and the linear projector [24, 50] are commonly used. Unlike employing complex composition functions, we adopt the simple linear projector in our method. + +# 4. Our approach + +We aim to disentangle attribute and object features for visual representation by learning from image pairs sharing the same attributes or objects. For example, by learning the object "flower" from the "purple flower" and the "red flower" and learning the attribute "yellow" from the "yellow bird" and the "yellow pear", we can infer what a "yellow flower" looks like. To this end, we propose ADE to learn cross-attentions as concept disentanglers with the regularization of a novel token earth mover's distance. The whole framework of our method is shown in Fig. 2. + +# 4.1. Disentanglement with cross-attention + +Multi-head self-attention in transformers [44] is powerful for extracting token connections. Attention maps each query token, and key-value token pairs to an output token. Every output token is a weighted sum of the values, where the weights is the similarity of the corresponding query token and the key tokens. The attention is formulated as: + +$$ +\operatorname {A t t e n t i o n} (Q, K, V) = \operatorname {s o f t m a x} \left(\frac {Q K ^ {T}}{\sqrt {d _ {k}}}\right) V \tag {3} +$$ + +![](images/e2ec8ae55dc8f89a72ef5576d46254e89c78dfad4c90c56be84a6ad613b8b42a.jpg) +Figure 3. Illustration of three types of attention. + +where three inputs are query tokens $(Q)$ , key tokens $(K)$ , and value tokens $(V)$ and the scaling factor $d_{k}$ is the dimension of the query and key. Self-attention uses the same input for $Q$ , $K$ , $V$ and effectively captures relationships among [CLS] and patch tokens of a single input image. Normally, the [CLS] token is exclusively used as a global representation of the input image for downstream tasks, but exclusive [CLS] token highly entangles attribute and object concepts. + +For CZSL task, we want to disentangle the exclusive concept by exploiting the semantic similarity between tokens from different concept-sharing features. For this purpose, we introduce a cross-attention mechanism to extract attribute-exclusive or object-exclusive features for paired images sharing the same attribute or object concept. The cross-attention has the same structure as the self-attention, but works on different inputs. Self-attention uses the same input $I$ for $Q$ , $K$ , $V$ (i.e., $Q = K = V = I$ ) while cross-attention uses one of the paired inputs $I$ for the query and the other $I'$ for the key and the value (i.e., $Q = I$ , $K = V = I'$ ). In the cross-attention, the query input and the key input play different roles. The cross-attention output is the weighted sum of the value (also the key) input based on the similarity between the query and key inputs. For a pair of input images, we swap the query and key inputs in computing cross-attention to derive two cross-attended outputs for the respective inputs. Cross-attention with query-key swapping (QKS) is illustrated in Fig. 3. + +The cross-attention outputs paired features of the exclusive concept with paired concept-sharing inputs. Taking the object-sharing pair as an example, object cross-attention leverages the shared object features of the key input to enhance the query input, thus making the outputs exclusive to object feature space, i.e., object-exclusive features $v_{o}$ and $v_{o}'$ . The same applies to attribute-exclusive features $v_{a}$ and $v_{a}'$ extracted from paired attribute-sharing images. We also use a standard self-attention to extract composition feature $v_{c}$ . + +To train cross-attentions, we adopt common cross entropy loss after MLP embedders $(\pi_{a},\pi_{c},\pi_{o})$ for attribute-exclusive features $(v_{a},v_{a}^{\prime})$ , object-exclusive features $(v_{o},v_{o}^{\prime})$ , and composition feature $(v_{c})$ . We denote any of these visual features as $v$ and the corresponding embedder as $\pi$ . We denote the word embedding as $w_{z}$ , where the concept $z\in \mathcal{Z}$ can be any of the attribute $a\in \mathcal{A}$ , the object $o\in \mathcal{O}$ , or the composition $c\in \mathcal{C}$ . The class probability of L2-normalized $\pi (v)$ and $w_{z}$ can be computed as: + +$$ +p _ {\pi} (z \mid v) = \frac {\exp (\pi (v) \cdot w _ {z} / \tau)}{\sum_ {\hat {z} \in \mathcal {Z}} \exp (\pi (v) \cdot w _ {\hat {z}} / \tau)}, z \in \mathcal {Z} \tag {4} +$$ + +where $\tau$ is the temperature. We then compute the cross entropy to classify visual features: + +$$ +H _ {\pi} (v, z) = - \log p _ {\pi} (z \mid v), z \in \mathcal {Z} \tag {5} +$$ + +Considering different classification objectives of attribute, object, and composition, the general Eq. (5) can be applied to five visual features, i.e., $v_{a}, v_{a}^{\prime}, v_{o}, v_{o}^{\prime}, v_{c}$ . Therefore, the training objective is composed of five cross entropy losses: + +$$ +\mathcal {L} _ {c e} = \underbrace {H _ {\pi_ {a}} (v _ {a} , a)} _ {\mathcal {L} _ {a t t r}} + \underbrace {H _ {\pi_ {a}} (v _ {a} ^ {\prime} , a)} _ {\mathcal {L} _ {a t t r} ^ {\prime}} + \underbrace {H _ {\pi_ {c}} (v _ {c} , c)} _ {\mathcal {L} _ {c o m}} + +$$ + +$$ +\underbrace {H _ {\pi_ {o}} \left(v _ {o} , o\right)} _ {\mathcal {L} _ {o b j}} + \underbrace {H _ {\pi_ {o}} \left(v _ {o} ^ {\prime} , o\right)} _ {\mathcal {L} _ {o b j} ^ {\prime}} \tag {6} +$$ + +where the attribute label $a\in \mathcal{A}$ , the object label $o\in \mathcal{O}$ , and the composition label $c = (a,o)\in \mathcal{C}_{test}$ + +# 4.2. Disentangling constraint at the attention level + +So far, we have enabled cross-attentions to disentangle concepts, but we want to further ensure that the attribute and the object disentanglers learn the corresponding attribute and object concepts instead of the opposite concepts. To this end, we introduce an attention-level earth mover's distance (EMD) to constrain disentanglers to learn the concept of interest. The EMD is formulated as an optimal transportation problem in [13]. Suppose we have supplies of $n_s$ sources $S = \{s_i\}_{i=1}^{n_s}$ and demands of $n_d$ destinations $D = \{d_j\}_{j=1}^{n_d}$ . Given the moving cost from the $i$ -th source to the $j$ -th destination $c_{ij}$ , an optimal transportation problem aims to find the minimal-cost flow $f_{ij}$ from sources to destinations: + +$$ +\underset {f _ {i j}} {\text {m i n i m i z e}} \quad \sum_ {i = 1} ^ {n _ {s}} \sum_ {j = 1} ^ {n _ {d}} c _ {i j} f _ {i j} \tag {7} +$$ + +$$ +\text {s u b j e c t} f _ {i j} \geqslant 0, i = 1, \dots , n _ {s}, j = 1, \dots , n _ {d} \tag {8} +$$ + +$$ +\sum_ {j = 1} ^ {n _ {d}} f _ {i j} = s _ {i}, i = 1, \dots , n _ {s} \tag {9} +$$ + +$$ +\sum_ {i = 1} ^ {n _ {s}} f _ {i j} = d _ {j}, j = 1, \dots , n _ {d} \tag {10} +$$ + +where the optimal flow $\tilde{f}_{ij}$ is computed by the moving cost $c_{ij}$ , the supplies $s_i$ , and the demands $d_j$ . The EMD can be further formulated as: + +$$ +\operatorname {E M D} \left(c _ {i j}, s _ {i}, d _ {j}\right) = \left(1 - c _ {i j}\right) \tilde {f} _ {i j}. \tag {11} +$$ + +When the EMD is greater, the distributions $S$ and $\mathcal{D}$ are closer. In Fig. 4, we show how to use the EMD as a feature similarity metric at the attention level in our cross-attention module. We can derive a cross-attention map from Eq. (3) and the counterpart cross-attention map after query-key swapping. We use the logits of [CLS]-to-patch attentions as supplies $s_i$ and demands $d_j$ , which represent how similar the global feature of one image is to the local patches of the + +![](images/2c42b119f70dfa9e38fac9430870a10d35ce499177dca99449bc897e3f48f4a9.jpg) +Figure 4. Illustration of the adapted EMD at the attention level. Branches 1 and 2 respectively denote using one of the paired inputs as the query $Q$ . We compute the EMD with two attention maps from 1 and 2 branches. We use the [CLS] -to-patch logits as the supplies $s_i$ and the demands $d_j$ , and one minus the mean matrix of patch-to-patch logits as the moving cost $c_{ij}$ . In this way, we adapt the EMD to our cross-attention module. + +other image. We use one minus the average map of patch-to-patch attentions as the moving cost $c_{ij}$ . In this way, we can compute an adapted EMD $\lambda$ for the cross-attention: + +$$ +\lambda_ {q} ^ {p} = \operatorname {E M D} \left(c _ {i j}, s _ {i}, d _ {j}; p, q\right), p, q \in \{a, o \} \tag {12} +$$ + +where $p$ represents the type of the cross-attention, i.e., attribute cross-attention when $p = a$ and object cross-attention when $p = o$ , and $q$ represents the type of the inputs, i.e., attribute-sharing inputs when $q = a$ and object-sharing inputs when $q = o$ . + +For attribute cross-attention, attribute-sharing inputs should have large EMD $\lambda_{a}^{a}$ while object-sharing inputs should have small EMD $\lambda_{o}^{a}$ . It is opposite for object cross-attention, i.e., small $\lambda_{a}^{o}$ of attribute-sharing inputs and large $\lambda_{o}^{o}$ of object-sharing inputs. Thus, we formulate the regularization term as: + +$$ +\mathcal {L} _ {\text {r e g}} = \lambda_ {o} ^ {a} + \lambda_ {a} ^ {o} - \lambda_ {a} ^ {a} - \lambda_ {o} ^ {o} \tag {13} +$$ + +# 4.3. Training and inference + +At the training phase, we formulate our final loss as a cross entropy with regularization for all inputs: + +$$ +\mathcal {L} = \mathcal {L} _ {c e} + \mathcal {L} _ {r e g} \tag {14} +$$ + +At inference phase, we feed the same test input into three attention branches in a self-attention manner, deriving three class probabilities $p(c), p(a)$ , and $p(o)^1$ , where $c = (a, o)$ . Unlike most methods modeling single $p(c)$ for prediction, we compute our prediction score by synthesizing attribute, object and composition probabilities: + +$$ +\hat {c} = \underset {c \in \mathcal {C} _ {\text {t e s t}}} {\arg \max } p (c) + \beta \cdot p (a) \cdot p (o) \tag {15} +$$ + +We first fix $\beta = 1.0$ during training and then validate $\beta = 0.0, 0.1, \dots, 1.0$ to choose the best $\beta$ on the validation set. Finally, we compute the composition prediction as Eq. (15) with the chosen $\beta$ , making the best prediction trade-off between generalized composition and independent concept. + +# 5. Experiments + +# 5.1. Experimental details + +Datasets We use three benchmark datasets in CZSL problem, namely Clothing16K [50], UT-Zappos50K [49], and C-GQA [29]. Clothing16K [50] contains different types of clothing (e.g., shirt, pants) with color attributes (e.g., white, black). UT-Zappos50K [49] is a fine-grained dataset consisting of different kinds of shoes (e.g., sneakers, sandals) with texture attributes (e.g., leather, canvas). C-GQA [29] is a split built on top of Stanford GQA dataset [14], composed of extensive common attribute concepts (e.g., old, wet) and object concepts (e.g., dog, bus) in real life. We follow the common data splits of these three datasets (see Table 1). + +
DatasetsCompositionTrainValTest
|A||O||A| × |O||Cs||X||Cs| / |Cu||X||Cs| / |Cu||X|
Clothing16K [50]987218724210 / 1055159 / 83413
UT-Zappos50K [49]1612192832299815 / 15321418 / 182914
C-GQA [29]4136742783625592269201252 / 10407280888 / 9235098
+ +Table 1. Summary of data split statistics. + +Open-world setting In addition to the standard closed-world setting, we also evaluate our model on the open-world setting [24], which is neglected by most previous works. The open-world setting considers all possible compositions, which requires a much larger testing space than the closed-world setting during inference. Taking UT-Zappos50K as an example (see Table 1), the closed world only considers 36 compositions in the testing set while the open world considers total 192 compositions, in which $\sim 81\%$ are ignored under the standard closed-world setting. + +Evaluation metrics Since CZSL models have an inherent bias for seen compositions, we follow the generalized CZSL evaluation protocol [36]. To overcome the negative bias for seen compositions, we apply different calibration terms to unseen compositions and compute the corresponding top-1 accuracy of seen and unseen compositions, where a larger bias makes higher unseen accuracy and lower seen accuracy, and vice versa. We treat seen accuracy as $x$ -axis and unseen accuracy as $y$ -axis to derive an unseen-seen accuracy curve. We can then compute the area under curve (AUC), the best harmonic mean, the best seen accuracy, and the best unseen accuracy from the curve. In our experiments, we report these four metrics for evaluation, among which AUC is the most representative and stable metric for measuring CZSL model performance. Note that the attribute accuracy or the object accuracy alone does not reflect CZSL performance, because the individual accuracy on attribute or object does not necessarily decide the accuracy of their composition. + +
Closed-world +ModelsClothing16KUT-Zappos50KC-GQA
AUCHMSeenUnseenAttrObjAUCHMSeenUnseenAttrObjAUCHMSeenUnseenAttrObj
SymNet [22]78.879.398.085.175.684.132.645.660.668.648.277.03.113.530.913.311.434.6
CompCos [24]90.387.298.596.890.291.831.848.158.863.845.572.42.912.830.712.210.433.9
GraphEmb [29]89.284.298.097.490.093.134.548.561.670.050.877.13.815.032.314.913.833.2
Co-CGE [25]88.387.998.594.787.491.430.844.660.962.646.073.53.614.731.614.312.634.6
SCEN [21]78.878.598.089.681.285.430.946.765.762.944.074.43.514.631.713.410.731.4
IVR [50]90.686.699.097.089.393.634.349.261.568.148.474.62.210.927.310.010.337.5
OADis [41]88.486.197.794.284.993.132.646.960.768.849.376.93.814.733.414.38.936.3
ADE (ours)92.488.798.297.790.293.635.151.163.064.346.374.05.218.035.017.716.832.3
+ +Table 2. Closed-world results on three datasets. We report the area under curve (AUC), the best harmonic mean (HM), the best seen accuracy (Seen), the best unseen accuracy (Unseen), the attribute accuracy (Attr), and the object accuracy (Obj) of the unseen-seen accuracy curve under the closed world-setting. AUC is the core CZSL metric. All models use the same DINO ViT-B-16 backbone. + +
Open-world +ModelsClothing16KUT-Zappos50KC-GQA
AUCHMSeenUnseenAttrObjAUCHMSeenUnseenAttrObjAUCHMSeenUnseenAttrObj
SymNet [22]57.468.398.260.757.681.225.040.660.451.038.275.00.774.930.13.218.437.5
CompCos [24]64.170.898.269.871.783.720.736.058.146.036.471.10.724.332.82.815.137.8
GraphEmb [29]62.068.398.569.771.882.423.540.060.647.037.169.30.814.832.73.217.236.7
Co-CGE [25]59.369.298.763.868.576.222.040.357.743.433.967.20.483.331.12.115.535.7
SCEN [21]53.761.596.762.363.679.122.538.064.847.534.973.30.342.529.51.514.832.3
IVR [50]63.672.098.769.070.384.825.342.360.750.038.471.40.945.730.64.016.936.5
OADis [41]53.463.298.058.657.385.425.341.658.753.940.374.70.714.233.02.614.639.7
ADE (ours)68.074.299.073.175.084.527.144.862.450.739.971.41.427.635.14.822.435.6
+ +Table 3. Open-world results on three datasets. Different from Table 2, open-world setting considers all possible compositions in testing. + +Implementation details We use a frozen ViT-B-16 [6] backbone pretrained with DINO [3] on ImageNet [5] in a self-supervised manner as our visual feature extractor. The ViT-B-16 outputs contain 197 tokens (1 [CLS] and 196 patch tokens) of 768 dimensions. For three attention disentangler modules, we implement one-layer multi-head attention framework following [44], changing the single input to paired inputs for cross-attention. The embedders $\pi_{a},\pi_{c},\pi_{o}$ are the two-layer MLPs following the previous works [24,50], projecting the 768-dimension visual features to 300-dimension word embedding space. The word embedding prototypes are initialized with word2vec [27] for all datasets and learnable during training. The composition function $\psi$ is one linear layer. We train our model using Adam optimizer [18] with a learning rate of $5\times 10^{-6}$ for UT-Zappos50K and Clothing16K, and $5\times 10^{-5}$ for C-GQA. All models are trained with 128 batch size for 300 epochs. + +# 5.2. Comparison + +To ensure a fair comparison and demonstrate that our improvement over baseline models is not merely by ViT, we adopt ViT backbone to state-of-the-art CZSL models and re-train all models. We compare our method with them: (1) OADis [41] disentangles attribute and object features from spatial convolutional maps; (2) SymNet [22] introduces the symmetry principle of attribute-object transformation and group theory as training objectives; (3) CompCos [24] extends CZSL to an open-world setting considering all possible compositions during inference, proposing a feasibility score based on data statistics to remove unfeasible compositions; + +(4) GraphEmb [29] and Co-CGE [25] propose to use graph convolutional networks (GCN) to represent attribute-object relationships and compositions; (5) SCEN [21] projects visual features to a Siamese contrastive space to capture concept prototypes, and introduces complex state transition module to produce virtual compositions; (6) IVR [50] proposes to disentangle visual features into concept-invariant domains from a perspective of domain generalization, by masking specific channels of visual features. + +Closed-world evaluation In Table 2, we compare our ADE model with the state-of-the-art methods. ADE consistently outperforms others by a significant margin. ADE increases the core metric AUC by 1.8 on Clothing16K, 0.6 on UT-Zappos50K, and 1.4 on C-GQA ( $\sim 37\%$ relatively). Similarly, ADE increases the best harmonic mean (HM) by $0.8\%$ on Clothing16K, $1.9\%$ on UT-Zappos50K, and $3.0\%$ on C-GQA. We notice that SymNet [22] and SCEN [21] perform badly on Clothing16K. The reason might be that not learning concept prototypes harms the word embedding expressivity on small-scale concepts. We also notice that IVR [50] performs very well on curated datasets Clothing16K and UT-Zappos50K but badly on larger-scale real-world dataset C-GQA. We hypothesize ideal concept-invariant domains might be difficult to learn from natural images and large-scale concepts of C-GQA. In contrast, our ADE model achieves state-of-the-art performance on all datasets. + +Open-world evaluation In Table 3, we consider the open-world setting to compare our ADE with other methods. Likewise, ADE also performs the best among all methods under open-world setting. ADE increases AUC by 3.9 on Cloth- + +
CAAAOARegAUCHMSeenUnseen
(0)✘✘✘✘23.841.159.048.9
(1)self✘✘✘25.342.361.149.9
(2)selfselfself✘26.744.661.949.8
(3)selfcrosscross✘26.944.563.448.7
(4)selfcrosscross✓27.144.862.450.7
+ +Table 4. Ablate the components in ADE on open-world UT-Zappos50K. CA, AA, and OA denote composition, attribute, and object attention. Reg denotes the regularization term. We test self- or cross-attention for AA and OA. + +ing16K, 1.8 on UT-Zappos50K, and 0.48 on C-GQA ( $\sim 51\%$ relatively). ADE also increases the best harmonic mean (HM) by $2.2\%$ on Clothing16K, $2.5\%$ on UT-Zappos50K, and $1.9\%$ on C-GQA ( $\sim 33\%$ relatively). From the above results, ADE surpasses others by a larger margin on open-world AUC and HM than closed-world ones, indicating ADE maintains utmost efficiency when turning from the closed world to the open world. It is worth mentioning that ADE does not apply any special operations (e.g., feasibility masking [24]) for the open world and deals with the two settings in exactly the same way. IVR [50] keeps its performance to a great extent but still lags behind our method significantly. + +# 5.3. Ablation study + +**Backbone:** ResNet vs ViT Our work leverages ViT as the default backbone to excavate more high-level sub-space information, while ResNet18 is the most common backbone in previous works. In Table 6, we compare our ADE to OADis [41] with both backbones. Our ADE performs similarly to OADis with ResNet18, but outperforms it significantly with ViT. Additionally, we present an ablation study on different components of our method with the ResNet18 backbone in the Appendix. These experiments indicate that our model benefits from ViT and all components of our method are effective regardless of the backbone. + +
Closed-worldClothing16KUT-Zappos50KC-GQA
BackboneModelsAUCHMAUCHMAUCHM
ResNet18OADis [41]85.584.730.044.43.113.6
ADE (ours)87.285.129.547.03.113.7
ViT-B-16OADis [41]88.486.132.646.93.814.7
ADE (ours)92.488.735.151.15.218.0
+ +Table 6. Compare ADE and OADis [41] with ResNet18 and ViT. + +Different parts of ADE We evaluate the effectiveness of attention disentanglers (composition, attribute, and object attention) and the regularization term in our model. We report the ablation study results on the open-world UT-Zappos50K in Table 4. Rows (0)-(2) show attention disentanglers can significantly improve the performance. Rows (2)-(3) show that cross-attention learns disentangled concepts better than self-attention for AA and OA. Rows (3)-(4) show the regularization term can further benefit the visual disentanglement, improving the unseen accuracy and overall AUC. + +
Inference formulationC-GQAClothing16K
AUCHMSeenUnseenAUCHMSeenUnseen
(0)p(c)4.616.835.116.092.488.898.297.7
(1)p(a) · p(o)4.015.831.415.157.366.396.763.1
(2)p(c) + p(a) · p(o)5.218.035.017.790.485.998.297.0
(3)p(c) + β · p(a) · p(o)5.218.035.017.792.488.798.297.7
+ +Table 5. Results on closed-world Clothing16K and C-GQA using different inference formulations. Rows (0)-(2) respectively represents the cases when $\beta = 0.0$ , $\beta = +\infty$ , and $\beta = 1.0$ . Row (3) is our inference formulation, which applies an $\beta$ optimized on the validation set. + +Inference formulation We also investigate the effect of our inference formulation $p(c) + \beta \cdot p(a) \cdot p(o)$ in Table 5. We report the results with extreme values of $\beta$ , i.e., $\beta = 0.0$ and $\beta = 1.0$ . Note that $\beta = 0.0$ means only using composition probability for prediction. In addition, we also test the performance only using the product of attribute and object probabilities $p(a) \cdot p(o)$ . We can observe that the best fixed $\beta$ value is unfixed among datasets. For example, $\beta = 1.0$ gives the highest AUC for C-GQA in row (2) while $\beta = 0.0$ for Clothing16K in row (0). In contrast, our validated $\beta$ consistently gives the best inference results for both datasets. Another observation on C-GQA is that $p(a) \cdot p(o)$ alone is not a good prediction, but adding it to $p(c)$ can increase the unseen accuracy. This indicates that the disentangled attribute prediction $p(a)$ and object prediction $p(o)$ indeed enhance the unseen generalization for CZSL problem. + +Effect of regularization term We propose an EMD-adapted regularization term at the attention level to force attentions to disentangle the concept of interest. We also investigate the effect of applying the regularization term at the feature level. Specifically, we compare our EMD-based distance to the cosine and euclidean feature distances. The results on open-world UT-Zappos50K are shown in Table 7. Our EMD-based regularization outperforms other distance forms, because our attention-level EMD distance considers token-wise similarity capturing the specific concept-related attention responses. + +
RegAUCHMSeenUnseen
Cosine26.844.763.048.6
Euclidean26.244.362.647.5
Ours (EMD)27.144.862.450.7
+ +Table 7. Comparison of different regularization terms on openworld UT-Zappos50K. + +# 5.4. Qualitative analysis + +Visual disentanglement in feature space is hard to visualize [41]. Inspired by previous work attempts [22, 30, 41, 50], we conduct qualitative analysis of image and text retrieval to show how our ADE model correlates the visual image and the concept composition. In addition, to further validate ADE is efficient to disentangle visual concepts, we conduct unseen-to-seen image retrieval based on their visual concept features extracted by attribute and object attentions. + +![](images/4d72df6e1f4a47e99d5df5ac13faaa7c3a585f4b090f6820485cda51e71b8f01.jpg) +(a) Top-5 text-to-image retrieval. + +![](images/96596a991f61678d701a70e4ccdb6daabee77ef6c03437aaf90739c3629d1c59.jpg) +(b) Top-5 image-to-text retrieval. +Figure 5. Qualitative analysis. (a) In the last row of "suede sandals", the wrong image (red box) is "fake leather sandals". (b) Each image has the ground-truth label (black text) and 5 retrieval results (colored text), in which the green text is the correct prediction. (c) We retrieve images sharing the same visual concepts by their visual concept features for unseen images of "yellow skirt" and "pink pants". + +![](images/43b9d3534ddefb34936bfe0e861b4f47e999213971b126ae3077f7589946977c.jpg) +(c) Top-5 visual concept retrieval. + +Image and text retrieval We first consider text-to-image retrieval. Given a text composition, e.g., "leather heels", we embed it and retrieve the top-5 closest visual features based on the feature distance. We display four text compositions of the different objects sharing the same attributes and vice versa in Fig. 5a. We can observe that the retrieved images are correct in most of the cases. One exception is when retrieving "suede sandals", the third closest image is "fake leather sandals". Although "suede sandals" and "fake leather sandals" are not the same composition, they are quite visually similar. We then consider image-to-text retrieval, shown in Fig. 5b. Given an image, e.g., the image of a "brown zebra", we extract its visual feature and retrieve the top-5 closest text composition embeddings. It is difficult to retrieve the ground-truth label in the top-1 closest text composition, but all top-5 results are all semantically related to the image. We take the image of "blond person" (row 3, col 2) as an example. Although the text composition "blond person" is not retrieved in the top-5 matches, the retrieved results "white shirts", "white outfit", "white shorts", "white pants", and "young girl" are all reasonable and actually present in the image. Image and text retrieval experiments validate that our ADE efficiently projects visual features and word embeddings into a uniform space. + +Visual concept retrieval Because the attribute and the object are visually coupled in an image to a high degree of entanglement, it is challenging to visualize the disentanglement in feature space [41]. Saini et al. [41] retrieve single attribute or object text from test images. However, this process is the same as multi-label classification and insufficient to validate that disentangled visual concepts are learned from images. Based on the disentanglement ability of ADE, we construct a visual concept retrieval experiment to investigate the distances between visual concept features, i.e., the embedded attribute feature $\pi_{a}(v_{a})$ and the embedded object feature $\pi_{o}(v_{o})$ , extracted from different images. Prior to our work, no existing models can do so, because none of them extracts concept-exclusive features like ADE. The results are shown in Fig. 5c. We first extract attribute features and object features from all seen images. Given an unseen image, we retrieve the top-5 closest images by measuring the feature + +distance between the attribute feature of the given image and that of all seen images, and the same goes for the object feature. For the image of "yellow skirt", all retrieval results for the visual concept "yellow" are all "yellow [OBJ]", and all retrieval results for "skirt" are "[ATTR] skirt". For the "pink pants" image, our model also perfectly retrieves the visual concepts, i.e., the attribute "pink" and the object "pants". Our experimental results demonstrate that our ADE model is effective to disentangle visual concepts from seen compositions and combine learned concept knowledge into unseen compositions. + +# 6. Conclusion + +In this paper, we tackle the problem of compositional zero-shot learning (CZSL). To disentangle visual concepts from the attribute-object composition, we propose ADE adopting cross-attentions to learn the individual concept from paired concept-sharing images. To constrain the disentanglers to learn the concept of interest, we employ a regularization term adapted from the earth mover's distance (EMD), which is used as a feature similarity metric in the cross-attention module. Moreover, to exploit the attribute and object prediction ability of ADE, we improve the inference process by combining attribute, object, and composition probabilities into the final prediction score. We empirically demonstrate ADE outperforms the current state-of-the-art methods under both closed- and open-world settings. We also conduct a comprehensive qualitative analysis to validate the disentanglement ability of attention disentanglers in ADE. + +Limitations Like existing CZSL methods, it is time- and computation-consuming to derive all composition embeddings when the numbers of attributes and objects are large. Moreover, it remains an open challenge to exploit concepts based on the actual semantics rather than solely on text; for instance, the "open" attribute in "open curtain" and "open computer" has completely different meanings. + +Acknowledgements This work is partially supported by Hong Kong Research Grant Council - Early Career Scheme (Grant No. 27208022) and HKU Seed Fund for Basic Research. + +# References + +[1] Jean-Baptiste Alayrac, Ivan Laptev, Josef Sivic, and Simon Lacoste-Julien. Joint discovery of object states and manipulation actions. In ICCV, 2017. 2 +[2] Yuval Atzmon, Felix Kreuk, Uri Shalit, and Gal Chechik. A causal view of compositional zero-shot recognition. 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In ECCV, 2022. 1, 2, 3, 5, 6, 7 \ No newline at end of file diff --git a/2023/Learning Attention As Disentangler for Compositional Zero-Shot Learning/images.zip b/2023/Learning Attention As Disentangler for Compositional Zero-Shot Learning/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..e28f10ae228f5e4e26fd610401c09f070a03f9d2 --- /dev/null +++ b/2023/Learning Attention As Disentangler for Compositional Zero-Shot Learning/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:44e4f9162e5c295357d366cfdc472ea1865066a29bfb29e6a85752f38b82e441 +size 581295 diff --git a/2023/Learning Attention As Disentangler for Compositional Zero-Shot Learning/layout.json b/2023/Learning Attention As Disentangler for Compositional Zero-Shot Learning/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..fa183917637ddaf064d8d35d3e98af74cb149b2d --- /dev/null +++ b/2023/Learning Attention As Disentangler for Compositional Zero-Shot Learning/layout.json @@ -0,0 +1,9374 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 67, + 103, + 525, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 103, + 525, + 121 + ], + "spans": [ + { + "bbox": [ + 67, + 103, + 525, + 121 + ], + "type": "text", + "content": "Learning Attention as Disentangler for Compositional Zero-shot Learning" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 168, + 143, + 425, + 172 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 168, + 143, + 425, + 172 + ], + "spans": [ + { + "bbox": [ + 168, + 143, + 425, + 172 + ], + "type": "text", + "content": "Shaozhe Hao Kai Han* Kwan-Yee K. Wong \nThe University of Hong Kong" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 176, + 174, + 414, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 176, + 174, + 414, + 185 + ], + "spans": [ + { + "bbox": [ + 176, + 174, + 414, + 185 + ], + "type": "text", + "content": "{szhao, kykwong}@cs.hku.hk kaihanx@hku.hk" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "spans": [ + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 239, + 290, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 239, + 290, + 502 + ], + "spans": [ + { + "bbox": [ + 45, + 239, + 290, + 502 + ], + "type": "text", + "content": "Compositional zero-shot learning (CZSL) aims at learning visual concepts (i.e., attributes and objects) from seen compositions and combining concept knowledge into unseen compositions. The key to CZSL is learning the disentanglement of the attribute-object composition. To this end, we propose to exploit cross-attention as compositional disentanglers to learn disentangled concept embeddings. For example, if we want to recognize an unseen composition \"yellow flower\", we can learn the attribute concept \"yellow\" and object concept \"flower\" from different yellow objects and different flowers respectively. To further constrain the disentanglers to learn the concept of interest, we employ a regularization at the attention level. Specifically, we adapt the earth mover's distance (EMD) as a feature similarity metric in the cross-attention module. Moreover, benefiting from concept disentanglement, we improve the inference process and tune the prediction score by combining multiple concept probabilities. Comprehensive experiments on three CZSL benchmark datasets demonstrate that our method significantly outperforms previous works in both closed- and open-world settings, establishing a new state-of-the-art. Project page: https://haoosz.github.io/ade-czsl/" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 527, + 127, + 540 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 527, + 127, + 540 + ], + "spans": [ + { + "bbox": [ + 47, + 527, + 127, + 540 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 45, + 548, + 288, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 548, + 288, + 693 + ], + "spans": [ + { + "bbox": [ + 45, + 548, + 288, + 693 + ], + "type": "text", + "content": "Suppose we have never seen white bears (i.e., polar bears) before. Can we picture what it would look like? This is not difficult because we have seen many white animals in daily life (e.g., white dogs and white rabbits) and different bears with various visual attributes in the zoo (e.g., brown bears and black bears). Humans have no difficulty in disentangling \"white\" and \"bear\" from seen instances and combining them into the unseen composition. Inspired by this property of human intelligence, researchers attempt to make machines learn compositions of concepts as well. Compositional zero-shot learning (CZSL) is a specific problem studying visual compositionality, aiming to learn visual concepts from seen" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 307, + 213, + 545, + 361 + ], + "blocks": [ + { + "bbox": [ + 307, + 213, + 545, + 361 + ], + "lines": [ + { + "bbox": [ + 307, + 213, + 545, + 361 + ], + "spans": [ + { + "bbox": [ + 307, + 213, + 545, + 361 + ], + "type": "image", + "image_path": "96a0d7012211e0c75550d61a06ff7e29e7d5473daf047868aa312de345224039.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 364, + 547, + 431 + ], + "lines": [ + { + "bbox": [ + 304, + 364, + 547, + 431 + ], + "spans": [ + { + "bbox": [ + 304, + 364, + 547, + 431 + ], + "type": "text", + "content": "Figure 1. Motivation illustration. Given images from seen attribute-object compositions, human can disentangle the attribute \"yellow\" from \"yellow bird\" and \"yellow pear\", and the object \"flower\" from \"purple flower\" and \"red flower\". After learning visual properties of the concepts \"yellow\" and \"flower\", human can then recognize images from the unseen composition \"yellow flower\"." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 437, + 546, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 437, + 546, + 461 + ], + "spans": [ + { + "bbox": [ + 304, + 437, + 546, + 461 + ], + "type": "text", + "content": "compositions of attributes and objects and generalize concept knowledge to unseen compositions." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 462, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 462, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 462, + 547, + 713 + ], + "type": "text", + "content": "Learning attribute-object compositions demands prior knowledge about attributes and objects. However, visual concepts of attributes and objects never appear alone in a natural image. To learn exclusive concepts for compositionality learning, we need to disentangle the attribute concept and the object concept. As illustrated in Fig. 1, if we want to recognize the image of \"yellow flower\", it is necessary to learn the \"yellow\" concept and the \"flower\" concept, i.e., disentangle visual concepts, from images of seen compositions. Previous works [22, 24, 25, 28-30, 36, 46] tackle CZSL by composing attribute and object word embeddings, and projecting word and visual embeddings to a joint space. They fail to disentangle visual concepts. Recently, some works [21, 40, 41, 50] consider visual disentanglement but still have limitations despite their good performance. SCEN [21] learns concept-constant samples contrastively without constructing concept embedding prototypes to avoid learning irrelevant concepts shared by positive samples. IVR [50] disentangles visual features into ideal concept-invariant domains. This ideal domain generalization setting requires a small discrepancy of attribute and object sets and would degenerate on vaster and more" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 703, + 135, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 703, + 135, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 703, + 135, + 712 + ], + "type": "text", + "content": "*Corresponding author" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15315" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 180 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 180 + ], + "type": "text", + "content": "complex concepts. ProtoProp [40] and OADis [41] learn local attribute and object prototypes from spatial features on convolutional feature maps. However, spatial disentanglement is sometimes infeasible because attribute and object concepts are highly entangled in spatial features. Taking an image of \"yellow flower\" as an example, the spatial positions related to the attribute \"yellow\" and the object \"flower\" completely overlap, which hinders effective attribute-object disentanglement." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 180, + 289, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 180, + 289, + 598 + ], + "spans": [ + { + "bbox": [ + 46, + 180, + 289, + 598 + ], + "type": "text", + "content": "To overcome the above limitations, we propose a simple visual disentangling framework exploiting Attention as DisEntangler (ADE) on top of vision transformers [6]. We notice that vision transformers (ViT) have access to more sub-space global information across multi-head attentions than CNNs [38]. Therefore, with the expressivity of different subspace representations, token attentions of ViT may provide a more effective way for disentangling visual features, compared to using traditional spatial attentions across local positions on convolutional features [40, 41]. Specifically, it is difficult to disentangle the attribute-object composition \"yellow flower\" by spatial positions, but it is possible for ViT multi-head attentions to project attribute concept \"yellow\" and object concept \"flower\" onto different subspaces. Inspired by this property, we propose to learn cross-attention between two inputs that share the same concept, e.g., \"yellow bird\" and \"yellow pear\" share the same attribute concept \"yellow\". In this way, we can derive attribute- and object-exclusive visual representations by cross-attention disentanglement. To ensure that the concept disentangler is exclusive to the specific concept, we also need to constrain the disentanglers to learn the concept of interest instead of the other concept. For example, given attribute-sharing images, the attribute attention should output similar attribute-exclusive features while the object attention should not. To achieve this goal, we apply a regularization term adapted from the earth mover's distance (EMD) [13] at the attention level. This regularization term forces cross-attention to learn the concept of interest by leveraging the feature similarity captured from all tokens. Mancini et al. [24] propose an open-world evaluation setting, which is neglected by most previous works. We consider both closed-world and the open-world settings in our experiments, demonstrating that our method is coherently efficient in both settings. The contributions of this paper are summarized below:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 53, + 600, + 288, + 711 + ], + "type": "list", + "angle": 0, + "index": 5, + "blocks": [ + { + "bbox": [ + 53, + 600, + 288, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 600, + 288, + 635 + ], + "spans": [ + { + "bbox": [ + 53, + 600, + 288, + 635 + ], + "type": "text", + "content": "- We propose a new CZSL approach, named ADE, using cross-attentions to disentangle attribute- and object-exclusive features from paired concept-sharing inputs." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 53, + 638, + 288, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 638, + 288, + 673 + ], + "spans": [ + { + "bbox": [ + 53, + 638, + 288, + 673 + ], + "type": "text", + "content": "- We force attention disentanglers to learn the concept of interest with a regularization term adapted from EMD, ensuring valid attribute-object disentanglement." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 53, + 675, + 288, + 711 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 675, + 288, + 711 + ], + "spans": [ + { + "bbox": [ + 53, + 675, + 288, + 711 + ], + "type": "text", + "content": "- We comprehensively evaluate our method in both closed-world and open-world settings on three CZSL datasets, achieving consistent state-of-the-art." + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 71, + 390, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 71, + 390, + 83 + ], + "spans": [ + { + "bbox": [ + 306, + 71, + 390, + 83 + ], + "type": "text", + "content": "2. Related work" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 91, + 547, + 270 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 91, + 547, + 270 + ], + "spans": [ + { + "bbox": [ + 304, + 91, + 547, + 270 + ], + "type": "text", + "content": "Visual attribute has been widely studied to understand how visual properties can be learned from objects. The pioneering work by Ferrari and Zisserman [10] learned visual attributes using a probabilistic generative model. The successive work by Lampert et al. [20] used visual attributes to detect unseen objects with an attribute-based multi-label classification. Similarly, Patterson et al. [35] proposed Economic Labeling Algorithm (ELA) to discover multi-label attributes for objects. Different from multi-label classification, other works [4,8,15,23] learned attribute-object relationship to generalize attribute feature across all object categories based on probabilistic models. Visual attributes also benefit downstream tasks, e.g., object recognition [7, 16, 31], action recognition [1,9,26], image captioning [19,33], and semi-supervised learning [42]." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 270, + 548, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 270, + 548, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 270, + 548, + 628 + ], + "type": "text", + "content": "Compositional zero-shot learning (CZSL) is a special case of zero-shot learning (ZSL) [34, 39, 43, 47, 48], aims at recognizing unseen attribute-object compositions learning from seen compositions. Misra et al. [28] first termed and studied CZSL by projecting composed primitives and visual features to a joint embedding space. Nagarajan et al. [30] formulated attributes as matrix operators applied on object vectors. Purushwalkam et al. [36] introduced a task-driven modular architecture to learn unseen compositions by re-weighting a set of sub-tasks. Wei et al. [46] generated attribute-object compositions with GAN [11] to match visual features. Li et al. [22] proposed symmetry principle of attribute-object transformation under the supervision of group axioms. Naeem et al. [29] and Mancini et al. [25] used graph convolutional networks to extract attribute-object representations. Recently, some works shift their interest from word composing to visual disentanglement. Atzmon et al. [2] solved CZSL from a causal perspective to learn disentangled representations. Ruis et al. [40] proposed to learn prototypical representations of objects and attributes. Li et al. [21] disentangled visual features into a Siamese contrastive space and entangled them with a generative model. Saini et al. [41] extracted visual similarity from spatial features to disentangle attributes and objects. Zhang et al. [50] treated CZSL as a domain generalization task, learning attribute- and object-invariant domains. A more realistic open-world CZSL setting was studied in [17, 24, 25], which considered all possible compositions in testing. Very recently, an inspiring work by Nayak et al. [32] introduced compositional soft prompts to CLIP [37] to tackle CZSL problem." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 630, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 547, + 715 + ], + "type": "text", + "content": "Attention mechanism has been well studied by non-local neural networks [45] in computer vision and transformers [44] in machine translation. Dosovitskiy et al. [6] adapted transformer architecture to computer vision field, proving its comparable efficiency over traditional CNNs. Inspired by the multi-head self-attention implemented by transformers, our work exploits efficient attention as disentangler for CZSL." + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "15316" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 54, + 70, + 427, + 235 + ], + "blocks": [ + { + "bbox": [ + 54, + 70, + 427, + 235 + ], + "lines": [ + { + "bbox": [ + 54, + 70, + 427, + 235 + ], + "spans": [ + { + "bbox": [ + 54, + 70, + 427, + 235 + ], + "type": "image", + "image_path": "925cc16c877a72219acffeb63e39e57ca1d8a082e63125eae57429d70ed42ed2.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 238, + 547, + 316 + ], + "lines": [ + { + "bbox": [ + 46, + 238, + 547, + 316 + ], + "spans": [ + { + "bbox": [ + 46, + 238, + 547, + 316 + ], + "type": "text", + "content": "Figure 2. Method overview. Left (our framework ADE): Given one target image of \"red bus\", we sample two auxiliary images of the same attribute \"red wall\" and of the same object \"blue bus\". We feed the three images into a frozen ViT initialized with DINO [3]. We then input all encoded tokens (i.e., [CLS] and patch tokens) to three attention modules: (1) attribute cross-attention taking paired attribute-sharing tokens as inputs; (2) object cross-attention taking paired object-sharing tokens as inputs; (3) composition self-attention taking tokens of single target image as input. We then project the [CLS] tokens of attention outputs with three MLP embeddings " + }, + { + "bbox": [ + 46, + 238, + 547, + 316 + ], + "type": "inline_equation", + "content": "\\pi_{a}" + }, + { + "bbox": [ + 46, + 238, + 547, + 316 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 238, + 547, + 316 + ], + "type": "inline_equation", + "content": "\\pi_{c}" + }, + { + "bbox": [ + 46, + 238, + 547, + 316 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 238, + 547, + 316 + ], + "type": "inline_equation", + "content": "\\pi_{o}" + }, + { + "bbox": [ + 46, + 238, + 547, + 316 + ], + "type": "text", + "content": ". We finally compute cross entropy losses of embedded visual features with three learnable word embeddings: attribute embeddings, object embeddings, and their linear fused composition embeddings. Right: Illustration of five losses in attribute, object, and composition embedding spaces." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 437, + 80, + 531, + 231 + ], + "blocks": [ + { + "bbox": [ + 437, + 80, + 531, + 231 + ], + "lines": [ + { + "bbox": [ + 437, + 80, + 531, + 231 + ], + "spans": [ + { + "bbox": [ + 437, + 80, + 531, + 231 + ], + "type": "image", + "image_path": "a9230fe046a161a5fbfffe9bd11e1a36a3fb687d622c98826d42bf7bba39abb3.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 323, + 124, + 337 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 323, + 124, + 337 + ], + "spans": [ + { + "bbox": [ + 47, + 323, + 124, + 337 + ], + "type": "text", + "content": "3. Preliminary" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 341, + 290, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 341, + 290, + 533 + ], + "spans": [ + { + "bbox": [ + 46, + 341, + 290, + 533 + ], + "type": "text", + "content": "Compositional zero-shot learning aims at learning a model from limited compositions of attributes (e.g., yellow) and objects (e.g., flower) to recognize an image from novel compositions. Given a set of all possible attributes " + }, + { + "bbox": [ + 46, + 341, + 290, + 533 + ], + "type": "inline_equation", + "content": "\\mathcal{A} = \\{a_0, a_1, \\dots, a_n\\}" + }, + { + "bbox": [ + 46, + 341, + 290, + 533 + ], + "type": "text", + "content": " and a set of all possible objects " + }, + { + "bbox": [ + 46, + 341, + 290, + 533 + ], + "type": "inline_equation", + "content": "\\mathcal{O} = \\{o_0, o_1, \\dots, o_m\\}" + }, + { + "bbox": [ + 46, + 341, + 290, + 533 + ], + "type": "text", + "content": ", a compositional class set " + }, + { + "bbox": [ + 46, + 341, + 290, + 533 + ], + "type": "inline_equation", + "content": "\\mathcal{C} = \\mathcal{A} \\times \\mathcal{O}" + }, + { + "bbox": [ + 46, + 341, + 290, + 533 + ], + "type": "text", + "content": " includes all attribute-object compositions. We divide " + }, + { + "bbox": [ + 46, + 341, + 290, + 533 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 46, + 341, + 290, + 533 + ], + "type": "text", + "content": " into two disjoint sets, namely the set of seen classes " + }, + { + "bbox": [ + 46, + 341, + 290, + 533 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_s" + }, + { + "bbox": [ + 46, + 341, + 290, + 533 + ], + "type": "text", + "content": " and the set of unseen classes " + }, + { + "bbox": [ + 46, + 341, + 290, + 533 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_u" + }, + { + "bbox": [ + 46, + 341, + 290, + 533 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 341, + 290, + 533 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_s \\cap \\mathcal{C}_u = \\emptyset" + }, + { + "bbox": [ + 46, + 341, + 290, + 533 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 341, + 290, + 533 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_s \\cup \\mathcal{C}_u = \\mathcal{C}" + }, + { + "bbox": [ + 46, + 341, + 290, + 533 + ], + "type": "text", + "content": ". Training images are only from classes in " + }, + { + "bbox": [ + 46, + 341, + 290, + 533 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_s" + }, + { + "bbox": [ + 46, + 341, + 290, + 533 + ], + "type": "text", + "content": " and testing images are from classes in " + }, + { + "bbox": [ + 46, + 341, + 290, + 533 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_{test} = \\mathcal{C}_s \\cup \\mathcal{C}_u'" + }, + { + "bbox": [ + 46, + 341, + 290, + 533 + ], + "type": "text", + "content": ". For closed-world evaluation, " + }, + { + "bbox": [ + 46, + 341, + 290, + 533 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_u'" + }, + { + "bbox": [ + 46, + 341, + 290, + 533 + ], + "type": "text", + "content": " is a predefined subset of " + }, + { + "bbox": [ + 46, + 341, + 290, + 533 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_u" + }, + { + "bbox": [ + 46, + 341, + 290, + 533 + ], + "type": "text", + "content": ", i.e., " + }, + { + "bbox": [ + 46, + 341, + 290, + 533 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_u' \\subset \\mathcal{C}_u" + }, + { + "bbox": [ + 46, + 341, + 290, + 533 + ], + "type": "text", + "content": ". For open-world evaluation, all possible compositions are considered for testing, i.e., " + }, + { + "bbox": [ + 46, + 341, + 290, + 533 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_u' = \\mathcal{C}_u" + }, + { + "bbox": [ + 46, + 341, + 290, + 533 + ], + "type": "text", + "content": ". CZSL task aims to learn a model " + }, + { + "bbox": [ + 46, + 341, + 290, + 533 + ], + "type": "inline_equation", + "content": "f: \\mathcal{X} \\to \\mathcal{C}_{test}" + }, + { + "bbox": [ + 46, + 341, + 290, + 533 + ], + "type": "text", + "content": " to predict labels in the testing composition set " + }, + { + "bbox": [ + 46, + 341, + 290, + 533 + ], + "type": "inline_equation", + "content": "c \\in \\mathcal{C}_{test}" + }, + { + "bbox": [ + 46, + 341, + 290, + 533 + ], + "type": "text", + "content": " for input images " + }, + { + "bbox": [ + 46, + 341, + 290, + 533 + ], + "type": "inline_equation", + "content": "x \\in \\mathcal{X}" + }, + { + "bbox": [ + 46, + 341, + 290, + 533 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 533, + 288, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 533, + 288, + 582 + ], + "spans": [ + { + "bbox": [ + 46, + 533, + 288, + 582 + ], + "type": "text", + "content": "To learn a CZSL model, a common method is to minimize the cosine similarity score between the visually encoded feature and the word embedding of attribute-object compositions. The similarity score can be expressed as" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 94, + 583, + 287, + 609 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 94, + 583, + 287, + 609 + ], + "spans": [ + { + "bbox": [ + 94, + 583, + 287, + 609 + ], + "type": "interline_equation", + "content": "s (x, (a, o)) = \\frac {\\phi (x)}{| | \\phi (x) | |} \\cdot \\frac {\\psi (a , o)}{| | \\psi (a , o) | |} \\tag {1}", + "image_path": "fd22e33acf94e0dc968b45ed3d6edf54d12117e248525ff087d8bd1c31dbd570.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 610, + 289, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 610, + 289, + 635 + ], + "spans": [ + { + "bbox": [ + 46, + 610, + 289, + 635 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 610, + 289, + 635 + ], + "type": "inline_equation", + "content": "\\phi (\\cdot)" + }, + { + "bbox": [ + 46, + 610, + 289, + 635 + ], + "type": "text", + "content": " is the visual encoder, and " + }, + { + "bbox": [ + 46, + 610, + 289, + 635 + ], + "type": "inline_equation", + "content": "\\psi (\\cdot ,\\cdot)" + }, + { + "bbox": [ + 46, + 610, + 289, + 635 + ], + "type": "text", + "content": " is the composition function. The CZSL model " + }, + { + "bbox": [ + 46, + 610, + 289, + 635 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 610, + 289, + 635 + ], + "type": "text", + "content": " can be formulated as" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 86, + 649, + 287, + 670 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 649, + 287, + 670 + ], + "spans": [ + { + "bbox": [ + 86, + 649, + 287, + 670 + ], + "type": "interline_equation", + "content": "f (x; \\theta_ {\\phi}, \\theta_ {\\psi}) = \\underset {a _ {i} \\in \\mathcal {A}, o _ {j} \\in \\mathcal {O}} {\\arg \\max } s (x, \\left(a _ {i}, o _ {j}\\right)) \\tag {2}", + "image_path": "8b6583f581cc84c7eeec80f441baeb986dccd9e3d6fe6fc9422276e161083a5a.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 677, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 289, + 714 + ], + "type": "text", + "content": "The model " + }, + { + "bbox": [ + 47, + 677, + 289, + 714 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 47, + 677, + 289, + 714 + ], + "type": "text", + "content": " is optimized by learning the model parameters " + }, + { + "bbox": [ + 47, + 677, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\theta_{\\phi}" + }, + { + "bbox": [ + 47, + 677, + 289, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 677, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\theta_{\\psi}" + }, + { + "bbox": [ + 47, + 677, + 289, + 714 + ], + "type": "text", + "content": " to match the input " + }, + { + "bbox": [ + 47, + 677, + 289, + 714 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 47, + 677, + 289, + 714 + ], + "type": "text", + "content": " with the most similar attribute-object composition. Visual encoder " + }, + { + "bbox": [ + 47, + 677, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 47, + 677, + 289, + 714 + ], + "type": "text", + "content": " and composition func" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 324, + 548, + 433 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 324, + 548, + 433 + ], + "spans": [ + { + "bbox": [ + 304, + 324, + 548, + 433 + ], + "type": "text", + "content": "tion " + }, + { + "bbox": [ + 304, + 324, + 548, + 433 + ], + "type": "inline_equation", + "content": "\\psi" + }, + { + "bbox": [ + 304, + 324, + 548, + 433 + ], + "type": "text", + "content": ", as two core components, take multiple forms in different methods. For visual encoder, works [40, 41, 50] manually design networks on top of a pretrained backbone (e.g., ResNet18 [12]) to disentangle attribute and object embeddings for visual features. For composition functions, the object conditioned network [41], the graph embedding [29, 40], and the linear projector [24, 50] are commonly used. Unlike employing complex composition functions, we adopt the simple linear projector in our method." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 443, + 394, + 456 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 443, + 394, + 456 + ], + "spans": [ + { + "bbox": [ + 305, + 443, + 394, + 456 + ], + "type": "text", + "content": "4. Our approach" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 463, + 547, + 583 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 463, + 547, + 583 + ], + "spans": [ + { + "bbox": [ + 304, + 463, + 547, + 583 + ], + "type": "text", + "content": "We aim to disentangle attribute and object features for visual representation by learning from image pairs sharing the same attributes or objects. For example, by learning the object \"flower\" from the \"purple flower\" and the \"red flower\" and learning the attribute \"yellow\" from the \"yellow bird\" and the \"yellow pear\", we can infer what a \"yellow flower\" looks like. To this end, we propose ADE to learn cross-attentions as concept disentanglers with the regularization of a novel token earth mover's distance. The whole framework of our method is shown in Fig. 2." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 590, + 503, + 604 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 590, + 503, + 604 + ], + "spans": [ + { + "bbox": [ + 305, + 590, + 503, + 604 + ], + "type": "text", + "content": "4.1. Disentanglement with cross-attention" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 609, + 546, + 681 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 609, + 546, + 681 + ], + "spans": [ + { + "bbox": [ + 304, + 609, + 546, + 681 + ], + "type": "text", + "content": "Multi-head self-attention in transformers [44] is powerful for extracting token connections. Attention maps each query token, and key-value token pairs to an output token. Every output token is a weighted sum of the values, where the weights is the similarity of the corresponding query token and the key tokens. The attention is formulated as:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 335, + 689, + 546, + 717 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 335, + 689, + 546, + 717 + ], + "spans": [ + { + "bbox": [ + 335, + 689, + 546, + 717 + ], + "type": "interline_equation", + "content": "\\operatorname {A t t e n t i o n} (Q, K, V) = \\operatorname {s o f t m a x} \\left(\\frac {Q K ^ {T}}{\\sqrt {d _ {k}}}\\right) V \\tag {3}", + "image_path": "a83a2ed97ea269df33494e94290f498ce47d2c217b9325979aa0b101236cb662.jpg" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "15317" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 70, + 286, + 134 + ], + "blocks": [ + { + "bbox": [ + 48, + 70, + 286, + 134 + ], + "lines": [ + { + "bbox": [ + 48, + 70, + 286, + 134 + ], + "spans": [ + { + "bbox": [ + 48, + 70, + 286, + 134 + ], + "type": "image", + "image_path": "e2ec8ae55dc8f89a72ef5576d46254e89c78dfad4c90c56be84a6ad613b8b42a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 80, + 137, + 253, + 147 + ], + "lines": [ + { + "bbox": [ + 80, + 137, + 253, + 147 + ], + "spans": [ + { + "bbox": [ + 80, + 137, + 253, + 147 + ], + "type": "text", + "content": "Figure 3. Illustration of three types of attention." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 158, + 287, + 255 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 158, + 287, + 255 + ], + "spans": [ + { + "bbox": [ + 47, + 158, + 287, + 255 + ], + "type": "text", + "content": "where three inputs are query tokens " + }, + { + "bbox": [ + 47, + 158, + 287, + 255 + ], + "type": "inline_equation", + "content": "(Q)" + }, + { + "bbox": [ + 47, + 158, + 287, + 255 + ], + "type": "text", + "content": ", key tokens " + }, + { + "bbox": [ + 47, + 158, + 287, + 255 + ], + "type": "inline_equation", + "content": "(K)" + }, + { + "bbox": [ + 47, + 158, + 287, + 255 + ], + "type": "text", + "content": ", and value tokens " + }, + { + "bbox": [ + 47, + 158, + 287, + 255 + ], + "type": "inline_equation", + "content": "(V)" + }, + { + "bbox": [ + 47, + 158, + 287, + 255 + ], + "type": "text", + "content": " and the scaling factor " + }, + { + "bbox": [ + 47, + 158, + 287, + 255 + ], + "type": "inline_equation", + "content": "d_{k}" + }, + { + "bbox": [ + 47, + 158, + 287, + 255 + ], + "type": "text", + "content": " is the dimension of the query and key. Self-attention uses the same input for " + }, + { + "bbox": [ + 47, + 158, + 287, + 255 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 47, + 158, + 287, + 255 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 158, + 287, + 255 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 47, + 158, + 287, + 255 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 158, + 287, + 255 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 47, + 158, + 287, + 255 + ], + "type": "text", + "content": " and effectively captures relationships among [CLS] and patch tokens of a single input image. Normally, the [CLS] token is exclusively used as a global representation of the input image for downstream tasks, but exclusive [CLS] token highly entangles attribute and object concepts." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 255, + 288, + 471 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 255, + 288, + 471 + ], + "spans": [ + { + "bbox": [ + 47, + 255, + 288, + 471 + ], + "type": "text", + "content": "For CZSL task, we want to disentangle the exclusive concept by exploiting the semantic similarity between tokens from different concept-sharing features. For this purpose, we introduce a cross-attention mechanism to extract attribute-exclusive or object-exclusive features for paired images sharing the same attribute or object concept. The cross-attention has the same structure as the self-attention, but works on different inputs. Self-attention uses the same input " + }, + { + "bbox": [ + 47, + 255, + 288, + 471 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 47, + 255, + 288, + 471 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 47, + 255, + 288, + 471 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 47, + 255, + 288, + 471 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 255, + 288, + 471 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 47, + 255, + 288, + 471 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 255, + 288, + 471 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 47, + 255, + 288, + 471 + ], + "type": "text", + "content": " (i.e., " + }, + { + "bbox": [ + 47, + 255, + 288, + 471 + ], + "type": "inline_equation", + "content": "Q = K = V = I" + }, + { + "bbox": [ + 47, + 255, + 288, + 471 + ], + "type": "text", + "content": ") while cross-attention uses one of the paired inputs " + }, + { + "bbox": [ + 47, + 255, + 288, + 471 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 47, + 255, + 288, + 471 + ], + "type": "text", + "content": " for the query and the other " + }, + { + "bbox": [ + 47, + 255, + 288, + 471 + ], + "type": "inline_equation", + "content": "I'" + }, + { + "bbox": [ + 47, + 255, + 288, + 471 + ], + "type": "text", + "content": " for the key and the value (i.e., " + }, + { + "bbox": [ + 47, + 255, + 288, + 471 + ], + "type": "inline_equation", + "content": "Q = I" + }, + { + "bbox": [ + 47, + 255, + 288, + 471 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 255, + 288, + 471 + ], + "type": "inline_equation", + "content": "K = V = I'" + }, + { + "bbox": [ + 47, + 255, + 288, + 471 + ], + "type": "text", + "content": "). In the cross-attention, the query input and the key input play different roles. The cross-attention output is the weighted sum of the value (also the key) input based on the similarity between the query and key inputs. For a pair of input images, we swap the query and key inputs in computing cross-attention to derive two cross-attended outputs for the respective inputs. Cross-attention with query-key swapping (QKS) is illustrated in Fig. 3." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 472, + 287, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 472, + 287, + 579 + ], + "spans": [ + { + "bbox": [ + 46, + 472, + 287, + 579 + ], + "type": "text", + "content": "The cross-attention outputs paired features of the exclusive concept with paired concept-sharing inputs. Taking the object-sharing pair as an example, object cross-attention leverages the shared object features of the key input to enhance the query input, thus making the outputs exclusive to object feature space, i.e., object-exclusive features " + }, + { + "bbox": [ + 46, + 472, + 287, + 579 + ], + "type": "inline_equation", + "content": "v_{o}" + }, + { + "bbox": [ + 46, + 472, + 287, + 579 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 472, + 287, + 579 + ], + "type": "inline_equation", + "content": "v_{o}'" + }, + { + "bbox": [ + 46, + 472, + 287, + 579 + ], + "type": "text", + "content": ". The same applies to attribute-exclusive features " + }, + { + "bbox": [ + 46, + 472, + 287, + 579 + ], + "type": "inline_equation", + "content": "v_{a}" + }, + { + "bbox": [ + 46, + 472, + 287, + 579 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 472, + 287, + 579 + ], + "type": "inline_equation", + "content": "v_{a}'" + }, + { + "bbox": [ + 46, + 472, + 287, + 579 + ], + "type": "text", + "content": " extracted from paired attribute-sharing images. We also use a standard self-attention to extract composition feature " + }, + { + "bbox": [ + 46, + 472, + 287, + 579 + ], + "type": "inline_equation", + "content": "v_{c}" + }, + { + "bbox": [ + 46, + 472, + 287, + 579 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 580, + 287, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 580, + 287, + 687 + ], + "spans": [ + { + "bbox": [ + 46, + 580, + 287, + 687 + ], + "type": "text", + "content": "To train cross-attentions, we adopt common cross entropy loss after MLP embedders " + }, + { + "bbox": [ + 46, + 580, + 287, + 687 + ], + "type": "inline_equation", + "content": "(\\pi_{a},\\pi_{c},\\pi_{o})" + }, + { + "bbox": [ + 46, + 580, + 287, + 687 + ], + "type": "text", + "content": " for attribute-exclusive features " + }, + { + "bbox": [ + 46, + 580, + 287, + 687 + ], + "type": "inline_equation", + "content": "(v_{a},v_{a}^{\\prime})" + }, + { + "bbox": [ + 46, + 580, + 287, + 687 + ], + "type": "text", + "content": ", object-exclusive features " + }, + { + "bbox": [ + 46, + 580, + 287, + 687 + ], + "type": "inline_equation", + "content": "(v_{o},v_{o}^{\\prime})" + }, + { + "bbox": [ + 46, + 580, + 287, + 687 + ], + "type": "text", + "content": ", and composition feature " + }, + { + "bbox": [ + 46, + 580, + 287, + 687 + ], + "type": "inline_equation", + "content": "(v_{c})" + }, + { + "bbox": [ + 46, + 580, + 287, + 687 + ], + "type": "text", + "content": ". We denote any of these visual features as " + }, + { + "bbox": [ + 46, + 580, + 287, + 687 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 46, + 580, + 287, + 687 + ], + "type": "text", + "content": " and the corresponding embedder as " + }, + { + "bbox": [ + 46, + 580, + 287, + 687 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 46, + 580, + 287, + 687 + ], + "type": "text", + "content": ". We denote the word embedding as " + }, + { + "bbox": [ + 46, + 580, + 287, + 687 + ], + "type": "inline_equation", + "content": "w_{z}" + }, + { + "bbox": [ + 46, + 580, + 287, + 687 + ], + "type": "text", + "content": ", where the concept " + }, + { + "bbox": [ + 46, + 580, + 287, + 687 + ], + "type": "inline_equation", + "content": "z\\in \\mathcal{Z}" + }, + { + "bbox": [ + 46, + 580, + 287, + 687 + ], + "type": "text", + "content": " can be any of the attribute " + }, + { + "bbox": [ + 46, + 580, + 287, + 687 + ], + "type": "inline_equation", + "content": "a\\in \\mathcal{A}" + }, + { + "bbox": [ + 46, + 580, + 287, + 687 + ], + "type": "text", + "content": ", the object " + }, + { + "bbox": [ + 46, + 580, + 287, + 687 + ], + "type": "inline_equation", + "content": "o\\in \\mathcal{O}" + }, + { + "bbox": [ + 46, + 580, + 287, + 687 + ], + "type": "text", + "content": ", or the composition " + }, + { + "bbox": [ + 46, + 580, + 287, + 687 + ], + "type": "inline_equation", + "content": "c\\in \\mathcal{C}" + }, + { + "bbox": [ + 46, + 580, + 287, + 687 + ], + "type": "text", + "content": ". The class probability of L2-normalized " + }, + { + "bbox": [ + 46, + 580, + 287, + 687 + ], + "type": "inline_equation", + "content": "\\pi (v)" + }, + { + "bbox": [ + 46, + 580, + 287, + 687 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 580, + 287, + 687 + ], + "type": "inline_equation", + "content": "w_{z}" + }, + { + "bbox": [ + 46, + 580, + 287, + 687 + ], + "type": "text", + "content": " can be computed as:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 72, + 689, + 287, + 716 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 72, + 689, + 287, + 716 + ], + "spans": [ + { + "bbox": [ + 72, + 689, + 287, + 716 + ], + "type": "interline_equation", + "content": "p _ {\\pi} (z \\mid v) = \\frac {\\exp (\\pi (v) \\cdot w _ {z} / \\tau)}{\\sum_ {\\hat {z} \\in \\mathcal {Z}} \\exp (\\pi (v) \\cdot w _ {\\hat {z}} / \\tau)}, z \\in \\mathcal {Z} \\tag {4}", + "image_path": "f34db4f3caf4fa65a876a172b600234a4da3d61f58a40df8111ea619c4f084a6.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 72, + 547, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 547, + 96 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 547, + 96 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 72, + 547, + 96 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 305, + 72, + 547, + 96 + ], + "type": "text", + "content": " is the temperature. We then compute the cross entropy to classify visual features:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 354, + 99, + 545, + 111 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 354, + 99, + 545, + 111 + ], + "spans": [ + { + "bbox": [ + 354, + 99, + 545, + 111 + ], + "type": "interline_equation", + "content": "H _ {\\pi} (v, z) = - \\log p _ {\\pi} (z \\mid v), z \\in \\mathcal {Z} \\tag {5}", + "image_path": "91113d28a08837ba510fcdbdfcd121823ccf7fed6d74d4cadc9b986b55870ccf.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 114, + 547, + 162 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 114, + 547, + 162 + ], + "spans": [ + { + "bbox": [ + 304, + 114, + 547, + 162 + ], + "type": "text", + "content": "Considering different classification objectives of attribute, object, and composition, the general Eq. (5) can be applied to five visual features, i.e., " + }, + { + "bbox": [ + 304, + 114, + 547, + 162 + ], + "type": "inline_equation", + "content": "v_{a}, v_{a}^{\\prime}, v_{o}, v_{o}^{\\prime}, v_{c}" + }, + { + "bbox": [ + 304, + 114, + 547, + 162 + ], + "type": "text", + "content": ". Therefore, the training objective is composed of five cross entropy losses:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 328, + 173, + 522, + 202 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 328, + 173, + 522, + 202 + ], + "spans": [ + { + "bbox": [ + 328, + 173, + 522, + 202 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {c e} = \\underbrace {H _ {\\pi_ {a}} (v _ {a} , a)} _ {\\mathcal {L} _ {a t t r}} + \\underbrace {H _ {\\pi_ {a}} (v _ {a} ^ {\\prime} , a)} _ {\\mathcal {L} _ {a t t r} ^ {\\prime}} + \\underbrace {H _ {\\pi_ {c}} (v _ {c} , c)} _ {\\mathcal {L} _ {c o m}} +", + "image_path": "ae6e83c9a5a0b1889fda9bd84201281bc251cd62961884882fe2ace09dbababd.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 356, + 205, + 545, + 236 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 356, + 205, + 545, + 236 + ], + "spans": [ + { + "bbox": [ + 356, + 205, + 545, + 236 + ], + "type": "interline_equation", + "content": "\\underbrace {H _ {\\pi_ {o}} \\left(v _ {o} , o\\right)} _ {\\mathcal {L} _ {o b j}} + \\underbrace {H _ {\\pi_ {o}} \\left(v _ {o} ^ {\\prime} , o\\right)} _ {\\mathcal {L} _ {o b j} ^ {\\prime}} \\tag {6}", + "image_path": "6d9085072cfc6371c86ea975008134e898242101c677b2a4811cc685c07bdef7.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 246, + 545, + 270 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 246, + 545, + 270 + ], + "spans": [ + { + "bbox": [ + 306, + 246, + 545, + 270 + ], + "type": "text", + "content": "where the attribute label " + }, + { + "bbox": [ + 306, + 246, + 545, + 270 + ], + "type": "inline_equation", + "content": "a\\in \\mathcal{A}" + }, + { + "bbox": [ + 306, + 246, + 545, + 270 + ], + "type": "text", + "content": " , the object label " + }, + { + "bbox": [ + 306, + 246, + 545, + 270 + ], + "type": "inline_equation", + "content": "o\\in \\mathcal{O}" + }, + { + "bbox": [ + 306, + 246, + 545, + 270 + ], + "type": "text", + "content": " , and the composition label " + }, + { + "bbox": [ + 306, + 246, + 545, + 270 + ], + "type": "inline_equation", + "content": "c = (a,o)\\in \\mathcal{C}_{test}" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 279, + 541, + 292 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 279, + 541, + 292 + ], + "spans": [ + { + "bbox": [ + 306, + 279, + 541, + 292 + ], + "type": "text", + "content": "4.2. Disentangling constraint at the attention level" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 298, + 547, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 298, + 547, + 441 + ], + "spans": [ + { + "bbox": [ + 304, + 298, + 547, + 441 + ], + "type": "text", + "content": "So far, we have enabled cross-attentions to disentangle concepts, but we want to further ensure that the attribute and the object disentanglers learn the corresponding attribute and object concepts instead of the opposite concepts. To this end, we introduce an attention-level earth mover's distance (EMD) to constrain disentanglers to learn the concept of interest. The EMD is formulated as an optimal transportation problem in [13]. Suppose we have supplies of " + }, + { + "bbox": [ + 304, + 298, + 547, + 441 + ], + "type": "inline_equation", + "content": "n_s" + }, + { + "bbox": [ + 304, + 298, + 547, + 441 + ], + "type": "text", + "content": " sources " + }, + { + "bbox": [ + 304, + 298, + 547, + 441 + ], + "type": "inline_equation", + "content": "S = \\{s_i\\}_{i=1}^{n_s}" + }, + { + "bbox": [ + 304, + 298, + 547, + 441 + ], + "type": "text", + "content": " and demands of " + }, + { + "bbox": [ + 304, + 298, + 547, + 441 + ], + "type": "inline_equation", + "content": "n_d" + }, + { + "bbox": [ + 304, + 298, + 547, + 441 + ], + "type": "text", + "content": " destinations " + }, + { + "bbox": [ + 304, + 298, + 547, + 441 + ], + "type": "inline_equation", + "content": "D = \\{d_j\\}_{j=1}^{n_d}" + }, + { + "bbox": [ + 304, + 298, + 547, + 441 + ], + "type": "text", + "content": ". Given the moving cost from the " + }, + { + "bbox": [ + 304, + 298, + 547, + 441 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 298, + 547, + 441 + ], + "type": "text", + "content": "-th source to the " + }, + { + "bbox": [ + 304, + 298, + 547, + 441 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 304, + 298, + 547, + 441 + ], + "type": "text", + "content": "-th destination " + }, + { + "bbox": [ + 304, + 298, + 547, + 441 + ], + "type": "inline_equation", + "content": "c_{ij}" + }, + { + "bbox": [ + 304, + 298, + 547, + 441 + ], + "type": "text", + "content": ", an optimal transportation problem aims to find the minimal-cost flow " + }, + { + "bbox": [ + 304, + 298, + 547, + 441 + ], + "type": "inline_equation", + "content": "f_{ij}" + }, + { + "bbox": [ + 304, + 298, + 547, + 441 + ], + "type": "text", + "content": " from sources to destinations:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 328, + 452, + 545, + 475 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 328, + 452, + 545, + 475 + ], + "spans": [ + { + "bbox": [ + 328, + 452, + 545, + 475 + ], + "type": "interline_equation", + "content": "\\underset {f _ {i j}} {\\text {m i n i m i z e}} \\quad \\sum_ {i = 1} ^ {n _ {s}} \\sum_ {j = 1} ^ {n _ {d}} c _ {i j} f _ {i j} \\tag {7}", + "image_path": "9d6824534cd3c8bdb6202bdc3cfafe4da543fb9af9a53761cc4eaa1582b04b7a.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 328, + 478, + 545, + 491 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 328, + 478, + 545, + 491 + ], + "spans": [ + { + "bbox": [ + 328, + 478, + 545, + 491 + ], + "type": "interline_equation", + "content": "\\text {s u b j e c t} f _ {i j} \\geqslant 0, i = 1, \\dots , n _ {s}, j = 1, \\dots , n _ {d} \\tag {8}", + "image_path": "75848594aac16d339cff71087e17b078edf6562b1aa121b7c96375f1c5c7a247.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 378, + 493, + 545, + 514 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 378, + 493, + 545, + 514 + ], + "spans": [ + { + "bbox": [ + 378, + 493, + 545, + 514 + ], + "type": "interline_equation", + "content": "\\sum_ {j = 1} ^ {n _ {d}} f _ {i j} = s _ {i}, i = 1, \\dots , n _ {s} \\tag {9}", + "image_path": "589f50261ea08ea138ce45fd1af967af8653e734ee54aadc4153a6f626093c7a.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 378, + 515, + 545, + 535 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 378, + 515, + 545, + 535 + ], + "spans": [ + { + "bbox": [ + 378, + 515, + 545, + 535 + ], + "type": "interline_equation", + "content": "\\sum_ {i = 1} ^ {n _ {s}} f _ {i j} = d _ {j}, j = 1, \\dots , n _ {d} \\tag {10}", + "image_path": "fd55dcc826c7be46bf27d7cb979be14abde66d188ec61007c87726220b17fdd3.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 546, + 545, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 546, + 545, + 582 + ], + "spans": [ + { + "bbox": [ + 305, + 546, + 545, + 582 + ], + "type": "text", + "content": "where the optimal flow " + }, + { + "bbox": [ + 305, + 546, + 545, + 582 + ], + "type": "inline_equation", + "content": "\\tilde{f}_{ij}" + }, + { + "bbox": [ + 305, + 546, + 545, + 582 + ], + "type": "text", + "content": " is computed by the moving cost " + }, + { + "bbox": [ + 305, + 546, + 545, + 582 + ], + "type": "inline_equation", + "content": "c_{ij}" + }, + { + "bbox": [ + 305, + 546, + 545, + 582 + ], + "type": "text", + "content": ", the supplies " + }, + { + "bbox": [ + 305, + 546, + 545, + 582 + ], + "type": "inline_equation", + "content": "s_i" + }, + { + "bbox": [ + 305, + 546, + 545, + 582 + ], + "type": "text", + "content": ", and the demands " + }, + { + "bbox": [ + 305, + 546, + 545, + 582 + ], + "type": "inline_equation", + "content": "d_j" + }, + { + "bbox": [ + 305, + 546, + 545, + 582 + ], + "type": "text", + "content": ". The EMD can be further formulated as:" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 358, + 593, + 545, + 607 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 358, + 593, + 545, + 607 + ], + "spans": [ + { + "bbox": [ + 358, + 593, + 545, + 607 + ], + "type": "interline_equation", + "content": "\\operatorname {E M D} \\left(c _ {i j}, s _ {i}, d _ {j}\\right) = \\left(1 - c _ {i j}\\right) \\tilde {f} _ {i j}. \\tag {11}", + "image_path": "b43dec6e9b5bae0e3a16483d680a521e2503121498008237af5bbffdd78539a8.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": "When the EMD is greater, the distributions " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": " are closer. In Fig. 4, we show how to use the EMD as a feature similarity metric at the attention level in our cross-attention module. We can derive a cross-attention map from Eq. (3) and the counterpart cross-attention map after query-key swapping. We use the logits of [CLS]-to-patch attentions as supplies " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "s_i" + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": " and demands " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "d_j" + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": ", which represent how similar the global feature of one image is to the local patches of the" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15318" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 71, + 285, + 222 + ], + "blocks": [ + { + "bbox": [ + 49, + 71, + 285, + 222 + ], + "lines": [ + { + "bbox": [ + 49, + 71, + 285, + 222 + ], + "spans": [ + { + "bbox": [ + 49, + 71, + 285, + 222 + ], + "type": "image", + "image_path": "2c42b119f70dfa9e38fac9430870a10d35ce499177dca99449bc897e3f48f4a9.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 224, + 289, + 302 + ], + "lines": [ + { + "bbox": [ + 46, + 224, + 289, + 302 + ], + "spans": [ + { + "bbox": [ + 46, + 224, + 289, + 302 + ], + "type": "text", + "content": "Figure 4. Illustration of the adapted EMD at the attention level. Branches 1 and 2 respectively denote using one of the paired inputs as the query " + }, + { + "bbox": [ + 46, + 224, + 289, + 302 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 46, + 224, + 289, + 302 + ], + "type": "text", + "content": ". We compute the EMD with two attention maps from 1 and 2 branches. We use the [CLS] -to-patch logits as the supplies " + }, + { + "bbox": [ + 46, + 224, + 289, + 302 + ], + "type": "inline_equation", + "content": "s_i" + }, + { + "bbox": [ + 46, + 224, + 289, + 302 + ], + "type": "text", + "content": " and the demands " + }, + { + "bbox": [ + 46, + 224, + 289, + 302 + ], + "type": "inline_equation", + "content": "d_j" + }, + { + "bbox": [ + 46, + 224, + 289, + 302 + ], + "type": "text", + "content": ", and one minus the mean matrix of patch-to-patch logits as the moving cost " + }, + { + "bbox": [ + 46, + 224, + 289, + 302 + ], + "type": "inline_equation", + "content": "c_{ij}" + }, + { + "bbox": [ + 46, + 224, + 289, + 302 + ], + "type": "text", + "content": ". In this way, we adapt the EMD to our cross-attention module." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 310, + 288, + 347 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 310, + 288, + 347 + ], + "spans": [ + { + "bbox": [ + 46, + 310, + 288, + 347 + ], + "type": "text", + "content": "other image. We use one minus the average map of patch-to-patch attentions as the moving cost " + }, + { + "bbox": [ + 46, + 310, + 288, + 347 + ], + "type": "inline_equation", + "content": "c_{ij}" + }, + { + "bbox": [ + 46, + 310, + 288, + 347 + ], + "type": "text", + "content": ". In this way, we can compute an adapted EMD " + }, + { + "bbox": [ + 46, + 310, + 288, + 347 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 46, + 310, + 288, + 347 + ], + "type": "text", + "content": " for the cross-attention:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 82, + 350, + 287, + 365 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 82, + 350, + 287, + 365 + ], + "spans": [ + { + "bbox": [ + 82, + 350, + 287, + 365 + ], + "type": "interline_equation", + "content": "\\lambda_ {q} ^ {p} = \\operatorname {E M D} \\left(c _ {i j}, s _ {i}, d _ {j}; p, q\\right), p, q \\in \\{a, o \\} \\tag {12}", + "image_path": "81c63daf988241acb112eb75e3a7f989960c48df41aa2ed77a62f7e0c1e72ba5.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 369, + 288, + 427 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 369, + 288, + 427 + ], + "spans": [ + { + "bbox": [ + 46, + 369, + 288, + 427 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 369, + 288, + 427 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 46, + 369, + 288, + 427 + ], + "type": "text", + "content": " represents the type of the cross-attention, i.e., attribute cross-attention when " + }, + { + "bbox": [ + 46, + 369, + 288, + 427 + ], + "type": "inline_equation", + "content": "p = a" + }, + { + "bbox": [ + 46, + 369, + 288, + 427 + ], + "type": "text", + "content": " and object cross-attention when " + }, + { + "bbox": [ + 46, + 369, + 288, + 427 + ], + "type": "inline_equation", + "content": "p = o" + }, + { + "bbox": [ + 46, + 369, + 288, + 427 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 369, + 288, + 427 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 46, + 369, + 288, + 427 + ], + "type": "text", + "content": " represents the type of the inputs, i.e., attribute-sharing inputs when " + }, + { + "bbox": [ + 46, + 369, + 288, + 427 + ], + "type": "inline_equation", + "content": "q = a" + }, + { + "bbox": [ + 46, + 369, + 288, + 427 + ], + "type": "text", + "content": " and object-sharing inputs when " + }, + { + "bbox": [ + 46, + 369, + 288, + 427 + ], + "type": "inline_equation", + "content": "q = o" + }, + { + "bbox": [ + 46, + 369, + 288, + 427 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 429, + 288, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 429, + 288, + 498 + ], + "spans": [ + { + "bbox": [ + 46, + 429, + 288, + 498 + ], + "type": "text", + "content": "For attribute cross-attention, attribute-sharing inputs should have large EMD " + }, + { + "bbox": [ + 46, + 429, + 288, + 498 + ], + "type": "inline_equation", + "content": "\\lambda_{a}^{a}" + }, + { + "bbox": [ + 46, + 429, + 288, + 498 + ], + "type": "text", + "content": " while object-sharing inputs should have small EMD " + }, + { + "bbox": [ + 46, + 429, + 288, + 498 + ], + "type": "inline_equation", + "content": "\\lambda_{o}^{a}" + }, + { + "bbox": [ + 46, + 429, + 288, + 498 + ], + "type": "text", + "content": ". It is opposite for object cross-attention, i.e., small " + }, + { + "bbox": [ + 46, + 429, + 288, + 498 + ], + "type": "inline_equation", + "content": "\\lambda_{a}^{o}" + }, + { + "bbox": [ + 46, + 429, + 288, + 498 + ], + "type": "text", + "content": " of attribute-sharing inputs and large " + }, + { + "bbox": [ + 46, + 429, + 288, + 498 + ], + "type": "inline_equation", + "content": "\\lambda_{o}^{o}" + }, + { + "bbox": [ + 46, + 429, + 288, + 498 + ], + "type": "text", + "content": " of object-sharing inputs. Thus, we formulate the regularization term as:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 110, + 502, + 287, + 517 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 110, + 502, + 287, + 517 + ], + "spans": [ + { + "bbox": [ + 110, + 502, + 287, + 517 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {r e g}} = \\lambda_ {o} ^ {a} + \\lambda_ {a} ^ {o} - \\lambda_ {a} ^ {a} - \\lambda_ {o} ^ {o} \\tag {13}", + "image_path": "35dc8bef719468ab511ed844b261cc1cbada45d08ef1f460eed8255da50f4da2.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 522, + 178, + 535 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 522, + 178, + 535 + ], + "spans": [ + { + "bbox": [ + 47, + 522, + 178, + 535 + ], + "type": "text", + "content": "4.3. Training and inference" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 541, + 287, + 565 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 541, + 287, + 565 + ], + "spans": [ + { + "bbox": [ + 46, + 541, + 287, + 565 + ], + "type": "text", + "content": "At the training phase, we formulate our final loss as a cross entropy with regularization for all inputs:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 132, + 568, + 287, + 581 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 132, + 568, + 287, + 581 + ], + "spans": [ + { + "bbox": [ + 132, + 568, + 287, + 581 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\mathcal {L} _ {c e} + \\mathcal {L} _ {r e g} \\tag {14}", + "image_path": "80d1c280e7a3d0fe2702be254d93ac3092a3089d41c2eb0a461bc8d2ab3a4cac.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 583, + 288, + 655 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 583, + 288, + 655 + ], + "spans": [ + { + "bbox": [ + 46, + 583, + 288, + 655 + ], + "type": "text", + "content": "At inference phase, we feed the same test input into three attention branches in a self-attention manner, deriving three class probabilities " + }, + { + "bbox": [ + 46, + 583, + 288, + 655 + ], + "type": "inline_equation", + "content": "p(c), p(a)" + }, + { + "bbox": [ + 46, + 583, + 288, + 655 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 583, + 288, + 655 + ], + "type": "inline_equation", + "content": "p(o)^1" + }, + { + "bbox": [ + 46, + 583, + 288, + 655 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 583, + 288, + 655 + ], + "type": "inline_equation", + "content": "c = (a, o)" + }, + { + "bbox": [ + 46, + 583, + 288, + 655 + ], + "type": "text", + "content": ". Unlike most methods modeling single " + }, + { + "bbox": [ + 46, + 583, + 288, + 655 + ], + "type": "inline_equation", + "content": "p(c)" + }, + { + "bbox": [ + 46, + 583, + 288, + 655 + ], + "type": "text", + "content": " for prediction, we compute our prediction score by synthesizing attribute, object and composition probabilities:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 94, + 665, + 287, + 685 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 94, + 665, + 287, + 685 + ], + "spans": [ + { + "bbox": [ + 94, + 665, + 287, + 685 + ], + "type": "interline_equation", + "content": "\\hat {c} = \\underset {c \\in \\mathcal {C} _ {\\text {t e s t}}} {\\arg \\max } p (c) + \\beta \\cdot p (a) \\cdot p (o) \\tag {15}", + "image_path": "6ac2e4369ab129e05b715bff75ebe543d9bfb8ef75dd69c11f10f0ec6cb693dd.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "text", + "content": "We first fix " + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "inline_equation", + "content": "\\beta = 1.0" + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "text", + "content": " during training and then validate " + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "inline_equation", + "content": "\\beta = 0.0, 0.1, \\dots, 1.0" + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "text", + "content": " to choose the best " + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "text", + "content": " on the validation set. Finally, we compute the composition prediction as Eq. (15) with the chosen " + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "text", + "content": ", making the best prediction trade-off between generalized composition and independent concept." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 142, + 388, + 155 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 142, + 388, + 155 + ], + "spans": [ + { + "bbox": [ + 306, + 142, + 388, + 155 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 162, + 425, + 174 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 162, + 425, + 174 + ], + "spans": [ + { + "bbox": [ + 306, + 162, + 425, + 174 + ], + "type": "text", + "content": "5.1. Experimental details" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 179, + 547, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 179, + 547, + 312 + ], + "spans": [ + { + "bbox": [ + 304, + 179, + 547, + 312 + ], + "type": "text", + "content": "Datasets We use three benchmark datasets in CZSL problem, namely Clothing16K [50], UT-Zappos50K [49], and C-GQA [29]. Clothing16K [50] contains different types of clothing (e.g., shirt, pants) with color attributes (e.g., white, black). UT-Zappos50K [49] is a fine-grained dataset consisting of different kinds of shoes (e.g., sneakers, sandals) with texture attributes (e.g., leather, canvas). C-GQA [29] is a split built on top of Stanford GQA dataset [14], composed of extensive common attribute concepts (e.g., old, wet) and object concepts (e.g., dog, bus) in real life. We follow the common data splits of these three datasets (see Table 1)." + } + ] + } + ], + "index": 16 + }, + { + "type": "table", + "bbox": [ + 307, + 316, + 548, + 360 + ], + "blocks": [ + { + "bbox": [ + 307, + 316, + 548, + 360 + ], + "lines": [ + { + "bbox": [ + 307, + 316, + 548, + 360 + ], + "spans": [ + { + "bbox": [ + 307, + 316, + 548, + 360 + ], + "type": "table", + "html": "
DatasetsCompositionTrainValTest
|A||O||A| × |O||Cs||X||Cs| / |Cu||X||Cs| / |Cu||X|
Clothing16K [50]987218724210 / 1055159 / 83413
UT-Zappos50K [49]1612192832299815 / 15321418 / 182914
C-GQA [29]4136742783625592269201252 / 10407280888 / 9235098
", + "image_path": "94bae43b3d4ea57d4290bb7527b88dd5cc57f7752da637675869729bf663975c.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "table_body" + } + ], + "index": 17 + }, + { + "bbox": [ + 351, + 361, + 499, + 371 + ], + "lines": [ + { + "bbox": [ + 351, + 361, + 499, + 371 + ], + "spans": [ + { + "bbox": [ + 351, + 361, + 499, + 371 + ], + "type": "text", + "content": "Table 1. Summary of data split statistics." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 374, + 547, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 374, + 547, + 495 + ], + "spans": [ + { + "bbox": [ + 304, + 374, + 547, + 495 + ], + "type": "text", + "content": "Open-world setting In addition to the standard closed-world setting, we also evaluate our model on the open-world setting [24], which is neglected by most previous works. The open-world setting considers all possible compositions, which requires a much larger testing space than the closed-world setting during inference. Taking UT-Zappos50K as an example (see Table 1), the closed world only considers 36 compositions in the testing set while the open world considers total 192 compositions, in which " + }, + { + "bbox": [ + 304, + 374, + 547, + 495 + ], + "type": "inline_equation", + "content": "\\sim 81\\%" + }, + { + "bbox": [ + 304, + 374, + 547, + 495 + ], + "type": "text", + "content": " are ignored under the standard closed-world setting." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 498, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 547, + 713 + ], + "type": "text", + "content": "Evaluation metrics Since CZSL models have an inherent bias for seen compositions, we follow the generalized CZSL evaluation protocol [36]. To overcome the negative bias for seen compositions, we apply different calibration terms to unseen compositions and compute the corresponding top-1 accuracy of seen and unseen compositions, where a larger bias makes higher unseen accuracy and lower seen accuracy, and vice versa. We treat seen accuracy as " + }, + { + "bbox": [ + 304, + 498, + 547, + 713 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 498, + 547, + 713 + ], + "type": "text", + "content": "-axis and unseen accuracy as " + }, + { + "bbox": [ + 304, + 498, + 547, + 713 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 304, + 498, + 547, + 713 + ], + "type": "text", + "content": "-axis to derive an unseen-seen accuracy curve. We can then compute the area under curve (AUC), the best harmonic mean, the best seen accuracy, and the best unseen accuracy from the curve. In our experiments, we report these four metrics for evaluation, among which AUC is the most representative and stable metric for measuring CZSL model performance. Note that the attribute accuracy or the object accuracy alone does not reflect CZSL performance, because the individual accuracy on attribute or object does not necessarily decide the accuracy of their composition." + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 47, + 693, + 288, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 693, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 693, + 288, + 713 + ], + "type": "text", + "content": "1Abbreviations for " + }, + { + "bbox": [ + 47, + 693, + 288, + 713 + ], + "type": "inline_equation", + "content": "p_{\\pi_c}(c|v_c),p_{\\pi_a}(a|v_a)" + }, + { + "bbox": [ + 47, + 693, + 288, + 713 + ], + "type": "text", + "content": " , and " + }, + { + "bbox": [ + 47, + 693, + 288, + 713 + ], + "type": "inline_equation", + "content": "p_{\\pi_o}(o|v_o)" + }, + { + "bbox": [ + 47, + 693, + 288, + 713 + ], + "type": "text", + "content": " , where " + }, + { + "bbox": [ + 47, + 693, + 288, + 713 + ], + "type": "inline_equation", + "content": "v_{c}" + }, + { + "bbox": [ + 47, + 693, + 288, + 713 + ], + "type": "inline_equation", + "content": "v_{a}" + }, + { + "bbox": [ + 47, + 693, + 288, + 713 + ], + "type": "text", + "content": " , and " + }, + { + "bbox": [ + 47, + 693, + 288, + 713 + ], + "type": "inline_equation", + "content": "v_{o}" + }, + { + "bbox": [ + 47, + 693, + 288, + 713 + ], + "type": "text", + "content": " are outputs from three self-attention." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15319" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 70, + 547, + 177 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 547, + 177 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 547, + 177 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 547, + 177 + ], + "type": "table", + "html": "
Closed-world \nModelsClothing16KUT-Zappos50KC-GQA
AUCHMSeenUnseenAttrObjAUCHMSeenUnseenAttrObjAUCHMSeenUnseenAttrObj
SymNet [22]78.879.398.085.175.684.132.645.660.668.648.277.03.113.530.913.311.434.6
CompCos [24]90.387.298.596.890.291.831.848.158.863.845.572.42.912.830.712.210.433.9
GraphEmb [29]89.284.298.097.490.093.134.548.561.670.050.877.13.815.032.314.913.833.2
Co-CGE [25]88.387.998.594.787.491.430.844.660.962.646.073.53.614.731.614.312.634.6
SCEN [21]78.878.598.089.681.285.430.946.765.762.944.074.43.514.631.713.410.731.4
IVR [50]90.686.699.097.089.393.634.349.261.568.148.474.62.210.927.310.010.337.5
OADis [41]88.486.197.794.284.993.132.646.960.768.849.376.93.814.733.414.38.936.3
ADE (ours)92.488.798.297.790.293.635.151.163.064.346.374.05.218.035.017.716.832.3
", + "image_path": "c594b8d84e62928d280c3b42a986bee93bee7b525f7127318fe56ad77c5f2be7.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 50, + 217, + 545, + 326 + ], + "blocks": [ + { + "bbox": [ + 47, + 178, + 546, + 212 + ], + "lines": [ + { + "bbox": [ + 47, + 178, + 546, + 212 + ], + "spans": [ + { + "bbox": [ + 47, + 178, + 546, + 212 + ], + "type": "text", + "content": "Table 2. Closed-world results on three datasets. We report the area under curve (AUC), the best harmonic mean (HM), the best seen accuracy (Seen), the best unseen accuracy (Unseen), the attribute accuracy (Attr), and the object accuracy (Obj) of the unseen-seen accuracy curve under the closed world-setting. AUC is the core CZSL metric. All models use the same DINO ViT-B-16 backbone." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 217, + 545, + 326 + ], + "lines": [ + { + "bbox": [ + 50, + 217, + 545, + 326 + ], + "spans": [ + { + "bbox": [ + 50, + 217, + 545, + 326 + ], + "type": "table", + "html": "
Open-world \nModelsClothing16KUT-Zappos50KC-GQA
AUCHMSeenUnseenAttrObjAUCHMSeenUnseenAttrObjAUCHMSeenUnseenAttrObj
SymNet [22]57.468.398.260.757.681.225.040.660.451.038.275.00.774.930.13.218.437.5
CompCos [24]64.170.898.269.871.783.720.736.058.146.036.471.10.724.332.82.815.137.8
GraphEmb [29]62.068.398.569.771.882.423.540.060.647.037.169.30.814.832.73.217.236.7
Co-CGE [25]59.369.298.763.868.576.222.040.357.743.433.967.20.483.331.12.115.535.7
SCEN [21]53.761.596.762.363.679.122.538.064.847.534.973.30.342.529.51.514.832.3
IVR [50]63.672.098.769.070.384.825.342.360.750.038.471.40.945.730.64.016.936.5
OADis [41]53.463.298.058.657.385.425.341.658.753.940.374.70.714.233.02.614.639.7
ADE (ours)68.074.299.073.175.084.527.144.862.450.739.971.41.427.635.14.822.435.6
", + "image_path": "5412042f095b816a022ad4e4f14d1c5b240bd91e8b9ba8f28d9e0fcfa600d102.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 51, + 327, + 541, + 338 + ], + "lines": [ + { + "bbox": [ + 51, + 327, + 541, + 338 + ], + "spans": [ + { + "bbox": [ + 51, + 327, + 541, + 338 + ], + "type": "text", + "content": "Table 3. Open-world results on three datasets. Different from Table 2, open-world setting considers all possible compositions in testing." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 346, + 289, + 550 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 346, + 289, + 550 + ], + "spans": [ + { + "bbox": [ + 46, + 346, + 289, + 550 + ], + "type": "text", + "content": "Implementation details We use a frozen ViT-B-16 [6] backbone pretrained with DINO [3] on ImageNet [5] in a self-supervised manner as our visual feature extractor. The ViT-B-16 outputs contain 197 tokens (1 [CLS] and 196 patch tokens) of 768 dimensions. For three attention disentangler modules, we implement one-layer multi-head attention framework following [44], changing the single input to paired inputs for cross-attention. The embedders " + }, + { + "bbox": [ + 46, + 346, + 289, + 550 + ], + "type": "inline_equation", + "content": "\\pi_{a},\\pi_{c},\\pi_{o}" + }, + { + "bbox": [ + 46, + 346, + 289, + 550 + ], + "type": "text", + "content": " are the two-layer MLPs following the previous works [24,50], projecting the 768-dimension visual features to 300-dimension word embedding space. The word embedding prototypes are initialized with word2vec [27] for all datasets and learnable during training. The composition function " + }, + { + "bbox": [ + 46, + 346, + 289, + 550 + ], + "type": "inline_equation", + "content": "\\psi" + }, + { + "bbox": [ + 46, + 346, + 289, + 550 + ], + "type": "text", + "content": " is one linear layer. We train our model using Adam optimizer [18] with a learning rate of " + }, + { + "bbox": [ + 46, + 346, + 289, + 550 + ], + "type": "inline_equation", + "content": "5\\times 10^{-6}" + }, + { + "bbox": [ + 46, + 346, + 289, + 550 + ], + "type": "text", + "content": " for UT-Zappos50K and Clothing16K, and " + }, + { + "bbox": [ + 46, + 346, + 289, + 550 + ], + "type": "inline_equation", + "content": "5\\times 10^{-5}" + }, + { + "bbox": [ + 46, + 346, + 289, + 550 + ], + "type": "text", + "content": " for C-GQA. All models are trained with 128 batch size for 300 epochs." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 562, + 128, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 562, + 128, + 574 + ], + "spans": [ + { + "bbox": [ + 47, + 562, + 128, + 574 + ], + "type": "text", + "content": "5.2. Comparison" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 582, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 289, + 714 + ], + "type": "text", + "content": "To ensure a fair comparison and demonstrate that our improvement over baseline models is not merely by ViT, we adopt ViT backbone to state-of-the-art CZSL models and re-train all models. We compare our method with them: (1) OADis [41] disentangles attribute and object features from spatial convolutional maps; (2) SymNet [22] introduces the symmetry principle of attribute-object transformation and group theory as training objectives; (3) CompCos [24] extends CZSL to an open-world setting considering all possible compositions during inference, proposing a feasibility score based on data statistics to remove unfeasible compositions;" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 346, + 547, + 454 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 346, + 547, + 454 + ], + "spans": [ + { + "bbox": [ + 304, + 346, + 547, + 454 + ], + "type": "text", + "content": "(4) GraphEmb [29] and Co-CGE [25] propose to use graph convolutional networks (GCN) to represent attribute-object relationships and compositions; (5) SCEN [21] projects visual features to a Siamese contrastive space to capture concept prototypes, and introduces complex state transition module to produce virtual compositions; (6) IVR [50] proposes to disentangle visual features into concept-invariant domains from a perspective of domain generalization, by masking specific channels of visual features." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 458, + 548, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 458, + 548, + 662 + ], + "spans": [ + { + "bbox": [ + 304, + 458, + 548, + 662 + ], + "type": "text", + "content": "Closed-world evaluation In Table 2, we compare our ADE model with the state-of-the-art methods. ADE consistently outperforms others by a significant margin. ADE increases the core metric AUC by 1.8 on Clothing16K, 0.6 on UT-Zappos50K, and 1.4 on C-GQA (" + }, + { + "bbox": [ + 304, + 458, + 548, + 662 + ], + "type": "inline_equation", + "content": "\\sim 37\\%" + }, + { + "bbox": [ + 304, + 458, + 548, + 662 + ], + "type": "text", + "content": " relatively). Similarly, ADE increases the best harmonic mean (HM) by " + }, + { + "bbox": [ + 304, + 458, + 548, + 662 + ], + "type": "inline_equation", + "content": "0.8\\%" + }, + { + "bbox": [ + 304, + 458, + 548, + 662 + ], + "type": "text", + "content": " on Clothing16K, " + }, + { + "bbox": [ + 304, + 458, + 548, + 662 + ], + "type": "inline_equation", + "content": "1.9\\%" + }, + { + "bbox": [ + 304, + 458, + 548, + 662 + ], + "type": "text", + "content": " on UT-Zappos50K, and " + }, + { + "bbox": [ + 304, + 458, + 548, + 662 + ], + "type": "inline_equation", + "content": "3.0\\%" + }, + { + "bbox": [ + 304, + 458, + 548, + 662 + ], + "type": "text", + "content": " on C-GQA. We notice that SymNet [22] and SCEN [21] perform badly on Clothing16K. The reason might be that not learning concept prototypes harms the word embedding expressivity on small-scale concepts. We also notice that IVR [50] performs very well on curated datasets Clothing16K and UT-Zappos50K but badly on larger-scale real-world dataset C-GQA. We hypothesize ideal concept-invariant domains might be difficult to learn from natural images and large-scale concepts of C-GQA. In contrast, our ADE model achieves state-of-the-art performance on all datasets." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 665, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 548, + 715 + ], + "type": "text", + "content": "Open-world evaluation In Table 3, we consider the open-world setting to compare our ADE with other methods. Likewise, ADE also performs the best among all methods under open-world setting. ADE increases AUC by 3.9 on Cloth-" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "15320" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 58, + 70, + 261, + 130 + ], + "blocks": [ + { + "bbox": [ + 58, + 70, + 261, + 130 + ], + "lines": [ + { + "bbox": [ + 58, + 70, + 261, + 130 + ], + "spans": [ + { + "bbox": [ + 58, + 70, + 261, + 130 + ], + "type": "table", + "html": "
CAAAOARegAUCHMSeenUnseen
(0)✘✘✘✘23.841.159.048.9
(1)self✘✘✘25.342.361.149.9
(2)selfselfself✘26.744.661.949.8
(3)selfcrosscross✘26.944.563.448.7
(4)selfcrosscross✓27.144.862.450.7
", + "image_path": "018e52e761bcc7301087bc016150f60778f25bffb6a3ad0f924381b16da78d2c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 46, + 133, + 269, + 175 + ], + "lines": [ + { + "bbox": [ + 46, + 133, + 269, + 175 + ], + "spans": [ + { + "bbox": [ + 46, + 133, + 269, + 175 + ], + "type": "text", + "content": "Table 4. Ablate the components in ADE on open-world UT-Zappos50K. CA, AA, and OA denote composition, attribute, and object attention. Reg denotes the regularization term. We test self- or cross-attention for AA and OA." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 185, + 289, + 330 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 185, + 289, + 330 + ], + "spans": [ + { + "bbox": [ + 46, + 185, + 289, + 330 + ], + "type": "text", + "content": "ing16K, 1.8 on UT-Zappos50K, and 0.48 on C-GQA (" + }, + { + "bbox": [ + 46, + 185, + 289, + 330 + ], + "type": "inline_equation", + "content": "\\sim 51\\%" + }, + { + "bbox": [ + 46, + 185, + 289, + 330 + ], + "type": "text", + "content": " relatively). ADE also increases the best harmonic mean (HM) by " + }, + { + "bbox": [ + 46, + 185, + 289, + 330 + ], + "type": "inline_equation", + "content": "2.2\\%" + }, + { + "bbox": [ + 46, + 185, + 289, + 330 + ], + "type": "text", + "content": " on Clothing16K, " + }, + { + "bbox": [ + 46, + 185, + 289, + 330 + ], + "type": "inline_equation", + "content": "2.5\\%" + }, + { + "bbox": [ + 46, + 185, + 289, + 330 + ], + "type": "text", + "content": " on UT-Zappos50K, and " + }, + { + "bbox": [ + 46, + 185, + 289, + 330 + ], + "type": "inline_equation", + "content": "1.9\\%" + }, + { + "bbox": [ + 46, + 185, + 289, + 330 + ], + "type": "text", + "content": " on C-GQA (" + }, + { + "bbox": [ + 46, + 185, + 289, + 330 + ], + "type": "inline_equation", + "content": "\\sim 33\\%" + }, + { + "bbox": [ + 46, + 185, + 289, + 330 + ], + "type": "text", + "content": " relatively). From the above results, ADE surpasses others by a larger margin on open-world AUC and HM than closed-world ones, indicating ADE maintains utmost efficiency when turning from the closed world to the open world. It is worth mentioning that ADE does not apply any special operations (e.g., feasibility masking [24]) for the open world and deals with the two settings in exactly the same way. IVR [50] keeps its performance to a great extent but still lags behind our method significantly." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 339, + 139, + 352 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 339, + 139, + 352 + ], + "spans": [ + { + "bbox": [ + 47, + 339, + 139, + 352 + ], + "type": "text", + "content": "5.3. Ablation study" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 359, + 288, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 359, + 288, + 491 + ], + "spans": [ + { + "bbox": [ + 46, + 359, + 288, + 491 + ], + "type": "text", + "content": "**Backbone:** ResNet vs ViT Our work leverages ViT as the default backbone to excavate more high-level sub-space information, while ResNet18 is the most common backbone in previous works. In Table 6, we compare our ADE to OADis [41] with both backbones. Our ADE performs similarly to OADis with ResNet18, but outperforms it significantly with ViT. Additionally, we present an ablation study on different components of our method with the ResNet18 backbone in the Appendix. These experiments indicate that our model benefits from ViT and all components of our method are effective regardless of the backbone." + } + ] + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 50, + 498, + 286, + 570 + ], + "blocks": [ + { + "bbox": [ + 50, + 498, + 286, + 570 + ], + "lines": [ + { + "bbox": [ + 50, + 498, + 286, + 570 + ], + "spans": [ + { + "bbox": [ + 50, + 498, + 286, + 570 + ], + "type": "table", + "html": "
Closed-worldClothing16KUT-Zappos50KC-GQA
BackboneModelsAUCHMAUCHMAUCHM
ResNet18OADis [41]85.584.730.044.43.113.6
ADE (ours)87.285.129.547.03.113.7
ViT-B-16OADis [41]88.486.132.646.93.814.7
ADE (ours)92.488.735.151.15.218.0
", + "image_path": "9db4d4725be8759c192483283da493c4e40648ac463a5bbadbb65612ecc05a52.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 49, + 571, + 285, + 582 + ], + "lines": [ + { + "bbox": [ + 49, + 571, + 285, + 582 + ], + "spans": [ + { + "bbox": [ + 49, + 571, + 285, + 582 + ], + "type": "text", + "content": "Table 6. Compare ADE and OADis [41] with ResNet18 and ViT." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 594, + 289, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 289, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 289, + 713 + ], + "type": "text", + "content": "Different parts of ADE We evaluate the effectiveness of attention disentanglers (composition, attribute, and object attention) and the regularization term in our model. We report the ablation study results on the open-world UT-Zappos50K in Table 4. Rows (0)-(2) show attention disentanglers can significantly improve the performance. Rows (2)-(3) show that cross-attention learns disentangled concepts better than self-attention for AA and OA. Rows (3)-(4) show the regularization term can further benefit the visual disentanglement, improving the unseen accuracy and overall AUC." + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 276, + 70, + 547, + 131 + ], + "blocks": [ + { + "bbox": [ + 276, + 70, + 547, + 131 + ], + "lines": [ + { + "bbox": [ + 276, + 70, + 547, + 131 + ], + "spans": [ + { + "bbox": [ + 276, + 70, + 547, + 131 + ], + "type": "table", + "html": "
Inference formulationC-GQAClothing16K
AUCHMSeenUnseenAUCHMSeenUnseen
(0)p(c)4.616.835.116.092.488.898.297.7
(1)p(a) · p(o)4.015.831.415.157.366.396.763.1
(2)p(c) + p(a) · p(o)5.218.035.017.790.485.998.297.0
(3)p(c) + β · p(a) · p(o)5.218.035.017.792.488.798.297.7
", + "image_path": "78c1a9361bb32d441453c48a16c84f617d62aa09813dd71b4099cd219eb22b6a.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 274, + 133, + 547, + 176 + ], + "lines": [ + { + "bbox": [ + 274, + 133, + 547, + 176 + ], + "spans": [ + { + "bbox": [ + 274, + 133, + 547, + 176 + ], + "type": "text", + "content": "Table 5. Results on closed-world Clothing16K and C-GQA using different inference formulations. Rows (0)-(2) respectively represents the cases when " + }, + { + "bbox": [ + 274, + 133, + 547, + 176 + ], + "type": "inline_equation", + "content": "\\beta = 0.0" + }, + { + "bbox": [ + 274, + 133, + 547, + 176 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 274, + 133, + 547, + 176 + ], + "type": "inline_equation", + "content": "\\beta = +\\infty" + }, + { + "bbox": [ + 274, + 133, + 547, + 176 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 274, + 133, + 547, + 176 + ], + "type": "inline_equation", + "content": "\\beta = 1.0" + }, + { + "bbox": [ + 274, + 133, + 547, + 176 + ], + "type": "text", + "content": ". Row (3) is our inference formulation, which applies an " + }, + { + "bbox": [ + 274, + 133, + 547, + 176 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 274, + 133, + 547, + 176 + ], + "type": "text", + "content": " optimized on the validation set." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 185, + 547, + 377 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 185, + 547, + 377 + ], + "spans": [ + { + "bbox": [ + 304, + 185, + 547, + 377 + ], + "type": "text", + "content": "Inference formulation We also investigate the effect of our inference formulation " + }, + { + "bbox": [ + 304, + 185, + 547, + 377 + ], + "type": "inline_equation", + "content": "p(c) + \\beta \\cdot p(a) \\cdot p(o)" + }, + { + "bbox": [ + 304, + 185, + 547, + 377 + ], + "type": "text", + "content": " in Table 5. We report the results with extreme values of " + }, + { + "bbox": [ + 304, + 185, + 547, + 377 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 185, + 547, + 377 + ], + "type": "text", + "content": ", i.e., " + }, + { + "bbox": [ + 304, + 185, + 547, + 377 + ], + "type": "inline_equation", + "content": "\\beta = 0.0" + }, + { + "bbox": [ + 304, + 185, + 547, + 377 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 185, + 547, + 377 + ], + "type": "inline_equation", + "content": "\\beta = 1.0" + }, + { + "bbox": [ + 304, + 185, + 547, + 377 + ], + "type": "text", + "content": ". Note that " + }, + { + "bbox": [ + 304, + 185, + 547, + 377 + ], + "type": "inline_equation", + "content": "\\beta = 0.0" + }, + { + "bbox": [ + 304, + 185, + 547, + 377 + ], + "type": "text", + "content": " means only using composition probability for prediction. In addition, we also test the performance only using the product of attribute and object probabilities " + }, + { + "bbox": [ + 304, + 185, + 547, + 377 + ], + "type": "inline_equation", + "content": "p(a) \\cdot p(o)" + }, + { + "bbox": [ + 304, + 185, + 547, + 377 + ], + "type": "text", + "content": ". We can observe that the best fixed " + }, + { + "bbox": [ + 304, + 185, + 547, + 377 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 185, + 547, + 377 + ], + "type": "text", + "content": " value is unfixed among datasets. For example, " + }, + { + "bbox": [ + 304, + 185, + 547, + 377 + ], + "type": "inline_equation", + "content": "\\beta = 1.0" + }, + { + "bbox": [ + 304, + 185, + 547, + 377 + ], + "type": "text", + "content": " gives the highest AUC for C-GQA in row (2) while " + }, + { + "bbox": [ + 304, + 185, + 547, + 377 + ], + "type": "inline_equation", + "content": "\\beta = 0.0" + }, + { + "bbox": [ + 304, + 185, + 547, + 377 + ], + "type": "text", + "content": " for Clothing16K in row (0). In contrast, our validated " + }, + { + "bbox": [ + 304, + 185, + 547, + 377 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 185, + 547, + 377 + ], + "type": "text", + "content": " consistently gives the best inference results for both datasets. Another observation on C-GQA is that " + }, + { + "bbox": [ + 304, + 185, + 547, + 377 + ], + "type": "inline_equation", + "content": "p(a) \\cdot p(o)" + }, + { + "bbox": [ + 304, + 185, + 547, + 377 + ], + "type": "text", + "content": " alone is not a good prediction, but adding it to " + }, + { + "bbox": [ + 304, + 185, + 547, + 377 + ], + "type": "inline_equation", + "content": "p(c)" + }, + { + "bbox": [ + 304, + 185, + 547, + 377 + ], + "type": "text", + "content": " can increase the unseen accuracy. This indicates that the disentangled attribute prediction " + }, + { + "bbox": [ + 304, + 185, + 547, + 377 + ], + "type": "inline_equation", + "content": "p(a)" + }, + { + "bbox": [ + 304, + 185, + 547, + 377 + ], + "type": "text", + "content": " and object prediction " + }, + { + "bbox": [ + 304, + 185, + 547, + 377 + ], + "type": "inline_equation", + "content": "p(o)" + }, + { + "bbox": [ + 304, + 185, + 547, + 377 + ], + "type": "text", + "content": " indeed enhance the unseen generalization for CZSL problem." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 381, + 547, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 381, + 547, + 514 + ], + "spans": [ + { + "bbox": [ + 304, + 381, + 547, + 514 + ], + "type": "text", + "content": "Effect of regularization term We propose an EMD-adapted regularization term at the attention level to force attentions to disentangle the concept of interest. We also investigate the effect of applying the regularization term at the feature level. Specifically, we compare our EMD-based distance to the cosine and euclidean feature distances. The results on open-world UT-Zappos50K are shown in Table 7. Our EMD-based regularization outperforms other distance forms, because our attention-level EMD distance considers token-wise similarity capturing the specific concept-related attention responses." + } + ] + } + ], + "index": 11 + }, + { + "type": "table", + "bbox": [ + 307, + 519, + 547, + 563 + ], + "blocks": [ + { + "bbox": [ + 307, + 519, + 547, + 563 + ], + "lines": [ + { + "bbox": [ + 307, + 519, + 547, + 563 + ], + "spans": [ + { + "bbox": [ + 307, + 519, + 547, + 563 + ], + "type": "table", + "html": "
RegAUCHMSeenUnseen
Cosine26.844.763.048.6
Euclidean26.244.362.647.5
Ours (EMD)27.144.862.450.7
", + "image_path": "74388ef1d9b10e21eb00214d2d75b8ad8fdee2f7a319c8fa1363d88f4b0359b3.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 304, + 564, + 547, + 586 + ], + "lines": [ + { + "bbox": [ + 304, + 564, + 547, + 586 + ], + "spans": [ + { + "bbox": [ + 304, + 564, + 547, + 586 + ], + "type": "text", + "content": "Table 7. Comparison of different regularization terms on openworld UT-Zappos50K." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 599, + 421, + 612 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 599, + 421, + 612 + ], + "spans": [ + { + "bbox": [ + 306, + 599, + 421, + 612 + ], + "type": "text", + "content": "5.4. Qualitative analysis" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "text", + "content": "Visual disentanglement in feature space is hard to visualize [41]. Inspired by previous work attempts [22, 30, 41, 50], we conduct qualitative analysis of image and text retrieval to show how our ADE model correlates the visual image and the concept composition. In addition, to further validate ADE is efficient to disentangle visual concepts, we conduct unseen-to-seen image retrieval based on their visual concept features extracted by attribute and object attentions." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15321" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 55, + 77, + 203, + 168 + ], + "blocks": [ + { + "bbox": [ + 55, + 77, + 203, + 168 + ], + "lines": [ + { + "bbox": [ + 55, + 77, + 203, + 168 + ], + "spans": [ + { + "bbox": [ + 55, + 77, + 203, + 168 + ], + "type": "image", + "image_path": "4d72df6e1f4a47e99d5df5ac13faaa7c3a585f4b090f6820485cda51e71b8f01.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 75, + 171, + 181, + 180 + ], + "lines": [ + { + "bbox": [ + 75, + 171, + 181, + 180 + ], + "spans": [ + { + "bbox": [ + 75, + 171, + 181, + 180 + ], + "type": "text", + "content": "(a) Top-5 text-to-image retrieval." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 211, + 78, + 384, + 169 + ], + "blocks": [ + { + "bbox": [ + 211, + 78, + 384, + 169 + ], + "lines": [ + { + "bbox": [ + 211, + 78, + 384, + 169 + ], + "spans": [ + { + "bbox": [ + 211, + 78, + 384, + 169 + ], + "type": "image", + "image_path": "96596a991f61678d701a70e4ccdb6daabee77ef6c03437aaf90739c3629d1c59.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 243, + 171, + 350, + 180 + ], + "lines": [ + { + "bbox": [ + 243, + 171, + 350, + 180 + ], + "spans": [ + { + "bbox": [ + 243, + 171, + 350, + 180 + ], + "type": "text", + "content": "(b) Top-5 image-to-text retrieval." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 182, + 547, + 216 + ], + "lines": [ + { + "bbox": [ + 46, + 182, + 547, + 216 + ], + "spans": [ + { + "bbox": [ + 46, + 182, + 547, + 216 + ], + "type": "text", + "content": "Figure 5. Qualitative analysis. (a) In the last row of \"suede sandals\", the wrong image (red box) is \"fake leather sandals\". (b) Each image has the ground-truth label (black text) and 5 retrieval results (colored text), in which the green text is the correct prediction. (c) We retrieve images sharing the same visual concepts by their visual concept features for unseen images of \"yellow skirt\" and \"pink pants\"." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 395, + 76, + 536, + 169 + ], + "blocks": [ + { + "bbox": [ + 395, + 76, + 536, + 169 + ], + "lines": [ + { + "bbox": [ + 395, + 76, + 536, + 169 + ], + "spans": [ + { + "bbox": [ + 395, + 76, + 536, + 169 + ], + "type": "image", + "image_path": "43b9d3534ddefb34936bfe0e861b4f47e999213971b126ae3077f7589946977c.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 410, + 171, + 518, + 180 + ], + "lines": [ + { + "bbox": [ + 410, + 171, + 518, + 180 + ], + "spans": [ + { + "bbox": [ + 410, + 171, + 518, + 180 + ], + "type": "text", + "content": "(c) Top-5 visual concept retrieval." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 220, + 289, + 508 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 220, + 289, + 508 + ], + "spans": [ + { + "bbox": [ + 46, + 220, + 289, + 508 + ], + "type": "text", + "content": "Image and text retrieval We first consider text-to-image retrieval. Given a text composition, e.g., \"leather heels\", we embed it and retrieve the top-5 closest visual features based on the feature distance. We display four text compositions of the different objects sharing the same attributes and vice versa in Fig. 5a. We can observe that the retrieved images are correct in most of the cases. One exception is when retrieving \"suede sandals\", the third closest image is \"fake leather sandals\". Although \"suede sandals\" and \"fake leather sandals\" are not the same composition, they are quite visually similar. We then consider image-to-text retrieval, shown in Fig. 5b. Given an image, e.g., the image of a \"brown zebra\", we extract its visual feature and retrieve the top-5 closest text composition embeddings. It is difficult to retrieve the ground-truth label in the top-1 closest text composition, but all top-5 results are all semantically related to the image. We take the image of \"blond person\" (row 3, col 2) as an example. Although the text composition \"blond person\" is not retrieved in the top-5 matches, the retrieved results \"white shirts\", \"white outfit\", \"white shorts\", \"white pants\", and \"young girl\" are all reasonable and actually present in the image. Image and text retrieval experiments validate that our ADE efficiently projects visual features and word embeddings into a uniform space." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 510, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 289, + 714 + ], + "type": "text", + "content": "Visual concept retrieval Because the attribute and the object are visually coupled in an image to a high degree of entanglement, it is challenging to visualize the disentanglement in feature space [41]. Saini et al. [41] retrieve single attribute or object text from test images. However, this process is the same as multi-label classification and insufficient to validate that disentangled visual concepts are learned from images. Based on the disentanglement ability of ADE, we construct a visual concept retrieval experiment to investigate the distances between visual concept features, i.e., the embedded attribute feature " + }, + { + "bbox": [ + 46, + 510, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\pi_{a}(v_{a})" + }, + { + "bbox": [ + 46, + 510, + 289, + 714 + ], + "type": "text", + "content": " and the embedded object feature " + }, + { + "bbox": [ + 46, + 510, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\pi_{o}(v_{o})" + }, + { + "bbox": [ + 46, + 510, + 289, + 714 + ], + "type": "text", + "content": ", extracted from different images. Prior to our work, no existing models can do so, because none of them extracts concept-exclusive features like ADE. The results are shown in Fig. 5c. We first extract attribute features and object features from all seen images. Given an unseen image, we retrieve the top-5 closest images by measuring the feature" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 220, + 547, + 353 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 220, + 547, + 353 + ], + "spans": [ + { + "bbox": [ + 304, + 220, + 547, + 353 + ], + "type": "text", + "content": "distance between the attribute feature of the given image and that of all seen images, and the same goes for the object feature. For the image of \"yellow skirt\", all retrieval results for the visual concept \"yellow\" are all \"yellow [OBJ]\", and all retrieval results for \"skirt\" are \"[ATTR] skirt\". For the \"pink pants\" image, our model also perfectly retrieves the visual concepts, i.e., the attribute \"pink\" and the object \"pants\". Our experimental results demonstrate that our ADE model is effective to disentangle visual concepts from seen compositions and combine learned concept knowledge into unseen compositions." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 360, + 378, + 372 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 360, + 378, + 372 + ], + "spans": [ + { + "bbox": [ + 306, + 360, + 378, + 372 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 380, + 547, + 571 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 380, + 547, + 571 + ], + "spans": [ + { + "bbox": [ + 304, + 380, + 547, + 571 + ], + "type": "text", + "content": "In this paper, we tackle the problem of compositional zero-shot learning (CZSL). To disentangle visual concepts from the attribute-object composition, we propose ADE adopting cross-attentions to learn the individual concept from paired concept-sharing images. To constrain the disentanglers to learn the concept of interest, we employ a regularization term adapted from the earth mover's distance (EMD), which is used as a feature similarity metric in the cross-attention module. Moreover, to exploit the attribute and object prediction ability of ADE, we improve the inference process by combining attribute, object, and composition probabilities into the final prediction score. We empirically demonstrate ADE outperforms the current state-of-the-art methods under both closed- and open-world settings. We also conduct a comprehensive qualitative analysis to validate the disentanglement ability of attention disentanglers in ADE." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 576, + 547, + 661 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 576, + 547, + 661 + ], + "spans": [ + { + "bbox": [ + 304, + 576, + 547, + 661 + ], + "type": "text", + "content": "Limitations Like existing CZSL methods, it is time- and computation-consuming to derive all composition embeddings when the numbers of attributes and objects are large. Moreover, it remains an open challenge to exploit concepts based on the actual semantics rather than solely on text; for instance, the \"open\" attribute in \"open curtain\" and \"open computer\" has completely different meanings." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 665, + 547, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 712 + ], + "type": "text", + "content": "Acknowledgements This work is partially supported by Hong Kong Research Grant Council - Early Career Scheme (Grant No. 27208022) and HKU Seed Fund for Basic Research." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15322" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 92, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 19, + "blocks": [ + { + "bbox": [ + 53, + 92, + 288, + 124 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 92, + 288, + 124 + ], + "spans": [ + { + "bbox": [ + 53, + 92, + 288, + 124 + ], + "type": "text", + "content": "[1] Jean-Baptiste Alayrac, Ivan Laptev, Josef Sivic, and Simon Lacoste-Julien. 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In ECCV, 2022. 1, 2, 3, 5, 6, 7" + } + ] + } + ], + "index": 13 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "15324" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Learning Attribute and Class-Specific Representation Duet for Fine-Grained Fashion Analysis/8a754c43-06a8-48b2-bbea-8eaf40d7cf09_content_list.json b/2023/Learning Attribute and Class-Specific Representation Duet for Fine-Grained Fashion Analysis/8a754c43-06a8-48b2-bbea-8eaf40d7cf09_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..7c245ee7f545f6835c4a317b8db295540510c5d2 --- /dev/null +++ b/2023/Learning Attribute and Class-Specific Representation Duet for Fine-Grained Fashion Analysis/8a754c43-06a8-48b2-bbea-8eaf40d7cf09_content_list.json @@ -0,0 +1,1709 @@ +[ + { + "type": "text", + "text": "Learning Attribute and Class-Specific Representation Duet for Fine-grained Fashion Analysis", + "text_level": 1, + "bbox": [ + 101, + 128, + 869, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Yang Jiao", + "bbox": [ + 217, + 204, + 299, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Amazon", + "bbox": [ + 223, + 223, + 292, + 237 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "jaoyan@amazon.com", + "bbox": [ + 183, + 242, + 334, + 255 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Yan Gao, Jingjing Meng, Jin Shang, Yi Sun", + "bbox": [ + 413, + 203, + 759, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Amazon", + "bbox": [ + 553, + 223, + 620, + 237 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{yanngao, ajmeng, imjshang, yisun}@amazon.com", + "bbox": [ + 385, + 241, + 782, + 256 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 291, + 313, + 306 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Fashion representation learning involves the analysis and understanding of various visual elements at different granularities and the interactions among them. Existing works often learn fine-grained fashion representations at the attribute level without considering their relationships and inter-dependencies across different classes. In this work, we propose to learn an attribute and class-specific fashion representation duet to better model such attribute relationships and inter-dependencies by leveraging prior knowledge about the taxonomy of fashion attributes and classes. Through two sub-networks for the attributes and classes, respectively, our proposed an embedding network progressively learns and refines the visual representation of a fashion image to improve its robustness for fashion retrieval. A multi-granularity loss consisting of attribute-level and class-level losses is proposed to introduce appropriate inductive bias to learn across different granularities of the fashion representations. Experimental results on three benchmark datasets demonstrate the effectiveness of our method, which outperforms the state-of-the-art methods by a large margin.", + "bbox": [ + 75, + 325, + 473, + 643 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 676, + 209, + 691 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Fashion products have become one of the most consumed products in online shopping. Unlike other types of products, fashion products are usually rich in visual elements at different levels of granularity. For instance, besides the overall visual appearance, a fashion product can be described by a set of attributes, such as \"shape\", \"color\" and \"style\", which focus on different aspects of the visual representation. Each attribute can be further categorized into various classes. For example, \"fit\", \"flare\" and \"pencil\" are different classes under attribute \"shape\" (Fig. 1). Therefore, modeling fashion representation in different granularities is essential for online shopping and other downstream applications, especially those that require analysis", + "bbox": [ + 75, + 704, + 470, + 902 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/643f6fe384ad817010b12640099376fded801bcef9b935eb82e69b1c88e7d3f5.jpg", + "image_caption": [ + "Figure 1. Left: existing fine-grained representation learning methods often learn attribute-specific representations for fashion products, thus may not be able to discern the two dresses that have different compositions of visual elements at the class level. Right: our proposed method (right) jointly learns attribute and class-specific representations. Therefore, it can discriminate between the two dresses by their class-specific representations." + ], + "image_footnote": [], + "bbox": [ + 506, + 292, + 888, + 482 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "of subtle or fine-grained details such as attribute-based fashion manipulation [1, 2, 27] and retrieval [6, 14, 19, 23, 24], fashion copyright [6, 19], and fashion compatibility analysis [11, 15, 21, 23].", + "bbox": [ + 496, + 625, + 892, + 684 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Fine-grained fashion modeling and analysis in recent years explore the attribute-specific representation learning. The focus has recently shifted from earlier works that learn separate representations for each attribute independently [1, 2] to multi-task learning, which uses a common backbone for different attributes while tailoring the learning for each specific attribute via mechanisms such as attention masks [6, 14, 19, 24]. Success of these attribute-specific representation learning methods for fine-grained fashion analysis can be attributed to their capabilities to discriminate visual features associated with different aspects of fashion products, which learning an image-level global representation finds challenging.", + "bbox": [ + 496, + 686, + 893, + 883 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "However, when it comes to classes, such attribute-", + "bbox": [ + 517, + 885, + 890, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "11050", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "specific representation methods face a similar challenge to the above. The reason is that due to the dynamic and aesthetic nature of fashion products, different visual elements are often composited together to achieve certain visual effects, making an attribute-level description insufficient to capture such interactions and granularity. For instance, under the same \"shape\" attribute, one may go for a dress design that combines classes \"fit\" and \"flare\" for a more casual look (top image, Fig. 1), but go for a different dress that combines \"fit\" and \"pencil\" for a more formal look while flattering one's natural curves (bottom image, Fig. 1). Therefore, an attribute-level representation is hard to differentiate the two dresses. Alternatively, one may directly learn a class-specific representation for each class under the \"shape\" attribute, which, however, faces the scalability issue. For instance, if a fashion image is associated with $N$ attributes and $M$ classes per attribute, one would need to learn $N \\times M$ class-specific representations.", + "bbox": [ + 76, + 90, + 472, + 362 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To better discriminate fashion products with distinct design considerations and model the interplay among various visual elements, we propose to leverage prior knowledge about fashion taxonomy to model fashion products. We jointly learn both attribute-specific and class-specific fashion representations through a multi-attribute multi-granularity multi-label embedding network (M3-Net). M3-Net consists of two sub-networks, for attributes and classes, respectively. Different attributes share the same backbone sub-network as well as two attribute-conditional attention modules, while different classes under a given attribute share two class-conditional attention modules.", + "bbox": [ + 76, + 363, + 472, + 542 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The shared backbone and conditional attention modules allow the network to better capture the inter-dependencies and shared visual statistics among the attributes and classes. Through multi-label learning on attribute-specific representations, we also improve the scalability of the proposed network by focusing class-specific representation learning on high likelihood classes only. Finally, a multi-granularity loss consisting of attribute-level and class-level losses is designed to introduce appropriate inductive bias for learning across different granularities.", + "bbox": [ + 76, + 545, + 472, + 696 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, our contributions are:", + "bbox": [ + 96, + 696, + 328, + 710 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose to model fashion products at both attribute and class levels based on fashion taxonomy to better capture the inter-dependencies of various visual elements and improve the discriminative power of learned fashion representations.", + "- We design a multi-attribute multi-granularity multi-label network (M3-Net) to jointly learn attributespecific and class-specific representation duet for fine-grained fashion analysis. Through two sub-networks and conditional attention modules, M3-Net is able to progressively learn discriminative representations at" + ], + "bbox": [ + 94, + 722, + 470, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "different granularities, with appropriate inductive bias introduced by the attribute-level and class-level losses.", + "bbox": [ + 529, + 90, + 890, + 121 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- Our model outperforms state-of-the-art methods in fine-grained fashion retrieval on three benchmark datasets. The experimental results demonstrate the efficacy of our proposed method.", + "bbox": [ + 517, + 132, + 893, + 191 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 215, + 640, + 231 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Generic Fashion Representation Learning", + "text_level": 1, + "bbox": [ + 500, + 239, + 857, + 257 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Earlier fashion representation learning works [7, 8, 16, 20, 25, 26] focus on the global representation of a fashion product by learning a generic metric embedding from the entire fashion image. The generic representations benefit tasks such as in-shop fashion retrieval [16, 22, 26], street-to-shop fashion retrieval [4, 7, 8, 13, 17, 18] and compatibility retrieval [11, 15, 20, 25]. For in-shop fashion retrieval, the images often have a consistent background and photo shooting angle. In comparison, street-to-shop retrieval is more challenging because the images are often taken in an uncontrolled environment with varying lighting conditions, scales, and viewing angles. Different from the above two tasks that focus on the overall similarity, compatibility retrieval focuses on a specific global attribute such as color, fabric, and style. Although effective in global representation learning, these works lack the capabilities to model fine-grain details and subtleties in fashion products.", + "bbox": [ + 496, + 263, + 890, + 521 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Multi-attribute Representation Learning", + "text_level": 1, + "bbox": [ + 500, + 530, + 849, + 546 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Many works tackle the problem of fine-grained fashion representation learning by analyzing fashion attributes. We have seen great success of such approaches in tasks such as attribute-specific retrieval [2, 6, 19, 24] and retrieval with attribute manipulation [1, 12, 27]. One group of works [12, 27] utilizes fully connected layers to transform generic representations into attribute-specific representations. However, the linear transformation function of fully connected layers neglects the spatial relationship within attribute-specific representations. Another group of works learns attribute-specific representations by leveraging region proposal, either via a dedicated network [13] or via global pooling layers [1, 2, 9]. For example, some works [1, 2] localize the spatial area of each attribute using global pooling layers, and crop the spatial feature maps for further attribute-specific learning. Although cropping spatial feature maps allows representation learning to focus on a local region, it rigidly limits the visual representation to a specific area and ignores other correlated visual elements in a larger area. In contrast, the third group of works uses attention masks to incorporate a global view into representation learning with the flexibility to bring in contexts from other regions. For instance, the authors of [6, 14, 19, 24] utilize", + "bbox": [ + 496, + 553, + 890, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "11051", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/cd0948f8e314fc00d4dd47317af5310eebf4f00e5e48d4cb88bda4ea2681264a.jpg", + "image_caption": [ + "Figure 2. The architecture of the proposed M3-Net. M3-Net first obtains a generic representation using a backbone CNN. It learns attribute-specific representations through two attribute-conditional attention modules (SCA-A and CCA-A). Taking the high-likelihood classes from the multi-label classification, M3-Net employs two class-conditional attention modules (SCA-C and CCA-C) to learn the class-specific representations. SCA-A and SCA-C are extended from the SCA module (Alg. 1), and CCA-A and CCA-C are extended from CCA module (Alg. 2)." + ], + "image_footnote": [], + "bbox": [ + 99, + 88, + 893, + 282 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "attention masks to dynamically assign weights to different dimensions of the global representation of an image for specific attributes. Veit, Belongie and Karaletsos [24] use attention masks to select and reweight relevant dimensions for each attribute to induce attribute-specific subspaces. Instead of learning attribute-specific weights, other works [6, 19] propose to learn attribute-aware spatial and channel attention modules. The attention modules are attached to the feature extraction network to enhance the participation of attributes in representation learning.", + "bbox": [ + 75, + 391, + 472, + 542 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.3. Multi-granularity Representation Learning", + "text_level": 1, + "bbox": [ + 76, + 558, + 447, + 574 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As attribute-level representations may still fall short of fashion tasks that require analysis of finer granular interactions, such as the one shown in Fig. 1, a few works propose to learn fashion representations in multiple granularities. Some works tackle the multi-granularity representation learning problem from the spatial domain, which essentially transforms multi-granularity learning into multi-scale learning. For instance, Dong, Ma and their co-authors [6, 19] propose to use a global branch and a local branch to learn two attribute-specific representations on two scales. Similarly, Bao, Zhang and their co-authors [3] propose a feature learning network that jointly learns the representation in two feature map scales and three image scales via a global, a part-base, and a local branch. Instead of multi-scale learning, Jiao, Xie and their co-authors [14] propose to segment the attribute-specific embedding spaces into class-specific embedding spaces using the cluster prototypes learned by online deep clustering. The proposed model achieves state-of-the-art performance on the fine-grained fashion retrieval task by prioritizing retrieval in class-specific embedding spaces. However, the representations are not optimized in", + "bbox": [ + 75, + 583, + 472, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "class-specific embedding spaces because the segmentation happens in the inference stage. In our work, we propose to jointly learn both attribute-specific and class-specific representations through a multi-granularity embedding network.", + "bbox": [ + 496, + 391, + 893, + 453 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Proposed Method", + "text_level": 1, + "bbox": [ + 500, + 465, + 671, + 482 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The proposed multi-attribute multi-granularity multi-label embedding network (M3-Net) is an end-to-end network that jointly learns the attribute and class level representations. As shown in Figure 2, M3-Net employs a backbone network, two attribute-conditional attention modules, two class-conditional attention modules, and a multi-label classification module. The backbone network shares learned weights across all attributes, which makes the embedding network scalable. It embeds an input image into a generic representation that represents the entire image. The generic representation is then fed through two attribute-conditional attention modules to focus learning on fine-grained attributes and obtain attribute-specific representations. Two class-conditional attention modules are further applied to learn more fine-grained class-specific representations. The shared backbone and conditional attention modules allow the network to better capture the interdependencies and shared visual statistics among the attributes and classes. The multi-label classification module serves to improve the scalability of the proposed network by focusing class-specific representation learning on high-likelihood classes.", + "bbox": [ + 496, + 491, + 890, + 821 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. M3-Net Architecture", + "text_level": 1, + "bbox": [ + 500, + 832, + 697, + 847 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given a set of fashion product images $\\{I\\}$ , we denote the set of attributes associated with these images as $\\{A_{n}\\}$ where $n \\in [1, N]$ . Similarly, we denote the set of classes", + "bbox": [ + 498, + 854, + 893, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "11052", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "associated with a given attribute $A_{n}$ as $\\{C_{m_n}\\}$ , where $m_{n} \\in [1, M_{n}]$ and $M_{n}$ is the number of classes under attribute $A_{n}$ . Given $A_{n}$ , an image $I \\in \\{I\\}$ can associate with a subset of labels in $\\{1, 2, \\dots, M_{n}\\}$ , which is represented by a vector $[y_{1_n}, \\dots, y_{m_n}, \\dots, y_{M_n}]$ , where $y_{m_n} = 1$ if and only if image $I$ is associated with class $C_{m_n}$ , and 0 otherwise.", + "bbox": [ + 76, + 90, + 468, + 181 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Generic representation. Denote the parameters of M3-Net as $\\theta$ and the parameters of the backbone network as $\\theta_{b}$ . Correspondingly, $f_{\\theta}$ represents M3-Net and $f_{\\theta_b}$ represents the backbone network. The generic visual representation of an image $I$ is then denoted by $\\psi = f_{\\theta_b}(I)$ , where $\\psi \\in \\mathbb{R}^{c\\times h\\times w}$ , $c,h,w$ are the number of channels, height, and width, respectively.", + "bbox": [ + 76, + 183, + 468, + 287 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "From here, we will use $\\psi$ to denote a generic feature map, use $\\phi$ to denote a spatially attended feature map and $\\varphi$ to denote a channel-wise attended feature map. Meanwhile, we use $x$ to denote the attribute-specific representation, and $\\overline{x}$ to denote the class-specific representation.", + "bbox": [ + 76, + 290, + 468, + 364 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Attribute-specific representation. The attribute-specific representation learning acts as a connector between the generic representations and the class-specific representations. It refines the generic representation by focusing learning on the attribute-specific visual features, and the resulting attribute-specific representation will be further refined in subsequent modules to obtain more fine-grained class-specific visual representations. To reduce the complexity of the class-specific representation learning, we conduct the attribute-specific representation learning in a multi-label setting. Therefore, instead of learning $N + \\sum_{n}^{N} M_{n}$ representations ( $N$ attribute-specific and $\\sum_{n}^{N} M_{n}$ class-specific representations), we can exclude unlikely classes, thus improve scalability.", + "bbox": [ + 76, + 367, + 468, + 580 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Motivated by the effectiveness of spatial and channel-wise attention for multi-attribute fashion representation learning in prior works, we utilize Spatial Conditional Attention module (SCA) and Channel-wise Conditional attention module (CCA) akin to the attribute-aware attention in [19]. Both SCA (Algorithm 1) and CCA (Algorithm 2) are applied to both attribute-specific and class-specific representation learning. The structures of SCA and CCA are shown in Figure 2.", + "bbox": [ + 76, + 582, + 468, + 717 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Attribute-conditional attention modules help representation learning focus on spatial locations and dimensions relevant to a given attribute. The Spatial Conditional Attention on Attribute (SCA-A) applies SCA (Algorithm 1) at the attribute level, while the Channel-wise Conditional Attention on Attribute (CCA-A) applies CCA (Algorithm 2) at the attribute level. Given the generic representation $\\psi$ and an attribute $A_{n}$ , SCA-A takes them as inputs and transforms them into feature maps with an identical size, $p_1(\\psi), p_2(A_n) \\in \\mathbb{R}^{c' \\times h \\times w}$ (step 5, 6 in Algorithm 1). The attention map $\\alpha_{n}$ is the Hadamard product between the image feature $p_1(\\psi)$ and attribute feature $p_2(A_n)$ with a scal", + "bbox": [ + 76, + 719, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Algorithm 1 Spatial Conditional Attention (SCA)", + "text_level": 1, + "bbox": [ + 501, + 90, + 831, + 106 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1: Input: a general feature map $\\psi \\in \\mathbb{R}^{c\\times h\\times w}$ , targeted label $l$ , intermediate channel number $c'$", + "2: Output: conditional spatial attention $\\alpha_{l}\\in \\mathbb{R}^{c\\times h\\times w}$", + "3: Define: feature transform function $T, T(\\psi) \\in \\mathbb{R}^{c' \\times h \\times w}$ , label embedding function $E_1, E_1(l) \\in \\mathbb{R}^{c' \\times 1}$ , linear function $W_1, W_1 \\in \\mathbb{R}^{c' \\times c'}$", + "4: Define: Hadamard product $\\odot$ , $J_{1,h,w} \\in \\mathbb{R}^{1 \\times h \\times w}$ and $J_{c,1} \\in \\mathbb{R}^{c \\times 1}$ are all-ones matrix for spatial duplication", + "5: Transform the input feature: $p_1(\\psi) = \\tanh (T(\\psi)), p_1(\\psi) \\in \\mathbb{R}^{c' \\times h \\times w}$", + "6: Embedding and transform the input label: $p_2(l) = \\tanh(W_1E_1(l)) \\cdot J_{1,h,w}$ , $p_2(l) \\in \\mathbb{R}^{c' \\times h \\times w}$", + "7: Calculate spatial attention:" + ], + "bbox": [ + 509, + 111, + 890, + 295 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\alpha_ {l} = J _ {c, 1} \\cdot s o f t m a x \\frac {\\sum_ {i} ^ {c ^ {\\prime}} [ p _ {2} (l) \\odot p _ {1} (\\psi) ] _ {i}}{\\sqrt {c ^ {\\prime}}}\n$$\n", + "text_format": "latex", + "bbox": [ + 527, + 295, + 764, + 318 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Algorithm 2 Channel-wise Conditional Attention (CCA)", + "text_level": 1, + "bbox": [ + 501, + 339, + 879, + 354 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1: Input: a general feature map $\\psi \\in \\mathbb{R}^{c\\times h\\times w}$ , targeted label $l$ , intermediate channel number $c'$", + "2: Output: conditional channel attention $\\beta_{l}\\in \\mathbb{R}^{c\\times 1}$", + "3: Define: label embedding function $E_2, E_2(l) \\in \\mathbb{R}^{c' \\times 1}$ , embedding transform function $W_2, W_2 \\in \\mathbb{R}^{c' \\times c'}$ , linear functions $W_3, W_4, W_3 \\in \\mathbb{R}^{c' \\times (c + c')}$ , and $W_4 \\in \\mathbb{R}^{c \\times c'}$", + "4: Define: feature vector concatenation $[a; b]$", + "5: Transform the input feature to vector:" + ], + "bbox": [ + 509, + 359, + 890, + 473 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nq _ {1} (\\psi) = \\sum_ {j} ^ {h \\times m ^ {\\prime}} p (\\psi), q _ {1} (\\psi) \\in \\mathbb {R} ^ {c \\times 1}\n$$\n", + "text_format": "latex", + "bbox": [ + 527, + 473, + 756, + 489 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "6: Embedding and transform the input label:", + "bbox": [ + 509, + 489, + 777, + 501 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nq _ {2} (l) = \\operatorname {r e l u} \\left(W _ {2} E _ {2} (l)\\right), q _ {2} (l) \\in \\mathbb {R} ^ {c ^ {\\prime} \\times 1}\n$$\n", + "text_format": "latex", + "bbox": [ + 527, + 501, + 767, + 517 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "7: Calculate channel attention:", + "bbox": [ + 509, + 517, + 696, + 527 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\beta_ {l} = \\operatorname {s i g m o i d} \\left(W _ {4} \\left(\\operatorname {r e l u} \\left(W _ {3} [ q _ {1} (\\psi); q _ {2} (l) ]\\right)\\right)\\right)\n$$\n", + "text_format": "latex", + "bbox": [ + 527, + 529, + 803, + 544 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "ing factor $\\sqrt{c'}$ (step 7). Then the spatially attended feature map is generated as", + "bbox": [ + 500, + 574, + 890, + 604 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\phi_ {n} = \\alpha_ {n} \\odot \\psi , \\phi_ {n} \\in \\mathbb {R} ^ {c \\times h \\times w}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 594, + 617, + 890, + 633 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\odot$ is Hadamard product. To further focus on the attribute-relevant dimensions, the Channel-wise Conditional Attention on Attribute, CCA-A (Algorithm 2), takes the spatially attended feature maps $\\phi_{n}$ and attribute $A_{n}$ as inputs, and transforms them into feature vectors $q_{1}(\\phi_{n})$ and $q_{2}(A_{n})$ (step 5, 6 in Algorithm 2), where $q_{1}(\\phi_{n})\\in \\mathbb{R}^{c\\times 1},q_{2}(A_{n})\\in \\mathbb{R}^{c^{\\prime}\\times 1}$ . The attention output $\\beta_{n}$ is obtained from the concatenation of $q_{1}(\\phi_{n})$ and $q_{2}(A_{n})$ (step 7). $\\beta_{n}\\in \\mathbb{R}^{c\\times 1}$ . Finally, the attribute-specific representation is generated as", + "bbox": [ + 496, + 647, + 890, + 797 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\varphi_ {n} = \\beta_ {n} \\odot q _ {1} (\\phi_ {n}), \\varphi_ {n} \\in \\mathbb {R} ^ {c \\times 1}. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 586, + 810, + 890, + 827 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Subsequently, to reduce the number of class-specific representations in learning, we involve the multi-label classification to exclude low-likelihood classes. As Eq. 3 shows, given an attribute-specific MLP module $g_{n}$ , the probability", + "bbox": [ + 496, + 839, + 890, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "11053", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "of all classes for an attribute-specific representation on $A_{n}$ is $P_{n}(I)$ .", + "bbox": [ + 75, + 90, + 468, + 121 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nP _ {n} (I) = \\left[ x _ {1 _ {n}}, \\dots , x _ {m _ {n}}, \\dots , x _ {M _ {n}} \\right] = g _ {n} (\\varphi_ {n}). \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 127, + 132, + 468, + 150 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "By setting a threshold $\\gamma$ , we obtain the multi-label class prediction $\\{\\widehat{l_n}\\} = \\{C_{m_n}|\\forall x_{m_n} > \\gamma \\}$ . $\\{\\widehat{l_n}\\}$ is the set of predicted high-likelihood classes. Empirically, with $\\gamma = 0.8$ we can exclude on average $94\\%$ of classes for an image. Please see the sensitivity analysis of $\\gamma$ in Suppl.", + "bbox": [ + 75, + 160, + 468, + 236 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Class-specific representation. As an attribute often involves multiple classes, the class-conditional attention modules help M3-Net focus on individual classes and learn class-specific representations.", + "bbox": [ + 75, + 237, + 468, + 296 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Class-conditional attention modules consist of Spatial Conditional Attention on Class (SCA-C) and Channelwise Conditional Attention on Class (CCA-C). SCA-C and CCA-C are attribute-specific. Different from the attribute-conditional attention modules, we expect them to focus on the relevant spatial locations and dimensions of corresponding classes.", + "bbox": [ + 75, + 297, + 468, + 402 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Given an attribute $A_{n}$ , its spatially attended feature map $\\phi_{n}$ , and class $C_{m_n} \\in \\{\\widehat{l_n}\\}$ , the SCA-C generates a class-conditional spatial attention map $\\overline{\\alpha_{m_n}}$ . We obtain the spatially attended feature map $\\overline{\\phi_{m_n}}$ as", + "bbox": [ + 76, + 402, + 468, + 465 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\overline {{\\phi_ {m _ {n}}}} = \\overline {{\\alpha_ {m _ {n}}}} \\odot \\phi_ {n}, \\overline {{\\phi_ {m _ {n}}}} \\in \\mathbb {R} ^ {c \\times h \\times w}. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 474, + 468, + 494 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$\\overline{\\phi_{m_n}}$ is subsequently fed through both attribute-conditional channel attention (CCA-A) and class-conditional channel attention (CCA-C). Especially, the CCA-A of $A_{n}$ outputs the attribute-conditional channel attention map $\\overline{\\beta_n}$ . The attended feature is", + "bbox": [ + 75, + 502, + 468, + 579 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\overline {{\\varphi_ {n}}} = \\overline {{\\beta_ {n}}} \\odot q _ {1} \\left(\\overline {{\\phi_ {m _ {n}}}}\\right), \\overline {{\\varphi_ {n}}} \\in \\mathbb {R} ^ {c \\times 1}. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 156, + 589, + 468, + 608 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The CCA-C of $A_{n}$ takes the feature vector $\\overline{\\varphi_n}$ and the class $C_{m_n}$ as inputs to generate the feature vector $q_{1}(\\overline{\\varphi_{n}})$ and gives the class-conditional channel-wise attention map $\\overline{\\beta_{m_n}}$ . The class-specific representation is obtained as", + "bbox": [ + 75, + 617, + 468, + 679 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\overline {{\\varphi_ {m _ {n}}}} = \\overline {{\\beta_ {m _ {n}}}} \\odot q _ {1} (\\overline {{\\varphi_ {n}}}), \\overline {{\\varphi_ {m _ {n}}}} \\in \\mathbb {R} ^ {c \\times 1}. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 145, + 688, + 468, + 707 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "M3-Net has three key outputs: the attribute-specific representation $\\varphi_{n}$ , class-specific-representation $\\overline{\\varphi_{m_n}}$ , and multi-label probability vector $P_{n}(I)$ . They are used to constrain the multi-granularity embedding spaces via a multi-granularity objective. In this part, we build our method upon the online clustering method and prototypical triplet loss in [14] and further extend them to learning two-granularity fine-grained representations.", + "bbox": [ + 75, + 717, + 468, + 838 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.2. Multi-granularity Objective", + "text_level": 1, + "bbox": [ + 76, + 847, + 328, + 863 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To learn across different granularities of the fashion representations in an end-to-end manner, we design two losses", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "to introduce appropriate inductive bias: an attribute-level loss and a class-level loss.", + "bbox": [ + 498, + 90, + 890, + 119 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Attribute-level loss. At the attribute level, we define the below multi-label classification loss to allow the representation learning on multi-label attributes. Given an image $I$ with $N$ attributes $\\{A_{n}\\}$ , each with $M_{n}$ classes $\\{C_{m_n}\\}$ and corresponding class labels $\\{y_{m_n}\\}$ , the loss of multi-label classification is a binary cross-entropy loss,", + "bbox": [ + 496, + 121, + 890, + 212 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {\\mathcal {M}} \\left(I, A _ {n} \\mid y _ {m _ {n}}\\right) = \\frac {1}{M _ {n}} \\left(\\sum_ {m = 1} ^ {M _ {n}} \\left[ - w _ {p} y _ {m _ {n}} \\cdot \\log x _ {m _ {n}} \\right. \\right. \\tag {7} \\\\ \\left. + \\left(1 - y _ {m _ {n}}\\right) \\cdot \\log \\left(1 - x _ {m _ {n}}\\right)\\right]\\left. \\right), \\forall x _ {m _ {n}} \\in P _ {n} (I), \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 217, + 890, + 277 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $x_{m_n}$ is the predicted probability of $I$ in class $C_{m_n}$ , $w_p$ is the weight on the positive samples to mitigate the class-imbalance problem.", + "bbox": [ + 498, + 282, + 890, + 327 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Class-level loss. At the class level, we propose to regularize the class-specific representation learning on both global and local structures via two triplet losses. For the global structure, we construct a prototypical triplet loss between an image representation, the representation of the positive prototype of the class that the image belongs to, and a negative representation. The triplet loss associated with the local structure involves instance-level representations to refine the local distance.", + "bbox": [ + 496, + 328, + 890, + 462 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "A classic triplet loss between an anchor, a positive, and a negative representation is defined as", + "bbox": [ + 498, + 464, + 890, + 494 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\triangle} (I, I ^ {+}, I ^ {-}) = \\max \\{0, \\zeta + d (I, I ^ {+}) - d (I, I ^ {-}) \\}, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 509, + 513, + 890, + 532 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\zeta = 0.4$ is a predefined margin, and $d$ is the cosine similarity.", + "bbox": [ + 498, + 537, + 890, + 566 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Given a triplet of images $[I, I^{+}, I^{-}]$ associated with classes $[C_{m_n}, C_{m_n}^{+}, C_{m_n}^{-}]$ in attribute $A_{n}$ , $C_{m_n} = C_{m_n}^{+} \\neq C_{m_n}^{-}$ . The prototypical triplet loss in the class-specific embedding spaces is defined as", + "bbox": [ + 498, + 566, + 890, + 627 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathcal {C C}} \\left(I, A _ {n}, C _ {m _ {n}}\\right) = \\mathcal {L} _ {\\triangle} \\left(\\overline {{\\varphi_ {m _ {n}} (I)}}, \\bar {\\varphi_ {C ^ {+}}}, \\overline {{\\varphi_ {m _ {n}} (I ^ {-})}}\\right), \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 513, + 632, + 890, + 650 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\overline{\\varphi_{m_n}(I)}$ is the anchor representation, $\\overline{\\varphi_{m_n}(I^-)}$ is a random negative representation in the class-specific embedding space, and $\\overline{\\varphi_{C^+}}$ is the positive class prototype in the space. The computation of $\\overline{\\varphi_{C^+}}$ is akin to [14].", + "bbox": [ + 496, + 655, + 890, + 717 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The instance triplet loss in the class-specific embedding spaces is defined as", + "bbox": [ + 498, + 718, + 890, + 747 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathcal {C I}} (I, A _ {n}, C _ {m _ {n}}) = \\mathcal {L} _ {\\triangle} (\\overline {{\\varphi_ {m _ {n}} (I)}}, \\overline {{\\varphi_ {m _ {n}} (I ^ {+})}}, \\overline {{\\varphi_ {m _ {n}} (I ^ {-})}}), \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 506, + 752, + 890, + 782 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\overline{\\varphi_{m_n}(I)}$ , $\\overline{\\varphi_{m_n}(I^+)}$ , $\\overline{\\varphi_{m_n}(I^-)}$ are the class-specific representations for the anchor, positive, and negative sample, respectively.", + "bbox": [ + 496, + 784, + 890, + 829 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Final objective function. The final objective function combines both attribute and class-level objectives and allows a simple end-to-end training, as shown in Eq.(11)", + "bbox": [ + 496, + 830, + 890, + 875 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\theta} \\left(\\lambda_ {M} \\mathcal {L} _ {\\mathcal {M}} + \\lambda_ {C C} \\mathcal {L} _ {\\mathcal {C C}} + \\lambda_ {C I} \\mathcal {L} _ {\\mathcal {C I}}\\right). \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 566, + 880, + 890, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "11054", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/fa004b5e3900cbc55fd462e441a5b1e103276afe75da18f3117baf16b7158d9b.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
DatasetAttr type# Attr# Class per attrTrain/val/test
DeepFashion [18]multi-label5156-230220K/28K/28K
FashionAI [28]single-label85-10144k/18k/18k
DARN [13]single-label97-55163k/20k/20k
", + "bbox": [ + 84, + 88, + 460, + 138 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Summary of the datasets used in experimental validations. \nAttr: attribute.", + "bbox": [ + 76, + 148, + 467, + 176 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where, $\\lambda_{M},\\lambda_{CC}$ and $\\lambda_{CI}$ are hyperparameters, which are set to 1 in our experiments.", + "bbox": [ + 76, + 205, + 467, + 236 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 252, + 209, + 268 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Datasets", + "text_level": 1, + "bbox": [ + 76, + 277, + 179, + 292 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In Table 1, we summarize the three benchmark datasets used in the experiments. DeepFashion is a large dataset containing image labels of fashion attributes, landmarks, etc. We use the coarsely-annotated attribute prediction subset, which is one of the most popular datasets in fashion retrieval, and is a multi-label dataset.", + "bbox": [ + 76, + 301, + 467, + 391 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Experimental Settings", + "text_level": 1, + "bbox": [ + 76, + 404, + 282, + 420 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We compare our proposed method with the state-of-the-art solutions [6, 14, 19] on the aforementioned datasets.", + "bbox": [ + 76, + 429, + 467, + 458 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Baselines. ASEIN networks are the state-of-the-art works on attribute-specific representation learning. ASEIN [19] learns 1024 dimensional attribute-specific representations by using an attribute-aware spatial attention and an attribute-aware channel attention. $\\mathrm{ASEN}_{v2}$ [19] builds a new attention module structure and achieves better performance than ASEIN. $\\mathrm{ASEN}++$ [6] further proposes a cascade network with a global branch and a local branch to learn multi-scale representations in 2,048 dimensions.", + "bbox": [ + 76, + 459, + 467, + 594 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "MODC [14] it is a fine-grained representation learning framework with online deep clustering to achieve retrieval in two granularities. It splits the attribute-specific embedding spaces into class-specific embedding spaces in the inference stage to enable retrieval at the finer granularity. MODC learns attribute-specific representations with 2048 dimensions and achieves the state-of-the-art results on multiple datasets.", + "bbox": [ + 76, + 595, + 467, + 715 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "M3-Net is our proposed method which jointly learns attribute-specific and class-specific representation duet for fine-grained fashion analysis. The attribute-specific and class-specific representations are 1024 dimensions. To isolate the effects of two-granularity attentions, we trained M3-Net with only the attribute-conditional attention modules, with only the class-conditional attention modules, and with both, called M3-Net $_a$ , M3-Net $_c$ , and M3-Net respectively.", + "bbox": [ + 76, + 718, + 467, + 838 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Training details M3-Net employs a ResNet50 [10] pretrained on ImageNet [5] as the shared backbone network, and removes the last residual block. It is identical to the backbone of the baselines for fair comparisons. To train", + "bbox": [ + 76, + 839, + 467, + 898 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "M3-Net, we use a learning rate $1 \\times 10^{-4}$ with a 0.975 decay per epoch and a batch size of 16. We sample 40k triplet of images each epoch of training. In training, We set $w_{p}$ to 100 for DeepFashion, and 1 for FashionAI and DARN. To train the baselines on DeepFashion, We follow the descriptions in [6, 14, 19].", + "bbox": [ + 496, + 90, + 890, + 181 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation Tasks and Metrics. We evaluate our proposed method in comparison with the above baselines on the fine-grained fashion retrieval task. Following the existing protocol for multi-granularity retrieval as proposed in MODC [14], the retrieval is prioritized in the class-specific embedding space, followed by retrieval in the attribute-specific embedding space. Same as existing works [6, 14, 19], we employ Mean Average Precision (MAP) and Recall as the evaluation metrics.", + "bbox": [ + 496, + 181, + 890, + 316 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Experimental Results", + "text_level": 1, + "bbox": [ + 500, + 330, + 700, + 345 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we discuss the experimental results and ablation study of M3-Net on multi-label attributes and single-label attributes. Table 2 presents the overall performance and the performance on each attribute of baselines and M3-Net on DeepFashion. Table 3 and Table 4 summarizes the performance on FashionAI and DARN. On all datasets, we show the ablation study of separately employing attribute-conditional attention modules (i.e., $\\mathrm{M3 - Net}_a$ ) and class-conditional attention modules (i.e., $\\mathrm{M3 - Net}_c$ ) to demonstrate the effectiveness of representation learning on attribute granularity and class granularity.", + "bbox": [ + 496, + 354, + 890, + 520 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3.1 Quantitative evaluation on multi-label dataset", + "text_level": 1, + "bbox": [ + 500, + 542, + 870, + 556 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2 summarizes the performance of fine-grained fashion retrieval on all attributes in DeepFashion. Note that $\\mathrm{ASEN}_{v2}$ [19] and $\\mathrm{ASEN}++$ [6] report performance on DeepFashion by treating it as a single-label dataset. To evaluate the performance in the multi-label setting, we split DeepFashion following the multi-class labels of each image in the dataset. The train/validation/test split is shown in Table 1. For the retrieval task, the validation set and test set are further split into the query and candidate sets by 1:4.", + "bbox": [ + 496, + 566, + 890, + 703 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "DeepFashion is an extremely challenging dataset for fine-grained fashion retrieval. Therefore, all methods perform much worse on DeepFashion than on other benchmark datasets Compared with the baselines, the proposed M3-Net consistently achieves the best performance with a large margin on all evaluation metrics on individual attributes and overall. Even when compared with the state-of-the-art multi-granularity method, MODC, the proposed M3-Net shows significant improvements over MODC on MAP@all (70.42%), MAP@100 (57.95%), and Recall@100 (112.5%). The results demonstrate the efficacy of the attribute and class-specific representations learned by M3-Net.", + "bbox": [ + 496, + 704, + 890, + 898 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "11055", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/0641c24a9053969212196f87046b72a7d85fdd015289caad3467f8c466d6192f.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ModelDeepFashion
MAP@allMAP@allMAP@100Recall@100
Attributetexturefabricshapepartstyleoveralloveralloverall
ASEN [19]21.0311.6114.687.814.6612.3320.605.10
ASENV2 [19]21.8611.6714.587.934.6812.5120.554.99
ASEN++ [6]22.2011.7114.708.154.7212.7420.795.21
MODC [14]22.2611.9814.687.965.2312.7822.216.06
M3-Neta27.3718.3422.9614.669.7419.0328.1410.59
M3-Netc30.0919.6025.2416.4311.3220.9230.5812.10
M3-Net30.7920.2027.1117.2811.6121.7835.0812.88
", + "bbox": [ + 210, + 88, + 759, + 218 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/94994219ed509fc6ebb8251fd37aea4dda9459f787d6c111fac25613da729098.jpg", + "table_caption": [ + "Table 2. Performance comparison on all attributes of the multi-label dataset, DeepFashion." + ], + "table_footnote": [], + "table_body": "
ModelFashionAI
MAP@allMAP@allMAP@100Recall@100
Attributeskirt lengthsleeve lengthcoat lengthpant lengthcollar designlapel designneckline designneck designoveralloveralloveralloverall
ASEN [19]64.6149.9849.7565.7670.3062.8652.1456.4257.3764.7022.77
ASENv2 [19]65.5854.4252.0367.4171.3666.7660.9159.5861.1367.8524.14
ASEN++ [6]66.3157.5155.4368.8372.7966.8566.7867.0264.2770.6225.30
MODC [14]74.5467.4868.2577.6981.1176.9077.4677.1074.3280.2930.26
M3-Neta73.2169.5865.2778.7980.8078.0577.0473.4073.9381.5730.48
M3-Netc74.3365.9164.2778.2682.0078.8574.8072.3972.8882.5830.77
M3-Net75.2770.0467.9079.3182.8278.5876.8175.5175.0487.0432.01
", + "bbox": [ + 96, + 253, + 874, + 359 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3. Performance comparison on all attributes of the single-label dataset, FashionAI.", + "bbox": [ + 220, + 369, + 746, + 383 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Ablation study on $\\mathrm{M3 - Net}_a$ , $\\mathrm{M3 - Net}_c$ and M3-Net suggests that employing more fine-grained attention on classes $(\\mathrm{M3 - Net}_c)$ performs better than attribute-level attention alone $(\\mathrm{M3 - Net}_a)$ . Yet combining attribute-conditional attentions and class-conditional attentions works the best (M3-Net). It shows that representations learned at the two granularities are complementary to each other.", + "bbox": [ + 75, + 411, + 468, + 516 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Furthermore, we analyze the performance on co-occurring classes on DeepFashion to evaluate the effectiveness of M3-Net in capturing the inter-dependencies between different classes in representation learning. We first calculate the pairwise co-occurrence rates of all classes in the dataset. Two classes are considered co-occurring if both are associated with the same image. The range of co-occurrence rate is [0, 0.03], i.e., the most frequently co-occurring class pairs appear in $3\\%$ of the images. We set the cut-off at 0.002 (corresponding to 565 co-occurrences), resulting in 468 class pairs from the 1M class pairs in the dataset. This gives us 122 unique classes. M3-Net achieves a MAP@all at 35.61 on this set of classes, which is $63.50\\%$ higher than the average of all classes. We hypothesize that M3-Net is able to incorporate the inter-dependencies between these classes into representation learning, thus performing better on them.", + "bbox": [ + 75, + 518, + 472, + 775 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3.2 Quantitative evaluation on single-label datasets", + "text_level": 1, + "bbox": [ + 76, + 799, + 460, + 814 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "For the two single-label datasets, FashionAI and DARN, we follow the same split as in [19]. On both datasets, we observe similar competence of the proposed M3-Net in fine-grained fashion retrieval. On FashionAI, M3-Net achieve the best performance overall on all evaluation met", + "bbox": [ + 75, + 824, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0f87d1ec8f177d1bb83c67c83fb2e091e732ac5b49687bd7561bc151357330a8.jpg", + "image_caption": [ + "Figure 3. Two-granularity attentions learned by M3-Net on DeepFashion. The attribute-conditional attention tends to focus on a wider range of regions in an image, while the class-conditional attention focuses more narrowly on a region relevant to each class. For instance, row 1: class \"slit\" focuses on the dress slit, \"elegant\" focuses on the waist; row 2: \"contrast trim\" focuses on the part with two different colors, \"stretch\" focuses on the strap; row 3: \"draped\" focuses on the drape decoration, and \"fit\" focuses on the waist. Best viewed in color on a computer screen." + ], + "image_footnote": [], + "bbox": [ + 501, + 410, + 890, + 568 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "rics (MAP@all, MAP@100, and Recall@100). It also outperforms the baselines on most individual attributes.", + "bbox": [ + 496, + 717, + 890, + 747 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "On DARN, we again observe a boost on all evaluation metrics. While baselines perform unsatisfactorily on \"clothes category\" and \"collar shape\", M3-Net improves them the most along with improvements on other attributes. Overall, M3-Net exceeds the best baseline, MODC, on MAP@all by $16.35\\%$ , MAP@100 by $14.59\\%$ , and Recall@100 by $18.24\\%$ . The results of M3-Net on single-label datasets again demonstrate the effectiveness of the attribute-specific and class-specific representations. Compared with MODC, which obtains class-specific representations by di", + "bbox": [ + 496, + 750, + 892, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "11056", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/7efede248cf20a17362fef634a1bd5780a60f46fce7e2b71d3c7a966acdd669e.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ModelDARN
MAP@allMAP@allMAP@100Recall@100
Attributeclothes categoryclothes buttonclothes colorclothes lengthclothes patternclothes shapecollar shapesleeve lengthsleeve shapeoveralloveralloverall
ASEN [19]36.6246.0152.7656.8554.8956.8534.4079.9558.0852.7558.7220.26
ASENv2 [19]37.9749.2452.2659.1355.3259.0636.8681.5458.8254.2959.6620.88
ASEN++ [6]40.2150.0453.1459.8357.4159.7037.4583.7060.4155.7861.0921.51
MODC [14]49.9460.7558.7966.3462.2468.4145.1487.4165.3262.5672.1626.76
M3-Neta59.1669.9468.1872.5872.8776.2160.2289.3671.5871.0678.1230.77
M3-Netc60.9870.9168.5274.9574.4879.1563.0990.3173.0072.7981.4631.64
M3-Net60.5470.3969.5273.9774.4077.8361.6390.0373.9472.4282.6931.34
", + "bbox": [ + 86, + 87, + 883, + 183 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 4. Performance comparison on all attributes of the single-label dataset, DARN.", + "bbox": [ + 230, + 191, + 736, + 208 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/dae655dc34bcf660402461606ff02120788b297f623535d6d3ebc7b19a48cc1d.jpg", + "image_caption": [ + "Figure 4. (a) single-label and (b) multi-label fashion retrieval by M3-Net and MODC on DeepFashion. Green: true positive retrieval; red: false positive retrieval. Best viewed in color on a computer screen." + ], + "image_footnote": [], + "bbox": [ + 81, + 220, + 495, + 409 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3f4f3253e43596aebe30db7d7ae9ccb597a7c9bd5dd074f9c62bde1f2a6ed336.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 500, + 220, + 893, + 409 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "rectly segmenting the attribute-specific representation into class-specific clusters in the same embedding space, M3-Net learns separate representation spaces for attributes and classes and performs better.", + "bbox": [ + 75, + 474, + 468, + 535 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Ablation study on FashionAI shows that overall having attentions on two granularities (M3-Net) performs better than attentions on either granularity alone $(\\mathrm{M}3 - \\mathrm{Net}_a$ and $\\mathrm{M}3 - \\mathrm{Net}_c)$ . On DARN, M3-Net's performance is comparable to that of $\\mathrm{M}3 - \\mathrm{Net}_c$ , which only has class-conditional attention modules. We speculate that this is due to discriminating attributes and classes is less challenging on single-label datasets than on multi-label attribute datasets.", + "bbox": [ + 75, + 536, + 470, + 656 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3.3 Qualitative evaluations", + "text_level": 1, + "bbox": [ + 76, + 678, + 290, + 694 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Figure 3 visualizes the two-granularity attentions learned by M3-Net. The attribute-conditional attention tends to focus on all regions that are likely to be associated with the attribute. For example, in the first row of Figure 3, the attention of attribute \"part\" involves areas covering various parts of the dress such as collar, belt area, and hemline (second image in the first row). On the contrary, the class-conditional attention tends to focus on class-specific regions in the image. For instance, class \"slit\" highlights the dress slit region (third image in the first row). The visualized attention is consistent with our hypothesis.", + "bbox": [ + 75, + 703, + 468, + 869 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Figure 4 presents examples of fine-grained fashion retrieval results on single-label and multi-label datasets. In", + "bbox": [ + 75, + 869, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "the figure, we compared the results from our proposed M3-Net with those from MODC (the best-performing baseline). Figure 4 (a) shows that on single-label retrieval, M3-Net can better discriminate fine-grained visual features than MODC, leading to more accurate retrieval results on individual classes. Moreover, on multi-label retrieval, M3-Net is able to retrieve images containing multiple class labels. For example, when searching an image on attribute \"texture\" with both \"print\" and \"tribal\" class labels (last example in Figure 4), M3-Net accurately retrieves related images, while MODC retrieves many other printed textures that is not \"tribal\".", + "bbox": [ + 496, + 474, + 892, + 656 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 669, + 617, + 684 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We have proposed a multi-attribute multi-granularity multi-label network (M3-Net) for fine-grained fashion analysis. Our proposed architecture learns both attribute and class-level representations for a fashion image through a shared backbone and two sub-networks with attribute and class conditional attention modules. This design, together with a multi-granularity loss, allows the network to effectively learn discriminative representations while capturing the inter-dependencies among various visual elements in different granularities. Our experiments show that the proposed M3-Net sets new state-of-the-art performance on both single-label and multi-label benchmark datasets in the fine-grained fashion retrieval task.", + "bbox": [ + 496, + 695, + 892, + 891 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "11057", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Kenan E Ak, Ashraf A Kassim, Joo Hwee Lim, and Jo Yew Tham. Learning attribute representations with localization for flexible fashion search. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops, pages 0-0, 2019." + ], + "bbox": [ + 78, + 90, + 468, + 287 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "11059", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Learning Attribute and Class-Specific Representation Duet for Fine-Grained Fashion Analysis/8a754c43-06a8-48b2-bbea-8eaf40d7cf09_model.json b/2023/Learning Attribute and Class-Specific Representation Duet for Fine-Grained Fashion Analysis/8a754c43-06a8-48b2-bbea-8eaf40d7cf09_model.json new file mode 100644 index 0000000000000000000000000000000000000000..1c3b9dadb875c33753a3353ec116faee640c8a65 --- /dev/null +++ b/2023/Learning Attribute and Class-Specific Representation Duet for Fine-Grained Fashion Analysis/8a754c43-06a8-48b2-bbea-8eaf40d7cf09_model.json @@ -0,0 +1,2134 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.102, + 0.13, + 0.87, + 0.178 + ], + "angle": 0, + "content": "Learning Attribute and Class-Specific Representation Duet for Fine-grained Fashion Analysis" + }, + { + "type": "text", + "bbox": [ + 0.218, + 0.205, + 0.3, + 0.222 + ], + "angle": 0, + "content": "Yang Jiao" + }, + { + "type": "text", + "bbox": [ + 0.224, + 0.224, + 0.294, + 0.238 + ], + "angle": 0, + "content": "Amazon" + }, + { + "type": "text", + "bbox": [ + 0.184, + 0.243, + 0.336, + 0.256 + ], + "angle": 0, + "content": "jaoyan@amazon.com" + }, + { + "type": "text", + "bbox": [ + 0.415, + 0.204, + 0.76, + 0.222 + ], + "angle": 0, + "content": "Yan Gao, Jingjing Meng, Jin Shang, Yi Sun" + }, + { + "type": "text", + "bbox": [ + 0.554, + 0.224, + 0.622, + 0.238 + ], + "angle": 0, + "content": "Amazon" + }, + { + "type": "text", + "bbox": [ + 0.387, + 0.242, + 0.784, + 0.257 + ], + "angle": 0, + "content": "{yanngao, ajmeng, imjshang, yisun}@amazon.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.292, + 0.314, + 0.308 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.326, + 0.474, + 0.645 + ], + "angle": 0, + "content": "Fashion representation learning involves the analysis and understanding of various visual elements at different granularities and the interactions among them. Existing works often learn fine-grained fashion representations at the attribute level without considering their relationships and inter-dependencies across different classes. In this work, we propose to learn an attribute and class-specific fashion representation duet to better model such attribute relationships and inter-dependencies by leveraging prior knowledge about the taxonomy of fashion attributes and classes. Through two sub-networks for the attributes and classes, respectively, our proposed an embedding network progressively learns and refines the visual representation of a fashion image to improve its robustness for fashion retrieval. A multi-granularity loss consisting of attribute-level and class-level losses is proposed to introduce appropriate inductive bias to learn across different granularities of the fashion representations. Experimental results on three benchmark datasets demonstrate the effectiveness of our method, which outperforms the state-of-the-art methods by a large margin." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.677, + 0.21, + 0.693 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Fashion products have become one of the most consumed products in online shopping. Unlike other types of products, fashion products are usually rich in visual elements at different levels of granularity. For instance, besides the overall visual appearance, a fashion product can be described by a set of attributes, such as \"shape\", \"color\" and \"style\", which focus on different aspects of the visual representation. Each attribute can be further categorized into various classes. For example, \"fit\", \"flare\" and \"pencil\" are different classes under attribute \"shape\" (Fig. 1). Therefore, modeling fashion representation in different granularities is essential for online shopping and other downstream applications, especially those that require analysis" + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.294, + 0.889, + 0.483 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.497, + 0.895, + 0.596 + ], + "angle": 0, + "content": "Figure 1. Left: existing fine-grained representation learning methods often learn attribute-specific representations for fashion products, thus may not be able to discern the two dresses that have different compositions of visual elements at the class level. Right: our proposed method (right) jointly learns attribute and class-specific representations. Therefore, it can discriminate between the two dresses by their class-specific representations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.625, + 0.893, + 0.685 + ], + "angle": 0, + "content": "of subtle or fine-grained details such as attribute-based fashion manipulation [1, 2, 27] and retrieval [6, 14, 19, 23, 24], fashion copyright [6, 19], and fashion compatibility analysis [11, 15, 21, 23]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.688, + 0.895, + 0.884 + ], + "angle": 0, + "content": "Fine-grained fashion modeling and analysis in recent years explore the attribute-specific representation learning. The focus has recently shifted from earlier works that learn separate representations for each attribute independently [1, 2] to multi-task learning, which uses a common backbone for different attributes while tailoring the learning for each specific attribute via mechanisms such as attention masks [6, 14, 19, 24]. Success of these attribute-specific representation learning methods for fine-grained fashion analysis can be attributed to their capabilities to discriminate visual features associated with different aspects of fashion products, which learning an image-level global representation finds challenging." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.886, + 0.892, + 0.901 + ], + "angle": 0, + "content": "However, when it comes to classes, such attribute-" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "11050" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.363 + ], + "angle": 0, + "content": "specific representation methods face a similar challenge to the above. The reason is that due to the dynamic and aesthetic nature of fashion products, different visual elements are often composited together to achieve certain visual effects, making an attribute-level description insufficient to capture such interactions and granularity. For instance, under the same \"shape\" attribute, one may go for a dress design that combines classes \"fit\" and \"flare\" for a more casual look (top image, Fig. 1), but go for a different dress that combines \"fit\" and \"pencil\" for a more formal look while flattering one's natural curves (bottom image, Fig. 1). Therefore, an attribute-level representation is hard to differentiate the two dresses. Alternatively, one may directly learn a class-specific representation for each class under the \"shape\" attribute, which, however, faces the scalability issue. For instance, if a fashion image is associated with \\(N\\) attributes and \\(M\\) classes per attribute, one would need to learn \\(N \\times M\\) class-specific representations." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.364, + 0.473, + 0.544 + ], + "angle": 0, + "content": "To better discriminate fashion products with distinct design considerations and model the interplay among various visual elements, we propose to leverage prior knowledge about fashion taxonomy to model fashion products. We jointly learn both attribute-specific and class-specific fashion representations through a multi-attribute multi-granularity multi-label embedding network (M3-Net). M3-Net consists of two sub-networks, for attributes and classes, respectively. Different attributes share the same backbone sub-network as well as two attribute-conditional attention modules, while different classes under a given attribute share two class-conditional attention modules." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.546, + 0.473, + 0.697 + ], + "angle": 0, + "content": "The shared backbone and conditional attention modules allow the network to better capture the inter-dependencies and shared visual statistics among the attributes and classes. Through multi-label learning on attribute-specific representations, we also improve the scalability of the proposed network by focusing class-specific representation learning on high likelihood classes only. Finally, a multi-granularity loss consisting of attribute-level and class-level losses is designed to introduce appropriate inductive bias for learning across different granularities." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.697, + 0.329, + 0.712 + ], + "angle": 0, + "content": "In summary, our contributions are:" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.723, + 0.47, + 0.8 + ], + "angle": 0, + "content": "- We propose to model fashion products at both attribute and class levels based on fashion taxonomy to better capture the inter-dependencies of various visual elements and improve the discriminative power of learned fashion representations." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.81, + 0.471, + 0.902 + ], + "angle": 0, + "content": "- We design a multi-attribute multi-granularity multi-label network (M3-Net) to jointly learn attributespecific and class-specific representation duet for fine-grained fashion analysis. Through two sub-networks and conditional attention modules, M3-Net is able to progressively learn discriminative representations at" + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.723, + 0.471, + 0.902 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.531, + 0.092, + 0.892, + 0.122 + ], + "angle": 0, + "content": "different granularities, with appropriate inductive bias introduced by the attribute-level and class-level losses." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.133, + 0.894, + 0.193 + ], + "angle": 0, + "content": "- Our model outperforms state-of-the-art methods in fine-grained fashion retrieval on three benchmark datasets. The experimental results demonstrate the efficacy of our proposed method." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.216, + 0.642, + 0.232 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.241, + 0.859, + 0.258 + ], + "angle": 0, + "content": "2.1. Generic Fashion Representation Learning" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.265, + 0.892, + 0.522 + ], + "angle": 0, + "content": "Earlier fashion representation learning works [7, 8, 16, 20, 25, 26] focus on the global representation of a fashion product by learning a generic metric embedding from the entire fashion image. The generic representations benefit tasks such as in-shop fashion retrieval [16, 22, 26], street-to-shop fashion retrieval [4, 7, 8, 13, 17, 18] and compatibility retrieval [11, 15, 20, 25]. For in-shop fashion retrieval, the images often have a consistent background and photo shooting angle. In comparison, street-to-shop retrieval is more challenging because the images are often taken in an uncontrolled environment with varying lighting conditions, scales, and viewing angles. Different from the above two tasks that focus on the overall similarity, compatibility retrieval focuses on a specific global attribute such as color, fabric, and style. Although effective in global representation learning, these works lack the capabilities to model fine-grain details and subtleties in fashion products." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.531, + 0.85, + 0.547 + ], + "angle": 0, + "content": "2.2. Multi-attribute Representation Learning" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.554, + 0.892, + 0.903 + ], + "angle": 0, + "content": "Many works tackle the problem of fine-grained fashion representation learning by analyzing fashion attributes. We have seen great success of such approaches in tasks such as attribute-specific retrieval [2, 6, 19, 24] and retrieval with attribute manipulation [1, 12, 27]. One group of works [12, 27] utilizes fully connected layers to transform generic representations into attribute-specific representations. However, the linear transformation function of fully connected layers neglects the spatial relationship within attribute-specific representations. Another group of works learns attribute-specific representations by leveraging region proposal, either via a dedicated network [13] or via global pooling layers [1, 2, 9]. For example, some works [1, 2] localize the spatial area of each attribute using global pooling layers, and crop the spatial feature maps for further attribute-specific learning. Although cropping spatial feature maps allows representation learning to focus on a local region, it rigidly limits the visual representation to a specific area and ignores other correlated visual elements in a larger area. In contrast, the third group of works uses attention masks to incorporate a global view into representation learning with the flexibility to bring in contexts from other regions. For instance, the authors of [6, 14, 19, 24] utilize" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "11051" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.1, + 0.089, + 0.895, + 0.284 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.296, + 0.895, + 0.366 + ], + "angle": 0, + "content": "Figure 2. The architecture of the proposed M3-Net. M3-Net first obtains a generic representation using a backbone CNN. It learns attribute-specific representations through two attribute-conditional attention modules (SCA-A and CCA-A). Taking the high-likelihood classes from the multi-label classification, M3-Net employs two class-conditional attention modules (SCA-C and CCA-C) to learn the class-specific representations. SCA-A and SCA-C are extended from the SCA module (Alg. 1), and CCA-A and CCA-C are extended from CCA module (Alg. 2)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.392, + 0.473, + 0.543 + ], + "angle": 0, + "content": "attention masks to dynamically assign weights to different dimensions of the global representation of an image for specific attributes. Veit, Belongie and Karaletsos [24] use attention masks to select and reweight relevant dimensions for each attribute to induce attribute-specific subspaces. Instead of learning attribute-specific weights, other works [6, 19] propose to learn attribute-aware spatial and channel attention modules. The attention modules are attached to the feature extraction network to enhance the participation of attributes in representation learning." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.559, + 0.449, + 0.575 + ], + "angle": 0, + "content": "2.3. Multi-granularity Representation Learning" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.584, + 0.473, + 0.903 + ], + "angle": 0, + "content": "As attribute-level representations may still fall short of fashion tasks that require analysis of finer granular interactions, such as the one shown in Fig. 1, a few works propose to learn fashion representations in multiple granularities. Some works tackle the multi-granularity representation learning problem from the spatial domain, which essentially transforms multi-granularity learning into multi-scale learning. For instance, Dong, Ma and their co-authors [6, 19] propose to use a global branch and a local branch to learn two attribute-specific representations on two scales. Similarly, Bao, Zhang and their co-authors [3] propose a feature learning network that jointly learns the representation in two feature map scales and three image scales via a global, a part-base, and a local branch. Instead of multi-scale learning, Jiao, Xie and their co-authors [14] propose to segment the attribute-specific embedding spaces into class-specific embedding spaces using the cluster prototypes learned by online deep clustering. The proposed model achieves state-of-the-art performance on the fine-grained fashion retrieval task by prioritizing retrieval in class-specific embedding spaces. However, the representations are not optimized in" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.392, + 0.895, + 0.454 + ], + "angle": 0, + "content": "class-specific embedding spaces because the segmentation happens in the inference stage. In our work, we propose to jointly learn both attribute-specific and class-specific representations through a multi-granularity embedding network." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.466, + 0.673, + 0.483 + ], + "angle": 0, + "content": "3. Proposed Method" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.492, + 0.892, + 0.822 + ], + "angle": 0, + "content": "The proposed multi-attribute multi-granularity multi-label embedding network (M3-Net) is an end-to-end network that jointly learns the attribute and class level representations. As shown in Figure 2, M3-Net employs a backbone network, two attribute-conditional attention modules, two class-conditional attention modules, and a multi-label classification module. The backbone network shares learned weights across all attributes, which makes the embedding network scalable. It embeds an input image into a generic representation that represents the entire image. The generic representation is then fed through two attribute-conditional attention modules to focus learning on fine-grained attributes and obtain attribute-specific representations. Two class-conditional attention modules are further applied to learn more fine-grained class-specific representations. The shared backbone and conditional attention modules allow the network to better capture the interdependencies and shared visual statistics among the attributes and classes. The multi-label classification module serves to improve the scalability of the proposed network by focusing class-specific representation learning on high-likelihood classes." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.833, + 0.698, + 0.848 + ], + "angle": 0, + "content": "3.1. M3-Net Architecture" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.894, + 0.903 + ], + "angle": 0, + "content": "Given a set of fashion product images \\(\\{I\\}\\), we denote the set of attributes associated with these images as \\(\\{A_{n}\\}\\) where \\(n \\in [1, N]\\). Similarly, we denote the set of classes" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "11052" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.091, + 0.47, + 0.183 + ], + "angle": 0, + "content": "associated with a given attribute \\(A_{n}\\) as \\(\\{C_{m_n}\\}\\), where \\(m_{n} \\in [1, M_{n}]\\) and \\(M_{n}\\) is the number of classes under attribute \\(A_{n}\\). Given \\(A_{n}\\), an image \\(I \\in \\{I\\}\\) can associate with a subset of labels in \\(\\{1, 2, \\dots, M_{n}\\}\\), which is represented by a vector \\([y_{1_n}, \\dots, y_{m_n}, \\dots, y_{M_n}]\\), where \\(y_{m_n} = 1\\) if and only if image \\(I\\) is associated with class \\(C_{m_n}\\), and 0 otherwise." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.184, + 0.469, + 0.289 + ], + "angle": 0, + "content": "Generic representation. Denote the parameters of M3-Net as \\(\\theta\\) and the parameters of the backbone network as \\(\\theta_{b}\\). Correspondingly, \\(f_{\\theta}\\) represents M3-Net and \\(f_{\\theta_b}\\) represents the backbone network. The generic visual representation of an image \\(I\\) is then denoted by \\(\\psi = f_{\\theta_b}(I)\\), where \\(\\psi \\in \\mathbb{R}^{c\\times h\\times w}\\), \\(c,h,w\\) are the number of channels, height, and width, respectively." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.291, + 0.469, + 0.366 + ], + "angle": 0, + "content": "From here, we will use \\(\\psi\\) to denote a generic feature map, use \\(\\phi\\) to denote a spatially attended feature map and \\(\\varphi\\) to denote a channel-wise attended feature map. Meanwhile, we use \\(x\\) to denote the attribute-specific representation, and \\(\\overline{x}\\) to denote the class-specific representation." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.368, + 0.469, + 0.581 + ], + "angle": 0, + "content": "Attribute-specific representation. The attribute-specific representation learning acts as a connector between the generic representations and the class-specific representations. It refines the generic representation by focusing learning on the attribute-specific visual features, and the resulting attribute-specific representation will be further refined in subsequent modules to obtain more fine-grained class-specific visual representations. To reduce the complexity of the class-specific representation learning, we conduct the attribute-specific representation learning in a multi-label setting. Therefore, instead of learning \\( N + \\sum_{n}^{N} M_{n} \\) representations (\\( N \\) attribute-specific and \\( \\sum_{n}^{N} M_{n} \\) class-specific representations), we can exclude unlikely classes, thus improve scalability." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.583, + 0.469, + 0.718 + ], + "angle": 0, + "content": "Motivated by the effectiveness of spatial and channel-wise attention for multi-attribute fashion representation learning in prior works, we utilize Spatial Conditional Attention module (SCA) and Channel-wise Conditional attention module (CCA) akin to the attribute-aware attention in [19]. Both SCA (Algorithm 1) and CCA (Algorithm 2) are applied to both attribute-specific and class-specific representation learning. The structures of SCA and CCA are shown in Figure 2." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.72, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Attribute-conditional attention modules help representation learning focus on spatial locations and dimensions relevant to a given attribute. The Spatial Conditional Attention on Attribute (SCA-A) applies SCA (Algorithm 1) at the attribute level, while the Channel-wise Conditional Attention on Attribute (CCA-A) applies CCA (Algorithm 2) at the attribute level. Given the generic representation \\(\\psi\\) and an attribute \\(A_{n}\\), SCA-A takes them as inputs and transforms them into feature maps with an identical size, \\(p_1(\\psi), p_2(A_n) \\in \\mathbb{R}^{c' \\times h \\times w}\\) (step 5, 6 in Algorithm 1). The attention map \\(\\alpha_{n}\\) is the Hadamard product between the image feature \\(p_1(\\psi)\\) and attribute feature \\(p_2(A_n)\\) with a scal" + }, + { + "type": "title", + "bbox": [ + 0.502, + 0.091, + 0.833, + 0.107 + ], + "angle": 0, + "content": "Algorithm 1 Spatial Conditional Attention (SCA)" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.112, + 0.892, + 0.139 + ], + "angle": 0, + "content": "1: Input: a general feature map \\(\\psi \\in \\mathbb{R}^{c\\times h\\times w}\\), targeted label \\(l\\), intermediate channel number \\(c'\\)" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.14, + 0.838, + 0.154 + ], + "angle": 0, + "content": "2: Output: conditional spatial attention \\(\\alpha_{l}\\in \\mathbb{R}^{c\\times h\\times w}\\)" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.155, + 0.892, + 0.2 + ], + "angle": 0, + "content": "3: Define: feature transform function \\( T, T(\\psi) \\in \\mathbb{R}^{c' \\times h \\times w} \\), label embedding function \\( E_1, E_1(l) \\in \\mathbb{R}^{c' \\times 1} \\), linear function \\( W_1, W_1 \\in \\mathbb{R}^{c' \\times c'} \\)" + }, + { + "type": "text", + "bbox": [ + 0.51, + 0.201, + 0.892, + 0.228 + ], + "angle": 0, + "content": "4: Define: Hadamard product \\(\\odot\\), \\(J_{1,h,w} \\in \\mathbb{R}^{1 \\times h \\times w}\\) and \\(J_{c,1} \\in \\mathbb{R}^{c \\times 1}\\) are all-ones matrix for spatial duplication" + }, + { + "type": "text", + "bbox": [ + 0.51, + 0.229, + 0.78, + 0.257 + ], + "angle": 0, + "content": "5: Transform the input feature: \\(p_1(\\psi) = \\tanh (T(\\psi)), p_1(\\psi) \\in \\mathbb{R}^{c' \\times h \\times w}\\)" + }, + { + "type": "text", + "bbox": [ + 0.51, + 0.257, + 0.846, + 0.284 + ], + "angle": 0, + "content": "6: Embedding and transform the input label: \\( p_2(l) = \\tanh(W_1E_1(l)) \\cdot J_{1,h,w} \\), \\( p_2(l) \\in \\mathbb{R}^{c' \\times h \\times w} \\)" + }, + { + "type": "text", + "bbox": [ + 0.51, + 0.284, + 0.69, + 0.296 + ], + "angle": 0, + "content": "7: Calculate spatial attention:" + }, + { + "type": "list", + "bbox": [ + 0.51, + 0.112, + 0.892, + 0.296 + ], + "angle": 0, + "content": null + }, + { + "type": "equation", + "bbox": [ + 0.529, + 0.296, + 0.765, + 0.319 + ], + "angle": 0, + "content": "\\[\n\\alpha_ {l} = J _ {c, 1} \\cdot s o f t m a x \\frac {\\sum_ {i} ^ {c ^ {\\prime}} [ p _ {2} (l) \\odot p _ {1} (\\psi) ] _ {i}}{\\sqrt {c ^ {\\prime}}}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.502, + 0.34, + 0.88, + 0.355 + ], + "angle": 0, + "content": "Algorithm 2 Channel-wise Conditional Attention (CCA)" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.361, + 0.892, + 0.388 + ], + "angle": 0, + "content": "1: Input: a general feature map \\(\\psi \\in \\mathbb{R}^{c\\times h\\times w}\\), targeted label \\(l\\), intermediate channel number \\(c'\\)" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.389, + 0.824, + 0.402 + ], + "angle": 0, + "content": "2: Output: conditional channel attention \\(\\beta_{l}\\in \\mathbb{R}^{c\\times 1}\\)" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.402, + 0.892, + 0.447 + ], + "angle": 0, + "content": "3: Define: label embedding function \\( E_2, E_2(l) \\in \\mathbb{R}^{c' \\times 1} \\), embedding transform function \\( W_2, W_2 \\in \\mathbb{R}^{c' \\times c'} \\), linear functions \\( W_3, W_4, W_3 \\in \\mathbb{R}^{c' \\times (c + c')} \\), and \\( W_4 \\in \\mathbb{R}^{c \\times c'} \\)" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.448, + 0.78, + 0.462 + ], + "angle": 0, + "content": "4: Define: feature vector concatenation \\([a; b]\\)" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.462, + 0.756, + 0.474 + ], + "angle": 0, + "content": "5: Transform the input feature to vector:" + }, + { + "type": "list", + "bbox": [ + 0.511, + 0.361, + 0.892, + 0.474 + ], + "angle": 0, + "content": null + }, + { + "type": "equation", + "bbox": [ + 0.529, + 0.474, + 0.757, + 0.49 + ], + "angle": 0, + "content": "\\[\nq _ {1} (\\psi) = \\sum_ {j} ^ {h \\times m ^ {\\prime}} p (\\psi), q _ {1} (\\psi) \\in \\mathbb {R} ^ {c \\times 1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.49, + 0.778, + 0.502 + ], + "angle": 0, + "content": "6: Embedding and transform the input label:" + }, + { + "type": "equation", + "bbox": [ + 0.529, + 0.502, + 0.769, + 0.518 + ], + "angle": 0, + "content": "\\[\nq _ {2} (l) = \\operatorname {r e l u} \\left(W _ {2} E _ {2} (l)\\right), q _ {2} (l) \\in \\mathbb {R} ^ {c ^ {\\prime} \\times 1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.518, + 0.697, + 0.529 + ], + "angle": 0, + "content": "7: Calculate channel attention:" + }, + { + "type": "equation", + "bbox": [ + 0.529, + 0.53, + 0.805, + 0.545 + ], + "angle": 0, + "content": "\\[\n\\beta_ {l} = \\operatorname {s i g m o i d} \\left(W _ {4} \\left(\\operatorname {r e l u} \\left(W _ {3} [ q _ {1} (\\psi); q _ {2} (l) ]\\right)\\right)\\right)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.575, + 0.892, + 0.606 + ], + "angle": 0, + "content": "ing factor \\(\\sqrt{c'}\\) (step 7). Then the spatially attended feature map is generated as" + }, + { + "type": "equation", + "bbox": [ + 0.595, + 0.618, + 0.892, + 0.635 + ], + "angle": 0, + "content": "\\[\n\\phi_ {n} = \\alpha_ {n} \\odot \\psi , \\phi_ {n} \\in \\mathbb {R} ^ {c \\times h \\times w}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.648, + 0.892, + 0.799 + ], + "angle": 0, + "content": "where \\(\\odot\\) is Hadamard product. To further focus on the attribute-relevant dimensions, the Channel-wise Conditional Attention on Attribute, CCA-A (Algorithm 2), takes the spatially attended feature maps \\(\\phi_{n}\\) and attribute \\(A_{n}\\) as inputs, and transforms them into feature vectors \\(q_{1}(\\phi_{n})\\) and \\(q_{2}(A_{n})\\) (step 5, 6 in Algorithm 2), where \\(q_{1}(\\phi_{n})\\in \\mathbb{R}^{c\\times 1},q_{2}(A_{n})\\in \\mathbb{R}^{c^{\\prime}\\times 1}\\). The attention output \\(\\beta_{n}\\) is obtained from the concatenation of \\(q_{1}(\\phi_{n})\\) and \\(q_{2}(A_{n})\\) (step 7). \\(\\beta_{n}\\in \\mathbb{R}^{c\\times 1}\\). Finally, the attribute-specific representation is generated as" + }, + { + "type": "equation", + "bbox": [ + 0.587, + 0.811, + 0.892, + 0.828 + ], + "angle": 0, + "content": "\\[\n\\varphi_ {n} = \\beta_ {n} \\odot q _ {1} (\\phi_ {n}), \\varphi_ {n} \\in \\mathbb {R} ^ {c \\times 1}. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Subsequently, to reduce the number of class-specific representations in learning, we involve the multi-label classification to exclude low-likelihood classes. As Eq. 3 shows, given an attribute-specific MLP module \\( g_{n} \\), the probability" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11053" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.122 + ], + "angle": 0, + "content": "of all classes for an attribute-specific representation on \\( A_{n} \\) is \\( P_{n}(I) \\)." + }, + { + "type": "equation", + "bbox": [ + 0.128, + 0.133, + 0.47, + 0.151 + ], + "angle": 0, + "content": "\\[\nP _ {n} (I) = \\left[ x _ {1 _ {n}}, \\dots , x _ {m _ {n}}, \\dots , x _ {M _ {n}} \\right] = g _ {n} (\\varphi_ {n}). \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.161, + 0.469, + 0.237 + ], + "angle": 0, + "content": "By setting a threshold \\(\\gamma\\), we obtain the multi-label class prediction \\(\\{\\widehat{l_n}\\} = \\{C_{m_n}|\\forall x_{m_n} > \\gamma \\}\\). \\(\\{\\widehat{l_n}\\}\\) is the set of predicted high-likelihood classes. Empirically, with \\(\\gamma = 0.8\\) we can exclude on average \\(94\\%\\) of classes for an image. Please see the sensitivity analysis of \\(\\gamma\\) in Suppl." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.238, + 0.469, + 0.297 + ], + "angle": 0, + "content": "Class-specific representation. As an attribute often involves multiple classes, the class-conditional attention modules help M3-Net focus on individual classes and learn class-specific representations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.298, + 0.469, + 0.403 + ], + "angle": 0, + "content": "Class-conditional attention modules consist of Spatial Conditional Attention on Class (SCA-C) and Channelwise Conditional Attention on Class (CCA-C). SCA-C and CCA-C are attribute-specific. Different from the attribute-conditional attention modules, we expect them to focus on the relevant spatial locations and dimensions of corresponding classes." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.404, + 0.469, + 0.466 + ], + "angle": 0, + "content": "Given an attribute \\(A_{n}\\), its spatially attended feature map \\(\\phi_{n}\\), and class \\(C_{m_n} \\in \\{\\widehat{l_n}\\}\\), the SCA-C generates a class-conditional spatial attention map \\(\\overline{\\alpha_{m_n}}\\). We obtain the spatially attended feature map \\(\\overline{\\phi_{m_n}}\\) as" + }, + { + "type": "equation", + "bbox": [ + 0.15, + 0.475, + 0.469, + 0.495 + ], + "angle": 0, + "content": "\\[\n\\overline {{\\phi_ {m _ {n}}}} = \\overline {{\\alpha_ {m _ {n}}}} \\odot \\phi_ {n}, \\overline {{\\phi_ {m _ {n}}}} \\in \\mathbb {R} ^ {c \\times h \\times w}. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.503, + 0.469, + 0.58 + ], + "angle": 0, + "content": "\\(\\overline{\\phi_{m_n}}\\) is subsequently fed through both attribute-conditional channel attention (CCA-A) and class-conditional channel attention (CCA-C). Especially, the CCA-A of \\(A_{n}\\) outputs the attribute-conditional channel attention map \\(\\overline{\\beta_n}\\). The attended feature is" + }, + { + "type": "equation", + "bbox": [ + 0.158, + 0.59, + 0.469, + 0.609 + ], + "angle": 0, + "content": "\\[\n\\overline {{\\varphi_ {n}}} = \\overline {{\\beta_ {n}}} \\odot q _ {1} \\left(\\overline {{\\phi_ {m _ {n}}}}\\right), \\overline {{\\varphi_ {n}}} \\in \\mathbb {R} ^ {c \\times 1}. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.618, + 0.469, + 0.68 + ], + "angle": 0, + "content": "The CCA-C of \\(A_{n}\\) takes the feature vector \\(\\overline{\\varphi_n}\\) and the class \\(C_{m_n}\\) as inputs to generate the feature vector \\(q_{1}(\\overline{\\varphi_{n}})\\) and gives the class-conditional channel-wise attention map \\(\\overline{\\beta_{m_n}}\\). The class-specific representation is obtained as" + }, + { + "type": "equation", + "bbox": [ + 0.146, + 0.689, + 0.469, + 0.708 + ], + "angle": 0, + "content": "\\[\n\\overline {{\\varphi_ {m _ {n}}}} = \\overline {{\\beta_ {m _ {n}}}} \\odot q _ {1} (\\overline {{\\varphi_ {n}}}), \\overline {{\\varphi_ {m _ {n}}}} \\in \\mathbb {R} ^ {c \\times 1}. \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.718, + 0.469, + 0.839 + ], + "angle": 0, + "content": "M3-Net has three key outputs: the attribute-specific representation \\(\\varphi_{n}\\), class-specific-representation \\(\\overline{\\varphi_{m_n}}\\), and multi-label probability vector \\(P_{n}(I)\\). They are used to constrain the multi-granularity embedding spaces via a multi-granularity objective. In this part, we build our method upon the online clustering method and prototypical triplet loss in [14] and further extend them to learning two-granularity fine-grained representations." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.848, + 0.329, + 0.864 + ], + "angle": 0, + "content": "3.2. Multi-granularity Objective" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "To learn across different granularities of the fashion representations in an end-to-end manner, we design two losses" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.12 + ], + "angle": 0, + "content": "to introduce appropriate inductive bias: an attribute-level loss and a class-level loss." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.122, + 0.892, + 0.213 + ], + "angle": 0, + "content": "Attribute-level loss. At the attribute level, we define the below multi-label classification loss to allow the representation learning on multi-label attributes. Given an image \\(I\\) with \\(N\\) attributes \\(\\{A_{n}\\}\\), each with \\(M_{n}\\) classes \\(\\{C_{m_n}\\}\\) and corresponding class labels \\(\\{y_{m_n}\\}\\), the loss of multi-label classification is a binary cross-entropy loss," + }, + { + "type": "equation", + "bbox": [ + 0.521, + 0.218, + 0.892, + 0.279 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {\\mathcal {M}} \\left(I, A _ {n} \\mid y _ {m _ {n}}\\right) = \\frac {1}{M _ {n}} \\left(\\sum_ {m = 1} ^ {M _ {n}} \\left[ - w _ {p} y _ {m _ {n}} \\cdot \\log x _ {m _ {n}} \\right. \\right. \\tag {7} \\\\ \\left. + \\left(1 - y _ {m _ {n}}\\right) \\cdot \\log \\left(1 - x _ {m _ {n}}\\right)\\right]\\left. \\right), \\forall x _ {m _ {n}} \\in P _ {n} (I), \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.283, + 0.892, + 0.328 + ], + "angle": 0, + "content": "where \\( x_{m_n} \\) is the predicted probability of \\( I \\) in class \\( C_{m_n} \\), \\( w_p \\) is the weight on the positive samples to mitigate the class-imbalance problem." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.329, + 0.892, + 0.463 + ], + "angle": 0, + "content": "Class-level loss. At the class level, we propose to regularize the class-specific representation learning on both global and local structures via two triplet losses. For the global structure, we construct a prototypical triplet loss between an image representation, the representation of the positive prototype of the class that the image belongs to, and a negative representation. The triplet loss associated with the local structure involves instance-level representations to refine the local distance." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.465, + 0.892, + 0.495 + ], + "angle": 0, + "content": "A classic triplet loss between an anchor, a positive, and a negative representation is defined as" + }, + { + "type": "equation", + "bbox": [ + 0.51, + 0.515, + 0.892, + 0.533 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\triangle} (I, I ^ {+}, I ^ {-}) = \\max \\{0, \\zeta + d (I, I ^ {+}) - d (I, I ^ {-}) \\}, \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.538, + 0.892, + 0.567 + ], + "angle": 0, + "content": "where \\(\\zeta = 0.4\\) is a predefined margin, and \\(d\\) is the cosine similarity." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.568, + 0.892, + 0.628 + ], + "angle": 0, + "content": "Given a triplet of images \\([I, I^{+}, I^{-}]\\) associated with classes \\([C_{m_n}, C_{m_n}^{+}, C_{m_n}^{-}]\\) in attribute \\(A_{n}\\), \\(C_{m_n} = C_{m_n}^{+} \\neq C_{m_n}^{-}\\). The prototypical triplet loss in the class-specific embedding spaces is defined as" + }, + { + "type": "equation", + "bbox": [ + 0.514, + 0.633, + 0.892, + 0.651 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathcal {C C}} \\left(I, A _ {n}, C _ {m _ {n}}\\right) = \\mathcal {L} _ {\\triangle} \\left(\\overline {{\\varphi_ {m _ {n}} (I)}}, \\bar {\\varphi_ {C ^ {+}}}, \\overline {{\\varphi_ {m _ {n}} (I ^ {-})}}\\right), \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.656, + 0.892, + 0.718 + ], + "angle": 0, + "content": "where \\(\\overline{\\varphi_{m_n}(I)}\\) is the anchor representation, \\(\\overline{\\varphi_{m_n}(I^-)}\\) is a random negative representation in the class-specific embedding space, and \\(\\overline{\\varphi_{C^+}}\\) is the positive class prototype in the space. The computation of \\(\\overline{\\varphi_{C^+}}\\) is akin to [14]." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.719, + 0.892, + 0.748 + ], + "angle": 0, + "content": "The instance triplet loss in the class-specific embedding spaces is defined as" + }, + { + "type": "equation", + "bbox": [ + 0.508, + 0.753, + 0.892, + 0.784 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathcal {C I}} (I, A _ {n}, C _ {m _ {n}}) = \\mathcal {L} _ {\\triangle} (\\overline {{\\varphi_ {m _ {n}} (I)}}, \\overline {{\\varphi_ {m _ {n}} (I ^ {+})}}, \\overline {{\\varphi_ {m _ {n}} (I ^ {-})}}), \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.785, + 0.892, + 0.83 + ], + "angle": 0, + "content": "where \\(\\overline{\\varphi_{m_n}(I)}\\), \\(\\overline{\\varphi_{m_n}(I^+)}\\), \\(\\overline{\\varphi_{m_n}(I^-)}\\) are the class-specific representations for the anchor, positive, and negative sample, respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.831, + 0.892, + 0.875 + ], + "angle": 0, + "content": "Final objective function. The final objective function combines both attribute and class-level objectives and allows a simple end-to-end training, as shown in Eq.(11)" + }, + { + "type": "equation", + "bbox": [ + 0.568, + 0.881, + 0.892, + 0.903 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\theta} \\left(\\lambda_ {M} \\mathcal {L} _ {\\mathcal {M}} + \\lambda_ {C C} \\mathcal {L} _ {\\mathcal {C C}} + \\lambda_ {C I} \\mathcal {L} _ {\\mathcal {C I}}\\right). \\tag {11}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11054" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.086, + 0.089, + 0.462, + 0.139 + ], + "angle": 0, + "content": "
DatasetAttr type# Attr# Class per attrTrain/val/test
DeepFashion [18]multi-label5156-230220K/28K/28K
FashionAI [28]single-label85-10144k/18k/18k
DARN [13]single-label97-55163k/20k/20k
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.15, + 0.468, + 0.178 + ], + "angle": 0, + "content": "Table 1. Summary of the datasets used in experimental validations. \nAttr: attribute." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.207, + 0.468, + 0.237 + ], + "angle": 0, + "content": "where, \\(\\lambda_{M},\\lambda_{CC}\\) and \\(\\lambda_{CI}\\) are hyperparameters, which are set to 1 in our experiments." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.253, + 0.21, + 0.27 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.279, + 0.18, + 0.293 + ], + "angle": 0, + "content": "4.1. Datasets" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.303, + 0.468, + 0.392 + ], + "angle": 0, + "content": "In Table 1, we summarize the three benchmark datasets used in the experiments. DeepFashion is a large dataset containing image labels of fashion attributes, landmarks, etc. We use the coarsely-annotated attribute prediction subset, which is one of the most popular datasets in fashion retrieval, and is a multi-label dataset." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.405, + 0.284, + 0.421 + ], + "angle": 0, + "content": "4.2. Experimental Settings" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.43, + 0.468, + 0.459 + ], + "angle": 0, + "content": "We compare our proposed method with the state-of-the-art solutions [6, 14, 19] on the aforementioned datasets." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.46, + 0.468, + 0.595 + ], + "angle": 0, + "content": "Baselines. ASEIN networks are the state-of-the-art works on attribute-specific representation learning. ASEIN [19] learns 1024 dimensional attribute-specific representations by using an attribute-aware spatial attention and an attribute-aware channel attention. \\(\\mathrm{ASEN}_{v2}\\) [19] builds a new attention module structure and achieves better performance than ASEIN. \\(\\mathrm{ASEN}++\\) [6] further proposes a cascade network with a global branch and a local branch to learn multi-scale representations in 2,048 dimensions." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.597, + 0.468, + 0.717 + ], + "angle": 0, + "content": "MODC [14] it is a fine-grained representation learning framework with online deep clustering to achieve retrieval in two granularities. It splits the attribute-specific embedding spaces into class-specific embedding spaces in the inference stage to enable retrieval at the finer granularity. MODC learns attribute-specific representations with 2048 dimensions and achieves the state-of-the-art results on multiple datasets." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.719, + 0.468, + 0.839 + ], + "angle": 0, + "content": "M3-Net is our proposed method which jointly learns attribute-specific and class-specific representation duet for fine-grained fashion analysis. The attribute-specific and class-specific representations are 1024 dimensions. To isolate the effects of two-granularity attentions, we trained M3-Net with only the attribute-conditional attention modules, with only the class-conditional attention modules, and with both, called M3-Net\\(_a\\), M3-Net\\(_c\\), and M3-Net respectively." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.84, + 0.468, + 0.9 + ], + "angle": 0, + "content": "Training details M3-Net employs a ResNet50 [10] pretrained on ImageNet [5] as the shared backbone network, and removes the last residual block. It is identical to the backbone of the baselines for fair comparisons. To train" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.091, + 0.892, + 0.182 + ], + "angle": 0, + "content": "M3-Net, we use a learning rate \\(1 \\times 10^{-4}\\) with a 0.975 decay per epoch and a batch size of 16. We sample 40k triplet of images each epoch of training. In training, We set \\(w_{p}\\) to 100 for DeepFashion, and 1 for FashionAI and DARN. To train the baselines on DeepFashion, We follow the descriptions in [6, 14, 19]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.183, + 0.892, + 0.318 + ], + "angle": 0, + "content": "Evaluation Tasks and Metrics. We evaluate our proposed method in comparison with the above baselines on the fine-grained fashion retrieval task. Following the existing protocol for multi-granularity retrieval as proposed in MODC [14], the retrieval is prioritized in the class-specific embedding space, followed by retrieval in the attribute-specific embedding space. Same as existing works [6, 14, 19], we employ Mean Average Precision (MAP) and Recall as the evaluation metrics." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.331, + 0.702, + 0.347 + ], + "angle": 0, + "content": "4.3. Experimental Results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.355, + 0.892, + 0.521 + ], + "angle": 0, + "content": "In this section, we discuss the experimental results and ablation study of M3-Net on multi-label attributes and single-label attributes. Table 2 presents the overall performance and the performance on each attribute of baselines and M3-Net on DeepFashion. Table 3 and Table 4 summarizes the performance on FashionAI and DARN. On all datasets, we show the ablation study of separately employing attribute-conditional attention modules (i.e., \\( \\mathrm{M3 - Net}_a \\)) and class-conditional attention modules (i.e., \\( \\mathrm{M3 - Net}_c \\)) to demonstrate the effectiveness of representation learning on attribute granularity and class granularity." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.543, + 0.872, + 0.558 + ], + "angle": 0, + "content": "4.3.1 Quantitative evaluation on multi-label dataset" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.568, + 0.892, + 0.704 + ], + "angle": 0, + "content": "Table 2 summarizes the performance of fine-grained fashion retrieval on all attributes in DeepFashion. Note that \\(\\mathrm{ASEN}_{v2}\\) [19] and \\(\\mathrm{ASEN}++\\) [6] report performance on DeepFashion by treating it as a single-label dataset. To evaluate the performance in the multi-label setting, we split DeepFashion following the multi-class labels of each image in the dataset. The train/validation/test split is shown in Table 1. For the retrieval task, the validation set and test set are further split into the query and candidate sets by 1:4." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.892, + 0.9 + ], + "angle": 0, + "content": "DeepFashion is an extremely challenging dataset for fine-grained fashion retrieval. Therefore, all methods perform much worse on DeepFashion than on other benchmark datasets Compared with the baselines, the proposed M3-Net consistently achieves the best performance with a large margin on all evaluation metrics on individual attributes and overall. Even when compared with the state-of-the-art multi-granularity method, MODC, the proposed M3-Net shows significant improvements over MODC on MAP@all (70.42%), MAP@100 (57.95%), and Recall@100 (112.5%). The results demonstrate the efficacy of the attribute and class-specific representations learned by M3-Net." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11055" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.212, + 0.089, + 0.761, + 0.219 + ], + "angle": 0, + "content": "
ModelDeepFashion
MAP@allMAP@allMAP@100Recall@100
Attributetexturefabricshapepartstyleoveralloveralloverall
ASEN [19]21.0311.6114.687.814.6612.3320.605.10
ASENV2 [19]21.8611.6714.587.934.6812.5120.554.99
ASEN++ [6]22.2011.7114.708.154.7212.7420.795.21
MODC [14]22.2611.9814.687.965.2312.7822.216.06
M3-Neta27.3718.3422.9614.669.7419.0328.1410.59
M3-Netc30.0919.6025.2416.4311.3220.9230.5812.10
M3-Net30.7920.2027.1117.2811.6121.7835.0812.88
" + }, + { + "type": "table_caption", + "bbox": [ + 0.217, + 0.227, + 0.752, + 0.241 + ], + "angle": 0, + "content": "Table 2. Performance comparison on all attributes of the multi-label dataset, DeepFashion." + }, + { + "type": "table", + "bbox": [ + 0.098, + 0.255, + 0.875, + 0.361 + ], + "angle": 0, + "content": "
ModelFashionAI
MAP@allMAP@allMAP@100Recall@100
Attributeskirt lengthsleeve lengthcoat lengthpant lengthcollar designlapel designneckline designneck designoveralloveralloveralloverall
ASEN [19]64.6149.9849.7565.7670.3062.8652.1456.4257.3764.7022.77
ASENv2 [19]65.5854.4252.0367.4171.3666.7660.9159.5861.1367.8524.14
ASEN++ [6]66.3157.5155.4368.8372.7966.8566.7867.0264.2770.6225.30
MODC [14]74.5467.4868.2577.6981.1176.9077.4677.1074.3280.2930.26
M3-Neta73.2169.5865.2778.7980.8078.0577.0473.4073.9381.5730.48
M3-Netc74.3365.9164.2778.2682.0078.8574.8072.3972.8882.5830.77
M3-Net75.2770.0467.9079.3182.8278.5876.8175.5175.0487.0432.01
" + }, + { + "type": "table_caption", + "bbox": [ + 0.221, + 0.371, + 0.747, + 0.384 + ], + "angle": 0, + "content": "Table 3. Performance comparison on all attributes of the single-label dataset, FashionAI." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.412, + 0.47, + 0.517 + ], + "angle": 0, + "content": "Ablation study on \\(\\mathrm{M3 - Net}_a\\), \\(\\mathrm{M3 - Net}_c\\) and M3-Net suggests that employing more fine-grained attention on classes \\((\\mathrm{M3 - Net}_c)\\) performs better than attribute-level attention alone \\((\\mathrm{M3 - Net}_a)\\). Yet combining attribute-conditional attentions and class-conditional attentions works the best (M3-Net). It shows that representations learned at the two granularities are complementary to each other." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.519, + 0.473, + 0.776 + ], + "angle": 0, + "content": "Furthermore, we analyze the performance on co-occurring classes on DeepFashion to evaluate the effectiveness of M3-Net in capturing the inter-dependencies between different classes in representation learning. We first calculate the pairwise co-occurrence rates of all classes in the dataset. Two classes are considered co-occurring if both are associated with the same image. The range of co-occurrence rate is [0, 0.03], i.e., the most frequently co-occurring class pairs appear in \\(3\\%\\) of the images. We set the cut-off at 0.002 (corresponding to 565 co-occurrences), resulting in 468 class pairs from the 1M class pairs in the dataset. This gives us 122 unique classes. M3-Net achieves a MAP@all at 35.61 on this set of classes, which is \\(63.50\\%\\) higher than the average of all classes. We hypothesize that M3-Net is able to incorporate the inter-dependencies between these classes into representation learning, thus performing better on them." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.8, + 0.461, + 0.815 + ], + "angle": 0, + "content": "4.3.2 Quantitative evaluation on single-label datasets" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.47, + 0.901 + ], + "angle": 0, + "content": "For the two single-label datasets, FashionAI and DARN, we follow the same split as in [19]. On both datasets, we observe similar competence of the proposed M3-Net in fine-grained fashion retrieval. On FashionAI, M3-Net achieve the best performance overall on all evaluation met" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.411, + 0.891, + 0.569 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.579, + 0.893, + 0.704 + ], + "angle": 0, + "content": "Figure 3. Two-granularity attentions learned by M3-Net on DeepFashion. The attribute-conditional attention tends to focus on a wider range of regions in an image, while the class-conditional attention focuses more narrowly on a region relevant to each class. For instance, row 1: class \"slit\" focuses on the dress slit, \"elegant\" focuses on the waist; row 2: \"contrast trim\" focuses on the part with two different colors, \"stretch\" focuses on the strap; row 3: \"draped\" focuses on the drape decoration, and \"fit\" focuses on the waist. Best viewed in color on a computer screen." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.718, + 0.891, + 0.748 + ], + "angle": 0, + "content": "rics (MAP@all, MAP@100, and Recall@100). It also outperforms the baselines on most individual attributes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.893, + 0.901 + ], + "angle": 0, + "content": "On DARN, we again observe a boost on all evaluation metrics. While baselines perform unsatisfactorily on \"clothes category\" and \"collar shape\", M3-Net improves them the most along with improvements on other attributes. Overall, M3-Net exceeds the best baseline, MODC, on MAP@all by \\(16.35\\%\\), MAP@100 by \\(14.59\\%\\), and Recall@100 by \\(18.24\\%\\). The results of M3-Net on single-label datasets again demonstrate the effectiveness of the attribute-specific and class-specific representations. Compared with MODC, which obtains class-specific representations by di" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "11056" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.088, + 0.088, + 0.885, + 0.184 + ], + "angle": 0, + "content": "
ModelDARN
MAP@allMAP@allMAP@100Recall@100
Attributeclothes categoryclothes buttonclothes colorclothes lengthclothes patternclothes shapecollar shapesleeve lengthsleeve shapeoveralloveralloverall
ASEN [19]36.6246.0152.7656.8554.8956.8534.4079.9558.0852.7558.7220.26
ASENv2 [19]37.9749.2452.2659.1355.3259.0636.8681.5458.8254.2959.6620.88
ASEN++ [6]40.2150.0453.1459.8357.4159.7037.4583.7060.4155.7861.0921.51
MODC [14]49.9460.7558.7966.3462.2468.4145.1487.4165.3262.5672.1626.76
M3-Neta59.1669.9468.1872.5872.8776.2160.2289.3671.5871.0678.1230.77
M3-Netc60.9870.9168.5274.9574.4879.1563.0990.3173.0072.7981.4631.64
M3-Net60.5470.3969.5273.9774.4077.8361.6390.0373.9472.4282.6931.34
" + }, + { + "type": "table_caption", + "bbox": [ + 0.232, + 0.193, + 0.738, + 0.209 + ], + "angle": 0, + "content": "Table 4. Performance comparison on all attributes of the single-label dataset, DARN." + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.222, + 0.496, + 0.41 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.222, + 0.895, + 0.41 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.42, + 0.893, + 0.449 + ], + "angle": 0, + "content": "Figure 4. (a) single-label and (b) multi-label fashion retrieval by M3-Net and MODC on DeepFashion. Green: true positive retrieval; red: false positive retrieval. Best viewed in color on a computer screen." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.476, + 0.47, + 0.536 + ], + "angle": 0, + "content": "rectly segmenting the attribute-specific representation into class-specific clusters in the same embedding space, M3-Net learns separate representation spaces for attributes and classes and performs better." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.537, + 0.471, + 0.657 + ], + "angle": 0, + "content": "Ablation study on FashionAI shows that overall having attentions on two granularities (M3-Net) performs better than attentions on either granularity alone \\((\\mathrm{M}3 - \\mathrm{Net}_a\\) and \\(\\mathrm{M}3 - \\mathrm{Net}_c)\\). On DARN, M3-Net's performance is comparable to that of \\(\\mathrm{M}3 - \\mathrm{Net}_c\\), which only has class-conditional attention modules. We speculate that this is due to discriminating attributes and classes is less challenging on single-label datasets than on multi-label attribute datasets." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.679, + 0.292, + 0.695 + ], + "angle": 0, + "content": "4.3.3 Qualitative evaluations" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.704, + 0.47, + 0.87 + ], + "angle": 0, + "content": "Figure 3 visualizes the two-granularity attentions learned by M3-Net. The attribute-conditional attention tends to focus on all regions that are likely to be associated with the attribute. For example, in the first row of Figure 3, the attention of attribute \"part\" involves areas covering various parts of the dress such as collar, belt area, and hemline (second image in the first row). On the contrary, the class-conditional attention tends to focus on class-specific regions in the image. For instance, class \"slit\" highlights the dress slit region (third image in the first row). The visualized attention is consistent with our hypothesis." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Figure 4 presents examples of fine-grained fashion retrieval results on single-label and multi-label datasets. In" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.476, + 0.893, + 0.657 + ], + "angle": 0, + "content": "the figure, we compared the results from our proposed M3-Net with those from MODC (the best-performing baseline). Figure 4 (a) shows that on single-label retrieval, M3-Net can better discriminate fine-grained visual features than MODC, leading to more accurate retrieval results on individual classes. Moreover, on multi-label retrieval, M3-Net is able to retrieve images containing multiple class labels. For example, when searching an image on attribute \"texture\" with both \"print\" and \"tribal\" class labels (last example in Figure 4), M3-Net accurately retrieves related images, while MODC retrieves many other printed textures that is not \"tribal\"." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.67, + 0.619, + 0.685 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.696, + 0.893, + 0.892 + ], + "angle": 0, + "content": "We have proposed a multi-attribute multi-granularity multi-label network (M3-Net) for fine-grained fashion analysis. Our proposed architecture learns both attribute and class-level representations for a fashion image through a shared backbone and two sub-networks with attribute and class conditional attention modules. This design, together with a multi-granularity loss, allows the network to effectively learn discriminative representations while capturing the inter-dependencies among various visual elements in different granularities. Our experiments show that the proposed M3-Net sets new state-of-the-art performance on both single-label and multi-label benchmark datasets in the fine-grained fashion retrieval task." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11057" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.184 + ], + "angle": 0, + "content": "[1] Kenan E Ak, Ashraf A Kassim, Joo Hwee Lim, and Jo Yew Tham. Learning attribute representations with localization for flexible fashion search. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops, pages 0-0, 2019." + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.47, + 0.289 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.519, + 0.956 + ], + "angle": 0, + "content": "11059" + } + ] +] \ No newline at end of file diff --git a/2023/Learning Attribute and Class-Specific Representation Duet for Fine-Grained Fashion Analysis/8a754c43-06a8-48b2-bbea-8eaf40d7cf09_origin.pdf b/2023/Learning Attribute and Class-Specific Representation Duet for Fine-Grained Fashion Analysis/8a754c43-06a8-48b2-bbea-8eaf40d7cf09_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..68d65dfce47bf48a09d8480eb1aee93108ebe9b7 --- /dev/null +++ b/2023/Learning Attribute and Class-Specific Representation Duet for Fine-Grained Fashion Analysis/8a754c43-06a8-48b2-bbea-8eaf40d7cf09_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:ee42b9a802005780c24346cd721a6c13ccc055ef6cce4c4521977249baa9d150 +size 5891601 diff --git a/2023/Learning Attribute and Class-Specific Representation Duet for Fine-Grained Fashion Analysis/full.md b/2023/Learning Attribute and Class-Specific Representation Duet for Fine-Grained Fashion Analysis/full.md new file mode 100644 index 0000000000000000000000000000000000000000..f546fdca3010f100893a236187ecea53386fa576 --- /dev/null +++ b/2023/Learning Attribute and Class-Specific Representation Duet for Fine-Grained Fashion Analysis/full.md @@ -0,0 +1,337 @@ +# Learning Attribute and Class-Specific Representation Duet for Fine-grained Fashion Analysis + +Yang Jiao + +Amazon + +jaoyan@amazon.com + +Yan Gao, Jingjing Meng, Jin Shang, Yi Sun + +Amazon + +{yanngao, ajmeng, imjshang, yisun}@amazon.com + +# Abstract + +Fashion representation learning involves the analysis and understanding of various visual elements at different granularities and the interactions among them. Existing works often learn fine-grained fashion representations at the attribute level without considering their relationships and inter-dependencies across different classes. In this work, we propose to learn an attribute and class-specific fashion representation duet to better model such attribute relationships and inter-dependencies by leveraging prior knowledge about the taxonomy of fashion attributes and classes. Through two sub-networks for the attributes and classes, respectively, our proposed an embedding network progressively learns and refines the visual representation of a fashion image to improve its robustness for fashion retrieval. A multi-granularity loss consisting of attribute-level and class-level losses is proposed to introduce appropriate inductive bias to learn across different granularities of the fashion representations. Experimental results on three benchmark datasets demonstrate the effectiveness of our method, which outperforms the state-of-the-art methods by a large margin. + +# 1. Introduction + +Fashion products have become one of the most consumed products in online shopping. Unlike other types of products, fashion products are usually rich in visual elements at different levels of granularity. For instance, besides the overall visual appearance, a fashion product can be described by a set of attributes, such as "shape", "color" and "style", which focus on different aspects of the visual representation. Each attribute can be further categorized into various classes. For example, "fit", "flare" and "pencil" are different classes under attribute "shape" (Fig. 1). Therefore, modeling fashion representation in different granularities is essential for online shopping and other downstream applications, especially those that require analysis + +![](images/643f6fe384ad817010b12640099376fded801bcef9b935eb82e69b1c88e7d3f5.jpg) +Figure 1. Left: existing fine-grained representation learning methods often learn attribute-specific representations for fashion products, thus may not be able to discern the two dresses that have different compositions of visual elements at the class level. Right: our proposed method (right) jointly learns attribute and class-specific representations. Therefore, it can discriminate between the two dresses by their class-specific representations. + +of subtle or fine-grained details such as attribute-based fashion manipulation [1, 2, 27] and retrieval [6, 14, 19, 23, 24], fashion copyright [6, 19], and fashion compatibility analysis [11, 15, 21, 23]. + +Fine-grained fashion modeling and analysis in recent years explore the attribute-specific representation learning. The focus has recently shifted from earlier works that learn separate representations for each attribute independently [1, 2] to multi-task learning, which uses a common backbone for different attributes while tailoring the learning for each specific attribute via mechanisms such as attention masks [6, 14, 19, 24]. Success of these attribute-specific representation learning methods for fine-grained fashion analysis can be attributed to their capabilities to discriminate visual features associated with different aspects of fashion products, which learning an image-level global representation finds challenging. + +However, when it comes to classes, such attribute- + +specific representation methods face a similar challenge to the above. The reason is that due to the dynamic and aesthetic nature of fashion products, different visual elements are often composited together to achieve certain visual effects, making an attribute-level description insufficient to capture such interactions and granularity. For instance, under the same "shape" attribute, one may go for a dress design that combines classes "fit" and "flare" for a more casual look (top image, Fig. 1), but go for a different dress that combines "fit" and "pencil" for a more formal look while flattering one's natural curves (bottom image, Fig. 1). Therefore, an attribute-level representation is hard to differentiate the two dresses. Alternatively, one may directly learn a class-specific representation for each class under the "shape" attribute, which, however, faces the scalability issue. For instance, if a fashion image is associated with $N$ attributes and $M$ classes per attribute, one would need to learn $N \times M$ class-specific representations. + +To better discriminate fashion products with distinct design considerations and model the interplay among various visual elements, we propose to leverage prior knowledge about fashion taxonomy to model fashion products. We jointly learn both attribute-specific and class-specific fashion representations through a multi-attribute multi-granularity multi-label embedding network (M3-Net). M3-Net consists of two sub-networks, for attributes and classes, respectively. Different attributes share the same backbone sub-network as well as two attribute-conditional attention modules, while different classes under a given attribute share two class-conditional attention modules. + +The shared backbone and conditional attention modules allow the network to better capture the inter-dependencies and shared visual statistics among the attributes and classes. Through multi-label learning on attribute-specific representations, we also improve the scalability of the proposed network by focusing class-specific representation learning on high likelihood classes only. Finally, a multi-granularity loss consisting of attribute-level and class-level losses is designed to introduce appropriate inductive bias for learning across different granularities. + +In summary, our contributions are: + +- We propose to model fashion products at both attribute and class levels based on fashion taxonomy to better capture the inter-dependencies of various visual elements and improve the discriminative power of learned fashion representations. +- We design a multi-attribute multi-granularity multi-label network (M3-Net) to jointly learn attributespecific and class-specific representation duet for fine-grained fashion analysis. Through two sub-networks and conditional attention modules, M3-Net is able to progressively learn discriminative representations at + +different granularities, with appropriate inductive bias introduced by the attribute-level and class-level losses. + +- Our model outperforms state-of-the-art methods in fine-grained fashion retrieval on three benchmark datasets. The experimental results demonstrate the efficacy of our proposed method. + +# 2. Related Work + +# 2.1. Generic Fashion Representation Learning + +Earlier fashion representation learning works [7, 8, 16, 20, 25, 26] focus on the global representation of a fashion product by learning a generic metric embedding from the entire fashion image. The generic representations benefit tasks such as in-shop fashion retrieval [16, 22, 26], street-to-shop fashion retrieval [4, 7, 8, 13, 17, 18] and compatibility retrieval [11, 15, 20, 25]. For in-shop fashion retrieval, the images often have a consistent background and photo shooting angle. In comparison, street-to-shop retrieval is more challenging because the images are often taken in an uncontrolled environment with varying lighting conditions, scales, and viewing angles. Different from the above two tasks that focus on the overall similarity, compatibility retrieval focuses on a specific global attribute such as color, fabric, and style. Although effective in global representation learning, these works lack the capabilities to model fine-grain details and subtleties in fashion products. + +# 2.2. Multi-attribute Representation Learning + +Many works tackle the problem of fine-grained fashion representation learning by analyzing fashion attributes. We have seen great success of such approaches in tasks such as attribute-specific retrieval [2, 6, 19, 24] and retrieval with attribute manipulation [1, 12, 27]. One group of works [12, 27] utilizes fully connected layers to transform generic representations into attribute-specific representations. However, the linear transformation function of fully connected layers neglects the spatial relationship within attribute-specific representations. Another group of works learns attribute-specific representations by leveraging region proposal, either via a dedicated network [13] or via global pooling layers [1, 2, 9]. For example, some works [1, 2] localize the spatial area of each attribute using global pooling layers, and crop the spatial feature maps for further attribute-specific learning. Although cropping spatial feature maps allows representation learning to focus on a local region, it rigidly limits the visual representation to a specific area and ignores other correlated visual elements in a larger area. In contrast, the third group of works uses attention masks to incorporate a global view into representation learning with the flexibility to bring in contexts from other regions. For instance, the authors of [6, 14, 19, 24] utilize + +![](images/cd0948f8e314fc00d4dd47317af5310eebf4f00e5e48d4cb88bda4ea2681264a.jpg) +Figure 2. The architecture of the proposed M3-Net. M3-Net first obtains a generic representation using a backbone CNN. It learns attribute-specific representations through two attribute-conditional attention modules (SCA-A and CCA-A). Taking the high-likelihood classes from the multi-label classification, M3-Net employs two class-conditional attention modules (SCA-C and CCA-C) to learn the class-specific representations. SCA-A and SCA-C are extended from the SCA module (Alg. 1), and CCA-A and CCA-C are extended from CCA module (Alg. 2). + +attention masks to dynamically assign weights to different dimensions of the global representation of an image for specific attributes. Veit, Belongie and Karaletsos [24] use attention masks to select and reweight relevant dimensions for each attribute to induce attribute-specific subspaces. Instead of learning attribute-specific weights, other works [6, 19] propose to learn attribute-aware spatial and channel attention modules. The attention modules are attached to the feature extraction network to enhance the participation of attributes in representation learning. + +# 2.3. Multi-granularity Representation Learning + +As attribute-level representations may still fall short of fashion tasks that require analysis of finer granular interactions, such as the one shown in Fig. 1, a few works propose to learn fashion representations in multiple granularities. Some works tackle the multi-granularity representation learning problem from the spatial domain, which essentially transforms multi-granularity learning into multi-scale learning. For instance, Dong, Ma and their co-authors [6, 19] propose to use a global branch and a local branch to learn two attribute-specific representations on two scales. Similarly, Bao, Zhang and their co-authors [3] propose a feature learning network that jointly learns the representation in two feature map scales and three image scales via a global, a part-base, and a local branch. Instead of multi-scale learning, Jiao, Xie and their co-authors [14] propose to segment the attribute-specific embedding spaces into class-specific embedding spaces using the cluster prototypes learned by online deep clustering. The proposed model achieves state-of-the-art performance on the fine-grained fashion retrieval task by prioritizing retrieval in class-specific embedding spaces. However, the representations are not optimized in + +class-specific embedding spaces because the segmentation happens in the inference stage. In our work, we propose to jointly learn both attribute-specific and class-specific representations through a multi-granularity embedding network. + +# 3. Proposed Method + +The proposed multi-attribute multi-granularity multi-label embedding network (M3-Net) is an end-to-end network that jointly learns the attribute and class level representations. As shown in Figure 2, M3-Net employs a backbone network, two attribute-conditional attention modules, two class-conditional attention modules, and a multi-label classification module. The backbone network shares learned weights across all attributes, which makes the embedding network scalable. It embeds an input image into a generic representation that represents the entire image. The generic representation is then fed through two attribute-conditional attention modules to focus learning on fine-grained attributes and obtain attribute-specific representations. Two class-conditional attention modules are further applied to learn more fine-grained class-specific representations. The shared backbone and conditional attention modules allow the network to better capture the interdependencies and shared visual statistics among the attributes and classes. The multi-label classification module serves to improve the scalability of the proposed network by focusing class-specific representation learning on high-likelihood classes. + +# 3.1. M3-Net Architecture + +Given a set of fashion product images $\{I\}$ , we denote the set of attributes associated with these images as $\{A_{n}\}$ where $n \in [1, N]$ . Similarly, we denote the set of classes + +associated with a given attribute $A_{n}$ as $\{C_{m_n}\}$ , where $m_{n} \in [1, M_{n}]$ and $M_{n}$ is the number of classes under attribute $A_{n}$ . Given $A_{n}$ , an image $I \in \{I\}$ can associate with a subset of labels in $\{1, 2, \dots, M_{n}\}$ , which is represented by a vector $[y_{1_n}, \dots, y_{m_n}, \dots, y_{M_n}]$ , where $y_{m_n} = 1$ if and only if image $I$ is associated with class $C_{m_n}$ , and 0 otherwise. + +Generic representation. Denote the parameters of M3-Net as $\theta$ and the parameters of the backbone network as $\theta_{b}$ . Correspondingly, $f_{\theta}$ represents M3-Net and $f_{\theta_b}$ represents the backbone network. The generic visual representation of an image $I$ is then denoted by $\psi = f_{\theta_b}(I)$ , where $\psi \in \mathbb{R}^{c\times h\times w}$ , $c,h,w$ are the number of channels, height, and width, respectively. + +From here, we will use $\psi$ to denote a generic feature map, use $\phi$ to denote a spatially attended feature map and $\varphi$ to denote a channel-wise attended feature map. Meanwhile, we use $x$ to denote the attribute-specific representation, and $\overline{x}$ to denote the class-specific representation. + +Attribute-specific representation. The attribute-specific representation learning acts as a connector between the generic representations and the class-specific representations. It refines the generic representation by focusing learning on the attribute-specific visual features, and the resulting attribute-specific representation will be further refined in subsequent modules to obtain more fine-grained class-specific visual representations. To reduce the complexity of the class-specific representation learning, we conduct the attribute-specific representation learning in a multi-label setting. Therefore, instead of learning $N + \sum_{n}^{N} M_{n}$ representations ( $N$ attribute-specific and $\sum_{n}^{N} M_{n}$ class-specific representations), we can exclude unlikely classes, thus improve scalability. + +Motivated by the effectiveness of spatial and channel-wise attention for multi-attribute fashion representation learning in prior works, we utilize Spatial Conditional Attention module (SCA) and Channel-wise Conditional attention module (CCA) akin to the attribute-aware attention in [19]. Both SCA (Algorithm 1) and CCA (Algorithm 2) are applied to both attribute-specific and class-specific representation learning. The structures of SCA and CCA are shown in Figure 2. + +Attribute-conditional attention modules help representation learning focus on spatial locations and dimensions relevant to a given attribute. The Spatial Conditional Attention on Attribute (SCA-A) applies SCA (Algorithm 1) at the attribute level, while the Channel-wise Conditional Attention on Attribute (CCA-A) applies CCA (Algorithm 2) at the attribute level. Given the generic representation $\psi$ and an attribute $A_{n}$ , SCA-A takes them as inputs and transforms them into feature maps with an identical size, $p_1(\psi), p_2(A_n) \in \mathbb{R}^{c' \times h \times w}$ (step 5, 6 in Algorithm 1). The attention map $\alpha_{n}$ is the Hadamard product between the image feature $p_1(\psi)$ and attribute feature $p_2(A_n)$ with a scal + +# Algorithm 1 Spatial Conditional Attention (SCA) + +1: Input: a general feature map $\psi \in \mathbb{R}^{c\times h\times w}$ , targeted label $l$ , intermediate channel number $c'$ +2: Output: conditional spatial attention $\alpha_{l}\in \mathbb{R}^{c\times h\times w}$ +3: Define: feature transform function $T, T(\psi) \in \mathbb{R}^{c' \times h \times w}$ , label embedding function $E_1, E_1(l) \in \mathbb{R}^{c' \times 1}$ , linear function $W_1, W_1 \in \mathbb{R}^{c' \times c'}$ +4: Define: Hadamard product $\odot$ , $J_{1,h,w} \in \mathbb{R}^{1 \times h \times w}$ and $J_{c,1} \in \mathbb{R}^{c \times 1}$ are all-ones matrix for spatial duplication +5: Transform the input feature: $p_1(\psi) = \tanh (T(\psi)), p_1(\psi) \in \mathbb{R}^{c' \times h \times w}$ +6: Embedding and transform the input label: $p_2(l) = \tanh(W_1E_1(l)) \cdot J_{1,h,w}$ , $p_2(l) \in \mathbb{R}^{c' \times h \times w}$ +7: Calculate spatial attention: + +$$ +\alpha_ {l} = J _ {c, 1} \cdot s o f t m a x \frac {\sum_ {i} ^ {c ^ {\prime}} [ p _ {2} (l) \odot p _ {1} (\psi) ] _ {i}}{\sqrt {c ^ {\prime}}} +$$ + +# Algorithm 2 Channel-wise Conditional Attention (CCA) + +1: Input: a general feature map $\psi \in \mathbb{R}^{c\times h\times w}$ , targeted label $l$ , intermediate channel number $c'$ +2: Output: conditional channel attention $\beta_{l}\in \mathbb{R}^{c\times 1}$ +3: Define: label embedding function $E_2, E_2(l) \in \mathbb{R}^{c' \times 1}$ , embedding transform function $W_2, W_2 \in \mathbb{R}^{c' \times c'}$ , linear functions $W_3, W_4, W_3 \in \mathbb{R}^{c' \times (c + c')}$ , and $W_4 \in \mathbb{R}^{c \times c'}$ +4: Define: feature vector concatenation $[a; b]$ +5: Transform the input feature to vector: + +$$ +q _ {1} (\psi) = \sum_ {j} ^ {h \times m ^ {\prime}} p (\psi), q _ {1} (\psi) \in \mathbb {R} ^ {c \times 1} +$$ + +6: Embedding and transform the input label: + +$$ +q _ {2} (l) = \operatorname {r e l u} \left(W _ {2} E _ {2} (l)\right), q _ {2} (l) \in \mathbb {R} ^ {c ^ {\prime} \times 1} +$$ + +7: Calculate channel attention: + +$$ +\beta_ {l} = \operatorname {s i g m o i d} \left(W _ {4} \left(\operatorname {r e l u} \left(W _ {3} [ q _ {1} (\psi); q _ {2} (l) ]\right)\right)\right) +$$ + +ing factor $\sqrt{c'}$ (step 7). Then the spatially attended feature map is generated as + +$$ +\phi_ {n} = \alpha_ {n} \odot \psi , \phi_ {n} \in \mathbb {R} ^ {c \times h \times w}, \tag {1} +$$ + +where $\odot$ is Hadamard product. To further focus on the attribute-relevant dimensions, the Channel-wise Conditional Attention on Attribute, CCA-A (Algorithm 2), takes the spatially attended feature maps $\phi_{n}$ and attribute $A_{n}$ as inputs, and transforms them into feature vectors $q_{1}(\phi_{n})$ and $q_{2}(A_{n})$ (step 5, 6 in Algorithm 2), where $q_{1}(\phi_{n})\in \mathbb{R}^{c\times 1},q_{2}(A_{n})\in \mathbb{R}^{c^{\prime}\times 1}$ . The attention output $\beta_{n}$ is obtained from the concatenation of $q_{1}(\phi_{n})$ and $q_{2}(A_{n})$ (step 7). $\beta_{n}\in \mathbb{R}^{c\times 1}$ . Finally, the attribute-specific representation is generated as + +$$ +\varphi_ {n} = \beta_ {n} \odot q _ {1} (\phi_ {n}), \varphi_ {n} \in \mathbb {R} ^ {c \times 1}. \tag {2} +$$ + +Subsequently, to reduce the number of class-specific representations in learning, we involve the multi-label classification to exclude low-likelihood classes. As Eq. 3 shows, given an attribute-specific MLP module $g_{n}$ , the probability + +of all classes for an attribute-specific representation on $A_{n}$ is $P_{n}(I)$ . + +$$ +P _ {n} (I) = \left[ x _ {1 _ {n}}, \dots , x _ {m _ {n}}, \dots , x _ {M _ {n}} \right] = g _ {n} (\varphi_ {n}). \tag {3} +$$ + +By setting a threshold $\gamma$ , we obtain the multi-label class prediction $\{\widehat{l_n}\} = \{C_{m_n}|\forall x_{m_n} > \gamma \}$ . $\{\widehat{l_n}\}$ is the set of predicted high-likelihood classes. Empirically, with $\gamma = 0.8$ we can exclude on average $94\%$ of classes for an image. Please see the sensitivity analysis of $\gamma$ in Suppl. + +Class-specific representation. As an attribute often involves multiple classes, the class-conditional attention modules help M3-Net focus on individual classes and learn class-specific representations. + +Class-conditional attention modules consist of Spatial Conditional Attention on Class (SCA-C) and Channelwise Conditional Attention on Class (CCA-C). SCA-C and CCA-C are attribute-specific. Different from the attribute-conditional attention modules, we expect them to focus on the relevant spatial locations and dimensions of corresponding classes. + +Given an attribute $A_{n}$ , its spatially attended feature map $\phi_{n}$ , and class $C_{m_n} \in \{\widehat{l_n}\}$ , the SCA-C generates a class-conditional spatial attention map $\overline{\alpha_{m_n}}$ . We obtain the spatially attended feature map $\overline{\phi_{m_n}}$ as + +$$ +\overline {{\phi_ {m _ {n}}}} = \overline {{\alpha_ {m _ {n}}}} \odot \phi_ {n}, \overline {{\phi_ {m _ {n}}}} \in \mathbb {R} ^ {c \times h \times w}. \tag {4} +$$ + +$\overline{\phi_{m_n}}$ is subsequently fed through both attribute-conditional channel attention (CCA-A) and class-conditional channel attention (CCA-C). Especially, the CCA-A of $A_{n}$ outputs the attribute-conditional channel attention map $\overline{\beta_n}$ . The attended feature is + +$$ +\overline {{\varphi_ {n}}} = \overline {{\beta_ {n}}} \odot q _ {1} \left(\overline {{\phi_ {m _ {n}}}}\right), \overline {{\varphi_ {n}}} \in \mathbb {R} ^ {c \times 1}. \tag {5} +$$ + +The CCA-C of $A_{n}$ takes the feature vector $\overline{\varphi_n}$ and the class $C_{m_n}$ as inputs to generate the feature vector $q_{1}(\overline{\varphi_{n}})$ and gives the class-conditional channel-wise attention map $\overline{\beta_{m_n}}$ . The class-specific representation is obtained as + +$$ +\overline {{\varphi_ {m _ {n}}}} = \overline {{\beta_ {m _ {n}}}} \odot q _ {1} (\overline {{\varphi_ {n}}}), \overline {{\varphi_ {m _ {n}}}} \in \mathbb {R} ^ {c \times 1}. \tag {6} +$$ + +M3-Net has three key outputs: the attribute-specific representation $\varphi_{n}$ , class-specific-representation $\overline{\varphi_{m_n}}$ , and multi-label probability vector $P_{n}(I)$ . They are used to constrain the multi-granularity embedding spaces via a multi-granularity objective. In this part, we build our method upon the online clustering method and prototypical triplet loss in [14] and further extend them to learning two-granularity fine-grained representations. + +# 3.2. Multi-granularity Objective + +To learn across different granularities of the fashion representations in an end-to-end manner, we design two losses + +to introduce appropriate inductive bias: an attribute-level loss and a class-level loss. + +Attribute-level loss. At the attribute level, we define the below multi-label classification loss to allow the representation learning on multi-label attributes. Given an image $I$ with $N$ attributes $\{A_{n}\}$ , each with $M_{n}$ classes $\{C_{m_n}\}$ and corresponding class labels $\{y_{m_n}\}$ , the loss of multi-label classification is a binary cross-entropy loss, + +$$ +\begin{array}{l} \mathcal {L} _ {\mathcal {M}} \left(I, A _ {n} \mid y _ {m _ {n}}\right) = \frac {1}{M _ {n}} \left(\sum_ {m = 1} ^ {M _ {n}} \left[ - w _ {p} y _ {m _ {n}} \cdot \log x _ {m _ {n}} \right. \right. \tag {7} \\ \left. + \left(1 - y _ {m _ {n}}\right) \cdot \log \left(1 - x _ {m _ {n}}\right)\right]\left. \right), \forall x _ {m _ {n}} \in P _ {n} (I), \\ \end{array} +$$ + +where $x_{m_n}$ is the predicted probability of $I$ in class $C_{m_n}$ , $w_p$ is the weight on the positive samples to mitigate the class-imbalance problem. + +Class-level loss. At the class level, we propose to regularize the class-specific representation learning on both global and local structures via two triplet losses. For the global structure, we construct a prototypical triplet loss between an image representation, the representation of the positive prototype of the class that the image belongs to, and a negative representation. The triplet loss associated with the local structure involves instance-level representations to refine the local distance. + +A classic triplet loss between an anchor, a positive, and a negative representation is defined as + +$$ +\mathcal {L} _ {\triangle} (I, I ^ {+}, I ^ {-}) = \max \{0, \zeta + d (I, I ^ {+}) - d (I, I ^ {-}) \}, \tag {8} +$$ + +where $\zeta = 0.4$ is a predefined margin, and $d$ is the cosine similarity. + +Given a triplet of images $[I, I^{+}, I^{-}]$ associated with classes $[C_{m_n}, C_{m_n}^{+}, C_{m_n}^{-}]$ in attribute $A_{n}$ , $C_{m_n} = C_{m_n}^{+} \neq C_{m_n}^{-}$ . The prototypical triplet loss in the class-specific embedding spaces is defined as + +$$ +\mathcal {L} _ {\mathcal {C C}} \left(I, A _ {n}, C _ {m _ {n}}\right) = \mathcal {L} _ {\triangle} \left(\overline {{\varphi_ {m _ {n}} (I)}}, \bar {\varphi_ {C ^ {+}}}, \overline {{\varphi_ {m _ {n}} (I ^ {-})}}\right), \tag {9} +$$ + +where $\overline{\varphi_{m_n}(I)}$ is the anchor representation, $\overline{\varphi_{m_n}(I^-)}$ is a random negative representation in the class-specific embedding space, and $\overline{\varphi_{C^+}}$ is the positive class prototype in the space. The computation of $\overline{\varphi_{C^+}}$ is akin to [14]. + +The instance triplet loss in the class-specific embedding spaces is defined as + +$$ +\mathcal {L} _ {\mathcal {C I}} (I, A _ {n}, C _ {m _ {n}}) = \mathcal {L} _ {\triangle} (\overline {{\varphi_ {m _ {n}} (I)}}, \overline {{\varphi_ {m _ {n}} (I ^ {+})}}, \overline {{\varphi_ {m _ {n}} (I ^ {-})}}), \tag {10} +$$ + +where $\overline{\varphi_{m_n}(I)}$ , $\overline{\varphi_{m_n}(I^+)}$ , $\overline{\varphi_{m_n}(I^-)}$ are the class-specific representations for the anchor, positive, and negative sample, respectively. + +Final objective function. The final objective function combines both attribute and class-level objectives and allows a simple end-to-end training, as shown in Eq.(11) + +$$ +\min _ {\theta} \left(\lambda_ {M} \mathcal {L} _ {\mathcal {M}} + \lambda_ {C C} \mathcal {L} _ {\mathcal {C C}} + \lambda_ {C I} \mathcal {L} _ {\mathcal {C I}}\right). \tag {11} +$$ + +
DatasetAttr type# Attr# Class per attrTrain/val/test
DeepFashion [18]multi-label5156-230220K/28K/28K
FashionAI [28]single-label85-10144k/18k/18k
DARN [13]single-label97-55163k/20k/20k
+ +Table 1. Summary of the datasets used in experimental validations. +Attr: attribute. + +where, $\lambda_{M},\lambda_{CC}$ and $\lambda_{CI}$ are hyperparameters, which are set to 1 in our experiments. + +# 4. Experiments + +# 4.1. Datasets + +In Table 1, we summarize the three benchmark datasets used in the experiments. DeepFashion is a large dataset containing image labels of fashion attributes, landmarks, etc. We use the coarsely-annotated attribute prediction subset, which is one of the most popular datasets in fashion retrieval, and is a multi-label dataset. + +# 4.2. Experimental Settings + +We compare our proposed method with the state-of-the-art solutions [6, 14, 19] on the aforementioned datasets. + +Baselines. ASEIN networks are the state-of-the-art works on attribute-specific representation learning. ASEIN [19] learns 1024 dimensional attribute-specific representations by using an attribute-aware spatial attention and an attribute-aware channel attention. $\mathrm{ASEN}_{v2}$ [19] builds a new attention module structure and achieves better performance than ASEIN. $\mathrm{ASEN}++$ [6] further proposes a cascade network with a global branch and a local branch to learn multi-scale representations in 2,048 dimensions. + +MODC [14] it is a fine-grained representation learning framework with online deep clustering to achieve retrieval in two granularities. It splits the attribute-specific embedding spaces into class-specific embedding spaces in the inference stage to enable retrieval at the finer granularity. MODC learns attribute-specific representations with 2048 dimensions and achieves the state-of-the-art results on multiple datasets. + +M3-Net is our proposed method which jointly learns attribute-specific and class-specific representation duet for fine-grained fashion analysis. The attribute-specific and class-specific representations are 1024 dimensions. To isolate the effects of two-granularity attentions, we trained M3-Net with only the attribute-conditional attention modules, with only the class-conditional attention modules, and with both, called M3-Net $_a$ , M3-Net $_c$ , and M3-Net respectively. + +Training details M3-Net employs a ResNet50 [10] pretrained on ImageNet [5] as the shared backbone network, and removes the last residual block. It is identical to the backbone of the baselines for fair comparisons. To train + +M3-Net, we use a learning rate $1 \times 10^{-4}$ with a 0.975 decay per epoch and a batch size of 16. We sample 40k triplet of images each epoch of training. In training, We set $w_{p}$ to 100 for DeepFashion, and 1 for FashionAI and DARN. To train the baselines on DeepFashion, We follow the descriptions in [6, 14, 19]. + +Evaluation Tasks and Metrics. We evaluate our proposed method in comparison with the above baselines on the fine-grained fashion retrieval task. Following the existing protocol for multi-granularity retrieval as proposed in MODC [14], the retrieval is prioritized in the class-specific embedding space, followed by retrieval in the attribute-specific embedding space. Same as existing works [6, 14, 19], we employ Mean Average Precision (MAP) and Recall as the evaluation metrics. + +# 4.3. Experimental Results + +In this section, we discuss the experimental results and ablation study of M3-Net on multi-label attributes and single-label attributes. Table 2 presents the overall performance and the performance on each attribute of baselines and M3-Net on DeepFashion. Table 3 and Table 4 summarizes the performance on FashionAI and DARN. On all datasets, we show the ablation study of separately employing attribute-conditional attention modules (i.e., $\mathrm{M3 - Net}_a$ ) and class-conditional attention modules (i.e., $\mathrm{M3 - Net}_c$ ) to demonstrate the effectiveness of representation learning on attribute granularity and class granularity. + +# 4.3.1 Quantitative evaluation on multi-label dataset + +Table 2 summarizes the performance of fine-grained fashion retrieval on all attributes in DeepFashion. Note that $\mathrm{ASEN}_{v2}$ [19] and $\mathrm{ASEN}++$ [6] report performance on DeepFashion by treating it as a single-label dataset. To evaluate the performance in the multi-label setting, we split DeepFashion following the multi-class labels of each image in the dataset. The train/validation/test split is shown in Table 1. For the retrieval task, the validation set and test set are further split into the query and candidate sets by 1:4. + +DeepFashion is an extremely challenging dataset for fine-grained fashion retrieval. Therefore, all methods perform much worse on DeepFashion than on other benchmark datasets Compared with the baselines, the proposed M3-Net consistently achieves the best performance with a large margin on all evaluation metrics on individual attributes and overall. Even when compared with the state-of-the-art multi-granularity method, MODC, the proposed M3-Net shows significant improvements over MODC on MAP@all (70.42%), MAP@100 (57.95%), and Recall@100 (112.5%). The results demonstrate the efficacy of the attribute and class-specific representations learned by M3-Net. + +
ModelDeepFashion
MAP@allMAP@allMAP@100Recall@100
Attributetexturefabricshapepartstyleoveralloveralloverall
ASEN [19]21.0311.6114.687.814.6612.3320.605.10
ASENV2 [19]21.8611.6714.587.934.6812.5120.554.99
ASEN++ [6]22.2011.7114.708.154.7212.7420.795.21
MODC [14]22.2611.9814.687.965.2312.7822.216.06
M3-Neta27.3718.3422.9614.669.7419.0328.1410.59
M3-Netc30.0919.6025.2416.4311.3220.9230.5812.10
M3-Net30.7920.2027.1117.2811.6121.7835.0812.88
+ +Table 2. Performance comparison on all attributes of the multi-label dataset, DeepFashion. + +
ModelFashionAI
MAP@allMAP@allMAP@100Recall@100
Attributeskirt lengthsleeve lengthcoat lengthpant lengthcollar designlapel designneckline designneck designoveralloveralloveralloverall
ASEN [19]64.6149.9849.7565.7670.3062.8652.1456.4257.3764.7022.77
ASENv2 [19]65.5854.4252.0367.4171.3666.7660.9159.5861.1367.8524.14
ASEN++ [6]66.3157.5155.4368.8372.7966.8566.7867.0264.2770.6225.30
MODC [14]74.5467.4868.2577.6981.1176.9077.4677.1074.3280.2930.26
M3-Neta73.2169.5865.2778.7980.8078.0577.0473.4073.9381.5730.48
M3-Netc74.3365.9164.2778.2682.0078.8574.8072.3972.8882.5830.77
M3-Net75.2770.0467.9079.3182.8278.5876.8175.5175.0487.0432.01
+ +Table 3. Performance comparison on all attributes of the single-label dataset, FashionAI. + +Ablation study on $\mathrm{M3 - Net}_a$ , $\mathrm{M3 - Net}_c$ and M3-Net suggests that employing more fine-grained attention on classes $(\mathrm{M3 - Net}_c)$ performs better than attribute-level attention alone $(\mathrm{M3 - Net}_a)$ . Yet combining attribute-conditional attentions and class-conditional attentions works the best (M3-Net). It shows that representations learned at the two granularities are complementary to each other. + +Furthermore, we analyze the performance on co-occurring classes on DeepFashion to evaluate the effectiveness of M3-Net in capturing the inter-dependencies between different classes in representation learning. We first calculate the pairwise co-occurrence rates of all classes in the dataset. Two classes are considered co-occurring if both are associated with the same image. The range of co-occurrence rate is [0, 0.03], i.e., the most frequently co-occurring class pairs appear in $3\%$ of the images. We set the cut-off at 0.002 (corresponding to 565 co-occurrences), resulting in 468 class pairs from the 1M class pairs in the dataset. This gives us 122 unique classes. M3-Net achieves a MAP@all at 35.61 on this set of classes, which is $63.50\%$ higher than the average of all classes. We hypothesize that M3-Net is able to incorporate the inter-dependencies between these classes into representation learning, thus performing better on them. + +# 4.3.2 Quantitative evaluation on single-label datasets + +For the two single-label datasets, FashionAI and DARN, we follow the same split as in [19]. On both datasets, we observe similar competence of the proposed M3-Net in fine-grained fashion retrieval. On FashionAI, M3-Net achieve the best performance overall on all evaluation met + +![](images/0f87d1ec8f177d1bb83c67c83fb2e091e732ac5b49687bd7561bc151357330a8.jpg) +Figure 3. Two-granularity attentions learned by M3-Net on DeepFashion. The attribute-conditional attention tends to focus on a wider range of regions in an image, while the class-conditional attention focuses more narrowly on a region relevant to each class. For instance, row 1: class "slit" focuses on the dress slit, "elegant" focuses on the waist; row 2: "contrast trim" focuses on the part with two different colors, "stretch" focuses on the strap; row 3: "draped" focuses on the drape decoration, and "fit" focuses on the waist. Best viewed in color on a computer screen. + +rics (MAP@all, MAP@100, and Recall@100). It also outperforms the baselines on most individual attributes. + +On DARN, we again observe a boost on all evaluation metrics. While baselines perform unsatisfactorily on "clothes category" and "collar shape", M3-Net improves them the most along with improvements on other attributes. Overall, M3-Net exceeds the best baseline, MODC, on MAP@all by $16.35\%$ , MAP@100 by $14.59\%$ , and Recall@100 by $18.24\%$ . The results of M3-Net on single-label datasets again demonstrate the effectiveness of the attribute-specific and class-specific representations. Compared with MODC, which obtains class-specific representations by di + +
ModelDARN
MAP@allMAP@allMAP@100Recall@100
Attributeclothes categoryclothes buttonclothes colorclothes lengthclothes patternclothes shapecollar shapesleeve lengthsleeve shapeoveralloveralloverall
ASEN [19]36.6246.0152.7656.8554.8956.8534.4079.9558.0852.7558.7220.26
ASENv2 [19]37.9749.2452.2659.1355.3259.0636.8681.5458.8254.2959.6620.88
ASEN++ [6]40.2150.0453.1459.8357.4159.7037.4583.7060.4155.7861.0921.51
MODC [14]49.9460.7558.7966.3462.2468.4145.1487.4165.3262.5672.1626.76
M3-Neta59.1669.9468.1872.5872.8776.2160.2289.3671.5871.0678.1230.77
M3-Netc60.9870.9168.5274.9574.4879.1563.0990.3173.0072.7981.4631.64
M3-Net60.5470.3969.5273.9774.4077.8361.6390.0373.9472.4282.6931.34
+ +Table 4. Performance comparison on all attributes of the single-label dataset, DARN. + +![](images/dae655dc34bcf660402461606ff02120788b297f623535d6d3ebc7b19a48cc1d.jpg) +Figure 4. (a) single-label and (b) multi-label fashion retrieval by M3-Net and MODC on DeepFashion. Green: true positive retrieval; red: false positive retrieval. Best viewed in color on a computer screen. + +![](images/3f4f3253e43596aebe30db7d7ae9ccb597a7c9bd5dd074f9c62bde1f2a6ed336.jpg) + +rectly segmenting the attribute-specific representation into class-specific clusters in the same embedding space, M3-Net learns separate representation spaces for attributes and classes and performs better. + +Ablation study on FashionAI shows that overall having attentions on two granularities (M3-Net) performs better than attentions on either granularity alone $(\mathrm{M}3 - \mathrm{Net}_a$ and $\mathrm{M}3 - \mathrm{Net}_c)$ . On DARN, M3-Net's performance is comparable to that of $\mathrm{M}3 - \mathrm{Net}_c$ , which only has class-conditional attention modules. We speculate that this is due to discriminating attributes and classes is less challenging on single-label datasets than on multi-label attribute datasets. + +# 4.3.3 Qualitative evaluations + +Figure 3 visualizes the two-granularity attentions learned by M3-Net. The attribute-conditional attention tends to focus on all regions that are likely to be associated with the attribute. For example, in the first row of Figure 3, the attention of attribute "part" involves areas covering various parts of the dress such as collar, belt area, and hemline (second image in the first row). On the contrary, the class-conditional attention tends to focus on class-specific regions in the image. For instance, class "slit" highlights the dress slit region (third image in the first row). The visualized attention is consistent with our hypothesis. + +Figure 4 presents examples of fine-grained fashion retrieval results on single-label and multi-label datasets. In + +the figure, we compared the results from our proposed M3-Net with those from MODC (the best-performing baseline). Figure 4 (a) shows that on single-label retrieval, M3-Net can better discriminate fine-grained visual features than MODC, leading to more accurate retrieval results on individual classes. Moreover, on multi-label retrieval, M3-Net is able to retrieve images containing multiple class labels. For example, when searching an image on attribute "texture" with both "print" and "tribal" class labels (last example in Figure 4), M3-Net accurately retrieves related images, while MODC retrieves many other printed textures that is not "tribal". + +# 5. Conclusion + +We have proposed a multi-attribute multi-granularity multi-label network (M3-Net) for fine-grained fashion analysis. Our proposed architecture learns both attribute and class-level representations for a fashion image through a shared backbone and two sub-networks with attribute and class conditional attention modules. This design, together with a multi-granularity loss, allows the network to effectively learn discriminative representations while capturing the inter-dependencies among various visual elements in different granularities. Our experiments show that the proposed M3-Net sets new state-of-the-art performance on both single-label and multi-label benchmark datasets in the fine-grained fashion retrieval task. + +# References + +[1] Kenan E Ak, Ashraf A Kassim, Joo Hwee Lim, and Jo Yew Tham. Learning attribute representations with localization for flexible fashion search. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 7708-7717, 2018. +[2] Kenan E Ak, Joo Hwee Lim, Jo Yew Tham, and Ashraf A Kassim. Efficient multi-attribute similarity learning towards attribute-based fashion search. In 2018 IEEE Winter Conference on Applications of Computer Vision (WACV), pages 1671–1679. IEEE, 2018. +[3] Chen Bao, Xudong Zhang, Jiazhou Chen, and Yongwei Miao. Mmf-net: multi-scale and multi-granularity feature learning for cross-domain fashion retrieval. Multimedia Tools and Applications, pages 1-33, 2022. +[4] Qiang Chen, Junshi Huang, Rogerio Feris, Lisa M Brown, Jian Dong, and Shuicheng Yan. Deep domain adaptation for describing people based on fine-grained clothing attributes. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 5315-5324, 2015. +[5] Jia Deng, Wei Dong, Richard Socher, Li-Jia Li, Kai Li, and Li Fei-Fei. Imagenet: A large-scale hierarchical image database. In 2009 IEEE conference on computer vision and pattern recognition, pages 248-255. IEEE, 2009. +[6] Jianfeng Dong, Zhe Ma, Xiaofeng Mao, Xun Yang, Yuan He, Richang Hong, and Shouling Ji. Fine-grained fashion similarity prediction by attribute-specific embedding learning. arXiv preprint arXiv:2104.02429, 2021. +[7] Bojana Gajic and Ramon Baldrich. Cross-domain fashion image retrieval. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition Workshops, pages 1869-1871, 2018. +[8] M Hadi Kiapour, Xufeng Han, Svetlana Lazebnik, Alexander C Berg, and Tamara L Berg. Where to buy it: Matching street clothing photos in online shops. In Proceedings of the IEEE international conference on computer vision, pages 3343-3351, 2015. +[9] Xintong Han, Zuxuan Wu, Phoenix X Huang, Xiao Zhang, Menglong Zhu, Yuan Li, Yang Zhao, and Larry S Davis. Automatic spatially-aware fashion concept discovery. In Proceedings of the IEEE international conference on computer vision, pages 1463-1471, 2017. +[10] Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 770-778, 2016. +[11] Ruining He, Charles Packer, and Julian McAuley. Learning compatibility across categories for heterogeneous item recommendation. In 2016 IEEE 16th International Conference on Data Mining (ICDM), pages 937-942. IEEE, 2016. +[12] Yuxin Hou, Eleonora Vig, Michael Donoser, and Loris Bazzani. Learning attribute-driven disentangled representations for interactive fashion retrieval. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 12147-12157, 2021. +[13] Junshi Huang, Rogerio S Feris, Qiang Chen, and Shuicheng Yan. Cross-domain image retrieval with a dual attribute + +aware ranking network. In Proceedings of the IEEE international conference on computer vision, pages 1062-1070, 2015. +[14] Yang Jiao, Ning Xie, Yan Gao, Chien-Chih Wang, and Yi Sun. Fine-grained fashion representation learning by online deep clustering. In European Conference on Computer Vision, pages 19-35. Springer, 2022. +[15] Donghyun Kim, Kuniaki Saito, Samarth Mishra, Stan Sclaroff, Kate Saenko, and Bryan A Plummer. Self-supervised visual attribute learning for fashion compatibility. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 1057-1066, 2021. +[16] Furkan Kinli, Baris Ozcan, and Furkan Kirac. Fashion image retrieval with capsule networks. In Proceedings of the IEEE/CVF International Conference on Computer Vision Workshops, pages 0-0, 2019. +[17] Zhanghui Kuang, Yiming Gao, Guanbin Li, Ping Luo, Yimin Chen, Liang Lin, and Wayne Zhang. Fashion retrieval via graph reasoning networks on a similarity pyramid. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 3066-3075, 2019. +[18] Ziwei Liu, Ping Luo, Shi Qiu, Xiaogang Wang, and Xiaou Tang. Deepfashion: Powering robust clothes recognition and retrieval with rich annotations. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 1096-1104, 2016. +[19] Zhe Ma, Jianfeng Dong, Zhongzi Long, Yao Zhang, Yuan He, Hui Xue, and Shouling Ji. Fine-grained fashion similarity learning by attribute-specific embedding network. In Proceedings of the AAAI Conference on Artificial Intelligence, pages 11741-11748, 2020. +[20] Julian McAuley, Christopher Targett, Qinfeng Shi, and Anton Van Den Hengel. Image-based recommendations on styles and substitutes. In Proceedings of the 38th international ACM SIGIR conference on research and development in information retrieval, pages 43-52, 2015. +[21] Ambareesh Revanur, Vijay Kumar, and Deepthi Sharma. Semi-supervised visual representation learning for fashion compatibility. In Fifteenth ACM Conference on Recommender Systems, pages 463-472, 2021. +[22] Devashish Shankar, Sujay Narumanchi, HA Ananya, Pramod Kompalli, and Krishnendu Chaudhury. Deep learning based large scale visual recommendation and search for e-commerce. arXiv preprint arXiv:1703.02344, 2017. +[23] Mariya I Vasileva, Bryan A Plummer, Krishna Dusad, Shreya Rajpal, Ranjitha Kumar, and David Forsyth. Learning type-aware embeddings for fashion compatibility. In Proceedings of the European Conference on Computer Vision (ECCV), pages 390-405, 2018. +[24] Andreas Veit, Serge Belongie, and Theofanis Karaletsos. Conditional similarity networks. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 830-838, 2017. +[25] Andreas Veit, Balazs Kovacs, Sean Bell, Julian McAuley, Kavita Bala, and Serge Belongie. Learning visual clothing style with heterogeneous dyadic co-occurrences. In Proceedings of the IEEE International Conference on Computer Vision, pages 4642–4650, 2015. + +[26] Zhonghao Wang, Yujun Gu, Ya Zhang, Jun Zhou, and Xiao Gu. Clothing retrieval with visual attention model. In 2017 IEEE Visual Communications and Image Processing (VCIP), pages 1-4. IEEE, 2017. +[27] Bo Zhao, Jiashi Feng, Xiao Wu, and Shuicheng Yan. Memory-augmented attribute manipulation networks for interactive fashion search. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 1520-1528, 2017. +[28] Xingxing Zou, Xiangheng Kong, Waikeung Wong, Congde Wang, Yuguang Liu, and Yang Cao. Fashionai: A hierarchical dataset for fashion understanding. 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Existing works often learn fine-grained fashion representations at the attribute level without considering their relationships and inter-dependencies across different classes. In this work, we propose to learn an attribute and class-specific fashion representation duet to better model such attribute relationships and inter-dependencies by leveraging prior knowledge about the taxonomy of fashion attributes and classes. Through two sub-networks for the attributes and classes, respectively, our proposed an embedding network progressively learns and refines the visual representation of a fashion image to improve its robustness for fashion retrieval. A multi-granularity loss consisting of attribute-level and class-level losses is proposed to introduce appropriate inductive bias to learn across different granularities of the fashion representations. Experimental results on three benchmark datasets demonstrate the effectiveness of our method, which outperforms the state-of-the-art methods by a large margin." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 536, + 128, + 548 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 536, + 128, + 548 + ], + "spans": [ + { + "bbox": [ + 47, + 536, + 128, + 548 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "text", + "content": "Fashion products have become one of the most consumed products in online shopping. Unlike other types of products, fashion products are usually rich in visual elements at different levels of granularity. For instance, besides the overall visual appearance, a fashion product can be described by a set of attributes, such as \"shape\", \"color\" and \"style\", which focus on different aspects of the visual representation. Each attribute can be further categorized into various classes. For example, \"fit\", \"flare\" and \"pencil\" are different classes under attribute \"shape\" (Fig. 1). Therefore, modeling fashion representation in different granularities is essential for online shopping and other downstream applications, especially those that require analysis" + } + ] + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 310, + 232, + 544, + 382 + ], + "blocks": [ + { + "bbox": [ + 310, + 232, + 544, + 382 + ], + "lines": [ + { + "bbox": [ + 310, + 232, + 544, + 382 + ], + "spans": [ + { + "bbox": [ + 310, + 232, + 544, + 382 + ], + "type": "image", + "image_path": "643f6fe384ad817010b12640099376fded801bcef9b935eb82e69b1c88e7d3f5.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 393, + 547, + 472 + ], + "lines": [ + { + "bbox": [ + 304, + 393, + 547, + 472 + ], + "spans": [ + { + "bbox": [ + 304, + 393, + 547, + 472 + ], + "type": "text", + "content": "Figure 1. Left: existing fine-grained representation learning methods often learn attribute-specific representations for fashion products, thus may not be able to discern the two dresses that have different compositions of visual elements at the class level. Right: our proposed method (right) jointly learns attribute and class-specific representations. Therefore, it can discriminate between the two dresses by their class-specific representations." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 495, + 546, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 495, + 546, + 542 + ], + "spans": [ + { + "bbox": [ + 304, + 495, + 546, + 542 + ], + "type": "text", + "content": "of subtle or fine-grained details such as attribute-based fashion manipulation [1, 2, 27] and retrieval [6, 14, 19, 23, 24], fashion copyright [6, 19], and fashion compatibility analysis [11, 15, 21, 23]." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 544, + 547, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 544, + 547, + 700 + ], + "spans": [ + { + "bbox": [ + 304, + 544, + 547, + 700 + ], + "type": "text", + "content": "Fine-grained fashion modeling and analysis in recent years explore the attribute-specific representation learning. The focus has recently shifted from earlier works that learn separate representations for each attribute independently [1, 2] to multi-task learning, which uses a common backbone for different attributes while tailoring the learning for each specific attribute via mechanisms such as attention masks [6, 14, 19, 24]. Success of these attribute-specific representation learning methods for fine-grained fashion analysis can be attributed to their capabilities to discriminate visual features associated with different aspects of fashion products, which learning an image-level global representation finds challenging." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 317, + 701, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 701, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 317, + 701, + 545, + 713 + ], + "type": "text", + "content": "However, when it comes to classes, such attribute-" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "11050" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 287 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 287 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 287 + ], + "type": "text", + "content": "specific representation methods face a similar challenge to the above. The reason is that due to the dynamic and aesthetic nature of fashion products, different visual elements are often composited together to achieve certain visual effects, making an attribute-level description insufficient to capture such interactions and granularity. For instance, under the same \"shape\" attribute, one may go for a dress design that combines classes \"fit\" and \"flare\" for a more casual look (top image, Fig. 1), but go for a different dress that combines \"fit\" and \"pencil\" for a more formal look while flattering one's natural curves (bottom image, Fig. 1). Therefore, an attribute-level representation is hard to differentiate the two dresses. Alternatively, one may directly learn a class-specific representation for each class under the \"shape\" attribute, which, however, faces the scalability issue. For instance, if a fashion image is associated with " + }, + { + "bbox": [ + 47, + 72, + 289, + 287 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 47, + 72, + 289, + 287 + ], + "type": "text", + "content": " attributes and " + }, + { + "bbox": [ + 47, + 72, + 289, + 287 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 47, + 72, + 289, + 287 + ], + "type": "text", + "content": " classes per attribute, one would need to learn " + }, + { + "bbox": [ + 47, + 72, + 289, + 287 + ], + "type": "inline_equation", + "content": "N \\times M" + }, + { + "bbox": [ + 47, + 72, + 289, + 287 + ], + "type": "text", + "content": " class-specific representations." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 288, + 289, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 288, + 289, + 430 + ], + "spans": [ + { + "bbox": [ + 47, + 288, + 289, + 430 + ], + "type": "text", + "content": "To better discriminate fashion products with distinct design considerations and model the interplay among various visual elements, we propose to leverage prior knowledge about fashion taxonomy to model fashion products. We jointly learn both attribute-specific and class-specific fashion representations through a multi-attribute multi-granularity multi-label embedding network (M3-Net). M3-Net consists of two sub-networks, for attributes and classes, respectively. Different attributes share the same backbone sub-network as well as two attribute-conditional attention modules, while different classes under a given attribute share two class-conditional attention modules." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 432, + 289, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 432, + 289, + 552 + ], + "spans": [ + { + "bbox": [ + 47, + 432, + 289, + 552 + ], + "type": "text", + "content": "The shared backbone and conditional attention modules allow the network to better capture the inter-dependencies and shared visual statistics among the attributes and classes. Through multi-label learning on attribute-specific representations, we also improve the scalability of the proposed network by focusing class-specific representation learning on high likelihood classes only. Finally, a multi-granularity loss consisting of attribute-level and class-level losses is designed to introduce appropriate inductive bias for learning across different granularities." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 59, + 552, + 201, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 552, + 201, + 563 + ], + "spans": [ + { + "bbox": [ + 59, + 552, + 201, + 563 + ], + "type": "text", + "content": "In summary, our contributions are:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 58, + 572, + 288, + 714 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 59, + 572, + 287, + 633 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 572, + 287, + 633 + ], + "spans": [ + { + "bbox": [ + 59, + 572, + 287, + 633 + ], + "type": "text", + "content": "- We propose to model fashion products at both attribute and class levels based on fashion taxonomy to better capture the inter-dependencies of various visual elements and improve the discriminative power of learned fashion representations." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 58, + 641, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 641, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 58, + 641, + 288, + 714 + ], + "type": "text", + "content": "- We design a multi-attribute multi-granularity multi-label network (M3-Net) to jointly learn attributespecific and class-specific representation duet for fine-grained fashion analysis. Through two sub-networks and conditional attention modules, M3-Net is able to progressively learn discriminative representations at" + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 324, + 72, + 545, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 324, + 72, + 545, + 96 + ], + "spans": [ + { + "bbox": [ + 324, + 72, + 545, + 96 + ], + "type": "text", + "content": "different granularities, with appropriate inductive bias introduced by the attribute-level and class-level losses." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 317, + 105, + 547, + 152 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 105, + 547, + 152 + ], + "spans": [ + { + "bbox": [ + 317, + 105, + 547, + 152 + ], + "type": "text", + "content": "- Our model outperforms state-of-the-art methods in fine-grained fashion retrieval on three benchmark datasets. The experimental results demonstrate the efficacy of our proposed method." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 171, + 392, + 183 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 171, + 392, + 183 + ], + "spans": [ + { + "bbox": [ + 306, + 171, + 392, + 183 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 190, + 525, + 204 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 190, + 525, + 204 + ], + "spans": [ + { + "bbox": [ + 306, + 190, + 525, + 204 + ], + "type": "text", + "content": "2.1. Generic Fashion Representation Learning" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 209, + 545, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 209, + 545, + 413 + ], + "spans": [ + { + "bbox": [ + 304, + 209, + 545, + 413 + ], + "type": "text", + "content": "Earlier fashion representation learning works [7, 8, 16, 20, 25, 26] focus on the global representation of a fashion product by learning a generic metric embedding from the entire fashion image. The generic representations benefit tasks such as in-shop fashion retrieval [16, 22, 26], street-to-shop fashion retrieval [4, 7, 8, 13, 17, 18] and compatibility retrieval [11, 15, 20, 25]. For in-shop fashion retrieval, the images often have a consistent background and photo shooting angle. In comparison, street-to-shop retrieval is more challenging because the images are often taken in an uncontrolled environment with varying lighting conditions, scales, and viewing angles. Different from the above two tasks that focus on the overall similarity, compatibility retrieval focuses on a specific global attribute such as color, fabric, and style. Although effective in global representation learning, these works lack the capabilities to model fine-grain details and subtleties in fashion products." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 420, + 520, + 433 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 420, + 520, + 433 + ], + "spans": [ + { + "bbox": [ + 306, + 420, + 520, + 433 + ], + "type": "text", + "content": "2.2. Multi-attribute Representation Learning" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 438, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 438, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 438, + 545, + 715 + ], + "type": "text", + "content": "Many works tackle the problem of fine-grained fashion representation learning by analyzing fashion attributes. We have seen great success of such approaches in tasks such as attribute-specific retrieval [2, 6, 19, 24] and retrieval with attribute manipulation [1, 12, 27]. One group of works [12, 27] utilizes fully connected layers to transform generic representations into attribute-specific representations. However, the linear transformation function of fully connected layers neglects the spatial relationship within attribute-specific representations. Another group of works learns attribute-specific representations by leveraging region proposal, either via a dedicated network [13] or via global pooling layers [1, 2, 9]. For example, some works [1, 2] localize the spatial area of each attribute using global pooling layers, and crop the spatial feature maps for further attribute-specific learning. Although cropping spatial feature maps allows representation learning to focus on a local region, it rigidly limits the visual representation to a specific area and ignores other correlated visual elements in a larger area. In contrast, the third group of works uses attention masks to incorporate a global view into representation learning with the flexibility to bring in contexts from other regions. For instance, the authors of [6, 14, 19, 24] utilize" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11051" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 70, + 547, + 224 + ], + "blocks": [ + { + "bbox": [ + 61, + 70, + 547, + 224 + ], + "lines": [ + { + "bbox": [ + 61, + 70, + 547, + 224 + ], + "spans": [ + { + "bbox": [ + 61, + 70, + 547, + 224 + ], + "type": "image", + "image_path": "cd0948f8e314fc00d4dd47317af5310eebf4f00e5e48d4cb88bda4ea2681264a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 234, + 547, + 289 + ], + "lines": [ + { + "bbox": [ + 46, + 234, + 547, + 289 + ], + "spans": [ + { + "bbox": [ + 46, + 234, + 547, + 289 + ], + "type": "text", + "content": "Figure 2. The architecture of the proposed M3-Net. M3-Net first obtains a generic representation using a backbone CNN. It learns attribute-specific representations through two attribute-conditional attention modules (SCA-A and CCA-A). Taking the high-likelihood classes from the multi-label classification, M3-Net employs two class-conditional attention modules (SCA-C and CCA-C) to learn the class-specific representations. SCA-A and SCA-C are extended from the SCA module (Alg. 1), and CCA-A and CCA-C are extended from CCA module (Alg. 2)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 310, + 289, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 310, + 289, + 430 + ], + "spans": [ + { + "bbox": [ + 46, + 310, + 289, + 430 + ], + "type": "text", + "content": "attention masks to dynamically assign weights to different dimensions of the global representation of an image for specific attributes. Veit, Belongie and Karaletsos [24] use attention masks to select and reweight relevant dimensions for each attribute to induce attribute-specific subspaces. Instead of learning attribute-specific weights, other works [6, 19] propose to learn attribute-aware spatial and channel attention modules. The attention modules are attached to the feature extraction network to enhance the participation of attributes in representation learning." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 442, + 274, + 455 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 442, + 274, + 455 + ], + "spans": [ + { + "bbox": [ + 47, + 442, + 274, + 455 + ], + "type": "text", + "content": "2.3. Multi-granularity Representation Learning" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 462, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 462, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 462, + 289, + 715 + ], + "type": "text", + "content": "As attribute-level representations may still fall short of fashion tasks that require analysis of finer granular interactions, such as the one shown in Fig. 1, a few works propose to learn fashion representations in multiple granularities. Some works tackle the multi-granularity representation learning problem from the spatial domain, which essentially transforms multi-granularity learning into multi-scale learning. For instance, Dong, Ma and their co-authors [6, 19] propose to use a global branch and a local branch to learn two attribute-specific representations on two scales. Similarly, Bao, Zhang and their co-authors [3] propose a feature learning network that jointly learns the representation in two feature map scales and three image scales via a global, a part-base, and a local branch. Instead of multi-scale learning, Jiao, Xie and their co-authors [14] propose to segment the attribute-specific embedding spaces into class-specific embedding spaces using the cluster prototypes learned by online deep clustering. The proposed model achieves state-of-the-art performance on the fine-grained fashion retrieval task by prioritizing retrieval in class-specific embedding spaces. However, the representations are not optimized in" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 310, + 547, + 359 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 310, + 547, + 359 + ], + "spans": [ + { + "bbox": [ + 304, + 310, + 547, + 359 + ], + "type": "text", + "content": "class-specific embedding spaces because the segmentation happens in the inference stage. In our work, we propose to jointly learn both attribute-specific and class-specific representations through a multi-granularity embedding network." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 369, + 411, + 382 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 369, + 411, + 382 + ], + "spans": [ + { + "bbox": [ + 306, + 369, + 411, + 382 + ], + "type": "text", + "content": "3. Proposed Method" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 389, + 545, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 389, + 545, + 651 + ], + "spans": [ + { + "bbox": [ + 304, + 389, + 545, + 651 + ], + "type": "text", + "content": "The proposed multi-attribute multi-granularity multi-label embedding network (M3-Net) is an end-to-end network that jointly learns the attribute and class level representations. As shown in Figure 2, M3-Net employs a backbone network, two attribute-conditional attention modules, two class-conditional attention modules, and a multi-label classification module. The backbone network shares learned weights across all attributes, which makes the embedding network scalable. It embeds an input image into a generic representation that represents the entire image. The generic representation is then fed through two attribute-conditional attention modules to focus learning on fine-grained attributes and obtain attribute-specific representations. Two class-conditional attention modules are further applied to learn more fine-grained class-specific representations. The shared backbone and conditional attention modules allow the network to better capture the interdependencies and shared visual statistics among the attributes and classes. The multi-label classification module serves to improve the scalability of the proposed network by focusing class-specific representation learning on high-likelihood classes." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 659, + 427, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 659, + 427, + 671 + ], + "spans": [ + { + "bbox": [ + 306, + 659, + 427, + 671 + ], + "type": "text", + "content": "3.1. M3-Net Architecture" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "type": "text", + "content": "Given a set of fashion product images " + }, + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\{I\\}" + }, + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "type": "text", + "content": ", we denote the set of attributes associated with these images as " + }, + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\{A_{n}\\}" + }, + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "type": "inline_equation", + "content": "n \\in [1, N]" + }, + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "type": "text", + "content": ". Similarly, we denote the set of classes" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "11052" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 144 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 144 + ], + "type": "text", + "content": "associated with a given attribute " + }, + { + "bbox": [ + 47, + 72, + 287, + 144 + ], + "type": "inline_equation", + "content": "A_{n}" + }, + { + "bbox": [ + 47, + 72, + 287, + 144 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 47, + 72, + 287, + 144 + ], + "type": "inline_equation", + "content": "\\{C_{m_n}\\}" + }, + { + "bbox": [ + 47, + 72, + 287, + 144 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 47, + 72, + 287, + 144 + ], + "type": "inline_equation", + "content": "m_{n} \\in [1, M_{n}]" + }, + { + "bbox": [ + 47, + 72, + 287, + 144 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 72, + 287, + 144 + ], + "type": "inline_equation", + "content": "M_{n}" + }, + { + "bbox": [ + 47, + 72, + 287, + 144 + ], + "type": "text", + "content": " is the number of classes under attribute " + }, + { + "bbox": [ + 47, + 72, + 287, + 144 + ], + "type": "inline_equation", + "content": "A_{n}" + }, + { + "bbox": [ + 47, + 72, + 287, + 144 + ], + "type": "text", + "content": ". Given " + }, + { + "bbox": [ + 47, + 72, + 287, + 144 + ], + "type": "inline_equation", + "content": "A_{n}" + }, + { + "bbox": [ + 47, + 72, + 287, + 144 + ], + "type": "text", + "content": ", an image " + }, + { + "bbox": [ + 47, + 72, + 287, + 144 + ], + "type": "inline_equation", + "content": "I \\in \\{I\\}" + }, + { + "bbox": [ + 47, + 72, + 287, + 144 + ], + "type": "text", + "content": " can associate with a subset of labels in " + }, + { + "bbox": [ + 47, + 72, + 287, + 144 + ], + "type": "inline_equation", + "content": "\\{1, 2, \\dots, M_{n}\\}" + }, + { + "bbox": [ + 47, + 72, + 287, + 144 + ], + "type": "text", + "content": ", which is represented by a vector " + }, + { + "bbox": [ + 47, + 72, + 287, + 144 + ], + "type": "inline_equation", + "content": "[y_{1_n}, \\dots, y_{m_n}, \\dots, y_{M_n}]" + }, + { + "bbox": [ + 47, + 72, + 287, + 144 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 47, + 72, + 287, + 144 + ], + "type": "inline_equation", + "content": "y_{m_n} = 1" + }, + { + "bbox": [ + 47, + 72, + 287, + 144 + ], + "type": "text", + "content": " if and only if image " + }, + { + "bbox": [ + 47, + 72, + 287, + 144 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 47, + 72, + 287, + 144 + ], + "type": "text", + "content": " is associated with class " + }, + { + "bbox": [ + 47, + 72, + 287, + 144 + ], + "type": "inline_equation", + "content": "C_{m_n}" + }, + { + "bbox": [ + 47, + 72, + 287, + 144 + ], + "type": "text", + "content": ", and 0 otherwise." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 145, + 287, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 145, + 287, + 228 + ], + "spans": [ + { + "bbox": [ + 47, + 145, + 287, + 228 + ], + "type": "text", + "content": "Generic representation. Denote the parameters of M3-Net as " + }, + { + "bbox": [ + 47, + 145, + 287, + 228 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 47, + 145, + 287, + 228 + ], + "type": "text", + "content": " and the parameters of the backbone network as " + }, + { + "bbox": [ + 47, + 145, + 287, + 228 + ], + "type": "inline_equation", + "content": "\\theta_{b}" + }, + { + "bbox": [ + 47, + 145, + 287, + 228 + ], + "type": "text", + "content": ". Correspondingly, " + }, + { + "bbox": [ + 47, + 145, + 287, + 228 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 47, + 145, + 287, + 228 + ], + "type": "text", + "content": " represents M3-Net and " + }, + { + "bbox": [ + 47, + 145, + 287, + 228 + ], + "type": "inline_equation", + "content": "f_{\\theta_b}" + }, + { + "bbox": [ + 47, + 145, + 287, + 228 + ], + "type": "text", + "content": " represents the backbone network. The generic visual representation of an image " + }, + { + "bbox": [ + 47, + 145, + 287, + 228 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 47, + 145, + 287, + 228 + ], + "type": "text", + "content": " is then denoted by " + }, + { + "bbox": [ + 47, + 145, + 287, + 228 + ], + "type": "inline_equation", + "content": "\\psi = f_{\\theta_b}(I)" + }, + { + "bbox": [ + 47, + 145, + 287, + 228 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 47, + 145, + 287, + 228 + ], + "type": "inline_equation", + "content": "\\psi \\in \\mathbb{R}^{c\\times h\\times w}" + }, + { + "bbox": [ + 47, + 145, + 287, + 228 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 145, + 287, + 228 + ], + "type": "inline_equation", + "content": "c,h,w" + }, + { + "bbox": [ + 47, + 145, + 287, + 228 + ], + "type": "text", + "content": " are the number of channels, height, and width, respectively." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 230, + 287, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 230, + 287, + 289 + ], + "spans": [ + { + "bbox": [ + 47, + 230, + 287, + 289 + ], + "type": "text", + "content": "From here, we will use " + }, + { + "bbox": [ + 47, + 230, + 287, + 289 + ], + "type": "inline_equation", + "content": "\\psi" + }, + { + "bbox": [ + 47, + 230, + 287, + 289 + ], + "type": "text", + "content": " to denote a generic feature map, use " + }, + { + "bbox": [ + 47, + 230, + 287, + 289 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 47, + 230, + 287, + 289 + ], + "type": "text", + "content": " to denote a spatially attended feature map and " + }, + { + "bbox": [ + 47, + 230, + 287, + 289 + ], + "type": "inline_equation", + "content": "\\varphi" + }, + { + "bbox": [ + 47, + 230, + 287, + 289 + ], + "type": "text", + "content": " to denote a channel-wise attended feature map. Meanwhile, we use " + }, + { + "bbox": [ + 47, + 230, + 287, + 289 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 47, + 230, + 287, + 289 + ], + "type": "text", + "content": " to denote the attribute-specific representation, and " + }, + { + "bbox": [ + 47, + 230, + 287, + 289 + ], + "type": "inline_equation", + "content": "\\overline{x}" + }, + { + "bbox": [ + 47, + 230, + 287, + 289 + ], + "type": "text", + "content": " to denote the class-specific representation." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 291, + 287, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 291, + 287, + 460 + ], + "spans": [ + { + "bbox": [ + 47, + 291, + 287, + 460 + ], + "type": "text", + "content": "Attribute-specific representation. The attribute-specific representation learning acts as a connector between the generic representations and the class-specific representations. It refines the generic representation by focusing learning on the attribute-specific visual features, and the resulting attribute-specific representation will be further refined in subsequent modules to obtain more fine-grained class-specific visual representations. To reduce the complexity of the class-specific representation learning, we conduct the attribute-specific representation learning in a multi-label setting. Therefore, instead of learning " + }, + { + "bbox": [ + 47, + 291, + 287, + 460 + ], + "type": "inline_equation", + "content": "N + \\sum_{n}^{N} M_{n}" + }, + { + "bbox": [ + 47, + 291, + 287, + 460 + ], + "type": "text", + "content": " representations (" + }, + { + "bbox": [ + 47, + 291, + 287, + 460 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 47, + 291, + 287, + 460 + ], + "type": "text", + "content": " attribute-specific and " + }, + { + "bbox": [ + 47, + 291, + 287, + 460 + ], + "type": "inline_equation", + "content": "\\sum_{n}^{N} M_{n}" + }, + { + "bbox": [ + 47, + 291, + 287, + 460 + ], + "type": "text", + "content": " class-specific representations), we can exclude unlikely classes, thus improve scalability." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 461, + 287, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 461, + 287, + 568 + ], + "spans": [ + { + "bbox": [ + 47, + 461, + 287, + 568 + ], + "type": "text", + "content": "Motivated by the effectiveness of spatial and channel-wise attention for multi-attribute fashion representation learning in prior works, we utilize Spatial Conditional Attention module (SCA) and Channel-wise Conditional attention module (CCA) akin to the attribute-aware attention in [19]. Both SCA (Algorithm 1) and CCA (Algorithm 2) are applied to both attribute-specific and class-specific representation learning. The structures of SCA and CCA are shown in Figure 2." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 570, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 570, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 570, + 287, + 713 + ], + "type": "text", + "content": "Attribute-conditional attention modules help representation learning focus on spatial locations and dimensions relevant to a given attribute. The Spatial Conditional Attention on Attribute (SCA-A) applies SCA (Algorithm 1) at the attribute level, while the Channel-wise Conditional Attention on Attribute (CCA-A) applies CCA (Algorithm 2) at the attribute level. Given the generic representation " + }, + { + "bbox": [ + 47, + 570, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\psi" + }, + { + "bbox": [ + 47, + 570, + 287, + 713 + ], + "type": "text", + "content": " and an attribute " + }, + { + "bbox": [ + 47, + 570, + 287, + 713 + ], + "type": "inline_equation", + "content": "A_{n}" + }, + { + "bbox": [ + 47, + 570, + 287, + 713 + ], + "type": "text", + "content": ", SCA-A takes them as inputs and transforms them into feature maps with an identical size, " + }, + { + "bbox": [ + 47, + 570, + 287, + 713 + ], + "type": "inline_equation", + "content": "p_1(\\psi), p_2(A_n) \\in \\mathbb{R}^{c' \\times h \\times w}" + }, + { + "bbox": [ + 47, + 570, + 287, + 713 + ], + "type": "text", + "content": " (step 5, 6 in Algorithm 1). The attention map " + }, + { + "bbox": [ + 47, + 570, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\alpha_{n}" + }, + { + "bbox": [ + 47, + 570, + 287, + 713 + ], + "type": "text", + "content": " is the Hadamard product between the image feature " + }, + { + "bbox": [ + 47, + 570, + 287, + 713 + ], + "type": "inline_equation", + "content": "p_1(\\psi)" + }, + { + "bbox": [ + 47, + 570, + 287, + 713 + ], + "type": "text", + "content": " and attribute feature " + }, + { + "bbox": [ + 47, + 570, + 287, + 713 + ], + "type": "inline_equation", + "content": "p_2(A_n)" + }, + { + "bbox": [ + 47, + 570, + 287, + 713 + ], + "type": "text", + "content": " with a scal" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 307, + 72, + 509, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 72, + 509, + 84 + ], + "spans": [ + { + "bbox": [ + 307, + 72, + 509, + 84 + ], + "type": "text", + "content": "Algorithm 1 Spatial Conditional Attention (SCA)" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 312, + 88, + 545, + 234 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 312, + 88, + 545, + 110 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 88, + 545, + 110 + ], + "spans": [ + { + "bbox": [ + 312, + 88, + 545, + 110 + ], + "type": "text", + "content": "1: Input: a general feature map " + }, + { + "bbox": [ + 312, + 88, + 545, + 110 + ], + "type": "inline_equation", + "content": "\\psi \\in \\mathbb{R}^{c\\times h\\times w}" + }, + { + "bbox": [ + 312, + 88, + 545, + 110 + ], + "type": "text", + "content": ", targeted label " + }, + { + "bbox": [ + 312, + 88, + 545, + 110 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 312, + 88, + 545, + 110 + ], + "type": "text", + "content": ", intermediate channel number " + }, + { + "bbox": [ + 312, + 88, + 545, + 110 + ], + "type": "inline_equation", + "content": "c'" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 312, + 110, + 512, + 121 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 110, + 512, + 121 + ], + "spans": [ + { + "bbox": [ + 312, + 110, + 512, + 121 + ], + "type": "text", + "content": "2: Output: conditional spatial attention " + }, + { + "bbox": [ + 312, + 110, + 512, + 121 + ], + "type": "inline_equation", + "content": "\\alpha_{l}\\in \\mathbb{R}^{c\\times h\\times w}" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 312, + 122, + 545, + 158 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 122, + 545, + 158 + ], + "spans": [ + { + "bbox": [ + 312, + 122, + 545, + 158 + ], + "type": "text", + "content": "3: Define: feature transform function " + }, + { + "bbox": [ + 312, + 122, + 545, + 158 + ], + "type": "inline_equation", + "content": "T, T(\\psi) \\in \\mathbb{R}^{c' \\times h \\times w}" + }, + { + "bbox": [ + 312, + 122, + 545, + 158 + ], + "type": "text", + "content": ", label embedding function " + }, + 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\\times h \\times w}" + }, + { + "bbox": [ + 312, + 159, + 545, + 180 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 312, + 159, + 545, + 180 + ], + "type": "inline_equation", + "content": "J_{c,1} \\in \\mathbb{R}^{c \\times 1}" + }, + { + "bbox": [ + 312, + 159, + 545, + 180 + ], + "type": "text", + "content": " are all-ones matrix for spatial duplication" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 312, + 181, + 477, + 203 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 181, + 477, + 203 + ], + "spans": [ + { + "bbox": [ + 312, + 181, + 477, + 203 + ], + "type": "text", + "content": "5: Transform the input feature: " + }, + { + "bbox": [ + 312, + 181, + 477, + 203 + ], + "type": "inline_equation", + "content": "p_1(\\psi) = \\tanh (T(\\psi)), p_1(\\psi) \\in \\mathbb{R}^{c' \\times h \\times w}" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 312, + 203, + 517, + 224 + ], + "type": "text", + "angle": 0, + "lines": [ + { 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"interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 323, + 234, + 468, + 252 + ], + "spans": [ + { + "bbox": [ + 323, + 234, + 468, + 252 + ], + "type": "interline_equation", + "content": "\\alpha_ {l} = J _ {c, 1} \\cdot s o f t m a x \\frac {\\sum_ {i} ^ {c ^ {\\prime}} [ p _ {2} (l) \\odot p _ {1} (\\psi) ] _ {i}}{\\sqrt {c ^ {\\prime}}}", + "image_path": "e723f0026c1891fb91b69e8c40c71b9f3148b700578130b3469641be6e724f1f.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 307, + 269, + 538, + 281 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 269, + 538, + 281 + ], + "spans": [ + { + "bbox": [ + 307, + 269, + 538, + 281 + ], + "type": "text", + "content": "Algorithm 2 Channel-wise Conditional Attention (CCA)" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 312, + 285, + 545, + 375 + ], + "type": "list", + "angle": 0, + "index": 22, + "blocks": [ + { + "bbox": [ + 312, + 285, + 545, + 307 + ], + "type": "text", + "angle": 0, + 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linear functions " + }, + { + "bbox": [ + 312, + 318, + 545, + 354 + ], + "type": "inline_equation", + "content": "W_3, W_4, W_3 \\in \\mathbb{R}^{c' \\times (c + c')}" + }, + { + "bbox": [ + 312, + 318, + 545, + 354 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 312, + 318, + 545, + 354 + ], + "type": "inline_equation", + "content": "W_4 \\in \\mathbb{R}^{c \\times c'}" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 312, + 354, + 477, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 354, + 477, + 365 + ], + "spans": [ + { + "bbox": [ + 312, + 354, + 477, + 365 + ], + "type": "text", + "content": "4: Define: feature vector concatenation " + }, + { + "bbox": [ + 312, + 354, + 477, + 365 + ], + "type": "inline_equation", + "content": "[a; b]" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 312, + 365, + 462, + 375 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 365, + 462, + 375 + ], + "spans": [ 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24 + }, + { + "bbox": [ + 323, + 397, + 470, + 410 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 323, + 397, + 470, + 410 + ], + "spans": [ + { + "bbox": [ + 323, + 397, + 470, + 410 + ], + "type": "interline_equation", + "content": "q _ {2} (l) = \\operatorname {r e l u} \\left(W _ {2} E _ {2} (l)\\right), q _ {2} (l) \\in \\mathbb {R} ^ {c ^ {\\prime} \\times 1}", + "image_path": "76746cc74bf5ea4a214bf0c3b901276469ecfb75dc678066296493b8e31d5a32.jpg" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 312, + 410, + 426, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 410, + 426, + 418 + ], + "spans": [ + { + "bbox": [ + 312, + 410, + 426, + 418 + ], + "type": "text", + "content": "7: Calculate channel attention:" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 323, + 419, + 492, + 431 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 323, + 419, + 492, + 431 + ], + "spans": [ + { + "bbox": [ + 323, + 419, + 492, + 431 + ], + "type": "interline_equation", + "content": "\\beta_ {l} = \\operatorname {s i g m o i d} \\left(W _ {4} \\left(\\operatorname {r e l u} \\left(W _ {3} [ q _ {1} (\\psi); q _ {2} (l) ]\\right)\\right)\\right)", + "image_path": "5e206da88bd63dedc12f84dc56e0b2e54aa40964bcc53f498e4ee7c638109230.jpg" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 306, + 455, + 545, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 455, + 545, + 479 + ], + "spans": [ + { + "bbox": [ + 306, + 455, + 545, + 479 + ], + "type": "text", + "content": "ing factor " + }, + { + "bbox": [ + 306, + 455, + 545, + 479 + ], + "type": "inline_equation", + "content": "\\sqrt{c'}" + }, + { + "bbox": [ + 306, + 455, + 545, + 479 + ], + "type": "text", + "content": " (step 7). Then the spatially attended feature map is generated as" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 364, + 489, + 545, + 502 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 364, + 489, + 545, + 502 + ], + "spans": [ + { + "bbox": [ + 364, + 489, + 545, + 502 + ], + "type": "interline_equation", + "content": "\\phi_ {n} = \\alpha_ {n} \\odot \\psi , \\phi_ {n} \\in \\mathbb {R} ^ {c \\times h \\times w}, \\tag {1}", + "image_path": "047559dd85f65e707460e5dd6857cec6868d00f2dc0156835fa978e44c99dabe.jpg" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 304, + 513, + 545, + 632 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 513, + 545, + 632 + ], + "spans": [ + { + "bbox": [ + 304, + 513, + 545, + 632 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 513, + 545, + 632 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 304, + 513, + 545, + 632 + ], + "type": "text", + "content": " is Hadamard product. To further focus on the attribute-relevant dimensions, the Channel-wise Conditional Attention on Attribute, CCA-A (Algorithm 2), takes the spatially attended feature maps " + }, + { + "bbox": [ + 304, + 513, + 545, + 632 + ], + "type": "inline_equation", + "content": "\\phi_{n}" + }, + { + "bbox": [ + 304, + 513, + 545, + 632 + ], + "type": "text", + "content": " and attribute " + }, + { + "bbox": [ + 304, + 513, + 545, + 632 + ], + "type": "inline_equation", + "content": "A_{n}" + }, + { + "bbox": [ + 304, + 513, + 545, + 632 + ], + "type": "text", + "content": " as inputs, and transforms them into feature vectors " + }, + { + "bbox": [ + 304, + 513, + 545, + 632 + ], + "type": "inline_equation", + "content": "q_{1}(\\phi_{n})" + }, + { + "bbox": [ + 304, + 513, + 545, + 632 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 513, + 545, + 632 + ], + "type": "inline_equation", + "content": "q_{2}(A_{n})" + }, + { + "bbox": [ + 304, + 513, + 545, + 632 + ], + "type": "text", + "content": " (step 5, 6 in Algorithm 2), where " + }, + { + "bbox": [ + 304, + 513, + 545, + 632 + ], + "type": "inline_equation", + "content": "q_{1}(\\phi_{n})\\in \\mathbb{R}^{c\\times 1},q_{2}(A_{n})\\in \\mathbb{R}^{c^{\\prime}\\times 1}" + }, + { + "bbox": [ + 304, + 513, + 545, + 632 + ], + "type": "text", + "content": ". The attention output " + }, + { + "bbox": [ + 304, + 513, + 545, + 632 + ], + "type": "inline_equation", + "content": "\\beta_{n}" + }, + { + "bbox": [ + 304, + 513, + 545, + 632 + ], + "type": "text", + "content": " is obtained from the concatenation of " + }, + { + "bbox": [ + 304, + 513, + 545, + 632 + ], + "type": "inline_equation", + "content": "q_{1}(\\phi_{n})" + }, + { + "bbox": [ + 304, + 513, + 545, + 632 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 513, + 545, + 632 + ], + "type": "inline_equation", + "content": "q_{2}(A_{n})" + }, + { + "bbox": [ + 304, + 513, + 545, + 632 + ], + "type": "text", + "content": " (step 7). " + }, + { + "bbox": [ + 304, + 513, + 545, + 632 + ], + "type": "inline_equation", + "content": "\\beta_{n}\\in \\mathbb{R}^{c\\times 1}" + }, + { + "bbox": [ + 304, + 513, + 545, + 632 + ], + "type": "text", + "content": ". Finally, the attribute-specific representation is generated as" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 359, + 642, + 545, + 655 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 359, + 642, + 545, + 655 + ], + "spans": [ + { + "bbox": [ + 359, + 642, + 545, + 655 + ], + "type": "interline_equation", + "content": "\\varphi_ {n} = \\beta_ {n} \\odot q _ {1} (\\phi_ {n}), \\varphi_ {n} \\in \\mathbb {R} ^ {c \\times 1}. \\tag {2}", + "image_path": "a72040b9f316f0f4927054e51d133b42c0f102eb1c287e600c27056af2f674de.jpg" + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 304, + 665, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 714 + ], + "type": "text", + "content": "Subsequently, to reduce the number of class-specific representations in learning, we involve the multi-label classification to exclude low-likelihood classes. As Eq. 3 shows, given an attribute-specific MLP module " + }, + { + "bbox": [ + 304, + 665, + 545, + 714 + ], + "type": "inline_equation", + "content": "g_{n}" + }, + { + "bbox": [ + 304, + 665, + 545, + 714 + ], + "type": "text", + "content": ", the probability" + } + ] + } + ], + "index": 32 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11053" + } + ] + } + ], + "index": 33 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 96 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 96 + ], + "type": "text", + "content": "of all classes for an attribute-specific representation on " + }, + { + "bbox": [ + 46, + 72, + 287, + 96 + ], + "type": "inline_equation", + "content": "A_{n}" + }, + { + "bbox": [ + 46, + 72, + 287, + 96 + ], + "type": "text", + "content": " is " + }, + { + "bbox": [ + 46, + 72, + 287, + 96 + ], + "type": "inline_equation", + "content": "P_{n}(I)" + }, + { + "bbox": [ + 46, + 72, + 287, + 96 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 78, + 105, + 287, + 119 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 78, + 105, + 287, + 119 + ], + "spans": [ + { + "bbox": [ + 78, + 105, + 287, + 119 + ], + "type": "interline_equation", + "content": "P _ {n} (I) = \\left[ x _ {1 _ {n}}, \\dots , x _ {m _ {n}}, \\dots , x _ {M _ {n}} \\right] = g _ {n} (\\varphi_ {n}). \\tag {3}", + "image_path": "b5c333527beb0485e01d6e4261be81088a01762fec0752efad3efae7a1b2150a.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 127, + 287, + 187 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 127, + 287, + 187 + ], + "spans": [ + { + "bbox": [ + 46, + 127, + 287, + 187 + ], + "type": "text", + "content": "By setting a threshold " + }, + { + "bbox": [ + 46, + 127, + 287, + 187 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 46, + 127, + 287, + 187 + ], + "type": "text", + "content": ", we obtain the multi-label class prediction " + }, + { + "bbox": [ + 46, + 127, + 287, + 187 + ], + "type": "inline_equation", + "content": "\\{\\widehat{l_n}\\} = \\{C_{m_n}|\\forall x_{m_n} > \\gamma \\}" + }, + { + "bbox": [ + 46, + 127, + 287, + 187 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 46, + 127, + 287, + 187 + ], + "type": "inline_equation", + "content": "\\{\\widehat{l_n}\\}" + }, + { + "bbox": [ + 46, + 127, + 287, + 187 + ], + "type": "text", + "content": " is the set of predicted high-likelihood classes. Empirically, with " + }, + { + "bbox": [ + 46, + 127, + 287, + 187 + ], + "type": "inline_equation", + "content": "\\gamma = 0.8" + }, + { + "bbox": [ + 46, + 127, + 287, + 187 + ], + "type": "text", + "content": " we can exclude on average " + }, + { + "bbox": [ + 46, + 127, + 287, + 187 + ], + "type": "inline_equation", + "content": "94\\%" + }, + { + "bbox": [ + 46, + 127, + 287, + 187 + ], + "type": "text", + "content": " of classes for an image. Please see the sensitivity analysis of " + }, + { + "bbox": [ + 46, + 127, + 287, + 187 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 46, + 127, + 287, + 187 + ], + "type": "text", + "content": " in Suppl." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 188, + 287, + 235 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 188, + 287, + 235 + ], + "spans": [ + { + "bbox": [ + 46, + 188, + 287, + 235 + ], + "type": "text", + "content": "Class-specific representation. As an attribute often involves multiple classes, the class-conditional attention modules help M3-Net focus on individual classes and learn class-specific representations." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 236, + 287, + 319 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 236, + 287, + 319 + ], + "spans": [ + { + "bbox": [ + 46, + 236, + 287, + 319 + ], + "type": "text", + "content": "Class-conditional attention modules consist of Spatial Conditional Attention on Class (SCA-C) and Channelwise Conditional Attention on Class (CCA-C). SCA-C and CCA-C are attribute-specific. Different from the attribute-conditional attention modules, we expect them to focus on the relevant spatial locations and dimensions of corresponding classes." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 319, + 287, + 369 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 319, + 287, + 369 + ], + "spans": [ + { + "bbox": [ + 47, + 319, + 287, + 369 + ], + "type": "text", + "content": "Given an attribute " + }, + { + "bbox": [ + 47, + 319, + 287, + 369 + ], + "type": "inline_equation", + "content": "A_{n}" + }, + { + "bbox": [ + 47, + 319, + 287, + 369 + ], + "type": "text", + "content": ", its spatially attended feature map " + }, + { + "bbox": [ + 47, + 319, + 287, + 369 + ], + "type": "inline_equation", + "content": "\\phi_{n}" + }, + { + "bbox": [ + 47, + 319, + 287, + 369 + ], + "type": "text", + "content": ", and class " + }, + { + "bbox": [ + 47, + 319, + 287, + 369 + ], + "type": "inline_equation", + "content": "C_{m_n} \\in \\{\\widehat{l_n}\\}" + }, + { + "bbox": [ + 47, + 319, + 287, + 369 + ], + "type": "text", + "content": ", the SCA-C generates a class-conditional spatial attention map " + }, + { + "bbox": [ + 47, + 319, + 287, + 369 + ], + "type": "inline_equation", + "content": "\\overline{\\alpha_{m_n}}" + }, + { + "bbox": [ + 47, + 319, + 287, + 369 + ], + "type": "text", + "content": ". We obtain the spatially attended feature map " + }, + { + "bbox": [ + 47, + 319, + 287, + 369 + ], + "type": "inline_equation", + "content": "\\overline{\\phi_{m_n}}" + }, + { + "bbox": [ + 47, + 319, + 287, + 369 + ], + "type": "text", + "content": " as" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 91, + 376, + 287, + 392 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 376, + 287, + 392 + ], + "spans": [ + { + "bbox": [ + 91, + 376, + 287, + 392 + ], + "type": "interline_equation", + "content": "\\overline {{\\phi_ {m _ {n}}}} = \\overline {{\\alpha_ {m _ {n}}}} \\odot \\phi_ {n}, \\overline {{\\phi_ {m _ {n}}}} \\in \\mathbb {R} ^ {c \\times h \\times w}. \\tag {4}", + "image_path": "a24d2db44c54b9728ce4e6a4841094bdb20bed3dccdcfb4a1688244efdfe4ea5.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 398, + 287, + 459 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 398, + 287, + 459 + ], + "spans": [ + { + "bbox": [ + 46, + 398, + 287, + 459 + ], + "type": "inline_equation", + "content": "\\overline{\\phi_{m_n}}" + }, + { + "bbox": [ + 46, + 398, + 287, + 459 + ], + "type": "text", + "content": " is subsequently fed through both attribute-conditional channel attention (CCA-A) and class-conditional channel attention (CCA-C). Especially, the CCA-A of " + }, + { + "bbox": [ + 46, + 398, + 287, + 459 + ], + "type": "inline_equation", + "content": "A_{n}" + }, + { + "bbox": [ + 46, + 398, + 287, + 459 + ], + "type": "text", + "content": " outputs the attribute-conditional channel attention map " + }, + { + "bbox": [ + 46, + 398, + 287, + 459 + ], + "type": "inline_equation", + "content": "\\overline{\\beta_n}" + }, + { + "bbox": [ + 46, + 398, + 287, + 459 + ], + "type": "text", + "content": ". The attended feature is" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 96, + 467, + 287, + 482 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 96, + 467, + 287, + 482 + ], + "spans": [ + { + "bbox": [ + 96, + 467, + 287, + 482 + ], + "type": "interline_equation", + "content": "\\overline {{\\varphi_ {n}}} = \\overline {{\\beta_ {n}}} \\odot q _ {1} \\left(\\overline {{\\phi_ {m _ {n}}}}\\right), \\overline {{\\varphi_ {n}}} \\in \\mathbb {R} ^ {c \\times 1}. \\tag {5}", + "image_path": "74ff5c9d8fd89a8d1e5d92e3c1f4be39433bb0a7ee971b5a4521b16f4ee985f0.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 489, + 287, + 538 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 489, + 287, + 538 + ], + "spans": [ + { + "bbox": [ + 46, + 489, + 287, + 538 + ], + "type": "text", + "content": "The CCA-C of " + }, + { + "bbox": [ + 46, + 489, + 287, + 538 + ], + "type": "inline_equation", + "content": "A_{n}" + }, + { + "bbox": [ + 46, + 489, + 287, + 538 + ], + "type": "text", + "content": " takes the feature vector " + }, + { + "bbox": [ + 46, + 489, + 287, + 538 + ], + "type": "inline_equation", + "content": "\\overline{\\varphi_n}" + }, + { + "bbox": [ + 46, + 489, + 287, + 538 + ], + "type": "text", + "content": " and the class " + }, + { + "bbox": [ + 46, + 489, + 287, + 538 + ], + "type": "inline_equation", + "content": "C_{m_n}" + }, + { + "bbox": [ + 46, + 489, + 287, + 538 + ], + "type": "text", + "content": " as inputs to generate the feature vector " + }, + { + "bbox": [ + 46, + 489, + 287, + 538 + ], + "type": "inline_equation", + "content": "q_{1}(\\overline{\\varphi_{n}})" + }, + { + "bbox": [ + 46, + 489, + 287, + 538 + ], + "type": "text", + "content": " and gives the class-conditional channel-wise attention map " + }, + { + "bbox": [ + 46, + 489, + 287, + 538 + ], + "type": "inline_equation", + "content": "\\overline{\\beta_{m_n}}" + }, + { + "bbox": [ + 46, + 489, + 287, + 538 + ], + "type": "text", + "content": ". The class-specific representation is obtained as" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 89, + 545, + 287, + 560 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 89, + 545, + 287, + 560 + ], + "spans": [ + { + "bbox": [ + 89, + 545, + 287, + 560 + ], + "type": "interline_equation", + "content": "\\overline {{\\varphi_ {m _ {n}}}} = \\overline {{\\beta_ {m _ {n}}}} \\odot q _ {1} (\\overline {{\\varphi_ {n}}}), \\overline {{\\varphi_ {m _ {n}}}} \\in \\mathbb {R} ^ {c \\times 1}. \\tag {6}", + "image_path": "e8c7725411278c0374e3642aabc29b8f422a39b06feeaa2bc137426cd1d6a512.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 568, + 287, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 568, + 287, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 568, + 287, + 664 + ], + "type": "text", + "content": "M3-Net has three key outputs: the attribute-specific representation " + }, + { + "bbox": [ + 46, + 568, + 287, + 664 + ], + "type": "inline_equation", + "content": "\\varphi_{n}" + }, + { + "bbox": [ + 46, + 568, + 287, + 664 + ], + "type": "text", + "content": ", class-specific-representation " + }, + { + "bbox": [ + 46, + 568, + 287, + 664 + ], + "type": "inline_equation", + "content": "\\overline{\\varphi_{m_n}}" + }, + { + "bbox": [ + 46, + 568, + 287, + 664 + ], + "type": "text", + "content": ", and multi-label probability vector " + }, + { + "bbox": [ + 46, + 568, + 287, + 664 + ], + "type": "inline_equation", + "content": "P_{n}(I)" + }, + { + "bbox": [ + 46, + 568, + 287, + 664 + ], + "type": "text", + "content": ". They are used to constrain the multi-granularity embedding spaces via a multi-granularity objective. In this part, we build our method upon the online clustering method and prototypical triplet loss in [14] and further extend them to learning two-granularity fine-grained representations." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 671, + 201, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 671, + 201, + 684 + ], + "spans": [ + { + "bbox": [ + 47, + 671, + 201, + 684 + ], + "type": "text", + "content": "3.2. Multi-granularity Objective" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "To learn across different granularities of the fashion representations in an end-to-end manner, we design two losses" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "type": "text", + "content": "to introduce appropriate inductive bias: an attribute-level loss and a class-level loss." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 96, + 545, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 96, + 545, + 168 + ], + "spans": [ + { + "bbox": [ + 304, + 96, + 545, + 168 + ], + "type": "text", + "content": "Attribute-level loss. At the attribute level, we define the below multi-label classification loss to allow the representation learning on multi-label attributes. Given an image " + }, + { + "bbox": [ + 304, + 96, + 545, + 168 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 304, + 96, + 545, + 168 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 304, + 96, + 545, + 168 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 96, + 545, + 168 + ], + "type": "text", + "content": " attributes " + }, + { + "bbox": [ + 304, + 96, + 545, + 168 + ], + "type": "inline_equation", + "content": "\\{A_{n}\\}" + }, + { + "bbox": [ + 304, + 96, + 545, + 168 + ], + "type": "text", + "content": ", each with " + }, + { + "bbox": [ + 304, + 96, + 545, + 168 + ], + "type": "inline_equation", + "content": "M_{n}" + }, + { + "bbox": [ + 304, + 96, + 545, + 168 + ], + "type": "text", + "content": " classes " + }, + { + "bbox": [ + 304, + 96, + 545, + 168 + ], + "type": "inline_equation", + "content": "\\{C_{m_n}\\}" + }, + { + "bbox": [ + 304, + 96, + 545, + 168 + ], + "type": "text", + "content": " and corresponding class labels " + }, + { + "bbox": [ + 304, + 96, + 545, + 168 + ], + "type": "inline_equation", + "content": "\\{y_{m_n}\\}" + }, + { + "bbox": [ + 304, + 96, + 545, + 168 + ], + "type": "text", + "content": ", the loss of multi-label classification is a binary cross-entropy loss," + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 318, + 172, + 545, + 220 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 172, + 545, + 220 + ], + "spans": [ + { + "bbox": [ + 318, + 172, + 545, + 220 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {\\mathcal {M}} \\left(I, A _ {n} \\mid y _ {m _ {n}}\\right) = \\frac {1}{M _ {n}} \\left(\\sum_ {m = 1} ^ {M _ {n}} \\left[ - w _ {p} y _ {m _ {n}} \\cdot \\log x _ {m _ {n}} \\right. \\right. \\tag {7} \\\\ \\left. + \\left(1 - y _ {m _ {n}}\\right) \\cdot \\log \\left(1 - x _ {m _ {n}}\\right)\\right]\\left. \\right), \\forall x _ {m _ {n}} \\in P _ {n} (I), \\\\ \\end{array}", + "image_path": "c7ec91791ff1712d3ffda277f75468336865decc489871e39c0d33fa2ec21b8d.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 224, + 545, + 259 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 224, + 545, + 259 + ], + "spans": [ + { + "bbox": [ + 305, + 224, + 545, + 259 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 224, + 545, + 259 + ], + "type": "inline_equation", + "content": "x_{m_n}" + }, + { + "bbox": [ + 305, + 224, + 545, + 259 + ], + "type": "text", + "content": " is the predicted probability of " + }, + { + "bbox": [ + 305, + 224, + 545, + 259 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 305, + 224, + 545, + 259 + ], + "type": "text", + "content": " in class " + }, + { + "bbox": [ + 305, + 224, + 545, + 259 + ], + "type": "inline_equation", + "content": "C_{m_n}" + }, + { + "bbox": [ + 305, + 224, + 545, + 259 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 224, + 545, + 259 + ], + "type": "inline_equation", + "content": "w_p" + }, + { + "bbox": [ + 305, + 224, + 545, + 259 + ], + "type": "text", + "content": " is the weight on the positive samples to mitigate the class-imbalance problem." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 260, + 545, + 366 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 260, + 545, + 366 + ], + "spans": [ + { + "bbox": [ + 304, + 260, + 545, + 366 + ], + "type": "text", + "content": "Class-level loss. At the class level, we propose to regularize the class-specific representation learning on both global and local structures via two triplet losses. For the global structure, we construct a prototypical triplet loss between an image representation, the representation of the positive prototype of the class that the image belongs to, and a negative representation. The triplet loss associated with the local structure involves instance-level representations to refine the local distance." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 368, + 545, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 368, + 545, + 392 + ], + "spans": [ + { + "bbox": [ + 305, + 368, + 545, + 392 + ], + "type": "text", + "content": "A classic triplet loss between an anchor, a positive, and a negative representation is defined as" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 312, + 407, + 545, + 422 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 407, + 545, + 422 + ], + "spans": [ + { + "bbox": [ + 312, + 407, + 545, + 422 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\triangle} (I, I ^ {+}, I ^ {-}) = \\max \\{0, \\zeta + d (I, I ^ {+}) - d (I, I ^ {-}) \\}, \\tag {8}", + "image_path": "cea100ff87860b5838333fe3b071cab06691cdaeb9edc8a80ba52084344e76ea.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 426, + 545, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 426, + 545, + 449 + ], + "spans": [ + { + "bbox": [ + 305, + 426, + 545, + 449 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 426, + 545, + 449 + ], + "type": "inline_equation", + "content": "\\zeta = 0.4" + }, + { + "bbox": [ + 305, + 426, + 545, + 449 + ], + "type": "text", + "content": " is a predefined margin, and " + }, + { + "bbox": [ + 305, + 426, + 545, + 449 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 305, + 426, + 545, + 449 + ], + "type": "text", + "content": " is the cosine similarity." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 305, + 449, + 545, + 497 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 449, + 545, + 497 + ], + "spans": [ + { + "bbox": [ + 305, + 449, + 545, + 497 + ], + "type": "text", + "content": "Given a triplet of images " + }, + { + "bbox": [ + 305, + 449, + 545, + 497 + ], + "type": "inline_equation", + "content": "[I, I^{+}, I^{-}]" + }, + { + "bbox": [ + 305, + 449, + 545, + 497 + ], + "type": "text", + "content": " associated with classes " + }, + { + "bbox": [ + 305, + 449, + 545, + 497 + ], + "type": "inline_equation", + "content": "[C_{m_n}, C_{m_n}^{+}, C_{m_n}^{-}]" + }, + { + "bbox": [ + 305, + 449, + 545, + 497 + ], + "type": "text", + "content": " in attribute " + }, + { + "bbox": [ + 305, + 449, + 545, + 497 + ], + "type": "inline_equation", + "content": "A_{n}" + }, + { + "bbox": [ + 305, + 449, + 545, + 497 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 449, + 545, + 497 + ], + "type": "inline_equation", + "content": "C_{m_n} = C_{m_n}^{+} \\neq C_{m_n}^{-}" + }, + { + "bbox": [ + 305, + 449, + 545, + 497 + ], + "type": "text", + "content": ". The prototypical triplet loss in the class-specific embedding spaces is defined as" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 314, + 501, + 545, + 515 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 501, + 545, + 515 + ], + "spans": [ + { + "bbox": [ + 314, + 501, + 545, + 515 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathcal {C C}} \\left(I, A _ {n}, C _ {m _ {n}}\\right) = \\mathcal {L} _ {\\triangle} \\left(\\overline {{\\varphi_ {m _ {n}} (I)}}, \\bar {\\varphi_ {C ^ {+}}}, \\overline {{\\varphi_ {m _ {n}} (I ^ {-})}}\\right), \\tag {9}", + "image_path": "d91432bb701d09e8a87eba99c9b93773a83585ff958e1e1abced61b5dcd348fb.jpg" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 519, + 545, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 519, + 545, + 568 + ], + "spans": [ + { + "bbox": [ + 304, + 519, + 545, + 568 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 519, + 545, + 568 + ], + "type": "inline_equation", + "content": "\\overline{\\varphi_{m_n}(I)}" + }, + { + "bbox": [ + 304, + 519, + 545, + 568 + ], + "type": "text", + "content": " is the anchor representation, " + }, + { + "bbox": [ + 304, + 519, + 545, + 568 + ], + "type": "inline_equation", + "content": "\\overline{\\varphi_{m_n}(I^-)}" + }, + { + "bbox": [ + 304, + 519, + 545, + 568 + ], + "type": "text", + "content": " is a random negative representation in the class-specific embedding space, and " + }, + { + "bbox": [ + 304, + 519, + 545, + 568 + ], + "type": "inline_equation", + "content": "\\overline{\\varphi_{C^+}}" + }, + { + "bbox": [ + 304, + 519, + 545, + 568 + ], + "type": "text", + "content": " is the positive class prototype in the space. The computation of " + }, + { + "bbox": [ + 304, + 519, + 545, + 568 + ], + "type": "inline_equation", + "content": "\\overline{\\varphi_{C^+}}" + }, + { + "bbox": [ + 304, + 519, + 545, + 568 + ], + "type": "text", + "content": " is akin to [14]." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 305, + 569, + 545, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 569, + 545, + 592 + ], + "spans": [ + { + "bbox": [ + 305, + 569, + 545, + 592 + ], + "type": "text", + "content": "The instance triplet loss in the class-specific embedding spaces is defined as" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 310, + 596, + 545, + 620 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 596, + 545, + 620 + ], + "spans": [ + { + "bbox": [ + 310, + 596, + 545, + 620 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathcal {C I}} (I, A _ {n}, C _ {m _ {n}}) = \\mathcal {L} _ {\\triangle} (\\overline {{\\varphi_ {m _ {n}} (I)}}, \\overline {{\\varphi_ {m _ {n}} (I ^ {+})}}, \\overline {{\\varphi_ {m _ {n}} (I ^ {-})}}), \\tag {10}", + "image_path": "5db1e1009d0db1d2327fd261b7ddaebfceef21eb865034c09d339b15d3b068e8.jpg" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 304, + 621, + 545, + 657 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 621, + 545, + 657 + ], + "spans": [ + { + "bbox": [ + 304, + 621, + 545, + 657 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 621, + 545, + 657 + ], + "type": "inline_equation", + "content": "\\overline{\\varphi_{m_n}(I)}" + }, + { + "bbox": [ + 304, + 621, + 545, + 657 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 621, + 545, + 657 + ], + "type": "inline_equation", + "content": "\\overline{\\varphi_{m_n}(I^+)}" + }, + { + "bbox": [ + 304, + 621, + 545, + 657 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 621, + 545, + 657 + ], + "type": "inline_equation", + "content": "\\overline{\\varphi_{m_n}(I^-)}" + }, + { + "bbox": [ + 304, + 621, + 545, + 657 + ], + "type": "text", + "content": " are the class-specific representations for the anchor, positive, and negative sample, respectively." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 304, + 658, + 545, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 658, + 545, + 693 + ], + "spans": [ + { + "bbox": [ + 304, + 658, + 545, + 693 + ], + "type": "text", + "content": "Final objective function. The final objective function combines both attribute and class-level objectives and allows a simple end-to-end training, as shown in Eq.(11)" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 347, + 697, + 545, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 347, + 697, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 347, + 697, + 545, + 715 + ], + "type": "interline_equation", + "content": "\\min _ {\\theta} \\left(\\lambda_ {M} \\mathcal {L} _ {\\mathcal {M}} + \\lambda_ {C C} \\mathcal {L} _ {\\mathcal {C C}} + \\lambda_ {C I} \\mathcal {L} _ {\\mathcal {C I}}\\right). \\tag {11}", + "image_path": "983f2bce40c1133fcc5a6ce53c9f9cee42ff89c51d79487fabc93e708addb608.jpg" + } + ] + } + ], + "index": 29 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11054" + } + ] + } + ], + "index": 30 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 52, + 70, + 282, + 110 + ], + "blocks": [ + { + "bbox": [ + 52, + 70, + 282, + 110 + ], + "lines": [ + { + "bbox": [ + 52, + 70, + 282, + 110 + ], + "spans": [ + { + "bbox": [ + 52, + 70, + 282, + 110 + ], + "type": "table", + "html": "
DatasetAttr type# Attr# Class per attrTrain/val/test
DeepFashion [18]multi-label5156-230220K/28K/28K
FashionAI [28]single-label85-10144k/18k/18k
DARN [13]single-label97-55163k/20k/20k
", + "image_path": "fa004b5e3900cbc55fd462e441a5b1e103276afe75da18f3117baf16b7158d9b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 118, + 286, + 140 + ], + "lines": [ + { + "bbox": [ + 47, + 118, + 286, + 140 + ], + "spans": [ + { + "bbox": [ + 47, + 118, + 286, + 140 + ], + "type": "text", + "content": "Table 1. Summary of the datasets used in experimental validations. \nAttr: attribute." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 47, + 163, + 286, + 187 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 163, + 286, + 187 + ], + "spans": [ + { + "bbox": [ + 47, + 163, + 286, + 187 + ], + "type": "text", + "content": "where, " + }, + { + "bbox": [ + 47, + 163, + 286, + 187 + ], + "type": "inline_equation", + "content": "\\lambda_{M},\\lambda_{CC}" + }, + { + "bbox": [ + 47, + 163, + 286, + 187 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 163, + 286, + 187 + ], + "type": "inline_equation", + "content": "\\lambda_{CI}" + }, + { + "bbox": [ + 47, + 163, + 286, + 187 + ], + "type": "text", + "content": " are hyperparameters, which are set to 1 in our experiments." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 200, + 128, + 213 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 200, + 128, + 213 + ], + "spans": [ + { + "bbox": [ + 47, + 200, + 128, + 213 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 220, + 110, + 232 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 220, + 110, + 232 + ], + "spans": [ + { + "bbox": [ + 47, + 220, + 110, + 232 + ], + "type": "text", + "content": "4.1. Datasets" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 239, + 286, + 310 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 239, + 286, + 310 + ], + "spans": [ + { + "bbox": [ + 47, + 239, + 286, + 310 + ], + "type": "text", + "content": "In Table 1, we summarize the three benchmark datasets used in the experiments. DeepFashion is a large dataset containing image labels of fashion attributes, landmarks, etc. We use the coarsely-annotated attribute prediction subset, which is one of the most popular datasets in fashion retrieval, and is a multi-label dataset." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 320, + 173, + 333 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 320, + 173, + 333 + ], + "spans": [ + { + "bbox": [ + 47, + 320, + 173, + 333 + ], + "type": "text", + "content": "4.2. Experimental Settings" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 340, + 286, + 363 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 340, + 286, + 363 + ], + "spans": [ + { + "bbox": [ + 47, + 340, + 286, + 363 + ], + "type": "text", + "content": "We compare our proposed method with the state-of-the-art solutions [6, 14, 19] on the aforementioned datasets." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 364, + 286, + 471 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 364, + 286, + 471 + ], + "spans": [ + { + "bbox": [ + 47, + 364, + 286, + 471 + ], + "type": "text", + "content": "Baselines. ASEIN networks are the state-of-the-art works on attribute-specific representation learning. ASEIN [19] learns 1024 dimensional attribute-specific representations by using an attribute-aware spatial attention and an attribute-aware channel attention. " + }, + { + "bbox": [ + 47, + 364, + 286, + 471 + ], + "type": "inline_equation", + "content": "\\mathrm{ASEN}_{v2}" + }, + { + "bbox": [ + 47, + 364, + 286, + 471 + ], + "type": "text", + "content": " [19] builds a new attention module structure and achieves better performance than ASEIN. " + }, + { + "bbox": [ + 47, + 364, + 286, + 471 + ], + "type": "inline_equation", + "content": "\\mathrm{ASEN}++" + }, + { + "bbox": [ + 47, + 364, + 286, + 471 + ], + "type": "text", + "content": " [6] further proposes a cascade network with a global branch and a local branch to learn multi-scale representations in 2,048 dimensions." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 472, + 286, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 472, + 286, + 567 + ], + "spans": [ + { + "bbox": [ + 47, + 472, + 286, + 567 + ], + "type": "text", + "content": "MODC [14] it is a fine-grained representation learning framework with online deep clustering to achieve retrieval in two granularities. It splits the attribute-specific embedding spaces into class-specific embedding spaces in the inference stage to enable retrieval at the finer granularity. MODC learns attribute-specific representations with 2048 dimensions and achieves the state-of-the-art results on multiple datasets." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 569, + 286, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 569, + 286, + 664 + ], + "spans": [ + { + "bbox": [ + 47, + 569, + 286, + 664 + ], + "type": "text", + "content": "M3-Net is our proposed method which jointly learns attribute-specific and class-specific representation duet for fine-grained fashion analysis. The attribute-specific and class-specific representations are 1024 dimensions. To isolate the effects of two-granularity attentions, we trained M3-Net with only the attribute-conditional attention modules, with only the class-conditional attention modules, and with both, called M3-Net" + }, + { + "bbox": [ + 47, + 569, + 286, + 664 + ], + "type": "inline_equation", + "content": "_a" + }, + { + "bbox": [ + 47, + 569, + 286, + 664 + ], + "type": "text", + "content": ", M3-Net" + }, + { + "bbox": [ + 47, + 569, + 286, + 664 + ], + "type": "inline_equation", + "content": "_c" + }, + { + "bbox": [ + 47, + 569, + 286, + 664 + ], + "type": "text", + "content": ", and M3-Net respectively." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 665, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 665, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 47, + 665, + 286, + 712 + ], + "type": "text", + "content": "Training details M3-Net employs a ResNet50 [10] pretrained on ImageNet [5] as the shared backbone network, and removes the last residual block. It is identical to the backbone of the baselines for fair comparisons. To train" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": "M3-Net, we use a learning rate " + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "inline_equation", + "content": "1 \\times 10^{-4}" + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": " with a 0.975 decay per epoch and a batch size of 16. We sample 40k triplet of images each epoch of training. In training, We set " + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "inline_equation", + "content": "w_{p}" + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": " to 100 for DeepFashion, and 1 for FashionAI and DARN. To train the baselines on DeepFashion, We follow the descriptions in [6, 14, 19]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 144, + 545, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 144, + 545, + 251 + ], + "spans": [ + { + "bbox": [ + 304, + 144, + 545, + 251 + ], + "type": "text", + "content": "Evaluation Tasks and Metrics. We evaluate our proposed method in comparison with the above baselines on the fine-grained fashion retrieval task. Following the existing protocol for multi-granularity retrieval as proposed in MODC [14], the retrieval is prioritized in the class-specific embedding space, followed by retrieval in the attribute-specific embedding space. Same as existing works [6, 14, 19], we employ Mean Average Precision (MAP) and Recall as the evaluation metrics." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 262, + 429, + 274 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 262, + 429, + 274 + ], + "spans": [ + { + "bbox": [ + 306, + 262, + 429, + 274 + ], + "type": "text", + "content": "4.3. Experimental Results" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 281, + 545, + 412 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 281, + 545, + 412 + ], + "spans": [ + { + "bbox": [ + 304, + 281, + 545, + 412 + ], + "type": "text", + "content": "In this section, we discuss the experimental results and ablation study of M3-Net on multi-label attributes and single-label attributes. Table 2 presents the overall performance and the performance on each attribute of baselines and M3-Net on DeepFashion. Table 3 and Table 4 summarizes the performance on FashionAI and DARN. On all datasets, we show the ablation study of separately employing attribute-conditional attention modules (i.e., " + }, + { + "bbox": [ + 304, + 281, + 545, + 412 + ], + "type": "inline_equation", + "content": "\\mathrm{M3 - Net}_a" + }, + { + "bbox": [ + 304, + 281, + 545, + 412 + ], + "type": "text", + "content": ") and class-conditional attention modules (i.e., " + }, + { + "bbox": [ + 304, + 281, + 545, + 412 + ], + "type": "inline_equation", + "content": "\\mathrm{M3 - Net}_c" + }, + { + "bbox": [ + 304, + 281, + 545, + 412 + ], + "type": "text", + "content": ") to demonstrate the effectiveness of representation learning on attribute granularity and class granularity." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 430, + 533, + 441 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 430, + 533, + 441 + ], + "spans": [ + { + "bbox": [ + 306, + 430, + 533, + 441 + ], + "type": "text", + "content": "4.3.1 Quantitative evaluation on multi-label dataset" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 449, + 545, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 449, + 545, + 557 + ], + "spans": [ + { + "bbox": [ + 304, + 449, + 545, + 557 + ], + "type": "text", + "content": "Table 2 summarizes the performance of fine-grained fashion retrieval on all attributes in DeepFashion. Note that " + }, + { + "bbox": [ + 304, + 449, + 545, + 557 + ], + "type": "inline_equation", + "content": "\\mathrm{ASEN}_{v2}" + }, + { + "bbox": [ + 304, + 449, + 545, + 557 + ], + "type": "text", + "content": " [19] and " + }, + { + "bbox": [ + 304, + 449, + 545, + 557 + ], + "type": "inline_equation", + "content": "\\mathrm{ASEN}++" + }, + { + "bbox": [ + 304, + 449, + 545, + 557 + ], + "type": "text", + "content": " [6] report performance on DeepFashion by treating it as a single-label dataset. To evaluate the performance in the multi-label setting, we split DeepFashion following the multi-class labels of each image in the dataset. The train/validation/test split is shown in Table 1. For the retrieval task, the validation set and test set are further split into the query and candidate sets by 1:4." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 558, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 545, + 712 + ], + "type": "text", + "content": "DeepFashion is an extremely challenging dataset for fine-grained fashion retrieval. Therefore, all methods perform much worse on DeepFashion than on other benchmark datasets Compared with the baselines, the proposed M3-Net consistently achieves the best performance with a large margin on all evaluation metrics on individual attributes and overall. Even when compared with the state-of-the-art multi-granularity method, MODC, the proposed M3-Net shows significant improvements over MODC on MAP@all (70.42%), MAP@100 (57.95%), and Recall@100 (112.5%). The results demonstrate the efficacy of the attribute and class-specific representations learned by M3-Net." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11055" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 129, + 70, + 465, + 173 + ], + "blocks": [ + { + "bbox": [ + 129, + 70, + 465, + 173 + ], + "lines": [ + { + "bbox": [ + 129, + 70, + 465, + 173 + ], + "spans": [ + { + "bbox": [ + 129, + 70, + 465, + 173 + ], + "type": "table", + "html": "
ModelDeepFashion
MAP@allMAP@allMAP@100Recall@100
Attributetexturefabricshapepartstyleoveralloveralloverall
ASEN [19]21.0311.6114.687.814.6612.3320.605.10
ASENV2 [19]21.8611.6714.587.934.6812.5120.554.99
ASEN++ [6]22.2011.7114.708.154.7212.7420.795.21
MODC [14]22.2611.9814.687.965.2312.7822.216.06
M3-Neta27.3718.3422.9614.669.7419.0328.1410.59
M3-Netc30.0919.6025.2416.4311.3220.9230.5812.10
M3-Net30.7920.2027.1117.2811.6121.7835.0812.88
", + "image_path": "0641c24a9053969212196f87046b72a7d85fdd015289caad3467f8c466d6192f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 59, + 201, + 535, + 285 + ], + "blocks": [ + { + "bbox": [ + 132, + 179, + 460, + 190 + ], + "lines": [ + { + "bbox": [ + 132, + 179, + 460, + 190 + ], + "spans": [ + { + "bbox": [ + 132, + 179, + 460, + 190 + ], + "type": "text", + "content": "Table 2. Performance comparison on all attributes of the multi-label dataset, DeepFashion." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 59, + 201, + 535, + 285 + ], + "lines": [ + { + "bbox": [ + 59, + 201, + 535, + 285 + ], + "spans": [ + { + "bbox": [ + 59, + 201, + 535, + 285 + ], + "type": "table", + "html": "
ModelFashionAI
MAP@allMAP@allMAP@100Recall@100
Attributeskirt lengthsleeve lengthcoat lengthpant lengthcollar designlapel designneckline designneck designoveralloveralloveralloverall
ASEN [19]64.6149.9849.7565.7670.3062.8652.1456.4257.3764.7022.77
ASENv2 [19]65.5854.4252.0367.4171.3666.7660.9159.5861.1367.8524.14
ASEN++ [6]66.3157.5155.4368.8372.7966.8566.7867.0264.2770.6225.30
MODC [14]74.5467.4868.2577.6981.1176.9077.4677.1074.3280.2930.26
M3-Neta73.2169.5865.2778.7980.8078.0577.0473.4073.9381.5730.48
M3-Netc74.3365.9164.2778.2682.0078.8574.8072.3972.8882.5830.77
M3-Net75.2770.0467.9079.3182.8278.5876.8175.5175.0487.0432.01
", + "image_path": "94994219ed509fc6ebb8251fd37aea4dda9459f787d6c111fac25613da729098.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 135, + 293, + 457, + 304 + ], + "lines": [ + { + "bbox": [ + 135, + 293, + 457, + 304 + ], + "spans": [ + { + "bbox": [ + 135, + 293, + 457, + 304 + ], + "type": "text", + "content": "Table 3. Performance comparison on all attributes of the single-label dataset, FashionAI." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 326, + 287, + 409 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 326, + 287, + 409 + ], + "spans": [ + { + "bbox": [ + 46, + 326, + 287, + 409 + ], + "type": "text", + "content": "Ablation study on " + }, + { + "bbox": [ + 46, + 326, + 287, + 409 + ], + "type": "inline_equation", + "content": "\\mathrm{M3 - Net}_a" + }, + { + "bbox": [ + 46, + 326, + 287, + 409 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 326, + 287, + 409 + ], + "type": "inline_equation", + "content": "\\mathrm{M3 - Net}_c" + }, + { + "bbox": [ + 46, + 326, + 287, + 409 + ], + "type": "text", + "content": " and M3-Net suggests that employing more fine-grained attention on classes " + }, + { + "bbox": [ + 46, + 326, + 287, + 409 + ], + "type": "inline_equation", + "content": "(\\mathrm{M3 - Net}_c)" + }, + { + "bbox": [ + 46, + 326, + 287, + 409 + ], + "type": "text", + "content": " performs better than attribute-level attention alone " + }, + { + "bbox": [ + 46, + 326, + 287, + 409 + ], + "type": "inline_equation", + "content": "(\\mathrm{M3 - Net}_a)" + }, + { + "bbox": [ + 46, + 326, + 287, + 409 + ], + "type": "text", + "content": ". Yet combining attribute-conditional attentions and class-conditional attentions works the best (M3-Net). It shows that representations learned at the two granularities are complementary to each other." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 411, + 289, + 614 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 411, + 289, + 614 + ], + "spans": [ + { + "bbox": [ + 46, + 411, + 289, + 614 + ], + "type": "text", + "content": "Furthermore, we analyze the performance on co-occurring classes on DeepFashion to evaluate the effectiveness of M3-Net in capturing the inter-dependencies between different classes in representation learning. We first calculate the pairwise co-occurrence rates of all classes in the dataset. Two classes are considered co-occurring if both are associated with the same image. The range of co-occurrence rate is [0, 0.03], i.e., the most frequently co-occurring class pairs appear in " + }, + { + "bbox": [ + 46, + 411, + 289, + 614 + ], + "type": "inline_equation", + "content": "3\\%" + }, + { + "bbox": [ + 46, + 411, + 289, + 614 + ], + "type": "text", + "content": " of the images. We set the cut-off at 0.002 (corresponding to 565 co-occurrences), resulting in 468 class pairs from the 1M class pairs in the dataset. This gives us 122 unique classes. M3-Net achieves a MAP@all at 35.61 on this set of classes, which is " + }, + { + "bbox": [ + 46, + 411, + 289, + 614 + ], + "type": "inline_equation", + "content": "63.50\\%" + }, + { + "bbox": [ + 46, + 411, + 289, + 614 + ], + "type": "text", + "content": " higher than the average of all classes. We hypothesize that M3-Net is able to incorporate the inter-dependencies between these classes into representation learning, thus performing better on them." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 633, + 282, + 645 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 633, + 282, + 645 + ], + "spans": [ + { + "bbox": [ + 47, + 633, + 282, + 645 + ], + "type": "text", + "content": "4.3.2 Quantitative evaluation on single-label datasets" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "text", + "content": "For the two single-label datasets, FashionAI and DARN, we follow the same split as in [19]. On both datasets, we observe similar competence of the proposed M3-Net in fine-grained fashion retrieval. On FashionAI, M3-Net achieve the best performance overall on all evaluation met" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 307, + 325, + 545, + 450 + ], + "blocks": [ + { + "bbox": [ + 307, + 325, + 545, + 450 + ], + "lines": [ + { + "bbox": [ + 307, + 325, + 545, + 450 + ], + "spans": [ + { + "bbox": [ + 307, + 325, + 545, + 450 + ], + "type": "image", + "image_path": "0f87d1ec8f177d1bb83c67c83fb2e091e732ac5b49687bd7561bc151357330a8.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 458, + 546, + 557 + ], + "lines": [ + { + "bbox": [ + 304, + 458, + 546, + 557 + ], + "spans": [ + { + "bbox": [ + 304, + 458, + 546, + 557 + ], + "type": "text", + "content": "Figure 3. Two-granularity attentions learned by M3-Net on DeepFashion. The attribute-conditional attention tends to focus on a wider range of regions in an image, while the class-conditional attention focuses more narrowly on a region relevant to each class. For instance, row 1: class \"slit\" focuses on the dress slit, \"elegant\" focuses on the waist; row 2: \"contrast trim\" focuses on the part with two different colors, \"stretch\" focuses on the strap; row 3: \"draped\" focuses on the drape decoration, and \"fit\" focuses on the waist. Best viewed in color on a computer screen." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 568, + 545, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 568, + 545, + 592 + ], + "spans": [ + { + "bbox": [ + 304, + 568, + 545, + 592 + ], + "type": "text", + "content": "rics (MAP@all, MAP@100, and Recall@100). It also outperforms the baselines on most individual attributes." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "text", + "content": "On DARN, we again observe a boost on all evaluation metrics. While baselines perform unsatisfactorily on \"clothes category\" and \"collar shape\", M3-Net improves them the most along with improvements on other attributes. Overall, M3-Net exceeds the best baseline, MODC, on MAP@all by " + }, + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "inline_equation", + "content": "16.35\\%" + }, + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "text", + "content": ", MAP@100 by " + }, + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "inline_equation", + "content": "14.59\\%" + }, + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "text", + "content": ", and Recall@100 by " + }, + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "inline_equation", + "content": "18.24\\%" + }, + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "text", + "content": ". The results of M3-Net on single-label datasets again demonstrate the effectiveness of the attribute-specific and class-specific representations. Compared with MODC, which obtains class-specific representations by di" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "11056" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 53, + 69, + 541, + 145 + ], + "blocks": [ + { + "bbox": [ + 53, + 69, + 541, + 145 + ], + "lines": [ + { + "bbox": [ + 53, + 69, + 541, + 145 + ], + "spans": [ + { + "bbox": [ + 53, + 69, + 541, + 145 + ], + "type": "table", + "html": "
ModelDARN
MAP@allMAP@allMAP@100Recall@100
Attributeclothes categoryclothes buttonclothes colorclothes lengthclothes patternclothes shapecollar shapesleeve lengthsleeve shapeoveralloveralloverall
ASEN [19]36.6246.0152.7656.8554.8956.8534.4079.9558.0852.7558.7220.26
ASENv2 [19]37.9749.2452.2659.1355.3259.0636.8681.5458.8254.2959.6620.88
ASEN++ [6]40.2150.0453.1459.8357.4159.7037.4583.7060.4155.7861.0921.51
MODC [14]49.9460.7558.7966.3462.2468.4145.1487.4165.3262.5672.1626.76
M3-Neta59.1669.9468.1872.5872.8776.2160.2289.3671.5871.0678.1230.77
M3-Netc60.9870.9168.5274.9574.4879.1563.0990.3173.0072.7981.4631.64
M3-Net60.5470.3969.5273.9774.4077.8361.6390.0373.9472.4282.6931.34
", + "image_path": "7efede248cf20a17362fef634a1bd5780a60f46fce7e2b71d3c7a966acdd669e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 141, + 152, + 451, + 165 + ], + "lines": [ + { + "bbox": [ + 141, + 152, + 451, + 165 + ], + "spans": [ + { + "bbox": [ + 141, + 152, + 451, + 165 + ], + "type": "text", + "content": "Table 4. Performance comparison on all attributes of the single-label dataset, DARN." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 50, + 175, + 303, + 324 + ], + "blocks": [ + { + "bbox": [ + 50, + 175, + 303, + 324 + ], + "lines": [ + { + "bbox": [ + 50, + 175, + 303, + 324 + ], + "spans": [ + { + "bbox": [ + 50, + 175, + 303, + 324 + ], + "type": "image", + "image_path": "dae655dc34bcf660402461606ff02120788b297f623535d6d3ebc7b19a48cc1d.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 332, + 546, + 355 + ], + "lines": [ + { + "bbox": [ + 46, + 332, + 546, + 355 + ], + "spans": [ + { + "bbox": [ + 46, + 332, + 546, + 355 + ], + "type": "text", + "content": "Figure 4. (a) single-label and (b) multi-label fashion retrieval by M3-Net and MODC on DeepFashion. Green: true positive retrieval; red: false positive retrieval. Best viewed in color on a computer screen." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 306, + 175, + 547, + 324 + ], + "blocks": [ + { + "bbox": [ + 306, + 175, + 547, + 324 + ], + "lines": [ + { + "bbox": [ + 306, + 175, + 547, + 324 + ], + "spans": [ + { + "bbox": [ + 306, + 175, + 547, + 324 + ], + "type": "image", + "image_path": "3f4f3253e43596aebe30db7d7ae9ccb597a7c9bd5dd074f9c62bde1f2a6ed336.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 376, + 287, + 424 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 376, + 287, + 424 + ], + "spans": [ + { + "bbox": [ + 46, + 376, + 287, + 424 + ], + "type": "text", + "content": "rectly segmenting the attribute-specific representation into class-specific clusters in the same embedding space, M3-Net learns separate representation spaces for attributes and classes and performs better." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 425, + 288, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 425, + 288, + 520 + ], + "spans": [ + { + "bbox": [ + 46, + 425, + 288, + 520 + ], + "type": "text", + "content": "Ablation study on FashionAI shows that overall having attentions on two granularities (M3-Net) performs better than attentions on either granularity alone " + }, + { + "bbox": [ + 46, + 425, + 288, + 520 + ], + "type": "inline_equation", + "content": "(\\mathrm{M}3 - \\mathrm{Net}_a" + }, + { + "bbox": [ + 46, + 425, + 288, + 520 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 425, + 288, + 520 + ], + "type": "inline_equation", + "content": "\\mathrm{M}3 - \\mathrm{Net}_c)" + }, + { + "bbox": [ + 46, + 425, + 288, + 520 + ], + "type": "text", + "content": ". On DARN, M3-Net's performance is comparable to that of " + }, + { + "bbox": [ + 46, + 425, + 288, + 520 + ], + "type": "inline_equation", + "content": "\\mathrm{M}3 - \\mathrm{Net}_c" + }, + { + "bbox": [ + 46, + 425, + 288, + 520 + ], + "type": "text", + "content": ", which only has class-conditional attention modules. We speculate that this is due to discriminating attributes and classes is less challenging on single-label datasets than on multi-label attribute datasets." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 537, + 178, + 550 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 537, + 178, + 550 + ], + "spans": [ + { + "bbox": [ + 47, + 537, + 178, + 550 + ], + "type": "text", + "content": "4.3.3 Qualitative evaluations" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 557, + 287, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 557, + 287, + 689 + ], + "spans": [ + { + "bbox": [ + 46, + 557, + 287, + 689 + ], + "type": "text", + "content": "Figure 3 visualizes the two-granularity attentions learned by M3-Net. The attribute-conditional attention tends to focus on all regions that are likely to be associated with the attribute. For example, in the first row of Figure 3, the attention of attribute \"part\" involves areas covering various parts of the dress such as collar, belt area, and hemline (second image in the first row). On the contrary, the class-conditional attention tends to focus on class-specific regions in the image. For instance, class \"slit\" highlights the dress slit region (third image in the first row). The visualized attention is consistent with our hypothesis." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "type": "text", + "content": "Figure 4 presents examples of fine-grained fashion retrieval results on single-label and multi-label datasets. In" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 376, + 546, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 376, + 546, + 520 + ], + "spans": [ + { + "bbox": [ + 304, + 376, + 546, + 520 + ], + "type": "text", + "content": "the figure, we compared the results from our proposed M3-Net with those from MODC (the best-performing baseline). Figure 4 (a) shows that on single-label retrieval, M3-Net can better discriminate fine-grained visual features than MODC, leading to more accurate retrieval results on individual classes. Moreover, on multi-label retrieval, M3-Net is able to retrieve images containing multiple class labels. For example, when searching an image on attribute \"texture\" with both \"print\" and \"tribal\" class labels (last example in Figure 4), M3-Net accurately retrieves related images, while MODC retrieves many other printed textures that is not \"tribal\"." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 530, + 378, + 542 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 530, + 378, + 542 + ], + "spans": [ + { + "bbox": [ + 306, + 530, + 378, + 542 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 551, + 546, + 706 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 551, + 546, + 706 + ], + "spans": [ + { + "bbox": [ + 304, + 551, + 546, + 706 + ], + "type": "text", + "content": "We have proposed a multi-attribute multi-granularity multi-label network (M3-Net) for fine-grained fashion analysis. Our proposed architecture learns both attribute and class-level representations for a fashion image through a shared backbone and two sub-networks with attribute and class conditional attention modules. This design, together with a multi-granularity loss, allows the network to effectively learn discriminative representations while capturing the inter-dependencies among various visual elements in different granularities. Our experiments show that the proposed M3-Net sets new state-of-the-art performance on both single-label and multi-label benchmark datasets in the fine-grained fashion retrieval task." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11057" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "text", + "content": "[1] Kenan E Ak, Ashraf A Kassim, Joo Hwee Lim, and Jo Yew Tham. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops, pages 0-0, 2019." + } + ] + } + ], + "index": 2 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "11059" + } + ] + } + ], + "index": 4 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Learning Audio-Visual Source Localization via False Negative Aware Contrastive Learning/e5b67298-ac49-4b7c-9b93-510776d56f4c_content_list.json b/2023/Learning Audio-Visual Source Localization via False Negative Aware Contrastive Learning/e5b67298-ac49-4b7c-9b93-510776d56f4c_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..9c897b990596d1e8bacd4a721e4af0f6bef03e6f --- /dev/null +++ b/2023/Learning Audio-Visual Source Localization via False Negative Aware Contrastive Learning/e5b67298-ac49-4b7c-9b93-510776d56f4c_content_list.json @@ -0,0 +1,1210 @@ +[ + { + "type": "text", + "text": "Learning Audio-Visual Source Localization via False Negative Aware Contrastive Learning", + "text_level": 1, + "bbox": [ + 248, + 130, + 722, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Weixuan Sun $^{1,5}$ , Jiayi Zhang $^{2}$ , Jianyuan Wang $^{3}$ , Zheyuan Liu $^{1}$ , Yiran Zhong $^{4}$ , Tianpeng Feng $^{5}$ , Yandong Guo $^{5}$ , Yanhao Zhang $^{5}$ , Nick Barnes $^{1}$ $^{1}$ Australian National University, $^{2}$ Beihang University, $^{3}$ The University of Oxford, $^{4}$ Shanghai AI Lab, $^{5}$ OPPO Research Institute.", + "bbox": [ + 161, + 202, + 807, + 273 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 291, + 313, + 306 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Self-supervised audio-visual source localization aims to locate sound-source objects in video frames without extra annotations. Recent methods often approach this goal with the help of contrastive learning, which assumes only the audio and visual contents from the same video are positive samples for each other. However, this assumption would suffer from false negative samples in real-world training. For example, for an audio sample, treating the frames from the same audio class as negative samples may mislead the model and therefore harm the learned representations (e.g., the audio of a siren wailing may reasonably correspond to the ambulances in multiple images). Based on this observation, we propose a new learning strategy named False Negative Aware Contrastive (FNAC) to mitigate the problem of misleading the training with such false negative samples. Specifically, we utilize the intra-modal similarities to identify potentially similar samples and construct corresponding adjacency matrices to guide contrastive learning. Further, we propose to strengthen the role of true negative samples by explicitly leveraging the visual features of sound sources to facilitate the differentiation of authentic sounding source regions. FNAC achieves state-of-the-art performances on Flickr-SoundNet, VGG-Sound, and AVSBench, which demonstrates the effectiveness of our method in mitigating the false negative issue. The code is available at https://github.com/OpenNLPLab/FNAC_AVL.", + "bbox": [ + 76, + 323, + 473, + 717 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 744, + 209, + 762 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "When hearing a sound, humans can naturally imagine the visual appearance of the source objects and locate them in the scene. This demonstrates that audio-visual correspondence is an important ability for scene understanding. Given that unlimited paired audio-visual data exists in nature, there is an emerging interest in developing multi-modal systems with audio-visual understanding abl", + "bbox": [ + 75, + 770, + 468, + 878 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/2d032ca1ccbd37fec2429de14bc9c3ffdc0962911c5cdd7a9c3efc0a14a525e3.jpg", + "image_caption": [ + "Figure 1. False negative in audio-visual contrastive learning. Audio-visual pairs with similar contents are falsely considered as negative samples to each other and pushed apart in the shared latent space, which we find would affect the model performance." + ], + "image_footnote": [], + "bbox": [ + 524, + 289, + 864, + 426 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ity. Various audio-visual tasks have been studied, including sound source localization [8, 19–21, 26–28], audio-visual event localization [32, 33, 35, 39], audio-visual video parsing [11, 18, 31] and audio-visual segmentation [37, 38]. In this work, we focus on unsupervised visual sound source localization, with the aim of localizing the sound-source objects in an image using its paired audio clip, but without relying on any manual annotations.", + "bbox": [ + 496, + 521, + 892, + 643 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The essence of unsupervised visual sound source localization is to leverage the co-occurrences between an audio clip and its corresponding image to extract representations. A major part of existing methods [8, 19–21, 28] formulates this task as contrastive learning. For each image sample, its paired audio clip is viewed as the positive sample, while all other audio clips are considered as negative. Likewise, each audio clip considers its paired image as positive and all others as negative. As such, the Noise Contrastive Estimation (NCE) loss [24, 30] is used to perform instance discrimination by pushing closer the distance between a positive audio-image pair, while pulling away any negative pairs. However, the contrastive learning scheme above suffers from the issue of false negatives during training, i.e., audio/image samples that belong to the semantically-matched class but are not regarded as a positive pair (due to the lack of manual labeling). A typical example is shown", + "bbox": [ + 496, + 643, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Indicates equal contribution", + "bbox": [ + 94, + 886, + 250, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "6420", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "in Fig. 1. Research shows [4, 16, 29, 36] that these false negatives will lead to contradictory objectives and harm the representation learning.", + "bbox": [ + 75, + 90, + 468, + 136 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Motivated by this observation, we assess the impact of false negatives in real-world training. We discover that with a batch size of 128, around $40\\%$ of the samples in VGG-Sound [9] will encounter at least one false negative sample during training. We then validate that false negatives indeed harm performance by artificially increasing the proportion of false negatives during training, and observing a noticeable performance drop. To make matters worse, larger batch sizes are often preferred in contrastive learning [24], but it may inadvertently increase the number of false negative samples during training and affect representation quality.", + "bbox": [ + 75, + 137, + 468, + 303 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To this end, we propose a false-negative aware audio-visual contrastive learning framework (FNAC), where we employ the intra-modal similarities as weak supervision. Specifically, we compute pair-wise similarities between all audio clips in a mini-batch without considering the visual to form an audio intra-modal adjacency matrix. Likewise, in the visual modality, we obtain an image adjacency matrix. We found that the adjacency matrices effectively identify potential samples of the same class within each modality (Fig. 4). The information can then be used to mitigate the false negatives and enhance the effect of true pairings.", + "bbox": [ + 75, + 303, + 467, + 469 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Specifically, we propose two complementary strategies: 1) FNS for False Negatives Suppression, and 2) TNE for True Negatives Enhancement. First, when optimizing the NCE loss, FNS regularizes the inter-modal and intra-modal similarities. Intrinsically, intra-modal adjacency explores potential false negatives by the similarity intensities and the pulling forces applied to these false negatives are canceled accordingly. Furthermore, we introduce TNE to emphasize the true negative influences in a region-wise manner, which in turn reduces the effect of false negative samples as well. We adopt the audio adjacency matrix to identify dissimilar samples, i.e., true negatives. Intuitively, dissimilar (true negative) sounds correspond to distinct regions, so the localized regions across the identified true negatives are regularized to be different. Such a mechanism encourages the model to discriminate genuine sound-source regions and suppress the co-occurring quiet objects. we conduct extensive analysis to demonstrate the effectiveness of our proposed method and report competitive performances across different settings and datasets. In summary, our main contributions are:", + "bbox": [ + 75, + 470, + 467, + 785 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We investigate the false negative issue in audio-visual contrastive learning. We quantitatively validate that this issue occurs and harms the representation quality.", + "- We exploit intra-modal similarities to identify potential false negatives and introduce FNS to suppress their impact." + ], + "bbox": [ + 94, + 797, + 467, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- We propose TNE, which emphasizes true negatives using different localization results between the identified true negatives, thus encouraging more discriminative sound source localizations.", + "bbox": [ + 517, + 90, + 890, + 148 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 167, + 640, + 184 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "False Negatives in Contrastive Learning. Typical contrastive learning employs instance discrimination [34] as a pretext task, in which two augmented views of the same image are considered as positive pairs, while views of all other images are treated as negative pairs, regardless of semantic similarities. Such a scheme inevitably suffers from the False Negatives issue [10, 13, 16, 36], which indicates that instances sharing the same semantic concepts are falsely treated as negatives, thus misleading model learning. Based on this, some works attempt to incorporate similar instances into model training to eliminate the impact of false negatives. For example, Zheng et al. [36] model a nearest neighbor graph for each batch of instances and execute a KNN-based multi-crop strategy to detect false negatives. Similarly, Dwibedi et al. [13] sample nearest neighbors from the dataset and treat them as positives for contrastive learning. More recently, [16] and [10] study how to identify false negatives without class labels and explicitly remove detected false negatives by two strategies, elimination and attraction, to improve contrastive loss. Other works use clustering-based methods to encode semantic structures [5, 7, 17] and then perform contrastive learning on these semantically similar cluster centers. In this paper, we propose and explore a similar problem in self-supervised audio-visual learning.", + "bbox": [ + 496, + 195, + 890, + 571 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Self-Supervised Sound Source Localization. Sound source localization aims to learn to locate sound-source regions in videos. Recent approaches extensively leverage contrastive learning based on audiovisual correspondence to address this issue. For example, [2, 3, 28] adopt a dual-stream architecture to extract unimodal features respectively and then calculate a contrastive loss to update the audiovisual network. The final localization map is usually obtained by calculating the cosine similarity between audio and visual features. Following the paradigm, Mo et al. [21] further propose an object-guided localization (OGL) module, an extra pre-trained visual encoder, to introduce visual priors into the localization results. Nevertheless, these works assume that the paired audio-visual signals are regularly aligned and all mismatched samples are heterogeneous. As aforementioned, the assumption ignores the semantic similarities between samples. Accordingly, Chen et al. [8] incorporate explicitly background regions with low correlation to the given audio into the framework and regard them as hard negatives. In a slightly different task", + "bbox": [ + 496, + 598, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "6421", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/f71a7b9b860136bb7e5a07e79031e6df49ba0d49008e031c5582caaf0858df6a.jpg", + "image_caption": [ + "Figure 2. Impact of false negatives on audio-visual representation learning. We adopt Consensus Intersection over Union (CIoU) [28] as an evaluation metric (higher is better) and report results on FlickrSoundNet [6] and VGG-SS [9] test sets, depicted by blue and brown, respectively. An obvious performance decline is observed as the proportion of false negative samples increases." + ], + "image_footnote": [], + "bbox": [ + 106, + 92, + 441, + 242 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "setting of audio-visual instance discrimination, false negative issues are also investigated. [23] detects false negatives by defining sets of positive and negative samples via cross-modal agreement, where positive samples are defined as similar samples in both modalities. [22] considers both false positive and false negative issues. For false negatives, they estimate the similarity across instances to compute a soft target distribution over instances so the contributions of false negatives are down-weighted. One work that explores a similar problem to us is [29], which treats top-K semantically similar audio-visual pairs as hard positives and explicitly integrates them into the contrastive loss. Unfortunately, this method relies on manually selected hypermeters K and a hard threshold. Unlike the previous methods, this paper uses intra-modal adjacency matrices to adaptively detect false negatives and eliminate their impact.", + "bbox": [ + 75, + 361, + 472, + 603 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 616, + 168, + 631 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we first investigate the problem raised by false negative samples in Sec. 3.1, and then propose to mitigate the problem. From two aspects, without supervision we identify the false negative samples to explicitly suppress them in training (Sec. 3.2), and use region-wise comparing learning to enhance the roles of true negative samples which hence relatively suppresses false negatives (Sec. 3.2).", + "bbox": [ + 75, + 642, + 468, + 748 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Revisiting Audio-visual Contrasting Learning", + "text_level": 1, + "bbox": [ + 76, + 756, + 464, + 773 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Various methods for audio-visual localization [18,21,28] employ a contrastive learning framework, in a manner of instance discrimination. Arguably, it assumes the audio-visual scenes from different videos are distinctive. Therefore the paired audio and image from the same video are considered a positive pair while the samples (audio or image) from other pairs are regarded as negatives. Specifically, we denote an audio-visual dataset as $\\mathcal{D} \\in \\{(a_i, v_i), i \\in$", + "bbox": [ + 75, + 779, + 470, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "$[0,n)\\}$ , where $(a_i,v_i)$ represents a sample with paired audio-visual content. Usually, a two-stream network is used to encode audio and visual signals and then map them into a shared latent space. The audio and visual representations extracted from $(a_i,v_i)$ are denoted as $Z_{i}^{a}\\in \\mathbb{R}^{1\\times d}$ and $Z_{i}^{v}\\in \\mathbb{R}^{1\\times d}$ with $d$ as feature dimension. Ideally, $Z_{i}^{a}$ and $Z_{i}^{v}$ represent the same semantic concept from the visual and audio perspectives, e.g., playing the drum. The optimization objective of contrastive learning is to maximize the similarity between audio and visual representations from the same video while minimizing the similarity between features from different videos. Mathematically, it can be formulated in a modal-symmetric way for a pair $(a_i,v_i)$ as:", + "bbox": [ + 498, + 90, + 890, + 287 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {\\text {c o n t r a s t . i}} = - \\log \\frac {\\exp \\left[ \\frac {1}{\\tau} \\operatorname {s i m} \\left(Z _ {i} ^ {a} , Z _ {i} ^ {v}\\right) \\right]}{\\sum_ {j} ^ {b} \\exp \\left[ \\frac {1}{\\tau} \\operatorname {s i m} \\left(Z _ {i} ^ {a} , Z _ {j} ^ {v}\\right) \\right]} \\\\ - \\log \\frac {\\exp \\left[ \\frac {1}{\\tau} \\operatorname {s i m} \\left(Z _ {i} ^ {v} , Z _ {i} ^ {a}\\right) \\right]}{\\sum_ {j} ^ {b} \\exp \\left[ \\frac {1}{\\tau} \\operatorname {s i m} \\left(Z _ {i} ^ {v} , Z _ {j} ^ {a}\\right) \\right]}, \\tag {1} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 534, + 294, + 890, + 377 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\tau$ is a temperature hyper-parameter, $b$ denotes batch size and sim represents the similarity function. Intuitively, this loss implies that each audio feature $Z_{i}^{a}$ is pushed close to its paired visual feature $Z_{i}^{v}$ in the shared latent space, while pulled apart from the rest $(b - 1)$ visual features $Z_{j,j\\neq i}^{v}$ . However, as discussed, there exist $\\hat{Z}_j^a$ and/or $\\hat{Z}_j^v$ that are semantically similar to $(Z_i^a,Z_i^v)$ , i.e., false negatives. In this situation, forcing $\\mathrm{sim}(Z_i^a,\\hat{Z}_j^v)$ or $\\mathrm{sim}(Z_i^v,\\hat{Z}_j^a)$ to be small might perplex the model training and lead to a non-optimal representation.", + "bbox": [ + 498, + 383, + 890, + 536 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Impact of False Negatives. Based on this observation, we conduct several pilot experiments to verify the issue of false negatives and their influence on audio-visual representation learning. For simplification, we reasonably assume that samples that share the same manually labeled category are False Negatives. Firstly, we examine the data distribution during the training procedure. We find that over $39.27\\%$ samples suffer from at least one false negative sample when training with a batch size of 128 on the VGG-Sound dataset [9] covering 309 categories. This ratio will undoubtedly increase when employing bigger batch sizes or fewer categories. Secondly, we examine how the false negative issue might affect audio-visual localization performance. Following prior works [8, 21], we adopt ResNet-18 as the backbone to encode audio and visual features and a standard NCE loss [24] is used. In particular, we manually substitute the true negatives with false negatives in the training samples. As shown in Fig 2, when the false negative rate is progressively increased, a significant performance decline is found, indicating that the model is perplexed by these similar samples. The experiments above demonstrate that false negatives substantially impact the model quality and cannot be disregarded.", + "bbox": [ + 496, + 553, + 890, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "6422", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/49d0e5bd7f38d374699852d5cc8ad2482079dd9aeb24b5b401a30bda6842ba0f.jpg", + "image_caption": [ + "Figure 3. An overview of False Negative Suppression (FNS). The main optimization objective is NCE [24] loss on audio-visual pairs. The audio adjacency matrix and visual adjacency matrix are respectively constructed to suppress false negatives by regularizing NCE loss." + ], + "image_footnote": [], + "bbox": [ + 230, + 90, + 733, + 239 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/066a33f2c98d9ff38a772814ff483ebfd51d9dab4e58e87312f1eebfdef90a98.jpg", + "image_caption": [ + "Figure 4. Qualitative samples of the found potential false negatives in visual and audio modalities. We report the nearest sample for every anchor. For the audio modality, we show the corresponding images here." + ], + "image_footnote": [], + "bbox": [ + 205, + 304, + 764, + 412 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Mitigating False Negatives in Audio Visual Learning", + "text_level": 1, + "bbox": [ + 76, + 477, + 470, + 508 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As discussed in Sec. 3.1, we prove that the unpaired positive samples (i.e., false negatives) existed in every minibatch that may harm the representations. Correspondingly, we propose to solve this problem by FNAC with two complementary methods, False Negatives Suppression (FNS) and True Negatives Enhancement (TNE). For the same goal of mitigating the false negative issue, FNS identifies the false negative samples and regularizes to reduce their effects, while TNE enhances the contribution of true negatives by region-wise comparison, which also inadvertently suppresses false negatives. Both methods can be seamlessly integrated into the audio-visual contrastive framework as regularization terms.", + "bbox": [ + 75, + 516, + 468, + 712 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "FNS: False Negatives Suppression. To suppress the false negative effects, two challenges are posed. First, distinguishing the potential false negative samples within the current mini-batch without extra supervision such as class labels. Second, eliminating the misleading effects of the identified false negatives.", + "bbox": [ + 75, + 734, + 468, + 824 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For the first challenge, we propose to leverage the unimodal feature representations to calculate pair-wise sample similarities, i.e., adjacency matrix. As shown in Fig. 3, the audio clips are fed into an audio encoder to obtain audio features $Z^{a} \\in \\mathbb{R}^{b \\times d}$ , then we calculate a dot product with", + "bbox": [ + 75, + 825, + 468, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$(Z^{a})^{T}$ followed by a row-wise softmax to obtain the pairwise self-similarity matrix $S^{a} \\in \\mathbb{R}^{b \\times b}$ , i.e., the audio adjacency matrix. Likewise, we average-pool the image features and obtain a visual adjacency matrix $S^{v} \\in \\mathbb{R}^{b \\times b}$ . Such adjacency matrices encode pair-wise similarities across a batch without considering inter-modal connection. For each audio-visual sample, we show its nearest sample by querying the adjacency matrices, as shown in Fig 4. It indicates that intra-modal adjacency matrices can effectively identify potential class-matched samples.", + "bbox": [ + 496, + 477, + 892, + 630 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Regarding the second challenge, we propose to impose intra-modal adjacency as a soft supervision signal for inter-modal contrastive learning, i.e., audio-visual similarities should be statistically consistent with the intramodal similarities. In other words, if two scenes are close, their audio features similarity value $\\mathrm{sim}(Z_i^a,Z_j^a)$ should be high, the visual similarity $\\mathrm{sim}(Z_i^v,Z_j^v)$ should match, and the cross-modal similarities $\\mathrm{sim}(Z_i^a,Z_j^v)$ or $\\mathrm{sim}(Z_i^v,Z_j^a)$ should also show consistency. Therefore, we leverage intramodal similarity as a supervision signal for audio-visual contrastive learning. Technically, we could utilize hard thresholds to achieve pseudo labels from intra-modal similarity like [8, 29, 36], which can serve to identify potential false negatives samples or areas. However, such methods require parameter tuning, and misassigned labels can exacerbate the false-negative problem. Differently, we propose FNS that directly regularizes the similarity scores. For a", + "bbox": [ + 496, + 643, + 893, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "6423", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/294c38639258ba3917471b7cc56233dc259609492e12634cfb807a6003a31404.jpg", + "image_caption": [ + "Figure 5. An overview of True Negative Enhancement (TNE). The visual features from localized regions are extracted to construct a sound-source visual feature adjacency matrix. The audio adjacency matrix is used to regularize the sound-source visual feature adjacency matrix to enhance true negatives." + ], + "image_footnote": [], + "bbox": [ + 230, + 88, + 723, + 244 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "sample $i$ , its optimization objective is formulated as:", + "bbox": [ + 76, + 334, + 423, + 349 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {F N S} - 1} = \\frac {1}{b} \\sum_ {j} ^ {b} \\mathcal {L} _ {\\text {d i s t}} \\left(\\operatorname {s i m} \\left(Z _ {i} ^ {a}, Z _ {j} ^ {v}\\right), \\operatorname {s i m} \\left(Z _ {i} ^ {a}, Z _ {j} ^ {a}\\right)\\right) \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 88, + 359, + 468, + 404 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {F N S} - 2} = \\frac {1}{b} \\sum_ {j} ^ {b} \\mathcal {L} _ {\\text {d i s t}} \\left(\\operatorname {s i m} \\left(Z _ {i} ^ {a}, Z _ {j} ^ {v}\\right), \\operatorname {s i m} \\left(Z _ {i} ^ {v}, Z _ {j} ^ {v}\\right)\\right) \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 88, + 406, + 468, + 449 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For an audio sample $a_i$ , the NCE loss $L_{\\text{contrast\\_i}}$ in Eq. 1 pushes all negatives away by encouraging $\\sin(Z_i^a, Z_j^v)_{j \\in [0,n), j \\neq i}$ to be close to 0, whereas FNS pulls back false negatives to suppress their effects. The suppression intensity corresponds to the values of $\\sin(Z_i^a, Z_j^a)$ and $\\sin(Z_i^v, Z_j^v)$ . In Eq. 3, the visual contrastive loss is calculated symmetrically. In practice, we calculate L1 distances between the inter-modal contrastive matrix and intra-modal adjacency matrices as shown in Fig. 3, so all pair-wise similarities are considered. Such a regularization term yields a parameter-free process so that we do not need to choose a hard threshold to determine the real false negatives, as the false negative effects can be adaptively regularized.", + "bbox": [ + 75, + 459, + 472, + 656 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "TNE: True Negatives Enhancement. To further reduce the misleading effect of false negatives, we propose to enhance the contribution of true negatives by region-wise comparison. As opponents, the impact of true negatives and that of false negatives are relative, so if the role of true negatives is raised, the role of false negatives would be suppressed. To improve the effect of true negatives in audio-visual learning, we turn back to its core concept, i.e., that the sound source objects are different both audibly and visually between the true negatives. Therefore, it is straightforward to put a particular emphasis on the possible regions of genuine sound-emitting objects.", + "bbox": [ + 75, + 672, + 468, + 854 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Specifically, we localize the sound-source objects by paired audio-visual samples, pop up their regional visual features, and encourage those of true negative samples to", + "bbox": [ + 75, + 854, + 470, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "be pulled away. The process is called true negative enhancement (TNE). It is worth noting that similar regularizations have been mentioned but disregarded by previous methods [8,21,29] because they did not distinguish the true negatives and false negatives samples.", + "bbox": [ + 496, + 334, + 890, + 409 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We show the paradigm of TNE in Fig. 5. Given an audio-visual pair $(a_i, v_i)$ , we obtain its localization result and use the localization map as a mask to extract the localized visual representation $Z_i^s \\in \\mathbb{R}^{d \\times h \\times w}$ , where $s$ indicates it is sounding region visual representation. In other words, $Z_i^s$ denotes the visual features that are aligned with the paired audio features. Then, consider another arbitrary audio-visual pair $(a_j, v_j)$ which localizes visual features $Z_j^s$ . If $a_i$ and $a_j$ are semantically different, i.e., $a_j$ is a true negative of $a_i$ , then the $Z_i^s$ should be dissimilar to $Z_j^s$ . It encourages the model to focus on different pixels so as to mine discriminative visual features according to the audio similarities. To leverage such a constraint in practice, we regularize the audio adjacency matrix and the similarities between the sounding region visual features. Formally, the TNE regularization is:", + "bbox": [ + 496, + 409, + 892, + 651 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {T N E}} = \\frac {1}{b} \\sum_ {j} ^ {b} \\mathcal {L} _ {\\text {d i s t}} \\left(\\operatorname {s i m} \\left(Z _ {i} ^ {a}, Z _ {j} ^ {a}\\right), \\operatorname {s i m} \\left(Z _ {i} ^ {s}, Z _ {j} ^ {s}\\right)\\right) \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 516, + 672, + 890, + 715 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "FNS and TNE are two general mechanisms for multimodal contrastive learning. FNS adopts audio and visual adjacency matrices to explore the potential false negatives and suppress their misleading effects on the NCE loss. TNE uses audio adjacency to discriminate the sound-source localization so the model tends to discover the genuine sound sources. Both methods can be seamlessly integrated with the existing contrastive learning framework as extra regularization terms. Our final optimization objective for the $i$ -th sample pair is:", + "bbox": [ + 496, + 723, + 893, + 875 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {i} = \\mathcal {L} _ {\\text {c o n t r a s t . i}} + \\alpha \\mathcal {L} _ {\\mathrm {F N S} _ {- 1}} + \\beta \\mathcal {L} _ {\\mathrm {F N S} _ {- 2}} + \\gamma \\mathcal {L} _ {\\mathrm {T N E}} \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 521, + 885, + 890, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "6424", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/eea832fbd6fc91cb2bf22b31db6c44fc4365456770245f66a0e7f6392e733dea.jpg", + "table_caption": [ + "Table 1. Quantitative results of the model trained with Flickr 10k and 144k. Note that 'EZ-VSL + OGL' corresponds to the main results reported in [21]. 'EZ-VSL' indicates our reproduced results without OGL, which are not reported in [21]. We reproduce the results with the trained weights and code provided by [21]." + ], + "table_footnote": [], + "table_body": "
Train setMethodFlickr CIoU(%)Flickr AUC(%)VGG-SS CIoU(%)VGG-SS AUC(%)
Flickr 10kAttention10k [28]43.6044.90--
CoursetoFine [26]52.2049.60--
AVObject [1]54.6050.40--
LVS [8]58.2052.50--
EZ-VSL* [21]62.2454.7419.8630.96
Ours84.3363.2635.2738.00
EZ-VSL + OGL [21]81.9362.5837.6139.21
Ours + OGL84.7364.3440.9740.38
Flickr 144kAttention10k [28]66.0055.80--
DMC [15]67.1056.80--
LVS [8]69.9057.30--
HardPos [29]75.2059.70--
EZ-VSL* [21]72.6958.7030.2735.92
Ours78.7159.3333.9337.29
EZ-VSL + OGL [21]83.1363.0641.0140.23
Ours + OGL83.9363.0641.1040.44
", + "bbox": [ + 181, + 141, + 792, + 345 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\alpha, \\beta, \\gamma$ are hyperparameters.", + "bbox": [ + 76, + 363, + 312, + 378 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 393, + 209, + 409 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Experimental Settings", + "text_level": 1, + "bbox": [ + 76, + 417, + 284, + 434 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets We train our audio-visual localization model on two datasets: Flickr SoundNet [6] and VGG-Sound [9]. Flickr SoundNet contains 2 million unconstrained videos from Flickr. For a fair comparison with the existing methods [8, 20, 21, 29], we conduct the training on two subsets of 10k and 144k paired samples from Flicker SoundNet. VGG-Sound includes 200k video clips from 309 classes. We also train on two subsets of 10k and 144k paired samples following the convention.", + "bbox": [ + 75, + 441, + 468, + 575 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Localization performances are measured on four benchmarks, Flickr [6], VGG-SS [9], Heard 110 and AVS-Bench [38]. The Flickr test set has 250 audio-visual pairs with manually labeled bounding boxes. VGG-SS is more challenging with 5,000 audio-visual pairs over 220 categories. Heard 110 is another subset of VGG-Sound to test the open-set learning ability. Its train set has 110 classes and the val set has another disjoint 110 unheard/unseen classes. Finally, AVSBench [38] is a recently proposed audio-visual dataset with 5,356 videos over 23 classes. It provides pixelwise labels for fine-grained localization evaluation.", + "bbox": [ + 75, + 578, + 470, + 744 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation Details We implement our method with PyTorch. The images are resized and randomly cropped into $224 \\times 224$ resolution, together with random horizontal flipping. The audio inputs are extracted from 3 seconds of audio clips and converted into log spectrogram maps. We also apply audio augmentation including Frequency mask and Time mask [25]. For both visual and audio encoders, we adopt ResNet18 [14] and the visual encoder is pretrained on ImageNet-1k [12]. The model is optimized for", + "bbox": [ + 75, + 763, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "30 epochs with Adam using a learning rate of $10^{-4}$ and a weight decay of $10^{-4}$ . To achieve a stable representation, we warm up the network with only NCE loss for 3 epochs, then integrate our regularization for the remaining epochs.", + "bbox": [ + 498, + 362, + 890, + 425 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Comparison on Flickr-SoundNet and VGG-SS", + "text_level": 1, + "bbox": [ + 498, + 433, + 890, + 450 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Flickr-SoundNet We train our model on Flickr 10k and 144k and report performances in Table 1. FNAC achieves superior performances over previous methods on both Flickr and VGG-SS test sets. Notably, compared to previous state-of-the-art EZ-VSL [21] on the Flickr test set, FNAC achieves a striking improvement of $22.09\\%$ CIOU with 10k training samples and $6.02\\%$ CIOU with 144k training samples. When tested on the more challenging VGGSS, FNAC also outperforms EZ-VSL by $15.41\\%$ CIOU and $3.49\\%$ CIOU respectively. Finally, Object-Guided localization (OGL) is a post-processing strategy that adopts pure visual-based localization results to refine audio-visual localization. For a fair comparison, we integrate FNAC with OGL to compare with EZ-VSL which also uses OGL. As shown, FNAC also outperforms EZ-VSL in most cases.", + "bbox": [ + 496, + 455, + 890, + 684 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "VGG-SS Performance of the model trained on VGG-Sound 10k and 144k is reported in Table 2. FNAC also beats all previous methods with a clear margin. For example, on the VGG-SS test set, we outperform EZ-VSL by $11.45\\%$ CIOU with 10k and $5.31\\%$ CIOU with 144k.", + "bbox": [ + 496, + 703, + 890, + 777 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We highlight two results as demonstrated in Table 1 and Table 2. First, FNAC achieves similar results on $10\\mathrm{k}$ and $144\\mathrm{k}$ training sets in both Flickr SoundNet and VGGSound, which is not observed in previous models. We believe that small-scale datasets (Flickr $10\\mathrm{k}$ , VGG-Sound $10\\mathrm{k}$ ) have fewer semantic classes and will encounter more false negatives during training, so previous methods have substantial performance gaps between the $10\\mathrm{k}$ and $144\\mathrm{k}$ training", + "bbox": [ + 496, + 779, + 893, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "6425", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/cdc1a934732517c888e23707e726f2c74eaa0c138779c8cc55c77df3c9f95d10.jpg", + "table_caption": [ + "Table 2. Quantitative results of models trained with VGG-SS 10k and 144k." + ], + "table_footnote": [], + "table_body": "
Train setMethodFlickr CIoU(%)Flickr AUC(%)VGG-SS CIoU(%)VGG-SS AUC(%)
VGGSound 10kLVS [8]61.8053.60--
EZ-VSL* [21]63.8554.4425.8433.68
Ours85.7463.6637.2938.99
EZ-VSL + OGL [21]78.7161.5338.7139.80
Ours + OGL82.1363.6440.6940.42
VGGSound 144kAttention10k [28]--18.5030.20
DMC [15]--29.1034.80
AVObject [1]--29.7035.70
LVS [8]73.5059.0034.4038.20
HardPos [29]76.8059.2034.6038.00
EZ-VSL [21]79.5161.1734.3837.70
Ours84.7363.7639.5039.66
EZ-VSL + OGL [21]83.9463.6038.8539.54
Ours + OGL85.1464.3041.8540.80
", + "bbox": [ + 179, + 114, + 794, + 295 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/2325884eff19fcd2fa1e9dae338b2ddfb9cf06e6b443ecae8189286b77ae8aba.jpg", + "table_caption": [ + "Table 3. Quantitative results on Heard 110 and Unheard 110. For a fair comparison, the results of EZ-VSL [21] and ours are integrated with the OGL module." + ], + "table_footnote": [], + "table_body": "
Test SetMethodCIoU(%)AUC(%)
Heard 110LVS [8]28.9036.20
EZ-VSL [21]37.2538.97
Ours39.5439.83
Unheard 110LVS [8]26.3034.70
EZ-VSL [21]39.5739.60
Ours42.9141.17
", + "bbox": [ + 125, + 369, + 424, + 465 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "sets. It indicates that FNAC can effectively address the false negative issue and has a strong ability for representation learning on small-scale datasets. Second, we show cross-dataset evaluation results in both tables, i.e., train on Flickr and test on VGG-SS or vice versa. FNAC achieves strong results and outperforms existing methods, which validates the cross-dataset generalization ability of FNAC. We show qualitative localization results in Fig. 6.", + "bbox": [ + 75, + 483, + 468, + 604 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Comparison on Heard 110 and AVSBench", + "text_level": 1, + "bbox": [ + 76, + 614, + 434, + 631 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Heard 110 To assess the generalization ability of FNAC in unseen/unheard audiovisual scenes, we conduct an open set experiment. We use the 70k samples covering 110 categories randomly sampled from VGGSound for training and then evaluate the model on the same 110 heard categories and another disjoint set with 110 unheard categories. As shown in Table 3, FNAC considerably outperforms previous methods, especially on Unheard 110 (42.91% vs. 39.57% of CIoU), which demonstrates the generalization ability of FNAC in unconstrained audio-visual data.", + "bbox": [ + 75, + 638, + 468, + 789 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "AVSbench AVSbench [38] is a newly proposed audiovisual segmentation benchmark with pixel-level annotations, which can be regarded as a fine-grained sound source localization task and used to accurately evaluate the localization ability of models. We directly perform a zero-shot evaluation on the AVSbench with metrics of mIoU and", + "bbox": [ + 75, + 809, + 470, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/8b7ccf5484e639c53e75d1838fb076ea1c8b5cd6a8cda12849dc5b15a8911e32.jpg", + "table_caption": [ + "Table 4. Zero-shot results on AVSBench S4 and MS3 [38]. All models are pretrained on VGGSound-144k dataset." + ], + "table_footnote": [], + "table_body": "
Test setMethodmIoUFScore
S4LVS23.69.251
EZ-VSL26.43.292
Ours27.15.314
MS3LVS18.54.174
EZ-VSL21.36.216
Ours21.98.225
", + "bbox": [ + 542, + 354, + 849, + 449 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/0f8221746c1ebf3f1721f35f145490b421321c05d21cb7b8e20cead5dad4a14c.jpg", + "table_caption": [ + "Table 5. Analysis of each component of the proposed FNAC. aud adj: audio adjacency matrix. img adj: image adjacency matrix." + ], + "table_footnote": [], + "table_body": "
FNSTNEFlickr CIoU(%)VGG-SS CIoU(%)
aud adjimg adj
77.9133.93
✓79.9135.85
✓81.9236.58
✓✓84.3336.92
✓81.1236.04
✓✓✓85.7437.29
", + "bbox": [ + 519, + 492, + 870, + 592 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "F-Score in two settings, Single Sound Source Segmentation (S4) and Multiple Sound Source Segmentation (MS3), without any fine-tuning. The results are reported in Table 4. The proposed method achieves outstanding performance on both S4 and MS3 settings, e.g., $27.15\\%$ and $21.98\\%$ mIoU when trained on VGGSound 144k. These results on the fine-grained localization benchmark validate the effectiveness of the TNE, which enables the model to discriminate authentic sound-source regions.", + "bbox": [ + 496, + 609, + 890, + 746 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Ablation Analysis of FNAC", + "text_level": 1, + "bbox": [ + 498, + 756, + 743, + 772 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We propose different regularization terms to guide audio-visual contrastive learning. In Table 5, we ablate each component individually. All results are obtained following the same hyperparameter setting on VGG-SS $10\\mathrm{k}$ and the baseline is trained with only NCE loss. First, the audio adjacency matrix and visual adjacency matrix are obtained in FNS to suppress the false negatives. We show that each adjacency matrix can improve the performances over the", + "bbox": [ + 496, + 780, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "6426", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3c38491ece96ba70245d9addb63d848af1d7d5d53f170f05794d1cc467c80ef0.jpg", + "image_caption": [ + "Figure 6. Visualization comparison on Flickr-SoundNet (left) and VGG-SS (right) test sets." + ], + "image_footnote": [], + "bbox": [ + 202, + 92, + 480, + 263 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/dc19afcddcd9dbd448ff4a0391ab6b86e069d234be21aae44bc8e3cfe68489b1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 490, + 93, + 767, + 263 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "baseline, which indicates that potential false negatives can be effectively suppressed in both audio and visual modalities. By combining the two adjacency matrices together, FNS achieves $84.33\\%$ CIoU on Flickr and $36.92\\%$ CIoU on VGG-SS. Second, by only deploying TNE, we achieve improved results over baseline (81.12% CIoU on Flickr and $36.04\\%$ CIoU on VGG-SS), indicating the effectiveness of TNE in enhancing true negatives. Finally, the combination of FNS and TNE achieves significant improvement over the baseline, showing the effectiveness of FNAC. We refer readers to supp. mat. for further ablation studies.", + "bbox": [ + 75, + 316, + 473, + 484 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5. Mining the Potential False Negatives", + "text_level": 1, + "bbox": [ + 76, + 506, + 393, + 523 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this section, we show quantitative and schematic analysis of the false negative mining ability of our method. Intuitively, a good audio-visual model should be able to generate similar feature representations for class matched samples. To validate this intuition, we construct a batch where all samples belong to the same category, i.e., all false negatives, and show the audio-visual similarity matrices of EZ-VSL [21] and ours in Fig. 7. As shown in the left, EZ-VSL only highlights the diagonal, since each audio feature is only similar to the paired image feature while all others are dissimilar despite all samples being from the same class. Differently, the similarity distribution of our matrix is more evenly spread as the majority of the samples are regarded as similar. It indicates that FNAC has implicitly learned semantically-aware features and clustered them in the latent space, so false negatives will be effectively identified as they are closer in terms of feature distance.", + "bbox": [ + 75, + 534, + 468, + 790 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Further, we show quantitative results of audio-visual similarities in Table 6. When the batch contains all true negatives, our average similarity score is lower than previous methods [8, 21]. When the batch contains all false negatives, our average similarity score is higher. The margin between the two similarities demonstrates our ability to distinguish false negatives and true negatives.", + "bbox": [ + 75, + 795, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c6c7b1babaa7784eda22c69796e87d12e55ed07dc3afb6ebf3de3bf4b1d4bd05.jpg", + "image_caption": [ + "Figure 7. Cross-modal similarity matrix predicted by EZ-VSL (left) and ours (right) when all samples in the batch belong to the same category, namely, they are false negatives of each other. All values are normalized between 0 to 1." + ], + "image_footnote": [], + "bbox": [ + 545, + 316, + 854, + 429 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/3dda753930d64ce813312b6a39a9444dc13816730a6be564c6b62d1295344305.jpg", + "table_caption": [ + "Table 6. Audio-visual similarities with different data. TN: all samples in the batch belong to different categories. FN: all samples in the batch belong to the same category." + ], + "table_footnote": [], + "table_body": "
MethodTN ↓FN ↑
LVS0.44840.5102
EZ-VS10.58580.5938
Ours0.38120.6554
", + "bbox": [ + 529, + 574, + 867, + 637 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 659, + 619, + 674 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we propose a simple yet effective strategy named FNAC to deal with the false negative issue in audio-visual sound source localization. We propose two complementary strategies to suppress false negatives (FNS) and enhance true negatives (TNE). The intra-modal adjacency matrices of audio and visual are generated to identify false negatives. Then two regularization terms are seamlessly incorporated with contrastive learning, which enable the model to learn semantic-aware features from audio-visual pairs. We show that FNAC can effectively mitigate the false negative issues and achieve state-of-the-art performance on several audio-visual localization benchmarks. We hope that our method can facilitate future research in audio-visual learning and other multi-modal tasks.", + "bbox": [ + 496, + 689, + 893, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "6427", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Triantafyllos Afouras, Andrew Owens, Joon Son Chung, and Andrew Zisserman. Self-supervised learning of audio-visual objects from video. In European Conference on Computer Vision, pages 208–224. Springer, 2020. 6, 7", + "[2] Relja Arandjelovic and Andrew Zisserman. Look, listen and learn. In Proceedings of the IEEE International Conference on Computer Vision, pages 609-617, 2017. 2", + "[3] Relja Arandjelovic and Andrew Zisserman. Objects that sound. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 8436-8444, 2021. 1" + ], + "bbox": [ + 78, + 90, + 468, + 810 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "6429", + "bbox": [ + 482, + 944, + 516, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Learning Audio-Visual Source Localization via False Negative Aware Contrastive Learning/e5b67298-ac49-4b7c-9b93-510776d56f4c_model.json b/2023/Learning Audio-Visual Source Localization via False Negative Aware Contrastive Learning/e5b67298-ac49-4b7c-9b93-510776d56f4c_model.json new file mode 100644 index 0000000000000000000000000000000000000000..7d8f661952bc2e7e570723cf0ce4e009b1a40568 --- /dev/null +++ b/2023/Learning Audio-Visual Source Localization via False Negative Aware Contrastive Learning/e5b67298-ac49-4b7c-9b93-510776d56f4c_model.json @@ -0,0 +1,1705 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.249, + 0.131, + 0.723, + 0.177 + ], + "angle": 0, + "content": "Learning Audio-Visual Source Localization via False Negative Aware Contrastive Learning" + }, + { + "type": "text", + "bbox": [ + 0.163, + 0.203, + 0.808, + 0.275 + ], + "angle": 0, + "content": "Weixuan Sun\\(^{1,5}\\), Jiayi Zhang\\(^{2}\\), Jianyuan Wang\\(^{3}\\), Zheyuan Liu\\(^{1}\\), Yiran Zhong\\(^{4}\\), Tianpeng Feng\\(^{5}\\), Yandong Guo\\(^{5}\\), Yanhao Zhang\\(^{5}\\), Nick Barnes\\(^{1}\\) \n\\(^{1}\\)Australian National University, \\(^{2}\\)Beihang University, \\(^{3}\\)The University of Oxford, \\(^{4}\\)Shanghai AI Lab, \\(^{5}\\)OPPO Research Institute." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.292, + 0.314, + 0.308 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.324, + 0.474, + 0.718 + ], + "angle": 0, + "content": "Self-supervised audio-visual source localization aims to locate sound-source objects in video frames without extra annotations. Recent methods often approach this goal with the help of contrastive learning, which assumes only the audio and visual contents from the same video are positive samples for each other. However, this assumption would suffer from false negative samples in real-world training. For example, for an audio sample, treating the frames from the same audio class as negative samples may mislead the model and therefore harm the learned representations (e.g., the audio of a siren wailing may reasonably correspond to the ambulances in multiple images). Based on this observation, we propose a new learning strategy named False Negative Aware Contrastive (FNAC) to mitigate the problem of misleading the training with such false negative samples. Specifically, we utilize the intra-modal similarities to identify potentially similar samples and construct corresponding adjacency matrices to guide contrastive learning. Further, we propose to strengthen the role of true negative samples by explicitly leveraging the visual features of sound sources to facilitate the differentiation of authentic sounding source regions. FNAC achieves state-of-the-art performances on Flickr-SoundNet, VGG-Sound, and AVSBench, which demonstrates the effectiveness of our method in mitigating the false negative issue. The code is available at https://github.com/OpenNLPLab/FNAC_AVL." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.746, + 0.21, + 0.763 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.771, + 0.47, + 0.879 + ], + "angle": 0, + "content": "When hearing a sound, humans can naturally imagine the visual appearance of the source objects and locate them in the scene. This demonstrates that audio-visual correspondence is an important ability for scene understanding. Given that unlimited paired audio-visual data exists in nature, there is an emerging interest in developing multi-modal systems with audio-visual understanding abl" + }, + { + "type": "image", + "bbox": [ + 0.526, + 0.29, + 0.865, + 0.427 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.446, + 0.892, + 0.504 + ], + "angle": 0, + "content": "Figure 1. False negative in audio-visual contrastive learning. Audio-visual pairs with similar contents are falsely considered as negative samples to each other and pushed apart in the shared latent space, which we find would affect the model performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.522, + 0.893, + 0.644 + ], + "angle": 0, + "content": "ity. Various audio-visual tasks have been studied, including sound source localization [8, 19–21, 26–28], audio-visual event localization [32, 33, 35, 39], audio-visual video parsing [11, 18, 31] and audio-visual segmentation [37, 38]. In this work, we focus on unsupervised visual sound source localization, with the aim of localizing the sound-source objects in an image using its paired audio clip, but without relying on any manual annotations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.645, + 0.895, + 0.903 + ], + "angle": 0, + "content": "The essence of unsupervised visual sound source localization is to leverage the co-occurrences between an audio clip and its corresponding image to extract representations. A major part of existing methods [8, 19–21, 28] formulates this task as contrastive learning. For each image sample, its paired audio clip is viewed as the positive sample, while all other audio clips are considered as negative. Likewise, each audio clip considers its paired image as positive and all others as negative. As such, the Noise Contrastive Estimation (NCE) loss [24, 30] is used to perform instance discrimination by pushing closer the distance between a positive audio-image pair, while pulling away any negative pairs. However, the contrastive learning scheme above suffers from the issue of false negatives during training, i.e., audio/image samples that belong to the semantically-matched class but are not regarded as a positive pair (due to the lack of manual labeling). A typical example is shown" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.251, + 0.9 + ], + "angle": 0, + "content": "*Indicates equal contribution" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6420" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.137 + ], + "angle": 0, + "content": "in Fig. 1. Research shows [4, 16, 29, 36] that these false negatives will lead to contradictory objectives and harm the representation learning." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.138, + 0.47, + 0.304 + ], + "angle": 0, + "content": "Motivated by this observation, we assess the impact of false negatives in real-world training. We discover that with a batch size of 128, around \\(40\\%\\) of the samples in VGG-Sound [9] will encounter at least one false negative sample during training. We then validate that false negatives indeed harm performance by artificially increasing the proportion of false negatives during training, and observing a noticeable performance drop. To make matters worse, larger batch sizes are often preferred in contrastive learning [24], but it may inadvertently increase the number of false negative samples during training and affect representation quality." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.304, + 0.468, + 0.47 + ], + "angle": 0, + "content": "To this end, we propose a false-negative aware audio-visual contrastive learning framework (FNAC), where we employ the intra-modal similarities as weak supervision. Specifically, we compute pair-wise similarities between all audio clips in a mini-batch without considering the visual to form an audio intra-modal adjacency matrix. Likewise, in the visual modality, we obtain an image adjacency matrix. We found that the adjacency matrices effectively identify potential samples of the same class within each modality (Fig. 4). The information can then be used to mitigate the false negatives and enhance the effect of true pairings." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.471, + 0.468, + 0.786 + ], + "angle": 0, + "content": "Specifically, we propose two complementary strategies: 1) FNS for False Negatives Suppression, and 2) TNE for True Negatives Enhancement. First, when optimizing the NCE loss, FNS regularizes the inter-modal and intra-modal similarities. Intrinsically, intra-modal adjacency explores potential false negatives by the similarity intensities and the pulling forces applied to these false negatives are canceled accordingly. Furthermore, we introduce TNE to emphasize the true negative influences in a region-wise manner, which in turn reduces the effect of false negative samples as well. We adopt the audio adjacency matrix to identify dissimilar samples, i.e., true negatives. Intuitively, dissimilar (true negative) sounds correspond to distinct regions, so the localized regions across the identified true negatives are regularized to be different. Such a mechanism encourages the model to discriminate genuine sound-source regions and suppress the co-occurring quiet objects. we conduct extensive analysis to demonstrate the effectiveness of our proposed method and report competitive performances across different settings and datasets. In summary, our main contributions are:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.798, + 0.468, + 0.844 + ], + "angle": 0, + "content": "- We investigate the false negative issue in audio-visual contrastive learning. We quantitatively validate that this issue occurs and harms the representation quality." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.856, + 0.468, + 0.901 + ], + "angle": 0, + "content": "- We exploit intra-modal similarities to identify potential false negatives and introduce FNS to suppress their impact." + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.798, + 0.468, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.092, + 0.892, + 0.15 + ], + "angle": 0, + "content": "- We propose TNE, which emphasizes true negatives using different localization results between the identified true negatives, thus encouraging more discriminative sound source localizations." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.169, + 0.642, + 0.185 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.196, + 0.892, + 0.573 + ], + "angle": 0, + "content": "False Negatives in Contrastive Learning. Typical contrastive learning employs instance discrimination [34] as a pretext task, in which two augmented views of the same image are considered as positive pairs, while views of all other images are treated as negative pairs, regardless of semantic similarities. Such a scheme inevitably suffers from the False Negatives issue [10, 13, 16, 36], which indicates that instances sharing the same semantic concepts are falsely treated as negatives, thus misleading model learning. Based on this, some works attempt to incorporate similar instances into model training to eliminate the impact of false negatives. For example, Zheng et al. [36] model a nearest neighbor graph for each batch of instances and execute a KNN-based multi-crop strategy to detect false negatives. Similarly, Dwibedi et al. [13] sample nearest neighbors from the dataset and treat them as positives for contrastive learning. More recently, [16] and [10] study how to identify false negatives without class labels and explicitly remove detected false negatives by two strategies, elimination and attraction, to improve contrastive loss. Other works use clustering-based methods to encode semantic structures [5, 7, 17] and then perform contrastive learning on these semantically similar cluster centers. In this paper, we propose and explore a similar problem in self-supervised audio-visual learning." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Self-Supervised Sound Source Localization. Sound source localization aims to learn to locate sound-source regions in videos. Recent approaches extensively leverage contrastive learning based on audiovisual correspondence to address this issue. For example, [2, 3, 28] adopt a dual-stream architecture to extract unimodal features respectively and then calculate a contrastive loss to update the audiovisual network. The final localization map is usually obtained by calculating the cosine similarity between audio and visual features. Following the paradigm, Mo et al. [21] further propose an object-guided localization (OGL) module, an extra pre-trained visual encoder, to introduce visual priors into the localization results. Nevertheless, these works assume that the paired audio-visual signals are regularly aligned and all mismatched samples are heterogeneous. As aforementioned, the assumption ignores the semantic similarities between samples. Accordingly, Chen et al. [8] incorporate explicitly background regions with low correlation to the given audio into the framework and regard them as hard negatives. In a slightly different task" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "6421" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.107, + 0.093, + 0.442, + 0.243 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.26, + 0.47, + 0.344 + ], + "angle": 0, + "content": "Figure 2. Impact of false negatives on audio-visual representation learning. We adopt Consensus Intersection over Union (CIoU) [28] as an evaluation metric (higher is better) and report results on FlickrSoundNet [6] and VGG-SS [9] test sets, depicted by blue and brown, respectively. An obvious performance decline is observed as the proportion of false negative samples increases." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.362, + 0.473, + 0.604 + ], + "angle": 0, + "content": "setting of audio-visual instance discrimination, false negative issues are also investigated. [23] detects false negatives by defining sets of positive and negative samples via cross-modal agreement, where positive samples are defined as similar samples in both modalities. [22] considers both false positive and false negative issues. For false negatives, they estimate the similarity across instances to compute a soft target distribution over instances so the contributions of false negatives are down-weighted. One work that explores a similar problem to us is [29], which treats top-K semantically similar audio-visual pairs as hard positives and explicitly integrates them into the contrastive loss. Unfortunately, this method relies on manually selected hypermeters K and a hard threshold. Unlike the previous methods, this paper uses intra-modal adjacency matrices to adaptively detect false negatives and eliminate their impact." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.617, + 0.169, + 0.632 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.643, + 0.47, + 0.749 + ], + "angle": 0, + "content": "In this section, we first investigate the problem raised by false negative samples in Sec. 3.1, and then propose to mitigate the problem. From two aspects, without supervision we identify the false negative samples to explicitly suppress them in training (Sec. 3.2), and use region-wise comparing learning to enhance the roles of true negative samples which hence relatively suppresses false negatives (Sec. 3.2)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.757, + 0.465, + 0.774 + ], + "angle": 0, + "content": "3.1. Revisiting Audio-visual Contrasting Learning" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Various methods for audio-visual localization [18,21,28] employ a contrastive learning framework, in a manner of instance discrimination. Arguably, it assumes the audio-visual scenes from different videos are distinctive. Therefore the paired audio and image from the same video are considered a positive pair while the samples (audio or image) from other pairs are regarded as negatives. Specifically, we denote an audio-visual dataset as \\(\\mathcal{D} \\in \\{(a_i, v_i), i \\in\\)" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.289 + ], + "angle": 0, + "content": "\\([0,n)\\}\\), where \\((a_i,v_i)\\) represents a sample with paired audio-visual content. Usually, a two-stream network is used to encode audio and visual signals and then map them into a shared latent space. The audio and visual representations extracted from \\((a_i,v_i)\\) are denoted as \\(Z_{i}^{a}\\in \\mathbb{R}^{1\\times d}\\) and \\(Z_{i}^{v}\\in \\mathbb{R}^{1\\times d}\\) with \\(d\\) as feature dimension. Ideally, \\(Z_{i}^{a}\\) and \\(Z_{i}^{v}\\) represent the same semantic concept from the visual and audio perspectives, e.g., playing the drum. The optimization objective of contrastive learning is to maximize the similarity between audio and visual representations from the same video while minimizing the similarity between features from different videos. Mathematically, it can be formulated in a modal-symmetric way for a pair \\((a_i,v_i)\\) as:" + }, + { + "type": "equation", + "bbox": [ + 0.535, + 0.295, + 0.892, + 0.378 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {\\text {c o n t r a s t . i}} = - \\log \\frac {\\exp \\left[ \\frac {1}{\\tau} \\operatorname {s i m} \\left(Z _ {i} ^ {a} , Z _ {i} ^ {v}\\right) \\right]}{\\sum_ {j} ^ {b} \\exp \\left[ \\frac {1}{\\tau} \\operatorname {s i m} \\left(Z _ {i} ^ {a} , Z _ {j} ^ {v}\\right) \\right]} \\\\ - \\log \\frac {\\exp \\left[ \\frac {1}{\\tau} \\operatorname {s i m} \\left(Z _ {i} ^ {v} , Z _ {i} ^ {a}\\right) \\right]}{\\sum_ {j} ^ {b} \\exp \\left[ \\frac {1}{\\tau} \\operatorname {s i m} \\left(Z _ {i} ^ {v} , Z _ {j} ^ {a}\\right) \\right]}, \\tag {1} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.384, + 0.892, + 0.537 + ], + "angle": 0, + "content": "where \\(\\tau\\) is a temperature hyper-parameter, \\(b\\) denotes batch size and sim represents the similarity function. Intuitively, this loss implies that each audio feature \\(Z_{i}^{a}\\) is pushed close to its paired visual feature \\(Z_{i}^{v}\\) in the shared latent space, while pulled apart from the rest \\((b - 1)\\) visual features \\(Z_{j,j\\neq i}^{v}\\). However, as discussed, there exist \\(\\hat{Z}_j^a\\) and/or \\(\\hat{Z}_j^v\\) that are semantically similar to \\((Z_i^a,Z_i^v)\\), i.e., false negatives. In this situation, forcing \\(\\mathrm{sim}(Z_i^a,\\hat{Z}_j^v)\\) or \\(\\mathrm{sim}(Z_i^v,\\hat{Z}_j^a)\\) to be small might perplex the model training and lead to a non-optimal representation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.554, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Impact of False Negatives. Based on this observation, we conduct several pilot experiments to verify the issue of false negatives and their influence on audio-visual representation learning. For simplification, we reasonably assume that samples that share the same manually labeled category are False Negatives. Firstly, we examine the data distribution during the training procedure. We find that over \\(39.27\\%\\) samples suffer from at least one false negative sample when training with a batch size of 128 on the VGG-Sound dataset [9] covering 309 categories. This ratio will undoubtedly increase when employing bigger batch sizes or fewer categories. Secondly, we examine how the false negative issue might affect audio-visual localization performance. Following prior works [8, 21], we adopt ResNet-18 as the backbone to encode audio and visual features and a standard NCE loss [24] is used. In particular, we manually substitute the true negatives with false negatives in the training samples. As shown in Fig 2, when the false negative rate is progressively increased, a significant performance decline is found, indicating that the model is perplexed by these similar samples. The experiments above demonstrate that false negatives substantially impact the model quality and cannot be disregarded." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6422" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.231, + 0.091, + 0.735, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.261, + 0.893, + 0.292 + ], + "angle": 0, + "content": "Figure 3. An overview of False Negative Suppression (FNS). The main optimization objective is NCE [24] loss on audio-visual pairs. The audio adjacency matrix and visual adjacency matrix are respectively constructed to suppress false negatives by regularizing NCE loss." + }, + { + "type": "image", + "bbox": [ + 0.206, + 0.305, + 0.765, + 0.414 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.424, + 0.893, + 0.455 + ], + "angle": 0, + "content": "Figure 4. Qualitative samples of the found potential false negatives in visual and audio modalities. We report the nearest sample for every anchor. For the audio modality, we show the corresponding images here." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.478, + 0.471, + 0.51 + ], + "angle": 0, + "content": "3.2. Mitigating False Negatives in Audio Visual Learning" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.517, + 0.47, + 0.713 + ], + "angle": 0, + "content": "As discussed in Sec. 3.1, we prove that the unpaired positive samples (i.e., false negatives) existed in every minibatch that may harm the representations. Correspondingly, we propose to solve this problem by FNAC with two complementary methods, False Negatives Suppression (FNS) and True Negatives Enhancement (TNE). For the same goal of mitigating the false negative issue, FNS identifies the false negative samples and regularizes to reduce their effects, while TNE enhances the contribution of true negatives by region-wise comparison, which also inadvertently suppresses false negatives. Both methods can be seamlessly integrated into the audio-visual contrastive framework as regularization terms." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.469, + 0.825 + ], + "angle": 0, + "content": "FNS: False Negatives Suppression. To suppress the false negative effects, two challenges are posed. First, distinguishing the potential false negative samples within the current mini-batch without extra supervision such as class labels. Second, eliminating the misleading effects of the identified false negatives." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.47, + 0.903 + ], + "angle": 0, + "content": "For the first challenge, we propose to leverage the unimodal feature representations to calculate pair-wise sample similarities, i.e., adjacency matrix. As shown in Fig. 3, the audio clips are fed into an audio encoder to obtain audio features \\( Z^{a} \\in \\mathbb{R}^{b \\times d} \\), then we calculate a dot product with" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.478, + 0.893, + 0.631 + ], + "angle": 0, + "content": "\\((Z^{a})^{T}\\) followed by a row-wise softmax to obtain the pairwise self-similarity matrix \\(S^{a} \\in \\mathbb{R}^{b \\times b}\\), i.e., the audio adjacency matrix. Likewise, we average-pool the image features and obtain a visual adjacency matrix \\(S^{v} \\in \\mathbb{R}^{b \\times b}\\). Such adjacency matrices encode pair-wise similarities across a batch without considering inter-modal connection. For each audio-visual sample, we show its nearest sample by querying the adjacency matrices, as shown in Fig 4. It indicates that intra-modal adjacency matrices can effectively identify potential class-matched samples." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.645, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Regarding the second challenge, we propose to impose intra-modal adjacency as a soft supervision signal for inter-modal contrastive learning, i.e., audio-visual similarities should be statistically consistent with the intramodal similarities. In other words, if two scenes are close, their audio features similarity value \\(\\mathrm{sim}(Z_i^a,Z_j^a)\\) should be high, the visual similarity \\(\\mathrm{sim}(Z_i^v,Z_j^v)\\) should match, and the cross-modal similarities \\(\\mathrm{sim}(Z_i^a,Z_j^v)\\) or \\(\\mathrm{sim}(Z_i^v,Z_j^a)\\) should also show consistency. Therefore, we leverage intramodal similarity as a supervision signal for audio-visual contrastive learning. Technically, we could utilize hard thresholds to achieve pseudo labels from intra-modal similarity like [8, 29, 36], which can serve to identify potential false negatives samples or areas. However, such methods require parameter tuning, and misassigned labels can exacerbate the false-negative problem. Differently, we propose FNS that directly regularizes the similarity scores. For a" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6423" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.231, + 0.089, + 0.725, + 0.246 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.268, + 0.895, + 0.311 + ], + "angle": 0, + "content": "Figure 5. An overview of True Negative Enhancement (TNE). The visual features from localized regions are extracted to construct a sound-source visual feature adjacency matrix. The audio adjacency matrix is used to regularize the sound-source visual feature adjacency matrix to enhance true negatives." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.335, + 0.424, + 0.35 + ], + "angle": 0, + "content": "sample \\(i\\), its optimization objective is formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.089, + 0.361, + 0.47, + 0.405 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {F N S} - 1} = \\frac {1}{b} \\sum_ {j} ^ {b} \\mathcal {L} _ {\\text {d i s t}} \\left(\\operatorname {s i m} \\left(Z _ {i} ^ {a}, Z _ {j} ^ {v}\\right), \\operatorname {s i m} \\left(Z _ {i} ^ {a}, Z _ {j} ^ {a}\\right)\\right) \\tag {2}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.089, + 0.407, + 0.47, + 0.45 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {F N S} - 2} = \\frac {1}{b} \\sum_ {j} ^ {b} \\mathcal {L} _ {\\text {d i s t}} \\left(\\operatorname {s i m} \\left(Z _ {i} ^ {a}, Z _ {j} ^ {v}\\right), \\operatorname {s i m} \\left(Z _ {i} ^ {v}, Z _ {j} ^ {v}\\right)\\right) \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.46, + 0.473, + 0.657 + ], + "angle": 0, + "content": "For an audio sample \\( a_i \\), the NCE loss \\( L_{\\text{contrast\\_i}} \\) in Eq. 1 pushes all negatives away by encouraging \\( \\sin(Z_i^a, Z_j^v)_{j \\in [0,n), j \\neq i} \\) to be close to 0, whereas FNS pulls back false negatives to suppress their effects. The suppression intensity corresponds to the values of \\( \\sin(Z_i^a, Z_j^a) \\) and \\( \\sin(Z_i^v, Z_j^v) \\). In Eq. 3, the visual contrastive loss is calculated symmetrically. In practice, we calculate L1 distances between the inter-modal contrastive matrix and intra-modal adjacency matrices as shown in Fig. 3, so all pair-wise similarities are considered. Such a regularization term yields a parameter-free process so that we do not need to choose a hard threshold to determine the real false negatives, as the false negative effects can be adaptively regularized." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.674, + 0.47, + 0.856 + ], + "angle": 0, + "content": "TNE: True Negatives Enhancement. To further reduce the misleading effect of false negatives, we propose to enhance the contribution of true negatives by region-wise comparison. As opponents, the impact of true negatives and that of false negatives are relative, so if the role of true negatives is raised, the role of false negatives would be suppressed. To improve the effect of true negatives in audio-visual learning, we turn back to its core concept, i.e., that the sound source objects are different both audibly and visually between the true negatives. Therefore, it is straightforward to put a particular emphasis on the possible regions of genuine sound-emitting objects." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Specifically, we localize the sound-source objects by paired audio-visual samples, pop up their regional visual features, and encourage those of true negative samples to" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.335, + 0.892, + 0.41 + ], + "angle": 0, + "content": "be pulled away. The process is called true negative enhancement (TNE). It is worth noting that similar regularizations have been mentioned but disregarded by previous methods [8,21,29] because they did not distinguish the true negatives and false negatives samples." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.41, + 0.893, + 0.652 + ], + "angle": 0, + "content": "We show the paradigm of TNE in Fig. 5. Given an audio-visual pair \\((a_i, v_i)\\), we obtain its localization result and use the localization map as a mask to extract the localized visual representation \\(Z_i^s \\in \\mathbb{R}^{d \\times h \\times w}\\), where \\(s\\) indicates it is sounding region visual representation. In other words, \\(Z_i^s\\) denotes the visual features that are aligned with the paired audio features. Then, consider another arbitrary audio-visual pair \\((a_j, v_j)\\) which localizes visual features \\(Z_j^s\\). If \\(a_i\\) and \\(a_j\\) are semantically different, i.e., \\(a_j\\) is a true negative of \\(a_i\\), then the \\(Z_i^s\\) should be dissimilar to \\(Z_j^s\\). It encourages the model to focus on different pixels so as to mine discriminative visual features according to the audio similarities. To leverage such a constraint in practice, we regularize the audio adjacency matrix and the similarities between the sounding region visual features. Formally, the TNE regularization is:" + }, + { + "type": "equation", + "bbox": [ + 0.517, + 0.673, + 0.892, + 0.716 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {T N E}} = \\frac {1}{b} \\sum_ {j} ^ {b} \\mathcal {L} _ {\\text {d i s t}} \\left(\\operatorname {s i m} \\left(Z _ {i} ^ {a}, Z _ {j} ^ {a}\\right), \\operatorname {s i m} \\left(Z _ {i} ^ {s}, Z _ {j} ^ {s}\\right)\\right) \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.724, + 0.895, + 0.876 + ], + "angle": 0, + "content": "FNS and TNE are two general mechanisms for multimodal contrastive learning. FNS adopts audio and visual adjacency matrices to explore the potential false negatives and suppress their misleading effects on the NCE loss. TNE uses audio adjacency to discriminate the sound-source localization so the model tends to discover the genuine sound sources. Both methods can be seamlessly integrated with the existing contrastive learning framework as extra regularization terms. Our final optimization objective for the \\(i\\)-th sample pair is:" + }, + { + "type": "equation", + "bbox": [ + 0.522, + 0.886, + 0.892, + 0.902 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {i} = \\mathcal {L} _ {\\text {c o n t r a s t . i}} + \\alpha \\mathcal {L} _ {\\mathrm {F N S} _ {- 1}} + \\beta \\mathcal {L} _ {\\mathrm {F N S} _ {- 2}} + \\gamma \\mathcal {L} _ {\\mathrm {T N E}} \\tag {5}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6424" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.895, + 0.133 + ], + "angle": 0, + "content": "Table 1. Quantitative results of the model trained with Flickr 10k and 144k. Note that 'EZ-VSL + OGL' corresponds to the main results reported in [21]. 'EZ-VSL' indicates our reproduced results without OGL, which are not reported in [21]. We reproduce the results with the trained weights and code provided by [21]." + }, + { + "type": "table", + "bbox": [ + 0.182, + 0.142, + 0.794, + 0.346 + ], + "angle": 0, + "content": "
Train setMethodFlickr CIoU(%)Flickr AUC(%)VGG-SS CIoU(%)VGG-SS AUC(%)
Flickr 10kAttention10k [28]43.6044.90--
CoursetoFine [26]52.2049.60--
AVObject [1]54.6050.40--
LVS [8]58.2052.50--
EZ-VSL* [21]62.2454.7419.8630.96
Ours84.3363.2635.2738.00
EZ-VSL + OGL [21]81.9362.5837.6139.21
Ours + OGL84.7364.3440.9740.38
Flickr 144kAttention10k [28]66.0055.80--
DMC [15]67.1056.80--
LVS [8]69.9057.30--
HardPos [29]75.2059.70--
EZ-VSL* [21]72.6958.7030.2735.92
Ours78.7159.3333.9337.29
EZ-VSL + OGL [21]83.1363.0641.0140.23
Ours + OGL83.9363.0641.1040.44
" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.364, + 0.313, + 0.38 + ], + "angle": 0, + "content": "where \\(\\alpha, \\beta, \\gamma\\) are hyperparameters." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.394, + 0.21, + 0.41 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.418, + 0.285, + 0.435 + ], + "angle": 0, + "content": "4.1. Experimental Settings" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.442, + 0.47, + 0.577 + ], + "angle": 0, + "content": "Datasets We train our audio-visual localization model on two datasets: Flickr SoundNet [6] and VGG-Sound [9]. Flickr SoundNet contains 2 million unconstrained videos from Flickr. For a fair comparison with the existing methods [8, 20, 21, 29], we conduct the training on two subsets of 10k and 144k paired samples from Flicker SoundNet. VGG-Sound includes 200k video clips from 309 classes. We also train on two subsets of 10k and 144k paired samples following the convention." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.579, + 0.471, + 0.745 + ], + "angle": 0, + "content": "Localization performances are measured on four benchmarks, Flickr [6], VGG-SS [9], Heard 110 and AVS-Bench [38]. The Flickr test set has 250 audio-visual pairs with manually labeled bounding boxes. VGG-SS is more challenging with 5,000 audio-visual pairs over 220 categories. Heard 110 is another subset of VGG-Sound to test the open-set learning ability. Its train set has 110 classes and the val set has another disjoint 110 unheard/unseen classes. Finally, AVSBench [38] is a recently proposed audio-visual dataset with 5,356 videos over 23 classes. It provides pixelwise labels for fine-grained localization evaluation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Implementation Details We implement our method with PyTorch. The images are resized and randomly cropped into \\(224 \\times 224\\) resolution, together with random horizontal flipping. The audio inputs are extracted from 3 seconds of audio clips and converted into log spectrogram maps. We also apply audio augmentation including Frequency mask and Time mask [25]. For both visual and audio encoders, we adopt ResNet18 [14] and the visual encoder is pretrained on ImageNet-1k [12]. The model is optimized for" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.363, + 0.892, + 0.426 + ], + "angle": 0, + "content": "30 epochs with Adam using a learning rate of \\(10^{-4}\\) and a weight decay of \\(10^{-4}\\). To achieve a stable representation, we warm up the network with only NCE loss for 3 epochs, then integrate our regularization for the remaining epochs." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.434, + 0.892, + 0.451 + ], + "angle": 0, + "content": "4.2. Comparison on Flickr-SoundNet and VGG-SS" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.457, + 0.892, + 0.685 + ], + "angle": 0, + "content": "Flickr-SoundNet We train our model on Flickr 10k and 144k and report performances in Table 1. FNAC achieves superior performances over previous methods on both Flickr and VGG-SS test sets. Notably, compared to previous state-of-the-art EZ-VSL [21] on the Flickr test set, FNAC achieves a striking improvement of \\(22.09\\%\\) CIOU with 10k training samples and \\(6.02\\%\\) CIOU with 144k training samples. When tested on the more challenging VGGSS, FNAC also outperforms EZ-VSL by \\(15.41\\%\\) CIOU and \\(3.49\\%\\) CIOU respectively. Finally, Object-Guided localization (OGL) is a post-processing strategy that adopts pure visual-based localization results to refine audio-visual localization. For a fair comparison, we integrate FNAC with OGL to compare with EZ-VSL which also uses OGL. As shown, FNAC also outperforms EZ-VSL in most cases." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.892, + 0.779 + ], + "angle": 0, + "content": "VGG-SS Performance of the model trained on VGG-Sound 10k and 144k is reported in Table 2. FNAC also beats all previous methods with a clear margin. For example, on the VGG-SS test set, we outperform EZ-VSL by \\(11.45\\%\\) CIOU with 10k and \\(5.31\\%\\) CIOU with 144k." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.895, + 0.902 + ], + "angle": 0, + "content": "We highlight two results as demonstrated in Table 1 and Table 2. First, FNAC achieves similar results on \\(10\\mathrm{k}\\) and \\(144\\mathrm{k}\\) training sets in both Flickr SoundNet and VGGSound, which is not observed in previous models. We believe that small-scale datasets (Flickr \\(10\\mathrm{k}\\), VGG-Sound \\(10\\mathrm{k}\\)) have fewer semantic classes and will encounter more false negatives during training, so previous methods have substantial performance gaps between the \\(10\\mathrm{k}\\) and \\(144\\mathrm{k}\\) training" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6425" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.26, + 0.089, + 0.71, + 0.104 + ], + "angle": 0, + "content": "Table 2. Quantitative results of models trained with VGG-SS 10k and 144k." + }, + { + "type": "table", + "bbox": [ + 0.18, + 0.115, + 0.795, + 0.296 + ], + "angle": 0, + "content": "
Train setMethodFlickr CIoU(%)Flickr AUC(%)VGG-SS CIoU(%)VGG-SS AUC(%)
VGGSound 10kLVS [8]61.8053.60--
EZ-VSL* [21]63.8554.4425.8433.68
Ours85.7463.6637.2938.99
EZ-VSL + OGL [21]78.7161.5338.7139.80
Ours + OGL82.1363.6440.6940.42
VGGSound 144kAttention10k [28]--18.5030.20
DMC [15]--29.1034.80
AVObject [1]--29.7035.70
LVS [8]73.5059.0034.4038.20
HardPos [29]76.8059.2034.6038.00
EZ-VSL [21]79.5161.1734.3837.70
Ours84.7363.7639.5039.66
EZ-VSL + OGL [21]83.9463.6038.8539.54
Ours + OGL85.1464.3041.8540.80
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.318, + 0.471, + 0.36 + ], + "angle": 0, + "content": "Table 3. Quantitative results on Heard 110 and Unheard 110. For a fair comparison, the results of EZ-VSL [21] and ours are integrated with the OGL module." + }, + { + "type": "table", + "bbox": [ + 0.127, + 0.37, + 0.426, + 0.466 + ], + "angle": 0, + "content": "
Test SetMethodCIoU(%)AUC(%)
Heard 110LVS [8]28.9036.20
EZ-VSL [21]37.2538.97
Ours39.5439.83
Unheard 110LVS [8]26.3034.70
EZ-VSL [21]39.5739.60
Ours42.9141.17
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.484, + 0.47, + 0.606 + ], + "angle": 0, + "content": "sets. It indicates that FNAC can effectively address the false negative issue and has a strong ability for representation learning on small-scale datasets. Second, we show cross-dataset evaluation results in both tables, i.e., train on Flickr and test on VGG-SS or vice versa. FNAC achieves strong results and outperforms existing methods, which validates the cross-dataset generalization ability of FNAC. We show qualitative localization results in Fig. 6." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.615, + 0.436, + 0.632 + ], + "angle": 0, + "content": "4.3. Comparison on Heard 110 and AVSBench" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.639, + 0.47, + 0.79 + ], + "angle": 0, + "content": "Heard 110 To assess the generalization ability of FNAC in unseen/unheard audiovisual scenes, we conduct an open set experiment. We use the 70k samples covering 110 categories randomly sampled from VGGSound for training and then evaluate the model on the same 110 heard categories and another disjoint set with 110 unheard categories. As shown in Table 3, FNAC considerably outperforms previous methods, especially on Unheard 110 (42.91% vs. 39.57% of CIoU), which demonstrates the generalization ability of FNAC in unconstrained audio-visual data." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.471, + 0.901 + ], + "angle": 0, + "content": "AVSbench AVSbench [38] is a newly proposed audiovisual segmentation benchmark with pixel-level annotations, which can be regarded as a fine-grained sound source localization task and used to accurately evaluate the localization ability of models. We directly perform a zero-shot evaluation on the AVSbench with metrics of mIoU and" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.318, + 0.892, + 0.346 + ], + "angle": 0, + "content": "Table 4. Zero-shot results on AVSBench S4 and MS3 [38]. All models are pretrained on VGGSound-144k dataset." + }, + { + "type": "table", + "bbox": [ + 0.543, + 0.356, + 0.85, + 0.45 + ], + "angle": 0, + "content": "
Test setMethodmIoUFScore
S4LVS23.69.251
EZ-VSL26.43.292
Ours27.15.314
MS3LVS18.54.174
EZ-VSL21.36.216
Ours21.98.225
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.454, + 0.892, + 0.483 + ], + "angle": 0, + "content": "Table 5. Analysis of each component of the proposed FNAC. aud adj: audio adjacency matrix. img adj: image adjacency matrix." + }, + { + "type": "table", + "bbox": [ + 0.521, + 0.493, + 0.872, + 0.593 + ], + "angle": 0, + "content": "
FNSTNEFlickr CIoU(%)VGG-SS CIoU(%)
aud adjimg adj
77.9133.93
✓79.9135.85
✓81.9236.58
✓✓84.3336.92
✓81.1236.04
✓✓✓85.7437.29
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.611, + 0.892, + 0.747 + ], + "angle": 0, + "content": "F-Score in two settings, Single Sound Source Segmentation (S4) and Multiple Sound Source Segmentation (MS3), without any fine-tuning. The results are reported in Table 4. The proposed method achieves outstanding performance on both S4 and MS3 settings, e.g., \\(27.15\\%\\) and \\(21.98\\%\\) mIoU when trained on VGGSound 144k. These results on the fine-grained localization benchmark validate the effectiveness of the TNE, which enables the model to discriminate authentic sound-source regions." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.757, + 0.744, + 0.773 + ], + "angle": 0, + "content": "4.4. Ablation Analysis of FNAC" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.781, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We propose different regularization terms to guide audio-visual contrastive learning. In Table 5, we ablate each component individually. All results are obtained following the same hyperparameter setting on VGG-SS \\(10\\mathrm{k}\\) and the baseline is trained with only NCE loss. First, the audio adjacency matrix and visual adjacency matrix are obtained in FNS to suppress the false negatives. We show that each adjacency matrix can improve the performances over the" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6426" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.204, + 0.093, + 0.482, + 0.265 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.491, + 0.094, + 0.768, + 0.265 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.213, + 0.278, + 0.756, + 0.293 + ], + "angle": 0, + "content": "Figure 6. Visualization comparison on Flickr-SoundNet (left) and VGG-SS (right) test sets." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.318, + 0.474, + 0.485 + ], + "angle": 0, + "content": "baseline, which indicates that potential false negatives can be effectively suppressed in both audio and visual modalities. By combining the two adjacency matrices together, FNS achieves \\(84.33\\%\\) CIoU on Flickr and \\(36.92\\%\\) CIoU on VGG-SS. Second, by only deploying TNE, we achieve improved results over baseline (81.12% CIoU on Flickr and \\(36.04\\%\\) CIoU on VGG-SS), indicating the effectiveness of TNE in enhancing true negatives. Finally, the combination of FNS and TNE achieves significant improvement over the baseline, showing the effectiveness of FNAC. We refer readers to supp. mat. for further ablation studies." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.507, + 0.395, + 0.525 + ], + "angle": 0, + "content": "4.5. Mining the Potential False Negatives" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.535, + 0.47, + 0.791 + ], + "angle": 0, + "content": "In this section, we show quantitative and schematic analysis of the false negative mining ability of our method. Intuitively, a good audio-visual model should be able to generate similar feature representations for class matched samples. To validate this intuition, we construct a batch where all samples belong to the same category, i.e., all false negatives, and show the audio-visual similarity matrices of EZ-VSL [21] and ours in Fig. 7. As shown in the left, EZ-VSL only highlights the diagonal, since each audio feature is only similar to the paired image feature while all others are dissimilar despite all samples being from the same class. Differently, the similarity distribution of our matrix is more evenly spread as the majority of the samples are regarded as similar. It indicates that FNAC has implicitly learned semantically-aware features and clustered them in the latent space, so false negatives will be effectively identified as they are closer in terms of feature distance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Further, we show quantitative results of audio-visual similarities in Table 6. When the batch contains all true negatives, our average similarity score is lower than previous methods [8, 21]. When the batch contains all false negatives, our average similarity score is higher. The margin between the two similarities demonstrates our ability to distinguish false negatives and true negatives." + }, + { + "type": "image", + "bbox": [ + 0.546, + 0.317, + 0.856, + 0.43 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.442, + 0.895, + 0.498 + ], + "angle": 0, + "content": "Figure 7. Cross-modal similarity matrix predicted by EZ-VSL (left) and ours (right) when all samples in the batch belong to the same category, namely, they are false negatives of each other. All values are normalized between 0 to 1." + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.523, + 0.895, + 0.566 + ], + "angle": 0, + "content": "Table 6. Audio-visual similarities with different data. TN: all samples in the batch belong to different categories. FN: all samples in the batch belong to the same category." + }, + { + "type": "table", + "bbox": [ + 0.53, + 0.575, + 0.868, + 0.638 + ], + "angle": 0, + "content": "
MethodTN ↓FN ↑
LVS0.44840.5102
EZ-VS10.58580.5938
Ours0.38120.6554
" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.66, + 0.62, + 0.675 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.69, + 0.895, + 0.901 + ], + "angle": 0, + "content": "In this paper, we propose a simple yet effective strategy named FNAC to deal with the false negative issue in audio-visual sound source localization. We propose two complementary strategies to suppress false negatives (FNS) and enhance true negatives (TNE). The intra-modal adjacency matrices of audio and visual are generated to identify false negatives. Then two regularization terms are seamlessly incorporated with contrastive learning, which enable the model to learn semantic-aware features from audio-visual pairs. We show that FNAC can effectively mitigate the false negative issues and achieve state-of-the-art performance on several audio-visual localization benchmarks. We hope that our method can facilitate future research in audio-visual learning and other multi-modal tasks." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6427" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.171 + ], + "angle": 0, + "content": "[1] Triantafyllos Afouras, Andrew Owens, Joon Son Chung, and Andrew Zisserman. Self-supervised learning of audio-visual objects from video. In European Conference on Computer Vision, pages 208–224. Springer, 2020. 6, 7" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.172, + 0.47, + 0.213 + ], + "angle": 0, + "content": "[2] Relja Arandjelovic and Andrew Zisserman. Look, listen and learn. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 8436-8444, 2021. 1" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.47, + 0.811 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.517, + 0.956 + ], + "angle": 0, + "content": "6429" + } + ] +] \ No newline at end of file diff --git a/2023/Learning Audio-Visual Source Localization via False Negative Aware Contrastive Learning/e5b67298-ac49-4b7c-9b93-510776d56f4c_origin.pdf b/2023/Learning Audio-Visual Source Localization via False Negative Aware Contrastive Learning/e5b67298-ac49-4b7c-9b93-510776d56f4c_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..33b89b654bba4696541c499e253753b0f0306e78 --- /dev/null +++ b/2023/Learning Audio-Visual Source Localization via False Negative Aware Contrastive Learning/e5b67298-ac49-4b7c-9b93-510776d56f4c_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:828da493d9a096f361b8c8a72326de9b44176588c7afa4e3f40caf2125017862 +size 4065751 diff --git a/2023/Learning Audio-Visual Source Localization via False Negative Aware Contrastive Learning/full.md b/2023/Learning Audio-Visual Source Localization via False Negative Aware Contrastive Learning/full.md new file mode 100644 index 0000000000000000000000000000000000000000..3dbf70f00eaa2d05084ad7822465768512d8b537 --- /dev/null +++ b/2023/Learning Audio-Visual Source Localization via False Negative Aware Contrastive Learning/full.md @@ -0,0 +1,236 @@ +# Learning Audio-Visual Source Localization via False Negative Aware Contrastive Learning + +Weixuan Sun $^{1,5}$ , Jiayi Zhang $^{2}$ , Jianyuan Wang $^{3}$ , Zheyuan Liu $^{1}$ , Yiran Zhong $^{4}$ , Tianpeng Feng $^{5}$ , Yandong Guo $^{5}$ , Yanhao Zhang $^{5}$ , Nick Barnes $^{1}$ $^{1}$ Australian National University, $^{2}$ Beihang University, $^{3}$ The University of Oxford, $^{4}$ Shanghai AI Lab, $^{5}$ OPPO Research Institute. + +# Abstract + +Self-supervised audio-visual source localization aims to locate sound-source objects in video frames without extra annotations. Recent methods often approach this goal with the help of contrastive learning, which assumes only the audio and visual contents from the same video are positive samples for each other. However, this assumption would suffer from false negative samples in real-world training. For example, for an audio sample, treating the frames from the same audio class as negative samples may mislead the model and therefore harm the learned representations (e.g., the audio of a siren wailing may reasonably correspond to the ambulances in multiple images). Based on this observation, we propose a new learning strategy named False Negative Aware Contrastive (FNAC) to mitigate the problem of misleading the training with such false negative samples. Specifically, we utilize the intra-modal similarities to identify potentially similar samples and construct corresponding adjacency matrices to guide contrastive learning. Further, we propose to strengthen the role of true negative samples by explicitly leveraging the visual features of sound sources to facilitate the differentiation of authentic sounding source regions. FNAC achieves state-of-the-art performances on Flickr-SoundNet, VGG-Sound, and AVSBench, which demonstrates the effectiveness of our method in mitigating the false negative issue. The code is available at https://github.com/OpenNLPLab/FNAC_AVL. + +# 1. Introduction + +When hearing a sound, humans can naturally imagine the visual appearance of the source objects and locate them in the scene. This demonstrates that audio-visual correspondence is an important ability for scene understanding. Given that unlimited paired audio-visual data exists in nature, there is an emerging interest in developing multi-modal systems with audio-visual understanding abl + +![](images/2d032ca1ccbd37fec2429de14bc9c3ffdc0962911c5cdd7a9c3efc0a14a525e3.jpg) +Figure 1. False negative in audio-visual contrastive learning. Audio-visual pairs with similar contents are falsely considered as negative samples to each other and pushed apart in the shared latent space, which we find would affect the model performance. + +ity. Various audio-visual tasks have been studied, including sound source localization [8, 19–21, 26–28], audio-visual event localization [32, 33, 35, 39], audio-visual video parsing [11, 18, 31] and audio-visual segmentation [37, 38]. In this work, we focus on unsupervised visual sound source localization, with the aim of localizing the sound-source objects in an image using its paired audio clip, but without relying on any manual annotations. + +The essence of unsupervised visual sound source localization is to leverage the co-occurrences between an audio clip and its corresponding image to extract representations. A major part of existing methods [8, 19–21, 28] formulates this task as contrastive learning. For each image sample, its paired audio clip is viewed as the positive sample, while all other audio clips are considered as negative. Likewise, each audio clip considers its paired image as positive and all others as negative. As such, the Noise Contrastive Estimation (NCE) loss [24, 30] is used to perform instance discrimination by pushing closer the distance between a positive audio-image pair, while pulling away any negative pairs. However, the contrastive learning scheme above suffers from the issue of false negatives during training, i.e., audio/image samples that belong to the semantically-matched class but are not regarded as a positive pair (due to the lack of manual labeling). A typical example is shown + +in Fig. 1. Research shows [4, 16, 29, 36] that these false negatives will lead to contradictory objectives and harm the representation learning. + +Motivated by this observation, we assess the impact of false negatives in real-world training. We discover that with a batch size of 128, around $40\%$ of the samples in VGG-Sound [9] will encounter at least one false negative sample during training. We then validate that false negatives indeed harm performance by artificially increasing the proportion of false negatives during training, and observing a noticeable performance drop. To make matters worse, larger batch sizes are often preferred in contrastive learning [24], but it may inadvertently increase the number of false negative samples during training and affect representation quality. + +To this end, we propose a false-negative aware audio-visual contrastive learning framework (FNAC), where we employ the intra-modal similarities as weak supervision. Specifically, we compute pair-wise similarities between all audio clips in a mini-batch without considering the visual to form an audio intra-modal adjacency matrix. Likewise, in the visual modality, we obtain an image adjacency matrix. We found that the adjacency matrices effectively identify potential samples of the same class within each modality (Fig. 4). The information can then be used to mitigate the false negatives and enhance the effect of true pairings. + +Specifically, we propose two complementary strategies: 1) FNS for False Negatives Suppression, and 2) TNE for True Negatives Enhancement. First, when optimizing the NCE loss, FNS regularizes the inter-modal and intra-modal similarities. Intrinsically, intra-modal adjacency explores potential false negatives by the similarity intensities and the pulling forces applied to these false negatives are canceled accordingly. Furthermore, we introduce TNE to emphasize the true negative influences in a region-wise manner, which in turn reduces the effect of false negative samples as well. We adopt the audio adjacency matrix to identify dissimilar samples, i.e., true negatives. Intuitively, dissimilar (true negative) sounds correspond to distinct regions, so the localized regions across the identified true negatives are regularized to be different. Such a mechanism encourages the model to discriminate genuine sound-source regions and suppress the co-occurring quiet objects. we conduct extensive analysis to demonstrate the effectiveness of our proposed method and report competitive performances across different settings and datasets. In summary, our main contributions are: + +- We investigate the false negative issue in audio-visual contrastive learning. We quantitatively validate that this issue occurs and harms the representation quality. +- We exploit intra-modal similarities to identify potential false negatives and introduce FNS to suppress their impact. + +- We propose TNE, which emphasizes true negatives using different localization results between the identified true negatives, thus encouraging more discriminative sound source localizations. + +# 2. Related Work + +False Negatives in Contrastive Learning. Typical contrastive learning employs instance discrimination [34] as a pretext task, in which two augmented views of the same image are considered as positive pairs, while views of all other images are treated as negative pairs, regardless of semantic similarities. Such a scheme inevitably suffers from the False Negatives issue [10, 13, 16, 36], which indicates that instances sharing the same semantic concepts are falsely treated as negatives, thus misleading model learning. Based on this, some works attempt to incorporate similar instances into model training to eliminate the impact of false negatives. For example, Zheng et al. [36] model a nearest neighbor graph for each batch of instances and execute a KNN-based multi-crop strategy to detect false negatives. Similarly, Dwibedi et al. [13] sample nearest neighbors from the dataset and treat them as positives for contrastive learning. More recently, [16] and [10] study how to identify false negatives without class labels and explicitly remove detected false negatives by two strategies, elimination and attraction, to improve contrastive loss. Other works use clustering-based methods to encode semantic structures [5, 7, 17] and then perform contrastive learning on these semantically similar cluster centers. In this paper, we propose and explore a similar problem in self-supervised audio-visual learning. + +Self-Supervised Sound Source Localization. Sound source localization aims to learn to locate sound-source regions in videos. Recent approaches extensively leverage contrastive learning based on audiovisual correspondence to address this issue. For example, [2, 3, 28] adopt a dual-stream architecture to extract unimodal features respectively and then calculate a contrastive loss to update the audiovisual network. The final localization map is usually obtained by calculating the cosine similarity between audio and visual features. Following the paradigm, Mo et al. [21] further propose an object-guided localization (OGL) module, an extra pre-trained visual encoder, to introduce visual priors into the localization results. Nevertheless, these works assume that the paired audio-visual signals are regularly aligned and all mismatched samples are heterogeneous. As aforementioned, the assumption ignores the semantic similarities between samples. Accordingly, Chen et al. [8] incorporate explicitly background regions with low correlation to the given audio into the framework and regard them as hard negatives. In a slightly different task + +![](images/f71a7b9b860136bb7e5a07e79031e6df49ba0d49008e031c5582caaf0858df6a.jpg) +Figure 2. Impact of false negatives on audio-visual representation learning. We adopt Consensus Intersection over Union (CIoU) [28] as an evaluation metric (higher is better) and report results on FlickrSoundNet [6] and VGG-SS [9] test sets, depicted by blue and brown, respectively. An obvious performance decline is observed as the proportion of false negative samples increases. + +setting of audio-visual instance discrimination, false negative issues are also investigated. [23] detects false negatives by defining sets of positive and negative samples via cross-modal agreement, where positive samples are defined as similar samples in both modalities. [22] considers both false positive and false negative issues. For false negatives, they estimate the similarity across instances to compute a soft target distribution over instances so the contributions of false negatives are down-weighted. One work that explores a similar problem to us is [29], which treats top-K semantically similar audio-visual pairs as hard positives and explicitly integrates them into the contrastive loss. Unfortunately, this method relies on manually selected hypermeters K and a hard threshold. Unlike the previous methods, this paper uses intra-modal adjacency matrices to adaptively detect false negatives and eliminate their impact. + +# 3. Method + +In this section, we first investigate the problem raised by false negative samples in Sec. 3.1, and then propose to mitigate the problem. From two aspects, without supervision we identify the false negative samples to explicitly suppress them in training (Sec. 3.2), and use region-wise comparing learning to enhance the roles of true negative samples which hence relatively suppresses false negatives (Sec. 3.2). + +# 3.1. Revisiting Audio-visual Contrasting Learning + +Various methods for audio-visual localization [18,21,28] employ a contrastive learning framework, in a manner of instance discrimination. Arguably, it assumes the audio-visual scenes from different videos are distinctive. Therefore the paired audio and image from the same video are considered a positive pair while the samples (audio or image) from other pairs are regarded as negatives. Specifically, we denote an audio-visual dataset as $\mathcal{D} \in \{(a_i, v_i), i \in$ + +$[0,n)\}$ , where $(a_i,v_i)$ represents a sample with paired audio-visual content. Usually, a two-stream network is used to encode audio and visual signals and then map them into a shared latent space. The audio and visual representations extracted from $(a_i,v_i)$ are denoted as $Z_{i}^{a}\in \mathbb{R}^{1\times d}$ and $Z_{i}^{v}\in \mathbb{R}^{1\times d}$ with $d$ as feature dimension. Ideally, $Z_{i}^{a}$ and $Z_{i}^{v}$ represent the same semantic concept from the visual and audio perspectives, e.g., playing the drum. The optimization objective of contrastive learning is to maximize the similarity between audio and visual representations from the same video while minimizing the similarity between features from different videos. Mathematically, it can be formulated in a modal-symmetric way for a pair $(a_i,v_i)$ as: + +$$ +\begin{array}{l} \mathcal {L} _ {\text {c o n t r a s t . i}} = - \log \frac {\exp \left[ \frac {1}{\tau} \operatorname {s i m} \left(Z _ {i} ^ {a} , Z _ {i} ^ {v}\right) \right]}{\sum_ {j} ^ {b} \exp \left[ \frac {1}{\tau} \operatorname {s i m} \left(Z _ {i} ^ {a} , Z _ {j} ^ {v}\right) \right]} \\ - \log \frac {\exp \left[ \frac {1}{\tau} \operatorname {s i m} \left(Z _ {i} ^ {v} , Z _ {i} ^ {a}\right) \right]}{\sum_ {j} ^ {b} \exp \left[ \frac {1}{\tau} \operatorname {s i m} \left(Z _ {i} ^ {v} , Z _ {j} ^ {a}\right) \right]}, \tag {1} \\ \end{array} +$$ + +where $\tau$ is a temperature hyper-parameter, $b$ denotes batch size and sim represents the similarity function. Intuitively, this loss implies that each audio feature $Z_{i}^{a}$ is pushed close to its paired visual feature $Z_{i}^{v}$ in the shared latent space, while pulled apart from the rest $(b - 1)$ visual features $Z_{j,j\neq i}^{v}$ . However, as discussed, there exist $\hat{Z}_j^a$ and/or $\hat{Z}_j^v$ that are semantically similar to $(Z_i^a,Z_i^v)$ , i.e., false negatives. In this situation, forcing $\mathrm{sim}(Z_i^a,\hat{Z}_j^v)$ or $\mathrm{sim}(Z_i^v,\hat{Z}_j^a)$ to be small might perplex the model training and lead to a non-optimal representation. + +Impact of False Negatives. Based on this observation, we conduct several pilot experiments to verify the issue of false negatives and their influence on audio-visual representation learning. For simplification, we reasonably assume that samples that share the same manually labeled category are False Negatives. Firstly, we examine the data distribution during the training procedure. We find that over $39.27\%$ samples suffer from at least one false negative sample when training with a batch size of 128 on the VGG-Sound dataset [9] covering 309 categories. This ratio will undoubtedly increase when employing bigger batch sizes or fewer categories. Secondly, we examine how the false negative issue might affect audio-visual localization performance. Following prior works [8, 21], we adopt ResNet-18 as the backbone to encode audio and visual features and a standard NCE loss [24] is used. In particular, we manually substitute the true negatives with false negatives in the training samples. As shown in Fig 2, when the false negative rate is progressively increased, a significant performance decline is found, indicating that the model is perplexed by these similar samples. The experiments above demonstrate that false negatives substantially impact the model quality and cannot be disregarded. + +![](images/49d0e5bd7f38d374699852d5cc8ad2482079dd9aeb24b5b401a30bda6842ba0f.jpg) +Figure 3. An overview of False Negative Suppression (FNS). The main optimization objective is NCE [24] loss on audio-visual pairs. The audio adjacency matrix and visual adjacency matrix are respectively constructed to suppress false negatives by regularizing NCE loss. + +![](images/066a33f2c98d9ff38a772814ff483ebfd51d9dab4e58e87312f1eebfdef90a98.jpg) +Figure 4. Qualitative samples of the found potential false negatives in visual and audio modalities. We report the nearest sample for every anchor. For the audio modality, we show the corresponding images here. + +# 3.2. Mitigating False Negatives in Audio Visual Learning + +As discussed in Sec. 3.1, we prove that the unpaired positive samples (i.e., false negatives) existed in every minibatch that may harm the representations. Correspondingly, we propose to solve this problem by FNAC with two complementary methods, False Negatives Suppression (FNS) and True Negatives Enhancement (TNE). For the same goal of mitigating the false negative issue, FNS identifies the false negative samples and regularizes to reduce their effects, while TNE enhances the contribution of true negatives by region-wise comparison, which also inadvertently suppresses false negatives. Both methods can be seamlessly integrated into the audio-visual contrastive framework as regularization terms. + +FNS: False Negatives Suppression. To suppress the false negative effects, two challenges are posed. First, distinguishing the potential false negative samples within the current mini-batch without extra supervision such as class labels. Second, eliminating the misleading effects of the identified false negatives. + +For the first challenge, we propose to leverage the unimodal feature representations to calculate pair-wise sample similarities, i.e., adjacency matrix. As shown in Fig. 3, the audio clips are fed into an audio encoder to obtain audio features $Z^{a} \in \mathbb{R}^{b \times d}$ , then we calculate a dot product with + +$(Z^{a})^{T}$ followed by a row-wise softmax to obtain the pairwise self-similarity matrix $S^{a} \in \mathbb{R}^{b \times b}$ , i.e., the audio adjacency matrix. Likewise, we average-pool the image features and obtain a visual adjacency matrix $S^{v} \in \mathbb{R}^{b \times b}$ . Such adjacency matrices encode pair-wise similarities across a batch without considering inter-modal connection. For each audio-visual sample, we show its nearest sample by querying the adjacency matrices, as shown in Fig 4. It indicates that intra-modal adjacency matrices can effectively identify potential class-matched samples. + +Regarding the second challenge, we propose to impose intra-modal adjacency as a soft supervision signal for inter-modal contrastive learning, i.e., audio-visual similarities should be statistically consistent with the intramodal similarities. In other words, if two scenes are close, their audio features similarity value $\mathrm{sim}(Z_i^a,Z_j^a)$ should be high, the visual similarity $\mathrm{sim}(Z_i^v,Z_j^v)$ should match, and the cross-modal similarities $\mathrm{sim}(Z_i^a,Z_j^v)$ or $\mathrm{sim}(Z_i^v,Z_j^a)$ should also show consistency. Therefore, we leverage intramodal similarity as a supervision signal for audio-visual contrastive learning. Technically, we could utilize hard thresholds to achieve pseudo labels from intra-modal similarity like [8, 29, 36], which can serve to identify potential false negatives samples or areas. However, such methods require parameter tuning, and misassigned labels can exacerbate the false-negative problem. Differently, we propose FNS that directly regularizes the similarity scores. For a + +![](images/294c38639258ba3917471b7cc56233dc259609492e12634cfb807a6003a31404.jpg) +Figure 5. An overview of True Negative Enhancement (TNE). The visual features from localized regions are extracted to construct a sound-source visual feature adjacency matrix. The audio adjacency matrix is used to regularize the sound-source visual feature adjacency matrix to enhance true negatives. + +sample $i$ , its optimization objective is formulated as: + +$$ +\mathcal {L} _ {\mathrm {F N S} - 1} = \frac {1}{b} \sum_ {j} ^ {b} \mathcal {L} _ {\text {d i s t}} \left(\operatorname {s i m} \left(Z _ {i} ^ {a}, Z _ {j} ^ {v}\right), \operatorname {s i m} \left(Z _ {i} ^ {a}, Z _ {j} ^ {a}\right)\right) \tag {2} +$$ + +$$ +\mathcal {L} _ {\mathrm {F N S} - 2} = \frac {1}{b} \sum_ {j} ^ {b} \mathcal {L} _ {\text {d i s t}} \left(\operatorname {s i m} \left(Z _ {i} ^ {a}, Z _ {j} ^ {v}\right), \operatorname {s i m} \left(Z _ {i} ^ {v}, Z _ {j} ^ {v}\right)\right) \tag {3} +$$ + +For an audio sample $a_i$ , the NCE loss $L_{\text{contrast\_i}}$ in Eq. 1 pushes all negatives away by encouraging $\sin(Z_i^a, Z_j^v)_{j \in [0,n), j \neq i}$ to be close to 0, whereas FNS pulls back false negatives to suppress their effects. The suppression intensity corresponds to the values of $\sin(Z_i^a, Z_j^a)$ and $\sin(Z_i^v, Z_j^v)$ . In Eq. 3, the visual contrastive loss is calculated symmetrically. In practice, we calculate L1 distances between the inter-modal contrastive matrix and intra-modal adjacency matrices as shown in Fig. 3, so all pair-wise similarities are considered. Such a regularization term yields a parameter-free process so that we do not need to choose a hard threshold to determine the real false negatives, as the false negative effects can be adaptively regularized. + +TNE: True Negatives Enhancement. To further reduce the misleading effect of false negatives, we propose to enhance the contribution of true negatives by region-wise comparison. As opponents, the impact of true negatives and that of false negatives are relative, so if the role of true negatives is raised, the role of false negatives would be suppressed. To improve the effect of true negatives in audio-visual learning, we turn back to its core concept, i.e., that the sound source objects are different both audibly and visually between the true negatives. Therefore, it is straightforward to put a particular emphasis on the possible regions of genuine sound-emitting objects. + +Specifically, we localize the sound-source objects by paired audio-visual samples, pop up their regional visual features, and encourage those of true negative samples to + +be pulled away. The process is called true negative enhancement (TNE). It is worth noting that similar regularizations have been mentioned but disregarded by previous methods [8,21,29] because they did not distinguish the true negatives and false negatives samples. + +We show the paradigm of TNE in Fig. 5. Given an audio-visual pair $(a_i, v_i)$ , we obtain its localization result and use the localization map as a mask to extract the localized visual representation $Z_i^s \in \mathbb{R}^{d \times h \times w}$ , where $s$ indicates it is sounding region visual representation. In other words, $Z_i^s$ denotes the visual features that are aligned with the paired audio features. Then, consider another arbitrary audio-visual pair $(a_j, v_j)$ which localizes visual features $Z_j^s$ . If $a_i$ and $a_j$ are semantically different, i.e., $a_j$ is a true negative of $a_i$ , then the $Z_i^s$ should be dissimilar to $Z_j^s$ . It encourages the model to focus on different pixels so as to mine discriminative visual features according to the audio similarities. To leverage such a constraint in practice, we regularize the audio adjacency matrix and the similarities between the sounding region visual features. Formally, the TNE regularization is: + +$$ +\mathcal {L} _ {\mathrm {T N E}} = \frac {1}{b} \sum_ {j} ^ {b} \mathcal {L} _ {\text {d i s t}} \left(\operatorname {s i m} \left(Z _ {i} ^ {a}, Z _ {j} ^ {a}\right), \operatorname {s i m} \left(Z _ {i} ^ {s}, Z _ {j} ^ {s}\right)\right) \tag {4} +$$ + +FNS and TNE are two general mechanisms for multimodal contrastive learning. FNS adopts audio and visual adjacency matrices to explore the potential false negatives and suppress their misleading effects on the NCE loss. TNE uses audio adjacency to discriminate the sound-source localization so the model tends to discover the genuine sound sources. Both methods can be seamlessly integrated with the existing contrastive learning framework as extra regularization terms. Our final optimization objective for the $i$ -th sample pair is: + +$$ +\mathcal {L} _ {i} = \mathcal {L} _ {\text {c o n t r a s t . i}} + \alpha \mathcal {L} _ {\mathrm {F N S} _ {- 1}} + \beta \mathcal {L} _ {\mathrm {F N S} _ {- 2}} + \gamma \mathcal {L} _ {\mathrm {T N E}} \tag {5} +$$ + +Table 1. Quantitative results of the model trained with Flickr 10k and 144k. Note that 'EZ-VSL + OGL' corresponds to the main results reported in [21]. 'EZ-VSL' indicates our reproduced results without OGL, which are not reported in [21]. We reproduce the results with the trained weights and code provided by [21]. + +
Train setMethodFlickr CIoU(%)Flickr AUC(%)VGG-SS CIoU(%)VGG-SS AUC(%)
Flickr 10kAttention10k [28]43.6044.90--
CoursetoFine [26]52.2049.60--
AVObject [1]54.6050.40--
LVS [8]58.2052.50--
EZ-VSL* [21]62.2454.7419.8630.96
Ours84.3363.2635.2738.00
EZ-VSL + OGL [21]81.9362.5837.6139.21
Ours + OGL84.7364.3440.9740.38
Flickr 144kAttention10k [28]66.0055.80--
DMC [15]67.1056.80--
LVS [8]69.9057.30--
HardPos [29]75.2059.70--
EZ-VSL* [21]72.6958.7030.2735.92
Ours78.7159.3333.9337.29
EZ-VSL + OGL [21]83.1363.0641.0140.23
Ours + OGL83.9363.0641.1040.44
+ +where $\alpha, \beta, \gamma$ are hyperparameters. + +# 4. Experiments + +# 4.1. Experimental Settings + +Datasets We train our audio-visual localization model on two datasets: Flickr SoundNet [6] and VGG-Sound [9]. Flickr SoundNet contains 2 million unconstrained videos from Flickr. For a fair comparison with the existing methods [8, 20, 21, 29], we conduct the training on two subsets of 10k and 144k paired samples from Flicker SoundNet. VGG-Sound includes 200k video clips from 309 classes. We also train on two subsets of 10k and 144k paired samples following the convention. + +Localization performances are measured on four benchmarks, Flickr [6], VGG-SS [9], Heard 110 and AVS-Bench [38]. The Flickr test set has 250 audio-visual pairs with manually labeled bounding boxes. VGG-SS is more challenging with 5,000 audio-visual pairs over 220 categories. Heard 110 is another subset of VGG-Sound to test the open-set learning ability. Its train set has 110 classes and the val set has another disjoint 110 unheard/unseen classes. Finally, AVSBench [38] is a recently proposed audio-visual dataset with 5,356 videos over 23 classes. It provides pixelwise labels for fine-grained localization evaluation. + +Implementation Details We implement our method with PyTorch. The images are resized and randomly cropped into $224 \times 224$ resolution, together with random horizontal flipping. The audio inputs are extracted from 3 seconds of audio clips and converted into log spectrogram maps. We also apply audio augmentation including Frequency mask and Time mask [25]. For both visual and audio encoders, we adopt ResNet18 [14] and the visual encoder is pretrained on ImageNet-1k [12]. The model is optimized for + +30 epochs with Adam using a learning rate of $10^{-4}$ and a weight decay of $10^{-4}$ . To achieve a stable representation, we warm up the network with only NCE loss for 3 epochs, then integrate our regularization for the remaining epochs. + +# 4.2. Comparison on Flickr-SoundNet and VGG-SS + +Flickr-SoundNet We train our model on Flickr 10k and 144k and report performances in Table 1. FNAC achieves superior performances over previous methods on both Flickr and VGG-SS test sets. Notably, compared to previous state-of-the-art EZ-VSL [21] on the Flickr test set, FNAC achieves a striking improvement of $22.09\%$ CIOU with 10k training samples and $6.02\%$ CIOU with 144k training samples. When tested on the more challenging VGGSS, FNAC also outperforms EZ-VSL by $15.41\%$ CIOU and $3.49\%$ CIOU respectively. Finally, Object-Guided localization (OGL) is a post-processing strategy that adopts pure visual-based localization results to refine audio-visual localization. For a fair comparison, we integrate FNAC with OGL to compare with EZ-VSL which also uses OGL. As shown, FNAC also outperforms EZ-VSL in most cases. + +VGG-SS Performance of the model trained on VGG-Sound 10k and 144k is reported in Table 2. FNAC also beats all previous methods with a clear margin. For example, on the VGG-SS test set, we outperform EZ-VSL by $11.45\%$ CIOU with 10k and $5.31\%$ CIOU with 144k. + +We highlight two results as demonstrated in Table 1 and Table 2. First, FNAC achieves similar results on $10\mathrm{k}$ and $144\mathrm{k}$ training sets in both Flickr SoundNet and VGGSound, which is not observed in previous models. We believe that small-scale datasets (Flickr $10\mathrm{k}$ , VGG-Sound $10\mathrm{k}$ ) have fewer semantic classes and will encounter more false negatives during training, so previous methods have substantial performance gaps between the $10\mathrm{k}$ and $144\mathrm{k}$ training + +Table 2. Quantitative results of models trained with VGG-SS 10k and 144k. + +
Train setMethodFlickr CIoU(%)Flickr AUC(%)VGG-SS CIoU(%)VGG-SS AUC(%)
VGGSound 10kLVS [8]61.8053.60--
EZ-VSL* [21]63.8554.4425.8433.68
Ours85.7463.6637.2938.99
EZ-VSL + OGL [21]78.7161.5338.7139.80
Ours + OGL82.1363.6440.6940.42
VGGSound 144kAttention10k [28]--18.5030.20
DMC [15]--29.1034.80
AVObject [1]--29.7035.70
LVS [8]73.5059.0034.4038.20
HardPos [29]76.8059.2034.6038.00
EZ-VSL [21]79.5161.1734.3837.70
Ours84.7363.7639.5039.66
EZ-VSL + OGL [21]83.9463.6038.8539.54
Ours + OGL85.1464.3041.8540.80
+ +Table 3. Quantitative results on Heard 110 and Unheard 110. For a fair comparison, the results of EZ-VSL [21] and ours are integrated with the OGL module. + +
Test SetMethodCIoU(%)AUC(%)
Heard 110LVS [8]28.9036.20
EZ-VSL [21]37.2538.97
Ours39.5439.83
Unheard 110LVS [8]26.3034.70
EZ-VSL [21]39.5739.60
Ours42.9141.17
+ +sets. It indicates that FNAC can effectively address the false negative issue and has a strong ability for representation learning on small-scale datasets. Second, we show cross-dataset evaluation results in both tables, i.e., train on Flickr and test on VGG-SS or vice versa. FNAC achieves strong results and outperforms existing methods, which validates the cross-dataset generalization ability of FNAC. We show qualitative localization results in Fig. 6. + +# 4.3. Comparison on Heard 110 and AVSBench + +Heard 110 To assess the generalization ability of FNAC in unseen/unheard audiovisual scenes, we conduct an open set experiment. We use the 70k samples covering 110 categories randomly sampled from VGGSound for training and then evaluate the model on the same 110 heard categories and another disjoint set with 110 unheard categories. As shown in Table 3, FNAC considerably outperforms previous methods, especially on Unheard 110 (42.91% vs. 39.57% of CIoU), which demonstrates the generalization ability of FNAC in unconstrained audio-visual data. + +AVSbench AVSbench [38] is a newly proposed audiovisual segmentation benchmark with pixel-level annotations, which can be regarded as a fine-grained sound source localization task and used to accurately evaluate the localization ability of models. We directly perform a zero-shot evaluation on the AVSbench with metrics of mIoU and + +Table 4. Zero-shot results on AVSBench S4 and MS3 [38]. All models are pretrained on VGGSound-144k dataset. + +
Test setMethodmIoUFScore
S4LVS23.69.251
EZ-VSL26.43.292
Ours27.15.314
MS3LVS18.54.174
EZ-VSL21.36.216
Ours21.98.225
+ +Table 5. Analysis of each component of the proposed FNAC. aud adj: audio adjacency matrix. img adj: image adjacency matrix. + +
FNSTNEFlickr CIoU(%)VGG-SS CIoU(%)
aud adjimg adj
77.9133.93
✓79.9135.85
✓81.9236.58
✓✓84.3336.92
✓81.1236.04
✓✓✓85.7437.29
+ +F-Score in two settings, Single Sound Source Segmentation (S4) and Multiple Sound Source Segmentation (MS3), without any fine-tuning. The results are reported in Table 4. The proposed method achieves outstanding performance on both S4 and MS3 settings, e.g., $27.15\%$ and $21.98\%$ mIoU when trained on VGGSound 144k. These results on the fine-grained localization benchmark validate the effectiveness of the TNE, which enables the model to discriminate authentic sound-source regions. + +# 4.4. Ablation Analysis of FNAC + +We propose different regularization terms to guide audio-visual contrastive learning. In Table 5, we ablate each component individually. All results are obtained following the same hyperparameter setting on VGG-SS $10\mathrm{k}$ and the baseline is trained with only NCE loss. First, the audio adjacency matrix and visual adjacency matrix are obtained in FNS to suppress the false negatives. We show that each adjacency matrix can improve the performances over the + +![](images/3c38491ece96ba70245d9addb63d848af1d7d5d53f170f05794d1cc467c80ef0.jpg) +Figure 6. Visualization comparison on Flickr-SoundNet (left) and VGG-SS (right) test sets. + +![](images/dc19afcddcd9dbd448ff4a0391ab6b86e069d234be21aae44bc8e3cfe68489b1.jpg) + +baseline, which indicates that potential false negatives can be effectively suppressed in both audio and visual modalities. By combining the two adjacency matrices together, FNS achieves $84.33\%$ CIoU on Flickr and $36.92\%$ CIoU on VGG-SS. Second, by only deploying TNE, we achieve improved results over baseline (81.12% CIoU on Flickr and $36.04\%$ CIoU on VGG-SS), indicating the effectiveness of TNE in enhancing true negatives. Finally, the combination of FNS and TNE achieves significant improvement over the baseline, showing the effectiveness of FNAC. We refer readers to supp. mat. for further ablation studies. + +# 4.5. Mining the Potential False Negatives + +In this section, we show quantitative and schematic analysis of the false negative mining ability of our method. Intuitively, a good audio-visual model should be able to generate similar feature representations for class matched samples. To validate this intuition, we construct a batch where all samples belong to the same category, i.e., all false negatives, and show the audio-visual similarity matrices of EZ-VSL [21] and ours in Fig. 7. As shown in the left, EZ-VSL only highlights the diagonal, since each audio feature is only similar to the paired image feature while all others are dissimilar despite all samples being from the same class. Differently, the similarity distribution of our matrix is more evenly spread as the majority of the samples are regarded as similar. It indicates that FNAC has implicitly learned semantically-aware features and clustered them in the latent space, so false negatives will be effectively identified as they are closer in terms of feature distance. + +Further, we show quantitative results of audio-visual similarities in Table 6. When the batch contains all true negatives, our average similarity score is lower than previous methods [8, 21]. When the batch contains all false negatives, our average similarity score is higher. The margin between the two similarities demonstrates our ability to distinguish false negatives and true negatives. + +![](images/c6c7b1babaa7784eda22c69796e87d12e55ed07dc3afb6ebf3de3bf4b1d4bd05.jpg) +Figure 7. Cross-modal similarity matrix predicted by EZ-VSL (left) and ours (right) when all samples in the batch belong to the same category, namely, they are false negatives of each other. All values are normalized between 0 to 1. + +Table 6. Audio-visual similarities with different data. TN: all samples in the batch belong to different categories. FN: all samples in the batch belong to the same category. + +
MethodTN ↓FN ↑
LVS0.44840.5102
EZ-VS10.58580.5938
Ours0.38120.6554
+ +# 5. Conclusion + +In this paper, we propose a simple yet effective strategy named FNAC to deal with the false negative issue in audio-visual sound source localization. We propose two complementary strategies to suppress false negatives (FNS) and enhance true negatives (TNE). The intra-modal adjacency matrices of audio and visual are generated to identify false negatives. Then two regularization terms are seamlessly incorporated with contrastive learning, which enable the model to learn semantic-aware features from audio-visual pairs. We show that FNAC can effectively mitigate the false negative issues and achieve state-of-the-art performance on several audio-visual localization benchmarks. We hope that our method can facilitate future research in audio-visual learning and other multi-modal tasks. + +# References + +[1] Triantafyllos Afouras, Andrew Owens, Joon Son Chung, and Andrew Zisserman. Self-supervised learning of audio-visual objects from video. 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], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 256, + 290, + 568 + ], + "spans": [ + { + "bbox": [ + 47, + 256, + 290, + 568 + ], + "type": "text", + "content": "Self-supervised audio-visual source localization aims to locate sound-source objects in video frames without extra annotations. Recent methods often approach this goal with the help of contrastive learning, which assumes only the audio and visual contents from the same video are positive samples for each other. However, this assumption would suffer from false negative samples in real-world training. For example, for an audio sample, treating the frames from the same audio class as negative samples may mislead the model and therefore harm the learned representations (e.g., the audio of a siren wailing may reasonably correspond to the ambulances in multiple images). Based on this observation, we propose a new learning strategy named False Negative Aware Contrastive (FNAC) to mitigate the problem of misleading the training with such false negative samples. Specifically, we utilize the intra-modal similarities to identify potentially similar samples and construct corresponding adjacency matrices to guide contrastive learning. Further, we propose to strengthen the role of true negative samples by explicitly leveraging the visual features of sound sources to facilitate the differentiation of authentic sounding source regions. FNAC achieves state-of-the-art performances on Flickr-SoundNet, VGG-Sound, and AVSBench, which demonstrates the effectiveness of our method in mitigating the false negative issue. The code is available at https://github.com/OpenNLPLab/FNAC_AVL." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 590, + 128, + 604 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 590, + 128, + 604 + ], + "spans": [ + { + "bbox": [ + 47, + 590, + 128, + 604 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 610, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 610, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 610, + 287, + 696 + ], + "type": "text", + "content": "When hearing a sound, humans can naturally imagine the visual appearance of the source objects and locate them in the scene. This demonstrates that audio-visual correspondence is an important ability for scene understanding. Given that unlimited paired audio-visual data exists in nature, there is an emerging interest in developing multi-modal systems with audio-visual understanding abl" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 321, + 229, + 529, + 338 + ], + "blocks": [ + { + "bbox": [ + 321, + 229, + 529, + 338 + ], + "lines": [ + { + "bbox": [ + 321, + 229, + 529, + 338 + ], + "spans": [ + { + "bbox": [ + 321, + 229, + 529, + 338 + ], + "type": "image", + "image_path": "2d032ca1ccbd37fec2429de14bc9c3ffdc0962911c5cdd7a9c3efc0a14a525e3.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 353, + 545, + 399 + ], + "lines": [ + { + "bbox": [ + 305, + 353, + 545, + 399 + ], + "spans": [ + { + "bbox": [ + 305, + 353, + 545, + 399 + ], + "type": "text", + "content": "Figure 1. False negative in audio-visual contrastive learning. Audio-visual pairs with similar contents are falsely considered as negative samples to each other and pushed apart in the shared latent space, which we find would affect the model performance." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 413, + 546, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 413, + 546, + 510 + ], + "spans": [ + { + "bbox": [ + 304, + 413, + 546, + 510 + ], + "type": "text", + "content": "ity. Various audio-visual tasks have been studied, including sound source localization [8, 19–21, 26–28], audio-visual event localization [32, 33, 35, 39], audio-visual video parsing [11, 18, 31] and audio-visual segmentation [37, 38]. In this work, we focus on unsupervised visual sound source localization, with the aim of localizing the sound-source objects in an image using its paired audio clip, but without relying on any manual annotations." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 510, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 547, + 715 + ], + "type": "text", + "content": "The essence of unsupervised visual sound source localization is to leverage the co-occurrences between an audio clip and its corresponding image to extract representations. A major part of existing methods [8, 19–21, 28] formulates this task as contrastive learning. For each image sample, its paired audio clip is viewed as the positive sample, while all other audio clips are considered as negative. Likewise, each audio clip considers its paired image as positive and all others as negative. As such, the Noise Contrastive Estimation (NCE) loss [24, 30] is used to perform instance discrimination by pushing closer the distance between a positive audio-image pair, while pulling away any negative pairs. However, the contrastive learning scheme above suffers from the issue of false negatives during training, i.e., audio/image samples that belong to the semantically-matched class but are not regarded as a positive pair (due to the lack of manual labeling). A typical example is shown" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 153, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 153, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 153, + 712 + ], + "type": "text", + "content": "*Indicates equal contribution" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6420" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "content": "in Fig. 1. Research shows [4, 16, 29, 36] that these false negatives will lead to contradictory objectives and harm the representation learning." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 109, + 287, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 109, + 287, + 240 + ], + "spans": [ + { + "bbox": [ + 46, + 109, + 287, + 240 + ], + "type": "text", + "content": "Motivated by this observation, we assess the impact of false negatives in real-world training. We discover that with a batch size of 128, around " + }, + { + "bbox": [ + 46, + 109, + 287, + 240 + ], + "type": "inline_equation", + "content": "40\\%" + }, + { + "bbox": [ + 46, + 109, + 287, + 240 + ], + "type": "text", + "content": " of the samples in VGG-Sound [9] will encounter at least one false negative sample during training. We then validate that false negatives indeed harm performance by artificially increasing the proportion of false negatives during training, and observing a noticeable performance drop. To make matters worse, larger batch sizes are often preferred in contrastive learning [24], but it may inadvertently increase the number of false negative samples during training and affect representation quality." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 240, + 286, + 372 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 240, + 286, + 372 + ], + "spans": [ + { + "bbox": [ + 46, + 240, + 286, + 372 + ], + "type": "text", + "content": "To this end, we propose a false-negative aware audio-visual contrastive learning framework (FNAC), where we employ the intra-modal similarities as weak supervision. Specifically, we compute pair-wise similarities between all audio clips in a mini-batch without considering the visual to form an audio intra-modal adjacency matrix. Likewise, in the visual modality, we obtain an image adjacency matrix. We found that the adjacency matrices effectively identify potential samples of the same class within each modality (Fig. 4). The information can then be used to mitigate the false negatives and enhance the effect of true pairings." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 373, + 286, + 622 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 373, + 286, + 622 + ], + "spans": [ + { + "bbox": [ + 46, + 373, + 286, + 622 + ], + "type": "text", + "content": "Specifically, we propose two complementary strategies: 1) FNS for False Negatives Suppression, and 2) TNE for True Negatives Enhancement. First, when optimizing the NCE loss, FNS regularizes the inter-modal and intra-modal similarities. Intrinsically, intra-modal adjacency explores potential false negatives by the similarity intensities and the pulling forces applied to these false negatives are canceled accordingly. Furthermore, we introduce TNE to emphasize the true negative influences in a region-wise manner, which in turn reduces the effect of false negative samples as well. We adopt the audio adjacency matrix to identify dissimilar samples, i.e., true negatives. Intuitively, dissimilar (true negative) sounds correspond to distinct regions, so the localized regions across the identified true negatives are regularized to be different. Such a mechanism encourages the model to discriminate genuine sound-source regions and suppress the co-occurring quiet objects. we conduct extensive analysis to demonstrate the effectiveness of our proposed method and report competitive performances across different settings and datasets. In summary, our main contributions are:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 58, + 632, + 286, + 713 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 58, + 632, + 286, + 668 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 632, + 286, + 668 + ], + "spans": [ + { + "bbox": [ + 58, + 632, + 286, + 668 + ], + "type": "text", + "content": "- We investigate the false negative issue in audio-visual contrastive learning. We quantitatively validate that this issue occurs and harms the representation quality." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 58, + 677, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 677, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 677, + 286, + 713 + ], + "type": "text", + "content": "- We exploit intra-modal similarities to identify potential false negatives and introduce FNS to suppress their impact." + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 317, + 72, + 545, + 118 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 72, + 545, + 118 + ], + "spans": [ + { + "bbox": [ + 317, + 72, + 545, + 118 + ], + "type": "text", + "content": "- We propose TNE, which emphasizes true negatives using different localization results between the identified true negatives, thus encouraging more discriminative sound source localizations." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 133, + 392, + 146 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 133, + 392, + 146 + ], + "spans": [ + { + "bbox": [ + 306, + 133, + 392, + 146 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 155, + 545, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 155, + 545, + 453 + ], + "spans": [ + { + "bbox": [ + 304, + 155, + 545, + 453 + ], + "type": "text", + "content": "False Negatives in Contrastive Learning. Typical contrastive learning employs instance discrimination [34] as a pretext task, in which two augmented views of the same image are considered as positive pairs, while views of all other images are treated as negative pairs, regardless of semantic similarities. Such a scheme inevitably suffers from the False Negatives issue [10, 13, 16, 36], which indicates that instances sharing the same semantic concepts are falsely treated as negatives, thus misleading model learning. Based on this, some works attempt to incorporate similar instances into model training to eliminate the impact of false negatives. For example, Zheng et al. [36] model a nearest neighbor graph for each batch of instances and execute a KNN-based multi-crop strategy to detect false negatives. Similarly, Dwibedi et al. [13] sample nearest neighbors from the dataset and treat them as positives for contrastive learning. More recently, [16] and [10] study how to identify false negatives without class labels and explicitly remove detected false negatives by two strategies, elimination and attraction, to improve contrastive loss. Other works use clustering-based methods to encode semantic structures [5, 7, 17] and then perform contrastive learning on these semantically similar cluster centers. In this paper, we propose and explore a similar problem in self-supervised audio-visual learning." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 474, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 545, + 713 + ], + "type": "text", + "content": "Self-Supervised Sound Source Localization. Sound source localization aims to learn to locate sound-source regions in videos. Recent approaches extensively leverage contrastive learning based on audiovisual correspondence to address this issue. For example, [2, 3, 28] adopt a dual-stream architecture to extract unimodal features respectively and then calculate a contrastive loss to update the audiovisual network. The final localization map is usually obtained by calculating the cosine similarity between audio and visual features. Following the paradigm, Mo et al. [21] further propose an object-guided localization (OGL) module, an extra pre-trained visual encoder, to introduce visual priors into the localization results. Nevertheless, these works assume that the paired audio-visual signals are regularly aligned and all mismatched samples are heterogeneous. As aforementioned, the assumption ignores the semantic similarities between samples. Accordingly, Chen et al. [8] incorporate explicitly background regions with low correlation to the given audio into the framework and regard them as hard negatives. In a slightly different task" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "6421" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 65, + 73, + 270, + 192 + ], + "blocks": [ + { + "bbox": [ + 65, + 73, + 270, + 192 + ], + "lines": [ + { + "bbox": [ + 65, + 73, + 270, + 192 + ], + "spans": [ + { + "bbox": [ + 65, + 73, + 270, + 192 + ], + "type": "image", + "image_path": "f71a7b9b860136bb7e5a07e79031e6df49ba0d49008e031c5582caaf0858df6a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 205, + 287, + 272 + ], + "lines": [ + { + "bbox": [ + 46, + 205, + 287, + 272 + ], + "spans": [ + { + "bbox": [ + 46, + 205, + 287, + 272 + ], + "type": "text", + "content": "Figure 2. Impact of false negatives on audio-visual representation learning. We adopt Consensus Intersection over Union (CIoU) [28] as an evaluation metric (higher is better) and report results on FlickrSoundNet [6] and VGG-SS [9] test sets, depicted by blue and brown, respectively. An obvious performance decline is observed as the proportion of false negative samples increases." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 286, + 289, + 478 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 286, + 289, + 478 + ], + "spans": [ + { + "bbox": [ + 46, + 286, + 289, + 478 + ], + "type": "text", + "content": "setting of audio-visual instance discrimination, false negative issues are also investigated. [23] detects false negatives by defining sets of positive and negative samples via cross-modal agreement, where positive samples are defined as similar samples in both modalities. [22] considers both false positive and false negative issues. For false negatives, they estimate the similarity across instances to compute a soft target distribution over instances so the contributions of false negatives are down-weighted. One work that explores a similar problem to us is [29], which treats top-K semantically similar audio-visual pairs as hard positives and explicitly integrates them into the contrastive loss. Unfortunately, this method relies on manually selected hypermeters K and a hard threshold. Unlike the previous methods, this paper uses intra-modal adjacency matrices to adaptively detect false negatives and eliminate their impact." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 488, + 103, + 500 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 488, + 103, + 500 + ], + "spans": [ + { + "bbox": [ + 47, + 488, + 103, + 500 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 509, + 287, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 509, + 287, + 593 + ], + "spans": [ + { + "bbox": [ + 46, + 509, + 287, + 593 + ], + "type": "text", + "content": "In this section, we first investigate the problem raised by false negative samples in Sec. 3.1, and then propose to mitigate the problem. From two aspects, without supervision we identify the false negative samples to explicitly suppress them in training (Sec. 3.2), and use region-wise comparing learning to enhance the roles of true negative samples which hence relatively suppresses false negatives (Sec. 3.2)." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 599, + 284, + 613 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 599, + 284, + 613 + ], + "spans": [ + { + "bbox": [ + 47, + 599, + 284, + 613 + ], + "type": "text", + "content": "3.1. Revisiting Audio-visual Contrasting Learning" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "type": "text", + "content": "Various methods for audio-visual localization [18,21,28] employ a contrastive learning framework, in a manner of instance discrimination. Arguably, it assumes the audio-visual scenes from different videos are distinctive. Therefore the paired audio and image from the same video are considered a positive pair while the samples (audio or image) from other pairs are regarded as negatives. Specifically, we denote an audio-visual dataset as " + }, + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{D} \\in \\{(a_i, v_i), i \\in" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 72, + 545, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 228 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 228 + ], + "type": "inline_equation", + "content": "[0,n)\\}" + }, + { + "bbox": [ + 305, + 72, + 545, + 228 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 305, + 72, + 545, + 228 + ], + "type": "inline_equation", + "content": "(a_i,v_i)" + }, + { + "bbox": [ + 305, + 72, + 545, + 228 + ], + "type": "text", + "content": " represents a sample with paired audio-visual content. Usually, a two-stream network is used to encode audio and visual signals and then map them into a shared latent space. The audio and visual representations extracted from " + }, + { + "bbox": [ + 305, + 72, + 545, + 228 + ], + "type": "inline_equation", + "content": "(a_i,v_i)" + }, + { + "bbox": [ + 305, + 72, + 545, + 228 + ], + "type": "text", + "content": " are denoted as " + }, + { + "bbox": [ + 305, + 72, + 545, + 228 + ], + "type": "inline_equation", + "content": "Z_{i}^{a}\\in \\mathbb{R}^{1\\times d}" + }, + { + "bbox": [ + 305, + 72, + 545, + 228 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 72, + 545, + 228 + ], + "type": "inline_equation", + "content": "Z_{i}^{v}\\in \\mathbb{R}^{1\\times d}" + }, + { + "bbox": [ + 305, + 72, + 545, + 228 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 305, + 72, + 545, + 228 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 305, + 72, + 545, + 228 + ], + "type": "text", + "content": " as feature dimension. Ideally, " + }, + { + "bbox": [ + 305, + 72, + 545, + 228 + ], + "type": "inline_equation", + "content": "Z_{i}^{a}" + }, + { + "bbox": [ + 305, + 72, + 545, + 228 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 72, + 545, + 228 + ], + "type": "inline_equation", + "content": "Z_{i}^{v}" + }, + { + "bbox": [ + 305, + 72, + 545, + 228 + ], + "type": "text", + "content": " represent the same semantic concept from the visual and audio perspectives, e.g., playing the drum. The optimization objective of contrastive learning is to maximize the similarity between audio and visual representations from the same video while minimizing the similarity between features from different videos. Mathematically, it can be formulated in a modal-symmetric way for a pair " + }, + { + "bbox": [ + 305, + 72, + 545, + 228 + ], + "type": "inline_equation", + "content": "(a_i,v_i)" + }, + { + "bbox": [ + 305, + 72, + 545, + 228 + ], + "type": "text", + "content": " as:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 327, + 233, + 545, + 299 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 327, + 233, + 545, + 299 + ], + "spans": [ + { + "bbox": [ + 327, + 233, + 545, + 299 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {\\text {c o n t r a s t . i}} = - \\log \\frac {\\exp \\left[ \\frac {1}{\\tau} \\operatorname {s i m} \\left(Z _ {i} ^ {a} , Z _ {i} ^ {v}\\right) \\right]}{\\sum_ {j} ^ {b} \\exp \\left[ \\frac {1}{\\tau} \\operatorname {s i m} \\left(Z _ {i} ^ {a} , Z _ {j} ^ {v}\\right) \\right]} \\\\ - \\log \\frac {\\exp \\left[ \\frac {1}{\\tau} \\operatorname {s i m} \\left(Z _ {i} ^ {v} , Z _ {i} ^ {a}\\right) \\right]}{\\sum_ {j} ^ {b} \\exp \\left[ \\frac {1}{\\tau} \\operatorname {s i m} \\left(Z _ {i} ^ {v} , Z _ {j} ^ {a}\\right) \\right]}, \\tag {1} \\\\ \\end{array}", + "image_path": "e02370b2d5193dd2a135cdfc53d31452842a8bfe5814c08df420d70eb618dd0d.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 304, + 545, + 425 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 304, + 545, + 425 + ], + "spans": [ + { + "bbox": [ + 305, + 304, + 545, + 425 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 304, + 545, + 425 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 305, + 304, + 545, + 425 + ], + "type": "text", + "content": " is a temperature hyper-parameter, " + }, + { + "bbox": [ + 305, + 304, + 545, + 425 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 305, + 304, + 545, + 425 + ], + "type": "text", + "content": " denotes batch size and sim represents the similarity function. Intuitively, this loss implies that each audio feature " + }, + { + "bbox": [ + 305, + 304, + 545, + 425 + ], + "type": "inline_equation", + "content": "Z_{i}^{a}" + }, + { + "bbox": [ + 305, + 304, + 545, + 425 + ], + "type": "text", + "content": " is pushed close to its paired visual feature " + }, + { + "bbox": [ + 305, + 304, + 545, + 425 + ], + "type": "inline_equation", + "content": "Z_{i}^{v}" + }, + { + "bbox": [ + 305, + 304, + 545, + 425 + ], + "type": "text", + "content": " in the shared latent space, while pulled apart from the rest " + }, + { + "bbox": [ + 305, + 304, + 545, + 425 + ], + "type": "inline_equation", + "content": "(b - 1)" + }, + { + "bbox": [ + 305, + 304, + 545, + 425 + ], + "type": "text", + "content": " visual features " + }, + { + "bbox": [ + 305, + 304, + 545, + 425 + ], + "type": "inline_equation", + "content": "Z_{j,j\\neq i}^{v}" + }, + { + "bbox": [ + 305, + 304, + 545, + 425 + ], + "type": "text", + "content": ". However, as discussed, there exist " + }, + { + "bbox": [ + 305, + 304, + 545, + 425 + ], + "type": "inline_equation", + "content": "\\hat{Z}_j^a" + }, + { + "bbox": [ + 305, + 304, + 545, + 425 + ], + "type": "text", + "content": " and/or " + }, + { + "bbox": [ + 305, + 304, + 545, + 425 + ], + "type": "inline_equation", + "content": "\\hat{Z}_j^v" + }, + { + "bbox": [ + 305, + 304, + 545, + 425 + ], + "type": "text", + "content": " that are semantically similar to " + }, + { + "bbox": [ + 305, + 304, + 545, + 425 + ], + "type": "inline_equation", + "content": "(Z_i^a,Z_i^v)" + }, + { + "bbox": [ + 305, + 304, + 545, + 425 + ], + "type": "text", + "content": ", i.e., false negatives. In this situation, forcing " + }, + { + "bbox": [ + 305, + 304, + 545, + 425 + ], + "type": "inline_equation", + "content": "\\mathrm{sim}(Z_i^a,\\hat{Z}_j^v)" + }, + { + "bbox": [ + 305, + 304, + 545, + 425 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 305, + 304, + 545, + 425 + ], + "type": "inline_equation", + "content": "\\mathrm{sim}(Z_i^v,\\hat{Z}_j^a)" + }, + { + "bbox": [ + 305, + 304, + 545, + 425 + ], + "type": "text", + "content": " to be small might perplex the model training and lead to a non-optimal representation." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 438, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 438, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 438, + 545, + 714 + ], + "type": "text", + "content": "Impact of False Negatives. Based on this observation, we conduct several pilot experiments to verify the issue of false negatives and their influence on audio-visual representation learning. For simplification, we reasonably assume that samples that share the same manually labeled category are False Negatives. Firstly, we examine the data distribution during the training procedure. We find that over " + }, + { + "bbox": [ + 304, + 438, + 545, + 714 + ], + "type": "inline_equation", + "content": "39.27\\%" + }, + { + "bbox": [ + 304, + 438, + 545, + 714 + ], + "type": "text", + "content": " samples suffer from at least one false negative sample when training with a batch size of 128 on the VGG-Sound dataset [9] covering 309 categories. This ratio will undoubtedly increase when employing bigger batch sizes or fewer categories. Secondly, we examine how the false negative issue might affect audio-visual localization performance. Following prior works [8, 21], we adopt ResNet-18 as the backbone to encode audio and visual features and a standard NCE loss [24] is used. In particular, we manually substitute the true negatives with false negatives in the training samples. As shown in Fig 2, when the false negative rate is progressively increased, a significant performance decline is found, indicating that the model is perplexed by these similar samples. The experiments above demonstrate that false negatives substantially impact the model quality and cannot be disregarded." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6422" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 141, + 72, + 449, + 190 + ], + "blocks": [ + { + "bbox": [ + 141, + 72, + 449, + 190 + ], + "lines": [ + { + "bbox": [ + 141, + 72, + 449, + 190 + ], + "spans": [ + { + "bbox": [ + 141, + 72, + 449, + 190 + ], + "type": "image", + "image_path": "49d0e5bd7f38d374699852d5cc8ad2482079dd9aeb24b5b401a30bda6842ba0f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 206, + 546, + 231 + ], + "lines": [ + { + "bbox": [ + 46, + 206, + 546, + 231 + ], + "spans": [ + { + "bbox": [ + 46, + 206, + 546, + 231 + ], + "type": "text", + "content": "Figure 3. An overview of False Negative Suppression (FNS). The main optimization objective is NCE [24] loss on audio-visual pairs. The audio adjacency matrix and visual adjacency matrix are respectively constructed to suppress false negatives by regularizing NCE loss." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 126, + 241, + 468, + 327 + ], + "blocks": [ + { + "bbox": [ + 126, + 241, + 468, + 327 + ], + "lines": [ + { + "bbox": [ + 126, + 241, + 468, + 327 + ], + "spans": [ + { + "bbox": [ + 126, + 241, + 468, + 327 + ], + "type": "image", + "image_path": "066a33f2c98d9ff38a772814ff483ebfd51d9dab4e58e87312f1eebfdef90a98.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 335, + 546, + 360 + ], + "lines": [ + { + "bbox": [ + 46, + 335, + 546, + 360 + ], + "spans": [ + { + "bbox": [ + 46, + 335, + 546, + 360 + ], + "type": "text", + "content": "Figure 4. Qualitative samples of the found potential false negatives in visual and audio modalities. We report the nearest sample for every anchor. For the audio modality, we show the corresponding images here." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 378, + 288, + 403 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 378, + 288, + 403 + ], + "spans": [ + { + "bbox": [ + 47, + 378, + 288, + 403 + ], + "type": "text", + "content": "3.2. Mitigating False Negatives in Audio Visual Learning" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 409, + 287, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 409, + 287, + 564 + ], + "spans": [ + { + "bbox": [ + 46, + 409, + 287, + 564 + ], + "type": "text", + "content": "As discussed in Sec. 3.1, we prove that the unpaired positive samples (i.e., false negatives) existed in every minibatch that may harm the representations. Correspondingly, we propose to solve this problem by FNAC with two complementary methods, False Negatives Suppression (FNS) and True Negatives Enhancement (TNE). For the same goal of mitigating the false negative issue, FNS identifies the false negative samples and regularizes to reduce their effects, while TNE enhances the contribution of true negatives by region-wise comparison, which also inadvertently suppresses false negatives. Both methods can be seamlessly integrated into the audio-visual contrastive framework as regularization terms." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 582, + 287, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 287, + 653 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 287, + 653 + ], + "type": "text", + "content": "FNS: False Negatives Suppression. To suppress the false negative effects, two challenges are posed. First, distinguishing the potential false negative samples within the current mini-batch without extra supervision such as class labels. Second, eliminating the misleading effects of the identified false negatives." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 654, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 287, + 715 + ], + "type": "text", + "content": "For the first challenge, we propose to leverage the unimodal feature representations to calculate pair-wise sample similarities, i.e., adjacency matrix. As shown in Fig. 3, the audio clips are fed into an audio encoder to obtain audio features " + }, + { + "bbox": [ + 46, + 654, + 287, + 715 + ], + "type": "inline_equation", + "content": "Z^{a} \\in \\mathbb{R}^{b \\times d}" + }, + { + "bbox": [ + 46, + 654, + 287, + 715 + ], + "type": "text", + "content": ", then we calculate a dot product with" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 378, + 546, + 499 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 378, + 546, + 499 + ], + "spans": [ + { + "bbox": [ + 304, + 378, + 546, + 499 + ], + "type": "inline_equation", + "content": "(Z^{a})^{T}" + }, + { + "bbox": [ + 304, + 378, + 546, + 499 + ], + "type": "text", + "content": " followed by a row-wise softmax to obtain the pairwise self-similarity matrix " + }, + { + "bbox": [ + 304, + 378, + 546, + 499 + ], + "type": "inline_equation", + "content": "S^{a} \\in \\mathbb{R}^{b \\times b}" + }, + { + "bbox": [ + 304, + 378, + 546, + 499 + ], + "type": "text", + "content": ", i.e., the audio adjacency matrix. Likewise, we average-pool the image features and obtain a visual adjacency matrix " + }, + { + "bbox": [ + 304, + 378, + 546, + 499 + ], + "type": "inline_equation", + "content": "S^{v} \\in \\mathbb{R}^{b \\times b}" + }, + { + "bbox": [ + 304, + 378, + 546, + 499 + ], + "type": "text", + "content": ". Such adjacency matrices encode pair-wise similarities across a batch without considering inter-modal connection. For each audio-visual sample, we show its nearest sample by querying the adjacency matrices, as shown in Fig 4. It indicates that intra-modal adjacency matrices can effectively identify potential class-matched samples." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 510, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 547, + 713 + ], + "type": "text", + "content": "Regarding the second challenge, we propose to impose intra-modal adjacency as a soft supervision signal for inter-modal contrastive learning, i.e., audio-visual similarities should be statistically consistent with the intramodal similarities. In other words, if two scenes are close, their audio features similarity value " + }, + { + "bbox": [ + 304, + 510, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{sim}(Z_i^a,Z_j^a)" + }, + { + "bbox": [ + 304, + 510, + 547, + 713 + ], + "type": "text", + "content": " should be high, the visual similarity " + }, + { + "bbox": [ + 304, + 510, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{sim}(Z_i^v,Z_j^v)" + }, + { + "bbox": [ + 304, + 510, + 547, + 713 + ], + "type": "text", + "content": " should match, and the cross-modal similarities " + }, + { + "bbox": [ + 304, + 510, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{sim}(Z_i^a,Z_j^v)" + }, + { + "bbox": [ + 304, + 510, + 547, + 713 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 304, + 510, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{sim}(Z_i^v,Z_j^a)" + }, + { + "bbox": [ + 304, + 510, + 547, + 713 + ], + "type": "text", + "content": " should also show consistency. Therefore, we leverage intramodal similarity as a supervision signal for audio-visual contrastive learning. Technically, we could utilize hard thresholds to achieve pseudo labels from intra-modal similarity like [8, 29, 36], which can serve to identify potential false negatives samples or areas. However, such methods require parameter tuning, and misassigned labels can exacerbate the false-negative problem. Differently, we propose FNS that directly regularizes the similarity scores. For a" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6423" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 141, + 70, + 443, + 194 + ], + "blocks": [ + { + "bbox": [ + 141, + 70, + 443, + 194 + ], + "lines": [ + { + "bbox": [ + 141, + 70, + 443, + 194 + ], + "spans": [ + { + "bbox": [ + 141, + 70, + 443, + 194 + ], + "type": "image", + "image_path": "294c38639258ba3917471b7cc56233dc259609492e12634cfb807a6003a31404.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 212, + 547, + 246 + ], + "lines": [ + { + "bbox": [ + 46, + 212, + 547, + 246 + ], + "spans": [ + { + "bbox": [ + 46, + 212, + 547, + 246 + ], + "type": "text", + "content": "Figure 5. An overview of True Negative Enhancement (TNE). The visual features from localized regions are extracted to construct a sound-source visual feature adjacency matrix. The audio adjacency matrix is used to regularize the sound-source visual feature adjacency matrix to enhance true negatives." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 265, + 259, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 265, + 259, + 277 + ], + "spans": [ + { + "bbox": [ + 47, + 265, + 259, + 277 + ], + "type": "text", + "content": "sample " + }, + { + "bbox": [ + 47, + 265, + 259, + 277 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 47, + 265, + 259, + 277 + ], + "type": "text", + "content": ", its optimization objective is formulated as:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 54, + 285, + 287, + 320 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 285, + 287, + 320 + ], + "spans": [ + { + "bbox": [ + 54, + 285, + 287, + 320 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {F N S} - 1} = \\frac {1}{b} \\sum_ {j} ^ {b} \\mathcal {L} _ {\\text {d i s t}} \\left(\\operatorname {s i m} \\left(Z _ {i} ^ {a}, Z _ {j} ^ {v}\\right), \\operatorname {s i m} \\left(Z _ {i} ^ {a}, Z _ {j} ^ {a}\\right)\\right) \\tag {2}", + "image_path": "343d9d119dd8e7a4b3383df7c756c409e35c9742dfec7abddb9634803285788c.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 54, + 322, + 287, + 356 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 322, + 287, + 356 + ], + "spans": [ + { + "bbox": [ + 54, + 322, + 287, + 356 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {F N S} - 2} = \\frac {1}{b} \\sum_ {j} ^ {b} \\mathcal {L} _ {\\text {d i s t}} \\left(\\operatorname {s i m} \\left(Z _ {i} ^ {a}, Z _ {j} ^ {v}\\right), \\operatorname {s i m} \\left(Z _ {i} ^ {v}, Z _ {j} ^ {v}\\right)\\right) \\tag {3}", + "image_path": "7fb68df791132220afc81e29f8806c0e4568c950edb2eea0039cab0232f1229d.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 364, + 289, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 364, + 289, + 520 + ], + "spans": [ + { + "bbox": [ + 46, + 364, + 289, + 520 + ], + "type": "text", + "content": "For an audio sample " + }, + { + "bbox": [ + 46, + 364, + 289, + 520 + ], + "type": "inline_equation", + "content": "a_i" + }, + { + "bbox": [ + 46, + 364, + 289, + 520 + ], + "type": "text", + "content": ", the NCE loss " + }, + { + "bbox": [ + 46, + 364, + 289, + 520 + ], + "type": "inline_equation", + "content": "L_{\\text{contrast\\_i}}" + }, + { + "bbox": [ + 46, + 364, + 289, + 520 + ], + "type": "text", + "content": " in Eq. 1 pushes all negatives away by encouraging " + }, + { + "bbox": [ + 46, + 364, + 289, + 520 + ], + "type": "inline_equation", + "content": "\\sin(Z_i^a, Z_j^v)_{j \\in [0,n), j \\neq i}" + }, + { + "bbox": [ + 46, + 364, + 289, + 520 + ], + "type": "text", + "content": " to be close to 0, whereas FNS pulls back false negatives to suppress their effects. The suppression intensity corresponds to the values of " + }, + { + "bbox": [ + 46, + 364, + 289, + 520 + ], + "type": "inline_equation", + "content": "\\sin(Z_i^a, Z_j^a)" + }, + { + "bbox": [ + 46, + 364, + 289, + 520 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 364, + 289, + 520 + ], + "type": "inline_equation", + "content": "\\sin(Z_i^v, Z_j^v)" + }, + { + "bbox": [ + 46, + 364, + 289, + 520 + ], + "type": "text", + "content": ". In Eq. 3, the visual contrastive loss is calculated symmetrically. In practice, we calculate L1 distances between the inter-modal contrastive matrix and intra-modal adjacency matrices as shown in Fig. 3, so all pair-wise similarities are considered. Such a regularization term yields a parameter-free process so that we do not need to choose a hard threshold to determine the real false negatives, as the false negative effects can be adaptively regularized." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 533, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 533, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 533, + 287, + 677 + ], + "type": "text", + "content": "TNE: True Negatives Enhancement. To further reduce the misleading effect of false negatives, we propose to enhance the contribution of true negatives by region-wise comparison. As opponents, the impact of true negatives and that of false negatives are relative, so if the role of true negatives is raised, the role of false negatives would be suppressed. To improve the effect of true negatives in audio-visual learning, we turn back to its core concept, i.e., that the sound source objects are different both audibly and visually between the true negatives. Therefore, it is straightforward to put a particular emphasis on the possible regions of genuine sound-emitting objects." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 677, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 288, + 713 + ], + "type": "text", + "content": "Specifically, we localize the sound-source objects by paired audio-visual samples, pop up their regional visual features, and encourage those of true negative samples to" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 265, + 545, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 265, + 545, + 324 + ], + "spans": [ + { + "bbox": [ + 304, + 265, + 545, + 324 + ], + "type": "text", + "content": "be pulled away. The process is called true negative enhancement (TNE). It is worth noting that similar regularizations have been mentioned but disregarded by previous methods [8,21,29] because they did not distinguish the true negatives and false negatives samples." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 324, + 546, + 516 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 324, + 546, + 516 + ], + "spans": [ + { + "bbox": [ + 304, + 324, + 546, + 516 + ], + "type": "text", + "content": "We show the paradigm of TNE in Fig. 5. Given an audio-visual pair " + }, + { + "bbox": [ + 304, + 324, + 546, + 516 + ], + "type": "inline_equation", + "content": "(a_i, v_i)" + }, + { + "bbox": [ + 304, + 324, + 546, + 516 + ], + "type": "text", + "content": ", we obtain its localization result and use the localization map as a mask to extract the localized visual representation " + }, + { + "bbox": [ + 304, + 324, + 546, + 516 + ], + "type": "inline_equation", + "content": "Z_i^s \\in \\mathbb{R}^{d \\times h \\times w}" + }, + { + "bbox": [ + 304, + 324, + 546, + 516 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 324, + 546, + 516 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 304, + 324, + 546, + 516 + ], + "type": "text", + "content": " indicates it is sounding region visual representation. In other words, " + }, + { + "bbox": [ + 304, + 324, + 546, + 516 + ], + "type": "inline_equation", + "content": "Z_i^s" + }, + { + "bbox": [ + 304, + 324, + 546, + 516 + ], + "type": "text", + "content": " denotes the visual features that are aligned with the paired audio features. Then, consider another arbitrary audio-visual pair " + }, + { + "bbox": [ + 304, + 324, + 546, + 516 + ], + "type": "inline_equation", + "content": "(a_j, v_j)" + }, + { + "bbox": [ + 304, + 324, + 546, + 516 + ], + "type": "text", + "content": " which localizes visual features " + }, + { + "bbox": [ + 304, + 324, + 546, + 516 + ], + "type": "inline_equation", + "content": "Z_j^s" + }, + { + "bbox": [ + 304, + 324, + 546, + 516 + ], + "type": "text", + "content": ". If " + }, + { + "bbox": [ + 304, + 324, + 546, + 516 + ], + "type": "inline_equation", + "content": "a_i" + }, + { + "bbox": [ + 304, + 324, + 546, + 516 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 324, + 546, + 516 + ], + "type": "inline_equation", + "content": "a_j" + }, + { + "bbox": [ + 304, + 324, + 546, + 516 + ], + "type": "text", + "content": " are semantically different, i.e., " + }, + { + "bbox": [ + 304, + 324, + 546, + 516 + ], + "type": "inline_equation", + "content": "a_j" + }, + { + "bbox": [ + 304, + 324, + 546, + 516 + ], + "type": "text", + "content": " is a true negative of " + }, + { + "bbox": [ + 304, + 324, + 546, + 516 + ], + "type": "inline_equation", + "content": "a_i" + }, + { + "bbox": [ + 304, + 324, + 546, + 516 + ], + "type": "text", + "content": ", then the " + }, + { + "bbox": [ + 304, + 324, + 546, + 516 + ], + "type": "inline_equation", + "content": "Z_i^s" + }, + { + "bbox": [ + 304, + 324, + 546, + 516 + ], + "type": "text", + "content": " should be dissimilar to " + }, + { + "bbox": [ + 304, + 324, + 546, + 516 + ], + "type": "inline_equation", + "content": "Z_j^s" + }, + { + "bbox": [ + 304, + 324, + 546, + 516 + ], + "type": "text", + "content": ". It encourages the model to focus on different pixels so as to mine discriminative visual features according to the audio similarities. To leverage such a constraint in practice, we regularize the audio adjacency matrix and the similarities between the sounding region visual features. Formally, the TNE regularization is:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 316, + 533, + 545, + 567 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 533, + 545, + 567 + ], + "spans": [ + { + "bbox": [ + 316, + 533, + 545, + 567 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {T N E}} = \\frac {1}{b} \\sum_ {j} ^ {b} \\mathcal {L} _ {\\text {d i s t}} \\left(\\operatorname {s i m} \\left(Z _ {i} ^ {a}, Z _ {j} ^ {a}\\right), \\operatorname {s i m} \\left(Z _ {i} ^ {s}, Z _ {j} ^ {s}\\right)\\right) \\tag {4}", + "image_path": "1b6f364b7e92a76a19a6bbe29df776fd2894c34ad85b2b6b9d2c007620202446.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 573, + 547, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 573, + 547, + 693 + ], + "spans": [ + { + "bbox": [ + 304, + 573, + 547, + 693 + ], + "type": "text", + "content": "FNS and TNE are two general mechanisms for multimodal contrastive learning. FNS adopts audio and visual adjacency matrices to explore the potential false negatives and suppress their misleading effects on the NCE loss. TNE uses audio adjacency to discriminate the sound-source localization so the model tends to discover the genuine sound sources. Both methods can be seamlessly integrated with the existing contrastive learning framework as extra regularization terms. Our final optimization objective for the " + }, + { + "bbox": [ + 304, + 573, + 547, + 693 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 573, + 547, + 693 + ], + "type": "text", + "content": "-th sample pair is:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 319, + 701, + 545, + 714 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 319, + 701, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 319, + 701, + 545, + 714 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {i} = \\mathcal {L} _ {\\text {c o n t r a s t . i}} + \\alpha \\mathcal {L} _ {\\mathrm {F N S} _ {- 1}} + \\beta \\mathcal {L} _ {\\mathrm {F N S} _ {- 2}} + \\gamma \\mathcal {L} _ {\\mathrm {T N E}} \\tag {5}", + "image_path": "920cff5bed20afdb5cd0dd5c89a6e5ab882c5f477e06b70ca71bb446109b421b.jpg" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6424" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 111, + 112, + 485, + 274 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "text", + "content": "Table 1. Quantitative results of the model trained with Flickr 10k and 144k. Note that 'EZ-VSL + OGL' corresponds to the main results reported in [21]. 'EZ-VSL' indicates our reproduced results without OGL, which are not reported in [21]. We reproduce the results with the trained weights and code provided by [21]." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 111, + 112, + 485, + 274 + ], + "lines": [ + { + "bbox": [ + 111, + 112, + 485, + 274 + ], + "spans": [ + { + "bbox": [ + 111, + 112, + 485, + 274 + ], + "type": "table", + "html": "
Train setMethodFlickr CIoU(%)Flickr AUC(%)VGG-SS CIoU(%)VGG-SS AUC(%)
Flickr 10kAttention10k [28]43.6044.90--
CoursetoFine [26]52.2049.60--
AVObject [1]54.6050.40--
LVS [8]58.2052.50--
EZ-VSL* [21]62.2454.7419.8630.96
Ours84.3363.2635.2738.00
EZ-VSL + OGL [21]81.9362.5837.6139.21
Ours + OGL84.7364.3440.9740.38
Flickr 144kAttention10k [28]66.0055.80--
DMC [15]67.1056.80--
LVS [8]69.9057.30--
HardPos [29]75.2059.70--
EZ-VSL* [21]72.6958.7030.2735.92
Ours78.7159.3333.9337.29
EZ-VSL + OGL [21]83.1363.0641.0140.23
Ours + OGL83.9363.0641.1040.44
", + "image_path": "eea832fbd6fc91cb2bf22b31db6c44fc4365456770245f66a0e7f6392e733dea.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 288, + 191, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 288, + 191, + 300 + ], + "spans": [ + { + "bbox": [ + 47, + 288, + 191, + 300 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 288, + 191, + 300 + ], + "type": "inline_equation", + "content": "\\alpha, \\beta, \\gamma" + }, + { + "bbox": [ + 47, + 288, + 191, + 300 + ], + "type": "text", + "content": " are hyperparameters." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 312, + 128, + 324 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 312, + 128, + 324 + ], + "spans": [ + { + "bbox": [ + 47, + 312, + 128, + 324 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 331, + 174, + 344 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 331, + 174, + 344 + ], + "spans": [ + { + "bbox": [ + 47, + 331, + 174, + 344 + ], + "type": "text", + "content": "4.1. Experimental Settings" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 350, + 287, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 350, + 287, + 456 + ], + "spans": [ + { + "bbox": [ + 46, + 350, + 287, + 456 + ], + "type": "text", + "content": "Datasets We train our audio-visual localization model on two datasets: Flickr SoundNet [6] and VGG-Sound [9]. Flickr SoundNet contains 2 million unconstrained videos from Flickr. For a fair comparison with the existing methods [8, 20, 21, 29], we conduct the training on two subsets of 10k and 144k paired samples from Flicker SoundNet. VGG-Sound includes 200k video clips from 309 classes. We also train on two subsets of 10k and 144k paired samples following the convention." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 458, + 288, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 458, + 288, + 590 + ], + "spans": [ + { + "bbox": [ + 46, + 458, + 288, + 590 + ], + "type": "text", + "content": "Localization performances are measured on four benchmarks, Flickr [6], VGG-SS [9], Heard 110 and AVS-Bench [38]. The Flickr test set has 250 audio-visual pairs with manually labeled bounding boxes. VGG-SS is more challenging with 5,000 audio-visual pairs over 220 categories. Heard 110 is another subset of VGG-Sound to test the open-set learning ability. Its train set has 110 classes and the val set has another disjoint 110 unheard/unseen classes. Finally, AVSBench [38] is a recently proposed audio-visual dataset with 5,356 videos over 23 classes. It provides pixelwise labels for fine-grained localization evaluation." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": "Implementation Details We implement our method with PyTorch. The images are resized and randomly cropped into " + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "inline_equation", + "content": "224 \\times 224" + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": " resolution, together with random horizontal flipping. The audio inputs are extracted from 3 seconds of audio clips and converted into log spectrogram maps. We also apply audio augmentation including Frequency mask and Time mask [25]. For both visual and audio encoders, we adopt ResNet18 [14] and the visual encoder is pretrained on ImageNet-1k [12]. The model is optimized for" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 287, + 545, + 337 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 287, + 545, + 337 + ], + "spans": [ + { + "bbox": [ + 305, + 287, + 545, + 337 + ], + "type": "text", + "content": "30 epochs with Adam using a learning rate of " + }, + { + "bbox": [ + 305, + 287, + 545, + 337 + ], + "type": "inline_equation", + "content": "10^{-4}" + }, + { + "bbox": [ + 305, + 287, + 545, + 337 + ], + "type": "text", + "content": " and a weight decay of " + }, + { + "bbox": [ + 305, + 287, + 545, + 337 + ], + "type": "inline_equation", + "content": "10^{-4}" + }, + { + "bbox": [ + 305, + 287, + 545, + 337 + ], + "type": "text", + "content": ". To achieve a stable representation, we warm up the network with only NCE loss for 3 epochs, then integrate our regularization for the remaining epochs." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 343, + 545, + 357 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 343, + 545, + 357 + ], + "spans": [ + { + "bbox": [ + 305, + 343, + 545, + 357 + ], + "type": "text", + "content": "4.2. Comparison on Flickr-SoundNet and VGG-SS" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 361, + 545, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 361, + 545, + 542 + ], + "spans": [ + { + "bbox": [ + 304, + 361, + 545, + 542 + ], + "type": "text", + "content": "Flickr-SoundNet We train our model on Flickr 10k and 144k and report performances in Table 1. FNAC achieves superior performances over previous methods on both Flickr and VGG-SS test sets. Notably, compared to previous state-of-the-art EZ-VSL [21] on the Flickr test set, FNAC achieves a striking improvement of " + }, + { + "bbox": [ + 304, + 361, + 545, + 542 + ], + "type": "inline_equation", + "content": "22.09\\%" + }, + { + "bbox": [ + 304, + 361, + 545, + 542 + ], + "type": "text", + "content": " CIOU with 10k training samples and " + }, + { + "bbox": [ + 304, + 361, + 545, + 542 + ], + "type": "inline_equation", + "content": "6.02\\%" + }, + { + "bbox": [ + 304, + 361, + 545, + 542 + ], + "type": "text", + "content": " CIOU with 144k training samples. When tested on the more challenging VGGSS, FNAC also outperforms EZ-VSL by " + }, + { + "bbox": [ + 304, + 361, + 545, + 542 + ], + "type": "inline_equation", + "content": "15.41\\%" + }, + { + "bbox": [ + 304, + 361, + 545, + 542 + ], + "type": "text", + "content": " CIOU and " + }, + { + "bbox": [ + 304, + 361, + 545, + 542 + ], + "type": "inline_equation", + "content": "3.49\\%" + }, + { + "bbox": [ + 304, + 361, + 545, + 542 + ], + "type": "text", + "content": " CIOU respectively. Finally, Object-Guided localization (OGL) is a post-processing strategy that adopts pure visual-based localization results to refine audio-visual localization. For a fair comparison, we integrate FNAC with OGL to compare with EZ-VSL which also uses OGL. As shown, FNAC also outperforms EZ-VSL in most cases." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 557, + 545, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 545, + 616 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 545, + 616 + ], + "type": "text", + "content": "VGG-SS Performance of the model trained on VGG-Sound 10k and 144k is reported in Table 2. FNAC also beats all previous methods with a clear margin. For example, on the VGG-SS test set, we outperform EZ-VSL by " + }, + { + "bbox": [ + 304, + 557, + 545, + 616 + ], + "type": "inline_equation", + "content": "11.45\\%" + }, + { + "bbox": [ + 304, + 557, + 545, + 616 + ], + "type": "text", + "content": " CIOU with 10k and " + }, + { + "bbox": [ + 304, + 557, + 545, + 616 + ], + "type": "inline_equation", + "content": "5.31\\%" + }, + { + "bbox": [ + 304, + 557, + 545, + 616 + ], + "type": "text", + "content": " CIOU with 144k." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "type": "text", + "content": "We highlight two results as demonstrated in Table 1 and Table 2. First, FNAC achieves similar results on " + }, + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "type": "inline_equation", + "content": "10\\mathrm{k}" + }, + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "type": "inline_equation", + "content": "144\\mathrm{k}" + }, + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "type": "text", + "content": " training sets in both Flickr SoundNet and VGGSound, which is not observed in previous models. We believe that small-scale datasets (Flickr " + }, + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "type": "inline_equation", + "content": "10\\mathrm{k}" + }, + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "type": "text", + "content": ", VGG-Sound " + }, + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "type": "inline_equation", + "content": "10\\mathrm{k}" + }, + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "type": "text", + "content": ") have fewer semantic classes and will encounter more false negatives during training, so previous methods have substantial performance gaps between the " + }, + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "type": "inline_equation", + "content": "10\\mathrm{k}" + }, + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "type": "inline_equation", + "content": "144\\mathrm{k}" + }, + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "type": "text", + "content": " training" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6425" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 110, + 91, + 486, + 234 + ], + "blocks": [ + { + "bbox": [ + 159, + 70, + 434, + 82 + ], + "lines": [ + { + "bbox": [ + 159, + 70, + 434, + 82 + ], + "spans": [ + { + "bbox": [ + 159, + 70, + 434, + 82 + ], + "type": "text", + "content": "Table 2. Quantitative results of models trained with VGG-SS 10k and 144k." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 110, + 91, + 486, + 234 + ], + "lines": [ + { + "bbox": [ + 110, + 91, + 486, + 234 + ], + "spans": [ + { + "bbox": [ + 110, + 91, + 486, + 234 + ], + "type": "table", + "html": "
Train setMethodFlickr CIoU(%)Flickr AUC(%)VGG-SS CIoU(%)VGG-SS AUC(%)
VGGSound 10kLVS [8]61.8053.60--
EZ-VSL* [21]63.8554.4425.8433.68
Ours85.7463.6637.2938.99
EZ-VSL + OGL [21]78.7161.5338.7139.80
Ours + OGL82.1363.6440.6940.42
VGGSound 144kAttention10k [28]--18.5030.20
DMC [15]--29.1034.80
AVObject [1]--29.7035.70
LVS [8]73.5059.0034.4038.20
HardPos [29]76.8059.2034.6038.00
EZ-VSL [21]79.5161.1734.3837.70
Ours84.7363.7639.5039.66
EZ-VSL + OGL [21]83.9463.6038.8539.54
Ours + OGL85.1464.3041.8540.80
", + "image_path": "cdc1a934732517c888e23707e726f2c74eaa0c138779c8cc55c77df3c9f95d10.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 77, + 293, + 260, + 369 + ], + "blocks": [ + { + "bbox": [ + 46, + 251, + 288, + 285 + ], + "lines": [ + { + "bbox": [ + 46, + 251, + 288, + 285 + ], + "spans": [ + { + "bbox": [ + 46, + 251, + 288, + 285 + ], + "type": "text", + "content": "Table 3. Quantitative results on Heard 110 and Unheard 110. For a fair comparison, the results of EZ-VSL [21] and ours are integrated with the OGL module." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 77, + 293, + 260, + 369 + ], + "lines": [ + { + "bbox": [ + 77, + 293, + 260, + 369 + ], + "spans": [ + { + "bbox": [ + 77, + 293, + 260, + 369 + ], + "type": "table", + "html": "
Test SetMethodCIoU(%)AUC(%)
Heard 110LVS [8]28.9036.20
EZ-VSL [21]37.2538.97
Ours39.5439.83
Unheard 110LVS [8]26.3034.70
EZ-VSL [21]39.5739.60
Ours42.9141.17
", + "image_path": "2325884eff19fcd2fa1e9dae338b2ddfb9cf06e6b443ecae8189286b77ae8aba.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 383, + 287, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 383, + 287, + 479 + ], + "spans": [ + { + "bbox": [ + 46, + 383, + 287, + 479 + ], + "type": "text", + "content": "sets. It indicates that FNAC can effectively address the false negative issue and has a strong ability for representation learning on small-scale datasets. Second, we show cross-dataset evaluation results in both tables, i.e., train on Flickr and test on VGG-SS or vice versa. FNAC achieves strong results and outperforms existing methods, which validates the cross-dataset generalization ability of FNAC. We show qualitative localization results in Fig. 6." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 487, + 266, + 500 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 487, + 266, + 500 + ], + "spans": [ + { + "bbox": [ + 47, + 487, + 266, + 500 + ], + "type": "text", + "content": "4.3. Comparison on Heard 110 and AVSBench" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 506, + 287, + 625 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 506, + 287, + 625 + ], + "spans": [ + { + "bbox": [ + 46, + 506, + 287, + 625 + ], + "type": "text", + "content": "Heard 110 To assess the generalization ability of FNAC in unseen/unheard audiovisual scenes, we conduct an open set experiment. We use the 70k samples covering 110 categories randomly sampled from VGGSound for training and then evaluate the model on the same 110 heard categories and another disjoint set with 110 unheard categories. As shown in Table 3, FNAC considerably outperforms previous methods, especially on Unheard 110 (42.91% vs. 39.57% of CIoU), which demonstrates the generalization ability of FNAC in unconstrained audio-visual data." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 641, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 288, + 713 + ], + "type": "text", + "content": "AVSbench AVSbench [38] is a newly proposed audiovisual segmentation benchmark with pixel-level annotations, which can be regarded as a fine-grained sound source localization task and used to accurately evaluate the localization ability of models. We directly perform a zero-shot evaluation on the AVSbench with metrics of mIoU and" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 332, + 281, + 520, + 356 + ], + "blocks": [ + { + "bbox": [ + 305, + 251, + 545, + 274 + ], + "lines": [ + { + "bbox": [ + 305, + 251, + 545, + 274 + ], + "spans": [ + { + "bbox": [ + 305, + 251, + 545, + 274 + ], + "type": "text", + "content": "Table 4. Zero-shot results on AVSBench S4 and MS3 [38]. All models are pretrained on VGGSound-144k dataset." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 332, + 281, + 520, + 356 + ], + "lines": [ + { + "bbox": [ + 332, + 281, + 520, + 356 + ], + "spans": [ + { + "bbox": [ + 332, + 281, + 520, + 356 + ], + "type": "table", + "html": "
Test setMethodmIoUFScore
S4LVS23.69.251
EZ-VSL26.43.292
Ours27.15.314
MS3LVS18.54.174
EZ-VSL21.36.216
Ours21.98.225
", + "image_path": "8b7ccf5484e639c53e75d1838fb076ea1c8b5cd6a8cda12849dc5b15a8911e32.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 318, + 390, + 533, + 469 + ], + "blocks": [ + { + "bbox": [ + 305, + 359, + 545, + 382 + ], + "lines": [ + { + "bbox": [ + 305, + 359, + 545, + 382 + ], + "spans": [ + { + "bbox": [ + 305, + 359, + 545, + 382 + ], + "type": "text", + "content": "Table 5. Analysis of each component of the proposed FNAC. aud adj: audio adjacency matrix. img adj: image adjacency matrix." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 318, + 390, + 533, + 469 + ], + "lines": [ + { + "bbox": [ + 318, + 390, + 533, + 469 + ], + "spans": [ + { + "bbox": [ + 318, + 390, + 533, + 469 + ], + "type": "table", + "html": "
FNSTNEFlickr CIoU(%)VGG-SS CIoU(%)
aud adjimg adj
77.9133.93
✓79.9135.85
✓81.9236.58
✓✓84.3336.92
✓81.1236.04
✓✓✓85.7437.29
", + "image_path": "0f8221746c1ebf3f1721f35f145490b421321c05d21cb7b8e20cead5dad4a14c.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 483, + 545, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 483, + 545, + 591 + ], + "spans": [ + { + "bbox": [ + 304, + 483, + 545, + 591 + ], + "type": "text", + "content": "F-Score in two settings, Single Sound Source Segmentation (S4) and Multiple Sound Source Segmentation (MS3), without any fine-tuning. The results are reported in Table 4. The proposed method achieves outstanding performance on both S4 and MS3 settings, e.g., " + }, + { + "bbox": [ + 304, + 483, + 545, + 591 + ], + "type": "inline_equation", + "content": "27.15\\%" + }, + { + "bbox": [ + 304, + 483, + 545, + 591 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 483, + 545, + 591 + ], + "type": "inline_equation", + "content": "21.98\\%" + }, + { + "bbox": [ + 304, + 483, + 545, + 591 + ], + "type": "text", + "content": " mIoU when trained on VGGSound 144k. These results on the fine-grained localization benchmark validate the effectiveness of the TNE, which enables the model to discriminate authentic sound-source regions." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 599, + 455, + 612 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 599, + 455, + 612 + ], + "spans": [ + { + "bbox": [ + 305, + 599, + 455, + 612 + ], + "type": "text", + "content": "4.4. Ablation Analysis of FNAC" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "type": "text", + "content": "We propose different regularization terms to guide audio-visual contrastive learning. In Table 5, we ablate each component individually. All results are obtained following the same hyperparameter setting on VGG-SS " + }, + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "type": "inline_equation", + "content": "10\\mathrm{k}" + }, + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "type": "text", + "content": " and the baseline is trained with only NCE loss. First, the audio adjacency matrix and visual adjacency matrix are obtained in FNS to suppress the false negatives. We show that each adjacency matrix can improve the performances over the" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "6426" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 124, + 73, + 294, + 209 + ], + "blocks": [ + { + "bbox": [ + 124, + 73, + 294, + 209 + ], + "lines": [ + { + "bbox": [ + 124, + 73, + 294, + 209 + ], + "spans": [ + { + "bbox": [ + 124, + 73, + 294, + 209 + ], + "type": "image", + "image_path": "3c38491ece96ba70245d9addb63d848af1d7d5d53f170f05794d1cc467c80ef0.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 130, + 220, + 462, + 232 + ], + "lines": [ + { + "bbox": [ + 130, + 220, + 462, + 232 + ], + "spans": [ + { + "bbox": [ + 130, + 220, + 462, + 232 + ], + "type": "text", + "content": "Figure 6. Visualization comparison on Flickr-SoundNet (left) and VGG-SS (right) test sets." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 300, + 74, + 470, + 209 + ], + "blocks": [ + { + "bbox": [ + 300, + 74, + 470, + 209 + ], + "lines": [ + { + "bbox": [ + 300, + 74, + 470, + 209 + ], + "spans": [ + { + "bbox": [ + 300, + 74, + 470, + 209 + ], + "type": "image", + "image_path": "dc19afcddcd9dbd448ff4a0391ab6b86e069d234be21aae44bc8e3cfe68489b1.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 251, + 290, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 251, + 290, + 384 + ], + "spans": [ + { + "bbox": [ + 46, + 251, + 290, + 384 + ], + "type": "text", + "content": "baseline, which indicates that potential false negatives can be effectively suppressed in both audio and visual modalities. By combining the two adjacency matrices together, FNS achieves " + }, + { + "bbox": [ + 46, + 251, + 290, + 384 + ], + "type": "inline_equation", + "content": "84.33\\%" + }, + { + "bbox": [ + 46, + 251, + 290, + 384 + ], + "type": "text", + "content": " CIoU on Flickr and " + }, + { + "bbox": [ + 46, + 251, + 290, + 384 + ], + "type": "inline_equation", + "content": "36.92\\%" + }, + { + "bbox": [ + 46, + 251, + 290, + 384 + ], + "type": "text", + "content": " CIoU on VGG-SS. Second, by only deploying TNE, we achieve improved results over baseline (81.12% CIoU on Flickr and " + }, + { + "bbox": [ + 46, + 251, + 290, + 384 + ], + "type": "inline_equation", + "content": "36.04\\%" + }, + { + "bbox": [ + 46, + 251, + 290, + 384 + ], + "type": "text", + "content": " CIoU on VGG-SS), indicating the effectiveness of TNE in enhancing true negatives. Finally, the combination of FNS and TNE achieves significant improvement over the baseline, showing the effectiveness of FNAC. We refer readers to supp. mat. for further ablation studies." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 401, + 241, + 415 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 401, + 241, + 415 + ], + "spans": [ + { + "bbox": [ + 47, + 401, + 241, + 415 + ], + "type": "text", + "content": "4.5. Mining the Potential False Negatives" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 423, + 287, + 626 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 423, + 287, + 626 + ], + "spans": [ + { + "bbox": [ + 46, + 423, + 287, + 626 + ], + "type": "text", + "content": "In this section, we show quantitative and schematic analysis of the false negative mining ability of our method. Intuitively, a good audio-visual model should be able to generate similar feature representations for class matched samples. To validate this intuition, we construct a batch where all samples belong to the same category, i.e., all false negatives, and show the audio-visual similarity matrices of EZ-VSL [21] and ours in Fig. 7. As shown in the left, EZ-VSL only highlights the diagonal, since each audio feature is only similar to the paired image feature while all others are dissimilar despite all samples being from the same class. Differently, the similarity distribution of our matrix is more evenly spread as the majority of the samples are regarded as similar. It indicates that FNAC has implicitly learned semantically-aware features and clustered them in the latent space, so false negatives will be effectively identified as they are closer in terms of feature distance." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 630, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 288, + 715 + ], + "type": "text", + "content": "Further, we show quantitative results of audio-visual similarities in Table 6. When the batch contains all true negatives, our average similarity score is lower than previous methods [8, 21]. When the batch contains all false negatives, our average similarity score is higher. The margin between the two similarities demonstrates our ability to distinguish false negatives and true negatives." + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 334, + 251, + 523, + 340 + ], + "blocks": [ + { + "bbox": [ + 334, + 251, + 523, + 340 + ], + "lines": [ + { + "bbox": [ + 334, + 251, + 523, + 340 + ], + "spans": [ + { + "bbox": [ + 334, + 251, + 523, + 340 + ], + "type": "image", + "image_path": "c6c7b1babaa7784eda22c69796e87d12e55ed07dc3afb6ebf3de3bf4b1d4bd05.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 350, + 547, + 394 + ], + "lines": [ + { + "bbox": [ + 305, + 350, + 547, + 394 + ], + "spans": [ + { + "bbox": [ + 305, + 350, + 547, + 394 + ], + "type": "text", + "content": "Figure 7. Cross-modal similarity matrix predicted by EZ-VSL (left) and ours (right) when all samples in the batch belong to the same category, namely, they are false negatives of each other. All values are normalized between 0 to 1." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 324, + 455, + 531, + 505 + ], + "blocks": [ + { + "bbox": [ + 305, + 414, + 547, + 448 + ], + "lines": [ + { + "bbox": [ + 305, + 414, + 547, + 448 + ], + "spans": [ + { + "bbox": [ + 305, + 414, + 547, + 448 + ], + "type": "text", + "content": "Table 6. Audio-visual similarities with different data. TN: all samples in the batch belong to different categories. FN: all samples in the batch belong to the same category." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 324, + 455, + 531, + 505 + ], + "lines": [ + { + "bbox": [ + 324, + 455, + 531, + 505 + ], + "spans": [ + { + "bbox": [ + 324, + 455, + 531, + 505 + ], + "type": "table", + "html": "
MethodTN ↓FN ↑
LVS0.44840.5102
EZ-VS10.58580.5938
Ours0.38120.6554
", + "image_path": "3dda753930d64ce813312b6a39a9444dc13816730a6be564c6b62d1295344305.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 522, + 379, + 534 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 522, + 379, + 534 + ], + "spans": [ + { + "bbox": [ + 306, + 522, + 379, + 534 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 546, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 546, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 546, + 547, + 713 + ], + "type": "text", + "content": "In this paper, we propose a simple yet effective strategy named FNAC to deal with the false negative issue in audio-visual sound source localization. We propose two complementary strategies to suppress false negatives (FNS) and enhance true negatives (TNE). The intra-modal adjacency matrices of audio and visual are generated to identify false negatives. Then two regularization terms are seamlessly incorporated with contrastive learning, which enable the model to learn semantic-aware features from audio-visual pairs. We show that FNAC can effectively mitigate the false negative issues and achieve state-of-the-art performance on several audio-visual localization benchmarks. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 8436-8444, 2021. 1" + } + ] + } + ], + "index": 11 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "text", + "content": "6429" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Learning Bottleneck Concepts in Image Classification/c0f445a3-9476-4f99-8d03-749bf8f8a370_content_list.json b/2023/Learning Bottleneck Concepts in Image Classification/c0f445a3-9476-4f99-8d03-749bf8f8a370_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..0287acc2ac711d08e9e887038845d6ab7f0ff4e6 --- /dev/null +++ b/2023/Learning Bottleneck Concepts in Image Classification/c0f445a3-9476-4f99-8d03-749bf8f8a370_content_list.json @@ -0,0 +1,2291 @@ +[ + { + "type": "text", + "text": "Learning Bottleneck Concepts in Image Classification", + "text_level": 1, + "bbox": [ + 214, + 130, + 756, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Bowen Wang $^{1}$ , Liangzhi Li $^{2*}$ , Yuta Nakashima $^{2}$ , Hajime Nagahara $^{2}$ , Osaka University, Japan", + "bbox": [ + 218, + 179, + 746, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "bowen.wang@is.ids.osaka-u.ac.jp", + "bbox": [ + 341, + 218, + 627, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "2{li, n-yuta, nagahara}@ids.osaka-u.ac.jp", + "bbox": [ + 300, + 234, + 661, + 252 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 286, + 313, + 301 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Interpreting and explaining the behavior of deep neural networks is critical for many tasks. Explainable AI provides a way to address this challenge, mostly by providing per-pixel relevance to the decision. Yet, interpreting such explanations may require expert knowledge. Some recent attempts toward interpretability adopt a concept-based framework, giving a higher-level relationship between some concepts and model decisions. This paper proposes Bottleneck Concept Learner (BotCL), which represents an image solely by the presence/absence of concepts learned through training over the target task without explicit supervision over the concepts. It uses self-supervision and tailored regularizers so that learned concepts can be human-understandable. Using some image classification tasks as our testbed, we demonstrate BotCL's potential to rebuild neural networks for better interpretability1.", + "bbox": [ + 75, + 316, + 473, + 561 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 587, + 209, + 603 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Understanding the behavior of deep neural networks (DNNs) is a major challenge in the explainable AI (XAI) community, especially for medical applications [19,38], for identifying biases in DNNs [2, 18, 42], etc. Tremendous research efforts have been devoted to the post-hoc paradigm for a posteriori explanation [29, 33]. This paradigm produces a relevance map to spot regions in the input image that interact with the model's decision. Yet the relevance map only tells low-level (or per-pixel) relationships and does not explicitly convey any semantics behind the decision. Interpretation of relevance maps may require expert knowledge.", + "bbox": [ + 75, + 612, + 468, + 779 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The concept-based framework [22, 37, 50] is inspired by the human capacity to learn a new concept by (subconsciously) finding finer-grained concepts and reuse them in different ways for better recognition [24]. Instead of giving per-pixel relevance, this framework offers higher-level", + "bbox": [ + 75, + 779, + 468, + 854 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/57c5c08570f5d3bb51eabe1f8d8a52da31021717facb6703e95af5a00db8e148.jpg", + "image_caption": [ + "Figure 1. Examples of concepts discovered by BotCL in ImageNet [10] and concepts in the input image. BotCL automatically discovers a set of concepts optimized for the target task and represents an image solely with the presence/absence of concepts." + ], + "image_footnote": [], + "bbox": [ + 519, + 284, + 870, + 458 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "relationships between the image and decision mediated by a limited number of concepts. That is, the decision is explained by giving a set of concepts found in the image. The interpretation of the decision is thus straightforward once the interpretation of each concept is established.", + "bbox": [ + 496, + 551, + 890, + 627 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Some works use concepts for the post-hoc paradigm for better interpretation of the decision [14, 50], while the link between the decision and concepts in the image is not obvious. The concept bottleneck structure [23] uses the presence/absence of concepts as image representation (referred to as concept activation). The classifier has access only to the concept activation, so the decision is strongly tied to the concepts. This bottleneck structure has become the mainstream of the concept-based framework [5, 20, 28, 31].", + "bbox": [ + 496, + 628, + 892, + 763 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "A major difficulty in this framework is designing a set of concepts that suits the target task. A promising approach is handcrafting them [4, 21, 48], which inherently offers better interpretability at the cost of extra annotations on the concepts. Recent attempts automatically discover concepts [1, 13, 14, 46]. Such concepts may not always be consistent with how humans (or models) see the world [25, 47] and may require some effort to interpret them, but concept discovery without supervision is a significant advantage.", + "bbox": [ + 496, + 763, + 893, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author.", + "bbox": [ + 94, + 862, + 222, + 875 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "$^{1}$ Code is available at https://github.com/webw520/BotCL and a simple demo is available at https://botcl.liangzhili.com/.", + "bbox": [ + 76, + 875, + 468, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "10962", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Inspired by these works, we propose bottleneck concept learner (BotCL) for simultaneously discovering concepts and learning the classifier. BotCL optimizes concepts for the given target image classification task without supervision for the concepts. An image is represented solely by the existence of concepts and is classified using them. We adopt a slot attention-based mechanism [26, 27] to spot the region in which each concept is found. This gives an extra signal for interpreting the decision since one can easily see what each learned concept represents by collectively showing training images with the detected concepts. Figure 1 shows examples from ImageNet [10]. BotCL discovers a predefined number of concepts in the dataset, which are exemplified by several images with attention maps. An image of Great White Shark is represented by the right part of mouth (Cpt.1) and fins (Cpt.3). BotCL uses a single fully-connected (FC) layer as a classifier, which is simple but enough to encode the co-occurrence of each concept and each class.", + "bbox": [ + 75, + 90, + 472, + 377 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Contribution. For better concept discovery, we propose to use self-supervision over concepts, inspired by the recent success in representation learning [9, 16]. Our ablation study demonstrates that self-supervision by contrastive loss is the key. We also try several constraints on concepts themselves, i.e., individual consistency to make a concept more selective and mutual distinctiveness for better coverage of various visual elements. These additional constraints regular the training process and help the model learn concepts of higher quality.", + "bbox": [ + 75, + 378, + 472, + 530 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 76, + 544, + 225, + 559 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Explainable AI", + "text_level": 1, + "bbox": [ + 76, + 569, + 230, + 585 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "XAI focuses on uncovering black-box deep neural networks [3, 6, 12, 32, 35, 36, 41, 43, 46]. A major approach is generating a relevance map that spots important regions for the model's decision. Various methods have been designed for specific architectures, e.g., CAM [49], and GradCAM [33] for convolutional neural networks; [7] for Transformers [40]. However, the interpretation of the relevance maps may not always be obvious, which spurs different approaches [34, 45], including context-based ones.", + "bbox": [ + 75, + 593, + 468, + 729 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Concept-based framework for interpretability", + "text_level": 1, + "bbox": [ + 76, + 739, + 465, + 757 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "A straightforward way to define a set of concepts for a target task is to utilize human knowledge [22,48]. Such concepts allow quantifying their importance for a decision [21]. A large corpus of concepts [4, 39] is beneficial for delving into hidden semantics in DNNs [50]. These methods are of the post-hoc XAI paradigm, but a handcrafted set of concepts can also be used as additional supervision for models with the concept bottleneck structure [15, 22, 31].", + "bbox": [ + 75, + 763, + 468, + 885 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Handcrafting a set of concepts offers better interpreabil", + "bbox": [ + 96, + 885, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ity as they suit human perception; however, the annotation cost is non-negligible. Moreover, such handcrafted concepts may not always be useful for DNNs [47]. These problems have motivated automatic concept discovery. Superpixels are a handy unit for finding low-level semantics, and concepts are defined by clustering them [13, 14, 30]. Another interesting approach is designing a set of concepts to be sufficient statistics of original DNN features [46]. These methods are designed purely for interpretation, and concept discovery is made aside from training on the target task.", + "bbox": [ + 496, + 90, + 890, + 241 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The concept bottleneck structure allows optimizing a set of concepts for the target task. ProtoPNet [8] adopts this structure and identifies concepts based on the distance between features and concepts. SENN [1] uses self-supervision by reconstruction loss for concept discovery.", + "bbox": [ + 496, + 242, + 890, + 316 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "SENN inspired us to use self-supervision, but instead of reconstruction loss, we adopt contrastive loss tailored. For a natural image classification task, this contrastive loss is essential for concept discovery.", + "bbox": [ + 496, + 316, + 890, + 378 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Model", + "text_level": 1, + "bbox": [ + 500, + 390, + 578, + 406 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Given a dataset $\\mathcal{D} = \\{(x_i, y_i) | i = 1, 2, \\dots, N\\}$ , where $x_i$ is an image and $y_i$ is the target class label in the set $\\Omega$ associated with $x_i$ . BotCL learns a set of $k$ concepts while learning the original classification task. Figure 2a shows an overview of BotCL's training scheme, consisting of a concept extractor, regularizers, and a classifier, as well as self-supervision (contrastive and reconstruction losses).", + "bbox": [ + 496, + 415, + 890, + 520 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "For a new image $x$ , we extract feature map $F = \\Phi(x) \\in \\mathbb{R}^{d \\times h \\times w}$ using a backbone convolutional neural network $\\Phi$ . $F$ is then fed into the concept extractor $g_{C}$ , where $C$ is a matrix, each of whose $\\kappa$ -th column vector $c_{\\kappa}$ is a concept prototype to be learned. The concept extractor produces concept bottleneck activations $t \\in [0,1]^k$ , indicating the presence of each concept, as well as concept features $V \\in \\mathbb{R}^{d \\times k}$ from regions where each concept exists. The concept activations in $t$ are used as input to the classifier to compute score $s \\in [0,1]^{|\\Omega|}$ . We use self-supervision and regularizers for training, taking $t$ and $V$ as input to constrain the concept prototypes.", + "bbox": [ + 496, + 521, + 890, + 703 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3.1. Concept Extractor", + "text_level": 1, + "bbox": [ + 500, + 710, + 679, + 727 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Concept extractor uses slot attention [26, 27]-based mechanism to discover visual concepts in $\\mathcal{D}$ . We first add position embedding $P$ to feature map $F$ to retain the spatial information, i.e., $F' = F + P$ . The spatial dimension of $F'$ is flattened, so its shape is $l \\times d$ , where $l = hw$ .", + "bbox": [ + 496, + 734, + 890, + 809 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The slot-attention computes attention over the spatial dimension for concept $\\kappa$ from $c_{\\kappa}$ and $F^{\\prime}$ . Let $Q(c_{\\kappa})\\in \\mathbb{R}^{d}$ , and $K(F^{\\prime})\\in \\mathbb{R}^{d\\times l}$ denote nonlinear transformations for $c_{\\kappa}$ and $F^{\\prime}$ , respectively, given as multi-layer perceptrons with three FC layers and a ReLU nonlinearity between them. Attention $a_{\\kappa}\\in [0,1]^{l}$ is given using a normalization function", + "bbox": [ + 496, + 810, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "10963", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/93cd9351f448be129dc709ec2a001ffe0d9e91a1be1bcf645de1be1904ae8caa.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 78, + 88, + 584, + 231 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/7ad52cdcbfc292d452281d9a91d3b445ae67870b6c54129097f8a07bd2fb6ac7.jpg", + "image_caption": [ + "(b)", + "Figure 2. (a) The model pipeline. (b) Self-supervision and regularizers." + ], + "image_footnote": [], + "bbox": [ + 591, + 88, + 893, + 234 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "$\\phi$ (refer to supp. material) as", + "bbox": [ + 76, + 306, + 277, + 321 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\na _ {\\kappa} = \\phi \\left(Q \\left(c _ {\\kappa}\\right) ^ {\\top} K \\left(F ^ {\\prime}\\right)\\right). \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 327, + 468, + 345 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "This attention indicates where concept $\\kappa$ presents in the image as shown in Figure 1. If concept $\\kappa$ is absent, corresponding entries of $a_{\\kappa}$ are all close to 0. We summarize the presence of each concept into concept activation $t_{\\kappa}$ by reducing the spatial dimension of $a_{\\kappa}$ as $t_{\\kappa} = \\tanh (\\sum_{m}a_{\\kappa m})$ where $a_{\\kappa m}$ is the $m$ -th element of $a_{\\kappa}$ .", + "bbox": [ + 76, + 351, + 468, + 443 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Feature Aggregation", + "text_level": 1, + "bbox": [ + 76, + 450, + 272, + 465 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For training, we also aggregate features in $F$ corresponding to concept $\\kappa$ into concept feature $v_{\\kappa}$ by", + "bbox": [ + 76, + 473, + 468, + 503 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nv _ {\\kappa} = F a _ {\\kappa}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 233, + 511, + 468, + 526 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "which gives the average of image features over the spatial dimension weighted by attention.", + "bbox": [ + 76, + 532, + 468, + 565 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.3.Classifier", + "text_level": 1, + "bbox": [ + 76, + 571, + 186, + 585 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We use a single FC layer without a bias term as the classifier, and concept activation $t = (t_{1},\\dots ,t_{k})^{\\top}$ is the only input, serving as the concept bottleneck [22]. Formally, letting $W$ be a learnable matrix, prediction $\\hat{y}\\in \\mathbb{R}^{|\\Omega |}$ is given by", + "bbox": [ + 76, + 594, + 468, + 669 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {y} = W t. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 240, + 670, + 468, + 686 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "This classifier can be roughly interpreted as learning the correlation between the class and concepts. Let $w_{\\omega}$ be the raw vector of $W$ corresponding to class $\\omega \\in \\Omega$ , and $w_{\\omega \\kappa}$ is its $\\kappa$ -th element. A positive value of $w_{\\omega \\kappa}$ means that concept $\\kappa$ co-occurs with class $\\omega$ in the dataset, so its presence in a new image positively supports class $\\omega$ . Meanwhile, a negative value means the concept rarely co-occurs.", + "bbox": [ + 76, + 689, + 468, + 796 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Training", + "text_level": 1, + "bbox": [ + 76, + 806, + 174, + 824 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.1. Self-supervision for Concept Discovery", + "text_level": 1, + "bbox": [ + 76, + 832, + 411, + 849 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The absence of concept labels motivates us to incorporate self-supervision for concept discovery. We employ two losses for different types of target tasks.", + "bbox": [ + 76, + 854, + 468, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Reconstruction loss. SENN [1] uses an autoencoder-like structure for learning better representation. We assume this structure works well when visual elements are strongly tied with the position since even discrete concepts should have sufficient information to reconstruct the original image. Based on this assumption, we design a reconstruction loss for self-supervision. As shown in Figure 2b, decoder $D$ only takes $t$ as input and reconstructs the original image. We define our reconstruction loss as", + "bbox": [ + 498, + 306, + 890, + 441 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nl _ {\\text {r e c}} = \\frac {1}{| \\mathcal {B} |} \\sum_ {x \\in \\mathcal {B}} \\| D (t) - x \\| ^ {2}. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 598, + 448, + 890, + 484 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Contrastive loss. The composition of natural images is rather arbitrary, so information in $t$ should be insufficient to reconstruct the original image. We thus design a simple loss for an alternative, borrowing the idea from the recent success of contrastive learning for self-supervision [9, 16].", + "bbox": [ + 498, + 501, + 890, + 575 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We leverage the image-level labels of the target classification task. Let $\\hat{t} = 2t - \\mathbf{1}_k$ , where $\\mathbf{1}_k$ is the $k$ -dimensional vector with all elements being 1. If a pair $(\\hat{t}, \\hat{t}')$ of concept activations belong to the same class (i.e., $y = y'$ for $y$ and $y'$ corresponding to $\\hat{t}$ and $\\hat{t}'$ ), they should be similar to each other since a similar set of concepts should be in the corresponding images, and otherwise dissimilar. The number $|\\Omega|$ of classes can be smaller than the number $|\\mathcal{B}|$ of images in a mini-batch so that a mini-batch can have multiple images of the same class. Therefore, we use sigmoid instead of softmax, leading to", + "bbox": [ + 498, + 577, + 890, + 743 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nl _ {\\text {r e t}} = - \\frac {1}{| \\mathcal {B} |} \\sum \\alpha (y, y ^ {\\prime}) \\log J (\\hat {t}, \\hat {t} ^ {\\prime}, y, y ^ {\\prime}), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 555, + 751, + 890, + 785 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\alpha$ is the weight to mitigate the class imbalance problem (see supp. material) and", + "bbox": [ + 498, + 792, + 890, + 823 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\underline {{J (\\hat {t} , \\hat {t} ^ {\\prime} , y , y ^ {\\prime}) =}} \\left\\{ \\begin{array}{l l} \\sigma (\\hat {t} ^ {\\top} \\hat {t} ^ {\\prime}) & \\text {f o r} y = y ^ {\\prime} \\\\ 1 - \\sigma (\\hat {t} ^ {\\top} \\hat {t} ^ {\\prime}) & \\text {o t h e r w i s e} \\end{array} . \\right. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 547, + 832, + 890, + 873 + ], + "page_idx": 2 + }, + { + "type": "page_footnote", + "text": "2For example, images of \"7\" in MNIST almost always have the acute angle in the top-right part.", + "bbox": [ + 500, + 875, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "10964", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.2. Concept Regularizers", + "text_level": 1, + "bbox": [ + 76, + 90, + 281, + 107 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We also employ concept regularizers to facilitate training. They constrain concept prototypes $\\{c_{\\kappa}\\}$ through $\\{v_{\\kappa}\\}$ .", + "bbox": [ + 76, + 113, + 468, + 146 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Individual consistency. For better interpretability, each learned concept should not have large variations. That is, the concept features $v_{\\kappa}$ and $v_{\\kappa}^{\\prime}$ of different images should be similar to each other if $t_{\\kappa}$ is close to 1. Let $\\mathcal{H}_{\\kappa}$ denote the set of all concept features of different images in a minibatch, whose activation is larger than the empirical threshold $\\xi$ , which is dynamically calculated as the mean of $t_{\\kappa}$ in a mini-batch. Using the cosine similarity $\\mathrm{sim}(\\cdot ,\\cdot)$ , we define the consistency loss as:", + "bbox": [ + 75, + 161, + 470, + 297 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nl _ {\\text {c o n}} = - \\frac {1}{k} \\sum_ {\\kappa} \\sum_ {v _ {\\kappa}, v _ {\\kappa} ^ {\\prime}} \\frac {\\sin \\left(v _ {\\kappa} , v _ {\\kappa} ^ {\\prime}\\right)}{\\left| \\mathcal {H} _ {\\kappa} \\right| \\left(\\left| \\mathcal {H} _ {\\kappa} \\right| - 1\\right)}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 145, + 301, + 468, + 342 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where the second summation is computed over all combinations of concept features $v_{\\kappa}$ and $v_{\\kappa}^{\\prime}$ . This loss penalizes a smaller similarity between $v_{\\kappa}$ and $v_{\\kappa}^{\\prime}$ .", + "bbox": [ + 76, + 348, + 468, + 395 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Mutual distinctiveness. To capture different aspects of images, different concepts should cover different visual elements. This means that the average image features of concept $\\kappa$ within a mini-batch, given by $\\bar{v}_{\\kappa} = \\sum_{v_{\\kappa}\\in \\mathcal{H}_{\\kappa}}v_{\\kappa}$ should be different from any other $v_{\\kappa^{\\prime}}$ . We can encode this into a loss term as", + "bbox": [ + 76, + 410, + 468, + 500 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nl _ {\\mathrm {d i s}} = \\sum_ {\\kappa , \\kappa^ {\\prime}} \\frac {\\operatorname {s i m} \\left(\\bar {v} _ {\\kappa} , \\bar {v} _ {\\kappa^ {\\prime}}\\right)}{k (k - 1)}, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 503, + 468, + 542 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where the summation is computed over all combinations of concepts. Note that concept $\\kappa$ is excluded from this loss if no image in a mini-batch has concept $\\kappa$ .", + "bbox": [ + 76, + 549, + 468, + 595 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.3. Quantization Loss", + "text_level": 1, + "bbox": [ + 76, + 601, + 254, + 617 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Concept activation $t$ can be sufficiently represented by a binary value, but we instead use a continuous value for training. We design a quantization loss to guarantee values are close to 0 or 1, given by", + "bbox": [ + 76, + 625, + 468, + 686 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nl _ {\\mathrm {q u a}} = \\frac {1}{k | \\mathcal {B} |} \\sum_ {x \\in \\mathcal {B}} \\left\\| \\operatorname {a b s} (\\hat {t}) - \\mathbf {1} _ {\\kappa} \\right\\| ^ {2}, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 158, + 691, + 468, + 727 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathrm{abs}(\\cdot)$ gives the element-wise absolute value and $\\| \\cdot \\|$ gives the Euclidean norm.", + "bbox": [ + 76, + 733, + 467, + 763 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.4. Total Loss", + "text_level": 1, + "bbox": [ + 76, + 771, + 192, + 786 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We use softmax cross-entropy for the target classification task's loss, donated by $l_{\\mathrm{cls}}$ . The overall loss of BotCL is defined by combining the losses above as", + "bbox": [ + 76, + 794, + 467, + 840 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL = l _ {\\mathrm {c l s}} + \\lambda_ {\\mathrm {R}} l _ {\\mathrm {R}} + \\lambda_ {\\mathrm {c o n}} l _ {\\mathrm {c o n}} + \\lambda_ {\\mathrm {d i s}} l _ {\\mathrm {d i s}} + \\lambda_ {\\mathrm {q u a l}} l _ {\\mathrm {q u a}}, \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 102, + 847, + 467, + 864 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $l_{\\mathrm{R}}$ is either $l_{\\mathrm{rec}}$ or $l_{\\mathrm{ret}}$ depending on the target domain, $\\lambda_{\\mathrm{qua}}, \\lambda_{\\mathrm{con}}, \\lambda_{\\mathrm{dis}}$ , and $\\lambda_{R}$ are weights to balance each term.", + "bbox": [ + 76, + 869, + 467, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "5. Results", + "text_level": 1, + "bbox": [ + 500, + 90, + 586, + 104 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "5.1. Experimental Settings", + "text_level": 1, + "bbox": [ + 500, + 117, + 705, + 133 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We evaluate BotCL on MNIST [11], CUB200 [44], and ImageNet [10]. For evaluating discovered concepts, we regenerated a synthetic shape dataset (Synthetic) [46].", + "bbox": [ + 500, + 143, + 890, + 189 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For MNIST, we applied the same networks as [1] for the backbone and the concept decoder. For CUB200 (same data split as [22]) and ImageNet, we used pre-trained ResNet [17] as the backbone with a $1 \\times 1$ convolutional layer to reduce the channel number (512 for ResNet-18 and 2048 for ResNet-101) to 128. We chose a concept number $k = 20$ for MNIST and $k = 50$ for the other natural image datasets. To generate Synthetic, we followed the setting of [46], where 18,000 images were generated for training and 2,000 for evaluation. We used $k = 15$ with ResNet-18 backbone.", + "bbox": [ + 498, + 191, + 890, + 343 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Images were resized to $256 \\times 256$ and cropped to $224 \\times 224$ (images in Synthetic were directly resized to $224 \\times 224$ ). Only random horizontal flip was applied as data augmentation during training. The weight of each loss was defaulted to $\\lambda_{\\mathrm{qua}} = 0.1$ , $\\lambda_{\\mathrm{con}} = 0.01$ , $\\lambda_{\\mathrm{dis}} = 0.05$ , and $\\lambda_{\\mathrm{R}} = 0.1$ .", + "bbox": [ + 498, + 347, + 890, + 424 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "5.2. Classification Performance", + "text_level": 1, + "bbox": [ + 500, + 441, + 741, + 455 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We compare the performance of BotCL with corresponding baselines (LeNet for MNIST and ResNet-18 for others with a linear classifier), our reimplementation of k-means and PCA in [46], and state-of-the-art concept-based models. Table 1 summarized the results. BotCL with contrastive loss $(\\mathrm{BotCL}_{\\mathrm{Cont}})$ achieves the best accuracy on CUB200, ImageNet, and Synthetic, outperforming the baseline linear classifiers. It is also comparable to the state-of-the-art on MNIST and Synthetic. BotCL with reconstruction loss $(\\mathrm{BotCL}_{\\mathrm{Rec}})$ shows a performance drop over CUB200, ImageNet, and Synthetic, while it outperforms $\\mathrm{BotCL}_{\\mathrm{Cont}}$ on MNIST. This behavior supports our assumption that the reconstruction loss is useful only when concepts are strongly tied to their spatial position. Otherwise, $t$ is insufficient to reconstruct the original image, and BotCL fails. Contrastive self-supervision is the key to facilitating concept discovery.", + "bbox": [ + 498, + 468, + 890, + 710 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We also explore the relationship between the number of classes and BotCL's accuracy over CUB200 and ImageNet. We used small and large variants of ResNet as the backbone. We extracted subsets of the datasets consisting of the first $n$ classes along with the class IDs. Figure 3 shows that BotCL has a competitive performance when the number of classes is less than 200. We conclude that BotCL hardly degrades the classification performance on small- or middle-sized datasets. However, this is not the case for $n > 200$ (refer to supp. material for larger $n$ and different $k$ 's).", + "bbox": [ + 498, + 713, + 890, + 864 + ], + "page_idx": 3 + }, + { + "type": "page_footnote", + "text": "3 Implementation details are in supp. material.", + "bbox": [ + 514, + 886, + 767, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "10965", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/84780a469a0780bcf43986dd8e3e608ef968a48c58084652eca318a3f7fc5142.jpg", + "image_caption": [ + "Figure 3. Classification accuracy vs. the number of classes. We used subsets of CUB200 and ImageNet with $k = 50$ and ResNet-18 and ResNet-101 backbones." + ], + "image_footnote": [], + "bbox": [ + 86, + 88, + 493, + 200 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/f522c58e4a2bd2bfbe6d3193555910f29361428d551c6201ca3af81bcaa68662.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 495, + 88, + 684, + 200 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/63f847b2ef16a25959ac120149bc5a6c942491ece6229324b63d6714c6ed0463.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 686, + 88, + 880, + 200 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/21abe34c316f4ccb3864f73d7989b63e23f3b9ebc903ecd100993504cc1b7d4e.jpg", + "table_caption": [ + "Table 1. Performance comparison in classification accuracy. The best concept-based method is highlighted in bold. $\\mathrm{BotCL_{Rec}}$ and $\\mathrm{BotCL_{Cont}}$ are both BotCL but with reconstruction and contrastive loss, respectively. For ImageNet, we used the first 200 classes." + ], + "table_footnote": [], + "table_body": "
CUB200ImageNetMNISTSynthetic
Baseline0.7310.7860.9880.999
k-means* [46]0.0630.4270.7810.747
PCA* [46]0.0440.1390.6530.645
SENN [1]0.6420.6730.9850.984
ProtoPNet [8]0.7250.7520.9810.992
BotCLRec0.6930.7200.9830.785
BotCLCont0.7400.7950.9800.998
", + "bbox": [ + 83, + 333, + 460, + 465 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.3. Interpretability", + "text_level": 1, + "bbox": [ + 76, + 494, + 233, + 512 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.3.1 Qualitative validation of discovered concepts", + "text_level": 1, + "bbox": [ + 76, + 521, + 442, + 537 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Figure 4a visualizes $a_{\\kappa}$ , showing concept $\\kappa$ in the image, over MNIST. We selected 5 concepts out of 20 that are most frequently activated (i.e., $t_{\\kappa} > 0.5$ ) in the training set. Taking digits 0 and 9 as an example, we can observe that they share Cpts.3-5 and the only difference is Cpt.2 that locates in the lower edge of the vertical stroke of 9. This stroke is specific to digit 9. We used BotCLRec, so we can remove Cpt.2 before reconstruction, which generates an image like 0 (refer to Section 5.3.3). Some concepts are incompatible with human intuition; yet we can interpret such concepts (e.g., Cpt.1 may attend to the missing stroke that completes a circle).", + "bbox": [ + 75, + 550, + 468, + 733 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For CUB200, we train $\\mathrm{BotCL}_{\\mathrm{Const}}$ with $n = 50$ and $k = 20$ . Figure 5a shows the attention maps of an image of yellow headed black bird. We can observe that the attentions for Cpts.1-5 cover different body parts, including the head, wing, back, and feet, which proves that BotCL can learn valid concepts from the natural image as well. Supp. material exemplifies all concepts discovered from MNIST and CUB200.", + "bbox": [ + 75, + 734, + 470, + 854 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.3.2 Consistency and distinctiveness of each concept", + "text_level": 1, + "bbox": [ + 500, + 268, + 883, + 284 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "BotCL is designed to discover individually consistent and mutually distinctive concepts. We qualitatively verify this by showing each concept with its top-5 activated images5 with attention maps in Figure 4b. For MNIST, different concepts cover different patterns, and each concept covers the same patterns in different samples (even the samples of different classes). Figure 5b for CUB200 shows that BotCL renders a similar behavior on the CUB200 dataset; that is, the top-5 concepts are responsible for different patterns, and each of them is consistent.", + "bbox": [ + 496, + 291, + 893, + 441 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.3.3 Contribution of each concept in inference", + "text_level": 1, + "bbox": [ + 498, + 460, + 841, + 476 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We can qualitatively see the contribution of each concept by removing the concept and seeing the changes in the corresponding self-supervision task's output. As shown in Figure 4c, when we set the activation of Cpt.2 (responsible for the vertical stroke of digit 9) to zero, the reconstructed image looks like digit 0. When Cpt.1, representing the absence of the circle in digit 7, is deactivated (i.e., $t_1$ is set to 0), a circle emerges in the upper part of the reconstructed image. The resulting image looks more like digit 9.", + "bbox": [ + 496, + 483, + 890, + 619 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For CUB200 shown in Figure 5c, we show images most similar to the input image in Figure 5a among the dataset in terms of $\\hat{t}^{\\top}\\hat{t}^{\\prime}$ , with ablating each concept. When Cpt.1 (responsible for the yellow head) is deactivated, more blackhead bird images appear in the top-8 images. Cpt.5 covers birds' feet and is common among most bird classes. Deactivating this concept does not change the top-8 images. These observations suggest that although some concepts do not contribute to classification performance, images are successfully represented by combinations of concepts.", + "bbox": [ + 496, + 619, + 890, + 771 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.4. Quantitative Evaluation on Synthetic", + "text_level": 1, + "bbox": [ + 500, + 779, + 821, + 796 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "One problem of the concept-based approach is the absence of established quantitative evaluations of concepts because the choice of concepts may be arbitrary and the same level of representability may be achieved with different sets of concepts. A single predefined set of concepts", + "bbox": [ + 496, + 803, + 890, + 878 + ], + "page_idx": 4 + }, + { + "type": "page_footnote", + "text": "4Cpts.1-5 are ordered based on the frequency counted in the dataset.", + "bbox": [ + 75, + 875, + 468, + 898 + ], + "page_idx": 4 + }, + { + "type": "page_footnote", + "text": "For each concept $\\kappa$ , five images whose $t_\\kappa$ is highest among $\\mathcal{D}$ .", + "bbox": [ + 514, + 886, + 857, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "10966", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/668f860605168c909be856f0a78bf471da8ab83ecfcc8a1b3d685d78bbcee359.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 117, + 90, + 364, + 261 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/fd4a0c9780aee08eb8187408059c7089b2c44a988a3da66d5395c0eb9b6ba531.jpg", + "image_caption": [ + "(b)" + ], + "image_footnote": [], + "bbox": [ + 372, + 90, + 599, + 261 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/5487ebc155c33e8beccc8b64d4b562e7db3f11335c51582ecee54d0e90c7d892.jpg", + "image_caption": [ + "(c)" + ], + "image_footnote": [], + "bbox": [ + 614, + 90, + 866, + 261 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/b18a7cf8c024aacf58f387223732feb540ed03b3fad7dc528aced3caeea96319.jpg", + "image_caption": [ + "(a)", + "Input" + ], + "image_footnote": [], + "bbox": [ + 140, + 357, + 181, + 390 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/becb6dd9c4268f4151bed3e16cd10a2d2ee396ef033ceb1bbbc14888dce58728.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 204, + 358, + 243, + 388 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/50287743766ff336afb75ff4d6641bd17e5dc2652732e4affb68208159280ebc.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 292, + 358, + 331, + 388 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/0652f11077c39740ced89e7475ba786808f693f69115b69e199d253ebcf9435a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 377, + 359, + 416, + 388 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/c0075e6ab4f82df310d28f3048a3b952c2c74bfa3e8622e82b4809aa784a572e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 464, + 359, + 503, + 388 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/6623cab36566e5883e4ee29ae7dc94eb9bef1122907d85104dd30cd9df723b8e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 552, + 359, + 591, + 388 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/917bf85335e8a2d28bd82769f71ed55908147912a228a5320005d2856e13e739.jpg", + "image_caption": [ + "Cpt.1", + "Top-5 Activation" + ], + "image_footnote": [], + "bbox": [ + 181, + 402, + 261, + 431 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/74807a28dee0666cf2b675093e6ac4c72ac50eeb6d60840bf6680ddb18d89b1b.jpg", + "image_caption": [ + "(b)" + ], + "image_footnote": [], + "bbox": [ + 183, + 434, + 259, + 492 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/c8bc659dbd9684b34759ee2a58f33db6312161830a72557e9ef19832a5b48caf.jpg", + "image_caption": [ + "Figure 5. Concepts learned for CUB200. (a) Visualization of 5 most important concepts for yellow headed black bird. (b) Top-5 activated concepts. (c) Image retrieval when all detected concepts were used (original) and when a certain concept was deactivated." + ], + "image_footnote": [], + "bbox": [ + 183, + 493, + 259, + 551 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/f28a10296593cfeee06fc12507e930f92e73c5674209bf40ea179e0e1aff5170.jpg", + "image_caption": [ + "Cpt.2" + ], + "image_footnote": [], + "bbox": [ + 271, + 402, + 349, + 431 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/c635bbc60deca00ab5190e33758ecf5e8c866152c0c588a3f6997883db295065.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 271, + 434, + 349, + 492 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/7df738de214667daf0750daf7d3b123a2dba9c56022c6f4327d71a188cf8ff83.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 271, + 493, + 349, + 551 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/73415367dccec47bb7ff2a5dc02319cdff85fd431b33822960b45e0aa125974a.jpg", + "image_caption": [ + "Cpt.3" + ], + "image_footnote": [], + "bbox": [ + 359, + 402, + 436, + 431 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/44421944b8f2f1faa08d859f20ccf3653dbf174e394486b5fe61386204dbd0c3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 359, + 434, + 436, + 492 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/34df0e268b588b0b52207c0a0ce42cfb08dca0728426b51c3e98f6dbe0f8850c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 359, + 493, + 436, + 551 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/d2283d0f0e9e24fea3bd0b54dcaa2a35295d3c7d10a2ddd4fe14b63249dae4da.jpg", + "image_caption": [ + "Cpt.4" + ], + "image_footnote": [], + "bbox": [ + 444, + 402, + 522, + 431 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/62337d64baa9236bcd2cb30a220c5e5dab5a0f661880e49f023ddf9e14199c91.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 444, + 434, + 522, + 492 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/8fcc4fdb45527369f2730e752391f942841d9ca8996d5bef8423388cb82e721c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 444, + 493, + 522, + 551 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/c5dacba753b21f8eca25c76d1a29637926725dcbad9aafa3059d60cff11f89ac.jpg", + "image_caption": [ + "Cpt.5" + ], + "image_footnote": [], + "bbox": [ + 531, + 402, + 609, + 431 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/698ff7b3a84e8a17f0600af887bfa2fb3d7b61d5d7024a7301ca893d0e5009a0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 531, + 434, + 607, + 463 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/9b178ced4986c4c2798ca8f7941f1da8b58cff1ed147deec0c05f5f809f89808.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 531, + 464, + 607, + 522 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/90ee06bcd6db828a9517082ac2390c89ae0ef9e500f78947106dcdadb8f47cca.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 531, + 523, + 607, + 551 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/516896f6287fce2e3e904196b7c13d983273b37c3adf24566fde9cc883dda50f.jpg", + "image_caption": [ + "Figure 4. Concepts for MNIST. (a) Attention maps for different input images. (b) Top-5 activated images (images in the dataset whose $t_\\kappa$ is largest) for each concept. (c) Images reconstructed by our concept decoder with all detected concepts (original) and with a certain concept deactivated.", + "(c)" + ], + "image_footnote": [], + "bbox": [ + 643, + 354, + 869, + 551 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "is not enough to evaluate the goodness of discovered concepts. Literature has evaluated concepts qualitatively (as Section 5.3) or by user study (as Section 5.5).", + "bbox": [ + 75, + 622, + 468, + 666 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We decided to use Synthetic [46] for quantitatively evaluating concepts. The task is a multi-label classification that involves 15 shapes. Combinations of the 5 shapes (shown in Figure 6a, S.1 to S.5) form 15 classes, and the other 10 shapes are noises6. We deem a shape is covered by concept $\\kappa$ when the shape's area and concept $\\kappa$ 's area (the area with $a_{\\kappa} > \\gamma$ for BotCL, where $\\gamma = 0.9$ is a predefined threshold) overlap. Let $h_{s\\kappa} = 1$ denote shape $s$ overlaps with concept $\\kappa$ , and $h_{s\\kappa} = 0$ otherwise. The coverage of $s$ by concept $\\kappa$ is given by", + "bbox": [ + 75, + 667, + 468, + 816 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {C o v e r a g e} _ {s \\kappa} = \\mathbb {E} \\left[ h _ {s \\kappa} \\right], \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 196, + 816, + 468, + 835 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where the expectation is computed over the images in the", + "bbox": [ + 76, + 839, + 468, + 854 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "test set with concept $\\kappa$ activated. The concepts and the 5 shapes are associated as a combinatorial optimization problem so that the sum of Coverage $_{s\\kappa}$ over $s$ are maximized.", + "bbox": [ + 496, + 622, + 890, + 666 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We use $k = 15$ to train BotCL. Figure 6a visualizes the concept associated with each shape7. A concept is located by $a_{\\kappa}$ for 6 images with the highest concept activations $t_{\\kappa}$ . The concepts cover the associated shapes with relatively small regions, but one concept usually covers multiple shapes. This can be further evident in Figure 6b that shows Coverages\\kappa. Cpt.8 only covers S.3, whereas Cpt.1 and Cpt.13 covers multiple shapes.", + "bbox": [ + 496, + 667, + 890, + 787 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We use three metrics other than accuracy to evaluate the performance of concept discovery: (i) Completeness measures how well a concept covers its associated shape in the dataset. (ii) Purity shows the ability to discover concepts that only cover a single shape. (iii) Distinctiveness quanti", + "bbox": [ + 496, + 789, + 890, + 864 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "6Images are generated with random shapes, so there can be multiple classes (combinations of shapes) in a single image, which forms a multi-label classification task.", + "bbox": [ + 75, + 862, + 468, + 898 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "7Note that in this experiment, only shapes matter but not colors.", + "bbox": [ + 514, + 875, + 854, + 887 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "Further details are in supp. material.", + "bbox": [ + 517, + 887, + 723, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "10967", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/d9f6e7d23c3c80f5bb6d87199c0893a83649c21c2d0b4c9e0bc43f361f0c8ad4.jpg", + "image_caption": [ + "Figure 6. Experiment on Synthetic. (a) S.1-S.5 are the five shapes of which combinations form classes. Attention maps next to each shape are of the concept that covers the shape. (b) Coverage $_{s\\kappa}$ (the concept associated with each of the five shapes is marked)." + ], + "image_footnote": [], + "bbox": [ + 106, + 88, + 424, + 281 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d9fd7f8b240cd20c97b3cae58f1b25024b111338cd5512a033924e3ceca864cd.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 433, + 90, + 872, + 281 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "fies the difference among concepts based on the coverage.", + "bbox": [ + 76, + 340, + 460, + 356 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "BotCL with contrastive loss is compared with ACE [14], and two baselines PCA and k-means in [46]. We apply k-means or PCA to $F$ of all images in the dataset after flattening the spatial dimensions. The cluster centers or the principal components are deemed as concepts. Attention maps can be computed by Euclidean distance or cosine similarity. Once the attention maps are obtained, we follow BotCL's process for classification.", + "bbox": [ + 75, + 357, + 468, + 477 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "As shown in Table 2, BotCL shows better completeness, distinctiveness, and accuracy scores than comparative methods. Although k-means is able to discover concepts, they are not optimized for the target classification task, and the performance is low. As we discussed, the concepts learned by BotCL tend to cover more than one target shape, causing a comparatively low purity. The cluster center of k-means is able to capture only one kind of shape at the cost of completeness. We can also observe that all methods are affected by concept number $k$ , and generally a larger $k$ ensure better performance on all metrics. This result is not surprising, but we confirmed that a larger $k$ is preferable for better interpretability. We detail the generation of the dataset, implementation of PCA and k-means, and formal definitions of metrics in supp. material.", + "bbox": [ + 75, + 479, + 468, + 705 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.5. User Study", + "text_level": 1, + "bbox": [ + 76, + 717, + 199, + 733 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Our user study is designed to evaluate BotCL with realistic datasets for the challenge of human understanding. Participants are asked to observe the test images with the attention map for concept $\\kappa$ (refer to Section 5.3.2) and select some phrases in the predefined vocabulary that best describes the concept (i.e., attended regions). They can also choose None of them if they cannot find any consistent visual elements. We recruited 20 participants for each concept", + "bbox": [ + 75, + 741, + 468, + 863 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/a56cc01c3219f9dc90eacfe5fefe0efbbbbdaa1899adbc91bc82ff635a20c0d8.jpg", + "table_caption": [ + "Table 2. Quantitative evaluation on Synthetic. Note that ACE uses concepts for post-hoc explanation and does not use them for classification. Comp., Dist., and Acc. mean completeness, distinctiveness, and accuracy, respectively." + ], + "table_footnote": [], + "table_body": "
Comp.PurityDist.Acc.
k=5ACE0.6620.2740.084—
k-means0.6300.7240.2150.652
PCA0.4580.1700.2980.571
BotCL0.6180.4530.2810.835
k=15ACE0.6140.2210.151—
k-means0.8160.9780.2720.747
PCA0.4320.1620.2860.645
BotCL0.9250.7440.4520.998
", + "bbox": [ + 540, + 406, + 848, + 536 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/a17fb73d974f3f86b6d63f2ac91f5ea5a57b31081280846cc11b58ca79fdd67f.jpg", + "table_caption": [ + "Table 3. Results of our user study." + ], + "table_footnote": [], + "table_body": "
DatasetConceptsCDR ↑CC ↑MIC ↓
MeanStdMeanStdMeanStd
MNISTAnnotated1.0000.0000.8380.1500.0710.047
BotCL0.8250.2880.5810.2740.1990.072
Random0.1220.0700.1630.0740.4380.039
CUB200Annotated0.9490.1150.5950.1130.5120.034
BotCL0.8740.1560.5300.1160.5490.036
Random0.2120.0810.1980.0390.5740.031
", + "bbox": [ + 504, + 573, + 890, + 686 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "of MNIST and 30 participants for CUB200 using Amazon Mechanical Turk.", + "bbox": [ + 498, + 704, + 890, + 733 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We defined three metrics to summarize the participants' responses. (i) Concept discovery rate (CDR): The ratio of the responses that are not None of them to all responses. A higher CDR means participants can find some consistent visual elements for many concepts. (ii) Concept consistency (CC): The ratio of exact matches out of all pairs of participants' responses. A high value means many participants use the same phrases to describe a concept. (iii) Mutual information between concepts (MIC): The similarity of the response distribution, computed over all possible pairs of concepts. This value is high when multiple concepts cover", + "bbox": [ + 496, + 734, + 892, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_footnote", + "text": "9SENN [1] and ProtoPNet [8] are not comparable. SENN's concepts globally cover a whole image. ProtoPNet requires way more concepts.", + "bbox": [ + 75, + 875, + 468, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "10968", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/589bceb8e937e8bfa1aefa978843209acb314dd8ed464c7a2ed93141c52d72cd.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 80, + 90, + 254, + 165 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b3e795580e69ad8beb823cc57b68d6ae0c7bca73fe6dea90027c8202d7fcfdaa.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 256, + 90, + 413, + 165 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/17c6932cdecf73f94b147e439c3dc70f2b46caa4e8e503f9442c43f60e95b9b7.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 416, + 90, + 571, + 166 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0366fc3d3dc05bbe606488ad455ff64e3f122e86aa4e0c05a0a4b27dbbd74003.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 575, + 90, + 730, + 166 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/67a66640a5f0007eebea833f5c1422f76c896422d519048ea6a167f332a3636e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 733, + 90, + 890, + 166 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/823c220e9bcef4c97bd3c08e6def3126a5ea9ed138eff67abcf2fb9063ac6c8d.jpg", + "image_caption": [ + "Figure 7. Results of ablation study. (a) Hyperparameter values vs. classification accuracy on ImageNet and CUB200. (b) Hyperparameter values vs. classification accuracy and other metrics on Synthetic." + ], + "image_footnote": [], + "bbox": [ + 80, + 183, + 254, + 270 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0596d4827d7a8b9782182f1405c55deb85c7c54368ce769bf312f668cfcee613.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 256, + 184, + 413, + 271 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/57007d38529c283143e8db2f3fe6a4a11bdb3132c1956995fd3fc3909b8dcf9d.jpg", + "image_caption": [ + "(b)" + ], + "image_footnote": [], + "bbox": [ + 416, + 184, + 571, + 271 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8bfb1423914005831d45a9d41642802d6f37f94662cce1f631e89537d748800d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 575, + 184, + 730, + 271 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8d8d3f72b281050304d8fe30e732e2b4877d7108667a613ef871958b6b749749.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 733, + 185, + 890, + 270 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "the same visual elements; therefore, lower is better.", + "bbox": [ + 75, + 351, + 415, + 364 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "For comparison, we also evaluated a manual annotation $^{10}$ and random scribbling for the same images. Table 3 shows that BotCL yields good scores for all metrics on both datasets (close to the manual annotation), showing the learned concepts are interpretable for humans (from CDR), consistent (from CC), and mutually distinct (from MIC). More details are in supp. material.", + "bbox": [ + 75, + 366, + 468, + 472 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.6. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 484, + 228, + 500 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We conducted ablation studies using the default hyperparameters except for the one to be explored. As there is no ground truth concept for CUB200 and ImageNet, only accuracy is evaluated (Figure 7a). For Synthetic, accuracy and the three metrics in Section 5.4 are employed (Figure 7b).", + "bbox": [ + 75, + 508, + 468, + 584 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Impact of $k$ . A small $k$ decreases the accuracy and other metrics, which means the necessity of searching the minimum number of concepts. Also, training tends to fail for all datasets when $k$ is large (detailed in the supp. materials). The number of concepts should be tuned for each dataset. This sensitivity is one of BotCL's limitations.", + "bbox": [ + 75, + 585, + 468, + 674 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Impact of $\\lambda_{qua}$ . This hyperparameter controls how close $t$ should be to a binary. The accuracy and the other metrics worsen when $\\lambda_{qua}$ gradually increases. BotCL encodes some information into $t$ (such as the area that a concept occupies), which is lost for larger $\\lambda_{qua}$ . An extreme value may also cause vanishing gradients.", + "bbox": [ + 75, + 676, + 468, + 767 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Impact of $\\lambda_{con}$ and $\\lambda_{dis}$ . The individual consistency and mutual distinctiveness losses hardly affect the performance on CUB200 and ImageNet, although we can see a slight drop when the values are zero for CUB200. For Synthetic, the performance metrics vary as they are designed to be. Meanwhile, the accuracy is relatively insensitive to these hyperparameters. The choice of concepts may be", + "bbox": [ + 75, + 768, + 468, + 875 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "highly arbitrary, and different sets of concepts may achieve similar classification performance. This arbitrariness may allow the designing of dedicated concept regularizers for the target task. However, training failures happen when they are set to be large. A small value benefits training.", + "bbox": [ + 496, + 351, + 890, + 426 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Impact of $\\lambda_{R}$ . Due to the lower performance of the reconstruction loss, we studied the impact of the contrastive loss only. The contrastive loss almost always improves the classification accuracy. The performance boost is significant in CUB200 and Synthetic. As ImageNet has more training data, this may imply that self-supervision greatly contributes to the learning of concepts when training samples are limited. These results demonstrate the importance of the contrastive loss. This is interesting since this loss uses the same labels as the classification loss.", + "bbox": [ + 496, + 426, + 890, + 577 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 594, + 617, + 609 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This paper presents BotCL for learning bottleneck concepts. Our qualitative and quantitative evaluation showed BotCL's ability to learn concepts without explicit supervision on them but through training for a target classification task. We also demonstrated that BotCL could provide interpretability on its decision and learned concepts themselves. Limitations. One limitation of BotCL is that it requires tuning the number $k$ of concepts for each dataset. It might be an interesting research direction to estimate $k$ , e.g., based on the number of classes in a given classification task. We will investigate the phenomenon to mitigate this problem.", + "bbox": [ + 496, + 619, + 890, + 787 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement This work is partly supported by JST CREST Grant No. JPMJCR20D3, JST FOREST Grant No. JPMJFR216O, JSPS KAKENHI Grant-in-Aid for Scientific Research (A). This work is also supported by JSPS KAKENHI Grant Number 19K10662, 20K23343, 21K17764, and 22H03353.", + "bbox": [ + 496, + 809, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_footnote", + "text": "10The authors annotated.", + "bbox": [ + 89, + 886, + 223, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "10969", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 80, + 90, + 171, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] David Alvarez-Melis and Tommi S Jaakkola. Towards robust interpretability with self-explaining neural networks. NeurIPS, 2018.", + "[2] Alejandro Barredo Arrieta, Natalia Diaz-Rodriguez, Javier Del Ser, Adrien Bennetot, Siham Tabik, Alberto Barbado, Salvador Garcia, Sergio Gil-Lopez, Daniel Molina, and Richard Benjamins. 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In ECCV, pages 119-134, 2018." + ], + "bbox": [ + 501, + 92, + 890, + 220 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "10971", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Learning Bottleneck Concepts in Image Classification/c0f445a3-9476-4f99-8d03-749bf8f8a370_model.json b/2023/Learning Bottleneck Concepts in Image Classification/c0f445a3-9476-4f99-8d03-749bf8f8a370_model.json new file mode 100644 index 0000000000000000000000000000000000000000..d1682ec3c170ea3fb1532bd839cab07a338c1df0 --- /dev/null +++ b/2023/Learning Bottleneck Concepts in Image Classification/c0f445a3-9476-4f99-8d03-749bf8f8a370_model.json @@ -0,0 +1,2937 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.215, + 0.131, + 0.757, + 0.154 + ], + "angle": 0, + "content": "Learning Bottleneck Concepts in Image Classification" + }, + { + "type": "text", + "bbox": [ + 0.22, + 0.18, + 0.748, + 0.217 + ], + "angle": 0, + "content": "Bowen Wang\\(^{1}\\), Liangzhi Li\\(^{2*}\\), Yuta Nakashima\\(^{2}\\), Hajime Nagahara\\(^{2}\\), Osaka University, Japan" + }, + { + "type": "text", + "bbox": [ + 0.342, + 0.219, + 0.628, + 0.234 + ], + "angle": 0, + "content": "bowen.wang@is.ids.osaka-u.ac.jp" + }, + { + "type": "text", + "bbox": [ + 0.302, + 0.236, + 0.662, + 0.253 + ], + "angle": 0, + "content": "2{li, n-yuta, nagahara}@ids.osaka-u.ac.jp" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.287, + 0.314, + 0.303 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.318, + 0.474, + 0.562 + ], + "angle": 0, + "content": "Interpreting and explaining the behavior of deep neural networks is critical for many tasks. Explainable AI provides a way to address this challenge, mostly by providing per-pixel relevance to the decision. Yet, interpreting such explanations may require expert knowledge. Some recent attempts toward interpretability adopt a concept-based framework, giving a higher-level relationship between some concepts and model decisions. This paper proposes Bottleneck Concept Learner (BotCL), which represents an image solely by the presence/absence of concepts learned through training over the target task without explicit supervision over the concepts. It uses self-supervision and tailored regularizers so that learned concepts can be human-understandable. Using some image classification tasks as our testbed, we demonstrate BotCL's potential to rebuild neural networks for better interpretability1." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.588, + 0.21, + 0.604 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.613, + 0.47, + 0.78 + ], + "angle": 0, + "content": "Understanding the behavior of deep neural networks (DNNs) is a major challenge in the explainable AI (XAI) community, especially for medical applications [19,38], for identifying biases in DNNs [2, 18, 42], etc. Tremendous research efforts have been devoted to the post-hoc paradigm for a posteriori explanation [29, 33]. This paradigm produces a relevance map to spot regions in the input image that interact with the model's decision. Yet the relevance map only tells low-level (or per-pixel) relationships and does not explicitly convey any semantics behind the decision. Interpretation of relevance maps may require expert knowledge." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.47, + 0.856 + ], + "angle": 0, + "content": "The concept-based framework [22, 37, 50] is inspired by the human capacity to learn a new concept by (subconsciously) finding finer-grained concepts and reuse them in different ways for better recognition [24]. Instead of giving per-pixel relevance, this framework offers higher-level" + }, + { + "type": "image", + "bbox": [ + 0.52, + 0.285, + 0.871, + 0.459 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.469, + 0.892, + 0.525 + ], + "angle": 0, + "content": "Figure 1. Examples of concepts discovered by BotCL in ImageNet [10] and concepts in the input image. BotCL automatically discovers a set of concepts optimized for the target task and represents an image solely with the presence/absence of concepts." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.553, + 0.892, + 0.628 + ], + "angle": 0, + "content": "relationships between the image and decision mediated by a limited number of concepts. That is, the decision is explained by giving a set of concepts found in the image. The interpretation of the decision is thus straightforward once the interpretation of each concept is established." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.893, + 0.764 + ], + "angle": 0, + "content": "Some works use concepts for the post-hoc paradigm for better interpretation of the decision [14, 50], while the link between the decision and concepts in the image is not obvious. The concept bottleneck structure [23] uses the presence/absence of concepts as image representation (referred to as concept activation). The classifier has access only to the concept activation, so the decision is strongly tied to the concepts. This bottleneck structure has become the mainstream of the concept-based framework [5, 20, 28, 31]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.895, + 0.902 + ], + "angle": 0, + "content": "A major difficulty in this framework is designing a set of concepts that suits the target task. A promising approach is handcrafting them [4, 21, 48], which inherently offers better interpretability at the cost of extra annotations on the concepts. Recent attempts automatically discover concepts [1, 13, 14, 46]. Such concepts may not always be consistent with how humans (or models) see the world [25, 47] and may require some effort to interpret them, but concept discovery without supervision is a significant advantage." + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.863, + 0.223, + 0.876 + ], + "angle": 0, + "content": "*Corresponding author." + }, + { + "type": "page_footnote", + "bbox": [ + 0.078, + 0.876, + 0.469, + 0.9 + ], + "angle": 0, + "content": "\\(^{1}\\)Code is available at https://github.com/webw520/BotCL and a simple demo is available at https://botcl.liangzhili.com/." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.863, + 0.469, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10962" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.378 + ], + "angle": 0, + "content": "Inspired by these works, we propose bottleneck concept learner (BotCL) for simultaneously discovering concepts and learning the classifier. BotCL optimizes concepts for the given target image classification task without supervision for the concepts. An image is represented solely by the existence of concepts and is classified using them. We adopt a slot attention-based mechanism [26, 27] to spot the region in which each concept is found. This gives an extra signal for interpreting the decision since one can easily see what each learned concept represents by collectively showing training images with the detected concepts. Figure 1 shows examples from ImageNet [10]. BotCL discovers a predefined number of concepts in the dataset, which are exemplified by several images with attention maps. An image of Great White Shark is represented by the right part of mouth (Cpt.1) and fins (Cpt.3). BotCL uses a single fully-connected (FC) layer as a classifier, which is simple but enough to encode the co-occurrence of each concept and each class." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.379, + 0.473, + 0.531 + ], + "angle": 0, + "content": "Contribution. For better concept discovery, we propose to use self-supervision over concepts, inspired by the recent success in representation learning [9, 16]. Our ablation study demonstrates that self-supervision by contrastive loss is the key. We also try several constraints on concepts themselves, i.e., individual consistency to make a concept more selective and mutual distinctiveness for better coverage of various visual elements. These additional constraints regular the training process and help the model learn concepts of higher quality." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.545, + 0.227, + 0.56 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.57, + 0.231, + 0.587 + ], + "angle": 0, + "content": "2.1. Explainable AI" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.594, + 0.47, + 0.731 + ], + "angle": 0, + "content": "XAI focuses on uncovering black-box deep neural networks [3, 6, 12, 32, 35, 36, 41, 43, 46]. A major approach is generating a relevance map that spots important regions for the model's decision. Various methods have been designed for specific architectures, e.g., CAM [49], and GradCAM [33] for convolutional neural networks; [7] for Transformers [40]. However, the interpretation of the relevance maps may not always be obvious, which spurs different approaches [34, 45], including context-based ones." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.741, + 0.466, + 0.758 + ], + "angle": 0, + "content": "2.2. Concept-based framework for interpretability" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.47, + 0.886 + ], + "angle": 0, + "content": "A straightforward way to define a set of concepts for a target task is to utilize human knowledge [22,48]. Such concepts allow quantifying their importance for a decision [21]. A large corpus of concepts [4, 39] is beneficial for delving into hidden semantics in DNNs [50]. These methods are of the post-hoc XAI paradigm, but a handcrafted set of concepts can also be used as additional supervision for models with the concept bottleneck structure [15, 22, 31]." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.886, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Handcrafting a set of concepts offers better interpreabil" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.242 + ], + "angle": 0, + "content": "ity as they suit human perception; however, the annotation cost is non-negligible. Moreover, such handcrafted concepts may not always be useful for DNNs [47]. These problems have motivated automatic concept discovery. Superpixels are a handy unit for finding low-level semantics, and concepts are defined by clustering them [13, 14, 30]. Another interesting approach is designing a set of concepts to be sufficient statistics of original DNN features [46]. These methods are designed purely for interpretation, and concept discovery is made aside from training on the target task." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.243, + 0.892, + 0.318 + ], + "angle": 0, + "content": "The concept bottleneck structure allows optimizing a set of concepts for the target task. ProtoPNet [8] adopts this structure and identifies concepts based on the distance between features and concepts. SENN [1] uses self-supervision by reconstruction loss for concept discovery." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.318, + 0.892, + 0.379 + ], + "angle": 0, + "content": "SENN inspired us to use self-supervision, but instead of reconstruction loss, we adopt contrastive loss tailored. For a natural image classification task, this contrastive loss is essential for concept discovery." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.391, + 0.58, + 0.407 + ], + "angle": 0, + "content": "3. Model" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.416, + 0.892, + 0.521 + ], + "angle": 0, + "content": "Given a dataset \\(\\mathcal{D} = \\{(x_i, y_i) | i = 1, 2, \\dots, N\\}\\), where \\(x_i\\) is an image and \\(y_i\\) is the target class label in the set \\(\\Omega\\) associated with \\(x_i\\). BotCL learns a set of \\(k\\) concepts while learning the original classification task. Figure 2a shows an overview of BotCL's training scheme, consisting of a concept extractor, regularizers, and a classifier, as well as self-supervision (contrastive and reconstruction losses)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.522, + 0.892, + 0.704 + ], + "angle": 0, + "content": "For a new image \\(x\\), we extract feature map \\(F = \\Phi(x) \\in \\mathbb{R}^{d \\times h \\times w}\\) using a backbone convolutional neural network \\(\\Phi\\). \\(F\\) is then fed into the concept extractor \\(g_{C}\\), where \\(C\\) is a matrix, each of whose \\(\\kappa\\)-th column vector \\(c_{\\kappa}\\) is a concept prototype to be learned. The concept extractor produces concept bottleneck activations \\(t \\in [0,1]^k\\), indicating the presence of each concept, as well as concept features \\(V \\in \\mathbb{R}^{d \\times k}\\) from regions where each concept exists. The concept activations in \\(t\\) are used as input to the classifier to compute score \\(s \\in [0,1]^{|\\Omega|}\\). We use self-supervision and regularizers for training, taking \\(t\\) and \\(V\\) as input to constrain the concept prototypes." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.712, + 0.681, + 0.728 + ], + "angle": 0, + "content": "3.1. Concept Extractor" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.81 + ], + "angle": 0, + "content": "Concept extractor uses slot attention [26, 27]-based mechanism to discover visual concepts in \\(\\mathcal{D}\\). We first add position embedding \\(P\\) to feature map \\(F\\) to retain the spatial information, i.e., \\(F' = F + P\\). The spatial dimension of \\(F'\\) is flattened, so its shape is \\(l \\times d\\), where \\(l = hw\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The slot-attention computes attention over the spatial dimension for concept \\(\\kappa\\) from \\(c_{\\kappa}\\) and \\(F^{\\prime}\\). Let \\(Q(c_{\\kappa})\\in \\mathbb{R}^{d}\\), and \\(K(F^{\\prime})\\in \\mathbb{R}^{d\\times l}\\) denote nonlinear transformations for \\(c_{\\kappa}\\) and \\(F^{\\prime}\\), respectively, given as multi-layer perceptrons with three FC layers and a ReLU nonlinearity between them. Attention \\(a_{\\kappa}\\in [0,1]^{l}\\) is given using a normalization function" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10963" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.08, + 0.089, + 0.585, + 0.232 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.325, + 0.239, + 0.344, + 0.252 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.593, + 0.089, + 0.895, + 0.235 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.734, + 0.24, + 0.753, + 0.253 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image_caption", + "bbox": [ + 0.273, + 0.266, + 0.696, + 0.28 + ], + "angle": 0, + "content": "Figure 2. (a) The model pipeline. (b) Self-supervision and regularizers." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.307, + 0.279, + 0.323 + ], + "angle": 0, + "content": "\\(\\phi\\) (refer to supp. material) as" + }, + { + "type": "equation", + "bbox": [ + 0.19, + 0.328, + 0.47, + 0.346 + ], + "angle": 0, + "content": "\\[\na _ {\\kappa} = \\phi \\left(Q \\left(c _ {\\kappa}\\right) ^ {\\top} K \\left(F ^ {\\prime}\\right)\\right). \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.352, + 0.47, + 0.444 + ], + "angle": 0, + "content": "This attention indicates where concept \\(\\kappa\\) presents in the image as shown in Figure 1. If concept \\(\\kappa\\) is absent, corresponding entries of \\(a_{\\kappa}\\) are all close to 0. We summarize the presence of each concept into concept activation \\(t_{\\kappa}\\) by reducing the spatial dimension of \\(a_{\\kappa}\\) as \\(t_{\\kappa} = \\tanh (\\sum_{m}a_{\\kappa m})\\) where \\(a_{\\kappa m}\\) is the \\(m\\)-th element of \\(a_{\\kappa}\\)." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.451, + 0.274, + 0.467 + ], + "angle": 0, + "content": "3.2. Feature Aggregation" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.474, + 0.469, + 0.505 + ], + "angle": 0, + "content": "For training, we also aggregate features in \\(F\\) corresponding to concept \\(\\kappa\\) into concept feature \\(v_{\\kappa}\\) by" + }, + { + "type": "equation", + "bbox": [ + 0.235, + 0.512, + 0.469, + 0.527 + ], + "angle": 0, + "content": "\\[\nv _ {\\kappa} = F a _ {\\kappa}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.534, + 0.47, + 0.566 + ], + "angle": 0, + "content": "which gives the average of image features over the spatial dimension weighted by attention." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.572, + 0.187, + 0.587 + ], + "angle": 0, + "content": "3.3.Classifier" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.595, + 0.469, + 0.67 + ], + "angle": 0, + "content": "We use a single FC layer without a bias term as the classifier, and concept activation \\(t = (t_{1},\\dots ,t_{k})^{\\top}\\) is the only input, serving as the concept bottleneck [22]. Formally, letting \\(W\\) be a learnable matrix, prediction \\(\\hat{y}\\in \\mathbb{R}^{|\\Omega |}\\) is given by" + }, + { + "type": "equation", + "bbox": [ + 0.241, + 0.671, + 0.469, + 0.687 + ], + "angle": 0, + "content": "\\[\n\\hat {y} = W t. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.69, + 0.47, + 0.797 + ], + "angle": 0, + "content": "This classifier can be roughly interpreted as learning the correlation between the class and concepts. Let \\( w_{\\omega} \\) be the raw vector of \\( W \\) corresponding to class \\( \\omega \\in \\Omega \\), and \\( w_{\\omega \\kappa} \\) is its \\( \\kappa \\)-th element. A positive value of \\( w_{\\omega \\kappa} \\) means that concept \\( \\kappa \\) co-occurs with class \\( \\omega \\) in the dataset, so its presence in a new image positively supports class \\( \\omega \\). Meanwhile, a negative value means the concept rarely co-occurs." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.808, + 0.176, + 0.825 + ], + "angle": 0, + "content": "4. Training" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.833, + 0.412, + 0.85 + ], + "angle": 0, + "content": "4.1. Self-supervision for Concept Discovery" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.47, + 0.902 + ], + "angle": 0, + "content": "The absence of concept labels motivates us to incorporate self-supervision for concept discovery. We employ two losses for different types of target tasks." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.307, + 0.892, + 0.442 + ], + "angle": 0, + "content": "Reconstruction loss. SENN [1] uses an autoencoder-like structure for learning better representation. We assume this structure works well when visual elements are strongly tied with the position since even discrete concepts should have sufficient information to reconstruct the original image. Based on this assumption, we design a reconstruction loss for self-supervision. As shown in Figure 2b, decoder \\( D \\) only takes \\( t \\) as input and reconstructs the original image. We define our reconstruction loss as" + }, + { + "type": "equation", + "bbox": [ + 0.599, + 0.449, + 0.892, + 0.486 + ], + "angle": 0, + "content": "\\[\nl _ {\\text {r e c}} = \\frac {1}{| \\mathcal {B} |} \\sum_ {x \\in \\mathcal {B}} \\| D (t) - x \\| ^ {2}. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.502, + 0.892, + 0.577 + ], + "angle": 0, + "content": "Contrastive loss. The composition of natural images is rather arbitrary, so information in \\( t \\) should be insufficient to reconstruct the original image. We thus design a simple loss for an alternative, borrowing the idea from the recent success of contrastive learning for self-supervision [9, 16]." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.578, + 0.892, + 0.744 + ], + "angle": 0, + "content": "We leverage the image-level labels of the target classification task. Let \\(\\hat{t} = 2t - \\mathbf{1}_k\\), where \\(\\mathbf{1}_k\\) is the \\(k\\)-dimensional vector with all elements being 1. If a pair \\((\\hat{t}, \\hat{t}')\\) of concept activations belong to the same class (i.e., \\(y = y'\\) for \\(y\\) and \\(y'\\) corresponding to \\(\\hat{t}\\) and \\(\\hat{t}'\\)), they should be similar to each other since a similar set of concepts should be in the corresponding images, and otherwise dissimilar. The number \\(|\\Omega|\\) of classes can be smaller than the number \\(|\\mathcal{B}|\\) of images in a mini-batch so that a mini-batch can have multiple images of the same class. Therefore, we use sigmoid instead of softmax, leading to" + }, + { + "type": "equation", + "bbox": [ + 0.557, + 0.752, + 0.892, + 0.786 + ], + "angle": 0, + "content": "\\[\nl _ {\\text {r e t}} = - \\frac {1}{| \\mathcal {B} |} \\sum \\alpha (y, y ^ {\\prime}) \\log J (\\hat {t}, \\hat {t} ^ {\\prime}, y, y ^ {\\prime}), \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.793, + 0.891, + 0.824 + ], + "angle": 0, + "content": "where \\(\\alpha\\) is the weight to mitigate the class imbalance problem (see supp. material) and" + }, + { + "type": "equation", + "bbox": [ + 0.549, + 0.833, + 0.892, + 0.874 + ], + "angle": 0, + "content": "\\[\n\\underline {{J (\\hat {t} , \\hat {t} ^ {\\prime} , y , y ^ {\\prime}) =}} \\left\\{ \\begin{array}{l l} \\sigma (\\hat {t} ^ {\\top} \\hat {t} ^ {\\prime}) & \\text {f o r} y = y ^ {\\prime} \\\\ 1 - \\sigma (\\hat {t} ^ {\\top} \\hat {t} ^ {\\prime}) & \\text {o t h e r w i s e} \\end{array} . \\right. \\tag {6}\n\\]" + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.875, + 0.892, + 0.901 + ], + "angle": 0, + "content": "2For example, images of \"7\" in MNIST almost always have the acute angle in the top-right part." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10964" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.077, + 0.091, + 0.282, + 0.108 + ], + "angle": 0, + "content": "4.2. Concept Regularizers" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.114, + 0.47, + 0.147 + ], + "angle": 0, + "content": "We also employ concept regularizers to facilitate training. They constrain concept prototypes \\(\\{c_{\\kappa}\\}\\) through \\(\\{v_{\\kappa}\\}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.162, + 0.471, + 0.298 + ], + "angle": 0, + "content": "Individual consistency. For better interpretability, each learned concept should not have large variations. That is, the concept features \\( v_{\\kappa} \\) and \\( v_{\\kappa}^{\\prime} \\) of different images should be similar to each other if \\( t_{\\kappa} \\) is close to 1. Let \\( \\mathcal{H}_{\\kappa} \\) denote the set of all concept features of different images in a minibatch, whose activation is larger than the empirical threshold \\( \\xi \\), which is dynamically calculated as the mean of \\( t_{\\kappa} \\) in a mini-batch. Using the cosine similarity \\( \\mathrm{sim}(\\cdot ,\\cdot) \\), we define the consistency loss as:" + }, + { + "type": "equation", + "bbox": [ + 0.147, + 0.303, + 0.47, + 0.343 + ], + "angle": 0, + "content": "\\[\nl _ {\\text {c o n}} = - \\frac {1}{k} \\sum_ {\\kappa} \\sum_ {v _ {\\kappa}, v _ {\\kappa} ^ {\\prime}} \\frac {\\sin \\left(v _ {\\kappa} , v _ {\\kappa} ^ {\\prime}\\right)}{\\left| \\mathcal {H} _ {\\kappa} \\right| \\left(\\left| \\mathcal {H} _ {\\kappa} \\right| - 1\\right)}, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.349, + 0.47, + 0.396 + ], + "angle": 0, + "content": "where the second summation is computed over all combinations of concept features \\( v_{\\kappa} \\) and \\( v_{\\kappa}^{\\prime} \\). This loss penalizes a smaller similarity between \\( v_{\\kappa} \\) and \\( v_{\\kappa}^{\\prime} \\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.411, + 0.47, + 0.501 + ], + "angle": 0, + "content": "Mutual distinctiveness. To capture different aspects of images, different concepts should cover different visual elements. This means that the average image features of concept \\(\\kappa\\) within a mini-batch, given by \\(\\bar{v}_{\\kappa} = \\sum_{v_{\\kappa}\\in \\mathcal{H}_{\\kappa}}v_{\\kappa}\\) should be different from any other \\(v_{\\kappa^{\\prime}}\\). We can encode this into a loss term as" + }, + { + "type": "equation", + "bbox": [ + 0.191, + 0.505, + 0.47, + 0.543 + ], + "angle": 0, + "content": "\\[\nl _ {\\mathrm {d i s}} = \\sum_ {\\kappa , \\kappa^ {\\prime}} \\frac {\\operatorname {s i m} \\left(\\bar {v} _ {\\kappa} , \\bar {v} _ {\\kappa^ {\\prime}}\\right)}{k (k - 1)}, \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.55, + 0.47, + 0.596 + ], + "angle": 0, + "content": "where the summation is computed over all combinations of concepts. Note that concept \\(\\kappa\\) is excluded from this loss if no image in a mini-batch has concept \\(\\kappa\\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.602, + 0.255, + 0.618 + ], + "angle": 0, + "content": "4.3. Quantization Loss" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.626, + 0.47, + 0.687 + ], + "angle": 0, + "content": "Concept activation \\( t \\) can be sufficiently represented by a binary value, but we instead use a continuous value for training. We design a quantization loss to guarantee values are close to 0 or 1, given by" + }, + { + "type": "equation", + "bbox": [ + 0.16, + 0.692, + 0.47, + 0.728 + ], + "angle": 0, + "content": "\\[\nl _ {\\mathrm {q u a}} = \\frac {1}{k | \\mathcal {B} |} \\sum_ {x \\in \\mathcal {B}} \\left\\| \\operatorname {a b s} (\\hat {t}) - \\mathbf {1} _ {\\kappa} \\right\\| ^ {2}, \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.734, + 0.468, + 0.765 + ], + "angle": 0, + "content": "where \\( \\mathrm{abs}(\\cdot) \\) gives the element-wise absolute value and \\( \\| \\cdot \\| \\) gives the Euclidean norm." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.772, + 0.194, + 0.787 + ], + "angle": 0, + "content": "4.4. Total Loss" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.795, + 0.468, + 0.841 + ], + "angle": 0, + "content": "We use softmax cross-entropy for the target classification task's loss, donated by \\( l_{\\mathrm{cls}} \\). The overall loss of BotCL is defined by combining the losses above as" + }, + { + "type": "equation", + "bbox": [ + 0.104, + 0.848, + 0.468, + 0.866 + ], + "angle": 0, + "content": "\\[\nL = l _ {\\mathrm {c l s}} + \\lambda_ {\\mathrm {R}} l _ {\\mathrm {R}} + \\lambda_ {\\mathrm {c o n}} l _ {\\mathrm {c o n}} + \\lambda_ {\\mathrm {d i s}} l _ {\\mathrm {d i s}} + \\lambda_ {\\mathrm {q u a l}} l _ {\\mathrm {q u a}}, \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.468, + 0.902 + ], + "angle": 0, + "content": "where \\(l_{\\mathrm{R}}\\) is either \\(l_{\\mathrm{rec}}\\) or \\(l_{\\mathrm{ret}}\\) depending on the target domain, \\(\\lambda_{\\mathrm{qua}}, \\lambda_{\\mathrm{con}}, \\lambda_{\\mathrm{dis}}\\), and \\(\\lambda_{R}\\) are weights to balance each term." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.091, + 0.587, + 0.106 + ], + "angle": 0, + "content": "5. Results" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.118, + 0.707, + 0.135 + ], + "angle": 0, + "content": "5.1. Experimental Settings" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.145, + 0.892, + 0.19 + ], + "angle": 0, + "content": "We evaluate BotCL on MNIST [11], CUB200 [44], and ImageNet [10]. For evaluating discovered concepts, we regenerated a synthetic shape dataset (Synthetic) [46]." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.193, + 0.892, + 0.344 + ], + "angle": 0, + "content": "For MNIST, we applied the same networks as [1] for the backbone and the concept decoder. For CUB200 (same data split as [22]) and ImageNet, we used pre-trained ResNet [17] as the backbone with a \\( 1 \\times 1 \\) convolutional layer to reduce the channel number (512 for ResNet-18 and 2048 for ResNet-101) to 128. We chose a concept number \\( k = 20 \\) for MNIST and \\( k = 50 \\) for the other natural image datasets. To generate Synthetic, we followed the setting of [46], where 18,000 images were generated for training and 2,000 for evaluation. We used \\( k = 15 \\) with ResNet-18 backbone." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.348, + 0.892, + 0.425 + ], + "angle": 0, + "content": "Images were resized to \\(256 \\times 256\\) and cropped to \\(224 \\times 224\\) (images in Synthetic were directly resized to \\(224 \\times 224\\)). Only random horizontal flip was applied as data augmentation during training. The weight of each loss was defaulted to \\(\\lambda_{\\mathrm{qua}} = 0.1\\), \\(\\lambda_{\\mathrm{con}} = 0.01\\), \\(\\lambda_{\\mathrm{dis}} = 0.05\\), and \\(\\lambda_{\\mathrm{R}} = 0.1\\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.443, + 0.743, + 0.457 + ], + "angle": 0, + "content": "5.2. Classification Performance" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.469, + 0.892, + 0.711 + ], + "angle": 0, + "content": "We compare the performance of BotCL with corresponding baselines (LeNet for MNIST and ResNet-18 for others with a linear classifier), our reimplementation of k-means and PCA in [46], and state-of-the-art concept-based models. Table 1 summarized the results. BotCL with contrastive loss \\((\\mathrm{BotCL}_{\\mathrm{Cont}})\\) achieves the best accuracy on CUB200, ImageNet, and Synthetic, outperforming the baseline linear classifiers. It is also comparable to the state-of-the-art on MNIST and Synthetic. BotCL with reconstruction loss \\((\\mathrm{BotCL}_{\\mathrm{Rec}})\\) shows a performance drop over CUB200, ImageNet, and Synthetic, while it outperforms \\(\\mathrm{BotCL}_{\\mathrm{Cont}}\\) on MNIST. This behavior supports our assumption that the reconstruction loss is useful only when concepts are strongly tied to their spatial position. Otherwise, \\(t\\) is insufficient to reconstruct the original image, and BotCL fails. Contrastive self-supervision is the key to facilitating concept discovery." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.714, + 0.892, + 0.866 + ], + "angle": 0, + "content": "We also explore the relationship between the number of classes and BotCL's accuracy over CUB200 and ImageNet. We used small and large variants of ResNet as the backbone. We extracted subsets of the datasets consisting of the first \\( n \\) classes along with the class IDs. Figure 3 shows that BotCL has a competitive performance when the number of classes is less than 200. We conclude that BotCL hardly degrades the classification performance on small- or middle-sized datasets. However, this is not the case for \\( n > 200 \\) (refer to supp. material for larger \\( n \\) and different \\( k \\)'s)." + }, + { + "type": "page_footnote", + "bbox": [ + 0.516, + 0.887, + 0.768, + 0.902 + ], + "angle": 0, + "content": "3 Implementation details are in supp. material." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10965" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.087, + 0.089, + 0.495, + 0.202 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.496, + 0.089, + 0.686, + 0.201 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.687, + 0.089, + 0.882, + 0.201 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.213, + 0.895, + 0.242 + ], + "angle": 0, + "content": "Figure 3. Classification accuracy vs. the number of classes. We used subsets of CUB200 and ImageNet with \\( k = 50 \\) and ResNet-18 and ResNet-101 backbones." + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.266, + 0.473, + 0.325 + ], + "angle": 0, + "content": "Table 1. Performance comparison in classification accuracy. The best concept-based method is highlighted in bold. \\(\\mathrm{BotCL_{Rec}}\\) and \\(\\mathrm{BotCL_{Cont}}\\) are both BotCL but with reconstruction and contrastive loss, respectively. For ImageNet, we used the first 200 classes." + }, + { + "type": "table", + "bbox": [ + 0.084, + 0.334, + 0.462, + 0.466 + ], + "angle": 0, + "content": "
CUB200ImageNetMNISTSynthetic
Baseline0.7310.7860.9880.999
k-means* [46]0.0630.4270.7810.747
PCA* [46]0.0440.1390.6530.645
SENN [1]0.6420.6730.9850.984
ProtoPNet [8]0.7250.7520.9810.992
BotCLRec0.6930.7200.9830.785
BotCLCont0.7400.7950.9800.998
" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.495, + 0.234, + 0.513 + ], + "angle": 0, + "content": "5.3. Interpretability" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.522, + 0.443, + 0.538 + ], + "angle": 0, + "content": "5.3.1 Qualitative validation of discovered concepts" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.551, + 0.47, + 0.734 + ], + "angle": 0, + "content": "Figure 4a visualizes \\( a_{\\kappa} \\), showing concept \\( \\kappa \\) in the image, over MNIST. We selected 5 concepts out of 20 that are most frequently activated (i.e., \\( t_{\\kappa} > 0.5 \\)) in the training set. Taking digits 0 and 9 as an example, we can observe that they share Cpts.3-5 and the only difference is Cpt.2 that locates in the lower edge of the vertical stroke of 9. This stroke is specific to digit 9. We used BotCLRec, so we can remove Cpt.2 before reconstruction, which generates an image like 0 (refer to Section 5.3.3). Some concepts are incompatible with human intuition; yet we can interpret such concepts (e.g., Cpt.1 may attend to the missing stroke that completes a circle)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.736, + 0.471, + 0.856 + ], + "angle": 0, + "content": "For CUB200, we train \\(\\mathrm{BotCL}_{\\mathrm{Const}}\\) with \\(n = 50\\) and \\(k = 20\\). Figure 5a shows the attention maps of an image of yellow headed black bird. We can observe that the attentions for Cpts.1-5 cover different body parts, including the head, wing, back, and feet, which proves that BotCL can learn valid concepts from the natural image as well. Supp. material exemplifies all concepts discovered from MNIST and CUB200." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.269, + 0.885, + 0.285 + ], + "angle": 0, + "content": "5.3.2 Consistency and distinctiveness of each concept" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.292, + 0.895, + 0.442 + ], + "angle": 0, + "content": "BotCL is designed to discover individually consistent and mutually distinctive concepts. We qualitatively verify this by showing each concept with its top-5 activated images5 with attention maps in Figure 4b. For MNIST, different concepts cover different patterns, and each concept covers the same patterns in different samples (even the samples of different classes). Figure 5b for CUB200 shows that BotCL renders a similar behavior on the CUB200 dataset; that is, the top-5 concepts are responsible for different patterns, and each of them is consistent." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.461, + 0.843, + 0.477 + ], + "angle": 0, + "content": "5.3.3 Contribution of each concept in inference" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.484, + 0.892, + 0.621 + ], + "angle": 0, + "content": "We can qualitatively see the contribution of each concept by removing the concept and seeing the changes in the corresponding self-supervision task's output. As shown in Figure 4c, when we set the activation of Cpt.2 (responsible for the vertical stroke of digit 9) to zero, the reconstructed image looks like digit 0. When Cpt.1, representing the absence of the circle in digit 7, is deactivated (i.e., \\( t_1 \\) is set to 0), a circle emerges in the upper part of the reconstructed image. The resulting image looks more like digit 9." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.621, + 0.892, + 0.772 + ], + "angle": 0, + "content": "For CUB200 shown in Figure 5c, we show images most similar to the input image in Figure 5a among the dataset in terms of \\(\\hat{t}^{\\top}\\hat{t}^{\\prime}\\), with ablating each concept. When Cpt.1 (responsible for the yellow head) is deactivated, more blackhead bird images appear in the top-8 images. Cpt.5 covers birds' feet and is common among most bird classes. Deactivating this concept does not change the top-8 images. These observations suggest that although some concepts do not contribute to classification performance, images are successfully represented by combinations of concepts." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.78, + 0.822, + 0.797 + ], + "angle": 0, + "content": "5.4. Quantitative Evaluation on Synthetic" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.804, + 0.892, + 0.88 + ], + "angle": 0, + "content": "One problem of the concept-based approach is the absence of established quantitative evaluations of concepts because the choice of concepts may be arbitrary and the same level of representability may be achieved with different sets of concepts. A single predefined set of concepts" + }, + { + "type": "page_footnote", + "bbox": [ + 0.076, + 0.875, + 0.47, + 0.9 + ], + "angle": 0, + "content": "4Cpts.1-5 are ordered based on the frequency counted in the dataset." + }, + { + "type": "page_footnote", + "bbox": [ + 0.516, + 0.887, + 0.858, + 0.902 + ], + "angle": 0, + "content": "For each concept \\(\\kappa\\), five images whose \\(t_\\kappa\\) is highest among \\(\\mathcal{D}\\)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "10966" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.119, + 0.092, + 0.365, + 0.262 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.232, + 0.266, + 0.25, + 0.278 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.373, + 0.092, + 0.6, + 0.262 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.488, + 0.265, + 0.505, + 0.277 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image", + "bbox": [ + 0.615, + 0.092, + 0.867, + 0.262 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.733, + 0.265, + 0.75, + 0.277 + ], + "angle": 0, + "content": "(c)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.291, + 0.895, + 0.334 + ], + "angle": 0, + "content": "Figure 4. Concepts for MNIST. (a) Attention maps for different input images. (b) Top-5 activated images (images in the dataset whose \\( t_\\kappa \\) is largest) for each concept. (c) Images reconstructed by our concept decoder with all detected concepts (original) and with a certain concept deactivated." + }, + { + "type": "image_caption", + "bbox": [ + 0.109, + 0.365, + 0.129, + 0.379 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.142, + 0.358, + 0.182, + 0.391 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.147, + 0.393, + 0.176, + 0.402 + ], + "angle": 0, + "content": "Input" + }, + { + "type": "image", + "bbox": [ + 0.205, + 0.359, + 0.245, + 0.39 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.205, + 0.393, + 0.242, + 0.402 + ], + "angle": 0, + "content": "Cpt.1" + }, + { + "type": "image", + "bbox": [ + 0.293, + 0.359, + 0.333, + 0.39 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.293, + 0.393, + 0.329, + 0.402 + ], + "angle": 0, + "content": "Cpt.2" + }, + { + "type": "image", + "bbox": [ + 0.379, + 0.36, + 0.418, + 0.39 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.38, + 0.393, + 0.418, + 0.402 + ], + "angle": 0, + "content": "Cpt.3" + }, + { + "type": "image", + "bbox": [ + 0.465, + 0.36, + 0.504, + 0.39 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.466, + 0.393, + 0.502, + 0.402 + ], + "angle": 0, + "content": "Cpt.4" + }, + { + "type": "image", + "bbox": [ + 0.553, + 0.361, + 0.592, + 0.39 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.553, + 0.393, + 0.591, + 0.402 + ], + "angle": 0, + "content": "Cpt.5" + }, + { + "type": "image_caption", + "bbox": [ + 0.108, + 0.474, + 0.129, + 0.487 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image_caption", + "bbox": [ + 0.147, + 0.436, + 0.165, + 0.523 + ], + "angle": 270, + "content": "Top-5 Activation" + }, + { + "type": "image", + "bbox": [ + 0.182, + 0.404, + 0.262, + 0.433 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.184, + 0.435, + 0.261, + 0.493 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.184, + 0.494, + 0.261, + 0.552 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.272, + 0.404, + 0.35, + 0.433 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.272, + 0.435, + 0.35, + 0.493 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.272, + 0.494, + 0.35, + 0.552 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.36, + 0.404, + 0.437, + 0.433 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.36, + 0.435, + 0.437, + 0.493 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.36, + 0.494, + 0.437, + 0.552 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.445, + 0.404, + 0.523, + 0.433 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.446, + 0.435, + 0.523, + 0.493 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.446, + 0.494, + 0.523, + 0.552 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.532, + 0.404, + 0.61, + 0.433 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.532, + 0.435, + 0.609, + 0.464 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.532, + 0.465, + 0.609, + 0.523 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.532, + 0.524, + 0.609, + 0.553 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.626, + 0.451, + 0.644, + 0.462 + ], + "angle": 0, + "content": "(c)" + }, + { + "type": "image", + "bbox": [ + 0.645, + 0.355, + 0.87, + 0.553 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.568, + 0.893, + 0.596 + ], + "angle": 0, + "content": "Figure 5. Concepts learned for CUB200. (a) Visualization of 5 most important concepts for yellow headed black bird. (b) Top-5 activated concepts. (c) Image retrieval when all detected concepts were used (original) and when a certain concept was deactivated." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.623, + 0.47, + 0.667 + ], + "angle": 0, + "content": "is not enough to evaluate the goodness of discovered concepts. Literature has evaluated concepts qualitatively (as Section 5.3) or by user study (as Section 5.5)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.668, + 0.47, + 0.817 + ], + "angle": 0, + "content": "We decided to use Synthetic [46] for quantitatively evaluating concepts. The task is a multi-label classification that involves 15 shapes. Combinations of the 5 shapes (shown in Figure 6a, S.1 to S.5) form 15 classes, and the other 10 shapes are noises6. We deem a shape is covered by concept \\(\\kappa\\) when the shape's area and concept \\(\\kappa\\)'s area (the area with \\(a_{\\kappa} > \\gamma\\) for BotCL, where \\(\\gamma = 0.9\\) is a predefined threshold) overlap. Let \\(h_{s\\kappa} = 1\\) denote shape \\(s\\) overlaps with concept \\(\\kappa\\), and \\(h_{s\\kappa} = 0\\) otherwise. The coverage of \\(s\\) by concept \\(\\kappa\\) is given by" + }, + { + "type": "equation", + "bbox": [ + 0.197, + 0.818, + 0.469, + 0.836 + ], + "angle": 0, + "content": "\\[\n\\operatorname {C o v e r a g e} _ {s \\kappa} = \\mathbb {E} \\left[ h _ {s \\kappa} \\right], \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.84, + 0.469, + 0.856 + ], + "angle": 0, + "content": "where the expectation is computed over the images in the" + }, + { + "type": "page_footnote", + "bbox": [ + 0.076, + 0.863, + 0.47, + 0.9 + ], + "angle": 0, + "content": "6Images are generated with random shapes, so there can be multiple classes (combinations of shapes) in a single image, which forms a multi-label classification task." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.623, + 0.892, + 0.667 + ], + "angle": 0, + "content": "test set with concept \\(\\kappa\\) activated. The concepts and the 5 shapes are associated as a combinatorial optimization problem so that the sum of Coverage\\(_{s\\kappa}\\) over \\(s\\) are maximized." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.668, + 0.892, + 0.789 + ], + "angle": 0, + "content": "We use \\( k = 15 \\) to train BotCL. Figure 6a visualizes the concept associated with each shape7. A concept is located by \\( a_{\\kappa} \\) for 6 images with the highest concept activations \\( t_{\\kappa} \\). The concepts cover the associated shapes with relatively small regions, but one concept usually covers multiple shapes. This can be further evident in Figure 6b that shows Coverages\\kappa. Cpt.8 only covers S.3, whereas Cpt.1 and Cpt.13 covers multiple shapes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.79, + 0.892, + 0.865 + ], + "angle": 0, + "content": "We use three metrics other than accuracy to evaluate the performance of concept discovery: (i) Completeness measures how well a concept covers its associated shape in the dataset. (ii) Purity shows the ability to discover concepts that only cover a single shape. (iii) Distinctiveness quanti" + }, + { + "type": "page_footnote", + "bbox": [ + 0.516, + 0.875, + 0.855, + 0.888 + ], + "angle": 0, + "content": "7Note that in this experiment, only shapes matter but not colors." + }, + { + "type": "page_footnote", + "bbox": [ + 0.519, + 0.888, + 0.724, + 0.901 + ], + "angle": 0, + "content": "Further details are in supp. material." + }, + { + "type": "list", + "bbox": [ + 0.516, + 0.875, + 0.855, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10967" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.107, + 0.089, + 0.426, + 0.282 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.434, + 0.092, + 0.874, + 0.282 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.297, + 0.893, + 0.327 + ], + "angle": 0, + "content": "Figure 6. Experiment on Synthetic. (a) S.1-S.5 are the five shapes of which combinations form classes. Attention maps next to each shape are of the concept that covers the shape. (b) Coverage\\(_{s\\kappa}\\) (the concept associated with each of the five shapes is marked)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.342, + 0.461, + 0.357 + ], + "angle": 0, + "content": "fies the difference among concepts based on the coverage." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.358, + 0.47, + 0.478 + ], + "angle": 0, + "content": "BotCL with contrastive loss is compared with ACE [14], and two baselines PCA and k-means in [46]. We apply k-means or PCA to \\(F\\) of all images in the dataset after flattening the spatial dimensions. The cluster centers or the principal components are deemed as concepts. Attention maps can be computed by Euclidean distance or cosine similarity. Once the attention maps are obtained, we follow BotCL's process for classification." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.48, + 0.47, + 0.707 + ], + "angle": 0, + "content": "As shown in Table 2, BotCL shows better completeness, distinctiveness, and accuracy scores than comparative methods. Although k-means is able to discover concepts, they are not optimized for the target classification task, and the performance is low. As we discussed, the concepts learned by BotCL tend to cover more than one target shape, causing a comparatively low purity. The cluster center of k-means is able to capture only one kind of shape at the cost of completeness. We can also observe that all methods are affected by concept number \\(k\\), and generally a larger \\(k\\) ensure better performance on all metrics. This result is not surprising, but we confirmed that a larger \\(k\\) is preferable for better interpretability. We detail the generation of the dataset, implementation of PCA and k-means, and formal definitions of metrics in supp. material." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.718, + 0.2, + 0.734 + ], + "angle": 0, + "content": "5.5. User Study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.742, + 0.47, + 0.864 + ], + "angle": 0, + "content": "Our user study is designed to evaluate BotCL with realistic datasets for the challenge of human understanding. Participants are asked to observe the test images with the attention map for concept \\(\\kappa\\) (refer to Section 5.3.2) and select some phrases in the predefined vocabulary that best describes the concept (i.e., attended regions). They can also choose None of them if they cannot find any consistent visual elements. We recruited 20 participants for each concept" + }, + { + "type": "page_footnote", + "bbox": [ + 0.076, + 0.875, + 0.469, + 0.903 + ], + "angle": 0, + "content": "9SENN [1] and ProtoPNet [8] are not comparable. SENN's concepts globally cover a whole image. ProtoPNet requires way more concepts." + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.34, + 0.893, + 0.396 + ], + "angle": 0, + "content": "Table 2. Quantitative evaluation on Synthetic. Note that ACE uses concepts for post-hoc explanation and does not use them for classification. Comp., Dist., and Acc. mean completeness, distinctiveness, and accuracy, respectively." + }, + { + "type": "table", + "bbox": [ + 0.541, + 0.407, + 0.849, + 0.537 + ], + "angle": 0, + "content": "
Comp.PurityDist.Acc.
k=5ACE0.6620.2740.084—
k-means0.6300.7240.2150.652
PCA0.4580.1700.2980.571
BotCL0.6180.4530.2810.835
k=15ACE0.6140.2210.151—
k-means0.8160.9780.2720.747
PCA0.4320.1620.2860.645
BotCL0.9250.7440.4520.998
" + }, + { + "type": "table_caption", + "bbox": [ + 0.593, + 0.549, + 0.799, + 0.563 + ], + "angle": 0, + "content": "Table 3. Results of our user study." + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.574, + 0.892, + 0.687 + ], + "angle": 0, + "content": "
DatasetConceptsCDR ↑CC ↑MIC ↓
MeanStdMeanStdMeanStd
MNISTAnnotated1.0000.0000.8380.1500.0710.047
BotCL0.8250.2880.5810.2740.1990.072
Random0.1220.0700.1630.0740.4380.039
CUB200Annotated0.9490.1150.5950.1130.5120.034
BotCL0.8740.1560.5300.1160.5490.036
Random0.2120.0810.1980.0390.5740.031
" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.705, + 0.891, + 0.734 + ], + "angle": 0, + "content": "of MNIST and 30 participants for CUB200 using Amazon Mechanical Turk." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.893, + 0.901 + ], + "angle": 0, + "content": "We defined three metrics to summarize the participants' responses. (i) Concept discovery rate (CDR): The ratio of the responses that are not None of them to all responses. A higher CDR means participants can find some consistent visual elements for many concepts. (ii) Concept consistency (CC): The ratio of exact matches out of all pairs of participants' responses. A high value means many participants use the same phrases to describe a concept. (iii) Mutual information between concepts (MIC): The similarity of the response distribution, computed over all possible pairs of concepts. This value is high when multiple concepts cover" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10968" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.091, + 0.255, + 0.166 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.257, + 0.092, + 0.414, + 0.166 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.417, + 0.092, + 0.573, + 0.167 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.576, + 0.092, + 0.732, + 0.167 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.735, + 0.092, + 0.892, + 0.167 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.477, + 0.171, + 0.493, + 0.182 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.184, + 0.256, + 0.271 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.257, + 0.185, + 0.414, + 0.272 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.417, + 0.185, + 0.573, + 0.272 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.576, + 0.185, + 0.731, + 0.272 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.735, + 0.186, + 0.891, + 0.271 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.477, + 0.277, + 0.495, + 0.289 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.301, + 0.893, + 0.329 + ], + "angle": 0, + "content": "Figure 7. Results of ablation study. (a) Hyperparameter values vs. classification accuracy on ImageNet and CUB200. (b) Hyperparameter values vs. classification accuracy and other metrics on Synthetic." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.352, + 0.416, + 0.365 + ], + "angle": 0, + "content": "the same visual elements; therefore, lower is better." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.367, + 0.469, + 0.473 + ], + "angle": 0, + "content": "For comparison, we also evaluated a manual annotation\\(^{10}\\) and random scribbling for the same images. Table 3 shows that BotCL yields good scores for all metrics on both datasets (close to the manual annotation), showing the learned concepts are interpretable for humans (from CDR), consistent (from CC), and mutually distinct (from MIC). More details are in supp. material." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.485, + 0.229, + 0.501 + ], + "angle": 0, + "content": "5.6. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.51, + 0.469, + 0.585 + ], + "angle": 0, + "content": "We conducted ablation studies using the default hyperparameters except for the one to be explored. As there is no ground truth concept for CUB200 and ImageNet, only accuracy is evaluated (Figure 7a). For Synthetic, accuracy and the three metrics in Section 5.4 are employed (Figure 7b)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.586, + 0.469, + 0.675 + ], + "angle": 0, + "content": "Impact of \\( k \\). A small \\( k \\) decreases the accuracy and other metrics, which means the necessity of searching the minimum number of concepts. Also, training tends to fail for all datasets when \\( k \\) is large (detailed in the supp. materials). The number of concepts should be tuned for each dataset. This sensitivity is one of BotCL's limitations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.678, + 0.469, + 0.768 + ], + "angle": 0, + "content": "Impact of \\(\\lambda_{qua}\\). This hyperparameter controls how close \\(t\\) should be to a binary. The accuracy and the other metrics worsen when \\(\\lambda_{qua}\\) gradually increases. BotCL encodes some information into \\(t\\) (such as the area that a concept occupies), which is lost for larger \\(\\lambda_{qua}\\). An extreme value may also cause vanishing gradients." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.769, + 0.469, + 0.875 + ], + "angle": 0, + "content": "Impact of \\(\\lambda_{con}\\) and \\(\\lambda_{dis}\\). The individual consistency and mutual distinctiveness losses hardly affect the performance on CUB200 and ImageNet, although we can see a slight drop when the values are zero for CUB200. For Synthetic, the performance metrics vary as they are designed to be. Meanwhile, the accuracy is relatively insensitive to these hyperparameters. The choice of concepts may be" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.352, + 0.892, + 0.427 + ], + "angle": 0, + "content": "highly arbitrary, and different sets of concepts may achieve similar classification performance. This arbitrariness may allow the designing of dedicated concept regularizers for the target task. However, training failures happen when they are set to be large. A small value benefits training." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.428, + 0.892, + 0.578 + ], + "angle": 0, + "content": "Impact of \\(\\lambda_{R}\\). Due to the lower performance of the reconstruction loss, we studied the impact of the contrastive loss only. The contrastive loss almost always improves the classification accuracy. The performance boost is significant in CUB200 and Synthetic. As ImageNet has more training data, this may imply that self-supervision greatly contributes to the learning of concepts when training samples are limited. These results demonstrate the importance of the contrastive loss. This is interesting since this loss uses the same labels as the classification loss." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.595, + 0.618, + 0.61 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.621, + 0.892, + 0.788 + ], + "angle": 0, + "content": "This paper presents BotCL for learning bottleneck concepts. Our qualitative and quantitative evaluation showed BotCL's ability to learn concepts without explicit supervision on them but through training for a target classification task. We also demonstrated that BotCL could provide interpretability on its decision and learned concepts themselves. Limitations. One limitation of BotCL is that it requires tuning the number \\( k \\) of concepts for each dataset. It might be an interesting research direction to estimate \\( k \\), e.g., based on the number of classes in a given classification task. We will investigate the phenomenon to mitigate this problem." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Acknowledgement This work is partly supported by JST CREST Grant No. JPMJCR20D3, JST FOREST Grant No. JPMJFR216O, JSPS KAKENHI Grant-in-Aid for Scientific Research (A). This work is also supported by JSPS KAKENHI Grant Number 19K10662, 20K23343, 21K17764, and 22H03353." + }, + { + "type": "page_footnote", + "bbox": [ + 0.091, + 0.887, + 0.225, + 0.899 + ], + "angle": 0, + "content": "10The authors annotated." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10969" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.081, + 0.091, + 0.173, + 0.105 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.468, + 0.155 + ], + "angle": 0, + "content": "[1] David Alvarez-Melis and Tommi S Jaakkola. Towards robust interpretability with self-explaining neural networks. 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Explainable AI provides a way to address this challenge, mostly by providing per-pixel relevance to the decision. Yet, interpreting such explanations may require expert knowledge. Some recent attempts toward interpretability adopt a concept-based framework, giving a higher-level relationship between some concepts and model decisions. This paper proposes Bottleneck Concept Learner (BotCL), which represents an image solely by the presence/absence of concepts learned through training over the target task without explicit supervision over the concepts. It uses self-supervision and tailored regularizers so that learned concepts can be human-understandable. Using some image classification tasks as our testbed, we demonstrate BotCL's potential to rebuild neural networks for better interpretability1. + +# 1. Introduction + +Understanding the behavior of deep neural networks (DNNs) is a major challenge in the explainable AI (XAI) community, especially for medical applications [19,38], for identifying biases in DNNs [2, 18, 42], etc. Tremendous research efforts have been devoted to the post-hoc paradigm for a posteriori explanation [29, 33]. This paradigm produces a relevance map to spot regions in the input image that interact with the model's decision. Yet the relevance map only tells low-level (or per-pixel) relationships and does not explicitly convey any semantics behind the decision. Interpretation of relevance maps may require expert knowledge. + +The concept-based framework [22, 37, 50] is inspired by the human capacity to learn a new concept by (subconsciously) finding finer-grained concepts and reuse them in different ways for better recognition [24]. Instead of giving per-pixel relevance, this framework offers higher-level + +![](images/57c5c08570f5d3bb51eabe1f8d8a52da31021717facb6703e95af5a00db8e148.jpg) +Figure 1. Examples of concepts discovered by BotCL in ImageNet [10] and concepts in the input image. BotCL automatically discovers a set of concepts optimized for the target task and represents an image solely with the presence/absence of concepts. + +relationships between the image and decision mediated by a limited number of concepts. That is, the decision is explained by giving a set of concepts found in the image. The interpretation of the decision is thus straightforward once the interpretation of each concept is established. + +Some works use concepts for the post-hoc paradigm for better interpretation of the decision [14, 50], while the link between the decision and concepts in the image is not obvious. The concept bottleneck structure [23] uses the presence/absence of concepts as image representation (referred to as concept activation). The classifier has access only to the concept activation, so the decision is strongly tied to the concepts. This bottleneck structure has become the mainstream of the concept-based framework [5, 20, 28, 31]. + +A major difficulty in this framework is designing a set of concepts that suits the target task. A promising approach is handcrafting them [4, 21, 48], which inherently offers better interpretability at the cost of extra annotations on the concepts. Recent attempts automatically discover concepts [1, 13, 14, 46]. Such concepts may not always be consistent with how humans (or models) see the world [25, 47] and may require some effort to interpret them, but concept discovery without supervision is a significant advantage. + +Inspired by these works, we propose bottleneck concept learner (BotCL) for simultaneously discovering concepts and learning the classifier. BotCL optimizes concepts for the given target image classification task without supervision for the concepts. An image is represented solely by the existence of concepts and is classified using them. We adopt a slot attention-based mechanism [26, 27] to spot the region in which each concept is found. This gives an extra signal for interpreting the decision since one can easily see what each learned concept represents by collectively showing training images with the detected concepts. Figure 1 shows examples from ImageNet [10]. BotCL discovers a predefined number of concepts in the dataset, which are exemplified by several images with attention maps. An image of Great White Shark is represented by the right part of mouth (Cpt.1) and fins (Cpt.3). BotCL uses a single fully-connected (FC) layer as a classifier, which is simple but enough to encode the co-occurrence of each concept and each class. + +Contribution. For better concept discovery, we propose to use self-supervision over concepts, inspired by the recent success in representation learning [9, 16]. Our ablation study demonstrates that self-supervision by contrastive loss is the key. We also try several constraints on concepts themselves, i.e., individual consistency to make a concept more selective and mutual distinctiveness for better coverage of various visual elements. These additional constraints regular the training process and help the model learn concepts of higher quality. + +# 2. Related Works + +# 2.1. Explainable AI + +XAI focuses on uncovering black-box deep neural networks [3, 6, 12, 32, 35, 36, 41, 43, 46]. A major approach is generating a relevance map that spots important regions for the model's decision. Various methods have been designed for specific architectures, e.g., CAM [49], and GradCAM [33] for convolutional neural networks; [7] for Transformers [40]. However, the interpretation of the relevance maps may not always be obvious, which spurs different approaches [34, 45], including context-based ones. + +# 2.2. Concept-based framework for interpretability + +A straightforward way to define a set of concepts for a target task is to utilize human knowledge [22,48]. Such concepts allow quantifying their importance for a decision [21]. A large corpus of concepts [4, 39] is beneficial for delving into hidden semantics in DNNs [50]. These methods are of the post-hoc XAI paradigm, but a handcrafted set of concepts can also be used as additional supervision for models with the concept bottleneck structure [15, 22, 31]. + +Handcrafting a set of concepts offers better interpreabil + +ity as they suit human perception; however, the annotation cost is non-negligible. Moreover, such handcrafted concepts may not always be useful for DNNs [47]. These problems have motivated automatic concept discovery. Superpixels are a handy unit for finding low-level semantics, and concepts are defined by clustering them [13, 14, 30]. Another interesting approach is designing a set of concepts to be sufficient statistics of original DNN features [46]. These methods are designed purely for interpretation, and concept discovery is made aside from training on the target task. + +The concept bottleneck structure allows optimizing a set of concepts for the target task. ProtoPNet [8] adopts this structure and identifies concepts based on the distance between features and concepts. SENN [1] uses self-supervision by reconstruction loss for concept discovery. + +SENN inspired us to use self-supervision, but instead of reconstruction loss, we adopt contrastive loss tailored. For a natural image classification task, this contrastive loss is essential for concept discovery. + +# 3. Model + +Given a dataset $\mathcal{D} = \{(x_i, y_i) | i = 1, 2, \dots, N\}$ , where $x_i$ is an image and $y_i$ is the target class label in the set $\Omega$ associated with $x_i$ . BotCL learns a set of $k$ concepts while learning the original classification task. Figure 2a shows an overview of BotCL's training scheme, consisting of a concept extractor, regularizers, and a classifier, as well as self-supervision (contrastive and reconstruction losses). + +For a new image $x$ , we extract feature map $F = \Phi(x) \in \mathbb{R}^{d \times h \times w}$ using a backbone convolutional neural network $\Phi$ . $F$ is then fed into the concept extractor $g_{C}$ , where $C$ is a matrix, each of whose $\kappa$ -th column vector $c_{\kappa}$ is a concept prototype to be learned. The concept extractor produces concept bottleneck activations $t \in [0,1]^k$ , indicating the presence of each concept, as well as concept features $V \in \mathbb{R}^{d \times k}$ from regions where each concept exists. The concept activations in $t$ are used as input to the classifier to compute score $s \in [0,1]^{|\Omega|}$ . We use self-supervision and regularizers for training, taking $t$ and $V$ as input to constrain the concept prototypes. + +# 3.1. Concept Extractor + +Concept extractor uses slot attention [26, 27]-based mechanism to discover visual concepts in $\mathcal{D}$ . We first add position embedding $P$ to feature map $F$ to retain the spatial information, i.e., $F' = F + P$ . The spatial dimension of $F'$ is flattened, so its shape is $l \times d$ , where $l = hw$ . + +The slot-attention computes attention over the spatial dimension for concept $\kappa$ from $c_{\kappa}$ and $F^{\prime}$ . Let $Q(c_{\kappa})\in \mathbb{R}^{d}$ , and $K(F^{\prime})\in \mathbb{R}^{d\times l}$ denote nonlinear transformations for $c_{\kappa}$ and $F^{\prime}$ , respectively, given as multi-layer perceptrons with three FC layers and a ReLU nonlinearity between them. Attention $a_{\kappa}\in [0,1]^{l}$ is given using a normalization function + +![](images/93cd9351f448be129dc709ec2a001ffe0d9e91a1be1bcf645de1be1904ae8caa.jpg) +(a) + +![](images/7ad52cdcbfc292d452281d9a91d3b445ae67870b6c54129097f8a07bd2fb6ac7.jpg) +(b) +Figure 2. (a) The model pipeline. (b) Self-supervision and regularizers. + +$\phi$ (refer to supp. material) as + +$$ +a _ {\kappa} = \phi \left(Q \left(c _ {\kappa}\right) ^ {\top} K \left(F ^ {\prime}\right)\right). \tag {1} +$$ + +This attention indicates where concept $\kappa$ presents in the image as shown in Figure 1. If concept $\kappa$ is absent, corresponding entries of $a_{\kappa}$ are all close to 0. We summarize the presence of each concept into concept activation $t_{\kappa}$ by reducing the spatial dimension of $a_{\kappa}$ as $t_{\kappa} = \tanh (\sum_{m}a_{\kappa m})$ where $a_{\kappa m}$ is the $m$ -th element of $a_{\kappa}$ . + +# 3.2. Feature Aggregation + +For training, we also aggregate features in $F$ corresponding to concept $\kappa$ into concept feature $v_{\kappa}$ by + +$$ +v _ {\kappa} = F a _ {\kappa}, \tag {2} +$$ + +which gives the average of image features over the spatial dimension weighted by attention. + +# 3.3.Classifier + +We use a single FC layer without a bias term as the classifier, and concept activation $t = (t_{1},\dots ,t_{k})^{\top}$ is the only input, serving as the concept bottleneck [22]. Formally, letting $W$ be a learnable matrix, prediction $\hat{y}\in \mathbb{R}^{|\Omega |}$ is given by + +$$ +\hat {y} = W t. \tag {3} +$$ + +This classifier can be roughly interpreted as learning the correlation between the class and concepts. Let $w_{\omega}$ be the raw vector of $W$ corresponding to class $\omega \in \Omega$ , and $w_{\omega \kappa}$ is its $\kappa$ -th element. A positive value of $w_{\omega \kappa}$ means that concept $\kappa$ co-occurs with class $\omega$ in the dataset, so its presence in a new image positively supports class $\omega$ . Meanwhile, a negative value means the concept rarely co-occurs. + +# 4. Training + +# 4.1. Self-supervision for Concept Discovery + +The absence of concept labels motivates us to incorporate self-supervision for concept discovery. We employ two losses for different types of target tasks. + +Reconstruction loss. SENN [1] uses an autoencoder-like structure for learning better representation. We assume this structure works well when visual elements are strongly tied with the position since even discrete concepts should have sufficient information to reconstruct the original image. Based on this assumption, we design a reconstruction loss for self-supervision. As shown in Figure 2b, decoder $D$ only takes $t$ as input and reconstructs the original image. We define our reconstruction loss as + +$$ +l _ {\text {r e c}} = \frac {1}{| \mathcal {B} |} \sum_ {x \in \mathcal {B}} \| D (t) - x \| ^ {2}. \tag {4} +$$ + +Contrastive loss. The composition of natural images is rather arbitrary, so information in $t$ should be insufficient to reconstruct the original image. We thus design a simple loss for an alternative, borrowing the idea from the recent success of contrastive learning for self-supervision [9, 16]. + +We leverage the image-level labels of the target classification task. Let $\hat{t} = 2t - \mathbf{1}_k$ , where $\mathbf{1}_k$ is the $k$ -dimensional vector with all elements being 1. If a pair $(\hat{t}, \hat{t}')$ of concept activations belong to the same class (i.e., $y = y'$ for $y$ and $y'$ corresponding to $\hat{t}$ and $\hat{t}'$ ), they should be similar to each other since a similar set of concepts should be in the corresponding images, and otherwise dissimilar. The number $|\Omega|$ of classes can be smaller than the number $|\mathcal{B}|$ of images in a mini-batch so that a mini-batch can have multiple images of the same class. Therefore, we use sigmoid instead of softmax, leading to + +$$ +l _ {\text {r e t}} = - \frac {1}{| \mathcal {B} |} \sum \alpha (y, y ^ {\prime}) \log J (\hat {t}, \hat {t} ^ {\prime}, y, y ^ {\prime}), \tag {5} +$$ + +where $\alpha$ is the weight to mitigate the class imbalance problem (see supp. material) and + +$$ +\underline {{J (\hat {t} , \hat {t} ^ {\prime} , y , y ^ {\prime}) =}} \left\{ \begin{array}{l l} \sigma (\hat {t} ^ {\top} \hat {t} ^ {\prime}) & \text {f o r} y = y ^ {\prime} \\ 1 - \sigma (\hat {t} ^ {\top} \hat {t} ^ {\prime}) & \text {o t h e r w i s e} \end{array} . \right. \tag {6} +$$ + +# 4.2. Concept Regularizers + +We also employ concept regularizers to facilitate training. They constrain concept prototypes $\{c_{\kappa}\}$ through $\{v_{\kappa}\}$ . + +Individual consistency. For better interpretability, each learned concept should not have large variations. That is, the concept features $v_{\kappa}$ and $v_{\kappa}^{\prime}$ of different images should be similar to each other if $t_{\kappa}$ is close to 1. Let $\mathcal{H}_{\kappa}$ denote the set of all concept features of different images in a minibatch, whose activation is larger than the empirical threshold $\xi$ , which is dynamically calculated as the mean of $t_{\kappa}$ in a mini-batch. Using the cosine similarity $\mathrm{sim}(\cdot ,\cdot)$ , we define the consistency loss as: + +$$ +l _ {\text {c o n}} = - \frac {1}{k} \sum_ {\kappa} \sum_ {v _ {\kappa}, v _ {\kappa} ^ {\prime}} \frac {\sin \left(v _ {\kappa} , v _ {\kappa} ^ {\prime}\right)}{\left| \mathcal {H} _ {\kappa} \right| \left(\left| \mathcal {H} _ {\kappa} \right| - 1\right)}, \tag {7} +$$ + +where the second summation is computed over all combinations of concept features $v_{\kappa}$ and $v_{\kappa}^{\prime}$ . This loss penalizes a smaller similarity between $v_{\kappa}$ and $v_{\kappa}^{\prime}$ . + +Mutual distinctiveness. To capture different aspects of images, different concepts should cover different visual elements. This means that the average image features of concept $\kappa$ within a mini-batch, given by $\bar{v}_{\kappa} = \sum_{v_{\kappa}\in \mathcal{H}_{\kappa}}v_{\kappa}$ should be different from any other $v_{\kappa^{\prime}}$ . We can encode this into a loss term as + +$$ +l _ {\mathrm {d i s}} = \sum_ {\kappa , \kappa^ {\prime}} \frac {\operatorname {s i m} \left(\bar {v} _ {\kappa} , \bar {v} _ {\kappa^ {\prime}}\right)}{k (k - 1)}, \tag {8} +$$ + +where the summation is computed over all combinations of concepts. Note that concept $\kappa$ is excluded from this loss if no image in a mini-batch has concept $\kappa$ . + +# 4.3. Quantization Loss + +Concept activation $t$ can be sufficiently represented by a binary value, but we instead use a continuous value for training. We design a quantization loss to guarantee values are close to 0 or 1, given by + +$$ +l _ {\mathrm {q u a}} = \frac {1}{k | \mathcal {B} |} \sum_ {x \in \mathcal {B}} \left\| \operatorname {a b s} (\hat {t}) - \mathbf {1} _ {\kappa} \right\| ^ {2}, \tag {9} +$$ + +where $\mathrm{abs}(\cdot)$ gives the element-wise absolute value and $\| \cdot \|$ gives the Euclidean norm. + +# 4.4. Total Loss + +We use softmax cross-entropy for the target classification task's loss, donated by $l_{\mathrm{cls}}$ . The overall loss of BotCL is defined by combining the losses above as + +$$ +L = l _ {\mathrm {c l s}} + \lambda_ {\mathrm {R}} l _ {\mathrm {R}} + \lambda_ {\mathrm {c o n}} l _ {\mathrm {c o n}} + \lambda_ {\mathrm {d i s}} l _ {\mathrm {d i s}} + \lambda_ {\mathrm {q u a l}} l _ {\mathrm {q u a}}, \tag {10} +$$ + +where $l_{\mathrm{R}}$ is either $l_{\mathrm{rec}}$ or $l_{\mathrm{ret}}$ depending on the target domain, $\lambda_{\mathrm{qua}}, \lambda_{\mathrm{con}}, \lambda_{\mathrm{dis}}$ , and $\lambda_{R}$ are weights to balance each term. + +# 5. Results + +# 5.1. Experimental Settings + +We evaluate BotCL on MNIST [11], CUB200 [44], and ImageNet [10]. For evaluating discovered concepts, we regenerated a synthetic shape dataset (Synthetic) [46]. + +For MNIST, we applied the same networks as [1] for the backbone and the concept decoder. For CUB200 (same data split as [22]) and ImageNet, we used pre-trained ResNet [17] as the backbone with a $1 \times 1$ convolutional layer to reduce the channel number (512 for ResNet-18 and 2048 for ResNet-101) to 128. We chose a concept number $k = 20$ for MNIST and $k = 50$ for the other natural image datasets. To generate Synthetic, we followed the setting of [46], where 18,000 images were generated for training and 2,000 for evaluation. We used $k = 15$ with ResNet-18 backbone. + +Images were resized to $256 \times 256$ and cropped to $224 \times 224$ (images in Synthetic were directly resized to $224 \times 224$ ). Only random horizontal flip was applied as data augmentation during training. The weight of each loss was defaulted to $\lambda_{\mathrm{qua}} = 0.1$ , $\lambda_{\mathrm{con}} = 0.01$ , $\lambda_{\mathrm{dis}} = 0.05$ , and $\lambda_{\mathrm{R}} = 0.1$ . + +# 5.2. Classification Performance + +We compare the performance of BotCL with corresponding baselines (LeNet for MNIST and ResNet-18 for others with a linear classifier), our reimplementation of k-means and PCA in [46], and state-of-the-art concept-based models. Table 1 summarized the results. BotCL with contrastive loss $(\mathrm{BotCL}_{\mathrm{Cont}})$ achieves the best accuracy on CUB200, ImageNet, and Synthetic, outperforming the baseline linear classifiers. It is also comparable to the state-of-the-art on MNIST and Synthetic. BotCL with reconstruction loss $(\mathrm{BotCL}_{\mathrm{Rec}})$ shows a performance drop over CUB200, ImageNet, and Synthetic, while it outperforms $\mathrm{BotCL}_{\mathrm{Cont}}$ on MNIST. This behavior supports our assumption that the reconstruction loss is useful only when concepts are strongly tied to their spatial position. Otherwise, $t$ is insufficient to reconstruct the original image, and BotCL fails. Contrastive self-supervision is the key to facilitating concept discovery. + +We also explore the relationship between the number of classes and BotCL's accuracy over CUB200 and ImageNet. We used small and large variants of ResNet as the backbone. We extracted subsets of the datasets consisting of the first $n$ classes along with the class IDs. Figure 3 shows that BotCL has a competitive performance when the number of classes is less than 200. We conclude that BotCL hardly degrades the classification performance on small- or middle-sized datasets. However, this is not the case for $n > 200$ (refer to supp. material for larger $n$ and different $k$ 's). + +![](images/84780a469a0780bcf43986dd8e3e608ef968a48c58084652eca318a3f7fc5142.jpg) +Figure 3. Classification accuracy vs. the number of classes. We used subsets of CUB200 and ImageNet with $k = 50$ and ResNet-18 and ResNet-101 backbones. + +![](images/f522c58e4a2bd2bfbe6d3193555910f29361428d551c6201ca3af81bcaa68662.jpg) + +![](images/63f847b2ef16a25959ac120149bc5a6c942491ece6229324b63d6714c6ed0463.jpg) + +Table 1. Performance comparison in classification accuracy. The best concept-based method is highlighted in bold. $\mathrm{BotCL_{Rec}}$ and $\mathrm{BotCL_{Cont}}$ are both BotCL but with reconstruction and contrastive loss, respectively. For ImageNet, we used the first 200 classes. + +
CUB200ImageNetMNISTSynthetic
Baseline0.7310.7860.9880.999
k-means* [46]0.0630.4270.7810.747
PCA* [46]0.0440.1390.6530.645
SENN [1]0.6420.6730.9850.984
ProtoPNet [8]0.7250.7520.9810.992
BotCLRec0.6930.7200.9830.785
BotCLCont0.7400.7950.9800.998
+ +# 5.3. Interpretability + +# 5.3.1 Qualitative validation of discovered concepts + +Figure 4a visualizes $a_{\kappa}$ , showing concept $\kappa$ in the image, over MNIST. We selected 5 concepts out of 20 that are most frequently activated (i.e., $t_{\kappa} > 0.5$ ) in the training set. Taking digits 0 and 9 as an example, we can observe that they share Cpts.3-5 and the only difference is Cpt.2 that locates in the lower edge of the vertical stroke of 9. This stroke is specific to digit 9. We used BotCLRec, so we can remove Cpt.2 before reconstruction, which generates an image like 0 (refer to Section 5.3.3). Some concepts are incompatible with human intuition; yet we can interpret such concepts (e.g., Cpt.1 may attend to the missing stroke that completes a circle). + +For CUB200, we train $\mathrm{BotCL}_{\mathrm{Const}}$ with $n = 50$ and $k = 20$ . Figure 5a shows the attention maps of an image of yellow headed black bird. We can observe that the attentions for Cpts.1-5 cover different body parts, including the head, wing, back, and feet, which proves that BotCL can learn valid concepts from the natural image as well. Supp. material exemplifies all concepts discovered from MNIST and CUB200. + +# 5.3.2 Consistency and distinctiveness of each concept + +BotCL is designed to discover individually consistent and mutually distinctive concepts. We qualitatively verify this by showing each concept with its top-5 activated images5 with attention maps in Figure 4b. For MNIST, different concepts cover different patterns, and each concept covers the same patterns in different samples (even the samples of different classes). Figure 5b for CUB200 shows that BotCL renders a similar behavior on the CUB200 dataset; that is, the top-5 concepts are responsible for different patterns, and each of them is consistent. + +# 5.3.3 Contribution of each concept in inference + +We can qualitatively see the contribution of each concept by removing the concept and seeing the changes in the corresponding self-supervision task's output. As shown in Figure 4c, when we set the activation of Cpt.2 (responsible for the vertical stroke of digit 9) to zero, the reconstructed image looks like digit 0. When Cpt.1, representing the absence of the circle in digit 7, is deactivated (i.e., $t_1$ is set to 0), a circle emerges in the upper part of the reconstructed image. The resulting image looks more like digit 9. + +For CUB200 shown in Figure 5c, we show images most similar to the input image in Figure 5a among the dataset in terms of $\hat{t}^{\top}\hat{t}^{\prime}$ , with ablating each concept. When Cpt.1 (responsible for the yellow head) is deactivated, more blackhead bird images appear in the top-8 images. Cpt.5 covers birds' feet and is common among most bird classes. Deactivating this concept does not change the top-8 images. These observations suggest that although some concepts do not contribute to classification performance, images are successfully represented by combinations of concepts. + +# 5.4. Quantitative Evaluation on Synthetic + +One problem of the concept-based approach is the absence of established quantitative evaluations of concepts because the choice of concepts may be arbitrary and the same level of representability may be achieved with different sets of concepts. A single predefined set of concepts + +![](images/668f860605168c909be856f0a78bf471da8ab83ecfcc8a1b3d685d78bbcee359.jpg) +(a) + +![](images/fd4a0c9780aee08eb8187408059c7089b2c44a988a3da66d5395c0eb9b6ba531.jpg) +(b) + +![](images/5487ebc155c33e8beccc8b64d4b562e7db3f11335c51582ecee54d0e90c7d892.jpg) +(c) + +![](images/b18a7cf8c024aacf58f387223732feb540ed03b3fad7dc528aced3caeea96319.jpg) +(a) +Input + +![](images/becb6dd9c4268f4151bed3e16cd10a2d2ee396ef033ceb1bbbc14888dce58728.jpg) + +![](images/50287743766ff336afb75ff4d6641bd17e5dc2652732e4affb68208159280ebc.jpg) + +![](images/0652f11077c39740ced89e7475ba786808f693f69115b69e199d253ebcf9435a.jpg) + +![](images/c0075e6ab4f82df310d28f3048a3b952c2c74bfa3e8622e82b4809aa784a572e.jpg) + +![](images/6623cab36566e5883e4ee29ae7dc94eb9bef1122907d85104dd30cd9df723b8e.jpg) + +![](images/917bf85335e8a2d28bd82769f71ed55908147912a228a5320005d2856e13e739.jpg) +Cpt.1 +Top-5 Activation + +![](images/74807a28dee0666cf2b675093e6ac4c72ac50eeb6d60840bf6680ddb18d89b1b.jpg) +(b) + +![](images/c8bc659dbd9684b34759ee2a58f33db6312161830a72557e9ef19832a5b48caf.jpg) +Figure 5. Concepts learned for CUB200. (a) Visualization of 5 most important concepts for yellow headed black bird. (b) Top-5 activated concepts. (c) Image retrieval when all detected concepts were used (original) and when a certain concept was deactivated. + +![](images/f28a10296593cfeee06fc12507e930f92e73c5674209bf40ea179e0e1aff5170.jpg) +Cpt.2 + +![](images/c635bbc60deca00ab5190e33758ecf5e8c866152c0c588a3f6997883db295065.jpg) + +![](images/7df738de214667daf0750daf7d3b123a2dba9c56022c6f4327d71a188cf8ff83.jpg) + +![](images/73415367dccec47bb7ff2a5dc02319cdff85fd431b33822960b45e0aa125974a.jpg) +Cpt.3 + +![](images/44421944b8f2f1faa08d859f20ccf3653dbf174e394486b5fe61386204dbd0c3.jpg) + +![](images/34df0e268b588b0b52207c0a0ce42cfb08dca0728426b51c3e98f6dbe0f8850c.jpg) + +![](images/d2283d0f0e9e24fea3bd0b54dcaa2a35295d3c7d10a2ddd4fe14b63249dae4da.jpg) +Cpt.4 + +![](images/62337d64baa9236bcd2cb30a220c5e5dab5a0f661880e49f023ddf9e14199c91.jpg) + +![](images/8fcc4fdb45527369f2730e752391f942841d9ca8996d5bef8423388cb82e721c.jpg) + +![](images/c5dacba753b21f8eca25c76d1a29637926725dcbad9aafa3059d60cff11f89ac.jpg) +Cpt.5 + +![](images/698ff7b3a84e8a17f0600af887bfa2fb3d7b61d5d7024a7301ca893d0e5009a0.jpg) + +![](images/9b178ced4986c4c2798ca8f7941f1da8b58cff1ed147deec0c05f5f809f89808.jpg) + +![](images/90ee06bcd6db828a9517082ac2390c89ae0ef9e500f78947106dcdadb8f47cca.jpg) + +![](images/516896f6287fce2e3e904196b7c13d983273b37c3adf24566fde9cc883dda50f.jpg) +Figure 4. Concepts for MNIST. (a) Attention maps for different input images. (b) Top-5 activated images (images in the dataset whose $t_\kappa$ is largest) for each concept. (c) Images reconstructed by our concept decoder with all detected concepts (original) and with a certain concept deactivated. +(c) + +is not enough to evaluate the goodness of discovered concepts. Literature has evaluated concepts qualitatively (as Section 5.3) or by user study (as Section 5.5). + +We decided to use Synthetic [46] for quantitatively evaluating concepts. The task is a multi-label classification that involves 15 shapes. Combinations of the 5 shapes (shown in Figure 6a, S.1 to S.5) form 15 classes, and the other 10 shapes are noises6. We deem a shape is covered by concept $\kappa$ when the shape's area and concept $\kappa$ 's area (the area with $a_{\kappa} > \gamma$ for BotCL, where $\gamma = 0.9$ is a predefined threshold) overlap. Let $h_{s\kappa} = 1$ denote shape $s$ overlaps with concept $\kappa$ , and $h_{s\kappa} = 0$ otherwise. The coverage of $s$ by concept $\kappa$ is given by + +$$ +\operatorname {C o v e r a g e} _ {s \kappa} = \mathbb {E} \left[ h _ {s \kappa} \right], \tag {11} +$$ + +where the expectation is computed over the images in the + +test set with concept $\kappa$ activated. The concepts and the 5 shapes are associated as a combinatorial optimization problem so that the sum of Coverage $_{s\kappa}$ over $s$ are maximized. + +We use $k = 15$ to train BotCL. Figure 6a visualizes the concept associated with each shape7. A concept is located by $a_{\kappa}$ for 6 images with the highest concept activations $t_{\kappa}$ . The concepts cover the associated shapes with relatively small regions, but one concept usually covers multiple shapes. This can be further evident in Figure 6b that shows Coverages\kappa. Cpt.8 only covers S.3, whereas Cpt.1 and Cpt.13 covers multiple shapes. + +We use three metrics other than accuracy to evaluate the performance of concept discovery: (i) Completeness measures how well a concept covers its associated shape in the dataset. (ii) Purity shows the ability to discover concepts that only cover a single shape. (iii) Distinctiveness quanti + +![](images/d9f6e7d23c3c80f5bb6d87199c0893a83649c21c2d0b4c9e0bc43f361f0c8ad4.jpg) +Figure 6. Experiment on Synthetic. (a) S.1-S.5 are the five shapes of which combinations form classes. Attention maps next to each shape are of the concept that covers the shape. (b) Coverage $_{s\kappa}$ (the concept associated with each of the five shapes is marked). + +![](images/d9fd7f8b240cd20c97b3cae58f1b25024b111338cd5512a033924e3ceca864cd.jpg) + +fies the difference among concepts based on the coverage. + +BotCL with contrastive loss is compared with ACE [14], and two baselines PCA and k-means in [46]. We apply k-means or PCA to $F$ of all images in the dataset after flattening the spatial dimensions. The cluster centers or the principal components are deemed as concepts. Attention maps can be computed by Euclidean distance or cosine similarity. Once the attention maps are obtained, we follow BotCL's process for classification. + +As shown in Table 2, BotCL shows better completeness, distinctiveness, and accuracy scores than comparative methods. Although k-means is able to discover concepts, they are not optimized for the target classification task, and the performance is low. As we discussed, the concepts learned by BotCL tend to cover more than one target shape, causing a comparatively low purity. The cluster center of k-means is able to capture only one kind of shape at the cost of completeness. We can also observe that all methods are affected by concept number $k$ , and generally a larger $k$ ensure better performance on all metrics. This result is not surprising, but we confirmed that a larger $k$ is preferable for better interpretability. We detail the generation of the dataset, implementation of PCA and k-means, and formal definitions of metrics in supp. material. + +# 5.5. User Study + +Our user study is designed to evaluate BotCL with realistic datasets for the challenge of human understanding. Participants are asked to observe the test images with the attention map for concept $\kappa$ (refer to Section 5.3.2) and select some phrases in the predefined vocabulary that best describes the concept (i.e., attended regions). They can also choose None of them if they cannot find any consistent visual elements. We recruited 20 participants for each concept + +Table 2. Quantitative evaluation on Synthetic. Note that ACE uses concepts for post-hoc explanation and does not use them for classification. Comp., Dist., and Acc. mean completeness, distinctiveness, and accuracy, respectively. + +
Comp.PurityDist.Acc.
k=5ACE0.6620.2740.084—
k-means0.6300.7240.2150.652
PCA0.4580.1700.2980.571
BotCL0.6180.4530.2810.835
k=15ACE0.6140.2210.151—
k-means0.8160.9780.2720.747
PCA0.4320.1620.2860.645
BotCL0.9250.7440.4520.998
+ +Table 3. Results of our user study. + +
DatasetConceptsCDR ↑CC ↑MIC ↓
MeanStdMeanStdMeanStd
MNISTAnnotated1.0000.0000.8380.1500.0710.047
BotCL0.8250.2880.5810.2740.1990.072
Random0.1220.0700.1630.0740.4380.039
CUB200Annotated0.9490.1150.5950.1130.5120.034
BotCL0.8740.1560.5300.1160.5490.036
Random0.2120.0810.1980.0390.5740.031
+ +of MNIST and 30 participants for CUB200 using Amazon Mechanical Turk. + +We defined three metrics to summarize the participants' responses. (i) Concept discovery rate (CDR): The ratio of the responses that are not None of them to all responses. A higher CDR means participants can find some consistent visual elements for many concepts. (ii) Concept consistency (CC): The ratio of exact matches out of all pairs of participants' responses. A high value means many participants use the same phrases to describe a concept. (iii) Mutual information between concepts (MIC): The similarity of the response distribution, computed over all possible pairs of concepts. This value is high when multiple concepts cover + +![](images/589bceb8e937e8bfa1aefa978843209acb314dd8ed464c7a2ed93141c52d72cd.jpg) + +![](images/b3e795580e69ad8beb823cc57b68d6ae0c7bca73fe6dea90027c8202d7fcfdaa.jpg) + +![](images/17c6932cdecf73f94b147e439c3dc70f2b46caa4e8e503f9442c43f60e95b9b7.jpg) +(a) + +![](images/0366fc3d3dc05bbe606488ad455ff64e3f122e86aa4e0c05a0a4b27dbbd74003.jpg) + +![](images/67a66640a5f0007eebea833f5c1422f76c896422d519048ea6a167f332a3636e.jpg) + +![](images/823c220e9bcef4c97bd3c08e6def3126a5ea9ed138eff67abcf2fb9063ac6c8d.jpg) +Figure 7. Results of ablation study. (a) Hyperparameter values vs. classification accuracy on ImageNet and CUB200. (b) Hyperparameter values vs. classification accuracy and other metrics on Synthetic. + +![](images/0596d4827d7a8b9782182f1405c55deb85c7c54368ce769bf312f668cfcee613.jpg) + +![](images/57007d38529c283143e8db2f3fe6a4a11bdb3132c1956995fd3fc3909b8dcf9d.jpg) +(b) + +![](images/8bfb1423914005831d45a9d41642802d6f37f94662cce1f631e89537d748800d.jpg) + +![](images/8d8d3f72b281050304d8fe30e732e2b4877d7108667a613ef871958b6b749749.jpg) + +the same visual elements; therefore, lower is better. + +For comparison, we also evaluated a manual annotation $^{10}$ and random scribbling for the same images. Table 3 shows that BotCL yields good scores for all metrics on both datasets (close to the manual annotation), showing the learned concepts are interpretable for humans (from CDR), consistent (from CC), and mutually distinct (from MIC). More details are in supp. material. + +# 5.6. Ablation Study + +We conducted ablation studies using the default hyperparameters except for the one to be explored. As there is no ground truth concept for CUB200 and ImageNet, only accuracy is evaluated (Figure 7a). For Synthetic, accuracy and the three metrics in Section 5.4 are employed (Figure 7b). + +Impact of $k$ . A small $k$ decreases the accuracy and other metrics, which means the necessity of searching the minimum number of concepts. Also, training tends to fail for all datasets when $k$ is large (detailed in the supp. materials). The number of concepts should be tuned for each dataset. This sensitivity is one of BotCL's limitations. + +Impact of $\lambda_{qua}$ . This hyperparameter controls how close $t$ should be to a binary. The accuracy and the other metrics worsen when $\lambda_{qua}$ gradually increases. BotCL encodes some information into $t$ (such as the area that a concept occupies), which is lost for larger $\lambda_{qua}$ . An extreme value may also cause vanishing gradients. + +Impact of $\lambda_{con}$ and $\lambda_{dis}$ . The individual consistency and mutual distinctiveness losses hardly affect the performance on CUB200 and ImageNet, although we can see a slight drop when the values are zero for CUB200. For Synthetic, the performance metrics vary as they are designed to be. Meanwhile, the accuracy is relatively insensitive to these hyperparameters. The choice of concepts may be + +highly arbitrary, and different sets of concepts may achieve similar classification performance. This arbitrariness may allow the designing of dedicated concept regularizers for the target task. However, training failures happen when they are set to be large. A small value benefits training. + +Impact of $\lambda_{R}$ . Due to the lower performance of the reconstruction loss, we studied the impact of the contrastive loss only. The contrastive loss almost always improves the classification accuracy. The performance boost is significant in CUB200 and Synthetic. As ImageNet has more training data, this may imply that self-supervision greatly contributes to the learning of concepts when training samples are limited. These results demonstrate the importance of the contrastive loss. This is interesting since this loss uses the same labels as the classification loss. + +# 6. Conclusion + +This paper presents BotCL for learning bottleneck concepts. Our qualitative and quantitative evaluation showed BotCL's ability to learn concepts without explicit supervision on them but through training for a target classification task. We also demonstrated that BotCL could provide interpretability on its decision and learned concepts themselves. Limitations. One limitation of BotCL is that it requires tuning the number $k$ of concepts for each dataset. It might be an interesting research direction to estimate $k$ , e.g., based on the number of classes in a given classification task. We will investigate the phenomenon to mitigate this problem. + +Acknowledgement This work is partly supported by JST CREST Grant No. JPMJCR20D3, JST FOREST Grant No. JPMJFR216O, JSPS KAKENHI Grant-in-Aid for Scientific Research (A). This work is also supported by JSPS KAKENHI Grant Number 19K10662, 20K23343, 21K17764, and 22H03353. + +# References + +[1] David Alvarez-Melis and Tommi S Jaakkola. Towards robust interpretability with self-explaining neural networks. NeurIPS, 2018. +[2] Alejandro Barredo Arrieta, Natalia Diaz-Rodriguez, Javier Del Ser, Adrien Bennetot, Siham Tabik, Alberto Barbado, Salvador Garcia, Sergio Gil-Lopez, Daniel Molina, and Richard Benjamins. Explainable artificial intelligence (XAI): Concepts, taxonomies, opportunities and challenges toward responsible AI. Information Fusion, 58:82-115, 2020. +[3] Sebastian Bach, Alexander Binder, Gregoire Montavon, Frederick Klauschen, Klaus-Robert Müller, and Wojciech Samek. 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Explainable AI provides a way to address this challenge, mostly by providing per-pixel relevance to the decision. Yet, interpreting such explanations may require expert knowledge. Some recent attempts toward interpretability adopt a concept-based framework, giving a higher-level relationship between some concepts and model decisions. This paper proposes Bottleneck Concept Learner (BotCL), which represents an image solely by the presence/absence of concepts learned through training over the target task without explicit supervision over the concepts. It uses self-supervision and tailored regularizers so that learned concepts can be human-understandable. Using some image classification tasks as our testbed, we demonstrate BotCL's potential to rebuild neural networks for better interpretability1." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 465, + 128, + 478 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 465, + 128, + 478 + ], + "spans": [ + { + "bbox": [ + 47, + 465, + 128, + 478 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 485, + 287, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 485, + 287, + 617 + ], + "spans": [ + { + "bbox": [ + 46, + 485, + 287, + 617 + ], + "type": "text", + "content": "Understanding the behavior of deep neural networks (DNNs) is a major challenge in the explainable AI (XAI) community, especially for medical applications [19,38], for identifying biases in DNNs [2, 18, 42], etc. Tremendous research efforts have been devoted to the post-hoc paradigm for a posteriori explanation [29, 33]. This paradigm produces a relevance map to spot regions in the input image that interact with the model's decision. Yet the relevance map only tells low-level (or per-pixel) relationships and does not explicitly convey any semantics behind the decision. Interpretation of relevance maps may require expert knowledge." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 617, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 287, + 677 + ], + "type": "text", + "content": "The concept-based framework [22, 37, 50] is inspired by the human capacity to learn a new concept by (subconsciously) finding finer-grained concepts and reuse them in different ways for better recognition [24]. Instead of giving per-pixel relevance, this framework offers higher-level" + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 318, + 225, + 533, + 363 + ], + "blocks": [ + { + "bbox": [ + 318, + 225, + 533, + 363 + ], + "lines": [ + { + "bbox": [ + 318, + 225, + 533, + 363 + ], + "spans": [ + { + "bbox": [ + 318, + 225, + 533, + 363 + ], + "type": "image", + "image_path": "57c5c08570f5d3bb51eabe1f8d8a52da31021717facb6703e95af5a00db8e148.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 371, + 545, + 415 + ], + "lines": [ + { + "bbox": [ + 305, + 371, + 545, + 415 + ], + "spans": [ + { + "bbox": [ + 305, + 371, + 545, + 415 + ], + "type": "text", + "content": "Figure 1. Examples of concepts discovered by BotCL in ImageNet [10] and concepts in the input image. BotCL automatically discovers a set of concepts optimized for the target task and represents an image solely with the presence/absence of concepts." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 437, + 545, + 497 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 437, + 545, + 497 + ], + "spans": [ + { + "bbox": [ + 304, + 437, + 545, + 497 + ], + "type": "text", + "content": "relationships between the image and decision mediated by a limited number of concepts. That is, the decision is explained by giving a set of concepts found in the image. The interpretation of the decision is thus straightforward once the interpretation of each concept is established." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 498, + 546, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 546, + 605 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 546, + 605 + ], + "type": "text", + "content": "Some works use concepts for the post-hoc paradigm for better interpretation of the decision [14, 50], while the link between the decision and concepts in the image is not obvious. The concept bottleneck structure [23] uses the presence/absence of concepts as image representation (referred to as concept activation). The classifier has access only to the concept activation, so the decision is strongly tied to the concepts. This bottleneck structure has become the mainstream of the concept-based framework [5, 20, 28, 31]." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 605, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 547, + 714 + ], + "type": "text", + "content": "A major difficulty in this framework is designing a set of concepts that suits the target task. A promising approach is handcrafting them [4, 21, 48], which inherently offers better interpretability at the cost of extra annotations on the concepts. Recent attempts automatically discover concepts [1, 13, 14, 46]. Such concepts may not always be consistent with how humans (or models) see the world [25, 47] and may require some effort to interpret them, but concept discovery without supervision is a significant advantage." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 683, + 136, + 693 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 683, + 136, + 693 + ], + "spans": [ + { + "bbox": [ + 58, + 683, + 136, + 693 + ], + "type": "text", + "content": "*Corresponding author." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 47, + 693, + 287, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 693, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 47, + 693, + 287, + 712 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 47, + 693, + 287, + 712 + ], + "type": "text", + "content": "Code is available at https://github.com/webw520/BotCL and a simple demo is available at https://botcl.liangzhili.com/." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10962" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 299 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 299 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 299 + ], + "type": "text", + "content": "Inspired by these works, we propose bottleneck concept learner (BotCL) for simultaneously discovering concepts and learning the classifier. BotCL optimizes concepts for the given target image classification task without supervision for the concepts. An image is represented solely by the existence of concepts and is classified using them. We adopt a slot attention-based mechanism [26, 27] to spot the region in which each concept is found. This gives an extra signal for interpreting the decision since one can easily see what each learned concept represents by collectively showing training images with the detected concepts. Figure 1 shows examples from ImageNet [10]. BotCL discovers a predefined number of concepts in the dataset, which are exemplified by several images with attention maps. An image of Great White Shark is represented by the right part of mouth (Cpt.1) and fins (Cpt.3). BotCL uses a single fully-connected (FC) layer as a classifier, which is simple but enough to encode the co-occurrence of each concept and each class." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 300, + 289, + 420 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 300, + 289, + 420 + ], + "spans": [ + { + "bbox": [ + 46, + 300, + 289, + 420 + ], + "type": "text", + "content": "Contribution. For better concept discovery, we propose to use self-supervision over concepts, inspired by the recent success in representation learning [9, 16]. Our ablation study demonstrates that self-supervision by contrastive loss is the key. We also try several constraints on concepts themselves, i.e., individual consistency to make a concept more selective and mutual distinctiveness for better coverage of various visual elements. These additional constraints regular the training process and help the model learn concepts of higher quality." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 431, + 138, + 443 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 431, + 138, + 443 + ], + "spans": [ + { + "bbox": [ + 47, + 431, + 138, + 443 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 451, + 141, + 464 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 451, + 141, + 464 + ], + "spans": [ + { + "bbox": [ + 47, + 451, + 141, + 464 + ], + "type": "text", + "content": "2.1. Explainable AI" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 470, + 287, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 470, + 287, + 578 + ], + "spans": [ + { + "bbox": [ + 46, + 470, + 287, + 578 + ], + "type": "text", + "content": "XAI focuses on uncovering black-box deep neural networks [3, 6, 12, 32, 35, 36, 41, 43, 46]. A major approach is generating a relevance map that spots important regions for the model's decision. Various methods have been designed for specific architectures, e.g., CAM [49], and GradCAM [33] for convolutional neural networks; [7] for Transformers [40]. However, the interpretation of the relevance maps may not always be obvious, which spurs different approaches [34, 45], including context-based ones." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 586, + 285, + 600 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 586, + 285, + 600 + ], + "spans": [ + { + "bbox": [ + 47, + 586, + 285, + 600 + ], + "type": "text", + "content": "2.2. Concept-based framework for interpretability" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 605, + 287, + 701 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 701 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 701 + ], + "type": "text", + "content": "A straightforward way to define a set of concepts for a target task is to utilize human knowledge [22,48]. Such concepts allow quantifying their importance for a decision [21]. A large corpus of concepts [4, 39] is beneficial for delving into hidden semantics in DNNs [50]. These methods are of the post-hoc XAI paradigm, but a handcrafted set of concepts can also be used as additional supervision for models with the concept bottleneck structure [15, 22, 31]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 59, + 701, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 701, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 59, + 701, + 287, + 713 + ], + "type": "text", + "content": "Handcrafting a set of concepts offers better interpreabil" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 72, + 545, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 191 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 191 + ], + "type": "text", + "content": "ity as they suit human perception; however, the annotation cost is non-negligible. Moreover, such handcrafted concepts may not always be useful for DNNs [47]. These problems have motivated automatic concept discovery. Superpixels are a handy unit for finding low-level semantics, and concepts are defined by clustering them [13, 14, 30]. Another interesting approach is designing a set of concepts to be sufficient statistics of original DNN features [46]. These methods are designed purely for interpretation, and concept discovery is made aside from training on the target task." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 192, + 545, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 192, + 545, + 251 + ], + "spans": [ + { + "bbox": [ + 304, + 192, + 545, + 251 + ], + "type": "text", + "content": "The concept bottleneck structure allows optimizing a set of concepts for the target task. ProtoPNet [8] adopts this structure and identifies concepts based on the distance between features and concepts. SENN [1] uses self-supervision by reconstruction loss for concept discovery." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 251, + 545, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 251, + 545, + 300 + ], + "spans": [ + { + "bbox": [ + 304, + 251, + 545, + 300 + ], + "type": "text", + "content": "SENN inspired us to use self-supervision, but instead of reconstruction loss, we adopt contrastive loss tailored. For a natural image classification task, this contrastive loss is essential for concept discovery." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 309, + 354, + 322 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 309, + 354, + 322 + ], + "spans": [ + { + "bbox": [ + 306, + 309, + 354, + 322 + ], + "type": "text", + "content": "3. Model" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 329, + 545, + 412 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 329, + 545, + 412 + ], + "spans": [ + { + "bbox": [ + 304, + 329, + 545, + 412 + ], + "type": "text", + "content": "Given a dataset " + }, + { + "bbox": [ + 304, + 329, + 545, + 412 + ], + "type": "inline_equation", + "content": "\\mathcal{D} = \\{(x_i, y_i) | i = 1, 2, \\dots, N\\}" + }, + { + "bbox": [ + 304, + 329, + 545, + 412 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 329, + 545, + 412 + ], + "type": "inline_equation", + "content": "x_i" + }, + { + "bbox": [ + 304, + 329, + 545, + 412 + ], + "type": "text", + "content": " is an image and " + }, + { + "bbox": [ + 304, + 329, + 545, + 412 + ], + "type": "inline_equation", + "content": "y_i" + }, + { + "bbox": [ + 304, + 329, + 545, + 412 + ], + "type": "text", + "content": " is the target class label in the set " + }, + { + "bbox": [ + 304, + 329, + 545, + 412 + ], + "type": "inline_equation", + "content": "\\Omega" + }, + { + "bbox": [ + 304, + 329, + 545, + 412 + ], + "type": "text", + "content": " associated with " + }, + { + "bbox": [ + 304, + 329, + 545, + 412 + ], + "type": "inline_equation", + "content": "x_i" + }, + { + "bbox": [ + 304, + 329, + 545, + 412 + ], + "type": "text", + "content": ". BotCL learns a set of " + }, + { + "bbox": [ + 304, + 329, + 545, + 412 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 329, + 545, + 412 + ], + "type": "text", + "content": " concepts while learning the original classification task. Figure 2a shows an overview of BotCL's training scheme, consisting of a concept extractor, regularizers, and a classifier, as well as self-supervision (contrastive and reconstruction losses)." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 413, + 545, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 413, + 545, + 557 + ], + "spans": [ + { + "bbox": [ + 304, + 413, + 545, + 557 + ], + "type": "text", + "content": "For a new image " + }, + { + "bbox": [ + 304, + 413, + 545, + 557 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 413, + 545, + 557 + ], + "type": "text", + "content": ", we extract feature map " + }, + { + "bbox": [ + 304, + 413, + 545, + 557 + ], + "type": "inline_equation", + "content": "F = \\Phi(x) \\in \\mathbb{R}^{d \\times h \\times w}" + }, + { + "bbox": [ + 304, + 413, + 545, + 557 + ], + "type": "text", + "content": " using a backbone convolutional neural network " + }, + { + "bbox": [ + 304, + 413, + 545, + 557 + ], + "type": "inline_equation", + "content": "\\Phi" + }, + { + "bbox": [ + 304, + 413, + 545, + 557 + ], + "type": "text", + "content": ". 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The concept extractor produces concept bottleneck activations " + }, + { + "bbox": [ + 304, + 413, + 545, + 557 + ], + "type": "inline_equation", + "content": "t \\in [0,1]^k" + }, + { + "bbox": [ + 304, + 413, + 545, + 557 + ], + "type": "text", + "content": ", indicating the presence of each concept, as well as concept features " + }, + { + "bbox": [ + 304, + 413, + 545, + 557 + ], + "type": "inline_equation", + "content": "V \\in \\mathbb{R}^{d \\times k}" + }, + { + "bbox": [ + 304, + 413, + 545, + 557 + ], + "type": "text", + "content": " from regions where each concept exists. The concept activations in " + }, + { + "bbox": [ + 304, + 413, + 545, + 557 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 413, + 545, + 557 + ], + "type": "text", + "content": " are used as input to the classifier to compute score " + }, + { + "bbox": [ + 304, + 413, + 545, + 557 + ], + "type": "inline_equation", + "content": "s \\in [0,1]^{|\\Omega|}" + }, + { + "bbox": [ + 304, + 413, + 545, + 557 + ], + "type": "text", + "content": ". We use self-supervision and regularizers for training, taking " + }, + { + "bbox": [ + 304, + 413, + 545, + 557 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 413, + 545, + 557 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 413, + 545, + 557 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 304, + 413, + 545, + 557 + ], + "type": "text", + "content": " as input to constrain the concept prototypes." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 563, + 416, + 576 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 563, + 416, + 576 + ], + "spans": [ + { + "bbox": [ + 306, + 563, + 416, + 576 + ], + "type": "text", + "content": "3.1. 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Attention " + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "inline_equation", + "content": "a_{\\kappa}\\in [0,1]^{l}" + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": " is given using a normalization function" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10963" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 70, + 358, + 183 + ], + "blocks": [ + { + "bbox": [ + 48, + 70, + 358, + 183 + ], + "lines": [ + { + "bbox": [ + 48, + 70, + 358, + 183 + ], + "spans": [ + { + "bbox": [ + 48, + 70, + 358, + 183 + ], + "type": "image", + "image_path": "93cd9351f448be129dc709ec2a001ffe0d9e91a1be1bcf645de1be1904ae8caa.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 198, + 189, + 210, + 199 + ], + "lines": [ + { + "bbox": [ + 198, + 189, + 210, + 199 + ], + "spans": [ + { + "bbox": [ + 198, + 189, + 210, + 199 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 362, + 70, + 547, + 186 + ], + "blocks": [ + { + "bbox": [ + 362, + 70, + 547, + 186 + ], + "lines": [ + { + "bbox": [ + 362, + 70, + 547, + 186 + ], + "spans": [ + { + "bbox": [ + 362, + 70, + 547, + 186 + ], + "type": "image", + "image_path": "7ad52cdcbfc292d452281d9a91d3b445ae67870b6c54129097f8a07bd2fb6ac7.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 449, + 190, + 460, + 200 + ], + "lines": [ + { + "bbox": [ + 449, + 190, + 460, + 200 + ], + "spans": [ + { + "bbox": [ + 449, + 190, + 460, + 200 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 167, + 210, + 425, + 221 + ], + "lines": [ + { + "bbox": [ + 167, + 210, + 425, + 221 + ], + "spans": [ + { + "bbox": [ + 167, + 210, + 425, + 221 + ], + "type": "text", + "content": "Figure 2. (a) The model pipeline. (b) Self-supervision and regularizers." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 243, + 170, + 255 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 243, + 170, + 255 + ], + "spans": [ + { + "bbox": [ + 47, + 243, + 170, + 255 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 47, + 243, + 170, + 255 + ], + "type": "text", + "content": " (refer to supp. material) as" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 116, + 259, + 287, + 274 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 259, + 287, + 274 + ], + "spans": [ + { + "bbox": [ + 116, + 259, + 287, + 274 + ], + "type": "interline_equation", + "content": "a _ {\\kappa} = \\phi \\left(Q \\left(c _ {\\kappa}\\right) ^ {\\top} K \\left(F ^ {\\prime}\\right)\\right). \\tag {1}", + "image_path": "1c9f45761f2af4767bbf68c00f678c9f0d4f7fed23837f31e7512fa1d5f50311.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 278, + 287, + 351 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 278, + 287, + 351 + ], + "spans": [ + { + "bbox": [ + 47, + 278, + 287, + 351 + ], + "type": "text", + "content": "This attention indicates where concept " + }, + { + "bbox": [ + 47, + 278, + 287, + 351 + ], + "type": "inline_equation", + "content": "\\kappa" + }, + { + "bbox": [ + 47, + 278, + 287, + 351 + ], + "type": "text", + "content": " presents in the image as shown in Figure 1. If concept " + }, + { + "bbox": [ + 47, + 278, + 287, + 351 + ], + "type": "inline_equation", + "content": "\\kappa" + }, + { + "bbox": [ + 47, + 278, + 287, + 351 + ], + "type": "text", + "content": " is absent, corresponding entries of " + }, + { + "bbox": [ + 47, + 278, + 287, + 351 + ], + "type": "inline_equation", + "content": "a_{\\kappa}" + }, + { + "bbox": [ + 47, + 278, + 287, + 351 + ], + "type": "text", + "content": " are all close to 0. We summarize the presence of each concept into concept activation " + }, + { + "bbox": [ + 47, + 278, + 287, + 351 + ], + "type": "inline_equation", + "content": "t_{\\kappa}" + }, + { + "bbox": [ + 47, + 278, + 287, + 351 + ], + "type": "text", + "content": " by reducing the spatial dimension of " + }, + { + "bbox": [ + 47, + 278, + 287, + 351 + ], + "type": "inline_equation", + "content": "a_{\\kappa}" + }, + { + "bbox": [ + 47, + 278, + 287, + 351 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 47, + 278, + 287, + 351 + ], + "type": "inline_equation", + "content": "t_{\\kappa} = \\tanh (\\sum_{m}a_{\\kappa m})" + }, + { + "bbox": [ + 47, + 278, + 287, + 351 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 47, + 278, + 287, + 351 + ], + "type": "inline_equation", + "content": "a_{\\kappa m}" + }, + { + "bbox": [ + 47, + 278, + 287, + 351 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 47, + 278, + 287, + 351 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 47, + 278, + 287, + 351 + ], + "type": "text", + "content": "-th element of " + }, + { + "bbox": [ + 47, + 278, + 287, + 351 + ], + "type": "inline_equation", + "content": "a_{\\kappa}" + }, + { + "bbox": [ + 47, + 278, + 287, + 351 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 357, + 167, + 369 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 357, + 167, + 369 + ], + "spans": [ + { + "bbox": [ + 47, + 357, + 167, + 369 + ], + "type": "text", + "content": "3.2. Feature Aggregation" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 375, + 287, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 375, + 287, + 399 + ], + "spans": [ + { + "bbox": [ + 47, + 375, + 287, + 399 + ], + "type": "text", + "content": "For training, we also aggregate features in " + }, + { + "bbox": [ + 47, + 375, + 287, + 399 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 47, + 375, + 287, + 399 + ], + "type": "text", + "content": " corresponding to concept " + }, + { + "bbox": [ + 47, + 375, + 287, + 399 + ], + "type": "inline_equation", + "content": "\\kappa" + }, + { + "bbox": [ + 47, + 375, + 287, + 399 + ], + "type": "text", + "content": " into concept feature " + }, + { + "bbox": [ + 47, + 375, + 287, + 399 + ], + "type": "inline_equation", + "content": "v_{\\kappa}" + }, + { + "bbox": [ + 47, + 375, + 287, + 399 + ], + "type": "text", + "content": " by" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 143, + 405, + 287, + 417 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 405, + 287, + 417 + ], + "spans": [ + { + "bbox": [ + 143, + 405, + 287, + 417 + ], + "type": "interline_equation", + "content": "v _ {\\kappa} = F a _ {\\kappa}, \\tag {2}", + "image_path": "0e7a448f11c68da52803be798fc0e813fbe13d2e8fb47250179d85bd9a4a80a1.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 422, + 287, + 448 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 422, + 287, + 448 + ], + "spans": [ + { + "bbox": [ + 47, + 422, + 287, + 448 + ], + "type": "text", + "content": "which gives the average of image features over the spatial dimension weighted by attention." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 453, + 114, + 464 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 453, + 114, + 464 + ], + "spans": [ + { + "bbox": [ + 47, + 453, + 114, + 464 + ], + "type": "text", + "content": "3.3.Classifier" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 471, + 287, + 530 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 471, + 287, + 530 + ], + "spans": [ + { + "bbox": [ + 47, + 471, + 287, + 530 + ], + "type": "text", + "content": "We use a single FC layer without a bias term as the classifier, and concept activation " + }, + { + "bbox": [ + 47, + 471, + 287, + 530 + ], + "type": "inline_equation", + "content": "t = (t_{1},\\dots ,t_{k})^{\\top}" + }, + { + "bbox": [ + 47, + 471, + 287, + 530 + ], + "type": "text", + "content": " is the only input, serving as the concept bottleneck [22]. Formally, letting " + }, + { + "bbox": [ + 47, + 471, + 287, + 530 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 47, + 471, + 287, + 530 + ], + "type": "text", + "content": " be a learnable matrix, prediction " + }, + { + "bbox": [ + 47, + 471, + 287, + 530 + ], + "type": "inline_equation", + "content": "\\hat{y}\\in \\mathbb{R}^{|\\Omega |}" + }, + { + "bbox": [ + 47, + 471, + 287, + 530 + ], + "type": "text", + "content": " is given by" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 147, + 531, + 287, + 544 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 147, + 531, + 287, + 544 + ], + "spans": [ + { + "bbox": [ + 147, + 531, + 287, + 544 + ], + "type": "interline_equation", + "content": "\\hat {y} = W t. \\tag {3}", + "image_path": "11825d44cba4fcd710ec7f301970cc7193fc06c6c9b5f8d819ef1bcfc6a3edc1.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 47, + 546, + 287, + 631 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 546, + 287, + 631 + ], + "spans": [ + { + "bbox": [ + 47, + 546, + 287, + 631 + ], + "type": "text", + "content": "This classifier can be roughly interpreted as learning the correlation between the class and concepts. Let " + }, + { + "bbox": [ + 47, + 546, + 287, + 631 + ], + "type": "inline_equation", + "content": "w_{\\omega}" + }, + { + "bbox": [ + 47, + 546, + 287, + 631 + ], + "type": "text", + "content": " be the raw vector of " + }, + { + "bbox": [ + 47, + 546, + 287, + 631 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 47, + 546, + 287, + 631 + ], + "type": "text", + "content": " corresponding to class " + }, + { + "bbox": [ + 47, + 546, + 287, + 631 + ], + "type": "inline_equation", + "content": "\\omega \\in \\Omega" + }, + { + "bbox": [ + 47, + 546, + 287, + 631 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 546, + 287, + 631 + ], + "type": "inline_equation", + "content": "w_{\\omega \\kappa}" + }, + { + "bbox": [ + 47, + 546, + 287, + 631 + ], + "type": "text", + "content": " is its " + }, + { + "bbox": [ + 47, + 546, + 287, + 631 + ], + "type": "inline_equation", + "content": "\\kappa" + }, + { + "bbox": [ + 47, + 546, + 287, + 631 + ], + "type": "text", + "content": "-th element. A positive value of " + }, + { + "bbox": [ + 47, + 546, + 287, + 631 + ], + "type": "inline_equation", + "content": "w_{\\omega \\kappa}" + }, + { + "bbox": [ + 47, + 546, + 287, + 631 + ], + "type": "text", + "content": " means that concept " + }, + { + "bbox": [ + 47, + 546, + 287, + 631 + ], + "type": "inline_equation", + "content": "\\kappa" + }, + { + "bbox": [ + 47, + 546, + 287, + 631 + ], + "type": "text", + "content": " co-occurs with class " + }, + { + "bbox": [ + 47, + 546, + 287, + 631 + ], + "type": "inline_equation", + "content": "\\omega" + }, + { + "bbox": [ + 47, + 546, + 287, + 631 + ], + "type": "text", + "content": " in the dataset, so its presence in a new image positively supports class " + }, + { + "bbox": [ + 47, + 546, + 287, + 631 + ], + "type": "inline_equation", + "content": "\\omega" + }, + { + "bbox": [ + 47, + 546, + 287, + 631 + ], + "type": "text", + "content": ". Meanwhile, a negative value means the concept rarely co-occurs." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 47, + 639, + 107, + 653 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 639, + 107, + 653 + ], + "spans": [ + { + "bbox": [ + 47, + 639, + 107, + 653 + ], + "type": "text", + "content": "4. Training" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 47, + 659, + 252, + 673 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 659, + 252, + 673 + ], + "spans": [ + { + "bbox": [ + 47, + 659, + 252, + 673 + ], + "type": "text", + "content": "4.1. Self-supervision for Concept Discovery" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "text", + "content": "The absence of concept labels motivates us to incorporate self-supervision for concept discovery. We employ two losses for different types of target tasks." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 243, + 545, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 243, + 545, + 350 + ], + "spans": [ + { + "bbox": [ + 305, + 243, + 545, + 350 + ], + "type": "text", + "content": "Reconstruction loss. SENN [1] uses an autoencoder-like structure for learning better representation. We assume this structure works well when visual elements are strongly tied with the position since even discrete concepts should have sufficient information to reconstruct the original image. Based on this assumption, we design a reconstruction loss for self-supervision. As shown in Figure 2b, decoder " + }, + { + "bbox": [ + 305, + 243, + 545, + 350 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 305, + 243, + 545, + 350 + ], + "type": "text", + "content": " only takes " + }, + { + "bbox": [ + 305, + 243, + 545, + 350 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 305, + 243, + 545, + 350 + ], + "type": "text", + "content": " as input and reconstructs the original image. We define our reconstruction loss as" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 366, + 355, + 545, + 384 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 366, + 355, + 545, + 384 + ], + "spans": [ + { + "bbox": [ + 366, + 355, + 545, + 384 + ], + "type": "interline_equation", + "content": "l _ {\\text {r e c}} = \\frac {1}{| \\mathcal {B} |} \\sum_ {x \\in \\mathcal {B}} \\| D (t) - x \\| ^ {2}. \\tag {4}", + "image_path": "39fc2e3f228d2ea3d882bb208dae97261bbad51dee5bb1192a810aae8fa4dcf2.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 397, + 545, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 397, + 545, + 456 + ], + "spans": [ + { + "bbox": [ + 305, + 397, + 545, + 456 + ], + "type": "text", + "content": "Contrastive loss. The composition of natural images is rather arbitrary, so information in " + }, + { + "bbox": [ + 305, + 397, + 545, + 456 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 305, + 397, + 545, + 456 + ], + "type": "text", + "content": " should be insufficient to reconstruct the original image. We thus design a simple loss for an alternative, borrowing the idea from the recent success of contrastive learning for self-supervision [9, 16]." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 305, + 457, + 545, + 589 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 457, + 545, + 589 + ], + "spans": [ + { + "bbox": [ + 305, + 457, + 545, + 589 + ], + "type": "text", + "content": "We leverage the image-level labels of the target classification task. Let " + }, + { + "bbox": [ + 305, + 457, + 545, + 589 + ], + "type": "inline_equation", + "content": "\\hat{t} = 2t - \\mathbf{1}_k" + }, + { + "bbox": [ + 305, + 457, + 545, + 589 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 305, + 457, + 545, + 589 + ], + "type": "inline_equation", + "content": "\\mathbf{1}_k" + }, + { + "bbox": [ + 305, + 457, + 545, + 589 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 305, + 457, + 545, + 589 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 305, + 457, + 545, + 589 + ], + "type": "text", + "content": "-dimensional vector with all elements being 1. If a pair " + }, + { + "bbox": [ + 305, + 457, + 545, + 589 + ], + "type": "inline_equation", + "content": "(\\hat{t}, \\hat{t}')" + }, + { + "bbox": [ + 305, + 457, + 545, + 589 + ], + "type": "text", + "content": " of concept activations belong to the same class (i.e., " + }, + { + "bbox": [ + 305, + 457, + 545, + 589 + ], + "type": "inline_equation", + "content": "y = y'" + }, + { + "bbox": [ + 305, + 457, + 545, + 589 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 305, + 457, + 545, + 589 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 305, + 457, + 545, + 589 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 457, + 545, + 589 + ], + "type": "inline_equation", + "content": "y'" + }, + { + "bbox": [ + 305, + 457, + 545, + 589 + ], + "type": "text", + "content": " corresponding to " + }, + { + "bbox": [ + 305, + 457, + 545, + 589 + ], + "type": "inline_equation", + "content": "\\hat{t}" + }, + { + "bbox": [ + 305, + 457, + 545, + 589 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 457, + 545, + 589 + ], + "type": "inline_equation", + "content": "\\hat{t}'" + }, + { + "bbox": [ + 305, + 457, + 545, + 589 + ], + "type": "text", + "content": "), they should be similar to each other since a similar set of concepts should be in the corresponding images, and otherwise dissimilar. The number " + }, + { + "bbox": [ + 305, + 457, + 545, + 589 + ], + "type": "inline_equation", + "content": "|\\Omega|" + }, + { + "bbox": [ + 305, + 457, + 545, + 589 + ], + "type": "text", + "content": " of classes can be smaller than the number " + }, + { + "bbox": [ + 305, + 457, + 545, + 589 + ], + "type": "inline_equation", + "content": "|\\mathcal{B}|" + }, + { + "bbox": [ + 305, + 457, + 545, + 589 + ], + "type": "text", + "content": " of images in a mini-batch so that a mini-batch can have multiple images of the same class. Therefore, we use sigmoid instead of softmax, leading to" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 340, + 595, + 545, + 622 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 340, + 595, + 545, + 622 + ], + "spans": [ + { + "bbox": [ + 340, + 595, + 545, + 622 + ], + "type": "interline_equation", + "content": "l _ {\\text {r e t}} = - \\frac {1}{| \\mathcal {B} |} \\sum \\alpha (y, y ^ {\\prime}) \\log J (\\hat {t}, \\hat {t} ^ {\\prime}, y, y ^ {\\prime}), \\tag {5}", + "image_path": "47fa9e0afea4bf35284b20728e6baa8272912511536968682cd5c398d3efd800.jpg" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 305, + 628, + 545, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 628, + 545, + 652 + ], + "spans": [ + { + "bbox": [ + 305, + 628, + 545, + 652 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 628, + 545, + 652 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 305, + 628, + 545, + 652 + ], + "type": "text", + "content": " is the weight to mitigate the class imbalance problem (see supp. material) and" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 335, + 659, + 545, + 692 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 335, + 659, + 545, + 692 + ], + "spans": [ + { + "bbox": [ + 335, + 659, + 545, + 692 + ], + "type": "interline_equation", + "content": "\\underline {{J (\\hat {t} , \\hat {t} ^ {\\prime} , y , y ^ {\\prime}) =}} \\left\\{ \\begin{array}{l l} \\sigma (\\hat {t} ^ {\\top} \\hat {t} ^ {\\prime}) & \\text {f o r} y = y ^ {\\prime} \\\\ 1 - \\sigma (\\hat {t} ^ {\\top} \\hat {t} ^ {\\prime}) & \\text {o t h e r w i s e} \\end{array} . \\right. \\tag {6}", + "image_path": "b7554ba5d74227e95dfb1b1444388b99606bfe03e2b3cf90cb4632f293718433.jpg" + } + ] + } + ], + "index": 25 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "text", + "content": "2For example, images of \"7\" in MNIST almost always have the acute angle in the top-right part." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10964" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 172, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 172, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 172, + 85 + ], + "type": "text", + "content": "4.2. Concept Regularizers" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 90, + 287, + 116 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 90, + 287, + 116 + ], + "spans": [ + { + "bbox": [ + 47, + 90, + 287, + 116 + ], + "type": "text", + "content": "We also employ concept regularizers to facilitate training. They constrain concept prototypes " + }, + { + "bbox": [ + 47, + 90, + 287, + 116 + ], + "type": "inline_equation", + "content": "\\{c_{\\kappa}\\}" + }, + { + "bbox": [ + 47, + 90, + 287, + 116 + ], + "type": "text", + "content": " through " + }, + { + "bbox": [ + 47, + 90, + 287, + 116 + ], + "type": "inline_equation", + "content": "\\{v_{\\kappa}\\}" + }, + { + "bbox": [ + 47, + 90, + 287, + 116 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 128, + 288, + 236 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 128, + 288, + 236 + ], + "spans": [ + { + "bbox": [ + 46, + 128, + 288, + 236 + ], + "type": "text", + "content": "Individual consistency. For better interpretability, each learned concept should not have large variations. That is, the concept features " + }, + { + "bbox": [ + 46, + 128, + 288, + 236 + ], + "type": "inline_equation", + "content": "v_{\\kappa}" + }, + { + "bbox": [ + 46, + 128, + 288, + 236 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 128, + 288, + 236 + ], + "type": "inline_equation", + "content": "v_{\\kappa}^{\\prime}" + }, + { + "bbox": [ + 46, + 128, + 288, + 236 + ], + "type": "text", + "content": " of different images should be similar to each other if " + }, + { + "bbox": [ + 46, + 128, + 288, + 236 + ], + "type": "inline_equation", + "content": "t_{\\kappa}" + }, + { + "bbox": [ + 46, + 128, + 288, + 236 + ], + "type": "text", + "content": " is close to 1. Let " + }, + { + "bbox": [ + 46, + 128, + 288, + 236 + ], + "type": "inline_equation", + "content": "\\mathcal{H}_{\\kappa}" + }, + { + "bbox": [ + 46, + 128, + 288, + 236 + ], + "type": "text", + "content": " denote the set of all concept features of different images in a minibatch, whose activation is larger than the empirical threshold " + }, + { + "bbox": [ + 46, + 128, + 288, + 236 + ], + "type": "inline_equation", + "content": "\\xi" + }, + { + "bbox": [ + 46, + 128, + 288, + 236 + ], + "type": "text", + "content": ", which is dynamically calculated as the mean of " + }, + { + "bbox": [ + 46, + 128, + 288, + 236 + ], + "type": "inline_equation", + "content": "t_{\\kappa}" + }, + { + "bbox": [ + 46, + 128, + 288, + 236 + ], + "type": "text", + "content": " in a mini-batch. Using the cosine similarity " + }, + { + "bbox": [ + 46, + 128, + 288, + 236 + ], + "type": "inline_equation", + "content": "\\mathrm{sim}(\\cdot ,\\cdot)" + }, + { + "bbox": [ + 46, + 128, + 288, + 236 + ], + "type": "text", + "content": ", we define the consistency loss as:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 89, + 239, + 287, + 271 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 89, + 239, + 287, + 271 + ], + "spans": [ + { + "bbox": [ + 89, + 239, + 287, + 271 + ], + "type": "interline_equation", + "content": "l _ {\\text {c o n}} = - \\frac {1}{k} \\sum_ {\\kappa} \\sum_ {v _ {\\kappa}, v _ {\\kappa} ^ {\\prime}} \\frac {\\sin \\left(v _ {\\kappa} , v _ {\\kappa} ^ {\\prime}\\right)}{\\left| \\mathcal {H} _ {\\kappa} \\right| \\left(\\left| \\mathcal {H} _ {\\kappa} \\right| - 1\\right)}, \\tag {7}", + "image_path": "a9c7176d19bf9e0f08bef9f1c46288072f9a31d575091856d8834ea0adc4ee18.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 276, + 287, + 313 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 276, + 287, + 313 + ], + "spans": [ + { + "bbox": [ + 47, + 276, + 287, + 313 + ], + "type": "text", + "content": "where the second summation is computed over all combinations of concept features " + }, + { + "bbox": [ + 47, + 276, + 287, + 313 + ], + "type": "inline_equation", + "content": "v_{\\kappa}" + }, + { + "bbox": [ + 47, + 276, + 287, + 313 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 276, + 287, + 313 + ], + "type": "inline_equation", + "content": "v_{\\kappa}^{\\prime}" + }, + { + "bbox": [ + 47, + 276, + 287, + 313 + ], + "type": "text", + "content": ". This loss penalizes a smaller similarity between " + }, + { + "bbox": [ + 47, + 276, + 287, + 313 + ], + "type": "inline_equation", + "content": "v_{\\kappa}" + }, + { + "bbox": [ + 47, + 276, + 287, + 313 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 276, + 287, + 313 + ], + "type": "inline_equation", + "content": "v_{\\kappa}^{\\prime}" + }, + { + "bbox": [ + 47, + 276, + 287, + 313 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 325, + 287, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 325, + 287, + 396 + ], + "spans": [ + { + "bbox": [ + 47, + 325, + 287, + 396 + ], + "type": "text", + "content": "Mutual distinctiveness. To capture different aspects of images, different concepts should cover different visual elements. This means that the average image features of concept " + }, + { + "bbox": [ + 47, + 325, + 287, + 396 + ], + "type": "inline_equation", + "content": "\\kappa" + }, + { + "bbox": [ + 47, + 325, + 287, + 396 + ], + "type": "text", + "content": " within a mini-batch, given by " + }, + { + "bbox": [ + 47, + 325, + 287, + 396 + ], + "type": "inline_equation", + "content": "\\bar{v}_{\\kappa} = \\sum_{v_{\\kappa}\\in \\mathcal{H}_{\\kappa}}v_{\\kappa}" + }, + { + "bbox": [ + 47, + 325, + 287, + 396 + ], + "type": "text", + "content": " should be different from any other " + }, + { + "bbox": [ + 47, + 325, + 287, + 396 + ], + "type": "inline_equation", + "content": "v_{\\kappa^{\\prime}}" + }, + { + "bbox": [ + 47, + 325, + 287, + 396 + ], + "type": "text", + "content": ". We can encode this into a loss term as" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 116, + 399, + 287, + 430 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 399, + 287, + 430 + ], + "spans": [ + { + "bbox": [ + 116, + 399, + 287, + 430 + ], + "type": "interline_equation", + "content": "l _ {\\mathrm {d i s}} = \\sum_ {\\kappa , \\kappa^ {\\prime}} \\frac {\\operatorname {s i m} \\left(\\bar {v} _ {\\kappa} , \\bar {v} _ {\\kappa^ {\\prime}}\\right)}{k (k - 1)}, \\tag {8}", + "image_path": "212e12a2df505ab35acf99f8478fdf3db978c5c9e7538cd6029f0ba67e4fb5f9.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 435, + 287, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 435, + 287, + 472 + ], + "spans": [ + { + "bbox": [ + 47, + 435, + 287, + 472 + ], + "type": "text", + "content": "where the summation is computed over all combinations of concepts. Note that concept " + }, + { + "bbox": [ + 47, + 435, + 287, + 472 + ], + "type": "inline_equation", + "content": "\\kappa" + }, + { + "bbox": [ + 47, + 435, + 287, + 472 + ], + "type": "text", + "content": " is excluded from this loss if no image in a mini-batch has concept " + }, + { + "bbox": [ + 47, + 435, + 287, + 472 + ], + "type": "inline_equation", + "content": "\\kappa" + }, + { + "bbox": [ + 47, + 435, + 287, + 472 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 476, + 156, + 489 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 476, + 156, + 489 + ], + "spans": [ + { + "bbox": [ + 47, + 476, + 156, + 489 + ], + "type": "text", + "content": "4.3. Quantization Loss" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 495, + 287, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 495, + 287, + 544 + ], + "spans": [ + { + "bbox": [ + 47, + 495, + 287, + 544 + ], + "type": "text", + "content": "Concept activation " + }, + { + "bbox": [ + 47, + 495, + 287, + 544 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 47, + 495, + 287, + 544 + ], + "type": "text", + "content": " can be sufficiently represented by a binary value, but we instead use a continuous value for training. We design a quantization loss to guarantee values are close to 0 or 1, given by" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 97, + 548, + 287, + 576 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 97, + 548, + 287, + 576 + ], + "spans": [ + { + "bbox": [ + 97, + 548, + 287, + 576 + ], + "type": "interline_equation", + "content": "l _ {\\mathrm {q u a}} = \\frac {1}{k | \\mathcal {B} |} \\sum_ {x \\in \\mathcal {B}} \\left\\| \\operatorname {a b s} (\\hat {t}) - \\mathbf {1} _ {\\kappa} \\right\\| ^ {2}, \\tag {9}", + "image_path": "91768ff6ce49ae4210901f5412c3a1684d55bb47a1dd60c686315c77e5f05479.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 581, + 286, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 581, + 286, + 605 + ], + "spans": [ + { + "bbox": [ + 47, + 581, + 286, + 605 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 581, + 286, + 605 + ], + "type": "inline_equation", + "content": "\\mathrm{abs}(\\cdot)" + }, + { + "bbox": [ + 47, + 581, + 286, + 605 + ], + "type": "text", + "content": " gives the element-wise absolute value and " + }, + { + "bbox": [ + 47, + 581, + 286, + 605 + ], + "type": "inline_equation", + "content": "\\| \\cdot \\|" + }, + { + "bbox": [ + 47, + 581, + 286, + 605 + ], + "type": "text", + "content": " gives the Euclidean norm." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 611, + 118, + 623 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 611, + 118, + 623 + ], + "spans": [ + { + "bbox": [ + 47, + 611, + 118, + 623 + ], + "type": "text", + "content": "4.4. Total Loss" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 629, + 286, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 629, + 286, + 666 + ], + "spans": [ + { + "bbox": [ + 47, + 629, + 286, + 666 + ], + "type": "text", + "content": "We use softmax cross-entropy for the target classification task's loss, donated by " + }, + { + "bbox": [ + 47, + 629, + 286, + 666 + ], + "type": "inline_equation", + "content": "l_{\\mathrm{cls}}" + }, + { + "bbox": [ + 47, + 629, + 286, + 666 + ], + "type": "text", + "content": ". The overall loss of BotCL is defined by combining the losses above as" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 63, + 671, + 286, + 685 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 671, + 286, + 685 + ], + "spans": [ + { + "bbox": [ + 63, + 671, + 286, + 685 + ], + "type": "interline_equation", + "content": "L = l _ {\\mathrm {c l s}} + \\lambda_ {\\mathrm {R}} l _ {\\mathrm {R}} + \\lambda_ {\\mathrm {c o n}} l _ {\\mathrm {c o n}} + \\lambda_ {\\mathrm {d i s}} l _ {\\mathrm {d i s}} + \\lambda_ {\\mathrm {q u a l}} l _ {\\mathrm {q u a}}, \\tag {10}", + "image_path": "0ff037fa2dd07e8761382a4c437c19ed586a743031a65fed20529e95c03d1a67.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 47, + 689, + 286, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 286, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 286, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 689, + 286, + 714 + ], + "type": "inline_equation", + "content": "l_{\\mathrm{R}}" + }, + { + "bbox": [ + 47, + 689, + 286, + 714 + ], + "type": "text", + "content": " is either " + }, + { + "bbox": [ + 47, + 689, + 286, + 714 + ], + "type": "inline_equation", + "content": "l_{\\mathrm{rec}}" + }, + { + "bbox": [ + 47, + 689, + 286, + 714 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 47, + 689, + 286, + 714 + ], + "type": "inline_equation", + "content": "l_{\\mathrm{ret}}" + }, + { + "bbox": [ + 47, + 689, + 286, + 714 + ], + "type": "text", + "content": " depending on the target domain, " + }, + { + "bbox": [ + 47, + 689, + 286, + 714 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{qua}}, \\lambda_{\\mathrm{con}}, \\lambda_{\\mathrm{dis}}" + }, + { + "bbox": [ + 47, + 689, + 286, + 714 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 689, + 286, + 714 + ], + "type": "inline_equation", + "content": "\\lambda_{R}" + }, + { + "bbox": [ + 47, + 689, + 286, + 714 + ], + "type": "text", + "content": " are weights to balance each term." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 72, + 359, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 359, + 83 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 359, + 83 + ], + "type": "text", + "content": "5. Results" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 93, + 432, + 106 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 93, + 432, + 106 + ], + "spans": [ + { + "bbox": [ + 306, + 93, + 432, + 106 + ], + "type": "text", + "content": "5.1. Experimental Settings" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 114, + 545, + 150 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 114, + 545, + 150 + ], + "spans": [ + { + "bbox": [ + 306, + 114, + 545, + 150 + ], + "type": "text", + "content": "We evaluate BotCL on MNIST [11], CUB200 [44], and ImageNet [10]. For evaluating discovered concepts, we regenerated a synthetic shape dataset (Synthetic) [46]." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 152, + 545, + 272 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 152, + 545, + 272 + ], + "spans": [ + { + "bbox": [ + 305, + 152, + 545, + 272 + ], + "type": "text", + "content": "For MNIST, we applied the same networks as [1] for the backbone and the concept decoder. For CUB200 (same data split as [22]) and ImageNet, we used pre-trained ResNet [17] as the backbone with a " + }, + { + "bbox": [ + 305, + 152, + 545, + 272 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 305, + 152, + 545, + 272 + ], + "type": "text", + "content": " convolutional layer to reduce the channel number (512 for ResNet-18 and 2048 for ResNet-101) to 128. We chose a concept number " + }, + { + "bbox": [ + 305, + 152, + 545, + 272 + ], + "type": "inline_equation", + "content": "k = 20" + }, + { + "bbox": [ + 305, + 152, + 545, + 272 + ], + "type": "text", + "content": " for MNIST and " + }, + { + "bbox": [ + 305, + 152, + 545, + 272 + ], + "type": "inline_equation", + "content": "k = 50" + }, + { + "bbox": [ + 305, + 152, + 545, + 272 + ], + "type": "text", + "content": " for the other natural image datasets. To generate Synthetic, we followed the setting of [46], where 18,000 images were generated for training and 2,000 for evaluation. We used " + }, + { + "bbox": [ + 305, + 152, + 545, + 272 + ], + "type": "inline_equation", + "content": "k = 15" + }, + { + "bbox": [ + 305, + 152, + 545, + 272 + ], + "type": "text", + "content": " with ResNet-18 backbone." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 275, + 545, + 336 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 275, + 545, + 336 + ], + "spans": [ + { + "bbox": [ + 305, + 275, + 545, + 336 + ], + "type": "text", + "content": "Images were resized to " + }, + { + "bbox": [ + 305, + 275, + 545, + 336 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 305, + 275, + 545, + 336 + ], + "type": "text", + "content": " and cropped to " + }, + { + "bbox": [ + 305, + 275, + 545, + 336 + ], + "type": "inline_equation", + "content": "224 \\times 224" + }, + { + "bbox": [ + 305, + 275, + 545, + 336 + ], + "type": "text", + "content": " (images in Synthetic were directly resized to " + }, + { + "bbox": [ + 305, + 275, + 545, + 336 + ], + "type": "inline_equation", + "content": "224 \\times 224" + }, + { + "bbox": [ + 305, + 275, + 545, + 336 + ], + "type": "text", + "content": "). Only random horizontal flip was applied as data augmentation during training. The weight of each loss was defaulted to " + }, + { + "bbox": [ + 305, + 275, + 545, + 336 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{qua}} = 0.1" + }, + { + "bbox": [ + 305, + 275, + 545, + 336 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 275, + 545, + 336 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{con}} = 0.01" + }, + { + "bbox": [ + 305, + 275, + 545, + 336 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 275, + 545, + 336 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{dis}} = 0.05" + }, + { + "bbox": [ + 305, + 275, + 545, + 336 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 305, + 275, + 545, + 336 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{R}} = 0.1" + }, + { + "bbox": [ + 305, + 275, + 545, + 336 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 350, + 454, + 361 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 350, + 454, + 361 + ], + "spans": [ + { + "bbox": [ + 306, + 350, + 454, + 361 + ], + "type": "text", + "content": "5.2. Classification Performance" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 305, + 371, + 545, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 371, + 545, + 563 + ], + "spans": [ + { + "bbox": [ + 305, + 371, + 545, + 563 + ], + "type": "text", + "content": "We compare the performance of BotCL with corresponding baselines (LeNet for MNIST and ResNet-18 for others with a linear classifier), our reimplementation of k-means and PCA in [46], and state-of-the-art concept-based models. Table 1 summarized the results. BotCL with contrastive loss " + }, + { + "bbox": [ + 305, + 371, + 545, + 563 + ], + "type": "inline_equation", + "content": "(\\mathrm{BotCL}_{\\mathrm{Cont}})" + }, + { + "bbox": [ + 305, + 371, + 545, + 563 + ], + "type": "text", + "content": " achieves the best accuracy on CUB200, ImageNet, and Synthetic, outperforming the baseline linear classifiers. It is also comparable to the state-of-the-art on MNIST and Synthetic. BotCL with reconstruction loss " + }, + { + "bbox": [ + 305, + 371, + 545, + 563 + ], + "type": "inline_equation", + "content": "(\\mathrm{BotCL}_{\\mathrm{Rec}})" + }, + { + "bbox": [ + 305, + 371, + 545, + 563 + ], + "type": "text", + "content": " shows a performance drop over CUB200, ImageNet, and Synthetic, while it outperforms " + }, + { + "bbox": [ + 305, + 371, + 545, + 563 + ], + "type": "inline_equation", + "content": "\\mathrm{BotCL}_{\\mathrm{Cont}}" + }, + { + "bbox": [ + 305, + 371, + 545, + 563 + ], + "type": "text", + "content": " on MNIST. This behavior supports our assumption that the reconstruction loss is useful only when concepts are strongly tied to their spatial position. Otherwise, " + }, + { + "bbox": [ + 305, + 371, + 545, + 563 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 305, + 371, + 545, + 563 + ], + "type": "text", + "content": " is insufficient to reconstruct the original image, and BotCL fails. Contrastive self-supervision is the key to facilitating concept discovery." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 305, + 565, + 545, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 565, + 545, + 685 + ], + "spans": [ + { + "bbox": [ + 305, + 565, + 545, + 685 + ], + "type": "text", + "content": "We also explore the relationship between the number of classes and BotCL's accuracy over CUB200 and ImageNet. We used small and large variants of ResNet as the backbone. We extracted subsets of the datasets consisting of the first " + }, + { + "bbox": [ + 305, + 565, + 545, + 685 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 305, + 565, + 545, + 685 + ], + "type": "text", + "content": " classes along with the class IDs. Figure 3 shows that BotCL has a competitive performance when the number of classes is less than 200. We conclude that BotCL hardly degrades the classification performance on small- or middle-sized datasets. However, this is not the case for " + }, + { + "bbox": [ + 305, + 565, + 545, + 685 + ], + "type": "inline_equation", + "content": "n > 200" + }, + { + "bbox": [ + 305, + 565, + 545, + 685 + ], + "type": "text", + "content": " (refer to supp. material for larger " + }, + { + "bbox": [ + 305, + 565, + 545, + 685 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 305, + 565, + 545, + 685 + ], + "type": "text", + "content": " and different " + }, + { + "bbox": [ + 305, + 565, + 545, + 685 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 305, + 565, + 545, + 685 + ], + "type": "text", + "content": "'s)." + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 315, + 702, + 470, + 714 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 702, + 470, + 714 + ], + "spans": [ + { + "bbox": [ + 315, + 702, + 470, + 714 + ], + "type": "text", + "content": "3 Implementation details are in supp. material." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10965" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 70, + 302, + 159 + ], + "blocks": [ + { + "bbox": [ + 53, + 70, + 302, + 159 + ], + "lines": [ + { + "bbox": [ + 53, + 70, + 302, + 159 + ], + "spans": [ + { + "bbox": [ + 53, + 70, + 302, + 159 + ], + "type": "image", + "image_path": "84780a469a0780bcf43986dd8e3e608ef968a48c58084652eca318a3f7fc5142.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 168, + 547, + 191 + ], + "lines": [ + { + "bbox": [ + 46, + 168, + 547, + 191 + ], + "spans": [ + { + "bbox": [ + 46, + 168, + 547, + 191 + ], + "type": "text", + "content": "Figure 3. Classification accuracy vs. the number of classes. We used subsets of CUB200 and ImageNet with " + }, + { + "bbox": [ + 46, + 168, + 547, + 191 + ], + "type": "inline_equation", + "content": "k = 50" + }, + { + "bbox": [ + 46, + 168, + 547, + 191 + ], + "type": "text", + "content": " and ResNet-18 and ResNet-101 backbones." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 303, + 70, + 419, + 159 + ], + "blocks": [ + { + "bbox": [ + 303, + 70, + 419, + 159 + ], + "lines": [ + { + "bbox": [ + 303, + 70, + 419, + 159 + ], + "spans": [ + { + "bbox": [ + 303, + 70, + 419, + 159 + ], + "type": "image", + "image_path": "f522c58e4a2bd2bfbe6d3193555910f29361428d551c6201ca3af81bcaa68662.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 420, + 70, + 539, + 159 + ], + "blocks": [ + { + "bbox": [ + 420, + 70, + 539, + 159 + ], + "lines": [ + { + "bbox": [ + 420, + 70, + 539, + 159 + ], + "spans": [ + { + "bbox": [ + 420, + 70, + 539, + 159 + ], + "type": "image", + "image_path": "63f847b2ef16a25959ac120149bc5a6c942491ece6229324b63d6714c6ed0463.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 51, + 264, + 282, + 369 + ], + "blocks": [ + { + "bbox": [ + 46, + 210, + 289, + 257 + ], + "lines": [ + { + "bbox": [ + 46, + 210, + 289, + 257 + ], + "spans": [ + { + "bbox": [ + 46, + 210, + 289, + 257 + ], + "type": "text", + "content": "Table 1. Performance comparison in classification accuracy. The best concept-based method is highlighted in bold. " + }, + { + "bbox": [ + 46, + 210, + 289, + 257 + ], + "type": "inline_equation", + "content": "\\mathrm{BotCL_{Rec}}" + }, + { + "bbox": [ + 46, + 210, + 289, + 257 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 210, + 289, + 257 + ], + "type": "inline_equation", + "content": "\\mathrm{BotCL_{Cont}}" + }, + { + "bbox": [ + 46, + 210, + 289, + 257 + ], + "type": "text", + "content": " are both BotCL but with reconstruction and contrastive loss, respectively. For ImageNet, we used the first 200 classes." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 51, + 264, + 282, + 369 + ], + "lines": [ + { + "bbox": [ + 51, + 264, + 282, + 369 + ], + "spans": [ + { + "bbox": [ + 51, + 264, + 282, + 369 + ], + "type": "table", + "html": "
CUB200ImageNetMNISTSynthetic
Baseline0.7310.7860.9880.999
k-means* [46]0.0630.4270.7810.747
PCA* [46]0.0440.1390.6530.645
SENN [1]0.6420.6730.9850.984
ProtoPNet [8]0.7250.7520.9810.992
BotCLRec0.6930.7200.9830.785
BotCLCont0.7400.7950.9800.998
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Interpretability" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 413, + 271, + 426 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 413, + 271, + 426 + ], + "spans": [ + { + "bbox": [ + 47, + 413, + 271, + 426 + ], + "type": "text", + "content": "5.3.1 Qualitative validation of discovered concepts" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 436, + 287, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 436, + 287, + 581 + ], + "spans": [ + { + "bbox": [ + 46, + 436, + 287, + 581 + ], + "type": "text", + "content": "Figure 4a visualizes " + }, + { + "bbox": [ + 46, + 436, + 287, + 581 + ], + "type": "inline_equation", + "content": "a_{\\kappa}" + }, + { + "bbox": [ + 46, + 436, + 287, + 581 + ], + "type": "text", + "content": ", showing concept " + }, + { + "bbox": [ + 46, + 436, + 287, + 581 + ], + "type": "inline_equation", + "content": "\\kappa" + }, + { + "bbox": [ + 46, + 436, + 287, + 581 + ], + "type": "text", + "content": " in the image, over MNIST. We selected 5 concepts out of 20 that are most frequently activated (i.e., " + }, + { + "bbox": [ + 46, + 436, + 287, + 581 + ], + "type": "inline_equation", + "content": "t_{\\kappa} > 0.5" + }, + { + "bbox": [ + 46, + 436, + 287, + 581 + ], + "type": "text", + "content": ") in the training set. Taking digits 0 and 9 as an example, we can observe that they share Cpts.3-5 and the only difference is Cpt.2 that locates in the lower edge of the vertical stroke of 9. This stroke is specific to digit 9. We used BotCLRec, so we can remove Cpt.2 before reconstruction, which generates an image like 0 (refer to Section 5.3.3). Some concepts are incompatible with human intuition; yet we can interpret such concepts (e.g., Cpt.1 may attend to the missing stroke that completes a circle)." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 582, + 288, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 288, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 288, + 677 + ], + "type": "text", + "content": "For CUB200, we train " + }, + { + "bbox": [ + 46, + 582, + 288, + 677 + ], + "type": "inline_equation", + "content": "\\mathrm{BotCL}_{\\mathrm{Const}}" + }, + { + "bbox": [ + 46, + 582, + 288, + 677 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 46, + 582, + 288, + 677 + ], + "type": "inline_equation", + "content": "n = 50" + }, + { + "bbox": [ + 46, + 582, + 288, + 677 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 582, + 288, + 677 + ], + "type": "inline_equation", + "content": "k = 20" + }, + { + "bbox": [ + 46, + 582, + 288, + 677 + ], + "type": "text", + "content": ". Figure 5a shows the attention maps of an image of yellow headed black bird. We can observe that the attentions for Cpts.1-5 cover different body parts, including the head, wing, back, and feet, which proves that BotCL can learn valid concepts from the natural image as well. Supp. material exemplifies all concepts discovered from MNIST and CUB200." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 213, + 541, + 225 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 213, + 541, + 225 + ], + "spans": [ + { + "bbox": [ + 306, + 213, + 541, + 225 + ], + "type": "text", + "content": "5.3.2 Consistency and distinctiveness of each concept" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 231, + 547, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 231, + 547, + 350 + ], + "spans": [ + { + "bbox": [ + 304, + 231, + 547, + 350 + ], + "type": "text", + "content": "BotCL is designed to discover individually consistent and mutually distinctive concepts. We qualitatively verify this by showing each concept with its top-5 activated images5 with attention maps in Figure 4b. For MNIST, different concepts cover different patterns, and each concept covers the same patterns in different samples (even the samples of different classes). Figure 5b for CUB200 shows that BotCL renders a similar behavior on the CUB200 dataset; that is, the top-5 concepts are responsible for different patterns, and each of them is consistent." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 365, + 515, + 377 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 365, + 515, + 377 + ], + "spans": [ + { + "bbox": [ + 305, + 365, + 515, + 377 + ], + "type": "text", + "content": "5.3.3 Contribution of each concept in inference" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 383, + 545, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 383, + 545, + 491 + ], + "spans": [ + { + "bbox": [ + 304, + 383, + 545, + 491 + ], + "type": "text", + "content": "We can qualitatively see the contribution of each concept by removing the concept and seeing the changes in the corresponding self-supervision task's output. As shown in Figure 4c, when we set the activation of Cpt.2 (responsible for the vertical stroke of digit 9) to zero, the reconstructed image looks like digit 0. When Cpt.1, representing the absence of the circle in digit 7, is deactivated (i.e., " + }, + { + "bbox": [ + 304, + 383, + 545, + 491 + ], + "type": "inline_equation", + "content": "t_1" + }, + { + "bbox": [ + 304, + 383, + 545, + 491 + ], + "type": "text", + "content": " is set to 0), a circle emerges in the upper part of the reconstructed image. The resulting image looks more like digit 9." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 491, + 545, + 611 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 491, + 545, + 611 + ], + "spans": [ + { + "bbox": [ + 304, + 491, + 545, + 611 + ], + "type": "text", + "content": "For CUB200 shown in Figure 5c, we show images most similar to the input image in Figure 5a among the dataset in terms of " + }, + { + "bbox": [ + 304, + 491, + 545, + 611 + ], + "type": "inline_equation", + "content": "\\hat{t}^{\\top}\\hat{t}^{\\prime}" + }, + { + "bbox": [ + 304, + 491, + 545, + 611 + ], + "type": "text", + "content": ", with ablating each concept. When Cpt.1 (responsible for the yellow head) is deactivated, more blackhead bird images appear in the top-8 images. Cpt.5 covers birds' feet and is common among most bird classes. Deactivating this concept does not change the top-8 images. These observations suggest that although some concepts do not contribute to classification performance, images are successfully represented by combinations of concepts." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 617, + 503, + 631 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 617, + 503, + 631 + ], + "spans": [ + { + "bbox": [ + 306, + 617, + 503, + 631 + ], + "type": "text", + "content": "5.4. Quantitative Evaluation on Synthetic" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 636, + 545, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 636, + 545, + 696 + ], + "spans": [ + { + "bbox": [ + 304, + 636, + 545, + 696 + ], + "type": "text", + "content": "One problem of the concept-based approach is the absence of established quantitative evaluations of concepts because the choice of concepts may be arbitrary and the same level of representability may be achieved with different sets of concepts. A single predefined set of concepts" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 46, + 693, + 287, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 693, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 693, + 287, + 712 + ], + "type": "text", + "content": "4Cpts.1-5 are ordered based on the frequency counted in the dataset." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 315, + 702, + 525, + 714 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 702, + 525, + 714 + ], + "spans": [ + { + "bbox": [ + 315, + 702, + 525, + 714 + ], + "type": "text", + "content": "For each concept " + }, + { + "bbox": [ + 315, + 702, + 525, + 714 + ], + "type": "inline_equation", + "content": "\\kappa" + }, + { + "bbox": [ + 315, + 702, + 525, + 714 + ], + "type": "text", + "content": ", five images whose " + }, + { + "bbox": [ + 315, + 702, + 525, + 714 + ], + "type": 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Concepts for MNIST. (a) Attention maps for different input images. (b) Top-5 activated images (images in the dataset whose " + }, + { + "bbox": [ + 46, + 230, + 547, + 264 + ], + "type": "inline_equation", + "content": "t_\\kappa" + }, + { + "bbox": [ + 46, + 230, + 547, + 264 + ], + "type": "text", + "content": " is largest) for each concept. (c) Images reconstructed by our concept decoder with all detected concepts (original) and with a certain concept deactivated." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 383, + 357, + 394, + 365 + ], + "lines": [ + { + "bbox": [ + 383, + 357, + 394, + 365 + ], + "spans": [ + { + "bbox": [ + 383, + 357, + 394, + 365 + ], + "type": "text", + "content": "(c)" + } + ] + } + ], + "index": 38, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 394, + 281, + 532, + 437 + ], + "lines": [ + { + "bbox": [ + 394, + 281, + 532, + 437 + ], + "spans": [ + { + "bbox": [ + 394, + 281, + 532, + 437 + ], + "type": "image", + "image_path": "516896f6287fce2e3e904196b7c13d983273b37c3adf24566fde9cc883dda50f.jpg" + } + ] + } + ], + "index": 39, + "angle": 0, + "type": "image_body" + } + ], + "index": 39 + }, + { + "bbox": [ + 46, + 493, + 287, + 528 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 493, + 287, + 528 + ], + "spans": [ + { + "bbox": [ + 46, + 493, + 287, + 528 + ], + "type": "text", + "content": "is not enough to evaluate the goodness of discovered concepts. Literature has evaluated concepts qualitatively (as Section 5.3) or by user study (as Section 5.5)." + } + ] + } + ], + "index": 41 + }, + { + "bbox": [ + 46, + 529, + 287, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 529, + 287, + 647 + ], + "spans": [ + { + "bbox": [ + 46, + 529, + 287, + 647 + ], + "type": "text", + "content": "We decided to use Synthetic [46] for quantitatively evaluating concepts. The task is a multi-label classification that involves 15 shapes. Combinations of the 5 shapes (shown in Figure 6a, S.1 to S.5) form 15 classes, and the other 10 shapes are noises6. We deem a shape is covered by concept " + }, + { + "bbox": [ + 46, + 529, + 287, + 647 + ], + "type": "inline_equation", + "content": "\\kappa" + }, + { + "bbox": [ + 46, + 529, + 287, + 647 + ], + "type": "text", + "content": " when the shape's area and concept " + }, + { + "bbox": [ + 46, + 529, + 287, + 647 + ], + "type": "inline_equation", + "content": "\\kappa" + }, + { + "bbox": [ + 46, + 529, + 287, + 647 + ], + "type": "text", + "content": "'s area (the area with " + }, + { + "bbox": [ + 46, + 529, + 287, + 647 + ], + "type": "inline_equation", + "content": "a_{\\kappa} > \\gamma" + }, + { + "bbox": [ + 46, + 529, + 287, + 647 + ], + "type": "text", + "content": " for BotCL, where " + }, + { + "bbox": [ + 46, + 529, + 287, + 647 + ], + "type": "inline_equation", + "content": "\\gamma = 0.9" + }, + { + "bbox": [ + 46, + 529, + 287, + 647 + ], + "type": "text", + "content": " is a predefined threshold) overlap. Let " + }, + { + "bbox": [ + 46, + 529, + 287, + 647 + ], + "type": "inline_equation", + "content": "h_{s\\kappa} = 1" + }, + { + "bbox": [ + 46, + 529, + 287, + 647 + ], + "type": "text", + "content": " denote shape " + }, + { + "bbox": [ + 46, + 529, + 287, + 647 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 46, + 529, + 287, + 647 + ], + "type": "text", + "content": " overlaps with concept " + }, + { + "bbox": [ + 46, + 529, + 287, + 647 + ], + "type": "inline_equation", + "content": "\\kappa" + }, + { + "bbox": [ + 46, + 529, + 287, + 647 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 529, + 287, + 647 + ], + "type": "inline_equation", + "content": "h_{s\\kappa} = 0" + }, + { + "bbox": [ + 46, + 529, + 287, + 647 + ], + "type": "text", + "content": " otherwise. The coverage of " + }, + { + "bbox": [ + 46, + 529, + 287, + 647 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 46, + 529, + 287, + 647 + ], + "type": "text", + "content": " by concept " + }, + { + "bbox": [ + 46, + 529, + 287, + 647 + ], + "type": "inline_equation", + "content": "\\kappa" + }, + { + "bbox": [ + 46, + 529, + 287, + 647 + ], + "type": "text", + "content": " is given by" + } + ] + } + ], + "index": 42 + }, + { + "bbox": [ + 120, + 647, + 287, + 662 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 120, + 647, + 287, + 662 + ], + "spans": [ + { + "bbox": [ + 120, + 647, + 287, + 662 + ], + "type": "interline_equation", + "content": "\\operatorname {C o v e r a g e} _ {s \\kappa} = \\mathbb {E} \\left[ h _ {s \\kappa} \\right], \\tag {11}", + "image_path": "0ec126db04f9feaf46f56e162f66522928aa0879464b26255d29c727ebd5e0e8.jpg" + } + ] + } + ], + "index": 43 + }, + { + "bbox": [ + 47, + 665, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 665, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 47, + 665, + 287, + 677 + ], + "type": "text", + "content": "where the expectation is computed over the images in the" + } + ] + } + ], + "index": 44 + }, + { + "bbox": [ + 304, + 493, + 545, + 528 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 493, + 545, + 528 + ], + "spans": [ + { + "bbox": [ + 304, + 493, + 545, + 528 + ], + "type": "text", + "content": "test set with concept " + }, + { + "bbox": [ + 304, + 493, + 545, + 528 + ], + "type": "inline_equation", + "content": "\\kappa" + }, + { + "bbox": [ + 304, + 493, + 545, + 528 + ], + "type": "text", + "content": " activated. The concepts and the 5 shapes are associated as a combinatorial optimization problem so that the sum of Coverage" + }, + { + "bbox": [ + 304, + 493, + 545, + 528 + ], + "type": "inline_equation", + "content": "_{s\\kappa}" + }, + { + "bbox": [ + 304, + 493, + 545, + 528 + ], + "type": "text", + "content": " over " + }, + { + "bbox": [ + 304, + 493, + 545, + 528 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 304, + 493, + 545, + 528 + ], + "type": "text", + "content": " are maximized." + } + ] + } + ], + "index": 46 + }, + { + "bbox": [ + 304, + 529, + 545, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 529, + 545, + 624 + ], + "spans": [ + { + "bbox": [ + 304, + 529, + 545, + 624 + ], + "type": "text", + "content": "We use " + }, + { + "bbox": [ + 304, + 529, + 545, + 624 + ], + "type": "inline_equation", + "content": "k = 15" + }, + { + "bbox": [ + 304, + 529, + 545, + 624 + ], + "type": "text", + "content": " to train BotCL. Figure 6a visualizes the concept associated with each shape7. A concept is located by " + }, + { + "bbox": [ + 304, + 529, + 545, + 624 + ], + "type": "inline_equation", + "content": "a_{\\kappa}" + }, + { + "bbox": [ + 304, + 529, + 545, + 624 + ], + "type": "text", + "content": " for 6 images with the highest concept activations " + }, + { + "bbox": [ + 304, + 529, + 545, + 624 + ], + "type": "inline_equation", + "content": "t_{\\kappa}" + }, + { + "bbox": [ + 304, + 529, + 545, + 624 + ], + "type": "text", + "content": ". The concepts cover the associated shapes with relatively small regions, but one concept usually covers multiple shapes. This can be further evident in Figure 6b that shows Coverages\\kappa. Cpt.8 only covers S.3, whereas Cpt.1 and Cpt.13 covers multiple shapes." + } + ] + } + ], + "index": 47 + }, + { + "bbox": [ + 304, + 625, + 545, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 625, + 545, + 685 + ], + "spans": [ + { + "bbox": [ + 304, + 625, + 545, + 685 + ], + "type": "text", + "content": "We use three metrics other than accuracy to evaluate the performance of concept discovery: (i) Completeness measures how well a concept covers its associated shape in the dataset. (ii) Purity shows the ability to discover concepts that only cover a single shape. (iii) Distinctiveness quanti" + } + ] + } + ], + "index": 48 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 46, + 683, + 287, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 683, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 683, + 287, + 712 + ], + "type": "text", + "content": "6Images are generated with random shapes, so there can be multiple classes (combinations of shapes) in a single image, which forms a multi-label classification task." + } + ] + } + ], + "index": 45 + }, + { + "bbox": [ + 315, + 693, + 523, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 693, + 523, + 703 + ], + "spans": [ + { + "bbox": [ + 315, + 693, + 523, + 703 + ], + "type": "text", + "content": "7Note that in this experiment, only shapes matter but not colors." + } + ] + } + ], + "index": 49 + }, + { + "bbox": [ + 317, + 703, + 443, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 703, + 443, + 713 + ], + "spans": [ + { + "bbox": [ + 317, + 703, + 443, + 713 + ], + "type": "text", + "content": "Further details are in supp. material." + } + ] + } + ], + "index": 50 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10967" + } + ] + } + ], + "index": 52 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 65, + 70, + 260, + 223 + ], + "blocks": [ + { + "bbox": [ + 65, + 70, + 260, + 223 + ], + "lines": [ + { + "bbox": [ + 65, + 70, + 260, + 223 + ], + "spans": [ + { + "bbox": [ + 65, + 70, + 260, + 223 + ], + "type": "image", + "image_path": "d9f6e7d23c3c80f5bb6d87199c0893a83649c21c2d0b4c9e0bc43f361f0c8ad4.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 235, + 546, + 258 + ], + "lines": [ + { + "bbox": [ + 46, + 235, + 546, + 258 + ], + "spans": [ + { + "bbox": [ + 46, + 235, + 546, + 258 + ], + "type": "text", + "content": "Figure 6. Experiment on Synthetic. (a) S.1-S.5 are the five shapes of which combinations form classes. Attention maps next to each shape are of the concept that covers the shape. (b) Coverage" + }, + { + "bbox": [ + 46, + 235, + 546, + 258 + ], + "type": "inline_equation", + "content": "_{s\\kappa}" + }, + { + "bbox": [ + 46, + 235, + 546, + 258 + ], + "type": "text", + "content": " (the concept associated with each of the five shapes is marked)." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 265, + 72, + 534, + 223 + ], + "blocks": [ + { + "bbox": [ + 265, + 72, + 534, + 223 + ], + "lines": [ + { + "bbox": [ + 265, + 72, + 534, + 223 + ], + "spans": [ + { + "bbox": [ + 265, + 72, + 534, + 223 + ], + "type": "image", + "image_path": "d9fd7f8b240cd20c97b3cae58f1b25024b111338cd5512a033924e3ceca864cd.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 270, + 282, + 282 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 270, + 282, + 282 + ], + "spans": [ + { + "bbox": [ + 47, + 270, + 282, + 282 + ], + "type": "text", + "content": "fies the difference among concepts based on the coverage." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 283, + 287, + 378 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 283, + 287, + 378 + ], + "spans": [ + { + "bbox": [ + 46, + 283, + 287, + 378 + ], + "type": "text", + "content": "BotCL with contrastive loss is compared with ACE [14], and two baselines PCA and k-means in [46]. We apply k-means or PCA to " + }, + { + "bbox": [ + 46, + 283, + 287, + 378 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 46, + 283, + 287, + 378 + ], + "type": "text", + "content": " of all images in the dataset after flattening the spatial dimensions. The cluster centers or the principal components are deemed as concepts. Attention maps can be computed by Euclidean distance or cosine similarity. Once the attention maps are obtained, we follow BotCL's process for classification." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 380, + 287, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 380, + 287, + 559 + ], + "spans": [ + { + "bbox": [ + 46, + 380, + 287, + 559 + ], + "type": "text", + "content": "As shown in Table 2, BotCL shows better completeness, distinctiveness, and accuracy scores than comparative methods. Although k-means is able to discover concepts, they are not optimized for the target classification task, and the performance is low. As we discussed, the concepts learned by BotCL tend to cover more than one target shape, causing a comparatively low purity. The cluster center of k-means is able to capture only one kind of shape at the cost of completeness. We can also observe that all methods are affected by concept number " + }, + { + "bbox": [ + 46, + 380, + 287, + 559 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 380, + 287, + 559 + ], + "type": "text", + "content": ", and generally a larger " + }, + { + "bbox": [ + 46, + 380, + 287, + 559 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 380, + 287, + 559 + ], + "type": "text", + "content": " ensure better performance on all metrics. This result is not surprising, but we confirmed that a larger " + }, + { + "bbox": [ + 46, + 380, + 287, + 559 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 380, + 287, + 559 + ], + "type": "text", + "content": " is preferable for better interpretability. We detail the generation of the dataset, implementation of PCA and k-means, and formal definitions of metrics in supp. material." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 568, + 122, + 581 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 568, + 122, + 581 + ], + "spans": [ + { + "bbox": [ + 47, + 568, + 122, + 581 + ], + "type": "text", + "content": "5.5. User Study" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 587, + 287, + 684 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 587, + 287, + 684 + ], + "spans": [ + { + "bbox": [ + 46, + 587, + 287, + 684 + ], + "type": "text", + "content": "Our user study is designed to evaluate BotCL with realistic datasets for the challenge of human understanding. Participants are asked to observe the test images with the attention map for concept " + }, + { + "bbox": [ + 46, + 587, + 287, + 684 + ], + "type": "inline_equation", + "content": "\\kappa" + }, + { + "bbox": [ + 46, + 587, + 287, + 684 + ], + "type": "text", + "content": " (refer to Section 5.3.2) and select some phrases in the predefined vocabulary that best describes the concept (i.e., attended regions). They can also choose None of them if they cannot find any consistent visual elements. We recruited 20 participants for each concept" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 331, + 322, + 519, + 425 + ], + "blocks": [ + { + "bbox": [ + 305, + 269, + 546, + 313 + ], + "lines": [ + { + "bbox": [ + 305, + 269, + 546, + 313 + ], + "spans": [ + { + "bbox": [ + 305, + 269, + 546, + 313 + ], + "type": "text", + "content": "Table 2. Quantitative evaluation on Synthetic. Note that ACE uses concepts for post-hoc explanation and does not use them for classification. Comp., Dist., and Acc. mean completeness, distinctiveness, and accuracy, respectively." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 331, + 322, + 519, + 425 + ], + "lines": [ + { + "bbox": [ + 331, + 322, + 519, + 425 + ], + "spans": [ + { + "bbox": [ + 331, + 322, + 519, + 425 + ], + "type": "table", + "html": "
Comp.PurityDist.Acc.
k=5ACE0.6620.2740.084—
k-means0.6300.7240.2150.652
PCA0.4580.1700.2980.571
BotCL0.6180.4530.2810.835
k=15ACE0.6140.2210.151—
k-means0.8160.9780.2720.747
PCA0.4320.1620.2860.645
BotCL0.9250.7440.4520.998
", + "image_path": "a56cc01c3219f9dc90eacfe5fefe0efbbbbdaa1899adbc91bc82ff635a20c0d8.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 309, + 454, + 545, + 544 + ], + "blocks": [ + { + "bbox": [ + 362, + 434, + 488, + 445 + ], + "lines": [ + { + "bbox": [ + 362, + 434, + 488, + 445 + ], + "spans": [ + { + "bbox": [ + 362, + 434, + 488, + 445 + ], + "type": "text", + "content": "Table 3. Results of our user study." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 309, + 454, + 545, + 544 + ], + "lines": [ + { + "bbox": [ + 309, + 454, + 545, + 544 + ], + "spans": [ + { + "bbox": [ + 309, + 454, + 545, + 544 + ], + "type": "table", + "html": "
DatasetConceptsCDR ↑CC ↑MIC ↓
MeanStdMeanStdMeanStd
MNISTAnnotated1.0000.0000.8380.1500.0710.047
BotCL0.8250.2880.5810.2740.1990.072
Random0.1220.0700.1630.0740.4380.039
CUB200Annotated0.9490.1150.5950.1130.5120.034
BotCL0.8740.1560.5300.1160.5490.036
Random0.2120.0810.1980.0390.5740.031
", + "image_path": "a17fb73d974f3f86b6d63f2ac91f5ea5a57b31081280846cc11b58ca79fdd67f.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 558, + 545, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 558, + 545, + 581 + ], + "spans": [ + { + "bbox": [ + 305, + 558, + 545, + 581 + ], + "type": "text", + "content": "of MNIST and 30 participants for CUB200 using Amazon Mechanical Turk." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 582, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 546, + 713 + ], + "type": "text", + "content": "We defined three metrics to summarize the participants' responses. (i) Concept discovery rate (CDR): The ratio of the responses that are not None of them to all responses. A higher CDR means participants can find some consistent visual elements for many concepts. (ii) Concept consistency (CC): The ratio of exact matches out of all pairs of participants' responses. A high value means many participants use the same phrases to describe a concept. (iii) Mutual information between concepts (MIC): The similarity of the response distribution, computed over all possible pairs of concepts. This value is high when multiple concepts cover" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 46, + 693, + 287, + 715 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 693, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 693, + 287, + 715 + ], + "type": "text", + "content": "9SENN [1] and ProtoPNet [8] are not comparable. SENN's concepts globally cover a whole image. ProtoPNet requires way more concepts." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10968" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 72, + 156, + 131 + ], + "blocks": [ + { + "bbox": [ + 49, + 72, + 156, + 131 + ], + "lines": [ + { + "bbox": [ + 49, + 72, + 156, + 131 + ], + "spans": [ + { + "bbox": [ + 49, + 72, + 156, + 131 + ], + "type": "image", + "image_path": "589bceb8e937e8bfa1aefa978843209acb314dd8ed464c7a2ed93141c52d72cd.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 157, + 72, + 253, + 131 + ], + "blocks": [ + { + "bbox": [ + 157, + 72, + 253, + 131 + ], + "lines": [ + { + "bbox": [ + 157, + 72, + 253, + 131 + ], + "spans": [ + { + "bbox": [ + 157, + 72, + 253, + 131 + ], + "type": "image", + "image_path": "b3e795580e69ad8beb823cc57b68d6ae0c7bca73fe6dea90027c8202d7fcfdaa.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 255, + 72, + 350, + 132 + ], + "blocks": [ + { + "bbox": [ + 255, + 72, + 350, + 132 + ], + "lines": [ + { + "bbox": [ + 255, + 72, + 350, + 132 + ], + "spans": [ + { + "bbox": [ + 255, + 72, + 350, + 132 + ], + "type": "image", + "image_path": "17c6932cdecf73f94b147e439c3dc70f2b46caa4e8e503f9442c43f60e95b9b7.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 291, + 135, + 301, + 144 + ], + "lines": [ + { + "bbox": [ + 291, + 135, + 301, + 144 + ], + "spans": [ + { + "bbox": [ + 291, + 135, + 301, + 144 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 352, + 72, + 447, + 132 + ], + "blocks": [ + { + "bbox": [ + 352, + 72, + 447, + 132 + ], + "lines": [ + { + "bbox": [ + 352, + 72, + 447, + 132 + ], + "spans": [ + { + "bbox": [ + 352, + 72, + 447, + 132 + ], + "type": "image", + "image_path": "0366fc3d3dc05bbe606488ad455ff64e3f122e86aa4e0c05a0a4b27dbbd74003.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 449, + 72, + 545, + 132 + ], + "blocks": [ + { + "bbox": [ + 449, + 72, + 545, + 132 + ], + "lines": [ + { + "bbox": [ + 449, + 72, + 545, + 132 + ], + "spans": [ + { + "bbox": [ + 449, + 72, + 545, + 132 + ], + "type": "image", + "image_path": "67a66640a5f0007eebea833f5c1422f76c896422d519048ea6a167f332a3636e.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 49, + 145, + 156, + 214 + ], + "blocks": [ + { + "bbox": [ + 49, + 145, + 156, + 214 + ], + "lines": [ + { + "bbox": [ + 49, + 145, + 156, + 214 + ], + "spans": [ + { + "bbox": [ + 49, + 145, + 156, + 214 + ], + "type": "image", + "image_path": "823c220e9bcef4c97bd3c08e6def3126a5ea9ed138eff67abcf2fb9063ac6c8d.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 238, + 546, + 260 + ], + "lines": [ + { + "bbox": [ + 46, + 238, + 546, + 260 + ], + "spans": [ + { + "bbox": [ + 46, + 238, + 546, + 260 + ], + "type": "text", + "content": "Figure 7. Results of ablation study. (a) Hyperparameter values vs. classification accuracy on ImageNet and CUB200. (b) Hyperparameter values vs. classification accuracy and other metrics on Synthetic." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 157, + 146, + 253, + 215 + ], + "blocks": [ + { + "bbox": [ + 157, + 146, + 253, + 215 + ], + "lines": [ + { + "bbox": [ + 157, + 146, + 253, + 215 + ], + "spans": [ + { + "bbox": [ + 157, + 146, + 253, + 215 + ], + "type": "image", + "image_path": "0596d4827d7a8b9782182f1405c55deb85c7c54368ce769bf312f668cfcee613.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 255, + 146, + 350, + 215 + ], + "blocks": [ + { + "bbox": [ + 255, + 146, + 350, + 215 + ], + "lines": [ + { + "bbox": [ + 255, + 146, + 350, + 215 + ], + "spans": [ + { + "bbox": [ + 255, + 146, + 350, + 215 + ], + "type": "image", + "image_path": "57007d38529c283143e8db2f3fe6a4a11bdb3132c1956995fd3fc3909b8dcf9d.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 291, + 219, + 302, + 228 + ], + "lines": [ + { + "bbox": [ + 291, + 219, + 302, + 228 + ], + "spans": [ + { + "bbox": [ + 291, + 219, + 302, + 228 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 352, + 146, + 447, + 215 + ], + "blocks": [ + { + "bbox": [ + 352, + 146, + 447, + 215 + ], + "lines": [ + { + "bbox": [ + 352, + 146, + 447, + 215 + ], + "spans": [ + { + "bbox": [ + 352, + 146, + 447, + 215 + ], + "type": "image", + "image_path": "8bfb1423914005831d45a9d41642802d6f37f94662cce1f631e89537d748800d.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 449, + 147, + 545, + 214 + ], + "blocks": [ + { + "bbox": [ + 449, + 147, + 545, + 214 + ], + "lines": [ + { + "bbox": [ + 449, + 147, + 545, + 214 + ], + "spans": [ + { + "bbox": [ + 449, + 147, + 545, + 214 + ], + "type": "image", + "image_path": "8d8d3f72b281050304d8fe30e732e2b4877d7108667a613ef871958b6b749749.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 278, + 254, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 278, + 254, + 289 + ], + "spans": [ + { + "bbox": [ + 46, + 278, + 254, + 289 + ], + "type": "text", + "content": "the same visual elements; therefore, lower is better." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 290, + 287, + 374 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 290, + 287, + 374 + ], + "spans": [ + { + "bbox": [ + 46, + 290, + 287, + 374 + ], + "type": "text", + "content": "For comparison, we also evaluated a manual annotation" + }, + { + "bbox": [ + 46, + 290, + 287, + 374 + ], + "type": "inline_equation", + "content": "^{10}" + }, + { + "bbox": [ + 46, + 290, + 287, + 374 + ], + "type": "text", + "content": " and random scribbling for the same images. Table 3 shows that BotCL yields good scores for all metrics on both datasets (close to the manual annotation), showing the learned concepts are interpretable for humans (from CDR), consistent (from CC), and mutually distinct (from MIC). More details are in supp. material." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 47, + 384, + 140, + 396 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 384, + 140, + 396 + ], + "spans": [ + { + "bbox": [ + 47, + 384, + 140, + 396 + ], + "type": "text", + "content": "5.6. Ablation Study" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 46, + 403, + 287, + 463 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 403, + 287, + 463 + ], + "spans": [ + { + "bbox": [ + 46, + 403, + 287, + 463 + ], + "type": "text", + "content": "We conducted ablation studies using the default hyperparameters except for the one to be explored. As there is no ground truth concept for CUB200 and ImageNet, only accuracy is evaluated (Figure 7a). For Synthetic, accuracy and the three metrics in Section 5.4 are employed (Figure 7b)." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 46, + 464, + 287, + 534 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 464, + 287, + 534 + ], + "spans": [ + { + "bbox": [ + 46, + 464, + 287, + 534 + ], + "type": "text", + "content": "Impact of " + }, + { + "bbox": [ + 46, + 464, + 287, + 534 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 464, + 287, + 534 + ], + "type": "text", + "content": ". A small " + }, + { + "bbox": [ + 46, + 464, + 287, + 534 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 464, + 287, + 534 + ], + "type": "text", + "content": " decreases the accuracy and other metrics, which means the necessity of searching the minimum number of concepts. Also, training tends to fail for all datasets when " + }, + { + "bbox": [ + 46, + 464, + 287, + 534 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 464, + 287, + 534 + ], + "type": "text", + "content": " is large (detailed in the supp. materials). The number of concepts should be tuned for each dataset. This sensitivity is one of BotCL's limitations." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 46, + 536, + 287, + 608 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 536, + 287, + 608 + ], + "spans": [ + { + "bbox": [ + 46, + 536, + 287, + 608 + ], + "type": "text", + "content": "Impact of " + }, + { + "bbox": [ + 46, + 536, + 287, + 608 + ], + "type": "inline_equation", + "content": "\\lambda_{qua}" + }, + { + "bbox": [ + 46, + 536, + 287, + 608 + ], + "type": "text", + "content": ". This hyperparameter controls how close " + }, + { + "bbox": [ + 46, + 536, + 287, + 608 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 536, + 287, + 608 + ], + "type": "text", + "content": " should be to a binary. The accuracy and the other metrics worsen when " + }, + { + "bbox": [ + 46, + 536, + 287, + 608 + ], + "type": "inline_equation", + "content": "\\lambda_{qua}" + }, + { + "bbox": [ + 46, + 536, + 287, + 608 + ], + "type": "text", + "content": " gradually increases. BotCL encodes some information into " + }, + { + "bbox": [ + 46, + 536, + 287, + 608 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 536, + 287, + 608 + ], + "type": "text", + "content": " (such as the area that a concept occupies), which is lost for larger " + }, + { + "bbox": [ + 46, + 536, + 287, + 608 + ], + "type": "inline_equation", + "content": "\\lambda_{qua}" + }, + { + "bbox": [ + 46, + 536, + 287, + 608 + ], + "type": "text", + "content": ". An extreme value may also cause vanishing gradients." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 46, + 609, + 287, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 609, + 287, + 693 + ], + "spans": [ + { + "bbox": [ + 46, + 609, + 287, + 693 + ], + "type": "text", + "content": "Impact of " + }, + { + "bbox": [ + 46, + 609, + 287, + 693 + ], + "type": "inline_equation", + "content": "\\lambda_{con}" + }, + { + "bbox": [ + 46, + 609, + 287, + 693 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 609, + 287, + 693 + ], + "type": "inline_equation", + "content": "\\lambda_{dis}" + }, + { + "bbox": [ + 46, + 609, + 287, + 693 + ], + "type": "text", + "content": ". The individual consistency and mutual distinctiveness losses hardly affect the performance on CUB200 and ImageNet, although we can see a slight drop when the values are zero for CUB200. For Synthetic, the performance metrics vary as they are designed to be. Meanwhile, the accuracy is relatively insensitive to these hyperparameters. The choice of concepts may be" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 278, + 545, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 278, + 545, + 338 + ], + "spans": [ + { + "bbox": [ + 304, + 278, + 545, + 338 + ], + "type": "text", + "content": "highly arbitrary, and different sets of concepts may achieve similar classification performance. This arbitrariness may allow the designing of dedicated concept regularizers for the target task. However, training failures happen when they are set to be large. A small value benefits training." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 338, + 545, + 457 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 338, + 545, + 457 + ], + "spans": [ + { + "bbox": [ + 304, + 338, + 545, + 457 + ], + "type": "text", + "content": "Impact of " + }, + { + "bbox": [ + 304, + 338, + 545, + 457 + ], + "type": "inline_equation", + "content": "\\lambda_{R}" + }, + { + "bbox": [ + 304, + 338, + 545, + 457 + ], + "type": "text", + "content": ". Due to the lower performance of the reconstruction loss, we studied the impact of the contrastive loss only. The contrastive loss almost always improves the classification accuracy. The performance boost is significant in CUB200 and Synthetic. As ImageNet has more training data, this may imply that self-supervision greatly contributes to the learning of concepts when training samples are limited. These results demonstrate the importance of the contrastive loss. This is interesting since this loss uses the same labels as the classification loss." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 471, + 378, + 483 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 471, + 378, + 483 + ], + "spans": [ + { + "bbox": [ + 306, + 471, + 378, + 483 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 491, + 545, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 491, + 545, + 624 + ], + "spans": [ + { + "bbox": [ + 304, + 491, + 545, + 624 + ], + "type": "text", + "content": "This paper presents BotCL for learning bottleneck concepts. Our qualitative and quantitative evaluation showed BotCL's ability to learn concepts without explicit supervision on them but through training for a target classification task. We also demonstrated that BotCL could provide interpretability on its decision and learned concepts themselves. Limitations. One limitation of BotCL is that it requires tuning the number " + }, + { + "bbox": [ + 304, + 491, + 545, + 624 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 491, + 545, + 624 + ], + "type": "text", + "content": " of concepts for each dataset. It might be an interesting research direction to estimate " + }, + { + "bbox": [ + 304, + 491, + 545, + 624 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 491, + 545, + 624 + ], + "type": "text", + "content": ", e.g., based on the number of classes in a given classification task. We will investigate the phenomenon to mitigate this problem." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 641, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 545, + 712 + ], + "type": "text", + "content": "Acknowledgement This work is partly supported by JST CREST Grant No. JPMJCR20D3, JST FOREST Grant No. JPMJFR216O, JSPS KAKENHI Grant-in-Aid for Scientific Research (A). This work is also supported by JSPS KAKENHI Grant Number 19K10662, 20K23343, 21K17764, and 22H03353." + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 55, + 702, + 137, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 702, + 137, + 712 + ], + "spans": [ + { + "bbox": [ + 55, + 702, + 137, + 712 + ], + "type": "text", + "content": "10The authors annotated." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10969" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 49, + 72, + 105, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 72, + 105, + 83 + ], + "spans": [ + { + "bbox": [ + 49, + 72, + 105, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 286, + 712 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 53, + 91, + 286, + 122 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 286, + 122 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 286, + 122 + ], + "type": "text", + "content": "[1] David Alvarez-Melis and Tommi S Jaakkola. 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However, both our preliminary investigation and recent studies suggest that they may be less effective in learning representations for fine-grained visual recognition (FGVR) since many features helpful for optimizing SSL objectives are not suitable for characterizing the subtle differences in FGVR. To overcome this issue, we propose learning an additional screening mechanism to identify discriminative clues commonly seen across instances and classes, dubbed as common rationales in this paper. Intuitively, common rationales tend to correspond to the discriminative patterns from the key parts of foreground objects. We show that a common rationale detector can be learned by simply exploiting the GradCAM induced from the SSL objective without using any pre-trained object parts or saliency detectors, making it seamlessly to be integrated with the existing SSL process. Specifically, we fit the GradCAM with a branch with limited fitting capacity, which allows the branch to capture the common rationales and discard the less common discriminative patterns. At the test stage, the branch generates a set of spatial weights to selectively aggregate features representing an instance. Extensive experimental results on four visual tasks demonstrate that the proposed method can lead to a significant improvement in different evaluation settings. $^{1}$", + "bbox": [ + 75, + 348, + 473, + 741 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 770, + 209, + 786 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, self-supervised representations Learning (SSL) has been shown to be effective for transferring the learned representations to different downstream", + "bbox": [ + 75, + 795, + 468, + 842 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/963e2f1dcaa63d6a061884dc1f04f852c10a152fc760e65901398dc487e6b7e1.jpg", + "image_caption": [ + "Figure 1. GradCAM [30] visualization for MoCo v2 [18], VICReg [4] and our method on the CUB-200-2011, Stanford Cars and FGVC Aircraft datasets. Compared with the existing method MoCo v2 and VICReg, which are prone to be distracted by background patterns, our method can identify features from the foreground and potentially the key parts of the object." + ], + "image_footnote": [], + "bbox": [ + 501, + 316, + 890, + 512 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tasks [2, 4, 5, 14, 18]. Methods such as contrastive learning [7, 9, 16, 18] have demonstrated state-of-the-art feature learning capability and have been intensively studied recently. However, recent studies [11] suggest that contrastive learning may have a \"coarse-grained bias\" and could be less effective for fine-grained classification problems whose goal is to distinguish visually similar subcategories of objects under the basic-level category.", + "bbox": [ + 496, + 640, + 893, + 762 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "This phenomenon is rooted in fine-grained visual recognition (FGVR) properties and the training objective of SSL. SSL tries to minimize a pretext task, e.g., contrastive learning minimizes the distance between same-instance features while maximizing the distance among different-instance features, and any visual patterns that could contribute to loss minimization will be learned. On the other hand, the discriminative patterns for FGVR can be subtle. It is more likely to reside on key object parts. Thus, the feature learned", + "bbox": [ + 496, + 763, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author. This work is supported by the Centre for Augmented Reasoning.", + "bbox": [ + 75, + 849, + 467, + 875 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "1The source code will be publicly available at: https://github. com/GANPerf/LCR", + "bbox": [ + 76, + 875, + 467, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "11392", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "from SSL may not necessarily be useful for FGVR. Figure 1 shows our investigation of this issue. As seen, the existing SSL paradigms, such as MoCo [18] and VICReg [4] are prone to learn patterns from irrelevant regions2. Existing works [31, 38, 42] usually handle this issue by recoursing to pre-trained object part detectors or saliency detectors to regularize SSL using patterns from valid regions to achieve the training objective. However, both the part detectors and saliency detectors could restrict the applicability of SSL for FGVR since part detectors are trained from human annotations, and the saliency regions are not always coincident with the discriminative regions.", + "bbox": [ + 75, + 90, + 472, + 271 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Therefore, this work aims to directly solve the problem from the target domain data. Specifically, we propose to learn an additional screening mechanism in addition to the contrastive learning process. The purpose of the screening mechanism is to filter out the patterns that might contribute to SSL objectives but are irrelevant to FGVR. Somehow surprisingly, we find that such a screening mechanism can be learned from the GradCAM [30] of the SSL loss via an extremely simple method. The whole process can be described as a \"fitting and masking\" procedure: At the training time, we use an additional branch with limited fitting capacity (see more discussion about it in Section 3.2) to fit the GradCAM calculated from the SSL objective. At the testing time, we apply this additional branch to predict an attention mask to perform weighted average pooling for the final presentation. The motivation for such a design is that the GradCAM fitting branch tends to characterize the discriminative patterns that commonly occur across samples due to its limited fitting capacity, and those common patterns, dubbed common rationale in this paper, are more likely corresponding to the discriminative clues from key object parts or at least foreground regions.", + "bbox": [ + 75, + 272, + 472, + 604 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We implement our method based on MoCo v2 [8], one of the state-of-the-art approaches in unsupervised feature learning, which also produces the best performance on FGVR in our setting. Our implementation uses the training objective of MoCo v2 to learn feature representations and derive the GradCAM. Through extensive experiments, we show that our approach can significantly boost the quality of the learned feature. For example, when evaluating the learned feature for retrieval tasks, our method achieves $49.69\\%$ on the CUB-200-2011 retrieval task, which is $32.62\\%$ higher than our baseline method (MoCo v2 [8]). In the linear evaluation phase, the proposed method achieves new state-of-the-art $71.31\\%$ Top-1 accuracy, which is $3.01\\%$ higher than MoCo v2.", + "bbox": [ + 75, + 604, + 472, + 816 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 89, + 640, + 106 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Self-supervised learning aims to learn feature representation from unlabeled data. It relies on a pretext task whose supervision could be derived from the data itself, e.g., image colorization [41], image inpainting [28], and rotation [24] prediction. Contrastive learning is recently identified as a promising framework for self-supervised learning and has been extensively studied [5, 7, 10, 13, 18, 36]. Despite the subtle differences, most contrastive learning approaches [15, 37, 43] try to minimize the distance between different views of the same images and push away the views of different images. The representative methods are SimCLR [7] and MoCo [18]. Besides contrastively learning, consistency-based approaches, such as BYOL [16], SimSiam [9] and masking-and-prediction-based approaches, such as MAE [17], BEiT [3], and ADIOS [32] are also proven effective for SSL.", + "bbox": [ + 496, + 145, + 893, + 388 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Improving SSL via Better Region Localization. A pipeline to improve the distinguishing ability is to design better data augmentations of SSL. Three such methods were recently proposed: DiLo [42], SAGA [39], and Contrastive-Crop [29]. DiLo uses a copy-and-pasting approach as a kind of augmentation to create an image with a different background. In such a way, the proposed method distills localization via learning invariance against backgrounds and improves the ability of SSL models to localize foreground objects. SAGA adopts self-augmentation with a guided attention strategy to augment input images based on predictive attention. In their method, an attention-guided crop is used to enhance the robustness of feature representation. ContrastiveCrop shows a better crop as an augmentation to generate better views in SSL and keep the semantic information of an image. All of these works locate the object by improving the data augmentations for SSL. In this work, our method is adaptive to locate the key regions for self-supervised learning without needing external augmentations. Another family of approaches tries to target the same problem as ours: making the learned feature capture more of the foreground region. CVSA [38] proposed a cross-view saliency alignment framework that first crops and swaps saliency regions of images as a novel view generation. Then it adopts a cross-view saliency alignment loss to encourage the model to learn features from foreground objects. CAST [31] encourages Grad-CAM attention to fit the salient image regions detected by a saliency detector. Those methods often rely on pre-trained saliency detection. This implicitly assumes that salient regions are more likely to be discriminative regions. This assumption, however, does not always hold, especially for FGVR.", + "bbox": [ + 496, + 417, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_footnote", + "text": "2The weakness of existing SSL methods on FGVR can also be quantitatively demonstrated by their performance on retrieval tasks shown in Section 4.3. As will be seen from our experiments, using only the features learned from SSL and without any further supervision from the target data, existing SSL methods achieve very poor performance in the retrieval task, i.e., based on feature similarity to identify same-class images.", + "bbox": [ + 75, + 825, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "11393", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 89, + 169, + 104 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we first briefly review self-supervised contrastive learning [8] and gradient-weighted class activation mapping (GradCAM) [30] as preliminary knowledge. Then, we introduce the proposed approach.", + "bbox": [ + 76, + 114, + 468, + 176 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Preliminary", + "text_level": 1, + "bbox": [ + 76, + 183, + 207, + 200 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Self-Supervised Contrastive Learning. Given an image $I$ from a batch of samples, $x = t(I)$ and $x' = t'(I)$ are the two augmented views, where the $t$ and $t'$ are two different transformations sampled from a set of data augmentations $\\mathcal{T}$ . Then the views $x$ and $x'$ are used as the input of an encoder $f_{\\theta}$ to generate their feature representations $u = f_{\\theta}(x)$ and $u' = f_{\\theta}(x')$ . Finally, the projector heads $g_{\\theta}$ are used to map $u$ and $u'$ onto the embeddings $z = g_{\\theta}(u)$ and $z' = g_{\\theta}(u')$ . Let $(z,z')$ be embeddings from the same image and are used as a positive pair. Let $z_k$ be the embedding from a different image, and $(z,z_k)$ thus composes a negative pair. SimCLR [7] adopts a contrastive loss to maximize the agreement of positive pairs over those of negative pairs. The MoCo [1, 10, 18] family adopts the same contrastive loss but adds a queue to store the image embeddings to alleviate the memory cost due to the large batch size. Formally, the contrastive loss takes the following form", + "bbox": [ + 76, + 207, + 470, + 464 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {C L} = - \\log \\frac {\\exp \\left(z \\cdot z ^ {\\prime} / t\\right)}{\\sum_ {i = 0} ^ {Q} \\exp \\left(z \\cdot z _ {i} / t\\right)}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 156, + 470, + 468, + 508 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $t$ denotes a temperature parameter, and $z_{i}$ is the embedding in the queue.", + "bbox": [ + 76, + 515, + 468, + 544 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Gradient-weighted Class Activation Mapping (GradCAM) is a commonly used way to produce a visual explanation. It identifies the important image regions contributing to the prediction by using the gradient of the loss function with respect to the feature map or input images. In this paper, we consider the gradient calculated with respect to the last convolutional layer feature maps. Formally, we consider the feature map of the last convolutional layer denoting as $\\phi(I) \\in \\mathbb{R}^{H \\times W \\times C}$ , $H$ , $W$ and $C$ are the height, width and number of channels of the feature map, respectively. In standard C-way classification, the GradCAM is calculated by:", + "bbox": [ + 76, + 545, + 468, + 726 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n[ \\operatorname {G r a d - C A M} (\\hat {y}) ] _ {i, j} = R e L U \\left(\\alpha_ {\\hat {y}} ^ {\\top} [ \\phi (I) ] _ {i, j}\\right)\n$$\n", + "text_format": "latex", + "bbox": [ + 125, + 734, + 416, + 753 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nw h e r e, \\alpha_ {\\hat {y}} = \\frac {\\partial \\mathcal {L} _ {C E} (P (y) , \\hat {y})}{\\partial [ \\phi (I) ] _ {i , j}} \\in \\mathbb {R} ^ {C}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 127, + 755, + 468, + 789 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_{CE}(P(y),\\hat{y})$ is the cross-entropy loss measuring the compatibility between the posterior probability $P(y)$ and ground-truth class label $\\hat{y}^3$ . $[\\phi (I)]_{i,j}\\in \\mathbb{R}^C$ denotes the", + "bbox": [ + 76, + 796, + 468, + 843 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/231d2cba7317d476c69e6e182c64a116164aa6f2cdd507bbe4b6738f1faee171.jpg", + "image_caption": [ + "Figure 2. The overview of our method. At the structure level, it has the following components: 1)Encoder: MoCo-based contrastive learning is used to create the image-level representation. 2) GradCAM fitting branch, which is a convolutional layer with $k$ filters followed by a channel-wise max-out operator. 3) Inference: at the inference time, the prediction from GFB is used as a spatial attention mask, and it is used to replace the GAP operation by weighted average pooling to obtain the image representation." + ], + "image_footnote": [], + "bbox": [ + 504, + 90, + 890, + 345 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "feature vector located at the $(i,j)$ -th grid. Grad-CAM $(\\hat{y})$ denotes GradCAM for the $\\hat{y}$ -th class. $[\\mathrm{Grad - CAM}(\\hat{y})]_{i,j}$ refers to the importance value of the $(i,j)$ th spatial grid for predicting the $\\hat{y}$ -th class.", + "bbox": [ + 498, + 493, + 890, + 554 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Note that although GradCAM is commonly used for supervised classification problems, it can be readily extended to other problems by changing the corresponding loss function.", + "bbox": [ + 498, + 554, + 890, + 612 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Our Method: Learning Common Rationale", + "text_level": 1, + "bbox": [ + 500, + 623, + 867, + 638 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Figure 2 gives an overview of the proposed method. Our method is extremely simple: we merely add one GradCAM fitting branch (GFB) and fit the GradCAM generated from the CL loss at the training time. At the test time, we let this GFB predict (normalized) GradCAM and use the prediction as an attention mask to perform weighted average pooling over the convolutional feature map. The details about this framework are elaborated as follows.", + "bbox": [ + 498, + 646, + 890, + 765 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "GradCAM Calculation. For self-supervised learning, we do not have access to ground-truth class labels. Therefore, we use the contrastive learning loss $\\mathcal{L}_{CL}$ in Eq. 1 to replace $\\mathcal{L}_{CE}$ in Eq. 2:", + "bbox": [ + 498, + 767, + 890, + 828 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n[ \\mathbf {G} ] _ {i, j} = R e L U \\left(\\frac {\\partial \\mathcal {L} _ {C L} (\\psi (\\phi (I)))}{\\partial [ \\phi (I) ] _ {i , j}} ^ {\\top} [ \\phi (I) ] _ {i, j}\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 524, + 835, + 890, + 877 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\psi (\\cdot)$ denotes the feature extractor. Note that in the", + "bbox": [ + 500, + 885, + 890, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_footnote", + "text": "$^3\\mathcal{L}_{CE}(P(y),\\hat{y}) = \\log P(\\hat{y})$ for the multi-classification problem and the gradient of $\\log P(y)$ is proportional to the gradient of the corresponding logit. Those equivalence forms lead to the different definitions of GradCAM in the literature.", + "bbox": [ + 76, + 849, + 468, + 898 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "11394", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "original GradCAM, the GradCAM weight indicates how important each region contributes to classifying the image into the $y$ -th class. Similarly, the GradCAM weight from $\\mathcal{L}_{CL}$ indicates the contribution of each region to the instance discrimination task in the contrastive learning objective. From Figure 1, we can see that existing Contrastive Learning approaches learn a diverse set of visual patterns, and not all of them are relevant to the FGVR task.", + "bbox": [ + 75, + 90, + 468, + 210 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Architecture of the GFB. The structure of the GFB plays an important role in our method. We expect this branch has a limited fitting capability, such that the branch will not overfit the GradCAM but only capture the commonly occurring discriminative patterns, i.e., common rationales. Inspired by [33], we use a convolutional layer with $K$ filter and $1 \\times 1$ kernel size followed by the max-out operation [33] as the fitting branch. Formally, such a branch applies the following operation to the local feature $[\\phi(I)]_{i,j}$ at the $(i,j)$ -th grid of the feature map:", + "bbox": [ + 75, + 210, + 470, + 363 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nA _ {i, j} = \\max _ {k} \\left\\{\\mathbf {w} _ {k} ^ {\\top} [ \\phi (I) ] _ {i, j} \\right\\}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 179, + 369, + 468, + 391 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $A_{i,j}$ will be the predicted GradCAM weight at the $(i,j)$ -th grid and $\\mathbf{w}_k$ is the $k$ -th filter (projector) in the convolutional layer. Intuitively, the convolutional layer can be seen as a collection of $K$ detectors and the above operation can be understood as follows: each projection vector $\\mathbf{w}_k$ detects an object part $\\mathcal{P}_k$ ; the max-out operation takes the maximum of $K$ projections at a given location, which will result in a high value if any of the $K$ object parts are detected. Varying $K$ could adjust the size of the detector pool and influence the fitting capability.", + "bbox": [ + 75, + 398, + 468, + 547 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Training Loss. In addition to the contrastive learning loss, we require the GFB to produce a similar attention map as the one produced from the GradCAM of $\\mathcal{L}_{CL}$ . We follow [33] to normalize the GradCAM into a probability distribution and adopt KL divergence as the loss function.", + "bbox": [ + 75, + 549, + 468, + 623 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Formally, we normalize the GradCAM $\\mathcal{G}$ and $\\mathcal{A}$ via the softmax function:", + "bbox": [ + 75, + 625, + 468, + 654 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n[ \\bar {\\mathbf {G}} ] _ {i, j} = \\frac {\\exp \\left([ \\mathbf {G} ] _ {i , j} / \\tau\\right)}{\\sum_ {i = 1} ^ {H} \\sum_ {j = 1} ^ {W} \\exp \\left([ \\mathbf {G} ] _ {i , j} / \\tau\\right)},\n$$\n", + "text_format": "latex", + "bbox": [ + 143, + 657, + 400, + 696 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n[ \\bar {\\mathbf {A}} ] _ {i, j} = \\frac {\\exp \\left([ \\mathbf {A} ] _ {i , j} / \\tau\\right)}{\\sum_ {i = 1} ^ {H} \\sum_ {j = 1} ^ {W} \\exp \\left([ \\mathbf {A} ] _ {i , j} / \\tau\\right)}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 143, + 698, + 468, + 736 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $[\\cdot ]_{i,j}$ denotes the $i,j$ -th element of the feature map. $\\tau$ is an empirical temperature parameter and we set it to 0.4 here. Thus, the objective can be expressed as follows:", + "bbox": [ + 76, + 741, + 468, + 786 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {K L} = \\sum_ {i = 1} ^ {H} \\sum_ {j = 1} ^ {W} [ \\bar {\\mathbf {A}} ] _ {i, j} \\log \\frac {[ \\bar {\\mathbf {A}} ] _ {i , j}}{[ \\bar {\\mathbf {G}} ] _ {i , j}}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 161, + 792, + 468, + 835 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Thus, the final loss function taken on all images over an unlabelled dataset is shown as followings.", + "bbox": [ + 76, + 843, + 468, + 872 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\lambda \\mathcal {L} _ {C L} + \\nu \\mathcal {L} _ {K L}. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 200, + 881, + 468, + 896 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Inference. At the inference time, the GradCAM fitting branch will be firstly used to produce an attention mask, i.e., prediction of GradCAM. This attention mask is firstly normalized using $A_{i,j}' = \\frac{A_{i,j} - \\min(A)}{1e^{-7} + \\max(A)}$ . Then we use the normalized attention to perform weighted average pooling of features from the last-layer convolutional feature map. Formally, it calculates:", + "bbox": [ + 496, + 90, + 890, + 200 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {f} = \\sum_ {i, j} \\left[ A ^ {\\prime} \\right] _ {i, j} [ \\phi (I) ] _ {i, j} \\in \\mathbb {R} ^ {C}. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 593, + 208, + 890, + 239 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "f is used for the downstream tasks.", + "bbox": [ + 498, + 250, + 732, + 262 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Discussion. Our approach is inspired by the SAM method in [33]. However, there are several important differences:", + "bbox": [ + 498, + 263, + 890, + 294 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- SAM method was proposed for supervised FGVC under a low-data regime, while our approach is designed for self-supervised learning.", + "- Most importantly, our study discovers that for self-supervised feature learning, the best strategy to interact with the GFB and the feature learning branch is different from what has been discovered in [33]. Table 1 summarizes the main differences. As seen, unlike either SAM or SAM-bilinear, we do not introduce any interaction between the feature learning branch and the GradCAM fitting branch during training but allow them to perform weighted average pooling at the test stage. In fact, we find that applying cross-branch interaction at the training stage will undermine the feature learning process. This is because applying cross-branch interaction, e.g., using A to weighted pool features will prevent CL from exploring discriminative patterns, especially when A has not been properly learned.", + "- For multiple projections, SAM uses bilinear pooling to aggregate $\\mathbf{A}$ and the original feature map, resulting in high-dimensional feature representation. Our work performs max-out on multiple projections, resulting in a single attention mask for performing weighted average pooling. Consequently, we could achieve a significant reduction of the feature dimensionality." + ], + "bbox": [ + 517, + 301, + 890, + 712 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To make our study comprehensive, we also explore several variants as baseline approaches. From the comparison with those methods, the benefit of our design could become more evident. For comparison, we use the following architectures as baselines for self-supervised pre-training:", + "bbox": [ + 496, + 719, + 890, + 794 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "SAM-SSL: this baseline extends SAM by changing its objective function from cross-entropy to the contrastive loss in MoCo V2. It shares the same architecture as SAM [33], where a projection is used as the GFB, and GradCAM fitting is trained as an auxiliary task to contrastive learning.", + "bbox": [ + 496, + 795, + 890, + 869 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "SAM-SSL-Bilinear: this baseline extends SAM-bilinear by using the contrastive loss in MoCo V2. The cross-branch", + "bbox": [ + 496, + 869, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "11395", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/5f4542668fd93974d0295ebd2017e8ca2de6f8aae8c87de0d73f4026394d56df.jpg", + "table_caption": [ + "Table 1. Upper part: summary of the major difference between our method and SAM method [33]. Lower part: two variants that are also investigated in this work." + ], + "table_footnote": [], + "table_body": "
MethodGradCAM Fitting BranchCross-branch InteractionFeature DimensionLoss Function
traintest
SAM1 proj××CCrossEntropy
SAM-Bilinearmax[K projs]bilinear poolingbilinear poolingC*KCrossEntropy
Oursmax[K projs]×weighted average poolingCContrastive
Ours-DualPoolingmax[K projs]weighted average poolingweighted average poolingCContrastive
Ours-MultiTaskmax[K projs]××CContrastive
", + "bbox": [ + 78, + 128, + 911, + 247 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "interaction of SAM-SSL-Bilinear follows the original SAM-Bilinear method.", + "bbox": [ + 75, + 272, + 468, + 301 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Besides the above two extensions of the SAM methods, we also consider two variants of our method. The first is called Ours-MultiTask, which does not perform weighted average pooling at the test stage but merely uses GradCAM fitting as an auxiliary task. Another is called Ours-DualPooling, which performs weighted average pooling at both training and testing stages. Those two variants are summarized in Table 1.", + "bbox": [ + 75, + 301, + 468, + 422 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 436, + 209, + 453 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we will evaluate our proposed method on three widely used fine-grained visual datasets (Caltech-UCSD Birds (CUB-200-2011) [35], Stanford Cars [25] and FGVC-Aircraft [27]), and a large-scale fine-grained dataset (iNaturalist2019 [34]). Our experiments aim to understand the effectiveness and the components of the proposed algorithm.", + "bbox": [ + 75, + 460, + 468, + 583 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Datasets and Settings", + "text_level": 1, + "bbox": [ + 76, + 590, + 277, + 606 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets. CUB-200-2011 contains 11,788 images with 200 bird species, where 5994 images are used for training and 5794 images for testing. Stanford Cars contains 16,185 images with 196 categories, where 8144 images are for training and 8041 images for testing. FGVC-Aircraft contains 10,000 images with 100 categories, where 6667 images are for training, and 3333 images are for testing. iNaturalist2019 in its 2019 version contains 1,010 categories, with a combined training and validation set of 268,243 images. Note that fine-grained visual task focus on distinguishing similar subcategories within a super-category, while there are six super-categories in iNaturalist2019.", + "bbox": [ + 75, + 613, + 468, + 808 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implementation Details. We adopt the ResNet-50 [19] as the network backbone, which is initialized using ImageNet-trained weights, and build our method on top of MoCo v2 [8]. Therefore the SSL loss term is identical to MoCo v2. The momentum value and memory size are set similarly to MoCo v2, i.e., 0.999 and 65536, respectively.", + "bbox": [ + 75, + 810, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The projector head $g_{\\theta}$ in MoCo v2 is composed of two fully-connected layers with ReLU and a third linear layer with batch normalization (BN) [21]. The size of all three layers is $2048 \\times 2048 \\times 256$ . We set the mini-batch size as 128 and used an SGD optimizer with a learning rate of 0.03, a momentum of 0.9, and a weight decay of 0.0001. 100 epochs are used to train the feature extractor. The images from the four FGVR datasets are resized to $224 \\times 224$ pixels during training times. During testing time, images are firstly resized to 256 pixels and then are centered cropped to $224 \\times 224$ on these four FGVR datasets.", + "bbox": [ + 496, + 272, + 893, + 438 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/1d524e1ef944fee21646c78ee698bb7c0852eb9ebee7a653e1a57d765689f84e.jpg", + "image_caption": [ + "4.2. Evaluation Protocols", + "Figure 3. Comparison of ResNet-50, MoCo v2 and Ours on the retrieval rank-1 on the iNaturalist2019 dataset. \"Amphibians\", \"Birds\", \"Fungi\", \"Reptiles\", and \"Insects\" are the superclasses in iNaturalist2019." + ], + "image_footnote": [], + "bbox": [ + 501, + 481, + 893, + 633 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We evaluate the proposed method in two settings: linear probing and image retrieval. Linear probing is a commonly used evaluation protocol in SSL. In linear probing, the feature extractor learned from the SSL algorithm will be fixed and a linear classifier will be trained on top of the learned features. The classification performance of the linear classifier indicates the quality of the learned feature.", + "bbox": [ + 496, + 719, + 890, + 824 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Besides linear probing, we also use image retrieval (also equivalent to the nearest neighbor classification task) task to evaluate the learned features, which was also explored in the literature [6,22,23]. This task aims to find the images with the same category as query images based on the", + "bbox": [ + 496, + 825, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "11396", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/38927331c5a6f6ab1faa017e166bde401cc5e998bfc2367f029d4468f21c72d2.jpg", + "table_caption": [ + "Table 2. Classification and retrieval of our method evaluated on the CUB-200-2011, Stanford Cars and FGVC Aircraft datasets. \"ResNet-50\" represents pre-training in the ImageNet dataset [12] in a supervised manner, then freezing the ResNet-50 backbone and only optimizing the supervised linear classifier in the classification task. We report the Top 1 and Top 5 (in %) on the classification task, rank-1, rank-5, and mAP (in %) on the retrieval task. 100, 50, and 20 are the three different label proportions (in %) in the classification task." + ], + "table_footnote": [], + "table_body": "
DatasetMethodClassificationRetrieval
Top 1/Top 5(100)Top 1/Top 5(50)Top 1/Top 5(20)rank-1rank-5mAP
CUB-200-2011ResNet-5068.17/90.4258.99/85.9046.54/77.0910.6529.325.09
MoCo v268.30/90.8560.96/87.0046.91/76.5917.0741.468.13
Ours71.31/92.0366.52/90.0655.33/83.5249.6975.2324.01
Stanford CarsResNet-5057.41/83.5546.23/74.3131.19/58.674.9116.982.34
MoCo v258.43/84.8550.17/77.3835.14/64.1010.9429.573.12
Ours60.75/86.4453.87/81.7240.88/69.1834.5660.758.87
FGVC AircraftResNet-5047.38/74.7337.83/67.1228.20/54.735.1614.222.61
MoCo v252.54/80.7445.52/73.8535.17/65.0819.3839.906.30
Ours55.87/84.7348.22/77.1438.55/68.5334.3361.0915.43
", + "bbox": [ + 81, + 155, + 888, + 337 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "learned feature. Note that, unlike linear probing, the image retrieval task does not involve a large amount of labeled data – which could be used to suppress the less relevant features. In this sense, succeeding in the image retrieval task imposes higher feature quality requirements. Moreover, image retrieval is a practically useful task, and unsupervised feature learning is an attractive solution to image retrieval since the whole retrieval system can be built without any human annotation and intervention. For the retrieval task, we use rank-1, rank-5, and mAP as evaluation metrics.", + "bbox": [ + 75, + 361, + 472, + 512 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Main Results", + "text_level": 1, + "bbox": [ + 76, + 525, + 217, + 540 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The Effectiveness of the Proposed Method. Our method is based on MoCo v2. We first compare our result against MoCo v2 to examine the performance gain. The results are reported in Table 2 and Figure 3.", + "bbox": [ + 75, + 550, + 468, + 611 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "From Table 2, we can see that our method has led to a significant improvement over MoCo v2. It achieves $71.31\\%$ top-1 accuracy and $92.03\\%$ top-5 accuracy on the CUB-200-2011 dataset with $100\\%$ label proportions, which is a $3.01\\%$ improvement on top-1 and $1.18\\%$ improvement on top-5 over MoCo v2. Similarly, significant improvement can also be found on the Stanford Cars and FGVC Aircraft datasets. This demonstrates that our methods improve the quality of the feature representations learned from the original MoCo v2. Notably, with the label proportions reduced from $100\\%$ to $20\\%$ , there is generally a better improvement in the performance of the proposed method, which demonstrates that the proposed method learns less noisy features, so that training with fewer data can generalize better.", + "bbox": [ + 75, + 612, + 470, + 838 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The advantage of the proposed method becomes more pronounced when evaluating the image retrieval task. As seen from Table 2, our method leads to a significant boost in performance on all datasets. Specifically, the rank-1,", + "bbox": [ + 75, + 839, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "rank-5 and mAP of ours ( $K = 32$ ) are $49.69\\%$ , $75.23\\%$ , and $24.01\\%$ , respectively on the CUB-200-2011 dataset, which is $32.62\\%$ , $33.77\\%$ , and $15.88\\%$ higher than the method of MoCo v2. Similar improvement can also be observed on the Stanford Cars and FGVC Aircraft datasets. On the large-scale fine-grained dataset, i.e., iNaturalist2019, our method also performs better than MoCo v2 shown in Figure 3. These indicate the proposed method is particularly good for retrieval tasks, which might be due to its ability to filter out less relevant patterns.", + "bbox": [ + 496, + 361, + 893, + 513 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Comparison with Other SSL Frameworks. In addition to the comparison on MoCo v2, we also compare the proposed method against other commonly used SSL approaches. We report the Top-1 accuracy, the running time, and the peak memory with two different batch sizes (32 & 128). The results are shown in Table 3. All methods are run on 4 V100 GPUs, each with 32G memory. We report the training speed, GPU memory usage, and performance. For classification performance, the blue marks mean the best classification results, and the green marks mean the second-best classification results. It is clear to see that our method achieves the best Top-1 performance on the CUB-200-2011, Stanford Cars, and FGVC Aircraft datasets. Also, when the GPU resources are limited, e.g., only 1 V100 GPU is available, the proposed method reduces the batch size but still remains a competitive classification performance compared to other SSL methods. Regarding training speed and GPU memory usage, the proposed method has the same running time as MoCo v2 and SimSiam, slightly more peak memory than SimSiam, but less peak memory, and quicker running time than SimCLR and BYOL. Although DINO uses the least training time and GPU memory usage, their performances are also the worst compared to ours and other self-supervised learning methods. Barlow Twins and VICReg", + "bbox": [ + 496, + 523, + 893, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "11397", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/08918a9edbff3881e2b78b51095d6db4f567f8b3eb9751bf2b2f06296ec98aa9.jpg", + "table_caption": [ + "Table 3. Compared to other state-of-the-art self-supervised learning frameworks with Top 1 accuracy on the CUB-200-2011, Stanford Cars and FGVC Aircraft datasets; running time and peak memory on the CUB-200-2011 dataset. The training time is measured on 4 Tesla V100 GPUs with 100 epochs, and the peak memory is calculated on a single GPU. Top 1 accuracy (\\%) is reported on linear classification with the frozen representations of their feature extractor. For fairness, all following models use the ResNet-50 as the network backbone and initialize the ResNet-50 architecture with ImageNet-trained weights. blue=best, green=second best." + ], + "table_footnote": [ + "Due to computational constraints, we are unable to evaluate on the batch size of 4096 as used in the original paper; we leave this for future work." + ], + "table_body": "
MethodBatch SizeTop 1(CUB)Top 1(Cars)Top 1(Aircraft)time(CUB)GPU Memory(CUB)
Supervised-81.3491.0287.13--
DINO [6]32/12812.37/16.669.27/10.518.52/12.931.5h/1.5h4.9G/8.4G
SimCLR [7]*32/12833.49/38.3944.31/49.4140.56/45.222.5h/2.5h7.1G/23.8G
BYOL [16]*32/12836.64/39.2743.66/45.2134.90/37.624.0h/4.0h7.4G/24.6G
SimSiam [9]32/12835.82/39.9756.87/58.8941.59/43.062.0h/2.0h4.4G/8.9G
MoCo v2 [8]32/12868.03/68.3052.61/58.4342.51/52.542.0h/2.0h6.1G/10.3G
BarlowTwins [40]32/12828.58/33.4523.34/31.9128.35/34.771.5h/1.5h7.0G/8.9G
VICReg [4]32/12830.07/37.7819.29/30.8029.97/36.001.0h/1.0h7.0G/9.0G
Ours32/12870.43 /71.3156.90/60.7546.92/55.872.0h/2.0h6.1G/10.3G
BYOL+Ours*32/12845.79/51.2048.53 /50.6440.08/45.944.0h/4.0h7.4G/24.6G
", + "bbox": [ + 78, + 169, + 906, + 340 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "have a quicker running time and less GPU memory than our proposed method with a batch size of 128, but their performances are much worse than ours.", + "bbox": [ + 75, + 380, + 470, + 425 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Our method also can be implemented with other self-supervised learning methods, e.g., BYOL, referring to \"BYOL+Ours\" presented in Table 3. As we can see, our method applied to the BYOL objective is consistently superior to the baseline of BYOL on three fine-grained datasets.", + "bbox": [ + 75, + 426, + 470, + 503 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Comparison with Alternative Solutions", + "text_level": 1, + "bbox": [ + 76, + 513, + 413, + 530 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Our method is featured by its capability of discovering the key discriminative regions, which is vital for FGVR. In this section, we compared the proposed method with nine alternative solutions to take object localization into account. The first is to simply use a bilinear network [26] for MoCo V2. Specifically, we follow the similar bilinear structure as in [33], which implicitly learns $K$ parts and aggregates features from those $K$ parts, and we set $K = 32$ to make a fair comparison to us (since we use 32 projections). We still use MoCo v2 as the SSL framework and denote this method MoCo v2 -Bilinear. The second and third are the methods of SAM-SSL and SAM-SSL-Bilinear introduced in Section 3.2 since our method is extended from the self-boosting attention mechanism (SAM) proposed in [33]. The fourth and fifth are the two variants considered in Section 3.2. The other four comparing methods are the very recently localization-based self-supervised methods, DiLo [42], CVSA [38], LEWEL [20], and ContrastiveCrop [29]. DiLo uses a copy-and-pasting approach as a kind of augmentation to create an image with a different background. The work of CVSA targets a similar problem as ours. They exploit self-supervised fine-grained contrastive learning via cross-view saliency alignment to crops and swaps saliency regions of images. LEWEL adap", + "bbox": [ + 73, + 537, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "tively aggregates spatial information of features using spatial aggregation operation between feature map and alignment map to guide the feature learning better. The work of ContrastiveCrop is based on the idea of using attention to guide image cropping, which localizes the object and improves the data augmentation for self-supervised learning.", + "bbox": [ + 496, + 380, + 893, + 472 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The comparison to those nine alternatives is shown in Table 4. As seen, by comparing the SAM-SSL and SAM-SSL-Bilinear, we observe that the proposed method can lead to overall better performance, achieving a significant boost on some datasets. Occasionally, SAM-SSL-Bilinear ( $K = 32$ ) can achieve comparable performance as ours, but at the cost of using a much higher feature dimensionality. This clearly shows the advantage of the proposed scheme over the scheme in [33]. Furthermore, our method and combined with ContrastiveCrop (i.e., ours+ContrastiveCrop) with the lowest feature dimensions but achieve the best Top 1 and rank-1 performance on the CUB-200-2011, Stanford Cars and FGVC Aircraft datasets, compared to those nine alternatives. Also, compared with the other localization-aware SSL methods, our method shows a clear advantage, especially for the retrieval task, e.g., ours vs. LEWEL. Finally, we find that the variant of our method does not produce a good performance. For example, when applying weighted average pooling at both training and testing, i.e., Ours-DualPooling, will make the feature learning fail completely, and the representations will collapse. On the other hand, not performing cross-branch interaction, i.e., Ours-MultiTask, does not bring too much improvement over the MoCo v2 baseline.", + "bbox": [ + 496, + 473, + 893, + 834 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.5. The Impact of Number of Projections", + "text_level": 1, + "bbox": [ + 500, + 845, + 823, + 863 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To explore the impact of the number of linear projections in our method, we conduct experiments with the different", + "bbox": [ + 498, + 869, + 893, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "11398", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/655ceca78ed0c6c7dce0291b61ec5a2ae4f4136ca86f317b4b701ab46d420b01.jpg", + "table_caption": [ + "Table 4. The linear Top 1 (%) and retrieval rank-1 (%) performance comparisons of recent alternative solutions and Ours on the CUB-200-2011, Stanford Cars and FGVC Aircraft datasets. blue=best, green=second best. Collapse means the model fails to produce meaningful performance." + ], + "table_footnote": [], + "table_body": "
MethodFeatureClassificationRetrieval
DimensionCUBCarsAircraftCUBCarsAircraft
MoCo v2 [8]C68.3058.4352.5417.0710.9419.38
MoCo v2 -BilinearC*K68.4458.0653.0141.2730.8930.80
SAM-SSLC68.5958.4952.9718.3814.2621.72
SAM-SSL-BilinearC*K71.5659.1255.1244.2035.3832.10
DiLo [38,42]C64.14-----
CVSA [38]C65.02-----
LEWEL [20]C*K69.2759.0254.3319.2312.0120.67
ContrastiveCrop [29]C68.8261.6654.4018.7113.6120.88
Ours-DualPoolingCcollapsecollapse
Ours-MultiTaskC68.5658.5552.8717.6213.9822.23
OursC71.3160.7555.8749.6934.5634.33
Ours+ContrastiveCropC72.8463.7156.0849.3633.5534.95
", + "bbox": [ + 140, + 141, + 831, + 369 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b8dedb35578b9e5b62f5371d0e922e8f582a9ad9fa9b59c80e7721b38a0abe1f.jpg", + "image_caption": [ + "Figure 4. Comparison of MoCo v2 (the blue plot) baseline with our method (the red plot) w.r.t. $K$ on the CUB-200-2011." + ], + "image_footnote": [], + "bbox": [ + 125, + 391, + 421, + 556 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "numbers of $K$ . Figure 4 shows the retrieval results of rank-1 w.r.t. eight different projections on the fine-grained dataset CUB-200-2011. As we can see, with the increase of linear projections $K$ , the rank-1 gradually increases—the final rank-1 peaks at $49.69\\%$ with $K$ around 32. After $K$ reaches 64, the performance decreases. When the number of projections is very large, the combination of $K$ -part detectors becomes spurious and overfits the correlated pattern, thus resulting in a drop in performance. From the curve, we can also see that choosing any value between 4 and 64 can lead to similar performance. So our method is not very sensitive to $K$ once it falls into a reasonable range.", + "bbox": [ + 75, + 623, + 468, + 805 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.6. Alternative Structure for GFB", + "text_level": 1, + "bbox": [ + 76, + 816, + 346, + 830 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this section, we investigate alternative designs for GFB. In particular, we consider using a two-layer (with 32 as the intermediate feature dimension) multi-layer perception (MLP) to replace the maximized projections in the pro", + "bbox": [ + 75, + 839, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/9b7a7d37ca4c3705830754877dd394516525526258b6a343159a3a30a6e56eef.jpg", + "table_caption": [ + "Table 5. Retrieval performance (%) of our methods and using MLP as the alternative GFB branch. The evaluation is on the Stanford Cars dataset." + ], + "table_footnote": [], + "table_body": "
DatasetArchitecturerank-1rank-5mAP
CarsOurs34.5660.758.87
MLP25.5750.915.92
", + "bbox": [ + 521, + 443, + 874, + 497 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "posed method. Compared with our GFB structure, an MLP has better fitting capacity due to the extra linear layer. We conduct experiments on the Stanford Cars dataset, and the result is shown in Table 5. We find that the performance dramatically decreases when using MLP. This demonstrates the importance of our GFB module design.", + "bbox": [ + 496, + 522, + 890, + 613 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion, Further Results (Appendix), Limitation and Future Work", + "text_level": 1, + "bbox": [ + 498, + 630, + 890, + 664 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we introduce a simple-but-effective way of learning an additional screening mechanism to self-supervised feature learning for fine-grained visual recognition. The idea is to identify discriminative clues commonly seen across instances and classes by fitting the GradCAM of the SSL loss with a fitting-capability-limited branch. Our method achieves state-of-the-art in the classification task and is particularly pronounced in retrieval tasks on fine-grained visual recognition problems. More experimental results, including adopting our method for non-fine-grained visual recognition problems, and visualizing each projection in the GFB, can be found in the Appendix. So far, the proposed method seems to be most effective for FGVR, which could be a limitation and we plan to extend the applicability of the proposed method in our future work.", + "bbox": [ + 496, + 674, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "11399", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Soroush Abbasi Koohpayegani, Ajinkya Tejankar, and Hamed Piriaviash. Compress: Self-supervised learning by compressing representations. Advances in Neural Information Processing Systems, 33:12980-12992, 2020. 3", + "[2] Philip Bachman, R Devon Hjelm, and William Buchwalter. Learning representations by maximizing mutual information across views. 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Advances in Neural Information Processing Systems, 34:2543-2555, 2021. 2" + ], + "bbox": [ + 501, + 90, + 892, + 400 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "11401", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Learning Common Rationale To Improve Self-Supervised Representation for Fine-Grained Visual Recognition Problems/f542c58d-1024-4f6c-81dd-99d6fba543cf_model.json b/2023/Learning Common Rationale To Improve Self-Supervised Representation for Fine-Grained Visual Recognition Problems/f542c58d-1024-4f6c-81dd-99d6fba543cf_model.json new file mode 100644 index 0000000000000000000000000000000000000000..cb417d29e1613de8bbd75ea88468b5dc8071cbeb --- /dev/null +++ b/2023/Learning Common Rationale To Improve Self-Supervised Representation for Fine-Grained Visual Recognition Problems/f542c58d-1024-4f6c-81dd-99d6fba543cf_model.json @@ -0,0 +1,1947 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.102, + 0.13, + 0.872, + 0.177 + ], + "angle": 0, + "content": "Learning Common Rationale to Improve Self-Supervised Representation for Fine-Grained Visual Recognition Problems" + }, + { + "type": "text", + "bbox": [ + 0.224, + 0.204, + 0.344, + 0.222 + ], + "angle": 0, + "content": "Yangyang Shu" + }, + { + "type": "text", + "bbox": [ + 0.4, + 0.204, + 0.581, + 0.222 + ], + "angle": 0, + "content": "Anton van den Hengel" + }, + { + "type": "text", + "bbox": [ + 0.638, + 0.204, + 0.753, + 0.222 + ], + "angle": 0, + "content": "Lingqiao Liu*" + }, + { + "type": "text", + "bbox": [ + 0.258, + 0.247, + 0.713, + 0.265 + ], + "angle": 0, + "content": "School of Computer Science, The University of Adelaide" + }, + { + "type": "text", + "bbox": [ + 0.21, + 0.268, + 0.756, + 0.283 + ], + "angle": 0, + "content": "{yangyang.shu,anton.vandenhengel,lingqiao.liu}@adelaide.edu.au" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.317, + 0.314, + 0.333 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.349, + 0.474, + 0.742 + ], + "angle": 0, + "content": "Self-supervised learning (SSL) strategies have demonstrated remarkable performance in various recognition tasks. However, both our preliminary investigation and recent studies suggest that they may be less effective in learning representations for fine-grained visual recognition (FGVR) since many features helpful for optimizing SSL objectives are not suitable for characterizing the subtle differences in FGVR. To overcome this issue, we propose learning an additional screening mechanism to identify discriminative clues commonly seen across instances and classes, dubbed as common rationales in this paper. Intuitively, common rationales tend to correspond to the discriminative patterns from the key parts of foreground objects. We show that a common rationale detector can be learned by simply exploiting the GradCAM induced from the SSL objective without using any pre-trained object parts or saliency detectors, making it seamlessly to be integrated with the existing SSL process. Specifically, we fit the GradCAM with a branch with limited fitting capacity, which allows the branch to capture the common rationales and discard the less common discriminative patterns. At the test stage, the branch generates a set of spatial weights to selectively aggregate features representing an instance. Extensive experimental results on four visual tasks demonstrate that the proposed method can lead to a significant improvement in different evaluation settings.\\(^{1}\\)" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.771, + 0.21, + 0.787 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.47, + 0.843 + ], + "angle": 0, + "content": "Recently, self-supervised representations Learning (SSL) has been shown to be effective for transferring the learned representations to different downstream" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.317, + 0.892, + 0.513 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.524, + 0.895, + 0.61 + ], + "angle": 0, + "content": "Figure 1. GradCAM [30] visualization for MoCo v2 [18], VICReg [4] and our method on the CUB-200-2011, Stanford Cars and FGVC Aircraft datasets. Compared with the existing method MoCo v2 and VICReg, which are prone to be distracted by background patterns, our method can identify features from the foreground and potentially the key parts of the object." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.641, + 0.895, + 0.763 + ], + "angle": 0, + "content": "tasks [2, 4, 5, 14, 18]. Methods such as contrastive learning [7, 9, 16, 18] have demonstrated state-of-the-art feature learning capability and have been intensively studied recently. However, recent studies [11] suggest that contrastive learning may have a \"coarse-grained bias\" and could be less effective for fine-grained classification problems whose goal is to distinguish visually similar subcategories of objects under the basic-level category." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.895, + 0.903 + ], + "angle": 0, + "content": "This phenomenon is rooted in fine-grained visual recognition (FGVR) properties and the training objective of SSL. SSL tries to minimize a pretext task, e.g., contrastive learning minimizes the distance between same-instance features while maximizing the distance among different-instance features, and any visual patterns that could contribute to loss minimization will be learned. On the other hand, the discriminative patterns for FGVR can be subtle. It is more likely to reside on key object parts. Thus, the feature learned" + }, + { + "type": "page_footnote", + "bbox": [ + 0.076, + 0.851, + 0.468, + 0.876 + ], + "angle": 0, + "content": "*Corresponding author. This work is supported by the Centre for Augmented Reasoning." + }, + { + "type": "page_footnote", + "bbox": [ + 0.077, + 0.876, + 0.468, + 0.9 + ], + "angle": 0, + "content": "1The source code will be publicly available at: https://github. com/GANPerf/LCR" + }, + { + "type": "list", + "bbox": [ + 0.076, + 0.851, + 0.468, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "11392" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.473, + 0.272 + ], + "angle": 0, + "content": "from SSL may not necessarily be useful for FGVR. Figure 1 shows our investigation of this issue. As seen, the existing SSL paradigms, such as MoCo [18] and VICReg [4] are prone to learn patterns from irrelevant regions2. Existing works [31, 38, 42] usually handle this issue by recoursing to pre-trained object part detectors or saliency detectors to regularize SSL using patterns from valid regions to achieve the training objective. However, both the part detectors and saliency detectors could restrict the applicability of SSL for FGVR since part detectors are trained from human annotations, and the saliency regions are not always coincident with the discriminative regions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.273, + 0.473, + 0.605 + ], + "angle": 0, + "content": "Therefore, this work aims to directly solve the problem from the target domain data. Specifically, we propose to learn an additional screening mechanism in addition to the contrastive learning process. The purpose of the screening mechanism is to filter out the patterns that might contribute to SSL objectives but are irrelevant to FGVR. Somehow surprisingly, we find that such a screening mechanism can be learned from the GradCAM [30] of the SSL loss via an extremely simple method. The whole process can be described as a \"fitting and masking\" procedure: At the training time, we use an additional branch with limited fitting capacity (see more discussion about it in Section 3.2) to fit the GradCAM calculated from the SSL objective. At the testing time, we apply this additional branch to predict an attention mask to perform weighted average pooling for the final presentation. The motivation for such a design is that the GradCAM fitting branch tends to characterize the discriminative patterns that commonly occur across samples due to its limited fitting capacity, and those common patterns, dubbed common rationale in this paper, are more likely corresponding to the discriminative clues from key object parts or at least foreground regions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.606, + 0.473, + 0.818 + ], + "angle": 0, + "content": "We implement our method based on MoCo v2 [8], one of the state-of-the-art approaches in unsupervised feature learning, which also produces the best performance on FGVR in our setting. Our implementation uses the training objective of MoCo v2 to learn feature representations and derive the GradCAM. Through extensive experiments, we show that our approach can significantly boost the quality of the learned feature. For example, when evaluating the learned feature for retrieval tasks, our method achieves \\(49.69\\%\\) on the CUB-200-2011 retrieval task, which is \\(32.62\\%\\) higher than our baseline method (MoCo v2 [8]). In the linear evaluation phase, the proposed method achieves new state-of-the-art \\(71.31\\%\\) Top-1 accuracy, which is \\(3.01\\%\\) higher than MoCo v2." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.09, + 0.642, + 0.107 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.146, + 0.895, + 0.389 + ], + "angle": 0, + "content": "Self-supervised learning aims to learn feature representation from unlabeled data. It relies on a pretext task whose supervision could be derived from the data itself, e.g., image colorization [41], image inpainting [28], and rotation [24] prediction. Contrastive learning is recently identified as a promising framework for self-supervised learning and has been extensively studied [5, 7, 10, 13, 18, 36]. Despite the subtle differences, most contrastive learning approaches [15, 37, 43] try to minimize the distance between different views of the same images and push away the views of different images. The representative methods are SimCLR [7] and MoCo [18]. Besides contrastively learning, consistency-based approaches, such as BYOL [16], SimSiam [9] and masking-and-prediction-based approaches, such as MAE [17], BEiT [3], and ADIOS [32] are also proven effective for SSL." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.418, + 0.895, + 0.904 + ], + "angle": 0, + "content": "Improving SSL via Better Region Localization. A pipeline to improve the distinguishing ability is to design better data augmentations of SSL. Three such methods were recently proposed: DiLo [42], SAGA [39], and Contrastive-Crop [29]. DiLo uses a copy-and-pasting approach as a kind of augmentation to create an image with a different background. In such a way, the proposed method distills localization via learning invariance against backgrounds and improves the ability of SSL models to localize foreground objects. SAGA adopts self-augmentation with a guided attention strategy to augment input images based on predictive attention. In their method, an attention-guided crop is used to enhance the robustness of feature representation. ContrastiveCrop shows a better crop as an augmentation to generate better views in SSL and keep the semantic information of an image. All of these works locate the object by improving the data augmentations for SSL. In this work, our method is adaptive to locate the key regions for self-supervised learning without needing external augmentations. Another family of approaches tries to target the same problem as ours: making the learned feature capture more of the foreground region. CVSA [38] proposed a cross-view saliency alignment framework that first crops and swaps saliency regions of images as a novel view generation. Then it adopts a cross-view saliency alignment loss to encourage the model to learn features from foreground objects. CAST [31] encourages Grad-CAM attention to fit the salient image regions detected by a saliency detector. Those methods often rely on pre-trained saliency detection. This implicitly assumes that salient regions are more likely to be discriminative regions. This assumption, however, does not always hold, especially for FGVR." + }, + { + "type": "page_footnote", + "bbox": [ + 0.076, + 0.827, + 0.473, + 0.903 + ], + "angle": 0, + "content": "2The weakness of existing SSL methods on FGVR can also be quantitatively demonstrated by their performance on retrieval tasks shown in Section 4.3. As will be seen from our experiments, using only the features learned from SSL and without any further supervision from the target data, existing SSL methods achieve very poor performance in the retrieval task, i.e., based on feature similarity to identify same-class images." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "11393" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.09, + 0.17, + 0.105 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.115, + 0.47, + 0.177 + ], + "angle": 0, + "content": "In this section, we first briefly review self-supervised contrastive learning [8] and gradient-weighted class activation mapping (GradCAM) [30] as preliminary knowledge. Then, we introduce the proposed approach." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.184, + 0.208, + 0.201 + ], + "angle": 0, + "content": "3.1. Preliminary" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.208, + 0.471, + 0.465 + ], + "angle": 0, + "content": "Self-Supervised Contrastive Learning. Given an image \\(I\\) from a batch of samples, \\(x = t(I)\\) and \\(x' = t'(I)\\) are the two augmented views, where the \\(t\\) and \\(t'\\) are two different transformations sampled from a set of data augmentations \\(\\mathcal{T}\\). Then the views \\(x\\) and \\(x'\\) are used as the input of an encoder \\(f_{\\theta}\\) to generate their feature representations \\(u = f_{\\theta}(x)\\) and \\(u' = f_{\\theta}(x')\\). Finally, the projector heads \\(g_{\\theta}\\) are used to map \\(u\\) and \\(u'\\) onto the embeddings \\(z = g_{\\theta}(u)\\) and \\(z' = g_{\\theta}(u')\\). Let \\((z,z')\\) be embeddings from the same image and are used as a positive pair. Let \\(z_k\\) be the embedding from a different image, and \\((z,z_k)\\) thus composes a negative pair. SimCLR [7] adopts a contrastive loss to maximize the agreement of positive pairs over those of negative pairs. The MoCo [1, 10, 18] family adopts the same contrastive loss but adds a queue to store the image embeddings to alleviate the memory cost due to the large batch size. Formally, the contrastive loss takes the following form" + }, + { + "type": "equation", + "bbox": [ + 0.157, + 0.472, + 0.47, + 0.509 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {C L} = - \\log \\frac {\\exp \\left(z \\cdot z ^ {\\prime} / t\\right)}{\\sum_ {i = 0} ^ {Q} \\exp \\left(z \\cdot z _ {i} / t\\right)}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.516, + 0.469, + 0.545 + ], + "angle": 0, + "content": "where \\(t\\) denotes a temperature parameter, and \\(z_{i}\\) is the embedding in the queue." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.546, + 0.47, + 0.727 + ], + "angle": 0, + "content": "Gradient-weighted Class Activation Mapping (GradCAM) is a commonly used way to produce a visual explanation. It identifies the important image regions contributing to the prediction by using the gradient of the loss function with respect to the feature map or input images. In this paper, we consider the gradient calculated with respect to the last convolutional layer feature maps. Formally, we consider the feature map of the last convolutional layer denoting as \\(\\phi(I) \\in \\mathbb{R}^{H \\times W \\times C}\\), \\(H\\), \\(W\\) and \\(C\\) are the height, width and number of channels of the feature map, respectively. In standard C-way classification, the GradCAM is calculated by:" + }, + { + "type": "equation", + "bbox": [ + 0.127, + 0.735, + 0.418, + 0.755 + ], + "angle": 0, + "content": "\\[\n[ \\operatorname {G r a d - C A M} (\\hat {y}) ] _ {i, j} = R e L U \\left(\\alpha_ {\\hat {y}} ^ {\\top} [ \\phi (I) ] _ {i, j}\\right)\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.128, + 0.756, + 0.469, + 0.79 + ], + "angle": 0, + "content": "\\[\nw h e r e, \\alpha_ {\\hat {y}} = \\frac {\\partial \\mathcal {L} _ {C E} (P (y) , \\hat {y})}{\\partial [ \\phi (I) ] _ {i , j}} \\in \\mathbb {R} ^ {C}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.797, + 0.469, + 0.844 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_{CE}(P(y),\\hat{y})\\) is the cross-entropy loss measuring the compatibility between the posterior probability \\(P(y)\\) and ground-truth class label \\(\\hat{y}^3\\). \\([\\phi (I)]_{i,j}\\in \\mathbb{R}^C\\) denotes the" + }, + { + "type": "page_footnote", + "bbox": [ + 0.077, + 0.85, + 0.469, + 0.9 + ], + "angle": 0, + "content": "\\(^3\\mathcal{L}_{CE}(P(y),\\hat{y}) = \\log P(\\hat{y})\\) for the multi-classification problem and the gradient of \\(\\log P(y)\\) is proportional to the gradient of the corresponding logit. Those equivalence forms lead to the different definitions of GradCAM in the literature." + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.091, + 0.891, + 0.346 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.359, + 0.892, + 0.47 + ], + "angle": 0, + "content": "Figure 2. The overview of our method. At the structure level, it has the following components: 1)Encoder: MoCo-based contrastive learning is used to create the image-level representation. 2) GradCAM fitting branch, which is a convolutional layer with \\( k \\) filters followed by a channel-wise max-out operator. 3) Inference: at the inference time, the prediction from GFB is used as a spatial attention mask, and it is used to replace the GAP operation by weighted average pooling to obtain the image representation." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.494, + 0.891, + 0.555 + ], + "angle": 0, + "content": "feature vector located at the \\((i,j)\\)-th grid. Grad-CAM \\((\\hat{y})\\) denotes GradCAM for the \\(\\hat{y}\\)-th class. \\([\\mathrm{Grad - CAM}(\\hat{y})]_{i,j}\\) refers to the importance value of the \\((i,j)\\)th spatial grid for predicting the \\(\\hat{y}\\)-th class." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.555, + 0.892, + 0.613 + ], + "angle": 0, + "content": "Note that although GradCAM is commonly used for supervised classification problems, it can be readily extended to other problems by changing the corresponding loss function." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.624, + 0.869, + 0.64 + ], + "angle": 0, + "content": "3.2. Our Method: Learning Common Rationale" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.647, + 0.892, + 0.766 + ], + "angle": 0, + "content": "Figure 2 gives an overview of the proposed method. Our method is extremely simple: we merely add one GradCAM fitting branch (GFB) and fit the GradCAM generated from the CL loss at the training time. At the test time, we let this GFB predict (normalized) GradCAM and use the prediction as an attention mask to perform weighted average pooling over the convolutional feature map. The details about this framework are elaborated as follows." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.768, + 0.891, + 0.829 + ], + "angle": 0, + "content": "GradCAM Calculation. For self-supervised learning, we do not have access to ground-truth class labels. Therefore, we use the contrastive learning loss \\(\\mathcal{L}_{CL}\\) in Eq. 1 to replace \\(\\mathcal{L}_{CE}\\) in Eq. 2:" + }, + { + "type": "equation", + "bbox": [ + 0.525, + 0.837, + 0.892, + 0.878 + ], + "angle": 0, + "content": "\\[\n[ \\mathbf {G} ] _ {i, j} = R e L U \\left(\\frac {\\partial \\mathcal {L} _ {C L} (\\psi (\\phi (I)))}{\\partial [ \\phi (I) ] _ {i , j}} ^ {\\top} [ \\phi (I) ] _ {i, j}\\right), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.886, + 0.891, + 0.902 + ], + "angle": 0, + "content": "where \\(\\psi (\\cdot)\\) denotes the feature extractor. Note that in the" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11394" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.211 + ], + "angle": 0, + "content": "original GradCAM, the GradCAM weight indicates how important each region contributes to classifying the image into the \\(y\\)-th class. Similarly, the GradCAM weight from \\(\\mathcal{L}_{CL}\\) indicates the contribution of each region to the instance discrimination task in the contrastive learning objective. From Figure 1, we can see that existing Contrastive Learning approaches learn a diverse set of visual patterns, and not all of them are relevant to the FGVR task." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.212, + 0.471, + 0.364 + ], + "angle": 0, + "content": "Architecture of the GFB. The structure of the GFB plays an important role in our method. We expect this branch has a limited fitting capability, such that the branch will not overfit the GradCAM but only capture the commonly occurring discriminative patterns, i.e., common rationales. Inspired by [33], we use a convolutional layer with \\( K \\) filter and \\( 1 \\times 1 \\) kernel size followed by the max-out operation [33] as the fitting branch. Formally, such a branch applies the following operation to the local feature \\( [\\phi(I)]_{i,j} \\) at the \\( (i,j) \\)-th grid of the feature map:" + }, + { + "type": "equation", + "bbox": [ + 0.18, + 0.37, + 0.47, + 0.392 + ], + "angle": 0, + "content": "\\[\nA _ {i, j} = \\max _ {k} \\left\\{\\mathbf {w} _ {k} ^ {\\top} [ \\phi (I) ] _ {i, j} \\right\\}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.399, + 0.47, + 0.549 + ], + "angle": 0, + "content": "where \\( A_{i,j} \\) will be the predicted GradCAM weight at the \\( (i,j) \\)-th grid and \\( \\mathbf{w}_k \\) is the \\( k \\)-th filter (projector) in the convolutional layer. Intuitively, the convolutional layer can be seen as a collection of \\( K \\) detectors and the above operation can be understood as follows: each projection vector \\( \\mathbf{w}_k \\) detects an object part \\( \\mathcal{P}_k \\); the max-out operation takes the maximum of \\( K \\) projections at a given location, which will result in a high value if any of the \\( K \\) object parts are detected. Varying \\( K \\) could adjust the size of the detector pool and influence the fitting capability." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.55, + 0.469, + 0.624 + ], + "angle": 0, + "content": "Training Loss. In addition to the contrastive learning loss, we require the GFB to produce a similar attention map as the one produced from the GradCAM of \\(\\mathcal{L}_{CL}\\). We follow [33] to normalize the GradCAM into a probability distribution and adopt KL divergence as the loss function." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.625, + 0.469, + 0.655 + ], + "angle": 0, + "content": "Formally, we normalize the GradCAM \\(\\mathcal{G}\\) and \\(\\mathcal{A}\\) via the softmax function:" + }, + { + "type": "equation", + "bbox": [ + 0.144, + 0.659, + 0.401, + 0.697 + ], + "angle": 0, + "content": "\\[\n[ \\bar {\\mathbf {G}} ] _ {i, j} = \\frac {\\exp \\left([ \\mathbf {G} ] _ {i , j} / \\tau\\right)}{\\sum_ {i = 1} ^ {H} \\sum_ {j = 1} ^ {W} \\exp \\left([ \\mathbf {G} ] _ {i , j} / \\tau\\right)},\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.144, + 0.699, + 0.469, + 0.737 + ], + "angle": 0, + "content": "\\[\n[ \\bar {\\mathbf {A}} ] _ {i, j} = \\frac {\\exp \\left([ \\mathbf {A} ] _ {i , j} / \\tau\\right)}{\\sum_ {i = 1} ^ {H} \\sum_ {j = 1} ^ {W} \\exp \\left([ \\mathbf {A} ] _ {i , j} / \\tau\\right)}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.742, + 0.469, + 0.787 + ], + "angle": 0, + "content": "where \\([\\cdot ]_{i,j}\\) denotes the \\(i,j\\)-th element of the feature map. \\(\\tau\\) is an empirical temperature parameter and we set it to 0.4 here. Thus, the objective can be expressed as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.162, + 0.794, + 0.469, + 0.837 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {K L} = \\sum_ {i = 1} ^ {H} \\sum_ {j = 1} ^ {W} [ \\bar {\\mathbf {A}} ] _ {i, j} \\log \\frac {[ \\bar {\\mathbf {A}} ] _ {i , j}}{[ \\bar {\\mathbf {G}} ] _ {i , j}}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.844, + 0.469, + 0.873 + ], + "angle": 0, + "content": "Thus, the final loss function taken on all images over an unlabelled dataset is shown as followings." + }, + { + "type": "equation", + "bbox": [ + 0.201, + 0.882, + 0.469, + 0.897 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\lambda \\mathcal {L} _ {C L} + \\nu \\mathcal {L} _ {K L}. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.201 + ], + "angle": 0, + "content": "Inference. At the inference time, the GradCAM fitting branch will be firstly used to produce an attention mask, i.e., prediction of GradCAM. This attention mask is firstly normalized using \\( A_{i,j}' = \\frac{A_{i,j} - \\min(A)}{1e^{-7} + \\max(A)} \\). Then we use the normalized attention to perform weighted average pooling of features from the last-layer convolutional feature map. Formally, it calculates:" + }, + { + "type": "equation", + "bbox": [ + 0.594, + 0.209, + 0.892, + 0.241 + ], + "angle": 0, + "content": "\\[\n\\mathbf {f} = \\sum_ {i, j} \\left[ A ^ {\\prime} \\right] _ {i, j} [ \\phi (I) ] _ {i, j} \\in \\mathbb {R} ^ {C}. \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.25, + 0.733, + 0.263 + ], + "angle": 0, + "content": "f is used for the downstream tasks." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.265, + 0.892, + 0.295 + ], + "angle": 0, + "content": "Discussion. Our approach is inspired by the SAM method in [33]. However, there are several important differences:" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.302, + 0.892, + 0.347 + ], + "angle": 0, + "content": "- SAM method was proposed for supervised FGVC under a low-data regime, while our approach is designed for self-supervised learning." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.356, + 0.892, + 0.598 + ], + "angle": 0, + "content": "- Most importantly, our study discovers that for self-supervised feature learning, the best strategy to interact with the GFB and the feature learning branch is different from what has been discovered in [33]. Table 1 summarizes the main differences. As seen, unlike either SAM or SAM-bilinear, we do not introduce any interaction between the feature learning branch and the GradCAM fitting branch during training but allow them to perform weighted average pooling at the test stage. In fact, we find that applying cross-branch interaction at the training stage will undermine the feature learning process. This is because applying cross-branch interaction, e.g., using A to weighted pool features will prevent CL from exploring discriminative patterns, especially when A has not been properly learned." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.607, + 0.892, + 0.713 + ], + "angle": 0, + "content": "- For multiple projections, SAM uses bilinear pooling to aggregate \\(\\mathbf{A}\\) and the original feature map, resulting in high-dimensional feature representation. Our work performs max-out on multiple projections, resulting in a single attention mask for performing weighted average pooling. Consequently, we could achieve a significant reduction of the feature dimensionality." + }, + { + "type": "list", + "bbox": [ + 0.518, + 0.302, + 0.892, + 0.713 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.892, + 0.795 + ], + "angle": 0, + "content": "To make our study comprehensive, we also explore several variants as baseline approaches. From the comparison with those methods, the benefit of our design could become more evident. For comparison, we use the following architectures as baselines for self-supervised pre-training:" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.892, + 0.87 + ], + "angle": 0, + "content": "SAM-SSL: this baseline extends SAM by changing its objective function from cross-entropy to the contrastive loss in MoCo V2. It shares the same architecture as SAM [33], where a projection is used as the GFB, and GradCAM fitting is trained as an auxiliary task to contrastive learning." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "SAM-SSL-Bilinear: this baseline extends SAM-bilinear by using the contrastive loss in MoCo V2. The cross-branch" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11395" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.892, + 0.118 + ], + "angle": 0, + "content": "Table 1. Upper part: summary of the major difference between our method and SAM method [33]. Lower part: two variants that are also investigated in this work." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.129, + 0.913, + 0.248 + ], + "angle": 0, + "content": "
MethodGradCAM Fitting BranchCross-branch InteractionFeature DimensionLoss Function
traintest
SAM1 proj××CCrossEntropy
SAM-Bilinearmax[K projs]bilinear poolingbilinear poolingC*KCrossEntropy
Oursmax[K projs]×weighted average poolingCContrastive
Ours-DualPoolingmax[K projs]weighted average poolingweighted average poolingCContrastive
Ours-MultiTaskmax[K projs]××CContrastive
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.273, + 0.469, + 0.302 + ], + "angle": 0, + "content": "interaction of SAM-SSL-Bilinear follows the original SAM-Bilinear method." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.303, + 0.469, + 0.424 + ], + "angle": 0, + "content": "Besides the above two extensions of the SAM methods, we also consider two variants of our method. The first is called Ours-MultiTask, which does not perform weighted average pooling at the test stage but merely uses GradCAM fitting as an auxiliary task. Another is called Ours-DualPooling, which performs weighted average pooling at both training and testing stages. Those two variants are summarized in Table 1." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.437, + 0.21, + 0.454 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.462, + 0.47, + 0.584 + ], + "angle": 0, + "content": "In this section, we will evaluate our proposed method on three widely used fine-grained visual datasets (Caltech-UCSD Birds (CUB-200-2011) [35], Stanford Cars [25] and FGVC-Aircraft [27]), and a large-scale fine-grained dataset (iNaturalist2019 [34]). Our experiments aim to understand the effectiveness and the components of the proposed algorithm." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.591, + 0.279, + 0.607 + ], + "angle": 0, + "content": "4.1. Datasets and Settings" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.614, + 0.469, + 0.809 + ], + "angle": 0, + "content": "Datasets. CUB-200-2011 contains 11,788 images with 200 bird species, where 5994 images are used for training and 5794 images for testing. Stanford Cars contains 16,185 images with 196 categories, where 8144 images are for training and 8041 images for testing. FGVC-Aircraft contains 10,000 images with 100 categories, where 6667 images are for training, and 3333 images are for testing. iNaturalist2019 in its 2019 version contains 1,010 categories, with a combined training and validation set of 268,243 images. Note that fine-grained visual task focus on distinguishing similar subcategories within a super-category, while there are six super-categories in iNaturalist2019." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Implementation Details. We adopt the ResNet-50 [19] as the network backbone, which is initialized using ImageNet-trained weights, and build our method on top of MoCo v2 [8]. Therefore the SSL loss term is identical to MoCo v2. The momentum value and memory size are set similarly to MoCo v2, i.e., 0.999 and 65536, respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.273, + 0.895, + 0.439 + ], + "angle": 0, + "content": "The projector head \\( g_{\\theta} \\) in MoCo v2 is composed of two fully-connected layers with ReLU and a third linear layer with batch normalization (BN) [21]. The size of all three layers is \\( 2048 \\times 2048 \\times 256 \\). We set the mini-batch size as 128 and used an SGD optimizer with a learning rate of 0.03, a momentum of 0.9, and a weight decay of 0.0001. 100 epochs are used to train the feature extractor. The images from the four FGVR datasets are resized to \\( 224 \\times 224 \\) pixels during training times. During testing time, images are firstly resized to 256 pixels and then are centered cropped to \\( 224 \\times 224 \\) on these four FGVR datasets." + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.448, + 0.697, + 0.464 + ], + "angle": 0, + "content": "4.2. Evaluation Protocols" + }, + { + "type": "image", + "bbox": [ + 0.502, + 0.482, + 0.895, + 0.635 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.645, + 0.892, + 0.702 + ], + "angle": 0, + "content": "Figure 3. Comparison of ResNet-50, MoCo v2 and Ours on the retrieval rank-1 on the iNaturalist2019 dataset. \"Amphibians\", \"Birds\", \"Fungi\", \"Reptiles\", and \"Insects\" are the superclasses in iNaturalist2019." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.892, + 0.825 + ], + "angle": 0, + "content": "We evaluate the proposed method in two settings: linear probing and image retrieval. Linear probing is a commonly used evaluation protocol in SSL. In linear probing, the feature extractor learned from the SSL algorithm will be fixed and a linear classifier will be trained on top of the learned features. The classification performance of the linear classifier indicates the quality of the learned feature." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Besides linear probing, we also use image retrieval (also equivalent to the nearest neighbor classification task) task to evaluate the learned features, which was also explored in the literature [6,22,23]. This task aims to find the images with the same category as query images based on the" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "11396" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.892, + 0.147 + ], + "angle": 0, + "content": "Table 2. Classification and retrieval of our method evaluated on the CUB-200-2011, Stanford Cars and FGVC Aircraft datasets. \"ResNet-50\" represents pre-training in the ImageNet dataset [12] in a supervised manner, then freezing the ResNet-50 backbone and only optimizing the supervised linear classifier in the classification task. We report the Top 1 and Top 5 (in %) on the classification task, rank-1, rank-5, and mAP (in %) on the retrieval task. 100, 50, and 20 are the three different label proportions (in %) in the classification task." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.156, + 0.89, + 0.338 + ], + "angle": 0, + "content": "
DatasetMethodClassificationRetrieval
Top 1/Top 5(100)Top 1/Top 5(50)Top 1/Top 5(20)rank-1rank-5mAP
CUB-200-2011ResNet-5068.17/90.4258.99/85.9046.54/77.0910.6529.325.09
MoCo v268.30/90.8560.96/87.0046.91/76.5917.0741.468.13
Ours71.31/92.0366.52/90.0655.33/83.5249.6975.2324.01
Stanford CarsResNet-5057.41/83.5546.23/74.3131.19/58.674.9116.982.34
MoCo v258.43/84.8550.17/77.3835.14/64.1010.9429.573.12
Ours60.75/86.4453.87/81.7240.88/69.1834.5660.758.87
FGVC AircraftResNet-5047.38/74.7337.83/67.1228.20/54.735.1614.222.61
MoCo v252.54/80.7445.52/73.8535.17/65.0819.3839.906.30
Ours55.87/84.7348.22/77.1438.55/68.5334.3361.0915.43
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.362, + 0.473, + 0.513 + ], + "angle": 0, + "content": "learned feature. Note that, unlike linear probing, the image retrieval task does not involve a large amount of labeled data – which could be used to suppress the less relevant features. In this sense, succeeding in the image retrieval task imposes higher feature quality requirements. Moreover, image retrieval is a practically useful task, and unsupervised feature learning is an attractive solution to image retrieval since the whole retrieval system can be built without any human annotation and intervention. For the retrieval task, we use rank-1, rank-5, and mAP as evaluation metrics." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.526, + 0.218, + 0.541 + ], + "angle": 0, + "content": "4.3. Main Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.551, + 0.47, + 0.612 + ], + "angle": 0, + "content": "The Effectiveness of the Proposed Method. Our method is based on MoCo v2. We first compare our result against MoCo v2 to examine the performance gain. The results are reported in Table 2 and Figure 3." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.613, + 0.471, + 0.839 + ], + "angle": 0, + "content": "From Table 2, we can see that our method has led to a significant improvement over MoCo v2. It achieves \\(71.31\\%\\) top-1 accuracy and \\(92.03\\%\\) top-5 accuracy on the CUB-200-2011 dataset with \\(100\\%\\) label proportions, which is a \\(3.01\\%\\) improvement on top-1 and \\(1.18\\%\\) improvement on top-5 over MoCo v2. Similarly, significant improvement can also be found on the Stanford Cars and FGVC Aircraft datasets. This demonstrates that our methods improve the quality of the feature representations learned from the original MoCo v2. Notably, with the label proportions reduced from \\(100\\%\\) to \\(20\\%\\), there is generally a better improvement in the performance of the proposed method, which demonstrates that the proposed method learns less noisy features, so that training with fewer data can generalize better." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.472, + 0.903 + ], + "angle": 0, + "content": "The advantage of the proposed method becomes more pronounced when evaluating the image retrieval task. As seen from Table 2, our method leads to a significant boost in performance on all datasets. Specifically, the rank-1," + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.362, + 0.895, + 0.514 + ], + "angle": 0, + "content": "rank-5 and mAP of ours (\\(K = 32\\)) are \\(49.69\\%\\), \\(75.23\\%\\), and \\(24.01\\%\\), respectively on the CUB-200-2011 dataset, which is \\(32.62\\%\\), \\(33.77\\%\\), and \\(15.88\\%\\) higher than the method of MoCo v2. Similar improvement can also be observed on the Stanford Cars and FGVC Aircraft datasets. On the large-scale fine-grained dataset, i.e., iNaturalist2019, our method also performs better than MoCo v2 shown in Figure 3. These indicate the proposed method is particularly good for retrieval tasks, which might be due to its ability to filter out less relevant patterns." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.524, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Comparison with Other SSL Frameworks. In addition to the comparison on MoCo v2, we also compare the proposed method against other commonly used SSL approaches. We report the Top-1 accuracy, the running time, and the peak memory with two different batch sizes (32 & 128). The results are shown in Table 3. All methods are run on 4 V100 GPUs, each with 32G memory. We report the training speed, GPU memory usage, and performance. For classification performance, the blue marks mean the best classification results, and the green marks mean the second-best classification results. It is clear to see that our method achieves the best Top-1 performance on the CUB-200-2011, Stanford Cars, and FGVC Aircraft datasets. Also, when the GPU resources are limited, e.g., only 1 V100 GPU is available, the proposed method reduces the batch size but still remains a competitive classification performance compared to other SSL methods. Regarding training speed and GPU memory usage, the proposed method has the same running time as MoCo v2 and SimSiam, slightly more peak memory than SimSiam, but less peak memory, and quicker running time than SimCLR and BYOL. Although DINO uses the least training time and GPU memory usage, their performances are also the worst compared to ours and other self-supervised learning methods. Barlow Twins and VICReg" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "11397" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.895, + 0.161 + ], + "angle": 0, + "content": "Table 3. Compared to other state-of-the-art self-supervised learning frameworks with Top 1 accuracy on the CUB-200-2011, Stanford Cars and FGVC Aircraft datasets; running time and peak memory on the CUB-200-2011 dataset. The training time is measured on 4 Tesla V100 GPUs with 100 epochs, and the peak memory is calculated on a single GPU. Top 1 accuracy (\\%) is reported on linear classification with the frozen representations of their feature extractor. For fairness, all following models use the ResNet-50 as the network backbone and initialize the ResNet-50 architecture with ImageNet-trained weights. blue=best, green=second best." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.17, + 0.907, + 0.342 + ], + "angle": 0, + "content": "
MethodBatch SizeTop 1(CUB)Top 1(Cars)Top 1(Aircraft)time(CUB)GPU Memory(CUB)
Supervised-81.3491.0287.13--
DINO [6]32/12812.37/16.669.27/10.518.52/12.931.5h/1.5h4.9G/8.4G
SimCLR [7]*32/12833.49/38.3944.31/49.4140.56/45.222.5h/2.5h7.1G/23.8G
BYOL [16]*32/12836.64/39.2743.66/45.2134.90/37.624.0h/4.0h7.4G/24.6G
SimSiam [9]32/12835.82/39.9756.87/58.8941.59/43.062.0h/2.0h4.4G/8.9G
MoCo v2 [8]32/12868.03/68.3052.61/58.4342.51/52.542.0h/2.0h6.1G/10.3G
BarlowTwins [40]32/12828.58/33.4523.34/31.9128.35/34.771.5h/1.5h7.0G/8.9G
VICReg [4]32/12830.07/37.7819.29/30.8029.97/36.001.0h/1.0h7.0G/9.0G
Ours32/12870.43 /71.3156.90/60.7546.92/55.872.0h/2.0h6.1G/10.3G
BYOL+Ours*32/12845.79/51.2048.53 /50.6440.08/45.944.0h/4.0h7.4G/24.6G
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.099, + 0.343, + 0.862, + 0.358 + ], + "angle": 0, + "content": "Due to computational constraints, we are unable to evaluate on the batch size of 4096 as used in the original paper; we leave this for future work." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.381, + 0.471, + 0.426 + ], + "angle": 0, + "content": "have a quicker running time and less GPU memory than our proposed method with a batch size of 128, but their performances are much worse than ours." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.427, + 0.472, + 0.504 + ], + "angle": 0, + "content": "Our method also can be implemented with other self-supervised learning methods, e.g., BYOL, referring to \"BYOL+Ours\" presented in Table 3. As we can see, our method applied to the BYOL objective is consistently superior to the baseline of BYOL on three fine-grained datasets." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.515, + 0.414, + 0.531 + ], + "angle": 0, + "content": "4.4. Comparison with Alternative Solutions" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.539, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Our method is featured by its capability of discovering the key discriminative regions, which is vital for FGVR. In this section, we compared the proposed method with nine alternative solutions to take object localization into account. The first is to simply use a bilinear network [26] for MoCo V2. Specifically, we follow the similar bilinear structure as in [33], which implicitly learns \\(K\\) parts and aggregates features from those \\(K\\) parts, and we set \\(K = 32\\) to make a fair comparison to us (since we use 32 projections). We still use MoCo v2 as the SSL framework and denote this method MoCo v2 -Bilinear. The second and third are the methods of SAM-SSL and SAM-SSL-Bilinear introduced in Section 3.2 since our method is extended from the self-boosting attention mechanism (SAM) proposed in [33]. The fourth and fifth are the two variants considered in Section 3.2. The other four comparing methods are the very recently localization-based self-supervised methods, DiLo [42], CVSA [38], LEWEL [20], and ContrastiveCrop [29]. DiLo uses a copy-and-pasting approach as a kind of augmentation to create an image with a different background. The work of CVSA targets a similar problem as ours. They exploit self-supervised fine-grained contrastive learning via cross-view saliency alignment to crops and swaps saliency regions of images. LEWEL adap" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.381, + 0.895, + 0.473 + ], + "angle": 0, + "content": "tively aggregates spatial information of features using spatial aggregation operation between feature map and alignment map to guide the feature learning better. The work of ContrastiveCrop is based on the idea of using attention to guide image cropping, which localizes the object and improves the data augmentation for self-supervised learning." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.474, + 0.895, + 0.835 + ], + "angle": 0, + "content": "The comparison to those nine alternatives is shown in Table 4. As seen, by comparing the SAM-SSL and SAM-SSL-Bilinear, we observe that the proposed method can lead to overall better performance, achieving a significant boost on some datasets. Occasionally, SAM-SSL-Bilinear (\\( K = 32 \\)) can achieve comparable performance as ours, but at the cost of using a much higher feature dimensionality. This clearly shows the advantage of the proposed scheme over the scheme in [33]. Furthermore, our method and combined with ContrastiveCrop (i.e., ours+ContrastiveCrop) with the lowest feature dimensions but achieve the best Top 1 and rank-1 performance on the CUB-200-2011, Stanford Cars and FGVC Aircraft datasets, compared to those nine alternatives. Also, compared with the other localization-aware SSL methods, our method shows a clear advantage, especially for the retrieval task, e.g., ours vs. LEWEL. Finally, we find that the variant of our method does not produce a good performance. For example, when applying weighted average pooling at both training and testing, i.e., Ours-DualPooling, will make the feature learning fail completely, and the representations will collapse. On the other hand, not performing cross-branch interaction, i.e., Ours-MultiTask, does not bring too much improvement over the MoCo v2 baseline." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.847, + 0.825, + 0.864 + ], + "angle": 0, + "content": "4.5. The Impact of Number of Projections" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.894, + 0.903 + ], + "angle": 0, + "content": "To explore the impact of the number of linear projections in our method, we conduct experiments with the different" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "11398" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.895, + 0.133 + ], + "angle": 0, + "content": "Table 4. The linear Top 1 (%) and retrieval rank-1 (%) performance comparisons of recent alternative solutions and Ours on the CUB-200-2011, Stanford Cars and FGVC Aircraft datasets. blue=best, green=second best. Collapse means the model fails to produce meaningful performance." + }, + { + "type": "table", + "bbox": [ + 0.141, + 0.142, + 0.833, + 0.37 + ], + "angle": 0, + "content": "
MethodFeatureClassificationRetrieval
DimensionCUBCarsAircraftCUBCarsAircraft
MoCo v2 [8]C68.3058.4352.5417.0710.9419.38
MoCo v2 -BilinearC*K68.4458.0653.0141.2730.8930.80
SAM-SSLC68.5958.4952.9718.3814.2621.72
SAM-SSL-BilinearC*K71.5659.1255.1244.2035.3832.10
DiLo [38,42]C64.14-----
CVSA [38]C65.02-----
LEWEL [20]C*K69.2759.0254.3319.2312.0120.67
ContrastiveCrop [29]C68.8261.6654.4018.7113.6120.88
Ours-DualPoolingCcollapsecollapse
Ours-MultiTaskC68.5658.5552.8717.6213.9822.23
OursC71.3160.7555.8749.6934.5634.33
Ours+ContrastiveCropC72.8463.7156.0849.3633.5534.95
" + }, + { + "type": "image", + "bbox": [ + 0.127, + 0.392, + 0.422, + 0.558 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.568, + 0.472, + 0.597 + ], + "angle": 0, + "content": "Figure 4. Comparison of MoCo v2 (the blue plot) baseline with our method (the red plot) w.r.t. \\( K \\) on the CUB-200-2011." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.624, + 0.47, + 0.806 + ], + "angle": 0, + "content": "numbers of \\( K \\). Figure 4 shows the retrieval results of rank-1 w.r.t. eight different projections on the fine-grained dataset CUB-200-2011. As we can see, with the increase of linear projections \\( K \\), the rank-1 gradually increases—the final rank-1 peaks at \\( 49.69\\% \\) with \\( K \\) around 32. After \\( K \\) reaches 64, the performance decreases. When the number of projections is very large, the combination of \\( K \\)-part detectors becomes spurious and overfits the correlated pattern, thus resulting in a drop in performance. From the curve, we can also see that choosing any value between 4 and 64 can lead to similar performance. So our method is not very sensitive to \\( K \\) once it falls into a reasonable range." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.817, + 0.347, + 0.832 + ], + "angle": 0, + "content": "4.6. Alternative Structure for GFB" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.903 + ], + "angle": 0, + "content": "In this section, we investigate alternative designs for GFB. In particular, we consider using a two-layer (with 32 as the intermediate feature dimension) multi-layer perception (MLP) to replace the maximized projections in the pro" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.39, + 0.892, + 0.432 + ], + "angle": 0, + "content": "Table 5. Retrieval performance (%) of our methods and using MLP as the alternative GFB branch. The evaluation is on the Stanford Cars dataset." + }, + { + "type": "table", + "bbox": [ + 0.522, + 0.444, + 0.875, + 0.498 + ], + "angle": 0, + "content": "
DatasetArchitecturerank-1rank-5mAP
CarsOurs34.5660.758.87
MLP25.5750.915.92
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.523, + 0.892, + 0.614 + ], + "angle": 0, + "content": "posed method. Compared with our GFB structure, an MLP has better fitting capacity due to the extra linear layer. We conduct experiments on the Stanford Cars dataset, and the result is shown in Table 5. We find that the performance dramatically decreases when using MLP. This demonstrates the importance of our GFB module design." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.631, + 0.892, + 0.665 + ], + "angle": 0, + "content": "5. Conclusion, Further Results (Appendix), Limitation and Future Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In this paper, we introduce a simple-but-effective way of learning an additional screening mechanism to self-supervised feature learning for fine-grained visual recognition. The idea is to identify discriminative clues commonly seen across instances and classes by fitting the GradCAM of the SSL loss with a fitting-capability-limited branch. Our method achieves state-of-the-art in the classification task and is particularly pronounced in retrieval tasks on fine-grained visual recognition problems. More experimental results, including adopting our method for non-fine-grained visual recognition problems, and visualizing each projection in the GFB, can be found in the Appendix. So far, the proposed method seems to be most effective for FGVR, which could be a limitation and we plan to extend the applicability of the proposed method in our future work." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "11399" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.105 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.17 + ], + "angle": 0, + "content": "[1] Soroush Abbasi Koohpayegani, Ajinkya Tejankar, and Hamed Piriaviash. Compress: Self-supervised learning by compressing representations. Advances in Neural Information Processing Systems, 33:12980-12992, 2020. 3" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.171, + 0.47, + 0.226 + ], + "angle": 0, + "content": "[2] Philip Bachman, R Devon Hjelm, and William Buchwalter. Learning representations by maximizing mutual information across views. 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Advances in Neural Information Processing Systems, 34:2543-2555, 2021. 2" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.092, + 0.893, + 0.401 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.956 + ], + "angle": 0, + "content": "11401" + } + ] +] \ No newline at end of file diff --git a/2023/Learning Common Rationale To Improve Self-Supervised Representation for Fine-Grained Visual Recognition Problems/f542c58d-1024-4f6c-81dd-99d6fba543cf_origin.pdf b/2023/Learning Common Rationale To Improve Self-Supervised Representation for Fine-Grained Visual Recognition Problems/f542c58d-1024-4f6c-81dd-99d6fba543cf_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..e8e20421d1b4520fcdf5adbcf58367b5520b11eb --- /dev/null +++ b/2023/Learning Common Rationale To Improve Self-Supervised Representation for Fine-Grained Visual Recognition Problems/f542c58d-1024-4f6c-81dd-99d6fba543cf_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:de6f1800c4695527d725f098af4632f74121d55b571e9084958adf2f2f028243 +size 2317636 diff --git a/2023/Learning Common Rationale To Improve Self-Supervised Representation for Fine-Grained Visual Recognition Problems/full.md b/2023/Learning Common Rationale To Improve Self-Supervised Representation for Fine-Grained Visual Recognition Problems/full.md new file mode 100644 index 0000000000000000000000000000000000000000..930a57baa0a82c14bd85e25a8235f5075a6156aa --- /dev/null +++ b/2023/Learning Common Rationale To Improve Self-Supervised Representation for Fine-Grained Visual Recognition Problems/full.md @@ -0,0 +1,278 @@ +# Learning Common Rationale to Improve Self-Supervised Representation for Fine-Grained Visual Recognition Problems + +Yangyang Shu + +Anton van den Hengel + +Lingqiao Liu* + +School of Computer Science, The University of Adelaide + +{yangyang.shu,anton.vandenhengel,lingqiao.liu}@adelaide.edu.au + +# Abstract + +Self-supervised learning (SSL) strategies have demonstrated remarkable performance in various recognition tasks. However, both our preliminary investigation and recent studies suggest that they may be less effective in learning representations for fine-grained visual recognition (FGVR) since many features helpful for optimizing SSL objectives are not suitable for characterizing the subtle differences in FGVR. To overcome this issue, we propose learning an additional screening mechanism to identify discriminative clues commonly seen across instances and classes, dubbed as common rationales in this paper. Intuitively, common rationales tend to correspond to the discriminative patterns from the key parts of foreground objects. We show that a common rationale detector can be learned by simply exploiting the GradCAM induced from the SSL objective without using any pre-trained object parts or saliency detectors, making it seamlessly to be integrated with the existing SSL process. Specifically, we fit the GradCAM with a branch with limited fitting capacity, which allows the branch to capture the common rationales and discard the less common discriminative patterns. At the test stage, the branch generates a set of spatial weights to selectively aggregate features representing an instance. Extensive experimental results on four visual tasks demonstrate that the proposed method can lead to a significant improvement in different evaluation settings. $^{1}$ + +# 1. Introduction + +Recently, self-supervised representations Learning (SSL) has been shown to be effective for transferring the learned representations to different downstream + +![](images/963e2f1dcaa63d6a061884dc1f04f852c10a152fc760e65901398dc487e6b7e1.jpg) +Figure 1. GradCAM [30] visualization for MoCo v2 [18], VICReg [4] and our method on the CUB-200-2011, Stanford Cars and FGVC Aircraft datasets. Compared with the existing method MoCo v2 and VICReg, which are prone to be distracted by background patterns, our method can identify features from the foreground and potentially the key parts of the object. + +tasks [2, 4, 5, 14, 18]. Methods such as contrastive learning [7, 9, 16, 18] have demonstrated state-of-the-art feature learning capability and have been intensively studied recently. However, recent studies [11] suggest that contrastive learning may have a "coarse-grained bias" and could be less effective for fine-grained classification problems whose goal is to distinguish visually similar subcategories of objects under the basic-level category. + +This phenomenon is rooted in fine-grained visual recognition (FGVR) properties and the training objective of SSL. SSL tries to minimize a pretext task, e.g., contrastive learning minimizes the distance between same-instance features while maximizing the distance among different-instance features, and any visual patterns that could contribute to loss minimization will be learned. On the other hand, the discriminative patterns for FGVR can be subtle. It is more likely to reside on key object parts. Thus, the feature learned + +from SSL may not necessarily be useful for FGVR. Figure 1 shows our investigation of this issue. As seen, the existing SSL paradigms, such as MoCo [18] and VICReg [4] are prone to learn patterns from irrelevant regions2. Existing works [31, 38, 42] usually handle this issue by recoursing to pre-trained object part detectors or saliency detectors to regularize SSL using patterns from valid regions to achieve the training objective. However, both the part detectors and saliency detectors could restrict the applicability of SSL for FGVR since part detectors are trained from human annotations, and the saliency regions are not always coincident with the discriminative regions. + +Therefore, this work aims to directly solve the problem from the target domain data. Specifically, we propose to learn an additional screening mechanism in addition to the contrastive learning process. The purpose of the screening mechanism is to filter out the patterns that might contribute to SSL objectives but are irrelevant to FGVR. Somehow surprisingly, we find that such a screening mechanism can be learned from the GradCAM [30] of the SSL loss via an extremely simple method. The whole process can be described as a "fitting and masking" procedure: At the training time, we use an additional branch with limited fitting capacity (see more discussion about it in Section 3.2) to fit the GradCAM calculated from the SSL objective. At the testing time, we apply this additional branch to predict an attention mask to perform weighted average pooling for the final presentation. The motivation for such a design is that the GradCAM fitting branch tends to characterize the discriminative patterns that commonly occur across samples due to its limited fitting capacity, and those common patterns, dubbed common rationale in this paper, are more likely corresponding to the discriminative clues from key object parts or at least foreground regions. + +We implement our method based on MoCo v2 [8], one of the state-of-the-art approaches in unsupervised feature learning, which also produces the best performance on FGVR in our setting. Our implementation uses the training objective of MoCo v2 to learn feature representations and derive the GradCAM. Through extensive experiments, we show that our approach can significantly boost the quality of the learned feature. For example, when evaluating the learned feature for retrieval tasks, our method achieves $49.69\%$ on the CUB-200-2011 retrieval task, which is $32.62\%$ higher than our baseline method (MoCo v2 [8]). In the linear evaluation phase, the proposed method achieves new state-of-the-art $71.31\%$ Top-1 accuracy, which is $3.01\%$ higher than MoCo v2. + +# 2. Related Work + +Self-supervised learning aims to learn feature representation from unlabeled data. It relies on a pretext task whose supervision could be derived from the data itself, e.g., image colorization [41], image inpainting [28], and rotation [24] prediction. Contrastive learning is recently identified as a promising framework for self-supervised learning and has been extensively studied [5, 7, 10, 13, 18, 36]. Despite the subtle differences, most contrastive learning approaches [15, 37, 43] try to minimize the distance between different views of the same images and push away the views of different images. The representative methods are SimCLR [7] and MoCo [18]. Besides contrastively learning, consistency-based approaches, such as BYOL [16], SimSiam [9] and masking-and-prediction-based approaches, such as MAE [17], BEiT [3], and ADIOS [32] are also proven effective for SSL. + +Improving SSL via Better Region Localization. A pipeline to improve the distinguishing ability is to design better data augmentations of SSL. Three such methods were recently proposed: DiLo [42], SAGA [39], and Contrastive-Crop [29]. DiLo uses a copy-and-pasting approach as a kind of augmentation to create an image with a different background. In such a way, the proposed method distills localization via learning invariance against backgrounds and improves the ability of SSL models to localize foreground objects. SAGA adopts self-augmentation with a guided attention strategy to augment input images based on predictive attention. In their method, an attention-guided crop is used to enhance the robustness of feature representation. ContrastiveCrop shows a better crop as an augmentation to generate better views in SSL and keep the semantic information of an image. All of these works locate the object by improving the data augmentations for SSL. In this work, our method is adaptive to locate the key regions for self-supervised learning without needing external augmentations. Another family of approaches tries to target the same problem as ours: making the learned feature capture more of the foreground region. CVSA [38] proposed a cross-view saliency alignment framework that first crops and swaps saliency regions of images as a novel view generation. Then it adopts a cross-view saliency alignment loss to encourage the model to learn features from foreground objects. CAST [31] encourages Grad-CAM attention to fit the salient image regions detected by a saliency detector. Those methods often rely on pre-trained saliency detection. This implicitly assumes that salient regions are more likely to be discriminative regions. This assumption, however, does not always hold, especially for FGVR. + +# 3. Method + +In this section, we first briefly review self-supervised contrastive learning [8] and gradient-weighted class activation mapping (GradCAM) [30] as preliminary knowledge. Then, we introduce the proposed approach. + +# 3.1. Preliminary + +Self-Supervised Contrastive Learning. Given an image $I$ from a batch of samples, $x = t(I)$ and $x' = t'(I)$ are the two augmented views, where the $t$ and $t'$ are two different transformations sampled from a set of data augmentations $\mathcal{T}$ . Then the views $x$ and $x'$ are used as the input of an encoder $f_{\theta}$ to generate their feature representations $u = f_{\theta}(x)$ and $u' = f_{\theta}(x')$ . Finally, the projector heads $g_{\theta}$ are used to map $u$ and $u'$ onto the embeddings $z = g_{\theta}(u)$ and $z' = g_{\theta}(u')$ . Let $(z,z')$ be embeddings from the same image and are used as a positive pair. Let $z_k$ be the embedding from a different image, and $(z,z_k)$ thus composes a negative pair. SimCLR [7] adopts a contrastive loss to maximize the agreement of positive pairs over those of negative pairs. The MoCo [1, 10, 18] family adopts the same contrastive loss but adds a queue to store the image embeddings to alleviate the memory cost due to the large batch size. Formally, the contrastive loss takes the following form + +$$ +\mathcal {L} _ {C L} = - \log \frac {\exp \left(z \cdot z ^ {\prime} / t\right)}{\sum_ {i = 0} ^ {Q} \exp \left(z \cdot z _ {i} / t\right)}, \tag {1} +$$ + +where $t$ denotes a temperature parameter, and $z_{i}$ is the embedding in the queue. + +Gradient-weighted Class Activation Mapping (GradCAM) is a commonly used way to produce a visual explanation. It identifies the important image regions contributing to the prediction by using the gradient of the loss function with respect to the feature map or input images. In this paper, we consider the gradient calculated with respect to the last convolutional layer feature maps. Formally, we consider the feature map of the last convolutional layer denoting as $\phi(I) \in \mathbb{R}^{H \times W \times C}$ , $H$ , $W$ and $C$ are the height, width and number of channels of the feature map, respectively. In standard C-way classification, the GradCAM is calculated by: + +$$ +[ \operatorname {G r a d - C A M} (\hat {y}) ] _ {i, j} = R e L U \left(\alpha_ {\hat {y}} ^ {\top} [ \phi (I) ] _ {i, j}\right) +$$ + +$$ +w h e r e, \alpha_ {\hat {y}} = \frac {\partial \mathcal {L} _ {C E} (P (y) , \hat {y})}{\partial [ \phi (I) ] _ {i , j}} \in \mathbb {R} ^ {C}, \tag {2} +$$ + +where $\mathcal{L}_{CE}(P(y),\hat{y})$ is the cross-entropy loss measuring the compatibility between the posterior probability $P(y)$ and ground-truth class label $\hat{y}^3$ . $[\phi (I)]_{i,j}\in \mathbb{R}^C$ denotes the + +![](images/231d2cba7317d476c69e6e182c64a116164aa6f2cdd507bbe4b6738f1faee171.jpg) +Figure 2. The overview of our method. At the structure level, it has the following components: 1)Encoder: MoCo-based contrastive learning is used to create the image-level representation. 2) GradCAM fitting branch, which is a convolutional layer with $k$ filters followed by a channel-wise max-out operator. 3) Inference: at the inference time, the prediction from GFB is used as a spatial attention mask, and it is used to replace the GAP operation by weighted average pooling to obtain the image representation. + +feature vector located at the $(i,j)$ -th grid. Grad-CAM $(\hat{y})$ denotes GradCAM for the $\hat{y}$ -th class. $[\mathrm{Grad - CAM}(\hat{y})]_{i,j}$ refers to the importance value of the $(i,j)$ th spatial grid for predicting the $\hat{y}$ -th class. + +Note that although GradCAM is commonly used for supervised classification problems, it can be readily extended to other problems by changing the corresponding loss function. + +# 3.2. Our Method: Learning Common Rationale + +Figure 2 gives an overview of the proposed method. Our method is extremely simple: we merely add one GradCAM fitting branch (GFB) and fit the GradCAM generated from the CL loss at the training time. At the test time, we let this GFB predict (normalized) GradCAM and use the prediction as an attention mask to perform weighted average pooling over the convolutional feature map. The details about this framework are elaborated as follows. + +GradCAM Calculation. For self-supervised learning, we do not have access to ground-truth class labels. Therefore, we use the contrastive learning loss $\mathcal{L}_{CL}$ in Eq. 1 to replace $\mathcal{L}_{CE}$ in Eq. 2: + +$$ +[ \mathbf {G} ] _ {i, j} = R e L U \left(\frac {\partial \mathcal {L} _ {C L} (\psi (\phi (I)))}{\partial [ \phi (I) ] _ {i , j}} ^ {\top} [ \phi (I) ] _ {i, j}\right), \tag {3} +$$ + +where $\psi (\cdot)$ denotes the feature extractor. Note that in the + +original GradCAM, the GradCAM weight indicates how important each region contributes to classifying the image into the $y$ -th class. Similarly, the GradCAM weight from $\mathcal{L}_{CL}$ indicates the contribution of each region to the instance discrimination task in the contrastive learning objective. From Figure 1, we can see that existing Contrastive Learning approaches learn a diverse set of visual patterns, and not all of them are relevant to the FGVR task. + +Architecture of the GFB. The structure of the GFB plays an important role in our method. We expect this branch has a limited fitting capability, such that the branch will not overfit the GradCAM but only capture the commonly occurring discriminative patterns, i.e., common rationales. Inspired by [33], we use a convolutional layer with $K$ filter and $1 \times 1$ kernel size followed by the max-out operation [33] as the fitting branch. Formally, such a branch applies the following operation to the local feature $[\phi(I)]_{i,j}$ at the $(i,j)$ -th grid of the feature map: + +$$ +A _ {i, j} = \max _ {k} \left\{\mathbf {w} _ {k} ^ {\top} [ \phi (I) ] _ {i, j} \right\}, \tag {4} +$$ + +where $A_{i,j}$ will be the predicted GradCAM weight at the $(i,j)$ -th grid and $\mathbf{w}_k$ is the $k$ -th filter (projector) in the convolutional layer. Intuitively, the convolutional layer can be seen as a collection of $K$ detectors and the above operation can be understood as follows: each projection vector $\mathbf{w}_k$ detects an object part $\mathcal{P}_k$ ; the max-out operation takes the maximum of $K$ projections at a given location, which will result in a high value if any of the $K$ object parts are detected. Varying $K$ could adjust the size of the detector pool and influence the fitting capability. + +Training Loss. In addition to the contrastive learning loss, we require the GFB to produce a similar attention map as the one produced from the GradCAM of $\mathcal{L}_{CL}$ . We follow [33] to normalize the GradCAM into a probability distribution and adopt KL divergence as the loss function. + +Formally, we normalize the GradCAM $\mathcal{G}$ and $\mathcal{A}$ via the softmax function: + +$$ +[ \bar {\mathbf {G}} ] _ {i, j} = \frac {\exp \left([ \mathbf {G} ] _ {i , j} / \tau\right)}{\sum_ {i = 1} ^ {H} \sum_ {j = 1} ^ {W} \exp \left([ \mathbf {G} ] _ {i , j} / \tau\right)}, +$$ + +$$ +[ \bar {\mathbf {A}} ] _ {i, j} = \frac {\exp \left([ \mathbf {A} ] _ {i , j} / \tau\right)}{\sum_ {i = 1} ^ {H} \sum_ {j = 1} ^ {W} \exp \left([ \mathbf {A} ] _ {i , j} / \tau\right)}, \tag {5} +$$ + +where $[\cdot ]_{i,j}$ denotes the $i,j$ -th element of the feature map. $\tau$ is an empirical temperature parameter and we set it to 0.4 here. Thus, the objective can be expressed as follows: + +$$ +\mathcal {L} _ {K L} = \sum_ {i = 1} ^ {H} \sum_ {j = 1} ^ {W} [ \bar {\mathbf {A}} ] _ {i, j} \log \frac {[ \bar {\mathbf {A}} ] _ {i , j}}{[ \bar {\mathbf {G}} ] _ {i , j}}, \tag {6} +$$ + +Thus, the final loss function taken on all images over an unlabelled dataset is shown as followings. + +$$ +\mathcal {L} = \lambda \mathcal {L} _ {C L} + \nu \mathcal {L} _ {K L}. \tag {7} +$$ + +Inference. At the inference time, the GradCAM fitting branch will be firstly used to produce an attention mask, i.e., prediction of GradCAM. This attention mask is firstly normalized using $A_{i,j}' = \frac{A_{i,j} - \min(A)}{1e^{-7} + \max(A)}$ . Then we use the normalized attention to perform weighted average pooling of features from the last-layer convolutional feature map. Formally, it calculates: + +$$ +\mathbf {f} = \sum_ {i, j} \left[ A ^ {\prime} \right] _ {i, j} [ \phi (I) ] _ {i, j} \in \mathbb {R} ^ {C}. \tag {8} +$$ + +f is used for the downstream tasks. + +Discussion. Our approach is inspired by the SAM method in [33]. However, there are several important differences: + +- SAM method was proposed for supervised FGVC under a low-data regime, while our approach is designed for self-supervised learning. +- Most importantly, our study discovers that for self-supervised feature learning, the best strategy to interact with the GFB and the feature learning branch is different from what has been discovered in [33]. Table 1 summarizes the main differences. As seen, unlike either SAM or SAM-bilinear, we do not introduce any interaction between the feature learning branch and the GradCAM fitting branch during training but allow them to perform weighted average pooling at the test stage. In fact, we find that applying cross-branch interaction at the training stage will undermine the feature learning process. This is because applying cross-branch interaction, e.g., using A to weighted pool features will prevent CL from exploring discriminative patterns, especially when A has not been properly learned. +- For multiple projections, SAM uses bilinear pooling to aggregate $\mathbf{A}$ and the original feature map, resulting in high-dimensional feature representation. Our work performs max-out on multiple projections, resulting in a single attention mask for performing weighted average pooling. Consequently, we could achieve a significant reduction of the feature dimensionality. + +To make our study comprehensive, we also explore several variants as baseline approaches. From the comparison with those methods, the benefit of our design could become more evident. For comparison, we use the following architectures as baselines for self-supervised pre-training: + +SAM-SSL: this baseline extends SAM by changing its objective function from cross-entropy to the contrastive loss in MoCo V2. It shares the same architecture as SAM [33], where a projection is used as the GFB, and GradCAM fitting is trained as an auxiliary task to contrastive learning. + +SAM-SSL-Bilinear: this baseline extends SAM-bilinear by using the contrastive loss in MoCo V2. The cross-branch + +Table 1. Upper part: summary of the major difference between our method and SAM method [33]. Lower part: two variants that are also investigated in this work. + +
MethodGradCAM Fitting BranchCross-branch InteractionFeature DimensionLoss Function
traintest
SAM1 proj××CCrossEntropy
SAM-Bilinearmax[K projs]bilinear poolingbilinear poolingC*KCrossEntropy
Oursmax[K projs]×weighted average poolingCContrastive
Ours-DualPoolingmax[K projs]weighted average poolingweighted average poolingCContrastive
Ours-MultiTaskmax[K projs]××CContrastive
+ +interaction of SAM-SSL-Bilinear follows the original SAM-Bilinear method. + +Besides the above two extensions of the SAM methods, we also consider two variants of our method. The first is called Ours-MultiTask, which does not perform weighted average pooling at the test stage but merely uses GradCAM fitting as an auxiliary task. Another is called Ours-DualPooling, which performs weighted average pooling at both training and testing stages. Those two variants are summarized in Table 1. + +# 4. Experiments + +In this section, we will evaluate our proposed method on three widely used fine-grained visual datasets (Caltech-UCSD Birds (CUB-200-2011) [35], Stanford Cars [25] and FGVC-Aircraft [27]), and a large-scale fine-grained dataset (iNaturalist2019 [34]). Our experiments aim to understand the effectiveness and the components of the proposed algorithm. + +# 4.1. Datasets and Settings + +Datasets. CUB-200-2011 contains 11,788 images with 200 bird species, where 5994 images are used for training and 5794 images for testing. Stanford Cars contains 16,185 images with 196 categories, where 8144 images are for training and 8041 images for testing. FGVC-Aircraft contains 10,000 images with 100 categories, where 6667 images are for training, and 3333 images are for testing. iNaturalist2019 in its 2019 version contains 1,010 categories, with a combined training and validation set of 268,243 images. Note that fine-grained visual task focus on distinguishing similar subcategories within a super-category, while there are six super-categories in iNaturalist2019. + +Implementation Details. We adopt the ResNet-50 [19] as the network backbone, which is initialized using ImageNet-trained weights, and build our method on top of MoCo v2 [8]. Therefore the SSL loss term is identical to MoCo v2. The momentum value and memory size are set similarly to MoCo v2, i.e., 0.999 and 65536, respectively. + +The projector head $g_{\theta}$ in MoCo v2 is composed of two fully-connected layers with ReLU and a third linear layer with batch normalization (BN) [21]. The size of all three layers is $2048 \times 2048 \times 256$ . We set the mini-batch size as 128 and used an SGD optimizer with a learning rate of 0.03, a momentum of 0.9, and a weight decay of 0.0001. 100 epochs are used to train the feature extractor. The images from the four FGVR datasets are resized to $224 \times 224$ pixels during training times. During testing time, images are firstly resized to 256 pixels and then are centered cropped to $224 \times 224$ on these four FGVR datasets. + +![](images/1d524e1ef944fee21646c78ee698bb7c0852eb9ebee7a653e1a57d765689f84e.jpg) +4.2. Evaluation Protocols +Figure 3. Comparison of ResNet-50, MoCo v2 and Ours on the retrieval rank-1 on the iNaturalist2019 dataset. "Amphibians", "Birds", "Fungi", "Reptiles", and "Insects" are the superclasses in iNaturalist2019. + +We evaluate the proposed method in two settings: linear probing and image retrieval. Linear probing is a commonly used evaluation protocol in SSL. In linear probing, the feature extractor learned from the SSL algorithm will be fixed and a linear classifier will be trained on top of the learned features. The classification performance of the linear classifier indicates the quality of the learned feature. + +Besides linear probing, we also use image retrieval (also equivalent to the nearest neighbor classification task) task to evaluate the learned features, which was also explored in the literature [6,22,23]. This task aims to find the images with the same category as query images based on the + +Table 2. Classification and retrieval of our method evaluated on the CUB-200-2011, Stanford Cars and FGVC Aircraft datasets. "ResNet-50" represents pre-training in the ImageNet dataset [12] in a supervised manner, then freezing the ResNet-50 backbone and only optimizing the supervised linear classifier in the classification task. We report the Top 1 and Top 5 (in %) on the classification task, rank-1, rank-5, and mAP (in %) on the retrieval task. 100, 50, and 20 are the three different label proportions (in %) in the classification task. + +
DatasetMethodClassificationRetrieval
Top 1/Top 5(100)Top 1/Top 5(50)Top 1/Top 5(20)rank-1rank-5mAP
CUB-200-2011ResNet-5068.17/90.4258.99/85.9046.54/77.0910.6529.325.09
MoCo v268.30/90.8560.96/87.0046.91/76.5917.0741.468.13
Ours71.31/92.0366.52/90.0655.33/83.5249.6975.2324.01
Stanford CarsResNet-5057.41/83.5546.23/74.3131.19/58.674.9116.982.34
MoCo v258.43/84.8550.17/77.3835.14/64.1010.9429.573.12
Ours60.75/86.4453.87/81.7240.88/69.1834.5660.758.87
FGVC AircraftResNet-5047.38/74.7337.83/67.1228.20/54.735.1614.222.61
MoCo v252.54/80.7445.52/73.8535.17/65.0819.3839.906.30
Ours55.87/84.7348.22/77.1438.55/68.5334.3361.0915.43
+ +learned feature. Note that, unlike linear probing, the image retrieval task does not involve a large amount of labeled data – which could be used to suppress the less relevant features. In this sense, succeeding in the image retrieval task imposes higher feature quality requirements. Moreover, image retrieval is a practically useful task, and unsupervised feature learning is an attractive solution to image retrieval since the whole retrieval system can be built without any human annotation and intervention. For the retrieval task, we use rank-1, rank-5, and mAP as evaluation metrics. + +# 4.3. Main Results + +The Effectiveness of the Proposed Method. Our method is based on MoCo v2. We first compare our result against MoCo v2 to examine the performance gain. The results are reported in Table 2 and Figure 3. + +From Table 2, we can see that our method has led to a significant improvement over MoCo v2. It achieves $71.31\%$ top-1 accuracy and $92.03\%$ top-5 accuracy on the CUB-200-2011 dataset with $100\%$ label proportions, which is a $3.01\%$ improvement on top-1 and $1.18\%$ improvement on top-5 over MoCo v2. Similarly, significant improvement can also be found on the Stanford Cars and FGVC Aircraft datasets. This demonstrates that our methods improve the quality of the feature representations learned from the original MoCo v2. Notably, with the label proportions reduced from $100\%$ to $20\%$ , there is generally a better improvement in the performance of the proposed method, which demonstrates that the proposed method learns less noisy features, so that training with fewer data can generalize better. + +The advantage of the proposed method becomes more pronounced when evaluating the image retrieval task. As seen from Table 2, our method leads to a significant boost in performance on all datasets. Specifically, the rank-1, + +rank-5 and mAP of ours ( $K = 32$ ) are $49.69\%$ , $75.23\%$ , and $24.01\%$ , respectively on the CUB-200-2011 dataset, which is $32.62\%$ , $33.77\%$ , and $15.88\%$ higher than the method of MoCo v2. Similar improvement can also be observed on the Stanford Cars and FGVC Aircraft datasets. On the large-scale fine-grained dataset, i.e., iNaturalist2019, our method also performs better than MoCo v2 shown in Figure 3. These indicate the proposed method is particularly good for retrieval tasks, which might be due to its ability to filter out less relevant patterns. + +Comparison with Other SSL Frameworks. In addition to the comparison on MoCo v2, we also compare the proposed method against other commonly used SSL approaches. We report the Top-1 accuracy, the running time, and the peak memory with two different batch sizes (32 & 128). The results are shown in Table 3. All methods are run on 4 V100 GPUs, each with 32G memory. We report the training speed, GPU memory usage, and performance. For classification performance, the blue marks mean the best classification results, and the green marks mean the second-best classification results. It is clear to see that our method achieves the best Top-1 performance on the CUB-200-2011, Stanford Cars, and FGVC Aircraft datasets. Also, when the GPU resources are limited, e.g., only 1 V100 GPU is available, the proposed method reduces the batch size but still remains a competitive classification performance compared to other SSL methods. Regarding training speed and GPU memory usage, the proposed method has the same running time as MoCo v2 and SimSiam, slightly more peak memory than SimSiam, but less peak memory, and quicker running time than SimCLR and BYOL. Although DINO uses the least training time and GPU memory usage, their performances are also the worst compared to ours and other self-supervised learning methods. Barlow Twins and VICReg + +Table 3. Compared to other state-of-the-art self-supervised learning frameworks with Top 1 accuracy on the CUB-200-2011, Stanford Cars and FGVC Aircraft datasets; running time and peak memory on the CUB-200-2011 dataset. The training time is measured on 4 Tesla V100 GPUs with 100 epochs, and the peak memory is calculated on a single GPU. Top 1 accuracy (\%) is reported on linear classification with the frozen representations of their feature extractor. For fairness, all following models use the ResNet-50 as the network backbone and initialize the ResNet-50 architecture with ImageNet-trained weights. blue=best, green=second best. + +
MethodBatch SizeTop 1(CUB)Top 1(Cars)Top 1(Aircraft)time(CUB)GPU Memory(CUB)
Supervised-81.3491.0287.13--
DINO [6]32/12812.37/16.669.27/10.518.52/12.931.5h/1.5h4.9G/8.4G
SimCLR [7]*32/12833.49/38.3944.31/49.4140.56/45.222.5h/2.5h7.1G/23.8G
BYOL [16]*32/12836.64/39.2743.66/45.2134.90/37.624.0h/4.0h7.4G/24.6G
SimSiam [9]32/12835.82/39.9756.87/58.8941.59/43.062.0h/2.0h4.4G/8.9G
MoCo v2 [8]32/12868.03/68.3052.61/58.4342.51/52.542.0h/2.0h6.1G/10.3G
BarlowTwins [40]32/12828.58/33.4523.34/31.9128.35/34.771.5h/1.5h7.0G/8.9G
VICReg [4]32/12830.07/37.7819.29/30.8029.97/36.001.0h/1.0h7.0G/9.0G
Ours32/12870.43 /71.3156.90/60.7546.92/55.872.0h/2.0h6.1G/10.3G
BYOL+Ours*32/12845.79/51.2048.53 /50.6440.08/45.944.0h/4.0h7.4G/24.6G
+ +Due to computational constraints, we are unable to evaluate on the batch size of 4096 as used in the original paper; we leave this for future work. + +have a quicker running time and less GPU memory than our proposed method with a batch size of 128, but their performances are much worse than ours. + +Our method also can be implemented with other self-supervised learning methods, e.g., BYOL, referring to "BYOL+Ours" presented in Table 3. As we can see, our method applied to the BYOL objective is consistently superior to the baseline of BYOL on three fine-grained datasets. + +# 4.4. Comparison with Alternative Solutions + +Our method is featured by its capability of discovering the key discriminative regions, which is vital for FGVR. In this section, we compared the proposed method with nine alternative solutions to take object localization into account. The first is to simply use a bilinear network [26] for MoCo V2. Specifically, we follow the similar bilinear structure as in [33], which implicitly learns $K$ parts and aggregates features from those $K$ parts, and we set $K = 32$ to make a fair comparison to us (since we use 32 projections). We still use MoCo v2 as the SSL framework and denote this method MoCo v2 -Bilinear. The second and third are the methods of SAM-SSL and SAM-SSL-Bilinear introduced in Section 3.2 since our method is extended from the self-boosting attention mechanism (SAM) proposed in [33]. The fourth and fifth are the two variants considered in Section 3.2. The other four comparing methods are the very recently localization-based self-supervised methods, DiLo [42], CVSA [38], LEWEL [20], and ContrastiveCrop [29]. DiLo uses a copy-and-pasting approach as a kind of augmentation to create an image with a different background. The work of CVSA targets a similar problem as ours. They exploit self-supervised fine-grained contrastive learning via cross-view saliency alignment to crops and swaps saliency regions of images. LEWEL adap + +tively aggregates spatial information of features using spatial aggregation operation between feature map and alignment map to guide the feature learning better. The work of ContrastiveCrop is based on the idea of using attention to guide image cropping, which localizes the object and improves the data augmentation for self-supervised learning. + +The comparison to those nine alternatives is shown in Table 4. As seen, by comparing the SAM-SSL and SAM-SSL-Bilinear, we observe that the proposed method can lead to overall better performance, achieving a significant boost on some datasets. Occasionally, SAM-SSL-Bilinear ( $K = 32$ ) can achieve comparable performance as ours, but at the cost of using a much higher feature dimensionality. This clearly shows the advantage of the proposed scheme over the scheme in [33]. Furthermore, our method and combined with ContrastiveCrop (i.e., ours+ContrastiveCrop) with the lowest feature dimensions but achieve the best Top 1 and rank-1 performance on the CUB-200-2011, Stanford Cars and FGVC Aircraft datasets, compared to those nine alternatives. Also, compared with the other localization-aware SSL methods, our method shows a clear advantage, especially for the retrieval task, e.g., ours vs. LEWEL. Finally, we find that the variant of our method does not produce a good performance. For example, when applying weighted average pooling at both training and testing, i.e., Ours-DualPooling, will make the feature learning fail completely, and the representations will collapse. On the other hand, not performing cross-branch interaction, i.e., Ours-MultiTask, does not bring too much improvement over the MoCo v2 baseline. + +# 4.5. The Impact of Number of Projections + +To explore the impact of the number of linear projections in our method, we conduct experiments with the different + +Table 4. The linear Top 1 (%) and retrieval rank-1 (%) performance comparisons of recent alternative solutions and Ours on the CUB-200-2011, Stanford Cars and FGVC Aircraft datasets. blue=best, green=second best. Collapse means the model fails to produce meaningful performance. + +
MethodFeatureClassificationRetrieval
DimensionCUBCarsAircraftCUBCarsAircraft
MoCo v2 [8]C68.3058.4352.5417.0710.9419.38
MoCo v2 -BilinearC*K68.4458.0653.0141.2730.8930.80
SAM-SSLC68.5958.4952.9718.3814.2621.72
SAM-SSL-BilinearC*K71.5659.1255.1244.2035.3832.10
DiLo [38,42]C64.14-----
CVSA [38]C65.02-----
LEWEL [20]C*K69.2759.0254.3319.2312.0120.67
ContrastiveCrop [29]C68.8261.6654.4018.7113.6120.88
Ours-DualPoolingCcollapsecollapse
Ours-MultiTaskC68.5658.5552.8717.6213.9822.23
OursC71.3160.7555.8749.6934.5634.33
Ours+ContrastiveCropC72.8463.7156.0849.3633.5534.95
+ +![](images/b8dedb35578b9e5b62f5371d0e922e8f582a9ad9fa9b59c80e7721b38a0abe1f.jpg) +Figure 4. Comparison of MoCo v2 (the blue plot) baseline with our method (the red plot) w.r.t. $K$ on the CUB-200-2011. + +numbers of $K$ . Figure 4 shows the retrieval results of rank-1 w.r.t. eight different projections on the fine-grained dataset CUB-200-2011. As we can see, with the increase of linear projections $K$ , the rank-1 gradually increases—the final rank-1 peaks at $49.69\%$ with $K$ around 32. After $K$ reaches 64, the performance decreases. When the number of projections is very large, the combination of $K$ -part detectors becomes spurious and overfits the correlated pattern, thus resulting in a drop in performance. From the curve, we can also see that choosing any value between 4 and 64 can lead to similar performance. So our method is not very sensitive to $K$ once it falls into a reasonable range. + +# 4.6. Alternative Structure for GFB + +In this section, we investigate alternative designs for GFB. In particular, we consider using a two-layer (with 32 as the intermediate feature dimension) multi-layer perception (MLP) to replace the maximized projections in the pro + +Table 5. Retrieval performance (%) of our methods and using MLP as the alternative GFB branch. The evaluation is on the Stanford Cars dataset. + +
DatasetArchitecturerank-1rank-5mAP
CarsOurs34.5660.758.87
MLP25.5750.915.92
+ +posed method. Compared with our GFB structure, an MLP has better fitting capacity due to the extra linear layer. We conduct experiments on the Stanford Cars dataset, and the result is shown in Table 5. We find that the performance dramatically decreases when using MLP. This demonstrates the importance of our GFB module design. + +# 5. Conclusion, Further Results (Appendix), Limitation and Future Work + +In this paper, we introduce a simple-but-effective way of learning an additional screening mechanism to self-supervised feature learning for fine-grained visual recognition. The idea is to identify discriminative clues commonly seen across instances and classes by fitting the GradCAM of the SSL loss with a fitting-capability-limited branch. Our method achieves state-of-the-art in the classification task and is particularly pronounced in retrieval tasks on fine-grained visual recognition problems. 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Adversarial masking for self-supervised learning. In International Conference on Machine Learning, pages 20026-20040. PMLR, 2022. 2 +[33] Yangyang Shu, Baosheng Yu, Haiming Xu, and Lingqiao Liu. Improving fine-grained visual recognition in low data regimes via self-boosting attention mechanism. In Computer Vision-ECCV 2022: 17th European Conference, Tel Aviv, Israel, October 23–27, 2022, Proceedings, Part XXV, pages 449–465. Springer, 2022. 4, 5, 7 +[34] Grant Van Horn, Oisin Mac Aodha, Yang Song, Yin Cui, Chen Sun, Alex Shepard, Hartwig Adam, Pietro Perona, and Serge Belongie. The inaturalist species classification and detection dataset. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 8769-8778, 2018. 5 +[35] Catherine Wah, Steve Branson, Peter Welinder, Pietro Perona, and Serge Belongie. The caltech-ucsd birds-200-2011 dataset. 2011. 5 +[36] Tongzhou Wang and Phillip Isola. Understanding contrastive representation learning through alignment and uniformity on the hypersphere. In International Conference on Machine Learning, pages 9929-9939. PMLR, 2020. 2 +[37] Xinlong Wang, Rufeng Zhang, Chunhua Shen, Tao Kong, and Lei Li. Dense contrastive learning for self-supervised visual pre-training. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 3024-3033, 2021. 2 +[38] Di Wu, Siyuan Li, Zelin Zang, Kai Wang, Lei Shang, Baigui Sun, Hao Li, and Stan Z Li. Align yourself: Self-supervised pre-training for fine-grained recognition via saliency alignment. arXiv preprint arXiv:2106.15788, 2021. 2, 7, 8 + +[39] Chun-Hsiao Yeh, Cheng-Yao Hong, Yen-Chi Hsu, and Tyng-Luh Liu. Saga: Self-augmentation with guided attention for representation learning. In ICASSP 2022-2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pages 3463-3467. 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Advances in Neural Information Processing Systems, 34:2543-2555, 2021. 2 \ No newline at end of file diff --git a/2023/Learning Common Rationale To Improve Self-Supervised Representation for Fine-Grained Visual Recognition Problems/images.zip b/2023/Learning Common Rationale To Improve Self-Supervised Representation for Fine-Grained Visual Recognition Problems/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..8d8cedead851721ba87d1b92cb70a5e3db258971 --- /dev/null +++ b/2023/Learning Common Rationale To Improve Self-Supervised Representation for Fine-Grained Visual Recognition Problems/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:a8272d5cb97bd1fc4d342a72c95d40b09c0b6bab5a7269c883f0bf3e30ebf12c +size 560425 diff --git a/2023/Learning Common Rationale To Improve Self-Supervised Representation for Fine-Grained Visual Recognition Problems/layout.json b/2023/Learning Common Rationale To Improve Self-Supervised Representation for Fine-Grained Visual Recognition Problems/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..4aa6d4e17d9ac6e88d1c372fe85f3b9f7d9bd82f --- /dev/null +++ b/2023/Learning Common Rationale To Improve Self-Supervised Representation for Fine-Grained Visual Recognition Problems/layout.json @@ -0,0 +1,7866 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 62, + 102, + 533, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 102, + 533, + 140 + ], + "spans": [ + { + "bbox": [ + 62, + 102, + 533, + 140 + ], + "type": "text", + "content": "Learning Common Rationale to Improve Self-Supervised Representation for Fine-Grained Visual Recognition Problems" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 137, + 161, + 210, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 137, + 161, + 210, + 175 + ], + "spans": [ + { + "bbox": [ + 137, + 161, + 210, + 175 + ], + "type": "text", + "content": "Yangyang Shu" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 244, + 161, + 355, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 244, + 161, + 355, + 175 + ], + "spans": [ + { + "bbox": [ + 244, + 161, + 355, + 175 + ], + "type": "text", + "content": "Anton van den Hengel" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 390, + 161, + 460, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 390, + 161, + 460, + 175 + ], + "spans": [ + { + "bbox": [ + 390, + 161, + 460, + 175 + ], + "type": "text", + "content": "Lingqiao Liu*" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 157, + 195, + 436, + 209 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 157, + 195, + 436, + 209 + ], + "spans": [ + { + "bbox": [ + 157, + 195, + 436, + 209 + ], + "type": "text", + "content": "School of Computer Science, The University of Adelaide" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 128, + 212, + 462, + 224 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 128, + 212, + 462, + 224 + ], + "spans": [ + { + "bbox": [ + 128, + 212, + 462, + 224 + ], + "type": "text", + "content": "{yangyang.shu,anton.vandenhengel,lingqiao.liu}@adelaide.edu.au" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 143, + 251, + 192, + 263 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 251, + 192, + 263 + ], + "spans": [ + { + "bbox": [ + 143, + 251, + 192, + 263 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 276, + 290, + 587 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 276, + 290, + 587 + ], + "spans": [ + { + "bbox": [ + 46, + 276, + 290, + 587 + ], + "type": "text", + "content": "Self-supervised learning (SSL) strategies have demonstrated remarkable performance in various recognition tasks. However, both our preliminary investigation and recent studies suggest that they may be less effective in learning representations for fine-grained visual recognition (FGVR) since many features helpful for optimizing SSL objectives are not suitable for characterizing the subtle differences in FGVR. To overcome this issue, we propose learning an additional screening mechanism to identify discriminative clues commonly seen across instances and classes, dubbed as common rationales in this paper. Intuitively, common rationales tend to correspond to the discriminative patterns from the key parts of foreground objects. We show that a common rationale detector can be learned by simply exploiting the GradCAM induced from the SSL objective without using any pre-trained object parts or saliency detectors, making it seamlessly to be integrated with the existing SSL process. Specifically, we fit the GradCAM with a branch with limited fitting capacity, which allows the branch to capture the common rationales and discard the less common discriminative patterns. At the test stage, the branch generates a set of spatial weights to selectively aggregate features representing an instance. Extensive experimental results on four visual tasks demonstrate that the proposed method can lead to a significant improvement in different evaluation settings." + }, + { + "bbox": [ + 46, + 276, + 290, + 587 + ], + "type": "inline_equation", + "content": "^{1}" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 610, + 128, + 623 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 610, + 128, + 623 + ], + "spans": [ + { + "bbox": [ + 47, + 610, + 128, + 623 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 630, + 287, + 667 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 287, + 667 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 287, + 667 + ], + "type": "text", + "content": "Recently, self-supervised representations Learning (SSL) has been shown to be effective for transferring the learned representations to different downstream" + } + ] + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 307, + 251, + 545, + 406 + ], + "blocks": [ + { + "bbox": [ + 307, + 251, + 545, + 406 + ], + "lines": [ + { + "bbox": [ + 307, + 251, + 545, + 406 + ], + "spans": [ + { + "bbox": [ + 307, + 251, + 545, + 406 + ], + "type": "image", + "image_path": "963e2f1dcaa63d6a061884dc1f04f852c10a152fc760e65901398dc487e6b7e1.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 415, + 547, + 483 + ], + "lines": [ + { + "bbox": [ + 305, + 415, + 547, + 483 + ], + "spans": [ + { + "bbox": [ + 305, + 415, + 547, + 483 + ], + "type": "text", + "content": "Figure 1. GradCAM [30] visualization for MoCo v2 [18], VICReg [4] and our method on the CUB-200-2011, Stanford Cars and FGVC Aircraft datasets. Compared with the existing method MoCo v2 and VICReg, which are prone to be distracted by background patterns, our method can identify features from the foreground and potentially the key parts of the object." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 507, + 547, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 507, + 547, + 604 + ], + "spans": [ + { + "bbox": [ + 304, + 507, + 547, + 604 + ], + "type": "text", + "content": "tasks [2, 4, 5, 14, 18]. Methods such as contrastive learning [7, 9, 16, 18] have demonstrated state-of-the-art feature learning capability and have been intensively studied recently. However, recent studies [11] suggest that contrastive learning may have a \"coarse-grained bias\" and could be less effective for fine-grained classification problems whose goal is to distinguish visually similar subcategories of objects under the basic-level category." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": "This phenomenon is rooted in fine-grained visual recognition (FGVR) properties and the training objective of SSL. SSL tries to minimize a pretext task, e.g., contrastive learning minimizes the distance between same-instance features while maximizing the distance among different-instance features, and any visual patterns that could contribute to loss minimization will be learned. On the other hand, the discriminative patterns for FGVR can be subtle. It is more likely to reside on key object parts. Thus, the feature learned" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 673, + 286, + 693 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 673, + 286, + 693 + ], + "spans": [ + { + "bbox": [ + 46, + 673, + 286, + 693 + ], + "type": "text", + "content": "*Corresponding author. This work is supported by the Centre for Augmented Reasoning." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 47, + 693, + 286, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 693, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 47, + 693, + 286, + 712 + ], + "type": "text", + "content": "1The source code will be publicly available at: https://github. com/GANPerf/LCR" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "11392" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "type": "text", + "content": "from SSL may not necessarily be useful for FGVR. Figure 1 shows our investigation of this issue. As seen, the existing SSL paradigms, such as MoCo [18] and VICReg [4] are prone to learn patterns from irrelevant regions2. Existing works [31, 38, 42] usually handle this issue by recoursing to pre-trained object part detectors or saliency detectors to regularize SSL using patterns from valid regions to achieve the training objective. However, both the part detectors and saliency detectors could restrict the applicability of SSL for FGVR since part detectors are trained from human annotations, and the saliency regions are not always coincident with the discriminative regions." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 216, + 289, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 216, + 289, + 479 + ], + "spans": [ + { + "bbox": [ + 46, + 216, + 289, + 479 + ], + "type": "text", + "content": "Therefore, this work aims to directly solve the problem from the target domain data. Specifically, we propose to learn an additional screening mechanism in addition to the contrastive learning process. The purpose of the screening mechanism is to filter out the patterns that might contribute to SSL objectives but are irrelevant to FGVR. Somehow surprisingly, we find that such a screening mechanism can be learned from the GradCAM [30] of the SSL loss via an extremely simple method. The whole process can be described as a \"fitting and masking\" procedure: At the training time, we use an additional branch with limited fitting capacity (see more discussion about it in Section 3.2) to fit the GradCAM calculated from the SSL objective. At the testing time, we apply this additional branch to predict an attention mask to perform weighted average pooling for the final presentation. The motivation for such a design is that the GradCAM fitting branch tends to characterize the discriminative patterns that commonly occur across samples due to its limited fitting capacity, and those common patterns, dubbed common rationale in this paper, are more likely corresponding to the discriminative clues from key object parts or at least foreground regions." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 479, + 289, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 479, + 289, + 647 + ], + "spans": [ + { + "bbox": [ + 46, + 479, + 289, + 647 + ], + "type": "text", + "content": "We implement our method based on MoCo v2 [8], one of the state-of-the-art approaches in unsupervised feature learning, which also produces the best performance on FGVR in our setting. Our implementation uses the training objective of MoCo v2 to learn feature representations and derive the GradCAM. Through extensive experiments, we show that our approach can significantly boost the quality of the learned feature. For example, when evaluating the learned feature for retrieval tasks, our method achieves " + }, + { + "bbox": [ + 46, + 479, + 289, + 647 + ], + "type": "inline_equation", + "content": "49.69\\%" + }, + { + "bbox": [ + 46, + 479, + 289, + 647 + ], + "type": "text", + "content": " on the CUB-200-2011 retrieval task, which is " + }, + { + "bbox": [ + 46, + 479, + 289, + 647 + ], + "type": "inline_equation", + "content": "32.62\\%" + }, + { + "bbox": [ + 46, + 479, + 289, + 647 + ], + "type": "text", + "content": " higher than our baseline method (MoCo v2 [8]). In the linear evaluation phase, the proposed method achieves new state-of-the-art " + }, + { + "bbox": [ + 46, + 479, + 289, + 647 + ], + "type": "inline_equation", + "content": "71.31\\%" + }, + { + "bbox": [ + 46, + 479, + 289, + 647 + ], + "type": "text", + "content": " Top-1 accuracy, which is " + }, + { + "bbox": [ + 46, + 479, + 289, + 647 + ], + "type": "inline_equation", + "content": "3.01\\%" + }, + { + "bbox": [ + 46, + 479, + 289, + 647 + ], + "type": "text", + "content": " higher than MoCo v2." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 306, + 71, + 392, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 71, + 392, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 71, + 392, + 84 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 115, + 547, + 308 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 115, + 547, + 308 + ], + "spans": [ + { + "bbox": [ + 304, + 115, + 547, + 308 + ], + "type": "text", + "content": "Self-supervised learning aims to learn feature representation from unlabeled data. It relies on a pretext task whose supervision could be derived from the data itself, e.g., image colorization [41], image inpainting [28], and rotation [24] prediction. Contrastive learning is recently identified as a promising framework for self-supervised learning and has been extensively studied [5, 7, 10, 13, 18, 36]. Despite the subtle differences, most contrastive learning approaches [15, 37, 43] try to minimize the distance between different views of the same images and push away the views of different images. The representative methods are SimCLR [7] and MoCo [18]. Besides contrastively learning, consistency-based approaches, such as BYOL [16], SimSiam [9] and masking-and-prediction-based approaches, such as MAE [17], BEiT [3], and ADIOS [32] are also proven effective for SSL." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 331, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 331, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 331, + 547, + 715 + ], + "type": "text", + "content": "Improving SSL via Better Region Localization. A pipeline to improve the distinguishing ability is to design better data augmentations of SSL. Three such methods were recently proposed: DiLo [42], SAGA [39], and Contrastive-Crop [29]. DiLo uses a copy-and-pasting approach as a kind of augmentation to create an image with a different background. In such a way, the proposed method distills localization via learning invariance against backgrounds and improves the ability of SSL models to localize foreground objects. SAGA adopts self-augmentation with a guided attention strategy to augment input images based on predictive attention. In their method, an attention-guided crop is used to enhance the robustness of feature representation. ContrastiveCrop shows a better crop as an augmentation to generate better views in SSL and keep the semantic information of an image. All of these works locate the object by improving the data augmentations for SSL. In this work, our method is adaptive to locate the key regions for self-supervised learning without needing external augmentations. Another family of approaches tries to target the same problem as ours: making the learned feature capture more of the foreground region. CVSA [38] proposed a cross-view saliency alignment framework that first crops and swaps saliency regions of images as a novel view generation. Then it adopts a cross-view saliency alignment loss to encourage the model to learn features from foreground objects. CAST [31] encourages Grad-CAM attention to fit the salient image regions detected by a saliency detector. Those methods often rely on pre-trained saliency detection. This implicitly assumes that salient regions are more likely to be discriminative regions. This assumption, however, does not always hold, especially for FGVR." + } + ] + } + ], + "index": 5 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 46, + 654, + 289, + 715 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 289, + 715 + ], + "type": "text", + "content": "2The weakness of existing SSL methods on FGVR can also be quantitatively demonstrated by their performance on retrieval tasks shown in Section 4.3. As will be seen from our experiments, using only the features learned from SSL and without any further supervision from the target data, existing SSL methods achieve very poor performance in the retrieval task, i.e., based on feature similarity to identify same-class images." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "11393" + } + ] + } + ], + "index": 7 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 71, + 104, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 71, + 104, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 104, + 83 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 91, + 287, + 140 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 91, + 287, + 140 + ], + "spans": [ + { + "bbox": [ + 47, + 91, + 287, + 140 + ], + "type": "text", + "content": "In this section, we first briefly review self-supervised contrastive learning [8] and gradient-weighted class activation mapping (GradCAM) [30] as preliminary knowledge. Then, we introduce the proposed approach." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 145, + 127, + 159 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 145, + 127, + 159 + ], + "spans": [ + { + "bbox": [ + 47, + 145, + 127, + 159 + ], + "type": "text", + "content": "3.1. Preliminary" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 164, + 288, + 368 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 164, + 288, + 368 + ], + "spans": [ + { + "bbox": [ + 47, + 164, + 288, + 368 + ], + "type": "text", + "content": "Self-Supervised Contrastive Learning. Given an image " + }, + { + "bbox": [ + 47, + 164, + 288, + 368 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 47, + 164, + 288, + 368 + ], + "type": "text", + "content": " from a batch of samples, " + }, + { + "bbox": [ + 47, + 164, + 288, + 368 + ], + "type": "inline_equation", + "content": "x = t(I)" + }, + { + "bbox": [ + 47, + 164, + 288, + 368 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 164, + 288, + 368 + ], + "type": "inline_equation", + "content": "x' = t'(I)" + }, + { + "bbox": [ + 47, + 164, + 288, + 368 + ], + "type": "text", + "content": " are the two augmented views, where the " + }, + { + "bbox": [ + 47, + 164, + 288, + 368 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 47, + 164, + 288, + 368 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 164, + 288, + 368 + ], + "type": "inline_equation", + "content": "t'" + }, + { + "bbox": [ + 47, + 164, + 288, + 368 + ], + "type": "text", + "content": " are two different transformations sampled from a set of data augmentations " + }, + { + "bbox": [ + 47, + 164, + 288, + 368 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 47, + 164, + 288, + 368 + ], + "type": "text", + "content": ". Then the views " + }, + { + "bbox": [ + 47, + 164, + 288, + 368 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 47, + 164, + 288, + 368 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 164, + 288, + 368 + ], + "type": "inline_equation", + "content": "x'" + }, + { + "bbox": [ + 47, + 164, + 288, + 368 + ], + "type": "text", + "content": " are used as the input of an encoder " + }, + { + "bbox": [ + 47, + 164, + 288, + 368 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 47, + 164, + 288, + 368 + ], + "type": "text", + "content": " to generate their feature representations " + }, + { + "bbox": [ + 47, + 164, + 288, + 368 + ], + "type": "inline_equation", + "content": "u = f_{\\theta}(x)" + }, + { + "bbox": [ + 47, + 164, + 288, + 368 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 164, + 288, + 368 + ], + "type": "inline_equation", + "content": "u' = f_{\\theta}(x')" + }, + { + "bbox": [ + 47, + 164, + 288, + 368 + ], + "type": "text", + "content": ". Finally, the projector heads " + }, + { + "bbox": [ + 47, + 164, + 288, + 368 + ], + "type": "inline_equation", + "content": "g_{\\theta}" + }, + { + "bbox": [ + 47, + 164, + 288, + 368 + ], + "type": "text", + "content": " are used to map " + }, + { + "bbox": [ + 47, + 164, + 288, + 368 + ], + "type": "inline_equation", + "content": "u" + }, + { + "bbox": [ + 47, + 164, + 288, + 368 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 164, + 288, + 368 + ], + "type": "inline_equation", + "content": "u'" + }, + { + "bbox": [ + 47, + 164, + 288, + 368 + ], + "type": "text", + "content": " onto the embeddings " + }, + { + "bbox": [ + 47, + 164, + 288, + 368 + ], + "type": "inline_equation", + "content": "z = g_{\\theta}(u)" + }, + { + "bbox": [ + 47, + 164, + 288, + 368 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 164, + 288, + 368 + ], + "type": "inline_equation", + "content": "z' = g_{\\theta}(u')" + }, + { + "bbox": [ + 47, + 164, + 288, + 368 + ], + "type": "text", + "content": ". Let " + }, + { + "bbox": [ + 47, + 164, + 288, + 368 + ], + "type": "inline_equation", + "content": "(z,z')" + }, + { + "bbox": [ + 47, + 164, + 288, + 368 + ], + "type": "text", + "content": " be embeddings from the same image and are used as a positive pair. Let " + }, + { + "bbox": [ + 47, + 164, + 288, + 368 + ], + "type": "inline_equation", + "content": "z_k" + }, + { + "bbox": [ + 47, + 164, + 288, + 368 + ], + "type": "text", + "content": " be the embedding from a different image, and " + }, + { + "bbox": [ + 47, + 164, + 288, + 368 + ], + "type": "inline_equation", + "content": "(z,z_k)" + }, + { + "bbox": [ + 47, + 164, + 288, + 368 + ], + "type": "text", + "content": " thus composes a negative pair. SimCLR [7] adopts a contrastive loss to maximize the agreement of positive pairs over those of negative pairs. The MoCo [1, 10, 18] family adopts the same contrastive loss but adds a queue to store the image embeddings to alleviate the memory cost due to the large batch size. Formally, the contrastive loss takes the following form" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 96, + 373, + 287, + 403 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 96, + 373, + 287, + 403 + ], + "spans": [ + { + "bbox": [ + 96, + 373, + 287, + 403 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {C L} = - \\log \\frac {\\exp \\left(z \\cdot z ^ {\\prime} / t\\right)}{\\sum_ {i = 0} ^ {Q} \\exp \\left(z \\cdot z _ {i} / t\\right)}, \\tag {1}", + "image_path": "ca1d2829fd6095074dc3fecb15dea311811aeac682b5c24ea2fb00764672fa06.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 408, + 287, + 431 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 408, + 287, + 431 + ], + "spans": [ + { + "bbox": [ + 47, + 408, + 287, + 431 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 408, + 287, + 431 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 47, + 408, + 287, + 431 + ], + "type": "text", + "content": " denotes a temperature parameter, and " + }, + { + "bbox": [ + 47, + 408, + 287, + 431 + ], + "type": "inline_equation", + "content": "z_{i}" + }, + { + "bbox": [ + 47, + 408, + 287, + 431 + ], + "type": "text", + "content": " is the embedding in the queue." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 432, + 287, + 575 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 432, + 287, + 575 + ], + "spans": [ + { + "bbox": [ + 47, + 432, + 287, + 575 + ], + "type": "text", + "content": "Gradient-weighted Class Activation Mapping (GradCAM) is a commonly used way to produce a visual explanation. It identifies the important image regions contributing to the prediction by using the gradient of the loss function with respect to the feature map or input images. In this paper, we consider the gradient calculated with respect to the last convolutional layer feature maps. Formally, we consider the feature map of the last convolutional layer denoting as " + }, + { + "bbox": [ + 47, + 432, + 287, + 575 + ], + "type": "inline_equation", + "content": "\\phi(I) \\in \\mathbb{R}^{H \\times W \\times C}" + }, + { + "bbox": [ + 47, + 432, + 287, + 575 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 432, + 287, + 575 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 47, + 432, + 287, + 575 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 432, + 287, + 575 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 47, + 432, + 287, + 575 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 432, + 287, + 575 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 47, + 432, + 287, + 575 + ], + "type": "text", + "content": " are the height, width and number of channels of the feature map, respectively. In standard C-way classification, the GradCAM is calculated by:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 77, + 582, + 255, + 597 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 582, + 255, + 597 + ], + "spans": [ + { + "bbox": [ + 77, + 582, + 255, + 597 + ], + "type": "interline_equation", + "content": "[ \\operatorname {G r a d - C A M} (\\hat {y}) ] _ {i, j} = R e L U \\left(\\alpha_ {\\hat {y}} ^ {\\top} [ \\phi (I) ] _ {i, j}\\right)", + "image_path": "63cb278c3c6cac1d35343944418247ef41fbc6c78b4a227d4c9b8c9843934304.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 78, + 598, + 287, + 625 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 78, + 598, + 287, + 625 + ], + "spans": [ + { + "bbox": [ + 78, + 598, + 287, + 625 + ], + "type": "interline_equation", + "content": "w h e r e, \\alpha_ {\\hat {y}} = \\frac {\\partial \\mathcal {L} _ {C E} (P (y) , \\hat {y})}{\\partial [ \\phi (I) ] _ {i , j}} \\in \\mathbb {R} ^ {C}, \\tag {2}", + "image_path": "fa1f213a583235c4b98e41a4f955fee2bc7ac00101c8c96835bca96ca80667a1.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 631, + 287, + 668 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 631, + 287, + 668 + ], + "spans": [ + { + "bbox": [ + 47, + 631, + 287, + 668 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 631, + 287, + 668 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{CE}(P(y),\\hat{y})" + }, + { + "bbox": [ + 47, + 631, + 287, + 668 + ], + "type": "text", + "content": " is the cross-entropy loss measuring the compatibility between the posterior probability " + }, + { + "bbox": [ + 47, + 631, + 287, + 668 + ], + "type": "inline_equation", + "content": "P(y)" + }, + { + "bbox": [ + 47, + 631, + 287, + 668 + ], + "type": "text", + "content": " and ground-truth class label " + }, + { + "bbox": [ + 47, + 631, + 287, + 668 + ], + "type": "inline_equation", + "content": "\\hat{y}^3" + }, + { + "bbox": [ + 47, + 631, + 287, + 668 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 47, + 631, + 287, + 668 + ], + "type": "inline_equation", + "content": "[\\phi (I)]_{i,j}\\in \\mathbb{R}^C" + }, + { + "bbox": [ + 47, + 631, + 287, + 668 + ], + "type": "text", + "content": " denotes the" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 309, + 72, + 545, + 274 + ], + "blocks": [ + { + "bbox": [ + 309, + 72, + 545, + 274 + ], + "lines": [ + { + "bbox": [ + 309, + 72, + 545, + 274 + ], + "spans": [ + { + "bbox": [ + 309, + 72, + 545, + 274 + ], + "type": "image", + "image_path": "231d2cba7317d476c69e6e182c64a116164aa6f2cdd507bbe4b6738f1faee171.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 284, + 545, + 372 + ], + "lines": [ + { + "bbox": [ + 305, + 284, + 545, + 372 + ], + "spans": [ + { + "bbox": [ + 305, + 284, + 545, + 372 + ], + "type": "text", + "content": "Figure 2. The overview of our method. At the structure level, it has the following components: 1)Encoder: MoCo-based contrastive learning is used to create the image-level representation. 2) GradCAM fitting branch, which is a convolutional layer with " + }, + { + "bbox": [ + 305, + 284, + 545, + 372 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 305, + 284, + 545, + 372 + ], + "type": "text", + "content": " filters followed by a channel-wise max-out operator. 3) Inference: at the inference time, the prediction from GFB is used as a spatial attention mask, and it is used to replace the GAP operation by weighted average pooling to obtain the image representation." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 391, + 545, + 439 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 391, + 545, + 439 + ], + "spans": [ + { + "bbox": [ + 305, + 391, + 545, + 439 + ], + "type": "text", + "content": "feature vector located at the " + }, + { + "bbox": [ + 305, + 391, + 545, + 439 + ], + "type": "inline_equation", + "content": "(i,j)" + }, + { + "bbox": [ + 305, + 391, + 545, + 439 + ], + "type": "text", + "content": "-th grid. Grad-CAM " + }, + { + "bbox": [ + 305, + 391, + 545, + 439 + ], + "type": "inline_equation", + "content": "(\\hat{y})" + }, + { + "bbox": [ + 305, + 391, + 545, + 439 + ], + "type": "text", + "content": " denotes GradCAM for the " + }, + { + "bbox": [ + 305, + 391, + 545, + 439 + ], + "type": "inline_equation", + "content": "\\hat{y}" + }, + { + "bbox": [ + 305, + 391, + 545, + 439 + ], + "type": "text", + "content": "-th class. " + }, + { + "bbox": [ + 305, + 391, + 545, + 439 + ], + "type": "inline_equation", + "content": "[\\mathrm{Grad - CAM}(\\hat{y})]_{i,j}" + }, + { + "bbox": [ + 305, + 391, + 545, + 439 + ], + "type": "text", + "content": " refers to the importance value of the " + }, + { + "bbox": [ + 305, + 391, + 545, + 439 + ], + "type": "inline_equation", + "content": "(i,j)" + }, + { + "bbox": [ + 305, + 391, + 545, + 439 + ], + "type": "text", + "content": "th spatial grid for predicting the " + }, + { + "bbox": [ + 305, + 391, + 545, + 439 + ], + "type": "inline_equation", + "content": "\\hat{y}" + }, + { + "bbox": [ + 305, + 391, + 545, + 439 + ], + "type": "text", + "content": "-th class." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 439, + 545, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 439, + 545, + 485 + ], + "spans": [ + { + "bbox": [ + 305, + 439, + 545, + 485 + ], + "type": "text", + "content": "Note that although GradCAM is commonly used for supervised classification problems, it can be readily extended to other problems by changing the corresponding loss function." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 494, + 531, + 506 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 494, + 531, + 506 + ], + "spans": [ + { + "bbox": [ + 306, + 494, + 531, + 506 + ], + "type": "text", + "content": "3.2. Our Method: Learning Common Rationale" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 512, + 545, + 606 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 512, + 545, + 606 + ], + "spans": [ + { + "bbox": [ + 305, + 512, + 545, + 606 + ], + "type": "text", + "content": "Figure 2 gives an overview of the proposed method. Our method is extremely simple: we merely add one GradCAM fitting branch (GFB) and fit the GradCAM generated from the CL loss at the training time. At the test time, we let this GFB predict (normalized) GradCAM and use the prediction as an attention mask to perform weighted average pooling over the convolutional feature map. The details about this framework are elaborated as follows." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 608, + 545, + 656 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 608, + 545, + 656 + ], + "spans": [ + { + "bbox": [ + 305, + 608, + 545, + 656 + ], + "type": "text", + "content": "GradCAM Calculation. For self-supervised learning, we do not have access to ground-truth class labels. Therefore, we use the contrastive learning loss " + }, + { + "bbox": [ + 305, + 608, + 545, + 656 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{CL}" + }, + { + "bbox": [ + 305, + 608, + 545, + 656 + ], + "type": "text", + "content": " in Eq. 1 to replace " + }, + { + "bbox": [ + 305, + 608, + 545, + 656 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{CE}" + }, + { + "bbox": [ + 305, + 608, + 545, + 656 + ], + "type": "text", + "content": " in Eq. 2:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 321, + 662, + 545, + 695 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 662, + 545, + 695 + ], + "spans": [ + { + "bbox": [ + 321, + 662, + 545, + 695 + ], + "type": "interline_equation", + "content": "[ \\mathbf {G} ] _ {i, j} = R e L U \\left(\\frac {\\partial \\mathcal {L} _ {C L} (\\psi (\\phi (I)))}{\\partial [ \\phi (I) ] _ {i , j}} ^ {\\top} [ \\phi (I) ] _ {i, j}\\right), \\tag {3}", + "image_path": "675d8ee1b6b3189ae9799e6f6452cefde4182ec70f6719f82b5c11ffe766e87b.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 701, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 701, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 701, + 545, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 701, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\psi (\\cdot)" + }, + { + "bbox": [ + 306, + 701, + 545, + 714 + ], + "type": "text", + "content": " denotes the feature extractor. Note that in the" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 47, + 673, + 287, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 673, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 47, + 673, + 287, + 712 + ], + "type": "inline_equation", + "content": "^3\\mathcal{L}_{CE}(P(y),\\hat{y}) = \\log P(\\hat{y})" + }, + { + "bbox": [ + 47, + 673, + 287, + 712 + ], + "type": "text", + "content": " for the multi-classification problem and the gradient of " + }, + { + "bbox": [ + 47, + 673, + 287, + 712 + ], + "type": "inline_equation", + "content": "\\log P(y)" + }, + { + "bbox": [ + 47, + 673, + 287, + 712 + ], + "type": "text", + "content": " is proportional to the gradient of the corresponding logit. Those equivalence forms lead to the different definitions of GradCAM in the literature." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "11394" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 167 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 167 + ], + "type": "text", + "content": "original GradCAM, the GradCAM weight indicates how important each region contributes to classifying the image into the " + }, + { + "bbox": [ + 46, + 72, + 287, + 167 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 72, + 287, + 167 + ], + "type": "text", + "content": "-th class. Similarly, the GradCAM weight from " + }, + { + "bbox": [ + 46, + 72, + 287, + 167 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{CL}" + }, + { + "bbox": [ + 46, + 72, + 287, + 167 + ], + "type": "text", + "content": " indicates the contribution of each region to the instance discrimination task in the contrastive learning objective. From Figure 1, we can see that existing Contrastive Learning approaches learn a diverse set of visual patterns, and not all of them are relevant to the FGVR task." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 167, + 288, + 288 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 167, + 288, + 288 + ], + "spans": [ + { + "bbox": [ + 46, + 167, + 288, + 288 + ], + "type": "text", + "content": "Architecture of the GFB. The structure of the GFB plays an important role in our method. We expect this branch has a limited fitting capability, such that the branch will not overfit the GradCAM but only capture the commonly occurring discriminative patterns, i.e., common rationales. Inspired by [33], we use a convolutional layer with " + }, + { + "bbox": [ + 46, + 167, + 288, + 288 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 167, + 288, + 288 + ], + "type": "text", + "content": " filter and " + }, + { + "bbox": [ + 46, + 167, + 288, + 288 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 46, + 167, + 288, + 288 + ], + "type": "text", + "content": " kernel size followed by the max-out operation [33] as the fitting branch. Formally, such a branch applies the following operation to the local feature " + }, + { + "bbox": [ + 46, + 167, + 288, + 288 + ], + "type": "inline_equation", + "content": "[\\phi(I)]_{i,j}" + }, + { + "bbox": [ + 46, + 167, + 288, + 288 + ], + "type": "text", + "content": " at the " + }, + { + "bbox": [ + 46, + 167, + 288, + 288 + ], + "type": "inline_equation", + "content": "(i,j)" + }, + { + "bbox": [ + 46, + 167, + 288, + 288 + ], + "type": "text", + "content": "-th grid of the feature map:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 110, + 293, + 287, + 310 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 110, + 293, + 287, + 310 + ], + "spans": [ + { + "bbox": [ + 110, + 293, + 287, + 310 + ], + "type": "interline_equation", + "content": "A _ {i, j} = \\max _ {k} \\left\\{\\mathbf {w} _ {k} ^ {\\top} [ \\phi (I) ] _ {i, j} \\right\\}, \\tag {4}", + "image_path": "38285fa0248429ad8b185f817701d223985668ef4fbb392e8136b17712cdd16c.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 316, + 287, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 316, + 287, + 434 + ], + "spans": [ + { + "bbox": [ + 46, + 316, + 287, + 434 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 316, + 287, + 434 + ], + "type": "inline_equation", + "content": "A_{i,j}" + }, + { + "bbox": [ + 46, + 316, + 287, + 434 + ], + "type": "text", + "content": " will be the predicted GradCAM weight at the " + }, + { + "bbox": [ + 46, + 316, + 287, + 434 + ], + "type": "inline_equation", + "content": "(i,j)" + }, + { + "bbox": [ + 46, + 316, + 287, + 434 + ], + "type": "text", + "content": "-th grid and " + }, + { + "bbox": [ + 46, + 316, + 287, + 434 + ], + "type": "inline_equation", + "content": "\\mathbf{w}_k" + }, + { + "bbox": [ + 46, + 316, + 287, + 434 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 46, + 316, + 287, + 434 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 316, + 287, + 434 + ], + "type": "text", + "content": "-th filter (projector) in the convolutional layer. Intuitively, the convolutional layer can be seen as a collection of " + }, + { + "bbox": [ + 46, + 316, + 287, + 434 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 316, + 287, + 434 + ], + "type": "text", + "content": " detectors and the above operation can be understood as follows: each projection vector " + }, + { + "bbox": [ + 46, + 316, + 287, + 434 + ], + "type": "inline_equation", + "content": "\\mathbf{w}_k" + }, + { + "bbox": [ + 46, + 316, + 287, + 434 + ], + "type": "text", + "content": " detects an object part " + }, + { + "bbox": [ + 46, + 316, + 287, + 434 + ], + "type": "inline_equation", + "content": "\\mathcal{P}_k" + }, + { + "bbox": [ + 46, + 316, + 287, + 434 + ], + "type": "text", + "content": "; the max-out operation takes the maximum of " + }, + { + "bbox": [ + 46, + 316, + 287, + 434 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 316, + 287, + 434 + ], + "type": "text", + "content": " projections at a given location, which will result in a high value if any of the " + }, + { + "bbox": [ + 46, + 316, + 287, + 434 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 316, + 287, + 434 + ], + "type": "text", + "content": " object parts are detected. Varying " + }, + { + "bbox": [ + 46, + 316, + 287, + 434 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 316, + 287, + 434 + ], + "type": "text", + "content": " could adjust the size of the detector pool and influence the fitting capability." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 435, + 287, + 494 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 435, + 287, + 494 + ], + "spans": [ + { + "bbox": [ + 46, + 435, + 287, + 494 + ], + "type": "text", + "content": "Training Loss. In addition to the contrastive learning loss, we require the GFB to produce a similar attention map as the one produced from the GradCAM of " + }, + { + "bbox": [ + 46, + 435, + 287, + 494 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{CL}" + }, + { + "bbox": [ + 46, + 435, + 287, + 494 + ], + "type": "text", + "content": ". We follow [33] to normalize the GradCAM into a probability distribution and adopt KL divergence as the loss function." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 495, + 287, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 495, + 287, + 518 + ], + "spans": [ + { + "bbox": [ + 46, + 495, + 287, + 518 + ], + "type": "text", + "content": "Formally, we normalize the GradCAM " + }, + { + "bbox": [ + 46, + 495, + 287, + 518 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 46, + 495, + 287, + 518 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 495, + 287, + 518 + ], + "type": "inline_equation", + "content": "\\mathcal{A}" + }, + { + "bbox": [ + 46, + 495, + 287, + 518 + ], + "type": "text", + "content": " via the softmax function:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 88, + 521, + 245, + 552 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 88, + 521, + 245, + 552 + ], + "spans": [ + { + "bbox": [ + 88, + 521, + 245, + 552 + ], + "type": "interline_equation", + "content": "[ \\bar {\\mathbf {G}} ] _ {i, j} = \\frac {\\exp \\left([ \\mathbf {G} ] _ {i , j} / \\tau\\right)}{\\sum_ {i = 1} ^ {H} \\sum_ {j = 1} ^ {W} \\exp \\left([ \\mathbf {G} ] _ {i , j} / \\tau\\right)},", + "image_path": "f436c97e555e8131a61136335e7c40c59204c40032c708c58166900ceb1bacb4.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 88, + 553, + 287, + 583 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 88, + 553, + 287, + 583 + ], + "spans": [ + { + "bbox": [ + 88, + 553, + 287, + 583 + ], + "type": "interline_equation", + "content": "[ \\bar {\\mathbf {A}} ] _ {i, j} = \\frac {\\exp \\left([ \\mathbf {A} ] _ {i , j} / \\tau\\right)}{\\sum_ {i = 1} ^ {H} \\sum_ {j = 1} ^ {W} \\exp \\left([ \\mathbf {A} ] _ {i , j} / \\tau\\right)}, \\tag {5}", + "image_path": "ac831c0ec29788d7df2264c61e9c6b87005c88d4d3601441cc55e7ef82f3a997.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 587, + 287, + 623 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 587, + 287, + 623 + ], + "spans": [ + { + "bbox": [ + 47, + 587, + 287, + 623 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 587, + 287, + 623 + ], + "type": "inline_equation", + "content": "[\\cdot ]_{i,j}" + }, + { + "bbox": [ + 47, + 587, + 287, + 623 + ], + "type": "text", + "content": " denotes the " + }, + { + "bbox": [ + 47, + 587, + 287, + 623 + ], + "type": "inline_equation", + "content": "i,j" + }, + { + "bbox": [ + 47, + 587, + 287, + 623 + ], + "type": "text", + "content": "-th element of the feature map. " + }, + { + "bbox": [ + 47, + 587, + 287, + 623 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 47, + 587, + 287, + 623 + ], + "type": "text", + "content": " is an empirical temperature parameter and we set it to 0.4 here. Thus, the objective can be expressed as follows:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 99, + 628, + 287, + 662 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 99, + 628, + 287, + 662 + ], + "spans": [ + { + "bbox": [ + 99, + 628, + 287, + 662 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {K L} = \\sum_ {i = 1} ^ {H} \\sum_ {j = 1} ^ {W} [ \\bar {\\mathbf {A}} ] _ {i, j} \\log \\frac {[ \\bar {\\mathbf {A}} ] _ {i , j}}{[ \\bar {\\mathbf {G}} ] _ {i , j}}, \\tag {6}", + "image_path": "60ab782d39c14d68dd56363ea481cc7b5b954842434e8ba1a5dae8dcf612bee7.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 668, + 287, + 691 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 668, + 287, + 691 + ], + "spans": [ + { + "bbox": [ + 47, + 668, + 287, + 691 + ], + "type": "text", + "content": "Thus, the final loss function taken on all images over an unlabelled dataset is shown as followings." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 123, + 698, + 287, + 710 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 123, + 698, + 287, + 710 + ], + "spans": [ + { + "bbox": [ + 123, + 698, + 287, + 710 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\lambda \\mathcal {L} _ {C L} + \\nu \\mathcal {L} _ {K L}. \\tag {7}", + "image_path": "b1951e81afb516e79b424c35a6d55285c8c49e95dd6a20c29ffa392e03688dd8.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 72, + 545, + 159 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 159 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 159 + ], + "type": "text", + "content": "Inference. At the inference time, the GradCAM fitting branch will be firstly used to produce an attention mask, i.e., prediction of GradCAM. This attention mask is firstly normalized using " + }, + { + "bbox": [ + 304, + 72, + 545, + 159 + ], + "type": "inline_equation", + "content": "A_{i,j}' = \\frac{A_{i,j} - \\min(A)}{1e^{-7} + \\max(A)}" + }, + { + "bbox": [ + 304, + 72, + 545, + 159 + ], + "type": "text", + "content": ". Then we use the normalized attention to perform weighted average pooling of features from the last-layer convolutional feature map. Formally, it calculates:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 363, + 165, + 545, + 190 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 363, + 165, + 545, + 190 + ], + "spans": [ + { + "bbox": [ + 363, + 165, + 545, + 190 + ], + "type": "interline_equation", + "content": "\\mathbf {f} = \\sum_ {i, j} \\left[ A ^ {\\prime} \\right] _ {i, j} [ \\phi (I) ] _ {i, j} \\in \\mathbb {R} ^ {C}. \\tag {8}", + "image_path": "73658bc0735a25b723e0d219ea832e93d14587c526bbb521bc33ab32fbb8f7b0.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 198, + 448, + 208 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 198, + 448, + 208 + ], + "spans": [ + { + "bbox": [ + 305, + 198, + 448, + 208 + ], + "type": "text", + "content": "f is used for the downstream tasks." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 209, + 545, + 233 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 209, + 545, + 233 + ], + "spans": [ + { + "bbox": [ + 305, + 209, + 545, + 233 + ], + "type": "text", + "content": "Discussion. Our approach is inspired by the SAM method in [33]. However, there are several important differences:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 317, + 239, + 545, + 564 + ], + "type": "list", + "angle": 0, + "index": 19, + "blocks": [ + { + "bbox": [ + 317, + 239, + 545, + 274 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 239, + 545, + 274 + ], + "spans": [ + { + "bbox": [ + 317, + 239, + 545, + 274 + ], + "type": "text", + "content": "- SAM method was proposed for supervised FGVC under a low-data regime, while our approach is designed for self-supervised learning." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 317, + 281, + 545, + 473 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 281, + 545, + 473 + ], + "spans": [ + { + "bbox": [ + 317, + 281, + 545, + 473 + ], + "type": "text", + "content": "- Most importantly, our study discovers that for self-supervised feature learning, the best strategy to interact with the GFB and the feature learning branch is different from what has been discovered in [33]. Table 1 summarizes the main differences. As seen, unlike either SAM or SAM-bilinear, we do not introduce any interaction between the feature learning branch and the GradCAM fitting branch during training but allow them to perform weighted average pooling at the test stage. In fact, we find that applying cross-branch interaction at the training stage will undermine the feature learning process. This is because applying cross-branch interaction, e.g., using A to weighted pool features will prevent CL from exploring discriminative patterns, especially when A has not been properly learned." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 317, + 480, + 545, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 480, + 545, + 564 + ], + "spans": [ + { + "bbox": [ + 317, + 480, + 545, + 564 + ], + "type": "text", + "content": "- For multiple projections, SAM uses bilinear pooling to aggregate " + }, + { + "bbox": [ + 317, + 480, + 545, + 564 + ], + "type": "inline_equation", + "content": "\\mathbf{A}" + }, + { + "bbox": [ + 317, + 480, + 545, + 564 + ], + "type": "text", + "content": " and the original feature map, resulting in high-dimensional feature representation. Our work performs max-out on multiple projections, resulting in a single attention mask for performing weighted average pooling. Consequently, we could achieve a significant reduction of the feature dimensionality." + } + ] + } + ], + "index": 18 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 304, + 570, + 545, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 545, + 629 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 545, + 629 + ], + "type": "text", + "content": "To make our study comprehensive, we also explore several variants as baseline approaches. From the comparison with those methods, the benefit of our design could become more evident. For comparison, we use the following architectures as baselines for self-supervised pre-training:" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 630, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 545, + 689 + ], + "type": "text", + "content": "SAM-SSL: this baseline extends SAM by changing its objective function from cross-entropy to the contrastive loss in MoCo V2. It shares the same architecture as SAM [33], where a projection is used as the GFB, and GradCAM fitting is trained as an auxiliary task to contrastive learning." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "text", + "content": "SAM-SSL-Bilinear: this baseline extends SAM-bilinear by using the contrastive loss in MoCo V2. The cross-branch" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "11395" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 102, + 558, + 196 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 545, + 93 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 545, + 93 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 545, + 93 + ], + "type": "text", + "content": "Table 1. Upper part: summary of the major difference between our method and SAM method [33]. Lower part: two variants that are also investigated in this work." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 102, + 558, + 196 + ], + "lines": [ + { + "bbox": [ + 48, + 102, + 558, + 196 + ], + "spans": [ + { + "bbox": [ + 48, + 102, + 558, + 196 + ], + "type": "table", + "html": "
MethodGradCAM Fitting BranchCross-branch InteractionFeature DimensionLoss Function
traintest
SAM1 proj××CCrossEntropy
SAM-Bilinearmax[K projs]bilinear poolingbilinear poolingC*KCrossEntropy
Oursmax[K projs]×weighted average poolingCContrastive
Ours-DualPoolingmax[K projs]weighted average poolingweighted average poolingCContrastive
Ours-MultiTaskmax[K projs]××CContrastive
", + "image_path": "5f4542668fd93974d0295ebd2017e8ca2de6f8aae8c87de0d73f4026394d56df.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 216, + 287, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 216, + 287, + 239 + ], + "spans": [ + { + "bbox": [ + 46, + 216, + 287, + 239 + ], + "type": "text", + "content": "interaction of SAM-SSL-Bilinear follows the original SAM-Bilinear method." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 239, + 287, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 239, + 287, + 335 + ], + "spans": [ + { + "bbox": [ + 46, + 239, + 287, + 335 + ], + "type": "text", + "content": "Besides the above two extensions of the SAM methods, we also consider two variants of our method. The first is called Ours-MultiTask, which does not perform weighted average pooling at the test stage but merely uses GradCAM fitting as an auxiliary task. Another is called Ours-DualPooling, which performs weighted average pooling at both training and testing stages. Those two variants are summarized in Table 1." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 346, + 128, + 359 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 346, + 128, + 359 + ], + "spans": [ + { + "bbox": [ + 47, + 346, + 128, + 359 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 365, + 287, + 462 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 365, + 287, + 462 + ], + "spans": [ + { + "bbox": [ + 46, + 365, + 287, + 462 + ], + "type": "text", + "content": "In this section, we will evaluate our proposed method on three widely used fine-grained visual datasets (Caltech-UCSD Birds (CUB-200-2011) [35], Stanford Cars [25] and FGVC-Aircraft [27]), and a large-scale fine-grained dataset (iNaturalist2019 [34]). Our experiments aim to understand the effectiveness and the components of the proposed algorithm." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 468, + 170, + 480 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 468, + 170, + 480 + ], + "spans": [ + { + "bbox": [ + 47, + 468, + 170, + 480 + ], + "type": "text", + "content": "4.1. Datasets and Settings" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 486, + 287, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 486, + 287, + 640 + ], + "spans": [ + { + "bbox": [ + 46, + 486, + 287, + 640 + ], + "type": "text", + "content": "Datasets. CUB-200-2011 contains 11,788 images with 200 bird species, where 5994 images are used for training and 5794 images for testing. Stanford Cars contains 16,185 images with 196 categories, where 8144 images are for training and 8041 images for testing. FGVC-Aircraft contains 10,000 images with 100 categories, where 6667 images are for training, and 3333 images are for testing. iNaturalist2019 in its 2019 version contains 1,010 categories, with a combined training and validation set of 268,243 images. Note that fine-grained visual task focus on distinguishing similar subcategories within a super-category, while there are six super-categories in iNaturalist2019." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 642, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 287, + 714 + ], + "type": "text", + "content": "Implementation Details. We adopt the ResNet-50 [19] as the network backbone, which is initialized using ImageNet-trained weights, and build our method on top of MoCo v2 [8]. Therefore the SSL loss term is identical to MoCo v2. The momentum value and memory size are set similarly to MoCo v2, i.e., 0.999 and 65536, respectively." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 216, + 547, + 347 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 216, + 547, + 347 + ], + "spans": [ + { + "bbox": [ + 304, + 216, + 547, + 347 + ], + "type": "text", + "content": "The projector head " + }, + { + "bbox": [ + 304, + 216, + 547, + 347 + ], + "type": "inline_equation", + "content": "g_{\\theta}" + }, + { + "bbox": [ + 304, + 216, + 547, + 347 + ], + "type": "text", + "content": " in MoCo v2 is composed of two fully-connected layers with ReLU and a third linear layer with batch normalization (BN) [21]. The size of all three layers is " + }, + { + "bbox": [ + 304, + 216, + 547, + 347 + ], + "type": "inline_equation", + "content": "2048 \\times 2048 \\times 256" + }, + { + "bbox": [ + 304, + 216, + 547, + 347 + ], + "type": "text", + "content": ". We set the mini-batch size as 128 and used an SGD optimizer with a learning rate of 0.03, a momentum of 0.9, and a weight decay of 0.0001. 100 epochs are used to train the feature extractor. The images from the four FGVR datasets are resized to " + }, + { + "bbox": [ + 304, + 216, + 547, + 347 + ], + "type": "inline_equation", + "content": "224 \\times 224" + }, + { + "bbox": [ + 304, + 216, + 547, + 347 + ], + "type": "text", + "content": " pixels during training times. During testing time, images are firstly resized to 256 pixels and then are centered cropped to " + }, + { + "bbox": [ + 304, + 216, + 547, + 347 + ], + "type": "inline_equation", + "content": "224 \\times 224" + }, + { + "bbox": [ + 304, + 216, + 547, + 347 + ], + "type": "text", + "content": " on these four FGVR datasets." + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 307, + 381, + 547, + 502 + ], + "blocks": [ + { + "bbox": [ + 306, + 354, + 426, + 367 + ], + "lines": [ + { + "bbox": [ + 306, + 354, + 426, + 367 + ], + "spans": [ + { + "bbox": [ + 306, + 354, + 426, + 367 + ], + "type": "text", + "content": "4.2. Evaluation Protocols" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 307, + 381, + 547, + 502 + ], + "lines": [ + { + "bbox": [ + 307, + 381, + 547, + 502 + ], + "spans": [ + { + "bbox": [ + 307, + 381, + 547, + 502 + ], + "type": "image", + "image_path": "1d524e1ef944fee21646c78ee698bb7c0852eb9ebee7a653e1a57d765689f84e.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 510, + 545, + 555 + ], + "lines": [ + { + "bbox": [ + 304, + 510, + 545, + 555 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 545, + 555 + ], + "type": "text", + "content": "Figure 3. Comparison of ResNet-50, MoCo v2 and Ours on the retrieval rank-1 on the iNaturalist2019 dataset. \"Amphibians\", \"Birds\", \"Fungi\", \"Reptiles\", and \"Insects\" are the superclasses in iNaturalist2019." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 570, + 545, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 545, + 653 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 545, + 653 + ], + "type": "text", + "content": "We evaluate the proposed method in two settings: linear probing and image retrieval. Linear probing is a commonly used evaluation protocol in SSL. In linear probing, the feature extractor learned from the SSL algorithm will be fixed and a linear classifier will be trained on top of the learned features. The classification performance of the linear classifier indicates the quality of the learned feature." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": "Besides linear probing, we also use image retrieval (also equivalent to the nearest neighbor classification task) task to evaluate the learned features, which was also explored in the literature [6,22,23]. This task aims to find the images with the same category as query images based on the" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "11396" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 123, + 544, + 267 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 545, + 116 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 545, + 116 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 545, + 116 + ], + "type": "text", + "content": "Table 2. Classification and retrieval of our method evaluated on the CUB-200-2011, Stanford Cars and FGVC Aircraft datasets. \"ResNet-50\" represents pre-training in the ImageNet dataset [12] in a supervised manner, then freezing the ResNet-50 backbone and only optimizing the supervised linear classifier in the classification task. We report the Top 1 and Top 5 (in %) on the classification task, rank-1, rank-5, and mAP (in %) on the retrieval task. 100, 50, and 20 are the three different label proportions (in %) in the classification task." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 123, + 544, + 267 + ], + "lines": [ + { + "bbox": [ + 50, + 123, + 544, + 267 + ], + "spans": [ + { + "bbox": [ + 50, + 123, + 544, + 267 + ], + "type": "table", + "html": "
DatasetMethodClassificationRetrieval
Top 1/Top 5(100)Top 1/Top 5(50)Top 1/Top 5(20)rank-1rank-5mAP
CUB-200-2011ResNet-5068.17/90.4258.99/85.9046.54/77.0910.6529.325.09
MoCo v268.30/90.8560.96/87.0046.91/76.5917.0741.468.13
Ours71.31/92.0366.52/90.0655.33/83.5249.6975.2324.01
Stanford CarsResNet-5057.41/83.5546.23/74.3131.19/58.674.9116.982.34
MoCo v258.43/84.8550.17/77.3835.14/64.1010.9429.573.12
Ours60.75/86.4453.87/81.7240.88/69.1834.5660.758.87
FGVC AircraftResNet-5047.38/74.7337.83/67.1228.20/54.735.1614.222.61
MoCo v252.54/80.7445.52/73.8535.17/65.0819.3839.906.30
Ours55.87/84.7348.22/77.1438.55/68.5334.3361.0915.43
", + "image_path": "38927331c5a6f6ab1faa017e166bde401cc5e998bfc2367f029d4468f21c72d2.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 286, + 289, + 406 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 286, + 289, + 406 + ], + "spans": [ + { + "bbox": [ + 46, + 286, + 289, + 406 + ], + "type": "text", + "content": "learned feature. Note that, unlike linear probing, the image retrieval task does not involve a large amount of labeled data – which could be used to suppress the less relevant features. In this sense, succeeding in the image retrieval task imposes higher feature quality requirements. Moreover, image retrieval is a practically useful task, and unsupervised feature learning is an attractive solution to image retrieval since the whole retrieval system can be built without any human annotation and intervention. For the retrieval task, we use rank-1, rank-5, and mAP as evaluation metrics." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 416, + 133, + 428 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 416, + 133, + 428 + ], + "spans": [ + { + "bbox": [ + 47, + 416, + 133, + 428 + ], + "type": "text", + "content": "4.3. Main Results" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 436, + 287, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 436, + 287, + 484 + ], + "spans": [ + { + "bbox": [ + 46, + 436, + 287, + 484 + ], + "type": "text", + "content": "The Effectiveness of the Proposed Method. Our method is based on MoCo v2. We first compare our result against MoCo v2 to examine the performance gain. The results are reported in Table 2 and Figure 3." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 485, + 288, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 485, + 288, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 485, + 288, + 664 + ], + "type": "text", + "content": "From Table 2, we can see that our method has led to a significant improvement over MoCo v2. It achieves " + }, + { + "bbox": [ + 46, + 485, + 288, + 664 + ], + "type": "inline_equation", + "content": "71.31\\%" + }, + { + "bbox": [ + 46, + 485, + 288, + 664 + ], + "type": "text", + "content": " top-1 accuracy and " + }, + { + "bbox": [ + 46, + 485, + 288, + 664 + ], + "type": "inline_equation", + "content": "92.03\\%" + }, + { + "bbox": [ + 46, + 485, + 288, + 664 + ], + "type": "text", + "content": " top-5 accuracy on the CUB-200-2011 dataset with " + }, + { + "bbox": [ + 46, + 485, + 288, + 664 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 46, + 485, + 288, + 664 + ], + "type": "text", + "content": " label proportions, which is a " + }, + { + "bbox": [ + 46, + 485, + 288, + 664 + ], + "type": "inline_equation", + "content": "3.01\\%" + }, + { + "bbox": [ + 46, + 485, + 288, + 664 + ], + "type": "text", + "content": " improvement on top-1 and " + }, + { + "bbox": [ + 46, + 485, + 288, + 664 + ], + "type": "inline_equation", + "content": "1.18\\%" + }, + { + "bbox": [ + 46, + 485, + 288, + 664 + ], + "type": "text", + "content": " improvement on top-5 over MoCo v2. Similarly, significant improvement can also be found on the Stanford Cars and FGVC Aircraft datasets. This demonstrates that our methods improve the quality of the feature representations learned from the original MoCo v2. Notably, with the label proportions reduced from " + }, + { + "bbox": [ + 46, + 485, + 288, + 664 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 46, + 485, + 288, + 664 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 485, + 288, + 664 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 46, + 485, + 288, + 664 + ], + "type": "text", + "content": ", there is generally a better improvement in the performance of the proposed method, which demonstrates that the proposed method learns less noisy features, so that training with fewer data can generalize better." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": "The advantage of the proposed method becomes more pronounced when evaluating the image retrieval task. As seen from Table 2, our method leads to a significant boost in performance on all datasets. Specifically, the rank-1," + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 286, + 547, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 286, + 547, + 407 + ], + "spans": [ + { + "bbox": [ + 304, + 286, + 547, + 407 + ], + "type": "text", + "content": "rank-5 and mAP of ours (" + }, + { + "bbox": [ + 304, + 286, + 547, + 407 + ], + "type": "inline_equation", + "content": "K = 32" + }, + { + "bbox": [ + 304, + 286, + 547, + 407 + ], + "type": "text", + "content": ") are " + }, + { + "bbox": [ + 304, + 286, + 547, + 407 + ], + "type": "inline_equation", + "content": "49.69\\%" + }, + { + "bbox": [ + 304, + 286, + 547, + 407 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 286, + 547, + 407 + ], + "type": "inline_equation", + "content": "75.23\\%" + }, + { + "bbox": [ + 304, + 286, + 547, + 407 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 286, + 547, + 407 + ], + "type": "inline_equation", + "content": "24.01\\%" + }, + { + "bbox": [ + 304, + 286, + 547, + 407 + ], + "type": "text", + "content": ", respectively on the CUB-200-2011 dataset, which is " + }, + { + "bbox": [ + 304, + 286, + 547, + 407 + ], + "type": "inline_equation", + "content": "32.62\\%" + }, + { + "bbox": [ + 304, + 286, + 547, + 407 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 286, + 547, + 407 + ], + "type": "inline_equation", + "content": "33.77\\%" + }, + { + "bbox": [ + 304, + 286, + 547, + 407 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 286, + 547, + 407 + ], + "type": "inline_equation", + "content": "15.88\\%" + }, + { + "bbox": [ + 304, + 286, + 547, + 407 + ], + "type": "text", + "content": " higher than the method of MoCo v2. Similar improvement can also be observed on the Stanford Cars and FGVC Aircraft datasets. On the large-scale fine-grained dataset, i.e., iNaturalist2019, our method also performs better than MoCo v2 shown in Figure 3. These indicate the proposed method is particularly good for retrieval tasks, which might be due to its ability to filter out less relevant patterns." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 415, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 415, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 415, + 547, + 715 + ], + "type": "text", + "content": "Comparison with Other SSL Frameworks. In addition to the comparison on MoCo v2, we also compare the proposed method against other commonly used SSL approaches. We report the Top-1 accuracy, the running time, and the peak memory with two different batch sizes (32 & 128). The results are shown in Table 3. All methods are run on 4 V100 GPUs, each with 32G memory. We report the training speed, GPU memory usage, and performance. For classification performance, the blue marks mean the best classification results, and the green marks mean the second-best classification results. It is clear to see that our method achieves the best Top-1 performance on the CUB-200-2011, Stanford Cars, and FGVC Aircraft datasets. Also, when the GPU resources are limited, e.g., only 1 V100 GPU is available, the proposed method reduces the batch size but still remains a competitive classification performance compared to other SSL methods. Regarding training speed and GPU memory usage, the proposed method has the same running time as MoCo v2 and SimSiam, slightly more peak memory than SimSiam, but less peak memory, and quicker running time than SimCLR and BYOL. Although DINO uses the least training time and GPU memory usage, their performances are also the worst compared to ours and other self-supervised learning methods. Barlow Twins and VICReg" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "11397" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 134, + 555, + 270 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 547, + 127 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 547, + 127 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 547, + 127 + ], + "type": "text", + "content": "Table 3. Compared to other state-of-the-art self-supervised learning frameworks with Top 1 accuracy on the CUB-200-2011, Stanford Cars and FGVC Aircraft datasets; running time and peak memory on the CUB-200-2011 dataset. The training time is measured on 4 Tesla V100 GPUs with 100 epochs, and the peak memory is calculated on a single GPU. Top 1 accuracy (\\%) is reported on linear classification with the frozen representations of their feature extractor. For fairness, all following models use the ResNet-50 as the network backbone and initialize the ResNet-50 architecture with ImageNet-trained weights. blue=best, green=second best." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 134, + 555, + 270 + ], + "lines": [ + { + "bbox": [ + 48, + 134, + 555, + 270 + ], + "spans": [ + { + "bbox": [ + 48, + 134, + 555, + 270 + ], + "type": "table", + "html": "
MethodBatch SizeTop 1(CUB)Top 1(Cars)Top 1(Aircraft)time(CUB)GPU Memory(CUB)
Supervised-81.3491.0287.13--
DINO [6]32/12812.37/16.669.27/10.518.52/12.931.5h/1.5h4.9G/8.4G
SimCLR [7]*32/12833.49/38.3944.31/49.4140.56/45.222.5h/2.5h7.1G/23.8G
BYOL [16]*32/12836.64/39.2743.66/45.2134.90/37.624.0h/4.0h7.4G/24.6G
SimSiam [9]32/12835.82/39.9756.87/58.8941.59/43.062.0h/2.0h4.4G/8.9G
MoCo v2 [8]32/12868.03/68.3052.61/58.4342.51/52.542.0h/2.0h6.1G/10.3G
BarlowTwins [40]32/12828.58/33.4523.34/31.9128.35/34.771.5h/1.5h7.0G/8.9G
VICReg [4]32/12830.07/37.7819.29/30.8029.97/36.001.0h/1.0h7.0G/9.0G
Ours32/12870.43 /71.3156.90/60.7546.92/55.872.0h/2.0h6.1G/10.3G
BYOL+Ours*32/12845.79/51.2048.53 /50.6440.08/45.944.0h/4.0h7.4G/24.6G
", + "image_path": "08918a9edbff3881e2b78b51095d6db4f567f8b3eb9751bf2b2f06296ec98aa9.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 60, + 271, + 527, + 283 + ], + "lines": [ + { + "bbox": [ + 60, + 271, + 527, + 283 + ], + "spans": [ + { + "bbox": [ + 60, + 271, + 527, + 283 + ], + "type": "text", + "content": "Due to computational constraints, we are unable to evaluate on the batch size of 4096 as used in the original paper; we leave this for future work." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 301, + 288, + 337 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 301, + 288, + 337 + ], + "spans": [ + { + "bbox": [ + 46, + 301, + 288, + 337 + ], + "type": "text", + "content": "have a quicker running time and less GPU memory than our proposed method with a batch size of 128, but their performances are much worse than ours." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 338, + 288, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 338, + 288, + 399 + ], + "spans": [ + { + "bbox": [ + 46, + 338, + 288, + 399 + ], + "type": "text", + "content": "Our method also can be implemented with other self-supervised learning methods, e.g., BYOL, referring to \"BYOL+Ours\" presented in Table 3. As we can see, our method applied to the BYOL objective is consistently superior to the baseline of BYOL on three fine-grained datasets." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 407, + 253, + 420 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 407, + 253, + 420 + ], + "spans": [ + { + "bbox": [ + 47, + 407, + 253, + 420 + ], + "type": "text", + "content": "4.4. Comparison with Alternative Solutions" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 426, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 426, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 45, + 426, + 288, + 715 + ], + "type": "text", + "content": "Our method is featured by its capability of discovering the key discriminative regions, which is vital for FGVR. In this section, we compared the proposed method with nine alternative solutions to take object localization into account. The first is to simply use a bilinear network [26] for MoCo V2. Specifically, we follow the similar bilinear structure as in [33], which implicitly learns " + }, + { + "bbox": [ + 45, + 426, + 288, + 715 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 45, + 426, + 288, + 715 + ], + "type": "text", + "content": " parts and aggregates features from those " + }, + { + "bbox": [ + 45, + 426, + 288, + 715 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 45, + 426, + 288, + 715 + ], + "type": "text", + "content": " parts, and we set " + }, + { + "bbox": [ + 45, + 426, + 288, + 715 + ], + "type": "inline_equation", + "content": "K = 32" + }, + { + "bbox": [ + 45, + 426, + 288, + 715 + ], + "type": "text", + "content": " to make a fair comparison to us (since we use 32 projections). We still use MoCo v2 as the SSL framework and denote this method MoCo v2 -Bilinear. The second and third are the methods of SAM-SSL and SAM-SSL-Bilinear introduced in Section 3.2 since our method is extended from the self-boosting attention mechanism (SAM) proposed in [33]. The fourth and fifth are the two variants considered in Section 3.2. The other four comparing methods are the very recently localization-based self-supervised methods, DiLo [42], CVSA [38], LEWEL [20], and ContrastiveCrop [29]. DiLo uses a copy-and-pasting approach as a kind of augmentation to create an image with a different background. The work of CVSA targets a similar problem as ours. They exploit self-supervised fine-grained contrastive learning via cross-view saliency alignment to crops and swaps saliency regions of images. LEWEL adap" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 301, + 547, + 374 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 301, + 547, + 374 + ], + "spans": [ + { + "bbox": [ + 304, + 301, + 547, + 374 + ], + "type": "text", + "content": "tively aggregates spatial information of features using spatial aggregation operation between feature map and alignment map to guide the feature learning better. The work of ContrastiveCrop is based on the idea of using attention to guide image cropping, which localizes the object and improves the data augmentation for self-supervised learning." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 375, + 547, + 661 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 375, + 547, + 661 + ], + "spans": [ + { + "bbox": [ + 304, + 375, + 547, + 661 + ], + "type": "text", + "content": "The comparison to those nine alternatives is shown in Table 4. As seen, by comparing the SAM-SSL and SAM-SSL-Bilinear, we observe that the proposed method can lead to overall better performance, achieving a significant boost on some datasets. Occasionally, SAM-SSL-Bilinear (" + }, + { + "bbox": [ + 304, + 375, + 547, + 661 + ], + "type": "inline_equation", + "content": "K = 32" + }, + { + "bbox": [ + 304, + 375, + 547, + 661 + ], + "type": "text", + "content": ") can achieve comparable performance as ours, but at the cost of using a much higher feature dimensionality. This clearly shows the advantage of the proposed scheme over the scheme in [33]. Furthermore, our method and combined with ContrastiveCrop (i.e., ours+ContrastiveCrop) with the lowest feature dimensions but achieve the best Top 1 and rank-1 performance on the CUB-200-2011, Stanford Cars and FGVC Aircraft datasets, compared to those nine alternatives. Also, compared with the other localization-aware SSL methods, our method shows a clear advantage, especially for the retrieval task, e.g., ours vs. LEWEL. Finally, we find that the variant of our method does not produce a good performance. For example, when applying weighted average pooling at both training and testing, i.e., Ours-DualPooling, will make the feature learning fail completely, and the representations will collapse. On the other hand, not performing cross-branch interaction, i.e., Ours-MultiTask, does not bring too much improvement over the MoCo v2 baseline." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 670, + 504, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 670, + 504, + 684 + ], + "spans": [ + { + "bbox": [ + 306, + 670, + 504, + 684 + ], + "type": "text", + "content": "4.5. The Impact of Number of Projections" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 689, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 547, + 715 + ], + "type": "text", + "content": "To explore the impact of the number of linear projections in our method, we conduct experiments with the different" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "11398" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 86, + 112, + 509, + 293 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "text", + "content": "Table 4. The linear Top 1 (%) and retrieval rank-1 (%) performance comparisons of recent alternative solutions and Ours on the CUB-200-2011, Stanford Cars and FGVC Aircraft datasets. blue=best, green=second best. Collapse means the model fails to produce meaningful performance." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 86, + 112, + 509, + 293 + ], + "lines": [ + { + "bbox": [ + 86, + 112, + 509, + 293 + ], + "spans": [ + { + "bbox": [ + 86, + 112, + 509, + 293 + ], + "type": "table", + "html": "
MethodFeatureClassificationRetrieval
DimensionCUBCarsAircraftCUBCarsAircraft
MoCo v2 [8]C68.3058.4352.5417.0710.9419.38
MoCo v2 -BilinearC*K68.4458.0653.0141.2730.8930.80
SAM-SSLC68.5958.4952.9718.3814.2621.72
SAM-SSL-BilinearC*K71.5659.1255.1244.2035.3832.10
DiLo [38,42]C64.14-----
CVSA [38]C65.02-----
LEWEL [20]C*K69.2759.0254.3319.2312.0120.67
ContrastiveCrop [29]C68.8261.6654.4018.7113.6120.88
Ours-DualPoolingCcollapsecollapse
Ours-MultiTaskC68.5658.5552.8717.6213.9822.23
OursC71.3160.7555.8749.6934.5634.33
Ours+ContrastiveCropC72.8463.7156.0849.3633.5534.95
", + "image_path": "655ceca78ed0c6c7dce0291b61ec5a2ae4f4136ca86f317b4b701ab46d420b01.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 77, + 310, + 258, + 441 + ], + "blocks": [ + { + "bbox": [ + 77, + 310, + 258, + 441 + ], + "lines": [ + { + "bbox": [ + 77, + 310, + 258, + 441 + ], + "spans": [ + { + "bbox": [ + 77, + 310, + 258, + 441 + ], + "type": "image", + "image_path": "b8dedb35578b9e5b62f5371d0e922e8f582a9ad9fa9b59c80e7721b38a0abe1f.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 449, + 288, + 472 + ], + "lines": [ + { + "bbox": [ + 46, + 449, + 288, + 472 + ], + "spans": [ + { + "bbox": [ + 46, + 449, + 288, + 472 + ], + "type": "text", + "content": "Figure 4. Comparison of MoCo v2 (the blue plot) baseline with our method (the red plot) w.r.t. " + }, + { + "bbox": [ + 46, + 449, + 288, + 472 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 449, + 288, + 472 + ], + "type": "text", + "content": " on the CUB-200-2011." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 494, + 287, + 638 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 494, + 287, + 638 + ], + "spans": [ + { + "bbox": [ + 46, + 494, + 287, + 638 + ], + "type": "text", + "content": "numbers of " + }, + { + "bbox": [ + 46, + 494, + 287, + 638 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 494, + 287, + 638 + ], + "type": "text", + "content": ". Figure 4 shows the retrieval results of rank-1 w.r.t. eight different projections on the fine-grained dataset CUB-200-2011. As we can see, with the increase of linear projections " + }, + { + "bbox": [ + 46, + 494, + 287, + 638 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 494, + 287, + 638 + ], + "type": "text", + "content": ", the rank-1 gradually increases—the final rank-1 peaks at " + }, + { + "bbox": [ + 46, + 494, + 287, + 638 + ], + "type": "inline_equation", + "content": "49.69\\%" + }, + { + "bbox": [ + 46, + 494, + 287, + 638 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 46, + 494, + 287, + 638 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 494, + 287, + 638 + ], + "type": "text", + "content": " around 32. After " + }, + { + "bbox": [ + 46, + 494, + 287, + 638 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 494, + 287, + 638 + ], + "type": "text", + "content": " reaches 64, the performance decreases. When the number of projections is very large, the combination of " + }, + { + "bbox": [ + 46, + 494, + 287, + 638 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 494, + 287, + 638 + ], + "type": "text", + "content": "-part detectors becomes spurious and overfits the correlated pattern, thus resulting in a drop in performance. From the curve, we can also see that choosing any value between 4 and 64 can lead to similar performance. So our method is not very sensitive to " + }, + { + "bbox": [ + 46, + 494, + 287, + 638 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 494, + 287, + 638 + ], + "type": "text", + "content": " once it falls into a reasonable range." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 647, + 212, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 647, + 212, + 658 + ], + "spans": [ + { + "bbox": [ + 47, + 647, + 212, + 658 + ], + "type": "text", + "content": "4.6. Alternative Structure for GFB" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": "In this section, we investigate alternative designs for GFB. In particular, we consider using a two-layer (with 32 as the intermediate feature dimension) multi-layer perception (MLP) to replace the maximized projections in the pro" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 319, + 351, + 535, + 394 + ], + "blocks": [ + { + "bbox": [ + 305, + 308, + 545, + 342 + ], + "lines": [ + { + "bbox": [ + 305, + 308, + 545, + 342 + ], + "spans": [ + { + "bbox": [ + 305, + 308, + 545, + 342 + ], + "type": "text", + "content": "Table 5. Retrieval performance (%) of our methods and using MLP as the alternative GFB branch. The evaluation is on the Stanford Cars dataset." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 319, + 351, + 535, + 394 + ], + "lines": [ + { + "bbox": [ + 319, + 351, + 535, + 394 + ], + "spans": [ + { + "bbox": [ + 319, + 351, + 535, + 394 + ], + "type": "table", + "html": "
DatasetArchitecturerank-1rank-5mAP
CarsOurs34.5660.758.87
MLP25.5750.915.92
", + "image_path": "9b7a7d37ca4c3705830754877dd394516525526258b6a343159a3a30a6e56eef.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 414, + 545, + 486 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 414, + 545, + 486 + ], + "spans": [ + { + "bbox": [ + 304, + 414, + 545, + 486 + ], + "type": "text", + "content": "posed method. Compared with our GFB structure, an MLP has better fitting capacity due to the extra linear layer. We conduct experiments on the Stanford Cars dataset, and the result is shown in Table 5. We find that the performance dramatically decreases when using MLP. This demonstrates the importance of our GFB module design." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 499, + 545, + 526 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 499, + 545, + 526 + ], + "spans": [ + { + "bbox": [ + 305, + 499, + 545, + 526 + ], + "type": "text", + "content": "5. Conclusion, Further Results (Appendix), Limitation and Future Work" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": "In this paper, we introduce a simple-but-effective way of learning an additional screening mechanism to self-supervised feature learning for fine-grained visual recognition. The idea is to identify discriminative clues commonly seen across instances and classes by fitting the GradCAM of the SSL loss with a fitting-capability-limited branch. Our method achieves state-of-the-art in the classification task and is particularly pronounced in retrieval tasks on fine-grained visual recognition problems. More experimental results, including adopting our method for non-fine-grained visual recognition problems, and visualizing each projection in the GFB, can be found in the Appendix. So far, the proposed method seems to be most effective for FGVR, which could be a limitation and we plan to extend the applicability of the proposed method in our future work." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "11399" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 713 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "text", + "content": "[1] Soroush Abbasi Koohpayegani, Ajinkya Tejankar, and Hamed Piriaviash. 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UltraLiDAR learns discrete representations from large-scale LiDAR point clouds and conduct realistic, scalable and controllable LiDAR completion and generation. Top row: Sparse-to-dense LiDAR completion; Second row: Controllable manipulation of real LiDAR with actor removal and insertion; Third row: Diverse LiDAR generation with realistic global structure and fine-grained details; Bottom row: Conditional scene generation with partially observed point clouds (highlighted in red). Please see supp. for more examples." + ], + "image_footnote": [], + "bbox": [ + 81, + 243, + 888, + 592 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 667, + 313, + 681 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "LiDAR provides accurate geometric measurements of the 3D world. Unfortunately, dense LiDARs are very expensive and the point clouds captured by low-beam LiDAR are often sparse. To address these issues, we present UltraLiDAR, a data-driven framework for scene-level LiDAR completion, LiDAR generation, and LiDAR manipulation. The crux of UltraLiDAR is a compact, discrete representation that encodes the point cloud's geometric structure, is robust to noise, and is easy to manipulate. We show that by aligning the representation of a sparse point cloud to that of a dense point cloud, we can densify the sparse point clouds as if they were captured by a real high-density LiDAR, drastically reducing the cost. Furthermore, by learning a prior over the discrete codebook, we can generate diverse, realistic LiDAR", + "bbox": [ + 75, + 689, + 470, + 900 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "point clouds for self-driving. We evaluate the effectiveness of UltraLiDAR on sparse-to-dense LiDAR completion and LiDAR generation. Experiments show that densifying real-world point clouds with our approach can significantly improve the performance of downstream perception systems. Compared to prior art on LiDAR generation, our approach generates much more realistic point clouds. According to A/B test, over $98.5\\%$ of the time human participants prefer our results over those of previous methods. Please refer to project page https://waabi.ai/research/ultralidar/ for more information.", + "bbox": [ + 496, + 667, + 893, + 835 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 501, + 847, + 632, + 863 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Building a robust 3D perception system is key to bringing self-driving vehicles into our daily lives. To effectively", + "bbox": [ + 500, + 869, + 892, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "1074", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "perceive their surroundings, existing autonomous systems primarily exploit LiDAR as the major sensing modality, since it can capture well the 3D geometry of the world. However, while LiDAR provides accurate geometric measurements, it comes with two major limitations: (i) the captured point clouds are inherently sparse; and (ii) the data collection process is difficult to scale up.", + "bbox": [ + 75, + 90, + 470, + 196 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Sparsity: Most popular self-driving LiDARs are time-of-flight and scan the environment by rotating emitter-detector pairs (i.e., beams) around the azimuth. At every time step, each emitter emits a light pulse which travels until it hits a target, gets reflected, and is received by the detector. Distance is measured by calculating the time of travel. Due to the design, the captured point cloud density inherently decreases as the distance to the sensor increases. For distant objects, it is often that only a few LiDAR points are captured, which greatly increases the difficulty for 3D perception. The sparsity problem becomes even more severe under poor weather conditions [47], or when LiDAR sensors have fewer beams [4]. One \"simple\" strategy is to increase the number of LiDAR beams. However, 128-beam LiDAR sensors are much more expensive than their 64/32-beam counterparts, not to mention that 512-beam LiDAR does not exist yet.", + "bbox": [ + 75, + 200, + 470, + 458 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Scalability: Training and testing perception systems in diverse situations are crucial for developing robust autonomous systems. However, due to their intricate design, LiDARs are much more expensive than cameras. A commercial 64-beam LiDAR usually costs over 25K USD. The price barrier makes LiDAR less accessible to the general public and restricts data collection to a small fraction of vehicles that populate our roads, significantly hindering scaling up. One way to circumvent the issue is to leverage existing LiDAR simulation suites to generate more data. While the simulated point clouds are realistic, these systems typically require one to manually create the scene or rely on multiple scans of the real world in advance, making such a solution less desirable.", + "bbox": [ + 75, + 462, + 468, + 672 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "With these challenges in mind, we propose UltraLiDAR, a novel framework for LiDAR completion and generation. The key idea is to learn a compact, discrete 3D representation (codebook) of LiDAR point clouds that encodes the geometric structure of the scene and the physical rules of our world (e.g., occlusion). Then, by aligning the representation of a sparse point cloud to that of a dense point cloud, we can densify the sparse point cloud as if it were captured by a high-density LiDAR (e.g., 512-beam LiDAR). Furthermore, we can learn a prior over the discrete codebook and generate novel, realistic driving scenes by sampling from it; we can also manipulate the discrete code of the scene and produce counterfactual scenarios, both of which can drastically improve the diversity and amount of LiDAR data. Fig. 1 shows some example outputs of UltraLiDAR.", + "bbox": [ + 75, + 674, + 470, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We demonstrate the effectiveness of UltraLiDAR on two tasks: sparse-to-dense LiDAR completion and LiDAR generation. For LiDAR completion, since there is no ground truth for high-density LiDAR, we exploit the performance of downstream perception tasks as a \"proxy\" measurement. Specifically, we evaluate 3D detection models on both sparse and densified point clouds and measure the performance difference. Experiments on Pandaset [46] and KITTI-360 [27] show that our completion model can generalize across datasets and the densified results can significantly improve the performance of 3D detection models. As for LiDAR generation, we compare our results with state-of-the-art LiDAR generative models [3, 53]. Our generated point clouds better match the statistics of those of ground truth data. We also conducted a human study where participants prefer our method over prior art over $98.5\\%$ (best $100\\%$ ) of the time; comparing to ground truth, our results were selected $32\\%$ of the time (best $50\\%$ ).", + "bbox": [ + 496, + 90, + 890, + 362 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To summarize, the main contributions of this paper are:", + "bbox": [ + 517, + 363, + 883, + 378 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. We present a LiDAR representation that can effectively capture data priors and enable various downstream applications, e.g., LiDAR completion and generation.", + "2. We propose a sparse-to-dense LiDAR completion pipeline that can accurately densify sparse point clouds and improve the performance and generalization ability of trained detection models across datasets.", + "3. We develop an (un)conditional LiDAR generative model that can synthesize high-quality LiDAR point clouds and supports various manipulations." + ], + "bbox": [ + 511, + 382, + 890, + 542 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 556, + 640, + 573 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "LiDAR / Depth Completion: Sparse LiDAR/depth completion is a beneficial task for many robotic applications as it can provide more accurate geometry for holistic scenes compared to images. LiDAR scene completion has been studied and attracted the computer vision community's attention in recent years [2,9,34,35,42,48], while the progress has been pushing forward, most of them focus on directly predicting semantic labels for the completed coarse voxels without fine-grained geometry information, thus no other downstream tasks are benefited. More recently, SPG [47] was proposed for unsupervised domain adaptation for 3D object detection via foreground point completion. However, its completion target is generated by heuristics, thus an improved holistic understanding of the scene is hard to achieve. Depth completion [43] instead solves the problem by relying on a sparse lidar sweep and a paired RGB image to compute a 2.5D pseudo-depth image. However, this problem is ill-posed as monocular images contain ambiguities and the field of view is also limited. Thus, the accuracy is hard to improve, and it's difficult to reconstruct whole scenes at scale. Our model instead tackles this problem", + "bbox": [ + 496, + 583, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "1075", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/a99ed84ed57f87533ac0c1cfcf5fda031d41ebcc92257c77782bcd44ad67e20f.jpg", + "image_caption": [ + "Figure 2. Overview of UltraLiDAR pipeline. For (a) LiDAR completion, the sparse encoder maps the sparse point cloud to discrete codes, and the dense decoder reconstructs dense data from them; For (b) LiDAR generation, the transformer model starts from a blank canvas or canvas with codes mapped from the partial observations; and iteratively predicts and updates the missing parts. The decoder produces the LiDAR output given the predicted code as the generation results." + ], + "image_footnote": [], + "bbox": [ + 84, + 70, + 467, + 175 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/1d11a8fea457eb093129d1040f1b12aa433898f74286c184fa79ca97e211f0dc.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 468, + 70, + 893, + 175 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "from a representation learning perspective. It captures the data prior in advance with robust discrete representations thus generalizing better. It also completes the full scene with a higher-beam LiDAR pattern, which is generic to various downstream tasks.", + "bbox": [ + 75, + 244, + 468, + 319 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3D Generation: Inspired by the tremendous progress in 2D image generation [11, 18, 25], 3D content generation has attracted more and more attention in recent years. Existing works demonstrated the high-quality generation in different representations including point cloud [1, 3, 50, 52], voxel grid [16, 21, 29, 41, 45], mesh [14, 17, 19, 39] or implicit geometry [5, 6, 38]. However, these works usually focus on the object level and cannot handle large scenes (due to noncompact representation, large memory footprint and limited model capacity). To enable larger-scale scene synthesis, recent works either define a more compact output space or procedurally generate the scenes [31, 32]. Unfortunately, the generated scenes are still quite limited (e.g., indoor environments) and there are only few works focusing on largescale scene generation for self-driving. In this paper, we focus on the generation of LiDAR point clouds that are highly unstructured, sparse, and non-uniform. [3] and [36] use the variational autoencoder (VAE) or generative adversarial network (GAN) on LiDAR point clouds but the generation realism is quite limited. Most recently, researchers propose a novel score-matching diffusion model for higher-quality LiDAR generation [53] but keep only limited local geometry details and global scenario structures. In contrast, we present a generic framework to learn discrete representations to better maintain the structure and semantic information for a more realistic and controllable generation.", + "bbox": [ + 76, + 330, + 472, + 724 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Learning Discrete Representations: VQ-VAE [44] proposed to learn discrete representations by compressing images into discrete latent space. It primarily consists of three components: an encoder that learns to map the input image into latent feature maps; a codebook that contains a set of learnable latent embeddings where the feature maps are quantized via nearest neighbor lookup; and a decoder that reconstructs the input image from the quantized code. [33] used a multi-scale hierarchical architecture to capture local and global information in separate codebooks. Based on the learned codebook and decoder in VQ-VAE, VQ-GAN [13]", + "bbox": [ + 75, + 734, + 468, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "proposed to use of a transformer model for image generation. More recently, MaskGIT [7] shows that the learned codebook and the decoder are capable of generating impressive realistic RGB images by using mask modeling with bidirectional transformers. However, all existing works focus on 2D natural images and it is non-trivial to handle sparse, unstructured LiDAR points. To our best knowledge, this paper is the first work that conducts discrete representation in the 3D domain and achieves state-of-the-art performance in large-scale LiDAR scene completion and generation.", + "bbox": [ + 496, + 244, + 893, + 396 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. UltraLiDAR", + "text_level": 1, + "bbox": [ + 498, + 402, + 629, + 417 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this paper, we seek to learn a compact 3D representation of scene-level LiDAR point clouds to enable a series of downstream applications, such as sparse-to-dense LiDAR completion, (un)conditional LiDAR generation, and LiDAR manipulation. Based on the observation that vector quantized (VQ) representations [13, 33, 44] are robust to noise, easy to manipulate, and naturally compatible with generative models, we propose to learn a discrete codebook for LiDAR point clouds and build our model on top of it.", + "bbox": [ + 496, + 424, + 890, + 559 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We start by reviewing the basics of vector-quantized variational autoencoder (VQ-VAE) [44], a building block of our approach. Then we showcase how to exploit similar concepts to encode 3D point clouds into a discrete codebook. Finally, we discuss how to exploit the discrete representation for different tasks.", + "bbox": [ + 496, + 560, + 890, + 650 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Discrete Representations for LiDAR", + "text_level": 1, + "bbox": [ + 500, + 654, + 815, + 671 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "VQ-VAE revisit: The goal of VQ-VAE is to learn a discrete latent representation that is expressive, robust to noise, and compatible with generative models. VQ-VAE consists of three parts: (i) an encoder $E$ that encodes the input signal, which for simplicity we assume to be an image, $\\mathbf{x} \\in \\mathbb{R}^{H \\times W \\times 3}$ to a continuous embedding map $\\mathbf{z} = E(\\mathbf{x}) \\in \\mathbb{R}^{h \\times w \\times D}$ , (ii) an element-wise quantization function $q$ that maps each embedding to its closest learnable latent code $\\mathbf{e}_k \\in \\mathbb{R}^D$ , with $k = 1, \\dots, K$ , and (iii) a decoder $G$ that takes as input the quantized representation $\\hat{\\mathbf{z}} = q(\\mathbf{z})$ and outputs the reconstructed image $\\hat{\\mathbf{x}} = G(\\hat{\\mathbf{z}})$ . The whole model can be trained end-to-end by minimizing:", + "bbox": [ + 496, + 676, + 890, + 859 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {v q}} = \\left\\| \\mathbf {x} - \\hat {\\mathbf {x}} \\right\\| _ {2} ^ {2} + \\left\\| \\operatorname {s g} [ E (\\mathbf {x}) ] - \\hat {\\mathbf {z}} \\right\\| _ {2} ^ {2} + \\left\\| \\operatorname {s g} [ \\hat {\\mathbf {z}} ] - E (\\mathbf {x}) \\right\\| _ {2} ^ {2}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 504, + 863, + 890, + 896 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "1076", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/c27b26e291d3a8af1e659942074d3566d7c064ef7cfe691069ca7ec00acbcac5.jpg", + "image_caption": [ + "Figure 3. LiDAR completion and 3D detection on Pandaset. With densified point clouds, the detection model can identify more objects and reduce false negatives. We show detection results in red boxes and ground truth in blue. The missing area far away from ego vehicle in the densified results is caused by uphill; we refer the reader to the supp. material for the explanation with camera visualization." + ], + "image_footnote": [], + "bbox": [ + 117, + 78, + 300, + 157 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/ca86c0d210437c115051eff47b7b9994bd416776f3b04b1a0055a37e8fe69f56.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 302, + 79, + 482, + 157 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/4f4a1653062125b1ce35a0f95dce6e2f9327e2f12ee83962e790ab1fd8370673.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 483, + 79, + 663, + 157 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/3673c1666333ae849dab567b408803cc9daa64f51acd7c2f490cddecd3325ba0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 666, + 79, + 846, + 157 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathrm{sg}[\\cdot ]$ denotes the stop-gradient operation.", + "bbox": [ + 76, + 217, + 393, + 232 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The limited number of discrete codes e stabilizes the input distribution of the decoder during training; it also forces the codes to capture meaningful, re-usable information as the decoder can no longer \"seek shortcut\" from the continuous signals for the reconstruction task. VQ-VAE has enjoyed great success across different modalities, such as natural images [7, 13], audio [44] and 2.5D images [40]. In this work, we further extend it to learn discrete representations for 3D LiDAR point clouds.", + "bbox": [ + 75, + 233, + 470, + 369 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "VQ-VAE for LiDAR: We aim to learn a discrete codebook that can effectively represent a set of LiDAR point clouds. Directly applying VQ-VAE, however, is challenging, since the fixed set of discrete latents will have to model point clouds that live in a continuous 3D space, and deal with the fact that each point cloud may have a different number of points. To address these issues, we propose to voxelize the point clouds and instead infer whether each voxel is occupied or not. By grounding the point clouds with a pre-defined grid (similar to the 2D pixel grid of images), we can foster the discrete codebook to learn the overall structure rather than the minor 3D positional variations. This representation also can naturally handle the varying number of points. While we may sacrifice some precision during the voxelization process, the impact is negligible for both LiDAR completion and generation (see Sec. 4).", + "bbox": [ + 75, + 383, + 468, + 626 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Now that we have a voxelized point cloud, the next step is to design the encoder $E$ and the decoder $G$ . For large scenes with high resolution, 3D convolution becomes very expensive since we need to infer the occupancy of each voxel densely. We thus convert the input to Birds-Eye-View (BEV) images by treating the height dimension of the voxel grids as feature channel $C$ and then adopt 2D convolutions instead. In this case, we can process 3D LiDAR data just like 2D images; we can also exploit existing model architectures designed for 2D images directly. We note that such BEV images have been widely adopted in the context of self-driving perception [8, 51], since they encode rich geometric information. The output of the decoder is a logit grid $\\hat{\\mathbf{x}} \\in \\mathbb{R}^{H \\times W \\times C}$ . It can be further converted to a binary voxel grid $\\hat{\\mathbf{x}}^{\\mathrm{bin}} \\in \\{0,1\\}^{H \\times W \\times C}$ through gumbel softmax [23].", + "bbox": [ + 75, + 627, + 470, + 854 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Finally, we train our LiDAR VQ-VAE model with Eq. 1, except that we replace the $\\ell_2$ reconstruction loss with a binary (occupied or not) cross-entropy loss. To improve the", + "bbox": [ + 75, + 854, + 470, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "realism of the reconstruction, we further adopt a pre-trained voxel-based detector $V$ and measure the feature difference, similar to perceptual loss [24]. Our full loss is:", + "bbox": [ + 496, + 217, + 893, + 263 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {f e a t}} = \\mathcal {L} _ {\\mathrm {v q}} + \\| V _ {\\mathrm {b}} (\\mathbf {x}) - V _ {\\mathrm {b}} \\left(\\hat {\\mathbf {x}} ^ {\\mathrm {b i n}}\\right) \\| _ {2} ^ {2}. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 573, + 273, + 890, + 292 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$V_{\\mathrm{b}}$ denotes the feature from the last backbone layer of $V$", + "bbox": [ + 500, + 304, + 877, + 320 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "LiDAR manipulation: Once we train the model, we can easily manipulate arbitrary LiDAR point clouds by editing their corresponding latent codes. Since objects are spatially apart in 3D, the model can dedicate specific codes for them. We can thus identify the codes for objects of interest (e.g., vehicles) and insert/remove them into/from the scene. As shown in Sec. 4, we can populate many vehicles on the street and create counterfactual scenarios.", + "bbox": [ + 496, + 329, + 890, + 450 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. LiDAR Completion", + "text_level": 1, + "bbox": [ + 500, + 460, + 686, + 477 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given a dataset of paired, voxelized LiDAR point clouds $\\{(\\mathbf{x}_1^{\\mathrm{sp}},\\mathbf{x}_1^{\\mathrm{den}}),\\dots,(\\mathbf{x}_N^{\\mathrm{sp}},\\mathbf{x}_N^{\\mathrm{den}})\\}$ , the goal of LiDAR completion is to learn a function $f$ that maps a sparse LiDAR point cloud $\\mathbf{x}^{\\mathrm{sp}}$ to its dense counterpart $\\mathbf{x}^{\\mathrm{den}}$ .", + "bbox": [ + 498, + 484, + 890, + 545 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "One straightforward strategy is to leverage the pairwise supervision and directly learn a pix2pix-style network [22] but on voxels. While this model performs well within the same data distribution, it degrades significantly when the input distribution shifts (e.g., when the sparse LiDAR point clouds come from different datasets). We conjecture that this is because there is no restriction on the learned representation, and the model learns to \"cheat\" by relying on non-generalizable details rather than the overall structure.", + "bbox": [ + 496, + 546, + 890, + 681 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this section, we investigate the use of discrete representations to alleviate the issue. We first learn a discrete codebook $\\{\\mathbf{e}_1^{\\mathrm{den}},\\dots,\\mathbf{e}_K^{\\mathrm{den}}\\}$ , an encoder $E^{\\mathrm{den}}$ , and a decoder $G^{\\mathrm{den}}$ for each dense LiDAR point cloud $\\mathbf{x}^{\\mathrm{den}}$ using the approach in Sec. 3.1. Then we learn a separate encoder $E^{\\mathrm{sp}}$ that maps each sparse LiDAR point cloud $\\mathbf{x}^{\\mathrm{sp}}$ to the same feature space $\\mathbf{z}^{\\mathrm{sp}} = E^{\\mathrm{sp}}(\\mathbf{x}^{\\mathrm{sp}})$ and quantize it with the dense discrete representation $\\mathbf{e}^{\\mathrm{den}}$ . Finally, we decode the quantized representation $\\hat{\\mathbf{z}}^{\\mathrm{sp}} = q(\\mathbf{z}^{\\mathrm{sp}})$ with the dense decoder $G^{\\mathrm{den}}$ and obtain a densified point cloud $\\hat{\\mathbf{x}}^{\\mathrm{sp - den}} = G^{\\mathrm{den}}(\\hat{\\mathbf{z}}^{\\mathrm{sp}})$ . With the help of the learned codebook, we can ensure the input to the dense decoder $G^{\\mathrm{den}}$ is in-domain and the reconstructed point clouds are high-quality; we can also denoise the embedding from the encoder and better handle the variations and distribution shift within the input data.", + "bbox": [ + 496, + 681, + 890, + 910 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "1077", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/9252da9e7fbd4452790022a4040585229f929dd88fc9a68fd51482aaf889aca3.jpg", + "image_caption": [ + "Real (not paired, reference only)" + ], + "image_footnote": [], + "bbox": [ + 127, + 80, + 308, + 157 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/35a5a762bee90959158c5215243e55f8081b443561edd54b4863c822300fa0dc.jpg", + "image_caption": [ + "Figure 4. Qualitative comparison against baselines on unconditional LiDAR generation. We compare with two state-of-the-art LiDAR generation methods Projected GAN [37] and LiDARGen [53] and include real data for reference. Our model can generate results with more structured layouts and clearer beam patterns." + ], + "image_footnote": [], + "bbox": [ + 127, + 159, + 307, + 234 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/98e300e1f5ea044f0dcb1396324a1e18843b63fafe94fce9414731f999985340.jpg", + "image_caption": [ + "Projected GAN" + ], + "image_footnote": [], + "bbox": [ + 313, + 80, + 491, + 157 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/5e0bcf986a2a0a823de48f564897eb0721fe150cfef48f0e5d339794b47f4446.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 313, + 159, + 491, + 234 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/fd792c45db063ee03cb813136cfb80060db61685094f937b1ab2df257fd81b49.jpg", + "image_caption": [ + "LiDAR Gen" + ], + "image_footnote": [], + "bbox": [ + 491, + 80, + 666, + 157 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/af05dafa663bce81ea100d3ecf2df21f5fc9b9c1d7eb6b1fbceabcd0ccde9dfb.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 491, + 159, + 666, + 234 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/32949c7fa4858e613b70c82435e8233447c8d3bc3c73328fed301ec877917ffd.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 668, + 80, + 846, + 157 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/460a44d1c3c409bbe299de86b58e89e1fbdcf8f6b6b17fa3b08e6df71cf2ae52.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 669, + 159, + 846, + 234 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Training: In practice, we jointly train the sparse encoder $E_{\\mathrm{sp}}$ and the dense VQ-VAE model, since it achieves slightly better performance than performing two-stage training. We hypothesize this is because joint training allows the model to learn a codebook that is easy to decode, and achieves low quantization error for both encoders $E_{\\mathrm{sp}}$ and $E_{\\mathrm{den}}$ . We use the same loss functions in Sec. 3.1 to train the whole model, except that the reconstructed target is always the dense point cloud (which we can obtain from the paired data).", + "bbox": [ + 75, + 286, + 468, + 421 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. LiDAR Generation", + "text_level": 1, + "bbox": [ + 76, + 431, + 261, + 446 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As we have alluded to earlier, the learned discrete representations can be naturally combined with generative models. In this section, we describe in detail how we exploit the discrete codebook to generate high-fidelity LiDAR point clouds, both unconditionally and conditionally.", + "bbox": [ + 75, + 455, + 468, + 532 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Unconditional generation: Given the learned codebook e and the decoder $G$ , the problem of LiDAR generation can be formulated as code map generation. Instead of directly generating LiDAR point clouds, we first generate discrete code maps in the form of code indices. Then we map the indices to discrete features by querying the codebook and decoding them back to LiDAR point clouds with the decoder. Following Chang et al. [7], we adopt a bi-directional self-attention Transformer [7, 20] to iteratively predict the code map. Specifically, we start from a blank canvas. At each iteration, we select a subset of the predicted codes with top confidence scores and update the canvas accordingly. With the help of the Transformer, we can aggregate context from the whole map and predict missing parts based on already predicted codes. In the end, the canvas will be filled with predicted code indices, from which we can decode LiDAR point clouds. We refer the reader to [7] for more details.", + "bbox": [ + 75, + 542, + 468, + 800 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Conditional generation: Our unconditional LiDAR generation pipeline can be easily extended to perform conditional generation. Instead of starting the generation process from an empty canvas, one can simply start with a partially filled code map and let the Transformer predict the rest. For instance, we can place [CAR] codes at regions of interest;", + "bbox": [ + 75, + 809, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "and run the model multiple times. We can then obtain different traffic scenarios with the pre-defined cars untouched. Please refer to supp. material for how we identify the codes.", + "bbox": [ + 496, + 286, + 890, + 330 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Free space suppression sampling: Our iterative generation procedure can be viewed as a variant of coarse-to-fine generation. The codes generated during early iterations determine the overall structure, while the ones generated at the end are in charge of fine-grained details. While this pipeline is effective for image generation [7], it may lead to degenerated results when generating LiDAR point clouds. One critical reason is that LiDAR point clouds are sparse, and a large portion of the scene is represented by the same [BLANK] codes. Since the [BLANK] codes occur frequently, the Transformer tends to predict them with high scores. If we naively sample the codes based on the output of the Transformer, we may fill most of the canvas with [BLANK] codes, and little structure will remain. To address this issue, we suppress the [BLANK] codes during the early generation stages by setting their probability to 0. This ensures the model generates meaningful structures in the beginning. We identify the [BLANK] codes by looking at the occurrence statistic of all codes across the whole dataset. We empirically select the top as [BLANK] codes.", + "bbox": [ + 496, + 335, + 892, + 637 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Iterative denoising: With free space suppression sampling, we can already obtain good results. However, the generated point clouds sometimes still contain high-frequency noise (e.g., there might be some floating points in the very far range). To mitigate this issue, we randomly mask out different regions of the output LiDAR point clouds and re-generate them. The intuition is that if we mask out a structured region, we can still recover it through the neighborhood context. However, if the masked region corresponds to pure noise that is irrelevant to the surrounding, it will likely be removed after multiple trials (since the model cannot infer it from the context).", + "bbox": [ + 496, + 648, + 890, + 829 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Training: We first encode all LiDAR point clouds into frozen discrete representations (code maps) learned in Sec. 3.1. Then, at each training iteration, we randomly mask out a subset of codes. Finally, we adopt the bi-directional", + "bbox": [ + 496, + 839, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "1078", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/50a744ac6e34170f8f3d519274b80549c98f3919592a212c4d018224f263b12a.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ModelSparse to DenseTwo-stage PINORPointPillar
APBEVAP3DAPBEVAP3D
Real / 64-79.362.275.562.3
Sim / 512-78.157.770.055.5
Sim / 512ContComp79.762.475.159.8
Sim / 512Ours80.364.376.062.8
", + "bbox": [ + 96, + 88, + 446, + 161 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Transformer to predict the correct code for those masked regions. Since we have GT code map, we supervise the model with cross-entropy loss. See [7] for more details.", + "bbox": [ + 76, + 214, + 468, + 258 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3.4. Implementation Details", + "text_level": 1, + "bbox": [ + 76, + 263, + 294, + 280 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we discuss implementation details that are crucial for learning discrete LiDAR representations.", + "bbox": [ + 76, + 287, + 468, + 318 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Voxel sizes matter: We set the input voxel size to be $15.625 \\times 15.625 \\times 15$ cm for x, y, z dimensions. We find that the downsampling ratio when mapping the BEV image to the discrete code has a huge impact on both reconstruction and generation performance. If the patch size that each discrete code represents is too large, a single fixed code does not have enough capacity to model the variations (e.g., a small position/rotation shift of a car inside the patch). We empirically find that downsampling $8 \\times$ achieves a good trade-off between preserving high-frequency information in the LiDAR data and maintaining high-level semantic meaning. Thus the patch size is $8 \\times 8$ , leading to $1.25 \\times 1.25$ m on the spatial dimension that each code represents.", + "bbox": [ + 75, + 325, + 468, + 522 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Model hyperparameters: As a typical BEV image usually has a large spatial range, the resolution of the image and the number of codes are high. We use Swin Transformer [28] instead of the vanilla Vision Transformer [12] to reduce the computational cost for our generative Transformer model. It has 24 layers and 8 heads, and the embedding dimension is set to 512. All other training hyperparameters like optimizer settings and label smoothing are kept the same as in [7]. For simplicity, we use the same architecture in our VQ-VAE learning. The encoder and decoder are both Swin Transformers with 12 layers, respectively. We set the codebook size to 1024 with 1024 hidden dimensions for each code.", + "bbox": [ + 75, + 530, + 468, + 724 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Codebook (re)-initialization: We empirically find that the codebook can easily collapse (only a few codes are used) during training. For better codebook learning, we use data-dependent codebook initialization. Specifically, we use a memory bank to store the continuous embedding output from the encoders at each iteration; and use K-Means centroids of the memory bank to initialize/reinitialize the codebook if the code utilization percentage is lower than a threshold (empirically, we define a code is not used for 256 iterations as \"dead code\" and set the threshold to be $50\\%$ ). During the first 2000 iterations of training, we gradually", + "bbox": [ + 75, + 734, + 468, + 901 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/37feb914afbdf9b893a3711aaa7f50956e618b3b12c5a7edf128ce1ad049bd1d.jpg", + "table_caption": [ + "Table 1. Results on PandaSet. We evaluate all models on PandaSet real 64-beam data, and perform sparse-to-dense during inference optionally with ContComp and our model." + ], + "table_footnote": [], + "table_body": "
ModelSparse to DenseTwo-stage PINORPointPillar
APBEVAP3DAPBEVAP3D
Real / 64-71.732.860.928.1
Sim / 512-66.933.258.528.0
Sim / 512ContComp74.941.567.736.9
Sim / 512Ours76.746.373.040.9
", + "bbox": [ + 519, + 88, + 867, + 161 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. PandaSet $\\rightarrow$ KITTI Cross-Dataset Evaluation. The detection and LiDAR completion models are trained on PandaSet, and no KITTI data is seen/used before evaluation. Our LiDAR completion model can do reliable completion on unseen data and significantly improve the detector performance in zero-shot.", + "bbox": [ + 500, + 162, + 890, + 231 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "shifted the decoder input from continuous to quantized embeddings as a warmup. We find these strategies help achieve good codebook learning and utilization.", + "bbox": [ + 500, + 242, + 890, + 287 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 301, + 632, + 316 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Perception with LiDAR Completion", + "text_level": 1, + "bbox": [ + 500, + 325, + 808, + 342 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We first conduct experiments to verify that UltraLiDAR can boost the performance of a 3D detection model performance by performing LiDAR completion and using the densified results as detection model input. To show that our model generalizes well and can generate reliable sparse-todense results across datasets with the learned discrete representations, we further test the models on KITTI [15] that are trained on PandaSet [46]. We also evaluate our model on the SemanticKITTI scene completion benchmark [2] and show that our model with a generic design can be on par with models on the leaderboard that are heavily tuned for this task.", + "bbox": [ + 496, + 343, + 890, + 523 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Dataset: We train UltraLiDAR and the 3D detection models on PandaSet [46]. We reimplement LiDARsim [30] to generate the 512-beam LiDAR data paired with the real 64-beam LiDAR sweeps (i.e., the actor placement and background are identical) and obtain the sparse-to-dense supervision. We use a custom train/validation split since there is no official split; we refer the readers to the supp. materials for more details. We use KITTI [15] dataset for cross-dataset generalization evaluation; the validation set is used to obtain results, and no model is trained on it. For SemanticKITTI, we use the official train and test split.", + "bbox": [ + 496, + 534, + 890, + 700 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation metrics: To evaluate 3D detection we use the KITTI metrics and report $\\mathrm{AP}_{\\mathrm{BEV}}$ and $\\mathrm{AP}_{\\mathrm{3D}}$ of the car category at IoU = 0.7. For the SemanticKITTI scene completion benchmark, we report Intersection-over-Union (IoU), which classifies a voxel as occupied or empty.", + "bbox": [ + 496, + 709, + 890, + 786 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Training and implementation details: We use two base detectors for the 3D detection benchmark: PointPillar [26] from mmdetection3d [10], and a BEV detector which we denote Two-stage_PIXOR, which improves over [49] by adding a second stage RoI refinement branch; more details of Two-stage_PIXOR can be found in the supp. materials. We also modified PointPillar to make it use binary voxels", + "bbox": [ + 496, + 794, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "1079", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/0cdd97fd5bede0fe4d15da7d11fdc87ff933da3a367aae6a0e1c03c6d22f061a.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
SCCNet [42]JS3C-Net [48]Local-DIFs [34]Ours
IoU29.856.657.756.0
", + "bbox": [ + 88, + 88, + 459, + 118 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "instead of pillar features as input; so that the LiDAR completion results from our model can be used. The voxel size for detectors is set to be the same as UltraLiDAR. For SemanticKITTI, the input data is preprocessed as voxel data, and we directly use it without modification.", + "bbox": [ + 75, + 185, + 468, + 261 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Baselines: We first train detectors on PandaSet real data with 64-beam and simulated data with 512-beam, denoted as Real/64 and Sim/512, respectively; during inference, we perform sparse-to-dense LiDAR completion to densify the sparse real data for the Sim/512 model. We also train a LiDAR completion model without the codebook and quantization function (the model thus behaves like an AutoEncoder with sparse-to-dense supervision) as another baseline, denoted as ContComp. We evaluate all models with PandaSet real data; when testing the generalization ability on KITTI dataset, we directly evaluate all models trained on PandaSet in zero-shot (i.e., no KITTI data is seen/used before the evaluation) with KITTI real data.", + "bbox": [ + 75, + 266, + 468, + 462 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "PandaSet results: From the first two rows in Tab. 1, we can see that the Sim/512 models perform worse than their Real/64 counterparts when evaluating on the real data. This is expected as there is a domain gap between the dense and sparse data, and the models may learn to rely on the richer geometry information in the dense data that does not exist in the sparse counterpart. However, if we perform the sparse-to-dense operation and lift the model to a higher density, we can see a decent performance improvement over the Sim/512 model. Moreover, we see that our model performs better than the ContComp model that uses continuous representations, indicating the effectiveness of using discrete representation in this task.", + "bbox": [ + 75, + 467, + 468, + 662 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Cross-dataset genearization results: To verify the generalization ability of our model, we directly test it on KITTI in a zero-shot manner, that is without seeing KITTI data in advance. As shown in Tab. 2, both entries that utilize sparse-to-dense achieve better performance, and even surpass the Real/64 model, showing the benefits of sparse-to-dense completion. Since the discrete representation is naturally more robust to noise because of the quantization operation, our model with discrete representations can outperform ContComp by a very significant margin when doing zero-shot generalization, once again showing the benefits of using discrete representations.", + "bbox": [ + 75, + 669, + 468, + 849 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "SemanticKITTI results: We further test our model on SemanticKITTI scene completion benchmark. As shown in Tab. 3, our model can achieve on-par performance with", + "bbox": [ + 75, + 854, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/709fbb9d0f005978b1f9c142b89d922f04d1d198279fbc22fe7e8267fab57905.jpg", + "table_caption": [ + "Table 3. SemanticKITTI semantic scene completion results. Our model with generic design can achieve on-par performance with state-of-the-art methods that employ architectures/modules heavily tuned for this task." + ], + "table_footnote": [], + "table_body": "
Method\\( MMD_{BEV} \\downarrow \\)\\( JSD_{BEV} \\downarrow \\)
LiDAR VAE [3]\\( 1.18 \\times 10^{-3} \\)0.256
LiDAR GAN [3]\\( 2.07 \\times 10^{-3} \\)0.275
Projected GAN [37]\\( 1.25 \\times 10^{-3} \\)0.190
LiDARGen [53]\\( 4.80 \\times 10^{-4} \\)0.140
Ours\\( 9.67 \\times 10^{-5} \\)0.132
", + "bbox": [ + 532, + 88, + 859, + 175 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 4. Quantitative results on KITTI-360. Our results show better statistical alignment with the real data.", + "bbox": [ + 498, + 180, + 890, + 209 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "state-of-the-art methods [34, 35, 48] that employ architectures and operations heavily tuned for this task, for example shape-aware point-voxel interaction [48] or multi-resolution scene representation [34, 35].", + "bbox": [ + 498, + 220, + 890, + 281 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. LiDAR Scene Generation", + "text_level": 1, + "bbox": [ + 500, + 290, + 732, + 306 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We first compare quantitative results on KITTI-360 [27] with other baselines in the unconditional generation setting. In this case, we directly train our model with the sparse-to-sparse reconstruction task without the dense encoder; and use the sparse encoder to generate code maps in the generative model training instead. We follow LiDArgen [53] and use the first two sequences as the validation set and use the rest for model training. In Fig. $4^{1}$ , we show the qualitative comparison between our model and two baselines; and include the real data for reference. We can see that our model can generate results that are much more similar to the real data, with more structured and reasonable scene layouts and more stable/clearer beam patterns. More unconditional generation results on KITTI-360 can be found in the second row of Fig. 1 and supp. materials.", + "bbox": [ + 496, + 315, + 890, + 542 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Quantitative results: Following [53], we use the Maximum-Mean Discrepancy (MMD) and Jensen-Shannon divergence (JSD) with a $100 \\times 100$ 2D histogram along the ground plane (x and y coordinates) as metrics. Since our model generates points based on voxels, the number of points may differ from the real point cloud. We thus use occupancy as a measurement when doing histogram bin count (i.e., points from the same voxel will only count once) for point clouds from real data and other baselines. We believe this change captures the global structure difference better and lowers the weight on the local point density estimation, which is more reasonable and aligns better with the perceptual quality. As shown in Tab. 4, our method achieves superior performance compared with the baselines.", + "bbox": [ + 496, + 556, + 890, + 782 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Model parameters: We calculate the number of parameters to make sure the model capacities are at the same level when compared with baselines. The number of parameters of LiDArgen [53] and our model are 29.7M and 40.3M, which are both smaller than a standard Swin-Small model.", + "bbox": [ + 496, + 797, + 890, + 873 + ], + "page_idx": 6 + }, + { + "type": "page_footnote", + "text": "1We contacted the authors of [53] to obtain outputs of all models they used for visualization and metrics calculation", + "bbox": [ + 500, + 875, + 890, + 898 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "1080", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/b4d2d4184ca997dee6fe1c9c8340466b624c667d3f733775f16ca735e26a21d8.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodPercent Prefer Ours
Ours vs LiDAR VAE [3]99.5%
Ours vs LiDAR GAN [3]100%
Ours vs ProjGAN [37]100%
Ours vs LiDARGen [53]98.5%
", + "bbox": [ + 119, + 88, + 426, + 161 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 5. Human study results on KITTI-360. Results from our model show significantly better visual quality.", + "bbox": [ + 76, + 162, + 468, + 191 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/789284817a91c0b75c7b056a0c99370cc736145e65e22580b171a42fdc4fa33c.jpg", + "image_caption": [ + "Figure 5. Unconditional generation results on Pandaset. We train our model on dense Pandaset data and generate dense results. The generated samples show diverse scenario layouts with proper actor placement (e.g., parked car in the right sample). The synthesized point clouds are realistic such that a pre-trained detector can directly work out-of-the-box." + ], + "image_footnote": [], + "bbox": [ + 83, + 198, + 467, + 267 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Human study: We perform an A/B test on a set of 8 researchers who have LiDAR expertise to better evaluate the visual quality of the generated samples. We use the same test system as [53], which shows a pair of randomly chosen images of two point clouds each time and lets the human decide which one is more realistic. We compare with four baselines as well as with the real data, with 200 image pairs each, leading to 1000 image pairs in total. We show the percentage of examples where participants believed our generations are more realistic against other baselines in Tab. 5. It is clear that our model can generate results with superior visual quality; over $98.5\\%$ of the time (100% for some baselines), the testers prefer our results over the baselines. It is worth noting that in $32\\%$ cases, people believe our results are more realistic than real data, which is very significant given the fact that for data that is indistinguishable from real, the winning ratio would be $50\\%$ with random choice.", + "bbox": [ + 75, + 363, + 472, + 621 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Unconditional generation: Besides the KITTI-360 results in Fig. 4 and 1, we also train our model on dense Panadset for dense point cloud generation; and additionally run detection models on the generated samples, shown in Fig. 5. We can see that our model is able to generate diverse scenes with proper actor placement (e.g., parked car in the right example), indicating the superiority of our model for this LiDAR generation task. Moreover, the excellent detection results showcase that the generated samples also have high fidelity w.r.t. the perception model.", + "bbox": [ + 75, + 632, + 468, + 784 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Conditional generation: We show conditional generation results on KITTI-360 in the bottom row of Fig. 1. Our model can fully exploit the visible part-colored by purple) as context, do reasonable extrapolation for the surrounding environment, and generate diverse scenes (e.g., curved road or crossroad) that align with the input condition well. See supp. materials for more results on KITTI-360/PandaSet.", + "bbox": [ + 75, + 794, + 468, + 902 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7496cfcace9317f6a1cd74a7cfdacdfea237ded06063f80646f101966d875e79.jpg", + "image_caption": [ + "Figure 6. Conditional LiDAR generation for dirt removal. We mask the red rectangular region in the range view image to mimic dirt occluder. Left: Original input. The masked region is not visible to the model. Right: Our generation results. Our model can successfully recover the vehicle that is partially observed." + ], + "image_footnote": [], + "bbox": [ + 504, + 90, + 890, + 193 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Meanwhile, we further consider a practical setting where the LiDAR sensor can fail for a specific region due to dirt or mechanical issues. To mimic this situation, we mask a part of the range images, as shown in Fig. 6. We can see that our model can still do accurate completion even on partially visible cars, recovering the occluded region, and potentially avoiding dangerous situations.", + "bbox": [ + 496, + 276, + 890, + 383 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Manipulation: We show manipulation results with actor insertion and removal in the second row of Fig. 1. This is achieved by explicitly changing the code indices on the code map and letting the decoder generate new results. For example, we can copy the codes for the ground plane and paste them to overwrite the region where a car exists, resulting in a controllable manipulation process. We refer the readers for more results in supp. materials.", + "bbox": [ + 496, + 388, + 892, + 511 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 516, + 617, + 531 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we propose a framework to learn novel LiDAR representations that effectively capture the data priors that enable various downstream applications, including scene completion and generation. Based on the learned representation, we propose a novel sparse-to-dense data reconstruction pipeline that can accurately densify the sparse input and improve the generalization ability of the trained detection models in a zero-shot manner. We further show that our model can generate high-quality LiDAR point clouds unconditionally and do reasonable conditional generation and manipulation, which leads to more realistic and controllable data-driven LiDAR simulation.", + "bbox": [ + 496, + 534, + 890, + 714 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "One potential future direction for improving our model is to exploit the structure in range view representations, including beam info (which point from which ray) and occlusion reasoning, and combine them with our existing model. This may potentially improve the fidelity of our results.", + "bbox": [ + 496, + 715, + 890, + 791 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement We thank Vlas Zyrianov and Shenlong Wang for providing A/B test code and baseline results, Arnaud Bonnet for infrastructure support, Siva Manivasagam for proofreading. We also thank the Waabi team for their valuable support. YX is partially supported by an NSERC scholarship and a Borealis AI fellowship. WCM is partially supported by a Siebel scholarship.", + "bbox": [ + 496, + 795, + 890, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "1081", + "bbox": [ + 483, + 944, + 513, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Panos Achlioptas, Olga Diamanti, Ioannis Mitliagkas, and Leonidas Guibas. 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In Proceedings of the European Conference on Computer Vision (ECCV), October 2022. 2, 3, 5, 7, 8" + ], + "bbox": [ + 501, + 92, + 890, + 881 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "1083", + "bbox": [ + 483, + 945, + 514, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Learning Compact Representations for LiDAR Completion and Generation/99e8a6b8-3456-496c-a230-7faca7e11fdf_model.json b/2023/Learning Compact Representations for LiDAR Completion and Generation/99e8a6b8-3456-496c-a230-7faca7e11fdf_model.json new file mode 100644 index 0000000000000000000000000000000000000000..13f7abc777345f5aaa0835063fefb071745015ec --- /dev/null +++ b/2023/Learning Compact Representations for LiDAR Completion and Generation/99e8a6b8-3456-496c-a230-7faca7e11fdf_model.json @@ -0,0 +1,2222 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.105, + 0.131, + 0.867, + 0.154 + ], + "angle": 0, + "content": "Learning Compact Representations for LiDAR Completion and Generation" + }, + { + "type": "text", + "bbox": [ + 0.151, + 0.179, + 0.282, + 0.198 + ], + "angle": 0, + "content": "Yuwen Xiong\\(^{1,2}\\)" + }, + { + "type": "text", + "bbox": [ + 0.323, + 0.181, + 0.45, + 0.197 + ], + "angle": 0, + "content": "Wei-Chiu Ma1,3" + }, + { + "type": "text", + "bbox": [ + 0.491, + 0.181, + 0.633, + 0.199 + ], + "angle": 0, + "content": "Jingkang Wang\\(^{1,2}\\)" + }, + { + "type": "text", + "bbox": [ + 0.674, + 0.181, + 0.818, + 0.199 + ], + "angle": 0, + "content": "Raquel Urtasun1,2" + }, + { + "type": "text", + "bbox": [ + 0.189, + 0.199, + 0.249, + 0.216 + ], + "angle": 0, + "content": "Waabi" + }, + { + "type": "text", + "bbox": [ + 0.27, + 0.199, + 0.45, + 0.217 + ], + "angle": 0, + "content": "\\(^{2}\\)University of Toronto" + }, + { + "type": "text", + "bbox": [ + 0.471, + 0.199, + 0.664, + 0.218 + ], + "angle": 0, + "content": "3Massachusetts Institute" + }, + { + "type": "text", + "bbox": [ + 0.675, + 0.199, + 0.782, + 0.218 + ], + "angle": 0, + "content": "of Technology" + }, + { + "type": "text", + "bbox": [ + 0.33, + 0.22, + 0.636, + 0.234 + ], + "angle": 0, + "content": "{yxiong, wma, jwang, urtasun}@waabi.ai" + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.244, + 0.89, + 0.593 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.597, + 0.893, + 0.653 + ], + "angle": 0, + "content": "Figure 1. UltraLiDAR learns discrete representations from large-scale LiDAR point clouds and conduct realistic, scalable and controllable LiDAR completion and generation. Top row: Sparse-to-dense LiDAR completion; Second row: Controllable manipulation of real LiDAR with actor removal and insertion; Third row: Diverse LiDAR generation with realistic global structure and fine-grained details; Bottom row: Conditional scene generation with partially observed point clouds (highlighted in red). Please see supp. for more examples." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.668, + 0.314, + 0.683 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.69, + 0.472, + 0.901 + ], + "angle": 0, + "content": "LiDAR provides accurate geometric measurements of the 3D world. Unfortunately, dense LiDARs are very expensive and the point clouds captured by low-beam LiDAR are often sparse. To address these issues, we present UltraLiDAR, a data-driven framework for scene-level LiDAR completion, LiDAR generation, and LiDAR manipulation. The crux of UltraLiDAR is a compact, discrete representation that encodes the point cloud's geometric structure, is robust to noise, and is easy to manipulate. We show that by aligning the representation of a sparse point cloud to that of a dense point cloud, we can densify the sparse point clouds as if they were captured by a real high-density LiDAR, drastically reducing the cost. Furthermore, by learning a prior over the discrete codebook, we can generate diverse, realistic LiDAR" + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.669, + 0.895, + 0.837 + ], + "angle": 0, + "content": "point clouds for self-driving. We evaluate the effectiveness of UltraLiDAR on sparse-to-dense LiDAR completion and LiDAR generation. Experiments show that densifying real-world point clouds with our approach can significantly improve the performance of downstream perception systems. Compared to prior art on LiDAR generation, our approach generates much more realistic point clouds. According to A/B test, over \\(98.5\\%\\) of the time human participants prefer our results over those of previous methods. Please refer to project page https://waabi.ai/research/ultralidar/ for more information." + }, + { + "type": "title", + "bbox": [ + 0.502, + 0.848, + 0.633, + 0.864 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.893, + 0.903 + ], + "angle": 0, + "content": "Building a robust 3D perception system is key to bringing self-driving vehicles into our daily lives. To effectively" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1074" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.471, + 0.198 + ], + "angle": 0, + "content": "perceive their surroundings, existing autonomous systems primarily exploit LiDAR as the major sensing modality, since it can capture well the 3D geometry of the world. However, while LiDAR provides accurate geometric measurements, it comes with two major limitations: (i) the captured point clouds are inherently sparse; and (ii) the data collection process is difficult to scale up." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.201, + 0.471, + 0.459 + ], + "angle": 0, + "content": "Sparsity: Most popular self-driving LiDARs are time-of-flight and scan the environment by rotating emitter-detector pairs (i.e., beams) around the azimuth. At every time step, each emitter emits a light pulse which travels until it hits a target, gets reflected, and is received by the detector. Distance is measured by calculating the time of travel. Due to the design, the captured point cloud density inherently decreases as the distance to the sensor increases. For distant objects, it is often that only a few LiDAR points are captured, which greatly increases the difficulty for 3D perception. The sparsity problem becomes even more severe under poor weather conditions [47], or when LiDAR sensors have fewer beams [4]. One \"simple\" strategy is to increase the number of LiDAR beams. However, 128-beam LiDAR sensors are much more expensive than their 64/32-beam counterparts, not to mention that 512-beam LiDAR does not exist yet." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.463, + 0.47, + 0.674 + ], + "angle": 0, + "content": "Scalability: Training and testing perception systems in diverse situations are crucial for developing robust autonomous systems. However, due to their intricate design, LiDARs are much more expensive than cameras. A commercial 64-beam LiDAR usually costs over 25K USD. The price barrier makes LiDAR less accessible to the general public and restricts data collection to a small fraction of vehicles that populate our roads, significantly hindering scaling up. One way to circumvent the issue is to leverage existing LiDAR simulation suites to generate more data. While the simulated point clouds are realistic, these systems typically require one to manually create the scene or rely on multiple scans of the real world in advance, making such a solution less desirable." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.675, + 0.471, + 0.901 + ], + "angle": 0, + "content": "With these challenges in mind, we propose UltraLiDAR, a novel framework for LiDAR completion and generation. The key idea is to learn a compact, discrete 3D representation (codebook) of LiDAR point clouds that encodes the geometric structure of the scene and the physical rules of our world (e.g., occlusion). Then, by aligning the representation of a sparse point cloud to that of a dense point cloud, we can densify the sparse point cloud as if it were captured by a high-density LiDAR (e.g., 512-beam LiDAR). Furthermore, we can learn a prior over the discrete codebook and generate novel, realistic driving scenes by sampling from it; we can also manipulate the discrete code of the scene and produce counterfactual scenarios, both of which can drastically improve the diversity and amount of LiDAR data. Fig. 1 shows some example outputs of UltraLiDAR." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.363 + ], + "angle": 0, + "content": "We demonstrate the effectiveness of UltraLiDAR on two tasks: sparse-to-dense LiDAR completion and LiDAR generation. For LiDAR completion, since there is no ground truth for high-density LiDAR, we exploit the performance of downstream perception tasks as a \"proxy\" measurement. Specifically, we evaluate 3D detection models on both sparse and densified point clouds and measure the performance difference. Experiments on Pandaset [46] and KITTI-360 [27] show that our completion model can generalize across datasets and the densified results can significantly improve the performance of 3D detection models. As for LiDAR generation, we compare our results with state-of-the-art LiDAR generative models [3, 53]. Our generated point clouds better match the statistics of those of ground truth data. We also conducted a human study where participants prefer our method over prior art over \\(98.5\\%\\) (best \\(100\\%\\)) of the time; comparing to ground truth, our results were selected \\(32\\%\\) of the time (best \\(50\\%\\))." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.364, + 0.885, + 0.379 + ], + "angle": 0, + "content": "To summarize, the main contributions of this paper are:" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.383, + 0.891, + 0.429 + ], + "angle": 0, + "content": "1. We present a LiDAR representation that can effectively capture data priors and enable various downstream applications, e.g., LiDAR completion and generation." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.433, + 0.892, + 0.492 + ], + "angle": 0, + "content": "2. We propose a sparse-to-dense LiDAR completion pipeline that can accurately densify sparse point clouds and improve the performance and generalization ability of trained detection models across datasets." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.498, + 0.892, + 0.543 + ], + "angle": 0, + "content": "3. We develop an (un)conditional LiDAR generative model that can synthesize high-quality LiDAR point clouds and supports various manipulations." + }, + { + "type": "list", + "bbox": [ + 0.512, + 0.383, + 0.892, + 0.543 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.558, + 0.642, + 0.574 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.584, + 0.892, + 0.901 + ], + "angle": 0, + "content": "LiDAR / Depth Completion: Sparse LiDAR/depth completion is a beneficial task for many robotic applications as it can provide more accurate geometry for holistic scenes compared to images. LiDAR scene completion has been studied and attracted the computer vision community's attention in recent years [2,9,34,35,42,48], while the progress has been pushing forward, most of them focus on directly predicting semantic labels for the completed coarse voxels without fine-grained geometry information, thus no other downstream tasks are benefited. More recently, SPG [47] was proposed for unsupervised domain adaptation for 3D object detection via foreground point completion. However, its completion target is generated by heuristics, thus an improved holistic understanding of the scene is hard to achieve. Depth completion [43] instead solves the problem by relying on a sparse lidar sweep and a paired RGB image to compute a 2.5D pseudo-depth image. However, this problem is ill-posed as monocular images contain ambiguities and the field of view is also limited. Thus, the accuracy is hard to improve, and it's difficult to reconstruct whole scenes at scale. Our model instead tackles this problem" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1075" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.086, + 0.071, + 0.468, + 0.176 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.47, + 0.071, + 0.895, + 0.176 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.18, + 0.894, + 0.237 + ], + "angle": 0, + "content": "Figure 2. Overview of UltraLiDAR pipeline. For (a) LiDAR completion, the sparse encoder maps the sparse point cloud to discrete codes, and the dense decoder reconstructs dense data from them; For (b) LiDAR generation, the transformer model starts from a blank canvas or canvas with codes mapped from the partial observations; and iteratively predicts and updates the missing parts. The decoder produces the LiDAR output given the predicted code as the generation results." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.245, + 0.47, + 0.32 + ], + "angle": 0, + "content": "from a representation learning perspective. It captures the data prior in advance with robust discrete representations thus generalizing better. It also completes the full scene with a higher-beam LiDAR pattern, which is generic to various downstream tasks." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.332, + 0.473, + 0.725 + ], + "angle": 0, + "content": "3D Generation: Inspired by the tremendous progress in 2D image generation [11, 18, 25], 3D content generation has attracted more and more attention in recent years. Existing works demonstrated the high-quality generation in different representations including point cloud [1, 3, 50, 52], voxel grid [16, 21, 29, 41, 45], mesh [14, 17, 19, 39] or implicit geometry [5, 6, 38]. However, these works usually focus on the object level and cannot handle large scenes (due to noncompact representation, large memory footprint and limited model capacity). To enable larger-scale scene synthesis, recent works either define a more compact output space or procedurally generate the scenes [31, 32]. Unfortunately, the generated scenes are still quite limited (e.g., indoor environments) and there are only few works focusing on largescale scene generation for self-driving. In this paper, we focus on the generation of LiDAR point clouds that are highly unstructured, sparse, and non-uniform. [3] and [36] use the variational autoencoder (VAE) or generative adversarial network (GAN) on LiDAR point clouds but the generation realism is quite limited. Most recently, researchers propose a novel score-matching diffusion model for higher-quality LiDAR generation [53] but keep only limited local geometry details and global scenario structures. In contrast, we present a generic framework to learn discrete representations to better maintain the structure and semantic information for a more realistic and controllable generation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Learning Discrete Representations: VQ-VAE [44] proposed to learn discrete representations by compressing images into discrete latent space. It primarily consists of three components: an encoder that learns to map the input image into latent feature maps; a codebook that contains a set of learnable latent embeddings where the feature maps are quantized via nearest neighbor lookup; and a decoder that reconstructs the input image from the quantized code. [33] used a multi-scale hierarchical architecture to capture local and global information in separate codebooks. Based on the learned codebook and decoder in VQ-VAE, VQ-GAN [13]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.245, + 0.895, + 0.397 + ], + "angle": 0, + "content": "proposed to use of a transformer model for image generation. More recently, MaskGIT [7] shows that the learned codebook and the decoder are capable of generating impressive realistic RGB images by using mask modeling with bidirectional transformers. However, all existing works focus on 2D natural images and it is non-trivial to handle sparse, unstructured LiDAR points. To our best knowledge, this paper is the first work that conducts discrete representation in the 3D domain and achieves state-of-the-art performance in large-scale LiDAR scene completion and generation." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.403, + 0.63, + 0.419 + ], + "angle": 0, + "content": "3. UltraLiDAR" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.425, + 0.892, + 0.56 + ], + "angle": 0, + "content": "In this paper, we seek to learn a compact 3D representation of scene-level LiDAR point clouds to enable a series of downstream applications, such as sparse-to-dense LiDAR completion, (un)conditional LiDAR generation, and LiDAR manipulation. Based on the observation that vector quantized (VQ) representations [13, 33, 44] are robust to noise, easy to manipulate, and naturally compatible with generative models, we propose to learn a discrete codebook for LiDAR point clouds and build our model on top of it." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.561, + 0.892, + 0.651 + ], + "angle": 0, + "content": "We start by reviewing the basics of vector-quantized variational autoencoder (VQ-VAE) [44], a building block of our approach. Then we showcase how to exploit similar concepts to encode 3D point clouds into a discrete codebook. Finally, we discuss how to exploit the discrete representation for different tasks." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.655, + 0.816, + 0.672 + ], + "angle": 0, + "content": "3.1. Discrete Representations for LiDAR" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.678, + 0.892, + 0.86 + ], + "angle": 0, + "content": "VQ-VAE revisit: The goal of VQ-VAE is to learn a discrete latent representation that is expressive, robust to noise, and compatible with generative models. VQ-VAE consists of three parts: (i) an encoder \\( E \\) that encodes the input signal, which for simplicity we assume to be an image, \\( \\mathbf{x} \\in \\mathbb{R}^{H \\times W \\times 3} \\) to a continuous embedding map \\( \\mathbf{z} = E(\\mathbf{x}) \\in \\mathbb{R}^{h \\times w \\times D} \\), (ii) an element-wise quantization function \\( q \\) that maps each embedding to its closest learnable latent code \\( \\mathbf{e}_k \\in \\mathbb{R}^D \\), with \\( k = 1, \\dots, K \\), and (iii) a decoder \\( G \\) that takes as input the quantized representation \\( \\hat{\\mathbf{z}} = q(\\mathbf{z}) \\) and outputs the reconstructed image \\( \\hat{\\mathbf{x}} = G(\\hat{\\mathbf{z}}) \\). The whole model can be trained end-to-end by minimizing:" + }, + { + "type": "equation", + "bbox": [ + 0.505, + 0.864, + 0.892, + 0.897 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {v q}} = \\left\\| \\mathbf {x} - \\hat {\\mathbf {x}} \\right\\| _ {2} ^ {2} + \\left\\| \\operatorname {s g} [ E (\\mathbf {x}) ] - \\hat {\\mathbf {z}} \\right\\| _ {2} ^ {2} + \\left\\| \\operatorname {s g} [ \\hat {\\mathbf {z}} ] - E (\\mathbf {x}) \\right\\| _ {2} ^ {2}, \\tag {1}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1076" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.118, + 0.079, + 0.301, + 0.159 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.303, + 0.08, + 0.483, + 0.159 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.484, + 0.08, + 0.665, + 0.159 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.668, + 0.08, + 0.848, + 0.159 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.16, + 0.895, + 0.203 + ], + "angle": 0, + "content": "Figure 3. LiDAR completion and 3D detection on Pandaset. With densified point clouds, the detection model can identify more objects and reduce false negatives. We show detection results in red boxes and ground truth in blue. The missing area far away from ego vehicle in the densified results is caused by uphill; we refer the reader to the supp. material for the explanation with camera visualization." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.218, + 0.395, + 0.233 + ], + "angle": 0, + "content": "where \\(\\mathrm{sg}[\\cdot ]\\) denotes the stop-gradient operation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.234, + 0.471, + 0.37 + ], + "angle": 0, + "content": "The limited number of discrete codes e stabilizes the input distribution of the decoder during training; it also forces the codes to capture meaningful, re-usable information as the decoder can no longer \"seek shortcut\" from the continuous signals for the reconstruction task. VQ-VAE has enjoyed great success across different modalities, such as natural images [7, 13], audio [44] and 2.5D images [40]. In this work, we further extend it to learn discrete representations for 3D LiDAR point clouds." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.385, + 0.47, + 0.627 + ], + "angle": 0, + "content": "VQ-VAE for LiDAR: We aim to learn a discrete codebook that can effectively represent a set of LiDAR point clouds. Directly applying VQ-VAE, however, is challenging, since the fixed set of discrete latents will have to model point clouds that live in a continuous 3D space, and deal with the fact that each point cloud may have a different number of points. To address these issues, we propose to voxelize the point clouds and instead infer whether each voxel is occupied or not. By grounding the point clouds with a pre-defined grid (similar to the 2D pixel grid of images), we can foster the discrete codebook to learn the overall structure rather than the minor 3D positional variations. This representation also can naturally handle the varying number of points. While we may sacrifice some precision during the voxelization process, the impact is negligible for both LiDAR completion and generation (see Sec. 4)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.628, + 0.471, + 0.856 + ], + "angle": 0, + "content": "Now that we have a voxelized point cloud, the next step is to design the encoder \\( E \\) and the decoder \\( G \\). For large scenes with high resolution, 3D convolution becomes very expensive since we need to infer the occupancy of each voxel densely. We thus convert the input to Birds-Eye-View (BEV) images by treating the height dimension of the voxel grids as feature channel \\( C \\) and then adopt 2D convolutions instead. In this case, we can process 3D LiDAR data just like 2D images; we can also exploit existing model architectures designed for 2D images directly. We note that such BEV images have been widely adopted in the context of self-driving perception [8, 51], since they encode rich geometric information. The output of the decoder is a logit grid \\( \\hat{\\mathbf{x}} \\in \\mathbb{R}^{H \\times W \\times C} \\). It can be further converted to a binary voxel grid \\( \\hat{\\mathbf{x}}^{\\mathrm{bin}} \\in \\{0,1\\}^{H \\times W \\times C} \\) through gumbel softmax [23]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Finally, we train our LiDAR VQ-VAE model with Eq. 1, except that we replace the \\(\\ell_2\\) reconstruction loss with a binary (occupied or not) cross-entropy loss. To improve the" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.218, + 0.895, + 0.264 + ], + "angle": 0, + "content": "realism of the reconstruction, we further adopt a pre-trained voxel-based detector \\(V\\) and measure the feature difference, similar to perceptual loss [24]. Our full loss is:" + }, + { + "type": "equation", + "bbox": [ + 0.574, + 0.275, + 0.892, + 0.293 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {f e a t}} = \\mathcal {L} _ {\\mathrm {v q}} + \\| V _ {\\mathrm {b}} (\\mathbf {x}) - V _ {\\mathrm {b}} \\left(\\hat {\\mathbf {x}} ^ {\\mathrm {b i n}}\\right) \\| _ {2} ^ {2}. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.305, + 0.879, + 0.321 + ], + "angle": 0, + "content": "\\(V_{\\mathrm{b}}\\) denotes the feature from the last backbone layer of \\(V\\)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.33, + 0.892, + 0.451 + ], + "angle": 0, + "content": "LiDAR manipulation: Once we train the model, we can easily manipulate arbitrary LiDAR point clouds by editing their corresponding latent codes. Since objects are spatially apart in 3D, the model can dedicate specific codes for them. We can thus identify the codes for objects of interest (e.g., vehicles) and insert/remove them into/from the scene. As shown in Sec. 4, we can populate many vehicles on the street and create counterfactual scenarios." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.462, + 0.687, + 0.478 + ], + "angle": 0, + "content": "3.2. LiDAR Completion" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.485, + 0.892, + 0.546 + ], + "angle": 0, + "content": "Given a dataset of paired, voxelized LiDAR point clouds \\(\\{(\\mathbf{x}_1^{\\mathrm{sp}},\\mathbf{x}_1^{\\mathrm{den}}),\\dots,(\\mathbf{x}_N^{\\mathrm{sp}},\\mathbf{x}_N^{\\mathrm{den}})\\}\\), the goal of LiDAR completion is to learn a function \\(f\\) that maps a sparse LiDAR point cloud \\(\\mathbf{x}^{\\mathrm{sp}}\\) to its dense counterpart \\(\\mathbf{x}^{\\mathrm{den}}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.547, + 0.892, + 0.682 + ], + "angle": 0, + "content": "One straightforward strategy is to leverage the pairwise supervision and directly learn a pix2pix-style network [22] but on voxels. While this model performs well within the same data distribution, it degrades significantly when the input distribution shifts (e.g., when the sparse LiDAR point clouds come from different datasets). We conjecture that this is because there is no restriction on the learned representation, and the model learns to \"cheat\" by relying on non-generalizable details rather than the overall structure." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.683, + 0.892, + 0.911 + ], + "angle": 0, + "content": "In this section, we investigate the use of discrete representations to alleviate the issue. We first learn a discrete codebook \\(\\{\\mathbf{e}_1^{\\mathrm{den}},\\dots,\\mathbf{e}_K^{\\mathrm{den}}\\}\\), an encoder \\(E^{\\mathrm{den}}\\), and a decoder \\(G^{\\mathrm{den}}\\) for each dense LiDAR point cloud \\(\\mathbf{x}^{\\mathrm{den}}\\) using the approach in Sec. 3.1. Then we learn a separate encoder \\(E^{\\mathrm{sp}}\\) that maps each sparse LiDAR point cloud \\(\\mathbf{x}^{\\mathrm{sp}}\\) to the same feature space \\(\\mathbf{z}^{\\mathrm{sp}} = E^{\\mathrm{sp}}(\\mathbf{x}^{\\mathrm{sp}})\\) and quantize it with the dense discrete representation \\(\\mathbf{e}^{\\mathrm{den}}\\). Finally, we decode the quantized representation \\(\\hat{\\mathbf{z}}^{\\mathrm{sp}} = q(\\mathbf{z}^{\\mathrm{sp}})\\) with the dense decoder \\(G^{\\mathrm{den}}\\) and obtain a densified point cloud \\(\\hat{\\mathbf{x}}^{\\mathrm{sp - den}} = G^{\\mathrm{den}}(\\hat{\\mathbf{z}}^{\\mathrm{sp}})\\). With the help of the learned codebook, we can ensure the input to the dense decoder \\(G^{\\mathrm{den}}\\) is in-domain and the reconstructed point clouds are high-quality; we can also denoise the embedding from the encoder and better handle the variations and distribution shift within the input data." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1077" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.127, + 0.067, + 0.317, + 0.08 + ], + "angle": 0, + "content": "Real (not paired, reference only)" + }, + { + "type": "image", + "bbox": [ + 0.128, + 0.081, + 0.31, + 0.158 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.128, + 0.16, + 0.308, + 0.236 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.357, + 0.068, + 0.447, + 0.08 + ], + "angle": 0, + "content": "Projected GAN" + }, + { + "type": "image", + "bbox": [ + 0.315, + 0.081, + 0.492, + 0.159 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.315, + 0.16, + 0.492, + 0.236 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.55, + 0.068, + 0.616, + 0.08 + ], + "angle": 0, + "content": "LiDAR Gen" + }, + { + "type": "image", + "bbox": [ + 0.493, + 0.081, + 0.667, + 0.158 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.493, + 0.16, + 0.668, + 0.236 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.742, + 0.069, + 0.774, + 0.08 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image", + "bbox": [ + 0.669, + 0.081, + 0.848, + 0.159 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.671, + 0.16, + 0.848, + 0.236 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.238, + 0.892, + 0.28 + ], + "angle": 0, + "content": "Figure 4. Qualitative comparison against baselines on unconditional LiDAR generation. We compare with two state-of-the-art LiDAR generation methods Projected GAN [37] and LiDARGen [53] and include real data for reference. Our model can generate results with more structured layouts and clearer beam patterns." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.287, + 0.47, + 0.422 + ], + "angle": 0, + "content": "Training: In practice, we jointly train the sparse encoder \\( E_{\\mathrm{sp}} \\) and the dense VQ-VAE model, since it achieves slightly better performance than performing two-stage training. We hypothesize this is because joint training allows the model to learn a codebook that is easy to decode, and achieves low quantization error for both encoders \\( E_{\\mathrm{sp}} \\) and \\( E_{\\mathrm{den}} \\). We use the same loss functions in Sec. 3.1 to train the whole model, except that the reconstructed target is always the dense point cloud (which we can obtain from the paired data)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.432, + 0.262, + 0.447 + ], + "angle": 0, + "content": "3.3. LiDAR Generation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.457, + 0.47, + 0.533 + ], + "angle": 0, + "content": "As we have alluded to earlier, the learned discrete representations can be naturally combined with generative models. In this section, we describe in detail how we exploit the discrete codebook to generate high-fidelity LiDAR point clouds, both unconditionally and conditionally." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.543, + 0.47, + 0.801 + ], + "angle": 0, + "content": "Unconditional generation: Given the learned codebook e and the decoder \\(G\\), the problem of LiDAR generation can be formulated as code map generation. Instead of directly generating LiDAR point clouds, we first generate discrete code maps in the form of code indices. Then we map the indices to discrete features by querying the codebook and decoding them back to LiDAR point clouds with the decoder. Following Chang et al. [7], we adopt a bi-directional self-attention Transformer [7, 20] to iteratively predict the code map. Specifically, we start from a blank canvas. At each iteration, we select a subset of the predicted codes with top confidence scores and update the canvas accordingly. With the help of the Transformer, we can aggregate context from the whole map and predict missing parts based on already predicted codes. In the end, the canvas will be filled with predicted code indices, from which we can decode LiDAR point clouds. We refer the reader to [7] for more details." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Conditional generation: Our unconditional LiDAR generation pipeline can be easily extended to perform conditional generation. Instead of starting the generation process from an empty canvas, one can simply start with a partially filled code map and let the Transformer predict the rest. For instance, we can place [CAR] codes at regions of interest;" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.287, + 0.892, + 0.332 + ], + "angle": 0, + "content": "and run the model multiple times. We can then obtain different traffic scenarios with the pre-defined cars untouched. Please refer to supp. material for how we identify the codes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.336, + 0.893, + 0.638 + ], + "angle": 0, + "content": "Free space suppression sampling: Our iterative generation procedure can be viewed as a variant of coarse-to-fine generation. The codes generated during early iterations determine the overall structure, while the ones generated at the end are in charge of fine-grained details. While this pipeline is effective for image generation [7], it may lead to degenerated results when generating LiDAR point clouds. One critical reason is that LiDAR point clouds are sparse, and a large portion of the scene is represented by the same [BLANK] codes. Since the [BLANK] codes occur frequently, the Transformer tends to predict them with high scores. If we naively sample the codes based on the output of the Transformer, we may fill most of the canvas with [BLANK] codes, and little structure will remain. To address this issue, we suppress the [BLANK] codes during the early generation stages by setting their probability to 0. This ensures the model generates meaningful structures in the beginning. We identify the [BLANK] codes by looking at the occurrence statistic of all codes across the whole dataset. We empirically select the top as [BLANK] codes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.649, + 0.892, + 0.83 + ], + "angle": 0, + "content": "Iterative denoising: With free space suppression sampling, we can already obtain good results. However, the generated point clouds sometimes still contain high-frequency noise (e.g., there might be some floating points in the very far range). To mitigate this issue, we randomly mask out different regions of the output LiDAR point clouds and re-generate them. The intuition is that if we mask out a structured region, we can still recover it through the neighborhood context. However, if the masked region corresponds to pure noise that is irrelevant to the surrounding, it will likely be removed after multiple trials (since the model cannot infer it from the context)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Training: We first encode all LiDAR point clouds into frozen discrete representations (code maps) learned in Sec. 3.1. Then, at each training iteration, we randomly mask out a subset of codes. Finally, we adopt the bi-directional" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1078" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.097, + 0.089, + 0.447, + 0.162 + ], + "angle": 0, + "content": "
ModelSparse to DenseTwo-stage PINORPointPillar
APBEVAP3DAPBEVAP3D
Real / 64-79.362.275.562.3
Sim / 512-78.157.770.055.5
Sim / 512ContComp79.762.475.159.8
Sim / 512Ours80.364.376.062.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.163, + 0.47, + 0.205 + ], + "angle": 0, + "content": "Table 1. Results on PandaSet. We evaluate all models on PandaSet real 64-beam data, and perform sparse-to-dense during inference optionally with ContComp and our model." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.215, + 0.469, + 0.26 + ], + "angle": 0, + "content": "Transformer to predict the correct code for those masked regions. Since we have GT code map, we supervise the model with cross-entropy loss. See [7] for more details." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.265, + 0.295, + 0.281 + ], + "angle": 0, + "content": "3.4. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.289, + 0.469, + 0.319 + ], + "angle": 0, + "content": "In this section, we discuss implementation details that are crucial for learning discrete LiDAR representations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.327, + 0.469, + 0.523 + ], + "angle": 0, + "content": "Voxel sizes matter: We set the input voxel size to be \\(15.625 \\times 15.625 \\times 15\\) cm for x, y, z dimensions. We find that the downsampling ratio when mapping the BEV image to the discrete code has a huge impact on both reconstruction and generation performance. If the patch size that each discrete code represents is too large, a single fixed code does not have enough capacity to model the variations (e.g., a small position/rotation shift of a car inside the patch). We empirically find that downsampling \\(8 \\times\\) achieves a good trade-off between preserving high-frequency information in the LiDAR data and maintaining high-level semantic meaning. Thus the patch size is \\(8 \\times 8\\), leading to \\(1.25 \\times 1.25\\) m on the spatial dimension that each code represents." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.531, + 0.469, + 0.726 + ], + "angle": 0, + "content": "Model hyperparameters: As a typical BEV image usually has a large spatial range, the resolution of the image and the number of codes are high. We use Swin Transformer [28] instead of the vanilla Vision Transformer [12] to reduce the computational cost for our generative Transformer model. It has 24 layers and 8 heads, and the embedding dimension is set to 512. All other training hyperparameters like optimizer settings and label smoothing are kept the same as in [7]. For simplicity, we use the same architecture in our VQ-VAE learning. The encoder and decoder are both Swin Transformers with 12 layers, respectively. We set the codebook size to 1024 with 1024 hidden dimensions for each code." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.469, + 0.902 + ], + "angle": 0, + "content": "Codebook (re)-initialization: We empirically find that the codebook can easily collapse (only a few codes are used) during training. For better codebook learning, we use data-dependent codebook initialization. Specifically, we use a memory bank to store the continuous embedding output from the encoders at each iteration; and use K-Means centroids of the memory bank to initialize/reinitialize the codebook if the code utilization percentage is lower than a threshold (empirically, we define a code is not used for 256 iterations as \"dead code\" and set the threshold to be \\(50\\%\\)). During the first 2000 iterations of training, we gradually" + }, + { + "type": "table", + "bbox": [ + 0.52, + 0.089, + 0.869, + 0.162 + ], + "angle": 0, + "content": "
ModelSparse to DenseTwo-stage PINORPointPillar
APBEVAP3DAPBEVAP3D
Real / 64-71.732.860.928.1
Sim / 512-66.933.258.528.0
Sim / 512ContComp74.941.567.736.9
Sim / 512Ours76.746.373.040.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.163, + 0.892, + 0.232 + ], + "angle": 0, + "content": "Table 2. PandaSet \\(\\rightarrow\\) KITTI Cross-Dataset Evaluation. The detection and LiDAR completion models are trained on PandaSet, and no KITTI data is seen/used before evaluation. Our LiDAR completion model can do reliable completion on unseen data and significantly improve the detector performance in zero-shot." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.243, + 0.892, + 0.289 + ], + "angle": 0, + "content": "shifted the decoder input from continuous to quantized embeddings as a warmup. We find these strategies help achieve good codebook learning and utilization." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.302, + 0.633, + 0.318 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.327, + 0.81, + 0.343 + ], + "angle": 0, + "content": "4.1. Perception with LiDAR Completion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.344, + 0.892, + 0.525 + ], + "angle": 0, + "content": "We first conduct experiments to verify that UltraLiDAR can boost the performance of a 3D detection model performance by performing LiDAR completion and using the densified results as detection model input. To show that our model generalizes well and can generate reliable sparse-todense results across datasets with the learned discrete representations, we further test the models on KITTI [15] that are trained on PandaSet [46]. We also evaluate our model on the SemanticKITTI scene completion benchmark [2] and show that our model with a generic design can be on par with models on the leaderboard that are heavily tuned for this task." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.535, + 0.892, + 0.702 + ], + "angle": 0, + "content": "Dataset: We train UltraLiDAR and the 3D detection models on PandaSet [46]. We reimplement LiDARsim [30] to generate the 512-beam LiDAR data paired with the real 64-beam LiDAR sweeps (i.e., the actor placement and background are identical) and obtain the sparse-to-dense supervision. We use a custom train/validation split since there is no official split; we refer the readers to the supp. materials for more details. We use KITTI [15] dataset for cross-dataset generalization evaluation; the validation set is used to obtain results, and no model is trained on it. For SemanticKITTI, we use the official train and test split." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.71, + 0.892, + 0.787 + ], + "angle": 0, + "content": "Evaluation metrics: To evaluate 3D detection we use the KITTI metrics and report \\(\\mathrm{AP}_{\\mathrm{BEV}}\\) and \\(\\mathrm{AP}_{\\mathrm{3D}}\\) of the car category at IoU = 0.7. For the SemanticKITTI scene completion benchmark, we report Intersection-over-Union (IoU), which classifies a voxel as occupied or empty." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Training and implementation details: We use two base detectors for the 3D detection benchmark: PointPillar [26] from mmdetection3d [10], and a BEV detector which we denote Two-stage_PIXOR, which improves over [49] by adding a second stage RoI refinement branch; more details of Two-stage_PIXOR can be found in the supp. materials. We also modified PointPillar to make it use binary voxels" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1079" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.089, + 0.089, + 0.46, + 0.119 + ], + "angle": 0, + "content": "
SCCNet [42]JS3C-Net [48]Local-DIFs [34]Ours
IoU29.856.657.756.0
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.123, + 0.47, + 0.178 + ], + "angle": 0, + "content": "Table 3. SemanticKITTI semantic scene completion results. Our model with generic design can achieve on-par performance with state-of-the-art methods that employ architectures/modules heavily tuned for this task." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.186, + 0.469, + 0.262 + ], + "angle": 0, + "content": "instead of pillar features as input; so that the LiDAR completion results from our model can be used. The voxel size for detectors is set to be the same as UltraLiDAR. For SemanticKITTI, the input data is preprocessed as voxel data, and we directly use it without modification." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.267, + 0.47, + 0.463 + ], + "angle": 0, + "content": "Baselines: We first train detectors on PandaSet real data with 64-beam and simulated data with 512-beam, denoted as Real/64 and Sim/512, respectively; during inference, we perform sparse-to-dense LiDAR completion to densify the sparse real data for the Sim/512 model. We also train a LiDAR completion model without the codebook and quantization function (the model thus behaves like an AutoEncoder with sparse-to-dense supervision) as another baseline, denoted as ContComp. We evaluate all models with PandaSet real data; when testing the generalization ability on KITTI dataset, we directly evaluate all models trained on PandaSet in zero-shot (i.e., no KITTI data is seen/used before the evaluation) with KITTI real data." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.468, + 0.469, + 0.664 + ], + "angle": 0, + "content": "PandaSet results: From the first two rows in Tab. 1, we can see that the Sim/512 models perform worse than their Real/64 counterparts when evaluating on the real data. This is expected as there is a domain gap between the dense and sparse data, and the models may learn to rely on the richer geometry information in the dense data that does not exist in the sparse counterpart. However, if we perform the sparse-to-dense operation and lift the model to a higher density, we can see a decent performance improvement over the Sim/512 model. Moreover, we see that our model performs better than the ContComp model that uses continuous representations, indicating the effectiveness of using discrete representation in this task." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.67, + 0.469, + 0.851 + ], + "angle": 0, + "content": "Cross-dataset genearization results: To verify the generalization ability of our model, we directly test it on KITTI in a zero-shot manner, that is without seeing KITTI data in advance. As shown in Tab. 2, both entries that utilize sparse-to-dense achieve better performance, and even surpass the Real/64 model, showing the benefits of sparse-to-dense completion. Since the discrete representation is naturally more robust to noise because of the quantization operation, our model with discrete representations can outperform ContComp by a very significant margin when doing zero-shot generalization, once again showing the benefits of using discrete representations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.469, + 0.901 + ], + "angle": 0, + "content": "SemanticKITTI results: We further test our model on SemanticKITTI scene completion benchmark. As shown in Tab. 3, our model can achieve on-par performance with" + }, + { + "type": "table", + "bbox": [ + 0.533, + 0.089, + 0.86, + 0.176 + ], + "angle": 0, + "content": "
Method\\( MMD_{BEV} \\downarrow \\)\\( JSD_{BEV} \\downarrow \\)
LiDAR VAE [3]\\( 1.18 \\times 10^{-3} \\)0.256
LiDAR GAN [3]\\( 2.07 \\times 10^{-3} \\)0.275
Projected GAN [37]\\( 1.25 \\times 10^{-3} \\)0.190
LiDARGen [53]\\( 4.80 \\times 10^{-4} \\)0.140
Ours\\( 9.67 \\times 10^{-5} \\)0.132
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.181, + 0.892, + 0.21 + ], + "angle": 0, + "content": "Table 4. Quantitative results on KITTI-360. Our results show better statistical alignment with the real data." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.221, + 0.892, + 0.282 + ], + "angle": 0, + "content": "state-of-the-art methods [34, 35, 48] that employ architectures and operations heavily tuned for this task, for example shape-aware point-voxel interaction [48] or multi-resolution scene representation [34, 35]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.291, + 0.733, + 0.307 + ], + "angle": 0, + "content": "4.2. LiDAR Scene Generation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.316, + 0.892, + 0.543 + ], + "angle": 0, + "content": "We first compare quantitative results on KITTI-360 [27] with other baselines in the unconditional generation setting. In this case, we directly train our model with the sparse-to-sparse reconstruction task without the dense encoder; and use the sparse encoder to generate code maps in the generative model training instead. We follow LiDArgen [53] and use the first two sequences as the validation set and use the rest for model training. In Fig. \\(4^{1}\\), we show the qualitative comparison between our model and two baselines; and include the real data for reference. We can see that our model can generate results that are much more similar to the real data, with more structured and reasonable scene layouts and more stable/clearer beam patterns. More unconditional generation results on KITTI-360 can be found in the second row of Fig. 1 and supp. materials." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.558, + 0.892, + 0.784 + ], + "angle": 0, + "content": "Quantitative results: Following [53], we use the Maximum-Mean Discrepancy (MMD) and Jensen-Shannon divergence (JSD) with a \\(100 \\times 100\\) 2D histogram along the ground plane (x and y coordinates) as metrics. Since our model generates points based on voxels, the number of points may differ from the real point cloud. We thus use occupancy as a measurement when doing histogram bin count (i.e., points from the same voxel will only count once) for point clouds from real data and other baselines. We believe this change captures the global structure difference better and lowers the weight on the local point density estimation, which is more reasonable and aligns better with the perceptual quality. As shown in Tab. 4, our method achieves superior performance compared with the baselines." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.799, + 0.892, + 0.874 + ], + "angle": 0, + "content": "Model parameters: We calculate the number of parameters to make sure the model capacities are at the same level when compared with baselines. The number of parameters of LiDArgen [53] and our model are 29.7M and 40.3M, which are both smaller than a standard Swin-Small model." + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.876, + 0.892, + 0.9 + ], + "angle": 0, + "content": "1We contacted the authors of [53] to obtain outputs of all models they used for visualization and metrics calculation" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1080" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.12, + 0.089, + 0.428, + 0.162 + ], + "angle": 0, + "content": "
MethodPercent Prefer Ours
Ours vs LiDAR VAE [3]99.5%
Ours vs LiDAR GAN [3]100%
Ours vs ProjGAN [37]100%
Ours vs LiDARGen [53]98.5%
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.164, + 0.47, + 0.192 + ], + "angle": 0, + "content": "Table 5. Human study results on KITTI-360. Results from our model show significantly better visual quality." + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.199, + 0.468, + 0.268 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.274, + 0.47, + 0.357 + ], + "angle": 0, + "content": "Figure 5. Unconditional generation results on Pandaset. We train our model on dense Pandaset data and generate dense results. The generated samples show diverse scenario layouts with proper actor placement (e.g., parked car in the right sample). The synthesized point clouds are realistic such that a pre-trained detector can directly work out-of-the-box." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.364, + 0.473, + 0.622 + ], + "angle": 0, + "content": "Human study: We perform an A/B test on a set of 8 researchers who have LiDAR expertise to better evaluate the visual quality of the generated samples. We use the same test system as [53], which shows a pair of randomly chosen images of two point clouds each time and lets the human decide which one is more realistic. We compare with four baselines as well as with the real data, with 200 image pairs each, leading to 1000 image pairs in total. We show the percentage of examples where participants believed our generations are more realistic against other baselines in Tab. 5. It is clear that our model can generate results with superior visual quality; over \\(98.5\\%\\) of the time (100% for some baselines), the testers prefer our results over the baselines. It is worth noting that in \\(32\\%\\) cases, people believe our results are more realistic than real data, which is very significant given the fact that for data that is indistinguishable from real, the winning ratio would be \\(50\\%\\) with random choice." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.633, + 0.47, + 0.785 + ], + "angle": 0, + "content": "Unconditional generation: Besides the KITTI-360 results in Fig. 4 and 1, we also train our model on dense Panadset for dense point cloud generation; and additionally run detection models on the generated samples, shown in Fig. 5. We can see that our model is able to generate diverse scenes with proper actor placement (e.g., parked car in the right example), indicating the superiority of our model for this LiDAR generation task. Moreover, the excellent detection results showcase that the generated samples also have high fidelity w.r.t. the perception model." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Conditional generation: We show conditional generation results on KITTI-360 in the bottom row of Fig. 1. Our model can fully exploit the visible part-colored by purple) as context, do reasonable extrapolation for the surrounding environment, and generate diverse scenes (e.g., curved road or crossroad) that align with the input condition well. See supp. materials for more results on KITTI-360/PandaSet." + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.091, + 0.891, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.2, + 0.893, + 0.271 + ], + "angle": 0, + "content": "Figure 6. Conditional LiDAR generation for dirt removal. We mask the red rectangular region in the range view image to mimic dirt occluder. Left: Original input. The masked region is not visible to the model. Right: Our generation results. Our model can successfully recover the vehicle that is partially observed." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.277, + 0.892, + 0.385 + ], + "angle": 0, + "content": "Meanwhile, we further consider a practical setting where the LiDAR sensor can fail for a specific region due to dirt or mechanical issues. To mimic this situation, we mask a part of the range images, as shown in Fig. 6. We can see that our model can still do accurate completion even on partially visible cars, recovering the occluded region, and potentially avoiding dangerous situations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.39, + 0.893, + 0.512 + ], + "angle": 0, + "content": "Manipulation: We show manipulation results with actor insertion and removal in the second row of Fig. 1. This is achieved by explicitly changing the code indices on the code map and letting the decoder generate new results. For example, we can copy the codes for the ground plane and paste them to overwrite the region where a car exists, resulting in a controllable manipulation process. We refer the readers for more results in supp. materials." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.517, + 0.619, + 0.532 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.535, + 0.892, + 0.715 + ], + "angle": 0, + "content": "In this paper, we propose a framework to learn novel LiDAR representations that effectively capture the data priors that enable various downstream applications, including scene completion and generation. Based on the learned representation, we propose a novel sparse-to-dense data reconstruction pipeline that can accurately densify the sparse input and improve the generalization ability of the trained detection models in a zero-shot manner. We further show that our model can generate high-quality LiDAR point clouds unconditionally and do reasonable conditional generation and manipulation, which leads to more realistic and controllable data-driven LiDAR simulation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.716, + 0.892, + 0.792 + ], + "angle": 0, + "content": "One potential future direction for improving our model is to exploit the structure in range view representations, including beam info (which point from which ray) and occlusion reasoning, and combine them with our existing model. This may potentially improve the fidelity of our results." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.892, + 0.903 + ], + "angle": 0, + "content": "Acknowledgement We thank Vlas Zyrianov and Shenlong Wang for providing A/B test code and baseline results, Arnaud Bonnet for infrastructure support, Siva Manivasagam for proofreading. We also thank the Waabi team for their valuable support. YX is partially supported by an NSERC scholarship and a Borealis AI fellowship. WCM is partially supported by a Siebel scholarship." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "1081" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.171 + ], + "angle": 0, + "content": "[1] Panos Achlioptas, Olga Diamanti, Ioannis Mitliagkas, and Leonidas Guibas. 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UltraLiDAR learns discrete representations from large-scale LiDAR point clouds and conduct realistic, scalable and controllable LiDAR completion and generation. Top row: Sparse-to-dense LiDAR completion; Second row: Controllable manipulation of real LiDAR with actor removal and insertion; Third row: Diverse LiDAR generation with realistic global structure and fine-grained details; Bottom row: Conditional scene generation with partially observed point clouds (highlighted in red). Please see supp. for more examples. + +# Abstract + +LiDAR provides accurate geometric measurements of the 3D world. Unfortunately, dense LiDARs are very expensive and the point clouds captured by low-beam LiDAR are often sparse. To address these issues, we present UltraLiDAR, a data-driven framework for scene-level LiDAR completion, LiDAR generation, and LiDAR manipulation. The crux of UltraLiDAR is a compact, discrete representation that encodes the point cloud's geometric structure, is robust to noise, and is easy to manipulate. We show that by aligning the representation of a sparse point cloud to that of a dense point cloud, we can densify the sparse point clouds as if they were captured by a real high-density LiDAR, drastically reducing the cost. Furthermore, by learning a prior over the discrete codebook, we can generate diverse, realistic LiDAR + +point clouds for self-driving. We evaluate the effectiveness of UltraLiDAR on sparse-to-dense LiDAR completion and LiDAR generation. Experiments show that densifying real-world point clouds with our approach can significantly improve the performance of downstream perception systems. Compared to prior art on LiDAR generation, our approach generates much more realistic point clouds. According to A/B test, over $98.5\%$ of the time human participants prefer our results over those of previous methods. Please refer to project page https://waabi.ai/research/ultralidar/ for more information. + +# 1. Introduction + +Building a robust 3D perception system is key to bringing self-driving vehicles into our daily lives. To effectively + +perceive their surroundings, existing autonomous systems primarily exploit LiDAR as the major sensing modality, since it can capture well the 3D geometry of the world. However, while LiDAR provides accurate geometric measurements, it comes with two major limitations: (i) the captured point clouds are inherently sparse; and (ii) the data collection process is difficult to scale up. + +Sparsity: Most popular self-driving LiDARs are time-of-flight and scan the environment by rotating emitter-detector pairs (i.e., beams) around the azimuth. At every time step, each emitter emits a light pulse which travels until it hits a target, gets reflected, and is received by the detector. Distance is measured by calculating the time of travel. Due to the design, the captured point cloud density inherently decreases as the distance to the sensor increases. For distant objects, it is often that only a few LiDAR points are captured, which greatly increases the difficulty for 3D perception. The sparsity problem becomes even more severe under poor weather conditions [47], or when LiDAR sensors have fewer beams [4]. One "simple" strategy is to increase the number of LiDAR beams. However, 128-beam LiDAR sensors are much more expensive than their 64/32-beam counterparts, not to mention that 512-beam LiDAR does not exist yet. + +Scalability: Training and testing perception systems in diverse situations are crucial for developing robust autonomous systems. However, due to their intricate design, LiDARs are much more expensive than cameras. A commercial 64-beam LiDAR usually costs over 25K USD. The price barrier makes LiDAR less accessible to the general public and restricts data collection to a small fraction of vehicles that populate our roads, significantly hindering scaling up. One way to circumvent the issue is to leverage existing LiDAR simulation suites to generate more data. While the simulated point clouds are realistic, these systems typically require one to manually create the scene or rely on multiple scans of the real world in advance, making such a solution less desirable. + +With these challenges in mind, we propose UltraLiDAR, a novel framework for LiDAR completion and generation. The key idea is to learn a compact, discrete 3D representation (codebook) of LiDAR point clouds that encodes the geometric structure of the scene and the physical rules of our world (e.g., occlusion). Then, by aligning the representation of a sparse point cloud to that of a dense point cloud, we can densify the sparse point cloud as if it were captured by a high-density LiDAR (e.g., 512-beam LiDAR). Furthermore, we can learn a prior over the discrete codebook and generate novel, realistic driving scenes by sampling from it; we can also manipulate the discrete code of the scene and produce counterfactual scenarios, both of which can drastically improve the diversity and amount of LiDAR data. Fig. 1 shows some example outputs of UltraLiDAR. + +We demonstrate the effectiveness of UltraLiDAR on two tasks: sparse-to-dense LiDAR completion and LiDAR generation. For LiDAR completion, since there is no ground truth for high-density LiDAR, we exploit the performance of downstream perception tasks as a "proxy" measurement. Specifically, we evaluate 3D detection models on both sparse and densified point clouds and measure the performance difference. Experiments on Pandaset [46] and KITTI-360 [27] show that our completion model can generalize across datasets and the densified results can significantly improve the performance of 3D detection models. As for LiDAR generation, we compare our results with state-of-the-art LiDAR generative models [3, 53]. Our generated point clouds better match the statistics of those of ground truth data. We also conducted a human study where participants prefer our method over prior art over $98.5\%$ (best $100\%$ ) of the time; comparing to ground truth, our results were selected $32\%$ of the time (best $50\%$ ). + +To summarize, the main contributions of this paper are: + +1. We present a LiDAR representation that can effectively capture data priors and enable various downstream applications, e.g., LiDAR completion and generation. +2. We propose a sparse-to-dense LiDAR completion pipeline that can accurately densify sparse point clouds and improve the performance and generalization ability of trained detection models across datasets. +3. We develop an (un)conditional LiDAR generative model that can synthesize high-quality LiDAR point clouds and supports various manipulations. + +# 2. Related Work + +LiDAR / Depth Completion: Sparse LiDAR/depth completion is a beneficial task for many robotic applications as it can provide more accurate geometry for holistic scenes compared to images. LiDAR scene completion has been studied and attracted the computer vision community's attention in recent years [2,9,34,35,42,48], while the progress has been pushing forward, most of them focus on directly predicting semantic labels for the completed coarse voxels without fine-grained geometry information, thus no other downstream tasks are benefited. More recently, SPG [47] was proposed for unsupervised domain adaptation for 3D object detection via foreground point completion. However, its completion target is generated by heuristics, thus an improved holistic understanding of the scene is hard to achieve. Depth completion [43] instead solves the problem by relying on a sparse lidar sweep and a paired RGB image to compute a 2.5D pseudo-depth image. However, this problem is ill-posed as monocular images contain ambiguities and the field of view is also limited. Thus, the accuracy is hard to improve, and it's difficult to reconstruct whole scenes at scale. Our model instead tackles this problem + +![](images/a99ed84ed57f87533ac0c1cfcf5fda031d41ebcc92257c77782bcd44ad67e20f.jpg) +Figure 2. Overview of UltraLiDAR pipeline. For (a) LiDAR completion, the sparse encoder maps the sparse point cloud to discrete codes, and the dense decoder reconstructs dense data from them; For (b) LiDAR generation, the transformer model starts from a blank canvas or canvas with codes mapped from the partial observations; and iteratively predicts and updates the missing parts. The decoder produces the LiDAR output given the predicted code as the generation results. + +![](images/1d11a8fea457eb093129d1040f1b12aa433898f74286c184fa79ca97e211f0dc.jpg) + +from a representation learning perspective. It captures the data prior in advance with robust discrete representations thus generalizing better. It also completes the full scene with a higher-beam LiDAR pattern, which is generic to various downstream tasks. + +3D Generation: Inspired by the tremendous progress in 2D image generation [11, 18, 25], 3D content generation has attracted more and more attention in recent years. Existing works demonstrated the high-quality generation in different representations including point cloud [1, 3, 50, 52], voxel grid [16, 21, 29, 41, 45], mesh [14, 17, 19, 39] or implicit geometry [5, 6, 38]. However, these works usually focus on the object level and cannot handle large scenes (due to noncompact representation, large memory footprint and limited model capacity). To enable larger-scale scene synthesis, recent works either define a more compact output space or procedurally generate the scenes [31, 32]. Unfortunately, the generated scenes are still quite limited (e.g., indoor environments) and there are only few works focusing on largescale scene generation for self-driving. In this paper, we focus on the generation of LiDAR point clouds that are highly unstructured, sparse, and non-uniform. [3] and [36] use the variational autoencoder (VAE) or generative adversarial network (GAN) on LiDAR point clouds but the generation realism is quite limited. Most recently, researchers propose a novel score-matching diffusion model for higher-quality LiDAR generation [53] but keep only limited local geometry details and global scenario structures. In contrast, we present a generic framework to learn discrete representations to better maintain the structure and semantic information for a more realistic and controllable generation. + +Learning Discrete Representations: VQ-VAE [44] proposed to learn discrete representations by compressing images into discrete latent space. It primarily consists of three components: an encoder that learns to map the input image into latent feature maps; a codebook that contains a set of learnable latent embeddings where the feature maps are quantized via nearest neighbor lookup; and a decoder that reconstructs the input image from the quantized code. [33] used a multi-scale hierarchical architecture to capture local and global information in separate codebooks. Based on the learned codebook and decoder in VQ-VAE, VQ-GAN [13] + +proposed to use of a transformer model for image generation. More recently, MaskGIT [7] shows that the learned codebook and the decoder are capable of generating impressive realistic RGB images by using mask modeling with bidirectional transformers. However, all existing works focus on 2D natural images and it is non-trivial to handle sparse, unstructured LiDAR points. To our best knowledge, this paper is the first work that conducts discrete representation in the 3D domain and achieves state-of-the-art performance in large-scale LiDAR scene completion and generation. + +# 3. UltraLiDAR + +In this paper, we seek to learn a compact 3D representation of scene-level LiDAR point clouds to enable a series of downstream applications, such as sparse-to-dense LiDAR completion, (un)conditional LiDAR generation, and LiDAR manipulation. Based on the observation that vector quantized (VQ) representations [13, 33, 44] are robust to noise, easy to manipulate, and naturally compatible with generative models, we propose to learn a discrete codebook for LiDAR point clouds and build our model on top of it. + +We start by reviewing the basics of vector-quantized variational autoencoder (VQ-VAE) [44], a building block of our approach. Then we showcase how to exploit similar concepts to encode 3D point clouds into a discrete codebook. Finally, we discuss how to exploit the discrete representation for different tasks. + +# 3.1. Discrete Representations for LiDAR + +VQ-VAE revisit: The goal of VQ-VAE is to learn a discrete latent representation that is expressive, robust to noise, and compatible with generative models. VQ-VAE consists of three parts: (i) an encoder $E$ that encodes the input signal, which for simplicity we assume to be an image, $\mathbf{x} \in \mathbb{R}^{H \times W \times 3}$ to a continuous embedding map $\mathbf{z} = E(\mathbf{x}) \in \mathbb{R}^{h \times w \times D}$ , (ii) an element-wise quantization function $q$ that maps each embedding to its closest learnable latent code $\mathbf{e}_k \in \mathbb{R}^D$ , with $k = 1, \dots, K$ , and (iii) a decoder $G$ that takes as input the quantized representation $\hat{\mathbf{z}} = q(\mathbf{z})$ and outputs the reconstructed image $\hat{\mathbf{x}} = G(\hat{\mathbf{z}})$ . The whole model can be trained end-to-end by minimizing: + +$$ +\mathcal {L} _ {\mathrm {v q}} = \left\| \mathbf {x} - \hat {\mathbf {x}} \right\| _ {2} ^ {2} + \left\| \operatorname {s g} [ E (\mathbf {x}) ] - \hat {\mathbf {z}} \right\| _ {2} ^ {2} + \left\| \operatorname {s g} [ \hat {\mathbf {z}} ] - E (\mathbf {x}) \right\| _ {2} ^ {2}, \tag {1} +$$ + +![](images/c27b26e291d3a8af1e659942074d3566d7c064ef7cfe691069ca7ec00acbcac5.jpg) +Figure 3. LiDAR completion and 3D detection on Pandaset. With densified point clouds, the detection model can identify more objects and reduce false negatives. We show detection results in red boxes and ground truth in blue. The missing area far away from ego vehicle in the densified results is caused by uphill; we refer the reader to the supp. material for the explanation with camera visualization. + +![](images/ca86c0d210437c115051eff47b7b9994bd416776f3b04b1a0055a37e8fe69f56.jpg) + +![](images/4f4a1653062125b1ce35a0f95dce6e2f9327e2f12ee83962e790ab1fd8370673.jpg) + +![](images/3673c1666333ae849dab567b408803cc9daa64f51acd7c2f490cddecd3325ba0.jpg) + +where $\mathrm{sg}[\cdot ]$ denotes the stop-gradient operation. + +The limited number of discrete codes e stabilizes the input distribution of the decoder during training; it also forces the codes to capture meaningful, re-usable information as the decoder can no longer "seek shortcut" from the continuous signals for the reconstruction task. VQ-VAE has enjoyed great success across different modalities, such as natural images [7, 13], audio [44] and 2.5D images [40]. In this work, we further extend it to learn discrete representations for 3D LiDAR point clouds. + +VQ-VAE for LiDAR: We aim to learn a discrete codebook that can effectively represent a set of LiDAR point clouds. Directly applying VQ-VAE, however, is challenging, since the fixed set of discrete latents will have to model point clouds that live in a continuous 3D space, and deal with the fact that each point cloud may have a different number of points. To address these issues, we propose to voxelize the point clouds and instead infer whether each voxel is occupied or not. By grounding the point clouds with a pre-defined grid (similar to the 2D pixel grid of images), we can foster the discrete codebook to learn the overall structure rather than the minor 3D positional variations. This representation also can naturally handle the varying number of points. While we may sacrifice some precision during the voxelization process, the impact is negligible for both LiDAR completion and generation (see Sec. 4). + +Now that we have a voxelized point cloud, the next step is to design the encoder $E$ and the decoder $G$ . For large scenes with high resolution, 3D convolution becomes very expensive since we need to infer the occupancy of each voxel densely. We thus convert the input to Birds-Eye-View (BEV) images by treating the height dimension of the voxel grids as feature channel $C$ and then adopt 2D convolutions instead. In this case, we can process 3D LiDAR data just like 2D images; we can also exploit existing model architectures designed for 2D images directly. We note that such BEV images have been widely adopted in the context of self-driving perception [8, 51], since they encode rich geometric information. The output of the decoder is a logit grid $\hat{\mathbf{x}} \in \mathbb{R}^{H \times W \times C}$ . It can be further converted to a binary voxel grid $\hat{\mathbf{x}}^{\mathrm{bin}} \in \{0,1\}^{H \times W \times C}$ through gumbel softmax [23]. + +Finally, we train our LiDAR VQ-VAE model with Eq. 1, except that we replace the $\ell_2$ reconstruction loss with a binary (occupied or not) cross-entropy loss. To improve the + +realism of the reconstruction, we further adopt a pre-trained voxel-based detector $V$ and measure the feature difference, similar to perceptual loss [24]. Our full loss is: + +$$ +\mathcal {L} _ {\text {f e a t}} = \mathcal {L} _ {\mathrm {v q}} + \| V _ {\mathrm {b}} (\mathbf {x}) - V _ {\mathrm {b}} \left(\hat {\mathbf {x}} ^ {\mathrm {b i n}}\right) \| _ {2} ^ {2}. \tag {2} +$$ + +$V_{\mathrm{b}}$ denotes the feature from the last backbone layer of $V$ + +LiDAR manipulation: Once we train the model, we can easily manipulate arbitrary LiDAR point clouds by editing their corresponding latent codes. Since objects are spatially apart in 3D, the model can dedicate specific codes for them. We can thus identify the codes for objects of interest (e.g., vehicles) and insert/remove them into/from the scene. As shown in Sec. 4, we can populate many vehicles on the street and create counterfactual scenarios. + +# 3.2. LiDAR Completion + +Given a dataset of paired, voxelized LiDAR point clouds $\{(\mathbf{x}_1^{\mathrm{sp}},\mathbf{x}_1^{\mathrm{den}}),\dots,(\mathbf{x}_N^{\mathrm{sp}},\mathbf{x}_N^{\mathrm{den}})\}$ , the goal of LiDAR completion is to learn a function $f$ that maps a sparse LiDAR point cloud $\mathbf{x}^{\mathrm{sp}}$ to its dense counterpart $\mathbf{x}^{\mathrm{den}}$ . + +One straightforward strategy is to leverage the pairwise supervision and directly learn a pix2pix-style network [22] but on voxels. While this model performs well within the same data distribution, it degrades significantly when the input distribution shifts (e.g., when the sparse LiDAR point clouds come from different datasets). We conjecture that this is because there is no restriction on the learned representation, and the model learns to "cheat" by relying on non-generalizable details rather than the overall structure. + +In this section, we investigate the use of discrete representations to alleviate the issue. We first learn a discrete codebook $\{\mathbf{e}_1^{\mathrm{den}},\dots,\mathbf{e}_K^{\mathrm{den}}\}$ , an encoder $E^{\mathrm{den}}$ , and a decoder $G^{\mathrm{den}}$ for each dense LiDAR point cloud $\mathbf{x}^{\mathrm{den}}$ using the approach in Sec. 3.1. Then we learn a separate encoder $E^{\mathrm{sp}}$ that maps each sparse LiDAR point cloud $\mathbf{x}^{\mathrm{sp}}$ to the same feature space $\mathbf{z}^{\mathrm{sp}} = E^{\mathrm{sp}}(\mathbf{x}^{\mathrm{sp}})$ and quantize it with the dense discrete representation $\mathbf{e}^{\mathrm{den}}$ . Finally, we decode the quantized representation $\hat{\mathbf{z}}^{\mathrm{sp}} = q(\mathbf{z}^{\mathrm{sp}})$ with the dense decoder $G^{\mathrm{den}}$ and obtain a densified point cloud $\hat{\mathbf{x}}^{\mathrm{sp - den}} = G^{\mathrm{den}}(\hat{\mathbf{z}}^{\mathrm{sp}})$ . With the help of the learned codebook, we can ensure the input to the dense decoder $G^{\mathrm{den}}$ is in-domain and the reconstructed point clouds are high-quality; we can also denoise the embedding from the encoder and better handle the variations and distribution shift within the input data. + +![](images/9252da9e7fbd4452790022a4040585229f929dd88fc9a68fd51482aaf889aca3.jpg) +Real (not paired, reference only) + +![](images/35a5a762bee90959158c5215243e55f8081b443561edd54b4863c822300fa0dc.jpg) +Figure 4. Qualitative comparison against baselines on unconditional LiDAR generation. We compare with two state-of-the-art LiDAR generation methods Projected GAN [37] and LiDARGen [53] and include real data for reference. Our model can generate results with more structured layouts and clearer beam patterns. + +![](images/98e300e1f5ea044f0dcb1396324a1e18843b63fafe94fce9414731f999985340.jpg) +Projected GAN + +![](images/5e0bcf986a2a0a823de48f564897eb0721fe150cfef48f0e5d339794b47f4446.jpg) + +![](images/fd792c45db063ee03cb813136cfb80060db61685094f937b1ab2df257fd81b49.jpg) +LiDAR Gen + +![](images/af05dafa663bce81ea100d3ecf2df21f5fc9b9c1d7eb6b1fbceabcd0ccde9dfb.jpg) + +![](images/32949c7fa4858e613b70c82435e8233447c8d3bc3c73328fed301ec877917ffd.jpg) +Ours + +![](images/460a44d1c3c409bbe299de86b58e89e1fbdcf8f6b6b17fa3b08e6df71cf2ae52.jpg) + +Training: In practice, we jointly train the sparse encoder $E_{\mathrm{sp}}$ and the dense VQ-VAE model, since it achieves slightly better performance than performing two-stage training. We hypothesize this is because joint training allows the model to learn a codebook that is easy to decode, and achieves low quantization error for both encoders $E_{\mathrm{sp}}$ and $E_{\mathrm{den}}$ . We use the same loss functions in Sec. 3.1 to train the whole model, except that the reconstructed target is always the dense point cloud (which we can obtain from the paired data). + +# 3.3. LiDAR Generation + +As we have alluded to earlier, the learned discrete representations can be naturally combined with generative models. In this section, we describe in detail how we exploit the discrete codebook to generate high-fidelity LiDAR point clouds, both unconditionally and conditionally. + +Unconditional generation: Given the learned codebook e and the decoder $G$ , the problem of LiDAR generation can be formulated as code map generation. Instead of directly generating LiDAR point clouds, we first generate discrete code maps in the form of code indices. Then we map the indices to discrete features by querying the codebook and decoding them back to LiDAR point clouds with the decoder. Following Chang et al. [7], we adopt a bi-directional self-attention Transformer [7, 20] to iteratively predict the code map. Specifically, we start from a blank canvas. At each iteration, we select a subset of the predicted codes with top confidence scores and update the canvas accordingly. With the help of the Transformer, we can aggregate context from the whole map and predict missing parts based on already predicted codes. In the end, the canvas will be filled with predicted code indices, from which we can decode LiDAR point clouds. We refer the reader to [7] for more details. + +Conditional generation: Our unconditional LiDAR generation pipeline can be easily extended to perform conditional generation. Instead of starting the generation process from an empty canvas, one can simply start with a partially filled code map and let the Transformer predict the rest. For instance, we can place [CAR] codes at regions of interest; + +and run the model multiple times. We can then obtain different traffic scenarios with the pre-defined cars untouched. Please refer to supp. material for how we identify the codes. + +Free space suppression sampling: Our iterative generation procedure can be viewed as a variant of coarse-to-fine generation. The codes generated during early iterations determine the overall structure, while the ones generated at the end are in charge of fine-grained details. While this pipeline is effective for image generation [7], it may lead to degenerated results when generating LiDAR point clouds. One critical reason is that LiDAR point clouds are sparse, and a large portion of the scene is represented by the same [BLANK] codes. Since the [BLANK] codes occur frequently, the Transformer tends to predict them with high scores. If we naively sample the codes based on the output of the Transformer, we may fill most of the canvas with [BLANK] codes, and little structure will remain. To address this issue, we suppress the [BLANK] codes during the early generation stages by setting their probability to 0. This ensures the model generates meaningful structures in the beginning. We identify the [BLANK] codes by looking at the occurrence statistic of all codes across the whole dataset. We empirically select the top as [BLANK] codes. + +Iterative denoising: With free space suppression sampling, we can already obtain good results. However, the generated point clouds sometimes still contain high-frequency noise (e.g., there might be some floating points in the very far range). To mitigate this issue, we randomly mask out different regions of the output LiDAR point clouds and re-generate them. The intuition is that if we mask out a structured region, we can still recover it through the neighborhood context. However, if the masked region corresponds to pure noise that is irrelevant to the surrounding, it will likely be removed after multiple trials (since the model cannot infer it from the context). + +Training: We first encode all LiDAR point clouds into frozen discrete representations (code maps) learned in Sec. 3.1. Then, at each training iteration, we randomly mask out a subset of codes. Finally, we adopt the bi-directional + +
ModelSparse to DenseTwo-stage PINORPointPillar
APBEVAP3DAPBEVAP3D
Real / 64-79.362.275.562.3
Sim / 512-78.157.770.055.5
Sim / 512ContComp79.762.475.159.8
Sim / 512Ours80.364.376.062.8
+ +Transformer to predict the correct code for those masked regions. Since we have GT code map, we supervise the model with cross-entropy loss. See [7] for more details. + +# 3.4. Implementation Details + +In this section, we discuss implementation details that are crucial for learning discrete LiDAR representations. + +Voxel sizes matter: We set the input voxel size to be $15.625 \times 15.625 \times 15$ cm for x, y, z dimensions. We find that the downsampling ratio when mapping the BEV image to the discrete code has a huge impact on both reconstruction and generation performance. If the patch size that each discrete code represents is too large, a single fixed code does not have enough capacity to model the variations (e.g., a small position/rotation shift of a car inside the patch). We empirically find that downsampling $8 \times$ achieves a good trade-off between preserving high-frequency information in the LiDAR data and maintaining high-level semantic meaning. Thus the patch size is $8 \times 8$ , leading to $1.25 \times 1.25$ m on the spatial dimension that each code represents. + +Model hyperparameters: As a typical BEV image usually has a large spatial range, the resolution of the image and the number of codes are high. We use Swin Transformer [28] instead of the vanilla Vision Transformer [12] to reduce the computational cost for our generative Transformer model. It has 24 layers and 8 heads, and the embedding dimension is set to 512. All other training hyperparameters like optimizer settings and label smoothing are kept the same as in [7]. For simplicity, we use the same architecture in our VQ-VAE learning. The encoder and decoder are both Swin Transformers with 12 layers, respectively. We set the codebook size to 1024 with 1024 hidden dimensions for each code. + +Codebook (re)-initialization: We empirically find that the codebook can easily collapse (only a few codes are used) during training. For better codebook learning, we use data-dependent codebook initialization. Specifically, we use a memory bank to store the continuous embedding output from the encoders at each iteration; and use K-Means centroids of the memory bank to initialize/reinitialize the codebook if the code utilization percentage is lower than a threshold (empirically, we define a code is not used for 256 iterations as "dead code" and set the threshold to be $50\%$ ). During the first 2000 iterations of training, we gradually + +Table 1. Results on PandaSet. We evaluate all models on PandaSet real 64-beam data, and perform sparse-to-dense during inference optionally with ContComp and our model. + +
ModelSparse to DenseTwo-stage PINORPointPillar
APBEVAP3DAPBEVAP3D
Real / 64-71.732.860.928.1
Sim / 512-66.933.258.528.0
Sim / 512ContComp74.941.567.736.9
Sim / 512Ours76.746.373.040.9
+ +Table 2. PandaSet $\rightarrow$ KITTI Cross-Dataset Evaluation. The detection and LiDAR completion models are trained on PandaSet, and no KITTI data is seen/used before evaluation. Our LiDAR completion model can do reliable completion on unseen data and significantly improve the detector performance in zero-shot. + +shifted the decoder input from continuous to quantized embeddings as a warmup. We find these strategies help achieve good codebook learning and utilization. + +# 4. Experiments + +# 4.1. Perception with LiDAR Completion + +We first conduct experiments to verify that UltraLiDAR can boost the performance of a 3D detection model performance by performing LiDAR completion and using the densified results as detection model input. To show that our model generalizes well and can generate reliable sparse-todense results across datasets with the learned discrete representations, we further test the models on KITTI [15] that are trained on PandaSet [46]. We also evaluate our model on the SemanticKITTI scene completion benchmark [2] and show that our model with a generic design can be on par with models on the leaderboard that are heavily tuned for this task. + +Dataset: We train UltraLiDAR and the 3D detection models on PandaSet [46]. We reimplement LiDARsim [30] to generate the 512-beam LiDAR data paired with the real 64-beam LiDAR sweeps (i.e., the actor placement and background are identical) and obtain the sparse-to-dense supervision. We use a custom train/validation split since there is no official split; we refer the readers to the supp. materials for more details. We use KITTI [15] dataset for cross-dataset generalization evaluation; the validation set is used to obtain results, and no model is trained on it. For SemanticKITTI, we use the official train and test split. + +Evaluation metrics: To evaluate 3D detection we use the KITTI metrics and report $\mathrm{AP}_{\mathrm{BEV}}$ and $\mathrm{AP}_{\mathrm{3D}}$ of the car category at IoU = 0.7. For the SemanticKITTI scene completion benchmark, we report Intersection-over-Union (IoU), which classifies a voxel as occupied or empty. + +Training and implementation details: We use two base detectors for the 3D detection benchmark: PointPillar [26] from mmdetection3d [10], and a BEV detector which we denote Two-stage_PIXOR, which improves over [49] by adding a second stage RoI refinement branch; more details of Two-stage_PIXOR can be found in the supp. materials. We also modified PointPillar to make it use binary voxels + +
SCCNet [42]JS3C-Net [48]Local-DIFs [34]Ours
IoU29.856.657.756.0
+ +instead of pillar features as input; so that the LiDAR completion results from our model can be used. The voxel size for detectors is set to be the same as UltraLiDAR. For SemanticKITTI, the input data is preprocessed as voxel data, and we directly use it without modification. + +Baselines: We first train detectors on PandaSet real data with 64-beam and simulated data with 512-beam, denoted as Real/64 and Sim/512, respectively; during inference, we perform sparse-to-dense LiDAR completion to densify the sparse real data for the Sim/512 model. We also train a LiDAR completion model without the codebook and quantization function (the model thus behaves like an AutoEncoder with sparse-to-dense supervision) as another baseline, denoted as ContComp. We evaluate all models with PandaSet real data; when testing the generalization ability on KITTI dataset, we directly evaluate all models trained on PandaSet in zero-shot (i.e., no KITTI data is seen/used before the evaluation) with KITTI real data. + +PandaSet results: From the first two rows in Tab. 1, we can see that the Sim/512 models perform worse than their Real/64 counterparts when evaluating on the real data. This is expected as there is a domain gap between the dense and sparse data, and the models may learn to rely on the richer geometry information in the dense data that does not exist in the sparse counterpart. However, if we perform the sparse-to-dense operation and lift the model to a higher density, we can see a decent performance improvement over the Sim/512 model. Moreover, we see that our model performs better than the ContComp model that uses continuous representations, indicating the effectiveness of using discrete representation in this task. + +Cross-dataset genearization results: To verify the generalization ability of our model, we directly test it on KITTI in a zero-shot manner, that is without seeing KITTI data in advance. As shown in Tab. 2, both entries that utilize sparse-to-dense achieve better performance, and even surpass the Real/64 model, showing the benefits of sparse-to-dense completion. Since the discrete representation is naturally more robust to noise because of the quantization operation, our model with discrete representations can outperform ContComp by a very significant margin when doing zero-shot generalization, once again showing the benefits of using discrete representations. + +SemanticKITTI results: We further test our model on SemanticKITTI scene completion benchmark. As shown in Tab. 3, our model can achieve on-par performance with + +Table 3. SemanticKITTI semantic scene completion results. Our model with generic design can achieve on-par performance with state-of-the-art methods that employ architectures/modules heavily tuned for this task. + +
Method\( MMD_{BEV} \downarrow \)\( JSD_{BEV} \downarrow \)
LiDAR VAE [3]\( 1.18 \times 10^{-3} \)0.256
LiDAR GAN [3]\( 2.07 \times 10^{-3} \)0.275
Projected GAN [37]\( 1.25 \times 10^{-3} \)0.190
LiDARGen [53]\( 4.80 \times 10^{-4} \)0.140
Ours\( 9.67 \times 10^{-5} \)0.132
+ +Table 4. Quantitative results on KITTI-360. Our results show better statistical alignment with the real data. + +state-of-the-art methods [34, 35, 48] that employ architectures and operations heavily tuned for this task, for example shape-aware point-voxel interaction [48] or multi-resolution scene representation [34, 35]. + +# 4.2. LiDAR Scene Generation + +We first compare quantitative results on KITTI-360 [27] with other baselines in the unconditional generation setting. In this case, we directly train our model with the sparse-to-sparse reconstruction task without the dense encoder; and use the sparse encoder to generate code maps in the generative model training instead. We follow LiDArgen [53] and use the first two sequences as the validation set and use the rest for model training. In Fig. $4^{1}$ , we show the qualitative comparison between our model and two baselines; and include the real data for reference. We can see that our model can generate results that are much more similar to the real data, with more structured and reasonable scene layouts and more stable/clearer beam patterns. More unconditional generation results on KITTI-360 can be found in the second row of Fig. 1 and supp. materials. + +Quantitative results: Following [53], we use the Maximum-Mean Discrepancy (MMD) and Jensen-Shannon divergence (JSD) with a $100 \times 100$ 2D histogram along the ground plane (x and y coordinates) as metrics. Since our model generates points based on voxels, the number of points may differ from the real point cloud. We thus use occupancy as a measurement when doing histogram bin count (i.e., points from the same voxel will only count once) for point clouds from real data and other baselines. We believe this change captures the global structure difference better and lowers the weight on the local point density estimation, which is more reasonable and aligns better with the perceptual quality. As shown in Tab. 4, our method achieves superior performance compared with the baselines. + +Model parameters: We calculate the number of parameters to make sure the model capacities are at the same level when compared with baselines. The number of parameters of LiDArgen [53] and our model are 29.7M and 40.3M, which are both smaller than a standard Swin-Small model. + +
MethodPercent Prefer Ours
Ours vs LiDAR VAE [3]99.5%
Ours vs LiDAR GAN [3]100%
Ours vs ProjGAN [37]100%
Ours vs LiDARGen [53]98.5%
+ +Table 5. Human study results on KITTI-360. Results from our model show significantly better visual quality. + +![](images/789284817a91c0b75c7b056a0c99370cc736145e65e22580b171a42fdc4fa33c.jpg) +Figure 5. Unconditional generation results on Pandaset. We train our model on dense Pandaset data and generate dense results. The generated samples show diverse scenario layouts with proper actor placement (e.g., parked car in the right sample). The synthesized point clouds are realistic such that a pre-trained detector can directly work out-of-the-box. + +Human study: We perform an A/B test on a set of 8 researchers who have LiDAR expertise to better evaluate the visual quality of the generated samples. We use the same test system as [53], which shows a pair of randomly chosen images of two point clouds each time and lets the human decide which one is more realistic. We compare with four baselines as well as with the real data, with 200 image pairs each, leading to 1000 image pairs in total. We show the percentage of examples where participants believed our generations are more realistic against other baselines in Tab. 5. It is clear that our model can generate results with superior visual quality; over $98.5\%$ of the time (100% for some baselines), the testers prefer our results over the baselines. It is worth noting that in $32\%$ cases, people believe our results are more realistic than real data, which is very significant given the fact that for data that is indistinguishable from real, the winning ratio would be $50\%$ with random choice. + +Unconditional generation: Besides the KITTI-360 results in Fig. 4 and 1, we also train our model on dense Panadset for dense point cloud generation; and additionally run detection models on the generated samples, shown in Fig. 5. We can see that our model is able to generate diverse scenes with proper actor placement (e.g., parked car in the right example), indicating the superiority of our model for this LiDAR generation task. Moreover, the excellent detection results showcase that the generated samples also have high fidelity w.r.t. the perception model. + +Conditional generation: We show conditional generation results on KITTI-360 in the bottom row of Fig. 1. Our model can fully exploit the visible part-colored by purple) as context, do reasonable extrapolation for the surrounding environment, and generate diverse scenes (e.g., curved road or crossroad) that align with the input condition well. See supp. materials for more results on KITTI-360/PandaSet. + +![](images/7496cfcace9317f6a1cd74a7cfdacdfea237ded06063f80646f101966d875e79.jpg) +Figure 6. Conditional LiDAR generation for dirt removal. We mask the red rectangular region in the range view image to mimic dirt occluder. Left: Original input. The masked region is not visible to the model. Right: Our generation results. Our model can successfully recover the vehicle that is partially observed. + +Meanwhile, we further consider a practical setting where the LiDAR sensor can fail for a specific region due to dirt or mechanical issues. To mimic this situation, we mask a part of the range images, as shown in Fig. 6. We can see that our model can still do accurate completion even on partially visible cars, recovering the occluded region, and potentially avoiding dangerous situations. + +Manipulation: We show manipulation results with actor insertion and removal in the second row of Fig. 1. This is achieved by explicitly changing the code indices on the code map and letting the decoder generate new results. For example, we can copy the codes for the ground plane and paste them to overwrite the region where a car exists, resulting in a controllable manipulation process. We refer the readers for more results in supp. materials. + +# 5. Conclusion + +In this paper, we propose a framework to learn novel LiDAR representations that effectively capture the data priors that enable various downstream applications, including scene completion and generation. Based on the learned representation, we propose a novel sparse-to-dense data reconstruction pipeline that can accurately densify the sparse input and improve the generalization ability of the trained detection models in a zero-shot manner. We further show that our model can generate high-quality LiDAR point clouds unconditionally and do reasonable conditional generation and manipulation, which leads to more realistic and controllable data-driven LiDAR simulation. + +One potential future direction for improving our model is to exploit the structure in range view representations, including beam info (which point from which ray) and occlusion reasoning, and combine them with our existing model. This may potentially improve the fidelity of our results. + +Acknowledgement We thank Vlas Zyrianov and Shenlong Wang for providing A/B test code and baseline results, Arnaud Bonnet for infrastructure support, Siva Manivasagam for proofreading. We also thank the Waabi team for their valuable support. YX is partially supported by an NSERC scholarship and a Borealis AI fellowship. WCM is partially supported by a Siebel scholarship. + +# References + +[1] Panos Achlioptas, Olga Diamanti, Ioannis Mitliagkas, and Leonidas Guibas. Learning representations and generative models for 3d point clouds. In International conference on machine learning, pages 40-49. PMLR, 2018. 3 +[2] Jens Behley, Martin Garbade, Andres Milioto, Jan Quenzel, Sven Behnke, Cyril Stachniss, and Jurgen Gall. Semantickitti: A dataset for semantic scene understanding of lidar sequences. 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UltraLiDAR learns discrete representations from large-scale LiDAR point clouds and conduct realistic, scalable and controllable LiDAR completion and generation. Top row: Sparse-to-dense LiDAR completion; Second row: Controllable manipulation of real LiDAR with actor removal and insertion; Third row: Diverse LiDAR generation with realistic global structure and fine-grained details; Bottom row: Conditional scene generation with partially observed point clouds (highlighted in red). Please see supp. for more examples." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 143, + 529, + 192, + 540 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 529, + 192, + 540 + ], + "spans": [ + { + "bbox": [ + 143, + 529, + 192, + 540 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 546, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 546, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 546, + 288, + 713 + ], + "type": "text", + "content": "LiDAR provides accurate geometric measurements of the 3D world. Unfortunately, dense LiDARs are very expensive and the point clouds captured by low-beam LiDAR are often sparse. To address these issues, we present UltraLiDAR, a data-driven framework for scene-level LiDAR completion, LiDAR generation, and LiDAR manipulation. The crux of UltraLiDAR is a compact, discrete representation that encodes the point cloud's geometric structure, is robust to noise, and is easy to manipulate. We show that by aligning the representation of a sparse point cloud to that of a dense point cloud, we can densify the sparse point clouds as if they were captured by a real high-density LiDAR, drastically reducing the cost. Furthermore, by learning a prior over the discrete codebook, we can generate diverse, realistic LiDAR" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 529, + 547, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 529, + 547, + 662 + ], + "spans": [ + { + "bbox": [ + 304, + 529, + 547, + 662 + ], + "type": "text", + "content": "point clouds for self-driving. We evaluate the effectiveness of UltraLiDAR on sparse-to-dense LiDAR completion and LiDAR generation. Experiments show that densifying real-world point clouds with our approach can significantly improve the performance of downstream perception systems. Compared to prior art on LiDAR generation, our approach generates much more realistic point clouds. According to A/B test, over " + }, + { + "bbox": [ + 304, + 529, + 547, + 662 + ], + "type": "inline_equation", + "content": "98.5\\%" + }, + { + "bbox": [ + 304, + 529, + 547, + 662 + ], + "type": "text", + "content": " of the time human participants prefer our results over those of previous methods. Please refer to project page https://waabi.ai/research/ultralidar/ for more information." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 307, + 671, + 387, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 671, + 387, + 684 + ], + "spans": [ + { + "bbox": [ + 307, + 671, + 387, + 684 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 689, + 546, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 546, + 715 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 546, + 715 + ], + "type": "text", + "content": "Building a robust 3D perception system is key to bringing self-driving vehicles into our daily lives. To effectively" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1074" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 156 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 156 + ], + "type": "text", + "content": "perceive their surroundings, existing autonomous systems primarily exploit LiDAR as the major sensing modality, since it can capture well the 3D geometry of the world. However, while LiDAR provides accurate geometric measurements, it comes with two major limitations: (i) the captured point clouds are inherently sparse; and (ii) the data collection process is difficult to scale up." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 159, + 288, + 363 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 159, + 288, + 363 + ], + "spans": [ + { + "bbox": [ + 46, + 159, + 288, + 363 + ], + "type": "text", + "content": "Sparsity: Most popular self-driving LiDARs are time-of-flight and scan the environment by rotating emitter-detector pairs (i.e., beams) around the azimuth. At every time step, each emitter emits a light pulse which travels until it hits a target, gets reflected, and is received by the detector. Distance is measured by calculating the time of travel. Due to the design, the captured point cloud density inherently decreases as the distance to the sensor increases. For distant objects, it is often that only a few LiDAR points are captured, which greatly increases the difficulty for 3D perception. The sparsity problem becomes even more severe under poor weather conditions [47], or when LiDAR sensors have fewer beams [4]. One \"simple\" strategy is to increase the number of LiDAR beams. However, 128-beam LiDAR sensors are much more expensive than their 64/32-beam counterparts, not to mention that 512-beam LiDAR does not exist yet." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 366, + 287, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 366, + 287, + 533 + ], + "spans": [ + { + "bbox": [ + 46, + 366, + 287, + 533 + ], + "type": "text", + "content": "Scalability: Training and testing perception systems in diverse situations are crucial for developing robust autonomous systems. However, due to their intricate design, LiDARs are much more expensive than cameras. A commercial 64-beam LiDAR usually costs over 25K USD. The price barrier makes LiDAR less accessible to the general public and restricts data collection to a small fraction of vehicles that populate our roads, significantly hindering scaling up. One way to circumvent the issue is to leverage existing LiDAR simulation suites to generate more data. While the simulated point clouds are realistic, these systems typically require one to manually create the scene or rely on multiple scans of the real world in advance, making such a solution less desirable." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 534, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 534, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 534, + 288, + 713 + ], + "type": "text", + "content": "With these challenges in mind, we propose UltraLiDAR, a novel framework for LiDAR completion and generation. The key idea is to learn a compact, discrete 3D representation (codebook) of LiDAR point clouds that encodes the geometric structure of the scene and the physical rules of our world (e.g., occlusion). Then, by aligning the representation of a sparse point cloud to that of a dense point cloud, we can densify the sparse point cloud as if it were captured by a high-density LiDAR (e.g., 512-beam LiDAR). Furthermore, we can learn a prior over the discrete codebook and generate novel, realistic driving scenes by sampling from it; we can also manipulate the discrete code of the scene and produce counterfactual scenarios, both of which can drastically improve the diversity and amount of LiDAR data. Fig. 1 shows some example outputs of UltraLiDAR." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 72, + 545, + 287 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 287 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 287 + ], + "type": "text", + "content": "We demonstrate the effectiveness of UltraLiDAR on two tasks: sparse-to-dense LiDAR completion and LiDAR generation. For LiDAR completion, since there is no ground truth for high-density LiDAR, we exploit the performance of downstream perception tasks as a \"proxy\" measurement. Specifically, we evaluate 3D detection models on both sparse and densified point clouds and measure the performance difference. Experiments on Pandaset [46] and KITTI-360 [27] show that our completion model can generalize across datasets and the densified results can significantly improve the performance of 3D detection models. As for LiDAR generation, we compare our results with state-of-the-art LiDAR generative models [3, 53]. Our generated point clouds better match the statistics of those of ground truth data. We also conducted a human study where participants prefer our method over prior art over " + }, + { + "bbox": [ + 304, + 72, + 545, + 287 + ], + "type": "inline_equation", + "content": "98.5\\%" + }, + { + "bbox": [ + 304, + 72, + 545, + 287 + ], + "type": "text", + "content": " (best " + }, + { + "bbox": [ + 304, + 72, + 545, + 287 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 304, + 72, + 545, + 287 + ], + "type": "text", + "content": ") of the time; comparing to ground truth, our results were selected " + }, + { + "bbox": [ + 304, + 72, + 545, + 287 + ], + "type": "inline_equation", + "content": "32\\%" + }, + { + "bbox": [ + 304, + 72, + 545, + 287 + ], + "type": "text", + "content": " of the time (best " + }, + { + "bbox": [ + 304, + 72, + 545, + 287 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 304, + 72, + 545, + 287 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 317, + 288, + 541, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 288, + 541, + 300 + ], + "spans": [ + { + "bbox": [ + 317, + 288, + 541, + 300 + ], + "type": "text", + "content": "To summarize, the main contributions of this paper are:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 313, + 303, + 545, + 430 + ], + "type": "list", + "angle": 0, + "index": 9, + "blocks": [ + { + "bbox": [ + 313, + 303, + 545, + 339 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 303, + 545, + 339 + ], + "spans": [ + { + "bbox": [ + 313, + 303, + 545, + 339 + ], + "type": "text", + "content": "1. We present a LiDAR representation that can effectively capture data priors and enable various downstream applications, e.g., LiDAR completion and generation." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 342, + 545, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 342, + 545, + 389 + ], + "spans": [ + { + "bbox": [ + 313, + 342, + 545, + 389 + ], + "type": "text", + "content": "2. We propose a sparse-to-dense LiDAR completion pipeline that can accurately densify sparse point clouds and improve the performance and generalization ability of trained detection models across datasets." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 394, + 545, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 394, + 545, + 430 + ], + "spans": [ + { + "bbox": [ + 313, + 394, + 545, + 430 + ], + "type": "text", + "content": "3. We develop an (un)conditional LiDAR generative model that can synthesize high-quality LiDAR point clouds and supports various manipulations." + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 441, + 392, + 454 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 441, + 392, + 454 + ], + "spans": [ + { + "bbox": [ + 306, + 441, + 392, + 454 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 462, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 462, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 462, + 545, + 713 + ], + "type": "text", + "content": "LiDAR / Depth Completion: Sparse LiDAR/depth completion is a beneficial task for many robotic applications as it can provide more accurate geometry for holistic scenes compared to images. LiDAR scene completion has been studied and attracted the computer vision community's attention in recent years [2,9,34,35,42,48], while the progress has been pushing forward, most of them focus on directly predicting semantic labels for the completed coarse voxels without fine-grained geometry information, thus no other downstream tasks are benefited. More recently, SPG [47] was proposed for unsupervised domain adaptation for 3D object detection via foreground point completion. However, its completion target is generated by heuristics, thus an improved holistic understanding of the scene is hard to achieve. Depth completion [43] instead solves the problem by relying on a sparse lidar sweep and a paired RGB image to compute a 2.5D pseudo-depth image. However, this problem is ill-posed as monocular images contain ambiguities and the field of view is also limited. Thus, the accuracy is hard to improve, and it's difficult to reconstruct whole scenes at scale. Our model instead tackles this problem" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1075" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 52, + 56, + 286, + 139 + ], + "blocks": [ + { + "bbox": [ + 52, + 56, + 286, + 139 + ], + "lines": [ + { + "bbox": [ + 52, + 56, + 286, + 139 + ], + "spans": [ + { + "bbox": [ + 52, + 56, + 286, + 139 + ], + "type": "image", + "image_path": "a99ed84ed57f87533ac0c1cfcf5fda031d41ebcc92257c77782bcd44ad67e20f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 142, + 547, + 187 + ], + "lines": [ + { + "bbox": [ + 45, + 142, + 547, + 187 + ], + "spans": [ + { + "bbox": [ + 45, + 142, + 547, + 187 + ], + "type": "text", + "content": "Figure 2. Overview of UltraLiDAR pipeline. For (a) LiDAR completion, the sparse encoder maps the sparse point cloud to discrete codes, and the dense decoder reconstructs dense data from them; For (b) LiDAR generation, the transformer model starts from a blank canvas or canvas with codes mapped from the partial observations; and iteratively predicts and updates the missing parts. The decoder produces the LiDAR output given the predicted code as the generation results." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 287, + 56, + 547, + 139 + ], + "blocks": [ + { + "bbox": [ + 287, + 56, + 547, + 139 + ], + "lines": [ + { + "bbox": [ + 287, + 56, + 547, + 139 + ], + "spans": [ + { + "bbox": [ + 287, + 56, + 547, + 139 + ], + "type": "image", + "image_path": "1d11a8fea457eb093129d1040f1b12aa433898f74286c184fa79ca97e211f0dc.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 194, + 287, + 253 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 194, + 287, + 253 + ], + "spans": [ + { + "bbox": [ + 46, + 194, + 287, + 253 + ], + "type": "text", + "content": "from a representation learning perspective. It captures the data prior in advance with robust discrete representations thus generalizing better. It also completes the full scene with a higher-beam LiDAR pattern, which is generic to various downstream tasks." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 262, + 289, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 262, + 289, + 574 + ], + "spans": [ + { + "bbox": [ + 47, + 262, + 289, + 574 + ], + "type": "text", + "content": "3D Generation: Inspired by the tremendous progress in 2D image generation [11, 18, 25], 3D content generation has attracted more and more attention in recent years. Existing works demonstrated the high-quality generation in different representations including point cloud [1, 3, 50, 52], voxel grid [16, 21, 29, 41, 45], mesh [14, 17, 19, 39] or implicit geometry [5, 6, 38]. However, these works usually focus on the object level and cannot handle large scenes (due to noncompact representation, large memory footprint and limited model capacity). To enable larger-scale scene synthesis, recent works either define a more compact output space or procedurally generate the scenes [31, 32]. Unfortunately, the generated scenes are still quite limited (e.g., indoor environments) and there are only few works focusing on largescale scene generation for self-driving. In this paper, we focus on the generation of LiDAR point clouds that are highly unstructured, sparse, and non-uniform. [3] and [36] use the variational autoencoder (VAE) or generative adversarial network (GAN) on LiDAR point clouds but the generation realism is quite limited. Most recently, researchers propose a novel score-matching diffusion model for higher-quality LiDAR generation [53] but keep only limited local geometry details and global scenario structures. In contrast, we present a generic framework to learn discrete representations to better maintain the structure and semantic information for a more realistic and controllable generation." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 582, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 287, + 715 + ], + "type": "text", + "content": "Learning Discrete Representations: VQ-VAE [44] proposed to learn discrete representations by compressing images into discrete latent space. It primarily consists of three components: an encoder that learns to map the input image into latent feature maps; a codebook that contains a set of learnable latent embeddings where the feature maps are quantized via nearest neighbor lookup; and a decoder that reconstructs the input image from the quantized code. [33] used a multi-scale hierarchical architecture to capture local and global information in separate codebooks. Based on the learned codebook and decoder in VQ-VAE, VQ-GAN [13]" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 194, + 547, + 314 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 194, + 547, + 314 + ], + "spans": [ + { + "bbox": [ + 304, + 194, + 547, + 314 + ], + "type": "text", + "content": "proposed to use of a transformer model for image generation. More recently, MaskGIT [7] shows that the learned codebook and the decoder are capable of generating impressive realistic RGB images by using mask modeling with bidirectional transformers. However, all existing works focus on 2D natural images and it is non-trivial to handle sparse, unstructured LiDAR points. To our best knowledge, this paper is the first work that conducts discrete representation in the 3D domain and achieves state-of-the-art performance in large-scale LiDAR scene completion and generation." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 319, + 385, + 331 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 319, + 385, + 331 + ], + "spans": [ + { + "bbox": [ + 305, + 319, + 385, + 331 + ], + "type": "text", + "content": "3. UltraLiDAR" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 336, + 545, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 336, + 545, + 443 + ], + "spans": [ + { + "bbox": [ + 304, + 336, + 545, + 443 + ], + "type": "text", + "content": "In this paper, we seek to learn a compact 3D representation of scene-level LiDAR point clouds to enable a series of downstream applications, such as sparse-to-dense LiDAR completion, (un)conditional LiDAR generation, and LiDAR manipulation. Based on the observation that vector quantized (VQ) representations [13, 33, 44] are robust to noise, easy to manipulate, and naturally compatible with generative models, we propose to learn a discrete codebook for LiDAR point clouds and build our model on top of it." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 444, + 545, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 444, + 545, + 515 + ], + "spans": [ + { + "bbox": [ + 304, + 444, + 545, + 515 + ], + "type": "text", + "content": "We start by reviewing the basics of vector-quantized variational autoencoder (VQ-VAE) [44], a building block of our approach. Then we showcase how to exploit similar concepts to encode 3D point clouds into a discrete codebook. Finally, we discuss how to exploit the discrete representation for different tasks." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 518, + 499, + 532 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 518, + 499, + 532 + ], + "spans": [ + { + "bbox": [ + 306, + 518, + 499, + 532 + ], + "type": "text", + "content": "3.1. Discrete Representations for LiDAR" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 536, + 545, + 681 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 536, + 545, + 681 + ], + "spans": [ + { + "bbox": [ + 304, + 536, + 545, + 681 + ], + "type": "text", + "content": "VQ-VAE revisit: The goal of VQ-VAE is to learn a discrete latent representation that is expressive, robust to noise, and compatible with generative models. VQ-VAE consists of three parts: (i) an encoder " + }, + { + "bbox": [ + 304, + 536, + 545, + 681 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 304, + 536, + 545, + 681 + ], + "type": "text", + "content": " that encodes the input signal, which for simplicity we assume to be an image, " + }, + { + "bbox": [ + 304, + 536, + 545, + 681 + ], + "type": "inline_equation", + "content": "\\mathbf{x} \\in \\mathbb{R}^{H \\times W \\times 3}" + }, + { + "bbox": [ + 304, + 536, + 545, + 681 + ], + "type": "text", + "content": " to a continuous embedding map " + }, + { + "bbox": [ + 304, + 536, + 545, + 681 + ], + "type": "inline_equation", + "content": "\\mathbf{z} = E(\\mathbf{x}) \\in \\mathbb{R}^{h \\times w \\times D}" + }, + { + "bbox": [ + 304, + 536, + 545, + 681 + ], + "type": "text", + "content": ", (ii) an element-wise quantization function " + }, + { + "bbox": [ + 304, + 536, + 545, + 681 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 304, + 536, + 545, + 681 + ], + "type": "text", + "content": " that maps each embedding to its closest learnable latent code " + }, + { + "bbox": [ + 304, + 536, + 545, + 681 + ], + "type": "inline_equation", + "content": "\\mathbf{e}_k \\in \\mathbb{R}^D" + }, + { + "bbox": [ + 304, + 536, + 545, + 681 + ], + "type": "text", + "content": ", with " + }, + { + "bbox": [ + 304, + 536, + 545, + 681 + ], + "type": "inline_equation", + "content": "k = 1, \\dots, K" + }, + { + "bbox": [ + 304, + 536, + 545, + 681 + ], + "type": "text", + "content": ", and (iii) a decoder " + }, + { + "bbox": [ + 304, + 536, + 545, + 681 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 304, + 536, + 545, + 681 + ], + "type": "text", + "content": " that takes as input the quantized representation " + }, + { + "bbox": [ + 304, + 536, + 545, + 681 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{z}} = q(\\mathbf{z})" + }, + { + "bbox": [ + 304, + 536, + 545, + 681 + ], + "type": "text", + "content": " and outputs the reconstructed image " + }, + { + "bbox": [ + 304, + 536, + 545, + 681 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{x}} = G(\\hat{\\mathbf{z}})" + }, + { + "bbox": [ + 304, + 536, + 545, + 681 + ], + "type": "text", + "content": ". The whole model can be trained end-to-end by minimizing:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 309, + 684, + 545, + 710 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 684, + 545, + 710 + ], + "spans": [ + { + "bbox": [ + 309, + 684, + 545, + 710 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {v q}} = \\left\\| \\mathbf {x} - \\hat {\\mathbf {x}} \\right\\| _ {2} ^ {2} + \\left\\| \\operatorname {s g} [ E (\\mathbf {x}) ] - \\hat {\\mathbf {z}} \\right\\| _ {2} ^ {2} + \\left\\| \\operatorname {s g} [ \\hat {\\mathbf {z}} ] - E (\\mathbf {x}) \\right\\| _ {2} ^ {2}, \\tag {1}", + "image_path": "86f6493656a0ab4e7f871a28736898906d28e3f3ca09bfec7a6da64ec5f4d2c7.jpg" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1076" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 72, + 62, + 184, + 125 + ], + "blocks": [ + { + "bbox": [ + 72, + 62, + 184, + 125 + ], + "lines": [ + { + "bbox": [ + 72, + 62, + 184, + 125 + ], + "spans": [ + { + "bbox": [ + 72, + 62, + 184, + 125 + ], + "type": "image", + "image_path": "c27b26e291d3a8af1e659942074d3566d7c064ef7cfe691069ca7ec00acbcac5.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 126, + 547, + 160 + ], + "lines": [ + { + "bbox": [ + 46, + 126, + 547, + 160 + ], + "spans": [ + { + "bbox": [ + 46, + 126, + 547, + 160 + ], + "type": "text", + "content": "Figure 3. LiDAR completion and 3D detection on Pandaset. With densified point clouds, the detection model can identify more objects and reduce false negatives. We show detection results in red boxes and ground truth in blue. The missing area far away from ego vehicle in the densified results is caused by uphill; we refer the reader to the supp. material for the explanation with camera visualization." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 185, + 63, + 295, + 125 + ], + "blocks": [ + { + "bbox": [ + 185, + 63, + 295, + 125 + ], + "lines": [ + { + "bbox": [ + 185, + 63, + 295, + 125 + ], + "spans": [ + { + "bbox": [ + 185, + 63, + 295, + 125 + ], + "type": "image", + "image_path": "ca86c0d210437c115051eff47b7b9994bd416776f3b04b1a0055a37e8fe69f56.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 296, + 63, + 406, + 125 + ], + "blocks": [ + { + "bbox": [ + 296, + 63, + 406, + 125 + ], + "lines": [ + { + "bbox": [ + 296, + 63, + 406, + 125 + ], + "spans": [ + { + "bbox": [ + 296, + 63, + 406, + 125 + ], + "type": "image", + "image_path": "4f4a1653062125b1ce35a0f95dce6e2f9327e2f12ee83962e790ab1fd8370673.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 408, + 63, + 518, + 125 + ], + "blocks": [ + { + "bbox": [ + 408, + 63, + 518, + 125 + ], + "lines": [ + { + "bbox": [ + 408, + 63, + 518, + 125 + ], + "spans": [ + { + "bbox": [ + 408, + 63, + 518, + 125 + ], + "type": "image", + "image_path": "3673c1666333ae849dab567b408803cc9daa64f51acd7c2f490cddecd3325ba0.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 172, + 241, + 184 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 172, + 241, + 184 + ], + "spans": [ + { + "bbox": [ + 47, + 172, + 241, + 184 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 172, + 241, + 184 + ], + "type": "inline_equation", + "content": "\\mathrm{sg}[\\cdot ]" + }, + { + "bbox": [ + 47, + 172, + 241, + 184 + ], + "type": "text", + "content": " denotes the stop-gradient operation." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 185, + 288, + 293 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 185, + 288, + 293 + ], + "spans": [ + { + "bbox": [ + 46, + 185, + 288, + 293 + ], + "type": "text", + "content": "The limited number of discrete codes e stabilizes the input distribution of the decoder during training; it also forces the codes to capture meaningful, re-usable information as the decoder can no longer \"seek shortcut\" from the continuous signals for the reconstruction task. VQ-VAE has enjoyed great success across different modalities, such as natural images [7, 13], audio [44] and 2.5D images [40]. In this work, we further extend it to learn discrete representations for 3D LiDAR point clouds." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 304, + 287, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 304, + 287, + 496 + ], + "spans": [ + { + "bbox": [ + 46, + 304, + 287, + 496 + ], + "type": "text", + "content": "VQ-VAE for LiDAR: We aim to learn a discrete codebook that can effectively represent a set of LiDAR point clouds. Directly applying VQ-VAE, however, is challenging, since the fixed set of discrete latents will have to model point clouds that live in a continuous 3D space, and deal with the fact that each point cloud may have a different number of points. To address these issues, we propose to voxelize the point clouds and instead infer whether each voxel is occupied or not. By grounding the point clouds with a pre-defined grid (similar to the 2D pixel grid of images), we can foster the discrete codebook to learn the overall structure rather than the minor 3D positional variations. This representation also can naturally handle the varying number of points. While we may sacrifice some precision during the voxelization process, the impact is negligible for both LiDAR completion and generation (see Sec. 4)." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 497, + 288, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 497, + 288, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 497, + 288, + 677 + ], + "type": "text", + "content": "Now that we have a voxelized point cloud, the next step is to design the encoder " + }, + { + "bbox": [ + 46, + 497, + 288, + 677 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 46, + 497, + 288, + 677 + ], + "type": "text", + "content": " and the decoder " + }, + { + "bbox": [ + 46, + 497, + 288, + 677 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 46, + 497, + 288, + 677 + ], + "type": "text", + "content": ". For large scenes with high resolution, 3D convolution becomes very expensive since we need to infer the occupancy of each voxel densely. We thus convert the input to Birds-Eye-View (BEV) images by treating the height dimension of the voxel grids as feature channel " + }, + { + "bbox": [ + 46, + 497, + 288, + 677 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 497, + 288, + 677 + ], + "type": "text", + "content": " and then adopt 2D convolutions instead. In this case, we can process 3D LiDAR data just like 2D images; we can also exploit existing model architectures designed for 2D images directly. We note that such BEV images have been widely adopted in the context of self-driving perception [8, 51], since they encode rich geometric information. The output of the decoder is a logit grid " + }, + { + "bbox": [ + 46, + 497, + 288, + 677 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{x}} \\in \\mathbb{R}^{H \\times W \\times C}" + }, + { + "bbox": [ + 46, + 497, + 288, + 677 + ], + "type": "text", + "content": ". It can be further converted to a binary voxel grid " + }, + { + "bbox": [ + 46, + 497, + 288, + 677 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{x}}^{\\mathrm{bin}} \\in \\{0,1\\}^{H \\times W \\times C}" + }, + { + "bbox": [ + 46, + 497, + 288, + 677 + ], + "type": "text", + "content": " through gumbel softmax [23]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 677, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 288, + 714 + ], + "type": "text", + "content": "Finally, we train our LiDAR VQ-VAE model with Eq. 1, except that we replace the " + }, + { + "bbox": [ + 46, + 677, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\ell_2" + }, + { + "bbox": [ + 46, + 677, + 288, + 714 + ], + "type": "text", + "content": " reconstruction loss with a binary (occupied or not) cross-entropy loss. To improve the" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 172, + 547, + 209 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 172, + 547, + 209 + ], + "spans": [ + { + "bbox": [ + 304, + 172, + 547, + 209 + ], + "type": "text", + "content": "realism of the reconstruction, we further adopt a pre-trained voxel-based detector " + }, + { + "bbox": [ + 304, + 172, + 547, + 209 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 304, + 172, + 547, + 209 + ], + "type": "text", + "content": " and measure the feature difference, similar to perceptual loss [24]. Our full loss is:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 351, + 217, + 545, + 232 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 351, + 217, + 545, + 232 + ], + "spans": [ + { + "bbox": [ + 351, + 217, + 545, + 232 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {f e a t}} = \\mathcal {L} _ {\\mathrm {v q}} + \\| V _ {\\mathrm {b}} (\\mathbf {x}) - V _ {\\mathrm {b}} \\left(\\hat {\\mathbf {x}} ^ {\\mathrm {b i n}}\\right) \\| _ {2} ^ {2}. \\tag {2}", + "image_path": "de6475d41e3c754bac0135af74a53a0c89d17edb6cdf5bd7d73aff2173fe0a5d.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 241, + 537, + 254 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 241, + 537, + 254 + ], + "spans": [ + { + "bbox": [ + 306, + 241, + 537, + 254 + ], + "type": "inline_equation", + "content": "V_{\\mathrm{b}}" + }, + { + "bbox": [ + 306, + 241, + 537, + 254 + ], + "type": "text", + "content": " denotes the feature from the last backbone layer of " + }, + { + "bbox": [ + 306, + 241, + 537, + 254 + ], + "type": "inline_equation", + "content": "V" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 261, + 545, + 357 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 261, + 545, + 357 + ], + "spans": [ + { + "bbox": [ + 304, + 261, + 545, + 357 + ], + "type": "text", + "content": "LiDAR manipulation: Once we train the model, we can easily manipulate arbitrary LiDAR point clouds by editing their corresponding latent codes. Since objects are spatially apart in 3D, the model can dedicate specific codes for them. We can thus identify the codes for objects of interest (e.g., vehicles) and insert/remove them into/from the scene. As shown in Sec. 4, we can populate many vehicles on the street and create counterfactual scenarios." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 365, + 420, + 378 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 365, + 420, + 378 + ], + "spans": [ + { + "bbox": [ + 306, + 365, + 420, + 378 + ], + "type": "text", + "content": "3.2. LiDAR Completion" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 384, + 545, + 432 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 384, + 545, + 432 + ], + "spans": [ + { + "bbox": [ + 305, + 384, + 545, + 432 + ], + "type": "text", + "content": "Given a dataset of paired, voxelized LiDAR point clouds " + }, + { + "bbox": [ + 305, + 384, + 545, + 432 + ], + "type": "inline_equation", + "content": "\\{(\\mathbf{x}_1^{\\mathrm{sp}},\\mathbf{x}_1^{\\mathrm{den}}),\\dots,(\\mathbf{x}_N^{\\mathrm{sp}},\\mathbf{x}_N^{\\mathrm{den}})\\}" + }, + { + "bbox": [ + 305, + 384, + 545, + 432 + ], + "type": "text", + "content": ", the goal of LiDAR completion is to learn a function " + }, + { + "bbox": [ + 305, + 384, + 545, + 432 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 305, + 384, + 545, + 432 + ], + "type": "text", + "content": " that maps a sparse LiDAR point cloud " + }, + { + "bbox": [ + 305, + 384, + 545, + 432 + ], + "type": "inline_equation", + "content": "\\mathbf{x}^{\\mathrm{sp}}" + }, + { + "bbox": [ + 305, + 384, + 545, + 432 + ], + "type": "text", + "content": " to its dense counterpart " + }, + { + "bbox": [ + 305, + 384, + 545, + 432 + ], + "type": "inline_equation", + "content": "\\mathbf{x}^{\\mathrm{den}}" + }, + { + "bbox": [ + 305, + 384, + 545, + 432 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 433, + 545, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 433, + 545, + 540 + ], + "spans": [ + { + "bbox": [ + 304, + 433, + 545, + 540 + ], + "type": "text", + "content": "One straightforward strategy is to leverage the pairwise supervision and directly learn a pix2pix-style network [22] but on voxels. While this model performs well within the same data distribution, it degrades significantly when the input distribution shifts (e.g., when the sparse LiDAR point clouds come from different datasets). We conjecture that this is because there is no restriction on the learned representation, and the model learns to \"cheat\" by relying on non-generalizable details rather than the overall structure." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 540, + 545, + 721 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 540, + 545, + 721 + ], + "spans": [ + { + "bbox": [ + 304, + 540, + 545, + 721 + ], + "type": "text", + "content": "In this section, we investigate the use of discrete representations to alleviate the issue. We first learn a discrete codebook " + }, + { + "bbox": [ + 304, + 540, + 545, + 721 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{e}_1^{\\mathrm{den}},\\dots,\\mathbf{e}_K^{\\mathrm{den}}\\}" + }, + { + "bbox": [ + 304, + 540, + 545, + 721 + ], + "type": "text", + "content": ", an encoder " + }, + { + "bbox": [ + 304, + 540, + 545, + 721 + ], + "type": "inline_equation", + "content": "E^{\\mathrm{den}}" + }, + { + "bbox": [ + 304, + 540, + 545, + 721 + ], + "type": "text", + "content": ", and a decoder " + }, + { + "bbox": [ + 304, + 540, + 545, + 721 + ], + "type": "inline_equation", + "content": "G^{\\mathrm{den}}" + }, + { + "bbox": [ + 304, + 540, + 545, + 721 + ], + "type": "text", + "content": " for each dense LiDAR point cloud " + }, + { + "bbox": [ + 304, + 540, + 545, + 721 + ], + "type": "inline_equation", + "content": "\\mathbf{x}^{\\mathrm{den}}" + }, + { + "bbox": [ + 304, + 540, + 545, + 721 + ], + "type": "text", + "content": " using the approach in Sec. 3.1. Then we learn a separate encoder " + }, + { + "bbox": [ + 304, + 540, + 545, + 721 + ], + "type": "inline_equation", + "content": "E^{\\mathrm{sp}}" + }, + { + "bbox": [ + 304, + 540, + 545, + 721 + ], + "type": "text", + "content": " that maps each sparse LiDAR point cloud " + }, + { + "bbox": [ + 304, + 540, + 545, + 721 + ], + "type": "inline_equation", + "content": "\\mathbf{x}^{\\mathrm{sp}}" + }, + { + "bbox": [ + 304, + 540, + 545, + 721 + ], + "type": "text", + "content": " to the same feature space " + }, + { + "bbox": [ + 304, + 540, + 545, + 721 + ], + "type": "inline_equation", + "content": "\\mathbf{z}^{\\mathrm{sp}} = E^{\\mathrm{sp}}(\\mathbf{x}^{\\mathrm{sp}})" + }, + { + "bbox": [ + 304, + 540, + 545, + 721 + ], + "type": "text", + "content": " and quantize it with the dense discrete representation " + }, + { + "bbox": [ + 304, + 540, + 545, + 721 + ], + "type": "inline_equation", + "content": "\\mathbf{e}^{\\mathrm{den}}" + }, + { + "bbox": [ + 304, + 540, + 545, + 721 + ], + "type": "text", + "content": ". Finally, we decode the quantized representation " + }, + { + "bbox": [ + 304, + 540, + 545, + 721 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{z}}^{\\mathrm{sp}} = q(\\mathbf{z}^{\\mathrm{sp}})" + }, + { + "bbox": [ + 304, + 540, + 545, + 721 + ], + "type": "text", + "content": " with the dense decoder " + }, + { + "bbox": [ + 304, + 540, + 545, + 721 + ], + "type": "inline_equation", + "content": "G^{\\mathrm{den}}" + }, + { + "bbox": [ + 304, + 540, + 545, + 721 + ], + "type": "text", + "content": " and obtain a densified point cloud " + }, + { + "bbox": [ + 304, + 540, + 545, + 721 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{x}}^{\\mathrm{sp - den}} = G^{\\mathrm{den}}(\\hat{\\mathbf{z}}^{\\mathrm{sp}})" + }, + { + "bbox": [ + 304, + 540, + 545, + 721 + ], + "type": "text", + "content": ". With the help of the learned codebook, we can ensure the input to the dense decoder " + }, + { + "bbox": [ + 304, + 540, + 545, + 721 + ], + "type": "inline_equation", + "content": "G^{\\mathrm{den}}" + }, + { + "bbox": [ + 304, + 540, + 545, + 721 + ], + "type": "text", + "content": " is in-domain and the reconstructed point clouds are high-quality; we can also denoise the embedding from the encoder and better handle the variations and distribution shift within the input data." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1077" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 78, + 64, + 189, + 125 + ], + "blocks": [ + { + "bbox": [ + 77, + 53, + 194, + 63 + ], + "lines": [ + { + "bbox": [ + 77, + 53, + 194, + 63 + ], + "spans": [ + { + "bbox": [ + 77, + 53, + 194, + 63 + ], + "type": "text", + "content": "Real (not paired, reference only)" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 78, + 64, + 189, + 125 + ], + "lines": [ + { + "bbox": [ + 78, + 64, + 189, + 125 + ], + "spans": [ + { + "bbox": [ + 78, + 64, + 189, + 125 + ], + "type": "image", + "image_path": "9252da9e7fbd4452790022a4040585229f929dd88fc9a68fd51482aaf889aca3.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 78, + 126, + 188, + 186 + ], + "blocks": [ + { + "bbox": [ + 78, + 126, + 188, + 186 + ], + "lines": [ + { + "bbox": [ + 78, + 126, + 188, + 186 + ], + "spans": [ + { + "bbox": [ + 78, + 126, + 188, + 186 + ], + "type": "image", + "image_path": "35a5a762bee90959158c5215243e55f8081b443561edd54b4863c822300fa0dc.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 188, + 545, + 221 + ], + "lines": [ + { + "bbox": [ + 46, + 188, + 545, + 221 + ], + "spans": [ + { + "bbox": [ + 46, + 188, + 545, + 221 + ], + "type": "text", + "content": "Figure 4. Qualitative comparison against baselines on unconditional LiDAR generation. We compare with two state-of-the-art LiDAR generation methods Projected GAN [37] and LiDARGen [53] and include real data for reference. Our model can generate results with more structured layouts and clearer beam patterns." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 192, + 64, + 301, + 125 + ], + "blocks": [ + { + "bbox": [ + 218, + 53, + 273, + 63 + ], + "lines": [ + { + "bbox": [ + 218, + 53, + 273, + 63 + ], + "spans": [ + { + "bbox": [ + 218, + 53, + 273, + 63 + ], + "type": "text", + "content": "Projected GAN" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 192, + 64, + 301, + 125 + ], + "lines": [ + { + "bbox": [ + 192, + 64, + 301, + 125 + ], + "spans": [ + { + "bbox": [ + 192, + 64, + 301, + 125 + ], + "type": "image", + "image_path": "98e300e1f5ea044f0dcb1396324a1e18843b63fafe94fce9414731f999985340.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 192, + 126, + 301, + 186 + ], + "blocks": [ + { + "bbox": [ + 192, + 126, + 301, + 186 + ], + "lines": [ + { + "bbox": [ + 192, + 126, + 301, + 186 + ], + "spans": [ + { + "bbox": [ + 192, + 126, + 301, + 186 + ], + "type": "image", + "image_path": "5e0bcf986a2a0a823de48f564897eb0721fe150cfef48f0e5d339794b47f4446.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 301, + 64, + 408, + 125 + ], + "blocks": [ + { + "bbox": [ + 336, + 53, + 376, + 63 + ], + "lines": [ + { + "bbox": [ + 336, + 53, + 376, + 63 + ], + "spans": [ + { + "bbox": [ + 336, + 53, + 376, + 63 + ], + "type": "text", + "content": "LiDAR Gen" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 301, + 64, + 408, + 125 + ], + "lines": [ + { + "bbox": [ + 301, + 64, + 408, + 125 + ], + "spans": [ + { + "bbox": [ + 301, + 64, + 408, + 125 + ], + "type": "image", + "image_path": "fd792c45db063ee03cb813136cfb80060db61685094f937b1ab2df257fd81b49.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 301, + 126, + 408, + 186 + ], + "blocks": [ + { + "bbox": [ + 301, + 126, + 408, + 186 + ], + "lines": [ + { + "bbox": [ + 301, + 126, + 408, + 186 + ], + "spans": [ + { + "bbox": [ + 301, + 126, + 408, + 186 + ], + "type": "image", + "image_path": "af05dafa663bce81ea100d3ecf2df21f5fc9b9c1d7eb6b1fbceabcd0ccde9dfb.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 409, + 64, + 518, + 125 + ], + "blocks": [ + { + "bbox": [ + 454, + 54, + 473, + 63 + ], + "lines": [ + { + "bbox": [ + 454, + 54, + 473, + 63 + ], + "spans": [ + { + "bbox": [ + 454, + 54, + 473, + 63 + ], + "type": "text", + "content": "Ours" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 409, + 64, + 518, + 125 + ], + "lines": [ + { + "bbox": [ + 409, + 64, + 518, + 125 + ], + "spans": [ + { + "bbox": [ + 409, + 64, + 518, + 125 + ], + "type": "image", + "image_path": "32949c7fa4858e613b70c82435e8233447c8d3bc3c73328fed301ec877917ffd.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 410, + 126, + 518, + 186 + ], + "blocks": [ + { + "bbox": [ + 410, + 126, + 518, + 186 + ], + "lines": [ + { + "bbox": [ + 410, + 126, + 518, + 186 + ], + "spans": [ + { + "bbox": [ + 410, + 126, + 518, + 186 + ], + "type": "image", + "image_path": "460a44d1c3c409bbe299de86b58e89e1fbdcf8f6b6b17fa3b08e6df71cf2ae52.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 227, + 287, + 334 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 227, + 287, + 334 + ], + "spans": [ + { + "bbox": [ + 46, + 227, + 287, + 334 + ], + "type": "text", + "content": "Training: In practice, we jointly train the sparse encoder " + }, + { + "bbox": [ + 46, + 227, + 287, + 334 + ], + "type": "inline_equation", + "content": "E_{\\mathrm{sp}}" + }, + { + "bbox": [ + 46, + 227, + 287, + 334 + ], + "type": "text", + "content": " and the dense VQ-VAE model, since it achieves slightly better performance than performing two-stage training. We hypothesize this is because joint training allows the model to learn a codebook that is easy to decode, and achieves low quantization error for both encoders " + }, + { + "bbox": [ + 46, + 227, + 287, + 334 + ], + "type": "inline_equation", + "content": "E_{\\mathrm{sp}}" + }, + { + "bbox": [ + 46, + 227, + 287, + 334 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 227, + 287, + 334 + ], + "type": "inline_equation", + "content": "E_{\\mathrm{den}}" + }, + { + "bbox": [ + 46, + 227, + 287, + 334 + ], + "type": "text", + "content": ". We use the same loss functions in Sec. 3.1 to train the whole model, except that the reconstructed target is always the dense point cloud (which we can obtain from the paired data)." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 47, + 342, + 160, + 354 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 342, + 160, + 354 + ], + "spans": [ + { + "bbox": [ + 47, + 342, + 160, + 354 + ], + "type": "text", + "content": "3.3. LiDAR Generation" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 361, + 287, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 361, + 287, + 422 + ], + "spans": [ + { + "bbox": [ + 46, + 361, + 287, + 422 + ], + "type": "text", + "content": "As we have alluded to earlier, the learned discrete representations can be naturally combined with generative models. In this section, we describe in detail how we exploit the discrete codebook to generate high-fidelity LiDAR point clouds, both unconditionally and conditionally." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 46, + 430, + 287, + 634 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 430, + 287, + 634 + ], + "spans": [ + { + "bbox": [ + 46, + 430, + 287, + 634 + ], + "type": "text", + "content": "Unconditional generation: Given the learned codebook e and the decoder " + }, + { + "bbox": [ + 46, + 430, + 287, + 634 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 46, + 430, + 287, + 634 + ], + "type": "text", + "content": ", the problem of LiDAR generation can be formulated as code map generation. Instead of directly generating LiDAR point clouds, we first generate discrete code maps in the form of code indices. Then we map the indices to discrete features by querying the codebook and decoding them back to LiDAR point clouds with the decoder. Following Chang et al. [7], we adopt a bi-directional self-attention Transformer [7, 20] to iteratively predict the code map. Specifically, we start from a blank canvas. At each iteration, we select a subset of the predicted codes with top confidence scores and update the canvas accordingly. With the help of the Transformer, we can aggregate context from the whole map and predict missing parts based on already predicted codes. In the end, the canvas will be filled with predicted code indices, from which we can decode LiDAR point clouds. We refer the reader to [7] for more details." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 46, + 641, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 287, + 714 + ], + "type": "text", + "content": "Conditional generation: Our unconditional LiDAR generation pipeline can be easily extended to perform conditional generation. Instead of starting the generation process from an empty canvas, one can simply start with a partially filled code map and let the Transformer predict the rest. For instance, we can place [CAR] codes at regions of interest;" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 227, + 545, + 262 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 227, + 545, + 262 + ], + "spans": [ + { + "bbox": [ + 304, + 227, + 545, + 262 + ], + "type": "text", + "content": "and run the model multiple times. We can then obtain different traffic scenarios with the pre-defined cars untouched. Please refer to supp. material for how we identify the codes." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 266, + 546, + 505 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 266, + 546, + 505 + ], + "spans": [ + { + "bbox": [ + 304, + 266, + 546, + 505 + ], + "type": "text", + "content": "Free space suppression sampling: Our iterative generation procedure can be viewed as a variant of coarse-to-fine generation. The codes generated during early iterations determine the overall structure, while the ones generated at the end are in charge of fine-grained details. While this pipeline is effective for image generation [7], it may lead to degenerated results when generating LiDAR point clouds. One critical reason is that LiDAR point clouds are sparse, and a large portion of the scene is represented by the same [BLANK] codes. Since the [BLANK] codes occur frequently, the Transformer tends to predict them with high scores. If we naively sample the codes based on the output of the Transformer, we may fill most of the canvas with [BLANK] codes, and little structure will remain. To address this issue, we suppress the [BLANK] codes during the early generation stages by setting their probability to 0. This ensures the model generates meaningful structures in the beginning. We identify the [BLANK] codes by looking at the occurrence statistic of all codes across the whole dataset. We empirically select the top as [BLANK] codes." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 514, + 545, + 657 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 514, + 545, + 657 + ], + "spans": [ + { + "bbox": [ + 304, + 514, + 545, + 657 + ], + "type": "text", + "content": "Iterative denoising: With free space suppression sampling, we can already obtain good results. However, the generated point clouds sometimes still contain high-frequency noise (e.g., there might be some floating points in the very far range). To mitigate this issue, we randomly mask out different regions of the output LiDAR point clouds and re-generate them. The intuition is that if we mask out a structured region, we can still recover it through the neighborhood context. However, if the masked region corresponds to pure noise that is irrelevant to the surrounding, it will likely be removed after multiple trials (since the model cannot infer it from the context)." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "Training: We first encode all LiDAR point clouds into frozen discrete representations (code maps) learned in Sec. 3.1. Then, at each training iteration, we randomly mask out a subset of codes. Finally, we adopt the bi-directional" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1078" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 59, + 70, + 273, + 128 + ], + "blocks": [ + { + "bbox": [ + 59, + 70, + 273, + 128 + ], + "lines": [ + { + "bbox": [ + 59, + 70, + 273, + 128 + ], + "spans": [ + { + "bbox": [ + 59, + 70, + 273, + 128 + ], + "type": "table", + "html": "
ModelSparse to DenseTwo-stage PINORPointPillar
APBEVAP3DAPBEVAP3D
Real / 64-79.362.275.562.3
Sim / 512-78.157.770.055.5
Sim / 512ContComp79.762.475.159.8
Sim / 512Ours80.364.376.062.8
", + "image_path": "50a744ac6e34170f8f3d519274b80549c98f3919592a212c4d018224f263b12a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 170, + 287, + 205 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 170, + 287, + 205 + ], + "spans": [ + { + "bbox": [ + 47, + 170, + 287, + 205 + ], + "type": "text", + "content": "Transformer to predict the correct code for those masked regions. Since we have GT code map, we supervise the model with cross-entropy loss. See [7] for more details." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 209, + 180, + 222 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 209, + 180, + 222 + ], + "spans": [ + { + "bbox": [ + 47, + 209, + 180, + 222 + ], + "type": "text", + "content": "3.4. Implementation Details" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 228, + 287, + 252 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 228, + 287, + 252 + ], + "spans": [ + { + "bbox": [ + 47, + 228, + 287, + 252 + ], + "type": "text", + "content": "In this section, we discuss implementation details that are crucial for learning discrete LiDAR representations." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 258, + 287, + 414 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 258, + 287, + 414 + ], + "spans": [ + { + "bbox": [ + 46, + 258, + 287, + 414 + ], + "type": "text", + "content": "Voxel sizes matter: We set the input voxel size to be " + }, + { + "bbox": [ + 46, + 258, + 287, + 414 + ], + "type": "inline_equation", + "content": "15.625 \\times 15.625 \\times 15" + }, + { + "bbox": [ + 46, + 258, + 287, + 414 + ], + "type": "text", + "content": " cm for x, y, z dimensions. We find that the downsampling ratio when mapping the BEV image to the discrete code has a huge impact on both reconstruction and generation performance. If the patch size that each discrete code represents is too large, a single fixed code does not have enough capacity to model the variations (e.g., a small position/rotation shift of a car inside the patch). We empirically find that downsampling " + }, + { + "bbox": [ + 46, + 258, + 287, + 414 + ], + "type": "inline_equation", + "content": "8 \\times" + }, + { + "bbox": [ + 46, + 258, + 287, + 414 + ], + "type": "text", + "content": " achieves a good trade-off between preserving high-frequency information in the LiDAR data and maintaining high-level semantic meaning. Thus the patch size is " + }, + { + "bbox": [ + 46, + 258, + 287, + 414 + ], + "type": "inline_equation", + "content": "8 \\times 8" + }, + { + "bbox": [ + 46, + 258, + 287, + 414 + ], + "type": "text", + "content": ", leading to " + }, + { + "bbox": [ + 46, + 258, + 287, + 414 + ], + "type": "inline_equation", + "content": "1.25 \\times 1.25" + }, + { + "bbox": [ + 46, + 258, + 287, + 414 + ], + "type": "text", + "content": " m on the spatial dimension that each code represents." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 420, + 287, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 420, + 287, + 574 + ], + "spans": [ + { + "bbox": [ + 46, + 420, + 287, + 574 + ], + "type": "text", + "content": "Model hyperparameters: As a typical BEV image usually has a large spatial range, the resolution of the image and the number of codes are high. We use Swin Transformer [28] instead of the vanilla Vision Transformer [12] to reduce the computational cost for our generative Transformer model. It has 24 layers and 8 heads, and the embedding dimension is set to 512. All other training hyperparameters like optimizer settings and label smoothing are kept the same as in [7]. For simplicity, we use the same architecture in our VQ-VAE learning. The encoder and decoder are both Swin Transformers with 12 layers, respectively. We set the codebook size to 1024 with 1024 hidden dimensions for each code." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "type": "text", + "content": "Codebook (re)-initialization: We empirically find that the codebook can easily collapse (only a few codes are used) during training. For better codebook learning, we use data-dependent codebook initialization. Specifically, we use a memory bank to store the continuous embedding output from the encoders at each iteration; and use K-Means centroids of the memory bank to initialize/reinitialize the codebook if the code utilization percentage is lower than a threshold (empirically, we define a code is not used for 256 iterations as \"dead code\" and set the threshold to be " + }, + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "type": "text", + "content": "). During the first 2000 iterations of training, we gradually" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 318, + 70, + 531, + 128 + ], + "blocks": [ + { + "bbox": [ + 47, + 129, + 287, + 162 + ], + "lines": [ + { + "bbox": [ + 47, + 129, + 287, + 162 + ], + "spans": [ + { + "bbox": [ + 47, + 129, + 287, + 162 + ], + "type": "text", + "content": "Table 1. Results on PandaSet. We evaluate all models on PandaSet real 64-beam data, and perform sparse-to-dense during inference optionally with ContComp and our model." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 318, + 70, + 531, + 128 + ], + "lines": [ + { + "bbox": [ + 318, + 70, + 531, + 128 + ], + "spans": [ + { + "bbox": [ + 318, + 70, + 531, + 128 + ], + "type": "table", + "html": "
ModelSparse to DenseTwo-stage PINORPointPillar
APBEVAP3DAPBEVAP3D
Real / 64-71.732.860.928.1
Sim / 512-66.933.258.528.0
Sim / 512ContComp74.941.567.736.9
Sim / 512Ours76.746.373.040.9
", + "image_path": "37feb914afbdf9b893a3711aaa7f50956e618b3b12c5a7edf128ce1ad049bd1d.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 129, + 545, + 183 + ], + "lines": [ + { + "bbox": [ + 306, + 129, + 545, + 183 + ], + "spans": [ + { + "bbox": [ + 306, + 129, + 545, + 183 + ], + "type": "text", + "content": "Table 2. PandaSet " + }, + { + "bbox": [ + 306, + 129, + 545, + 183 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 306, + 129, + 545, + 183 + ], + "type": "text", + "content": " KITTI Cross-Dataset Evaluation. The detection and LiDAR completion models are trained on PandaSet, and no KITTI data is seen/used before evaluation. Our LiDAR completion model can do reliable completion on unseen data and significantly improve the detector performance in zero-shot." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 306, + 192, + 545, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 192, + 545, + 228 + ], + "spans": [ + { + "bbox": [ + 306, + 192, + 545, + 228 + ], + "type": "text", + "content": "shifted the decoder input from continuous to quantized embeddings as a warmup. We find these strategies help achieve good codebook learning and utilization." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 239, + 387, + 251 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 239, + 387, + 251 + ], + "spans": [ + { + "bbox": [ + 306, + 239, + 387, + 251 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 258, + 495, + 271 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 258, + 495, + 271 + ], + "spans": [ + { + "bbox": [ + 306, + 258, + 495, + 271 + ], + "type": "text", + "content": "4.1. Perception with LiDAR Completion" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 272, + 545, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 272, + 545, + 415 + ], + "spans": [ + { + "bbox": [ + 304, + 272, + 545, + 415 + ], + "type": "text", + "content": "We first conduct experiments to verify that UltraLiDAR can boost the performance of a 3D detection model performance by performing LiDAR completion and using the densified results as detection model input. To show that our model generalizes well and can generate reliable sparse-todense results across datasets with the learned discrete representations, we further test the models on KITTI [15] that are trained on PandaSet [46]. We also evaluate our model on the SemanticKITTI scene completion benchmark [2] and show that our model with a generic design can be on par with models on the leaderboard that are heavily tuned for this task." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 423, + 545, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 423, + 545, + 555 + ], + "spans": [ + { + "bbox": [ + 304, + 423, + 545, + 555 + ], + "type": "text", + "content": "Dataset: We train UltraLiDAR and the 3D detection models on PandaSet [46]. We reimplement LiDARsim [30] to generate the 512-beam LiDAR data paired with the real 64-beam LiDAR sweeps (i.e., the actor placement and background are identical) and obtain the sparse-to-dense supervision. We use a custom train/validation split since there is no official split; we refer the readers to the supp. materials for more details. We use KITTI [15] dataset for cross-dataset generalization evaluation; the validation set is used to obtain results, and no model is trained on it. For SemanticKITTI, we use the official train and test split." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 562, + 545, + 623 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 562, + 545, + 623 + ], + "spans": [ + { + "bbox": [ + 304, + 562, + 545, + 623 + ], + "type": "text", + "content": "Evaluation metrics: To evaluate 3D detection we use the KITTI metrics and report " + }, + { + "bbox": [ + 304, + 562, + 545, + 623 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_{\\mathrm{BEV}}" + }, + { + "bbox": [ + 304, + 562, + 545, + 623 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 562, + 545, + 623 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_{\\mathrm{3D}}" + }, + { + "bbox": [ + 304, + 562, + 545, + 623 + ], + "type": "text", + "content": " of the car category at IoU = 0.7. For the SemanticKITTI scene completion benchmark, we report Intersection-over-Union (IoU), which classifies a voxel as occupied or empty." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": "Training and implementation details: We use two base detectors for the 3D detection benchmark: PointPillar [26] from mmdetection3d [10], and a BEV detector which we denote Two-stage_PIXOR, which improves over [49] by adding a second stage RoI refinement branch; more details of Two-stage_PIXOR can be found in the supp. materials. We also modified PointPillar to make it use binary voxels" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1079" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 54, + 70, + 281, + 94 + ], + "blocks": [ + { + "bbox": [ + 54, + 70, + 281, + 94 + ], + "lines": [ + { + "bbox": [ + 54, + 70, + 281, + 94 + ], + "spans": [ + { + "bbox": [ + 54, + 70, + 281, + 94 + ], + "type": "table", + "html": "
SCCNet [42]JS3C-Net [48]Local-DIFs [34]Ours
IoU29.856.657.756.0
", + "image_path": "0cdd97fd5bede0fe4d15da7d11fdc87ff933da3a367aae6a0e1c03c6d22f061a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 147, + 287, + 207 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 147, + 287, + 207 + ], + "spans": [ + { + "bbox": [ + 46, + 147, + 287, + 207 + ], + "type": "text", + "content": "instead of pillar features as input; so that the LiDAR completion results from our model can be used. The voxel size for detectors is set to be the same as UltraLiDAR. For SemanticKITTI, the input data is preprocessed as voxel data, and we directly use it without modification." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 211, + 287, + 366 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 211, + 287, + 366 + ], + "spans": [ + { + "bbox": [ + 46, + 211, + 287, + 366 + ], + "type": "text", + "content": "Baselines: We first train detectors on PandaSet real data with 64-beam and simulated data with 512-beam, denoted as Real/64 and Sim/512, respectively; during inference, we perform sparse-to-dense LiDAR completion to densify the sparse real data for the Sim/512 model. We also train a LiDAR completion model without the codebook and quantization function (the model thus behaves like an AutoEncoder with sparse-to-dense supervision) as another baseline, denoted as ContComp. We evaluate all models with PandaSet real data; when testing the generalization ability on KITTI dataset, we directly evaluate all models trained on PandaSet in zero-shot (i.e., no KITTI data is seen/used before the evaluation) with KITTI real data." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 370, + 287, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 370, + 287, + 525 + ], + "spans": [ + { + "bbox": [ + 46, + 370, + 287, + 525 + ], + "type": "text", + "content": "PandaSet results: From the first two rows in Tab. 1, we can see that the Sim/512 models perform worse than their Real/64 counterparts when evaluating on the real data. This is expected as there is a domain gap between the dense and sparse data, and the models may learn to rely on the richer geometry information in the dense data that does not exist in the sparse counterpart. However, if we perform the sparse-to-dense operation and lift the model to a higher density, we can see a decent performance improvement over the Sim/512 model. Moreover, we see that our model performs better than the ContComp model that uses continuous representations, indicating the effectiveness of using discrete representation in this task." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 530, + 287, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 530, + 287, + 673 + ], + "spans": [ + { + "bbox": [ + 46, + 530, + 287, + 673 + ], + "type": "text", + "content": "Cross-dataset genearization results: To verify the generalization ability of our model, we directly test it on KITTI in a zero-shot manner, that is without seeing KITTI data in advance. As shown in Tab. 2, both entries that utilize sparse-to-dense achieve better performance, and even surpass the Real/64 model, showing the benefits of sparse-to-dense completion. Since the discrete representation is naturally more robust to noise because of the quantization operation, our model with discrete representations can outperform ContComp by a very significant margin when doing zero-shot generalization, once again showing the benefits of using discrete representations." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": "SemanticKITTI results: We further test our model on SemanticKITTI scene completion benchmark. As shown in Tab. 3, our model can achieve on-par performance with" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 326, + 70, + 526, + 139 + ], + "blocks": [ + { + "bbox": [ + 47, + 97, + 287, + 140 + ], + "lines": [ + { + "bbox": [ + 47, + 97, + 287, + 140 + ], + "spans": [ + { + "bbox": [ + 47, + 97, + 287, + 140 + ], + "type": "text", + "content": "Table 3. SemanticKITTI semantic scene completion results. Our model with generic design can achieve on-par performance with state-of-the-art methods that employ architectures/modules heavily tuned for this task." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 326, + 70, + 526, + 139 + ], + "lines": [ + { + "bbox": [ + 326, + 70, + 526, + 139 + ], + "spans": [ + { + "bbox": [ + 326, + 70, + 526, + 139 + ], + "type": "table", + "html": "
Method\\( MMD_{BEV} \\downarrow \\)\\( JSD_{BEV} \\downarrow \\)
LiDAR VAE [3]\\( 1.18 \\times 10^{-3} \\)0.256
LiDAR GAN [3]\\( 2.07 \\times 10^{-3} \\)0.275
Projected GAN [37]\\( 1.25 \\times 10^{-3} \\)0.190
LiDARGen [53]\\( 4.80 \\times 10^{-4} \\)0.140
Ours\\( 9.67 \\times 10^{-5} \\)0.132
", + "image_path": "709fbb9d0f005978b1f9c142b89d922f04d1d198279fbc22fe7e8267fab57905.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 143, + 545, + 166 + ], + "lines": [ + { + "bbox": [ + 305, + 143, + 545, + 166 + ], + "spans": [ + { + "bbox": [ + 305, + 143, + 545, + 166 + ], + "type": "text", + "content": "Table 4. Quantitative results on KITTI-360. Our results show better statistical alignment with the real data." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 175, + 545, + 223 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 175, + 545, + 223 + ], + "spans": [ + { + "bbox": [ + 305, + 175, + 545, + 223 + ], + "type": "text", + "content": "state-of-the-art methods [34, 35, 48] that employ architectures and operations heavily tuned for this task, for example shape-aware point-voxel interaction [48] or multi-resolution scene representation [34, 35]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 230, + 448, + 243 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 230, + 448, + 243 + ], + "spans": [ + { + "bbox": [ + 306, + 230, + 448, + 243 + ], + "type": "text", + "content": "4.2. LiDAR Scene Generation" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 250, + 545, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 250, + 545, + 430 + ], + "spans": [ + { + "bbox": [ + 304, + 250, + 545, + 430 + ], + "type": "text", + "content": "We first compare quantitative results on KITTI-360 [27] with other baselines in the unconditional generation setting. In this case, we directly train our model with the sparse-to-sparse reconstruction task without the dense encoder; and use the sparse encoder to generate code maps in the generative model training instead. We follow LiDArgen [53] and use the first two sequences as the validation set and use the rest for model training. In Fig. " + }, + { + "bbox": [ + 304, + 250, + 545, + 430 + ], + "type": "inline_equation", + "content": "4^{1}" + }, + { + "bbox": [ + 304, + 250, + 545, + 430 + ], + "type": "text", + "content": ", we show the qualitative comparison between our model and two baselines; and include the real data for reference. We can see that our model can generate results that are much more similar to the real data, with more structured and reasonable scene layouts and more stable/clearer beam patterns. More unconditional generation results on KITTI-360 can be found in the second row of Fig. 1 and supp. materials." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 441, + 545, + 620 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 441, + 545, + 620 + ], + "spans": [ + { + "bbox": [ + 304, + 441, + 545, + 620 + ], + "type": "text", + "content": "Quantitative results: Following [53], we use the Maximum-Mean Discrepancy (MMD) and Jensen-Shannon divergence (JSD) with a " + }, + { + "bbox": [ + 304, + 441, + 545, + 620 + ], + "type": "inline_equation", + "content": "100 \\times 100" + }, + { + "bbox": [ + 304, + 441, + 545, + 620 + ], + "type": "text", + "content": " 2D histogram along the ground plane (x and y coordinates) as metrics. Since our model generates points based on voxels, the number of points may differ from the real point cloud. We thus use occupancy as a measurement when doing histogram bin count (i.e., points from the same voxel will only count once) for point clouds from real data and other baselines. We believe this change captures the global structure difference better and lowers the weight on the local point density estimation, which is more reasonable and aligns better with the perceptual quality. As shown in Tab. 4, our method achieves superior performance compared with the baselines." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 632, + 545, + 692 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 632, + 545, + 692 + ], + "spans": [ + { + "bbox": [ + 304, + 632, + 545, + 692 + ], + "type": "text", + "content": "Model parameters: We calculate the number of parameters to make sure the model capacities are at the same level when compared with baselines. The number of parameters of LiDArgen [53] and our model are 29.7M and 40.3M, which are both smaller than a standard Swin-Small model." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 306, + 693, + 545, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 693, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 306, + 693, + 545, + 712 + ], + "type": "text", + "content": "1We contacted the authors of [53] to obtain outputs of all models they used for visualization and metrics calculation" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1080" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 73, + 70, + 261, + 128 + ], + "blocks": [ + { + "bbox": [ + 73, + 70, + 261, + 128 + ], + "lines": [ + { + "bbox": [ + 73, + 70, + 261, + 128 + ], + "spans": [ + { + "bbox": [ + 73, + 70, + 261, + 128 + ], + "type": "table", + "html": "
MethodPercent Prefer Ours
Ours vs LiDAR VAE [3]99.5%
Ours vs LiDAR GAN [3]100%
Ours vs ProjGAN [37]100%
Ours vs LiDARGen [53]98.5%
", + "image_path": "b4d2d4184ca997dee6fe1c9c8340466b624c667d3f733775f16ca735e26a21d8.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 129, + 287, + 152 + ], + "lines": [ + { + "bbox": [ + 47, + 129, + 287, + 152 + ], + "spans": [ + { + "bbox": [ + 47, + 129, + 287, + 152 + ], + "type": "text", + "content": "Table 5. Human study results on KITTI-360. Results from our model show significantly better visual quality." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 51, + 157, + 286, + 212 + ], + "blocks": [ + { + "bbox": [ + 51, + 157, + 286, + 212 + ], + "lines": [ + { + "bbox": [ + 51, + 157, + 286, + 212 + ], + "spans": [ + { + "bbox": [ + 51, + 157, + 286, + 212 + ], + "type": "image", + "image_path": "789284817a91c0b75c7b056a0c99370cc736145e65e22580b171a42fdc4fa33c.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 217, + 287, + 282 + ], + "lines": [ + { + "bbox": [ + 46, + 217, + 287, + 282 + ], + "spans": [ + { + "bbox": [ + 46, + 217, + 287, + 282 + ], + "type": "text", + "content": "Figure 5. Unconditional generation results on Pandaset. We train our model on dense Pandaset data and generate dense results. The generated samples show diverse scenario layouts with proper actor placement (e.g., parked car in the right sample). The synthesized point clouds are realistic such that a pre-trained detector can directly work out-of-the-box." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 288, + 289, + 492 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 288, + 289, + 492 + ], + "spans": [ + { + "bbox": [ + 46, + 288, + 289, + 492 + ], + "type": "text", + "content": "Human study: We perform an A/B test on a set of 8 researchers who have LiDAR expertise to better evaluate the visual quality of the generated samples. We use the same test system as [53], which shows a pair of randomly chosen images of two point clouds each time and lets the human decide which one is more realistic. We compare with four baselines as well as with the real data, with 200 image pairs each, leading to 1000 image pairs in total. We show the percentage of examples where participants believed our generations are more realistic against other baselines in Tab. 5. It is clear that our model can generate results with superior visual quality; over " + }, + { + "bbox": [ + 46, + 288, + 289, + 492 + ], + "type": "inline_equation", + "content": "98.5\\%" + }, + { + "bbox": [ + 46, + 288, + 289, + 492 + ], + "type": "text", + "content": " of the time (100% for some baselines), the testers prefer our results over the baselines. It is worth noting that in " + }, + { + "bbox": [ + 46, + 288, + 289, + 492 + ], + "type": "inline_equation", + "content": "32\\%" + }, + { + "bbox": [ + 46, + 288, + 289, + 492 + ], + "type": "text", + "content": " cases, people believe our results are more realistic than real data, which is very significant given the fact that for data that is indistinguishable from real, the winning ratio would be " + }, + { + "bbox": [ + 46, + 288, + 289, + 492 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 46, + 288, + 289, + 492 + ], + "type": "text", + "content": " with random choice." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 501, + 287, + 621 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 501, + 287, + 621 + ], + "spans": [ + { + "bbox": [ + 46, + 501, + 287, + 621 + ], + "type": "text", + "content": "Unconditional generation: Besides the KITTI-360 results in Fig. 4 and 1, we also train our model on dense Panadset for dense point cloud generation; and additionally run detection models on the generated samples, shown in Fig. 5. We can see that our model is able to generate diverse scenes with proper actor placement (e.g., parked car in the right example), indicating the superiority of our model for this LiDAR generation task. Moreover, the excellent detection results showcase that the generated samples also have high fidelity w.r.t. the perception model." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "content": "Conditional generation: We show conditional generation results on KITTI-360 in the bottom row of Fig. 1. Our model can fully exploit the visible part-colored by purple) as context, do reasonable extrapolation for the surrounding environment, and generate diverse scenes (e.g., curved road or crossroad) that align with the input condition well. See supp. materials for more results on KITTI-360/PandaSet." + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 309, + 72, + 545, + 153 + ], + "blocks": [ + { + "bbox": [ + 309, + 72, + 545, + 153 + ], + "lines": [ + { + "bbox": [ + 309, + 72, + 545, + 153 + ], + "spans": [ + { + "bbox": [ + 309, + 72, + 545, + 153 + ], + "type": "image", + "image_path": "7496cfcace9317f6a1cd74a7cfdacdfea237ded06063f80646f101966d875e79.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 158, + 546, + 214 + ], + "lines": [ + { + "bbox": [ + 304, + 158, + 546, + 214 + ], + "spans": [ + { + "bbox": [ + 304, + 158, + 546, + 214 + ], + "type": "text", + "content": "Figure 6. Conditional LiDAR generation for dirt removal. We mask the red rectangular region in the range view image to mimic dirt occluder. Left: Original input. The masked region is not visible to the model. Right: Our generation results. Our model can successfully recover the vehicle that is partially observed." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 219, + 545, + 304 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 219, + 545, + 304 + ], + "spans": [ + { + "bbox": [ + 304, + 219, + 545, + 304 + ], + "type": "text", + "content": "Meanwhile, we further consider a practical setting where the LiDAR sensor can fail for a specific region due to dirt or mechanical issues. To mimic this situation, we mask a part of the range images, as shown in Fig. 6. We can see that our model can still do accurate completion even on partially visible cars, recovering the occluded region, and potentially avoiding dangerous situations." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 308, + 546, + 405 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 308, + 546, + 405 + ], + "spans": [ + { + "bbox": [ + 304, + 308, + 546, + 405 + ], + "type": "text", + "content": "Manipulation: We show manipulation results with actor insertion and removal in the second row of Fig. 1. This is achieved by explicitly changing the code indices on the code map and letting the decoder generate new results. For example, we can copy the codes for the ground plane and paste them to overwrite the region where a car exists, resulting in a controllable manipulation process. We refer the readers for more results in supp. materials." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 409, + 378, + 421 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 409, + 378, + 421 + ], + "spans": [ + { + "bbox": [ + 306, + 409, + 378, + 421 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 423, + 545, + 566 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 423, + 545, + 566 + ], + "spans": [ + { + "bbox": [ + 304, + 423, + 545, + 566 + ], + "type": "text", + "content": "In this paper, we propose a framework to learn novel LiDAR representations that effectively capture the data priors that enable various downstream applications, including scene completion and generation. Based on the learned representation, we propose a novel sparse-to-dense data reconstruction pipeline that can accurately densify the sparse input and improve the generalization ability of the trained detection models in a zero-shot manner. We further show that our model can generate high-quality LiDAR point clouds unconditionally and do reasonable conditional generation and manipulation, which leads to more realistic and controllable data-driven LiDAR simulation." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 567, + 545, + 627 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 567, + 545, + 627 + ], + "spans": [ + { + "bbox": [ + 304, + 567, + 545, + 627 + ], + "type": "text", + "content": "One potential future direction for improving our model is to exploit the structure in range view representations, including beam info (which point from which ray) and occlusion reasoning, and combine them with our existing model. This may potentially improve the fidelity of our results." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 630, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 545, + 715 + ], + "type": "text", + "content": "Acknowledgement We thank Vlas Zyrianov and Shenlong Wang for providing A/B test code and baseline results, Arnaud Bonnet for infrastructure support, Siva Manivasagam for proofreading. We also thank the Waabi team for their valuable support. YX is partially supported by an NSERC scholarship and a Borealis AI fellowship. WCM is partially supported by a Siebel scholarship." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 314, + 757 + ], + "type": "text", + "content": "1081" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "text", + "content": "[1] Panos Achlioptas, Olga Diamanti, Ioannis Mitliagkas, and Leonidas Guibas. 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In Proceedings of the European Conference on Computer Vision (ECCV), October 2022. 2, 3, 5, 7, 8" + } + ] + } + ], + "index": 27 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 749, + 315, + 757 + ], + "type": "text", + "content": "1083" + } + ] + } + ], + "index": 29 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Learning Conditional Attributes for Compositional Zero-Shot Learning/c4434e76-0cd3-4a7c-8473-28f0e15837c1_content_list.json b/2023/Learning Conditional Attributes for Compositional Zero-Shot Learning/c4434e76-0cd3-4a7c-8473-28f0e15837c1_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..713dc2b61feca61be961f7652a3ea986bb81fa1f --- /dev/null +++ b/2023/Learning Conditional Attributes for Compositional Zero-Shot Learning/c4434e76-0cd3-4a7c-8473-28f0e15837c1_content_list.json @@ -0,0 +1,1549 @@ +[ + { + "type": "text", + "text": "Learning Conditional Attributes for Compositional Zero-Shot Learning", + "text_level": 1, + "bbox": [ + 124, + 130, + 846, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Qingsheng Wang $^{1*}$ , Lingqiao Liu $^{2}$ , Chenchen Jing $^{3}$ , Hao Chen $^{3}$ , Guoqiang Liang $^{1}$ , Peng Wang $^{1\\dagger}$ , Chunhua Shen $^{3}$", + "bbox": [ + 173, + 179, + 826, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ School of Computer Science and Ningbo Institute, Northwestern Polytechnical University, Xi'an, China \n $^{2}$ School of Computer Science, University of Adelaide, Adelaide, Australia \n $^{3}$ School of Computer Science, Zhejiang University, Hangzhou, China", + "bbox": [ + 88, + 215, + 913, + 271 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 303, + 312, + 319 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Compositional Zero-Shot Learning (CZSL) aims to train models to recognize novel compositional concepts based on learned concepts such as attribute-object combinations. One of the challenges is to model attributes interacted with different objects, e.g., the attribute \"wet\" in \"wet apple\" and \"wet cat\" is different. As a solution, we provide analysis and argue that attributes are conditioned on the recognized object and input image and explore learning conditional attribute embeddings by a proposed attribute learning framework containing an attribute hyper learner and an attribute base learner. By encoding conditional attributes, our model enables to generate flexible attribute embeddings for generalization from seen to unseen compositions. Experiments on CZSL benchmarks, including the more challenging C-GQA dataset, demonstrate better performances compared with other state-of-the-art approaches and validate the importance of learning conditional attributes. Code‡ is available at https://github.com/wqshmzh/CANet-CZSL.", + "bbox": [ + 75, + 335, + 473, + 625 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 656, + 207, + 671 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Deep machine learning algorithms today can learn knowledge of concepts to recognize patterns. Can a machine compose different learned concepts to generalize to new compositions? Compositional generalization is one of the hallmarks of human intelligence [3, 18]. To make the models equipped with this ability, Compositional Zero-Shot Learning (CZSL) [25] is proposed, where the models are trained to recognize images of unseen compositions composed of seen concepts. In this work, we concentrate on the situation where each composition is composed by attribute (e.g., wet) and object (e.g., apple). For example, given im", + "bbox": [ + 75, + 681, + 468, + 849 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/69262c50c4ac7806465c5b0b08c667f6aa0279201f77b98db022df5d7afb0a37.jpg", + "image_caption": [ + "Figure 1. The diagram of our work. We aim to learn conditional attributes conditioned on the recognized object and input image through an attribute learning framework containing an attribute hyper learner and an attribute base learner. We first recognize the object in the input image. Then, we feed prior knowledge extracted from the conditions, which are recognized object word embedding and input image visual embedding, to the attribute hyper learner. Finally, conditional attribute embeddings are produced by the attribute base learner parameterized by the attribute hyper learner." + ], + "image_footnote": [], + "bbox": [ + 501, + 301, + 879, + 523 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ages of wet apple and dry cat, a well-trained model can recognize images of new compositions dry apple and wet cat.", + "bbox": [ + 496, + 684, + 890, + 715 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Compositional Zero-Shot Learning of attribute-object compositions requires modeling attributes, objects, and the contextuality between them. Learning to model objects in CZSL is similar to conventional supervised object classification task since the model has access to all objects in CZSL task [33]. Learning to model contextuality between attribute and object is mostly addressed in the literature [23,25,26,31,39-41]. One of the main challenges of CZSL is the appearance diversity of an attribute when composed with different objects, e.g., attribute wet in wet apple and wet cat is different. This reveals that the information of each attribute is dependent on different objects. However, most", + "bbox": [ + 496, + 719, + 892, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*E-mail: wqshmzh@mail.nwpu.edu.cn", + "bbox": [ + 93, + 862, + 303, + 875 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "†Corresponding author. E-mail: peng.wang@nwpu.edu.cn", + "bbox": [ + 96, + 875, + 403, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "‡Gitee: https://gitee.com/wqshmzh/canet-czsl", + "bbox": [ + 96, + 887, + 421, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "11197", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "recent works in CZSL [4,27,32,33,42,45] extract attribute representations irrelevant to the object from seen compositions to infer the unseen compositions. These approaches neglect the nature of attribute diversity and learn concrete attribute representation agnostic to different objects.", + "bbox": [ + 75, + 90, + 468, + 167 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we learn conditional attributes rather than learning concrete ones in a proposed Conditional Attribute Network (CANet). We first conduct analysis to determine the exact conditions by considering the recognition of attribute and object as computing a classification probability of attribute and object conditioned on the input image. By decomposing this probability, we demonstrate that the probability of the input image belonging to an attribute is conditioned on the recognized object and the input image.", + "bbox": [ + 75, + 167, + 467, + 303 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We present an attribute learning framework to learn conditional attribute embeddings conditioned on the above two conditions. The framework contains an attribute hyper learner and an attribute base learner, which are sketched in Fig. 1. The attribute hyper learner learns from prior knowledge extracted from the conditions. The attribute base learner is parameterized by the attribute hyper learner and is designed to encode all attribute word embeddings into conditional attribute embeddings. With the attribute learning framework, the attribute embeddings are changed along with the recognized object and input image. Finally, the attribute matching is processed in an attribute space where the input image embedding is projected. The attribute classification logits are computed by cosine similarities between the projected input image embedding and all conditional attribute embeddings. Additionally, we model the contextuality between attribute and object as composing attribute and object word embeddings. We use cosine similarities between the projected input image embedding and all composed attribute-object embeddings to get the classification logits.", + "bbox": [ + 75, + 303, + 467, + 619 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our main contributions are as follows:", + "bbox": [ + 96, + 619, + 351, + 633 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose to learn attributes conditioned on the recognized object and input image.", + "- We propose an attribute learning framework containing an attribute hyper learner and an attribute base learner for learning conditional attribute embeddings.", + "- Experiments and ablation studies indicate the effectiveness of our proposed conditional attribute network, which further validates the importance of learning conditional attributes in the CZSL task." + ], + "bbox": [ + 94, + 635, + 467, + 768 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 784, + 217, + 799 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Compositional Zero-Shot Learning. Given descriptions only, we can recognize objects that are never seen before. In conventional Zero-Shot Learning (ZSL), models have access both to images of seen classes and descriptions of seen and unseen classes [19]. In contrast, CZSL presents no description of seen and unseen attribute-object", + "bbox": [ + 75, + 809, + 467, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "compositions while all attributes and objects as concepts are seen during training. Recently, works in CZSL are divided into two main streams. One extracts attribute and object words or visual features independently from a composition during training, including learning attributes as linear transformations of objects [27], learning to hierarchically decompose compositions and recompose the concepts with learned visual concepts [41], learning independent prototypes of attributes and objects and compositing prototypes via graph network [32], and learning decomposed prototypes of visual concept features [33] via siamese contrastive embedding network [20]. The other is to learn a compositional space [23], a graph network [2, 26], an episode-based cross-attention module [39], and a contrastive space [1] for contextuality modeling. Also, Yang et al. [42] rethink the CZSL task in a decomposable causal way and learn three spaces for attribute, object, and composition classifications. Additionally, with pre-trained large vision language models like CLIP, Nayak et al. [30] propose to tune soft prompts as concept embeddings.", + "bbox": [ + 496, + 90, + 890, + 393 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recent work in [12] addresses the problem of attribute diversity. They propose to learn translational attribute features conditionally dependent on the object prototypes. Specifically, they add generic object embedding as the object prototype to the concatenated attribute and object embedding. However, this approach makes the model concentrate more on the composition instead of the attribute, causing the attribute learning degrade to learning the contextuality between attribute and object. On the contrary, we explicitly focus on learning conditional attribute embeddings. The learned conditional attribute embeddings can be changed along with the objects and input images.", + "bbox": [ + 496, + 393, + 890, + 575 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Attribute Learning. Learning features of attributes is explored by a large community including image search [16, 34], sentence generation [17], and zero-shot classification [9, 29]. Conventional attribute learning approaches map the attributes into high-dimensional space and train a discriminative classification head without considering the diverse nature of attributes [22, 35, 37]. Our work also learns high-dimensional embeddings to represent attributes. The main difference is that our learned attribute embeddings are conditioned on different objects and input images.", + "bbox": [ + 496, + 575, + 890, + 728 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Approach", + "text_level": 1, + "bbox": [ + 500, + 744, + 607, + 762 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3.1. Task Definition", + "text_level": 1, + "bbox": [ + 500, + 768, + 653, + 784 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The task of CZSL aims to learn to classify an image $i$ into a composition $c$ composed by multiple seen concepts, where $i$ and $c$ are unseen during training. Denote sets of images, compositions, attributes, and objects as $\\mathcal{I}$ , $\\mathcal{C}$ , $\\mathcal{A}$ , and $\\mathcal{O}$ , we have $i \\in \\mathcal{I}$ , $c \\in \\mathcal{C}$ , $a \\in \\mathcal{A}$ , $o \\in \\mathcal{O}$ , and $\\mathcal{C} = \\mathcal{A} \\times \\mathcal{O}$ . During training, machines have access to seen set $\\mathcal{D}_{\\text{seen}} = \\{(i^s, c^s) | i^s \\in \\mathcal{I}^s, \\mathcal{I}^s \\subsetneq \\mathcal{I}, c \\in \\mathcal{C}^s, \\mathcal{C}^s \\subsetneq \\mathcal{C}\\}$ ,", + "bbox": [ + 496, + 794, + 890, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "11198", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/68e891a309253c233f3774ac087fc178d18b2a535b0403dc8c0bc3c537a93f6b.jpg", + "image_caption": [ + "Figure 2. Structure of our proposed CANet. The symbol $\\oplus$ is channel-wise concatenation. The mapping networks $\\omega_{o},\\omega_{a}$ , and $\\omega_{c}$ map the input image embedding $\\mathbf{x}$ into object, attribute, and composition spaces $S_{o},S_{a}$ , and $S_{c}$ . All object word embeddings $\\mathbf{v}_{o}$ along with the object-mapped input image embedding are used in $S_{o}$ to compute loss $\\mathcal{L}_o$ and get the recognized object $o^{*}$ . The attribute hyper learner $\\mathcal{H}$ learns to parameterize the attribute base learner $\\mathcal{G}$ using the prior knowledge $\\beta$ extracted from the recognized object word embedding $\\mathbf{v}_{o^*}$ and $\\mathbf{x}$ . The conditional attribute embeddings $\\mathbf{e}_a$ are encoded by $\\mathcal{G}$ parameterized by $\\mathcal{H}$ . Using all $\\mathbf{e}_a$ along with the attribute-mapped input image embedding in space $S_{a}$ to compute loss $\\mathcal{L}_a$ . Loss $\\mathcal{L}_{a,o}$ is computed using all compositional word embeddings produced by composing network $\\mathcal{C}$ and the composition-mapped input image embedding in space $S_{c}$ ." + ], + "image_footnote": [], + "bbox": [ + 83, + 95, + 885, + 359 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "attribute set $\\mathcal{A}$ , and object set $\\mathcal{O}$ , where $\\mathcal{I}^s$ and $\\mathcal{C}^s$ are sets of images and compositions seen when training. Also, evaluation of algorithms requires unseen set $\\mathcal{D}_{\\text{unseen}} = \\{(i^u, c^u) | i^u \\in \\mathcal{I}^u, c^u \\in \\mathcal{C}^u, \\mathcal{I}^u \\subsetneq \\mathcal{I}, \\mathcal{C}^u \\subsetneq \\mathcal{C}\\}$ used for validation and testing. In conventional ZSL, $\\mathcal{I}^s \\cap \\mathcal{I}^u = \\emptyset$ , $\\mathcal{C}^s \\cap \\mathcal{C}^u = \\emptyset$ , i.e. unseen images and compositions are not overlapped with the seen ones. Here, we follow the setting of Generalized Zero-Shot Learning (GZSL) where images in $\\mathcal{I}^s$ and $\\mathcal{I}^u$ and labels in $\\mathcal{C}^s$ and $\\mathcal{C}^u$ appear during validation and testing. GZSL is a challenging setting with larger label space and a strong bias of seen compositions to unseen ones, relaxing the less realistic assumption in conventional ZSL that test data only belongs to unseen classes.", + "bbox": [ + 75, + 486, + 468, + 681 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Conditional Attribute Network", + "text_level": 1, + "bbox": [ + 76, + 691, + 352, + 705 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Determining Conditions. In CZSL, it is common to learn to classify attributes and objects besides compositions. We first assume that the model recognizes the input image $i$ as attribute $a^*$ and object $o^*$ . The recognizing score can be formulated as a conditional probability $P(a^*, o^* | i)$ conditioned on input image $i$ . We propose to decompose this probability to express the attribute and object recognition as a one-label classification task. According to multi-variable conditional probability formulation, we have:", + "bbox": [ + 75, + 714, + 468, + 849 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nP \\left(a ^ {*}, o ^ {*} \\mid i\\right) = P \\left(a ^ {*} \\mid o ^ {*}, i\\right) P \\left(o ^ {*} \\mid i\\right) \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 158, + 852, + 467, + 868 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $P(o^{*}|i)$ is probability of image $i$ belonging to object $o^{*}$ and $P(a^{*}|o^{*},i)$ represents the probability of attribute $a^{*}$", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "conditioned on the joint presentation of $o^*$ and $i$ . This indicates that the recognition of an attribute is conditioned on the recognized object and input image. To better solve the attribute diversity problem, we consider the information of the recognized object and input image as conditions for conditional attribute encoding.", + "bbox": [ + 496, + 486, + 890, + 577 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Object Recognition. Object recognition requires learning to map the input image embedding into an object space. To incorporate object semantic information, we compute cosine similarities between object-mapped image embedding $\\omega_{o}(\\mathbf{x})$ and all object word embeddings $\\mathbf{v}_{o}$ instead of directly learning a classification head:", + "bbox": [ + 496, + 580, + 890, + 671 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\langle \\omega_ {o} (\\mathbf {x}), \\mathbf {v} _ {o} \\right\\rangle = \\frac {\\omega_ {o} (\\mathbf {x}) ^ {\\top} \\mathbf {v} _ {o}}{\\| \\omega_ {o} (\\mathbf {x}) \\| _ {2} \\| \\mathbf {v} _ {o} \\| _ {2}} \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 589, + 672, + 890, + 705 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathbf{x} = f(i) \\in \\mathcal{X}$ is the visual embedding of input image $i$ in visual space $\\mathcal{X}$ extracted by image backbone $f$ (e.g., ResNet-18 [11]), $\\omega_{o}$ is the mapping from $\\mathcal{X}$ to object semantic space $S_{o}$ , $\\mathbf{v}_{o} = \\phi(o)$ , $\\mathbf{v}_{o} \\in S_{o}$ is object word embedding in $S_{o}$ extracted by word embedder $\\phi$ (e.g., word2vec [24], FastText [7]). The recognized object $o^{*} = \\underset{o \\in \\mathcal{O}}{\\arg \\max} \\langle \\omega_{o}(\\mathbf{x}), \\phi(o) \\rangle$ .", + "bbox": [ + 496, + 707, + 890, + 821 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Learning Conditional Attributes. With the recognized object $o^*$ and visual embedding $\\mathbf{x}$ of input image $i$ , we learn the attribute hyper learner $\\mathcal{H}$ and attribute base learner $\\mathcal{G}$ in the proposed attribute learning framework to extract attribute embeddings conditioned on the recognized object $o^*$ .", + "bbox": [ + 496, + 825, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "11199", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "and input image $i$ . We consider the information of $o^*$ and $i$ as prior knowledge for $\\mathcal{H}$ . Specifically, the prior knowledge is implemented as a feature vector $\\beta$ :", + "bbox": [ + 75, + 90, + 468, + 135 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\beta = \\mathcal {P} \\left(\\operatorname {c a t} \\left(\\mathbf {v} _ {o ^ {*}}, \\mathbf {x}\\right)\\right) \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 202, + 138, + 468, + 154 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{v}_{o^*} = \\phi(o^*)$ is word embedding of $o^*$ , $\\mathcal{P}$ is a composing network for $\\mathbf{v}_{o^*}$ and $\\mathbf{x}$ , $\\operatorname{cat}(\\cdot)$ is channel-wise concatenation operation. With the prior knowledge, the attribute hyper learner $\\mathcal{H}$ can parameterize $\\mathcal{G}$ as:", + "bbox": [ + 75, + 156, + 468, + 215 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {\\Theta} _ {\\mathcal {G}} = \\mathcal {H} (\\beta ; \\boldsymbol {\\Theta} _ {\\mathcal {H}}) \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 210, + 219, + 468, + 234 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\Theta_{\\mathcal{H}}$ is the set of randomly initialized parameters of $\\mathcal{H}$ , $\\Theta_{\\mathcal{G}}$ is the set of generated parameters of $\\mathcal{G}$ . In this way, the attribute embeddings $\\mathbf{e}_a$ conditioned on $o^*$ and $i$ can be encoded via $\\mathcal{G}$ parameterized by $\\mathcal{H}$ :", + "bbox": [ + 76, + 237, + 468, + 297 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {e} _ {a} = \\mathcal {G} \\left(\\mathbf {v} _ {a}; \\boldsymbol {\\Theta} _ {\\mathcal {G}}\\right) \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 214, + 300, + 468, + 315 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{v}_a = \\phi(a)$ is word embedding of attribute word $a$ .", + "bbox": [ + 75, + 316, + 454, + 332 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Modeling Contextuality. Although the conditional attribute embeddings are related to the recognized object and input image, object embeddings are also supposed to be influenced by attributes. Therefore, we model the contextuality of attribute-object compositions to address the relationships between them. We follow the work of Mancini et al. [23] in their closed world setting that contextuality is modeled as the mixture of attribute and object word embeddings to extract attribute-object compositional embeddings:", + "bbox": [ + 75, + 333, + 468, + 468 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {v} _ {a, o} = \\mathcal {C} (\\operatorname {c a t} \\left(\\mathbf {v} _ {a}, \\mathbf {v} _ {o}\\right)) \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 194, + 470, + 468, + 486 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{C}$ is a composing network for $\\mathbf{v}_a$ and $\\mathbf{v}_o$ .", + "bbox": [ + 76, + 488, + 390, + 503 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The entire structure of our model is shown in Fig. 2.", + "bbox": [ + 96, + 503, + 439, + 518 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Training Objectives", + "text_level": 1, + "bbox": [ + 76, + 527, + 264, + 542 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Similar to object recognition, attribute or composition recognition is also implemented by computing cosine similarities $\\langle \\omega_{a}(\\mathbf{x}),\\mathbf{v}_{a}\\rangle$ or $\\langle \\omega_c(\\mathbf{x}),\\mathbf{v}_{a,o}\\rangle$ between attribute-mapped or composition-mapped image embeddings, i.e., $\\omega_{a}(\\mathbf{x})$ or $\\omega_{c}(\\mathbf{x})$ , and attribute word embeddings or attribute-object compositional embeddings, i.e., $\\mathbf{v}_a$ or $\\mathbf{v}_{a,o}$ :", + "bbox": [ + 75, + 551, + 468, + 642 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\langle \\omega_ {a} (\\mathbf {x}), \\mathbf {e} _ {a} \\right\\rangle = \\frac {\\omega_ {a} (\\mathbf {x}) ^ {\\top} \\mathbf {e} _ {a}}{\\| \\omega_ {a} (\\mathbf {x}) \\| _ {2} \\| \\mathbf {e} _ {a} \\| _ {2}} \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 166, + 643, + 468, + 676 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\langle \\omega_ {c} (\\mathbf {x}), \\mathbf {v} _ {a, o} \\right\\rangle = \\frac {\\omega_ {c} (\\mathbf {x}) ^ {\\top} \\mathbf {v} _ {a , o}}{\\| \\omega_ {c} (\\mathbf {x}) \\| _ {2} \\| \\mathbf {v} _ {a , o} \\| _ {2}} \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 156, + 678, + 468, + 712 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The recognition probability $P(o^{*}|i)$ , $P(a^{*}|o^{*},i)$ , and $P(c^{*}|i)$ are normalized cosine similarities, where $P(c^{*}|i)$ is the probability of input image $i$ belonging to the recognized attribute-object composition $c^{*}$ . As shown in Fig. 2, our model learns three embedding spaces: attribute space $S_{a}$ , object space $S_{o}$ , and attribute-object compositional space $S_{c}$ . Therefore, we incorporate three separate cross-entropy losses to maximize the three recognition probabilities to make the model optimized in these three spaces. The losses are as follows:", + "bbox": [ + 75, + 715, + 468, + 864 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {a} = - \\sum_ {a \\in \\mathcal {A}} \\log \\frac {\\exp \\left(\\left\\langle \\omega_ {a} (\\mathbf {x}), \\mathbf {e} _ {a} \\right\\rangle / \\tau\\right)}{\\sum_ {a ^ {\\prime} \\in \\mathcal {A}} \\exp \\left(\\left\\langle \\omega_ {a} (\\mathbf {x}), \\mathbf {e} _ {a ^ {\\prime}} \\right\\rangle / \\tau\\right)} \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 119, + 866, + 468, + 902 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {o} = - \\sum_ {o \\in \\mathcal {O}} \\log \\frac {\\exp \\left(\\left\\langle \\omega_ {o} (\\mathbf {x}) , \\mathbf {v} _ {o} \\right\\rangle / \\tau\\right)}{\\sum_ {o ^ {\\prime} \\in \\mathcal {O}} \\exp \\left(\\left\\langle \\omega_ {o} (\\mathbf {x}) , \\mathbf {v} _ {o} ^ {\\prime} \\right\\rangle / \\tau\\right)} \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 542, + 88, + 890, + 125 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Also, for composition recognition, we have:", + "bbox": [ + 500, + 131, + 790, + 145 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {a, o} = - \\sum_ {(a, o) \\in \\mathcal {C}} \\log \\frac {\\exp \\left(\\left\\langle \\omega_ {c} (\\mathbf {x}), \\mathbf {v} _ {a , o} \\right\\rangle / \\tau\\right)}{\\sum_ {\\left(a ^ {\\prime} , o ^ {\\prime}\\right) \\in \\mathcal {C}} \\exp \\left(\\left\\langle \\omega_ {c} (\\mathbf {x}), \\mathbf {v} _ {a ^ {\\prime} , o ^ {\\prime}} \\right\\rangle / \\tau\\right)} \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 509, + 147, + 890, + 199 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\tau$ is temperature factor [46]. Finally, the training loss as a whole linearly combines the three losses above:", + "bbox": [ + 498, + 199, + 890, + 228 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\frac {\\mathcal {L} _ {a} + \\mathcal {L} _ {o}}{2} + \\mathcal {L} _ {a, o} \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 620, + 229, + 890, + 258 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Inference", + "text_level": 1, + "bbox": [ + 500, + 267, + 607, + 281 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "During validation and testing, we incorporate a linear normalization function $g$ for cosine similarities:", + "bbox": [ + 498, + 290, + 890, + 320 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\ng (d) = (1 + d) * 0. 5 \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 624, + 321, + 890, + 338 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Then, we have $P(a|o^{*},i) = g(\\langle \\omega_{a}(\\mathbf{x}),\\mathbf{e}_{a}\\rangle),P(o|i) = g(\\langle \\omega_{o}(\\mathbf{x}),\\mathbf{v}_{o}\\rangle)$ , and $P(c|i) = g(\\langle \\omega_c(\\mathbf{x}),\\mathbf{v}_{a,o}\\rangle)$ . The inference rule is parameterized as:", + "bbox": [ + 498, + 339, + 890, + 385 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\ns = (1 - \\alpha) P (c | i) + \\alpha P (a | o ^ {*}, i) P (o | i) \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 560, + 387, + 890, + 404 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\alpha$ is the weight factor controlling balance.", + "bbox": [ + 498, + 406, + 821, + 421 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 498, + 435, + 630, + 452 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this section, experiments are conducted following the concrete introductions of datasets, metrics, implementation details, and baselines. Then, we report ablation results to demonstrate the effectiveness of our model.", + "bbox": [ + 496, + 459, + 890, + 518 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 498, + 530, + 689, + 546 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Datasets We conduct experiments with three widely adopted datasets in the CZSL task, which are MIT-States [14], UT-Zappos50K [43, 44], and C-GQA [26]. MIT-States contains 53753 crawled web images labeled with 1962 attribute-object (e.g., mossy highway) compositions. This dataset has 30338, 10420, and 12995 training, validation, and testing images [31] labeled with 1262, 600, and 800 compositions. In validation and test sets, the numbers of seen and unseen compositions are the same. All compositions are composed of 115 attributes and 245 objects. UT-Zappos50K is made up of 50025 images labeled with 116 fine-grained shoe classes composed of 16 attributes (e.g., rubber) and 12 objects (e.g., sneaker). This dataset has 22998, 3214, and 2914 training, validation, and testing images [31] labeled with 83, 30, and 36 compositions. Also, numbers of seen and unseen compositions in validation and test sets share the same quantity. C-GQA is created based on Stanford GQA dataset [13] used for VQA task. C-GQA contains 39298 images labeled with over $9.5\\mathrm{k}$ compositions composed of 453 attributes and 870 objects. This dataset has 26920, 7280, and 5098 training, validation, and testing images labeled with 6963, 2541, and 2069 compositions. Detailed splits are presented in Tab. 1.", + "bbox": [ + 496, + 553, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "11200", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/3f00ecb4155a0fb916d5b9821a4fbfa239e18c80a43596885e3e8ead4898137c.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
DatasetTrainingValidationTest
AOCsICsCuICsCuI
UT-Zappos50K [43,44]161283229981515321418182914
MIT-States [14]1152451262303383003001042040040012995
C-GQA [26]453870696326920117313687280102210475098
", + "bbox": [ + 78, + 88, + 893, + 186 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 1. Detailed dataset splits of UT-Zappos50K, MIT-States, and C-GQA in training, validation, and test sets.", + "bbox": [ + 153, + 195, + 815, + 209 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Metrics To demonstrate the advances in attribute learning, we report the attribute and object classification accuracies (best attr and best obj). The setting of GZSL requires both seen and unseen compositions to exist during validation and testing. As a result, there is an inherent bias of seen against unseen compositions. We follow the evaluation protocols proposed in [8] where a scalar bias is added to final activations of classes of seen compositions to calibrate the model. As the scalar varies from negative infinity to positive infinity, there must be a best operating point at which the bias between seen and unseen compositions is the lowest. We report the results in terms of the best accuracies of seen images (best seen), unseen images (best unseen), best Harmonic Mean (best HM), and Area Under Curve (AUC) with different scalar biases.", + "bbox": [ + 75, + 223, + 472, + 449 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implementations We consider image backbone $f$ as ResNet-18 pre-trained on ImageNet [10] to extract 512 dimension vectors following preceding works. The mapping networks $\\omega_{a}$ , $\\omega_{o}$ , and $\\omega_{c}$ share the similar structure of two Fully Connected (FC) layers with ReLU [28], LayerNorm [5], and Dropout [36] following the first FC layer. We adopt word embedder $\\phi$ as 600-dimensional word2vec+FastText for MIT-States, 300-dimensional FastText for UT-Zappos50K, and word2vec for C-GQA. The layer structures of $\\mathcal{G}$ , $\\mathcal{P}$ , and $\\mathcal{C}$ are the same as the mapping networks, where ReLU is added in $\\mathcal{P}$ and $\\mathcal{C}$ to the last FC layer. Weight generation for the attribute base learner $\\mathcal{G}$ through the attribute hyper learner $\\mathcal{H}$ requires more parameters and makes learning difficult, as noted by Bertinetto et al. [6]. Therefore, we adopt weight factorization in [38] to reduce parameters for the attribute hyper learner $\\mathcal{H}$ , that is", + "bbox": [ + 75, + 450, + 472, + 691 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {e} _ {a} ^ {(i)} = \\left(\\mathbf {v} _ {a} \\mathbf {W} _ {\\mathcal {G}} ^ {(i)} + \\mathbf {b} _ {\\mathcal {G}} ^ {(i)}\\right) \\odot \\boldsymbol {\\lambda} _ {\\mathcal {G}} ^ {(i)} \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 166, + 693, + 467, + 712 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {\\lambda} _ {\\mathcal {G}} ^ {(i)} = \\mathcal {H} (\\beta ; \\boldsymbol {\\Theta} _ {\\mathcal {H}} ^ {(i)}) \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 209, + 713, + 467, + 734 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $(i)$ indicates $i$ th FC layer, $\\mathbf{W}_{\\mathcal{G}}^{(i)}$ and $\\mathbf{b}_{\\mathcal{G}}^{(i)}$ are the weight matrix and bias vector of $i$ th FC layer in $\\mathcal{G}$ , $\\{\\mathbf{W}_{\\mathcal{G}}^{(i)}, \\mathbf{b}_{\\mathcal{G}}^{(i)}\\} \\subset \\Theta_{\\mathcal{G}}, \\Theta_{\\mathcal{H}}^{(i)} \\subset \\Theta_{\\mathcal{H}}$ , and $\\odot$ denotes elementwise multiplication. During training, we fix the image backbone $f$ and train other modules using Adam [15] optimizer and an Nvidia GeForce GTX 1080Ti GPU with a learning rate and weight decay of 0.00005. The batch size is 256. The temperature factor $\\tau$ , weight factor $\\alpha$ , and the maximum number of epochs are set to 0.02, 0.4, and 500 for UT-Zappos50K; 0.05, 0.2, and 800 for MIT-States; and 0.05, 0.4, and 1000 for C-GQA.", + "bbox": [ + 75, + 729, + 472, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Baselines We conduct experiments with the following algorithms: 1) AttrAsOp [27] treats attributes as linear transformations on object vectors instead of data points in some high-dimensional space and optimizes the transformations through several regularizers in the loss function. 2) TMN [31] constructs task-driven modular networks in semantic space configured through a gating function conditioned on the task. 3) SymNet [21] proposes symmetry property in attribute-object compositions and group axioms as objectives in an end-to-end manner. 4) $CGE_{\\mathrm{ff}}$ [26] exploits dependencies between attributes, objects, and compositions through an end-to-end graph formulation where \"ff\" means fixed image feature backbone. 5) CompCos [23] learns a mapping from image features to semantic space of compositions and computes cosine similarities between them. 6) DeCa [42] rethinks the CZSL task in a decomposable causal perspective and learns three independent mappings from image feature space to attribute, object, and composition semantic space. Cosine similarities are also adopted. 7) SCN [20] computes visual prototypes of attributes and objects in a siamese contrastive space and proposes a designed State Transition Module to increase the diversity of training compositions.", + "bbox": [ + 496, + 223, + 893, + 571 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Quantitative Analysis", + "text_level": 1, + "bbox": [ + 498, + 585, + 702, + 602 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "All results are computed on test sets of all datasets and from their published papers and [26] for a fair comparison. We report quantitative results with the best AUC in Tab. 2.", + "bbox": [ + 496, + 609, + 890, + 655 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "From Tab.2, our model outperforms other state-of-the-art algorithms in terms of best attr, best unseen, and AUC in all three datasets including the recently proposed C-GQA, indicating the better attribute learning performance and generalization ability from seen to unseen compositions. Specifically, our model performs much better on C-GQA with more state-of-the-art results although it is a much more challenging dataset than MIT-States and UT-Zappos50K.", + "bbox": [ + 496, + 657, + 890, + 777 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For UT-Zappos50K, the observations are that our model boosts attribute recognition accuracy, unseen image classification accuracy, and AUC from $47.3\\%$ , $63.1\\%$ , and $32.0\\%$ of SCEN to the new state-of-the-art of $48.4\\%$ , $66.3\\%$ , and $33.1\\%$ with $1.1\\%$ , $3.2\\%$ , and $1.1\\%$ improvement respectively. For MIT-States, our model achieves $30.2\\%$ , $32.6\\%$ , $26.2\\%$ , and $5.4\\%$ accuracies for attribute and object classification, unseen image classification, and AUC on the test", + "bbox": [ + 496, + 779, + 893, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "11201", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/936ada382740ba78a02f5e619d5f3ce12b1095f27a117599aa3c7e1f0b0817c8.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
AlgorithmUT-Zappos50KMIT-StatesC-GQA
NameVenueAtt.Obj.S.U.HMAUCAtt.Obj.S.U.HMAUCAtt.Obj.S.U.HMAUC
AttrAsOp [27]ECCV'1838.969.659.854.240.825.921.123.614.317.49.91.68.312.511.83.92.90.3
TMN [31]ICCV'1940.869.958.760.045.029.323.326.520.220.113.02.99.720.521.66.37.71.1
SymNet [21]CVPR'2041.368.649.857.440.423.426.328.324.425.216.13.015.023.127.010.810.92.2
CGEff [26]CVPR'2145.073.956.863.641.226.427.932.028.725.317.25.112.726.927.511.711.92.5
CompCos [23]CVPR'2144.773.559.862.543.528.727.931.825.324.616.44.5------
DeCa [42]TMM'22--62.763.146.331.6--29.825.218.25.3------
SCEN [20]CVPR'2247.375.663.563.147.832.028.232.229.925.218.45.313.627.928.912.112.42.9
Ours48.472.661.066.347.333.130.232.629.026.217.95.417.522.330.013.214.53.3
", + "bbox": [ + 76, + 88, + 895, + 277 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. Quantitative results on test sets of all datasets with the state-of-the-art in terms of best attr (Att.), best obj (Obj.), best seen (S.), best unseen (U.), best HM (HM), and AUC.", + "bbox": [ + 75, + 285, + 892, + 314 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "set, providing $2.0\\%$ , $0.4\\%$ , $1.0\\%$ , and $0.1\\%$ improvements on the recently proposed SCEN as the new state-of-the-art results. This indicates that the proposed conditional attribute network can truly improve the attribute recognition performance and consequently the unseen image classification and AUC.", + "bbox": [ + 75, + 328, + 470, + 417 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For the more challenging dataset C-GQA, since it is significantly harder than MIT-States and UT-Zappos50K with $5.5 \\times$ and $0.9 \\times$ composition labels and images in the training set compared with MIT-States, our model outperforms all other algorithms except best obj with $3.9\\%$ , $1.1\\%$ , $1.1\\%$ , $2.1\\%$ , and $0.4\\%$ boosting in terms of best attr, best seen, best unseen, best HM, and AUC in the testing set. This indicates that the proposed conditional attribute network makes a critical contribution when facing a more challenging dataset even if the object recognition accuracy is lower.", + "bbox": [ + 75, + 422, + 468, + 575 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We give an analysis of the importance that attributes should be conditioned on objects. First, note that although DeCa also learns attribute, object, and composition spaces separately, it learns attributes as static embeddings independent from objects, causing lower best unseen and AUC on UT-Zappos50K and MIT-States compared with ours in Tab. 2. Next, different baselines incorporate different techniques to handle the CZSL task though, they learn static attribute embeddings too, producing lower best attr, best unseen, and AUC. Then, the proposed method performs much better on C-GQA compared with other baselines. All the above phenomena demonstrate that attributes should be conditioned on objects and performance on datasets with larger label space can gain more boosts in this way.", + "bbox": [ + 75, + 579, + 468, + 792 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "From the results of the three datasets above, we observe an interesting phenomenon. Although the results of best obj in three datasets are all lower than that of SCEN, results of best unseen are all higher accompanied by higher results of best attr. We speculate the reason is that some objects have more attributes (or are more dominated) in unseen compositions and the misclassified objects recognized", + "bbox": [ + 75, + 795, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "by our model are less dominated (i.e. have few attributes or are long-tailed in terms of attribute). As a result, with the correctly predicted objects dominated in unseen compositions, the more correctly classified attributes, the higher the results of best unseen.", + "bbox": [ + 496, + 328, + 893, + 405 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Qualitative Analysis", + "text_level": 1, + "bbox": [ + 498, + 419, + 692, + 436 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we present some qualitative results of novel compositions with top-3 predictions on UT-Zappos50K, MIT-States, and C-GQA in Fig. 3. We show results for each dataset in each row. Images whose top prediction matches the label are shown in the first three columns and the rest columns show wrong results. For UT-Zappos50K, the remaining two answers of all images can match at least one label factor. For some instances in MIT-States, we can notice that the top and second predictions can both describe the image. For example, for the image labeled with winding stream, there is sunlight reflecting from the stream and creek is the synonym of stream. Therefore, sunny creek can also be the label of the image. Another example is that image labeled with wide valley also present cloudy cloud in the blue sky located in the upper part. As a result, the model has difficulty deciding what to predict. This reflects that labels in MIT-States are heavy in noise. For C-GQA where labels are clear, our model can produce more answers that match the label factors in the remaining two predictions, which indicates the better performance and robustness of our model.", + "bbox": [ + 496, + 445, + 893, + 762 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Additionally, we present wrong predictions in the last two columns. It can be noticed that our model can predict correct answers in most top-3 predictions. As for the image of MIT-States labeled as broken bottle, our model predicts the attribute as small because it is difficult to focus on a certain attribute of the bottle since the bottle in this image is both small and broken. Besides, images in the training set are limited in the status of objects. For example, training images of sheep hardly present the action of laying down", + "bbox": [ + 496, + 763, + 893, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "11202", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/c04e57793a1bfca4bcdc59ab816715be7d9fde460105abaca0a14eabda3b2e19.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
VariantUT-Zappos50KC-GQA
#NameAtt.Obj.S.U.HMAUCAtt.Obj.S.U.HMAUC
(1)w/o L_a + L_o46.174.361.564.746.131.710.830.629.812.813.43.0
(2)w/o L_c41.960.759.554.745.728.314.817.128.111.212.42.6
(3)w/o G + H + P47.074.059.965.846.331.714.827.829.913.114.63.1
(4)w/o P46.773.260.764.547.531.614.526.430.113.014.53.1
(5)w/o H46.270.358.562.746.330.513.925.829.111.212.52.4
(6)w/o x for H45.671.361.662.844.830.113.420.830.212.713.92.9
(7)Full48.472.661.066.347.333.117.522.330.013.214.53.3
", + "bbox": [ + 81, + 88, + 890, + 258 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3. Ablation results on test sets in terms of best attr (Att.), best obj (Obj.), best seen (S.), best unseen (U.), best HM (HM), and AUC.", + "bbox": [ + 76, + 268, + 890, + 282 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/bf70401301edb7578a26bec565f6b220fee8b211a66ef07939ab6a0cd1040436.jpg", + "image_caption": [ + "Figure 3. Qualitative Results. We demonstrate top-3 predictions of some instances using our proposed model." + ], + "image_footnote": [], + "bbox": [ + 80, + 287, + 888, + 488 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "causing our model mistakenly classify the sheep in the image labeled as light sheep into elephant. Thus, with the recognized object elephant, the model can only focus on attributes conditioned on elephant and find the appropriate attribute that matches the image.", + "bbox": [ + 75, + 527, + 470, + 603 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 617, + 230, + 633 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, we ablate the proposed model to evaluate the performance of each module. The ablation study is conducted on test sets of UT-Zappos50K, C-GQA. To achieve more convincing ablation results, we do not choose MIT-States because images in MIT-States are labeled using automatic search. As a result, the noise of labels is too heavy to be used for evaluations, as is pointed out by Atzmon et.al. [4]. Ablation results are reported in Tab. 3. The detailed ablation process is as follows:", + "bbox": [ + 75, + 642, + 468, + 777 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We first study the effects of recognizing compositions only and recognizing attributes and objects without compositions, which are corresponded to variants (1) and (2) in Tab. 3, and report results in terms of six metrics used in Tab. 2. Compared with variant (6), the results of each variant mostly decline, indicating the importance of recognizing attributes, objects, and compositions jointly. As to the results of Obj. in UT-Zappos50K and C-GQA from variants", + "bbox": [ + 75, + 780, + 470, + 901 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "(1) and (6), we can observe that those object classification accuracies decline. This is mainly because when recognizing objects individually each object presents visual diversity caused by different attributes, e.g., sliced apple is different from apple in visual appearance since a sliced apple is sliced into multiple pieces. However, this phenomenon does not affect other results, especially for the dataset with larger label space, e.g., C-GQA.", + "bbox": [ + 496, + 527, + 890, + 650 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Next, with attributes, objects, and compositions being recognized, we ablate $\\mathcal{G} + \\mathcal{H} + \\mathcal{P}$ (where attribute word embeddings are directly used in $S_{a}$ ), $\\mathcal{H}$ (where the concatenation of $\\beta$ and $\\mathbf{v}_a$ is fed to $\\mathcal{G}$ ), $\\mathcal{P}$ (where the concatenation of $\\mathbf{v}_{o^*}$ and $\\mathbf{x}$ is directly fed to $\\mathcal{H}$ ), and $\\mathbf{x}$ in $\\beta$ that is fed to $\\mathcal{H}$ , which are corresponded to variants (3)-(6) in Tab. 3. Note that if $\\mathcal{P}$ is presented then $\\mathcal{G}$ is required to be presented also because the concatenation of $\\beta$ and $\\mathbf{v}_a$ requires changing the number of dimensions to that of $\\mathbf{x}$ through $\\mathcal{G}$ . Also, $\\mathcal{G}$ can not be ablated only otherwise the model changes to variant (3). Compared to variant (7), all results are mostly declined, indicating that optimizing the model with $\\mathcal{G}$ , $\\mathcal{H}$ , $\\mathcal{P}$ , and $\\mathbf{x}$ is essential. As for variant (5), it performs worse on seen and unseen images compared with variant (4), indicating the importance of using the attribute hyper learner. Comparing results of variants (5) with (6), we observe that", + "bbox": [ + 496, + 659, + 892, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "11203", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6dc1096afc1924895fd146605ee1180b4c2e7330c74e9be8c0743040ebe049c6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 76, + 88, + 349, + 239 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/2e2087136a868572667efafb1833479fd344d62fa00301798e16c29cb245f808.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 349, + 88, + 620, + 239 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b927075be46c20eb35a24fb5a79e03a953902c49ceba1d492d331530162941ad.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 622, + 88, + 893, + 239 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ce7c3b094c98fb9e9e380289233ed066ef12d07ac5a34b6ea56d0e947325a5c6.jpg", + "image_caption": [ + "Figure 4. Influence of weighting factor $\\alpha$ on AUC, seen accuracy, and unseen accuracy." + ], + "image_footnote": [], + "bbox": [ + 78, + 241, + 349, + 375 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d092a4294e42482f5a6987c4a906fd2100f835417fc42d74d361f749af9c33b5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 349, + 241, + 620, + 375 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/47f179b52754c14b8b7b2b6c861761344dcbae469df4a7064525551e6c798108.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 622, + 241, + 893, + 375 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "adding the attribute hyper learner $\\mathcal{H}$ for $\\mathcal{G}$ without image visual embedding $\\mathbf{x}$ marginally increases overfitting to seen images. Results of variant (6) present the best generalization compared with variants (3)-(5) because adding $\\mathbf{x}$ in $\\beta$ for $\\mathcal{H}$ provides diverse instances that are seen for $\\mathcal{H}$ during training since the number of image visual embeddings is far more than the number of object word embeddings.", + "bbox": [ + 75, + 415, + 470, + 521 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Lastly, we conduct experiments to study the impact of weighting factor $\\alpha$ in Eq. (14) on all datasets. In detail, we present results of AUC, seen accuracy, and unseen accuracy in Fig. 4 with $\\alpha \\in [0,1]$ with an interval of 0.1. It can be observed that all results of AUC increase first and then decrease with $\\alpha$ increases from 0.0. The peaks of AUC are reached when $\\alpha$ equals 0.5, 0.1, and 0.3 in UT-Zappos50K, MIT-States, and C-GQA. This phenomenon reveals that learning to classify attributes, objects, and compositions all contribute to making our model reach optimal. Additionally, it can be noticed that the results of AUC are all generally declined when $\\alpha$ changes from 0.0 to 1.0. This is because attribute-object compositions involve not only the side information of attribute and object, but also the contextuality between attribute and object. As for the results of seen and unseen accuracies reported in the second row, the same trend can be observed. Specifically, results of unseen accuracy are more sensitive than seen accuracy and also have peaks with various $\\alpha$ , indicating that $\\alpha$ also has an impact on the generalization ability of our model. In conclusion, using a small weighting factor $\\alpha$ is always better than using a larger one, indicating that modeling contextuality between attribute and object is a bit more beneficial to the CZSL task than separately classifying attributes and objects.", + "bbox": [ + 75, + 523, + 470, + 901 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 414, + 619, + 430 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this work, we address the attribute diversity problem in Compositional Zero-Shot Learning. As a solution, we propose a Conditional Attribute Network (CANet) to learn attributes conditioned on the recognized object and input image. We first decompose the probability of attribute and object recognition conditioned on the input image to lay a foundation for learning conditional attributes. Then, we build an attribute learning framework to encode conditional attribute embeddings. Experiments show that our model outperforms recent CZSL approaches and achieves new state-of-the-art results. Despite the better attribute recognition performance, a limitation is that our model is less qualified to handle object long-tailed distribution in terms of attribute mentioned in Sec. 4.2. Future works can be focused on solving the problem above while learning conditional attributes.", + "bbox": [ + 496, + 439, + 893, + 680 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Acknowledgements", + "text_level": 1, + "bbox": [ + 500, + 695, + 687, + 713 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was supported by National Key R&D Program of China (No.2020AAA0106900), the National Natural Science Foundation of China (No.U19B2037), Shaanxi Provincial Key R&D Program (No.2021KWZ-03), and Natural Science Basic Research Program of Shaanxi (No.2021JCW-03).", + "bbox": [ + 496, + 720, + 893, + 811 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "11204", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Muhammad Umer Anwaar, Rayyan Ahmad Khan, Zhihui Pan, and Martin Kleinsteuber. A contrastive learning approach for compositional zero-shot learning. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 10823-10832, 2019. 4" + ], + "bbox": [ + 501, + 92, + 890, + 373 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "11206", + "bbox": [ + 480, + 945, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Learning Conditional Attributes for Compositional Zero-Shot Learning/c4434e76-0cd3-4a7c-8473-28f0e15837c1_model.json b/2023/Learning Conditional Attributes for Compositional Zero-Shot Learning/c4434e76-0cd3-4a7c-8473-28f0e15837c1_model.json new file mode 100644 index 0000000000000000000000000000000000000000..8d9360028e11b8a1b149781c317f4a2b816f83f4 --- /dev/null +++ b/2023/Learning Conditional Attributes for Compositional Zero-Shot Learning/c4434e76-0cd3-4a7c-8473-28f0e15837c1_model.json @@ -0,0 +1,2046 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.125, + 0.131, + 0.848, + 0.154 + ], + "angle": 0, + "content": "Learning Conditional Attributes for Compositional Zero-Shot Learning" + }, + { + "type": "text", + "bbox": [ + 0.174, + 0.18, + 0.827, + 0.217 + ], + "angle": 0, + "content": "Qingsheng Wang\\(^{1*}\\), Lingqiao Liu\\(^{2}\\), Chenchen Jing\\(^{3}\\), Hao Chen\\(^{3}\\), Guoqiang Liang\\(^{1}\\), Peng Wang\\(^{1\\dagger}\\), Chunhua Shen\\(^{3}\\)" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.217, + 0.914, + 0.272 + ], + "angle": 0, + "content": "\\(^{1}\\)School of Computer Science and Ningbo Institute, Northwestern Polytechnical University, Xi'an, China \n\\(^{2}\\)School of Computer Science, University of Adelaide, Adelaide, Australia \n\\(^{3}\\)School of Computer Science, Zhejiang University, Hangzhou, China" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.304, + 0.313, + 0.32 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.337, + 0.474, + 0.625 + ], + "angle": 0, + "content": "Compositional Zero-Shot Learning (CZSL) aims to train models to recognize novel compositional concepts based on learned concepts such as attribute-object combinations. One of the challenges is to model attributes interacted with different objects, e.g., the attribute \"wet\" in \"wet apple\" and \"wet cat\" is different. As a solution, we provide analysis and argue that attributes are conditioned on the recognized object and input image and explore learning conditional attribute embeddings by a proposed attribute learning framework containing an attribute hyper learner and an attribute base learner. By encoding conditional attributes, our model enables to generate flexible attribute embeddings for generalization from seen to unseen compositions. Experiments on CZSL benchmarks, including the more challenging C-GQA dataset, demonstrate better performances compared with other state-of-the-art approaches and validate the importance of learning conditional attributes. Code‡ is available at https://github.com/wqshmzh/CANet-CZSL." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.657, + 0.208, + 0.672 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.683, + 0.47, + 0.851 + ], + "angle": 0, + "content": "Deep machine learning algorithms today can learn knowledge of concepts to recognize patterns. Can a machine compose different learned concepts to generalize to new compositions? Compositional generalization is one of the hallmarks of human intelligence [3, 18]. To make the models equipped with this ability, Compositional Zero-Shot Learning (CZSL) [25] is proposed, where the models are trained to recognize images of unseen compositions composed of seen concepts. In this work, we concentrate on the situation where each composition is composed by attribute (e.g., wet) and object (e.g., apple). For example, given im" + }, + { + "type": "image", + "bbox": [ + 0.502, + 0.302, + 0.88, + 0.525 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.537, + 0.892, + 0.663 + ], + "angle": 0, + "content": "Figure 1. The diagram of our work. We aim to learn conditional attributes conditioned on the recognized object and input image through an attribute learning framework containing an attribute hyper learner and an attribute base learner. We first recognize the object in the input image. Then, we feed prior knowledge extracted from the conditions, which are recognized object word embedding and input image visual embedding, to the attribute hyper learner. Finally, conditional attribute embeddings are produced by the attribute base learner parameterized by the attribute hyper learner." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.685, + 0.891, + 0.716 + ], + "angle": 0, + "content": "ages of wet apple and dry cat, a well-trained model can recognize images of new compositions dry apple and wet cat." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Compositional Zero-Shot Learning of attribute-object compositions requires modeling attributes, objects, and the contextuality between them. Learning to model objects in CZSL is similar to conventional supervised object classification task since the model has access to all objects in CZSL task [33]. Learning to model contextuality between attribute and object is mostly addressed in the literature [23,25,26,31,39-41]. One of the main challenges of CZSL is the appearance diversity of an attribute when composed with different objects, e.g., attribute wet in wet apple and wet cat is different. This reveals that the information of each attribute is dependent on different objects. However, most" + }, + { + "type": "page_footnote", + "bbox": [ + 0.094, + 0.863, + 0.305, + 0.876 + ], + "angle": 0, + "content": "*E-mail: wqshmzh@mail.nwpu.edu.cn" + }, + { + "type": "page_footnote", + "bbox": [ + 0.097, + 0.876, + 0.404, + 0.888 + ], + "angle": 0, + "content": "†Corresponding author. E-mail: peng.wang@nwpu.edu.cn" + }, + { + "type": "page_footnote", + "bbox": [ + 0.097, + 0.888, + 0.423, + 0.9 + ], + "angle": 0, + "content": "‡Gitee: https://gitee.com/wqshmzh/canet-czsl" + }, + { + "type": "list", + "bbox": [ + 0.094, + 0.863, + 0.423, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11197" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.168 + ], + "angle": 0, + "content": "recent works in CZSL [4,27,32,33,42,45] extract attribute representations irrelevant to the object from seen compositions to infer the unseen compositions. These approaches neglect the nature of attribute diversity and learn concrete attribute representation agnostic to different objects." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.168, + 0.468, + 0.304 + ], + "angle": 0, + "content": "In this paper, we learn conditional attributes rather than learning concrete ones in a proposed Conditional Attribute Network (CANet). We first conduct analysis to determine the exact conditions by considering the recognition of attribute and object as computing a classification probability of attribute and object conditioned on the input image. By decomposing this probability, we demonstrate that the probability of the input image belonging to an attribute is conditioned on the recognized object and the input image." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.304, + 0.468, + 0.62 + ], + "angle": 0, + "content": "We present an attribute learning framework to learn conditional attribute embeddings conditioned on the above two conditions. The framework contains an attribute hyper learner and an attribute base learner, which are sketched in Fig. 1. The attribute hyper learner learns from prior knowledge extracted from the conditions. The attribute base learner is parameterized by the attribute hyper learner and is designed to encode all attribute word embeddings into conditional attribute embeddings. With the attribute learning framework, the attribute embeddings are changed along with the recognized object and input image. Finally, the attribute matching is processed in an attribute space where the input image embedding is projected. The attribute classification logits are computed by cosine similarities between the projected input image embedding and all conditional attribute embeddings. Additionally, we model the contextuality between attribute and object as composing attribute and object word embeddings. We use cosine similarities between the projected input image embedding and all composed attribute-object embeddings to get the classification logits." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.621, + 0.352, + 0.634 + ], + "angle": 0, + "content": "Our main contributions are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.636, + 0.468, + 0.665 + ], + "angle": 0, + "content": "- We propose to learn attributes conditioned on the recognized object and input image." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.666, + 0.468, + 0.709 + ], + "angle": 0, + "content": "- We propose an attribute learning framework containing an attribute hyper learner and an attribute base learner for learning conditional attribute embeddings." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.711, + 0.468, + 0.769 + ], + "angle": 0, + "content": "- Experiments and ablation studies indicate the effectiveness of our proposed conditional attribute network, which further validates the importance of learning conditional attributes in the CZSL task." + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.636, + 0.468, + 0.769 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.785, + 0.218, + 0.8 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Compositional Zero-Shot Learning. Given descriptions only, we can recognize objects that are never seen before. In conventional Zero-Shot Learning (ZSL), models have access both to images of seen classes and descriptions of seen and unseen classes [19]. In contrast, CZSL presents no description of seen and unseen attribute-object" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.394 + ], + "angle": 0, + "content": "compositions while all attributes and objects as concepts are seen during training. Recently, works in CZSL are divided into two main streams. One extracts attribute and object words or visual features independently from a composition during training, including learning attributes as linear transformations of objects [27], learning to hierarchically decompose compositions and recompose the concepts with learned visual concepts [41], learning independent prototypes of attributes and objects and compositing prototypes via graph network [32], and learning decomposed prototypes of visual concept features [33] via siamese contrastive embedding network [20]. The other is to learn a compositional space [23], a graph network [2, 26], an episode-based cross-attention module [39], and a contrastive space [1] for contextuality modeling. Also, Yang et al. [42] rethink the CZSL task in a decomposable causal way and learn three spaces for attribute, object, and composition classifications. Additionally, with pre-trained large vision language models like CLIP, Nayak et al. [30] propose to tune soft prompts as concept embeddings." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.395, + 0.892, + 0.576 + ], + "angle": 0, + "content": "Recent work in [12] addresses the problem of attribute diversity. They propose to learn translational attribute features conditionally dependent on the object prototypes. Specifically, they add generic object embedding as the object prototype to the concatenated attribute and object embedding. However, this approach makes the model concentrate more on the composition instead of the attribute, causing the attribute learning degrade to learning the contextuality between attribute and object. On the contrary, we explicitly focus on learning conditional attribute embeddings. The learned conditional attribute embeddings can be changed along with the objects and input images." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.577, + 0.892, + 0.729 + ], + "angle": 0, + "content": "Attribute Learning. Learning features of attributes is explored by a large community including image search [16, 34], sentence generation [17], and zero-shot classification [9, 29]. Conventional attribute learning approaches map the attributes into high-dimensional space and train a discriminative classification head without considering the diverse nature of attributes [22, 35, 37]. Our work also learns high-dimensional embeddings to represent attributes. The main difference is that our learned attribute embeddings are conditioned on different objects and input images." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.745, + 0.608, + 0.763 + ], + "angle": 0, + "content": "3. Approach" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.77, + 0.654, + 0.785 + ], + "angle": 0, + "content": "3.1. Task Definition" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.892, + 0.903 + ], + "angle": 0, + "content": "The task of CZSL aims to learn to classify an image \\(i\\) into a composition \\(c\\) composed by multiple seen concepts, where \\(i\\) and \\(c\\) are unseen during training. Denote sets of images, compositions, attributes, and objects as \\(\\mathcal{I}\\), \\(\\mathcal{C}\\), \\(\\mathcal{A}\\), and \\(\\mathcal{O}\\), we have \\(i \\in \\mathcal{I}\\), \\(c \\in \\mathcal{C}\\), \\(a \\in \\mathcal{A}\\), \\(o \\in \\mathcal{O}\\), and \\(\\mathcal{C} = \\mathcal{A} \\times \\mathcal{O}\\). During training, machines have access to seen set \\(\\mathcal{D}_{\\text{seen}} = \\{(i^s, c^s) | i^s \\in \\mathcal{I}^s, \\mathcal{I}^s \\subsetneq \\mathcal{I}, c \\in \\mathcal{C}^s, \\mathcal{C}^s \\subsetneq \\mathcal{C}\\}\\)," + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11198" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.096, + 0.887, + 0.361 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.375, + 0.892, + 0.472 + ], + "angle": 0, + "content": "Figure 2. Structure of our proposed CANet. The symbol \\(\\oplus\\) is channel-wise concatenation. The mapping networks \\(\\omega_{o},\\omega_{a}\\), and \\(\\omega_{c}\\) map the input image embedding \\(\\mathbf{x}\\) into object, attribute, and composition spaces \\(S_{o},S_{a}\\), and \\(S_{c}\\). All object word embeddings \\(\\mathbf{v}_{o}\\) along with the object-mapped input image embedding are used in \\(S_{o}\\) to compute loss \\(\\mathcal{L}_o\\) and get the recognized object \\(o^{*}\\). The attribute hyper learner \\(\\mathcal{H}\\) learns to parameterize the attribute base learner \\(\\mathcal{G}\\) using the prior knowledge \\(\\beta\\) extracted from the recognized object word embedding \\(\\mathbf{v}_{o^*}\\) and \\(\\mathbf{x}\\). The conditional attribute embeddings \\(\\mathbf{e}_a\\) are encoded by \\(\\mathcal{G}\\) parameterized by \\(\\mathcal{H}\\). Using all \\(\\mathbf{e}_a\\) along with the attribute-mapped input image embedding in space \\(S_{a}\\) to compute loss \\(\\mathcal{L}_a\\). Loss \\(\\mathcal{L}_{a,o}\\) is computed using all compositional word embeddings produced by composing network \\(\\mathcal{C}\\) and the composition-mapped input image embedding in space \\(S_{c}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.487, + 0.47, + 0.683 + ], + "angle": 0, + "content": "attribute set \\(\\mathcal{A}\\), and object set \\(\\mathcal{O}\\), where \\(\\mathcal{I}^s\\) and \\(\\mathcal{C}^s\\) are sets of images and compositions seen when training. Also, evaluation of algorithms requires unseen set \\(\\mathcal{D}_{\\text{unseen}} = \\{(i^u, c^u) | i^u \\in \\mathcal{I}^u, c^u \\in \\mathcal{C}^u, \\mathcal{I}^u \\subsetneq \\mathcal{I}, \\mathcal{C}^u \\subsetneq \\mathcal{C}\\}\\) used for validation and testing. In conventional ZSL, \\(\\mathcal{I}^s \\cap \\mathcal{I}^u = \\emptyset\\), \\(\\mathcal{C}^s \\cap \\mathcal{C}^u = \\emptyset\\), i.e. unseen images and compositions are not overlapped with the seen ones. Here, we follow the setting of Generalized Zero-Shot Learning (GZSL) where images in \\(\\mathcal{I}^s\\) and \\(\\mathcal{I}^u\\) and labels in \\(\\mathcal{C}^s\\) and \\(\\mathcal{C}^u\\) appear during validation and testing. GZSL is a challenging setting with larger label space and a strong bias of seen compositions to unseen ones, relaxing the less realistic assumption in conventional ZSL that test data only belongs to unseen classes." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.692, + 0.353, + 0.706 + ], + "angle": 0, + "content": "3.2. Conditional Attribute Network" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.715, + 0.469, + 0.85 + ], + "angle": 0, + "content": "Determining Conditions. In CZSL, it is common to learn to classify attributes and objects besides compositions. We first assume that the model recognizes the input image \\( i \\) as attribute \\( a^* \\) and object \\( o^* \\). The recognizing score can be formulated as a conditional probability \\( P(a^*, o^* | i) \\) conditioned on input image \\( i \\). We propose to decompose this probability to express the attribute and object recognition as a one-label classification task. According to multi-variable conditional probability formulation, we have:" + }, + { + "type": "equation", + "bbox": [ + 0.16, + 0.853, + 0.468, + 0.869 + ], + "angle": 0, + "content": "\\[\nP \\left(a ^ {*}, o ^ {*} \\mid i\\right) = P \\left(a ^ {*} \\mid o ^ {*}, i\\right) P \\left(o ^ {*} \\mid i\\right) \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "where \\( P(o^{*}|i) \\) is probability of image \\( i \\) belonging to object \\( o^{*} \\) and \\( P(a^{*}|o^{*},i) \\) represents the probability of attribute \\( a^{*} \\)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.487, + 0.892, + 0.578 + ], + "angle": 0, + "content": "conditioned on the joint presentation of \\( o^* \\) and \\( i \\). This indicates that the recognition of an attribute is conditioned on the recognized object and input image. To better solve the attribute diversity problem, we consider the information of the recognized object and input image as conditions for conditional attribute encoding." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.582, + 0.892, + 0.672 + ], + "angle": 0, + "content": "Object Recognition. Object recognition requires learning to map the input image embedding into an object space. To incorporate object semantic information, we compute cosine similarities between object-mapped image embedding \\(\\omega_{o}(\\mathbf{x})\\) and all object word embeddings \\(\\mathbf{v}_{o}\\) instead of directly learning a classification head:" + }, + { + "type": "equation", + "bbox": [ + 0.59, + 0.673, + 0.892, + 0.707 + ], + "angle": 0, + "content": "\\[\n\\left\\langle \\omega_ {o} (\\mathbf {x}), \\mathbf {v} _ {o} \\right\\rangle = \\frac {\\omega_ {o} (\\mathbf {x}) ^ {\\top} \\mathbf {v} _ {o}}{\\| \\omega_ {o} (\\mathbf {x}) \\| _ {2} \\| \\mathbf {v} _ {o} \\| _ {2}} \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.708, + 0.892, + 0.822 + ], + "angle": 0, + "content": "where \\(\\mathbf{x} = f(i) \\in \\mathcal{X}\\) is the visual embedding of input image \\(i\\) in visual space \\(\\mathcal{X}\\) extracted by image backbone \\(f\\) (e.g., ResNet-18 [11]), \\(\\omega_{o}\\) is the mapping from \\(\\mathcal{X}\\) to object semantic space \\(S_{o}\\), \\(\\mathbf{v}_{o} = \\phi(o)\\), \\(\\mathbf{v}_{o} \\in S_{o}\\) is object word embedding in \\(S_{o}\\) extracted by word embedder \\(\\phi\\) (e.g., word2vec [24], FastText [7]). The recognized object \\(o^{*} = \\underset{o \\in \\mathcal{O}}{\\arg \\max} \\langle \\omega_{o}(\\mathbf{x}), \\phi(o) \\rangle\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Learning Conditional Attributes. With the recognized object \\(o^*\\) and visual embedding \\(\\mathbf{x}\\) of input image \\(i\\), we learn the attribute hyper learner \\(\\mathcal{H}\\) and attribute base learner \\(\\mathcal{G}\\) in the proposed attribute learning framework to extract attribute embeddings conditioned on the recognized object \\(o^*\\)." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11199" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.136 + ], + "angle": 0, + "content": "and input image \\(i\\). We consider the information of \\(o^*\\) and \\(i\\) as prior knowledge for \\(\\mathcal{H}\\). Specifically, the prior knowledge is implemented as a feature vector \\(\\beta\\):" + }, + { + "type": "equation", + "bbox": [ + 0.203, + 0.14, + 0.469, + 0.155 + ], + "angle": 0, + "content": "\\[\n\\beta = \\mathcal {P} \\left(\\operatorname {c a t} \\left(\\mathbf {v} _ {o ^ {*}}, \\mathbf {x}\\right)\\right) \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.157, + 0.469, + 0.217 + ], + "angle": 0, + "content": "where \\(\\mathbf{v}_{o^*} = \\phi(o^*)\\) is word embedding of \\(o^*\\), \\(\\mathcal{P}\\) is a composing network for \\(\\mathbf{v}_{o^*}\\) and \\(\\mathbf{x}\\), \\(\\operatorname{cat}(\\cdot)\\) is channel-wise concatenation operation. With the prior knowledge, the attribute hyper learner \\(\\mathcal{H}\\) can parameterize \\(\\mathcal{G}\\) as:" + }, + { + "type": "equation", + "bbox": [ + 0.212, + 0.22, + 0.469, + 0.236 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {\\Theta} _ {\\mathcal {G}} = \\mathcal {H} (\\beta ; \\boldsymbol {\\Theta} _ {\\mathcal {H}}) \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.238, + 0.469, + 0.298 + ], + "angle": 0, + "content": "where \\(\\Theta_{\\mathcal{H}}\\) is the set of randomly initialized parameters of \\(\\mathcal{H}\\), \\(\\Theta_{\\mathcal{G}}\\) is the set of generated parameters of \\(\\mathcal{G}\\). In this way, the attribute embeddings \\(\\mathbf{e}_a\\) conditioned on \\(o^*\\) and \\(i\\) can be encoded via \\(\\mathcal{G}\\) parameterized by \\(\\mathcal{H}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.215, + 0.301, + 0.469, + 0.316 + ], + "angle": 0, + "content": "\\[\n\\mathbf {e} _ {a} = \\mathcal {G} \\left(\\mathbf {v} _ {a}; \\boldsymbol {\\Theta} _ {\\mathcal {G}}\\right) \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.318, + 0.455, + 0.333 + ], + "angle": 0, + "content": "where \\(\\mathbf{v}_a = \\phi(a)\\) is word embedding of attribute word \\(a\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.334, + 0.469, + 0.469 + ], + "angle": 0, + "content": "Modeling Contextuality. Although the conditional attribute embeddings are related to the recognized object and input image, object embeddings are also supposed to be influenced by attributes. Therefore, we model the contextuality of attribute-object compositions to address the relationships between them. We follow the work of Mancini et al. [23] in their closed world setting that contextuality is modeled as the mixture of attribute and object word embeddings to extract attribute-object compositional embeddings:" + }, + { + "type": "equation", + "bbox": [ + 0.196, + 0.471, + 0.469, + 0.487 + ], + "angle": 0, + "content": "\\[\n\\mathbf {v} _ {a, o} = \\mathcal {C} (\\operatorname {c a t} \\left(\\mathbf {v} _ {a}, \\mathbf {v} _ {o}\\right)) \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.489, + 0.392, + 0.504 + ], + "angle": 0, + "content": "where \\(\\mathcal{C}\\) is a composing network for \\(\\mathbf{v}_a\\) and \\(\\mathbf{v}_o\\)." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.504, + 0.441, + 0.52 + ], + "angle": 0, + "content": "The entire structure of our model is shown in Fig. 2." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.528, + 0.266, + 0.544 + ], + "angle": 0, + "content": "3.3. Training Objectives" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.552, + 0.469, + 0.643 + ], + "angle": 0, + "content": "Similar to object recognition, attribute or composition recognition is also implemented by computing cosine similarities \\(\\langle \\omega_{a}(\\mathbf{x}),\\mathbf{v}_{a}\\rangle\\) or \\(\\langle \\omega_c(\\mathbf{x}),\\mathbf{v}_{a,o}\\rangle\\) between attribute-mapped or composition-mapped image embeddings, i.e., \\(\\omega_{a}(\\mathbf{x})\\) or \\(\\omega_{c}(\\mathbf{x})\\), and attribute word embeddings or attribute-object compositional embeddings, i.e., \\(\\mathbf{v}_a\\) or \\(\\mathbf{v}_{a,o}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.168, + 0.644, + 0.469, + 0.678 + ], + "angle": 0, + "content": "\\[\n\\left\\langle \\omega_ {a} (\\mathbf {x}), \\mathbf {e} _ {a} \\right\\rangle = \\frac {\\omega_ {a} (\\mathbf {x}) ^ {\\top} \\mathbf {e} _ {a}}{\\| \\omega_ {a} (\\mathbf {x}) \\| _ {2} \\| \\mathbf {e} _ {a} \\| _ {2}} \\tag {7}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.158, + 0.679, + 0.469, + 0.713 + ], + "angle": 0, + "content": "\\[\n\\left\\langle \\omega_ {c} (\\mathbf {x}), \\mathbf {v} _ {a, o} \\right\\rangle = \\frac {\\omega_ {c} (\\mathbf {x}) ^ {\\top} \\mathbf {v} _ {a , o}}{\\| \\omega_ {c} (\\mathbf {x}) \\| _ {2} \\| \\mathbf {v} _ {a , o} \\| _ {2}} \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.717, + 0.469, + 0.866 + ], + "angle": 0, + "content": "The recognition probability \\( P(o^{*}|i) \\), \\( P(a^{*}|o^{*},i) \\), and \\( P(c^{*}|i) \\) are normalized cosine similarities, where \\( P(c^{*}|i) \\) is the probability of input image \\( i \\) belonging to the recognized attribute-object composition \\( c^{*} \\). As shown in Fig. 2, our model learns three embedding spaces: attribute space \\( S_{a} \\), object space \\( S_{o} \\), and attribute-object compositional space \\( S_{c} \\). Therefore, we incorporate three separate cross-entropy losses to maximize the three recognition probabilities to make the model optimized in these three spaces. The losses are as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.12, + 0.867, + 0.469, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {a} = - \\sum_ {a \\in \\mathcal {A}} \\log \\frac {\\exp \\left(\\left\\langle \\omega_ {a} (\\mathbf {x}), \\mathbf {e} _ {a} \\right\\rangle / \\tau\\right)}{\\sum_ {a ^ {\\prime} \\in \\mathcal {A}} \\exp \\left(\\left\\langle \\omega_ {a} (\\mathbf {x}), \\mathbf {e} _ {a ^ {\\prime}} \\right\\rangle / \\tau\\right)} \\tag {9}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.544, + 0.089, + 0.891, + 0.126 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {o} = - \\sum_ {o \\in \\mathcal {O}} \\log \\frac {\\exp \\left(\\left\\langle \\omega_ {o} (\\mathbf {x}) , \\mathbf {v} _ {o} \\right\\rangle / \\tau\\right)}{\\sum_ {o ^ {\\prime} \\in \\mathcal {O}} \\exp \\left(\\left\\langle \\omega_ {o} (\\mathbf {x}) , \\mathbf {v} _ {o} ^ {\\prime} \\right\\rangle / \\tau\\right)} \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.132, + 0.792, + 0.146 + ], + "angle": 0, + "content": "Also, for composition recognition, we have:" + }, + { + "type": "equation", + "bbox": [ + 0.51, + 0.148, + 0.891, + 0.2 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {a, o} = - \\sum_ {(a, o) \\in \\mathcal {C}} \\log \\frac {\\exp \\left(\\left\\langle \\omega_ {c} (\\mathbf {x}), \\mathbf {v} _ {a , o} \\right\\rangle / \\tau\\right)}{\\sum_ {\\left(a ^ {\\prime} , o ^ {\\prime}\\right) \\in \\mathcal {C}} \\exp \\left(\\left\\langle \\omega_ {c} (\\mathbf {x}), \\mathbf {v} _ {a ^ {\\prime} , o ^ {\\prime}} \\right\\rangle / \\tau\\right)} \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.2, + 0.891, + 0.229 + ], + "angle": 0, + "content": "where \\(\\tau\\) is temperature factor [46]. Finally, the training loss as a whole linearly combines the three losses above:" + }, + { + "type": "equation", + "bbox": [ + 0.621, + 0.23, + 0.891, + 0.26 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\frac {\\mathcal {L} _ {a} + \\mathcal {L} _ {o}}{2} + \\mathcal {L} _ {a, o} \\tag {12}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.268, + 0.609, + 0.282 + ], + "angle": 0, + "content": "3.4. Inference" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.291, + 0.891, + 0.321 + ], + "angle": 0, + "content": "During validation and testing, we incorporate a linear normalization function \\( g \\) for cosine similarities:" + }, + { + "type": "equation", + "bbox": [ + 0.625, + 0.323, + 0.891, + 0.339 + ], + "angle": 0, + "content": "\\[\ng (d) = (1 + d) * 0. 5 \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.34, + 0.891, + 0.386 + ], + "angle": 0, + "content": "Then, we have \\( P(a|o^{*},i) = g(\\langle \\omega_{a}(\\mathbf{x}),\\mathbf{e}_{a}\\rangle),P(o|i) = g(\\langle \\omega_{o}(\\mathbf{x}),\\mathbf{v}_{o}\\rangle) \\), and \\( P(c|i) = g(\\langle \\omega_c(\\mathbf{x}),\\mathbf{v}_{a,o}\\rangle) \\). The inference rule is parameterized as:" + }, + { + "type": "equation", + "bbox": [ + 0.561, + 0.388, + 0.891, + 0.405 + ], + "angle": 0, + "content": "\\[\ns = (1 - \\alpha) P (c | i) + \\alpha P (a | o ^ {*}, i) P (o | i) \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.407, + 0.822, + 0.422 + ], + "angle": 0, + "content": "where \\(\\alpha\\) is the weight factor controlling balance." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.436, + 0.631, + 0.453 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.46, + 0.891, + 0.52 + ], + "angle": 0, + "content": "In this section, experiments are conducted following the concrete introductions of datasets, metrics, implementation details, and baselines. Then, we report ablation results to demonstrate the effectiveness of our model." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.531, + 0.69, + 0.547 + ], + "angle": 0, + "content": "4.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.554, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Datasets We conduct experiments with three widely adopted datasets in the CZSL task, which are MIT-States [14], UT-Zappos50K [43, 44], and C-GQA [26]. MIT-States contains 53753 crawled web images labeled with 1962 attribute-object (e.g., mossy highway) compositions. This dataset has 30338, 10420, and 12995 training, validation, and testing images [31] labeled with 1262, 600, and 800 compositions. In validation and test sets, the numbers of seen and unseen compositions are the same. All compositions are composed of 115 attributes and 245 objects. UT-Zappos50K is made up of 50025 images labeled with 116 fine-grained shoe classes composed of 16 attributes (e.g., rubber) and 12 objects (e.g., sneaker). This dataset has 22998, 3214, and 2914 training, validation, and testing images [31] labeled with 83, 30, and 36 compositions. Also, numbers of seen and unseen compositions in validation and test sets share the same quantity. C-GQA is created based on Stanford GQA dataset [13] used for VQA task. C-GQA contains 39298 images labeled with over \\(9.5\\mathrm{k}\\) compositions composed of 453 attributes and 870 objects. This dataset has 26920, 7280, and 5098 training, validation, and testing images labeled with 6963, 2541, and 2069 compositions. Detailed splits are presented in Tab. 1." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11200" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.08, + 0.089, + 0.895, + 0.187 + ], + "angle": 0, + "content": "
DatasetTrainingValidationTest
AOCsICsCuICsCuI
UT-Zappos50K [43,44]161283229981515321418182914
MIT-States [14]1152451262303383003001042040040012995
C-GQA [26]453870696326920117313687280102210475098
" + }, + { + "type": "table_caption", + "bbox": [ + 0.154, + 0.196, + 0.816, + 0.21 + ], + "angle": 0, + "content": "Table 1. Detailed dataset splits of UT-Zappos50K, MIT-States, and C-GQA in training, validation, and test sets." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.224, + 0.473, + 0.45 + ], + "angle": 0, + "content": "Metrics To demonstrate the advances in attribute learning, we report the attribute and object classification accuracies (best attr and best obj). The setting of GZSL requires both seen and unseen compositions to exist during validation and testing. As a result, there is an inherent bias of seen against unseen compositions. We follow the evaluation protocols proposed in [8] where a scalar bias is added to final activations of classes of seen compositions to calibrate the model. As the scalar varies from negative infinity to positive infinity, there must be a best operating point at which the bias between seen and unseen compositions is the lowest. We report the results in terms of the best accuracies of seen images (best seen), unseen images (best unseen), best Harmonic Mean (best HM), and Area Under Curve (AUC) with different scalar biases." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.451, + 0.473, + 0.692 + ], + "angle": 0, + "content": "Implementations We consider image backbone \\( f \\) as ResNet-18 pre-trained on ImageNet [10] to extract 512 dimension vectors following preceding works. The mapping networks \\( \\omega_{a} \\), \\( \\omega_{o} \\), and \\( \\omega_{c} \\) share the similar structure of two Fully Connected (FC) layers with ReLU [28], LayerNorm [5], and Dropout [36] following the first FC layer. We adopt word embedder \\( \\phi \\) as 600-dimensional word2vec+FastText for MIT-States, 300-dimensional FastText for UT-Zappos50K, and word2vec for C-GQA. The layer structures of \\( \\mathcal{G} \\), \\( \\mathcal{P} \\), and \\( \\mathcal{C} \\) are the same as the mapping networks, where ReLU is added in \\( \\mathcal{P} \\) and \\( \\mathcal{C} \\) to the last FC layer. Weight generation for the attribute base learner \\( \\mathcal{G} \\) through the attribute hyper learner \\( \\mathcal{H} \\) requires more parameters and makes learning difficult, as noted by Bertinetto et al. [6]. Therefore, we adopt weight factorization in [38] to reduce parameters for the attribute hyper learner \\( \\mathcal{H} \\), that is" + }, + { + "type": "equation", + "bbox": [ + 0.167, + 0.694, + 0.468, + 0.713 + ], + "angle": 0, + "content": "\\[\n\\mathbf {e} _ {a} ^ {(i)} = \\left(\\mathbf {v} _ {a} \\mathbf {W} _ {\\mathcal {G}} ^ {(i)} + \\mathbf {b} _ {\\mathcal {G}} ^ {(i)}\\right) \\odot \\boldsymbol {\\lambda} _ {\\mathcal {G}} ^ {(i)} \\tag {15}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.21, + 0.714, + 0.468, + 0.735 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {\\lambda} _ {\\mathcal {G}} ^ {(i)} = \\mathcal {H} (\\beta ; \\boldsymbol {\\Theta} _ {\\mathcal {H}} ^ {(i)}) \\tag {16}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.731, + 0.473, + 0.902 + ], + "angle": 0, + "content": "where \\((i)\\) indicates \\(i\\)th FC layer, \\(\\mathbf{W}_{\\mathcal{G}}^{(i)}\\) and \\(\\mathbf{b}_{\\mathcal{G}}^{(i)}\\) are the weight matrix and bias vector of \\(i\\)th FC layer in \\(\\mathcal{G}\\), \\(\\{\\mathbf{W}_{\\mathcal{G}}^{(i)}, \\mathbf{b}_{\\mathcal{G}}^{(i)}\\} \\subset \\Theta_{\\mathcal{G}}, \\Theta_{\\mathcal{H}}^{(i)} \\subset \\Theta_{\\mathcal{H}}\\), and \\(\\odot\\) denotes elementwise multiplication. During training, we fix the image backbone \\(f\\) and train other modules using Adam [15] optimizer and an Nvidia GeForce GTX 1080Ti GPU with a learning rate and weight decay of 0.00005. The batch size is 256. The temperature factor \\(\\tau\\), weight factor \\(\\alpha\\), and the maximum number of epochs are set to 0.02, 0.4, and 500 for UT-Zappos50K; 0.05, 0.2, and 800 for MIT-States; and 0.05, 0.4, and 1000 for C-GQA." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.224, + 0.895, + 0.572 + ], + "angle": 0, + "content": "Baselines We conduct experiments with the following algorithms: 1) AttrAsOp [27] treats attributes as linear transformations on object vectors instead of data points in some high-dimensional space and optimizes the transformations through several regularizers in the loss function. 2) TMN [31] constructs task-driven modular networks in semantic space configured through a gating function conditioned on the task. 3) SymNet [21] proposes symmetry property in attribute-object compositions and group axioms as objectives in an end-to-end manner. 4) \\( CGE_{\\mathrm{ff}} \\) [26] exploits dependencies between attributes, objects, and compositions through an end-to-end graph formulation where \"ff\" means fixed image feature backbone. 5) CompCos [23] learns a mapping from image features to semantic space of compositions and computes cosine similarities between them. 6) DeCa [42] rethinks the CZSL task in a decomposable causal perspective and learns three independent mappings from image feature space to attribute, object, and composition semantic space. Cosine similarities are also adopted. 7) SCN [20] computes visual prototypes of attributes and objects in a siamese contrastive space and proposes a designed State Transition Module to increase the diversity of training compositions." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.587, + 0.704, + 0.603 + ], + "angle": 0, + "content": "4.2. Quantitative Analysis" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.611, + 0.892, + 0.656 + ], + "angle": 0, + "content": "All results are computed on test sets of all datasets and from their published papers and [26] for a fair comparison. We report quantitative results with the best AUC in Tab. 2." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.658, + 0.892, + 0.779 + ], + "angle": 0, + "content": "From Tab.2, our model outperforms other state-of-the-art algorithms in terms of best attr, best unseen, and AUC in all three datasets including the recently proposed C-GQA, indicating the better attribute learning performance and generalization ability from seen to unseen compositions. Specifically, our model performs much better on C-GQA with more state-of-the-art results although it is a much more challenging dataset than MIT-States and UT-Zappos50K." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.895, + 0.901 + ], + "angle": 0, + "content": "For UT-Zappos50K, the observations are that our model boosts attribute recognition accuracy, unseen image classification accuracy, and AUC from \\(47.3\\%\\), \\(63.1\\%\\), and \\(32.0\\%\\) of SCEN to the new state-of-the-art of \\(48.4\\%\\), \\(66.3\\%\\), and \\(33.1\\%\\) with \\(1.1\\%\\), \\(3.2\\%\\), and \\(1.1\\%\\) improvement respectively. For MIT-States, our model achieves \\(30.2\\%\\), \\(32.6\\%\\), \\(26.2\\%\\), and \\(5.4\\%\\) accuracies for attribute and object classification, unseen image classification, and AUC on the test" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "11201" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.078, + 0.089, + 0.896, + 0.278 + ], + "angle": 0, + "content": "
AlgorithmUT-Zappos50KMIT-StatesC-GQA
NameVenueAtt.Obj.S.U.HMAUCAtt.Obj.S.U.HMAUCAtt.Obj.S.U.HMAUC
AttrAsOp [27]ECCV'1838.969.659.854.240.825.921.123.614.317.49.91.68.312.511.83.92.90.3
TMN [31]ICCV'1940.869.958.760.045.029.323.326.520.220.113.02.99.720.521.66.37.71.1
SymNet [21]CVPR'2041.368.649.857.440.423.426.328.324.425.216.13.015.023.127.010.810.92.2
CGEff [26]CVPR'2145.073.956.863.641.226.427.932.028.725.317.25.112.726.927.511.711.92.5
CompCos [23]CVPR'2144.773.559.862.543.528.727.931.825.324.616.44.5------
DeCa [42]TMM'22--62.763.146.331.6--29.825.218.25.3------
SCEN [20]CVPR'2247.375.663.563.147.832.028.232.229.925.218.45.313.627.928.912.112.42.9
Ours48.472.661.066.347.333.130.232.629.026.217.95.417.522.330.013.214.53.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.286, + 0.893, + 0.315 + ], + "angle": 0, + "content": "Table 2. Quantitative results on test sets of all datasets with the state-of-the-art in terms of best attr (Att.), best obj (Obj.), best seen (S.), best unseen (U.), best HM (HM), and AUC." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.329, + 0.471, + 0.419 + ], + "angle": 0, + "content": "set, providing \\(2.0\\%\\), \\(0.4\\%\\), \\(1.0\\%\\), and \\(0.1\\%\\) improvements on the recently proposed SCEN as the new state-of-the-art results. This indicates that the proposed conditional attribute network can truly improve the attribute recognition performance and consequently the unseen image classification and AUC." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.424, + 0.47, + 0.576 + ], + "angle": 0, + "content": "For the more challenging dataset C-GQA, since it is significantly harder than MIT-States and UT-Zappos50K with \\(5.5 \\times\\) and \\(0.9 \\times\\) composition labels and images in the training set compared with MIT-States, our model outperforms all other algorithms except best obj with \\(3.9\\%\\), \\(1.1\\%\\), \\(1.1\\%\\), \\(2.1\\%\\), and \\(0.4\\%\\) boosting in terms of best attr, best seen, best unseen, best HM, and AUC in the testing set. This indicates that the proposed conditional attribute network makes a critical contribution when facing a more challenging dataset even if the object recognition accuracy is lower." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.58, + 0.47, + 0.793 + ], + "angle": 0, + "content": "We give an analysis of the importance that attributes should be conditioned on objects. First, note that although DeCa also learns attribute, object, and composition spaces separately, it learns attributes as static embeddings independent from objects, causing lower best unseen and AUC on UT-Zappos50K and MIT-States compared with ours in Tab. 2. Next, different baselines incorporate different techniques to handle the CZSL task though, they learn static attribute embeddings too, producing lower best attr, best unseen, and AUC. Then, the proposed method performs much better on C-GQA compared with other baselines. All the above phenomena demonstrate that attributes should be conditioned on objects and performance on datasets with larger label space can gain more boosts in this way." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.471, + 0.903 + ], + "angle": 0, + "content": "From the results of the three datasets above, we observe an interesting phenomenon. Although the results of best obj in three datasets are all lower than that of SCEN, results of best unseen are all higher accompanied by higher results of best attr. We speculate the reason is that some objects have more attributes (or are more dominated) in unseen compositions and the misclassified objects recognized" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.329, + 0.895, + 0.406 + ], + "angle": 0, + "content": "by our model are less dominated (i.e. have few attributes or are long-tailed in terms of attribute). As a result, with the correctly predicted objects dominated in unseen compositions, the more correctly classified attributes, the higher the results of best unseen." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.42, + 0.693, + 0.438 + ], + "angle": 0, + "content": "4.3. Qualitative Analysis" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.446, + 0.895, + 0.763 + ], + "angle": 0, + "content": "In this section, we present some qualitative results of novel compositions with top-3 predictions on UT-Zappos50K, MIT-States, and C-GQA in Fig. 3. We show results for each dataset in each row. Images whose top prediction matches the label are shown in the first three columns and the rest columns show wrong results. For UT-Zappos50K, the remaining two answers of all images can match at least one label factor. For some instances in MIT-States, we can notice that the top and second predictions can both describe the image. For example, for the image labeled with winding stream, there is sunlight reflecting from the stream and creek is the synonym of stream. Therefore, sunny creek can also be the label of the image. Another example is that image labeled with wide valley also present cloudy cloud in the blue sky located in the upper part. As a result, the model has difficulty deciding what to predict. This reflects that labels in MIT-States are heavy in noise. For C-GQA where labels are clear, our model can produce more answers that match the label factors in the remaining two predictions, which indicates the better performance and robustness of our model." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Additionally, we present wrong predictions in the last two columns. It can be noticed that our model can predict correct answers in most top-3 predictions. As for the image of MIT-States labeled as broken bottle, our model predicts the attribute as small because it is difficult to focus on a certain attribute of the bottle since the bottle in this image is both small and broken. Besides, images in the training set are limited in the status of objects. For example, training images of sheep hardly present the action of laying down" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "11202" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.089, + 0.891, + 0.259 + ], + "angle": 0, + "content": "
VariantUT-Zappos50KC-GQA
#NameAtt.Obj.S.U.HMAUCAtt.Obj.S.U.HMAUC
(1)w/o L_a + L_o46.174.361.564.746.131.710.830.629.812.813.43.0
(2)w/o L_c41.960.759.554.745.728.314.817.128.111.212.42.6
(3)w/o G + H + P47.074.059.965.846.331.714.827.829.913.114.63.1
(4)w/o P46.773.260.764.547.531.614.526.430.113.014.53.1
(5)w/o H46.270.358.562.746.330.513.925.829.111.212.52.4
(6)w/o x for H45.671.361.662.844.830.113.420.830.212.713.92.9
(7)Full48.472.661.066.347.333.117.522.330.013.214.53.3
" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.269, + 0.891, + 0.283 + ], + "angle": 0, + "content": "Table 3. Ablation results on test sets in terms of best attr (Att.), best obj (Obj.), best seen (S.), best unseen (U.), best HM (HM), and AUC." + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.288, + 0.889, + 0.489 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.16, + 0.5, + 0.807, + 0.515 + ], + "angle": 0, + "content": "Figure 3. Qualitative Results. We demonstrate top-3 predictions of some instances using our proposed model." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.528, + 0.471, + 0.604 + ], + "angle": 0, + "content": "causing our model mistakenly classify the sheep in the image labeled as light sheep into elephant. Thus, with the recognized object elephant, the model can only focus on attributes conditioned on elephant and find the appropriate attribute that matches the image." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.618, + 0.231, + 0.634 + ], + "angle": 0, + "content": "4.4. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.643, + 0.47, + 0.779 + ], + "angle": 0, + "content": "In this section, we ablate the proposed model to evaluate the performance of each module. The ablation study is conducted on test sets of UT-Zappos50K, C-GQA. To achieve more convincing ablation results, we do not choose MIT-States because images in MIT-States are labeled using automatic search. As a result, the noise of labels is too heavy to be used for evaluations, as is pointed out by Atzmon et.al. [4]. Ablation results are reported in Tab. 3. The detailed ablation process is as follows:" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.471, + 0.902 + ], + "angle": 0, + "content": "We first study the effects of recognizing compositions only and recognizing attributes and objects without compositions, which are corresponded to variants (1) and (2) in Tab. 3, and report results in terms of six metrics used in Tab. 2. Compared with variant (6), the results of each variant mostly decline, indicating the importance of recognizing attributes, objects, and compositions jointly. As to the results of Obj. in UT-Zappos50K and C-GQA from variants" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.528, + 0.892, + 0.651 + ], + "angle": 0, + "content": "(1) and (6), we can observe that those object classification accuracies decline. This is mainly because when recognizing objects individually each object presents visual diversity caused by different attributes, e.g., sliced apple is different from apple in visual appearance since a sliced apple is sliced into multiple pieces. However, this phenomenon does not affect other results, especially for the dataset with larger label space, e.g., C-GQA." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.66, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Next, with attributes, objects, and compositions being recognized, we ablate \\(\\mathcal{G} + \\mathcal{H} + \\mathcal{P}\\) (where attribute word embeddings are directly used in \\(S_{a}\\)), \\(\\mathcal{H}\\) (where the concatenation of \\(\\beta\\) and \\(\\mathbf{v}_a\\) is fed to \\(\\mathcal{G}\\)), \\(\\mathcal{P}\\) (where the concatenation of \\(\\mathbf{v}_{o^*}\\) and \\(\\mathbf{x}\\) is directly fed to \\(\\mathcal{H}\\)), and \\(\\mathbf{x}\\) in \\(\\beta\\) that is fed to \\(\\mathcal{H}\\), which are corresponded to variants (3)-(6) in Tab. 3. Note that if \\(\\mathcal{P}\\) is presented then \\(\\mathcal{G}\\) is required to be presented also because the concatenation of \\(\\beta\\) and \\(\\mathbf{v}_a\\) requires changing the number of dimensions to that of \\(\\mathbf{x}\\) through \\(\\mathcal{G}\\). Also, \\(\\mathcal{G}\\) can not be ablated only otherwise the model changes to variant (3). Compared to variant (7), all results are mostly declined, indicating that optimizing the model with \\(\\mathcal{G}\\), \\(\\mathcal{H}\\), \\(\\mathcal{P}\\), and \\(\\mathbf{x}\\) is essential. As for variant (5), it performs worse on seen and unseen images compared with variant (4), indicating the importance of using the attribute hyper learner. Comparing results of variants (5) with (6), we observe that" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11203" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.089, + 0.35, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.35, + 0.089, + 0.621, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.623, + 0.089, + 0.895, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.079, + 0.242, + 0.35, + 0.376 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.35, + 0.242, + 0.621, + 0.376 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.623, + 0.242, + 0.895, + 0.376 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.225, + 0.389, + 0.744, + 0.404 + ], + "angle": 0, + "content": "Figure 4. Influence of weighting factor \\(\\alpha\\) on AUC, seen accuracy, and unseen accuracy." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.416, + 0.471, + 0.522 + ], + "angle": 0, + "content": "adding the attribute hyper learner \\(\\mathcal{H}\\) for \\(\\mathcal{G}\\) without image visual embedding \\(\\mathbf{x}\\) marginally increases overfitting to seen images. Results of variant (6) present the best generalization compared with variants (3)-(5) because adding \\(\\mathbf{x}\\) in \\(\\beta\\) for \\(\\mathcal{H}\\) provides diverse instances that are seen for \\(\\mathcal{H}\\) during training since the number of image visual embeddings is far more than the number of object word embeddings." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.524, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Lastly, we conduct experiments to study the impact of weighting factor \\(\\alpha\\) in Eq. (14) on all datasets. In detail, we present results of AUC, seen accuracy, and unseen accuracy in Fig. 4 with \\(\\alpha \\in [0,1]\\) with an interval of 0.1. It can be observed that all results of AUC increase first and then decrease with \\(\\alpha\\) increases from 0.0. The peaks of AUC are reached when \\(\\alpha\\) equals 0.5, 0.1, and 0.3 in UT-Zappos50K, MIT-States, and C-GQA. This phenomenon reveals that learning to classify attributes, objects, and compositions all contribute to making our model reach optimal. Additionally, it can be noticed that the results of AUC are all generally declined when \\(\\alpha\\) changes from 0.0 to 1.0. This is because attribute-object compositions involve not only the side information of attribute and object, but also the contextuality between attribute and object. As for the results of seen and unseen accuracies reported in the second row, the same trend can be observed. Specifically, results of unseen accuracy are more sensitive than seen accuracy and also have peaks with various \\(\\alpha\\), indicating that \\(\\alpha\\) also has an impact on the generalization ability of our model. In conclusion, using a small weighting factor \\(\\alpha\\) is always better than using a larger one, indicating that modeling contextuality between attribute and object is a bit more beneficial to the CZSL task than separately classifying attributes and objects." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.415, + 0.62, + 0.431 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.44, + 0.895, + 0.681 + ], + "angle": 0, + "content": "In this work, we address the attribute diversity problem in Compositional Zero-Shot Learning. As a solution, we propose a Conditional Attribute Network (CANet) to learn attributes conditioned on the recognized object and input image. We first decompose the probability of attribute and object recognition conditioned on the input image to lay a foundation for learning conditional attributes. Then, we build an attribute learning framework to encode conditional attribute embeddings. Experiments show that our model outperforms recent CZSL approaches and achieves new state-of-the-art results. Despite the better attribute recognition performance, a limitation is that our model is less qualified to handle object long-tailed distribution in terms of attribute mentioned in Sec. 4.2. Future works can be focused on solving the problem above while learning conditional attributes." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.696, + 0.688, + 0.714 + ], + "angle": 0, + "content": "6. Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.721, + 0.894, + 0.812 + ], + "angle": 0, + "content": "This work was supported by National Key R&D Program of China (No.2020AAA0106900), the National Natural Science Foundation of China (No.U19B2037), Shaanxi Provincial Key R&D Program (No.2021KWZ-03), and Natural Science Basic Research Program of Shaanxi (No.2021JCW-03)." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "11204" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.185 + ], + "angle": 0, + "content": "[1] Muhammad Umer Anwaar, Rayyan Ahmad Khan, Zhihui Pan, and Martin Kleinsteuber. A contrastive learning approach for compositional zero-shot learning. 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One of the challenges is to model attributes interacted with different objects, e.g., the attribute "wet" in "wet apple" and "wet cat" is different. As a solution, we provide analysis and argue that attributes are conditioned on the recognized object and input image and explore learning conditional attribute embeddings by a proposed attribute learning framework containing an attribute hyper learner and an attribute base learner. By encoding conditional attributes, our model enables to generate flexible attribute embeddings for generalization from seen to unseen compositions. Experiments on CZSL benchmarks, including the more challenging C-GQA dataset, demonstrate better performances compared with other state-of-the-art approaches and validate the importance of learning conditional attributes. Code‡ is available at https://github.com/wqshmzh/CANet-CZSL. + +# 1. Introduction + +Deep machine learning algorithms today can learn knowledge of concepts to recognize patterns. Can a machine compose different learned concepts to generalize to new compositions? Compositional generalization is one of the hallmarks of human intelligence [3, 18]. To make the models equipped with this ability, Compositional Zero-Shot Learning (CZSL) [25] is proposed, where the models are trained to recognize images of unseen compositions composed of seen concepts. In this work, we concentrate on the situation where each composition is composed by attribute (e.g., wet) and object (e.g., apple). For example, given im + +![](images/69262c50c4ac7806465c5b0b08c667f6aa0279201f77b98db022df5d7afb0a37.jpg) +Figure 1. The diagram of our work. We aim to learn conditional attributes conditioned on the recognized object and input image through an attribute learning framework containing an attribute hyper learner and an attribute base learner. We first recognize the object in the input image. Then, we feed prior knowledge extracted from the conditions, which are recognized object word embedding and input image visual embedding, to the attribute hyper learner. Finally, conditional attribute embeddings are produced by the attribute base learner parameterized by the attribute hyper learner. + +ages of wet apple and dry cat, a well-trained model can recognize images of new compositions dry apple and wet cat. + +Compositional Zero-Shot Learning of attribute-object compositions requires modeling attributes, objects, and the contextuality between them. Learning to model objects in CZSL is similar to conventional supervised object classification task since the model has access to all objects in CZSL task [33]. Learning to model contextuality between attribute and object is mostly addressed in the literature [23,25,26,31,39-41]. One of the main challenges of CZSL is the appearance diversity of an attribute when composed with different objects, e.g., attribute wet in wet apple and wet cat is different. This reveals that the information of each attribute is dependent on different objects. However, most + +recent works in CZSL [4,27,32,33,42,45] extract attribute representations irrelevant to the object from seen compositions to infer the unseen compositions. These approaches neglect the nature of attribute diversity and learn concrete attribute representation agnostic to different objects. + +In this paper, we learn conditional attributes rather than learning concrete ones in a proposed Conditional Attribute Network (CANet). We first conduct analysis to determine the exact conditions by considering the recognition of attribute and object as computing a classification probability of attribute and object conditioned on the input image. By decomposing this probability, we demonstrate that the probability of the input image belonging to an attribute is conditioned on the recognized object and the input image. + +We present an attribute learning framework to learn conditional attribute embeddings conditioned on the above two conditions. The framework contains an attribute hyper learner and an attribute base learner, which are sketched in Fig. 1. The attribute hyper learner learns from prior knowledge extracted from the conditions. The attribute base learner is parameterized by the attribute hyper learner and is designed to encode all attribute word embeddings into conditional attribute embeddings. With the attribute learning framework, the attribute embeddings are changed along with the recognized object and input image. Finally, the attribute matching is processed in an attribute space where the input image embedding is projected. The attribute classification logits are computed by cosine similarities between the projected input image embedding and all conditional attribute embeddings. Additionally, we model the contextuality between attribute and object as composing attribute and object word embeddings. We use cosine similarities between the projected input image embedding and all composed attribute-object embeddings to get the classification logits. + +Our main contributions are as follows: + +- We propose to learn attributes conditioned on the recognized object and input image. +- We propose an attribute learning framework containing an attribute hyper learner and an attribute base learner for learning conditional attribute embeddings. +- Experiments and ablation studies indicate the effectiveness of our proposed conditional attribute network, which further validates the importance of learning conditional attributes in the CZSL task. + +# 2. Related Work + +Compositional Zero-Shot Learning. Given descriptions only, we can recognize objects that are never seen before. In conventional Zero-Shot Learning (ZSL), models have access both to images of seen classes and descriptions of seen and unseen classes [19]. In contrast, CZSL presents no description of seen and unseen attribute-object + +compositions while all attributes and objects as concepts are seen during training. Recently, works in CZSL are divided into two main streams. One extracts attribute and object words or visual features independently from a composition during training, including learning attributes as linear transformations of objects [27], learning to hierarchically decompose compositions and recompose the concepts with learned visual concepts [41], learning independent prototypes of attributes and objects and compositing prototypes via graph network [32], and learning decomposed prototypes of visual concept features [33] via siamese contrastive embedding network [20]. The other is to learn a compositional space [23], a graph network [2, 26], an episode-based cross-attention module [39], and a contrastive space [1] for contextuality modeling. Also, Yang et al. [42] rethink the CZSL task in a decomposable causal way and learn three spaces for attribute, object, and composition classifications. Additionally, with pre-trained large vision language models like CLIP, Nayak et al. [30] propose to tune soft prompts as concept embeddings. + +Recent work in [12] addresses the problem of attribute diversity. They propose to learn translational attribute features conditionally dependent on the object prototypes. Specifically, they add generic object embedding as the object prototype to the concatenated attribute and object embedding. However, this approach makes the model concentrate more on the composition instead of the attribute, causing the attribute learning degrade to learning the contextuality between attribute and object. On the contrary, we explicitly focus on learning conditional attribute embeddings. The learned conditional attribute embeddings can be changed along with the objects and input images. + +Attribute Learning. Learning features of attributes is explored by a large community including image search [16, 34], sentence generation [17], and zero-shot classification [9, 29]. Conventional attribute learning approaches map the attributes into high-dimensional space and train a discriminative classification head without considering the diverse nature of attributes [22, 35, 37]. Our work also learns high-dimensional embeddings to represent attributes. The main difference is that our learned attribute embeddings are conditioned on different objects and input images. + +# 3. Approach + +# 3.1. Task Definition + +The task of CZSL aims to learn to classify an image $i$ into a composition $c$ composed by multiple seen concepts, where $i$ and $c$ are unseen during training. Denote sets of images, compositions, attributes, and objects as $\mathcal{I}$ , $\mathcal{C}$ , $\mathcal{A}$ , and $\mathcal{O}$ , we have $i \in \mathcal{I}$ , $c \in \mathcal{C}$ , $a \in \mathcal{A}$ , $o \in \mathcal{O}$ , and $\mathcal{C} = \mathcal{A} \times \mathcal{O}$ . During training, machines have access to seen set $\mathcal{D}_{\text{seen}} = \{(i^s, c^s) | i^s \in \mathcal{I}^s, \mathcal{I}^s \subsetneq \mathcal{I}, c \in \mathcal{C}^s, \mathcal{C}^s \subsetneq \mathcal{C}\}$ , + +![](images/68e891a309253c233f3774ac087fc178d18b2a535b0403dc8c0bc3c537a93f6b.jpg) +Figure 2. Structure of our proposed CANet. The symbol $\oplus$ is channel-wise concatenation. The mapping networks $\omega_{o},\omega_{a}$ , and $\omega_{c}$ map the input image embedding $\mathbf{x}$ into object, attribute, and composition spaces $S_{o},S_{a}$ , and $S_{c}$ . All object word embeddings $\mathbf{v}_{o}$ along with the object-mapped input image embedding are used in $S_{o}$ to compute loss $\mathcal{L}_o$ and get the recognized object $o^{*}$ . The attribute hyper learner $\mathcal{H}$ learns to parameterize the attribute base learner $\mathcal{G}$ using the prior knowledge $\beta$ extracted from the recognized object word embedding $\mathbf{v}_{o^*}$ and $\mathbf{x}$ . The conditional attribute embeddings $\mathbf{e}_a$ are encoded by $\mathcal{G}$ parameterized by $\mathcal{H}$ . Using all $\mathbf{e}_a$ along with the attribute-mapped input image embedding in space $S_{a}$ to compute loss $\mathcal{L}_a$ . Loss $\mathcal{L}_{a,o}$ is computed using all compositional word embeddings produced by composing network $\mathcal{C}$ and the composition-mapped input image embedding in space $S_{c}$ . + +attribute set $\mathcal{A}$ , and object set $\mathcal{O}$ , where $\mathcal{I}^s$ and $\mathcal{C}^s$ are sets of images and compositions seen when training. Also, evaluation of algorithms requires unseen set $\mathcal{D}_{\text{unseen}} = \{(i^u, c^u) | i^u \in \mathcal{I}^u, c^u \in \mathcal{C}^u, \mathcal{I}^u \subsetneq \mathcal{I}, \mathcal{C}^u \subsetneq \mathcal{C}\}$ used for validation and testing. In conventional ZSL, $\mathcal{I}^s \cap \mathcal{I}^u = \emptyset$ , $\mathcal{C}^s \cap \mathcal{C}^u = \emptyset$ , i.e. unseen images and compositions are not overlapped with the seen ones. Here, we follow the setting of Generalized Zero-Shot Learning (GZSL) where images in $\mathcal{I}^s$ and $\mathcal{I}^u$ and labels in $\mathcal{C}^s$ and $\mathcal{C}^u$ appear during validation and testing. GZSL is a challenging setting with larger label space and a strong bias of seen compositions to unseen ones, relaxing the less realistic assumption in conventional ZSL that test data only belongs to unseen classes. + +# 3.2. Conditional Attribute Network + +Determining Conditions. In CZSL, it is common to learn to classify attributes and objects besides compositions. We first assume that the model recognizes the input image $i$ as attribute $a^*$ and object $o^*$ . The recognizing score can be formulated as a conditional probability $P(a^*, o^* | i)$ conditioned on input image $i$ . We propose to decompose this probability to express the attribute and object recognition as a one-label classification task. According to multi-variable conditional probability formulation, we have: + +$$ +P \left(a ^ {*}, o ^ {*} \mid i\right) = P \left(a ^ {*} \mid o ^ {*}, i\right) P \left(o ^ {*} \mid i\right) \tag {1} +$$ + +where $P(o^{*}|i)$ is probability of image $i$ belonging to object $o^{*}$ and $P(a^{*}|o^{*},i)$ represents the probability of attribute $a^{*}$ + +conditioned on the joint presentation of $o^*$ and $i$ . This indicates that the recognition of an attribute is conditioned on the recognized object and input image. To better solve the attribute diversity problem, we consider the information of the recognized object and input image as conditions for conditional attribute encoding. + +Object Recognition. Object recognition requires learning to map the input image embedding into an object space. To incorporate object semantic information, we compute cosine similarities between object-mapped image embedding $\omega_{o}(\mathbf{x})$ and all object word embeddings $\mathbf{v}_{o}$ instead of directly learning a classification head: + +$$ +\left\langle \omega_ {o} (\mathbf {x}), \mathbf {v} _ {o} \right\rangle = \frac {\omega_ {o} (\mathbf {x}) ^ {\top} \mathbf {v} _ {o}}{\| \omega_ {o} (\mathbf {x}) \| _ {2} \| \mathbf {v} _ {o} \| _ {2}} \tag {2} +$$ + +where $\mathbf{x} = f(i) \in \mathcal{X}$ is the visual embedding of input image $i$ in visual space $\mathcal{X}$ extracted by image backbone $f$ (e.g., ResNet-18 [11]), $\omega_{o}$ is the mapping from $\mathcal{X}$ to object semantic space $S_{o}$ , $\mathbf{v}_{o} = \phi(o)$ , $\mathbf{v}_{o} \in S_{o}$ is object word embedding in $S_{o}$ extracted by word embedder $\phi$ (e.g., word2vec [24], FastText [7]). The recognized object $o^{*} = \underset{o \in \mathcal{O}}{\arg \max} \langle \omega_{o}(\mathbf{x}), \phi(o) \rangle$ . + +Learning Conditional Attributes. With the recognized object $o^*$ and visual embedding $\mathbf{x}$ of input image $i$ , we learn the attribute hyper learner $\mathcal{H}$ and attribute base learner $\mathcal{G}$ in the proposed attribute learning framework to extract attribute embeddings conditioned on the recognized object $o^*$ . + +and input image $i$ . We consider the information of $o^*$ and $i$ as prior knowledge for $\mathcal{H}$ . Specifically, the prior knowledge is implemented as a feature vector $\beta$ : + +$$ +\beta = \mathcal {P} \left(\operatorname {c a t} \left(\mathbf {v} _ {o ^ {*}}, \mathbf {x}\right)\right) \tag {3} +$$ + +where $\mathbf{v}_{o^*} = \phi(o^*)$ is word embedding of $o^*$ , $\mathcal{P}$ is a composing network for $\mathbf{v}_{o^*}$ and $\mathbf{x}$ , $\operatorname{cat}(\cdot)$ is channel-wise concatenation operation. With the prior knowledge, the attribute hyper learner $\mathcal{H}$ can parameterize $\mathcal{G}$ as: + +$$ +\boldsymbol {\Theta} _ {\mathcal {G}} = \mathcal {H} (\beta ; \boldsymbol {\Theta} _ {\mathcal {H}}) \tag {4} +$$ + +where $\Theta_{\mathcal{H}}$ is the set of randomly initialized parameters of $\mathcal{H}$ , $\Theta_{\mathcal{G}}$ is the set of generated parameters of $\mathcal{G}$ . In this way, the attribute embeddings $\mathbf{e}_a$ conditioned on $o^*$ and $i$ can be encoded via $\mathcal{G}$ parameterized by $\mathcal{H}$ : + +$$ +\mathbf {e} _ {a} = \mathcal {G} \left(\mathbf {v} _ {a}; \boldsymbol {\Theta} _ {\mathcal {G}}\right) \tag {5} +$$ + +where $\mathbf{v}_a = \phi(a)$ is word embedding of attribute word $a$ . + +Modeling Contextuality. Although the conditional attribute embeddings are related to the recognized object and input image, object embeddings are also supposed to be influenced by attributes. Therefore, we model the contextuality of attribute-object compositions to address the relationships between them. We follow the work of Mancini et al. [23] in their closed world setting that contextuality is modeled as the mixture of attribute and object word embeddings to extract attribute-object compositional embeddings: + +$$ +\mathbf {v} _ {a, o} = \mathcal {C} (\operatorname {c a t} \left(\mathbf {v} _ {a}, \mathbf {v} _ {o}\right)) \tag {6} +$$ + +where $\mathcal{C}$ is a composing network for $\mathbf{v}_a$ and $\mathbf{v}_o$ . + +The entire structure of our model is shown in Fig. 2. + +# 3.3. Training Objectives + +Similar to object recognition, attribute or composition recognition is also implemented by computing cosine similarities $\langle \omega_{a}(\mathbf{x}),\mathbf{v}_{a}\rangle$ or $\langle \omega_c(\mathbf{x}),\mathbf{v}_{a,o}\rangle$ between attribute-mapped or composition-mapped image embeddings, i.e., $\omega_{a}(\mathbf{x})$ or $\omega_{c}(\mathbf{x})$ , and attribute word embeddings or attribute-object compositional embeddings, i.e., $\mathbf{v}_a$ or $\mathbf{v}_{a,o}$ : + +$$ +\left\langle \omega_ {a} (\mathbf {x}), \mathbf {e} _ {a} \right\rangle = \frac {\omega_ {a} (\mathbf {x}) ^ {\top} \mathbf {e} _ {a}}{\| \omega_ {a} (\mathbf {x}) \| _ {2} \| \mathbf {e} _ {a} \| _ {2}} \tag {7} +$$ + +$$ +\left\langle \omega_ {c} (\mathbf {x}), \mathbf {v} _ {a, o} \right\rangle = \frac {\omega_ {c} (\mathbf {x}) ^ {\top} \mathbf {v} _ {a , o}}{\| \omega_ {c} (\mathbf {x}) \| _ {2} \| \mathbf {v} _ {a , o} \| _ {2}} \tag {8} +$$ + +The recognition probability $P(o^{*}|i)$ , $P(a^{*}|o^{*},i)$ , and $P(c^{*}|i)$ are normalized cosine similarities, where $P(c^{*}|i)$ is the probability of input image $i$ belonging to the recognized attribute-object composition $c^{*}$ . As shown in Fig. 2, our model learns three embedding spaces: attribute space $S_{a}$ , object space $S_{o}$ , and attribute-object compositional space $S_{c}$ . Therefore, we incorporate three separate cross-entropy losses to maximize the three recognition probabilities to make the model optimized in these three spaces. The losses are as follows: + +$$ +\mathcal {L} _ {a} = - \sum_ {a \in \mathcal {A}} \log \frac {\exp \left(\left\langle \omega_ {a} (\mathbf {x}), \mathbf {e} _ {a} \right\rangle / \tau\right)}{\sum_ {a ^ {\prime} \in \mathcal {A}} \exp \left(\left\langle \omega_ {a} (\mathbf {x}), \mathbf {e} _ {a ^ {\prime}} \right\rangle / \tau\right)} \tag {9} +$$ + +$$ +\mathcal {L} _ {o} = - \sum_ {o \in \mathcal {O}} \log \frac {\exp \left(\left\langle \omega_ {o} (\mathbf {x}) , \mathbf {v} _ {o} \right\rangle / \tau\right)}{\sum_ {o ^ {\prime} \in \mathcal {O}} \exp \left(\left\langle \omega_ {o} (\mathbf {x}) , \mathbf {v} _ {o} ^ {\prime} \right\rangle / \tau\right)} \tag {10} +$$ + +Also, for composition recognition, we have: + +$$ +\mathcal {L} _ {a, o} = - \sum_ {(a, o) \in \mathcal {C}} \log \frac {\exp \left(\left\langle \omega_ {c} (\mathbf {x}), \mathbf {v} _ {a , o} \right\rangle / \tau\right)}{\sum_ {\left(a ^ {\prime} , o ^ {\prime}\right) \in \mathcal {C}} \exp \left(\left\langle \omega_ {c} (\mathbf {x}), \mathbf {v} _ {a ^ {\prime} , o ^ {\prime}} \right\rangle / \tau\right)} \tag {11} +$$ + +where $\tau$ is temperature factor [46]. Finally, the training loss as a whole linearly combines the three losses above: + +$$ +\mathcal {L} = \frac {\mathcal {L} _ {a} + \mathcal {L} _ {o}}{2} + \mathcal {L} _ {a, o} \tag {12} +$$ + +# 3.4. Inference + +During validation and testing, we incorporate a linear normalization function $g$ for cosine similarities: + +$$ +g (d) = (1 + d) * 0. 5 \tag {13} +$$ + +Then, we have $P(a|o^{*},i) = g(\langle \omega_{a}(\mathbf{x}),\mathbf{e}_{a}\rangle),P(o|i) = g(\langle \omega_{o}(\mathbf{x}),\mathbf{v}_{o}\rangle)$ , and $P(c|i) = g(\langle \omega_c(\mathbf{x}),\mathbf{v}_{a,o}\rangle)$ . The inference rule is parameterized as: + +$$ +s = (1 - \alpha) P (c | i) + \alpha P (a | o ^ {*}, i) P (o | i) \tag {14} +$$ + +where $\alpha$ is the weight factor controlling balance. + +# 4. Experiments + +In this section, experiments are conducted following the concrete introductions of datasets, metrics, implementation details, and baselines. Then, we report ablation results to demonstrate the effectiveness of our model. + +# 4.1. Experimental Setup + +Datasets We conduct experiments with three widely adopted datasets in the CZSL task, which are MIT-States [14], UT-Zappos50K [43, 44], and C-GQA [26]. MIT-States contains 53753 crawled web images labeled with 1962 attribute-object (e.g., mossy highway) compositions. This dataset has 30338, 10420, and 12995 training, validation, and testing images [31] labeled with 1262, 600, and 800 compositions. In validation and test sets, the numbers of seen and unseen compositions are the same. All compositions are composed of 115 attributes and 245 objects. UT-Zappos50K is made up of 50025 images labeled with 116 fine-grained shoe classes composed of 16 attributes (e.g., rubber) and 12 objects (e.g., sneaker). This dataset has 22998, 3214, and 2914 training, validation, and testing images [31] labeled with 83, 30, and 36 compositions. Also, numbers of seen and unseen compositions in validation and test sets share the same quantity. C-GQA is created based on Stanford GQA dataset [13] used for VQA task. C-GQA contains 39298 images labeled with over $9.5\mathrm{k}$ compositions composed of 453 attributes and 870 objects. This dataset has 26920, 7280, and 5098 training, validation, and testing images labeled with 6963, 2541, and 2069 compositions. Detailed splits are presented in Tab. 1. + +
DatasetTrainingValidationTest
AOCsICsCuICsCuI
UT-Zappos50K [43,44]161283229981515321418182914
MIT-States [14]1152451262303383003001042040040012995
C-GQA [26]453870696326920117313687280102210475098
+ +Table 1. Detailed dataset splits of UT-Zappos50K, MIT-States, and C-GQA in training, validation, and test sets. + +Metrics To demonstrate the advances in attribute learning, we report the attribute and object classification accuracies (best attr and best obj). The setting of GZSL requires both seen and unseen compositions to exist during validation and testing. As a result, there is an inherent bias of seen against unseen compositions. We follow the evaluation protocols proposed in [8] where a scalar bias is added to final activations of classes of seen compositions to calibrate the model. As the scalar varies from negative infinity to positive infinity, there must be a best operating point at which the bias between seen and unseen compositions is the lowest. We report the results in terms of the best accuracies of seen images (best seen), unseen images (best unseen), best Harmonic Mean (best HM), and Area Under Curve (AUC) with different scalar biases. + +Implementations We consider image backbone $f$ as ResNet-18 pre-trained on ImageNet [10] to extract 512 dimension vectors following preceding works. The mapping networks $\omega_{a}$ , $\omega_{o}$ , and $\omega_{c}$ share the similar structure of two Fully Connected (FC) layers with ReLU [28], LayerNorm [5], and Dropout [36] following the first FC layer. We adopt word embedder $\phi$ as 600-dimensional word2vec+FastText for MIT-States, 300-dimensional FastText for UT-Zappos50K, and word2vec for C-GQA. The layer structures of $\mathcal{G}$ , $\mathcal{P}$ , and $\mathcal{C}$ are the same as the mapping networks, where ReLU is added in $\mathcal{P}$ and $\mathcal{C}$ to the last FC layer. Weight generation for the attribute base learner $\mathcal{G}$ through the attribute hyper learner $\mathcal{H}$ requires more parameters and makes learning difficult, as noted by Bertinetto et al. [6]. Therefore, we adopt weight factorization in [38] to reduce parameters for the attribute hyper learner $\mathcal{H}$ , that is + +$$ +\mathbf {e} _ {a} ^ {(i)} = \left(\mathbf {v} _ {a} \mathbf {W} _ {\mathcal {G}} ^ {(i)} + \mathbf {b} _ {\mathcal {G}} ^ {(i)}\right) \odot \boldsymbol {\lambda} _ {\mathcal {G}} ^ {(i)} \tag {15} +$$ + +$$ +\boldsymbol {\lambda} _ {\mathcal {G}} ^ {(i)} = \mathcal {H} (\beta ; \boldsymbol {\Theta} _ {\mathcal {H}} ^ {(i)}) \tag {16} +$$ + +where $(i)$ indicates $i$ th FC layer, $\mathbf{W}_{\mathcal{G}}^{(i)}$ and $\mathbf{b}_{\mathcal{G}}^{(i)}$ are the weight matrix and bias vector of $i$ th FC layer in $\mathcal{G}$ , $\{\mathbf{W}_{\mathcal{G}}^{(i)}, \mathbf{b}_{\mathcal{G}}^{(i)}\} \subset \Theta_{\mathcal{G}}, \Theta_{\mathcal{H}}^{(i)} \subset \Theta_{\mathcal{H}}$ , and $\odot$ denotes elementwise multiplication. During training, we fix the image backbone $f$ and train other modules using Adam [15] optimizer and an Nvidia GeForce GTX 1080Ti GPU with a learning rate and weight decay of 0.00005. The batch size is 256. The temperature factor $\tau$ , weight factor $\alpha$ , and the maximum number of epochs are set to 0.02, 0.4, and 500 for UT-Zappos50K; 0.05, 0.2, and 800 for MIT-States; and 0.05, 0.4, and 1000 for C-GQA. + +Baselines We conduct experiments with the following algorithms: 1) AttrAsOp [27] treats attributes as linear transformations on object vectors instead of data points in some high-dimensional space and optimizes the transformations through several regularizers in the loss function. 2) TMN [31] constructs task-driven modular networks in semantic space configured through a gating function conditioned on the task. 3) SymNet [21] proposes symmetry property in attribute-object compositions and group axioms as objectives in an end-to-end manner. 4) $CGE_{\mathrm{ff}}$ [26] exploits dependencies between attributes, objects, and compositions through an end-to-end graph formulation where "ff" means fixed image feature backbone. 5) CompCos [23] learns a mapping from image features to semantic space of compositions and computes cosine similarities between them. 6) DeCa [42] rethinks the CZSL task in a decomposable causal perspective and learns three independent mappings from image feature space to attribute, object, and composition semantic space. Cosine similarities are also adopted. 7) SCN [20] computes visual prototypes of attributes and objects in a siamese contrastive space and proposes a designed State Transition Module to increase the diversity of training compositions. + +# 4.2. Quantitative Analysis + +All results are computed on test sets of all datasets and from their published papers and [26] for a fair comparison. We report quantitative results with the best AUC in Tab. 2. + +From Tab.2, our model outperforms other state-of-the-art algorithms in terms of best attr, best unseen, and AUC in all three datasets including the recently proposed C-GQA, indicating the better attribute learning performance and generalization ability from seen to unseen compositions. Specifically, our model performs much better on C-GQA with more state-of-the-art results although it is a much more challenging dataset than MIT-States and UT-Zappos50K. + +For UT-Zappos50K, the observations are that our model boosts attribute recognition accuracy, unseen image classification accuracy, and AUC from $47.3\%$ , $63.1\%$ , and $32.0\%$ of SCEN to the new state-of-the-art of $48.4\%$ , $66.3\%$ , and $33.1\%$ with $1.1\%$ , $3.2\%$ , and $1.1\%$ improvement respectively. For MIT-States, our model achieves $30.2\%$ , $32.6\%$ , $26.2\%$ , and $5.4\%$ accuracies for attribute and object classification, unseen image classification, and AUC on the test + +
AlgorithmUT-Zappos50KMIT-StatesC-GQA
NameVenueAtt.Obj.S.U.HMAUCAtt.Obj.S.U.HMAUCAtt.Obj.S.U.HMAUC
AttrAsOp [27]ECCV'1838.969.659.854.240.825.921.123.614.317.49.91.68.312.511.83.92.90.3
TMN [31]ICCV'1940.869.958.760.045.029.323.326.520.220.113.02.99.720.521.66.37.71.1
SymNet [21]CVPR'2041.368.649.857.440.423.426.328.324.425.216.13.015.023.127.010.810.92.2
CGEff [26]CVPR'2145.073.956.863.641.226.427.932.028.725.317.25.112.726.927.511.711.92.5
CompCos [23]CVPR'2144.773.559.862.543.528.727.931.825.324.616.44.5------
DeCa [42]TMM'22--62.763.146.331.6--29.825.218.25.3------
SCEN [20]CVPR'2247.375.663.563.147.832.028.232.229.925.218.45.313.627.928.912.112.42.9
Ours48.472.661.066.347.333.130.232.629.026.217.95.417.522.330.013.214.53.3
+ +Table 2. Quantitative results on test sets of all datasets with the state-of-the-art in terms of best attr (Att.), best obj (Obj.), best seen (S.), best unseen (U.), best HM (HM), and AUC. + +set, providing $2.0\%$ , $0.4\%$ , $1.0\%$ , and $0.1\%$ improvements on the recently proposed SCEN as the new state-of-the-art results. This indicates that the proposed conditional attribute network can truly improve the attribute recognition performance and consequently the unseen image classification and AUC. + +For the more challenging dataset C-GQA, since it is significantly harder than MIT-States and UT-Zappos50K with $5.5 \times$ and $0.9 \times$ composition labels and images in the training set compared with MIT-States, our model outperforms all other algorithms except best obj with $3.9\%$ , $1.1\%$ , $1.1\%$ , $2.1\%$ , and $0.4\%$ boosting in terms of best attr, best seen, best unseen, best HM, and AUC in the testing set. This indicates that the proposed conditional attribute network makes a critical contribution when facing a more challenging dataset even if the object recognition accuracy is lower. + +We give an analysis of the importance that attributes should be conditioned on objects. First, note that although DeCa also learns attribute, object, and composition spaces separately, it learns attributes as static embeddings independent from objects, causing lower best unseen and AUC on UT-Zappos50K and MIT-States compared with ours in Tab. 2. Next, different baselines incorporate different techniques to handle the CZSL task though, they learn static attribute embeddings too, producing lower best attr, best unseen, and AUC. Then, the proposed method performs much better on C-GQA compared with other baselines. All the above phenomena demonstrate that attributes should be conditioned on objects and performance on datasets with larger label space can gain more boosts in this way. + +From the results of the three datasets above, we observe an interesting phenomenon. Although the results of best obj in three datasets are all lower than that of SCEN, results of best unseen are all higher accompanied by higher results of best attr. We speculate the reason is that some objects have more attributes (or are more dominated) in unseen compositions and the misclassified objects recognized + +by our model are less dominated (i.e. have few attributes or are long-tailed in terms of attribute). As a result, with the correctly predicted objects dominated in unseen compositions, the more correctly classified attributes, the higher the results of best unseen. + +# 4.3. Qualitative Analysis + +In this section, we present some qualitative results of novel compositions with top-3 predictions on UT-Zappos50K, MIT-States, and C-GQA in Fig. 3. We show results for each dataset in each row. Images whose top prediction matches the label are shown in the first three columns and the rest columns show wrong results. For UT-Zappos50K, the remaining two answers of all images can match at least one label factor. For some instances in MIT-States, we can notice that the top and second predictions can both describe the image. For example, for the image labeled with winding stream, there is sunlight reflecting from the stream and creek is the synonym of stream. Therefore, sunny creek can also be the label of the image. Another example is that image labeled with wide valley also present cloudy cloud in the blue sky located in the upper part. As a result, the model has difficulty deciding what to predict. This reflects that labels in MIT-States are heavy in noise. For C-GQA where labels are clear, our model can produce more answers that match the label factors in the remaining two predictions, which indicates the better performance and robustness of our model. + +Additionally, we present wrong predictions in the last two columns. It can be noticed that our model can predict correct answers in most top-3 predictions. As for the image of MIT-States labeled as broken bottle, our model predicts the attribute as small because it is difficult to focus on a certain attribute of the bottle since the bottle in this image is both small and broken. Besides, images in the training set are limited in the status of objects. For example, training images of sheep hardly present the action of laying down + +
VariantUT-Zappos50KC-GQA
#NameAtt.Obj.S.U.HMAUCAtt.Obj.S.U.HMAUC
(1)w/o L_a + L_o46.174.361.564.746.131.710.830.629.812.813.43.0
(2)w/o L_c41.960.759.554.745.728.314.817.128.111.212.42.6
(3)w/o G + H + P47.074.059.965.846.331.714.827.829.913.114.63.1
(4)w/o P46.773.260.764.547.531.614.526.430.113.014.53.1
(5)w/o H46.270.358.562.746.330.513.925.829.111.212.52.4
(6)w/o x for H45.671.361.662.844.830.113.420.830.212.713.92.9
(7)Full48.472.661.066.347.333.117.522.330.013.214.53.3
+ +Table 3. Ablation results on test sets in terms of best attr (Att.), best obj (Obj.), best seen (S.), best unseen (U.), best HM (HM), and AUC. + +![](images/bf70401301edb7578a26bec565f6b220fee8b211a66ef07939ab6a0cd1040436.jpg) +Figure 3. Qualitative Results. We demonstrate top-3 predictions of some instances using our proposed model. + +causing our model mistakenly classify the sheep in the image labeled as light sheep into elephant. Thus, with the recognized object elephant, the model can only focus on attributes conditioned on elephant and find the appropriate attribute that matches the image. + +# 4.4. Ablation Study + +In this section, we ablate the proposed model to evaluate the performance of each module. The ablation study is conducted on test sets of UT-Zappos50K, C-GQA. To achieve more convincing ablation results, we do not choose MIT-States because images in MIT-States are labeled using automatic search. As a result, the noise of labels is too heavy to be used for evaluations, as is pointed out by Atzmon et.al. [4]. Ablation results are reported in Tab. 3. The detailed ablation process is as follows: + +We first study the effects of recognizing compositions only and recognizing attributes and objects without compositions, which are corresponded to variants (1) and (2) in Tab. 3, and report results in terms of six metrics used in Tab. 2. Compared with variant (6), the results of each variant mostly decline, indicating the importance of recognizing attributes, objects, and compositions jointly. As to the results of Obj. in UT-Zappos50K and C-GQA from variants + +(1) and (6), we can observe that those object classification accuracies decline. This is mainly because when recognizing objects individually each object presents visual diversity caused by different attributes, e.g., sliced apple is different from apple in visual appearance since a sliced apple is sliced into multiple pieces. However, this phenomenon does not affect other results, especially for the dataset with larger label space, e.g., C-GQA. + +Next, with attributes, objects, and compositions being recognized, we ablate $\mathcal{G} + \mathcal{H} + \mathcal{P}$ (where attribute word embeddings are directly used in $S_{a}$ ), $\mathcal{H}$ (where the concatenation of $\beta$ and $\mathbf{v}_a$ is fed to $\mathcal{G}$ ), $\mathcal{P}$ (where the concatenation of $\mathbf{v}_{o^*}$ and $\mathbf{x}$ is directly fed to $\mathcal{H}$ ), and $\mathbf{x}$ in $\beta$ that is fed to $\mathcal{H}$ , which are corresponded to variants (3)-(6) in Tab. 3. Note that if $\mathcal{P}$ is presented then $\mathcal{G}$ is required to be presented also because the concatenation of $\beta$ and $\mathbf{v}_a$ requires changing the number of dimensions to that of $\mathbf{x}$ through $\mathcal{G}$ . Also, $\mathcal{G}$ can not be ablated only otherwise the model changes to variant (3). Compared to variant (7), all results are mostly declined, indicating that optimizing the model with $\mathcal{G}$ , $\mathcal{H}$ , $\mathcal{P}$ , and $\mathbf{x}$ is essential. As for variant (5), it performs worse on seen and unseen images compared with variant (4), indicating the importance of using the attribute hyper learner. Comparing results of variants (5) with (6), we observe that + +![](images/6dc1096afc1924895fd146605ee1180b4c2e7330c74e9be8c0743040ebe049c6.jpg) + +![](images/2e2087136a868572667efafb1833479fd344d62fa00301798e16c29cb245f808.jpg) + +![](images/b927075be46c20eb35a24fb5a79e03a953902c49ceba1d492d331530162941ad.jpg) + +![](images/ce7c3b094c98fb9e9e380289233ed066ef12d07ac5a34b6ea56d0e947325a5c6.jpg) +Figure 4. Influence of weighting factor $\alpha$ on AUC, seen accuracy, and unseen accuracy. + +![](images/d092a4294e42482f5a6987c4a906fd2100f835417fc42d74d361f749af9c33b5.jpg) + +![](images/47f179b52754c14b8b7b2b6c861761344dcbae469df4a7064525551e6c798108.jpg) + +adding the attribute hyper learner $\mathcal{H}$ for $\mathcal{G}$ without image visual embedding $\mathbf{x}$ marginally increases overfitting to seen images. Results of variant (6) present the best generalization compared with variants (3)-(5) because adding $\mathbf{x}$ in $\beta$ for $\mathcal{H}$ provides diverse instances that are seen for $\mathcal{H}$ during training since the number of image visual embeddings is far more than the number of object word embeddings. + +Lastly, we conduct experiments to study the impact of weighting factor $\alpha$ in Eq. (14) on all datasets. In detail, we present results of AUC, seen accuracy, and unseen accuracy in Fig. 4 with $\alpha \in [0,1]$ with an interval of 0.1. It can be observed that all results of AUC increase first and then decrease with $\alpha$ increases from 0.0. The peaks of AUC are reached when $\alpha$ equals 0.5, 0.1, and 0.3 in UT-Zappos50K, MIT-States, and C-GQA. This phenomenon reveals that learning to classify attributes, objects, and compositions all contribute to making our model reach optimal. Additionally, it can be noticed that the results of AUC are all generally declined when $\alpha$ changes from 0.0 to 1.0. This is because attribute-object compositions involve not only the side information of attribute and object, but also the contextuality between attribute and object. As for the results of seen and unseen accuracies reported in the second row, the same trend can be observed. Specifically, results of unseen accuracy are more sensitive than seen accuracy and also have peaks with various $\alpha$ , indicating that $\alpha$ also has an impact on the generalization ability of our model. In conclusion, using a small weighting factor $\alpha$ is always better than using a larger one, indicating that modeling contextuality between attribute and object is a bit more beneficial to the CZSL task than separately classifying attributes and objects. + +# 5. Conclusion + +In this work, we address the attribute diversity problem in Compositional Zero-Shot Learning. As a solution, we propose a Conditional Attribute Network (CANet) to learn attributes conditioned on the recognized object and input image. We first decompose the probability of attribute and object recognition conditioned on the input image to lay a foundation for learning conditional attributes. Then, we build an attribute learning framework to encode conditional attribute embeddings. Experiments show that our model outperforms recent CZSL approaches and achieves new state-of-the-art results. Despite the better attribute recognition performance, a limitation is that our model is less qualified to handle object long-tailed distribution in terms of attribute mentioned in Sec. 4.2. Future works can be focused on solving the problem above while learning conditional attributes. + +# 6. Acknowledgements + +This work was supported by National Key R&D Program of China (No.2020AAA0106900), the National Natural Science Foundation of China (No.U19B2037), Shaanxi Provincial Key R&D Program (No.2021KWZ-03), and Natural Science Basic Research Program of Shaanxi (No.2021JCW-03). + +# References + +[1] Muhammad Umer Anwaar, Rayyan Ahmad Khan, Zhihui Pan, and Martin Kleinsteuber. A contrastive learning approach for compositional zero-shot learning. In Proceedings of the 2021 International Conference on Multimodal Interaction, pages 34-42, 2021. 2 +[2] Muhammad Umer Anhaar, Zhihui Pan, and Martin Kleinsteuber. 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One of the challenges is to model attributes interacted with different objects, e.g., the attribute \"wet\" in \"wet apple\" and \"wet cat\" is different. As a solution, we provide analysis and argue that attributes are conditioned on the recognized object and input image and explore learning conditional attribute embeddings by a proposed attribute learning framework containing an attribute hyper learner and an attribute base learner. By encoding conditional attributes, our model enables to generate flexible attribute embeddings for generalization from seen to unseen compositions. Experiments on CZSL benchmarks, including the more challenging C-GQA dataset, demonstrate better performances compared with other state-of-the-art approaches and validate the importance of learning conditional attributes. Code‡ is available at https://github.com/wqshmzh/CANet-CZSL." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 520, + 127, + 532 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 520, + 127, + 532 + ], + "spans": [ + { + "bbox": [ + 47, + 520, + 127, + 532 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 540, + 287, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 540, + 287, + 673 + ], + "spans": [ + { + "bbox": [ + 46, + 540, + 287, + 673 + ], + "type": "text", + "content": "Deep machine learning algorithms today can learn knowledge of concepts to recognize patterns. Can a machine compose different learned concepts to generalize to new compositions? Compositional generalization is one of the hallmarks of human intelligence [3, 18]. To make the models equipped with this ability, Compositional Zero-Shot Learning (CZSL) [25] is proposed, where the models are trained to recognize images of unseen compositions composed of seen concepts. In this work, we concentrate on the situation where each composition is composed by attribute (e.g., wet) and object (e.g., apple). For example, given im" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 307, + 239, + 538, + 415 + ], + "blocks": [ + { + "bbox": [ + 307, + 239, + 538, + 415 + ], + "lines": [ + { + "bbox": [ + 307, + 239, + 538, + 415 + ], + "spans": [ + { + "bbox": [ + 307, + 239, + 538, + 415 + ], + "type": "image", + "image_path": "69262c50c4ac7806465c5b0b08c667f6aa0279201f77b98db022df5d7afb0a37.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 425, + 545, + 525 + ], + "lines": [ + { + "bbox": [ + 304, + 425, + 545, + 525 + ], + "spans": [ + { + "bbox": [ + 304, + 425, + 545, + 525 + ], + "type": "text", + "content": "Figure 1. The diagram of our work. We aim to learn conditional attributes conditioned on the recognized object and input image through an attribute learning framework containing an attribute hyper learner and an attribute base learner. We first recognize the object in the input image. Then, we feed prior knowledge extracted from the conditions, which are recognized object word embedding and input image visual embedding, to the attribute hyper learner. Finally, conditional attribute embeddings are produced by the attribute base learner parameterized by the attribute hyper learner." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 542, + 545, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 542, + 545, + 567 + ], + "spans": [ + { + "bbox": [ + 304, + 542, + 545, + 567 + ], + "type": "text", + "content": "ages of wet apple and dry cat, a well-trained model can recognize images of new compositions dry apple and wet cat." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "text", + "content": "Compositional Zero-Shot Learning of attribute-object compositions requires modeling attributes, objects, and the contextuality between them. Learning to model objects in CZSL is similar to conventional supervised object classification task since the model has access to all objects in CZSL task [33]. Learning to model contextuality between attribute and object is mostly addressed in the literature [23,25,26,31,39-41]. One of the main challenges of CZSL is the appearance diversity of an attribute when composed with different objects, e.g., attribute wet in wet apple and wet cat is different. This reveals that the information of each attribute is dependent on different objects. However, most" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 57, + 683, + 186, + 693 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 683, + 186, + 693 + ], + "spans": [ + { + "bbox": [ + 57, + 683, + 186, + 693 + ], + "type": "text", + "content": "*E-mail: wqshmzh@mail.nwpu.edu.cn" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 59, + 693, + 247, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 693, + 247, + 703 + ], + "spans": [ + { + "bbox": [ + 59, + 693, + 247, + 703 + ], + "type": "text", + "content": "†Corresponding author. E-mail: peng.wang@nwpu.edu.cn" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 59, + 703, + 258, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 703, + 258, + 712 + ], + "spans": [ + { + "bbox": [ + 59, + 703, + 258, + 712 + ], + "type": "text", + "content": "‡Gitee: https://gitee.com/wqshmzh/canet-czsl" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11197" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "text", + "content": "recent works in CZSL [4,27,32,33,42,45] extract attribute representations irrelevant to the object from seen compositions to infer the unseen compositions. These approaches neglect the nature of attribute diversity and learn concrete attribute representation agnostic to different objects." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 133, + 286, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 133, + 286, + 240 + ], + "spans": [ + { + "bbox": [ + 46, + 133, + 286, + 240 + ], + "type": "text", + "content": "In this paper, we learn conditional attributes rather than learning concrete ones in a proposed Conditional Attribute Network (CANet). We first conduct analysis to determine the exact conditions by considering the recognition of attribute and object as computing a classification probability of attribute and object conditioned on the input image. By decomposing this probability, we demonstrate that the probability of the input image belonging to an attribute is conditioned on the recognized object and the input image." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 240, + 286, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 240, + 286, + 491 + ], + "spans": [ + { + "bbox": [ + 46, + 240, + 286, + 491 + ], + "type": "text", + "content": "We present an attribute learning framework to learn conditional attribute embeddings conditioned on the above two conditions. The framework contains an attribute hyper learner and an attribute base learner, which are sketched in Fig. 1. The attribute hyper learner learns from prior knowledge extracted from the conditions. The attribute base learner is parameterized by the attribute hyper learner and is designed to encode all attribute word embeddings into conditional attribute embeddings. With the attribute learning framework, the attribute embeddings are changed along with the recognized object and input image. Finally, the attribute matching is processed in an attribute space where the input image embedding is projected. The attribute classification logits are computed by cosine similarities between the projected input image embedding and all conditional attribute embeddings. Additionally, we model the contextuality between attribute and object as composing attribute and object word embeddings. We use cosine similarities between the projected input image embedding and all composed attribute-object embeddings to get the classification logits." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 59, + 491, + 215, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 491, + 215, + 502 + ], + "spans": [ + { + "bbox": [ + 59, + 491, + 215, + 502 + ], + "type": "text", + "content": "Our main contributions are as follows:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 58, + 503, + 286, + 609 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 58, + 503, + 286, + 526 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 503, + 286, + 526 + ], + "spans": [ + { + "bbox": [ + 58, + 503, + 286, + 526 + ], + "type": "text", + "content": "- We propose to learn attributes conditioned on the recognized object and input image." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 58, + 527, + 286, + 561 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 527, + 286, + 561 + ], + "spans": [ + { + "bbox": [ + 58, + 527, + 286, + 561 + ], + "type": "text", + "content": "- We propose an attribute learning framework containing an attribute hyper learner and an attribute base learner for learning conditional attribute embeddings." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 58, + 563, + 286, + 609 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 563, + 286, + 609 + ], + "spans": [ + { + "bbox": [ + 58, + 563, + 286, + 609 + ], + "type": "text", + "content": "- Experiments and ablation studies indicate the effectiveness of our proposed conditional attribute network, which further validates the importance of learning conditional attributes in the CZSL task." + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 621, + 133, + 633 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 621, + 133, + 633 + ], + "spans": [ + { + "bbox": [ + 47, + 621, + 133, + 633 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 641, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 286, + 713 + ], + "type": "text", + "content": "Compositional Zero-Shot Learning. Given descriptions only, we can recognize objects that are never seen before. In conventional Zero-Shot Learning (ZSL), models have access both to images of seen classes and descriptions of seen and unseen classes [19]. In contrast, CZSL presents no description of seen and unseen attribute-object" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 72, + 545, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 312 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 312 + ], + "type": "text", + "content": "compositions while all attributes and objects as concepts are seen during training. Recently, works in CZSL are divided into two main streams. One extracts attribute and object words or visual features independently from a composition during training, including learning attributes as linear transformations of objects [27], learning to hierarchically decompose compositions and recompose the concepts with learned visual concepts [41], learning independent prototypes of attributes and objects and compositing prototypes via graph network [32], and learning decomposed prototypes of visual concept features [33] via siamese contrastive embedding network [20]. The other is to learn a compositional space [23], a graph network [2, 26], an episode-based cross-attention module [39], and a contrastive space [1] for contextuality modeling. Also, Yang et al. [42] rethink the CZSL task in a decomposable causal way and learn three spaces for attribute, object, and composition classifications. Additionally, with pre-trained large vision language models like CLIP, Nayak et al. [30] propose to tune soft prompts as concept embeddings." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 312, + 545, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 312, + 545, + 456 + ], + "spans": [ + { + "bbox": [ + 304, + 312, + 545, + 456 + ], + "type": "text", + "content": "Recent work in [12] addresses the problem of attribute diversity. They propose to learn translational attribute features conditionally dependent on the object prototypes. Specifically, they add generic object embedding as the object prototype to the concatenated attribute and object embedding. However, this approach makes the model concentrate more on the composition instead of the attribute, causing the attribute learning degrade to learning the contextuality between attribute and object. On the contrary, we explicitly focus on learning conditional attribute embeddings. The learned conditional attribute embeddings can be changed along with the objects and input images." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 456, + 545, + 577 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 456, + 545, + 577 + ], + "spans": [ + { + "bbox": [ + 304, + 456, + 545, + 577 + ], + "type": "text", + "content": "Attribute Learning. Learning features of attributes is explored by a large community including image search [16, 34], sentence generation [17], and zero-shot classification [9, 29]. Conventional attribute learning approaches map the attributes into high-dimensional space and train a discriminative classification head without considering the diverse nature of attributes [22, 35, 37]. Our work also learns high-dimensional embeddings to represent attributes. The main difference is that our learned attribute embeddings are conditioned on different objects and input images." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 590, + 372, + 604 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 590, + 372, + 604 + ], + "spans": [ + { + "bbox": [ + 306, + 590, + 372, + 604 + ], + "type": "text", + "content": "3. Approach" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 609, + 400, + 621 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 609, + 400, + 621 + ], + "spans": [ + { + "bbox": [ + 306, + 609, + 400, + 621 + ], + "type": "text", + "content": "3.1. 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Structure of our proposed CANet. The symbol " + }, + { + "bbox": [ + 46, + 297, + 545, + 373 + ], + "type": "inline_equation", + "content": "\\oplus" + }, + { + "bbox": [ + 46, + 297, + 545, + 373 + ], + "type": "text", + "content": " is channel-wise concatenation. 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Loss " + }, + { + "bbox": [ + 46, + 297, + 545, + 373 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{a,o}" + }, + { + "bbox": [ + 46, + 297, + 545, + 373 + ], + "type": "text", + "content": " is computed using all compositional word embeddings produced by composing network " + }, + { + "bbox": [ + 46, + 297, + 545, + 373 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 46, + 297, + 545, + 373 + ], + "type": "text", + "content": " and the composition-mapped input image embedding in space " + }, + { + "bbox": [ + 46, + 297, + 545, + 373 + ], + "type": "inline_equation", + "content": "S_{c}" + }, + { + "bbox": [ + 46, + 297, + 545, + 373 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 385, + 287, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 385, + 287, + 540 + ], + "spans": [ + { + "bbox": [ + 46, + 385, + 287, + 540 + ], + "type": "text", + "content": "attribute set " + }, + { + "bbox": [ + 46, + 385, + 287, + 540 + ], + "type": "inline_equation", + "content": "\\mathcal{A}" + }, + { + "bbox": [ + 46, + 385, + 287, + 540 + ], + "type": "text", + "content": ", and object set " + }, + { + "bbox": [ + 46, + 385, + 287, + 540 + ], + "type": "inline_equation", + "content": "\\mathcal{O}" + }, + { + "bbox": [ + 46, + 385, + 287, + 540 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 385, + 287, + 540 + ], + "type": "inline_equation", + "content": "\\mathcal{I}^s" + }, + { + "bbox": [ + 46, + 385, + 287, + 540 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 385, + 287, + 540 + ], + "type": "inline_equation", + "content": "\\mathcal{C}^s" + }, + { + "bbox": [ + 46, + 385, + 287, + 540 + ], + "type": "text", + "content": " are sets of images and compositions seen when training. Also, evaluation of algorithms requires unseen set " + }, + { + "bbox": [ + 46, + 385, + 287, + 540 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\text{unseen}} = \\{(i^u, c^u) | i^u \\in \\mathcal{I}^u, c^u \\in \\mathcal{C}^u, \\mathcal{I}^u \\subsetneq \\mathcal{I}, \\mathcal{C}^u \\subsetneq \\mathcal{C}\\}" + }, + { + "bbox": [ + 46, + 385, + 287, + 540 + ], + "type": "text", + "content": " used for validation and testing. In conventional ZSL, " + }, + { + "bbox": [ + 46, + 385, + 287, + 540 + ], + "type": "inline_equation", + "content": "\\mathcal{I}^s \\cap \\mathcal{I}^u = \\emptyset" + }, + { + "bbox": [ + 46, + 385, + 287, + 540 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 385, + 287, + 540 + ], + "type": "inline_equation", + "content": "\\mathcal{C}^s \\cap \\mathcal{C}^u = \\emptyset" + }, + { + "bbox": [ + 46, + 385, + 287, + 540 + ], + "type": "text", + "content": ", i.e. unseen images and compositions are not overlapped with the seen ones. Here, we follow the setting of Generalized Zero-Shot Learning (GZSL) where images in " + }, + { + "bbox": [ + 46, + 385, + 287, + 540 + ], + "type": "inline_equation", + "content": "\\mathcal{I}^s" + }, + { + "bbox": [ + 46, + 385, + 287, + 540 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 385, + 287, + 540 + ], + "type": "inline_equation", + "content": "\\mathcal{I}^u" + }, + { + "bbox": [ + 46, + 385, + 287, + 540 + ], + "type": "text", + "content": " and labels in " + }, + { + "bbox": [ + 46, + 385, + 287, + 540 + ], + "type": "inline_equation", + "content": "\\mathcal{C}^s" + }, + { + "bbox": [ + 46, + 385, + 287, + 540 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 385, + 287, + 540 + ], + "type": "inline_equation", + "content": "\\mathcal{C}^u" + }, + { + "bbox": [ + 46, + 385, + 287, + 540 + ], + "type": "text", + "content": " appear during validation and testing. GZSL is a challenging setting with larger label space and a strong bias of seen compositions to unseen ones, relaxing the less realistic assumption in conventional ZSL that test data only belongs to unseen classes." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 548, + 216, + 559 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 548, + 216, + 559 + ], + "spans": [ + { + "bbox": [ + 47, + 548, + 216, + 559 + ], + "type": "text", + "content": "3.2. Conditional Attribute Network" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 566, + 287, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 566, + 287, + 673 + ], + "spans": [ + { + "bbox": [ + 46, + 566, + 287, + 673 + ], + "type": "text", + "content": "Determining Conditions. In CZSL, it is common to learn to classify attributes and objects besides compositions. We first assume that the model recognizes the input image " + }, + { + "bbox": [ + 46, + 566, + 287, + 673 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 566, + 287, + 673 + ], + "type": "text", + "content": " as attribute " + }, + { + "bbox": [ + 46, + 566, + 287, + 673 + ], + "type": "inline_equation", + "content": "a^*" + }, + { + "bbox": [ + 46, + 566, + 287, + 673 + ], + "type": "text", + "content": " and object " + }, + { + "bbox": [ + 46, + 566, + 287, + 673 + ], + "type": "inline_equation", + "content": "o^*" + }, + { + "bbox": [ + 46, + 566, + 287, + 673 + ], + "type": "text", + "content": ". The recognizing score can be formulated as a conditional probability " + }, + { + "bbox": [ + 46, + 566, + 287, + 673 + ], + "type": "inline_equation", + "content": "P(a^*, o^* | i)" + }, + { + "bbox": [ + 46, + 566, + 287, + 673 + ], + "type": "text", + "content": " conditioned on input image " + }, + { + "bbox": [ + 46, + 566, + 287, + 673 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 566, + 287, + 673 + ], + "type": "text", + "content": ". We propose to decompose this probability to express the attribute and object recognition as a one-label classification task. According to multi-variable conditional probability formulation, we have:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 97, + 675, + 286, + 688 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 97, + 675, + 286, + 688 + ], + "spans": [ + { + "bbox": [ + 97, + 675, + 286, + 688 + ], + "type": "interline_equation", + "content": "P \\left(a ^ {*}, o ^ {*} \\mid i\\right) = P \\left(a ^ {*} \\mid o ^ {*}, i\\right) P \\left(o ^ {*} \\mid i\\right) \\tag {1}", + "image_path": "151387b82beaf92c487c37750d02e2b70447dfc2d1c22363340b896ba64d09e8.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "inline_equation", + "content": "P(o^{*}|i)" + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": " is probability of image " + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": " belonging to object " + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "inline_equation", + "content": "o^{*}" + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "inline_equation", + "content": "P(a^{*}|o^{*},i)" + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": " represents the probability of attribute " + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "inline_equation", + "content": "a^{*}" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 385, + 545, + 457 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 385, + 545, + 457 + ], + "spans": [ + { + "bbox": [ + 304, + 385, + 545, + 457 + ], + "type": "text", + "content": "conditioned on the joint presentation of " + }, + { + "bbox": [ + 304, + 385, + 545, + 457 + ], + "type": "inline_equation", + "content": "o^*" + }, + { + "bbox": [ + 304, + 385, + 545, + 457 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 385, + 545, + 457 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 385, + 545, + 457 + ], + "type": "text", + "content": ". This indicates that the recognition of an attribute is conditioned on the recognized object and input image. To better solve the attribute diversity problem, we consider the information of the recognized object and input image as conditions for conditional attribute encoding." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 460, + 545, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 460, + 545, + 532 + ], + "spans": [ + { + "bbox": [ + 304, + 460, + 545, + 532 + ], + "type": "text", + "content": "Object Recognition. Object recognition requires learning to map the input image embedding into an object space. To incorporate object semantic information, we compute cosine similarities between object-mapped image embedding " + }, + { + "bbox": [ + 304, + 460, + 545, + 532 + ], + "type": "inline_equation", + "content": "\\omega_{o}(\\mathbf{x})" + }, + { + "bbox": [ + 304, + 460, + 545, + 532 + ], + "type": "text", + "content": " and all object word embeddings " + }, + { + "bbox": [ + 304, + 460, + 545, + 532 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_{o}" + }, + { + "bbox": [ + 304, + 460, + 545, + 532 + ], + "type": "text", + "content": " instead of directly learning a classification head:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 361, + 533, + 545, + 559 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 361, + 533, + 545, + 559 + ], + "spans": [ + { + "bbox": [ + 361, + 533, + 545, + 559 + ], + "type": "interline_equation", + "content": "\\left\\langle \\omega_ {o} (\\mathbf {x}), \\mathbf {v} _ {o} \\right\\rangle = \\frac {\\omega_ {o} (\\mathbf {x}) ^ {\\top} \\mathbf {v} _ {o}}{\\| \\omega_ {o} (\\mathbf {x}) \\| _ {2} \\| \\mathbf {v} _ {o} \\| _ {2}} \\tag {2}", + "image_path": "8e2e5ceaba61cd366272b312d18c5a58d9531b685164fa28291e78b98f6f2f9e.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 560, + 545, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 560, + 545, + 651 + ], + "spans": [ + { + "bbox": [ + 304, + 560, + 545, + 651 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 560, + 545, + 651 + ], + "type": "inline_equation", + "content": "\\mathbf{x} = f(i) \\in \\mathcal{X}" + }, + { + "bbox": [ + 304, + 560, + 545, + 651 + ], + "type": "text", + "content": " is the visual embedding of input image " + }, + { + "bbox": [ + 304, + 560, + 545, + 651 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 560, + 545, + 651 + ], + "type": "text", + "content": " in visual space " + }, + { + "bbox": [ + 304, + 560, + 545, + 651 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 304, + 560, + 545, + 651 + ], + "type": "text", + "content": " extracted by image backbone " + }, + { + "bbox": [ + 304, + 560, + 545, + 651 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 560, + 545, + 651 + ], + "type": "text", + "content": " (e.g., ResNet-18 [11]), " + }, + { + "bbox": [ + 304, + 560, + 545, + 651 + ], + "type": "inline_equation", + "content": "\\omega_{o}" + }, + { + "bbox": [ + 304, + 560, + 545, + 651 + ], + "type": "text", + "content": " is the mapping from " + }, + { + "bbox": [ + 304, + 560, + 545, + 651 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 304, + 560, + 545, + 651 + ], + "type": "text", + "content": " to object semantic space " + }, + { + "bbox": [ + 304, + 560, + 545, + 651 + ], + "type": "inline_equation", + "content": "S_{o}" + }, + { + "bbox": [ + 304, + 560, + 545, + 651 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 560, + 545, + 651 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_{o} = \\phi(o)" + }, + { + "bbox": [ + 304, + 560, + 545, + 651 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 560, + 545, + 651 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_{o} \\in S_{o}" + }, + { + "bbox": [ + 304, + 560, + 545, + 651 + ], + "type": "text", + "content": " is object word embedding in " + }, + { + "bbox": [ + 304, + 560, + 545, + 651 + ], + "type": "inline_equation", + "content": "S_{o}" + }, + { + "bbox": [ + 304, + 560, + 545, + 651 + ], + "type": "text", + "content": " extracted by word embedder " + }, + { + "bbox": [ + 304, + 560, + 545, + 651 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 304, + 560, + 545, + 651 + ], + "type": "text", + "content": " (e.g., word2vec [24], FastText [7]). The recognized object " + }, + { + "bbox": [ + 304, + 560, + 545, + 651 + ], + "type": "inline_equation", + "content": "o^{*} = \\underset{o \\in \\mathcal{O}}{\\arg \\max} \\langle \\omega_{o}(\\mathbf{x}), \\phi(o) \\rangle" + }, + { + "bbox": [ + 304, + 560, + 545, + 651 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": "Learning Conditional Attributes. With the recognized object " + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "inline_equation", + "content": "o^*" + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": " and visual embedding " + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": " of input image " + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": ", we learn the attribute hyper learner " + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{H}" + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": " and attribute base learner " + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": " in the proposed attribute learning framework to extract attribute embeddings conditioned on the recognized object " + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "inline_equation", + "content": "o^*" + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "11199" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 107 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 107 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 107 + ], + "type": "text", + "content": "and input image " + }, + { + "bbox": [ + 46, + 72, + 287, + 107 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 72, + 287, + 107 + ], + "type": "text", + "content": ". We consider the information of " + }, + { + "bbox": [ + 46, + 72, + 287, + 107 + ], + "type": "inline_equation", + "content": "o^*" + }, + { + "bbox": [ + 46, + 72, + 287, + 107 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 72, + 287, + 107 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 72, + 287, + 107 + ], + "type": "text", + "content": " as prior knowledge for " + }, + { + "bbox": [ + 46, + 72, + 287, + 107 + ], + "type": "inline_equation", + "content": "\\mathcal{H}" + }, + { + "bbox": [ + 46, + 72, + 287, + 107 + ], + "type": "text", + "content": ". Specifically, the prior knowledge is implemented as a feature vector " + }, + { + "bbox": [ + 46, + 72, + 287, + 107 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 72, + 287, + 107 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 124, + 110, + 287, + 122 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 124, + 110, + 287, + 122 + ], + "spans": [ + { + "bbox": [ + 124, + 110, + 287, + 122 + ], + "type": "interline_equation", + "content": "\\beta = \\mathcal {P} \\left(\\operatorname {c a t} \\left(\\mathbf {v} _ {o ^ {*}}, \\mathbf {x}\\right)\\right) \\tag {3}", + "image_path": "35c0ce43839b170e93f23cda16bc44fae9317e36421bb5f90930303e0acc040a.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 124, + 287, + 171 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 124, + 287, + 171 + ], + "spans": [ + { + "bbox": [ + 46, + 124, + 287, + 171 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 124, + 287, + 171 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_{o^*} = \\phi(o^*)" + }, + { + "bbox": [ + 46, + 124, + 287, + 171 + ], + "type": "text", + "content": " is word embedding of " + }, + { + "bbox": [ + 46, + 124, + 287, + 171 + ], + "type": "inline_equation", + "content": "o^*" + }, + { + "bbox": [ + 46, + 124, + 287, + 171 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 124, + 287, + 171 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 46, + 124, + 287, + 171 + ], + "type": "text", + "content": " is a composing network for " + }, + { + "bbox": [ + 46, + 124, + 287, + 171 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_{o^*}" + }, + { + "bbox": [ + 46, + 124, + 287, + 171 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 124, + 287, + 171 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 46, + 124, + 287, + 171 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 124, + 287, + 171 + ], + "type": "inline_equation", + "content": "\\operatorname{cat}(\\cdot)" + }, + { + "bbox": [ + 46, + 124, + 287, + 171 + ], + "type": "text", + "content": " is channel-wise concatenation operation. With the prior knowledge, the attribute hyper learner " + }, + { + "bbox": [ + 46, + 124, + 287, + 171 + ], + "type": "inline_equation", + "content": "\\mathcal{H}" + }, + { + "bbox": [ + 46, + 124, + 287, + 171 + ], + "type": "text", + "content": " can parameterize " + }, + { + "bbox": [ + 46, + 124, + 287, + 171 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 46, + 124, + 287, + 171 + ], + "type": "text", + "content": " as:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 129, + 174, + 287, + 186 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 129, + 174, + 287, + 186 + ], + "spans": [ + { + "bbox": [ + 129, + 174, + 287, + 186 + ], + "type": "interline_equation", + "content": "\\boldsymbol {\\Theta} _ {\\mathcal {G}} = \\mathcal {H} (\\beta ; \\boldsymbol {\\Theta} _ {\\mathcal {H}}) \\tag {4}", + "image_path": "19ea432ce957f536f5b680bb2d8e1ec4b8a864ba1826b027912acb4bdac7356d.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 188, + 287, + 236 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 188, + 287, + 236 + ], + "spans": [ + { + "bbox": [ + 47, + 188, + 287, + 236 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 188, + 287, + 236 + ], + "type": "inline_equation", + "content": "\\Theta_{\\mathcal{H}}" + }, + { + "bbox": [ + 47, + 188, + 287, + 236 + ], + "type": "text", + "content": " is the set of randomly initialized parameters of " + }, + { + "bbox": [ + 47, + 188, + 287, + 236 + ], + "type": "inline_equation", + "content": "\\mathcal{H}" + }, + { + "bbox": [ + 47, + 188, + 287, + 236 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 188, + 287, + 236 + ], + "type": "inline_equation", + "content": "\\Theta_{\\mathcal{G}}" + }, + { + "bbox": [ + 47, + 188, + 287, + 236 + ], + "type": "text", + "content": " is the set of generated parameters of " + }, + { + "bbox": [ + 47, + 188, + 287, + 236 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 47, + 188, + 287, + 236 + ], + "type": "text", + "content": ". In this way, the attribute embeddings " + }, + { + "bbox": [ + 47, + 188, + 287, + 236 + ], + "type": "inline_equation", + "content": "\\mathbf{e}_a" + }, + { + "bbox": [ + 47, + 188, + 287, + 236 + ], + "type": "text", + "content": " conditioned on " + }, + { + "bbox": [ + 47, + 188, + 287, + 236 + ], + "type": "inline_equation", + "content": "o^*" + }, + { + "bbox": [ + 47, + 188, + 287, + 236 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 188, + 287, + 236 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 47, + 188, + 287, + 236 + ], + "type": "text", + "content": " can be encoded via " + }, + { + "bbox": [ + 47, + 188, + 287, + 236 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 47, + 188, + 287, + 236 + ], + "type": "text", + "content": " parameterized by " + }, + { + "bbox": [ + 47, + 188, + 287, + 236 + ], + "type": "inline_equation", + "content": "\\mathcal{H}" + }, + { + "bbox": [ + 47, + 188, + 287, + 236 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 131, + 238, + 287, + 250 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 131, + 238, + 287, + 250 + ], + "spans": [ + { + "bbox": [ + 131, + 238, + 287, + 250 + ], + "type": "interline_equation", + "content": "\\mathbf {e} _ {a} = \\mathcal {G} \\left(\\mathbf {v} _ {a}; \\boldsymbol {\\Theta} _ {\\mathcal {G}}\\right) \\tag {5}", + "image_path": "d144ac89a644114fb6f53eba6700006a1b021a789d0c6ff843a1ef4e58ba2350.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 251, + 278, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 251, + 278, + 263 + ], + "spans": [ + { + "bbox": [ + 46, + 251, + 278, + 263 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 251, + 278, + 263 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_a = \\phi(a)" + }, + { + "bbox": [ + 46, + 251, + 278, + 263 + ], + "type": "text", + "content": " is word embedding of attribute word " + }, + { + "bbox": [ + 46, + 251, + 278, + 263 + ], + "type": "inline_equation", + "content": "a" + }, + { + "bbox": [ + 46, + 251, + 278, + 263 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 264, + 287, + 371 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 264, + 287, + 371 + ], + "spans": [ + { + "bbox": [ + 46, + 264, + 287, + 371 + ], + "type": "text", + "content": "Modeling Contextuality. Although the conditional attribute embeddings are related to the recognized object and input image, object embeddings are also supposed to be influenced by attributes. Therefore, we model the contextuality of attribute-object compositions to address the relationships between them. We follow the work of Mancini et al. [23] in their closed world setting that contextuality is modeled as the mixture of attribute and object word embeddings to extract attribute-object compositional embeddings:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 119, + 373, + 287, + 385 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 119, + 373, + 287, + 385 + ], + "spans": [ + { + "bbox": [ + 119, + 373, + 287, + 385 + ], + "type": "interline_equation", + "content": "\\mathbf {v} _ {a, o} = \\mathcal {C} (\\operatorname {c a t} \\left(\\mathbf {v} _ {a}, \\mathbf {v} _ {o}\\right)) \\tag {6}", + "image_path": "302fc3d6f476701025beb6d5fe6ddb9160801a955424a5cac17c40bd9c026578.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 387, + 239, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 387, + 239, + 399 + ], + "spans": [ + { + "bbox": [ + 47, + 387, + 239, + 399 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 387, + 239, + 399 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 47, + 387, + 239, + 399 + ], + "type": "text", + "content": " is a composing network for " + }, + { + "bbox": [ + 47, + 387, + 239, + 399 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_a" + }, + { + "bbox": [ + 47, + 387, + 239, + 399 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 387, + 239, + 399 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_o" + }, + { + "bbox": [ + 47, + 387, + 239, + 399 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 59, + 399, + 269, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 399, + 269, + 411 + ], + "spans": [ + { + "bbox": [ + 59, + 399, + 269, + 411 + ], + "type": "text", + "content": "The entire structure of our model is shown in Fig. 2." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 418, + 162, + 430 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 418, + 162, + 430 + ], + "spans": [ + { + "bbox": [ + 47, + 418, + 162, + 430 + ], + "type": "text", + "content": "3.3. Training Objectives" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 437, + 287, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 437, + 287, + 509 + ], + "spans": [ + { + "bbox": [ + 46, + 437, + 287, + 509 + ], + "type": "text", + "content": "Similar to object recognition, attribute or composition recognition is also implemented by computing cosine similarities " + }, + { + "bbox": [ + 46, + 437, + 287, + 509 + ], + "type": "inline_equation", + "content": "\\langle \\omega_{a}(\\mathbf{x}),\\mathbf{v}_{a}\\rangle" + }, + { + "bbox": [ + 46, + 437, + 287, + 509 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 46, + 437, + 287, + 509 + ], + "type": "inline_equation", + "content": "\\langle \\omega_c(\\mathbf{x}),\\mathbf{v}_{a,o}\\rangle" + }, + { + "bbox": [ + 46, + 437, + 287, + 509 + ], + "type": "text", + "content": " between attribute-mapped or composition-mapped image embeddings, i.e., " + }, + { + "bbox": [ + 46, + 437, + 287, + 509 + ], + "type": "inline_equation", + "content": "\\omega_{a}(\\mathbf{x})" + }, + { + "bbox": [ + 46, + 437, + 287, + 509 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 46, + 437, + 287, + 509 + ], + "type": "inline_equation", + "content": "\\omega_{c}(\\mathbf{x})" + }, + { + "bbox": [ + 46, + 437, + 287, + 509 + ], + "type": "text", + "content": ", and attribute word embeddings or attribute-object compositional embeddings, i.e., " + }, + { + "bbox": [ + 46, + 437, + 287, + 509 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_a" + }, + { + "bbox": [ + 46, + 437, + 287, + 509 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 46, + 437, + 287, + 509 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_{a,o}" + }, + { + "bbox": [ + 46, + 437, + 287, + 509 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 102, + 510, + 287, + 536 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 102, + 510, + 287, + 536 + ], + "spans": [ + { + "bbox": [ + 102, + 510, + 287, + 536 + ], + "type": "interline_equation", + "content": "\\left\\langle \\omega_ {a} (\\mathbf {x}), \\mathbf {e} _ {a} \\right\\rangle = \\frac {\\omega_ {a} (\\mathbf {x}) ^ {\\top} \\mathbf {e} _ {a}}{\\| \\omega_ {a} (\\mathbf {x}) \\| _ {2} \\| \\mathbf {e} _ {a} \\| _ {2}} \\tag {7}", + "image_path": "a5ed20f374e3dd23e8fa5ae00db2823eb6101261d0fe49b95903f5e065ef4bba.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 96, + 537, + 287, + 564 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 96, + 537, + 287, + 564 + ], + "spans": [ + { + "bbox": [ + 96, + 537, + 287, + 564 + ], + "type": "interline_equation", + "content": "\\left\\langle \\omega_ {c} (\\mathbf {x}), \\mathbf {v} _ {a, o} \\right\\rangle = \\frac {\\omega_ {c} (\\mathbf {x}) ^ {\\top} \\mathbf {v} _ {a , o}}{\\| \\omega_ {c} (\\mathbf {x}) \\| _ {2} \\| \\mathbf {v} _ {a , o} \\| _ {2}} \\tag {8}", + "image_path": "29fb9f91416c2597bd7de9e42b1b09f5b9882ee76e156ef8f4a67cde2a562f42.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 567, + 287, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 567, + 287, + 685 + ], + "spans": [ + { + "bbox": [ + 46, + 567, + 287, + 685 + ], + "type": "text", + "content": "The recognition probability " + }, + { + "bbox": [ + 46, + 567, + 287, + 685 + ], + "type": "inline_equation", + "content": "P(o^{*}|i)" + }, + { + "bbox": [ + 46, + 567, + 287, + 685 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 567, + 287, + 685 + ], + "type": "inline_equation", + "content": "P(a^{*}|o^{*},i)" + }, + { + "bbox": [ + 46, + 567, + 287, + 685 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 567, + 287, + 685 + ], + "type": "inline_equation", + "content": "P(c^{*}|i)" + }, + { + "bbox": [ + 46, + 567, + 287, + 685 + ], + "type": "text", + "content": " are normalized cosine similarities, where " + }, + { + "bbox": [ + 46, + 567, + 287, + 685 + ], + "type": "inline_equation", + "content": "P(c^{*}|i)" + }, + { + "bbox": [ + 46, + 567, + 287, + 685 + ], + "type": "text", + "content": " is the probability of input image " + }, + { + "bbox": [ + 46, + 567, + 287, + 685 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 567, + 287, + 685 + ], + "type": "text", + "content": " belonging to the recognized attribute-object composition " + }, + { + "bbox": [ + 46, + 567, + 287, + 685 + ], + "type": "inline_equation", + "content": "c^{*}" + }, + { + "bbox": [ + 46, + 567, + 287, + 685 + ], + "type": "text", + "content": ". As shown in Fig. 2, our model learns three embedding spaces: attribute space " + }, + { + "bbox": [ + 46, + 567, + 287, + 685 + ], + "type": "inline_equation", + "content": "S_{a}" + }, + { + "bbox": [ + 46, + 567, + 287, + 685 + ], + "type": "text", + "content": ", object space " + }, + { + "bbox": [ + 46, + 567, + 287, + 685 + ], + "type": "inline_equation", + "content": "S_{o}" + }, + { + "bbox": [ + 46, + 567, + 287, + 685 + ], + "type": "text", + "content": ", and attribute-object compositional space " + }, + { + "bbox": [ + 46, + 567, + 287, + 685 + ], + "type": "inline_equation", + "content": "S_{c}" + }, + { + "bbox": [ + 46, + 567, + 287, + 685 + ], + "type": "text", + "content": ". Therefore, we incorporate three separate cross-entropy losses to maximize the three recognition probabilities to make the model optimized in these three spaces. The losses are as follows:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 73, + 686, + 287, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 73, + 686, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 73, + 686, + 287, + 715 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {a} = - \\sum_ {a \\in \\mathcal {A}} \\log \\frac {\\exp \\left(\\left\\langle \\omega_ {a} (\\mathbf {x}), \\mathbf {e} _ {a} \\right\\rangle / \\tau\\right)}{\\sum_ {a ^ {\\prime} \\in \\mathcal {A}} \\exp \\left(\\left\\langle \\omega_ {a} (\\mathbf {x}), \\mathbf {e} _ {a ^ {\\prime}} \\right\\rangle / \\tau\\right)} \\tag {9}", + "image_path": "6e162685ae17833391822f1b0c71686e8f55cce489d80a35248bebf08b472698.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 332, + 70, + 545, + 99 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 332, + 70, + 545, + 99 + ], + "spans": [ + { + "bbox": [ + 332, + 70, + 545, + 99 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {o} = - \\sum_ {o \\in \\mathcal {O}} \\log \\frac {\\exp \\left(\\left\\langle \\omega_ {o} (\\mathbf {x}) , \\mathbf {v} _ {o} \\right\\rangle / \\tau\\right)}{\\sum_ {o ^ {\\prime} \\in \\mathcal {O}} \\exp \\left(\\left\\langle \\omega_ {o} (\\mathbf {x}) , \\mathbf {v} _ {o} ^ {\\prime} \\right\\rangle / \\tau\\right)} \\tag {10}", + "image_path": "9d880d8f348219c2681073a48c91a0c244c43c14c2b007e99b11239858968d38.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 104, + 484, + 115 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 104, + 484, + 115 + ], + "spans": [ + { + "bbox": [ + 306, + 104, + 484, + 115 + ], + "type": "text", + "content": "Also, for composition recognition, we have:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 312, + 117, + 545, + 158 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 117, + 545, + 158 + ], + "spans": [ + { + "bbox": [ + 312, + 117, + 545, + 158 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {a, o} = - \\sum_ {(a, o) \\in \\mathcal {C}} \\log \\frac {\\exp \\left(\\left\\langle \\omega_ {c} (\\mathbf {x}), \\mathbf {v} _ {a , o} \\right\\rangle / \\tau\\right)}{\\sum_ {\\left(a ^ {\\prime} , o ^ {\\prime}\\right) \\in \\mathcal {C}} \\exp \\left(\\left\\langle \\omega_ {c} (\\mathbf {x}), \\mathbf {v} _ {a ^ {\\prime} , o ^ {\\prime}} \\right\\rangle / \\tau\\right)} \\tag {11}", + "image_path": "e2dd8f024544ea2dd05b09cb751494d55c9c4cd5da4a8852039222e88ebb8d00.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 158, + 545, + 181 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 158, + 545, + 181 + ], + "spans": [ + { + "bbox": [ + 305, + 158, + 545, + 181 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 158, + 545, + 181 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 305, + 158, + 545, + 181 + ], + "type": "text", + "content": " is temperature factor [46]. Finally, the training loss as a whole linearly combines the three losses above:" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 380, + 182, + 545, + 205 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 380, + 182, + 545, + 205 + ], + "spans": [ + { + "bbox": [ + 380, + 182, + 545, + 205 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\frac {\\mathcal {L} _ {a} + \\mathcal {L} _ {o}}{2} + \\mathcal {L} _ {a, o} \\tag {12}", + "image_path": "66de680011ea39b87e51e498b9564ea2c6985308340cbe1cbb418be406d96020.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 212, + 372, + 223 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 212, + 372, + 223 + ], + "spans": [ + { + "bbox": [ + 306, + 212, + 372, + 223 + ], + "type": "text", + "content": "3.4. Inference" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 305, + 230, + 545, + 254 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 230, + 545, + 254 + ], + "spans": [ + { + "bbox": [ + 305, + 230, + 545, + 254 + ], + "type": "text", + "content": "During validation and testing, we incorporate a linear normalization function " + }, + { + "bbox": [ + 305, + 230, + 545, + 254 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 305, + 230, + 545, + 254 + ], + "type": "text", + "content": " for cosine similarities:" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 382, + 255, + 545, + 268 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 382, + 255, + 545, + 268 + ], + "spans": [ + { + "bbox": [ + 382, + 255, + 545, + 268 + ], + "type": "interline_equation", + "content": "g (d) = (1 + d) * 0. 5 \\tag {13}", + "image_path": "4f9fc07a53d3741eeb98eb1b22f1d2d37c2e878ca8119bc9fb5cb3fc26e18537.jpg" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 305, + 269, + 545, + 305 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 269, + 545, + 305 + ], + "spans": [ + { + "bbox": [ + 305, + 269, + 545, + 305 + ], + "type": "text", + "content": "Then, we have " + }, + { + "bbox": [ + 305, + 269, + 545, + 305 + ], + "type": "inline_equation", + "content": "P(a|o^{*},i) = g(\\langle \\omega_{a}(\\mathbf{x}),\\mathbf{e}_{a}\\rangle),P(o|i) = g(\\langle \\omega_{o}(\\mathbf{x}),\\mathbf{v}_{o}\\rangle)" + }, + { + "bbox": [ + 305, + 269, + 545, + 305 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 305, + 269, + 545, + 305 + ], + "type": "inline_equation", + "content": "P(c|i) = g(\\langle \\omega_c(\\mathbf{x}),\\mathbf{v}_{a,o}\\rangle)" + }, + { + "bbox": [ + 305, + 269, + 545, + 305 + ], + "type": "text", + "content": ". The inference rule is parameterized as:" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 343, + 307, + 545, + 320 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 343, + 307, + 545, + 320 + ], + "spans": [ + { + "bbox": [ + 343, + 307, + 545, + 320 + ], + "type": "interline_equation", + "content": "s = (1 - \\alpha) P (c | i) + \\alpha P (a | o ^ {*}, i) P (o | i) \\tag {14}", + "image_path": "f60fd25c69767560136a8f1e2afca49c086e0a686ceb9c274046f944753a0c04.jpg" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 305, + 322, + 503, + 334 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 322, + 503, + 334 + ], + "spans": [ + { + "bbox": [ + 305, + 322, + 503, + 334 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 322, + 503, + 334 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 305, + 322, + 503, + 334 + ], + "type": "text", + "content": " is the weight factor controlling balance." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 305, + 345, + 386, + 358 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 345, + 386, + 358 + ], + "spans": [ + { + "bbox": [ + 305, + 345, + 386, + 358 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 304, + 364, + 545, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 364, + 545, + 411 + ], + "spans": [ + { + "bbox": [ + 304, + 364, + 545, + 411 + ], + "type": "text", + "content": "In this section, experiments are conducted following the concrete introductions of datasets, metrics, implementation details, and baselines. Then, we report ablation results to demonstrate the effectiveness of our model." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 305, + 420, + 422, + 433 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 420, + 422, + 433 + ], + "spans": [ + { + "bbox": [ + 305, + 420, + 422, + 433 + ], + "type": "text", + "content": "4.1. Experimental Setup" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 304, + 438, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 438, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 438, + 545, + 713 + ], + "type": "text", + "content": "Datasets We conduct experiments with three widely adopted datasets in the CZSL task, which are MIT-States [14], UT-Zappos50K [43, 44], and C-GQA [26]. MIT-States contains 53753 crawled web images labeled with 1962 attribute-object (e.g., mossy highway) compositions. This dataset has 30338, 10420, and 12995 training, validation, and testing images [31] labeled with 1262, 600, and 800 compositions. In validation and test sets, the numbers of seen and unseen compositions are the same. All compositions are composed of 115 attributes and 245 objects. UT-Zappos50K is made up of 50025 images labeled with 116 fine-grained shoe classes composed of 16 attributes (e.g., rubber) and 12 objects (e.g., sneaker). This dataset has 22998, 3214, and 2914 training, validation, and testing images [31] labeled with 83, 30, and 36 compositions. Also, numbers of seen and unseen compositions in validation and test sets share the same quantity. C-GQA is created based on Stanford GQA dataset [13] used for VQA task. C-GQA contains 39298 images labeled with over " + }, + { + "bbox": [ + 304, + 438, + 545, + 713 + ], + "type": "inline_equation", + "content": "9.5\\mathrm{k}" + }, + { + "bbox": [ + 304, + 438, + 545, + 713 + ], + "type": "text", + "content": " compositions composed of 453 attributes and 870 objects. This dataset has 26920, 7280, and 5098 training, validation, and testing images labeled with 6963, 2541, and 2069 compositions. Detailed splits are presented in Tab. 1." + } + ] + } + ], + "index": 31 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11200" + } + ] + } + ], + "index": 32 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 70, + 547, + 148 + ], + "blocks": [ + { + "bbox": [ + 48, + 70, + 547, + 148 + ], + "lines": [ + { + "bbox": [ + 48, + 70, + 547, + 148 + ], + "spans": [ + { + "bbox": [ + 48, + 70, + 547, + 148 + ], + "type": "table", + "html": "
DatasetTrainingValidationTest
AOCsICsCuICsCuI
UT-Zappos50K [43,44]161283229981515321418182914
MIT-States [14]1152451262303383003001042040040012995
C-GQA [26]453870696326920117313687280102210475098
", + "image_path": "3f00ecb4155a0fb916d5b9821a4fbfa239e18c80a43596885e3e8ead4898137c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 94, + 155, + 499, + 166 + ], + "lines": [ + { + "bbox": [ + 94, + 155, + 499, + 166 + ], + "spans": [ + { + "bbox": [ + 94, + 155, + 499, + 166 + ], + "type": "text", + "content": "Table 1. Detailed dataset splits of UT-Zappos50K, MIT-States, and C-GQA in training, validation, and test sets." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 177, + 289, + 356 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 177, + 289, + 356 + ], + "spans": [ + { + "bbox": [ + 46, + 177, + 289, + 356 + ], + "type": "text", + "content": "Metrics To demonstrate the advances in attribute learning, we report the attribute and object classification accuracies (best attr and best obj). The setting of GZSL requires both seen and unseen compositions to exist during validation and testing. As a result, there is an inherent bias of seen against unseen compositions. We follow the evaluation protocols proposed in [8] where a scalar bias is added to final activations of classes of seen compositions to calibrate the model. As the scalar varies from negative infinity to positive infinity, there must be a best operating point at which the bias between seen and unseen compositions is the lowest. We report the results in terms of the best accuracies of seen images (best seen), unseen images (best unseen), best Harmonic Mean (best HM), and Area Under Curve (AUC) with different scalar biases." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 357, + 289, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 357, + 289, + 548 + ], + "spans": [ + { + "bbox": [ + 46, + 357, + 289, + 548 + ], + "type": "text", + "content": "Implementations We consider image backbone " + }, + { + "bbox": [ + 46, + 357, + 289, + 548 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 357, + 289, + 548 + ], + "type": "text", + "content": " as ResNet-18 pre-trained on ImageNet [10] to extract 512 dimension vectors following preceding works. The mapping networks " + }, + { + "bbox": [ + 46, + 357, + 289, + 548 + ], + "type": "inline_equation", + "content": "\\omega_{a}" + }, + { + "bbox": [ + 46, + 357, + 289, + 548 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 357, + 289, + 548 + ], + "type": "inline_equation", + "content": "\\omega_{o}" + }, + { + "bbox": [ + 46, + 357, + 289, + 548 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 357, + 289, + 548 + ], + "type": "inline_equation", + "content": "\\omega_{c}" + }, + { + "bbox": [ + 46, + 357, + 289, + 548 + ], + "type": "text", + "content": " share the similar structure of two Fully Connected (FC) layers with ReLU [28], LayerNorm [5], and Dropout [36] following the first FC layer. We adopt word embedder " + }, + { + "bbox": [ + 46, + 357, + 289, + 548 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 46, + 357, + 289, + 548 + ], + "type": "text", + "content": " as 600-dimensional word2vec+FastText for MIT-States, 300-dimensional FastText for UT-Zappos50K, and word2vec for C-GQA. The layer structures of " + }, + { + "bbox": [ + 46, + 357, + 289, + 548 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 46, + 357, + 289, + 548 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 357, + 289, + 548 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 46, + 357, + 289, + 548 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 357, + 289, + 548 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 46, + 357, + 289, + 548 + ], + "type": "text", + "content": " are the same as the mapping networks, where ReLU is added in " + }, + { + "bbox": [ + 46, + 357, + 289, + 548 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 46, + 357, + 289, + 548 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 357, + 289, + 548 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 46, + 357, + 289, + 548 + ], + "type": "text", + "content": " to the last FC layer. Weight generation for the attribute base learner " + }, + { + "bbox": [ + 46, + 357, + 289, + 548 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 46, + 357, + 289, + 548 + ], + "type": "text", + "content": " through the attribute hyper learner " + }, + { + "bbox": [ + 46, + 357, + 289, + 548 + ], + "type": "inline_equation", + "content": "\\mathcal{H}" + }, + { + "bbox": [ + 46, + 357, + 289, + 548 + ], + "type": "text", + "content": " requires more parameters and makes learning difficult, as noted by Bertinetto et al. [6]. Therefore, we adopt weight factorization in [38] to reduce parameters for the attribute hyper learner " + }, + { + "bbox": [ + 46, + 357, + 289, + 548 + ], + "type": "inline_equation", + "content": "\\mathcal{H}" + }, + { + "bbox": [ + 46, + 357, + 289, + 548 + ], + "type": "text", + "content": ", that is" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 102, + 549, + 286, + 564 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 102, + 549, + 286, + 564 + ], + "spans": [ + { + "bbox": [ + 102, + 549, + 286, + 564 + ], + "type": "interline_equation", + "content": "\\mathbf {e} _ {a} ^ {(i)} = \\left(\\mathbf {v} _ {a} \\mathbf {W} _ {\\mathcal {G}} ^ {(i)} + \\mathbf {b} _ {\\mathcal {G}} ^ {(i)}\\right) \\odot \\boldsymbol {\\lambda} _ {\\mathcal {G}} ^ {(i)} \\tag {15}", + "image_path": "e4997af6e94712246da8c17ebf2ef08b512a45055ec57f9a25f37e4926789532.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 128, + 565, + 286, + 582 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 128, + 565, + 286, + 582 + ], + "spans": [ + { + "bbox": [ + 128, + 565, + 286, + 582 + ], + "type": "interline_equation", + "content": "\\boldsymbol {\\lambda} _ {\\mathcal {G}} ^ {(i)} = \\mathcal {H} (\\beta ; \\boldsymbol {\\Theta} _ {\\mathcal {H}} ^ {(i)}) \\tag {16}", + "image_path": "41528763bfbdd14cfb275957a46084753906e93f80aabe9776600338fdcf8ab3.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 578, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 578, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 578, + 289, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 578, + 289, + 714 + ], + "type": "inline_equation", + "content": "(i)" + }, + { + "bbox": [ + 46, + 578, + 289, + 714 + ], + "type": "text", + "content": " indicates " + }, + { + "bbox": [ + 46, + 578, + 289, + 714 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 578, + 289, + 714 + ], + "type": "text", + "content": "th FC layer, " + }, + { + "bbox": [ + 46, + 578, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_{\\mathcal{G}}^{(i)}" + }, + { + "bbox": [ + 46, + 578, + 289, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 578, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{b}_{\\mathcal{G}}^{(i)}" + }, + { + "bbox": [ + 46, + 578, + 289, + 714 + ], + "type": "text", + "content": " are the weight matrix and bias vector of " + }, + { + "bbox": [ + 46, + 578, + 289, + 714 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 578, + 289, + 714 + ], + "type": "text", + "content": "th FC layer in " + }, + { + "bbox": [ + 46, + 578, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 46, + 578, + 289, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 578, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{W}_{\\mathcal{G}}^{(i)}, \\mathbf{b}_{\\mathcal{G}}^{(i)}\\} \\subset \\Theta_{\\mathcal{G}}, \\Theta_{\\mathcal{H}}^{(i)} \\subset \\Theta_{\\mathcal{H}}" + }, + { + "bbox": [ + 46, + 578, + 289, + 714 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 578, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 46, + 578, + 289, + 714 + ], + "type": "text", + "content": " denotes elementwise multiplication. During training, we fix the image backbone " + }, + { + "bbox": [ + 46, + 578, + 289, + 714 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 578, + 289, + 714 + ], + "type": "text", + "content": " and train other modules using Adam [15] optimizer and an Nvidia GeForce GTX 1080Ti GPU with a learning rate and weight decay of 0.00005. The batch size is 256. The temperature factor " + }, + { + "bbox": [ + 46, + 578, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 46, + 578, + 289, + 714 + ], + "type": "text", + "content": ", weight factor " + }, + { + "bbox": [ + 46, + 578, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 578, + 289, + 714 + ], + "type": "text", + "content": ", and the maximum number of epochs are set to 0.02, 0.4, and 500 for UT-Zappos50K; 0.05, 0.2, and 800 for MIT-States; and 0.05, 0.4, and 1000 for C-GQA." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 177, + 547, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 177, + 547, + 453 + ], + "spans": [ + { + "bbox": [ + 304, + 177, + 547, + 453 + ], + "type": "text", + "content": "Baselines We conduct experiments with the following algorithms: 1) AttrAsOp [27] treats attributes as linear transformations on object vectors instead of data points in some high-dimensional space and optimizes the transformations through several regularizers in the loss function. 2) TMN [31] constructs task-driven modular networks in semantic space configured through a gating function conditioned on the task. 3) SymNet [21] proposes symmetry property in attribute-object compositions and group axioms as objectives in an end-to-end manner. 4) " + }, + { + "bbox": [ + 304, + 177, + 547, + 453 + ], + "type": "inline_equation", + "content": "CGE_{\\mathrm{ff}}" + }, + { + "bbox": [ + 304, + 177, + 547, + 453 + ], + "type": "text", + "content": " [26] exploits dependencies between attributes, objects, and compositions through an end-to-end graph formulation where \"ff\" means fixed image feature backbone. 5) CompCos [23] learns a mapping from image features to semantic space of compositions and computes cosine similarities between them. 6) DeCa [42] rethinks the CZSL task in a decomposable causal perspective and learns three independent mappings from image feature space to attribute, object, and composition semantic space. Cosine similarities are also adopted. 7) SCN [20] computes visual prototypes of attributes and objects in a siamese contrastive space and proposes a designed State Transition Module to increase the diversity of training compositions." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 464, + 430, + 477 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 464, + 430, + 477 + ], + "spans": [ + { + "bbox": [ + 305, + 464, + 430, + 477 + ], + "type": "text", + "content": "4.2. Quantitative Analysis" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 483, + 545, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 483, + 545, + 519 + ], + "spans": [ + { + "bbox": [ + 304, + 483, + 545, + 519 + ], + "type": "text", + "content": "All results are computed on test sets of all datasets and from their published papers and [26] for a fair comparison. We report quantitative results with the best AUC in Tab. 2." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 521, + 545, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 545, + 616 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 545, + 616 + ], + "type": "text", + "content": "From Tab.2, our model outperforms other state-of-the-art algorithms in terms of best attr, best unseen, and AUC in all three datasets including the recently proposed C-GQA, indicating the better attribute learning performance and generalization ability from seen to unseen compositions. Specifically, our model performs much better on C-GQA with more state-of-the-art results although it is a much more challenging dataset than MIT-States and UT-Zappos50K." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "text", + "content": "For UT-Zappos50K, the observations are that our model boosts attribute recognition accuracy, unseen image classification accuracy, and AUC from " + }, + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "inline_equation", + "content": "47.3\\%" + }, + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "inline_equation", + "content": "63.1\\%" + }, + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "inline_equation", + "content": "32.0\\%" + }, + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "text", + "content": " of SCEN to the new state-of-the-art of " + }, + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "inline_equation", + "content": "48.4\\%" + }, + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "inline_equation", + "content": "66.3\\%" + }, + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "inline_equation", + "content": "33.1\\%" + }, + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "inline_equation", + "content": "1.1\\%" + }, + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "inline_equation", + "content": "3.2\\%" + }, + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "inline_equation", + "content": "1.1\\%" + }, + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "text", + "content": " improvement respectively. For MIT-States, our model achieves " + }, + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "inline_equation", + "content": "30.2\\%" + }, + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "inline_equation", + "content": "32.6\\%" + }, + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "inline_equation", + "content": "26.2\\%" + }, + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "inline_equation", + "content": "5.4\\%" + }, + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "text", + "content": " accuracies for attribute and object classification, unseen image classification, and AUC on the test" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11201" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 47, + 70, + 548, + 220 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 548, + 220 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 548, + 220 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 548, + 220 + ], + "type": "table", + "html": "
AlgorithmUT-Zappos50KMIT-StatesC-GQA
NameVenueAtt.Obj.S.U.HMAUCAtt.Obj.S.U.HMAUCAtt.Obj.S.U.HMAUC
AttrAsOp [27]ECCV'1838.969.659.854.240.825.921.123.614.317.49.91.68.312.511.83.92.90.3
TMN [31]ICCV'1940.869.958.760.045.029.323.326.520.220.113.02.99.720.521.66.37.71.1
SymNet [21]CVPR'2041.368.649.857.440.423.426.328.324.425.216.13.015.023.127.010.810.92.2
CGEff [26]CVPR'2145.073.956.863.641.226.427.932.028.725.317.25.112.726.927.511.711.92.5
CompCos [23]CVPR'2144.773.559.862.543.528.727.931.825.324.616.44.5------
DeCa [42]TMM'22--62.763.146.331.6--29.825.218.25.3------
SCEN [20]CVPR'2247.375.663.563.147.832.028.232.229.925.218.45.313.627.928.912.112.42.9
Ours48.472.661.066.347.333.130.232.629.026.217.95.417.522.330.013.214.53.3
", + "image_path": "936ada382740ba78a02f5e619d5f3ce12b1095f27a117599aa3c7e1f0b0817c8.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 226, + 546, + 249 + ], + "lines": [ + { + "bbox": [ + 46, + 226, + 546, + 249 + ], + "spans": [ + { + "bbox": [ + 46, + 226, + 546, + 249 + ], + "type": "text", + "content": "Table 2. Quantitative results on test sets of all datasets with the state-of-the-art in terms of best attr (Att.), best obj (Obj.), best seen (S.), best unseen (U.), best HM (HM), and AUC." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 260, + 288, + 331 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 260, + 288, + 331 + ], + "spans": [ + { + "bbox": [ + 46, + 260, + 288, + 331 + ], + "type": "text", + "content": "set, providing " + }, + { + "bbox": [ + 46, + 260, + 288, + 331 + ], + "type": "inline_equation", + "content": "2.0\\%" + }, + { + "bbox": [ + 46, + 260, + 288, + 331 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 260, + 288, + 331 + ], + "type": "inline_equation", + "content": "0.4\\%" + }, + { + "bbox": [ + 46, + 260, + 288, + 331 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 260, + 288, + 331 + ], + "type": "inline_equation", + "content": "1.0\\%" + }, + { + "bbox": [ + 46, + 260, + 288, + 331 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 260, + 288, + 331 + ], + "type": "inline_equation", + "content": "0.1\\%" + }, + { + "bbox": [ + 46, + 260, + 288, + 331 + ], + "type": "text", + "content": " improvements on the recently proposed SCEN as the new state-of-the-art results. This indicates that the proposed conditional attribute network can truly improve the attribute recognition performance and consequently the unseen image classification and AUC." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 335, + 287, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 335, + 287, + 456 + ], + "spans": [ + { + "bbox": [ + 46, + 335, + 287, + 456 + ], + "type": "text", + "content": "For the more challenging dataset C-GQA, since it is significantly harder than MIT-States and UT-Zappos50K with " + }, + { + "bbox": [ + 46, + 335, + 287, + 456 + ], + "type": "inline_equation", + "content": "5.5 \\times" + }, + { + "bbox": [ + 46, + 335, + 287, + 456 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 335, + 287, + 456 + ], + "type": "inline_equation", + "content": "0.9 \\times" + }, + { + "bbox": [ + 46, + 335, + 287, + 456 + ], + "type": "text", + "content": " composition labels and images in the training set compared with MIT-States, our model outperforms all other algorithms except best obj with " + }, + { + "bbox": [ + 46, + 335, + 287, + 456 + ], + "type": "inline_equation", + "content": "3.9\\%" + }, + { + "bbox": [ + 46, + 335, + 287, + 456 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 335, + 287, + 456 + ], + "type": "inline_equation", + "content": "1.1\\%" + }, + { + "bbox": [ + 46, + 335, + 287, + 456 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 335, + 287, + 456 + ], + "type": "inline_equation", + "content": "1.1\\%" + }, + { + "bbox": [ + 46, + 335, + 287, + 456 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 335, + 287, + 456 + ], + "type": "inline_equation", + "content": "2.1\\%" + }, + { + "bbox": [ + 46, + 335, + 287, + 456 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 335, + 287, + 456 + ], + "type": "inline_equation", + "content": "0.4\\%" + }, + { + "bbox": [ + 46, + 335, + 287, + 456 + ], + "type": "text", + "content": " boosting in terms of best attr, best seen, best unseen, best HM, and AUC in the testing set. This indicates that the proposed conditional attribute network makes a critical contribution when facing a more challenging dataset even if the object recognition accuracy is lower." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 459, + 287, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 459, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 459, + 287, + 628 + ], + "type": "text", + "content": "We give an analysis of the importance that attributes should be conditioned on objects. First, note that although DeCa also learns attribute, object, and composition spaces separately, it learns attributes as static embeddings independent from objects, causing lower best unseen and AUC on UT-Zappos50K and MIT-States compared with ours in Tab. 2. Next, different baselines incorporate different techniques to handle the CZSL task though, they learn static attribute embeddings too, producing lower best attr, best unseen, and AUC. Then, the proposed method performs much better on C-GQA compared with other baselines. All the above phenomena demonstrate that attributes should be conditioned on objects and performance on datasets with larger label space can gain more boosts in this way." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 630, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 288, + 715 + ], + "type": "text", + "content": "From the results of the three datasets above, we observe an interesting phenomenon. Although the results of best obj in three datasets are all lower than that of SCEN, results of best unseen are all higher accompanied by higher results of best attr. We speculate the reason is that some objects have more attributes (or are more dominated) in unseen compositions and the misclassified objects recognized" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 260, + 547, + 321 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 260, + 547, + 321 + ], + "spans": [ + { + "bbox": [ + 304, + 260, + 547, + 321 + ], + "type": "text", + "content": "by our model are less dominated (i.e. have few attributes or are long-tailed in terms of attribute). As a result, with the correctly predicted objects dominated in unseen compositions, the more correctly classified attributes, the higher the results of best unseen." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 332, + 424, + 346 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 332, + 424, + 346 + ], + "spans": [ + { + "bbox": [ + 305, + 332, + 424, + 346 + ], + "type": "text", + "content": "4.3. Qualitative Analysis" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 353, + 547, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 353, + 547, + 604 + ], + "spans": [ + { + "bbox": [ + 304, + 353, + 547, + 604 + ], + "type": "text", + "content": "In this section, we present some qualitative results of novel compositions with top-3 predictions on UT-Zappos50K, MIT-States, and C-GQA in Fig. 3. We show results for each dataset in each row. Images whose top prediction matches the label are shown in the first three columns and the rest columns show wrong results. For UT-Zappos50K, the remaining two answers of all images can match at least one label factor. For some instances in MIT-States, we can notice that the top and second predictions can both describe the image. For example, for the image labeled with winding stream, there is sunlight reflecting from the stream and creek is the synonym of stream. Therefore, sunny creek can also be the label of the image. Another example is that image labeled with wide valley also present cloudy cloud in the blue sky located in the upper part. As a result, the model has difficulty deciding what to predict. This reflects that labels in MIT-States are heavy in noise. For C-GQA where labels are clear, our model can produce more answers that match the label factors in the remaining two predictions, which indicates the better performance and robustness of our model." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": "Additionally, we present wrong predictions in the last two columns. It can be noticed that our model can predict correct answers in most top-3 predictions. As for the image of MIT-States labeled as broken bottle, our model predicts the attribute as small because it is difficult to focus on a certain attribute of the bottle since the bottle in this image is both small and broken. Besides, images in the training set are limited in the status of objects. For example, training images of sheep hardly present the action of laying down" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "11202" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 70, + 545, + 205 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 545, + 205 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 545, + 205 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 545, + 205 + ], + "type": "table", + "html": "
VariantUT-Zappos50KC-GQA
#NameAtt.Obj.S.U.HMAUCAtt.Obj.S.U.HMAUC
(1)w/o L_a + L_o46.174.361.564.746.131.710.830.629.812.813.43.0
(2)w/o L_c41.960.759.554.745.728.314.817.128.111.212.42.6
(3)w/o G + H + P47.074.059.965.846.331.714.827.829.913.114.63.1
(4)w/o P46.773.260.764.547.531.614.526.430.113.014.53.1
(5)w/o H46.270.358.562.746.330.513.925.829.111.212.52.4
(6)w/o x for H45.671.361.662.844.830.113.420.830.212.713.92.9
(7)Full48.472.661.066.347.333.117.522.330.013.214.53.3
", + "image_path": "c04e57793a1bfca4bcdc59ab816715be7d9fde460105abaca0a14eabda3b2e19.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 213, + 545, + 224 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 213, + 545, + 224 + ], + "spans": [ + { + "bbox": [ + 47, + 213, + 545, + 224 + ], + "type": "text", + "content": "Table 3. Ablation results on test sets in terms of best attr (Att.), best obj (Obj.), best seen (S.), best unseen (U.), best HM (HM), and AUC." + } + ] + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 49, + 228, + 544, + 387 + ], + "blocks": [ + { + "bbox": [ + 49, + 228, + 544, + 387 + ], + "lines": [ + { + "bbox": [ + 49, + 228, + 544, + 387 + ], + "spans": [ + { + "bbox": [ + 49, + 228, + 544, + 387 + ], + "type": "image", + "image_path": "bf70401301edb7578a26bec565f6b220fee8b211a66ef07939ab6a0cd1040436.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 97, + 396, + 493, + 407 + ], + "lines": [ + { + "bbox": [ + 97, + 396, + 493, + 407 + ], + "spans": [ + { + "bbox": [ + 97, + 396, + 493, + 407 + ], + "type": "text", + "content": "Figure 3. Qualitative Results. We demonstrate top-3 predictions of some instances using our proposed model." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 418, + 288, + 478 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 418, + 288, + 478 + ], + "spans": [ + { + "bbox": [ + 46, + 418, + 288, + 478 + ], + "type": "text", + "content": "causing our model mistakenly classify the sheep in the image labeled as light sheep into elephant. Thus, with the recognized object elephant, the model can only focus on attributes conditioned on elephant and find the appropriate attribute that matches the image." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 489, + 141, + 502 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 489, + 141, + 502 + ], + "spans": [ + { + "bbox": [ + 47, + 489, + 141, + 502 + ], + "type": "text", + "content": "4.4. Ablation Study" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 509, + 287, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 509, + 287, + 616 + ], + "spans": [ + { + "bbox": [ + 46, + 509, + 287, + 616 + ], + "type": "text", + "content": "In this section, we ablate the proposed model to evaluate the performance of each module. The ablation study is conducted on test sets of UT-Zappos50K, C-GQA. To achieve more convincing ablation results, we do not choose MIT-States because images in MIT-States are labeled using automatic search. As a result, the noise of labels is too heavy to be used for evaluations, as is pointed out by Atzmon et.al. [4]. Ablation results are reported in Tab. 3. The detailed ablation process is as follows:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "type": "text", + "content": "We first study the effects of recognizing compositions only and recognizing attributes and objects without compositions, which are corresponded to variants (1) and (2) in Tab. 3, and report results in terms of six metrics used in Tab. 2. Compared with variant (6), the results of each variant mostly decline, indicating the importance of recognizing attributes, objects, and compositions jointly. As to the results of Obj. in UT-Zappos50K and C-GQA from variants" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 418, + 545, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 418, + 545, + 515 + ], + "spans": [ + { + "bbox": [ + 304, + 418, + 545, + 515 + ], + "type": "text", + "content": "(1) and (6), we can observe that those object classification accuracies decline. This is mainly because when recognizing objects individually each object presents visual diversity caused by different attributes, e.g., sliced apple is different from apple in visual appearance since a sliced apple is sliced into multiple pieces. However, this phenomenon does not affect other results, especially for the dataset with larger label space, e.g., C-GQA." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "text", + "content": "Next, with attributes, objects, and compositions being recognized, we ablate " + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{G} + \\mathcal{H} + \\mathcal{P}" + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "text", + "content": " (where attribute word embeddings are directly used in " + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "inline_equation", + "content": "S_{a}" + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "text", + "content": "), " + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{H}" + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "text", + "content": " (where the concatenation of " + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_a" + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "text", + "content": " is fed to " + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "text", + "content": "), " + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "text", + "content": " (where the concatenation of " + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_{o^*}" + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "text", + "content": " is directly fed to " + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{H}" + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "text", + "content": "), and " + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "text", + "content": " that is fed to " + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{H}" + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "text", + "content": ", which are corresponded to variants (3)-(6) in Tab. 3. Note that if " + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "text", + "content": " is presented then " + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "text", + "content": " is required to be presented also because the concatenation of " + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_a" + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "text", + "content": " requires changing the number of dimensions to that of " + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "text", + "content": " through " + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "text", + "content": ". Also, " + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "text", + "content": " can not be ablated only otherwise the model changes to variant (3). Compared to variant (7), all results are mostly declined, indicating that optimizing the model with " + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{H}" + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "text", + "content": " is essential. As for variant (5), it performs worse on seen and unseen images compared with variant (4), indicating the importance of using the attribute hyper learner. Comparing results of variants (5) with (6), we observe that" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11203" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 70, + 214, + 190 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 214, + 190 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 214, + 190 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 214, + 190 + ], + "type": "image", + "image_path": "6dc1096afc1924895fd146605ee1180b4c2e7330c74e9be8c0743040ebe049c6.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 214, + 70, + 380, + 190 + ], + "blocks": [ + { + "bbox": [ + 214, + 70, + 380, + 190 + ], + "lines": [ + { + "bbox": [ + 214, + 70, + 380, + 190 + ], + "spans": [ + { + "bbox": [ + 214, + 70, + 380, + 190 + ], + "type": "image", + "image_path": "2e2087136a868572667efafb1833479fd344d62fa00301798e16c29cb245f808.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 381, + 70, + 547, + 190 + ], + "blocks": [ + { + "bbox": [ + 381, + 70, + 547, + 190 + ], + "lines": [ + { + "bbox": [ + 381, + 70, + 547, + 190 + ], + "spans": [ + { + "bbox": [ + 381, + 70, + 547, + 190 + ], + "type": "image", + "image_path": "b927075be46c20eb35a24fb5a79e03a953902c49ceba1d492d331530162941ad.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 48, + 191, + 214, + 297 + ], + "blocks": [ + { + "bbox": [ + 48, + 191, + 214, + 297 + ], + "lines": [ + { + "bbox": [ + 48, + 191, + 214, + 297 + ], + "spans": [ + { + "bbox": [ + 48, + 191, + 214, + 297 + ], + "type": "image", + "image_path": "ce7c3b094c98fb9e9e380289233ed066ef12d07ac5a34b6ea56d0e947325a5c6.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 137, + 308, + 455, + 319 + ], + "lines": [ + { + "bbox": [ + 137, + 308, + 455, + 319 + ], + "spans": [ + { + "bbox": [ + 137, + 308, + 455, + 319 + ], + "type": "text", + "content": "Figure 4. Influence of weighting factor " + }, + { + "bbox": [ + 137, + 308, + 455, + 319 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 137, + 308, + 455, + 319 + ], + "type": "text", + "content": " on AUC, seen accuracy, and unseen accuracy." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 214, + 191, + 380, + 297 + ], + "blocks": [ + { + "bbox": [ + 214, + 191, + 380, + 297 + ], + "lines": [ + { + "bbox": [ + 214, + 191, + 380, + 297 + ], + "spans": [ + { + "bbox": [ + 214, + 191, + 380, + 297 + ], + "type": "image", + "image_path": "d092a4294e42482f5a6987c4a906fd2100f835417fc42d74d361f749af9c33b5.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 381, + 191, + 547, + 297 + ], + "blocks": [ + { + "bbox": [ + 381, + 191, + 547, + 297 + ], + "lines": [ + { + "bbox": [ + 381, + 191, + 547, + 297 + ], + "spans": [ + { + "bbox": [ + 381, + 191, + 547, + 297 + ], + "type": "image", + "image_path": "47f179b52754c14b8b7b2b6c861761344dcbae469df4a7064525551e6c798108.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 329, + 288, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 329, + 288, + 413 + ], + "spans": [ + { + "bbox": [ + 46, + 329, + 288, + 413 + ], + "type": "text", + "content": "adding the attribute hyper learner " + }, + { + "bbox": [ + 46, + 329, + 288, + 413 + ], + "type": "inline_equation", + "content": "\\mathcal{H}" + }, + { + "bbox": [ + 46, + 329, + 288, + 413 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 46, + 329, + 288, + 413 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 46, + 329, + 288, + 413 + ], + "type": "text", + "content": " without image visual embedding " + }, + { + "bbox": [ + 46, + 329, + 288, + 413 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 46, + 329, + 288, + 413 + ], + "type": "text", + "content": " marginally increases overfitting to seen images. Results of variant (6) present the best generalization compared with variants (3)-(5) because adding " + }, + { + "bbox": [ + 46, + 329, + 288, + 413 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 46, + 329, + 288, + 413 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 46, + 329, + 288, + 413 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 329, + 288, + 413 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 46, + 329, + 288, + 413 + ], + "type": "inline_equation", + "content": "\\mathcal{H}" + }, + { + "bbox": [ + 46, + 329, + 288, + 413 + ], + "type": "text", + "content": " provides diverse instances that are seen for " + }, + { + "bbox": [ + 46, + 329, + 288, + 413 + ], + "type": "inline_equation", + "content": "\\mathcal{H}" + }, + { + "bbox": [ + 46, + 329, + 288, + 413 + ], + "type": "text", + "content": " during training since the number of image visual embeddings is far more than the number of object word embeddings." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 415, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 415, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 415, + 288, + 714 + ], + "type": "text", + "content": "Lastly, we conduct experiments to study the impact of weighting factor " + }, + { + "bbox": [ + 46, + 415, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 415, + 288, + 714 + ], + "type": "text", + "content": " in Eq. (14) on all datasets. In detail, we present results of AUC, seen accuracy, and unseen accuracy in Fig. 4 with " + }, + { + "bbox": [ + 46, + 415, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\alpha \\in [0,1]" + }, + { + "bbox": [ + 46, + 415, + 288, + 714 + ], + "type": "text", + "content": " with an interval of 0.1. It can be observed that all results of AUC increase first and then decrease with " + }, + { + "bbox": [ + 46, + 415, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 415, + 288, + 714 + ], + "type": "text", + "content": " increases from 0.0. The peaks of AUC are reached when " + }, + { + "bbox": [ + 46, + 415, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 415, + 288, + 714 + ], + "type": "text", + "content": " equals 0.5, 0.1, and 0.3 in UT-Zappos50K, MIT-States, and C-GQA. This phenomenon reveals that learning to classify attributes, objects, and compositions all contribute to making our model reach optimal. Additionally, it can be noticed that the results of AUC are all generally declined when " + }, + { + "bbox": [ + 46, + 415, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 415, + 288, + 714 + ], + "type": "text", + "content": " changes from 0.0 to 1.0. This is because attribute-object compositions involve not only the side information of attribute and object, but also the contextuality between attribute and object. As for the results of seen and unseen accuracies reported in the second row, the same trend can be observed. Specifically, results of unseen accuracy are more sensitive than seen accuracy and also have peaks with various " + }, + { + "bbox": [ + 46, + 415, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 415, + 288, + 714 + ], + "type": "text", + "content": ", indicating that " + }, + { + "bbox": [ + 46, + 415, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 415, + 288, + 714 + ], + "type": "text", + "content": " also has an impact on the generalization ability of our model. In conclusion, using a small weighting factor " + }, + { + "bbox": [ + 46, + 415, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 415, + 288, + 714 + ], + "type": "text", + "content": " is always better than using a larger one, indicating that modeling contextuality between attribute and object is a bit more beneficial to the CZSL task than separately classifying attributes and objects." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 328, + 379, + 341 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 328, + 379, + 341 + ], + "spans": [ + { + "bbox": [ + 306, + 328, + 379, + 341 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 348, + 547, + 539 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 348, + 547, + 539 + ], + "spans": [ + { + "bbox": [ + 304, + 348, + 547, + 539 + ], + "type": "text", + "content": "In this work, we address the attribute diversity problem in Compositional Zero-Shot Learning. As a solution, we propose a Conditional Attribute Network (CANet) to learn attributes conditioned on the recognized object and input image. We first decompose the probability of attribute and object recognition conditioned on the input image to lay a foundation for learning conditional attributes. Then, we build an attribute learning framework to encode conditional attribute embeddings. Experiments show that our model outperforms recent CZSL approaches and achieves new state-of-the-art results. Despite the better attribute recognition performance, a limitation is that our model is less qualified to handle object long-tailed distribution in terms of attribute mentioned in Sec. 4.2. Future works can be focused on solving the problem above while learning conditional attributes." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 551, + 421, + 565 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 551, + 421, + 565 + ], + "spans": [ + { + "bbox": [ + 306, + 551, + 421, + 565 + ], + "type": "text", + "content": "6. Acknowledgements" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 571, + 547, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 571, + 547, + 643 + ], + "spans": [ + { + "bbox": [ + 304, + 571, + 547, + 643 + ], + "type": "text", + "content": "This work was supported by National Key R&D Program of China (No.2020AAA0106900), the National Natural Science Foundation of China (No.U19B2037), Shaanxi Provincial Key R&D Program (No.2021KWZ-03), and Natural Science Basic Research Program of Shaanxi (No.2021JCW-03)." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "11204" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 146 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 146 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 146 + ], + "type": "text", + "content": "[1] Muhammad Umer Anwaar, Rayyan Ahmad Khan, Zhihui Pan, and Martin Kleinsteuber. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 10823-10832, 2019. 4" + } + ] + } + ], + "index": 20 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "text", + "content": "11206" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Learning Correspondence Uncertainty via Differentiable Nonlinear Least Squares/8f30fa60-e502-4ee5-838a-d9c7713dcf6d_content_list.json b/2023/Learning Correspondence Uncertainty via Differentiable Nonlinear Least Squares/8f30fa60-e502-4ee5-838a-d9c7713dcf6d_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..5222fde087b44613cdd09db3d666635a8782a224 --- /dev/null +++ b/2023/Learning Correspondence Uncertainty via Differentiable Nonlinear Least Squares/8f30fa60-e502-4ee5-838a-d9c7713dcf6d_content_list.json @@ -0,0 +1,1783 @@ +[ + { + "type": "text", + "text": "Learning Correspondence Uncertainty via Differentiable Nonlinear Least Squares", + "text_level": 1, + "bbox": [ + 267, + 130, + 702, + 179 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Dominik Muhle1,2 \n1TU Munich", + "bbox": [ + 86, + 205, + 235, + 239 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Lukas Koestler $^{1,2}$", + "bbox": [ + 285, + 205, + 428, + 223 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Krishna Murthy Jatavallabhula4", + "bbox": [ + 480, + 207, + 732, + 224 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Daniel Cremers1,2,3", + "bbox": [ + 785, + 205, + 941, + 222 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "2Munich Center for Machine Learning", + "bbox": [ + 276, + 224, + 581, + 243 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{3}$ University of Oxford", + "bbox": [ + 633, + 224, + 808, + 242 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{4}$ MIT", + "bbox": [ + 862, + 224, + 908, + 239 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{dominik.muhle, lukas.koestler, cremers}@tum.de jkrishna@mit.edu", + "bbox": [ + 215, + 244, + 810, + 260 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "images with correspondences", + "bbox": [ + 179, + 286, + 331, + 297 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/1b84e559e923c5aebadce76925f11adac34b5822314ed1b79298475374c4609c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 81, + 297, + 294, + 354 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/e8cddea1f1b77514392f23b15d7e006badca92b2740500998d99c237bb64db43.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 294, + 297, + 406, + 349 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/4ded2522acfb42dfc6f33f42b99df32a9b55a7fd46c7fc3366c3f37f17618514.jpg", + "image_caption": [ + "uncertainty estimates from images" + ], + "image_footnote": [], + "bbox": [ + 81, + 354, + 294, + 412 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/bb69457b3eeab57802812bcafb9df5e6c8d6e8feb5d8323df774fd9ea9573e37.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 294, + 354, + 406, + 412 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/230ca915a5199cf01d184cd2f7a859e7ab082227beb40ac99658ff08a0fbef1c.jpg", + "image_caption": [ + "Figure 1. We present a differentiable nonlinear least squares (DNLS) framework for learning feature correspondence quality by computing per-feature positional uncertainty. The uncertainty estimates (left, bottom images) are regressed from a pose estimation error (middle), enabling the framework across a range of (handcrafted, learned) feature extractors. Our learned covariances (right, orange trajectory) improve orientation estimation by up to $11\\%$ over state-of-the-art probabilistic pose estimation methods on the KITTI dataset [21]." + ], + "image_footnote": [], + "bbox": [ + 411, + 289, + 571, + 424 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/07c047a63adcaf8f25897f98fe52484315c72cf001ae413d0cb5740812d0bbef.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 576, + 286, + 888, + 422 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 500, + 313, + 515 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We propose a differentiable nonlinear least squares framework to account for uncertainty in relative pose estimation from feature correspondences. Specifically, we introduce a symmetric version of the probabilistic normal epipolar constraint, and an approach to estimate the covariance of feature positions by differentiating through the camera pose estimation procedure. We evaluate our approach on synthetic, as well as the KITTI and EuRoC real-world datasets. On the synthetic dataset, we confirm that our learned covariances accurately approximate the true noise distribution. In real world experiments, we find that our approach consistently outperforms state-of-the-art nonprobabilistic and probabilistic approaches, regardless of the feature extraction algorithm of choice.", + "bbox": [ + 73, + 531, + 470, + 743 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 762, + 207, + 777 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Estimating the relative pose between two images given mutual feature correspondences is a fundamental problem in computer vision. It is a key component of structure from motion (SfM) and visual odometry (VO) methods which in turn fuel a plethora of applications from autonomous vehicles or robots to augmented and virtual reality.", + "bbox": [ + 75, + 787, + 468, + 878 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Estimating the relative pose - rotation and translation - between two images, is often formulated as a geometric problem that can be solved by estimating the essential matrix [42] for calibrated cameras, or the fundamental matrix [24] for uncalibrated cameras. Related algorithms like the eight-point algorithm [23, 42] provide fast solutions. However, essential matrix based approaches suffer issues such as solution multiplicity [18, 24] and planar degeneracy [33]. The normal epipolar constraint (NEC) [34] addresses issues such as by estimating the issues such as which leads to more accurate relative poses [33].", + "bbox": [ + 500, + 500, + 890, + 667 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Neither of the aforementioned algorithms takes into account the quality of feature correspondences – an important cue that potentially improves pose estimation accuracy. Instead, feature correspondences are classified into inliers and outliers through a RANSAC scheme [11]. However, keypoint detectors [12, 56] for feature correspondences or tracking algorithms [63] yield imperfect points [40] that exhibit a richer family of error distributions, as opposed to an inlier-outlier distribution family. Algorithms, that make use of feature correspondence quality have been proposed for essential/fundamental matrix estimation [7, 53] and for the NEC [48], respectively.", + "bbox": [ + 496, + 670, + 892, + 852 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "While estimating the relative pose can be formulated as a classical optimization problem [15, 33], the rise in popularity of deep learning has led to several works augmenting", + "bbox": [ + 498, + 856, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "Project Page: https://dominikmuhle.github.io/dnls_covs/", + "bbox": [ + 99, + 888, + 398, + 901 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "13102", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/6ae52ad7dfb3af692a5e97429cd7ca162b89034198b0a988a2748753037aa58b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 125, + 88, + 483, + 172 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/b542b81cb7ec3599f81598486d9a8660e9b0dd0a0613b12c0d16997c85847200.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 486, + 88, + 843, + 172 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/7436d32d3240a57c0a2ca596cf36c1c79147156b8e05f7ceef48a47d4fea599c.jpg", + "image_caption": [ + "(a) covariances from [48] per pixel", + "(c) learned covariances per pixel (Ours)" + ], + "image_footnote": [], + "bbox": [ + 122, + 189, + 480, + 273 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/bad77c254c535aeb660e76ba6bf3884c3eac9a4e58651da5492e0ce55eb4ede0.jpg", + "image_caption": [ + "(b) points and covariances [48]", + "(d) points and learned covariances (Ours)", + "Figure 2. Comparison between covariances used in [48] (first row) and our learned covariances (second row). The first column shows a dense color coded $(s, \\alpha, \\beta$ mapped to HLS with $\\gamma$ correction) representation for each pixel, while the second column shows subsampled keypoints and their corresponding (enlarged) covariances. The higher saturation in (a) shows that the covariances are more anisotropic. The learned covariances (c) show a more fine-grained detail in the scale (brightness) and less blurring than the covariances in (a)." + ], + "image_footnote": [], + "bbox": [ + 483, + 188, + 841, + 273 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "VO or visual simultaneous localisation and mapping (VSLAM) pipelines with learned components. GN-Net [67] learns robust feature representations for direct methods like DSO [15]. For feature based methods Superpoint [12] provides learned features, while Superglue [57] uses graph neural networks to find corresponding matches between feature points in two images. DSAC introduces a differential relaxation to RANSAC that allows gradient flow through the otherwise non-differentiable operation. In [53] a network learns to re-weight correspondences for estimating the fundamental matrix. PixLoc [58] estimates the pose from an image and a 3D model based on direct alignment.", + "bbox": [ + 75, + 349, + 468, + 532 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work we combine the predictive power of deep learning with the precision of geometric modeling for highly accurate relative pose estimation. Estimating the noise distributions for the feature positions of different feature extractors allows us to incorporate this information into relative pose estimation. Instead of modeling the noise for each feature extractor explicitly, we present a method to learn these distributions from data, using the same domain that the feature extractors work with - images. We achieve this based on the following technical contributions:", + "bbox": [ + 75, + 534, + 468, + 686 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We introduce a symmetric version of the probabilistic normal epipolar constraint (PNEC), that more accurately models the geometry of relative pose estimation with uncertain feature positions.", + "- We propose a learning strategy to minimize the relative pose error by learning feature position uncertainty through differentiable nonlinear least squares (DNLS), see Fig. 1.", + "- We show with synthetic experiments, that using the gradient from the relative pose error leads to meaningful estimates of the positional uncertainty that reflect the correct error distribution.", + "- We validate our approach on real-world data in a visual odometry setting and compare our method to non" + ], + "bbox": [ + 76, + 689, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "probabilistic relative pose estimation algorithms, namely Nister 5pt [50], and NEC [33], as well as to the PNEC with non-learned covariances [48].", + "bbox": [ + 511, + 349, + 890, + 396 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We show that our method is able to generalize to different feature extraction algorithms such as SuperPoint [12] and feature tracking approaches on real-world data.", + "- We release the code for all experiments and the training setup to facilitate future research." + ], + "bbox": [ + 500, + 396, + 890, + 470 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 492, + 638, + 508 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "This work is on deep learning for improving frame-to-frame relative pose estimation by incorporating feature position uncertainty with applications to visual odometry. We therefore restrict our discussion of related work to relative pose estimation in visual odometry, weighting correspondences for relative pose estimation, and deep learning in the context of VSLAM. For a broader overview over VSLAM we refer the reader to more topic-specific overview papers [10, 65] and to the excellent books by Hartley and Zisserman [24] and by Szeliski [62].", + "bbox": [ + 496, + 520, + 890, + 671 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Relative Pose Estimation in Visual Odometry. Finding the relative pose between two images has a long history in computer vision, with the first solution for perspective images reaching back to 1913 by Kruppa [35]. Modern methods for solving this problem can be classified into feature-based and direct methods. The former rely on feature points extracted in the images together with geometric constraints like the epipolar constraint or the normal epipolar constraint [34] to calculate the relative pose. The latter optimize the pose by directly considering the intensity differences between the two images and rose to popularity with LSD-SLAM [16] and DSO [15]. Since direct methods work on the assumption of brightness or irradiance constancy they require the appearance to be somewhat similar across images. In turn, keypoint based methods rely", + "bbox": [ + 496, + 674, + 892, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "13103", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "on suitable feature extractors which can exhibit significant amounts of noise and uncertainty. In this paper we propose a method to learn the intrinsic noise of keypoint detectors – therefore, the following will focus on feature based relative pose estimation.", + "bbox": [ + 75, + 90, + 470, + 167 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "One of the most widely used parameterizations for reconstructing the relative pose from feature correspondences is the essential matrix, given calibrated cameras, or the fundamental matrix in the general setting. Several solutions based on the essential matrix have been proposed [36, 38, 42, 50, 61]. They include the linear solver by Longuet-Higgins [42], requiring 8 correspondences, or the solver by Nister et al. [51] requiring the minimal number of 5 correspondences. However, due to their construction, essential matrix methods deteriorate for purely rotational motion with noise-free correspondences [33]. As an alternative, methods that do not use the essential matrix have been proposed - they either estimate the relative pose using quaternions [17] or make use of the normal epipolar constraint (NEC) by Kneip and Lynen [33, 34]. The latter addresses the problems of the essential matrix by estimating rotation independent of the translation. [6] shows how to obtain the global minimum for the NEC. Further work, that disentangles rotation and translation can be found in [39].", + "bbox": [ + 75, + 169, + 470, + 455 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Weighting of Feature Correspondences. Keypoints in images can exhibit significant noise, deteriorating the performance for pose estimation significantly [22]. The noise characteristics of the keypoint positions depend on the feature extractor. For Kanade-Lucas-Tomasi (KLT) tracking [44, 63] approaches, the position uncertainty has been investigated in several works [20, 59, 60, 72]. The uncertainty was directly integrated into the tracking in [14]. [71] proposed a method to obtain anisotropic and inhomogeneous covariances for SIFT [43] and SURF [3].", + "bbox": [ + 75, + 459, + 468, + 609 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given the imperfect keypoint positions, not all correspondences are equally well suited for estimating the relative pose. [22] showed the effect of the noise level on the accuracy of the pose estimation. Limiting the influence of bad feature correspondences has been studied from a geometrical and a probabilistic perspective. Random sample consensus (RANSAC) [19] is a popular method to classify datapoints into inliers and outliers that can be easily integrated into feature based relative pose estimation pipelines. Ranftl et al. [53] relax the hard classification for inlier and outlier and use deep learning to find a robust fundamental matrix estimator in the presence of outliers in an iteratively reweighted least squares (IRLS) fashion. DSAC [5] models RANSAC as a probabilistic process to make it differentiable. Other lines of work integrate information about position uncertainty directly into the alignment problem. For radar based SLAM, [8] incorporates keypoint uncertainty in radar images, with a deep network predicting the uncertainty. Image based position uncertainty was investigated", + "bbox": [ + 75, + 613, + 470, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "from the statistical, [27, 28], the photogrammetry [46] and the computer vision perspective [7, 29]. [7] and [29] debated the benefit of incorporating position uncertainty into fundamental matrix estimation. We base our method on the probabilistic normal epipolar constraint (PNEC) [48], that improved on the NEC by extending it to a probabilistic view. It achieved better results on real-world data with covariances approximated using the Boltzmann distribution [4]. We expand on this idea by learning covariances (see Fig. 2) agnostic of the keypoints extractor used to further improve pose estimation.", + "bbox": [ + 496, + 90, + 890, + 256 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Deep Learning in VSLAM. Deep Learning has transformed computer vision in the last decade. While deep networks have been successfully used for tasks like detection [54], semantic segmentation [41], and recently novel view synthesis [47], they have also found application in VSLAM pipelines. DVSO [69] and D3VO [68] leveraged deep learning to improve the precision for direct methods, while GN-Net [67] predicts robust and dense feature maps. Several works proposed to learn keypoint extractors, for feature based pose estimation, such as SuperPoint [12] and LIFT [70]. SuperGlue [57] enabled feature matching with graph neural networks. Other lines of work leverage deep learning for localization by making parts of the pose estimation pipeline differentiable [2,5,58,64]. Works, that directly predicting the pose include PoseNet [30] and CTCNet [25] that uses self-supervised learning with a cycle-consistency loss for VO. [40] learns image representations by refining keypoint positions and camera poses in a post-processing step of a structure-from-motion pipeline. $\\nabla$ SLAM [26] presents a differentiable dense SLAM system with several components (e.g., the Levenberg-Marquardt [37, 45] optimizer).", + "bbox": [ + 496, + 257, + 892, + 575 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 500, + 585, + 589, + 602 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In the following, we present our framework to estimate positional uncertainty of feature points by leveraging DNLS. We learn the noise covariances through a forward and backward step. In the forward step, the covariances are used in a probabilistic pose estimation optimization, namely the PNEC. In the backward step, the gradient from the pose error is back-propagated through the optimization to the covariances. From there we can train a neural network to predict the keypoint position uncertainty from the images. We start by summarizing the asymmetric PNEC [48] and for the first time introduce its symmetric counterpart.", + "bbox": [ + 496, + 612, + 890, + 779 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Prerequisites", + "text_level": 1, + "bbox": [ + 500, + 787, + 635, + 801 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Notation. We follow the notation of [48]. Bold lowercase letters (e.g. $\\pmb{f}$ ) denote vectors, whereas bold uppercase letters (e.g. $\\pmb{\\Sigma}$ ) denote matrices. $\\hat{\\pmb{u}} \\in \\mathbb{R}^{3 \\times 3}$ represents the skew-symmetric matrix of the vector $\\pmb{u} \\in \\mathbb{R}^3$ such that the cross product between two vectors can be rewritten as a matrix-vector operation, i.e. $\\pmb{u} \\times \\pmb{v} = \\hat{\\pmb{u}}\\pmb{v}$ . The transpose is", + "bbox": [ + 496, + 809, + 890, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "13104", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/43455a9955841ec37d299f9eea2d6cdac9368debcb666b186a52bc6fea6d0013.jpg", + "image_caption": [ + "Figure 3. Architecture: We extract the uncertainty per image for every pixel using a UNet [55] backbone. Using keypoint locations from a keypoint detector, we obtain the keypoints with their estimated positional uncertainty. The relative pose is then estimated using a DNLS optimization. The UNet is updated by backpropagating the gradient (obtained by implicit differentiation) to the network output." + ], + "image_footnote": [], + "bbox": [ + 109, + 88, + 856, + 253 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "denoted by the superscript $\\top$ . We deviate from [48] in the following: variables of the second frame are marked with the ' superscript, while variables of the first frame do not have a superscript. We represent the relative pose between images as a rigid-body transformation consisting of a rotation matrix $R \\in SO(3)$ and a unit length translation $t \\in \\mathbb{R}^3$ ( $\\| t \\| = 1$ is imposed due to scale-invariance).", + "bbox": [ + 75, + 301, + 473, + 409 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. The Probabilistic Normal Epipolar Constraint", + "text_level": 1, + "bbox": [ + 76, + 419, + 468, + 435 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The asymmetric probabilistic normal epipolar constraint (PNEC) estimates the relative pose, give two images $I, I'$ of the same scene under the assumption of uncertain feature positions in the second image. A feature correspondences is given by $\\pmb{p}_i, \\pmb{p}_i'$ in the image plane, where the uncertainty of $\\pmb{p}_i'$ is represented by the corresponding covariance $\\Sigma_{2\\mathrm{D},i}'$ . To get the epipolar geometry for the PNEC the feature points are unprojected using the camera intrinsics, giving unit length bearing vectors $\\pmb{f}_i, \\pmb{f}_i'$ . The uncertainty of $\\pmb{f}_i'$ is now represented by $\\Sigma_i'$ . Estimating the relative pose is done by minimizing the PNEC cost function as defined in [48]. For convenience we recap the energy function", + "bbox": [ + 75, + 443, + 472, + 625 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nE (\\boldsymbol {R}, \\boldsymbol {t}) = \\sum_ {i} \\frac {e _ {i} ^ {2}}{\\sigma_ {i} ^ {2}} = \\sum_ {i} \\frac {| \\boldsymbol {t} ^ {\\top} (\\boldsymbol {f} _ {i} \\times \\boldsymbol {R} \\boldsymbol {f} _ {i} ^ {\\prime}) | ^ {2}}{\\boldsymbol {t} ^ {\\top} \\hat {\\boldsymbol {f}} _ {i} \\boldsymbol {R} \\boldsymbol {\\Sigma} _ {i} ^ {\\prime} \\boldsymbol {R} ^ {\\top} \\hat {\\boldsymbol {f}} _ {i} ^ {\\top} \\boldsymbol {t}}, (1)\n$$\n", + "text_format": "latex", + "bbox": [ + 114, + 636, + 468, + 676 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "in our notation. As mentioned previously, this asymmetric PNEC in [48] only considers uncertainties $\\Sigma^{\\prime}$ in the second frame. While this assumption might hold for the KLT tracking [66] used in [48], this leaves out important information when using other keypoint detectors like ORB [56] or SuperPoint [12]. Therefore, we will introduce a symmetric version of the PNEC that is more suitable for our task in the following.", + "bbox": [ + 75, + 686, + 468, + 806 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Making the PNEC symmetric. As in [48] we assume the covariance of the bearing vectors $\\pmb{f}_i$ and $\\pmb{f}_i'$ to be gaussian, their covariance matrices denoted by $\\pmb{\\Sigma}_i$ and $\\pmb{\\Sigma}_i'$ , respectively. The new variance can be approximated as", + "bbox": [ + 75, + 808, + 470, + 869 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\sigma_ {s, i} ^ {2} = \\boldsymbol {t} ^ {\\top} \\left(\\left(\\boldsymbol {R} \\hat {\\boldsymbol {f}} _ {i} ^ {\\prime}\\right) \\boldsymbol {\\Sigma} _ {i} \\left(\\boldsymbol {R} \\hat {\\boldsymbol {f}} _ {i} ^ {\\prime}\\right) ^ {\\top} + \\hat {\\boldsymbol {f}} _ {i} \\boldsymbol {R} \\boldsymbol {\\Sigma} _ {i} ^ {\\prime} \\boldsymbol {R} ^ {\\top} \\hat {\\boldsymbol {f}} _ {i} ^ {\\top}\\right) \\boldsymbol {t}. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 94, + 882, + 468, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In the supplementary material we derive the variance and show the validity of this approximation given the geometry of the problem. This new variance now gives us the new symmetric PNEC with its following energy function", + "bbox": [ + 496, + 301, + 892, + 363 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nE _ {s} (\\boldsymbol {R}, \\boldsymbol {t}) = \\sum_ {i} \\frac {e _ {i} ^ {2}}{\\sigma_ {s , i} ^ {2}} \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 624, + 373, + 890, + 411 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. DNLS for Learning Covariances", + "text_level": 1, + "bbox": [ + 500, + 422, + 785, + 436 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We want to estimate covariances $\\Sigma_{2\\mathrm{D}}$ and $\\Sigma_{2\\mathrm{D}}^{\\prime}$ (in the following collectively denoted as $\\Sigma_{2\\mathrm{D}}$ for better readability) in the image plane", + "bbox": [ + 496, + 445, + 892, + 491 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {\\Sigma} _ {2 \\mathrm {D}} = \\underset {\\boldsymbol {\\Sigma} _ {2 \\mathrm {D}}} {\\arg \\min } \\mathcal {L}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 630, + 503, + 890, + 526 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "such that they minimize a loss function $\\mathcal{L}$ of the estimated pose. Since we found that the rotational error of the PNEC is more stable than the translational error, we chose to minimize only the rotational error", + "bbox": [ + 496, + 537, + 893, + 597 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\ne _ {\\text {r o t}} = \\angle \\tilde {\\boldsymbol {R}} ^ {\\top} \\boldsymbol {R} \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 683, + 608, + 890, + 626 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} (\\tilde {\\boldsymbol {R}}, \\boldsymbol {R}; \\boldsymbol {\\Sigma} _ {2 \\mathrm {D}}) = e _ {\\mathrm {r o t}} \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 609, + 630, + 890, + 647 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "between the ground truth rotation $\\tilde{\\pmb{R}}$ and the estimated rotation $\\pmb{R}$ . We obtain", + "bbox": [ + 496, + 661, + 890, + 691 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {R} = \\arg \\min _ {\\boldsymbol {R}} E _ {s} (\\boldsymbol {R}, t; \\Sigma_ {2 \\mathrm {D}}) \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 599, + 704, + 890, + 726 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "by minimizing Eq. 3. To learn the covariances that minimize the rotational error, we can follow the gradient $d\\mathcal{L} / d\\Sigma_{2\\mathrm{D}}$ . Implicit differentiation allows us to compute the gradient as", + "bbox": [ + 496, + 737, + 890, + 797 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {d \\mathcal {L}}{d \\boldsymbol {\\Sigma} _ {2 \\mathrm {D}}} = - \\frac {\\partial^ {2} E _ {s}}{\\partial \\boldsymbol {\\Sigma} _ {2 \\mathrm {D}} \\partial \\boldsymbol {R} ^ {\\top}} \\left(\\frac {\\partial^ {2} E _ {s}}{\\partial \\boldsymbol {R} \\partial \\boldsymbol {R} ^ {\\top}}\\right) ^ {- 1} \\frac {e _ {\\text {r o t}}}{\\partial \\boldsymbol {R}}. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 544, + 809, + 890, + 845 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For a detailed derivation of Eq. 8 and other methods, that unroll the optimization, to obtain the gradient we refer the interested reader to [13].", + "bbox": [ + 496, + 854, + 892, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "13105", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/6a7ae7993f2e1a6147cf413b4d48274275ae7abfa8e14fa7366fd5cb1c9e1767.jpg", + "image_caption": [ + "(a) $e_{\\mathrm{rot}}$ during training" + ], + "image_footnote": [], + "bbox": [ + 80, + 88, + 271, + 176 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/1f71886f6535a19698c9ae4a0a949eeac1600bdc7cfb158d4821fc1edad4a2cf.jpg", + "image_caption": [ + "(b) $\\sigma_{norm}^2$ error during training" + ], + "image_footnote": [], + "bbox": [ + 272, + 89, + 467, + 176 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/f21aa1be7d28aa2e0aac6295ff8bde7db74602f93907582731cf394ba994536f.jpg", + "image_caption": [ + "Figure 4. Rotational error (a) and differences between the true residual variance $\\tilde{\\sigma}^2$ and the learned variance $\\sigma^2$ (b) over the training epochs. Starting from uniform covariances, our method adapts the covariances for each keypoint to minimize the rotational error. Simultaneously, this leads to a better estimate of $\\sigma^2$ ." + ], + "image_footnote": [], + "bbox": [ + 89, + 268, + 459, + 400 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/d0e316f93a7aef38fa4a46b97b9d16a9d87d491db9c8834e9ed6a4f48e7006ec.jpg", + "image_caption": [ + "(a) covariance matrices in the 1st frame after 100 epochs training", + "(b) covariance matrices in the 2nd frame after 100 epochs training", + "Figure 5. Estimated (red) covariance ellipses in the first (a) and the second (b) frame, learned from 128000 examples. Ground truth (green) covariances as comparison. Although the gradient minimizes the rotational error (see Fig. 4a), it is not capable of learning the correct covariance in the image plane." + ], + "image_footnote": [], + "bbox": [ + 89, + 416, + 457, + 547 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Supervised Learning. The goal of the paper is for a neural network $F$ learn the noise distributions of a keypoint detector. Given an image and a keypoint position, the network should predict the covariance of the noise $\\Sigma_{2\\mathrm{D},i} = F(\\boldsymbol {I},\\boldsymbol {p}_i)$ . The gradient $d\\mathcal{L} / d\\Sigma_{2\\mathrm{D}}$ allows for the network to learn the covariance matrices in an end-to-end manner by regression on the relative pose error. Given a dataset with known ground truth poses, we can use", + "bbox": [ + 75, + 648, + 468, + 768 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\sup } = e _ {\\text {r o t}} \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 233, + 782, + 468, + 797 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "as a training loss. This ensures, that learned covariances effectively minimize the rotational error. See Fig. 3 for overview of the training process.", + "bbox": [ + 75, + 810, + 468, + 854 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Self-Supervised Learning. Finding a suitable annotated dataset for a specific task is often non-trivial. For our task, we need accurate ground truth poses that are difficult to ac", + "bbox": [ + 75, + 854, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "quire. But given a stream of images, like in VO, our method can be adapted to train a network in a self-supervised manner without the need for ground truth poses. For this, we follow the approach of [25] to exploit the cycle-consistency between a tuple of images. The cycle-consistency loss for a triplet $\\{I_1, I_2, I_3\\}$ of images is given by", + "bbox": [ + 496, + 90, + 890, + 181 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {c y c l}} = \\angle \\prod_ {(i, j) \\in \\mathcal {P}} \\boldsymbol {R} _ {i j}, \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 619, + 194, + 890, + 227 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf{R}_{ij}$ is the estimated rotation between images $I_{i}$ and $I_{j}$ and $\\mathcal{P} = \\{(1,2),(2,3),(3,1)\\}$ defines the cycle. As in [25], we also define an anchor loss", + "bbox": [ + 498, + 239, + 890, + 285 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {a n c h o r}} = \\sum_ {(i, j) \\in \\mathcal {P}} \\angle R _ {i j} R _ {i j, \\mathrm {N E C}} ^ {\\top} \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 591, + 297, + 890, + 330 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "with the NEC rotation estimate, as a regularising term. In contrast to [25], our method does not risk learning degenerate solutions from the cycle-consistency loss, since the rotation is estimated using independently detected keypoints. The final loss is then given by", + "bbox": [ + 496, + 342, + 890, + 417 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {s e l f}} = \\mathcal {L} _ {\\text {c y c l}} + \\lambda \\mathcal {L} _ {\\text {a n c h o r}}. \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 612, + 431, + 890, + 448 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 460, + 632, + 479 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We evaluate our method in both synthetic and real-world experiments. Over the synthetic data, we investigate the ability of the gradient to learn the underlying noise distribution correctly by overfitting covariance estimates directly. We also investigate if better noise estimation leads to a reduces rotational error.", + "bbox": [ + 496, + 487, + 890, + 577 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "On real-world data, we use the gradient to train a network to predicts the noise distributions from images for different keypoint detectors. We explore fully supervised and self-supervised learning techniques for SuperPoint [12] and Basalt [66] KLT-Tracks to verify that our method is agnostic to the type of feature descriptor used (classical vs learned). We evaluate the performance of the learned covariances in a visual odometry setting on the popular KITTI odometry and the EuRoC dataset. We also evaluate generalization capabilities from the KITTI to the EuRoC dataset.", + "bbox": [ + 496, + 579, + 890, + 729 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For our experiments we implement Eq. 3 in both Theseus [52] and ceres [1]. We use the Theseus implementation to train our network, since it allows for batched optimization and provides the needed gradient (see Eq. 8). However, we use the ceres implementation for our evaluation. We found the Levenberg-Marquardt optimization of ceres to be faster and more stable than its theseus counterpart.", + "bbox": [ + 496, + 729, + 890, + 835 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Simulated Experiments", + "text_level": 1, + "bbox": [ + 500, + 845, + 715, + 863 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In the simulated experiments we overfit covariance estimates for a single relative pose estimation problem using", + "bbox": [ + 500, + 869, + 890, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "13106", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/a4b616e032eafc2ed38439704b3002ade950df0f9942281d46d3f46f3bdef8f5.jpg", + "image_caption": [ + "(a) $e_{\\mathrm{rot}}$ during training" + ], + "image_footnote": [], + "bbox": [ + 80, + 89, + 271, + 178 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/d3c7bd319872a4185cc7ac9241beec52f03f1100a4505dfe71995ca03170e7c4.jpg", + "image_caption": [ + "(b) $\\sigma_{norm}^2$ error during training" + ], + "image_footnote": [], + "bbox": [ + 272, + 88, + 467, + 178 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/7118faac46243aca99c028df3a74f866901f9501ab60f43311d429339cb77bbb.jpg", + "image_caption": [ + "Figure 6. Rotational error (a) and differences between the true residual variance $\\tilde{\\sigma}^2$ and the learned variance $\\sigma^2$ (b) over the training epochs. As previously, our method learns to adapt the covariances for each keypoint to minimize rotational error. Minimizing the rotational error leads to a significantly better estimate of $\\sigma^2$ .", + "(a) covariance matrices in the 2nd frame after 100 epochs training", + "Figure 7. Estimated (red) covariance ellipses in the second frame, learned from 128000 examples. Ground truth (green) covariances as comparison. Training data with enough variety gives a gradient that allows to correctly learn the covariances even in the image plane, overcoming the unobservabilities of the first experiment." + ], + "image_footnote": [], + "bbox": [ + 89, + 270, + 459, + 402 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "the gradient from Eq. 8. For this, We create a random relative pose estimation problem consisting of two cameraframes observing randomly generated points in 3D space. The points are projected into camera frames using a pin-hole camera model. Each projected point is assigned a random gaussian noise distribution. From this 128000 random problems are sampled. We learn the noise distributions by initializing all covariance estimates as scaled identity matrices, solving the relative pose estimation problem using the PNEC and updating the parameters of the distribution using the gradient of Eq. 8 directly. We train for 100 epochs with the ADAM [31] optimizer with (0.9, 0.99) as parameters and a batch size of 12800 for a stable gradient.", + "bbox": [ + 75, + 494, + 468, + 690 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Fig. 4a shows the decrease of the rotation error over the epochs. The learned covariances decrease the error by $8\\%$ and $16\\%$ compared to unit covariances and the NEC, respectively. This validates the importance of good covariances for the PNEC, shown in [48]. Fig. 4b shows the average error for the normalized variance $\\sigma_{norm}^2$ , given by", + "bbox": [ + 75, + 691, + 468, + 784 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\sigma_ {i, n o r m} ^ {2} = \\frac {N \\cdot \\sigma_ {i} ^ {2}}{\\sum_ {j = 0} ^ {N} \\sigma_ {j} ^ {2}} \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 200, + 792, + 468, + 830 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "over the training epochs, obtained at the ground truth relative pose. We compare the normalized error variance, as the scale of $\\sigma^2$ is not observable from the gradient. The covariances that minimize the rotational error also approximate", + "bbox": [ + 75, + 840, + 468, + 902 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/d0e6806c6fdff765b963cf66588aae4e30a257e57004c90c1d0fc6a659390887.jpg", + "image_caption": [ + "Figure 8. Qualitative trajectory comparison for KITTI seq. 00. Since we compare monocular methods, that cannot estimate the correct scale from a pair of images, we use the scale of the ground truth translations for visualization purposes. Both, our supervised and self-supervised approaches lead to significant improvements in the trajectory. There is little drift even without additional rotation averaging [11] or loop closure [49]." + ], + "image_footnote": [], + "bbox": [ + 531, + 88, + 859, + 321 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "the residual uncertainty $\\sigma^2$ very closely. However, while the residual uncertainty is approximated well, the learned 2D covariances in the image plane do not correspond to the correct covariances (see Fig. 5). This is due to two different reasons. First, due to $\\sigma_i^2$ dependence on both $\\Sigma_{\\mathrm{2D},i}$ and $\\Sigma_{\\mathrm{2D},i}^{\\prime}$ , there is not a single unique solution. Secondly, the direction of the gradient is dependent on the translation between the images (see the supplementary material for more details). In this experimental setup, the information flow to the images is limited and we can only learn the true distribution for $\\sigma^2$ but not for the 2D images covariances.", + "bbox": [ + 496, + 422, + 892, + 589 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To address the problems with limited information flow of the previous experiment, we propose a second experiment to negate the influence of these aforementioned factors. First, each individual problem has a randomly sampled relative pose, where the first frame stays fixed. This removes the influence of the translation on the gradient direction. The noise is still drawn from the same distributions as earlier. Second, we fix the noise in the first frame to be small, isotropic, and homogeneous in nature. Furthermore, we only learn the covariances in the second frame and provide the optimization with the ground truth noise in the first frame. Fig. 6 and Fig. 7 show, that under these constraints, we are not only able to learn the distribution for $\\sigma^2$ but also $\\Sigma_{2\\mathrm{D}}'$ . Together, both experiments show, that we can learn the correct distributions from noisy data by following the gradient that minimizes the rotational error.", + "bbox": [ + 496, + 590, + 892, + 832 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Real World Data", + "text_level": 1, + "bbox": [ + 500, + 845, + 666, + 859 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We evaluate our method on the KITTI [21] and EuRoC [9] dataset. Since KITTI shows outdoor driving sequences", + "bbox": [ + 500, + 869, + 892, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "13107", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/d64154659931de7090e864269fee34369a9e2bf84ead86b78592a08a7068c216.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
NISTÉR-5PT [50]NEC [33]NEC-LSWEIGHTED NEC-LSOURS SUPERVISEDOURS SELF-SUPERVISED
Seq.RPE1RPEnetRPE1RPEnetRPE1RPEnetRPE1RPEnetRPE1RPEnetRPE1RPEnet
080.19517.0204.240.0818.2843.660.0567.0042.500.0546.0592.500.0504.0672.460.0504.1182.46
090.1425.7541.740.0531.6461.430.0521.5530.710.0511.3540.700.0491.3170.710.0491.2780.70
100.29516.6786.570.1679.2644.430.0644.7871.790.0634.3891.760.0633.5131.640.0653.8211.65
train0.24911.5064.130.14110.1272.970.0826.9101.720.0816.4101.720.0772.3781.690.0772.5051.69
test0.20014.3494.070.0896.9173.280.0565.3531.960.0554.6761.950.0523.3331.910.0533.4081.91
", + "bbox": [ + 86, + 88, + 879, + 222 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/f5b7787cd139cf151d9ed7a4f21acd819ae560b946e28a56f8999012deb94e94.jpg", + "table_caption": [ + "Table 1. Quantitative comparison on the KITTI [21] dataset with SuperPoint [12] keypoints. We compare two rotation and one translation metric. The results are shown for each test sequence together with the mean results on the training and test set weighted by the sequence length. Both our training setups outperform the non-probabilitic algorithms but also the weighted NEC-LS using SuperGlue confidences consistently across unseen data. The learned uncertainties are able to generalise well and improve the relative pose estimation significantly." + ], + "table_footnote": [], + "table_body": "
NISTÉR-5PT [50]NEC [33]NEC-LSKLT-PNEC [48]OURS SUPERVISEDOURS SELF-SUPERVISED
Seq.RPE1RPEnetRPE1RPEnetRPE1RPEnetRPE1RPEnetRPE1RPEnetRPE1RPEnet
080.1266.9293.440.0883.9028.910.0532.9082.490.0542.5242.420.0482.3732.360.0471.7062.36
090.0902.5441.280.0542.0276.760.0522.3070.740.0461.0030.690.0431.2440.640.0421.1410.64
100.18811.5544.430.1198.3028.530.0664.5761.780.0634.4801.710.0583.7891.580.0563.6231.60
train0.2049.6773.190.1738.3018.590.1033.9551.730.1044.2131.660.0942.7821.600.0962.7371.61
test0.1296.7223.110.0854.2378.340.0553.0601.960.0542.5141.900.0482.3591.820.0481.9101.83
", + "bbox": [ + 86, + 281, + 879, + 415 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2. Quantitative comparison on the KITTI [21] dataset with KLT tracks [66]. As in Tab. 1, we show the results on the test set together with the mean on the train and test set weighted by the sequence lengths. As for SuperPoint, our methods improve all metrics consistently for unseen data. Our learned covariances are significantly better for relative pose estimation than the approximation used in [48].", + "bbox": [ + 75, + 416, + 892, + 459 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "and EuRoC shows indoor scenes captured with a drone, they exhibit different motion models as well as a variety of images. For KITTI we choose sequences 00-07 as the training set for both supervised and self-supervised training. Sequences 08-10 are used as the test set. We use a smaller UNet [55] architecture as our network to predict the covariances for the whole image. We chose this network since it gives us a good balance between batch size, training time and performance. The network predicts the parameters for the covariances directly. We choose", + "bbox": [ + 75, + 467, + 472, + 619 + ], + "page_idx": 6 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {\\Sigma} _ {2 \\mathrm {D}} (s, \\alpha , \\beta) = s \\boldsymbol {R} _ {\\alpha} \\left( \\begin{array}{c c} \\beta & 0 \\\\ 0 & 1 - \\beta \\end{array} \\right) \\boldsymbol {R} _ {\\alpha} ^ {\\top} \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 140, + 628, + 468, + 664 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "as a parameterization [7]. To ensure that our network predicts valid covariances the network output is filtered with", + "bbox": [ + 75, + 672, + 468, + 705 + ], + "page_idx": 6 + }, + { + "type": "equation", + "text": "\n$$\nf _ {1} (x) = \\left(1 + | x |\\right) ^ {\\operatorname {s i g n} (\\mathrm {x})} \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 192, + 714, + 468, + 733 + ], + "page_idx": 6 + }, + { + "type": "equation", + "text": "\n$$\nf _ {2} (x) = x \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 194, + 734, + 468, + 751 + ], + "page_idx": 6 + }, + { + "type": "equation", + "text": "\n$$\nf _ {3} (x) = \\frac {1}{1 + e ^ {- x}} \\tag {17}\n$$\n", + "text_format": "latex", + "bbox": [ + 194, + 753, + 468, + 782 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "for $s, \\alpha, \\beta$ , respectively. Feature points that have subpixel accuracy use the nearest pixel covariance. See the supplementary material for more details on the training setup.", + "bbox": [ + 75, + 794, + 468, + 840 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Supervised Learning. To show that our method generalizes to different keypoint detectors, we train two networks, one for SuperPoint [12] and one for KLT tracks obtained from [66]. The SuperPoint keypoints are matched", + "bbox": [ + 75, + 840, + 468, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "using SuperGlue [57]. For training we use a batch size of 8 images pairs for SuperPoint and 16 images pairs for KLT tracks. We trained for 100 epochs for both SuperPoint and KLT tracks. More training details are provided in the supplementary material. To ensure our network does not overfit on specific keypoint locations, we randomly crop the images before finding correspondences during training time. During evaluation we use the uncropped images to obtain features. During training we randomly perturb the ground truth pose as a starting point. To increase robustness, we first use the eigenvalue based optimization of the NEC in a RANSAC scheme [32] to filter outliers. This is followed by a custom least squares implementation of the NEC (NECLS), followed by optimizing Eq. 3. As reported in [48] we found, that such a multi-stage optimization provides the most robust and accurate results. We show examples of how the DNLS-learned covariances change the energy function landscape in the supplementary material.", + "bbox": [ + 496, + 467, + 893, + 739 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Self-Supervised Learning. We evaluate our self-supervised training setup on the same data as our supervised training. Due to needing image tuples instead of pairs, we reduce the batch size to 12 for KLT image triplets. This gives us 24 and 36 images pairs per batch, respectively. The training epochs are reduced to 50. More training details for the supervised and self-supervised training can be found in the supplementary material.", + "bbox": [ + 496, + 743, + 893, + 866 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results. We evaluate the learned covariances in a VO setting. We compare the proposed DNLS approach to the", + "bbox": [ + 498, + 869, + 893, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "13108", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/0825f3548ae77f77624077907a246648b67367d081110ae4e3600dc1ea5d1995.jpg", + "table_caption": [], + "table_footnote": [ + "Table 3. Quantitative comparison on the Vicon sequences of the EuRoC dataset [9] with SuperPoint [12] keypoints. The dataset is more difficult than KITTI (see Tab. 2 and Tab. 1) with SuperPoint and SuperGlue [57] finding far fewer matches. As reported in [48] the least squares implementations struggle with bad initialization under these adverse conditions with NEC-LS performing especially poor. From all least squares optimizations, our learned covariances consistently perform the best, even outperforming the NEC most of the time." + ], + "table_body": "
NISTÉR-5PT [51]NEC [33]NEC-LSWEIGHTED NEC-LSOURS SELF-SUPERVISEDOURS TAB. 1
Seq.RPE1RPEnetRPE1RPEnetRPE1RPEnetRPE1RPEnetRPE1RPEnetRPE1RPEnetRPE1RPEnet
V1_010.50171.8731.860.32039.5043.120.38752.9246.310.38856.5246.820.32731.1235.560.33231.8134.01
V1_020.54132.0120.360.38928.1126.950.54070.0828.940.54268.3529.810.44430.3921.980.43629.0721.29
V1_030.66027.3925.000.49225.4231.060.55276.7231.580.55578.1432.250.51029.5224.190.52031.1824.13
V2_010.51561.4533.510.31631.9539.790.31035.8439.000.31438.6239.620.28517.6132.400.29522.4130.58
V2_020.54543.7322.240.39625.4832.210.36926.9625.360.36525.0925.810.38225.3221.160.38621.9120.34
V2_031.12336.7128.770.97648.2637.600.939107.1136.740.941100.7336.710.94252.7231.130.99155.4130.40
mean0.63148.4527.560.46333.5136.030.49458.9035.610.49658.9536.110.46130.5728.460.47231.4427.44
", + "bbox": [ + 78, + 88, + 895, + 250 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "popular 5pt algorithm [51] and the NEC [33] as implemented in [32]. To investigate the benefit of our learned covariances we include the NEC-LS implementation as well as the symmetric PNEC with the covariances from [48] in Tab. 2. For Tab. 1 we additionally include a weighted version of our custom NEC-LS implementation with matching confidence from SuperGlue as weights. All methods are given the same feature matches and use a constant motion model for initializing the optimizations. We evaluate on the rotational versions of the $\\mathrm{RPE}_1$ and $\\mathrm{RPE}_n$ and the cosine error $e_t$ for the translation as defined in [11, 48]. Tab. 1 and Tab. 2 show the average results on the test set over 5 runs for SuperPoint and KLT tracks on KITTI [21], respectively. We show additional results in the supplementary material. Our methods consistently perform the best over all sequences, with the self-supervised being on par with our supervised training. Compared to its non-probabilistic counterpart NEC-LS, our method improves the $\\mathrm{RPE}_1$ by $7\\%$ and $13\\%$ and the $\\mathrm{RPE}_n$ by $37\\%$ and $23\\%$ for different keypoint detectors on unseen data. It also improves upon weighted methods, like weighted NEC-LS and the nonlearned covariances for the PNEC [48]. This demonstrates the importance of correctly modeling the feature correspondence quality. We show an example trajectory in Fig. 8.", + "bbox": [ + 75, + 324, + 472, + 686 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Tab. 3 shows the results on the EuRoC dataset for SuperPoint. Pose estimation is significantly more difficult compared to KITTI, often having few correspondences between images. However, our method generalizes to different datasets, with the network trained on KITTI and our self-supervised approach, outperforming the others most of the time. Especially a direct comparison with NEC-LS, the closest non-probabilistic method, shows significant improvements of $7\\%$ for $\\mathrm{RPE}_1$ and $48\\%$ for the $\\mathrm{RPE}_n$ .", + "bbox": [ + 75, + 688, + 470, + 828 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Discussion and Limitations", + "text_level": 1, + "bbox": [ + 76, + 843, + 328, + 859 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Our experiments demonstrate the capability of our framework to correctly learn positional uncertainty, lead", + "bbox": [ + 76, + 869, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ing to improved results for relative pose estimation for VO. Our approach generalizes to different feature extractors and to different datasets, providing a unified approach to estimate the noise distribution of keypoint detectors. However, our method requires more computational resources than the original uncertainty estimation for the PNEC.", + "bbox": [ + 496, + 324, + 893, + 414 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We evaluate our learned covariances in a visual odometry setting, showing that they lead to reduced errors and especially less drift in the trajectory. However, this does not guarantee that the covariances are calibrated. Our framework inherits the ambiguity of the PNEC with regard to the noise scale. The true scale of the noise is not observable from relative pose estimation alone and only the relative scale between covariances can be learned. For the purposes of VO, this scale ambiguity is negligible.", + "bbox": [ + 496, + 415, + 893, + 551 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "As our synthetic experiments show, diverse data is needed to correctly identify the 2D noise distribution. However, obtaining the noise distribution is difficult for keypoint detectors - hence learning it from pose regression. Further limitations are addressed in the supplementary material.", + "bbox": [ + 496, + 551, + 893, + 628 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 642, + 619, + 657 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We present a novel DNLS framework for estimating positional uncertainty. Our framework can be combined with any feature extraction algorithm, making it extremely versatile. Regressing the noise distribution from relative pose estimation, ensures that learned covariance matrices are suitable for visual odometry tasks. In synthetic experiments, our framework is capable to learn the correct noise distribution from noisy data. We showed the practical application of our framework on real-world data for different feature extractors. Our learned uncertainty consistently outperforms a variety of non-probabilistic relative pose estimation algorithms as well as other uncertainty estimation methods.", + "bbox": [ + 496, + 667, + 893, + 849 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements. This work was supported by the ERC Advanced Grant SIMULACRON, by the Munich Center for Machine Learning and by the EPSRC Programme Grant VisualAI EP/T028572/1.", + "bbox": [ + 496, + 862, + 893, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "13109", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Sameer Agarwal, Keir Mierle, and Others. Ceres solver. http://ceres-solver.org.5", + "[2] Relja Arandjelovic, Petr Gronat, Akihiko Torii, Tomas Pajdla, and Josef Sivic. Netvlad: Cnn architecture for weakly supervised place recognition. In CVPR, 2016. 3", + "[3] Herbert Bay, Tinne Tuytelaars, and Luc Van Gool. Surf: Speeded up robust features. In ECCV, 2006. 3", + "[4] Christopher M. Bishop. Pattern recognition and machine learning, 5th Edition. 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Springer, 2017. 3" + ], + "bbox": [ + 78, + 90, + 468, + 191 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "13112", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Learning Correspondence Uncertainty via Differentiable Nonlinear Least Squares/8f30fa60-e502-4ee5-838a-d9c7713dcf6d_model.json b/2023/Learning Correspondence Uncertainty via Differentiable Nonlinear Least Squares/8f30fa60-e502-4ee5-838a-d9c7713dcf6d_model.json new file mode 100644 index 0000000000000000000000000000000000000000..473fd9ed86dddb474d555c2234a2098b753429cc --- /dev/null +++ b/2023/Learning Correspondence Uncertainty via Differentiable Nonlinear Least Squares/8f30fa60-e502-4ee5-838a-d9c7713dcf6d_model.json @@ -0,0 +1,2708 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.269, + 0.131, + 0.703, + 0.18 + ], + "angle": 0, + "content": "Learning Correspondence Uncertainty via Differentiable Nonlinear Least Squares" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.207, + 0.236, + 0.241 + ], + "angle": 0, + "content": "Dominik Muhle1,2 \n1TU Munich" + }, + { + "type": "text", + "bbox": [ + 0.287, + 0.207, + 0.429, + 0.224 + ], + "angle": 0, + "content": "Lukas Koestler\\(^{1,2}\\)" + }, + { + "type": "text", + "bbox": [ + 0.482, + 0.208, + 0.733, + 0.225 + ], + "angle": 0, + "content": "Krishna Murthy Jatavallabhula4" + }, + { + "type": "text", + "bbox": [ + 0.787, + 0.207, + 0.942, + 0.223 + ], + "angle": 0, + "content": "Daniel Cremers1,2,3" + }, + { + "type": "text", + "bbox": [ + 0.277, + 0.226, + 0.583, + 0.244 + ], + "angle": 0, + "content": "2Munich Center for Machine Learning" + }, + { + "type": "text", + "bbox": [ + 0.635, + 0.225, + 0.81, + 0.243 + ], + "angle": 0, + "content": "\\(^{3}\\)University of Oxford" + }, + { + "type": "text", + "bbox": [ + 0.863, + 0.225, + 0.91, + 0.241 + ], + "angle": 0, + "content": "\\(^{4}\\)MIT" + }, + { + "type": "text", + "bbox": [ + 0.216, + 0.246, + 0.812, + 0.261 + ], + "angle": 0, + "content": "{dominik.muhle, lukas.koestler, cremers}@tum.de jkrishna@mit.edu" + }, + { + "type": "text", + "bbox": [ + 0.181, + 0.287, + 0.333, + 0.298 + ], + "angle": 0, + "content": "images with correspondences" + }, + { + "type": "image", + "bbox": [ + 0.083, + 0.298, + 0.295, + 0.356 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.295, + 0.298, + 0.407, + 0.351 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.083, + 0.356, + 0.295, + 0.414 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.295, + 0.356, + 0.407, + 0.414 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.17, + 0.415, + 0.347, + 0.424 + ], + "angle": 0, + "content": "uncertainty estimates from images" + }, + { + "type": "image", + "bbox": [ + 0.412, + 0.29, + 0.573, + 0.425 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.577, + 0.287, + 0.89, + 0.424 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.431, + 0.893, + 0.488 + ], + "angle": 0, + "content": "Figure 1. We present a differentiable nonlinear least squares (DNLS) framework for learning feature correspondence quality by computing per-feature positional uncertainty. The uncertainty estimates (left, bottom images) are regressed from a pose estimation error (middle), enabling the framework across a range of (handcrafted, learned) feature extractors. Our learned covariances (right, orange trajectory) improve orientation estimation by up to \\(11\\%\\) over state-of-the-art probabilistic pose estimation methods on the KITTI dataset [21]." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.5, + 0.314, + 0.516 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.532, + 0.472, + 0.744 + ], + "angle": 0, + "content": "We propose a differentiable nonlinear least squares framework to account for uncertainty in relative pose estimation from feature correspondences. Specifically, we introduce a symmetric version of the probabilistic normal epipolar constraint, and an approach to estimate the covariance of feature positions by differentiating through the camera pose estimation procedure. We evaluate our approach on synthetic, as well as the KITTI and EuRoC real-world datasets. On the synthetic dataset, we confirm that our learned covariances accurately approximate the true noise distribution. In real world experiments, we find that our approach consistently outperforms state-of-the-art nonprobabilistic and probabilistic approaches, regardless of the feature extraction algorithm of choice." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.763, + 0.208, + 0.779 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.788, + 0.47, + 0.88 + ], + "angle": 0, + "content": "Estimating the relative pose between two images given mutual feature correspondences is a fundamental problem in computer vision. It is a key component of structure from motion (SfM) and visual odometry (VO) methods which in turn fuel a plethora of applications from autonomous vehicles or robots to augmented and virtual reality." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.501, + 0.892, + 0.669 + ], + "angle": 0, + "content": "Estimating the relative pose - rotation and translation - between two images, is often formulated as a geometric problem that can be solved by estimating the essential matrix [42] for calibrated cameras, or the fundamental matrix [24] for uncalibrated cameras. Related algorithms like the eight-point algorithm [23, 42] provide fast solutions. However, essential matrix based approaches suffer issues such as solution multiplicity [18, 24] and planar degeneracy [33]. The normal epipolar constraint (NEC) [34] addresses issues such as by estimating the issues such as which leads to more accurate relative poses [33]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.671, + 0.893, + 0.853 + ], + "angle": 0, + "content": "Neither of the aforementioned algorithms takes into account the quality of feature correspondences – an important cue that potentially improves pose estimation accuracy. Instead, feature correspondences are classified into inliers and outliers through a RANSAC scheme [11]. However, keypoint detectors [12, 56] for feature correspondences or tracking algorithms [63] yield imperfect points [40] that exhibit a richer family of error distributions, as opposed to an inlier-outlier distribution family. Algorithms, that make use of feature correspondence quality have been proposed for essential/fundamental matrix estimation [7, 53] and for the NEC [48], respectively." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.857, + 0.894, + 0.903 + ], + "angle": 0, + "content": "While estimating the relative pose can be formulated as a classical optimization problem [15, 33], the rise in popularity of deep learning has led to several works augmenting" + }, + { + "type": "page_footnote", + "bbox": [ + 0.1, + 0.889, + 0.399, + 0.902 + ], + "angle": 0, + "content": "Project Page: https://dominikmuhle.github.io/dnls_covs/" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13102" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.127, + 0.089, + 0.484, + 0.174 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.214, + 0.177, + 0.397, + 0.189 + ], + "angle": 0, + "content": "(a) covariances from [48] per pixel" + }, + { + "type": "image", + "bbox": [ + 0.487, + 0.089, + 0.844, + 0.174 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.584, + 0.177, + 0.747, + 0.189 + ], + "angle": 0, + "content": "(b) points and covariances [48]" + }, + { + "type": "image", + "bbox": [ + 0.124, + 0.19, + 0.482, + 0.275 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.199, + 0.277, + 0.408, + 0.289 + ], + "angle": 0, + "content": "(c) learned covariances per pixel (Ours)" + }, + { + "type": "image", + "bbox": [ + 0.484, + 0.189, + 0.842, + 0.275 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.555, + 0.277, + 0.772, + 0.289 + ], + "angle": 0, + "content": "(d) points and learned covariances (Ours)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.29, + 0.892, + 0.346 + ], + "angle": 0, + "content": "Figure 2. Comparison between covariances used in [48] (first row) and our learned covariances (second row). The first column shows a dense color coded \\((s, \\alpha, \\beta\\) mapped to HLS with \\(\\gamma\\) correction) representation for each pixel, while the second column shows subsampled keypoints and their corresponding (enlarged) covariances. The higher saturation in (a) shows that the covariances are more anisotropic. The learned covariances (c) show a more fine-grained detail in the scale (brightness) and less blurring than the covariances in (a)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.351, + 0.469, + 0.533 + ], + "angle": 0, + "content": "VO or visual simultaneous localisation and mapping (VSLAM) pipelines with learned components. GN-Net [67] learns robust feature representations for direct methods like DSO [15]. For feature based methods Superpoint [12] provides learned features, while Superglue [57] uses graph neural networks to find corresponding matches between feature points in two images. DSAC introduces a differential relaxation to RANSAC that allows gradient flow through the otherwise non-differentiable operation. In [53] a network learns to re-weight correspondences for estimating the fundamental matrix. PixLoc [58] estimates the pose from an image and a 3D model based on direct alignment." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.535, + 0.469, + 0.687 + ], + "angle": 0, + "content": "In this work we combine the predictive power of deep learning with the precision of geometric modeling for highly accurate relative pose estimation. Estimating the noise distributions for the feature positions of different feature extractors allows us to incorporate this information into relative pose estimation. Instead of modeling the noise for each feature extractor explicitly, we present a method to learn these distributions from data, using the same domain that the feature extractors work with - images. We achieve this based on the following technical contributions:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.69, + 0.469, + 0.749 + ], + "angle": 0, + "content": "- We introduce a symmetric version of the probabilistic normal epipolar constraint (PNEC), that more accurately models the geometry of relative pose estimation with uncertain feature positions." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.75, + 0.468, + 0.81 + ], + "angle": 0, + "content": "- We propose a learning strategy to minimize the relative pose error by learning feature position uncertainty through differentiable nonlinear least squares (DNLS), see Fig. 1." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.811, + 0.468, + 0.87 + ], + "angle": 0, + "content": "- We show with synthetic experiments, that using the gradient from the relative pose error leads to meaningful estimates of the positional uncertainty that reflect the correct error distribution." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.871, + 0.468, + 0.901 + ], + "angle": 0, + "content": "- We validate our approach on real-world data in a visual odometry setting and compare our method to non" + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.69, + 0.469, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.351, + 0.892, + 0.397 + ], + "angle": 0, + "content": "probabilistic relative pose estimation algorithms, namely Nister 5pt [50], and NEC [33], as well as to the PNEC with non-learned covariances [48]." + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.397, + 0.892, + 0.442 + ], + "angle": 0, + "content": "- We show that our method is able to generalize to different feature extraction algorithms such as SuperPoint [12] and feature tracking approaches on real-world data." + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.442, + 0.892, + 0.472 + ], + "angle": 0, + "content": "- We release the code for all experiments and the training setup to facilitate future research." + }, + { + "type": "list", + "bbox": [ + 0.501, + 0.397, + 0.892, + 0.472 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.493, + 0.64, + 0.509 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.521, + 0.892, + 0.672 + ], + "angle": 0, + "content": "This work is on deep learning for improving frame-to-frame relative pose estimation by incorporating feature position uncertainty with applications to visual odometry. We therefore restrict our discussion of related work to relative pose estimation in visual odometry, weighting correspondences for relative pose estimation, and deep learning in the context of VSLAM. For a broader overview over VSLAM we refer the reader to more topic-specific overview papers [10, 65] and to the excellent books by Hartley and Zisserman [24] and by Szeliski [62]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Relative Pose Estimation in Visual Odometry. Finding the relative pose between two images has a long history in computer vision, with the first solution for perspective images reaching back to 1913 by Kruppa [35]. Modern methods for solving this problem can be classified into feature-based and direct methods. The former rely on feature points extracted in the images together with geometric constraints like the epipolar constraint or the normal epipolar constraint [34] to calculate the relative pose. The latter optimize the pose by directly considering the intensity differences between the two images and rose to popularity with LSD-SLAM [16] and DSO [15]. Since direct methods work on the assumption of brightness or irradiance constancy they require the appearance to be somewhat similar across images. In turn, keypoint based methods rely" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "13103" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.471, + 0.168 + ], + "angle": 0, + "content": "on suitable feature extractors which can exhibit significant amounts of noise and uncertainty. In this paper we propose a method to learn the intrinsic noise of keypoint detectors – therefore, the following will focus on feature based relative pose estimation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.17, + 0.472, + 0.457 + ], + "angle": 0, + "content": "One of the most widely used parameterizations for reconstructing the relative pose from feature correspondences is the essential matrix, given calibrated cameras, or the fundamental matrix in the general setting. Several solutions based on the essential matrix have been proposed [36, 38, 42, 50, 61]. They include the linear solver by Longuet-Higgins [42], requiring 8 correspondences, or the solver by Nister et al. [51] requiring the minimal number of 5 correspondences. However, due to their construction, essential matrix methods deteriorate for purely rotational motion with noise-free correspondences [33]. As an alternative, methods that do not use the essential matrix have been proposed - they either estimate the relative pose using quaternions [17] or make use of the normal epipolar constraint (NEC) by Kneip and Lynen [33, 34]. The latter addresses the problems of the essential matrix by estimating rotation independent of the translation. [6] shows how to obtain the global minimum for the NEC. Further work, that disentangles rotation and translation can be found in [39]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.46, + 0.47, + 0.611 + ], + "angle": 0, + "content": "Weighting of Feature Correspondences. Keypoints in images can exhibit significant noise, deteriorating the performance for pose estimation significantly [22]. The noise characteristics of the keypoint positions depend on the feature extractor. For Kanade-Lucas-Tomasi (KLT) tracking [44, 63] approaches, the position uncertainty has been investigated in several works [20, 59, 60, 72]. The uncertainty was directly integrated into the tracking in [14]. [71] proposed a method to obtain anisotropic and inhomogeneous covariances for SIFT [43] and SURF [3]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.614, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Given the imperfect keypoint positions, not all correspondences are equally well suited for estimating the relative pose. [22] showed the effect of the noise level on the accuracy of the pose estimation. Limiting the influence of bad feature correspondences has been studied from a geometrical and a probabilistic perspective. Random sample consensus (RANSAC) [19] is a popular method to classify datapoints into inliers and outliers that can be easily integrated into feature based relative pose estimation pipelines. Ranftl et al. [53] relax the hard classification for inlier and outlier and use deep learning to find a robust fundamental matrix estimator in the presence of outliers in an iteratively reweighted least squares (IRLS) fashion. DSAC [5] models RANSAC as a probabilistic process to make it differentiable. Other lines of work integrate information about position uncertainty directly into the alignment problem. For radar based SLAM, [8] incorporates keypoint uncertainty in radar images, with a deep network predicting the uncertainty. Image based position uncertainty was investigated" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.257 + ], + "angle": 0, + "content": "from the statistical, [27, 28], the photogrammetry [46] and the computer vision perspective [7, 29]. [7] and [29] debated the benefit of incorporating position uncertainty into fundamental matrix estimation. We base our method on the probabilistic normal epipolar constraint (PNEC) [48], that improved on the NEC by extending it to a probabilistic view. It achieved better results on real-world data with covariances approximated using the Boltzmann distribution [4]. We expand on this idea by learning covariances (see Fig. 2) agnostic of the keypoints extractor used to further improve pose estimation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.258, + 0.893, + 0.576 + ], + "angle": 0, + "content": "Deep Learning in VSLAM. Deep Learning has transformed computer vision in the last decade. While deep networks have been successfully used for tasks like detection [54], semantic segmentation [41], and recently novel view synthesis [47], they have also found application in VSLAM pipelines. DVSO [69] and D3VO [68] leveraged deep learning to improve the precision for direct methods, while GN-Net [67] predicts robust and dense feature maps. Several works proposed to learn keypoint extractors, for feature based pose estimation, such as SuperPoint [12] and LIFT [70]. SuperGlue [57] enabled feature matching with graph neural networks. Other lines of work leverage deep learning for localization by making parts of the pose estimation pipeline differentiable [2,5,58,64]. Works, that directly predicting the pose include PoseNet [30] and CTCNet [25] that uses self-supervised learning with a cycle-consistency loss for VO. [40] learns image representations by refining keypoint positions and camera poses in a post-processing step of a structure-from-motion pipeline. \\(\\nabla\\) SLAM [26] presents a differentiable dense SLAM system with several components (e.g., the Levenberg-Marquardt [37, 45] optimizer)." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.587, + 0.591, + 0.603 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.613, + 0.892, + 0.78 + ], + "angle": 0, + "content": "In the following, we present our framework to estimate positional uncertainty of feature points by leveraging DNLS. We learn the noise covariances through a forward and backward step. In the forward step, the covariances are used in a probabilistic pose estimation optimization, namely the PNEC. In the backward step, the gradient from the pose error is back-propagated through the optimization to the covariances. From there we can train a neural network to predict the keypoint position uncertainty from the images. We start by summarizing the asymmetric PNEC [48] and for the first time introduce its symmetric counterpart." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.788, + 0.637, + 0.803 + ], + "angle": 0, + "content": "3.1. Prerequisites" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.892, + 0.903 + ], + "angle": 0, + "content": "Notation. We follow the notation of [48]. Bold lowercase letters (e.g. \\( \\pmb{f} \\)) denote vectors, whereas bold uppercase letters (e.g. \\( \\pmb{\\Sigma} \\)) denote matrices. \\( \\hat{\\pmb{u}} \\in \\mathbb{R}^{3 \\times 3} \\) represents the skew-symmetric matrix of the vector \\( \\pmb{u} \\in \\mathbb{R}^3 \\) such that the cross product between two vectors can be rewritten as a matrix-vector operation, i.e. \\( \\pmb{u} \\times \\pmb{v} = \\hat{\\pmb{u}}\\pmb{v} \\). The transpose is" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13104" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.11, + 0.089, + 0.857, + 0.254 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.256, + 0.895, + 0.299 + ], + "angle": 0, + "content": "Figure 3. Architecture: We extract the uncertainty per image for every pixel using a UNet [55] backbone. Using keypoint locations from a keypoint detector, we obtain the keypoints with their estimated positional uncertainty. The relative pose is then estimated using a DNLS optimization. The UNet is updated by backpropagating the gradient (obtained by implicit differentiation) to the network output." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.302, + 0.474, + 0.41 + ], + "angle": 0, + "content": "denoted by the superscript \\(\\top\\). We deviate from [48] in the following: variables of the second frame are marked with the ' superscript, while variables of the first frame do not have a superscript. We represent the relative pose between images as a rigid-body transformation consisting of a rotation matrix \\( R \\in SO(3) \\) and a unit length translation \\( t \\in \\mathbb{R}^3 \\) (\\( \\| t \\| = 1 \\) is imposed due to scale-invariance)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.42, + 0.47, + 0.436 + ], + "angle": 0, + "content": "3.2. The Probabilistic Normal Epipolar Constraint" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.444, + 0.473, + 0.626 + ], + "angle": 0, + "content": "The asymmetric probabilistic normal epipolar constraint (PNEC) estimates the relative pose, give two images \\(I, I'\\) of the same scene under the assumption of uncertain feature positions in the second image. A feature correspondences is given by \\(\\pmb{p}_i, \\pmb{p}_i'\\) in the image plane, where the uncertainty of \\(\\pmb{p}_i'\\) is represented by the corresponding covariance \\(\\Sigma_{2\\mathrm{D},i}'\\). To get the epipolar geometry for the PNEC the feature points are unprojected using the camera intrinsics, giving unit length bearing vectors \\(\\pmb{f}_i, \\pmb{f}_i'\\). The uncertainty of \\(\\pmb{f}_i'\\) is now represented by \\(\\Sigma_i'\\). Estimating the relative pose is done by minimizing the PNEC cost function as defined in [48]. For convenience we recap the energy function" + }, + { + "type": "equation", + "bbox": [ + 0.116, + 0.637, + 0.47, + 0.677 + ], + "angle": 0, + "content": "\\[\nE (\\boldsymbol {R}, \\boldsymbol {t}) = \\sum_ {i} \\frac {e _ {i} ^ {2}}{\\sigma_ {i} ^ {2}} = \\sum_ {i} \\frac {| \\boldsymbol {t} ^ {\\top} (\\boldsymbol {f} _ {i} \\times \\boldsymbol {R} \\boldsymbol {f} _ {i} ^ {\\prime}) | ^ {2}}{\\boldsymbol {t} ^ {\\top} \\hat {\\boldsymbol {f}} _ {i} \\boldsymbol {R} \\boldsymbol {\\Sigma} _ {i} ^ {\\prime} \\boldsymbol {R} ^ {\\top} \\hat {\\boldsymbol {f}} _ {i} ^ {\\top} \\boldsymbol {t}}, (1)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.687, + 0.47, + 0.808 + ], + "angle": 0, + "content": "in our notation. As mentioned previously, this asymmetric PNEC in [48] only considers uncertainties \\(\\Sigma^{\\prime}\\) in the second frame. While this assumption might hold for the KLT tracking [66] used in [48], this leaves out important information when using other keypoint detectors like ORB [56] or SuperPoint [12]. Therefore, we will introduce a symmetric version of the PNEC that is more suitable for our task in the following." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.809, + 0.471, + 0.871 + ], + "angle": 0, + "content": "Making the PNEC symmetric. As in [48] we assume the covariance of the bearing vectors \\(\\pmb{f}_i\\) and \\(\\pmb{f}_i'\\) to be gaussian, their covariance matrices denoted by \\(\\pmb{\\Sigma}_i\\) and \\(\\pmb{\\Sigma}_i'\\), respectively. The new variance can be approximated as" + }, + { + "type": "equation", + "bbox": [ + 0.095, + 0.883, + 0.47, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\sigma_ {s, i} ^ {2} = \\boldsymbol {t} ^ {\\top} \\left(\\left(\\boldsymbol {R} \\hat {\\boldsymbol {f}} _ {i} ^ {\\prime}\\right) \\boldsymbol {\\Sigma} _ {i} \\left(\\boldsymbol {R} \\hat {\\boldsymbol {f}} _ {i} ^ {\\prime}\\right) ^ {\\top} + \\hat {\\boldsymbol {f}} _ {i} \\boldsymbol {R} \\boldsymbol {\\Sigma} _ {i} ^ {\\prime} \\boldsymbol {R} ^ {\\top} \\hat {\\boldsymbol {f}} _ {i} ^ {\\top}\\right) \\boldsymbol {t}. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.303, + 0.893, + 0.364 + ], + "angle": 0, + "content": "In the supplementary material we derive the variance and show the validity of this approximation given the geometry of the problem. This new variance now gives us the new symmetric PNEC with its following energy function" + }, + { + "type": "equation", + "bbox": [ + 0.625, + 0.374, + 0.892, + 0.412 + ], + "angle": 0, + "content": "\\[\nE _ {s} (\\boldsymbol {R}, \\boldsymbol {t}) = \\sum_ {i} \\frac {e _ {i} ^ {2}}{\\sigma_ {s , i} ^ {2}} \\tag {3}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.423, + 0.787, + 0.438 + ], + "angle": 0, + "content": "3.3. DNLS for Learning Covariances" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.446, + 0.893, + 0.492 + ], + "angle": 0, + "content": "We want to estimate covariances \\(\\Sigma_{2\\mathrm{D}}\\) and \\(\\Sigma_{2\\mathrm{D}}^{\\prime}\\) (in the following collectively denoted as \\(\\Sigma_{2\\mathrm{D}}\\) for better readability) in the image plane" + }, + { + "type": "equation", + "bbox": [ + 0.631, + 0.504, + 0.892, + 0.527 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {\\Sigma} _ {2 \\mathrm {D}} = \\underset {\\boldsymbol {\\Sigma} _ {2 \\mathrm {D}}} {\\arg \\min } \\mathcal {L}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.538, + 0.894, + 0.598 + ], + "angle": 0, + "content": "such that they minimize a loss function \\(\\mathcal{L}\\) of the estimated pose. Since we found that the rotational error of the PNEC is more stable than the translational error, we chose to minimize only the rotational error" + }, + { + "type": "equation", + "bbox": [ + 0.684, + 0.609, + 0.891, + 0.627 + ], + "angle": 0, + "content": "\\[\ne _ {\\text {r o t}} = \\angle \\tilde {\\boldsymbol {R}} ^ {\\top} \\boldsymbol {R} \\tag {5}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.61, + 0.631, + 0.892, + 0.648 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} (\\tilde {\\boldsymbol {R}}, \\boldsymbol {R}; \\boldsymbol {\\Sigma} _ {2 \\mathrm {D}}) = e _ {\\mathrm {r o t}} \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.662, + 0.892, + 0.692 + ], + "angle": 0, + "content": "between the ground truth rotation \\(\\tilde{\\pmb{R}}\\) and the estimated rotation \\(\\pmb{R}\\). We obtain" + }, + { + "type": "equation", + "bbox": [ + 0.6, + 0.705, + 0.892, + 0.727 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {R} = \\arg \\min _ {\\boldsymbol {R}} E _ {s} (\\boldsymbol {R}, t; \\Sigma_ {2 \\mathrm {D}}) \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.738, + 0.892, + 0.798 + ], + "angle": 0, + "content": "by minimizing Eq. 3. To learn the covariances that minimize the rotational error, we can follow the gradient \\(d\\mathcal{L} / d\\Sigma_{2\\mathrm{D}}\\). Implicit differentiation allows us to compute the gradient as" + }, + { + "type": "equation", + "bbox": [ + 0.545, + 0.81, + 0.892, + 0.846 + ], + "angle": 0, + "content": "\\[\n\\frac {d \\mathcal {L}}{d \\boldsymbol {\\Sigma} _ {2 \\mathrm {D}}} = - \\frac {\\partial^ {2} E _ {s}}{\\partial \\boldsymbol {\\Sigma} _ {2 \\mathrm {D}} \\partial \\boldsymbol {R} ^ {\\top}} \\left(\\frac {\\partial^ {2} E _ {s}}{\\partial \\boldsymbol {R} \\partial \\boldsymbol {R} ^ {\\top}}\\right) ^ {- 1} \\frac {e _ {\\text {r o t}}}{\\partial \\boldsymbol {R}}. \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.893, + 0.901 + ], + "angle": 0, + "content": "For a detailed derivation of Eq. 8 and other methods, that unroll the optimization, to obtain the gradient we refer the interested reader to [13]." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13105" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.089, + 0.272, + 0.178 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.117, + 0.181, + 0.237, + 0.193 + ], + "angle": 0, + "content": "(a) \\(e_{\\mathrm{rot}}\\) during training" + }, + { + "type": "image", + "bbox": [ + 0.274, + 0.09, + 0.468, + 0.178 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.286, + 0.18, + 0.456, + 0.194 + ], + "angle": 0, + "content": "(b) \\(\\sigma_{norm}^2\\) error during training" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.197, + 0.468, + 0.266 + ], + "angle": 0, + "content": "Figure 4. Rotational error (a) and differences between the true residual variance \\(\\tilde{\\sigma}^2\\) and the learned variance \\(\\sigma^2\\) (b) over the training epochs. Starting from uniform covariances, our method adapts the covariances for each keypoint to minimize the rotational error. Simultaneously, this leads to a better estimate of \\(\\sigma^2\\)." + }, + { + "type": "image", + "bbox": [ + 0.09, + 0.269, + 0.46, + 0.401 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.102, + 0.404, + 0.446, + 0.416 + ], + "angle": 0, + "content": "(a) covariance matrices in the 1st frame after 100 epochs training" + }, + { + "type": "image", + "bbox": [ + 0.091, + 0.417, + 0.458, + 0.549 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.099, + 0.552, + 0.449, + 0.565 + ], + "angle": 0, + "content": "(b) covariance matrices in the 2nd frame after 100 epochs training" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.568, + 0.47, + 0.638 + ], + "angle": 0, + "content": "Figure 5. Estimated (red) covariance ellipses in the first (a) and the second (b) frame, learned from 128000 examples. Ground truth (green) covariances as comparison. Although the gradient minimizes the rotational error (see Fig. 4a), it is not capable of learning the correct covariance in the image plane." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.649, + 0.47, + 0.77 + ], + "angle": 0, + "content": "Supervised Learning. The goal of the paper is for a neural network \\( F \\) learn the noise distributions of a keypoint detector. Given an image and a keypoint position, the network should predict the covariance of the noise \\( \\Sigma_{2\\mathrm{D},i} = F(\\boldsymbol {I},\\boldsymbol {p}_i) \\). The gradient \\( d\\mathcal{L} / d\\Sigma_{2\\mathrm{D}} \\) allows for the network to learn the covariance matrices in an end-to-end manner by regression on the relative pose error. Given a dataset with known ground truth poses, we can use" + }, + { + "type": "equation", + "bbox": [ + 0.235, + 0.783, + 0.469, + 0.799 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\sup } = e _ {\\text {r o t}} \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.469, + 0.856 + ], + "angle": 0, + "content": "as a training loss. This ensures, that learned covariances effectively minimize the rotational error. See Fig. 3 for overview of the training process." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Self-Supervised Learning. Finding a suitable annotated dataset for a specific task is often non-trivial. For our task, we need accurate ground truth poses that are difficult to ac" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.183 + ], + "angle": 0, + "content": "quire. But given a stream of images, like in VO, our method can be adapted to train a network in a self-supervised manner without the need for ground truth poses. For this, we follow the approach of [25] to exploit the cycle-consistency between a tuple of images. The cycle-consistency loss for a triplet \\(\\{I_1, I_2, I_3\\}\\) of images is given by" + }, + { + "type": "equation", + "bbox": [ + 0.62, + 0.195, + 0.892, + 0.228 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {c y c l}} = \\angle \\prod_ {(i, j) \\in \\mathcal {P}} \\boldsymbol {R} _ {i j}, \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.241, + 0.892, + 0.286 + ], + "angle": 0, + "content": "where \\( \\mathbf{R}_{ij} \\) is the estimated rotation between images \\( I_{i} \\) and \\( I_{j} \\) and \\( \\mathcal{P} = \\{(1,2),(2,3),(3,1)\\} \\) defines the cycle. As in [25], we also define an anchor loss" + }, + { + "type": "equation", + "bbox": [ + 0.593, + 0.298, + 0.891, + 0.332 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {a n c h o r}} = \\sum_ {(i, j) \\in \\mathcal {P}} \\angle R _ {i j} R _ {i j, \\mathrm {N E C}} ^ {\\top} \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.343, + 0.892, + 0.419 + ], + "angle": 0, + "content": "with the NEC rotation estimate, as a regularising term. In contrast to [25], our method does not risk learning degenerate solutions from the cycle-consistency loss, since the rotation is estimated using independently detected keypoints. The final loss is then given by" + }, + { + "type": "equation", + "bbox": [ + 0.613, + 0.432, + 0.891, + 0.449 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {s e l f}} = \\mathcal {L} _ {\\text {c y c l}} + \\lambda \\mathcal {L} _ {\\text {a n c h o r}}. \\tag {12}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.462, + 0.633, + 0.48 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.488, + 0.892, + 0.578 + ], + "angle": 0, + "content": "We evaluate our method in both synthetic and real-world experiments. Over the synthetic data, we investigate the ability of the gradient to learn the underlying noise distribution correctly by overfitting covariance estimates directly. We also investigate if better noise estimation leads to a reduces rotational error." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.58, + 0.892, + 0.73 + ], + "angle": 0, + "content": "On real-world data, we use the gradient to train a network to predicts the noise distributions from images for different keypoint detectors. We explore fully supervised and self-supervised learning techniques for SuperPoint [12] and Basalt [66] KLT-Tracks to verify that our method is agnostic to the type of feature descriptor used (classical vs learned). We evaluate the performance of the learned covariances in a visual odometry setting on the popular KITTI odometry and the EuRoC dataset. We also evaluate generalization capabilities from the KITTI to the EuRoC dataset." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.731, + 0.892, + 0.837 + ], + "angle": 0, + "content": "For our experiments we implement Eq. 3 in both Theseus [52] and ceres [1]. We use the Theseus implementation to train our network, since it allows for batched optimization and provides the needed gradient (see Eq. 8). However, we use the ceres implementation for our evaluation. We found the Levenberg-Marquardt optimization of ceres to be faster and more stable than its theseus counterpart." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.847, + 0.717, + 0.864 + ], + "angle": 0, + "content": "4.1. Simulated Experiments" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "In the simulated experiments we overfit covariance estimates for a single relative pose estimation problem using" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13106" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.09, + 0.272, + 0.179 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.117, + 0.182, + 0.237, + 0.194 + ], + "angle": 0, + "content": "(a) \\(e_{\\mathrm{rot}}\\) during training" + }, + { + "type": "image", + "bbox": [ + 0.274, + 0.089, + 0.468, + 0.179 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.286, + 0.18, + 0.456, + 0.195 + ], + "angle": 0, + "content": "(b) \\(\\sigma_{norm}^2\\) error during training" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.197, + 0.47, + 0.268 + ], + "angle": 0, + "content": "Figure 6. Rotational error (a) and differences between the true residual variance \\(\\tilde{\\sigma}^2\\) and the learned variance \\(\\sigma^2\\) (b) over the training epochs. As previously, our method learns to adapt the covariances for each keypoint to minimize rotational error. Minimizing the rotational error leads to a significantly better estimate of \\(\\sigma^2\\)." + }, + { + "type": "image", + "bbox": [ + 0.09, + 0.271, + 0.46, + 0.404 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.099, + 0.406, + 0.449, + 0.419 + ], + "angle": 0, + "content": "(a) covariance matrices in the 2nd frame after 100 epochs training" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.42, + 0.47, + 0.492 + ], + "angle": 0, + "content": "Figure 7. Estimated (red) covariance ellipses in the second frame, learned from 128000 examples. Ground truth (green) covariances as comparison. Training data with enough variety gives a gradient that allows to correctly learn the covariances even in the image plane, overcoming the unobservabilities of the first experiment." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.495, + 0.47, + 0.691 + ], + "angle": 0, + "content": "the gradient from Eq. 8. For this, We create a random relative pose estimation problem consisting of two cameraframes observing randomly generated points in 3D space. The points are projected into camera frames using a pin-hole camera model. Each projected point is assigned a random gaussian noise distribution. From this 128000 random problems are sampled. We learn the noise distributions by initializing all covariance estimates as scaled identity matrices, solving the relative pose estimation problem using the PNEC and updating the parameters of the distribution using the gradient of Eq. 8 directly. We train for 100 epochs with the ADAM [31] optimizer with (0.9, 0.99) as parameters and a batch size of 12800 for a stable gradient." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.692, + 0.47, + 0.785 + ], + "angle": 0, + "content": "Fig. 4a shows the decrease of the rotation error over the epochs. The learned covariances decrease the error by \\(8\\%\\) and \\(16\\%\\) compared to unit covariances and the NEC, respectively. This validates the importance of good covariances for the PNEC, shown in [48]. Fig. 4b shows the average error for the normalized variance \\(\\sigma_{norm}^2\\), given by" + }, + { + "type": "equation", + "bbox": [ + 0.201, + 0.793, + 0.47, + 0.832 + ], + "angle": 0, + "content": "\\[\n\\sigma_ {i, n o r m} ^ {2} = \\frac {N \\cdot \\sigma_ {i} ^ {2}}{\\sum_ {j = 0} ^ {N} \\sigma_ {j} ^ {2}} \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.841, + 0.47, + 0.903 + ], + "angle": 0, + "content": "over the training epochs, obtained at the ground truth relative pose. We compare the normalized error variance, as the scale of \\(\\sigma^2\\) is not observable from the gradient. The covariances that minimize the rotational error also approximate" + }, + { + "type": "image", + "bbox": [ + 0.532, + 0.089, + 0.86, + 0.322 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.324, + 0.892, + 0.422 + ], + "angle": 0, + "content": "Figure 8. Qualitative trajectory comparison for KITTI seq. 00. Since we compare monocular methods, that cannot estimate the correct scale from a pair of images, we use the scale of the ground truth translations for visualization purposes. Both, our supervised and self-supervised approaches lead to significant improvements in the trajectory. There is little drift even without additional rotation averaging [11] or loop closure [49]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.424, + 0.893, + 0.59 + ], + "angle": 0, + "content": "the residual uncertainty \\(\\sigma^2\\) very closely. However, while the residual uncertainty is approximated well, the learned 2D covariances in the image plane do not correspond to the correct covariances (see Fig. 5). This is due to two different reasons. First, due to \\(\\sigma_i^2\\) dependence on both \\(\\Sigma_{\\mathrm{2D},i}\\) and \\(\\Sigma_{\\mathrm{2D},i}^{\\prime}\\), there is not a single unique solution. Secondly, the direction of the gradient is dependent on the translation between the images (see the supplementary material for more details). In this experimental setup, the information flow to the images is limited and we can only learn the true distribution for \\(\\sigma^2\\) but not for the 2D images covariances." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.591, + 0.893, + 0.833 + ], + "angle": 0, + "content": "To address the problems with limited information flow of the previous experiment, we propose a second experiment to negate the influence of these aforementioned factors. First, each individual problem has a randomly sampled relative pose, where the first frame stays fixed. This removes the influence of the translation on the gradient direction. The noise is still drawn from the same distributions as earlier. Second, we fix the noise in the first frame to be small, isotropic, and homogeneous in nature. Furthermore, we only learn the covariances in the second frame and provide the optimization with the ground truth noise in the first frame. Fig. 6 and Fig. 7 show, that under these constraints, we are not only able to learn the distribution for \\(\\sigma^2\\) but also \\(\\Sigma_{2\\mathrm{D}}'\\). Together, both experiments show, that we can learn the correct distributions from noisy data by following the gradient that minimizes the rotational error." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.846, + 0.667, + 0.861 + ], + "angle": 0, + "content": "4.2. Real World Data" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.893, + 0.902 + ], + "angle": 0, + "content": "We evaluate our method on the KITTI [21] and EuRoC [9] dataset. Since KITTI shows outdoor driving sequences" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13107" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.087, + 0.089, + 0.88, + 0.223 + ], + "angle": 0, + "content": "
NISTÉR-5PT [50]NEC [33]NEC-LSWEIGHTED NEC-LSOURS SUPERVISEDOURS SELF-SUPERVISED
Seq.RPE1RPEnetRPE1RPEnetRPE1RPEnetRPE1RPEnetRPE1RPEnetRPE1RPEnet
080.19517.0204.240.0818.2843.660.0567.0042.500.0546.0592.500.0504.0672.460.0504.1182.46
090.1425.7541.740.0531.6461.430.0521.5530.710.0511.3540.700.0491.3170.710.0491.2780.70
100.29516.6786.570.1679.2644.430.0644.7871.790.0634.3891.760.0633.5131.640.0653.8211.65
train0.24911.5064.130.14110.1272.970.0826.9101.720.0816.4101.720.0772.3781.690.0772.5051.69
test0.20014.3494.070.0896.9173.280.0565.3531.960.0554.6761.950.0523.3331.910.0533.4081.91
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.224, + 0.895, + 0.281 + ], + "angle": 0, + "content": "Table 1. Quantitative comparison on the KITTI [21] dataset with SuperPoint [12] keypoints. We compare two rotation and one translation metric. The results are shown for each test sequence together with the mean results on the training and test set weighted by the sequence length. Both our training setups outperform the non-probabilitic algorithms but also the weighted NEC-LS using SuperGlue confidences consistently across unseen data. The learned uncertainties are able to generalise well and improve the relative pose estimation significantly." + }, + { + "type": "table", + "bbox": [ + 0.088, + 0.282, + 0.88, + 0.416 + ], + "angle": 0, + "content": "
NISTÉR-5PT [50]NEC [33]NEC-LSKLT-PNEC [48]OURS SUPERVISEDOURS SELF-SUPERVISED
Seq.RPE1RPEnetRPE1RPEnetRPE1RPEnetRPE1RPEnetRPE1RPEnetRPE1RPEnet
080.1266.9293.440.0883.9028.910.0532.9082.490.0542.5242.420.0482.3732.360.0471.7062.36
090.0902.5441.280.0542.0276.760.0522.3070.740.0461.0030.690.0431.2440.640.0421.1410.64
100.18811.5544.430.1198.3028.530.0664.5761.780.0634.4801.710.0583.7891.580.0563.6231.60
train0.2049.6773.190.1738.3018.590.1033.9551.730.1044.2131.660.0942.7821.600.0962.7371.61
test0.1296.7223.110.0854.2378.340.0553.0601.960.0542.5141.900.0482.3591.820.0481.9101.83
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.417, + 0.893, + 0.46 + ], + "angle": 0, + "content": "Table 2. Quantitative comparison on the KITTI [21] dataset with KLT tracks [66]. As in Tab. 1, we show the results on the test set together with the mean on the train and test set weighted by the sequence lengths. As for SuperPoint, our methods improve all metrics consistently for unseen data. Our learned covariances are significantly better for relative pose estimation than the approximation used in [48]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.468, + 0.473, + 0.62 + ], + "angle": 0, + "content": "and EuRoC shows indoor scenes captured with a drone, they exhibit different motion models as well as a variety of images. For KITTI we choose sequences 00-07 as the training set for both supervised and self-supervised training. Sequences 08-10 are used as the test set. We use a smaller UNet [55] architecture as our network to predict the covariances for the whole image. We chose this network since it gives us a good balance between batch size, training time and performance. The network predicts the parameters for the covariances directly. We choose" + }, + { + "type": "equation", + "bbox": [ + 0.142, + 0.63, + 0.47, + 0.665 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {\\Sigma} _ {2 \\mathrm {D}} (s, \\alpha , \\beta) = s \\boldsymbol {R} _ {\\alpha} \\left( \\begin{array}{c c} \\beta & 0 \\\\ 0 & 1 - \\beta \\end{array} \\right) \\boldsymbol {R} _ {\\alpha} ^ {\\top} \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.674, + 0.47, + 0.706 + ], + "angle": 0, + "content": "as a parameterization [7]. To ensure that our network predicts valid covariances the network output is filtered with" + }, + { + "type": "equation", + "bbox": [ + 0.194, + 0.715, + 0.469, + 0.734 + ], + "angle": 0, + "content": "\\[\nf _ {1} (x) = \\left(1 + | x |\\right) ^ {\\operatorname {s i g n} (\\mathrm {x})} \\tag {15}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.196, + 0.736, + 0.469, + 0.752 + ], + "angle": 0, + "content": "\\[\nf _ {2} (x) = x \\tag {16}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.196, + 0.755, + 0.469, + 0.784 + ], + "angle": 0, + "content": "\\[\nf _ {3} (x) = \\frac {1}{1 + e ^ {- x}} \\tag {17}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.47, + 0.841 + ], + "angle": 0, + "content": "for \\( s, \\alpha, \\beta \\), respectively. Feature points that have subpixel accuracy use the nearest pixel covariance. See the supplementary material for more details on the training setup." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.841, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Supervised Learning. To show that our method generalizes to different keypoint detectors, we train two networks, one for SuperPoint [12] and one for KLT tracks obtained from [66]. The SuperPoint keypoints are matched" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.468, + 0.895, + 0.74 + ], + "angle": 0, + "content": "using SuperGlue [57]. For training we use a batch size of 8 images pairs for SuperPoint and 16 images pairs for KLT tracks. We trained for 100 epochs for both SuperPoint and KLT tracks. More training details are provided in the supplementary material. To ensure our network does not overfit on specific keypoint locations, we randomly crop the images before finding correspondences during training time. During evaluation we use the uncropped images to obtain features. During training we randomly perturb the ground truth pose as a starting point. To increase robustness, we first use the eigenvalue based optimization of the NEC in a RANSAC scheme [32] to filter outliers. This is followed by a custom least squares implementation of the NEC (NECLS), followed by optimizing Eq. 3. As reported in [48] we found, that such a multi-stage optimization provides the most robust and accurate results. We show examples of how the DNLS-learned covariances change the energy function landscape in the supplementary material." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.744, + 0.895, + 0.867 + ], + "angle": 0, + "content": "Self-Supervised Learning. We evaluate our self-supervised training setup on the same data as our supervised training. Due to needing image tuples instead of pairs, we reduce the batch size to 12 for KLT image triplets. This gives us 24 and 36 images pairs per batch, respectively. The training epochs are reduced to 50. More training details for the supervised and self-supervised training can be found in the supplementary material." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Results. We evaluate the learned covariances in a VO setting. We compare the proposed DNLS approach to the" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "13108" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.079, + 0.089, + 0.896, + 0.251 + ], + "angle": 0, + "content": "
NISTÉR-5PT [51]NEC [33]NEC-LSWEIGHTED NEC-LSOURS SELF-SUPERVISEDOURS TAB. 1
Seq.RPE1RPEnetRPE1RPEnetRPE1RPEnetRPE1RPEnetRPE1RPEnetRPE1RPEnetRPE1RPEnet
V1_010.50171.8731.860.32039.5043.120.38752.9246.310.38856.5246.820.32731.1235.560.33231.8134.01
V1_020.54132.0120.360.38928.1126.950.54070.0828.940.54268.3529.810.44430.3921.980.43629.0721.29
V1_030.66027.3925.000.49225.4231.060.55276.7231.580.55578.1432.250.51029.5224.190.52031.1824.13
V2_010.51561.4533.510.31631.9539.790.31035.8439.000.31438.6239.620.28517.6132.400.29522.4130.58
V2_020.54543.7322.240.39625.4832.210.36926.9625.360.36525.0925.810.38225.3221.160.38621.9120.34
V2_031.12336.7128.770.97648.2637.600.939107.1136.740.941100.7336.710.94252.7231.130.99155.4130.40
mean0.63148.4527.560.46333.5136.030.49458.9035.610.49658.9536.110.46130.5728.460.47231.4427.44
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.076, + 0.253, + 0.894, + 0.311 + ], + "angle": 0, + "content": "Table 3. Quantitative comparison on the Vicon sequences of the EuRoC dataset [9] with SuperPoint [12] keypoints. The dataset is more difficult than KITTI (see Tab. 2 and Tab. 1) with SuperPoint and SuperGlue [57] finding far fewer matches. As reported in [48] the least squares implementations struggle with bad initialization under these adverse conditions with NEC-LS performing especially poor. From all least squares optimizations, our learned covariances consistently perform the best, even outperforming the NEC most of the time." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.325, + 0.473, + 0.688 + ], + "angle": 0, + "content": "popular 5pt algorithm [51] and the NEC [33] as implemented in [32]. To investigate the benefit of our learned covariances we include the NEC-LS implementation as well as the symmetric PNEC with the covariances from [48] in Tab. 2. For Tab. 1 we additionally include a weighted version of our custom NEC-LS implementation with matching confidence from SuperGlue as weights. All methods are given the same feature matches and use a constant motion model for initializing the optimizations. We evaluate on the rotational versions of the \\(\\mathrm{RPE}_1\\) and \\(\\mathrm{RPE}_n\\) and the cosine error \\(e_t\\) for the translation as defined in [11, 48]. Tab. 1 and Tab. 2 show the average results on the test set over 5 runs for SuperPoint and KLT tracks on KITTI [21], respectively. We show additional results in the supplementary material. Our methods consistently perform the best over all sequences, with the self-supervised being on par with our supervised training. Compared to its non-probabilistic counterpart NEC-LS, our method improves the \\(\\mathrm{RPE}_1\\) by \\(7\\%\\) and \\(13\\%\\) and the \\(\\mathrm{RPE}_n\\) by \\(37\\%\\) and \\(23\\%\\) for different keypoint detectors on unseen data. It also improves upon weighted methods, like weighted NEC-LS and the nonlearned covariances for the PNEC [48]. This demonstrates the importance of correctly modeling the feature correspondence quality. We show an example trajectory in Fig. 8." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.472, + 0.829 + ], + "angle": 0, + "content": "Tab. 3 shows the results on the EuRoC dataset for SuperPoint. Pose estimation is significantly more difficult compared to KITTI, often having few correspondences between images. However, our method generalizes to different datasets, with the network trained on KITTI and our self-supervised approach, outperforming the others most of the time. Especially a direct comparison with NEC-LS, the closest non-probabilistic method, shows significant improvements of \\(7\\%\\) for \\(\\mathrm{RPE}_1\\) and \\(48\\%\\) for the \\(\\mathrm{RPE}_n\\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.844, + 0.33, + 0.86 + ], + "angle": 0, + "content": "5. Discussion and Limitations" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.472, + 0.903 + ], + "angle": 0, + "content": "Our experiments demonstrate the capability of our framework to correctly learn positional uncertainty, lead" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.325, + 0.895, + 0.415 + ], + "angle": 0, + "content": "ing to improved results for relative pose estimation for VO. Our approach generalizes to different feature extractors and to different datasets, providing a unified approach to estimate the noise distribution of keypoint detectors. However, our method requires more computational resources than the original uncertainty estimation for the PNEC." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.416, + 0.895, + 0.552 + ], + "angle": 0, + "content": "We evaluate our learned covariances in a visual odometry setting, showing that they lead to reduced errors and especially less drift in the trajectory. However, this does not guarantee that the covariances are calibrated. Our framework inherits the ambiguity of the PNEC with regard to the noise scale. The true scale of the noise is not observable from relative pose estimation alone and only the relative scale between covariances can be learned. For the purposes of VO, this scale ambiguity is negligible." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.553, + 0.895, + 0.629 + ], + "angle": 0, + "content": "As our synthetic experiments show, diverse data is needed to correctly identify the 2D noise distribution. However, obtaining the noise distribution is difficult for keypoint detectors - hence learning it from pose regression. Further limitations are addressed in the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.643, + 0.62, + 0.658 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.668, + 0.895, + 0.851 + ], + "angle": 0, + "content": "We present a novel DNLS framework for estimating positional uncertainty. Our framework can be combined with any feature extraction algorithm, making it extremely versatile. Regressing the noise distribution from relative pose estimation, ensures that learned covariance matrices are suitable for visual odometry tasks. In synthetic experiments, our framework is capable to learn the correct noise distribution from noisy data. We showed the practical application of our framework on real-world data for different feature extractors. Our learned uncertainty consistently outperforms a variety of non-probabilistic relative pose estimation algorithms as well as other uncertainty estimation methods." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.863, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Acknowledgements. This work was supported by the ERC Advanced Grant SIMULACRON, by the Munich Center for Machine Learning and by the EPSRC Programme Grant VisualAI EP/T028572/1." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "13109" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.105 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.468, + 0.143 + ], + "angle": 0, + "content": "[1] Sameer Agarwal, Keir Mierle, and Others. 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Springer, 2017. 3" + }, + { + "type": "list", + "bbox": [ + 0.079, + 0.092, + 0.47, + 0.192 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.519, + 0.956 + ], + "angle": 0, + "content": "13112" + } + ] +] \ No newline at end of file diff --git a/2023/Learning Correspondence Uncertainty via Differentiable Nonlinear Least Squares/8f30fa60-e502-4ee5-838a-d9c7713dcf6d_origin.pdf b/2023/Learning Correspondence Uncertainty via Differentiable Nonlinear Least Squares/8f30fa60-e502-4ee5-838a-d9c7713dcf6d_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..1f10c11e5f131c43aaba13aee108685c91390479 --- /dev/null +++ b/2023/Learning Correspondence Uncertainty via Differentiable Nonlinear Least Squares/8f30fa60-e502-4ee5-838a-d9c7713dcf6d_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:e97a96ca3aef594ed4c22de87d6f9e4fb1e8c2b95cf7d20e41145ce10b1b8659 +size 7831110 diff --git a/2023/Learning Correspondence Uncertainty via Differentiable Nonlinear Least Squares/full.md b/2023/Learning Correspondence Uncertainty via Differentiable Nonlinear Least Squares/full.md new file mode 100644 index 0000000000000000000000000000000000000000..021690f54e69681b77fdb211a37cff236ed15b51 --- /dev/null +++ b/2023/Learning Correspondence Uncertainty via Differentiable Nonlinear Least Squares/full.md @@ -0,0 +1,388 @@ +# Learning Correspondence Uncertainty via Differentiable Nonlinear Least Squares + +Dominik Muhle1,2 +1TU Munich + +Lukas Koestler $^{1,2}$ + +Krishna Murthy Jatavallabhula4 + +Daniel Cremers1,2,3 + +2Munich Center for Machine Learning + +$^{3}$ University of Oxford + +$^{4}$ MIT + +{dominik.muhle, lukas.koestler, cremers}@tum.de jkrishna@mit.edu + +images with correspondences + +![](images/1b84e559e923c5aebadce76925f11adac34b5822314ed1b79298475374c4609c.jpg) + +![](images/e8cddea1f1b77514392f23b15d7e006badca92b2740500998d99c237bb64db43.jpg) + +![](images/4ded2522acfb42dfc6f33f42b99df32a9b55a7fd46c7fc3366c3f37f17618514.jpg) +uncertainty estimates from images + +![](images/bb69457b3eeab57802812bcafb9df5e6c8d6e8feb5d8323df774fd9ea9573e37.jpg) + +![](images/230ca915a5199cf01d184cd2f7a859e7ab082227beb40ac99658ff08a0fbef1c.jpg) +Figure 1. We present a differentiable nonlinear least squares (DNLS) framework for learning feature correspondence quality by computing per-feature positional uncertainty. The uncertainty estimates (left, bottom images) are regressed from a pose estimation error (middle), enabling the framework across a range of (handcrafted, learned) feature extractors. Our learned covariances (right, orange trajectory) improve orientation estimation by up to $11\%$ over state-of-the-art probabilistic pose estimation methods on the KITTI dataset [21]. + +![](images/07c047a63adcaf8f25897f98fe52484315c72cf001ae413d0cb5740812d0bbef.jpg) + +# Abstract + +We propose a differentiable nonlinear least squares framework to account for uncertainty in relative pose estimation from feature correspondences. Specifically, we introduce a symmetric version of the probabilistic normal epipolar constraint, and an approach to estimate the covariance of feature positions by differentiating through the camera pose estimation procedure. We evaluate our approach on synthetic, as well as the KITTI and EuRoC real-world datasets. On the synthetic dataset, we confirm that our learned covariances accurately approximate the true noise distribution. In real world experiments, we find that our approach consistently outperforms state-of-the-art nonprobabilistic and probabilistic approaches, regardless of the feature extraction algorithm of choice. + +# 1. Introduction + +Estimating the relative pose between two images given mutual feature correspondences is a fundamental problem in computer vision. It is a key component of structure from motion (SfM) and visual odometry (VO) methods which in turn fuel a plethora of applications from autonomous vehicles or robots to augmented and virtual reality. + +Estimating the relative pose - rotation and translation - between two images, is often formulated as a geometric problem that can be solved by estimating the essential matrix [42] for calibrated cameras, or the fundamental matrix [24] for uncalibrated cameras. Related algorithms like the eight-point algorithm [23, 42] provide fast solutions. However, essential matrix based approaches suffer issues such as solution multiplicity [18, 24] and planar degeneracy [33]. The normal epipolar constraint (NEC) [34] addresses issues such as by estimating the issues such as which leads to more accurate relative poses [33]. + +Neither of the aforementioned algorithms takes into account the quality of feature correspondences – an important cue that potentially improves pose estimation accuracy. Instead, feature correspondences are classified into inliers and outliers through a RANSAC scheme [11]. However, keypoint detectors [12, 56] for feature correspondences or tracking algorithms [63] yield imperfect points [40] that exhibit a richer family of error distributions, as opposed to an inlier-outlier distribution family. Algorithms, that make use of feature correspondence quality have been proposed for essential/fundamental matrix estimation [7, 53] and for the NEC [48], respectively. + +While estimating the relative pose can be formulated as a classical optimization problem [15, 33], the rise in popularity of deep learning has led to several works augmenting + +![](images/6ae52ad7dfb3af692a5e97429cd7ca162b89034198b0a988a2748753037aa58b.jpg) + +![](images/b542b81cb7ec3599f81598486d9a8660e9b0dd0a0613b12c0d16997c85847200.jpg) + +![](images/7436d32d3240a57c0a2ca596cf36c1c79147156b8e05f7ceef48a47d4fea599c.jpg) +(a) covariances from [48] per pixel +(c) learned covariances per pixel (Ours) + +![](images/bad77c254c535aeb660e76ba6bf3884c3eac9a4e58651da5492e0ce55eb4ede0.jpg) +(b) points and covariances [48] +(d) points and learned covariances (Ours) +Figure 2. Comparison between covariances used in [48] (first row) and our learned covariances (second row). The first column shows a dense color coded $(s, \alpha, \beta$ mapped to HLS with $\gamma$ correction) representation for each pixel, while the second column shows subsampled keypoints and their corresponding (enlarged) covariances. The higher saturation in (a) shows that the covariances are more anisotropic. The learned covariances (c) show a more fine-grained detail in the scale (brightness) and less blurring than the covariances in (a). + +VO or visual simultaneous localisation and mapping (VSLAM) pipelines with learned components. GN-Net [67] learns robust feature representations for direct methods like DSO [15]. For feature based methods Superpoint [12] provides learned features, while Superglue [57] uses graph neural networks to find corresponding matches between feature points in two images. DSAC introduces a differential relaxation to RANSAC that allows gradient flow through the otherwise non-differentiable operation. In [53] a network learns to re-weight correspondences for estimating the fundamental matrix. PixLoc [58] estimates the pose from an image and a 3D model based on direct alignment. + +In this work we combine the predictive power of deep learning with the precision of geometric modeling for highly accurate relative pose estimation. Estimating the noise distributions for the feature positions of different feature extractors allows us to incorporate this information into relative pose estimation. Instead of modeling the noise for each feature extractor explicitly, we present a method to learn these distributions from data, using the same domain that the feature extractors work with - images. We achieve this based on the following technical contributions: + +- We introduce a symmetric version of the probabilistic normal epipolar constraint (PNEC), that more accurately models the geometry of relative pose estimation with uncertain feature positions. +- We propose a learning strategy to minimize the relative pose error by learning feature position uncertainty through differentiable nonlinear least squares (DNLS), see Fig. 1. +- We show with synthetic experiments, that using the gradient from the relative pose error leads to meaningful estimates of the positional uncertainty that reflect the correct error distribution. +- We validate our approach on real-world data in a visual odometry setting and compare our method to non + +probabilistic relative pose estimation algorithms, namely Nister 5pt [50], and NEC [33], as well as to the PNEC with non-learned covariances [48]. + +- We show that our method is able to generalize to different feature extraction algorithms such as SuperPoint [12] and feature tracking approaches on real-world data. +- We release the code for all experiments and the training setup to facilitate future research. + +# 2. Related Work + +This work is on deep learning for improving frame-to-frame relative pose estimation by incorporating feature position uncertainty with applications to visual odometry. We therefore restrict our discussion of related work to relative pose estimation in visual odometry, weighting correspondences for relative pose estimation, and deep learning in the context of VSLAM. For a broader overview over VSLAM we refer the reader to more topic-specific overview papers [10, 65] and to the excellent books by Hartley and Zisserman [24] and by Szeliski [62]. + +Relative Pose Estimation in Visual Odometry. Finding the relative pose between two images has a long history in computer vision, with the first solution for perspective images reaching back to 1913 by Kruppa [35]. Modern methods for solving this problem can be classified into feature-based and direct methods. The former rely on feature points extracted in the images together with geometric constraints like the epipolar constraint or the normal epipolar constraint [34] to calculate the relative pose. The latter optimize the pose by directly considering the intensity differences between the two images and rose to popularity with LSD-SLAM [16] and DSO [15]. Since direct methods work on the assumption of brightness or irradiance constancy they require the appearance to be somewhat similar across images. In turn, keypoint based methods rely + +on suitable feature extractors which can exhibit significant amounts of noise and uncertainty. In this paper we propose a method to learn the intrinsic noise of keypoint detectors – therefore, the following will focus on feature based relative pose estimation. + +One of the most widely used parameterizations for reconstructing the relative pose from feature correspondences is the essential matrix, given calibrated cameras, or the fundamental matrix in the general setting. Several solutions based on the essential matrix have been proposed [36, 38, 42, 50, 61]. They include the linear solver by Longuet-Higgins [42], requiring 8 correspondences, or the solver by Nister et al. [51] requiring the minimal number of 5 correspondences. However, due to their construction, essential matrix methods deteriorate for purely rotational motion with noise-free correspondences [33]. As an alternative, methods that do not use the essential matrix have been proposed - they either estimate the relative pose using quaternions [17] or make use of the normal epipolar constraint (NEC) by Kneip and Lynen [33, 34]. The latter addresses the problems of the essential matrix by estimating rotation independent of the translation. [6] shows how to obtain the global minimum for the NEC. Further work, that disentangles rotation and translation can be found in [39]. + +Weighting of Feature Correspondences. Keypoints in images can exhibit significant noise, deteriorating the performance for pose estimation significantly [22]. The noise characteristics of the keypoint positions depend on the feature extractor. For Kanade-Lucas-Tomasi (KLT) tracking [44, 63] approaches, the position uncertainty has been investigated in several works [20, 59, 60, 72]. The uncertainty was directly integrated into the tracking in [14]. [71] proposed a method to obtain anisotropic and inhomogeneous covariances for SIFT [43] and SURF [3]. + +Given the imperfect keypoint positions, not all correspondences are equally well suited for estimating the relative pose. [22] showed the effect of the noise level on the accuracy of the pose estimation. Limiting the influence of bad feature correspondences has been studied from a geometrical and a probabilistic perspective. Random sample consensus (RANSAC) [19] is a popular method to classify datapoints into inliers and outliers that can be easily integrated into feature based relative pose estimation pipelines. Ranftl et al. [53] relax the hard classification for inlier and outlier and use deep learning to find a robust fundamental matrix estimator in the presence of outliers in an iteratively reweighted least squares (IRLS) fashion. DSAC [5] models RANSAC as a probabilistic process to make it differentiable. Other lines of work integrate information about position uncertainty directly into the alignment problem. For radar based SLAM, [8] incorporates keypoint uncertainty in radar images, with a deep network predicting the uncertainty. Image based position uncertainty was investigated + +from the statistical, [27, 28], the photogrammetry [46] and the computer vision perspective [7, 29]. [7] and [29] debated the benefit of incorporating position uncertainty into fundamental matrix estimation. We base our method on the probabilistic normal epipolar constraint (PNEC) [48], that improved on the NEC by extending it to a probabilistic view. It achieved better results on real-world data with covariances approximated using the Boltzmann distribution [4]. We expand on this idea by learning covariances (see Fig. 2) agnostic of the keypoints extractor used to further improve pose estimation. + +Deep Learning in VSLAM. Deep Learning has transformed computer vision in the last decade. While deep networks have been successfully used for tasks like detection [54], semantic segmentation [41], and recently novel view synthesis [47], they have also found application in VSLAM pipelines. DVSO [69] and D3VO [68] leveraged deep learning to improve the precision for direct methods, while GN-Net [67] predicts robust and dense feature maps. Several works proposed to learn keypoint extractors, for feature based pose estimation, such as SuperPoint [12] and LIFT [70]. SuperGlue [57] enabled feature matching with graph neural networks. Other lines of work leverage deep learning for localization by making parts of the pose estimation pipeline differentiable [2,5,58,64]. Works, that directly predicting the pose include PoseNet [30] and CTCNet [25] that uses self-supervised learning with a cycle-consistency loss for VO. [40] learns image representations by refining keypoint positions and camera poses in a post-processing step of a structure-from-motion pipeline. $\nabla$ SLAM [26] presents a differentiable dense SLAM system with several components (e.g., the Levenberg-Marquardt [37, 45] optimizer). + +# 3. Method + +In the following, we present our framework to estimate positional uncertainty of feature points by leveraging DNLS. We learn the noise covariances through a forward and backward step. In the forward step, the covariances are used in a probabilistic pose estimation optimization, namely the PNEC. In the backward step, the gradient from the pose error is back-propagated through the optimization to the covariances. From there we can train a neural network to predict the keypoint position uncertainty from the images. We start by summarizing the asymmetric PNEC [48] and for the first time introduce its symmetric counterpart. + +# 3.1. Prerequisites + +Notation. We follow the notation of [48]. Bold lowercase letters (e.g. $\pmb{f}$ ) denote vectors, whereas bold uppercase letters (e.g. $\pmb{\Sigma}$ ) denote matrices. $\hat{\pmb{u}} \in \mathbb{R}^{3 \times 3}$ represents the skew-symmetric matrix of the vector $\pmb{u} \in \mathbb{R}^3$ such that the cross product between two vectors can be rewritten as a matrix-vector operation, i.e. $\pmb{u} \times \pmb{v} = \hat{\pmb{u}}\pmb{v}$ . The transpose is + +![](images/43455a9955841ec37d299f9eea2d6cdac9368debcb666b186a52bc6fea6d0013.jpg) +Figure 3. Architecture: We extract the uncertainty per image for every pixel using a UNet [55] backbone. Using keypoint locations from a keypoint detector, we obtain the keypoints with their estimated positional uncertainty. The relative pose is then estimated using a DNLS optimization. The UNet is updated by backpropagating the gradient (obtained by implicit differentiation) to the network output. + +denoted by the superscript $\top$ . We deviate from [48] in the following: variables of the second frame are marked with the ' superscript, while variables of the first frame do not have a superscript. We represent the relative pose between images as a rigid-body transformation consisting of a rotation matrix $R \in SO(3)$ and a unit length translation $t \in \mathbb{R}^3$ ( $\| t \| = 1$ is imposed due to scale-invariance). + +# 3.2. The Probabilistic Normal Epipolar Constraint + +The asymmetric probabilistic normal epipolar constraint (PNEC) estimates the relative pose, give two images $I, I'$ of the same scene under the assumption of uncertain feature positions in the second image. A feature correspondences is given by $\pmb{p}_i, \pmb{p}_i'$ in the image plane, where the uncertainty of $\pmb{p}_i'$ is represented by the corresponding covariance $\Sigma_{2\mathrm{D},i}'$ . To get the epipolar geometry for the PNEC the feature points are unprojected using the camera intrinsics, giving unit length bearing vectors $\pmb{f}_i, \pmb{f}_i'$ . The uncertainty of $\pmb{f}_i'$ is now represented by $\Sigma_i'$ . Estimating the relative pose is done by minimizing the PNEC cost function as defined in [48]. For convenience we recap the energy function + +$$ +E (\boldsymbol {R}, \boldsymbol {t}) = \sum_ {i} \frac {e _ {i} ^ {2}}{\sigma_ {i} ^ {2}} = \sum_ {i} \frac {| \boldsymbol {t} ^ {\top} (\boldsymbol {f} _ {i} \times \boldsymbol {R} \boldsymbol {f} _ {i} ^ {\prime}) | ^ {2}}{\boldsymbol {t} ^ {\top} \hat {\boldsymbol {f}} _ {i} \boldsymbol {R} \boldsymbol {\Sigma} _ {i} ^ {\prime} \boldsymbol {R} ^ {\top} \hat {\boldsymbol {f}} _ {i} ^ {\top} \boldsymbol {t}}, (1) +$$ + +in our notation. As mentioned previously, this asymmetric PNEC in [48] only considers uncertainties $\Sigma^{\prime}$ in the second frame. While this assumption might hold for the KLT tracking [66] used in [48], this leaves out important information when using other keypoint detectors like ORB [56] or SuperPoint [12]. Therefore, we will introduce a symmetric version of the PNEC that is more suitable for our task in the following. + +Making the PNEC symmetric. As in [48] we assume the covariance of the bearing vectors $\pmb{f}_i$ and $\pmb{f}_i'$ to be gaussian, their covariance matrices denoted by $\pmb{\Sigma}_i$ and $\pmb{\Sigma}_i'$ , respectively. The new variance can be approximated as + +$$ +\sigma_ {s, i} ^ {2} = \boldsymbol {t} ^ {\top} \left(\left(\boldsymbol {R} \hat {\boldsymbol {f}} _ {i} ^ {\prime}\right) \boldsymbol {\Sigma} _ {i} \left(\boldsymbol {R} \hat {\boldsymbol {f}} _ {i} ^ {\prime}\right) ^ {\top} + \hat {\boldsymbol {f}} _ {i} \boldsymbol {R} \boldsymbol {\Sigma} _ {i} ^ {\prime} \boldsymbol {R} ^ {\top} \hat {\boldsymbol {f}} _ {i} ^ {\top}\right) \boldsymbol {t}. \tag {2} +$$ + +In the supplementary material we derive the variance and show the validity of this approximation given the geometry of the problem. This new variance now gives us the new symmetric PNEC with its following energy function + +$$ +E _ {s} (\boldsymbol {R}, \boldsymbol {t}) = \sum_ {i} \frac {e _ {i} ^ {2}}{\sigma_ {s , i} ^ {2}} \tag {3} +$$ + +# 3.3. DNLS for Learning Covariances + +We want to estimate covariances $\Sigma_{2\mathrm{D}}$ and $\Sigma_{2\mathrm{D}}^{\prime}$ (in the following collectively denoted as $\Sigma_{2\mathrm{D}}$ for better readability) in the image plane + +$$ +\boldsymbol {\Sigma} _ {2 \mathrm {D}} = \underset {\boldsymbol {\Sigma} _ {2 \mathrm {D}}} {\arg \min } \mathcal {L}, \tag {4} +$$ + +such that they minimize a loss function $\mathcal{L}$ of the estimated pose. Since we found that the rotational error of the PNEC is more stable than the translational error, we chose to minimize only the rotational error + +$$ +e _ {\text {r o t}} = \angle \tilde {\boldsymbol {R}} ^ {\top} \boldsymbol {R} \tag {5} +$$ + +$$ +\mathcal {L} (\tilde {\boldsymbol {R}}, \boldsymbol {R}; \boldsymbol {\Sigma} _ {2 \mathrm {D}}) = e _ {\mathrm {r o t}} \tag {6} +$$ + +between the ground truth rotation $\tilde{\pmb{R}}$ and the estimated rotation $\pmb{R}$ . We obtain + +$$ +\boldsymbol {R} = \arg \min _ {\boldsymbol {R}} E _ {s} (\boldsymbol {R}, t; \Sigma_ {2 \mathrm {D}}) \tag {7} +$$ + +by minimizing Eq. 3. To learn the covariances that minimize the rotational error, we can follow the gradient $d\mathcal{L} / d\Sigma_{2\mathrm{D}}$ . Implicit differentiation allows us to compute the gradient as + +$$ +\frac {d \mathcal {L}}{d \boldsymbol {\Sigma} _ {2 \mathrm {D}}} = - \frac {\partial^ {2} E _ {s}}{\partial \boldsymbol {\Sigma} _ {2 \mathrm {D}} \partial \boldsymbol {R} ^ {\top}} \left(\frac {\partial^ {2} E _ {s}}{\partial \boldsymbol {R} \partial \boldsymbol {R} ^ {\top}}\right) ^ {- 1} \frac {e _ {\text {r o t}}}{\partial \boldsymbol {R}}. \tag {8} +$$ + +For a detailed derivation of Eq. 8 and other methods, that unroll the optimization, to obtain the gradient we refer the interested reader to [13]. + +![](images/6a7ae7993f2e1a6147cf413b4d48274275ae7abfa8e14fa7366fd5cb1c9e1767.jpg) +(a) $e_{\mathrm{rot}}$ during training + +![](images/1f71886f6535a19698c9ae4a0a949eeac1600bdc7cfb158d4821fc1edad4a2cf.jpg) +(b) $\sigma_{norm}^2$ error during training + +![](images/f21aa1be7d28aa2e0aac6295ff8bde7db74602f93907582731cf394ba994536f.jpg) +Figure 4. Rotational error (a) and differences between the true residual variance $\tilde{\sigma}^2$ and the learned variance $\sigma^2$ (b) over the training epochs. Starting from uniform covariances, our method adapts the covariances for each keypoint to minimize the rotational error. Simultaneously, this leads to a better estimate of $\sigma^2$ . + +![](images/d0e316f93a7aef38fa4a46b97b9d16a9d87d491db9c8834e9ed6a4f48e7006ec.jpg) +(a) covariance matrices in the 1st frame after 100 epochs training +(b) covariance matrices in the 2nd frame after 100 epochs training +Figure 5. Estimated (red) covariance ellipses in the first (a) and the second (b) frame, learned from 128000 examples. Ground truth (green) covariances as comparison. Although the gradient minimizes the rotational error (see Fig. 4a), it is not capable of learning the correct covariance in the image plane. + +Supervised Learning. The goal of the paper is for a neural network $F$ learn the noise distributions of a keypoint detector. Given an image and a keypoint position, the network should predict the covariance of the noise $\Sigma_{2\mathrm{D},i} = F(\boldsymbol {I},\boldsymbol {p}_i)$ . The gradient $d\mathcal{L} / d\Sigma_{2\mathrm{D}}$ allows for the network to learn the covariance matrices in an end-to-end manner by regression on the relative pose error. Given a dataset with known ground truth poses, we can use + +$$ +\mathcal {L} _ {\sup } = e _ {\text {r o t}} \tag {9} +$$ + +as a training loss. This ensures, that learned covariances effectively minimize the rotational error. See Fig. 3 for overview of the training process. + +Self-Supervised Learning. Finding a suitable annotated dataset for a specific task is often non-trivial. For our task, we need accurate ground truth poses that are difficult to ac + +quire. But given a stream of images, like in VO, our method can be adapted to train a network in a self-supervised manner without the need for ground truth poses. For this, we follow the approach of [25] to exploit the cycle-consistency between a tuple of images. The cycle-consistency loss for a triplet $\{I_1, I_2, I_3\}$ of images is given by + +$$ +\mathcal {L} _ {\text {c y c l}} = \angle \prod_ {(i, j) \in \mathcal {P}} \boldsymbol {R} _ {i j}, \tag {10} +$$ + +where $\mathbf{R}_{ij}$ is the estimated rotation between images $I_{i}$ and $I_{j}$ and $\mathcal{P} = \{(1,2),(2,3),(3,1)\}$ defines the cycle. As in [25], we also define an anchor loss + +$$ +\mathcal {L} _ {\text {a n c h o r}} = \sum_ {(i, j) \in \mathcal {P}} \angle R _ {i j} R _ {i j, \mathrm {N E C}} ^ {\top} \tag {11} +$$ + +with the NEC rotation estimate, as a regularising term. In contrast to [25], our method does not risk learning degenerate solutions from the cycle-consistency loss, since the rotation is estimated using independently detected keypoints. The final loss is then given by + +$$ +\mathcal {L} _ {\text {s e l f}} = \mathcal {L} _ {\text {c y c l}} + \lambda \mathcal {L} _ {\text {a n c h o r}}. \tag {12} +$$ + +# 4. Experiments + +We evaluate our method in both synthetic and real-world experiments. Over the synthetic data, we investigate the ability of the gradient to learn the underlying noise distribution correctly by overfitting covariance estimates directly. We also investigate if better noise estimation leads to a reduces rotational error. + +On real-world data, we use the gradient to train a network to predicts the noise distributions from images for different keypoint detectors. We explore fully supervised and self-supervised learning techniques for SuperPoint [12] and Basalt [66] KLT-Tracks to verify that our method is agnostic to the type of feature descriptor used (classical vs learned). We evaluate the performance of the learned covariances in a visual odometry setting on the popular KITTI odometry and the EuRoC dataset. We also evaluate generalization capabilities from the KITTI to the EuRoC dataset. + +For our experiments we implement Eq. 3 in both Theseus [52] and ceres [1]. We use the Theseus implementation to train our network, since it allows for batched optimization and provides the needed gradient (see Eq. 8). However, we use the ceres implementation for our evaluation. We found the Levenberg-Marquardt optimization of ceres to be faster and more stable than its theseus counterpart. + +# 4.1. Simulated Experiments + +In the simulated experiments we overfit covariance estimates for a single relative pose estimation problem using + +![](images/a4b616e032eafc2ed38439704b3002ade950df0f9942281d46d3f46f3bdef8f5.jpg) +(a) $e_{\mathrm{rot}}$ during training + +![](images/d3c7bd319872a4185cc7ac9241beec52f03f1100a4505dfe71995ca03170e7c4.jpg) +(b) $\sigma_{norm}^2$ error during training + +![](images/7118faac46243aca99c028df3a74f866901f9501ab60f43311d429339cb77bbb.jpg) +Figure 6. Rotational error (a) and differences between the true residual variance $\tilde{\sigma}^2$ and the learned variance $\sigma^2$ (b) over the training epochs. As previously, our method learns to adapt the covariances for each keypoint to minimize rotational error. Minimizing the rotational error leads to a significantly better estimate of $\sigma^2$ . +(a) covariance matrices in the 2nd frame after 100 epochs training +Figure 7. Estimated (red) covariance ellipses in the second frame, learned from 128000 examples. Ground truth (green) covariances as comparison. Training data with enough variety gives a gradient that allows to correctly learn the covariances even in the image plane, overcoming the unobservabilities of the first experiment. + +the gradient from Eq. 8. For this, We create a random relative pose estimation problem consisting of two cameraframes observing randomly generated points in 3D space. The points are projected into camera frames using a pin-hole camera model. Each projected point is assigned a random gaussian noise distribution. From this 128000 random problems are sampled. We learn the noise distributions by initializing all covariance estimates as scaled identity matrices, solving the relative pose estimation problem using the PNEC and updating the parameters of the distribution using the gradient of Eq. 8 directly. We train for 100 epochs with the ADAM [31] optimizer with (0.9, 0.99) as parameters and a batch size of 12800 for a stable gradient. + +Fig. 4a shows the decrease of the rotation error over the epochs. The learned covariances decrease the error by $8\%$ and $16\%$ compared to unit covariances and the NEC, respectively. This validates the importance of good covariances for the PNEC, shown in [48]. Fig. 4b shows the average error for the normalized variance $\sigma_{norm}^2$ , given by + +$$ +\sigma_ {i, n o r m} ^ {2} = \frac {N \cdot \sigma_ {i} ^ {2}}{\sum_ {j = 0} ^ {N} \sigma_ {j} ^ {2}} \tag {13} +$$ + +over the training epochs, obtained at the ground truth relative pose. We compare the normalized error variance, as the scale of $\sigma^2$ is not observable from the gradient. The covariances that minimize the rotational error also approximate + +![](images/d0e6806c6fdff765b963cf66588aae4e30a257e57004c90c1d0fc6a659390887.jpg) +Figure 8. Qualitative trajectory comparison for KITTI seq. 00. Since we compare monocular methods, that cannot estimate the correct scale from a pair of images, we use the scale of the ground truth translations for visualization purposes. Both, our supervised and self-supervised approaches lead to significant improvements in the trajectory. There is little drift even without additional rotation averaging [11] or loop closure [49]. + +the residual uncertainty $\sigma^2$ very closely. However, while the residual uncertainty is approximated well, the learned 2D covariances in the image plane do not correspond to the correct covariances (see Fig. 5). This is due to two different reasons. First, due to $\sigma_i^2$ dependence on both $\Sigma_{\mathrm{2D},i}$ and $\Sigma_{\mathrm{2D},i}^{\prime}$ , there is not a single unique solution. Secondly, the direction of the gradient is dependent on the translation between the images (see the supplementary material for more details). In this experimental setup, the information flow to the images is limited and we can only learn the true distribution for $\sigma^2$ but not for the 2D images covariances. + +To address the problems with limited information flow of the previous experiment, we propose a second experiment to negate the influence of these aforementioned factors. First, each individual problem has a randomly sampled relative pose, where the first frame stays fixed. This removes the influence of the translation on the gradient direction. The noise is still drawn from the same distributions as earlier. Second, we fix the noise in the first frame to be small, isotropic, and homogeneous in nature. Furthermore, we only learn the covariances in the second frame and provide the optimization with the ground truth noise in the first frame. Fig. 6 and Fig. 7 show, that under these constraints, we are not only able to learn the distribution for $\sigma^2$ but also $\Sigma_{2\mathrm{D}}'$ . Together, both experiments show, that we can learn the correct distributions from noisy data by following the gradient that minimizes the rotational error. + +# 4.2. Real World Data + +We evaluate our method on the KITTI [21] and EuRoC [9] dataset. Since KITTI shows outdoor driving sequences + +
NISTÉR-5PT [50]NEC [33]NEC-LSWEIGHTED NEC-LSOURS SUPERVISEDOURS SELF-SUPERVISED
Seq.RPE1RPEnetRPE1RPEnetRPE1RPEnetRPE1RPEnetRPE1RPEnetRPE1RPEnet
080.19517.0204.240.0818.2843.660.0567.0042.500.0546.0592.500.0504.0672.460.0504.1182.46
090.1425.7541.740.0531.6461.430.0521.5530.710.0511.3540.700.0491.3170.710.0491.2780.70
100.29516.6786.570.1679.2644.430.0644.7871.790.0634.3891.760.0633.5131.640.0653.8211.65
train0.24911.5064.130.14110.1272.970.0826.9101.720.0816.4101.720.0772.3781.690.0772.5051.69
test0.20014.3494.070.0896.9173.280.0565.3531.960.0554.6761.950.0523.3331.910.0533.4081.91
+ +Table 1. Quantitative comparison on the KITTI [21] dataset with SuperPoint [12] keypoints. We compare two rotation and one translation metric. The results are shown for each test sequence together with the mean results on the training and test set weighted by the sequence length. Both our training setups outperform the non-probabilitic algorithms but also the weighted NEC-LS using SuperGlue confidences consistently across unseen data. The learned uncertainties are able to generalise well and improve the relative pose estimation significantly. + +
NISTÉR-5PT [50]NEC [33]NEC-LSKLT-PNEC [48]OURS SUPERVISEDOURS SELF-SUPERVISED
Seq.RPE1RPEnetRPE1RPEnetRPE1RPEnetRPE1RPEnetRPE1RPEnetRPE1RPEnet
080.1266.9293.440.0883.9028.910.0532.9082.490.0542.5242.420.0482.3732.360.0471.7062.36
090.0902.5441.280.0542.0276.760.0522.3070.740.0461.0030.690.0431.2440.640.0421.1410.64
100.18811.5544.430.1198.3028.530.0664.5761.780.0634.4801.710.0583.7891.580.0563.6231.60
train0.2049.6773.190.1738.3018.590.1033.9551.730.1044.2131.660.0942.7821.600.0962.7371.61
test0.1296.7223.110.0854.2378.340.0553.0601.960.0542.5141.900.0482.3591.820.0481.9101.83
+ +Table 2. Quantitative comparison on the KITTI [21] dataset with KLT tracks [66]. As in Tab. 1, we show the results on the test set together with the mean on the train and test set weighted by the sequence lengths. As for SuperPoint, our methods improve all metrics consistently for unseen data. Our learned covariances are significantly better for relative pose estimation than the approximation used in [48]. + +and EuRoC shows indoor scenes captured with a drone, they exhibit different motion models as well as a variety of images. For KITTI we choose sequences 00-07 as the training set for both supervised and self-supervised training. Sequences 08-10 are used as the test set. We use a smaller UNet [55] architecture as our network to predict the covariances for the whole image. We chose this network since it gives us a good balance between batch size, training time and performance. The network predicts the parameters for the covariances directly. We choose + +$$ +\boldsymbol {\Sigma} _ {2 \mathrm {D}} (s, \alpha , \beta) = s \boldsymbol {R} _ {\alpha} \left( \begin{array}{c c} \beta & 0 \\ 0 & 1 - \beta \end{array} \right) \boldsymbol {R} _ {\alpha} ^ {\top} \tag {14} +$$ + +as a parameterization [7]. To ensure that our network predicts valid covariances the network output is filtered with + +$$ +f _ {1} (x) = \left(1 + | x |\right) ^ {\operatorname {s i g n} (\mathrm {x})} \tag {15} +$$ + +$$ +f _ {2} (x) = x \tag {16} +$$ + +$$ +f _ {3} (x) = \frac {1}{1 + e ^ {- x}} \tag {17} +$$ + +for $s, \alpha, \beta$ , respectively. Feature points that have subpixel accuracy use the nearest pixel covariance. See the supplementary material for more details on the training setup. + +Supervised Learning. To show that our method generalizes to different keypoint detectors, we train two networks, one for SuperPoint [12] and one for KLT tracks obtained from [66]. The SuperPoint keypoints are matched + +using SuperGlue [57]. For training we use a batch size of 8 images pairs for SuperPoint and 16 images pairs for KLT tracks. We trained for 100 epochs for both SuperPoint and KLT tracks. More training details are provided in the supplementary material. To ensure our network does not overfit on specific keypoint locations, we randomly crop the images before finding correspondences during training time. During evaluation we use the uncropped images to obtain features. During training we randomly perturb the ground truth pose as a starting point. To increase robustness, we first use the eigenvalue based optimization of the NEC in a RANSAC scheme [32] to filter outliers. This is followed by a custom least squares implementation of the NEC (NECLS), followed by optimizing Eq. 3. As reported in [48] we found, that such a multi-stage optimization provides the most robust and accurate results. We show examples of how the DNLS-learned covariances change the energy function landscape in the supplementary material. + +Self-Supervised Learning. We evaluate our self-supervised training setup on the same data as our supervised training. Due to needing image tuples instead of pairs, we reduce the batch size to 12 for KLT image triplets. This gives us 24 and 36 images pairs per batch, respectively. The training epochs are reduced to 50. More training details for the supervised and self-supervised training can be found in the supplementary material. + +Results. We evaluate the learned covariances in a VO setting. We compare the proposed DNLS approach to the + +
NISTÉR-5PT [51]NEC [33]NEC-LSWEIGHTED NEC-LSOURS SELF-SUPERVISEDOURS TAB. 1
Seq.RPE1RPEnetRPE1RPEnetRPE1RPEnetRPE1RPEnetRPE1RPEnetRPE1RPEnetRPE1RPEnet
V1_010.50171.8731.860.32039.5043.120.38752.9246.310.38856.5246.820.32731.1235.560.33231.8134.01
V1_020.54132.0120.360.38928.1126.950.54070.0828.940.54268.3529.810.44430.3921.980.43629.0721.29
V1_030.66027.3925.000.49225.4231.060.55276.7231.580.55578.1432.250.51029.5224.190.52031.1824.13
V2_010.51561.4533.510.31631.9539.790.31035.8439.000.31438.6239.620.28517.6132.400.29522.4130.58
V2_020.54543.7322.240.39625.4832.210.36926.9625.360.36525.0925.810.38225.3221.160.38621.9120.34
V2_031.12336.7128.770.97648.2637.600.939107.1136.740.941100.7336.710.94252.7231.130.99155.4130.40
mean0.63148.4527.560.46333.5136.030.49458.9035.610.49658.9536.110.46130.5728.460.47231.4427.44
+ +Table 3. Quantitative comparison on the Vicon sequences of the EuRoC dataset [9] with SuperPoint [12] keypoints. The dataset is more difficult than KITTI (see Tab. 2 and Tab. 1) with SuperPoint and SuperGlue [57] finding far fewer matches. As reported in [48] the least squares implementations struggle with bad initialization under these adverse conditions with NEC-LS performing especially poor. From all least squares optimizations, our learned covariances consistently perform the best, even outperforming the NEC most of the time. + +popular 5pt algorithm [51] and the NEC [33] as implemented in [32]. To investigate the benefit of our learned covariances we include the NEC-LS implementation as well as the symmetric PNEC with the covariances from [48] in Tab. 2. For Tab. 1 we additionally include a weighted version of our custom NEC-LS implementation with matching confidence from SuperGlue as weights. All methods are given the same feature matches and use a constant motion model for initializing the optimizations. We evaluate on the rotational versions of the $\mathrm{RPE}_1$ and $\mathrm{RPE}_n$ and the cosine error $e_t$ for the translation as defined in [11, 48]. Tab. 1 and Tab. 2 show the average results on the test set over 5 runs for SuperPoint and KLT tracks on KITTI [21], respectively. We show additional results in the supplementary material. Our methods consistently perform the best over all sequences, with the self-supervised being on par with our supervised training. Compared to its non-probabilistic counterpart NEC-LS, our method improves the $\mathrm{RPE}_1$ by $7\%$ and $13\%$ and the $\mathrm{RPE}_n$ by $37\%$ and $23\%$ for different keypoint detectors on unseen data. It also improves upon weighted methods, like weighted NEC-LS and the nonlearned covariances for the PNEC [48]. This demonstrates the importance of correctly modeling the feature correspondence quality. We show an example trajectory in Fig. 8. + +Tab. 3 shows the results on the EuRoC dataset for SuperPoint. Pose estimation is significantly more difficult compared to KITTI, often having few correspondences between images. However, our method generalizes to different datasets, with the network trained on KITTI and our self-supervised approach, outperforming the others most of the time. Especially a direct comparison with NEC-LS, the closest non-probabilistic method, shows significant improvements of $7\%$ for $\mathrm{RPE}_1$ and $48\%$ for the $\mathrm{RPE}_n$ . + +# 5. Discussion and Limitations + +Our experiments demonstrate the capability of our framework to correctly learn positional uncertainty, lead + +ing to improved results for relative pose estimation for VO. Our approach generalizes to different feature extractors and to different datasets, providing a unified approach to estimate the noise distribution of keypoint detectors. However, our method requires more computational resources than the original uncertainty estimation for the PNEC. + +We evaluate our learned covariances in a visual odometry setting, showing that they lead to reduced errors and especially less drift in the trajectory. However, this does not guarantee that the covariances are calibrated. Our framework inherits the ambiguity of the PNEC with regard to the noise scale. The true scale of the noise is not observable from relative pose estimation alone and only the relative scale between covariances can be learned. For the purposes of VO, this scale ambiguity is negligible. + +As our synthetic experiments show, diverse data is needed to correctly identify the 2D noise distribution. However, obtaining the noise distribution is difficult for keypoint detectors - hence learning it from pose regression. Further limitations are addressed in the supplementary material. + +# 6. Conclusion + +We present a novel DNLS framework for estimating positional uncertainty. Our framework can be combined with any feature extraction algorithm, making it extremely versatile. Regressing the noise distribution from relative pose estimation, ensures that learned covariance matrices are suitable for visual odometry tasks. In synthetic experiments, our framework is capable to learn the correct noise distribution from noisy data. We showed the practical application of our framework on real-world data for different feature extractors. Our learned uncertainty consistently outperforms a variety of non-probabilistic relative pose estimation algorithms as well as other uncertainty estimation methods. + +Acknowledgements. This work was supported by the ERC Advanced Grant SIMULACRON, by the Munich Center for Machine Learning and by the EPSRC Programme Grant VisualAI EP/T028572/1. + +# References + +[1] Sameer Agarwal, Keir Mierle, and Others. 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We present a differentiable nonlinear least squares (DNLS) framework for learning feature correspondence quality by computing per-feature positional uncertainty. The uncertainty estimates (left, bottom images) are regressed from a pose estimation error (middle), enabling the framework across a range of (handcrafted, learned) feature extractors. 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Specifically, we introduce a symmetric version of the probabilistic normal epipolar constraint, and an approach to estimate the covariance of feature positions by differentiating through the camera pose estimation procedure. We evaluate our approach on synthetic, as well as the KITTI and EuRoC real-world datasets. On the synthetic dataset, we confirm that our learned covariances accurately approximate the true noise distribution. In real world experiments, we find that our approach consistently outperforms state-of-the-art nonprobabilistic and probabilistic approaches, regardless of the feature extraction algorithm of choice." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 47, + 604, + 127, + 616 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 604, + 127, + 616 + ], + "spans": [ + { + "bbox": [ + 47, + 604, + 127, + 616 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 46, + 624, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 624, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 624, + 287, + 696 + ], + "type": "text", + "content": "Estimating the relative pose between two images given mutual feature correspondences is a fundamental problem in computer vision. It is a key component of structure from motion (SfM) and visual odometry (VO) methods which in turn fuel a plethora of applications from autonomous vehicles or robots to augmented and virtual reality." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 306, + 396, + 545, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 396, + 545, + 529 + ], + "spans": [ + { + "bbox": [ + 306, + 396, + 545, + 529 + ], + "type": "text", + "content": "Estimating the relative pose - rotation and translation - between two images, is often formulated as a geometric problem that can be solved by estimating the essential matrix [42] for calibrated cameras, or the fundamental matrix [24] for uncalibrated cameras. Related algorithms like the eight-point algorithm [23, 42] provide fast solutions. However, essential matrix based approaches suffer issues such as solution multiplicity [18, 24] and planar degeneracy [33]. The normal epipolar constraint (NEC) [34] addresses issues such as by estimating the issues such as which leads to more accurate relative poses [33]." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 531, + 546, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 531, + 546, + 675 + ], + "spans": [ + { + "bbox": [ + 304, + 531, + 546, + 675 + ], + "type": "text", + "content": "Neither of the aforementioned algorithms takes into account the quality of feature correspondences – an important cue that potentially improves pose estimation accuracy. Instead, feature correspondences are classified into inliers and outliers through a RANSAC scheme [11]. However, keypoint detectors [12, 56] for feature correspondences or tracking algorithms [63] yield imperfect points [40] that exhibit a richer family of error distributions, as opposed to an inlier-outlier distribution family. Algorithms, that make use of feature correspondence quality have been proposed for essential/fundamental matrix estimation [7, 53] and for the NEC [48], respectively." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 305, + 678, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 678, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 678, + 547, + 715 + ], + "type": "text", + "content": "While estimating the relative pose can be formulated as a classical optimization problem [15, 33], the rise in popularity of deep learning has led to several works augmenting" + } + ] + } + ], + "index": 26 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 61, + 704, + 244, + 714 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 704, + 244, + 714 + ], + "spans": [ + { + "bbox": [ + 61, + 704, + 244, + 714 + ], + "type": "text", + "content": "Project Page: https://dominikmuhle.github.io/dnls_covs/" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13102" + } + ] + } + ], + "index": 28 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 77, + 70, + 296, + 137 + ], + "blocks": [ + { + "bbox": [ + 77, + 70, + 296, + 137 + ], + "lines": [ + { + "bbox": [ + 77, + 70, + 296, + 137 + ], + "spans": [ + { + "bbox": [ + 77, + 70, + 296, + 137 + ], + "type": "image", + "image_path": "6ae52ad7dfb3af692a5e97429cd7ca162b89034198b0a988a2748753037aa58b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 298, + 70, + 516, + 137 + ], + "blocks": [ + { + "bbox": [ + 298, + 70, + 516, + 137 + ], + "lines": [ + { + "bbox": [ + 298, + 70, + 516, + 137 + ], + "spans": [ + { + "bbox": [ + 298, + 70, + 516, + 137 + ], + "type": "image", + "image_path": "b542b81cb7ec3599f81598486d9a8660e9b0dd0a0613b12c0d16997c85847200.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 75, + 150, + 294, + 217 + ], + "blocks": [ + { + "bbox": [ + 130, + 140, + 242, + 149 + ], + "lines": [ + { + "bbox": [ + 130, + 140, + 242, + 149 + ], + "spans": [ + { + "bbox": [ + 130, + 140, + 242, + 149 + ], + "type": "text", + "content": "(a) covariances from [48] per pixel" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 75, + 150, + 294, + 217 + ], + "lines": [ + { + "bbox": [ + 75, + 150, + 294, + 217 + ], + "spans": [ + { + "bbox": [ + 75, + 150, + 294, + 217 + ], + "type": "image", + "image_path": "7436d32d3240a57c0a2ca596cf36c1c79147156b8e05f7ceef48a47d4fea599c.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 121, + 219, + 249, + 228 + ], + "lines": [ + { + "bbox": [ + 121, + 219, + 249, + 228 + ], + "spans": [ + { + "bbox": [ + 121, + 219, + 249, + 228 + ], + "type": "text", + "content": "(c) learned covariances per pixel (Ours)" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 296, + 149, + 515, + 217 + ], + "blocks": [ + { + "bbox": [ + 357, + 140, + 457, + 149 + ], + "lines": [ + { + "bbox": [ + 357, + 140, + 457, + 149 + ], + "spans": [ + { + "bbox": [ + 357, + 140, + 457, + 149 + ], + "type": "text", + "content": "(b) points and covariances [48]" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 296, + 149, + 515, + 217 + ], + "lines": [ + { + "bbox": [ + 296, + 149, + 515, + 217 + ], + "spans": [ + { + "bbox": [ + 296, + 149, + 515, + 217 + ], + "type": "image", + "image_path": "bad77c254c535aeb660e76ba6bf3884c3eac9a4e58651da5492e0ce55eb4ede0.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 339, + 219, + 472, + 228 + ], + "lines": [ + { + "bbox": [ + 339, + 219, + 472, + 228 + ], + "spans": [ + { + "bbox": [ + 339, + 219, + 472, + 228 + ], + "type": "text", + "content": "(d) points and learned covariances (Ours)" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 229, + 545, + 274 + ], + "lines": [ + { + "bbox": [ + 46, + 229, + 545, + 274 + ], + "spans": [ + { + "bbox": [ + 46, + 229, + 545, + 274 + ], + "type": "text", + "content": "Figure 2. Comparison between covariances used in [48] (first row) and our learned covariances (second row). The first column shows a dense color coded " + }, + { + "bbox": [ + 46, + 229, + 545, + 274 + ], + "type": "inline_equation", + "content": "(s, \\alpha, \\beta" + }, + { + "bbox": [ + 46, + 229, + 545, + 274 + ], + "type": "text", + "content": " mapped to HLS with " + }, + { + "bbox": [ + 46, + 229, + 545, + 274 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 46, + 229, + 545, + 274 + ], + "type": "text", + "content": " correction) representation for each pixel, while the second column shows subsampled keypoints and their corresponding (enlarged) covariances. The higher saturation in (a) shows that the covariances are more anisotropic. The learned covariances (c) show a more fine-grained detail in the scale (brightness) and less blurring than the covariances in (a)." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 277, + 287, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 277, + 287, + 422 + ], + "spans": [ + { + "bbox": [ + 46, + 277, + 287, + 422 + ], + "type": "text", + "content": "VO or visual simultaneous localisation and mapping (VSLAM) pipelines with learned components. GN-Net [67] learns robust feature representations for direct methods like DSO [15]. For feature based methods Superpoint [12] provides learned features, while Superglue [57] uses graph neural networks to find corresponding matches between feature points in two images. DSAC introduces a differential relaxation to RANSAC that allows gradient flow through the otherwise non-differentiable operation. In [53] a network learns to re-weight correspondences for estimating the fundamental matrix. PixLoc [58] estimates the pose from an image and a 3D model based on direct alignment." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 423, + 287, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 423, + 287, + 544 + ], + "spans": [ + { + "bbox": [ + 46, + 423, + 287, + 544 + ], + "type": "text", + "content": "In this work we combine the predictive power of deep learning with the precision of geometric modeling for highly accurate relative pose estimation. Estimating the noise distributions for the feature positions of different feature extractors allows us to incorporate this information into relative pose estimation. Instead of modeling the noise for each feature extractor explicitly, we present a method to learn these distributions from data, using the same domain that the feature extractors work with - images. We achieve this based on the following technical contributions:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 546, + 287, + 713 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 47, + 546, + 287, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 546, + 287, + 593 + ], + "spans": [ + { + "bbox": [ + 47, + 546, + 287, + 593 + ], + "type": "text", + "content": "- We introduce a symmetric version of the probabilistic normal epipolar constraint (PNEC), that more accurately models the geometry of relative pose estimation with uncertain feature positions." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 594, + 286, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 594, + 286, + 641 + ], + "spans": [ + { + "bbox": [ + 47, + 594, + 286, + 641 + ], + "type": "text", + "content": "- We propose a learning strategy to minimize the relative pose error by learning feature position uncertainty through differentiable nonlinear least squares (DNLS), see Fig. 1." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 642, + 286, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 642, + 286, + 689 + ], + "spans": [ + { + "bbox": [ + 47, + 642, + 286, + 689 + ], + "type": "text", + "content": "- We show with synthetic experiments, that using the gradient from the relative pose error leads to meaningful estimates of the positional uncertainty that reflect the correct error distribution." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 47, + 689, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 286, + 713 + ], + "type": "text", + "content": "- We validate our approach on real-world data in a visual odometry setting and compare our method to non" + } + ] + } + ], + "index": 14 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 313, + 277, + 545, + 314 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 277, + 545, + 314 + ], + "spans": [ + { + "bbox": [ + 313, + 277, + 545, + 314 + ], + "type": "text", + "content": "probabilistic relative pose estimation algorithms, namely Nister 5pt [50], and NEC [33], as well as to the PNEC with non-learned covariances [48]." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 314, + 545, + 373 + ], + "type": "list", + "angle": 0, + "index": 19, + "blocks": [ + { + "bbox": [ + 306, + 314, + 545, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 314, + 545, + 350 + ], + "spans": [ + { + "bbox": [ + 306, + 314, + 545, + 350 + ], + "type": "text", + "content": "- We show that our method is able to generalize to different feature extraction algorithms such as SuperPoint [12] and feature tracking approaches on real-world data." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 350, + 545, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 350, + 545, + 373 + ], + "spans": [ + { + "bbox": [ + 306, + 350, + 545, + 373 + ], + "type": "text", + "content": "- We release the code for all experiments and the training setup to facilitate future research." + } + ] + } + ], + "index": 18 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 390, + 391, + 403 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 390, + 391, + 403 + ], + "spans": [ + { + "bbox": [ + 306, + 390, + 391, + 403 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 412, + 545, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 412, + 545, + 532 + ], + "spans": [ + { + "bbox": [ + 304, + 412, + 545, + 532 + ], + "type": "text", + "content": "This work is on deep learning for improving frame-to-frame relative pose estimation by incorporating feature position uncertainty with applications to visual odometry. We therefore restrict our discussion of related work to relative pose estimation in visual odometry, weighting correspondences for relative pose estimation, and deep learning in the context of VSLAM. For a broader overview over VSLAM we refer the reader to more topic-specific overview papers [10, 65] and to the excellent books by Hartley and Zisserman [24] and by Szeliski [62]." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 534, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 546, + 713 + ], + "type": "text", + "content": "Relative Pose Estimation in Visual Odometry. Finding the relative pose between two images has a long history in computer vision, with the first solution for perspective images reaching back to 1913 by Kruppa [35]. Modern methods for solving this problem can be classified into feature-based and direct methods. The former rely on feature points extracted in the images together with geometric constraints like the epipolar constraint or the normal epipolar constraint [34] to calculate the relative pose. The latter optimize the pose by directly considering the intensity differences between the two images and rose to popularity with LSD-SLAM [16] and DSO [15]. Since direct methods work on the assumption of brightness or irradiance constancy they require the appearance to be somewhat similar across images. In turn, keypoint based methods rely" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13103" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 133 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 133 + ], + "type": "text", + "content": "on suitable feature extractors which can exhibit significant amounts of noise and uncertainty. In this paper we propose a method to learn the intrinsic noise of keypoint detectors – therefore, the following will focus on feature based relative pose estimation." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 134, + 288, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 134, + 288, + 361 + ], + "spans": [ + { + "bbox": [ + 46, + 134, + 288, + 361 + ], + "type": "text", + "content": "One of the most widely used parameterizations for reconstructing the relative pose from feature correspondences is the essential matrix, given calibrated cameras, or the fundamental matrix in the general setting. Several solutions based on the essential matrix have been proposed [36, 38, 42, 50, 61]. They include the linear solver by Longuet-Higgins [42], requiring 8 correspondences, or the solver by Nister et al. [51] requiring the minimal number of 5 correspondences. However, due to their construction, essential matrix methods deteriorate for purely rotational motion with noise-free correspondences [33]. As an alternative, methods that do not use the essential matrix have been proposed - they either estimate the relative pose using quaternions [17] or make use of the normal epipolar constraint (NEC) by Kneip and Lynen [33, 34]. The latter addresses the problems of the essential matrix by estimating rotation independent of the translation. [6] shows how to obtain the global minimum for the NEC. Further work, that disentangles rotation and translation can be found in [39]." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 364, + 287, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 364, + 287, + 483 + ], + "spans": [ + { + "bbox": [ + 46, + 364, + 287, + 483 + ], + "type": "text", + "content": "Weighting of Feature Correspondences. Keypoints in images can exhibit significant noise, deteriorating the performance for pose estimation significantly [22]. The noise characteristics of the keypoint positions depend on the feature extractor. For Kanade-Lucas-Tomasi (KLT) tracking [44, 63] approaches, the position uncertainty has been investigated in several works [20, 59, 60, 72]. The uncertainty was directly integrated into the tracking in [14]. [71] proposed a method to obtain anisotropic and inhomogeneous covariances for SIFT [43] and SURF [3]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 486, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 486, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 486, + 288, + 715 + ], + "type": "text", + "content": "Given the imperfect keypoint positions, not all correspondences are equally well suited for estimating the relative pose. [22] showed the effect of the noise level on the accuracy of the pose estimation. Limiting the influence of bad feature correspondences has been studied from a geometrical and a probabilistic perspective. Random sample consensus (RANSAC) [19] is a popular method to classify datapoints into inliers and outliers that can be easily integrated into feature based relative pose estimation pipelines. Ranftl et al. [53] relax the hard classification for inlier and outlier and use deep learning to find a robust fundamental matrix estimator in the presence of outliers in an iteratively reweighted least squares (IRLS) fashion. DSAC [5] models RANSAC as a probabilistic process to make it differentiable. Other lines of work integrate information about position uncertainty directly into the alignment problem. For radar based SLAM, [8] incorporates keypoint uncertainty in radar images, with a deep network predicting the uncertainty. Image based position uncertainty was investigated" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 72, + 545, + 203 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 203 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 203 + ], + "type": "text", + "content": "from the statistical, [27, 28], the photogrammetry [46] and the computer vision perspective [7, 29]. [7] and [29] debated the benefit of incorporating position uncertainty into fundamental matrix estimation. We base our method on the probabilistic normal epipolar constraint (PNEC) [48], that improved on the NEC by extending it to a probabilistic view. It achieved better results on real-world data with covariances approximated using the Boltzmann distribution [4]. We expand on this idea by learning covariances (see Fig. 2) agnostic of the keypoints extractor used to further improve pose estimation." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 204, + 546, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 204, + 546, + 456 + ], + "spans": [ + { + "bbox": [ + 304, + 204, + 546, + 456 + ], + "type": "text", + "content": "Deep Learning in VSLAM. Deep Learning has transformed computer vision in the last decade. While deep networks have been successfully used for tasks like detection [54], semantic segmentation [41], and recently novel view synthesis [47], they have also found application in VSLAM pipelines. DVSO [69] and D3VO [68] leveraged deep learning to improve the precision for direct methods, while GN-Net [67] predicts robust and dense feature maps. Several works proposed to learn keypoint extractors, for feature based pose estimation, such as SuperPoint [12] and LIFT [70]. SuperGlue [57] enabled feature matching with graph neural networks. Other lines of work leverage deep learning for localization by making parts of the pose estimation pipeline differentiable [2,5,58,64]. Works, that directly predicting the pose include PoseNet [30] and CTCNet [25] that uses self-supervised learning with a cycle-consistency loss for VO. [40] learns image representations by refining keypoint positions and camera poses in a post-processing step of a structure-from-motion pipeline. " + }, + { + "bbox": [ + 304, + 204, + 546, + 456 + ], + "type": "inline_equation", + "content": "\\nabla" + }, + { + "bbox": [ + 304, + 204, + 546, + 456 + ], + "type": "text", + "content": " SLAM [26] presents a differentiable dense SLAM system with several components (e.g., the Levenberg-Marquardt [37, 45] optimizer)." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 464, + 361, + 477 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 464, + 361, + 477 + ], + "spans": [ + { + "bbox": [ + 306, + 464, + 361, + 477 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 485, + 545, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 485, + 545, + 617 + ], + "spans": [ + { + "bbox": [ + 304, + 485, + 545, + 617 + ], + "type": "text", + "content": "In the following, we present our framework to estimate positional uncertainty of feature points by leveraging DNLS. We learn the noise covariances through a forward and backward step. In the forward step, the covariances are used in a probabilistic pose estimation optimization, namely the PNEC. In the backward step, the gradient from the pose error is back-propagated through the optimization to the covariances. From there we can train a neural network to predict the keypoint position uncertainty from the images. We start by summarizing the asymmetric PNEC [48] and for the first time introduce its symmetric counterpart." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 624, + 389, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 624, + 389, + 635 + ], + "spans": [ + { + "bbox": [ + 306, + 624, + 389, + 635 + ], + "type": "text", + "content": "3.1. Prerequisites" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 641, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 545, + 715 + ], + "type": "text", + "content": "Notation. We follow the notation of [48]. Bold lowercase letters (e.g. " + }, + { + "bbox": [ + 304, + 641, + 545, + 715 + ], + "type": "inline_equation", + "content": "\\pmb{f}" + }, + { + "bbox": [ + 304, + 641, + 545, + 715 + ], + "type": "text", + "content": ") denote vectors, whereas bold uppercase letters (e.g. " + }, + { + "bbox": [ + 304, + 641, + 545, + 715 + ], + "type": "inline_equation", + "content": "\\pmb{\\Sigma}" + }, + { + "bbox": [ + 304, + 641, + 545, + 715 + ], + "type": "text", + "content": ") denote matrices. " + }, + { + "bbox": [ + 304, + 641, + 545, + 715 + ], + "type": "inline_equation", + "content": "\\hat{\\pmb{u}} \\in \\mathbb{R}^{3 \\times 3}" + }, + { + "bbox": [ + 304, + 641, + 545, + 715 + ], + "type": "text", + "content": " represents the skew-symmetric matrix of the vector " + }, + { + "bbox": [ + 304, + 641, + 545, + 715 + ], + "type": "inline_equation", + "content": "\\pmb{u} \\in \\mathbb{R}^3" + }, + { + "bbox": [ + 304, + 641, + 545, + 715 + ], + "type": "text", + "content": " such that the cross product between two vectors can be rewritten as a matrix-vector operation, i.e. " + }, + { + "bbox": [ + 304, + 641, + 545, + 715 + ], + "type": "inline_equation", + "content": "\\pmb{u} \\times \\pmb{v} = \\hat{\\pmb{u}}\\pmb{v}" + }, + { + "bbox": [ + 304, + 641, + 545, + 715 + ], + "type": "text", + "content": ". The transpose is" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13104" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 67, + 70, + 524, + 201 + ], + "blocks": [ + { + "bbox": [ + 67, + 70, + 524, + 201 + ], + "lines": [ + { + "bbox": [ + 67, + 70, + 524, + 201 + ], + "spans": [ + { + "bbox": [ + 67, + 70, + 524, + 201 + ], + "type": "image", + "image_path": "43455a9955841ec37d299f9eea2d6cdac9368debcb666b186a52bc6fea6d0013.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 202, + 547, + 236 + ], + "lines": [ + { + "bbox": [ + 46, + 202, + 547, + 236 + ], + "spans": [ + { + "bbox": [ + 46, + 202, + 547, + 236 + ], + "type": "text", + "content": "Figure 3. Architecture: We extract the uncertainty per image for every pixel using a UNet [55] backbone. Using keypoint locations from a keypoint detector, we obtain the keypoints with their estimated positional uncertainty. The relative pose is then estimated using a DNLS optimization. The UNet is updated by backpropagating the gradient (obtained by implicit differentiation) to the network output." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 239, + 290, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 239, + 290, + 324 + ], + "spans": [ + { + "bbox": [ + 46, + 239, + 290, + 324 + ], + "type": "text", + "content": "denoted by the superscript " + }, + { + "bbox": [ + 46, + 239, + 290, + 324 + ], + "type": "inline_equation", + "content": "\\top" + }, + { + "bbox": [ + 46, + 239, + 290, + 324 + ], + "type": "text", + "content": ". We deviate from [48] in the following: variables of the second frame are marked with the ' superscript, while variables of the first frame do not have a superscript. We represent the relative pose between images as a rigid-body transformation consisting of a rotation matrix " + }, + { + "bbox": [ + 46, + 239, + 290, + 324 + ], + "type": "inline_equation", + "content": "R \\in SO(3)" + }, + { + "bbox": [ + 46, + 239, + 290, + 324 + ], + "type": "text", + "content": " and a unit length translation " + }, + { + "bbox": [ + 46, + 239, + 290, + 324 + ], + "type": "inline_equation", + "content": "t \\in \\mathbb{R}^3" + }, + { + "bbox": [ + 46, + 239, + 290, + 324 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 46, + 239, + 290, + 324 + ], + "type": "inline_equation", + "content": "\\| t \\| = 1" + }, + { + "bbox": [ + 46, + 239, + 290, + 324 + ], + "type": "text", + "content": " is imposed due to scale-invariance)." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 332, + 287, + 345 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 332, + 287, + 345 + ], + "spans": [ + { + "bbox": [ + 47, + 332, + 287, + 345 + ], + "type": "text", + "content": "3.2. The Probabilistic Normal Epipolar Constraint" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 351, + 289, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 351, + 289, + 495 + ], + "spans": [ + { + "bbox": [ + 46, + 351, + 289, + 495 + ], + "type": "text", + "content": "The asymmetric probabilistic normal epipolar constraint (PNEC) estimates the relative pose, give two images " + }, + { + "bbox": [ + 46, + 351, + 289, + 495 + ], + "type": "inline_equation", + "content": "I, I'" + }, + { + "bbox": [ + 46, + 351, + 289, + 495 + ], + "type": "text", + "content": " of the same scene under the assumption of uncertain feature positions in the second image. A feature correspondences is given by " + }, + { + "bbox": [ + 46, + 351, + 289, + 495 + ], + "type": "inline_equation", + "content": "\\pmb{p}_i, \\pmb{p}_i'" + }, + { + "bbox": [ + 46, + 351, + 289, + 495 + ], + "type": "text", + "content": " in the image plane, where the uncertainty of " + }, + { + "bbox": [ + 46, + 351, + 289, + 495 + ], + "type": "inline_equation", + "content": "\\pmb{p}_i'" + }, + { + "bbox": [ + 46, + 351, + 289, + 495 + ], + "type": "text", + "content": " is represented by the corresponding covariance " + }, + { + "bbox": [ + 46, + 351, + 289, + 495 + ], + "type": "inline_equation", + "content": "\\Sigma_{2\\mathrm{D},i}'" + }, + { + "bbox": [ + 46, + 351, + 289, + 495 + ], + "type": "text", + "content": ". To get the epipolar geometry for the PNEC the feature points are unprojected using the camera intrinsics, giving unit length bearing vectors " + }, + { + "bbox": [ + 46, + 351, + 289, + 495 + ], + "type": "inline_equation", + "content": "\\pmb{f}_i, \\pmb{f}_i'" + }, + { + "bbox": [ + 46, + 351, + 289, + 495 + ], + "type": "text", + "content": ". The uncertainty of " + }, + { + "bbox": [ + 46, + 351, + 289, + 495 + ], + "type": "inline_equation", + "content": "\\pmb{f}_i'" + }, + { + "bbox": [ + 46, + 351, + 289, + 495 + ], + "type": "text", + "content": " is now represented by " + }, + { + "bbox": [ + 46, + 351, + 289, + 495 + ], + "type": "inline_equation", + "content": "\\Sigma_i'" + }, + { + "bbox": [ + 46, + 351, + 289, + 495 + ], + "type": "text", + "content": ". Estimating the relative pose is done by minimizing the PNEC cost function as defined in [48]. For convenience we recap the energy function" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 70, + 504, + 287, + 536 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 504, + 287, + 536 + ], + "spans": [ + { + "bbox": [ + 70, + 504, + 287, + 536 + ], + "type": "interline_equation", + "content": "E (\\boldsymbol {R}, \\boldsymbol {t}) = \\sum_ {i} \\frac {e _ {i} ^ {2}}{\\sigma_ {i} ^ {2}} = \\sum_ {i} \\frac {| \\boldsymbol {t} ^ {\\top} (\\boldsymbol {f} _ {i} \\times \\boldsymbol {R} \\boldsymbol {f} _ {i} ^ {\\prime}) | ^ {2}}{\\boldsymbol {t} ^ {\\top} \\hat {\\boldsymbol {f}} _ {i} \\boldsymbol {R} \\boldsymbol {\\Sigma} _ {i} ^ {\\prime} \\boldsymbol {R} ^ {\\top} \\hat {\\boldsymbol {f}} _ {i} ^ {\\top} \\boldsymbol {t}}, (1)", + "image_path": "de69594d538871ffe09cea5bd473313ea18a63d9005febf5f576186f6cc3b858.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 544, + 287, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 544, + 287, + 639 + ], + "spans": [ + { + "bbox": [ + 46, + 544, + 287, + 639 + ], + "type": "text", + "content": "in our notation. As mentioned previously, this asymmetric PNEC in [48] only considers uncertainties " + }, + { + "bbox": [ + 46, + 544, + 287, + 639 + ], + "type": "inline_equation", + "content": "\\Sigma^{\\prime}" + }, + { + "bbox": [ + 46, + 544, + 287, + 639 + ], + "type": "text", + "content": " in the second frame. While this assumption might hold for the KLT tracking [66] used in [48], this leaves out important information when using other keypoint detectors like ORB [56] or SuperPoint [12]. Therefore, we will introduce a symmetric version of the PNEC that is more suitable for our task in the following." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 640, + 288, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 640, + 288, + 689 + ], + "spans": [ + { + "bbox": [ + 46, + 640, + 288, + 689 + ], + "type": "text", + "content": "Making the PNEC symmetric. As in [48] we assume the covariance of the bearing vectors " + }, + { + "bbox": [ + 46, + 640, + 288, + 689 + ], + "type": "inline_equation", + "content": "\\pmb{f}_i" + }, + { + "bbox": [ + 46, + 640, + 288, + 689 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 640, + 288, + 689 + ], + "type": "inline_equation", + "content": "\\pmb{f}_i'" + }, + { + "bbox": [ + 46, + 640, + 288, + 689 + ], + "type": "text", + "content": " to be gaussian, their covariance matrices denoted by " + }, + { + "bbox": [ + 46, + 640, + 288, + 689 + ], + "type": "inline_equation", + "content": "\\pmb{\\Sigma}_i" + }, + { + "bbox": [ + 46, + 640, + 288, + 689 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 640, + 288, + 689 + ], + "type": "inline_equation", + "content": "\\pmb{\\Sigma}_i'" + }, + { + "bbox": [ + 46, + 640, + 288, + 689 + ], + "type": "text", + "content": ", respectively. The new variance can be approximated as" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 58, + 699, + 287, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 699, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 58, + 699, + 287, + 715 + ], + "type": "interline_equation", + "content": "\\sigma_ {s, i} ^ {2} = \\boldsymbol {t} ^ {\\top} \\left(\\left(\\boldsymbol {R} \\hat {\\boldsymbol {f}} _ {i} ^ {\\prime}\\right) \\boldsymbol {\\Sigma} _ {i} \\left(\\boldsymbol {R} \\hat {\\boldsymbol {f}} _ {i} ^ {\\prime}\\right) ^ {\\top} + \\hat {\\boldsymbol {f}} _ {i} \\boldsymbol {R} \\boldsymbol {\\Sigma} _ {i} ^ {\\prime} \\boldsymbol {R} ^ {\\top} \\hat {\\boldsymbol {f}} _ {i} ^ {\\top}\\right) \\boldsymbol {t}. \\tag {2}", + "image_path": "352f8442e3faf82d69e92dab7070939496d11dc85ab259564327c84149ffec65.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 239, + 546, + 288 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 239, + 546, + 288 + ], + "spans": [ + { + "bbox": [ + 304, + 239, + 546, + 288 + ], + "type": "text", + "content": "In the supplementary material we derive the variance and show the validity of this approximation given the geometry of the problem. This new variance now gives us the new symmetric PNEC with its following energy function" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 382, + 296, + 545, + 326 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 382, + 296, + 545, + 326 + ], + "spans": [ + { + "bbox": [ + 382, + 296, + 545, + 326 + ], + "type": "interline_equation", + "content": "E _ {s} (\\boldsymbol {R}, \\boldsymbol {t}) = \\sum_ {i} \\frac {e _ {i} ^ {2}}{\\sigma_ {s , i} ^ {2}} \\tag {3}", + "image_path": "0ba333d821a15e6ef7962c014e05933dc4060c321dbf4199ab24757e626032ff.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 335, + 481, + 346 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 335, + 481, + 346 + ], + "spans": [ + { + "bbox": [ + 306, + 335, + 481, + 346 + ], + "type": "text", + "content": "3.3. DNLS for Learning Covariances" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 353, + 546, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 353, + 546, + 389 + ], + "spans": [ + { + "bbox": [ + 304, + 353, + 546, + 389 + ], + "type": "text", + "content": "We want to estimate covariances " + }, + { + "bbox": [ + 304, + 353, + 546, + 389 + ], + "type": "inline_equation", + "content": "\\Sigma_{2\\mathrm{D}}" + }, + { + "bbox": [ + 304, + 353, + 546, + 389 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 353, + 546, + 389 + ], + "type": "inline_equation", + "content": "\\Sigma_{2\\mathrm{D}}^{\\prime}" + }, + { + "bbox": [ + 304, + 353, + 546, + 389 + ], + "type": "text", + "content": " (in the following collectively denoted as " + }, + { + "bbox": [ + 304, + 353, + 546, + 389 + ], + "type": "inline_equation", + "content": "\\Sigma_{2\\mathrm{D}}" + }, + { + "bbox": [ + 304, + 353, + 546, + 389 + ], + "type": "text", + "content": " for better readability) in the image plane" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 386, + 399, + 545, + 417 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 386, + 399, + 545, + 417 + ], + "spans": [ + { + "bbox": [ + 386, + 399, + 545, + 417 + ], + "type": "interline_equation", + "content": "\\boldsymbol {\\Sigma} _ {2 \\mathrm {D}} = \\underset {\\boldsymbol {\\Sigma} _ {2 \\mathrm {D}}} {\\arg \\min } \\mathcal {L}, \\tag {4}", + "image_path": "928a2d7303892af402b09b294369d75a5355809cd1b066221b47a476ac4934e9.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 426, + 547, + 473 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 426, + 547, + 473 + ], + "spans": [ + { + "bbox": [ + 304, + 426, + 547, + 473 + ], + "type": "text", + "content": "such that they minimize a loss function " + }, + { + "bbox": [ + 304, + 426, + 547, + 473 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 304, + 426, + 547, + 473 + ], + "type": "text", + "content": " of the estimated pose. Since we found that the rotational error of the PNEC is more stable than the translational error, we chose to minimize only the rotational error" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 418, + 482, + 545, + 496 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 418, + 482, + 545, + 496 + ], + "spans": [ + { + "bbox": [ + 418, + 482, + 545, + 496 + ], + "type": "interline_equation", + "content": "e _ {\\text {r o t}} = \\angle \\tilde {\\boldsymbol {R}} ^ {\\top} \\boldsymbol {R} \\tag {5}", + "image_path": "1e8f5ac8ced507ca135512c1f8250c0c7bbf4d1ffc0e5efd1acb4991a58b8870.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 373, + 499, + 545, + 513 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 373, + 499, + 545, + 513 + ], + "spans": [ + { + "bbox": [ + 373, + 499, + 545, + 513 + ], + "type": "interline_equation", + "content": "\\mathcal {L} (\\tilde {\\boldsymbol {R}}, \\boldsymbol {R}; \\boldsymbol {\\Sigma} _ {2 \\mathrm {D}}) = e _ {\\mathrm {r o t}} \\tag {6}", + "image_path": "2f2305e7ef65c48a9aa34fdf732d1a87f613e906b4ea975b65f9c4c4766d30b2.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 524, + 545, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 524, + 545, + 548 + ], + "spans": [ + { + "bbox": [ + 304, + 524, + 545, + 548 + ], + "type": "text", + "content": "between the ground truth rotation " + }, + { + "bbox": [ + 304, + 524, + 545, + 548 + ], + "type": "inline_equation", + "content": "\\tilde{\\pmb{R}}" + }, + { + "bbox": [ + 304, + 524, + 545, + 548 + ], + "type": "text", + "content": " and the estimated rotation " + }, + { + "bbox": [ + 304, + 524, + 545, + 548 + ], + "type": "inline_equation", + "content": "\\pmb{R}" + }, + { + "bbox": [ + 304, + 524, + 545, + 548 + ], + "type": "text", + "content": ". We obtain" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 367, + 558, + 545, + 575 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 367, + 558, + 545, + 575 + ], + "spans": [ + { + "bbox": [ + 367, + 558, + 545, + 575 + ], + "type": "interline_equation", + "content": "\\boldsymbol {R} = \\arg \\min _ {\\boldsymbol {R}} E _ {s} (\\boldsymbol {R}, t; \\Sigma_ {2 \\mathrm {D}}) \\tag {7}", + "image_path": "f4c249d77e8c6ccc4c7d63600697a708a05351f419f81045b3ae67641084a4e7.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 584, + 545, + 632 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 584, + 545, + 632 + ], + "spans": [ + { + "bbox": [ + 304, + 584, + 545, + 632 + ], + "type": "text", + "content": "by minimizing Eq. 3. To learn the covariances that minimize the rotational error, we can follow the gradient " + }, + { + "bbox": [ + 304, + 584, + 545, + 632 + ], + "type": "inline_equation", + "content": "d\\mathcal{L} / d\\Sigma_{2\\mathrm{D}}" + }, + { + "bbox": [ + 304, + 584, + 545, + 632 + ], + "type": "text", + "content": ". Implicit differentiation allows us to compute the gradient as" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 333, + 641, + 545, + 670 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 333, + 641, + 545, + 670 + ], + "spans": [ + { + "bbox": [ + 333, + 641, + 545, + 670 + ], + "type": "interline_equation", + "content": "\\frac {d \\mathcal {L}}{d \\boldsymbol {\\Sigma} _ {2 \\mathrm {D}}} = - \\frac {\\partial^ {2} E _ {s}}{\\partial \\boldsymbol {\\Sigma} _ {2 \\mathrm {D}} \\partial \\boldsymbol {R} ^ {\\top}} \\left(\\frac {\\partial^ {2} E _ {s}}{\\partial \\boldsymbol {R} \\partial \\boldsymbol {R} ^ {\\top}}\\right) ^ {- 1} \\frac {e _ {\\text {r o t}}}{\\partial \\boldsymbol {R}}. \\tag {8}", + "image_path": "115b941d70ffd54ce1f19be2b59c19511eafc702da28770dbf354d55784a8523.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 677, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 546, + 713 + ], + "type": "text", + "content": "For a detailed derivation of Eq. 8 and other methods, that unroll the optimization, to obtain the gradient we refer the interested reader to [13]." + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13105" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 70, + 166, + 140 + ], + "blocks": [ + { + "bbox": [ + 49, + 70, + 166, + 140 + ], + "lines": [ + { + "bbox": [ + 49, + 70, + 166, + 140 + ], + "spans": [ + { + "bbox": [ + 49, + 70, + 166, + 140 + ], + "type": "image", + "image_path": "6a7ae7993f2e1a6147cf413b4d48274275ae7abfa8e14fa7366fd5cb1c9e1767.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 71, + 143, + 145, + 152 + ], + "lines": [ + { + "bbox": [ + 71, + 143, + 145, + 152 + ], + "spans": [ + { + "bbox": [ + 71, + 143, + 145, + 152 + ], + "type": "text", + "content": "(a) " + }, + { + "bbox": [ + 71, + 143, + 145, + 152 + ], + "type": "inline_equation", + "content": "e_{\\mathrm{rot}}" + }, + { + "bbox": [ + 71, + 143, + 145, + 152 + ], + "type": "text", + "content": " during training" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 167, + 71, + 286, + 140 + ], + "blocks": [ + { + "bbox": [ + 167, + 71, + 286, + 140 + ], + "lines": [ + { + "bbox": [ + 167, + 71, + 286, + 140 + ], + "spans": [ + { + "bbox": [ + 167, + 71, + 286, + 140 + ], + "type": "image", + "image_path": "1f71886f6535a19698c9ae4a0a949eeac1600bdc7cfb158d4821fc1edad4a2cf.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 175, + 142, + 279, + 153 + ], + "lines": [ + { + "bbox": [ + 175, + 142, + 279, + 153 + ], + "spans": [ + { + "bbox": [ + 175, + 142, + 279, + 153 + ], + "type": "text", + "content": "(b) " + }, + { + "bbox": [ + 175, + 142, + 279, + 153 + ], + "type": "inline_equation", + "content": "\\sigma_{norm}^2" + }, + { + "bbox": [ + 175, + 142, + 279, + 153 + ], + "type": "text", + "content": " error during training" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 55, + 213, + 281, + 317 + ], + "blocks": [ + { + "bbox": [ + 46, + 156, + 286, + 210 + ], + "lines": [ + { + "bbox": [ + 46, + 156, + 286, + 210 + ], + "spans": [ + { + "bbox": [ + 46, + 156, + 286, + 210 + ], + "type": "text", + "content": "Figure 4. Rotational error (a) and differences between the true residual variance " + }, + { + "bbox": [ + 46, + 156, + 286, + 210 + ], + "type": "inline_equation", + "content": "\\tilde{\\sigma}^2" + }, + { + "bbox": [ + 46, + 156, + 286, + 210 + ], + "type": "text", + "content": " and the learned variance " + }, + { + "bbox": [ + 46, + 156, + 286, + 210 + ], + "type": "inline_equation", + "content": "\\sigma^2" + }, + { + "bbox": [ + 46, + 156, + 286, + 210 + ], + "type": "text", + "content": " (b) over the training epochs. Starting from uniform covariances, our method adapts the covariances for each keypoint to minimize the rotational error. Simultaneously, this leads to a better estimate of " + }, + { + "bbox": [ + 46, + 156, + 286, + 210 + ], + "type": "inline_equation", + "content": "\\sigma^2" + }, + { + "bbox": [ + 46, + 156, + 286, + 210 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 55, + 213, + 281, + 317 + ], + "lines": [ + { + "bbox": [ + 55, + 213, + 281, + 317 + ], + "spans": [ + { + "bbox": [ + 55, + 213, + 281, + 317 + ], + "type": "image", + "image_path": "f21aa1be7d28aa2e0aac6295ff8bde7db74602f93907582731cf394ba994536f.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 55, + 330, + 280, + 434 + ], + "blocks": [ + { + "bbox": [ + 62, + 319, + 272, + 329 + ], + "lines": [ + { + "bbox": [ + 62, + 319, + 272, + 329 + ], + "spans": [ + { + "bbox": [ + 62, + 319, + 272, + 329 + ], + "type": "text", + "content": "(a) covariance matrices in the 1st frame after 100 epochs training" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 55, + 330, + 280, + 434 + ], + "lines": [ + { + "bbox": [ + 55, + 330, + 280, + 434 + ], + "spans": [ + { + "bbox": [ + 55, + 330, + 280, + 434 + ], + "type": "image", + "image_path": "d0e316f93a7aef38fa4a46b97b9d16a9d87d491db9c8834e9ed6a4f48e7006ec.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 60, + 437, + 274, + 447 + ], + "lines": [ + { + "bbox": [ + 60, + 437, + 274, + 447 + ], + "spans": [ + { + "bbox": [ + 60, + 437, + 274, + 447 + ], + "type": "text", + "content": "(b) covariance matrices in the 2nd frame after 100 epochs training" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 449, + 287, + 505 + ], + "lines": [ + { + "bbox": [ + 46, + 449, + 287, + 505 + ], + "spans": [ + { + "bbox": [ + 46, + 449, + 287, + 505 + ], + "type": "text", + "content": "Figure 5. Estimated (red) covariance ellipses in the first (a) and the second (b) frame, learned from 128000 examples. Ground truth (green) covariances as comparison. Although the gradient minimizes the rotational error (see Fig. 4a), it is not capable of learning the correct covariance in the image plane." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 514, + 287, + 609 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 514, + 287, + 609 + ], + "spans": [ + { + "bbox": [ + 46, + 514, + 287, + 609 + ], + "type": "text", + "content": "Supervised Learning. The goal of the paper is for a neural network " + }, + { + "bbox": [ + 46, + 514, + 287, + 609 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 46, + 514, + 287, + 609 + ], + "type": "text", + "content": " learn the noise distributions of a keypoint detector. Given an image and a keypoint position, the network should predict the covariance of the noise " + }, + { + "bbox": [ + 46, + 514, + 287, + 609 + ], + "type": "inline_equation", + "content": "\\Sigma_{2\\mathrm{D},i} = F(\\boldsymbol {I},\\boldsymbol {p}_i)" + }, + { + "bbox": [ + 46, + 514, + 287, + 609 + ], + "type": "text", + "content": ". The gradient " + }, + { + "bbox": [ + 46, + 514, + 287, + 609 + ], + "type": "inline_equation", + "content": "d\\mathcal{L} / d\\Sigma_{2\\mathrm{D}}" + }, + { + "bbox": [ + 46, + 514, + 287, + 609 + ], + "type": "text", + "content": " allows for the network to learn the covariance matrices in an end-to-end manner by regression on the relative pose error. Given a dataset with known ground truth poses, we can use" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 143, + 620, + 287, + 632 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 620, + 287, + 632 + ], + "spans": [ + { + "bbox": [ + 143, + 620, + 287, + 632 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\sup } = e _ {\\text {r o t}} \\tag {9}", + "image_path": "328831a99278aaea1810808371a0042fa5d674a701b3bd2de419e2386f25c71d.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 642, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 287, + 677 + ], + "type": "text", + "content": "as a training loss. This ensures, that learned covariances effectively minimize the rotational error. See Fig. 3 for overview of the training process." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": "Self-Supervised Learning. Finding a suitable annotated dataset for a specific task is often non-trivial. For our task, we need accurate ground truth poses that are difficult to ac" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": "quire. But given a stream of images, like in VO, our method can be adapted to train a network in a self-supervised manner without the need for ground truth poses. For this, we follow the approach of [25] to exploit the cycle-consistency between a tuple of images. The cycle-consistency loss for a triplet " + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "inline_equation", + "content": "\\{I_1, I_2, I_3\\}" + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": " of images is given by" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 379, + 154, + 545, + 180 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 379, + 154, + 545, + 180 + ], + "spans": [ + { + "bbox": [ + 379, + 154, + 545, + 180 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {c y c l}} = \\angle \\prod_ {(i, j) \\in \\mathcal {P}} \\boldsymbol {R} _ {i j}, \\tag {10}", + "image_path": "d5f2593d349c8097d10617721f8d967f21414668cad478ad4d2699b9369ce6ff.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 190, + 545, + 226 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 190, + 545, + 226 + ], + "spans": [ + { + "bbox": [ + 305, + 190, + 545, + 226 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 190, + 545, + 226 + ], + "type": "inline_equation", + "content": "\\mathbf{R}_{ij}" + }, + { + "bbox": [ + 305, + 190, + 545, + 226 + ], + "type": "text", + "content": " is the estimated rotation between images " + }, + { + "bbox": [ + 305, + 190, + 545, + 226 + ], + "type": "inline_equation", + "content": "I_{i}" + }, + { + "bbox": [ + 305, + 190, + 545, + 226 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 190, + 545, + 226 + ], + "type": "inline_equation", + "content": "I_{j}" + }, + { + "bbox": [ + 305, + 190, + 545, + 226 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 190, + 545, + 226 + ], + "type": "inline_equation", + "content": "\\mathcal{P} = \\{(1,2),(2,3),(3,1)\\}" + }, + { + "bbox": [ + 305, + 190, + 545, + 226 + ], + "type": "text", + "content": " defines the cycle. As in [25], we also define an anchor loss" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 362, + 236, + 545, + 262 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 362, + 236, + 545, + 262 + ], + "spans": [ + { + "bbox": [ + 362, + 236, + 545, + 262 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {a n c h o r}} = \\sum_ {(i, j) \\in \\mathcal {P}} \\angle R _ {i j} R _ {i j, \\mathrm {N E C}} ^ {\\top} \\tag {11}", + "image_path": "d9c49da1f4552f7e33c5b2b255dae36ad643b429919ecd2d23c24b6c969ae0a9.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 271, + 545, + 331 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 271, + 545, + 331 + ], + "spans": [ + { + "bbox": [ + 304, + 271, + 545, + 331 + ], + "type": "text", + "content": "with the NEC rotation estimate, as a regularising term. In contrast to [25], our method does not risk learning degenerate solutions from the cycle-consistency loss, since the rotation is estimated using independently detected keypoints. The final loss is then given by" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 375, + 342, + 545, + 355 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 375, + 342, + 545, + 355 + ], + "spans": [ + { + "bbox": [ + 375, + 342, + 545, + 355 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {s e l f}} = \\mathcal {L} _ {\\text {c y c l}} + \\lambda \\mathcal {L} _ {\\text {a n c h o r}}. \\tag {12}", + "image_path": "9a0b42eda74be06c5377b54bc92e28fafe1bddba82e74bc32c8867147072a86a.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 365, + 387, + 380 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 365, + 387, + 380 + ], + "spans": [ + { + "bbox": [ + 306, + 365, + 387, + 380 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 386, + 545, + 457 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 386, + 545, + 457 + ], + "spans": [ + { + "bbox": [ + 304, + 386, + 545, + 457 + ], + "type": "text", + "content": "We evaluate our method in both synthetic and real-world experiments. Over the synthetic data, we investigate the ability of the gradient to learn the underlying noise distribution correctly by overfitting covariance estimates directly. We also investigate if better noise estimation leads to a reduces rotational error." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 459, + 545, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 459, + 545, + 578 + ], + "spans": [ + { + "bbox": [ + 304, + 459, + 545, + 578 + ], + "type": "text", + "content": "On real-world data, we use the gradient to train a network to predicts the noise distributions from images for different keypoint detectors. We explore fully supervised and self-supervised learning techniques for SuperPoint [12] and Basalt [66] KLT-Tracks to verify that our method is agnostic to the type of feature descriptor used (classical vs learned). We evaluate the performance of the learned covariances in a visual odometry setting on the popular KITTI odometry and the EuRoC dataset. We also evaluate generalization capabilities from the KITTI to the EuRoC dataset." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 578, + 545, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 578, + 545, + 662 + ], + "spans": [ + { + "bbox": [ + 304, + 578, + 545, + 662 + ], + "type": "text", + "content": "For our experiments we implement Eq. 3 in both Theseus [52] and ceres [1]. We use the Theseus implementation to train our network, since it allows for batched optimization and provides the needed gradient (see Eq. 8). However, we use the ceres implementation for our evaluation. We found the Levenberg-Marquardt optimization of ceres to be faster and more stable than its theseus counterpart." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 306, + 670, + 438, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 670, + 438, + 684 + ], + "spans": [ + { + "bbox": [ + 306, + 670, + 438, + 684 + ], + "type": "text", + "content": "4.1. Simulated Experiments" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "content": "In the simulated experiments we overfit covariance estimates for a single relative pose estimation problem using" + } + ] + } + ], + "index": 25 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13106" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 71, + 166, + 141 + ], + "blocks": [ + { + "bbox": [ + 49, + 71, + 166, + 141 + ], + "lines": [ + { + "bbox": [ + 49, + 71, + 166, + 141 + ], + "spans": [ + { + "bbox": [ + 49, + 71, + 166, + 141 + ], + "type": "image", + "image_path": "a4b616e032eafc2ed38439704b3002ade950df0f9942281d46d3f46f3bdef8f5.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 71, + 144, + 145, + 153 + ], + "lines": [ + { + "bbox": [ + 71, + 144, + 145, + 153 + ], + "spans": [ + { + "bbox": [ + 71, + 144, + 145, + 153 + ], + "type": "text", + "content": "(a) " + }, + { + "bbox": [ + 71, + 144, + 145, + 153 + ], + "type": "inline_equation", + "content": "e_{\\mathrm{rot}}" + }, + { + "bbox": [ + 71, + 144, + 145, + 153 + ], + "type": "text", + "content": " during training" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 167, + 70, + 286, + 141 + ], + "blocks": [ + { + "bbox": [ + 167, + 70, + 286, + 141 + ], + "lines": [ + { + "bbox": [ + 167, + 70, + 286, + 141 + ], + "spans": [ + { + "bbox": [ + 167, + 70, + 286, + 141 + ], + "type": "image", + "image_path": "d3c7bd319872a4185cc7ac9241beec52f03f1100a4505dfe71995ca03170e7c4.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 175, + 142, + 279, + 154 + ], + "lines": [ + { + "bbox": [ + 175, + 142, + 279, + 154 + ], + "spans": [ + { + "bbox": [ + 175, + 142, + 279, + 154 + ], + "type": "text", + "content": "(b) " + }, + { + "bbox": [ + 175, + 142, + 279, + 154 + ], + "type": "inline_equation", + "content": "\\sigma_{norm}^2" + }, + { + "bbox": [ + 175, + 142, + 279, + 154 + ], + "type": "text", + "content": " error during training" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 55, + 214, + 281, + 319 + ], + "blocks": [ + { + "bbox": [ + 46, + 156, + 287, + 212 + ], + "lines": [ + { + "bbox": [ + 46, + 156, + 287, + 212 + ], + "spans": [ + { + "bbox": [ + 46, + 156, + 287, + 212 + ], + "type": "text", + "content": "Figure 6. Rotational error (a) and differences between the true residual variance " + }, + { + "bbox": [ + 46, + 156, + 287, + 212 + ], + "type": "inline_equation", + "content": "\\tilde{\\sigma}^2" + }, + { + "bbox": [ + 46, + 156, + 287, + 212 + ], + "type": "text", + "content": " and the learned variance " + }, + { + "bbox": [ + 46, + 156, + 287, + 212 + ], + "type": "inline_equation", + "content": "\\sigma^2" + }, + { + "bbox": [ + 46, + 156, + 287, + 212 + ], + "type": "text", + "content": " (b) over the training epochs. As previously, our method learns to adapt the covariances for each keypoint to minimize rotational error. Minimizing the rotational error leads to a significantly better estimate of " + }, + { + "bbox": [ + 46, + 156, + 287, + 212 + ], + "type": "inline_equation", + "content": "\\sigma^2" + }, + { + "bbox": [ + 46, + 156, + 287, + 212 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 55, + 214, + 281, + 319 + ], + "lines": [ + { + "bbox": [ + 55, + 214, + 281, + 319 + ], + "spans": [ + { + "bbox": [ + 55, + 214, + 281, + 319 + ], + "type": "image", + "image_path": "7118faac46243aca99c028df3a74f866901f9501ab60f43311d429339cb77bbb.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 60, + 321, + 274, + 331 + ], + "lines": [ + { + "bbox": [ + 60, + 321, + 274, + 331 + ], + "spans": [ + { + "bbox": [ + 60, + 321, + 274, + 331 + ], + "type": "text", + "content": "(a) covariance matrices in the 2nd frame after 100 epochs training" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 332, + 287, + 389 + ], + "lines": [ + { + "bbox": [ + 46, + 332, + 287, + 389 + ], + "spans": [ + { + "bbox": [ + 46, + 332, + 287, + 389 + ], + "type": "text", + "content": "Figure 7. Estimated (red) covariance ellipses in the second frame, learned from 128000 examples. Ground truth (green) covariances as comparison. Training data with enough variety gives a gradient that allows to correctly learn the covariances even in the image plane, overcoming the unobservabilities of the first experiment." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 392, + 287, + 547 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 392, + 287, + 547 + ], + "spans": [ + { + "bbox": [ + 46, + 392, + 287, + 547 + ], + "type": "text", + "content": "the gradient from Eq. 8. For this, We create a random relative pose estimation problem consisting of two cameraframes observing randomly generated points in 3D space. The points are projected into camera frames using a pin-hole camera model. Each projected point is assigned a random gaussian noise distribution. From this 128000 random problems are sampled. We learn the noise distributions by initializing all covariance estimates as scaled identity matrices, solving the relative pose estimation problem using the PNEC and updating the parameters of the distribution using the gradient of Eq. 8 directly. We train for 100 epochs with the ADAM [31] optimizer with (0.9, 0.99) as parameters and a batch size of 12800 for a stable gradient." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 548, + 287, + 621 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 548, + 287, + 621 + ], + "spans": [ + { + "bbox": [ + 46, + 548, + 287, + 621 + ], + "type": "text", + "content": "Fig. 4a shows the decrease of the rotation error over the epochs. The learned covariances decrease the error by " + }, + { + "bbox": [ + 46, + 548, + 287, + 621 + ], + "type": "inline_equation", + "content": "8\\%" + }, + { + "bbox": [ + 46, + 548, + 287, + 621 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 548, + 287, + 621 + ], + "type": "inline_equation", + "content": "16\\%" + }, + { + "bbox": [ + 46, + 548, + 287, + 621 + ], + "type": "text", + "content": " compared to unit covariances and the NEC, respectively. This validates the importance of good covariances for the PNEC, shown in [48]. Fig. 4b shows the average error for the normalized variance " + }, + { + "bbox": [ + 46, + 548, + 287, + 621 + ], + "type": "inline_equation", + "content": "\\sigma_{norm}^2" + }, + { + "bbox": [ + 46, + 548, + 287, + 621 + ], + "type": "text", + "content": ", given by" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 123, + 628, + 287, + 658 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 123, + 628, + 287, + 658 + ], + "spans": [ + { + "bbox": [ + 123, + 628, + 287, + 658 + ], + "type": "interline_equation", + "content": "\\sigma_ {i, n o r m} ^ {2} = \\frac {N \\cdot \\sigma_ {i} ^ {2}}{\\sum_ {j = 0} ^ {N} \\sigma_ {j} ^ {2}} \\tag {13}", + "image_path": "5c64ba6069f5be01cdafea050bb42752680f6fd8709a5620fb0566f769cd2d8f.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 666, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 666, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 666, + 287, + 715 + ], + "type": "text", + "content": "over the training epochs, obtained at the ground truth relative pose. We compare the normalized error variance, as the scale of " + }, + { + "bbox": [ + 46, + 666, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\sigma^2" + }, + { + "bbox": [ + 46, + 666, + 287, + 715 + ], + "type": "text", + "content": " is not observable from the gradient. The covariances that minimize the rotational error also approximate" + } + ] + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 325, + 70, + 526, + 255 + ], + "blocks": [ + { + "bbox": [ + 325, + 70, + 526, + 255 + ], + "lines": [ + { + "bbox": [ + 325, + 70, + 526, + 255 + ], + "spans": [ + { + "bbox": [ + 325, + 70, + 526, + 255 + ], + "type": "image", + "image_path": "d0e6806c6fdff765b963cf66588aae4e30a257e57004c90c1d0fc6a659390887.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 256, + 545, + 334 + ], + "lines": [ + { + "bbox": [ + 304, + 256, + 545, + 334 + ], + "spans": [ + { + "bbox": [ + 304, + 256, + 545, + 334 + ], + "type": "text", + "content": "Figure 8. Qualitative trajectory comparison for KITTI seq. 00. Since we compare monocular methods, that cannot estimate the correct scale from a pair of images, we use the scale of the ground truth translations for visualization purposes. Both, our supervised and self-supervised approaches lead to significant improvements in the trajectory. There is little drift even without additional rotation averaging [11] or loop closure [49]." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 335, + 546, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 335, + 546, + 467 + ], + "spans": [ + { + "bbox": [ + 304, + 335, + 546, + 467 + ], + "type": "text", + "content": "the residual uncertainty " + }, + { + "bbox": [ + 304, + 335, + 546, + 467 + ], + "type": "inline_equation", + "content": "\\sigma^2" + }, + { + "bbox": [ + 304, + 335, + 546, + 467 + ], + "type": "text", + "content": " very closely. However, while the residual uncertainty is approximated well, the learned 2D covariances in the image plane do not correspond to the correct covariances (see Fig. 5). This is due to two different reasons. First, due to " + }, + { + "bbox": [ + 304, + 335, + 546, + 467 + ], + "type": "inline_equation", + "content": "\\sigma_i^2" + }, + { + "bbox": [ + 304, + 335, + 546, + 467 + ], + "type": "text", + "content": " dependence on both " + }, + { + "bbox": [ + 304, + 335, + 546, + 467 + ], + "type": "inline_equation", + "content": "\\Sigma_{\\mathrm{2D},i}" + }, + { + "bbox": [ + 304, + 335, + 546, + 467 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 335, + 546, + 467 + ], + "type": "inline_equation", + "content": "\\Sigma_{\\mathrm{2D},i}^{\\prime}" + }, + { + "bbox": [ + 304, + 335, + 546, + 467 + ], + "type": "text", + "content": ", there is not a single unique solution. Secondly, the direction of the gradient is dependent on the translation between the images (see the supplementary material for more details). In this experimental setup, the information flow to the images is limited and we can only learn the true distribution for " + }, + { + "bbox": [ + 304, + 335, + 546, + 467 + ], + "type": "inline_equation", + "content": "\\sigma^2" + }, + { + "bbox": [ + 304, + 335, + 546, + 467 + ], + "type": "text", + "content": " but not for the 2D images covariances." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 468, + 546, + 659 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 468, + 546, + 659 + ], + "spans": [ + { + "bbox": [ + 304, + 468, + 546, + 659 + ], + "type": "text", + "content": "To address the problems with limited information flow of the previous experiment, we propose a second experiment to negate the influence of these aforementioned factors. First, each individual problem has a randomly sampled relative pose, where the first frame stays fixed. This removes the influence of the translation on the gradient direction. The noise is still drawn from the same distributions as earlier. Second, we fix the noise in the first frame to be small, isotropic, and homogeneous in nature. Furthermore, we only learn the covariances in the second frame and provide the optimization with the ground truth noise in the first frame. Fig. 6 and Fig. 7 show, that under these constraints, we are not only able to learn the distribution for " + }, + { + "bbox": [ + 304, + 468, + 546, + 659 + ], + "type": "inline_equation", + "content": "\\sigma^2" + }, + { + "bbox": [ + 304, + 468, + 546, + 659 + ], + "type": "text", + "content": " but also " + }, + { + "bbox": [ + 304, + 468, + 546, + 659 + ], + "type": "inline_equation", + "content": "\\Sigma_{2\\mathrm{D}}'" + }, + { + "bbox": [ + 304, + 468, + 546, + 659 + ], + "type": "text", + "content": ". Together, both experiments show, that we can learn the correct distributions from noisy data by following the gradient that minimizes the rotational error." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 670, + 408, + 681 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 670, + 408, + 681 + ], + "spans": [ + { + "bbox": [ + 306, + 670, + 408, + 681 + ], + "type": "text", + "content": "4.2. Real World Data" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 689, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 546, + 714 + ], + "type": "text", + "content": "We evaluate our method on the KITTI [21] and EuRoC [9] dataset. Since KITTI shows outdoor driving sequences" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13107" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 53, + 70, + 538, + 176 + ], + "blocks": [ + { + "bbox": [ + 53, + 70, + 538, + 176 + ], + "lines": [ + { + "bbox": [ + 53, + 70, + 538, + 176 + ], + "spans": [ + { + "bbox": [ + 53, + 70, + 538, + 176 + ], + "type": "table", + "html": "
NISTÉR-5PT [50]NEC [33]NEC-LSWEIGHTED NEC-LSOURS SUPERVISEDOURS SELF-SUPERVISED
Seq.RPE1RPEnetRPE1RPEnetRPE1RPEnetRPE1RPEnetRPE1RPEnetRPE1RPEnet
080.19517.0204.240.0818.2843.660.0567.0042.500.0546.0592.500.0504.0672.460.0504.1182.46
090.1425.7541.740.0531.6461.430.0521.5530.710.0511.3540.700.0491.3170.710.0491.2780.70
100.29516.6786.570.1679.2644.430.0644.7871.790.0634.3891.760.0633.5131.640.0653.8211.65
train0.24911.5064.130.14110.1272.970.0826.9101.720.0816.4101.720.0772.3781.690.0772.5051.69
test0.20014.3494.070.0896.9173.280.0565.3531.960.0554.6761.950.0523.3331.910.0533.4081.91
", + "image_path": "d64154659931de7090e864269fee34369a9e2bf84ead86b78592a08a7068c216.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 53, + 223, + 538, + 329 + ], + "blocks": [ + { + "bbox": [ + 46, + 177, + 547, + 222 + ], + "lines": [ + { + "bbox": [ + 46, + 177, + 547, + 222 + ], + "spans": [ + { + "bbox": [ + 46, + 177, + 547, + 222 + ], + "type": "text", + "content": "Table 1. Quantitative comparison on the KITTI [21] dataset with SuperPoint [12] keypoints. We compare two rotation and one translation metric. The results are shown for each test sequence together with the mean results on the training and test set weighted by the sequence length. Both our training setups outperform the non-probabilitic algorithms but also the weighted NEC-LS using SuperGlue confidences consistently across unseen data. The learned uncertainties are able to generalise well and improve the relative pose estimation significantly." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 53, + 223, + 538, + 329 + ], + "lines": [ + { + "bbox": [ + 53, + 223, + 538, + 329 + ], + "spans": [ + { + "bbox": [ + 53, + 223, + 538, + 329 + ], + "type": "table", + "html": "
NISTÉR-5PT [50]NEC [33]NEC-LSKLT-PNEC [48]OURS SUPERVISEDOURS SELF-SUPERVISED
Seq.RPE1RPEnetRPE1RPEnetRPE1RPEnetRPE1RPEnetRPE1RPEnetRPE1RPEnet
080.1266.9293.440.0883.9028.910.0532.9082.490.0542.5242.420.0482.3732.360.0471.7062.36
090.0902.5441.280.0542.0276.760.0522.3070.740.0461.0030.690.0431.2440.640.0421.1410.64
100.18811.5544.430.1198.3028.530.0664.5761.780.0634.4801.710.0583.7891.580.0563.6231.60
train0.2049.6773.190.1738.3018.590.1033.9551.730.1044.2131.660.0942.7821.600.0962.7371.61
test0.1296.7223.110.0854.2378.340.0553.0601.960.0542.5141.900.0482.3591.820.0481.9101.83
", + "image_path": "f5b7787cd139cf151d9ed7a4f21acd819ae560b946e28a56f8999012deb94e94.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 330, + 546, + 364 + ], + "lines": [ + { + "bbox": [ + 46, + 330, + 546, + 364 + ], + "spans": [ + { + "bbox": [ + 46, + 330, + 546, + 364 + ], + "type": "text", + "content": "Table 2. Quantitative comparison on the KITTI [21] dataset with KLT tracks [66]. As in Tab. 1, we show the results on the test set together with the mean on the train and test set weighted by the sequence lengths. As for SuperPoint, our methods improve all metrics consistently for unseen data. Our learned covariances are significantly better for relative pose estimation than the approximation used in [48]." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 370, + 289, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 370, + 289, + 491 + ], + "spans": [ + { + "bbox": [ + 46, + 370, + 289, + 491 + ], + "type": "text", + "content": "and EuRoC shows indoor scenes captured with a drone, they exhibit different motion models as well as a variety of images. For KITTI we choose sequences 00-07 as the training set for both supervised and self-supervised training. Sequences 08-10 are used as the test set. We use a smaller UNet [55] architecture as our network to predict the covariances for the whole image. We chose this network since it gives us a good balance between batch size, training time and performance. The network predicts the parameters for the covariances directly. We choose" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 86, + 498, + 287, + 526 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 498, + 287, + 526 + ], + "spans": [ + { + "bbox": [ + 86, + 498, + 287, + 526 + ], + "type": "interline_equation", + "content": "\\boldsymbol {\\Sigma} _ {2 \\mathrm {D}} (s, \\alpha , \\beta) = s \\boldsymbol {R} _ {\\alpha} \\left( \\begin{array}{c c} \\beta & 0 \\\\ 0 & 1 - \\beta \\end{array} \\right) \\boldsymbol {R} _ {\\alpha} ^ {\\top} \\tag {14}", + "image_path": "3e1515104e825a039ec565574e165e7260b72a78166c339d5c6a7bb8a0a6fefd.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 533, + 287, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 533, + 287, + 559 + ], + "spans": [ + { + "bbox": [ + 46, + 533, + 287, + 559 + ], + "type": "text", + "content": "as a parameterization [7]. To ensure that our network predicts valid covariances the network output is filtered with" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 118, + 566, + 287, + 581 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 118, + 566, + 287, + 581 + ], + "spans": [ + { + "bbox": [ + 118, + 566, + 287, + 581 + ], + "type": "interline_equation", + "content": "f _ {1} (x) = \\left(1 + | x |\\right) ^ {\\operatorname {s i g n} (\\mathrm {x})} \\tag {15}", + "image_path": "193347c6871cdb4896d616360a20e0e3e87d07b63bd569f0ab59a6994d0ee2cf.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 119, + 582, + 287, + 595 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 119, + 582, + 287, + 595 + ], + "spans": [ + { + "bbox": [ + 119, + 582, + 287, + 595 + ], + "type": "interline_equation", + "content": "f _ {2} (x) = x \\tag {16}", + "image_path": "b013b14a26a01884da210b4d440584cbbed4004533b0b086e3dcbcf74aecbb43.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 119, + 597, + 287, + 620 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 119, + 597, + 287, + 620 + ], + "spans": [ + { + "bbox": [ + 119, + 597, + 287, + 620 + ], + "type": "interline_equation", + "content": "f _ {3} (x) = \\frac {1}{1 + e ^ {- x}} \\tag {17}", + "image_path": "ecced1ef14f307b1ebf795bbc97b54da71f8ee3b011c35ca7fa3112cf0c8d0f8.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 629, + 287, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 287, + 666 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 287, + 666 + ], + "type": "text", + "content": "for " + }, + { + "bbox": [ + 46, + 629, + 287, + 666 + ], + "type": "inline_equation", + "content": "s, \\alpha, \\beta" + }, + { + "bbox": [ + 46, + 629, + 287, + 666 + ], + "type": "text", + "content": ", respectively. Feature points that have subpixel accuracy use the nearest pixel covariance. See the supplementary material for more details on the training setup." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 666, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 666, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 666, + 287, + 715 + ], + "type": "text", + "content": "Supervised Learning. To show that our method generalizes to different keypoint detectors, we train two networks, one for SuperPoint [12] and one for KLT tracks obtained from [66]. The SuperPoint keypoints are matched" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 370, + 547, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 370, + 547, + 586 + ], + "spans": [ + { + "bbox": [ + 304, + 370, + 547, + 586 + ], + "type": "text", + "content": "using SuperGlue [57]. For training we use a batch size of 8 images pairs for SuperPoint and 16 images pairs for KLT tracks. We trained for 100 epochs for both SuperPoint and KLT tracks. More training details are provided in the supplementary material. To ensure our network does not overfit on specific keypoint locations, we randomly crop the images before finding correspondences during training time. During evaluation we use the uncropped images to obtain features. During training we randomly perturb the ground truth pose as a starting point. To increase robustness, we first use the eigenvalue based optimization of the NEC in a RANSAC scheme [32] to filter outliers. This is followed by a custom least squares implementation of the NEC (NECLS), followed by optimizing Eq. 3. As reported in [48] we found, that such a multi-stage optimization provides the most robust and accurate results. We show examples of how the DNLS-learned covariances change the energy function landscape in the supplementary material." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 589, + 547, + 686 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 589, + 547, + 686 + ], + "spans": [ + { + "bbox": [ + 304, + 589, + 547, + 686 + ], + "type": "text", + "content": "Self-Supervised Learning. We evaluate our self-supervised training setup on the same data as our supervised training. Due to needing image tuples instead of pairs, we reduce the batch size to 12 for KLT image triplets. This gives us 24 and 36 images pairs per batch, respectively. The training epochs are reduced to 50. More training details for the supervised and self-supervised training can be found in the supplementary material." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 689, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 547, + 715 + ], + "type": "text", + "content": "Results. We evaluate the learned covariances in a VO setting. We compare the proposed DNLS approach to the" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "13108" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 70, + 548, + 198 + ], + "blocks": [ + { + "bbox": [ + 48, + 70, + 548, + 198 + ], + "lines": [ + { + "bbox": [ + 48, + 70, + 548, + 198 + ], + "spans": [ + { + "bbox": [ + 48, + 70, + 548, + 198 + ], + "type": "table", + "html": "
NISTÉR-5PT [51]NEC [33]NEC-LSWEIGHTED NEC-LSOURS SELF-SUPERVISEDOURS TAB. 1
Seq.RPE1RPEnetRPE1RPEnetRPE1RPEnetRPE1RPEnetRPE1RPEnetRPE1RPEnetRPE1RPEnet
V1_010.50171.8731.860.32039.5043.120.38752.9246.310.38856.5246.820.32731.1235.560.33231.8134.01
V1_020.54132.0120.360.38928.1126.950.54070.0828.940.54268.3529.810.44430.3921.980.43629.0721.29
V1_030.66027.3925.000.49225.4231.060.55276.7231.580.55578.1432.250.51029.5224.190.52031.1824.13
V2_010.51561.4533.510.31631.9539.790.31035.8439.000.31438.6239.620.28517.6132.400.29522.4130.58
V2_020.54543.7322.240.39625.4832.210.36926.9625.360.36525.0925.810.38225.3221.160.38621.9120.34
V2_031.12336.7128.770.97648.2637.600.939107.1136.740.941100.7336.710.94252.7231.130.99155.4130.40
mean0.63148.4527.560.46333.5136.030.49458.9035.610.49658.9536.110.46130.5728.460.47231.4427.44
", + "image_path": "0825f3548ae77f77624077907a246648b67367d081110ae4e3600dc1ea5d1995.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 46, + 200, + 547, + 246 + ], + "lines": [ + { + "bbox": [ + 46, + 200, + 547, + 246 + ], + "spans": [ + { + "bbox": [ + 46, + 200, + 547, + 246 + ], + "type": "text", + "content": "Table 3. Quantitative comparison on the Vicon sequences of the EuRoC dataset [9] with SuperPoint [12] keypoints. The dataset is more difficult than KITTI (see Tab. 2 and Tab. 1) with SuperPoint and SuperGlue [57] finding far fewer matches. As reported in [48] the least squares implementations struggle with bad initialization under these adverse conditions with NEC-LS performing especially poor. From all least squares optimizations, our learned covariances consistently perform the best, even outperforming the NEC most of the time." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 257, + 289, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 257, + 289, + 544 + ], + "spans": [ + { + "bbox": [ + 46, + 257, + 289, + 544 + ], + "type": "text", + "content": "popular 5pt algorithm [51] and the NEC [33] as implemented in [32]. To investigate the benefit of our learned covariances we include the NEC-LS implementation as well as the symmetric PNEC with the covariances from [48] in Tab. 2. For Tab. 1 we additionally include a weighted version of our custom NEC-LS implementation with matching confidence from SuperGlue as weights. All methods are given the same feature matches and use a constant motion model for initializing the optimizations. We evaluate on the rotational versions of the " + }, + { + "bbox": [ + 46, + 257, + 289, + 544 + ], + "type": "inline_equation", + "content": "\\mathrm{RPE}_1" + }, + { + "bbox": [ + 46, + 257, + 289, + 544 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 257, + 289, + 544 + ], + "type": "inline_equation", + "content": "\\mathrm{RPE}_n" + }, + { + "bbox": [ + 46, + 257, + 289, + 544 + ], + "type": "text", + "content": " and the cosine error " + }, + { + "bbox": [ + 46, + 257, + 289, + 544 + ], + "type": "inline_equation", + "content": "e_t" + }, + { + "bbox": [ + 46, + 257, + 289, + 544 + ], + "type": "text", + "content": " for the translation as defined in [11, 48]. Tab. 1 and Tab. 2 show the average results on the test set over 5 runs for SuperPoint and KLT tracks on KITTI [21], respectively. We show additional results in the supplementary material. Our methods consistently perform the best over all sequences, with the self-supervised being on par with our supervised training. Compared to its non-probabilistic counterpart NEC-LS, our method improves the " + }, + { + "bbox": [ + 46, + 257, + 289, + 544 + ], + "type": "inline_equation", + "content": "\\mathrm{RPE}_1" + }, + { + "bbox": [ + 46, + 257, + 289, + 544 + ], + "type": "text", + "content": " by " + }, + { + "bbox": [ + 46, + 257, + 289, + 544 + ], + "type": "inline_equation", + "content": "7\\%" + }, + { + "bbox": [ + 46, + 257, + 289, + 544 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 257, + 289, + 544 + ], + "type": "inline_equation", + "content": "13\\%" + }, + { + "bbox": [ + 46, + 257, + 289, + 544 + ], + "type": "text", + "content": " and the " + }, + { + "bbox": [ + 46, + 257, + 289, + 544 + ], + "type": "inline_equation", + "content": "\\mathrm{RPE}_n" + }, + { + "bbox": [ + 46, + 257, + 289, + 544 + ], + "type": "text", + "content": " by " + }, + { + "bbox": [ + 46, + 257, + 289, + 544 + ], + "type": "inline_equation", + "content": "37\\%" + }, + { + "bbox": [ + 46, + 257, + 289, + 544 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 257, + 289, + 544 + ], + "type": "inline_equation", + "content": "23\\%" + }, + { + "bbox": [ + 46, + 257, + 289, + 544 + ], + "type": "text", + "content": " for different keypoint detectors on unseen data. It also improves upon weighted methods, like weighted NEC-LS and the nonlearned covariances for the PNEC [48]. This demonstrates the importance of correctly modeling the feature correspondence quality. We show an example trajectory in Fig. 8." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 545, + 288, + 656 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 288, + 656 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 288, + 656 + ], + "type": "text", + "content": "Tab. 3 shows the results on the EuRoC dataset for SuperPoint. Pose estimation is significantly more difficult compared to KITTI, often having few correspondences between images. However, our method generalizes to different datasets, with the network trained on KITTI and our self-supervised approach, outperforming the others most of the time. Especially a direct comparison with NEC-LS, the closest non-probabilistic method, shows significant improvements of " + }, + { + "bbox": [ + 46, + 545, + 288, + 656 + ], + "type": "inline_equation", + "content": "7\\%" + }, + { + "bbox": [ + 46, + 545, + 288, + 656 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 46, + 545, + 288, + 656 + ], + "type": "inline_equation", + "content": "\\mathrm{RPE}_1" + }, + { + "bbox": [ + 46, + 545, + 288, + 656 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 545, + 288, + 656 + ], + "type": "inline_equation", + "content": "48\\%" + }, + { + "bbox": [ + 46, + 545, + 288, + 656 + ], + "type": "text", + "content": " for the " + }, + { + "bbox": [ + 46, + 545, + 288, + 656 + ], + "type": "inline_equation", + "content": "\\mathrm{RPE}_n" + }, + { + "bbox": [ + 46, + 545, + 288, + 656 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 668, + 201, + 681 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 668, + 201, + 681 + ], + "spans": [ + { + "bbox": [ + 47, + 668, + 201, + 681 + ], + "type": "text", + "content": "5. Discussion and Limitations" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "type": "text", + "content": "Our experiments demonstrate the capability of our framework to correctly learn positional uncertainty, lead" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 257, + 547, + 328 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 257, + 547, + 328 + ], + "spans": [ + { + "bbox": [ + 304, + 257, + 547, + 328 + ], + "type": "text", + "content": "ing to improved results for relative pose estimation for VO. Our approach generalizes to different feature extractors and to different datasets, providing a unified approach to estimate the noise distribution of keypoint detectors. However, our method requires more computational resources than the original uncertainty estimation for the PNEC." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 329, + 547, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 329, + 547, + 437 + ], + "spans": [ + { + "bbox": [ + 304, + 329, + 547, + 437 + ], + "type": "text", + "content": "We evaluate our learned covariances in a visual odometry setting, showing that they lead to reduced errors and especially less drift in the trajectory. However, this does not guarantee that the covariances are calibrated. Our framework inherits the ambiguity of the PNEC with regard to the noise scale. The true scale of the noise is not observable from relative pose estimation alone and only the relative scale between covariances can be learned. For the purposes of VO, this scale ambiguity is negligible." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 437, + 547, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 437, + 547, + 498 + ], + "spans": [ + { + "bbox": [ + 304, + 437, + 547, + 498 + ], + "type": "text", + "content": "As our synthetic experiments show, diverse data is needed to correctly identify the 2D noise distribution. However, obtaining the noise distribution is difficult for keypoint detectors - hence learning it from pose regression. Further limitations are addressed in the supplementary material." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 509, + 379, + 521 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 509, + 379, + 521 + ], + "spans": [ + { + "bbox": [ + 306, + 509, + 379, + 521 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 529, + 547, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 529, + 547, + 673 + ], + "spans": [ + { + "bbox": [ + 304, + 529, + 547, + 673 + ], + "type": "text", + "content": "We present a novel DNLS framework for estimating positional uncertainty. Our framework can be combined with any feature extraction algorithm, making it extremely versatile. Regressing the noise distribution from relative pose estimation, ensures that learned covariance matrices are suitable for visual odometry tasks. In synthetic experiments, our framework is capable to learn the correct noise distribution from noisy data. We showed the practical application of our framework on real-world data for different feature extractors. Our learned uncertainty consistently outperforms a variety of non-probabilistic relative pose estimation algorithms as well as other uncertainty estimation methods." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 683, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 683, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 683, + 547, + 715 + ], + "type": "text", + "content": "Acknowledgements. This work was supported by the ERC Advanced Grant SIMULACRON, by the Munich Center for Machine Learning and by the EPSRC Programme Grant VisualAI EP/T028572/1." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "13109" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 286, + 712 + ], + "type": "list", + "angle": 0, + "index": 18, + "blocks": [ + { + "bbox": [ + 53, + 91, + 286, + 113 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 286, + 113 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 286, + 113 + ], + "type": "text", + "content": "[1] Sameer Agarwal, Keir Mierle, and Others. 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Springer, 2017. 3" + } + ] + } + ], + "index": 1 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "13112" + } + ] + } + ], + "index": 3 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Learning Customized Visual Models With Retrieval-Augmented Knowledge/5534a4dd-73bd-49cc-aaa8-1125042ab403_content_list.json b/2023/Learning Customized Visual Models With Retrieval-Augmented Knowledge/5534a4dd-73bd-49cc-aaa8-1125042ab403_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..f980ed42c28af0dd2f0890661c309cb694f3d3b5 --- /dev/null +++ b/2023/Learning Customized Visual Models With Retrieval-Augmented Knowledge/5534a4dd-73bd-49cc-aaa8-1125042ab403_content_list.json @@ -0,0 +1,2070 @@ +[ + { + "type": "text", + "text": "Learning Customized Visual Models with Retrieval-Augmented Knowledge", + "text_level": 1, + "bbox": [ + 106, + 130, + 864, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Haotian Liu†§◆ Kilho Son‡ Jianwei Yang‡ Ce Liu‡ Jianfeng Gao‡ Yong Jae Lee† Chunyuan Li†¶ University of Wisconsin–Madison ‡ Microsoft {lht,yongjaeelee}@cs.wisc.edu {kilhoson, jianwyan, ce.liu, jfgao, chunyl}@microsoft.com https://react-v1.github.io", + "bbox": [ + 106, + 180, + 861, + 251 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 286, + 313, + 301 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Image-text contrastive learning models such as CLIP have demonstrated strong task transfer ability. The high generality and usability of these visual models is achieved via a web-scale data collection process to ensure broad concept coverage, followed by expensive pre-training to feed all the knowledge into model weights. Alternatively, we propose REACT, REtrieval-Augmented CusTomization, a framework to acquire the relevant web knowledge to build customized visual models for target domains. We retrieve the most relevant image-text pairs ( $\\sim 3\\%$ of CLIP pre-training data) from the web-scale database as external knowledge and propose to customize the model by only training new modularized blocks while freezing all the original weights. The effectiveness of REACT is demonstrated via extensive experiments on classification, retrieval, detection and segmentation tasks, including zero, few, and full-shot settings. Particularly, on the zero-shot classification task, compared with CLIP, it achieves up to $5.4\\%$ improvement on ImageNet and $3.7\\%$ on the ELEVATER benchmark (20 datasets).", + "bbox": [ + 75, + 318, + 473, + 606 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 654, + 209, + 669 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "It has been a fundamental research problem in computer vision (CV) to build a transferable visual system that can easily adapt to a wide range of downstream tasks. With remarkable advances in deep learning, a de facto solution to achieve this is to train deep neural networks on a large amount of data to pursue the so-called generic visual representations. This dates back to the standard supervised training on ImageNet [10], whose superb representation power is further demonstrated in BiT [23]/ViT [12] by scaling up the training to JFT300M [50]. Along the way, recent efforts have been applied to the popular image self-supervised learning [6, 16, 17] to reduce the demand for labeled data. The", + "bbox": [ + 75, + 680, + 470, + 863 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "third approach is image-text contrastive learning trained on billion-scale web-crawled image-text pairs. Such models, like CLIP [43] and ALIGN [20], are able to achieve great performance on different downstream domains, without the need of any human labels.", + "bbox": [ + 500, + 287, + 893, + 363 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Excellent empirical performance has been achieved with the above three pre-training methods, by following the well established two-stage pre-training then adaptation pipeline: model pre-training from scratch on large data, then model adaptation directly on downstream tasks. Specifically, the pre-trained models are adapted to downstream tasks by considering the available task-specific samples only: either evaluated in a zero-shot task transfer manner, or updated using linear probing (LP) [43], finetuning (FT) [27], or prompt tuning [44, 71]. Following this two-stage pipeline, most research has reverted to the faith that building transferable visual systems is equivalent to developing more generic visual models by feeding all knowledge in the model pre-training stage. Therefore, the community has been witnessing a trend in exploring scaling success of pre-training model and data size with less care on the target domain, hoping that the model can adapt to any downstream scenario.", + "bbox": [ + 496, + 364, + 895, + 623 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this paper, we argue that the conventional two-stage pipeline above is over-simplified and less efficient, in achieving the goal of building a transferable visual system in real-world settings. Instead, we propose a customization stage in between the pre-training and adaptation, where customization is implemented by systematically leveraging retrieved external knowledge. The inspiration comes from how humans are specialized in society for better generalization: instead of trying to memorize all concepts, humans are trained/prepared in a relevant subject to master a certain skill, while maintaining the basic skills in pre-training.", + "bbox": [ + 496, + 626, + 895, + 792 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To this end, we explore a systematic approach to acquire and learn with external knowledge sources from a large image-text corpus for model customization. The process of collecting external image-text knowledge is fully automatic without extra human annotation. The acquired knowledge typically contains richer information about the concept: relevant images that never appear in the downstream training", + "bbox": [ + 496, + 795, + 895, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "$\\spadesuit$ core contribution; equal advising; work initiated during an internship at Microsoft.", + "bbox": [ + 75, + 875, + 468, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "15148", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/e6247859f1503f6566ad699b8aba5f6c5dd7dc2bc67e17751012a9694eb7de18.jpg", + "image_caption": [ + "Figure 1. REACT achieves the best zero-shot ImageNet performance among public checkpoints (Left), achieves new SoTA on semi-supervised ImageNet classification in the $1\\%$ labeled data setting (Middle), and consistently transfer better than CLIP on across a variety of tasks, including ImageNet classification, zero/few/full-shot classification on 20 datasets in ELEVATER benchmark, image-text retrieval, object detection and segmentation (Right). Please see the detailed numbers and settings in the experimental section. For the left figure, circle size indicates model size." + ], + "image_footnote": [], + "bbox": [ + 81, + 89, + 261, + 242 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/05195f77dc9feea22cc3d7c26014c010cd81a603a8286b190d05658467e9afc8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 266, + 90, + 437, + 242 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/ae4b32cdce349650530b2ed5da356abb50406c1cf8adc128c44c620a3176d167.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 450, + 90, + 875, + 244 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "and evaluation set, and richer text descriptions about concept semantics. Such multi-modal knowledge sources are generally available on the web, and further open-sourced like LAION [45, 46]. They cover a variety of domains, making it possible to develop customized visual models for task-level transfer. Similar retrieval-augmented intuitions have been exploited in computer vision for class-level transfer [32], but not yet for task-level transfer (similar to that of CLIP). Our main findings/contributions can be summarized as follows.", + "bbox": [ + 75, + 330, + 470, + 467 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We propose to explore the potential of the web-scale image-text corpus as external knowledge to significantly improve task-level transfer performance on the target domain at an affordable cost. A simple and effective strategy is proposed. To begin with, we build a large-scale multimodal indexing system to retrieve the relevant image-text pairs using CLIP features and approximate nearest neighbor search. For a CV problem, the task instruction is often sufficiently specified with text such as class names, which allows us to utilize them as queries to retrieve the relevant image-text pair knowledge from the indexing system. No images from the CV problem are needed. To efficiently build the customized visual model, we propose a novel modularized learning strategy: only updating the additional trainable weights on the retrieved knowledge, and freezing the original model weights. Hence, the model masters the new skill without forgetting basic skills.", + "bbox": [ + 75, + 472, + 470, + 729 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The generality and effectiveness of the proposed customization strategy is demonstrated on four CV problems. We instantiate it with CLIP, and develop the customized visual models for image classification on ImageNet and 20 datasets in ELEVATER [27], image-text retrieval on COCO [30]/Flickr [41], as well as object detection and semantic segmentation on COCO [30]. The knowledge bases are considered as LAION [46] and larger web-crawled multimodal data. The retrieval-augmented knowledge ( $\\sim 3\\%$ image-text pairs compared with the original training data) significantly improves the model's zero-shot performance", + "bbox": [ + 75, + 734, + 470, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "without the need of accessing any images on downstream tasks. See Figure 1 for highlighted results. For example, our ViT-L/14 checkpoint achieves $78.5\\%$ zero-shot accuracy on ImageNet [10], surpassing all public checkpoints from CLIP [43] and OpenCLIP [18], including those with larger model size and trained on a much larger LAION-2B [45]. The new customized models demonstrate higher few/full-shot performance than the generic model counterparts.", + "bbox": [ + 496, + 330, + 893, + 450 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our retrieval system, codebase, and pre-trained models are publicly available. To make this line of research more accessible, our retrieved subsets for both ELEVATER and ImageNet will also be made available, with an easy-to-use toolkit to download the subsets without storing the whole dataset locally. It poses a feasible direction for leveraging the ever-increasing data from the Internet for customized visual recognition, especially for the low-resource regimes.", + "bbox": [ + 496, + 453, + 893, + 575 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 588, + 640, + 604 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Vision-Language Pretraining. Learning transferable visual representations from natural language supervision is an emerging research area. The pioneering works of CLIP [43] and ALIGN [20] make use of contrastive learning to pretrain models on billion-scale web-crawled image-text pairs. There are an increasing number of studies to improve their generality from various modeling perspectives, including training objectives [11,13,14,38,65,68], scaling techniques [9,40,65], data efficiency [25,28], and leveraging multilingual correlations [9, 19]. In academia, several works demonstrate techniques to improve the learned semantic representations on datasets at a smaller scale (e.g. CC3M [47], CC12M [4], YFCC15M [43, 51]), by exploring pretraining on a unified image-text-label space [59], token-level contrastive loss [61], and auxiliary within-modality contrastive loss [29,37,58,63]. Complementary to the above works, we build on top of existing pre-trained generic models, and aim to improve the model's performance by customizing them using retrieved relevant image-text pairs.", + "bbox": [ + 496, + 612, + 895, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "15149", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Retrieval-Augmented Models. In natural language processing, several works augment large language models with external data encoded with structured language and relation representations [3, 15, 22, 26, 31, 39, 66]. Motivated by retrieval-augmented models in NLP, several recent works leverage visual and / or textual knowledge to improve classification [32], question answering [7, 35, 56, 60], image generation [2, 8, 49, 72], and multi-modal tasks simultaneously [62]. RAC [32] improves long-tail classification by retrieving from a non-parametric memory consisting of pre-encoded images and text. K-LITE [48] enhances the text prompts with the retrieved external knowledge that is encoded in natural language. Our paper leverages the paired knowledge of image-text and aims to improve task transfer performance for core vision problems such as classification, retrieval, detection and segmentation.", + "bbox": [ + 75, + 90, + 472, + 332 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Adaptation of Vision-Language models. CLIP demonstrates impressive zero-shot and linear probing performance on different downstream domains. Several works explore improving the domain adaptation performance on CLIP models. ELEVATER [27] leverages the text encoder outputs to initialize the task-specific linear head to improve the linear probe and finetuning performance of CLIP. Inspired by prompting techniques in NLP, recent works [44, 71] make use of learnable prompts that are trained on a few samples on downstream tasks. Similar to these works, this paper aims to improve CLIP's performance on downstream tasks, while making use of relevant image-text pairs data to improve the model's performance, without access to the downstream images. Furthermore, when downstream samples are available, they are complimentary to our method.", + "bbox": [ + 75, + 337, + 473, + 565 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Retrieval-Augmented Customization", + "text_level": 1, + "bbox": [ + 76, + 571, + 408, + 588 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Preliminaries", + "text_level": 1, + "bbox": [ + 76, + 593, + 217, + 607 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Computer vision models have achieved strong transfer performance, when learning with large-scale image data only [17], image-label data [23] and/or image-caption data [43,59,67]. Without loss of generality, we follow [59] and define a unified triplet-wise format $(\\pmb{x},\\pmb{t},y)$ for imagetext-label data, where $\\pmb{x}\\in \\mathcal{X}$ is an image, $t\\in \\mathcal{T}$ is its language description, and $y\\in \\mathcal{V}$ is a label indicating the index of the unique language description in the dataset. In a general form, the language description is a text sequence $\\pmb{t} = [t_1,\\dots ,t_L]$ . It ranges from simple category names representing visual concepts when $L$ is small, to more freeform and semantic-rich sentences such as captions when $L$ is relatively large.", + "bbox": [ + 75, + 613, + 470, + 809 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "A typical transfer learning pipeline follows the procedure of pre-training then adaptation: (i) With large-scale pre-training, an image encoder foundation model $f_{\\theta}$ parameterized by $\\pmb{\\theta}$ is first trained to represent image $\\pmb{x}$ as a visual feature vector $\\tilde{\\pmb{v}} \\in \\mathbb{R}^{P \\times 1}$ : $\\tilde{\\pmb{v}} = f_{\\pmb{\\theta}}(\\pmb{x})$ . For recent language-image models [43], a dual-encoder architecture is often em", + "bbox": [ + 75, + 810, + 472, + 901 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/f674ef5e8723b3692b6a283aac0be7715c7d250628eabf9d4ba752065d26ca35.jpg", + "image_caption": [ + "Figure 2. Illustration of the proposed REACT framework." + ], + "image_footnote": [], + "bbox": [ + 514, + 92, + 874, + 311 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "ployed, where an additional text encoder $f_{\\phi}(\\pmb{t})$ parameterized by $\\phi$ represents the sentence $\\tilde{\\pmb{u}} \\in \\mathbb{R}^{P \\times 1} : \\tilde{\\pmb{u}} = f_{\\phi}(\\pmb{t})$ . (ii) Given a downstream task, model adaptation is typically performed using the available task-specific information, or task instruction $\\mathcal{I}$ . For example, the task-level transfer of a language-image model is described as:", + "bbox": [ + 496, + 344, + 893, + 434 + ], + "page_idx": 2 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Zero-shot. In a customized setting, the simplest task definition can be provided as a set of category names for visual recognition, leading to the task instruction $\\mathcal{I}_0 = \\{t\\}$ . No training image $x$ is available, not to mention the corresponding label $y$ .", + "- Few/Full-shot. The users may spend annotation cost to curate $N$ image-label pairs as the training instances, making the task instruction more specific, $\\mathcal{I}_{\\mathrm{F}} = \\{(x_{n},t_{n},y_{n})\\}_{n = 1}^{N}$ , which allows updating the image encoder model $f_{\\theta}$ for better adaptation performance." + ], + "bbox": [ + 506, + 438, + 893, + 595 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this paper, we assume there exists a web-scale image-text corpus as the external knowledge source $S = \\{(x_{m}, t_{m})\\}_{m=1}^{M}$ , where $M$ is the database size, e.g. 400M for LAION [46]. One may use the task instruction $\\mathcal{I}$ as a query to seek additional relevant knowledge to build a more transferable visual system. Given the downstream task instruction $\\mathcal{I}$ and an external knowledge source $S$ , our goal is to learn customized visual-semantic representations, which are readily transferable to the downstream task of interest, whose training and evaluation images are not observed during the customization process. To this end, we propose REACT. We illustrate the high-level idea in Figure 2, and describe the process as follows.", + "bbox": [ + 496, + 598, + 893, + 795 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Multi-modal External Knowledge", + "text_level": 1, + "bbox": [ + 500, + 804, + 795, + 820 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Knowledge Base Construction. We explore web-scale image-text data as the multi-modal knowledge base $S$ in this paper. Ideally, one may consider the entire web as the knowledge base, and use Google or Bing search to retrieve the relevant knowledge. We consider two large static datasets", + "bbox": [ + 496, + 824, + 893, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "15150", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "with image-text pairs. To control the experiment complexity and ensure reproducibility, we use LAION-400M [46], a publicly available database with 400M pairs, for most of the experiments. To further study the scaling influence of the retrieval base, we conduct comparisons on Web-800M, a privately collected web database with 800M pairs.", + "bbox": [ + 75, + 90, + 468, + 181 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To facilitate an efficient knowledge acquisition process, we use pre-trained contrastive models (e.g. CLIP) as the feature extractor, and build a cross-modal retrieval system using FAISS [21]. We use its Hierarchical Navigable Small World (HNSW) approximate $k$ -NN lookup [34] to balance performance and efficiency. Please see appendix for more details. After the retrieval system is built on the designated retrieval pool, it can be efficiently used for retrieving relevant image-text pairs for various downstream domains.", + "bbox": [ + 75, + 181, + 470, + 316 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Retrieval-Augmented Task Instruction. To facilitate the same interface for various customized visual tasks in the wild, it is desirable to have the same uniform task instruction schema. In NLP, all task instructions can follow the same uniform schema, composed of task definition and positive/negative examples [36, 55]. Here, the task definition defines a given task in natural language, completely specifying how an input is expected to be mapped to an output text. We note a coherence connection between this NLP task schema and the customized zero/few/full-shot CV settings in Section 3.1. Following a similar schema, the minimum requirement to specify a visual task is the task definition $\\mathcal{I}_0$ , where category names illustrate the target visual concepts in natural language. Though adding human-annotated examples is a natural way to clarify the task and yield the complete schema $\\mathcal{I}_{\\mathrm{F}}$ , extra cost is introduced.", + "bbox": [ + 75, + 323, + 468, + 564 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "It is of high interest to clarify the task using relevant examples, without human curating cost. Therefore, we propose to augment the task instruction with the retrieved examples from the external multi-modal knowledge base $S$ . For each concept $t \\in \\mathcal{I}_0$ in a given task, we first represent it in natural language $q = g_{prompt}(t)$ using the language prompt as in [43], through inserting the concept into a set of task-specific templates $\\mathcal{P}$ . The task definition is expanded in its natural language form:", + "bbox": [ + 75, + 566, + 470, + 702 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {Q} = \\left\\{\\boldsymbol {q} \\mid \\boldsymbol {q} = g _ {\\text {p r o m p t}} (\\boldsymbol {t}), \\forall \\boldsymbol {t} \\in \\mathcal {I} _ {0}, \\text {p r o m p t} \\in \\mathcal {P} \\right\\}. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 96, + 714, + 470, + 732 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Next, we perform our knowledge retrieval process to acquire the relevant image-text pair $s = g_{\\text{retrieve}}(q)$ from the source $S$ . Two types of retrieval processes are considered to acquire the top- $K$ pairs:", + "bbox": [ + 75, + 744, + 468, + 806 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "- Text-to-Text (T2T) retrieval allows us to retrieve more relevant examples as they have a better match with our target concept. The T2T-retrieved set for $\\mathcal{I}_0$ is:", + "bbox": [ + 83, + 809, + 468, + 854 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {S} ^ {T 2 T} = \\left\\{\\left(\\boldsymbol {x}, \\boldsymbol {t}\\right) \\in \\mathcal {S}: \\underset {\\boldsymbol {t} \\in \\mathbb {T}, | \\mathbb {T} | = K} {\\operatorname {a r g m a x}} f _ {\\phi} (\\boldsymbol {t}) ^ {\\top} f _ {\\phi} (\\boldsymbol {q}), \\forall \\boldsymbol {q} \\in \\mathcal {Q} \\right\\} \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 867, + 468, + 893 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "- Text-to-image (T2I) retrieval allows us to have more diversity in the text descriptions in our retrieved examples. The T2I-retrieved set for $\\mathcal{I}_0$ is:", + "bbox": [ + 506, + 90, + 893, + 135 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {S} ^ {T 2 I} = \\left\\{\\left(\\boldsymbol {x}, \\boldsymbol {t}\\right) \\in \\mathcal {S}: \\underset {\\boldsymbol {x} \\in \\mathbb {X}, | \\mathbb {X} | = K} {\\operatorname {a r g m a x}} f _ {\\boldsymbol {\\theta}} (\\boldsymbol {x}) ^ {\\top} f _ {\\boldsymbol {\\phi}} (\\boldsymbol {q}), \\forall \\boldsymbol {q} \\in \\mathcal {Q} \\right\\} \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 143, + 893, + 170 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Both $S^{T2T}$ and $S^{T2I}$ are retrieved examples to augment the task definition $\\mathcal{I}_0$ , without accessing the images in the training or validation set of the task. Compared to $\\mathcal{I}_{\\mathrm{F}}$ , they are \"free\" external knowledge to clarify the task and can be used to build a more transferable system.", + "bbox": [ + 496, + 178, + 893, + 255 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Model Customization", + "text_level": 1, + "bbox": [ + 500, + 263, + 702, + 277 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "After retrieving the relevant multi-modal examples, one may employ the naive customization solution by fine-tuning the full-model initialized from pre-trained weights, as in Figure 3(a). Alternatively, we propose an affordable solution to endow pre-trained models with a new capability to leverage this external knowledge. The pre-trained generic visual models have gained strong transfer abilities and access to a large amount of internal knowledge stored in the model weights. We freeze the weights of these models so that their initial capacity remains unchanged. To bridge these pretrained models harmoniously to the customized domain, we consider locked-text gated-image tuning with the following two techniques, illustrated in Figure 3(d).", + "bbox": [ + 496, + 279, + 893, + 474 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Modularized Image Encoder. In order to provide sufficient expressivity to the model and make it able to adapt well on retrieved knowledge, we insert gated self-attention dense blocks in between the original layers of the image encoder, and train the new blocks from scratch. Those blocks are made of a self-attention layer, that attends the early layer inputs, followed by an extra dense feed-forward layer. Please see a visual illustration of this gated block in the rightmost of Figure 3(d). We denote the parameters of all new modules as $\\theta^{\\prime}$ . This design is inspired by the gated cross-attention-dense blocks in Flamingo [1] and frozen multi-modal model [52]. The difference is that the trainable module is introduced in Flamingo to enable cross-modal conditioning, while we adapt it for model growing in new customized domains.", + "bbox": [ + 496, + 479, + 893, + 691 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Frozen Text Encoder. The text encoder in language-image contrast models represents the task semantic space. To maintain it, we propose locked-text tuning, which freezes the text model weights so that the generic task encoding knowledge remains locked; see Figure 3(c). This is in contrast with locked-image tuning (LiT) [68] in Figure 3(b), where the image encoder is frozen and the text encoder is fine-tuned, which teaches a text model to read out good representations from a pre-trained image model for new tasks.", + "bbox": [ + 496, + 696, + 893, + 830 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We extract the normalized feature vectors in a hypersphere using $\\pmb{u}_i = \\frac{f_{\\{\\theta,\\theta'\\}}(\\pmb{x}_i)}{\\|f_{\\{\\theta,\\theta'\\}}(\\pmb{x}_i)\\|}$ and $\\pmb{v}_j = \\frac{f_\\phi(\\pmb{t}_j)}{\\|f_\\phi(\\pmb{t}_j)\\|}$ . To customize the model wrt task definition $\\mathcal{I}_0$ , we update $\\pmb{\\theta}'$ using a bidirectional learning objective between images and", + "bbox": [ + 496, + 832, + 893, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "15151", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/3df86e83fc2f06e2971e5ba6a241053f435a20de8cfe0867cf3119e51ef536a3.jpg", + "image_caption": [ + "(a) Full-Model Tuning" + ], + "image_footnote": [], + "bbox": [ + 96, + 89, + 236, + 167 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/198e42f8f7eb524f7277a0d5e1397cde87666638f9c4b175258af7e39de42044.jpg", + "image_caption": [ + "(b) Locked-Image Tuning" + ], + "image_footnote": [], + "bbox": [ + 251, + 90, + 385, + 167 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/d78649bbb20b100f35b173ed6c8b5612a7cb576d4441c247b84f70cadd3ea9ec.jpg", + "image_caption": [ + "(c) Locked-Text Tuning" + ], + "image_footnote": [], + "bbox": [ + 401, + 90, + 535, + 167 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/8551b6c257124e74960d84c541ec0e015c7470c253853ceb26dcb6209140e602.jpg", + "image_caption": [ + "(d) Locked-Text Gated-Image Tuning" + ], + "image_footnote": [], + "bbox": [ + 563, + 90, + 694, + 167 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/eee419d6ba26107e5e71a72b76ec94de1b06e9b0cd8f588d3be4d9ec30a086b0.jpg", + "image_caption": [ + "Figure 3. Illustrative comparisons across different model tuning methods. (a) and (b) are existing baseline tuning methods. For model customization in a target domain, we found that (c) and (d) work better. One layer of the proposed modularized image encoder in locked-text gated-image tuning is illustrated in right side." + ], + "image_footnote": [], + "bbox": [ + 709, + 90, + 874, + 196 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "language on the retrieved knowledge pool $S^{T2T}$ and/or $S^{T2I}$ :", + "bbox": [ + 76, + 258, + 470, + 275 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\min _ {\\left\\{\\boldsymbol {\\theta} ^ {\\prime} \\right\\}} \\mathcal {L} _ {\\mathrm {C}} = \\mathcal {L} _ {i 2 t} + \\mathcal {L} _ {t 2 i}, \\text {w i t h} \\mathcal {B} \\sim \\mathcal {S} ^ {T 2 T} \\text {o r} \\mathcal {S} ^ {T 2 I} (4) \\\\ \\mathcal {L} _ {i 2 t} = - \\sum_ {i \\in \\mathcal {B}} \\frac {1}{| \\mathcal {P} (i) |} \\sum_ {k \\in \\mathcal {P} (i)} \\log \\frac {\\exp \\left(\\tau \\boldsymbol {u} _ {i} ^ {\\top} \\boldsymbol {v} _ {k}\\right)}{\\sum_ {j \\in \\mathcal {B}} \\exp \\left(\\tau \\boldsymbol {u} _ {i} ^ {\\top} \\boldsymbol {v} _ {j}\\right)} \\quad \\text {a n d} (5) \\\\ \\mathcal {L} _ {t 2 i} = - \\sum_ {j \\in \\mathcal {B}} \\frac {1}{| \\mathcal {Q} (j) |} \\sum_ {k \\in \\mathcal {Q} (j)} \\log \\frac {\\exp (\\tau \\boldsymbol {u} _ {k} ^ {\\top} \\boldsymbol {v} _ {j})}{\\sum_ {i \\in \\mathcal {B}} \\exp (\\tau \\boldsymbol {u} _ {i} ^ {\\top} \\boldsymbol {v} _ {j})} (6) \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 91, + 297, + 470, + 402 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\tau$ is a temperature hyper-parameter controlling the strength of penalties on hard negative samples, and $\\mathcal{P}(i) = \\{k|k\\in \\mathcal{B},\\pmb{v}_k^\\top \\pmb{v}_i\\geq \\gamma \\}$ , $\\mathcal{Q}(j) = \\{k|k\\in \\mathcal{B},\\pmb{v}_k^\\top \\pmb{v}_j\\geq \\gamma \\}$ . We set $\\gamma = 0.9$ for classification tasks to force image-text pairs sharing the similar text to be positive. Note (4) is a general form; it reduces to UniCL [59] when $\\gamma = 1.0$ ; it further reduces to the training objective of CLIP [43] when there is a one-to-one mapping between an image and its paired caption in a batch, i.e. $\\mathcal{P}(i) = \\{i\\}$ and $\\mathcal{Q}(j) = \\{j\\}$ .", + "bbox": [ + 76, + 410, + 468, + 545 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In our empirical study we find that locked pre-trained image and text encoders with trainable gated modules in image encoder work best. Once the customized visual models are trained with the retrieved knowledge, we transfer it to the downstream domain for zero/few/full-shot evaluation.", + "bbox": [ + 75, + 546, + 470, + 619 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 633, + 209, + 648 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we conduct experiments to answer three research questions: (1) What are the unique advantages of retrieval-augmented image-text knowledge for task transfer? (2) How does our design choice of locked-text gated-image tuning compare to existing methods for model customization? (3) Is customization still beneficial in settings where the training data in downstream tasks are observed, i.e., in few-shot or full-shot settings? (4) Does customization scales well to dense prediction tasks like detection/segmentation?", + "bbox": [ + 75, + 659, + 468, + 794 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We evaluate our models on four CV problems: image classification, image-text retrieval, object detection, and semantic segmentation. We first consider ImageNet [10] for zero-shot task transfer. We then further evaluate our model on ELEVATER [27], which is an open-set image classification benchmark that contains 20 datasets. We also conduct experiments on image-text retrieval with MSCOCO [30] and", + "bbox": [ + 75, + 795, + 470, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Flickr [64] dataset. Finally, we evaluate on object detection and semantic segmentation with MSCOCO [30] dataset.", + "bbox": [ + 498, + 258, + 890, + 290 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "One of the most intriguing benefits of REACT is that it does not need access to any images from the downstream task. Therefore, we first evaluate on task-level zero-shot transfer, which requires no images in the target to be observed [27, 43, 48]. This setting is different from traditional class-level zero-shot [57], where both the category and images in evaluation should not be observed in training. We argue that ImageNet concepts have been observed in CLIP (Sec. 2.2 of [43]) and other web-scale trained models [28], as WordNet synsets and common words in English Wikipedia are explicitly added in the query list when searching for (image, text) pairs in their training data construction process.", + "bbox": [ + 496, + 291, + 893, + 473 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Image Classification", + "text_level": 1, + "bbox": [ + 500, + 484, + 691, + 501 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1.1 Zero-Shot on ImageNet-1K", + "text_level": 1, + "bbox": [ + 500, + 508, + 743, + 525 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As shown in Table 1, by customizing the generic model CLIP/OpenCLIP on 10M retrieved image-text pairs from LAION-400M, REACT achieves a significant and consistent gain (up to $5.4\\%$ ) on zero-shot image classification on ImageNet-1K, with different backbones and original pretraining datasets. There are three interesting findings.", + "bbox": [ + 496, + 535, + 893, + 626 + ], + "page_idx": 4 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "F1: REACT can benefit from model's own pre-training data. Compared to OpenCLIP [18] (ViT-B/32) trained on LAION-400M, by training on 10M relevant pairs from the same LAION-400M dataset, REACT improves over OpenCLIP by $3.5\\%$ . Note that the model purely uses the image-text pairs that it has seen during its pre-training, and does not see any extra data. This shows that REACT can more adequately adapt to the target domain during the model customization stage, suggesting a favorable property that no new data is required for customization.", + "F2: REACT efficiently explores new image-text sources, even for large models. We customize CLIP [43] ViT-L/14 on 10M retrieved relevant image-text pairs, and the model achieves a $2.8\\%$ improvement to $78.1\\%$ . This surpasses the checkpoint with a much larger ViT-H/14 backbone and trained on a much larger LAION-2B dataset. This suggests that REACT is a more sample-efficient approach to improve the model performance on the domain-of-interest." + ], + "bbox": [ + 496, + 628, + 893, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "15152", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/49ed044e36e49bef23578deafef9c305b827faefca5000912cedbbec61de5013.jpg", + "image_caption": [ + "Figure 4. Zero-shot comparison on ELEVATER ICinW 20 datasets. REACT (B32) improves over the base checkpoints on most datasets." + ], + "image_footnote": [], + "bbox": [ + 130, + 90, + 831, + 234 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/75e472f09623f8d6a4e80c86324d0d9ae0d63f7a479f73788c24b26bf4840880.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
fθPretrain DataRetrieved DataMethodImageNet-1K Zero-Shot
DatasetSize
B/32WIT-400M--CLIP63.2
L-400M10MREACT68.6 (+5.4)
LAION-400M--OpenCLIP62.9
L-400M10MREACT66.4 (+3.5)
L/14WIT-400M--CLIP75.3
L-400M6MREACT77.6 (+2.3)
L-400M10MREACT78.1 (+2.8)
W-800M†6MREACT78.5 (+3.2)
LAION-400M--OpenCLIP72.8
LAION-2B--OpenCLIP75.3
H/14LAION-2B--OpenCLIP78.0
G/14LAION-2B--OpenCLIP80.1
L-2B12MREACT81.0 (+0.9)
", + "bbox": [ + 81, + 265, + 460, + 465 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "F3: Scaling up the retrieval pool increases performance. We perform REACT in a privately collected dataset with over 800M pairs, and train a customized model on 6M retrieved pairs. The performance is increased to $78.5\\%$ , yielding $0.9\\%$ gain compared with 6M pairs retrieved from LAION-400M. This suggests that REACT scales well with the larger retrieval pool. It showcases REACT as a cost-efficient approach to leveraging the ever-increasing web image-text corpus.", + "bbox": [ + 75, + 569, + 468, + 691 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1.2 Zero-, Few-, and Full-Shot on ELEVATER", + "text_level": 1, + "bbox": [ + 75, + 702, + 418, + 715 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "As a proxy for performing vision tasks for many customized scenarios in the wild, we consider the image classification in the wild (ICinW) benchmark in ELEVATER [27]. It consists of 20 datasets from a diverse selection of domains and covers a wide range of concepts, totaling 1151 classes.", + "bbox": [ + 75, + 719, + 468, + 794 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We perform multi-modal knowledge retrieval for 20 datasets together – the retrieved samples are around 10M image-text pairs in total, on which one single customized visual model is trained. After the process, we feed the customized model to different downstream tasks separately. For each downstream dataset, we use the official ELEVATER toolkit to obtain the train/val/test splits, and perform zero-", + "bbox": [ + 75, + 795, + 470, + 901 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/10b13eac23f60ed9015355823a0731a414c3bffd1e0317b8616dd05514f9e086.jpg", + "table_caption": [ + "Table 1. Comparison of zero-shot task transfer with public checkpoints from CLIP [43] and OpenCLIP [18]. LAION [45, 46] is abbreviated as \"L\" in the table. Web-800M†: a privately collected web database with 800M image-text pairs. By continue pretraining on only $\\sim 10\\mathrm{M}$ retrieved data, REACT outperforms all public CLIP/OpenCLIP checkpoints." + ], + "table_footnote": [], + "table_body": "
MethodZero-ShotFew-shotFull-shot
LPFTLPFT
CLIP56.865.463.378.480.4
REACT60.668.968.480.481.8
Gains(+3.8)(+3.5)(+5.1)(+2.0)(+1.4)
", + "bbox": [ + 509, + 265, + 879, + 354 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. The average scores of image classification performance on 20 datasets in ELEVATER. REACT consistently outperforms CLIP in both data-limited and data-rich regimes.", + "bbox": [ + 498, + 366, + 890, + 409 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "shot, few-shot, and full-shot evaluation.", + "bbox": [ + 500, + 426, + 763, + 440 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We report the average scores in Table 2. It achieves $3.8\\%$ improvement in the zero-shot setting, even when we do not perform a separate customization for different datasets. This demonstrates the robustness of our customization process. Further, we see the consistent improvement in few-shot and full-shot settings, including both linear probe (LP) and finetuning (FT). This result is encouraging, as it demonstrates that when we have access to some or all data from the downstream task, the proposed model customization stage remains beneficial. Therefore, we advocate model customization process in both data-limited and data-rich settings.", + "bbox": [ + 496, + 441, + 893, + 608 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Breakdown Analysis. Next, we ask why does the retrieved image-text knowledge improve the zero-shot task transfer performance on a broad range of datasets? We compare the breakdown performance on all 20 datasets in Figure 4 for the zero-shot settings. Out of 20 datasets, the retrieval-augmented knowledge shows superior/comparable/inferior performance to the baseline on $15/1/4$ datasets for CLIP and $14/0/6$ datasets for OpenCLIP, respectively. Most of the improved and failure datasets are consistent for both checkpoints. For the top two datasets that gains the most, i.e. StanfordCars and FGVC Aircraft, relevant image-text knowledge is retrieved from the web-crawled data LAION-400M to describe the concepts; see Fig. 5a. Interestingly, this observation is complementary to K-LITE [48], which failed on these two datasets, because no knowledge was extracted from Wiktionary for them, as it often requires domain-specific knowledge and even visual knowledge to best define a car brand (e.g. BMW X6 SUV or Audi R8) or an aircraft model type (e.g. DC-10 or A321).", + "bbox": [ + 496, + 613, + 893, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "15153", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/e32cb8ae3b4f71c97e183d1e5aa3ff1116fad3ba1d09aa4fdc00302304dbab0d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 80, + 90, + 99, + 104 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Task Samples", + "text_level": 1, + "bbox": [ + 102, + 93, + 184, + 104 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/501d8113c135f49941c2a54b4d435c12a4eb0ea65f782176423fccfdff0c6184.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 202, + 90, + 225, + 106 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Retrieved Image-Text Pairs", + "text_level": 1, + "bbox": [ + 230, + 93, + 387, + 104 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7e75ce7af7f12d489dc52627f6527f033876ac57037b65ff3eb1d3a272ab872e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 80, + 114, + 98, + 178 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a21e636a02e86ab3b9d1c317aaf20f5b78b667ab2752f96b5fca5a118f4e53c5.jpg", + "image_caption": [ + "BMW X6 SUV 2012" + ], + "image_footnote": [], + "bbox": [ + 107, + 111, + 194, + 138 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/13f46a21b96d7c9e34e16ad617eb387af41d45a7e28c71b6b676203e397fc69a.jpg", + "image_caption": [ + "Audi R8 Coupe 2012" + ], + "image_footnote": [], + "bbox": [ + 138, + 148, + 194, + 176 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/fd9fd6b19c7b89211f3ab403349de2abcad6cce003c9b71391f0b17a6f07298e.jpg", + "image_caption": [ + "Picture of 2012 BMW X6" + ], + "image_footnote": [], + "bbox": [ + 200, + 109, + 297, + 137 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/836326942944125799689230331d1999a3d4c8c5a5b66776d9baa0e09d726690.jpg", + "image_caption": [ + "Audi R8 At Moscow International Exhibition Motorshow 2008" + ], + "image_footnote": [], + "bbox": [ + 202, + 148, + 282, + 176 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/1a695ce25d5afa064e0e4245f2c6f7e24242eee0dc836c6a7ca75c360b957845.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 284, + 109, + 354, + 137 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/28b72d4390785e996dcc268a3cf3cfec8eaafcde4c760e5a9be19e0b3247655e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 354, + 109, + 403, + 137 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2253028c789170a085211bcf9a271783457a93622497549e658a56c6aea682fd.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 403, + 109, + 465, + 137 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/79028b1589bfb82e3fd1c68e62f964aa2e65d9d4dc74ba72e300f495aca50a7d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 84, + 191, + 98, + 255 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/951ec2d5c6466d8f91df5c338df43646c21d4812e36bd56ca9b4ce75ceed6cb8.jpg", + "image_caption": [ + "DC-10" + ], + "image_footnote": [], + "bbox": [ + 142, + 186, + 194, + 214 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/78910bc06d56426ebe91ca1176b9c35baa4795cb05d9086dc544a3f7dfbef4f1.jpg", + "image_caption": [ + "A321" + ], + "image_footnote": [], + "bbox": [ + 140, + 226, + 192, + 255 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6a7ebb974dcdc446242d6b7584c0fa4e2643f730261fd0d000fb8138b4b770d7.jpg", + "image_caption": [ + "DC-10 makes last passage" + ], + "image_footnote": [], + "bbox": [ + 200, + 186, + 266, + 215 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "", + "bbox": [ + 202, + 226, + 266, + 255 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "B-6007 - Airbus A320-2", + "bbox": [ + 202, + 255, + 297, + 262 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5e563c4433bb06c646b81e13144d8f0384d6b809c8064a460b93ed4598cb7102.jpg", + "image_caption": [ + "at passenger flight.", + "" + ], + "image_footnote": [], + "bbox": [ + 269, + 186, + 352, + 215 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/dad41504b79e475f8d840c0b7848556d42161ee16e20ceb33f341f113f2ea47b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 352, + 186, + 403, + 215 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/746ae41fc3f37b06a387684a4855d4e3932765f576cfc3ea419ab8c46b61d3bc.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 403, + 186, + 465, + 215 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/86a82a17da674cede984bb6f737b6a04f2a1b9defefd854ea553104f335fd440.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 410, + 215, + 465, + 255 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "", + "bbox": [ + 202, + 226, + 266, + 255 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a3410ba4a3ffa171156fab8a1489ea77b7c07b90a6f8128451ea85ab5e98eeb1.jpg", + "image_caption": [ + "B-6007-AirbusA320-2", + "tern Airlines" + ], + "image_footnote": [], + "bbox": [ + 269, + 226, + 352, + 255 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "A320-2", + "bbox": [ + 269, + 255, + 297, + 262 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a7469fb36b7d9f46b8dc5f5eb1a2927774849c55195a9adb0d0867343f0a079e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 352, + 226, + 403, + 255 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/9095605e1b0e945d0091944fe5810c91f6a2dde2f70b35728335d4b8b352fbbe.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 83, + 318, + 171, + 329 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4c13db2ddc6546ddcb6bca9907274fd0d11a771fc2f3d59898fd2de96d530f54.jpg", + "image_caption": [ + "lymph node", + "(b) Failure case. The dataset with the largest degradation in Fig. 4: PatchCamelyon [54]. LAION-400M has a low concept coverage on this domain, and the retrieved samples are in a different distribution from the target set.", + "Figure 5. Success and failure cases in ELEVATER benchmark. We show class name and the caption of the first retrieved image-text pairs, others are similar and omitted due to limited space." + ], + "image_footnote": [], + "bbox": [ + 80, + 330, + 140, + 378 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/79ce1fae714fd120da65ec24119407e9d2429f21986e46dbeec39bc309187135.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 143, + 325, + 204, + 332 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ba1f9c885d54741ac5426591119c4dbf4dd1fb216b587956ce9a58809e9b8439.jpg", + "image_caption": [ + "lymph ... tumor..." + ], + "image_footnote": [], + "bbox": [ + 143, + 332, + 204, + 378 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/9ff699e9f404b83eaf25e9fe24358c5a54964e08f4274f3a5be26f3a3b8fc94f.jpg", + "image_caption": [ + "(a) Success examples. The two datasets with largest improvement in Fig. 4: Stanford-Cars [24] and FGVC-Aircraft [33]. There is a high concept coverage for these datasets in LAION, resulting in a relevant and diverse retrieved set." + ], + "image_footnote": [], + "bbox": [ + 207, + 315, + 233, + 332 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/372387ae16abf53bc916284e86f3b202807404217d0b1c6cd43fe901256c7212.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 233, + 318, + 366, + 329 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2f05c6e4a0a51a07f25bef66fad85880e78726199f489cadc2ed23551512b93b.jpg", + "image_caption": [ + "Microscopic enlargement", + "ment of a mast cell." + ], + "image_footnote": [], + "bbox": [ + 207, + 330, + 279, + 378 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d8262108760abd6332cb4221c6c52239ede3d2f87b0f3f1e8c84687b4f7da9f2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 279, + 330, + 352, + 378 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ffc75e3e7e33f09274b6090e2162f07a9d6dcb13a3a3cd95441d6955f5e7c316.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 352, + 330, + 403, + 378 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/156c7230170a6f3b37a04fe854edfa0a6c3d5e94868782646c0e72258bf41dd9.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 406, + 330, + 467, + 378 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Limitations. As shown in Fig. 4, REACT struggles on the PatchCamelyon dataset, a cancer cell recognition benchmark. We visualize the retrieved samples and the samples from the original training set in Fig. 5b. The retrieved images are either instruction photos and from another sensing method, which exhibits a different visual distribution from PatchCamelyon. This suggests the importance of ensuring the retrieval quality for the domain-of-interest.", + "bbox": [ + 75, + 489, + 468, + 609 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Image-Text Retrieval", + "text_level": 1, + "bbox": [ + 76, + 619, + 274, + 636 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To demonstrate the generality of REACT, we consider Flickr30K [64] and MSCOCO [30] image-text retrieval tasks, in both zero-shot and full-shot settings. We use the standard image-text contrastive objective [43]. For image-text retrieval task, following [20, 43], we use the CLIP-L/14 with 336x336 input resolution in both zero-shot, customization, and fine-tuning stage. We use the captions from MSCOCO as queries to retrieve 6M image-text pairs and perform customization. Note that none of the caption queries are used in the model training stage.", + "bbox": [ + 75, + 643, + 468, + 795 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "As shown in Table 3, REACT improves the generic CLIP counterparts on both zero-shot and full-shot retrieval for Flickr30K and MSCOCO datasets. The gain on zero-shot task transfer is large. On Flickr30K, it achieves $3.4\\% /10.0\\%$ recall improvement for I2T and T2I retrieval, respectively. Afer fine-tuning on full training data, REACT still improves over the baseline slightly. It provides another piece of ev", + "bbox": [ + 75, + 795, + 470, + 901 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/4b10f50ab96134b5a712b78b58329ff2ee1426c755825636730a8a7cb2f58fd1.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodFlickr30KMSCOCO
Img → TextText → ImgImg → TextText → Img
R@1R@5R@1R@5R@1R@5R@1R@5
Zero-ShotImgBert [42]70.790.254.379.644.071.232.359.0
ALIGN [20]88.698.775.793.858.683.045.669.8
CLIP [43]88.098.768.790.658.481.537.862.4
CLIP†87.098.366.588.059.280.737.862.4
REACT90.499.176.593.763.385.147.572.0
Bletchley†90.898.278.094.066.785.648.972.7
REACT92.198.779.294.767.785.950.574.4
Fine-tunedGPO [5]88.798.976.194.568.190.252.780.2
ALIGN [20]95.399.884.997.477.093.559.983.3
CLIP†96.499.886.597.978.393.860.983.8
REACT96.699.986.898.078.794.061.184.1
", + "bbox": [ + 509, + 89, + 880, + 275 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/798cab432288ece2033a03bc4a4222da4d9d6fe5e8b0c7122b25a410b898a0a7.jpg", + "table_caption": [ + "Table 3. Image-text retrieval results on Flickr30K [41] and MSCOCO [30] datasets. CLIP†, Bletchley†: our evaluation." + ], + "table_footnote": [], + "table_body": "
Pretrain MethodBackboneRegion \nProposalsMSCOCO AP50
NovelBaseAll
Zero-ShotCLIPResNet-50GT58.658.258.3
REACTResNet-50GT58.9 (+0.3)59.4 (+1.2)59.3 (+1.0)
CLIPResNet-50RPN29.724.025.5
REACTResNet-50RPN31.6 (+1.9)25.4 (+1.4)27.0 (+1.5)
OVDCLIPResNet-50-14.252.842.7
REACTResNet-50-20.6 (+6.4)55.1 (+2.3)46.1 (+3.4)
", + "bbox": [ + 508, + 311, + 883, + 422 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 4. Zero-shot and open-vocabulary object detection results on MSCOCO [30] dataset using RegionCLIP [69] pipeline.", + "bbox": [ + 500, + 425, + 890, + 453 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "idence for REACT in data-rich settings. Furthermore, we conduct the same customization procedure of REACT on a large checkpoint Bletchley [53] with 864M parameters, and observe consistent gains over both datasets. It demonstrates that REACT scales well with model size on retrieval tasks.", + "bbox": [ + 498, + 469, + 890, + 544 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Dense Prediction Tasks", + "text_level": 1, + "bbox": [ + 500, + 555, + 714, + 569 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Although REACT is optimized with the image-level contrastive loss during the customization stage, we find it beneficial for dense prediction tasks as well. We showcase its application to dense prediction tasks on object detection and semantic segmentation.", + "bbox": [ + 498, + 578, + 893, + 654 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Object Detection. For object detection, we choose the state-of-the-art RegionCLIP [69] as our framework. We conduct experiments in two settings: zero-shot inference and open-vocabulary object detection (OVD) on MSCOCO dataset. We perform the model customization following the same setting as Sec. 4.2. Following RegionCLIP, we conduct experiments on ResNet50 backbone. The results are shown in Table 4. REACT consistently improves over CLIP checkpoint under all settings.", + "bbox": [ + 496, + 657, + 893, + 794 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "For zero-shot inference, when ground-truth region proposal is used, REACT improves over CLIP by $+1.0$ on overall AP50; when the pretrained RPN is used, REACT demonstrates $+1.5 / + 1.4 / + 1.9$ AP50 improvements on novel, base, and all classes, respectively.", + "bbox": [ + 496, + 795, + 893, + 869 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "For OVD, we can see that with the REACT, the detector yields improved performance on base with $+2.3$ AP50, and", + "bbox": [ + 498, + 869, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "15154", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/83e846449c46ffb3280b37904d5c81bfe91cb3cb33d3605a26fb0ed5168b9975.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodmIoU
zero-shotw/ refinew/ finetune
MaskCLIP [70]12.514.618.1
REACT (Locked-Text)14.4 (+1.9)18.2 (+3.6)20.7 (+2.6)
REACT (Locked-Text Gated-Image)14.5 (+2.0)16.3 (+1.7)19.2 (+1.1)
", + "bbox": [ + 81, + 89, + 460, + 152 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "importantly, it significantly improves novel categories with +6.4 AP50. This suggests that the injected knowledge during the model customization stage improves the learned fine-grained visual feature that is beneficial to both seen and unseen categories for object detection, when the downstream coarse-grained data is available. This is favored, because (1) the weakly-supervised data such as the coarse-grained image-text pairs requires much less human annotation cost than fine-grained bounding box annotation, (2) the paired data in REACT is free, as it is retrieved from the web, where COCO image-text pairs are not used in customized training.", + "bbox": [ + 75, + 196, + 468, + 362 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Semantic Segmentation. For semantic segmentation, we choose the state-of-the-art MaskCLIP [70] as the framework. It investigates three evaluation settings for segmentation. First, it makes use of the pretrained CLIP checkpoint to discover the alignment between grid visual features and the text prompt features, so as to perform zero-shot semantic segmentation. Second, to further improve the performance, MaskCLIP [70] proposes two techniques for refining its zero-shot predictions: key smoothing and prompt denoising. Lastly, when the training images are available, without the need to access the training labels, it further proposes MaskCLIP + [70] to perform full-shot finetuning on the target training set using pseudo-labels. Following MaskCLIP [70], we use ViT-B/16 checkpoints, and use their official code base to train and evaluate models. We report results in Table 5.", + "bbox": [ + 75, + 364, + 470, + 589 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "On all of the three settings, REACT demonstrates improvements over the MaskCLIP. Notably, when refinement techniques are used, REACT with locked-text tuning demonstrates a significant $3.6\\%$ gain in mIoU. Surprisingly, without seeing the downstream COCO images, the zero-shot evaluation of REACT (18.2) even slightly outperforms MaskCLIP+ (18.1), which is finetuned on the downstream training COCO images with self-training.", + "bbox": [ + 75, + 590, + 468, + 712 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Summary. These results are encouraging, as it shows that the customized knowledge from REACT transfers well to dense prediction tasks like detection and segmentation.", + "bbox": [ + 75, + 714, + 467, + 758 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Ablation Studies", + "text_level": 1, + "bbox": [ + 76, + 771, + 240, + 786 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We ablate REACT on ImageNet with CLIP ViT-B/32 checkpoint, with 10M retrieved image-text pairs from LAION-400M. See more ablations in supplementary.", + "bbox": [ + 75, + 792, + 467, + 838 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Tuning strategy. We ablate the design choices in the model customization stage: (1) direct tuning the pre-trained weights vs. training gated blocks from scratch; (2) updating visual vs.text encoder. We report results in Table 6. First, a frozen text", + "bbox": [ + 75, + 839, + 468, + 898 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/1a8452e49127c1cfd40ec3047b19ed1c48d9002393ab571babb539135bf76a81.jpg", + "table_caption": [ + "Table 5. Zero-shot and annotation-free semantic segmentation results on COCO Stuff [30] using MaskCLIP [70] (ViT-B/16)." + ], + "table_footnote": [], + "table_body": "
MethodVisualText# Train.IN1K Acc.COCO R@1 T2II2T
DirectCLIP [43]XX-63.248.829.9
Locked-Image [68]X✓63.4M63.750.534.2
Locked-Text✓X88.1M66.951.136.1
Full-model✓✓151.3M64.354.337.9
GatedX✓18.9M63.049.533.5
Locked-Text Gated-Image✓X42.5M68.653.438.1
✓✓89.8M68.754.339.9
", + "bbox": [ + 501, + 88, + 883, + 179 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "encoder consistently outperforms a frozen visual encoder. We conjecture the phenomenon is due to that the retrieved texts have a much more limited space, comparing to text space in the original pre-training set (e.g. LAION-400M), as the concepts are limited to the query classes from the target domain. Therefore, fine-tuning the text encoder may tend to collapse the pre-trained semantic space.", + "bbox": [ + 496, + 247, + 893, + 353 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We advocate two tuning methods for model customization. Locked-text gated-image tuning has a strong adaptation power, and is efficient in the model customization stage, with fewer trainable parameters. Locked-text tuning is also an effective way of customizing the models to downstream tasks, without the need of adding extra parameters. By default, we use gated blocks for its superior performance and efficiency.", + "bbox": [ + 496, + 356, + 893, + 462 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Retrieval size. We observe that training with a small retrieval size is more likely to overfit. We find that a larger retrieval size generally yields better performance, and saturates at around 6-10M image-text pairs.", + "bbox": [ + 498, + 469, + 893, + 529 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/7a90056d3408b9113084d99178a8581430d2989ab8245cc09d0eb7e525e69a30.jpg", + "table_caption": [ + "Table 6. Ablation: tuning strategy. For our model customization purpose, we advocate locked-text (gated-image) tuning methods in gray rows. $\\checkmark$ : trainable, $\\mathcal{X}$ : locked." + ], + "table_footnote": [], + "table_body": "
Retrieval Size01M3M6M10M
ImageNet-1K Accuracy63.264.866.968.668.6
", + "bbox": [ + 513, + 536, + 875, + 564 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 593, + 617, + 608 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We presented REACT, a plug-and-play framework for leveraging large-scale image-text corpus as external knowledge to efficiently customize models on downstream tasks. Extensive experiments demonstrate its generality and effectiveness in image classification, image-text retrieval, object detection, and semantic segmentation, on more than 20 different downstream datasets. We highly advocate the model customization stage for building more transferable visual system for different downstream tasks.", + "bbox": [ + 496, + 621, + 893, + 756 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement. This work was supported in part by NSF CAREER IIS2150012, NASA 80NSSC21K0295, and Institute of Information & communications Technology Planning & Evaluation(IITP) grants funded by the Korea government(MSIT) (No. 2022- 0-00871, Development of AI Autonomy and Knowledge Enhancement for AI Agent Collaboration) and (No. RS-2022-00187238, Development of Large Korean Language Model Technology for Efficient Pre-training).", + "bbox": [ + 496, + 763, + 893, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "15155", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Jean-Baptiste Alayrac, Jeff Donahue, Pauline Luc, Antoine Miech, Iain Barr, Yana Hasson, Karel Lenc, Arthur Mensch, Katie Millican, Malcolm Reynolds, et al. 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Lafite2: Few-shot text-to-image generation. arXiv preprint arXiv:2210.14124, 2022. 3" + ], + "bbox": [ + 503, + 92, + 893, + 388 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "15158", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Learning Customized Visual Models With Retrieval-Augmented Knowledge/5534a4dd-73bd-49cc-aaa8-1125042ab403_model.json b/2023/Learning Customized Visual Models With Retrieval-Augmented Knowledge/5534a4dd-73bd-49cc-aaa8-1125042ab403_model.json new file mode 100644 index 0000000000000000000000000000000000000000..e7c60c978f9d8bba000a50016e826d38558a9623 --- /dev/null +++ b/2023/Learning Customized Visual Models With Retrieval-Augmented Knowledge/5534a4dd-73bd-49cc-aaa8-1125042ab403_model.json @@ -0,0 +1,3027 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.107, + 0.131, + 0.865, + 0.154 + ], + "angle": 0, + "content": "Learning Customized Visual Models with Retrieval-Augmented Knowledge" + }, + { + "type": "text", + "bbox": [ + 0.107, + 0.181, + 0.862, + 0.252 + ], + "angle": 0, + "content": "Haotian Liu†§◆ Kilho Son‡ Jianwei Yang‡ Ce Liu‡ Jianfeng Gao‡ Yong Jae Lee† Chunyuan Li†¶ University of Wisconsin–Madison ‡ Microsoft {lht,yongjaeelee}@cs.wisc.edu {kilhoson, jianwyan, ce.liu, jfgao, chunyl}@microsoft.com https://react-v1.github.io" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.287, + 0.314, + 0.303 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.319, + 0.474, + 0.607 + ], + "angle": 0, + "content": "Image-text contrastive learning models such as CLIP have demonstrated strong task transfer ability. The high generality and usability of these visual models is achieved via a web-scale data collection process to ensure broad concept coverage, followed by expensive pre-training to feed all the knowledge into model weights. Alternatively, we propose REACT, REtrieval-Augmented CusTomization, a framework to acquire the relevant web knowledge to build customized visual models for target domains. We retrieve the most relevant image-text pairs (\\(\\sim 3\\%\\) of CLIP pre-training data) from the web-scale database as external knowledge and propose to customize the model by only training new modularized blocks while freezing all the original weights. The effectiveness of REACT is demonstrated via extensive experiments on classification, retrieval, detection and segmentation tasks, including zero, few, and full-shot settings. Particularly, on the zero-shot classification task, compared with CLIP, it achieves up to \\(5.4\\%\\) improvement on ImageNet and \\(3.7\\%\\) on the ELEVATER benchmark (20 datasets)." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.655, + 0.21, + 0.67 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.681, + 0.472, + 0.864 + ], + "angle": 0, + "content": "It has been a fundamental research problem in computer vision (CV) to build a transferable visual system that can easily adapt to a wide range of downstream tasks. With remarkable advances in deep learning, a de facto solution to achieve this is to train deep neural networks on a large amount of data to pursue the so-called generic visual representations. This dates back to the standard supervised training on ImageNet [10], whose superb representation power is further demonstrated in BiT [23]/ViT [12] by scaling up the training to JFT300M [50]. Along the way, recent efforts have been applied to the popular image self-supervised learning [6, 16, 17] to reduce the demand for labeled data. The" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.288, + 0.895, + 0.364 + ], + "angle": 0, + "content": "third approach is image-text contrastive learning trained on billion-scale web-crawled image-text pairs. Such models, like CLIP [43] and ALIGN [20], are able to achieve great performance on different downstream domains, without the need of any human labels." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.366, + 0.896, + 0.624 + ], + "angle": 0, + "content": "Excellent empirical performance has been achieved with the above three pre-training methods, by following the well established two-stage pre-training then adaptation pipeline: model pre-training from scratch on large data, then model adaptation directly on downstream tasks. Specifically, the pre-trained models are adapted to downstream tasks by considering the available task-specific samples only: either evaluated in a zero-shot task transfer manner, or updated using linear probing (LP) [43], finetuning (FT) [27], or prompt tuning [44, 71]. Following this two-stage pipeline, most research has reverted to the faith that building transferable visual systems is equivalent to developing more generic visual models by feeding all knowledge in the model pre-training stage. Therefore, the community has been witnessing a trend in exploring scaling success of pre-training model and data size with less care on the target domain, hoping that the model can adapt to any downstream scenario." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.627, + 0.897, + 0.793 + ], + "angle": 0, + "content": "In this paper, we argue that the conventional two-stage pipeline above is over-simplified and less efficient, in achieving the goal of building a transferable visual system in real-world settings. Instead, we propose a customization stage in between the pre-training and adaptation, where customization is implemented by systematically leveraging retrieved external knowledge. The inspiration comes from how humans are specialized in society for better generalization: instead of trying to memorize all concepts, humans are trained/prepared in a relevant subject to master a certain skill, while maintaining the basic skills in pre-training." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.897, + 0.903 + ], + "angle": 0, + "content": "To this end, we explore a systematic approach to acquire and learn with external knowledge sources from a large image-text corpus for model customization. The process of collecting external image-text knowledge is fully automatic without extra human annotation. The acquired knowledge typically contains richer information about the concept: relevant images that never appear in the downstream training" + }, + { + "type": "page_footnote", + "bbox": [ + 0.076, + 0.875, + 0.47, + 0.901 + ], + "angle": 0, + "content": "\\(\\spadesuit\\) core contribution; equal advising; work initiated during an internship at Microsoft." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "15148" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.09, + 0.262, + 0.243 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.267, + 0.091, + 0.438, + 0.243 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.451, + 0.091, + 0.877, + 0.245 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.249, + 0.895, + 0.318 + ], + "angle": 0, + "content": "Figure 1. REACT achieves the best zero-shot ImageNet performance among public checkpoints (Left), achieves new SoTA on semi-supervised ImageNet classification in the \\(1\\%\\) labeled data setting (Middle), and consistently transfer better than CLIP on across a variety of tasks, including ImageNet classification, zero/few/full-shot classification on 20 datasets in ELEVATER benchmark, image-text retrieval, object detection and segmentation (Right). Please see the detailed numbers and settings in the experimental section. For the left figure, circle size indicates model size." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.331, + 0.471, + 0.468 + ], + "angle": 0, + "content": "and evaluation set, and richer text descriptions about concept semantics. Such multi-modal knowledge sources are generally available on the web, and further open-sourced like LAION [45, 46]. They cover a variety of domains, making it possible to develop customized visual models for task-level transfer. Similar retrieval-augmented intuitions have been exploited in computer vision for class-level transfer [32], but not yet for task-level transfer (similar to that of CLIP). Our main findings/contributions can be summarized as follows." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.473, + 0.471, + 0.73 + ], + "angle": 0, + "content": "We propose to explore the potential of the web-scale image-text corpus as external knowledge to significantly improve task-level transfer performance on the target domain at an affordable cost. A simple and effective strategy is proposed. To begin with, we build a large-scale multimodal indexing system to retrieve the relevant image-text pairs using CLIP features and approximate nearest neighbor search. For a CV problem, the task instruction is often sufficiently specified with text such as class names, which allows us to utilize them as queries to retrieve the relevant image-text pair knowledge from the indexing system. No images from the CV problem are needed. To efficiently build the customized visual model, we propose a novel modularized learning strategy: only updating the additional trainable weights on the retrieved knowledge, and freezing the original model weights. Hence, the model masters the new skill without forgetting basic skills." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.472, + 0.903 + ], + "angle": 0, + "content": "The generality and effectiveness of the proposed customization strategy is demonstrated on four CV problems. We instantiate it with CLIP, and develop the customized visual models for image classification on ImageNet and 20 datasets in ELEVATER [27], image-text retrieval on COCO [30]/Flickr [41], as well as object detection and semantic segmentation on COCO [30]. The knowledge bases are considered as LAION [46] and larger web-crawled multimodal data. The retrieval-augmented knowledge (\\(\\sim 3\\%\\) image-text pairs compared with the original training data) significantly improves the model's zero-shot performance" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.331, + 0.895, + 0.452 + ], + "angle": 0, + "content": "without the need of accessing any images on downstream tasks. See Figure 1 for highlighted results. For example, our ViT-L/14 checkpoint achieves \\(78.5\\%\\) zero-shot accuracy on ImageNet [10], surpassing all public checkpoints from CLIP [43] and OpenCLIP [18], including those with larger model size and trained on a much larger LAION-2B [45]. The new customized models demonstrate higher few/full-shot performance than the generic model counterparts." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.454, + 0.895, + 0.577 + ], + "angle": 0, + "content": "Our retrieval system, codebase, and pre-trained models are publicly available. To make this line of research more accessible, our retrieved subsets for both ELEVATER and ImageNet will also be made available, with an easy-to-use toolkit to download the subsets without storing the whole dataset locally. It poses a feasible direction for leveraging the ever-increasing data from the Internet for customized visual recognition, especially for the low-resource regimes." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.589, + 0.642, + 0.605 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.613, + 0.897, + 0.902 + ], + "angle": 0, + "content": "Vision-Language Pretraining. Learning transferable visual representations from natural language supervision is an emerging research area. The pioneering works of CLIP [43] and ALIGN [20] make use of contrastive learning to pretrain models on billion-scale web-crawled image-text pairs. There are an increasing number of studies to improve their generality from various modeling perspectives, including training objectives [11,13,14,38,65,68], scaling techniques [9,40,65], data efficiency [25,28], and leveraging multilingual correlations [9, 19]. In academia, several works demonstrate techniques to improve the learned semantic representations on datasets at a smaller scale (e.g. CC3M [47], CC12M [4], YFCC15M [43, 51]), by exploring pretraining on a unified image-text-label space [59], token-level contrastive loss [61], and auxiliary within-modality contrastive loss [29,37,58,63]. Complementary to the above works, we build on top of existing pre-trained generic models, and aim to improve the model's performance by customizing them using retrieved relevant image-text pairs." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "15149" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.333 + ], + "angle": 0, + "content": "Retrieval-Augmented Models. In natural language processing, several works augment large language models with external data encoded with structured language and relation representations [3, 15, 22, 26, 31, 39, 66]. Motivated by retrieval-augmented models in NLP, several recent works leverage visual and / or textual knowledge to improve classification [32], question answering [7, 35, 56, 60], image generation [2, 8, 49, 72], and multi-modal tasks simultaneously [62]. RAC [32] improves long-tail classification by retrieving from a non-parametric memory consisting of pre-encoded images and text. K-LITE [48] enhances the text prompts with the retrieved external knowledge that is encoded in natural language. Our paper leverages the paired knowledge of image-text and aims to improve task transfer performance for core vision problems such as classification, retrieval, detection and segmentation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.338, + 0.474, + 0.566 + ], + "angle": 0, + "content": "Adaptation of Vision-Language models. CLIP demonstrates impressive zero-shot and linear probing performance on different downstream domains. Several works explore improving the domain adaptation performance on CLIP models. ELEVATER [27] leverages the text encoder outputs to initialize the task-specific linear head to improve the linear probe and finetuning performance of CLIP. Inspired by prompting techniques in NLP, recent works [44, 71] make use of learnable prompts that are trained on a few samples on downstream tasks. Similar to these works, this paper aims to improve CLIP's performance on downstream tasks, while making use of relevant image-text pairs data to improve the model's performance, without access to the downstream images. Furthermore, when downstream samples are available, they are complimentary to our method." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.572, + 0.409, + 0.589 + ], + "angle": 0, + "content": "3. Retrieval-Augmented Customization" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.594, + 0.218, + 0.608 + ], + "angle": 0, + "content": "3.1. Preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.614, + 0.471, + 0.81 + ], + "angle": 0, + "content": "Computer vision models have achieved strong transfer performance, when learning with large-scale image data only [17], image-label data [23] and/or image-caption data [43,59,67]. Without loss of generality, we follow [59] and define a unified triplet-wise format \\((\\pmb{x},\\pmb{t},y)\\) for imagetext-label data, where \\(\\pmb{x}\\in \\mathcal{X}\\) is an image, \\(t\\in \\mathcal{T}\\) is its language description, and \\(y\\in \\mathcal{V}\\) is a label indicating the index of the unique language description in the dataset. In a general form, the language description is a text sequence \\(\\pmb{t} = [t_1,\\dots ,t_L]\\). It ranges from simple category names representing visual concepts when \\(L\\) is small, to more freeform and semantic-rich sentences such as captions when \\(L\\) is relatively large." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.473, + 0.902 + ], + "angle": 0, + "content": "A typical transfer learning pipeline follows the procedure of pre-training then adaptation: (i) With large-scale pre-training, an image encoder foundation model \\( f_{\\theta} \\) parameterized by \\( \\pmb{\\theta} \\) is first trained to represent image \\( \\pmb{x} \\) as a visual feature vector \\( \\tilde{\\pmb{v}} \\in \\mathbb{R}^{P \\times 1} \\): \\( \\tilde{\\pmb{v}} = f_{\\pmb{\\theta}}(\\pmb{x}) \\). For recent language-image models [43], a dual-encoder architecture is often em" + }, + { + "type": "image", + "bbox": [ + 0.516, + 0.093, + 0.875, + 0.313 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.525, + 0.318, + 0.866, + 0.333 + ], + "angle": 0, + "content": "Figure 2. Illustration of the proposed REACT framework." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.345, + 0.895, + 0.435 + ], + "angle": 0, + "content": "ployed, where an additional text encoder \\( f_{\\phi}(\\pmb{t}) \\) parameterized by \\( \\phi \\) represents the sentence \\( \\tilde{\\pmb{u}} \\in \\mathbb{R}^{P \\times 1} : \\tilde{\\pmb{u}} = f_{\\phi}(\\pmb{t}) \\). (ii) Given a downstream task, model adaptation is typically performed using the available task-specific information, or task instruction \\( \\mathcal{I} \\). For example, the task-level transfer of a language-image model is described as:" + }, + { + "type": "text", + "bbox": [ + 0.507, + 0.439, + 0.892, + 0.515 + ], + "angle": 0, + "content": "- Zero-shot. In a customized setting, the simplest task definition can be provided as a set of category names for visual recognition, leading to the task instruction \\(\\mathcal{I}_0 = \\{t\\}\\). No training image \\(x\\) is available, not to mention the corresponding label \\(y\\)." + }, + { + "type": "text", + "bbox": [ + 0.507, + 0.52, + 0.894, + 0.596 + ], + "angle": 0, + "content": "- Few/Full-shot. The users may spend annotation cost to curate \\(N\\) image-label pairs as the training instances, making the task instruction more specific, \\(\\mathcal{I}_{\\mathrm{F}} = \\{(x_{n},t_{n},y_{n})\\}_{n = 1}^{N}\\), which allows updating the image encoder model \\(f_{\\theta}\\) for better adaptation performance." + }, + { + "type": "list", + "bbox": [ + 0.507, + 0.439, + 0.894, + 0.596 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.895, + 0.796 + ], + "angle": 0, + "content": "In this paper, we assume there exists a web-scale image-text corpus as the external knowledge source \\( S = \\{(x_{m}, t_{m})\\}_{m=1}^{M} \\), where \\( M \\) is the database size, e.g. 400M for LAION [46]. One may use the task instruction \\( \\mathcal{I} \\) as a query to seek additional relevant knowledge to build a more transferable visual system. Given the downstream task instruction \\( \\mathcal{I} \\) and an external knowledge source \\( S \\), our goal is to learn customized visual-semantic representations, which are readily transferable to the downstream task of interest, whose training and evaluation images are not observed during the customization process. To this end, we propose REACT. We illustrate the high-level idea in Figure 2, and describe the process as follows." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.805, + 0.796, + 0.821 + ], + "angle": 0, + "content": "3.2. Multi-modal External Knowledge" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Knowledge Base Construction. We explore web-scale image-text data as the multi-modal knowledge base \\( S \\) in this paper. Ideally, one may consider the entire web as the knowledge base, and use Google or Bing search to retrieve the relevant knowledge. We consider two large static datasets" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "15150" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.182 + ], + "angle": 0, + "content": "with image-text pairs. To control the experiment complexity and ensure reproducibility, we use LAION-400M [46], a publicly available database with 400M pairs, for most of the experiments. To further study the scaling influence of the retrieval base, we conduct comparisons on Web-800M, a privately collected web database with 800M pairs." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.183, + 0.471, + 0.318 + ], + "angle": 0, + "content": "To facilitate an efficient knowledge acquisition process, we use pre-trained contrastive models (e.g. CLIP) as the feature extractor, and build a cross-modal retrieval system using FAISS [21]. We use its Hierarchical Navigable Small World (HNSW) approximate \\( k \\)-NN lookup [34] to balance performance and efficiency. Please see appendix for more details. After the retrieval system is built on the designated retrieval pool, it can be efficiently used for retrieving relevant image-text pairs for various downstream domains." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.324, + 0.47, + 0.565 + ], + "angle": 0, + "content": "Retrieval-Augmented Task Instruction. To facilitate the same interface for various customized visual tasks in the wild, it is desirable to have the same uniform task instruction schema. In NLP, all task instructions can follow the same uniform schema, composed of task definition and positive/negative examples [36, 55]. Here, the task definition defines a given task in natural language, completely specifying how an input is expected to be mapped to an output text. We note a coherence connection between this NLP task schema and the customized zero/few/full-shot CV settings in Section 3.1. Following a similar schema, the minimum requirement to specify a visual task is the task definition \\(\\mathcal{I}_0\\), where category names illustrate the target visual concepts in natural language. Though adding human-annotated examples is a natural way to clarify the task and yield the complete schema \\(\\mathcal{I}_{\\mathrm{F}}\\), extra cost is introduced." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.567, + 0.471, + 0.703 + ], + "angle": 0, + "content": "It is of high interest to clarify the task using relevant examples, without human curating cost. Therefore, we propose to augment the task instruction with the retrieved examples from the external multi-modal knowledge base \\( S \\). For each concept \\( t \\in \\mathcal{I}_0 \\) in a given task, we first represent it in natural language \\( q = g_{prompt}(t) \\) using the language prompt as in [43], through inserting the concept into a set of task-specific templates \\( \\mathcal{P} \\). The task definition is expanded in its natural language form:" + }, + { + "type": "equation", + "bbox": [ + 0.097, + 0.715, + 0.471, + 0.733 + ], + "angle": 0, + "content": "\\[\n\\mathcal {Q} = \\left\\{\\boldsymbol {q} \\mid \\boldsymbol {q} = g _ {\\text {p r o m p t}} (\\boldsymbol {t}), \\forall \\boldsymbol {t} \\in \\mathcal {I} _ {0}, \\text {p r o m p t} \\in \\mathcal {P} \\right\\}. \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.746, + 0.47, + 0.807 + ], + "angle": 0, + "content": "Next, we perform our knowledge retrieval process to acquire the relevant image-text pair \\( s = g_{\\text{retrieve}}(q) \\) from the source \\( S \\). Two types of retrieval processes are considered to acquire the top- \\( K \\) pairs:" + }, + { + "type": "text", + "bbox": [ + 0.084, + 0.81, + 0.47, + 0.856 + ], + "angle": 0, + "content": "- Text-to-Text (T2T) retrieval allows us to retrieve more relevant examples as they have a better match with our target concept. The T2T-retrieved set for \\(\\mathcal{I}_0\\) is:" + }, + { + "type": "equation", + "bbox": [ + 0.1, + 0.868, + 0.47, + 0.894 + ], + "angle": 0, + "content": "\\[\n\\mathcal {S} ^ {T 2 T} = \\left\\{\\left(\\boldsymbol {x}, \\boldsymbol {t}\\right) \\in \\mathcal {S}: \\underset {\\boldsymbol {t} \\in \\mathbb {T}, | \\mathbb {T} | = K} {\\operatorname {a r g m a x}} f _ {\\phi} (\\boldsymbol {t}) ^ {\\top} f _ {\\phi} (\\boldsymbol {q}), \\forall \\boldsymbol {q} \\in \\mathcal {Q} \\right\\} \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.507, + 0.092, + 0.894, + 0.136 + ], + "angle": 0, + "content": "- Text-to-image (T2I) retrieval allows us to have more diversity in the text descriptions in our retrieved examples. The T2I-retrieved set for \\(\\mathcal{I}_0\\) is:" + }, + { + "type": "equation", + "bbox": [ + 0.521, + 0.145, + 0.894, + 0.171 + ], + "angle": 0, + "content": "\\[\n\\mathcal {S} ^ {T 2 I} = \\left\\{\\left(\\boldsymbol {x}, \\boldsymbol {t}\\right) \\in \\mathcal {S}: \\underset {\\boldsymbol {x} \\in \\mathbb {X}, | \\mathbb {X} | = K} {\\operatorname {a r g m a x}} f _ {\\boldsymbol {\\theta}} (\\boldsymbol {x}) ^ {\\top} f _ {\\boldsymbol {\\phi}} (\\boldsymbol {q}), \\forall \\boldsymbol {q} \\in \\mathcal {Q} \\right\\} \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.179, + 0.894, + 0.256 + ], + "angle": 0, + "content": "Both \\( S^{T2T} \\) and \\( S^{T2I} \\) are retrieved examples to augment the task definition \\( \\mathcal{I}_0 \\), without accessing the images in the training or validation set of the task. Compared to \\( \\mathcal{I}_{\\mathrm{F}} \\), they are \"free\" external knowledge to clarify the task and can be used to build a more transferable system." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.264, + 0.704, + 0.278 + ], + "angle": 0, + "content": "3.3. Model Customization" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.28, + 0.894, + 0.476 + ], + "angle": 0, + "content": "After retrieving the relevant multi-modal examples, one may employ the naive customization solution by fine-tuning the full-model initialized from pre-trained weights, as in Figure 3(a). Alternatively, we propose an affordable solution to endow pre-trained models with a new capability to leverage this external knowledge. The pre-trained generic visual models have gained strong transfer abilities and access to a large amount of internal knowledge stored in the model weights. We freeze the weights of these models so that their initial capacity remains unchanged. To bridge these pretrained models harmoniously to the customized domain, we consider locked-text gated-image tuning with the following two techniques, illustrated in Figure 3(d)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.481, + 0.894, + 0.692 + ], + "angle": 0, + "content": "Modularized Image Encoder. In order to provide sufficient expressivity to the model and make it able to adapt well on retrieved knowledge, we insert gated self-attention dense blocks in between the original layers of the image encoder, and train the new blocks from scratch. Those blocks are made of a self-attention layer, that attends the early layer inputs, followed by an extra dense feed-forward layer. Please see a visual illustration of this gated block in the rightmost of Figure 3(d). We denote the parameters of all new modules as \\(\\theta^{\\prime}\\). This design is inspired by the gated cross-attention-dense blocks in Flamingo [1] and frozen multi-modal model [52]. The difference is that the trainable module is introduced in Flamingo to enable cross-modal conditioning, while we adapt it for model growing in new customized domains." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.697, + 0.894, + 0.832 + ], + "angle": 0, + "content": "Frozen Text Encoder. The text encoder in language-image contrast models represents the task semantic space. To maintain it, we propose locked-text tuning, which freezes the text model weights so that the generic task encoding knowledge remains locked; see Figure 3(c). This is in contrast with locked-image tuning (LiT) [68] in Figure 3(b), where the image encoder is frozen and the text encoder is fine-tuned, which teaches a text model to read out good representations from a pre-trained image model for new tasks." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.833, + 0.894, + 0.901 + ], + "angle": 0, + "content": "We extract the normalized feature vectors in a hypersphere using \\(\\pmb{u}_i = \\frac{f_{\\{\\theta,\\theta'\\}}(\\pmb{x}_i)}{\\|f_{\\{\\theta,\\theta'\\}}(\\pmb{x}_i)\\|}\\) and \\(\\pmb{v}_j = \\frac{f_\\phi(\\pmb{t}_j)}{\\|f_\\phi(\\pmb{t}_j)\\|}\\). To customize the model wrt task definition \\(\\mathcal{I}_0\\), we update \\(\\pmb{\\theta}'\\) using a bidirectional learning objective between images and" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "15151" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.098, + 0.09, + 0.237, + 0.168 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.109, + 0.177, + 0.22, + 0.19 + ], + "angle": 0, + "content": "(a) Full-Model Tuning" + }, + { + "type": "image", + "bbox": [ + 0.252, + 0.091, + 0.387, + 0.168 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.252, + 0.177, + 0.378, + 0.19 + ], + "angle": 0, + "content": "(b) Locked-Image Tuning" + }, + { + "type": "image", + "bbox": [ + 0.403, + 0.091, + 0.536, + 0.168 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.408, + 0.178, + 0.524, + 0.191 + ], + "angle": 0, + "content": "(c) Locked-Text Tuning" + }, + { + "type": "image", + "bbox": [ + 0.564, + 0.091, + 0.696, + 0.168 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.572, + 0.173, + 0.676, + 0.197 + ], + "angle": 0, + "content": "(d) Locked-Text Gated-Image Tuning" + }, + { + "type": "image", + "bbox": [ + 0.71, + 0.091, + 0.875, + 0.198 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.202, + 0.894, + 0.245 + ], + "angle": 0, + "content": "Figure 3. Illustrative comparisons across different model tuning methods. (a) and (b) are existing baseline tuning methods. For model customization in a target domain, we found that (c) and (d) work better. One layer of the proposed modularized image encoder in locked-text gated-image tuning is illustrated in right side." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.259, + 0.471, + 0.276 + ], + "angle": 0, + "content": "language on the retrieved knowledge pool \\(S^{T2T}\\) and/or \\(S^{T2I}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.092, + 0.298, + 0.471, + 0.403 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\min _ {\\left\\{\\boldsymbol {\\theta} ^ {\\prime} \\right\\}} \\mathcal {L} _ {\\mathrm {C}} = \\mathcal {L} _ {i 2 t} + \\mathcal {L} _ {t 2 i}, \\text {w i t h} \\mathcal {B} \\sim \\mathcal {S} ^ {T 2 T} \\text {o r} \\mathcal {S} ^ {T 2 I} (4) \\\\ \\mathcal {L} _ {i 2 t} = - \\sum_ {i \\in \\mathcal {B}} \\frac {1}{| \\mathcal {P} (i) |} \\sum_ {k \\in \\mathcal {P} (i)} \\log \\frac {\\exp \\left(\\tau \\boldsymbol {u} _ {i} ^ {\\top} \\boldsymbol {v} _ {k}\\right)}{\\sum_ {j \\in \\mathcal {B}} \\exp \\left(\\tau \\boldsymbol {u} _ {i} ^ {\\top} \\boldsymbol {v} _ {j}\\right)} \\quad \\text {a n d} (5) \\\\ \\mathcal {L} _ {t 2 i} = - \\sum_ {j \\in \\mathcal {B}} \\frac {1}{| \\mathcal {Q} (j) |} \\sum_ {k \\in \\mathcal {Q} (j)} \\log \\frac {\\exp (\\tau \\boldsymbol {u} _ {k} ^ {\\top} \\boldsymbol {v} _ {j})}{\\sum_ {i \\in \\mathcal {B}} \\exp (\\tau \\boldsymbol {u} _ {i} ^ {\\top} \\boldsymbol {v} _ {j})} (6) \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.411, + 0.469, + 0.546 + ], + "angle": 0, + "content": "where \\(\\tau\\) is a temperature hyper-parameter controlling the strength of penalties on hard negative samples, and \\(\\mathcal{P}(i) = \\{k|k\\in \\mathcal{B},\\pmb{v}_k^\\top \\pmb{v}_i\\geq \\gamma \\}\\), \\(\\mathcal{Q}(j) = \\{k|k\\in \\mathcal{B},\\pmb{v}_k^\\top \\pmb{v}_j\\geq \\gamma \\}\\). We set \\(\\gamma = 0.9\\) for classification tasks to force image-text pairs sharing the similar text to be positive. Note (4) is a general form; it reduces to UniCL [59] when \\(\\gamma = 1.0\\); it further reduces to the training objective of CLIP [43] when there is a one-to-one mapping between an image and its paired caption in a batch, i.e. \\(\\mathcal{P}(i) = \\{i\\}\\) and \\(\\mathcal{Q}(j) = \\{j\\}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.547, + 0.471, + 0.621 + ], + "angle": 0, + "content": "In our empirical study we find that locked pre-trained image and text encoders with trainable gated modules in image encoder work best. Once the customized visual models are trained with the retrieved knowledge, we transfer it to the downstream domain for zero/few/full-shot evaluation." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.634, + 0.21, + 0.65 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.66, + 0.47, + 0.795 + ], + "angle": 0, + "content": "In this section, we conduct experiments to answer three research questions: (1) What are the unique advantages of retrieval-augmented image-text knowledge for task transfer? (2) How does our design choice of locked-text gated-image tuning compare to existing methods for model customization? (3) Is customization still beneficial in settings where the training data in downstream tasks are observed, i.e., in few-shot or full-shot settings? (4) Does customization scales well to dense prediction tasks like detection/segmentation?" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.471, + 0.901 + ], + "angle": 0, + "content": "We evaluate our models on four CV problems: image classification, image-text retrieval, object detection, and semantic segmentation. We first consider ImageNet [10] for zero-shot task transfer. We then further evaluate our model on ELEVATER [27], which is an open-set image classification benchmark that contains 20 datasets. We also conduct experiments on image-text retrieval with MSCOCO [30] and" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.26, + 0.892, + 0.291 + ], + "angle": 0, + "content": "Flickr [64] dataset. Finally, we evaluate on object detection and semantic segmentation with MSCOCO [30] dataset." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.292, + 0.895, + 0.474 + ], + "angle": 0, + "content": "One of the most intriguing benefits of REACT is that it does not need access to any images from the downstream task. Therefore, we first evaluate on task-level zero-shot transfer, which requires no images in the target to be observed [27, 43, 48]. This setting is different from traditional class-level zero-shot [57], where both the category and images in evaluation should not be observed in training. We argue that ImageNet concepts have been observed in CLIP (Sec. 2.2 of [43]) and other web-scale trained models [28], as WordNet synsets and common words in English Wikipedia are explicitly added in the query list when searching for (image, text) pairs in their training data construction process." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.486, + 0.692, + 0.502 + ], + "angle": 0, + "content": "4.1. Image Classification" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.51, + 0.744, + 0.526 + ], + "angle": 0, + "content": "4.1.1 Zero-Shot on ImageNet-1K" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.536, + 0.894, + 0.627 + ], + "angle": 0, + "content": "As shown in Table 1, by customizing the generic model CLIP/OpenCLIP on 10M retrieved image-text pairs from LAION-400M, REACT achieves a significant and consistent gain (up to \\(5.4\\%\\)) on zero-shot image classification on ImageNet-1K, with different backbones and original pretraining datasets. There are three interesting findings." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.894, + 0.779 + ], + "angle": 0, + "content": "F1: REACT can benefit from model's own pre-training data. Compared to OpenCLIP [18] (ViT-B/32) trained on LAION-400M, by training on 10M relevant pairs from the same LAION-400M dataset, REACT improves over OpenCLIP by \\(3.5\\%\\). Note that the model purely uses the image-text pairs that it has seen during its pre-training, and does not see any extra data. This shows that REACT can more adequately adapt to the target domain during the model customization stage, suggesting a favorable property that no new data is required for customization." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.781, + 0.894, + 0.901 + ], + "angle": 0, + "content": "F2: REACT efficiently explores new image-text sources, even for large models. We customize CLIP [43] ViT-L/14 on 10M retrieved relevant image-text pairs, and the model achieves a \\(2.8\\%\\) improvement to \\(78.1\\%\\). This surpasses the checkpoint with a much larger ViT-H/14 backbone and trained on a much larger LAION-2B dataset. This suggests that REACT is a more sample-efficient approach to improve the model performance on the domain-of-interest." + }, + { + "type": "list", + "bbox": [ + 0.498, + 0.629, + 0.894, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15152" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.132, + 0.092, + 0.833, + 0.235 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.085, + 0.238, + 0.882, + 0.253 + ], + "angle": 0, + "content": "Figure 4. Zero-shot comparison on ELEVATER ICinW 20 datasets. REACT (B32) improves over the base checkpoints on most datasets." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.266, + 0.462, + 0.466 + ], + "angle": 0, + "content": "
fθPretrain DataRetrieved DataMethodImageNet-1K Zero-Shot
DatasetSize
B/32WIT-400M--CLIP63.2
L-400M10MREACT68.6 (+5.4)
LAION-400M--OpenCLIP62.9
L-400M10MREACT66.4 (+3.5)
L/14WIT-400M--CLIP75.3
L-400M6MREACT77.6 (+2.3)
L-400M10MREACT78.1 (+2.8)
W-800M†6MREACT78.5 (+3.2)
LAION-400M--OpenCLIP72.8
LAION-2B--OpenCLIP75.3
H/14LAION-2B--OpenCLIP78.0
G/14LAION-2B--OpenCLIP80.1
L-2B12MREACT81.0 (+0.9)
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.469, + 0.472, + 0.554 + ], + "angle": 0, + "content": "Table 1. Comparison of zero-shot task transfer with public checkpoints from CLIP [43] and OpenCLIP [18]. LAION [45, 46] is abbreviated as \"L\" in the table. Web-800M†: a privately collected web database with 800M image-text pairs. By continue pretraining on only \\(\\sim 10\\mathrm{M}\\) retrieved data, REACT outperforms all public CLIP/OpenCLIP checkpoints." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.57, + 0.47, + 0.692 + ], + "angle": 0, + "content": "F3: Scaling up the retrieval pool increases performance. We perform REACT in a privately collected dataset with over 800M pairs, and train a customized model on 6M retrieved pairs. The performance is increased to \\(78.5\\%\\), yielding \\(0.9\\%\\) gain compared with 6M pairs retrieved from LAION-400M. This suggests that REACT scales well with the larger retrieval pool. It showcases REACT as a cost-efficient approach to leveraging the ever-increasing web image-text corpus." + }, + { + "type": "title", + "bbox": [ + 0.076, + 0.703, + 0.419, + 0.717 + ], + "angle": 0, + "content": "4.1.2 Zero-, Few-, and Full-Shot on ELEVATER" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.47, + 0.795 + ], + "angle": 0, + "content": "As a proxy for performing vision tasks for many customized scenarios in the wild, we consider the image classification in the wild (ICinW) benchmark in ELEVATER [27]. It consists of 20 datasets from a diverse selection of domains and covers a wide range of concepts, totaling 1151 classes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.471, + 0.902 + ], + "angle": 0, + "content": "We perform multi-modal knowledge retrieval for 20 datasets together – the retrieved samples are around 10M image-text pairs in total, on which one single customized visual model is trained. After the process, we feed the customized model to different downstream tasks separately. For each downstream dataset, we use the official ELEVATER toolkit to obtain the train/val/test splits, and perform zero-" + }, + { + "type": "table", + "bbox": [ + 0.51, + 0.266, + 0.88, + 0.356 + ], + "angle": 0, + "content": "
MethodZero-ShotFew-shotFull-shot
LPFTLPFT
CLIP56.865.463.378.480.4
REACT60.668.968.480.481.8
Gains(+3.8)(+3.5)(+5.1)(+2.0)(+1.4)
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.367, + 0.892, + 0.41 + ], + "angle": 0, + "content": "Table 2. The average scores of image classification performance on 20 datasets in ELEVATER. REACT consistently outperforms CLIP in both data-limited and data-rich regimes." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.427, + 0.764, + 0.441 + ], + "angle": 0, + "content": "shot, few-shot, and full-shot evaluation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.442, + 0.895, + 0.609 + ], + "angle": 0, + "content": "We report the average scores in Table 2. It achieves \\(3.8\\%\\) improvement in the zero-shot setting, even when we do not perform a separate customization for different datasets. This demonstrates the robustness of our customization process. Further, we see the consistent improvement in few-shot and full-shot settings, including both linear probe (LP) and finetuning (FT). This result is encouraging, as it demonstrates that when we have access to some or all data from the downstream task, the proposed model customization stage remains beneficial. Therefore, we advocate model customization process in both data-limited and data-rich settings." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Breakdown Analysis. Next, we ask why does the retrieved image-text knowledge improve the zero-shot task transfer performance on a broad range of datasets? We compare the breakdown performance on all 20 datasets in Figure 4 for the zero-shot settings. Out of 20 datasets, the retrieval-augmented knowledge shows superior/comparable/inferior performance to the baseline on \\(15/1/4\\) datasets for CLIP and \\(14/0/6\\) datasets for OpenCLIP, respectively. Most of the improved and failure datasets are consistent for both checkpoints. For the top two datasets that gains the most, i.e. StanfordCars and FGVC Aircraft, relevant image-text knowledge is retrieved from the web-crawled data LAION-400M to describe the concepts; see Fig. 5a. Interestingly, this observation is complementary to K-LITE [48], which failed on these two datasets, because no knowledge was extracted from Wiktionary for them, as it often requires domain-specific knowledge and even visual knowledge to best define a car brand (e.g. BMW X6 SUV or Audi R8) or an aircraft model type (e.g. DC-10 or A321)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15153" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.092, + 0.101, + 0.106 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.104, + 0.094, + 0.186, + 0.106 + ], + "angle": 0, + "content": "Task Samples" + }, + { + "type": "image", + "bbox": [ + 0.204, + 0.092, + 0.226, + 0.107 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.232, + 0.094, + 0.388, + 0.106 + ], + "angle": 0, + "content": "Retrieved Image-Text Pairs" + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.116, + 0.099, + 0.179 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.109, + 0.112, + 0.195, + 0.14 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.114, + 0.14, + 0.193, + 0.147 + ], + "angle": 0, + "content": "BMW X6 SUV 2012" + }, + { + "type": "image", + "bbox": [ + 0.139, + 0.15, + 0.195, + 0.177 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.108, + 0.179, + 0.194, + 0.186 + ], + "angle": 0, + "content": "Audi R8 Coupe 2012" + }, + { + "type": "image", + "bbox": [ + 0.202, + 0.111, + 0.299, + 0.138 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.202, + 0.14, + 0.304, + 0.147 + ], + "angle": 0, + "content": "Picture of 2012 BMW X6" + }, + { + "type": "image", + "bbox": [ + 0.204, + 0.149, + 0.284, + 0.177 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.285, + 0.111, + 0.355, + 0.138 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.356, + 0.111, + 0.404, + 0.138 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.405, + 0.111, + 0.467, + 0.138 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.204, + 0.178, + 0.449, + 0.186 + ], + "angle": 0, + "content": "Audi R8 At Moscow International Exhibition Motorshow 2008" + }, + { + "type": "image", + "bbox": [ + 0.085, + 0.193, + 0.099, + 0.256 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.143, + 0.188, + 0.195, + 0.215 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.166, + 0.217, + 0.193, + 0.224 + ], + "angle": 0, + "content": "DC-10" + }, + { + "type": "image", + "bbox": [ + 0.141, + 0.227, + 0.194, + 0.256 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.169, + 0.256, + 0.193, + 0.263 + ], + "angle": 0, + "content": "A321" + }, + { + "type": "image", + "bbox": [ + 0.202, + 0.188, + 0.267, + 0.216 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.202, + 0.217, + 0.298, + 0.225 + ], + "angle": 0, + "content": "DC-10 makes last passage" + }, + { + "type": "image", + "bbox": [ + 0.203, + 0.227, + 0.267, + 0.256 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.203, + 0.256, + 0.298, + 0.263 + ], + "angle": 0, + "content": "B-6007 - Airbus A320-2" + }, + { + "type": "image", + "bbox": [ + 0.27, + 0.188, + 0.353, + 0.216 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.27, + 0.217, + 0.342, + 0.225 + ], + "angle": 0, + "content": "at passenger flight." + }, + { + "type": "image", + "bbox": [ + 0.354, + 0.188, + 0.404, + 0.216 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.354, + 0.217, + 0.404, + 0.225 + ], + "angle": 0, + "content": "" + }, + { + "type": "image", + "bbox": [ + 0.405, + 0.188, + 0.467, + 0.216 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.411, + 0.217, + 0.466, + 0.256 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.203, + 0.227, + 0.267, + 0.256 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.204, + 0.256, + 0.298, + 0.264 + ], + "angle": 0, + "content": "B-6007-AirbusA320-2" + }, + { + "type": "image", + "bbox": [ + 0.27, + 0.227, + 0.353, + 0.256 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.27, + 0.256, + 0.298, + 0.263 + ], + "angle": 0, + "content": "A320-2" + }, + { + "type": "image", + "bbox": [ + 0.354, + 0.227, + 0.405, + 0.256 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.354, + 0.256, + 0.402, + 0.264 + ], + "angle": 0, + "content": "tern Airlines" + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.266, + 0.47, + 0.313 + ], + "angle": 0, + "content": "(a) Success examples. The two datasets with largest improvement in Fig. 4: Stanford-Cars [24] and FGVC-Aircraft [33]. There is a high concept coverage for these datasets in LAION, resulting in a relevant and diverse retrieved set." + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.319, + 0.173, + 0.33 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.331, + 0.142, + 0.379 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.083, + 0.38, + 0.125, + 0.387 + ], + "angle": 0, + "content": "lymph node" + }, + { + "type": "image", + "bbox": [ + 0.144, + 0.327, + 0.205, + 0.333 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.144, + 0.333, + 0.205, + 0.379 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.146, + 0.38, + 0.204, + 0.387 + ], + "angle": 0, + "content": "lymph ... tumor..." + }, + { + "type": "image", + "bbox": [ + 0.208, + 0.316, + 0.234, + 0.333 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.235, + 0.319, + 0.367, + 0.33 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.208, + 0.331, + 0.28, + 0.379 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.21, + 0.38, + 0.296, + 0.388 + ], + "angle": 0, + "content": "Microscopic enlargement" + }, + { + "type": "image", + "bbox": [ + 0.281, + 0.331, + 0.353, + 0.379 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.281, + 0.38, + 0.345, + 0.388 + ], + "angle": 0, + "content": "ment of a mast cell." + }, + { + "type": "image", + "bbox": [ + 0.354, + 0.331, + 0.405, + 0.379 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.408, + 0.331, + 0.468, + 0.379 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.39, + 0.47, + 0.427 + ], + "angle": 0, + "content": "(b) Failure case. The dataset with the largest degradation in Fig. 4: PatchCamelyon [54]. LAION-400M has a low concept coverage on this domain, and the retrieved samples are in a different distribution from the target set." + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.433, + 0.469, + 0.475 + ], + "angle": 0, + "content": "Figure 5. Success and failure cases in ELEVATER benchmark. We show class name and the caption of the first retrieved image-text pairs, others are similar and omitted due to limited space." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.491, + 0.47, + 0.611 + ], + "angle": 0, + "content": "Limitations. As shown in Fig. 4, REACT struggles on the PatchCamelyon dataset, a cancer cell recognition benchmark. We visualize the retrieved samples and the samples from the original training set in Fig. 5b. The retrieved images are either instruction photos and from another sensing method, which exhibits a different visual distribution from PatchCamelyon. This suggests the importance of ensuring the retrieval quality for the domain-of-interest." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.621, + 0.276, + 0.637 + ], + "angle": 0, + "content": "4.2. Image-Text Retrieval" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.645, + 0.47, + 0.796 + ], + "angle": 0, + "content": "To demonstrate the generality of REACT, we consider Flickr30K [64] and MSCOCO [30] image-text retrieval tasks, in both zero-shot and full-shot settings. We use the standard image-text contrastive objective [43]. For image-text retrieval task, following [20, 43], we use the CLIP-L/14 with 336x336 input resolution in both zero-shot, customization, and fine-tuning stage. We use the captions from MSCOCO as queries to retrieve 6M image-text pairs and perform customization. Note that none of the caption queries are used in the model training stage." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.471, + 0.902 + ], + "angle": 0, + "content": "As shown in Table 3, REACT improves the generic CLIP counterparts on both zero-shot and full-shot retrieval for Flickr30K and MSCOCO datasets. The gain on zero-shot task transfer is large. On Flickr30K, it achieves \\(3.4\\% /10.0\\%\\) recall improvement for I2T and T2I retrieval, respectively. Afer fine-tuning on full training data, REACT still improves over the baseline slightly. It provides another piece of ev" + }, + { + "type": "table", + "bbox": [ + 0.51, + 0.09, + 0.882, + 0.276 + ], + "angle": 0, + "content": "
MethodFlickr30KMSCOCO
Img → TextText → ImgImg → TextText → Img
R@1R@5R@1R@5R@1R@5R@1R@5
Zero-ShotImgBert [42]70.790.254.379.644.071.232.359.0
ALIGN [20]88.698.775.793.858.683.045.669.8
CLIP [43]88.098.768.790.658.481.537.862.4
CLIP†87.098.366.588.059.280.737.862.4
REACT90.499.176.593.763.385.147.572.0
Bletchley†90.898.278.094.066.785.648.972.7
REACT92.198.779.294.767.785.950.574.4
Fine-tunedGPO [5]88.798.976.194.568.190.252.780.2
ALIGN [20]95.399.884.997.477.093.559.983.3
CLIP†96.499.886.597.978.393.860.983.8
REACT96.699.986.898.078.794.061.184.1
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.28, + 0.892, + 0.308 + ], + "angle": 0, + "content": "Table 3. Image-text retrieval results on Flickr30K [41] and MSCOCO [30] datasets. CLIP†, Bletchley†: our evaluation." + }, + { + "type": "table", + "bbox": [ + 0.509, + 0.313, + 0.885, + 0.424 + ], + "angle": 0, + "content": "
Pretrain MethodBackboneRegion \nProposalsMSCOCO AP50
NovelBaseAll
Zero-ShotCLIPResNet-50GT58.658.258.3
REACTResNet-50GT58.9 (+0.3)59.4 (+1.2)59.3 (+1.0)
CLIPResNet-50RPN29.724.025.5
REACTResNet-50RPN31.6 (+1.9)25.4 (+1.4)27.0 (+1.5)
OVDCLIPResNet-50-14.252.842.7
REACTResNet-50-20.6 (+6.4)55.1 (+2.3)46.1 (+3.4)
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.426, + 0.891, + 0.454 + ], + "angle": 0, + "content": "Table 4. Zero-shot and open-vocabulary object detection results on MSCOCO [30] dataset using RegionCLIP [69] pipeline." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.47, + 0.892, + 0.545 + ], + "angle": 0, + "content": "idence for REACT in data-rich settings. Furthermore, we conduct the same customization procedure of REACT on a large checkpoint Bletchley [53] with 864M parameters, and observe consistent gains over both datasets. It demonstrates that REACT scales well with model size on retrieval tasks." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.556, + 0.715, + 0.57 + ], + "angle": 0, + "content": "4.3. Dense Prediction Tasks" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.579, + 0.894, + 0.655 + ], + "angle": 0, + "content": "Although REACT is optimized with the image-level contrastive loss during the customization stage, we find it beneficial for dense prediction tasks as well. We showcase its application to dense prediction tasks on object detection and semantic segmentation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.659, + 0.894, + 0.795 + ], + "angle": 0, + "content": "Object Detection. For object detection, we choose the state-of-the-art RegionCLIP [69] as our framework. We conduct experiments in two settings: zero-shot inference and open-vocabulary object detection (OVD) on MSCOCO dataset. We perform the model customization following the same setting as Sec. 4.2. Following RegionCLIP, we conduct experiments on ResNet50 backbone. The results are shown in Table 4. REACT consistently improves over CLIP checkpoint under all settings." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.894, + 0.87 + ], + "angle": 0, + "content": "For zero-shot inference, when ground-truth region proposal is used, REACT improves over CLIP by \\(+1.0\\) on overall AP50; when the pretrained RPN is used, REACT demonstrates \\(+1.5 / + 1.4 / + 1.9\\) AP50 improvements on novel, base, and all classes, respectively." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "For OVD, we can see that with the REACT, the detector yields improved performance on base with \\(+2.3\\) AP50, and" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15154" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.09, + 0.462, + 0.153 + ], + "angle": 0, + "content": "
MethodmIoU
zero-shotw/ refinew/ finetune
MaskCLIP [70]12.514.618.1
REACT (Locked-Text)14.4 (+1.9)18.2 (+3.6)20.7 (+2.6)
REACT (Locked-Text Gated-Image)14.5 (+2.0)16.3 (+1.7)19.2 (+1.1)
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.158, + 0.468, + 0.186 + ], + "angle": 0, + "content": "Table 5. Zero-shot and annotation-free semantic segmentation results on COCO Stuff [30] using MaskCLIP [70] (ViT-B/16)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.197, + 0.47, + 0.363 + ], + "angle": 0, + "content": "importantly, it significantly improves novel categories with +6.4 AP50. This suggests that the injected knowledge during the model customization stage improves the learned fine-grained visual feature that is beneficial to both seen and unseen categories for object detection, when the downstream coarse-grained data is available. This is favored, because (1) the weakly-supervised data such as the coarse-grained image-text pairs requires much less human annotation cost than fine-grained bounding box annotation, (2) the paired data in REACT is free, as it is retrieved from the web, where COCO image-text pairs are not used in customized training." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.365, + 0.471, + 0.59 + ], + "angle": 0, + "content": "Semantic Segmentation. For semantic segmentation, we choose the state-of-the-art MaskCLIP [70] as the framework. It investigates three evaluation settings for segmentation. First, it makes use of the pretrained CLIP checkpoint to discover the alignment between grid visual features and the text prompt features, so as to perform zero-shot semantic segmentation. Second, to further improve the performance, MaskCLIP [70] proposes two techniques for refining its zero-shot predictions: key smoothing and prompt denoising. Lastly, when the training images are available, without the need to access the training labels, it further proposes MaskCLIP + [70] to perform full-shot finetuning on the target training set using pseudo-labels. Following MaskCLIP [70], we use ViT-B/16 checkpoints, and use their official code base to train and evaluate models. We report results in Table 5." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.592, + 0.47, + 0.713 + ], + "angle": 0, + "content": "On all of the three settings, REACT demonstrates improvements over the MaskCLIP. Notably, when refinement techniques are used, REACT with locked-text tuning demonstrates a significant \\(3.6\\%\\) gain in mIoU. Surprisingly, without seeing the downstream COCO images, the zero-shot evaluation of REACT (18.2) even slightly outperforms MaskCLIP+ (18.1), which is finetuned on the downstream training COCO images with self-training." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.715, + 0.468, + 0.76 + ], + "angle": 0, + "content": "Summary. These results are encouraging, as it shows that the customized knowledge from REACT transfers well to dense prediction tasks like detection and segmentation." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.772, + 0.241, + 0.787 + ], + "angle": 0, + "content": "4.4. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.793, + 0.468, + 0.839 + ], + "angle": 0, + "content": "We ablate REACT on ImageNet with CLIP ViT-B/32 checkpoint, with 10M retrieved image-text pairs from LAION-400M. See more ablations in supplementary." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.47, + 0.9 + ], + "angle": 0, + "content": "Tuning strategy. We ablate the design choices in the model customization stage: (1) direct tuning the pre-trained weights vs. training gated blocks from scratch; (2) updating visual vs.text encoder. We report results in Table 6. First, a frozen text" + }, + { + "type": "table", + "bbox": [ + 0.503, + 0.089, + 0.885, + 0.18 + ], + "angle": 0, + "content": "
MethodVisualText# Train.IN1K Acc.COCO R@1 T2II2T
DirectCLIP [43]XX-63.248.829.9
Locked-Image [68]X✓63.4M63.750.534.2
Locked-Text✓X88.1M66.951.136.1
Full-model✓✓151.3M64.354.337.9
GatedX✓18.9M63.049.533.5
Locked-Text Gated-Image✓X42.5M68.653.438.1
✓✓89.8M68.754.339.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.186, + 0.892, + 0.228 + ], + "angle": 0, + "content": "Table 6. Ablation: tuning strategy. For our model customization purpose, we advocate locked-text (gated-image) tuning methods in gray rows. \\(\\checkmark\\): trainable, \\(\\mathcal{X}\\): locked." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.248, + 0.894, + 0.354 + ], + "angle": 0, + "content": "encoder consistently outperforms a frozen visual encoder. We conjecture the phenomenon is due to that the retrieved texts have a much more limited space, comparing to text space in the original pre-training set (e.g. LAION-400M), as the concepts are limited to the query classes from the target domain. Therefore, fine-tuning the text encoder may tend to collapse the pre-trained semantic space." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.357, + 0.894, + 0.463 + ], + "angle": 0, + "content": "We advocate two tuning methods for model customization. Locked-text gated-image tuning has a strong adaptation power, and is efficient in the model customization stage, with fewer trainable parameters. Locked-text tuning is also an effective way of customizing the models to downstream tasks, without the need of adding extra parameters. By default, we use gated blocks for its superior performance and efficiency." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.47, + 0.894, + 0.53 + ], + "angle": 0, + "content": "Retrieval size. We observe that training with a small retrieval size is more likely to overfit. We find that a larger retrieval size generally yields better performance, and saturates at around 6-10M image-text pairs." + }, + { + "type": "table", + "bbox": [ + 0.514, + 0.537, + 0.876, + 0.565 + ], + "angle": 0, + "content": "
Retrieval Size01M3M6M10M
ImageNet-1K Accuracy63.264.866.968.668.6
" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.594, + 0.619, + 0.609 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.622, + 0.894, + 0.757 + ], + "angle": 0, + "content": "We presented REACT, a plug-and-play framework for leveraging large-scale image-text corpus as external knowledge to efficiently customize models on downstream tasks. Extensive experiments demonstrate its generality and effectiveness in image classification, image-text retrieval, object detection, and semantic segmentation, on more than 20 different downstream datasets. We highly advocate the model customization stage for building more transferable visual system for different downstream tasks." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Acknowledgement. This work was supported in part by NSF CAREER IIS2150012, NASA 80NSSC21K0295, and Institute of Information & communications Technology Planning & Evaluation(IITP) grants funded by the Korea government(MSIT) (No. 2022- 0-00871, Development of AI Autonomy and Knowledge Enhancement for AI Agent Collaboration) and (No. RS-2022-00187238, Development of Large Korean Language Model Technology for Efficient Pre-training)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15155" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.175, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.185 + ], + "angle": 0, + "content": "[1] Jean-Baptiste Alayrac, Jeff Donahue, Pauline Luc, Antoine Miech, Iain Barr, Yana Hasson, Karel Lenc, Arthur Mensch, Katie Millican, Malcolm Reynolds, et al. 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Lafite2: Few-shot text-to-image generation. arXiv preprint arXiv:2210.14124, 2022. 3" + }, + { + "type": "list", + "bbox": [ + 0.504, + 0.093, + 0.894, + 0.389 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15158" + } + ] +] \ No newline at end of file diff --git a/2023/Learning Customized Visual Models With Retrieval-Augmented Knowledge/5534a4dd-73bd-49cc-aaa8-1125042ab403_origin.pdf b/2023/Learning Customized Visual Models With Retrieval-Augmented Knowledge/5534a4dd-73bd-49cc-aaa8-1125042ab403_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..850b5cb638f8469e0df770256f50dff0706913db --- /dev/null +++ b/2023/Learning Customized Visual Models With Retrieval-Augmented Knowledge/5534a4dd-73bd-49cc-aaa8-1125042ab403_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:40ac3606145c453cd4a3b9ed4e0a07f8f2f3716fefef96df667666303b446930 +size 1478230 diff --git a/2023/Learning Customized Visual Models With Retrieval-Augmented Knowledge/full.md b/2023/Learning Customized Visual Models With Retrieval-Augmented Knowledge/full.md new file mode 100644 index 0000000000000000000000000000000000000000..f01f6028879cc436021a6ee97a81f38ee6b6fbf3 --- /dev/null +++ b/2023/Learning Customized Visual Models With Retrieval-Augmented Knowledge/full.md @@ -0,0 +1,407 @@ +# Learning Customized Visual Models with Retrieval-Augmented Knowledge + +Haotian Liu†§◆ Kilho Son‡ Jianwei Yang‡ Ce Liu‡ Jianfeng Gao‡ Yong Jae Lee† Chunyuan Li†¶ University of Wisconsin–Madison ‡ Microsoft {lht,yongjaeelee}@cs.wisc.edu {kilhoson, jianwyan, ce.liu, jfgao, chunyl}@microsoft.com https://react-v1.github.io + +# Abstract + +Image-text contrastive learning models such as CLIP have demonstrated strong task transfer ability. The high generality and usability of these visual models is achieved via a web-scale data collection process to ensure broad concept coverage, followed by expensive pre-training to feed all the knowledge into model weights. Alternatively, we propose REACT, REtrieval-Augmented CusTomization, a framework to acquire the relevant web knowledge to build customized visual models for target domains. We retrieve the most relevant image-text pairs ( $\sim 3\%$ of CLIP pre-training data) from the web-scale database as external knowledge and propose to customize the model by only training new modularized blocks while freezing all the original weights. The effectiveness of REACT is demonstrated via extensive experiments on classification, retrieval, detection and segmentation tasks, including zero, few, and full-shot settings. Particularly, on the zero-shot classification task, compared with CLIP, it achieves up to $5.4\%$ improvement on ImageNet and $3.7\%$ on the ELEVATER benchmark (20 datasets). + +# 1. Introduction + +It has been a fundamental research problem in computer vision (CV) to build a transferable visual system that can easily adapt to a wide range of downstream tasks. With remarkable advances in deep learning, a de facto solution to achieve this is to train deep neural networks on a large amount of data to pursue the so-called generic visual representations. This dates back to the standard supervised training on ImageNet [10], whose superb representation power is further demonstrated in BiT [23]/ViT [12] by scaling up the training to JFT300M [50]. Along the way, recent efforts have been applied to the popular image self-supervised learning [6, 16, 17] to reduce the demand for labeled data. The + +third approach is image-text contrastive learning trained on billion-scale web-crawled image-text pairs. Such models, like CLIP [43] and ALIGN [20], are able to achieve great performance on different downstream domains, without the need of any human labels. + +Excellent empirical performance has been achieved with the above three pre-training methods, by following the well established two-stage pre-training then adaptation pipeline: model pre-training from scratch on large data, then model adaptation directly on downstream tasks. Specifically, the pre-trained models are adapted to downstream tasks by considering the available task-specific samples only: either evaluated in a zero-shot task transfer manner, or updated using linear probing (LP) [43], finetuning (FT) [27], or prompt tuning [44, 71]. Following this two-stage pipeline, most research has reverted to the faith that building transferable visual systems is equivalent to developing more generic visual models by feeding all knowledge in the model pre-training stage. Therefore, the community has been witnessing a trend in exploring scaling success of pre-training model and data size with less care on the target domain, hoping that the model can adapt to any downstream scenario. + +In this paper, we argue that the conventional two-stage pipeline above is over-simplified and less efficient, in achieving the goal of building a transferable visual system in real-world settings. Instead, we propose a customization stage in between the pre-training and adaptation, where customization is implemented by systematically leveraging retrieved external knowledge. The inspiration comes from how humans are specialized in society for better generalization: instead of trying to memorize all concepts, humans are trained/prepared in a relevant subject to master a certain skill, while maintaining the basic skills in pre-training. + +To this end, we explore a systematic approach to acquire and learn with external knowledge sources from a large image-text corpus for model customization. The process of collecting external image-text knowledge is fully automatic without extra human annotation. The acquired knowledge typically contains richer information about the concept: relevant images that never appear in the downstream training + +![](images/e6247859f1503f6566ad699b8aba5f6c5dd7dc2bc67e17751012a9694eb7de18.jpg) +Figure 1. REACT achieves the best zero-shot ImageNet performance among public checkpoints (Left), achieves new SoTA on semi-supervised ImageNet classification in the $1\%$ labeled data setting (Middle), and consistently transfer better than CLIP on across a variety of tasks, including ImageNet classification, zero/few/full-shot classification on 20 datasets in ELEVATER benchmark, image-text retrieval, object detection and segmentation (Right). Please see the detailed numbers and settings in the experimental section. For the left figure, circle size indicates model size. + +![](images/05195f77dc9feea22cc3d7c26014c010cd81a603a8286b190d05658467e9afc8.jpg) + +![](images/ae4b32cdce349650530b2ed5da356abb50406c1cf8adc128c44c620a3176d167.jpg) + +and evaluation set, and richer text descriptions about concept semantics. Such multi-modal knowledge sources are generally available on the web, and further open-sourced like LAION [45, 46]. They cover a variety of domains, making it possible to develop customized visual models for task-level transfer. Similar retrieval-augmented intuitions have been exploited in computer vision for class-level transfer [32], but not yet for task-level transfer (similar to that of CLIP). Our main findings/contributions can be summarized as follows. + +We propose to explore the potential of the web-scale image-text corpus as external knowledge to significantly improve task-level transfer performance on the target domain at an affordable cost. A simple and effective strategy is proposed. To begin with, we build a large-scale multimodal indexing system to retrieve the relevant image-text pairs using CLIP features and approximate nearest neighbor search. For a CV problem, the task instruction is often sufficiently specified with text such as class names, which allows us to utilize them as queries to retrieve the relevant image-text pair knowledge from the indexing system. No images from the CV problem are needed. To efficiently build the customized visual model, we propose a novel modularized learning strategy: only updating the additional trainable weights on the retrieved knowledge, and freezing the original model weights. Hence, the model masters the new skill without forgetting basic skills. + +The generality and effectiveness of the proposed customization strategy is demonstrated on four CV problems. We instantiate it with CLIP, and develop the customized visual models for image classification on ImageNet and 20 datasets in ELEVATER [27], image-text retrieval on COCO [30]/Flickr [41], as well as object detection and semantic segmentation on COCO [30]. The knowledge bases are considered as LAION [46] and larger web-crawled multimodal data. The retrieval-augmented knowledge ( $\sim 3\%$ image-text pairs compared with the original training data) significantly improves the model's zero-shot performance + +without the need of accessing any images on downstream tasks. See Figure 1 for highlighted results. For example, our ViT-L/14 checkpoint achieves $78.5\%$ zero-shot accuracy on ImageNet [10], surpassing all public checkpoints from CLIP [43] and OpenCLIP [18], including those with larger model size and trained on a much larger LAION-2B [45]. The new customized models demonstrate higher few/full-shot performance than the generic model counterparts. + +Our retrieval system, codebase, and pre-trained models are publicly available. To make this line of research more accessible, our retrieved subsets for both ELEVATER and ImageNet will also be made available, with an easy-to-use toolkit to download the subsets without storing the whole dataset locally. It poses a feasible direction for leveraging the ever-increasing data from the Internet for customized visual recognition, especially for the low-resource regimes. + +# 2. Related Work + +Vision-Language Pretraining. Learning transferable visual representations from natural language supervision is an emerging research area. The pioneering works of CLIP [43] and ALIGN [20] make use of contrastive learning to pretrain models on billion-scale web-crawled image-text pairs. There are an increasing number of studies to improve their generality from various modeling perspectives, including training objectives [11,13,14,38,65,68], scaling techniques [9,40,65], data efficiency [25,28], and leveraging multilingual correlations [9, 19]. In academia, several works demonstrate techniques to improve the learned semantic representations on datasets at a smaller scale (e.g. CC3M [47], CC12M [4], YFCC15M [43, 51]), by exploring pretraining on a unified image-text-label space [59], token-level contrastive loss [61], and auxiliary within-modality contrastive loss [29,37,58,63]. Complementary to the above works, we build on top of existing pre-trained generic models, and aim to improve the model's performance by customizing them using retrieved relevant image-text pairs. + +Retrieval-Augmented Models. In natural language processing, several works augment large language models with external data encoded with structured language and relation representations [3, 15, 22, 26, 31, 39, 66]. Motivated by retrieval-augmented models in NLP, several recent works leverage visual and / or textual knowledge to improve classification [32], question answering [7, 35, 56, 60], image generation [2, 8, 49, 72], and multi-modal tasks simultaneously [62]. RAC [32] improves long-tail classification by retrieving from a non-parametric memory consisting of pre-encoded images and text. K-LITE [48] enhances the text prompts with the retrieved external knowledge that is encoded in natural language. Our paper leverages the paired knowledge of image-text and aims to improve task transfer performance for core vision problems such as classification, retrieval, detection and segmentation. + +Adaptation of Vision-Language models. CLIP demonstrates impressive zero-shot and linear probing performance on different downstream domains. Several works explore improving the domain adaptation performance on CLIP models. ELEVATER [27] leverages the text encoder outputs to initialize the task-specific linear head to improve the linear probe and finetuning performance of CLIP. Inspired by prompting techniques in NLP, recent works [44, 71] make use of learnable prompts that are trained on a few samples on downstream tasks. Similar to these works, this paper aims to improve CLIP's performance on downstream tasks, while making use of relevant image-text pairs data to improve the model's performance, without access to the downstream images. Furthermore, when downstream samples are available, they are complimentary to our method. + +# 3. Retrieval-Augmented Customization + +# 3.1. Preliminaries + +Computer vision models have achieved strong transfer performance, when learning with large-scale image data only [17], image-label data [23] and/or image-caption data [43,59,67]. Without loss of generality, we follow [59] and define a unified triplet-wise format $(\pmb{x},\pmb{t},y)$ for imagetext-label data, where $\pmb{x}\in \mathcal{X}$ is an image, $t\in \mathcal{T}$ is its language description, and $y\in \mathcal{V}$ is a label indicating the index of the unique language description in the dataset. In a general form, the language description is a text sequence $\pmb{t} = [t_1,\dots ,t_L]$ . It ranges from simple category names representing visual concepts when $L$ is small, to more freeform and semantic-rich sentences such as captions when $L$ is relatively large. + +A typical transfer learning pipeline follows the procedure of pre-training then adaptation: (i) With large-scale pre-training, an image encoder foundation model $f_{\theta}$ parameterized by $\pmb{\theta}$ is first trained to represent image $\pmb{x}$ as a visual feature vector $\tilde{\pmb{v}} \in \mathbb{R}^{P \times 1}$ : $\tilde{\pmb{v}} = f_{\pmb{\theta}}(\pmb{x})$ . For recent language-image models [43], a dual-encoder architecture is often em + +![](images/f674ef5e8723b3692b6a283aac0be7715c7d250628eabf9d4ba752065d26ca35.jpg) +Figure 2. Illustration of the proposed REACT framework. + +ployed, where an additional text encoder $f_{\phi}(\pmb{t})$ parameterized by $\phi$ represents the sentence $\tilde{\pmb{u}} \in \mathbb{R}^{P \times 1} : \tilde{\pmb{u}} = f_{\phi}(\pmb{t})$ . (ii) Given a downstream task, model adaptation is typically performed using the available task-specific information, or task instruction $\mathcal{I}$ . For example, the task-level transfer of a language-image model is described as: + +- Zero-shot. In a customized setting, the simplest task definition can be provided as a set of category names for visual recognition, leading to the task instruction $\mathcal{I}_0 = \{t\}$ . No training image $x$ is available, not to mention the corresponding label $y$ . +- Few/Full-shot. The users may spend annotation cost to curate $N$ image-label pairs as the training instances, making the task instruction more specific, $\mathcal{I}_{\mathrm{F}} = \{(x_{n},t_{n},y_{n})\}_{n = 1}^{N}$ , which allows updating the image encoder model $f_{\theta}$ for better adaptation performance. + +In this paper, we assume there exists a web-scale image-text corpus as the external knowledge source $S = \{(x_{m}, t_{m})\}_{m=1}^{M}$ , where $M$ is the database size, e.g. 400M for LAION [46]. One may use the task instruction $\mathcal{I}$ as a query to seek additional relevant knowledge to build a more transferable visual system. Given the downstream task instruction $\mathcal{I}$ and an external knowledge source $S$ , our goal is to learn customized visual-semantic representations, which are readily transferable to the downstream task of interest, whose training and evaluation images are not observed during the customization process. To this end, we propose REACT. We illustrate the high-level idea in Figure 2, and describe the process as follows. + +# 3.2. Multi-modal External Knowledge + +Knowledge Base Construction. We explore web-scale image-text data as the multi-modal knowledge base $S$ in this paper. Ideally, one may consider the entire web as the knowledge base, and use Google or Bing search to retrieve the relevant knowledge. We consider two large static datasets + +with image-text pairs. To control the experiment complexity and ensure reproducibility, we use LAION-400M [46], a publicly available database with 400M pairs, for most of the experiments. To further study the scaling influence of the retrieval base, we conduct comparisons on Web-800M, a privately collected web database with 800M pairs. + +To facilitate an efficient knowledge acquisition process, we use pre-trained contrastive models (e.g. CLIP) as the feature extractor, and build a cross-modal retrieval system using FAISS [21]. We use its Hierarchical Navigable Small World (HNSW) approximate $k$ -NN lookup [34] to balance performance and efficiency. Please see appendix for more details. After the retrieval system is built on the designated retrieval pool, it can be efficiently used for retrieving relevant image-text pairs for various downstream domains. + +Retrieval-Augmented Task Instruction. To facilitate the same interface for various customized visual tasks in the wild, it is desirable to have the same uniform task instruction schema. In NLP, all task instructions can follow the same uniform schema, composed of task definition and positive/negative examples [36, 55]. Here, the task definition defines a given task in natural language, completely specifying how an input is expected to be mapped to an output text. We note a coherence connection between this NLP task schema and the customized zero/few/full-shot CV settings in Section 3.1. Following a similar schema, the minimum requirement to specify a visual task is the task definition $\mathcal{I}_0$ , where category names illustrate the target visual concepts in natural language. Though adding human-annotated examples is a natural way to clarify the task and yield the complete schema $\mathcal{I}_{\mathrm{F}}$ , extra cost is introduced. + +It is of high interest to clarify the task using relevant examples, without human curating cost. Therefore, we propose to augment the task instruction with the retrieved examples from the external multi-modal knowledge base $S$ . For each concept $t \in \mathcal{I}_0$ in a given task, we first represent it in natural language $q = g_{prompt}(t)$ using the language prompt as in [43], through inserting the concept into a set of task-specific templates $\mathcal{P}$ . The task definition is expanded in its natural language form: + +$$ +\mathcal {Q} = \left\{\boldsymbol {q} \mid \boldsymbol {q} = g _ {\text {p r o m p t}} (\boldsymbol {t}), \forall \boldsymbol {t} \in \mathcal {I} _ {0}, \text {p r o m p t} \in \mathcal {P} \right\}. \tag {1} +$$ + +Next, we perform our knowledge retrieval process to acquire the relevant image-text pair $s = g_{\text{retrieve}}(q)$ from the source $S$ . Two types of retrieval processes are considered to acquire the top- $K$ pairs: + +- Text-to-Text (T2T) retrieval allows us to retrieve more relevant examples as they have a better match with our target concept. The T2T-retrieved set for $\mathcal{I}_0$ is: + +$$ +\mathcal {S} ^ {T 2 T} = \left\{\left(\boldsymbol {x}, \boldsymbol {t}\right) \in \mathcal {S}: \underset {\boldsymbol {t} \in \mathbb {T}, | \mathbb {T} | = K} {\operatorname {a r g m a x}} f _ {\phi} (\boldsymbol {t}) ^ {\top} f _ {\phi} (\boldsymbol {q}), \forall \boldsymbol {q} \in \mathcal {Q} \right\} \tag {2} +$$ + +- Text-to-image (T2I) retrieval allows us to have more diversity in the text descriptions in our retrieved examples. The T2I-retrieved set for $\mathcal{I}_0$ is: + +$$ +\mathcal {S} ^ {T 2 I} = \left\{\left(\boldsymbol {x}, \boldsymbol {t}\right) \in \mathcal {S}: \underset {\boldsymbol {x} \in \mathbb {X}, | \mathbb {X} | = K} {\operatorname {a r g m a x}} f _ {\boldsymbol {\theta}} (\boldsymbol {x}) ^ {\top} f _ {\boldsymbol {\phi}} (\boldsymbol {q}), \forall \boldsymbol {q} \in \mathcal {Q} \right\} \tag {3} +$$ + +Both $S^{T2T}$ and $S^{T2I}$ are retrieved examples to augment the task definition $\mathcal{I}_0$ , without accessing the images in the training or validation set of the task. Compared to $\mathcal{I}_{\mathrm{F}}$ , they are "free" external knowledge to clarify the task and can be used to build a more transferable system. + +# 3.3. Model Customization + +After retrieving the relevant multi-modal examples, one may employ the naive customization solution by fine-tuning the full-model initialized from pre-trained weights, as in Figure 3(a). Alternatively, we propose an affordable solution to endow pre-trained models with a new capability to leverage this external knowledge. The pre-trained generic visual models have gained strong transfer abilities and access to a large amount of internal knowledge stored in the model weights. We freeze the weights of these models so that their initial capacity remains unchanged. To bridge these pretrained models harmoniously to the customized domain, we consider locked-text gated-image tuning with the following two techniques, illustrated in Figure 3(d). + +Modularized Image Encoder. In order to provide sufficient expressivity to the model and make it able to adapt well on retrieved knowledge, we insert gated self-attention dense blocks in between the original layers of the image encoder, and train the new blocks from scratch. Those blocks are made of a self-attention layer, that attends the early layer inputs, followed by an extra dense feed-forward layer. Please see a visual illustration of this gated block in the rightmost of Figure 3(d). We denote the parameters of all new modules as $\theta^{\prime}$ . This design is inspired by the gated cross-attention-dense blocks in Flamingo [1] and frozen multi-modal model [52]. The difference is that the trainable module is introduced in Flamingo to enable cross-modal conditioning, while we adapt it for model growing in new customized domains. + +Frozen Text Encoder. The text encoder in language-image contrast models represents the task semantic space. To maintain it, we propose locked-text tuning, which freezes the text model weights so that the generic task encoding knowledge remains locked; see Figure 3(c). This is in contrast with locked-image tuning (LiT) [68] in Figure 3(b), where the image encoder is frozen and the text encoder is fine-tuned, which teaches a text model to read out good representations from a pre-trained image model for new tasks. + +We extract the normalized feature vectors in a hypersphere using $\pmb{u}_i = \frac{f_{\{\theta,\theta'\}}(\pmb{x}_i)}{\|f_{\{\theta,\theta'\}}(\pmb{x}_i)\|}$ and $\pmb{v}_j = \frac{f_\phi(\pmb{t}_j)}{\|f_\phi(\pmb{t}_j)\|}$ . To customize the model wrt task definition $\mathcal{I}_0$ , we update $\pmb{\theta}'$ using a bidirectional learning objective between images and + +![](images/3df86e83fc2f06e2971e5ba6a241053f435a20de8cfe0867cf3119e51ef536a3.jpg) +(a) Full-Model Tuning + +![](images/198e42f8f7eb524f7277a0d5e1397cde87666638f9c4b175258af7e39de42044.jpg) +(b) Locked-Image Tuning + +![](images/d78649bbb20b100f35b173ed6c8b5612a7cb576d4441c247b84f70cadd3ea9ec.jpg) +(c) Locked-Text Tuning + +![](images/8551b6c257124e74960d84c541ec0e015c7470c253853ceb26dcb6209140e602.jpg) +(d) Locked-Text Gated-Image Tuning + +![](images/eee419d6ba26107e5e71a72b76ec94de1b06e9b0cd8f588d3be4d9ec30a086b0.jpg) +Figure 3. Illustrative comparisons across different model tuning methods. (a) and (b) are existing baseline tuning methods. For model customization in a target domain, we found that (c) and (d) work better. One layer of the proposed modularized image encoder in locked-text gated-image tuning is illustrated in right side. + +language on the retrieved knowledge pool $S^{T2T}$ and/or $S^{T2I}$ : + +$$ +\begin{array}{l} \min _ {\left\{\boldsymbol {\theta} ^ {\prime} \right\}} \mathcal {L} _ {\mathrm {C}} = \mathcal {L} _ {i 2 t} + \mathcal {L} _ {t 2 i}, \text {w i t h} \mathcal {B} \sim \mathcal {S} ^ {T 2 T} \text {o r} \mathcal {S} ^ {T 2 I} (4) \\ \mathcal {L} _ {i 2 t} = - \sum_ {i \in \mathcal {B}} \frac {1}{| \mathcal {P} (i) |} \sum_ {k \in \mathcal {P} (i)} \log \frac {\exp \left(\tau \boldsymbol {u} _ {i} ^ {\top} \boldsymbol {v} _ {k}\right)}{\sum_ {j \in \mathcal {B}} \exp \left(\tau \boldsymbol {u} _ {i} ^ {\top} \boldsymbol {v} _ {j}\right)} \quad \text {a n d} (5) \\ \mathcal {L} _ {t 2 i} = - \sum_ {j \in \mathcal {B}} \frac {1}{| \mathcal {Q} (j) |} \sum_ {k \in \mathcal {Q} (j)} \log \frac {\exp (\tau \boldsymbol {u} _ {k} ^ {\top} \boldsymbol {v} _ {j})}{\sum_ {i \in \mathcal {B}} \exp (\tau \boldsymbol {u} _ {i} ^ {\top} \boldsymbol {v} _ {j})} (6) \\ \end{array} +$$ + +where $\tau$ is a temperature hyper-parameter controlling the strength of penalties on hard negative samples, and $\mathcal{P}(i) = \{k|k\in \mathcal{B},\pmb{v}_k^\top \pmb{v}_i\geq \gamma \}$ , $\mathcal{Q}(j) = \{k|k\in \mathcal{B},\pmb{v}_k^\top \pmb{v}_j\geq \gamma \}$ . We set $\gamma = 0.9$ for classification tasks to force image-text pairs sharing the similar text to be positive. Note (4) is a general form; it reduces to UniCL [59] when $\gamma = 1.0$ ; it further reduces to the training objective of CLIP [43] when there is a one-to-one mapping between an image and its paired caption in a batch, i.e. $\mathcal{P}(i) = \{i\}$ and $\mathcal{Q}(j) = \{j\}$ . + +In our empirical study we find that locked pre-trained image and text encoders with trainable gated modules in image encoder work best. Once the customized visual models are trained with the retrieved knowledge, we transfer it to the downstream domain for zero/few/full-shot evaluation. + +# 4. Experiments + +In this section, we conduct experiments to answer three research questions: (1) What are the unique advantages of retrieval-augmented image-text knowledge for task transfer? (2) How does our design choice of locked-text gated-image tuning compare to existing methods for model customization? (3) Is customization still beneficial in settings where the training data in downstream tasks are observed, i.e., in few-shot or full-shot settings? (4) Does customization scales well to dense prediction tasks like detection/segmentation? + +We evaluate our models on four CV problems: image classification, image-text retrieval, object detection, and semantic segmentation. We first consider ImageNet [10] for zero-shot task transfer. We then further evaluate our model on ELEVATER [27], which is an open-set image classification benchmark that contains 20 datasets. We also conduct experiments on image-text retrieval with MSCOCO [30] and + +Flickr [64] dataset. Finally, we evaluate on object detection and semantic segmentation with MSCOCO [30] dataset. + +One of the most intriguing benefits of REACT is that it does not need access to any images from the downstream task. Therefore, we first evaluate on task-level zero-shot transfer, which requires no images in the target to be observed [27, 43, 48]. This setting is different from traditional class-level zero-shot [57], where both the category and images in evaluation should not be observed in training. We argue that ImageNet concepts have been observed in CLIP (Sec. 2.2 of [43]) and other web-scale trained models [28], as WordNet synsets and common words in English Wikipedia are explicitly added in the query list when searching for (image, text) pairs in their training data construction process. + +# 4.1. Image Classification + +# 4.1.1 Zero-Shot on ImageNet-1K + +As shown in Table 1, by customizing the generic model CLIP/OpenCLIP on 10M retrieved image-text pairs from LAION-400M, REACT achieves a significant and consistent gain (up to $5.4\%$ ) on zero-shot image classification on ImageNet-1K, with different backbones and original pretraining datasets. There are three interesting findings. + +F1: REACT can benefit from model's own pre-training data. Compared to OpenCLIP [18] (ViT-B/32) trained on LAION-400M, by training on 10M relevant pairs from the same LAION-400M dataset, REACT improves over OpenCLIP by $3.5\%$ . Note that the model purely uses the image-text pairs that it has seen during its pre-training, and does not see any extra data. This shows that REACT can more adequately adapt to the target domain during the model customization stage, suggesting a favorable property that no new data is required for customization. +F2: REACT efficiently explores new image-text sources, even for large models. We customize CLIP [43] ViT-L/14 on 10M retrieved relevant image-text pairs, and the model achieves a $2.8\%$ improvement to $78.1\%$ . This surpasses the checkpoint with a much larger ViT-H/14 backbone and trained on a much larger LAION-2B dataset. This suggests that REACT is a more sample-efficient approach to improve the model performance on the domain-of-interest. + +![](images/49ed044e36e49bef23578deafef9c305b827faefca5000912cedbbec61de5013.jpg) +Figure 4. Zero-shot comparison on ELEVATER ICinW 20 datasets. REACT (B32) improves over the base checkpoints on most datasets. + +
fθPretrain DataRetrieved DataMethodImageNet-1K Zero-Shot
DatasetSize
B/32WIT-400M--CLIP63.2
L-400M10MREACT68.6 (+5.4)
LAION-400M--OpenCLIP62.9
L-400M10MREACT66.4 (+3.5)
L/14WIT-400M--CLIP75.3
L-400M6MREACT77.6 (+2.3)
L-400M10MREACT78.1 (+2.8)
W-800M†6MREACT78.5 (+3.2)
LAION-400M--OpenCLIP72.8
LAION-2B--OpenCLIP75.3
H/14LAION-2B--OpenCLIP78.0
G/14LAION-2B--OpenCLIP80.1
L-2B12MREACT81.0 (+0.9)
+ +F3: Scaling up the retrieval pool increases performance. We perform REACT in a privately collected dataset with over 800M pairs, and train a customized model on 6M retrieved pairs. The performance is increased to $78.5\%$ , yielding $0.9\%$ gain compared with 6M pairs retrieved from LAION-400M. This suggests that REACT scales well with the larger retrieval pool. It showcases REACT as a cost-efficient approach to leveraging the ever-increasing web image-text corpus. + +# 4.1.2 Zero-, Few-, and Full-Shot on ELEVATER + +As a proxy for performing vision tasks for many customized scenarios in the wild, we consider the image classification in the wild (ICinW) benchmark in ELEVATER [27]. It consists of 20 datasets from a diverse selection of domains and covers a wide range of concepts, totaling 1151 classes. + +We perform multi-modal knowledge retrieval for 20 datasets together – the retrieved samples are around 10M image-text pairs in total, on which one single customized visual model is trained. After the process, we feed the customized model to different downstream tasks separately. For each downstream dataset, we use the official ELEVATER toolkit to obtain the train/val/test splits, and perform zero- + +Table 1. Comparison of zero-shot task transfer with public checkpoints from CLIP [43] and OpenCLIP [18]. LAION [45, 46] is abbreviated as "L" in the table. Web-800M†: a privately collected web database with 800M image-text pairs. By continue pretraining on only $\sim 10\mathrm{M}$ retrieved data, REACT outperforms all public CLIP/OpenCLIP checkpoints. + +
MethodZero-ShotFew-shotFull-shot
LPFTLPFT
CLIP56.865.463.378.480.4
REACT60.668.968.480.481.8
Gains(+3.8)(+3.5)(+5.1)(+2.0)(+1.4)
+ +Table 2. The average scores of image classification performance on 20 datasets in ELEVATER. REACT consistently outperforms CLIP in both data-limited and data-rich regimes. + +shot, few-shot, and full-shot evaluation. + +We report the average scores in Table 2. It achieves $3.8\%$ improvement in the zero-shot setting, even when we do not perform a separate customization for different datasets. This demonstrates the robustness of our customization process. Further, we see the consistent improvement in few-shot and full-shot settings, including both linear probe (LP) and finetuning (FT). This result is encouraging, as it demonstrates that when we have access to some or all data from the downstream task, the proposed model customization stage remains beneficial. Therefore, we advocate model customization process in both data-limited and data-rich settings. + +Breakdown Analysis. Next, we ask why does the retrieved image-text knowledge improve the zero-shot task transfer performance on a broad range of datasets? We compare the breakdown performance on all 20 datasets in Figure 4 for the zero-shot settings. Out of 20 datasets, the retrieval-augmented knowledge shows superior/comparable/inferior performance to the baseline on $15/1/4$ datasets for CLIP and $14/0/6$ datasets for OpenCLIP, respectively. Most of the improved and failure datasets are consistent for both checkpoints. For the top two datasets that gains the most, i.e. StanfordCars and FGVC Aircraft, relevant image-text knowledge is retrieved from the web-crawled data LAION-400M to describe the concepts; see Fig. 5a. Interestingly, this observation is complementary to K-LITE [48], which failed on these two datasets, because no knowledge was extracted from Wiktionary for them, as it often requires domain-specific knowledge and even visual knowledge to best define a car brand (e.g. BMW X6 SUV or Audi R8) or an aircraft model type (e.g. DC-10 or A321). + +![](images/e32cb8ae3b4f71c97e183d1e5aa3ff1116fad3ba1d09aa4fdc00302304dbab0d.jpg) + +# Task Samples + +![](images/501d8113c135f49941c2a54b4d435c12a4eb0ea65f782176423fccfdff0c6184.jpg) + +# Retrieved Image-Text Pairs + +![](images/7e75ce7af7f12d489dc52627f6527f033876ac57037b65ff3eb1d3a272ab872e.jpg) + +![](images/a21e636a02e86ab3b9d1c317aaf20f5b78b667ab2752f96b5fca5a118f4e53c5.jpg) +BMW X6 SUV 2012 + +![](images/13f46a21b96d7c9e34e16ad617eb387af41d45a7e28c71b6b676203e397fc69a.jpg) +Audi R8 Coupe 2012 + +![](images/fd9fd6b19c7b89211f3ab403349de2abcad6cce003c9b71391f0b17a6f07298e.jpg) +Picture of 2012 BMW X6 + +![](images/836326942944125799689230331d1999a3d4c8c5a5b66776d9baa0e09d726690.jpg) +Audi R8 At Moscow International Exhibition Motorshow 2008 + +![](images/1a695ce25d5afa064e0e4245f2c6f7e24242eee0dc836c6a7ca75c360b957845.jpg) + +![](images/28b72d4390785e996dcc268a3cf3cfec8eaafcde4c760e5a9be19e0b3247655e.jpg) + +![](images/2253028c789170a085211bcf9a271783457a93622497549e658a56c6aea682fd.jpg) + +![](images/79028b1589bfb82e3fd1c68e62f964aa2e65d9d4dc74ba72e300f495aca50a7d.jpg) + +![](images/951ec2d5c6466d8f91df5c338df43646c21d4812e36bd56ca9b4ce75ceed6cb8.jpg) +DC-10 + +![](images/78910bc06d56426ebe91ca1176b9c35baa4795cb05d9086dc544a3f7dfbef4f1.jpg) +A321 + +![](images/6a7ebb974dcdc446242d6b7584c0fa4e2643f730261fd0d000fb8138b4b770d7.jpg) +DC-10 makes last passage + +B-6007 - Airbus A320-2 + +![](images/5e563c4433bb06c646b81e13144d8f0384d6b809c8064a460b93ed4598cb7102.jpg) +at passenger flight. + +![](images/dad41504b79e475f8d840c0b7848556d42161ee16e20ceb33f341f113f2ea47b.jpg) + +![](images/746ae41fc3f37b06a387684a4855d4e3932765f576cfc3ea419ab8c46b61d3bc.jpg) + +![](images/86a82a17da674cede984bb6f737b6a04f2a1b9defefd854ea553104f335fd440.jpg) + +![](images/a3410ba4a3ffa171156fab8a1489ea77b7c07b90a6f8128451ea85ab5e98eeb1.jpg) +B-6007-AirbusA320-2 +tern Airlines + +A320-2 + +![](images/a7469fb36b7d9f46b8dc5f5eb1a2927774849c55195a9adb0d0867343f0a079e.jpg) + +![](images/9095605e1b0e945d0091944fe5810c91f6a2dde2f70b35728335d4b8b352fbbe.jpg) + +![](images/4c13db2ddc6546ddcb6bca9907274fd0d11a771fc2f3d59898fd2de96d530f54.jpg) +lymph node +(b) Failure case. The dataset with the largest degradation in Fig. 4: PatchCamelyon [54]. LAION-400M has a low concept coverage on this domain, and the retrieved samples are in a different distribution from the target set. +Figure 5. Success and failure cases in ELEVATER benchmark. We show class name and the caption of the first retrieved image-text pairs, others are similar and omitted due to limited space. + +![](images/79ce1fae714fd120da65ec24119407e9d2429f21986e46dbeec39bc309187135.jpg) + +![](images/ba1f9c885d54741ac5426591119c4dbf4dd1fb216b587956ce9a58809e9b8439.jpg) +lymph ... tumor... + +![](images/9ff699e9f404b83eaf25e9fe24358c5a54964e08f4274f3a5be26f3a3b8fc94f.jpg) +(a) Success examples. The two datasets with largest improvement in Fig. 4: Stanford-Cars [24] and FGVC-Aircraft [33]. There is a high concept coverage for these datasets in LAION, resulting in a relevant and diverse retrieved set. + +![](images/372387ae16abf53bc916284e86f3b202807404217d0b1c6cd43fe901256c7212.jpg) + +![](images/2f05c6e4a0a51a07f25bef66fad85880e78726199f489cadc2ed23551512b93b.jpg) +Microscopic enlargement +ment of a mast cell. + +![](images/d8262108760abd6332cb4221c6c52239ede3d2f87b0f3f1e8c84687b4f7da9f2.jpg) + +![](images/ffc75e3e7e33f09274b6090e2162f07a9d6dcb13a3a3cd95441d6955f5e7c316.jpg) + +![](images/156c7230170a6f3b37a04fe854edfa0a6c3d5e94868782646c0e72258bf41dd9.jpg) + +Limitations. As shown in Fig. 4, REACT struggles on the PatchCamelyon dataset, a cancer cell recognition benchmark. We visualize the retrieved samples and the samples from the original training set in Fig. 5b. The retrieved images are either instruction photos and from another sensing method, which exhibits a different visual distribution from PatchCamelyon. This suggests the importance of ensuring the retrieval quality for the domain-of-interest. + +# 4.2. Image-Text Retrieval + +To demonstrate the generality of REACT, we consider Flickr30K [64] and MSCOCO [30] image-text retrieval tasks, in both zero-shot and full-shot settings. We use the standard image-text contrastive objective [43]. For image-text retrieval task, following [20, 43], we use the CLIP-L/14 with 336x336 input resolution in both zero-shot, customization, and fine-tuning stage. We use the captions from MSCOCO as queries to retrieve 6M image-text pairs and perform customization. Note that none of the caption queries are used in the model training stage. + +As shown in Table 3, REACT improves the generic CLIP counterparts on both zero-shot and full-shot retrieval for Flickr30K and MSCOCO datasets. The gain on zero-shot task transfer is large. On Flickr30K, it achieves $3.4\% /10.0\%$ recall improvement for I2T and T2I retrieval, respectively. Afer fine-tuning on full training data, REACT still improves over the baseline slightly. It provides another piece of ev + +
MethodFlickr30KMSCOCO
Img → TextText → ImgImg → TextText → Img
R@1R@5R@1R@5R@1R@5R@1R@5
Zero-ShotImgBert [42]70.790.254.379.644.071.232.359.0
ALIGN [20]88.698.775.793.858.683.045.669.8
CLIP [43]88.098.768.790.658.481.537.862.4
CLIP†87.098.366.588.059.280.737.862.4
REACT90.499.176.593.763.385.147.572.0
Bletchley†90.898.278.094.066.785.648.972.7
REACT92.198.779.294.767.785.950.574.4
Fine-tunedGPO [5]88.798.976.194.568.190.252.780.2
ALIGN [20]95.399.884.997.477.093.559.983.3
CLIP†96.499.886.597.978.393.860.983.8
REACT96.699.986.898.078.794.061.184.1
+ +Table 3. Image-text retrieval results on Flickr30K [41] and MSCOCO [30] datasets. CLIP†, Bletchley†: our evaluation. + +
Pretrain MethodBackboneRegion +ProposalsMSCOCO AP50
NovelBaseAll
Zero-ShotCLIPResNet-50GT58.658.258.3
REACTResNet-50GT58.9 (+0.3)59.4 (+1.2)59.3 (+1.0)
CLIPResNet-50RPN29.724.025.5
REACTResNet-50RPN31.6 (+1.9)25.4 (+1.4)27.0 (+1.5)
OVDCLIPResNet-50-14.252.842.7
REACTResNet-50-20.6 (+6.4)55.1 (+2.3)46.1 (+3.4)
+ +Table 4. Zero-shot and open-vocabulary object detection results on MSCOCO [30] dataset using RegionCLIP [69] pipeline. + +idence for REACT in data-rich settings. Furthermore, we conduct the same customization procedure of REACT on a large checkpoint Bletchley [53] with 864M parameters, and observe consistent gains over both datasets. It demonstrates that REACT scales well with model size on retrieval tasks. + +# 4.3. Dense Prediction Tasks + +Although REACT is optimized with the image-level contrastive loss during the customization stage, we find it beneficial for dense prediction tasks as well. We showcase its application to dense prediction tasks on object detection and semantic segmentation. + +Object Detection. For object detection, we choose the state-of-the-art RegionCLIP [69] as our framework. We conduct experiments in two settings: zero-shot inference and open-vocabulary object detection (OVD) on MSCOCO dataset. We perform the model customization following the same setting as Sec. 4.2. Following RegionCLIP, we conduct experiments on ResNet50 backbone. The results are shown in Table 4. REACT consistently improves over CLIP checkpoint under all settings. + +For zero-shot inference, when ground-truth region proposal is used, REACT improves over CLIP by $+1.0$ on overall AP50; when the pretrained RPN is used, REACT demonstrates $+1.5 / + 1.4 / + 1.9$ AP50 improvements on novel, base, and all classes, respectively. + +For OVD, we can see that with the REACT, the detector yields improved performance on base with $+2.3$ AP50, and + +
MethodmIoU
zero-shotw/ refinew/ finetune
MaskCLIP [70]12.514.618.1
REACT (Locked-Text)14.4 (+1.9)18.2 (+3.6)20.7 (+2.6)
REACT (Locked-Text Gated-Image)14.5 (+2.0)16.3 (+1.7)19.2 (+1.1)
+ +importantly, it significantly improves novel categories with +6.4 AP50. This suggests that the injected knowledge during the model customization stage improves the learned fine-grained visual feature that is beneficial to both seen and unseen categories for object detection, when the downstream coarse-grained data is available. This is favored, because (1) the weakly-supervised data such as the coarse-grained image-text pairs requires much less human annotation cost than fine-grained bounding box annotation, (2) the paired data in REACT is free, as it is retrieved from the web, where COCO image-text pairs are not used in customized training. + +Semantic Segmentation. For semantic segmentation, we choose the state-of-the-art MaskCLIP [70] as the framework. It investigates three evaluation settings for segmentation. First, it makes use of the pretrained CLIP checkpoint to discover the alignment between grid visual features and the text prompt features, so as to perform zero-shot semantic segmentation. Second, to further improve the performance, MaskCLIP [70] proposes two techniques for refining its zero-shot predictions: key smoothing and prompt denoising. Lastly, when the training images are available, without the need to access the training labels, it further proposes MaskCLIP + [70] to perform full-shot finetuning on the target training set using pseudo-labels. Following MaskCLIP [70], we use ViT-B/16 checkpoints, and use their official code base to train and evaluate models. We report results in Table 5. + +On all of the three settings, REACT demonstrates improvements over the MaskCLIP. Notably, when refinement techniques are used, REACT with locked-text tuning demonstrates a significant $3.6\%$ gain in mIoU. Surprisingly, without seeing the downstream COCO images, the zero-shot evaluation of REACT (18.2) even slightly outperforms MaskCLIP+ (18.1), which is finetuned on the downstream training COCO images with self-training. + +Summary. These results are encouraging, as it shows that the customized knowledge from REACT transfers well to dense prediction tasks like detection and segmentation. + +# 4.4. Ablation Studies + +We ablate REACT on ImageNet with CLIP ViT-B/32 checkpoint, with 10M retrieved image-text pairs from LAION-400M. See more ablations in supplementary. + +Tuning strategy. We ablate the design choices in the model customization stage: (1) direct tuning the pre-trained weights vs. training gated blocks from scratch; (2) updating visual vs.text encoder. We report results in Table 6. First, a frozen text + +Table 5. Zero-shot and annotation-free semantic segmentation results on COCO Stuff [30] using MaskCLIP [70] (ViT-B/16). + +
MethodVisualText# Train.IN1K Acc.COCO R@1 T2II2T
DirectCLIP [43]XX-63.248.829.9
Locked-Image [68]X✓63.4M63.750.534.2
Locked-Text✓X88.1M66.951.136.1
Full-model✓✓151.3M64.354.337.9
GatedX✓18.9M63.049.533.5
Locked-Text Gated-Image✓X42.5M68.653.438.1
✓✓89.8M68.754.339.9
+ +encoder consistently outperforms a frozen visual encoder. We conjecture the phenomenon is due to that the retrieved texts have a much more limited space, comparing to text space in the original pre-training set (e.g. LAION-400M), as the concepts are limited to the query classes from the target domain. Therefore, fine-tuning the text encoder may tend to collapse the pre-trained semantic space. + +We advocate two tuning methods for model customization. Locked-text gated-image tuning has a strong adaptation power, and is efficient in the model customization stage, with fewer trainable parameters. Locked-text tuning is also an effective way of customizing the models to downstream tasks, without the need of adding extra parameters. By default, we use gated blocks for its superior performance and efficiency. + +Retrieval size. We observe that training with a small retrieval size is more likely to overfit. We find that a larger retrieval size generally yields better performance, and saturates at around 6-10M image-text pairs. + +Table 6. Ablation: tuning strategy. For our model customization purpose, we advocate locked-text (gated-image) tuning methods in gray rows. $\checkmark$ : trainable, $\mathcal{X}$ : locked. + +
Retrieval Size01M3M6M10M
ImageNet-1K Accuracy63.264.866.968.668.6
+ +# 5. Conclusion + +We presented REACT, a plug-and-play framework for leveraging large-scale image-text corpus as external knowledge to efficiently customize models on downstream tasks. Extensive experiments demonstrate its generality and effectiveness in image classification, image-text retrieval, object detection, and semantic segmentation, on more than 20 different downstream datasets. We highly advocate the model customization stage for building more transferable visual system for different downstream tasks. + +Acknowledgement. This work was supported in part by NSF CAREER IIS2150012, NASA 80NSSC21K0295, and Institute of Information & communications Technology Planning & Evaluation(IITP) grants funded by the Korea government(MSIT) (No. 2022- 0-00871, Development of AI Autonomy and Knowledge Enhancement for AI Agent Collaboration) and (No. RS-2022-00187238, Development of Large Korean Language Model Technology for Efficient Pre-training). + +# References + +[1] Jean-Baptiste Alayrac, Jeff Donahue, Pauline Luc, Antoine Miech, Iain Barr, Yana Hasson, Karel Lenc, Arthur Mensch, Katie Millican, Malcolm Reynolds, et al. Flamingo: a visual language model for few-shot learning. arXiv preprint arXiv:2204.14198, 2022. 4 +[2] Andreas Blattmann, Robin Rombach, Kaan Oktay, and Björn Ommer. 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Lafite2: Few-shot text-to-image generation. arXiv preprint arXiv:2210.14124, 2022. 3 \ No newline at end of file diff --git a/2023/Learning Customized Visual Models With Retrieval-Augmented Knowledge/images.zip b/2023/Learning Customized Visual Models With Retrieval-Augmented Knowledge/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..f05162223f927050e445a6829cfcf0be0a481585 --- /dev/null +++ b/2023/Learning Customized Visual Models With Retrieval-Augmented Knowledge/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:f1d4fee7a8315442c308faeb078a0ad5f0effde28ca2fa58eb5e7c1ab4e8f40d +size 501345 diff --git a/2023/Learning Customized Visual Models With Retrieval-Augmented Knowledge/layout.json b/2023/Learning Customized Visual Models With Retrieval-Augmented Knowledge/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..f6cf54047e04efdc8c34130807b55203c6de42f4 --- /dev/null +++ b/2023/Learning Customized Visual Models With Retrieval-Augmented Knowledge/layout.json @@ -0,0 +1,11189 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 65, + 103, + 529, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 103, + 529, + 121 + ], + "spans": [ + { + "bbox": [ + 65, + 103, + 529, + 121 + ], + "type": "text", + "content": "Learning Customized Visual Models with Retrieval-Augmented Knowledge" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 65, + 143, + 527, + 199 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 143, + 527, + 199 + ], + "spans": [ + { + "bbox": [ + 65, + 143, + 527, + 199 + ], + "type": "text", + "content": "Haotian Liu†§◆ Kilho Son‡ Jianwei Yang‡ Ce Liu‡ Jianfeng Gao‡ Yong Jae Lee† Chunyuan Li†¶ University of Wisconsin–Madison ‡ Microsoft {lht,yongjaeelee}@cs.wisc.edu {kilhoson, jianwyan, ce.liu, jfgao, chunyl}@microsoft.com https://react-v1.github.io" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 143, + 227, + 192, + 239 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 227, + 192, + 239 + ], + "spans": [ + { + "bbox": [ + 143, + 227, + 192, + 239 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 252, + 290, + 480 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 252, + 290, + 480 + ], + "spans": [ + { + "bbox": [ + 46, + 252, + 290, + 480 + ], + "type": "text", + "content": "Image-text contrastive learning models such as CLIP have demonstrated strong task transfer ability. The high generality and usability of these visual models is achieved via a web-scale data collection process to ensure broad concept coverage, followed by expensive pre-training to feed all the knowledge into model weights. Alternatively, we propose REACT, REtrieval-Augmented CusTomization, a framework to acquire the relevant web knowledge to build customized visual models for target domains. We retrieve the most relevant image-text pairs (" + }, + { + "bbox": [ + 46, + 252, + 290, + 480 + ], + "type": "inline_equation", + "content": "\\sim 3\\%" + }, + { + "bbox": [ + 46, + 252, + 290, + 480 + ], + "type": "text", + "content": " of CLIP pre-training data) from the web-scale database as external knowledge and propose to customize the model by only training new modularized blocks while freezing all the original weights. The effectiveness of REACT is demonstrated via extensive experiments on classification, retrieval, detection and segmentation tasks, including zero, few, and full-shot settings. Particularly, on the zero-shot classification task, compared with CLIP, it achieves up to " + }, + { + "bbox": [ + 46, + 252, + 290, + 480 + ], + "type": "inline_equation", + "content": "5.4\\%" + }, + { + "bbox": [ + 46, + 252, + 290, + 480 + ], + "type": "text", + "content": " improvement on ImageNet and " + }, + { + "bbox": [ + 46, + 252, + 290, + 480 + ], + "type": "inline_equation", + "content": "3.7\\%" + }, + { + "bbox": [ + 46, + 252, + 290, + 480 + ], + "type": "text", + "content": " on the ELEVATER benchmark (20 datasets)." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 518, + 128, + 530 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 518, + 128, + 530 + ], + "spans": [ + { + "bbox": [ + 47, + 518, + 128, + 530 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 539, + 288, + 684 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 539, + 288, + 684 + ], + "spans": [ + { + "bbox": [ + 46, + 539, + 288, + 684 + ], + "type": "text", + "content": "It has been a fundamental research problem in computer vision (CV) to build a transferable visual system that can easily adapt to a wide range of downstream tasks. With remarkable advances in deep learning, a de facto solution to achieve this is to train deep neural networks on a large amount of data to pursue the so-called generic visual representations. This dates back to the standard supervised training on ImageNet [10], whose superb representation power is further demonstrated in BiT [23]/ViT [12] by scaling up the training to JFT300M [50]. Along the way, recent efforts have been applied to the popular image self-supervised learning [6, 16, 17] to reduce the demand for labeled data. The" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 228, + 547, + 288 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 228, + 547, + 288 + ], + "spans": [ + { + "bbox": [ + 306, + 228, + 547, + 288 + ], + "type": "text", + "content": "third approach is image-text contrastive learning trained on billion-scale web-crawled image-text pairs. Such models, like CLIP [43] and ALIGN [20], are able to achieve great performance on different downstream domains, without the need of any human labels." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 289, + 548, + 494 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 289, + 548, + 494 + ], + "spans": [ + { + "bbox": [ + 304, + 289, + 548, + 494 + ], + "type": "text", + "content": "Excellent empirical performance has been achieved with the above three pre-training methods, by following the well established two-stage pre-training then adaptation pipeline: model pre-training from scratch on large data, then model adaptation directly on downstream tasks. Specifically, the pre-trained models are adapted to downstream tasks by considering the available task-specific samples only: either evaluated in a zero-shot task transfer manner, or updated using linear probing (LP) [43], finetuning (FT) [27], or prompt tuning [44, 71]. Following this two-stage pipeline, most research has reverted to the faith that building transferable visual systems is equivalent to developing more generic visual models by feeding all knowledge in the model pre-training stage. Therefore, the community has been witnessing a trend in exploring scaling success of pre-training model and data size with less care on the target domain, hoping that the model can adapt to any downstream scenario." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 496, + 548, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 496, + 548, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 496, + 548, + 628 + ], + "type": "text", + "content": "In this paper, we argue that the conventional two-stage pipeline above is over-simplified and less efficient, in achieving the goal of building a transferable visual system in real-world settings. Instead, we propose a customization stage in between the pre-training and adaptation, where customization is implemented by systematically leveraging retrieved external knowledge. The inspiration comes from how humans are specialized in society for better generalization: instead of trying to memorize all concepts, humans are trained/prepared in a relevant subject to master a certain skill, while maintaining the basic skills in pre-training." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 630, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 548, + 715 + ], + "type": "text", + "content": "To this end, we explore a systematic approach to acquire and learn with external knowledge sources from a large image-text corpus for model customization. The process of collecting external image-text knowledge is fully automatic without extra human annotation. The acquired knowledge typically contains richer information about the concept: relevant images that never appear in the downstream training" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 693, + 287, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 693, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 693, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\spadesuit" + }, + { + "bbox": [ + 46, + 693, + 287, + 713 + ], + "type": "text", + "content": " core contribution; equal advising; work initiated during an internship at Microsoft." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "15148" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 71, + 160, + 192 + ], + "blocks": [ + { + "bbox": [ + 50, + 71, + 160, + 192 + ], + "lines": [ + { + "bbox": [ + 50, + 71, + 160, + 192 + ], + "spans": [ + { + "bbox": [ + 50, + 71, + 160, + 192 + ], + "type": "image", + "image_path": "e6247859f1503f6566ad699b8aba5f6c5dd7dc2bc67e17751012a9694eb7de18.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 197, + 547, + 251 + ], + "lines": [ + { + "bbox": [ + 46, + 197, + 547, + 251 + ], + "spans": [ + { + "bbox": [ + 46, + 197, + 547, + 251 + ], + "type": "text", + "content": "Figure 1. REACT achieves the best zero-shot ImageNet performance among public checkpoints (Left), achieves new SoTA on semi-supervised ImageNet classification in the " + }, + { + "bbox": [ + 46, + 197, + 547, + 251 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 46, + 197, + 547, + 251 + ], + "type": "text", + "content": " labeled data setting (Middle), and consistently transfer better than CLIP on across a variety of tasks, including ImageNet classification, zero/few/full-shot classification on 20 datasets in ELEVATER benchmark, image-text retrieval, object detection and segmentation (Right). Please see the detailed numbers and settings in the experimental section. For the left figure, circle size indicates model size." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 163, + 72, + 268, + 192 + ], + "blocks": [ + { + "bbox": [ + 163, + 72, + 268, + 192 + ], + "lines": [ + { + "bbox": [ + 163, + 72, + 268, + 192 + ], + "spans": [ + { + "bbox": [ + 163, + 72, + 268, + 192 + ], + "type": "image", + "image_path": "05195f77dc9feea22cc3d7c26014c010cd81a603a8286b190d05658467e9afc8.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 276, + 72, + 536, + 194 + ], + "blocks": [ + { + "bbox": [ + 276, + 72, + 536, + 194 + ], + "lines": [ + { + "bbox": [ + 276, + 72, + 536, + 194 + ], + "spans": [ + { + "bbox": [ + 276, + 72, + 536, + 194 + ], + "type": "image", + "image_path": "ae4b32cdce349650530b2ed5da356abb50406c1cf8adc128c44c620a3176d167.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 262, + 288, + 370 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 262, + 288, + 370 + ], + "spans": [ + { + "bbox": [ + 46, + 262, + 288, + 370 + ], + "type": "text", + "content": "and evaluation set, and richer text descriptions about concept semantics. Such multi-modal knowledge sources are generally available on the web, and further open-sourced like LAION [45, 46]. They cover a variety of domains, making it possible to develop customized visual models for task-level transfer. Similar retrieval-augmented intuitions have been exploited in computer vision for class-level transfer [32], but not yet for task-level transfer (similar to that of CLIP). Our main findings/contributions can be summarized as follows." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 374, + 288, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 374, + 288, + 578 + ], + "spans": [ + { + "bbox": [ + 46, + 374, + 288, + 578 + ], + "type": "text", + "content": "We propose to explore the potential of the web-scale image-text corpus as external knowledge to significantly improve task-level transfer performance on the target domain at an affordable cost. A simple and effective strategy is proposed. To begin with, we build a large-scale multimodal indexing system to retrieve the relevant image-text pairs using CLIP features and approximate nearest neighbor search. For a CV problem, the task instruction is often sufficiently specified with text such as class names, which allows us to utilize them as queries to retrieve the relevant image-text pair knowledge from the indexing system. No images from the CV problem are needed. To efficiently build the customized visual model, we propose a novel modularized learning strategy: only updating the additional trainable weights on the retrieved knowledge, and freezing the original model weights. Hence, the model masters the new skill without forgetting basic skills." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "text", + "content": "The generality and effectiveness of the proposed customization strategy is demonstrated on four CV problems. We instantiate it with CLIP, and develop the customized visual models for image classification on ImageNet and 20 datasets in ELEVATER [27], image-text retrieval on COCO [30]/Flickr [41], as well as object detection and semantic segmentation on COCO [30]. The knowledge bases are considered as LAION [46] and larger web-crawled multimodal data. The retrieval-augmented knowledge (" + }, + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\sim 3\\%" + }, + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "text", + "content": " image-text pairs compared with the original training data) significantly improves the model's zero-shot performance" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 262, + 547, + 357 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 262, + 547, + 357 + ], + "spans": [ + { + "bbox": [ + 304, + 262, + 547, + 357 + ], + "type": "text", + "content": "without the need of accessing any images on downstream tasks. See Figure 1 for highlighted results. For example, our ViT-L/14 checkpoint achieves " + }, + { + "bbox": [ + 304, + 262, + 547, + 357 + ], + "type": "inline_equation", + "content": "78.5\\%" + }, + { + "bbox": [ + 304, + 262, + 547, + 357 + ], + "type": "text", + "content": " zero-shot accuracy on ImageNet [10], surpassing all public checkpoints from CLIP [43] and OpenCLIP [18], including those with larger model size and trained on a much larger LAION-2B [45]. The new customized models demonstrate higher few/full-shot performance than the generic model counterparts." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 359, + 547, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 359, + 547, + 456 + ], + "spans": [ + { + "bbox": [ + 304, + 359, + 547, + 456 + ], + "type": "text", + "content": "Our retrieval system, codebase, and pre-trained models are publicly available. To make this line of research more accessible, our retrieved subsets for both ELEVATER and ImageNet will also be made available, with an easy-to-use toolkit to download the subsets without storing the whole dataset locally. It poses a feasible direction for leveraging the ever-increasing data from the Internet for customized visual recognition, especially for the low-resource regimes." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 466, + 392, + 479 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 466, + 392, + 479 + ], + "spans": [ + { + "bbox": [ + 306, + 466, + 392, + 479 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 485, + 548, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 485, + 548, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 485, + 548, + 714 + ], + "type": "text", + "content": "Vision-Language Pretraining. Learning transferable visual representations from natural language supervision is an emerging research area. The pioneering works of CLIP [43] and ALIGN [20] make use of contrastive learning to pretrain models on billion-scale web-crawled image-text pairs. There are an increasing number of studies to improve their generality from various modeling perspectives, including training objectives [11,13,14,38,65,68], scaling techniques [9,40,65], data efficiency [25,28], and leveraging multilingual correlations [9, 19]. In academia, several works demonstrate techniques to improve the learned semantic representations on datasets at a smaller scale (e.g. CC3M [47], CC12M [4], YFCC15M [43, 51]), by exploring pretraining on a unified image-text-label space [59], token-level contrastive loss [61], and auxiliary within-modality contrastive loss [29,37,58,63]. Complementary to the above works, we build on top of existing pre-trained generic models, and aim to improve the model's performance by customizing them using retrieved relevant image-text pairs." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "15149" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 263 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 263 + ], + "type": "text", + "content": "Retrieval-Augmented Models. In natural language processing, several works augment large language models with external data encoded with structured language and relation representations [3, 15, 22, 26, 31, 39, 66]. Motivated by retrieval-augmented models in NLP, several recent works leverage visual and / or textual knowledge to improve classification [32], question answering [7, 35, 56, 60], image generation [2, 8, 49, 72], and multi-modal tasks simultaneously [62]. RAC [32] improves long-tail classification by retrieving from a non-parametric memory consisting of pre-encoded images and text. K-LITE [48] enhances the text prompts with the retrieved external knowledge that is encoded in natural language. Our paper leverages the paired knowledge of image-text and aims to improve task transfer performance for core vision problems such as classification, retrieval, detection and segmentation." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 267, + 290, + 448 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 267, + 290, + 448 + ], + "spans": [ + { + "bbox": [ + 46, + 267, + 290, + 448 + ], + "type": "text", + "content": "Adaptation of Vision-Language models. CLIP demonstrates impressive zero-shot and linear probing performance on different downstream domains. Several works explore improving the domain adaptation performance on CLIP models. ELEVATER [27] leverages the text encoder outputs to initialize the task-specific linear head to improve the linear probe and finetuning performance of CLIP. Inspired by prompting techniques in NLP, recent works [44, 71] make use of learnable prompts that are trained on a few samples on downstream tasks. Similar to these works, this paper aims to improve CLIP's performance on downstream tasks, while making use of relevant image-text pairs data to improve the model's performance, without access to the downstream images. Furthermore, when downstream samples are available, they are complimentary to our method." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 453, + 250, + 466 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 453, + 250, + 466 + ], + "spans": [ + { + "bbox": [ + 47, + 453, + 250, + 466 + ], + "type": "text", + "content": "3. Retrieval-Augmented Customization" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 470, + 133, + 481 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 470, + 133, + 481 + ], + "spans": [ + { + "bbox": [ + 47, + 470, + 133, + 481 + ], + "type": "text", + "content": "3.1. Preliminaries" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 486, + 288, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 486, + 288, + 641 + ], + "spans": [ + { + "bbox": [ + 46, + 486, + 288, + 641 + ], + "type": "text", + "content": "Computer vision models have achieved strong transfer performance, when learning with large-scale image data only [17], image-label data [23] and/or image-caption data [43,59,67]. Without loss of generality, we follow [59] and define a unified triplet-wise format " + }, + { + "bbox": [ + 46, + 486, + 288, + 641 + ], + "type": "inline_equation", + "content": "(\\pmb{x},\\pmb{t},y)" + }, + { + "bbox": [ + 46, + 486, + 288, + 641 + ], + "type": "text", + "content": " for imagetext-label data, where " + }, + { + "bbox": [ + 46, + 486, + 288, + 641 + ], + "type": "inline_equation", + "content": "\\pmb{x}\\in \\mathcal{X}" + }, + { + "bbox": [ + 46, + 486, + 288, + 641 + ], + "type": "text", + "content": " is an image, " + }, + { + "bbox": [ + 46, + 486, + 288, + 641 + ], + "type": "inline_equation", + "content": "t\\in \\mathcal{T}" + }, + { + "bbox": [ + 46, + 486, + 288, + 641 + ], + "type": "text", + "content": " is its language description, and " + }, + { + "bbox": [ + 46, + 486, + 288, + 641 + ], + "type": "inline_equation", + "content": "y\\in \\mathcal{V}" + }, + { + "bbox": [ + 46, + 486, + 288, + 641 + ], + "type": "text", + "content": " is a label indicating the index of the unique language description in the dataset. In a general form, the language description is a text sequence " + }, + { + "bbox": [ + 46, + 486, + 288, + 641 + ], + "type": "inline_equation", + "content": "\\pmb{t} = [t_1,\\dots ,t_L]" + }, + { + "bbox": [ + 46, + 486, + 288, + 641 + ], + "type": "text", + "content": ". It ranges from simple category names representing visual concepts when " + }, + { + "bbox": [ + 46, + 486, + 288, + 641 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 486, + 288, + 641 + ], + "type": "text", + "content": " is small, to more freeform and semantic-rich sentences such as captions when " + }, + { + "bbox": [ + 46, + 486, + 288, + 641 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 486, + 288, + 641 + ], + "type": "text", + "content": " is relatively large." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 642, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 289, + 714 + ], + "type": "text", + "content": "A typical transfer learning pipeline follows the procedure of pre-training then adaptation: (i) With large-scale pre-training, an image encoder foundation model " + }, + { + "bbox": [ + 46, + 642, + 289, + 714 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 46, + 642, + 289, + 714 + ], + "type": "text", + "content": " parameterized by " + }, + { + "bbox": [ + 46, + 642, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\pmb{\\theta}" + }, + { + "bbox": [ + 46, + 642, + 289, + 714 + ], + "type": "text", + "content": " is first trained to represent image " + }, + { + "bbox": [ + 46, + 642, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\pmb{x}" + }, + { + "bbox": [ + 46, + 642, + 289, + 714 + ], + "type": "text", + "content": " as a visual feature vector " + }, + { + "bbox": [ + 46, + 642, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\tilde{\\pmb{v}} \\in \\mathbb{R}^{P \\times 1}" + }, + { + "bbox": [ + 46, + 642, + 289, + 714 + ], + "type": "text", + "content": ": " + }, + { + "bbox": [ + 46, + 642, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\tilde{\\pmb{v}} = f_{\\pmb{\\theta}}(\\pmb{x})" + }, + { + "bbox": [ + 46, + 642, + 289, + 714 + ], + "type": "text", + "content": ". For recent language-image models [43], a dual-encoder architecture is often em" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 315, + 73, + 535, + 247 + ], + "blocks": [ + { + "bbox": [ + 315, + 73, + 535, + 247 + ], + "lines": [ + { + "bbox": [ + 315, + 73, + 535, + 247 + ], + "spans": [ + { + "bbox": [ + 315, + 73, + 535, + 247 + ], + "type": "image", + "image_path": "f674ef5e8723b3692b6a283aac0be7715c7d250628eabf9d4ba752065d26ca35.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 321, + 251, + 529, + 263 + ], + "lines": [ + { + "bbox": [ + 321, + 251, + 529, + 263 + ], + "spans": [ + { + "bbox": [ + 321, + 251, + 529, + 263 + ], + "type": "text", + "content": "Figure 2. Illustration of the proposed REACT framework." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 273, + 547, + 344 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 273, + 547, + 344 + ], + "spans": [ + { + "bbox": [ + 304, + 273, + 547, + 344 + ], + "type": "text", + "content": "ployed, where an additional text encoder " + }, + { + "bbox": [ + 304, + 273, + 547, + 344 + ], + "type": "inline_equation", + "content": "f_{\\phi}(\\pmb{t})" + }, + { + "bbox": [ + 304, + 273, + 547, + 344 + ], + "type": "text", + "content": " parameterized by " + }, + { + "bbox": [ + 304, + 273, + 547, + 344 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 304, + 273, + 547, + 344 + ], + "type": "text", + "content": " represents the sentence " + }, + { + "bbox": [ + 304, + 273, + 547, + 344 + ], + "type": "inline_equation", + "content": "\\tilde{\\pmb{u}} \\in \\mathbb{R}^{P \\times 1} : \\tilde{\\pmb{u}} = f_{\\phi}(\\pmb{t})" + }, + { + "bbox": [ + 304, + 273, + 547, + 344 + ], + "type": "text", + "content": ". (ii) Given a downstream task, model adaptation is typically performed using the available task-specific information, or task instruction " + }, + { + "bbox": [ + 304, + 273, + 547, + 344 + ], + "type": "inline_equation", + "content": "\\mathcal{I}" + }, + { + "bbox": [ + 304, + 273, + 547, + 344 + ], + "type": "text", + "content": ". For example, the task-level transfer of a language-image model is described as:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 310, + 347, + 547, + 472 + ], + "type": "list", + "angle": 0, + "index": 11, + "blocks": [ + { + "bbox": [ + 310, + 347, + 545, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 347, + 545, + 407 + ], + "spans": [ + { + "bbox": [ + 310, + 347, + 545, + 407 + ], + "type": "text", + "content": "- Zero-shot. In a customized setting, the simplest task definition can be provided as a set of category names for visual recognition, leading to the task instruction " + }, + { + "bbox": [ + 310, + 347, + 545, + 407 + ], + "type": "inline_equation", + "content": "\\mathcal{I}_0 = \\{t\\}" + }, + { + "bbox": [ + 310, + 347, + 545, + 407 + ], + "type": "text", + "content": ". No training image " + }, + { + "bbox": [ + 310, + 347, + 545, + 407 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 310, + 347, + 545, + 407 + ], + "type": "text", + "content": " is available, not to mention the corresponding label " + }, + { + "bbox": [ + 310, + 347, + 545, + 407 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 310, + 347, + 545, + 407 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 310, + 411, + 547, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 411, + 547, + 472 + ], + "spans": [ + { + "bbox": [ + 310, + 411, + 547, + 472 + ], + "type": "text", + "content": "- Few/Full-shot. The users may spend annotation cost to curate " + }, + { + "bbox": [ + 310, + 411, + 547, + 472 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 310, + 411, + 547, + 472 + ], + "type": "text", + "content": " image-label pairs as the training instances, making the task instruction more specific, " + }, + { + "bbox": [ + 310, + 411, + 547, + 472 + ], + "type": "inline_equation", + "content": "\\mathcal{I}_{\\mathrm{F}} = \\{(x_{n},t_{n},y_{n})\\}_{n = 1}^{N}" + }, + { + "bbox": [ + 310, + 411, + 547, + 472 + ], + "type": "text", + "content": ", which allows updating the image encoder model " + }, + { + "bbox": [ + 310, + 411, + 547, + 472 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 310, + 411, + 547, + 472 + ], + "type": "text", + "content": " for better adaptation performance." + } + ] + } + ], + "index": 10 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 304, + 474, + 547, + 630 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 547, + 630 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 547, + 630 + ], + "type": "text", + "content": "In this paper, we assume there exists a web-scale image-text corpus as the external knowledge source " + }, + { + "bbox": [ + 304, + 474, + 547, + 630 + ], + "type": "inline_equation", + "content": "S = \\{(x_{m}, t_{m})\\}_{m=1}^{M}" + }, + { + "bbox": [ + 304, + 474, + 547, + 630 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 474, + 547, + 630 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 474, + 547, + 630 + ], + "type": "text", + "content": " is the database size, e.g. 400M for LAION [46]. One may use the task instruction " + }, + { + "bbox": [ + 304, + 474, + 547, + 630 + ], + "type": "inline_equation", + "content": "\\mathcal{I}" + }, + { + "bbox": [ + 304, + 474, + 547, + 630 + ], + "type": "text", + "content": " as a query to seek additional relevant knowledge to build a more transferable visual system. Given the downstream task instruction " + }, + { + "bbox": [ + 304, + 474, + 547, + 630 + ], + "type": "inline_equation", + "content": "\\mathcal{I}" + }, + { + "bbox": [ + 304, + 474, + 547, + 630 + ], + "type": "text", + "content": " and an external knowledge source " + }, + { + "bbox": [ + 304, + 474, + 547, + 630 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 474, + 547, + 630 + ], + "type": "text", + "content": ", our goal is to learn customized visual-semantic representations, which are readily transferable to the downstream task of interest, whose training and evaluation images are not observed during the customization process. To this end, we propose REACT. We illustrate the high-level idea in Figure 2, and describe the process as follows." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 637, + 487, + 650 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 637, + 487, + 650 + ], + "spans": [ + { + "bbox": [ + 306, + 637, + 487, + 650 + ], + "type": "text", + "content": "3.2. Multi-modal External Knowledge" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 653, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 547, + 713 + ], + "type": "text", + "content": "Knowledge Base Construction. We explore web-scale image-text data as the multi-modal knowledge base " + }, + { + "bbox": [ + 304, + 653, + 547, + 713 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 653, + 547, + 713 + ], + "type": "text", + "content": " in this paper. Ideally, one may consider the entire web as the knowledge base, and use Google or Bing search to retrieve the relevant knowledge. We consider two large static datasets" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "15150" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "type": "text", + "content": "with image-text pairs. To control the experiment complexity and ensure reproducibility, we use LAION-400M [46], a publicly available database with 400M pairs, for most of the experiments. To further study the scaling influence of the retrieval base, we conduct comparisons on Web-800M, a privately collected web database with 800M pairs." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 144, + 288, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 144, + 288, + 251 + ], + "spans": [ + { + "bbox": [ + 46, + 144, + 288, + 251 + ], + "type": "text", + "content": "To facilitate an efficient knowledge acquisition process, we use pre-trained contrastive models (e.g. CLIP) as the feature extractor, and build a cross-modal retrieval system using FAISS [21]. We use its Hierarchical Navigable Small World (HNSW) approximate " + }, + { + "bbox": [ + 46, + 144, + 288, + 251 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 144, + 288, + 251 + ], + "type": "text", + "content": "-NN lookup [34] to balance performance and efficiency. Please see appendix for more details. After the retrieval system is built on the designated retrieval pool, it can be efficiently used for retrieving relevant image-text pairs for various downstream domains." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 256, + 287, + 447 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 256, + 287, + 447 + ], + "spans": [ + { + "bbox": [ + 46, + 256, + 287, + 447 + ], + "type": "text", + "content": "Retrieval-Augmented Task Instruction. To facilitate the same interface for various customized visual tasks in the wild, it is desirable to have the same uniform task instruction schema. In NLP, all task instructions can follow the same uniform schema, composed of task definition and positive/negative examples [36, 55]. Here, the task definition defines a given task in natural language, completely specifying how an input is expected to be mapped to an output text. We note a coherence connection between this NLP task schema and the customized zero/few/full-shot CV settings in Section 3.1. Following a similar schema, the minimum requirement to specify a visual task is the task definition " + }, + { + "bbox": [ + 46, + 256, + 287, + 447 + ], + "type": "inline_equation", + "content": "\\mathcal{I}_0" + }, + { + "bbox": [ + 46, + 256, + 287, + 447 + ], + "type": "text", + "content": ", where category names illustrate the target visual concepts in natural language. Though adding human-annotated examples is a natural way to clarify the task and yield the complete schema " + }, + { + "bbox": [ + 46, + 256, + 287, + 447 + ], + "type": "inline_equation", + "content": "\\mathcal{I}_{\\mathrm{F}}" + }, + { + "bbox": [ + 46, + 256, + 287, + 447 + ], + "type": "text", + "content": ", extra cost is introduced." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 449, + 288, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 449, + 288, + 556 + ], + "spans": [ + { + "bbox": [ + 46, + 449, + 288, + 556 + ], + "type": "text", + "content": "It is of high interest to clarify the task using relevant examples, without human curating cost. Therefore, we propose to augment the task instruction with the retrieved examples from the external multi-modal knowledge base " + }, + { + "bbox": [ + 46, + 449, + 288, + 556 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 449, + 288, + 556 + ], + "type": "text", + "content": ". For each concept " + }, + { + "bbox": [ + 46, + 449, + 288, + 556 + ], + "type": "inline_equation", + "content": "t \\in \\mathcal{I}_0" + }, + { + "bbox": [ + 46, + 449, + 288, + 556 + ], + "type": "text", + "content": " in a given task, we first represent it in natural language " + }, + { + "bbox": [ + 46, + 449, + 288, + 556 + ], + "type": "inline_equation", + "content": "q = g_{prompt}(t)" + }, + { + "bbox": [ + 46, + 449, + 288, + 556 + ], + "type": "text", + "content": " using the language prompt as in [43], through inserting the concept into a set of task-specific templates " + }, + { + "bbox": [ + 46, + 449, + 288, + 556 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 46, + 449, + 288, + 556 + ], + "type": "text", + "content": ". The task definition is expanded in its natural language form:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 59, + 566, + 288, + 580 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 566, + 288, + 580 + ], + "spans": [ + { + "bbox": [ + 59, + 566, + 288, + 580 + ], + "type": "interline_equation", + "content": "\\mathcal {Q} = \\left\\{\\boldsymbol {q} \\mid \\boldsymbol {q} = g _ {\\text {p r o m p t}} (\\boldsymbol {t}), \\forall \\boldsymbol {t} \\in \\mathcal {I} _ {0}, \\text {p r o m p t} \\in \\mathcal {P} \\right\\}. \\tag {1}", + "image_path": "090bde9246ea12540556118ef86dde7c57db414d2f7e0a9e764554c4da0fd4b7.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 590, + 287, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 590, + 287, + 639 + ], + "spans": [ + { + "bbox": [ + 46, + 590, + 287, + 639 + ], + "type": "text", + "content": "Next, we perform our knowledge retrieval process to acquire the relevant image-text pair " + }, + { + "bbox": [ + 46, + 590, + 287, + 639 + ], + "type": "inline_equation", + "content": "s = g_{\\text{retrieve}}(q)" + }, + { + "bbox": [ + 46, + 590, + 287, + 639 + ], + "type": "text", + "content": " from the source " + }, + { + "bbox": [ + 46, + 590, + 287, + 639 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 590, + 287, + 639 + ], + "type": "text", + "content": ". Two types of retrieval processes are considered to acquire the top- " + }, + { + "bbox": [ + 46, + 590, + 287, + 639 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 590, + 287, + 639 + ], + "type": "text", + "content": " pairs:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 51, + 641, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 641, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 51, + 641, + 287, + 677 + ], + "type": "text", + "content": "- Text-to-Text (T2T) retrieval allows us to retrieve more relevant examples as they have a better match with our target concept. The T2T-retrieved set for " + }, + { + "bbox": [ + 51, + 641, + 287, + 677 + ], + "type": "inline_equation", + "content": "\\mathcal{I}_0" + }, + { + "bbox": [ + 51, + 641, + 287, + 677 + ], + "type": "text", + "content": " is:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 61, + 687, + 287, + 708 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 687, + 287, + 708 + ], + "spans": [ + { + "bbox": [ + 61, + 687, + 287, + 708 + ], + "type": "interline_equation", + "content": "\\mathcal {S} ^ {T 2 T} = \\left\\{\\left(\\boldsymbol {x}, \\boldsymbol {t}\\right) \\in \\mathcal {S}: \\underset {\\boldsymbol {t} \\in \\mathbb {T}, | \\mathbb {T} | = K} {\\operatorname {a r g m a x}} f _ {\\phi} (\\boldsymbol {t}) ^ {\\top} f _ {\\phi} (\\boldsymbol {q}), \\forall \\boldsymbol {q} \\in \\mathcal {Q} \\right\\} \\tag {2}", + "image_path": "90bb0117af2b7e7dcfa9f83bb11b2829cfff38621bd25f952aa9c8aaa97430f1.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 310, + 72, + 547, + 107 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 72, + 547, + 107 + ], + "spans": [ + { + "bbox": [ + 310, + 72, + 547, + 107 + ], + "type": "text", + "content": "- Text-to-image (T2I) retrieval allows us to have more diversity in the text descriptions in our retrieved examples. The T2I-retrieved set for " + }, + { + "bbox": [ + 310, + 72, + 547, + 107 + ], + "type": "inline_equation", + "content": "\\mathcal{I}_0" + }, + { + "bbox": [ + 310, + 72, + 547, + 107 + ], + "type": "text", + "content": " is:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 318, + 114, + 547, + 135 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 114, + 547, + 135 + ], + "spans": [ + { + "bbox": [ + 318, + 114, + 547, + 135 + ], + "type": "interline_equation", + "content": "\\mathcal {S} ^ {T 2 I} = \\left\\{\\left(\\boldsymbol {x}, \\boldsymbol {t}\\right) \\in \\mathcal {S}: \\underset {\\boldsymbol {x} \\in \\mathbb {X}, | \\mathbb {X} | = K} {\\operatorname {a r g m a x}} f _ {\\boldsymbol {\\theta}} (\\boldsymbol {x}) ^ {\\top} f _ {\\boldsymbol {\\phi}} (\\boldsymbol {q}), \\forall \\boldsymbol {q} \\in \\mathcal {Q} \\right\\} \\tag {3}", + "image_path": "21dc9603b75c05dcf008516bea5004ed17160e69997d3069aa498d110442e6c2.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 141, + 547, + 202 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 141, + 547, + 202 + ], + "spans": [ + { + "bbox": [ + 304, + 141, + 547, + 202 + ], + "type": "text", + "content": "Both " + }, + { + "bbox": [ + 304, + 141, + 547, + 202 + ], + "type": "inline_equation", + "content": "S^{T2T}" + }, + { + "bbox": [ + 304, + 141, + 547, + 202 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 141, + 547, + 202 + ], + "type": "inline_equation", + "content": "S^{T2I}" + }, + { + "bbox": [ + 304, + 141, + 547, + 202 + ], + "type": "text", + "content": " are retrieved examples to augment the task definition " + }, + { + "bbox": [ + 304, + 141, + 547, + 202 + ], + "type": "inline_equation", + "content": "\\mathcal{I}_0" + }, + { + "bbox": [ + 304, + 141, + 547, + 202 + ], + "type": "text", + "content": ", without accessing the images in the training or validation set of the task. Compared to " + }, + { + "bbox": [ + 304, + 141, + 547, + 202 + ], + "type": "inline_equation", + "content": "\\mathcal{I}_{\\mathrm{F}}" + }, + { + "bbox": [ + 304, + 141, + 547, + 202 + ], + "type": "text", + "content": ", they are \"free\" external knowledge to clarify the task and can be used to build a more transferable system." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 209, + 430, + 220 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 209, + 430, + 220 + ], + "spans": [ + { + "bbox": [ + 306, + 209, + 430, + 220 + ], + "type": "text", + "content": "3.3. Model Customization" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 221, + 547, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 221, + 547, + 376 + ], + "spans": [ + { + "bbox": [ + 304, + 221, + 547, + 376 + ], + "type": "text", + "content": "After retrieving the relevant multi-modal examples, one may employ the naive customization solution by fine-tuning the full-model initialized from pre-trained weights, as in Figure 3(a). Alternatively, we propose an affordable solution to endow pre-trained models with a new capability to leverage this external knowledge. The pre-trained generic visual models have gained strong transfer abilities and access to a large amount of internal knowledge stored in the model weights. We freeze the weights of these models so that their initial capacity remains unchanged. To bridge these pretrained models harmoniously to the customized domain, we consider locked-text gated-image tuning with the following two techniques, illustrated in Figure 3(d)." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 380, + 547, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 380, + 547, + 548 + ], + "spans": [ + { + "bbox": [ + 304, + 380, + 547, + 548 + ], + "type": "text", + "content": "Modularized Image Encoder. In order to provide sufficient expressivity to the model and make it able to adapt well on retrieved knowledge, we insert gated self-attention dense blocks in between the original layers of the image encoder, and train the new blocks from scratch. Those blocks are made of a self-attention layer, that attends the early layer inputs, followed by an extra dense feed-forward layer. Please see a visual illustration of this gated block in the rightmost of Figure 3(d). We denote the parameters of all new modules as " + }, + { + "bbox": [ + 304, + 380, + 547, + 548 + ], + "type": "inline_equation", + "content": "\\theta^{\\prime}" + }, + { + "bbox": [ + 304, + 380, + 547, + 548 + ], + "type": "text", + "content": ". This design is inspired by the gated cross-attention-dense blocks in Flamingo [1] and frozen multi-modal model [52]. The difference is that the trainable module is introduced in Flamingo to enable cross-modal conditioning, while we adapt it for model growing in new customized domains." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 552, + 547, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 552, + 547, + 658 + ], + "spans": [ + { + "bbox": [ + 304, + 552, + 547, + 658 + ], + "type": "text", + "content": "Frozen Text Encoder. The text encoder in language-image contrast models represents the task semantic space. To maintain it, we propose locked-text tuning, which freezes the text model weights so that the generic task encoding knowledge remains locked; see Figure 3(c). This is in contrast with locked-image tuning (LiT) [68] in Figure 3(b), where the image encoder is frozen and the text encoder is fine-tuned, which teaches a text model to read out good representations from a pre-trained image model for new tasks." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 659, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 659, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 659, + 547, + 713 + ], + "type": "text", + "content": "We extract the normalized feature vectors in a hypersphere using " + }, + { + "bbox": [ + 304, + 659, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\pmb{u}_i = \\frac{f_{\\{\\theta,\\theta'\\}}(\\pmb{x}_i)}{\\|f_{\\{\\theta,\\theta'\\}}(\\pmb{x}_i)\\|}" + }, + { + "bbox": [ + 304, + 659, + 547, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 659, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\pmb{v}_j = \\frac{f_\\phi(\\pmb{t}_j)}{\\|f_\\phi(\\pmb{t}_j)\\|}" + }, + { + "bbox": [ + 304, + 659, + 547, + 713 + ], + "type": "text", + "content": ". To customize the model wrt task definition " + }, + { + "bbox": [ + 304, + 659, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{I}_0" + }, + { + "bbox": [ + 304, + 659, + 547, + 713 + ], + "type": "text", + "content": ", we update " + }, + { + "bbox": [ + 304, + 659, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\pmb{\\theta}'" + }, + { + "bbox": [ + 304, + 659, + 547, + 713 + ], + "type": "text", + "content": " using a bidirectional learning objective between images and" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15151" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 59, + 71, + 145, + 133 + ], + "blocks": [ + { + "bbox": [ + 59, + 71, + 145, + 133 + ], + "lines": [ + { + "bbox": [ + 59, + 71, + 145, + 133 + ], + "spans": [ + { + "bbox": [ + 59, + 71, + 145, + 133 + ], + "type": "image", + "image_path": "3df86e83fc2f06e2971e5ba6a241053f435a20de8cfe0867cf3119e51ef536a3.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 66, + 140, + 134, + 150 + ], + "lines": [ + { + "bbox": [ + 66, + 140, + 134, + 150 + ], + "spans": [ + { + "bbox": [ + 66, + 140, + 134, + 150 + ], + "type": "text", + "content": "(a) Full-Model Tuning" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 154, + 72, + 236, + 133 + ], + "blocks": [ + { + "bbox": [ + 154, + 72, + 236, + 133 + ], + "lines": [ + { + "bbox": [ + 154, + 72, + 236, + 133 + ], + "spans": [ + { + "bbox": [ + 154, + 72, + 236, + 133 + ], + "type": "image", + "image_path": "198e42f8f7eb524f7277a0d5e1397cde87666638f9c4b175258af7e39de42044.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 154, + 140, + 231, + 150 + ], + "lines": [ + { + "bbox": [ + 154, + 140, + 231, + 150 + ], + "spans": [ + { + "bbox": [ + 154, + 140, + 231, + 150 + ], + "type": "text", + "content": "(b) Locked-Image Tuning" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 246, + 72, + 328, + 133 + ], + "blocks": [ + { + "bbox": [ + 246, + 72, + 328, + 133 + ], + "lines": [ + { + "bbox": [ + 246, + 72, + 328, + 133 + ], + "spans": [ + { + "bbox": [ + 246, + 72, + 328, + 133 + ], + "type": "image", + "image_path": "d78649bbb20b100f35b173ed6c8b5612a7cb576d4441c247b84f70cadd3ea9ec.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 249, + 140, + 320, + 151 + ], + "lines": [ + { + "bbox": [ + 249, + 140, + 320, + 151 + ], + "spans": [ + { + "bbox": [ + 249, + 140, + 320, + 151 + ], + "type": "text", + "content": "(c) Locked-Text Tuning" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 345, + 72, + 425, + 133 + ], + "blocks": [ + { + "bbox": [ + 345, + 72, + 425, + 133 + ], + "lines": [ + { + "bbox": [ + 345, + 72, + 425, + 133 + ], + "spans": [ + { + "bbox": [ + 345, + 72, + 425, + 133 + ], + "type": "image", + "image_path": "8551b6c257124e74960d84c541ec0e015c7470c253853ceb26dcb6209140e602.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 350, + 137, + 413, + 156 + ], + "lines": [ + { + "bbox": [ + 350, + 137, + 413, + 156 + ], + "spans": [ + { + "bbox": [ + 350, + 137, + 413, + 156 + ], + "type": "text", + "content": "(d) Locked-Text Gated-Image Tuning" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 434, + 72, + 535, + 156 + ], + "blocks": [ + { + "bbox": [ + 434, + 72, + 535, + 156 + ], + "lines": [ + { + "bbox": [ + 434, + 72, + 535, + 156 + ], + "spans": [ + { + "bbox": [ + 434, + 72, + 535, + 156 + ], + "type": "image", + "image_path": "eee419d6ba26107e5e71a72b76ec94de1b06e9b0cd8f588d3be4d9ec30a086b0.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 159, + 547, + 194 + ], + "lines": [ + { + "bbox": [ + 46, + 159, + 547, + 194 + ], + "spans": [ + { + "bbox": [ + 46, + 159, + 547, + 194 + ], + "type": "text", + "content": "Figure 3. Illustrative comparisons across different model tuning methods. (a) and (b) are existing baseline tuning methods. For model customization in a target domain, we found that (c) and (d) work better. One layer of the proposed modularized image encoder in locked-text gated-image tuning is illustrated in right side." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 205, + 288, + 218 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 205, + 288, + 218 + ], + "spans": [ + { + "bbox": [ + 47, + 205, + 288, + 218 + ], + "type": "text", + "content": "language on the retrieved knowledge pool " + }, + { + "bbox": [ + 47, + 205, + 288, + 218 + ], + "type": "inline_equation", + "content": "S^{T2T}" + }, + { + "bbox": [ + 47, + 205, + 288, + 218 + ], + "type": "text", + "content": " and/or " + }, + { + "bbox": [ + 47, + 205, + 288, + 218 + ], + "type": "inline_equation", + "content": "S^{T2I}" + }, + { + "bbox": [ + 47, + 205, + 288, + 218 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 56, + 236, + 288, + 319 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 236, + 288, + 319 + ], + "spans": [ + { + "bbox": [ + 56, + 236, + 288, + 319 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\min _ {\\left\\{\\boldsymbol {\\theta} ^ {\\prime} \\right\\}} \\mathcal {L} _ {\\mathrm {C}} = \\mathcal {L} _ {i 2 t} + \\mathcal {L} _ {t 2 i}, \\text {w i t h} \\mathcal {B} \\sim \\mathcal {S} ^ {T 2 T} \\text {o r} \\mathcal {S} ^ {T 2 I} (4) \\\\ \\mathcal {L} _ {i 2 t} = - \\sum_ {i \\in \\mathcal {B}} \\frac {1}{| \\mathcal {P} (i) |} \\sum_ {k \\in \\mathcal {P} (i)} \\log \\frac {\\exp \\left(\\tau \\boldsymbol {u} _ {i} ^ {\\top} \\boldsymbol {v} _ {k}\\right)}{\\sum_ {j \\in \\mathcal {B}} \\exp \\left(\\tau \\boldsymbol {u} _ {i} ^ {\\top} \\boldsymbol {v} _ {j}\\right)} \\quad \\text {a n d} (5) \\\\ \\mathcal {L} _ {t 2 i} = - \\sum_ {j \\in \\mathcal {B}} \\frac {1}{| \\mathcal {Q} (j) |} \\sum_ {k \\in \\mathcal {Q} (j)} \\log \\frac {\\exp (\\tau \\boldsymbol {u} _ {k} ^ {\\top} \\boldsymbol {v} _ {j})}{\\sum_ {i \\in \\mathcal {B}} \\exp (\\tau \\boldsymbol {u} _ {i} ^ {\\top} \\boldsymbol {v} _ {j})} (6) \\\\ \\end{array}", + "image_path": "5f8288daaccb096ef4e6f0d02185a165c6bfd37b7a85aa228cbc579523ecc681.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 325, + 287, + 432 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 325, + 287, + 432 + ], + "spans": [ + { + "bbox": [ + 47, + 325, + 287, + 432 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 325, + 287, + 432 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 47, + 325, + 287, + 432 + ], + "type": "text", + "content": " is a temperature hyper-parameter controlling the strength of penalties on hard negative samples, and " + }, + { + "bbox": [ + 47, + 325, + 287, + 432 + ], + "type": "inline_equation", + "content": "\\mathcal{P}(i) = \\{k|k\\in \\mathcal{B},\\pmb{v}_k^\\top \\pmb{v}_i\\geq \\gamma \\}" + }, + { + "bbox": [ + 47, + 325, + 287, + 432 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 325, + 287, + 432 + ], + "type": "inline_equation", + "content": "\\mathcal{Q}(j) = \\{k|k\\in \\mathcal{B},\\pmb{v}_k^\\top \\pmb{v}_j\\geq \\gamma \\}" + }, + { + "bbox": [ + 47, + 325, + 287, + 432 + ], + "type": "text", + "content": ". We set " + }, + { + "bbox": [ + 47, + 325, + 287, + 432 + ], + "type": "inline_equation", + "content": "\\gamma = 0.9" + }, + { + "bbox": [ + 47, + 325, + 287, + 432 + ], + "type": "text", + "content": " for classification tasks to force image-text pairs sharing the similar text to be positive. Note (4) is a general form; it reduces to UniCL [59] when " + }, + { + "bbox": [ + 47, + 325, + 287, + 432 + ], + "type": "inline_equation", + "content": "\\gamma = 1.0" + }, + { + "bbox": [ + 47, + 325, + 287, + 432 + ], + "type": "text", + "content": "; it further reduces to the training objective of CLIP [43] when there is a one-to-one mapping between an image and its paired caption in a batch, i.e. " + }, + { + "bbox": [ + 47, + 325, + 287, + 432 + ], + "type": "inline_equation", + "content": "\\mathcal{P}(i) = \\{i\\}" + }, + { + "bbox": [ + 47, + 325, + 287, + 432 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 325, + 287, + 432 + ], + "type": "inline_equation", + "content": "\\mathcal{Q}(j) = \\{j\\}" + }, + { + "bbox": [ + 47, + 325, + 287, + 432 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 433, + 288, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 433, + 288, + 491 + ], + "spans": [ + { + "bbox": [ + 46, + 433, + 288, + 491 + ], + "type": "text", + "content": "In our empirical study we find that locked pre-trained image and text encoders with trainable gated modules in image encoder work best. Once the customized visual models are trained with the retrieved knowledge, we transfer it to the downstream domain for zero/few/full-shot evaluation." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 47, + 502, + 128, + 514 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 502, + 128, + 514 + ], + "spans": [ + { + "bbox": [ + 47, + 502, + 128, + 514 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 522, + 287, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 522, + 287, + 629 + ], + "spans": [ + { + "bbox": [ + 46, + 522, + 287, + 629 + ], + "type": "text", + "content": "In this section, we conduct experiments to answer three research questions: (1) What are the unique advantages of retrieval-augmented image-text knowledge for task transfer? (2) How does our design choice of locked-text gated-image tuning compare to existing methods for model customization? (3) Is customization still beneficial in settings where the training data in downstream tasks are observed, i.e., in few-shot or full-shot settings? (4) Does customization scales well to dense prediction tasks like detection/segmentation?" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 46, + 630, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 288, + 713 + ], + "type": "text", + "content": "We evaluate our models on four CV problems: image classification, image-text retrieval, object detection, and semantic segmentation. We first consider ImageNet [10] for zero-shot task transfer. We then further evaluate our model on ELEVATER [27], which is an open-set image classification benchmark that contains 20 datasets. We also conduct experiments on image-text retrieval with MSCOCO [30] and" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 205, + 545, + 230 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 205, + 545, + 230 + ], + "spans": [ + { + "bbox": [ + 305, + 205, + 545, + 230 + ], + "type": "text", + "content": "Flickr [64] dataset. Finally, we evaluate on object detection and semantic segmentation with MSCOCO [30] dataset." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 231, + 547, + 375 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 231, + 547, + 375 + ], + "spans": [ + { + "bbox": [ + 304, + 231, + 547, + 375 + ], + "type": "text", + "content": "One of the most intriguing benefits of REACT is that it does not need access to any images from the downstream task. Therefore, we first evaluate on task-level zero-shot transfer, which requires no images in the target to be observed [27, 43, 48]. This setting is different from traditional class-level zero-shot [57], where both the category and images in evaluation should not be observed in training. We argue that ImageNet concepts have been observed in CLIP (Sec. 2.2 of [43]) and other web-scale trained models [28], as WordNet synsets and common words in English Wikipedia are explicitly added in the query list when searching for (image, text) pairs in their training data construction process." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 384, + 423, + 397 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 384, + 423, + 397 + ], + "spans": [ + { + "bbox": [ + 306, + 384, + 423, + 397 + ], + "type": "text", + "content": "4.1. Image Classification" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 403, + 455, + 416 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 403, + 455, + 416 + ], + "spans": [ + { + "bbox": [ + 306, + 403, + 455, + 416 + ], + "type": "text", + "content": "4.1.1 Zero-Shot on ImageNet-1K" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 424, + 547, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 424, + 547, + 496 + ], + "spans": [ + { + "bbox": [ + 304, + 424, + 547, + 496 + ], + "type": "text", + "content": "As shown in Table 1, by customizing the generic model CLIP/OpenCLIP on 10M retrieved image-text pairs from LAION-400M, REACT achieves a significant and consistent gain (up to " + }, + { + "bbox": [ + 304, + 424, + 547, + 496 + ], + "type": "inline_equation", + "content": "5.4\\%" + }, + { + "bbox": [ + 304, + 424, + 547, + 496 + ], + "type": "text", + "content": ") on zero-shot image classification on ImageNet-1K, with different backbones and original pretraining datasets. There are three interesting findings." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 498, + 547, + 713 + ], + "type": "list", + "angle": 0, + "index": 24, + "blocks": [ + { + "bbox": [ + 304, + 498, + 547, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 547, + 616 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 547, + 616 + ], + "type": "text", + "content": "F1: REACT can benefit from model's own pre-training data. Compared to OpenCLIP [18] (ViT-B/32) trained on LAION-400M, by training on 10M relevant pairs from the same LAION-400M dataset, REACT improves over OpenCLIP by " + }, + { + "bbox": [ + 304, + 498, + 547, + 616 + ], + "type": "inline_equation", + "content": "3.5\\%" + }, + { + "bbox": [ + 304, + 498, + 547, + 616 + ], + "type": "text", + "content": ". Note that the model purely uses the image-text pairs that it has seen during its pre-training, and does not see any extra data. This shows that REACT can more adequately adapt to the target domain during the model customization stage, suggesting a favorable property that no new data is required for customization." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 618, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 618, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 618, + 547, + 713 + ], + "type": "text", + "content": "F2: REACT efficiently explores new image-text sources, even for large models. We customize CLIP [43] ViT-L/14 on 10M retrieved relevant image-text pairs, and the model achieves a " + }, + { + "bbox": [ + 304, + 618, + 547, + 713 + ], + "type": "inline_equation", + "content": "2.8\\%" + }, + { + "bbox": [ + 304, + 618, + 547, + 713 + ], + "type": "text", + "content": " improvement to " + }, + { + "bbox": [ + 304, + 618, + 547, + 713 + ], + "type": "inline_equation", + "content": "78.1\\%" + }, + { + "bbox": [ + 304, + 618, + 547, + 713 + ], + "type": "text", + "content": ". This surpasses the checkpoint with a much larger ViT-H/14 backbone and trained on a much larger LAION-2B dataset. This suggests that REACT is a more sample-efficient approach to improve the model performance on the domain-of-interest." + } + ] + } + ], + "index": 23 + } + ], + "sub_type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15152" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 80, + 72, + 509, + 186 + ], + "blocks": [ + { + "bbox": [ + 80, + 72, + 509, + 186 + ], + "lines": [ + { + "bbox": [ + 80, + 72, + 509, + 186 + ], + "spans": [ + { + "bbox": [ + 80, + 72, + 509, + 186 + ], + "type": "image", + "image_path": "49ed044e36e49bef23578deafef9c305b827faefca5000912cedbbec61de5013.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 52, + 188, + 539, + 200 + ], + "lines": [ + { + "bbox": [ + 52, + 188, + 539, + 200 + ], + "spans": [ + { + "bbox": [ + 52, + 188, + 539, + 200 + ], + "type": "text", + "content": "Figure 4. Zero-shot comparison on ELEVATER ICinW 20 datasets. REACT (B32) improves over the base checkpoints on most datasets." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 50, + 210, + 282, + 369 + ], + "blocks": [ + { + "bbox": [ + 50, + 210, + 282, + 369 + ], + "lines": [ + { + "bbox": [ + 50, + 210, + 282, + 369 + ], + "spans": [ + { + "bbox": [ + 50, + 210, + 282, + 369 + ], + "type": "table", + "html": "
fθPretrain DataRetrieved DataMethodImageNet-1K Zero-Shot
DatasetSize
B/32WIT-400M--CLIP63.2
L-400M10MREACT68.6 (+5.4)
LAION-400M--OpenCLIP62.9
L-400M10MREACT66.4 (+3.5)
L/14WIT-400M--CLIP75.3
L-400M6MREACT77.6 (+2.3)
L-400M10MREACT78.1 (+2.8)
W-800M†6MREACT78.5 (+3.2)
LAION-400M--OpenCLIP72.8
LAION-2B--OpenCLIP75.3
H/14LAION-2B--OpenCLIP78.0
G/14LAION-2B--OpenCLIP80.1
L-2B12MREACT81.0 (+0.9)
", + "image_path": "75e472f09623f8d6a4e80c86324d0d9ae0d63f7a479f73788c24b26bf4840880.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 451, + 287, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 451, + 287, + 548 + ], + "spans": [ + { + "bbox": [ + 46, + 451, + 287, + 548 + ], + "type": "text", + "content": "F3: Scaling up the retrieval pool increases performance. We perform REACT in a privately collected dataset with over 800M pairs, and train a customized model on 6M retrieved pairs. The performance is increased to " + }, + { + "bbox": [ + 46, + 451, + 287, + 548 + ], + "type": "inline_equation", + "content": "78.5\\%" + }, + { + "bbox": [ + 46, + 451, + 287, + 548 + ], + "type": "text", + "content": ", yielding " + }, + { + "bbox": [ + 46, + 451, + 287, + 548 + ], + "type": "inline_equation", + "content": "0.9\\%" + }, + { + "bbox": [ + 46, + 451, + 287, + 548 + ], + "type": "text", + "content": " gain compared with 6M pairs retrieved from LAION-400M. This suggests that REACT scales well with the larger retrieval pool. It showcases REACT as a cost-efficient approach to leveraging the ever-increasing web image-text corpus." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 556, + 256, + 567 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 556, + 256, + 567 + ], + "spans": [ + { + "bbox": [ + 46, + 556, + 256, + 567 + ], + "type": "text", + "content": "4.1.2 Zero-, Few-, and Full-Shot on ELEVATER" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 570, + 287, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 287, + 629 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 287, + 629 + ], + "type": "text", + "content": "As a proxy for performing vision tasks for many customized scenarios in the wild, we consider the image classification in the wild (ICinW) benchmark in ELEVATER [27]. It consists of 20 datasets from a diverse selection of domains and covers a wide range of concepts, totaling 1151 classes." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "text", + "content": "We perform multi-modal knowledge retrieval for 20 datasets together – the retrieved samples are around 10M image-text pairs in total, on which one single customized visual model is trained. After the process, we feed the customized model to different downstream tasks separately. For each downstream dataset, we use the official ELEVATER toolkit to obtain the train/val/test splits, and perform zero-" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 312, + 210, + 538, + 281 + ], + "blocks": [ + { + "bbox": [ + 46, + 371, + 288, + 438 + ], + "lines": [ + { + "bbox": [ + 46, + 371, + 288, + 438 + ], + "spans": [ + { + "bbox": [ + 46, + 371, + 288, + 438 + ], + "type": "text", + "content": "Table 1. Comparison of zero-shot task transfer with public checkpoints from CLIP [43] and OpenCLIP [18]. LAION [45, 46] is abbreviated as \"L\" in the table. Web-800M†: a privately collected web database with 800M image-text pairs. By continue pretraining on only " + }, + { + "bbox": [ + 46, + 371, + 288, + 438 + ], + "type": "inline_equation", + "content": "\\sim 10\\mathrm{M}" + }, + { + "bbox": [ + 46, + 371, + 288, + 438 + ], + "type": "text", + "content": " retrieved data, REACT outperforms all public CLIP/OpenCLIP checkpoints." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 312, + 210, + 538, + 281 + ], + "lines": [ + { + "bbox": [ + 312, + 210, + 538, + 281 + ], + "spans": [ + { + "bbox": [ + 312, + 210, + 538, + 281 + ], + "type": "table", + "html": "
MethodZero-ShotFew-shotFull-shot
LPFTLPFT
CLIP56.865.463.378.480.4
REACT60.668.968.480.481.8
Gains(+3.8)(+3.5)(+5.1)(+2.0)(+1.4)
", + "image_path": "10b13eac23f60ed9015355823a0731a414c3bffd1e0317b8616dd05514f9e086.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 290, + 545, + 324 + ], + "lines": [ + { + "bbox": [ + 305, + 290, + 545, + 324 + ], + "spans": [ + { + "bbox": [ + 305, + 290, + 545, + 324 + ], + "type": "text", + "content": "Table 2. The average scores of image classification performance on 20 datasets in ELEVATER. REACT consistently outperforms CLIP in both data-limited and data-rich regimes." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 306, + 338, + 467, + 349 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 338, + 467, + 349 + ], + "spans": [ + { + "bbox": [ + 306, + 338, + 467, + 349 + ], + "type": "text", + "content": "shot, few-shot, and full-shot evaluation." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 350, + 547, + 482 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 350, + 547, + 482 + ], + "spans": [ + { + "bbox": [ + 304, + 350, + 547, + 482 + ], + "type": "text", + "content": "We report the average scores in Table 2. It achieves " + }, + { + "bbox": [ + 304, + 350, + 547, + 482 + ], + "type": "inline_equation", + "content": "3.8\\%" + }, + { + "bbox": [ + 304, + 350, + 547, + 482 + ], + "type": "text", + "content": " improvement in the zero-shot setting, even when we do not perform a separate customization for different datasets. This demonstrates the robustness of our customization process. Further, we see the consistent improvement in few-shot and full-shot settings, including both linear probe (LP) and finetuning (FT). This result is encouraging, as it demonstrates that when we have access to some or all data from the downstream task, the proposed model customization stage remains beneficial. Therefore, we advocate model customization process in both data-limited and data-rich settings." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 486, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 486, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 547, + 713 + ], + "type": "text", + "content": "Breakdown Analysis. Next, we ask why does the retrieved image-text knowledge improve the zero-shot task transfer performance on a broad range of datasets? We compare the breakdown performance on all 20 datasets in Figure 4 for the zero-shot settings. Out of 20 datasets, the retrieval-augmented knowledge shows superior/comparable/inferior performance to the baseline on " + }, + { + "bbox": [ + 304, + 486, + 547, + 713 + ], + "type": "inline_equation", + "content": "15/1/4" + }, + { + "bbox": [ + 304, + 486, + 547, + 713 + ], + "type": "text", + "content": " datasets for CLIP and " + }, + { + "bbox": [ + 304, + 486, + 547, + 713 + ], + "type": "inline_equation", + "content": "14/0/6" + }, + { + "bbox": [ + 304, + 486, + 547, + 713 + ], + "type": "text", + "content": " datasets for OpenCLIP, respectively. Most of the improved and failure datasets are consistent for both checkpoints. For the top two datasets that gains the most, i.e. StanfordCars and FGVC Aircraft, relevant image-text knowledge is retrieved from the web-crawled data LAION-400M to describe the concepts; see Fig. 5a. Interestingly, this observation is complementary to K-LITE [48], which failed on these two datasets, because no knowledge was extracted from Wiktionary for them, as it often requires domain-specific knowledge and even visual knowledge to best define a car brand (e.g. BMW X6 SUV or Audi R8) or an aircraft model type (e.g. DC-10 or A321)." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15153" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 72, + 61, + 83 + ], + "blocks": [ + { + "bbox": [ + 49, + 72, + 61, + 83 + ], + "lines": [ + { + "bbox": [ + 49, + 72, + 61, + 83 + ], + "spans": [ + { + "bbox": [ + 49, + 72, + 61, + 83 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The dataset with the largest degradation in Fig. 4: PatchCamelyon [54]. LAION-400M has a low concept coverage on this domain, and the retrieved samples are in a different distribution from the target set." + } + ] + } + ], + "index": 52, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 47, + 342, + 287, + 376 + ], + "lines": [ + { + "bbox": [ + 47, + 342, + 287, + 376 + ], + "spans": [ + { + "bbox": [ + 47, + 342, + 287, + 376 + ], + "type": "text", + "content": "Figure 5. Success and failure cases in ELEVATER benchmark. We show class name and the caption of the first retrieved image-text pairs, others are similar and omitted due to limited space." + } + ] + } + ], + "index": 53, + "angle": 0, + "type": "image_caption" + } + ], + "index": 39 + }, + { + "type": "image", + "bbox": [ + 88, + 258, + 125, + 263 + ], + "blocks": [ + { + "bbox": [ + 88, + 258, + 125, + 263 + ], + "lines": [ + { + "bbox": [ + 88, + 258, + 125, + 263 + ], + "spans": [ + { + "bbox": [ + 88, + 258, + 125, + 263 + ], + "type": "image", + "image_path": "79ce1fae714fd120da65ec24119407e9d2429f21986e46dbeec39bc309187135.jpg" + } + ] + } + ], + "index": 41, + "angle": 0, + "type": "image_body" + } + ], + "index": 41 + }, + { + "type": "image", + "bbox": [ + 88, + 263, + 125, + 300 + ], + "blocks": [ + { + "bbox": [ + 88, + 263, + 125, + 300 + ], + "lines": [ + { + "bbox": [ + 88, + 263, + 125, + 300 + ], + "spans": [ + { + "bbox": [ + 88, + 263, + 125, + 300 + ], + "type": "image", + "image_path": "ba1f9c885d54741ac5426591119c4dbf4dd1fb216b587956ce9a58809e9b8439.jpg" + } + ] + } + ], + "index": 42, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 89, + 300, + 124, + 306 + ], + "lines": [ + { + "bbox": [ + 89, + 300, + 124, + 306 + ], + "spans": [ + { + "bbox": [ + 89, + 300, + 124, + 306 + ], + "type": "text", + "content": "lymph ... tumor..." + } + ] + } + ], + "index": 43, + "angle": 0, + "type": "image_caption" + } + ], + "index": 42 + }, + { + "type": "image", + "bbox": [ + 127, + 250, + 143, + 263 + ], + "blocks": [ + { + "bbox": [ + 47, + 210, + 287, + 247 + ], + "lines": [ + { + "bbox": [ + 47, + 210, + 287, + 247 + ], + "spans": [ + { + "bbox": [ + 47, + 210, + 287, + 247 + ], + "type": "text", + "content": "(a) Success examples. The two datasets with largest improvement in Fig. 4: Stanford-Cars [24] and FGVC-Aircraft [33]. There is a high concept coverage for these datasets in LAION, resulting in a relevant and diverse retrieved set." + } + ] + } + ], + "index": 37, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 127, + 250, + 143, + 263 + ], + "lines": [ + { + "bbox": [ + 127, + 250, + 143, + 263 + ], + "spans": [ + { + "bbox": [ + 127, + 250, + 143, + 263 + ], + "type": "image", + "image_path": "9ff699e9f404b83eaf25e9fe24358c5a54964e08f4274f3a5be26f3a3b8fc94f.jpg" + } + ] + } + ], + "index": 44, + "angle": 0, + "type": "image_body" + } + ], + "index": 44 + }, + { + "type": "image", + "bbox": [ + 143, + 252, + 224, + 261 + ], + "blocks": [ + { + "bbox": [ + 143, + 252, + 224, + 261 + ], + "lines": [ + { + "bbox": [ + 143, + 252, + 224, + 261 + ], + "spans": [ + { + "bbox": [ + 143, + 252, + 224, + 261 + ], + "type": "image", + "image_path": "372387ae16abf53bc916284e86f3b202807404217d0b1c6cd43fe901256c7212.jpg" + } + ] + } + ], + "index": 45, + "angle": 0, + "type": "image_body" + } + ], + "index": 45 + }, + { + "type": "image", + "bbox": [ + 127, + 262, + 171, + 300 + ], + "blocks": [ + { + "bbox": [ + 127, + 262, + 171, + 300 + ], + "lines": [ + { + "bbox": [ + 127, + 262, + 171, + 300 + ], + "spans": [ + { + "bbox": [ + 127, + 262, + 171, + 300 + ], + "type": "image", + "image_path": "2f05c6e4a0a51a07f25bef66fad85880e78726199f489cadc2ed23551512b93b.jpg" + } + ] + } + ], + "index": 46, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 128, + 300, + 181, + 307 + ], + "lines": [ + { + "bbox": [ + 128, + 300, + 181, + 307 + ], + "spans": [ + { + "bbox": [ + 128, + 300, + 181, + 307 + ], + "type": "text", + "content": "Microscopic enlargement" + } + ] + } + ], + "index": 47, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 171, + 300, + 211, + 307 + ], + "lines": [ + { + "bbox": [ + 171, + 300, + 211, + 307 + ], + "spans": [ + { + "bbox": [ + 171, + 300, + 211, + 307 + ], + "type": "text", + "content": "ment of a mast cell." + } + ] + } + ], + "index": 49, + "angle": 0, + "type": "image_caption" + } + ], + "index": 46 + }, + { + "type": "image", + "bbox": [ + 171, + 262, + 216, + 300 + ], + "blocks": [ + { + "bbox": [ + 171, + 262, + 216, + 300 + ], + "lines": [ + { + "bbox": [ + 171, + 262, + 216, + 300 + ], + "spans": [ + { + "bbox": [ + 171, + 262, + 216, + 300 + ], + "type": "image", + "image_path": "d8262108760abd6332cb4221c6c52239ede3d2f87b0f3f1e8c84687b4f7da9f2.jpg" + } + ] + } + ], + "index": 48, + "angle": 0, + "type": "image_body" + } + ], + "index": 48 + }, + { + "type": "image", + "bbox": [ + 216, + 262, + 247, + 300 + ], + "blocks": [ + { + "bbox": [ + 216, + 262, + 247, + 300 + ], + "lines": [ + { + "bbox": [ + 216, + 262, + 247, + 300 + ], + "spans": [ + { + "bbox": [ + 216, + 262, + 247, + 300 + ], + "type": "image", + "image_path": "ffc75e3e7e33f09274b6090e2162f07a9d6dcb13a3a3cd95441d6955f5e7c316.jpg" + } + ] + } + ], + "index": 50, + "angle": 0, + "type": "image_body" + } + ], + "index": 50 + }, + { + "type": "image", + "bbox": [ + 249, + 262, + 286, + 300 + ], + "blocks": [ + { + "bbox": [ + 249, + 262, + 286, + 300 + ], + "lines": [ + { + "bbox": [ + 249, + 262, + 286, + 300 + ], + "spans": [ + { + "bbox": [ + 249, + 262, + 286, + 300 + ], + "type": "image", + "image_path": "156c7230170a6f3b37a04fe854edfa0a6c3d5e94868782646c0e72258bf41dd9.jpg" + } + ] + } + ], + "index": 51, + "angle": 0, + "type": "image_body" + } + ], + "index": 51 + }, + { + "bbox": [ + 46, + 388, + 287, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 388, + 287, + 483 + ], + "spans": [ + { + "bbox": [ + 46, + 388, + 287, + 483 + ], + "type": "text", + "content": "Limitations. As shown in Fig. 4, REACT struggles on the PatchCamelyon dataset, a cancer cell recognition benchmark. We visualize the retrieved samples and the samples from the original training set in Fig. 5b. The retrieved images are either instruction photos and from another sensing method, which exhibits a different visual distribution from PatchCamelyon. This suggests the importance of ensuring the retrieval quality for the domain-of-interest." + } + ] + } + ], + "index": 54 + }, + { + "bbox": [ + 47, + 491, + 168, + 504 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 491, + 168, + 504 + ], + "spans": [ + { + "bbox": [ + 47, + 491, + 168, + 504 + ], + "type": "text", + "content": "4.2. Image-Text Retrieval" + } + ] + } + ], + "index": 55 + }, + { + "bbox": [ + 46, + 510, + 287, + 630 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 287, + 630 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 287, + 630 + ], + "type": "text", + "content": "To demonstrate the generality of REACT, we consider Flickr30K [64] and MSCOCO [30] image-text retrieval tasks, in both zero-shot and full-shot settings. We use the standard image-text contrastive objective [43]. For image-text retrieval task, following [20, 43], we use the CLIP-L/14 with 336x336 input resolution in both zero-shot, customization, and fine-tuning stage. We use the captions from MSCOCO as queries to retrieve 6M image-text pairs and perform customization. Note that none of the caption queries are used in the model training stage." + } + ] + } + ], + "index": 56 + }, + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "text", + "content": "As shown in Table 3, REACT improves the generic CLIP counterparts on both zero-shot and full-shot retrieval for Flickr30K and MSCOCO datasets. The gain on zero-shot task transfer is large. On Flickr30K, it achieves " + }, + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "inline_equation", + "content": "3.4\\% /10.0\\%" + }, + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "text", + "content": " recall improvement for I2T and T2I retrieval, respectively. Afer fine-tuning on full training data, REACT still improves over the baseline slightly. It provides another piece of ev" + } + ] + } + ], + "index": 57 + }, + { + "type": "table", + "bbox": [ + 312, + 71, + 539, + 218 + ], + "blocks": [ + { + "bbox": [ + 312, + 71, + 539, + 218 + ], + "lines": [ + { + "bbox": [ + 312, + 71, + 539, + 218 + ], + "spans": [ + { + "bbox": [ + 312, + 71, + 539, + 218 + ], + "type": "table", + "html": "
MethodFlickr30KMSCOCO
Img → TextText → ImgImg → TextText → Img
R@1R@5R@1R@5R@1R@5R@1R@5
Zero-ShotImgBert [42]70.790.254.379.644.071.232.359.0
ALIGN [20]88.698.775.793.858.683.045.669.8
CLIP [43]88.098.768.790.658.481.537.862.4
CLIP†87.098.366.588.059.280.737.862.4
REACT90.499.176.593.763.385.147.572.0
Bletchley†90.898.278.094.066.785.648.972.7
REACT92.198.779.294.767.785.950.574.4
Fine-tunedGPO [5]88.798.976.194.568.190.252.780.2
ALIGN [20]95.399.884.997.477.093.559.983.3
CLIP†96.499.886.597.978.393.860.983.8
REACT96.699.986.898.078.794.061.184.1
", + "image_path": "4b10f50ab96134b5a712b78b58329ff2ee1426c755825636730a8a7cb2f58fd1.jpg" + } + ] + } + ], + "index": 58, + "angle": 0, + "type": "table_body" + } + ], + "index": 58 + }, + { + "type": "table", + "bbox": [ + 311, + 247, + 541, + 335 + ], + "blocks": [ + { + "bbox": [ + 306, + 221, + 545, + 243 + ], + "lines": [ + { + "bbox": [ + 306, + 221, + 545, + 243 + ], + "spans": [ + { + "bbox": [ + 306, + 221, + 545, + 243 + ], + "type": "text", + "content": "Table 3. Image-text retrieval results on Flickr30K [41] and MSCOCO [30] datasets. CLIP†, Bletchley†: our evaluation." + } + ] + } + ], + "index": 59, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 311, + 247, + 541, + 335 + ], + "lines": [ + { + "bbox": [ + 311, + 247, + 541, + 335 + ], + "spans": [ + { + "bbox": [ + 311, + 247, + 541, + 335 + ], + "type": "table", + "html": "
Pretrain MethodBackboneRegion \nProposalsMSCOCO AP50
NovelBaseAll
Zero-ShotCLIPResNet-50GT58.658.258.3
REACTResNet-50GT58.9 (+0.3)59.4 (+1.2)59.3 (+1.0)
CLIPResNet-50RPN29.724.025.5
REACTResNet-50RPN31.6 (+1.9)25.4 (+1.4)27.0 (+1.5)
OVDCLIPResNet-50-14.252.842.7
REACTResNet-50-20.6 (+6.4)55.1 (+2.3)46.1 (+3.4)
", + "image_path": "798cab432288ece2033a03bc4a4222da4d9d6fe5e8b0c7122b25a410b898a0a7.jpg" + } + ] + } + ], + "index": 60, + "angle": 0, + "type": "table_body" + } + ], + "index": 60 + }, + { + "bbox": [ + 306, + 337, + 545, + 359 + ], + "lines": [ + { + "bbox": [ + 306, + 337, + 545, + 359 + ], + "spans": [ + { + "bbox": [ + 306, + 337, + 545, + 359 + ], + "type": "text", + "content": "Table 4. Zero-shot and open-vocabulary object detection results on MSCOCO [30] dataset using RegionCLIP [69] pipeline." + } + ] + } + ], + "index": 61, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 372, + 545, + 431 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 372, + 545, + 431 + ], + "spans": [ + { + "bbox": [ + 305, + 372, + 545, + 431 + ], + "type": "text", + "content": "idence for REACT in data-rich settings. Furthermore, we conduct the same customization procedure of REACT on a large checkpoint Bletchley [53] with 864M parameters, and observe consistent gains over both datasets. It demonstrates that REACT scales well with model size on retrieval tasks." + } + ] + } + ], + "index": 62 + }, + { + "bbox": [ + 306, + 440, + 437, + 451 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 440, + 437, + 451 + ], + "spans": [ + { + "bbox": [ + 306, + 440, + 437, + 451 + ], + "type": "text", + "content": "4.3. Dense Prediction Tasks" + } + ] + } + ], + "index": 63 + }, + { + "bbox": [ + 305, + 458, + 547, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 458, + 547, + 518 + ], + "spans": [ + { + "bbox": [ + 305, + 458, + 547, + 518 + ], + "type": "text", + "content": "Although REACT is optimized with the image-level contrastive loss during the customization stage, we find it beneficial for dense prediction tasks as well. We showcase its application to dense prediction tasks on object detection and semantic segmentation." + } + ] + } + ], + "index": 64 + }, + { + "bbox": [ + 304, + 521, + 547, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 547, + 629 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 547, + 629 + ], + "type": "text", + "content": "Object Detection. For object detection, we choose the state-of-the-art RegionCLIP [69] as our framework. We conduct experiments in two settings: zero-shot inference and open-vocabulary object detection (OVD) on MSCOCO dataset. We perform the model customization following the same setting as Sec. 4.2. Following RegionCLIP, we conduct experiments on ResNet50 backbone. The results are shown in Table 4. REACT consistently improves over CLIP checkpoint under all settings." + } + ] + } + ], + "index": 65 + }, + { + "bbox": [ + 304, + 630, + 547, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 547, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 547, + 689 + ], + "type": "text", + "content": "For zero-shot inference, when ground-truth region proposal is used, REACT improves over CLIP by " + }, + { + "bbox": [ + 304, + 630, + 547, + 689 + ], + "type": "inline_equation", + "content": "+1.0" + }, + { + "bbox": [ + 304, + 630, + 547, + 689 + ], + "type": "text", + "content": " on overall AP50; when the pretrained RPN is used, REACT demonstrates " + }, + { + "bbox": [ + 304, + 630, + 547, + 689 + ], + "type": "inline_equation", + "content": "+1.5 / + 1.4 / + 1.9" + }, + { + "bbox": [ + 304, + 630, + 547, + 689 + ], + "type": "text", + "content": " AP50 improvements on novel, base, and all classes, respectively." + } + ] + } + ], + "index": 66 + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": "For OVD, we can see that with the REACT, the detector yields improved performance on base with " + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "inline_equation", + "content": "+2.3" + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": " AP50, and" + } + ] + } + ], + "index": 67 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15154" + } + ] + } + ], + "index": 68 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 71, + 282, + 121 + ], + "blocks": [ + { + "bbox": [ + 50, + 71, + 282, + 121 + ], + "lines": [ + { + "bbox": [ + 50, + 71, + 282, + 121 + ], + "spans": [ + { + "bbox": [ + 50, + 71, + 282, + 121 + ], + "type": "table", + "html": "
MethodmIoU
zero-shotw/ refinew/ finetune
MaskCLIP [70]12.514.618.1
REACT (Locked-Text)14.4 (+1.9)18.2 (+3.6)20.7 (+2.6)
REACT (Locked-Text Gated-Image)14.5 (+2.0)16.3 (+1.7)19.2 (+1.1)
", + "image_path": "83e846449c46ffb3280b37904d5c81bfe91cb3cb33d3605a26fb0ed5168b9975.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 156, + 287, + 287 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 156, + 287, + 287 + ], + "spans": [ + { + "bbox": [ + 46, + 156, + 287, + 287 + ], + "type": "text", + "content": "importantly, it significantly improves novel categories with +6.4 AP50. This suggests that the injected knowledge during the model customization stage improves the learned fine-grained visual feature that is beneficial to both seen and unseen categories for object detection, when the downstream coarse-grained data is available. This is favored, because (1) the weakly-supervised data such as the coarse-grained image-text pairs requires much less human annotation cost than fine-grained bounding box annotation, (2) the paired data in REACT is free, as it is retrieved from the web, where COCO image-text pairs are not used in customized training." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 289, + 288, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 289, + 288, + 467 + ], + "spans": [ + { + "bbox": [ + 46, + 289, + 288, + 467 + ], + "type": "text", + "content": "Semantic Segmentation. For semantic segmentation, we choose the state-of-the-art MaskCLIP [70] as the framework. It investigates three evaluation settings for segmentation. First, it makes use of the pretrained CLIP checkpoint to discover the alignment between grid visual features and the text prompt features, so as to perform zero-shot semantic segmentation. Second, to further improve the performance, MaskCLIP [70] proposes two techniques for refining its zero-shot predictions: key smoothing and prompt denoising. Lastly, when the training images are available, without the need to access the training labels, it further proposes MaskCLIP + [70] to perform full-shot finetuning on the target training set using pseudo-labels. Following MaskCLIP [70], we use ViT-B/16 checkpoints, and use their official code base to train and evaluate models. We report results in Table 5." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 468, + 287, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 468, + 287, + 564 + ], + "spans": [ + { + "bbox": [ + 46, + 468, + 287, + 564 + ], + "type": "text", + "content": "On all of the three settings, REACT demonstrates improvements over the MaskCLIP. Notably, when refinement techniques are used, REACT with locked-text tuning demonstrates a significant " + }, + { + "bbox": [ + 46, + 468, + 287, + 564 + ], + "type": "inline_equation", + "content": "3.6\\%" + }, + { + "bbox": [ + 46, + 468, + 287, + 564 + ], + "type": "text", + "content": " gain in mIoU. Surprisingly, without seeing the downstream COCO images, the zero-shot evaluation of REACT (18.2) even slightly outperforms MaskCLIP+ (18.1), which is finetuned on the downstream training COCO images with self-training." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 566, + 286, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 566, + 286, + 601 + ], + "spans": [ + { + "bbox": [ + 46, + 566, + 286, + 601 + ], + "type": "text", + "content": "Summary. These results are encouraging, as it shows that the customized knowledge from REACT transfers well to dense prediction tasks like detection and segmentation." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 611, + 147, + 623 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 611, + 147, + 623 + ], + "spans": [ + { + "bbox": [ + 47, + 611, + 147, + 623 + ], + "type": "text", + "content": "4.4. Ablation Studies" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 628, + 286, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 628, + 286, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 628, + 286, + 664 + ], + "type": "text", + "content": "We ablate REACT on ImageNet with CLIP ViT-B/32 checkpoint, with 10M retrieved image-text pairs from LAION-400M. See more ablations in supplementary." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 665, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 712 + ], + "type": "text", + "content": "Tuning strategy. We ablate the design choices in the model customization stage: (1) direct tuning the pre-trained weights vs. training gated blocks from scratch; (2) updating visual vs.text encoder. We report results in Table 6. First, a frozen text" + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 307, + 70, + 541, + 142 + ], + "blocks": [ + { + "bbox": [ + 47, + 125, + 286, + 147 + ], + "lines": [ + { + "bbox": [ + 47, + 125, + 286, + 147 + ], + "spans": [ + { + "bbox": [ + 47, + 125, + 286, + 147 + ], + "type": "text", + "content": "Table 5. Zero-shot and annotation-free semantic segmentation results on COCO Stuff [30] using MaskCLIP [70] (ViT-B/16)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 70, + 541, + 142 + ], + "lines": [ + { + "bbox": [ + 307, + 70, + 541, + 142 + ], + "spans": [ + { + "bbox": [ + 307, + 70, + 541, + 142 + ], + "type": "table", + "html": "
MethodVisualText# Train.IN1K Acc.COCO R@1 T2II2T
DirectCLIP [43]XX-63.248.829.9
Locked-Image [68]X✓63.4M63.750.534.2
Locked-Text✓X88.1M66.951.136.1
Full-model✓✓151.3M64.354.337.9
GatedX✓18.9M63.049.533.5
Locked-Text Gated-Image✓X42.5M68.653.438.1
✓✓89.8M68.754.339.9
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Retrieval Size01M3M6M10M
ImageNet-1K Accuracy63.264.866.968.668.6
", + "image_path": "7a90056d3408b9113084d99178a8581430d2989ab8245cc09d0eb7e525e69a30.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "table_body" + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 470, + 378, + 482 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 470, + 378, + 482 + ], + "spans": [ + { + "bbox": [ + 306, + 470, + 378, + 482 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 492, + 547, + 599 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 492, + 547, + 599 + ], + "spans": [ + { + "bbox": [ + 304, + 492, + 547, + 599 + ], + "type": "text", + "content": "We presented REACT, a plug-and-play framework for leveraging large-scale image-text corpus as external knowledge to efficiently customize models on downstream tasks. Extensive experiments demonstrate its generality and effectiveness in image classification, image-text retrieval, object detection, and semantic segmentation, on more than 20 different downstream datasets. We highly advocate the model customization stage for building more transferable visual system for different downstream tasks." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 605, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 547, + 713 + ], + "type": "text", + "content": "Acknowledgement. This work was supported in part by NSF CAREER IIS2150012, NASA 80NSSC21K0295, and Institute of Information & communications Technology Planning & Evaluation(IITP) grants funded by the Korea government(MSIT) (No. 2022- 0-00871, Development of AI Autonomy and Knowledge Enhancement for AI Agent Collaboration) and (No. RS-2022-00187238, Development of Large Korean Language Model Technology for Efficient Pre-training)." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15155" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 712 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 146 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 146 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 146 + ], + "type": "text", + "content": "[1] Jean-Baptiste Alayrac, Jeff Donahue, Pauline Luc, Antoine Miech, Iain Barr, Yana Hasson, Karel Lenc, Arthur Mensch, Katie Millican, Malcolm Reynolds, et al. 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Lafite2: Few-shot text-to-image generation. arXiv preprint arXiv:2210.14124, 2022. 3" + } + ] + } + ], + "index": 20 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "15158" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Learning Debiased Representations via Conditional Attribute Interpolation/35e0c901-be24-4ae3-9fbb-72a8952235b2_content_list.json b/2023/Learning Debiased Representations via Conditional Attribute Interpolation/35e0c901-be24-4ae3-9fbb-72a8952235b2_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..20bc3aad43f478147c5b1231ff1d2a3f3294b166 --- /dev/null +++ b/2023/Learning Debiased Representations via Conditional Attribute Interpolation/35e0c901-be24-4ae3-9fbb-72a8952235b2_content_list.json @@ -0,0 +1,1534 @@ +[ + { + "type": "text", + "text": "Learning Debiased Representations via Conditional Attribute Interpolation", + "text_level": 1, + "bbox": [ + 104, + 130, + 864, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Yi-Kai Zhang, Qi-Wei Wang, De-Chuan Zhan, Han-Jia Ye $^{\\text{®}}$ \nState Key Laboratory for Novel Software Technology, Nanjing University", + "bbox": [ + 192, + 180, + 776, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{zhangyk, wangqiwei, zhandc, yehj}@lamda.nju.edu.cn", + "bbox": [ + 269, + 219, + 694, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 268, + 313, + 284 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "An image is usually described by more than one attribute like \"shape\" and \"color\". When a dataset is biased, i.e., most samples have attributes spuriously correlated with the target label, a Deep Neural Network (DNN) is prone to make predictions by the \"unintended\" attribute, especially if it is easier to learn. To improve the generalization ability when training on such a biased dataset, we propose a $\\chi^2$ -model to learn debiased representations. First, we design a $\\chi$ -shape pattern to match the training dynamics of a DNN and find Intermediate Attribute Samples (IASs) — samples near the attribute decision boundaries, which indicate how the value of an attribute changes from one extreme to another. Then we rectify the representation with a $\\chi$ -structured metric learning objective. Conditional interpolation among IASs eliminates the negative effect of peripheral attributes and facilitates retaining the intra-class compactness. Experiments show that $\\chi^2$ -model learns debiased representation effectively and achieves remarkable improvements on various datasets. Code is available at: https://github.com/ZhangYikaii/ch-square", + "bbox": [ + 75, + 300, + 473, + 603 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 632, + 209, + 648 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Deep neural networks (DNNs) have emerged as an epoch-making technology in various machine learning tasks with impressive performance [5,26]. In some real applications, an object may possess multiple attributes, and some of them are only spuriously correlated to the target label. For example, in Figure 1, the intrinsic attribute of an image annotated by \"lifeboats\" is its shape. Although there are many lifeboats colored orange, a learner can not make predictions through the color, i.e., there is a misleading correlation from attribute as one containing \"orange\" color is the target \"lifeboats\". When the major training samples can be well discerned by such peripheral attribute, especially learning on it is easier than on the intrinsic one, a DNN is prone to bias towards that \"unintended\" bias attribute [6, 11, 21, 43, 47, 48, 51], like recognizing a \"cyclist\" wearing orange as a \"lifeboat\". Similar spurious attribute also exists in various applications", + "bbox": [ + 75, + 659, + 470, + 901 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/1cf6d30b931cf83503022d4275a14b514b47312b5fd2ca6559f6ef395d1d2a9b.jpg", + "image_caption": [ + "(a) Orange lifeboat" + ], + "image_footnote": [], + "bbox": [ + 553, + 270, + 671, + 362 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "97.8% lifeboat", + "bbox": [ + 555, + 382, + 645, + 393 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "0.5% beacon", + "bbox": [ + 560, + 396, + 643, + 407 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "0.4% container ship", + "bbox": [ + 560, + 409, + 676, + 421 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/15712e1742b0095e18d2b345765b98e6134c72465c35a19dc41c20c7d86240ea.jpg", + "image_caption": [ + "(b) Orange cyclists", + "Figure 1. Classification of a standard ResNet-50 of (a) an orange lifeboat in the training set (with both color and shape attributes), and (b) an orange cyclist for the test (aligned with color attribute but conflicting with the shape one). Most of the lifeboats in the training set are orange. The biased model is prone to predict via the \"unintended\" color attribute rather than the intrinsic shape." + ], + "image_footnote": [], + "bbox": [ + 707, + 270, + 826, + 363 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "57.0% lifeboat", + "bbox": [ + 707, + 383, + 797, + 393 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "13.8% bicycle-built-for-two", + "bbox": [ + 710, + 396, + 862, + 407 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "9.0% toyshop", + "bbox": [ + 714, + 409, + 799, + 421 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "such as recommendation system [8, 35, 53, 59] and neural language processing [13, 14, 33, 41, 56].", + "bbox": [ + 496, + 545, + 890, + 575 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Given such a biased training dataset, how to get rid of the negative effect of the misleading correlations? One intuitive solution is to perform special operations on those samples highly correlated to the bias attributes, which requires additional supervision, such as the pre-defined bias type [1,4,11,12,22,30,34,46,50]. Since prior knowledge of the dataset bias requires expensive manual annotations and is naturally missing in some applications, learning a debiased model without additional supervision about bias is in demand. Nam et al. [36] identify samples with intrinsic attributes based on the observation that malignant bias attributes are often easier-to-learn than others. Then the valuable samples for a debiasing scheme could be dynamically reweighted or augmented [11,27,34]. However, the restricted number of such samples implies uncertain representations and limits its ability to assist in debiasing.", + "bbox": [ + 496, + 580, + 893, + 821 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To leverage more valuable-for-debiasing knowledge, we take a further step in analyzing the representation space of naively-training dynamics, especially focusing on the discrepancies in attributes with a different learning difficulty. As we will later illustrate in Figure 2, an attribute-based", + "bbox": [ + 496, + 824, + 893, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "7599", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "DNN pushes and fits on the easier bias attribute initially. The intrinsic attribute is then forced to shift in a \"lazy\" manner. The bias attribute that is pushed away first leaves a large margin boundary. Since the space of the other intrinsic attribute is filled with many different samples on bias attribute, it has a large intra-class variance, like a \"hollow\". The representation is biased toward one side of the \"hollow\", i.e., those samples aligned with the bias attribute. Without the true intra-class structure, the model becomes biased.", + "bbox": [ + 75, + 90, + 472, + 226 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "From the above observation, it is crucial to fill intra-class \"hollow\" and remodel representation compactness. Notice that the samples shifting to the two sides of the \"hollow\" have different characteristics, as aligned with the bias attribute and conflicting with it, respectively. We can find samples with an intermediate state between the above two. We call this type of sample the Intermediate Attribute Samples (IASs) which are near the decision boundary. When we condition (fix) on the intrinsic attribute, IASs vary on the other bias attribute and are exactly located in the \"hollow\" with low-density structural knowledge. Further, we can mine samples, including IASs, based on the distinct training dynamics.", + "bbox": [ + 73, + 229, + 472, + 412 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To this end, we propose our two-stage $\\chi^2$ -model. In the first stage, we train a vanilla model on the biased dataset and record the sample-wise training dynamics w.r.t. both the target and the most obvious non-target classes (as the bias ones) along the epochs. An IAS is often predicted as a nontarget class in the beginning and then switched to its target class gradually, making its dynamics plot a $\\chi$ -shape. Following this observation, we design a $\\chi$ -shape pattern to match the training samples. The matching score ranks the mined samples according to the bias level, i.e., how much they are biased towards the side of the bias attribute. Benefiting from the IASs, we conduct conditional attribute interpolation, i.e., fixing the value of the target attribute. We interpolate the class-specific prototypes around IASs with various bias ratios. These conditional interpolated prototypes precisely \"average out\" on the bias attribute. From that, we design a $\\chi$ -structured metric learning objective. It pulls samples close to those same-class interpolated prototypes, then intra-class samples become compact, and the influence of the bias attribute is removed. Our $\\chi^2$ -model learns debiased representation effectively and achieves remarkable improvements on various datasets. Our contributions are summarized as", + "bbox": [ + 75, + 414, + 472, + 746 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We claim and verify that Intermediate Attribute Samples (IASs) distributed around attribute decision boundaries facilitate learning a debiased representation.", + "- Based on the diverse learning behavior of different attribute types, we mine samples with varying bias levels, especially IASs. From that, we interpolate bias attribute conditioned on the intrinsic one and compact intra-class samples to remove the negative effect of bias.", + "- Experiments on benchmarks and a newly constructed real-world dataset from NICO [17] validate the effectiveness" + ], + "bbox": [ + 76, + 750, + 470, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "of our $\\chi^2$ -model in learning debiased representations.", + "bbox": [ + 511, + 90, + 867, + 107 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. A Closer Look at Learning on Bias Attribute", + "text_level": 1, + "bbox": [ + 500, + 119, + 890, + 137 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "After the background of learning on a biased dataset in subsection, we analyze the training dynamics of the model.", + "bbox": [ + 500, + 145, + 890, + 176 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Problem Definition", + "text_level": 1, + "bbox": [ + 500, + 184, + 683, + 199 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Given a training set $\\mathcal{D}_{\\mathrm{train}} = \\{(\\mathbf{x}_i,y_i)\\}_{i = 1}^N$ , each sample $\\mathbf{x}_i$ is associated with a class label $y\\in \\{1,2,\\dots ,C\\}$ . We aim to find a decision rule $h_\\theta$ that maps a sample to its label. $h_\\theta$ is optimized by fitting all the training samples, e.g., minimizing the cross entropy loss as follows:", + "bbox": [ + 498, + 205, + 893, + 284 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {C E}} = \\mathbb {E} _ {\\left(\\mathbf {x} _ {i}, y _ {i}\\right) \\sim \\mathcal {D} _ {\\text {t r a i n}}} \\left[ - \\log \\Pr \\left(h _ {\\boldsymbol {\\theta}} \\left(\\mathbf {x} _ {i}\\right) = y _ {i} \\mid \\mathbf {x} _ {i}\\right) \\right]. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 294, + 893, + 313 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We denote $h_{\\theta} = \\arg \\max_{c\\in [C]}\\mathbf{w}_c^\\top f_\\phi (\\mathbf{x})$ , where $f_{\\phi}\\rightarrow$ $\\mathbb{R}^d$ is the feature extraction network and $\\{\\mathbf{w}_c\\}_{c\\in [C]}$ is toplayer $C$ -class classifier. The $\\pmb{\\theta}$ represents the union of learnable parameters $\\phi$ and $\\mathbf{W}$ . We expect the learned $h_\\theta$ to have the high discerning ability over the test set $\\mathcal{D}_{\\mathrm{test}}$ which has the same form as the training set $\\mathcal{D}_{\\mathrm{train}}$", + "bbox": [ + 498, + 324, + 893, + 417 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In addition to its class label, a sample could be described based on various attributes. If an attribute is spuriously correlated with the target label, we name it non-target bias attribute $a_{b}$ . The attribute that intrinsically determines the class label is the target attribute $a_{y}$ . For example, when we draw different handwritten digits in the MNIST dataset with specific colors [22], the color attribute will not help in the model generalization since we need to discern digits by the shape, e.g., \"1\" is like the stick. However, if almost all training images labeled \"1\" are in the same \"yellow\" color, the decision rule image in \"yellow\" is digit \"1\" will perform well on a such biased training set.", + "bbox": [ + 496, + 417, + 893, + 598 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In the task of learning with a biased training set [22, 29, 36], the bias attribute $a_{b}$ on most of the same-class samples are consistent, and spuriously correlated with the target label (as example digit \"1\" in \"yellow\" above), so a model $h_{\\theta}$ that relies on $a_{b}$ or the target attribute $a_{y}$ will both perform well on $\\mathcal{D}_{\\mathrm{train}}$ . In real-world applications, it is often easier to learn to rely on $a_{b}$ than on $a_{y}$ , such as \"background\" or \"texture\" is easier-to-learn than the object [42, 51]. Therefore a model is prone to recognize based on the $a_{b}$ . Such a simplicity bias [3, 37, 38, 42] dramatically hurts the generalization of an unbiased test set. Nam et al. [36] also observe that the loss dynamics indicate the easier $a_{b}$ is learned first, where the model is distracted and fails to learn $a_{y}$ .", + "bbox": [ + 496, + 598, + 893, + 795 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Based on the behaviors of the \"ultimate\" biased model, samples in $\\mathcal{D}_{\\mathrm{train}}$ are split into two sets. Those training samples that could be correctly predicted based on the bias attribute $a_{b}$ are named as Bias-Aligned (BA) samples (as example \"yellow digit 1\" above), while the remaining ones are Bias-Conflicting (BC) samples (as digit \"1\" of other colors). The number of BC samples is extremely small, and previous", + "bbox": [ + 496, + 795, + 893, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "7600", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/c40b7b9532fbf4bf8cf0735509a804cd0069a6e7934d4509db60c9feb56dfbc3.jpg", + "image_caption": [ + "Figure 2. An illustration of the training dynamics of a naively-trained model on a biased dataset. The different attribute classes are drawn with a specific color (top row) or shape (bottom row). The first three columns correspond to the sequential training progress of these two classifiers, and the final column shows the test scenario. The easier-to-learn color is fitted first, which leaves a large margin on decision boundary and correspondingly triggers the shape attribute intra-class \"hollow\". \"UB\" and \"BB\" are the abbreviations of \"unbiased boundary\" and \"biased boundary\". The biased model cannot generalize well as the shadow area in the last column frames the shape-misclassified samples. We use yellow stars to indicate the shifted class centers of the training samples and gray stars for those of the test samples." + ], + "image_footnote": [], + "bbox": [ + 161, + 87, + 815, + 380 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "methods emphasize their role with various strategies [11, 27, 34, 36]. For additional related methods of learning a debiased model [2, 7, 9, 10, 18, 24, 25, 29, 31, 40, 49, 60] please see the supplementary material. They can be extrapolated and applied to other application scenarios [16, 45, 52, 54, 57, 58].", + "bbox": [ + 75, + 498, + 473, + 575 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. The Training Dynamics of Biased Dataset", + "text_level": 1, + "bbox": [ + 76, + 585, + 431, + 602 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We analyze the training dynamics of a naively trained model in Eq. 1 on the Colored MNIST dataset. The non-target bias attribute is the color and the target attribute is the shape. For visualization shown in Figure 2, we set the output dimension of the penultimate layer as two. In addition to the learned classifier on shape attribute $a_{y}$ , simultaneously, we add another linear classifier on top of the embedding to show how the decision boundary of color attribute $a_{b}$ changes. More details are described in the supplementary material. Focusing on the precedence relationship for learning $a_{y}$ and $a_{b}$ , we have the following observations:", + "bbox": [ + 75, + 609, + 470, + 775 + ], + "page_idx": 2 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- The easier-to-learn bias attribute color is fitted soon. The early training stage is shown in the first column. Both color and shape attribute classifiers discern by different colors and do correctly on almost all BA samples (red “0” and blue “2”, about $95\\%$ of the training set).", + "- The target attribute shape is learned later in a \"lazy\" manner. To further fit all shape labels, the model focuses on the limited BC samples (blue \"0\" and red \"2\", corre" + ], + "bbox": [ + 76, + 780, + 473, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "spondingly about $5\\%$ ) that cannot be perfectly classified by color. It pushes minor BC representations to the other (correct) side instead of adjusting the decision boundary.", + "bbox": [ + 509, + 498, + 892, + 545 + ], + "page_idx": 2 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- The ahead-color and lagged-shape learning process leaves a large margin of color attribute boundary, which further triggers the shape attribute intra-class \"hollow\". Because the representation of different colors is continuously pushed away (classified) before that of the shape, the gaps between different color attribute clusters are significantly larger than that of the shape attribute.", + "- Since there is an intra-class \"hollow\" between BA and BC samples which is conditioned on a particular shape, the true class representation is deviated toward color. The fourth column shows that the training class centers (yellow stars) and the test ones (gray stars) are mismatched. The true class center is located in the low-density \"hollow\" between shape-conditioned BA and BC samples." + ], + "bbox": [ + 500, + 546, + 893, + 755 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Previous observations indicate that the before-and-latter learning process on attributes of different learning difficulties leaves the model to lose intra-class compactness, primarily when learning relying on the bias attribute is easier. To alleviate class center deviation towards the BA samples, only emphasizing the BC samples is insufficient due to their scarcity. In addition, we propose to utilize Intermediate Attribute Samples (IASs), i.e., the samples near the attribute decision boundary and remodel the shifted representation.", + "bbox": [ + 496, + 763, + 893, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "7601", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/c3f2a145d37ce5f6322b4c1b41a250943454e9a9793b821c066c3654aa01ffe8.jpg", + "image_caption": [ + "Figure 3. An illustration of the $\\chi^2$ -model. In the first stage (top row, left to right), we match and mine all samples with a $\\chi$ -shape pattern. As shown in the right part, the images are getting biased towards the side of peripheral bias attribute from top to bottom, i.e., from various colors or backgrounds to a single red or sunset. Different shapes ( $\\bigcirc$ or $\\Delta$ ) and colors (orange or green) drawn in the Representation Space indicate the target and bias attribute, respectively. In the second stage (bottom row, right to left), we construct prototypes by conditional interpolating around IASs with various ratios and design the $\\chi$ -structured metric learning objective to pull the intra-class samples." + ], + "image_footnote": [], + "bbox": [ + 169, + 87, + 815, + 329 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Especially when conditioned on the target attribute, the IASs vary on bias attribute and fill in the low-density intra-class \"hollow\" between BA and BC samples.", + "bbox": [ + 73, + 434, + 470, + 481 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3. $\\chi^2$ -Model", + "text_level": 1, + "bbox": [ + 75, + 493, + 183, + 510 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To mitigate the representation deviation and compact the intra-class \"hollow\", we leverage IASs to encode how bias attribute changes from one extreme (major BA side) to another (BC side). Then, the variety of the bias attribute could be interpolated when conditioned on a particular target attribute. We propose our two-stage $\\chi^2$ -model, whose notion is illustrated in Figure 3. First, the $\\chi^2$ -model discovers IASs based on the training dynamics of the vanilla model in subsection 3.1. Next, we analyze where the top-ranked samples with a $\\chi$ -shape pattern are as well as their effectiveness in debiasing in subsection 3.2. A conditional attribute interpolation step with IASs then fills in the low-density \"hollow\" to get a better estimation of class-specific prototype. By pulling samples to the corresponding prototype, the $\\chi$ -structured metric learning makes intra-class samples compact in subsection 3.3. We further investigate the Colored MNIST dataset. Results on other datasets are consistent.", + "bbox": [ + 73, + 518, + 473, + 776 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1. Scoring Samples with a $\\chi$ -shape Pattern", + "text_level": 1, + "bbox": [ + 75, + 786, + 419, + 803 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "From the observations in the previous section, we aim to collect IASs to reveal how BC samples shift and leave the intra-class \"hollow\" between them and BA ones. As discussed in subsection 2.2, the vanilla model fits BC samples later than BA ones, which motivates us to score the samples from their training dynamics. Once we have the score pattern", + "bbox": [ + 75, + 810, + 470, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "to match and distinguish BA and BC samples, IASs, with intermediate scores can be extracted and available for the next debiasing stage. In the following, we denote the posterior of the Ground-Truth class (GT-class) $y_{i}$ for a sample $\\mathbf{x}_i$ as", + "bbox": [ + 496, + 434, + 893, + 494 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname * {P r} \\left(h _ {\\boldsymbol {\\theta}} (\\mathbf {x} _ {i}) = y _ {i} \\mid \\mathbf {x} _ {i}\\right) = \\operatorname {s o f t m a x} \\left(\\mathbf {w} _ {c} ^ {\\top} f _ {\\boldsymbol {\\phi}} (\\mathbf {x})\\right) _ {y _ {i}}, \\quad (2)\n$$\n", + "text_format": "latex", + "bbox": [ + 522, + 506, + 892, + 525 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "the larger the posterior, the more confident a model predicts $\\mathbf{x}_i$ with $y_{i}$ . For notation simplicity, we abbreviate the posterior as $\\operatorname*{Pr}(y_i\\mid \\mathbf{x}_i)$ . The target posterior of a BA sample reaches one or becomes much higher than other categories soon after training several epochs, while the posterior of a BC sample has a delayed increase. To capture the clues on the change of bias attribute, we also analyze the posterior of the most obvious non-GT attribute, which reveals crucial bias influences. Denote the model at the $t$ -th epoch plus the superscript $t$ , such as $h_\\theta^t$ . We take the bias class for the sample $\\mathbf{x}_i$ at epoch $t$ as $b_i^t = \\arg \\max_{c\\in [C],c\\neq y_i}\\left(\\mathbf{w}_c^\\top f_\\phi (\\mathbf{x})\\right)^t$ . Then, we define the non-GT bias class as the most frequent $b_i^t$ along all epochs, i.e., $b_{i} = \\max_{-}\\mathrm{freq}\\{b_{i}^{t}\\}_{t = 1}^{T}$ . A sample has a larger bias class posterior when it has low confidence in its target class and vice versa.", + "bbox": [ + 496, + 535, + 893, + 763 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Taking posteriors of both $y_{i}$ and $b_{i}$ into account, a BA sample has larger $\\operatorname{Pr}(y_i \\mid \\mathbf{x}_i)$ and small $\\operatorname{Pr}(b_i \\mid \\mathbf{x}_i)$ along all its training epochs. For a BC sample, $\\operatorname{Pr}(y_i \\mid \\mathbf{x}_i)$ increases gradually and meanwhile $\\operatorname{Pr}(b_i \\mid \\mathbf{x}_i)$ decreases. We verify the phenomenon on Colored MNIST dataset in Figure 4 (left). For BA samples (yellow \"1\"), the two curves demonstrate a \"rectangle\", while for BC samples (blue \"1\"), the two curves have an obvious intersection and reveal a \"x\" shape. The statistics for the change of posteriors are shown", + "bbox": [ + 496, + 763, + 895, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "7602", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/b4f6b6e93c679d14333aab2af654687a7a5f6f9ca9a94b2f72a09b3c125e1c04.jpg", + "image_caption": [ + "Figure 4. Left: The change of posterior over the GT-class (green curve) as well as the bias class (red curve) over four samples. The two curves over BC samples and IAS demonstrate a $\\chi$ -shape, which is different from the curves over the BA sample. Right: The change of prediction frequencies of BC or BA samples along with the training epochs. The statistics are calculated over all BC or BA samples. A BA sample is easily predicted as the GT-class from the initial training stage, while a BC sample changes its prediction from the bias class to the GT-class gradually." + ], + "image_footnote": [], + "bbox": [ + 114, + 85, + 318, + 233 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/7d3216a2a9d89f10e726b182f8b88e68dcd2fd4e3f5987f055344430fa848ccd.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 323, + 85, + 529, + 234 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/ecd76dd2fa41ac5c6bdd450b4646f7df87225034c68b3f1d38b7d0ccfd79bc3b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 545, + 85, + 849, + 234 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "in Figure 4 (right). Therefore, how much the training dynamics match the \" $\\chi$ \" shape reveals the probability of a sample that shifts from the major BA clusters to minor BC ones. We design a $\\chi$ -shape for the dynamics of losses to capture such BC-specific properties. The change of sample-specific loss for ground-truth label and bias label over $T$ epochs could be summarized by $\\mathcal{L}_{\\mathrm{CE}}$ . Then, we use two exponential $\\chi$ -shape functions $\\chi_{\\mathrm{pattern}}$ to capture the ideal loss shape of the BC sample, i.e., the severely shifted case.", + "bbox": [ + 75, + 330, + 472, + 468 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {C E}} \\left(\\mathbf {x} _ {i}\\right) = \\left( \\begin{array}{c} \\mathcal {L} _ {\\mathrm {C E}} ^ {g t} \\left(\\mathbf {x} _ {i}\\right) = \\left\\{- \\log \\operatorname * {P r} ^ {t} \\left(y _ {i} \\mid \\mathbf {x} _ {i}\\right) \\right\\} _ {t = 1} ^ {T} \\\\ \\mathcal {L} _ {\\mathrm {C E}} ^ {b} \\left(\\mathbf {x} _ {i}\\right) = \\left\\{- \\log \\operatorname * {P r} ^ {t} \\left(b _ {i} \\mid \\mathbf {x} _ {i}\\right) \\right\\} _ {t = 1} ^ {T} \\end{array} \\right),\n$$\n", + "text_format": "latex", + "bbox": [ + 78, + 487, + 465, + 529 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\chi_ {\\text {p a t t e r n}} = \\left( \\begin{array}{l} \\mathrm {p} ^ {g t} = \\left\\{e ^ {- A _ {1} t} \\right\\} _ {t = 1} ^ {T} \\\\ \\mathrm {p} ^ {b} = \\left\\{e ^ {A _ {2} t} \\right\\} _ {t = 1} ^ {T} \\end{array} \\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 531, + 468, + 571 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $A_{1}$ and $A_{2}$ are the matching factors. They could be determined based on the dynamics of prediction fluctuations. For more details please see the supplementary material. The $\\chi_{\\mathrm{pattern}}$ encodes the observations for the most deviated BC samples. To match the loss dynamics with the pattern, we use the inner product over the two curves:", + "bbox": [ + 76, + 590, + 468, + 680 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathbf {s} \\left(\\mathbf {x} _ {i}\\right) = \\left\\langle \\mathcal {L} _ {\\mathrm {C E}} \\left(\\mathbf {x} _ {i}\\right), \\chi_ {\\text {s h a p e}} \\right\\rangle \\tag {4} \\\\ = \\left\\langle \\mathcal {L} _ {\\mathrm {C E}} ^ {g t} \\left(\\mathbf {x} _ {i}\\right), \\mathrm {p} ^ {g t} \\right\\rangle + \\left\\langle \\mathcal {L} _ {\\mathrm {C E}} ^ {b} \\left(\\mathbf {x} _ {i}\\right), \\mathrm {p} ^ {b} \\right\\rangle \\\\ = \\sum_ {t = 1} ^ {T} \\left(- e ^ {- A _ {1} t} \\cdot \\log \\Pr \\left(h _ {\\boldsymbol {\\theta}} \\left(\\mathbf {x} _ {i}\\right) = y _ {i} \\mid \\mathbf {x} _ {i}\\right) \\right. \\\\ - e ^ {A _ {2} t} \\cdot \\log \\operatorname * {P r} \\left(h _ {\\boldsymbol {\\theta}} \\left(\\mathbf {x} _ {i}\\right) = b _ {i} \\mid \\mathbf {x} _ {i}\\right). \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 104, + 700, + 468, + 805 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The inner product $\\mathbf{s}(\\mathbf{x}_i)$ takes the area under the curves (AUC) into account, which is more robust w.r.t. the volatile loss changes. When $\\mathbf{s}(\\mathbf{x}_i)$ score goes from low to high, the sample varies on the bias level, i.e., from BA samples to IASs, and then to BC samples.", + "bbox": [ + 75, + 825, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 1. The classification accuracy on the unbiased test sets of vanilla models. Various training sampling strategies are compared. \"0-1\" denotes only using BC samples. \"Step-wise\" denotes applying uniformly higher and lower weights on BC and BA samples. \"χ-pattern\" denotes sampling with scores calculated by our $\\chi^2$ -model. The best results are in bold, while the second-best ones are with underlines. C-CIFAR-10 is a similarly biased dataset as C-MNIST.", + "bbox": [ + 496, + 329, + 893, + 428 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/d286407795cc964c3b5d649aca44bcf4bdc22eb1fadd01558b8b1bf528ce7704.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Dataset Ratio (%)C-MNISTC-CIFAR-10
99.999.599.999.5
Vanilla28.5859.2926.9130.16
+ 0-154.7870.4118.7325.06
+ Step-wise41.6873.5232.1235.91
+χ-pattern52.6780.2935.4737.83
", + "bbox": [ + 540, + 438, + 852, + 539 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.2. Where IASs Are and Why IASs Can Help to Learn a Debiased Representation?", + "text_level": 1, + "bbox": [ + 498, + 569, + 890, + 599 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Combining the analysis in subsection 2.2 and collecting ranked samples by $\\mathbf{s}(\\mathbf{x}_i)$ , we find there are two types of IASs according to the representation near the target attribute decision boundary (as \"0\" for complex shapes in Figure 3), or that of the bias attribute (as helicopter in intermediate transitional \"sunset\" background). (1) If an IAS has an intermediate target attribute value, it may be a difficult samples and contains rich information about the target class boundaries. (2) If an IAS is in an intermediate state on the bias attribute, it may help to fill in the intra-class vacant \"hollow\" when conditioning (fixing) on the target attribute. Both types of IASs are similar to BC samples but from two directions, i.e., compared to the BA samples, they contain richer semantics on target or bias attributes. In the representation space, they are scattered between BA and BC samples, compensating for the sparsity of BC samples and valuable for debiasing. We will show how $\\chi$ -structured objective with IASs help to remodel the true class centers in the following subsection.", + "bbox": [ + 496, + 609, + 893, + 882 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We illustrate the importance of IASs with simple experi", + "bbox": [ + 519, + 885, + 893, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "7603", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/ff2f345aed3d2a455b6cb50414f851c650f07d21cd2f9fc086a6db5fb2ba4ef8.jpg", + "image_caption": [ + "Biased Model" + ], + "image_footnote": [], + "bbox": [ + 148, + 107, + 315, + 258 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/e3313ebc03b52da3fb69dc859af1c6c1a3d2ab9eadac3defe1509df2c025e7d1.jpg", + "image_caption": [ + "Figure 5. Heatmap of the mean distance from the sample to its conditional interpolated prototypes. We construct the prototype with mixing over the same-class subset but with different ratios of BC samples. Then the mean distances between the sample and those prototypes are measured. For a biased model (left two), when the BC ratio $\\gamma$ of interpolated prototype $\\mathbf{p}_{\\gamma}$ changes from low to high (horizontal direction), the distance of a sample to different $\\mathbf{p}_{\\gamma}$ varies hugely. The BA samples are closer to the low ratio ones, while the BC samples behave the opposite. An intra-class \"hollow\" exists. For an unbiased model (right two), the distances from any sample to $\\mathbf{p}_{\\gamma}$ with different ratios are almost the same." + ], + "image_footnote": [], + "bbox": [ + 323, + 108, + 462, + 258 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/2944384d775bc741062c6bf9774ddc647457f211d24c7c60b20ee9caa86d902b.jpg", + "image_caption": [ + "Unbiased Model" + ], + "image_footnote": [], + "bbox": [ + 483, + 108, + 616, + 258 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/98aeac472b9b9c12ed52083ea9c9628980d8ac06e55f26c040cd6f2b145e423a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 627, + 108, + 764, + 258 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/65803eb4e27b2c9e6d9ebe845f64c9c2ae67b3f659076b95883047b1ad189a46.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 774, + 117, + 826, + 258 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "ments on biased Colored-MNIST and Corrupted CIFAR-10 datasets. The datasets are described in subsection 4.1. We investigate whether various reweighting strategies on the vanilla model improve the generalization ability over an unbiased test set. We use \"0-1\" to denote the strategy that utilizes only the BC samples. \"step-wise\" means we apply uniformly higher (ratio of BA samples) and lower weights (one minus above ratio) to BC and BA samples. Our \"x-pattern\" smoothly reweights all samples with the matched scores, where BC samples as well as IASs have relatively larger weights than the remaining BA ones. The results in Table 1 show that simple reweighting strategies can improve the performance of a vanilla classifier, supporting the significance of emphasizing BC-like samples. Our \"x-pattern\" gets the best results in most scenarios, indicating that higher resampling weights on the IASs and BC samples assist the vanilla model to better frame the representation space.", + "bbox": [ + 75, + 375, + 472, + 632 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3.3. Learning from a $\\chi$ -Structured Objective", + "text_level": 1, + "bbox": [ + 76, + 646, + 421, + 662 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Although the BA samples are severely biased towards the bias attribute, the BC samples, integrating the rich bias attribute semantics, naturally make the representation independent of the biased influence [19]. An intuitive approach for debiasing is to average over BC samples and classified by the BC class centers. However, the sparsity of BC samples induces an erratic estimation which is far from the true class center, as shown in Figure 2.", + "bbox": [ + 75, + 672, + 470, + 792 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Benefiting from the analysis that BC-like IASs better estimate the intra-class structure, we target conditional interpolating around it, i.e., mixing the same-class samples with different BC-like scores to remodel the intermediate samples between BA and BC samples. From that, we can construct many prototypes closer to the real class center and pull samples to these prototypes to compact the intra-class", + "bbox": [ + 75, + 794, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "space. Combined with the soft ranking score from the $\\chi$ -pattern in the previous stage, we build two pools (subsets) of the samples denoted as $\\mathcal{D}_{\\parallel}$ and $\\mathcal{D}_{\\perp}$ . The $\\mathcal{D}_{\\perp}$ pool collects the top-rank samplers and most of them are BC samples and IASs. The $\\mathcal{D}_{\\parallel}$ pool is sampled from the remaining (BA) part according to the score. With the help of $\\mathcal{D}_{\\parallel}$ and $\\mathcal{D}_{\\perp}$ , we construct multiple bias bags (subset) $\\mathcal{B}_{\\gamma}$ with bootstrapping where the ratio of BC samples is $\\gamma$ .", + "bbox": [ + 496, + 375, + 893, + 496 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {B} _ {\\gamma} = \\left\\{\\left(\\mathbf {x} _ {i}, y _ {i}\\right) \\mid \\operatorname {n u m} \\left(\\mathcal {D} _ {\\perp}\\right): \\operatorname {n u m} \\left(\\mathcal {D} _ {\\|}\\right) = \\gamma \\right\\}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 544, + 502, + 890, + 520 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\mathrm{num}(\\mathcal{D})$ equals the number of samples in $\\mathcal{D}$ . When $\\gamma$ is low to high, the $\\mathcal{B}_{\\gamma}$ contains samples ranging from the extremes of BA samples to the IASs, and then to the BC ones. Based on $\\mathcal{B}_{\\gamma}$ , we compute the prototype, i.e., averaged on $\\mathcal{B}_{\\gamma}$ to interpolate bias attribute conditioned on the particular target attribute. For example, the prototype conditioned on class $c$ is formalized as $\\mathbf{p}_{\\gamma,c}$ :", + "bbox": [ + 496, + 526, + 893, + 633 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {p} _ {\\gamma , c} = \\frac {1}{K} \\sum_ {\\left(\\mathbf {x} _ {i}, y _ {i}\\right) \\in \\mathcal {B} _ {\\gamma}} f _ {\\phi} \\left(\\mathbf {x} _ {i}\\right) \\cdot \\mathbb {I} [ y _ {i} = c ]. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 555, + 642, + 890, + 680 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To further demonstrate the significance of intra-class compactness, we design the experiments to study the difference between a biased vanilla model and the unbiased oracle model (well-trained on an unbiased training set). We measure the mean distance between samples and their multiple conditional interpolated prototypes with changing ratio $\\gamma$ . If the prototypes are shifted with changing $\\gamma$ , that indicates a large intra-class deviation exists. As shown in Figure 5, for a biased model, when $\\gamma$ decreases, $\\mathbf{p}_{\\gamma}$ is interpolated closer to the BA samples. Opposite phenomena are observed in the BC samples. As for the unbiased oracle model, no matter how the BC ratio $\\gamma$ changes, such mean distance is almost unchanged and shows a lower variance. This coincides with the observation in Figure 2.", + "bbox": [ + 496, + 689, + 893, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "7604", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/612b3b030a33ae911f2741ae7bab0fa82af92337eababc280060029850850010.jpg", + "table_caption": [ + "Table 2. The classification performance on unbiased test set (in %; higher is better) evaluated on unbiased test sets of Colored MNIST and Corrupted CIFAR-10 with training on varying BA samples ratios. We denote bias pre-provided type by $\\bigcirc$ (without any information), $\\bullet$ (bias prior knowledge), and $\\bullet$ (explicit bias supervision). The best result is in bold, while the second-best is with underlines." + ], + "table_footnote": [], + "table_body": "
Dataset Ratio (%)Colored MNISTCorrupted CIFAR-10
99.999.599.095.099.999.599.095.0
Vanilla + p [44]○28.5859.2974.4287.1326.9130.1637.7141.60
○31.0164.8276.8487.8626.5529.4838.0742.30
RUBi [7]●27.8270.8086.5896.7733.7034.7034.5947.23
ReBias [4]●27.7172.8985.9596.8733.6534.4035.8247.45
End [46]●28.1981.8188.1096.9931.3033.8334.0238.77
DI [50]●33.1880.6386.2898.3632.0933.3737.6551.27
LfF [36]○30.2468.9076.6996.8129.8933.6835.2845.38
LFA [27]○22.3164.1381.8395.4532.4935.7439.6347.25
x-pattern + p●60.3364.1593.5398.3035.3339.3141.3253.37
x²-model (Ours)○66.9188.7392.1597.8735.6737.6140.7449.04
", + "bbox": [ + 174, + 142, + 797, + 339 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Motivated by mimicking the oracle, we adopt the conditional interpolated prototypes and construct a customized $\\chi$ -structured metric learning task. Assuming $\\gamma$ is large, we use $\\mathbf{p}_{\\gamma}$ and $\\mathbf{p}_{1 - \\gamma}$ to denote prototypes in bias bags $\\mathcal{B}$ with high and low BC ratios. The model should prioritize pulling the majority of low BC ratio bias bag $\\mathcal{B}_{1 - \\gamma}$ closer to $\\mathbf{p}_{\\gamma}$ , which interpolated into the high BC space. Similarly, the high BC bias bag $\\mathcal{B}_{\\gamma}$ should be pulled to low BC interpolated $\\mathbf{p}_{1 - \\gamma}$ . We optimize the cross-entropy loss $\\mathcal{L}_{\\mathrm{CE}}$ to enable the pulling operation. Concretely, the posterior via the distance $\\left(\\cdot ,\\cdot\\right)$ in the representation space is formalized as:", + "bbox": [ + 75, + 362, + 472, + 530 + ], + "page_idx": 6 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname * {P r} \\left(y _ {i} \\mid \\mathbf {x} _ {i}\\right) = \\frac {\\exp \\left(- \\mathrm {d} \\left(f _ {\\phi} \\left(\\mathbf {x} _ {i}\\right) , \\mathbf {p} _ {\\gamma , y _ {i}}\\right) / \\tau\\right)}{\\sum_ {c \\in [ C ]} \\exp \\left(- \\mathrm {d} \\left(f _ {\\phi} \\left(\\mathbf {x} _ {i}\\right) , \\mathbf {p} _ {\\gamma , c}\\right) / \\tau\\right)}, (7)\n$$\n", + "text_format": "latex", + "bbox": [ + 86, + 541, + 470, + 578 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "where $\\tau$ is a scaled temperature. One of the branches of the $\\chi$ -structure classification task is optimizing the $\\mathcal{L}_{\\mathrm{CE}}$ between samples in the $\\mathcal{B}_{1 - \\gamma}$ and $\\mathbf{p}_{\\gamma}$ . Similarly, the other branch is optimizing between $\\mathcal{B}_{\\gamma}$ and $\\mathbf{p}_{1 - \\gamma}$ at the same time. As shown in Figure 3, such a high-and-low correspondence captures and compacts the intra-class \"hollow\". In summary, The bias bags of high BC ratios $\\mathcal{B}_{\\gamma}$ with corresponding low BC interpolated prototypes conditioning on the target attribute $\\mathbf{p}_{1 - \\gamma}$ , and $\\mathcal{B}_{1 - \\gamma}$ with $\\mathbf{p}_{\\gamma}$ form the $\\chi$ -structure crossover objective.", + "bbox": [ + 75, + 587, + 473, + 739 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 753, + 209, + 771 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We conduct experiments to verify whether $\\chi^2$ -model has effective debiasing capability. We begin by introducing bias details in each dataset (as in subsection 4.1). We present the comparison approaches and training details. In subsection 4.2, the experiments show that $\\chi^2$ -model achieves superior performance in each stage. Furthermore, we exemplify the inherent quality of the prototype-based classification for debiasing tasks and offer ablation studies in subsection 4.3.", + "bbox": [ + 75, + 779, + 472, + 902 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/b352d742dead58bd51036dbcabd461b778ddb4f2d6e3e162e87306ca57f57725.jpg", + "table_caption": [ + "Table 3. The classification performance on the unbiased CelebA and NICO test set. The data source $BA$ denotes the measurement on BA samples and $BC$ is corresponding the BC samples." + ], + "table_footnote": [], + "table_body": "
Data SourceBiased CelebANICO
BABCAllAll
LfF [36]73.6970.4172.0534.44
DFA [27]94.0158.9876.5033.10
\\( \\chi^2 \\)-model97.6660.7979.2336.99
", + "bbox": [ + 550, + 414, + 839, + 501 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.1. Experimental Setups", + "text_level": 1, + "bbox": [ + 500, + 523, + 697, + 540 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Datasets. To cover more general and challenging cases of bias impact, we validate $\\chi^2$ -model in a variety of datasets, including two synthetic bias datasets (Colored MNIST [4], Corrupted CIFAR-10 [36]) and two real-world datasets (Biased CelebA [32] and Biased NICO).", + "bbox": [ + 496, + 550, + 893, + 626 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The BA samples ratio $\\rho$ in the training set is usually high (over $95\\%$ ), so the bias attribute is highly correlated with the target label. For instance, in the Colored MNIST dataset, each digit is linked to a pre-defined bias color. Similarly, there is an object target with corruption bias in Corrupted CIFAR-10 and a gender target with hair color bias in Biased CelebA. Following the previous works [19], we use the BA ratio $\\rho \\in \\{95.0\\%, 99.0\\%, 99.5\\%, 99.9\\% \\}$ for Colored MNIST and Corrupted CIFAR-10, respectively, and approximately $96\\%$ for Biased CelebA. The Biased NICO dataset is dedicatedly sampled in NICO [17], initially designed for OOD (Out-of-Distribution) image classification. NICO is enriched with variations in the object and context dimensions. We select the bias attribute with the highest co-occurrence frequency to the target one, e.g., helicopter to sunset in training set correlates strongly (see BA samples in Figure 3). The correlation ratio is roughly controlled to $86\\%$ . For more details please see the supplementary material.", + "bbox": [ + 496, + 628, + 895, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "7605", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/2c59797a4a4da0ffbe44b88ae0f0fd6b642ecd3da33c9dd4d7cc234fdec3e49c.jpg", + "table_caption": [ + "Table 4. The performance of BC samples mining on Colored MNIST with $99.5\\%$ BA ratio. Acc. denotes mean accuracy of ranking with top-300. $98\\% - \\sigma$ denotes the number of samples required to contain $98\\%$ of BC samples. $AP$ is average precision. $\\uparrow$ means higher is better, while $\\downarrow$ is the opposite." + ], + "table_footnote": [], + "table_body": "
MeasureAcc. ↑98%-σ ↓AP ↑
Entropy [20]78.3363283.52
Confidence [28]80.3359085.61
Loss [36]94.3941898.22
Pleiss et al. [39]82.6768689.24
Zhao et al. [55]90.3345196.04
χ-pattern (Ours)95.8437298.44
", + "bbox": [ + 112, + 162, + 431, + 277 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Baselines. We carefully select the classic and the latest trending approaches as baselines: (1) Vanilla model training with cross entropy as described in subsection 2.1. (2) Bias-tailored approaches with pre-provided bias type: RUBi, Rebias. (3) Explicit approaches under the guidance of total bias supervision: EnD and DI. (4) Implicit methods through general bias properties: LfF and DFA.", + "bbox": [ + 75, + 294, + 468, + 398 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Implementation details. Following the existing popular benchmarks [19, 23], we use the four-layer CNN with kernel size $7 \\times 7$ for the Colored MNIST dataset and ResNet-18 [15] for Corrupted CIFAR-10, Biased CelebA, and Biased NICO datasets. For a fair comparison, we re-implemented the baselines with the same configuration. We mainly focus on unbiased test accuracy for all categories. All models are trained on an NVIDIA RTX 3090 GPU.", + "bbox": [ + 75, + 400, + 468, + 520 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Baselines for the first stage. To better demonstrate the effectiveness of $\\chi$ -pattern, we consider related sample-specific scoring methods [39, 55] and report average precision, top-threshold accuracy, and the minimum samples (threshold) required for $98\\%$ accuracy. For more results, such as PR curves, please see the supplementary material.", + "bbox": [ + 75, + 521, + 470, + 612 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.2. Quantitative Evaluation", + "text_level": 1, + "bbox": [ + 76, + 619, + 299, + 636 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Performance of $\\chi$ -shape pattern. As shown in Table 4, our $\\chi$ -pattern matching achieves state-of-the-art performance on various evaluation metrics. Thus, the $\\chi$ -structure metric learning objective can leverage more IASs cues to interpolate bias attribute and further learn the debiased representation.", + "bbox": [ + 75, + 643, + 468, + 718 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "$\\chi^2$ -model in different types of bias constructions. (1) Synthetic bias on Colored MNIST and Corrupted CIFAR-10: From Table 2 we find that under extreme bias influence, as $\\rho$ is $99.9\\%$ , the performance of the vanilla model and other baselines decreases catastrophically. In contrast, Our $\\chi^2$ -model maintains the robust and efficient debiasing capability on the unbiased dataset. Further, more results in Figure 2 present the remarkable performance of our $\\chi^2$ -model compared to other methods. (2) Real-world bias on Biased CelebA and Biased NICO: Table 3 shows that compared to the recent methods which do not pre-provide any bias information as the same as ours, our method also achieves", + "bbox": [ + 75, + 719, + 470, + 900 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/2bfb29a0f9fa4db8be93aff5b33213ece4e09f52c713c79a66f091a6ec9e7838.jpg", + "image_caption": [ + "(a) t-SNE on $a_{t}$" + ], + "image_footnote": [], + "bbox": [ + 506, + 92, + 612, + 174 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/5f900d9cda0fd89e3aa3704b65b98bf5d7e8669686bb9587f153296bb6d0b0f1.jpg", + "image_caption": [ + "(b) t-SNE on $a_{b}$" + ], + "image_footnote": [], + "bbox": [ + 625, + 93, + 728, + 172 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7517b9cec2c4f684b35dac79150f64c8f5f463f90a50865c6dd0c64fb079cbb6.jpg", + "image_caption": [ + "(c) ablation study of $A_{1}, A_{2}$", + "Figure 6. (a) and (b) show the t-SNE visualization of our unbiased representation in terms of digit (the target attribute) and color (the bias one) in Colored MNIST, respectively. (c) displays the top-300 mean accuracy of mining BC samples on Colored MNIST with $99.5\\%$ BA ratio when $A_{1}$ and $A_{2}$ are changed." + ], + "image_footnote": [], + "bbox": [ + 740, + 90, + 890, + 176 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "outstanding performance. The above experiments indicate that conditional interpolation among IASs feedback the shift of the intrinsic knowledge and facilitate learning debiased representations even in extremely biased conditions.", + "bbox": [ + 496, + 296, + 892, + 357 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3. Further analysis", + "text_level": 1, + "bbox": [ + 500, + 372, + 663, + 387 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The inherent debiasing capability of prototype-based classification. We directly construct the prototype by averaging the trained representations of the vanilla model (as in Table 2 line two named “+ p”). The results show that on some datasets like Colored MNIST, the prototype-based classifier without training achieves performance improvement.", + "bbox": [ + 496, + 397, + 893, + 487 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Visualize the test set representation on 2D embedding space via t-SNE. Figure 6 shows the 2D projection of the feature extracted by $\\chi^2$ -model on Colored MNIST. We color the target and bias attributes separately. The representations follow the target attribute to cluster into classes which indicates that our model learns the debiased representations.", + "bbox": [ + 496, + 489, + 893, + 580 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Ablation studies. We further perform the ablation analysis of the matching factors $A_{1}, A_{2}$ in Eq. 3, which directly determine the $\\chi$ -shape curves. The results show the first stage of $\\chi^2$ -model is robust to changes in hyperparameters. For more related experiments like on different BC identification thresholds, please see the supplementary material.", + "bbox": [ + 496, + 582, + 893, + 672 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 691, + 617, + 707 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Although intra-class biased samples with a \"hollow\" structure impede learning debiased representations, we propose the $\\chi^2$ -model to leverage Intermediate Attribute Samples (IASs) to remodel the representation compactness. $\\chi^2$ -model works in a two-stage manner, matching and ranking possible IASs based on their $\\chi$ -shape training dynamics followed by a $\\chi$ -branch metric-based debiasing objective with conditional attribute interpolation.", + "bbox": [ + 496, + 719, + 893, + 839 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments. This research was supported by NSFC (61773198,61921006,62006112), Collaborative Innovation Center of Novel Software Technology and Industrialization, NSF of Jiangsu Province (BK20200313).", + "bbox": [ + 496, + 839, + 893, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "7606", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Vedika Agarwal, Rakshith Shetty, and Mario Fritz. Towards causal VQA: revealing and reducing spurious correlations by invariant and covariant semantic editing. In CVPR, pages 9687-9695, 2020. 1", + "[2] Martin Arjovsky, Léon Bottou, Ishaan Gulrajani, and David Lopez-Paz. Invariant risk minimization. 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In ICCV, pages 14982-14992, 2021. 3" + ], + "bbox": [ + 501, + 90, + 893, + 571 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "7608", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Learning Debiased Representations via Conditional Attribute Interpolation/35e0c901-be24-4ae3-9fbb-72a8952235b2_model.json b/2023/Learning Debiased Representations via Conditional Attribute Interpolation/35e0c901-be24-4ae3-9fbb-72a8952235b2_model.json new file mode 100644 index 0000000000000000000000000000000000000000..174cb475911f6f6bcec1c84ae1bc99ae99194bf5 --- /dev/null +++ b/2023/Learning Debiased Representations via Conditional Attribute Interpolation/35e0c901-be24-4ae3-9fbb-72a8952235b2_model.json @@ -0,0 +1,2310 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.106, + 0.131, + 0.865, + 0.154 + ], + "angle": 0, + "content": "Learning Debiased Representations via Conditional Attribute Interpolation" + }, + { + "type": "text", + "bbox": [ + 0.193, + 0.181, + 0.777, + 0.217 + ], + "angle": 0, + "content": "Yi-Kai Zhang, Qi-Wei Wang, De-Chuan Zhan, Han-Jia Ye\\(^{\\text{®}}\\) \nState Key Laboratory for Novel Software Technology, Nanjing University" + }, + { + "type": "text", + "bbox": [ + 0.271, + 0.22, + 0.695, + 0.234 + ], + "angle": 0, + "content": "{zhangyk, wangqiwei, zhandc, yehj}@lamda.nju.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.269, + 0.314, + 0.285 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.301, + 0.474, + 0.604 + ], + "angle": 0, + "content": "An image is usually described by more than one attribute like \"shape\" and \"color\". When a dataset is biased, i.e., most samples have attributes spuriously correlated with the target label, a Deep Neural Network (DNN) is prone to make predictions by the \"unintended\" attribute, especially if it is easier to learn. To improve the generalization ability when training on such a biased dataset, we propose a \\(\\chi^2\\)-model to learn debiased representations. First, we design a \\(\\chi\\)-shape pattern to match the training dynamics of a DNN and find Intermediate Attribute Samples (IASs) — samples near the attribute decision boundaries, which indicate how the value of an attribute changes from one extreme to another. Then we rectify the representation with a \\(\\chi\\)-structured metric learning objective. Conditional interpolation among IASs eliminates the negative effect of peripheral attributes and facilitates retaining the intra-class compactness. Experiments show that \\(\\chi^2\\)-model learns debiased representation effectively and achieves remarkable improvements on various datasets. Code is available at: https://github.com/ZhangYikaii/ch-square" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.633, + 0.21, + 0.649 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.66, + 0.472, + 0.902 + ], + "angle": 0, + "content": "Deep neural networks (DNNs) have emerged as an epoch-making technology in various machine learning tasks with impressive performance [5,26]. In some real applications, an object may possess multiple attributes, and some of them are only spuriously correlated to the target label. For example, in Figure 1, the intrinsic attribute of an image annotated by \"lifeboats\" is its shape. Although there are many lifeboats colored orange, a learner can not make predictions through the color, i.e., there is a misleading correlation from attribute as one containing \"orange\" color is the target \"lifeboats\". When the major training samples can be well discerned by such peripheral attribute, especially learning on it is easier than on the intrinsic one, a DNN is prone to bias towards that \"unintended\" bias attribute [6, 11, 21, 43, 47, 48, 51], like recognizing a \"cyclist\" wearing orange as a \"lifeboat\". Similar spurious attribute also exists in various applications" + }, + { + "type": "image", + "bbox": [ + 0.554, + 0.271, + 0.673, + 0.363 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.554, + 0.365, + 0.661, + 0.377 + ], + "angle": 0, + "content": "(a) Orange lifeboat" + }, + { + "type": "text", + "bbox": [ + 0.556, + 0.383, + 0.646, + 0.395 + ], + "angle": 0, + "content": "97.8% lifeboat" + }, + { + "type": "text", + "bbox": [ + 0.561, + 0.397, + 0.644, + 0.409 + ], + "angle": 0, + "content": "0.5% beacon" + }, + { + "type": "text", + "bbox": [ + 0.562, + 0.41, + 0.678, + 0.422 + ], + "angle": 0, + "content": "0.4% container ship" + }, + { + "type": "image", + "bbox": [ + 0.708, + 0.271, + 0.828, + 0.364 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.708, + 0.365, + 0.814, + 0.378 + ], + "angle": 0, + "content": "(b) Orange cyclists" + }, + { + "type": "text", + "bbox": [ + 0.708, + 0.384, + 0.799, + 0.395 + ], + "angle": 0, + "content": "57.0% lifeboat" + }, + { + "type": "text", + "bbox": [ + 0.711, + 0.397, + 0.863, + 0.409 + ], + "angle": 0, + "content": "13.8% bicycle-built-for-two" + }, + { + "type": "text", + "bbox": [ + 0.715, + 0.41, + 0.8, + 0.422 + ], + "angle": 0, + "content": "9.0% toyshop" + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.436, + 0.895, + 0.52 + ], + "angle": 0, + "content": "Figure 1. Classification of a standard ResNet-50 of (a) an orange lifeboat in the training set (with both color and shape attributes), and (b) an orange cyclist for the test (aligned with color attribute but conflicting with the shape one). Most of the lifeboats in the training set are orange. The biased model is prone to predict via the \"unintended\" color attribute rather than the intrinsic shape." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.546, + 0.892, + 0.577 + ], + "angle": 0, + "content": "such as recommendation system [8, 35, 53, 59] and neural language processing [13, 14, 33, 41, 56]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.581, + 0.895, + 0.822 + ], + "angle": 0, + "content": "Given such a biased training dataset, how to get rid of the negative effect of the misleading correlations? One intuitive solution is to perform special operations on those samples highly correlated to the bias attributes, which requires additional supervision, such as the pre-defined bias type [1,4,11,12,22,30,34,46,50]. Since prior knowledge of the dataset bias requires expensive manual annotations and is naturally missing in some applications, learning a debiased model without additional supervision about bias is in demand. Nam et al. [36] identify samples with intrinsic attributes based on the observation that malignant bias attributes are often easier-to-learn than others. Then the valuable samples for a debiasing scheme could be dynamically reweighted or augmented [11,27,34]. However, the restricted number of such samples implies uncertain representations and limits its ability to assist in debiasing." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.895, + 0.901 + ], + "angle": 0, + "content": "To leverage more valuable-for-debiasing knowledge, we take a further step in analyzing the representation space of naively-training dynamics, especially focusing on the discrepancies in attributes with a different learning difficulty. As we will later illustrate in Figure 2, an attribute-based" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7599" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.227 + ], + "angle": 0, + "content": "DNN pushes and fits on the easier bias attribute initially. The intrinsic attribute is then forced to shift in a \"lazy\" manner. The bias attribute that is pushed away first leaves a large margin boundary. Since the space of the other intrinsic attribute is filled with many different samples on bias attribute, it has a large intra-class variance, like a \"hollow\". The representation is biased toward one side of the \"hollow\", i.e., those samples aligned with the bias attribute. Without the true intra-class structure, the model becomes biased." + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.231, + 0.473, + 0.413 + ], + "angle": 0, + "content": "From the above observation, it is crucial to fill intra-class \"hollow\" and remodel representation compactness. Notice that the samples shifting to the two sides of the \"hollow\" have different characteristics, as aligned with the bias attribute and conflicting with it, respectively. We can find samples with an intermediate state between the above two. We call this type of sample the Intermediate Attribute Samples (IASs) which are near the decision boundary. When we condition (fix) on the intrinsic attribute, IASs vary on the other bias attribute and are exactly located in the \"hollow\" with low-density structural knowledge. Further, we can mine samples, including IASs, based on the distinct training dynamics." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.415, + 0.473, + 0.747 + ], + "angle": 0, + "content": "To this end, we propose our two-stage \\(\\chi^2\\)-model. In the first stage, we train a vanilla model on the biased dataset and record the sample-wise training dynamics w.r.t. both the target and the most obvious non-target classes (as the bias ones) along the epochs. An IAS is often predicted as a nontarget class in the beginning and then switched to its target class gradually, making its dynamics plot a \\(\\chi\\)-shape. Following this observation, we design a \\(\\chi\\)-shape pattern to match the training samples. The matching score ranks the mined samples according to the bias level, i.e., how much they are biased towards the side of the bias attribute. Benefiting from the IASs, we conduct conditional attribute interpolation, i.e., fixing the value of the target attribute. We interpolate the class-specific prototypes around IASs with various bias ratios. These conditional interpolated prototypes precisely \"average out\" on the bias attribute. From that, we design a \\(\\chi\\)-structured metric learning objective. It pulls samples close to those same-class interpolated prototypes, then intra-class samples become compact, and the influence of the bias attribute is removed. Our \\(\\chi^2\\)-model learns debiased representation effectively and achieves remarkable improvements on various datasets. Our contributions are summarized as" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.75, + 0.47, + 0.796 + ], + "angle": 0, + "content": "- We claim and verify that Intermediate Attribute Samples (IASs) distributed around attribute decision boundaries facilitate learning a debiased representation." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.796, + 0.472, + 0.871 + ], + "angle": 0, + "content": "- Based on the diverse learning behavior of different attribute types, we mine samples with varying bias levels, especially IASs. From that, we interpolate bias attribute conditioned on the intrinsic one and compact intra-class samples to remove the negative effect of bias." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.871, + 0.472, + 0.902 + ], + "angle": 0, + "content": "- Experiments on benchmarks and a newly constructed real-world dataset from NICO [17] validate the effectiveness" + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.75, + 0.472, + 0.902 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.092, + 0.868, + 0.108 + ], + "angle": 0, + "content": "of our \\(\\chi^2\\)-model in learning debiased representations." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.12, + 0.892, + 0.138 + ], + "angle": 0, + "content": "2. A Closer Look at Learning on Bias Attribute" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.146, + 0.892, + 0.177 + ], + "angle": 0, + "content": "After the background of learning on a biased dataset in subsection, we analyze the training dynamics of the model." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.185, + 0.684, + 0.2 + ], + "angle": 0, + "content": "2.1. Problem Definition" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.207, + 0.894, + 0.285 + ], + "angle": 0, + "content": "Given a training set \\(\\mathcal{D}_{\\mathrm{train}} = \\{(\\mathbf{x}_i,y_i)\\}_{i = 1}^N\\) , each sample \\(\\mathbf{x}_i\\) is associated with a class label \\(y\\in \\{1,2,\\dots ,C\\}\\) . We aim to find a decision rule \\(h_\\theta\\) that maps a sample to its label. \\(h_\\theta\\) is optimized by fitting all the training samples, e.g., minimizing the cross entropy loss as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.515, + 0.295, + 0.894, + 0.314 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {C E}} = \\mathbb {E} _ {\\left(\\mathbf {x} _ {i}, y _ {i}\\right) \\sim \\mathcal {D} _ {\\text {t r a i n}}} \\left[ - \\log \\Pr \\left(h _ {\\boldsymbol {\\theta}} \\left(\\mathbf {x} _ {i}\\right) = y _ {i} \\mid \\mathbf {x} _ {i}\\right) \\right]. \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.325, + 0.895, + 0.418 + ], + "angle": 0, + "content": "We denote \\(h_{\\theta} = \\arg \\max_{c\\in [C]}\\mathbf{w}_c^\\top f_\\phi (\\mathbf{x})\\) , where \\(f_{\\phi}\\rightarrow\\) \\(\\mathbb{R}^d\\) is the feature extraction network and \\(\\{\\mathbf{w}_c\\}_{c\\in [C]}\\) is toplayer \\(C\\) -class classifier. The \\(\\pmb{\\theta}\\) represents the union of learnable parameters \\(\\phi\\) and \\(\\mathbf{W}\\) . We expect the learned \\(h_\\theta\\) to have the high discerning ability over the test set \\(\\mathcal{D}_{\\mathrm{test}}\\) which has the same form as the training set \\(\\mathcal{D}_{\\mathrm{train}}\\)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.419, + 0.895, + 0.599 + ], + "angle": 0, + "content": "In addition to its class label, a sample could be described based on various attributes. If an attribute is spuriously correlated with the target label, we name it non-target bias attribute \\(a_{b}\\). The attribute that intrinsically determines the class label is the target attribute \\(a_{y}\\). For example, when we draw different handwritten digits in the MNIST dataset with specific colors [22], the color attribute will not help in the model generalization since we need to discern digits by the shape, e.g., \"1\" is like the stick. However, if almost all training images labeled \"1\" are in the same \"yellow\" color, the decision rule image in \"yellow\" is digit \"1\" will perform well on a such biased training set." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.895, + 0.796 + ], + "angle": 0, + "content": "In the task of learning with a biased training set [22, 29, 36], the bias attribute \\(a_{b}\\) on most of the same-class samples are consistent, and spuriously correlated with the target label (as example digit \"1\" in \"yellow\" above), so a model \\(h_{\\theta}\\) that relies on \\(a_{b}\\) or the target attribute \\(a_{y}\\) will both perform well on \\(\\mathcal{D}_{\\mathrm{train}}\\). In real-world applications, it is often easier to learn to rely on \\(a_{b}\\) than on \\(a_{y}\\), such as \"background\" or \"texture\" is easier-to-learn than the object [42, 51]. Therefore a model is prone to recognize based on the \\(a_{b}\\). Such a simplicity bias [3, 37, 38, 42] dramatically hurts the generalization of an unbiased test set. Nam et al. [36] also observe that the loss dynamics indicate the easier \\(a_{b}\\) is learned first, where the model is distracted and fails to learn \\(a_{y}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Based on the behaviors of the \"ultimate\" biased model, samples in \\(\\mathcal{D}_{\\mathrm{train}}\\) are split into two sets. Those training samples that could be correctly predicted based on the bias attribute \\(a_{b}\\) are named as Bias-Aligned (BA) samples (as example \"yellow digit 1\" above), while the remaining ones are Bias-Conflicting (BC) samples (as digit \"1\" of other colors). The number of BC samples is extremely small, and previous" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7600" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.162, + 0.088, + 0.816, + 0.381 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.392, + 0.897, + 0.477 + ], + "angle": 0, + "content": "Figure 2. An illustration of the training dynamics of a naively-trained model on a biased dataset. The different attribute classes are drawn with a specific color (top row) or shape (bottom row). The first three columns correspond to the sequential training progress of these two classifiers, and the final column shows the test scenario. The easier-to-learn color is fitted first, which leaves a large margin on decision boundary and correspondingly triggers the shape attribute intra-class \"hollow\". \"UB\" and \"BB\" are the abbreviations of \"unbiased boundary\" and \"biased boundary\". The biased model cannot generalize well as the shadow area in the last column frames the shape-misclassified samples. We use yellow stars to indicate the shifted class centers of the training samples and gray stars for those of the test samples." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.499, + 0.475, + 0.577 + ], + "angle": 0, + "content": "methods emphasize their role with various strategies [11, 27, 34, 36]. For additional related methods of learning a debiased model [2, 7, 9, 10, 18, 24, 25, 29, 31, 40, 49, 60] please see the supplementary material. They can be extrapolated and applied to other application scenarios [16, 45, 52, 54, 57, 58]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.587, + 0.433, + 0.603 + ], + "angle": 0, + "content": "2.2. The Training Dynamics of Biased Dataset" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.61, + 0.471, + 0.776 + ], + "angle": 0, + "content": "We analyze the training dynamics of a naively trained model in Eq. 1 on the Colored MNIST dataset. The non-target bias attribute is the color and the target attribute is the shape. For visualization shown in Figure 2, we set the output dimension of the penultimate layer as two. In addition to the learned classifier on shape attribute \\(a_{y}\\), simultaneously, we add another linear classifier on top of the embedding to show how the decision boundary of color attribute \\(a_{b}\\) changes. More details are described in the supplementary material. Focusing on the precedence relationship for learning \\(a_{y}\\) and \\(a_{b}\\), we have the following observations:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.781, + 0.473, + 0.856 + ], + "angle": 0, + "content": "- The easier-to-learn bias attribute color is fitted soon. The early training stage is shown in the first column. Both color and shape attribute classifiers discern by different colors and do correctly on almost all BA samples (red “0” and blue “2”, about \\(95\\%\\) of the training set)." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.856, + 0.474, + 0.901 + ], + "angle": 0, + "content": "- The target attribute shape is learned later in a \"lazy\" manner. To further fit all shape labels, the model focuses on the limited BC samples (blue \"0\" and red \"2\", corre" + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.781, + 0.474, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.499, + 0.893, + 0.546 + ], + "angle": 0, + "content": "spondingly about \\(5\\%\\) ) that cannot be perfectly classified by color. It pushes minor BC representations to the other (correct) side instead of adjusting the decision boundary." + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.547, + 0.895, + 0.65 + ], + "angle": 0, + "content": "- The ahead-color and lagged-shape learning process leaves a large margin of color attribute boundary, which further triggers the shape attribute intra-class \"hollow\". Because the representation of different colors is continuously pushed away (classified) before that of the shape, the gaps between different color attribute clusters are significantly larger than that of the shape attribute." + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.651, + 0.894, + 0.756 + ], + "angle": 0, + "content": "- Since there is an intra-class \"hollow\" between BA and BC samples which is conditioned on a particular shape, the true class representation is deviated toward color. The fourth column shows that the training class centers (yellow stars) and the test ones (gray stars) are mismatched. The true class center is located in the low-density \"hollow\" between shape-conditioned BA and BC samples." + }, + { + "type": "list", + "bbox": [ + 0.501, + 0.547, + 0.895, + 0.756 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Previous observations indicate that the before-and-latter learning process on attributes of different learning difficulties leaves the model to lose intra-class compactness, primarily when learning relying on the bias attribute is easier. To alleviate class center deviation towards the BA samples, only emphasizing the BC samples is insufficient due to their scarcity. In addition, we propose to utilize Intermediate Attribute Samples (IASs), i.e., the samples near the attribute decision boundary and remodel the shifted representation." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "7601" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.171, + 0.088, + 0.816, + 0.33 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.341, + 0.896, + 0.412 + ], + "angle": 0, + "content": "Figure 3. An illustration of the \\(\\chi^2\\)-model. In the first stage (top row, left to right), we match and mine all samples with a \\(\\chi\\)-shape pattern. As shown in the right part, the images are getting biased towards the side of peripheral bias attribute from top to bottom, i.e., from various colors or backgrounds to a single red or sunset. Different shapes (\\(\\bigcirc\\) or \\(\\Delta\\)) and colors (orange or green) drawn in the Representation Space indicate the target and bias attribute, respectively. In the second stage (bottom row, right to left), we construct prototypes by conditional interpolating around IASs with various ratios and design the \\(\\chi\\)-structured metric learning objective to pull the intra-class samples." + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.435, + 0.471, + 0.482 + ], + "angle": 0, + "content": "Especially when conditioned on the target attribute, the IASs vary on bias attribute and fill in the low-density intra-class \"hollow\" between BA and BC samples." + }, + { + "type": "title", + "bbox": [ + 0.076, + 0.494, + 0.184, + 0.511 + ], + "angle": 0, + "content": "3. \\(\\chi^2\\)-Model" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.52, + 0.474, + 0.777 + ], + "angle": 0, + "content": "To mitigate the representation deviation and compact the intra-class \"hollow\", we leverage IASs to encode how bias attribute changes from one extreme (major BA side) to another (BC side). Then, the variety of the bias attribute could be interpolated when conditioned on a particular target attribute. We propose our two-stage \\(\\chi^2\\)-model, whose notion is illustrated in Figure 3. First, the \\(\\chi^2\\)-model discovers IASs based on the training dynamics of the vanilla model in subsection 3.1. Next, we analyze where the top-ranked samples with a \\(\\chi\\)-shape pattern are as well as their effectiveness in debiasing in subsection 3.2. A conditional attribute interpolation step with IASs then fills in the low-density \"hollow\" to get a better estimation of class-specific prototype. By pulling samples to the corresponding prototype, the \\(\\chi\\)-structured metric learning makes intra-class samples compact in subsection 3.3. We further investigate the Colored MNIST dataset. Results on other datasets are consistent." + }, + { + "type": "title", + "bbox": [ + 0.076, + 0.787, + 0.421, + 0.804 + ], + "angle": 0, + "content": "3.1. Scoring Samples with a \\(\\chi\\)-shape Pattern" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.471, + 0.903 + ], + "angle": 0, + "content": "From the observations in the previous section, we aim to collect IASs to reveal how BC samples shift and leave the intra-class \"hollow\" between them and BA ones. As discussed in subsection 2.2, the vanilla model fits BC samples later than BA ones, which motivates us to score the samples from their training dynamics. Once we have the score pattern" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.435, + 0.895, + 0.496 + ], + "angle": 0, + "content": "to match and distinguish BA and BC samples, IASs, with intermediate scores can be extracted and available for the next debiasing stage. In the following, we denote the posterior of the Ground-Truth class (GT-class) \\( y_{i} \\) for a sample \\( \\mathbf{x}_i \\) as" + }, + { + "type": "equation", + "bbox": [ + 0.524, + 0.507, + 0.893, + 0.526 + ], + "angle": 0, + "content": "\\[\n\\operatorname * {P r} \\left(h _ {\\boldsymbol {\\theta}} (\\mathbf {x} _ {i}) = y _ {i} \\mid \\mathbf {x} _ {i}\\right) = \\operatorname {s o f t m a x} \\left(\\mathbf {w} _ {c} ^ {\\top} f _ {\\boldsymbol {\\phi}} (\\mathbf {x})\\right) _ {y _ {i}}, \\quad (2)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.536, + 0.895, + 0.765 + ], + "angle": 0, + "content": "the larger the posterior, the more confident a model predicts \\(\\mathbf{x}_i\\) with \\(y_{i}\\). For notation simplicity, we abbreviate the posterior as \\(\\operatorname*{Pr}(y_i\\mid \\mathbf{x}_i)\\). The target posterior of a BA sample reaches one or becomes much higher than other categories soon after training several epochs, while the posterior of a BC sample has a delayed increase. To capture the clues on the change of bias attribute, we also analyze the posterior of the most obvious non-GT attribute, which reveals crucial bias influences. Denote the model at the \\(t\\)-th epoch plus the superscript \\(t\\), such as \\(h_\\theta^t\\). We take the bias class for the sample \\(\\mathbf{x}_i\\) at epoch \\(t\\) as \\(b_i^t = \\arg \\max_{c\\in [C],c\\neq y_i}\\left(\\mathbf{w}_c^\\top f_\\phi (\\mathbf{x})\\right)^t\\). Then, we define the non-GT bias class as the most frequent \\(b_i^t\\) along all epochs, i.e., \\(b_{i} = \\max_{-}\\mathrm{freq}\\{b_{i}^{t}\\}_{t = 1}^{T}\\). A sample has a larger bias class posterior when it has low confidence in its target class and vice versa." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.896, + 0.902 + ], + "angle": 0, + "content": "Taking posteriors of both \\( y_{i} \\) and \\( b_{i} \\) into account, a BA sample has larger \\( \\operatorname{Pr}(y_i \\mid \\mathbf{x}_i) \\) and small \\( \\operatorname{Pr}(b_i \\mid \\mathbf{x}_i) \\) along all its training epochs. For a BC sample, \\( \\operatorname{Pr}(y_i \\mid \\mathbf{x}_i) \\) increases gradually and meanwhile \\( \\operatorname{Pr}(b_i \\mid \\mathbf{x}_i) \\) decreases. We verify the phenomenon on Colored MNIST dataset in Figure 4 (left). For BA samples (yellow \"1\"), the two curves demonstrate a \"rectangle\", while for BC samples (blue \"1\"), the two curves have an obvious intersection and reveal a \"x\" shape. The statistics for the change of posteriors are shown" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7602" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.115, + 0.086, + 0.32, + 0.234 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.324, + 0.087, + 0.53, + 0.236 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.547, + 0.087, + 0.85, + 0.235 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.243, + 0.895, + 0.314 + ], + "angle": 0, + "content": "Figure 4. Left: The change of posterior over the GT-class (green curve) as well as the bias class (red curve) over four samples. The two curves over BC samples and IAS demonstrate a \\(\\chi\\)-shape, which is different from the curves over the BA sample. Right: The change of prediction frequencies of BC or BA samples along with the training epochs. The statistics are calculated over all BC or BA samples. A BA sample is easily predicted as the GT-class from the initial training stage, while a BC sample changes its prediction from the bias class to the GT-class gradually." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.332, + 0.473, + 0.469 + ], + "angle": 0, + "content": "in Figure 4 (right). Therefore, how much the training dynamics match the \" \\( \\chi \\) \" shape reveals the probability of a sample that shifts from the major BA clusters to minor BC ones. We design a \\( \\chi \\)-shape for the dynamics of losses to capture such BC-specific properties. The change of sample-specific loss for ground-truth label and bias label over \\( T \\) epochs could be summarized by \\( \\mathcal{L}_{\\mathrm{CE}} \\). Then, we use two exponential \\( \\chi \\)-shape functions \\( \\chi_{\\mathrm{pattern}} \\) to capture the ideal loss shape of the BC sample, i.e., the severely shifted case." + }, + { + "type": "equation", + "bbox": [ + 0.08, + 0.488, + 0.466, + 0.53 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {C E}} \\left(\\mathbf {x} _ {i}\\right) = \\left( \\begin{array}{c} \\mathcal {L} _ {\\mathrm {C E}} ^ {g t} \\left(\\mathbf {x} _ {i}\\right) = \\left\\{- \\log \\operatorname * {P r} ^ {t} \\left(y _ {i} \\mid \\mathbf {x} _ {i}\\right) \\right\\} _ {t = 1} ^ {T} \\\\ \\mathcal {L} _ {\\mathrm {C E}} ^ {b} \\left(\\mathbf {x} _ {i}\\right) = \\left\\{- \\log \\operatorname * {P r} ^ {t} \\left(b _ {i} \\mid \\mathbf {x} _ {i}\\right) \\right\\} _ {t = 1} ^ {T} \\end{array} \\right),\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.15, + 0.532, + 0.47, + 0.573 + ], + "angle": 0, + "content": "\\[\n\\chi_ {\\text {p a t t e r n}} = \\left( \\begin{array}{l} \\mathrm {p} ^ {g t} = \\left\\{e ^ {- A _ {1} t} \\right\\} _ {t = 1} ^ {T} \\\\ \\mathrm {p} ^ {b} = \\left\\{e ^ {A _ {2} t} \\right\\} _ {t = 1} ^ {T} \\end{array} \\right), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.591, + 0.47, + 0.681 + ], + "angle": 0, + "content": "where \\(A_{1}\\) and \\(A_{2}\\) are the matching factors. They could be determined based on the dynamics of prediction fluctuations. For more details please see the supplementary material. The \\(\\chi_{\\mathrm{pattern}}\\) encodes the observations for the most deviated BC samples. To match the loss dynamics with the pattern, we use the inner product over the two curves:" + }, + { + "type": "equation", + "bbox": [ + 0.106, + 0.702, + 0.47, + 0.806 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathbf {s} \\left(\\mathbf {x} _ {i}\\right) = \\left\\langle \\mathcal {L} _ {\\mathrm {C E}} \\left(\\mathbf {x} _ {i}\\right), \\chi_ {\\text {s h a p e}} \\right\\rangle \\tag {4} \\\\ = \\left\\langle \\mathcal {L} _ {\\mathrm {C E}} ^ {g t} \\left(\\mathbf {x} _ {i}\\right), \\mathrm {p} ^ {g t} \\right\\rangle + \\left\\langle \\mathcal {L} _ {\\mathrm {C E}} ^ {b} \\left(\\mathbf {x} _ {i}\\right), \\mathrm {p} ^ {b} \\right\\rangle \\\\ = \\sum_ {t = 1} ^ {T} \\left(- e ^ {- A _ {1} t} \\cdot \\log \\Pr \\left(h _ {\\boldsymbol {\\theta}} \\left(\\mathbf {x} _ {i}\\right) = y _ {i} \\mid \\mathbf {x} _ {i}\\right) \\right. \\\\ - e ^ {A _ {2} t} \\cdot \\log \\operatorname * {P r} \\left(h _ {\\boldsymbol {\\theta}} \\left(\\mathbf {x} _ {i}\\right) = b _ {i} \\mid \\mathbf {x} _ {i}\\right). \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.47, + 0.901 + ], + "angle": 0, + "content": "The inner product \\(\\mathbf{s}(\\mathbf{x}_i)\\) takes the area under the curves (AUC) into account, which is more robust w.r.t. the volatile loss changes. When \\(\\mathbf{s}(\\mathbf{x}_i)\\) score goes from low to high, the sample varies on the bias level, i.e., from BA samples to IASs, and then to BC samples." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.33, + 0.895, + 0.429 + ], + "angle": 0, + "content": "Table 1. The classification accuracy on the unbiased test sets of vanilla models. Various training sampling strategies are compared. \"0-1\" denotes only using BC samples. \"Step-wise\" denotes applying uniformly higher and lower weights on BC and BA samples. \"χ-pattern\" denotes sampling with scores calculated by our \\(\\chi^2\\)-model. The best results are in bold, while the second-best ones are with underlines. C-CIFAR-10 is a similarly biased dataset as C-MNIST." + }, + { + "type": "table", + "bbox": [ + 0.541, + 0.439, + 0.853, + 0.54 + ], + "angle": 0, + "content": "
Dataset Ratio (%)C-MNISTC-CIFAR-10
99.999.599.999.5
Vanilla28.5859.2926.9130.16
+ 0-154.7870.4118.7325.06
+ Step-wise41.6873.5232.1235.91
+χ-pattern52.6780.2935.4737.83
" + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.57, + 0.892, + 0.601 + ], + "angle": 0, + "content": "3.2. Where IASs Are and Why IASs Can Help to Learn a Debiased Representation?" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.611, + 0.895, + 0.883 + ], + "angle": 0, + "content": "Combining the analysis in subsection 2.2 and collecting ranked samples by \\(\\mathbf{s}(\\mathbf{x}_i)\\), we find there are two types of IASs according to the representation near the target attribute decision boundary (as \"0\" for complex shapes in Figure 3), or that of the bias attribute (as helicopter in intermediate transitional \"sunset\" background). (1) If an IAS has an intermediate target attribute value, it may be a difficult samples and contains rich information about the target class boundaries. (2) If an IAS is in an intermediate state on the bias attribute, it may help to fill in the intra-class vacant \"hollow\" when conditioning (fixing) on the target attribute. Both types of IASs are similar to BC samples but from two directions, i.e., compared to the BA samples, they contain richer semantics on target or bias attributes. In the representation space, they are scattered between BA and BC samples, compensating for the sparsity of BC samples and valuable for debiasing. We will show how \\(\\chi\\)-structured objective with IASs help to remodel the true class centers in the following subsection." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.886, + 0.895, + 0.902 + ], + "angle": 0, + "content": "We illustrate the importance of IASs with simple experi" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7603" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.277, + 0.087, + 0.362, + 0.099 + ], + "angle": 0, + "content": "Biased Model" + }, + { + "type": "image", + "bbox": [ + 0.15, + 0.108, + 0.316, + 0.259 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.324, + 0.109, + 0.464, + 0.26 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.572, + 0.087, + 0.675, + 0.099 + ], + "angle": 0, + "content": "Unbiased Model" + }, + { + "type": "image", + "bbox": [ + 0.484, + 0.109, + 0.617, + 0.259 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.629, + 0.109, + 0.765, + 0.259 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.776, + 0.118, + 0.828, + 0.26 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.269, + 0.895, + 0.352 + ], + "angle": 0, + "content": "Figure 5. Heatmap of the mean distance from the sample to its conditional interpolated prototypes. We construct the prototype with mixing over the same-class subset but with different ratios of BC samples. Then the mean distances between the sample and those prototypes are measured. For a biased model (left two), when the BC ratio \\(\\gamma\\) of interpolated prototype \\(\\mathbf{p}_{\\gamma}\\) changes from low to high (horizontal direction), the distance of a sample to different \\(\\mathbf{p}_{\\gamma}\\) varies hugely. The BA samples are closer to the low ratio ones, while the BC samples behave the opposite. An intra-class \"hollow\" exists. For an unbiased model (right two), the distances from any sample to \\(\\mathbf{p}_{\\gamma}\\) with different ratios are almost the same." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.375, + 0.473, + 0.633 + ], + "angle": 0, + "content": "ments on biased Colored-MNIST and Corrupted CIFAR-10 datasets. The datasets are described in subsection 4.1. We investigate whether various reweighting strategies on the vanilla model improve the generalization ability over an unbiased test set. We use \"0-1\" to denote the strategy that utilizes only the BC samples. \"step-wise\" means we apply uniformly higher (ratio of BA samples) and lower weights (one minus above ratio) to BC and BA samples. Our \"x-pattern\" smoothly reweights all samples with the matched scores, where BC samples as well as IASs have relatively larger weights than the remaining BA ones. The results in Table 1 show that simple reweighting strategies can improve the performance of a vanilla classifier, supporting the significance of emphasizing BC-like samples. Our \"x-pattern\" gets the best results in most scenarios, indicating that higher resampling weights on the IASs and BC samples assist the vanilla model to better frame the representation space." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.647, + 0.423, + 0.664 + ], + "angle": 0, + "content": "3.3. Learning from a \\(\\chi\\)-Structured Objective" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.673, + 0.471, + 0.794 + ], + "angle": 0, + "content": "Although the BA samples are severely biased towards the bias attribute, the BC samples, integrating the rich bias attribute semantics, naturally make the representation independent of the biased influence [19]. An intuitive approach for debiasing is to average over BC samples and classified by the BC class centers. However, the sparsity of BC samples induces an erratic estimation which is far from the true class center, as shown in Figure 2." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Benefiting from the analysis that BC-like IASs better estimate the intra-class structure, we target conditional interpolating around it, i.e., mixing the same-class samples with different BC-like scores to remodel the intermediate samples between BA and BC samples. From that, we can construct many prototypes closer to the real class center and pull samples to these prototypes to compact the intra-class" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.375, + 0.895, + 0.497 + ], + "angle": 0, + "content": "space. Combined with the soft ranking score from the \\(\\chi\\)-pattern in the previous stage, we build two pools (subsets) of the samples denoted as \\(\\mathcal{D}_{\\parallel}\\) and \\(\\mathcal{D}_{\\perp}\\). The \\(\\mathcal{D}_{\\perp}\\) pool collects the top-rank samplers and most of them are BC samples and IASs. The \\(\\mathcal{D}_{\\parallel}\\) pool is sampled from the remaining (BA) part according to the score. With the help of \\(\\mathcal{D}_{\\parallel}\\) and \\(\\mathcal{D}_{\\perp}\\), we construct multiple bias bags (subset) \\(\\mathcal{B}_{\\gamma}\\) with bootstrapping where the ratio of BC samples is \\(\\gamma\\)." + }, + { + "type": "equation", + "bbox": [ + 0.545, + 0.503, + 0.892, + 0.521 + ], + "angle": 0, + "content": "\\[\n\\mathcal {B} _ {\\gamma} = \\left\\{\\left(\\mathbf {x} _ {i}, y _ {i}\\right) \\mid \\operatorname {n u m} \\left(\\mathcal {D} _ {\\perp}\\right): \\operatorname {n u m} \\left(\\mathcal {D} _ {\\|}\\right) = \\gamma \\right\\}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.527, + 0.895, + 0.635 + ], + "angle": 0, + "content": "where \\(\\mathrm{num}(\\mathcal{D})\\) equals the number of samples in \\(\\mathcal{D}\\). When \\(\\gamma\\) is low to high, the \\(\\mathcal{B}_{\\gamma}\\) contains samples ranging from the extremes of BA samples to the IASs, and then to the BC ones. Based on \\(\\mathcal{B}_{\\gamma}\\), we compute the prototype, i.e., averaged on \\(\\mathcal{B}_{\\gamma}\\) to interpolate bias attribute conditioned on the particular target attribute. For example, the prototype conditioned on class \\(c\\) is formalized as \\(\\mathbf{p}_{\\gamma,c}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.556, + 0.643, + 0.892, + 0.681 + ], + "angle": 0, + "content": "\\[\n\\mathbf {p} _ {\\gamma , c} = \\frac {1}{K} \\sum_ {\\left(\\mathbf {x} _ {i}, y _ {i}\\right) \\in \\mathcal {B} _ {\\gamma}} f _ {\\phi} \\left(\\mathbf {x} _ {i}\\right) \\cdot \\mathbb {I} [ y _ {i} = c ]. \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.69, + 0.895, + 0.901 + ], + "angle": 0, + "content": "To further demonstrate the significance of intra-class compactness, we design the experiments to study the difference between a biased vanilla model and the unbiased oracle model (well-trained on an unbiased training set). We measure the mean distance between samples and their multiple conditional interpolated prototypes with changing ratio \\(\\gamma\\). If the prototypes are shifted with changing \\(\\gamma\\), that indicates a large intra-class deviation exists. As shown in Figure 5, for a biased model, when \\(\\gamma\\) decreases, \\(\\mathbf{p}_{\\gamma}\\) is interpolated closer to the BA samples. Opposite phenomena are observed in the BC samples. As for the unbiased oracle model, no matter how the BC ratio \\(\\gamma\\) changes, such mean distance is almost unchanged and shows a lower variance. This coincides with the observation in Figure 2." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7604" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.895, + 0.133 + ], + "angle": 0, + "content": "Table 2. The classification performance on unbiased test set (in %; higher is better) evaluated on unbiased test sets of Colored MNIST and Corrupted CIFAR-10 with training on varying BA samples ratios. We denote bias pre-provided type by \\(\\bigcirc\\) (without any information), \\(\\bullet\\) (bias prior knowledge), and \\(\\bullet\\) (explicit bias supervision). The best result is in bold, while the second-best is with underlines." + }, + { + "type": "table", + "bbox": [ + 0.176, + 0.143, + 0.798, + 0.34 + ], + "angle": 0, + "content": "
Dataset Ratio (%)Colored MNISTCorrupted CIFAR-10
99.999.599.095.099.999.599.095.0
Vanilla + p [44]○28.5859.2974.4287.1326.9130.1637.7141.60
○31.0164.8276.8487.8626.5529.4838.0742.30
RUBi [7]●27.8270.8086.5896.7733.7034.7034.5947.23
ReBias [4]●27.7172.8985.9596.8733.6534.4035.8247.45
End [46]●28.1981.8188.1096.9931.3033.8334.0238.77
DI [50]●33.1880.6386.2898.3632.0933.3737.6551.27
LfF [36]○30.2468.9076.6996.8129.8933.6835.2845.38
LFA [27]○22.3164.1381.8395.4532.4935.7439.6347.25
x-pattern + p●60.3364.1593.5398.3035.3339.3141.3253.37
x²-model (Ours)○66.9188.7392.1597.8735.6737.6140.7449.04
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.363, + 0.473, + 0.531 + ], + "angle": 0, + "content": "Motivated by mimicking the oracle, we adopt the conditional interpolated prototypes and construct a customized \\(\\chi\\)-structured metric learning task. Assuming \\(\\gamma\\) is large, we use \\(\\mathbf{p}_{\\gamma}\\) and \\(\\mathbf{p}_{1 - \\gamma}\\) to denote prototypes in bias bags \\(\\mathcal{B}\\) with high and low BC ratios. The model should prioritize pulling the majority of low BC ratio bias bag \\(\\mathcal{B}_{1 - \\gamma}\\) closer to \\(\\mathbf{p}_{\\gamma}\\), which interpolated into the high BC space. Similarly, the high BC bias bag \\(\\mathcal{B}_{\\gamma}\\) should be pulled to low BC interpolated \\(\\mathbf{p}_{1 - \\gamma}\\). We optimize the cross-entropy loss \\(\\mathcal{L}_{\\mathrm{CE}}\\) to enable the pulling operation. Concretely, the posterior via the distance \\(\\left(\\cdot ,\\cdot\\right)\\) in the representation space is formalized as:" + }, + { + "type": "equation", + "bbox": [ + 0.087, + 0.542, + 0.472, + 0.579 + ], + "angle": 0, + "content": "\\[\n\\operatorname * {P r} \\left(y _ {i} \\mid \\mathbf {x} _ {i}\\right) = \\frac {\\exp \\left(- \\mathrm {d} \\left(f _ {\\phi} \\left(\\mathbf {x} _ {i}\\right) , \\mathbf {p} _ {\\gamma , y _ {i}}\\right) / \\tau\\right)}{\\sum_ {c \\in [ C ]} \\exp \\left(- \\mathrm {d} \\left(f _ {\\phi} \\left(\\mathbf {x} _ {i}\\right) , \\mathbf {p} _ {\\gamma , c}\\right) / \\tau\\right)}, (7)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.588, + 0.475, + 0.741 + ], + "angle": 0, + "content": "where \\(\\tau\\) is a scaled temperature. One of the branches of the \\(\\chi\\)-structure classification task is optimizing the \\(\\mathcal{L}_{\\mathrm{CE}}\\) between samples in the \\(\\mathcal{B}_{1 - \\gamma}\\) and \\(\\mathbf{p}_{\\gamma}\\). Similarly, the other branch is optimizing between \\(\\mathcal{B}_{\\gamma}\\) and \\(\\mathbf{p}_{1 - \\gamma}\\) at the same time. As shown in Figure 3, such a high-and-low correspondence captures and compacts the intra-class \"hollow\". In summary, The bias bags of high BC ratios \\(\\mathcal{B}_{\\gamma}\\) with corresponding low BC interpolated prototypes conditioning on the target attribute \\(\\mathbf{p}_{1 - \\gamma}\\), and \\(\\mathcal{B}_{1 - \\gamma}\\) with \\(\\mathbf{p}_{\\gamma}\\) form the \\(\\chi\\)-structure crossover objective." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.755, + 0.21, + 0.772 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.473, + 0.903 + ], + "angle": 0, + "content": "We conduct experiments to verify whether \\(\\chi^2\\)-model has effective debiasing capability. We begin by introducing bias details in each dataset (as in subsection 4.1). We present the comparison approaches and training details. In subsection 4.2, the experiments show that \\(\\chi^2\\)-model achieves superior performance in each stage. Furthermore, we exemplify the inherent quality of the prototype-based classification for debiasing tasks and offer ablation studies in subsection 4.3." + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.361, + 0.895, + 0.406 + ], + "angle": 0, + "content": "Table 3. The classification performance on the unbiased CelebA and NICO test set. The data source \\( BA \\) denotes the measurement on BA samples and \\( BC \\) is corresponding the BC samples." + }, + { + "type": "table", + "bbox": [ + 0.552, + 0.415, + 0.84, + 0.502 + ], + "angle": 0, + "content": "
Data SourceBiased CelebANICO
BABCAllAll
LfF [36]73.6970.4172.0534.44
DFA [27]94.0158.9876.5033.10
\\( \\chi^2 \\)-model97.6660.7979.2336.99
" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.525, + 0.698, + 0.541 + ], + "angle": 0, + "content": "4.1. Experimental Setups" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.551, + 0.895, + 0.627 + ], + "angle": 0, + "content": "Datasets. To cover more general and challenging cases of bias impact, we validate \\(\\chi^2\\)-model in a variety of datasets, including two synthetic bias datasets (Colored MNIST [4], Corrupted CIFAR-10 [36]) and two real-world datasets (Biased CelebA [32] and Biased NICO)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.897, + 0.902 + ], + "angle": 0, + "content": "The BA samples ratio \\(\\rho\\) in the training set is usually high (over \\(95\\%\\)), so the bias attribute is highly correlated with the target label. For instance, in the Colored MNIST dataset, each digit is linked to a pre-defined bias color. Similarly, there is an object target with corruption bias in Corrupted CIFAR-10 and a gender target with hair color bias in Biased CelebA. Following the previous works [19], we use the BA ratio \\(\\rho \\in \\{95.0\\%, 99.0\\%, 99.5\\%, 99.9\\% \\}\\) for Colored MNIST and Corrupted CIFAR-10, respectively, and approximately \\(96\\%\\) for Biased CelebA. The Biased NICO dataset is dedicatedly sampled in NICO [17], initially designed for OOD (Out-of-Distribution) image classification. NICO is enriched with variations in the object and context dimensions. We select the bias attribute with the highest co-occurrence frequency to the target one, e.g., helicopter to sunset in training set correlates strongly (see BA samples in Figure 3). The correlation ratio is roughly controlled to \\(86\\%\\). For more details please see the supplementary material." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7605" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.083, + 0.473, + 0.155 + ], + "angle": 0, + "content": "Table 4. The performance of BC samples mining on Colored MNIST with \\(99.5\\%\\) BA ratio. Acc. denotes mean accuracy of ranking with top-300. \\(98\\% - \\sigma\\) denotes the number of samples required to contain \\(98\\%\\) of BC samples. \\(AP\\) is average precision. \\(\\uparrow\\) means higher is better, while \\(\\downarrow\\) is the opposite." + }, + { + "type": "table", + "bbox": [ + 0.114, + 0.164, + 0.432, + 0.279 + ], + "angle": 0, + "content": "
MeasureAcc. ↑98%-σ ↓AP ↑
Entropy [20]78.3363283.52
Confidence [28]80.3359085.61
Loss [36]94.3941898.22
Pleiss et al. [39]82.6768689.24
Zhao et al. [55]90.3345196.04
χ-pattern (Ours)95.8437298.44
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.295, + 0.47, + 0.4 + ], + "angle": 0, + "content": "Baselines. We carefully select the classic and the latest trending approaches as baselines: (1) Vanilla model training with cross entropy as described in subsection 2.1. (2) Bias-tailored approaches with pre-provided bias type: RUBi, Rebias. (3) Explicit approaches under the guidance of total bias supervision: EnD and DI. (4) Implicit methods through general bias properties: LfF and DFA." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.401, + 0.47, + 0.521 + ], + "angle": 0, + "content": "Implementation details. Following the existing popular benchmarks [19, 23], we use the four-layer CNN with kernel size \\(7 \\times 7\\) for the Colored MNIST dataset and ResNet-18 [15] for Corrupted CIFAR-10, Biased CelebA, and Biased NICO datasets. For a fair comparison, we re-implemented the baselines with the same configuration. We mainly focus on unbiased test accuracy for all categories. All models are trained on an NVIDIA RTX 3090 GPU." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.522, + 0.471, + 0.613 + ], + "angle": 0, + "content": "Baselines for the first stage. To better demonstrate the effectiveness of \\(\\chi\\)-pattern, we consider related sample-specific scoring methods [39, 55] and report average precision, top-threshold accuracy, and the minimum samples (threshold) required for \\(98\\%\\) accuracy. For more results, such as PR curves, please see the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.621, + 0.3, + 0.637 + ], + "angle": 0, + "content": "4.2. Quantitative Evaluation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.645, + 0.47, + 0.719 + ], + "angle": 0, + "content": "Performance of \\(\\chi\\)-shape pattern. As shown in Table 4, our \\(\\chi\\)-pattern matching achieves state-of-the-art performance on various evaluation metrics. Thus, the \\(\\chi\\)-structure metric learning objective can leverage more IASs cues to interpolate bias attribute and further learn the debiased representation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.471, + 0.901 + ], + "angle": 0, + "content": "\\(\\chi^2\\)-model in different types of bias constructions. (1) Synthetic bias on Colored MNIST and Corrupted CIFAR-10: From Table 2 we find that under extreme bias influence, as \\(\\rho\\) is \\(99.9\\%\\), the performance of the vanilla model and other baselines decreases catastrophically. In contrast, Our \\(\\chi^2\\)-model maintains the robust and efficient debiasing capability on the unbiased dataset. Further, more results in Figure 2 present the remarkable performance of our \\(\\chi^2\\)-model compared to other methods. (2) Real-world bias on Biased CelebA and Biased NICO: Table 3 shows that compared to the recent methods which do not pre-provide any bias information as the same as ours, our method also achieves" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.093, + 0.613, + 0.175 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.522, + 0.183, + 0.598, + 0.194 + ], + "angle": 0, + "content": "(a) t-SNE on \\(a_{t}\\)" + }, + { + "type": "image", + "bbox": [ + 0.627, + 0.094, + 0.73, + 0.174 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.64, + 0.183, + 0.716, + 0.194 + ], + "angle": 0, + "content": "(b) t-SNE on \\(a_{b}\\)" + }, + { + "type": "image", + "bbox": [ + 0.741, + 0.092, + 0.891, + 0.177 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.747, + 0.181, + 0.882, + 0.193 + ], + "angle": 0, + "content": "(c) ablation study of \\(A_{1}, A_{2}\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.202, + 0.894, + 0.273 + ], + "angle": 0, + "content": "Figure 6. (a) and (b) show the t-SNE visualization of our unbiased representation in terms of digit (the target attribute) and color (the bias one) in Colored MNIST, respectively. (c) displays the top-300 mean accuracy of mining BC samples on Colored MNIST with \\(99.5\\%\\) BA ratio when \\(A_{1}\\) and \\(A_{2}\\) are changed." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.297, + 0.893, + 0.358 + ], + "angle": 0, + "content": "outstanding performance. The above experiments indicate that conditional interpolation among IASs feedback the shift of the intrinsic knowledge and facilitate learning debiased representations even in extremely biased conditions." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.373, + 0.664, + 0.388 + ], + "angle": 0, + "content": "4.3. Further analysis" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.398, + 0.894, + 0.488 + ], + "angle": 0, + "content": "The inherent debiasing capability of prototype-based classification. We directly construct the prototype by averaging the trained representations of the vanilla model (as in Table 2 line two named “+ p”). The results show that on some datasets like Colored MNIST, the prototype-based classifier without training achieves performance improvement." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.49, + 0.894, + 0.581 + ], + "angle": 0, + "content": "Visualize the test set representation on 2D embedding space via t-SNE. Figure 6 shows the 2D projection of the feature extracted by \\(\\chi^2\\)-model on Colored MNIST. We color the target and bias attributes separately. The representations follow the target attribute to cluster into classes which indicates that our model learns the debiased representations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.583, + 0.894, + 0.674 + ], + "angle": 0, + "content": "Ablation studies. We further perform the ablation analysis of the matching factors \\( A_{1}, A_{2} \\) in Eq. 3, which directly determine the \\( \\chi \\)-shape curves. The results show the first stage of \\( \\chi^2 \\)-model is robust to changes in hyperparameters. For more related experiments like on different BC identification thresholds, please see the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.693, + 0.619, + 0.708 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.895, + 0.84 + ], + "angle": 0, + "content": "Although intra-class biased samples with a \"hollow\" structure impede learning debiased representations, we propose the \\(\\chi^2\\)-model to leverage Intermediate Attribute Samples (IASs) to remodel the representation compactness. \\(\\chi^2\\)-model works in a two-stage manner, matching and ranking possible IASs based on their \\(\\chi\\)-shape training dynamics followed by a \\(\\chi\\)-branch metric-based debiasing objective with conditional attribute interpolation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Acknowledgments. This research was supported by NSFC (61773198,61921006,62006112), Collaborative Innovation Center of Novel Software Technology and Industrialization, NSF of Jiangsu Province (BK20200313)." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "7606" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.17 + ], + "angle": 0, + "content": "[1] Vedika Agarwal, Rakshith Shetty, and Mario Fritz. Towards causal VQA: revealing and reducing spurious correlations by invariant and covariant semantic editing. In CVPR, pages 9687-9695, 2020. 1" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.173, + 0.472, + 0.213 + ], + "angle": 0, + "content": "[2] Martin Arjovsky, Léon Bottou, Ishaan Gulrajani, and David Lopez-Paz. Invariant risk minimization. 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In ICCV, pages 14982-14992, 2021. 3" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.092, + 0.895, + 0.573 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "7608" + } + ] +] \ No newline at end of file diff --git a/2023/Learning Debiased Representations via Conditional Attribute Interpolation/35e0c901-be24-4ae3-9fbb-72a8952235b2_origin.pdf b/2023/Learning Debiased Representations via Conditional Attribute Interpolation/35e0c901-be24-4ae3-9fbb-72a8952235b2_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..6383883dc16ae49022863db518b3a742c4f3e8c2 --- /dev/null +++ b/2023/Learning Debiased Representations via Conditional Attribute Interpolation/35e0c901-be24-4ae3-9fbb-72a8952235b2_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:b2b15d5da4442d24da252e6e5cbe78954236258607022221cb18899f6b4480c3 +size 5890289 diff --git a/2023/Learning Debiased Representations via Conditional Attribute Interpolation/full.md b/2023/Learning Debiased Representations via Conditional Attribute Interpolation/full.md new file mode 100644 index 0000000000000000000000000000000000000000..6d09d58f7458216a028b5c4334692c970551a4b3 --- /dev/null +++ b/2023/Learning Debiased Representations via Conditional Attribute Interpolation/full.md @@ -0,0 +1,319 @@ +# Learning Debiased Representations via Conditional Attribute Interpolation + +Yi-Kai Zhang, Qi-Wei Wang, De-Chuan Zhan, Han-Jia Ye $^{\text{®}}$ +State Key Laboratory for Novel Software Technology, Nanjing University + +{zhangyk, wangqiwei, zhandc, yehj}@lamda.nju.edu.cn + +# Abstract + +An image is usually described by more than one attribute like "shape" and "color". When a dataset is biased, i.e., most samples have attributes spuriously correlated with the target label, a Deep Neural Network (DNN) is prone to make predictions by the "unintended" attribute, especially if it is easier to learn. To improve the generalization ability when training on such a biased dataset, we propose a $\chi^2$ -model to learn debiased representations. First, we design a $\chi$ -shape pattern to match the training dynamics of a DNN and find Intermediate Attribute Samples (IASs) — samples near the attribute decision boundaries, which indicate how the value of an attribute changes from one extreme to another. Then we rectify the representation with a $\chi$ -structured metric learning objective. Conditional interpolation among IASs eliminates the negative effect of peripheral attributes and facilitates retaining the intra-class compactness. Experiments show that $\chi^2$ -model learns debiased representation effectively and achieves remarkable improvements on various datasets. Code is available at: https://github.com/ZhangYikaii/ch-square + +# 1. Introduction + +Deep neural networks (DNNs) have emerged as an epoch-making technology in various machine learning tasks with impressive performance [5,26]. In some real applications, an object may possess multiple attributes, and some of them are only spuriously correlated to the target label. For example, in Figure 1, the intrinsic attribute of an image annotated by "lifeboats" is its shape. Although there are many lifeboats colored orange, a learner can not make predictions through the color, i.e., there is a misleading correlation from attribute as one containing "orange" color is the target "lifeboats". When the major training samples can be well discerned by such peripheral attribute, especially learning on it is easier than on the intrinsic one, a DNN is prone to bias towards that "unintended" bias attribute [6, 11, 21, 43, 47, 48, 51], like recognizing a "cyclist" wearing orange as a "lifeboat". Similar spurious attribute also exists in various applications + +![](images/1cf6d30b931cf83503022d4275a14b514b47312b5fd2ca6559f6ef395d1d2a9b.jpg) +(a) Orange lifeboat + +97.8% lifeboat + +0.5% beacon + +0.4% container ship + +![](images/15712e1742b0095e18d2b345765b98e6134c72465c35a19dc41c20c7d86240ea.jpg) +(b) Orange cyclists +Figure 1. Classification of a standard ResNet-50 of (a) an orange lifeboat in the training set (with both color and shape attributes), and (b) an orange cyclist for the test (aligned with color attribute but conflicting with the shape one). Most of the lifeboats in the training set are orange. The biased model is prone to predict via the "unintended" color attribute rather than the intrinsic shape. + +57.0% lifeboat + +13.8% bicycle-built-for-two + +9.0% toyshop + +such as recommendation system [8, 35, 53, 59] and neural language processing [13, 14, 33, 41, 56]. + +Given such a biased training dataset, how to get rid of the negative effect of the misleading correlations? One intuitive solution is to perform special operations on those samples highly correlated to the bias attributes, which requires additional supervision, such as the pre-defined bias type [1,4,11,12,22,30,34,46,50]. Since prior knowledge of the dataset bias requires expensive manual annotations and is naturally missing in some applications, learning a debiased model without additional supervision about bias is in demand. Nam et al. [36] identify samples with intrinsic attributes based on the observation that malignant bias attributes are often easier-to-learn than others. Then the valuable samples for a debiasing scheme could be dynamically reweighted or augmented [11,27,34]. However, the restricted number of such samples implies uncertain representations and limits its ability to assist in debiasing. + +To leverage more valuable-for-debiasing knowledge, we take a further step in analyzing the representation space of naively-training dynamics, especially focusing on the discrepancies in attributes with a different learning difficulty. As we will later illustrate in Figure 2, an attribute-based + +DNN pushes and fits on the easier bias attribute initially. The intrinsic attribute is then forced to shift in a "lazy" manner. The bias attribute that is pushed away first leaves a large margin boundary. Since the space of the other intrinsic attribute is filled with many different samples on bias attribute, it has a large intra-class variance, like a "hollow". The representation is biased toward one side of the "hollow", i.e., those samples aligned with the bias attribute. Without the true intra-class structure, the model becomes biased. + +From the above observation, it is crucial to fill intra-class "hollow" and remodel representation compactness. Notice that the samples shifting to the two sides of the "hollow" have different characteristics, as aligned with the bias attribute and conflicting with it, respectively. We can find samples with an intermediate state between the above two. We call this type of sample the Intermediate Attribute Samples (IASs) which are near the decision boundary. When we condition (fix) on the intrinsic attribute, IASs vary on the other bias attribute and are exactly located in the "hollow" with low-density structural knowledge. Further, we can mine samples, including IASs, based on the distinct training dynamics. + +To this end, we propose our two-stage $\chi^2$ -model. In the first stage, we train a vanilla model on the biased dataset and record the sample-wise training dynamics w.r.t. both the target and the most obvious non-target classes (as the bias ones) along the epochs. An IAS is often predicted as a nontarget class in the beginning and then switched to its target class gradually, making its dynamics plot a $\chi$ -shape. Following this observation, we design a $\chi$ -shape pattern to match the training samples. The matching score ranks the mined samples according to the bias level, i.e., how much they are biased towards the side of the bias attribute. Benefiting from the IASs, we conduct conditional attribute interpolation, i.e., fixing the value of the target attribute. We interpolate the class-specific prototypes around IASs with various bias ratios. These conditional interpolated prototypes precisely "average out" on the bias attribute. From that, we design a $\chi$ -structured metric learning objective. It pulls samples close to those same-class interpolated prototypes, then intra-class samples become compact, and the influence of the bias attribute is removed. Our $\chi^2$ -model learns debiased representation effectively and achieves remarkable improvements on various datasets. Our contributions are summarized as + +- We claim and verify that Intermediate Attribute Samples (IASs) distributed around attribute decision boundaries facilitate learning a debiased representation. +- Based on the diverse learning behavior of different attribute types, we mine samples with varying bias levels, especially IASs. From that, we interpolate bias attribute conditioned on the intrinsic one and compact intra-class samples to remove the negative effect of bias. +- Experiments on benchmarks and a newly constructed real-world dataset from NICO [17] validate the effectiveness + +of our $\chi^2$ -model in learning debiased representations. + +# 2. A Closer Look at Learning on Bias Attribute + +After the background of learning on a biased dataset in subsection, we analyze the training dynamics of the model. + +# 2.1. Problem Definition + +Given a training set $\mathcal{D}_{\mathrm{train}} = \{(\mathbf{x}_i,y_i)\}_{i = 1}^N$ , each sample $\mathbf{x}_i$ is associated with a class label $y\in \{1,2,\dots ,C\}$ . We aim to find a decision rule $h_\theta$ that maps a sample to its label. $h_\theta$ is optimized by fitting all the training samples, e.g., minimizing the cross entropy loss as follows: + +$$ +\mathcal {L} _ {\mathrm {C E}} = \mathbb {E} _ {\left(\mathbf {x} _ {i}, y _ {i}\right) \sim \mathcal {D} _ {\text {t r a i n}}} \left[ - \log \Pr \left(h _ {\boldsymbol {\theta}} \left(\mathbf {x} _ {i}\right) = y _ {i} \mid \mathbf {x} _ {i}\right) \right]. \tag {1} +$$ + +We denote $h_{\theta} = \arg \max_{c\in [C]}\mathbf{w}_c^\top f_\phi (\mathbf{x})$ , where $f_{\phi}\rightarrow$ $\mathbb{R}^d$ is the feature extraction network and $\{\mathbf{w}_c\}_{c\in [C]}$ is toplayer $C$ -class classifier. The $\pmb{\theta}$ represents the union of learnable parameters $\phi$ and $\mathbf{W}$ . We expect the learned $h_\theta$ to have the high discerning ability over the test set $\mathcal{D}_{\mathrm{test}}$ which has the same form as the training set $\mathcal{D}_{\mathrm{train}}$ + +In addition to its class label, a sample could be described based on various attributes. If an attribute is spuriously correlated with the target label, we name it non-target bias attribute $a_{b}$ . The attribute that intrinsically determines the class label is the target attribute $a_{y}$ . For example, when we draw different handwritten digits in the MNIST dataset with specific colors [22], the color attribute will not help in the model generalization since we need to discern digits by the shape, e.g., "1" is like the stick. However, if almost all training images labeled "1" are in the same "yellow" color, the decision rule image in "yellow" is digit "1" will perform well on a such biased training set. + +In the task of learning with a biased training set [22, 29, 36], the bias attribute $a_{b}$ on most of the same-class samples are consistent, and spuriously correlated with the target label (as example digit "1" in "yellow" above), so a model $h_{\theta}$ that relies on $a_{b}$ or the target attribute $a_{y}$ will both perform well on $\mathcal{D}_{\mathrm{train}}$ . In real-world applications, it is often easier to learn to rely on $a_{b}$ than on $a_{y}$ , such as "background" or "texture" is easier-to-learn than the object [42, 51]. Therefore a model is prone to recognize based on the $a_{b}$ . Such a simplicity bias [3, 37, 38, 42] dramatically hurts the generalization of an unbiased test set. Nam et al. [36] also observe that the loss dynamics indicate the easier $a_{b}$ is learned first, where the model is distracted and fails to learn $a_{y}$ . + +Based on the behaviors of the "ultimate" biased model, samples in $\mathcal{D}_{\mathrm{train}}$ are split into two sets. Those training samples that could be correctly predicted based on the bias attribute $a_{b}$ are named as Bias-Aligned (BA) samples (as example "yellow digit 1" above), while the remaining ones are Bias-Conflicting (BC) samples (as digit "1" of other colors). The number of BC samples is extremely small, and previous + +![](images/c40b7b9532fbf4bf8cf0735509a804cd0069a6e7934d4509db60c9feb56dfbc3.jpg) +Figure 2. An illustration of the training dynamics of a naively-trained model on a biased dataset. The different attribute classes are drawn with a specific color (top row) or shape (bottom row). The first three columns correspond to the sequential training progress of these two classifiers, and the final column shows the test scenario. The easier-to-learn color is fitted first, which leaves a large margin on decision boundary and correspondingly triggers the shape attribute intra-class "hollow". "UB" and "BB" are the abbreviations of "unbiased boundary" and "biased boundary". The biased model cannot generalize well as the shadow area in the last column frames the shape-misclassified samples. We use yellow stars to indicate the shifted class centers of the training samples and gray stars for those of the test samples. + +methods emphasize their role with various strategies [11, 27, 34, 36]. For additional related methods of learning a debiased model [2, 7, 9, 10, 18, 24, 25, 29, 31, 40, 49, 60] please see the supplementary material. They can be extrapolated and applied to other application scenarios [16, 45, 52, 54, 57, 58]. + +# 2.2. The Training Dynamics of Biased Dataset + +We analyze the training dynamics of a naively trained model in Eq. 1 on the Colored MNIST dataset. The non-target bias attribute is the color and the target attribute is the shape. For visualization shown in Figure 2, we set the output dimension of the penultimate layer as two. In addition to the learned classifier on shape attribute $a_{y}$ , simultaneously, we add another linear classifier on top of the embedding to show how the decision boundary of color attribute $a_{b}$ changes. More details are described in the supplementary material. Focusing on the precedence relationship for learning $a_{y}$ and $a_{b}$ , we have the following observations: + +- The easier-to-learn bias attribute color is fitted soon. The early training stage is shown in the first column. Both color and shape attribute classifiers discern by different colors and do correctly on almost all BA samples (red “0” and blue “2”, about $95\%$ of the training set). +- The target attribute shape is learned later in a "lazy" manner. To further fit all shape labels, the model focuses on the limited BC samples (blue "0" and red "2", corre + +spondingly about $5\%$ ) that cannot be perfectly classified by color. It pushes minor BC representations to the other (correct) side instead of adjusting the decision boundary. + +- The ahead-color and lagged-shape learning process leaves a large margin of color attribute boundary, which further triggers the shape attribute intra-class "hollow". Because the representation of different colors is continuously pushed away (classified) before that of the shape, the gaps between different color attribute clusters are significantly larger than that of the shape attribute. +- Since there is an intra-class "hollow" between BA and BC samples which is conditioned on a particular shape, the true class representation is deviated toward color. The fourth column shows that the training class centers (yellow stars) and the test ones (gray stars) are mismatched. The true class center is located in the low-density "hollow" between shape-conditioned BA and BC samples. + +Previous observations indicate that the before-and-latter learning process on attributes of different learning difficulties leaves the model to lose intra-class compactness, primarily when learning relying on the bias attribute is easier. To alleviate class center deviation towards the BA samples, only emphasizing the BC samples is insufficient due to their scarcity. In addition, we propose to utilize Intermediate Attribute Samples (IASs), i.e., the samples near the attribute decision boundary and remodel the shifted representation. + +![](images/c3f2a145d37ce5f6322b4c1b41a250943454e9a9793b821c066c3654aa01ffe8.jpg) +Figure 3. An illustration of the $\chi^2$ -model. In the first stage (top row, left to right), we match and mine all samples with a $\chi$ -shape pattern. As shown in the right part, the images are getting biased towards the side of peripheral bias attribute from top to bottom, i.e., from various colors or backgrounds to a single red or sunset. Different shapes ( $\bigcirc$ or $\Delta$ ) and colors (orange or green) drawn in the Representation Space indicate the target and bias attribute, respectively. In the second stage (bottom row, right to left), we construct prototypes by conditional interpolating around IASs with various ratios and design the $\chi$ -structured metric learning objective to pull the intra-class samples. + +Especially when conditioned on the target attribute, the IASs vary on bias attribute and fill in the low-density intra-class "hollow" between BA and BC samples. + +# 3. $\chi^2$ -Model + +To mitigate the representation deviation and compact the intra-class "hollow", we leverage IASs to encode how bias attribute changes from one extreme (major BA side) to another (BC side). Then, the variety of the bias attribute could be interpolated when conditioned on a particular target attribute. We propose our two-stage $\chi^2$ -model, whose notion is illustrated in Figure 3. First, the $\chi^2$ -model discovers IASs based on the training dynamics of the vanilla model in subsection 3.1. Next, we analyze where the top-ranked samples with a $\chi$ -shape pattern are as well as their effectiveness in debiasing in subsection 3.2. A conditional attribute interpolation step with IASs then fills in the low-density "hollow" to get a better estimation of class-specific prototype. By pulling samples to the corresponding prototype, the $\chi$ -structured metric learning makes intra-class samples compact in subsection 3.3. We further investigate the Colored MNIST dataset. Results on other datasets are consistent. + +# 3.1. Scoring Samples with a $\chi$ -shape Pattern + +From the observations in the previous section, we aim to collect IASs to reveal how BC samples shift and leave the intra-class "hollow" between them and BA ones. As discussed in subsection 2.2, the vanilla model fits BC samples later than BA ones, which motivates us to score the samples from their training dynamics. Once we have the score pattern + +to match and distinguish BA and BC samples, IASs, with intermediate scores can be extracted and available for the next debiasing stage. In the following, we denote the posterior of the Ground-Truth class (GT-class) $y_{i}$ for a sample $\mathbf{x}_i$ as + +$$ +\operatorname * {P r} \left(h _ {\boldsymbol {\theta}} (\mathbf {x} _ {i}) = y _ {i} \mid \mathbf {x} _ {i}\right) = \operatorname {s o f t m a x} \left(\mathbf {w} _ {c} ^ {\top} f _ {\boldsymbol {\phi}} (\mathbf {x})\right) _ {y _ {i}}, \quad (2) +$$ + +the larger the posterior, the more confident a model predicts $\mathbf{x}_i$ with $y_{i}$ . For notation simplicity, we abbreviate the posterior as $\operatorname*{Pr}(y_i\mid \mathbf{x}_i)$ . The target posterior of a BA sample reaches one or becomes much higher than other categories soon after training several epochs, while the posterior of a BC sample has a delayed increase. To capture the clues on the change of bias attribute, we also analyze the posterior of the most obvious non-GT attribute, which reveals crucial bias influences. Denote the model at the $t$ -th epoch plus the superscript $t$ , such as $h_\theta^t$ . We take the bias class for the sample $\mathbf{x}_i$ at epoch $t$ as $b_i^t = \arg \max_{c\in [C],c\neq y_i}\left(\mathbf{w}_c^\top f_\phi (\mathbf{x})\right)^t$ . Then, we define the non-GT bias class as the most frequent $b_i^t$ along all epochs, i.e., $b_{i} = \max_{-}\mathrm{freq}\{b_{i}^{t}\}_{t = 1}^{T}$ . A sample has a larger bias class posterior when it has low confidence in its target class and vice versa. + +Taking posteriors of both $y_{i}$ and $b_{i}$ into account, a BA sample has larger $\operatorname{Pr}(y_i \mid \mathbf{x}_i)$ and small $\operatorname{Pr}(b_i \mid \mathbf{x}_i)$ along all its training epochs. For a BC sample, $\operatorname{Pr}(y_i \mid \mathbf{x}_i)$ increases gradually and meanwhile $\operatorname{Pr}(b_i \mid \mathbf{x}_i)$ decreases. We verify the phenomenon on Colored MNIST dataset in Figure 4 (left). For BA samples (yellow "1"), the two curves demonstrate a "rectangle", while for BC samples (blue "1"), the two curves have an obvious intersection and reveal a "x" shape. The statistics for the change of posteriors are shown + +![](images/b4f6b6e93c679d14333aab2af654687a7a5f6f9ca9a94b2f72a09b3c125e1c04.jpg) +Figure 4. Left: The change of posterior over the GT-class (green curve) as well as the bias class (red curve) over four samples. The two curves over BC samples and IAS demonstrate a $\chi$ -shape, which is different from the curves over the BA sample. Right: The change of prediction frequencies of BC or BA samples along with the training epochs. The statistics are calculated over all BC or BA samples. A BA sample is easily predicted as the GT-class from the initial training stage, while a BC sample changes its prediction from the bias class to the GT-class gradually. + +![](images/7d3216a2a9d89f10e726b182f8b88e68dcd2fd4e3f5987f055344430fa848ccd.jpg) + +![](images/ecd76dd2fa41ac5c6bdd450b4646f7df87225034c68b3f1d38b7d0ccfd79bc3b.jpg) + +in Figure 4 (right). Therefore, how much the training dynamics match the " $\chi$ " shape reveals the probability of a sample that shifts from the major BA clusters to minor BC ones. We design a $\chi$ -shape for the dynamics of losses to capture such BC-specific properties. The change of sample-specific loss for ground-truth label and bias label over $T$ epochs could be summarized by $\mathcal{L}_{\mathrm{CE}}$ . Then, we use two exponential $\chi$ -shape functions $\chi_{\mathrm{pattern}}$ to capture the ideal loss shape of the BC sample, i.e., the severely shifted case. + +$$ +\mathcal {L} _ {\mathrm {C E}} \left(\mathbf {x} _ {i}\right) = \left( \begin{array}{c} \mathcal {L} _ {\mathrm {C E}} ^ {g t} \left(\mathbf {x} _ {i}\right) = \left\{- \log \operatorname * {P r} ^ {t} \left(y _ {i} \mid \mathbf {x} _ {i}\right) \right\} _ {t = 1} ^ {T} \\ \mathcal {L} _ {\mathrm {C E}} ^ {b} \left(\mathbf {x} _ {i}\right) = \left\{- \log \operatorname * {P r} ^ {t} \left(b _ {i} \mid \mathbf {x} _ {i}\right) \right\} _ {t = 1} ^ {T} \end{array} \right), +$$ + +$$ +\chi_ {\text {p a t t e r n}} = \left( \begin{array}{l} \mathrm {p} ^ {g t} = \left\{e ^ {- A _ {1} t} \right\} _ {t = 1} ^ {T} \\ \mathrm {p} ^ {b} = \left\{e ^ {A _ {2} t} \right\} _ {t = 1} ^ {T} \end{array} \right), \tag {3} +$$ + +where $A_{1}$ and $A_{2}$ are the matching factors. They could be determined based on the dynamics of prediction fluctuations. For more details please see the supplementary material. The $\chi_{\mathrm{pattern}}$ encodes the observations for the most deviated BC samples. To match the loss dynamics with the pattern, we use the inner product over the two curves: + +$$ +\begin{array}{l} \mathbf {s} \left(\mathbf {x} _ {i}\right) = \left\langle \mathcal {L} _ {\mathrm {C E}} \left(\mathbf {x} _ {i}\right), \chi_ {\text {s h a p e}} \right\rangle \tag {4} \\ = \left\langle \mathcal {L} _ {\mathrm {C E}} ^ {g t} \left(\mathbf {x} _ {i}\right), \mathrm {p} ^ {g t} \right\rangle + \left\langle \mathcal {L} _ {\mathrm {C E}} ^ {b} \left(\mathbf {x} _ {i}\right), \mathrm {p} ^ {b} \right\rangle \\ = \sum_ {t = 1} ^ {T} \left(- e ^ {- A _ {1} t} \cdot \log \Pr \left(h _ {\boldsymbol {\theta}} \left(\mathbf {x} _ {i}\right) = y _ {i} \mid \mathbf {x} _ {i}\right) \right. \\ - e ^ {A _ {2} t} \cdot \log \operatorname * {P r} \left(h _ {\boldsymbol {\theta}} \left(\mathbf {x} _ {i}\right) = b _ {i} \mid \mathbf {x} _ {i}\right). \\ \end{array} +$$ + +The inner product $\mathbf{s}(\mathbf{x}_i)$ takes the area under the curves (AUC) into account, which is more robust w.r.t. the volatile loss changes. When $\mathbf{s}(\mathbf{x}_i)$ score goes from low to high, the sample varies on the bias level, i.e., from BA samples to IASs, and then to BC samples. + +Table 1. The classification accuracy on the unbiased test sets of vanilla models. Various training sampling strategies are compared. "0-1" denotes only using BC samples. "Step-wise" denotes applying uniformly higher and lower weights on BC and BA samples. "χ-pattern" denotes sampling with scores calculated by our $\chi^2$ -model. The best results are in bold, while the second-best ones are with underlines. C-CIFAR-10 is a similarly biased dataset as C-MNIST. + +
Dataset Ratio (%)C-MNISTC-CIFAR-10
99.999.599.999.5
Vanilla28.5859.2926.9130.16
+ 0-154.7870.4118.7325.06
+ Step-wise41.6873.5232.1235.91
+χ-pattern52.6780.2935.4737.83
+ +# 3.2. Where IASs Are and Why IASs Can Help to Learn a Debiased Representation? + +Combining the analysis in subsection 2.2 and collecting ranked samples by $\mathbf{s}(\mathbf{x}_i)$ , we find there are two types of IASs according to the representation near the target attribute decision boundary (as "0" for complex shapes in Figure 3), or that of the bias attribute (as helicopter in intermediate transitional "sunset" background). (1) If an IAS has an intermediate target attribute value, it may be a difficult samples and contains rich information about the target class boundaries. (2) If an IAS is in an intermediate state on the bias attribute, it may help to fill in the intra-class vacant "hollow" when conditioning (fixing) on the target attribute. Both types of IASs are similar to BC samples but from two directions, i.e., compared to the BA samples, they contain richer semantics on target or bias attributes. In the representation space, they are scattered between BA and BC samples, compensating for the sparsity of BC samples and valuable for debiasing. We will show how $\chi$ -structured objective with IASs help to remodel the true class centers in the following subsection. + +We illustrate the importance of IASs with simple experi + +![](images/ff2f345aed3d2a455b6cb50414f851c650f07d21cd2f9fc086a6db5fb2ba4ef8.jpg) +Biased Model + +![](images/e3313ebc03b52da3fb69dc859af1c6c1a3d2ab9eadac3defe1509df2c025e7d1.jpg) +Figure 5. Heatmap of the mean distance from the sample to its conditional interpolated prototypes. We construct the prototype with mixing over the same-class subset but with different ratios of BC samples. Then the mean distances between the sample and those prototypes are measured. For a biased model (left two), when the BC ratio $\gamma$ of interpolated prototype $\mathbf{p}_{\gamma}$ changes from low to high (horizontal direction), the distance of a sample to different $\mathbf{p}_{\gamma}$ varies hugely. The BA samples are closer to the low ratio ones, while the BC samples behave the opposite. An intra-class "hollow" exists. For an unbiased model (right two), the distances from any sample to $\mathbf{p}_{\gamma}$ with different ratios are almost the same. + +![](images/2944384d775bc741062c6bf9774ddc647457f211d24c7c60b20ee9caa86d902b.jpg) +Unbiased Model + +![](images/98aeac472b9b9c12ed52083ea9c9628980d8ac06e55f26c040cd6f2b145e423a.jpg) + +![](images/65803eb4e27b2c9e6d9ebe845f64c9c2ae67b3f659076b95883047b1ad189a46.jpg) + +ments on biased Colored-MNIST and Corrupted CIFAR-10 datasets. The datasets are described in subsection 4.1. We investigate whether various reweighting strategies on the vanilla model improve the generalization ability over an unbiased test set. We use "0-1" to denote the strategy that utilizes only the BC samples. "step-wise" means we apply uniformly higher (ratio of BA samples) and lower weights (one minus above ratio) to BC and BA samples. Our "x-pattern" smoothly reweights all samples with the matched scores, where BC samples as well as IASs have relatively larger weights than the remaining BA ones. The results in Table 1 show that simple reweighting strategies can improve the performance of a vanilla classifier, supporting the significance of emphasizing BC-like samples. Our "x-pattern" gets the best results in most scenarios, indicating that higher resampling weights on the IASs and BC samples assist the vanilla model to better frame the representation space. + +# 3.3. Learning from a $\chi$ -Structured Objective + +Although the BA samples are severely biased towards the bias attribute, the BC samples, integrating the rich bias attribute semantics, naturally make the representation independent of the biased influence [19]. An intuitive approach for debiasing is to average over BC samples and classified by the BC class centers. However, the sparsity of BC samples induces an erratic estimation which is far from the true class center, as shown in Figure 2. + +Benefiting from the analysis that BC-like IASs better estimate the intra-class structure, we target conditional interpolating around it, i.e., mixing the same-class samples with different BC-like scores to remodel the intermediate samples between BA and BC samples. From that, we can construct many prototypes closer to the real class center and pull samples to these prototypes to compact the intra-class + +space. Combined with the soft ranking score from the $\chi$ -pattern in the previous stage, we build two pools (subsets) of the samples denoted as $\mathcal{D}_{\parallel}$ and $\mathcal{D}_{\perp}$ . The $\mathcal{D}_{\perp}$ pool collects the top-rank samplers and most of them are BC samples and IASs. The $\mathcal{D}_{\parallel}$ pool is sampled from the remaining (BA) part according to the score. With the help of $\mathcal{D}_{\parallel}$ and $\mathcal{D}_{\perp}$ , we construct multiple bias bags (subset) $\mathcal{B}_{\gamma}$ with bootstrapping where the ratio of BC samples is $\gamma$ . + +$$ +\mathcal {B} _ {\gamma} = \left\{\left(\mathbf {x} _ {i}, y _ {i}\right) \mid \operatorname {n u m} \left(\mathcal {D} _ {\perp}\right): \operatorname {n u m} \left(\mathcal {D} _ {\|}\right) = \gamma \right\}, \tag {5} +$$ + +where $\mathrm{num}(\mathcal{D})$ equals the number of samples in $\mathcal{D}$ . When $\gamma$ is low to high, the $\mathcal{B}_{\gamma}$ contains samples ranging from the extremes of BA samples to the IASs, and then to the BC ones. Based on $\mathcal{B}_{\gamma}$ , we compute the prototype, i.e., averaged on $\mathcal{B}_{\gamma}$ to interpolate bias attribute conditioned on the particular target attribute. For example, the prototype conditioned on class $c$ is formalized as $\mathbf{p}_{\gamma,c}$ : + +$$ +\mathbf {p} _ {\gamma , c} = \frac {1}{K} \sum_ {\left(\mathbf {x} _ {i}, y _ {i}\right) \in \mathcal {B} _ {\gamma}} f _ {\phi} \left(\mathbf {x} _ {i}\right) \cdot \mathbb {I} [ y _ {i} = c ]. \tag {6} +$$ + +To further demonstrate the significance of intra-class compactness, we design the experiments to study the difference between a biased vanilla model and the unbiased oracle model (well-trained on an unbiased training set). We measure the mean distance between samples and their multiple conditional interpolated prototypes with changing ratio $\gamma$ . If the prototypes are shifted with changing $\gamma$ , that indicates a large intra-class deviation exists. As shown in Figure 5, for a biased model, when $\gamma$ decreases, $\mathbf{p}_{\gamma}$ is interpolated closer to the BA samples. Opposite phenomena are observed in the BC samples. As for the unbiased oracle model, no matter how the BC ratio $\gamma$ changes, such mean distance is almost unchanged and shows a lower variance. This coincides with the observation in Figure 2. + +Table 2. The classification performance on unbiased test set (in %; higher is better) evaluated on unbiased test sets of Colored MNIST and Corrupted CIFAR-10 with training on varying BA samples ratios. We denote bias pre-provided type by $\bigcirc$ (without any information), $\bullet$ (bias prior knowledge), and $\bullet$ (explicit bias supervision). The best result is in bold, while the second-best is with underlines. + +
Dataset Ratio (%)Colored MNISTCorrupted CIFAR-10
99.999.599.095.099.999.599.095.0
Vanilla + p [44]○28.5859.2974.4287.1326.9130.1637.7141.60
○31.0164.8276.8487.8626.5529.4838.0742.30
RUBi [7]●27.8270.8086.5896.7733.7034.7034.5947.23
ReBias [4]●27.7172.8985.9596.8733.6534.4035.8247.45
End [46]●28.1981.8188.1096.9931.3033.8334.0238.77
DI [50]●33.1880.6386.2898.3632.0933.3737.6551.27
LfF [36]○30.2468.9076.6996.8129.8933.6835.2845.38
LFA [27]○22.3164.1381.8395.4532.4935.7439.6347.25
x-pattern + p●60.3364.1593.5398.3035.3339.3141.3253.37
x²-model (Ours)○66.9188.7392.1597.8735.6737.6140.7449.04
+ +Motivated by mimicking the oracle, we adopt the conditional interpolated prototypes and construct a customized $\chi$ -structured metric learning task. Assuming $\gamma$ is large, we use $\mathbf{p}_{\gamma}$ and $\mathbf{p}_{1 - \gamma}$ to denote prototypes in bias bags $\mathcal{B}$ with high and low BC ratios. The model should prioritize pulling the majority of low BC ratio bias bag $\mathcal{B}_{1 - \gamma}$ closer to $\mathbf{p}_{\gamma}$ , which interpolated into the high BC space. Similarly, the high BC bias bag $\mathcal{B}_{\gamma}$ should be pulled to low BC interpolated $\mathbf{p}_{1 - \gamma}$ . We optimize the cross-entropy loss $\mathcal{L}_{\mathrm{CE}}$ to enable the pulling operation. Concretely, the posterior via the distance $\left(\cdot ,\cdot\right)$ in the representation space is formalized as: + +$$ +\operatorname * {P r} \left(y _ {i} \mid \mathbf {x} _ {i}\right) = \frac {\exp \left(- \mathrm {d} \left(f _ {\phi} \left(\mathbf {x} _ {i}\right) , \mathbf {p} _ {\gamma , y _ {i}}\right) / \tau\right)}{\sum_ {c \in [ C ]} \exp \left(- \mathrm {d} \left(f _ {\phi} \left(\mathbf {x} _ {i}\right) , \mathbf {p} _ {\gamma , c}\right) / \tau\right)}, (7) +$$ + +where $\tau$ is a scaled temperature. One of the branches of the $\chi$ -structure classification task is optimizing the $\mathcal{L}_{\mathrm{CE}}$ between samples in the $\mathcal{B}_{1 - \gamma}$ and $\mathbf{p}_{\gamma}$ . Similarly, the other branch is optimizing between $\mathcal{B}_{\gamma}$ and $\mathbf{p}_{1 - \gamma}$ at the same time. As shown in Figure 3, such a high-and-low correspondence captures and compacts the intra-class "hollow". In summary, The bias bags of high BC ratios $\mathcal{B}_{\gamma}$ with corresponding low BC interpolated prototypes conditioning on the target attribute $\mathbf{p}_{1 - \gamma}$ , and $\mathcal{B}_{1 - \gamma}$ with $\mathbf{p}_{\gamma}$ form the $\chi$ -structure crossover objective. + +# 4. Experiments + +We conduct experiments to verify whether $\chi^2$ -model has effective debiasing capability. We begin by introducing bias details in each dataset (as in subsection 4.1). We present the comparison approaches and training details. In subsection 4.2, the experiments show that $\chi^2$ -model achieves superior performance in each stage. Furthermore, we exemplify the inherent quality of the prototype-based classification for debiasing tasks and offer ablation studies in subsection 4.3. + +Table 3. The classification performance on the unbiased CelebA and NICO test set. The data source $BA$ denotes the measurement on BA samples and $BC$ is corresponding the BC samples. + +
Data SourceBiased CelebANICO
BABCAllAll
LfF [36]73.6970.4172.0534.44
DFA [27]94.0158.9876.5033.10
\( \chi^2 \)-model97.6660.7979.2336.99
+ +# 4.1. Experimental Setups + +Datasets. To cover more general and challenging cases of bias impact, we validate $\chi^2$ -model in a variety of datasets, including two synthetic bias datasets (Colored MNIST [4], Corrupted CIFAR-10 [36]) and two real-world datasets (Biased CelebA [32] and Biased NICO). + +The BA samples ratio $\rho$ in the training set is usually high (over $95\%$ ), so the bias attribute is highly correlated with the target label. For instance, in the Colored MNIST dataset, each digit is linked to a pre-defined bias color. Similarly, there is an object target with corruption bias in Corrupted CIFAR-10 and a gender target with hair color bias in Biased CelebA. Following the previous works [19], we use the BA ratio $\rho \in \{95.0\%, 99.0\%, 99.5\%, 99.9\% \}$ for Colored MNIST and Corrupted CIFAR-10, respectively, and approximately $96\%$ for Biased CelebA. The Biased NICO dataset is dedicatedly sampled in NICO [17], initially designed for OOD (Out-of-Distribution) image classification. NICO is enriched with variations in the object and context dimensions. We select the bias attribute with the highest co-occurrence frequency to the target one, e.g., helicopter to sunset in training set correlates strongly (see BA samples in Figure 3). The correlation ratio is roughly controlled to $86\%$ . For more details please see the supplementary material. + +Table 4. The performance of BC samples mining on Colored MNIST with $99.5\%$ BA ratio. Acc. denotes mean accuracy of ranking with top-300. $98\% - \sigma$ denotes the number of samples required to contain $98\%$ of BC samples. $AP$ is average precision. $\uparrow$ means higher is better, while $\downarrow$ is the opposite. + +
MeasureAcc. ↑98%-σ ↓AP ↑
Entropy [20]78.3363283.52
Confidence [28]80.3359085.61
Loss [36]94.3941898.22
Pleiss et al. [39]82.6768689.24
Zhao et al. [55]90.3345196.04
χ-pattern (Ours)95.8437298.44
+ +Baselines. We carefully select the classic and the latest trending approaches as baselines: (1) Vanilla model training with cross entropy as described in subsection 2.1. (2) Bias-tailored approaches with pre-provided bias type: RUBi, Rebias. (3) Explicit approaches under the guidance of total bias supervision: EnD and DI. (4) Implicit methods through general bias properties: LfF and DFA. + +Implementation details. Following the existing popular benchmarks [19, 23], we use the four-layer CNN with kernel size $7 \times 7$ for the Colored MNIST dataset and ResNet-18 [15] for Corrupted CIFAR-10, Biased CelebA, and Biased NICO datasets. For a fair comparison, we re-implemented the baselines with the same configuration. We mainly focus on unbiased test accuracy for all categories. All models are trained on an NVIDIA RTX 3090 GPU. + +Baselines for the first stage. To better demonstrate the effectiveness of $\chi$ -pattern, we consider related sample-specific scoring methods [39, 55] and report average precision, top-threshold accuracy, and the minimum samples (threshold) required for $98\%$ accuracy. For more results, such as PR curves, please see the supplementary material. + +# 4.2. Quantitative Evaluation + +Performance of $\chi$ -shape pattern. As shown in Table 4, our $\chi$ -pattern matching achieves state-of-the-art performance on various evaluation metrics. Thus, the $\chi$ -structure metric learning objective can leverage more IASs cues to interpolate bias attribute and further learn the debiased representation. + +$\chi^2$ -model in different types of bias constructions. (1) Synthetic bias on Colored MNIST and Corrupted CIFAR-10: From Table 2 we find that under extreme bias influence, as $\rho$ is $99.9\%$ , the performance of the vanilla model and other baselines decreases catastrophically. In contrast, Our $\chi^2$ -model maintains the robust and efficient debiasing capability on the unbiased dataset. Further, more results in Figure 2 present the remarkable performance of our $\chi^2$ -model compared to other methods. (2) Real-world bias on Biased CelebA and Biased NICO: Table 3 shows that compared to the recent methods which do not pre-provide any bias information as the same as ours, our method also achieves + +![](images/2bfb29a0f9fa4db8be93aff5b33213ece4e09f52c713c79a66f091a6ec9e7838.jpg) +(a) t-SNE on $a_{t}$ + +![](images/5f900d9cda0fd89e3aa3704b65b98bf5d7e8669686bb9587f153296bb6d0b0f1.jpg) +(b) t-SNE on $a_{b}$ + +![](images/7517b9cec2c4f684b35dac79150f64c8f5f463f90a50865c6dd0c64fb079cbb6.jpg) +(c) ablation study of $A_{1}, A_{2}$ +Figure 6. (a) and (b) show the t-SNE visualization of our unbiased representation in terms of digit (the target attribute) and color (the bias one) in Colored MNIST, respectively. (c) displays the top-300 mean accuracy of mining BC samples on Colored MNIST with $99.5\%$ BA ratio when $A_{1}$ and $A_{2}$ are changed. + +outstanding performance. The above experiments indicate that conditional interpolation among IASs feedback the shift of the intrinsic knowledge and facilitate learning debiased representations even in extremely biased conditions. + +# 4.3. Further analysis + +The inherent debiasing capability of prototype-based classification. We directly construct the prototype by averaging the trained representations of the vanilla model (as in Table 2 line two named “+ p”). The results show that on some datasets like Colored MNIST, the prototype-based classifier without training achieves performance improvement. + +Visualize the test set representation on 2D embedding space via t-SNE. Figure 6 shows the 2D projection of the feature extracted by $\chi^2$ -model on Colored MNIST. We color the target and bias attributes separately. The representations follow the target attribute to cluster into classes which indicates that our model learns the debiased representations. + +Ablation studies. We further perform the ablation analysis of the matching factors $A_{1}, A_{2}$ in Eq. 3, which directly determine the $\chi$ -shape curves. The results show the first stage of $\chi^2$ -model is robust to changes in hyperparameters. For more related experiments like on different BC identification thresholds, please see the supplementary material. + +# 5. Conclusion + +Although intra-class biased samples with a "hollow" structure impede learning debiased representations, we propose the $\chi^2$ -model to leverage Intermediate Attribute Samples (IASs) to remodel the representation compactness. $\chi^2$ -model works in a two-stage manner, matching and ranking possible IASs based on their $\chi$ -shape training dynamics followed by a $\chi$ -branch metric-based debiasing objective with conditional attribute interpolation. + +Acknowledgments. This research was supported by NSFC (61773198,61921006,62006112), Collaborative Innovation Center of Novel Software Technology and Industrialization, NSF of Jiangsu Province (BK20200313). + +# References + +[1] Vedika Agarwal, Rakshith Shetty, and Mario Fritz. Towards causal VQA: revealing and reducing spurious correlations by invariant and covariant semantic editing. In CVPR, pages 9687-9695, 2020. 1 +[2] Martin Arjovsky, Léon Bottou, Ishaan Gulrajani, and David Lopez-Paz. 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When a dataset is biased, i.e., most samples have attributes spuriously correlated with the target label, a Deep Neural Network (DNN) is prone to make predictions by the \"unintended\" attribute, especially if it is easier to learn. To improve the generalization ability when training on such a biased dataset, we propose a " + }, + { + "bbox": [ + 46, + 238, + 290, + 478 + ], + "type": "inline_equation", + "content": "\\chi^2" + }, + { + "bbox": [ + 46, + 238, + 290, + 478 + ], + "type": "text", + "content": "-model to learn debiased representations. First, we design a " + }, + { + "bbox": [ + 46, + 238, + 290, + 478 + ], + "type": "inline_equation", + "content": "\\chi" + }, + { + "bbox": [ + 46, + 238, + 290, + 478 + ], + "type": "text", + "content": "-shape pattern to match the training dynamics of a DNN and find Intermediate Attribute Samples (IASs) — samples near the attribute decision boundaries, which indicate how the value of an attribute changes from one extreme to another. 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Classification of a standard ResNet-50 of (a) an orange lifeboat in the training set (with both color and shape attributes), and (b) an orange cyclist for the test (aligned with color attribute but conflicting with the shape one). Most of the lifeboats in the training set are orange. The biased model is prone to predict via the \"unintended\" color attribute rather than the intrinsic shape." + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "bbox": [ + 433, + 304, + 488, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 433, + 304, + 488, + 312 + ], + "spans": [ + { + "bbox": [ + 433, + 304, + 488, + 312 + ], + "type": "text", + "content": "57.0% lifeboat" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 435, + 314, + 528, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 435, + 314, + 528, + 323 + ], + "spans": [ + { + "bbox": [ + 435, + 314, + 528, + 323 + ], + "type": "text", + "content": "13.8% bicycle-built-for-two" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 437, + 324, + 489, + 334 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 437, + 324, + 489, + 334 + ], + "spans": [ + { + "bbox": [ + 437, + 324, + 489, + 334 + ], + "type": "text", + "content": "9.0% toyshop" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 432, + 545, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 432, + 545, + 456 + ], + "spans": [ + { + "bbox": [ + 304, + 432, + 545, + 456 + ], + "type": "text", + "content": "such as recommendation system [8, 35, 53, 59] and neural language processing [13, 14, 33, 41, 56]." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 460, + 547, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 460, + 547, + 651 + ], + "spans": [ + { + "bbox": [ + 304, + 460, + 547, + 651 + ], + "type": "text", + "content": "Given such a biased training dataset, how to get rid of the negative effect of the misleading correlations? One intuitive solution is to perform special operations on those samples highly correlated to the bias attributes, which requires additional supervision, such as the pre-defined bias type [1,4,11,12,22,30,34,46,50]. Since prior knowledge of the dataset bias requires expensive manual annotations and is naturally missing in some applications, learning a debiased model without additional supervision about bias is in demand. Nam et al. [36] identify samples with intrinsic attributes based on the observation that malignant bias attributes are often easier-to-learn than others. Then the valuable samples for a debiasing scheme could be dynamically reweighted or augmented [11,27,34]. However, the restricted number of such samples implies uncertain representations and limits its ability to assist in debiasing." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 653, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 547, + 713 + ], + "type": "text", + "content": "To leverage more valuable-for-debiasing knowledge, we take a further step in analyzing the representation space of naively-training dynamics, especially focusing on the discrepancies in attributes with a different learning difficulty. As we will later illustrate in Figure 2, an attribute-based" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7599" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 179 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 179 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 179 + ], + "type": "text", + "content": "DNN pushes and fits on the easier bias attribute initially. The intrinsic attribute is then forced to shift in a \"lazy\" manner. The bias attribute that is pushed away first leaves a large margin boundary. Since the space of the other intrinsic attribute is filled with many different samples on bias attribute, it has a large intra-class variance, like a \"hollow\". The representation is biased toward one side of the \"hollow\", i.e., those samples aligned with the bias attribute. Without the true intra-class structure, the model becomes biased." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 182, + 289, + 327 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 182, + 289, + 327 + ], + "spans": [ + { + "bbox": [ + 45, + 182, + 289, + 327 + ], + "type": "text", + "content": "From the above observation, it is crucial to fill intra-class \"hollow\" and remodel representation compactness. Notice that the samples shifting to the two sides of the \"hollow\" have different characteristics, as aligned with the bias attribute and conflicting with it, respectively. We can find samples with an intermediate state between the above two. We call this type of sample the Intermediate Attribute Samples (IASs) which are near the decision boundary. When we condition (fix) on the intrinsic attribute, IASs vary on the other bias attribute and are exactly located in the \"hollow\" with low-density structural knowledge. Further, we can mine samples, including IASs, based on the distinct training dynamics." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 328, + 289, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 328, + 289, + 591 + ], + "spans": [ + { + "bbox": [ + 46, + 328, + 289, + 591 + ], + "type": "text", + "content": "To this end, we propose our two-stage " + }, + { + "bbox": [ + 46, + 328, + 289, + 591 + ], + "type": "inline_equation", + "content": "\\chi^2" + }, + { + "bbox": [ + 46, + 328, + 289, + 591 + ], + "type": "text", + "content": "-model. In the first stage, we train a vanilla model on the biased dataset and record the sample-wise training dynamics w.r.t. both the target and the most obvious non-target classes (as the bias ones) along the epochs. An IAS is often predicted as a nontarget class in the beginning and then switched to its target class gradually, making its dynamics plot a " + }, + { + "bbox": [ + 46, + 328, + 289, + 591 + ], + "type": "inline_equation", + "content": "\\chi" + }, + { + "bbox": [ + 46, + 328, + 289, + 591 + ], + "type": "text", + "content": "-shape. Following this observation, we design a " + }, + { + "bbox": [ + 46, + 328, + 289, + 591 + ], + "type": "inline_equation", + "content": "\\chi" + }, + { + "bbox": [ + 46, + 328, + 289, + 591 + ], + "type": "text", + "content": "-shape pattern to match the training samples. The matching score ranks the mined samples according to the bias level, i.e., how much they are biased towards the side of the bias attribute. Benefiting from the IASs, we conduct conditional attribute interpolation, i.e., fixing the value of the target attribute. We interpolate the class-specific prototypes around IASs with various bias ratios. These conditional interpolated prototypes precisely \"average out\" on the bias attribute. From that, we design a " + }, + { + "bbox": [ + 46, + 328, + 289, + 591 + ], + "type": "inline_equation", + "content": "\\chi" + }, + { + "bbox": [ + 46, + 328, + 289, + 591 + ], + "type": "text", + "content": "-structured metric learning objective. It pulls samples close to those same-class interpolated prototypes, then intra-class samples become compact, and the influence of the bias attribute is removed. Our " + }, + { + "bbox": [ + 46, + 328, + 289, + 591 + ], + "type": "inline_equation", + "content": "\\chi^2" + }, + { + "bbox": [ + 46, + 328, + 289, + 591 + ], + "type": "text", + "content": "-model learns debiased representation effectively and achieves remarkable improvements on various datasets. Our contributions are summarized as" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 594, + 288, + 714 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 47, + 594, + 287, + 630 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 594, + 287, + 630 + ], + "spans": [ + { + "bbox": [ + 47, + 594, + 287, + 630 + ], + "type": "text", + "content": "- We claim and verify that Intermediate Attribute Samples (IASs) distributed around attribute decision boundaries facilitate learning a debiased representation." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 630, + 288, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 630, + 288, + 689 + ], + "spans": [ + { + "bbox": [ + 47, + 630, + 288, + 689 + ], + "type": "text", + "content": "- Based on the diverse learning behavior of different attribute types, we mine samples with varying bias levels, especially IASs. From that, we interpolate bias attribute conditioned on the intrinsic one and compact intra-class samples to remove the negative effect of bias." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "type": "text", + "content": "- Experiments on benchmarks and a newly constructed real-world dataset from NICO [17] validate the effectiveness" + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 313, + 72, + 531, + 85 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 531, + 85 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 531, + 85 + ], + "type": "text", + "content": "of our " + }, + { + "bbox": [ + 313, + 72, + 531, + 85 + ], + "type": "inline_equation", + "content": "\\chi^2" + }, + { + "bbox": [ + 313, + 72, + 531, + 85 + ], + "type": "text", + "content": "-model in learning debiased representations." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 95, + 545, + 109 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 95, + 545, + 109 + ], + "spans": [ + { + "bbox": [ + 306, + 95, + 545, + 109 + ], + "type": "text", + "content": "2. A Closer Look at Learning on Bias Attribute" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 115, + 545, + 140 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 115, + 545, + 140 + ], + "spans": [ + { + "bbox": [ + 306, + 115, + 545, + 140 + ], + "type": "text", + "content": "After the background of learning on a biased dataset in subsection, we analyze the training dynamics of the model." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 146, + 418, + 158 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 146, + 418, + 158 + ], + "spans": [ + { + "bbox": [ + 306, + 146, + 418, + 158 + ], + "type": "text", + "content": "2.1. Problem Definition" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 163, + 547, + 225 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 163, + 547, + 225 + ], + "spans": [ + { + "bbox": [ + 305, + 163, + 547, + 225 + ], + "type": "text", + "content": "Given a training set " + }, + { + "bbox": [ + 305, + 163, + 547, + 225 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{train}} = \\{(\\mathbf{x}_i,y_i)\\}_{i = 1}^N" + }, + { + "bbox": [ + 305, + 163, + 547, + 225 + ], + "type": "text", + "content": " , each sample " + }, + { + "bbox": [ + 305, + 163, + 547, + 225 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i" + }, + { + "bbox": [ + 305, + 163, + 547, + 225 + ], + "type": "text", + "content": " is associated with a class label " + }, + { + "bbox": [ + 305, + 163, + 547, + 225 + ], + "type": "inline_equation", + "content": "y\\in \\{1,2,\\dots ,C\\}" + }, + { + "bbox": [ + 305, + 163, + 547, + 225 + ], + "type": "text", + "content": " . We aim to find a decision rule " + }, + { + "bbox": [ + 305, + 163, + 547, + 225 + ], + "type": "inline_equation", + "content": "h_\\theta" + }, + { + "bbox": [ + 305, + 163, + 547, + 225 + ], + "type": "text", + "content": " that maps a sample to its label. " + }, + { + "bbox": [ + 305, + 163, + 547, + 225 + ], + "type": "inline_equation", + "content": "h_\\theta" + }, + { + "bbox": [ + 305, + 163, + 547, + 225 + ], + "type": "text", + "content": " is optimized by fitting all the training samples, e.g., minimizing the cross entropy loss as follows:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 315, + 233, + 547, + 248 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 233, + 547, + 248 + ], + "spans": [ + { + "bbox": [ + 315, + 233, + 547, + 248 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {C E}} = \\mathbb {E} _ {\\left(\\mathbf {x} _ {i}, y _ {i}\\right) \\sim \\mathcal {D} _ {\\text {t r a i n}}} \\left[ - \\log \\Pr \\left(h _ {\\boldsymbol {\\theta}} \\left(\\mathbf {x} _ {i}\\right) = y _ {i} \\mid \\mathbf {x} _ {i}\\right) \\right]. \\tag {1}", + "image_path": "ce786e1e8dd268da58cf365a838cdad28db18697969dbbda1258fdd94806c0f3.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 257, + 547, + 331 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 257, + 547, + 331 + ], + "spans": [ + { + "bbox": [ + 305, + 257, + 547, + 331 + ], + "type": "text", + "content": "We denote " + }, + { + "bbox": [ + 305, + 257, + 547, + 331 + ], + "type": "inline_equation", + "content": "h_{\\theta} = \\arg \\max_{c\\in [C]}\\mathbf{w}_c^\\top f_\\phi (\\mathbf{x})" + }, + { + "bbox": [ + 305, + 257, + 547, + 331 + ], + "type": "text", + "content": " , where " + }, + { + "bbox": [ + 305, + 257, + 547, + 331 + ], + "type": "inline_equation", + "content": "f_{\\phi}\\rightarrow" + }, + { + "bbox": [ + 305, + 257, + 547, + 331 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^d" + }, + { + "bbox": [ + 305, + 257, + 547, + 331 + ], + "type": "text", + "content": " is the feature extraction network and " + }, + { + "bbox": [ + 305, + 257, + 547, + 331 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{w}_c\\}_{c\\in [C]}" + }, + { + "bbox": [ + 305, + 257, + 547, + 331 + ], + "type": "text", + "content": " is toplayer " + }, + { + "bbox": [ + 305, + 257, + 547, + 331 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 305, + 257, + 547, + 331 + ], + "type": "text", + "content": " -class classifier. The " + }, + { + "bbox": [ + 305, + 257, + 547, + 331 + ], + "type": "inline_equation", + "content": "\\pmb{\\theta}" + }, + { + "bbox": [ + 305, + 257, + 547, + 331 + ], + "type": "text", + "content": " represents the union of learnable parameters " + }, + { + "bbox": [ + 305, + 257, + 547, + 331 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 305, + 257, + 547, + 331 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 257, + 547, + 331 + ], + "type": "inline_equation", + "content": "\\mathbf{W}" + }, + { + "bbox": [ + 305, + 257, + 547, + 331 + ], + "type": "text", + "content": " . We expect the learned " + }, + { + "bbox": [ + 305, + 257, + 547, + 331 + ], + "type": "inline_equation", + "content": "h_\\theta" + }, + { + "bbox": [ + 305, + 257, + 547, + 331 + ], + "type": "text", + "content": " to have the high discerning ability over the test set " + }, + { + "bbox": [ + 305, + 257, + 547, + 331 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{test}}" + }, + { + "bbox": [ + 305, + 257, + 547, + 331 + ], + "type": "text", + "content": " which has the same form as the training set " + }, + { + "bbox": [ + 305, + 257, + 547, + 331 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{train}}" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 331, + 547, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 331, + 547, + 474 + ], + "spans": [ + { + "bbox": [ + 304, + 331, + 547, + 474 + ], + "type": "text", + "content": "In addition to its class label, a sample could be described based on various attributes. If an attribute is spuriously correlated with the target label, we name it non-target bias attribute " + }, + { + "bbox": [ + 304, + 331, + 547, + 474 + ], + "type": "inline_equation", + "content": "a_{b}" + }, + { + "bbox": [ + 304, + 331, + 547, + 474 + ], + "type": "text", + "content": ". The attribute that intrinsically determines the class label is the target attribute " + }, + { + "bbox": [ + 304, + 331, + 547, + 474 + ], + "type": "inline_equation", + "content": "a_{y}" + }, + { + "bbox": [ + 304, + 331, + 547, + 474 + ], + "type": "text", + "content": ". For example, when we draw different handwritten digits in the MNIST dataset with specific colors [22], the color attribute will not help in the model generalization since we need to discern digits by the shape, e.g., \"1\" is like the stick. However, if almost all training images labeled \"1\" are in the same \"yellow\" color, the decision rule image in \"yellow\" is digit \"1\" will perform well on a such biased training set." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 474, + 547, + 630 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 547, + 630 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 547, + 630 + ], + "type": "text", + "content": "In the task of learning with a biased training set [22, 29, 36], the bias attribute " + }, + { + "bbox": [ + 304, + 474, + 547, + 630 + ], + "type": "inline_equation", + "content": "a_{b}" + }, + { + "bbox": [ + 304, + 474, + 547, + 630 + ], + "type": "text", + "content": " on most of the same-class samples are consistent, and spuriously correlated with the target label (as example digit \"1\" in \"yellow\" above), so a model " + }, + { + "bbox": [ + 304, + 474, + 547, + 630 + ], + "type": "inline_equation", + "content": "h_{\\theta}" + }, + { + "bbox": [ + 304, + 474, + 547, + 630 + ], + "type": "text", + "content": " that relies on " + }, + { + "bbox": [ + 304, + 474, + 547, + 630 + ], + "type": "inline_equation", + "content": "a_{b}" + }, + { + "bbox": [ + 304, + 474, + 547, + 630 + ], + "type": "text", + "content": " or the target attribute " + }, + { + "bbox": [ + 304, + 474, + 547, + 630 + ], + "type": "inline_equation", + "content": "a_{y}" + }, + { + "bbox": [ + 304, + 474, + 547, + 630 + ], + "type": "text", + "content": " will both perform well on " + }, + { + "bbox": [ + 304, + 474, + 547, + 630 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{train}}" + }, + { + "bbox": [ + 304, + 474, + 547, + 630 + ], + "type": "text", + "content": ". In real-world applications, it is often easier to learn to rely on " + }, + { + "bbox": [ + 304, + 474, + 547, + 630 + ], + "type": "inline_equation", + "content": "a_{b}" + }, + { + "bbox": [ + 304, + 474, + 547, + 630 + ], + "type": "text", + "content": " than on " + }, + { + "bbox": [ + 304, + 474, + 547, + 630 + ], + "type": "inline_equation", + "content": "a_{y}" + }, + { + "bbox": [ + 304, + 474, + 547, + 630 + ], + "type": "text", + "content": ", such as \"background\" or \"texture\" is easier-to-learn than the object [42, 51]. Therefore a model is prone to recognize based on the " + }, + { + "bbox": [ + 304, + 474, + 547, + 630 + ], + "type": "inline_equation", + "content": "a_{b}" + }, + { + "bbox": [ + 304, + 474, + 547, + 630 + ], + "type": "text", + "content": ". Such a simplicity bias [3, 37, 38, 42] dramatically hurts the generalization of an unbiased test set. Nam et al. [36] also observe that the loss dynamics indicate the easier " + }, + { + "bbox": [ + 304, + 474, + 547, + 630 + ], + "type": "inline_equation", + "content": "a_{b}" + }, + { + "bbox": [ + 304, + 474, + 547, + 630 + ], + "type": "text", + "content": " is learned first, where the model is distracted and fails to learn " + }, + { + "bbox": [ + 304, + 474, + 547, + 630 + ], + "type": "inline_equation", + "content": "a_{y}" + }, + { + "bbox": [ + 304, + 474, + 547, + 630 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 630, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 547, + 714 + ], + "type": "text", + "content": "Based on the behaviors of the \"ultimate\" biased model, samples in " + }, + { + "bbox": [ + 304, + 630, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{train}}" + }, + { + "bbox": [ + 304, + 630, + 547, + 714 + ], + "type": "text", + "content": " are split into two sets. Those training samples that could be correctly predicted based on the bias attribute " + }, + { + "bbox": [ + 304, + 630, + 547, + 714 + ], + "type": "inline_equation", + "content": "a_{b}" + }, + { + "bbox": [ + 304, + 630, + 547, + 714 + ], + "type": "text", + "content": " are named as Bias-Aligned (BA) samples (as example \"yellow digit 1\" above), while the remaining ones are Bias-Conflicting (BC) samples (as digit \"1\" of other colors). The number of BC samples is extremely small, and previous" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7600" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 99, + 69, + 499, + 301 + ], + "blocks": [ + { + "bbox": [ + 99, + 69, + 499, + 301 + ], + "lines": [ + { + "bbox": [ + 99, + 69, + 499, + 301 + ], + "spans": [ + { + "bbox": [ + 99, + 69, + 499, + 301 + ], + "type": "image", + "image_path": "c40b7b9532fbf4bf8cf0735509a804cd0069a6e7934d4509db60c9feb56dfbc3.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 310, + 548, + 377 + ], + "lines": [ + { + "bbox": [ + 46, + 310, + 548, + 377 + ], + "spans": [ + { + "bbox": [ + 46, + 310, + 548, + 377 + ], + "type": "text", + "content": "Figure 2. An illustration of the training dynamics of a naively-trained model on a biased dataset. The different attribute classes are drawn with a specific color (top row) or shape (bottom row). The first three columns correspond to the sequential training progress of these two classifiers, and the final column shows the test scenario. The easier-to-learn color is fitted first, which leaves a large margin on decision boundary and correspondingly triggers the shape attribute intra-class \"hollow\". \"UB\" and \"BB\" are the abbreviations of \"unbiased boundary\" and \"biased boundary\". The biased model cannot generalize well as the shadow area in the last column frames the shape-misclassified samples. We use yellow stars to indicate the shifted class centers of the training samples and gray stars for those of the test samples." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 395, + 290, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 395, + 290, + 456 + ], + "spans": [ + { + "bbox": [ + 46, + 395, + 290, + 456 + ], + "type": "text", + "content": "methods emphasize their role with various strategies [11, 27, 34, 36]. For additional related methods of learning a debiased model [2, 7, 9, 10, 18, 24, 25, 29, 31, 40, 49, 60] please see the supplementary material. They can be extrapolated and applied to other application scenarios [16, 45, 52, 54, 57, 58]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 464, + 264, + 477 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 464, + 264, + 477 + ], + "spans": [ + { + "bbox": [ + 47, + 464, + 264, + 477 + ], + "type": "text", + "content": "2.2. The Training Dynamics of Biased Dataset" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 483, + 288, + 614 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 483, + 288, + 614 + ], + "spans": [ + { + "bbox": [ + 46, + 483, + 288, + 614 + ], + "type": "text", + "content": "We analyze the training dynamics of a naively trained model in Eq. 1 on the Colored MNIST dataset. The non-target bias attribute is the color and the target attribute is the shape. For visualization shown in Figure 2, we set the output dimension of the penultimate layer as two. In addition to the learned classifier on shape attribute " + }, + { + "bbox": [ + 46, + 483, + 288, + 614 + ], + "type": "inline_equation", + "content": "a_{y}" + }, + { + "bbox": [ + 46, + 483, + 288, + 614 + ], + "type": "text", + "content": ", simultaneously, we add another linear classifier on top of the embedding to show how the decision boundary of color attribute " + }, + { + "bbox": [ + 46, + 483, + 288, + 614 + ], + "type": "inline_equation", + "content": "a_{b}" + }, + { + "bbox": [ + 46, + 483, + 288, + 614 + ], + "type": "text", + "content": " changes. More details are described in the supplementary material. Focusing on the precedence relationship for learning " + }, + { + "bbox": [ + 46, + 483, + 288, + 614 + ], + "type": "inline_equation", + "content": "a_{y}" + }, + { + "bbox": [ + 46, + 483, + 288, + 614 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 483, + 288, + 614 + ], + "type": "inline_equation", + "content": "a_{b}" + }, + { + "bbox": [ + 46, + 483, + 288, + 614 + ], + "type": "text", + "content": ", we have the following observations:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 618, + 290, + 713 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 47, + 618, + 289, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 618, + 289, + 677 + ], + "spans": [ + { + "bbox": [ + 47, + 618, + 289, + 677 + ], + "type": "text", + "content": "- The easier-to-learn bias attribute color is fitted soon. The early training stage is shown in the first column. Both color and shape attribute classifiers discern by different colors and do correctly on almost all BA samples (red “0” and blue “2”, about " + }, + { + "bbox": [ + 47, + 618, + 289, + 677 + ], + "type": "inline_equation", + "content": "95\\%" + }, + { + "bbox": [ + 47, + 618, + 289, + 677 + ], + "type": "text", + "content": " of the training set)." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 677, + 290, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 290, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 290, + 713 + ], + "type": "text", + "content": "- The target attribute shape is learned later in a \"lazy\" manner. To further fit all shape labels, the model focuses on the limited BC samples (blue \"0\" and red \"2\", corre" + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 312, + 395, + 546, + 432 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 395, + 546, + 432 + ], + "spans": [ + { + "bbox": [ + 312, + 395, + 546, + 432 + ], + "type": "text", + "content": "spondingly about " + }, + { + "bbox": [ + 312, + 395, + 546, + 432 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 312, + 395, + 546, + 432 + ], + "type": "text", + "content": " ) that cannot be perfectly classified by color. It pushes minor BC representations to the other (correct) side instead of adjusting the decision boundary." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 433, + 547, + 598 + ], + "type": "list", + "angle": 0, + "index": 11, + "blocks": [ + { + "bbox": [ + 306, + 433, + 547, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 433, + 547, + 514 + ], + "spans": [ + { + "bbox": [ + 306, + 433, + 547, + 514 + ], + "type": "text", + "content": "- The ahead-color and lagged-shape learning process leaves a large margin of color attribute boundary, which further triggers the shape attribute intra-class \"hollow\". Because the representation of different colors is continuously pushed away (classified) before that of the shape, the gaps between different color attribute clusters are significantly larger than that of the shape attribute." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 515, + 547, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 515, + 547, + 598 + ], + "spans": [ + { + "bbox": [ + 306, + 515, + 547, + 598 + ], + "type": "text", + "content": "- Since there is an intra-class \"hollow\" between BA and BC samples which is conditioned on a particular shape, the true class representation is deviated toward color. The fourth column shows that the training class centers (yellow stars) and the test ones (gray stars) are mismatched. The true class center is located in the low-density \"hollow\" between shape-conditioned BA and BC samples." + } + ] + } + ], + "index": 10 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 304, + 605, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 547, + 713 + ], + "type": "text", + "content": "Previous observations indicate that the before-and-latter learning process on attributes of different learning difficulties leaves the model to lose intra-class compactness, primarily when learning relying on the bias attribute is easier. To alleviate class center deviation towards the BA samples, only emphasizing the BC samples is insufficient due to their scarcity. In addition, we propose to utilize Intermediate Attribute Samples (IASs), i.e., the samples near the attribute decision boundary and remodel the shifted representation." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "7601" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 104, + 69, + 499, + 261 + ], + "blocks": [ + { + "bbox": [ + 104, + 69, + 499, + 261 + ], + "lines": [ + { + "bbox": [ + 104, + 69, + 499, + 261 + ], + "spans": [ + { + "bbox": [ + 104, + 69, + 499, + 261 + ], + "type": "image", + "image_path": "c3f2a145d37ce5f6322b4c1b41a250943454e9a9793b821c066c3654aa01ffe8.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 270, + 548, + 326 + ], + "lines": [ + { + "bbox": [ + 45, + 270, + 548, + 326 + ], + "spans": [ + { + "bbox": [ + 45, + 270, + 548, + 326 + ], + "type": "text", + "content": "Figure 3. An illustration of the " + }, + { + "bbox": [ + 45, + 270, + 548, + 326 + ], + "type": "inline_equation", + "content": "\\chi^2" + }, + { + "bbox": [ + 45, + 270, + 548, + 326 + ], + "type": "text", + "content": "-model. In the first stage (top row, left to right), we match and mine all samples with a " + }, + { + "bbox": [ + 45, + 270, + 548, + 326 + ], + "type": "inline_equation", + "content": "\\chi" + }, + { + "bbox": [ + 45, + 270, + 548, + 326 + ], + "type": "text", + "content": "-shape pattern. As shown in the right part, the images are getting biased towards the side of peripheral bias attribute from top to bottom, i.e., from various colors or backgrounds to a single red or sunset. Different shapes (" + }, + { + "bbox": [ + 45, + 270, + 548, + 326 + ], + "type": "inline_equation", + "content": "\\bigcirc" + }, + { + "bbox": [ + 45, + 270, + 548, + 326 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 45, + 270, + 548, + 326 + ], + "type": "inline_equation", + "content": "\\Delta" + }, + { + "bbox": [ + 45, + 270, + 548, + 326 + ], + "type": "text", + "content": ") and colors (orange or green) drawn in the Representation Space indicate the target and bias attribute, respectively. In the second stage (bottom row, right to left), we construct prototypes by conditional interpolating around IASs with various ratios and design the " + }, + { + "bbox": [ + 45, + 270, + 548, + 326 + ], + "type": "inline_equation", + "content": "\\chi" + }, + { + "bbox": [ + 45, + 270, + 548, + 326 + ], + "type": "text", + "content": "-structured metric learning objective to pull the intra-class samples." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 344, + 288, + 381 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 344, + 288, + 381 + ], + "spans": [ + { + "bbox": [ + 45, + 344, + 288, + 381 + ], + "type": "text", + "content": "Especially when conditioned on the target attribute, the IASs vary on bias attribute and fill in the low-density intra-class \"hollow\" between BA and BC samples." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 391, + 112, + 404 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 391, + 112, + 404 + ], + "spans": [ + { + "bbox": [ + 46, + 391, + 112, + 404 + ], + "type": "text", + "content": "3. " + }, + { + "bbox": [ + 46, + 391, + 112, + 404 + ], + "type": "inline_equation", + "content": "\\chi^2" + }, + { + "bbox": [ + 46, + 391, + 112, + 404 + ], + "type": "text", + "content": "-Model" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 411, + 290, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 411, + 290, + 615 + ], + "spans": [ + { + "bbox": [ + 45, + 411, + 290, + 615 + ], + "type": "text", + "content": "To mitigate the representation deviation and compact the intra-class \"hollow\", we leverage IASs to encode how bias attribute changes from one extreme (major BA side) to another (BC side). Then, the variety of the bias attribute could be interpolated when conditioned on a particular target attribute. We propose our two-stage " + }, + { + "bbox": [ + 45, + 411, + 290, + 615 + ], + "type": "inline_equation", + "content": "\\chi^2" + }, + { + "bbox": [ + 45, + 411, + 290, + 615 + ], + "type": "text", + "content": "-model, whose notion is illustrated in Figure 3. First, the " + }, + { + "bbox": [ + 45, + 411, + 290, + 615 + ], + "type": "inline_equation", + "content": "\\chi^2" + }, + { + "bbox": [ + 45, + 411, + 290, + 615 + ], + "type": "text", + "content": "-model discovers IASs based on the training dynamics of the vanilla model in subsection 3.1. Next, we analyze where the top-ranked samples with a " + }, + { + "bbox": [ + 45, + 411, + 290, + 615 + ], + "type": "inline_equation", + "content": "\\chi" + }, + { + "bbox": [ + 45, + 411, + 290, + 615 + ], + "type": "text", + "content": "-shape pattern are as well as their effectiveness in debiasing in subsection 3.2. A conditional attribute interpolation step with IASs then fills in the low-density \"hollow\" to get a better estimation of class-specific prototype. By pulling samples to the corresponding prototype, the " + }, + { + "bbox": [ + 45, + 411, + 290, + 615 + ], + "type": "inline_equation", + "content": "\\chi" + }, + { + "bbox": [ + 45, + 411, + 290, + 615 + ], + "type": "text", + "content": "-structured metric learning makes intra-class samples compact in subsection 3.3. We further investigate the Colored MNIST dataset. Results on other datasets are consistent." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 623, + 257, + 636 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 623, + 257, + 636 + ], + "spans": [ + { + "bbox": [ + 46, + 623, + 257, + 636 + ], + "type": "text", + "content": "3.1. Scoring Samples with a " + }, + { + "bbox": [ + 46, + 623, + 257, + 636 + ], + "type": "inline_equation", + "content": "\\chi" + }, + { + "bbox": [ + 46, + 623, + 257, + 636 + ], + "type": "text", + "content": "-shape Pattern" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 642, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 288, + 715 + ], + "type": "text", + "content": "From the observations in the previous section, we aim to collect IASs to reveal how BC samples shift and leave the intra-class \"hollow\" between them and BA ones. As discussed in subsection 2.2, the vanilla model fits BC samples later than BA ones, which motivates us to score the samples from their training dynamics. Once we have the score pattern" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 344, + 547, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 344, + 547, + 392 + ], + "spans": [ + { + "bbox": [ + 304, + 344, + 547, + 392 + ], + "type": "text", + "content": "to match and distinguish BA and BC samples, IASs, with intermediate scores can be extracted and available for the next debiasing stage. In the following, we denote the posterior of the Ground-Truth class (GT-class) " + }, + { + "bbox": [ + 304, + 344, + 547, + 392 + ], + "type": "inline_equation", + "content": "y_{i}" + }, + { + "bbox": [ + 304, + 344, + 547, + 392 + ], + "type": "text", + "content": " for a sample " + }, + { + "bbox": [ + 304, + 344, + 547, + 392 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i" + }, + { + "bbox": [ + 304, + 344, + 547, + 392 + ], + "type": "text", + "content": " as" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 320, + 401, + 546, + 416 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 401, + 546, + 416 + ], + "spans": [ + { + "bbox": [ + 320, + 401, + 546, + 416 + ], + "type": "interline_equation", + "content": "\\operatorname * {P r} \\left(h _ {\\boldsymbol {\\theta}} (\\mathbf {x} _ {i}) = y _ {i} \\mid \\mathbf {x} _ {i}\\right) = \\operatorname {s o f t m a x} \\left(\\mathbf {w} _ {c} ^ {\\top} f _ {\\boldsymbol {\\phi}} (\\mathbf {x})\\right) _ {y _ {i}}, \\quad (2)", + "image_path": "00cddcd1c80d00ac1b2cbb94d5fd18d8fc3a170a1e64385ae7b76700b58ee626.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 424, + 547, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 424, + 547, + 605 + ], + "spans": [ + { + "bbox": [ + 304, + 424, + 547, + 605 + ], + "type": "text", + "content": "the larger the posterior, the more confident a model predicts " + }, + { + "bbox": [ + 304, + 424, + 547, + 605 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i" + }, + { + "bbox": [ + 304, + 424, + 547, + 605 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 304, + 424, + 547, + 605 + ], + "type": "inline_equation", + "content": "y_{i}" + }, + { + "bbox": [ + 304, + 424, + 547, + 605 + ], + "type": "text", + "content": ". For notation simplicity, we abbreviate the posterior as " + }, + { + "bbox": [ + 304, + 424, + 547, + 605 + ], + "type": "inline_equation", + "content": "\\operatorname*{Pr}(y_i\\mid \\mathbf{x}_i)" + }, + { + "bbox": [ + 304, + 424, + 547, + 605 + ], + "type": "text", + "content": ". The target posterior of a BA sample reaches one or becomes much higher than other categories soon after training several epochs, while the posterior of a BC sample has a delayed increase. To capture the clues on the change of bias attribute, we also analyze the posterior of the most obvious non-GT attribute, which reveals crucial bias influences. Denote the model at the " + }, + { + "bbox": [ + 304, + 424, + 547, + 605 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 424, + 547, + 605 + ], + "type": "text", + "content": "-th epoch plus the superscript " + }, + { + "bbox": [ + 304, + 424, + 547, + 605 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 424, + 547, + 605 + ], + "type": "text", + "content": ", such as " + }, + { + "bbox": [ + 304, + 424, + 547, + 605 + ], + "type": "inline_equation", + "content": "h_\\theta^t" + }, + { + "bbox": [ + 304, + 424, + 547, + 605 + ], + "type": "text", + "content": ". We take the bias class for the sample " + }, + { + "bbox": [ + 304, + 424, + 547, + 605 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i" + }, + { + "bbox": [ + 304, + 424, + 547, + 605 + ], + "type": "text", + "content": " at epoch " + }, + { + "bbox": [ + 304, + 424, + 547, + 605 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 424, + 547, + 605 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 304, + 424, + 547, + 605 + ], + "type": "inline_equation", + "content": "b_i^t = \\arg \\max_{c\\in [C],c\\neq y_i}\\left(\\mathbf{w}_c^\\top f_\\phi (\\mathbf{x})\\right)^t" + }, + { + "bbox": [ + 304, + 424, + 547, + 605 + ], + "type": "text", + "content": ". Then, we define the non-GT bias class as the most frequent " + }, + { + "bbox": [ + 304, + 424, + 547, + 605 + ], + "type": "inline_equation", + "content": "b_i^t" + }, + { + "bbox": [ + 304, + 424, + 547, + 605 + ], + "type": "text", + "content": " along all epochs, i.e., " + }, + { + "bbox": [ + 304, + 424, + 547, + 605 + ], + "type": "inline_equation", + "content": "b_{i} = \\max_{-}\\mathrm{freq}\\{b_{i}^{t}\\}_{t = 1}^{T}" + }, + { + "bbox": [ + 304, + 424, + 547, + 605 + ], + "type": "text", + "content": ". A sample has a larger bias class posterior when it has low confidence in its target class and vice versa." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 605, + 548, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 548, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 548, + 714 + ], + "type": "text", + "content": "Taking posteriors of both " + }, + { + "bbox": [ + 304, + 605, + 548, + 714 + ], + "type": "inline_equation", + "content": "y_{i}" + }, + { + "bbox": [ + 304, + 605, + 548, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 605, + 548, + 714 + ], + "type": "inline_equation", + "content": "b_{i}" + }, + { + "bbox": [ + 304, + 605, + 548, + 714 + ], + "type": "text", + "content": " into account, a BA sample has larger " + }, + { + "bbox": [ + 304, + 605, + 548, + 714 + ], + "type": "inline_equation", + "content": "\\operatorname{Pr}(y_i \\mid \\mathbf{x}_i)" + }, + { + "bbox": [ + 304, + 605, + 548, + 714 + ], + "type": "text", + "content": " and small " + }, + { + "bbox": [ + 304, + 605, + 548, + 714 + ], + "type": "inline_equation", + "content": "\\operatorname{Pr}(b_i \\mid \\mathbf{x}_i)" + }, + { + "bbox": [ + 304, + 605, + 548, + 714 + ], + "type": "text", + "content": " along all its training epochs. For a BC sample, " + }, + { + "bbox": [ + 304, + 605, + 548, + 714 + ], + "type": "inline_equation", + "content": "\\operatorname{Pr}(y_i \\mid \\mathbf{x}_i)" + }, + { + "bbox": [ + 304, + 605, + 548, + 714 + ], + "type": "text", + "content": " increases gradually and meanwhile " + }, + { + "bbox": [ + 304, + 605, + 548, + 714 + ], + "type": "inline_equation", + "content": "\\operatorname{Pr}(b_i \\mid \\mathbf{x}_i)" + }, + { + "bbox": [ + 304, + 605, + 548, + 714 + ], + "type": "text", + "content": " decreases. We verify the phenomenon on Colored MNIST dataset in Figure 4 (left). For BA samples (yellow \"1\"), the two curves demonstrate a \"rectangle\", while for BC samples (blue \"1\"), the two curves have an obvious intersection and reveal a \"x\" shape. The statistics for the change of posteriors are shown" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7602" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 70, + 68, + 195, + 185 + ], + "blocks": [ + { + "bbox": [ + 70, + 68, + 195, + 185 + ], + "lines": [ + { + "bbox": [ + 70, + 68, + 195, + 185 + ], + "spans": [ + { + "bbox": [ + 70, + 68, + 195, + 185 + ], + "type": "image", + "image_path": "b4f6b6e93c679d14333aab2af654687a7a5f6f9ca9a94b2f72a09b3c125e1c04.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 192, + 547, + 248 + ], + "lines": [ + { + "bbox": [ + 46, + 192, + 547, + 248 + ], + "spans": [ + { + "bbox": [ + 46, + 192, + 547, + 248 + ], + "type": "text", + "content": "Figure 4. Left: The change of posterior over the GT-class (green curve) as well as the bias class (red curve) over four samples. The two curves over BC samples and IAS demonstrate a " + }, + { + "bbox": [ + 46, + 192, + 547, + 248 + ], + "type": "inline_equation", + "content": "\\chi" + }, + { + "bbox": [ + 46, + 192, + 547, + 248 + ], + "type": "text", + "content": "-shape, which is different from the curves over the BA sample. Right: The change of prediction frequencies of BC or BA samples along with the training epochs. The statistics are calculated over all BC or BA samples. A BA sample is easily predicted as the GT-class from the initial training stage, while a BC sample changes its prediction from the bias class to the GT-class gradually." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 198, + 68, + 324, + 186 + ], + "blocks": [ + { + "bbox": [ + 198, + 68, + 324, + 186 + ], + "lines": [ + { + "bbox": [ + 198, + 68, + 324, + 186 + ], + "spans": [ + { + "bbox": [ + 198, + 68, + 324, + 186 + ], + "type": "image", + "image_path": "7d3216a2a9d89f10e726b182f8b88e68dcd2fd4e3f5987f055344430fa848ccd.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 334, + 68, + 520, + 186 + ], + "blocks": [ + { + "bbox": [ + 334, + 68, + 520, + 186 + ], + "lines": [ + { + "bbox": [ + 334, + 68, + 520, + 186 + ], + "spans": [ + { + "bbox": [ + 334, + 68, + 520, + 186 + ], + "type": "image", + "image_path": "ecd76dd2fa41ac5c6bdd450b4646f7df87225034c68b3f1d38b7d0ccfd79bc3b.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 262, + 289, + 371 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 262, + 289, + 371 + ], + "spans": [ + { + "bbox": [ + 46, + 262, + 289, + 371 + ], + "type": "text", + "content": "in Figure 4 (right). Therefore, how much the training dynamics match the \" " + }, + { + "bbox": [ + 46, + 262, + 289, + 371 + ], + "type": "inline_equation", + "content": "\\chi" + }, + { + "bbox": [ + 46, + 262, + 289, + 371 + ], + "type": "text", + "content": " \" shape reveals the probability of a sample that shifts from the major BA clusters to minor BC ones. We design a " + }, + { + "bbox": [ + 46, + 262, + 289, + 371 + ], + "type": "inline_equation", + "content": "\\chi" + }, + { + "bbox": [ + 46, + 262, + 289, + 371 + ], + "type": "text", + "content": "-shape for the dynamics of losses to capture such BC-specific properties. The change of sample-specific loss for ground-truth label and bias label over " + }, + { + "bbox": [ + 46, + 262, + 289, + 371 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 262, + 289, + 371 + ], + "type": "text", + "content": " epochs could be summarized by " + }, + { + "bbox": [ + 46, + 262, + 289, + 371 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{CE}}" + }, + { + "bbox": [ + 46, + 262, + 289, + 371 + ], + "type": "text", + "content": ". Then, we use two exponential " + }, + { + "bbox": [ + 46, + 262, + 289, + 371 + ], + "type": "inline_equation", + "content": "\\chi" + }, + { + "bbox": [ + 46, + 262, + 289, + 371 + ], + "type": "text", + "content": "-shape functions " + }, + { + "bbox": [ + 46, + 262, + 289, + 371 + ], + "type": "inline_equation", + "content": "\\chi_{\\mathrm{pattern}}" + }, + { + "bbox": [ + 46, + 262, + 289, + 371 + ], + "type": "text", + "content": " to capture the ideal loss shape of the BC sample, i.e., the severely shifted case." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 48, + 386, + 285, + 419 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 386, + 285, + 419 + ], + "spans": [ + { + "bbox": [ + 48, + 386, + 285, + 419 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {C E}} \\left(\\mathbf {x} _ {i}\\right) = \\left( \\begin{array}{c} \\mathcal {L} _ {\\mathrm {C E}} ^ {g t} \\left(\\mathbf {x} _ {i}\\right) = \\left\\{- \\log \\operatorname * {P r} ^ {t} \\left(y _ {i} \\mid \\mathbf {x} _ {i}\\right) \\right\\} _ {t = 1} ^ {T} \\\\ \\mathcal {L} _ {\\mathrm {C E}} ^ {b} \\left(\\mathbf {x} _ {i}\\right) = \\left\\{- \\log \\operatorname * {P r} ^ {t} \\left(b _ {i} \\mid \\mathbf {x} _ {i}\\right) \\right\\} _ {t = 1} ^ {T} \\end{array} \\right),", + "image_path": "e789835d45716572d4e9d71a65485a2a8e894dfa9caea71340d62ec2d867d45b.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 91, + 421, + 287, + 453 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 421, + 287, + 453 + ], + "spans": [ + { + "bbox": [ + 91, + 421, + 287, + 453 + ], + "type": "interline_equation", + "content": "\\chi_ {\\text {p a t t e r n}} = \\left( \\begin{array}{l} \\mathrm {p} ^ {g t} = \\left\\{e ^ {- A _ {1} t} \\right\\} _ {t = 1} ^ {T} \\\\ \\mathrm {p} ^ {b} = \\left\\{e ^ {A _ {2} t} \\right\\} _ {t = 1} ^ {T} \\end{array} \\right), \\tag {3}", + "image_path": "0c0b75e722611bb4284087b17708193ae2ed12f07d4fbf9bee83d11384153b81.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 468, + 287, + 539 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 468, + 287, + 539 + ], + "spans": [ + { + "bbox": [ + 47, + 468, + 287, + 539 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 468, + 287, + 539 + ], + "type": "inline_equation", + "content": "A_{1}" + }, + { + "bbox": [ + 47, + 468, + 287, + 539 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 468, + 287, + 539 + ], + "type": "inline_equation", + "content": "A_{2}" + }, + { + "bbox": [ + 47, + 468, + 287, + 539 + ], + "type": "text", + "content": " are the matching factors. They could be determined based on the dynamics of prediction fluctuations. For more details please see the supplementary material. The " + }, + { + "bbox": [ + 47, + 468, + 287, + 539 + ], + "type": "inline_equation", + "content": "\\chi_{\\mathrm{pattern}}" + }, + { + "bbox": [ + 47, + 468, + 287, + 539 + ], + "type": "text", + "content": " encodes the observations for the most deviated BC samples. To match the loss dynamics with the pattern, we use the inner product over the two curves:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 64, + 555, + 287, + 638 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 64, + 555, + 287, + 638 + ], + "spans": [ + { + "bbox": [ + 64, + 555, + 287, + 638 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathbf {s} \\left(\\mathbf {x} _ {i}\\right) = \\left\\langle \\mathcal {L} _ {\\mathrm {C E}} \\left(\\mathbf {x} _ {i}\\right), \\chi_ {\\text {s h a p e}} \\right\\rangle \\tag {4} \\\\ = \\left\\langle \\mathcal {L} _ {\\mathrm {C E}} ^ {g t} \\left(\\mathbf {x} _ {i}\\right), \\mathrm {p} ^ {g t} \\right\\rangle + \\left\\langle \\mathcal {L} _ {\\mathrm {C E}} ^ {b} \\left(\\mathbf {x} _ {i}\\right), \\mathrm {p} ^ {b} \\right\\rangle \\\\ = \\sum_ {t = 1} ^ {T} \\left(- e ^ {- A _ {1} t} \\cdot \\log \\Pr \\left(h _ {\\boldsymbol {\\theta}} \\left(\\mathbf {x} _ {i}\\right) = y _ {i} \\mid \\mathbf {x} _ {i}\\right) \\right. \\\\ - e ^ {A _ {2} t} \\cdot \\log \\operatorname * {P r} \\left(h _ {\\boldsymbol {\\theta}} \\left(\\mathbf {x} _ {i}\\right) = b _ {i} \\mid \\mathbf {x} _ {i}\\right). \\\\ \\end{array}", + "image_path": "9833c4ba2010fcf305a30523650cfc7d039cd4f3350068a15febcbd86b56fe10.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "text", + "content": "The inner product " + }, + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{s}(\\mathbf{x}_i)" + }, + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "text", + "content": " takes the area under the curves (AUC) into account, which is more robust w.r.t. the volatile loss changes. When " + }, + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{s}(\\mathbf{x}_i)" + }, + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "text", + "content": " score goes from low to high, the sample varies on the bias level, i.e., from BA samples to IASs, and then to BC samples." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 261, + 547, + 339 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 261, + 547, + 339 + ], + "spans": [ + { + "bbox": [ + 304, + 261, + 547, + 339 + ], + "type": "text", + "content": "Table 1. The classification accuracy on the unbiased test sets of vanilla models. Various training sampling strategies are compared. \"0-1\" denotes only using BC samples. \"Step-wise\" denotes applying uniformly higher and lower weights on BC and BA samples. \"χ-pattern\" denotes sampling with scores calculated by our " + }, + { + "bbox": [ + 304, + 261, + 547, + 339 + ], + "type": "inline_equation", + "content": "\\chi^2" + }, + { + "bbox": [ + 304, + 261, + 547, + 339 + ], + "type": "text", + "content": "-model. The best results are in bold, while the second-best ones are with underlines. C-CIFAR-10 is a similarly biased dataset as C-MNIST." + } + ] + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 331, + 347, + 522, + 427 + ], + "blocks": [ + { + "bbox": [ + 331, + 347, + 522, + 427 + ], + "lines": [ + { + "bbox": [ + 331, + 347, + 522, + 427 + ], + "spans": [ + { + "bbox": [ + 331, + 347, + 522, + 427 + ], + "type": "table", + "html": "
Dataset Ratio (%)C-MNISTC-CIFAR-10
99.999.599.999.5
Vanilla28.5859.2926.9130.16
+ 0-154.7870.4118.7325.06
+ Step-wise41.6873.5232.1235.91
+χ-pattern52.6780.2935.4737.83
", + "image_path": "d286407795cc964c3b5d649aca44bcf4bdc22eb1fadd01558b8b1bf528ce7704.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 451, + 545, + 475 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 451, + 545, + 475 + ], + "spans": [ + { + "bbox": [ + 305, + 451, + 545, + 475 + ], + "type": "text", + "content": "3.2. Where IASs Are and Why IASs Can Help to Learn a Debiased Representation?" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 483, + 547, + 699 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 483, + 547, + 699 + ], + "spans": [ + { + "bbox": [ + 304, + 483, + 547, + 699 + ], + "type": "text", + "content": "Combining the analysis in subsection 2.2 and collecting ranked samples by " + }, + { + "bbox": [ + 304, + 483, + 547, + 699 + ], + "type": "inline_equation", + "content": "\\mathbf{s}(\\mathbf{x}_i)" + }, + { + "bbox": [ + 304, + 483, + 547, + 699 + ], + "type": "text", + "content": ", we find there are two types of IASs according to the representation near the target attribute decision boundary (as \"0\" for complex shapes in Figure 3), or that of the bias attribute (as helicopter in intermediate transitional \"sunset\" background). (1) If an IAS has an intermediate target attribute value, it may be a difficult samples and contains rich information about the target class boundaries. (2) If an IAS is in an intermediate state on the bias attribute, it may help to fill in the intra-class vacant \"hollow\" when conditioning (fixing) on the target attribute. Both types of IASs are similar to BC samples but from two directions, i.e., compared to the BA samples, they contain richer semantics on target or bias attributes. In the representation space, they are scattered between BA and BC samples, compensating for the sparsity of BC samples and valuable for debiasing. We will show how " + }, + { + "bbox": [ + 304, + 483, + 547, + 699 + ], + "type": "inline_equation", + "content": "\\chi" + }, + { + "bbox": [ + 304, + 483, + 547, + 699 + ], + "type": "text", + "content": "-structured objective with IASs help to remodel the true class centers in the following subsection." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 318, + 701, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 701, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 318, + 701, + 547, + 714 + ], + "type": "text", + "content": "We illustrate the importance of IASs with simple experi" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7603" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 91, + 85, + 193, + 205 + ], + "blocks": [ + { + "bbox": [ + 169, + 68, + 221, + 78 + ], + "lines": [ + { + "bbox": [ + 169, + 68, + 221, + 78 + ], + "spans": [ + { + "bbox": [ + 169, + 68, + 221, + 78 + ], + "type": "text", + "content": "Biased Model" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 91, + 85, + 193, + 205 + ], + "lines": [ + { + "bbox": [ + 91, + 85, + 193, + 205 + ], + "spans": [ + { + "bbox": [ + 91, + 85, + 193, + 205 + ], + "type": "image", + "image_path": "ff2f345aed3d2a455b6cb50414f851c650f07d21cd2f9fc086a6db5fb2ba4ef8.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 198, + 86, + 283, + 205 + ], + "blocks": [ + { + "bbox": [ + 198, + 86, + 283, + 205 + ], + "lines": [ + { + "bbox": [ + 198, + 86, + 283, + 205 + ], + "spans": [ + { + "bbox": [ + 198, + 86, + 283, + 205 + ], + "type": "image", + "image_path": "e3313ebc03b52da3fb69dc859af1c6c1a3d2ab9eadac3defe1509df2c025e7d1.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 213, + 547, + 278 + ], + "lines": [ + { + "bbox": [ + 46, + 213, + 547, + 278 + ], + "spans": [ + { + "bbox": [ + 46, + 213, + 547, + 278 + ], + "type": "text", + "content": "Figure 5. Heatmap of the mean distance from the sample to its conditional interpolated prototypes. We construct the prototype with mixing over the same-class subset but with different ratios of BC samples. Then the mean distances between the sample and those prototypes are measured. For a biased model (left two), when the BC ratio " + }, + { + "bbox": [ + 46, + 213, + 547, + 278 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 46, + 213, + 547, + 278 + ], + "type": "text", + "content": " of interpolated prototype " + }, + { + "bbox": [ + 46, + 213, + 547, + 278 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_{\\gamma}" + }, + { + "bbox": [ + 46, + 213, + 547, + 278 + ], + "type": "text", + "content": " changes from low to high (horizontal direction), the distance of a sample to different " + }, + { + "bbox": [ + 46, + 213, + 547, + 278 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_{\\gamma}" + }, + { + "bbox": [ + 46, + 213, + 547, + 278 + ], + "type": "text", + "content": " varies hugely. The BA samples are closer to the low ratio ones, while the BC samples behave the opposite. An intra-class \"hollow\" exists. For an unbiased model (right two), the distances from any sample to " + }, + { + "bbox": [ + 46, + 213, + 547, + 278 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_{\\gamma}" + }, + { + "bbox": [ + 46, + 213, + 547, + 278 + ], + "type": "text", + "content": " with different ratios are almost the same." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 296, + 86, + 377, + 205 + ], + "blocks": [ + { + "bbox": [ + 350, + 68, + 413, + 78 + ], + "lines": [ + { + "bbox": [ + 350, + 68, + 413, + 78 + ], + "spans": [ + { + "bbox": [ + 350, + 68, + 413, + 78 + ], + "type": "text", + "content": "Unbiased Model" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 296, + 86, + 377, + 205 + ], + "lines": [ + { + "bbox": [ + 296, + 86, + 377, + 205 + ], + "spans": [ + { + "bbox": [ + 296, + 86, + 377, + 205 + ], + "type": "image", + "image_path": "2944384d775bc741062c6bf9774ddc647457f211d24c7c60b20ee9caa86d902b.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 384, + 86, + 468, + 205 + ], + "blocks": [ + { + "bbox": [ + 384, + 86, + 468, + 205 + ], + "lines": [ + { + "bbox": [ + 384, + 86, + 468, + 205 + ], + "spans": [ + { + "bbox": [ + 384, + 86, + 468, + 205 + ], + "type": "image", + "image_path": "98aeac472b9b9c12ed52083ea9c9628980d8ac06e55f26c040cd6f2b145e423a.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 474, + 93, + 506, + 205 + ], + "blocks": [ + { + "bbox": [ + 474, + 93, + 506, + 205 + ], + "lines": [ + { + "bbox": [ + 474, + 93, + 506, + 205 + ], + "spans": [ + { + "bbox": [ + 474, + 93, + 506, + 205 + ], + "type": "image", + "image_path": "65803eb4e27b2c9e6d9ebe845f64c9c2ae67b3f659076b95883047b1ad189a46.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 297, + 289, + 501 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 297, + 289, + 501 + ], + "spans": [ + { + "bbox": [ + 46, + 297, + 289, + 501 + ], + "type": "text", + "content": "ments on biased Colored-MNIST and Corrupted CIFAR-10 datasets. The datasets are described in subsection 4.1. We investigate whether various reweighting strategies on the vanilla model improve the generalization ability over an unbiased test set. We use \"0-1\" to denote the strategy that utilizes only the BC samples. \"step-wise\" means we apply uniformly higher (ratio of BA samples) and lower weights (one minus above ratio) to BC and BA samples. Our \"x-pattern\" smoothly reweights all samples with the matched scores, where BC samples as well as IASs have relatively larger weights than the remaining BA ones. The results in Table 1 show that simple reweighting strategies can improve the performance of a vanilla classifier, supporting the significance of emphasizing BC-like samples. Our \"x-pattern\" gets the best results in most scenarios, indicating that higher resampling weights on the IASs and BC samples assist the vanilla model to better frame the representation space." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 512, + 258, + 525 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 512, + 258, + 525 + ], + "spans": [ + { + "bbox": [ + 47, + 512, + 258, + 525 + ], + "type": "text", + "content": "3.3. Learning from a " + }, + { + "bbox": [ + 47, + 512, + 258, + 525 + ], + "type": "inline_equation", + "content": "\\chi" + }, + { + "bbox": [ + 47, + 512, + 258, + 525 + ], + "type": "text", + "content": "-Structured Objective" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 533, + 288, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 533, + 288, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 533, + 288, + 628 + ], + "type": "text", + "content": "Although the BA samples are severely biased towards the bias attribute, the BC samples, integrating the rich bias attribute semantics, naturally make the representation independent of the biased influence [19]. An intuitive approach for debiasing is to average over BC samples and classified by the BC class centers. However, the sparsity of BC samples induces an erratic estimation which is far from the true class center, as shown in Figure 2." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "content": "Benefiting from the analysis that BC-like IASs better estimate the intra-class structure, we target conditional interpolating around it, i.e., mixing the same-class samples with different BC-like scores to remodel the intermediate samples between BA and BC samples. From that, we can construct many prototypes closer to the real class center and pull samples to these prototypes to compact the intra-class" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 297, + 547, + 393 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 297, + 547, + 393 + ], + "spans": [ + { + "bbox": [ + 304, + 297, + 547, + 393 + ], + "type": "text", + "content": "space. Combined with the soft ranking score from the " + }, + { + "bbox": [ + 304, + 297, + 547, + 393 + ], + "type": "inline_equation", + "content": "\\chi" + }, + { + "bbox": [ + 304, + 297, + 547, + 393 + ], + "type": "text", + "content": "-pattern in the previous stage, we build two pools (subsets) of the samples denoted as " + }, + { + "bbox": [ + 304, + 297, + 547, + 393 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\parallel}" + }, + { + "bbox": [ + 304, + 297, + 547, + 393 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 297, + 547, + 393 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\perp}" + }, + { + "bbox": [ + 304, + 297, + 547, + 393 + ], + "type": "text", + "content": ". The " + }, + { + "bbox": [ + 304, + 297, + 547, + 393 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\perp}" + }, + { + "bbox": [ + 304, + 297, + 547, + 393 + ], + "type": "text", + "content": " pool collects the top-rank samplers and most of them are BC samples and IASs. The " + }, + { + "bbox": [ + 304, + 297, + 547, + 393 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\parallel}" + }, + { + "bbox": [ + 304, + 297, + 547, + 393 + ], + "type": "text", + "content": " pool is sampled from the remaining (BA) part according to the score. With the help of " + }, + { + "bbox": [ + 304, + 297, + 547, + 393 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\parallel}" + }, + { + "bbox": [ + 304, + 297, + 547, + 393 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 297, + 547, + 393 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\perp}" + }, + { + "bbox": [ + 304, + 297, + 547, + 393 + ], + "type": "text", + "content": ", we construct multiple bias bags (subset) " + }, + { + "bbox": [ + 304, + 297, + 547, + 393 + ], + "type": "inline_equation", + "content": "\\mathcal{B}_{\\gamma}" + }, + { + "bbox": [ + 304, + 297, + 547, + 393 + ], + "type": "text", + "content": " with bootstrapping where the ratio of BC samples is " + }, + { + "bbox": [ + 304, + 297, + 547, + 393 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 304, + 297, + 547, + 393 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 333, + 398, + 545, + 412 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 333, + 398, + 545, + 412 + ], + "spans": [ + { + "bbox": [ + 333, + 398, + 545, + 412 + ], + "type": "interline_equation", + "content": "\\mathcal {B} _ {\\gamma} = \\left\\{\\left(\\mathbf {x} _ {i}, y _ {i}\\right) \\mid \\operatorname {n u m} \\left(\\mathcal {D} _ {\\perp}\\right): \\operatorname {n u m} \\left(\\mathcal {D} _ {\\|}\\right) = \\gamma \\right\\}, \\tag {5}", + "image_path": "b3f054a66d23cd2e5c5d508a4cc9d365585f6587faa8fe76b58b5599c12a868d.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 417, + 547, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 417, + 547, + 502 + ], + "spans": [ + { + "bbox": [ + 304, + 417, + 547, + 502 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 417, + 547, + 502 + ], + "type": "inline_equation", + "content": "\\mathrm{num}(\\mathcal{D})" + }, + { + "bbox": [ + 304, + 417, + 547, + 502 + ], + "type": "text", + "content": " equals the number of samples in " + }, + { + "bbox": [ + 304, + 417, + 547, + 502 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 304, + 417, + 547, + 502 + ], + "type": "text", + "content": ". When " + }, + { + "bbox": [ + 304, + 417, + 547, + 502 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 304, + 417, + 547, + 502 + ], + "type": "text", + "content": " is low to high, the " + }, + { + "bbox": [ + 304, + 417, + 547, + 502 + ], + "type": "inline_equation", + "content": "\\mathcal{B}_{\\gamma}" + }, + { + "bbox": [ + 304, + 417, + 547, + 502 + ], + "type": "text", + "content": " contains samples ranging from the extremes of BA samples to the IASs, and then to the BC ones. Based on " + }, + { + "bbox": [ + 304, + 417, + 547, + 502 + ], + "type": "inline_equation", + "content": "\\mathcal{B}_{\\gamma}" + }, + { + "bbox": [ + 304, + 417, + 547, + 502 + ], + "type": "text", + "content": ", we compute the prototype, i.e., averaged on " + }, + { + "bbox": [ + 304, + 417, + 547, + 502 + ], + "type": "inline_equation", + "content": "\\mathcal{B}_{\\gamma}" + }, + { + "bbox": [ + 304, + 417, + 547, + 502 + ], + "type": "text", + "content": " to interpolate bias attribute conditioned on the particular target attribute. For example, the prototype conditioned on class " + }, + { + "bbox": [ + 304, + 417, + 547, + 502 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 417, + 547, + 502 + ], + "type": "text", + "content": " is formalized as " + }, + { + "bbox": [ + 304, + 417, + 547, + 502 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_{\\gamma,c}" + }, + { + "bbox": [ + 304, + 417, + 547, + 502 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 340, + 509, + 545, + 539 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 340, + 509, + 545, + 539 + ], + "spans": [ + { + "bbox": [ + 340, + 509, + 545, + 539 + ], + "type": "interline_equation", + "content": "\\mathbf {p} _ {\\gamma , c} = \\frac {1}{K} \\sum_ {\\left(\\mathbf {x} _ {i}, y _ {i}\\right) \\in \\mathcal {B} _ {\\gamma}} f _ {\\phi} \\left(\\mathbf {x} _ {i}\\right) \\cdot \\mathbb {I} [ y _ {i} = c ]. \\tag {6}", + "image_path": "469ce69bebf92fe2f8a67ac527b58f6caa348393215b7ddc256796f7075c0e49.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 546, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 546, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 546, + 547, + 713 + ], + "type": "text", + "content": "To further demonstrate the significance of intra-class compactness, we design the experiments to study the difference between a biased vanilla model and the unbiased oracle model (well-trained on an unbiased training set). We measure the mean distance between samples and their multiple conditional interpolated prototypes with changing ratio " + }, + { + "bbox": [ + 304, + 546, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 304, + 546, + 547, + 713 + ], + "type": "text", + "content": ". If the prototypes are shifted with changing " + }, + { + "bbox": [ + 304, + 546, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 304, + 546, + 547, + 713 + ], + "type": "text", + "content": ", that indicates a large intra-class deviation exists. As shown in Figure 5, for a biased model, when " + }, + { + "bbox": [ + 304, + 546, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 304, + 546, + 547, + 713 + ], + "type": "text", + "content": " decreases, " + }, + { + "bbox": [ + 304, + 546, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_{\\gamma}" + }, + { + "bbox": [ + 304, + 546, + 547, + 713 + ], + "type": "text", + "content": " is interpolated closer to the BA samples. Opposite phenomena are observed in the BC samples. As for the unbiased oracle model, no matter how the BC ratio " + }, + { + "bbox": [ + 304, + 546, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 304, + 546, + 547, + 713 + ], + "type": "text", + "content": " changes, such mean distance is almost unchanged and shows a lower variance. This coincides with the observation in Figure 2." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7604" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 107, + 113, + 488, + 269 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "text", + "content": "Table 2. The classification performance on unbiased test set (in %; higher is better) evaluated on unbiased test sets of Colored MNIST and Corrupted CIFAR-10 with training on varying BA samples ratios. We denote bias pre-provided type by " + }, + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "inline_equation", + "content": "\\bigcirc" + }, + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "text", + "content": " (without any information), " + }, + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "inline_equation", + "content": "\\bullet" + }, + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "text", + "content": " (bias prior knowledge), and " + }, + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "inline_equation", + "content": "\\bullet" + }, + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "text", + "content": " (explicit bias supervision). The best result is in bold, while the second-best is with underlines." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 107, + 113, + 488, + 269 + ], + "lines": [ + { + "bbox": [ + 107, + 113, + 488, + 269 + ], + "spans": [ + { + "bbox": [ + 107, + 113, + 488, + 269 + ], + "type": "table", + "html": "
Dataset Ratio (%)Colored MNISTCorrupted CIFAR-10
99.999.599.095.099.999.599.095.0
Vanilla + p [44]○28.5859.2974.4287.1326.9130.1637.7141.60
○31.0164.8276.8487.8626.5529.4838.0742.30
RUBi [7]●27.8270.8086.5896.7733.7034.7034.5947.23
ReBias [4]●27.7172.8985.9596.8733.6534.4035.8247.45
End [46]●28.1981.8188.1096.9931.3033.8334.0238.77
DI [50]●33.1880.6386.2898.3632.0933.3737.6551.27
LfF [36]○30.2468.9076.6996.8129.8933.6835.2845.38
LFA [27]○22.3164.1381.8395.4532.4935.7439.6347.25
x-pattern + p●60.3364.1593.5398.3035.3339.3141.3253.37
x²-model (Ours)○66.9188.7392.1597.8735.6737.6140.7449.04
", + "image_path": "612b3b030a33ae911f2741ae7bab0fa82af92337eababc280060029850850010.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 287, + 289, + 420 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 287, + 289, + 420 + ], + "spans": [ + { + "bbox": [ + 46, + 287, + 289, + 420 + ], + "type": "text", + "content": "Motivated by mimicking the oracle, we adopt the conditional interpolated prototypes and construct a customized " + }, + { + "bbox": [ + 46, + 287, + 289, + 420 + ], + "type": "inline_equation", + "content": "\\chi" + }, + { + "bbox": [ + 46, + 287, + 289, + 420 + ], + "type": "text", + "content": "-structured metric learning task. Assuming " + }, + { + "bbox": [ + 46, + 287, + 289, + 420 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 46, + 287, + 289, + 420 + ], + "type": "text", + "content": " is large, we use " + }, + { + "bbox": [ + 46, + 287, + 289, + 420 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_{\\gamma}" + }, + { + "bbox": [ + 46, + 287, + 289, + 420 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 287, + 289, + 420 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_{1 - \\gamma}" + }, + { + "bbox": [ + 46, + 287, + 289, + 420 + ], + "type": "text", + "content": " to denote prototypes in bias bags " + }, + { + "bbox": [ + 46, + 287, + 289, + 420 + ], + "type": "inline_equation", + "content": "\\mathcal{B}" + }, + { + "bbox": [ + 46, + 287, + 289, + 420 + ], + "type": "text", + "content": " with high and low BC ratios. The model should prioritize pulling the majority of low BC ratio bias bag " + }, + { + "bbox": [ + 46, + 287, + 289, + 420 + ], + "type": "inline_equation", + "content": "\\mathcal{B}_{1 - \\gamma}" + }, + { + "bbox": [ + 46, + 287, + 289, + 420 + ], + "type": "text", + "content": " closer to " + }, + { + "bbox": [ + 46, + 287, + 289, + 420 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_{\\gamma}" + }, + { + "bbox": [ + 46, + 287, + 289, + 420 + ], + "type": "text", + "content": ", which interpolated into the high BC space. Similarly, the high BC bias bag " + }, + { + "bbox": [ + 46, + 287, + 289, + 420 + ], + "type": "inline_equation", + "content": "\\mathcal{B}_{\\gamma}" + }, + { + "bbox": [ + 46, + 287, + 289, + 420 + ], + "type": "text", + "content": " should be pulled to low BC interpolated " + }, + { + "bbox": [ + 46, + 287, + 289, + 420 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_{1 - \\gamma}" + }, + { + "bbox": [ + 46, + 287, + 289, + 420 + ], + "type": "text", + "content": ". We optimize the cross-entropy loss " + }, + { + "bbox": [ + 46, + 287, + 289, + 420 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{CE}}" + }, + { + "bbox": [ + 46, + 287, + 289, + 420 + ], + "type": "text", + "content": " to enable the pulling operation. Concretely, the posterior via the distance " + }, + { + "bbox": [ + 46, + 287, + 289, + 420 + ], + "type": "inline_equation", + "content": "\\left(\\cdot ,\\cdot\\right)" + }, + { + "bbox": [ + 46, + 287, + 289, + 420 + ], + "type": "text", + "content": " in the representation space is formalized as:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 53, + 429, + 288, + 458 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 429, + 288, + 458 + ], + "spans": [ + { + "bbox": [ + 53, + 429, + 288, + 458 + ], + "type": "interline_equation", + "content": "\\operatorname * {P r} \\left(y _ {i} \\mid \\mathbf {x} _ {i}\\right) = \\frac {\\exp \\left(- \\mathrm {d} \\left(f _ {\\phi} \\left(\\mathbf {x} _ {i}\\right) , \\mathbf {p} _ {\\gamma , y _ {i}}\\right) / \\tau\\right)}{\\sum_ {c \\in [ C ]} \\exp \\left(- \\mathrm {d} \\left(f _ {\\phi} \\left(\\mathbf {x} _ {i}\\right) , \\mathbf {p} _ {\\gamma , c}\\right) / \\tau\\right)}, (7)", + "image_path": "7b60515d4116d74c8210ded2529643d5b1ab393a64d6104535b558ddb1461d2e.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 465, + 290, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 465, + 290, + 586 + ], + "spans": [ + { + "bbox": [ + 46, + 465, + 290, + 586 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 465, + 290, + 586 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 46, + 465, + 290, + 586 + ], + "type": "text", + "content": " is a scaled temperature. One of the branches of the " + }, + { + "bbox": [ + 46, + 465, + 290, + 586 + ], + "type": "inline_equation", + "content": "\\chi" + }, + { + "bbox": [ + 46, + 465, + 290, + 586 + ], + "type": "text", + "content": "-structure classification task is optimizing the " + }, + { + "bbox": [ + 46, + 465, + 290, + 586 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{CE}}" + }, + { + "bbox": [ + 46, + 465, + 290, + 586 + ], + "type": "text", + "content": " between samples in the " + }, + { + "bbox": [ + 46, + 465, + 290, + 586 + ], + "type": "inline_equation", + "content": "\\mathcal{B}_{1 - \\gamma}" + }, + { + "bbox": [ + 46, + 465, + 290, + 586 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 465, + 290, + 586 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_{\\gamma}" + }, + { + "bbox": [ + 46, + 465, + 290, + 586 + ], + "type": "text", + "content": ". Similarly, the other branch is optimizing between " + }, + { + "bbox": [ + 46, + 465, + 290, + 586 + ], + "type": "inline_equation", + "content": "\\mathcal{B}_{\\gamma}" + }, + { + "bbox": [ + 46, + 465, + 290, + 586 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 465, + 290, + 586 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_{1 - \\gamma}" + }, + { + "bbox": [ + 46, + 465, + 290, + 586 + ], + "type": "text", + "content": " at the same time. As shown in Figure 3, such a high-and-low correspondence captures and compacts the intra-class \"hollow\". In summary, The bias bags of high BC ratios " + }, + { + "bbox": [ + 46, + 465, + 290, + 586 + ], + "type": "inline_equation", + "content": "\\mathcal{B}_{\\gamma}" + }, + { + "bbox": [ + 46, + 465, + 290, + 586 + ], + "type": "text", + "content": " with corresponding low BC interpolated prototypes conditioning on the target attribute " + }, + { + "bbox": [ + 46, + 465, + 290, + 586 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_{1 - \\gamma}" + }, + { + "bbox": [ + 46, + 465, + 290, + 586 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 465, + 290, + 586 + ], + "type": "inline_equation", + "content": "\\mathcal{B}_{1 - \\gamma}" + }, + { + "bbox": [ + 46, + 465, + 290, + 586 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 46, + 465, + 290, + 586 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_{\\gamma}" + }, + { + "bbox": [ + 46, + 465, + 290, + 586 + ], + "type": "text", + "content": " form the " + }, + { + "bbox": [ + 46, + 465, + 290, + 586 + ], + "type": "inline_equation", + "content": "\\chi" + }, + { + "bbox": [ + 46, + 465, + 290, + 586 + ], + "type": "text", + "content": "-structure crossover objective." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 597, + 128, + 611 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 597, + 128, + 611 + ], + "spans": [ + { + "bbox": [ + 47, + 597, + 128, + 611 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "text", + "content": "We conduct experiments to verify whether " + }, + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\chi^2" + }, + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "text", + "content": "-model has effective debiasing capability. We begin by introducing bias details in each dataset (as in subsection 4.1). We present the comparison approaches and training details. In subsection 4.2, the experiments show that " + }, + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\chi^2" + }, + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "text", + "content": "-model achieves superior performance in each stage. Furthermore, we exemplify the inherent quality of the prototype-based classification for debiasing tasks and offer ablation studies in subsection 4.3." + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 337, + 328, + 514, + 397 + ], + "blocks": [ + { + "bbox": [ + 304, + 285, + 547, + 321 + ], + "lines": [ + { + "bbox": [ + 304, + 285, + 547, + 321 + ], + "spans": [ + { + "bbox": [ + 304, + 285, + 547, + 321 + ], + "type": "text", + "content": "Table 3. The classification performance on the unbiased CelebA and NICO test set. The data source " + }, + { + "bbox": [ + 304, + 285, + 547, + 321 + ], + "type": "inline_equation", + "content": "BA" + }, + { + "bbox": [ + 304, + 285, + 547, + 321 + ], + "type": "text", + "content": " denotes the measurement on BA samples and " + }, + { + "bbox": [ + 304, + 285, + 547, + 321 + ], + "type": "inline_equation", + "content": "BC" + }, + { + "bbox": [ + 304, + 285, + 547, + 321 + ], + "type": "text", + "content": " is corresponding the BC samples." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 337, + 328, + 514, + 397 + ], + "lines": [ + { + "bbox": [ + 337, + 328, + 514, + 397 + ], + "spans": [ + { + "bbox": [ + 337, + 328, + 514, + 397 + ], + "type": "table", + "html": "
Data SourceBiased CelebANICO
BABCAllAll
LfF [36]73.6970.4172.0534.44
DFA [27]94.0158.9876.5033.10
\\( \\chi^2 \\)-model97.6660.7979.2336.99
", + "image_path": "b352d742dead58bd51036dbcabd461b778ddb4f2d6e3e162e87306ca57f57725.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 415, + 427, + 428 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 415, + 427, + 428 + ], + "spans": [ + { + "bbox": [ + 306, + 415, + 427, + 428 + ], + "type": "text", + "content": "4.1. Experimental Setups" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 436, + 547, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 436, + 547, + 496 + ], + "spans": [ + { + "bbox": [ + 304, + 436, + 547, + 496 + ], + "type": "text", + "content": "Datasets. To cover more general and challenging cases of bias impact, we validate " + }, + { + "bbox": [ + 304, + 436, + 547, + 496 + ], + "type": "inline_equation", + "content": "\\chi^2" + }, + { + "bbox": [ + 304, + 436, + 547, + 496 + ], + "type": "text", + "content": "-model in a variety of datasets, including two synthetic bias datasets (Colored MNIST [4], Corrupted CIFAR-10 [36]) and two real-world datasets (Biased CelebA [32] and Biased NICO)." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 498, + 548, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 548, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 548, + 714 + ], + "type": "text", + "content": "The BA samples ratio " + }, + { + "bbox": [ + 304, + 498, + 548, + 714 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 304, + 498, + 548, + 714 + ], + "type": "text", + "content": " in the training set is usually high (over " + }, + { + "bbox": [ + 304, + 498, + 548, + 714 + ], + "type": "inline_equation", + "content": "95\\%" + }, + { + "bbox": [ + 304, + 498, + 548, + 714 + ], + "type": "text", + "content": "), so the bias attribute is highly correlated with the target label. For instance, in the Colored MNIST dataset, each digit is linked to a pre-defined bias color. Similarly, there is an object target with corruption bias in Corrupted CIFAR-10 and a gender target with hair color bias in Biased CelebA. Following the previous works [19], we use the BA ratio " + }, + { + "bbox": [ + 304, + 498, + 548, + 714 + ], + "type": "inline_equation", + "content": "\\rho \\in \\{95.0\\%, 99.0\\%, 99.5\\%, 99.9\\% \\}" + }, + { + "bbox": [ + 304, + 498, + 548, + 714 + ], + "type": "text", + "content": " for Colored MNIST and Corrupted CIFAR-10, respectively, and approximately " + }, + { + "bbox": [ + 304, + 498, + 548, + 714 + ], + "type": "inline_equation", + "content": "96\\%" + }, + { + "bbox": [ + 304, + 498, + 548, + 714 + ], + "type": "text", + "content": " for Biased CelebA. The Biased NICO dataset is dedicatedly sampled in NICO [17], initially designed for OOD (Out-of-Distribution) image classification. NICO is enriched with variations in the object and context dimensions. We select the bias attribute with the highest co-occurrence frequency to the target one, e.g., helicopter to sunset in training set correlates strongly (see BA samples in Figure 3). The correlation ratio is roughly controlled to " + }, + { + "bbox": [ + 304, + 498, + 548, + 714 + ], + "type": "inline_equation", + "content": "86\\%" + }, + { + "bbox": [ + 304, + 498, + 548, + 714 + ], + "type": "text", + "content": ". For more details please see the supplementary material." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7605" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 69, + 129, + 264, + 220 + ], + "blocks": [ + { + "bbox": [ + 46, + 65, + 289, + 122 + ], + "lines": [ + { + "bbox": [ + 46, + 65, + 289, + 122 + ], + "spans": [ + { + "bbox": [ + 46, + 65, + 289, + 122 + ], + "type": "text", + "content": "Table 4. The performance of BC samples mining on Colored MNIST with " + }, + { + "bbox": [ + 46, + 65, + 289, + 122 + ], + "type": "inline_equation", + "content": "99.5\\%" + }, + { + "bbox": [ + 46, + 65, + 289, + 122 + ], + "type": "text", + "content": " BA ratio. Acc. denotes mean accuracy of ranking with top-300. " + }, + { + "bbox": [ + 46, + 65, + 289, + 122 + ], + "type": "inline_equation", + "content": "98\\% - \\sigma" + }, + { + "bbox": [ + 46, + 65, + 289, + 122 + ], + "type": "text", + "content": " denotes the number of samples required to contain " + }, + { + "bbox": [ + 46, + 65, + 289, + 122 + ], + "type": "inline_equation", + "content": "98\\%" + }, + { + "bbox": [ + 46, + 65, + 289, + 122 + ], + "type": "text", + "content": " of BC samples. " + }, + { + "bbox": [ + 46, + 65, + 289, + 122 + ], + "type": "inline_equation", + "content": "AP" + }, + { + "bbox": [ + 46, + 65, + 289, + 122 + ], + "type": "text", + "content": " is average precision. " + }, + { + "bbox": [ + 46, + 65, + 289, + 122 + ], + "type": "inline_equation", + "content": "\\uparrow" + }, + { + "bbox": [ + 46, + 65, + 289, + 122 + ], + "type": "text", + "content": " means higher is better, while " + }, + { + "bbox": [ + 46, + 65, + 289, + 122 + ], + "type": "inline_equation", + "content": "\\downarrow" + }, + { + "bbox": [ + 46, + 65, + 289, + 122 + ], + "type": "text", + "content": " is the opposite." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 69, + 129, + 264, + 220 + ], + "lines": [ + { + "bbox": [ + 69, + 129, + 264, + 220 + ], + "spans": [ + { + "bbox": [ + 69, + 129, + 264, + 220 + ], + "type": "table", + "html": "
MeasureAcc. ↑98%-σ ↓AP ↑
Entropy [20]78.3363283.52
Confidence [28]80.3359085.61
Loss [36]94.3941898.22
Pleiss et al. [39]82.6768689.24
Zhao et al. [55]90.3345196.04
χ-pattern (Ours)95.8437298.44
", + "image_path": "2c59797a4a4da0ffbe44b88ae0f0fd6b642ecd3da33c9dd4d7cc234fdec3e49c.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 233, + 287, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 233, + 287, + 316 + ], + "spans": [ + { + "bbox": [ + 46, + 233, + 287, + 316 + ], + "type": "text", + "content": "Baselines. We carefully select the classic and the latest trending approaches as baselines: (1) Vanilla model training with cross entropy as described in subsection 2.1. (2) Bias-tailored approaches with pre-provided bias type: RUBi, Rebias. (3) Explicit approaches under the guidance of total bias supervision: EnD and DI. (4) Implicit methods through general bias properties: LfF and DFA." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 317, + 287, + 412 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 317, + 287, + 412 + ], + "spans": [ + { + "bbox": [ + 46, + 317, + 287, + 412 + ], + "type": "text", + "content": "Implementation details. Following the existing popular benchmarks [19, 23], we use the four-layer CNN with kernel size " + }, + { + "bbox": [ + 46, + 317, + 287, + 412 + ], + "type": "inline_equation", + "content": "7 \\times 7" + }, + { + "bbox": [ + 46, + 317, + 287, + 412 + ], + "type": "text", + "content": " for the Colored MNIST dataset and ResNet-18 [15] for Corrupted CIFAR-10, Biased CelebA, and Biased NICO datasets. For a fair comparison, we re-implemented the baselines with the same configuration. We mainly focus on unbiased test accuracy for all categories. All models are trained on an NVIDIA RTX 3090 GPU." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 413, + 288, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 413, + 288, + 485 + ], + "spans": [ + { + "bbox": [ + 46, + 413, + 288, + 485 + ], + "type": "text", + "content": "Baselines for the first stage. To better demonstrate the effectiveness of " + }, + { + "bbox": [ + 46, + 413, + 288, + 485 + ], + "type": "inline_equation", + "content": "\\chi" + }, + { + "bbox": [ + 46, + 413, + 288, + 485 + ], + "type": "text", + "content": "-pattern, we consider related sample-specific scoring methods [39, 55] and report average precision, top-threshold accuracy, and the minimum samples (threshold) required for " + }, + { + "bbox": [ + 46, + 413, + 288, + 485 + ], + "type": "inline_equation", + "content": "98\\%" + }, + { + "bbox": [ + 46, + 413, + 288, + 485 + ], + "type": "text", + "content": " accuracy. For more results, such as PR curves, please see the supplementary material." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 491, + 183, + 504 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 491, + 183, + 504 + ], + "spans": [ + { + "bbox": [ + 47, + 491, + 183, + 504 + ], + "type": "text", + "content": "4.2. Quantitative Evaluation" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 510, + 287, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 287, + 569 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 287, + 569 + ], + "type": "text", + "content": "Performance of " + }, + { + "bbox": [ + 46, + 510, + 287, + 569 + ], + "type": "inline_equation", + "content": "\\chi" + }, + { + "bbox": [ + 46, + 510, + 287, + 569 + ], + "type": "text", + "content": "-shape pattern. As shown in Table 4, our " + }, + { + "bbox": [ + 46, + 510, + 287, + 569 + ], + "type": "inline_equation", + "content": "\\chi" + }, + { + "bbox": [ + 46, + 510, + 287, + 569 + ], + "type": "text", + "content": "-pattern matching achieves state-of-the-art performance on various evaluation metrics. Thus, the " + }, + { + "bbox": [ + 46, + 510, + 287, + 569 + ], + "type": "inline_equation", + "content": "\\chi" + }, + { + "bbox": [ + 46, + 510, + 287, + 569 + ], + "type": "text", + "content": "-structure metric learning objective can leverage more IASs cues to interpolate bias attribute and further learn the debiased representation." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 570, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\chi^2" + }, + { + "bbox": [ + 46, + 570, + 288, + 713 + ], + "type": "text", + "content": "-model in different types of bias constructions. (1) Synthetic bias on Colored MNIST and Corrupted CIFAR-10: From Table 2 we find that under extreme bias influence, as " + }, + { + "bbox": [ + 46, + 570, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 46, + 570, + 288, + 713 + ], + "type": "text", + "content": " is " + }, + { + "bbox": [ + 46, + 570, + 288, + 713 + ], + "type": "inline_equation", + "content": "99.9\\%" + }, + { + "bbox": [ + 46, + 570, + 288, + 713 + ], + "type": "text", + "content": ", the performance of the vanilla model and other baselines decreases catastrophically. In contrast, Our " + }, + { + "bbox": [ + 46, + 570, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\chi^2" + }, + { + "bbox": [ + 46, + 570, + 288, + 713 + ], + "type": "text", + "content": "-model maintains the robust and efficient debiasing capability on the unbiased dataset. Further, more results in Figure 2 present the remarkable performance of our " + }, + { + "bbox": [ + 46, + 570, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\chi^2" + }, + { + "bbox": [ + 46, + 570, + 288, + 713 + ], + "type": "text", + "content": "-model compared to other methods. (2) Real-world bias on Biased CelebA and Biased NICO: Table 3 shows that compared to the recent methods which do not pre-provide any bias information as the same as ours, our method also achieves" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 310, + 73, + 375, + 138 + ], + "blocks": [ + { + "bbox": [ + 310, + 73, + 375, + 138 + ], + "lines": [ + { + "bbox": [ + 310, + 73, + 375, + 138 + ], + "spans": [ + { + "bbox": [ + 310, + 73, + 375, + 138 + ], + "type": "image", + "image_path": "2bfb29a0f9fa4db8be93aff5b33213ece4e09f52c713c79a66f091a6ec9e7838.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 319, + 144, + 365, + 153 + ], + "lines": [ + { + "bbox": [ + 319, + 144, + 365, + 153 + ], + "spans": [ + { + "bbox": [ + 319, + 144, + 365, + 153 + ], + "type": "text", + "content": "(a) t-SNE on " + }, + { + "bbox": [ + 319, + 144, + 365, + 153 + ], + "type": "inline_equation", + "content": "a_{t}" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 383, + 74, + 446, + 137 + ], + "blocks": [ + { + "bbox": [ + 383, + 74, + 446, + 137 + ], + "lines": [ + { + "bbox": [ + 383, + 74, + 446, + 137 + ], + "spans": [ + { + "bbox": [ + 383, + 74, + 446, + 137 + ], + "type": "image", + "image_path": "5f900d9cda0fd89e3aa3704b65b98bf5d7e8669686bb9587f153296bb6d0b0f1.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 391, + 144, + 438, + 153 + ], + "lines": [ + { + "bbox": [ + 391, + 144, + 438, + 153 + ], + "spans": [ + { + "bbox": [ + 391, + 144, + 438, + 153 + ], + "type": "text", + "content": "(b) t-SNE on " + }, + { + "bbox": [ + 391, + 144, + 438, + 153 + ], + "type": "inline_equation", + "content": "a_{b}" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 453, + 72, + 545, + 140 + ], + "blocks": [ + { + "bbox": [ + 453, + 72, + 545, + 140 + ], + "lines": [ + { + "bbox": [ + 453, + 72, + 545, + 140 + ], + "spans": [ + { + "bbox": [ + 453, + 72, + 545, + 140 + ], + "type": "image", + "image_path": "7517b9cec2c4f684b35dac79150f64c8f5f463f90a50865c6dd0c64fb079cbb6.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 457, + 143, + 539, + 152 + ], + "lines": [ + { + "bbox": [ + 457, + 143, + 539, + 152 + ], + "spans": [ + { + "bbox": [ + 457, + 143, + 539, + 152 + ], + "type": "text", + "content": "(c) ablation study of " + }, + { + "bbox": [ + 457, + 143, + 539, + 152 + ], + "type": "inline_equation", + "content": "A_{1}, A_{2}" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 304, + 159, + 547, + 216 + ], + "lines": [ + { + "bbox": [ + 304, + 159, + 547, + 216 + ], + "spans": [ + { + "bbox": [ + 304, + 159, + 547, + 216 + ], + "type": "text", + "content": "Figure 6. (a) and (b) show the t-SNE visualization of our unbiased representation in terms of digit (the target attribute) and color (the bias one) in Colored MNIST, respectively. (c) displays the top-300 mean accuracy of mining BC samples on Colored MNIST with " + }, + { + "bbox": [ + 304, + 159, + 547, + 216 + ], + "type": "inline_equation", + "content": "99.5\\%" + }, + { + "bbox": [ + 304, + 159, + 547, + 216 + ], + "type": "text", + "content": " BA ratio when " + }, + { + "bbox": [ + 304, + 159, + 547, + 216 + ], + "type": "inline_equation", + "content": "A_{1}" + }, + { + "bbox": [ + 304, + 159, + 547, + 216 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 159, + 547, + 216 + ], + "type": "inline_equation", + "content": "A_{2}" + }, + { + "bbox": [ + 304, + 159, + 547, + 216 + ], + "type": "text", + "content": " are changed." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 235, + 546, + 283 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 235, + 546, + 283 + ], + "spans": [ + { + "bbox": [ + 304, + 235, + 546, + 283 + ], + "type": "text", + "content": "outstanding performance. The above experiments indicate that conditional interpolation among IASs feedback the shift of the intrinsic knowledge and facilitate learning debiased representations even in extremely biased conditions." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 295, + 406, + 307 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 295, + 406, + 307 + ], + "spans": [ + { + "bbox": [ + 306, + 295, + 406, + 307 + ], + "type": "text", + "content": "4.3. Further analysis" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 315, + 547, + 386 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 315, + 547, + 386 + ], + "spans": [ + { + "bbox": [ + 304, + 315, + 547, + 386 + ], + "type": "text", + "content": "The inherent debiasing capability of prototype-based classification. We directly construct the prototype by averaging the trained representations of the vanilla model (as in Table 2 line two named “+ p”). The results show that on some datasets like Colored MNIST, the prototype-based classifier without training achieves performance improvement." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 388, + 547, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 388, + 547, + 460 + ], + "spans": [ + { + "bbox": [ + 304, + 388, + 547, + 460 + ], + "type": "text", + "content": "Visualize the test set representation on 2D embedding space via t-SNE. Figure 6 shows the 2D projection of the feature extracted by " + }, + { + "bbox": [ + 304, + 388, + 547, + 460 + ], + "type": "inline_equation", + "content": "\\chi^2" + }, + { + "bbox": [ + 304, + 388, + 547, + 460 + ], + "type": "text", + "content": "-model on Colored MNIST. We color the target and bias attributes separately. The representations follow the target attribute to cluster into classes which indicates that our model learns the debiased representations." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 461, + 547, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 461, + 547, + 533 + ], + "spans": [ + { + "bbox": [ + 304, + 461, + 547, + 533 + ], + "type": "text", + "content": "Ablation studies. We further perform the ablation analysis of the matching factors " + }, + { + "bbox": [ + 304, + 461, + 547, + 533 + ], + "type": "inline_equation", + "content": "A_{1}, A_{2}" + }, + { + "bbox": [ + 304, + 461, + 547, + 533 + ], + "type": "text", + "content": " in Eq. 3, which directly determine the " + }, + { + "bbox": [ + 304, + 461, + 547, + 533 + ], + "type": "inline_equation", + "content": "\\chi" + }, + { + "bbox": [ + 304, + 461, + 547, + 533 + ], + "type": "text", + "content": "-shape curves. The results show the first stage of " + }, + { + "bbox": [ + 304, + 461, + 547, + 533 + ], + "type": "inline_equation", + "content": "\\chi^2" + }, + { + "bbox": [ + 304, + 461, + 547, + 533 + ], + "type": "text", + "content": "-model is robust to changes in hyperparameters. For more related experiments like on different BC identification thresholds, please see the supplementary material." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 548, + 378, + 560 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 548, + 378, + 560 + ], + "spans": [ + { + "bbox": [ + 306, + 548, + 378, + 560 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 570, + 547, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 547, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 547, + 665 + ], + "type": "text", + "content": "Although intra-class biased samples with a \"hollow\" structure impede learning debiased representations, we propose the " + }, + { + "bbox": [ + 304, + 570, + 547, + 665 + ], + "type": "inline_equation", + "content": "\\chi^2" + }, + { + "bbox": [ + 304, + 570, + 547, + 665 + ], + "type": "text", + "content": "-model to leverage Intermediate Attribute Samples (IASs) to remodel the representation compactness. " + }, + { + "bbox": [ + 304, + 570, + 547, + 665 + ], + "type": "inline_equation", + "content": "\\chi^2" + }, + { + "bbox": [ + 304, + 570, + 547, + 665 + ], + "type": "text", + "content": "-model works in a two-stage manner, matching and ranking possible IASs based on their " + }, + { + "bbox": [ + 304, + 570, + 547, + 665 + ], + "type": "inline_equation", + "content": "\\chi" + }, + { + "bbox": [ + 304, + 570, + 547, + 665 + ], + "type": "text", + "content": "-shape training dynamics followed by a " + }, + { + "bbox": [ + 304, + 570, + 547, + 665 + ], + "type": "inline_equation", + "content": "\\chi" + }, + { + "bbox": [ + 304, + 570, + 547, + 665 + ], + "type": "text", + "content": "-branch metric-based debiasing objective with conditional attribute interpolation." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "content": "Acknowledgments. This research was supported by NSFC (61773198,61921006,62006112), Collaborative Innovation Center of Novel Software Technology and Industrialization, NSF of Jiangsu Province (BK20200313)." + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7606" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 714 + ], + "type": "list", + "angle": 0, + "index": 17, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "text", + "content": "[1] Vedika Agarwal, Rakshith Shetty, and Mario Fritz. 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In ICCV, pages 14982-14992, 2021. 3" + } + ] + } + ], + "index": 27 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7608" + } + ] + } + ], + "index": 29 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Learning Decorrelated Representations Efficiently Using Fast Fourier Transform/2745a979-d548-4430-88ec-679e29ec0301_content_list.json b/2023/Learning Decorrelated Representations Efficiently Using Fast Fourier Transform/2745a979-d548-4430-88ec-679e29ec0301_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..98e63d71fbaeb85ca0101b0cbd45d612309f7fe3 --- /dev/null +++ b/2023/Learning Decorrelated Representations Efficiently Using Fast Fourier Transform/2745a979-d548-4430-88ec-679e29ec0301_content_list.json @@ -0,0 +1,1798 @@ +[ + { + "type": "text", + "text": "Learning Decorrelated Representations Efficiently Using Fast Fourier Transform", + "text_level": 1, + "bbox": [ + 230, + 130, + 738, + 174 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Yutaro Shigeto* Masashi Shimbo* Yuya Yoshikawa Akikazu Takeuchi {shigeto, shimbo, yoshikawa, takeuchi}@staircenter STAIR Lab, Chiba Institute of Technology, Narashino, Chiba, Japan", + "bbox": [ + 189, + 203, + 781, + 257 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 291, + 313, + 306 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Barlow Twins and VICReg are self-supervised representation learning models that use regularizers to decorrelate features. Although these models are as effective as conventional representation learning models, their training can be computationally demanding if the dimension $d$ of the projected embeddings is high. As the regularizers are defined in terms of individual elements of a cross-correlation or covariance matrix, computing the loss for $n$ samples takes $O(nd^2)$ time. In this paper, we propose a relaxed decorrelating regularizer that can be computed in $O(nd\\log d)$ time by Fast Fourier Transform. We also propose an inexpensive technique to mitigate undesirable local minima that develop with the relaxation. The proposed regularizer exhibits accuracy comparable to that of existing regularizers in downstream tasks, whereas their training requires less memory and is faster for large $d$ . The source code is available. $^1$", + "bbox": [ + 73, + 323, + 473, + 565 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 595, + 209, + 611 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Self-supervised learning (SSL) of representations [1, 3-5, 10, 13, 15, 27-30] has become an integral part of deep learning applications in computer vision. Most SSL models for visual representations employ a multi-view, Siamese network architecture. First, an input image is altered by different transformations that preserve its original semantics. The two augmented examples are then fed to a neural network (or in some cases, two different networks) that consists of a backbone network cascaded with a small projection network (usually a multi-layer perceptron) to produce \"twin\" projected embeddings, or views, of the original. Finally, the network weights are trained so that the twin embeddings (referred to as a \"positive pair\") are similar, reflecting the fact that they represent the same original image. After training, the projection network is discarded, while the backbone network is reused for down", + "bbox": [ + 73, + 621, + 470, + 864 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "stream tasks; the idea is that the pretrained backbone should produce generic representations of images that also benefit downstream tasks.", + "bbox": [ + 500, + 292, + 890, + 337 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "One major issue in SSL is to sidestep collapsed embeddings, or the presence of trivial solutions such that all examples are projected to a single embedding vector. Contrastive approaches [3, 4, 15, 27, 28] eliminate such solutions by a loss term that repels embeddings of different original images (known as \"negative pairs\") from each other. Considering all possible negative pairs is infeasible, and negative sampling is usually performed.", + "bbox": [ + 496, + 337, + 892, + 458 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recent studies have explored non-contrastive SSL models. Among these models, Barlow Twins [29] and VICReg [1] use loss functions to penalize features (components of embedding vectors) with a small variance, which are characteristic of collapsed embeddings. Also notable in these loss functions are regularization terms for feature decorrelation. They reduce redundancy in the learned features and make Barlow Twins and VICReg perform as well as contrastive models. However, since the regularizers are defined in terms of elements in a sample cross-correlation or covariance matrix, they require $O(nd^2)$ time to compute, where $n$ is the number of examples in a batch, and $d$ is the dimensionality of the projected embeddings. This is problematic, as an increased $d$ has been reported to improve the performance of both Barlow Twins and VICReg [1, 29].", + "bbox": [ + 496, + 458, + 893, + 685 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Contributions. We propose a relaxed decorrelating regularizer to address the inefficiency of Barlow Twins and VICReg. The proposed regularizer does not require the explicit calculation of cross-correlation or covariance matrices and can be computed in $O(nd\\log d)$ time by means of Fast Fourier Transform (FFT) [7]. Although undesirable local minima develop as a result of relaxation, they can be mitigated by feature permutation; we give an account of why this simple technique works. The SSL models using the proposed regularizer achieve competitive performance with Barlow Twins and VICReg in downstream tasks, with substantially less computation time for large $d$ . With $d = 8192$ , training is 1.2 (with a ResNet-50 backbone) or 2.2 (with a", + "bbox": [ + 496, + 703, + 893, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Equal contribution.", + "bbox": [ + 94, + 875, + 205, + 886 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "$^{1}$ https://github.com/yutaro-s/scalable-decorrelation-ssl.git", + "bbox": [ + 96, + 886, + 441, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "2052", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "lightweight ResNet-18 backbone) times as fast as Barlow Twins. The proposed method also reduces memory consumption, which allows for larger batch size.", + "bbox": [ + 75, + 90, + 468, + 137 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Notation. We use zero-based indexing for vector and matrix components unless stated otherwise; thus, for a vector $\\mathbf{x} \\in \\mathbb{R}^d$ , the component index ranges from 0 to $d - 1$ . We use $[\\mathbf{x}]_i$ to denote the $i$ th component of vector $\\mathbf{x}$ , and $[\\mathbf{M}]_{ij}$ to denote the $(i,j)$ th element of matrix $\\mathbf{M}$ . For a complex vector $\\mathbf{c}$ , $\\bar{\\mathbf{c}}$ denotes its componentwise complex conjugate. For vectors $\\mathbf{x}$ and $\\mathbf{y}$ , $\\mathbf{x} \\circ \\mathbf{y}$ denotes their componentwise product.", + "bbox": [ + 75, + 155, + 470, + 261 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 275, + 218, + 290 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Contrastive SSL. Contrastive SSL uses positive and negative pairs of augmented samples [3, 4, 6, 9, 15, 24, 27, 28]. The commonly used InfoNCE loss [27] consists of an alignment term, which maximizes the similarity between positive pairs, and a uniformity term, which minimizes the similarity between negative pairs [28]. SimCLR [3] is a state-of-the-art contrastive SSL method. However, to obtain effective representations, SimCLR requires a large number of negative pairs [3], or, in other words, a large batch (or memory bank) size $n$ . This can be a computational bottleneck, as the loss computation of SimCLR takes $O(n^{2}d)$ time where $d$ is the dimensionality of the projected embeddings.", + "bbox": [ + 75, + 300, + 470, + 481 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Non-contrastive SSL Using Asymmetric Architecture. Recently, researchers have started exploring non-contrastive approaches to SSL, i.e., those that do not use negative pairs for training. To overcome collapsed embeddings, models such as BYOL [13] and SimSiam [5] introduce asymmetry in the architecture, e.g., by suppressing gradient updates and/or using the moving average of network parameters for one branch of the Siamese network. These methods are heuristically motivated, as collapsed embeddings are not explicitly penalized; however, they are effective in practice.", + "bbox": [ + 75, + 500, + 468, + 667 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Non-contrastive SSL by Decorating Regularization. A line of work exists that maintains a standard (symmetric) Siamese network but introduces loss functions to suppress collapsed embeddings. These loss functions also have regularization terms to promote feature decorrelation. Barlow Twins [29] is the first method in this line. It uses a decorrelating regularizer based on cross-correlation across two views. VICReg [1] uses regularizers that are defined in terms of covariance matrices of individual views. We review these methods in detail in Sec. 3.", + "bbox": [ + 75, + 685, + 467, + 835 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Non-contrastive SSL by Whitening. Some authors [10, 18] have used whitening to explicitly decorrelate features during training, as opposed to performing regularization.", + "bbox": [ + 75, + 854, + 468, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Subsequent work [30] whitened both features and instances. Because the whitening procedures used in these approaches require the computation of all the eigenvalues of the covariance matrices, a training epoch takes $O(\\min (dn^2, nd^2))$ time, which is inefficient with large $d$ or $n$ .", + "bbox": [ + 496, + 90, + 890, + 167 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Use of Convolution in Machine Learning. Convolution is the fundamental building block of convolution neural networks (CNNs). CNNs take (linear) convolution of input vectors with small learnable kernels to extract local features. Although FFT reduces the asymptotic complexity of convolution computation, it is seldom used with CNNs, because the size of kernels is typically too small to benefit from speed-up by FFT. In contrast to CNNs, we use (circular) convolution to compute summary statistics of covariance and cross-correlation matrices.", + "bbox": [ + 496, + 184, + 890, + 334 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In other areas of machine learning, circular convolution and its non-commutative analogue, circular correlation, have been used for implementing associative memory [2,20,22]. The idea has recently been applied to knowledge graph embeddings (KGEs) [19], with the resulting model later shown [14] to be isomorphic to complex-valued KGEs [25] by means of the convolution theorem.", + "bbox": [ + 496, + 335, + 890, + 441 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. SSL Using Decorating Regularizers", + "text_level": 1, + "bbox": [ + 498, + 454, + 843, + 472 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "This section reviews Barlow Twins [29] and VICReg [1]. Given a batch of $n$ original training examples, these models apply two randomly chosen transformations to each example. The transformed examples are then processed independently by a neural network to produce twin embeddings (views) of the original. Let $\\mathbf{a}^{(k)}, \\mathbf{b}^{(k)} \\in \\mathbb{R}^d$ denote the twin embeddings thus obtained for the $k$ th example, and let $\\mathrm{A} = \\{\\mathbf{a}^{(k)}\\}_{k=1}^n$ , $\\mathrm{B} = \\{\\mathbf{b}^{(k)}\\}_{k=1}^n$ be the sets of embeddings for individual views. Given these embeddings, the network is trained to minimize the loss function specific to each model.", + "bbox": [ + 496, + 479, + 890, + 631 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Barlow Twins. Barlow Twins optimizes the loss function defined in terms of the cross-correlation matrix $\\mathbf{C}(\\mathbf{A},\\mathbf{B})\\in$ $\\mathbb{R}^{d\\times d}$ between views A and B:", + "bbox": [ + 496, + 650, + 890, + 694 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\mathrm {B T}} = \\sum_ {i = 0} ^ {d - 1} (1 - [ \\mathbf {C} (\\mathrm {A}, \\mathrm {B}) ] _ {i i}) ^ {2} + \\lambda R _ {\\text {o f f}} (\\mathbf {C} (\\mathrm {A}, \\mathrm {B})), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 524, + 702, + 890, + 744 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "where hyperparameter $\\lambda \\geq 0$ controls the strength of regularization, and $R_{\\mathrm{off}}:\\mathbb{R}^{d\\times d}\\to \\mathbb{R}$ is a regularizer function defined as", + "bbox": [ + 496, + 753, + 890, + 797 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\nR _ {\\text {o f f}} (\\mathbf {M}) = \\sum_ {i = 0} ^ {d - 1} \\sum_ {j = 0 \\atop j \\neq i} ^ {d - 1} [ \\mathbf {M} ] _ {i j} ^ {2}. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 609, + 808, + 890, + 859 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The first term in Eq. (1) is minimized when the corresponding features of two views are fully correlated, i.e.,", + "bbox": [ + 496, + 869, + 890, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "2053", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "$[\\mathbf{C}(\\mathrm{A},\\mathrm{B})]_{ii} = 1$ for $i = 0,\\dots ,d - 1$ . This term can be efficiently computed in $O(nd)$ time. Regularizer $R_{\\mathrm{off}}(\\mathbf{C}(\\mathrm{A},\\mathrm{B}))$ in the second term is responsible for feature decorrelation, as it is minimized when all the off-diagonal elements in $\\mathbf{C}(\\mathrm{A},\\mathrm{B})$ are zero. For a large $d$ , $R_{\\mathrm{off}}(\\mathbf{C}(\\mathrm{A},\\mathrm{B}))$ can be a computational burden, as it takes $O(nd^2)$ time to compute due to the $d\\times d$ matrix $\\mathbf{C}(\\mathrm{A},\\mathrm{B})$ .", + "bbox": [ + 76, + 90, + 472, + 196 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "VICReg. Let $\\mathbf{K}(\\mathrm{A}),\\mathbf{K}(\\mathrm{B})\\in \\mathbb{R}^{d\\times d}$ be the covariance matrices of A and B, respectively. The VICReg loss function is", + "bbox": [ + 76, + 220, + 468, + 265 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} L _ {\\mathrm {V I C}} = \\frac {\\alpha}{n} \\sum_ {k = 1} ^ {n} \\| \\mathbf {a} ^ {(k)} - \\mathbf {b} ^ {(k)} \\| _ {2} ^ {2} \\\\ + \\frac {\\mu}{d} (R _ {\\text {v a r}} (\\mathbf {K} (\\mathrm {A})) + R _ {\\text {v a r}} (\\mathbf {K} (\\mathrm {B}))) \\\\ + \\frac {\\nu}{d} \\left(R _ {\\text {o f f}} (\\mathbf {K} (\\mathrm {A})) + R _ {\\text {o f f}} (\\mathbf {K} (\\mathrm {B}))\\right), \\tag {3} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 135, + 277, + 468, + 373 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where hyperparameters $\\alpha, \\mu, \\nu \\geq 0$ control the importance of individual terms, and $R_{\\mathrm{var}}$ is the regularizer defined as", + "bbox": [ + 76, + 385, + 468, + 415 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nR _ {\\text {v a r}} (\\mathbf {M}) = \\sum_ {i = 0} ^ {d - 1} \\max (0, \\gamma - \\sqrt {[ \\mathbf {M} ] _ {i i}}), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 151, + 429, + 468, + 469 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "with the target standard deviation $\\gamma > 0$ . Function $R_{\\mathrm{off}}$ is the same regularizer as used in Barlow Twins (Eq. (2)), but here, it is applied to $\\mathbf{K}(\\mathbf{A})$ and $\\mathbf{K}(\\mathbf{B})$ instead of $\\mathbf{C}(\\mathbf{A}, \\mathbf{B})$ .", + "bbox": [ + 76, + 482, + 468, + 527 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The first term in Eq. (3) brings two embeddings of the same example closer. Regularizer $R_{\\mathrm{var}}$ penalizes collapsed embeddings with zero variance, whereas $R_{\\mathrm{off}}$ promotes the diversity of features by encouraging the feature covariance to be zero. The time complexity of calculating $R_{\\mathrm{off}}(\\mathbf{K}(\\mathbf{A}))$ and $R_{\\mathrm{off}}(\\mathbf{K}(\\mathbf{B}))$ is $O(nd^2)$ , identical to that of $R_{\\mathrm{off}}(\\mathbf{C}(\\mathbf{A},\\mathbf{B}))$ in Barlow Twins.", + "bbox": [ + 76, + 527, + 470, + 635 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Proposed Method", + "text_level": 1, + "bbox": [ + 76, + 651, + 250, + 667 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We propose a weaker but efficiently computable alternative to the regularizer function $R_{\\mathrm{off}}$ . In the following, our regularizer is presented in terms of cross-correlation matrix $\\mathbf{C}(\\mathbf{A},\\mathbf{B})$ , similarly to Barlow Twins. However, if applied instead to $\\mathbf{K}(\\mathbf{A})$ and $\\mathbf{K}(\\mathbf{B})$ , it produces a relaxed version of the corresponding regularization terms in the VICReg loss.", + "bbox": [ + 76, + 676, + 468, + 768 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.1. Regularizer Based on Sums of Cross-correlations", + "text_level": 1, + "bbox": [ + 76, + 781, + 468, + 810 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Recall that the Barlow Twins loss is based on the cross-correlation matrix $\\mathbf{C} = \\mathbf{C}(\\mathbf{A},\\mathbf{B})$ of two views $\\mathrm{A} = \\{\\mathbf{a}^{(k)}\\}_{k = 1}^n$ and $\\mathbf{B} = \\{\\mathbf{b}^{(k)}\\}_{k = 1}^n$ . For brevity, assume that both $A$ and $B$ are standardized. Then, we can simply write $\\mathbf{C} = (1 / (n - 1))\\sum_{k = 1}^{n}\\mathbf{a}^{(k)}\\mathbf{b}^{(k)^{\\mathrm{T}}}$ .", + "bbox": [ + 76, + 820, + 468, + 902 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/2e20bb4a5aa16d81709ed344a36120428f5186062bde9c317df86ae9e5ca7c1a.jpg", + "image_caption": [ + "Figure 1. A $3 \\times 3$ cross-correlation matrix $\\mathbf{C} = [c_{ij}]$ $(i,j = 0,1,2)$ and sumvec $(\\mathbf{C}) = [\\nu_0\\nu_1\\nu_2]^{\\mathrm{T}}$" + ], + "image_footnote": [], + "bbox": [ + 514, + 90, + 658, + 196 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\{ \\begin{array}{l} v _ {0} = c _ {0 0} + c _ {1 1} + c _ {2 2} \\\\ v _ {1} = c _ {0 1} + c _ {1 2} + c _ {2 0} \\\\ v _ {2} = c _ {0 2} + c _ {1 0} + c _ {2 1} \\end{array} \\right.\n$$\n", + "text_format": "latex", + "bbox": [ + 745, + 130, + 857, + 172 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our regularizer is defined in terms of a $d$ -dimensional \"summary\" vector of the $d \\times d$ matrix $\\mathbf{C}$ . This vector, denoted by sumvec( $\\mathbf{C}$ ), is given componentwise by", + "bbox": [ + 498, + 268, + 890, + 314 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n[ \\operatorname {s u m v e c} (\\mathbf {C}) ] _ {i} = \\sum_ {j = 0} ^ {d - 1} [ \\mathbf {C} ] _ {j, (i + j) \\bmod d}. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 573, + 325, + 890, + 367 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Note the zero-based component indices. The zeroth component $\\left[\\operatorname{sumvec}(\\mathbf{C})\\right]_0$ is the trace of $\\mathbf{C}$ . Each of the remaining $d - 1$ components corresponds to a sum of $d$ different off-diagonal elements of $\\mathbf{C}$ , with no single element appearing in two distinct sums. Thus, every element in $\\mathbf{C}$ appears exactly once in the summations in Eq. (5). The calculation of a summary vector for a $3 \\times 3$ covariance matrix is illustrated in Fig. 1.", + "bbox": [ + 498, + 378, + 890, + 500 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Now, we define a regularizer in terms of all but the zeroth component of sumvec(C):", + "bbox": [ + 498, + 500, + 890, + 531 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nR _ {\\text {s u m}} (\\mathbf {C}) = \\sum_ {i = 1} ^ {d - 1} \\| [ \\operatorname {s u m v e c} (\\mathbf {C}) ] _ {i} \\| _ {q} ^ {q}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 581, + 542, + 890, + 583 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where hyperparameter $q \\in \\{1,2\\}$ . This function $R_{\\mathrm{sum}}$ can be used as a drop-in replacement for $R_{\\mathrm{off}}$ in the Barlow Twins loss (Eq. (1)). The zeroth component $[\\mathrm{sumvec}(\\mathbf{C})]_0$ is excluded in Eq. (6), because it concerns the diagonal elements of $\\mathbf{C}$ that are irrelevant to feature decorrelation; they do not appear in Barlow Twin's regularizer $R_{\\mathrm{off}}(\\mathbf{C})$ either.", + "bbox": [ + 498, + 594, + 890, + 685 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The regularizer $R_{\\mathrm{sum}}$ is weaker than $R_{\\mathrm{off}}$ in that it imposes constraints on the components of the summary vector, or the sums of $d$ elements of $\\mathbf{C}$ , whereas $R_{\\mathrm{off}}$ constrains individual elements. Indeed, the minimizers of $R_{\\mathrm{off}}(\\mathbf{C})$ also minimize $R_{\\mathrm{sum}}(\\mathbf{C})$ , but the converse does not necessarily hold. However, as we discuss in Sec. 4.2, $R_{\\mathrm{sum}}$ allows faster computation. Furthermore, in Sec. 4.3, we provide a simple technique to mitigate the weakness of $R_{\\mathrm{sum}}$ .", + "bbox": [ + 496, + 686, + 890, + 806 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.2. Efficient Computation", + "text_level": 1, + "bbox": [ + 500, + 816, + 707, + 832 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Computing sumvec(C) by Eq. (5) requires the cross-correlation matrix $\\mathbf{C}(\\mathbf{A},\\mathbf{B})$ , whose calculation incurs the same computational cost as that of the Barlow Twins loss. However, by means of the Fourier transform, sumvec(C)", + "bbox": [ + 498, + 839, + 890, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "2054", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "can be calculated directly from the vectors in A and B without explicit calculation of their cross-correlation matrix. To this end, we use involution and circular convolution.", + "bbox": [ + 75, + 90, + 468, + 135 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For a vector $\\mathbf{x} \\in \\mathbb{R}^d$ , its involution [22] (also called flipping [23]) $\\mathrm{inv}(\\mathbf{x})$ is the vector obtained by reversing the order of its first (not the zeroth) to $(d - 1)\\mathrm{st}$ components; i.e., $[\\mathrm{inv}(\\mathbf{x})]_i = [\\mathbf{x}]_{(d - i) \\bmod d}$ for $i = 0, \\ldots, d - 1$ .", + "bbox": [ + 75, + 136, + 467, + 196 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For vectors $\\mathbf{x},\\mathbf{y}\\in \\mathbb{R}^d$ , their circular convolution $\\mathbf{x}*\\mathbf{y}$ is a $d$ -dimensional vector with components given as", + "bbox": [ + 76, + 196, + 467, + 226 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left[ \\mathbf {x} * \\mathbf {y} \\right] _ {i} = \\sum_ {j = 0} ^ {d - 1} \\left[ \\mathbf {x y} ^ {\\mathrm {T}} \\right] _ {j, (i - j) \\bmod d}. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 160, + 237, + 467, + 280 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As a result, circular convolution is known as the \"compressed outer product.\"", + "bbox": [ + 76, + 291, + 467, + 319 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Now, for each twin embedding pair $\\mathbf{a}^{(k)}\\in \\mathrm{A}$ and $\\mathbf{b}^{(k)}\\in$ $\\mathbf{B}(k = 1,\\dots ,n)$ , let us consider vector $\\operatorname {inv}(\\mathbf{a}^{(k)})*\\mathbf{b}^{(k)}\\in$ $\\mathbb{R}^d$ . Noting the indices altered by involution, we see that this vector is given componentwise by", + "bbox": [ + 76, + 319, + 467, + 380 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left[ \\operatorname {i n v} \\left(\\mathbf {a} ^ {(k)}\\right) * \\mathbf {b} ^ {(k)} \\right] _ {i} = \\sum_ {j = 0} ^ {d - 1} \\left[ \\mathbf {a} ^ {(k)} \\mathbf {b} ^ {(k) ^ {\\mathrm {T}}} \\right] _ {j, (i + j) \\bmod d}. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 96, + 392, + 467, + 434 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Substituting $\\mathbf{C} = (1 / (n - 1))\\sum_{k = 1}^{n}\\mathbf{a}^{(k)}\\mathbf{b}^{(k)^{\\mathrm{T}}}$ into Eq. (5) and using Eq. (8), we have", + "bbox": [ + 76, + 446, + 467, + 479 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} [ \\operatorname {s u m v e c} (\\mathbf {C}) ] _ {i} = \\sum_ {j = 0} ^ {d - 1} \\overbrace {\\left[ \\frac {1}{n - 1} \\sum_ {k = 1} ^ {n} \\mathbf {a} ^ {(k)} \\mathbf {b} ^ {(k) ^ {\\mathrm {T}}} \\right] _ {j , (i + j) \\bmod d}} ^ {\\mathbf {c}} \\\\ = \\frac {1}{n - 1} \\sum_ {k = 1} ^ {n} \\sum_ {j = 0} ^ {d - 1} \\left[ \\mathbf {a} ^ {(k)} \\mathbf {b} ^ {(k) ^ {\\mathrm {T}}} \\right] _ {j, (i + j) \\bmod d} \\\\ = \\frac {1}{n - 1} \\sum_ {k = 1} ^ {n} \\left[ \\operatorname {i n v} \\left(\\mathbf {a} ^ {(k)}\\right) * \\mathbf {b} ^ {(k)} \\right] _ {i}, \\tag {9} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 91, + 491, + 468, + 643 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "or, as a vector,", + "bbox": [ + 76, + 654, + 174, + 666 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {s u m v e c} (\\mathbf {C}) = \\frac {1}{n - 1} \\sum_ {k = 1} ^ {n} \\operatorname {i n v} \\left(\\mathbf {a} ^ {(k)}\\right) * \\mathbf {b} ^ {(k)}. \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 135, + 676, + 467, + 715 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Let $\\mathcal{F}$ and $\\mathcal{F}^{-1}$ denote the discrete Fourier transform and inverse discrete Fourier transform, respectively. Noting that $\\mathcal{F}(\\mathrm{inv}(\\mathbf{x})) = \\overline{\\mathcal{F}(\\mathbf{x})}$ for any $\\mathbf{x} \\in \\mathbb{R}^d$ (see e.g., [23], Section 7.4.2) and using the convolution theorem $\\mathcal{F}(\\mathbf{x} * \\mathbf{y}) = \\mathcal{F}(\\mathbf{x}) \\circ \\mathcal{F}(\\mathbf{y})$ , we have", + "bbox": [ + 76, + 728, + 467, + 805 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {i n v} \\left(\\mathbf {a} ^ {(k)}\\right) * \\mathbf {b} ^ {(k)} = \\mathcal {F} ^ {- 1} \\left(\\overline {{\\mathcal {F} \\left(\\mathbf {a} ^ {(k)}\\right)}} \\circ \\mathcal {F} \\left(\\mathbf {b} ^ {(k)}\\right)\\right). \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 109, + 816, + 467, + 840 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Substituting Eq. (11) into Eq. (10), we obtain", + "bbox": [ + 500, + 90, + 799, + 106 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\operatorname {s u m v e c} (\\mathbf {C}) = \\frac {1}{n - 1} \\sum_ {k = 1} ^ {n} \\overbrace {\\mathcal {F} ^ {- 1} \\left(\\overline {{\\mathcal {F} \\left(\\mathbf {a} ^ {(k)}\\right)}} \\circ \\mathcal {F} \\left(\\mathbf {b} ^ {(k)}\\right)\\right)} ^ {\\operatorname {i n v} \\left(\\mathbf {a} ^ {(k)}\\right) * \\mathbf {b} ^ {(k)}} \\\\ = \\frac {1}{n - 1} \\mathcal {F} ^ {- 1} \\left(\\sum_ {k = 1} ^ {n} \\overline {{\\mathcal {F} (\\mathbf {a} ^ {(k)})}} \\circ \\mathcal {F} (\\mathbf {b} ^ {(k)})\\right). \\tag {12} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 116, + 888, + 218 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Using this equation, we can compute sumvec(C) directly from the embedding vectors $\\{\\mathbf{a}^{(k)},\\mathbf{b}^{(k)}\\}_{k = 1}^{n}$ , bypassing the cumbersome calculation of C. Noting that the (inverse) Fourier transform of a $d$ -dimensional vector can be performed in $O(d\\log d)$ time by the FFT algorithm, while the calculation of complex conjugates, component products, and the sum of $n$ vectors takes $O(nd)$ time, we can see that the overall time to obtain sumvec(C) is $O(nd\\log d)$ , which is also the time needed to compute $R_{\\mathrm{sum}}(\\mathbf{C})$ . This is a substantial improvement over the $O(nd^2)$ computation time of $R_{\\mathrm{off}}(\\mathbf{C})$ in the Barlow Twins loss.", + "bbox": [ + 496, + 227, + 890, + 392 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Furthermore, the space complexity of computing $R_{\\mathrm{sum}}(\\mathbf{C})$ is $O(nd)$ , which is optimal if the $O(nd)$ space needed to store input vectors A and B is considered as part of the complexity. In contrast, Barlow Twins requires extra $O(d^2)$ space to store C.", + "bbox": [ + 498, + 393, + 890, + 468 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.3. Feature Permutation to Mitigate Undesirable Local Minima", + "text_level": 1, + "bbox": [ + 498, + 478, + 890, + 507 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As seen from Eq. (5), the components of sumvec(C) are the sums of $d$ elements in C, and the proposed regularizer $R_{\\mathrm{sum}}$ (Eq. (6)) encourages these sums to be close to zero. This is weaker than the regularizer $R_{\\mathrm{off}}$ (Eq. (2)) in the Barlow Twins loss, which pushes individual elements of C towards zero. Indeed, $R_{\\mathrm{sum}}(\\mathbf{C})$ can be close to zero even if individual elements in C are not; the summands in Eq. (5) can cancel each other, since they can be either positive or negative. As a result, undesirable local minima develop in the parameter space, rendering our regularizer ineffective.", + "bbox": [ + 496, + 516, + 890, + 667 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Here, we propose a technique to eliminate these local minima: we randomly permute feature indices during training so that sums of different cross-correlation terms constitute sumvec(C). To understand why this simple technique is effective, consider minimizing $R_{\\mathrm{sum}}(\\mathbf{C})$ , regarding the elements of C as independent3 variables. It is easy to see that the minimum is attained by the solutions to a homogeneous system of linear equations:", + "bbox": [ + 496, + 667, + 890, + 787 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\overbrace {\\sum_ {j = 0} ^ {d - 1} [ \\mathbf {C} ] _ {j , (i + j) \\bmod d}} ^ {\\left[ \\operatorname {s u m v e c} (\\mathbf {C}) \\right] _ {i}} = 0, \\qquad \\text {f o r} i = 1, \\dots , d - 1.\n$$\n", + "text_format": "latex", + "bbox": [ + 531, + 797, + 856, + 864 + ], + "page_idx": 3 + }, + { + "type": "page_footnote", + "text": "2The vector $\\mathrm{inv}(\\mathbf{x})*\\mathbf{y}$ is known as the circular (cross-)correlation of $\\mathbf{x}$ and $\\mathbf{y}$ [20, 22, 23]. We opt not to use this term in this paper to avoid confusion with the cross-correlation of random vectors, which is used in Barlow Twins.", + "bbox": [ + 75, + 849, + 468, + 898 + ], + "page_idx": 3 + }, + { + "type": "page_footnote", + "text": "3This assumption is not unrealistic given the high capacity of modern neural networks.", + "bbox": [ + 500, + 875, + 890, + 898 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "2055", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "This is an underdetermined system, with only $d - 1$ equations but with $d(d - 1)$ unknowns, namely, $[\\mathbf{C}]_{j\\ell}, j, \\ell = 0, \\dots, d - 1, j \\neq \\ell$ . This underdeterminacy is the cause of nontrivial solutions such that $[\\mathbf{C}]_{j\\ell} \\neq 0$ , that is, undesirable solutions in which summands with opposite signs cancel each other in an equation.", + "bbox": [ + 75, + 90, + 468, + 181 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Now, by repeatedly permuting the feature indices and minimizing the loss, we effectively introduce additional equations to the system, since permutation can produce different sets of linear equations over the unknowns, and these new constraints eventually render nontrivial solutions inadmissible.", + "bbox": [ + 75, + 181, + 470, + 271 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For ease of implementation, we permute feature indices randomly during training, instead of generating all permutations systematically at once, similarly to the way that stochastic gradient descent is a modification to full gradient descent. Note that the permuted feature indices need not be identical across mini-batches, even within a single epoch; indeed, in the experiments presented in Sec. 5, we use a different random permutation of features in every mini-batch in every epoch.", + "bbox": [ + 75, + 272, + 470, + 407 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.4. Feature Grouping to Control the Degree of Relaxation", + "text_level": 1, + "bbox": [ + 76, + 417, + 468, + 446 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Instead of computing a summary vector for an entire cross-correlation matrix $\\mathbf{C}$ , we can compute summaries at a more fine-grained level. Specifically, we partition $d$ features into groups of size $b$ each4. This partitioning induces in $\\mathbf{C}$ a total of $\\lceil d / b \\rceil^2$ block submatrices of size $b \\times b$ , i.e., $\\mathbf{C} = [\\mathbf{C}_{ij}](i,j = 1,\\dots,\\lceil d / b \\rceil)$ with submatrices $\\mathbf{C}_{ij} \\in \\mathbb{R}^{b \\times b}$ . We then define the regularizer as", + "bbox": [ + 75, + 455, + 470, + 561 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} R _ {\\operatorname {s u m}} ^ {(b)} (\\mathbf {C}) = \\sum_ {i = 1} ^ {\\lceil d / b \\rceil} \\sum_ {\\ell = 1} ^ {b - 1} \\| [ \\operatorname {s u m v e c} (\\mathbf {C} _ {i i}) ] _ {\\ell} \\| _ {q} ^ {q} \\\\ + \\sum_ {\\substack {i, j = 1 \\\\ i \\neq j}} ^ {\\lceil d / b \\rceil} \\sum_ {\\ell = 0} ^ {b - 1} \\left\\| \\left[ \\operatorname {sumvec} \\left(\\mathbf{C}_{ij}\\right) \\right] _ {\\ell} \\right\\| _ {q} ^ {q}. \\tag{13} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 104, + 573, + 468, + 670 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As before, $\\mathrm{sumvec}(\\mathbf{C}_{ij})$ can be computed without explicitly computing $\\mathbf{C}_{ij}$ by means of involution, circular convolution (of subvectors of embeddings), and the Fourier transform. Calculating a single $\\mathrm{sumvec}(\\mathbf{C}_{ij})$ takes $O(nb\\log b)$ time using FFT, and since there are $\\lceil d / b\\rceil^2$ blocks, the total time needed to compute $R_{\\mathrm{sum}}^{(b)}$ is $O((nd^2 /b)\\log b)$ .", + "bbox": [ + 75, + 681, + 468, + 787 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The block size hyperparameter $b$ controls the granularity of the summary computation and interpolates the proposed and existing regularizers. On one hand, the regularizer $R_{\\mathrm{sum}}^{(1)}(\\mathbf{C})$ reduces $R_{\\mathrm{off}}(\\mathbf{C})$ of Barlow Twins when $b = 1$ , provided that $q = 2$ . On the other hand, when $b = d$ , we", + "bbox": [ + 75, + 789, + 468, + 866 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "recover $R_{\\mathrm{sum}}^{(d)}(\\mathbf{C}) = R_{\\mathrm{sum}}(\\mathbf{C})$ given in Eq. (6). Thus, this grouping formulation provides a generalization of Barlow Twins, with parameter $b$ controlling the trade-off between the computational efficiency and the degree of relaxed regularization. Empirically, the performance can be slightly improved by the use of a feature group of moderate size, with no substantial degradation observed in training time and memory usage; see Sec. 5.", + "bbox": [ + 496, + 89, + 890, + 210 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "It should be noted that the permutation and grouping of features are compatible and can be combined.", + "bbox": [ + 498, + 212, + 890, + 242 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.5. Regularizer Based on Sums of Feature Covariances", + "text_level": 1, + "bbox": [ + 498, + 250, + 890, + 280 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The function $R_{\\mathrm{sum}}$ can also be used to define a VICReg-style regularizer based on covariance, simply by replacing $R_{\\mathrm{off}}$ with $R_{\\mathrm{sum}}$ in Eq. (3), and passing correlation matrices $\\mathbf{K}(\\mathbf{A})$ or $\\mathbf{K}(\\mathbf{B})$ instead of $\\mathbf{C}(\\mathbf{A}, \\mathbf{B})$ as the argument. Fast computation is possible with FFT, and the grouping version is also straightforward; this is described in greater detail in Supplementary Material.", + "bbox": [ + 498, + 287, + 890, + 393 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.6. Summary of Proposed Models", + "text_level": 1, + "bbox": [ + 500, + 402, + 767, + 417 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The loss functions of the proposed models are summarized below. Let the function $R = R_{\\mathrm{sum}}^{(b)}$ if feature grouping is used with block size $b$ , or let $R = R_{\\mathrm{sum}}$ if grouping is not used.", + "bbox": [ + 498, + 426, + 890, + 484 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For Barlow Twins-style cross-correlation regularization, the loss function is", + "bbox": [ + 498, + 487, + 890, + 516 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL = \\sum_ {i} (1 - [ \\mathbf {C} (\\mathrm {A}, \\mathrm {B}) ] _ {i i}) ^ {2} + \\lambda R (\\mathbf {C} (\\mathrm {A}, \\mathrm {B})), \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 503, + 523, + 890, + 554 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "whereas for VICReg-style covariance regularization, we use", + "bbox": [ + 500, + 561, + 890, + 577 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} L = \\frac {\\alpha}{n} \\sum_ {i} \\| \\mathbf {a} ^ {(i)} - \\mathbf {b} ^ {(i)} \\| _ {2} ^ {2} + \\frac {\\mu}{d} \\left(R _ {\\text {v a r}} (\\mathbf {K} (\\mathbf {A})) + R _ {\\text {v a r}} (\\mathbf {K} (\\mathbf {B}))\\right) \\\\ + \\frac {\\nu}{d} (R (\\mathbf {K} (\\mathrm {A})) + R (\\mathbf {K} (\\mathrm {B}))). \\tag {15} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 504, + 583, + 890, + 643 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Setting $R = R_{\\mathrm{off}}$ in these formulas gives the original Barlow Twins and VICReg, when hyperparameter $q = 2$ .", + "bbox": [ + 498, + 651, + 890, + 681 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 500, + 694, + 632, + 710 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We empirically evaluate the effect of the proposed regularizers. To be precise, we train SSL models using the Barlow Twins-style loss function of Eq. (14) and the VICReg-style loss function of Eq. (15) and compare their performance with Barlow Twins and VICReg in downstream tasks. The training time and memory consumption are also evaluated. For our models, feature permutation is performed in every batch iteration except for the ablation study.", + "bbox": [ + 496, + 719, + 890, + 839 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In the following, we briefly present the tasks and datasets used in the experiments. See Supplementary Material for the complete experimental setup, including the hyperparameter values and the results of additional experiments.", + "bbox": [ + 496, + 840, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_footnote", + "text": "4If $d$ is not divisible by $b$ , pad dummy features that are constantly 0 in the last group.", + "bbox": [ + 75, + 875, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "2056", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/ae7b25bbb499f12e5d317662540f46ef8141b874ac4c2e752b9c85aa6a031005.jpg", + "table_caption": [ + "Table 1. Linear evaluation accuracy (\\%) on ImageNet-100 with $d = 2048$ . Bold numbers indicate the best performance within each family (cross-correlation regularization, covariance regularization, or other SSL models). †: quoted from the solo-learn [26] GitHub repository as of December 28, 2022; ‡: quoted from [30]." + ], + "table_footnote": [], + "table_body": "
ModelTop-1Top-5
Barlow Twins†80.1695.14
Barlow Twins80.1295.24
Proposed (Barlow Twins-style; no grouping)79.9494.76
Proposed (Barlow Twins-style; b = 128)81.0295.24
VICReg†79.4095.02
VICReg79.3094.30
Proposed (VICReg-style; no grouping)79.2094.96
Proposed (VICReg-style; b = 128)80.0494.98
W-MSE† [10]69.0691.22
Zero-FCL‡ [30]79.3294.94
Zero-CL‡ [30]79.2694.98
NNCLR† [9]80.1695.30
BYOL† [13]80.3294.94
MoCo V3† [6]80.3694.96
", + "bbox": [ + 93, + 170, + 452, + 383 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Tasks and Datasets", + "text_level": 1, + "bbox": [ + 76, + 410, + 261, + 425 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Models are pretrained with images in the ImageNet dataset [8] or its subset, ImageNet-100 [24], depending on the experiment. ResNet-50 [16] is used as the backbone for ImageNet, while ResNet-18 is used for ImageNet-100.", + "bbox": [ + 75, + 433, + 468, + 494 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To evaluate downstream SSL performance, we follow the standard linear evaluation protocol: After the backbone network is pretrained by a SSL method, we train a linear classifier on top of the frozen backbone using labeled data from the ImageNet or ImageNet-100 training set. The resulting classifier is then evaluated by the top-1 and top-5 accuracy on the respective validation sets.", + "bbox": [ + 75, + 494, + 468, + 601 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For transfer learning evaluation, we apply the pretrained models to an object detection task on Pascal VOC07+12 [11]. Following previous studies [1, 15, 29], we use the trainval set of VOC2007 and VOC2012 for training and the test split of VOC2007 for testing. We fine-tune Faster R-CNN [21] with R50-C4. Models are evaluated by three types of average precision (AP): AP, $\\mathrm{AP}_{50}$ , and $\\mathrm{AP}_{75}$ , where $\\mathrm{AP}_x$ signifies the intersection-over-union (IoU) threshold of $x\\%$ . We report the average scores over five trials.", + "bbox": [ + 75, + 601, + 470, + 738 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Results and Discussion", + "text_level": 1, + "bbox": [ + 76, + 748, + 290, + 763 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Linear evaluation on ImageNet-100. Tab. 1 presents the results. We can see that the accuracy of the proposed models is comparable to that of all existing models in the table, including Barlow Twins and VICReg, with or without feature grouping.", + "bbox": [ + 75, + 772, + 468, + 849 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Linear evaluation on ImageNet. Tab. 2 presents the results. Due to the high computational cost of this large-scale", + "bbox": [ + 75, + 869, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/12cc1d34e4b86ce4280c8f759a8901cdea1ced527ba6a7be31140e64cf9e7cbe.jpg", + "table_caption": [ + "Table 2. Linear evaluation accuracy (\\%) on ImageNet; highest accuracy over 100 epochs of linear head training. $d = 8192$ for the proposed model, Barlow Twins, and VICReg. †: quoted from the original papers of the respective methods; ‡: quoted from the MoCo V3 GitHub repository." + ], + "table_footnote": [], + "table_body": "
ModelEpochsTop-1Top-5
Barlow Twins†100073.291.0
Barlow Twins100072.490.6
Proposed (Barlow Twins-style; no grouping)100073.091.2
Proposed (Barlow Twins-style; b = 128)100073.291.3
VICReg†100073.291.1
VICReg100072.690.9
Proposed (VICReg-style; no grouping)100072.891.1
W-MSE 4† [10]40072.6—
Zero-CL† [30]40072.690.5
SimCLR† [3]100069.389.0
NNCLR† [9]100075.492.3
BYOL† [13]100074.391.6
MoCo V3‡ [6]100074.6—
", + "bbox": [ + 503, + 170, + 888, + 372 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/a500cf19dd3895f7fb543290c47f07265dc0fc8b654df11d54ec291d0fbc92e1.jpg", + "table_caption": [ + "Table 3. Results of transfer learning for object detection on VOC07+12. †: quoted from original papers; ‡: quoted from [15]." + ], + "table_footnote": [], + "table_body": "
ModelAP50APAP75
Supervised‡81.353.558.8
Barlow Twins†82.656.863.4
Proposed (Barlow Twins-style; no grouping)82.555.061.1
VICReg†82.4——
Proposed (VICReg-style; no grouping)82.356.162.1
", + "bbox": [ + 501, + 425, + 890, + 529 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "experiment, we do not evaluate feature grouping with the VICReg-style regularization. The proposed models perform slightly worse than NNCLR, BYOL, and MoCo V3, but have comparable performance to that of Barlow Twins and VICReg.", + "bbox": [ + 496, + 555, + 893, + 631 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Transfer learning evaluation on Pascal VOC object detection. Tab. 3 presents the results of transfer learning. Again, the proposed models demonstrate performance comparable to that of Barlow Twins and VICReg.", + "bbox": [ + 496, + 650, + 890, + 712 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Training time on ImageNet. Tab. 4 presents the training time over 1000 epochs on ImageNet. We tested two situations: training using 8 and 4 GPUs. In both situations, we set the per GPU batch size to 128, which leads to the effective batch size of 1024 for 8 GPUs and 512 for 4 GPUs. As indicated in Tab. 4, the accuracy of the proposed model is comparable to that of Barlow Twins, with a noticeable reduction in training time. More precise evaluation of train", + "bbox": [ + 496, + 731, + 890, + 853 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "5This experiment was conducted on a commercial cloud platform that limits a session to a maximum of three days. To finish training Barlow Twins with 8 GPUs for 1000 epochs, three sessions were required, whereas", + "bbox": [ + 498, + 862, + 893, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "2057", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/b44c9cc292c6865ed21f789cf761b513488cae597949341d521d3884daddcba9.jpg", + "table_caption": [ + "Table 4. Linear evaluation accuracy (\\%) and the total training time on ImageNet with ResNet-50 backbone ( $d = 8192$ ). The per GPU batch size is 128. Proposed refers to the proposed method using the Barlow Twins-style regularizer without grouping. Barlow Twins* refers to the results quoted from [29, Figure 2]." + ], + "table_footnote": [], + "table_body": "
# GPUs (Batch size)ModelTop-1Top-5Time
8 (1024)Barlow Twins*73.291.0—
Barlow Twins72.490.76d 14h 0m
Proposed73.091.35d 14h 58m
4 (512)Barlow Twins*———
Barlow Twins72.190.212d 19h 30m
Proposed72.891.210d 21h 6m
", + "bbox": [ + 83, + 169, + 464, + 277 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/62895c1f535980ecf6c66164d29d030ff2b99711dbccff2786582daa2af725bf.jpg", + "table_caption": [ + "Table 5. The effect of feature permutation: accuracy (\\%) and training time per 10 epochs (second) on ImageNet-100.", + "(a) Barlow Twins-style cross-correlation regularization" + ], + "table_footnote": [], + "table_body": "
GroupingPermutationTop-1Top-5Time
nono59.6485.201646.2
yes79.9494.761668.7
b = 128no73.5893.361697.5
yes81.0295.241709.6
", + "bbox": [ + 116, + 349, + 434, + 433 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/5c7feaa46d210331a807901e30825efa1f8bfee94686b50ea00a2281fbba8aab.jpg", + "table_caption": [ + "(b) VICReg-style covariance regularization" + ], + "table_footnote": [], + "table_body": "
GroupingPermutationTop-1Top-5Time
nono57.4284.261692.2
yes79.2094.961718.0
b = 128no66.2689.681802.1
yes80.0494.981813.3
", + "bbox": [ + 119, + 462, + 431, + 547 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ing speed is provided in the next experiment, and additional results are provided in Supplementary Material.", + "bbox": [ + 76, + 575, + 468, + 606 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Dimensionality of embeddings and computational cost.", + "text_level": 1, + "bbox": [ + 76, + 635, + 467, + 648 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Fig. 2 presents the elapsed time and the peak GPU memory allocation over 10 epochs on ImageNet-100 on a single GPU, with varying dimensionality of the projected embeddings: $d \\in \\{2048, 4096, 8192, 16384\\}$ . The improvement over Barlow Twins and VICReg becomes noticeable as $d$ is increased; at $d = 8192$ , the proposed models (without grouping) are 2.8 times as fast as VICReg, and 2.2 times as fast as Barlow Twins; while at $d = 16384$ , they are 5.7 times as fast as VICReg, and 4.0 times as fast as Barlow Twins. For both $d = 8192$ and 16384, memory consumption is reduced by more than half. See Supplementary Material for the results with the ResNet-50 backbone on multiple GPUs and the detail of forward/backward/loss computation time.", + "bbox": [ + 75, + 650, + 468, + 845 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/06a30355c7053310aef768faacbdc33bb1dff7a99c81d4cc9326b940b9d8d1e7.jpg", + "table_caption": [ + "Table 6. The regularizers of Barlow Twins and VICReg applied to the embeddings produced by the proposed models. Perm.: permutation; Diff: difference to the baselines.", + "(a) Barlow Twins-style cross-correlation regularization" + ], + "table_footnote": [], + "table_body": "
ModelGroupingPerm.Normalized Barlow Twins loss (Eq. (16))Diff
Barlow Twins——0.0050
Proposednono0.5640.559
yes0.0100.005
b = 128no0.0490.044
yes0.0090.004
", + "bbox": [ + 516, + 157, + 879, + 271 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/ee35fca641c8efb772ad3a61a9351ba81c19399f7955209e8f1e9c7d3972aec6.jpg", + "table_caption": [ + "(b) VICReg-style covariance regularization" + ], + "table_footnote": [], + "table_body": "
ModelGroupingPerm.Normalized VICReg loss (Eq. (17))Diff
VICReg——0.0020
Proposednono1.9991.997
yes0.0110.009
b = 128no0.3790.377
yes0.0070.005
", + "bbox": [ + 516, + 301, + 879, + 414 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effectiveness of feature permutation. Tab. 5 presents the effect of feature permutation on ImageNet-100 at $d = 2048$ . Regardless of whether grouping is used, the accuracy decreases significantly without permutation, suggesting that feature permutation is essential for the effectiveness of our proposed regularizer. As illustrated in the column \"Time\" in Tab. 5, the cost of permutation is negligible, even though it was performed as frequently as every batch iteration.", + "bbox": [ + 496, + 438, + 890, + 559 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We also quantitatively evaluate the degree of decorrelation obtained by feature permutation. After the proposed models are trained, we compute the normalized values of Barlow Twins' and VICReg's regularizers applied to the embeddings $A, B$ output by the proposed models, given as follows:", + "bbox": [ + 496, + 560, + 890, + 648 + ], + "page_idx": 6 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {R _ {\\text {o f f}} (\\mathbf {C} (\\mathrm {A} , \\mathrm {B}))}{d (d - 1)} \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 607, + 656, + 890, + 688 + ], + "page_idx": 6 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {R _ {\\text {o f f}} (\\mathbf {K} (\\mathrm {A})) + R _ {\\text {o f f}} (\\mathbf {K} (\\mathrm {B}))}{2 d (d - 1)} \\tag {17}\n$$\n", + "text_format": "latex", + "bbox": [ + 609, + 690, + 890, + 722 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The normalization factor $d(d - 1)$ is to make the resulting values the means over $d(d - 1)$ off-diagonal elements of $\\mathbf{K}(\\mathbf{A})$ , $\\mathbf{K}(\\mathbf{B})$ , and $\\mathbf{C}(\\mathbf{A},\\mathbf{B})$ . Since VICReg has regularization terms for $\\mathbf{K}(\\mathbf{A})$ and $\\mathbf{K}(\\mathbf{B})$ , its loss is further divided by 2. Tab. 6 presents the results on ImageNet-100 ( $d = 2048$ ). We observe that feature permutation promotes decorrelation from the point of view of the baseline loss functions.", + "bbox": [ + 496, + 731, + 890, + 835 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Impact of block size in feature grouping. To evaluate the effect of feature grouping on ImageNet-100, we fix the embedding dimension at $d = 2048$ and change the block", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_footnote", + "text": "the proposed model required two sessions. The time reported in Tab. 4 is the total run time of these sessions, which includes time (3 to 5 seconds) for reinitialization at the beginning of each session.", + "bbox": [ + 75, + 862, + 467, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "2058", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3cd714293187435b8b7b5b08b272339485223117c32f6271f194c137a4a64b3a.jpg", + "image_caption": [ + "Figure 2. Training time and memory usage on ImageNet-100 with ResNet-18 on a single GPU." + ], + "image_footnote": [], + "bbox": [ + 93, + 88, + 877, + 392 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6bddb76b3e3ce5eeb518e01b5ae48d50d449dee4f20cac63243d0a4e4c1de1f0.jpg", + "image_caption": [ + "(a) Top-1 accuracy" + ], + "image_footnote": [], + "bbox": [ + 119, + 438, + 334, + 555 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/fb065f6641478ca7630c27870e267848eba0414cef6e4d9a32b9442063cdf979.jpg", + "image_caption": [ + "(b) Elapsed training time" + ], + "image_footnote": [], + "bbox": [ + 375, + 438, + 591, + 555 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c8920ee0e4b62c47f44253eb5d370d2be719e51b2ba25cff4131730f33836079.jpg", + "image_caption": [ + "(c) Peak GPU memory allocated", + "Figure 3. The impact of the block size on ImageNet-100. The $x$ -axis indicates the block size $b$ ." + ], + "image_footnote": [], + "bbox": [ + 635, + 439, + 849, + 555 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "size $b \\in \\{2, 4, 8, \\dots, 2048\\}$ . The block size $b = d = 2048$ corresponds to no feature grouping. Figure 3 presents the result, which indicates that unless $b$ is extremely small (i.e., 8 or less), there is no significant increase in training time or GPU memory usage. Setting $b$ to a moderate size, such as $b = 128$ , improves performance.", + "bbox": [ + 75, + 632, + 470, + 724 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 76, + 739, + 194, + 753 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We have proposed a new decorrelating regularizer for non-contrastive SSL. Given $d$ -dimensional embeddings of $n$ samples, the regularizer can be computed in $O(nd\\log d)$ time, which is an improvement over the $O(nd^2)$ time required by the existing models (Barlow Twins and VICReg). The reduced memory consumption allows for a larger batch size, which in general enables more effective models to be learned. We also proposed a feature permutation technique to alleviate the weakness of our regularizer.", + "bbox": [ + 75, + 763, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "With our regularizer, the speed-up is most notable with networks with a lightweight backbone, wherein computation at the loss node takes a large part of training time. This makes our method an attractive option to use with knowledge-distilled backbones [12, 17].", + "bbox": [ + 496, + 633, + 890, + 708 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The proposed method is not limited to SSL but potentially useful to a wider range of applications that involve decorrelation. We plan to pursue this avenue in future work.", + "bbox": [ + 496, + 717, + 890, + 763 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments", + "text_level": 1, + "bbox": [ + 500, + 805, + 658, + 821 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We thank anonymous reviewers for their helpful comments. This work was partially supported by the New Energy and Industrial Technology Development Organization (NEDO) and JSPS Kakenhi Grant 19H04173.", + "bbox": [ + 496, + 839, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "2059", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 106 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Adrien Bardes, Jean Ponce, and Yann LeCun. VI-CReg: Variance-invariance-covariance regularization for self-supervised learning. In ICLR, 2022. 1, 2, 6", + "[2] A. Borsellino and T. Poggio. Convolution and correlation algebras. Kybernetik, 13(2):113-122, 1973. 2", + "[3] Ting Chen, Simon Kornblith, Mohammad Norouzi, and Geoffrey Hinton. A simple framework for contrastive learning of visual representations. 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In ICLR, 2022. 1, 2, 6" + ], + "bbox": [ + 501, + 92, + 890, + 800 + ], + "page_idx": 8 + }, + { + "type": "page_number", + "text": "2060", + "bbox": [ + 482, + 944, + 516, + 955 + ], + "page_idx": 8 + } +] \ No newline at end of file diff --git a/2023/Learning Decorrelated Representations Efficiently Using Fast Fourier Transform/2745a979-d548-4430-88ec-679e29ec0301_model.json b/2023/Learning Decorrelated Representations Efficiently Using Fast Fourier Transform/2745a979-d548-4430-88ec-679e29ec0301_model.json new file mode 100644 index 0000000000000000000000000000000000000000..514f82124c618db5327102fa6759145219c7fe76 --- /dev/null +++ b/2023/Learning Decorrelated Representations Efficiently Using Fast Fourier Transform/2745a979-d548-4430-88ec-679e29ec0301_model.json @@ -0,0 +1,2198 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.232, + 0.131, + 0.74, + 0.175 + ], + "angle": 0, + "content": "Learning Decorrelated Representations Efficiently Using Fast Fourier Transform" + }, + { + "type": "text", + "bbox": [ + 0.19, + 0.204, + 0.782, + 0.258 + ], + "angle": 0, + "content": "Yutaro Shigeto* Masashi Shimbo* Yuya Yoshikawa Akikazu Takeuchi {shigeto, shimbo, yoshikawa, takeuchi}@staircenter STAIR Lab, Chiba Institute of Technology, Narashino, Chiba, Japan" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.292, + 0.314, + 0.308 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.324, + 0.474, + 0.566 + ], + "angle": 0, + "content": "Barlow Twins and VICReg are self-supervised representation learning models that use regularizers to decorrelate features. Although these models are as effective as conventional representation learning models, their training can be computationally demanding if the dimension \\( d \\) of the projected embeddings is high. As the regularizers are defined in terms of individual elements of a cross-correlation or covariance matrix, computing the loss for \\( n \\) samples takes \\( O(nd^2) \\) time. In this paper, we propose a relaxed decorrelating regularizer that can be computed in \\( O(nd\\log d) \\) time by Fast Fourier Transform. We also propose an inexpensive technique to mitigate undesirable local minima that develop with the relaxation. The proposed regularizer exhibits accuracy comparable to that of existing regularizers in downstream tasks, whereas their training requires less memory and is faster for large \\( d \\). The source code is available.\\(^1\\)" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.597, + 0.21, + 0.612 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.622, + 0.471, + 0.865 + ], + "angle": 0, + "content": "Self-supervised learning (SSL) of representations [1, 3-5, 10, 13, 15, 27-30] has become an integral part of deep learning applications in computer vision. Most SSL models for visual representations employ a multi-view, Siamese network architecture. First, an input image is altered by different transformations that preserve its original semantics. The two augmented examples are then fed to a neural network (or in some cases, two different networks) that consists of a backbone network cascaded with a small projection network (usually a multi-layer perceptron) to produce \"twin\" projected embeddings, or views, of the original. Finally, the network weights are trained so that the twin embeddings (referred to as a \"positive pair\") are similar, reflecting the fact that they represent the same original image. After training, the projection network is discarded, while the backbone network is reused for down" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.293, + 0.892, + 0.338 + ], + "angle": 0, + "content": "stream tasks; the idea is that the pretrained backbone should produce generic representations of images that also benefit downstream tasks." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.338, + 0.893, + 0.459 + ], + "angle": 0, + "content": "One major issue in SSL is to sidestep collapsed embeddings, or the presence of trivial solutions such that all examples are projected to a single embedding vector. Contrastive approaches [3, 4, 15, 27, 28] eliminate such solutions by a loss term that repels embeddings of different original images (known as \"negative pairs\") from each other. Considering all possible negative pairs is infeasible, and negative sampling is usually performed." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.459, + 0.895, + 0.686 + ], + "angle": 0, + "content": "Recent studies have explored non-contrastive SSL models. Among these models, Barlow Twins [29] and VICReg [1] use loss functions to penalize features (components of embedding vectors) with a small variance, which are characteristic of collapsed embeddings. Also notable in these loss functions are regularization terms for feature decorrelation. They reduce redundancy in the learned features and make Barlow Twins and VICReg perform as well as contrastive models. However, since the regularizers are defined in terms of elements in a sample cross-correlation or covariance matrix, they require \\( O(nd^2) \\) time to compute, where \\( n \\) is the number of examples in a batch, and \\( d \\) is the dimensionality of the projected embeddings. This is problematic, as an increased \\( d \\) has been reported to improve the performance of both Barlow Twins and VICReg [1, 29]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Contributions. We propose a relaxed decorrelating regularizer to address the inefficiency of Barlow Twins and VICReg. The proposed regularizer does not require the explicit calculation of cross-correlation or covariance matrices and can be computed in \\( O(nd\\log d) \\) time by means of Fast Fourier Transform (FFT) [7]. Although undesirable local minima develop as a result of relaxation, they can be mitigated by feature permutation; we give an account of why this simple technique works. The SSL models using the proposed regularizer achieve competitive performance with Barlow Twins and VICReg in downstream tasks, with substantially less computation time for large \\( d \\). With \\( d = 8192 \\), training is 1.2 (with a ResNet-50 backbone) or 2.2 (with a" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.875, + 0.207, + 0.887 + ], + "angle": 0, + "content": "*Equal contribution." + }, + { + "type": "page_footnote", + "bbox": [ + 0.097, + 0.887, + 0.442, + 0.901 + ], + "angle": 0, + "content": "\\(^{1}\\)https://github.com/yutaro-s/scalable-decorrelation-ssl.git" + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.875, + 0.442, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2052" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.138 + ], + "angle": 0, + "content": "lightweight ResNet-18 backbone) times as fast as Barlow Twins. The proposed method also reduces memory consumption, which allows for larger batch size." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.156, + 0.471, + 0.262 + ], + "angle": 0, + "content": "Notation. We use zero-based indexing for vector and matrix components unless stated otherwise; thus, for a vector \\(\\mathbf{x} \\in \\mathbb{R}^d\\), the component index ranges from 0 to \\(d - 1\\). We use \\([\\mathbf{x}]_i\\) to denote the \\(i\\)th component of vector \\(\\mathbf{x}\\), and \\([\\mathbf{M}]_{ij}\\) to denote the \\((i,j)\\)th element of matrix \\(\\mathbf{M}\\). For a complex vector \\(\\mathbf{c}\\), \\(\\bar{\\mathbf{c}}\\) denotes its componentwise complex conjugate. For vectors \\(\\mathbf{x}\\) and \\(\\mathbf{y}\\), \\(\\mathbf{x} \\circ \\mathbf{y}\\) denotes their componentwise product." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.276, + 0.22, + 0.291 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.301, + 0.471, + 0.482 + ], + "angle": 0, + "content": "Contrastive SSL. Contrastive SSL uses positive and negative pairs of augmented samples [3, 4, 6, 9, 15, 24, 27, 28]. The commonly used InfoNCE loss [27] consists of an alignment term, which maximizes the similarity between positive pairs, and a uniformity term, which minimizes the similarity between negative pairs [28]. SimCLR [3] is a state-of-the-art contrastive SSL method. However, to obtain effective representations, SimCLR requires a large number of negative pairs [3], or, in other words, a large batch (or memory bank) size \\( n \\). This can be a computational bottleneck, as the loss computation of SimCLR takes \\( O(n^{2}d) \\) time where \\( d \\) is the dimensionality of the projected embeddings." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.501, + 0.47, + 0.668 + ], + "angle": 0, + "content": "Non-contrastive SSL Using Asymmetric Architecture. Recently, researchers have started exploring non-contrastive approaches to SSL, i.e., those that do not use negative pairs for training. To overcome collapsed embeddings, models such as BYOL [13] and SimSiam [5] introduce asymmetry in the architecture, e.g., by suppressing gradient updates and/or using the moving average of network parameters for one branch of the Siamese network. These methods are heuristically motivated, as collapsed embeddings are not explicitly penalized; however, they are effective in practice." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.686, + 0.468, + 0.837 + ], + "angle": 0, + "content": "Non-contrastive SSL by Decorating Regularization. A line of work exists that maintains a standard (symmetric) Siamese network but introduces loss functions to suppress collapsed embeddings. These loss functions also have regularization terms to promote feature decorrelation. Barlow Twins [29] is the first method in this line. It uses a decorrelating regularizer based on cross-correlation across two views. VICReg [1] uses regularizers that are defined in terms of covariance matrices of individual views. We review these methods in detail in Sec. 3." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Non-contrastive SSL by Whitening. Some authors [10, 18] have used whitening to explicitly decorrelate features during training, as opposed to performing regularization." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.168 + ], + "angle": 0, + "content": "Subsequent work [30] whitened both features and instances. Because the whitening procedures used in these approaches require the computation of all the eigenvalues of the covariance matrices, a training epoch takes \\( O(\\min (dn^2, nd^2)) \\) time, which is inefficient with large \\( d \\) or \\( n \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.185, + 0.892, + 0.335 + ], + "angle": 0, + "content": "Use of Convolution in Machine Learning. Convolution is the fundamental building block of convolution neural networks (CNNs). CNNs take (linear) convolution of input vectors with small learnable kernels to extract local features. Although FFT reduces the asymptotic complexity of convolution computation, it is seldom used with CNNs, because the size of kernels is typically too small to benefit from speed-up by FFT. In contrast to CNNs, we use (circular) convolution to compute summary statistics of covariance and cross-correlation matrices." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.337, + 0.892, + 0.442 + ], + "angle": 0, + "content": "In other areas of machine learning, circular convolution and its non-commutative analogue, circular correlation, have been used for implementing associative memory [2,20,22]. The idea has recently been applied to knowledge graph embeddings (KGEs) [19], with the resulting model later shown [14] to be isomorphic to complex-valued KGEs [25] by means of the convolution theorem." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.455, + 0.844, + 0.473 + ], + "angle": 0, + "content": "3. SSL Using Decorating Regularizers" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.481, + 0.892, + 0.632 + ], + "angle": 0, + "content": "This section reviews Barlow Twins [29] and VICReg [1]. Given a batch of \\( n \\) original training examples, these models apply two randomly chosen transformations to each example. The transformed examples are then processed independently by a neural network to produce twin embeddings (views) of the original. Let \\( \\mathbf{a}^{(k)}, \\mathbf{b}^{(k)} \\in \\mathbb{R}^d \\) denote the twin embeddings thus obtained for the \\( k \\)th example, and let \\( \\mathrm{A} = \\{\\mathbf{a}^{(k)}\\}_{k=1}^n \\), \\( \\mathrm{B} = \\{\\mathbf{b}^{(k)}\\}_{k=1}^n \\) be the sets of embeddings for individual views. Given these embeddings, the network is trained to minimize the loss function specific to each model." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.651, + 0.892, + 0.695 + ], + "angle": 0, + "content": "Barlow Twins. Barlow Twins optimizes the loss function defined in terms of the cross-correlation matrix \\(\\mathbf{C}(\\mathbf{A},\\mathbf{B})\\in\\) \\(\\mathbb{R}^{d\\times d}\\) between views A and B:" + }, + { + "type": "equation", + "bbox": [ + 0.525, + 0.703, + 0.892, + 0.745 + ], + "angle": 0, + "content": "\\[\nL _ {\\mathrm {B T}} = \\sum_ {i = 0} ^ {d - 1} (1 - [ \\mathbf {C} (\\mathrm {A}, \\mathrm {B}) ] _ {i i}) ^ {2} + \\lambda R _ {\\text {o f f}} (\\mathbf {C} (\\mathrm {A}, \\mathrm {B})), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.755, + 0.892, + 0.799 + ], + "angle": 0, + "content": "where hyperparameter \\(\\lambda \\geq 0\\) controls the strength of regularization, and \\(R_{\\mathrm{off}}:\\mathbb{R}^{d\\times d}\\to \\mathbb{R}\\) is a regularizer function defined as" + }, + { + "type": "equation", + "bbox": [ + 0.611, + 0.809, + 0.892, + 0.861 + ], + "angle": 0, + "content": "\\[\nR _ {\\text {o f f}} (\\mathbf {M}) = \\sum_ {i = 0} ^ {d - 1} \\sum_ {j = 0 \\atop j \\neq i} ^ {d - 1} [ \\mathbf {M} ] _ {i j} ^ {2}. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "The first term in Eq. (1) is minimized when the corresponding features of two views are fully correlated, i.e.," + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2053" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.091, + 0.473, + 0.198 + ], + "angle": 0, + "content": "\\([\\mathbf{C}(\\mathrm{A},\\mathrm{B})]_{ii} = 1\\) for \\(i = 0,\\dots ,d - 1\\). This term can be efficiently computed in \\(O(nd)\\) time. Regularizer \\(R_{\\mathrm{off}}(\\mathbf{C}(\\mathrm{A},\\mathrm{B}))\\) in the second term is responsible for feature decorrelation, as it is minimized when all the off-diagonal elements in \\(\\mathbf{C}(\\mathrm{A},\\mathrm{B})\\) are zero. For a large \\(d\\), \\(R_{\\mathrm{off}}(\\mathbf{C}(\\mathrm{A},\\mathrm{B}))\\) can be a computational burden, as it takes \\(O(nd^2)\\) time to compute due to the \\(d\\times d\\) matrix \\(\\mathbf{C}(\\mathrm{A},\\mathrm{B})\\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.221, + 0.47, + 0.266 + ], + "angle": 0, + "content": "VICReg. Let \\(\\mathbf{K}(\\mathrm{A}),\\mathbf{K}(\\mathrm{B})\\in \\mathbb{R}^{d\\times d}\\) be the covariance matrices of A and B, respectively. The VICReg loss function is" + }, + { + "type": "equation", + "bbox": [ + 0.136, + 0.278, + 0.469, + 0.374 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} L _ {\\mathrm {V I C}} = \\frac {\\alpha}{n} \\sum_ {k = 1} ^ {n} \\| \\mathbf {a} ^ {(k)} - \\mathbf {b} ^ {(k)} \\| _ {2} ^ {2} \\\\ + \\frac {\\mu}{d} (R _ {\\text {v a r}} (\\mathbf {K} (\\mathrm {A})) + R _ {\\text {v a r}} (\\mathbf {K} (\\mathrm {B}))) \\\\ + \\frac {\\nu}{d} \\left(R _ {\\text {o f f}} (\\mathbf {K} (\\mathrm {A})) + R _ {\\text {o f f}} (\\mathbf {K} (\\mathrm {B}))\\right), \\tag {3} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.386, + 0.47, + 0.416 + ], + "angle": 0, + "content": "where hyperparameters \\(\\alpha, \\mu, \\nu \\geq 0\\) control the importance of individual terms, and \\(R_{\\mathrm{var}}\\) is the regularizer defined as" + }, + { + "type": "equation", + "bbox": [ + 0.152, + 0.43, + 0.47, + 0.47 + ], + "angle": 0, + "content": "\\[\nR _ {\\text {v a r}} (\\mathbf {M}) = \\sum_ {i = 0} ^ {d - 1} \\max (0, \\gamma - \\sqrt {[ \\mathbf {M} ] _ {i i}}), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.483, + 0.47, + 0.528 + ], + "angle": 0, + "content": "with the target standard deviation \\(\\gamma > 0\\). Function \\(R_{\\mathrm{off}}\\) is the same regularizer as used in Barlow Twins (Eq. (2)), but here, it is applied to \\(\\mathbf{K}(\\mathbf{A})\\) and \\(\\mathbf{K}(\\mathbf{B})\\) instead of \\(\\mathbf{C}(\\mathbf{A}, \\mathbf{B})\\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.529, + 0.472, + 0.636 + ], + "angle": 0, + "content": "The first term in Eq. (3) brings two embeddings of the same example closer. Regularizer \\( R_{\\mathrm{var}} \\) penalizes collapsed embeddings with zero variance, whereas \\( R_{\\mathrm{off}} \\) promotes the diversity of features by encouraging the feature covariance to be zero. The time complexity of calculating \\( R_{\\mathrm{off}}(\\mathbf{K}(\\mathbf{A})) \\) and \\( R_{\\mathrm{off}}(\\mathbf{K}(\\mathbf{B})) \\) is \\( O(nd^2) \\), identical to that of \\( R_{\\mathrm{off}}(\\mathbf{C}(\\mathbf{A},\\mathbf{B})) \\) in Barlow Twins." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.652, + 0.251, + 0.669 + ], + "angle": 0, + "content": "4. Proposed Method" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.678, + 0.47, + 0.77 + ], + "angle": 0, + "content": "We propose a weaker but efficiently computable alternative to the regularizer function \\( R_{\\mathrm{off}} \\). In the following, our regularizer is presented in terms of cross-correlation matrix \\( \\mathbf{C}(\\mathbf{A},\\mathbf{B}) \\), similarly to Barlow Twins. However, if applied instead to \\( \\mathbf{K}(\\mathbf{A}) \\) and \\( \\mathbf{K}(\\mathbf{B}) \\), it produces a relaxed version of the corresponding regularization terms in the VICReg loss." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.782, + 0.469, + 0.811 + ], + "angle": 0, + "content": "4.1. Regularizer Based on Sums of Cross-correlations" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.821, + 0.47, + 0.904 + ], + "angle": 0, + "content": "Recall that the Barlow Twins loss is based on the cross-correlation matrix \\(\\mathbf{C} = \\mathbf{C}(\\mathbf{A},\\mathbf{B})\\) of two views \\(\\mathrm{A} = \\{\\mathbf{a}^{(k)}\\}_{k = 1}^n\\) and \\(\\mathbf{B} = \\{\\mathbf{b}^{(k)}\\}_{k = 1}^n\\). For brevity, assume that both \\(A\\) and \\(B\\) are standardized. Then, we can simply write \\(\\mathbf{C} = (1 / (n - 1))\\sum_{k = 1}^{n}\\mathbf{a}^{(k)}\\mathbf{b}^{(k)^{\\mathrm{T}}}\\)." + }, + { + "type": "image", + "bbox": [ + 0.515, + 0.091, + 0.66, + 0.198 + ], + "angle": 0, + "content": null + }, + { + "type": "equation", + "bbox": [ + 0.746, + 0.131, + 0.858, + 0.173 + ], + "angle": 0, + "content": "\\[\n\\left\\{ \\begin{array}{l} v _ {0} = c _ {0 0} + c _ {1 1} + c _ {2 2} \\\\ v _ {1} = c _ {0 1} + c _ {1 2} + c _ {2 0} \\\\ v _ {2} = c _ {0 2} + c _ {1 0} + c _ {2 1} \\end{array} \\right.\n\\]" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.211, + 0.892, + 0.243 + ], + "angle": 0, + "content": "Figure 1. A \\(3 \\times 3\\) cross-correlation matrix \\(\\mathbf{C} = [c_{ij}]\\) \\((i,j = 0,1,2)\\) and sumvec \\((\\mathbf{C}) = [\\nu_0\\nu_1\\nu_2]^{\\mathrm{T}}\\)" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.269, + 0.892, + 0.315 + ], + "angle": 0, + "content": "Our regularizer is defined in terms of a \\(d\\)-dimensional \"summary\" vector of the \\(d \\times d\\) matrix \\(\\mathbf{C}\\). This vector, denoted by sumvec(\\(\\mathbf{C}\\)), is given componentwise by" + }, + { + "type": "equation", + "bbox": [ + 0.575, + 0.326, + 0.892, + 0.368 + ], + "angle": 0, + "content": "\\[\n[ \\operatorname {s u m v e c} (\\mathbf {C}) ] _ {i} = \\sum_ {j = 0} ^ {d - 1} [ \\mathbf {C} ] _ {j, (i + j) \\bmod d}. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.38, + 0.892, + 0.501 + ], + "angle": 0, + "content": "Note the zero-based component indices. The zeroth component \\(\\left[\\operatorname{sumvec}(\\mathbf{C})\\right]_0\\) is the trace of \\(\\mathbf{C}\\). Each of the remaining \\(d - 1\\) components corresponds to a sum of \\(d\\) different off-diagonal elements of \\(\\mathbf{C}\\), with no single element appearing in two distinct sums. Thus, every element in \\(\\mathbf{C}\\) appears exactly once in the summations in Eq. (5). The calculation of a summary vector for a \\(3 \\times 3\\) covariance matrix is illustrated in Fig. 1." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.501, + 0.892, + 0.532 + ], + "angle": 0, + "content": "Now, we define a regularizer in terms of all but the zeroth component of sumvec(C):" + }, + { + "type": "equation", + "bbox": [ + 0.582, + 0.543, + 0.892, + 0.584 + ], + "angle": 0, + "content": "\\[\nR _ {\\text {s u m}} (\\mathbf {C}) = \\sum_ {i = 1} ^ {d - 1} \\| [ \\operatorname {s u m v e c} (\\mathbf {C}) ] _ {i} \\| _ {q} ^ {q}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.595, + 0.892, + 0.686 + ], + "angle": 0, + "content": "where hyperparameter \\(q \\in \\{1,2\\}\\). This function \\(R_{\\mathrm{sum}}\\) can be used as a drop-in replacement for \\(R_{\\mathrm{off}}\\) in the Barlow Twins loss (Eq. (1)). The zeroth component \\([\\mathrm{sumvec}(\\mathbf{C})]_0\\) is excluded in Eq. (6), because it concerns the diagonal elements of \\(\\mathbf{C}\\) that are irrelevant to feature decorrelation; they do not appear in Barlow Twin's regularizer \\(R_{\\mathrm{off}}(\\mathbf{C})\\) either." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.687, + 0.892, + 0.807 + ], + "angle": 0, + "content": "The regularizer \\( R_{\\mathrm{sum}} \\) is weaker than \\( R_{\\mathrm{off}} \\) in that it imposes constraints on the components of the summary vector, or the sums of \\( d \\) elements of \\( \\mathbf{C} \\), whereas \\( R_{\\mathrm{off}} \\) constrains individual elements. Indeed, the minimizers of \\( R_{\\mathrm{off}}(\\mathbf{C}) \\) also minimize \\( R_{\\mathrm{sum}}(\\mathbf{C}) \\), but the converse does not necessarily hold. However, as we discuss in Sec. 4.2, \\( R_{\\mathrm{sum}} \\) allows faster computation. Furthermore, in Sec. 4.3, we provide a simple technique to mitigate the weakness of \\( R_{\\mathrm{sum}} \\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.817, + 0.708, + 0.833 + ], + "angle": 0, + "content": "4.2. Efficient Computation" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.84, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Computing sumvec(C) by Eq. (5) requires the cross-correlation matrix \\(\\mathbf{C}(\\mathbf{A},\\mathbf{B})\\), whose calculation incurs the same computational cost as that of the Barlow Twins loss. However, by means of the Fourier transform, sumvec(C)" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2054" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.136 + ], + "angle": 0, + "content": "can be calculated directly from the vectors in A and B without explicit calculation of their cross-correlation matrix. To this end, we use involution and circular convolution." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.137, + 0.468, + 0.198 + ], + "angle": 0, + "content": "For a vector \\(\\mathbf{x} \\in \\mathbb{R}^d\\), its involution [22] (also called flipping [23]) \\(\\mathrm{inv}(\\mathbf{x})\\) is the vector obtained by reversing the order of its first (not the zeroth) to \\((d - 1)\\mathrm{st}\\) components; i.e., \\([\\mathrm{inv}(\\mathbf{x})]_i = [\\mathbf{x}]_{(d - i) \\bmod d}\\) for \\(i = 0, \\ldots, d - 1\\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.198, + 0.468, + 0.227 + ], + "angle": 0, + "content": "For vectors \\(\\mathbf{x},\\mathbf{y}\\in \\mathbb{R}^d\\) , their circular convolution \\(\\mathbf{x}*\\mathbf{y}\\) is a \\(d\\) -dimensional vector with components given as" + }, + { + "type": "equation", + "bbox": [ + 0.161, + 0.238, + 0.468, + 0.281 + ], + "angle": 0, + "content": "\\[\n\\left[ \\mathbf {x} * \\mathbf {y} \\right] _ {i} = \\sum_ {j = 0} ^ {d - 1} \\left[ \\mathbf {x y} ^ {\\mathrm {T}} \\right] _ {j, (i - j) \\bmod d}. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.292, + 0.468, + 0.32 + ], + "angle": 0, + "content": "As a result, circular convolution is known as the \"compressed outer product.\"" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.32, + 0.468, + 0.381 + ], + "angle": 0, + "content": "Now, for each twin embedding pair \\(\\mathbf{a}^{(k)}\\in \\mathrm{A}\\) and \\(\\mathbf{b}^{(k)}\\in\\) \\(\\mathbf{B}(k = 1,\\dots ,n)\\), let us consider vector \\(\\operatorname {inv}(\\mathbf{a}^{(k)})*\\mathbf{b}^{(k)}\\in\\) \\(\\mathbb{R}^d\\). Noting the indices altered by involution, we see that this vector is given componentwise by" + }, + { + "type": "equation", + "bbox": [ + 0.098, + 0.393, + 0.468, + 0.435 + ], + "angle": 0, + "content": "\\[\n\\left[ \\operatorname {i n v} \\left(\\mathbf {a} ^ {(k)}\\right) * \\mathbf {b} ^ {(k)} \\right] _ {i} = \\sum_ {j = 0} ^ {d - 1} \\left[ \\mathbf {a} ^ {(k)} \\mathbf {b} ^ {(k) ^ {\\mathrm {T}}} \\right] _ {j, (i + j) \\bmod d}. \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.447, + 0.468, + 0.481 + ], + "angle": 0, + "content": "Substituting \\(\\mathbf{C} = (1 / (n - 1))\\sum_{k = 1}^{n}\\mathbf{a}^{(k)}\\mathbf{b}^{(k)^{\\mathrm{T}}}\\) into Eq. (5) and using Eq. (8), we have" + }, + { + "type": "equation", + "bbox": [ + 0.093, + 0.492, + 0.469, + 0.644 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} [ \\operatorname {s u m v e c} (\\mathbf {C}) ] _ {i} = \\sum_ {j = 0} ^ {d - 1} \\overbrace {\\left[ \\frac {1}{n - 1} \\sum_ {k = 1} ^ {n} \\mathbf {a} ^ {(k)} \\mathbf {b} ^ {(k) ^ {\\mathrm {T}}} \\right] _ {j , (i + j) \\bmod d}} ^ {\\mathbf {c}} \\\\ = \\frac {1}{n - 1} \\sum_ {k = 1} ^ {n} \\sum_ {j = 0} ^ {d - 1} \\left[ \\mathbf {a} ^ {(k)} \\mathbf {b} ^ {(k) ^ {\\mathrm {T}}} \\right] _ {j, (i + j) \\bmod d} \\\\ = \\frac {1}{n - 1} \\sum_ {k = 1} ^ {n} \\left[ \\operatorname {i n v} \\left(\\mathbf {a} ^ {(k)}\\right) * \\mathbf {b} ^ {(k)} \\right] _ {i}, \\tag {9} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.655, + 0.176, + 0.667 + ], + "angle": 0, + "content": "or, as a vector," + }, + { + "type": "equation", + "bbox": [ + 0.137, + 0.678, + 0.468, + 0.717 + ], + "angle": 0, + "content": "\\[\n\\operatorname {s u m v e c} (\\mathbf {C}) = \\frac {1}{n - 1} \\sum_ {k = 1} ^ {n} \\operatorname {i n v} \\left(\\mathbf {a} ^ {(k)}\\right) * \\mathbf {b} ^ {(k)}. \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.729, + 0.468, + 0.806 + ], + "angle": 0, + "content": "Let \\(\\mathcal{F}\\) and \\(\\mathcal{F}^{-1}\\) denote the discrete Fourier transform and inverse discrete Fourier transform, respectively. Noting that \\(\\mathcal{F}(\\mathrm{inv}(\\mathbf{x})) = \\overline{\\mathcal{F}(\\mathbf{x})}\\) for any \\(\\mathbf{x} \\in \\mathbb{R}^d\\) (see e.g., [23], Section 7.4.2) and using the convolution theorem \\(\\mathcal{F}(\\mathbf{x} * \\mathbf{y}) = \\mathcal{F}(\\mathbf{x}) \\circ \\mathcal{F}(\\mathbf{y})\\), we have" + }, + { + "type": "equation", + "bbox": [ + 0.111, + 0.817, + 0.468, + 0.842 + ], + "angle": 0, + "content": "\\[\n\\operatorname {i n v} \\left(\\mathbf {a} ^ {(k)}\\right) * \\mathbf {b} ^ {(k)} = \\mathcal {F} ^ {- 1} \\left(\\overline {{\\mathcal {F} \\left(\\mathbf {a} ^ {(k)}\\right)}} \\circ \\mathcal {F} \\left(\\mathbf {b} ^ {(k)}\\right)\\right). \\tag {11}\n\\]" + }, + { + "type": "page_footnote", + "bbox": [ + 0.076, + 0.851, + 0.469, + 0.899 + ], + "angle": 0, + "content": "2The vector \\(\\mathrm{inv}(\\mathbf{x})*\\mathbf{y}\\) is known as the circular (cross-)correlation of \\(\\mathbf{x}\\) and \\(\\mathbf{y}\\) [20, 22, 23]. We opt not to use this term in this paper to avoid confusion with the cross-correlation of random vectors, which is used in Barlow Twins." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.8, + 0.107 + ], + "angle": 0, + "content": "Substituting Eq. (11) into Eq. (10), we obtain" + }, + { + "type": "equation", + "bbox": [ + 0.516, + 0.117, + 0.89, + 0.219 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\operatorname {s u m v e c} (\\mathbf {C}) = \\frac {1}{n - 1} \\sum_ {k = 1} ^ {n} \\overbrace {\\mathcal {F} ^ {- 1} \\left(\\overline {{\\mathcal {F} \\left(\\mathbf {a} ^ {(k)}\\right)}} \\circ \\mathcal {F} \\left(\\mathbf {b} ^ {(k)}\\right)\\right)} ^ {\\operatorname {i n v} \\left(\\mathbf {a} ^ {(k)}\\right) * \\mathbf {b} ^ {(k)}} \\\\ = \\frac {1}{n - 1} \\mathcal {F} ^ {- 1} \\left(\\sum_ {k = 1} ^ {n} \\overline {{\\mathcal {F} (\\mathbf {a} ^ {(k)})}} \\circ \\mathcal {F} (\\mathbf {b} ^ {(k)})\\right). \\tag {12} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.228, + 0.892, + 0.393 + ], + "angle": 0, + "content": "Using this equation, we can compute sumvec(C) directly from the embedding vectors \\(\\{\\mathbf{a}^{(k)},\\mathbf{b}^{(k)}\\}_{k = 1}^{n}\\), bypassing the cumbersome calculation of C. Noting that the (inverse) Fourier transform of a \\(d\\) -dimensional vector can be performed in \\(O(d\\log d)\\) time by the FFT algorithm, while the calculation of complex conjugates, component products, and the sum of \\(n\\) vectors takes \\(O(nd)\\) time, we can see that the overall time to obtain sumvec(C) is \\(O(nd\\log d)\\), which is also the time needed to compute \\(R_{\\mathrm{sum}}(\\mathbf{C})\\). This is a substantial improvement over the \\(O(nd^2)\\) computation time of \\(R_{\\mathrm{off}}(\\mathbf{C})\\) in the Barlow Twins loss." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.394, + 0.892, + 0.469 + ], + "angle": 0, + "content": "Furthermore, the space complexity of computing \\( R_{\\mathrm{sum}}(\\mathbf{C}) \\) is \\( O(nd) \\), which is optimal if the \\( O(nd) \\) space needed to store input vectors A and B is considered as part of the complexity. In contrast, Barlow Twins requires extra \\( O(d^2) \\) space to store C." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.479, + 0.891, + 0.508 + ], + "angle": 0, + "content": "4.3. Feature Permutation to Mitigate Undesirable Local Minima" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.517, + 0.892, + 0.668 + ], + "angle": 0, + "content": "As seen from Eq. (5), the components of sumvec(C) are the sums of \\(d\\) elements in C, and the proposed regularizer \\(R_{\\mathrm{sum}}\\) (Eq. (6)) encourages these sums to be close to zero. This is weaker than the regularizer \\(R_{\\mathrm{off}}\\) (Eq. (2)) in the Barlow Twins loss, which pushes individual elements of C towards zero. Indeed, \\(R_{\\mathrm{sum}}(\\mathbf{C})\\) can be close to zero even if individual elements in C are not; the summands in Eq. (5) can cancel each other, since they can be either positive or negative. As a result, undesirable local minima develop in the parameter space, rendering our regularizer ineffective." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.669, + 0.892, + 0.789 + ], + "angle": 0, + "content": "Here, we propose a technique to eliminate these local minima: we randomly permute feature indices during training so that sums of different cross-correlation terms constitute sumvec(C). To understand why this simple technique is effective, consider minimizing \\( R_{\\mathrm{sum}}(\\mathbf{C}) \\), regarding the elements of C as independent3 variables. It is easy to see that the minimum is attained by the solutions to a homogeneous system of linear equations:" + }, + { + "type": "equation", + "bbox": [ + 0.532, + 0.799, + 0.857, + 0.866 + ], + "angle": 0, + "content": "\\[\n\\overbrace {\\sum_ {j = 0} ^ {d - 1} [ \\mathbf {C} ] _ {j , (i + j) \\bmod d}} ^ {\\left[ \\operatorname {s u m v e c} (\\mathbf {C}) \\right] _ {i}} = 0, \\qquad \\text {f o r} i = 1, \\dots , d - 1.\n\\]" + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.875, + 0.891, + 0.899 + ], + "angle": 0, + "content": "3This assumption is not unrealistic given the high capacity of modern neural networks." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.515, + 0.957 + ], + "angle": 0, + "content": "2055" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.182 + ], + "angle": 0, + "content": "This is an underdetermined system, with only \\( d - 1 \\) equations but with \\( d(d - 1) \\) unknowns, namely, \\( [\\mathbf{C}]_{j\\ell}, j, \\ell = 0, \\dots, d - 1, j \\neq \\ell \\). This underdeterminacy is the cause of nontrivial solutions such that \\( [\\mathbf{C}]_{j\\ell} \\neq 0 \\), that is, undesirable solutions in which summands with opposite signs cancel each other in an equation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.183, + 0.471, + 0.272 + ], + "angle": 0, + "content": "Now, by repeatedly permuting the feature indices and minimizing the loss, we effectively introduce additional equations to the system, since permutation can produce different sets of linear equations over the unknowns, and these new constraints eventually render nontrivial solutions inadmissible." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.273, + 0.471, + 0.409 + ], + "angle": 0, + "content": "For ease of implementation, we permute feature indices randomly during training, instead of generating all permutations systematically at once, similarly to the way that stochastic gradient descent is a modification to full gradient descent. Note that the permuted feature indices need not be identical across mini-batches, even within a single epoch; indeed, in the experiments presented in Sec. 5, we use a different random permutation of features in every mini-batch in every epoch." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.418, + 0.47, + 0.448 + ], + "angle": 0, + "content": "4.4. Feature Grouping to Control the Degree of Relaxation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.457, + 0.471, + 0.563 + ], + "angle": 0, + "content": "Instead of computing a summary vector for an entire cross-correlation matrix \\(\\mathbf{C}\\), we can compute summaries at a more fine-grained level. Specifically, we partition \\(d\\) features into groups of size \\(b\\) each4. This partitioning induces in \\(\\mathbf{C}\\) a total of \\(\\lceil d / b \\rceil^2\\) block submatrices of size \\(b \\times b\\), i.e., \\(\\mathbf{C} = [\\mathbf{C}_{ij}](i,j = 1,\\dots,\\lceil d / b \\rceil)\\) with submatrices \\(\\mathbf{C}_{ij} \\in \\mathbb{R}^{b \\times b}\\). We then define the regularizer as" + }, + { + "type": "equation", + "bbox": [ + 0.106, + 0.574, + 0.469, + 0.671 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} R _ {\\operatorname {s u m}} ^ {(b)} (\\mathbf {C}) = \\sum_ {i = 1} ^ {\\lceil d / b \\rceil} \\sum_ {\\ell = 1} ^ {b - 1} \\| [ \\operatorname {s u m v e c} (\\mathbf {C} _ {i i}) ] _ {\\ell} \\| _ {q} ^ {q} \\\\ + \\sum_ {\\substack {i, j = 1 \\\\ i \\neq j}} ^ {\\lceil d / b \\rceil} \\sum_ {\\ell = 0} ^ {b - 1} \\left\\| \\left[ \\operatorname {sumvec} \\left(\\mathbf{C}_{ij}\\right) \\right] _ {\\ell} \\right\\| _ {q} ^ {q}. \\tag{13} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.682, + 0.47, + 0.789 + ], + "angle": 0, + "content": "As before, \\(\\mathrm{sumvec}(\\mathbf{C}_{ij})\\) can be computed without explicitly computing \\(\\mathbf{C}_{ij}\\) by means of involution, circular convolution (of subvectors of embeddings), and the Fourier transform. Calculating a single \\(\\mathrm{sumvec}(\\mathbf{C}_{ij})\\) takes \\(O(nb\\log b)\\) time using FFT, and since there are \\(\\lceil d / b\\rceil^2\\) blocks, the total time needed to compute \\(R_{\\mathrm{sum}}^{(b)}\\) is \\(O((nd^2 /b)\\log b)\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.79, + 0.469, + 0.867 + ], + "angle": 0, + "content": "The block size hyperparameter \\( b \\) controls the granularity of the summary computation and interpolates the proposed and existing regularizers. On one hand, the regularizer \\( R_{\\mathrm{sum}}^{(1)}(\\mathbf{C}) \\) reduces \\( R_{\\mathrm{off}}(\\mathbf{C}) \\) of Barlow Twins when \\( b = 1 \\), provided that \\( q = 2 \\). On the other hand, when \\( b = d \\), we" + }, + { + "type": "page_footnote", + "bbox": [ + 0.076, + 0.875, + 0.47, + 0.901 + ], + "angle": 0, + "content": "4If \\(d\\) is not divisible by \\(b\\), pad dummy features that are constantly 0 in the last group." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.09, + 0.892, + 0.212 + ], + "angle": 0, + "content": "recover \\( R_{\\mathrm{sum}}^{(d)}(\\mathbf{C}) = R_{\\mathrm{sum}}(\\mathbf{C}) \\) given in Eq. (6). Thus, this grouping formulation provides a generalization of Barlow Twins, with parameter \\( b \\) controlling the trade-off between the computational efficiency and the degree of relaxed regularization. Empirically, the performance can be slightly improved by the use of a feature group of moderate size, with no substantial degradation observed in training time and memory usage; see Sec. 5." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.213, + 0.892, + 0.243 + ], + "angle": 0, + "content": "It should be noted that the permutation and grouping of features are compatible and can be combined." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.25, + 0.892, + 0.281 + ], + "angle": 0, + "content": "4.5. Regularizer Based on Sums of Feature Covariances" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.289, + 0.892, + 0.395 + ], + "angle": 0, + "content": "The function \\( R_{\\mathrm{sum}} \\) can also be used to define a VICReg-style regularizer based on covariance, simply by replacing \\( R_{\\mathrm{off}} \\) with \\( R_{\\mathrm{sum}} \\) in Eq. (3), and passing correlation matrices \\( \\mathbf{K}(\\mathbf{A}) \\) or \\( \\mathbf{K}(\\mathbf{B}) \\) instead of \\( \\mathbf{C}(\\mathbf{A}, \\mathbf{B}) \\) as the argument. Fast computation is possible with FFT, and the grouping version is also straightforward; this is described in greater detail in Supplementary Material." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.403, + 0.768, + 0.419 + ], + "angle": 0, + "content": "4.6. Summary of Proposed Models" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.427, + 0.892, + 0.486 + ], + "angle": 0, + "content": "The loss functions of the proposed models are summarized below. Let the function \\( R = R_{\\mathrm{sum}}^{(b)} \\) if feature grouping is used with block size \\( b \\), or let \\( R = R_{\\mathrm{sum}} \\) if grouping is not used." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.488, + 0.892, + 0.517 + ], + "angle": 0, + "content": "For Barlow Twins-style cross-correlation regularization, the loss function is" + }, + { + "type": "equation", + "bbox": [ + 0.504, + 0.524, + 0.892, + 0.555 + ], + "angle": 0, + "content": "\\[\nL = \\sum_ {i} (1 - [ \\mathbf {C} (\\mathrm {A}, \\mathrm {B}) ] _ {i i}) ^ {2} + \\lambda R (\\mathbf {C} (\\mathrm {A}, \\mathrm {B})), \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.563, + 0.892, + 0.578 + ], + "angle": 0, + "content": "whereas for VICReg-style covariance regularization, we use" + }, + { + "type": "equation", + "bbox": [ + 0.505, + 0.584, + 0.891, + 0.645 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} L = \\frac {\\alpha}{n} \\sum_ {i} \\| \\mathbf {a} ^ {(i)} - \\mathbf {b} ^ {(i)} \\| _ {2} ^ {2} + \\frac {\\mu}{d} \\left(R _ {\\text {v a r}} (\\mathbf {K} (\\mathbf {A})) + R _ {\\text {v a r}} (\\mathbf {K} (\\mathbf {B}))\\right) \\\\ + \\frac {\\nu}{d} (R (\\mathbf {K} (\\mathrm {A})) + R (\\mathbf {K} (\\mathrm {B}))). \\tag {15} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.652, + 0.892, + 0.683 + ], + "angle": 0, + "content": "Setting \\( R = R_{\\mathrm{off}} \\) in these formulas gives the original Barlow Twins and VICReg, when hyperparameter \\( q = 2 \\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.695, + 0.633, + 0.712 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.892, + 0.84 + ], + "angle": 0, + "content": "We empirically evaluate the effect of the proposed regularizers. To be precise, we train SSL models using the Barlow Twins-style loss function of Eq. (14) and the VICReg-style loss function of Eq. (15) and compare their performance with Barlow Twins and VICReg in downstream tasks. The training time and memory consumption are also evaluated. For our models, feature permutation is performed in every batch iteration except for the ablation study." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.841, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In the following, we briefly present the tasks and datasets used in the experiments. See Supplementary Material for the complete experimental setup, including the hyperparameter values and the results of additional experiments." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2056" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.472, + 0.16 + ], + "angle": 0, + "content": "Table 1. Linear evaluation accuracy (\\%) on ImageNet-100 with \\( d = 2048 \\). Bold numbers indicate the best performance within each family (cross-correlation regularization, covariance regularization, or other SSL models). †: quoted from the solo-learn [26] GitHub repository as of December 28, 2022; ‡: quoted from [30]." + }, + { + "type": "table", + "bbox": [ + 0.094, + 0.171, + 0.454, + 0.385 + ], + "angle": 0, + "content": "
ModelTop-1Top-5
Barlow Twins†80.1695.14
Barlow Twins80.1295.24
Proposed (Barlow Twins-style; no grouping)79.9494.76
Proposed (Barlow Twins-style; b = 128)81.0295.24
VICReg†79.4095.02
VICReg79.3094.30
Proposed (VICReg-style; no grouping)79.2094.96
Proposed (VICReg-style; b = 128)80.0494.98
W-MSE† [10]69.0691.22
Zero-FCL‡ [30]79.3294.94
Zero-CL‡ [30]79.2694.98
NNCLR† [9]80.1695.30
BYOL† [13]80.3294.94
MoCo V3† [6]80.3694.96
" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.411, + 0.262, + 0.426 + ], + "angle": 0, + "content": "5.1. Tasks and Datasets" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.434, + 0.47, + 0.496 + ], + "angle": 0, + "content": "Models are pretrained with images in the ImageNet dataset [8] or its subset, ImageNet-100 [24], depending on the experiment. ResNet-50 [16] is used as the backbone for ImageNet, while ResNet-18 is used for ImageNet-100." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.495, + 0.47, + 0.602 + ], + "angle": 0, + "content": "To evaluate downstream SSL performance, we follow the standard linear evaluation protocol: After the backbone network is pretrained by a SSL method, we train a linear classifier on top of the frozen backbone using labeled data from the ImageNet or ImageNet-100 training set. The resulting classifier is then evaluated by the top-1 and top-5 accuracy on the respective validation sets." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.602, + 0.471, + 0.739 + ], + "angle": 0, + "content": "For transfer learning evaluation, we apply the pretrained models to an object detection task on Pascal VOC07+12 [11]. Following previous studies [1, 15, 29], we use the trainval set of VOC2007 and VOC2012 for training and the test split of VOC2007 for testing. We fine-tune Faster R-CNN [21] with R50-C4. Models are evaluated by three types of average precision (AP): AP, \\(\\mathrm{AP}_{50}\\), and \\(\\mathrm{AP}_{75}\\), where \\(\\mathrm{AP}_x\\) signifies the intersection-over-union (IoU) threshold of \\(x\\%\\). We report the average scores over five trials." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.749, + 0.291, + 0.765 + ], + "angle": 0, + "content": "5.2. Results and Discussion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.773, + 0.47, + 0.851 + ], + "angle": 0, + "content": "Linear evaluation on ImageNet-100. Tab. 1 presents the results. We can see that the accuracy of the proposed models is comparable to that of all existing models in the table, including Barlow Twins and VICReg, with or without feature grouping." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Linear evaluation on ImageNet. Tab. 2 presents the results. Due to the high computational cost of this large-scale" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.089, + 0.894, + 0.16 + ], + "angle": 0, + "content": "Table 2. Linear evaluation accuracy (\\%) on ImageNet; highest accuracy over 100 epochs of linear head training. \\( d = 8192 \\) for the proposed model, Barlow Twins, and VICReg. †: quoted from the original papers of the respective methods; ‡: quoted from the MoCo V3 GitHub repository." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.171, + 0.89, + 0.373 + ], + "angle": 0, + "content": "
ModelEpochsTop-1Top-5
Barlow Twins†100073.291.0
Barlow Twins100072.490.6
Proposed (Barlow Twins-style; no grouping)100073.091.2
Proposed (Barlow Twins-style; b = 128)100073.291.3
VICReg†100073.291.1
VICReg100072.690.9
Proposed (VICReg-style; no grouping)100072.891.1
W-MSE 4† [10]40072.6—
Zero-CL† [30]40072.690.5
SimCLR† [3]100069.389.0
NNCLR† [9]100075.492.3
BYOL† [13]100074.391.6
MoCo V3‡ [6]100074.6—
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.387, + 0.892, + 0.416 + ], + "angle": 0, + "content": "Table 3. Results of transfer learning for object detection on VOC07+12. †: quoted from original papers; ‡: quoted from [15]." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.426, + 0.892, + 0.53 + ], + "angle": 0, + "content": "
ModelAP50APAP75
Supervised‡81.353.558.8
Barlow Twins†82.656.863.4
Proposed (Barlow Twins-style; no grouping)82.555.061.1
VICReg†82.4——
Proposed (VICReg-style; no grouping)82.356.162.1
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.556, + 0.894, + 0.632 + ], + "angle": 0, + "content": "experiment, we do not evaluate feature grouping with the VICReg-style regularization. The proposed models perform slightly worse than NNCLR, BYOL, and MoCo V3, but have comparable performance to that of Barlow Twins and VICReg." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.651, + 0.892, + 0.713 + ], + "angle": 0, + "content": "Transfer learning evaluation on Pascal VOC object detection. Tab. 3 presents the results of transfer learning. Again, the proposed models demonstrate performance comparable to that of Barlow Twins and VICReg." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.732, + 0.892, + 0.854 + ], + "angle": 0, + "content": "Training time on ImageNet. Tab. 4 presents the training time over 1000 epochs on ImageNet. We tested two situations: training using 8 and 4 GPUs. In both situations, we set the per GPU batch size to 128, which leads to the effective batch size of 1024 for 8 GPUs and 512 for 4 GPUs. As indicated in Tab. 4, the accuracy of the proposed model is comparable to that of Barlow Twins, with a noticeable reduction in training time. More precise evaluation of train" + }, + { + "type": "page_footnote", + "bbox": [ + 0.499, + 0.863, + 0.894, + 0.901 + ], + "angle": 0, + "content": "5This experiment was conducted on a commercial cloud platform that limits a session to a maximum of three days. To finish training Barlow Twins with 8 GPUs for 1000 epochs, three sessions were required, whereas" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2057" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.473, + 0.16 + ], + "angle": 0, + "content": "Table 4. Linear evaluation accuracy (\\%) and the total training time on ImageNet with ResNet-50 backbone (\\( d = 8192 \\)). The per GPU batch size is 128. Proposed refers to the proposed method using the Barlow Twins-style regularizer without grouping. Barlow Twins* refers to the results quoted from [29, Figure 2]." + }, + { + "type": "table", + "bbox": [ + 0.084, + 0.17, + 0.465, + 0.278 + ], + "angle": 0, + "content": "
# GPUs (Batch size)ModelTop-1Top-5Time
8 (1024)Barlow Twins*73.291.0—
Barlow Twins72.490.76d 14h 0m
Proposed73.091.35d 14h 58m
4 (512)Barlow Twins*———
Barlow Twins72.190.212d 19h 30m
Proposed72.891.210d 21h 6m
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.295, + 0.47, + 0.324 + ], + "angle": 0, + "content": "Table 5. The effect of feature permutation: accuracy (\\%) and training time per 10 epochs (second) on ImageNet-100." + }, + { + "type": "table_caption", + "bbox": [ + 0.128, + 0.335, + 0.42, + 0.348 + ], + "angle": 0, + "content": "(a) Barlow Twins-style cross-correlation regularization" + }, + { + "type": "table", + "bbox": [ + 0.117, + 0.35, + 0.435, + 0.434 + ], + "angle": 0, + "content": "
GroupingPermutationTop-1Top-5Time
nono59.6485.201646.2
yes79.9494.761668.7
b = 128no73.5893.361697.5
yes81.0295.241709.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.159, + 0.448, + 0.388, + 0.461 + ], + "angle": 0, + "content": "(b) VICReg-style covariance regularization" + }, + { + "type": "table", + "bbox": [ + 0.12, + 0.463, + 0.432, + 0.548 + ], + "angle": 0, + "content": "
GroupingPermutationTop-1Top-5Time
nono57.4284.261692.2
yes79.2094.961718.0
b = 128no66.2689.681802.1
yes80.0494.981813.3
" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.576, + 0.47, + 0.607 + ], + "angle": 0, + "content": "ing speed is provided in the next experiment, and additional results are provided in Supplementary Material." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.636, + 0.468, + 0.65 + ], + "angle": 0, + "content": "Dimensionality of embeddings and computational cost." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.651, + 0.47, + 0.846 + ], + "angle": 0, + "content": "Fig. 2 presents the elapsed time and the peak GPU memory allocation over 10 epochs on ImageNet-100 on a single GPU, with varying dimensionality of the projected embeddings: \\( d \\in \\{2048, 4096, 8192, 16384\\} \\). The improvement over Barlow Twins and VICReg becomes noticeable as \\( d \\) is increased; at \\( d = 8192 \\), the proposed models (without grouping) are 2.8 times as fast as VICReg, and 2.2 times as fast as Barlow Twins; while at \\( d = 16384 \\), they are 5.7 times as fast as VICReg, and 4.0 times as fast as Barlow Twins. For both \\( d = 8192 \\) and 16384, memory consumption is reduced by more than half. See Supplementary Material for the results with the ResNet-50 backbone on multiple GPUs and the detail of forward/backward/loss computation time." + }, + { + "type": "page_footnote", + "bbox": [ + 0.076, + 0.863, + 0.468, + 0.901 + ], + "angle": 0, + "content": "the proposed model required two sessions. The time reported in Tab. 4 is the total run time of these sessions, which includes time (3 to 5 seconds) for reinitialization at the beginning of each session." + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.089, + 0.892, + 0.13 + ], + "angle": 0, + "content": "Table 6. The regularizers of Barlow Twins and VICReg applied to the embeddings produced by the proposed models. Perm.: permutation; Diff: difference to the baselines." + }, + { + "type": "table_caption", + "bbox": [ + 0.55, + 0.144, + 0.842, + 0.156 + ], + "angle": 0, + "content": "(a) Barlow Twins-style cross-correlation regularization" + }, + { + "type": "table", + "bbox": [ + 0.517, + 0.158, + 0.88, + 0.272 + ], + "angle": 0, + "content": "
ModelGroupingPerm.Normalized Barlow Twins loss (Eq. (16))Diff
Barlow Twins——0.0050
Proposednono0.5640.559
yes0.0100.005
b = 128no0.0490.044
yes0.0090.004
" + }, + { + "type": "table_caption", + "bbox": [ + 0.582, + 0.287, + 0.811, + 0.3 + ], + "angle": 0, + "content": "(b) VICReg-style covariance regularization" + }, + { + "type": "table", + "bbox": [ + 0.517, + 0.302, + 0.88, + 0.415 + ], + "angle": 0, + "content": "
ModelGroupingPerm.Normalized VICReg loss (Eq. (17))Diff
VICReg——0.0020
Proposednono1.9991.997
yes0.0110.009
b = 128no0.3790.377
yes0.0070.005
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.439, + 0.892, + 0.56 + ], + "angle": 0, + "content": "Effectiveness of feature permutation. Tab. 5 presents the effect of feature permutation on ImageNet-100 at \\( d = 2048 \\). Regardless of whether grouping is used, the accuracy decreases significantly without permutation, suggesting that feature permutation is essential for the effectiveness of our proposed regularizer. As illustrated in the column \"Time\" in Tab. 5, the cost of permutation is negligible, even though it was performed as frequently as every batch iteration." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.561, + 0.892, + 0.649 + ], + "angle": 0, + "content": "We also quantitatively evaluate the degree of decorrelation obtained by feature permutation. After the proposed models are trained, we compute the normalized values of Barlow Twins' and VICReg's regularizers applied to the embeddings \\( A, B \\) output by the proposed models, given as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.608, + 0.657, + 0.891, + 0.689 + ], + "angle": 0, + "content": "\\[\n\\frac {R _ {\\text {o f f}} (\\mathbf {C} (\\mathrm {A} , \\mathrm {B}))}{d (d - 1)} \\tag {16}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.61, + 0.691, + 0.891, + 0.723 + ], + "angle": 0, + "content": "\\[\n\\frac {R _ {\\text {o f f}} (\\mathbf {K} (\\mathrm {A})) + R _ {\\text {o f f}} (\\mathbf {K} (\\mathrm {B}))}{2 d (d - 1)} \\tag {17}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.732, + 0.892, + 0.837 + ], + "angle": 0, + "content": "The normalization factor \\( d(d - 1) \\) is to make the resulting values the means over \\( d(d - 1) \\) off-diagonal elements of \\( \\mathbf{K}(\\mathbf{A}) \\), \\( \\mathbf{K}(\\mathbf{B}) \\), and \\( \\mathbf{C}(\\mathbf{A},\\mathbf{B}) \\). Since VICReg has regularization terms for \\( \\mathbf{K}(\\mathbf{A}) \\) and \\( \\mathbf{K}(\\mathbf{B}) \\), its loss is further divided by 2. Tab. 6 presents the results on ImageNet-100 (\\( d = 2048 \\)). We observe that feature permutation promotes decorrelation from the point of view of the baseline loss functions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Impact of block size in feature grouping. To evaluate the effect of feature grouping on ImageNet-100, we fix the embedding dimension at \\( d = 2048 \\) and change the block" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2058" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.094, + 0.089, + 0.878, + 0.393 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.202, + 0.404, + 0.768, + 0.42 + ], + "angle": 0, + "content": "Figure 2. Training time and memory usage on ImageNet-100 with ResNet-18 on a single GPU." + }, + { + "type": "image", + "bbox": [ + 0.12, + 0.439, + 0.335, + 0.556 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.177, + 0.568, + 0.278, + 0.581 + ], + "angle": 0, + "content": "(a) Top-1 accuracy" + }, + { + "type": "image", + "bbox": [ + 0.377, + 0.439, + 0.593, + 0.556 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.418, + 0.568, + 0.551, + 0.581 + ], + "angle": 0, + "content": "(b) Elapsed training time" + }, + { + "type": "image", + "bbox": [ + 0.637, + 0.44, + 0.851, + 0.556 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.658, + 0.568, + 0.831, + 0.581 + ], + "angle": 0, + "content": "(c) Peak GPU memory allocated" + }, + { + "type": "image_caption", + "bbox": [ + 0.202, + 0.592, + 0.766, + 0.607 + ], + "angle": 0, + "content": "Figure 3. The impact of the block size on ImageNet-100. The \\(x\\)-axis indicates the block size \\(b\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.633, + 0.471, + 0.725 + ], + "angle": 0, + "content": "size \\( b \\in \\{2, 4, 8, \\dots, 2048\\} \\). The block size \\( b = d = 2048 \\) corresponds to no feature grouping. Figure 3 presents the result, which indicates that unless \\( b \\) is extremely small (i.e., 8 or less), there is no significant increase in training time or GPU memory usage. Setting \\( b \\) to a moderate size, such as \\( b = 128 \\), improves performance." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.74, + 0.196, + 0.755 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.471, + 0.903 + ], + "angle": 0, + "content": "We have proposed a new decorrelating regularizer for non-contrastive SSL. Given \\(d\\)-dimensional embeddings of \\(n\\) samples, the regularizer can be computed in \\(O(nd\\log d)\\) time, which is an improvement over the \\(O(nd^2)\\) time required by the existing models (Barlow Twins and VICReg). The reduced memory consumption allows for a larger batch size, which in general enables more effective models to be learned. We also proposed a feature permutation technique to alleviate the weakness of our regularizer." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.634, + 0.892, + 0.709 + ], + "angle": 0, + "content": "With our regularizer, the speed-up is most notable with networks with a lightweight backbone, wherein computation at the loss node takes a large part of training time. This makes our method an attractive option to use with knowledge-distilled backbones [12, 17]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.718, + 0.892, + 0.765 + ], + "angle": 0, + "content": "The proposed method is not limited to SSL but potentially useful to a wider range of applications that involve decorrelation. We plan to pursue this avenue in future work." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.806, + 0.66, + 0.823 + ], + "angle": 0, + "content": "Acknowledgments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We thank anonymous reviewers for their helpful comments. This work was partially supported by the New Energy and Industrial Technology Development Organization (NEDO) and JSPS Kakenhi Grant 19H04173." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2059" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.175, + 0.107 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.117, + 0.47, + 0.158 + ], + "angle": 0, + "content": "[1] Adrien Bardes, Jean Ponce, and Yann LeCun. VI-CReg: Variance-invariance-covariance regularization for self-supervised learning. In ICLR, 2022. 1, 2, 6" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.161, + 0.469, + 0.188 + ], + "angle": 0, + "content": "[2] A. Borsellino and T. Poggio. Convolution and correlation algebras. 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In ICLR, 2022. 1, 2, 6" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.801 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.517, + 0.957 + ], + "angle": 0, + "content": "2060" + } + ] +] \ No newline at end of file diff --git a/2023/Learning Decorrelated Representations Efficiently Using Fast Fourier Transform/2745a979-d548-4430-88ec-679e29ec0301_origin.pdf b/2023/Learning Decorrelated Representations Efficiently Using Fast Fourier Transform/2745a979-d548-4430-88ec-679e29ec0301_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..9105c773c21214b4f2aa11b075f3955c659cd637 --- /dev/null +++ b/2023/Learning Decorrelated Representations Efficiently Using Fast Fourier Transform/2745a979-d548-4430-88ec-679e29ec0301_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:045ea57cda6b4cd7574d91a40dd9ef6ed540593a6d64031b4eda3708f6a87d9f +size 308771 diff --git a/2023/Learning Decorrelated Representations Efficiently Using Fast Fourier Transform/full.md b/2023/Learning Decorrelated Representations Efficiently Using Fast Fourier Transform/full.md new file mode 100644 index 0000000000000000000000000000000000000000..bb9e3916650a3f0637363bcdf0bc2e86ea725055 --- /dev/null +++ b/2023/Learning Decorrelated Representations Efficiently Using Fast Fourier Transform/full.md @@ -0,0 +1,355 @@ +# Learning Decorrelated Representations Efficiently Using Fast Fourier Transform + +Yutaro Shigeto* Masashi Shimbo* Yuya Yoshikawa Akikazu Takeuchi {shigeto, shimbo, yoshikawa, takeuchi}@staircenter STAIR Lab, Chiba Institute of Technology, Narashino, Chiba, Japan + +# Abstract + +Barlow Twins and VICReg are self-supervised representation learning models that use regularizers to decorrelate features. Although these models are as effective as conventional representation learning models, their training can be computationally demanding if the dimension $d$ of the projected embeddings is high. As the regularizers are defined in terms of individual elements of a cross-correlation or covariance matrix, computing the loss for $n$ samples takes $O(nd^2)$ time. In this paper, we propose a relaxed decorrelating regularizer that can be computed in $O(nd\log d)$ time by Fast Fourier Transform. We also propose an inexpensive technique to mitigate undesirable local minima that develop with the relaxation. The proposed regularizer exhibits accuracy comparable to that of existing regularizers in downstream tasks, whereas their training requires less memory and is faster for large $d$ . The source code is available. $^1$ + +# 1. Introduction + +Self-supervised learning (SSL) of representations [1, 3-5, 10, 13, 15, 27-30] has become an integral part of deep learning applications in computer vision. Most SSL models for visual representations employ a multi-view, Siamese network architecture. First, an input image is altered by different transformations that preserve its original semantics. The two augmented examples are then fed to a neural network (or in some cases, two different networks) that consists of a backbone network cascaded with a small projection network (usually a multi-layer perceptron) to produce "twin" projected embeddings, or views, of the original. Finally, the network weights are trained so that the twin embeddings (referred to as a "positive pair") are similar, reflecting the fact that they represent the same original image. After training, the projection network is discarded, while the backbone network is reused for down + +stream tasks; the idea is that the pretrained backbone should produce generic representations of images that also benefit downstream tasks. + +One major issue in SSL is to sidestep collapsed embeddings, or the presence of trivial solutions such that all examples are projected to a single embedding vector. Contrastive approaches [3, 4, 15, 27, 28] eliminate such solutions by a loss term that repels embeddings of different original images (known as "negative pairs") from each other. Considering all possible negative pairs is infeasible, and negative sampling is usually performed. + +Recent studies have explored non-contrastive SSL models. Among these models, Barlow Twins [29] and VICReg [1] use loss functions to penalize features (components of embedding vectors) with a small variance, which are characteristic of collapsed embeddings. Also notable in these loss functions are regularization terms for feature decorrelation. They reduce redundancy in the learned features and make Barlow Twins and VICReg perform as well as contrastive models. However, since the regularizers are defined in terms of elements in a sample cross-correlation or covariance matrix, they require $O(nd^2)$ time to compute, where $n$ is the number of examples in a batch, and $d$ is the dimensionality of the projected embeddings. This is problematic, as an increased $d$ has been reported to improve the performance of both Barlow Twins and VICReg [1, 29]. + +Contributions. We propose a relaxed decorrelating regularizer to address the inefficiency of Barlow Twins and VICReg. The proposed regularizer does not require the explicit calculation of cross-correlation or covariance matrices and can be computed in $O(nd\log d)$ time by means of Fast Fourier Transform (FFT) [7]. Although undesirable local minima develop as a result of relaxation, they can be mitigated by feature permutation; we give an account of why this simple technique works. The SSL models using the proposed regularizer achieve competitive performance with Barlow Twins and VICReg in downstream tasks, with substantially less computation time for large $d$ . With $d = 8192$ , training is 1.2 (with a ResNet-50 backbone) or 2.2 (with a + +lightweight ResNet-18 backbone) times as fast as Barlow Twins. The proposed method also reduces memory consumption, which allows for larger batch size. + +Notation. We use zero-based indexing for vector and matrix components unless stated otherwise; thus, for a vector $\mathbf{x} \in \mathbb{R}^d$ , the component index ranges from 0 to $d - 1$ . We use $[\mathbf{x}]_i$ to denote the $i$ th component of vector $\mathbf{x}$ , and $[\mathbf{M}]_{ij}$ to denote the $(i,j)$ th element of matrix $\mathbf{M}$ . For a complex vector $\mathbf{c}$ , $\bar{\mathbf{c}}$ denotes its componentwise complex conjugate. For vectors $\mathbf{x}$ and $\mathbf{y}$ , $\mathbf{x} \circ \mathbf{y}$ denotes their componentwise product. + +# 2. Related Work + +Contrastive SSL. Contrastive SSL uses positive and negative pairs of augmented samples [3, 4, 6, 9, 15, 24, 27, 28]. The commonly used InfoNCE loss [27] consists of an alignment term, which maximizes the similarity between positive pairs, and a uniformity term, which minimizes the similarity between negative pairs [28]. SimCLR [3] is a state-of-the-art contrastive SSL method. However, to obtain effective representations, SimCLR requires a large number of negative pairs [3], or, in other words, a large batch (or memory bank) size $n$ . This can be a computational bottleneck, as the loss computation of SimCLR takes $O(n^{2}d)$ time where $d$ is the dimensionality of the projected embeddings. + +Non-contrastive SSL Using Asymmetric Architecture. Recently, researchers have started exploring non-contrastive approaches to SSL, i.e., those that do not use negative pairs for training. To overcome collapsed embeddings, models such as BYOL [13] and SimSiam [5] introduce asymmetry in the architecture, e.g., by suppressing gradient updates and/or using the moving average of network parameters for one branch of the Siamese network. These methods are heuristically motivated, as collapsed embeddings are not explicitly penalized; however, they are effective in practice. + +Non-contrastive SSL by Decorating Regularization. A line of work exists that maintains a standard (symmetric) Siamese network but introduces loss functions to suppress collapsed embeddings. These loss functions also have regularization terms to promote feature decorrelation. Barlow Twins [29] is the first method in this line. It uses a decorrelating regularizer based on cross-correlation across two views. VICReg [1] uses regularizers that are defined in terms of covariance matrices of individual views. We review these methods in detail in Sec. 3. + +Non-contrastive SSL by Whitening. Some authors [10, 18] have used whitening to explicitly decorrelate features during training, as opposed to performing regularization. + +Subsequent work [30] whitened both features and instances. Because the whitening procedures used in these approaches require the computation of all the eigenvalues of the covariance matrices, a training epoch takes $O(\min (dn^2, nd^2))$ time, which is inefficient with large $d$ or $n$ . + +Use of Convolution in Machine Learning. Convolution is the fundamental building block of convolution neural networks (CNNs). CNNs take (linear) convolution of input vectors with small learnable kernels to extract local features. Although FFT reduces the asymptotic complexity of convolution computation, it is seldom used with CNNs, because the size of kernels is typically too small to benefit from speed-up by FFT. In contrast to CNNs, we use (circular) convolution to compute summary statistics of covariance and cross-correlation matrices. + +In other areas of machine learning, circular convolution and its non-commutative analogue, circular correlation, have been used for implementing associative memory [2,20,22]. The idea has recently been applied to knowledge graph embeddings (KGEs) [19], with the resulting model later shown [14] to be isomorphic to complex-valued KGEs [25] by means of the convolution theorem. + +# 3. SSL Using Decorating Regularizers + +This section reviews Barlow Twins [29] and VICReg [1]. Given a batch of $n$ original training examples, these models apply two randomly chosen transformations to each example. The transformed examples are then processed independently by a neural network to produce twin embeddings (views) of the original. Let $\mathbf{a}^{(k)}, \mathbf{b}^{(k)} \in \mathbb{R}^d$ denote the twin embeddings thus obtained for the $k$ th example, and let $\mathrm{A} = \{\mathbf{a}^{(k)}\}_{k=1}^n$ , $\mathrm{B} = \{\mathbf{b}^{(k)}\}_{k=1}^n$ be the sets of embeddings for individual views. Given these embeddings, the network is trained to minimize the loss function specific to each model. + +Barlow Twins. Barlow Twins optimizes the loss function defined in terms of the cross-correlation matrix $\mathbf{C}(\mathbf{A},\mathbf{B})\in$ $\mathbb{R}^{d\times d}$ between views A and B: + +$$ +L _ {\mathrm {B T}} = \sum_ {i = 0} ^ {d - 1} (1 - [ \mathbf {C} (\mathrm {A}, \mathrm {B}) ] _ {i i}) ^ {2} + \lambda R _ {\text {o f f}} (\mathbf {C} (\mathrm {A}, \mathrm {B})), \tag {1} +$$ + +where hyperparameter $\lambda \geq 0$ controls the strength of regularization, and $R_{\mathrm{off}}:\mathbb{R}^{d\times d}\to \mathbb{R}$ is a regularizer function defined as + +$$ +R _ {\text {o f f}} (\mathbf {M}) = \sum_ {i = 0} ^ {d - 1} \sum_ {j = 0 \atop j \neq i} ^ {d - 1} [ \mathbf {M} ] _ {i j} ^ {2}. \tag {2} +$$ + +The first term in Eq. (1) is minimized when the corresponding features of two views are fully correlated, i.e., + +$[\mathbf{C}(\mathrm{A},\mathrm{B})]_{ii} = 1$ for $i = 0,\dots ,d - 1$ . This term can be efficiently computed in $O(nd)$ time. Regularizer $R_{\mathrm{off}}(\mathbf{C}(\mathrm{A},\mathrm{B}))$ in the second term is responsible for feature decorrelation, as it is minimized when all the off-diagonal elements in $\mathbf{C}(\mathrm{A},\mathrm{B})$ are zero. For a large $d$ , $R_{\mathrm{off}}(\mathbf{C}(\mathrm{A},\mathrm{B}))$ can be a computational burden, as it takes $O(nd^2)$ time to compute due to the $d\times d$ matrix $\mathbf{C}(\mathrm{A},\mathrm{B})$ . + +VICReg. Let $\mathbf{K}(\mathrm{A}),\mathbf{K}(\mathrm{B})\in \mathbb{R}^{d\times d}$ be the covariance matrices of A and B, respectively. The VICReg loss function is + +$$ +\begin{array}{l} L _ {\mathrm {V I C}} = \frac {\alpha}{n} \sum_ {k = 1} ^ {n} \| \mathbf {a} ^ {(k)} - \mathbf {b} ^ {(k)} \| _ {2} ^ {2} \\ + \frac {\mu}{d} (R _ {\text {v a r}} (\mathbf {K} (\mathrm {A})) + R _ {\text {v a r}} (\mathbf {K} (\mathrm {B}))) \\ + \frac {\nu}{d} \left(R _ {\text {o f f}} (\mathbf {K} (\mathrm {A})) + R _ {\text {o f f}} (\mathbf {K} (\mathrm {B}))\right), \tag {3} \\ \end{array} +$$ + +where hyperparameters $\alpha, \mu, \nu \geq 0$ control the importance of individual terms, and $R_{\mathrm{var}}$ is the regularizer defined as + +$$ +R _ {\text {v a r}} (\mathbf {M}) = \sum_ {i = 0} ^ {d - 1} \max (0, \gamma - \sqrt {[ \mathbf {M} ] _ {i i}}), \tag {4} +$$ + +with the target standard deviation $\gamma > 0$ . Function $R_{\mathrm{off}}$ is the same regularizer as used in Barlow Twins (Eq. (2)), but here, it is applied to $\mathbf{K}(\mathbf{A})$ and $\mathbf{K}(\mathbf{B})$ instead of $\mathbf{C}(\mathbf{A}, \mathbf{B})$ . + +The first term in Eq. (3) brings two embeddings of the same example closer. Regularizer $R_{\mathrm{var}}$ penalizes collapsed embeddings with zero variance, whereas $R_{\mathrm{off}}$ promotes the diversity of features by encouraging the feature covariance to be zero. The time complexity of calculating $R_{\mathrm{off}}(\mathbf{K}(\mathbf{A}))$ and $R_{\mathrm{off}}(\mathbf{K}(\mathbf{B}))$ is $O(nd^2)$ , identical to that of $R_{\mathrm{off}}(\mathbf{C}(\mathbf{A},\mathbf{B}))$ in Barlow Twins. + +# 4. Proposed Method + +We propose a weaker but efficiently computable alternative to the regularizer function $R_{\mathrm{off}}$ . In the following, our regularizer is presented in terms of cross-correlation matrix $\mathbf{C}(\mathbf{A},\mathbf{B})$ , similarly to Barlow Twins. However, if applied instead to $\mathbf{K}(\mathbf{A})$ and $\mathbf{K}(\mathbf{B})$ , it produces a relaxed version of the corresponding regularization terms in the VICReg loss. + +# 4.1. Regularizer Based on Sums of Cross-correlations + +Recall that the Barlow Twins loss is based on the cross-correlation matrix $\mathbf{C} = \mathbf{C}(\mathbf{A},\mathbf{B})$ of two views $\mathrm{A} = \{\mathbf{a}^{(k)}\}_{k = 1}^n$ and $\mathbf{B} = \{\mathbf{b}^{(k)}\}_{k = 1}^n$ . For brevity, assume that both $A$ and $B$ are standardized. Then, we can simply write $\mathbf{C} = (1 / (n - 1))\sum_{k = 1}^{n}\mathbf{a}^{(k)}\mathbf{b}^{(k)^{\mathrm{T}}}$ . + +![](images/2e20bb4a5aa16d81709ed344a36120428f5186062bde9c317df86ae9e5ca7c1a.jpg) +Figure 1. A $3 \times 3$ cross-correlation matrix $\mathbf{C} = [c_{ij}]$ $(i,j = 0,1,2)$ and sumvec $(\mathbf{C}) = [\nu_0\nu_1\nu_2]^{\mathrm{T}}$ + +$$ +\left\{ \begin{array}{l} v _ {0} = c _ {0 0} + c _ {1 1} + c _ {2 2} \\ v _ {1} = c _ {0 1} + c _ {1 2} + c _ {2 0} \\ v _ {2} = c _ {0 2} + c _ {1 0} + c _ {2 1} \end{array} \right. +$$ + +Our regularizer is defined in terms of a $d$ -dimensional "summary" vector of the $d \times d$ matrix $\mathbf{C}$ . This vector, denoted by sumvec( $\mathbf{C}$ ), is given componentwise by + +$$ +[ \operatorname {s u m v e c} (\mathbf {C}) ] _ {i} = \sum_ {j = 0} ^ {d - 1} [ \mathbf {C} ] _ {j, (i + j) \bmod d}. \tag {5} +$$ + +Note the zero-based component indices. The zeroth component $\left[\operatorname{sumvec}(\mathbf{C})\right]_0$ is the trace of $\mathbf{C}$ . Each of the remaining $d - 1$ components corresponds to a sum of $d$ different off-diagonal elements of $\mathbf{C}$ , with no single element appearing in two distinct sums. Thus, every element in $\mathbf{C}$ appears exactly once in the summations in Eq. (5). The calculation of a summary vector for a $3 \times 3$ covariance matrix is illustrated in Fig. 1. + +Now, we define a regularizer in terms of all but the zeroth component of sumvec(C): + +$$ +R _ {\text {s u m}} (\mathbf {C}) = \sum_ {i = 1} ^ {d - 1} \| [ \operatorname {s u m v e c} (\mathbf {C}) ] _ {i} \| _ {q} ^ {q}, \tag {6} +$$ + +where hyperparameter $q \in \{1,2\}$ . This function $R_{\mathrm{sum}}$ can be used as a drop-in replacement for $R_{\mathrm{off}}$ in the Barlow Twins loss (Eq. (1)). The zeroth component $[\mathrm{sumvec}(\mathbf{C})]_0$ is excluded in Eq. (6), because it concerns the diagonal elements of $\mathbf{C}$ that are irrelevant to feature decorrelation; they do not appear in Barlow Twin's regularizer $R_{\mathrm{off}}(\mathbf{C})$ either. + +The regularizer $R_{\mathrm{sum}}$ is weaker than $R_{\mathrm{off}}$ in that it imposes constraints on the components of the summary vector, or the sums of $d$ elements of $\mathbf{C}$ , whereas $R_{\mathrm{off}}$ constrains individual elements. Indeed, the minimizers of $R_{\mathrm{off}}(\mathbf{C})$ also minimize $R_{\mathrm{sum}}(\mathbf{C})$ , but the converse does not necessarily hold. However, as we discuss in Sec. 4.2, $R_{\mathrm{sum}}$ allows faster computation. Furthermore, in Sec. 4.3, we provide a simple technique to mitigate the weakness of $R_{\mathrm{sum}}$ . + +# 4.2. Efficient Computation + +Computing sumvec(C) by Eq. (5) requires the cross-correlation matrix $\mathbf{C}(\mathbf{A},\mathbf{B})$ , whose calculation incurs the same computational cost as that of the Barlow Twins loss. However, by means of the Fourier transform, sumvec(C) + +can be calculated directly from the vectors in A and B without explicit calculation of their cross-correlation matrix. To this end, we use involution and circular convolution. + +For a vector $\mathbf{x} \in \mathbb{R}^d$ , its involution [22] (also called flipping [23]) $\mathrm{inv}(\mathbf{x})$ is the vector obtained by reversing the order of its first (not the zeroth) to $(d - 1)\mathrm{st}$ components; i.e., $[\mathrm{inv}(\mathbf{x})]_i = [\mathbf{x}]_{(d - i) \bmod d}$ for $i = 0, \ldots, d - 1$ . + +For vectors $\mathbf{x},\mathbf{y}\in \mathbb{R}^d$ , their circular convolution $\mathbf{x}*\mathbf{y}$ is a $d$ -dimensional vector with components given as + +$$ +\left[ \mathbf {x} * \mathbf {y} \right] _ {i} = \sum_ {j = 0} ^ {d - 1} \left[ \mathbf {x y} ^ {\mathrm {T}} \right] _ {j, (i - j) \bmod d}. \tag {7} +$$ + +As a result, circular convolution is known as the "compressed outer product." + +Now, for each twin embedding pair $\mathbf{a}^{(k)}\in \mathrm{A}$ and $\mathbf{b}^{(k)}\in$ $\mathbf{B}(k = 1,\dots ,n)$ , let us consider vector $\operatorname {inv}(\mathbf{a}^{(k)})*\mathbf{b}^{(k)}\in$ $\mathbb{R}^d$ . Noting the indices altered by involution, we see that this vector is given componentwise by + +$$ +\left[ \operatorname {i n v} \left(\mathbf {a} ^ {(k)}\right) * \mathbf {b} ^ {(k)} \right] _ {i} = \sum_ {j = 0} ^ {d - 1} \left[ \mathbf {a} ^ {(k)} \mathbf {b} ^ {(k) ^ {\mathrm {T}}} \right] _ {j, (i + j) \bmod d}. \tag {8} +$$ + +Substituting $\mathbf{C} = (1 / (n - 1))\sum_{k = 1}^{n}\mathbf{a}^{(k)}\mathbf{b}^{(k)^{\mathrm{T}}}$ into Eq. (5) and using Eq. (8), we have + +$$ +\begin{array}{l} [ \operatorname {s u m v e c} (\mathbf {C}) ] _ {i} = \sum_ {j = 0} ^ {d - 1} \overbrace {\left[ \frac {1}{n - 1} \sum_ {k = 1} ^ {n} \mathbf {a} ^ {(k)} \mathbf {b} ^ {(k) ^ {\mathrm {T}}} \right] _ {j , (i + j) \bmod d}} ^ {\mathbf {c}} \\ = \frac {1}{n - 1} \sum_ {k = 1} ^ {n} \sum_ {j = 0} ^ {d - 1} \left[ \mathbf {a} ^ {(k)} \mathbf {b} ^ {(k) ^ {\mathrm {T}}} \right] _ {j, (i + j) \bmod d} \\ = \frac {1}{n - 1} \sum_ {k = 1} ^ {n} \left[ \operatorname {i n v} \left(\mathbf {a} ^ {(k)}\right) * \mathbf {b} ^ {(k)} \right] _ {i}, \tag {9} \\ \end{array} +$$ + +or, as a vector, + +$$ +\operatorname {s u m v e c} (\mathbf {C}) = \frac {1}{n - 1} \sum_ {k = 1} ^ {n} \operatorname {i n v} \left(\mathbf {a} ^ {(k)}\right) * \mathbf {b} ^ {(k)}. \tag {10} +$$ + +Let $\mathcal{F}$ and $\mathcal{F}^{-1}$ denote the discrete Fourier transform and inverse discrete Fourier transform, respectively. Noting that $\mathcal{F}(\mathrm{inv}(\mathbf{x})) = \overline{\mathcal{F}(\mathbf{x})}$ for any $\mathbf{x} \in \mathbb{R}^d$ (see e.g., [23], Section 7.4.2) and using the convolution theorem $\mathcal{F}(\mathbf{x} * \mathbf{y}) = \mathcal{F}(\mathbf{x}) \circ \mathcal{F}(\mathbf{y})$ , we have + +$$ +\operatorname {i n v} \left(\mathbf {a} ^ {(k)}\right) * \mathbf {b} ^ {(k)} = \mathcal {F} ^ {- 1} \left(\overline {{\mathcal {F} \left(\mathbf {a} ^ {(k)}\right)}} \circ \mathcal {F} \left(\mathbf {b} ^ {(k)}\right)\right). \tag {11} +$$ + +Substituting Eq. (11) into Eq. (10), we obtain + +$$ +\begin{array}{l} \operatorname {s u m v e c} (\mathbf {C}) = \frac {1}{n - 1} \sum_ {k = 1} ^ {n} \overbrace {\mathcal {F} ^ {- 1} \left(\overline {{\mathcal {F} \left(\mathbf {a} ^ {(k)}\right)}} \circ \mathcal {F} \left(\mathbf {b} ^ {(k)}\right)\right)} ^ {\operatorname {i n v} \left(\mathbf {a} ^ {(k)}\right) * \mathbf {b} ^ {(k)}} \\ = \frac {1}{n - 1} \mathcal {F} ^ {- 1} \left(\sum_ {k = 1} ^ {n} \overline {{\mathcal {F} (\mathbf {a} ^ {(k)})}} \circ \mathcal {F} (\mathbf {b} ^ {(k)})\right). \tag {12} \\ \end{array} +$$ + +Using this equation, we can compute sumvec(C) directly from the embedding vectors $\{\mathbf{a}^{(k)},\mathbf{b}^{(k)}\}_{k = 1}^{n}$ , bypassing the cumbersome calculation of C. Noting that the (inverse) Fourier transform of a $d$ -dimensional vector can be performed in $O(d\log d)$ time by the FFT algorithm, while the calculation of complex conjugates, component products, and the sum of $n$ vectors takes $O(nd)$ time, we can see that the overall time to obtain sumvec(C) is $O(nd\log d)$ , which is also the time needed to compute $R_{\mathrm{sum}}(\mathbf{C})$ . This is a substantial improvement over the $O(nd^2)$ computation time of $R_{\mathrm{off}}(\mathbf{C})$ in the Barlow Twins loss. + +Furthermore, the space complexity of computing $R_{\mathrm{sum}}(\mathbf{C})$ is $O(nd)$ , which is optimal if the $O(nd)$ space needed to store input vectors A and B is considered as part of the complexity. In contrast, Barlow Twins requires extra $O(d^2)$ space to store C. + +# 4.3. Feature Permutation to Mitigate Undesirable Local Minima + +As seen from Eq. (5), the components of sumvec(C) are the sums of $d$ elements in C, and the proposed regularizer $R_{\mathrm{sum}}$ (Eq. (6)) encourages these sums to be close to zero. This is weaker than the regularizer $R_{\mathrm{off}}$ (Eq. (2)) in the Barlow Twins loss, which pushes individual elements of C towards zero. Indeed, $R_{\mathrm{sum}}(\mathbf{C})$ can be close to zero even if individual elements in C are not; the summands in Eq. (5) can cancel each other, since they can be either positive or negative. As a result, undesirable local minima develop in the parameter space, rendering our regularizer ineffective. + +Here, we propose a technique to eliminate these local minima: we randomly permute feature indices during training so that sums of different cross-correlation terms constitute sumvec(C). To understand why this simple technique is effective, consider minimizing $R_{\mathrm{sum}}(\mathbf{C})$ , regarding the elements of C as independent3 variables. It is easy to see that the minimum is attained by the solutions to a homogeneous system of linear equations: + +$$ +\overbrace {\sum_ {j = 0} ^ {d - 1} [ \mathbf {C} ] _ {j , (i + j) \bmod d}} ^ {\left[ \operatorname {s u m v e c} (\mathbf {C}) \right] _ {i}} = 0, \qquad \text {f o r} i = 1, \dots , d - 1. +$$ + +This is an underdetermined system, with only $d - 1$ equations but with $d(d - 1)$ unknowns, namely, $[\mathbf{C}]_{j\ell}, j, \ell = 0, \dots, d - 1, j \neq \ell$ . This underdeterminacy is the cause of nontrivial solutions such that $[\mathbf{C}]_{j\ell} \neq 0$ , that is, undesirable solutions in which summands with opposite signs cancel each other in an equation. + +Now, by repeatedly permuting the feature indices and minimizing the loss, we effectively introduce additional equations to the system, since permutation can produce different sets of linear equations over the unknowns, and these new constraints eventually render nontrivial solutions inadmissible. + +For ease of implementation, we permute feature indices randomly during training, instead of generating all permutations systematically at once, similarly to the way that stochastic gradient descent is a modification to full gradient descent. Note that the permuted feature indices need not be identical across mini-batches, even within a single epoch; indeed, in the experiments presented in Sec. 5, we use a different random permutation of features in every mini-batch in every epoch. + +# 4.4. Feature Grouping to Control the Degree of Relaxation + +Instead of computing a summary vector for an entire cross-correlation matrix $\mathbf{C}$ , we can compute summaries at a more fine-grained level. Specifically, we partition $d$ features into groups of size $b$ each4. This partitioning induces in $\mathbf{C}$ a total of $\lceil d / b \rceil^2$ block submatrices of size $b \times b$ , i.e., $\mathbf{C} = [\mathbf{C}_{ij}](i,j = 1,\dots,\lceil d / b \rceil)$ with submatrices $\mathbf{C}_{ij} \in \mathbb{R}^{b \times b}$ . We then define the regularizer as + +$$ +\begin{array}{l} R _ {\operatorname {s u m}} ^ {(b)} (\mathbf {C}) = \sum_ {i = 1} ^ {\lceil d / b \rceil} \sum_ {\ell = 1} ^ {b - 1} \| [ \operatorname {s u m v e c} (\mathbf {C} _ {i i}) ] _ {\ell} \| _ {q} ^ {q} \\ + \sum_ {\substack {i, j = 1 \\ i \neq j}} ^ {\lceil d / b \rceil} \sum_ {\ell = 0} ^ {b - 1} \left\| \left[ \operatorname {sumvec} \left(\mathbf{C}_{ij}\right) \right] _ {\ell} \right\| _ {q} ^ {q}. \tag{13} \\ \end{array} +$$ + +As before, $\mathrm{sumvec}(\mathbf{C}_{ij})$ can be computed without explicitly computing $\mathbf{C}_{ij}$ by means of involution, circular convolution (of subvectors of embeddings), and the Fourier transform. Calculating a single $\mathrm{sumvec}(\mathbf{C}_{ij})$ takes $O(nb\log b)$ time using FFT, and since there are $\lceil d / b\rceil^2$ blocks, the total time needed to compute $R_{\mathrm{sum}}^{(b)}$ is $O((nd^2 /b)\log b)$ . + +The block size hyperparameter $b$ controls the granularity of the summary computation and interpolates the proposed and existing regularizers. On one hand, the regularizer $R_{\mathrm{sum}}^{(1)}(\mathbf{C})$ reduces $R_{\mathrm{off}}(\mathbf{C})$ of Barlow Twins when $b = 1$ , provided that $q = 2$ . On the other hand, when $b = d$ , we + +recover $R_{\mathrm{sum}}^{(d)}(\mathbf{C}) = R_{\mathrm{sum}}(\mathbf{C})$ given in Eq. (6). Thus, this grouping formulation provides a generalization of Barlow Twins, with parameter $b$ controlling the trade-off between the computational efficiency and the degree of relaxed regularization. Empirically, the performance can be slightly improved by the use of a feature group of moderate size, with no substantial degradation observed in training time and memory usage; see Sec. 5. + +It should be noted that the permutation and grouping of features are compatible and can be combined. + +# 4.5. Regularizer Based on Sums of Feature Covariances + +The function $R_{\mathrm{sum}}$ can also be used to define a VICReg-style regularizer based on covariance, simply by replacing $R_{\mathrm{off}}$ with $R_{\mathrm{sum}}$ in Eq. (3), and passing correlation matrices $\mathbf{K}(\mathbf{A})$ or $\mathbf{K}(\mathbf{B})$ instead of $\mathbf{C}(\mathbf{A}, \mathbf{B})$ as the argument. Fast computation is possible with FFT, and the grouping version is also straightforward; this is described in greater detail in Supplementary Material. + +# 4.6. Summary of Proposed Models + +The loss functions of the proposed models are summarized below. Let the function $R = R_{\mathrm{sum}}^{(b)}$ if feature grouping is used with block size $b$ , or let $R = R_{\mathrm{sum}}$ if grouping is not used. + +For Barlow Twins-style cross-correlation regularization, the loss function is + +$$ +L = \sum_ {i} (1 - [ \mathbf {C} (\mathrm {A}, \mathrm {B}) ] _ {i i}) ^ {2} + \lambda R (\mathbf {C} (\mathrm {A}, \mathrm {B})), \tag {14} +$$ + +whereas for VICReg-style covariance regularization, we use + +$$ +\begin{array}{l} L = \frac {\alpha}{n} \sum_ {i} \| \mathbf {a} ^ {(i)} - \mathbf {b} ^ {(i)} \| _ {2} ^ {2} + \frac {\mu}{d} \left(R _ {\text {v a r}} (\mathbf {K} (\mathbf {A})) + R _ {\text {v a r}} (\mathbf {K} (\mathbf {B}))\right) \\ + \frac {\nu}{d} (R (\mathbf {K} (\mathrm {A})) + R (\mathbf {K} (\mathrm {B}))). \tag {15} \\ \end{array} +$$ + +Setting $R = R_{\mathrm{off}}$ in these formulas gives the original Barlow Twins and VICReg, when hyperparameter $q = 2$ . + +# 5. Experiments + +We empirically evaluate the effect of the proposed regularizers. To be precise, we train SSL models using the Barlow Twins-style loss function of Eq. (14) and the VICReg-style loss function of Eq. (15) and compare their performance with Barlow Twins and VICReg in downstream tasks. The training time and memory consumption are also evaluated. For our models, feature permutation is performed in every batch iteration except for the ablation study. + +In the following, we briefly present the tasks and datasets used in the experiments. See Supplementary Material for the complete experimental setup, including the hyperparameter values and the results of additional experiments. + +Table 1. Linear evaluation accuracy (\%) on ImageNet-100 with $d = 2048$ . Bold numbers indicate the best performance within each family (cross-correlation regularization, covariance regularization, or other SSL models). †: quoted from the solo-learn [26] GitHub repository as of December 28, 2022; ‡: quoted from [30]. + +
ModelTop-1Top-5
Barlow Twins†80.1695.14
Barlow Twins80.1295.24
Proposed (Barlow Twins-style; no grouping)79.9494.76
Proposed (Barlow Twins-style; b = 128)81.0295.24
VICReg†79.4095.02
VICReg79.3094.30
Proposed (VICReg-style; no grouping)79.2094.96
Proposed (VICReg-style; b = 128)80.0494.98
W-MSE† [10]69.0691.22
Zero-FCL‡ [30]79.3294.94
Zero-CL‡ [30]79.2694.98
NNCLR† [9]80.1695.30
BYOL† [13]80.3294.94
MoCo V3† [6]80.3694.96
+ +# 5.1. Tasks and Datasets + +Models are pretrained with images in the ImageNet dataset [8] or its subset, ImageNet-100 [24], depending on the experiment. ResNet-50 [16] is used as the backbone for ImageNet, while ResNet-18 is used for ImageNet-100. + +To evaluate downstream SSL performance, we follow the standard linear evaluation protocol: After the backbone network is pretrained by a SSL method, we train a linear classifier on top of the frozen backbone using labeled data from the ImageNet or ImageNet-100 training set. The resulting classifier is then evaluated by the top-1 and top-5 accuracy on the respective validation sets. + +For transfer learning evaluation, we apply the pretrained models to an object detection task on Pascal VOC07+12 [11]. Following previous studies [1, 15, 29], we use the trainval set of VOC2007 and VOC2012 for training and the test split of VOC2007 for testing. We fine-tune Faster R-CNN [21] with R50-C4. Models are evaluated by three types of average precision (AP): AP, $\mathrm{AP}_{50}$ , and $\mathrm{AP}_{75}$ , where $\mathrm{AP}_x$ signifies the intersection-over-union (IoU) threshold of $x\%$ . We report the average scores over five trials. + +# 5.2. Results and Discussion + +Linear evaluation on ImageNet-100. Tab. 1 presents the results. We can see that the accuracy of the proposed models is comparable to that of all existing models in the table, including Barlow Twins and VICReg, with or without feature grouping. + +Linear evaluation on ImageNet. Tab. 2 presents the results. Due to the high computational cost of this large-scale + +Table 2. Linear evaluation accuracy (\%) on ImageNet; highest accuracy over 100 epochs of linear head training. $d = 8192$ for the proposed model, Barlow Twins, and VICReg. †: quoted from the original papers of the respective methods; ‡: quoted from the MoCo V3 GitHub repository. + +
ModelEpochsTop-1Top-5
Barlow Twins†100073.291.0
Barlow Twins100072.490.6
Proposed (Barlow Twins-style; no grouping)100073.091.2
Proposed (Barlow Twins-style; b = 128)100073.291.3
VICReg†100073.291.1
VICReg100072.690.9
Proposed (VICReg-style; no grouping)100072.891.1
W-MSE 4† [10]40072.6—
Zero-CL† [30]40072.690.5
SimCLR† [3]100069.389.0
NNCLR† [9]100075.492.3
BYOL† [13]100074.391.6
MoCo V3‡ [6]100074.6—
+ +Table 3. Results of transfer learning for object detection on VOC07+12. †: quoted from original papers; ‡: quoted from [15]. + +
ModelAP50APAP75
Supervised‡81.353.558.8
Barlow Twins†82.656.863.4
Proposed (Barlow Twins-style; no grouping)82.555.061.1
VICReg†82.4——
Proposed (VICReg-style; no grouping)82.356.162.1
+ +experiment, we do not evaluate feature grouping with the VICReg-style regularization. The proposed models perform slightly worse than NNCLR, BYOL, and MoCo V3, but have comparable performance to that of Barlow Twins and VICReg. + +Transfer learning evaluation on Pascal VOC object detection. Tab. 3 presents the results of transfer learning. Again, the proposed models demonstrate performance comparable to that of Barlow Twins and VICReg. + +Training time on ImageNet. Tab. 4 presents the training time over 1000 epochs on ImageNet. We tested two situations: training using 8 and 4 GPUs. In both situations, we set the per GPU batch size to 128, which leads to the effective batch size of 1024 for 8 GPUs and 512 for 4 GPUs. As indicated in Tab. 4, the accuracy of the proposed model is comparable to that of Barlow Twins, with a noticeable reduction in training time. More precise evaluation of train + +Table 4. Linear evaluation accuracy (\%) and the total training time on ImageNet with ResNet-50 backbone ( $d = 8192$ ). The per GPU batch size is 128. Proposed refers to the proposed method using the Barlow Twins-style regularizer without grouping. Barlow Twins* refers to the results quoted from [29, Figure 2]. + +
# GPUs (Batch size)ModelTop-1Top-5Time
8 (1024)Barlow Twins*73.291.0—
Barlow Twins72.490.76d 14h 0m
Proposed73.091.35d 14h 58m
4 (512)Barlow Twins*———
Barlow Twins72.190.212d 19h 30m
Proposed72.891.210d 21h 6m
+ +Table 5. The effect of feature permutation: accuracy (\%) and training time per 10 epochs (second) on ImageNet-100. +(a) Barlow Twins-style cross-correlation regularization + +
GroupingPermutationTop-1Top-5Time
nono59.6485.201646.2
yes79.9494.761668.7
b = 128no73.5893.361697.5
yes81.0295.241709.6
+ +(b) VICReg-style covariance regularization + +
GroupingPermutationTop-1Top-5Time
nono57.4284.261692.2
yes79.2094.961718.0
b = 128no66.2689.681802.1
yes80.0494.981813.3
+ +ing speed is provided in the next experiment, and additional results are provided in Supplementary Material. + +# Dimensionality of embeddings and computational cost. + +Fig. 2 presents the elapsed time and the peak GPU memory allocation over 10 epochs on ImageNet-100 on a single GPU, with varying dimensionality of the projected embeddings: $d \in \{2048, 4096, 8192, 16384\}$ . The improvement over Barlow Twins and VICReg becomes noticeable as $d$ is increased; at $d = 8192$ , the proposed models (without grouping) are 2.8 times as fast as VICReg, and 2.2 times as fast as Barlow Twins; while at $d = 16384$ , they are 5.7 times as fast as VICReg, and 4.0 times as fast as Barlow Twins. For both $d = 8192$ and 16384, memory consumption is reduced by more than half. See Supplementary Material for the results with the ResNet-50 backbone on multiple GPUs and the detail of forward/backward/loss computation time. + +Table 6. The regularizers of Barlow Twins and VICReg applied to the embeddings produced by the proposed models. Perm.: permutation; Diff: difference to the baselines. +(a) Barlow Twins-style cross-correlation regularization + +
ModelGroupingPerm.Normalized Barlow Twins loss (Eq. (16))Diff
Barlow Twins——0.0050
Proposednono0.5640.559
yes0.0100.005
b = 128no0.0490.044
yes0.0090.004
+ +(b) VICReg-style covariance regularization + +
ModelGroupingPerm.Normalized VICReg loss (Eq. (17))Diff
VICReg——0.0020
Proposednono1.9991.997
yes0.0110.009
b = 128no0.3790.377
yes0.0070.005
+ +Effectiveness of feature permutation. Tab. 5 presents the effect of feature permutation on ImageNet-100 at $d = 2048$ . Regardless of whether grouping is used, the accuracy decreases significantly without permutation, suggesting that feature permutation is essential for the effectiveness of our proposed regularizer. As illustrated in the column "Time" in Tab. 5, the cost of permutation is negligible, even though it was performed as frequently as every batch iteration. + +We also quantitatively evaluate the degree of decorrelation obtained by feature permutation. After the proposed models are trained, we compute the normalized values of Barlow Twins' and VICReg's regularizers applied to the embeddings $A, B$ output by the proposed models, given as follows: + +$$ +\frac {R _ {\text {o f f}} (\mathbf {C} (\mathrm {A} , \mathrm {B}))}{d (d - 1)} \tag {16} +$$ + +$$ +\frac {R _ {\text {o f f}} (\mathbf {K} (\mathrm {A})) + R _ {\text {o f f}} (\mathbf {K} (\mathrm {B}))}{2 d (d - 1)} \tag {17} +$$ + +The normalization factor $d(d - 1)$ is to make the resulting values the means over $d(d - 1)$ off-diagonal elements of $\mathbf{K}(\mathbf{A})$ , $\mathbf{K}(\mathbf{B})$ , and $\mathbf{C}(\mathbf{A},\mathbf{B})$ . Since VICReg has regularization terms for $\mathbf{K}(\mathbf{A})$ and $\mathbf{K}(\mathbf{B})$ , its loss is further divided by 2. Tab. 6 presents the results on ImageNet-100 ( $d = 2048$ ). We observe that feature permutation promotes decorrelation from the point of view of the baseline loss functions. + +Impact of block size in feature grouping. To evaluate the effect of feature grouping on ImageNet-100, we fix the embedding dimension at $d = 2048$ and change the block + +![](images/3cd714293187435b8b7b5b08b272339485223117c32f6271f194c137a4a64b3a.jpg) +Figure 2. Training time and memory usage on ImageNet-100 with ResNet-18 on a single GPU. + +![](images/6bddb76b3e3ce5eeb518e01b5ae48d50d449dee4f20cac63243d0a4e4c1de1f0.jpg) +(a) Top-1 accuracy + +![](images/fb065f6641478ca7630c27870e267848eba0414cef6e4d9a32b9442063cdf979.jpg) +(b) Elapsed training time + +![](images/c8920ee0e4b62c47f44253eb5d370d2be719e51b2ba25cff4131730f33836079.jpg) +(c) Peak GPU memory allocated +Figure 3. The impact of the block size on ImageNet-100. The $x$ -axis indicates the block size $b$ . + +size $b \in \{2, 4, 8, \dots, 2048\}$ . The block size $b = d = 2048$ corresponds to no feature grouping. Figure 3 presents the result, which indicates that unless $b$ is extremely small (i.e., 8 or less), there is no significant increase in training time or GPU memory usage. Setting $b$ to a moderate size, such as $b = 128$ , improves performance. + +# 6. Conclusion + +We have proposed a new decorrelating regularizer for non-contrastive SSL. Given $d$ -dimensional embeddings of $n$ samples, the regularizer can be computed in $O(nd\log d)$ time, which is an improvement over the $O(nd^2)$ time required by the existing models (Barlow Twins and VICReg). The reduced memory consumption allows for a larger batch size, which in general enables more effective models to be learned. We also proposed a feature permutation technique to alleviate the weakness of our regularizer. + +With our regularizer, the speed-up is most notable with networks with a lightweight backbone, wherein computation at the loss node takes a large part of training time. This makes our method an attractive option to use with knowledge-distilled backbones [12, 17]. + +The proposed method is not limited to SSL but potentially useful to a wider range of applications that involve decorrelation. We plan to pursue this avenue in future work. + +# Acknowledgments + +We thank anonymous reviewers for their helpful comments. This work was partially supported by the New Energy and Industrial Technology Development Organization (NEDO) and JSPS Kakenhi Grant 19H04173. + +# References + +[1] Adrien Bardes, Jean Ponce, and Yann LeCun. VI-CReg: Variance-invariance-covariance regularization for self-supervised learning. In ICLR, 2022. 1, 2, 6 +[2] A. Borsellino and T. Poggio. Convolution and correlation algebras. Kybernetik, 13(2):113-122, 1973. 2 +[3] Ting Chen, Simon Kornblith, Mohammad Norouzi, and Geoffrey Hinton. A simple framework for contrastive learning of visual representations. In ICML, pages 1597-1607, 2020. 1, 2, 6 +[4] Ting Chen, Simon Kornblith, Kevin Swersky, Mohammad Norouzi, and Geoffrey E. Hinton. Big self-supervised models are strong semi-supervised learners. In NeurIPS, pages 22243-22255, 2020. 1, 2 +[5] Xinlei Chen and Kaiming He. Exploring simple Siamese representation learning. In CVPR, pages 15750-15758, 2021. 1, 2 +[6] Xinlei Chen, Saining Xie, and Kaiming He. An empirical study of training self-supervised vision transformers. In ICCV, pages 9640-9649, 2021. 2, 6 +[7] James W. Cooley and John W. Tukey. An algorithm for the machine calculation of complex Fourier series. Mathematics of Computation, 19(90):297-301, 1965. 1 +[8] Jia Deng, Wei Dong, Richard Socher, Li-Jia Li, Kai Li, and Li Fei-Fei. ImageNet: A large-scale hierarchical image database. In CVPR, pages 248–255, 2009. 6 +[9] Debidatta Dwibedi, Yusuf Aytar, Jonathan Tompson, Pierre Sermanet, and Andrew Zisserman. 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Mathematics of the Discrete Fourier Transform (DFT) with Audio Applications. W3K Publishing, 2nd edition, 2008. 4 +[24] Yonglong Tian, Dilip Krishnan, and Phillip Isola. Contrastive multiview coding. In ECCV, pages 776-794, 2020. 2, 6 +[25] Théo Trouillon, Johannes Welbl, Sebastian Riedel, Éric Gaussier, and Guillaume Bouchard. Complex embeddings for simple link prediction. In ICML, pages 2071-2080, 2016. 2 +[26] Victor G. Turrisi da Costa, Enrico Fini, Moin Nabi, Nicu Sebe, and Elisa Ricci. solo-learn: A library of self-supervised methods for visual representation learning. Journal of Machine Learning Research, 23(56):1-6, 2022. 6 +[27] Aaron van den Oord, Yazhe Li, and Oriol Vinyals. Representation learning with contrastive predictive coding. arXiv.cs preprint, 1807.03748, 2018. 1, 2 +[28] Tongzhou Wang and Phillip Isola. Understanding contrastive representation learning through alignment and uniformity on the hypersphere. In ICML, pages 9929-9939, 2020. 1, 2 +[29] Jure Zbontar, Li Jing, Ishan Misra, Yann LeCun, and Stéhane Deny. Barlow Twins: Self-supervised learning via redundancy reduction. In ICML, pages 12310-12320, 2021. 1, 2, 6, 7 +[30] Shaofeng Zhang, Feng Zhu, Junchi Yan, Rui Zhao, and Xiaokang Yang. Zero-CL: Instance and feature decorrelation for negative-free symmetric contrastive learning. In ICLR, 2022. 1, 2, 6 \ No newline at end of file diff --git a/2023/Learning Decorrelated Representations Efficiently Using Fast Fourier Transform/images.zip b/2023/Learning Decorrelated Representations Efficiently Using Fast Fourier Transform/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..cfdd5b2ba40e371beace0e2dd5a691a2a0c4f980 --- /dev/null +++ b/2023/Learning Decorrelated Representations Efficiently Using Fast Fourier Transform/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:b23739f8a4a90db02ce7af4c2ec127892b4b40f0920562b1f0ddb5c0a91ca69e +size 460207 diff --git a/2023/Learning Decorrelated Representations Efficiently Using Fast Fourier Transform/layout.json b/2023/Learning Decorrelated Representations Efficiently Using Fast Fourier Transform/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..e8992ce8df353e726c11efd6a6313b32a4db0566 --- /dev/null +++ b/2023/Learning Decorrelated Representations Efficiently Using Fast Fourier Transform/layout.json @@ -0,0 +1,11091 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 141, + 103, + 452, + 138 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 103, + 452, + 138 + ], + "spans": [ + { + "bbox": [ + 141, + 103, + 452, + 138 + ], + "type": "text", + "content": "Learning Decorrelated Representations Efficiently Using Fast Fourier Transform" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 116, + 161, + 478, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 161, + 478, + 204 + ], + "spans": [ + { + "bbox": [ + 116, + 161, + 478, + 204 + ], + "type": "text", + "content": "Yutaro Shigeto* Masashi Shimbo* Yuya Yoshikawa Akikazu Takeuchi {shigeto, shimbo, yoshikawa, takeuchi}@staircenter STAIR Lab, Chiba Institute of Technology, Narashino, Chiba, Japan" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 143, + 231, + 192, + 243 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 231, + 192, + 243 + ], + "spans": [ + { + "bbox": [ + 143, + 231, + 192, + 243 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 45, + 256, + 290, + 448 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 256, + 290, + 448 + ], + "spans": [ + { + "bbox": [ + 45, + 256, + 290, + 448 + ], + "type": "text", + "content": "Barlow Twins and VICReg are self-supervised representation learning models that use regularizers to decorrelate features. 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Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 693, + 126, + 702 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 693, + 126, + 702 + ], + "spans": [ + { + "bbox": [ + 58, + 693, + 126, + 702 + ], + "type": "text", + "content": "*Equal contribution." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 59, + 702, + 270, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 702, + 270, + 713 + ], + "spans": [ + { + "bbox": [ + 59, + 702, + 270, + 713 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 59, + 702, + 270, + 713 + ], + "type": "text", + "content": "https://github.com/yutaro-s/scalable-decorrelation-ssl.git" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2052" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "type": "text", + "content": "lightweight ResNet-18 backbone) times as fast as Barlow Twins. The proposed method also reduces memory consumption, which allows for larger batch size." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 123, + 288, + 207 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 123, + 288, + 207 + ], + "spans": [ + { + "bbox": [ + 46, + 123, + 288, + 207 + ], + "type": "text", + "content": "Notation. We use zero-based indexing for vector and matrix components unless stated otherwise; thus, for a vector " + }, + { + "bbox": [ + 46, + 123, + 288, + 207 + ], + "type": "inline_equation", + "content": "\\mathbf{x} \\in \\mathbb{R}^d" + }, + { + "bbox": [ + 46, + 123, + 288, + 207 + ], + "type": "text", + "content": ", the component index ranges from 0 to " + }, + { + "bbox": [ + 46, + 123, + 288, + 207 + ], + "type": "inline_equation", + "content": "d - 1" + }, + { + "bbox": [ + 46, + 123, + 288, + 207 + ], + "type": "text", + "content": ". We use " + }, + { + "bbox": [ + 46, + 123, + 288, + 207 + ], + "type": "inline_equation", + "content": "[\\mathbf{x}]_i" + }, + { + "bbox": [ + 46, + 123, + 288, + 207 + ], + "type": "text", + "content": " to denote the " + }, + { + "bbox": [ + 46, + 123, + 288, + 207 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 123, + 288, + 207 + ], + "type": "text", + "content": "th component of vector " + }, + { + "bbox": [ + 46, + 123, + 288, + 207 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 46, + 123, + 288, + 207 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 123, + 288, + 207 + ], + "type": "inline_equation", + "content": "[\\mathbf{M}]_{ij}" + }, + { + "bbox": [ + 46, + 123, + 288, + 207 + ], + "type": "text", + "content": " to denote the " + }, + { + "bbox": [ + 46, + 123, + 288, + 207 + ], + "type": "inline_equation", + "content": "(i,j)" + }, + { + "bbox": [ + 46, + 123, + 288, + 207 + ], + "type": "text", + "content": "th element of matrix " + }, + { + "bbox": [ + 46, + 123, + 288, + 207 + ], + "type": "inline_equation", + "content": "\\mathbf{M}" + }, + { + "bbox": [ + 46, + 123, + 288, + 207 + ], + "type": "text", + "content": ". For a complex vector " + }, + { + "bbox": [ + 46, + 123, + 288, + 207 + ], + "type": "inline_equation", + "content": "\\mathbf{c}" + }, + { + "bbox": [ + 46, + 123, + 288, + 207 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 123, + 288, + 207 + ], + "type": "inline_equation", + "content": "\\bar{\\mathbf{c}}" + }, + { + "bbox": [ + 46, + 123, + 288, + 207 + ], + "type": "text", + "content": " denotes its componentwise complex conjugate. For vectors " + }, + { + "bbox": [ + 46, + 123, + 288, + 207 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 46, + 123, + 288, + 207 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 123, + 288, + 207 + ], + "type": "inline_equation", + "content": "\\mathbf{y}" + }, + { + "bbox": [ + 46, + 123, + 288, + 207 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 123, + 288, + 207 + ], + "type": "inline_equation", + "content": "\\mathbf{x} \\circ \\mathbf{y}" + }, + { + "bbox": [ + 46, + 123, + 288, + 207 + ], + "type": "text", + "content": " denotes their componentwise product." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 218, + 134, + 230 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 218, + 134, + 230 + ], + "spans": [ + { + "bbox": [ + 47, + 218, + 134, + 230 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 238, + 288, + 381 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 238, + 288, + 381 + ], + "spans": [ + { + "bbox": [ + 46, + 238, + 288, + 381 + ], + "type": "text", + "content": "Contrastive SSL. Contrastive SSL uses positive and negative pairs of augmented samples [3, 4, 6, 9, 15, 24, 27, 28]. The commonly used InfoNCE loss [27] consists of an alignment term, which maximizes the similarity between positive pairs, and a uniformity term, which minimizes the similarity between negative pairs [28]. SimCLR [3] is a state-of-the-art contrastive SSL method. However, to obtain effective representations, SimCLR requires a large number of negative pairs [3], or, in other words, a large batch (or memory bank) size " + }, + { + "bbox": [ + 46, + 238, + 288, + 381 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 238, + 288, + 381 + ], + "type": "text", + "content": ". This can be a computational bottleneck, as the loss computation of SimCLR takes " + }, + { + "bbox": [ + 46, + 238, + 288, + 381 + ], + "type": "inline_equation", + "content": "O(n^{2}d)" + }, + { + "bbox": [ + 46, + 238, + 288, + 381 + ], + "type": "text", + "content": " time where " + }, + { + "bbox": [ + 46, + 238, + 288, + 381 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 238, + 288, + 381 + ], + "type": "text", + "content": " is the dimensionality of the projected embeddings." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 396, + 287, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 396, + 287, + 529 + ], + "spans": [ + { + "bbox": [ + 46, + 396, + 287, + 529 + ], + "type": "text", + "content": "Non-contrastive SSL Using Asymmetric Architecture. Recently, researchers have started exploring non-contrastive approaches to SSL, i.e., those that do not use negative pairs for training. To overcome collapsed embeddings, models such as BYOL [13] and SimSiam [5] introduce asymmetry in the architecture, e.g., by suppressing gradient updates and/or using the moving average of network parameters for one branch of the Siamese network. These methods are heuristically motivated, as collapsed embeddings are not explicitly penalized; however, they are effective in practice." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 543, + 286, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 543, + 286, + 662 + ], + "spans": [ + { + "bbox": [ + 46, + 543, + 286, + 662 + ], + "type": "text", + "content": "Non-contrastive SSL by Decorating Regularization. A line of work exists that maintains a standard (symmetric) Siamese network but introduces loss functions to suppress collapsed embeddings. These loss functions also have regularization terms to promote feature decorrelation. Barlow Twins [29] is the first method in this line. It uses a decorrelating regularizer based on cross-correlation across two views. VICReg [1] uses regularizers that are defined in terms of covariance matrices of individual views. We review these methods in detail in Sec. 3." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "text", + "content": "Non-contrastive SSL by Whitening. Some authors [10, 18] have used whitening to explicitly decorrelate features during training, as opposed to performing regularization." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": "Subsequent work [30] whitened both features and instances. Because the whitening procedures used in these approaches require the computation of all the eigenvalues of the covariance matrices, a training epoch takes " + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "inline_equation", + "content": "O(\\min (dn^2, nd^2))" + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": " time, which is inefficient with large " + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 146, + 545, + 265 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 146, + 545, + 265 + ], + "spans": [ + { + "bbox": [ + 304, + 146, + 545, + 265 + ], + "type": "text", + "content": "Use of Convolution in Machine Learning. Convolution is the fundamental building block of convolution neural networks (CNNs). CNNs take (linear) convolution of input vectors with small learnable kernels to extract local features. Although FFT reduces the asymptotic complexity of convolution computation, it is seldom used with CNNs, because the size of kernels is typically too small to benefit from speed-up by FFT. In contrast to CNNs, we use (circular) convolution to compute summary statistics of covariance and cross-correlation matrices." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 266, + 545, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 266, + 545, + 350 + ], + "spans": [ + { + "bbox": [ + 304, + 266, + 545, + 350 + ], + "type": "text", + "content": "In other areas of machine learning, circular convolution and its non-commutative analogue, circular correlation, have been used for implementing associative memory [2,20,22]. The idea has recently been applied to knowledge graph embeddings (KGEs) [19], with the resulting model later shown [14] to be isomorphic to complex-valued KGEs [25] by means of the convolution theorem." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 360, + 516, + 374 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 360, + 516, + 374 + ], + "spans": [ + { + "bbox": [ + 305, + 360, + 516, + 374 + ], + "type": "text", + "content": "3. SSL Using Decorating Regularizers" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 380, + 545, + 500 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 380, + 545, + 500 + ], + "spans": [ + { + "bbox": [ + 304, + 380, + 545, + 500 + ], + "type": "text", + "content": "This section reviews Barlow Twins [29] and VICReg [1]. Given a batch of " + }, + { + "bbox": [ + 304, + 380, + 545, + 500 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 380, + 545, + 500 + ], + "type": "text", + "content": " original training examples, these models apply two randomly chosen transformations to each example. The transformed examples are then processed independently by a neural network to produce twin embeddings (views) of the original. Let " + }, + { + "bbox": [ + 304, + 380, + 545, + 500 + ], + "type": "inline_equation", + "content": "\\mathbf{a}^{(k)}, \\mathbf{b}^{(k)} \\in \\mathbb{R}^d" + }, + { + "bbox": [ + 304, + 380, + 545, + 500 + ], + "type": "text", + "content": " denote the twin embeddings thus obtained for the " + }, + { + "bbox": [ + 304, + 380, + 545, + 500 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 380, + 545, + 500 + ], + "type": "text", + "content": "th example, and let " + }, + { + "bbox": [ + 304, + 380, + 545, + 500 + ], + "type": "inline_equation", + "content": "\\mathrm{A} = \\{\\mathbf{a}^{(k)}\\}_{k=1}^n" + }, + { + "bbox": [ + 304, + 380, + 545, + 500 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 380, + 545, + 500 + ], + "type": "inline_equation", + "content": "\\mathrm{B} = \\{\\mathbf{b}^{(k)}\\}_{k=1}^n" + }, + { + "bbox": [ + 304, + 380, + 545, + 500 + ], + "type": "text", + "content": " be the sets of embeddings for individual views. Given these embeddings, the network is trained to minimize the loss function specific to each model." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 515, + 545, + 550 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 515, + 545, + 550 + ], + "spans": [ + { + "bbox": [ + 304, + 515, + 545, + 550 + ], + "type": "text", + "content": "Barlow Twins. Barlow Twins optimizes the loss function defined in terms of the cross-correlation matrix " + }, + { + "bbox": [ + 304, + 515, + 545, + 550 + ], + "type": "inline_equation", + "content": "\\mathbf{C}(\\mathbf{A},\\mathbf{B})\\in" + }, + { + "bbox": [ + 304, + 515, + 545, + 550 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{d\\times d}" + }, + { + "bbox": [ + 304, + 515, + 545, + 550 + ], + "type": "text", + "content": " between views A and B:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 321, + 556, + 545, + 590 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 556, + 545, + 590 + ], + "spans": [ + { + "bbox": [ + 321, + 556, + 545, + 590 + ], + "type": "interline_equation", + "content": "L _ {\\mathrm {B T}} = \\sum_ {i = 0} ^ {d - 1} (1 - [ \\mathbf {C} (\\mathrm {A}, \\mathrm {B}) ] _ {i i}) ^ {2} + \\lambda R _ {\\text {o f f}} (\\mathbf {C} (\\mathrm {A}, \\mathrm {B})), \\tag {1}", + "image_path": "07f4ef074450f2995573b7600067c00042319ac631b515c5ed9154a66ae9da7a.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 597, + 545, + 632 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 597, + 545, + 632 + ], + "spans": [ + { + "bbox": [ + 304, + 597, + 545, + 632 + ], + "type": "text", + "content": "where hyperparameter " + }, + { + "bbox": [ + 304, + 597, + 545, + 632 + ], + "type": "inline_equation", + "content": "\\lambda \\geq 0" + }, + { + "bbox": [ + 304, + 597, + 545, + 632 + ], + "type": "text", + "content": " controls the strength of regularization, and " + }, + { + "bbox": [ + 304, + 597, + 545, + 632 + ], + "type": "inline_equation", + "content": "R_{\\mathrm{off}}:\\mathbb{R}^{d\\times d}\\to \\mathbb{R}" + }, + { + "bbox": [ + 304, + 597, + 545, + 632 + ], + "type": "text", + "content": " is a regularizer function defined as" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 373, + 640, + 545, + 681 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 373, + 640, + 545, + 681 + ], + "spans": [ + { + "bbox": [ + 373, + 640, + 545, + 681 + ], + "type": "interline_equation", + "content": "R _ {\\text {o f f}} (\\mathbf {M}) = \\sum_ {i = 0} ^ {d - 1} \\sum_ {j = 0 \\atop j \\neq i} ^ {d - 1} [ \\mathbf {M} ] _ {i j} ^ {2}. \\tag {2}", + "image_path": "0f16b96bc8e74d08cc6b4aef947fae96d3b296d0f58c1f88f2e6c4a42c0e4c52.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "text", + "content": "The first term in Eq. (1) is minimized when the corresponding features of two views are fully correlated, i.e.," + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2053" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 156 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 156 + ], + "type": "inline_equation", + "content": "[\\mathbf{C}(\\mathrm{A},\\mathrm{B})]_{ii} = 1" + }, + { + "bbox": [ + 47, + 72, + 289, + 156 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 47, + 72, + 289, + 156 + ], + "type": "inline_equation", + "content": "i = 0,\\dots ,d - 1" + }, + { + "bbox": [ + 47, + 72, + 289, + 156 + ], + "type": "text", + "content": ". This term can be efficiently computed in " + }, + { + "bbox": [ + 47, + 72, + 289, + 156 + ], + "type": "inline_equation", + "content": "O(nd)" + }, + { + "bbox": [ + 47, + 72, + 289, + 156 + ], + "type": "text", + "content": " time. Regularizer " + }, + { + "bbox": [ + 47, + 72, + 289, + 156 + ], + "type": "inline_equation", + "content": "R_{\\mathrm{off}}(\\mathbf{C}(\\mathrm{A},\\mathrm{B}))" + }, + { + "bbox": [ + 47, + 72, + 289, + 156 + ], + "type": "text", + "content": " in the second term is responsible for feature decorrelation, as it is minimized when all the off-diagonal elements in " + }, + { + "bbox": [ + 47, + 72, + 289, + 156 + ], + "type": "inline_equation", + "content": "\\mathbf{C}(\\mathrm{A},\\mathrm{B})" + }, + { + "bbox": [ + 47, + 72, + 289, + 156 + ], + "type": "text", + "content": " are zero. For a large " + }, + { + "bbox": [ + 47, + 72, + 289, + 156 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 47, + 72, + 289, + 156 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 72, + 289, + 156 + ], + "type": "inline_equation", + "content": "R_{\\mathrm{off}}(\\mathbf{C}(\\mathrm{A},\\mathrm{B}))" + }, + { + "bbox": [ + 47, + 72, + 289, + 156 + ], + "type": "text", + "content": " can be a computational burden, as it takes " + }, + { + "bbox": [ + 47, + 72, + 289, + 156 + ], + "type": "inline_equation", + "content": "O(nd^2)" + }, + { + "bbox": [ + 47, + 72, + 289, + 156 + ], + "type": "text", + "content": " time to compute due to the " + }, + { + "bbox": [ + 47, + 72, + 289, + 156 + ], + "type": "inline_equation", + "content": "d\\times d" + }, + { + "bbox": [ + 47, + 72, + 289, + 156 + ], + "type": "text", + "content": " matrix " + }, + { + "bbox": [ + 47, + 72, + 289, + 156 + ], + "type": "inline_equation", + "content": "\\mathbf{C}(\\mathrm{A},\\mathrm{B})" + }, + { + "bbox": [ + 47, + 72, + 289, + 156 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 175, + 287, + 210 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 175, + 287, + 210 + ], + "spans": [ + { + "bbox": [ + 47, + 175, + 287, + 210 + ], + "type": "text", + "content": "VICReg. Let " + }, + { + "bbox": [ + 47, + 175, + 287, + 210 + ], + "type": "inline_equation", + "content": "\\mathbf{K}(\\mathrm{A}),\\mathbf{K}(\\mathrm{B})\\in \\mathbb{R}^{d\\times d}" + }, + { + "bbox": [ + 47, + 175, + 287, + 210 + ], + "type": "text", + "content": " be the covariance matrices of A and B, respectively. The VICReg loss function is" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 83, + 220, + 287, + 296 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 220, + 287, + 296 + ], + "spans": [ + { + "bbox": [ + 83, + 220, + 287, + 296 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} L _ {\\mathrm {V I C}} = \\frac {\\alpha}{n} \\sum_ {k = 1} ^ {n} \\| \\mathbf {a} ^ {(k)} - \\mathbf {b} ^ {(k)} \\| _ {2} ^ {2} \\\\ + \\frac {\\mu}{d} (R _ {\\text {v a r}} (\\mathbf {K} (\\mathrm {A})) + R _ {\\text {v a r}} (\\mathbf {K} (\\mathrm {B}))) \\\\ + \\frac {\\nu}{d} \\left(R _ {\\text {o f f}} (\\mathbf {K} (\\mathrm {A})) + R _ {\\text {o f f}} (\\mathbf {K} (\\mathrm {B}))\\right), \\tag {3} \\\\ \\end{array}", + "image_path": "0ac2cf5d909629163343ab9db96c9ee4106a492d9e2ab90b23087033d3ef2cf1.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 305, + 287, + 329 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 305, + 287, + 329 + ], + "spans": [ + { + "bbox": [ + 47, + 305, + 287, + 329 + ], + "type": "text", + "content": "where hyperparameters " + }, + { + "bbox": [ + 47, + 305, + 287, + 329 + ], + "type": "inline_equation", + "content": "\\alpha, \\mu, \\nu \\geq 0" + }, + { + "bbox": [ + 47, + 305, + 287, + 329 + ], + "type": "text", + "content": " control the importance of individual terms, and " + }, + { + "bbox": [ + 47, + 305, + 287, + 329 + ], + "type": "inline_equation", + "content": "R_{\\mathrm{var}}" + }, + { + "bbox": [ + 47, + 305, + 287, + 329 + ], + "type": "text", + "content": " is the regularizer defined as" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 93, + 340, + 287, + 372 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 93, + 340, + 287, + 372 + ], + "spans": [ + { + "bbox": [ + 93, + 340, + 287, + 372 + ], + "type": "interline_equation", + "content": "R _ {\\text {v a r}} (\\mathbf {M}) = \\sum_ {i = 0} ^ {d - 1} \\max (0, \\gamma - \\sqrt {[ \\mathbf {M} ] _ {i i}}), \\tag {4}", + "image_path": "490f1906d31bed65b9df8006f1d998f3403e324b95c2be6e9e3067d68aa8150b.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 382, + 287, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 382, + 287, + 418 + ], + "spans": [ + { + "bbox": [ + 47, + 382, + 287, + 418 + ], + "type": "text", + "content": "with the target standard deviation " + }, + { + "bbox": [ + 47, + 382, + 287, + 418 + ], + "type": "inline_equation", + "content": "\\gamma > 0" + }, + { + "bbox": [ + 47, + 382, + 287, + 418 + ], + "type": "text", + "content": ". Function " + }, + { + "bbox": [ + 47, + 382, + 287, + 418 + ], + "type": "inline_equation", + "content": "R_{\\mathrm{off}}" + }, + { + "bbox": [ + 47, + 382, + 287, + 418 + ], + "type": "text", + "content": " is the same regularizer as used in Barlow Twins (Eq. (2)), but here, it is applied to " + }, + { + "bbox": [ + 47, + 382, + 287, + 418 + ], + "type": "inline_equation", + "content": "\\mathbf{K}(\\mathbf{A})" + }, + { + "bbox": [ + 47, + 382, + 287, + 418 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 382, + 287, + 418 + ], + "type": "inline_equation", + "content": "\\mathbf{K}(\\mathbf{B})" + }, + { + "bbox": [ + 47, + 382, + 287, + 418 + ], + "type": "text", + "content": " instead of " + }, + { + "bbox": [ + 47, + 382, + 287, + 418 + ], + "type": "inline_equation", + "content": "\\mathbf{C}(\\mathbf{A}, \\mathbf{B})" + }, + { + "bbox": [ + 47, + 382, + 287, + 418 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 418, + 288, + 503 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 418, + 288, + 503 + ], + "spans": [ + { + "bbox": [ + 47, + 418, + 288, + 503 + ], + "type": "text", + "content": "The first term in Eq. (3) brings two embeddings of the same example closer. Regularizer " + }, + { + "bbox": [ + 47, + 418, + 288, + 503 + ], + "type": "inline_equation", + "content": "R_{\\mathrm{var}}" + }, + { + "bbox": [ + 47, + 418, + 288, + 503 + ], + "type": "text", + "content": " penalizes collapsed embeddings with zero variance, whereas " + }, + { + "bbox": [ + 47, + 418, + 288, + 503 + ], + "type": "inline_equation", + "content": "R_{\\mathrm{off}}" + }, + { + "bbox": [ + 47, + 418, + 288, + 503 + ], + "type": "text", + "content": " promotes the diversity of features by encouraging the feature covariance to be zero. The time complexity of calculating " + }, + { + "bbox": [ + 47, + 418, + 288, + 503 + ], + "type": "inline_equation", + "content": "R_{\\mathrm{off}}(\\mathbf{K}(\\mathbf{A}))" + }, + { + "bbox": [ + 47, + 418, + 288, + 503 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 418, + 288, + 503 + ], + "type": "inline_equation", + "content": "R_{\\mathrm{off}}(\\mathbf{K}(\\mathbf{B}))" + }, + { + "bbox": [ + 47, + 418, + 288, + 503 + ], + "type": "text", + "content": " is " + }, + { + "bbox": [ + 47, + 418, + 288, + 503 + ], + "type": "inline_equation", + "content": "O(nd^2)" + }, + { + "bbox": [ + 47, + 418, + 288, + 503 + ], + "type": "text", + "content": ", identical to that of " + }, + { + "bbox": [ + 47, + 418, + 288, + 503 + ], + "type": "inline_equation", + "content": "R_{\\mathrm{off}}(\\mathbf{C}(\\mathbf{A},\\mathbf{B}))" + }, + { + "bbox": [ + 47, + 418, + 288, + 503 + ], + "type": "text", + "content": " in Barlow Twins." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 516, + 153, + 529 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 516, + 153, + 529 + ], + "spans": [ + { + "bbox": [ + 47, + 516, + 153, + 529 + ], + "type": "text", + "content": "4. Proposed Method" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 536, + 287, + 609 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 536, + 287, + 609 + ], + "spans": [ + { + "bbox": [ + 47, + 536, + 287, + 609 + ], + "type": "text", + "content": "We propose a weaker but efficiently computable alternative to the regularizer function " + }, + { + "bbox": [ + 47, + 536, + 287, + 609 + ], + "type": "inline_equation", + "content": "R_{\\mathrm{off}}" + }, + { + "bbox": [ + 47, + 536, + 287, + 609 + ], + "type": "text", + "content": ". In the following, our regularizer is presented in terms of cross-correlation matrix " + }, + { + "bbox": [ + 47, + 536, + 287, + 609 + ], + "type": "inline_equation", + "content": "\\mathbf{C}(\\mathbf{A},\\mathbf{B})" + }, + { + "bbox": [ + 47, + 536, + 287, + 609 + ], + "type": "text", + "content": ", similarly to Barlow Twins. However, if applied instead to " + }, + { + "bbox": [ + 47, + 536, + 287, + 609 + ], + "type": "inline_equation", + "content": "\\mathbf{K}(\\mathbf{A})" + }, + { + "bbox": [ + 47, + 536, + 287, + 609 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 536, + 287, + 609 + ], + "type": "inline_equation", + "content": "\\mathbf{K}(\\mathbf{B})" + }, + { + "bbox": [ + 47, + 536, + 287, + 609 + ], + "type": "text", + "content": ", it produces a relaxed version of the corresponding regularization terms in the VICReg loss." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 619, + 287, + 642 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 619, + 287, + 642 + ], + "spans": [ + { + "bbox": [ + 47, + 619, + 287, + 642 + ], + "type": "text", + "content": "4.1. Regularizer Based on Sums of Cross-correlations" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 650, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 650, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 650, + 287, + 715 + ], + "type": "text", + "content": "Recall that the Barlow Twins loss is based on the cross-correlation matrix " + }, + { + "bbox": [ + 47, + 650, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{C} = \\mathbf{C}(\\mathbf{A},\\mathbf{B})" + }, + { + "bbox": [ + 47, + 650, + 287, + 715 + ], + "type": "text", + "content": " of two views " + }, + { + "bbox": [ + 47, + 650, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathrm{A} = \\{\\mathbf{a}^{(k)}\\}_{k = 1}^n" + }, + { + "bbox": [ + 47, + 650, + 287, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 650, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{B} = \\{\\mathbf{b}^{(k)}\\}_{k = 1}^n" + }, + { + "bbox": [ + 47, + 650, + 287, + 715 + ], + "type": "text", + "content": ". For brevity, assume that both " + }, + { + "bbox": [ + 47, + 650, + 287, + 715 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 47, + 650, + 287, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 650, + 287, + 715 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 47, + 650, + 287, + 715 + ], + "type": "text", + "content": " are standardized. Then, we can simply write " + }, + { + "bbox": [ + 47, + 650, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{C} = (1 / (n - 1))\\sum_{k = 1}^{n}\\mathbf{a}^{(k)}\\mathbf{b}^{(k)^{\\mathrm{T}}}" + }, + { + "bbox": [ + 47, + 650, + 287, + 715 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 315, + 72, + 403, + 156 + ], + "blocks": [ + { + "bbox": [ + 315, + 72, + 403, + 156 + ], + "lines": [ + { + "bbox": [ + 315, + 72, + 403, + 156 + ], + "spans": [ + { + "bbox": [ + 315, + 72, + 403, + 156 + ], + "type": "image", + "image_path": "2e20bb4a5aa16d81709ed344a36120428f5186062bde9c317df86ae9e5ca7c1a.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 167, + 545, + 192 + ], + "lines": [ + { + "bbox": [ + 305, + 167, + 545, + 192 + ], + "spans": [ + { + "bbox": [ + 305, + 167, + 545, + 192 + ], + "type": "text", + "content": "Figure 1. A " + }, + { + "bbox": [ + 305, + 167, + 545, + 192 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 305, + 167, + 545, + 192 + ], + "type": "text", + "content": " cross-correlation matrix " + }, + { + "bbox": [ + 305, + 167, + 545, + 192 + ], + "type": "inline_equation", + "content": "\\mathbf{C} = [c_{ij}]" + }, + { + "bbox": [ + 305, + 167, + 545, + 192 + ], + "type": "inline_equation", + "content": "(i,j = 0,1,2)" + }, + { + "bbox": [ + 305, + 167, + 545, + 192 + ], + "type": "text", + "content": " and sumvec " + }, + { + "bbox": [ + 305, + 167, + 545, + 192 + ], + "type": "inline_equation", + "content": "(\\mathbf{C}) = [\\nu_0\\nu_1\\nu_2]^{\\mathrm{T}}" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 456, + 103, + 525, + 137 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 456, + 103, + 525, + 137 + ], + "spans": [ + { + "bbox": [ + 456, + 103, + 525, + 137 + ], + "type": "interline_equation", + "content": "\\left\\{ \\begin{array}{l} v _ {0} = c _ {0 0} + c _ {1 1} + c _ {2 2} \\\\ v _ {1} = c _ {0 1} + c _ {1 2} + c _ {2 0} \\\\ v _ {2} = c _ {0 2} + c _ {1 0} + c _ {2 1} \\end{array} \\right.", + "image_path": "d7744df96402bf934c8f7eecd1d646739a921ad9e939ba11923e5478fde8adec.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 213, + 545, + 249 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 213, + 545, + 249 + ], + "spans": [ + { + "bbox": [ + 305, + 213, + 545, + 249 + ], + "type": "text", + "content": "Our regularizer is defined in terms of a " + }, + { + "bbox": [ + 305, + 213, + 545, + 249 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 305, + 213, + 545, + 249 + ], + "type": "text", + "content": "-dimensional \"summary\" vector of the " + }, + { + "bbox": [ + 305, + 213, + 545, + 249 + ], + "type": "inline_equation", + "content": "d \\times d" + }, + { + "bbox": [ + 305, + 213, + 545, + 249 + ], + "type": "text", + "content": " matrix " + }, + { + "bbox": [ + 305, + 213, + 545, + 249 + ], + "type": "inline_equation", + "content": "\\mathbf{C}" + }, + { + "bbox": [ + 305, + 213, + 545, + 249 + ], + "type": "text", + "content": ". This vector, denoted by sumvec(" + }, + { + "bbox": [ + 305, + 213, + 545, + 249 + ], + "type": "inline_equation", + "content": "\\mathbf{C}" + }, + { + "bbox": [ + 305, + 213, + 545, + 249 + ], + "type": "text", + "content": "), is given componentwise by" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 351, + 258, + 545, + 291 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 351, + 258, + 545, + 291 + ], + "spans": [ + { + "bbox": [ + 351, + 258, + 545, + 291 + ], + "type": "interline_equation", + "content": "[ \\operatorname {s u m v e c} (\\mathbf {C}) ] _ {i} = \\sum_ {j = 0} ^ {d - 1} [ \\mathbf {C} ] _ {j, (i + j) \\bmod d}. \\tag {5}", + "image_path": "b7859144648a1585d6373d29a9d3db52e6b15a766a78f780c4af2b70ccd75505.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 300, + 545, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 300, + 545, + 396 + ], + "spans": [ + { + "bbox": [ + 305, + 300, + 545, + 396 + ], + "type": "text", + "content": "Note the zero-based component indices. The zeroth component " + }, + { + "bbox": [ + 305, + 300, + 545, + 396 + ], + "type": "inline_equation", + "content": "\\left[\\operatorname{sumvec}(\\mathbf{C})\\right]_0" + }, + { + "bbox": [ + 305, + 300, + 545, + 396 + ], + "type": "text", + "content": " is the trace of " + }, + { + "bbox": [ + 305, + 300, + 545, + 396 + ], + "type": "inline_equation", + "content": "\\mathbf{C}" + }, + { + "bbox": [ + 305, + 300, + 545, + 396 + ], + "type": "text", + "content": ". Each of the remaining " + }, + { + "bbox": [ + 305, + 300, + 545, + 396 + ], + "type": "inline_equation", + "content": "d - 1" + }, + { + "bbox": [ + 305, + 300, + 545, + 396 + ], + "type": "text", + "content": " components corresponds to a sum of " + }, + { + "bbox": [ + 305, + 300, + 545, + 396 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 305, + 300, + 545, + 396 + ], + "type": "text", + "content": " different off-diagonal elements of " + }, + { + "bbox": [ + 305, + 300, + 545, + 396 + ], + "type": "inline_equation", + "content": "\\mathbf{C}" + }, + { + "bbox": [ + 305, + 300, + 545, + 396 + ], + "type": "text", + "content": ", with no single element appearing in two distinct sums. Thus, every element in " + }, + { + "bbox": [ + 305, + 300, + 545, + 396 + ], + "type": "inline_equation", + "content": "\\mathbf{C}" + }, + { + "bbox": [ + 305, + 300, + 545, + 396 + ], + "type": "text", + "content": " appears exactly once in the summations in Eq. (5). The calculation of a summary vector for a " + }, + { + "bbox": [ + 305, + 300, + 545, + 396 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 305, + 300, + 545, + 396 + ], + "type": "text", + "content": " covariance matrix is illustrated in Fig. 1." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 396, + 545, + 421 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 396, + 545, + 421 + ], + "spans": [ + { + "bbox": [ + 305, + 396, + 545, + 421 + ], + "type": "text", + "content": "Now, we define a regularizer in terms of all but the zeroth component of sumvec(C):" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 356, + 430, + 545, + 462 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 356, + 430, + 545, + 462 + ], + "spans": [ + { + "bbox": [ + 356, + 430, + 545, + 462 + ], + "type": "interline_equation", + "content": "R _ {\\text {s u m}} (\\mathbf {C}) = \\sum_ {i = 1} ^ {d - 1} \\| [ \\operatorname {s u m v e c} (\\mathbf {C}) ] _ {i} \\| _ {q} ^ {q}, \\tag {6}", + "image_path": "f6cf67608cc9eb07080f7d3c3e7a4629e6d74f9aae4060f592d5115c2269bbd0.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 471, + 545, + 543 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 471, + 545, + 543 + ], + "spans": [ + { + "bbox": [ + 305, + 471, + 545, + 543 + ], + "type": "text", + "content": "where hyperparameter " + }, + { + "bbox": [ + 305, + 471, + 545, + 543 + ], + "type": "inline_equation", + "content": "q \\in \\{1,2\\}" + }, + { + "bbox": [ + 305, + 471, + 545, + 543 + ], + "type": "text", + "content": ". This function " + }, + { + "bbox": [ + 305, + 471, + 545, + 543 + ], + "type": "inline_equation", + "content": "R_{\\mathrm{sum}}" + }, + { + "bbox": [ + 305, + 471, + 545, + 543 + ], + "type": "text", + "content": " can be used as a drop-in replacement for " + }, + { + "bbox": [ + 305, + 471, + 545, + 543 + ], + "type": "inline_equation", + "content": "R_{\\mathrm{off}}" + }, + { + "bbox": [ + 305, + 471, + 545, + 543 + ], + "type": "text", + "content": " in the Barlow Twins loss (Eq. (1)). The zeroth component " + }, + { + "bbox": [ + 305, + 471, + 545, + 543 + ], + "type": "inline_equation", + "content": "[\\mathrm{sumvec}(\\mathbf{C})]_0" + }, + { + "bbox": [ + 305, + 471, + 545, + 543 + ], + "type": "text", + "content": " is excluded in Eq. (6), because it concerns the diagonal elements of " + }, + { + "bbox": [ + 305, + 471, + 545, + 543 + ], + "type": "inline_equation", + "content": "\\mathbf{C}" + }, + { + "bbox": [ + 305, + 471, + 545, + 543 + ], + "type": "text", + "content": " that are irrelevant to feature decorrelation; they do not appear in Barlow Twin's regularizer " + }, + { + "bbox": [ + 305, + 471, + 545, + 543 + ], + "type": "inline_equation", + "content": "R_{\\mathrm{off}}(\\mathbf{C})" + }, + { + "bbox": [ + 305, + 471, + 545, + 543 + ], + "type": "text", + "content": " either." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 544, + 545, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 544, + 545, + 639 + ], + "spans": [ + { + "bbox": [ + 304, + 544, + 545, + 639 + ], + "type": "text", + "content": "The regularizer " + }, + { + "bbox": [ + 304, + 544, + 545, + 639 + ], + "type": "inline_equation", + "content": "R_{\\mathrm{sum}}" + }, + { + "bbox": [ + 304, + 544, + 545, + 639 + ], + "type": "text", + "content": " is weaker than " + }, + { + "bbox": [ + 304, + 544, + 545, + 639 + ], + "type": "inline_equation", + "content": "R_{\\mathrm{off}}" + }, + { + "bbox": [ + 304, + 544, + 545, + 639 + ], + "type": "text", + "content": " in that it imposes constraints on the components of the summary vector, or the sums of " + }, + { + "bbox": [ + 304, + 544, + 545, + 639 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 544, + 545, + 639 + ], + "type": "text", + "content": " elements of " + }, + { + "bbox": [ + 304, + 544, + 545, + 639 + ], + "type": "inline_equation", + "content": "\\mathbf{C}" + }, + { + "bbox": [ + 304, + 544, + 545, + 639 + ], + "type": "text", + "content": ", whereas " + }, + { + "bbox": [ + 304, + 544, + 545, + 639 + ], + "type": "inline_equation", + "content": "R_{\\mathrm{off}}" + }, + { + "bbox": [ + 304, + 544, + 545, + 639 + ], + "type": "text", + "content": " constrains individual elements. Indeed, the minimizers of " + }, + { + "bbox": [ + 304, + 544, + 545, + 639 + ], + "type": "inline_equation", + "content": "R_{\\mathrm{off}}(\\mathbf{C})" + }, + { + "bbox": [ + 304, + 544, + 545, + 639 + ], + "type": "text", + "content": " also minimize " + }, + { + "bbox": [ + 304, + 544, + 545, + 639 + ], + "type": "inline_equation", + "content": "R_{\\mathrm{sum}}(\\mathbf{C})" + }, + { + "bbox": [ + 304, + 544, + 545, + 639 + ], + "type": "text", + "content": ", but the converse does not necessarily hold. However, as we discuss in Sec. 4.2, " + }, + { + "bbox": [ + 304, + 544, + 545, + 639 + ], + "type": "inline_equation", + "content": "R_{\\mathrm{sum}}" + }, + { + "bbox": [ + 304, + 544, + 545, + 639 + ], + "type": "text", + "content": " allows faster computation. Furthermore, in Sec. 4.3, we provide a simple technique to mitigate the weakness of " + }, + { + "bbox": [ + 304, + 544, + 545, + 639 + ], + "type": "inline_equation", + "content": "R_{\\mathrm{sum}}" + }, + { + "bbox": [ + 304, + 544, + 545, + 639 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 647, + 433, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 647, + 433, + 659 + ], + "spans": [ + { + "bbox": [ + 306, + 647, + 433, + 659 + ], + "type": "text", + "content": "4.2. Efficient Computation" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 305, + 665, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 665, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 665, + 545, + 714 + ], + "type": "text", + "content": "Computing sumvec(C) by Eq. (5) requires the cross-correlation matrix " + }, + { + "bbox": [ + 305, + 665, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{C}(\\mathbf{A},\\mathbf{B})" + }, + { + "bbox": [ + 305, + 665, + 545, + 714 + ], + "type": "text", + "content": ", whose calculation incurs the same computational cost as that of the Barlow Twins loss. However, by means of the Fourier transform, sumvec(C)" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2054" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 107 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 107 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 107 + ], + "type": "text", + "content": "can be calculated directly from the vectors in A and B without explicit calculation of their cross-correlation matrix. To this end, we use involution and circular convolution." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 108, + 286, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 108, + 286, + 156 + ], + "spans": [ + { + "bbox": [ + 46, + 108, + 286, + 156 + ], + "type": "text", + "content": "For a vector " + }, + { + "bbox": [ + 46, + 108, + 286, + 156 + ], + "type": "inline_equation", + "content": "\\mathbf{x} \\in \\mathbb{R}^d" + }, + { + "bbox": [ + 46, + 108, + 286, + 156 + ], + "type": "text", + "content": ", its involution [22] (also called flipping [23]) " + }, + { + "bbox": [ + 46, + 108, + 286, + 156 + ], + "type": "inline_equation", + "content": "\\mathrm{inv}(\\mathbf{x})" + }, + { + "bbox": [ + 46, + 108, + 286, + 156 + ], + "type": "text", + "content": " is the vector obtained by reversing the order of its first (not the zeroth) to " + }, + { + "bbox": [ + 46, + 108, + 286, + 156 + ], + "type": "inline_equation", + "content": "(d - 1)\\mathrm{st}" + }, + { + "bbox": [ + 46, + 108, + 286, + 156 + ], + "type": "text", + "content": " components; i.e., " + }, + { + "bbox": [ + 46, + 108, + 286, + 156 + ], + "type": "inline_equation", + "content": "[\\mathrm{inv}(\\mathbf{x})]_i = [\\mathbf{x}]_{(d - i) \\bmod d}" + }, + { + "bbox": [ + 46, + 108, + 286, + 156 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 46, + 108, + 286, + 156 + ], + "type": "inline_equation", + "content": "i = 0, \\ldots, d - 1" + }, + { + "bbox": [ + 46, + 108, + 286, + 156 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 156, + 286, + 179 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 156, + 286, + 179 + ], + "spans": [ + { + "bbox": [ + 47, + 156, + 286, + 179 + ], + "type": "text", + "content": "For vectors " + }, + { + "bbox": [ + 47, + 156, + 286, + 179 + ], + "type": "inline_equation", + "content": "\\mathbf{x},\\mathbf{y}\\in \\mathbb{R}^d" + }, + { + "bbox": [ + 47, + 156, + 286, + 179 + ], + "type": "text", + "content": " , their circular convolution " + }, + { + "bbox": [ + 47, + 156, + 286, + 179 + ], + "type": "inline_equation", + "content": "\\mathbf{x}*\\mathbf{y}" + }, + { + "bbox": [ + 47, + 156, + 286, + 179 + ], + "type": "text", + "content": " is a " + }, + { + "bbox": [ + 47, + 156, + 286, + 179 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 47, + 156, + 286, + 179 + ], + "type": "text", + "content": " -dimensional vector with components given as" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 98, + 188, + 286, + 222 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 98, + 188, + 286, + 222 + ], + "spans": [ + { + "bbox": [ + 98, + 188, + 286, + 222 + ], + "type": "interline_equation", + "content": "\\left[ \\mathbf {x} * \\mathbf {y} \\right] _ {i} = \\sum_ {j = 0} ^ {d - 1} \\left[ \\mathbf {x y} ^ {\\mathrm {T}} \\right] _ {j, (i - j) \\bmod d}. \\tag {7}", + "image_path": "7ca7f00b594349f98548bebc60fd2bd801227f6d5e053a0a391abf6ca967e75b.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 231, + 286, + 253 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 231, + 286, + 253 + ], + "spans": [ + { + "bbox": [ + 47, + 231, + 286, + 253 + ], + "type": "text", + "content": "As a result, circular convolution is known as the \"compressed outer product.\"" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 253, + 286, + 301 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 253, + 286, + 301 + ], + "spans": [ + { + "bbox": [ + 47, + 253, + 286, + 301 + ], + "type": "text", + "content": "Now, for each twin embedding pair " + }, + { + "bbox": [ + 47, + 253, + 286, + 301 + ], + "type": "inline_equation", + "content": "\\mathbf{a}^{(k)}\\in \\mathrm{A}" + }, + { + "bbox": [ + 47, + 253, + 286, + 301 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 253, + 286, + 301 + ], + "type": "inline_equation", + "content": "\\mathbf{b}^{(k)}\\in" + }, + { + "bbox": [ + 47, + 253, + 286, + 301 + ], + "type": "inline_equation", + "content": "\\mathbf{B}(k = 1,\\dots ,n)" + }, + { + "bbox": [ + 47, + 253, + 286, + 301 + ], + "type": "text", + "content": ", let us consider vector " + }, + { + "bbox": [ + 47, + 253, + 286, + 301 + ], + "type": "inline_equation", + "content": "\\operatorname {inv}(\\mathbf{a}^{(k)})*\\mathbf{b}^{(k)}\\in" + }, + { + "bbox": [ + 47, + 253, + 286, + 301 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^d" + }, + { + "bbox": [ + 47, + 253, + 286, + 301 + ], + "type": "text", + "content": ". Noting the indices altered by involution, we see that this vector is given componentwise by" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 59, + 311, + 286, + 344 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 311, + 286, + 344 + ], + "spans": [ + { + "bbox": [ + 59, + 311, + 286, + 344 + ], + "type": "interline_equation", + "content": "\\left[ \\operatorname {i n v} \\left(\\mathbf {a} ^ {(k)}\\right) * \\mathbf {b} ^ {(k)} \\right] _ {i} = \\sum_ {j = 0} ^ {d - 1} \\left[ \\mathbf {a} ^ {(k)} \\mathbf {b} ^ {(k) ^ {\\mathrm {T}}} \\right] _ {j, (i + j) \\bmod d}. \\tag {8}", + "image_path": "b3c59a74cd0fe95d02babd1017b4b6291828aa30fcc30bd6ec22578842a91f2c.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 354, + 286, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 354, + 286, + 380 + ], + "spans": [ + { + "bbox": [ + 47, + 354, + 286, + 380 + ], + "type": "text", + "content": "Substituting " + }, + { + "bbox": [ + 47, + 354, + 286, + 380 + ], + "type": "inline_equation", + "content": "\\mathbf{C} = (1 / (n - 1))\\sum_{k = 1}^{n}\\mathbf{a}^{(k)}\\mathbf{b}^{(k)^{\\mathrm{T}}}" + }, + { + "bbox": [ + 47, + 354, + 286, + 380 + ], + "type": "text", + "content": " into Eq. (5) and using Eq. (8), we have" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 56, + 389, + 287, + 510 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 389, + 287, + 510 + ], + "spans": [ + { + "bbox": [ + 56, + 389, + 287, + 510 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} [ \\operatorname {s u m v e c} (\\mathbf {C}) ] _ {i} = \\sum_ {j = 0} ^ {d - 1} \\overbrace {\\left[ \\frac {1}{n - 1} \\sum_ {k = 1} ^ {n} \\mathbf {a} ^ {(k)} \\mathbf {b} ^ {(k) ^ {\\mathrm {T}}} \\right] _ {j , (i + j) \\bmod d}} ^ {\\mathbf {c}} \\\\ = \\frac {1}{n - 1} \\sum_ {k = 1} ^ {n} \\sum_ {j = 0} ^ {d - 1} \\left[ \\mathbf {a} ^ {(k)} \\mathbf {b} ^ {(k) ^ {\\mathrm {T}}} \\right] _ {j, (i + j) \\bmod d} \\\\ = \\frac {1}{n - 1} \\sum_ {k = 1} ^ {n} \\left[ \\operatorname {i n v} \\left(\\mathbf {a} ^ {(k)}\\right) * \\mathbf {b} ^ {(k)} \\right] _ {i}, \\tag {9} \\\\ \\end{array}", + "image_path": "5433ad717b5222bd350bb6c4225996a67de7c9bd9c5fa6b256e396fce106fdd8.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 518, + 107, + 528 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 518, + 107, + 528 + ], + "spans": [ + { + "bbox": [ + 47, + 518, + 107, + 528 + ], + "type": "text", + "content": "or, as a vector," + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 83, + 536, + 286, + 567 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 536, + 286, + 567 + ], + "spans": [ + { + "bbox": [ + 83, + 536, + 286, + 567 + ], + "type": "interline_equation", + "content": "\\operatorname {s u m v e c} (\\mathbf {C}) = \\frac {1}{n - 1} \\sum_ {k = 1} ^ {n} \\operatorname {i n v} \\left(\\mathbf {a} ^ {(k)}\\right) * \\mathbf {b} ^ {(k)}. \\tag {10}", + "image_path": "2329c011578abe12cbc04266eaba682bd588ecf0bc1df4c3c180bede89b61e89.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 577, + 286, + 638 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 577, + 286, + 638 + ], + "spans": [ + { + "bbox": [ + 47, + 577, + 286, + 638 + ], + "type": "text", + "content": "Let " + }, + { + "bbox": [ + 47, + 577, + 286, + 638 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 47, + 577, + 286, + 638 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 577, + 286, + 638 + ], + "type": "inline_equation", + "content": "\\mathcal{F}^{-1}" + }, + { + "bbox": [ + 47, + 577, + 286, + 638 + ], + "type": "text", + "content": " denote the discrete Fourier transform and inverse discrete Fourier transform, respectively. Noting that " + }, + { + "bbox": [ + 47, + 577, + 286, + 638 + ], + "type": "inline_equation", + "content": "\\mathcal{F}(\\mathrm{inv}(\\mathbf{x})) = \\overline{\\mathcal{F}(\\mathbf{x})}" + }, + { + "bbox": [ + 47, + 577, + 286, + 638 + ], + "type": "text", + "content": " for any " + }, + { + "bbox": [ + 47, + 577, + 286, + 638 + ], + "type": "inline_equation", + "content": "\\mathbf{x} \\in \\mathbb{R}^d" + }, + { + "bbox": [ + 47, + 577, + 286, + 638 + ], + "type": "text", + "content": " (see e.g., [23], Section 7.4.2) and using the convolution theorem " + }, + { + "bbox": [ + 47, + 577, + 286, + 638 + ], + "type": "inline_equation", + "content": "\\mathcal{F}(\\mathbf{x} * \\mathbf{y}) = \\mathcal{F}(\\mathbf{x}) \\circ \\mathcal{F}(\\mathbf{y})" + }, + { + "bbox": [ + 47, + 577, + 286, + 638 + ], + "type": "text", + "content": ", we have" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 67, + 647, + 286, + 666 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 647, + 286, + 666 + ], + "spans": [ + { + "bbox": [ + 67, + 647, + 286, + 666 + ], + "type": "interline_equation", + "content": "\\operatorname {i n v} \\left(\\mathbf {a} ^ {(k)}\\right) * \\mathbf {b} ^ {(k)} = \\mathcal {F} ^ {- 1} \\left(\\overline {{\\mathcal {F} \\left(\\mathbf {a} ^ {(k)}\\right)}} \\circ \\mathcal {F} \\left(\\mathbf {b} ^ {(k)}\\right)\\right). \\tag {11}", + "image_path": "c1ec0dac4793cd454f012680c7f0ed21245e850c9425f48ef393b22b6cb40e71.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 72, + 489, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 489, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 489, + 84 + ], + "type": "text", + "content": "Substituting Eq. (11) into Eq. (10), we obtain" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 315, + 92, + 544, + 173 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 92, + 544, + 173 + ], + "spans": [ + { + "bbox": [ + 315, + 92, + 544, + 173 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\operatorname {s u m v e c} (\\mathbf {C}) = \\frac {1}{n - 1} \\sum_ {k = 1} ^ {n} \\overbrace {\\mathcal {F} ^ {- 1} \\left(\\overline {{\\mathcal {F} \\left(\\mathbf {a} ^ {(k)}\\right)}} \\circ \\mathcal {F} \\left(\\mathbf {b} ^ {(k)}\\right)\\right)} ^ {\\operatorname {i n v} \\left(\\mathbf {a} ^ {(k)}\\right) * \\mathbf {b} ^ {(k)}} \\\\ = \\frac {1}{n - 1} \\mathcal {F} ^ {- 1} \\left(\\sum_ {k = 1} ^ {n} \\overline {{\\mathcal {F} (\\mathbf {a} ^ {(k)})}} \\circ \\mathcal {F} (\\mathbf {b} ^ {(k)})\\right). \\tag {12} \\\\ \\end{array}", + "image_path": "cac38959ec1f61f80aa81ec8fc3a548071106378b5a9d2e62792ef5d6d38674d.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 180, + 545, + 311 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 180, + 545, + 311 + ], + "spans": [ + { + "bbox": [ + 304, + 180, + 545, + 311 + ], + "type": "text", + "content": "Using this equation, we can compute sumvec(C) directly from the embedding vectors " + }, + { + "bbox": [ + 304, + 180, + 545, + 311 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{a}^{(k)},\\mathbf{b}^{(k)}\\}_{k = 1}^{n}" + }, + { + "bbox": [ + 304, + 180, + 545, + 311 + ], + "type": "text", + "content": ", bypassing the cumbersome calculation of C. Noting that the (inverse) Fourier transform of a " + }, + { + "bbox": [ + 304, + 180, + 545, + 311 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 180, + 545, + 311 + ], + "type": "text", + "content": " -dimensional vector can be performed in " + }, + { + "bbox": [ + 304, + 180, + 545, + 311 + ], + "type": "inline_equation", + "content": "O(d\\log d)" + }, + { + "bbox": [ + 304, + 180, + 545, + 311 + ], + "type": "text", + "content": " time by the FFT algorithm, while the calculation of complex conjugates, component products, and the sum of " + }, + { + "bbox": [ + 304, + 180, + 545, + 311 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 180, + 545, + 311 + ], + "type": "text", + "content": " vectors takes " + }, + { + "bbox": [ + 304, + 180, + 545, + 311 + ], + "type": "inline_equation", + "content": "O(nd)" + }, + { + "bbox": [ + 304, + 180, + 545, + 311 + ], + "type": "text", + "content": " time, we can see that the overall time to obtain sumvec(C) is " + }, + { + "bbox": [ + 304, + 180, + 545, + 311 + ], + "type": "inline_equation", + "content": "O(nd\\log d)" + }, + { + "bbox": [ + 304, + 180, + 545, + 311 + ], + "type": "text", + "content": ", which is also the time needed to compute " + }, + { + "bbox": [ + 304, + 180, + 545, + 311 + ], + "type": "inline_equation", + "content": "R_{\\mathrm{sum}}(\\mathbf{C})" + }, + { + "bbox": [ + 304, + 180, + 545, + 311 + ], + "type": "text", + "content": ". This is a substantial improvement over the " + }, + { + "bbox": [ + 304, + 180, + 545, + 311 + ], + "type": "inline_equation", + "content": "O(nd^2)" + }, + { + "bbox": [ + 304, + 180, + 545, + 311 + ], + "type": "text", + "content": " computation time of " + }, + { + "bbox": [ + 304, + 180, + 545, + 311 + ], + "type": "inline_equation", + "content": "R_{\\mathrm{off}}(\\mathbf{C})" + }, + { + "bbox": [ + 304, + 180, + 545, + 311 + ], + "type": "text", + "content": " in the Barlow Twins loss." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 312, + 545, + 371 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 312, + 545, + 371 + ], + "spans": [ + { + "bbox": [ + 305, + 312, + 545, + 371 + ], + "type": "text", + "content": "Furthermore, the space complexity of computing " + }, + { + "bbox": [ + 305, + 312, + 545, + 371 + ], + "type": "inline_equation", + "content": "R_{\\mathrm{sum}}(\\mathbf{C})" + }, + { + "bbox": [ + 305, + 312, + 545, + 371 + ], + "type": "text", + "content": " is " + }, + { + "bbox": [ + 305, + 312, + 545, + 371 + ], + "type": "inline_equation", + "content": "O(nd)" + }, + { + "bbox": [ + 305, + 312, + 545, + 371 + ], + "type": "text", + "content": ", which is optimal if the " + }, + { + "bbox": [ + 305, + 312, + 545, + 371 + ], + "type": "inline_equation", + "content": "O(nd)" + }, + { + "bbox": [ + 305, + 312, + 545, + 371 + ], + "type": "text", + "content": " space needed to store input vectors A and B is considered as part of the complexity. In contrast, Barlow Twins requires extra " + }, + { + "bbox": [ + 305, + 312, + 545, + 371 + ], + "type": "inline_equation", + "content": "O(d^2)" + }, + { + "bbox": [ + 305, + 312, + 545, + 371 + ], + "type": "text", + "content": " space to store C." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 379, + 545, + 402 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 379, + 545, + 402 + ], + "spans": [ + { + "bbox": [ + 305, + 379, + 545, + 402 + ], + "type": "text", + "content": "4.3. Feature Permutation to Mitigate Undesirable Local Minima" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 409, + 545, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 409, + 545, + 529 + ], + "spans": [ + { + "bbox": [ + 304, + 409, + 545, + 529 + ], + "type": "text", + "content": "As seen from Eq. (5), the components of sumvec(C) are the sums of " + }, + { + "bbox": [ + 304, + 409, + 545, + 529 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 409, + 545, + 529 + ], + "type": "text", + "content": " elements in C, and the proposed regularizer " + }, + { + "bbox": [ + 304, + 409, + 545, + 529 + ], + "type": "inline_equation", + "content": "R_{\\mathrm{sum}}" + }, + { + "bbox": [ + 304, + 409, + 545, + 529 + ], + "type": "text", + "content": " (Eq. (6)) encourages these sums to be close to zero. This is weaker than the regularizer " + }, + { + "bbox": [ + 304, + 409, + 545, + 529 + ], + "type": "inline_equation", + "content": "R_{\\mathrm{off}}" + }, + { + "bbox": [ + 304, + 409, + 545, + 529 + ], + "type": "text", + "content": " (Eq. (2)) in the Barlow Twins loss, which pushes individual elements of C towards zero. Indeed, " + }, + { + "bbox": [ + 304, + 409, + 545, + 529 + ], + "type": "inline_equation", + "content": "R_{\\mathrm{sum}}(\\mathbf{C})" + }, + { + "bbox": [ + 304, + 409, + 545, + 529 + ], + "type": "text", + "content": " can be close to zero even if individual elements in C are not; the summands in Eq. (5) can cancel each other, since they can be either positive or negative. As a result, undesirable local minima develop in the parameter space, rendering our regularizer ineffective." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 529, + 545, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 529, + 545, + 624 + ], + "spans": [ + { + "bbox": [ + 304, + 529, + 545, + 624 + ], + "type": "text", + "content": "Here, we propose a technique to eliminate these local minima: we randomly permute feature indices during training so that sums of different cross-correlation terms constitute sumvec(C). To understand why this simple technique is effective, consider minimizing " + }, + { + "bbox": [ + 304, + 529, + 545, + 624 + ], + "type": "inline_equation", + "content": "R_{\\mathrm{sum}}(\\mathbf{C})" + }, + { + "bbox": [ + 304, + 529, + 545, + 624 + ], + "type": "text", + "content": ", regarding the elements of C as independent3 variables. It is easy to see that the minimum is attained by the solutions to a homogeneous system of linear equations:" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 325, + 632, + 524, + 685 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 325, + 632, + 524, + 685 + ], + "spans": [ + { + "bbox": [ + 325, + 632, + 524, + 685 + ], + "type": "interline_equation", + "content": "\\overbrace {\\sum_ {j = 0} ^ {d - 1} [ \\mathbf {C} ] _ {j , (i + j) \\bmod d}} ^ {\\left[ \\operatorname {s u m v e c} (\\mathbf {C}) \\right] _ {i}} = 0, \\qquad \\text {f o r} i = 1, \\dots , d - 1.", + "image_path": "aa1b477fb64e8df8d10da189827376a0b5a610e10d4b437c88f55fdfb7a1e6e7.jpg" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 46, + 673, + 287, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 673, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 673, + 287, + 712 + ], + "type": "text", + "content": "2The vector " + }, + { + "bbox": [ + 46, + 673, + 287, + 712 + ], + "type": "inline_equation", + "content": "\\mathrm{inv}(\\mathbf{x})*\\mathbf{y}" + }, + { + "bbox": [ + 46, + 673, + 287, + 712 + ], + "type": "text", + "content": " is known as the circular (cross-)correlation of " + }, + { + "bbox": [ + 46, + 673, + 287, + 712 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 46, + 673, + 287, + 712 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 673, + 287, + 712 + ], + "type": "inline_equation", + "content": "\\mathbf{y}" + }, + { + "bbox": [ + 46, + 673, + 287, + 712 + ], + "type": "text", + "content": " [20, 22, 23]. We opt not to use this term in this paper to avoid confusion with the cross-correlation of random vectors, which is used in Barlow Twins." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 693, + 545, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 693, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 306, + 693, + 545, + 712 + ], + "type": "text", + "content": "3This assumption is not unrealistic given the high capacity of modern neural networks." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2055" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "type": "text", + "content": "This is an underdetermined system, with only " + }, + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "type": "inline_equation", + "content": "d - 1" + }, + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "type": "text", + "content": " equations but with " + }, + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "type": "inline_equation", + "content": "d(d - 1)" + }, + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "type": "text", + "content": " unknowns, namely, " + }, + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "type": "inline_equation", + "content": "[\\mathbf{C}]_{j\\ell}, j, \\ell = 0, \\dots, d - 1, j \\neq \\ell" + }, + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "type": "text", + "content": ". This underdeterminacy is the cause of nontrivial solutions such that " + }, + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "type": "inline_equation", + "content": "[\\mathbf{C}]_{j\\ell} \\neq 0" + }, + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "type": "text", + "content": ", that is, undesirable solutions in which summands with opposite signs cancel each other in an equation." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 144, + 288, + 215 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 144, + 288, + 215 + ], + "spans": [ + { + "bbox": [ + 46, + 144, + 288, + 215 + ], + "type": "text", + "content": "Now, by repeatedly permuting the feature indices and minimizing the loss, we effectively introduce additional equations to the system, since permutation can produce different sets of linear equations over the unknowns, and these new constraints eventually render nontrivial solutions inadmissible." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 216, + 288, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 216, + 288, + 323 + ], + "spans": [ + { + "bbox": [ + 46, + 216, + 288, + 323 + ], + "type": "text", + "content": "For ease of implementation, we permute feature indices randomly during training, instead of generating all permutations systematically at once, similarly to the way that stochastic gradient descent is a modification to full gradient descent. Note that the permuted feature indices need not be identical across mini-batches, even within a single epoch; indeed, in the experiments presented in Sec. 5, we use a different random permutation of features in every mini-batch in every epoch." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 331, + 287, + 354 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 331, + 287, + 354 + ], + "spans": [ + { + "bbox": [ + 47, + 331, + 287, + 354 + ], + "type": "text", + "content": "4.4. Feature Grouping to Control the Degree of Relaxation" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 361, + 288, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 361, + 288, + 445 + ], + "spans": [ + { + "bbox": [ + 46, + 361, + 288, + 445 + ], + "type": "text", + "content": "Instead of computing a summary vector for an entire cross-correlation matrix " + }, + { + "bbox": [ + 46, + 361, + 288, + 445 + ], + "type": "inline_equation", + "content": "\\mathbf{C}" + }, + { + "bbox": [ + 46, + 361, + 288, + 445 + ], + "type": "text", + "content": ", we can compute summaries at a more fine-grained level. Specifically, we partition " + }, + { + "bbox": [ + 46, + 361, + 288, + 445 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 361, + 288, + 445 + ], + "type": "text", + "content": " features into groups of size " + }, + { + "bbox": [ + 46, + 361, + 288, + 445 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 46, + 361, + 288, + 445 + ], + "type": "text", + "content": " each4. This partitioning induces in " + }, + { + "bbox": [ + 46, + 361, + 288, + 445 + ], + "type": "inline_equation", + "content": "\\mathbf{C}" + }, + { + "bbox": [ + 46, + 361, + 288, + 445 + ], + "type": "text", + "content": " a total of " + }, + { + "bbox": [ + 46, + 361, + 288, + 445 + ], + "type": "inline_equation", + "content": "\\lceil d / b \\rceil^2" + }, + { + "bbox": [ + 46, + 361, + 288, + 445 + ], + "type": "text", + "content": " block submatrices of size " + }, + { + "bbox": [ + 46, + 361, + 288, + 445 + ], + "type": "inline_equation", + "content": "b \\times b" + }, + { + "bbox": [ + 46, + 361, + 288, + 445 + ], + "type": "text", + "content": ", i.e., " + }, + { + "bbox": [ + 46, + 361, + 288, + 445 + ], + "type": "inline_equation", + "content": "\\mathbf{C} = [\\mathbf{C}_{ij}](i,j = 1,\\dots,\\lceil d / b \\rceil)" + }, + { + "bbox": [ + 46, + 361, + 288, + 445 + ], + "type": "text", + "content": " with submatrices " + }, + { + "bbox": [ + 46, + 361, + 288, + 445 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_{ij} \\in \\mathbb{R}^{b \\times b}" + }, + { + "bbox": [ + 46, + 361, + 288, + 445 + ], + "type": "text", + "content": ". We then define the regularizer as" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 64, + 454, + 287, + 531 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 64, + 454, + 287, + 531 + ], + "spans": [ + { + "bbox": [ + 64, + 454, + 287, + 531 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} R _ {\\operatorname {s u m}} ^ {(b)} (\\mathbf {C}) = \\sum_ {i = 1} ^ {\\lceil d / b \\rceil} \\sum_ {\\ell = 1} ^ {b - 1} \\| [ \\operatorname {s u m v e c} (\\mathbf {C} _ {i i}) ] _ {\\ell} \\| _ {q} ^ {q} \\\\ + \\sum_ {\\substack {i, j = 1 \\\\ i \\neq j}} ^ {\\lceil d / b \\rceil} \\sum_ {\\ell = 0} ^ {b - 1} \\left\\| \\left[ \\operatorname {sumvec} \\left(\\mathbf{C}_{ij}\\right) \\right] _ {\\ell} \\right\\| _ {q} ^ {q}. \\tag{13} \\\\ \\end{array}", + "image_path": "ed81acd121e723f4ace504dd0d386db828f1aa4c5e538633044b9bddc4c36629.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 540, + 287, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 540, + 287, + 624 + ], + "spans": [ + { + "bbox": [ + 46, + 540, + 287, + 624 + ], + "type": "text", + "content": "As before, " + }, + { + "bbox": [ + 46, + 540, + 287, + 624 + ], + "type": "inline_equation", + "content": "\\mathrm{sumvec}(\\mathbf{C}_{ij})" + }, + { + "bbox": [ + 46, + 540, + 287, + 624 + ], + "type": "text", + "content": " can be computed without explicitly computing " + }, + { + "bbox": [ + 46, + 540, + 287, + 624 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_{ij}" + }, + { + "bbox": [ + 46, + 540, + 287, + 624 + ], + "type": "text", + "content": " by means of involution, circular convolution (of subvectors of embeddings), and the Fourier transform. Calculating a single " + }, + { + "bbox": [ + 46, + 540, + 287, + 624 + ], + "type": "inline_equation", + "content": "\\mathrm{sumvec}(\\mathbf{C}_{ij})" + }, + { + "bbox": [ + 46, + 540, + 287, + 624 + ], + "type": "text", + "content": " takes " + }, + { + "bbox": [ + 46, + 540, + 287, + 624 + ], + "type": "inline_equation", + "content": "O(nb\\log b)" + }, + { + "bbox": [ + 46, + 540, + 287, + 624 + ], + "type": "text", + "content": " time using FFT, and since there are " + }, + { + "bbox": [ + 46, + 540, + 287, + 624 + ], + "type": "inline_equation", + "content": "\\lceil d / b\\rceil^2" + }, + { + "bbox": [ + 46, + 540, + 287, + 624 + ], + "type": "text", + "content": " blocks, the total time needed to compute " + }, + { + "bbox": [ + 46, + 540, + 287, + 624 + ], + "type": "inline_equation", + "content": "R_{\\mathrm{sum}}^{(b)}" + }, + { + "bbox": [ + 46, + 540, + 287, + 624 + ], + "type": "text", + "content": " is " + }, + { + "bbox": [ + 46, + 540, + 287, + 624 + ], + "type": "inline_equation", + "content": "O((nd^2 /b)\\log b)" + }, + { + "bbox": [ + 46, + 540, + 287, + 624 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 625, + 287, + 686 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 625, + 287, + 686 + ], + "spans": [ + { + "bbox": [ + 46, + 625, + 287, + 686 + ], + "type": "text", + "content": "The block size hyperparameter " + }, + { + "bbox": [ + 46, + 625, + 287, + 686 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 46, + 625, + 287, + 686 + ], + "type": "text", + "content": " controls the granularity of the summary computation and interpolates the proposed and existing regularizers. On one hand, the regularizer " + }, + { + "bbox": [ + 46, + 625, + 287, + 686 + ], + "type": "inline_equation", + "content": "R_{\\mathrm{sum}}^{(1)}(\\mathbf{C})" + }, + { + "bbox": [ + 46, + 625, + 287, + 686 + ], + "type": "text", + "content": " reduces " + }, + { + "bbox": [ + 46, + 625, + 287, + 686 + ], + "type": "inline_equation", + "content": "R_{\\mathrm{off}}(\\mathbf{C})" + }, + { + "bbox": [ + 46, + 625, + 287, + 686 + ], + "type": "text", + "content": " of Barlow Twins when " + }, + { + "bbox": [ + 46, + 625, + 287, + 686 + ], + "type": "inline_equation", + "content": "b = 1" + }, + { + "bbox": [ + 46, + 625, + 287, + 686 + ], + "type": "text", + "content": ", provided that " + }, + { + "bbox": [ + 46, + 625, + 287, + 686 + ], + "type": "inline_equation", + "content": "q = 2" + }, + { + "bbox": [ + 46, + 625, + 287, + 686 + ], + "type": "text", + "content": ". On the other hand, when " + }, + { + "bbox": [ + 46, + 625, + 287, + 686 + ], + "type": "inline_equation", + "content": "b = d" + }, + { + "bbox": [ + 46, + 625, + 287, + 686 + ], + "type": "text", + "content": ", we" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 71, + 545, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 71, + 545, + 167 + ], + "spans": [ + { + "bbox": [ + 304, + 71, + 545, + 167 + ], + "type": "text", + "content": "recover " + }, + { + "bbox": [ + 304, + 71, + 545, + 167 + ], + "type": "inline_equation", + "content": "R_{\\mathrm{sum}}^{(d)}(\\mathbf{C}) = R_{\\mathrm{sum}}(\\mathbf{C})" + }, + { + "bbox": [ + 304, + 71, + 545, + 167 + ], + "type": "text", + "content": " given in Eq. (6). Thus, this grouping formulation provides a generalization of Barlow Twins, with parameter " + }, + { + "bbox": [ + 304, + 71, + 545, + 167 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 304, + 71, + 545, + 167 + ], + "type": "text", + "content": " controlling the trade-off between the computational efficiency and the degree of relaxed regularization. Empirically, the performance can be slightly improved by the use of a feature group of moderate size, with no substantial degradation observed in training time and memory usage; see Sec. 5." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 168, + 545, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 168, + 545, + 192 + ], + "spans": [ + { + "bbox": [ + 305, + 168, + 545, + 192 + ], + "type": "text", + "content": "It should be noted that the permutation and grouping of features are compatible and can be combined." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 198, + 545, + 222 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 198, + 545, + 222 + ], + "spans": [ + { + "bbox": [ + 305, + 198, + 545, + 222 + ], + "type": "text", + "content": "4.5. Regularizer Based on Sums of Feature Covariances" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 228, + 545, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 228, + 545, + 312 + ], + "spans": [ + { + "bbox": [ + 305, + 228, + 545, + 312 + ], + "type": "text", + "content": "The function " + }, + { + "bbox": [ + 305, + 228, + 545, + 312 + ], + "type": "inline_equation", + "content": "R_{\\mathrm{sum}}" + }, + { + "bbox": [ + 305, + 228, + 545, + 312 + ], + "type": "text", + "content": " can also be used to define a VICReg-style regularizer based on covariance, simply by replacing " + }, + { + "bbox": [ + 305, + 228, + 545, + 312 + ], + "type": "inline_equation", + "content": "R_{\\mathrm{off}}" + }, + { + "bbox": [ + 305, + 228, + 545, + 312 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 305, + 228, + 545, + 312 + ], + "type": "inline_equation", + "content": "R_{\\mathrm{sum}}" + }, + { + "bbox": [ + 305, + 228, + 545, + 312 + ], + "type": "text", + "content": " in Eq. (3), and passing correlation matrices " + }, + { + "bbox": [ + 305, + 228, + 545, + 312 + ], + "type": "inline_equation", + "content": "\\mathbf{K}(\\mathbf{A})" + }, + { + "bbox": [ + 305, + 228, + 545, + 312 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 305, + 228, + 545, + 312 + ], + "type": "inline_equation", + "content": "\\mathbf{K}(\\mathbf{B})" + }, + { + "bbox": [ + 305, + 228, + 545, + 312 + ], + "type": "text", + "content": " instead of " + }, + { + "bbox": [ + 305, + 228, + 545, + 312 + ], + "type": "inline_equation", + "content": "\\mathbf{C}(\\mathbf{A}, \\mathbf{B})" + }, + { + "bbox": [ + 305, + 228, + 545, + 312 + ], + "type": "text", + "content": " as the argument. Fast computation is possible with FFT, and the grouping version is also straightforward; this is described in greater detail in Supplementary Material." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 319, + 470, + 331 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 319, + 470, + 331 + ], + "spans": [ + { + "bbox": [ + 306, + 319, + 470, + 331 + ], + "type": "text", + "content": "4.6. Summary of Proposed Models" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 338, + 545, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 338, + 545, + 384 + ], + "spans": [ + { + "bbox": [ + 305, + 338, + 545, + 384 + ], + "type": "text", + "content": "The loss functions of the proposed models are summarized below. Let the function " + }, + { + "bbox": [ + 305, + 338, + 545, + 384 + ], + "type": "inline_equation", + "content": "R = R_{\\mathrm{sum}}^{(b)}" + }, + { + "bbox": [ + 305, + 338, + 545, + 384 + ], + "type": "text", + "content": " if feature grouping is used with block size " + }, + { + "bbox": [ + 305, + 338, + 545, + 384 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 305, + 338, + 545, + 384 + ], + "type": "text", + "content": ", or let " + }, + { + "bbox": [ + 305, + 338, + 545, + 384 + ], + "type": "inline_equation", + "content": "R = R_{\\mathrm{sum}}" + }, + { + "bbox": [ + 305, + 338, + 545, + 384 + ], + "type": "text", + "content": " if grouping is not used." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 386, + 545, + 409 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 386, + 545, + 409 + ], + "spans": [ + { + "bbox": [ + 305, + 386, + 545, + 409 + ], + "type": "text", + "content": "For Barlow Twins-style cross-correlation regularization, the loss function is" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 308, + 415, + 545, + 439 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 415, + 545, + 439 + ], + "spans": [ + { + "bbox": [ + 308, + 415, + 545, + 439 + ], + "type": "interline_equation", + "content": "L = \\sum_ {i} (1 - [ \\mathbf {C} (\\mathrm {A}, \\mathrm {B}) ] _ {i i}) ^ {2} + \\lambda R (\\mathbf {C} (\\mathrm {A}, \\mathrm {B})), \\tag {14}", + "image_path": "46671ef8caab881c7d26ac29c80fcbed1ef8d029d1cdbc2371cd47e7de2db0a4.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 445, + 545, + 457 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 445, + 545, + 457 + ], + "spans": [ + { + "bbox": [ + 306, + 445, + 545, + 457 + ], + "type": "text", + "content": "whereas for VICReg-style covariance regularization, we use" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 309, + 462, + 545, + 510 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 462, + 545, + 510 + ], + "spans": [ + { + "bbox": [ + 309, + 462, + 545, + 510 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} L = \\frac {\\alpha}{n} \\sum_ {i} \\| \\mathbf {a} ^ {(i)} - \\mathbf {b} ^ {(i)} \\| _ {2} ^ {2} + \\frac {\\mu}{d} \\left(R _ {\\text {v a r}} (\\mathbf {K} (\\mathbf {A})) + R _ {\\text {v a r}} (\\mathbf {K} (\\mathbf {B}))\\right) \\\\ + \\frac {\\nu}{d} (R (\\mathbf {K} (\\mathrm {A})) + R (\\mathbf {K} (\\mathrm {B}))). \\tag {15} \\\\ \\end{array}", + "image_path": "1b965cde2ee04154350e72d313a756d973bfcf2a2bf9305388b1da8bdf09b60a.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 516, + 545, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 516, + 545, + 540 + ], + "spans": [ + { + "bbox": [ + 305, + 516, + 545, + 540 + ], + "type": "text", + "content": "Setting " + }, + { + "bbox": [ + 305, + 516, + 545, + 540 + ], + "type": "inline_equation", + "content": "R = R_{\\mathrm{off}}" + }, + { + "bbox": [ + 305, + 516, + 545, + 540 + ], + "type": "text", + "content": " in these formulas gives the original Barlow Twins and VICReg, when hyperparameter " + }, + { + "bbox": [ + 305, + 516, + 545, + 540 + ], + "type": "inline_equation", + "content": "q = 2" + }, + { + "bbox": [ + 305, + 516, + 545, + 540 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 550, + 387, + 563 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 550, + 387, + 563 + ], + "spans": [ + { + "bbox": [ + 306, + 550, + 387, + 563 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 570, + 545, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 545, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 545, + 665 + ], + "type": "text", + "content": "We empirically evaluate the effect of the proposed regularizers. To be precise, we train SSL models using the Barlow Twins-style loss function of Eq. (14) and the VICReg-style loss function of Eq. (15) and compare their performance with Barlow Twins and VICReg in downstream tasks. The training time and memory consumption are also evaluated. For our models, feature permutation is performed in every batch iteration except for the ablation study." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 666, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 666, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 666, + 545, + 713 + ], + "type": "text", + "content": "In the following, we briefly present the tasks and datasets used in the experiments. See Supplementary Material for the complete experimental setup, including the hyperparameter values and the results of additional experiments." + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 46, + 693, + 287, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 693, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 693, + 287, + 713 + ], + "type": "text", + "content": "4If " + }, + { + "bbox": [ + 46, + 693, + 287, + 713 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 693, + 287, + 713 + ], + "type": "text", + "content": " is not divisible by " + }, + { + "bbox": [ + 46, + 693, + 287, + 713 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 46, + 693, + 287, + 713 + ], + "type": "text", + "content": ", pad dummy features that are constantly 0 in the last group." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2056" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 57, + 135, + 277, + 304 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 288, + 126 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 288, + 126 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 288, + 126 + ], + "type": "text", + "content": "Table 1. Linear evaluation accuracy (\\%) on ImageNet-100 with " + }, + { + "bbox": [ + 46, + 70, + 288, + 126 + ], + "type": "inline_equation", + "content": "d = 2048" + }, + { + "bbox": [ + 46, + 70, + 288, + 126 + ], + "type": "text", + "content": ". Bold numbers indicate the best performance within each family (cross-correlation regularization, covariance regularization, or other SSL models). †: quoted from the solo-learn [26] GitHub repository as of December 28, 2022; ‡: quoted from [30]." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 57, + 135, + 277, + 304 + ], + "lines": [ + { + "bbox": [ + 57, + 135, + 277, + 304 + ], + "spans": [ + { + "bbox": [ + 57, + 135, + 277, + 304 + ], + "type": "table", + "html": "
ModelTop-1Top-5
Barlow Twins†80.1695.14
Barlow Twins80.1295.24
Proposed (Barlow Twins-style; no grouping)79.9494.76
Proposed (Barlow Twins-style; b = 128)81.0295.24
VICReg†79.4095.02
VICReg79.3094.30
Proposed (VICReg-style; no grouping)79.2094.96
Proposed (VICReg-style; b = 128)80.0494.98
W-MSE† [10]69.0691.22
Zero-FCL‡ [30]79.3294.94
Zero-CL‡ [30]79.2694.98
NNCLR† [9]80.1695.30
BYOL† [13]80.3294.94
MoCo V3† [6]80.3694.96
", + "image_path": "ae7b25bbb499f12e5d317662540f46ef8141b874ac4c2e752b9c85aa6a031005.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 325, + 160, + 337 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 325, + 160, + 337 + ], + "spans": [ + { + "bbox": [ + 47, + 325, + 160, + 337 + ], + "type": "text", + "content": "5.1. Tasks and Datasets" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 343, + 287, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 343, + 287, + 392 + ], + "spans": [ + { + "bbox": [ + 46, + 343, + 287, + 392 + ], + "type": "text", + "content": "Models are pretrained with images in the ImageNet dataset [8] or its subset, ImageNet-100 [24], depending on the experiment. ResNet-50 [16] is used as the backbone for ImageNet, while ResNet-18 is used for ImageNet-100." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 392, + 287, + 476 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 392, + 287, + 476 + ], + "spans": [ + { + "bbox": [ + 46, + 392, + 287, + 476 + ], + "type": "text", + "content": "To evaluate downstream SSL performance, we follow the standard linear evaluation protocol: After the backbone network is pretrained by a SSL method, we train a linear classifier on top of the frozen backbone using labeled data from the ImageNet or ImageNet-100 training set. The resulting classifier is then evaluated by the top-1 and top-5 accuracy on the respective validation sets." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 476, + 288, + 585 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 476, + 288, + 585 + ], + "spans": [ + { + "bbox": [ + 46, + 476, + 288, + 585 + ], + "type": "text", + "content": "For transfer learning evaluation, we apply the pretrained models to an object detection task on Pascal VOC07+12 [11]. Following previous studies [1, 15, 29], we use the trainval set of VOC2007 and VOC2012 for training and the test split of VOC2007 for testing. We fine-tune Faster R-CNN [21] with R50-C4. Models are evaluated by three types of average precision (AP): AP, " + }, + { + "bbox": [ + 46, + 476, + 288, + 585 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_{50}" + }, + { + "bbox": [ + 46, + 476, + 288, + 585 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 476, + 288, + 585 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_{75}" + }, + { + "bbox": [ + 46, + 476, + 288, + 585 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 476, + 288, + 585 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_x" + }, + { + "bbox": [ + 46, + 476, + 288, + 585 + ], + "type": "text", + "content": " signifies the intersection-over-union (IoU) threshold of " + }, + { + "bbox": [ + 46, + 476, + 288, + 585 + ], + "type": "inline_equation", + "content": "x\\%" + }, + { + "bbox": [ + 46, + 476, + 288, + 585 + ], + "type": "text", + "content": ". We report the average scores over five trials." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 593, + 178, + 605 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 593, + 178, + 605 + ], + "spans": [ + { + "bbox": [ + 47, + 593, + 178, + 605 + ], + "type": "text", + "content": "5.2. Results and Discussion" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 612, + 287, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 612, + 287, + 673 + ], + "spans": [ + { + "bbox": [ + 46, + 612, + 287, + 673 + ], + "type": "text", + "content": "Linear evaluation on ImageNet-100. Tab. 1 presents the results. We can see that the accuracy of the proposed models is comparable to that of all existing models in the table, including Barlow Twins and VICReg, with or without feature grouping." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "type": "text", + "content": "Linear evaluation on ImageNet. Tab. 2 presents the results. Due to the high computational cost of this large-scale" + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 308, + 135, + 544, + 295 + ], + "blocks": [ + { + "bbox": [ + 304, + 70, + 547, + 126 + ], + "lines": [ + { + "bbox": [ + 304, + 70, + 547, + 126 + ], + "spans": [ + { + "bbox": [ + 304, + 70, + 547, + 126 + ], + "type": "text", + "content": "Table 2. Linear evaluation accuracy (\\%) on ImageNet; highest accuracy over 100 epochs of linear head training. " + }, + { + "bbox": [ + 304, + 70, + 547, + 126 + ], + "type": "inline_equation", + "content": "d = 8192" + }, + { + "bbox": [ + 304, + 70, + 547, + 126 + ], + "type": "text", + "content": " for the proposed model, Barlow Twins, and VICReg. †: quoted from the original papers of the respective methods; ‡: quoted from the MoCo V3 GitHub repository." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 135, + 544, + 295 + ], + "lines": [ + { + "bbox": [ + 308, + 135, + 544, + 295 + ], + "spans": [ + { + "bbox": [ + 308, + 135, + 544, + 295 + ], + "type": "table", + "html": "
ModelEpochsTop-1Top-5
Barlow Twins†100073.291.0
Barlow Twins100072.490.6
Proposed (Barlow Twins-style; no grouping)100073.091.2
Proposed (Barlow Twins-style; b = 128)100073.291.3
VICReg†100073.291.1
VICReg100072.690.9
Proposed (VICReg-style; no grouping)100072.891.1
W-MSE 4† [10]40072.6—
Zero-CL† [30]40072.690.5
SimCLR† [3]100069.389.0
NNCLR† [9]100075.492.3
BYOL† [13]100074.391.6
MoCo V3‡ [6]100074.6—
", + "image_path": "12cc1d34e4b86ce4280c8f759a8901cdea1ced527ba6a7be31140e64cf9e7cbe.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 307, + 337, + 545, + 419 + ], + "blocks": [ + { + "bbox": [ + 305, + 306, + 545, + 329 + ], + "lines": [ + { + "bbox": [ + 305, + 306, + 545, + 329 + ], + "spans": [ + { + "bbox": [ + 305, + 306, + 545, + 329 + ], + "type": "text", + "content": "Table 3. Results of transfer learning for object detection on VOC07+12. †: quoted from original papers; ‡: quoted from [15]." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 337, + 545, + 419 + ], + "lines": [ + { + "bbox": [ + 307, + 337, + 545, + 419 + ], + "spans": [ + { + "bbox": [ + 307, + 337, + 545, + 419 + ], + "type": "table", + "html": "
ModelAP50APAP75
Supervised‡81.353.558.8
Barlow Twins†82.656.863.4
Proposed (Barlow Twins-style; no grouping)82.555.061.1
VICReg†82.4——
Proposed (VICReg-style; no grouping)82.356.162.1
", + "image_path": "a500cf19dd3895f7fb543290c47f07265dc0fc8b654df11d54ec291d0fbc92e1.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 440, + 547, + 500 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 440, + 547, + 500 + ], + "spans": [ + { + "bbox": [ + 304, + 440, + 547, + 500 + ], + "type": "text", + "content": "experiment, we do not evaluate feature grouping with the VICReg-style regularization. The proposed models perform slightly worse than NNCLR, BYOL, and MoCo V3, but have comparable performance to that of Barlow Twins and VICReg." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 515, + 545, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 515, + 545, + 564 + ], + "spans": [ + { + "bbox": [ + 304, + 515, + 545, + 564 + ], + "type": "text", + "content": "Transfer learning evaluation on Pascal VOC object detection. Tab. 3 presents the results of transfer learning. Again, the proposed models demonstrate performance comparable to that of Barlow Twins and VICReg." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 579, + 545, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 579, + 545, + 676 + ], + "spans": [ + { + "bbox": [ + 304, + 579, + 545, + 676 + ], + "type": "text", + "content": "Training time on ImageNet. Tab. 4 presents the training time over 1000 epochs on ImageNet. We tested two situations: training using 8 and 4 GPUs. In both situations, we set the per GPU batch size to 128, which leads to the effective batch size of 1024 for 8 GPUs and 512 for 4 GPUs. As indicated in Tab. 4, the accuracy of the proposed model is comparable to that of Barlow Twins, with a noticeable reduction in training time. More precise evaluation of train" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 305, + 683, + 547, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 683, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 683, + 547, + 713 + ], + "type": "text", + "content": "5This experiment was conducted on a commercial cloud platform that limits a session to a maximum of three days. To finish training Barlow Twins with 8 GPUs for 1000 epochs, three sessions were required, whereas" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2057" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 51, + 134, + 284, + 220 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 289, + 126 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 289, + 126 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 289, + 126 + ], + "type": "text", + "content": "Table 4. Linear evaluation accuracy (\\%) and the total training time on ImageNet with ResNet-50 backbone (" + }, + { + "bbox": [ + 47, + 70, + 289, + 126 + ], + "type": "inline_equation", + "content": "d = 8192" + }, + { + "bbox": [ + 47, + 70, + 289, + 126 + ], + "type": "text", + "content": "). The per GPU batch size is 128. Proposed refers to the proposed method using the Barlow Twins-style regularizer without grouping. Barlow Twins* refers to the results quoted from [29, Figure 2]." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 51, + 134, + 284, + 220 + ], + "lines": [ + { + "bbox": [ + 51, + 134, + 284, + 220 + ], + "spans": [ + { + "bbox": [ + 51, + 134, + 284, + 220 + ], + "type": "table", + "html": "
# GPUs (Batch size)ModelTop-1Top-5Time
8 (1024)Barlow Twins*73.291.0—
Barlow Twins72.490.76d 14h 0m
Proposed73.091.35d 14h 58m
4 (512)Barlow Twins*———
Barlow Twins72.190.212d 19h 30m
Proposed72.891.210d 21h 6m
", + "image_path": "b44c9cc292c6865ed21f789cf761b513488cae597949341d521d3884daddcba9.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 71, + 277, + 266, + 343 + ], + "blocks": [ + { + "bbox": [ + 47, + 233, + 287, + 256 + ], + "lines": [ + { + "bbox": [ + 47, + 233, + 287, + 256 + ], + "spans": [ + { + "bbox": [ + 47, + 233, + 287, + 256 + ], + "type": "text", + "content": "Table 5. The effect of feature permutation: accuracy (\\%) and training time per 10 epochs (second) on ImageNet-100." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 78, + 265, + 257, + 275 + ], + "lines": [ + { + "bbox": [ + 78, + 265, + 257, + 275 + ], + "spans": [ + { + "bbox": [ + 78, + 265, + 257, + 275 + ], + "type": "text", + "content": "(a) Barlow Twins-style cross-correlation regularization" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 71, + 277, + 266, + 343 + ], + "lines": [ + { + "bbox": [ + 71, + 277, + 266, + 343 + ], + "spans": [ + { + "bbox": [ + 71, + 277, + 266, + 343 + ], + "type": "table", + "html": "
GroupingPermutationTop-1Top-5Time
nono59.6485.201646.2
yes79.9494.761668.7
b = 128no73.5893.361697.5
yes81.0295.241709.6
", + "image_path": "62895c1f535980ecf6c66164d29d030ff2b99711dbccff2786582daa2af725bf.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 73, + 366, + 264, + 434 + ], + "blocks": [ + { + "bbox": [ + 97, + 354, + 237, + 365 + ], + "lines": [ + { + "bbox": [ + 97, + 354, + 237, + 365 + ], + "spans": [ + { + "bbox": [ + 97, + 354, + 237, + 365 + ], + "type": "text", + "content": "(b) VICReg-style covariance regularization" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 73, + 366, + 264, + 434 + ], + "lines": [ + { + "bbox": [ + 73, + 366, + 264, + 434 + ], + "spans": [ + { + "bbox": [ + 73, + 366, + 264, + 434 + ], + "type": "table", + "html": "
GroupingPermutationTop-1Top-5Time
nono57.4284.261692.2
yes79.2094.961718.0
b = 128no66.2689.681802.1
yes80.0494.981813.3
", + "image_path": "5c7feaa46d210331a807901e30825efa1f8bfee94686b50ea00a2281fbba8aab.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 456, + 287, + 480 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 456, + 287, + 480 + ], + "spans": [ + { + "bbox": [ + 47, + 456, + 287, + 480 + ], + "type": "text", + "content": "ing speed is provided in the next experiment, and additional results are provided in Supplementary Material." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 503, + 286, + 514 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 503, + 286, + 514 + ], + "spans": [ + { + "bbox": [ + 47, + 503, + 286, + 514 + ], + "type": "text", + "content": "Dimensionality of embeddings and computational cost." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 515, + 287, + 670 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 515, + 287, + 670 + ], + "spans": [ + { + "bbox": [ + 46, + 515, + 287, + 670 + ], + "type": "text", + "content": "Fig. 2 presents the elapsed time and the peak GPU memory allocation over 10 epochs on ImageNet-100 on a single GPU, with varying dimensionality of the projected embeddings: " + }, + { + "bbox": [ + 46, + 515, + 287, + 670 + ], + "type": "inline_equation", + "content": "d \\in \\{2048, 4096, 8192, 16384\\}" + }, + { + "bbox": [ + 46, + 515, + 287, + 670 + ], + "type": "text", + "content": ". The improvement over Barlow Twins and VICReg becomes noticeable as " + }, + { + "bbox": [ + 46, + 515, + 287, + 670 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 515, + 287, + 670 + ], + "type": "text", + "content": " is increased; at " + }, + { + "bbox": [ + 46, + 515, + 287, + 670 + ], + "type": "inline_equation", + "content": "d = 8192" + }, + { + "bbox": [ + 46, + 515, + 287, + 670 + ], + "type": "text", + "content": ", the proposed models (without grouping) are 2.8 times as fast as VICReg, and 2.2 times as fast as Barlow Twins; while at " + }, + { + "bbox": [ + 46, + 515, + 287, + 670 + ], + "type": "inline_equation", + "content": "d = 16384" + }, + { + "bbox": [ + 46, + 515, + 287, + 670 + ], + "type": "text", + "content": ", they are 5.7 times as fast as VICReg, and 4.0 times as fast as Barlow Twins. For both " + }, + { + "bbox": [ + 46, + 515, + 287, + 670 + ], + "type": "inline_equation", + "content": "d = 8192" + }, + { + "bbox": [ + 46, + 515, + 287, + 670 + ], + "type": "text", + "content": " and 16384, memory consumption is reduced by more than half. See Supplementary Material for the results with the ResNet-50 backbone on multiple GPUs and the detail of forward/backward/loss computation time." + } + ] + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 316, + 125, + 538, + 215 + ], + "blocks": [ + { + "bbox": [ + 305, + 70, + 545, + 102 + ], + "lines": [ + { + "bbox": [ + 305, + 70, + 545, + 102 + ], + "spans": [ + { + "bbox": [ + 305, + 70, + 545, + 102 + ], + "type": "text", + "content": "Table 6. The regularizers of Barlow Twins and VICReg applied to the embeddings produced by the proposed models. Perm.: permutation; Diff: difference to the baselines." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 336, + 114, + 515, + 123 + ], + "lines": [ + { + "bbox": [ + 336, + 114, + 515, + 123 + ], + "spans": [ + { + "bbox": [ + 336, + 114, + 515, + 123 + ], + "type": "text", + "content": "(a) Barlow Twins-style cross-correlation regularization" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 316, + 125, + 538, + 215 + ], + "lines": [ + { + "bbox": [ + 316, + 125, + 538, + 215 + ], + "spans": [ + { + "bbox": [ + 316, + 125, + 538, + 215 + ], + "type": "table", + "html": "
ModelGroupingPerm.Normalized Barlow Twins loss (Eq. (16))Diff
Barlow Twins——0.0050
Proposednono0.5640.559
yes0.0100.005
b = 128no0.0490.044
yes0.0090.004
", + "image_path": "06a30355c7053310aef768faacbdc33bb1dff7a99c81d4cc9326b940b9d8d1e7.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_body" + } + ], + "index": 13 + }, + { + "type": "table", + "bbox": [ + 316, + 239, + 538, + 328 + ], + "blocks": [ + { + "bbox": [ + 356, + 227, + 496, + 237 + ], + "lines": [ + { + "bbox": [ + 356, + 227, + 496, + 237 + ], + "spans": [ + { + "bbox": [ + 356, + 227, + 496, + 237 + ], + "type": "text", + "content": "(b) VICReg-style covariance regularization" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 316, + 239, + 538, + 328 + ], + "lines": [ + { + "bbox": [ + 316, + 239, + 538, + 328 + ], + "spans": [ + { + "bbox": [ + 316, + 239, + 538, + 328 + ], + "type": "table", + "html": "
ModelGroupingPerm.Normalized VICReg loss (Eq. (17))Diff
VICReg——0.0020
Proposednono1.9991.997
yes0.0110.009
b = 128no0.3790.377
yes0.0070.005
", + "image_path": "ee35fca641c8efb772ad3a61a9351ba81c19399f7955209e8f1e9c7d3972aec6.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "table_body" + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 347, + 545, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 347, + 545, + 443 + ], + "spans": [ + { + "bbox": [ + 304, + 347, + 545, + 443 + ], + "type": "text", + "content": "Effectiveness of feature permutation. Tab. 5 presents the effect of feature permutation on ImageNet-100 at " + }, + { + "bbox": [ + 304, + 347, + 545, + 443 + ], + "type": "inline_equation", + "content": "d = 2048" + }, + { + "bbox": [ + 304, + 347, + 545, + 443 + ], + "type": "text", + "content": ". Regardless of whether grouping is used, the accuracy decreases significantly without permutation, suggesting that feature permutation is essential for the effectiveness of our proposed regularizer. As illustrated in the column \"Time\" in Tab. 5, the cost of permutation is negligible, even though it was performed as frequently as every batch iteration." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 444, + 545, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 444, + 545, + 514 + ], + "spans": [ + { + "bbox": [ + 304, + 444, + 545, + 514 + ], + "type": "text", + "content": "We also quantitatively evaluate the degree of decorrelation obtained by feature permutation. After the proposed models are trained, we compute the normalized values of Barlow Twins' and VICReg's regularizers applied to the embeddings " + }, + { + "bbox": [ + 304, + 444, + 545, + 514 + ], + "type": "inline_equation", + "content": "A, B" + }, + { + "bbox": [ + 304, + 444, + 545, + 514 + ], + "type": "text", + "content": " output by the proposed models, given as follows:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 372, + 520, + 545, + 545 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 372, + 520, + 545, + 545 + ], + "spans": [ + { + "bbox": [ + 372, + 520, + 545, + 545 + ], + "type": "interline_equation", + "content": "\\frac {R _ {\\text {o f f}} (\\mathbf {C} (\\mathrm {A} , \\mathrm {B}))}{d (d - 1)} \\tag {16}", + "image_path": "6f722b35b008c1d29d59803f1d7b77de484fe209898a65a559cd76bf101a3faf.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 373, + 547, + 545, + 572 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 373, + 547, + 545, + 572 + ], + "spans": [ + { + "bbox": [ + 373, + 547, + 545, + 572 + ], + "type": "interline_equation", + "content": "\\frac {R _ {\\text {o f f}} (\\mathbf {K} (\\mathrm {A})) + R _ {\\text {o f f}} (\\mathbf {K} (\\mathrm {B}))}{2 d (d - 1)} \\tag {17}", + "image_path": "b9c29535a22fff06d14b6fc286f80a2bbf06097484c3298edf6df6949f96d5d4.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 579, + 545, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 579, + 545, + 662 + ], + "spans": [ + { + "bbox": [ + 304, + 579, + 545, + 662 + ], + "type": "text", + "content": "The normalization factor " + }, + { + "bbox": [ + 304, + 579, + 545, + 662 + ], + "type": "inline_equation", + "content": "d(d - 1)" + }, + { + "bbox": [ + 304, + 579, + 545, + 662 + ], + "type": "text", + "content": " is to make the resulting values the means over " + }, + { + "bbox": [ + 304, + 579, + 545, + 662 + ], + "type": "inline_equation", + "content": "d(d - 1)" + }, + { + "bbox": [ + 304, + 579, + 545, + 662 + ], + "type": "text", + "content": " off-diagonal elements of " + }, + { + "bbox": [ + 304, + 579, + 545, + 662 + ], + "type": "inline_equation", + "content": "\\mathbf{K}(\\mathbf{A})" + }, + { + "bbox": [ + 304, + 579, + 545, + 662 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 579, + 545, + 662 + ], + "type": "inline_equation", + "content": "\\mathbf{K}(\\mathbf{B})" + }, + { + "bbox": [ + 304, + 579, + 545, + 662 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 579, + 545, + 662 + ], + "type": "inline_equation", + "content": "\\mathbf{C}(\\mathbf{A},\\mathbf{B})" + }, + { + "bbox": [ + 304, + 579, + 545, + 662 + ], + "type": "text", + "content": ". Since VICReg has regularization terms for " + }, + { + "bbox": [ + 304, + 579, + 545, + 662 + ], + "type": "inline_equation", + "content": "\\mathbf{K}(\\mathbf{A})" + }, + { + "bbox": [ + 304, + 579, + 545, + 662 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 579, + 545, + 662 + ], + "type": "inline_equation", + "content": "\\mathbf{K}(\\mathbf{B})" + }, + { + "bbox": [ + 304, + 579, + 545, + 662 + ], + "type": "text", + "content": ", its loss is further divided by 2. Tab. 6 presents the results on ImageNet-100 (" + }, + { + "bbox": [ + 304, + 579, + 545, + 662 + ], + "type": "inline_equation", + "content": "d = 2048" + }, + { + "bbox": [ + 304, + 579, + 545, + 662 + ], + "type": "text", + "content": "). We observe that feature permutation promotes decorrelation from the point of view of the baseline loss functions." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": "Impact of block size in feature grouping. To evaluate the effect of feature grouping on ImageNet-100, we fix the embedding dimension at " + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "inline_equation", + "content": "d = 2048" + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": " and change the block" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 46, + 683, + 286, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 683, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 683, + 286, + 713 + ], + "type": "text", + "content": "the proposed model required two sessions. The time reported in Tab. 4 is the total run time of these sessions, which includes time (3 to 5 seconds) for reinitialization at the beginning of each session." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2058" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 57, + 70, + 537, + 311 + ], + "blocks": [ + { + "bbox": [ + 57, + 70, + 537, + 311 + ], + "lines": [ + { + "bbox": [ + 57, + 70, + 537, + 311 + ], + "spans": [ + { + "bbox": [ + 57, + 70, + 537, + 311 + ], + "type": "image", + "image_path": "3cd714293187435b8b7b5b08b272339485223117c32f6271f194c137a4a64b3a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 123, + 319, + 470, + 332 + ], + "lines": [ + { + "bbox": [ + 123, + 319, + 470, + 332 + ], + "spans": [ + { + "bbox": [ + 123, + 319, + 470, + 332 + ], + "type": "text", + "content": "Figure 2. 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The impact of the block size on ImageNet-100. The " + }, + { + "bbox": [ + 123, + 468, + 468, + 480 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 123, + 468, + 468, + 480 + ], + "type": "text", + "content": "-axis indicates the block size " + }, + { + "bbox": [ + 123, + 468, + 468, + 480 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 123, + 468, + 468, + 480 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 501, + 288, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 501, + 288, + 574 + ], + "spans": [ + { + "bbox": [ + 46, + 501, + 288, + 574 + ], + "type": "text", + "content": "size " + }, + { + "bbox": [ + 46, + 501, + 288, + 574 + ], + "type": "inline_equation", + "content": "b \\in \\{2, 4, 8, \\dots, 2048\\}" + }, + { + "bbox": [ + 46, + 501, + 288, + 574 + ], + "type": "text", + "content": ". The block size " + }, + { + "bbox": [ + 46, + 501, + 288, + 574 + ], + "type": "inline_equation", + "content": "b = d = 2048" + }, + { + "bbox": [ + 46, + 501, + 288, + 574 + ], + "type": "text", + "content": " corresponds to no feature grouping. Figure 3 presents the result, which indicates that unless " + }, + { + "bbox": [ + 46, + 501, + 288, + 574 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 46, + 501, + 288, + 574 + ], + "type": "text", + "content": " is extremely small (i.e., 8 or less), there is no significant increase in training time or GPU memory usage. Setting " + }, + { + "bbox": [ + 46, + 501, + 288, + 574 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 46, + 501, + 288, + 574 + ], + "type": "text", + "content": " to a moderate size, such as " + }, + { + "bbox": [ + 46, + 501, + 288, + 574 + ], + "type": "inline_equation", + "content": "b = 128" + }, + { + "bbox": [ + 46, + 501, + 288, + 574 + ], + "type": "text", + "content": ", improves performance." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 586, + 119, + 597 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 586, + 119, + 597 + ], + "spans": [ + { + "bbox": [ + 47, + 586, + 119, + 597 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": "We have proposed a new decorrelating regularizer for non-contrastive SSL. Given " + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": "-dimensional embeddings of " + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": " samples, the regularizer can be computed in " + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "inline_equation", + "content": "O(nd\\log d)" + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": " time, which is an improvement over the " + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "inline_equation", + "content": "O(nd^2)" + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": " time required by the existing models (Barlow Twins and VICReg). The reduced memory consumption allows for a larger batch size, which in general enables more effective models to be learned. We also proposed a feature permutation technique to alleviate the weakness of our regularizer." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 502, + 545, + 561 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 502, + 545, + 561 + ], + "spans": [ + { + "bbox": [ + 304, + 502, + 545, + 561 + ], + "type": "text", + "content": "With our regularizer, the speed-up is most notable with networks with a lightweight backbone, wherein computation at the loss node takes a large part of training time. This makes our method an attractive option to use with knowledge-distilled backbones [12, 17]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 568, + 545, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 568, + 545, + 605 + ], + "spans": [ + { + "bbox": [ + 304, + 568, + 545, + 605 + ], + "type": "text", + "content": "The proposed method is not limited to SSL but potentially useful to a wider range of applications that involve decorrelation. We plan to pursue this avenue in future work." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 638, + 403, + 651 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 638, + 403, + 651 + ], + "spans": [ + { + "bbox": [ + 306, + 638, + 403, + 651 + ], + "type": "text", + "content": "Acknowledgments" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "We thank anonymous reviewers for their helpful comments. This work was partially supported by the New Energy and Industrial Technology Development Organization (NEDO) and JSPS Kakenhi Grant 19H04173." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2059" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 92, + 287, + 712 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 53, + 92, + 287, + 125 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 92, + 287, + 125 + ], + "spans": [ + { + "bbox": [ + 53, + 92, + 287, + 125 + ], + "type": "text", + "content": "[1] Adrien Bardes, Jean Ponce, and Yann LeCun. 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In ICLR, 2022. 1, 2, 6" + } + ] + } + ], + "index": 31 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "text", + "content": "2060" + } + ] + } + ], + "index": 33 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 8 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Learning Detailed Radiance Manifolds for High-Fidelity and 3D-Consistent Portrait Synthesis From Monocular Image/ee76865a-ff6b-45fe-83d5-c6e1d7d201e2_content_list.json b/2023/Learning Detailed Radiance Manifolds for High-Fidelity and 3D-Consistent Portrait Synthesis From Monocular Image/ee76865a-ff6b-45fe-83d5-c6e1d7d201e2_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..08ef7b820cd724cb6bbcf8ed2da2468f727d94dd --- /dev/null +++ b/2023/Learning Detailed Radiance Manifolds for High-Fidelity and 3D-Consistent Portrait Synthesis From Monocular Image/ee76865a-ff6b-45fe-83d5-c6e1d7d201e2_content_list.json @@ -0,0 +1,1606 @@ +[ + { + "type": "text", + "text": "Learning Detailed Radiance Manifolds for High-Fidelity and 3D-Consistent Portrait Synthesis from Monocular Image", + "text_level": 1, + "bbox": [ + 106, + 128, + 867, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Yu Deng Baoyuan Wang Heung-Yeung Shum Xiaobing.AI", + "bbox": [ + 284, + 203, + 684, + 239 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/29846e2c8625222bcd5704a3d43ae06412ed0157076ed2e5b21f9a5c9b09de9f.jpg", + "image_caption": [ + "Input", + "Figure 1. Novel view synthesis results by our method. It can generate novel views of a portrait image with high-fidelity and strong 3D-consistency via single forward pass (e.g., see the bangs and wrinkles). Best viewed with zoom-in and see the video for animations." + ], + "image_footnote": [], + "bbox": [ + 80, + 255, + 480, + 489 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/aadd97515b37a598846b96f00d4eb745b50e4817a7da68ad971b381276442641.jpg", + "image_caption": [ + "Input", + "Novel views" + ], + "image_footnote": [], + "bbox": [ + 488, + 255, + 890, + 489 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 555, + 313, + 571 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "A key challenge for novel view synthesis of monocular portrait images is 3D consistency under continuous pose variations. Most existing methods rely on 2D generative models which often leads to obvious 3D inconsistency artifacts. We present a 3D-consistent novel view synthesis approach for monocular portrait images based on a recent proposed 3D-aware GAN, namely Generative Radiance Manifolds (GRAM) [13], which has shown strong 3D consistency at multiview image generation of virtual subjects via the radiance manifolds representation. However, simply learning an encoder to map a real image into the latent space of GRAM can only reconstruct coarse radiance manifolds without faithful fine details, while improving the reconstruction fidelity via instance-specific optimization is time-consuming. We introduce a novel detail manifolds reconstructor to learn 3D-consistent fine details on the radiance manifolds from monocular images, and combine them with the coarse radiance manifolds for high-fidelity reconstruction. The 3D priors derived from the coarse radiance manifolds are used to regulate the learned details to ensure reasonable synthesized results", + "bbox": [ + 75, + 585, + 472, + 902 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "at novel views. Trained on in-the-wild 2D images, our method achieves high-fidelity and 3D-consistent portrait synthesis largely outperforming the prior art. Project page: https://yudeng.github.io/GRAMInverter/", + "bbox": [ + 498, + 556, + 893, + 617 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 500, + 648, + 632, + 666 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Synthesizing photorealistic portrait images of a person from an arbitrary viewpoint is an important task that can benefit diverse downstream applications such as virtual avatar creation and immersive online communication. Thanks to the thriving of 2D Generative Adversarial Networks (GANs) [18,25,26], people can now generate high-quality portraits at desired views given only monocular images as input, via a simple invert-then-edit strategy by conducting GAN inversion [1,38,52] and latent space editing [12,20,41,50]. However, existing 2D GAN-based methods still have deficiencies when applied to applications that require more strict 3D consistency (e.g. VR&AR). Due to the non-physical rendering process of the 2D CNN-based generators, their synthesized images under pose changes usually bear certain kinds of multiview inconsistency, such", + "bbox": [ + 496, + 675, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "4423", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "as geometry distortions [3,5] and texture sticking or flickering [24, 55]. These artifacts may not be significant enough when inspecting each static image but can be easily captured by human eyes under continuous image variations.", + "bbox": [ + 75, + 90, + 468, + 151 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recently, there are an emerging group of 3D-aware GANs [9, 10, 13, 19, 39, 40] targeting at image generation with 3D pose disentanglement. By incorporating Neural Radiance Field (NeRF) [29] and its variants into the adversarial learning process of GANs, they can produce realistic images with strong 3D-consistency across different views, given only a set of monocular images as training data. As a result, 3D-aware GANs have shown greater potential than 2D GANs for pose manipulations of portraits. However, even though 3D-aware GANs are capable of generating 3D-consistent portraits of virtual subjects, leveraging them for real image pose editing is still a challenging task. To obtain faithful reconstructions of real images, most existing methods [9, 10, 13, 27, 46, 47, 67] turn to a time-consuming and instance-specific optimization to invert the given images into the latent space of a pre-trained 3D-aware GAN, which is hard to scale-up. And simply enforcing an encoder-based 3D-aware GAN inversion [7, 46] often fails to preserve fine details in the original image.", + "bbox": [ + 75, + 154, + 470, + 441 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we propose a novel approach GRAMInverter, for high-fidelity and 3D-consistent novel view synthesis of monocular portraits via single forward pass. Our method is built upon the recent GRAM [13] that can synthesize high-quality virtual images with strong 3D consistency via the radiance manifolds representation [13]. Nevertheless, GRAM suffers from the same lack-of-fidelity issue when combined with a general encoder-based GAN inversion approach [52]. The main reason is that the obtained semantically-meaningful low-dimensional latent code cannot well record detail information of the input, as also indicated by some recent 2D GAN inversion methods [52, 55].", + "bbox": [ + 75, + 444, + 468, + 625 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To tackle this problem, our motivation is to further learn 3D-space high-frequency details and combine them with the coarse radiance manifolds obtained from the general encoder-based inversion of GRAM, to achieve faithful reconstruction and 3D-consistent view synthesis. A straightforward way to achieve this is to extract a high-resolution 3D voxel from the input image and combine it with the coarse radiance manifolds. However, this is prohibited by modern GPUs due to the high memory cost of the 3D voxel. To tackle this problem, we turn to learn a high resolution detail manifolds, taking the advantage of the radiance manifolds representation of GRAM, instead of learning the memory-consuming 3D voxel. We introduce a novel detail manifolds reconstructor to extract detail manifolds from the input images. It leverages manifold super-resolution [60] to predict high-resolution detail manifolds from a low resolution feature voxel. This can be effectively achieved by a set of memory-efficient 2D convolution blocks. The obtained", + "bbox": [ + 75, + 628, + 470, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "high resolution detail manifolds can still maintain strict 3D consistency due to lying in the 3D space. We also propose dedicated losses to regulate the detail manifolds via 3D priors derived from the coarse radiance manifolds, to ensure reasonable novel view results.", + "bbox": [ + 496, + 90, + 890, + 165 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Another contribution of our method is an improvement upon the memory and time-consuming GRAM, without which it is difficult to be integrated into our GAN inversion framework. We replace the original MLP-based radiance generator [13] in GRAM with a StyleGAN2 [26]-based triplane generator proposed by [9]. The efficient GRAM requires only $1/4$ memory cost with $7 \\times$ speed up, without sacrificing the image generation quality and 3D consistency.", + "bbox": [ + 496, + 167, + 890, + 287 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We train our method on FFHQ dataset [25] and conduct multiple experiments to demonstrate its advantages on pose control of portrait images. Once trained, GRAMInverter takes a monocular image as input and predicts its radiance manifolds representation for novel view synthesis at 3 FPS on a single GPU. The generated novel views well preserve fine details in the original image with strong 3D consistency, outperforming prior art by a large margin. We believe our method takes a solid step towards efficient 3D-aware content creation for real applications.", + "bbox": [ + 496, + 289, + 890, + 439 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 455, + 640, + 472 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3D-aware generative model. Learned with monocular 2D images, 3D-aware GANs [9, 10, 13, 17, 19, 30, 31, 34, 39, 40, 45, 60, 62] achieve an explicit disentanglement of camera pose by introducing underlying 3D representations. Earlier works [30, 42, 48] utilize voxel or mesh as the intermediate representation. Later works [9, 10, 13, 34, 39, 62, 69] leverage NeRF [29] and its variants [13, 33, 54, 64] to achieve more strict 3D consistency. Among them, methods that directly render their 3D representations for image synthesis achieve the best multiview consistency [10, 13, 17, 40, 45]. We propose a novel approach for high-quality pose editing of given portraits based on GRAM [13], which is a recent 3D-aware GAN with state-of-the-art multiview consistency.", + "bbox": [ + 496, + 483, + 890, + 679 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "GAN inversion. GAN inversion aims to map a given real image into the latent space of a pre-trained generator for image reconstruction and manipulation. Numerous methods [1,4,6,26,37,38,52,55,63,72,73] try to find a latent code which can faithfully reconstruct the given image meanwhile falls inside a semantically meaningful latent space that supports reasonable editing. They either adopt optimization-based approach [1, 2, 26, 73], introduce an extra image encoder [4, 37, 52], or utilize a hybrid version of the former two [6, 72]. Nevertheless, recent studies [38, 52, 55, 74] reveal that it is difficult to achieve high-fidelity reconstruction and artifacts-free editing at once given only low-bitrate latent code as representation. As a result, several methods propose to further fine-tune the pre-trained generator [38]", + "bbox": [ + 496, + 688, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "4424", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/2bf3075ab1ad6cef8deb70c3bae9951a4e794c76adc874da2f3ee44726339ea7.jpg", + "image_caption": [ + "Figure 2. Overview of the GRAMInverter. An input portrait image goes through two stages to obtain the final radiance manifolds for novel view synthesis. The first general inversion stage maps the input image to the latent space of a pre-trained efficient GRAM to obtain coarse radiance manifolds. The second detail-specific stage then extracts detail feature manifolds from the input image and combines them with the coarse results for high-fidelity image synthesis. See the text for more details." + ], + "image_footnote": [], + "bbox": [ + 83, + 88, + 883, + 282 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "or allow more detailed features from the input images to leak into the generator during inversion [55, 63].", + "bbox": [ + 75, + 359, + 468, + 390 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "While the above methods target at the inversion of 2D GANs, inverting a given image with 3D-aware GANs shares a similar spirit. An advantage of 3D-aware GAN inversion compare to its 2D counterpart is a natural disentanglement of the 3D pose. Once inverted, novel view synthesis can be easily achieved without further latent space exploration [20, 41]. The majority of existing 3D-aware GAN inversion methods [9, 10, 13, 27, 46, 47, 51, 57] leverage optimization-based or a hybrid approach for faithful reconstruction, which are time-consuming and hard to scale-up. A recent method [7] explores GAN inversion with a single forward of an encoder, yet it struggles to preserve fine image details. Our proposed method is also an encoder-based inversion approach which yields high-quality reconstruction and novel view synthesis thanks to our novel design.", + "bbox": [ + 75, + 391, + 470, + 618 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Pose editing of monocular portraits. Editing the camera pose of a monocular portrait for novel view synthesis is a longstanding task and has witnessed the emergence of diverse methods. Some of them [8,35,59,61,75,76] achieve pose editing by first conducting 3D reconstruction and then rendering the obtained mesh at novel views. Due to the imperfect reconstruction results, they often have difficulties handling non-face regions and unseen parts at the input view. Others [15, 16, 32, 36, 43, 44, 56, 58, 66, 70] generate novel views in a face-reenactment paradigm, where warping flows are often learned from video data to transform a source image to a target viewpoint. These methods may encounter geometry distortions at novel views due to the lack of an explicit 3D constraint. More recently, plenty of works [3,7,12,22,28,41,46,47,50] have studied pose editing of an image by inverting it into a prior model such as GAN. With the strong prior bearing in a pre-trained generator, synthesizing novel views of a given portrait can be achieved", + "bbox": [ + 75, + 628, + 470, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "without any 3D or video data during training. Among them, methods using 3D-aware GANs [7,9,13,46,47] have shown better 3D consistency under pose variations. Our method is also based on 3D-aware GAN and largely improves the efficiency, reconstruction quality, as well as 3D consistency.", + "bbox": [ + 496, + 359, + 890, + 436 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Approach", + "text_level": 1, + "bbox": [ + 500, + 449, + 609, + 467 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given a monocular portrait image $\\hat{I}$ , we aim to synthesize its novel views at some arbitrary camera viewpoints by leveraging the prior knowledge of a pre-trained 3D-aware GAN, as shown in Fig. 2. To guarantee high-quality and 3D-consistent novel view synthesis, we adopt GRAM [13] as our underlying image generator and design an efficient version of it that requires much less computation and memory cost so as to incorporate it into our whole framework (Sec. 3.1). With the efficient GRAM, we first utilize a general encoder-based GAN inversion to reconstruct the coarse radiance manifolds from the input image (Sec. 3.2). We then introduce a detail-specific reconstruction stage to learn high-resolution detail manifolds that cannot be well captured by the coarse result, via our proposed novel detail manifolds reconstructor (Sec. 3.3). Multiple losses are enforced to regulate the predicted detail manifolds to ensure reasonable synthesized results at novel views, by leveraging the 3D priors derived from the coarse radiance manifolds (Sec. 3.4). We describe each part in details below.", + "bbox": [ + 496, + 474, + 892, + 762 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Efficient Generative Radiance Manifolds", + "text_level": 1, + "bbox": [ + 498, + 771, + 848, + 787 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We start with a brief review of the original GRAM proposed in [13]. The core of GRAM is its underlying radiance manifolds representation, which regulates radiance field learning on a set of surface manifolds in the 3D space instead of predicting it in the whole volumetric space as done by [29]. The surface manifolds are defined as a set of iso-surfaces $\\{S_i\\}$ in a 3D scalar field represented by a", + "bbox": [ + 496, + 794, + 890, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "4425", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "light-weight MLP called the manifold predictor $\\mathcal{M}$ :", + "bbox": [ + 76, + 90, + 421, + 107 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {M}: \\boldsymbol {x} \\in \\mathbb {R} ^ {3} \\rightarrow s \\in \\mathbb {R}, \\mathcal {S} _ {i} = \\{\\boldsymbol {x} | \\mathcal {M} (\\boldsymbol {x}) = l _ {i} \\}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 116, + 114, + 468, + 133 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\{l_i\\}$ are $N$ predefined scalar levels. During image generation, only intersections $\\{\\pmb{x}_i\\}$ between a viewing ray $\\pmb{r}$ and the surface manifolds will be sent into an MLP-based radiance generator $\\Phi$ for radiance prediction:", + "bbox": [ + 76, + 143, + 468, + 204 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\Phi : \\left(\\boldsymbol {z}, \\boldsymbol {x} _ {i}\\right) \\in \\mathbb {R} ^ {d _ {z}} \\times \\mathbb {R} ^ {3} \\rightarrow (\\boldsymbol {c}, \\alpha) \\in \\mathbb {R} ^ {4}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 137, + 210, + 468, + 229 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $z$ is a latent code determining the radiance, $c$ is the color, and $\\alpha$ is the occupancy. The final color of each ray can be computed via manifold rendering [13, 71]:", + "bbox": [ + 76, + 237, + 468, + 282 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nC (\\boldsymbol {r}) = \\sum_ {i = 1} ^ {N} \\prod_ {j < i} (1 - \\alpha (\\boldsymbol {x} _ {j})) \\alpha (\\boldsymbol {x} _ {i}) \\boldsymbol {c} (\\boldsymbol {x} _ {i}). \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 135, + 290, + 468, + 333 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The high mometry cost of GRAM lies in its MLP-based radiance generator $\\Phi$ , which requires millions of forward steps to generate a single image. Inspired by the recent EG3D [9], we substitute the original radiance generator with a tri-plane generator [9] based on StyleGAN2 structure [26]. Its efficient coarse-to-fine structure helps to reduce memory and computation costs by a large margin. Given the new radiance generator, the color and occupancy for points on the surface manifolds can be obtained by first generating tri-plane features by a 2D CNN $\\Psi$ , and then conducting tri-plane sampling and sending the sampled features into a small MLP-based decoder $m$ as done in [9]. Note that although we take the tri-plane generator from EG3D to improve efficiency, we do not use its 2D super-resolution module but keep strictly to the radiance manifolds representation. This helps us to maintain the strong 3D consistency brought by the manifold rendering. In addition, we calculate ray-manifold intersections at $1/4$ resolution of the final image to further speed up our image generation process (details in the suppl. material).", + "bbox": [ + 75, + 340, + 468, + 642 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The efficient GRAM serves as a strong prior for generating realistic multiview images of virtual subjects. By combining it with our two-stage manifolds reconstruction method, we achieve high-quality novel view synthesis of real portraits, as described in the following sections.", + "bbox": [ + 75, + 643, + 468, + 718 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. General Inversion Stage", + "text_level": 1, + "bbox": [ + 76, + 726, + 299, + 742 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given a pre-trained efficient GRAM following a typical 3D-aware GAN training paradigm [13], we first introduce an image inverter $E_{w}$ that maps a given image to the latent space of the efficient GRAM, as shown in Fig. 2. Inspired by previous StyleGAN-based inversion methods [1, 52, 55], we invert the given image into a latent code $\\boldsymbol{w} + = [\\boldsymbol{w}_1, \\boldsymbol{w}_2, \\dots, \\boldsymbol{w}_L]$ in $\\mathcal{W}+$ space [1] of the tri-plane generator $\\Psi$ for a proper trade-off between inversion fidelity and pose editing quality, where $L$ is the number of layers in $\\Psi$ 's synthesis sub-network. We leverage", + "bbox": [ + 75, + 750, + 470, + 901 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/1ad64f830a6e5c88291c4e0265c3486b01788878969db49e1788fac887900797.jpg", + "image_caption": [ + "Figure 3. The detail encoder $E_{detail}$ extracts a camera space feature voxel from an input image. The voxel corresponds to a quadrangular frustum in the 3D space bounded by the near and far planes of the camera and the outermost viewing rays." + ], + "image_footnote": [], + "bbox": [ + 501, + 89, + 890, + 200 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "the e4e encoder [52] as the backbone of $E_{w}$ . Given $\\pmb{w} +$ , we can obtain a coarse radiance manifolds $\\Phi(\\pmb{w} +, \\{S_i\\}) = m \\circ \\Psi(\\pmb{w} +, \\{S_i\\})$ via Eq. (1) and (2), and further obtain a coarse inversion image $I_{w}$ by rendering the radiance manifolds at input viewpoint $\\hat{\\theta}$ via Eq. (3), where $\\hat{\\theta}$ can be obtained by off-the-shelf 3D face reconstruction method [14].", + "bbox": [ + 496, + 282, + 890, + 373 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We fixed the pre-trained efficient GRAM and learn the image inverter $E_{w}$ following the training process of [52], except that we replaced the adversarial loss in [52] with a naive L2 loss between predicted $w+$ and the average latent code of the $\\mathcal{W}+$ space. To further improve the reconstruction fidelity, we fixed the trained $E_{w}$ and finetuned the efficient GRAM via the pivot tuning strategy [38] using all training images. Details for the above training processes can be found in the suppl. material.", + "bbox": [ + 496, + 373, + 892, + 508 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "After training, the general inversion stage can already synthesize reasonable multiview images of the input, yet it cannot faithfully preserve the fine details, making the inverted result looks less like the original image (see Fig. 6). Therefore, we introduce a detail-specific stage for faithful detail reconstruction, as described below.", + "bbox": [ + 496, + 508, + 893, + 599 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Detail-Specific Reconstruction Stage", + "text_level": 1, + "bbox": [ + 500, + 608, + 815, + 625 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The detail-specific stage aims to extract fine details from the input image that cannot be well described by the coarse radiance manifolds to improve the reconstruction fidelity. The intuition is to learn high-resolution details in 3D space so that their combination with the coarse radiance manifolds still remains strong 3D consistency under pose variations. To achieve this goal, we design a detail manifolds recon. structor consisting of two modules: a detail encoder $E_{detail}$ that extracts low-resolution feature voxel from the input image, and a super-resolution module $\\mathcal{U}$ to predict highresolution detail manifolds from the low-resolution voxel.", + "bbox": [ + 496, + 632, + 890, + 797 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Specifically, $E_{detail}$ takes an image $\\hat{I}$ as input and predicts a camera space feature voxel as shown in Fig. 3:", + "bbox": [ + 496, + 797, + 890, + 828 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nE _ {\\text {d e t a i l}}: \\hat {I} \\in \\mathbb {R} ^ {H \\times W \\times 3} \\rightarrow V \\in \\mathbb {R} ^ {H _ {l r} \\times W _ {l r} \\times D _ {l r} \\times d _ {V}}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 511, + 835, + 890, + 854 + ], + "page_idx": 3 + }, + { + "type": "page_footnote", + "text": "In practice, we find that concatenating $\\hat{I}$ with an extra difference map $\\Delta = \\hat{I} - I_w$ as input yields better reconstruction quality, where $I_w$ is the inversion image obtained by the general inversion stage.", + "bbox": [ + 500, + 862, + 893, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "4426", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $d_V$ is the feature dimension. We implement $E_{detail}$ as a 3D U-Net with skip connections to extract both global geometry structures as well as local fine textures from the input image. We refer the readers to the suppl. material for detailed network structure.", + "bbox": [ + 75, + 90, + 468, + 167 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The feature voxel is defined in camera space instead of world space (i.e. space where tri-plane features of efficient GRAM are defined) as it is easier for $E_{detail}$ to extract image-aligned features than to learn transformed world space features (see Sec. 4.3). Given the feature voxel $V$ , we can obtain the corresponding feature $f^{lr} \\in \\mathbb{R}^{d_V}$ for a point $\\boldsymbol{x} \\in \\mathbb{R}^3$ in the world space via:", + "bbox": [ + 75, + 172, + 470, + 280 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nf ^ {l r} = \\operatorname {g r i d \\_ s a m p l e} (V, \\operatorname {w o r l d 2 c a m} (\\boldsymbol {x})), \\qquad (5)\n$$\n", + "text_format": "latex", + "bbox": [ + 138, + 303, + 468, + 321 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where grid_sample is a tri-linear interpolation function, and world2cam is a rigid transformation function between the world space and the camera space.", + "bbox": [ + 76, + 343, + 468, + 390 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Nevertheless, since $V$ is a low-resolution voxel, directly combining it with the feature manifolds obtained from the general inversion stage leads to a blurry inversion result, while predicting a high-resolution voxel (e.g. $256^{3}$ ) instead causes unaffordable memory cost. Inspired by [60], we take the advantage of our radiance manifolds representation to obtain high-resolution detail manifolds from the low-resolution voxel via manifold super-resolution. Specifically, we first obtain low-resolution detail manifolds $f^{lr}(\\{S_i\\})$ by querying features from $V$ via Eq. (5) for low-resolution points grid on the surface manifolds $\\{S_i\\}$ . We then flatten each manifold to a low-resolution feature map $F_{i}^{lr}$ and send it to the super-resolution module $\\mathcal{U}$ to obtain a high-resolution feature map $F_{i}^{hr} = \\mathcal{U}(F_{i}^{lr})$ , where $\\mathcal{U}$ is a simple 2D CNN of 4 convolution blocks and 2 bilinear upsampling blocks. Finally, we obtain the high-resolution detail manifolds $f^{hr}(\\{S_i\\})$ by re-projecting each flattened feature map $F_{i}^{hr}$ to the surface manifolds. Since we conduct super-resolution for 3D space surface manifolds, 3D consistency across different views can be naturally maintained during this process. Note that although the manifold super-resolution strategy is proposed in [60], it does not leverage it in a reconstruction scenario but to generate random fine details. By contrast, we utilize it for faithful reconstruction of high-frequency details in the original image.", + "bbox": [ + 75, + 396, + 470, + 773 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Given $f^{hr}(\\{S_i\\})$ from the detail-specific stage, we add it to the coarse feature manifolds $\\Psi(\\boldsymbol{w} + \\{\\mathcal{S}_i\\})$ from the general inversion stage, and send each feature point on the manifolds to the MLP-based decoder $m$ to obtain the final radiance manifolds, as shown in Fig. 2. The final inversion image $I$ can then be obtained similarly via manifold rendering at input view $\\hat{\\theta}$ . Novel views can also be easily generated given an arbitrary camera pose $\\theta$ during rendering.", + "bbox": [ + 75, + 779, + 468, + 902 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/3ecf9551fb0e3f1bcdd01b5bf88fd7ba6a5ee3ef012b8b4ff61e9dafd3278f3b.jpg", + "image_caption": [ + "Figure 4. Visualization of the novel view regularization." + ], + "image_footnote": [], + "bbox": [ + 511, + 88, + 882, + 247 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Detail Manifolds Learning", + "text_level": 1, + "bbox": [ + 500, + 287, + 740, + 303 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We fix the image inverter $E_{w}$ and the efficient GRAM from the general inversion stage, and learn the detail manifolds reconstructor with the following losses.", + "bbox": [ + 498, + 309, + 890, + 356 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Image reconstruction loss. A multi-level reconstruction loss is applied between the final inversion image $I$ and the input image $\\hat{I}$ :", + "bbox": [ + 498, + 358, + 890, + 402 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {r} = \\left\\| I - \\hat {I} \\right\\| ^ {2} + \\operatorname {L P I P S} (I, \\hat {I}) + \\left(1 - \\langle f _ {i d} (I), f _ {i d} (\\hat {I}) \\rangle\\right), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 509, + 409, + 890, + 428 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathrm{LPIPS}(\\cdot ,\\cdot)$ is the perceptual loss defined by [68], and $f_{id}$ is a pre-trained face recognition network [11].", + "bbox": [ + 498, + 435, + 890, + 465 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Novel view regularization. The reconstruction loss guarantees a faithful inversion result at the input viewpoint, yet artifacts can still occur when rendering the radiance manifolds at other views. We, therefore, design a regularization term to ensure reasonable novel view synthesis results:", + "bbox": [ + 498, + 469, + 890, + 545 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {n v} = \\operatorname {L P I P S} (M \\odot I (\\boldsymbol {\\theta}), M \\odot I _ {w} (\\boldsymbol {\\theta})), \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 558, + 551, + 890, + 568 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $I(\\pmb{\\theta})$ and $I_w(\\pmb{\\theta})$ are final and coarse inversion image rendered at novel view $\\pmb{\\theta}$ respectively, $\\odot$ is element-wise multiplication, and $M$ is a binary mask:", + "bbox": [ + 498, + 574, + 890, + 621 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nM (u, v) = \\mathbb {I} (- \\boldsymbol {r} (\\hat {\\boldsymbol {\\theta}}) \\cdot N _ {w} (\\boldsymbol {\\theta}) (u, v) < \\tau). \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 557, + 626, + 890, + 643 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Here $(u,v)$ is the image space coordinate, $\\mathbb{I}$ is the indicator function, $\\pmb{r}(\\hat{\\pmb{\\theta}})$ is the camera lookat direction of the input image $\\hat{I}$ , $N_w(\\pmb {\\theta})$ is the surface normal map of $I_{w}(\\pmb {\\theta})$ , and $\\tau$ is a scalar threshold. The intuition behind this regularization is that the details for regions unobserved in the input image should stay close to the coarse inversion result at novel views, as the coarse inversion image is more reasonable at new views due to leveraging the priors from the pre-trained GRAM. The normal map $N_w(\\pmb {\\theta})$ in Eq. (8) can be effectively calculated via the following equation:", + "bbox": [ + 496, + 650, + 890, + 803 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nN _ {w} (\\boldsymbol {\\theta}) (u, v) = - \\frac {1}{\\eta} \\sum_ {i = 1} ^ {N} T \\left(\\alpha \\left(\\boldsymbol {x} _ {i}\\right)\\right) \\alpha \\left(\\boldsymbol {x} _ {i}\\right) \\frac {\\partial \\alpha \\left(\\boldsymbol {x} _ {i}\\right)}{\\partial \\boldsymbol {x} _ {i}}, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 522, + 809, + 890, + 849 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\pmb{x}_i$ are intersections along the ray that $(u, v)$ corresponds to, $T(\\alpha(\\pmb{x}_i)) = \\prod_{j < i} (1 - \\alpha(\\pmb{x}_j))$ is the accumulated transparency, and $\\eta$ is a normalizing scalar. The partial", + "bbox": [ + 498, + 854, + 890, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "4427", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "gradient $\\partial \\alpha (\\pmb {x}_i) / \\partial \\pmb {x}_i$ can be easily computed via backpropagating the MLP-based decoder $m$ . Visualizations of the normal map $N_{w}(\\theta)$ and the binary mask $M$ are in Fig. 4.", + "bbox": [ + 75, + 90, + 468, + 137 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Depth regularization. We further enforce a depth regularization to the HR detail manifolds $f^{hr}(\\{\\mathcal{S}_i\\})$ to ensure that details are predicted near the geometry surface:", + "bbox": [ + 75, + 140, + 468, + 186 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {d e p t h}} = \\left\\{ \\begin{array}{l l} \\lambda \\| f ^ {h r} (\\boldsymbol {x} _ {i}) \\| ^ {2} & | z (\\boldsymbol {x} _ {i}) - z _ {\\text {s u r f}} | > \\epsilon \\\\ 0 & | z (\\boldsymbol {x} _ {i}) - z _ {\\text {s u r f}} | \\leq \\epsilon \\end{array} , \\right. \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 94, + 196, + 468, + 238 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\pmb{x}_i$ are intersections along the viewing rays at input viewpoint $\\hat{\\theta}$ , $z(\\pmb{x}_i)$ is the depth of $\\pmb{x}_i$ , $z_{surf} = \\sum_{i=1}^{N} T(\\alpha(\\pmb{x}_i)) \\alpha(\\pmb{x}_i) z(\\pmb{x}_i)$ is the depth of the approximated surface, and $\\epsilon$ is a threshold. This regularization ensures correct parallax for the learned details (see Sec. 4.3).", + "bbox": [ + 75, + 248, + 468, + 325 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 340, + 209, + 357 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation details. We train our method on the FFHQ [25] dataset at $256^2$ resolution and test it on the CelebA-HQ [23] dataset. All images are pre-processed following the procedure in [13]. The camera pose of input images is estimated by the face reconstruction method of [14]. We train our models on 4 Tesla V100 GPUs with 32GB memory. The whole training process takes around 6 days, where training the efficient GRAM takes 2 days, training the image inverter and finetuning the efficient GRAM takes 2 days and 1 day respectively, and training the detail manifolds reconstructor takes 1 day. More in the suppl. material.", + "bbox": [ + 75, + 364, + 468, + 532 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Novel View Synthesis Results", + "text_level": 1, + "bbox": [ + 76, + 541, + 336, + 558 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Figure 1 shows the novel view synthesis results of our method given different portrait images. Our method well preserves fine details (e.g. hair bangs, wrinkles, moles) of the input images and produces their 3D consistent novel views. The whole inversion and novel view synthesis process runs at 3 FPS on a V100 GPU without specialized acceleration, which largely improves the efficiency upon previous optimization-based 3D-aware GAN inversions. With the manifold caching technique in [13], we can further increase the free view rendering speed to 180FPS. More examples and video results are in the suppl. material.", + "bbox": [ + 75, + 565, + 468, + 731 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Comparison with Prior Arts", + "text_level": 1, + "bbox": [ + 76, + 739, + 331, + 757 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Comparison with GRAM. We first compare our efficient version of GRAM with the original one [13]. We measure the image generation quality by the Fréchet Inception Distances (FID) [21] between 20K randomly generated images and 20K sampled real images. The 3D consistency is measured by the reconstruction quality of NeuS [54] (i.e. $\\mathrm{PSNR}_{mv}$ and $\\mathrm{SSIM}_{mv}$ ) on multiview images of 50 generated instances following [60]. As shown in Tab. 1, our efficient GRAM largely reduces the memory cost and increases", + "bbox": [ + 75, + 763, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/335e3ca8bd54c5b2ce69db615b8d63d12b089239fa56329941e5ff38745f672e.jpg", + "table_caption": [ + "Table 1. Comparison between efficient GRAM and GRAM [13]. *: Inference on a Tesla V100 GPU with a batchsize of 1." + ], + "table_footnote": [], + "table_body": "
MethodsMemory* ↓FPS* ↑FID ↓PSNRm v ↑SSIMm v ↑
EG3D2.8G206.0234.00.928
GRAM12G215.038.00.966
Ours3.3G1414.237.60.969
", + "bbox": [ + 501, + 126, + 890, + 193 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "the inference speed upon the original one without sacrificing image generation quality or 3D consistency, by introducing the StyleGAN2-based radiance generator and the efficient intersection calculation strategy. This improvement enables our following GRAMinverter method, otherwise, it is difficult, if not impossible, to leverage the memory-consuming GRAM for encoder-based GAN inversion. We also list the performance of the state-of-the-art EG3D [9] as a reference. Although EG3D has better image quality, it sacrifices the 3D consistency which we argue is a key factor for 3D-aware generation.", + "bbox": [ + 496, + 210, + 890, + 377 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Comparison with pose editing methods. We compare with existing methods that achieve 3D pose editing of a given portrait via single forward pass, including 2D GAN inversion-based methods: e4e [52] + InterFaceGAN [41], HFGI [55] + InterFaceGAN, and HFGI + StyleHEAT [65]; 3D-aware GAN inversion-based methods: pix2NeRF [7] and IDE-3D [46]; and face reenactment methods: PIRenderer [36] and Face-vid2vid [56].", + "bbox": [ + 496, + 383, + 890, + 505 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We first evaluate the inversion fidelity among GAN inversion-based methods (Tab. 2). We report PSNR, SSIM, LPIPS, identity similarity (i.e. ID) measured by cosine distance of face recognition features [53], and FID. All metrics are calculated between the first 1K images of CelebAHQ and their corresponding inverted results. Since different methods may generate images of different resolutions and alignments, we pre-process all results following [13] and resize them to $256 \\times 256$ for a fair comparison. As shown, our method significantly outperforms other 3D-aware GAN inversion methods across all metrics. We also exceed the StyleGAN2-based inversion method e4e and achieve comparable results with the state-of-the-art method HFGI.", + "bbox": [ + 496, + 506, + 890, + 702 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We further compare our method with other approaches on pose editing of portrait images. We generate novel views (see the suppl. material) of the 1K test images using different methods and evaluate their identity similarity and FID to the original input in Tab. 2. Higher $\\mathrm{ID}_{nv}$ and lower $\\mathrm{FID}_{nv}$ indicate that a method can better keep the identity and image quality while changing the camera pose. Our method yields the best result among all competitors. We also surpass PIRenderer and Face-vid2vid which require video data for training, while ours is merely trained on monocular in-the-wild images. Figure 5 shows a visual comparison.", + "bbox": [ + 496, + 703, + 890, + 869 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Finally, we measure the 3D consistency of all methods during continuous variation of the camera viewpoint. Fol-", + "bbox": [ + 498, + 869, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "4428", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/830cc18579d1383a438279b021e0708b0b53473fd88c898b405e44a748a492d1.jpg", + "table_caption": [ + "Table 2. Quantitative comparison with existing portrait editing methods. See the text for details." + ], + "table_footnote": [], + "table_body": "
MethodsInversion fidelityNovel view quality3D consistency
PSNR↑SSIM↑LPIPS↓ID↑FID↓ID_nv↑FID_nv↓PSNR_mv↑SSIM_mv↑
PIRendererer [36]-----0.47642.6436.720.958
Face-vid2vid [56]-----0.41641.7636.100.942
e4e [52] + InterfaceGAN [41]19.230.4510.2130.70635.920.48938.0434.290.909
HFGI [55] + InterfaceGAN [41]22.300.5790.1350.82726.410.51645.2333.990.917
HFGI [55] + StyleHEAT [65]22.300.5790.1350.82726.410.45758.3335.930.951
pix2NeRF [7]16.950.3940.4520.466108.30.378115.650.660.997
IDE-3D (encoder) [46]16.730.3820.2900.39351.510.32447.5637.570.950
Ours21.510.6500.1270.93628.170.63536.0239.530.974
", + "bbox": [ + 99, + 112, + 870, + 263 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e88218ac2bf0cac65b8f2a05c5a5dff025c070aaa8e2677d397a322b693a45f2.jpg", + "image_caption": [ + "PIRenderer" + ], + "image_footnote": [], + "bbox": [ + 89, + 273, + 261, + 472 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8a459be36fbfda0be2047cae6b8fe6c29babc06e11a23b4f7947bda791caa145.jpg", + "image_caption": [ + "Face-vid2vid" + ], + "image_footnote": [], + "bbox": [ + 264, + 275, + 436, + 472 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0ca813fdd37f67f2a9120a1c2a535adafecf1c1d5386ce027eddd3289a74cc88.jpg", + "image_caption": [ + "e4e+InterFaceGAN" + ], + "image_footnote": [], + "bbox": [ + 437, + 275, + 609, + 472 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/51829ec42b39c987656518b27b80f6a705ec88c7d2f72d9cbf779cab8ec7b662.jpg", + "image_caption": [ + "HFGI+InterFaceGAN" + ], + "image_footnote": [], + "bbox": [ + 614, + 275, + 785, + 472 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/9c1b64e766e297443d588fe6919295ee25604d4a0b65a1aedf43847df1c3f95f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 787, + 275, + 875, + 472 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/1ac13ac7403fb35869f523a3569d7767e02d0a6b4d245f9604c9b3a776c7a7a2.jpg", + "image_caption": [ + "StyleHEAT", + "Figure 5. Pose editing comparison. Texture images with smoothly tilted strips indicate better 3D consistency. Best viewed with zoom-in." + ], + "image_footnote": [], + "bbox": [ + 89, + 484, + 261, + 681 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/032666ffa92d1d0caf50b91593f5fa849d5bd34c6f7411356ef360cab8555adb.jpg", + "image_caption": [ + "pix2NeRF" + ], + "image_footnote": [], + "bbox": [ + 264, + 484, + 436, + 681 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ead55e557a1d1f94c26fc07593070e0f8ee0233816297a532d5b8de1a8590541.jpg", + "image_caption": [ + "IDE-3D (encoder)" + ], + "image_footnote": [], + "bbox": [ + 437, + 484, + 609, + 681 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3448794f8fd1994804ff3263b52b9f558880f224ba79573ec9a7c36995fbb58e.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 614, + 484, + 785, + 681 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e31c7e08e60ec00ba5030b23ec1095787526cba4f70e5ec3845469b994709782.jpg", + "image_caption": [ + "Input", + "Input" + ], + "image_footnote": [], + "bbox": [ + 787, + 484, + 875, + 681 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "lowing [60], for each method, we generate 30 images under different views for 50 test instances in CelebA-HQ, and measure the multiview reconstruction quality of NeuS on them (i.e. $\\mathrm{PSNR}_{mv}$ and $\\mathrm{SSIM}_{mv}$ ). In theory, better 3D consistency across different views would reduce the learning difficulty of NeuS, thus leading to higher PSNR and SSIM. Table 2 shows that our method has the second best 3D consistency among all methods, while the best one (i.e. pix2NeRF) generates over-smooth images of low quality as shown in Fig. 5 and indicated by the high FID score in Tab. 2. Our method outperforms IDE-3D in that it utilizes", + "bbox": [ + 75, + 732, + 470, + 898 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "a 2D super-resolution module in its 3D-aware GAN which lowers the 3D consistency to some extent. Nevertheless, all 3D-aware GAN-based methods yield better 3D consistency compared to other 2D methods, indicating the importance of 3D-aware GAN for pose editing of images. A further comparison with the full pipeline of IDE-3D which includes an extra optimization step is in the suppl. material.", + "bbox": [ + 496, + 732, + 890, + 838 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Figure 5 further shows the visual comparison of 3D consistency, where we draw the stacked texture image of a fixed horizontal line segment during continuous camera movement following [60]. Methods with strong 3D consistency", + "bbox": [ + 496, + 839, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "4429", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5c20b35819820c21bf2762bc1c7f69ccfdaf18e7d5be411978156fd83f5af115.jpg", + "image_caption": [ + "Figure 6. Visual comparison between different alternatives. Our final solution yields the best result. Best viewed with zoom-in." + ], + "image_footnote": [], + "bbox": [ + 76, + 88, + 468, + 344 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/c9b8ac05717fcb16ecb37f3f0488a1acb3ab15e83b41b8419dcb373471c2107c.jpg", + "table_caption": [ + "Table 3. Ablation study of our proposed framework." + ], + "table_footnote": [], + "table_body": "
MethodsPSNR ↑LPIPS ↓ID ↑FID_nv ↓
General17.680.2650.64844.43
General - pretrain17.450.2800.47252.12
General + finetune18.000.2540.67843.46
Detail (Ours)21.510.1270.93636.02
Detail - world2cam19.960.1710.90838.74
Detail - superres21.060.1650.92638.45
Detail - L_nv22.320.1060.94936.49
Detail - mask19.080.2110.84043.25
Detail - L_depth23.680.0940.96035.60
", + "bbox": [ + 84, + 414, + 460, + 565 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "will result in texture images with smoothly tilted strips, while methods with low 3D consistency produce twisted textures (i.e. geometry distortions and texture flickering issues) or vertical lines (i.e. texture sticking issues). Our method clearly produces a more reasonable texture image compared to the others. See the suppl. material and the accompanying video for more results.", + "bbox": [ + 75, + 585, + 468, + 694 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 704, + 230, + 720 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We conduct an ablation study to validate the efficacy of our proposed framework and report the results in Tab. 3 and Fig. 6. All metrics are calculated similarly as in Sec. 4.2.", + "bbox": [ + 75, + 727, + 468, + 773 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Inversion stage. Table 3 shows the performance of different stages. General stands for the general inversion stage without finetuned generator. General - pretrain denotes learning the efficient GRAM with $E_{w}$ together instead of pre-training it via the 3D-aware GAN framework. General + finetune denotes finetuning the pre-trained efficient GRAM as described in Sec. 3.2, and Detail denotes our final approach with detail-specific reconstruction. As shown,", + "bbox": [ + 75, + 780, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "the general stage alone cannot produce faithful reconstruction result, whether the efficient GRAM is further finetuned or not. By contrast, introducing the detail-specific reconstruction significantly improves the inversion fidelity upon the previous stage without sacrificing novel view quality. Learning the efficient GRAM together with the encoder without pre-training leads to a significant performance drop, indicating the importance of leveraging the prior knowledge of a pre-trained 3D-aware GAN.", + "bbox": [ + 496, + 90, + 890, + 227 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Network architecture. We ablate the architecture of the detail manifolds reconstructor. As shown in Tab. 3 and Fig. 6, learning the low-resolution detail voxel in world space instead of in camera space (- world2cam) harms the reconstruction fidelity. And removing the super-resolution module for high-resolution manifold prediction (- superres) leads to blurry inversion results.", + "bbox": [ + 496, + 231, + 890, + 338 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Regularization. We further validate our proposed regularization for detail manifolds learning. As shown in Tab. 3 and Fig. 6, removing the novel view regularization $(- \\mathcal{L}_{nv})$ causes obvious artifacts at new views and leads to the increase of $\\mathrm{FID}_{nv}$ , though it improves the reconstruction quality at the input viewpoint. Simply enforcing $\\mathcal{L}_{nv}$ without the normal-aware mask (-mask) damages fine texture preservation at visible regions. Finally, although learning without the depth regularization $(- \\mathcal{L}_{depth})$ results in better metrics, we find that it cannot well preserve certain fine details at novel views due to incorrect parallax brought by the depth error (e.g. mole in Fig. 6). We conjecture that such dynamic artifact can hardly be captured by the current feature extractor [49] for FID computation.", + "bbox": [ + 496, + 342, + 892, + 554 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusions", + "text_level": 1, + "bbox": [ + 500, + 568, + 627, + 583 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We presented GRAMinverter, a novel approach for high-fidelity and 3D-consistent portrait synthesis from monocular images via single forward pass. The core idea is to learn a detail manifolds reconstructor to predict 3D-consistent fine details on the radiance manifolds from a input image, and combine them with the coarse radiance manifolds obtained via an encoder-based inversion of the pre-trained GRAM. Extensive experiments have demonstrated our superior results over previous works. We believe our method paves a new way for efficient 3D-aware portrait creation.", + "bbox": [ + 496, + 593, + 890, + 744 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitations and future works. Our GRAMinverter has several limitations. Based on the radiance manifold representation, it produces layered artifacts at large viewing angles. It cannot well handle occlusions of hands and other accessories. Its performance is also affected by the training data and may produce inferior results for out-of-distribution input. Besides, it does not support editing of attributes beyond camera viewpoints as done in previous 2D GAN inversions. Better 3D representations and inversion strategies should be further explored to alleviate these problems.", + "bbox": [ + 496, + 750, + 892, + 901 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "4430", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Rameen Abdul, Yipeng Qin, and Peter Wonka. Image2stylegan: How to embed images into the stylegan latent space? 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Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.107, + 0.13, + 0.868, + 0.177 + ], + "angle": 0, + "content": "Learning Detailed Radiance Manifolds for High-Fidelity and 3D-Consistent Portrait Synthesis from Monocular Image" + }, + { + "type": "text", + "bbox": [ + 0.285, + 0.204, + 0.686, + 0.241 + ], + "angle": 0, + "content": "Yu Deng Baoyuan Wang Heung-Yeung Shum Xiaobing.AI" + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.256, + 0.481, + 0.49 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.117, + 0.49, + 0.149, + 0.501 + ], + "angle": 0, + "content": "Input" + }, + { + "type": "image", + "bbox": [ + 0.489, + 0.256, + 0.892, + 0.49 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.526, + 0.49, + 0.558, + 0.501 + ], + "angle": 0, + "content": "Input" + }, + { + "type": "image_caption", + "bbox": [ + 0.704, + 0.49, + 0.776, + 0.5 + ], + "angle": 0, + "content": "Novel views" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.507, + 0.893, + 0.537 + ], + "angle": 0, + "content": "Figure 1. Novel view synthesis results by our method. It can generate novel views of a portrait image with high-fidelity and strong 3D-consistency via single forward pass (e.g., see the bangs and wrinkles). Best viewed with zoom-in and see the video for animations." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.556, + 0.314, + 0.572 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.586, + 0.473, + 0.903 + ], + "angle": 0, + "content": "A key challenge for novel view synthesis of monocular portrait images is 3D consistency under continuous pose variations. Most existing methods rely on 2D generative models which often leads to obvious 3D inconsistency artifacts. We present a 3D-consistent novel view synthesis approach for monocular portrait images based on a recent proposed 3D-aware GAN, namely Generative Radiance Manifolds (GRAM) [13], which has shown strong 3D consistency at multiview image generation of virtual subjects via the radiance manifolds representation. However, simply learning an encoder to map a real image into the latent space of GRAM can only reconstruct coarse radiance manifolds without faithful fine details, while improving the reconstruction fidelity via instance-specific optimization is time-consuming. We introduce a novel detail manifolds reconstructor to learn 3D-consistent fine details on the radiance manifolds from monocular images, and combine them with the coarse radiance manifolds for high-fidelity reconstruction. The 3D priors derived from the coarse radiance manifolds are used to regulate the learned details to ensure reasonable synthesized results" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.557, + 0.895, + 0.618 + ], + "angle": 0, + "content": "at novel views. Trained on in-the-wild 2D images, our method achieves high-fidelity and 3D-consistent portrait synthesis largely outperforming the prior art. Project page: https://yudeng.github.io/GRAMInverter/" + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.65, + 0.633, + 0.667 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.676, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Synthesizing photorealistic portrait images of a person from an arbitrary viewpoint is an important task that can benefit diverse downstream applications such as virtual avatar creation and immersive online communication. Thanks to the thriving of 2D Generative Adversarial Networks (GANs) [18,25,26], people can now generate high-quality portraits at desired views given only monocular images as input, via a simple invert-then-edit strategy by conducting GAN inversion [1,38,52] and latent space editing [12,20,41,50]. However, existing 2D GAN-based methods still have deficiencies when applied to applications that require more strict 3D consistency (e.g. VR&AR). Due to the non-physical rendering process of the 2D CNN-based generators, their synthesized images under pose changes usually bear certain kinds of multiview inconsistency, such" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4423" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.152 + ], + "angle": 0, + "content": "as geometry distortions [3,5] and texture sticking or flickering [24, 55]. These artifacts may not be significant enough when inspecting each static image but can be easily captured by human eyes under continuous image variations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.155, + 0.471, + 0.442 + ], + "angle": 0, + "content": "Recently, there are an emerging group of 3D-aware GANs [9, 10, 13, 19, 39, 40] targeting at image generation with 3D pose disentanglement. By incorporating Neural Radiance Field (NeRF) [29] and its variants into the adversarial learning process of GANs, they can produce realistic images with strong 3D-consistency across different views, given only a set of monocular images as training data. As a result, 3D-aware GANs have shown greater potential than 2D GANs for pose manipulations of portraits. However, even though 3D-aware GANs are capable of generating 3D-consistent portraits of virtual subjects, leveraging them for real image pose editing is still a challenging task. To obtain faithful reconstructions of real images, most existing methods [9, 10, 13, 27, 46, 47, 67] turn to a time-consuming and instance-specific optimization to invert the given images into the latent space of a pre-trained 3D-aware GAN, which is hard to scale-up. And simply enforcing an encoder-based 3D-aware GAN inversion [7, 46] often fails to preserve fine details in the original image." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.445, + 0.47, + 0.626 + ], + "angle": 0, + "content": "In this paper, we propose a novel approach GRAMInverter, for high-fidelity and 3D-consistent novel view synthesis of monocular portraits via single forward pass. Our method is built upon the recent GRAM [13] that can synthesize high-quality virtual images with strong 3D consistency via the radiance manifolds representation [13]. Nevertheless, GRAM suffers from the same lack-of-fidelity issue when combined with a general encoder-based GAN inversion approach [52]. The main reason is that the obtained semantically-meaningful low-dimensional latent code cannot well record detail information of the input, as also indicated by some recent 2D GAN inversion methods [52, 55]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.629, + 0.471, + 0.901 + ], + "angle": 0, + "content": "To tackle this problem, our motivation is to further learn 3D-space high-frequency details and combine them with the coarse radiance manifolds obtained from the general encoder-based inversion of GRAM, to achieve faithful reconstruction and 3D-consistent view synthesis. A straightforward way to achieve this is to extract a high-resolution 3D voxel from the input image and combine it with the coarse radiance manifolds. However, this is prohibited by modern GPUs due to the high memory cost of the 3D voxel. To tackle this problem, we turn to learn a high resolution detail manifolds, taking the advantage of the radiance manifolds representation of GRAM, instead of learning the memory-consuming 3D voxel. We introduce a novel detail manifolds reconstructor to extract detail manifolds from the input images. It leverages manifold super-resolution [60] to predict high-resolution detail manifolds from a low resolution feature voxel. This can be effectively achieved by a set of memory-efficient 2D convolution blocks. The obtained" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.166 + ], + "angle": 0, + "content": "high resolution detail manifolds can still maintain strict 3D consistency due to lying in the 3D space. We also propose dedicated losses to regulate the detail manifolds via 3D priors derived from the coarse radiance manifolds, to ensure reasonable novel view results." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.168, + 0.892, + 0.289 + ], + "angle": 0, + "content": "Another contribution of our method is an improvement upon the memory and time-consuming GRAM, without which it is difficult to be integrated into our GAN inversion framework. We replace the original MLP-based radiance generator [13] in GRAM with a StyleGAN2 [26]-based triplane generator proposed by [9]. The efficient GRAM requires only \\( 1/4 \\) memory cost with \\( 7 \\times \\) speed up, without sacrificing the image generation quality and 3D consistency." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.29, + 0.892, + 0.44 + ], + "angle": 0, + "content": "We train our method on FFHQ dataset [25] and conduct multiple experiments to demonstrate its advantages on pose control of portrait images. Once trained, GRAMInverter takes a monocular image as input and predicts its radiance manifolds representation for novel view synthesis at 3 FPS on a single GPU. The generated novel views well preserve fine details in the original image with strong 3D consistency, outperforming prior art by a large margin. We believe our method takes a solid step towards efficient 3D-aware content creation for real applications." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.457, + 0.642, + 0.473 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.484, + 0.892, + 0.68 + ], + "angle": 0, + "content": "3D-aware generative model. Learned with monocular 2D images, 3D-aware GANs [9, 10, 13, 17, 19, 30, 31, 34, 39, 40, 45, 60, 62] achieve an explicit disentanglement of camera pose by introducing underlying 3D representations. Earlier works [30, 42, 48] utilize voxel or mesh as the intermediate representation. Later works [9, 10, 13, 34, 39, 62, 69] leverage NeRF [29] and its variants [13, 33, 54, 64] to achieve more strict 3D consistency. Among them, methods that directly render their 3D representations for image synthesis achieve the best multiview consistency [10, 13, 17, 40, 45]. We propose a novel approach for high-quality pose editing of given portraits based on GRAM [13], which is a recent 3D-aware GAN with state-of-the-art multiview consistency." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.892, + 0.901 + ], + "angle": 0, + "content": "GAN inversion. GAN inversion aims to map a given real image into the latent space of a pre-trained generator for image reconstruction and manipulation. Numerous methods [1,4,6,26,37,38,52,55,63,72,73] try to find a latent code which can faithfully reconstruct the given image meanwhile falls inside a semantically meaningful latent space that supports reasonable editing. They either adopt optimization-based approach [1, 2, 26, 73], introduce an extra image encoder [4, 37, 52], or utilize a hybrid version of the former two [6, 72]. Nevertheless, recent studies [38, 52, 55, 74] reveal that it is difficult to achieve high-fidelity reconstruction and artifacts-free editing at once given only low-bitrate latent code as representation. As a result, several methods propose to further fine-tune the pre-trained generator [38]" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "4424" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.089, + 0.885, + 0.284 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.288, + 0.893, + 0.348 + ], + "angle": 0, + "content": "Figure 2. Overview of the GRAMInverter. An input portrait image goes through two stages to obtain the final radiance manifolds for novel view synthesis. The first general inversion stage maps the input image to the latent space of a pre-trained efficient GRAM to obtain coarse radiance manifolds. The second detail-specific stage then extracts detail feature manifolds from the input image and combines them with the coarse results for high-fidelity image synthesis. See the text for more details." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.361, + 0.47, + 0.391 + ], + "angle": 0, + "content": "or allow more detailed features from the input images to leak into the generator during inversion [55, 63]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.392, + 0.471, + 0.619 + ], + "angle": 0, + "content": "While the above methods target at the inversion of 2D GANs, inverting a given image with 3D-aware GANs shares a similar spirit. An advantage of 3D-aware GAN inversion compare to its 2D counterpart is a natural disentanglement of the 3D pose. Once inverted, novel view synthesis can be easily achieved without further latent space exploration [20, 41]. The majority of existing 3D-aware GAN inversion methods [9, 10, 13, 27, 46, 47, 51, 57] leverage optimization-based or a hybrid approach for faithful reconstruction, which are time-consuming and hard to scale-up. A recent method [7] explores GAN inversion with a single forward of an encoder, yet it struggles to preserve fine image details. Our proposed method is also an encoder-based inversion approach which yields high-quality reconstruction and novel view synthesis thanks to our novel design." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.629, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Pose editing of monocular portraits. Editing the camera pose of a monocular portrait for novel view synthesis is a longstanding task and has witnessed the emergence of diverse methods. Some of them [8,35,59,61,75,76] achieve pose editing by first conducting 3D reconstruction and then rendering the obtained mesh at novel views. Due to the imperfect reconstruction results, they often have difficulties handling non-face regions and unseen parts at the input view. Others [15, 16, 32, 36, 43, 44, 56, 58, 66, 70] generate novel views in a face-reenactment paradigm, where warping flows are often learned from video data to transform a source image to a target viewpoint. These methods may encounter geometry distortions at novel views due to the lack of an explicit 3D constraint. More recently, plenty of works [3,7,12,22,28,41,46,47,50] have studied pose editing of an image by inverting it into a prior model such as GAN. With the strong prior bearing in a pre-trained generator, synthesizing novel views of a given portrait can be achieved" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.361, + 0.892, + 0.437 + ], + "angle": 0, + "content": "without any 3D or video data during training. Among them, methods using 3D-aware GANs [7,9,13,46,47] have shown better 3D consistency under pose variations. Our method is also based on 3D-aware GAN and largely improves the efficiency, reconstruction quality, as well as 3D consistency." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.45, + 0.61, + 0.468 + ], + "angle": 0, + "content": "3. Approach" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.475, + 0.893, + 0.763 + ], + "angle": 0, + "content": "Given a monocular portrait image \\(\\hat{I}\\), we aim to synthesize its novel views at some arbitrary camera viewpoints by leveraging the prior knowledge of a pre-trained 3D-aware GAN, as shown in Fig. 2. To guarantee high-quality and 3D-consistent novel view synthesis, we adopt GRAM [13] as our underlying image generator and design an efficient version of it that requires much less computation and memory cost so as to incorporate it into our whole framework (Sec. 3.1). With the efficient GRAM, we first utilize a general encoder-based GAN inversion to reconstruct the coarse radiance manifolds from the input image (Sec. 3.2). We then introduce a detail-specific reconstruction stage to learn high-resolution detail manifolds that cannot be well captured by the coarse result, via our proposed novel detail manifolds reconstructor (Sec. 3.3). Multiple losses are enforced to regulate the predicted detail manifolds to ensure reasonable synthesized results at novel views, by leveraging the 3D priors derived from the coarse radiance manifolds (Sec. 3.4). We describe each part in details below." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.772, + 0.849, + 0.788 + ], + "angle": 0, + "content": "3.1. Efficient Generative Radiance Manifolds" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.892, + 0.903 + ], + "angle": 0, + "content": "We start with a brief review of the original GRAM proposed in [13]. The core of GRAM is its underlying radiance manifolds representation, which regulates radiance field learning on a set of surface manifolds in the 3D space instead of predicting it in the whole volumetric space as done by [29]. The surface manifolds are defined as a set of iso-surfaces \\(\\{S_i\\}\\) in a 3D scalar field represented by a" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4425" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.423, + 0.108 + ], + "angle": 0, + "content": "light-weight MLP called the manifold predictor \\(\\mathcal{M}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.117, + 0.116, + 0.47, + 0.134 + ], + "angle": 0, + "content": "\\[\n\\mathcal {M}: \\boldsymbol {x} \\in \\mathbb {R} ^ {3} \\rightarrow s \\in \\mathbb {R}, \\mathcal {S} _ {i} = \\{\\boldsymbol {x} | \\mathcal {M} (\\boldsymbol {x}) = l _ {i} \\}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.144, + 0.47, + 0.205 + ], + "angle": 0, + "content": "where \\(\\{l_i\\}\\) are \\(N\\) predefined scalar levels. During image generation, only intersections \\(\\{\\pmb{x}_i\\}\\) between a viewing ray \\(\\pmb{r}\\) and the surface manifolds will be sent into an MLP-based radiance generator \\(\\Phi\\) for radiance prediction:" + }, + { + "type": "equation", + "bbox": [ + 0.138, + 0.212, + 0.469, + 0.23 + ], + "angle": 0, + "content": "\\[\n\\Phi : \\left(\\boldsymbol {z}, \\boldsymbol {x} _ {i}\\right) \\in \\mathbb {R} ^ {d _ {z}} \\times \\mathbb {R} ^ {3} \\rightarrow (\\boldsymbol {c}, \\alpha) \\in \\mathbb {R} ^ {4}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.238, + 0.47, + 0.284 + ], + "angle": 0, + "content": "where \\( z \\) is a latent code determining the radiance, \\( c \\) is the color, and \\( \\alpha \\) is the occupancy. The final color of each ray can be computed via manifold rendering [13, 71]:" + }, + { + "type": "equation", + "bbox": [ + 0.137, + 0.291, + 0.469, + 0.334 + ], + "angle": 0, + "content": "\\[\nC (\\boldsymbol {r}) = \\sum_ {i = 1} ^ {N} \\prod_ {j < i} (1 - \\alpha (\\boldsymbol {x} _ {j})) \\alpha (\\boldsymbol {x} _ {i}) \\boldsymbol {c} (\\boldsymbol {x} _ {i}). \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.341, + 0.47, + 0.643 + ], + "angle": 0, + "content": "The high mometry cost of GRAM lies in its MLP-based radiance generator \\(\\Phi\\), which requires millions of forward steps to generate a single image. Inspired by the recent EG3D [9], we substitute the original radiance generator with a tri-plane generator [9] based on StyleGAN2 structure [26]. Its efficient coarse-to-fine structure helps to reduce memory and computation costs by a large margin. Given the new radiance generator, the color and occupancy for points on the surface manifolds can be obtained by first generating tri-plane features by a 2D CNN \\(\\Psi\\), and then conducting tri-plane sampling and sending the sampled features into a small MLP-based decoder \\(m\\) as done in [9]. Note that although we take the tri-plane generator from EG3D to improve efficiency, we do not use its 2D super-resolution module but keep strictly to the radiance manifolds representation. This helps us to maintain the strong 3D consistency brought by the manifold rendering. In addition, we calculate ray-manifold intersections at \\(1/4\\) resolution of the final image to further speed up our image generation process (details in the suppl. material)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.644, + 0.47, + 0.719 + ], + "angle": 0, + "content": "The efficient GRAM serves as a strong prior for generating realistic multiview images of virtual subjects. By combining it with our two-stage manifolds reconstruction method, we achieve high-quality novel view synthesis of real portraits, as described in the following sections." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.727, + 0.3, + 0.743 + ], + "angle": 0, + "content": "3.2. General Inversion Stage" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Given a pre-trained efficient GRAM following a typical 3D-aware GAN training paradigm [13], we first introduce an image inverter \\( E_{w} \\) that maps a given image to the latent space of the efficient GRAM, as shown in Fig. 2. Inspired by previous StyleGAN-based inversion methods [1, 52, 55], we invert the given image into a latent code \\( \\boldsymbol{w} + = [\\boldsymbol{w}_1, \\boldsymbol{w}_2, \\dots, \\boldsymbol{w}_L] \\) in \\( \\mathcal{W}+ \\) space [1] of the tri-plane generator \\( \\Psi \\) for a proper trade-off between inversion fidelity and pose editing quality, where \\( L \\) is the number of layers in \\( \\Psi \\)'s synthesis sub-network. We leverage" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.09, + 0.891, + 0.202 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.211, + 0.894, + 0.268 + ], + "angle": 0, + "content": "Figure 3. The detail encoder \\( E_{detail} \\) extracts a camera space feature voxel from an input image. The voxel corresponds to a quadrangular frustum in the 3D space bounded by the near and far planes of the camera and the outermost viewing rays." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.283, + 0.892, + 0.374 + ], + "angle": 0, + "content": "the e4e encoder [52] as the backbone of \\( E_{w} \\). Given \\( \\pmb{w} + \\), we can obtain a coarse radiance manifolds \\( \\Phi(\\pmb{w} +, \\{S_i\\}) = m \\circ \\Psi(\\pmb{w} +, \\{S_i\\}) \\) via Eq. (1) and (2), and further obtain a coarse inversion image \\( I_{w} \\) by rendering the radiance manifolds at input viewpoint \\( \\hat{\\theta} \\) via Eq. (3), where \\( \\hat{\\theta} \\) can be obtained by off-the-shelf 3D face reconstruction method [14]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.374, + 0.893, + 0.51 + ], + "angle": 0, + "content": "We fixed the pre-trained efficient GRAM and learn the image inverter \\( E_{w} \\) following the training process of [52], except that we replaced the adversarial loss in [52] with a naive L2 loss between predicted \\( w+ \\) and the average latent code of the \\( \\mathcal{W}+ \\) space. To further improve the reconstruction fidelity, we fixed the trained \\( E_{w} \\) and finetuned the efficient GRAM via the pivot tuning strategy [38] using all training images. Details for the above training processes can be found in the suppl. material." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.51, + 0.894, + 0.6 + ], + "angle": 0, + "content": "After training, the general inversion stage can already synthesize reasonable multiview images of the input, yet it cannot faithfully preserve the fine details, making the inverted result looks less like the original image (see Fig. 6). Therefore, we introduce a detail-specific stage for faithful detail reconstruction, as described below." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.609, + 0.816, + 0.626 + ], + "angle": 0, + "content": "3.3. Detail-Specific Reconstruction Stage" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.633, + 0.892, + 0.798 + ], + "angle": 0, + "content": "The detail-specific stage aims to extract fine details from the input image that cannot be well described by the coarse radiance manifolds to improve the reconstruction fidelity. The intuition is to learn high-resolution details in 3D space so that their combination with the coarse radiance manifolds still remains strong 3D consistency under pose variations. To achieve this goal, we design a detail manifolds recon. structor consisting of two modules: a detail encoder \\(E_{detail}\\) that extracts low-resolution feature voxel from the input image, and a super-resolution module \\(\\mathcal{U}\\) to predict highresolution detail manifolds from the low-resolution voxel." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.798, + 0.892, + 0.829 + ], + "angle": 0, + "content": "Specifically, \\( E_{detail} \\) takes an image \\( \\hat{I} \\) as input and predicts a camera space feature voxel as shown in Fig. 3:" + }, + { + "type": "equation", + "bbox": [ + 0.512, + 0.836, + 0.892, + 0.855 + ], + "angle": 0, + "content": "\\[\nE _ {\\text {d e t a i l}}: \\hat {I} \\in \\mathbb {R} ^ {H \\times W \\times 3} \\rightarrow V \\in \\mathbb {R} ^ {H _ {l r} \\times W _ {l r} \\times D _ {l r} \\times d _ {V}}, \\tag {4}\n\\]" + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.863, + 0.894, + 0.901 + ], + "angle": 0, + "content": "In practice, we find that concatenating \\(\\hat{I}\\) with an extra difference map \\(\\Delta = \\hat{I} - I_w\\) as input yields better reconstruction quality, where \\(I_w\\) is the inversion image obtained by the general inversion stage." + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4426" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.168 + ], + "angle": 0, + "content": "where \\( d_V \\) is the feature dimension. We implement \\( E_{detail} \\) as a 3D U-Net with skip connections to extract both global geometry structures as well as local fine textures from the input image. We refer the readers to the suppl. material for detailed network structure." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.174, + 0.471, + 0.281 + ], + "angle": 0, + "content": "The feature voxel is defined in camera space instead of world space (i.e. space where tri-plane features of efficient GRAM are defined) as it is easier for \\( E_{detail} \\) to extract image-aligned features than to learn transformed world space features (see Sec. 4.3). Given the feature voxel \\( V \\), we can obtain the corresponding feature \\( f^{lr} \\in \\mathbb{R}^{d_V} \\) for a point \\( \\boldsymbol{x} \\in \\mathbb{R}^3 \\) in the world space via:" + }, + { + "type": "equation", + "bbox": [ + 0.14, + 0.304, + 0.47, + 0.323 + ], + "angle": 0, + "content": "\\[\nf ^ {l r} = \\operatorname {g r i d \\_ s a m p l e} (V, \\operatorname {w o r l d 2 c a m} (\\boldsymbol {x})), \\qquad (5)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.344, + 0.47, + 0.391 + ], + "angle": 0, + "content": "where grid_sample is a tri-linear interpolation function, and world2cam is a rigid transformation function between the world space and the camera space." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.397, + 0.471, + 0.775 + ], + "angle": 0, + "content": "Nevertheless, since \\(V\\) is a low-resolution voxel, directly combining it with the feature manifolds obtained from the general inversion stage leads to a blurry inversion result, while predicting a high-resolution voxel (e.g. \\(256^{3}\\)) instead causes unaffordable memory cost. Inspired by [60], we take the advantage of our radiance manifolds representation to obtain high-resolution detail manifolds from the low-resolution voxel via manifold super-resolution. Specifically, we first obtain low-resolution detail manifolds \\(f^{lr}(\\{S_i\\})\\) by querying features from \\(V\\) via Eq. (5) for low-resolution points grid on the surface manifolds \\(\\{S_i\\}\\). We then flatten each manifold to a low-resolution feature map \\(F_{i}^{lr}\\) and send it to the super-resolution module \\(\\mathcal{U}\\) to obtain a high-resolution feature map \\(F_{i}^{hr} = \\mathcal{U}(F_{i}^{lr})\\), where \\(\\mathcal{U}\\) is a simple 2D CNN of 4 convolution blocks and 2 bilinear upsampling blocks. Finally, we obtain the high-resolution detail manifolds \\(f^{hr}(\\{S_i\\})\\) by re-projecting each flattened feature map \\(F_{i}^{hr}\\) to the surface manifolds. Since we conduct super-resolution for 3D space surface manifolds, 3D consistency across different views can be naturally maintained during this process. Note that although the manifold super-resolution strategy is proposed in [60], it does not leverage it in a reconstruction scenario but to generate random fine details. By contrast, we utilize it for faithful reconstruction of high-frequency details in the original image." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Given \\( f^{hr}(\\{S_i\\}) \\) from the detail-specific stage, we add it to the coarse feature manifolds \\( \\Psi(\\boldsymbol{w} + \\{\\mathcal{S}_i\\}) \\) from the general inversion stage, and send each feature point on the manifolds to the MLP-based decoder \\( m \\) to obtain the final radiance manifolds, as shown in Fig. 2. The final inversion image \\( I \\) can then be obtained similarly via manifold rendering at input view \\( \\hat{\\theta} \\). Novel views can also be easily generated given an arbitrary camera pose \\( \\theta \\) during rendering." + }, + { + "type": "image", + "bbox": [ + 0.513, + 0.089, + 0.883, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.529, + 0.258, + 0.862, + 0.273 + ], + "angle": 0, + "content": "Figure 4. Visualization of the novel view regularization." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.288, + 0.741, + 0.304 + ], + "angle": 0, + "content": "3.4. Detail Manifolds Learning" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.31, + 0.892, + 0.357 + ], + "angle": 0, + "content": "We fix the image inverter \\( E_{w} \\) and the efficient GRAM from the general inversion stage, and learn the detail manifolds reconstructor with the following losses." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.359, + 0.892, + 0.404 + ], + "angle": 0, + "content": "Image reconstruction loss. A multi-level reconstruction loss is applied between the final inversion image \\(I\\) and the input image \\(\\hat{I}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.51, + 0.41, + 0.892, + 0.429 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {r} = \\left\\| I - \\hat {I} \\right\\| ^ {2} + \\operatorname {L P I P S} (I, \\hat {I}) + \\left(1 - \\langle f _ {i d} (I), f _ {i d} (\\hat {I}) \\rangle\\right), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.436, + 0.892, + 0.467 + ], + "angle": 0, + "content": "where \\(\\mathrm{LPIPS}(\\cdot ,\\cdot)\\) is the perceptual loss defined by [68], and \\(f_{id}\\) is a pre-trained face recognition network [11]." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.47, + 0.892, + 0.546 + ], + "angle": 0, + "content": "Novel view regularization. The reconstruction loss guarantees a faithful inversion result at the input viewpoint, yet artifacts can still occur when rendering the radiance manifolds at other views. We, therefore, design a regularization term to ensure reasonable novel view synthesis results:" + }, + { + "type": "equation", + "bbox": [ + 0.56, + 0.552, + 0.892, + 0.569 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {n v} = \\operatorname {L P I P S} (M \\odot I (\\boldsymbol {\\theta}), M \\odot I _ {w} (\\boldsymbol {\\theta})), \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.575, + 0.892, + 0.622 + ], + "angle": 0, + "content": "where \\(I(\\pmb{\\theta})\\) and \\(I_w(\\pmb{\\theta})\\) are final and coarse inversion image rendered at novel view \\(\\pmb{\\theta}\\) respectively, \\(\\odot\\) is element-wise multiplication, and \\(M\\) is a binary mask:" + }, + { + "type": "equation", + "bbox": [ + 0.558, + 0.627, + 0.892, + 0.645 + ], + "angle": 0, + "content": "\\[\nM (u, v) = \\mathbb {I} (- \\boldsymbol {r} (\\hat {\\boldsymbol {\\theta}}) \\cdot N _ {w} (\\boldsymbol {\\theta}) (u, v) < \\tau). \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.651, + 0.892, + 0.804 + ], + "angle": 0, + "content": "Here \\((u,v)\\) is the image space coordinate, \\(\\mathbb{I}\\) is the indicator function, \\(\\pmb{r}(\\hat{\\pmb{\\theta}})\\) is the camera lookat direction of the input image \\(\\hat{I}\\), \\(N_w(\\pmb {\\theta})\\) is the surface normal map of \\(I_{w}(\\pmb {\\theta})\\), and \\(\\tau\\) is a scalar threshold. The intuition behind this regularization is that the details for regions unobserved in the input image should stay close to the coarse inversion result at novel views, as the coarse inversion image is more reasonable at new views due to leveraging the priors from the pre-trained GRAM. The normal map \\(N_w(\\pmb {\\theta})\\) in Eq. (8) can be effectively calculated via the following equation:" + }, + { + "type": "equation", + "bbox": [ + 0.523, + 0.81, + 0.892, + 0.851 + ], + "angle": 0, + "content": "\\[\nN _ {w} (\\boldsymbol {\\theta}) (u, v) = - \\frac {1}{\\eta} \\sum_ {i = 1} ^ {N} T \\left(\\alpha \\left(\\boldsymbol {x} _ {i}\\right)\\right) \\alpha \\left(\\boldsymbol {x} _ {i}\\right) \\frac {\\partial \\alpha \\left(\\boldsymbol {x} _ {i}\\right)}{\\partial \\boldsymbol {x} _ {i}}, \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.892, + 0.902 + ], + "angle": 0, + "content": "where \\( \\pmb{x}_i \\) are intersections along the ray that \\( (u, v) \\) corresponds to, \\( T(\\alpha(\\pmb{x}_i)) = \\prod_{j < i} (1 - \\alpha(\\pmb{x}_j)) \\) is the accumulated transparency, and \\( \\eta \\) is a normalizing scalar. The partial" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4427" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.47, + 0.138 + ], + "angle": 0, + "content": "gradient \\(\\partial \\alpha (\\pmb {x}_i) / \\partial \\pmb {x}_i\\) can be easily computed via backpropagating the MLP-based decoder \\(m\\). Visualizations of the normal map \\(N_{w}(\\theta)\\) and the binary mask \\(M\\) are in Fig. 4." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.141, + 0.47, + 0.187 + ], + "angle": 0, + "content": "Depth regularization. We further enforce a depth regularization to the HR detail manifolds \\( f^{hr}(\\{\\mathcal{S}_i\\}) \\) to ensure that details are predicted near the geometry surface:" + }, + { + "type": "equation", + "bbox": [ + 0.096, + 0.198, + 0.47, + 0.239 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {d e p t h}} = \\left\\{ \\begin{array}{l l} \\lambda \\| f ^ {h r} (\\boldsymbol {x} _ {i}) \\| ^ {2} & | z (\\boldsymbol {x} _ {i}) - z _ {\\text {s u r f}} | > \\epsilon \\\\ 0 & | z (\\boldsymbol {x} _ {i}) - z _ {\\text {s u r f}} | \\leq \\epsilon \\end{array} , \\right. \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.249, + 0.469, + 0.327 + ], + "angle": 0, + "content": "where \\(\\pmb{x}_i\\) are intersections along the viewing rays at input viewpoint \\(\\hat{\\theta}\\), \\(z(\\pmb{x}_i)\\) is the depth of \\(\\pmb{x}_i\\), \\(z_{surf} = \\sum_{i=1}^{N} T(\\alpha(\\pmb{x}_i)) \\alpha(\\pmb{x}_i) z(\\pmb{x}_i)\\) is the depth of the approximated surface, and \\(\\epsilon\\) is a threshold. This regularization ensures correct parallax for the learned details (see Sec. 4.3)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.341, + 0.21, + 0.358 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.366, + 0.47, + 0.534 + ], + "angle": 0, + "content": "Implementation details. We train our method on the FFHQ [25] dataset at \\(256^2\\) resolution and test it on the CelebA-HQ [23] dataset. All images are pre-processed following the procedure in [13]. The camera pose of input images is estimated by the face reconstruction method of [14]. We train our models on 4 Tesla V100 GPUs with 32GB memory. The whole training process takes around 6 days, where training the efficient GRAM takes 2 days, training the image inverter and finetuning the efficient GRAM takes 2 days and 1 day respectively, and training the detail manifolds reconstructor takes 1 day. More in the suppl. material." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.542, + 0.337, + 0.559 + ], + "angle": 0, + "content": "4.1. Novel View Synthesis Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.566, + 0.47, + 0.732 + ], + "angle": 0, + "content": "Figure 1 shows the novel view synthesis results of our method given different portrait images. Our method well preserves fine details (e.g. hair bangs, wrinkles, moles) of the input images and produces their 3D consistent novel views. The whole inversion and novel view synthesis process runs at 3 FPS on a V100 GPU without specialized acceleration, which largely improves the efficiency upon previous optimization-based 3D-aware GAN inversions. With the manifold caching technique in [13], we can further increase the free view rendering speed to 180FPS. More examples and video results are in the suppl. material." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.741, + 0.332, + 0.758 + ], + "angle": 0, + "content": "4.2. Comparison with Prior Arts" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Comparison with GRAM. We first compare our efficient version of GRAM with the original one [13]. We measure the image generation quality by the Fréchet Inception Distances (FID) [21] between 20K randomly generated images and 20K sampled real images. The 3D consistency is measured by the reconstruction quality of NeuS [54] (i.e. \\(\\mathrm{PSNR}_{mv}\\) and \\(\\mathrm{SSIM}_{mv}\\)) on multiview images of 50 generated instances following [60]. As shown in Tab. 1, our efficient GRAM largely reduces the memory cost and increases" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.089, + 0.892, + 0.117 + ], + "angle": 0, + "content": "Table 1. Comparison between efficient GRAM and GRAM [13]. *: Inference on a Tesla V100 GPU with a batchsize of 1." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.127, + 0.892, + 0.194 + ], + "angle": 0, + "content": "
MethodsMemory* ↓FPS* ↑FID ↓PSNRm v ↑SSIMm v ↑
EG3D2.8G206.0234.00.928
GRAM12G215.038.00.966
Ours3.3G1414.237.60.969
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.212, + 0.892, + 0.378 + ], + "angle": 0, + "content": "the inference speed upon the original one without sacrificing image generation quality or 3D consistency, by introducing the StyleGAN2-based radiance generator and the efficient intersection calculation strategy. This improvement enables our following GRAMinverter method, otherwise, it is difficult, if not impossible, to leverage the memory-consuming GRAM for encoder-based GAN inversion. We also list the performance of the state-of-the-art EG3D [9] as a reference. Although EG3D has better image quality, it sacrifices the 3D consistency which we argue is a key factor for 3D-aware generation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.385, + 0.892, + 0.506 + ], + "angle": 0, + "content": "Comparison with pose editing methods. We compare with existing methods that achieve 3D pose editing of a given portrait via single forward pass, including 2D GAN inversion-based methods: e4e [52] + InterFaceGAN [41], HFGI [55] + InterFaceGAN, and HFGI + StyleHEAT [65]; 3D-aware GAN inversion-based methods: pix2NeRF [7] and IDE-3D [46]; and face reenactment methods: PIRenderer [36] and Face-vid2vid [56]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.507, + 0.892, + 0.703 + ], + "angle": 0, + "content": "We first evaluate the inversion fidelity among GAN inversion-based methods (Tab. 2). We report PSNR, SSIM, LPIPS, identity similarity (i.e. ID) measured by cosine distance of face recognition features [53], and FID. All metrics are calculated between the first 1K images of CelebAHQ and their corresponding inverted results. Since different methods may generate images of different resolutions and alignments, we pre-process all results following [13] and resize them to \\(256 \\times 256\\) for a fair comparison. As shown, our method significantly outperforms other 3D-aware GAN inversion methods across all metrics. We also exceed the StyleGAN2-based inversion method e4e and achieve comparable results with the state-of-the-art method HFGI." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.892, + 0.87 + ], + "angle": 0, + "content": "We further compare our method with other approaches on pose editing of portrait images. We generate novel views (see the suppl. material) of the 1K test images using different methods and evaluate their identity similarity and FID to the original input in Tab. 2. Higher \\(\\mathrm{ID}_{nv}\\) and lower \\(\\mathrm{FID}_{nv}\\) indicate that a method can better keep the identity and image quality while changing the camera pose. Our method yields the best result among all competitors. We also surpass PIRenderer and Face-vid2vid which require video data for training, while ours is merely trained on monocular in-the-wild images. Figure 5 shows a visual comparison." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Finally, we measure the 3D consistency of all methods during continuous variation of the camera viewpoint. Fol-" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4428" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.201, + 0.09, + 0.768, + 0.104 + ], + "angle": 0, + "content": "Table 2. Quantitative comparison with existing portrait editing methods. See the text for details." + }, + { + "type": "table", + "bbox": [ + 0.1, + 0.113, + 0.872, + 0.264 + ], + "angle": 0, + "content": "
MethodsInversion fidelityNovel view quality3D consistency
PSNR↑SSIM↑LPIPS↓ID↑FID↓ID_nv↑FID_nv↓PSNR_mv↑SSIM_mv↑
PIRendererer [36]-----0.47642.6436.720.958
Face-vid2vid [56]-----0.41641.7636.100.942
e4e [52] + InterfaceGAN [41]19.230.4510.2130.70635.920.48938.0434.290.909
HFGI [55] + InterfaceGAN [41]22.300.5790.1350.82726.410.51645.2333.990.917
HFGI [55] + StyleHEAT [65]22.300.5790.1350.82726.410.45758.3335.930.951
pix2NeRF [7]16.950.3940.4520.466108.30.378115.650.660.997
IDE-3D (encoder) [46]16.730.3820.2900.39351.510.32447.5637.570.950
Ours21.510.6500.1270.93628.170.63536.0239.530.974
" + }, + { + "type": "image", + "bbox": [ + 0.091, + 0.275, + 0.263, + 0.473 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.143, + 0.474, + 0.213, + 0.484 + ], + "angle": 0, + "content": "PIRenderer" + }, + { + "type": "image", + "bbox": [ + 0.265, + 0.276, + 0.437, + 0.473 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.311, + 0.474, + 0.391, + 0.484 + ], + "angle": 0, + "content": "Face-vid2vid" + }, + { + "type": "image", + "bbox": [ + 0.439, + 0.276, + 0.611, + 0.473 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.465, + 0.474, + 0.583, + 0.484 + ], + "angle": 0, + "content": "e4e+InterFaceGAN" + }, + { + "type": "image", + "bbox": [ + 0.615, + 0.276, + 0.787, + 0.473 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.633, + 0.474, + 0.765, + 0.484 + ], + "angle": 0, + "content": "HFGI+InterFaceGAN" + }, + { + "type": "image", + "bbox": [ + 0.788, + 0.276, + 0.876, + 0.473 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.816, + 0.474, + 0.849, + 0.485 + ], + "angle": 0, + "content": "Input" + }, + { + "type": "image", + "bbox": [ + 0.091, + 0.485, + 0.263, + 0.682 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.142, + 0.683, + 0.212, + 0.695 + ], + "angle": 0, + "content": "StyleHEAT" + }, + { + "type": "image", + "bbox": [ + 0.265, + 0.485, + 0.437, + 0.682 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.319, + 0.683, + 0.382, + 0.695 + ], + "angle": 0, + "content": "pix2NeRF" + }, + { + "type": "image", + "bbox": [ + 0.439, + 0.485, + 0.611, + 0.682 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.47, + 0.683, + 0.579, + 0.695 + ], + "angle": 0, + "content": "IDE-3D (encoder)" + }, + { + "type": "image", + "bbox": [ + 0.615, + 0.485, + 0.787, + 0.682 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.685, + 0.684, + 0.715, + 0.694 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image", + "bbox": [ + 0.788, + 0.485, + 0.876, + 0.682 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.816, + 0.684, + 0.849, + 0.695 + ], + "angle": 0, + "content": "Input" + }, + { + "type": "image_caption", + "bbox": [ + 0.078, + 0.701, + 0.891, + 0.715 + ], + "angle": 0, + "content": "Figure 5. Pose editing comparison. Texture images with smoothly tilted strips indicate better 3D consistency. Best viewed with zoom-in." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.733, + 0.471, + 0.899 + ], + "angle": 0, + "content": "lowing [60], for each method, we generate 30 images under different views for 50 test instances in CelebA-HQ, and measure the multiview reconstruction quality of NeuS on them (i.e. \\(\\mathrm{PSNR}_{mv}\\) and \\(\\mathrm{SSIM}_{mv}\\)). In theory, better 3D consistency across different views would reduce the learning difficulty of NeuS, thus leading to higher PSNR and SSIM. Table 2 shows that our method has the second best 3D consistency among all methods, while the best one (i.e. pix2NeRF) generates over-smooth images of low quality as shown in Fig. 5 and indicated by the high FID score in Tab. 2. Our method outperforms IDE-3D in that it utilizes" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.733, + 0.892, + 0.839 + ], + "angle": 0, + "content": "a 2D super-resolution module in its 3D-aware GAN which lowers the 3D consistency to some extent. Nevertheless, all 3D-aware GAN-based methods yield better 3D consistency compared to other 2D methods, indicating the importance of 3D-aware GAN for pose editing of images. A further comparison with the full pipeline of IDE-3D which includes an extra optimization step is in the suppl. material." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Figure 5 further shows the visual comparison of 3D consistency, where we draw the stacked texture image of a fixed horizontal line segment during continuous camera movement following [60]. Methods with strong 3D consistency" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4429" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.089, + 0.47, + 0.345 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.355, + 0.47, + 0.384 + ], + "angle": 0, + "content": "Figure 6. Visual comparison between different alternatives. Our final solution yields the best result. Best viewed with zoom-in." + }, + { + "type": "table_caption", + "bbox": [ + 0.117, + 0.39, + 0.429, + 0.404 + ], + "angle": 0, + "content": "Table 3. Ablation study of our proposed framework." + }, + { + "type": "table", + "bbox": [ + 0.086, + 0.415, + 0.462, + 0.566 + ], + "angle": 0, + "content": "
MethodsPSNR ↑LPIPS ↓ID ↑FID_nv ↓
General17.680.2650.64844.43
General - pretrain17.450.2800.47252.12
General + finetune18.000.2540.67843.46
Detail (Ours)21.510.1270.93636.02
Detail - world2cam19.960.1710.90838.74
Detail - superres21.060.1650.92638.45
Detail - L_nv22.320.1060.94936.49
Detail - mask19.080.2110.84043.25
Detail - L_depth23.680.0940.96035.60
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.587, + 0.47, + 0.695 + ], + "angle": 0, + "content": "will result in texture images with smoothly tilted strips, while methods with low 3D consistency produce twisted textures (i.e. geometry distortions and texture flickering issues) or vertical lines (i.e. texture sticking issues). Our method clearly produces a more reasonable texture image compared to the others. See the suppl. material and the accompanying video for more results." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.705, + 0.231, + 0.721 + ], + "angle": 0, + "content": "4.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.728, + 0.47, + 0.775 + ], + "angle": 0, + "content": "We conduct an ablation study to validate the efficacy of our proposed framework and report the results in Tab. 3 and Fig. 6. All metrics are calculated similarly as in Sec. 4.2." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Inversion stage. Table 3 shows the performance of different stages. General stands for the general inversion stage without finetuned generator. General - pretrain denotes learning the efficient GRAM with \\( E_{w} \\) together instead of pre-training it via the 3D-aware GAN framework. General + finetune denotes finetuning the pre-trained efficient GRAM as described in Sec. 3.2, and Detail denotes our final approach with detail-specific reconstruction. As shown," + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.228 + ], + "angle": 0, + "content": "the general stage alone cannot produce faithful reconstruction result, whether the efficient GRAM is further finetuned or not. By contrast, introducing the detail-specific reconstruction significantly improves the inversion fidelity upon the previous stage without sacrificing novel view quality. Learning the efficient GRAM together with the encoder without pre-training leads to a significant performance drop, indicating the importance of leveraging the prior knowledge of a pre-trained 3D-aware GAN." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.232, + 0.892, + 0.339 + ], + "angle": 0, + "content": "Network architecture. We ablate the architecture of the detail manifolds reconstructor. As shown in Tab. 3 and Fig. 6, learning the low-resolution detail voxel in world space instead of in camera space (- world2cam) harms the reconstruction fidelity. And removing the super-resolution module for high-resolution manifold prediction (- superres) leads to blurry inversion results." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.343, + 0.893, + 0.555 + ], + "angle": 0, + "content": "Regularization. We further validate our proposed regularization for detail manifolds learning. As shown in Tab. 3 and Fig. 6, removing the novel view regularization \\((- \\mathcal{L}_{nv})\\) causes obvious artifacts at new views and leads to the increase of \\(\\mathrm{FID}_{nv}\\), though it improves the reconstruction quality at the input viewpoint. Simply enforcing \\(\\mathcal{L}_{nv}\\) without the normal-aware mask (-mask) damages fine texture preservation at visible regions. Finally, although learning without the depth regularization \\((- \\mathcal{L}_{depth})\\) results in better metrics, we find that it cannot well preserve certain fine details at novel views due to incorrect parallax brought by the depth error (e.g. mole in Fig. 6). We conjecture that such dynamic artifact can hardly be captured by the current feature extractor [49] for FID computation." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.569, + 0.628, + 0.584 + ], + "angle": 0, + "content": "5. Conclusions" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.594, + 0.892, + 0.746 + ], + "angle": 0, + "content": "We presented GRAMinverter, a novel approach for high-fidelity and 3D-consistent portrait synthesis from monocular images via single forward pass. The core idea is to learn a detail manifolds reconstructor to predict 3D-consistent fine details on the radiance manifolds from a input image, and combine them with the coarse radiance manifolds obtained via an encoder-based inversion of the pre-trained GRAM. Extensive experiments have demonstrated our superior results over previous works. We believe our method paves a new way for efficient 3D-aware portrait creation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.893, + 0.902 + ], + "angle": 0, + "content": "Limitations and future works. Our GRAMinverter has several limitations. Based on the radiance manifold representation, it produces layered artifacts at large viewing angles. It cannot well handle occlusions of hands and other accessories. Its performance is also affected by the training data and may produce inferior results for out-of-distribution input. Besides, it does not support editing of attributes beyond camera viewpoints as done in previous 2D GAN inversions. Better 3D representations and inversion strategies should be further explored to alleviate these problems." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4430" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.171 + ], + "angle": 0, + "content": "[1] Rameen Abdul, Yipeng Qin, and Peter Wonka. Image2stylegan: How to embed images into the stylegan latent space? 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In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 787-796, 2015. 3" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.698 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "4433" + } + ] +] \ No newline at end of file diff --git a/2023/Learning Detailed Radiance Manifolds for High-Fidelity and 3D-Consistent Portrait Synthesis From Monocular Image/ee76865a-ff6b-45fe-83d5-c6e1d7d201e2_origin.pdf b/2023/Learning Detailed Radiance Manifolds for High-Fidelity and 3D-Consistent Portrait Synthesis From Monocular Image/ee76865a-ff6b-45fe-83d5-c6e1d7d201e2_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..c40c40f1a760a0f1f9fac7b5f28870518c3965b9 --- /dev/null +++ b/2023/Learning Detailed Radiance Manifolds for High-Fidelity and 3D-Consistent Portrait Synthesis From Monocular Image/ee76865a-ff6b-45fe-83d5-c6e1d7d201e2_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:e4a03e0dc8446ac326fd90fce491d4cb15890c625989490c05c10b2a95a5cf39 +size 7261522 diff --git a/2023/Learning Detailed Radiance Manifolds for High-Fidelity and 3D-Consistent Portrait Synthesis From Monocular Image/full.md b/2023/Learning Detailed Radiance Manifolds for High-Fidelity and 3D-Consistent Portrait Synthesis From Monocular Image/full.md new file mode 100644 index 0000000000000000000000000000000000000000..21e7095764c452941ada2ac6ab8ac9167bd22da7 --- /dev/null +++ b/2023/Learning Detailed Radiance Manifolds for High-Fidelity and 3D-Consistent Portrait Synthesis From Monocular Image/full.md @@ -0,0 +1,344 @@ +# Learning Detailed Radiance Manifolds for High-Fidelity and 3D-Consistent Portrait Synthesis from Monocular Image + +Yu Deng Baoyuan Wang Heung-Yeung Shum Xiaobing.AI + +![](images/29846e2c8625222bcd5704a3d43ae06412ed0157076ed2e5b21f9a5c9b09de9f.jpg) +Input +Figure 1. Novel view synthesis results by our method. It can generate novel views of a portrait image with high-fidelity and strong 3D-consistency via single forward pass (e.g., see the bangs and wrinkles). Best viewed with zoom-in and see the video for animations. + +![](images/aadd97515b37a598846b96f00d4eb745b50e4817a7da68ad971b381276442641.jpg) +Input +Novel views + +# Abstract + +A key challenge for novel view synthesis of monocular portrait images is 3D consistency under continuous pose variations. Most existing methods rely on 2D generative models which often leads to obvious 3D inconsistency artifacts. We present a 3D-consistent novel view synthesis approach for monocular portrait images based on a recent proposed 3D-aware GAN, namely Generative Radiance Manifolds (GRAM) [13], which has shown strong 3D consistency at multiview image generation of virtual subjects via the radiance manifolds representation. However, simply learning an encoder to map a real image into the latent space of GRAM can only reconstruct coarse radiance manifolds without faithful fine details, while improving the reconstruction fidelity via instance-specific optimization is time-consuming. We introduce a novel detail manifolds reconstructor to learn 3D-consistent fine details on the radiance manifolds from monocular images, and combine them with the coarse radiance manifolds for high-fidelity reconstruction. The 3D priors derived from the coarse radiance manifolds are used to regulate the learned details to ensure reasonable synthesized results + +at novel views. Trained on in-the-wild 2D images, our method achieves high-fidelity and 3D-consistent portrait synthesis largely outperforming the prior art. Project page: https://yudeng.github.io/GRAMInverter/ + +# 1. Introduction + +Synthesizing photorealistic portrait images of a person from an arbitrary viewpoint is an important task that can benefit diverse downstream applications such as virtual avatar creation and immersive online communication. Thanks to the thriving of 2D Generative Adversarial Networks (GANs) [18,25,26], people can now generate high-quality portraits at desired views given only monocular images as input, via a simple invert-then-edit strategy by conducting GAN inversion [1,38,52] and latent space editing [12,20,41,50]. However, existing 2D GAN-based methods still have deficiencies when applied to applications that require more strict 3D consistency (e.g. VR&AR). Due to the non-physical rendering process of the 2D CNN-based generators, their synthesized images under pose changes usually bear certain kinds of multiview inconsistency, such + +as geometry distortions [3,5] and texture sticking or flickering [24, 55]. These artifacts may not be significant enough when inspecting each static image but can be easily captured by human eyes under continuous image variations. + +Recently, there are an emerging group of 3D-aware GANs [9, 10, 13, 19, 39, 40] targeting at image generation with 3D pose disentanglement. By incorporating Neural Radiance Field (NeRF) [29] and its variants into the adversarial learning process of GANs, they can produce realistic images with strong 3D-consistency across different views, given only a set of monocular images as training data. As a result, 3D-aware GANs have shown greater potential than 2D GANs for pose manipulations of portraits. However, even though 3D-aware GANs are capable of generating 3D-consistent portraits of virtual subjects, leveraging them for real image pose editing is still a challenging task. To obtain faithful reconstructions of real images, most existing methods [9, 10, 13, 27, 46, 47, 67] turn to a time-consuming and instance-specific optimization to invert the given images into the latent space of a pre-trained 3D-aware GAN, which is hard to scale-up. And simply enforcing an encoder-based 3D-aware GAN inversion [7, 46] often fails to preserve fine details in the original image. + +In this paper, we propose a novel approach GRAMInverter, for high-fidelity and 3D-consistent novel view synthesis of monocular portraits via single forward pass. Our method is built upon the recent GRAM [13] that can synthesize high-quality virtual images with strong 3D consistency via the radiance manifolds representation [13]. Nevertheless, GRAM suffers from the same lack-of-fidelity issue when combined with a general encoder-based GAN inversion approach [52]. The main reason is that the obtained semantically-meaningful low-dimensional latent code cannot well record detail information of the input, as also indicated by some recent 2D GAN inversion methods [52, 55]. + +To tackle this problem, our motivation is to further learn 3D-space high-frequency details and combine them with the coarse radiance manifolds obtained from the general encoder-based inversion of GRAM, to achieve faithful reconstruction and 3D-consistent view synthesis. A straightforward way to achieve this is to extract a high-resolution 3D voxel from the input image and combine it with the coarse radiance manifolds. However, this is prohibited by modern GPUs due to the high memory cost of the 3D voxel. To tackle this problem, we turn to learn a high resolution detail manifolds, taking the advantage of the radiance manifolds representation of GRAM, instead of learning the memory-consuming 3D voxel. We introduce a novel detail manifolds reconstructor to extract detail manifolds from the input images. It leverages manifold super-resolution [60] to predict high-resolution detail manifolds from a low resolution feature voxel. This can be effectively achieved by a set of memory-efficient 2D convolution blocks. The obtained + +high resolution detail manifolds can still maintain strict 3D consistency due to lying in the 3D space. We also propose dedicated losses to regulate the detail manifolds via 3D priors derived from the coarse radiance manifolds, to ensure reasonable novel view results. + +Another contribution of our method is an improvement upon the memory and time-consuming GRAM, without which it is difficult to be integrated into our GAN inversion framework. We replace the original MLP-based radiance generator [13] in GRAM with a StyleGAN2 [26]-based triplane generator proposed by [9]. The efficient GRAM requires only $1/4$ memory cost with $7 \times$ speed up, without sacrificing the image generation quality and 3D consistency. + +We train our method on FFHQ dataset [25] and conduct multiple experiments to demonstrate its advantages on pose control of portrait images. Once trained, GRAMInverter takes a monocular image as input and predicts its radiance manifolds representation for novel view synthesis at 3 FPS on a single GPU. The generated novel views well preserve fine details in the original image with strong 3D consistency, outperforming prior art by a large margin. We believe our method takes a solid step towards efficient 3D-aware content creation for real applications. + +# 2. Related Work + +3D-aware generative model. Learned with monocular 2D images, 3D-aware GANs [9, 10, 13, 17, 19, 30, 31, 34, 39, 40, 45, 60, 62] achieve an explicit disentanglement of camera pose by introducing underlying 3D representations. Earlier works [30, 42, 48] utilize voxel or mesh as the intermediate representation. Later works [9, 10, 13, 34, 39, 62, 69] leverage NeRF [29] and its variants [13, 33, 54, 64] to achieve more strict 3D consistency. Among them, methods that directly render their 3D representations for image synthesis achieve the best multiview consistency [10, 13, 17, 40, 45]. We propose a novel approach for high-quality pose editing of given portraits based on GRAM [13], which is a recent 3D-aware GAN with state-of-the-art multiview consistency. + +GAN inversion. GAN inversion aims to map a given real image into the latent space of a pre-trained generator for image reconstruction and manipulation. Numerous methods [1,4,6,26,37,38,52,55,63,72,73] try to find a latent code which can faithfully reconstruct the given image meanwhile falls inside a semantically meaningful latent space that supports reasonable editing. They either adopt optimization-based approach [1, 2, 26, 73], introduce an extra image encoder [4, 37, 52], or utilize a hybrid version of the former two [6, 72]. Nevertheless, recent studies [38, 52, 55, 74] reveal that it is difficult to achieve high-fidelity reconstruction and artifacts-free editing at once given only low-bitrate latent code as representation. As a result, several methods propose to further fine-tune the pre-trained generator [38] + +![](images/2bf3075ab1ad6cef8deb70c3bae9951a4e794c76adc874da2f3ee44726339ea7.jpg) +Figure 2. Overview of the GRAMInverter. An input portrait image goes through two stages to obtain the final radiance manifolds for novel view synthesis. The first general inversion stage maps the input image to the latent space of a pre-trained efficient GRAM to obtain coarse radiance manifolds. The second detail-specific stage then extracts detail feature manifolds from the input image and combines them with the coarse results for high-fidelity image synthesis. See the text for more details. + +or allow more detailed features from the input images to leak into the generator during inversion [55, 63]. + +While the above methods target at the inversion of 2D GANs, inverting a given image with 3D-aware GANs shares a similar spirit. An advantage of 3D-aware GAN inversion compare to its 2D counterpart is a natural disentanglement of the 3D pose. Once inverted, novel view synthesis can be easily achieved without further latent space exploration [20, 41]. The majority of existing 3D-aware GAN inversion methods [9, 10, 13, 27, 46, 47, 51, 57] leverage optimization-based or a hybrid approach for faithful reconstruction, which are time-consuming and hard to scale-up. A recent method [7] explores GAN inversion with a single forward of an encoder, yet it struggles to preserve fine image details. Our proposed method is also an encoder-based inversion approach which yields high-quality reconstruction and novel view synthesis thanks to our novel design. + +Pose editing of monocular portraits. Editing the camera pose of a monocular portrait for novel view synthesis is a longstanding task and has witnessed the emergence of diverse methods. Some of them [8,35,59,61,75,76] achieve pose editing by first conducting 3D reconstruction and then rendering the obtained mesh at novel views. Due to the imperfect reconstruction results, they often have difficulties handling non-face regions and unseen parts at the input view. Others [15, 16, 32, 36, 43, 44, 56, 58, 66, 70] generate novel views in a face-reenactment paradigm, where warping flows are often learned from video data to transform a source image to a target viewpoint. These methods may encounter geometry distortions at novel views due to the lack of an explicit 3D constraint. More recently, plenty of works [3,7,12,22,28,41,46,47,50] have studied pose editing of an image by inverting it into a prior model such as GAN. With the strong prior bearing in a pre-trained generator, synthesizing novel views of a given portrait can be achieved + +without any 3D or video data during training. Among them, methods using 3D-aware GANs [7,9,13,46,47] have shown better 3D consistency under pose variations. Our method is also based on 3D-aware GAN and largely improves the efficiency, reconstruction quality, as well as 3D consistency. + +# 3. Approach + +Given a monocular portrait image $\hat{I}$ , we aim to synthesize its novel views at some arbitrary camera viewpoints by leveraging the prior knowledge of a pre-trained 3D-aware GAN, as shown in Fig. 2. To guarantee high-quality and 3D-consistent novel view synthesis, we adopt GRAM [13] as our underlying image generator and design an efficient version of it that requires much less computation and memory cost so as to incorporate it into our whole framework (Sec. 3.1). With the efficient GRAM, we first utilize a general encoder-based GAN inversion to reconstruct the coarse radiance manifolds from the input image (Sec. 3.2). We then introduce a detail-specific reconstruction stage to learn high-resolution detail manifolds that cannot be well captured by the coarse result, via our proposed novel detail manifolds reconstructor (Sec. 3.3). Multiple losses are enforced to regulate the predicted detail manifolds to ensure reasonable synthesized results at novel views, by leveraging the 3D priors derived from the coarse radiance manifolds (Sec. 3.4). We describe each part in details below. + +# 3.1. Efficient Generative Radiance Manifolds + +We start with a brief review of the original GRAM proposed in [13]. The core of GRAM is its underlying radiance manifolds representation, which regulates radiance field learning on a set of surface manifolds in the 3D space instead of predicting it in the whole volumetric space as done by [29]. The surface manifolds are defined as a set of iso-surfaces $\{S_i\}$ in a 3D scalar field represented by a + +light-weight MLP called the manifold predictor $\mathcal{M}$ : + +$$ +\mathcal {M}: \boldsymbol {x} \in \mathbb {R} ^ {3} \rightarrow s \in \mathbb {R}, \mathcal {S} _ {i} = \{\boldsymbol {x} | \mathcal {M} (\boldsymbol {x}) = l _ {i} \}, \tag {1} +$$ + +where $\{l_i\}$ are $N$ predefined scalar levels. During image generation, only intersections $\{\pmb{x}_i\}$ between a viewing ray $\pmb{r}$ and the surface manifolds will be sent into an MLP-based radiance generator $\Phi$ for radiance prediction: + +$$ +\Phi : \left(\boldsymbol {z}, \boldsymbol {x} _ {i}\right) \in \mathbb {R} ^ {d _ {z}} \times \mathbb {R} ^ {3} \rightarrow (\boldsymbol {c}, \alpha) \in \mathbb {R} ^ {4}, \tag {2} +$$ + +where $z$ is a latent code determining the radiance, $c$ is the color, and $\alpha$ is the occupancy. The final color of each ray can be computed via manifold rendering [13, 71]: + +$$ +C (\boldsymbol {r}) = \sum_ {i = 1} ^ {N} \prod_ {j < i} (1 - \alpha (\boldsymbol {x} _ {j})) \alpha (\boldsymbol {x} _ {i}) \boldsymbol {c} (\boldsymbol {x} _ {i}). \tag {3} +$$ + +The high mometry cost of GRAM lies in its MLP-based radiance generator $\Phi$ , which requires millions of forward steps to generate a single image. Inspired by the recent EG3D [9], we substitute the original radiance generator with a tri-plane generator [9] based on StyleGAN2 structure [26]. Its efficient coarse-to-fine structure helps to reduce memory and computation costs by a large margin. Given the new radiance generator, the color and occupancy for points on the surface manifolds can be obtained by first generating tri-plane features by a 2D CNN $\Psi$ , and then conducting tri-plane sampling and sending the sampled features into a small MLP-based decoder $m$ as done in [9]. Note that although we take the tri-plane generator from EG3D to improve efficiency, we do not use its 2D super-resolution module but keep strictly to the radiance manifolds representation. This helps us to maintain the strong 3D consistency brought by the manifold rendering. In addition, we calculate ray-manifold intersections at $1/4$ resolution of the final image to further speed up our image generation process (details in the suppl. material). + +The efficient GRAM serves as a strong prior for generating realistic multiview images of virtual subjects. By combining it with our two-stage manifolds reconstruction method, we achieve high-quality novel view synthesis of real portraits, as described in the following sections. + +# 3.2. General Inversion Stage + +Given a pre-trained efficient GRAM following a typical 3D-aware GAN training paradigm [13], we first introduce an image inverter $E_{w}$ that maps a given image to the latent space of the efficient GRAM, as shown in Fig. 2. Inspired by previous StyleGAN-based inversion methods [1, 52, 55], we invert the given image into a latent code $\boldsymbol{w} + = [\boldsymbol{w}_1, \boldsymbol{w}_2, \dots, \boldsymbol{w}_L]$ in $\mathcal{W}+$ space [1] of the tri-plane generator $\Psi$ for a proper trade-off between inversion fidelity and pose editing quality, where $L$ is the number of layers in $\Psi$ 's synthesis sub-network. We leverage + +![](images/1ad64f830a6e5c88291c4e0265c3486b01788878969db49e1788fac887900797.jpg) +Figure 3. The detail encoder $E_{detail}$ extracts a camera space feature voxel from an input image. The voxel corresponds to a quadrangular frustum in the 3D space bounded by the near and far planes of the camera and the outermost viewing rays. + +the e4e encoder [52] as the backbone of $E_{w}$ . Given $\pmb{w} +$ , we can obtain a coarse radiance manifolds $\Phi(\pmb{w} +, \{S_i\}) = m \circ \Psi(\pmb{w} +, \{S_i\})$ via Eq. (1) and (2), and further obtain a coarse inversion image $I_{w}$ by rendering the radiance manifolds at input viewpoint $\hat{\theta}$ via Eq. (3), where $\hat{\theta}$ can be obtained by off-the-shelf 3D face reconstruction method [14]. + +We fixed the pre-trained efficient GRAM and learn the image inverter $E_{w}$ following the training process of [52], except that we replaced the adversarial loss in [52] with a naive L2 loss between predicted $w+$ and the average latent code of the $\mathcal{W}+$ space. To further improve the reconstruction fidelity, we fixed the trained $E_{w}$ and finetuned the efficient GRAM via the pivot tuning strategy [38] using all training images. Details for the above training processes can be found in the suppl. material. + +After training, the general inversion stage can already synthesize reasonable multiview images of the input, yet it cannot faithfully preserve the fine details, making the inverted result looks less like the original image (see Fig. 6). Therefore, we introduce a detail-specific stage for faithful detail reconstruction, as described below. + +# 3.3. Detail-Specific Reconstruction Stage + +The detail-specific stage aims to extract fine details from the input image that cannot be well described by the coarse radiance manifolds to improve the reconstruction fidelity. The intuition is to learn high-resolution details in 3D space so that their combination with the coarse radiance manifolds still remains strong 3D consistency under pose variations. To achieve this goal, we design a detail manifolds recon. structor consisting of two modules: a detail encoder $E_{detail}$ that extracts low-resolution feature voxel from the input image, and a super-resolution module $\mathcal{U}$ to predict highresolution detail manifolds from the low-resolution voxel. + +Specifically, $E_{detail}$ takes an image $\hat{I}$ as input and predicts a camera space feature voxel as shown in Fig. 3: + +$$ +E _ {\text {d e t a i l}}: \hat {I} \in \mathbb {R} ^ {H \times W \times 3} \rightarrow V \in \mathbb {R} ^ {H _ {l r} \times W _ {l r} \times D _ {l r} \times d _ {V}}, \tag {4} +$$ + +where $d_V$ is the feature dimension. We implement $E_{detail}$ as a 3D U-Net with skip connections to extract both global geometry structures as well as local fine textures from the input image. We refer the readers to the suppl. material for detailed network structure. + +The feature voxel is defined in camera space instead of world space (i.e. space where tri-plane features of efficient GRAM are defined) as it is easier for $E_{detail}$ to extract image-aligned features than to learn transformed world space features (see Sec. 4.3). Given the feature voxel $V$ , we can obtain the corresponding feature $f^{lr} \in \mathbb{R}^{d_V}$ for a point $\boldsymbol{x} \in \mathbb{R}^3$ in the world space via: + +$$ +f ^ {l r} = \operatorname {g r i d \_ s a m p l e} (V, \operatorname {w o r l d 2 c a m} (\boldsymbol {x})), \qquad (5) +$$ + +where grid_sample is a tri-linear interpolation function, and world2cam is a rigid transformation function between the world space and the camera space. + +Nevertheless, since $V$ is a low-resolution voxel, directly combining it with the feature manifolds obtained from the general inversion stage leads to a blurry inversion result, while predicting a high-resolution voxel (e.g. $256^{3}$ ) instead causes unaffordable memory cost. Inspired by [60], we take the advantage of our radiance manifolds representation to obtain high-resolution detail manifolds from the low-resolution voxel via manifold super-resolution. Specifically, we first obtain low-resolution detail manifolds $f^{lr}(\{S_i\})$ by querying features from $V$ via Eq. (5) for low-resolution points grid on the surface manifolds $\{S_i\}$ . We then flatten each manifold to a low-resolution feature map $F_{i}^{lr}$ and send it to the super-resolution module $\mathcal{U}$ to obtain a high-resolution feature map $F_{i}^{hr} = \mathcal{U}(F_{i}^{lr})$ , where $\mathcal{U}$ is a simple 2D CNN of 4 convolution blocks and 2 bilinear upsampling blocks. Finally, we obtain the high-resolution detail manifolds $f^{hr}(\{S_i\})$ by re-projecting each flattened feature map $F_{i}^{hr}$ to the surface manifolds. Since we conduct super-resolution for 3D space surface manifolds, 3D consistency across different views can be naturally maintained during this process. Note that although the manifold super-resolution strategy is proposed in [60], it does not leverage it in a reconstruction scenario but to generate random fine details. By contrast, we utilize it for faithful reconstruction of high-frequency details in the original image. + +Given $f^{hr}(\{S_i\})$ from the detail-specific stage, we add it to the coarse feature manifolds $\Psi(\boldsymbol{w} + \{\mathcal{S}_i\})$ from the general inversion stage, and send each feature point on the manifolds to the MLP-based decoder $m$ to obtain the final radiance manifolds, as shown in Fig. 2. The final inversion image $I$ can then be obtained similarly via manifold rendering at input view $\hat{\theta}$ . Novel views can also be easily generated given an arbitrary camera pose $\theta$ during rendering. + +![](images/3ecf9551fb0e3f1bcdd01b5bf88fd7ba6a5ee3ef012b8b4ff61e9dafd3278f3b.jpg) +Figure 4. Visualization of the novel view regularization. + +# 3.4. Detail Manifolds Learning + +We fix the image inverter $E_{w}$ and the efficient GRAM from the general inversion stage, and learn the detail manifolds reconstructor with the following losses. + +Image reconstruction loss. A multi-level reconstruction loss is applied between the final inversion image $I$ and the input image $\hat{I}$ : + +$$ +\mathcal {L} _ {r} = \left\| I - \hat {I} \right\| ^ {2} + \operatorname {L P I P S} (I, \hat {I}) + \left(1 - \langle f _ {i d} (I), f _ {i d} (\hat {I}) \rangle\right), \tag {6} +$$ + +where $\mathrm{LPIPS}(\cdot ,\cdot)$ is the perceptual loss defined by [68], and $f_{id}$ is a pre-trained face recognition network [11]. + +Novel view regularization. The reconstruction loss guarantees a faithful inversion result at the input viewpoint, yet artifacts can still occur when rendering the radiance manifolds at other views. We, therefore, design a regularization term to ensure reasonable novel view synthesis results: + +$$ +\mathcal {L} _ {n v} = \operatorname {L P I P S} (M \odot I (\boldsymbol {\theta}), M \odot I _ {w} (\boldsymbol {\theta})), \tag {7} +$$ + +where $I(\pmb{\theta})$ and $I_w(\pmb{\theta})$ are final and coarse inversion image rendered at novel view $\pmb{\theta}$ respectively, $\odot$ is element-wise multiplication, and $M$ is a binary mask: + +$$ +M (u, v) = \mathbb {I} (- \boldsymbol {r} (\hat {\boldsymbol {\theta}}) \cdot N _ {w} (\boldsymbol {\theta}) (u, v) < \tau). \tag {8} +$$ + +Here $(u,v)$ is the image space coordinate, $\mathbb{I}$ is the indicator function, $\pmb{r}(\hat{\pmb{\theta}})$ is the camera lookat direction of the input image $\hat{I}$ , $N_w(\pmb {\theta})$ is the surface normal map of $I_{w}(\pmb {\theta})$ , and $\tau$ is a scalar threshold. The intuition behind this regularization is that the details for regions unobserved in the input image should stay close to the coarse inversion result at novel views, as the coarse inversion image is more reasonable at new views due to leveraging the priors from the pre-trained GRAM. The normal map $N_w(\pmb {\theta})$ in Eq. (8) can be effectively calculated via the following equation: + +$$ +N _ {w} (\boldsymbol {\theta}) (u, v) = - \frac {1}{\eta} \sum_ {i = 1} ^ {N} T \left(\alpha \left(\boldsymbol {x} _ {i}\right)\right) \alpha \left(\boldsymbol {x} _ {i}\right) \frac {\partial \alpha \left(\boldsymbol {x} _ {i}\right)}{\partial \boldsymbol {x} _ {i}}, \tag {9} +$$ + +where $\pmb{x}_i$ are intersections along the ray that $(u, v)$ corresponds to, $T(\alpha(\pmb{x}_i)) = \prod_{j < i} (1 - \alpha(\pmb{x}_j))$ is the accumulated transparency, and $\eta$ is a normalizing scalar. The partial + +gradient $\partial \alpha (\pmb {x}_i) / \partial \pmb {x}_i$ can be easily computed via backpropagating the MLP-based decoder $m$ . Visualizations of the normal map $N_{w}(\theta)$ and the binary mask $M$ are in Fig. 4. + +Depth regularization. We further enforce a depth regularization to the HR detail manifolds $f^{hr}(\{\mathcal{S}_i\})$ to ensure that details are predicted near the geometry surface: + +$$ +\mathcal {L} _ {\text {d e p t h}} = \left\{ \begin{array}{l l} \lambda \| f ^ {h r} (\boldsymbol {x} _ {i}) \| ^ {2} & | z (\boldsymbol {x} _ {i}) - z _ {\text {s u r f}} | > \epsilon \\ 0 & | z (\boldsymbol {x} _ {i}) - z _ {\text {s u r f}} | \leq \epsilon \end{array} , \right. \tag {10} +$$ + +where $\pmb{x}_i$ are intersections along the viewing rays at input viewpoint $\hat{\theta}$ , $z(\pmb{x}_i)$ is the depth of $\pmb{x}_i$ , $z_{surf} = \sum_{i=1}^{N} T(\alpha(\pmb{x}_i)) \alpha(\pmb{x}_i) z(\pmb{x}_i)$ is the depth of the approximated surface, and $\epsilon$ is a threshold. This regularization ensures correct parallax for the learned details (see Sec. 4.3). + +# 4. Experiments + +Implementation details. We train our method on the FFHQ [25] dataset at $256^2$ resolution and test it on the CelebA-HQ [23] dataset. All images are pre-processed following the procedure in [13]. The camera pose of input images is estimated by the face reconstruction method of [14]. We train our models on 4 Tesla V100 GPUs with 32GB memory. The whole training process takes around 6 days, where training the efficient GRAM takes 2 days, training the image inverter and finetuning the efficient GRAM takes 2 days and 1 day respectively, and training the detail manifolds reconstructor takes 1 day. More in the suppl. material. + +# 4.1. Novel View Synthesis Results + +Figure 1 shows the novel view synthesis results of our method given different portrait images. Our method well preserves fine details (e.g. hair bangs, wrinkles, moles) of the input images and produces their 3D consistent novel views. The whole inversion and novel view synthesis process runs at 3 FPS on a V100 GPU without specialized acceleration, which largely improves the efficiency upon previous optimization-based 3D-aware GAN inversions. With the manifold caching technique in [13], we can further increase the free view rendering speed to 180FPS. More examples and video results are in the suppl. material. + +# 4.2. Comparison with Prior Arts + +Comparison with GRAM. We first compare our efficient version of GRAM with the original one [13]. We measure the image generation quality by the Fréchet Inception Distances (FID) [21] between 20K randomly generated images and 20K sampled real images. The 3D consistency is measured by the reconstruction quality of NeuS [54] (i.e. $\mathrm{PSNR}_{mv}$ and $\mathrm{SSIM}_{mv}$ ) on multiview images of 50 generated instances following [60]. As shown in Tab. 1, our efficient GRAM largely reduces the memory cost and increases + +Table 1. Comparison between efficient GRAM and GRAM [13]. *: Inference on a Tesla V100 GPU with a batchsize of 1. + +
MethodsMemory* ↓FPS* ↑FID ↓PSNRm v ↑SSIMm v ↑
EG3D2.8G206.0234.00.928
GRAM12G215.038.00.966
Ours3.3G1414.237.60.969
+ +the inference speed upon the original one without sacrificing image generation quality or 3D consistency, by introducing the StyleGAN2-based radiance generator and the efficient intersection calculation strategy. This improvement enables our following GRAMinverter method, otherwise, it is difficult, if not impossible, to leverage the memory-consuming GRAM for encoder-based GAN inversion. We also list the performance of the state-of-the-art EG3D [9] as a reference. Although EG3D has better image quality, it sacrifices the 3D consistency which we argue is a key factor for 3D-aware generation. + +Comparison with pose editing methods. We compare with existing methods that achieve 3D pose editing of a given portrait via single forward pass, including 2D GAN inversion-based methods: e4e [52] + InterFaceGAN [41], HFGI [55] + InterFaceGAN, and HFGI + StyleHEAT [65]; 3D-aware GAN inversion-based methods: pix2NeRF [7] and IDE-3D [46]; and face reenactment methods: PIRenderer [36] and Face-vid2vid [56]. + +We first evaluate the inversion fidelity among GAN inversion-based methods (Tab. 2). We report PSNR, SSIM, LPIPS, identity similarity (i.e. ID) measured by cosine distance of face recognition features [53], and FID. All metrics are calculated between the first 1K images of CelebAHQ and their corresponding inverted results. Since different methods may generate images of different resolutions and alignments, we pre-process all results following [13] and resize them to $256 \times 256$ for a fair comparison. As shown, our method significantly outperforms other 3D-aware GAN inversion methods across all metrics. We also exceed the StyleGAN2-based inversion method e4e and achieve comparable results with the state-of-the-art method HFGI. + +We further compare our method with other approaches on pose editing of portrait images. We generate novel views (see the suppl. material) of the 1K test images using different methods and evaluate their identity similarity and FID to the original input in Tab. 2. Higher $\mathrm{ID}_{nv}$ and lower $\mathrm{FID}_{nv}$ indicate that a method can better keep the identity and image quality while changing the camera pose. Our method yields the best result among all competitors. We also surpass PIRenderer and Face-vid2vid which require video data for training, while ours is merely trained on monocular in-the-wild images. Figure 5 shows a visual comparison. + +Finally, we measure the 3D consistency of all methods during continuous variation of the camera viewpoint. Fol- + +Table 2. Quantitative comparison with existing portrait editing methods. See the text for details. + +
MethodsInversion fidelityNovel view quality3D consistency
PSNR↑SSIM↑LPIPS↓ID↑FID↓ID_nv↑FID_nv↓PSNR_mv↑SSIM_mv↑
PIRendererer [36]-----0.47642.6436.720.958
Face-vid2vid [56]-----0.41641.7636.100.942
e4e [52] + InterfaceGAN [41]19.230.4510.2130.70635.920.48938.0434.290.909
HFGI [55] + InterfaceGAN [41]22.300.5790.1350.82726.410.51645.2333.990.917
HFGI [55] + StyleHEAT [65]22.300.5790.1350.82726.410.45758.3335.930.951
pix2NeRF [7]16.950.3940.4520.466108.30.378115.650.660.997
IDE-3D (encoder) [46]16.730.3820.2900.39351.510.32447.5637.570.950
Ours21.510.6500.1270.93628.170.63536.0239.530.974
+ +![](images/e88218ac2bf0cac65b8f2a05c5a5dff025c070aaa8e2677d397a322b693a45f2.jpg) +PIRenderer + +![](images/8a459be36fbfda0be2047cae6b8fe6c29babc06e11a23b4f7947bda791caa145.jpg) +Face-vid2vid + +![](images/0ca813fdd37f67f2a9120a1c2a535adafecf1c1d5386ce027eddd3289a74cc88.jpg) +e4e+InterFaceGAN + +![](images/51829ec42b39c987656518b27b80f6a705ec88c7d2f72d9cbf779cab8ec7b662.jpg) +HFGI+InterFaceGAN + +![](images/9c1b64e766e297443d588fe6919295ee25604d4a0b65a1aedf43847df1c3f95f.jpg) + +![](images/1ac13ac7403fb35869f523a3569d7767e02d0a6b4d245f9604c9b3a776c7a7a2.jpg) +StyleHEAT +Figure 5. Pose editing comparison. Texture images with smoothly tilted strips indicate better 3D consistency. Best viewed with zoom-in. + +![](images/032666ffa92d1d0caf50b91593f5fa849d5bd34c6f7411356ef360cab8555adb.jpg) +pix2NeRF + +![](images/ead55e557a1d1f94c26fc07593070e0f8ee0233816297a532d5b8de1a8590541.jpg) +IDE-3D (encoder) + +![](images/3448794f8fd1994804ff3263b52b9f558880f224ba79573ec9a7c36995fbb58e.jpg) +Ours + +![](images/e31c7e08e60ec00ba5030b23ec1095787526cba4f70e5ec3845469b994709782.jpg) +Input +Input + +lowing [60], for each method, we generate 30 images under different views for 50 test instances in CelebA-HQ, and measure the multiview reconstruction quality of NeuS on them (i.e. $\mathrm{PSNR}_{mv}$ and $\mathrm{SSIM}_{mv}$ ). In theory, better 3D consistency across different views would reduce the learning difficulty of NeuS, thus leading to higher PSNR and SSIM. Table 2 shows that our method has the second best 3D consistency among all methods, while the best one (i.e. pix2NeRF) generates over-smooth images of low quality as shown in Fig. 5 and indicated by the high FID score in Tab. 2. Our method outperforms IDE-3D in that it utilizes + +a 2D super-resolution module in its 3D-aware GAN which lowers the 3D consistency to some extent. Nevertheless, all 3D-aware GAN-based methods yield better 3D consistency compared to other 2D methods, indicating the importance of 3D-aware GAN for pose editing of images. A further comparison with the full pipeline of IDE-3D which includes an extra optimization step is in the suppl. material. + +Figure 5 further shows the visual comparison of 3D consistency, where we draw the stacked texture image of a fixed horizontal line segment during continuous camera movement following [60]. Methods with strong 3D consistency + +![](images/5c20b35819820c21bf2762bc1c7f69ccfdaf18e7d5be411978156fd83f5af115.jpg) +Figure 6. Visual comparison between different alternatives. Our final solution yields the best result. Best viewed with zoom-in. + +Table 3. Ablation study of our proposed framework. + +
MethodsPSNR ↑LPIPS ↓ID ↑FID_nv ↓
General17.680.2650.64844.43
General - pretrain17.450.2800.47252.12
General + finetune18.000.2540.67843.46
Detail (Ours)21.510.1270.93636.02
Detail - world2cam19.960.1710.90838.74
Detail - superres21.060.1650.92638.45
Detail - L_nv22.320.1060.94936.49
Detail - mask19.080.2110.84043.25
Detail - L_depth23.680.0940.96035.60
+ +will result in texture images with smoothly tilted strips, while methods with low 3D consistency produce twisted textures (i.e. geometry distortions and texture flickering issues) or vertical lines (i.e. texture sticking issues). Our method clearly produces a more reasonable texture image compared to the others. See the suppl. material and the accompanying video for more results. + +# 4.3. Ablation Study + +We conduct an ablation study to validate the efficacy of our proposed framework and report the results in Tab. 3 and Fig. 6. All metrics are calculated similarly as in Sec. 4.2. + +Inversion stage. Table 3 shows the performance of different stages. General stands for the general inversion stage without finetuned generator. General - pretrain denotes learning the efficient GRAM with $E_{w}$ together instead of pre-training it via the 3D-aware GAN framework. General + finetune denotes finetuning the pre-trained efficient GRAM as described in Sec. 3.2, and Detail denotes our final approach with detail-specific reconstruction. As shown, + +the general stage alone cannot produce faithful reconstruction result, whether the efficient GRAM is further finetuned or not. By contrast, introducing the detail-specific reconstruction significantly improves the inversion fidelity upon the previous stage without sacrificing novel view quality. Learning the efficient GRAM together with the encoder without pre-training leads to a significant performance drop, indicating the importance of leveraging the prior knowledge of a pre-trained 3D-aware GAN. + +Network architecture. We ablate the architecture of the detail manifolds reconstructor. As shown in Tab. 3 and Fig. 6, learning the low-resolution detail voxel in world space instead of in camera space (- world2cam) harms the reconstruction fidelity. And removing the super-resolution module for high-resolution manifold prediction (- superres) leads to blurry inversion results. + +Regularization. We further validate our proposed regularization for detail manifolds learning. As shown in Tab. 3 and Fig. 6, removing the novel view regularization $(- \mathcal{L}_{nv})$ causes obvious artifacts at new views and leads to the increase of $\mathrm{FID}_{nv}$ , though it improves the reconstruction quality at the input viewpoint. Simply enforcing $\mathcal{L}_{nv}$ without the normal-aware mask (-mask) damages fine texture preservation at visible regions. Finally, although learning without the depth regularization $(- \mathcal{L}_{depth})$ results in better metrics, we find that it cannot well preserve certain fine details at novel views due to incorrect parallax brought by the depth error (e.g. mole in Fig. 6). We conjecture that such dynamic artifact can hardly be captured by the current feature extractor [49] for FID computation. + +# 5. Conclusions + +We presented GRAMinverter, a novel approach for high-fidelity and 3D-consistent portrait synthesis from monocular images via single forward pass. The core idea is to learn a detail manifolds reconstructor to predict 3D-consistent fine details on the radiance manifolds from a input image, and combine them with the coarse radiance manifolds obtained via an encoder-based inversion of the pre-trained GRAM. Extensive experiments have demonstrated our superior results over previous works. We believe our method paves a new way for efficient 3D-aware portrait creation. + +Limitations and future works. Our GRAMinverter has several limitations. Based on the radiance manifold representation, it produces layered artifacts at large viewing angles. It cannot well handle occlusions of hands and other accessories. Its performance is also affected by the training data and may produce inferior results for out-of-distribution input. 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Novel view synthesis results by our method. It can generate novel views of a portrait image with high-fidelity and strong 3D-consistency via single forward pass (e.g., see the bangs and wrinkles). Best viewed with zoom-in and see the video for animations." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 299, + 202, + 545, + 388 + ], + "blocks": [ + { + "bbox": [ + 299, + 202, + 545, + 388 + ], + "lines": [ + { + "bbox": [ + 299, + 202, + 545, + 388 + ], + "spans": [ + { + "bbox": [ + 299, + 202, + 545, + 388 + ], + "type": "image", + "image_path": "aadd97515b37a598846b96f00d4eb745b50e4817a7da68ad971b381276442641.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 321, + 388, + 341, + 396 + ], + "lines": [ + { + "bbox": [ + 321, + 388, + 341, + 396 + ], + "spans": [ + { + "bbox": [ + 321, + 388, + 341, + 396 + ], + "type": "text", + "content": "Input" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 430, + 388, + 474, + 396 + ], + "lines": [ + { + "bbox": [ + 430, + 388, + 474, + 396 + ], + "spans": [ + { + "bbox": [ + 430, + 388, + 474, + 396 + ], + "type": "text", + "content": "Novel views" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 143, + 440, + 192, + 453 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 440, + 192, + 453 + ], + "spans": [ + { + "bbox": [ + 143, + 440, + 192, + 453 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 464, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 464, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 464, + 289, + 715 + ], + "type": "text", + "content": "A key challenge for novel view synthesis of monocular portrait images is 3D consistency under continuous pose variations. Most existing methods rely on 2D generative models which often leads to obvious 3D inconsistency artifacts. We present a 3D-consistent novel view synthesis approach for monocular portrait images based on a recent proposed 3D-aware GAN, namely Generative Radiance Manifolds (GRAM) [13], which has shown strong 3D consistency at multiview image generation of virtual subjects via the radiance manifolds representation. However, simply learning an encoder to map a real image into the latent space of GRAM can only reconstruct coarse radiance manifolds without faithful fine details, while improving the reconstruction fidelity via instance-specific optimization is time-consuming. We introduce a novel detail manifolds reconstructor to learn 3D-consistent fine details on the radiance manifolds from monocular images, and combine them with the coarse radiance manifolds for high-fidelity reconstruction. The 3D priors derived from the coarse radiance manifolds are used to regulate the learned details to ensure reasonable synthesized results" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 441, + 547, + 489 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 441, + 547, + 489 + ], + "spans": [ + { + "bbox": [ + 305, + 441, + 547, + 489 + ], + "type": "text", + "content": "at novel views. Trained on in-the-wild 2D images, our method achieves high-fidelity and 3D-consistent portrait synthesis largely outperforming the prior art. Project page: https://yudeng.github.io/GRAMInverter/" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 514, + 387, + 528 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 514, + 387, + 528 + ], + "spans": [ + { + "bbox": [ + 306, + 514, + 387, + 528 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 535, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 535, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 535, + 547, + 715 + ], + "type": "text", + "content": "Synthesizing photorealistic portrait images of a person from an arbitrary viewpoint is an important task that can benefit diverse downstream applications such as virtual avatar creation and immersive online communication. Thanks to the thriving of 2D Generative Adversarial Networks (GANs) [18,25,26], people can now generate high-quality portraits at desired views given only monocular images as input, via a simple invert-then-edit strategy by conducting GAN inversion [1,38,52] and latent space editing [12,20,41,50]. However, existing 2D GAN-based methods still have deficiencies when applied to applications that require more strict 3D consistency (e.g. VR&AR). Due to the non-physical rendering process of the 2D CNN-based generators, their synthesized images under pose changes usually bear certain kinds of multiview inconsistency, such" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4423" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": "as geometry distortions [3,5] and texture sticking or flickering [24, 55]. These artifacts may not be significant enough when inspecting each static image but can be easily captured by human eyes under continuous image variations." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 122, + 288, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 122, + 288, + 350 + ], + "spans": [ + { + "bbox": [ + 46, + 122, + 288, + 350 + ], + "type": "text", + "content": "Recently, there are an emerging group of 3D-aware GANs [9, 10, 13, 19, 39, 40] targeting at image generation with 3D pose disentanglement. By incorporating Neural Radiance Field (NeRF) [29] and its variants into the adversarial learning process of GANs, they can produce realistic images with strong 3D-consistency across different views, given only a set of monocular images as training data. As a result, 3D-aware GANs have shown greater potential than 2D GANs for pose manipulations of portraits. However, even though 3D-aware GANs are capable of generating 3D-consistent portraits of virtual subjects, leveraging them for real image pose editing is still a challenging task. To obtain faithful reconstructions of real images, most existing methods [9, 10, 13, 27, 46, 47, 67] turn to a time-consuming and instance-specific optimization to invert the given images into the latent space of a pre-trained 3D-aware GAN, which is hard to scale-up. And simply enforcing an encoder-based 3D-aware GAN inversion [7, 46] often fails to preserve fine details in the original image." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 352, + 287, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 352, + 287, + 495 + ], + "spans": [ + { + "bbox": [ + 46, + 352, + 287, + 495 + ], + "type": "text", + "content": "In this paper, we propose a novel approach GRAMInverter, for high-fidelity and 3D-consistent novel view synthesis of monocular portraits via single forward pass. Our method is built upon the recent GRAM [13] that can synthesize high-quality virtual images with strong 3D consistency via the radiance manifolds representation [13]. Nevertheless, GRAM suffers from the same lack-of-fidelity issue when combined with a general encoder-based GAN inversion approach [52]. The main reason is that the obtained semantically-meaningful low-dimensional latent code cannot well record detail information of the input, as also indicated by some recent 2D GAN inversion methods [52, 55]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 498, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 288, + 713 + ], + "type": "text", + "content": "To tackle this problem, our motivation is to further learn 3D-space high-frequency details and combine them with the coarse radiance manifolds obtained from the general encoder-based inversion of GRAM, to achieve faithful reconstruction and 3D-consistent view synthesis. A straightforward way to achieve this is to extract a high-resolution 3D voxel from the input image and combine it with the coarse radiance manifolds. However, this is prohibited by modern GPUs due to the high memory cost of the 3D voxel. To tackle this problem, we turn to learn a high resolution detail manifolds, taking the advantage of the radiance manifolds representation of GRAM, instead of learning the memory-consuming 3D voxel. We introduce a novel detail manifolds reconstructor to extract detail manifolds from the input images. It leverages manifold super-resolution [60] to predict high-resolution detail manifolds from a low resolution feature voxel. This can be effectively achieved by a set of memory-efficient 2D convolution blocks. The obtained" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 72, + 545, + 131 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 131 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 131 + ], + "type": "text", + "content": "high resolution detail manifolds can still maintain strict 3D consistency due to lying in the 3D space. We also propose dedicated losses to regulate the detail manifolds via 3D priors derived from the coarse radiance manifolds, to ensure reasonable novel view results." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 133, + 545, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 133, + 545, + 228 + ], + "spans": [ + { + "bbox": [ + 304, + 133, + 545, + 228 + ], + "type": "text", + "content": "Another contribution of our method is an improvement upon the memory and time-consuming GRAM, without which it is difficult to be integrated into our GAN inversion framework. We replace the original MLP-based radiance generator [13] in GRAM with a StyleGAN2 [26]-based triplane generator proposed by [9]. The efficient GRAM requires only " + }, + { + "bbox": [ + 304, + 133, + 545, + 228 + ], + "type": "inline_equation", + "content": "1/4" + }, + { + "bbox": [ + 304, + 133, + 545, + 228 + ], + "type": "text", + "content": " memory cost with " + }, + { + "bbox": [ + 304, + 133, + 545, + 228 + ], + "type": "inline_equation", + "content": "7 \\times" + }, + { + "bbox": [ + 304, + 133, + 545, + 228 + ], + "type": "text", + "content": " speed up, without sacrificing the image generation quality and 3D consistency." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 229, + 545, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 229, + 545, + 348 + ], + "spans": [ + { + "bbox": [ + 304, + 229, + 545, + 348 + ], + "type": "text", + "content": "We train our method on FFHQ dataset [25] and conduct multiple experiments to demonstrate its advantages on pose control of portrait images. Once trained, GRAMInverter takes a monocular image as input and predicts its radiance manifolds representation for novel view synthesis at 3 FPS on a single GPU. The generated novel views well preserve fine details in the original image with strong 3D consistency, outperforming prior art by a large margin. We believe our method takes a solid step towards efficient 3D-aware content creation for real applications." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 361, + 392, + 374 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 361, + 392, + 374 + ], + "spans": [ + { + "bbox": [ + 306, + 361, + 392, + 374 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 383, + 545, + 538 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 383, + 545, + 538 + ], + "spans": [ + { + "bbox": [ + 304, + 383, + 545, + 538 + ], + "type": "text", + "content": "3D-aware generative model. Learned with monocular 2D images, 3D-aware GANs [9, 10, 13, 17, 19, 30, 31, 34, 39, 40, 45, 60, 62] achieve an explicit disentanglement of camera pose by introducing underlying 3D representations. Earlier works [30, 42, 48] utilize voxel or mesh as the intermediate representation. Later works [9, 10, 13, 34, 39, 62, 69] leverage NeRF [29] and its variants [13, 33, 54, 64] to achieve more strict 3D consistency. Among them, methods that directly render their 3D representations for image synthesis achieve the best multiview consistency [10, 13, 17, 40, 45]. We propose a novel approach for high-quality pose editing of given portraits based on GRAM [13], which is a recent 3D-aware GAN with state-of-the-art multiview consistency." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": "GAN inversion. GAN inversion aims to map a given real image into the latent space of a pre-trained generator for image reconstruction and manipulation. Numerous methods [1,4,6,26,37,38,52,55,63,72,73] try to find a latent code which can faithfully reconstruct the given image meanwhile falls inside a semantically meaningful latent space that supports reasonable editing. They either adopt optimization-based approach [1, 2, 26, 73], introduce an extra image encoder [4, 37, 52], or utilize a hybrid version of the former two [6, 72]. Nevertheless, recent studies [38, 52, 55, 74] reveal that it is difficult to achieve high-fidelity reconstruction and artifacts-free editing at once given only low-bitrate latent code as representation. As a result, several methods propose to further fine-tune the pre-trained generator [38]" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4424" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 70, + 541, + 224 + ], + "blocks": [ + { + "bbox": [ + 51, + 70, + 541, + 224 + ], + "lines": [ + { + "bbox": [ + 51, + 70, + 541, + 224 + ], + "spans": [ + { + "bbox": [ + 51, + 70, + 541, + 224 + ], + "type": "image", + "image_path": "2bf3075ab1ad6cef8deb70c3bae9951a4e794c76adc874da2f3ee44726339ea7.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 228, + 546, + 275 + ], + "lines": [ + { + "bbox": [ + 46, + 228, + 546, + 275 + ], + "spans": [ + { + "bbox": [ + 46, + 228, + 546, + 275 + ], + "type": "text", + "content": "Figure 2. Overview of the GRAMInverter. An input portrait image goes through two stages to obtain the final radiance manifolds for novel view synthesis. The first general inversion stage maps the input image to the latent space of a pre-trained efficient GRAM to obtain coarse radiance manifolds. The second detail-specific stage then extracts detail feature manifolds from the input image and combines them with the coarse results for high-fidelity image synthesis. See the text for more details." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 285, + 287, + 309 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 285, + 287, + 309 + ], + "spans": [ + { + "bbox": [ + 46, + 285, + 287, + 309 + ], + "type": "text", + "content": "or allow more detailed features from the input images to leak into the generator during inversion [55, 63]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 310, + 288, + 490 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 310, + 288, + 490 + ], + "spans": [ + { + "bbox": [ + 46, + 310, + 288, + 490 + ], + "type": "text", + "content": "While the above methods target at the inversion of 2D GANs, inverting a given image with 3D-aware GANs shares a similar spirit. An advantage of 3D-aware GAN inversion compare to its 2D counterpart is a natural disentanglement of the 3D pose. Once inverted, novel view synthesis can be easily achieved without further latent space exploration [20, 41]. The majority of existing 3D-aware GAN inversion methods [9, 10, 13, 27, 46, 47, 51, 57] leverage optimization-based or a hybrid approach for faithful reconstruction, which are time-consuming and hard to scale-up. A recent method [7] explores GAN inversion with a single forward of an encoder, yet it struggles to preserve fine image details. Our proposed method is also an encoder-based inversion approach which yields high-quality reconstruction and novel view synthesis thanks to our novel design." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 498, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 288, + 714 + ], + "type": "text", + "content": "Pose editing of monocular portraits. Editing the camera pose of a monocular portrait for novel view synthesis is a longstanding task and has witnessed the emergence of diverse methods. Some of them [8,35,59,61,75,76] achieve pose editing by first conducting 3D reconstruction and then rendering the obtained mesh at novel views. Due to the imperfect reconstruction results, they often have difficulties handling non-face regions and unseen parts at the input view. Others [15, 16, 32, 36, 43, 44, 56, 58, 66, 70] generate novel views in a face-reenactment paradigm, where warping flows are often learned from video data to transform a source image to a target viewpoint. These methods may encounter geometry distortions at novel views due to the lack of an explicit 3D constraint. More recently, plenty of works [3,7,12,22,28,41,46,47,50] have studied pose editing of an image by inverting it into a prior model such as GAN. With the strong prior bearing in a pre-trained generator, synthesizing novel views of a given portrait can be achieved" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 285, + 545, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 285, + 545, + 346 + ], + "spans": [ + { + "bbox": [ + 304, + 285, + 545, + 346 + ], + "type": "text", + "content": "without any 3D or video data during training. Among them, methods using 3D-aware GANs [7,9,13,46,47] have shown better 3D consistency under pose variations. Our method is also based on 3D-aware GAN and largely improves the efficiency, reconstruction quality, as well as 3D consistency." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 356, + 373, + 370 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 356, + 373, + 370 + ], + "spans": [ + { + "bbox": [ + 306, + 356, + 373, + 370 + ], + "type": "text", + "content": "3. Approach" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 376, + 546, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 376, + 546, + 604 + ], + "spans": [ + { + "bbox": [ + 304, + 376, + 546, + 604 + ], + "type": "text", + "content": "Given a monocular portrait image " + }, + { + "bbox": [ + 304, + 376, + 546, + 604 + ], + "type": "inline_equation", + "content": "\\hat{I}" + }, + { + "bbox": [ + 304, + 376, + 546, + 604 + ], + "type": "text", + "content": ", we aim to synthesize its novel views at some arbitrary camera viewpoints by leveraging the prior knowledge of a pre-trained 3D-aware GAN, as shown in Fig. 2. To guarantee high-quality and 3D-consistent novel view synthesis, we adopt GRAM [13] as our underlying image generator and design an efficient version of it that requires much less computation and memory cost so as to incorporate it into our whole framework (Sec. 3.1). With the efficient GRAM, we first utilize a general encoder-based GAN inversion to reconstruct the coarse radiance manifolds from the input image (Sec. 3.2). We then introduce a detail-specific reconstruction stage to learn high-resolution detail manifolds that cannot be well captured by the coarse result, via our proposed novel detail manifolds reconstructor (Sec. 3.3). Multiple losses are enforced to regulate the predicted detail manifolds to ensure reasonable synthesized results at novel views, by leveraging the 3D priors derived from the coarse radiance manifolds (Sec. 3.4). We describe each part in details below." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 611, + 519, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 611, + 519, + 624 + ], + "spans": [ + { + "bbox": [ + 305, + 611, + 519, + 624 + ], + "type": "text", + "content": "3.1. Efficient Generative Radiance Manifolds" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 629, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 545, + 715 + ], + "type": "text", + "content": "We start with a brief review of the original GRAM proposed in [13]. The core of GRAM is its underlying radiance manifolds representation, which regulates radiance field learning on a set of surface manifolds in the 3D space instead of predicting it in the whole volumetric space as done by [29]. The surface manifolds are defined as a set of iso-surfaces " + }, + { + "bbox": [ + 304, + 629, + 545, + 715 + ], + "type": "inline_equation", + "content": "\\{S_i\\}" + }, + { + "bbox": [ + 304, + 629, + 545, + 715 + ], + "type": "text", + "content": " in a 3D scalar field represented by a" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4425" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 258, + 85 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 258, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 258, + 85 + ], + "type": "text", + "content": "light-weight MLP called the manifold predictor " + }, + { + "bbox": [ + 47, + 72, + 258, + 85 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 47, + 72, + 258, + 85 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 71, + 91, + 287, + 106 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 71, + 91, + 287, + 106 + ], + "spans": [ + { + "bbox": [ + 71, + 91, + 287, + 106 + ], + "type": "interline_equation", + "content": "\\mathcal {M}: \\boldsymbol {x} \\in \\mathbb {R} ^ {3} \\rightarrow s \\in \\mathbb {R}, \\mathcal {S} _ {i} = \\{\\boldsymbol {x} | \\mathcal {M} (\\boldsymbol {x}) = l _ {i} \\}, \\tag {1}", + "image_path": "e15372809594c9352459cc24fa1a4ad8a25b44eeaa0be04a39211403984781b1.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 114, + 287, + 162 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 114, + 287, + 162 + ], + "spans": [ + { + "bbox": [ + 47, + 114, + 287, + 162 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 114, + 287, + 162 + ], + "type": "inline_equation", + "content": "\\{l_i\\}" + }, + { + "bbox": [ + 47, + 114, + 287, + 162 + ], + "type": "text", + "content": " are " + }, + { + "bbox": [ + 47, + 114, + 287, + 162 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 47, + 114, + 287, + 162 + ], + "type": "text", + "content": " predefined scalar levels. During image generation, only intersections " + }, + { + "bbox": [ + 47, + 114, + 287, + 162 + ], + "type": "inline_equation", + "content": "\\{\\pmb{x}_i\\}" + }, + { + "bbox": [ + 47, + 114, + 287, + 162 + ], + "type": "text", + "content": " between a viewing ray " + }, + { + "bbox": [ + 47, + 114, + 287, + 162 + ], + "type": "inline_equation", + "content": "\\pmb{r}" + }, + { + "bbox": [ + 47, + 114, + 287, + 162 + ], + "type": "text", + "content": " and the surface manifolds will be sent into an MLP-based radiance generator " + }, + { + "bbox": [ + 47, + 114, + 287, + 162 + ], + "type": "inline_equation", + "content": "\\Phi" + }, + { + "bbox": [ + 47, + 114, + 287, + 162 + ], + "type": "text", + "content": " for radiance prediction:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 84, + 167, + 287, + 182 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 84, + 167, + 287, + 182 + ], + "spans": [ + { + "bbox": [ + 84, + 167, + 287, + 182 + ], + "type": "interline_equation", + "content": "\\Phi : \\left(\\boldsymbol {z}, \\boldsymbol {x} _ {i}\\right) \\in \\mathbb {R} ^ {d _ {z}} \\times \\mathbb {R} ^ {3} \\rightarrow (\\boldsymbol {c}, \\alpha) \\in \\mathbb {R} ^ {4}, \\tag {2}", + "image_path": "d906f44f161abde58536eed2af75542ad459a43c1f2a4e64e57107119159ad95.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 188, + 287, + 224 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 188, + 287, + 224 + ], + "spans": [ + { + "bbox": [ + 47, + 188, + 287, + 224 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 188, + 287, + 224 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 47, + 188, + 287, + 224 + ], + "type": "text", + "content": " is a latent code determining the radiance, " + }, + { + "bbox": [ + 47, + 188, + 287, + 224 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 47, + 188, + 287, + 224 + ], + "type": "text", + "content": " is the color, and " + }, + { + "bbox": [ + 47, + 188, + 287, + 224 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 47, + 188, + 287, + 224 + ], + "type": "text", + "content": " is the occupancy. The final color of each ray can be computed via manifold rendering [13, 71]:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 83, + 230, + 287, + 264 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 230, + 287, + 264 + ], + "spans": [ + { + "bbox": [ + 83, + 230, + 287, + 264 + ], + "type": "interline_equation", + "content": "C (\\boldsymbol {r}) = \\sum_ {i = 1} ^ {N} \\prod_ {j < i} (1 - \\alpha (\\boldsymbol {x} _ {j})) \\alpha (\\boldsymbol {x} _ {i}) \\boldsymbol {c} (\\boldsymbol {x} _ {i}). \\tag {3}", + "image_path": "8b30542432c07ba913a7304682ca3c1b85f5981f1f3bfcd6202448a4a58e6ec5.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 270, + 287, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 270, + 287, + 509 + ], + "spans": [ + { + "bbox": [ + 46, + 270, + 287, + 509 + ], + "type": "text", + "content": "The high mometry cost of GRAM lies in its MLP-based radiance generator " + }, + { + "bbox": [ + 46, + 270, + 287, + 509 + ], + "type": "inline_equation", + "content": "\\Phi" + }, + { + "bbox": [ + 46, + 270, + 287, + 509 + ], + "type": "text", + "content": ", which requires millions of forward steps to generate a single image. Inspired by the recent EG3D [9], we substitute the original radiance generator with a tri-plane generator [9] based on StyleGAN2 structure [26]. Its efficient coarse-to-fine structure helps to reduce memory and computation costs by a large margin. Given the new radiance generator, the color and occupancy for points on the surface manifolds can be obtained by first generating tri-plane features by a 2D CNN " + }, + { + "bbox": [ + 46, + 270, + 287, + 509 + ], + "type": "inline_equation", + "content": "\\Psi" + }, + { + "bbox": [ + 46, + 270, + 287, + 509 + ], + "type": "text", + "content": ", and then conducting tri-plane sampling and sending the sampled features into a small MLP-based decoder " + }, + { + "bbox": [ + 46, + 270, + 287, + 509 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 270, + 287, + 509 + ], + "type": "text", + "content": " as done in [9]. Note that although we take the tri-plane generator from EG3D to improve efficiency, we do not use its 2D super-resolution module but keep strictly to the radiance manifolds representation. This helps us to maintain the strong 3D consistency brought by the manifold rendering. In addition, we calculate ray-manifold intersections at " + }, + { + "bbox": [ + 46, + 270, + 287, + 509 + ], + "type": "inline_equation", + "content": "1/4" + }, + { + "bbox": [ + 46, + 270, + 287, + 509 + ], + "type": "text", + "content": " resolution of the final image to further speed up our image generation process (details in the suppl. material)." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 510, + 287, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 287, + 569 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 287, + 569 + ], + "type": "text", + "content": "The efficient GRAM serves as a strong prior for generating realistic multiview images of virtual subjects. By combining it with our two-stage manifolds reconstruction method, we achieve high-quality novel view synthesis of real portraits, as described in the following sections." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 575, + 183, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 575, + 183, + 588 + ], + "spans": [ + { + "bbox": [ + 47, + 575, + 183, + 588 + ], + "type": "text", + "content": "3.2. General Inversion Stage" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": "Given a pre-trained efficient GRAM following a typical 3D-aware GAN training paradigm [13], we first introduce an image inverter " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "E_{w}" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": " that maps a given image to the latent space of the efficient GRAM, as shown in Fig. 2. Inspired by previous StyleGAN-based inversion methods [1, 52, 55], we invert the given image into a latent code " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\boldsymbol{w} + = [\\boldsymbol{w}_1, \\boldsymbol{w}_2, \\dots, \\boldsymbol{w}_L]" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{W}+" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": " space [1] of the tri-plane generator " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\Psi" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": " for a proper trade-off between inversion fidelity and pose editing quality, where " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": " is the number of layers in " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\Psi" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": "'s synthesis sub-network. We leverage" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 307, + 71, + 545, + 159 + ], + "blocks": [ + { + "bbox": [ + 307, + 71, + 545, + 159 + ], + "lines": [ + { + "bbox": [ + 307, + 71, + 545, + 159 + ], + "spans": [ + { + "bbox": [ + 307, + 71, + 545, + 159 + ], + "type": "image", + "image_path": "1ad64f830a6e5c88291c4e0265c3486b01788878969db49e1788fac887900797.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 167, + 547, + 212 + ], + "lines": [ + { + "bbox": [ + 304, + 167, + 547, + 212 + ], + "spans": [ + { + "bbox": [ + 304, + 167, + 547, + 212 + ], + "type": "text", + "content": "Figure 3. The detail encoder " + }, + { + "bbox": [ + 304, + 167, + 547, + 212 + ], + "type": "inline_equation", + "content": "E_{detail}" + }, + { + "bbox": [ + 304, + 167, + 547, + 212 + ], + "type": "text", + "content": " extracts a camera space feature voxel from an input image. The voxel corresponds to a quadrangular frustum in the 3D space bounded by the near and far planes of the camera and the outermost viewing rays." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 224, + 545, + 296 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 224, + 545, + 296 + ], + "spans": [ + { + "bbox": [ + 304, + 224, + 545, + 296 + ], + "type": "text", + "content": "the e4e encoder [52] as the backbone of " + }, + { + "bbox": [ + 304, + 224, + 545, + 296 + ], + "type": "inline_equation", + "content": "E_{w}" + }, + { + "bbox": [ + 304, + 224, + 545, + 296 + ], + "type": "text", + "content": ". Given " + }, + { + "bbox": [ + 304, + 224, + 545, + 296 + ], + "type": "inline_equation", + "content": "\\pmb{w} +" + }, + { + "bbox": [ + 304, + 224, + 545, + 296 + ], + "type": "text", + "content": ", we can obtain a coarse radiance manifolds " + }, + { + "bbox": [ + 304, + 224, + 545, + 296 + ], + "type": "inline_equation", + "content": "\\Phi(\\pmb{w} +, \\{S_i\\}) = m \\circ \\Psi(\\pmb{w} +, \\{S_i\\})" + }, + { + "bbox": [ + 304, + 224, + 545, + 296 + ], + "type": "text", + "content": " via Eq. (1) and (2), and further obtain a coarse inversion image " + }, + { + "bbox": [ + 304, + 224, + 545, + 296 + ], + "type": "inline_equation", + "content": "I_{w}" + }, + { + "bbox": [ + 304, + 224, + 545, + 296 + ], + "type": "text", + "content": " by rendering the radiance manifolds at input viewpoint " + }, + { + "bbox": [ + 304, + 224, + 545, + 296 + ], + "type": "inline_equation", + "content": "\\hat{\\theta}" + }, + { + "bbox": [ + 304, + 224, + 545, + 296 + ], + "type": "text", + "content": " via Eq. (3), where " + }, + { + "bbox": [ + 304, + 224, + 545, + 296 + ], + "type": "inline_equation", + "content": "\\hat{\\theta}" + }, + { + "bbox": [ + 304, + 224, + 545, + 296 + ], + "type": "text", + "content": " can be obtained by off-the-shelf 3D face reconstruction method [14]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 296, + 546, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 296, + 546, + 403 + ], + "spans": [ + { + "bbox": [ + 304, + 296, + 546, + 403 + ], + "type": "text", + "content": "We fixed the pre-trained efficient GRAM and learn the image inverter " + }, + { + "bbox": [ + 304, + 296, + 546, + 403 + ], + "type": "inline_equation", + "content": "E_{w}" + }, + { + "bbox": [ + 304, + 296, + 546, + 403 + ], + "type": "text", + "content": " following the training process of [52], except that we replaced the adversarial loss in [52] with a naive L2 loss between predicted " + }, + { + "bbox": [ + 304, + 296, + 546, + 403 + ], + "type": "inline_equation", + "content": "w+" + }, + { + "bbox": [ + 304, + 296, + 546, + 403 + ], + "type": "text", + "content": " and the average latent code of the " + }, + { + "bbox": [ + 304, + 296, + 546, + 403 + ], + "type": "inline_equation", + "content": "\\mathcal{W}+" + }, + { + "bbox": [ + 304, + 296, + 546, + 403 + ], + "type": "text", + "content": " space. To further improve the reconstruction fidelity, we fixed the trained " + }, + { + "bbox": [ + 304, + 296, + 546, + 403 + ], + "type": "inline_equation", + "content": "E_{w}" + }, + { + "bbox": [ + 304, + 296, + 546, + 403 + ], + "type": "text", + "content": " and finetuned the efficient GRAM via the pivot tuning strategy [38] using all training images. Details for the above training processes can be found in the suppl. material." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 403, + 547, + 475 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 403, + 547, + 475 + ], + "spans": [ + { + "bbox": [ + 304, + 403, + 547, + 475 + ], + "type": "text", + "content": "After training, the general inversion stage can already synthesize reasonable multiview images of the input, yet it cannot faithfully preserve the fine details, making the inverted result looks less like the original image (see Fig. 6). Therefore, we introduce a detail-specific stage for faithful detail reconstruction, as described below." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 482, + 499, + 495 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 482, + 499, + 495 + ], + "spans": [ + { + "bbox": [ + 306, + 482, + 499, + 495 + ], + "type": "text", + "content": "3.3. Detail-Specific Reconstruction Stage" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 501, + 545, + 632 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 501, + 545, + 632 + ], + "spans": [ + { + "bbox": [ + 304, + 501, + 545, + 632 + ], + "type": "text", + "content": "The detail-specific stage aims to extract fine details from the input image that cannot be well described by the coarse radiance manifolds to improve the reconstruction fidelity. The intuition is to learn high-resolution details in 3D space so that their combination with the coarse radiance manifolds still remains strong 3D consistency under pose variations. To achieve this goal, we design a detail manifolds recon. structor consisting of two modules: a detail encoder " + }, + { + "bbox": [ + 304, + 501, + 545, + 632 + ], + "type": "inline_equation", + "content": "E_{detail}" + }, + { + "bbox": [ + 304, + 501, + 545, + 632 + ], + "type": "text", + "content": " that extracts low-resolution feature voxel from the input image, and a super-resolution module " + }, + { + "bbox": [ + 304, + 501, + 545, + 632 + ], + "type": "inline_equation", + "content": "\\mathcal{U}" + }, + { + "bbox": [ + 304, + 501, + 545, + 632 + ], + "type": "text", + "content": " to predict highresolution detail manifolds from the low-resolution voxel." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 632, + 545, + 656 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 632, + 545, + 656 + ], + "spans": [ + { + "bbox": [ + 304, + 632, + 545, + 656 + ], + "type": "text", + "content": "Specifically, " + }, + { + "bbox": [ + 304, + 632, + 545, + 656 + ], + "type": "inline_equation", + "content": "E_{detail}" + }, + { + "bbox": [ + 304, + 632, + 545, + 656 + ], + "type": "text", + "content": " takes an image " + }, + { + "bbox": [ + 304, + 632, + 545, + 656 + ], + "type": "inline_equation", + "content": "\\hat{I}" + }, + { + "bbox": [ + 304, + 632, + 545, + 656 + ], + "type": "text", + "content": " as input and predicts a camera space feature voxel as shown in Fig. 3:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 313, + 662, + 545, + 677 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 662, + 545, + 677 + ], + "spans": [ + { + "bbox": [ + 313, + 662, + 545, + 677 + ], + "type": "interline_equation", + "content": "E _ {\\text {d e t a i l}}: \\hat {I} \\in \\mathbb {R} ^ {H \\times W \\times 3} \\rightarrow V \\in \\mathbb {R} ^ {H _ {l r} \\times W _ {l r} \\times D _ {l r} \\times d _ {V}}, \\tag {4}", + "image_path": "bf4c6666baaa95441c97d75525ce22572a42f15f091edbd485a0a2d035b27045.jpg" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 306, + 683, + 547, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 683, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 683, + 547, + 713 + ], + "type": "text", + "content": "In practice, we find that concatenating " + }, + { + "bbox": [ + 306, + 683, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\hat{I}" + }, + { + "bbox": [ + 306, + 683, + 547, + 713 + ], + "type": "text", + "content": " with an extra difference map " + }, + { + "bbox": [ + 306, + 683, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\Delta = \\hat{I} - I_w" + }, + { + "bbox": [ + 306, + 683, + 547, + 713 + ], + "type": "text", + "content": " as input yields better reconstruction quality, where " + }, + { + "bbox": [ + 306, + 683, + 547, + 713 + ], + "type": "inline_equation", + "content": "I_w" + }, + { + "bbox": [ + 306, + 683, + 547, + 713 + ], + "type": "text", + "content": " is the inversion image obtained by the general inversion stage." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "4426" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "inline_equation", + "content": "d_V" + }, + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "text", + "content": " is the feature dimension. We implement " + }, + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "inline_equation", + "content": "E_{detail}" + }, + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "text", + "content": " as a 3D U-Net with skip connections to extract both global geometry structures as well as local fine textures from the input image. We refer the readers to the suppl. material for detailed network structure." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 137, + 288, + 222 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 137, + 288, + 222 + ], + "spans": [ + { + "bbox": [ + 46, + 137, + 288, + 222 + ], + "type": "text", + "content": "The feature voxel is defined in camera space instead of world space (i.e. space where tri-plane features of efficient GRAM are defined) as it is easier for " + }, + { + "bbox": [ + 46, + 137, + 288, + 222 + ], + "type": "inline_equation", + "content": "E_{detail}" + }, + { + "bbox": [ + 46, + 137, + 288, + 222 + ], + "type": "text", + "content": " to extract image-aligned features than to learn transformed world space features (see Sec. 4.3). Given the feature voxel " + }, + { + "bbox": [ + 46, + 137, + 288, + 222 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 46, + 137, + 288, + 222 + ], + "type": "text", + "content": ", we can obtain the corresponding feature " + }, + { + "bbox": [ + 46, + 137, + 288, + 222 + ], + "type": "inline_equation", + "content": "f^{lr} \\in \\mathbb{R}^{d_V}" + }, + { + "bbox": [ + 46, + 137, + 288, + 222 + ], + "type": "text", + "content": " for a point " + }, + { + "bbox": [ + 46, + 137, + 288, + 222 + ], + "type": "inline_equation", + "content": "\\boldsymbol{x} \\in \\mathbb{R}^3" + }, + { + "bbox": [ + 46, + 137, + 288, + 222 + ], + "type": "text", + "content": " in the world space via:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 85, + 240, + 287, + 255 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 240, + 287, + 255 + ], + "spans": [ + { + "bbox": [ + 85, + 240, + 287, + 255 + ], + "type": "interline_equation", + "content": "f ^ {l r} = \\operatorname {g r i d \\_ s a m p l e} (V, \\operatorname {w o r l d 2 c a m} (\\boldsymbol {x})), \\qquad (5)", + "image_path": "75e71db44f7805059fcba21a5a14e75d7e6e727f3873b5609a617bf97f9a496c.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 272, + 287, + 309 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 272, + 287, + 309 + ], + "spans": [ + { + "bbox": [ + 47, + 272, + 287, + 309 + ], + "type": "text", + "content": "where grid_sample is a tri-linear interpolation function, and world2cam is a rigid transformation function between the world space and the camera space." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 314, + 288, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 314, + 288, + 613 + ], + "spans": [ + { + "bbox": [ + 46, + 314, + 288, + 613 + ], + "type": "text", + "content": "Nevertheless, since " + }, + { + "bbox": [ + 46, + 314, + 288, + 613 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 46, + 314, + 288, + 613 + ], + "type": "text", + "content": " is a low-resolution voxel, directly combining it with the feature manifolds obtained from the general inversion stage leads to a blurry inversion result, while predicting a high-resolution voxel (e.g. " + }, + { + "bbox": [ + 46, + 314, + 288, + 613 + ], + "type": "inline_equation", + "content": "256^{3}" + }, + { + "bbox": [ + 46, + 314, + 288, + 613 + ], + "type": "text", + "content": ") instead causes unaffordable memory cost. Inspired by [60], we take the advantage of our radiance manifolds representation to obtain high-resolution detail manifolds from the low-resolution voxel via manifold super-resolution. Specifically, we first obtain low-resolution detail manifolds " + }, + { + "bbox": [ + 46, + 314, + 288, + 613 + ], + "type": "inline_equation", + "content": "f^{lr}(\\{S_i\\})" + }, + { + "bbox": [ + 46, + 314, + 288, + 613 + ], + "type": "text", + "content": " by querying features from " + }, + { + "bbox": [ + 46, + 314, + 288, + 613 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 46, + 314, + 288, + 613 + ], + "type": "text", + "content": " via Eq. (5) for low-resolution points grid on the surface manifolds " + }, + { + "bbox": [ + 46, + 314, + 288, + 613 + ], + "type": "inline_equation", + "content": "\\{S_i\\}" + }, + { + "bbox": [ + 46, + 314, + 288, + 613 + ], + "type": "text", + "content": ". We then flatten each manifold to a low-resolution feature map " + }, + { + "bbox": [ + 46, + 314, + 288, + 613 + ], + "type": "inline_equation", + "content": "F_{i}^{lr}" + }, + { + "bbox": [ + 46, + 314, + 288, + 613 + ], + "type": "text", + "content": " and send it to the super-resolution module " + }, + { + "bbox": [ + 46, + 314, + 288, + 613 + ], + "type": "inline_equation", + "content": "\\mathcal{U}" + }, + { + "bbox": [ + 46, + 314, + 288, + 613 + ], + "type": "text", + "content": " to obtain a high-resolution feature map " + }, + { + "bbox": [ + 46, + 314, + 288, + 613 + ], + "type": "inline_equation", + "content": "F_{i}^{hr} = \\mathcal{U}(F_{i}^{lr})" + }, + { + "bbox": [ + 46, + 314, + 288, + 613 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 314, + 288, + 613 + ], + "type": "inline_equation", + "content": "\\mathcal{U}" + }, + { + "bbox": [ + 46, + 314, + 288, + 613 + ], + "type": "text", + "content": " is a simple 2D CNN of 4 convolution blocks and 2 bilinear upsampling blocks. Finally, we obtain the high-resolution detail manifolds " + }, + { + "bbox": [ + 46, + 314, + 288, + 613 + ], + "type": "inline_equation", + "content": "f^{hr}(\\{S_i\\})" + }, + { + "bbox": [ + 46, + 314, + 288, + 613 + ], + "type": "text", + "content": " by re-projecting each flattened feature map " + }, + { + "bbox": [ + 46, + 314, + 288, + 613 + ], + "type": "inline_equation", + "content": "F_{i}^{hr}" + }, + { + "bbox": [ + 46, + 314, + 288, + 613 + ], + "type": "text", + "content": " to the surface manifolds. Since we conduct super-resolution for 3D space surface manifolds, 3D consistency across different views can be naturally maintained during this process. Note that although the manifold super-resolution strategy is proposed in [60], it does not leverage it in a reconstruction scenario but to generate random fine details. By contrast, we utilize it for faithful reconstruction of high-frequency details in the original image." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "type": "text", + "content": "Given " + }, + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "type": "inline_equation", + "content": "f^{hr}(\\{S_i\\})" + }, + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "type": "text", + "content": " from the detail-specific stage, we add it to the coarse feature manifolds " + }, + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\Psi(\\boldsymbol{w} + \\{\\mathcal{S}_i\\})" + }, + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "type": "text", + "content": " from the general inversion stage, and send each feature point on the manifolds to the MLP-based decoder " + }, + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "type": "text", + "content": " to obtain the final radiance manifolds, as shown in Fig. 2. The final inversion image " + }, + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "type": "text", + "content": " can then be obtained similarly via manifold rendering at input view " + }, + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\hat{\\theta}" + }, + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "type": "text", + "content": ". Novel views can also be easily generated given an arbitrary camera pose " + }, + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "type": "text", + "content": " during rendering." + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 313, + 70, + 540, + 196 + ], + "blocks": [ + { + "bbox": [ + 313, + 70, + 540, + 196 + ], + "lines": [ + { + "bbox": [ + 313, + 70, + 540, + 196 + ], + "spans": [ + { + "bbox": [ + 313, + 70, + 540, + 196 + ], + "type": "image", + "image_path": "3ecf9551fb0e3f1bcdd01b5bf88fd7ba6a5ee3ef012b8b4ff61e9dafd3278f3b.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 323, + 204, + 527, + 216 + ], + "lines": [ + { + "bbox": [ + 323, + 204, + 527, + 216 + ], + "spans": [ + { + "bbox": [ + 323, + 204, + 527, + 216 + ], + "type": "text", + "content": "Figure 4. Visualization of the novel view regularization." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 228, + 453, + 240 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 228, + 453, + 240 + ], + "spans": [ + { + "bbox": [ + 306, + 228, + 453, + 240 + ], + "type": "text", + "content": "3.4. Detail Manifolds Learning" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 245, + 545, + 282 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 245, + 545, + 282 + ], + "spans": [ + { + "bbox": [ + 305, + 245, + 545, + 282 + ], + "type": "text", + "content": "We fix the image inverter " + }, + { + "bbox": [ + 305, + 245, + 545, + 282 + ], + "type": "inline_equation", + "content": "E_{w}" + }, + { + "bbox": [ + 305, + 245, + 545, + 282 + ], + "type": "text", + "content": " and the efficient GRAM from the general inversion stage, and learn the detail manifolds reconstructor with the following losses." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 284, + 545, + 319 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 284, + 545, + 319 + ], + "spans": [ + { + "bbox": [ + 305, + 284, + 545, + 319 + ], + "type": "text", + "content": "Image reconstruction loss. A multi-level reconstruction loss is applied between the final inversion image " + }, + { + "bbox": [ + 305, + 284, + 545, + 319 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 305, + 284, + 545, + 319 + ], + "type": "text", + "content": " and the input image " + }, + { + "bbox": [ + 305, + 284, + 545, + 319 + ], + "type": "inline_equation", + "content": "\\hat{I}" + }, + { + "bbox": [ + 305, + 284, + 545, + 319 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 312, + 324, + 545, + 339 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 324, + 545, + 339 + ], + "spans": [ + { + "bbox": [ + 312, + 324, + 545, + 339 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {r} = \\left\\| I - \\hat {I} \\right\\| ^ {2} + \\operatorname {L P I P S} (I, \\hat {I}) + \\left(1 - \\langle f _ {i d} (I), f _ {i d} (\\hat {I}) \\rangle\\right), \\tag {6}", + "image_path": "791ce2d42698f3d2ae9cd5eba5b7da314ffdb3153d28c498939d1c465ce4ab6d.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 345, + 545, + 369 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 345, + 545, + 369 + ], + "spans": [ + { + "bbox": [ + 305, + 345, + 545, + 369 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 345, + 545, + 369 + ], + "type": "inline_equation", + "content": "\\mathrm{LPIPS}(\\cdot ,\\cdot)" + }, + { + "bbox": [ + 305, + 345, + 545, + 369 + ], + "type": "text", + "content": " is the perceptual loss defined by [68], and " + }, + { + "bbox": [ + 305, + 345, + 545, + 369 + ], + "type": "inline_equation", + "content": "f_{id}" + }, + { + "bbox": [ + 305, + 345, + 545, + 369 + ], + "type": "text", + "content": " is a pre-trained face recognition network [11]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 372, + 545, + 432 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 372, + 545, + 432 + ], + "spans": [ + { + "bbox": [ + 305, + 372, + 545, + 432 + ], + "type": "text", + "content": "Novel view regularization. The reconstruction loss guarantees a faithful inversion result at the input viewpoint, yet artifacts can still occur when rendering the radiance manifolds at other views. We, therefore, design a regularization term to ensure reasonable novel view synthesis results:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 342, + 437, + 545, + 450 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 342, + 437, + 545, + 450 + ], + "spans": [ + { + "bbox": [ + 342, + 437, + 545, + 450 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {n v} = \\operatorname {L P I P S} (M \\odot I (\\boldsymbol {\\theta}), M \\odot I _ {w} (\\boldsymbol {\\theta})), \\tag {7}", + "image_path": "2a1b9bdcbca7d003cc84ad9ee671d146c92c57cff9e9355ff2c8f13a7cbbf645.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 455, + 545, + 492 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 455, + 545, + 492 + ], + "spans": [ + { + "bbox": [ + 305, + 455, + 545, + 492 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 455, + 545, + 492 + ], + "type": "inline_equation", + "content": "I(\\pmb{\\theta})" + }, + { + "bbox": [ + 305, + 455, + 545, + 492 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 455, + 545, + 492 + ], + "type": "inline_equation", + "content": "I_w(\\pmb{\\theta})" + }, + { + "bbox": [ + 305, + 455, + 545, + 492 + ], + "type": "text", + "content": " are final and coarse inversion image rendered at novel view " + }, + { + "bbox": [ + 305, + 455, + 545, + 492 + ], + "type": "inline_equation", + "content": "\\pmb{\\theta}" + }, + { + "bbox": [ + 305, + 455, + 545, + 492 + ], + "type": "text", + "content": " respectively, " + }, + { + "bbox": [ + 305, + 455, + 545, + 492 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 305, + 455, + 545, + 492 + ], + "type": "text", + "content": " is element-wise multiplication, and " + }, + { + "bbox": [ + 305, + 455, + 545, + 492 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 305, + 455, + 545, + 492 + ], + "type": "text", + "content": " is a binary mask:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 341, + 496, + 545, + 510 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 341, + 496, + 545, + 510 + ], + "spans": [ + { + "bbox": [ + 341, + 496, + 545, + 510 + ], + "type": "interline_equation", + "content": "M (u, v) = \\mathbb {I} (- \\boldsymbol {r} (\\hat {\\boldsymbol {\\theta}}) \\cdot N _ {w} (\\boldsymbol {\\theta}) (u, v) < \\tau). \\tag {8}", + "image_path": "193ba99e762aa89bbd04281c89d902853c4a51866ef5e29a2c6863974c6189e9.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 515, + 545, + 636 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 515, + 545, + 636 + ], + "spans": [ + { + "bbox": [ + 304, + 515, + 545, + 636 + ], + "type": "text", + "content": "Here " + }, + { + "bbox": [ + 304, + 515, + 545, + 636 + ], + "type": "inline_equation", + "content": "(u,v)" + }, + { + "bbox": [ + 304, + 515, + 545, + 636 + ], + "type": "text", + "content": " is the image space coordinate, " + }, + { + "bbox": [ + 304, + 515, + 545, + 636 + ], + "type": "inline_equation", + "content": "\\mathbb{I}" + }, + { + "bbox": [ + 304, + 515, + 545, + 636 + ], + "type": "text", + "content": " is the indicator function, " + }, + { + "bbox": [ + 304, + 515, + 545, + 636 + ], + "type": "inline_equation", + "content": "\\pmb{r}(\\hat{\\pmb{\\theta}})" + }, + { + "bbox": [ + 304, + 515, + 545, + 636 + ], + "type": "text", + "content": " is the camera lookat direction of the input image " + }, + { + "bbox": [ + 304, + 515, + 545, + 636 + ], + "type": "inline_equation", + "content": "\\hat{I}" + }, + { + "bbox": [ + 304, + 515, + 545, + 636 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 515, + 545, + 636 + ], + "type": "inline_equation", + "content": "N_w(\\pmb {\\theta})" + }, + { + "bbox": [ + 304, + 515, + 545, + 636 + ], + "type": "text", + "content": " is the surface normal map of " + }, + { + "bbox": [ + 304, + 515, + 545, + 636 + ], + "type": "inline_equation", + "content": "I_{w}(\\pmb {\\theta})" + }, + { + "bbox": [ + 304, + 515, + 545, + 636 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 515, + 545, + 636 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 515, + 545, + 636 + ], + "type": "text", + "content": " is a scalar threshold. The intuition behind this regularization is that the details for regions unobserved in the input image should stay close to the coarse inversion result at novel views, as the coarse inversion image is more reasonable at new views due to leveraging the priors from the pre-trained GRAM. The normal map " + }, + { + "bbox": [ + 304, + 515, + 545, + 636 + ], + "type": "inline_equation", + "content": "N_w(\\pmb {\\theta})" + }, + { + "bbox": [ + 304, + 515, + 545, + 636 + ], + "type": "text", + "content": " in Eq. (8) can be effectively calculated via the following equation:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 320, + 641, + 545, + 673 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 641, + 545, + 673 + ], + "spans": [ + { + "bbox": [ + 320, + 641, + 545, + 673 + ], + "type": "interline_equation", + "content": "N _ {w} (\\boldsymbol {\\theta}) (u, v) = - \\frac {1}{\\eta} \\sum_ {i = 1} ^ {N} T \\left(\\alpha \\left(\\boldsymbol {x} _ {i}\\right)\\right) \\alpha \\left(\\boldsymbol {x} _ {i}\\right) \\frac {\\partial \\alpha \\left(\\boldsymbol {x} _ {i}\\right)}{\\partial \\boldsymbol {x} _ {i}}, \\tag {9}", + "image_path": "f2ed9ce93a3309b33653dfe66bfdf1ad0909940d2b569b2d9e27aee7a84b49c7.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 677, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 545, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 677, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\pmb{x}_i" + }, + { + "bbox": [ + 305, + 677, + 545, + 714 + ], + "type": "text", + "content": " are intersections along the ray that " + }, + { + "bbox": [ + 305, + 677, + 545, + 714 + ], + "type": "inline_equation", + "content": "(u, v)" + }, + { + "bbox": [ + 305, + 677, + 545, + 714 + ], + "type": "text", + "content": " corresponds to, " + }, + { + "bbox": [ + 305, + 677, + 545, + 714 + ], + "type": "inline_equation", + "content": "T(\\alpha(\\pmb{x}_i)) = \\prod_{j < i} (1 - \\alpha(\\pmb{x}_j))" + }, + { + "bbox": [ + 305, + 677, + 545, + 714 + ], + "type": "text", + "content": " is the accumulated transparency, and " + }, + { + "bbox": [ + 305, + 677, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 305, + 677, + 545, + 714 + ], + "type": "text", + "content": " is a normalizing scalar. The partial" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "4427" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "type": "text", + "content": "gradient " + }, + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "type": "inline_equation", + "content": "\\partial \\alpha (\\pmb {x}_i) / \\partial \\pmb {x}_i" + }, + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "type": "text", + "content": " can be easily computed via backpropagating the MLP-based decoder " + }, + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "type": "text", + "content": ". Visualizations of the normal map " + }, + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "type": "inline_equation", + "content": "N_{w}(\\theta)" + }, + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "type": "text", + "content": " and the binary mask " + }, + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "type": "text", + "content": " are in Fig. 4." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 111, + 287, + 148 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 111, + 287, + 148 + ], + "spans": [ + { + "bbox": [ + 46, + 111, + 287, + 148 + ], + "type": "text", + "content": "Depth regularization. We further enforce a depth regularization to the HR detail manifolds " + }, + { + "bbox": [ + 46, + 111, + 287, + 148 + ], + "type": "inline_equation", + "content": "f^{hr}(\\{\\mathcal{S}_i\\})" + }, + { + "bbox": [ + 46, + 111, + 287, + 148 + ], + "type": "text", + "content": " to ensure that details are predicted near the geometry surface:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 156, + 287, + 189 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 156, + 287, + 189 + ], + "spans": [ + { + "bbox": [ + 58, + 156, + 287, + 189 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {d e p t h}} = \\left\\{ \\begin{array}{l l} \\lambda \\| f ^ {h r} (\\boldsymbol {x} _ {i}) \\| ^ {2} & | z (\\boldsymbol {x} _ {i}) - z _ {\\text {s u r f}} | > \\epsilon \\\\ 0 & | z (\\boldsymbol {x} _ {i}) - z _ {\\text {s u r f}} | \\leq \\epsilon \\end{array} , \\right. \\tag {10}", + "image_path": "dd581bce2407f06dad0ae2415329fbfe69a4d4b242427c9c18c16000435a1c99.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 197, + 287, + 258 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 197, + 287, + 258 + ], + "spans": [ + { + "bbox": [ + 46, + 197, + 287, + 258 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 197, + 287, + 258 + ], + "type": "inline_equation", + "content": "\\pmb{x}_i" + }, + { + "bbox": [ + 46, + 197, + 287, + 258 + ], + "type": "text", + "content": " are intersections along the viewing rays at input viewpoint " + }, + { + "bbox": [ + 46, + 197, + 287, + 258 + ], + "type": "inline_equation", + "content": "\\hat{\\theta}" + }, + { + "bbox": [ + 46, + 197, + 287, + 258 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 197, + 287, + 258 + ], + "type": "inline_equation", + "content": "z(\\pmb{x}_i)" + }, + { + "bbox": [ + 46, + 197, + 287, + 258 + ], + "type": "text", + "content": " is the depth of " + }, + { + "bbox": [ + 46, + 197, + 287, + 258 + ], + "type": "inline_equation", + "content": "\\pmb{x}_i" + }, + { + "bbox": [ + 46, + 197, + 287, + 258 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 197, + 287, + 258 + ], + "type": "inline_equation", + "content": "z_{surf} = \\sum_{i=1}^{N} T(\\alpha(\\pmb{x}_i)) \\alpha(\\pmb{x}_i) z(\\pmb{x}_i)" + }, + { + "bbox": [ + 46, + 197, + 287, + 258 + ], + "type": "text", + "content": " is the depth of the approximated surface, and " + }, + { + "bbox": [ + 46, + 197, + 287, + 258 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 46, + 197, + 287, + 258 + ], + "type": "text", + "content": " is a threshold. This regularization ensures correct parallax for the learned details (see Sec. 4.3)." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 270, + 128, + 283 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 270, + 128, + 283 + ], + "spans": [ + { + "bbox": [ + 47, + 270, + 128, + 283 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 289, + 287, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 289, + 287, + 422 + ], + "spans": [ + { + "bbox": [ + 46, + 289, + 287, + 422 + ], + "type": "text", + "content": "Implementation details. We train our method on the FFHQ [25] dataset at " + }, + { + "bbox": [ + 46, + 289, + 287, + 422 + ], + "type": "inline_equation", + "content": "256^2" + }, + { + "bbox": [ + 46, + 289, + 287, + 422 + ], + "type": "text", + "content": " resolution and test it on the CelebA-HQ [23] dataset. All images are pre-processed following the procedure in [13]. The camera pose of input images is estimated by the face reconstruction method of [14]. We train our models on 4 Tesla V100 GPUs with 32GB memory. The whole training process takes around 6 days, where training the efficient GRAM takes 2 days, training the image inverter and finetuning the efficient GRAM takes 2 days and 1 day respectively, and training the detail manifolds reconstructor takes 1 day. More in the suppl. material." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 429, + 206, + 442 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 429, + 206, + 442 + ], + "spans": [ + { + "bbox": [ + 47, + 429, + 206, + 442 + ], + "type": "text", + "content": "4.1. Novel View Synthesis Results" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 448, + 287, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 448, + 287, + 579 + ], + "spans": [ + { + "bbox": [ + 46, + 448, + 287, + 579 + ], + "type": "text", + "content": "Figure 1 shows the novel view synthesis results of our method given different portrait images. Our method well preserves fine details (e.g. hair bangs, wrinkles, moles) of the input images and produces their 3D consistent novel views. The whole inversion and novel view synthesis process runs at 3 FPS on a V100 GPU without specialized acceleration, which largely improves the efficiency upon previous optimization-based 3D-aware GAN inversions. With the manifold caching technique in [13], we can further increase the free view rendering speed to 180FPS. More examples and video results are in the suppl. material." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 586, + 203, + 600 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 586, + 203, + 600 + ], + "spans": [ + { + "bbox": [ + 47, + 586, + 203, + 600 + ], + "type": "text", + "content": "4.2. Comparison with Prior Arts" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "content": "Comparison with GRAM. We first compare our efficient version of GRAM with the original one [13]. We measure the image generation quality by the Fréchet Inception Distances (FID) [21] between 20K randomly generated images and 20K sampled real images. The 3D consistency is measured by the reconstruction quality of NeuS [54] (i.e. " + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{PSNR}_{mv}" + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{SSIM}_{mv}" + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "content": ") on multiview images of 50 generated instances following [60]. As shown in Tab. 1, our efficient GRAM largely reduces the memory cost and increases" + } + ] + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 307, + 100, + 545, + 153 + ], + "blocks": [ + { + "bbox": [ + 306, + 70, + 545, + 92 + ], + "lines": [ + { + "bbox": [ + 306, + 70, + 545, + 92 + ], + "spans": [ + { + "bbox": [ + 306, + 70, + 545, + 92 + ], + "type": "text", + "content": "Table 1. Comparison between efficient GRAM and GRAM [13]. *: Inference on a Tesla V100 GPU with a batchsize of 1." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 100, + 545, + 153 + ], + "lines": [ + { + "bbox": [ + 307, + 100, + 545, + 153 + ], + "spans": [ + { + "bbox": [ + 307, + 100, + 545, + 153 + ], + "type": "table", + "html": "
MethodsMemory* ↓FPS* ↑FID ↓PSNRm v ↑SSIMm v ↑
EG3D2.8G206.0234.00.928
GRAM12G215.038.00.966
Ours3.3G1414.237.60.969
", + "image_path": "335e3ca8bd54c5b2ce69db615b8d63d12b089239fa56329941e5ff38745f672e.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 167, + 545, + 299 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 167, + 545, + 299 + ], + "spans": [ + { + "bbox": [ + 304, + 167, + 545, + 299 + ], + "type": "text", + "content": "the inference speed upon the original one without sacrificing image generation quality or 3D consistency, by introducing the StyleGAN2-based radiance generator and the efficient intersection calculation strategy. This improvement enables our following GRAMinverter method, otherwise, it is difficult, if not impossible, to leverage the memory-consuming GRAM for encoder-based GAN inversion. We also list the performance of the state-of-the-art EG3D [9] as a reference. Although EG3D has better image quality, it sacrifices the 3D consistency which we argue is a key factor for 3D-aware generation." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 304, + 545, + 400 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 304, + 545, + 400 + ], + "spans": [ + { + "bbox": [ + 304, + 304, + 545, + 400 + ], + "type": "text", + "content": "Comparison with pose editing methods. We compare with existing methods that achieve 3D pose editing of a given portrait via single forward pass, including 2D GAN inversion-based methods: e4e [52] + InterFaceGAN [41], HFGI [55] + InterFaceGAN, and HFGI + StyleHEAT [65]; 3D-aware GAN inversion-based methods: pix2NeRF [7] and IDE-3D [46]; and face reenactment methods: PIRenderer [36] and Face-vid2vid [56]." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 401, + 545, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 401, + 545, + 556 + ], + "spans": [ + { + "bbox": [ + 304, + 401, + 545, + 556 + ], + "type": "text", + "content": "We first evaluate the inversion fidelity among GAN inversion-based methods (Tab. 2). We report PSNR, SSIM, LPIPS, identity similarity (i.e. ID) measured by cosine distance of face recognition features [53], and FID. All metrics are calculated between the first 1K images of CelebAHQ and their corresponding inverted results. Since different methods may generate images of different resolutions and alignments, we pre-process all results following [13] and resize them to " + }, + { + "bbox": [ + 304, + 401, + 545, + 556 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 304, + 401, + 545, + 556 + ], + "type": "text", + "content": " for a fair comparison. As shown, our method significantly outperforms other 3D-aware GAN inversion methods across all metrics. We also exceed the StyleGAN2-based inversion method e4e and achieve comparable results with the state-of-the-art method HFGI." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 557, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 545, + 689 + ], + "type": "text", + "content": "We further compare our method with other approaches on pose editing of portrait images. We generate novel views (see the suppl. material) of the 1K test images using different methods and evaluate their identity similarity and FID to the original input in Tab. 2. Higher " + }, + { + "bbox": [ + 304, + 557, + 545, + 689 + ], + "type": "inline_equation", + "content": "\\mathrm{ID}_{nv}" + }, + { + "bbox": [ + 304, + 557, + 545, + 689 + ], + "type": "text", + "content": " and lower " + }, + { + "bbox": [ + 304, + 557, + 545, + 689 + ], + "type": "inline_equation", + "content": "\\mathrm{FID}_{nv}" + }, + { + "bbox": [ + 304, + 557, + 545, + 689 + ], + "type": "text", + "content": " indicate that a method can better keep the identity and image quality while changing the camera pose. Our method yields the best result among all competitors. We also surpass PIRenderer and Face-vid2vid which require video data for training, while ours is merely trained on monocular in-the-wild images. Figure 5 shows a visual comparison." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": "Finally, we measure the 3D consistency of all methods during continuous variation of the camera viewpoint. Fol-" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4428" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 61, + 89, + 533, + 209 + ], + "blocks": [ + { + "bbox": [ + 123, + 71, + 470, + 82 + ], + "lines": [ + { + "bbox": [ + 123, + 71, + 470, + 82 + ], + "spans": [ + { + "bbox": [ + 123, + 71, + 470, + 82 + ], + "type": "text", + "content": "Table 2. Quantitative comparison with existing portrait editing methods. See the text for details." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 61, + 89, + 533, + 209 + ], + "lines": [ + { + "bbox": [ + 61, + 89, + 533, + 209 + ], + "spans": [ + { + "bbox": [ + 61, + 89, + 533, + 209 + ], + "type": "table", + "html": "
MethodsInversion fidelityNovel view quality3D consistency
PSNR↑SSIM↑LPIPS↓ID↑FID↓ID_nv↑FID_nv↓PSNR_mv↑SSIM_mv↑
PIRendererer [36]-----0.47642.6436.720.958
Face-vid2vid [56]-----0.41641.7636.100.942
e4e [52] + InterfaceGAN [41]19.230.4510.2130.70635.920.48938.0434.290.909
HFGI [55] + InterfaceGAN [41]22.300.5790.1350.82726.410.51645.2333.990.917
HFGI [55] + StyleHEAT [65]22.300.5790.1350.82726.410.45758.3335.930.951
pix2NeRF [7]16.950.3940.4520.466108.30.378115.650.660.997
IDE-3D (encoder) [46]16.730.3820.2900.39351.510.32447.5637.570.950
Ours21.510.6500.1270.93628.170.63536.0239.530.974
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Pose editing comparison. Texture images with smoothly tilted strips indicate better 3D consistency. Best viewed with zoom-in." + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 162, + 384, + 267, + 540 + ], + "blocks": [ + { + "bbox": [ + 162, + 384, + 267, + 540 + ], + "lines": [ + { + "bbox": [ + 162, + 384, + 267, + 540 + ], + "spans": [ + { + "bbox": [ + 162, + 384, + 267, + 540 + ], + "type": "image", + "image_path": "032666ffa92d1d0caf50b91593f5fa849d5bd34c6f7411356ef360cab8555adb.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 195, + 540, + 233, + 550 + ], + "lines": [ + { + "bbox": [ + 195, + 540, + 233, + 550 + ], + "spans": [ + { + "bbox": [ + 195, + 540, + 233, + 550 + ], + "type": "text", + "content": "pix2NeRF" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 268, + 384, + 373, + 540 + ], + "blocks": [ + { + "bbox": [ + 268, + 384, + 373, + 540 + ], + "lines": [ + { + "bbox": [ + 268, + 384, + 373, + 540 + ], + "spans": [ + { + "bbox": [ + 268, + 384, + 373, + 540 + ], + "type": "image", + "image_path": "ead55e557a1d1f94c26fc07593070e0f8ee0233816297a532d5b8de1a8590541.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 287, + 540, + 354, + 550 + ], + "lines": [ + { + "bbox": [ + 287, + 540, + 354, + 550 + ], + "spans": [ + { + "bbox": [ + 287, + 540, + 354, + 550 + ], + "type": "text", + "content": "IDE-3D (encoder)" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 376, + 384, + 481, + 540 + ], + "blocks": [ + { + "bbox": [ + 376, + 384, + 481, + 540 + ], + "lines": [ + { + "bbox": [ + 376, + 384, + 481, + 540 + ], + "spans": [ + { + "bbox": [ + 376, + 384, + 481, + 540 + ], + "type": "image", + "image_path": "3448794f8fd1994804ff3263b52b9f558880f224ba79573ec9a7c36995fbb58e.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 419, + 541, + 437, + 549 + ], + "lines": [ + { + "bbox": [ + 419, + 541, + 437, + 549 + ], + "spans": [ + { + "bbox": [ + 419, + 541, + 437, + 549 + ], + "type": "text", + "content": "Ours" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + } + ], + "index": 18 + }, + { + "type": "image", + "bbox": [ + 482, + 384, + 536, + 540 + ], + "blocks": [ + { + "bbox": [ + 499, + 375, + 519, + 384 + ], + "lines": [ + { + "bbox": [ + 499, + 375, + 519, + 384 + ], + "spans": [ + { + "bbox": [ + 499, + 375, + 519, + 384 + ], + "type": "text", + "content": "Input" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 482, + 384, + 536, + 540 + ], + "lines": [ + { + "bbox": [ + 482, + 384, + 536, + 540 + ], + "spans": [ + { + "bbox": [ + 482, + 384, + 536, + 540 + ], + "type": "image", + "image_path": "e31c7e08e60ec00ba5030b23ec1095787526cba4f70e5ec3845469b994709782.jpg" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 499, + 541, + 519, + 550 + ], + "lines": [ + { + "bbox": [ + 499, + 541, + 519, + 550 + ], + "spans": [ + { + "bbox": [ + 499, + 541, + 519, + 550 + ], + "type": "text", + "content": "Input" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_caption" + } + ], + "index": 20 + }, + { + "bbox": [ + 46, + 580, + 288, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 580, + 288, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 580, + 288, + 712 + ], + "type": "text", + "content": "lowing [60], for each method, we generate 30 images under different views for 50 test instances in CelebA-HQ, and measure the multiview reconstruction quality of NeuS on them (i.e. " + }, + { + "bbox": [ + 46, + 580, + 288, + 712 + ], + "type": "inline_equation", + "content": "\\mathrm{PSNR}_{mv}" + }, + { + "bbox": [ + 46, + 580, + 288, + 712 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 580, + 288, + 712 + ], + "type": "inline_equation", + "content": "\\mathrm{SSIM}_{mv}" + }, + { + "bbox": [ + 46, + 580, + 288, + 712 + ], + "type": "text", + "content": "). In theory, better 3D consistency across different views would reduce the learning difficulty of NeuS, thus leading to higher PSNR and SSIM. Table 2 shows that our method has the second best 3D consistency among all methods, while the best one (i.e. pix2NeRF) generates over-smooth images of low quality as shown in Fig. 5 and indicated by the high FID score in Tab. 2. Our method outperforms IDE-3D in that it utilizes" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 580, + 545, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 580, + 545, + 664 + ], + "spans": [ + { + "bbox": [ + 304, + 580, + 545, + 664 + ], + "type": "text", + "content": "a 2D super-resolution module in its 3D-aware GAN which lowers the 3D consistency to some extent. Nevertheless, all 3D-aware GAN-based methods yield better 3D consistency compared to other 2D methods, indicating the importance of 3D-aware GAN for pose editing of images. A further comparison with the full pipeline of IDE-3D which includes an extra optimization step is in the suppl. material." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "Figure 5 further shows the visual comparison of 3D consistency, where we draw the stacked texture image of a fixed horizontal line segment during continuous camera movement following [60]. Methods with strong 3D consistency" + } + ] + } + ], + "index": 25 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4429" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 70, + 287, + 273 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 287, + 273 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 287, + 273 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 287, + 273 + ], + "type": "image", + "image_path": "5c20b35819820c21bf2762bc1c7f69ccfdaf18e7d5be411978156fd83f5af115.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 281, + 287, + 304 + ], + "lines": [ + { + "bbox": [ + 47, + 281, + 287, + 304 + ], + "spans": [ + { + "bbox": [ + 47, + 281, + 287, + 304 + ], + "type": "text", + "content": "Figure 6. Visual comparison between different alternatives. Our final solution yields the best result. Best viewed with zoom-in." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 52, + 328, + 282, + 448 + ], + "blocks": [ + { + "bbox": [ + 71, + 308, + 262, + 319 + ], + "lines": [ + { + "bbox": [ + 71, + 308, + 262, + 319 + ], + "spans": [ + { + "bbox": [ + 71, + 308, + 262, + 319 + ], + "type": "text", + "content": "Table 3. Ablation study of our proposed framework." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 52, + 328, + 282, + 448 + ], + "lines": [ + { + "bbox": [ + 52, + 328, + 282, + 448 + ], + "spans": [ + { + "bbox": [ + 52, + 328, + 282, + 448 + ], + "type": "table", + "html": "
MethodsPSNR ↑LPIPS ↓ID ↑FID_nv ↓
General17.680.2650.64844.43
General - pretrain17.450.2800.47252.12
General + finetune18.000.2540.67843.46
Detail (Ours)21.510.1270.93636.02
Detail - world2cam19.960.1710.90838.74
Detail - superres21.060.1650.92638.45
Detail - L_nv22.320.1060.94936.49
Detail - mask19.080.2110.84043.25
Detail - L_depth23.680.0940.96035.60
", + "image_path": "c9b8ac05717fcb16ecb37f3f0488a1acb3ab15e83b41b8419dcb373471c2107c.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 464, + 287, + 550 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 464, + 287, + 550 + ], + "spans": [ + { + "bbox": [ + 46, + 464, + 287, + 550 + ], + "type": "text", + "content": "will result in texture images with smoothly tilted strips, while methods with low 3D consistency produce twisted textures (i.e. geometry distortions and texture flickering issues) or vertical lines (i.e. texture sticking issues). Our method clearly produces a more reasonable texture image compared to the others. See the suppl. material and the accompanying video for more results." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 558, + 141, + 571 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 558, + 141, + 571 + ], + "spans": [ + { + "bbox": [ + 47, + 558, + 141, + 571 + ], + "type": "text", + "content": "4.3. Ablation Study" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 576, + 287, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 576, + 287, + 613 + ], + "spans": [ + { + "bbox": [ + 46, + 576, + 287, + 613 + ], + "type": "text", + "content": "We conduct an ablation study to validate the efficacy of our proposed framework and report the results in Tab. 3 and Fig. 6. All metrics are calculated similarly as in Sec. 4.2." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 618, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 618, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 618, + 288, + 715 + ], + "type": "text", + "content": "Inversion stage. Table 3 shows the performance of different stages. General stands for the general inversion stage without finetuned generator. General - pretrain denotes learning the efficient GRAM with " + }, + { + "bbox": [ + 46, + 618, + 288, + 715 + ], + "type": "inline_equation", + "content": "E_{w}" + }, + { + "bbox": [ + 46, + 618, + 288, + 715 + ], + "type": "text", + "content": " together instead of pre-training it via the 3D-aware GAN framework. General + finetune denotes finetuning the pre-trained efficient GRAM as described in Sec. 3.2, and Detail denotes our final approach with detail-specific reconstruction. As shown," + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "text", + "content": "the general stage alone cannot produce faithful reconstruction result, whether the efficient GRAM is further finetuned or not. By contrast, introducing the detail-specific reconstruction significantly improves the inversion fidelity upon the previous stage without sacrificing novel view quality. Learning the efficient GRAM together with the encoder without pre-training leads to a significant performance drop, indicating the importance of leveraging the prior knowledge of a pre-trained 3D-aware GAN." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 183, + 545, + 268 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 183, + 545, + 268 + ], + "spans": [ + { + "bbox": [ + 304, + 183, + 545, + 268 + ], + "type": "text", + "content": "Network architecture. We ablate the architecture of the detail manifolds reconstructor. As shown in Tab. 3 and Fig. 6, learning the low-resolution detail voxel in world space instead of in camera space (- world2cam) harms the reconstruction fidelity. And removing the super-resolution module for high-resolution manifold prediction (- superres) leads to blurry inversion results." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 271, + 546, + 439 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 271, + 546, + 439 + ], + "spans": [ + { + "bbox": [ + 304, + 271, + 546, + 439 + ], + "type": "text", + "content": "Regularization. We further validate our proposed regularization for detail manifolds learning. As shown in Tab. 3 and Fig. 6, removing the novel view regularization " + }, + { + "bbox": [ + 304, + 271, + 546, + 439 + ], + "type": "inline_equation", + "content": "(- \\mathcal{L}_{nv})" + }, + { + "bbox": [ + 304, + 271, + 546, + 439 + ], + "type": "text", + "content": " causes obvious artifacts at new views and leads to the increase of " + }, + { + "bbox": [ + 304, + 271, + 546, + 439 + ], + "type": "inline_equation", + "content": "\\mathrm{FID}_{nv}" + }, + { + "bbox": [ + 304, + 271, + 546, + 439 + ], + "type": "text", + "content": ", though it improves the reconstruction quality at the input viewpoint. Simply enforcing " + }, + { + "bbox": [ + 304, + 271, + 546, + 439 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{nv}" + }, + { + "bbox": [ + 304, + 271, + 546, + 439 + ], + "type": "text", + "content": " without the normal-aware mask (-mask) damages fine texture preservation at visible regions. Finally, although learning without the depth regularization " + }, + { + "bbox": [ + 304, + 271, + 546, + 439 + ], + "type": "inline_equation", + "content": "(- \\mathcal{L}_{depth})" + }, + { + "bbox": [ + 304, + 271, + 546, + 439 + ], + "type": "text", + "content": " results in better metrics, we find that it cannot well preserve certain fine details at novel views due to incorrect parallax brought by the depth error (e.g. mole in Fig. 6). We conjecture that such dynamic artifact can hardly be captured by the current feature extractor [49] for FID computation." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 450, + 384, + 462 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 450, + 384, + 462 + ], + "spans": [ + { + "bbox": [ + 306, + 450, + 384, + 462 + ], + "type": "text", + "content": "5. Conclusions" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 470, + 545, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 470, + 545, + 590 + ], + "spans": [ + { + "bbox": [ + 304, + 470, + 545, + 590 + ], + "type": "text", + "content": "We presented GRAMinverter, a novel approach for high-fidelity and 3D-consistent portrait synthesis from monocular images via single forward pass. The core idea is to learn a detail manifolds reconstructor to predict 3D-consistent fine details on the radiance manifolds from a input image, and combine them with the coarse radiance manifolds obtained via an encoder-based inversion of the pre-trained GRAM. Extensive experiments have demonstrated our superior results over previous works. We believe our method paves a new way for efficient 3D-aware portrait creation." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 594, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 546, + 714 + ], + "type": "text", + "content": "Limitations and future works. Our GRAMinverter has several limitations. Based on the radiance manifold representation, it produces layered artifacts at large viewing angles. It cannot well handle occlusions of hands and other accessories. Its performance is also affected by the training data and may produce inferior results for out-of-distribution input. Besides, it does not support editing of attributes beyond camera viewpoints as done in previous 2D GAN inversions. 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In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 787-796, 2015. 3" + } + ] + } + ], + "index": 24 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4433" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Learning Discriminative Representations for Skeleton Based Action Recognition/d7b634f0-e078-4d7a-89da-58619960a3b5_content_list.json b/2023/Learning Discriminative Representations for Skeleton Based Action Recognition/d7b634f0-e078-4d7a-89da-58619960a3b5_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..28163d9b4f76438eaf47f76a5da4604f12a6de17 --- /dev/null +++ b/2023/Learning Discriminative Representations for Skeleton Based Action Recognition/d7b634f0-e078-4d7a-89da-58619960a3b5_content_list.json @@ -0,0 +1,1557 @@ +[ + { + "type": "text", + "text": "Learning Discriminative Representations for Skeleton Based Action Recognition", + "text_level": 1, + "bbox": [ + 81, + 130, + 888, + 151 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Huanyu Zhou $^{1}$ , Qingjie Liu $^{1,2,3,*}$ , Yunhong Wang $^{1}$", + "bbox": [ + 290, + 179, + 686, + 198 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ State Key Laboratory of Virtual Reality Technology and Systems, Beihang University, Beijing, China $^{2}$ Zhongguancun Laboratory, $^{3}$ Hangzhou Innovation Institute of Beihang University", + "bbox": [ + 88, + 198, + 892, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{zhysora, qingjie.liu, yhwang}@buaa.edu.cn", + "bbox": [ + 300, + 236, + 671, + 251 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 286, + 312, + 301 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Human action recognition aims at classifying the category of human action from a segment of a video. Recently, people have dived into designing GCN-based models to extract features from skeletons for performing this task, because skeleton representations are much more efficient and robust than other modalities such as RGB frames. However, when employing the skeleton data, some important clues like related items are also discarded. It results in some ambiguous actions that are hard to be distinguished and tend to be misclassified. To alleviate this problem, we propose an auxiliary feature refinement head (FR Head), which consists of spatial-temporal decoupling and contrastive feature refinement, to obtain discriminative representations of skeletons. Ambiguous samples are dynamically discovered and calibrated in the feature space. Furthermore, FR Head could be imposed on different stages of GCNs to build a multi-level refinement for stronger supervision. Extensive experiments are conducted on NTU RGB+D, NTU RGB+D 120, and NW-UCLA datasets. Our proposed models obtain competitive results from state-of-the-art methods and can help to discriminate those ambiguous samples. Codes are available at https://github.com/zhysora/FR-Head.", + "bbox": [ + 76, + 318, + 473, + 651 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 681, + 207, + 698 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In human-to-human communication, action plays a particularly important role. The behaviors convey intrinsic information like emotions and potential intentions and thus help to understand the person. Empowering intelligent machines with the same ability to understand human behaviors is critical for natural human-computer interaction and many other practical applications, and has been attracting much attention recently.", + "bbox": [ + 75, + 708, + 468, + 828 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Nowadays, obtaining 2D/3D skeletons of humans has become much easier thanks to the advanced sensor technology and human pose estimation algorithms. Skeletons", + "bbox": [ + 76, + 829, + 468, + 875 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/952023fb34e46a439957a7f3c6804a64de423d59d971732dbd3cb0fdff6312d8.jpg", + "image_caption": [ + "Figure 1. There are some actions that are hard to recognize because the skeleton representations lack important interactive objects and contexts, which make them easily confused with each other." + ], + "image_footnote": [], + "bbox": [ + 514, + 291, + 883, + 588 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "are compact and robust representations that are immune to viewpoint changes and cluttered backgrounds, making them attractive for action recognition. A typical way to use skeletons for action recognition is to build Graph Convolutional Networks (GCNs) [38]. The joints and bones in the human body naturally form graphs, which make GCNs a perfect tool to extract topological features of skeletons. GCN-based methods have become more and more popular, with another merit that the models can be built lightweight and have high computational efficiency compared with models processing video frames.", + "bbox": [ + 496, + 688, + 892, + 853 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "However, using skeletons to recognize actions has some limitations. A major problem is that skeleton representation lacks important interactive objects and contextual informa", + "bbox": [ + 498, + 854, + 890, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author", + "bbox": [ + 94, + 886, + 218, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "10608", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tion for distinguishing similar actions. As shown in Fig. 1, it is hard to distinguish \"Writing\", \"Reading\" and \"Typing on a keyboard\" based on the skeleton view alone. In contrast, a model can recognize them from RGB frames by focusing on the related items. These actions are easily confused with each other and should be given more attention.", + "bbox": [ + 75, + 90, + 470, + 181 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To alleviate this drawback, we propose a feature refinement module using contrastive learning to lift the discriminative ability of features between ambiguous actions. We first decouple hidden features into spatial and temporal components so that the network can better focus on discriminative parts among ambiguous actions along the topological and temporal dimensions. Then we identify the confident and ambiguous samples based on the model prediction during training. Confident samples are used to maintain a prototype for each class, which is achieved by a contrastive learning loss to constrain intra-class and inter-class distances. Meanwhile, ambiguous samples are calibrated by being closer to or far away from confident samples in the feature space. Furthermore, the aforementioned feature refinement module can be embedded into multiple types of GCNs to improve hierarchical feature learning. It will produce a multi-level contrastive loss, which is jointly trained with the classification loss to improve the performance of ambiguous actions. Our main contributions are summarized as follows:", + "bbox": [ + 75, + 181, + 473, + 484 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a discriminative feature refinement module to improve the performance of ambiguous actions in skeleton based action recognition. It uses contrastive learning to constrain the distance between confident samples and ambiguous samples. It also decouples the raw feature map into spatial and temporal components in a lightweight way for efficient feature enhancement.", + "- The feature refinement module is plug-and-play and compatible with most GCN-based models. It can be jointly trained with other losses but discarded in the inference stage.", + "- We conduct extensive experiments on NTU RGB+D, NTU RGB+D 120, and NW-UCLA datasets to compare our proposed methods with the state-of-the-art models. Experimental results demonstrate the significant improvement of our methods." + ], + "bbox": [ + 93, + 497, + 468, + 777 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 791, + 218, + 806 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Human Pose Estimation", + "text_level": 1, + "bbox": [ + 76, + 816, + 299, + 832 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Human pose estimation is an essential building block for a wide range of intelligent systems in fields such as AR, sports analysis, and healthcare, thus receiving much attention in recent years. Recent approaches leverage the", + "bbox": [ + 75, + 839, + 470, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "temporal information of 2D pose sequences to alleviate the depth ambiguity in 3D poses [1, 13, 19, 20, 23]. Hossain et al. [13] tackle the task as a sequence-to-sequence problem and build RNNs to learn the mapping. Cai et al. [1] exploit the spatial-temporal relations from the 2D sequences via an encoder-decoder like GCN. Li et al. [19] use Transformer [31] to capture the long-range relationships in the 2D pose sequence.", + "bbox": [ + 496, + 90, + 893, + 212 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Skeleton Based Action Recognition", + "text_level": 1, + "bbox": [ + 500, + 220, + 805, + 238 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Action recognition benefits a lot from human pose estimation. Early works treat the recognition as a sequence classification task. Su et al. [30] design an auto-encoder with RNNs to learn high-level features from the sequence. Another stream converts the skeleton sequence to image-like data using hand-crafted schemes [9, 37]. Duan et al. [10] concatenate an RGB frame with a 2D skeleton heat map and use 3D CNNs to extract features. These works do not explicitly exploit the spatial structure of the human body.", + "bbox": [ + 496, + 244, + 893, + 393 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The mainstream in this field is to use GCNs to extract the high-level features from skeletons since the joints and bones in the human body naturally construct a graph [5,22,38,42]. In this way, the topology of the human body is fully exploited. Yan et al. [38] is the first attempt to use GCNs for skeleton based human action recognition. They define the basic connections of spatial and temporal dimensions and introduce an efficient pipeline. Zhang et al. [42] build a two-stream architecture for both joint and bone modalities. Chen et al. [5] improve the design of GCNs in [38] and propose to dynamically learn different topologies and effectively aggregate joint features in each channel.", + "bbox": [ + 496, + 396, + 893, + 579 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.3. Contrastive Learning", + "text_level": 1, + "bbox": [ + 500, + 587, + 702, + 603 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recently, contrastive learning has achieved remarkable progress in diverse fields. Typically, contrastive learning requires generating a set of transformed versions (or \"views\") of an image using data augmentations, then training the network to distinguish the different views of the image. Chen et al. [2] explore the strategies of data augmentations and use a huge batch size to obtain the enhanced representation. He et al. [3,4,12] realize contrastive learning in a more efficient way using a momentum encoder and a dynamic queue. Wang et al. [33] define the positive and negative samples in a supervised manner. They design a metric function loss to calibrate these misclassified feature representations for better intra-class consistency and segmentation performance. Inspired by this, our work tries to use a similar spirit to refine the skeleton representations for ambiguous actions.", + "bbox": [ + 496, + 611, + 893, + 838 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.4. Ambiguous Sample", + "text_level": 1, + "bbox": [ + 500, + 847, + 687, + 863 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Most of the recognition tasks for solving ambiguous samples focus on fine-grained image classification. For ex", + "bbox": [ + 500, + 869, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "10609", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/e25c349f0a1fde0f8ecfaa18f0d31c538edd112a372a7d6159fb6f2fdfac18d1.jpg", + "image_caption": [ + "Figure 2. overview of the proposed method." + ], + "image_footnote": [], + "bbox": [ + 83, + 90, + 877, + 470 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "ample, Lin et al. [32] perform bilinear pooling on the representations of two local patches to learn the discriminative feature. Dubey et al. [11] model similarity between image pairs and leverage metric learning to improve the feature distributions. Zhuang et al. [43] design a module to adaptively discover contrastive cues from a pair of images and attentively distinguish them via pairwise interaction. However, we have not found works that aim at solving skeleton-based action recognition.", + "bbox": [ + 75, + 523, + 468, + 659 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 76, + 674, + 210, + 691 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We now give the details of our method. The overview of it is depicted in Fig. 2.", + "bbox": [ + 75, + 700, + 470, + 729 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Backbone", + "text_level": 1, + "bbox": [ + 76, + 741, + 191, + 755 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The input of our model is a sequence of skeletons with a shape of $T \\times V \\times 3$ , which means $T$ frames of $V$ joints in a 3D space. We build our approach on [5]. However, we will show in the experimental section that it can improve any GCNs. The backbone consists of 10 basic units, termed TGN. TGN is constructed by a series of Temporal CNNs (TCNs) and Graph Convolution Networks (GCNs). Concretely, TCNs extract the temporal features by imposing 1D CNNs on the temporal dimension; GCNs extract the spa", + "bbox": [ + 75, + 763, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "tial features with a learnable topological graph defined on the spatial dimension. Note that two of the basic units are stripped TGNs implemented by stripped 1D CNNs. They are used to generate multi-scale features by decreasing the temporal dimension while increasing the channel dimension. Then, a pooling layer is applied to get the 1D high-level feature vectors. Finally, a fully-connected (FC) layer with softmax activation maps the feature to a probability distribution of $K$ candidate categories.", + "bbox": [ + 496, + 523, + 890, + 660 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "It is noted that the detailed implementation of the backbone is not the main concern of our method. The implementation of the basic unit can be replaced by any other GCN-based networks like [26, 38].", + "bbox": [ + 496, + 662, + 890, + 722 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Feature Refinement Head", + "text_level": 1, + "bbox": [ + 500, + 738, + 733, + 753 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our main idea is to improve the performance of the skeleton based model on ambiguous actions that are quite similar and easily misclassified. To achieve this, we propose a plug-and-play module to optimize multi-level features within the backbone network, termed Feature Refinement Head (FR Head). It first decouples the hidden feature maps into spatial and temporal components and then applies a contrastive learning loss with global class prototypes and ambiguous samples. It is worth noting that the proposed FR", + "bbox": [ + 496, + 763, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "10610", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Head is added only for training. There is no additional computational cost or memory consumption during inference.", + "bbox": [ + 76, + 90, + 468, + 121 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2.1 Multi-Level Feature Selection", + "text_level": 1, + "bbox": [ + 76, + 143, + 336, + 157 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To learn more discriminative feature representations, we divide the backbone into four stages, respectively at the 1st, 5th, 8th, and last layer of TGN, and impose a FR Head on each of them. The 5th and the 8th layers employ a strided operation. Each FR Head refines the corresponding hidden features by calculating a contrastive learning (CL) loss, whose details will be discussed in Section 3.2.3. To balance the different levels, we add a weighting parameter for each stage and the multi-level CL loss can be defined as a weighted average sum:", + "bbox": [ + 75, + 169, + 470, + 320 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {C L} = \\sum_ {i = 1} ^ {4} \\lambda_ {i} \\cdot \\mathcal {L} _ {C L} ^ {i} \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 200, + 335, + 468, + 375 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_{CL}$ is the multi-level CL loss, $\\lambda_{i}$ is the hyperparameter to control stage $i$ and $\\mathcal{L}_{CL}^{i}$ is the local CL loss calculated by stage $i$ .", + "bbox": [ + 76, + 383, + 470, + 431 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2.2 Spatial-Temporal Decoupling", + "text_level": 1, + "bbox": [ + 76, + 452, + 336, + 468 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Due to the complexity of human activities, coarse modelling features will lead to confusion between ambiguous actions with similar spatial appearances or temporal transformations.", + "bbox": [ + 76, + 478, + 468, + 537 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For example, \"put sth. into a bag\" can be easily distinguished from \"take sth. out of a bag\" using temporal clues. However, compared to the \"reach into pockets\", more concentrations on the spatial information are required. Therefore, we propose a spatial-temporal decouple module that mines the spatial and temporal information simultaneously to improve the discriminative ability of action representations.", + "bbox": [ + 75, + 539, + 468, + 657 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As Fig. 2 describes, the raw feature map is fed into two parallel branches for efficient feature enhancement. Concretely, each branch comprises a spatial/temporal pooling layer which only keeps the average value of the related dimension and a $1 \\times 1$ convolution layer which is used to squeeze the feature to a fixed size. Then the output feature is flattened to a unified representation with the channel size of $C_h$ . Finally, a CL loss is added on top of each branch. We accomplish the Spatial-Temporal Decoupling feature refinement by summing losses from the two branches:", + "bbox": [ + 75, + 660, + 468, + 811 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {C L} ^ {i} = \\operatorname {C L} \\left(F _ {s} ^ {i}\\right) + \\operatorname {C L} \\left(F _ {t} ^ {i}\\right) \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 181, + 828, + 468, + 847 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $F_{s}^{i}$ and $F_{t}^{i}$ stand for the spatial feature and the temporal feature of stage $i$ , respectively. $\\mathrm{CL}(\\cdot)$ is the function to calculate the CL loss with a specific feature vector.", + "bbox": [ + 76, + 854, + 468, + 902 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/cf52a4991b93331d0cc154e828fec3003e02df88972f780e3c6b31ce0ddfdd3b.jpg", + "image_caption": [ + "Figure 3. Discovering the confident and ambiguous samples for action \"writing\"." + ], + "image_footnote": [], + "bbox": [ + 501, + 85, + 893, + 304 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2.3 Contrastive Feature Refinement", + "text_level": 1, + "bbox": [ + 500, + 369, + 777, + 383 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As Fig. 2 shows, we conduct the feature refinement in a manner of contrastive learning. The idea is inspired by [33]. Each sample will be refined by both its ground truth actions and other ambiguous actions.", + "bbox": [ + 498, + 393, + 892, + 454 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Confident Sample Clustering. Given an action label $k$ , if a sample is predicted correctly, namely as a True Positive (TP), we consider it a confident sample to distinguish it from ambiguous samples. Apparently, features from confident samples tend to have better intra-class consistency. As Fig. 3 shows, we gather those features to update the global representation (i.e., prototype) of the corresponding classes via exponential moving average (EMA). Assuming $s_{TP}^{k}$ is the set of confident samples for action $k$ in a batch and its size is $n_{TP}^{k}$ , the EMA operation can be defined as:", + "bbox": [ + 498, + 454, + 890, + 607 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nP _ {k} = (1 - \\alpha) \\cdot \\frac {1}{n _ {T P} ^ {k}} \\sum_ {i \\in s _ {T P} ^ {k}} F _ {i} + \\alpha \\cdot P _ {k} \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 563, + 616, + 890, + 656 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $P_{k}$ is the prototype of action $k$ , $F_{i}$ is the feature extracted from sample $i$ . $\\alpha$ is the momentum term, we set it to 0.9 by experience. Over the training procedure, the prototype becomes a stable estimation of the clustering center for action $k$ . It is capable of refining the feature of a newly arrived sample. Each sample should be close to the related prototype while far away from other prototypes. The distance between two feature vectors is defined as $\\mathrm{dis}(\\cdot ,\\cdot)$ , which is implemented by cosine distance:", + "bbox": [ + 498, + 662, + 890, + 799 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {d i s} (\\boldsymbol {u}, \\boldsymbol {v}) = \\frac {\\boldsymbol {u} \\boldsymbol {v} ^ {T}}{| | \\boldsymbol {u} | | _ {2} | | \\boldsymbol {v} | | _ {2}} \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 612, + 809, + 890, + 844 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{u},\\mathbf{v}$ stand for 1D vectors. $\\| \\cdot \\| _2$ is $L_{2}$ norm.", + "bbox": [ + 500, + 854, + 839, + 869 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Ambiguous Sample Discovering. To discover the ambiguous samples during the training stages, we gather the", + "bbox": [ + 498, + 869, + 890, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "10611", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "misclassified samples which tend to be quite similar to other categories. Given an action label $k$ , there are two types of ambiguous samples. If a sample of action $k$ is misclassified as other categories, it is termed as False Negative (FN). If a sample of other categories is misclassified as action $k$ , it is termed as False Positive (FP). Supposing $s_{FN}^{k}, s_{FP}^{k}$ are sets of FN and FP samples for action $k$ and the sizes of them are $n_{FN}^{k}, n_{FP}^{k}$ . As fig. 3 shows, We gather those samples in a batch and calculate the mean values as the center representations:", + "bbox": [ + 75, + 90, + 472, + 241 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {\\mu} _ {F N} ^ {k} = \\frac {1}{n _ {F N} ^ {k}} \\sum_ {j \\in s _ {F N} ^ {k}} F _ {j}, \\quad \\boldsymbol {\\mu} _ {F P} ^ {k} = \\frac {1}{n _ {F P} ^ {k}} \\sum_ {j \\in s _ {F P} ^ {k}} F _ {j} \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 247, + 468, + 287 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\pmb{\\mu}_{FN}^{k},\\pmb{\\mu}_{FP}^{k}$ stand for the center representation of FN and FP samples of class $k$ . Note that, we do not maintain a global representation for those ambiguous samples because the prediction of those samples is not stable in the training stage and the amount is much less than TP samples.", + "bbox": [ + 75, + 297, + 468, + 373 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Ambiguous Sample Calibration. To calibrate the prediction of ambiguous samples, we take confident sample $i$ of action $k$ as the anchor and calculate an auxiliary term in the feature space. For those FN samples which should be classified as action $k$ , a compensation term $\\phi_{i}$ is introduced:", + "bbox": [ + 75, + 375, + 468, + 449 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\phi_ {i} = \\left\\{ \\begin{array}{c} 1 - \\operatorname {d i s} \\left(F _ {i}, \\boldsymbol {\\mu} _ {F N} ^ {k}\\right), \\text {i f} i \\in s _ {T P} ^ {k} \\text {a n d} n _ {F N} ^ {k} > 0; \\\\ 0, \\text {o t h e r w i s e .} \\end{array} \\right. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 458, + 468, + 500 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "By minimizing the compensation term $\\phi_{i}$ , FN samples are supposed to be closer to the confident sample in the feature space. When there are no FN samples or the cosine distance converges to 1, $\\phi_{i}$ reaches the minimum value 0. This may motivate the model to correct these ambiguous samples as action $k$ .", + "bbox": [ + 75, + 506, + 468, + 595 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "On the other hand, for those FP samples which belong to other categories, a penalty term $\\psi_{i}$ is introduced:", + "bbox": [ + 76, + 597, + 468, + 627 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\psi_ {i} = \\left\\{ \\begin{array}{c} 1 + \\operatorname {d i s} \\left(F _ {i}, \\boldsymbol {\\mu} _ {F P} ^ {k}\\right), \\text {i f} i \\in s _ {T P} ^ {k} \\text {a n d} n _ {F P} ^ {k} > 0; \\\\ 0, \\text {o t h e r w i s e .} \\end{array} \\right. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 636, + 468, + 676 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Similarly, the penalty term $\\psi_{i}$ penalizes the distance between the FP samples and the confident samples in the feature space. When there are no FP samples or the cosine distance converges to $-1$ , $\\psi_{i}$ reaches the minimum value 0. This may prevent the model from recognizing these ambiguous samples as action $k$ .", + "bbox": [ + 75, + 685, + 468, + 773 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Finally, taking sample $i$ as an anchor, the proposed CL loss function can be defined as:", + "bbox": [ + 76, + 775, + 468, + 804 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\operatorname {C L} \\left(F _ {i}\\right) = - \\log \\frac {e ^ {\\operatorname {d i s} \\left(F _ {i} , P _ {k}\\right) / \\tau - (1 - p _ {i k}) \\psi_ {i}}}{e ^ {\\operatorname {d i s} \\left(F _ {i} , P _ {k}\\right) / \\tau - (1 - p _ {i k}) \\psi_ {i}} + \\sum_ {l \\neq k} e ^ {\\operatorname {d i s} \\left(F _ {i} , P _ {l}\\right) / \\tau}} \\\\ - \\log \\frac {e ^ {\\operatorname {d i s} \\left(F _ {i} , P _ {k}\\right) / \\tau - \\left(1 - p _ {i k}\\right) \\phi_ {i}}}{e ^ {\\operatorname {d i s} \\left(F _ {i} , P _ {k}\\right) / \\tau - \\left(1 - p _ {i k}\\right) \\psi_ {i}} + \\sum_ {l \\neq k} e ^ {\\operatorname {d i s} \\left(F _ {i} , P _ {l}\\right) / \\tau}} \\tag {8} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 811, + 475, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $p_{ik}$ is the predicted probability score of sample $i$ for class $k$ . It means that the TP samples with weaker confidence get stronger supervision from those ambiguous samples.", + "bbox": [ + 496, + 90, + 890, + 151 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Training Objective", + "text_level": 1, + "bbox": [ + 500, + 162, + 681, + 179 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We use Cross-Entropy (CE) loss to train our network:", + "bbox": [ + 517, + 186, + 872, + 202 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {C E} = - \\frac {1}{N} \\sum_ {i} \\sum_ {c} y _ {i c} \\log \\left(p _ {i c}\\right) \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 584, + 214, + 890, + 250 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $N$ is the number of samples in a batch. $y_{ic}$ is the one-hot presentation of the label of sample $i$ . If and only if $c$ is the target class of sample $i$ , $y_{ic} = 1$ . $p_{ic}$ is the probability score of sample $i$ belonging to class $k$ predicted by the network.", + "bbox": [ + 496, + 261, + 890, + 335 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Finally, CE loss is combined with our proposed multilevel CL loss to form the full learning objective function:", + "bbox": [ + 496, + 338, + 890, + 368 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {C E} + w _ {c l} \\cdot \\mathcal {L} _ {C L} \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 617, + 382, + 890, + 398 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_{CL}$ and $\\mathcal{L}_{CE}$ are defined in Eqs. 1 and 9. $w_{cl}$ is the balanced hyper-parameter for CL loss.", + "bbox": [ + 496, + 411, + 890, + 441 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 457, + 630, + 474 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Datasets", + "text_level": 1, + "bbox": [ + 500, + 483, + 601, + 497 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "NTU RGB+D. NTU RGB+D [24] is a widely used dataset containing 56,880 samples. 40 participants are invited to perform 60 actions including daily behaviors and health-related actions. Each action is performed by 1 or 2 people. The human skeleton is presented by 25 3D joints, which are captured by 3 Microsoft Kinect v2 cameras with different horizontal angle settings. It provides two benchmarks: (1) Cross-Subject (X-Sub): the dataset is divided according to the subjects. The training set consists of 20 subjects while the testing set consists of other 20 subjects. (2) Cross-View (X-View): the dataset is split by the camera views. They select camera views 2 and 3 to construct the training data while camera view 1 is used for testing.", + "bbox": [ + 496, + 506, + 890, + 703 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "NTU RGB+D 120. NTU RGB+D 120 [21] extends NTU RGB+D with extra 57,367 samples by introducing new 60 action classes, making it the largest skeleton based action recognition dataset. In total, it collects 113,945 skeleton sequences over 120 different classes performed by 106 participants. It also increases the number of camera setups to 32 by using different places and backgrounds. Two evaluation protocols are recommended: (1) Cross-Subject (X-Sub): samples from 56 subjects are selected to form the training set, and the reaming 50 subjects are used for testing. (2) Cross-Set (X-Set): samples with even setup IDs are used for training, while samples with odd setup IDs are used for testing.", + "bbox": [ + 496, + 704, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "10612", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/020ec7d402d3494ffb8f5bf94c7d8900e18ecceae60d15179793159d20732c6c.jpg", + "table_caption": [ + "Table 1. Ablation studies of our method on NTU-RGB+D 120 dataset under the X-Sub setting with the joint input modality." + ], + "table_footnote": [], + "table_body": "
MethodParams.Acc (%)
Baseline1.46M84.5
+ CL Loss1.53M85.0↑0.5
+ ST Decouple1.59M85.3↑0.8
+ ML Refine1.61M84.7↑0.2
Ours1.99M85.5↑1.0
", + "bbox": [ + 135, + 128, + 411, + 252 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/53350a50e9d1de678db54b741849b9d09a72c7bb968d14ce912b292dbb724603.jpg", + "table_caption": [ + "Table 2. Hyper-parameter exploration of our proposed method on NTU-RGB+D 120 dataset under the X-Sub setting with the joint input modality. The best one is in **bold**." + ], + "table_footnote": [], + "table_body": "
wclλ1λ2λ3λ4Acc (%)
1000184.4
0.1000185.3
0.01000185.0
111184.5
10.20.2184.7
10.50.20.184.1
0.10.10.11185.2
0.10.10.1185.1
0.10.20.2185.4
0.10.20.5185.5
", + "bbox": [ + 129, + 316, + 418, + 510 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "NW-UCLA. Northwestern-UCLA dataset [34] contains 1494 video clips performed by 10 volunteers. 3 Kinect cameras are used to capture 3D skeletons with 20 joints from multiple views. Totally 10 action categories are covered. We adopt the evaluation protocols recommended by the author: training data comes from the first two cameras, while testing data is from the other camera.", + "bbox": [ + 75, + 535, + 468, + 642 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Implementation Details", + "text_level": 1, + "bbox": [ + 76, + 650, + 294, + 666 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We adopt [5] as the backbone and implement the proposed method with the PyTorch deep learning framework. All experiments are conducted on one RTX 2080Ti GPU. The Stochastic Gradient Descent (SGD) optimizer is employed with a momentum of 0.9 and a weight decay of 0.0004 to train the models. In the first 5 epochs, we apply a warmup strategy for stable training. The initial learning rate is set to 0.1 and we decrease it at epoch 35 and 55 with a factor of 0.1. We train all models with 70 epochs and select the best performance. The base channel $C$ is set to 64 and the hidden channel $C_h$ is set to 256. The hyper-parameters in our methods are set as: $\\lambda_1 = 0.1$ , $\\lambda_2 = 0.2$ , $\\lambda_3 = 0.5$ , $\\lambda_4 = 1$ , $w_{cl} = 0.1$ . For NTU RGB+D and NTU RGB+D 120, we follow the data preprocessing in [41] and set the batch size to 64. All samples are resized to 64 frames. For NW", + "bbox": [ + 75, + 674, + 470, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "UCLA, we follow the data preprocessing in [8] and set the batch size to 16.", + "bbox": [ + 498, + 90, + 890, + 119 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 131, + 653, + 148 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We conduct ablation studies and evaluate the different hyper-parameter settings on the X-Sub benchmark of NTU RGB+D 120 dataset to verify the effectiveness of the proposed module.", + "bbox": [ + 496, + 155, + 890, + 215 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The results of ablation studies are displayed in Table 1. We remove all additional heads and train the network with CE loss to build the baseline. We also divide the proposed module into different sub-modules and design 3 variants: (1) CL Loss: we directly employ the CL loss to refine features from the last layer without any additional operations. (2) ST Decouple: we decouple the features into spatial and temporal components before refinement. (3) ML Refine: we impose the refinement on proposed multi-level stages in the training pipeline. It can be seen that all these sub-modules can improve the performance of the baseline. Among them, the contributions from CL loss and ST Decouple are relatively dominant. Moreover, when combining all of them, the result becomes better. We also report the count of trainable parameters of different models. The extra cost of parameters may increase the time of the training procedure but does not affect the inference stage.", + "bbox": [ + 496, + 215, + 892, + 473 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We analyze the configurations on the hyper-parameters of our method, and the results are available in Table 2. First, we try 3 different values of $w_{cl}$ to find the balance between the CL loss and CE loss with the fixed combination of $\\lambda_1 = \\lambda_2 = \\lambda_3 = 0, \\lambda_4 = 1$ for an efficient experiment. It seems that bigger $w_{cl}$ may hurt the performance while too small values only provide a little improvement. Then, we try more combinations of $\\lambda_i$ to balance the importance of different stages. From the results, we can observe that giving higher weight to the previous layers may obtain negative influence and increase the importance gradually from the early stage to the last stage and thus lead to an optimal result. It is concluded that the refinement of the high-level features from the final stage plays a major role and the low-level features provide the auxiliary effects. Finally, we choose the configuration of $\\lambda_1 = 0.1, \\lambda_2 = 0.2, \\lambda_3 = 0.5, \\lambda_4 = 1, w_{cl} = 0.1$ for the following experiments.", + "bbox": [ + 496, + 474, + 892, + 746 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.4. Combined with Other Backbones", + "text_level": 1, + "bbox": [ + 500, + 756, + 792, + 771 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Our proposed module is plug-and-play and compatible with most GCN-based backbones. To examine its universality, we apply it to 5 widely used GCN-based backbones [5, 17, 26, 35, 38] and evaluate them on the X-Sub and X-Set of NTU RGB+D 120 dataset. For fair comparisons, we reimplement them and use the same data preprocessing without the multi-stream fusion. Table 3 reports the performance and number of parameters of different methods. It is", + "bbox": [ + 496, + 779, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "10613", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/46760e0a5954771ebfcac585e61ae5d015f009d75256c268afea4d084ddf5a94.jpg", + "table_caption": [ + "Table 3. Performance of our proposed method using different GCN-based backbones on NTU-RGB+D 120 dataset with the joint input modality." + ], + "table_footnote": [], + "table_body": "
MethodParams.NTU-RGB+D 120
X-Sub (%)X-Set (%)
ST-GCN [38]2.11M83.485.1
+ FR Head2.65M84.4↑1.086.5↑1.4
2s-AGCN [26]3.80M84.385.9
+ FR Head4.33M84.6↑0.386.6↑0.7
CTR-GCN [5]1.46M84.586.6
+ FR Head1.99M85.5↑1.087.3↑0.7
TCA-GCN [35]5.65M85.086.3
+ FR Head6.18M85.2↑0.287.4↑1.1
HD-GCN [17]1.68M85.187.2
+ FR Head2.21M85.4↑0.387.7↑0.5
", + "bbox": [ + 76, + 142, + 478, + 371 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/df21168a5cf57c1dbf72f0198c0fc11e1e2f861ff143998c6b0435b60251b00e.jpg", + "table_caption": [ + "Table 4. Accuracy (\\%) on different difficult level actions for NTU-RGB+D 120 dataset under the X-Sub setting with the joint input modality." + ], + "table_footnote": [], + "table_body": "
MethodNTU-RGB+D 120
HardMediumEasy
ST-GCN [38]57.480.994.7
2s-AGCN [26]58.982.095.0
CTR-GCN [5]59.682.495.1
Ours61.683.395.7
Δ2.00.90.6
", + "bbox": [ + 122, + 436, + 424, + 569 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "observed that all models obtain an obvious gain of accuracy by employing the FR Head. The improvement is around $1.0\\%$ . In most cases, the models with lower accuracy are improved more than those with higher initial accuracy. The reason behind it may be that our modules utilize the knowledge from the misclassified samples. The lower accuracy of means the misclassified samples are more sufficient. The additional count of parameters introduced by the FR Head is around 0.5M and can be ignored in the inference stage.", + "bbox": [ + 75, + 594, + 468, + 731 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.5. Performance on Ambiguous Actions", + "text_level": 1, + "bbox": [ + 76, + 739, + 390, + 758 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We spilt NTU-RGB+D 120 dataset into 3 subsets with different difficulty levels. Specifically, according to the results of CTR-GCN [5], we gather actions whose accuracy is lower than $70\\%$ as Hard Level, between $70\\%$ and $90\\%$ as Medium Level, and over $90\\%$ as Easy Level. The results are displayed in Table 4. The experiment is under the X-Subsetting with only the joint input modality. Because ambiguous actions are quite similar and easy to be misclassified, these actions usually fall into Hard Level. From the", + "bbox": [ + 75, + 763, + 468, + 902 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/dc79be0a46ef8262f50fb5e591bd41f3997cb86db5f50f580274ad4465ee81ae.jpg", + "image_caption": [ + "Figure 4. The group-wise accuracy difference $(\\%)$ between our method and CTR-GCN [5] on ambiguous actions for NTU-RGB+D 120 dataset under the X-Sub setting with the joint input modality." + ], + "image_footnote": [], + "bbox": [ + 504, + 92, + 890, + 239 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/429fda840fd97c3e07d4afb7078fd0e775a11a418027e6986db527569c037ece.jpg", + "image_caption": [ + "Figure 5. Visualization of latent representation by t-SNE for ambiguous groups from NTU RGB+D 120 dataset. Different colors indicate different classes. The upper one is from the CTR-GCN [5], while the bottom one is from our method." + ], + "image_footnote": [], + "bbox": [ + 503, + 323, + 890, + 438 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "results, we can see that our method makes a great improvement in Hard Level actions, which demonstrates the ability to distinguish those ambiguous actions.", + "bbox": [ + 496, + 534, + 890, + 580 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Furthermore, we define ambiguous groups, which collect several related ambiguous actions to verify the performance of ambiguous samples. We first pick a class as an anchor class, for example, \"writing\". Then we gather the misclassified samples on \"writing\" and obtain the top-3 actions with the highest frequency, like \"reading\", \"typing on a keyboard\" and \"playing with phone\". These 4 actions will be constructed as an ambiguous group. The group-wise accuracy will be the average accuracy of all actions included by the group. Here, we randomly pick 60 anchor actions and constructed corresponding ambiguous groups from NTU-RGB+D 120 dataset. We compare our results with a SOTA model CTR-GCN [5] and display the results in Fig. 4. Our method gains great improvement in most ambiguous groups.", + "bbox": [ + 496, + 580, + 892, + 808 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We randomly pick some ambiguous groups and visualize the distribution of them in the feature space using t-SNE. As mentioned before, each ambiguous group contains four classes, including an anchor class and three ambiguous classes. We compare our method with CTR-GCN [5]. Fig. 5 shows that our model achieves a more compact clustering.", + "bbox": [ + 496, + 810, + 893, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "10614", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/6773a5571be44201e551e3a72001de974c741cbe778aa05cd1f8a034236f8c44.jpg", + "table_caption": [ + "Table 5. Performance comparison of skeleton-based action recognition in top-1 accuracy (\\%). The best one is in bold and the second one is underlined." + ], + "table_footnote": [], + "table_body": "
MethodPublicationNTU RGB+DNTU RGB+D 120NW-UCLA
X-SubX-ViewX-SubX-Set
ST-GCN [38]AAAI201881.588.3---
Ind-RNN [18]CVPR201881.888.0---
RotClips+MTCNN [15]TIP2018--62.261.8-
2s-AGCN [26]CVPR201988.595.182.984.9-
AGC-LSTM [27]CVPR201989.295.0--93.3
DGNN [25]CVPR201989.996.1---
PA-ResGCN-B19 [28]ACMMM202090.996.087.388.3-
Dynamic GCN [39]ACMMM202091.596.087.388.6-
SGN [41]CVPR202089.094.579.281.5-
Shift-GCN [8]CVPR202090.796.585.987.694.6
MS-G3D [22]CVPR202091.596.286.988.4-
DDGCN [16]ECCV202091.197.1---
DC-GCN+ADG [7]ECCV202090.896.686.588.195.3
MST-GCN [6]AAAI202191.596.687.588.8-
Skeletal-GNN [40]ICCV202191.696.787.589.2-
CTR-GCN [5]ICCV202192.496.888.990.696.5
STF [14]AAAI202292.596.988.989.9-
Ta-CNN [36]AAAI202290.494.885.486.896.1
EfficientGCN-B4 [29]TPAMI202291.795.788.389.1-
Ours-92.896.889.590.996.8
", + "bbox": [ + 145, + 127, + 823, + 483 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.6. Comparison with the State-of-the-Art", + "text_level": 1, + "bbox": [ + 76, + 508, + 406, + 525 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this section, we conduct a comparison with the state-of-the-art methods on NTU RGB+D 120, NTU RGB+D, and NW-UCLA datasets to demonstrate the competitive ability of our proposed module. The quantitative results are displayed in Table 5. It is noted that most of the state-of-the-art methods employ a multi-stream fusion framework. For a fair comparison, we follow the same framework as [5,35]. We make a fusion with the results from four modalities including joint, bone, joint motion, and bone motion as the final report result.", + "bbox": [ + 75, + 531, + 470, + 681 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "It is observed that our methods outperform most existing methods on these three datasets. On both settings of NTU-RGB+D 120, X-Sub of NTU-RGB+D, and NW-UCLA datasets, our model obtains the best results. On X-View of NTU-RGB+D, our model reaches state-of-the-art results with a reasonable gap between the best one, which demonstrates the great potential of our proposed module. Notably, our method is the first to propose a way to solve ambiguous actions, which are very important in skeleton based action recognition.", + "bbox": [ + 75, + 683, + 468, + 834 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 76, + 844, + 194, + 861 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we present a novel feature refinement module equipped with contrastive learning to solve the", + "bbox": [ + 76, + 869, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ambiguous actions for skeleton based action recognition. Multi-level features extracted from GCN-based backbone are leveraged and enhanced on both the spatial and temporal dimensions. The contrastive learning is conducted with the samples with high confidence and calibrated by the FP and FN samples to make full use of the misclassified actions.", + "bbox": [ + 496, + 508, + 890, + 616 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The extensive experiments demonstrate the effectiveness of the proposed module to distinguish the confusing categories and the university to be compatible with most GCN-based backbones. On three widely used benchmarks, our proposed method obtains satisfactory results and outperforms those state-of-the-art methods.", + "bbox": [ + 496, + 619, + 890, + 709 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Discussion. Despite the performance of our proposed module on three public large-scale datasets, the ambiguous actions in a few-shot setting with insufficient data remain to be explored. We will concentrate on it in our future work. In addition, there are some potential negative societal impacts to be considered. Our method may be applied in some controversial fields, such as surveillance. Besides, applying our module will introduce extra training costs, which should be discussed in the carbon emission problem.", + "bbox": [ + 496, + 714, + 890, + 851 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements. This paper was founded by National Natural Science Foundation of China under grants U20B2069 and 62176017.", + "bbox": [ + 498, + 854, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "10615", + "bbox": [ + 480, + 944, + 517, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Yujun Cai, Liuhao Ge, Jun Liu, Jianfei Cai, Tat-Jen Cham, Junsong Yuan, and Nadia Magnenat Thalmann. Exploiting spatial-temporal relationships for 3d pose estimation via graph convolutional networks. In Proceedings of the IEEE International Conference on Computer Vision, pages 2272-2281, 2019. 2", + "[2] Ting Chen, Simon Kornblith, Mohammad Norouzi, and Geoffrey Hinton. A simple framework for contrastive learning of visual representations. In International Conference on Machine Learning, pages 1597-1607. 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In Proceedings of the AAAI Conference on Artificial Intelligence, volume 34, pages 13130-13137, 2020. 3" + ], + "bbox": [ + 501, + 90, + 892, + 429 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "10617", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Learning Discriminative Representations for Skeleton Based Action Recognition/d7b634f0-e078-4d7a-89da-58619960a3b5_model.json b/2023/Learning Discriminative Representations for Skeleton Based Action Recognition/d7b634f0-e078-4d7a-89da-58619960a3b5_model.json new file mode 100644 index 0000000000000000000000000000000000000000..eb30f7e07c8665ad3c8cdb807aa691af52959b2e --- /dev/null +++ b/2023/Learning Discriminative Representations for Skeleton Based Action Recognition/d7b634f0-e078-4d7a-89da-58619960a3b5_model.json @@ -0,0 +1,2068 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.082, + 0.131, + 0.89, + 0.152 + ], + "angle": 0, + "content": "Learning Discriminative Representations for Skeleton Based Action Recognition" + }, + { + "type": "text", + "bbox": [ + 0.291, + 0.18, + 0.687, + 0.199 + ], + "angle": 0, + "content": "Huanyu Zhou\\(^{1}\\), Qingjie Liu\\(^{1,2,3,*}\\), Yunhong Wang\\(^{1}\\)" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.199, + 0.893, + 0.234 + ], + "angle": 0, + "content": "\\(^{1}\\)State Key Laboratory of Virtual Reality Technology and Systems, Beihang University, Beijing, China \\(^{2}\\)Zhongguancun Laboratory, \\(^{3}\\)Hangzhou Innovation Institute of Beihang University" + }, + { + "type": "text", + "bbox": [ + 0.302, + 0.237, + 0.673, + 0.252 + ], + "angle": 0, + "content": "{zhysora, qingjie.liu, yhwang}@buaa.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.287, + 0.313, + 0.303 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.319, + 0.474, + 0.652 + ], + "angle": 0, + "content": "Human action recognition aims at classifying the category of human action from a segment of a video. Recently, people have dived into designing GCN-based models to extract features from skeletons for performing this task, because skeleton representations are much more efficient and robust than other modalities such as RGB frames. However, when employing the skeleton data, some important clues like related items are also discarded. It results in some ambiguous actions that are hard to be distinguished and tend to be misclassified. To alleviate this problem, we propose an auxiliary feature refinement head (FR Head), which consists of spatial-temporal decoupling and contrastive feature refinement, to obtain discriminative representations of skeletons. Ambiguous samples are dynamically discovered and calibrated in the feature space. Furthermore, FR Head could be imposed on different stages of GCNs to build a multi-level refinement for stronger supervision. Extensive experiments are conducted on NTU RGB+D, NTU RGB+D 120, and NW-UCLA datasets. Our proposed models obtain competitive results from state-of-the-art methods and can help to discriminate those ambiguous samples. Codes are available at https://github.com/zhysora/FR-Head." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.682, + 0.208, + 0.699 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.709, + 0.469, + 0.829 + ], + "angle": 0, + "content": "In human-to-human communication, action plays a particularly important role. The behaviors convey intrinsic information like emotions and potential intentions and thus help to understand the person. Empowering intelligent machines with the same ability to understand human behaviors is critical for natural human-computer interaction and many other practical applications, and has been attracting much attention recently." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.83, + 0.469, + 0.876 + ], + "angle": 0, + "content": "Nowadays, obtaining 2D/3D skeletons of humans has become much easier thanks to the advanced sensor technology and human pose estimation algorithms. Skeletons" + }, + { + "type": "image", + "bbox": [ + 0.516, + 0.292, + 0.885, + 0.589 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.606, + 0.892, + 0.66 + ], + "angle": 0, + "content": "Figure 1. There are some actions that are hard to recognize because the skeleton representations lack important interactive objects and contexts, which make them easily confused with each other." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.893, + 0.854 + ], + "angle": 0, + "content": "are compact and robust representations that are immune to viewpoint changes and cluttered backgrounds, making them attractive for action recognition. A typical way to use skeletons for action recognition is to build Graph Convolutional Networks (GCNs) [38]. The joints and bones in the human body naturally form graphs, which make GCNs a perfect tool to extract topological features of skeletons. GCN-based methods have become more and more popular, with another merit that the models can be built lightweight and have high computational efficiency compared with models processing video frames." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "However, using skeletons to recognize actions has some limitations. A major problem is that skeleton representation lacks important interactive objects and contextual informa" + }, + { + "type": "page_footnote", + "bbox": [ + 0.095, + 0.887, + 0.22, + 0.9 + ], + "angle": 0, + "content": "*Corresponding author" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10608" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.471, + 0.182 + ], + "angle": 0, + "content": "tion for distinguishing similar actions. As shown in Fig. 1, it is hard to distinguish \"Writing\", \"Reading\" and \"Typing on a keyboard\" based on the skeleton view alone. In contrast, a model can recognize them from RGB frames by focusing on the related items. These actions are easily confused with each other and should be given more attention." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.183, + 0.474, + 0.485 + ], + "angle": 0, + "content": "To alleviate this drawback, we propose a feature refinement module using contrastive learning to lift the discriminative ability of features between ambiguous actions. We first decouple hidden features into spatial and temporal components so that the network can better focus on discriminative parts among ambiguous actions along the topological and temporal dimensions. Then we identify the confident and ambiguous samples based on the model prediction during training. Confident samples are used to maintain a prototype for each class, which is achieved by a contrastive learning loss to constrain intra-class and inter-class distances. Meanwhile, ambiguous samples are calibrated by being closer to or far away from confident samples in the feature space. Furthermore, the aforementioned feature refinement module can be embedded into multiple types of GCNs to improve hierarchical feature learning. It will produce a multi-level contrastive loss, which is jointly trained with the classification loss to improve the performance of ambiguous actions. Our main contributions are summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.094, + 0.498, + 0.47, + 0.619 + ], + "angle": 0, + "content": "- We propose a discriminative feature refinement module to improve the performance of ambiguous actions in skeleton based action recognition. It uses contrastive learning to constrain the distance between confident samples and ambiguous samples. It also decouples the raw feature map into spatial and temporal components in a lightweight way for efficient feature enhancement." + }, + { + "type": "text", + "bbox": [ + 0.094, + 0.63, + 0.47, + 0.692 + ], + "angle": 0, + "content": "- The feature refinement module is plug-and-play and compatible with most GCN-based models. It can be jointly trained with other losses but discarded in the inference stage." + }, + { + "type": "text", + "bbox": [ + 0.094, + 0.702, + 0.47, + 0.778 + ], + "angle": 0, + "content": "- We conduct extensive experiments on NTU RGB+D, NTU RGB+D 120, and NW-UCLA datasets to compare our proposed methods with the state-of-the-art models. Experimental results demonstrate the significant improvement of our methods." + }, + { + "type": "list", + "bbox": [ + 0.094, + 0.498, + 0.47, + 0.778 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.792, + 0.22, + 0.808 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.817, + 0.3, + 0.833 + ], + "angle": 0, + "content": "2.1. Human Pose Estimation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Human pose estimation is an essential building block for a wide range of intelligent systems in fields such as AR, sports analysis, and healthcare, thus receiving much attention in recent years. Recent approaches leverage the" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.213 + ], + "angle": 0, + "content": "temporal information of 2D pose sequences to alleviate the depth ambiguity in 3D poses [1, 13, 19, 20, 23]. Hossain et al. [13] tackle the task as a sequence-to-sequence problem and build RNNs to learn the mapping. Cai et al. [1] exploit the spatial-temporal relations from the 2D sequences via an encoder-decoder like GCN. Li et al. [19] use Transformer [31] to capture the long-range relationships in the 2D pose sequence." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.222, + 0.806, + 0.239 + ], + "angle": 0, + "content": "2.2. Skeleton Based Action Recognition" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.245, + 0.895, + 0.395 + ], + "angle": 0, + "content": "Action recognition benefits a lot from human pose estimation. Early works treat the recognition as a sequence classification task. Su et al. [30] design an auto-encoder with RNNs to learn high-level features from the sequence. Another stream converts the skeleton sequence to image-like data using hand-crafted schemes [9, 37]. Duan et al. [10] concatenate an RGB frame with a 2D skeleton heat map and use 3D CNNs to extract features. These works do not explicitly exploit the spatial structure of the human body." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.397, + 0.895, + 0.58 + ], + "angle": 0, + "content": "The mainstream in this field is to use GCNs to extract the high-level features from skeletons since the joints and bones in the human body naturally construct a graph [5,22,38,42]. In this way, the topology of the human body is fully exploited. Yan et al. [38] is the first attempt to use GCNs for skeleton based human action recognition. They define the basic connections of spatial and temporal dimensions and introduce an efficient pipeline. Zhang et al. [42] build a two-stream architecture for both joint and bone modalities. Chen et al. [5] improve the design of GCNs in [38] and propose to dynamically learn different topologies and effectively aggregate joint features in each channel." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.588, + 0.704, + 0.604 + ], + "angle": 0, + "content": "2.3. Contrastive Learning" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.612, + 0.894, + 0.839 + ], + "angle": 0, + "content": "Recently, contrastive learning has achieved remarkable progress in diverse fields. Typically, contrastive learning requires generating a set of transformed versions (or \"views\") of an image using data augmentations, then training the network to distinguish the different views of the image. Chen et al. [2] explore the strategies of data augmentations and use a huge batch size to obtain the enhanced representation. He et al. [3,4,12] realize contrastive learning in a more efficient way using a momentum encoder and a dynamic queue. Wang et al. [33] define the positive and negative samples in a supervised manner. They design a metric function loss to calibrate these misclassified feature representations for better intra-class consistency and segmentation performance. Inspired by this, our work tries to use a similar spirit to refine the skeleton representations for ambiguous actions." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.848, + 0.688, + 0.864 + ], + "angle": 0, + "content": "2.4. Ambiguous Sample" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.894, + 0.903 + ], + "angle": 0, + "content": "Most of the recognition tasks for solving ambiguous samples focus on fine-grained image classification. For ex" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "10609" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.092, + 0.878, + 0.472 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.353, + 0.483, + 0.616, + 0.499 + ], + "angle": 0, + "content": "Figure 2. overview of the proposed method." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.525, + 0.47, + 0.66 + ], + "angle": 0, + "content": "ample, Lin et al. [32] perform bilinear pooling on the representations of two local patches to learn the discriminative feature. Dubey et al. [11] model similarity between image pairs and leverage metric learning to improve the feature distributions. Zhuang et al. [43] design a module to adaptively discover contrastive cues from a pair of images and attentively distinguish them via pairwise interaction. However, we have not found works that aim at solving skeleton-based action recognition." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.675, + 0.212, + 0.692 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.701, + 0.471, + 0.731 + ], + "angle": 0, + "content": "We now give the details of our method. The overview of it is depicted in Fig. 2." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.742, + 0.192, + 0.756 + ], + "angle": 0, + "content": "3.1. Backbone" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.47, + 0.901 + ], + "angle": 0, + "content": "The input of our model is a sequence of skeletons with a shape of \\( T \\times V \\times 3 \\), which means \\( T \\) frames of \\( V \\) joints in a 3D space. We build our approach on [5]. However, we will show in the experimental section that it can improve any GCNs. The backbone consists of 10 basic units, termed TGN. TGN is constructed by a series of Temporal CNNs (TCNs) and Graph Convolution Networks (GCNs). Concretely, TCNs extract the temporal features by imposing 1D CNNs on the temporal dimension; GCNs extract the spa" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.524, + 0.892, + 0.661 + ], + "angle": 0, + "content": "tial features with a learnable topological graph defined on the spatial dimension. Note that two of the basic units are stripped TGNs implemented by stripped 1D CNNs. They are used to generate multi-scale features by decreasing the temporal dimension while increasing the channel dimension. Then, a pooling layer is applied to get the 1D high-level feature vectors. Finally, a fully-connected (FC) layer with softmax activation maps the feature to a probability distribution of \\( K \\) candidate categories." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.663, + 0.892, + 0.723 + ], + "angle": 0, + "content": "It is noted that the detailed implementation of the backbone is not the main concern of our method. The implementation of the basic unit can be replaced by any other GCN-based networks like [26, 38]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.739, + 0.734, + 0.754 + ], + "angle": 0, + "content": "3.2. Feature Refinement Head" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Our main idea is to improve the performance of the skeleton based model on ambiguous actions that are quite similar and easily misclassified. To achieve this, we propose a plug-and-play module to optimize multi-level features within the backbone network, termed Feature Refinement Head (FR Head). It first decouples the hidden feature maps into spatial and temporal components and then applies a contrastive learning loss with global class prototypes and ambiguous samples. It is worth noting that the proposed FR" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "10610" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.122 + ], + "angle": 0, + "content": "Head is added only for training. There is no additional computational cost or memory consumption during inference." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.145, + 0.338, + 0.159 + ], + "angle": 0, + "content": "3.2.1 Multi-Level Feature Selection" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.17, + 0.471, + 0.321 + ], + "angle": 0, + "content": "To learn more discriminative feature representations, we divide the backbone into four stages, respectively at the 1st, 5th, 8th, and last layer of TGN, and impose a FR Head on each of them. The 5th and the 8th layers employ a strided operation. Each FR Head refines the corresponding hidden features by calculating a contrastive learning (CL) loss, whose details will be discussed in Section 3.2.3. To balance the different levels, we add a weighting parameter for each stage and the multi-level CL loss can be defined as a weighted average sum:" + }, + { + "type": "equation", + "bbox": [ + 0.202, + 0.336, + 0.47, + 0.376 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {C L} = \\sum_ {i = 1} ^ {4} \\lambda_ {i} \\cdot \\mathcal {L} _ {C L} ^ {i} \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.385, + 0.471, + 0.432 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_{CL}\\) is the multi-level CL loss, \\(\\lambda_{i}\\) is the hyperparameter to control stage \\(i\\) and \\(\\mathcal{L}_{CL}^{i}\\) is the local CL loss calculated by stage \\(i\\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.453, + 0.338, + 0.469 + ], + "angle": 0, + "content": "3.2.2 Spatial-Temporal Decoupling" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.479, + 0.47, + 0.538 + ], + "angle": 0, + "content": "Due to the complexity of human activities, coarse modelling features will lead to confusion between ambiguous actions with similar spatial appearances or temporal transformations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.54, + 0.47, + 0.659 + ], + "angle": 0, + "content": "For example, \"put sth. into a bag\" can be easily distinguished from \"take sth. out of a bag\" using temporal clues. However, compared to the \"reach into pockets\", more concentrations on the spatial information are required. Therefore, we propose a spatial-temporal decouple module that mines the spatial and temporal information simultaneously to improve the discriminative ability of action representations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.661, + 0.47, + 0.812 + ], + "angle": 0, + "content": "As Fig. 2 describes, the raw feature map is fed into two parallel branches for efficient feature enhancement. Concretely, each branch comprises a spatial/temporal pooling layer which only keeps the average value of the related dimension and a \\(1 \\times 1\\) convolution layer which is used to squeeze the feature to a fixed size. Then the output feature is flattened to a unified representation with the channel size of \\(C_h\\). Finally, a CL loss is added on top of each branch. We accomplish the Spatial-Temporal Decoupling feature refinement by summing losses from the two branches:" + }, + { + "type": "equation", + "bbox": [ + 0.182, + 0.829, + 0.469, + 0.848 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {C L} ^ {i} = \\operatorname {C L} \\left(F _ {s} ^ {i}\\right) + \\operatorname {C L} \\left(F _ {t} ^ {i}\\right) \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.855, + 0.47, + 0.903 + ], + "angle": 0, + "content": "where \\( F_{s}^{i} \\) and \\( F_{t}^{i} \\) stand for the spatial feature and the temporal feature of stage \\( i \\), respectively. \\( \\mathrm{CL}(\\cdot) \\) is the function to calculate the CL loss with a specific feature vector." + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.087, + 0.895, + 0.305 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.315, + 0.894, + 0.344 + ], + "angle": 0, + "content": "Figure 3. Discovering the confident and ambiguous samples for action \"writing\"." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.371, + 0.779, + 0.385 + ], + "angle": 0, + "content": "3.2.3 Contrastive Feature Refinement" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.394, + 0.893, + 0.455 + ], + "angle": 0, + "content": "As Fig. 2 shows, we conduct the feature refinement in a manner of contrastive learning. The idea is inspired by [33]. Each sample will be refined by both its ground truth actions and other ambiguous actions." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.455, + 0.892, + 0.608 + ], + "angle": 0, + "content": "Confident Sample Clustering. Given an action label \\( k \\), if a sample is predicted correctly, namely as a True Positive (TP), we consider it a confident sample to distinguish it from ambiguous samples. Apparently, features from confident samples tend to have better intra-class consistency. As Fig. 3 shows, we gather those features to update the global representation (i.e., prototype) of the corresponding classes via exponential moving average (EMA). Assuming \\( s_{TP}^{k} \\) is the set of confident samples for action \\( k \\) in a batch and its size is \\( n_{TP}^{k} \\), the EMA operation can be defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.565, + 0.617, + 0.892, + 0.657 + ], + "angle": 0, + "content": "\\[\nP _ {k} = (1 - \\alpha) \\cdot \\frac {1}{n _ {T P} ^ {k}} \\sum_ {i \\in s _ {T P} ^ {k}} F _ {i} + \\alpha \\cdot P _ {k} \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.663, + 0.892, + 0.8 + ], + "angle": 0, + "content": "where \\(P_{k}\\) is the prototype of action \\(k\\), \\(F_{i}\\) is the feature extracted from sample \\(i\\). \\(\\alpha\\) is the momentum term, we set it to 0.9 by experience. Over the training procedure, the prototype becomes a stable estimation of the clustering center for action \\(k\\). It is capable of refining the feature of a newly arrived sample. Each sample should be close to the related prototype while far away from other prototypes. The distance between two feature vectors is defined as \\(\\mathrm{dis}(\\cdot ,\\cdot)\\), which is implemented by cosine distance:" + }, + { + "type": "equation", + "bbox": [ + 0.614, + 0.81, + 0.892, + 0.845 + ], + "angle": 0, + "content": "\\[\n\\operatorname {d i s} (\\boldsymbol {u}, \\boldsymbol {v}) = \\frac {\\boldsymbol {u} \\boldsymbol {v} ^ {T}}{| | \\boldsymbol {u} | | _ {2} | | \\boldsymbol {v} | | _ {2}} \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.855, + 0.84, + 0.871 + ], + "angle": 0, + "content": "where \\(\\mathbf{u},\\mathbf{v}\\) stand for 1D vectors. \\(\\| \\cdot \\| _2\\) is \\(L_{2}\\) norm." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Ambiguous Sample Discovering. To discover the ambiguous samples during the training stages, we gather the" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "10611" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.242 + ], + "angle": 0, + "content": "misclassified samples which tend to be quite similar to other categories. Given an action label \\( k \\), there are two types of ambiguous samples. If a sample of action \\( k \\) is misclassified as other categories, it is termed as False Negative (FN). If a sample of other categories is misclassified as action \\( k \\), it is termed as False Positive (FP). Supposing \\( s_{FN}^{k}, s_{FP}^{k} \\) are sets of FN and FP samples for action \\( k \\) and the sizes of them are \\( n_{FN}^{k}, n_{FP}^{k} \\). As fig. 3 shows, We gather those samples in a batch and calculate the mean values as the center representations:" + }, + { + "type": "equation", + "bbox": [ + 0.101, + 0.248, + 0.47, + 0.289 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {\\mu} _ {F N} ^ {k} = \\frac {1}{n _ {F N} ^ {k}} \\sum_ {j \\in s _ {F N} ^ {k}} F _ {j}, \\quad \\boldsymbol {\\mu} _ {F P} ^ {k} = \\frac {1}{n _ {F P} ^ {k}} \\sum_ {j \\in s _ {F P} ^ {k}} F _ {j} \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.298, + 0.47, + 0.374 + ], + "angle": 0, + "content": "where \\(\\pmb{\\mu}_{FN}^{k},\\pmb{\\mu}_{FP}^{k}\\) stand for the center representation of FN and FP samples of class \\(k\\). Note that, we do not maintain a global representation for those ambiguous samples because the prediction of those samples is not stable in the training stage and the amount is much less than TP samples." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.375, + 0.47, + 0.45 + ], + "angle": 0, + "content": "Ambiguous Sample Calibration. To calibrate the prediction of ambiguous samples, we take confident sample \\(i\\) of action \\(k\\) as the anchor and calculate an auxiliary term in the feature space. For those FN samples which should be classified as action \\(k\\), a compensation term \\(\\phi_{i}\\) is introduced:" + }, + { + "type": "equation", + "bbox": [ + 0.09, + 0.459, + 0.469, + 0.5 + ], + "angle": 0, + "content": "\\[\n\\phi_ {i} = \\left\\{ \\begin{array}{c} 1 - \\operatorname {d i s} \\left(F _ {i}, \\boldsymbol {\\mu} _ {F N} ^ {k}\\right), \\text {i f} i \\in s _ {T P} ^ {k} \\text {a n d} n _ {F N} ^ {k} > 0; \\\\ 0, \\text {o t h e r w i s e .} \\end{array} \\right. \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.507, + 0.469, + 0.596 + ], + "angle": 0, + "content": "By minimizing the compensation term \\(\\phi_{i}\\), FN samples are supposed to be closer to the confident sample in the feature space. When there are no FN samples or the cosine distance converges to 1, \\(\\phi_{i}\\) reaches the minimum value 0. This may motivate the model to correct these ambiguous samples as action \\(k\\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.598, + 0.469, + 0.628 + ], + "angle": 0, + "content": "On the other hand, for those FP samples which belong to other categories, a penalty term \\(\\psi_{i}\\) is introduced:" + }, + { + "type": "equation", + "bbox": [ + 0.091, + 0.637, + 0.469, + 0.677 + ], + "angle": 0, + "content": "\\[\n\\psi_ {i} = \\left\\{ \\begin{array}{c} 1 + \\operatorname {d i s} \\left(F _ {i}, \\boldsymbol {\\mu} _ {F P} ^ {k}\\right), \\text {i f} i \\in s _ {T P} ^ {k} \\text {a n d} n _ {F P} ^ {k} > 0; \\\\ 0, \\text {o t h e r w i s e .} \\end{array} \\right. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.686, + 0.469, + 0.775 + ], + "angle": 0, + "content": "Similarly, the penalty term \\(\\psi_{i}\\) penalizes the distance between the FP samples and the confident samples in the feature space. When there are no FP samples or the cosine distance converges to \\(-1\\), \\(\\psi_{i}\\) reaches the minimum value 0. This may prevent the model from recognizing these ambiguous samples as action \\(k\\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.776, + 0.469, + 0.805 + ], + "angle": 0, + "content": "Finally, taking sample \\( i \\) as an anchor, the proposed CL loss function can be defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.077, + 0.812, + 0.476, + 0.902 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\operatorname {C L} \\left(F _ {i}\\right) = - \\log \\frac {e ^ {\\operatorname {d i s} \\left(F _ {i} , P _ {k}\\right) / \\tau - (1 - p _ {i k}) \\psi_ {i}}}{e ^ {\\operatorname {d i s} \\left(F _ {i} , P _ {k}\\right) / \\tau - (1 - p _ {i k}) \\psi_ {i}} + \\sum_ {l \\neq k} e ^ {\\operatorname {d i s} \\left(F _ {i} , P _ {l}\\right) / \\tau}} \\\\ - \\log \\frac {e ^ {\\operatorname {d i s} \\left(F _ {i} , P _ {k}\\right) / \\tau - \\left(1 - p _ {i k}\\right) \\phi_ {i}}}{e ^ {\\operatorname {d i s} \\left(F _ {i} , P _ {k}\\right) / \\tau - \\left(1 - p _ {i k}\\right) \\psi_ {i}} + \\sum_ {l \\neq k} e ^ {\\operatorname {d i s} \\left(F _ {i} , P _ {l}\\right) / \\tau}} \\tag {8} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.152 + ], + "angle": 0, + "content": "where \\( p_{ik} \\) is the predicted probability score of sample \\( i \\) for class \\( k \\). It means that the TP samples with weaker confidence get stronger supervision from those ambiguous samples." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.164, + 0.682, + 0.18 + ], + "angle": 0, + "content": "3.3. Training Objective" + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.188, + 0.874, + 0.203 + ], + "angle": 0, + "content": "We use Cross-Entropy (CE) loss to train our network:" + }, + { + "type": "equation", + "bbox": [ + 0.586, + 0.215, + 0.892, + 0.25 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {C E} = - \\frac {1}{N} \\sum_ {i} \\sum_ {c} y _ {i c} \\log \\left(p _ {i c}\\right) \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.262, + 0.892, + 0.336 + ], + "angle": 0, + "content": "where \\(N\\) is the number of samples in a batch. \\(y_{ic}\\) is the one-hot presentation of the label of sample \\(i\\). If and only if \\(c\\) is the target class of sample \\(i\\), \\(y_{ic} = 1\\). \\(p_{ic}\\) is the probability score of sample \\(i\\) belonging to class \\(k\\) predicted by the network." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.339, + 0.892, + 0.369 + ], + "angle": 0, + "content": "Finally, CE loss is combined with our proposed multilevel CL loss to form the full learning objective function:" + }, + { + "type": "equation", + "bbox": [ + 0.618, + 0.383, + 0.891, + 0.399 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {C E} + w _ {c l} \\cdot \\mathcal {L} _ {C L} \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.412, + 0.892, + 0.442 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_{CL}\\) and \\(\\mathcal{L}_{CE}\\) are defined in Eqs. 1 and 9. \\(w_{cl}\\) is the balanced hyper-parameter for CL loss." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.458, + 0.632, + 0.475 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.484, + 0.602, + 0.498 + ], + "angle": 0, + "content": "4.1. Datasets" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.507, + 0.892, + 0.704 + ], + "angle": 0, + "content": "NTU RGB+D. NTU RGB+D [24] is a widely used dataset containing 56,880 samples. 40 participants are invited to perform 60 actions including daily behaviors and health-related actions. Each action is performed by 1 or 2 people. The human skeleton is presented by 25 3D joints, which are captured by 3 Microsoft Kinect v2 cameras with different horizontal angle settings. It provides two benchmarks: (1) Cross-Subject (X-Sub): the dataset is divided according to the subjects. The training set consists of 20 subjects while the testing set consists of other 20 subjects. (2) Cross-View (X-View): the dataset is split by the camera views. They select camera views 2 and 3 to construct the training data while camera view 1 is used for testing." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.892, + 0.901 + ], + "angle": 0, + "content": "NTU RGB+D 120. NTU RGB+D 120 [21] extends NTU RGB+D with extra 57,367 samples by introducing new 60 action classes, making it the largest skeleton based action recognition dataset. In total, it collects 113,945 skeleton sequences over 120 different classes performed by 106 participants. It also increases the number of camera setups to 32 by using different places and backgrounds. Two evaluation protocols are recommended: (1) Cross-Subject (X-Sub): samples from 56 subjects are selected to form the training set, and the reaming 50 subjects are used for testing. (2) Cross-Set (X-Set): samples with even setup IDs are used for training, while samples with odd setup IDs are used for testing." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10612" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.47, + 0.118 + ], + "angle": 0, + "content": "Table 1. Ablation studies of our method on NTU-RGB+D 120 dataset under the X-Sub setting with the joint input modality." + }, + { + "type": "table", + "bbox": [ + 0.136, + 0.129, + 0.413, + 0.253 + ], + "angle": 0, + "content": "
MethodParams.Acc (%)
Baseline1.46M84.5
+ CL Loss1.53M85.0↑0.5
+ ST Decouple1.59M85.3↑0.8
+ ML Refine1.61M84.7↑0.2
Ours1.99M85.5↑1.0
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.266, + 0.47, + 0.308 + ], + "angle": 0, + "content": "Table 2. Hyper-parameter exploration of our proposed method on NTU-RGB+D 120 dataset under the X-Sub setting with the joint input modality. The best one is in **bold**." + }, + { + "type": "table", + "bbox": [ + 0.13, + 0.318, + 0.419, + 0.511 + ], + "angle": 0, + "content": "
wclλ1λ2λ3λ4Acc (%)
1000184.4
0.1000185.3
0.01000185.0
111184.5
10.20.2184.7
10.50.20.184.1
0.10.10.11185.2
0.10.10.1185.1
0.10.20.2185.4
0.10.20.5185.5
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.536, + 0.47, + 0.643 + ], + "angle": 0, + "content": "NW-UCLA. Northwestern-UCLA dataset [34] contains 1494 video clips performed by 10 volunteers. 3 Kinect cameras are used to capture 3D skeletons with 20 joints from multiple views. Totally 10 action categories are covered. We adopt the evaluation protocols recommended by the author: training data comes from the first two cameras, while testing data is from the other camera." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.651, + 0.295, + 0.667 + ], + "angle": 0, + "content": "4.2. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.675, + 0.471, + 0.901 + ], + "angle": 0, + "content": "We adopt [5] as the backbone and implement the proposed method with the PyTorch deep learning framework. All experiments are conducted on one RTX 2080Ti GPU. The Stochastic Gradient Descent (SGD) optimizer is employed with a momentum of 0.9 and a weight decay of 0.0004 to train the models. In the first 5 epochs, we apply a warmup strategy for stable training. The initial learning rate is set to 0.1 and we decrease it at epoch 35 and 55 with a factor of 0.1. We train all models with 70 epochs and select the best performance. The base channel \\( C \\) is set to 64 and the hidden channel \\( C_h \\) is set to 256. The hyper-parameters in our methods are set as: \\( \\lambda_1 = 0.1 \\), \\( \\lambda_2 = 0.2 \\), \\( \\lambda_3 = 0.5 \\), \\( \\lambda_4 = 1 \\), \\( w_{cl} = 0.1 \\). For NTU RGB+D and NTU RGB+D 120, we follow the data preprocessing in [41] and set the batch size to 64. All samples are resized to 64 frames. For NW" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.121 + ], + "angle": 0, + "content": "UCLA, we follow the data preprocessing in [8] and set the batch size to 16." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.132, + 0.655, + 0.149 + ], + "angle": 0, + "content": "4.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.156, + 0.892, + 0.216 + ], + "angle": 0, + "content": "We conduct ablation studies and evaluate the different hyper-parameter settings on the X-Sub benchmark of NTU RGB+D 120 dataset to verify the effectiveness of the proposed module." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.217, + 0.893, + 0.474 + ], + "angle": 0, + "content": "The results of ablation studies are displayed in Table 1. We remove all additional heads and train the network with CE loss to build the baseline. We also divide the proposed module into different sub-modules and design 3 variants: (1) CL Loss: we directly employ the CL loss to refine features from the last layer without any additional operations. (2) ST Decouple: we decouple the features into spatial and temporal components before refinement. (3) ML Refine: we impose the refinement on proposed multi-level stages in the training pipeline. It can be seen that all these sub-modules can improve the performance of the baseline. Among them, the contributions from CL loss and ST Decouple are relatively dominant. Moreover, when combining all of them, the result becomes better. We also report the count of trainable parameters of different models. The extra cost of parameters may increase the time of the training procedure but does not affect the inference stage." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.475, + 0.893, + 0.747 + ], + "angle": 0, + "content": "We analyze the configurations on the hyper-parameters of our method, and the results are available in Table 2. First, we try 3 different values of \\( w_{cl} \\) to find the balance between the CL loss and CE loss with the fixed combination of \\( \\lambda_1 = \\lambda_2 = \\lambda_3 = 0, \\lambda_4 = 1 \\) for an efficient experiment. It seems that bigger \\( w_{cl} \\) may hurt the performance while too small values only provide a little improvement. Then, we try more combinations of \\( \\lambda_i \\) to balance the importance of different stages. From the results, we can observe that giving higher weight to the previous layers may obtain negative influence and increase the importance gradually from the early stage to the last stage and thus lead to an optimal result. It is concluded that the refinement of the high-level features from the final stage plays a major role and the low-level features provide the auxiliary effects. Finally, we choose the configuration of \\( \\lambda_1 = 0.1, \\lambda_2 = 0.2, \\lambda_3 = 0.5, \\lambda_4 = 1, w_{cl} = 0.1 \\) for the following experiments." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.757, + 0.794, + 0.772 + ], + "angle": 0, + "content": "4.4. Combined with Other Backbones" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Our proposed module is plug-and-play and compatible with most GCN-based backbones. To examine its universality, we apply it to 5 widely used GCN-based backbones [5, 17, 26, 35, 38] and evaluate them on the X-Sub and X-Set of NTU RGB+D 120 dataset. For fair comparisons, we reimplement them and use the same data preprocessing without the multi-stream fusion. Table 3 reports the performance and number of parameters of different methods. It is" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10613" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.472, + 0.132 + ], + "angle": 0, + "content": "Table 3. Performance of our proposed method using different GCN-based backbones on NTU-RGB+D 120 dataset with the joint input modality." + }, + { + "type": "table", + "bbox": [ + 0.078, + 0.143, + 0.479, + 0.372 + ], + "angle": 0, + "content": "
MethodParams.NTU-RGB+D 120
X-Sub (%)X-Set (%)
ST-GCN [38]2.11M83.485.1
+ FR Head2.65M84.4↑1.086.5↑1.4
2s-AGCN [26]3.80M84.385.9
+ FR Head4.33M84.6↑0.386.6↑0.7
CTR-GCN [5]1.46M84.586.6
+ FR Head1.99M85.5↑1.087.3↑0.7
TCA-GCN [35]5.65M85.086.3
+ FR Head6.18M85.2↑0.287.4↑1.1
HD-GCN [17]1.68M85.187.2
+ FR Head2.21M85.4↑0.387.7↑0.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.383, + 0.471, + 0.426 + ], + "angle": 0, + "content": "Table 4. Accuracy (\\%) on different difficult level actions for NTU-RGB+D 120 dataset under the X-Sub setting with the joint input modality." + }, + { + "type": "table", + "bbox": [ + 0.124, + 0.437, + 0.426, + 0.57 + ], + "angle": 0, + "content": "
MethodNTU-RGB+D 120
HardMediumEasy
ST-GCN [38]57.480.994.7
2s-AGCN [26]58.982.095.0
CTR-GCN [5]59.682.495.1
Ours61.683.395.7
Δ2.00.90.6
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.595, + 0.47, + 0.732 + ], + "angle": 0, + "content": "observed that all models obtain an obvious gain of accuracy by employing the FR Head. The improvement is around \\(1.0\\%\\). In most cases, the models with lower accuracy are improved more than those with higher initial accuracy. The reason behind it may be that our modules utilize the knowledge from the misclassified samples. The lower accuracy of means the misclassified samples are more sufficient. The additional count of parameters introduced by the FR Head is around 0.5M and can be ignored in the inference stage." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.741, + 0.391, + 0.759 + ], + "angle": 0, + "content": "4.5. Performance on Ambiguous Actions" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.47, + 0.903 + ], + "angle": 0, + "content": "We spilt NTU-RGB+D 120 dataset into 3 subsets with different difficulty levels. Specifically, according to the results of CTR-GCN [5], we gather actions whose accuracy is lower than \\(70\\%\\) as Hard Level, between \\(70\\%\\) and \\(90\\%\\) as Medium Level, and over \\(90\\%\\) as Easy Level. The results are displayed in Table 4. The experiment is under the X-Subsetting with only the joint input modality. Because ambiguous actions are quite similar and easy to be misclassified, these actions usually fall into Hard Level. From the" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.093, + 0.891, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.251, + 0.895, + 0.308 + ], + "angle": 0, + "content": "Figure 4. The group-wise accuracy difference \\((\\%)\\) between our method and CTR-GCN [5] on ambiguous actions for NTU-RGB+D 120 dataset under the X-Sub setting with the joint input modality." + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.324, + 0.891, + 0.439 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.448, + 0.892, + 0.505 + ], + "angle": 0, + "content": "Figure 5. Visualization of latent representation by t-SNE for ambiguous groups from NTU RGB+D 120 dataset. Different colors indicate different classes. The upper one is from the CTR-GCN [5], while the bottom one is from our method." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.535, + 0.892, + 0.581 + ], + "angle": 0, + "content": "results, we can see that our method makes a great improvement in Hard Level actions, which demonstrates the ability to distinguish those ambiguous actions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.582, + 0.893, + 0.809 + ], + "angle": 0, + "content": "Furthermore, we define ambiguous groups, which collect several related ambiguous actions to verify the performance of ambiguous samples. We first pick a class as an anchor class, for example, \"writing\". Then we gather the misclassified samples on \"writing\" and obtain the top-3 actions with the highest frequency, like \"reading\", \"typing on a keyboard\" and \"playing with phone\". These 4 actions will be constructed as an ambiguous group. The group-wise accuracy will be the average accuracy of all actions included by the group. Here, we randomly pick 60 anchor actions and constructed corresponding ambiguous groups from NTU-RGB+D 120 dataset. We compare our results with a SOTA model CTR-GCN [5] and display the results in Fig. 4. Our method gains great improvement in most ambiguous groups." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.894, + 0.903 + ], + "angle": 0, + "content": "We randomly pick some ambiguous groups and visualize the distribution of them in the feature space using t-SNE. As mentioned before, each ambiguous group contains four classes, including an anchor class and three ambiguous classes. We compare our method with CTR-GCN [5]. Fig. 5 shows that our model achieves a more compact clustering." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "10614" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.894, + 0.119 + ], + "angle": 0, + "content": "Table 5. Performance comparison of skeleton-based action recognition in top-1 accuracy (\\%). The best one is in bold and the second one is underlined." + }, + { + "type": "table", + "bbox": [ + 0.147, + 0.128, + 0.825, + 0.484 + ], + "angle": 0, + "content": "
MethodPublicationNTU RGB+DNTU RGB+D 120NW-UCLA
X-SubX-ViewX-SubX-Set
ST-GCN [38]AAAI201881.588.3---
Ind-RNN [18]CVPR201881.888.0---
RotClips+MTCNN [15]TIP2018--62.261.8-
2s-AGCN [26]CVPR201988.595.182.984.9-
AGC-LSTM [27]CVPR201989.295.0--93.3
DGNN [25]CVPR201989.996.1---
PA-ResGCN-B19 [28]ACMMM202090.996.087.388.3-
Dynamic GCN [39]ACMMM202091.596.087.388.6-
SGN [41]CVPR202089.094.579.281.5-
Shift-GCN [8]CVPR202090.796.585.987.694.6
MS-G3D [22]CVPR202091.596.286.988.4-
DDGCN [16]ECCV202091.197.1---
DC-GCN+ADG [7]ECCV202090.896.686.588.195.3
MST-GCN [6]AAAI202191.596.687.588.8-
Skeletal-GNN [40]ICCV202191.696.787.589.2-
CTR-GCN [5]ICCV202192.496.888.990.696.5
STF [14]AAAI202292.596.988.989.9-
Ta-CNN [36]AAAI202290.494.885.486.896.1
EfficientGCN-B4 [29]TPAMI202291.795.788.389.1-
Ours-92.896.889.590.996.8
" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.509, + 0.407, + 0.526 + ], + "angle": 0, + "content": "4.6. Comparison with the State-of-the-Art" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.532, + 0.471, + 0.683 + ], + "angle": 0, + "content": "In this section, we conduct a comparison with the state-of-the-art methods on NTU RGB+D 120, NTU RGB+D, and NW-UCLA datasets to demonstrate the competitive ability of our proposed module. The quantitative results are displayed in Table 5. It is noted that most of the state-of-the-art methods employ a multi-stream fusion framework. For a fair comparison, we follow the same framework as [5,35]. We make a fusion with the results from four modalities including joint, bone, joint motion, and bone motion as the final report result." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.684, + 0.47, + 0.835 + ], + "angle": 0, + "content": "It is observed that our methods outperform most existing methods on these three datasets. On both settings of NTU-RGB+D 120, X-Sub of NTU-RGB+D, and NW-UCLA datasets, our model obtains the best results. On X-View of NTU-RGB+D, our model reaches state-of-the-art results with a reasonable gap between the best one, which demonstrates the great potential of our proposed module. Notably, our method is the first to propose a way to solve ambiguous actions, which are very important in skeleton based action recognition." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.845, + 0.196, + 0.862 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.471, + 0.903 + ], + "angle": 0, + "content": "In this paper, we present a novel feature refinement module equipped with contrastive learning to solve the" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.51, + 0.892, + 0.617 + ], + "angle": 0, + "content": "ambiguous actions for skeleton based action recognition. Multi-level features extracted from GCN-based backbone are leveraged and enhanced on both the spatial and temporal dimensions. The contrastive learning is conducted with the samples with high confidence and calibrated by the FP and FN samples to make full use of the misclassified actions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.62, + 0.892, + 0.71 + ], + "angle": 0, + "content": "The extensive experiments demonstrate the effectiveness of the proposed module to distinguish the confusing categories and the university to be compatible with most GCN-based backbones. On three widely used benchmarks, our proposed method obtains satisfactory results and outperforms those state-of-the-art methods." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.715, + 0.892, + 0.852 + ], + "angle": 0, + "content": "Discussion. Despite the performance of our proposed module on three public large-scale datasets, the ambiguous actions in a few-shot setting with insufficient data remain to be explored. We will concentrate on it in our future work. In addition, there are some potential negative societal impacts to be considered. Our method may be applied in some controversial fields, such as surveillance. Besides, applying our module will introduce extra training costs, which should be discussed in the carbon emission problem." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Acknowledgements. This paper was founded by National Natural Science Foundation of China under grants U20B2069 and 62176017." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.958 + ], + "angle": 0, + "content": "10615" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.105 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.197 + ], + "angle": 0, + "content": "[1] Yujun Cai, Liuhao Ge, Jun Liu, Jianfei Cai, Tat-Jen Cham, Junsong Yuan, and Nadia Magnenat Thalmann. Exploiting spatial-temporal relationships for 3d pose estimation via graph convolutional networks. In Proceedings of the IEEE International Conference on Computer Vision, pages 2272-2281, 2019. 2" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.2, + 0.472, + 0.255 + ], + "angle": 0, + "content": "[2] Ting Chen, Simon Kornblith, Mohammad Norouzi, and Geoffrey Hinton. 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Recently, people have dived into designing GCN-based models to extract features from skeletons for performing this task, because skeleton representations are much more efficient and robust than other modalities such as RGB frames. However, when employing the skeleton data, some important clues like related items are also discarded. It results in some ambiguous actions that are hard to be distinguished and tend to be misclassified. To alleviate this problem, we propose an auxiliary feature refinement head (FR Head), which consists of spatial-temporal decoupling and contrastive feature refinement, to obtain discriminative representations of skeletons. Ambiguous samples are dynamically discovered and calibrated in the feature space. Furthermore, FR Head could be imposed on different stages of GCNs to build a multi-level refinement for stronger supervision. Extensive experiments are conducted on NTU RGB+D, NTU RGB+D 120, and NW-UCLA datasets. Our proposed models obtain competitive results from state-of-the-art methods and can help to discriminate those ambiguous samples. Codes are available at https://github.com/zhysora/FR-Head. + +# 1. Introduction + +In human-to-human communication, action plays a particularly important role. The behaviors convey intrinsic information like emotions and potential intentions and thus help to understand the person. Empowering intelligent machines with the same ability to understand human behaviors is critical for natural human-computer interaction and many other practical applications, and has been attracting much attention recently. + +Nowadays, obtaining 2D/3D skeletons of humans has become much easier thanks to the advanced sensor technology and human pose estimation algorithms. Skeletons + +![](images/952023fb34e46a439957a7f3c6804a64de423d59d971732dbd3cb0fdff6312d8.jpg) +Figure 1. There are some actions that are hard to recognize because the skeleton representations lack important interactive objects and contexts, which make them easily confused with each other. + +are compact and robust representations that are immune to viewpoint changes and cluttered backgrounds, making them attractive for action recognition. A typical way to use skeletons for action recognition is to build Graph Convolutional Networks (GCNs) [38]. The joints and bones in the human body naturally form graphs, which make GCNs a perfect tool to extract topological features of skeletons. GCN-based methods have become more and more popular, with another merit that the models can be built lightweight and have high computational efficiency compared with models processing video frames. + +However, using skeletons to recognize actions has some limitations. A major problem is that skeleton representation lacks important interactive objects and contextual informa + +tion for distinguishing similar actions. As shown in Fig. 1, it is hard to distinguish "Writing", "Reading" and "Typing on a keyboard" based on the skeleton view alone. In contrast, a model can recognize them from RGB frames by focusing on the related items. These actions are easily confused with each other and should be given more attention. + +To alleviate this drawback, we propose a feature refinement module using contrastive learning to lift the discriminative ability of features between ambiguous actions. We first decouple hidden features into spatial and temporal components so that the network can better focus on discriminative parts among ambiguous actions along the topological and temporal dimensions. Then we identify the confident and ambiguous samples based on the model prediction during training. Confident samples are used to maintain a prototype for each class, which is achieved by a contrastive learning loss to constrain intra-class and inter-class distances. Meanwhile, ambiguous samples are calibrated by being closer to or far away from confident samples in the feature space. Furthermore, the aforementioned feature refinement module can be embedded into multiple types of GCNs to improve hierarchical feature learning. It will produce a multi-level contrastive loss, which is jointly trained with the classification loss to improve the performance of ambiguous actions. Our main contributions are summarized as follows: + +- We propose a discriminative feature refinement module to improve the performance of ambiguous actions in skeleton based action recognition. It uses contrastive learning to constrain the distance between confident samples and ambiguous samples. It also decouples the raw feature map into spatial and temporal components in a lightweight way for efficient feature enhancement. +- The feature refinement module is plug-and-play and compatible with most GCN-based models. It can be jointly trained with other losses but discarded in the inference stage. +- We conduct extensive experiments on NTU RGB+D, NTU RGB+D 120, and NW-UCLA datasets to compare our proposed methods with the state-of-the-art models. Experimental results demonstrate the significant improvement of our methods. + +# 2. Related Work + +# 2.1. Human Pose Estimation + +Human pose estimation is an essential building block for a wide range of intelligent systems in fields such as AR, sports analysis, and healthcare, thus receiving much attention in recent years. Recent approaches leverage the + +temporal information of 2D pose sequences to alleviate the depth ambiguity in 3D poses [1, 13, 19, 20, 23]. Hossain et al. [13] tackle the task as a sequence-to-sequence problem and build RNNs to learn the mapping. Cai et al. [1] exploit the spatial-temporal relations from the 2D sequences via an encoder-decoder like GCN. Li et al. [19] use Transformer [31] to capture the long-range relationships in the 2D pose sequence. + +# 2.2. Skeleton Based Action Recognition + +Action recognition benefits a lot from human pose estimation. Early works treat the recognition as a sequence classification task. Su et al. [30] design an auto-encoder with RNNs to learn high-level features from the sequence. Another stream converts the skeleton sequence to image-like data using hand-crafted schemes [9, 37]. Duan et al. [10] concatenate an RGB frame with a 2D skeleton heat map and use 3D CNNs to extract features. These works do not explicitly exploit the spatial structure of the human body. + +The mainstream in this field is to use GCNs to extract the high-level features from skeletons since the joints and bones in the human body naturally construct a graph [5,22,38,42]. In this way, the topology of the human body is fully exploited. Yan et al. [38] is the first attempt to use GCNs for skeleton based human action recognition. They define the basic connections of spatial and temporal dimensions and introduce an efficient pipeline. Zhang et al. [42] build a two-stream architecture for both joint and bone modalities. Chen et al. [5] improve the design of GCNs in [38] and propose to dynamically learn different topologies and effectively aggregate joint features in each channel. + +# 2.3. Contrastive Learning + +Recently, contrastive learning has achieved remarkable progress in diverse fields. Typically, contrastive learning requires generating a set of transformed versions (or "views") of an image using data augmentations, then training the network to distinguish the different views of the image. Chen et al. [2] explore the strategies of data augmentations and use a huge batch size to obtain the enhanced representation. He et al. [3,4,12] realize contrastive learning in a more efficient way using a momentum encoder and a dynamic queue. Wang et al. [33] define the positive and negative samples in a supervised manner. They design a metric function loss to calibrate these misclassified feature representations for better intra-class consistency and segmentation performance. Inspired by this, our work tries to use a similar spirit to refine the skeleton representations for ambiguous actions. + +# 2.4. Ambiguous Sample + +Most of the recognition tasks for solving ambiguous samples focus on fine-grained image classification. For ex + +![](images/e25c349f0a1fde0f8ecfaa18f0d31c538edd112a372a7d6159fb6f2fdfac18d1.jpg) +Figure 2. overview of the proposed method. + +ample, Lin et al. [32] perform bilinear pooling on the representations of two local patches to learn the discriminative feature. Dubey et al. [11] model similarity between image pairs and leverage metric learning to improve the feature distributions. Zhuang et al. [43] design a module to adaptively discover contrastive cues from a pair of images and attentively distinguish them via pairwise interaction. However, we have not found works that aim at solving skeleton-based action recognition. + +# 3. Methodology + +We now give the details of our method. The overview of it is depicted in Fig. 2. + +# 3.1. Backbone + +The input of our model is a sequence of skeletons with a shape of $T \times V \times 3$ , which means $T$ frames of $V$ joints in a 3D space. We build our approach on [5]. However, we will show in the experimental section that it can improve any GCNs. The backbone consists of 10 basic units, termed TGN. TGN is constructed by a series of Temporal CNNs (TCNs) and Graph Convolution Networks (GCNs). Concretely, TCNs extract the temporal features by imposing 1D CNNs on the temporal dimension; GCNs extract the spa + +tial features with a learnable topological graph defined on the spatial dimension. Note that two of the basic units are stripped TGNs implemented by stripped 1D CNNs. They are used to generate multi-scale features by decreasing the temporal dimension while increasing the channel dimension. Then, a pooling layer is applied to get the 1D high-level feature vectors. Finally, a fully-connected (FC) layer with softmax activation maps the feature to a probability distribution of $K$ candidate categories. + +It is noted that the detailed implementation of the backbone is not the main concern of our method. The implementation of the basic unit can be replaced by any other GCN-based networks like [26, 38]. + +# 3.2. Feature Refinement Head + +Our main idea is to improve the performance of the skeleton based model on ambiguous actions that are quite similar and easily misclassified. To achieve this, we propose a plug-and-play module to optimize multi-level features within the backbone network, termed Feature Refinement Head (FR Head). It first decouples the hidden feature maps into spatial and temporal components and then applies a contrastive learning loss with global class prototypes and ambiguous samples. It is worth noting that the proposed FR + +Head is added only for training. There is no additional computational cost or memory consumption during inference. + +# 3.2.1 Multi-Level Feature Selection + +To learn more discriminative feature representations, we divide the backbone into four stages, respectively at the 1st, 5th, 8th, and last layer of TGN, and impose a FR Head on each of them. The 5th and the 8th layers employ a strided operation. Each FR Head refines the corresponding hidden features by calculating a contrastive learning (CL) loss, whose details will be discussed in Section 3.2.3. To balance the different levels, we add a weighting parameter for each stage and the multi-level CL loss can be defined as a weighted average sum: + +$$ +\mathcal {L} _ {C L} = \sum_ {i = 1} ^ {4} \lambda_ {i} \cdot \mathcal {L} _ {C L} ^ {i} \tag {1} +$$ + +where $\mathcal{L}_{CL}$ is the multi-level CL loss, $\lambda_{i}$ is the hyperparameter to control stage $i$ and $\mathcal{L}_{CL}^{i}$ is the local CL loss calculated by stage $i$ . + +# 3.2.2 Spatial-Temporal Decoupling + +Due to the complexity of human activities, coarse modelling features will lead to confusion between ambiguous actions with similar spatial appearances or temporal transformations. + +For example, "put sth. into a bag" can be easily distinguished from "take sth. out of a bag" using temporal clues. However, compared to the "reach into pockets", more concentrations on the spatial information are required. Therefore, we propose a spatial-temporal decouple module that mines the spatial and temporal information simultaneously to improve the discriminative ability of action representations. + +As Fig. 2 describes, the raw feature map is fed into two parallel branches for efficient feature enhancement. Concretely, each branch comprises a spatial/temporal pooling layer which only keeps the average value of the related dimension and a $1 \times 1$ convolution layer which is used to squeeze the feature to a fixed size. Then the output feature is flattened to a unified representation with the channel size of $C_h$ . Finally, a CL loss is added on top of each branch. We accomplish the Spatial-Temporal Decoupling feature refinement by summing losses from the two branches: + +$$ +\mathcal {L} _ {C L} ^ {i} = \operatorname {C L} \left(F _ {s} ^ {i}\right) + \operatorname {C L} \left(F _ {t} ^ {i}\right) \tag {2} +$$ + +where $F_{s}^{i}$ and $F_{t}^{i}$ stand for the spatial feature and the temporal feature of stage $i$ , respectively. $\mathrm{CL}(\cdot)$ is the function to calculate the CL loss with a specific feature vector. + +![](images/cf52a4991b93331d0cc154e828fec3003e02df88972f780e3c6b31ce0ddfdd3b.jpg) +Figure 3. Discovering the confident and ambiguous samples for action "writing". + +# 3.2.3 Contrastive Feature Refinement + +As Fig. 2 shows, we conduct the feature refinement in a manner of contrastive learning. The idea is inspired by [33]. Each sample will be refined by both its ground truth actions and other ambiguous actions. + +Confident Sample Clustering. Given an action label $k$ , if a sample is predicted correctly, namely as a True Positive (TP), we consider it a confident sample to distinguish it from ambiguous samples. Apparently, features from confident samples tend to have better intra-class consistency. As Fig. 3 shows, we gather those features to update the global representation (i.e., prototype) of the corresponding classes via exponential moving average (EMA). Assuming $s_{TP}^{k}$ is the set of confident samples for action $k$ in a batch and its size is $n_{TP}^{k}$ , the EMA operation can be defined as: + +$$ +P _ {k} = (1 - \alpha) \cdot \frac {1}{n _ {T P} ^ {k}} \sum_ {i \in s _ {T P} ^ {k}} F _ {i} + \alpha \cdot P _ {k} \tag {3} +$$ + +where $P_{k}$ is the prototype of action $k$ , $F_{i}$ is the feature extracted from sample $i$ . $\alpha$ is the momentum term, we set it to 0.9 by experience. Over the training procedure, the prototype becomes a stable estimation of the clustering center for action $k$ . It is capable of refining the feature of a newly arrived sample. Each sample should be close to the related prototype while far away from other prototypes. The distance between two feature vectors is defined as $\mathrm{dis}(\cdot ,\cdot)$ , which is implemented by cosine distance: + +$$ +\operatorname {d i s} (\boldsymbol {u}, \boldsymbol {v}) = \frac {\boldsymbol {u} \boldsymbol {v} ^ {T}}{| | \boldsymbol {u} | | _ {2} | | \boldsymbol {v} | | _ {2}} \tag {4} +$$ + +where $\mathbf{u},\mathbf{v}$ stand for 1D vectors. $\| \cdot \| _2$ is $L_{2}$ norm. + +Ambiguous Sample Discovering. To discover the ambiguous samples during the training stages, we gather the + +misclassified samples which tend to be quite similar to other categories. Given an action label $k$ , there are two types of ambiguous samples. If a sample of action $k$ is misclassified as other categories, it is termed as False Negative (FN). If a sample of other categories is misclassified as action $k$ , it is termed as False Positive (FP). Supposing $s_{FN}^{k}, s_{FP}^{k}$ are sets of FN and FP samples for action $k$ and the sizes of them are $n_{FN}^{k}, n_{FP}^{k}$ . As fig. 3 shows, We gather those samples in a batch and calculate the mean values as the center representations: + +$$ +\boldsymbol {\mu} _ {F N} ^ {k} = \frac {1}{n _ {F N} ^ {k}} \sum_ {j \in s _ {F N} ^ {k}} F _ {j}, \quad \boldsymbol {\mu} _ {F P} ^ {k} = \frac {1}{n _ {F P} ^ {k}} \sum_ {j \in s _ {F P} ^ {k}} F _ {j} \tag {5} +$$ + +where $\pmb{\mu}_{FN}^{k},\pmb{\mu}_{FP}^{k}$ stand for the center representation of FN and FP samples of class $k$ . Note that, we do not maintain a global representation for those ambiguous samples because the prediction of those samples is not stable in the training stage and the amount is much less than TP samples. + +Ambiguous Sample Calibration. To calibrate the prediction of ambiguous samples, we take confident sample $i$ of action $k$ as the anchor and calculate an auxiliary term in the feature space. For those FN samples which should be classified as action $k$ , a compensation term $\phi_{i}$ is introduced: + +$$ +\phi_ {i} = \left\{ \begin{array}{c} 1 - \operatorname {d i s} \left(F _ {i}, \boldsymbol {\mu} _ {F N} ^ {k}\right), \text {i f} i \in s _ {T P} ^ {k} \text {a n d} n _ {F N} ^ {k} > 0; \\ 0, \text {o t h e r w i s e .} \end{array} \right. \tag {6} +$$ + +By minimizing the compensation term $\phi_{i}$ , FN samples are supposed to be closer to the confident sample in the feature space. When there are no FN samples or the cosine distance converges to 1, $\phi_{i}$ reaches the minimum value 0. This may motivate the model to correct these ambiguous samples as action $k$ . + +On the other hand, for those FP samples which belong to other categories, a penalty term $\psi_{i}$ is introduced: + +$$ +\psi_ {i} = \left\{ \begin{array}{c} 1 + \operatorname {d i s} \left(F _ {i}, \boldsymbol {\mu} _ {F P} ^ {k}\right), \text {i f} i \in s _ {T P} ^ {k} \text {a n d} n _ {F P} ^ {k} > 0; \\ 0, \text {o t h e r w i s e .} \end{array} \right. \tag {7} +$$ + +Similarly, the penalty term $\psi_{i}$ penalizes the distance between the FP samples and the confident samples in the feature space. When there are no FP samples or the cosine distance converges to $-1$ , $\psi_{i}$ reaches the minimum value 0. This may prevent the model from recognizing these ambiguous samples as action $k$ . + +Finally, taking sample $i$ as an anchor, the proposed CL loss function can be defined as: + +$$ +\begin{array}{l} \operatorname {C L} \left(F _ {i}\right) = - \log \frac {e ^ {\operatorname {d i s} \left(F _ {i} , P _ {k}\right) / \tau - (1 - p _ {i k}) \psi_ {i}}}{e ^ {\operatorname {d i s} \left(F _ {i} , P _ {k}\right) / \tau - (1 - p _ {i k}) \psi_ {i}} + \sum_ {l \neq k} e ^ {\operatorname {d i s} \left(F _ {i} , P _ {l}\right) / \tau}} \\ - \log \frac {e ^ {\operatorname {d i s} \left(F _ {i} , P _ {k}\right) / \tau - \left(1 - p _ {i k}\right) \phi_ {i}}}{e ^ {\operatorname {d i s} \left(F _ {i} , P _ {k}\right) / \tau - \left(1 - p _ {i k}\right) \psi_ {i}} + \sum_ {l \neq k} e ^ {\operatorname {d i s} \left(F _ {i} , P _ {l}\right) / \tau}} \tag {8} \\ \end{array} +$$ + +where $p_{ik}$ is the predicted probability score of sample $i$ for class $k$ . It means that the TP samples with weaker confidence get stronger supervision from those ambiguous samples. + +# 3.3. Training Objective + +We use Cross-Entropy (CE) loss to train our network: + +$$ +\mathcal {L} _ {C E} = - \frac {1}{N} \sum_ {i} \sum_ {c} y _ {i c} \log \left(p _ {i c}\right) \tag {9} +$$ + +where $N$ is the number of samples in a batch. $y_{ic}$ is the one-hot presentation of the label of sample $i$ . If and only if $c$ is the target class of sample $i$ , $y_{ic} = 1$ . $p_{ic}$ is the probability score of sample $i$ belonging to class $k$ predicted by the network. + +Finally, CE loss is combined with our proposed multilevel CL loss to form the full learning objective function: + +$$ +\mathcal {L} = \mathcal {L} _ {C E} + w _ {c l} \cdot \mathcal {L} _ {C L} \tag {10} +$$ + +where $\mathcal{L}_{CL}$ and $\mathcal{L}_{CE}$ are defined in Eqs. 1 and 9. $w_{cl}$ is the balanced hyper-parameter for CL loss. + +# 4. Experiments + +# 4.1. Datasets + +NTU RGB+D. NTU RGB+D [24] is a widely used dataset containing 56,880 samples. 40 participants are invited to perform 60 actions including daily behaviors and health-related actions. Each action is performed by 1 or 2 people. The human skeleton is presented by 25 3D joints, which are captured by 3 Microsoft Kinect v2 cameras with different horizontal angle settings. It provides two benchmarks: (1) Cross-Subject (X-Sub): the dataset is divided according to the subjects. The training set consists of 20 subjects while the testing set consists of other 20 subjects. (2) Cross-View (X-View): the dataset is split by the camera views. They select camera views 2 and 3 to construct the training data while camera view 1 is used for testing. + +NTU RGB+D 120. NTU RGB+D 120 [21] extends NTU RGB+D with extra 57,367 samples by introducing new 60 action classes, making it the largest skeleton based action recognition dataset. In total, it collects 113,945 skeleton sequences over 120 different classes performed by 106 participants. It also increases the number of camera setups to 32 by using different places and backgrounds. Two evaluation protocols are recommended: (1) Cross-Subject (X-Sub): samples from 56 subjects are selected to form the training set, and the reaming 50 subjects are used for testing. (2) Cross-Set (X-Set): samples with even setup IDs are used for training, while samples with odd setup IDs are used for testing. + +Table 1. Ablation studies of our method on NTU-RGB+D 120 dataset under the X-Sub setting with the joint input modality. + +
MethodParams.Acc (%)
Baseline1.46M84.5
+ CL Loss1.53M85.0↑0.5
+ ST Decouple1.59M85.3↑0.8
+ ML Refine1.61M84.7↑0.2
Ours1.99M85.5↑1.0
+ +Table 2. Hyper-parameter exploration of our proposed method on NTU-RGB+D 120 dataset under the X-Sub setting with the joint input modality. The best one is in **bold**. + +
wclλ1λ2λ3λ4Acc (%)
1000184.4
0.1000185.3
0.01000185.0
111184.5
10.20.2184.7
10.50.20.184.1
0.10.10.11185.2
0.10.10.1185.1
0.10.20.2185.4
0.10.20.5185.5
+ +NW-UCLA. Northwestern-UCLA dataset [34] contains 1494 video clips performed by 10 volunteers. 3 Kinect cameras are used to capture 3D skeletons with 20 joints from multiple views. Totally 10 action categories are covered. We adopt the evaluation protocols recommended by the author: training data comes from the first two cameras, while testing data is from the other camera. + +# 4.2. Implementation Details + +We adopt [5] as the backbone and implement the proposed method with the PyTorch deep learning framework. All experiments are conducted on one RTX 2080Ti GPU. The Stochastic Gradient Descent (SGD) optimizer is employed with a momentum of 0.9 and a weight decay of 0.0004 to train the models. In the first 5 epochs, we apply a warmup strategy for stable training. The initial learning rate is set to 0.1 and we decrease it at epoch 35 and 55 with a factor of 0.1. We train all models with 70 epochs and select the best performance. The base channel $C$ is set to 64 and the hidden channel $C_h$ is set to 256. The hyper-parameters in our methods are set as: $\lambda_1 = 0.1$ , $\lambda_2 = 0.2$ , $\lambda_3 = 0.5$ , $\lambda_4 = 1$ , $w_{cl} = 0.1$ . For NTU RGB+D and NTU RGB+D 120, we follow the data preprocessing in [41] and set the batch size to 64. All samples are resized to 64 frames. For NW + +UCLA, we follow the data preprocessing in [8] and set the batch size to 16. + +# 4.3. Ablation Study + +We conduct ablation studies and evaluate the different hyper-parameter settings on the X-Sub benchmark of NTU RGB+D 120 dataset to verify the effectiveness of the proposed module. + +The results of ablation studies are displayed in Table 1. We remove all additional heads and train the network with CE loss to build the baseline. We also divide the proposed module into different sub-modules and design 3 variants: (1) CL Loss: we directly employ the CL loss to refine features from the last layer without any additional operations. (2) ST Decouple: we decouple the features into spatial and temporal components before refinement. (3) ML Refine: we impose the refinement on proposed multi-level stages in the training pipeline. It can be seen that all these sub-modules can improve the performance of the baseline. Among them, the contributions from CL loss and ST Decouple are relatively dominant. Moreover, when combining all of them, the result becomes better. We also report the count of trainable parameters of different models. The extra cost of parameters may increase the time of the training procedure but does not affect the inference stage. + +We analyze the configurations on the hyper-parameters of our method, and the results are available in Table 2. First, we try 3 different values of $w_{cl}$ to find the balance between the CL loss and CE loss with the fixed combination of $\lambda_1 = \lambda_2 = \lambda_3 = 0, \lambda_4 = 1$ for an efficient experiment. It seems that bigger $w_{cl}$ may hurt the performance while too small values only provide a little improvement. Then, we try more combinations of $\lambda_i$ to balance the importance of different stages. From the results, we can observe that giving higher weight to the previous layers may obtain negative influence and increase the importance gradually from the early stage to the last stage and thus lead to an optimal result. It is concluded that the refinement of the high-level features from the final stage plays a major role and the low-level features provide the auxiliary effects. Finally, we choose the configuration of $\lambda_1 = 0.1, \lambda_2 = 0.2, \lambda_3 = 0.5, \lambda_4 = 1, w_{cl} = 0.1$ for the following experiments. + +# 4.4. Combined with Other Backbones + +Our proposed module is plug-and-play and compatible with most GCN-based backbones. To examine its universality, we apply it to 5 widely used GCN-based backbones [5, 17, 26, 35, 38] and evaluate them on the X-Sub and X-Set of NTU RGB+D 120 dataset. For fair comparisons, we reimplement them and use the same data preprocessing without the multi-stream fusion. Table 3 reports the performance and number of parameters of different methods. It is + +Table 3. Performance of our proposed method using different GCN-based backbones on NTU-RGB+D 120 dataset with the joint input modality. + +
MethodParams.NTU-RGB+D 120
X-Sub (%)X-Set (%)
ST-GCN [38]2.11M83.485.1
+ FR Head2.65M84.4↑1.086.5↑1.4
2s-AGCN [26]3.80M84.385.9
+ FR Head4.33M84.6↑0.386.6↑0.7
CTR-GCN [5]1.46M84.586.6
+ FR Head1.99M85.5↑1.087.3↑0.7
TCA-GCN [35]5.65M85.086.3
+ FR Head6.18M85.2↑0.287.4↑1.1
HD-GCN [17]1.68M85.187.2
+ FR Head2.21M85.4↑0.387.7↑0.5
+ +Table 4. Accuracy (\%) on different difficult level actions for NTU-RGB+D 120 dataset under the X-Sub setting with the joint input modality. + +
MethodNTU-RGB+D 120
HardMediumEasy
ST-GCN [38]57.480.994.7
2s-AGCN [26]58.982.095.0
CTR-GCN [5]59.682.495.1
Ours61.683.395.7
Δ2.00.90.6
+ +observed that all models obtain an obvious gain of accuracy by employing the FR Head. The improvement is around $1.0\%$ . In most cases, the models with lower accuracy are improved more than those with higher initial accuracy. The reason behind it may be that our modules utilize the knowledge from the misclassified samples. The lower accuracy of means the misclassified samples are more sufficient. The additional count of parameters introduced by the FR Head is around 0.5M and can be ignored in the inference stage. + +# 4.5. Performance on Ambiguous Actions + +We spilt NTU-RGB+D 120 dataset into 3 subsets with different difficulty levels. Specifically, according to the results of CTR-GCN [5], we gather actions whose accuracy is lower than $70\%$ as Hard Level, between $70\%$ and $90\%$ as Medium Level, and over $90\%$ as Easy Level. The results are displayed in Table 4. The experiment is under the X-Subsetting with only the joint input modality. Because ambiguous actions are quite similar and easy to be misclassified, these actions usually fall into Hard Level. From the + +![](images/dc79be0a46ef8262f50fb5e591bd41f3997cb86db5f50f580274ad4465ee81ae.jpg) +Figure 4. The group-wise accuracy difference $(\%)$ between our method and CTR-GCN [5] on ambiguous actions for NTU-RGB+D 120 dataset under the X-Sub setting with the joint input modality. + +![](images/429fda840fd97c3e07d4afb7078fd0e775a11a418027e6986db527569c037ece.jpg) +Figure 5. Visualization of latent representation by t-SNE for ambiguous groups from NTU RGB+D 120 dataset. Different colors indicate different classes. The upper one is from the CTR-GCN [5], while the bottom one is from our method. + +results, we can see that our method makes a great improvement in Hard Level actions, which demonstrates the ability to distinguish those ambiguous actions. + +Furthermore, we define ambiguous groups, which collect several related ambiguous actions to verify the performance of ambiguous samples. We first pick a class as an anchor class, for example, "writing". Then we gather the misclassified samples on "writing" and obtain the top-3 actions with the highest frequency, like "reading", "typing on a keyboard" and "playing with phone". These 4 actions will be constructed as an ambiguous group. The group-wise accuracy will be the average accuracy of all actions included by the group. Here, we randomly pick 60 anchor actions and constructed corresponding ambiguous groups from NTU-RGB+D 120 dataset. We compare our results with a SOTA model CTR-GCN [5] and display the results in Fig. 4. Our method gains great improvement in most ambiguous groups. + +We randomly pick some ambiguous groups and visualize the distribution of them in the feature space using t-SNE. As mentioned before, each ambiguous group contains four classes, including an anchor class and three ambiguous classes. We compare our method with CTR-GCN [5]. Fig. 5 shows that our model achieves a more compact clustering. + +Table 5. Performance comparison of skeleton-based action recognition in top-1 accuracy (\%). The best one is in bold and the second one is underlined. + +
MethodPublicationNTU RGB+DNTU RGB+D 120NW-UCLA
X-SubX-ViewX-SubX-Set
ST-GCN [38]AAAI201881.588.3---
Ind-RNN [18]CVPR201881.888.0---
RotClips+MTCNN [15]TIP2018--62.261.8-
2s-AGCN [26]CVPR201988.595.182.984.9-
AGC-LSTM [27]CVPR201989.295.0--93.3
DGNN [25]CVPR201989.996.1---
PA-ResGCN-B19 [28]ACMMM202090.996.087.388.3-
Dynamic GCN [39]ACMMM202091.596.087.388.6-
SGN [41]CVPR202089.094.579.281.5-
Shift-GCN [8]CVPR202090.796.585.987.694.6
MS-G3D [22]CVPR202091.596.286.988.4-
DDGCN [16]ECCV202091.197.1---
DC-GCN+ADG [7]ECCV202090.896.686.588.195.3
MST-GCN [6]AAAI202191.596.687.588.8-
Skeletal-GNN [40]ICCV202191.696.787.589.2-
CTR-GCN [5]ICCV202192.496.888.990.696.5
STF [14]AAAI202292.596.988.989.9-
Ta-CNN [36]AAAI202290.494.885.486.896.1
EfficientGCN-B4 [29]TPAMI202291.795.788.389.1-
Ours-92.896.889.590.996.8
+ +# 4.6. Comparison with the State-of-the-Art + +In this section, we conduct a comparison with the state-of-the-art methods on NTU RGB+D 120, NTU RGB+D, and NW-UCLA datasets to demonstrate the competitive ability of our proposed module. The quantitative results are displayed in Table 5. It is noted that most of the state-of-the-art methods employ a multi-stream fusion framework. For a fair comparison, we follow the same framework as [5,35]. We make a fusion with the results from four modalities including joint, bone, joint motion, and bone motion as the final report result. + +It is observed that our methods outperform most existing methods on these three datasets. On both settings of NTU-RGB+D 120, X-Sub of NTU-RGB+D, and NW-UCLA datasets, our model obtains the best results. On X-View of NTU-RGB+D, our model reaches state-of-the-art results with a reasonable gap between the best one, which demonstrates the great potential of our proposed module. Notably, our method is the first to propose a way to solve ambiguous actions, which are very important in skeleton based action recognition. + +# 5. Conclusion + +In this paper, we present a novel feature refinement module equipped with contrastive learning to solve the + +ambiguous actions for skeleton based action recognition. Multi-level features extracted from GCN-based backbone are leveraged and enhanced on both the spatial and temporal dimensions. The contrastive learning is conducted with the samples with high confidence and calibrated by the FP and FN samples to make full use of the misclassified actions. + +The extensive experiments demonstrate the effectiveness of the proposed module to distinguish the confusing categories and the university to be compatible with most GCN-based backbones. On three widely used benchmarks, our proposed method obtains satisfactory results and outperforms those state-of-the-art methods. + +Discussion. Despite the performance of our proposed module on three public large-scale datasets, the ambiguous actions in a few-shot setting with insufficient data remain to be explored. We will concentrate on it in our future work. In addition, there are some potential negative societal impacts to be considered. Our method may be applied in some controversial fields, such as surveillance. Besides, applying our module will introduce extra training costs, which should be discussed in the carbon emission problem. + +Acknowledgements. This paper was founded by National Natural Science Foundation of China under grants U20B2069 and 62176017. + +# References + +[1] Yujun Cai, Liuhao Ge, Jun Liu, Jianfei Cai, Tat-Jen Cham, Junsong Yuan, and Nadia Magnenat Thalmann. Exploiting spatial-temporal relationships for 3d pose estimation via graph convolutional networks. 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In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 7922-7931, 2019. 2 +[38] Sijie Yan, Yuanjun Xiong, and Dahua Lin. Spatial temporal graph convolutional networks for skeleton-based action recognition. In Proceedings of the AAAI Conference on Artificial Intelligence, pages 7444-7452, 2018. 1, 2, 3, 6, 7, 8 + +[39] Fanfan Ye, Shiliang Pu, Qiaoyong Zhong, Chao Li, Di Xie, and Huiming Tang. Dynamic gcn: Context-enriched topology learning for skeleton-based action recognition. In Proceedings of the ACM International Conference on Multimedia, pages 55-63, 2020. 8 +[40] Ailing Zeng, Xiao Sun, Lei Yang, Nanxuan Zhao, Minhao Liu, and Qiang Xu. Learning skeletal graph neural networks for hard 3d pose estimation. In Proceedings of the IEEE International Conference on Computer Vision, pages 11436-11445, 2021. 8 +[41] Pengfei Zhang, Cuiling Lan, Wenjun Zeng, Junliang Xing, Jianru Xue, and Nanning Zheng. 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Recently, people have dived into designing GCN-based models to extract features from skeletons for performing this task, because skeleton representations are much more efficient and robust than other modalities such as RGB frames. However, when employing the skeleton data, some important clues like related items are also discarded. It results in some ambiguous actions that are hard to be distinguished and tend to be misclassified. To alleviate this problem, we propose an auxiliary feature refinement head (FR Head), which consists of spatial-temporal decoupling and contrastive feature refinement, to obtain discriminative representations of skeletons. Ambiguous samples are dynamically discovered and calibrated in the feature space. Furthermore, FR Head could be imposed on different stages of GCNs to build a multi-level refinement for stronger supervision. Extensive experiments are conducted on NTU RGB+D, NTU RGB+D 120, and NW-UCLA datasets. Our proposed models obtain competitive results from state-of-the-art methods and can help to discriminate those ambiguous samples. Codes are available at https://github.com/zhysora/FR-Head." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 540, + 127, + 553 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 540, + 127, + 553 + ], + "spans": [ + { + "bbox": [ + 47, + 540, + 127, + 553 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 561, + 287, + 656 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 561, + 287, + 656 + ], + "spans": [ + { + "bbox": [ + 46, + 561, + 287, + 656 + ], + "type": "text", + "content": "In human-to-human communication, action plays a particularly important role. The behaviors convey intrinsic information like emotions and potential intentions and thus help to understand the person. Empowering intelligent machines with the same ability to understand human behaviors is critical for natural human-computer interaction and many other practical applications, and has been attracting much attention recently." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 657, + 287, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 657, + 287, + 693 + ], + "spans": [ + { + "bbox": [ + 47, + 657, + 287, + 693 + ], + "type": "text", + "content": "Nowadays, obtaining 2D/3D skeletons of humans has become much easier thanks to the advanced sensor technology and human pose estimation algorithms. Skeletons" + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 315, + 231, + 541, + 466 + ], + "blocks": [ + { + "bbox": [ + 315, + 231, + 541, + 466 + ], + "lines": [ + { + "bbox": [ + 315, + 231, + 541, + 466 + ], + "spans": [ + { + "bbox": [ + 315, + 231, + 541, + 466 + ], + "type": "image", + "image_path": "952023fb34e46a439957a7f3c6804a64de423d59d971732dbd3cb0fdff6312d8.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 479, + 545, + 522 + ], + "lines": [ + { + "bbox": [ + 305, + 479, + 545, + 522 + ], + "spans": [ + { + "bbox": [ + 305, + 479, + 545, + 522 + ], + "type": "text", + "content": "Figure 1. There are some actions that are hard to recognize because the skeleton representations lack important interactive objects and contexts, which make them easily confused with each other." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 545, + 546, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 546, + 676 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 546, + 676 + ], + "type": "text", + "content": "are compact and robust representations that are immune to viewpoint changes and cluttered backgrounds, making them attractive for action recognition. A typical way to use skeletons for action recognition is to build Graph Convolutional Networks (GCNs) [38]. The joints and bones in the human body naturally form graphs, which make GCNs a perfect tool to extract topological features of skeletons. GCN-based methods have become more and more popular, with another merit that the models can be built lightweight and have high computational efficiency compared with models processing video frames." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "content": "However, using skeletons to recognize actions has some limitations. A major problem is that skeleton representation lacks important interactive objects and contextual informa" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 134, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 134, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 134, + 712 + ], + "type": "text", + "content": "*Corresponding author" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10608" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 144 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 144 + ], + "type": "text", + "content": "tion for distinguishing similar actions. As shown in Fig. 1, it is hard to distinguish \"Writing\", \"Reading\" and \"Typing on a keyboard\" based on the skeleton view alone. In contrast, a model can recognize them from RGB frames by focusing on the related items. These actions are easily confused with each other and should be given more attention." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 144, + 290, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 144, + 290, + 384 + ], + "spans": [ + { + "bbox": [ + 46, + 144, + 290, + 384 + ], + "type": "text", + "content": "To alleviate this drawback, we propose a feature refinement module using contrastive learning to lift the discriminative ability of features between ambiguous actions. We first decouple hidden features into spatial and temporal components so that the network can better focus on discriminative parts among ambiguous actions along the topological and temporal dimensions. Then we identify the confident and ambiguous samples based on the model prediction during training. Confident samples are used to maintain a prototype for each class, which is achieved by a contrastive learning loss to constrain intra-class and inter-class distances. Meanwhile, ambiguous samples are calibrated by being closer to or far away from confident samples in the feature space. Furthermore, the aforementioned feature refinement module can be embedded into multiple types of GCNs to improve hierarchical feature learning. It will produce a multi-level contrastive loss, which is jointly trained with the classification loss to improve the performance of ambiguous actions. Our main contributions are summarized as follows:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 57, + 394, + 287, + 616 + ], + "type": "list", + "angle": 0, + "index": 5, + "blocks": [ + { + "bbox": [ + 57, + 394, + 287, + 490 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 394, + 287, + 490 + ], + "spans": [ + { + "bbox": [ + 57, + 394, + 287, + 490 + ], + "type": "text", + "content": "- We propose a discriminative feature refinement module to improve the performance of ambiguous actions in skeleton based action recognition. It uses contrastive learning to constrain the distance between confident samples and ambiguous samples. It also decouples the raw feature map into spatial and temporal components in a lightweight way for efficient feature enhancement." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 57, + 498, + 287, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 498, + 287, + 548 + ], + "spans": [ + { + "bbox": [ + 57, + 498, + 287, + 548 + ], + "type": "text", + "content": "- The feature refinement module is plug-and-play and compatible with most GCN-based models. It can be jointly trained with other losses but discarded in the inference stage." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 57, + 555, + 287, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 555, + 287, + 616 + ], + "spans": [ + { + "bbox": [ + 57, + 555, + 287, + 616 + ], + "type": "text", + "content": "- We conduct extensive experiments on NTU RGB+D, NTU RGB+D 120, and NW-UCLA datasets to compare our proposed methods with the state-of-the-art models. Experimental results demonstrate the significant improvement of our methods." + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 627, + 134, + 639 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 627, + 134, + 639 + ], + "spans": [ + { + "bbox": [ + 47, + 627, + 134, + 639 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 647, + 183, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 647, + 183, + 659 + ], + "spans": [ + { + "bbox": [ + 47, + 647, + 183, + 659 + ], + "type": "text", + "content": "2.1. Human Pose Estimation" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": "Human pose estimation is an essential building block for a wide range of intelligent systems in fields such as AR, sports analysis, and healthcare, thus receiving much attention in recent years. Recent approaches leverage the" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 72, + 547, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 168 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 168 + ], + "type": "text", + "content": "temporal information of 2D pose sequences to alleviate the depth ambiguity in 3D poses [1, 13, 19, 20, 23]. Hossain et al. [13] tackle the task as a sequence-to-sequence problem and build RNNs to learn the mapping. Cai et al. [1] exploit the spatial-temporal relations from the 2D sequences via an encoder-decoder like GCN. Li et al. [19] use Transformer [31] to capture the long-range relationships in the 2D pose sequence." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 175, + 493, + 189 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 175, + 493, + 189 + ], + "spans": [ + { + "bbox": [ + 306, + 175, + 493, + 189 + ], + "type": "text", + "content": "2.2. Skeleton Based Action Recognition" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 194, + 547, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 194, + 547, + 312 + ], + "spans": [ + { + "bbox": [ + 304, + 194, + 547, + 312 + ], + "type": "text", + "content": "Action recognition benefits a lot from human pose estimation. Early works treat the recognition as a sequence classification task. Su et al. [30] design an auto-encoder with RNNs to learn high-level features from the sequence. Another stream converts the skeleton sequence to image-like data using hand-crafted schemes [9, 37]. Duan et al. [10] concatenate an RGB frame with a 2D skeleton heat map and use 3D CNNs to extract features. These works do not explicitly exploit the spatial structure of the human body." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 314, + 547, + 459 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 314, + 547, + 459 + ], + "spans": [ + { + "bbox": [ + 304, + 314, + 547, + 459 + ], + "type": "text", + "content": "The mainstream in this field is to use GCNs to extract the high-level features from skeletons since the joints and bones in the human body naturally construct a graph [5,22,38,42]. In this way, the topology of the human body is fully exploited. Yan et al. [38] is the first attempt to use GCNs for skeleton based human action recognition. They define the basic connections of spatial and temporal dimensions and introduce an efficient pipeline. Zhang et al. [42] build a two-stream architecture for both joint and bone modalities. Chen et al. [5] improve the design of GCNs in [38] and propose to dynamically learn different topologies and effectively aggregate joint features in each channel." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 465, + 430, + 478 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 465, + 430, + 478 + ], + "spans": [ + { + "bbox": [ + 306, + 465, + 430, + 478 + ], + "type": "text", + "content": "2.3. Contrastive Learning" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 484, + 547, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 484, + 547, + 664 + ], + "spans": [ + { + "bbox": [ + 304, + 484, + 547, + 664 + ], + "type": "text", + "content": "Recently, contrastive learning has achieved remarkable progress in diverse fields. Typically, contrastive learning requires generating a set of transformed versions (or \"views\") of an image using data augmentations, then training the network to distinguish the different views of the image. Chen et al. [2] explore the strategies of data augmentations and use a huge batch size to obtain the enhanced representation. He et al. [3,4,12] realize contrastive learning in a more efficient way using a momentum encoder and a dynamic queue. Wang et al. [33] define the positive and negative samples in a supervised manner. They design a metric function loss to calibrate these misclassified feature representations for better intra-class consistency and segmentation performance. Inspired by this, our work tries to use a similar spirit to refine the skeleton representations for ambiguous actions." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 671, + 421, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 671, + 421, + 684 + ], + "spans": [ + { + "bbox": [ + 306, + 671, + 421, + 684 + ], + "type": "text", + "content": "2.4. Ambiguous Sample" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 689, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 547, + 715 + ], + "type": "text", + "content": "Most of the recognition tasks for solving ambiguous samples focus on fine-grained image classification. For ex" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "10609" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 72, + 537, + 373 + ], + "blocks": [ + { + "bbox": [ + 51, + 72, + 537, + 373 + ], + "lines": [ + { + "bbox": [ + 51, + 72, + 537, + 373 + ], + "spans": [ + { + "bbox": [ + 51, + 72, + 537, + 373 + ], + "type": "image", + "image_path": "e25c349f0a1fde0f8ecfaa18f0d31c538edd112a372a7d6159fb6f2fdfac18d1.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 216, + 382, + 376, + 395 + ], + "lines": [ + { + "bbox": [ + 216, + 382, + 376, + 395 + ], + "spans": [ + { + "bbox": [ + 216, + 382, + 376, + 395 + ], + "type": "text", + "content": "Figure 2. overview of the proposed method." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 415, + 287, + 522 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 415, + 287, + 522 + ], + "spans": [ + { + "bbox": [ + 46, + 415, + 287, + 522 + ], + "type": "text", + "content": "ample, Lin et al. [32] perform bilinear pooling on the representations of two local patches to learn the discriminative feature. Dubey et al. [11] model similarity between image pairs and leverage metric learning to improve the feature distributions. Zhuang et al. [43] design a module to adaptively discover contrastive cues from a pair of images and attentively distinguish them via pairwise interaction. However, we have not found works that aim at solving skeleton-based action recognition." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 534, + 129, + 548 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 534, + 129, + 548 + ], + "spans": [ + { + "bbox": [ + 47, + 534, + 129, + 548 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 555, + 288, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 555, + 288, + 578 + ], + "spans": [ + { + "bbox": [ + 46, + 555, + 288, + 578 + ], + "type": "text", + "content": "We now give the details of our method. The overview of it is depicted in Fig. 2." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 587, + 117, + 598 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 587, + 117, + 598 + ], + "spans": [ + { + "bbox": [ + 47, + 587, + 117, + 598 + ], + "type": "text", + "content": "3.1. Backbone" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "content": "The input of our model is a sequence of skeletons with a shape of " + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "inline_equation", + "content": "T \\times V \\times 3" + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "content": ", which means " + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "content": " frames of " + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "content": " joints in a 3D space. We build our approach on [5]. However, we will show in the experimental section that it can improve any GCNs. The backbone consists of 10 basic units, termed TGN. TGN is constructed by a series of Temporal CNNs (TCNs) and Graph Convolution Networks (GCNs). Concretely, TCNs extract the temporal features by imposing 1D CNNs on the temporal dimension; GCNs extract the spa" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 415, + 545, + 523 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 415, + 545, + 523 + ], + "spans": [ + { + "bbox": [ + 304, + 415, + 545, + 523 + ], + "type": "text", + "content": "tial features with a learnable topological graph defined on the spatial dimension. Note that two of the basic units are stripped TGNs implemented by stripped 1D CNNs. They are used to generate multi-scale features by decreasing the temporal dimension while increasing the channel dimension. Then, a pooling layer is applied to get the 1D high-level feature vectors. Finally, a fully-connected (FC) layer with softmax activation maps the feature to a probability distribution of " + }, + { + "bbox": [ + 304, + 415, + 545, + 523 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 415, + 545, + 523 + ], + "type": "text", + "content": " candidate categories." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 525, + 545, + 572 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 525, + 545, + 572 + ], + "spans": [ + { + "bbox": [ + 304, + 525, + 545, + 572 + ], + "type": "text", + "content": "It is noted that the detailed implementation of the backbone is not the main concern of our method. The implementation of the basic unit can be replaced by any other GCN-based networks like [26, 38]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 585, + 449, + 597 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 585, + 449, + 597 + ], + "spans": [ + { + "bbox": [ + 306, + 585, + 449, + 597 + ], + "type": "text", + "content": "3.2. Feature Refinement Head" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": "Our main idea is to improve the performance of the skeleton based model on ambiguous actions that are quite similar and easily misclassified. To achieve this, we propose a plug-and-play module to optimize multi-level features within the backbone network, termed Feature Refinement Head (FR Head). It first decouples the hidden feature maps into spatial and temporal components and then applies a contrastive learning loss with global class prototypes and ambiguous samples. It is worth noting that the proposed FR" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "10610" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "content": "Head is added only for training. There is no additional computational cost or memory consumption during inference." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 114, + 206, + 125 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 114, + 206, + 125 + ], + "spans": [ + { + "bbox": [ + 47, + 114, + 206, + 125 + ], + "type": "text", + "content": "3.2.1 Multi-Level Feature Selection" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 134, + 288, + 254 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 134, + 288, + 254 + ], + "spans": [ + { + "bbox": [ + 46, + 134, + 288, + 254 + ], + "type": "text", + "content": "To learn more discriminative feature representations, we divide the backbone into four stages, respectively at the 1st, 5th, 8th, and last layer of TGN, and impose a FR Head on each of them. The 5th and the 8th layers employ a strided operation. Each FR Head refines the corresponding hidden features by calculating a contrastive learning (CL) loss, whose details will be discussed in Section 3.2.3. To balance the different levels, we add a weighting parameter for each stage and the multi-level CL loss can be defined as a weighted average sum:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 123, + 266, + 287, + 297 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 123, + 266, + 287, + 297 + ], + "spans": [ + { + "bbox": [ + 123, + 266, + 287, + 297 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {C L} = \\sum_ {i = 1} ^ {4} \\lambda_ {i} \\cdot \\mathcal {L} _ {C L} ^ {i} \\tag {1}", + "image_path": "adaf499864b3a28b7c39e6d3fa3e3977238f8bf8f4ae66cebc8893061a4c4996.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 304, + 288, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 304, + 288, + 342 + ], + "spans": [ + { + "bbox": [ + 47, + 304, + 288, + 342 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 304, + 288, + 342 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{CL}" + }, + { + "bbox": [ + 47, + 304, + 288, + 342 + ], + "type": "text", + "content": " is the multi-level CL loss, " + }, + { + "bbox": [ + 47, + 304, + 288, + 342 + ], + "type": "inline_equation", + "content": "\\lambda_{i}" + }, + { + "bbox": [ + 47, + 304, + 288, + 342 + ], + "type": "text", + "content": " is the hyperparameter to control stage " + }, + { + "bbox": [ + 47, + 304, + 288, + 342 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 47, + 304, + 288, + 342 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 304, + 288, + 342 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{CL}^{i}" + }, + { + "bbox": [ + 47, + 304, + 288, + 342 + ], + "type": "text", + "content": " is the local CL loss calculated by stage " + }, + { + "bbox": [ + 47, + 304, + 288, + 342 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 47, + 304, + 288, + 342 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 358, + 206, + 371 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 358, + 206, + 371 + ], + "spans": [ + { + "bbox": [ + 47, + 358, + 206, + 371 + ], + "type": "text", + "content": "3.2.2 Spatial-Temporal Decoupling" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 379, + 287, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 379, + 287, + 426 + ], + "spans": [ + { + "bbox": [ + 47, + 379, + 287, + 426 + ], + "type": "text", + "content": "Due to the complexity of human activities, coarse modelling features will lead to confusion between ambiguous actions with similar spatial appearances or temporal transformations." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 427, + 287, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 427, + 287, + 521 + ], + "spans": [ + { + "bbox": [ + 46, + 427, + 287, + 521 + ], + "type": "text", + "content": "For example, \"put sth. into a bag\" can be easily distinguished from \"take sth. out of a bag\" using temporal clues. However, compared to the \"reach into pockets\", more concentrations on the spatial information are required. Therefore, we propose a spatial-temporal decouple module that mines the spatial and temporal information simultaneously to improve the discriminative ability of action representations." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 523, + 287, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 523, + 287, + 643 + ], + "spans": [ + { + "bbox": [ + 46, + 523, + 287, + 643 + ], + "type": "text", + "content": "As Fig. 2 describes, the raw feature map is fed into two parallel branches for efficient feature enhancement. Concretely, each branch comprises a spatial/temporal pooling layer which only keeps the average value of the related dimension and a " + }, + { + "bbox": [ + 46, + 523, + 287, + 643 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 46, + 523, + 287, + 643 + ], + "type": "text", + "content": " convolution layer which is used to squeeze the feature to a fixed size. Then the output feature is flattened to a unified representation with the channel size of " + }, + { + "bbox": [ + 46, + 523, + 287, + 643 + ], + "type": "inline_equation", + "content": "C_h" + }, + { + "bbox": [ + 46, + 523, + 287, + 643 + ], + "type": "text", + "content": ". Finally, a CL loss is added on top of each branch. We accomplish the Spatial-Temporal Decoupling feature refinement by summing losses from the two branches:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 111, + 656, + 287, + 671 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 111, + 656, + 287, + 671 + ], + "spans": [ + { + "bbox": [ + 111, + 656, + 287, + 671 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {C L} ^ {i} = \\operatorname {C L} \\left(F _ {s} ^ {i}\\right) + \\operatorname {C L} \\left(F _ {t} ^ {i}\\right) \\tag {2}", + "image_path": "52cbdb662bd815e0960c9a076026097417465e197700d48879235eb18ebd0718.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "inline_equation", + "content": "F_{s}^{i}" + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "inline_equation", + "content": "F_{t}^{i}" + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "text", + "content": " stand for the spatial feature and the temporal feature of stage " + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "text", + "content": ", respectively. " + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathrm{CL}(\\cdot)" + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "text", + "content": " is the function to calculate the CL loss with a specific feature vector." + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 307, + 68, + 547, + 241 + ], + "blocks": [ + { + "bbox": [ + 307, + 68, + 547, + 241 + ], + "lines": [ + { + "bbox": [ + 307, + 68, + 547, + 241 + ], + "spans": [ + { + "bbox": [ + 307, + 68, + 547, + 241 + ], + "type": "image", + "image_path": "cf52a4991b93331d0cc154e828fec3003e02df88972f780e3c6b31ce0ddfdd3b.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 249, + 547, + 272 + ], + "lines": [ + { + "bbox": [ + 305, + 249, + 547, + 272 + ], + "spans": [ + { + "bbox": [ + 305, + 249, + 547, + 272 + ], + "type": "text", + "content": "Figure 3. Discovering the confident and ambiguous samples for action \"writing\"." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 293, + 476, + 304 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 293, + 476, + 304 + ], + "spans": [ + { + "bbox": [ + 306, + 293, + 476, + 304 + ], + "type": "text", + "content": "3.2.3 Contrastive Feature Refinement" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 312, + 546, + 360 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 312, + 546, + 360 + ], + "spans": [ + { + "bbox": [ + 305, + 312, + 546, + 360 + ], + "type": "text", + "content": "As Fig. 2 shows, we conduct the feature refinement in a manner of contrastive learning. The idea is inspired by [33]. Each sample will be refined by both its ground truth actions and other ambiguous actions." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 360, + 545, + 481 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 360, + 545, + 481 + ], + "spans": [ + { + "bbox": [ + 305, + 360, + 545, + 481 + ], + "type": "text", + "content": "Confident Sample Clustering. Given an action label " + }, + { + "bbox": [ + 305, + 360, + 545, + 481 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 305, + 360, + 545, + 481 + ], + "type": "text", + "content": ", if a sample is predicted correctly, namely as a True Positive (TP), we consider it a confident sample to distinguish it from ambiguous samples. Apparently, features from confident samples tend to have better intra-class consistency. As Fig. 3 shows, we gather those features to update the global representation (i.e., prototype) of the corresponding classes via exponential moving average (EMA). Assuming " + }, + { + "bbox": [ + 305, + 360, + 545, + 481 + ], + "type": "inline_equation", + "content": "s_{TP}^{k}" + }, + { + "bbox": [ + 305, + 360, + 545, + 481 + ], + "type": "text", + "content": " is the set of confident samples for action " + }, + { + "bbox": [ + 305, + 360, + 545, + 481 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 305, + 360, + 545, + 481 + ], + "type": "text", + "content": " in a batch and its size is " + }, + { + "bbox": [ + 305, + 360, + 545, + 481 + ], + "type": "inline_equation", + "content": "n_{TP}^{k}" + }, + { + "bbox": [ + 305, + 360, + 545, + 481 + ], + "type": "text", + "content": ", the EMA operation can be defined as:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 345, + 488, + 545, + 520 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 345, + 488, + 545, + 520 + ], + "spans": [ + { + "bbox": [ + 345, + 488, + 545, + 520 + ], + "type": "interline_equation", + "content": "P _ {k} = (1 - \\alpha) \\cdot \\frac {1}{n _ {T P} ^ {k}} \\sum_ {i \\in s _ {T P} ^ {k}} F _ {i} + \\alpha \\cdot P _ {k} \\tag {3}", + "image_path": "02bd65503f8c3fd7c6f8521c50f69ac3b0dfb80fb035f576cd750ecaef100850.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 525, + 545, + 633 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 525, + 545, + 633 + ], + "spans": [ + { + "bbox": [ + 305, + 525, + 545, + 633 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 525, + 545, + 633 + ], + "type": "inline_equation", + "content": "P_{k}" + }, + { + "bbox": [ + 305, + 525, + 545, + 633 + ], + "type": "text", + "content": " is the prototype of action " + }, + { + "bbox": [ + 305, + 525, + 545, + 633 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 305, + 525, + 545, + 633 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 525, + 545, + 633 + ], + "type": "inline_equation", + "content": "F_{i}" + }, + { + "bbox": [ + 305, + 525, + 545, + 633 + ], + "type": "text", + "content": " is the feature extracted from sample " + }, + { + "bbox": [ + 305, + 525, + 545, + 633 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 305, + 525, + 545, + 633 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 305, + 525, + 545, + 633 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 305, + 525, + 545, + 633 + ], + "type": "text", + "content": " is the momentum term, we set it to 0.9 by experience. Over the training procedure, the prototype becomes a stable estimation of the clustering center for action " + }, + { + "bbox": [ + 305, + 525, + 545, + 633 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 305, + 525, + 545, + 633 + ], + "type": "text", + "content": ". It is capable of refining the feature of a newly arrived sample. Each sample should be close to the related prototype while far away from other prototypes. The distance between two feature vectors is defined as " + }, + { + "bbox": [ + 305, + 525, + 545, + 633 + ], + "type": "inline_equation", + "content": "\\mathrm{dis}(\\cdot ,\\cdot)" + }, + { + "bbox": [ + 305, + 525, + 545, + 633 + ], + "type": "text", + "content": ", which is implemented by cosine distance:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 375, + 641, + 545, + 669 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 375, + 641, + 545, + 669 + ], + "spans": [ + { + "bbox": [ + 375, + 641, + 545, + 669 + ], + "type": "interline_equation", + "content": "\\operatorname {d i s} (\\boldsymbol {u}, \\boldsymbol {v}) = \\frac {\\boldsymbol {u} \\boldsymbol {v} ^ {T}}{| | \\boldsymbol {u} | | _ {2} | | \\boldsymbol {v} | | _ {2}} \\tag {4}", + "image_path": "cb3662920ac963cbc2b23c70e9eecca81c5c1546bb4db1edab30eed96017a6a4.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 677, + 514, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 677, + 514, + 689 + ], + "spans": [ + { + "bbox": [ + 306, + 677, + 514, + 689 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 677, + 514, + 689 + ], + "type": "inline_equation", + "content": "\\mathbf{u},\\mathbf{v}" + }, + { + "bbox": [ + 306, + 677, + 514, + 689 + ], + "type": "text", + "content": " stand for 1D vectors. " + }, + { + "bbox": [ + 306, + 677, + 514, + 689 + ], + "type": "inline_equation", + "content": "\\| \\cdot \\| _2" + }, + { + "bbox": [ + 306, + 677, + 514, + 689 + ], + "type": "text", + "content": " is " + }, + { + "bbox": [ + 306, + 677, + 514, + 689 + ], + "type": "inline_equation", + "content": "L_{2}" + }, + { + "bbox": [ + 306, + 677, + 514, + 689 + ], + "type": "text", + "content": " norm." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "content": "Ambiguous Sample Discovering. To discover the ambiguous samples during the training stages, we gather the" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10611" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "text", + "content": "misclassified samples which tend to be quite similar to other categories. Given an action label " + }, + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "text", + "content": ", there are two types of ambiguous samples. If a sample of action " + }, + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "text", + "content": " is misclassified as other categories, it is termed as False Negative (FN). If a sample of other categories is misclassified as action " + }, + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "text", + "content": ", it is termed as False Positive (FP). Supposing " + }, + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "inline_equation", + "content": "s_{FN}^{k}, s_{FP}^{k}" + }, + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "text", + "content": " are sets of FN and FP samples for action " + }, + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "text", + "content": " and the sizes of them are " + }, + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "inline_equation", + "content": "n_{FN}^{k}, n_{FP}^{k}" + }, + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "text", + "content": ". As fig. 3 shows, We gather those samples in a batch and calculate the mean values as the center representations:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 61, + 196, + 287, + 228 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 196, + 287, + 228 + ], + "spans": [ + { + "bbox": [ + 61, + 196, + 287, + 228 + ], + "type": "interline_equation", + "content": "\\boldsymbol {\\mu} _ {F N} ^ {k} = \\frac {1}{n _ {F N} ^ {k}} \\sum_ {j \\in s _ {F N} ^ {k}} F _ {j}, \\quad \\boldsymbol {\\mu} _ {F P} ^ {k} = \\frac {1}{n _ {F P} ^ {k}} \\sum_ {j \\in s _ {F P} ^ {k}} F _ {j} \\tag {5}", + "image_path": "bf4626470da0a8b54d792ce5fe5e6b8dc4a32ba3bb8370d867396bc1601451c3.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 236, + 287, + 296 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 236, + 287, + 296 + ], + "spans": [ + { + "bbox": [ + 46, + 236, + 287, + 296 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 236, + 287, + 296 + ], + "type": "inline_equation", + "content": "\\pmb{\\mu}_{FN}^{k},\\pmb{\\mu}_{FP}^{k}" + }, + { + "bbox": [ + 46, + 236, + 287, + 296 + ], + "type": "text", + "content": " stand for the center representation of FN and FP samples of class " + }, + { + "bbox": [ + 46, + 236, + 287, + 296 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 236, + 287, + 296 + ], + "type": "text", + "content": ". Note that, we do not maintain a global representation for those ambiguous samples because the prediction of those samples is not stable in the training stage and the amount is much less than TP samples." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 297, + 287, + 356 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 297, + 287, + 356 + ], + "spans": [ + { + "bbox": [ + 46, + 297, + 287, + 356 + ], + "type": "text", + "content": "Ambiguous Sample Calibration. To calibrate the prediction of ambiguous samples, we take confident sample " + }, + { + "bbox": [ + 46, + 297, + 287, + 356 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 297, + 287, + 356 + ], + "type": "text", + "content": " of action " + }, + { + "bbox": [ + 46, + 297, + 287, + 356 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 297, + 287, + 356 + ], + "type": "text", + "content": " as the anchor and calculate an auxiliary term in the feature space. For those FN samples which should be classified as action " + }, + { + "bbox": [ + 46, + 297, + 287, + 356 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 297, + 287, + 356 + ], + "type": "text", + "content": ", a compensation term " + }, + { + "bbox": [ + 46, + 297, + 287, + 356 + ], + "type": "inline_equation", + "content": "\\phi_{i}" + }, + { + "bbox": [ + 46, + 297, + 287, + 356 + ], + "type": "text", + "content": " is introduced:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 363, + 287, + 396 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 363, + 287, + 396 + ], + "spans": [ + { + "bbox": [ + 55, + 363, + 287, + 396 + ], + "type": "interline_equation", + "content": "\\phi_ {i} = \\left\\{ \\begin{array}{c} 1 - \\operatorname {d i s} \\left(F _ {i}, \\boldsymbol {\\mu} _ {F N} ^ {k}\\right), \\text {i f} i \\in s _ {T P} ^ {k} \\text {a n d} n _ {F N} ^ {k} > 0; \\\\ 0, \\text {o t h e r w i s e .} \\end{array} \\right. \\tag {6}", + "image_path": "98b993191482d92273d08bfe93be98f00bb07c24e4b10f3ad5fdfb62719c9b83.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 401, + 287, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 401, + 287, + 472 + ], + "spans": [ + { + "bbox": [ + 46, + 401, + 287, + 472 + ], + "type": "text", + "content": "By minimizing the compensation term " + }, + { + "bbox": [ + 46, + 401, + 287, + 472 + ], + "type": "inline_equation", + "content": "\\phi_{i}" + }, + { + "bbox": [ + 46, + 401, + 287, + 472 + ], + "type": "text", + "content": ", FN samples are supposed to be closer to the confident sample in the feature space. When there are no FN samples or the cosine distance converges to 1, " + }, + { + "bbox": [ + 46, + 401, + 287, + 472 + ], + "type": "inline_equation", + "content": "\\phi_{i}" + }, + { + "bbox": [ + 46, + 401, + 287, + 472 + ], + "type": "text", + "content": " reaches the minimum value 0. This may motivate the model to correct these ambiguous samples as action " + }, + { + "bbox": [ + 46, + 401, + 287, + 472 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 401, + 287, + 472 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 473, + 287, + 497 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 473, + 287, + 497 + ], + "spans": [ + { + "bbox": [ + 47, + 473, + 287, + 497 + ], + "type": "text", + "content": "On the other hand, for those FP samples which belong to other categories, a penalty term " + }, + { + "bbox": [ + 47, + 473, + 287, + 497 + ], + "type": "inline_equation", + "content": "\\psi_{i}" + }, + { + "bbox": [ + 47, + 473, + 287, + 497 + ], + "type": "text", + "content": " is introduced:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 504, + 287, + 536 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 504, + 287, + 536 + ], + "spans": [ + { + "bbox": [ + 55, + 504, + 287, + 536 + ], + "type": "interline_equation", + "content": "\\psi_ {i} = \\left\\{ \\begin{array}{c} 1 + \\operatorname {d i s} \\left(F _ {i}, \\boldsymbol {\\mu} _ {F P} ^ {k}\\right), \\text {i f} i \\in s _ {T P} ^ {k} \\text {a n d} n _ {F P} ^ {k} > 0; \\\\ 0, \\text {o t h e r w i s e .} \\end{array} \\right. \\tag {7}", + "image_path": "57b491bc7ebafe2e2ee5defb39785158241a8f1ac0fd7107aa9816a99383f565.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 543, + 287, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 543, + 287, + 613 + ], + "spans": [ + { + "bbox": [ + 46, + 543, + 287, + 613 + ], + "type": "text", + "content": "Similarly, the penalty term " + }, + { + "bbox": [ + 46, + 543, + 287, + 613 + ], + "type": "inline_equation", + "content": "\\psi_{i}" + }, + { + "bbox": [ + 46, + 543, + 287, + 613 + ], + "type": "text", + "content": " penalizes the distance between the FP samples and the confident samples in the feature space. When there are no FP samples or the cosine distance converges to " + }, + { + "bbox": [ + 46, + 543, + 287, + 613 + ], + "type": "inline_equation", + "content": "-1" + }, + { + "bbox": [ + 46, + 543, + 287, + 613 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 543, + 287, + 613 + ], + "type": "inline_equation", + "content": "\\psi_{i}" + }, + { + "bbox": [ + 46, + 543, + 287, + 613 + ], + "type": "text", + "content": " reaches the minimum value 0. This may prevent the model from recognizing these ambiguous samples as action " + }, + { + "bbox": [ + 46, + 543, + 287, + 613 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 543, + 287, + 613 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 614, + 287, + 637 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 614, + 287, + 637 + ], + "spans": [ + { + "bbox": [ + 47, + 614, + 287, + 637 + ], + "type": "text", + "content": "Finally, taking sample " + }, + { + "bbox": [ + 47, + 614, + 287, + 637 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 47, + 614, + 287, + 637 + ], + "type": "text", + "content": " as an anchor, the proposed CL loss function can be defined as:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 643, + 291, + 714 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 643, + 291, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 643, + 291, + 714 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\operatorname {C L} \\left(F _ {i}\\right) = - \\log \\frac {e ^ {\\operatorname {d i s} \\left(F _ {i} , P _ {k}\\right) / \\tau - (1 - p _ {i k}) \\psi_ {i}}}{e ^ {\\operatorname {d i s} \\left(F _ {i} , P _ {k}\\right) / \\tau - (1 - p _ {i k}) \\psi_ {i}} + \\sum_ {l \\neq k} e ^ {\\operatorname {d i s} \\left(F _ {i} , P _ {l}\\right) / \\tau}} \\\\ - \\log \\frac {e ^ {\\operatorname {d i s} \\left(F _ {i} , P _ {k}\\right) / \\tau - \\left(1 - p _ {i k}\\right) \\phi_ {i}}}{e ^ {\\operatorname {d i s} \\left(F _ {i} , P _ {k}\\right) / \\tau - \\left(1 - p _ {i k}\\right) \\psi_ {i}} + \\sum_ {l \\neq k} e ^ {\\operatorname {d i s} \\left(F _ {i} , P _ {l}\\right) / \\tau}} \\tag {8} \\\\ \\end{array}", + "image_path": "4cb6b84e2750e1248ee389320223b28bcb9e5e45a165d1a7c4faa2e5ba163e3a.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "inline_equation", + "content": "p_{ik}" + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": " is the predicted probability score of sample " + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": " for class " + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": ". It means that the TP samples with weaker confidence get stronger supervision from those ambiguous samples." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 129, + 417, + 142 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 129, + 417, + 142 + ], + "spans": [ + { + "bbox": [ + 306, + 129, + 417, + 142 + ], + "type": "text", + "content": "3.3. Training Objective" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 317, + 148, + 534, + 160 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 148, + 534, + 160 + ], + "spans": [ + { + "bbox": [ + 317, + 148, + 534, + 160 + ], + "type": "text", + "content": "We use Cross-Entropy (CE) loss to train our network:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 358, + 170, + 545, + 198 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 358, + 170, + 545, + 198 + ], + "spans": [ + { + "bbox": [ + 358, + 170, + 545, + 198 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {C E} = - \\frac {1}{N} \\sum_ {i} \\sum_ {c} y _ {i c} \\log \\left(p _ {i c}\\right) \\tag {9}", + "image_path": "90b8de7b4d8dd4b5eb040e7f6cb30971d253e8924e289aea0c0e5a6a51ac8afa.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 207, + 545, + 266 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 207, + 545, + 266 + ], + "spans": [ + { + "bbox": [ + 304, + 207, + 545, + 266 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 207, + 545, + 266 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 207, + 545, + 266 + ], + "type": "text", + "content": " is the number of samples in a batch. " + }, + { + "bbox": [ + 304, + 207, + 545, + 266 + ], + "type": "inline_equation", + "content": "y_{ic}" + }, + { + "bbox": [ + 304, + 207, + 545, + 266 + ], + "type": "text", + "content": " is the one-hot presentation of the label of sample " + }, + { + "bbox": [ + 304, + 207, + 545, + 266 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 207, + 545, + 266 + ], + "type": "text", + "content": ". If and only if " + }, + { + "bbox": [ + 304, + 207, + 545, + 266 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 207, + 545, + 266 + ], + "type": "text", + "content": " is the target class of sample " + }, + { + "bbox": [ + 304, + 207, + 545, + 266 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 207, + 545, + 266 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 207, + 545, + 266 + ], + "type": "inline_equation", + "content": "y_{ic} = 1" + }, + { + "bbox": [ + 304, + 207, + 545, + 266 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 207, + 545, + 266 + ], + "type": "inline_equation", + "content": "p_{ic}" + }, + { + "bbox": [ + 304, + 207, + 545, + 266 + ], + "type": "text", + "content": " is the probability score of sample " + }, + { + "bbox": [ + 304, + 207, + 545, + 266 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 207, + 545, + 266 + ], + "type": "text", + "content": " belonging to class " + }, + { + "bbox": [ + 304, + 207, + 545, + 266 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 207, + 545, + 266 + ], + "type": "text", + "content": " predicted by the network." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 268, + 545, + 292 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 268, + 545, + 292 + ], + "spans": [ + { + "bbox": [ + 304, + 268, + 545, + 292 + ], + "type": "text", + "content": "Finally, CE loss is combined with our proposed multilevel CL loss to form the full learning objective function:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 378, + 303, + 545, + 316 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 378, + 303, + 545, + 316 + ], + "spans": [ + { + "bbox": [ + 378, + 303, + 545, + 316 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\mathcal {L} _ {C E} + w _ {c l} \\cdot \\mathcal {L} _ {C L} \\tag {10}", + "image_path": "6b122e9ce80ff13f5502e3e5af41a20c905b2a1f25fb8a2ffe2925683d970936.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 326, + 545, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 326, + 545, + 350 + ], + "spans": [ + { + "bbox": [ + 304, + 326, + 545, + 350 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 326, + 545, + 350 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{CL}" + }, + { + "bbox": [ + 304, + 326, + 545, + 350 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 326, + 545, + 350 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{CE}" + }, + { + "bbox": [ + 304, + 326, + 545, + 350 + ], + "type": "text", + "content": " are defined in Eqs. 1 and 9. " + }, + { + "bbox": [ + 304, + 326, + 545, + 350 + ], + "type": "inline_equation", + "content": "w_{cl}" + }, + { + "bbox": [ + 304, + 326, + 545, + 350 + ], + "type": "text", + "content": " is the balanced hyper-parameter for CL loss." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 362, + 386, + 376 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 362, + 386, + 376 + ], + "spans": [ + { + "bbox": [ + 306, + 362, + 386, + 376 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 383, + 368, + 394 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 383, + 368, + 394 + ], + "spans": [ + { + "bbox": [ + 306, + 383, + 368, + 394 + ], + "type": "text", + "content": "4.1. Datasets" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 401, + 545, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 401, + 545, + 557 + ], + "spans": [ + { + "bbox": [ + 304, + 401, + 545, + 557 + ], + "type": "text", + "content": "NTU RGB+D. NTU RGB+D [24] is a widely used dataset containing 56,880 samples. 40 participants are invited to perform 60 actions including daily behaviors and health-related actions. Each action is performed by 1 or 2 people. The human skeleton is presented by 25 3D joints, which are captured by 3 Microsoft Kinect v2 cameras with different horizontal angle settings. It provides two benchmarks: (1) Cross-Subject (X-Sub): the dataset is divided according to the subjects. The training set consists of 20 subjects while the testing set consists of other 20 subjects. (2) Cross-View (X-View): the dataset is split by the camera views. They select camera views 2 and 3 to construct the training data while camera view 1 is used for testing." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "content": "NTU RGB+D 120. NTU RGB+D 120 [21] extends NTU RGB+D with extra 57,367 samples by introducing new 60 action classes, making it the largest skeleton based action recognition dataset. In total, it collects 113,945 skeleton sequences over 120 different classes performed by 106 participants. It also increases the number of camera setups to 32 by using different places and backgrounds. Two evaluation protocols are recommended: (1) Cross-Subject (X-Sub): samples from 56 subjects are selected to form the training set, and the reaming 50 subjects are used for testing. (2) Cross-Set (X-Set): samples with even setup IDs are used for training, while samples with odd setup IDs are used for testing." + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10612" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 83, + 102, + 252, + 200 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 287, + 93 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 287, + 93 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 287, + 93 + ], + "type": "text", + "content": "Table 1. Ablation studies of our method on NTU-RGB+D 120 dataset under the X-Sub setting with the joint input modality." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 83, + 102, + 252, + 200 + ], + "lines": [ + { + "bbox": [ + 83, + 102, + 252, + 200 + ], + "spans": [ + { + "bbox": [ + 83, + 102, + 252, + 200 + ], + "type": "table", + "html": "
MethodParams.Acc (%)
Baseline1.46M84.5
+ CL Loss1.53M85.0↑0.5
+ ST Decouple1.59M85.3↑0.8
+ ML Refine1.61M84.7↑0.2
Ours1.99M85.5↑1.0
", + "image_path": "020ec7d402d3494ffb8f5bf94c7d8900e18ecceae60d15179793159d20732c6c.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 79, + 251, + 256, + 404 + ], + "blocks": [ + { + "bbox": [ + 47, + 210, + 287, + 243 + ], + "lines": [ + { + "bbox": [ + 47, + 210, + 287, + 243 + ], + "spans": [ + { + "bbox": [ + 47, + 210, + 287, + 243 + ], + "type": "text", + "content": "Table 2. Hyper-parameter exploration of our proposed method on NTU-RGB+D 120 dataset under the X-Sub setting with the joint input modality. The best one is in **bold**." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 79, + 251, + 256, + 404 + ], + "lines": [ + { + "bbox": [ + 79, + 251, + 256, + 404 + ], + "spans": [ + { + "bbox": [ + 79, + 251, + 256, + 404 + ], + "type": "table", + "html": "
wclλ1λ2λ3λ4Acc (%)
1000184.4
0.1000185.3
0.01000185.0
111184.5
10.20.2184.7
10.50.20.184.1
0.10.10.11185.2
0.10.10.1185.1
0.10.20.2185.4
0.10.20.5185.5
", + "image_path": "53350a50e9d1de678db54b741849b9d09a72c7bb968d14ce912b292dbb724603.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 424, + 287, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 424, + 287, + 509 + ], + "spans": [ + { + "bbox": [ + 46, + 424, + 287, + 509 + ], + "type": "text", + "content": "NW-UCLA. Northwestern-UCLA dataset [34] contains 1494 video clips performed by 10 volunteers. 3 Kinect cameras are used to capture 3D skeletons with 20 joints from multiple views. Totally 10 action categories are covered. We adopt the evaluation protocols recommended by the author: training data comes from the first two cameras, while testing data is from the other camera." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 515, + 180, + 528 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 515, + 180, + 528 + ], + "spans": [ + { + "bbox": [ + 47, + 515, + 180, + 528 + ], + "type": "text", + "content": "4.2. Implementation Details" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 534, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 534, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 534, + 288, + 713 + ], + "type": "text", + "content": "We adopt [5] as the backbone and implement the proposed method with the PyTorch deep learning framework. All experiments are conducted on one RTX 2080Ti GPU. The Stochastic Gradient Descent (SGD) optimizer is employed with a momentum of 0.9 and a weight decay of 0.0004 to train the models. In the first 5 epochs, we apply a warmup strategy for stable training. The initial learning rate is set to 0.1 and we decrease it at epoch 35 and 55 with a factor of 0.1. We train all models with 70 epochs and select the best performance. The base channel " + }, + { + "bbox": [ + 46, + 534, + 288, + 713 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 534, + 288, + 713 + ], + "type": "text", + "content": " is set to 64 and the hidden channel " + }, + { + "bbox": [ + 46, + 534, + 288, + 713 + ], + "type": "inline_equation", + "content": "C_h" + }, + { + "bbox": [ + 46, + 534, + 288, + 713 + ], + "type": "text", + "content": " is set to 256. The hyper-parameters in our methods are set as: " + }, + { + "bbox": [ + 46, + 534, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\lambda_1 = 0.1" + }, + { + "bbox": [ + 46, + 534, + 288, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 534, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\lambda_2 = 0.2" + }, + { + "bbox": [ + 46, + 534, + 288, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 534, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\lambda_3 = 0.5" + }, + { + "bbox": [ + 46, + 534, + 288, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 534, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\lambda_4 = 1" + }, + { + "bbox": [ + 46, + 534, + 288, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 534, + 288, + 713 + ], + "type": "inline_equation", + "content": "w_{cl} = 0.1" + }, + { + "bbox": [ + 46, + 534, + 288, + 713 + ], + "type": "text", + "content": ". For NTU RGB+D and NTU RGB+D 120, we follow the data preprocessing in [41] and set the batch size to 64. All samples are resized to 64 frames. For NW" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "type": "text", + "content": "UCLA, we follow the data preprocessing in [8] and set the batch size to 16." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 104, + 400, + 118 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 104, + 400, + 118 + ], + "spans": [ + { + "bbox": [ + 306, + 104, + 400, + 118 + ], + "type": "text", + "content": "4.3. Ablation Study" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 123, + 545, + 171 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 123, + 545, + 171 + ], + "spans": [ + { + "bbox": [ + 304, + 123, + 545, + 171 + ], + "type": "text", + "content": "We conduct ablation studies and evaluate the different hyper-parameter settings on the X-Sub benchmark of NTU RGB+D 120 dataset to verify the effectiveness of the proposed module." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 171, + 546, + 375 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 171, + 546, + 375 + ], + "spans": [ + { + "bbox": [ + 304, + 171, + 546, + 375 + ], + "type": "text", + "content": "The results of ablation studies are displayed in Table 1. We remove all additional heads and train the network with CE loss to build the baseline. We also divide the proposed module into different sub-modules and design 3 variants: (1) CL Loss: we directly employ the CL loss to refine features from the last layer without any additional operations. (2) ST Decouple: we decouple the features into spatial and temporal components before refinement. (3) ML Refine: we impose the refinement on proposed multi-level stages in the training pipeline. It can be seen that all these sub-modules can improve the performance of the baseline. Among them, the contributions from CL loss and ST Decouple are relatively dominant. Moreover, when combining all of them, the result becomes better. We also report the count of trainable parameters of different models. The extra cost of parameters may increase the time of the training procedure but does not affect the inference stage." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 376, + 546, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 376, + 546, + 591 + ], + "spans": [ + { + "bbox": [ + 304, + 376, + 546, + 591 + ], + "type": "text", + "content": "We analyze the configurations on the hyper-parameters of our method, and the results are available in Table 2. First, we try 3 different values of " + }, + { + "bbox": [ + 304, + 376, + 546, + 591 + ], + "type": "inline_equation", + "content": "w_{cl}" + }, + { + "bbox": [ + 304, + 376, + 546, + 591 + ], + "type": "text", + "content": " to find the balance between the CL loss and CE loss with the fixed combination of " + }, + { + "bbox": [ + 304, + 376, + 546, + 591 + ], + "type": "inline_equation", + "content": "\\lambda_1 = \\lambda_2 = \\lambda_3 = 0, \\lambda_4 = 1" + }, + { + "bbox": [ + 304, + 376, + 546, + 591 + ], + "type": "text", + "content": " for an efficient experiment. It seems that bigger " + }, + { + "bbox": [ + 304, + 376, + 546, + 591 + ], + "type": "inline_equation", + "content": "w_{cl}" + }, + { + "bbox": [ + 304, + 376, + 546, + 591 + ], + "type": "text", + "content": " may hurt the performance while too small values only provide a little improvement. Then, we try more combinations of " + }, + { + "bbox": [ + 304, + 376, + 546, + 591 + ], + "type": "inline_equation", + "content": "\\lambda_i" + }, + { + "bbox": [ + 304, + 376, + 546, + 591 + ], + "type": "text", + "content": " to balance the importance of different stages. From the results, we can observe that giving higher weight to the previous layers may obtain negative influence and increase the importance gradually from the early stage to the last stage and thus lead to an optimal result. It is concluded that the refinement of the high-level features from the final stage plays a major role and the low-level features provide the auxiliary effects. Finally, we choose the configuration of " + }, + { + "bbox": [ + 304, + 376, + 546, + 591 + ], + "type": "inline_equation", + "content": "\\lambda_1 = 0.1, \\lambda_2 = 0.2, \\lambda_3 = 0.5, \\lambda_4 = 1, w_{cl} = 0.1" + }, + { + "bbox": [ + 304, + 376, + 546, + 591 + ], + "type": "text", + "content": " for the following experiments." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 599, + 485, + 611 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 599, + 485, + 611 + ], + "spans": [ + { + "bbox": [ + 306, + 599, + 485, + 611 + ], + "type": "text", + "content": "4.4. Combined with Other Backbones" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": "Our proposed module is plug-and-play and compatible with most GCN-based backbones. To examine its universality, we apply it to 5 widely used GCN-based backbones [5, 17, 26, 35, 38] and evaluate them on the X-Sub and X-Set of NTU RGB+D 120 dataset. For fair comparisons, we reimplement them and use the same data preprocessing without the multi-stream fusion. Table 3 reports the performance and number of parameters of different methods. It is" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10613" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 47, + 113, + 293, + 294 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 288, + 104 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 288, + 104 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 288, + 104 + ], + "type": "text", + "content": "Table 3. Performance of our proposed method using different GCN-based backbones on NTU-RGB+D 120 dataset with the joint input modality." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 47, + 113, + 293, + 294 + ], + "lines": [ + { + "bbox": [ + 47, + 113, + 293, + 294 + ], + "spans": [ + { + "bbox": [ + 47, + 113, + 293, + 294 + ], + "type": "table", + "html": "
MethodParams.NTU-RGB+D 120
X-Sub (%)X-Set (%)
ST-GCN [38]2.11M83.485.1
+ FR Head2.65M84.4↑1.086.5↑1.4
2s-AGCN [26]3.80M84.385.9
+ FR Head4.33M84.6↑0.386.6↑0.7
CTR-GCN [5]1.46M84.586.6
+ FR Head1.99M85.5↑1.087.3↑0.7
TCA-GCN [35]5.65M85.086.3
+ FR Head6.18M85.2↑0.287.4↑1.1
HD-GCN [17]1.68M85.187.2
+ FR Head2.21M85.4↑0.387.7↑0.5
", + "image_path": "46760e0a5954771ebfcac585e61ae5d015f009d75256c268afea4d084ddf5a94.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 75, + 346, + 260, + 451 + ], + "blocks": [ + { + "bbox": [ + 46, + 303, + 288, + 337 + ], + "lines": [ + { + "bbox": [ + 46, + 303, + 288, + 337 + ], + "spans": [ + { + "bbox": [ + 46, + 303, + 288, + 337 + ], + "type": "text", + "content": "Table 4. Accuracy (\\%) on different difficult level actions for NTU-RGB+D 120 dataset under the X-Sub setting with the joint input modality." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 75, + 346, + 260, + 451 + ], + "lines": [ + { + "bbox": [ + 75, + 346, + 260, + 451 + ], + "spans": [ + { + "bbox": [ + 75, + 346, + 260, + 451 + ], + "type": "table", + "html": "
MethodNTU-RGB+D 120
HardMediumEasy
ST-GCN [38]57.480.994.7
2s-AGCN [26]58.982.095.0
CTR-GCN [5]59.682.495.1
Ours61.683.395.7
Δ2.00.90.6
", + "image_path": "df21168a5cf57c1dbf72f0198c0fc11e1e2f861ff143998c6b0435b60251b00e.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 471, + 287, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 471, + 287, + 579 + ], + "spans": [ + { + "bbox": [ + 46, + 471, + 287, + 579 + ], + "type": "text", + "content": "observed that all models obtain an obvious gain of accuracy by employing the FR Head. The improvement is around " + }, + { + "bbox": [ + 46, + 471, + 287, + 579 + ], + "type": "inline_equation", + "content": "1.0\\%" + }, + { + "bbox": [ + 46, + 471, + 287, + 579 + ], + "type": "text", + "content": ". In most cases, the models with lower accuracy are improved more than those with higher initial accuracy. The reason behind it may be that our modules utilize the knowledge from the misclassified samples. The lower accuracy of means the misclassified samples are more sufficient. The additional count of parameters introduced by the FR Head is around 0.5M and can be ignored in the inference stage." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 586, + 239, + 601 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 586, + 239, + 601 + ], + "spans": [ + { + "bbox": [ + 47, + 586, + 239, + 601 + ], + "type": "text", + "content": "4.5. Performance on Ambiguous Actions" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "type": "text", + "content": "We spilt NTU-RGB+D 120 dataset into 3 subsets with different difficulty levels. Specifically, according to the results of CTR-GCN [5], we gather actions whose accuracy is lower than " + }, + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "type": "inline_equation", + "content": "70\\%" + }, + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "type": "text", + "content": " as Hard Level, between " + }, + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "type": "inline_equation", + "content": "70\\%" + }, + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "type": "inline_equation", + "content": "90\\%" + }, + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "type": "text", + "content": " as Medium Level, and over " + }, + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "type": "inline_equation", + "content": "90\\%" + }, + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "type": "text", + "content": " as Easy Level. The results are displayed in Table 4. The experiment is under the X-Subsetting with only the joint input modality. Because ambiguous actions are quite similar and easy to be misclassified, these actions usually fall into Hard Level. From the" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 309, + 73, + 545, + 190 + ], + "blocks": [ + { + "bbox": [ + 309, + 73, + 545, + 190 + ], + "lines": [ + { + "bbox": [ + 309, + 73, + 545, + 190 + ], + "spans": [ + { + "bbox": [ + 309, + 73, + 545, + 190 + ], + "type": "image", + "image_path": "dc79be0a46ef8262f50fb5e591bd41f3997cb86db5f50f580274ad4465ee81ae.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 198, + 547, + 243 + ], + "lines": [ + { + "bbox": [ + 304, + 198, + 547, + 243 + ], + "spans": [ + { + "bbox": [ + 304, + 198, + 547, + 243 + ], + "type": "text", + "content": "Figure 4. The group-wise accuracy difference " + }, + { + "bbox": [ + 304, + 198, + 547, + 243 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 304, + 198, + 547, + 243 + ], + "type": "text", + "content": " between our method and CTR-GCN [5] on ambiguous actions for NTU-RGB+D 120 dataset under the X-Sub setting with the joint input modality." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 308, + 256, + 545, + 347 + ], + "blocks": [ + { + "bbox": [ + 308, + 256, + 545, + 347 + ], + "lines": [ + { + "bbox": [ + 308, + 256, + 545, + 347 + ], + "spans": [ + { + "bbox": [ + 308, + 256, + 545, + 347 + ], + "type": "image", + "image_path": "429fda840fd97c3e07d4afb7078fd0e775a11a418027e6986db527569c037ece.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 354, + 545, + 399 + ], + "lines": [ + { + "bbox": [ + 304, + 354, + 545, + 399 + ], + "spans": [ + { + "bbox": [ + 304, + 354, + 545, + 399 + ], + "type": "text", + "content": "Figure 5. Visualization of latent representation by t-SNE for ambiguous groups from NTU RGB+D 120 dataset. Different colors indicate different classes. The upper one is from the CTR-GCN [5], while the bottom one is from our method." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 423, + 545, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 423, + 545, + 460 + ], + "spans": [ + { + "bbox": [ + 304, + 423, + 545, + 460 + ], + "type": "text", + "content": "results, we can see that our method makes a great improvement in Hard Level actions, which demonstrates the ability to distinguish those ambiguous actions." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 460, + 546, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 460, + 546, + 640 + ], + "spans": [ + { + "bbox": [ + 304, + 460, + 546, + 640 + ], + "type": "text", + "content": "Furthermore, we define ambiguous groups, which collect several related ambiguous actions to verify the performance of ambiguous samples. We first pick a class as an anchor class, for example, \"writing\". Then we gather the misclassified samples on \"writing\" and obtain the top-3 actions with the highest frequency, like \"reading\", \"typing on a keyboard\" and \"playing with phone\". These 4 actions will be constructed as an ambiguous group. The group-wise accuracy will be the average accuracy of all actions included by the group. Here, we randomly pick 60 anchor actions and constructed corresponding ambiguous groups from NTU-RGB+D 120 dataset. We compare our results with a SOTA model CTR-GCN [5] and display the results in Fig. 4. Our method gains great improvement in most ambiguous groups." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "type": "text", + "content": "We randomly pick some ambiguous groups and visualize the distribution of them in the feature space using t-SNE. As mentioned before, each ambiguous group contains four classes, including an anchor class and three ambiguous classes. We compare our method with CTR-GCN [5]. Fig. 5 shows that our model achieves a more compact clustering." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "10614" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 89, + 101, + 504, + 383 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 547, + 94 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 547, + 94 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 547, + 94 + ], + "type": "text", + "content": "Table 5. Performance comparison of skeleton-based action recognition in top-1 accuracy (\\%). The best one is in bold and the second one is underlined." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 89, + 101, + 504, + 383 + ], + "lines": [ + { + "bbox": [ + 89, + 101, + 504, + 383 + ], + "spans": [ + { + "bbox": [ + 89, + 101, + 504, + 383 + ], + "type": "table", + "html": "
MethodPublicationNTU RGB+DNTU RGB+D 120NW-UCLA
X-SubX-ViewX-SubX-Set
ST-GCN [38]AAAI201881.588.3---
Ind-RNN [18]CVPR201881.888.0---
RotClips+MTCNN [15]TIP2018--62.261.8-
2s-AGCN [26]CVPR201988.595.182.984.9-
AGC-LSTM [27]CVPR201989.295.0--93.3
DGNN [25]CVPR201989.996.1---
PA-ResGCN-B19 [28]ACMMM202090.996.087.388.3-
Dynamic GCN [39]ACMMM202091.596.087.388.6-
SGN [41]CVPR202089.094.579.281.5-
Shift-GCN [8]CVPR202090.796.585.987.694.6
MS-G3D [22]CVPR202091.596.286.988.4-
DDGCN [16]ECCV202091.197.1---
DC-GCN+ADG [7]ECCV202090.896.686.588.195.3
MST-GCN [6]AAAI202191.596.687.588.8-
Skeletal-GNN [40]ICCV202191.696.787.589.2-
CTR-GCN [5]ICCV202192.496.888.990.696.5
STF [14]AAAI202292.596.988.989.9-
Ta-CNN [36]AAAI202290.494.885.486.896.1
EfficientGCN-B4 [29]TPAMI202291.795.788.389.1-
Ours-92.896.889.590.996.8
", + "image_path": "6773a5571be44201e551e3a72001de974c741cbe778aa05cd1f8a034236f8c44.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 403, + 249, + 416 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 403, + 249, + 416 + ], + "spans": [ + { + "bbox": [ + 47, + 403, + 249, + 416 + ], + "type": "text", + "content": "4.6. Comparison with the State-of-the-Art" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 421, + 288, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 421, + 288, + 540 + ], + "spans": [ + { + "bbox": [ + 46, + 421, + 288, + 540 + ], + "type": "text", + "content": "In this section, we conduct a comparison with the state-of-the-art methods on NTU RGB+D 120, NTU RGB+D, and NW-UCLA datasets to demonstrate the competitive ability of our proposed module. The quantitative results are displayed in Table 5. It is noted that most of the state-of-the-art methods employ a multi-stream fusion framework. For a fair comparison, we follow the same framework as [5,35]. We make a fusion with the results from four modalities including joint, bone, joint motion, and bone motion as the final report result." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 541, + 287, + 661 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 541, + 287, + 661 + ], + "spans": [ + { + "bbox": [ + 46, + 541, + 287, + 661 + ], + "type": "text", + "content": "It is observed that our methods outperform most existing methods on these three datasets. On both settings of NTU-RGB+D 120, X-Sub of NTU-RGB+D, and NW-UCLA datasets, our model obtains the best results. On X-View of NTU-RGB+D, our model reaches state-of-the-art results with a reasonable gap between the best one, which demonstrates the great potential of our proposed module. Notably, our method is the first to propose a way to solve ambiguous actions, which are very important in skeleton based action recognition." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 669, + 119, + 682 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 669, + 119, + 682 + ], + "spans": [ + { + "bbox": [ + 47, + 669, + 119, + 682 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "type": "text", + "content": "In this paper, we present a novel feature refinement module equipped with contrastive learning to solve the" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 403, + 545, + 488 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 403, + 545, + 488 + ], + "spans": [ + { + "bbox": [ + 304, + 403, + 545, + 488 + ], + "type": "text", + "content": "ambiguous actions for skeleton based action recognition. Multi-level features extracted from GCN-based backbone are leveraged and enhanced on both the spatial and temporal dimensions. The contrastive learning is conducted with the samples with high confidence and calibrated by the FP and FN samples to make full use of the misclassified actions." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 491, + 545, + 562 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 491, + 545, + 562 + ], + "spans": [ + { + "bbox": [ + 304, + 491, + 545, + 562 + ], + "type": "text", + "content": "The extensive experiments demonstrate the effectiveness of the proposed module to distinguish the confusing categories and the university to be compatible with most GCN-based backbones. On three widely used benchmarks, our proposed method obtains satisfactory results and outperforms those state-of-the-art methods." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 566, + 545, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 566, + 545, + 674 + ], + "spans": [ + { + "bbox": [ + 304, + 566, + 545, + 674 + ], + "type": "text", + "content": "Discussion. Despite the performance of our proposed module on three public large-scale datasets, the ambiguous actions in a few-shot setting with insufficient data remain to be explored. We will concentrate on it in our future work. In addition, there are some potential negative societal impacts to be considered. Our method may be applied in some controversial fields, such as surveillance. Besides, applying our module will introduce extra training costs, which should be discussed in the carbon emission problem." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "content": "Acknowledgements. This paper was founded by National Natural Science Foundation of China under grants U20B2069 and 62176017." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 758 + ], + "type": "text", + "content": "10615" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 156 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 156 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 156 + ], + "type": "text", + "content": "[1] Yujun Cai, Liuhao Ge, Jun Liu, Jianfei Cai, Tat-Jen Cham, Junsong Yuan, and Nadia Magnenat Thalmann. 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In Proceedings of the AAAI Conference on Artificial Intelligence, volume 34, pages 13130-13137, 2020. 3" + } + ] + } + ], + "index": 18 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "10617" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Learning Distortion Invariant Representation for Image Restoration From a Causality Perspective/bf96eb62-eb0a-4620-9268-36a8377665e9_content_list.json b/2023/Learning Distortion Invariant Representation for Image Restoration From a Causality Perspective/bf96eb62-eb0a-4620-9268-36a8377665e9_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..adbfadb3e59bb2355bdaa5915bc0c52be7fa68ee --- /dev/null +++ b/2023/Learning Distortion Invariant Representation for Image Restoration From a Causality Perspective/bf96eb62-eb0a-4620-9268-36a8377665e9_content_list.json @@ -0,0 +1,1680 @@ +[ + { + "type": "text", + "text": "Learning Distortion Invariant Representation for Image Restoration from A Causality Perspective", + "text_level": 1, + "bbox": [ + 140, + 130, + 828, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Xin Li $^{1}$ , Bingchen Li $^{1}$ , Xin Jin $^{2}$ , Cuiling Lan $^{3\\dagger}$ , Zhibo Chen $^{1\\dagger}$ $^{1}$ University of Science and Technology of China $^{2}$ Eastern Institute for Advanced Study \n $^{3}$ Microsoft Research Asia", + "bbox": [ + 133, + 202, + 834, + 253 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{lixin666, lbc31415926}@mail.ustc.edu.cn, jinxin@eias.ac.cn,", + "bbox": [ + 218, + 258, + 746, + 273 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "culan@microsoft.com, chenzhibo@ustc.edu.cn", + "bbox": [ + 297, + 277, + 671, + 291 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 325, + 313, + 343 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In recent years, we have witnessed the great advancement of Deep neural networks (DNNs) in image restoration. However, a critical limitation is that they cannot generalize well to real-world degradations with different degrees or types. In this paper, we are the first to propose a novel training strategy for image restoration from the causality perspective, to improve the generalization ability of DNNs for unknown degradations. Our method, termed Distortion Invariant representation Learning (DIL), treats each distortion type and degree as one specific confounder, and learns the distortion-invariant representation by eliminating the harmful confounding effect of each degradation. We derive our DIL with the back-door criterion in causality by modeling the interventions of different distortions from the optimization perspective. Particularly, we introduce counterfactual distortion augmentation to simulate the virtual distortion types and degrees as the confounders. Then, we instantiate the intervention of each distortion with a virtual model updating based on corresponding distorted images, and eliminate them from the meta-learning perspective. Extensive experiments demonstrate the generalization capability of our DIL on unseen distortion types and degrees. Our code will be available at https://github.com/lixinustc/Causal-IR-DIL.", + "bbox": [ + 75, + 359, + 472, + 720 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 753, + 209, + 768 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Image restoration (IR) tasks [7, 8, 32, 51], including image super-resolution [11, 24, 43, 46, 56, 57], deblurring [41, 75], denoising [3, 23, 40], compression artifacts removal [28, 53], etc, have achieved amazing/uplifting performances, powered by deep learning. A series of backbones are elaborately and carefully designed to boost the", + "bbox": [ + 75, + 781, + 468, + 875 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/ca1f35bdb9b6dc03efc6b463b172cd755568d61b882db27830d2c9fb233c5fce.jpg", + "image_caption": [ + "Figure 1. A comparison between ERM and our DIL with RRDB as backbone. The results are tested on Set5 with Gaussian noise." + ], + "image_footnote": [], + "bbox": [ + 522, + 325, + 870, + 487 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "restoration performances for specific degradation. Convolution neural networks (CNNs) [20] and transformers [12,34] are two commonly-used designed choices for the backbones of image restoration. However, these works inevitably suffer from severe performance drops when they encounter unseen degradations as shown in Fig. 1, where the restoration degree in training corresponds to the noise of standard deviation 20 and the degrees in testing are different. The commonly-used training paradigm in image restoration, i.e., empirical risk minimization (ERM), does not work well for out-of-distribution degradations. Particularly, the restoration networks trained with ERM merely mine the correlation between distorted image $I_{d}$ and its ideal reconstructed image $I_{o}$ by minimizing the distance between $I_{o}$ and the corresponding clean image $I_{c}$ . However, a spurious correlation [44] is also captured which introduces the bad confounding effects of specific degradation $d$ . It means the conditional probability $P(I_{o}|I_{d})$ is also conditioned on the distortion types or degrees $d$ (i.e., $d \\nmid I_{o}|I_{d}$ ).", + "bbox": [ + 496, + 535, + 890, + 823 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "A robust/generalizable restoration network should be distortion-invariant (i.e., $d \\perp I_{o}|I_{d}$ ). For instance, given two distorted images with the same content $I_{c}$ but different degradations $d_{1}$ and $d_{2}$ , the robust restoration network is expected to recover the same reconstructed image $I_{o}$", + "bbox": [ + 496, + 824, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "†Corresponding Author", + "bbox": [ + 94, + 886, + 223, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "1714", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "from these two distorted images (i.e., $P(I_{o}|I_{d}, d = d_{1}) = P(I_{o}|I_{d}, d = d_{2})$ ), respectively. Previous works for the robustness of the restoration network can be roughly divided into two categories, distortion adaptation-based schemes, and domain adaptation/translation-based schemes. Distortion adaptation-based schemes [60] aim to estimate the distortion types or representations, and then, handle the different distortions by adaptively modulating the restoration network. Domain adaptation/translation-based schemes [13, 35,48] regard different distortions as different domains, and introduce the domain adaptation/translation strategies to the image restoration field. Notwithstanding, the above works ignore the exploration of the intrinsic reasons for the poor generalization capability of the restoration network. In this paper, we take the first step to the causality-inspired image restoration, where novel distortion invariant representation learning from the causality perspective is proposed, to improve the generalization capability of the restoration network.", + "bbox": [ + 76, + 90, + 472, + 377 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "As depicted in [17, 44], correlation is not equivalent to causation. Learning distortion invariant representation for image restoration requires obtaining the causal effects between the distorted and ideal reconstructed images instead of only their correlation. There are two typical adjustment criteria for causal effects estimation [17], the back-door criterion, and the front-door criterion, respectively. In particular, the back-door criterion aims to remove the bad confounding effects by traversing over known confounders, while the front-door criterion is to solve the challenge that confounders cannot be identified. To improve the generalization capability of the restoration network, we build a structural causal graph in Fig. 2 for the image restoration process and propose the Distortion-Invariant representation Learning (DIL) for image restoration by implementing the back-door criterion from the optimization perspective. There are two challenges for achieving this. The first challenge is how to construct the confounder sets (i.e., distortion sets). From the causality perspective [17, 44], it is better to keep other factors in the distorted image invariant except for distortion types. However, in the real world, collecting distorted/clean image pairs, especially with different real distortions but the same content is impractical. Inspired by counterfactual [44] in causality and the distortion simulation [55, 71], we propose counterfactual distortion augmentation, which selects amounts of high-quality images from the commonly-used dataset [2, 49], and simulate the different distortion degrees or types on these images as the confounders.", + "bbox": [ + 76, + 383, + 472, + 821 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Another challenge of implementing DIL stems from finding a stable and proper instantiating scheme for the back-door criterion. Previous works [36,37,54,64,65] have incorporated causal inference in high-level tasks by instantiating the back-door criterion [17] with attention interven-", + "bbox": [ + 76, + 824, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "tion [64], feature interventions [66], etc, which are arduous to be exploited in the low-level task of image restoration. In this work, we theoretically derive our distortion-invariant representation learning DIL by instantiating the back-door criterion from the optimization perspective. Particularly, we model the intervention of simulated distortions for the restoration process by virtually updating the restoration network with the samples from the corresponding distortions. Then, we eliminate the confounding effects of distortions by introducing the optimization strategy from Meta-Learning to our proposed DIL. In this way, we can instantiate the causal learning in image restoration and enable the DIL based on the back-door criterion.", + "bbox": [ + 496, + 90, + 893, + 286 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The contributions of this paper are listed as follows:", + "bbox": [ + 517, + 287, + 861, + 301 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We revisit the image restoration task from a causality view and pinpoint that the reason for the poor generalization of the restoration network, is that the restoration network is not independent to the distortions in the training dataset.", + "- Based on the back-door criterion in causality, we propose a novel training paradigm, Distortion Invariant representation Learning (DIL) for image restoration, where the intervention is instantiated by a virtually model updating under the counterfactual distortion augmentation and is eliminated with the optimization based on meta-learning.", + "- Extensive experiments on different image restoration tasks have demonstrated the effectiveness of our DIL for improving the generalization ability on unseen distortion types and degrees." + ], + "bbox": [ + 517, + 304, + 890, + 551 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 500, + 563, + 648, + 579 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Image Restoration", + "text_level": 1, + "bbox": [ + 500, + 582, + 679, + 597 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Image Restoration (IR) [7, 22, 26, 32, 33, 51, 67] aims to recover high-quality images from the corresponding distorted images, which plays a prominent role in improving the human visual experience. With the advancement of deep learning, a series of works have achieved remarkable progress in lots of IR tasks, including image denoising [3, 40, 73], deblurring [41, 50, 75], super-resolution (SR) [9, 11, 27, 58, 61, 62, 74], etc. Particularly, most of them are devoted to elaborately designing the frameworks for different IR tasks based on their degradation process, which can be roughly divided into two categories, CNN-based framework [9, 11, 74], and Transformer-based framework [7, 24, 32, 67]. Despite that, the above works only explore how to improve the ability of inductive bias toward specific degradation, which lacks enough generalization capability. To improve the model's robustness, some works seek to incorporate the domain translation [13, 35, 48] or distortion-adaptive learning [60] into image restoration. In contrast, we introduce causal learning [17] to image restoration. We answer the reason for the bad robustness of the", + "bbox": [ + 496, + 598, + 893, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "1715", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "restoration network and propose distortion-invariant representation learning from a causality perspective.", + "bbox": [ + 75, + 90, + 468, + 121 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Causal Inference", + "text_level": 1, + "bbox": [ + 76, + 122, + 243, + 136 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Causal Inference is proposed to eliminate the harmful bias of confounders and discover the causal relationship between multiple variables [17]. A do operation is implemented with adjustment criteria, e.g., front-door or back-door, to estimate the causal effects [44]. In recent years, deep learning has boosted the vast development of a series of intelligent tasks, e.g., image classification [10, 12, 34], segmentation [19, 47], detection [6, 30], low-level processing [7, 51]. However, prominent works focus on fitting the correlation between inputs and their outputs while ignoring the causation. Due to the existence of confounders, the networks are easy to capture the spurious correlation between inputs and their outputs. For instance, if most lions lie in the grass in the training data, the model inevitably mistakes the grass for a lion. To get rid of the harmful bias of confounders, some studies seek to incorporate causal inference into deep learning. [54, 66] model the interventions of confounders from the feature perspective [64] integrate the front-door criterion to vision-language task from the attention perspective. To improve the generalization capability, [29, 36, 37, 65] introduce the causal learning to domain adaptation/generalization. However, the above causality-inspired methods merely focus on the high-level tasks. In this paper, for the first time, we investigate the causality-based image restoration, which aims to improve the generalization capability of restoration networks on different distortion types and degrees.", + "bbox": [ + 75, + 138, + 472, + 547 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methods", + "text_level": 1, + "bbox": [ + 76, + 561, + 174, + 577 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. A Causal View for Image Restoration", + "text_level": 1, + "bbox": [ + 76, + 580, + 400, + 595 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Image restoration aims to restore the distorted images, of which the degradation process can be represented as a function $I_{d} = g(I_{c},D)$ . Here, $I_{c},I_{d},D$ denote the clean, distorted images, and distortions, respectively. $D$ contains distortion types $D_{t}$ and degrees $D_{l}$ . A restoration network $f$ is trained with the loss function to minimize the difference between its ideal reconstructed images $I_{o}$ and the original clean image $I_{c}$ . We model this whole process with a structure causal graph as shown in Fig. 2. Here, $D\\rightarrow I_d\\leftarrow I_c$ denotes the degradation process of $I_{d} = g(I_{c},D)$ . $I_{c}\\rightarrow I_{o}$ denotes $I_{o}$ is learned with the supervision of $I_{c}$ by maximizing the probability of $P(I_c|I_o)$ . In addition, $D\\to I_o$ refers to the knowledge learned from $D$ to $I_{o}$ . $I_{d}\\rightarrow I_{o}$ means the restoration process with restoration network $f$ .", + "bbox": [ + 75, + 598, + 468, + 809 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "From the causality perspective, the causal representation of image restoration requires that the restoration network $f$ obtains the causal relationship between $I_{d} \\rightarrow I_{o}$ . However, there are two extra paths $I_{d} \\leftarrow D \\rightarrow I_{o}$ and $I_{d} \\leftarrow I_{c} \\rightarrow I_{o}$ introducing the spurious correlation to $I_{d}$ and $I_{o}$ , where $I_{c}$ and $D$ are confounders in causality. Importantly, the $I_{c}$ are", + "bbox": [ + 75, + 810, + 470, + 901 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/fa13543cf2c61f5a168cea4d798641af881d33d9b2ac0941a30535d521fc6cad.jpg", + "image_caption": [ + "Figure 2. Structure causal graph for image restoration." + ], + "image_footnote": [], + "bbox": [ + 540, + 88, + 679, + 220 + ], + "page_idx": 2 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "$D$ Distortion Set", + "$D_{t}$ Distortion Types", + "$D_{l}$ Distortion Degrees", + "$I_{d}$ Distorted Images", + "$I_{o}$ Ideal Reconstructed Images", + "$I_{c}$ Clean Images", + "$f$ Restoration Network", + "$d$ Distortion sampled from $D$" + ], + "bbox": [ + 686, + 92, + 851, + 220 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "commonly diverse in the datasets and bring more vivid textures to reconstructed image $I_{o}$ , which is a favorable confounder. We do not take into account the confounder $I_{c}$ in our paper.", + "bbox": [ + 496, + 255, + 890, + 315 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We aim to improve the robustness of the restoration network to unseen or unknown distortions, which are inhibited by the bad confounding effects from confounders $D$ . But, how do the confounders $D$ limit the generalization capability of the restoration network? As shown in Fig. 2, the existing of $I_{d} \\gets D \\to I_{o}$ causes the conditional probability $P(I_{o}|I_{d})$ learned by restoration network $f$ is also condition on distortions $D$ , i.e., the fitting conditional probability of $f$ is in fact as $P(I_{o}|I_{d},D)$ . Consequently, the restoration network $f$ is not robust to different distortions due to that it is not independent of different distortions $D$ .", + "bbox": [ + 496, + 316, + 892, + 481 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "A robust restoration network $f$ should be independent of different distortions (i.e., $D \\perp I_o|I_d$ ). To achieve this, we adopt the back-door criterion in causal inference to realize distortion-invariant learning (DIL) through a \"do\" operation. Here, a \"do\" operation [17, 44] is exploited to cut off the connection from the distortion $D$ to $I_d$ , thereby removing the bad confounding effects of $D$ to the path $I_d \\to I_o$ , and learning the distortion-invariant feature representation (i.e., $D \\perp I_o|I_d$ ). We formulate the back-door criterion in image restoration as Equ. 1.", + "bbox": [ + 496, + 482, + 892, + 633 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nP \\left(I _ {o} | d o \\left(I _ {d}\\right)\\right) = \\sum_ {d _ {i} \\in D} P \\left(I _ {o} \\mid I _ {d}, d _ {i}\\right) P \\left(d _ {i}\\right), P \\left(d _ {i}\\right) = \\frac {1}{n}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 508, + 641, + 890, + 679 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where the causal conditional probability $P(I_{o}|do(I_{d}))$ is the optimization direction for restoration network $f$ towards distortion invariant learning. To simplify the optimization, we set the probability of each distortion $d_{i}$ as $1 / n$ , where $n$ is the number of distortion types and degrees that existed in confounders. From Equ. 1, two crucial challenges for achieving it arise. 1) How to construct the virtual confounders (i.e., different distortion types or degrees)? since collecting different real distorted images with the same contents are nontrivial in the real world. 2) How to instantiate the intervention of different distortions to the reconstruction process (i.e., the $P(I_{o}|I_{d},d_{i})$ ) in image restoration. We achieve this through counterfactual distortion augmentation and distortion-invariant representation learning as described", + "bbox": [ + 496, + 688, + 893, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "1716", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "in the following sections.", + "bbox": [ + 76, + 90, + 246, + 104 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Counterfactual Distortion Augmentation", + "text_level": 1, + "bbox": [ + 76, + 114, + 426, + 130 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To learn the distortion-invariant representation for the restoration network, it is vital to construct the distortion set $D$ (i.e., confounders). For instance, if we expect the restoration network to have the generalization capability for different distortion degrees, we require to construct the distortion set $D$ with the distortions at different levels. Similarly, we can increase the generalization capability of the restoration network for unknown distortion types by constructing the $D$ with different but related distortion types. Furthermore, to avoid the effects of different image contents, it is better for each clean image to have corresponding distorted images with various distortion types or degrees in $D$ . However, it is non-trivial to collect datasets that satisfy the above principles in the real world, which is labor-intensive and arduous.", + "bbox": [ + 75, + 137, + 468, + 348 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this paper, we construct the distortion set $D$ with synthesized distortions, which we can call virtual confounders in causality. Concretely, we collected a series of high-quality images $I_{c}$ , and generated the distorted images by modifying the degradation process as $I_{d} = g(I_{c}, d_{i}), d_{i} \\in D$ . We can also prove the rightness of the above distortion augmentation from the counterfactuals in causality [17], where we answer the counterfactual question that \"if $D$ is $d_{i}$ , what the $I_{d}$ would be with $I_{c}$ invariant?\". The proof can be found in the Supplementary.", + "bbox": [ + 75, + 349, + 470, + 501 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Distortion-invariant Representation Learning", + "text_level": 1, + "bbox": [ + 76, + 508, + 465, + 523 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "After constructing the virtual confounders/distortions set $D = \\{d_i | 1 \\leq i \\leq n\\}$ . We are able to achieve the distortion-invariant representation learning by implementing the back-door criterion as Eq. 1 for image restoration. Let us first introduce the relationship between the probability $P(I_o|I_d)$ and the commonly-used training paradigm ERM (empirical risk minimization). In image restoration, an ideal reconstruction $I_o$ is expected to learn by maximizing the condition probability $P(I_o|I_d)$ with loss function as $\\mathcal{L}(f_{\\theta}(I_d), I_c)$ , where $f_{\\theta}$ is the restoration network with the parameters $\\theta$ and $L$ denotes the loss function, such as the commonly-used $\\mathcal{L}_1$ or $\\mathcal{L}_2$ loss. The ERM is used to optimize the network $f_{\\theta}$ (with parameters denoted by $\\theta$ ) by minimizing the loss function overall training dataset $\\mathcal{D} = \\{I_d, I_c | d \\in D\\}$ as:", + "bbox": [ + 75, + 531, + 468, + 758 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\theta^ {*} = \\arg \\min _ {\\theta} \\mathbb {E} _ {(I _ {d}, I _ {c}) \\sim \\mathcal {D}} [ \\mathcal {L} (f _ {\\theta} (I _ {d}), I _ {c}) ], \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 135, + 765, + 468, + 787 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\theta^{*}$ enables the restoration network $f$ to maximize the $P(I_{o}|I_{d})\\approx P(I_{c}|I_{d})$ . However, the above training process also leads the $P(I_{o}|I_{d})$ to be not independent to the distortions $d\\in D$ in the training dataset $\\mathcal{D}$ , which eliminate the generalization ability of $f$ on the out-of-distribution distortions (i.e., when $d\\notin D$ ). To achieve the distortion-invariant representation learning, we aim to maximize the", + "bbox": [ + 75, + 794, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "causal conditional probability $P(I_{o}|do(I_{d}))$ as instead of $P(I_{o}|I_{d})$ . The key challenge stems from how to model the conditional probability $P(I_{o}|I_{d},d_{i})$ in Eq. 1 (i.e., how to model the intervention from the distortion $d_{i}\\in D$ for the restoration process $P(I_o|I_d)$ ).", + "bbox": [ + 496, + 90, + 890, + 167 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this paper, we propose to model the intervention from $d_{i} \\in D$ to the restoration process (i.e., $P(I_{o}|I_{d},d_{i})$ ) through the optimization of the network parameters $\\theta$ . From the above analysis, we know that the restoration network $f_{\\theta}$ trained with ERM on the paired training data $(I_{d_i},I_c)$ is condition on the distortion $d_{i}$ . This inspires us to instantiate the intervention of different distortion types or degrees $d_{i} \\in D$ through updating the model parameter $\\theta$ to $\\phi_{d_i}$ based on ERM with the training distorted-and-clean image pairs $(I_{d_i},I_c)$ as:", + "bbox": [ + 496, + 167, + 890, + 318 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\phi_ {d _ {i}} = \\theta - \\alpha \\nabla_ {\\theta} \\mathcal {L} \\left(f _ {\\theta} \\left(I _ {d _ {i}}\\right), I _ {c}\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 591, + 325, + 890, + 342 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\phi_{d_i}$ denotes the parameters of the restoration network after one-step update, which is conditioned on the confounder $d_i$ . Consequently, the maximum of the conditional probability $P(I_o|I_d,d_i)$ can be obtained by minimizing the loss $\\mathcal{L}(f_{\\phi_{d_i}}(I_d),I_c)$ . The optimization direction toward maximizing the causal condition probability $P(I_o|do(I_d))$ in Eq. 1 can be derived as:", + "bbox": [ + 496, + 349, + 890, + 455 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\theta^ {*} = \\arg \\min _ {\\theta} \\mathbb {E} _ {(I _ {d}, I _ {c}) \\sim \\mathcal {D}} [ \\sum_ {d _ {i} \\in D} \\mathcal {L} \\left(f _ {\\phi_ {d _ {i}}} (I _ {d}), I _ {c}\\right) ], \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 526, + 463, + 890, + 494 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $D$ denotes the confounder set which contains $n$ distortion degrees or types. Based on the above optimization objective, we learn distortion-invariant representation learning from a causality perspective.", + "bbox": [ + 496, + 501, + 890, + 561 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Implementations of DIL from Meta-Learning", + "text_level": 1, + "bbox": [ + 500, + 570, + 883, + 585 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "An interesting finding is that the derived optimization direction of DIL from causality perspective in Eq. 4 is consistent with one typical meta-learning strategy termed as MAML [14], even they have different purposes. MAML aims to enable the fast adaptation capability of a network for few-shot tasks, while ours aims to improve the generalization capability of the restoration network. We facilitate our DIL in image restoration based on this meta-learning strategy.", + "bbox": [ + 496, + 593, + 890, + 728 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "However, it is arduous to directly incorporate the optimization direction of Eq. 4 into the practical training process, which is computationally prohibitive. The reason is that it requires multiple gradient computing and updating, which is expensive, especially for the pixel-wise image restoration. To simplify this process, we utilize the Talyor expansion and inverse expansion to derive Eq. 4 as:", + "bbox": [ + 496, + 729, + 890, + 835 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\theta^ {*} = \\arg \\min _ {\\theta} \\mathbb {E} _ {(I _ {d}, I _ {c}) \\sim \\mathcal {D}} [ \\mathcal {L} (f _ {\\phi_ {\\bar {d}}} (I _ {d}), I _ {c}) ],\n$$\n", + "text_format": "latex", + "bbox": [ + 542, + 842, + 823, + 864 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nw h e r e \\phi_ {\\tilde {d}} = \\theta - \\alpha \\nabla_ {\\theta} \\sum_ {d _ {i} \\in D} \\frac {1}{n} \\mathcal {L} \\left(f _ {\\theta} \\left(I _ {d _ {i}}\\right), I _ {c}\\right), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 545, + 864, + 890, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "1717", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/4f8ea8a2faae326c60ea341dae7ecaeeacd6283936d3474c3e520f8864e0bc97.jpg", + "table_caption": [ + "Table 1. Quantitative comparison for image denoising on several benchmark datasets. Results are tested on three different unseen distortion degrees in terms of PSNR/SSIM on RGB channel. Best performances are bolded." + ], + "table_footnote": [], + "table_body": "
DatasetsLevelsMethods
ERMDILsfDILpfDILssDILps
CBSD68 [38]30 (unseen)24.90/0.58130.29(5.39↑)/0.86629.92(5.02↑)/0.85827.48(2.58↑)/0.80929.14(4.24↑)/0.802
40 (unseen)21.12/0.40028.35(7.23↑)/0.82528.10(6.98↑)/0.81225.90(4.78↑)/0.74625.74(4.62↑)/0.629
50 (unseen)18.96/0.30726.64(7.68↑)/0.77926.61(7.65↑)/0.76624.63(5.67↑)/0.68623.34(4.38↑)/0.501
Kodak24 [15]30 (unseen)25.12/0.53331.39(6.27↑)/0.86730.87(5.75↑)/0.85827.92(2.80↑)/0.80129.86(4.74↑)/0.782
40 (unseen)21.22/0.35229.49(8.27↑)/0.83129.15(7.93↑)/0.81726.46(5.24↑)/0.73826.13(4.91↑)/0.588
50 (unseen)19.02/0.26327.76(8.74↑)/0.78827.67(8.65↑)/0.77525.24(6.22↑)/0.67723.60(4.58↑)/0.457
McMaster [72]30 (unseen)25.65/0.56931.70(6.05↑)/0.87331.04(5.39↑)/0.85328.15(2.50↑)/0.79430.09(4.44↑)/0.800
40 (unseen)21.73/0.37329.81(8.08↑)/0.83129.07(7.34↑)/0.80226.59(4.86↑)/0.72826.24(4.51↑)/0.605
50 (unseen)19.47/0.27828.02(8.55↑)/0.78327.31(7.84↑)/0.74925.20(5.73↑)/0.66423.60(4.13↑)/0.466
Urban100 [21]30 (unseen)25.46/0.64830.93(5.47↑)/0.89830.26(4.80↑)/0.88426.95(1.49↑)/0.82529.73(4.27↑)/0.841
40 (unseen)21.53/0.47928.82(7.29↑)/0.86628.32(6.79↑)/0.84825.26(3.73↑)/0.76726.25(4.72↑)/0.691
50 (unseen)19.28/0.38926.88(7.60↑)/0.82926.63(7.35↑)/0.81123.85(4.57↑)/0.71023.71(4.43↑)/0.575
Manga109 [39]30 (unseen)26.62/0.65331.97(5.35↑)/0.91031.14(4.52↑)/0.90126.02(-0.6↑)/0.83331.05(4.43↑)/0.858
40 (unseen)22.34/0.44229.02(6.68↑)/0.88828.53(6.19↑)/0.87524.31(1.97↑)/0.78427.29(4.95↑)/0.704
50 (unseen)19.95/0.34226.52(6.57↑)/0.86026.34(6.39↑)/0.84622.82(2.87↑)/0.73424.47(4.52↑)/0.564
", + "bbox": [ + 94, + 127, + 870, + 361 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/19fe6461f33bd73401998bf50a2844f3f5e5db71f85b8f5689b6a2b85e01e2d6.jpg", + "image_caption": [ + "(a) Serial sampling based" + ], + "image_footnote": [], + "bbox": [ + 98, + 368, + 272, + 445 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/5c790d5b0d3bfaf8351aaf64c0c0d9352d0130eadc4e6f6f23c74c27c8080e42.jpg", + "image_caption": [ + "(b) Parallel sampling based", + "Figure 3. The comparison of serial sampling and parallel sampling." + ], + "image_footnote": [], + "bbox": [ + 285, + 380, + 450, + 425 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\phi_{\\bar{d}}$ denotes the parameters of restoration network $f$ that is virtually updated with loss function with samples overall all distortions $D = \\{d_i\\}, 1 \\leq i \\leq n$ . We define it as parallel sampling for DIL, which reduces the complex training process of DIL to two steps. In this paper, we call the original sampling strategy as serial sampling. The comparison between serial sampling and parallel sampling are shown in Fig. 3. The detailed derivation for Eq. 5 are described in the Supplementary.", + "bbox": [ + 75, + 503, + 468, + 638 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We also investigate two different gradient updating strategy for DIL. From Eq. 4 and Eq. 5, we can observe that they require the second-order gradient since the gradient is computed with two-step forward through $\\phi_{d_i}$ , which is shown in Fig. 3. To simplify it, Reptile [42] proposes an alternative strategy (i.e., approximating the second-order gradient by the sequential parameter updating with one-order gradient. The optimization direction (i.e., gradient) is computed with the deviation between the initial and last-step parameters. We integrate it into our DIL and call it first-order optimization. In contrast, the original optimization in Eq. 5 is termed second-order optimization. In summary, we propose four variants for DIL following the above two strategies. $\\mathrm{DIL}_{sf}$ adopts the serial sampling and first-order gradient optimization. $\\mathrm{DIL}_{pf}$ utilizes the parallel sampling and first-order optimization. $\\mathrm{DIL}_{ss} / \\mathrm{DIL}_{ps}$ exploits the second-order optimization and serial/parallel sampling.", + "bbox": [ + 75, + 643, + 470, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 369, + 633, + 386 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we first describe the implementation details. Then, we validate the effectiveness of our DIL from two typical out-of-distribution settings, i.e., Cross Distortion Degrees, and Cross Distortion Types. Particularly, for cross-distortion degrees, we train the restoration network with seen distortion degrees while testing it with unseen distortion degrees. For cross-distortion types, the restoration network is trained with synthesized distortions and validated on the corresponding real-world or other distortions.", + "bbox": [ + 496, + 393, + 890, + 531 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Implementation", + "text_level": 1, + "bbox": [ + 500, + 541, + 660, + 556 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We adopt the typical RRDB [56] as our image restoration backbone, which has demonstrated remarkable performances towards various low-level image tasks [52, 55]. All the experiments are done with four NVIDIA 2080Ti GPUs. Adam optimizer is adopted to optimize network parameters in both ERM and DIL training paradigms. More details are given in the Supplementary.", + "bbox": [ + 496, + 564, + 890, + 672 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Cross Distortion Degrees", + "text_level": 1, + "bbox": [ + 500, + 680, + 725, + 696 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Results on Image Denoising. For image denoising, the training data are composed of distorted images with noise levels [5, 10, 15, 20] and their corresponding clean images. After training the restoration network, we validate it on the test datasets with unseen noise degrees, including [30, 40, 50]. We compare the empirical risk minimization (ERM) and four variants of our proposed DIL, i.e., $\\mathrm{DIL}_{sf}$ , $\\mathrm{DIL}_{pf}$ , $\\mathrm{DIL}_{ss}$ , and $\\mathrm{DIL}_{ps}$ , respectively.", + "bbox": [ + 496, + 703, + 890, + 825 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The experimental results are shown in Table 1. We can observe that all four variants of DIL achieve great generalization ability on multiple unseen noise levels compared with commonly-used empirical risk minimization (ERM). On several typical scenarios, including natural im", + "bbox": [ + 496, + 824, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "1718", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/409366f20b6cf9f6610b259f054e6153f66750f8f34033750827dc40e9f62ffa.jpg", + "table_caption": [ + "Table 2. Quantitative comparison for image deblurring on several benchmark datasets. Results are tested on the five unseen blur degrees [4.2, 4.4, 4.6, 4.8, 5.0] in terms of PSNR/SSIM on RGB channel." + ], + "table_footnote": [], + "table_body": "
DatasetsMethodsLevels
4.2 (unseen)4.4 (unseen)4.6 (unseen)4.8 (unseen)5.0 (unseen)
Set5 [4]ERM29.31/0.84426.55/0.77624.43/0.70922.96/0.64822.00/0.602
DIL29.58(0.27↑)/0.84827.52(0.97↑)/0.80225.66(1.23↑)/0.75124.38(1.42↑)/0.70823.46(1.46↑)/0.671
Set14 [68]ERM27.22/0.78124.93/0.72623.16/0.67121.89/0.62420.88/0.583
DIL27.24(0.02↑)/0.77825.78(0.85↑)/0.74624.35(1.19↑)/0.70823.23(1.34↑)/0.67222.37(1.49↑)/0.640
BSD100 [38]ERM27.20/0.78425.17/0.73223.50/0.68222.24/0.63921.28/0.602
DIL27.37(0.17↑)/0.78126.16(0.99↑)/0.75324.91(1.41↑)/0.71923.86(1.62↑)/0.68623.02(1.74↑)/0.658
Urban100 [21]ERM24.95/0.79722.41/0.72320.59/0.65719.33/0.60618.40/0.565
DIL24.97(0.02↑)/0.79323.26(0.85↑)/0.74321.76(1.17↑)/0.69320.70(1.37↑)/0.65119.92(1.52↑)/0.618
Manga109 [39]ERM28.16/0.86523.96/0.79121.21/0.71319.63/0.65218.63/0.606
DIL28.09(-0.07↑)/0.86725.41(1.45↑)/0.82223.15(1.94↑)/0.77121.69(2.06↑)/0.72620.72(2.09↑)/0.691
", + "bbox": [ + 94, + 127, + 870, + 285 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/e41d7b63df26f9e4cf1aae939e241f8af967c59095bcfe8a90716db9628206a8.jpg", + "image_caption": [ + "Figure 4. Visual comparison of the commonly-used ERM and our proposed four variants of DIL with the unseen noise level 30." + ], + "image_footnote": [], + "bbox": [ + 98, + 287, + 225, + 435 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/a0bcd4fe07642ca273399569ed69719607fee115db1e4883a27725f0c42b073e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 225, + 287, + 354, + 434 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/b374fee163614a213f0d36327064b1ff9848d26270ccd678e6295e7ec4847f96.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 354, + 287, + 483, + 436 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/e7468a204711b4189c8661aeb4ac9c89de2f019fac45c83399b57e8e53bc1e41.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 483, + 287, + 612, + 435 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/dc7da7b4ff92f8a5684ef926d84a32c24cb466a7f052c76b89e9ddbcb154282a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 612, + 287, + 738, + 435 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/61a78efa12bae7831cf2f4fc084d7e46f896ff1554c0280c75b762a5aaf194ce.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 738, + 287, + 870, + 435 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/325a6634240d45f27a184dfa7f51e98c06dd62eb7918fc2b0a0c170c2322681c.jpg", + "table_caption": [ + "Table 3. Quantitative comparison for hybrid distortion removal. Results are tested on three different distortion levels in terms of PSNR/SSIM on Y channel." + ], + "table_footnote": [], + "table_body": "
DatasetsMethodsDistortion level
Mild (unseen)Moderate (unseen)Severe (seen)
BSD100 [38]ERM25.31/0.68724.62/0.64225.27/0.617
DIL26.37/0.69125.23/0.64525.22/0.613
Urban100 [21]ERM23.97/0.73622.51/0.67423.38/0.655
DIL25.00/0.74723.13/0.68223.20/0.645
Manga109 [39]ERM27.43/0.86324.85/0.80826.50/0.815
DIL28.41/0.86825.30/0.81026.19/0.766
DIV2K [2]ERM26.19/0.76625.94/0.74427.42/0.742
DIL27.84/0.78526.89/0.75627.38/0.737
", + "bbox": [ + 78, + 522, + 468, + 683 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "ages (i.e., CBSD68 [38], Kodak24 [15], McMaster [72]), building images (Urban100 [21]), cartoon images (i.e., Manga109 [39]), our DIL even outperforms the ERM by a promising/amazing gain of $8.74\\mathrm{dB}$ at most. Moreover, with the increase of the distribution gap between training and testing data, ours can achieve larger improvements for ERM. Furthermore, for cross distortion degree, $\\mathrm{DIL}_{sf}$ shows the best generalization capability compared with the other three variants by serial sampling and first-order optimization. We also visualize the reconstructed images of the above methods in Fig. 4. For the unseen distortion degree $(\\sigma = 30)$ , the ERM cannot remove the noise well and the reconstructed image also contains obvious noise distortion.", + "bbox": [ + 75, + 703, + 470, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "However, our $\\mathrm{DIL}_{sf}$ enables the restoration network to recover more vivid and clean images from the unseen noise degrees, which validates the correctness and effectiveness of our proposed DIL.", + "bbox": [ + 496, + 470, + 890, + 532 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Results on Image Deblurring. We also validate the generalization capability of our DIL on the challenging image deblurring. Under this scenarios, we train the restoration network with our proposed DIL with the gaussian blurring level [1.0, 2.0, 3.0, 4.0], and validate its generalization capability on the more severe and difficult blurring levels, including 4.2, 4.4, 4.6, 4.8, and 5.0.", + "bbox": [ + 496, + 534, + 892, + 638 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "As shown in Table. 2, we validate our DIL on five benchmark datasets, including Set5 [4], Set14 [68], BSD100 [38], Urban100 [21], and Manga109 [39]. With the increase of blurring level, the restoration network trained with ERM suffers from a severe performance drop, since the unseen blurring levels are far away from the blurring levels used for training. But our DIL can improve ERM on each unseen blurring level for five datasets. In particular, we achieve the gain of $2.09\\mathrm{dB}$ for the cartoon scene Manga109 [39] on the blurring level 5.0.", + "bbox": [ + 496, + 641, + 893, + 792 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Results on Hybrid-distorted Image Restoration. Except for the above single distortion, we also explore the generalization capability of our DIL on hybrid-distorted image restoration. Following [26], the hybrid distorted images are degraded with blur, noise, and Jpeg compression in a sequence manner. Based on the distortion degree, it can be divided into three levels from low to high, i.e., mild, mod-", + "bbox": [ + 496, + 795, + 893, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "1719", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/e77dfd0ca5de4da949a4e3f0d4ae838d926e391084a921e73ce2dfd21e0dcee1.jpg", + "table_caption": [ + "Table 4. Quantitative results of network generalization capability on real image denoising and synthetic image deraining tasks. Results are tested on Y channel in terms of PSNR/SSIM, except for DND where we obtain our results from official online benchmark." + ], + "table_footnote": [], + "table_body": "
MethodsDatasets (Real Denoising)Datasets (Deraining)
SIDD [1]DND [45]Rain100L [63]Rain12 [31]Rain800 [70]
ERM38.90/0.937938.67/0.954927.61/0.857731.44/0.894723.36/0.8199
DILsf39.96(1.06↑)/0.941039.16(0.49↑)/0.953128.15(0.54↑)/0.867932.43(0.99↑)/0.916323.41(0.05↑)/0.8261
DILps39.92(1.02↑)/0.938539.03(0.36↑)/0.955328.37(0.76↑)/0.873933.07(1.63↑)/0.926623.52(0.16↑)/0.8281
", + "bbox": [ + 156, + 127, + 810, + 290 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Figure 5. Visual comparison of the commonly-used ERM and our proposed DIL for unseen hybrid-distorted (mild) image restoration.", + "bbox": [ + 86, + 300, + 879, + 315 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "erate, and severe. In this setting, the restoration network is trained with severe hybrid distortions and validated on the mild and moderate levels.", + "bbox": [ + 75, + 320, + 468, + 364 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "As shown in Table 3, our DIL achieves an average gain of $1.05\\mathrm{dB}$ , and $0.66\\mathrm{dB}$ on the mild-level, and moderate-level hybrid distortions than ERM, which has a large distribution gap with severe-level hybrid distortions. We can also notice that with the increase of the distribution gap, ours can preserve more performances on the restoration of the out-of-distribution distortions. We also conduct the subjective comparison of our methods with the commonly-used ERM in Fig. 5. We can observe that the restoration network trained with ERM suffers from new artifacts for unseen hybrid-distorted images. But our DIL can eliminate the artifacts well and generate more promising results.", + "bbox": [ + 75, + 366, + 472, + 547 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Cross Distortion Types", + "text_level": 1, + "bbox": [ + 76, + 558, + 290, + 574 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, we investigate the effects of our proposed DIL on the cross-distortion type setting, which is more challenging than the cross-degree setting.", + "bbox": [ + 75, + 582, + 468, + 627 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results on Real Image Super-resolution Real Image Super-resolution (RealSR) has attracted great attention since it is urgently required in real life, where the distorted image contains complex hybrid distortions, such as blurring, low resolution, noise, etc. However, the distorted/clean pairs for RealSR are hard to be collected. Simulating distortions like Real-world distortion has been a popular solution for RealSR [55, 71]. In this paper, we follow the Real-ESRGAN [55] and utilize its proposed RealSR distortion simulating to generate image pairs as training datasets. Then we test the restoration network on the out-of-distribution datasets, RealSR V3 [5], DRealSR [59], which are two commonly-used datasets for RealSR evaluation.", + "bbox": [ + 75, + 628, + 468, + 838 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We show the experimental results on RealSR in Table. 5. Without access to any training samples in RealSR V3, DRealSR, our $\\mathrm{DIL}_{sf}$ can outperform the ERM by $0.29\\mathrm{dB}$ on RealSR V3 [5] and $0.26\\mathrm{dB}$ on DRealSR dataset [59].", + "bbox": [ + 75, + 839, + 468, + 901 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/8ee93464eec12863df522fdf31aaa6e13edf964b9c1ecacae6307c579bf3bf91.jpg", + "table_caption": [ + "Table 5. Quantitative results of the network generalization capability on RealSR tasks. Results are tested on the Y channel in terms of PSNR/SSIM." + ], + "table_footnote": [], + "table_body": "
MethodsDatasets
RealSR V3 [5] (unseen)DrealSR [59] (unseen)
Real-ESRNet [55]26.19/0.798928.22/0.8470
BSRNet [71]27.46/0.808229.45/0.8579
ERM27.65/0.809829.73/0.8628
DILsf27.94(0.29↑)/0.809829.99(0.26↑)/0.8648
DILps28.12(0.47↑)/0.806730.58(0.85↑)/0.8712
", + "bbox": [ + 506, + 369, + 879, + 465 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/100f6f12eed2fd82a6154264aeb515d67de764bc39614d8122c31bd0ae82b7ac.jpg", + "table_caption": [ + "Table 6. Quantitative results of our DIL on different backbones. Results are tested on the unseen noise level 30 in terms of PSNR/SSIM." + ], + "table_footnote": [], + "table_body": "
ModelsMethodsDatasets
CBSD68 [38]Kodak24 [15]Urban100 [21]
RRDBERM24.90/0.58125.12/0.53325.46/0.648
DIL30.28/0.86631.39/0.86730.93/0.898
SwinIRERM24.22/0.55124.22/0.49324.73/0.618
DIL29.08/0.79829.71/0.77429.72/0.834
", + "bbox": [ + 514, + 527, + 869, + 611 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Particularly, we notice that $\\mathrm{DIL}_{ps}$ is more suitable for cross-distortion type scenarios than $\\mathrm{DIL}_{sf}$ , which exceeds the ERM by a 0.47dB on RealSR V3, and 0.85dB on DRealSR dataset. The reason for that we guess is that $\\mathrm{DIL}_{ps}$ is more capable of improving the generalization for the large distribution gap in image restoration. We also visualize the comparison corresponding to the subjective quality for different methods. As shown in Fig. 6, Real-ESRNet [55] and BSRNet [71] cause the overshooting at the edge of the text. But our $\\mathrm{DIL}_{ps}$ can eliminate the artifacts and achieve a high-quality restoration", + "bbox": [ + 496, + 626, + 890, + 792 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results on Real Image Denoising. We also study the generalization capability of our training paradigm DIL on the Real Image Denoising task. Concretely, we select four synthesized distortions based on four categories of color space among camera ISP process [18], and generate training image pairs from DF2K [2, 49] in an online manner. Then we verify its generalization on the commonly-used Real De", + "bbox": [ + 496, + 795, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "1720", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/94f109de9c64b5ac92048328b4566f9f14e9b61c556dccef349418977a299f59.jpg", + "image_caption": [ + "Input" + ], + "image_footnote": [], + "bbox": [ + 84, + 87, + 272, + 183 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/31f134a90e396f293ab79f3b59c28fce2738a62e01699f697f3ea8195b3bb509.jpg", + "image_caption": [ + "Bicubic" + ], + "image_footnote": [], + "bbox": [ + 274, + 88, + 372, + 183 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b51d25b4c8ada72f5bbd6d5a692212836b782f5ff1c2e980e982211824a19d0c.jpg", + "image_caption": [ + "Real-ESRNet" + ], + "image_footnote": [], + "bbox": [ + 372, + 88, + 470, + 183 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/2c68de85be65692a8c757c43675e68badbf16563161c2bf34f88c1174fbc18dc.jpg", + "image_caption": [ + "BSRNet", + "Figure 6. Visual comparison with state-of-the-art methods on DRealSR [59]." + ], + "image_footnote": [], + "bbox": [ + 472, + 88, + 573, + 183 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ed0f34b0219d39d82e98fd08e8fa00b14afeb8efd521b7238e9da3fd9df2c3db.jpg", + "image_caption": [ + "ERM" + ], + "image_footnote": [], + "bbox": [ + 573, + 88, + 673, + 183 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e09bfbadf6c8dc5c61f05b70937858b1887cfcd9a29c9958fc22c01a5e81f58b.jpg", + "image_caption": [ + "DILps" + ], + "image_footnote": [], + "bbox": [ + 674, + 88, + 776, + 183 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/da3cc8c948fdcdcbed2a6888acb69dd98d1bdff5036ac1d15fa517e4deddf81d.jpg", + "image_caption": [ + "Ground Truth" + ], + "image_footnote": [], + "bbox": [ + 779, + 90, + 870, + 186 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/5654d0cde447d2449426b5a7d2c1a538e5b207a404d855f6a4011240b5257475.jpg", + "table_caption": [ + "Table 7. Quantitative comparison between different distortion augmentation methods. $\\mathrm{D}_1$ and $\\mathrm{D}_2$ are the first order distortion and the second order distortion derived from [55] respectively. Results are tested on RealSR datasets in terms of PSNR/SSIM." + ], + "table_footnote": [], + "table_body": "
AugmentationMethodsDatasets
RealSR V3 [5]DrealSR [59]
D1ERM27.65/0.809829.73/0.8628
DIL27.94/0.809829.99/0.8648
D2ERM27.39/0.807729.41/0.8591
DIL27.65/0.802729.85/0.8677
", + "bbox": [ + 102, + 286, + 434, + 363 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "noising dataset SIDD [1] and DND [45]. As Table 4 illustrated, our $\\mathrm{DIL}_{ps}$ achieves the PSNR of $39.92\\mathrm{dB}$ , which outperforms the ERM by $1.02\\mathrm{dB}$ , which is almost the same with $\\mathrm{DIL}_{sf}$ .", + "bbox": [ + 75, + 376, + 468, + 436 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Results on Image Deraining. As an extension experiment, we introduce our DIL to the experiments of image deraining task. Particularly, the raining types and degrees between different datasets are severely different in image deraining. Here, we optimize the restoration network with three image deraining datasets, including DID-MDN [69], Rain14000 [16], and Heavy Rain Dataset [25]. Then we validate the generalization capability of the restoration network on three unseen deraining datasets, i.e., Rain100L [63], Rain12 [31], and Rain800 [70]. We report the experimental results in Table 4. Our DIL $(\\mathrm{DIL}_{ps})$ enables the restoration network to have a better generalization capability than ERM, which obtains a gain of 0.76dB on Rain100L [63] and 1.63dB on Rain12 [31] dataset.", + "bbox": [ + 75, + 438, + 468, + 650 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Ablation Studies", + "text_level": 1, + "bbox": [ + 76, + 662, + 240, + 676 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Impact of different restoration networks. We demonstrate the effectiveness of DIL across different network backbones. In addition to the convolution-based RRDB [56] network, we also incorporate our DIL into the transformer-based SwinIR [32]. The performances are reported in Table 6, which reveals that our DIL can also improve the generalization capability of Transformer-based backbones. This study reveals our DIL is a general training paradigm for different backbones.", + "bbox": [ + 75, + 686, + 468, + 823 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effects of different variants for DIL As shown in Table. 1, and 4, we can observe that $\\mathrm{DIL}_{sf}$ is more proper for cross-distortion degrees. But for cross-distortion types, $\\mathrm{DIL}_{ps}$ achieves better performance for RealSR and Image Deraining. It is noteworthy that the distribution gap of dif", + "bbox": [ + 75, + 824, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ferent distortion types is larger than different degrees. The first-order optimization is more stable but lacks enough capability for a severe distribution gap compared to second-order optimization. But all of them are competent in improving the generalization capability.", + "bbox": [ + 496, + 220, + 890, + 297 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Discussion on Limitations", + "text_level": 1, + "bbox": [ + 500, + 299, + 740, + 314 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The performance on training data. We also report the performance of our DIL on the seen training data in Table 3. It can be seen that our DIL will cause a slight performance drop but the generalization capability is improved obviously. The reason for that is our DIL implements distortion invariant representation learning, which prevents the restoration network from over-fitting to the training data.", + "bbox": [ + 496, + 316, + 890, + 422 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The impact of different distortion augmentation. As shown in Table 7, despite that our DIL achieves the improvement of the generalization capability. The final generalization performance is still related to the distortion augmentation strategy. It is vital to find a universal distortion augmentation strategy, which requires more exploration. We believe it will be a potential/important direction to improve the generalization ability of the restoration network.", + "bbox": [ + 496, + 422, + 890, + 542 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 549, + 617, + 564 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we propose a novel distortion invariant representation learning (DIL) training paradigm for image restoration from the causality perspective. In particular, we provide a causal view of the image restoration process, and clarify why the restoration network lacks the generalization capability for different degradations. Based on that, we treat the distortion types and degrees as confounders, of which the confounding effects can be removed with our proposed DIL. Concretely, we produce the spurious confounders by simulating the different distortion types and degrees. Then, an instantiation of the back-door criterion in causality is introduced from the optimization perspective, which enables the restoration network to remove the harmful bias from different degradations. Extensive experiments on the settings, cross distortion degrees, and cross distortion types, have demonstrated that our DIL improves the generalization capability of the restoration network effectively.", + "bbox": [ + 496, + 568, + 890, + 824 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements", + "text_level": 1, + "bbox": [ + 500, + 834, + 666, + 849 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was supported in part by NSFC under Grant U1908209, 62021001, and ZJNSFC under Grant LQ23F010008.", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "1721", + "bbox": [ + 483, + 945, + 513, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Abdelrahman Abdelhamed, Stephen Lin, and Michael S Brown. 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IEEE Transactions on Pattern Analysis and Machine Intelligence, 43(7):2480-2495, 2020. 1, 2" + ], + "bbox": [ + 501, + 92, + 890, + 712 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "1724", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Learning Distortion Invariant Representation for Image Restoration From a Causality Perspective/bf96eb62-eb0a-4620-9268-36a8377665e9_model.json b/2023/Learning Distortion Invariant Representation for Image Restoration From a Causality Perspective/bf96eb62-eb0a-4620-9268-36a8377665e9_model.json new file mode 100644 index 0000000000000000000000000000000000000000..d4c11b38273487d24e0823334226ad1d01a0cc1b --- /dev/null +++ b/2023/Learning Distortion Invariant Representation for Image Restoration From a Causality Perspective/bf96eb62-eb0a-4620-9268-36a8377665e9_model.json @@ -0,0 +1,2686 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.141, + 0.131, + 0.83, + 0.177 + ], + "angle": 0, + "content": "Learning Distortion Invariant Representation for Image Restoration from A Causality Perspective" + }, + { + "type": "text", + "bbox": [ + 0.134, + 0.203, + 0.836, + 0.255 + ], + "angle": 0, + "content": "Xin Li\\(^{1}\\), Bingchen Li\\(^{1}\\), Xin Jin\\(^{2}\\), Cuiling Lan\\(^{3\\dagger}\\), Zhibo Chen\\(^{1\\dagger}\\) \n\\(^{1}\\)University of Science and Technology of China \\(^{2}\\)Eastern Institute for Advanced Study \n\\(^{3}\\)Microsoft Research Asia" + }, + { + "type": "text", + "bbox": [ + 0.22, + 0.259, + 0.747, + 0.275 + ], + "angle": 0, + "content": "{lixin666, lbc31415926}@mail.ustc.edu.cn, jinxin@eias.ac.cn," + }, + { + "type": "text", + "bbox": [ + 0.299, + 0.278, + 0.672, + 0.292 + ], + "angle": 0, + "content": "culan@microsoft.com, chenzhibo@ustc.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.327, + 0.314, + 0.344 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.36, + 0.473, + 0.722 + ], + "angle": 0, + "content": "In recent years, we have witnessed the great advancement of Deep neural networks (DNNs) in image restoration. However, a critical limitation is that they cannot generalize well to real-world degradations with different degrees or types. In this paper, we are the first to propose a novel training strategy for image restoration from the causality perspective, to improve the generalization ability of DNNs for unknown degradations. Our method, termed Distortion Invariant representation Learning (DIL), treats each distortion type and degree as one specific confounder, and learns the distortion-invariant representation by eliminating the harmful confounding effect of each degradation. We derive our DIL with the back-door criterion in causality by modeling the interventions of different distortions from the optimization perspective. Particularly, we introduce counterfactual distortion augmentation to simulate the virtual distortion types and degrees as the confounders. Then, we instantiate the intervention of each distortion with a virtual model updating based on corresponding distorted images, and eliminate them from the meta-learning perspective. Extensive experiments demonstrate the generalization capability of our DIL on unseen distortion types and degrees. Our code will be available at https://github.com/lixinustc/Causal-IR-DIL." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.755, + 0.21, + 0.77 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.782, + 0.47, + 0.875 + ], + "angle": 0, + "content": "Image restoration (IR) tasks [7, 8, 32, 51], including image super-resolution [11, 24, 43, 46, 56, 57], deblurring [41, 75], denoising [3, 23, 40], compression artifacts removal [28, 53], etc, have achieved amazing/uplifting performances, powered by deep learning. A series of backbones are elaborately and carefully designed to boost the" + }, + { + "type": "image", + "bbox": [ + 0.523, + 0.326, + 0.872, + 0.488 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.497, + 0.892, + 0.527 + ], + "angle": 0, + "content": "Figure 1. A comparison between ERM and our DIL with RRDB as backbone. The results are tested on Set5 with Gaussian noise." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.536, + 0.892, + 0.824 + ], + "angle": 0, + "content": "restoration performances for specific degradation. Convolution neural networks (CNNs) [20] and transformers [12,34] are two commonly-used designed choices for the backbones of image restoration. However, these works inevitably suffer from severe performance drops when they encounter unseen degradations as shown in Fig. 1, where the restoration degree in training corresponds to the noise of standard deviation 20 and the degrees in testing are different. The commonly-used training paradigm in image restoration, i.e., empirical risk minimization (ERM), does not work well for out-of-distribution degradations. Particularly, the restoration networks trained with ERM merely mine the correlation between distorted image \\( I_{d} \\) and its ideal reconstructed image \\( I_{o} \\) by minimizing the distance between \\( I_{o} \\) and the corresponding clean image \\( I_{c} \\). However, a spurious correlation [44] is also captured which introduces the bad confounding effects of specific degradation \\( d \\). It means the conditional probability \\( P(I_{o}|I_{d}) \\) is also conditioned on the distortion types or degrees \\( d \\) (i.e., \\( d \\nmid I_{o}|I_{d} \\))." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.895, + 0.903 + ], + "angle": 0, + "content": "A robust/generalizable restoration network should be distortion-invariant (i.e., \\(d \\perp I_{o}|I_{d}\\)). For instance, given two distorted images with the same content \\(I_{c}\\) but different degradations \\(d_{1}\\) and \\(d_{2}\\), the robust restoration network is expected to recover the same reconstructed image \\(I_{o}\\)" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.225, + 0.9 + ], + "angle": 0, + "content": "†Corresponding Author" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1714" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.091, + 0.473, + 0.378 + ], + "angle": 0, + "content": "from these two distorted images (i.e., \\( P(I_{o}|I_{d}, d = d_{1}) = P(I_{o}|I_{d}, d = d_{2}) \\)), respectively. Previous works for the robustness of the restoration network can be roughly divided into two categories, distortion adaptation-based schemes, and domain adaptation/translation-based schemes. Distortion adaptation-based schemes [60] aim to estimate the distortion types or representations, and then, handle the different distortions by adaptively modulating the restoration network. Domain adaptation/translation-based schemes [13, 35,48] regard different distortions as different domains, and introduce the domain adaptation/translation strategies to the image restoration field. Notwithstanding, the above works ignore the exploration of the intrinsic reasons for the poor generalization capability of the restoration network. In this paper, we take the first step to the causality-inspired image restoration, where novel distortion invariant representation learning from the causality perspective is proposed, to improve the generalization capability of the restoration network." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.384, + 0.473, + 0.822 + ], + "angle": 0, + "content": "As depicted in [17, 44], correlation is not equivalent to causation. Learning distortion invariant representation for image restoration requires obtaining the causal effects between the distorted and ideal reconstructed images instead of only their correlation. There are two typical adjustment criteria for causal effects estimation [17], the back-door criterion, and the front-door criterion, respectively. In particular, the back-door criterion aims to remove the bad confounding effects by traversing over known confounders, while the front-door criterion is to solve the challenge that confounders cannot be identified. To improve the generalization capability of the restoration network, we build a structural causal graph in Fig. 2 for the image restoration process and propose the Distortion-Invariant representation Learning (DIL) for image restoration by implementing the back-door criterion from the optimization perspective. There are two challenges for achieving this. The first challenge is how to construct the confounder sets (i.e., distortion sets). From the causality perspective [17, 44], it is better to keep other factors in the distorted image invariant except for distortion types. However, in the real world, collecting distorted/clean image pairs, especially with different real distortions but the same content is impractical. Inspired by counterfactual [44] in causality and the distortion simulation [55, 71], we propose counterfactual distortion augmentation, which selects amounts of high-quality images from the commonly-used dataset [2, 49], and simulate the different distortion degrees or types on these images as the confounders." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.825, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Another challenge of implementing DIL stems from finding a stable and proper instantiating scheme for the back-door criterion. Previous works [36,37,54,64,65] have incorporated causal inference in high-level tasks by instantiating the back-door criterion [17] with attention interven-" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.287 + ], + "angle": 0, + "content": "tion [64], feature interventions [66], etc, which are arduous to be exploited in the low-level task of image restoration. In this work, we theoretically derive our distortion-invariant representation learning DIL by instantiating the back-door criterion from the optimization perspective. Particularly, we model the intervention of simulated distortions for the restoration process by virtually updating the restoration network with the samples from the corresponding distortions. Then, we eliminate the confounding effects of distortions by introducing the optimization strategy from Meta-Learning to our proposed DIL. In this way, we can instantiate the causal learning in image restoration and enable the DIL based on the back-door criterion." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.289, + 0.862, + 0.303 + ], + "angle": 0, + "content": "The contributions of this paper are listed as follows:" + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.305, + 0.892, + 0.38 + ], + "angle": 0, + "content": "- We revisit the image restoration task from a causality view and pinpoint that the reason for the poor generalization of the restoration network, is that the restoration network is not independent to the distortions in the training dataset." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.385, + 0.892, + 0.49 + ], + "angle": 0, + "content": "- Based on the back-door criterion in causality, we propose a novel training paradigm, Distortion Invariant representation Learning (DIL) for image restoration, where the intervention is instantiated by a virtually model updating under the counterfactual distortion augmentation and is eliminated with the optimization based on meta-learning." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.492, + 0.892, + 0.552 + ], + "angle": 0, + "content": "- Extensive experiments on different image restoration tasks have demonstrated the effectiveness of our DIL for improving the generalization ability on unseen distortion types and degrees." + }, + { + "type": "list", + "bbox": [ + 0.519, + 0.305, + 0.892, + 0.552 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.564, + 0.65, + 0.58 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.583, + 0.68, + 0.598 + ], + "angle": 0, + "content": "2.1. Image Restoration" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Image Restoration (IR) [7, 22, 26, 32, 33, 51, 67] aims to recover high-quality images from the corresponding distorted images, which plays a prominent role in improving the human visual experience. With the advancement of deep learning, a series of works have achieved remarkable progress in lots of IR tasks, including image denoising [3, 40, 73], deblurring [41, 50, 75], super-resolution (SR) [9, 11, 27, 58, 61, 62, 74], etc. Particularly, most of them are devoted to elaborately designing the frameworks for different IR tasks based on their degradation process, which can be roughly divided into two categories, CNN-based framework [9, 11, 74], and Transformer-based framework [7, 24, 32, 67]. Despite that, the above works only explore how to improve the ability of inductive bias toward specific degradation, which lacks enough generalization capability. To improve the model's robustness, some works seek to incorporate the domain translation [13, 35, 48] or distortion-adaptive learning [60] into image restoration. In contrast, we introduce causal learning [17] to image restoration. We answer the reason for the bad robustness of the" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1715" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.122 + ], + "angle": 0, + "content": "restoration network and propose distortion-invariant representation learning from a causality perspective." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.123, + 0.245, + 0.137 + ], + "angle": 0, + "content": "2.2. Causal Inference" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.14, + 0.473, + 0.549 + ], + "angle": 0, + "content": "Causal Inference is proposed to eliminate the harmful bias of confounders and discover the causal relationship between multiple variables [17]. A do operation is implemented with adjustment criteria, e.g., front-door or back-door, to estimate the causal effects [44]. In recent years, deep learning has boosted the vast development of a series of intelligent tasks, e.g., image classification [10, 12, 34], segmentation [19, 47], detection [6, 30], low-level processing [7, 51]. However, prominent works focus on fitting the correlation between inputs and their outputs while ignoring the causation. Due to the existence of confounders, the networks are easy to capture the spurious correlation between inputs and their outputs. For instance, if most lions lie in the grass in the training data, the model inevitably mistakes the grass for a lion. To get rid of the harmful bias of confounders, some studies seek to incorporate causal inference into deep learning. [54, 66] model the interventions of confounders from the feature perspective [64] integrate the front-door criterion to vision-language task from the attention perspective. To improve the generalization capability, [29, 36, 37, 65] introduce the causal learning to domain adaptation/generalization. However, the above causality-inspired methods merely focus on the high-level tasks. In this paper, for the first time, we investigate the causality-based image restoration, which aims to improve the generalization capability of restoration networks on different distortion types and degrees." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.563, + 0.176, + 0.578 + ], + "angle": 0, + "content": "3. Methods" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.581, + 0.401, + 0.597 + ], + "angle": 0, + "content": "3.1. A Causal View for Image Restoration" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.599, + 0.47, + 0.81 + ], + "angle": 0, + "content": "Image restoration aims to restore the distorted images, of which the degradation process can be represented as a function \\( I_{d} = g(I_{c},D) \\). Here, \\( I_{c},I_{d},D \\) denote the clean, distorted images, and distortions, respectively. \\( D \\) contains distortion types \\( D_{t} \\) and degrees \\( D_{l} \\). A restoration network \\( f \\) is trained with the loss function to minimize the difference between its ideal reconstructed images \\( I_{o} \\) and the original clean image \\( I_{c} \\). We model this whole process with a structure causal graph as shown in Fig. 2. Here, \\( D\\rightarrow I_d\\leftarrow I_c \\) denotes the degradation process of \\( I_{d} = g(I_{c},D) \\). \\( I_{c}\\rightarrow I_{o} \\) denotes \\( I_{o} \\) is learned with the supervision of \\( I_{c} \\) by maximizing the probability of \\( P(I_c|I_o) \\). In addition, \\( D\\to I_o \\) refers to the knowledge learned from \\( D \\) to \\( I_{o} \\). \\( I_{d}\\rightarrow I_{o} \\) means the restoration process with restoration network \\( f \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.471, + 0.902 + ], + "angle": 0, + "content": "From the causality perspective, the causal representation of image restoration requires that the restoration network \\( f \\) obtains the causal relationship between \\( I_{d} \\rightarrow I_{o} \\). However, there are two extra paths \\( I_{d} \\leftarrow D \\rightarrow I_{o} \\) and \\( I_{d} \\leftarrow I_{c} \\rightarrow I_{o} \\) introducing the spurious correlation to \\( I_{d} \\) and \\( I_{o} \\), where \\( I_{c} \\) and \\( D \\) are confounders in causality. Importantly, the \\( I_{c} \\) are" + }, + { + "type": "image", + "bbox": [ + 0.541, + 0.089, + 0.681, + 0.222 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.687, + 0.093, + 0.783, + 0.105 + ], + "angle": 0, + "content": "\\(D\\) Distortion Set" + }, + { + "type": "text", + "bbox": [ + 0.688, + 0.11, + 0.796, + 0.123 + ], + "angle": 0, + "content": "\\(D_{t}\\) Distortion Types" + }, + { + "type": "text", + "bbox": [ + 0.688, + 0.126, + 0.807, + 0.139 + ], + "angle": 0, + "content": "\\(D_{l}\\) Distortion Degrees" + }, + { + "type": "text", + "bbox": [ + 0.688, + 0.144, + 0.798, + 0.157 + ], + "angle": 0, + "content": "\\(I_{d}\\) Distorted Images" + }, + { + "type": "text", + "bbox": [ + 0.688, + 0.161, + 0.852, + 0.174 + ], + "angle": 0, + "content": "\\(I_{o}\\) Ideal Reconstructed Images" + }, + { + "type": "text", + "bbox": [ + 0.688, + 0.178, + 0.782, + 0.191 + ], + "angle": 0, + "content": "\\(I_{c}\\) Clean Images" + }, + { + "type": "text", + "bbox": [ + 0.688, + 0.193, + 0.819, + 0.206 + ], + "angle": 0, + "content": "\\(f\\) Restoration Network" + }, + { + "type": "text", + "bbox": [ + 0.688, + 0.208, + 0.85, + 0.221 + ], + "angle": 0, + "content": "\\(d\\) Distortion sampled from \\(D\\)" + }, + { + "type": "list", + "bbox": [ + 0.687, + 0.093, + 0.852, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.533, + 0.234, + 0.858, + 0.248 + ], + "angle": 0, + "content": "Figure 2. Structure causal graph for image restoration." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.256, + 0.892, + 0.316 + ], + "angle": 0, + "content": "commonly diverse in the datasets and bring more vivid textures to reconstructed image \\( I_{o} \\), which is a favorable confounder. We do not take into account the confounder \\( I_{c} \\) in our paper." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.317, + 0.893, + 0.482 + ], + "angle": 0, + "content": "We aim to improve the robustness of the restoration network to unseen or unknown distortions, which are inhibited by the bad confounding effects from confounders \\( D \\). But, how do the confounders \\( D \\) limit the generalization capability of the restoration network? As shown in Fig. 2, the existing of \\( I_{d} \\gets D \\to I_{o} \\) causes the conditional probability \\( P(I_{o}|I_{d}) \\) learned by restoration network \\( f \\) is also condition on distortions \\( D \\), i.e., the fitting conditional probability of \\( f \\) is in fact as \\( P(I_{o}|I_{d},D) \\). Consequently, the restoration network \\( f \\) is not robust to different distortions due to that it is not independent of different distortions \\( D \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.483, + 0.893, + 0.634 + ], + "angle": 0, + "content": "A robust restoration network \\( f \\) should be independent of different distortions (i.e., \\( D \\perp I_o|I_d \\)). To achieve this, we adopt the back-door criterion in causal inference to realize distortion-invariant learning (DIL) through a \"do\" operation. Here, a \"do\" operation [17, 44] is exploited to cut off the connection from the distortion \\( D \\) to \\( I_d \\), thereby removing the bad confounding effects of \\( D \\) to the path \\( I_d \\to I_o \\), and learning the distortion-invariant feature representation (i.e., \\( D \\perp I_o|I_d \\)). We formulate the back-door criterion in image restoration as Equ. 1." + }, + { + "type": "equation", + "bbox": [ + 0.509, + 0.642, + 0.892, + 0.68 + ], + "angle": 0, + "content": "\\[\nP \\left(I _ {o} | d o \\left(I _ {d}\\right)\\right) = \\sum_ {d _ {i} \\in D} P \\left(I _ {o} \\mid I _ {d}, d _ {i}\\right) P \\left(d _ {i}\\right), P \\left(d _ {i}\\right) = \\frac {1}{n}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.895, + 0.901 + ], + "angle": 0, + "content": "where the causal conditional probability \\( P(I_{o}|do(I_{d})) \\) is the optimization direction for restoration network \\( f \\) towards distortion invariant learning. To simplify the optimization, we set the probability of each distortion \\( d_{i} \\) as \\( 1 / n \\), where \\( n \\) is the number of distortion types and degrees that existed in confounders. From Equ. 1, two crucial challenges for achieving it arise. 1) How to construct the virtual confounders (i.e., different distortion types or degrees)? since collecting different real distorted images with the same contents are nontrivial in the real world. 2) How to instantiate the intervention of different distortions to the reconstruction process (i.e., the \\( P(I_{o}|I_{d},d_{i}) \\)) in image restoration. We achieve this through counterfactual distortion augmentation and distortion-invariant representation learning as described" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1716" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.248, + 0.106 + ], + "angle": 0, + "content": "in the following sections." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.115, + 0.427, + 0.131 + ], + "angle": 0, + "content": "3.2. Counterfactual Distortion Augmentation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.138, + 0.47, + 0.349 + ], + "angle": 0, + "content": "To learn the distortion-invariant representation for the restoration network, it is vital to construct the distortion set \\( D \\) (i.e., confounders). For instance, if we expect the restoration network to have the generalization capability for different distortion degrees, we require to construct the distortion set \\( D \\) with the distortions at different levels. Similarly, we can increase the generalization capability of the restoration network for unknown distortion types by constructing the \\( D \\) with different but related distortion types. Furthermore, to avoid the effects of different image contents, it is better for each clean image to have corresponding distorted images with various distortion types or degrees in \\( D \\). However, it is non-trivial to collect datasets that satisfy the above principles in the real world, which is labor-intensive and arduous." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.35, + 0.471, + 0.502 + ], + "angle": 0, + "content": "In this paper, we construct the distortion set \\( D \\) with synthesized distortions, which we can call virtual confounders in causality. Concretely, we collected a series of high-quality images \\( I_{c} \\), and generated the distorted images by modifying the degradation process as \\( I_{d} = g(I_{c}, d_{i}), d_{i} \\in D \\). We can also prove the rightness of the above distortion augmentation from the counterfactuals in causality [17], where we answer the counterfactual question that \"if \\( D \\) is \\( d_{i} \\), what the \\( I_{d} \\) would be with \\( I_{c} \\) invariant?\". The proof can be found in the Supplementary." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.509, + 0.466, + 0.525 + ], + "angle": 0, + "content": "3.3. Distortion-invariant Representation Learning" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.532, + 0.47, + 0.759 + ], + "angle": 0, + "content": "After constructing the virtual confounders/distortions set \\( D = \\{d_i | 1 \\leq i \\leq n\\} \\). We are able to achieve the distortion-invariant representation learning by implementing the back-door criterion as Eq. 1 for image restoration. Let us first introduce the relationship between the probability \\( P(I_o|I_d) \\) and the commonly-used training paradigm ERM (empirical risk minimization). In image restoration, an ideal reconstruction \\( I_o \\) is expected to learn by maximizing the condition probability \\( P(I_o|I_d) \\) with loss function as \\( \\mathcal{L}(f_{\\theta}(I_d), I_c) \\), where \\( f_{\\theta} \\) is the restoration network with the parameters \\( \\theta \\) and \\( L \\) denotes the loss function, such as the commonly-used \\( \\mathcal{L}_1 \\) or \\( \\mathcal{L}_2 \\) loss. The ERM is used to optimize the network \\( f_{\\theta} \\) (with parameters denoted by \\( \\theta \\)) by minimizing the loss function overall training dataset \\( \\mathcal{D} = \\{I_d, I_c | d \\in D\\} \\) as:" + }, + { + "type": "equation", + "bbox": [ + 0.137, + 0.766, + 0.469, + 0.788 + ], + "angle": 0, + "content": "\\[\n\\theta^ {*} = \\arg \\min _ {\\theta} \\mathbb {E} _ {(I _ {d}, I _ {c}) \\sim \\mathcal {D}} [ \\mathcal {L} (f _ {\\theta} (I _ {d}), I _ {c}) ], \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.47, + 0.901 + ], + "angle": 0, + "content": "where \\(\\theta^{*}\\) enables the restoration network \\(f\\) to maximize the \\(P(I_{o}|I_{d})\\approx P(I_{c}|I_{d})\\). However, the above training process also leads the \\(P(I_{o}|I_{d})\\) to be not independent to the distortions \\(d\\in D\\) in the training dataset \\(\\mathcal{D}\\), which eliminate the generalization ability of \\(f\\) on the out-of-distribution distortions (i.e., when \\(d\\notin D\\)). To achieve the distortion-invariant representation learning, we aim to maximize the" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.168 + ], + "angle": 0, + "content": "causal conditional probability \\( P(I_{o}|do(I_{d})) \\) as instead of \\( P(I_{o}|I_{d}) \\). The key challenge stems from how to model the conditional probability \\( P(I_{o}|I_{d},d_{i}) \\) in Eq. 1 (i.e., how to model the intervention from the distortion \\( d_{i}\\in D \\) for the restoration process \\( P(I_o|I_d) \\))." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.168, + 0.892, + 0.319 + ], + "angle": 0, + "content": "In this paper, we propose to model the intervention from \\( d_{i} \\in D \\) to the restoration process (i.e., \\( P(I_{o}|I_{d},d_{i}) \\)) through the optimization of the network parameters \\( \\theta \\). From the above analysis, we know that the restoration network \\( f_{\\theta} \\) trained with ERM on the paired training data \\( (I_{d_i},I_c) \\) is condition on the distortion \\( d_{i} \\). This inspires us to instantiate the intervention of different distortion types or degrees \\( d_{i} \\in D \\) through updating the model parameter \\( \\theta \\) to \\( \\phi_{d_i} \\) based on ERM with the training distorted-and-clean image pairs \\( (I_{d_i},I_c) \\) as:" + }, + { + "type": "equation", + "bbox": [ + 0.592, + 0.327, + 0.892, + 0.343 + ], + "angle": 0, + "content": "\\[\n\\phi_ {d _ {i}} = \\theta - \\alpha \\nabla_ {\\theta} \\mathcal {L} \\left(f _ {\\theta} \\left(I _ {d _ {i}}\\right), I _ {c}\\right), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.35, + 0.892, + 0.456 + ], + "angle": 0, + "content": "where \\(\\phi_{d_i}\\) denotes the parameters of the restoration network after one-step update, which is conditioned on the confounder \\(d_i\\). Consequently, the maximum of the conditional probability \\(P(I_o|I_d,d_i)\\) can be obtained by minimizing the loss \\(\\mathcal{L}(f_{\\phi_{d_i}}(I_d),I_c)\\). The optimization direction toward maximizing the causal condition probability \\(P(I_o|do(I_d))\\) in Eq. 1 can be derived as:" + }, + { + "type": "equation", + "bbox": [ + 0.527, + 0.464, + 0.892, + 0.496 + ], + "angle": 0, + "content": "\\[\n\\theta^ {*} = \\arg \\min _ {\\theta} \\mathbb {E} _ {(I _ {d}, I _ {c}) \\sim \\mathcal {D}} [ \\sum_ {d _ {i} \\in D} \\mathcal {L} \\left(f _ {\\phi_ {d _ {i}}} (I _ {d}), I _ {c}\\right) ], \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.502, + 0.892, + 0.563 + ], + "angle": 0, + "content": "where \\(D\\) denotes the confounder set which contains \\(n\\) distortion degrees or types. Based on the above optimization objective, we learn distortion-invariant representation learning from a causality perspective." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.571, + 0.885, + 0.587 + ], + "angle": 0, + "content": "3.4. Implementations of DIL from Meta-Learning" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.594, + 0.892, + 0.729 + ], + "angle": 0, + "content": "An interesting finding is that the derived optimization direction of DIL from causality perspective in Eq. 4 is consistent with one typical meta-learning strategy termed as MAML [14], even they have different purposes. MAML aims to enable the fast adaptation capability of a network for few-shot tasks, while ours aims to improve the generalization capability of the restoration network. We facilitate our DIL in image restoration based on this meta-learning strategy." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.73, + 0.892, + 0.836 + ], + "angle": 0, + "content": "However, it is arduous to directly incorporate the optimization direction of Eq. 4 into the practical training process, which is computationally prohibitive. The reason is that it requires multiple gradient computing and updating, which is expensive, especially for the pixel-wise image restoration. To simplify this process, we utilize the Talyor expansion and inverse expansion to derive Eq. 4 as:" + }, + { + "type": "equation", + "bbox": [ + 0.544, + 0.843, + 0.824, + 0.865 + ], + "angle": 0, + "content": "\\[\n\\theta^ {*} = \\arg \\min _ {\\theta} \\mathbb {E} _ {(I _ {d}, I _ {c}) \\sim \\mathcal {D}} [ \\mathcal {L} (f _ {\\phi_ {\\bar {d}}} (I _ {d}), I _ {c}) ],\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.547, + 0.866, + 0.892, + 0.904 + ], + "angle": 0, + "content": "\\[\nw h e r e \\phi_ {\\tilde {d}} = \\theta - \\alpha \\nabla_ {\\theta} \\sum_ {d _ {i} \\in D} \\frac {1}{n} \\mathcal {L} \\left(f _ {\\theta} \\left(I _ {d _ {i}}\\right), I _ {c}\\right), \\tag {5}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1717" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.895, + 0.119 + ], + "angle": 0, + "content": "Table 1. Quantitative comparison for image denoising on several benchmark datasets. Results are tested on three different unseen distortion degrees in terms of PSNR/SSIM on RGB channel. Best performances are bolded." + }, + { + "type": "table", + "bbox": [ + 0.095, + 0.128, + 0.872, + 0.362 + ], + "angle": 0, + "content": "
DatasetsLevelsMethods
ERMDILsfDILpfDILssDILps
CBSD68 [38]30 (unseen)24.90/0.58130.29(5.39↑)/0.86629.92(5.02↑)/0.85827.48(2.58↑)/0.80929.14(4.24↑)/0.802
40 (unseen)21.12/0.40028.35(7.23↑)/0.82528.10(6.98↑)/0.81225.90(4.78↑)/0.74625.74(4.62↑)/0.629
50 (unseen)18.96/0.30726.64(7.68↑)/0.77926.61(7.65↑)/0.76624.63(5.67↑)/0.68623.34(4.38↑)/0.501
Kodak24 [15]30 (unseen)25.12/0.53331.39(6.27↑)/0.86730.87(5.75↑)/0.85827.92(2.80↑)/0.80129.86(4.74↑)/0.782
40 (unseen)21.22/0.35229.49(8.27↑)/0.83129.15(7.93↑)/0.81726.46(5.24↑)/0.73826.13(4.91↑)/0.588
50 (unseen)19.02/0.26327.76(8.74↑)/0.78827.67(8.65↑)/0.77525.24(6.22↑)/0.67723.60(4.58↑)/0.457
McMaster [72]30 (unseen)25.65/0.56931.70(6.05↑)/0.87331.04(5.39↑)/0.85328.15(2.50↑)/0.79430.09(4.44↑)/0.800
40 (unseen)21.73/0.37329.81(8.08↑)/0.83129.07(7.34↑)/0.80226.59(4.86↑)/0.72826.24(4.51↑)/0.605
50 (unseen)19.47/0.27828.02(8.55↑)/0.78327.31(7.84↑)/0.74925.20(5.73↑)/0.66423.60(4.13↑)/0.466
Urban100 [21]30 (unseen)25.46/0.64830.93(5.47↑)/0.89830.26(4.80↑)/0.88426.95(1.49↑)/0.82529.73(4.27↑)/0.841
40 (unseen)21.53/0.47928.82(7.29↑)/0.86628.32(6.79↑)/0.84825.26(3.73↑)/0.76726.25(4.72↑)/0.691
50 (unseen)19.28/0.38926.88(7.60↑)/0.82926.63(7.35↑)/0.81123.85(4.57↑)/0.71023.71(4.43↑)/0.575
Manga109 [39]30 (unseen)26.62/0.65331.97(5.35↑)/0.91031.14(4.52↑)/0.90126.02(-0.6↑)/0.83331.05(4.43↑)/0.858
40 (unseen)22.34/0.44229.02(6.68↑)/0.88828.53(6.19↑)/0.87524.31(1.97↑)/0.78427.29(4.95↑)/0.704
50 (unseen)19.95/0.34226.52(6.57↑)/0.86026.34(6.39↑)/0.84622.82(2.87↑)/0.73424.47(4.52↑)/0.564
" + }, + { + "type": "image", + "bbox": [ + 0.099, + 0.369, + 0.273, + 0.446 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.126, + 0.447, + 0.245, + 0.457 + ], + "angle": 0, + "content": "(a) Serial sampling based" + }, + { + "type": "image", + "bbox": [ + 0.286, + 0.381, + 0.451, + 0.426 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.306, + 0.444, + 0.434, + 0.456 + ], + "angle": 0, + "content": "(b) Parallel sampling based" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.468, + 0.47, + 0.498 + ], + "angle": 0, + "content": "Figure 3. The comparison of serial sampling and parallel sampling." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.504, + 0.47, + 0.64 + ], + "angle": 0, + "content": "where \\(\\phi_{\\bar{d}}\\) denotes the parameters of restoration network \\(f\\) that is virtually updated with loss function with samples overall all distortions \\(D = \\{d_i\\}, 1 \\leq i \\leq n\\). We define it as parallel sampling for DIL, which reduces the complex training process of DIL to two steps. In this paper, we call the original sampling strategy as serial sampling. The comparison between serial sampling and parallel sampling are shown in Fig. 3. The detailed derivation for Eq. 5 are described in the Supplementary." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.644, + 0.471, + 0.902 + ], + "angle": 0, + "content": "We also investigate two different gradient updating strategy for DIL. From Eq. 4 and Eq. 5, we can observe that they require the second-order gradient since the gradient is computed with two-step forward through \\(\\phi_{d_i}\\), which is shown in Fig. 3. To simplify it, Reptile [42] proposes an alternative strategy (i.e., approximating the second-order gradient by the sequential parameter updating with one-order gradient. The optimization direction (i.e., gradient) is computed with the deviation between the initial and last-step parameters. We integrate it into our DIL and call it first-order optimization. In contrast, the original optimization in Eq. 5 is termed second-order optimization. In summary, we propose four variants for DIL following the above two strategies. \\(\\mathrm{DIL}_{sf}\\) adopts the serial sampling and first-order gradient optimization. \\(\\mathrm{DIL}_{pf}\\) utilizes the parallel sampling and first-order optimization. \\(\\mathrm{DIL}_{ss} / \\mathrm{DIL}_{ps}\\) exploits the second-order optimization and serial/parallel sampling." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.37, + 0.634, + 0.387 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.395, + 0.892, + 0.532 + ], + "angle": 0, + "content": "In this section, we first describe the implementation details. Then, we validate the effectiveness of our DIL from two typical out-of-distribution settings, i.e., Cross Distortion Degrees, and Cross Distortion Types. Particularly, for cross-distortion degrees, we train the restoration network with seen distortion degrees while testing it with unseen distortion degrees. For cross-distortion types, the restoration network is trained with synthesized distortions and validated on the corresponding real-world or other distortions." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.542, + 0.661, + 0.558 + ], + "angle": 0, + "content": "4.1. Implementation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.565, + 0.892, + 0.673 + ], + "angle": 0, + "content": "We adopt the typical RRDB [56] as our image restoration backbone, which has demonstrated remarkable performances towards various low-level image tasks [52, 55]. All the experiments are done with four NVIDIA 2080Ti GPUs. Adam optimizer is adopted to optimize network parameters in both ERM and DIL training paradigms. More details are given in the Supplementary." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.681, + 0.727, + 0.698 + ], + "angle": 0, + "content": "4.2. Cross Distortion Degrees" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.892, + 0.826 + ], + "angle": 0, + "content": "Results on Image Denoising. For image denoising, the training data are composed of distorted images with noise levels [5, 10, 15, 20] and their corresponding clean images. After training the restoration network, we validate it on the test datasets with unseen noise degrees, including [30, 40, 50]. We compare the empirical risk minimization (ERM) and four variants of our proposed DIL, i.e., \\(\\mathrm{DIL}_{sf}\\), \\(\\mathrm{DIL}_{pf}\\), \\(\\mathrm{DIL}_{ss}\\), and \\(\\mathrm{DIL}_{ps}\\), respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The experimental results are shown in Table 1. We can observe that all four variants of DIL achieve great generalization ability on multiple unseen noise levels compared with commonly-used empirical risk minimization (ERM). On several typical scenarios, including natural im" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1718" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.09, + 0.892, + 0.119 + ], + "angle": 0, + "content": "Table 2. Quantitative comparison for image deblurring on several benchmark datasets. Results are tested on the five unseen blur degrees [4.2, 4.4, 4.6, 4.8, 5.0] in terms of PSNR/SSIM on RGB channel." + }, + { + "type": "table", + "bbox": [ + 0.095, + 0.128, + 0.872, + 0.286 + ], + "angle": 0, + "content": "
DatasetsMethodsLevels
4.2 (unseen)4.4 (unseen)4.6 (unseen)4.8 (unseen)5.0 (unseen)
Set5 [4]ERM29.31/0.84426.55/0.77624.43/0.70922.96/0.64822.00/0.602
DIL29.58(0.27↑)/0.84827.52(0.97↑)/0.80225.66(1.23↑)/0.75124.38(1.42↑)/0.70823.46(1.46↑)/0.671
Set14 [68]ERM27.22/0.78124.93/0.72623.16/0.67121.89/0.62420.88/0.583
DIL27.24(0.02↑)/0.77825.78(0.85↑)/0.74624.35(1.19↑)/0.70823.23(1.34↑)/0.67222.37(1.49↑)/0.640
BSD100 [38]ERM27.20/0.78425.17/0.73223.50/0.68222.24/0.63921.28/0.602
DIL27.37(0.17↑)/0.78126.16(0.99↑)/0.75324.91(1.41↑)/0.71923.86(1.62↑)/0.68623.02(1.74↑)/0.658
Urban100 [21]ERM24.95/0.79722.41/0.72320.59/0.65719.33/0.60618.40/0.565
DIL24.97(0.02↑)/0.79323.26(0.85↑)/0.74321.76(1.17↑)/0.69320.70(1.37↑)/0.65119.92(1.52↑)/0.618
Manga109 [39]ERM28.16/0.86523.96/0.79121.21/0.71319.63/0.65218.63/0.606
DIL28.09(-0.07↑)/0.86725.41(1.45↑)/0.82223.15(1.94↑)/0.77121.69(2.06↑)/0.72620.72(2.09↑)/0.691
" + }, + { + "type": "image", + "bbox": [ + 0.099, + 0.288, + 0.227, + 0.436 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.227, + 0.288, + 0.356, + 0.435 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.356, + 0.288, + 0.484, + 0.437 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.484, + 0.288, + 0.613, + 0.436 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.613, + 0.288, + 0.74, + 0.436 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.74, + 0.288, + 0.871, + 0.436 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.107, + 0.449, + 0.862, + 0.464 + ], + "angle": 0, + "content": "Figure 4. Visual comparison of the commonly-used ERM and our proposed four variants of DIL with the unseen noise level 30." + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.47, + 0.471, + 0.512 + ], + "angle": 0, + "content": "Table 3. Quantitative comparison for hybrid distortion removal. Results are tested on three different distortion levels in terms of PSNR/SSIM on Y channel." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.523, + 0.47, + 0.684 + ], + "angle": 0, + "content": "
DatasetsMethodsDistortion level
Mild (unseen)Moderate (unseen)Severe (seen)
BSD100 [38]ERM25.31/0.68724.62/0.64225.27/0.617
DIL26.37/0.69125.23/0.64525.22/0.613
Urban100 [21]ERM23.97/0.73622.51/0.67423.38/0.655
DIL25.00/0.74723.13/0.68223.20/0.645
Manga109 [39]ERM27.43/0.86324.85/0.80826.50/0.815
DIL28.41/0.86825.30/0.81026.19/0.766
DIV2K [2]ERM26.19/0.76625.94/0.74427.42/0.742
DIL27.84/0.78526.89/0.75627.38/0.737
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.704, + 0.471, + 0.901 + ], + "angle": 0, + "content": "ages (i.e., CBSD68 [38], Kodak24 [15], McMaster [72]), building images (Urban100 [21]), cartoon images (i.e., Manga109 [39]), our DIL even outperforms the ERM by a promising/amazing gain of \\(8.74\\mathrm{dB}\\) at most. Moreover, with the increase of the distribution gap between training and testing data, ours can achieve larger improvements for ERM. Furthermore, for cross distortion degree, \\(\\mathrm{DIL}_{sf}\\) shows the best generalization capability compared with the other three variants by serial sampling and first-order optimization. We also visualize the reconstructed images of the above methods in Fig. 4. For the unseen distortion degree \\((\\sigma = 30)\\), the ERM cannot remove the noise well and the reconstructed image also contains obvious noise distortion." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.472, + 0.892, + 0.533 + ], + "angle": 0, + "content": "However, our \\(\\mathrm{DIL}_{sf}\\) enables the restoration network to recover more vivid and clean images from the unseen noise degrees, which validates the correctness and effectiveness of our proposed DIL." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.535, + 0.893, + 0.64 + ], + "angle": 0, + "content": "Results on Image Deblurring. We also validate the generalization capability of our DIL on the challenging image deblurring. Under this scenarios, we train the restoration network with our proposed DIL with the gaussian blurring level [1.0, 2.0, 3.0, 4.0], and validate its generalization capability on the more severe and difficult blurring levels, including 4.2, 4.4, 4.6, 4.8, and 5.0." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.642, + 0.895, + 0.793 + ], + "angle": 0, + "content": "As shown in Table. 2, we validate our DIL on five benchmark datasets, including Set5 [4], Set14 [68], BSD100 [38], Urban100 [21], and Manga109 [39]. With the increase of blurring level, the restoration network trained with ERM suffers from a severe performance drop, since the unseen blurring levels are far away from the blurring levels used for training. But our DIL can improve ERM on each unseen blurring level for five datasets. In particular, we achieve the gain of \\(2.09\\mathrm{dB}\\) for the cartoon scene Manga109 [39] on the blurring level 5.0." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Results on Hybrid-distorted Image Restoration. Except for the above single distortion, we also explore the generalization capability of our DIL on hybrid-distorted image restoration. Following [26], the hybrid distorted images are degraded with blur, noise, and Jpeg compression in a sequence manner. Based on the distortion degree, it can be divided into three levels from low to high, i.e., mild, mod-" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1719" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.895, + 0.119 + ], + "angle": 0, + "content": "Table 4. Quantitative results of network generalization capability on real image denoising and synthetic image deraining tasks. Results are tested on Y channel in terms of PSNR/SSIM, except for DND where we obtain our results from official online benchmark." + }, + { + "type": "table", + "bbox": [ + 0.157, + 0.128, + 0.812, + 0.291 + ], + "angle": 0, + "content": "
MethodsDatasets (Real Denoising)Datasets (Deraining)
SIDD [1]DND [45]Rain100L [63]Rain12 [31]Rain800 [70]
ERM38.90/0.937938.67/0.954927.61/0.857731.44/0.894723.36/0.8199
DILsf39.96(1.06↑)/0.941039.16(0.49↑)/0.953128.15(0.54↑)/0.867932.43(0.99↑)/0.916323.41(0.05↑)/0.8261
DILps39.92(1.02↑)/0.938539.03(0.36↑)/0.955328.37(0.76↑)/0.873933.07(1.63↑)/0.926623.52(0.16↑)/0.8281
" + }, + { + "type": "image_caption", + "bbox": [ + 0.088, + 0.301, + 0.88, + 0.316 + ], + "angle": 0, + "content": "Figure 5. Visual comparison of the commonly-used ERM and our proposed DIL for unseen hybrid-distorted (mild) image restoration." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.321, + 0.47, + 0.365 + ], + "angle": 0, + "content": "erate, and severe. In this setting, the restoration network is trained with severe hybrid distortions and validated on the mild and moderate levels." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.367, + 0.473, + 0.549 + ], + "angle": 0, + "content": "As shown in Table 3, our DIL achieves an average gain of \\(1.05\\mathrm{dB}\\), and \\(0.66\\mathrm{dB}\\) on the mild-level, and moderate-level hybrid distortions than ERM, which has a large distribution gap with severe-level hybrid distortions. We can also notice that with the increase of the distribution gap, ours can preserve more performances on the restoration of the out-of-distribution distortions. We also conduct the subjective comparison of our methods with the commonly-used ERM in Fig. 5. We can observe that the restoration network trained with ERM suffers from new artifacts for unseen hybrid-distorted images. But our DIL can eliminate the artifacts well and generate more promising results." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.559, + 0.291, + 0.575 + ], + "angle": 0, + "content": "4.3. Cross Distortion Types" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.583, + 0.47, + 0.628 + ], + "angle": 0, + "content": "In this section, we investigate the effects of our proposed DIL on the cross-distortion type setting, which is more challenging than the cross-degree setting." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.629, + 0.47, + 0.839 + ], + "angle": 0, + "content": "Results on Real Image Super-resolution Real Image Super-resolution (RealSR) has attracted great attention since it is urgently required in real life, where the distorted image contains complex hybrid distortions, such as blurring, low resolution, noise, etc. However, the distorted/clean pairs for RealSR are hard to be collected. Simulating distortions like Real-world distortion has been a popular solution for RealSR [55, 71]. In this paper, we follow the Real-ESRGAN [55] and utilize its proposed RealSR distortion simulating to generate image pairs as training datasets. Then we test the restoration network on the out-of-distribution datasets, RealSR V3 [5], DRealSR [59], which are two commonly-used datasets for RealSR evaluation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.47, + 0.902 + ], + "angle": 0, + "content": "We show the experimental results on RealSR in Table. 5. Without access to any training samples in RealSR V3, DRealSR, our \\(\\mathrm{DIL}_{sf}\\) can outperform the ERM by \\(0.29\\mathrm{dB}\\) on RealSR V3 [5] and \\(0.26\\mathrm{dB}\\) on DRealSR dataset [59]." + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.319, + 0.892, + 0.36 + ], + "angle": 0, + "content": "Table 5. Quantitative results of the network generalization capability on RealSR tasks. Results are tested on the Y channel in terms of PSNR/SSIM." + }, + { + "type": "table", + "bbox": [ + 0.507, + 0.371, + 0.88, + 0.466 + ], + "angle": 0, + "content": "
MethodsDatasets
RealSR V3 [5] (unseen)DrealSR [59] (unseen)
Real-ESRNet [55]26.19/0.798928.22/0.8470
BSRNet [71]27.46/0.808229.45/0.8579
ERM27.65/0.809829.73/0.8628
DILsf27.94(0.29↑)/0.809829.99(0.26↑)/0.8648
DILps28.12(0.47↑)/0.806730.58(0.85↑)/0.8712
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.476, + 0.892, + 0.517 + ], + "angle": 0, + "content": "Table 6. Quantitative results of our DIL on different backbones. Results are tested on the unseen noise level 30 in terms of PSNR/SSIM." + }, + { + "type": "table", + "bbox": [ + 0.516, + 0.529, + 0.87, + 0.612 + ], + "angle": 0, + "content": "
ModelsMethodsDatasets
CBSD68 [38]Kodak24 [15]Urban100 [21]
RRDBERM24.90/0.58125.12/0.53325.46/0.648
DIL30.28/0.86631.39/0.86730.93/0.898
SwinIRERM24.22/0.55124.22/0.49324.73/0.618
DIL29.08/0.79829.71/0.77429.72/0.834
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.627, + 0.892, + 0.793 + ], + "angle": 0, + "content": "Particularly, we notice that \\(\\mathrm{DIL}_{ps}\\) is more suitable for cross-distortion type scenarios than \\(\\mathrm{DIL}_{sf}\\), which exceeds the ERM by a 0.47dB on RealSR V3, and 0.85dB on DRealSR dataset. The reason for that we guess is that \\(\\mathrm{DIL}_{ps}\\) is more capable of improving the generalization for the large distribution gap in image restoration. We also visualize the comparison corresponding to the subjective quality for different methods. As shown in Fig. 6, Real-ESRNet [55] and BSRNet [71] cause the overshooting at the edge of the text. But our \\(\\mathrm{DIL}_{ps}\\) can eliminate the artifacts and achieve a high-quality restoration" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Results on Real Image Denoising. We also study the generalization capability of our training paradigm DIL on the Real Image Denoising task. Concretely, we select four synthesized distortions based on four categories of color space among camera ISP process [18], and generate training image pairs from DF2K [2, 49] in an online manner. Then we verify its generalization on the commonly-used Real De" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1720" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.086, + 0.088, + 0.273, + 0.184 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.173, + 0.187, + 0.203, + 0.197 + ], + "angle": 0, + "content": "Input" + }, + { + "type": "image", + "bbox": [ + 0.275, + 0.089, + 0.373, + 0.184 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.305, + 0.187, + 0.344, + 0.196 + ], + "angle": 0, + "content": "Bicubic" + }, + { + "type": "image", + "bbox": [ + 0.373, + 0.089, + 0.472, + 0.184 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.393, + 0.187, + 0.459, + 0.196 + ], + "angle": 0, + "content": "Real-ESRNet" + }, + { + "type": "image", + "bbox": [ + 0.473, + 0.089, + 0.574, + 0.184 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.506, + 0.187, + 0.547, + 0.196 + ], + "angle": 0, + "content": "BSRNet" + }, + { + "type": "image", + "bbox": [ + 0.575, + 0.089, + 0.674, + 0.184 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.613, + 0.187, + 0.642, + 0.196 + ], + "angle": 0, + "content": "ERM" + }, + { + "type": "image", + "bbox": [ + 0.675, + 0.089, + 0.777, + 0.184 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.718, + 0.187, + 0.75, + 0.197 + ], + "angle": 0, + "content": "DILps" + }, + { + "type": "image", + "bbox": [ + 0.781, + 0.091, + 0.871, + 0.187 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.795, + 0.187, + 0.866, + 0.196 + ], + "angle": 0, + "content": "Ground Truth" + }, + { + "type": "image_caption", + "bbox": [ + 0.256, + 0.203, + 0.714, + 0.217 + ], + "angle": 0, + "content": "Figure 6. Visual comparison with state-of-the-art methods on DRealSR [59]." + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.22, + 0.47, + 0.275 + ], + "angle": 0, + "content": "Table 7. Quantitative comparison between different distortion augmentation methods. \\( \\mathrm{D}_1 \\) and \\( \\mathrm{D}_2 \\) are the first order distortion and the second order distortion derived from [55] respectively. Results are tested on RealSR datasets in terms of PSNR/SSIM." + }, + { + "type": "table", + "bbox": [ + 0.104, + 0.287, + 0.436, + 0.364 + ], + "angle": 0, + "content": "
AugmentationMethodsDatasets
RealSR V3 [5]DrealSR [59]
D1ERM27.65/0.809829.73/0.8628
DIL27.94/0.809829.99/0.8648
D2ERM27.39/0.807729.41/0.8591
DIL27.65/0.802729.85/0.8677
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.377, + 0.469, + 0.437 + ], + "angle": 0, + "content": "noising dataset SIDD [1] and DND [45]. As Table 4 illustrated, our \\(\\mathrm{DIL}_{ps}\\) achieves the PSNR of \\(39.92\\mathrm{dB}\\), which outperforms the ERM by \\(1.02\\mathrm{dB}\\), which is almost the same with \\(\\mathrm{DIL}_{sf}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.439, + 0.47, + 0.651 + ], + "angle": 0, + "content": "Results on Image Deraining. As an extension experiment, we introduce our DIL to the experiments of image deraining task. Particularly, the raining types and degrees between different datasets are severely different in image deraining. Here, we optimize the restoration network with three image deraining datasets, including DID-MDN [69], Rain14000 [16], and Heavy Rain Dataset [25]. Then we validate the generalization capability of the restoration network on three unseen deraining datasets, i.e., Rain100L [63], Rain12 [31], and Rain800 [70]. We report the experimental results in Table 4. Our DIL \\((\\mathrm{DIL}_{ps})\\) enables the restoration network to have a better generalization capability than ERM, which obtains a gain of 0.76dB on Rain100L [63] and 1.63dB on Rain12 [31] dataset." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.664, + 0.241, + 0.678 + ], + "angle": 0, + "content": "4.4. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.688, + 0.469, + 0.824 + ], + "angle": 0, + "content": "Impact of different restoration networks. We demonstrate the effectiveness of DIL across different network backbones. In addition to the convolution-based RRDB [56] network, we also incorporate our DIL into the transformer-based SwinIR [32]. The performances are reported in Table 6, which reveals that our DIL can also improve the generalization capability of Transformer-based backbones. This study reveals our DIL is a general training paradigm for different backbones." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Effects of different variants for DIL As shown in Table. 1, and 4, we can observe that \\(\\mathrm{DIL}_{sf}\\) is more proper for cross-distortion degrees. But for cross-distortion types, \\(\\mathrm{DIL}_{ps}\\) achieves better performance for RealSR and Image Deraining. It is noteworthy that the distribution gap of dif" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.222, + 0.892, + 0.298 + ], + "angle": 0, + "content": "ferent distortion types is larger than different degrees. The first-order optimization is more stable but lacks enough capability for a severe distribution gap compared to second-order optimization. But all of them are competent in improving the generalization capability." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.3, + 0.741, + 0.315 + ], + "angle": 0, + "content": "5. Discussion on Limitations" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.318, + 0.892, + 0.424 + ], + "angle": 0, + "content": "The performance on training data. We also report the performance of our DIL on the seen training data in Table 3. It can be seen that our DIL will cause a slight performance drop but the generalization capability is improved obviously. The reason for that is our DIL implements distortion invariant representation learning, which prevents the restoration network from over-fitting to the training data." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.424, + 0.892, + 0.544 + ], + "angle": 0, + "content": "The impact of different distortion augmentation. As shown in Table 7, despite that our DIL achieves the improvement of the generalization capability. The final generalization performance is still related to the distortion augmentation strategy. It is vital to find a universal distortion augmentation strategy, which requires more exploration. We believe it will be a potential/important direction to improve the generalization ability of the restoration network." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.55, + 0.619, + 0.565 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.569, + 0.892, + 0.825 + ], + "angle": 0, + "content": "In this paper, we propose a novel distortion invariant representation learning (DIL) training paradigm for image restoration from the causality perspective. In particular, we provide a causal view of the image restoration process, and clarify why the restoration network lacks the generalization capability for different degradations. Based on that, we treat the distortion types and degrees as confounders, of which the confounding effects can be removed with our proposed DIL. Concretely, we produce the spurious confounders by simulating the different distortion types and degrees. Then, an instantiation of the back-door criterion in causality is introduced from the optimization perspective, which enables the restoration network to remove the harmful bias from different degradations. Extensive experiments on the settings, cross distortion degrees, and cross distortion types, have demonstrated that our DIL improves the generalization capability of the restoration network effectively." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.835, + 0.667, + 0.851 + ], + "angle": 0, + "content": "Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "This work was supported in part by NSFC under Grant U1908209, 62021001, and ZJNSFC under Grant LQ23F010008." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.946, + 0.514, + 0.957 + ], + "angle": 0, + "content": "1721" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.184 + ], + "angle": 0, + "content": "[1] Abdelrahman Abdelhamed, Stephen Lin, and Michael S Brown. 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However, a critical limitation is that they cannot generalize well to real-world degradations with different degrees or types. In this paper, we are the first to propose a novel training strategy for image restoration from the causality perspective, to improve the generalization ability of DNNs for unknown degradations. Our method, termed Distortion Invariant representation Learning (DIL), treats each distortion type and degree as one specific confounder, and learns the distortion-invariant representation by eliminating the harmful confounding effect of each degradation. We derive our DIL with the back-door criterion in causality by modeling the interventions of different distortions from the optimization perspective. Particularly, we introduce counterfactual distortion augmentation to simulate the virtual distortion types and degrees as the confounders. Then, we instantiate the intervention of each distortion with a virtual model updating based on corresponding distorted images, and eliminate them from the meta-learning perspective. Extensive experiments demonstrate the generalization capability of our DIL on unseen distortion types and degrees. Our code will be available at https://github.com/lixinustc/Causal-IR-DIL. + +# 1. Introduction + +Image restoration (IR) tasks [7, 8, 32, 51], including image super-resolution [11, 24, 43, 46, 56, 57], deblurring [41, 75], denoising [3, 23, 40], compression artifacts removal [28, 53], etc, have achieved amazing/uplifting performances, powered by deep learning. A series of backbones are elaborately and carefully designed to boost the + +![](images/ca1f35bdb9b6dc03efc6b463b172cd755568d61b882db27830d2c9fb233c5fce.jpg) +Figure 1. A comparison between ERM and our DIL with RRDB as backbone. The results are tested on Set5 with Gaussian noise. + +restoration performances for specific degradation. Convolution neural networks (CNNs) [20] and transformers [12,34] are two commonly-used designed choices for the backbones of image restoration. However, these works inevitably suffer from severe performance drops when they encounter unseen degradations as shown in Fig. 1, where the restoration degree in training corresponds to the noise of standard deviation 20 and the degrees in testing are different. The commonly-used training paradigm in image restoration, i.e., empirical risk minimization (ERM), does not work well for out-of-distribution degradations. Particularly, the restoration networks trained with ERM merely mine the correlation between distorted image $I_{d}$ and its ideal reconstructed image $I_{o}$ by minimizing the distance between $I_{o}$ and the corresponding clean image $I_{c}$ . However, a spurious correlation [44] is also captured which introduces the bad confounding effects of specific degradation $d$ . It means the conditional probability $P(I_{o}|I_{d})$ is also conditioned on the distortion types or degrees $d$ (i.e., $d \nmid I_{o}|I_{d}$ ). + +A robust/generalizable restoration network should be distortion-invariant (i.e., $d \perp I_{o}|I_{d}$ ). For instance, given two distorted images with the same content $I_{c}$ but different degradations $d_{1}$ and $d_{2}$ , the robust restoration network is expected to recover the same reconstructed image $I_{o}$ + +from these two distorted images (i.e., $P(I_{o}|I_{d}, d = d_{1}) = P(I_{o}|I_{d}, d = d_{2})$ ), respectively. Previous works for the robustness of the restoration network can be roughly divided into two categories, distortion adaptation-based schemes, and domain adaptation/translation-based schemes. Distortion adaptation-based schemes [60] aim to estimate the distortion types or representations, and then, handle the different distortions by adaptively modulating the restoration network. Domain adaptation/translation-based schemes [13, 35,48] regard different distortions as different domains, and introduce the domain adaptation/translation strategies to the image restoration field. Notwithstanding, the above works ignore the exploration of the intrinsic reasons for the poor generalization capability of the restoration network. In this paper, we take the first step to the causality-inspired image restoration, where novel distortion invariant representation learning from the causality perspective is proposed, to improve the generalization capability of the restoration network. + +As depicted in [17, 44], correlation is not equivalent to causation. Learning distortion invariant representation for image restoration requires obtaining the causal effects between the distorted and ideal reconstructed images instead of only their correlation. There are two typical adjustment criteria for causal effects estimation [17], the back-door criterion, and the front-door criterion, respectively. In particular, the back-door criterion aims to remove the bad confounding effects by traversing over known confounders, while the front-door criterion is to solve the challenge that confounders cannot be identified. To improve the generalization capability of the restoration network, we build a structural causal graph in Fig. 2 for the image restoration process and propose the Distortion-Invariant representation Learning (DIL) for image restoration by implementing the back-door criterion from the optimization perspective. There are two challenges for achieving this. The first challenge is how to construct the confounder sets (i.e., distortion sets). From the causality perspective [17, 44], it is better to keep other factors in the distorted image invariant except for distortion types. However, in the real world, collecting distorted/clean image pairs, especially with different real distortions but the same content is impractical. Inspired by counterfactual [44] in causality and the distortion simulation [55, 71], we propose counterfactual distortion augmentation, which selects amounts of high-quality images from the commonly-used dataset [2, 49], and simulate the different distortion degrees or types on these images as the confounders. + +Another challenge of implementing DIL stems from finding a stable and proper instantiating scheme for the back-door criterion. Previous works [36,37,54,64,65] have incorporated causal inference in high-level tasks by instantiating the back-door criterion [17] with attention interven- + +tion [64], feature interventions [66], etc, which are arduous to be exploited in the low-level task of image restoration. In this work, we theoretically derive our distortion-invariant representation learning DIL by instantiating the back-door criterion from the optimization perspective. Particularly, we model the intervention of simulated distortions for the restoration process by virtually updating the restoration network with the samples from the corresponding distortions. Then, we eliminate the confounding effects of distortions by introducing the optimization strategy from Meta-Learning to our proposed DIL. In this way, we can instantiate the causal learning in image restoration and enable the DIL based on the back-door criterion. + +The contributions of this paper are listed as follows: + +- We revisit the image restoration task from a causality view and pinpoint that the reason for the poor generalization of the restoration network, is that the restoration network is not independent to the distortions in the training dataset. +- Based on the back-door criterion in causality, we propose a novel training paradigm, Distortion Invariant representation Learning (DIL) for image restoration, where the intervention is instantiated by a virtually model updating under the counterfactual distortion augmentation and is eliminated with the optimization based on meta-learning. +- Extensive experiments on different image restoration tasks have demonstrated the effectiveness of our DIL for improving the generalization ability on unseen distortion types and degrees. + +# 2. Related Works + +# 2.1. Image Restoration + +Image Restoration (IR) [7, 22, 26, 32, 33, 51, 67] aims to recover high-quality images from the corresponding distorted images, which plays a prominent role in improving the human visual experience. With the advancement of deep learning, a series of works have achieved remarkable progress in lots of IR tasks, including image denoising [3, 40, 73], deblurring [41, 50, 75], super-resolution (SR) [9, 11, 27, 58, 61, 62, 74], etc. Particularly, most of them are devoted to elaborately designing the frameworks for different IR tasks based on their degradation process, which can be roughly divided into two categories, CNN-based framework [9, 11, 74], and Transformer-based framework [7, 24, 32, 67]. Despite that, the above works only explore how to improve the ability of inductive bias toward specific degradation, which lacks enough generalization capability. To improve the model's robustness, some works seek to incorporate the domain translation [13, 35, 48] or distortion-adaptive learning [60] into image restoration. In contrast, we introduce causal learning [17] to image restoration. We answer the reason for the bad robustness of the + +restoration network and propose distortion-invariant representation learning from a causality perspective. + +# 2.2. Causal Inference + +Causal Inference is proposed to eliminate the harmful bias of confounders and discover the causal relationship between multiple variables [17]. A do operation is implemented with adjustment criteria, e.g., front-door or back-door, to estimate the causal effects [44]. In recent years, deep learning has boosted the vast development of a series of intelligent tasks, e.g., image classification [10, 12, 34], segmentation [19, 47], detection [6, 30], low-level processing [7, 51]. However, prominent works focus on fitting the correlation between inputs and their outputs while ignoring the causation. Due to the existence of confounders, the networks are easy to capture the spurious correlation between inputs and their outputs. For instance, if most lions lie in the grass in the training data, the model inevitably mistakes the grass for a lion. To get rid of the harmful bias of confounders, some studies seek to incorporate causal inference into deep learning. [54, 66] model the interventions of confounders from the feature perspective [64] integrate the front-door criterion to vision-language task from the attention perspective. To improve the generalization capability, [29, 36, 37, 65] introduce the causal learning to domain adaptation/generalization. However, the above causality-inspired methods merely focus on the high-level tasks. In this paper, for the first time, we investigate the causality-based image restoration, which aims to improve the generalization capability of restoration networks on different distortion types and degrees. + +# 3. Methods + +# 3.1. A Causal View for Image Restoration + +Image restoration aims to restore the distorted images, of which the degradation process can be represented as a function $I_{d} = g(I_{c},D)$ . Here, $I_{c},I_{d},D$ denote the clean, distorted images, and distortions, respectively. $D$ contains distortion types $D_{t}$ and degrees $D_{l}$ . A restoration network $f$ is trained with the loss function to minimize the difference between its ideal reconstructed images $I_{o}$ and the original clean image $I_{c}$ . We model this whole process with a structure causal graph as shown in Fig. 2. Here, $D\rightarrow I_d\leftarrow I_c$ denotes the degradation process of $I_{d} = g(I_{c},D)$ . $I_{c}\rightarrow I_{o}$ denotes $I_{o}$ is learned with the supervision of $I_{c}$ by maximizing the probability of $P(I_c|I_o)$ . In addition, $D\to I_o$ refers to the knowledge learned from $D$ to $I_{o}$ . $I_{d}\rightarrow I_{o}$ means the restoration process with restoration network $f$ . + +From the causality perspective, the causal representation of image restoration requires that the restoration network $f$ obtains the causal relationship between $I_{d} \rightarrow I_{o}$ . However, there are two extra paths $I_{d} \leftarrow D \rightarrow I_{o}$ and $I_{d} \leftarrow I_{c} \rightarrow I_{o}$ introducing the spurious correlation to $I_{d}$ and $I_{o}$ , where $I_{c}$ and $D$ are confounders in causality. Importantly, the $I_{c}$ are + +![](images/fa13543cf2c61f5a168cea4d798641af881d33d9b2ac0941a30535d521fc6cad.jpg) +Figure 2. Structure causal graph for image restoration. + +$D$ Distortion Set +$D_{t}$ Distortion Types +$D_{l}$ Distortion Degrees +$I_{d}$ Distorted Images +$I_{o}$ Ideal Reconstructed Images +$I_{c}$ Clean Images +$f$ Restoration Network +$d$ Distortion sampled from $D$ + +commonly diverse in the datasets and bring more vivid textures to reconstructed image $I_{o}$ , which is a favorable confounder. We do not take into account the confounder $I_{c}$ in our paper. + +We aim to improve the robustness of the restoration network to unseen or unknown distortions, which are inhibited by the bad confounding effects from confounders $D$ . But, how do the confounders $D$ limit the generalization capability of the restoration network? As shown in Fig. 2, the existing of $I_{d} \gets D \to I_{o}$ causes the conditional probability $P(I_{o}|I_{d})$ learned by restoration network $f$ is also condition on distortions $D$ , i.e., the fitting conditional probability of $f$ is in fact as $P(I_{o}|I_{d},D)$ . Consequently, the restoration network $f$ is not robust to different distortions due to that it is not independent of different distortions $D$ . + +A robust restoration network $f$ should be independent of different distortions (i.e., $D \perp I_o|I_d$ ). To achieve this, we adopt the back-door criterion in causal inference to realize distortion-invariant learning (DIL) through a "do" operation. Here, a "do" operation [17, 44] is exploited to cut off the connection from the distortion $D$ to $I_d$ , thereby removing the bad confounding effects of $D$ to the path $I_d \to I_o$ , and learning the distortion-invariant feature representation (i.e., $D \perp I_o|I_d$ ). We formulate the back-door criterion in image restoration as Equ. 1. + +$$ +P \left(I _ {o} | d o \left(I _ {d}\right)\right) = \sum_ {d _ {i} \in D} P \left(I _ {o} \mid I _ {d}, d _ {i}\right) P \left(d _ {i}\right), P \left(d _ {i}\right) = \frac {1}{n}, \tag {1} +$$ + +where the causal conditional probability $P(I_{o}|do(I_{d}))$ is the optimization direction for restoration network $f$ towards distortion invariant learning. To simplify the optimization, we set the probability of each distortion $d_{i}$ as $1 / n$ , where $n$ is the number of distortion types and degrees that existed in confounders. From Equ. 1, two crucial challenges for achieving it arise. 1) How to construct the virtual confounders (i.e., different distortion types or degrees)? since collecting different real distorted images with the same contents are nontrivial in the real world. 2) How to instantiate the intervention of different distortions to the reconstruction process (i.e., the $P(I_{o}|I_{d},d_{i})$ ) in image restoration. We achieve this through counterfactual distortion augmentation and distortion-invariant representation learning as described + +in the following sections. + +# 3.2. Counterfactual Distortion Augmentation + +To learn the distortion-invariant representation for the restoration network, it is vital to construct the distortion set $D$ (i.e., confounders). For instance, if we expect the restoration network to have the generalization capability for different distortion degrees, we require to construct the distortion set $D$ with the distortions at different levels. Similarly, we can increase the generalization capability of the restoration network for unknown distortion types by constructing the $D$ with different but related distortion types. Furthermore, to avoid the effects of different image contents, it is better for each clean image to have corresponding distorted images with various distortion types or degrees in $D$ . However, it is non-trivial to collect datasets that satisfy the above principles in the real world, which is labor-intensive and arduous. + +In this paper, we construct the distortion set $D$ with synthesized distortions, which we can call virtual confounders in causality. Concretely, we collected a series of high-quality images $I_{c}$ , and generated the distorted images by modifying the degradation process as $I_{d} = g(I_{c}, d_{i}), d_{i} \in D$ . We can also prove the rightness of the above distortion augmentation from the counterfactuals in causality [17], where we answer the counterfactual question that "if $D$ is $d_{i}$ , what the $I_{d}$ would be with $I_{c}$ invariant?". The proof can be found in the Supplementary. + +# 3.3. Distortion-invariant Representation Learning + +After constructing the virtual confounders/distortions set $D = \{d_i | 1 \leq i \leq n\}$ . We are able to achieve the distortion-invariant representation learning by implementing the back-door criterion as Eq. 1 for image restoration. Let us first introduce the relationship between the probability $P(I_o|I_d)$ and the commonly-used training paradigm ERM (empirical risk minimization). In image restoration, an ideal reconstruction $I_o$ is expected to learn by maximizing the condition probability $P(I_o|I_d)$ with loss function as $\mathcal{L}(f_{\theta}(I_d), I_c)$ , where $f_{\theta}$ is the restoration network with the parameters $\theta$ and $L$ denotes the loss function, such as the commonly-used $\mathcal{L}_1$ or $\mathcal{L}_2$ loss. The ERM is used to optimize the network $f_{\theta}$ (with parameters denoted by $\theta$ ) by minimizing the loss function overall training dataset $\mathcal{D} = \{I_d, I_c | d \in D\}$ as: + +$$ +\theta^ {*} = \arg \min _ {\theta} \mathbb {E} _ {(I _ {d}, I _ {c}) \sim \mathcal {D}} [ \mathcal {L} (f _ {\theta} (I _ {d}), I _ {c}) ], \tag {2} +$$ + +where $\theta^{*}$ enables the restoration network $f$ to maximize the $P(I_{o}|I_{d})\approx P(I_{c}|I_{d})$ . However, the above training process also leads the $P(I_{o}|I_{d})$ to be not independent to the distortions $d\in D$ in the training dataset $\mathcal{D}$ , which eliminate the generalization ability of $f$ on the out-of-distribution distortions (i.e., when $d\notin D$ ). To achieve the distortion-invariant representation learning, we aim to maximize the + +causal conditional probability $P(I_{o}|do(I_{d}))$ as instead of $P(I_{o}|I_{d})$ . The key challenge stems from how to model the conditional probability $P(I_{o}|I_{d},d_{i})$ in Eq. 1 (i.e., how to model the intervention from the distortion $d_{i}\in D$ for the restoration process $P(I_o|I_d)$ ). + +In this paper, we propose to model the intervention from $d_{i} \in D$ to the restoration process (i.e., $P(I_{o}|I_{d},d_{i})$ ) through the optimization of the network parameters $\theta$ . From the above analysis, we know that the restoration network $f_{\theta}$ trained with ERM on the paired training data $(I_{d_i},I_c)$ is condition on the distortion $d_{i}$ . This inspires us to instantiate the intervention of different distortion types or degrees $d_{i} \in D$ through updating the model parameter $\theta$ to $\phi_{d_i}$ based on ERM with the training distorted-and-clean image pairs $(I_{d_i},I_c)$ as: + +$$ +\phi_ {d _ {i}} = \theta - \alpha \nabla_ {\theta} \mathcal {L} \left(f _ {\theta} \left(I _ {d _ {i}}\right), I _ {c}\right), \tag {3} +$$ + +where $\phi_{d_i}$ denotes the parameters of the restoration network after one-step update, which is conditioned on the confounder $d_i$ . Consequently, the maximum of the conditional probability $P(I_o|I_d,d_i)$ can be obtained by minimizing the loss $\mathcal{L}(f_{\phi_{d_i}}(I_d),I_c)$ . The optimization direction toward maximizing the causal condition probability $P(I_o|do(I_d))$ in Eq. 1 can be derived as: + +$$ +\theta^ {*} = \arg \min _ {\theta} \mathbb {E} _ {(I _ {d}, I _ {c}) \sim \mathcal {D}} [ \sum_ {d _ {i} \in D} \mathcal {L} \left(f _ {\phi_ {d _ {i}}} (I _ {d}), I _ {c}\right) ], \tag {4} +$$ + +where $D$ denotes the confounder set which contains $n$ distortion degrees or types. Based on the above optimization objective, we learn distortion-invariant representation learning from a causality perspective. + +# 3.4. Implementations of DIL from Meta-Learning + +An interesting finding is that the derived optimization direction of DIL from causality perspective in Eq. 4 is consistent with one typical meta-learning strategy termed as MAML [14], even they have different purposes. MAML aims to enable the fast adaptation capability of a network for few-shot tasks, while ours aims to improve the generalization capability of the restoration network. We facilitate our DIL in image restoration based on this meta-learning strategy. + +However, it is arduous to directly incorporate the optimization direction of Eq. 4 into the practical training process, which is computationally prohibitive. The reason is that it requires multiple gradient computing and updating, which is expensive, especially for the pixel-wise image restoration. To simplify this process, we utilize the Talyor expansion and inverse expansion to derive Eq. 4 as: + +$$ +\theta^ {*} = \arg \min _ {\theta} \mathbb {E} _ {(I _ {d}, I _ {c}) \sim \mathcal {D}} [ \mathcal {L} (f _ {\phi_ {\bar {d}}} (I _ {d}), I _ {c}) ], +$$ + +$$ +w h e r e \phi_ {\tilde {d}} = \theta - \alpha \nabla_ {\theta} \sum_ {d _ {i} \in D} \frac {1}{n} \mathcal {L} \left(f _ {\theta} \left(I _ {d _ {i}}\right), I _ {c}\right), \tag {5} +$$ + +Table 1. Quantitative comparison for image denoising on several benchmark datasets. Results are tested on three different unseen distortion degrees in terms of PSNR/SSIM on RGB channel. Best performances are bolded. + +
DatasetsLevelsMethods
ERMDILsfDILpfDILssDILps
CBSD68 [38]30 (unseen)24.90/0.58130.29(5.39↑)/0.86629.92(5.02↑)/0.85827.48(2.58↑)/0.80929.14(4.24↑)/0.802
40 (unseen)21.12/0.40028.35(7.23↑)/0.82528.10(6.98↑)/0.81225.90(4.78↑)/0.74625.74(4.62↑)/0.629
50 (unseen)18.96/0.30726.64(7.68↑)/0.77926.61(7.65↑)/0.76624.63(5.67↑)/0.68623.34(4.38↑)/0.501
Kodak24 [15]30 (unseen)25.12/0.53331.39(6.27↑)/0.86730.87(5.75↑)/0.85827.92(2.80↑)/0.80129.86(4.74↑)/0.782
40 (unseen)21.22/0.35229.49(8.27↑)/0.83129.15(7.93↑)/0.81726.46(5.24↑)/0.73826.13(4.91↑)/0.588
50 (unseen)19.02/0.26327.76(8.74↑)/0.78827.67(8.65↑)/0.77525.24(6.22↑)/0.67723.60(4.58↑)/0.457
McMaster [72]30 (unseen)25.65/0.56931.70(6.05↑)/0.87331.04(5.39↑)/0.85328.15(2.50↑)/0.79430.09(4.44↑)/0.800
40 (unseen)21.73/0.37329.81(8.08↑)/0.83129.07(7.34↑)/0.80226.59(4.86↑)/0.72826.24(4.51↑)/0.605
50 (unseen)19.47/0.27828.02(8.55↑)/0.78327.31(7.84↑)/0.74925.20(5.73↑)/0.66423.60(4.13↑)/0.466
Urban100 [21]30 (unseen)25.46/0.64830.93(5.47↑)/0.89830.26(4.80↑)/0.88426.95(1.49↑)/0.82529.73(4.27↑)/0.841
40 (unseen)21.53/0.47928.82(7.29↑)/0.86628.32(6.79↑)/0.84825.26(3.73↑)/0.76726.25(4.72↑)/0.691
50 (unseen)19.28/0.38926.88(7.60↑)/0.82926.63(7.35↑)/0.81123.85(4.57↑)/0.71023.71(4.43↑)/0.575
Manga109 [39]30 (unseen)26.62/0.65331.97(5.35↑)/0.91031.14(4.52↑)/0.90126.02(-0.6↑)/0.83331.05(4.43↑)/0.858
40 (unseen)22.34/0.44229.02(6.68↑)/0.88828.53(6.19↑)/0.87524.31(1.97↑)/0.78427.29(4.95↑)/0.704
50 (unseen)19.95/0.34226.52(6.57↑)/0.86026.34(6.39↑)/0.84622.82(2.87↑)/0.73424.47(4.52↑)/0.564
+ +![](images/19fe6461f33bd73401998bf50a2844f3f5e5db71f85b8f5689b6a2b85e01e2d6.jpg) +(a) Serial sampling based + +![](images/5c790d5b0d3bfaf8351aaf64c0c0d9352d0130eadc4e6f6f23c74c27c8080e42.jpg) +(b) Parallel sampling based +Figure 3. The comparison of serial sampling and parallel sampling. + +where $\phi_{\bar{d}}$ denotes the parameters of restoration network $f$ that is virtually updated with loss function with samples overall all distortions $D = \{d_i\}, 1 \leq i \leq n$ . We define it as parallel sampling for DIL, which reduces the complex training process of DIL to two steps. In this paper, we call the original sampling strategy as serial sampling. The comparison between serial sampling and parallel sampling are shown in Fig. 3. The detailed derivation for Eq. 5 are described in the Supplementary. + +We also investigate two different gradient updating strategy for DIL. From Eq. 4 and Eq. 5, we can observe that they require the second-order gradient since the gradient is computed with two-step forward through $\phi_{d_i}$ , which is shown in Fig. 3. To simplify it, Reptile [42] proposes an alternative strategy (i.e., approximating the second-order gradient by the sequential parameter updating with one-order gradient. The optimization direction (i.e., gradient) is computed with the deviation between the initial and last-step parameters. We integrate it into our DIL and call it first-order optimization. In contrast, the original optimization in Eq. 5 is termed second-order optimization. In summary, we propose four variants for DIL following the above two strategies. $\mathrm{DIL}_{sf}$ adopts the serial sampling and first-order gradient optimization. $\mathrm{DIL}_{pf}$ utilizes the parallel sampling and first-order optimization. $\mathrm{DIL}_{ss} / \mathrm{DIL}_{ps}$ exploits the second-order optimization and serial/parallel sampling. + +# 4. Experiments + +In this section, we first describe the implementation details. Then, we validate the effectiveness of our DIL from two typical out-of-distribution settings, i.e., Cross Distortion Degrees, and Cross Distortion Types. Particularly, for cross-distortion degrees, we train the restoration network with seen distortion degrees while testing it with unseen distortion degrees. For cross-distortion types, the restoration network is trained with synthesized distortions and validated on the corresponding real-world or other distortions. + +# 4.1. Implementation + +We adopt the typical RRDB [56] as our image restoration backbone, which has demonstrated remarkable performances towards various low-level image tasks [52, 55]. All the experiments are done with four NVIDIA 2080Ti GPUs. Adam optimizer is adopted to optimize network parameters in both ERM and DIL training paradigms. More details are given in the Supplementary. + +# 4.2. Cross Distortion Degrees + +Results on Image Denoising. For image denoising, the training data are composed of distorted images with noise levels [5, 10, 15, 20] and their corresponding clean images. After training the restoration network, we validate it on the test datasets with unseen noise degrees, including [30, 40, 50]. We compare the empirical risk minimization (ERM) and four variants of our proposed DIL, i.e., $\mathrm{DIL}_{sf}$ , $\mathrm{DIL}_{pf}$ , $\mathrm{DIL}_{ss}$ , and $\mathrm{DIL}_{ps}$ , respectively. + +The experimental results are shown in Table 1. We can observe that all four variants of DIL achieve great generalization ability on multiple unseen noise levels compared with commonly-used empirical risk minimization (ERM). On several typical scenarios, including natural im + +Table 2. Quantitative comparison for image deblurring on several benchmark datasets. Results are tested on the five unseen blur degrees [4.2, 4.4, 4.6, 4.8, 5.0] in terms of PSNR/SSIM on RGB channel. + +
DatasetsMethodsLevels
4.2 (unseen)4.4 (unseen)4.6 (unseen)4.8 (unseen)5.0 (unseen)
Set5 [4]ERM29.31/0.84426.55/0.77624.43/0.70922.96/0.64822.00/0.602
DIL29.58(0.27↑)/0.84827.52(0.97↑)/0.80225.66(1.23↑)/0.75124.38(1.42↑)/0.70823.46(1.46↑)/0.671
Set14 [68]ERM27.22/0.78124.93/0.72623.16/0.67121.89/0.62420.88/0.583
DIL27.24(0.02↑)/0.77825.78(0.85↑)/0.74624.35(1.19↑)/0.70823.23(1.34↑)/0.67222.37(1.49↑)/0.640
BSD100 [38]ERM27.20/0.78425.17/0.73223.50/0.68222.24/0.63921.28/0.602
DIL27.37(0.17↑)/0.78126.16(0.99↑)/0.75324.91(1.41↑)/0.71923.86(1.62↑)/0.68623.02(1.74↑)/0.658
Urban100 [21]ERM24.95/0.79722.41/0.72320.59/0.65719.33/0.60618.40/0.565
DIL24.97(0.02↑)/0.79323.26(0.85↑)/0.74321.76(1.17↑)/0.69320.70(1.37↑)/0.65119.92(1.52↑)/0.618
Manga109 [39]ERM28.16/0.86523.96/0.79121.21/0.71319.63/0.65218.63/0.606
DIL28.09(-0.07↑)/0.86725.41(1.45↑)/0.82223.15(1.94↑)/0.77121.69(2.06↑)/0.72620.72(2.09↑)/0.691
+ +![](images/e41d7b63df26f9e4cf1aae939e241f8af967c59095bcfe8a90716db9628206a8.jpg) +Figure 4. Visual comparison of the commonly-used ERM and our proposed four variants of DIL with the unseen noise level 30. + +![](images/a0bcd4fe07642ca273399569ed69719607fee115db1e4883a27725f0c42b073e.jpg) + +![](images/b374fee163614a213f0d36327064b1ff9848d26270ccd678e6295e7ec4847f96.jpg) + +![](images/e7468a204711b4189c8661aeb4ac9c89de2f019fac45c83399b57e8e53bc1e41.jpg) + +![](images/dc7da7b4ff92f8a5684ef926d84a32c24cb466a7f052c76b89e9ddbcb154282a.jpg) + +![](images/61a78efa12bae7831cf2f4fc084d7e46f896ff1554c0280c75b762a5aaf194ce.jpg) + +Table 3. Quantitative comparison for hybrid distortion removal. Results are tested on three different distortion levels in terms of PSNR/SSIM on Y channel. + +
DatasetsMethodsDistortion level
Mild (unseen)Moderate (unseen)Severe (seen)
BSD100 [38]ERM25.31/0.68724.62/0.64225.27/0.617
DIL26.37/0.69125.23/0.64525.22/0.613
Urban100 [21]ERM23.97/0.73622.51/0.67423.38/0.655
DIL25.00/0.74723.13/0.68223.20/0.645
Manga109 [39]ERM27.43/0.86324.85/0.80826.50/0.815
DIL28.41/0.86825.30/0.81026.19/0.766
DIV2K [2]ERM26.19/0.76625.94/0.74427.42/0.742
DIL27.84/0.78526.89/0.75627.38/0.737
+ +ages (i.e., CBSD68 [38], Kodak24 [15], McMaster [72]), building images (Urban100 [21]), cartoon images (i.e., Manga109 [39]), our DIL even outperforms the ERM by a promising/amazing gain of $8.74\mathrm{dB}$ at most. Moreover, with the increase of the distribution gap between training and testing data, ours can achieve larger improvements for ERM. Furthermore, for cross distortion degree, $\mathrm{DIL}_{sf}$ shows the best generalization capability compared with the other three variants by serial sampling and first-order optimization. We also visualize the reconstructed images of the above methods in Fig. 4. For the unseen distortion degree $(\sigma = 30)$ , the ERM cannot remove the noise well and the reconstructed image also contains obvious noise distortion. + +However, our $\mathrm{DIL}_{sf}$ enables the restoration network to recover more vivid and clean images from the unseen noise degrees, which validates the correctness and effectiveness of our proposed DIL. + +Results on Image Deblurring. We also validate the generalization capability of our DIL on the challenging image deblurring. Under this scenarios, we train the restoration network with our proposed DIL with the gaussian blurring level [1.0, 2.0, 3.0, 4.0], and validate its generalization capability on the more severe and difficult blurring levels, including 4.2, 4.4, 4.6, 4.8, and 5.0. + +As shown in Table. 2, we validate our DIL on five benchmark datasets, including Set5 [4], Set14 [68], BSD100 [38], Urban100 [21], and Manga109 [39]. With the increase of blurring level, the restoration network trained with ERM suffers from a severe performance drop, since the unseen blurring levels are far away from the blurring levels used for training. But our DIL can improve ERM on each unseen blurring level for five datasets. In particular, we achieve the gain of $2.09\mathrm{dB}$ for the cartoon scene Manga109 [39] on the blurring level 5.0. + +Results on Hybrid-distorted Image Restoration. Except for the above single distortion, we also explore the generalization capability of our DIL on hybrid-distorted image restoration. Following [26], the hybrid distorted images are degraded with blur, noise, and Jpeg compression in a sequence manner. Based on the distortion degree, it can be divided into three levels from low to high, i.e., mild, mod- + +Table 4. Quantitative results of network generalization capability on real image denoising and synthetic image deraining tasks. Results are tested on Y channel in terms of PSNR/SSIM, except for DND where we obtain our results from official online benchmark. + +
MethodsDatasets (Real Denoising)Datasets (Deraining)
SIDD [1]DND [45]Rain100L [63]Rain12 [31]Rain800 [70]
ERM38.90/0.937938.67/0.954927.61/0.857731.44/0.894723.36/0.8199
DILsf39.96(1.06↑)/0.941039.16(0.49↑)/0.953128.15(0.54↑)/0.867932.43(0.99↑)/0.916323.41(0.05↑)/0.8261
DILps39.92(1.02↑)/0.938539.03(0.36↑)/0.955328.37(0.76↑)/0.873933.07(1.63↑)/0.926623.52(0.16↑)/0.8281
+ +Figure 5. Visual comparison of the commonly-used ERM and our proposed DIL for unseen hybrid-distorted (mild) image restoration. + +erate, and severe. In this setting, the restoration network is trained with severe hybrid distortions and validated on the mild and moderate levels. + +As shown in Table 3, our DIL achieves an average gain of $1.05\mathrm{dB}$ , and $0.66\mathrm{dB}$ on the mild-level, and moderate-level hybrid distortions than ERM, which has a large distribution gap with severe-level hybrid distortions. We can also notice that with the increase of the distribution gap, ours can preserve more performances on the restoration of the out-of-distribution distortions. We also conduct the subjective comparison of our methods with the commonly-used ERM in Fig. 5. We can observe that the restoration network trained with ERM suffers from new artifacts for unseen hybrid-distorted images. But our DIL can eliminate the artifacts well and generate more promising results. + +# 4.3. Cross Distortion Types + +In this section, we investigate the effects of our proposed DIL on the cross-distortion type setting, which is more challenging than the cross-degree setting. + +Results on Real Image Super-resolution Real Image Super-resolution (RealSR) has attracted great attention since it is urgently required in real life, where the distorted image contains complex hybrid distortions, such as blurring, low resolution, noise, etc. However, the distorted/clean pairs for RealSR are hard to be collected. Simulating distortions like Real-world distortion has been a popular solution for RealSR [55, 71]. In this paper, we follow the Real-ESRGAN [55] and utilize its proposed RealSR distortion simulating to generate image pairs as training datasets. Then we test the restoration network on the out-of-distribution datasets, RealSR V3 [5], DRealSR [59], which are two commonly-used datasets for RealSR evaluation. + +We show the experimental results on RealSR in Table. 5. Without access to any training samples in RealSR V3, DRealSR, our $\mathrm{DIL}_{sf}$ can outperform the ERM by $0.29\mathrm{dB}$ on RealSR V3 [5] and $0.26\mathrm{dB}$ on DRealSR dataset [59]. + +Table 5. Quantitative results of the network generalization capability on RealSR tasks. Results are tested on the Y channel in terms of PSNR/SSIM. + +
MethodsDatasets
RealSR V3 [5] (unseen)DrealSR [59] (unseen)
Real-ESRNet [55]26.19/0.798928.22/0.8470
BSRNet [71]27.46/0.808229.45/0.8579
ERM27.65/0.809829.73/0.8628
DILsf27.94(0.29↑)/0.809829.99(0.26↑)/0.8648
DILps28.12(0.47↑)/0.806730.58(0.85↑)/0.8712
+ +Table 6. Quantitative results of our DIL on different backbones. Results are tested on the unseen noise level 30 in terms of PSNR/SSIM. + +
ModelsMethodsDatasets
CBSD68 [38]Kodak24 [15]Urban100 [21]
RRDBERM24.90/0.58125.12/0.53325.46/0.648
DIL30.28/0.86631.39/0.86730.93/0.898
SwinIRERM24.22/0.55124.22/0.49324.73/0.618
DIL29.08/0.79829.71/0.77429.72/0.834
+ +Particularly, we notice that $\mathrm{DIL}_{ps}$ is more suitable for cross-distortion type scenarios than $\mathrm{DIL}_{sf}$ , which exceeds the ERM by a 0.47dB on RealSR V3, and 0.85dB on DRealSR dataset. The reason for that we guess is that $\mathrm{DIL}_{ps}$ is more capable of improving the generalization for the large distribution gap in image restoration. We also visualize the comparison corresponding to the subjective quality for different methods. As shown in Fig. 6, Real-ESRNet [55] and BSRNet [71] cause the overshooting at the edge of the text. But our $\mathrm{DIL}_{ps}$ can eliminate the artifacts and achieve a high-quality restoration + +Results on Real Image Denoising. We also study the generalization capability of our training paradigm DIL on the Real Image Denoising task. Concretely, we select four synthesized distortions based on four categories of color space among camera ISP process [18], and generate training image pairs from DF2K [2, 49] in an online manner. Then we verify its generalization on the commonly-used Real De + +![](images/94f109de9c64b5ac92048328b4566f9f14e9b61c556dccef349418977a299f59.jpg) +Input + +![](images/31f134a90e396f293ab79f3b59c28fce2738a62e01699f697f3ea8195b3bb509.jpg) +Bicubic + +![](images/b51d25b4c8ada72f5bbd6d5a692212836b782f5ff1c2e980e982211824a19d0c.jpg) +Real-ESRNet + +![](images/2c68de85be65692a8c757c43675e68badbf16563161c2bf34f88c1174fbc18dc.jpg) +BSRNet +Figure 6. Visual comparison with state-of-the-art methods on DRealSR [59]. + +![](images/ed0f34b0219d39d82e98fd08e8fa00b14afeb8efd521b7238e9da3fd9df2c3db.jpg) +ERM + +![](images/e09bfbadf6c8dc5c61f05b70937858b1887cfcd9a29c9958fc22c01a5e81f58b.jpg) +DILps + +![](images/da3cc8c948fdcdcbed2a6888acb69dd98d1bdff5036ac1d15fa517e4deddf81d.jpg) +Ground Truth + +Table 7. Quantitative comparison between different distortion augmentation methods. $\mathrm{D}_1$ and $\mathrm{D}_2$ are the first order distortion and the second order distortion derived from [55] respectively. Results are tested on RealSR datasets in terms of PSNR/SSIM. + +
AugmentationMethodsDatasets
RealSR V3 [5]DrealSR [59]
D1ERM27.65/0.809829.73/0.8628
DIL27.94/0.809829.99/0.8648
D2ERM27.39/0.807729.41/0.8591
DIL27.65/0.802729.85/0.8677
+ +noising dataset SIDD [1] and DND [45]. As Table 4 illustrated, our $\mathrm{DIL}_{ps}$ achieves the PSNR of $39.92\mathrm{dB}$ , which outperforms the ERM by $1.02\mathrm{dB}$ , which is almost the same with $\mathrm{DIL}_{sf}$ . + +Results on Image Deraining. As an extension experiment, we introduce our DIL to the experiments of image deraining task. Particularly, the raining types and degrees between different datasets are severely different in image deraining. Here, we optimize the restoration network with three image deraining datasets, including DID-MDN [69], Rain14000 [16], and Heavy Rain Dataset [25]. Then we validate the generalization capability of the restoration network on three unseen deraining datasets, i.e., Rain100L [63], Rain12 [31], and Rain800 [70]. We report the experimental results in Table 4. Our DIL $(\mathrm{DIL}_{ps})$ enables the restoration network to have a better generalization capability than ERM, which obtains a gain of 0.76dB on Rain100L [63] and 1.63dB on Rain12 [31] dataset. + +# 4.4. Ablation Studies + +Impact of different restoration networks. We demonstrate the effectiveness of DIL across different network backbones. In addition to the convolution-based RRDB [56] network, we also incorporate our DIL into the transformer-based SwinIR [32]. The performances are reported in Table 6, which reveals that our DIL can also improve the generalization capability of Transformer-based backbones. This study reveals our DIL is a general training paradigm for different backbones. + +Effects of different variants for DIL As shown in Table. 1, and 4, we can observe that $\mathrm{DIL}_{sf}$ is more proper for cross-distortion degrees. But for cross-distortion types, $\mathrm{DIL}_{ps}$ achieves better performance for RealSR and Image Deraining. It is noteworthy that the distribution gap of dif + +ferent distortion types is larger than different degrees. The first-order optimization is more stable but lacks enough capability for a severe distribution gap compared to second-order optimization. But all of them are competent in improving the generalization capability. + +# 5. Discussion on Limitations + +The performance on training data. We also report the performance of our DIL on the seen training data in Table 3. It can be seen that our DIL will cause a slight performance drop but the generalization capability is improved obviously. The reason for that is our DIL implements distortion invariant representation learning, which prevents the restoration network from over-fitting to the training data. + +The impact of different distortion augmentation. As shown in Table 7, despite that our DIL achieves the improvement of the generalization capability. The final generalization performance is still related to the distortion augmentation strategy. It is vital to find a universal distortion augmentation strategy, which requires more exploration. We believe it will be a potential/important direction to improve the generalization ability of the restoration network. + +# 6. Conclusion + +In this paper, we propose a novel distortion invariant representation learning (DIL) training paradigm for image restoration from the causality perspective. In particular, we provide a causal view of the image restoration process, and clarify why the restoration network lacks the generalization capability for different degradations. Based on that, we treat the distortion types and degrees as confounders, of which the confounding effects can be removed with our proposed DIL. Concretely, we produce the spurious confounders by simulating the different distortion types and degrees. Then, an instantiation of the back-door criterion in causality is introduced from the optimization perspective, which enables the restoration network to remove the harmful bias from different degradations. Extensive experiments on the settings, cross distortion degrees, and cross distortion types, have demonstrated that our DIL improves the generalization capability of the restoration network effectively. + +# Acknowledgements + +This work was supported in part by NSFC under Grant U1908209, 62021001, and ZJNSFC under Grant LQ23F010008. + +# References + +[1] Abdelrahman Abdelhamed, Stephen Lin, and Michael S Brown. A high-quality denoising dataset for smartphone cameras. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 1692-1700, 2018. 7, 8 +[2] Eirikur Agustsson and Radu Timofte. Ntire 2017 challenge on single image super-resolution: Dataset and study. 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IEEE Transactions on Pattern Analysis and Machine Intelligence, 43(7):2480-2495, 2020. 1, 2 \ No newline at end of file diff --git a/2023/Learning Distortion Invariant Representation for Image Restoration From a Causality Perspective/images.zip b/2023/Learning Distortion Invariant Representation for Image Restoration From a Causality Perspective/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..db68387b6705f6203a611b9142b2e4a24edc8efe --- /dev/null +++ b/2023/Learning Distortion Invariant Representation for Image Restoration From a Causality Perspective/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:09d1e12a8abb8b07ce3d58b32c0881116c2aa0d855e5ddbb76bd57fa572aeb4f +size 719681 diff --git a/2023/Learning Distortion Invariant Representation for Image Restoration From a Causality Perspective/layout.json b/2023/Learning Distortion Invariant Representation for Image Restoration From a Causality Perspective/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..b476ff2e9964e9eef33823281cb620eecdef8906 --- /dev/null +++ b/2023/Learning Distortion Invariant Representation for Image Restoration From a Causality Perspective/layout.json @@ -0,0 +1,11592 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 86, + 103, + 507, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 103, + 507, + 140 + ], + "spans": [ + { + "bbox": [ + 86, + 103, + 507, + 140 + ], + "type": "text", + "content": "Learning Distortion Invariant Representation for Image Restoration from A Causality Perspective" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 82, + 160, + 511, + 201 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 82, + 160, + 511, + 201 + ], + "spans": [ + { + "bbox": [ + 82, + 160, + 511, + 201 + ], + "type": "text", + "content": "Xin Li" + }, + { + "bbox": [ + 82, + 160, + 511, + 201 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 82, + 160, + 511, + 201 + ], + "type": "text", + "content": ", Bingchen Li" + }, + { + "bbox": [ + 82, + 160, + 511, + 201 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 82, + 160, + 511, + 201 + ], + "type": "text", + "content": ", Xin Jin" + }, + { + "bbox": [ + 82, + 160, + 511, + 201 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 82, + 160, + 511, + 201 + ], + "type": "text", + "content": ", Cuiling Lan" + }, + { + "bbox": [ + 82, + 160, + 511, + 201 + ], + "type": "inline_equation", + "content": "^{3\\dagger}" + }, + { + "bbox": [ + 82, + 160, + 511, + 201 + ], + "type": "text", + "content": ", Zhibo Chen" + }, + { + "bbox": [ + 82, + 160, + 511, + 201 + ], + "type": "inline_equation", + "content": "^{1\\dagger}" + }, + { + "bbox": [ + 82, + 160, + 511, + 201 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 82, + 160, + 511, + 201 + ], + "type": "text", + "content": "University of Science and Technology of China " + }, + { + "bbox": [ + 82, + 160, + 511, + 201 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 82, + 160, + 511, + 201 + ], + "type": "text", + "content": "Eastern Institute for Advanced Study \n" + }, + { + "bbox": [ + 82, + 160, + 511, + 201 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 82, + 160, + 511, + 201 + ], + "type": "text", + "content": "Microsoft Research Asia" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 134, + 205, + 457, + 217 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 134, + 205, + 457, + 217 + ], + "spans": [ + { + "bbox": [ + 134, + 205, + 457, + 217 + ], + "type": "text", + "content": "{lixin666, lbc31415926}@mail.ustc.edu.cn, jinxin@eias.ac.cn," + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 182, + 220, + 411, + 231 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 182, + 220, + 411, + 231 + ], + "spans": [ + { + "bbox": [ + 182, + 220, + 411, + 231 + ], + "type": "text", + "content": "culan@microsoft.com, chenzhibo@ustc.edu.cn" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 143, + 258, + 192, + 272 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 258, + 192, + 272 + ], + "spans": [ + { + "bbox": [ + 143, + 258, + 192, + 272 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 285, + 289, + 571 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 285, + 289, + 571 + ], + "spans": [ + { + "bbox": [ + 46, + 285, + 289, + 571 + ], + "type": "text", + "content": "In recent years, we have witnessed the great advancement of Deep neural networks (DNNs) in image restoration. However, a critical limitation is that they cannot generalize well to real-world degradations with different degrees or types. In this paper, we are the first to propose a novel training strategy for image restoration from the causality perspective, to improve the generalization ability of DNNs for unknown degradations. Our method, termed Distortion Invariant representation Learning (DIL), treats each distortion type and degree as one specific confounder, and learns the distortion-invariant representation by eliminating the harmful confounding effect of each degradation. We derive our DIL with the back-door criterion in causality by modeling the interventions of different distortions from the optimization perspective. Particularly, we introduce counterfactual distortion augmentation to simulate the virtual distortion types and degrees as the confounders. Then, we instantiate the intervention of each distortion with a virtual model updating based on corresponding distorted images, and eliminate them from the meta-learning perspective. Extensive experiments demonstrate the generalization capability of our DIL on unseen distortion types and degrees. Our code will be available at https://github.com/lixinustc/Causal-IR-DIL." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 597, + 128, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 597, + 128, + 609 + ], + "spans": [ + { + "bbox": [ + 47, + 597, + 128, + 609 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 619, + 287, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 619, + 287, + 693 + ], + "spans": [ + { + "bbox": [ + 46, + 619, + 287, + 693 + ], + "type": "text", + "content": "Image restoration (IR) tasks [7, 8, 32, 51], including image super-resolution [11, 24, 43, 46, 56, 57], deblurring [41, 75], denoising [3, 23, 40], compression artifacts removal [28, 53], etc, have achieved amazing/uplifting performances, powered by deep learning. A series of backbones are elaborately and carefully designed to boost the" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 320, + 258, + 533, + 386 + ], + "blocks": [ + { + "bbox": [ + 320, + 258, + 533, + 386 + ], + "lines": [ + { + "bbox": [ + 320, + 258, + 533, + 386 + ], + "spans": [ + { + "bbox": [ + 320, + 258, + 533, + 386 + ], + "type": "image", + "image_path": "ca1f35bdb9b6dc03efc6b463b172cd755568d61b882db27830d2c9fb233c5fce.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 393, + 545, + 417 + ], + "lines": [ + { + "bbox": [ + 305, + 393, + 545, + 417 + ], + "spans": [ + { + "bbox": [ + 305, + 393, + 545, + 417 + ], + "type": "text", + "content": "Figure 1. A comparison between ERM and our DIL with RRDB as backbone. The results are tested on Set5 with Gaussian noise." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 424, + 545, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 424, + 545, + 652 + ], + "spans": [ + { + "bbox": [ + 304, + 424, + 545, + 652 + ], + "type": "text", + "content": "restoration performances for specific degradation. Convolution neural networks (CNNs) [20] and transformers [12,34] are two commonly-used designed choices for the backbones of image restoration. However, these works inevitably suffer from severe performance drops when they encounter unseen degradations as shown in Fig. 1, where the restoration degree in training corresponds to the noise of standard deviation 20 and the degrees in testing are different. The commonly-used training paradigm in image restoration, i.e., empirical risk minimization (ERM), does not work well for out-of-distribution degradations. Particularly, the restoration networks trained with ERM merely mine the correlation between distorted image " + }, + { + "bbox": [ + 304, + 424, + 545, + 652 + ], + "type": "inline_equation", + "content": "I_{d}" + }, + { + "bbox": [ + 304, + 424, + 545, + 652 + ], + "type": "text", + "content": " and its ideal reconstructed image " + }, + { + "bbox": [ + 304, + 424, + 545, + 652 + ], + "type": "inline_equation", + "content": "I_{o}" + }, + { + "bbox": [ + 304, + 424, + 545, + 652 + ], + "type": "text", + "content": " by minimizing the distance between " + }, + { + "bbox": [ + 304, + 424, + 545, + 652 + ], + "type": "inline_equation", + "content": "I_{o}" + }, + { + "bbox": [ + 304, + 424, + 545, + 652 + ], + "type": "text", + "content": " and the corresponding clean image " + }, + { + "bbox": [ + 304, + 424, + 545, + 652 + ], + "type": "inline_equation", + "content": "I_{c}" + }, + { + "bbox": [ + 304, + 424, + 545, + 652 + ], + "type": "text", + "content": ". However, a spurious correlation [44] is also captured which introduces the bad confounding effects of specific degradation " + }, + { + "bbox": [ + 304, + 424, + 545, + 652 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 424, + 545, + 652 + ], + "type": "text", + "content": ". It means the conditional probability " + }, + { + "bbox": [ + 304, + 424, + 545, + 652 + ], + "type": "inline_equation", + "content": "P(I_{o}|I_{d})" + }, + { + "bbox": [ + 304, + 424, + 545, + 652 + ], + "type": "text", + "content": " is also conditioned on the distortion types or degrees " + }, + { + "bbox": [ + 304, + 424, + 545, + 652 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 424, + 545, + 652 + ], + "type": "text", + "content": " (i.e., " + }, + { + "bbox": [ + 304, + 424, + 545, + 652 + ], + "type": "inline_equation", + "content": "d \\nmid I_{o}|I_{d}" + }, + { + "bbox": [ + 304, + 424, + 545, + 652 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "text", + "content": "A robust/generalizable restoration network should be distortion-invariant (i.e., " + }, + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "inline_equation", + "content": "d \\perp I_{o}|I_{d}" + }, + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "text", + "content": "). For instance, given two distorted images with the same content " + }, + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "inline_equation", + "content": "I_{c}" + }, + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "text", + "content": " but different degradations " + }, + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "inline_equation", + "content": "d_{1}" + }, + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "inline_equation", + "content": "d_{2}" + }, + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "text", + "content": ", the robust restoration network is expected to recover the same reconstructed image " + }, + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "inline_equation", + "content": "I_{o}" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 137, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 137, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 137, + 712 + ], + "type": "text", + "content": "†Corresponding Author" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1714" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 299 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 299 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 299 + ], + "type": "text", + "content": "from these two distorted images (i.e., " + }, + { + "bbox": [ + 47, + 72, + 289, + 299 + ], + "type": "inline_equation", + "content": "P(I_{o}|I_{d}, d = d_{1}) = P(I_{o}|I_{d}, d = d_{2})" + }, + { + "bbox": [ + 47, + 72, + 289, + 299 + ], + "type": "text", + "content": "), respectively. Previous works for the robustness of the restoration network can be roughly divided into two categories, distortion adaptation-based schemes, and domain adaptation/translation-based schemes. Distortion adaptation-based schemes [60] aim to estimate the distortion types or representations, and then, handle the different distortions by adaptively modulating the restoration network. Domain adaptation/translation-based schemes [13, 35,48] regard different distortions as different domains, and introduce the domain adaptation/translation strategies to the image restoration field. Notwithstanding, the above works ignore the exploration of the intrinsic reasons for the poor generalization capability of the restoration network. In this paper, we take the first step to the causality-inspired image restoration, where novel distortion invariant representation learning from the causality perspective is proposed, to improve the generalization capability of the restoration network." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 304, + 289, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 304, + 289, + 651 + ], + "spans": [ + { + "bbox": [ + 47, + 304, + 289, + 651 + ], + "type": "text", + "content": "As depicted in [17, 44], correlation is not equivalent to causation. Learning distortion invariant representation for image restoration requires obtaining the causal effects between the distorted and ideal reconstructed images instead of only their correlation. There are two typical adjustment criteria for causal effects estimation [17], the back-door criterion, and the front-door criterion, respectively. In particular, the back-door criterion aims to remove the bad confounding effects by traversing over known confounders, while the front-door criterion is to solve the challenge that confounders cannot be identified. To improve the generalization capability of the restoration network, we build a structural causal graph in Fig. 2 for the image restoration process and propose the Distortion-Invariant representation Learning (DIL) for image restoration by implementing the back-door criterion from the optimization perspective. There are two challenges for achieving this. The first challenge is how to construct the confounder sets (i.e., distortion sets). From the causality perspective [17, 44], it is better to keep other factors in the distorted image invariant except for distortion types. However, in the real world, collecting distorted/clean image pairs, especially with different real distortions but the same content is impractical. Inspired by counterfactual [44] in causality and the distortion simulation [55, 71], we propose counterfactual distortion augmentation, which selects amounts of high-quality images from the commonly-used dataset [2, 49], and simulate the different distortion degrees or types on these images as the confounders." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 653, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 653, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 653, + 289, + 715 + ], + "type": "text", + "content": "Another challenge of implementing DIL stems from finding a stable and proper instantiating scheme for the back-door criterion. Previous works [36,37,54,64,65] have incorporated causal inference in high-level tasks by instantiating the back-door criterion [17] with attention interven-" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 304, + 72, + 547, + 227 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 227 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 227 + ], + "type": "text", + "content": "tion [64], feature interventions [66], etc, which are arduous to be exploited in the low-level task of image restoration. In this work, we theoretically derive our distortion-invariant representation learning DIL by instantiating the back-door criterion from the optimization perspective. Particularly, we model the intervention of simulated distortions for the restoration process by virtually updating the restoration network with the samples from the corresponding distortions. Then, we eliminate the confounding effects of distortions by introducing the optimization strategy from Meta-Learning to our proposed DIL. In this way, we can instantiate the causal learning in image restoration and enable the DIL based on the back-door criterion." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 317, + 228, + 527, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 228, + 527, + 239 + ], + "spans": [ + { + "bbox": [ + 317, + 228, + 527, + 239 + ], + "type": "text", + "content": "The contributions of this paper are listed as follows:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 317, + 241, + 545, + 437 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 317, + 241, + 545, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 241, + 545, + 300 + ], + "spans": [ + { + "bbox": [ + 317, + 241, + 545, + 300 + ], + "type": "text", + "content": "- We revisit the image restoration task from a causality view and pinpoint that the reason for the poor generalization of the restoration network, is that the restoration network is not independent to the distortions in the training dataset." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 317, + 304, + 545, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 304, + 545, + 388 + ], + "spans": [ + { + "bbox": [ + 317, + 304, + 545, + 388 + ], + "type": "text", + "content": "- Based on the back-door criterion in causality, we propose a novel training paradigm, Distortion Invariant representation Learning (DIL) for image restoration, where the intervention is instantiated by a virtually model updating under the counterfactual distortion augmentation and is eliminated with the optimization based on meta-learning." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 317, + 389, + 545, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 389, + 545, + 437 + ], + "spans": [ + { + "bbox": [ + 317, + 389, + 545, + 437 + ], + "type": "text", + "content": "- Extensive experiments on different image restoration tasks have demonstrated the effectiveness of our DIL for improving the generalization ability on unseen distortion types and degrees." + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 446, + 397, + 459 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 446, + 397, + 459 + ], + "spans": [ + { + "bbox": [ + 306, + 446, + 397, + 459 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 461, + 416, + 473 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 461, + 416, + 473 + ], + "spans": [ + { + "bbox": [ + 306, + 461, + 416, + 473 + ], + "type": "text", + "content": "2.1. Image Restoration" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 474, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 547, + 713 + ], + "type": "text", + "content": "Image Restoration (IR) [7, 22, 26, 32, 33, 51, 67] aims to recover high-quality images from the corresponding distorted images, which plays a prominent role in improving the human visual experience. With the advancement of deep learning, a series of works have achieved remarkable progress in lots of IR tasks, including image denoising [3, 40, 73], deblurring [41, 50, 75], super-resolution (SR) [9, 11, 27, 58, 61, 62, 74], etc. Particularly, most of them are devoted to elaborately designing the frameworks for different IR tasks based on their degradation process, which can be roughly divided into two categories, CNN-based framework [9, 11, 74], and Transformer-based framework [7, 24, 32, 67]. Despite that, the above works only explore how to improve the ability of inductive bias toward specific degradation, which lacks enough generalization capability. To improve the model's robustness, some works seek to incorporate the domain translation [13, 35, 48] or distortion-adaptive learning [60] into image restoration. In contrast, we introduce causal learning [17] to image restoration. We answer the reason for the bad robustness of the" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1715" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 96 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 96 + ], + "type": "text", + "content": "restoration network and propose distortion-invariant representation learning from a causality perspective." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 97, + 149, + 108 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 97, + 149, + 108 + ], + "spans": [ + { + "bbox": [ + 47, + 97, + 149, + 108 + ], + "type": "text", + "content": "2.2. Causal Inference" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 110, + 289, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 110, + 289, + 434 + ], + "spans": [ + { + "bbox": [ + 46, + 110, + 289, + 434 + ], + "type": "text", + "content": "Causal Inference is proposed to eliminate the harmful bias of confounders and discover the causal relationship between multiple variables [17]. A do operation is implemented with adjustment criteria, e.g., front-door or back-door, to estimate the causal effects [44]. In recent years, deep learning has boosted the vast development of a series of intelligent tasks, e.g., image classification [10, 12, 34], segmentation [19, 47], detection [6, 30], low-level processing [7, 51]. However, prominent works focus on fitting the correlation between inputs and their outputs while ignoring the causation. Due to the existence of confounders, the networks are easy to capture the spurious correlation between inputs and their outputs. For instance, if most lions lie in the grass in the training data, the model inevitably mistakes the grass for a lion. To get rid of the harmful bias of confounders, some studies seek to incorporate causal inference into deep learning. [54, 66] model the interventions of confounders from the feature perspective [64] integrate the front-door criterion to vision-language task from the attention perspective. To improve the generalization capability, [29, 36, 37, 65] introduce the causal learning to domain adaptation/generalization. However, the above causality-inspired methods merely focus on the high-level tasks. In this paper, for the first time, we investigate the causality-based image restoration, which aims to improve the generalization capability of restoration networks on different distortion types and degrees." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 445, + 107, + 457 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 445, + 107, + 457 + ], + "spans": [ + { + "bbox": [ + 47, + 445, + 107, + 457 + ], + "type": "text", + "content": "3. Methods" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 460, + 245, + 472 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 460, + 245, + 472 + ], + "spans": [ + { + "bbox": [ + 47, + 460, + 245, + 472 + ], + "type": "text", + "content": "3.1. A Causal View for Image Restoration" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 474, + 287, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 474, + 287, + 641 + ], + "spans": [ + { + "bbox": [ + 46, + 474, + 287, + 641 + ], + "type": "text", + "content": "Image restoration aims to restore the distorted images, of which the degradation process can be represented as a function " + }, + { + "bbox": [ + 46, + 474, + 287, + 641 + ], + "type": "inline_equation", + "content": "I_{d} = g(I_{c},D)" + }, + { + "bbox": [ + 46, + 474, + 287, + 641 + ], + "type": "text", + "content": ". Here, " + }, + { + "bbox": [ + 46, + 474, + 287, + 641 + ], + "type": "inline_equation", + "content": "I_{c},I_{d},D" + }, + { + "bbox": [ + 46, + 474, + 287, + 641 + ], + "type": "text", + "content": " denote the clean, distorted images, and distortions, respectively. " + }, + { + "bbox": [ + 46, + 474, + 287, + 641 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 46, + 474, + 287, + 641 + ], + "type": "text", + "content": " contains distortion types " + }, + { + "bbox": [ + 46, + 474, + 287, + 641 + ], + "type": "inline_equation", + "content": "D_{t}" + }, + { + "bbox": [ + 46, + 474, + 287, + 641 + ], + "type": "text", + "content": " and degrees " + }, + { + "bbox": [ + 46, + 474, + 287, + 641 + ], + "type": "inline_equation", + "content": "D_{l}" + }, + { + "bbox": [ + 46, + 474, + 287, + 641 + ], + "type": "text", + "content": ". A restoration network " + }, + { + "bbox": [ + 46, + 474, + 287, + 641 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 474, + 287, + 641 + ], + "type": "text", + "content": " is trained with the loss function to minimize the difference between its ideal reconstructed images " + }, + { + "bbox": [ + 46, + 474, + 287, + 641 + ], + "type": "inline_equation", + "content": "I_{o}" + }, + { + "bbox": [ + 46, + 474, + 287, + 641 + ], + "type": "text", + "content": " and the original clean image " + }, + { + "bbox": [ + 46, + 474, + 287, + 641 + ], + "type": "inline_equation", + "content": "I_{c}" + }, + { + "bbox": [ + 46, + 474, + 287, + 641 + ], + "type": "text", + "content": ". We model this whole process with a structure causal graph as shown in Fig. 2. Here, " + }, + { + "bbox": [ + 46, + 474, + 287, + 641 + ], + "type": "inline_equation", + "content": "D\\rightarrow I_d\\leftarrow I_c" + }, + { + "bbox": [ + 46, + 474, + 287, + 641 + ], + "type": "text", + "content": " denotes the degradation process of " + }, + { + "bbox": [ + 46, + 474, + 287, + 641 + ], + "type": "inline_equation", + "content": "I_{d} = g(I_{c},D)" + }, + { + "bbox": [ + 46, + 474, + 287, + 641 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 46, + 474, + 287, + 641 + ], + "type": "inline_equation", + "content": "I_{c}\\rightarrow I_{o}" + }, + { + "bbox": [ + 46, + 474, + 287, + 641 + ], + "type": "text", + "content": " denotes " + }, + { + "bbox": [ + 46, + 474, + 287, + 641 + ], + "type": "inline_equation", + "content": "I_{o}" + }, + { + "bbox": [ + 46, + 474, + 287, + 641 + ], + "type": "text", + "content": " is learned with the supervision of " + }, + { + "bbox": [ + 46, + 474, + 287, + 641 + ], + "type": "inline_equation", + "content": "I_{c}" + }, + { + "bbox": [ + 46, + 474, + 287, + 641 + ], + "type": "text", + "content": " by maximizing the probability of " + }, + { + "bbox": [ + 46, + 474, + 287, + 641 + ], + "type": "inline_equation", + "content": "P(I_c|I_o)" + }, + { + "bbox": [ + 46, + 474, + 287, + 641 + ], + "type": "text", + "content": ". In addition, " + }, + { + "bbox": [ + 46, + 474, + 287, + 641 + ], + "type": "inline_equation", + "content": "D\\to I_o" + }, + { + "bbox": [ + 46, + 474, + 287, + 641 + ], + "type": "text", + "content": " refers to the knowledge learned from " + }, + { + "bbox": [ + 46, + 474, + 287, + 641 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 46, + 474, + 287, + 641 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 474, + 287, + 641 + ], + "type": "inline_equation", + "content": "I_{o}" + }, + { + "bbox": [ + 46, + 474, + 287, + 641 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 46, + 474, + 287, + 641 + ], + "type": "inline_equation", + "content": "I_{d}\\rightarrow I_{o}" + }, + { + "bbox": [ + 46, + 474, + 287, + 641 + ], + "type": "text", + "content": " means the restoration process with restoration network " + }, + { + "bbox": [ + 46, + 474, + 287, + 641 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 474, + 287, + 641 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "content": "From the causality perspective, the causal representation of image restoration requires that the restoration network " + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "content": " obtains the causal relationship between " + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "inline_equation", + "content": "I_{d} \\rightarrow I_{o}" + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "content": ". However, there are two extra paths " + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "inline_equation", + "content": "I_{d} \\leftarrow D \\rightarrow I_{o}" + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "inline_equation", + "content": "I_{d} \\leftarrow I_{c} \\rightarrow I_{o}" + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "content": " introducing the spurious correlation to " + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "inline_equation", + "content": "I_{d}" + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "inline_equation", + "content": "I_{o}" + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "inline_equation", + "content": "I_{c}" + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "content": " are confounders in causality. Importantly, the " + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "inline_equation", + "content": "I_{c}" + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "content": " are" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 331, + 70, + 416, + 175 + ], + "blocks": [ + { + "bbox": [ + 331, + 70, + 416, + 175 + ], + "lines": [ + { + "bbox": [ + 331, + 70, + 416, + 175 + ], + "spans": [ + { + "bbox": [ + 331, + 70, + 416, + 175 + ], + "type": "image", + "image_path": "fa13543cf2c61f5a168cea4d798641af881d33d9b2ac0941a30535d521fc6cad.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 326, + 185, + 525, + 196 + ], + "lines": [ + { + "bbox": [ + 326, + 185, + 525, + 196 + ], + "spans": [ + { + "bbox": [ + 326, + 185, + 525, + 196 + ], + "type": "text", + "content": "Figure 2. Structure causal graph for image restoration." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 420, + 73, + 521, + 175 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 420, + 73, + 479, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 420, + 73, + 479, + 83 + ], + "spans": [ + { + "bbox": [ + 420, + 73, + 479, + 83 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 420, + 73, + 479, + 83 + ], + "type": "text", + "content": " Distortion Set" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 421, + 87, + 487, + 97 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 421, + 87, + 487, + 97 + ], + "spans": [ + { + "bbox": [ + 421, + 87, + 487, + 97 + ], + "type": "inline_equation", + "content": "D_{t}" + }, + { + "bbox": [ + 421, + 87, + 487, + 97 + ], + "type": "text", + "content": " Distortion Types" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 421, + 99, + 493, + 110 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 421, + 99, + 493, + 110 + ], + "spans": [ + { + "bbox": [ + 421, + 99, + 493, + 110 + ], + "type": "inline_equation", + "content": "D_{l}" + }, + { + "bbox": [ + 421, + 99, + 493, + 110 + ], + "type": "text", + "content": " Distortion Degrees" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 421, + 114, + 488, + 124 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 421, + 114, + 488, + 124 + ], + "spans": [ + { + "bbox": [ + 421, + 114, + 488, + 124 + ], + "type": "inline_equation", + "content": "I_{d}" + }, + { + "bbox": [ + 421, + 114, + 488, + 124 + ], + "type": "text", + "content": " Distorted Images" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 421, + 127, + 521, + 137 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 421, + 127, + 521, + 137 + ], + "spans": [ + { + "bbox": [ + 421, + 127, + 521, + 137 + ], + "type": "inline_equation", + "content": "I_{o}" + }, + { + "bbox": [ + 421, + 127, + 521, + 137 + ], + "type": "text", + "content": " Ideal Reconstructed Images" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 421, + 140, + 478, + 151 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 421, + 140, + 478, + 151 + ], + "spans": [ + { + "bbox": [ + 421, + 140, + 478, + 151 + ], + "type": "inline_equation", + "content": "I_{c}" + }, + { + "bbox": [ + 421, + 140, + 478, + 151 + ], + "type": "text", + "content": " Clean Images" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 421, + 152, + 501, + 163 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 421, + 152, + 501, + 163 + ], + "spans": [ + { + "bbox": [ + 421, + 152, + 501, + 163 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 421, + 152, + 501, + 163 + ], + "type": "text", + "content": " Restoration Network" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 421, + 164, + 520, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 421, + 164, + 520, + 175 + ], + "spans": [ + { + "bbox": [ + 421, + 164, + 520, + 175 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 421, + 164, + 520, + 175 + ], + "type": "text", + "content": " Distortion sampled from " + }, + { + "bbox": [ + 421, + 164, + 520, + 175 + ], + "type": "inline_equation", + "content": "D" + } + ] + } + ], + "index": 15 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 304, + 202, + 545, + 250 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 202, + 545, + 250 + ], + "spans": [ + { + "bbox": [ + 304, + 202, + 545, + 250 + ], + "type": "text", + "content": "commonly diverse in the datasets and bring more vivid textures to reconstructed image " + }, + { + "bbox": [ + 304, + 202, + 545, + 250 + ], + "type": "inline_equation", + "content": "I_{o}" + }, + { + "bbox": [ + 304, + 202, + 545, + 250 + ], + "type": "text", + "content": ", which is a favorable confounder. We do not take into account the confounder " + }, + { + "bbox": [ + 304, + 202, + 545, + 250 + ], + "type": "inline_equation", + "content": "I_{c}" + }, + { + "bbox": [ + 304, + 202, + 545, + 250 + ], + "type": "text", + "content": " in our paper." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 251, + 546, + 381 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 251, + 546, + 381 + ], + "spans": [ + { + "bbox": [ + 304, + 251, + 546, + 381 + ], + "type": "text", + "content": "We aim to improve the robustness of the restoration network to unseen or unknown distortions, which are inhibited by the bad confounding effects from confounders " + }, + { + "bbox": [ + 304, + 251, + 546, + 381 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 251, + 546, + 381 + ], + "type": "text", + "content": ". But, how do the confounders " + }, + { + "bbox": [ + 304, + 251, + 546, + 381 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 251, + 546, + 381 + ], + "type": "text", + "content": " limit the generalization capability of the restoration network? As shown in Fig. 2, the existing of " + }, + { + "bbox": [ + 304, + 251, + 546, + 381 + ], + "type": "inline_equation", + "content": "I_{d} \\gets D \\to I_{o}" + }, + { + "bbox": [ + 304, + 251, + 546, + 381 + ], + "type": "text", + "content": " causes the conditional probability " + }, + { + "bbox": [ + 304, + 251, + 546, + 381 + ], + "type": "inline_equation", + "content": "P(I_{o}|I_{d})" + }, + { + "bbox": [ + 304, + 251, + 546, + 381 + ], + "type": "text", + "content": " learned by restoration network " + }, + { + "bbox": [ + 304, + 251, + 546, + 381 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 251, + 546, + 381 + ], + "type": "text", + "content": " is also condition on distortions " + }, + { + "bbox": [ + 304, + 251, + 546, + 381 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 251, + 546, + 381 + ], + "type": "text", + "content": ", i.e., the fitting conditional probability of " + }, + { + "bbox": [ + 304, + 251, + 546, + 381 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 251, + 546, + 381 + ], + "type": "text", + "content": " is in fact as " + }, + { + "bbox": [ + 304, + 251, + 546, + 381 + ], + "type": "inline_equation", + "content": "P(I_{o}|I_{d},D)" + }, + { + "bbox": [ + 304, + 251, + 546, + 381 + ], + "type": "text", + "content": ". Consequently, the restoration network " + }, + { + "bbox": [ + 304, + 251, + 546, + 381 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 251, + 546, + 381 + ], + "type": "text", + "content": " is not robust to different distortions due to that it is not independent of different distortions " + }, + { + "bbox": [ + 304, + 251, + 546, + 381 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 251, + 546, + 381 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 382, + 546, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 382, + 546, + 502 + ], + "spans": [ + { + "bbox": [ + 304, + 382, + 546, + 502 + ], + "type": "text", + "content": "A robust restoration network " + }, + { + "bbox": [ + 304, + 382, + 546, + 502 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 382, + 546, + 502 + ], + "type": "text", + "content": " should be independent of different distortions (i.e., " + }, + { + "bbox": [ + 304, + 382, + 546, + 502 + ], + "type": "inline_equation", + "content": "D \\perp I_o|I_d" + }, + { + "bbox": [ + 304, + 382, + 546, + 502 + ], + "type": "text", + "content": "). To achieve this, we adopt the back-door criterion in causal inference to realize distortion-invariant learning (DIL) through a \"do\" operation. Here, a \"do\" operation [17, 44] is exploited to cut off the connection from the distortion " + }, + { + "bbox": [ + 304, + 382, + 546, + 502 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 382, + 546, + 502 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 382, + 546, + 502 + ], + "type": "inline_equation", + "content": "I_d" + }, + { + "bbox": [ + 304, + 382, + 546, + 502 + ], + "type": "text", + "content": ", thereby removing the bad confounding effects of " + }, + { + "bbox": [ + 304, + 382, + 546, + 502 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 382, + 546, + 502 + ], + "type": "text", + "content": " to the path " + }, + { + "bbox": [ + 304, + 382, + 546, + 502 + ], + "type": "inline_equation", + "content": "I_d \\to I_o" + }, + { + "bbox": [ + 304, + 382, + 546, + 502 + ], + "type": "text", + "content": ", and learning the distortion-invariant feature representation (i.e., " + }, + { + "bbox": [ + 304, + 382, + 546, + 502 + ], + "type": "inline_equation", + "content": "D \\perp I_o|I_d" + }, + { + "bbox": [ + 304, + 382, + 546, + 502 + ], + "type": "text", + "content": "). We formulate the back-door criterion in image restoration as Equ. 1." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 311, + 508, + 545, + 538 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 311, + 508, + 545, + 538 + ], + "spans": [ + { + "bbox": [ + 311, + 508, + 545, + 538 + ], + "type": "interline_equation", + "content": "P \\left(I _ {o} | d o \\left(I _ {d}\\right)\\right) = \\sum_ {d _ {i} \\in D} P \\left(I _ {o} \\mid I _ {d}, d _ {i}\\right) P \\left(d _ {i}\\right), P \\left(d _ {i}\\right) = \\frac {1}{n}, \\tag {1}", + "image_path": "df31b160d62c42eaf2d0e3a52b8fc4e7f9d9883f0a8d00810629df63a8019bbd.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 545, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 547, + 713 + ], + "type": "text", + "content": "where the causal conditional probability " + }, + { + "bbox": [ + 304, + 545, + 547, + 713 + ], + "type": "inline_equation", + "content": "P(I_{o}|do(I_{d}))" + }, + { + "bbox": [ + 304, + 545, + 547, + 713 + ], + "type": "text", + "content": " is the optimization direction for restoration network " + }, + { + "bbox": [ + 304, + 545, + 547, + 713 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 545, + 547, + 713 + ], + "type": "text", + "content": " towards distortion invariant learning. To simplify the optimization, we set the probability of each distortion " + }, + { + "bbox": [ + 304, + 545, + 547, + 713 + ], + "type": "inline_equation", + "content": "d_{i}" + }, + { + "bbox": [ + 304, + 545, + 547, + 713 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 304, + 545, + 547, + 713 + ], + "type": "inline_equation", + "content": "1 / n" + }, + { + "bbox": [ + 304, + 545, + 547, + 713 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 545, + 547, + 713 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 545, + 547, + 713 + ], + "type": "text", + "content": " is the number of distortion types and degrees that existed in confounders. From Equ. 1, two crucial challenges for achieving it arise. 1) How to construct the virtual confounders (i.e., different distortion types or degrees)? since collecting different real distorted images with the same contents are nontrivial in the real world. 2) How to instantiate the intervention of different distortions to the reconstruction process (i.e., the " + }, + { + "bbox": [ + 304, + 545, + 547, + 713 + ], + "type": "inline_equation", + "content": "P(I_{o}|I_{d},d_{i})" + }, + { + "bbox": [ + 304, + 545, + 547, + 713 + ], + "type": "text", + "content": ") in image restoration. We achieve this through counterfactual distortion augmentation and distortion-invariant representation learning as described" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1716" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 151, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 151, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 151, + 83 + ], + "type": "text", + "content": "in the following sections." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 91, + 261, + 103 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 91, + 261, + 103 + ], + "spans": [ + { + "bbox": [ + 47, + 91, + 261, + 103 + ], + "type": "text", + "content": "3.2. Counterfactual Distortion Augmentation" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 109, + 287, + 276 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 109, + 287, + 276 + ], + "spans": [ + { + "bbox": [ + 46, + 109, + 287, + 276 + ], + "type": "text", + "content": "To learn the distortion-invariant representation for the restoration network, it is vital to construct the distortion set " + }, + { + "bbox": [ + 46, + 109, + 287, + 276 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 46, + 109, + 287, + 276 + ], + "type": "text", + "content": " (i.e., confounders). For instance, if we expect the restoration network to have the generalization capability for different distortion degrees, we require to construct the distortion set " + }, + { + "bbox": [ + 46, + 109, + 287, + 276 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 46, + 109, + 287, + 276 + ], + "type": "text", + "content": " with the distortions at different levels. Similarly, we can increase the generalization capability of the restoration network for unknown distortion types by constructing the " + }, + { + "bbox": [ + 46, + 109, + 287, + 276 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 46, + 109, + 287, + 276 + ], + "type": "text", + "content": " with different but related distortion types. Furthermore, to avoid the effects of different image contents, it is better for each clean image to have corresponding distorted images with various distortion types or degrees in " + }, + { + "bbox": [ + 46, + 109, + 287, + 276 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 46, + 109, + 287, + 276 + ], + "type": "text", + "content": ". However, it is non-trivial to collect datasets that satisfy the above principles in the real world, which is labor-intensive and arduous." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 277, + 288, + 397 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 277, + 288, + 397 + ], + "spans": [ + { + "bbox": [ + 46, + 277, + 288, + 397 + ], + "type": "text", + "content": "In this paper, we construct the distortion set " + }, + { + "bbox": [ + 46, + 277, + 288, + 397 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 46, + 277, + 288, + 397 + ], + "type": "text", + "content": " with synthesized distortions, which we can call virtual confounders in causality. Concretely, we collected a series of high-quality images " + }, + { + "bbox": [ + 46, + 277, + 288, + 397 + ], + "type": "inline_equation", + "content": "I_{c}" + }, + { + "bbox": [ + 46, + 277, + 288, + 397 + ], + "type": "text", + "content": ", and generated the distorted images by modifying the degradation process as " + }, + { + "bbox": [ + 46, + 277, + 288, + 397 + ], + "type": "inline_equation", + "content": "I_{d} = g(I_{c}, d_{i}), d_{i} \\in D" + }, + { + "bbox": [ + 46, + 277, + 288, + 397 + ], + "type": "text", + "content": ". We can also prove the rightness of the above distortion augmentation from the counterfactuals in causality [17], where we answer the counterfactual question that \"if " + }, + { + "bbox": [ + 46, + 277, + 288, + 397 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 46, + 277, + 288, + 397 + ], + "type": "text", + "content": " is " + }, + { + "bbox": [ + 46, + 277, + 288, + 397 + ], + "type": "inline_equation", + "content": "d_{i}" + }, + { + "bbox": [ + 46, + 277, + 288, + 397 + ], + "type": "text", + "content": ", what the " + }, + { + "bbox": [ + 46, + 277, + 288, + 397 + ], + "type": "inline_equation", + "content": "I_{d}" + }, + { + "bbox": [ + 46, + 277, + 288, + 397 + ], + "type": "text", + "content": " would be with " + }, + { + "bbox": [ + 46, + 277, + 288, + 397 + ], + "type": "inline_equation", + "content": "I_{c}" + }, + { + "bbox": [ + 46, + 277, + 288, + 397 + ], + "type": "text", + "content": " invariant?\". The proof can be found in the Supplementary." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 403, + 285, + 415 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 403, + 285, + 415 + ], + "spans": [ + { + "bbox": [ + 47, + 403, + 285, + 415 + ], + "type": "text", + "content": "3.3. Distortion-invariant Representation Learning" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 421, + 287, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 421, + 287, + 601 + ], + "spans": [ + { + "bbox": [ + 46, + 421, + 287, + 601 + ], + "type": "text", + "content": "After constructing the virtual confounders/distortions set " + }, + { + "bbox": [ + 46, + 421, + 287, + 601 + ], + "type": "inline_equation", + "content": "D = \\{d_i | 1 \\leq i \\leq n\\}" + }, + { + "bbox": [ + 46, + 421, + 287, + 601 + ], + "type": "text", + "content": ". We are able to achieve the distortion-invariant representation learning by implementing the back-door criterion as Eq. 1 for image restoration. Let us first introduce the relationship between the probability " + }, + { + "bbox": [ + 46, + 421, + 287, + 601 + ], + "type": "inline_equation", + "content": "P(I_o|I_d)" + }, + { + "bbox": [ + 46, + 421, + 287, + 601 + ], + "type": "text", + "content": " and the commonly-used training paradigm ERM (empirical risk minimization). In image restoration, an ideal reconstruction " + }, + { + "bbox": [ + 46, + 421, + 287, + 601 + ], + "type": "inline_equation", + "content": "I_o" + }, + { + "bbox": [ + 46, + 421, + 287, + 601 + ], + "type": "text", + "content": " is expected to learn by maximizing the condition probability " + }, + { + "bbox": [ + 46, + 421, + 287, + 601 + ], + "type": "inline_equation", + "content": "P(I_o|I_d)" + }, + { + "bbox": [ + 46, + 421, + 287, + 601 + ], + "type": "text", + "content": " with loss function as " + }, + { + "bbox": [ + 46, + 421, + 287, + 601 + ], + "type": "inline_equation", + "content": "\\mathcal{L}(f_{\\theta}(I_d), I_c)" + }, + { + "bbox": [ + 46, + 421, + 287, + 601 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 421, + 287, + 601 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 46, + 421, + 287, + 601 + ], + "type": "text", + "content": " is the restoration network with the parameters " + }, + { + "bbox": [ + 46, + 421, + 287, + 601 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 421, + 287, + 601 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 421, + 287, + 601 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 421, + 287, + 601 + ], + "type": "text", + "content": " denotes the loss function, such as the commonly-used " + }, + { + "bbox": [ + 46, + 421, + 287, + 601 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_1" + }, + { + "bbox": [ + 46, + 421, + 287, + 601 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 46, + 421, + 287, + 601 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_2" + }, + { + "bbox": [ + 46, + 421, + 287, + 601 + ], + "type": "text", + "content": " loss. The ERM is used to optimize the network " + }, + { + "bbox": [ + 46, + 421, + 287, + 601 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 46, + 421, + 287, + 601 + ], + "type": "text", + "content": " (with parameters denoted by " + }, + { + "bbox": [ + 46, + 421, + 287, + 601 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 421, + 287, + 601 + ], + "type": "text", + "content": ") by minimizing the loss function overall training dataset " + }, + { + "bbox": [ + 46, + 421, + 287, + 601 + ], + "type": "inline_equation", + "content": "\\mathcal{D} = \\{I_d, I_c | d \\in D\\}" + }, + { + "bbox": [ + 46, + 421, + 287, + 601 + ], + "type": "text", + "content": " as:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 83, + 606, + 287, + 624 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 606, + 287, + 624 + ], + "spans": [ + { + "bbox": [ + 83, + 606, + 287, + 624 + ], + "type": "interline_equation", + "content": "\\theta^ {*} = \\arg \\min _ {\\theta} \\mathbb {E} _ {(I _ {d}, I _ {c}) \\sim \\mathcal {D}} [ \\mathcal {L} (f _ {\\theta} (I _ {d}), I _ {c}) ], \\tag {2}", + "image_path": "6b976cec54d02c203f30ecdc97c835c12fd11ec0ce27b9d039ba87c4d5201bcc.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\theta^{*}" + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "content": " enables the restoration network " + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "content": " to maximize the " + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "inline_equation", + "content": "P(I_{o}|I_{d})\\approx P(I_{c}|I_{d})" + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "content": ". However, the above training process also leads the " + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "inline_equation", + "content": "P(I_{o}|I_{d})" + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "content": " to be not independent to the distortions " + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "inline_equation", + "content": "d\\in D" + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "content": " in the training dataset " + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "content": ", which eliminate the generalization ability of " + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "content": " on the out-of-distribution distortions (i.e., when " + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "inline_equation", + "content": "d\\notin D" + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "content": "). To achieve the distortion-invariant representation learning, we aim to maximize the" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": "causal conditional probability " + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "inline_equation", + "content": "P(I_{o}|do(I_{d}))" + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": " as instead of " + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "inline_equation", + "content": "P(I_{o}|I_{d})" + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": ". The key challenge stems from how to model the conditional probability " + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "inline_equation", + "content": "P(I_{o}|I_{d},d_{i})" + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": " in Eq. 1 (i.e., how to model the intervention from the distortion " + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "inline_equation", + "content": "d_{i}\\in D" + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": " for the restoration process " + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "inline_equation", + "content": "P(I_o|I_d)" + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 133, + 545, + 252 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 133, + 545, + 252 + ], + "spans": [ + { + "bbox": [ + 304, + 133, + 545, + 252 + ], + "type": "text", + "content": "In this paper, we propose to model the intervention from " + }, + { + "bbox": [ + 304, + 133, + 545, + 252 + ], + "type": "inline_equation", + "content": "d_{i} \\in D" + }, + { + "bbox": [ + 304, + 133, + 545, + 252 + ], + "type": "text", + "content": " to the restoration process (i.e., " + }, + { + "bbox": [ + 304, + 133, + 545, + 252 + ], + "type": "inline_equation", + "content": "P(I_{o}|I_{d},d_{i})" + }, + { + "bbox": [ + 304, + 133, + 545, + 252 + ], + "type": "text", + "content": ") through the optimization of the network parameters " + }, + { + "bbox": [ + 304, + 133, + 545, + 252 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 133, + 545, + 252 + ], + "type": "text", + "content": ". From the above analysis, we know that the restoration network " + }, + { + "bbox": [ + 304, + 133, + 545, + 252 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 304, + 133, + 545, + 252 + ], + "type": "text", + "content": " trained with ERM on the paired training data " + }, + { + "bbox": [ + 304, + 133, + 545, + 252 + ], + "type": "inline_equation", + "content": "(I_{d_i},I_c)" + }, + { + "bbox": [ + 304, + 133, + 545, + 252 + ], + "type": "text", + "content": " is condition on the distortion " + }, + { + "bbox": [ + 304, + 133, + 545, + 252 + ], + "type": "inline_equation", + "content": "d_{i}" + }, + { + "bbox": [ + 304, + 133, + 545, + 252 + ], + "type": "text", + "content": ". This inspires us to instantiate the intervention of different distortion types or degrees " + }, + { + "bbox": [ + 304, + 133, + 545, + 252 + ], + "type": "inline_equation", + "content": "d_{i} \\in D" + }, + { + "bbox": [ + 304, + 133, + 545, + 252 + ], + "type": "text", + "content": " through updating the model parameter " + }, + { + "bbox": [ + 304, + 133, + 545, + 252 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 133, + 545, + 252 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 133, + 545, + 252 + ], + "type": "inline_equation", + "content": "\\phi_{d_i}" + }, + { + "bbox": [ + 304, + 133, + 545, + 252 + ], + "type": "text", + "content": " based on ERM with the training distorted-and-clean image pairs " + }, + { + "bbox": [ + 304, + 133, + 545, + 252 + ], + "type": "inline_equation", + "content": "(I_{d_i},I_c)" + }, + { + "bbox": [ + 304, + 133, + 545, + 252 + ], + "type": "text", + "content": " as:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 362, + 258, + 545, + 271 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 362, + 258, + 545, + 271 + ], + "spans": [ + { + "bbox": [ + 362, + 258, + 545, + 271 + ], + "type": "interline_equation", + "content": "\\phi_ {d _ {i}} = \\theta - \\alpha \\nabla_ {\\theta} \\mathcal {L} \\left(f _ {\\theta} \\left(I _ {d _ {i}}\\right), I _ {c}\\right), \\tag {3}", + "image_path": "0b45c442237894a4b41f93e44496dfc48dfcea23c216061bfc66187765c6fb00.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 277, + 545, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 277, + 545, + 361 + ], + "spans": [ + { + "bbox": [ + 304, + 277, + 545, + 361 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 277, + 545, + 361 + ], + "type": "inline_equation", + "content": "\\phi_{d_i}" + }, + { + "bbox": [ + 304, + 277, + 545, + 361 + ], + "type": "text", + "content": " denotes the parameters of the restoration network after one-step update, which is conditioned on the confounder " + }, + { + "bbox": [ + 304, + 277, + 545, + 361 + ], + "type": "inline_equation", + "content": "d_i" + }, + { + "bbox": [ + 304, + 277, + 545, + 361 + ], + "type": "text", + "content": ". Consequently, the maximum of the conditional probability " + }, + { + "bbox": [ + 304, + 277, + 545, + 361 + ], + "type": "inline_equation", + "content": "P(I_o|I_d,d_i)" + }, + { + "bbox": [ + 304, + 277, + 545, + 361 + ], + "type": "text", + "content": " can be obtained by minimizing the loss " + }, + { + "bbox": [ + 304, + 277, + 545, + 361 + ], + "type": "inline_equation", + "content": "\\mathcal{L}(f_{\\phi_{d_i}}(I_d),I_c)" + }, + { + "bbox": [ + 304, + 277, + 545, + 361 + ], + "type": "text", + "content": ". The optimization direction toward maximizing the causal condition probability " + }, + { + "bbox": [ + 304, + 277, + 545, + 361 + ], + "type": "inline_equation", + "content": "P(I_o|do(I_d))" + }, + { + "bbox": [ + 304, + 277, + 545, + 361 + ], + "type": "text", + "content": " in Eq. 1 can be derived as:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 322, + 367, + 545, + 392 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 322, + 367, + 545, + 392 + ], + "spans": [ + { + "bbox": [ + 322, + 367, + 545, + 392 + ], + "type": "interline_equation", + "content": "\\theta^ {*} = \\arg \\min _ {\\theta} \\mathbb {E} _ {(I _ {d}, I _ {c}) \\sim \\mathcal {D}} [ \\sum_ {d _ {i} \\in D} \\mathcal {L} \\left(f _ {\\phi_ {d _ {i}}} (I _ {d}), I _ {c}\\right) ], \\tag {4}", + "image_path": "95bc36f29c4294697596464ac0d6a20aafcb538f53acd39fff8eee1d8857310e.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 397, + 545, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 397, + 545, + 445 + ], + "spans": [ + { + "bbox": [ + 304, + 397, + 545, + 445 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 397, + 545, + 445 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 397, + 545, + 445 + ], + "type": "text", + "content": " denotes the confounder set which contains " + }, + { + "bbox": [ + 304, + 397, + 545, + 445 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 397, + 545, + 445 + ], + "type": "text", + "content": " distortion degrees or types. Based on the above optimization objective, we learn distortion-invariant representation learning from a causality perspective." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 452, + 541, + 464 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 452, + 541, + 464 + ], + "spans": [ + { + "bbox": [ + 306, + 452, + 541, + 464 + ], + "type": "text", + "content": "3.4. Implementations of DIL from Meta-Learning" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 470, + 545, + 577 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 470, + 545, + 577 + ], + "spans": [ + { + "bbox": [ + 304, + 470, + 545, + 577 + ], + "type": "text", + "content": "An interesting finding is that the derived optimization direction of DIL from causality perspective in Eq. 4 is consistent with one typical meta-learning strategy termed as MAML [14], even they have different purposes. MAML aims to enable the fast adaptation capability of a network for few-shot tasks, while ours aims to improve the generalization capability of the restoration network. We facilitate our DIL in image restoration based on this meta-learning strategy." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 578, + 545, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 578, + 545, + 662 + ], + "spans": [ + { + "bbox": [ + 304, + 578, + 545, + 662 + ], + "type": "text", + "content": "However, it is arduous to directly incorporate the optimization direction of Eq. 4 into the practical training process, which is computationally prohibitive. The reason is that it requires multiple gradient computing and updating, which is expensive, especially for the pixel-wise image restoration. To simplify this process, we utilize the Talyor expansion and inverse expansion to derive Eq. 4 as:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 332, + 667, + 504, + 685 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 332, + 667, + 504, + 685 + ], + "spans": [ + { + "bbox": [ + 332, + 667, + 504, + 685 + ], + "type": "interline_equation", + "content": "\\theta^ {*} = \\arg \\min _ {\\theta} \\mathbb {E} _ {(I _ {d}, I _ {c}) \\sim \\mathcal {D}} [ \\mathcal {L} (f _ {\\phi_ {\\bar {d}}} (I _ {d}), I _ {c}) ],", + "image_path": "15e0f37c2086bd552ccf0a3c081ff0690244224f9d424268ab33717b8e441c31.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 334, + 685, + 545, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 334, + 685, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 334, + 685, + 545, + 715 + ], + "type": "interline_equation", + "content": "w h e r e \\phi_ {\\tilde {d}} = \\theta - \\alpha \\nabla_ {\\theta} \\sum_ {d _ {i} \\in D} \\frac {1}{n} \\mathcal {L} \\left(f _ {\\theta} \\left(I _ {d _ {i}}\\right), I _ {c}\\right), \\tag {5}", + "image_path": "d11f7a536ccfbcd4496ceb4ecca9bf7cc56788baf88c9459e598af71a5c604a8.jpg" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "1717" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 58, + 101, + 533, + 286 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 547, + 94 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 547, + 94 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 547, + 94 + ], + "type": "text", + "content": "Table 1. Quantitative comparison for image denoising on several benchmark datasets. Results are tested on three different unseen distortion degrees in terms of PSNR/SSIM on RGB channel. Best performances are bolded." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 58, + 101, + 533, + 286 + ], + "lines": [ + { + "bbox": [ + 58, + 101, + 533, + 286 + ], + "spans": [ + { + "bbox": [ + 58, + 101, + 533, + 286 + ], + "type": "table", + "html": "
DatasetsLevelsMethods
ERMDILsfDILpfDILssDILps
CBSD68 [38]30 (unseen)24.90/0.58130.29(5.39↑)/0.86629.92(5.02↑)/0.85827.48(2.58↑)/0.80929.14(4.24↑)/0.802
40 (unseen)21.12/0.40028.35(7.23↑)/0.82528.10(6.98↑)/0.81225.90(4.78↑)/0.74625.74(4.62↑)/0.629
50 (unseen)18.96/0.30726.64(7.68↑)/0.77926.61(7.65↑)/0.76624.63(5.67↑)/0.68623.34(4.38↑)/0.501
Kodak24 [15]30 (unseen)25.12/0.53331.39(6.27↑)/0.86730.87(5.75↑)/0.85827.92(2.80↑)/0.80129.86(4.74↑)/0.782
40 (unseen)21.22/0.35229.49(8.27↑)/0.83129.15(7.93↑)/0.81726.46(5.24↑)/0.73826.13(4.91↑)/0.588
50 (unseen)19.02/0.26327.76(8.74↑)/0.78827.67(8.65↑)/0.77525.24(6.22↑)/0.67723.60(4.58↑)/0.457
McMaster [72]30 (unseen)25.65/0.56931.70(6.05↑)/0.87331.04(5.39↑)/0.85328.15(2.50↑)/0.79430.09(4.44↑)/0.800
40 (unseen)21.73/0.37329.81(8.08↑)/0.83129.07(7.34↑)/0.80226.59(4.86↑)/0.72826.24(4.51↑)/0.605
50 (unseen)19.47/0.27828.02(8.55↑)/0.78327.31(7.84↑)/0.74925.20(5.73↑)/0.66423.60(4.13↑)/0.466
Urban100 [21]30 (unseen)25.46/0.64830.93(5.47↑)/0.89830.26(4.80↑)/0.88426.95(1.49↑)/0.82529.73(4.27↑)/0.841
40 (unseen)21.53/0.47928.82(7.29↑)/0.86628.32(6.79↑)/0.84825.26(3.73↑)/0.76726.25(4.72↑)/0.691
50 (unseen)19.28/0.38926.88(7.60↑)/0.82926.63(7.35↑)/0.81123.85(4.57↑)/0.71023.71(4.43↑)/0.575
Manga109 [39]30 (unseen)26.62/0.65331.97(5.35↑)/0.91031.14(4.52↑)/0.90126.02(-0.6↑)/0.83331.05(4.43↑)/0.858
40 (unseen)22.34/0.44229.02(6.68↑)/0.88828.53(6.19↑)/0.87524.31(1.97↑)/0.78427.29(4.95↑)/0.704
50 (unseen)19.95/0.34226.52(6.57↑)/0.86026.34(6.39↑)/0.84622.82(2.87↑)/0.73424.47(4.52↑)/0.564
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The comparison of serial sampling and parallel sampling." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 399, + 287, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 399, + 287, + 506 + ], + "spans": [ + { + "bbox": [ + 46, + 399, + 287, + 506 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 399, + 287, + 506 + ], + "type": "inline_equation", + "content": "\\phi_{\\bar{d}}" + }, + { + "bbox": [ + 46, + 399, + 287, + 506 + ], + "type": "text", + "content": " denotes the parameters of restoration network " + }, + { + "bbox": [ + 46, + 399, + 287, + 506 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 399, + 287, + 506 + ], + "type": "text", + "content": " that is virtually updated with loss function with samples overall all distortions " + }, + { + "bbox": [ + 46, + 399, + 287, + 506 + ], + "type": "inline_equation", + "content": "D = \\{d_i\\}, 1 \\leq i \\leq n" + }, + { + "bbox": [ + 46, + 399, + 287, + 506 + ], + "type": "text", + "content": ". We define it as parallel sampling for DIL, which reduces the complex training process of DIL to two steps. In this paper, we call the original sampling strategy as serial sampling. The comparison between serial sampling and parallel sampling are shown in Fig. 3. The detailed derivation for Eq. 5 are described in the Supplementary." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 510, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 288, + 714 + ], + "type": "text", + "content": "We also investigate two different gradient updating strategy for DIL. From Eq. 4 and Eq. 5, we can observe that they require the second-order gradient since the gradient is computed with two-step forward through " + }, + { + "bbox": [ + 46, + 510, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\phi_{d_i}" + }, + { + "bbox": [ + 46, + 510, + 288, + 714 + ], + "type": "text", + "content": ", which is shown in Fig. 3. To simplify it, Reptile [42] proposes an alternative strategy (i.e., approximating the second-order gradient by the sequential parameter updating with one-order gradient. The optimization direction (i.e., gradient) is computed with the deviation between the initial and last-step parameters. We integrate it into our DIL and call it first-order optimization. In contrast, the original optimization in Eq. 5 is termed second-order optimization. In summary, we propose four variants for DIL following the above two strategies. " + }, + { + "bbox": [ + 46, + 510, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathrm{DIL}_{sf}" + }, + { + "bbox": [ + 46, + 510, + 288, + 714 + ], + "type": "text", + "content": " adopts the serial sampling and first-order gradient optimization. " + }, + { + "bbox": [ + 46, + 510, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathrm{DIL}_{pf}" + }, + { + "bbox": [ + 46, + 510, + 288, + 714 + ], + "type": "text", + "content": " utilizes the parallel sampling and first-order optimization. " + }, + { + "bbox": [ + 46, + 510, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathrm{DIL}_{ss} / \\mathrm{DIL}_{ps}" + }, + { + "bbox": [ + 46, + 510, + 288, + 714 + ], + "type": "text", + "content": " exploits the second-order optimization and serial/parallel sampling." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 293, + 388, + 306 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 293, + 388, + 306 + ], + "spans": [ + { + "bbox": [ + 306, + 293, + 388, + 306 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 312, + 545, + 421 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 312, + 545, + 421 + ], + "spans": [ + { + "bbox": [ + 304, + 312, + 545, + 421 + ], + "type": "text", + "content": "In this section, we first describe the implementation details. Then, we validate the effectiveness of our DIL from two typical out-of-distribution settings, i.e., Cross Distortion Degrees, and Cross Distortion Types. Particularly, for cross-distortion degrees, we train the restoration network with seen distortion degrees while testing it with unseen distortion degrees. For cross-distortion types, the restoration network is trained with synthesized distortions and validated on the corresponding real-world or other distortions." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 429, + 404, + 441 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 429, + 404, + 441 + ], + "spans": [ + { + "bbox": [ + 306, + 429, + 404, + 441 + ], + "type": "text", + "content": "4.1. Implementation" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 447, + 545, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 447, + 545, + 533 + ], + "spans": [ + { + "bbox": [ + 304, + 447, + 545, + 533 + ], + "type": "text", + "content": "We adopt the typical RRDB [56] as our image restoration backbone, which has demonstrated remarkable performances towards various low-level image tasks [52, 55]. All the experiments are done with four NVIDIA 2080Ti GPUs. Adam optimizer is adopted to optimize network parameters in both ERM and DIL training paradigms. More details are given in the Supplementary." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 539, + 444, + 552 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 539, + 444, + 552 + ], + "spans": [ + { + "bbox": [ + 306, + 539, + 444, + 552 + ], + "type": "text", + "content": "4.2. Cross Distortion Degrees" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 557, + 545, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 545, + 654 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 545, + 654 + ], + "type": "text", + "content": "Results on Image Denoising. For image denoising, the training data are composed of distorted images with noise levels [5, 10, 15, 20] and their corresponding clean images. After training the restoration network, we validate it on the test datasets with unseen noise degrees, including [30, 40, 50]. We compare the empirical risk minimization (ERM) and four variants of our proposed DIL, i.e., " + }, + { + "bbox": [ + 304, + 557, + 545, + 654 + ], + "type": "inline_equation", + "content": "\\mathrm{DIL}_{sf}" + }, + { + "bbox": [ + 304, + 557, + 545, + 654 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 557, + 545, + 654 + ], + "type": "inline_equation", + "content": "\\mathrm{DIL}_{pf}" + }, + { + "bbox": [ + 304, + 557, + 545, + 654 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 557, + 545, + 654 + ], + "type": "inline_equation", + "content": "\\mathrm{DIL}_{ss}" + }, + { + "bbox": [ + 304, + 557, + 545, + 654 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 557, + 545, + 654 + ], + "type": "inline_equation", + "content": "\\mathrm{DIL}_{ps}" + }, + { + "bbox": [ + 304, + 557, + 545, + 654 + ], + "type": "text", + "content": ", respectively." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "content": "The experimental results are shown in Table 1. We can observe that all four variants of DIL achieve great generalization ability on multiple unseen noise levels compared with commonly-used empirical risk minimization (ERM). On several typical scenarios, including natural im" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1718" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 58, + 101, + 533, + 226 + ], + "blocks": [ + { + "bbox": [ + 47, + 71, + 545, + 94 + ], + "lines": [ + { + "bbox": [ + 47, + 71, + 545, + 94 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 545, + 94 + ], + "type": "text", + "content": "Table 2. Quantitative comparison for image deblurring on several benchmark datasets. Results are tested on the five unseen blur degrees [4.2, 4.4, 4.6, 4.8, 5.0] in terms of PSNR/SSIM on RGB channel." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 58, + 101, + 533, + 226 + ], + "lines": [ + { + "bbox": [ + 58, + 101, + 533, + 226 + ], + "spans": [ + { + "bbox": [ + 58, + 101, + 533, + 226 + ], + "type": "table", + "html": "
DatasetsMethodsLevels
4.2 (unseen)4.4 (unseen)4.6 (unseen)4.8 (unseen)5.0 (unseen)
Set5 [4]ERM29.31/0.84426.55/0.77624.43/0.70922.96/0.64822.00/0.602
DIL29.58(0.27↑)/0.84827.52(0.97↑)/0.80225.66(1.23↑)/0.75124.38(1.42↑)/0.70823.46(1.46↑)/0.671
Set14 [68]ERM27.22/0.78124.93/0.72623.16/0.67121.89/0.62420.88/0.583
DIL27.24(0.02↑)/0.77825.78(0.85↑)/0.74624.35(1.19↑)/0.70823.23(1.34↑)/0.67222.37(1.49↑)/0.640
BSD100 [38]ERM27.20/0.78425.17/0.73223.50/0.68222.24/0.63921.28/0.602
DIL27.37(0.17↑)/0.78126.16(0.99↑)/0.75324.91(1.41↑)/0.71923.86(1.62↑)/0.68623.02(1.74↑)/0.658
Urban100 [21]ERM24.95/0.79722.41/0.72320.59/0.65719.33/0.60618.40/0.565
DIL24.97(0.02↑)/0.79323.26(0.85↑)/0.74321.76(1.17↑)/0.69320.70(1.37↑)/0.65119.92(1.52↑)/0.618
Manga109 [39]ERM28.16/0.86523.96/0.79121.21/0.71319.63/0.65218.63/0.606
DIL28.09(-0.07↑)/0.86725.41(1.45↑)/0.82223.15(1.94↑)/0.77121.69(2.06↑)/0.72620.72(2.09↑)/0.691
", + "image_path": "409366f20b6cf9f6610b259f054e6153f66750f8f34033750827dc40e9f62ffa.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 60, + 228, + 138, + 345 + ], + "blocks": [ + { + "bbox": [ + 60, + 228, + 138, + 345 + ], + "lines": [ + { + "bbox": [ + 60, + 228, + 138, + 345 + ], + "spans": [ + { + "bbox": [ + 60, + 228, + 138, + 345 + ], + "type": "image", + "image_path": "e41d7b63df26f9e4cf1aae939e241f8af967c59095bcfe8a90716db9628206a8.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 65, + 355, + 527, + 367 + ], + "lines": [ + { + "bbox": [ + 65, + 355, + 527, + 367 + ], + "spans": [ + { + "bbox": [ + 65, + 355, + 527, + 367 + ], + "type": "text", + "content": "Figure 4. Visual comparison of the commonly-used ERM and our proposed four variants of DIL with the unseen noise level 30." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 138, + 228, + 217, + 344 + ], + "blocks": [ + { + "bbox": [ + 138, + 228, + 217, + 344 + ], + "lines": [ + { + "bbox": [ + 138, + 228, + 217, + 344 + ], + "spans": [ + { + "bbox": [ + 138, + 228, + 217, + 344 + ], + "type": "image", + "image_path": "a0bcd4fe07642ca273399569ed69719607fee115db1e4883a27725f0c42b073e.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 217, + 228, + 296, + 346 + ], + "blocks": [ + { + "bbox": [ + 217, + 228, + 296, + 346 + ], + "lines": [ + { + "bbox": [ + 217, + 228, + 296, + 346 + ], + "spans": [ + { + "bbox": [ + 217, + 228, + 296, + 346 + ], + "type": "image", + "image_path": "b374fee163614a213f0d36327064b1ff9848d26270ccd678e6295e7ec4847f96.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 296, + 228, + 375, + 345 + ], + "blocks": [ + { + "bbox": [ + 296, + 228, + 375, + 345 + ], + "lines": [ + { + "bbox": [ + 296, + 228, + 375, + 345 + ], + "spans": [ + { + "bbox": [ + 296, + 228, + 375, + 345 + ], + "type": "image", + "image_path": "e7468a204711b4189c8661aeb4ac9c89de2f019fac45c83399b57e8e53bc1e41.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 375, + 228, + 452, + 345 + ], + "blocks": [ + { + "bbox": [ + 375, + 228, + 452, + 345 + ], + "lines": [ + { + "bbox": [ + 375, + 228, + 452, + 345 + ], + "spans": [ + { + "bbox": [ + 375, + 228, + 452, + 345 + ], + "type": "image", + "image_path": "dc7da7b4ff92f8a5684ef926d84a32c24cb466a7f052c76b89e9ddbcb154282a.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 452, + 228, + 533, + 345 + ], + "blocks": [ + { + "bbox": [ + 452, + 228, + 533, + 345 + ], + "lines": [ + { + "bbox": [ + 452, + 228, + 533, + 345 + ], + "spans": [ + { + "bbox": [ + 452, + 228, + 533, + 345 + ], + "type": "image", + "image_path": "61a78efa12bae7831cf2f4fc084d7e46f896ff1554c0280c75b762a5aaf194ce.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 48, + 414, + 287, + 541 + ], + "blocks": [ + { + "bbox": [ + 47, + 372, + 288, + 405 + ], + "lines": [ + { + "bbox": [ + 47, + 372, + 288, + 405 + ], + "spans": [ + { + "bbox": [ + 47, + 372, + 288, + 405 + ], + "type": "text", + "content": "Table 3. Quantitative comparison for hybrid distortion removal. Results are tested on three different distortion levels in terms of PSNR/SSIM on Y channel." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 414, + 287, + 541 + ], + "lines": [ + { + "bbox": [ + 48, + 414, + 287, + 541 + ], + "spans": [ + { + "bbox": [ + 48, + 414, + 287, + 541 + ], + "type": "table", + "html": "
DatasetsMethodsDistortion level
Mild (unseen)Moderate (unseen)Severe (seen)
BSD100 [38]ERM25.31/0.68724.62/0.64225.27/0.617
DIL26.37/0.69125.23/0.64525.22/0.613
Urban100 [21]ERM23.97/0.73622.51/0.67423.38/0.655
DIL25.00/0.74723.13/0.68223.20/0.645
Manga109 [39]ERM27.43/0.86324.85/0.80826.50/0.815
DIL28.41/0.86825.30/0.81026.19/0.766
DIV2K [2]ERM26.19/0.76625.94/0.74427.42/0.742
DIL27.84/0.78526.89/0.75627.38/0.737
", + "image_path": "325a6634240d45f27a184dfa7f51e98c06dd62eb7918fc2b0a0c170c2322681c.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 557, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 557, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 557, + 288, + 713 + ], + "type": "text", + "content": "ages (i.e., CBSD68 [38], Kodak24 [15], McMaster [72]), building images (Urban100 [21]), cartoon images (i.e., Manga109 [39]), our DIL even outperforms the ERM by a promising/amazing gain of " + }, + { + "bbox": [ + 46, + 557, + 288, + 713 + ], + "type": "inline_equation", + "content": "8.74\\mathrm{dB}" + }, + { + "bbox": [ + 46, + 557, + 288, + 713 + ], + "type": "text", + "content": " at most. Moreover, with the increase of the distribution gap between training and testing data, ours can achieve larger improvements for ERM. Furthermore, for cross distortion degree, " + }, + { + "bbox": [ + 46, + 557, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{DIL}_{sf}" + }, + { + "bbox": [ + 46, + 557, + 288, + 713 + ], + "type": "text", + "content": " shows the best generalization capability compared with the other three variants by serial sampling and first-order optimization. We also visualize the reconstructed images of the above methods in Fig. 4. For the unseen distortion degree " + }, + { + "bbox": [ + 46, + 557, + 288, + 713 + ], + "type": "inline_equation", + "content": "(\\sigma = 30)" + }, + { + "bbox": [ + 46, + 557, + 288, + 713 + ], + "type": "text", + "content": ", the ERM cannot remove the noise well and the reconstructed image also contains obvious noise distortion." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 373, + 545, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 373, + 545, + 422 + ], + "spans": [ + { + "bbox": [ + 304, + 373, + 545, + 422 + ], + "type": "text", + "content": "However, our " + }, + { + "bbox": [ + 304, + 373, + 545, + 422 + ], + "type": "inline_equation", + "content": "\\mathrm{DIL}_{sf}" + }, + { + "bbox": [ + 304, + 373, + 545, + 422 + ], + "type": "text", + "content": " enables the restoration network to recover more vivid and clean images from the unseen noise degrees, which validates the correctness and effectiveness of our proposed DIL." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 423, + 546, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 423, + 546, + 506 + ], + "spans": [ + { + "bbox": [ + 304, + 423, + 546, + 506 + ], + "type": "text", + "content": "Results on Image Deblurring. We also validate the generalization capability of our DIL on the challenging image deblurring. Under this scenarios, we train the restoration network with our proposed DIL with the gaussian blurring level [1.0, 2.0, 3.0, 4.0], and validate its generalization capability on the more severe and difficult blurring levels, including 4.2, 4.4, 4.6, 4.8, and 5.0." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 508, + 547, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 508, + 547, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 508, + 547, + 628 + ], + "type": "text", + "content": "As shown in Table. 2, we validate our DIL on five benchmark datasets, including Set5 [4], Set14 [68], BSD100 [38], Urban100 [21], and Manga109 [39]. With the increase of blurring level, the restoration network trained with ERM suffers from a severe performance drop, since the unseen blurring levels are far away from the blurring levels used for training. But our DIL can improve ERM on each unseen blurring level for five datasets. In particular, we achieve the gain of " + }, + { + "bbox": [ + 304, + 508, + 547, + 628 + ], + "type": "inline_equation", + "content": "2.09\\mathrm{dB}" + }, + { + "bbox": [ + 304, + 508, + 547, + 628 + ], + "type": "text", + "content": " for the cartoon scene Manga109 [39] on the blurring level 5.0." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 630, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 547, + 713 + ], + "type": "text", + "content": "Results on Hybrid-distorted Image Restoration. Except for the above single distortion, we also explore the generalization capability of our DIL on hybrid-distorted image restoration. Following [26], the hybrid distorted images are degraded with blur, noise, and Jpeg compression in a sequence manner. Based on the distortion degree, it can be divided into three levels from low to high, i.e., mild, mod-" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1719" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 96, + 101, + 496, + 230 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 547, + 94 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 547, + 94 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 547, + 94 + ], + "type": "text", + "content": "Table 4. Quantitative results of network generalization capability on real image denoising and synthetic image deraining tasks. Results are tested on Y channel in terms of PSNR/SSIM, except for DND where we obtain our results from official online benchmark." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 96, + 101, + 496, + 230 + ], + "lines": [ + { + "bbox": [ + 96, + 101, + 496, + 230 + ], + "spans": [ + { + "bbox": [ + 96, + 101, + 496, + 230 + ], + "type": "table", + "html": "
MethodsDatasets (Real Denoising)Datasets (Deraining)
SIDD [1]DND [45]Rain100L [63]Rain12 [31]Rain800 [70]
ERM38.90/0.937938.67/0.954927.61/0.857731.44/0.894723.36/0.8199
DILsf39.96(1.06↑)/0.941039.16(0.49↑)/0.953128.15(0.54↑)/0.867932.43(0.99↑)/0.916323.41(0.05↑)/0.8261
DILps39.92(1.02↑)/0.938539.03(0.36↑)/0.955328.37(0.76↑)/0.873933.07(1.63↑)/0.926623.52(0.16↑)/0.8281
", + "image_path": "e77dfd0ca5de4da949a4e3f0d4ae838d926e391084a921e73ce2dfd21e0dcee1.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 53, + 238, + 538, + 250 + ], + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 238, + 538, + 250 + ], + "spans": [ + { + "bbox": [ + 53, + 238, + 538, + 250 + ], + "type": "text", + "content": "Figure 5. Visual comparison of the commonly-used ERM and our proposed DIL for unseen hybrid-distorted (mild) image restoration." + } + ] + } + ], + "index": 2, + "type": "text" + }, + { + "bbox": [ + 46, + 254, + 287, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 254, + 287, + 289 + ], + "spans": [ + { + "bbox": [ + 46, + 254, + 287, + 289 + ], + "type": "text", + "content": "erate, and severe. In this setting, the restoration network is trained with severe hybrid distortions and validated on the mild and moderate levels." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 290, + 289, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 290, + 289, + 434 + ], + "spans": [ + { + "bbox": [ + 46, + 290, + 289, + 434 + ], + "type": "text", + "content": "As shown in Table 3, our DIL achieves an average gain of " + }, + { + "bbox": [ + 46, + 290, + 289, + 434 + ], + "type": "inline_equation", + "content": "1.05\\mathrm{dB}" + }, + { + "bbox": [ + 46, + 290, + 289, + 434 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 290, + 289, + 434 + ], + "type": "inline_equation", + "content": "0.66\\mathrm{dB}" + }, + { + "bbox": [ + 46, + 290, + 289, + 434 + ], + "type": "text", + "content": " on the mild-level, and moderate-level hybrid distortions than ERM, which has a large distribution gap with severe-level hybrid distortions. We can also notice that with the increase of the distribution gap, ours can preserve more performances on the restoration of the out-of-distribution distortions. We also conduct the subjective comparison of our methods with the commonly-used ERM in Fig. 5. We can observe that the restoration network trained with ERM suffers from new artifacts for unseen hybrid-distorted images. But our DIL can eliminate the artifacts well and generate more promising results." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 442, + 178, + 455 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 442, + 178, + 455 + ], + "spans": [ + { + "bbox": [ + 47, + 442, + 178, + 455 + ], + "type": "text", + "content": "4.3. Cross Distortion Types" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 461, + 287, + 497 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 461, + 287, + 497 + ], + "spans": [ + { + "bbox": [ + 46, + 461, + 287, + 497 + ], + "type": "text", + "content": "In this section, we investigate the effects of our proposed DIL on the cross-distortion type setting, which is more challenging than the cross-degree setting." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 498, + 287, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 287, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 287, + 664 + ], + "type": "text", + "content": "Results on Real Image Super-resolution Real Image Super-resolution (RealSR) has attracted great attention since it is urgently required in real life, where the distorted image contains complex hybrid distortions, such as blurring, low resolution, noise, etc. However, the distorted/clean pairs for RealSR are hard to be collected. Simulating distortions like Real-world distortion has been a popular solution for RealSR [55, 71]. In this paper, we follow the Real-ESRGAN [55] and utilize its proposed RealSR distortion simulating to generate image pairs as training datasets. Then we test the restoration network on the out-of-distribution datasets, RealSR V3 [5], DRealSR [59], which are two commonly-used datasets for RealSR evaluation." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "content": "We show the experimental results on RealSR in Table. 5. Without access to any training samples in RealSR V3, DRealSR, our " + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathrm{DIL}_{sf}" + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "content": " can outperform the ERM by " + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "inline_equation", + "content": "0.29\\mathrm{dB}" + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "content": " on RealSR V3 [5] and " + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "inline_equation", + "content": "0.26\\mathrm{dB}" + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "content": " on DRealSR dataset [59]." + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 310, + 293, + 538, + 369 + ], + "blocks": [ + { + "bbox": [ + 305, + 252, + 545, + 285 + ], + "lines": [ + { + "bbox": [ + 305, + 252, + 545, + 285 + ], + "spans": [ + { + "bbox": [ + 305, + 252, + 545, + 285 + ], + "type": "text", + "content": "Table 5. Quantitative results of the network generalization capability on RealSR tasks. Results are tested on the Y channel in terms of PSNR/SSIM." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 310, + 293, + 538, + 369 + ], + "lines": [ + { + "bbox": [ + 310, + 293, + 538, + 369 + ], + "spans": [ + { + "bbox": [ + 310, + 293, + 538, + 369 + ], + "type": "table", + "html": "
MethodsDatasets
RealSR V3 [5] (unseen)DrealSR [59] (unseen)
Real-ESRNet [55]26.19/0.798928.22/0.8470
BSRNet [71]27.46/0.808229.45/0.8579
ERM27.65/0.809829.73/0.8628
DILsf27.94(0.29↑)/0.809829.99(0.26↑)/0.8648
DILps28.12(0.47↑)/0.806730.58(0.85↑)/0.8712
", + "image_path": "8ee93464eec12863df522fdf31aaa6e13edf964b9c1ecacae6307c579bf3bf91.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 315, + 418, + 532, + 484 + ], + "blocks": [ + { + "bbox": [ + 305, + 376, + 545, + 409 + ], + "lines": [ + { + "bbox": [ + 305, + 376, + 545, + 409 + ], + "spans": [ + { + "bbox": [ + 305, + 376, + 545, + 409 + ], + "type": "text", + "content": "Table 6. Quantitative results of our DIL on different backbones. Results are tested on the unseen noise level 30 in terms of PSNR/SSIM." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 315, + 418, + 532, + 484 + ], + "lines": [ + { + "bbox": [ + 315, + 418, + 532, + 484 + ], + "spans": [ + { + "bbox": [ + 315, + 418, + 532, + 484 + ], + "type": "table", + "html": "
ModelsMethodsDatasets
CBSD68 [38]Kodak24 [15]Urban100 [21]
RRDBERM24.90/0.58125.12/0.53325.46/0.648
DIL30.28/0.86631.39/0.86730.93/0.898
SwinIRERM24.22/0.55124.22/0.49324.73/0.618
DIL29.08/0.79829.71/0.77429.72/0.834
", + "image_path": "100f6f12eed2fd82a6154264aeb515d67de764bc39614d8122c31bd0ae82b7ac.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 496, + 545, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 496, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 496, + 545, + 628 + ], + "type": "text", + "content": "Particularly, we notice that " + }, + { + "bbox": [ + 304, + 496, + 545, + 628 + ], + "type": "inline_equation", + "content": "\\mathrm{DIL}_{ps}" + }, + { + "bbox": [ + 304, + 496, + 545, + 628 + ], + "type": "text", + "content": " is more suitable for cross-distortion type scenarios than " + }, + { + "bbox": [ + 304, + 496, + 545, + 628 + ], + "type": "inline_equation", + "content": "\\mathrm{DIL}_{sf}" + }, + { + "bbox": [ + 304, + 496, + 545, + 628 + ], + "type": "text", + "content": ", which exceeds the ERM by a 0.47dB on RealSR V3, and 0.85dB on DRealSR dataset. The reason for that we guess is that " + }, + { + "bbox": [ + 304, + 496, + 545, + 628 + ], + "type": "inline_equation", + "content": "\\mathrm{DIL}_{ps}" + }, + { + "bbox": [ + 304, + 496, + 545, + 628 + ], + "type": "text", + "content": " is more capable of improving the generalization for the large distribution gap in image restoration. We also visualize the comparison corresponding to the subjective quality for different methods. As shown in Fig. 6, Real-ESRNet [55] and BSRNet [71] cause the overshooting at the edge of the text. But our " + }, + { + "bbox": [ + 304, + 496, + 545, + 628 + ], + "type": "inline_equation", + "content": "\\mathrm{DIL}_{ps}" + }, + { + "bbox": [ + 304, + 496, + 545, + 628 + ], + "type": "text", + "content": " can eliminate the artifacts and achieve a high-quality restoration" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": "Results on Real Image Denoising. We also study the generalization capability of our training paradigm DIL on the Real Image Denoising task. Concretely, we select four synthesized distortions based on four categories of color space among camera ISP process [18], and generate training image pairs from DF2K [2, 49] in an online manner. Then we verify its generalization on the commonly-used Real De" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1720" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 52, + 69, + 167, + 145 + ], + "blocks": [ + { + "bbox": [ + 52, + 69, + 167, + 145 + ], + "lines": [ + { + "bbox": [ + 52, + 69, + 167, + 145 + ], + "spans": [ + { + "bbox": [ + 52, + 69, + 167, + 145 + ], + "type": "image", + "image_path": "94f109de9c64b5ac92048328b4566f9f14e9b61c556dccef349418977a299f59.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 105, + 148, + 124, + 156 + ], + "lines": [ + { + "bbox": [ + 105, + 148, + 124, + 156 + ], + "spans": [ + { + "bbox": [ + 105, + 148, + 124, + 156 + ], + "type": "text", + "content": "Input" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 168, + 70, + 228, + 145 + ], + "blocks": [ + { + "bbox": [ + 168, + 70, + 228, + 145 + ], + "lines": [ + { + "bbox": [ + 168, + 70, + 228, + 145 + ], + "spans": [ + { + "bbox": [ + 168, + 70, + 228, + 145 + ], + "type": "image", + "image_path": "31f134a90e396f293ab79f3b59c28fce2738a62e01699f697f3ea8195b3bb509.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 186, + 148, + 210, + 155 + ], + "lines": [ + { + "bbox": [ + 186, + 148, + 210, + 155 + ], + "spans": [ + { + "bbox": [ + 186, + 148, + 210, + 155 + ], + "type": "text", + "content": "Bicubic" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 228, + 70, + 288, + 145 + ], + "blocks": [ + { + "bbox": [ + 228, + 70, + 288, + 145 + ], + "lines": [ + { + "bbox": [ + 228, + 70, + 288, + 145 + ], + "spans": [ + { + "bbox": [ + 228, + 70, + 288, + 145 + ], + "type": "image", + "image_path": "b51d25b4c8ada72f5bbd6d5a692212836b782f5ff1c2e980e982211824a19d0c.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 240, + 148, + 280, + 155 + ], + "lines": [ + { + "bbox": [ + 240, + 148, + 280, + 155 + ], + "spans": [ + { + "bbox": [ + 240, + 148, + 280, + 155 + ], + "type": "text", + "content": "Real-ESRNet" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 289, + 70, + 351, + 145 + ], + "blocks": [ + { + "bbox": [ + 289, + 70, + 351, + 145 + ], + "lines": [ + { + "bbox": [ + 289, + 70, + 351, + 145 + ], + "spans": [ + { + "bbox": [ + 289, + 70, + 351, + 145 + ], + "type": "image", + "image_path": "2c68de85be65692a8c757c43675e68badbf16563161c2bf34f88c1174fbc18dc.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 309, + 148, + 334, + 155 + ], + "lines": [ + { + "bbox": [ + 309, + 148, + 334, + 155 + ], + "spans": [ + { + "bbox": [ + 309, + 148, + 334, + 155 + ], + "type": "text", + "content": "BSRNet" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 156, + 160, + 436, + 171 + ], + "lines": [ + { + "bbox": [ + 156, + 160, + 436, + 171 + ], + "spans": [ + { + "bbox": [ + 156, + 160, + 436, + 171 + ], + "type": "text", + "content": "Figure 6. Visual comparison with state-of-the-art methods on DRealSR [59]." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 351, + 70, + 412, + 145 + ], + "blocks": [ + { + "bbox": [ + 351, + 70, + 412, + 145 + ], + "lines": [ + { + "bbox": [ + 351, + 70, + 412, + 145 + ], + "spans": [ + { + "bbox": [ + 351, + 70, + 412, + 145 + ], + "type": "image", + "image_path": "ed0f34b0219d39d82e98fd08e8fa00b14afeb8efd521b7238e9da3fd9df2c3db.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 375, + 148, + 392, + 155 + ], + "lines": [ + { + "bbox": [ + 375, + 148, + 392, + 155 + ], + "spans": [ + { + "bbox": [ + 375, + 148, + 392, + 155 + ], + "type": "text", + "content": "ERM" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 413, + 70, + 475, + 145 + ], + "blocks": [ + { + "bbox": [ + 413, + 70, + 475, + 145 + ], + "lines": [ + { + "bbox": [ + 413, + 70, + 475, + 145 + ], + "spans": [ + { + "bbox": [ + 413, + 70, + 475, + 145 + ], + "type": "image", + "image_path": "e09bfbadf6c8dc5c61f05b70937858b1887cfcd9a29c9958fc22c01a5e81f58b.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 439, + 148, + 459, + 156 + ], + "lines": [ + { + "bbox": [ + 439, + 148, + 459, + 156 + ], + "spans": [ + { + "bbox": [ + 439, + 148, + 459, + 156 + ], + "type": "text", + "content": "DILps" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 477, + 72, + 533, + 148 + ], + "blocks": [ + { + "bbox": [ + 477, + 72, + 533, + 148 + ], + "lines": [ + { + "bbox": [ + 477, + 72, + 533, + 148 + ], + "spans": [ + { + "bbox": [ + 477, + 72, + 533, + 148 + ], + "type": "image", + "image_path": "da3cc8c948fdcdcbed2a6888acb69dd98d1bdff5036ac1d15fa517e4deddf81d.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 486, + 148, + 529, + 155 + ], + "lines": [ + { + "bbox": [ + 486, + 148, + 529, + 155 + ], + "spans": [ + { + "bbox": [ + 486, + 148, + 529, + 155 + ], + "type": "text", + "content": "Ground Truth" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "type": "table", + "bbox": [ + 63, + 227, + 266, + 288 + ], + "blocks": [ + { + "bbox": [ + 46, + 174, + 287, + 217 + ], + "lines": [ + { + "bbox": [ + 46, + 174, + 287, + 217 + ], + "spans": [ + { + "bbox": [ + 46, + 174, + 287, + 217 + ], + "type": "text", + "content": "Table 7. Quantitative comparison between different distortion augmentation methods. " + }, + { + "bbox": [ + 46, + 174, + 287, + 217 + ], + "type": "inline_equation", + "content": "\\mathrm{D}_1" + }, + { + "bbox": [ + 46, + 174, + 287, + 217 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 174, + 287, + 217 + ], + "type": "inline_equation", + "content": "\\mathrm{D}_2" + }, + { + "bbox": [ + 46, + 174, + 287, + 217 + ], + "type": "text", + "content": " are the first order distortion and the second order distortion derived from [55] respectively. Results are tested on RealSR datasets in terms of PSNR/SSIM." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 63, + 227, + 266, + 288 + ], + "lines": [ + { + "bbox": [ + 63, + 227, + 266, + 288 + ], + "spans": [ + { + "bbox": [ + 63, + 227, + 266, + 288 + ], + "type": "table", + "html": "
AugmentationMethodsDatasets
RealSR V3 [5]DrealSR [59]
D1ERM27.65/0.809829.73/0.8628
DIL27.94/0.809829.99/0.8648
D2ERM27.39/0.807729.41/0.8591
DIL27.65/0.802729.85/0.8677
", + "image_path": "5654d0cde447d2449426b5a7d2c1a538e5b207a404d855f6a4011240b5257475.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "table_body" + } + ], + "index": 16 + }, + { + "bbox": [ + 46, + 298, + 287, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 298, + 287, + 346 + ], + "spans": [ + { + "bbox": [ + 46, + 298, + 287, + 346 + ], + "type": "text", + "content": "noising dataset SIDD [1] and DND [45]. As Table 4 illustrated, our " + }, + { + "bbox": [ + 46, + 298, + 287, + 346 + ], + "type": "inline_equation", + "content": "\\mathrm{DIL}_{ps}" + }, + { + "bbox": [ + 46, + 298, + 287, + 346 + ], + "type": "text", + "content": " achieves the PSNR of " + }, + { + "bbox": [ + 46, + 298, + 287, + 346 + ], + "type": "inline_equation", + "content": "39.92\\mathrm{dB}" + }, + { + "bbox": [ + 46, + 298, + 287, + 346 + ], + "type": "text", + "content": ", which outperforms the ERM by " + }, + { + "bbox": [ + 46, + 298, + 287, + 346 + ], + "type": "inline_equation", + "content": "1.02\\mathrm{dB}" + }, + { + "bbox": [ + 46, + 298, + 287, + 346 + ], + "type": "text", + "content": ", which is almost the same with " + }, + { + "bbox": [ + 46, + 298, + 287, + 346 + ], + "type": "inline_equation", + "content": "\\mathrm{DIL}_{sf}" + }, + { + "bbox": [ + 46, + 298, + 287, + 346 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 46, + 347, + 287, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 347, + 287, + 515 + ], + "spans": [ + { + "bbox": [ + 46, + 347, + 287, + 515 + ], + "type": "text", + "content": "Results on Image Deraining. As an extension experiment, we introduce our DIL to the experiments of image deraining task. Particularly, the raining types and degrees between different datasets are severely different in image deraining. Here, we optimize the restoration network with three image deraining datasets, including DID-MDN [69], Rain14000 [16], and Heavy Rain Dataset [25]. Then we validate the generalization capability of the restoration network on three unseen deraining datasets, i.e., Rain100L [63], Rain12 [31], and Rain800 [70]. We report the experimental results in Table 4. Our DIL " + }, + { + "bbox": [ + 46, + 347, + 287, + 515 + ], + "type": "inline_equation", + "content": "(\\mathrm{DIL}_{ps})" + }, + { + "bbox": [ + 46, + 347, + 287, + 515 + ], + "type": "text", + "content": " enables the restoration network to have a better generalization capability than ERM, which obtains a gain of 0.76dB on Rain100L [63] and 1.63dB on Rain12 [31] dataset." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 47, + 525, + 147, + 536 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 525, + 147, + 536 + ], + "spans": [ + { + "bbox": [ + 47, + 525, + 147, + 536 + ], + "type": "text", + "content": "4.4. Ablation Studies" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 46, + 544, + 287, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 544, + 287, + 652 + ], + "spans": [ + { + "bbox": [ + 46, + 544, + 287, + 652 + ], + "type": "text", + "content": "Impact of different restoration networks. We demonstrate the effectiveness of DIL across different network backbones. In addition to the convolution-based RRDB [56] network, we also incorporate our DIL into the transformer-based SwinIR [32]. The performances are reported in Table 6, which reveals that our DIL can also improve the generalization capability of Transformer-based backbones. This study reveals our DIL is a general training paradigm for different backbones." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "text", + "content": "Effects of different variants for DIL As shown in Table. 1, and 4, we can observe that " + }, + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{DIL}_{sf}" + }, + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "text", + "content": " is more proper for cross-distortion degrees. But for cross-distortion types, " + }, + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{DIL}_{ps}" + }, + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "text", + "content": " achieves better performance for RealSR and Image Deraining. It is noteworthy that the distribution gap of dif" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 175, + 545, + 236 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 175, + 545, + 236 + ], + "spans": [ + { + "bbox": [ + 304, + 175, + 545, + 236 + ], + "type": "text", + "content": "ferent distortion types is larger than different degrees. The first-order optimization is more stable but lacks enough capability for a severe distribution gap compared to second-order optimization. But all of them are competent in improving the generalization capability." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 306, + 237, + 453, + 249 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 237, + 453, + 249 + ], + "spans": [ + { + "bbox": [ + 306, + 237, + 453, + 249 + ], + "type": "text", + "content": "5. Discussion on Limitations" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 251, + 545, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 251, + 545, + 335 + ], + "spans": [ + { + "bbox": [ + 304, + 251, + 545, + 335 + ], + "type": "text", + "content": "The performance on training data. We also report the performance of our DIL on the seen training data in Table 3. It can be seen that our DIL will cause a slight performance drop but the generalization capability is improved obviously. The reason for that is our DIL implements distortion invariant representation learning, which prevents the restoration network from over-fitting to the training data." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 335, + 545, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 335, + 545, + 430 + ], + "spans": [ + { + "bbox": [ + 304, + 335, + 545, + 430 + ], + "type": "text", + "content": "The impact of different distortion augmentation. As shown in Table 7, despite that our DIL achieves the improvement of the generalization capability. The final generalization performance is still related to the distortion augmentation strategy. It is vital to find a universal distortion augmentation strategy, which requires more exploration. We believe it will be a potential/important direction to improve the generalization ability of the restoration network." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 306, + 435, + 378, + 447 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 435, + 378, + 447 + ], + "spans": [ + { + "bbox": [ + 306, + 435, + 378, + 447 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 304, + 450, + 545, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 450, + 545, + 653 + ], + "spans": [ + { + "bbox": [ + 304, + 450, + 545, + 653 + ], + "type": "text", + "content": "In this paper, we propose a novel distortion invariant representation learning (DIL) training paradigm for image restoration from the causality perspective. In particular, we provide a causal view of the image restoration process, and clarify why the restoration network lacks the generalization capability for different degradations. Based on that, we treat the distortion types and degrees as confounders, of which the confounding effects can be removed with our proposed DIL. Concretely, we produce the spurious confounders by simulating the different distortion types and degrees. Then, an instantiation of the back-door criterion in causality is introduced from the optimization perspective, which enables the restoration network to remove the harmful bias from different degradations. Extensive experiments on the settings, cross distortion degrees, and cross distortion types, have demonstrated that our DIL improves the generalization capability of the restoration network effectively." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 306, + 661, + 408, + 673 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 661, + 408, + 673 + ], + "spans": [ + { + "bbox": [ + 306, + 661, + 408, + 673 + ], + "type": "text", + "content": "Acknowledgements" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": "This work was supported in part by NSFC under Grant U1908209, 62021001, and ZJNSFC under Grant LQ23F010008." + } + ] + } + ], + "index": 29 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 749, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 749, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 749, + 314, + 757 + ], + "type": "text", + "content": "1721" + } + ] + } + ], + "index": 30 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 712 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "text", + "content": "[1] Abdelrahman Abdelhamed, Stephen Lin, and Michael S Brown. 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IEEE Transactions on Pattern Analysis and Machine Intelligence, 43(7):2480-2495, 2020. 1, 2" + } + ] + } + ], + "index": 22 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1724" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Learning Dynamic Style Kernels for Artistic Style Transfer/d30e13bb-a2dd-4b9a-b639-90ba30ba2cc5_content_list.json b/2023/Learning Dynamic Style Kernels for Artistic Style Transfer/d30e13bb-a2dd-4b9a-b639-90ba30ba2cc5_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..29639c521e443f8ce5d8c2f58bec0fe16ff8ecdc --- /dev/null +++ b/2023/Learning Dynamic Style Kernels for Artistic Style Transfer/d30e13bb-a2dd-4b9a-b639-90ba30ba2cc5_content_list.json @@ -0,0 +1,1647 @@ +[ + { + "type": "text", + "text": "Learning Dynamic Style Kernels for Artistic Style Transfer", + "text_level": 1, + "bbox": [ + 186, + 130, + 782, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Wenju Xu \nOPPO US Research Center \nPalo Alto, CA, USA \nxuwenjul23@gmail.com", + "bbox": [ + 94, + 181, + 313, + 250 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Chengjiang Long Meta Reality Lab Burlingame, CA, USA clong1@meta.com", + "bbox": [ + 349, + 181, + 531, + 250 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Yongwei Nie \nSouth China University of Technology \nGuangzhou, Guangdong, China \nnieyongwei@scut.edu.cn", + "bbox": [ + 568, + 181, + 872, + 250 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/313ddfc5b7669a445d989fbdc7ad86c9f2ef5a4168fa818e6b8ebcd5bbe24a61.jpg", + "image_caption": [ + "Figure 1. The first two rows show comparisons with state-of-the-art methods. The last row shows results of our proposed method, which can faithfully transfer various styles and preserve the content structure." + ], + "image_footnote": [], + "bbox": [ + 83, + 263, + 888, + 469 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 512, + 313, + 527 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Arbitrary style transfer has been demonstrated to be efficient in artistic image generation. Previous methods either globally modulate the content feature ignoring local details, or overly focus on the local structure details leading to style leakage. In contrast to the literature, we propose a new scheme \"style kernel\" that learns spatially adaptive kernels for per-pixel stylization, where the convolutional kernels are dynamically generated from the global style-content aligned feature and then the learned kernels are applied to modulate the content feature at each spatial position. This new scheme allows flexible both global and local interactions between the content and style features such that the wanted styles can be easily transferred to the content image while at the same time the content structure can be easily preserved. To further enhance the flexibility of our style transfer method, we propose a Style Alignment Encoding (SAE) module complemented with a Content-based Gating Modulation (CGM) module for learning the dynamic style kernels in focusing regions. Extensive experiments strongly demonstrate that our proposed method outperforms state-of-the-art methods and exhibits superior performance in terms of visual quality and efficiency.", + "bbox": [ + 73, + 550, + 472, + 883 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 501, + 512, + 630, + 527 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Artistic style transfer [48] refers to a hot computer vision technology that allows us to recompose the content of an image in the style of an artistic work. Figure 1 shows several vivid examples. We might have ever imagined what a photo might look like if it were painted by a famous artist like Pablo Picasso or Van Gogh. Now style transfer is the computer vision technique that turns this into a reality. It has great potential values in various real-world applications and therefore attracts a lot of researchers to constantly put efforts to make progress towards both quality and efficiency.", + "bbox": [ + 496, + 537, + 890, + 688 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Most of existing style transfer works [6, 15, 18, 26, 33] either globally modulate the content feature ignoring local details or overly focus on the local structure details leading to style leakage. In particular, [15, 18] seeks to match global statistics between content and style images, resulting in inconsistent stylizations that either remain large parts of the content unchanged or contain local content with distorted style patterns. SANet [33] and AdaAttN [31] improve the content similarity by learning attention maps that match the semantics between the style and stylized images, but these methods tend to distort object instances when improper style patterns are involved. Recently, IEC [5] adopts contrastive learning to pull close both the content and style representations between input and output images. MAST [16]", + "bbox": [ + 496, + 689, + 892, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "10083", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "seeks to balance the style and content via manifold alignment. Although both IEC and MAST have achieved some success in most cases, they are still far from satisfactory to well balance two important requirements, i.e., style consistency and structure similarity.", + "bbox": [ + 75, + 90, + 470, + 167 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we develop a novel style transfer framework in a manner of encoder-decoder structure, as illustrated in Figure 2, which contains two important modules: (1) a Style Alignment Encoding (SAE) module enhanced by Content-based Gating Modulation (CGM), which is used to generate content-style aligned features, and (2) a Style Kernel Generation (SKG) module used to transform the output features of SAE to convolutional kernels. In such a framework, we propose a new style transfer scheme, \"style kernel\", which treats the features of the style images as dynamic convolutional kernels and then transfer the style information to the content image by convolving the content image by the learned dynamic style kernels. This allows fine-grained local interactions between the style and content features, the flexibility of which makes both style transferring and content structure preserving much easier.", + "bbox": [ + 75, + 169, + 468, + 412 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To enforce the global correlation between the content and style features, we simulate the self-attention mechanism of Transformer [41] in the SAE module. This treats the content and style features as the queries and keys of the self-attention operator respectively and computes a large attention map the elements of which measure for each local content context the similarity to each local style context. With the attention map, we can aggregate for each pixel of the content image all the style features in a weighted manner to obtain content-style aligned features. We also design a Content-based Gating Modulation (CGM) operator that further thresholds the attention map and zeros the places where similarities are too small, seeking an adaptive number of correlated neighbors as a focusing region for each query point. Then, we use another set of convolutions that constitute the SKG module to further transform the content-style aligned features, and view (reshape) the output of SKG as dynamic style kernels. In order to improve the efficiency of the dynamic convolutions, SKG predicts separable local filters (two 1D filters and a bias) instead of a spatial 2D filter that has more parameters. The learned style kernels already integrate the information of the given content and style images. We further apply the learned dynamic style kernels to the content image feature for transferring the target style to the content image.", + "bbox": [ + 75, + 414, + 470, + 792 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We shall emphasize that unlike \"style code\" in AdaIN [15], DRB-GAN [48], and AdaConv [2] modeled as the dynamic parameters (e.g. mean, variance, convolution kernel) which are shared over all spatial positions globally without distinguishing the semantic regions, the learned dynamic kernels via our \"style kernel\" are point-wisely modeled upon the globally style-content aligned feature, and", + "bbox": [ + 75, + 795, + 468, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "therefore is able to make full use of the point-wise semantic structure correlation to modulate content feature for better artistic style transfer. Our learned dynamic style kernels are good at transferring the globally aggregated and locally semantic-aligned style features to local regions. This ensures our style transfer model that works well on consistent stylization with well preserved structure, overcoming the shortages of existing style transfer methods which either globally modulate the content feature ignoring local details (e.g. AdaIN, WCT [28]) or overly focus on the local structure details leading to style leakage (e.g. AdaAttN [31] and MAST [16]).", + "bbox": [ + 496, + 90, + 890, + 271 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The main contributions of this work are 3-fold as follows:", + "bbox": [ + 498, + 272, + 890, + 299 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We are the first to propose the \"style kernel\" scheme for artistic style transfer, which converts the globally style-content alignment features into position pointwisely dynamic convolutional kernels to convolve the features of content images together for style transfer.", + "- We design a novel architecture, i.e. SAE and CGM, to generate the dynamic style kernels by employing the correlation between the content and style image adaptively.", + "- Extensive experiments demonstrate that our method produces visually plausible stylization results with fine-grained style details and coherence content with the input content images." + ], + "bbox": [ + 517, + 301, + 890, + 500 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 500, + 512, + 648, + 527 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Artistic Style Transfer was initially solved by Gatys et al. [12] a pre-trained neural network to synthesize stylizations in an iterative optimization manner, and then a bunch of neural style transfer methods [3,5,11,18,31,38,39] were developed. In particular, AdaIN [15] introduces the adaptive instance normalization to globally match the statistics between the content and style features. For the same purpose, WCT [28] utilizes the whitening and coloring transforms, and LST [27] introduces a linear transformation matrix predicted on content and style features. [7,22,42,51] seek different ways to match the feature distribution. SANet [33] seeks to align the semantics between the content and style features via a self-attention network. $\\mathrm{StrTr}^2$ [8] resorts to the transformers [41, 47]. To further preserve the content details, AdaAttN [31] perform attentive normalization on per-point basis, IEC [5] employs stylization relations with contrastive learning and MAST [16] introduces manifold alignment to balance the style and content. However, emphasizing on content details prevents the transfer adequate style information to some degree, and results in style leakage. Recently, dynamic network based style transfer methods [3, 15, 18, 38] extend the model generalization. As a generic extension of AdaIN, AdaConv [2] introduces a parameter network that predicts network parameters used by", + "bbox": [ + 496, + 537, + 890, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "10084", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/887aa71401cc7c9022db7435e7967a0ee5c94bac99576acbe9a7444f7f293b76.jpg", + "image_caption": [ + "Figure 2. Overview of our proposed scheme \"style kernel\". A pretrained VGG encoder takes in the content and style image as input to produce the content feature $Z_{c}$ and style feature $Z_{s}$ . The style-alignment encoding model employs an attention mechanism by taking the $Z_{c}$ as query and $Z_{s}$ as key and value to exploit their semantics matching. The content-based gating module (CGM) learns a dynamic threshold and adaptively adjusts attention weights for a globally content-style aligned feature $Z_{cs}$ , which is transformed by style kernel generation module to dynamic style kernels. Finally, we conduct convolution operations on the channel-wisely grouped and shuffled (GS) content feature with the learned dynamic style kernels to get $\\bar{Z}_{cs}$ fed into the decoder to produce the stylizations." + ], + "image_footnote": [], + "bbox": [ + 81, + 89, + 885, + 314 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "another network for style transfer. DRB-GAN [48] models \"style code\" as the global mean and variance for dynamic convolutions to conduct style transfer. Different from all the above methods, we propose a new scheme \"style kernel\" to learn dynamic convolutional kernels from the style-content alignment feature to point-wisely modulate the content feature for artistic style transfer.", + "bbox": [ + 75, + 416, + 470, + 521 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Self-Attention Mechanism is introduced in Transformer [41] as a new attention mechanism. Similar to non-local neural networks [13,21,41,45], Transformer directly works on sequences of image patches to aggregate information for long-range dependencies. The recent researches demonstrate it has been successfully applied in various vision tasks like image recognition [4, 10, 14, 29], object detection [1, 44, 46], image captioning [9], image enhancement [49, 50], and text conditioned image generation [35, 37]. Our model takes the self-attention mechanism to align the semantics of the style feature to that of the content image.", + "bbox": [ + 75, + 523, + 468, + 690 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Dynamic Network consists of convolution layers for which the filter parameters are predicted by another sub-network. Recently, there is rapid progress in vision applications [17, 32, 36, 48, 52] that benefits from dynamic network for image/video enhancement. [19] employs dynamic upsampling filters for high-resolution image reconstruction. [52] predicts filters from spatio-temporal features for video deblurring. Differently, our StyleKernel learns spatially adaptive kernel for per-pixel stylization.", + "bbox": [ + 75, + 691, + 468, + 828 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Our Method", + "text_level": 1, + "bbox": [ + 76, + 844, + 207, + 859 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "While existing dynamic kernel based methods [2, 15, 48] can efficiently generate stylizations, we observe that their", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "visual-quality is limited in two aspects. (1) As the dynamic kernels are predicted based on the style feature without distinguishing the content-style correlation, the transferred style only globally reflects the style characters of the style image, ruining local content details. (2) The completeness of semantic regions is not well preserved. This is because the dynamic kernels used by the layers are spatially shared.", + "bbox": [ + 496, + 416, + 890, + 522 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To alleviate these problems, we propose to align the semantics of the style image to those of the content image and transform the content features for per-pixel stylization in a separable convolution manner. The pipeline of our proposed model is shown in Figure 2. The content image $I_{c}$ and style image $I_{s}$ are first fed into a fixed VGG encoder to produce the content and style feature maps $Z_{c} \\in \\mathbb{R}^{H_{c} \\times W_{c} \\times C_{in}}$ and $Z_{s} \\in \\mathbb{R}^{H_{s} \\times W_{s} \\times C_{in}}$ , where $H, W$ and $C_{in}$ represent the height, width and channel size of the feature map, respectively. Then in SAE, we align the content and style features by using the content features $Z_{c}$ as the queries and the style features $Z_{s}$ as the keys in a self-attention mechanism. The CGM module is conducted on the attention map to seek a focusing region for each query point. Thereafter, we predict by SKG the dynamic style kernels $F$ from the content-style aligned features $Z_{cs}$ . Finally, we group and shuffle (GS) $Z_{c}$ to break down the correlation within the channel-wise feature and apply convolutions parameterized by the learned kernels to the grouped and shuffled $Z_{c}$ to obtain $\\bar{Z}_{cs}$ which is further decoded to the target stylized image by a decoder.", + "bbox": [ + 496, + 523, + 892, + 825 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Style Alignment Encoding", + "text_level": 1, + "bbox": [ + 500, + 832, + 736, + 848 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "This module takes the content and style features as input, aligns between them by learning content-style alignment attention, and finally attentively adjusts the attention map by", + "bbox": [ + 500, + 854, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "10085", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/64286c43330aafe74e9fc9c07d79b037222aac4d2c22970b76d6546ed7781a75.jpg", + "image_caption": [ + "Content & Style" + ], + "image_footnote": [], + "bbox": [ + 86, + 88, + 209, + 213 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/5d37e1cb30e8d6a1be3a2c68d9f3944d2b4f98ad317e754b858ab8e2ceeb5aa6.jpg", + "image_caption": [ + "SANet" + ], + "image_footnote": [], + "bbox": [ + 210, + 88, + 334, + 215 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/7b8817ec17e7eb42d6485be6105e06f3589a5374ccf96cf5637eb2418e9cd9b2.jpg", + "image_caption": [ + "$\\mathrm{SANet} + \\mathrm{topK}$", + "Figure 3. The impact of the feature aggregation. Left: We compare the performances of models conducting different feature aggregation strategies. The SANet takes an attention module to aggregate information across all the nodes. The SANet + topK only acquires information from the nodes with top K attention scores. SANet + CGM takes our content-based gating modulation to aggregate information from a dynamic number of nodes. Our CGM is learned to masked out nodes with low attention score, leading to stylizations with well preserved structure content. The second row shows the distributions of selected nodes (highlighted in colors) and the focused areas (masked-out by black rectangles) learned by CGM. Right: we demonstrate the relation between the content/style loss and the number of selected nodes." + ], + "image_footnote": [], + "bbox": [ + 334, + 88, + 457, + 215 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/211aa4e2cc0e5ee06e7b753747b1bce36c4f77839ea5bf250820841c4a7453aa.jpg", + "image_caption": [ + "$\\mathrm{SANet} + \\mathrm{CGM}$" + ], + "image_footnote": [], + "bbox": [ + 459, + 88, + 581, + 213 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/fc182095be7056785c527fc4b43c4cfb17847f1a875c487850bb0ae5984452a5.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 583, + 88, + 705, + 215 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/edf5695a5d2536fbe27159e4d9c36b5aa9e4a75c2366a5acd0d6ee0c9923f7b2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 707, + 94, + 883, + 210 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "a content-based gating modulation module.", + "bbox": [ + 75, + 330, + 364, + 345 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Content-Style Alignment Attention. By taking the content feature $Z_{c}$ as the query, and the style feature $Z_{s}$ as the key and value, we compute the content-style alignment attention that seeks to aggregate information from the style feature map according to the matched content information. This warps the style feature to align with the content feature. To this end, we calculate the pairwise feature correlation $\\mathcal{M}^{s\\rightarrow c}\\in \\mathbb{R}^{H_cW_c\\times H_sW_s}$ . This results in an attention map $\\mathcal{A}\\in \\mathbb{R}^{H_cW_c\\times H_sW_s}$ by:", + "bbox": [ + 75, + 345, + 468, + 482 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {A} (u, v) = \\operatorname {s o f t m a x} (\\alpha \\mathcal {M} ^ {s \\rightarrow c}) = \\operatorname {s o f t m a x} (\\alpha \\frac {Z _ {c} (u) ^ {T} Z _ {s} (v)}{\\| Z _ {c} (u) \\| \\| Z _ {s} (v) \\|}), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 492, + 491, + 537 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\alpha$ is the coefficient that controls the sharpness of the softmax. $Z_{c}(u)$ and $Z_{s}(v)$ stands for the feature of $Z_{c}$ and $Z_{s}$ at position $u\\in \\mathbb{R}^{H_cW_c}$ and $v\\in \\mathbb{R}^{H_sW_s}$ . The $u$ -th row of the attention map $\\mathcal{A}$ represents similarities between the $u$ -th node of the content feature and all the nodes of the style feature.", + "bbox": [ + 75, + 547, + 468, + 637 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To align the semantics of the style feature to that of the content feature, we aggregate information in $Z_{s}$ based on the attention score map $\\mathcal{A}$ and obtain $Z_{cs} \\in \\mathcal{R}^{H_c W_c \\times C}$ by calculating their weighted average:", + "bbox": [ + 75, + 638, + 468, + 699 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nZ _ {c s} (u) = \\sum_ {v} \\mathcal {A} (u, v) \\cdot Z _ {s} (v). \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 176, + 709, + 468, + 738 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $Z_{cs}(u)$ represents the feature at position $u$ of $Z_{cs}$ . In the following, we denote the $Z_{cs} \\in \\mathcal{R}^{H_c \\times W_c \\times C}$ , which is obtained by reshaping.", + "bbox": [ + 75, + 750, + 468, + 795 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In Eq. 2, all style features are taken into consideration when computing the content-style aligned features $Z_{cs}$ . We find that this yields inferior results because many irrelevant features are involved into the computation. We therefore introduce the Content-based Gating Modulation (CGM) operator which creates dynamic thresholds that further filter out irrelevant style features.", + "bbox": [ + 75, + 795, + 470, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Content-based Gating Modulation is used to further adapt the attention map by the content feature $Z_{c}$ . Taking $Z_{c}$ as input, we employ a convolution network $E_{f}$ to generate a scale parameter $\\lambda$ and a bias parameter $\\beta$ . We then perform a row average operator on the attention matrix $A$ by:", + "bbox": [ + 498, + 330, + 892, + 407 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {A} _ {r} (i) = \\frac {1}{H _ {c}} \\sum_ {j = 1} ^ {H _ {c}} \\mathcal {A} _ {i, j}, \\forall i \\in [ 1, W _ {c} ]. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 573, + 417, + 890, + 460 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{A}_r$ is the obtained column vector after the average operator. Then, we obtain the threshold matrix $\\mathcal{T}$ by the following equation:", + "bbox": [ + 498, + 470, + 890, + 516 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {T} = \\mathcal {A} (\\lambda \\mathcal {A} _ {r} + \\beta). \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 627, + 527, + 890, + 545 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Finally, we update the attention $\\mathcal{A}$ by:", + "bbox": [ + 500, + 556, + 751, + 571 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\bar {\\mathcal {A}} = \\mathcal {A} \\cdot \\operatorname {S i g n} (\\mathcal {A} - \\mathcal {T}), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 617, + 583, + 890, + 599 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where the dot indicates element-wise multiplication and Sign is a function returning 1 given positive input and 0 otherwise. We use $\\bar{A}$ instead of $\\mathcal{A}$ in Eq. 2 to compute $Z_{cs}$ .", + "bbox": [ + 498, + 611, + 890, + 655 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$\\bar{\\mathcal{A}}$ is a dynamically learned mask, with which our model creates focused areas and filter out irrelevant style features. This allows our model to aggregate features from fairly correlated features, which is essential to preserve the completeness of semantic regions. In Figure 3 we compare the intermediate visualizations and stylized results. We see that the CGM works to recognize focused areas, where the style information is aggregated by the query point. By contrast, the attention learned by the SANet is distributed over the entire image, including visually less correlated points, such as corners and background.", + "bbox": [ + 496, + 656, + 890, + 823 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Style Kernel Generation", + "text_level": 1, + "bbox": [ + 500, + 832, + 720, + 847 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We propose the Style Kernel (SK) Generation network to further transform the content-style aligned features of SAE to dynamic style kernels. It takes the globally content-style", + "bbox": [ + 498, + 854, + 892, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "10086", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/6209a129f1388485dcb9f341011d6165b9875c3e68dc324453ae2b4e0260c933.jpg", + "table_caption": [ + "Table 1. Average inference time, measured on a Tesla V100 GPU, for different methods with a batch size of 1 and an input image of $256 \\times 256$ and $512 \\times 512$ ." + ], + "table_footnote": [], + "table_body": "
MethodAdaIN'17LST'19AvatarNet'18SANet'19IEC'21DRB-GAN'21AdaAttN'21MAST'21AdaConv'21StrTr²'22Ours
T256 ↓0.0040.0040.8730.0110.0120.0050.0240.1260.0190.0340.017
T256 ↓0.0050.0050.9620.0370.0210.0060.0420.2390.0360.0860.035
", + "bbox": [ + 78, + 118, + 893, + 186 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "aligned feature $Z_{cs}$ as input to predict the dynamic style filters $F, B = \\{F_1^{ij}, F_2^{ij}, B^{ij}\\}$ .", + "bbox": [ + 76, + 196, + 468, + 227 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Given the content-style aligned feature $Z_{cs}$ , we take two convolution layers to predict the filters $F \\in \\mathbb{R}^{H_c \\times W_c \\times C \\times 2k}$ , which has two 1-dim filters $F_1 = \\{F_1^{ij}\\}$ and $F_2 = \\{F_2^{ij}\\}$ of the sizes $k \\times 1$ and $1 \\times k$ , respectively, and one bias vector $B = \\{B^{ij}\\} \\in \\mathbb{R}^{H_c \\times W_c \\times C \\times 1}$ . Finally, we conduct convolution operations on the content feature $Z_{c}$ with the learned dynamic style kernels $F_1$ , $F_2$ and $B$ . The output after the convolutions is the feature called $\\bar{Z}_{cs}$ :", + "bbox": [ + 76, + 229, + 472, + 353 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\bar {Z} _ {c s} = \\frac {Z _ {c} - \\mu}{\\sigma} * F _ {1} * F _ {2} + B, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 176, + 367, + 468, + 393 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mu$ and $\\sigma$ are the affine parameters in normalization layer and $^*$ is the convolution operator. $\\bar{Z}_{cs}$ is then passed to the decoder to generate the stylized image $I_{cs}$ .", + "bbox": [ + 76, + 407, + 468, + 455 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Remarks. Note that different from \"style code\" [48] modeled as the parameters (e.g. mean and variance) which are shared over all spatial positions globally without taking different semantic regions into consideration, our learned dynamic style kernels are position point-wisely inferred from the globally style-content aligned feature, and therefore are able to fully explore the point-wise semantic structure correlation to modulate local content feature for better artistic style transfer. Our dynamic style kernels make it possible to transfer both the globally aggregated content-style aligned features to local regions in the content images. This ensures our new scheme \"style kernel\" works well on consistent stylization with well preserved structure, and alleviates the shortages of existing style transfer methods [15, 16, 28, 31] which either globally modulate the content feature ignoring local details or overly focus on the local structure details leading to style leakage.", + "bbox": [ + 76, + 460, + 472, + 718 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Loss Functions", + "text_level": 1, + "bbox": [ + 76, + 734, + 230, + 750 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The loss function is formulated with an adversarial loss $\\mathcal{L}_{adv}$ , a reconstruction loss $\\mathcal{L}_{rec}$ , a REMD loss $\\mathcal{L}_{REMD}$ , a style loss $\\mathcal{L}_{sty}$ [20] and a content loss $\\mathcal{L}_{cont}$ [33] as:", + "bbox": [ + 76, + 758, + 468, + 806 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {\\text {a d v}} + \\lambda_ {\\text {r e c}} \\mathcal {L} _ {\\text {r e c}} + \\lambda_ {\\text {c o n t}} \\mathcal {L} _ {\\text {c o n t}} + \\lambda_ {\\text {s t y}} \\mathcal {L} _ {\\text {s t y}} + \\lambda_ {\\text {R E M D}} \\mathcal {L} _ {\\text {R E M D}} \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 823, + 496, + 854 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\lambda_{adv}$ , $\\lambda_{rec}$ , $\\lambda_{cont}$ , $\\lambda_{sty}$ and $\\lambda_{REMD}$ are the hyperparameters used to balance the loss during training.", + "bbox": [ + 76, + 869, + 468, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Reconstruction Loss $\\mathcal{L}_{rec}$ is defined as:", + "bbox": [ + 500, + 196, + 769, + 212 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {r e c} = \\lambda_ {r e c 1} \\big (| | I _ {c c} - I _ {c} | | _ {2} + | | I _ {s s} - I _ {s} | | _ {2} \\big) \\\\ + \\lambda_ {r e c 2} \\sum_ {l = 1} ^ {L} \\left(\\left\\| \\phi_ {l} \\left(I _ {c c}\\right) - \\phi_ {l} \\left(I _ {c}\\right) \\right\\| _ {2} + \\left\\| \\phi_ {l} \\left(I _ {s s}\\right) - \\phi_ {l} \\left(I _ {s}\\right) \\right\\| _ {2}\\right), \\tag {8} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 222, + 892, + 292 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $I_{cc}$ and $I_{ss}$ are the reconstructed images when both the input content and style images are $I_{c}$ and $I_{s}$ , respectively. $\\phi_l$ refers to the $l_{th}$ layer in VGG. We chose features from Relu2_1, Relu3_1, Relu4_1 and Relu5_1 layers.", + "bbox": [ + 498, + 305, + 892, + 364 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "REMD Loss $\\mathcal{L}_{\\text{REMD}}$ [25] adapts the relaxed earth mover distance (REMD) to align the manifold surface of style features. It is formulated as:", + "bbox": [ + 498, + 364, + 890, + 409 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {R E M D} = \\max \\left(\\frac {1}{W _ {s} H _ {s}} \\sum_ {i} \\min _ {j} C _ {i j}, \\frac {1}{W _ {c} H _ {c}} \\sum_ {j} \\min _ {i} C _ {i j}\\right), \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 511, + 417, + 890, + 465 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $C_{ij}$ denotes the pair-wise cosine distance matrix between the $i_{th}$ and $j_{th}$ feature vector in $Z_{cs}$ and $Z_{s}$ .", + "bbox": [ + 498, + 477, + 890, + 508 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 521, + 633, + 539 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We train our proposed method on content images from the MS-COCO [30] dataset, and style images from WikiArt [23] database. Each dataset has around 80k images. The training images are first resized to 512, and then $256 \\times 256$ patches are randomly cropped from the images as inputs. Note that our model can be applied to images of any resolution at the testing stage. Our model is implemented by PyTorch [34]. The Adam [24] is adopted as the optimization solver. We train our model for 160k iterations with a batch size of 16. The learning rate is set to 0.0001.", + "bbox": [ + 496, + 546, + 893, + 698 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The hyperparameters in loss functions are set to $\\lambda_{cont} = 1$ , $\\lambda_{rec} = 1$ , $\\lambda_{sty} = 1$ , $\\lambda_{rec1} = 20$ , $\\lambda_{rec2} = 0.5$ , $\\lambda_{REMD} = 3$ , and $\\lambda_{adv} = 1$ . The encoder is a pretrained VGG-16 network [40], whose parameters are fixed during model training. A multi-scale discriminator is adopted from [43]. We update the discriminator one time after two generator iterations.", + "bbox": [ + 498, + 698, + 893, + 804 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Comparison with State-of-the-Art Methods", + "text_level": 1, + "bbox": [ + 498, + 813, + 867, + 829 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Qualitative Evaluation. As shown in Figure 4, we present qualitative results of different style transfer methods i.e., AdaConv [2], DRB-GAN [48], statistics matching based method like AdaIN [15], attention based methods including", + "bbox": [ + 498, + 839, + 893, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "10087", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/d6b6fb1168881785c745bb9d5457e39f4a919107b0f5b2bdedf7cd1275be5f9e.jpg", + "image_caption": [ + "Figure 4. Qualitative performance comparison on stylized results." + ], + "image_footnote": [], + "bbox": [ + 80, + 88, + 890, + 506 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/a579c9f6a830248f4fa65b410024d3e406f631b3f7cf1710acc6dbfcca2ac82a.jpg", + "table_caption": [ + "Table 2. Quantitative comparison with state-of-the-art methods. We compute the average style loss and the LPIPS score of different methods to indicate how well the style and content are transferred." + ], + "table_footnote": [], + "table_body": "
MethodAdaIN'17LST'19AvatarNet'18SANet'19IEC'21DRB-GAN'21AdaAttN'21MAST'21AdaConv'21StrTr²²Ours
Sty Loss↓1.772.675.911.411.811.511.14-1.041.070.98
LPIPS ↓0.370.330.340.360.310.330.320.320.420.330.30
", + "bbox": [ + 76, + 555, + 895, + 623 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "AdaAttN [31] and IEC [5], and feature modification methods like $\\mathrm{StrTr}^2$ [8] and MAST [16]. For a fair comparison, we deploy all competing methods for style transfer on images of the smaller dimension resized to 512 while the aspect ratio is preserved. Note that we use the public released code and follow the default configurations for testing.", + "bbox": [ + 75, + 632, + 468, + 724 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The comparison in Figure 4 shows the outperformance of our method in terms of visual quality. These images produced by our method faithfully reflect the style characters (e.g., stroke sizes and colors) with no artifact in the regions, and most importantly, they preserve the structural similarity of the content images. On the contrary, AdaIN [15] and MAST [16] fail to generate sharp details and fine strokes. AdaConv [2] yields distorted patterns as it cannot always recover the original style patterns. We also observe nonnegligible artificial structures in those images obtained by $\\mathrm{StrTr}^2$ [8], DRB-GAN [48] and AdaIN [15]. These meth", + "bbox": [ + 75, + 734, + 472, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "ods struggle to preserve the consistency in semantic regions such as the sky. In addition, AdaAttN [31] and IEC [5] and MAST [16] tend to overly preserve the structural similarity and fail to transfer the style to the content image, which makes the results look like the content images.", + "bbox": [ + 496, + 633, + 893, + 709 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Quantitative Evaluation. (1) Style Loss. Following WCT [28], we adopt the style loss to measure the style consistency between the generated stylizations and the style references. The results of different methods are reported in Table 2. As we can observe, our method achieves the lowest style loss, which indicates that our method mostly transfers the style information to the output. (2) LPIPS. We conduct LPIPS to measure the stability and consistency of rendered video clips by following IEC [5]. This metric is to compute the average perceptual distances between consecutive frames and the lower LPIPS score indicates a better stable and consistent performance. We synthesize 10 video clips", + "bbox": [ + 496, + 719, + 893, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "10088", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/f232a4ce0e872f74b2d993bccf2b7954e25677987aa41a6f536de27315883cf3.jpg", + "image_caption": [ + "Figure 5. Qualitative performance comparison on stylized results of different model variants. The results of SANet are also listed as reference. Please zoom in to observe the detailed difference." + ], + "image_footnote": [], + "bbox": [ + 80, + 88, + 893, + 258 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ff832659753253a2c706d1da2144ef11e4deaba740d36ceabefefb850353fd9f.jpg", + "image_caption": [ + "Figure 6. Effectiveness of the Content-based Gating Module (CGM). The results of AdaAttN are also listed as reference." + ], + "image_footnote": [], + "bbox": [ + 91, + 303, + 455, + 445 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5d87ca800903838f16dca8eda18032ccfc8e8071b3f73514cccafeeee581c732.jpg", + "image_caption": [ + "Figure 7. Impact of grouped shuffling: we randomly take 100 content-style pairs to create stylizations. From their feature maps extracted by VGG network, we measure the mean activation value channel-wisely and report the overall distribution." + ], + "image_footnote": [], + "bbox": [ + 151, + 483, + 392, + 607 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "for each method. In Table 2 we observe that our approach produces the lowest LPIPS score among all methods.", + "bbox": [ + 75, + 684, + 468, + 715 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Efficiency Analysis. In Table 1, we compare the inference time of different methods on image resolutions of $256 \\times 256$ and $512 \\times 512$ . All experiments are conducted using a single Tesla V100 GPU. Our method can achieve 25 fps on $512 \\times 512$ images, which is comparable with SOTA methods such as AdaAttN and IEC. It worth pointing out that the operation of our style kernel takes FLOPs cost of $H_{c} \\times W_{c} \\times C_{in} \\times (k + k + 1)$ while vanilla convolution operation has FLOPS cost of $H_{c} \\times W_{c} \\times C_{out} \\times (C_{in} \\times k \\times k + 1)$ . In Table 3, we compare the inference time given different kernel sizes. Note we set $k = 3$ as a trade-off between the efficiency and performance.", + "bbox": [ + 75, + 719, + 470, + 901 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/cd95f33141491ba1d20f07b8a904be8a131ae0509d87c0b5ee7468965a8b040d.jpg", + "table_caption": [ + "Table 3. Results of different sizes of style kernel." + ], + "table_footnote": [], + "table_body": "
SettingSty Loss↓LPIPS ↓T256 ↓T512 ↓
k=11.040.300.0150.034
k=30.980.300.0170.035
k=50.970.310.0210.044
", + "bbox": [ + 511, + 319, + 875, + 396 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 404, + 653, + 422 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We conduct ablation studies to highlight the effectiveness of different modeling components used by our method.", + "bbox": [ + 498, + 428, + 890, + 459 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effectiveness of Style Kernel. This module works to fully explore the point-wise semantic structure correlation to modulate local content features for better artistic style transfer. As shown in Figure 5, our dynamic style kernels make it possible to transfer both the globally aggregated content- style aligned features to local regions in the content images. This ensures our new scheme \"style kernel\" works well on consistent stylization with well preserved structure.", + "bbox": [ + 498, + 462, + 892, + 584 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effectiveness of Grouped Shuffling. To verify this module, we report the statistic distribution of activation strength in Table 7. The distribution gap between the results and real artworks is significantly reduced via using grouped shuffling. Without using GS module, the model fails to produce stylizations consistent to the style reference as shown in Figure 5. This demonstrates that the GS shrinks the statistic gap between the generated images and the style images.", + "bbox": [ + 498, + 587, + 890, + 709 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effectiveness of CGM. We summarized the results of our model w/ and w/o CGM in Figure 6. The model w/o CGM produces images containing regions with corrupted patterns and the stylization is not consistent to the style reference. While our model w/ CGM faithfully preserves the completeness of semantic regions. This is because our CGM aims to select focusing regions, where query points can aggregate style information from fairly correlated nodes.", + "bbox": [ + 496, + 710, + 890, + 833 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. More Discussions", + "text_level": 1, + "bbox": [ + 500, + 843, + 669, + 857 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Generalization of CGM. Our content-based gating modulation can be flexibly deployed as a plug-in module. To ver-", + "bbox": [ + 500, + 869, + 890, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "10089", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/641f9ab3d2660407056cf5a96f53936841ba51fe2ceabe9f174671452cde4b4f.jpg", + "image_caption": [ + "Content" + ], + "image_footnote": [], + "bbox": [ + 81, + 88, + 196, + 261 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3d61363950f9d892e9f7c652559ef196554146e58cc321b1276b4e36a3c52d3e.jpg", + "image_caption": [ + "Style" + ], + "image_footnote": [], + "bbox": [ + 197, + 88, + 313, + 260 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/66deb22b5d879562e458d026494ba4f44fdc6acb003a002df27c9f50c6f35071.jpg", + "image_caption": [ + "SANet" + ], + "image_footnote": [], + "bbox": [ + 313, + 88, + 424, + 261 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/37b5de4e3fa216924f3549c15dd1665f65fa2375d1080eede7ec91b371d8ba9f.jpg", + "image_caption": [ + "SANet + CGM" + ], + "image_footnote": [], + "bbox": [ + 426, + 88, + 542, + 261 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/04ae50f08249f8ce823a78b5e95dba9d1f8b7da4d02cad8c3132ca69c3452b24.jpg", + "image_caption": [ + "IEC" + ], + "image_footnote": [], + "bbox": [ + 542, + 88, + 656, + 261 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/85c614c8d5634895f29882dc7ed76797cdf140d6ccb84ea4b38beda074d0a981.jpg", + "image_caption": [ + "IEC + CGM" + ], + "image_footnote": [], + "bbox": [ + 656, + 88, + 772, + 261 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/cf1c3304e24d03fbb192e2c94b8585d8b980361e544e6421b3139da0f8938a77.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 772, + 88, + 887, + 261 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/00ab646d4d0c79eae12b32c401d017fa0f92623b28262c39836a3ac8a9cf3f23.jpg", + "image_caption": [ + "Content & Style", + "Figure 9. Comparisons on video style transfer. The 1st column lists 2 frames from a video clip as content images. The style image is at the bottom-right corner." + ], + "image_footnote": [], + "bbox": [ + 81, + 315, + 207, + 443 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/59a41d33b03310aaa22a29584e4e3e94e28edab51d9ccbdd89704498296b02c8.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 210, + 315, + 336, + 443 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/73c4cc5df329188124e3cfcf8af80b33c2bb2e0fca6e726e30df02d28e1d34ff.jpg", + "image_caption": [ + "DRB-GAN" + ], + "image_footnote": [], + "bbox": [ + 338, + 315, + 465, + 443 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "if the generalization, we conduct experiments by replacing the attention module in SANet and IEC with our CGM module. The refactored models are denoted as SANet + CGM and IEC + CGM. We train these models with the default settings and compare the performances in Figure 8. We can observe there are nonneglectable artifacts and distorted regions in the results of original SANet and IEC. By plugging-in our CGM, the artifacts are removed and the semantic regions are well preserved. This further proves the effectiveness of our CGM in aggregating semantically consistent information.", + "bbox": [ + 75, + 513, + 468, + 678 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Real-world Video Style Transfer. To verify the performance on real-world video stylization, we collect a 1080P video clip consist of 1377 images and compare our method with DRB-GAN [48]. As shown in Figure 9, our approach outperforms existing style transfer methods in terms of style consistency and stability. This can be attributed to the fact that our style kernels are good at transferring the globally aggregated and locally semantic-aligned style features to local regions.", + "bbox": [ + 75, + 683, + 468, + 820 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Social Impact and Future Work. Our model achieves impressive image stylizations with well preserved content structure and consistent style characteristics, as shown in Figure 10. This can definitely benefit our society. In the future, we will incorporate text information for text condi", + "bbox": [ + 75, + 824, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/50b63598938ed7f852beed901fd876d7e02e8a6bf1df8870b4aaa7b0502b46c0.jpg", + "image_caption": [ + "Figure 8. Generalization of our Content-based Gating Module (CGM). By replacing the attention module in SANet and IEC with our CGM, the artifacts and distorted regions in the results of original SANet and IEC are removed and the semantic regions are well preserved.", + "Ours", + "Figure 10. Demonstration of the performance of our method in terms of style consistency and structural similarity." + ], + "image_footnote": [], + "bbox": [ + 519, + 314, + 763, + 542 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/fb7885e43e8ffb8cf351d96e7369ff28a07e00438a44c54e4849428448612b40.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 766, + 315, + 872, + 429 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7d497f3e307bdf49abe266035da881092573f73c9331a27ccbd21564cdb76dac.jpg", + "image_caption": [ + "Style" + ], + "image_footnote": [], + "bbox": [ + 766, + 430, + 872, + 542 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "tioned image stylization.", + "bbox": [ + 500, + 595, + 663, + 611 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 625, + 617, + 640 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we present a new scheme \"style kernel\" for artistic style transfer. Our method learns an attention map with focusing regions using the proposed content-based gating operator. The style feature is then aligned to match the semantics in the content feature based on the learned attention map. In the style kernel generation module, the dynamic parameters \"style kernel\" are learned from the content-style aligned feature and then applied to modulate the content feature for style transfer. Extensive experimental results demonstrate the remarkable performance of our model in generating synthetic style images with better quality than the state-of-the-art.", + "bbox": [ + 496, + 650, + 890, + 830 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement", + "text_level": 1, + "bbox": [ + 500, + 845, + 658, + 862 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This research was sponsored by Prof. Yongwei Nie's Natural Science Foundation of China (62072191).", + "bbox": [ + 500, + 869, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "10090", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Nicolas Carion, Francisco Massa, Gabriel Synnaeve, Nicolas Usunier, Alexander Kirillov, and Sergey Zagoruyko. 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In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 2482-2491, 2019. 3" + ], + "bbox": [ + 501, + 92, + 890, + 893 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "10092", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Learning Dynamic Style Kernels for Artistic Style Transfer/d30e13bb-a2dd-4b9a-b639-90ba30ba2cc5_model.json b/2023/Learning Dynamic Style Kernels for Artistic Style Transfer/d30e13bb-a2dd-4b9a-b639-90ba30ba2cc5_model.json new file mode 100644 index 0000000000000000000000000000000000000000..7503499052782633ba3ace2a52295cf09fe65cfd --- /dev/null +++ b/2023/Learning Dynamic Style Kernels for Artistic Style Transfer/d30e13bb-a2dd-4b9a-b639-90ba30ba2cc5_model.json @@ -0,0 +1,2398 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.187, + 0.131, + 0.784, + 0.154 + ], + "angle": 0, + "content": "Learning Dynamic Style Kernels for Artistic Style Transfer" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.182, + 0.314, + 0.251 + ], + "angle": 0, + "content": "Wenju Xu \nOPPO US Research Center \nPalo Alto, CA, USA \nxuwenjul23@gmail.com" + }, + { + "type": "text", + "bbox": [ + 0.35, + 0.182, + 0.532, + 0.251 + ], + "angle": 0, + "content": "Chengjiang Long Meta Reality Lab Burlingame, CA, USA clong1@meta.com" + }, + { + "type": "text", + "bbox": [ + 0.569, + 0.182, + 0.874, + 0.251 + ], + "angle": 0, + "content": "Yongwei Nie \nSouth China University of Technology \nGuangzhou, Guangdong, China \nnieyongwei@scut.edu.cn" + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.265, + 0.889, + 0.47 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.473, + 0.893, + 0.501 + ], + "angle": 0, + "content": "Figure 1. The first two rows show comparisons with state-of-the-art methods. The last row shows results of our proposed method, which can faithfully transfer various styles and preserve the content structure." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.513, + 0.314, + 0.529 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.551, + 0.473, + 0.884 + ], + "angle": 0, + "content": "Arbitrary style transfer has been demonstrated to be efficient in artistic image generation. Previous methods either globally modulate the content feature ignoring local details, or overly focus on the local structure details leading to style leakage. In contrast to the literature, we propose a new scheme \"style kernel\" that learns spatially adaptive kernels for per-pixel stylization, where the convolutional kernels are dynamically generated from the global style-content aligned feature and then the learned kernels are applied to modulate the content feature at each spatial position. This new scheme allows flexible both global and local interactions between the content and style features such that the wanted styles can be easily transferred to the content image while at the same time the content structure can be easily preserved. To further enhance the flexibility of our style transfer method, we propose a Style Alignment Encoding (SAE) module complemented with a Content-based Gating Modulation (CGM) module for learning the dynamic style kernels in focusing regions. Extensive experiments strongly demonstrate that our proposed method outperforms state-of-the-art methods and exhibits superior performance in terms of visual quality and efficiency." + }, + { + "type": "title", + "bbox": [ + 0.502, + 0.513, + 0.631, + 0.529 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.539, + 0.892, + 0.689 + ], + "angle": 0, + "content": "Artistic style transfer [48] refers to a hot computer vision technology that allows us to recompose the content of an image in the style of an artistic work. Figure 1 shows several vivid examples. We might have ever imagined what a photo might look like if it were painted by a famous artist like Pablo Picasso or Van Gogh. Now style transfer is the computer vision technique that turns this into a reality. It has great potential values in various real-world applications and therefore attracts a lot of researchers to constantly put efforts to make progress towards both quality and efficiency." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.69, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Most of existing style transfer works [6, 15, 18, 26, 33] either globally modulate the content feature ignoring local details or overly focus on the local structure details leading to style leakage. In particular, [15, 18] seeks to match global statistics between content and style images, resulting in inconsistent stylizations that either remain large parts of the content unchanged or contain local content with distorted style patterns. SANet [33] and AdaAttN [31] improve the content similarity by learning attention maps that match the semantics between the style and stylized images, but these methods tend to distort object instances when improper style patterns are involved. Recently, IEC [5] adopts contrastive learning to pull close both the content and style representations between input and output images. MAST [16]" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.956 + ], + "angle": 0, + "content": "10083" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.471, + 0.168 + ], + "angle": 0, + "content": "seeks to balance the style and content via manifold alignment. Although both IEC and MAST have achieved some success in most cases, they are still far from satisfactory to well balance two important requirements, i.e., style consistency and structure similarity." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.17, + 0.47, + 0.413 + ], + "angle": 0, + "content": "In this paper, we develop a novel style transfer framework in a manner of encoder-decoder structure, as illustrated in Figure 2, which contains two important modules: (1) a Style Alignment Encoding (SAE) module enhanced by Content-based Gating Modulation (CGM), which is used to generate content-style aligned features, and (2) a Style Kernel Generation (SKG) module used to transform the output features of SAE to convolutional kernels. In such a framework, we propose a new style transfer scheme, \"style kernel\", which treats the features of the style images as dynamic convolutional kernels and then transfer the style information to the content image by convolving the content image by the learned dynamic style kernels. This allows fine-grained local interactions between the style and content features, the flexibility of which makes both style transferring and content structure preserving much easier." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.415, + 0.471, + 0.793 + ], + "angle": 0, + "content": "To enforce the global correlation between the content and style features, we simulate the self-attention mechanism of Transformer [41] in the SAE module. This treats the content and style features as the queries and keys of the self-attention operator respectively and computes a large attention map the elements of which measure for each local content context the similarity to each local style context. With the attention map, we can aggregate for each pixel of the content image all the style features in a weighted manner to obtain content-style aligned features. We also design a Content-based Gating Modulation (CGM) operator that further thresholds the attention map and zeros the places where similarities are too small, seeking an adaptive number of correlated neighbors as a focusing region for each query point. Then, we use another set of convolutions that constitute the SKG module to further transform the content-style aligned features, and view (reshape) the output of SKG as dynamic style kernels. In order to improve the efficiency of the dynamic convolutions, SKG predicts separable local filters (two 1D filters and a bias) instead of a spatial 2D filter that has more parameters. The learned style kernels already integrate the information of the given content and style images. We further apply the learned dynamic style kernels to the content image feature for transferring the target style to the content image." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.47, + 0.903 + ], + "angle": 0, + "content": "We shall emphasize that unlike \"style code\" in AdaIN [15], DRB-GAN [48], and AdaConv [2] modeled as the dynamic parameters (e.g. mean, variance, convolution kernel) which are shared over all spatial positions globally without distinguishing the semantic regions, the learned dynamic kernels via our \"style kernel\" are point-wisely modeled upon the globally style-content aligned feature, and" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.272 + ], + "angle": 0, + "content": "therefore is able to make full use of the point-wise semantic structure correlation to modulate content feature for better artistic style transfer. Our learned dynamic style kernels are good at transferring the globally aggregated and locally semantic-aligned style features to local regions. This ensures our style transfer model that works well on consistent stylization with well preserved structure, overcoming the shortages of existing style transfer methods which either globally modulate the content feature ignoring local details (e.g. AdaIN, WCT [28]) or overly focus on the local structure details leading to style leakage (e.g. AdaAttN [31] and MAST [16])." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.273, + 0.892, + 0.3 + ], + "angle": 0, + "content": "The main contributions of this work are 3-fold as follows:" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.303, + 0.892, + 0.378 + ], + "angle": 0, + "content": "- We are the first to propose the \"style kernel\" scheme for artistic style transfer, which converts the globally style-content alignment features into position pointwisely dynamic convolutional kernels to convolve the features of content images together for style transfer." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.38, + 0.892, + 0.439 + ], + "angle": 0, + "content": "- We design a novel architecture, i.e. SAE and CGM, to generate the dynamic style kernels by employing the correlation between the content and style image adaptively." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.442, + 0.892, + 0.501 + ], + "angle": 0, + "content": "- Extensive experiments demonstrate that our method produces visually plausible stylization results with fine-grained style details and coherence content with the input content images." + }, + { + "type": "list", + "bbox": [ + 0.518, + 0.303, + 0.892, + 0.501 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.513, + 0.65, + 0.529 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.539, + 0.892, + 0.903 + ], + "angle": 0, + "content": "Artistic Style Transfer was initially solved by Gatys et al. [12] a pre-trained neural network to synthesize stylizations in an iterative optimization manner, and then a bunch of neural style transfer methods [3,5,11,18,31,38,39] were developed. In particular, AdaIN [15] introduces the adaptive instance normalization to globally match the statistics between the content and style features. For the same purpose, WCT [28] utilizes the whitening and coloring transforms, and LST [27] introduces a linear transformation matrix predicted on content and style features. [7,22,42,51] seek different ways to match the feature distribution. SANet [33] seeks to align the semantics between the content and style features via a self-attention network. \\(\\mathrm{StrTr}^2\\) [8] resorts to the transformers [41, 47]. To further preserve the content details, AdaAttN [31] perform attentive normalization on per-point basis, IEC [5] employs stylization relations with contrastive learning and MAST [16] introduces manifold alignment to balance the style and content. However, emphasizing on content details prevents the transfer adequate style information to some degree, and results in style leakage. Recently, dynamic network based style transfer methods [3, 15, 18, 38] extend the model generalization. As a generic extension of AdaIN, AdaConv [2] introduces a parameter network that predicts network parameters used by" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "10084" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.09, + 0.887, + 0.315 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.322, + 0.896, + 0.406 + ], + "angle": 0, + "content": "Figure 2. Overview of our proposed scheme \"style kernel\". A pretrained VGG encoder takes in the content and style image as input to produce the content feature \\( Z_{c} \\) and style feature \\( Z_{s} \\). The style-alignment encoding model employs an attention mechanism by taking the \\( Z_{c} \\) as query and \\( Z_{s} \\) as key and value to exploit their semantics matching. The content-based gating module (CGM) learns a dynamic threshold and adaptively adjusts attention weights for a globally content-style aligned feature \\( Z_{cs} \\), which is transformed by style kernel generation module to dynamic style kernels. Finally, we conduct convolution operations on the channel-wisely grouped and shuffled (GS) content feature with the learned dynamic style kernels to get \\( \\bar{Z}_{cs} \\) fed into the decoder to produce the stylizations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.417, + 0.471, + 0.522 + ], + "angle": 0, + "content": "another network for style transfer. DRB-GAN [48] models \"style code\" as the global mean and variance for dynamic convolutions to conduct style transfer. Different from all the above methods, we propose a new scheme \"style kernel\" to learn dynamic convolutional kernels from the style-content alignment feature to point-wisely modulate the content feature for artistic style transfer." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.524, + 0.47, + 0.691 + ], + "angle": 0, + "content": "Self-Attention Mechanism is introduced in Transformer [41] as a new attention mechanism. Similar to non-local neural networks [13,21,41,45], Transformer directly works on sequences of image patches to aggregate information for long-range dependencies. The recent researches demonstrate it has been successfully applied in various vision tasks like image recognition [4, 10, 14, 29], object detection [1, 44, 46], image captioning [9], image enhancement [49, 50], and text conditioned image generation [35, 37]. Our model takes the self-attention mechanism to align the semantics of the style feature to that of the content image." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.692, + 0.47, + 0.829 + ], + "angle": 0, + "content": "Dynamic Network consists of convolution layers for which the filter parameters are predicted by another sub-network. Recently, there is rapid progress in vision applications [17, 32, 36, 48, 52] that benefits from dynamic network for image/video enhancement. [19] employs dynamic upsampling filters for high-resolution image reconstruction. [52] predicts filters from spatio-temporal features for video deblurring. Differently, our StyleKernel learns spatially adaptive kernel for per-pixel stylization." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.845, + 0.208, + 0.86 + ], + "angle": 0, + "content": "3. Our Method" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "While existing dynamic kernel based methods [2, 15, 48] can efficiently generate stylizations, we observe that their" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.417, + 0.892, + 0.523 + ], + "angle": 0, + "content": "visual-quality is limited in two aspects. (1) As the dynamic kernels are predicted based on the style feature without distinguishing the content-style correlation, the transferred style only globally reflects the style characters of the style image, ruining local content details. (2) The completeness of semantic regions is not well preserved. This is because the dynamic kernels used by the layers are spatially shared." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.524, + 0.893, + 0.826 + ], + "angle": 0, + "content": "To alleviate these problems, we propose to align the semantics of the style image to those of the content image and transform the content features for per-pixel stylization in a separable convolution manner. The pipeline of our proposed model is shown in Figure 2. The content image \\( I_{c} \\) and style image \\( I_{s} \\) are first fed into a fixed VGG encoder to produce the content and style feature maps \\( Z_{c} \\in \\mathbb{R}^{H_{c} \\times W_{c} \\times C_{in}} \\) and \\( Z_{s} \\in \\mathbb{R}^{H_{s} \\times W_{s} \\times C_{in}} \\), where \\( H, W \\) and \\( C_{in} \\) represent the height, width and channel size of the feature map, respectively. Then in SAE, we align the content and style features by using the content features \\( Z_{c} \\) as the queries and the style features \\( Z_{s} \\) as the keys in a self-attention mechanism. The CGM module is conducted on the attention map to seek a focusing region for each query point. Thereafter, we predict by SKG the dynamic style kernels \\( F \\) from the content-style aligned features \\( Z_{cs} \\). Finally, we group and shuffle (GS) \\( Z_{c} \\) to break down the correlation within the channel-wise feature and apply convolutions parameterized by the learned kernels to the grouped and shuffled \\( Z_{c} \\) to obtain \\( \\bar{Z}_{cs} \\) which is further decoded to the target stylized image by a decoder." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.833, + 0.738, + 0.849 + ], + "angle": 0, + "content": "3.1. Style Alignment Encoding" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "This module takes the content and style features as input, aligns between them by learning content-style alignment attention, and finally attentively adjusts the attention map by" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "10085" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.088, + 0.089, + 0.21, + 0.214 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.111, + 0.219, + 0.19, + 0.23 + ], + "angle": 0, + "content": "Content & Style" + }, + { + "type": "image", + "bbox": [ + 0.212, + 0.089, + 0.335, + 0.216 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.254, + 0.219, + 0.288, + 0.229 + ], + "angle": 0, + "content": "SANet" + }, + { + "type": "image", + "bbox": [ + 0.336, + 0.089, + 0.458, + 0.216 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.362, + 0.219, + 0.432, + 0.23 + ], + "angle": 0, + "content": "\\(\\mathrm{SANet} + \\mathrm{topK}\\)" + }, + { + "type": "image", + "bbox": [ + 0.46, + 0.089, + 0.582, + 0.214 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.492, + 0.219, + 0.565, + 0.229 + ], + "angle": 0, + "content": "\\(\\mathrm{SANet} + \\mathrm{CGM}\\)" + }, + { + "type": "image", + "bbox": [ + 0.584, + 0.089, + 0.706, + 0.216 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.629, + 0.219, + 0.655, + 0.229 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image", + "bbox": [ + 0.708, + 0.095, + 0.884, + 0.212 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.232, + 0.894, + 0.318 + ], + "angle": 0, + "content": "Figure 3. The impact of the feature aggregation. Left: We compare the performances of models conducting different feature aggregation strategies. The SANet takes an attention module to aggregate information across all the nodes. The SANet + topK only acquires information from the nodes with top K attention scores. SANet + CGM takes our content-based gating modulation to aggregate information from a dynamic number of nodes. Our CGM is learned to masked out nodes with low attention score, leading to stylizations with well preserved structure content. The second row shows the distributions of selected nodes (highlighted in colors) and the focused areas (masked-out by black rectangles) learned by CGM. Right: we demonstrate the relation between the content/style loss and the number of selected nodes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.332, + 0.365, + 0.346 + ], + "angle": 0, + "content": "a content-based gating modulation module." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.347, + 0.47, + 0.483 + ], + "angle": 0, + "content": "Content-Style Alignment Attention. By taking the content feature \\( Z_{c} \\) as the query, and the style feature \\( Z_{s} \\) as the key and value, we compute the content-style alignment attention that seeks to aggregate information from the style feature map according to the matched content information. This warps the style feature to align with the content feature. To this end, we calculate the pairwise feature correlation \\( \\mathcal{M}^{s\\rightarrow c}\\in \\mathbb{R}^{H_cW_c\\times H_sW_s} \\). This results in an attention map \\( \\mathcal{A}\\in \\mathbb{R}^{H_cW_c\\times H_sW_s} \\) by:" + }, + { + "type": "equation", + "bbox": [ + 0.077, + 0.493, + 0.493, + 0.539 + ], + "angle": 0, + "content": "\\[\n\\mathcal {A} (u, v) = \\operatorname {s o f t m a x} (\\alpha \\mathcal {M} ^ {s \\rightarrow c}) = \\operatorname {s o f t m a x} (\\alpha \\frac {Z _ {c} (u) ^ {T} Z _ {s} (v)}{\\| Z _ {c} (u) \\| \\| Z _ {s} (v) \\|}), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.549, + 0.469, + 0.638 + ], + "angle": 0, + "content": "where \\(\\alpha\\) is the coefficient that controls the sharpness of the softmax. \\(Z_{c}(u)\\) and \\(Z_{s}(v)\\) stands for the feature of \\(Z_{c}\\) and \\(Z_{s}\\) at position \\(u\\in \\mathbb{R}^{H_cW_c}\\) and \\(v\\in \\mathbb{R}^{H_sW_s}\\). The \\(u\\)-th row of the attention map \\(\\mathcal{A}\\) represents similarities between the \\(u\\)-th node of the content feature and all the nodes of the style feature." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.64, + 0.47, + 0.7 + ], + "angle": 0, + "content": "To align the semantics of the style feature to that of the content feature, we aggregate information in \\( Z_{s} \\) based on the attention score map \\( \\mathcal{A} \\) and obtain \\( Z_{cs} \\in \\mathcal{R}^{H_c W_c \\times C} \\) by calculating their weighted average:" + }, + { + "type": "equation", + "bbox": [ + 0.177, + 0.71, + 0.469, + 0.739 + ], + "angle": 0, + "content": "\\[\nZ _ {c s} (u) = \\sum_ {v} \\mathcal {A} (u, v) \\cdot Z _ {s} (v). \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.47, + 0.796 + ], + "angle": 0, + "content": "where \\(Z_{cs}(u)\\) represents the feature at position \\(u\\) of \\(Z_{cs}\\). In the following, we denote the \\(Z_{cs} \\in \\mathcal{R}^{H_c \\times W_c \\times C}\\), which is obtained by reshaping." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.471, + 0.902 + ], + "angle": 0, + "content": "In Eq. 2, all style features are taken into consideration when computing the content-style aligned features \\( Z_{cs} \\). We find that this yields inferior results because many irrelevant features are involved into the computation. We therefore introduce the Content-based Gating Modulation (CGM) operator which creates dynamic thresholds that further filter out irrelevant style features." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.332, + 0.893, + 0.409 + ], + "angle": 0, + "content": "Content-based Gating Modulation is used to further adapt the attention map by the content feature \\( Z_{c} \\). Taking \\( Z_{c} \\) as input, we employ a convolution network \\( E_{f} \\) to generate a scale parameter \\( \\lambda \\) and a bias parameter \\( \\beta \\). We then perform a row average operator on the attention matrix \\( A \\) by:" + }, + { + "type": "equation", + "bbox": [ + 0.575, + 0.419, + 0.892, + 0.462 + ], + "angle": 0, + "content": "\\[\n\\mathcal {A} _ {r} (i) = \\frac {1}{H _ {c}} \\sum_ {j = 1} ^ {H _ {c}} \\mathcal {A} _ {i, j}, \\forall i \\in [ 1, W _ {c} ]. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.472, + 0.892, + 0.517 + ], + "angle": 0, + "content": "where \\(\\mathcal{A}_r\\) is the obtained column vector after the average operator. Then, we obtain the threshold matrix \\(\\mathcal{T}\\) by the following equation:" + }, + { + "type": "equation", + "bbox": [ + 0.628, + 0.529, + 0.892, + 0.546 + ], + "angle": 0, + "content": "\\[\n\\mathcal {T} = \\mathcal {A} (\\lambda \\mathcal {A} _ {r} + \\beta). \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.557, + 0.753, + 0.573 + ], + "angle": 0, + "content": "Finally, we update the attention \\(\\mathcal{A}\\) by:" + }, + { + "type": "equation", + "bbox": [ + 0.619, + 0.584, + 0.892, + 0.6 + ], + "angle": 0, + "content": "\\[\n\\bar {\\mathcal {A}} = \\mathcal {A} \\cdot \\operatorname {S i g n} (\\mathcal {A} - \\mathcal {T}), \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.612, + 0.892, + 0.656 + ], + "angle": 0, + "content": "where the dot indicates element-wise multiplication and Sign is a function returning 1 given positive input and 0 otherwise. We use \\(\\bar{A}\\) instead of \\(\\mathcal{A}\\) in Eq. 2 to compute \\(Z_{cs}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.657, + 0.892, + 0.824 + ], + "angle": 0, + "content": "\\(\\bar{\\mathcal{A}}\\) is a dynamically learned mask, with which our model creates focused areas and filter out irrelevant style features. This allows our model to aggregate features from fairly correlated features, which is essential to preserve the completeness of semantic regions. In Figure 3 we compare the intermediate visualizations and stylized results. We see that the CGM works to recognize focused areas, where the style information is aggregated by the query point. By contrast, the attention learned by the SANet is distributed over the entire image, including visually less correlated points, such as corners and background." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.833, + 0.722, + 0.848 + ], + "angle": 0, + "content": "3.2. Style Kernel Generation" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.893, + 0.902 + ], + "angle": 0, + "content": "We propose the Style Kernel (SK) Generation network to further transform the content-style aligned features of SAE to dynamic style kernels. It takes the globally content-style" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "10086" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.895, + 0.117 + ], + "angle": 0, + "content": "Table 1. Average inference time, measured on a Tesla V100 GPU, for different methods with a batch size of 1 and an input image of \\(256 \\times 256\\) and \\(512 \\times 512\\)." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.119, + 0.895, + 0.188 + ], + "angle": 0, + "content": "
MethodAdaIN'17LST'19AvatarNet'18SANet'19IEC'21DRB-GAN'21AdaAttN'21MAST'21AdaConv'21StrTr²'22Ours
T256 ↓0.0040.0040.8730.0110.0120.0050.0240.1260.0190.0340.017
T256 ↓0.0050.0050.9620.0370.0210.0060.0420.2390.0360.0860.035
" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.197, + 0.47, + 0.228 + ], + "angle": 0, + "content": "aligned feature \\( Z_{cs} \\) as input to predict the dynamic style filters \\( F, B = \\{F_1^{ij}, F_2^{ij}, B^{ij}\\} \\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.23, + 0.473, + 0.354 + ], + "angle": 0, + "content": "Given the content-style aligned feature \\( Z_{cs} \\), we take two convolution layers to predict the filters \\( F \\in \\mathbb{R}^{H_c \\times W_c \\times C \\times 2k} \\), which has two 1-dim filters \\( F_1 = \\{F_1^{ij}\\} \\) and \\( F_2 = \\{F_2^{ij}\\} \\) of the sizes \\( k \\times 1 \\) and \\( 1 \\times k \\), respectively, and one bias vector \\( B = \\{B^{ij}\\} \\in \\mathbb{R}^{H_c \\times W_c \\times C \\times 1} \\). Finally, we conduct convolution operations on the content feature \\( Z_{c} \\) with the learned dynamic style kernels \\( F_1 \\), \\( F_2 \\) and \\( B \\). The output after the convolutions is the feature called \\( \\bar{Z}_{cs} \\):" + }, + { + "type": "equation", + "bbox": [ + 0.177, + 0.368, + 0.47, + 0.395 + ], + "angle": 0, + "content": "\\[\n\\bar {Z} _ {c s} = \\frac {Z _ {c} - \\mu}{\\sigma} * F _ {1} * F _ {2} + B, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.409, + 0.47, + 0.456 + ], + "angle": 0, + "content": "where \\(\\mu\\) and \\(\\sigma\\) are the affine parameters in normalization layer and \\(^*\\) is the convolution operator. \\(\\bar{Z}_{cs}\\) is then passed to the decoder to generate the stylized image \\(I_{cs}\\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.461, + 0.473, + 0.719 + ], + "angle": 0, + "content": "Remarks. Note that different from \"style code\" [48] modeled as the parameters (e.g. mean and variance) which are shared over all spatial positions globally without taking different semantic regions into consideration, our learned dynamic style kernels are position point-wisely inferred from the globally style-content aligned feature, and therefore are able to fully explore the point-wise semantic structure correlation to modulate local content feature for better artistic style transfer. Our dynamic style kernels make it possible to transfer both the globally aggregated content-style aligned features to local regions in the content images. This ensures our new scheme \"style kernel\" works well on consistent stylization with well preserved structure, and alleviates the shortages of existing style transfer methods [15, 16, 28, 31] which either globally modulate the content feature ignoring local details or overly focus on the local structure details leading to style leakage." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.735, + 0.231, + 0.75 + ], + "angle": 0, + "content": "3.3. Loss Functions" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.76, + 0.47, + 0.807 + ], + "angle": 0, + "content": "The loss function is formulated with an adversarial loss \\(\\mathcal{L}_{adv}\\), a reconstruction loss \\(\\mathcal{L}_{rec}\\), a REMD loss \\(\\mathcal{L}_{REMD}\\), a style loss \\(\\mathcal{L}_{sty}\\) [20] and a content loss \\(\\mathcal{L}_{cont}\\) [33] as:" + }, + { + "type": "equation", + "bbox": [ + 0.078, + 0.824, + 0.498, + 0.855 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {\\text {a d v}} + \\lambda_ {\\text {r e c}} \\mathcal {L} _ {\\text {r e c}} + \\lambda_ {\\text {c o n t}} \\mathcal {L} _ {\\text {c o n t}} + \\lambda_ {\\text {s t y}} \\mathcal {L} _ {\\text {s t y}} + \\lambda_ {\\text {R E M D}} \\mathcal {L} _ {\\text {R E M D}} \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.903 + ], + "angle": 0, + "content": "where \\(\\lambda_{adv}\\), \\(\\lambda_{rec}\\), \\(\\lambda_{cont}\\), \\(\\lambda_{sty}\\) and \\(\\lambda_{REMD}\\) are the hyperparameters used to balance the loss during training." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.197, + 0.771, + 0.213 + ], + "angle": 0, + "content": "Reconstruction Loss \\(\\mathcal{L}_{rec}\\) is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.5, + 0.223, + 0.893, + 0.294 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {r e c} = \\lambda_ {r e c 1} \\big (| | I _ {c c} - I _ {c} | | _ {2} + | | I _ {s s} - I _ {s} | | _ {2} \\big) \\\\ + \\lambda_ {r e c 2} \\sum_ {l = 1} ^ {L} \\left(\\left\\| \\phi_ {l} \\left(I _ {c c}\\right) - \\phi_ {l} \\left(I _ {c}\\right) \\right\\| _ {2} + \\left\\| \\phi_ {l} \\left(I _ {s s}\\right) - \\phi_ {l} \\left(I _ {s}\\right) \\right\\| _ {2}\\right), \\tag {8} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.306, + 0.893, + 0.366 + ], + "angle": 0, + "content": "where \\( I_{cc} \\) and \\( I_{ss} \\) are the reconstructed images when both the input content and style images are \\( I_{c} \\) and \\( I_{s} \\), respectively. \\( \\phi_l \\) refers to the \\( l_{th} \\) layer in VGG. We chose features from Relu2_1, Relu3_1, Relu4_1 and Relu5_1 layers." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.366, + 0.892, + 0.41 + ], + "angle": 0, + "content": "REMD Loss \\(\\mathcal{L}_{\\text{REMD}}\\) [25] adapts the relaxed earth mover distance (REMD) to align the manifold surface of style features. It is formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.512, + 0.419, + 0.892, + 0.466 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {R E M D} = \\max \\left(\\frac {1}{W _ {s} H _ {s}} \\sum_ {i} \\min _ {j} C _ {i j}, \\frac {1}{W _ {c} H _ {c}} \\sum_ {j} \\min _ {i} C _ {i j}\\right), \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.478, + 0.892, + 0.509 + ], + "angle": 0, + "content": "where \\( C_{ij} \\) denotes the pair-wise cosine distance matrix between the \\( i_{th} \\) and \\( j_{th} \\) feature vector in \\( Z_{cs} \\) and \\( Z_{s} \\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.522, + 0.634, + 0.54 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.547, + 0.894, + 0.699 + ], + "angle": 0, + "content": "We train our proposed method on content images from the MS-COCO [30] dataset, and style images from WikiArt [23] database. Each dataset has around 80k images. The training images are first resized to 512, and then \\(256 \\times 256\\) patches are randomly cropped from the images as inputs. Note that our model can be applied to images of any resolution at the testing stage. Our model is implemented by PyTorch [34]. The Adam [24] is adopted as the optimization solver. We train our model for 160k iterations with a batch size of 16. The learning rate is set to 0.0001." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.699, + 0.894, + 0.805 + ], + "angle": 0, + "content": "The hyperparameters in loss functions are set to \\(\\lambda_{cont} = 1\\), \\(\\lambda_{rec} = 1\\), \\(\\lambda_{sty} = 1\\), \\(\\lambda_{rec1} = 20\\), \\(\\lambda_{rec2} = 0.5\\), \\(\\lambda_{REMD} = 3\\), and \\(\\lambda_{adv} = 1\\). The encoder is a pretrained VGG-16 network [40], whose parameters are fixed during model training. A multi-scale discriminator is adopted from [43]. We update the discriminator one time after two generator iterations." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.814, + 0.869, + 0.83 + ], + "angle": 0, + "content": "4.1. Comparison with State-of-the-Art Methods" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.84, + 0.894, + 0.902 + ], + "angle": 0, + "content": "Qualitative Evaluation. As shown in Figure 4, we present qualitative results of different style transfer methods i.e., AdaConv [2], DRB-GAN [48], statistics matching based method like AdaIN [15], attention based methods including" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10087" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.089, + 0.891, + 0.507 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.289, + 0.51, + 0.68, + 0.522 + ], + "angle": 0, + "content": "Figure 4. Qualitative performance comparison on stylized results." + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.526, + 0.893, + 0.554 + ], + "angle": 0, + "content": "Table 2. Quantitative comparison with state-of-the-art methods. We compute the average style loss and the LPIPS score of different methods to indicate how well the style and content are transferred." + }, + { + "type": "table", + "bbox": [ + 0.078, + 0.556, + 0.897, + 0.624 + ], + "angle": 0, + "content": "
MethodAdaIN'17LST'19AvatarNet'18SANet'19IEC'21DRB-GAN'21AdaAttN'21MAST'21AdaConv'21StrTr²²Ours
Sty Loss↓1.772.675.911.411.811.511.14-1.041.070.98
LPIPS ↓0.370.330.340.360.310.330.320.320.420.330.30
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.633, + 0.47, + 0.725 + ], + "angle": 0, + "content": "AdaAttN [31] and IEC [5], and feature modification methods like \\(\\mathrm{StrTr}^2\\) [8] and MAST [16]. For a fair comparison, we deploy all competing methods for style transfer on images of the smaller dimension resized to 512 while the aspect ratio is preserved. Note that we use the public released code and follow the default configurations for testing." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.473, + 0.903 + ], + "angle": 0, + "content": "The comparison in Figure 4 shows the outperformance of our method in terms of visual quality. These images produced by our method faithfully reflect the style characters (e.g., stroke sizes and colors) with no artifact in the regions, and most importantly, they preserve the structural similarity of the content images. On the contrary, AdaIN [15] and MAST [16] fail to generate sharp details and fine strokes. AdaConv [2] yields distorted patterns as it cannot always recover the original style patterns. We also observe nonnegligible artificial structures in those images obtained by \\(\\mathrm{StrTr}^2\\) [8], DRB-GAN [48] and AdaIN [15]. These meth" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.634, + 0.895, + 0.71 + ], + "angle": 0, + "content": "ods struggle to preserve the consistency in semantic regions such as the sky. In addition, AdaAttN [31] and IEC [5] and MAST [16] tend to overly preserve the structural similarity and fail to transfer the style to the content image, which makes the results look like the content images." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Quantitative Evaluation. (1) Style Loss. Following WCT [28], we adopt the style loss to measure the style consistency between the generated stylizations and the style references. The results of different methods are reported in Table 2. As we can observe, our method achieves the lowest style loss, which indicates that our method mostly transfers the style information to the output. (2) LPIPS. We conduct LPIPS to measure the stability and consistency of rendered video clips by following IEC [5]. This metric is to compute the average perceptual distances between consecutive frames and the lower LPIPS score indicates a better stable and consistent performance. We synthesize 10 video clips" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "10088" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.089, + 0.894, + 0.26 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.262, + 0.893, + 0.292 + ], + "angle": 0, + "content": "Figure 5. Qualitative performance comparison on stylized results of different model variants. The results of SANet are also listed as reference. Please zoom in to observe the detailed difference." + }, + { + "type": "image", + "bbox": [ + 0.092, + 0.304, + 0.457, + 0.446 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.448, + 0.47, + 0.476 + ], + "angle": 0, + "content": "Figure 6. Effectiveness of the Content-based Gating Module (CGM). The results of AdaAttN are also listed as reference." + }, + { + "type": "image", + "bbox": [ + 0.152, + 0.484, + 0.393, + 0.608 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.609, + 0.471, + 0.667 + ], + "angle": 0, + "content": "Figure 7. Impact of grouped shuffling: we randomly take 100 content-style pairs to create stylizations. From their feature maps extracted by VGG network, we measure the mean activation value channel-wisely and report the overall distribution." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.685, + 0.47, + 0.716 + ], + "angle": 0, + "content": "for each method. In Table 2 we observe that our approach produces the lowest LPIPS score among all methods." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Efficiency Analysis. In Table 1, we compare the inference time of different methods on image resolutions of \\(256 \\times 256\\) and \\(512 \\times 512\\). All experiments are conducted using a single Tesla V100 GPU. Our method can achieve 25 fps on \\(512 \\times 512\\) images, which is comparable with SOTA methods such as AdaAttN and IEC. It worth pointing out that the operation of our style kernel takes FLOPs cost of \\(H_{c} \\times W_{c} \\times C_{in} \\times (k + k + 1)\\) while vanilla convolution operation has FLOPS cost of \\(H_{c} \\times W_{c} \\times C_{out} \\times (C_{in} \\times k \\times k + 1)\\). In Table 3, we compare the inference time given different kernel sizes. Note we set \\(k = 3\\) as a trade-off between the efficiency and performance." + }, + { + "type": "table_caption", + "bbox": [ + 0.549, + 0.305, + 0.842, + 0.318 + ], + "angle": 0, + "content": "Table 3. Results of different sizes of style kernel." + }, + { + "type": "table", + "bbox": [ + 0.513, + 0.32, + 0.877, + 0.397 + ], + "angle": 0, + "content": "
SettingSty Loss↓LPIPS ↓T256 ↓T512 ↓
k=11.040.300.0150.034
k=30.980.300.0170.035
k=50.970.310.0210.044
" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.405, + 0.654, + 0.423 + ], + "angle": 0, + "content": "4.2. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.429, + 0.892, + 0.46 + ], + "angle": 0, + "content": "We conduct ablation studies to highlight the effectiveness of different modeling components used by our method." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.463, + 0.893, + 0.585 + ], + "angle": 0, + "content": "Effectiveness of Style Kernel. This module works to fully explore the point-wise semantic structure correlation to modulate local content features for better artistic style transfer. As shown in Figure 5, our dynamic style kernels make it possible to transfer both the globally aggregated content- style aligned features to local regions in the content images. This ensures our new scheme \"style kernel\" works well on consistent stylization with well preserved structure." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.588, + 0.892, + 0.71 + ], + "angle": 0, + "content": "Effectiveness of Grouped Shuffling. To verify this module, we report the statistic distribution of activation strength in Table 7. The distribution gap between the results and real artworks is significantly reduced via using grouped shuffling. Without using GS module, the model fails to produce stylizations consistent to the style reference as shown in Figure 5. This demonstrates that the GS shrinks the statistic gap between the generated images and the style images." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.712, + 0.892, + 0.834 + ], + "angle": 0, + "content": "Effectiveness of CGM. We summarized the results of our model w/ and w/o CGM in Figure 6. The model w/o CGM produces images containing regions with corrupted patterns and the stylization is not consistent to the style reference. While our model w/ CGM faithfully preserves the completeness of semantic regions. This is because our CGM aims to select focusing regions, where query points can aggregate style information from fairly correlated nodes." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.844, + 0.671, + 0.858 + ], + "angle": 0, + "content": "4.3. More Discussions" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Generalization of CGM. Our content-based gating modulation can be flexibly deployed as a plug-in module. To ver-" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10089" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.089, + 0.197, + 0.262 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.136, + 0.265, + 0.176, + 0.275 + ], + "angle": 0, + "content": "Content" + }, + { + "type": "image", + "bbox": [ + 0.198, + 0.089, + 0.314, + 0.261 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.253, + 0.265, + 0.28, + 0.275 + ], + "angle": 0, + "content": "Style" + }, + { + "type": "image", + "bbox": [ + 0.315, + 0.089, + 0.426, + 0.262 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.356, + 0.265, + 0.39, + 0.275 + ], + "angle": 0, + "content": "SANet" + }, + { + "type": "image", + "bbox": [ + 0.427, + 0.089, + 0.543, + 0.262 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.455, + 0.265, + 0.527, + 0.275 + ], + "angle": 0, + "content": "SANet + CGM" + }, + { + "type": "image", + "bbox": [ + 0.543, + 0.089, + 0.657, + 0.262 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.595, + 0.265, + 0.615, + 0.275 + ], + "angle": 0, + "content": "IEC" + }, + { + "type": "image", + "bbox": [ + 0.657, + 0.089, + 0.773, + 0.262 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.681, + 0.265, + 0.74, + 0.275 + ], + "angle": 0, + "content": "IEC + CGM" + }, + { + "type": "image", + "bbox": [ + 0.773, + 0.089, + 0.888, + 0.262 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.805, + 0.265, + 0.83, + 0.275 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.278, + 0.892, + 0.307 + ], + "angle": 0, + "content": "Figure 8. Generalization of our Content-based Gating Module (CGM). By replacing the attention module in SANet and IEC with our CGM, the artifacts and distorted regions in the results of original SANet and IEC are removed and the semantic regions are well preserved." + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.316, + 0.209, + 0.444 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.106, + 0.446, + 0.184, + 0.457 + ], + "angle": 0, + "content": "Content & Style" + }, + { + "type": "image", + "bbox": [ + 0.211, + 0.316, + 0.338, + 0.444 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.256, + 0.446, + 0.282, + 0.456 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image", + "bbox": [ + 0.339, + 0.316, + 0.466, + 0.444 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.371, + 0.446, + 0.426, + 0.456 + ], + "angle": 0, + "content": "DRB-GAN" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.46, + 0.469, + 0.501 + ], + "angle": 0, + "content": "Figure 9. Comparisons on video style transfer. The 1st column lists 2 frames from a video clip as content images. The style image is at the bottom-right corner." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.514, + 0.469, + 0.679 + ], + "angle": 0, + "content": "if the generalization, we conduct experiments by replacing the attention module in SANet and IEC with our CGM module. The refactored models are denoted as SANet + CGM and IEC + CGM. We train these models with the default settings and compare the performances in Figure 8. We can observe there are nonneglectable artifacts and distorted regions in the results of original SANet and IEC. By plugging-in our CGM, the artifacts are removed and the semantic regions are well preserved. This further proves the effectiveness of our CGM in aggregating semantically consistent information." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.684, + 0.469, + 0.821 + ], + "angle": 0, + "content": "Real-world Video Style Transfer. To verify the performance on real-world video stylization, we collect a 1080P video clip consist of 1377 images and compare our method with DRB-GAN [48]. As shown in Figure 9, our approach outperforms existing style transfer methods in terms of style consistency and stability. This can be attributed to the fact that our style kernels are good at transferring the globally aggregated and locally semantic-aligned style features to local regions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Social Impact and Future Work. Our model achieves impressive image stylizations with well preserved content structure and consistent style characteristics, as shown in Figure 10. This can definitely benefit our society. In the future, we will incorporate text information for text condi" + }, + { + "type": "image", + "bbox": [ + 0.52, + 0.315, + 0.764, + 0.544 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.627, + 0.546, + 0.652, + 0.556 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image", + "bbox": [ + 0.767, + 0.316, + 0.874, + 0.43 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.767, + 0.431, + 0.874, + 0.544 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.809, + 0.546, + 0.836, + 0.557 + ], + "angle": 0, + "content": "Style" + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.56, + 0.892, + 0.588 + ], + "angle": 0, + "content": "Figure 10. Demonstration of the performance of our method in terms of style consistency and structural similarity." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.597, + 0.665, + 0.612 + ], + "angle": 0, + "content": "tioned image stylization." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.625, + 0.619, + 0.641 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.651, + 0.892, + 0.832 + ], + "angle": 0, + "content": "In this paper, we present a new scheme \"style kernel\" for artistic style transfer. Our method learns an attention map with focusing regions using the proposed content-based gating operator. The style feature is then aligned to match the semantics in the content feature based on the learned attention map. In the style kernel generation module, the dynamic parameters \"style kernel\" are learned from the content-style aligned feature and then applied to modulate the content feature for style transfer. Extensive experimental results demonstrate the remarkable performance of our model in generating synthetic style images with better quality than the state-of-the-art." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.846, + 0.66, + 0.863 + ], + "angle": 0, + "content": "Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.891, + 0.901 + ], + "angle": 0, + "content": "This research was sponsored by Prof. Yongwei Nie's Natural Science Foundation of China (62072191)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10090" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.183 + ], + "angle": 0, + "content": "[1] Nicolas Carion, Francisco Massa, Gabriel Synnaeve, Nicolas Usunier, Alexander Kirillov, and Sergey Zagoruyko. 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In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 2482-2491, 2019. 3" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.894 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "10092" + } + ] +] \ No newline at end of file diff --git a/2023/Learning Dynamic Style Kernels for Artistic Style Transfer/d30e13bb-a2dd-4b9a-b639-90ba30ba2cc5_origin.pdf b/2023/Learning Dynamic Style Kernels for Artistic Style Transfer/d30e13bb-a2dd-4b9a-b639-90ba30ba2cc5_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..4edee3d2382d2527e438d0fb8a319544736a50d1 --- /dev/null +++ b/2023/Learning Dynamic Style Kernels for Artistic Style Transfer/d30e13bb-a2dd-4b9a-b639-90ba30ba2cc5_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:77af72306a75d100fe893e3f78919a5c0b724bc7383e7f7aa11fb729c6046eb6 +size 9252811 diff --git a/2023/Learning Dynamic Style Kernels for Artistic Style Transfer/full.md b/2023/Learning Dynamic Style Kernels for Artistic Style Transfer/full.md new file mode 100644 index 0000000000000000000000000000000000000000..772a64059bf064daa1d1435985c2d187b994cb40 --- /dev/null +++ b/2023/Learning Dynamic Style Kernels for Artistic Style Transfer/full.md @@ -0,0 +1,344 @@ +# Learning Dynamic Style Kernels for Artistic Style Transfer + +Wenju Xu +OPPO US Research Center +Palo Alto, CA, USA +xuwenjul23@gmail.com + +Chengjiang Long Meta Reality Lab Burlingame, CA, USA clong1@meta.com + +Yongwei Nie +South China University of Technology +Guangzhou, Guangdong, China +nieyongwei@scut.edu.cn + +![](images/313ddfc5b7669a445d989fbdc7ad86c9f2ef5a4168fa818e6b8ebcd5bbe24a61.jpg) +Figure 1. The first two rows show comparisons with state-of-the-art methods. The last row shows results of our proposed method, which can faithfully transfer various styles and preserve the content structure. + +# Abstract + +Arbitrary style transfer has been demonstrated to be efficient in artistic image generation. Previous methods either globally modulate the content feature ignoring local details, or overly focus on the local structure details leading to style leakage. In contrast to the literature, we propose a new scheme "style kernel" that learns spatially adaptive kernels for per-pixel stylization, where the convolutional kernels are dynamically generated from the global style-content aligned feature and then the learned kernels are applied to modulate the content feature at each spatial position. This new scheme allows flexible both global and local interactions between the content and style features such that the wanted styles can be easily transferred to the content image while at the same time the content structure can be easily preserved. To further enhance the flexibility of our style transfer method, we propose a Style Alignment Encoding (SAE) module complemented with a Content-based Gating Modulation (CGM) module for learning the dynamic style kernels in focusing regions. Extensive experiments strongly demonstrate that our proposed method outperforms state-of-the-art methods and exhibits superior performance in terms of visual quality and efficiency. + +# 1. Introduction + +Artistic style transfer [48] refers to a hot computer vision technology that allows us to recompose the content of an image in the style of an artistic work. Figure 1 shows several vivid examples. We might have ever imagined what a photo might look like if it were painted by a famous artist like Pablo Picasso or Van Gogh. Now style transfer is the computer vision technique that turns this into a reality. It has great potential values in various real-world applications and therefore attracts a lot of researchers to constantly put efforts to make progress towards both quality and efficiency. + +Most of existing style transfer works [6, 15, 18, 26, 33] either globally modulate the content feature ignoring local details or overly focus on the local structure details leading to style leakage. In particular, [15, 18] seeks to match global statistics between content and style images, resulting in inconsistent stylizations that either remain large parts of the content unchanged or contain local content with distorted style patterns. SANet [33] and AdaAttN [31] improve the content similarity by learning attention maps that match the semantics between the style and stylized images, but these methods tend to distort object instances when improper style patterns are involved. Recently, IEC [5] adopts contrastive learning to pull close both the content and style representations between input and output images. MAST [16] + +seeks to balance the style and content via manifold alignment. Although both IEC and MAST have achieved some success in most cases, they are still far from satisfactory to well balance two important requirements, i.e., style consistency and structure similarity. + +In this paper, we develop a novel style transfer framework in a manner of encoder-decoder structure, as illustrated in Figure 2, which contains two important modules: (1) a Style Alignment Encoding (SAE) module enhanced by Content-based Gating Modulation (CGM), which is used to generate content-style aligned features, and (2) a Style Kernel Generation (SKG) module used to transform the output features of SAE to convolutional kernels. In such a framework, we propose a new style transfer scheme, "style kernel", which treats the features of the style images as dynamic convolutional kernels and then transfer the style information to the content image by convolving the content image by the learned dynamic style kernels. This allows fine-grained local interactions between the style and content features, the flexibility of which makes both style transferring and content structure preserving much easier. + +To enforce the global correlation between the content and style features, we simulate the self-attention mechanism of Transformer [41] in the SAE module. This treats the content and style features as the queries and keys of the self-attention operator respectively and computes a large attention map the elements of which measure for each local content context the similarity to each local style context. With the attention map, we can aggregate for each pixel of the content image all the style features in a weighted manner to obtain content-style aligned features. We also design a Content-based Gating Modulation (CGM) operator that further thresholds the attention map and zeros the places where similarities are too small, seeking an adaptive number of correlated neighbors as a focusing region for each query point. Then, we use another set of convolutions that constitute the SKG module to further transform the content-style aligned features, and view (reshape) the output of SKG as dynamic style kernels. In order to improve the efficiency of the dynamic convolutions, SKG predicts separable local filters (two 1D filters and a bias) instead of a spatial 2D filter that has more parameters. The learned style kernels already integrate the information of the given content and style images. We further apply the learned dynamic style kernels to the content image feature for transferring the target style to the content image. + +We shall emphasize that unlike "style code" in AdaIN [15], DRB-GAN [48], and AdaConv [2] modeled as the dynamic parameters (e.g. mean, variance, convolution kernel) which are shared over all spatial positions globally without distinguishing the semantic regions, the learned dynamic kernels via our "style kernel" are point-wisely modeled upon the globally style-content aligned feature, and + +therefore is able to make full use of the point-wise semantic structure correlation to modulate content feature for better artistic style transfer. Our learned dynamic style kernels are good at transferring the globally aggregated and locally semantic-aligned style features to local regions. This ensures our style transfer model that works well on consistent stylization with well preserved structure, overcoming the shortages of existing style transfer methods which either globally modulate the content feature ignoring local details (e.g. AdaIN, WCT [28]) or overly focus on the local structure details leading to style leakage (e.g. AdaAttN [31] and MAST [16]). + +The main contributions of this work are 3-fold as follows: + +- We are the first to propose the "style kernel" scheme for artistic style transfer, which converts the globally style-content alignment features into position pointwisely dynamic convolutional kernels to convolve the features of content images together for style transfer. +- We design a novel architecture, i.e. SAE and CGM, to generate the dynamic style kernels by employing the correlation between the content and style image adaptively. +- Extensive experiments demonstrate that our method produces visually plausible stylization results with fine-grained style details and coherence content with the input content images. + +# 2. Related Works + +Artistic Style Transfer was initially solved by Gatys et al. [12] a pre-trained neural network to synthesize stylizations in an iterative optimization manner, and then a bunch of neural style transfer methods [3,5,11,18,31,38,39] were developed. In particular, AdaIN [15] introduces the adaptive instance normalization to globally match the statistics between the content and style features. For the same purpose, WCT [28] utilizes the whitening and coloring transforms, and LST [27] introduces a linear transformation matrix predicted on content and style features. [7,22,42,51] seek different ways to match the feature distribution. SANet [33] seeks to align the semantics between the content and style features via a self-attention network. $\mathrm{StrTr}^2$ [8] resorts to the transformers [41, 47]. To further preserve the content details, AdaAttN [31] perform attentive normalization on per-point basis, IEC [5] employs stylization relations with contrastive learning and MAST [16] introduces manifold alignment to balance the style and content. However, emphasizing on content details prevents the transfer adequate style information to some degree, and results in style leakage. Recently, dynamic network based style transfer methods [3, 15, 18, 38] extend the model generalization. As a generic extension of AdaIN, AdaConv [2] introduces a parameter network that predicts network parameters used by + +![](images/887aa71401cc7c9022db7435e7967a0ee5c94bac99576acbe9a7444f7f293b76.jpg) +Figure 2. Overview of our proposed scheme "style kernel". A pretrained VGG encoder takes in the content and style image as input to produce the content feature $Z_{c}$ and style feature $Z_{s}$ . The style-alignment encoding model employs an attention mechanism by taking the $Z_{c}$ as query and $Z_{s}$ as key and value to exploit their semantics matching. The content-based gating module (CGM) learns a dynamic threshold and adaptively adjusts attention weights for a globally content-style aligned feature $Z_{cs}$ , which is transformed by style kernel generation module to dynamic style kernels. Finally, we conduct convolution operations on the channel-wisely grouped and shuffled (GS) content feature with the learned dynamic style kernels to get $\bar{Z}_{cs}$ fed into the decoder to produce the stylizations. + +another network for style transfer. DRB-GAN [48] models "style code" as the global mean and variance for dynamic convolutions to conduct style transfer. Different from all the above methods, we propose a new scheme "style kernel" to learn dynamic convolutional kernels from the style-content alignment feature to point-wisely modulate the content feature for artistic style transfer. + +Self-Attention Mechanism is introduced in Transformer [41] as a new attention mechanism. Similar to non-local neural networks [13,21,41,45], Transformer directly works on sequences of image patches to aggregate information for long-range dependencies. The recent researches demonstrate it has been successfully applied in various vision tasks like image recognition [4, 10, 14, 29], object detection [1, 44, 46], image captioning [9], image enhancement [49, 50], and text conditioned image generation [35, 37]. Our model takes the self-attention mechanism to align the semantics of the style feature to that of the content image. + +Dynamic Network consists of convolution layers for which the filter parameters are predicted by another sub-network. Recently, there is rapid progress in vision applications [17, 32, 36, 48, 52] that benefits from dynamic network for image/video enhancement. [19] employs dynamic upsampling filters for high-resolution image reconstruction. [52] predicts filters from spatio-temporal features for video deblurring. Differently, our StyleKernel learns spatially adaptive kernel for per-pixel stylization. + +# 3. Our Method + +While existing dynamic kernel based methods [2, 15, 48] can efficiently generate stylizations, we observe that their + +visual-quality is limited in two aspects. (1) As the dynamic kernels are predicted based on the style feature without distinguishing the content-style correlation, the transferred style only globally reflects the style characters of the style image, ruining local content details. (2) The completeness of semantic regions is not well preserved. This is because the dynamic kernels used by the layers are spatially shared. + +To alleviate these problems, we propose to align the semantics of the style image to those of the content image and transform the content features for per-pixel stylization in a separable convolution manner. The pipeline of our proposed model is shown in Figure 2. The content image $I_{c}$ and style image $I_{s}$ are first fed into a fixed VGG encoder to produce the content and style feature maps $Z_{c} \in \mathbb{R}^{H_{c} \times W_{c} \times C_{in}}$ and $Z_{s} \in \mathbb{R}^{H_{s} \times W_{s} \times C_{in}}$ , where $H, W$ and $C_{in}$ represent the height, width and channel size of the feature map, respectively. Then in SAE, we align the content and style features by using the content features $Z_{c}$ as the queries and the style features $Z_{s}$ as the keys in a self-attention mechanism. The CGM module is conducted on the attention map to seek a focusing region for each query point. Thereafter, we predict by SKG the dynamic style kernels $F$ from the content-style aligned features $Z_{cs}$ . Finally, we group and shuffle (GS) $Z_{c}$ to break down the correlation within the channel-wise feature and apply convolutions parameterized by the learned kernels to the grouped and shuffled $Z_{c}$ to obtain $\bar{Z}_{cs}$ which is further decoded to the target stylized image by a decoder. + +# 3.1. Style Alignment Encoding + +This module takes the content and style features as input, aligns between them by learning content-style alignment attention, and finally attentively adjusts the attention map by + +![](images/64286c43330aafe74e9fc9c07d79b037222aac4d2c22970b76d6546ed7781a75.jpg) +Content & Style + +![](images/5d37e1cb30e8d6a1be3a2c68d9f3944d2b4f98ad317e754b858ab8e2ceeb5aa6.jpg) +SANet + +![](images/7b8817ec17e7eb42d6485be6105e06f3589a5374ccf96cf5637eb2418e9cd9b2.jpg) +$\mathrm{SANet} + \mathrm{topK}$ +Figure 3. The impact of the feature aggregation. Left: We compare the performances of models conducting different feature aggregation strategies. The SANet takes an attention module to aggregate information across all the nodes. The SANet + topK only acquires information from the nodes with top K attention scores. SANet + CGM takes our content-based gating modulation to aggregate information from a dynamic number of nodes. Our CGM is learned to masked out nodes with low attention score, leading to stylizations with well preserved structure content. The second row shows the distributions of selected nodes (highlighted in colors) and the focused areas (masked-out by black rectangles) learned by CGM. Right: we demonstrate the relation between the content/style loss and the number of selected nodes. + +![](images/211aa4e2cc0e5ee06e7b753747b1bce36c4f77839ea5bf250820841c4a7453aa.jpg) +$\mathrm{SANet} + \mathrm{CGM}$ + +![](images/fc182095be7056785c527fc4b43c4cfb17847f1a875c487850bb0ae5984452a5.jpg) +Ours + +![](images/edf5695a5d2536fbe27159e4d9c36b5aa9e4a75c2366a5acd0d6ee0c9923f7b2.jpg) + +a content-based gating modulation module. + +Content-Style Alignment Attention. By taking the content feature $Z_{c}$ as the query, and the style feature $Z_{s}$ as the key and value, we compute the content-style alignment attention that seeks to aggregate information from the style feature map according to the matched content information. This warps the style feature to align with the content feature. To this end, we calculate the pairwise feature correlation $\mathcal{M}^{s\rightarrow c}\in \mathbb{R}^{H_cW_c\times H_sW_s}$ . This results in an attention map $\mathcal{A}\in \mathbb{R}^{H_cW_c\times H_sW_s}$ by: + +$$ +\mathcal {A} (u, v) = \operatorname {s o f t m a x} (\alpha \mathcal {M} ^ {s \rightarrow c}) = \operatorname {s o f t m a x} (\alpha \frac {Z _ {c} (u) ^ {T} Z _ {s} (v)}{\| Z _ {c} (u) \| \| Z _ {s} (v) \|}), \tag {1} +$$ + +where $\alpha$ is the coefficient that controls the sharpness of the softmax. $Z_{c}(u)$ and $Z_{s}(v)$ stands for the feature of $Z_{c}$ and $Z_{s}$ at position $u\in \mathbb{R}^{H_cW_c}$ and $v\in \mathbb{R}^{H_sW_s}$ . The $u$ -th row of the attention map $\mathcal{A}$ represents similarities between the $u$ -th node of the content feature and all the nodes of the style feature. + +To align the semantics of the style feature to that of the content feature, we aggregate information in $Z_{s}$ based on the attention score map $\mathcal{A}$ and obtain $Z_{cs} \in \mathcal{R}^{H_c W_c \times C}$ by calculating their weighted average: + +$$ +Z _ {c s} (u) = \sum_ {v} \mathcal {A} (u, v) \cdot Z _ {s} (v). \tag {2} +$$ + +where $Z_{cs}(u)$ represents the feature at position $u$ of $Z_{cs}$ . In the following, we denote the $Z_{cs} \in \mathcal{R}^{H_c \times W_c \times C}$ , which is obtained by reshaping. + +In Eq. 2, all style features are taken into consideration when computing the content-style aligned features $Z_{cs}$ . We find that this yields inferior results because many irrelevant features are involved into the computation. We therefore introduce the Content-based Gating Modulation (CGM) operator which creates dynamic thresholds that further filter out irrelevant style features. + +Content-based Gating Modulation is used to further adapt the attention map by the content feature $Z_{c}$ . Taking $Z_{c}$ as input, we employ a convolution network $E_{f}$ to generate a scale parameter $\lambda$ and a bias parameter $\beta$ . We then perform a row average operator on the attention matrix $A$ by: + +$$ +\mathcal {A} _ {r} (i) = \frac {1}{H _ {c}} \sum_ {j = 1} ^ {H _ {c}} \mathcal {A} _ {i, j}, \forall i \in [ 1, W _ {c} ]. \tag {3} +$$ + +where $\mathcal{A}_r$ is the obtained column vector after the average operator. Then, we obtain the threshold matrix $\mathcal{T}$ by the following equation: + +$$ +\mathcal {T} = \mathcal {A} (\lambda \mathcal {A} _ {r} + \beta). \tag {4} +$$ + +Finally, we update the attention $\mathcal{A}$ by: + +$$ +\bar {\mathcal {A}} = \mathcal {A} \cdot \operatorname {S i g n} (\mathcal {A} - \mathcal {T}), \tag {5} +$$ + +where the dot indicates element-wise multiplication and Sign is a function returning 1 given positive input and 0 otherwise. We use $\bar{A}$ instead of $\mathcal{A}$ in Eq. 2 to compute $Z_{cs}$ . + +$\bar{\mathcal{A}}$ is a dynamically learned mask, with which our model creates focused areas and filter out irrelevant style features. This allows our model to aggregate features from fairly correlated features, which is essential to preserve the completeness of semantic regions. In Figure 3 we compare the intermediate visualizations and stylized results. We see that the CGM works to recognize focused areas, where the style information is aggregated by the query point. By contrast, the attention learned by the SANet is distributed over the entire image, including visually less correlated points, such as corners and background. + +# 3.2. Style Kernel Generation + +We propose the Style Kernel (SK) Generation network to further transform the content-style aligned features of SAE to dynamic style kernels. It takes the globally content-style + +Table 1. Average inference time, measured on a Tesla V100 GPU, for different methods with a batch size of 1 and an input image of $256 \times 256$ and $512 \times 512$ . + +
MethodAdaIN'17LST'19AvatarNet'18SANet'19IEC'21DRB-GAN'21AdaAttN'21MAST'21AdaConv'21StrTr²'22Ours
T256 ↓0.0040.0040.8730.0110.0120.0050.0240.1260.0190.0340.017
T256 ↓0.0050.0050.9620.0370.0210.0060.0420.2390.0360.0860.035
+ +aligned feature $Z_{cs}$ as input to predict the dynamic style filters $F, B = \{F_1^{ij}, F_2^{ij}, B^{ij}\}$ . + +Given the content-style aligned feature $Z_{cs}$ , we take two convolution layers to predict the filters $F \in \mathbb{R}^{H_c \times W_c \times C \times 2k}$ , which has two 1-dim filters $F_1 = \{F_1^{ij}\}$ and $F_2 = \{F_2^{ij}\}$ of the sizes $k \times 1$ and $1 \times k$ , respectively, and one bias vector $B = \{B^{ij}\} \in \mathbb{R}^{H_c \times W_c \times C \times 1}$ . Finally, we conduct convolution operations on the content feature $Z_{c}$ with the learned dynamic style kernels $F_1$ , $F_2$ and $B$ . The output after the convolutions is the feature called $\bar{Z}_{cs}$ : + +$$ +\bar {Z} _ {c s} = \frac {Z _ {c} - \mu}{\sigma} * F _ {1} * F _ {2} + B, \tag {6} +$$ + +where $\mu$ and $\sigma$ are the affine parameters in normalization layer and $^*$ is the convolution operator. $\bar{Z}_{cs}$ is then passed to the decoder to generate the stylized image $I_{cs}$ . + +Remarks. Note that different from "style code" [48] modeled as the parameters (e.g. mean and variance) which are shared over all spatial positions globally without taking different semantic regions into consideration, our learned dynamic style kernels are position point-wisely inferred from the globally style-content aligned feature, and therefore are able to fully explore the point-wise semantic structure correlation to modulate local content feature for better artistic style transfer. Our dynamic style kernels make it possible to transfer both the globally aggregated content-style aligned features to local regions in the content images. This ensures our new scheme "style kernel" works well on consistent stylization with well preserved structure, and alleviates the shortages of existing style transfer methods [15, 16, 28, 31] which either globally modulate the content feature ignoring local details or overly focus on the local structure details leading to style leakage. + +# 3.3. Loss Functions + +The loss function is formulated with an adversarial loss $\mathcal{L}_{adv}$ , a reconstruction loss $\mathcal{L}_{rec}$ , a REMD loss $\mathcal{L}_{REMD}$ , a style loss $\mathcal{L}_{sty}$ [20] and a content loss $\mathcal{L}_{cont}$ [33] as: + +$$ +\mathcal {L} = \mathcal {L} _ {\text {a d v}} + \lambda_ {\text {r e c}} \mathcal {L} _ {\text {r e c}} + \lambda_ {\text {c o n t}} \mathcal {L} _ {\text {c o n t}} + \lambda_ {\text {s t y}} \mathcal {L} _ {\text {s t y}} + \lambda_ {\text {R E M D}} \mathcal {L} _ {\text {R E M D}} \tag {7} +$$ + +where $\lambda_{adv}$ , $\lambda_{rec}$ , $\lambda_{cont}$ , $\lambda_{sty}$ and $\lambda_{REMD}$ are the hyperparameters used to balance the loss during training. + +Reconstruction Loss $\mathcal{L}_{rec}$ is defined as: + +$$ +\begin{array}{l} \mathcal {L} _ {r e c} = \lambda_ {r e c 1} \big (| | I _ {c c} - I _ {c} | | _ {2} + | | I _ {s s} - I _ {s} | | _ {2} \big) \\ + \lambda_ {r e c 2} \sum_ {l = 1} ^ {L} \left(\left\| \phi_ {l} \left(I _ {c c}\right) - \phi_ {l} \left(I _ {c}\right) \right\| _ {2} + \left\| \phi_ {l} \left(I _ {s s}\right) - \phi_ {l} \left(I _ {s}\right) \right\| _ {2}\right), \tag {8} \\ \end{array} +$$ + +where $I_{cc}$ and $I_{ss}$ are the reconstructed images when both the input content and style images are $I_{c}$ and $I_{s}$ , respectively. $\phi_l$ refers to the $l_{th}$ layer in VGG. We chose features from Relu2_1, Relu3_1, Relu4_1 and Relu5_1 layers. + +REMD Loss $\mathcal{L}_{\text{REMD}}$ [25] adapts the relaxed earth mover distance (REMD) to align the manifold surface of style features. It is formulated as: + +$$ +\mathcal {L} _ {R E M D} = \max \left(\frac {1}{W _ {s} H _ {s}} \sum_ {i} \min _ {j} C _ {i j}, \frac {1}{W _ {c} H _ {c}} \sum_ {j} \min _ {i} C _ {i j}\right), \tag {9} +$$ + +where $C_{ij}$ denotes the pair-wise cosine distance matrix between the $i_{th}$ and $j_{th}$ feature vector in $Z_{cs}$ and $Z_{s}$ . + +# 4. Experiments + +We train our proposed method on content images from the MS-COCO [30] dataset, and style images from WikiArt [23] database. Each dataset has around 80k images. The training images are first resized to 512, and then $256 \times 256$ patches are randomly cropped from the images as inputs. Note that our model can be applied to images of any resolution at the testing stage. Our model is implemented by PyTorch [34]. The Adam [24] is adopted as the optimization solver. We train our model for 160k iterations with a batch size of 16. The learning rate is set to 0.0001. + +The hyperparameters in loss functions are set to $\lambda_{cont} = 1$ , $\lambda_{rec} = 1$ , $\lambda_{sty} = 1$ , $\lambda_{rec1} = 20$ , $\lambda_{rec2} = 0.5$ , $\lambda_{REMD} = 3$ , and $\lambda_{adv} = 1$ . The encoder is a pretrained VGG-16 network [40], whose parameters are fixed during model training. A multi-scale discriminator is adopted from [43]. We update the discriminator one time after two generator iterations. + +# 4.1. Comparison with State-of-the-Art Methods + +Qualitative Evaluation. As shown in Figure 4, we present qualitative results of different style transfer methods i.e., AdaConv [2], DRB-GAN [48], statistics matching based method like AdaIN [15], attention based methods including + +![](images/d6b6fb1168881785c745bb9d5457e39f4a919107b0f5b2bdedf7cd1275be5f9e.jpg) +Figure 4. Qualitative performance comparison on stylized results. + +Table 2. Quantitative comparison with state-of-the-art methods. We compute the average style loss and the LPIPS score of different methods to indicate how well the style and content are transferred. + +
MethodAdaIN'17LST'19AvatarNet'18SANet'19IEC'21DRB-GAN'21AdaAttN'21MAST'21AdaConv'21StrTr²²Ours
Sty Loss↓1.772.675.911.411.811.511.14-1.041.070.98
LPIPS ↓0.370.330.340.360.310.330.320.320.420.330.30
+ +AdaAttN [31] and IEC [5], and feature modification methods like $\mathrm{StrTr}^2$ [8] and MAST [16]. For a fair comparison, we deploy all competing methods for style transfer on images of the smaller dimension resized to 512 while the aspect ratio is preserved. Note that we use the public released code and follow the default configurations for testing. + +The comparison in Figure 4 shows the outperformance of our method in terms of visual quality. These images produced by our method faithfully reflect the style characters (e.g., stroke sizes and colors) with no artifact in the regions, and most importantly, they preserve the structural similarity of the content images. On the contrary, AdaIN [15] and MAST [16] fail to generate sharp details and fine strokes. AdaConv [2] yields distorted patterns as it cannot always recover the original style patterns. We also observe nonnegligible artificial structures in those images obtained by $\mathrm{StrTr}^2$ [8], DRB-GAN [48] and AdaIN [15]. These meth + +ods struggle to preserve the consistency in semantic regions such as the sky. In addition, AdaAttN [31] and IEC [5] and MAST [16] tend to overly preserve the structural similarity and fail to transfer the style to the content image, which makes the results look like the content images. + +Quantitative Evaluation. (1) Style Loss. Following WCT [28], we adopt the style loss to measure the style consistency between the generated stylizations and the style references. The results of different methods are reported in Table 2. As we can observe, our method achieves the lowest style loss, which indicates that our method mostly transfers the style information to the output. (2) LPIPS. We conduct LPIPS to measure the stability and consistency of rendered video clips by following IEC [5]. This metric is to compute the average perceptual distances between consecutive frames and the lower LPIPS score indicates a better stable and consistent performance. We synthesize 10 video clips + +![](images/f232a4ce0e872f74b2d993bccf2b7954e25677987aa41a6f536de27315883cf3.jpg) +Figure 5. Qualitative performance comparison on stylized results of different model variants. The results of SANet are also listed as reference. Please zoom in to observe the detailed difference. + +![](images/ff832659753253a2c706d1da2144ef11e4deaba740d36ceabefefb850353fd9f.jpg) +Figure 6. Effectiveness of the Content-based Gating Module (CGM). The results of AdaAttN are also listed as reference. + +![](images/5d87ca800903838f16dca8eda18032ccfc8e8071b3f73514cccafeeee581c732.jpg) +Figure 7. Impact of grouped shuffling: we randomly take 100 content-style pairs to create stylizations. From their feature maps extracted by VGG network, we measure the mean activation value channel-wisely and report the overall distribution. + +for each method. In Table 2 we observe that our approach produces the lowest LPIPS score among all methods. + +Efficiency Analysis. In Table 1, we compare the inference time of different methods on image resolutions of $256 \times 256$ and $512 \times 512$ . All experiments are conducted using a single Tesla V100 GPU. Our method can achieve 25 fps on $512 \times 512$ images, which is comparable with SOTA methods such as AdaAttN and IEC. It worth pointing out that the operation of our style kernel takes FLOPs cost of $H_{c} \times W_{c} \times C_{in} \times (k + k + 1)$ while vanilla convolution operation has FLOPS cost of $H_{c} \times W_{c} \times C_{out} \times (C_{in} \times k \times k + 1)$ . In Table 3, we compare the inference time given different kernel sizes. Note we set $k = 3$ as a trade-off between the efficiency and performance. + +Table 3. Results of different sizes of style kernel. + +
SettingSty Loss↓LPIPS ↓T256 ↓T512 ↓
k=11.040.300.0150.034
k=30.980.300.0170.035
k=50.970.310.0210.044
+ +# 4.2. Ablation Study + +We conduct ablation studies to highlight the effectiveness of different modeling components used by our method. + +Effectiveness of Style Kernel. This module works to fully explore the point-wise semantic structure correlation to modulate local content features for better artistic style transfer. As shown in Figure 5, our dynamic style kernels make it possible to transfer both the globally aggregated content- style aligned features to local regions in the content images. This ensures our new scheme "style kernel" works well on consistent stylization with well preserved structure. + +Effectiveness of Grouped Shuffling. To verify this module, we report the statistic distribution of activation strength in Table 7. The distribution gap between the results and real artworks is significantly reduced via using grouped shuffling. Without using GS module, the model fails to produce stylizations consistent to the style reference as shown in Figure 5. This demonstrates that the GS shrinks the statistic gap between the generated images and the style images. + +Effectiveness of CGM. We summarized the results of our model w/ and w/o CGM in Figure 6. The model w/o CGM produces images containing regions with corrupted patterns and the stylization is not consistent to the style reference. While our model w/ CGM faithfully preserves the completeness of semantic regions. This is because our CGM aims to select focusing regions, where query points can aggregate style information from fairly correlated nodes. + +# 4.3. More Discussions + +Generalization of CGM. Our content-based gating modulation can be flexibly deployed as a plug-in module. To ver- + +![](images/641f9ab3d2660407056cf5a96f53936841ba51fe2ceabe9f174671452cde4b4f.jpg) +Content + +![](images/3d61363950f9d892e9f7c652559ef196554146e58cc321b1276b4e36a3c52d3e.jpg) +Style + +![](images/66deb22b5d879562e458d026494ba4f44fdc6acb003a002df27c9f50c6f35071.jpg) +SANet + +![](images/37b5de4e3fa216924f3549c15dd1665f65fa2375d1080eede7ec91b371d8ba9f.jpg) +SANet + CGM + +![](images/04ae50f08249f8ce823a78b5e95dba9d1f8b7da4d02cad8c3132ca69c3452b24.jpg) +IEC + +![](images/85c614c8d5634895f29882dc7ed76797cdf140d6ccb84ea4b38beda074d0a981.jpg) +IEC + CGM + +![](images/cf1c3304e24d03fbb192e2c94b8585d8b980361e544e6421b3139da0f8938a77.jpg) +Ours + +![](images/00ab646d4d0c79eae12b32c401d017fa0f92623b28262c39836a3ac8a9cf3f23.jpg) +Content & Style +Figure 9. Comparisons on video style transfer. The 1st column lists 2 frames from a video clip as content images. The style image is at the bottom-right corner. + +![](images/59a41d33b03310aaa22a29584e4e3e94e28edab51d9ccbdd89704498296b02c8.jpg) +Ours + +![](images/73c4cc5df329188124e3cfcf8af80b33c2bb2e0fca6e726e30df02d28e1d34ff.jpg) +DRB-GAN + +if the generalization, we conduct experiments by replacing the attention module in SANet and IEC with our CGM module. The refactored models are denoted as SANet + CGM and IEC + CGM. We train these models with the default settings and compare the performances in Figure 8. We can observe there are nonneglectable artifacts and distorted regions in the results of original SANet and IEC. By plugging-in our CGM, the artifacts are removed and the semantic regions are well preserved. This further proves the effectiveness of our CGM in aggregating semantically consistent information. + +Real-world Video Style Transfer. To verify the performance on real-world video stylization, we collect a 1080P video clip consist of 1377 images and compare our method with DRB-GAN [48]. As shown in Figure 9, our approach outperforms existing style transfer methods in terms of style consistency and stability. This can be attributed to the fact that our style kernels are good at transferring the globally aggregated and locally semantic-aligned style features to local regions. + +Social Impact and Future Work. Our model achieves impressive image stylizations with well preserved content structure and consistent style characteristics, as shown in Figure 10. This can definitely benefit our society. In the future, we will incorporate text information for text condi + +![](images/50b63598938ed7f852beed901fd876d7e02e8a6bf1df8870b4aaa7b0502b46c0.jpg) +Figure 8. Generalization of our Content-based Gating Module (CGM). By replacing the attention module in SANet and IEC with our CGM, the artifacts and distorted regions in the results of original SANet and IEC are removed and the semantic regions are well preserved. +Ours +Figure 10. Demonstration of the performance of our method in terms of style consistency and structural similarity. + +![](images/fb7885e43e8ffb8cf351d96e7369ff28a07e00438a44c54e4849428448612b40.jpg) + +![](images/7d497f3e307bdf49abe266035da881092573f73c9331a27ccbd21564cdb76dac.jpg) +Style + +tioned image stylization. + +# 5. Conclusion + +In this paper, we present a new scheme "style kernel" for artistic style transfer. Our method learns an attention map with focusing regions using the proposed content-based gating operator. The style feature is then aligned to match the semantics in the content feature based on the learned attention map. In the style kernel generation module, the dynamic parameters "style kernel" are learned from the content-style aligned feature and then applied to modulate the content feature for style transfer. Extensive experimental results demonstrate the remarkable performance of our model in generating synthetic style images with better quality than the state-of-the-art. + +# Acknowledgement + +This research was sponsored by Prof. Yongwei Nie's Natural Science Foundation of China (62072191). + +# References + +[1] Nicolas Carion, Francisco Massa, Gabriel Synnaeve, Nicolas Usunier, Alexander Kirillov, and Sergey Zagoruyko. End-to-end object detection with transformers. In European Conference on Computer Vision, pages 213-229. Springer, 2020. 3 +[2] Prashanth Chandran, Gaspard Zoss, Paulo Gotardo, Markus Gross, and Derek Bradley. Adaptive convolutions for structure-aware style transfer. 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The first two rows show comparisons with state-of-the-art methods. The last row shows results of our proposed method, which can faithfully transfer various styles and preserve the content structure." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 143, + 406, + 192, + 418 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 406, + 192, + 418 + ], + "spans": [ + { + "bbox": [ + 143, + 406, + 192, + 418 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 45, + 436, + 289, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 436, + 289, + 700 + ], + "spans": [ + { + "bbox": [ + 45, + 436, + 289, + 700 + ], + "type": "text", + "content": "Arbitrary style transfer has been demonstrated to be efficient in artistic image generation. Previous methods either globally modulate the content feature ignoring local details, or overly focus on the local structure details leading to style leakage. In contrast to the literature, we propose a new scheme \"style kernel\" that learns spatially adaptive kernels for per-pixel stylization, where the convolutional kernels are dynamically generated from the global style-content aligned feature and then the learned kernels are applied to modulate the content feature at each spatial position. This new scheme allows flexible both global and local interactions between the content and style features such that the wanted styles can be easily transferred to the content image while at the same time the content structure can be easily preserved. To further enhance the flexibility of our style transfer method, we propose a Style Alignment Encoding (SAE) module complemented with a Content-based Gating Modulation (CGM) module for learning the dynamic style kernels in focusing regions. Extensive experiments strongly demonstrate that our proposed method outperforms state-of-the-art methods and exhibits superior performance in terms of visual quality and efficiency." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 307, + 406, + 386, + 418 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 406, + 386, + 418 + ], + "spans": [ + { + "bbox": [ + 307, + 406, + 386, + 418 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 426, + 545, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 426, + 545, + 545 + ], + "spans": [ + { + "bbox": [ + 304, + 426, + 545, + 545 + ], + "type": "text", + "content": "Artistic style transfer [48] refers to a hot computer vision technology that allows us to recompose the content of an image in the style of an artistic work. Figure 1 shows several vivid examples. We might have ever imagined what a photo might look like if it were painted by a famous artist like Pablo Picasso or Van Gogh. Now style transfer is the computer vision technique that turns this into a reality. It has great potential values in various real-world applications and therefore attracts a lot of researchers to constantly put efforts to make progress towards both quality and efficiency." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "type": "text", + "content": "Most of existing style transfer works [6, 15, 18, 26, 33] either globally modulate the content feature ignoring local details or overly focus on the local structure details leading to style leakage. In particular, [15, 18] seeks to match global statistics between content and style images, resulting in inconsistent stylizations that either remain large parts of the content unchanged or contain local content with distorted style patterns. SANet [33] and AdaAttN [31] improve the content similarity by learning attention maps that match the semantics between the style and stylized images, but these methods tend to distort object instances when improper style patterns are involved. Recently, IEC [5] adopts contrastive learning to pull close both the content and style representations between input and output images. MAST [16]" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10083" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 133 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 133 + ], + "type": "text", + "content": "seeks to balance the style and content via manifold alignment. Although both IEC and MAST have achieved some success in most cases, they are still far from satisfactory to well balance two important requirements, i.e., style consistency and structure similarity." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 134, + 287, + 327 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 134, + 287, + 327 + ], + "spans": [ + { + "bbox": [ + 46, + 134, + 287, + 327 + ], + "type": "text", + "content": "In this paper, we develop a novel style transfer framework in a manner of encoder-decoder structure, as illustrated in Figure 2, which contains two important modules: (1) a Style Alignment Encoding (SAE) module enhanced by Content-based Gating Modulation (CGM), which is used to generate content-style aligned features, and (2) a Style Kernel Generation (SKG) module used to transform the output features of SAE to convolutional kernels. In such a framework, we propose a new style transfer scheme, \"style kernel\", which treats the features of the style images as dynamic convolutional kernels and then transfer the style information to the content image by convolving the content image by the learned dynamic style kernels. This allows fine-grained local interactions between the style and content features, the flexibility of which makes both style transferring and content structure preserving much easier." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 328, + 288, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 328, + 288, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 328, + 288, + 628 + ], + "type": "text", + "content": "To enforce the global correlation between the content and style features, we simulate the self-attention mechanism of Transformer [41] in the SAE module. This treats the content and style features as the queries and keys of the self-attention operator respectively and computes a large attention map the elements of which measure for each local content context the similarity to each local style context. With the attention map, we can aggregate for each pixel of the content image all the style features in a weighted manner to obtain content-style aligned features. We also design a Content-based Gating Modulation (CGM) operator that further thresholds the attention map and zeros the places where similarities are too small, seeking an adaptive number of correlated neighbors as a focusing region for each query point. Then, we use another set of convolutions that constitute the SKG module to further transform the content-style aligned features, and view (reshape) the output of SKG as dynamic style kernels. In order to improve the efficiency of the dynamic convolutions, SKG predicts separable local filters (two 1D filters and a bias) instead of a spatial 2D filter that has more parameters. The learned style kernels already integrate the information of the given content and style images. We further apply the learned dynamic style kernels to the content image feature for transferring the target style to the content image." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 630, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 287, + 715 + ], + "type": "text", + "content": "We shall emphasize that unlike \"style code\" in AdaIN [15], DRB-GAN [48], and AdaConv [2] modeled as the dynamic parameters (e.g. mean, variance, convolution kernel) which are shared over all spatial positions globally without distinguishing the semantic regions, the learned dynamic kernels via our \"style kernel\" are point-wisely modeled upon the globally style-content aligned feature, and" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 72, + 545, + 215 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 215 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 215 + ], + "type": "text", + "content": "therefore is able to make full use of the point-wise semantic structure correlation to modulate content feature for better artistic style transfer. Our learned dynamic style kernels are good at transferring the globally aggregated and locally semantic-aligned style features to local regions. This ensures our style transfer model that works well on consistent stylization with well preserved structure, overcoming the shortages of existing style transfer methods which either globally modulate the content feature ignoring local details (e.g. AdaIN, WCT [28]) or overly focus on the local structure details leading to style leakage (e.g. AdaAttN [31] and MAST [16])." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 305, + 216, + 545, + 237 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 216, + 545, + 237 + ], + "spans": [ + { + "bbox": [ + 305, + 216, + 545, + 237 + ], + "type": "text", + "content": "The main contributions of this work are 3-fold as follows:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 317, + 239, + 545, + 396 + ], + "type": "list", + "angle": 0, + "index": 9, + "blocks": [ + { + "bbox": [ + 317, + 239, + 545, + 299 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 239, + 545, + 299 + ], + "spans": [ + { + "bbox": [ + 317, + 239, + 545, + 299 + ], + "type": "text", + "content": "- We are the first to propose the \"style kernel\" scheme for artistic style transfer, which converts the globally style-content alignment features into position pointwisely dynamic convolutional kernels to convolve the features of content images together for style transfer." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 317, + 300, + 545, + 347 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 300, + 545, + 347 + ], + "spans": [ + { + "bbox": [ + 317, + 300, + 545, + 347 + ], + "type": "text", + "content": "- We design a novel architecture, i.e. SAE and CGM, to generate the dynamic style kernels by employing the correlation between the content and style image adaptively." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 317, + 350, + 545, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 350, + 545, + 396 + ], + "spans": [ + { + "bbox": [ + 317, + 350, + 545, + 396 + ], + "type": "text", + "content": "- Extensive experiments demonstrate that our method produces visually plausible stylization results with fine-grained style details and coherence content with the input content images." + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 406, + 397, + 418 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 406, + 397, + 418 + ], + "spans": [ + { + "bbox": [ + 306, + 406, + 397, + 418 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 426, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 426, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 426, + 545, + 715 + ], + "type": "text", + "content": "Artistic Style Transfer was initially solved by Gatys et al. [12] a pre-trained neural network to synthesize stylizations in an iterative optimization manner, and then a bunch of neural style transfer methods [3,5,11,18,31,38,39] were developed. In particular, AdaIN [15] introduces the adaptive instance normalization to globally match the statistics between the content and style features. For the same purpose, WCT [28] utilizes the whitening and coloring transforms, and LST [27] introduces a linear transformation matrix predicted on content and style features. [7,22,42,51] seek different ways to match the feature distribution. SANet [33] seeks to align the semantics between the content and style features via a self-attention network. " + }, + { + "bbox": [ + 304, + 426, + 545, + 715 + ], + "type": "inline_equation", + "content": "\\mathrm{StrTr}^2" + }, + { + "bbox": [ + 304, + 426, + 545, + 715 + ], + "type": "text", + "content": " [8] resorts to the transformers [41, 47]. To further preserve the content details, AdaAttN [31] perform attentive normalization on per-point basis, IEC [5] employs stylization relations with contrastive learning and MAST [16] introduces manifold alignment to balance the style and content. However, emphasizing on content details prevents the transfer adequate style information to some degree, and results in style leakage. Recently, dynamic network based style transfer methods [3, 15, 18, 38] extend the model generalization. As a generic extension of AdaIN, AdaConv [2] introduces a parameter network that predicts network parameters used by" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "10084" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 71, + 542, + 249 + ], + "blocks": [ + { + "bbox": [ + 50, + 71, + 542, + 249 + ], + "lines": [ + { + "bbox": [ + 50, + 71, + 542, + 249 + ], + "spans": [ + { + "bbox": [ + 50, + 71, + 542, + 249 + ], + "type": "image", + "image_path": "887aa71401cc7c9022db7435e7967a0ee5c94bac99576acbe9a7444f7f293b76.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 255, + 548, + 321 + ], + "lines": [ + { + "bbox": [ + 46, + 255, + 548, + 321 + ], + "spans": [ + { + "bbox": [ + 46, + 255, + 548, + 321 + ], + "type": "text", + "content": "Figure 2. Overview of our proposed scheme \"style kernel\". A pretrained VGG encoder takes in the content and style image as input to produce the content feature " + }, + { + "bbox": [ + 46, + 255, + 548, + 321 + ], + "type": "inline_equation", + "content": "Z_{c}" + }, + { + "bbox": [ + 46, + 255, + 548, + 321 + ], + "type": "text", + "content": " and style feature " + }, + { + "bbox": [ + 46, + 255, + 548, + 321 + ], + "type": "inline_equation", + "content": "Z_{s}" + }, + { + "bbox": [ + 46, + 255, + 548, + 321 + ], + "type": "text", + "content": ". The style-alignment encoding model employs an attention mechanism by taking the " + }, + { + "bbox": [ + 46, + 255, + 548, + 321 + ], + "type": "inline_equation", + "content": "Z_{c}" + }, + { + "bbox": [ + 46, + 255, + 548, + 321 + ], + "type": "text", + "content": " as query and " + }, + { + "bbox": [ + 46, + 255, + 548, + 321 + ], + "type": "inline_equation", + "content": "Z_{s}" + }, + { + "bbox": [ + 46, + 255, + 548, + 321 + ], + "type": "text", + "content": " as key and value to exploit their semantics matching. The content-based gating module (CGM) learns a dynamic threshold and adaptively adjusts attention weights for a globally content-style aligned feature " + }, + { + "bbox": [ + 46, + 255, + 548, + 321 + ], + "type": "inline_equation", + "content": "Z_{cs}" + }, + { + "bbox": [ + 46, + 255, + 548, + 321 + ], + "type": "text", + "content": ", which is transformed by style kernel generation module to dynamic style kernels. Finally, we conduct convolution operations on the channel-wisely grouped and shuffled (GS) content feature with the learned dynamic style kernels to get " + }, + { + "bbox": [ + 46, + 255, + 548, + 321 + ], + "type": "inline_equation", + "content": "\\bar{Z}_{cs}" + }, + { + "bbox": [ + 46, + 255, + 548, + 321 + ], + "type": "text", + "content": " fed into the decoder to produce the stylizations." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 330, + 288, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 330, + 288, + 413 + ], + "spans": [ + { + "bbox": [ + 46, + 330, + 288, + 413 + ], + "type": "text", + "content": "another network for style transfer. DRB-GAN [48] models \"style code\" as the global mean and variance for dynamic convolutions to conduct style transfer. Different from all the above methods, we propose a new scheme \"style kernel\" to learn dynamic convolutional kernels from the style-content alignment feature to point-wisely modulate the content feature for artistic style transfer." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 415, + 287, + 547 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 415, + 287, + 547 + ], + "spans": [ + { + "bbox": [ + 46, + 415, + 287, + 547 + ], + "type": "text", + "content": "Self-Attention Mechanism is introduced in Transformer [41] as a new attention mechanism. Similar to non-local neural networks [13,21,41,45], Transformer directly works on sequences of image patches to aggregate information for long-range dependencies. The recent researches demonstrate it has been successfully applied in various vision tasks like image recognition [4, 10, 14, 29], object detection [1, 44, 46], image captioning [9], image enhancement [49, 50], and text conditioned image generation [35, 37]. Our model takes the self-attention mechanism to align the semantics of the style feature to that of the content image." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 548, + 287, + 656 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 548, + 287, + 656 + ], + "spans": [ + { + "bbox": [ + 46, + 548, + 287, + 656 + ], + "type": "text", + "content": "Dynamic Network consists of convolution layers for which the filter parameters are predicted by another sub-network. Recently, there is rapid progress in vision applications [17, 32, 36, 48, 52] that benefits from dynamic network for image/video enhancement. [19] employs dynamic upsampling filters for high-resolution image reconstruction. [52] predicts filters from spatio-temporal features for video deblurring. Differently, our StyleKernel learns spatially adaptive kernel for per-pixel stylization." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 669, + 127, + 681 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 669, + 127, + 681 + ], + "spans": [ + { + "bbox": [ + 47, + 669, + 127, + 681 + ], + "type": "text", + "content": "3. Our Method" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "While existing dynamic kernel based methods [2, 15, 48] can efficiently generate stylizations, we observe that their" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 330, + 545, + 414 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 330, + 545, + 414 + ], + "spans": [ + { + "bbox": [ + 304, + 330, + 545, + 414 + ], + "type": "text", + "content": "visual-quality is limited in two aspects. (1) As the dynamic kernels are predicted based on the style feature without distinguishing the content-style correlation, the transferred style only globally reflects the style characters of the style image, ruining local content details. (2) The completeness of semantic regions is not well preserved. This is because the dynamic kernels used by the layers are spatially shared." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 415, + 546, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 415, + 546, + 654 + ], + "spans": [ + { + "bbox": [ + 304, + 415, + 546, + 654 + ], + "type": "text", + "content": "To alleviate these problems, we propose to align the semantics of the style image to those of the content image and transform the content features for per-pixel stylization in a separable convolution manner. The pipeline of our proposed model is shown in Figure 2. The content image " + }, + { + "bbox": [ + 304, + 415, + 546, + 654 + ], + "type": "inline_equation", + "content": "I_{c}" + }, + { + "bbox": [ + 304, + 415, + 546, + 654 + ], + "type": "text", + "content": " and style image " + }, + { + "bbox": [ + 304, + 415, + 546, + 654 + ], + "type": "inline_equation", + "content": "I_{s}" + }, + { + "bbox": [ + 304, + 415, + 546, + 654 + ], + "type": "text", + "content": " are first fed into a fixed VGG encoder to produce the content and style feature maps " + }, + { + "bbox": [ + 304, + 415, + 546, + 654 + ], + "type": "inline_equation", + "content": "Z_{c} \\in \\mathbb{R}^{H_{c} \\times W_{c} \\times C_{in}}" + }, + { + "bbox": [ + 304, + 415, + 546, + 654 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 415, + 546, + 654 + ], + "type": "inline_equation", + "content": "Z_{s} \\in \\mathbb{R}^{H_{s} \\times W_{s} \\times C_{in}}" + }, + { + "bbox": [ + 304, + 415, + 546, + 654 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 415, + 546, + 654 + ], + "type": "inline_equation", + "content": "H, W" + }, + { + "bbox": [ + 304, + 415, + 546, + 654 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 415, + 546, + 654 + ], + "type": "inline_equation", + "content": "C_{in}" + }, + { + "bbox": [ + 304, + 415, + 546, + 654 + ], + "type": "text", + "content": " represent the height, width and channel size of the feature map, respectively. Then in SAE, we align the content and style features by using the content features " + }, + { + "bbox": [ + 304, + 415, + 546, + 654 + ], + "type": "inline_equation", + "content": "Z_{c}" + }, + { + "bbox": [ + 304, + 415, + 546, + 654 + ], + "type": "text", + "content": " as the queries and the style features " + }, + { + "bbox": [ + 304, + 415, + 546, + 654 + ], + "type": "inline_equation", + "content": "Z_{s}" + }, + { + "bbox": [ + 304, + 415, + 546, + 654 + ], + "type": "text", + "content": " as the keys in a self-attention mechanism. The CGM module is conducted on the attention map to seek a focusing region for each query point. Thereafter, we predict by SKG the dynamic style kernels " + }, + { + "bbox": [ + 304, + 415, + 546, + 654 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 304, + 415, + 546, + 654 + ], + "type": "text", + "content": " from the content-style aligned features " + }, + { + "bbox": [ + 304, + 415, + 546, + 654 + ], + "type": "inline_equation", + "content": "Z_{cs}" + }, + { + "bbox": [ + 304, + 415, + 546, + 654 + ], + "type": "text", + "content": ". Finally, we group and shuffle (GS) " + }, + { + "bbox": [ + 304, + 415, + 546, + 654 + ], + "type": "inline_equation", + "content": "Z_{c}" + }, + { + "bbox": [ + 304, + 415, + 546, + 654 + ], + "type": "text", + "content": " to break down the correlation within the channel-wise feature and apply convolutions parameterized by the learned kernels to the grouped and shuffled " + }, + { + "bbox": [ + 304, + 415, + 546, + 654 + ], + "type": "inline_equation", + "content": "Z_{c}" + }, + { + "bbox": [ + 304, + 415, + 546, + 654 + ], + "type": "text", + "content": " to obtain " + }, + { + "bbox": [ + 304, + 415, + 546, + 654 + ], + "type": "inline_equation", + "content": "\\bar{Z}_{cs}" + }, + { + "bbox": [ + 304, + 415, + 546, + 654 + ], + "type": "text", + "content": " which is further decoded to the target stylized image by a decoder." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 659, + 451, + 672 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 659, + 451, + 672 + ], + "spans": [ + { + "bbox": [ + 306, + 659, + 451, + 672 + ], + "type": "text", + "content": "3.1. Style Alignment Encoding" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 677, + 545, + 713 + ], + "type": "text", + "content": "This module takes the content and style features as input, aligns between them by learning content-style alignment attention, and finally attentively adjusts the attention map by" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10085" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 70, + 128, + 169 + ], + "blocks": [ + { + "bbox": [ + 53, + 70, + 128, + 169 + ], + "lines": [ + { + "bbox": [ + 53, + 70, + 128, + 169 + ], + "spans": [ + { + "bbox": [ + 53, + 70, + 128, + 169 + ], + "type": "image", + "image_path": "64286c43330aafe74e9fc9c07d79b037222aac4d2c22970b76d6546ed7781a75.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 67, + 173, + 116, + 182 + ], + "lines": [ + { + "bbox": [ + 67, + 173, + 116, + 182 + ], + "spans": [ + { + "bbox": [ + 67, + 173, + 116, + 182 + ], + "type": "text", + "content": "Content & Style" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 129, + 70, + 205, + 171 + ], + "blocks": [ + { + "bbox": [ + 129, + 70, + 205, + 171 + ], + "lines": [ + { + "bbox": [ + 129, + 70, + 205, + 171 + ], + "spans": [ + { + "bbox": [ + 129, + 70, + 205, + 171 + ], + "type": "image", + "image_path": "5d37e1cb30e8d6a1be3a2c68d9f3944d2b4f98ad317e754b858ab8e2ceeb5aa6.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 155, + 173, + 176, + 181 + ], + "lines": [ + { + "bbox": [ + 155, + 173, + 176, + 181 + ], + "spans": [ + { + "bbox": [ + 155, + 173, + 176, + 181 + ], + "type": "text", + "content": "SANet" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 205, + 70, + 280, + 171 + ], + "blocks": [ + { + "bbox": [ + 205, + 70, + 280, + 171 + ], + "lines": [ + { + "bbox": [ + 205, + 70, + 280, + 171 + ], + "spans": [ + { + "bbox": [ + 205, + 70, + 280, + 171 + ], + "type": "image", + "image_path": "7b8817ec17e7eb42d6485be6105e06f3589a5374ccf96cf5637eb2418e9cd9b2.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 221, + 173, + 264, + 182 + ], + "lines": [ + { + "bbox": [ + 221, + 173, + 264, + 182 + ], + "spans": [ + { + "bbox": [ + 221, + 173, + 264, + 182 + ], + "type": "inline_equation", + "content": "\\mathrm{SANet} + \\mathrm{topK}" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 183, + 547, + 251 + ], + "lines": [ + { + "bbox": [ + 46, + 183, + 547, + 251 + ], + "spans": [ + { + "bbox": [ + 46, + 183, + 547, + 251 + ], + "type": "text", + "content": "Figure 3. The impact of the feature aggregation. Left: We compare the performances of models conducting different feature aggregation strategies. The SANet takes an attention module to aggregate information across all the nodes. The SANet + topK only acquires information from the nodes with top K attention scores. SANet + CGM takes our content-based gating modulation to aggregate information from a dynamic number of nodes. Our CGM is learned to masked out nodes with low attention score, leading to stylizations with well preserved structure content. The second row shows the distributions of selected nodes (highlighted in colors) and the focused areas (masked-out by black rectangles) learned by CGM. Right: we demonstrate the relation between the content/style loss and the number of selected nodes." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 281, + 70, + 356, + 169 + ], + "blocks": [ + { + "bbox": [ + 281, + 70, + 356, + 169 + ], + "lines": [ + { + "bbox": [ + 281, + 70, + 356, + 169 + ], + "spans": [ + { + "bbox": [ + 281, + 70, + 356, + 169 + ], + "type": "image", + "image_path": "211aa4e2cc0e5ee06e7b753747b1bce36c4f77839ea5bf250820841c4a7453aa.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 301, + 173, + 345, + 181 + ], + "lines": [ + { + "bbox": [ + 301, + 173, + 345, + 181 + ], + "spans": [ + { + "bbox": [ + 301, + 173, + 345, + 181 + ], + "type": "inline_equation", + "content": "\\mathrm{SANet} + \\mathrm{CGM}" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 357, + 70, + 432, + 171 + ], + "blocks": [ + { + "bbox": [ + 357, + 70, + 432, + 171 + ], + "lines": [ + { + "bbox": [ + 357, + 70, + 432, + 171 + ], + "spans": [ + { + "bbox": [ + 357, + 70, + 432, + 171 + ], + "type": "image", + "image_path": "fc182095be7056785c527fc4b43c4cfb17847f1a875c487850bb0ae5984452a5.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 384, + 173, + 400, + 181 + ], + "lines": [ + { + "bbox": [ + 384, + 173, + 400, + 181 + ], + "spans": [ + { + "bbox": [ + 384, + 173, + 400, + 181 + ], + "type": "text", + "content": "Ours" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 433, + 75, + 541, + 167 + ], + "blocks": [ + { + "bbox": [ + 433, + 75, + 541, + 167 + ], + "lines": [ + { + "bbox": [ + 433, + 75, + 541, + 167 + ], + "spans": [ + { + "bbox": [ + 433, + 75, + 541, + 167 + ], + "type": "image", + "image_path": "edf5695a5d2536fbe27159e4d9c36b5aa9e4a75c2366a5acd0d6ee0c9923f7b2.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 262, + 223, + 274 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 262, + 223, + 274 + ], + "spans": [ + { + "bbox": [ + 46, + 262, + 223, + 274 + ], + "type": "text", + "content": "a content-based gating modulation module." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 274, + 287, + 382 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 274, + 287, + 382 + ], + "spans": [ + { + "bbox": [ + 46, + 274, + 287, + 382 + ], + "type": "text", + "content": "Content-Style Alignment Attention. By taking the content feature " + }, + { + "bbox": [ + 46, + 274, + 287, + 382 + ], + "type": "inline_equation", + "content": "Z_{c}" + }, + { + "bbox": [ + 46, + 274, + 287, + 382 + ], + "type": "text", + "content": " as the query, and the style feature " + }, + { + "bbox": [ + 46, + 274, + 287, + 382 + ], + "type": "inline_equation", + "content": "Z_{s}" + }, + { + "bbox": [ + 46, + 274, + 287, + 382 + ], + "type": "text", + "content": " as the key and value, we compute the content-style alignment attention that seeks to aggregate information from the style feature map according to the matched content information. This warps the style feature to align with the content feature. To this end, we calculate the pairwise feature correlation " + }, + { + "bbox": [ + 46, + 274, + 287, + 382 + ], + "type": "inline_equation", + "content": "\\mathcal{M}^{s\\rightarrow c}\\in \\mathbb{R}^{H_cW_c\\times H_sW_s}" + }, + { + "bbox": [ + 46, + 274, + 287, + 382 + ], + "type": "text", + "content": ". This results in an attention map " + }, + { + "bbox": [ + 46, + 274, + 287, + 382 + ], + "type": "inline_equation", + "content": "\\mathcal{A}\\in \\mathbb{R}^{H_cW_c\\times H_sW_s}" + }, + { + "bbox": [ + 46, + 274, + 287, + 382 + ], + "type": "text", + "content": " by:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 47, + 390, + 301, + 426 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 390, + 301, + 426 + ], + "spans": [ + { + "bbox": [ + 47, + 390, + 301, + 426 + ], + "type": "interline_equation", + "content": "\\mathcal {A} (u, v) = \\operatorname {s o f t m a x} (\\alpha \\mathcal {M} ^ {s \\rightarrow c}) = \\operatorname {s o f t m a x} (\\alpha \\frac {Z _ {c} (u) ^ {T} Z _ {s} (v)}{\\| Z _ {c} (u) \\| \\| Z _ {s} (v) \\|}), \\tag {1}", + "image_path": "3f4ae57166ce99b9a21690b4fad2c87f516c454352647cdc7011f28000ca744a.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 434, + 287, + 505 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 434, + 287, + 505 + ], + "spans": [ + { + "bbox": [ + 46, + 434, + 287, + 505 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 434, + 287, + 505 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 434, + 287, + 505 + ], + "type": "text", + "content": " is the coefficient that controls the sharpness of the softmax. " + }, + { + "bbox": [ + 46, + 434, + 287, + 505 + ], + "type": "inline_equation", + "content": "Z_{c}(u)" + }, + { + "bbox": [ + 46, + 434, + 287, + 505 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 434, + 287, + 505 + ], + "type": "inline_equation", + "content": "Z_{s}(v)" + }, + { + "bbox": [ + 46, + 434, + 287, + 505 + ], + "type": "text", + "content": " stands for the feature of " + }, + { + "bbox": [ + 46, + 434, + 287, + 505 + ], + "type": "inline_equation", + "content": "Z_{c}" + }, + { + "bbox": [ + 46, + 434, + 287, + 505 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 434, + 287, + 505 + ], + "type": "inline_equation", + "content": "Z_{s}" + }, + { + "bbox": [ + 46, + 434, + 287, + 505 + ], + "type": "text", + "content": " at position " + }, + { + "bbox": [ + 46, + 434, + 287, + 505 + ], + "type": "inline_equation", + "content": "u\\in \\mathbb{R}^{H_cW_c}" + }, + { + "bbox": [ + 46, + 434, + 287, + 505 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 434, + 287, + 505 + ], + "type": "inline_equation", + "content": "v\\in \\mathbb{R}^{H_sW_s}" + }, + { + "bbox": [ + 46, + 434, + 287, + 505 + ], + "type": "text", + "content": ". The " + }, + { + "bbox": [ + 46, + 434, + 287, + 505 + ], + "type": "inline_equation", + "content": "u" + }, + { + "bbox": [ + 46, + 434, + 287, + 505 + ], + "type": "text", + "content": "-th row of the attention map " + }, + { + "bbox": [ + 46, + 434, + 287, + 505 + ], + "type": "inline_equation", + "content": "\\mathcal{A}" + }, + { + "bbox": [ + 46, + 434, + 287, + 505 + ], + "type": "text", + "content": " represents similarities between the " + }, + { + "bbox": [ + 46, + 434, + 287, + 505 + ], + "type": "inline_equation", + "content": "u" + }, + { + "bbox": [ + 46, + 434, + 287, + 505 + ], + "type": "text", + "content": "-th node of the content feature and all the nodes of the style feature." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 46, + 506, + 287, + 554 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 506, + 287, + 554 + ], + "spans": [ + { + "bbox": [ + 46, + 506, + 287, + 554 + ], + "type": "text", + "content": "To align the semantics of the style feature to that of the content feature, we aggregate information in " + }, + { + "bbox": [ + 46, + 506, + 287, + 554 + ], + "type": "inline_equation", + "content": "Z_{s}" + }, + { + "bbox": [ + 46, + 506, + 287, + 554 + ], + "type": "text", + "content": " based on the attention score map " + }, + { + "bbox": [ + 46, + 506, + 287, + 554 + ], + "type": "inline_equation", + "content": "\\mathcal{A}" + }, + { + "bbox": [ + 46, + 506, + 287, + 554 + ], + "type": "text", + "content": " and obtain " + }, + { + "bbox": [ + 46, + 506, + 287, + 554 + ], + "type": "inline_equation", + "content": "Z_{cs} \\in \\mathcal{R}^{H_c W_c \\times C}" + }, + { + "bbox": [ + 46, + 506, + 287, + 554 + ], + "type": "text", + "content": " by calculating their weighted average:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 108, + 562, + 287, + 585 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 562, + 287, + 585 + ], + "spans": [ + { + "bbox": [ + 108, + 562, + 287, + 585 + ], + "type": "interline_equation", + "content": "Z _ {c s} (u) = \\sum_ {v} \\mathcal {A} (u, v) \\cdot Z _ {s} (v). \\tag {2}", + "image_path": "52ff6815907b2ef213d1354b1b299d5f86824e51d17dd5ea0e6842846ef3cf00.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 46, + 594, + 287, + 630 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 287, + 630 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 287, + 630 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 594, + 287, + 630 + ], + "type": "inline_equation", + "content": "Z_{cs}(u)" + }, + { + "bbox": [ + 46, + 594, + 287, + 630 + ], + "type": "text", + "content": " represents the feature at position " + }, + { + "bbox": [ + 46, + 594, + 287, + 630 + ], + "type": "inline_equation", + "content": "u" + }, + { + "bbox": [ + 46, + 594, + 287, + 630 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 46, + 594, + 287, + 630 + ], + "type": "inline_equation", + "content": "Z_{cs}" + }, + { + "bbox": [ + 46, + 594, + 287, + 630 + ], + "type": "text", + "content": ". In the following, we denote the " + }, + { + "bbox": [ + 46, + 594, + 287, + 630 + ], + "type": "inline_equation", + "content": "Z_{cs} \\in \\mathcal{R}^{H_c \\times W_c \\times C}" + }, + { + "bbox": [ + 46, + 594, + 287, + 630 + ], + "type": "text", + "content": ", which is obtained by reshaping." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "text", + "content": "In Eq. 2, all style features are taken into consideration when computing the content-style aligned features " + }, + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "inline_equation", + "content": "Z_{cs}" + }, + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "text", + "content": ". We find that this yields inferior results because many irrelevant features are involved into the computation. We therefore introduce the Content-based Gating Modulation (CGM) operator which creates dynamic thresholds that further filter out irrelevant style features." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 262, + 546, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 262, + 546, + 323 + ], + "spans": [ + { + "bbox": [ + 305, + 262, + 546, + 323 + ], + "type": "text", + "content": "Content-based Gating Modulation is used to further adapt the attention map by the content feature " + }, + { + "bbox": [ + 305, + 262, + 546, + 323 + ], + "type": "inline_equation", + "content": "Z_{c}" + }, + { + "bbox": [ + 305, + 262, + 546, + 323 + ], + "type": "text", + "content": ". Taking " + }, + { + "bbox": [ + 305, + 262, + 546, + 323 + ], + "type": "inline_equation", + "content": "Z_{c}" + }, + { + "bbox": [ + 305, + 262, + 546, + 323 + ], + "type": "text", + "content": " as input, we employ a convolution network " + }, + { + "bbox": [ + 305, + 262, + 546, + 323 + ], + "type": "inline_equation", + "content": "E_{f}" + }, + { + "bbox": [ + 305, + 262, + 546, + 323 + ], + "type": "text", + "content": " to generate a scale parameter " + }, + { + "bbox": [ + 305, + 262, + 546, + 323 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 305, + 262, + 546, + 323 + ], + "type": "text", + "content": " and a bias parameter " + }, + { + "bbox": [ + 305, + 262, + 546, + 323 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 305, + 262, + 546, + 323 + ], + "type": "text", + "content": ". We then perform a row average operator on the attention matrix " + }, + { + "bbox": [ + 305, + 262, + 546, + 323 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 305, + 262, + 546, + 323 + ], + "type": "text", + "content": " by:" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 351, + 331, + 545, + 365 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 351, + 331, + 545, + 365 + ], + "spans": [ + { + "bbox": [ + 351, + 331, + 545, + 365 + ], + "type": "interline_equation", + "content": "\\mathcal {A} _ {r} (i) = \\frac {1}{H _ {c}} \\sum_ {j = 1} ^ {H _ {c}} \\mathcal {A} _ {i, j}, \\forall i \\in [ 1, W _ {c} ]. \\tag {3}", + "image_path": "70d584519666b0c6dc8c9fcd6df136039cfed2e2e720085fb9f8f48994fe0f86.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 305, + 373, + 545, + 409 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 373, + 545, + 409 + ], + "spans": [ + { + "bbox": [ + 305, + 373, + 545, + 409 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 373, + 545, + 409 + ], + "type": "inline_equation", + "content": "\\mathcal{A}_r" + }, + { + "bbox": [ + 305, + 373, + 545, + 409 + ], + "type": "text", + "content": " is the obtained column vector after the average operator. Then, we obtain the threshold matrix " + }, + { + "bbox": [ + 305, + 373, + 545, + 409 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 305, + 373, + 545, + 409 + ], + "type": "text", + "content": " by the following equation:" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 384, + 418, + 545, + 432 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 384, + 418, + 545, + 432 + ], + "spans": [ + { + "bbox": [ + 384, + 418, + 545, + 432 + ], + "type": "interline_equation", + "content": "\\mathcal {T} = \\mathcal {A} (\\lambda \\mathcal {A} _ {r} + \\beta). \\tag {4}", + "image_path": "d276db2e4233a6f3a3e78f0b9f4a9cacc50066b7d53b5e6fd85477c58fe305bb.jpg" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 306, + 441, + 460, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 441, + 460, + 453 + ], + "spans": [ + { + "bbox": [ + 306, + 441, + 460, + 453 + ], + "type": "text", + "content": "Finally, we update the attention " + }, + { + "bbox": [ + 306, + 441, + 460, + 453 + ], + "type": "inline_equation", + "content": "\\mathcal{A}" + }, + { + "bbox": [ + 306, + 441, + 460, + 453 + ], + "type": "text", + "content": " by:" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 378, + 462, + 545, + 475 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 378, + 462, + 545, + 475 + ], + "spans": [ + { + "bbox": [ + 378, + 462, + 545, + 475 + ], + "type": "interline_equation", + "content": "\\bar {\\mathcal {A}} = \\mathcal {A} \\cdot \\operatorname {S i g n} (\\mathcal {A} - \\mathcal {T}), \\tag {5}", + "image_path": "f9dbbe1e8f877909dbe64b730c3fb1fabed573c67a6cc21d3a5a6e80127234e5.jpg" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 305, + 484, + 545, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 484, + 545, + 519 + ], + "spans": [ + { + "bbox": [ + 305, + 484, + 545, + 519 + ], + "type": "text", + "content": "where the dot indicates element-wise multiplication and Sign is a function returning 1 given positive input and 0 otherwise. We use " + }, + { + "bbox": [ + 305, + 484, + 545, + 519 + ], + "type": "inline_equation", + "content": "\\bar{A}" + }, + { + "bbox": [ + 305, + 484, + 545, + 519 + ], + "type": "text", + "content": " instead of " + }, + { + "bbox": [ + 305, + 484, + 545, + 519 + ], + "type": "inline_equation", + "content": "\\mathcal{A}" + }, + { + "bbox": [ + 305, + 484, + 545, + 519 + ], + "type": "text", + "content": " in Eq. 2 to compute " + }, + { + "bbox": [ + 305, + 484, + 545, + 519 + ], + "type": "inline_equation", + "content": "Z_{cs}" + }, + { + "bbox": [ + 305, + 484, + 545, + 519 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 304, + 520, + 545, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 520, + 545, + 652 + ], + "spans": [ + { + "bbox": [ + 304, + 520, + 545, + 652 + ], + "type": "inline_equation", + "content": "\\bar{\\mathcal{A}}" + }, + { + "bbox": [ + 304, + 520, + 545, + 652 + ], + "type": "text", + "content": " is a dynamically learned mask, with which our model creates focused areas and filter out irrelevant style features. This allows our model to aggregate features from fairly correlated features, which is essential to preserve the completeness of semantic regions. In Figure 3 we compare the intermediate visualizations and stylized results. We see that the CGM works to recognize focused areas, where the style information is aggregated by the query point. By contrast, the attention learned by the SANet is distributed over the entire image, including visually less correlated points, such as corners and background." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 306, + 659, + 441, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 659, + 441, + 671 + ], + "spans": [ + { + "bbox": [ + 306, + 659, + 441, + 671 + ], + "type": "text", + "content": "3.2. Style Kernel Generation" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 305, + 677, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 546, + 714 + ], + "type": "text", + "content": "We propose the Style Kernel (SK) Generation network to further transform the content-style aligned features of SAE to dynamic style kernels. It takes the globally content-style" + } + ] + } + ], + "index": 29 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "10086" + } + ] + } + ], + "index": 30 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 94, + 547, + 148 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 547, + 92 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 547, + 92 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 547, + 92 + ], + "type": "text", + "content": "Table 1. Average inference time, measured on a Tesla V100 GPU, for different methods with a batch size of 1 and an input image of " + }, + { + "bbox": [ + 47, + 70, + 547, + 92 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 47, + 70, + 547, + 92 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 70, + 547, + 92 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 47, + 70, + 547, + 92 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 94, + 547, + 148 + ], + "lines": [ + { + "bbox": [ + 48, + 94, + 547, + 148 + ], + "spans": [ + { + "bbox": [ + 48, + 94, + 547, + 148 + ], + "type": "table", + "html": "
MethodAdaIN'17LST'19AvatarNet'18SANet'19IEC'21DRB-GAN'21AdaAttN'21MAST'21AdaConv'21StrTr²'22Ours
T256 ↓0.0040.0040.8730.0110.0120.0050.0240.1260.0190.0340.017
T256 ↓0.0050.0050.9620.0370.0210.0060.0420.2390.0360.0860.035
", + "image_path": "6209a129f1388485dcb9f341011d6165b9875c3e68dc324453ae2b4e0260c933.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 156, + 287, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 156, + 287, + 180 + ], + "spans": [ + { + "bbox": [ + 47, + 156, + 287, + 180 + ], + "type": "text", + "content": "aligned feature " + }, + { + "bbox": [ + 47, + 156, + 287, + 180 + ], + "type": "inline_equation", + "content": "Z_{cs}" + }, + { + "bbox": [ + 47, + 156, + 287, + 180 + ], + "type": "text", + "content": " as input to predict the dynamic style filters " + }, + { + "bbox": [ + 47, + 156, + 287, + 180 + ], + "type": "inline_equation", + "content": "F, B = \\{F_1^{ij}, F_2^{ij}, B^{ij}\\}" + }, + { + "bbox": [ + 47, + 156, + 287, + 180 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 182, + 289, + 280 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 182, + 289, + 280 + ], + "spans": [ + { + "bbox": [ + 47, + 182, + 289, + 280 + ], + "type": "text", + "content": "Given the content-style aligned feature " + }, + { + "bbox": [ + 47, + 182, + 289, + 280 + ], + "type": "inline_equation", + "content": "Z_{cs}" + }, + { + "bbox": [ + 47, + 182, + 289, + 280 + ], + "type": "text", + "content": ", we take two convolution layers to predict the filters " + }, + { + "bbox": [ + 47, + 182, + 289, + 280 + ], + "type": "inline_equation", + "content": "F \\in \\mathbb{R}^{H_c \\times W_c \\times C \\times 2k}" + }, + { + "bbox": [ + 47, + 182, + 289, + 280 + ], + "type": "text", + "content": ", which has two 1-dim filters " + }, + { + "bbox": [ + 47, + 182, + 289, + 280 + ], + "type": "inline_equation", + "content": "F_1 = \\{F_1^{ij}\\}" + }, + { + "bbox": [ + 47, + 182, + 289, + 280 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 182, + 289, + 280 + ], + "type": "inline_equation", + "content": "F_2 = \\{F_2^{ij}\\}" + }, + { + "bbox": [ + 47, + 182, + 289, + 280 + ], + "type": "text", + "content": " of the sizes " + }, + { + "bbox": [ + 47, + 182, + 289, + 280 + ], + "type": "inline_equation", + "content": "k \\times 1" + }, + { + "bbox": [ + 47, + 182, + 289, + 280 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 182, + 289, + 280 + ], + "type": "inline_equation", + "content": "1 \\times k" + }, + { + "bbox": [ + 47, + 182, + 289, + 280 + ], + "type": "text", + "content": ", respectively, and one bias vector " + }, + { + "bbox": [ + 47, + 182, + 289, + 280 + ], + "type": "inline_equation", + "content": "B = \\{B^{ij}\\} \\in \\mathbb{R}^{H_c \\times W_c \\times C \\times 1}" + }, + { + "bbox": [ + 47, + 182, + 289, + 280 + ], + "type": "text", + "content": ". Finally, we conduct convolution operations on the content feature " + }, + { + "bbox": [ + 47, + 182, + 289, + 280 + ], + "type": "inline_equation", + "content": "Z_{c}" + }, + { + "bbox": [ + 47, + 182, + 289, + 280 + ], + "type": "text", + "content": " with the learned dynamic style kernels " + }, + { + "bbox": [ + 47, + 182, + 289, + 280 + ], + "type": "inline_equation", + "content": "F_1" + }, + { + "bbox": [ + 47, + 182, + 289, + 280 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 182, + 289, + 280 + ], + "type": "inline_equation", + "content": "F_2" + }, + { + "bbox": [ + 47, + 182, + 289, + 280 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 182, + 289, + 280 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 47, + 182, + 289, + 280 + ], + "type": "text", + "content": ". The output after the convolutions is the feature called " + }, + { + "bbox": [ + 47, + 182, + 289, + 280 + ], + "type": "inline_equation", + "content": "\\bar{Z}_{cs}" + }, + { + "bbox": [ + 47, + 182, + 289, + 280 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 108, + 291, + 287, + 312 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 291, + 287, + 312 + ], + "spans": [ + { + "bbox": [ + 108, + 291, + 287, + 312 + ], + "type": "interline_equation", + "content": "\\bar {Z} _ {c s} = \\frac {Z _ {c} - \\mu}{\\sigma} * F _ {1} * F _ {2} + B, \\tag {6}", + "image_path": "12b45ef9efd976d8a7803ed4b8f218542657b4e749af839e88f7a3cf59fd332e.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 323, + 287, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 323, + 287, + 361 + ], + "spans": [ + { + "bbox": [ + 47, + 323, + 287, + 361 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 323, + 287, + 361 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 47, + 323, + 287, + 361 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 323, + 287, + 361 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 47, + 323, + 287, + 361 + ], + "type": "text", + "content": " are the affine parameters in normalization layer and " + }, + { + "bbox": [ + 47, + 323, + 287, + 361 + ], + "type": "inline_equation", + "content": "^*" + }, + { + "bbox": [ + 47, + 323, + 287, + 361 + ], + "type": "text", + "content": " is the convolution operator. " + }, + { + "bbox": [ + 47, + 323, + 287, + 361 + ], + "type": "inline_equation", + "content": "\\bar{Z}_{cs}" + }, + { + "bbox": [ + 47, + 323, + 287, + 361 + ], + "type": "text", + "content": " is then passed to the decoder to generate the stylized image " + }, + { + "bbox": [ + 47, + 323, + 287, + 361 + ], + "type": "inline_equation", + "content": "I_{cs}" + }, + { + "bbox": [ + 47, + 323, + 287, + 361 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 365, + 289, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 365, + 289, + 569 + ], + "spans": [ + { + "bbox": [ + 47, + 365, + 289, + 569 + ], + "type": "text", + "content": "Remarks. Note that different from \"style code\" [48] modeled as the parameters (e.g. mean and variance) which are shared over all spatial positions globally without taking different semantic regions into consideration, our learned dynamic style kernels are position point-wisely inferred from the globally style-content aligned feature, and therefore are able to fully explore the point-wise semantic structure correlation to modulate local content feature for better artistic style transfer. Our dynamic style kernels make it possible to transfer both the globally aggregated content-style aligned features to local regions in the content images. This ensures our new scheme \"style kernel\" works well on consistent stylization with well preserved structure, and alleviates the shortages of existing style transfer methods [15, 16, 28, 31] which either globally modulate the content feature ignoring local details or overly focus on the local structure details leading to style leakage." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 582, + 141, + 594 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 582, + 141, + 594 + ], + "spans": [ + { + "bbox": [ + 47, + 582, + 141, + 594 + ], + "type": "text", + "content": "3.3. Loss Functions" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 601, + 287, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 601, + 287, + 639 + ], + "spans": [ + { + "bbox": [ + 47, + 601, + 287, + 639 + ], + "type": "text", + "content": "The loss function is formulated with an adversarial loss " + }, + { + "bbox": [ + 47, + 601, + 287, + 639 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{adv}" + }, + { + "bbox": [ + 47, + 601, + 287, + 639 + ], + "type": "text", + "content": ", a reconstruction loss " + }, + { + "bbox": [ + 47, + 601, + 287, + 639 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{rec}" + }, + { + "bbox": [ + 47, + 601, + 287, + 639 + ], + "type": "text", + "content": ", a REMD loss " + }, + { + "bbox": [ + 47, + 601, + 287, + 639 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{REMD}" + }, + { + "bbox": [ + 47, + 601, + 287, + 639 + ], + "type": "text", + "content": ", a style loss " + }, + { + "bbox": [ + 47, + 601, + 287, + 639 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{sty}" + }, + { + "bbox": [ + 47, + 601, + 287, + 639 + ], + "type": "text", + "content": " [20] and a content loss " + }, + { + "bbox": [ + 47, + 601, + 287, + 639 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{cont}" + }, + { + "bbox": [ + 47, + 601, + 287, + 639 + ], + "type": "text", + "content": " [33] as:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 652, + 304, + 677 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 652, + 304, + 677 + ], + "spans": [ + { + "bbox": [ + 47, + 652, + 304, + 677 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\mathcal {L} _ {\\text {a d v}} + \\lambda_ {\\text {r e c}} \\mathcal {L} _ {\\text {r e c}} + \\lambda_ {\\text {c o n t}} \\mathcal {L} _ {\\text {c o n t}} + \\lambda_ {\\text {s t y}} \\mathcal {L} _ {\\text {s t y}} + \\lambda_ {\\text {R E M D}} \\mathcal {L} _ {\\text {R E M D}} \\tag {7}", + "image_path": "594cfa198d02fd83363465550cc2a4e8fe18bb42cb3f0ce6d5e4fd41ec7d0b60.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\lambda_{adv}" + }, + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\lambda_{rec}" + }, + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\lambda_{cont}" + }, + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\lambda_{sty}" + }, + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\lambda_{REMD}" + }, + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "content": " are the hyperparameters used to balance the loss during training." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 156, + 471, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 156, + 471, + 168 + ], + "spans": [ + { + "bbox": [ + 306, + 156, + 471, + 168 + ], + "type": "text", + "content": "Reconstruction Loss " + }, + { + "bbox": [ + 306, + 156, + 471, + 168 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{rec}" + }, + { + "bbox": [ + 306, + 156, + 471, + 168 + ], + "type": "text", + "content": " is defined as:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 176, + 546, + 232 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 176, + 546, + 232 + ], + "spans": [ + { + "bbox": [ + 306, + 176, + 546, + 232 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {r e c} = \\lambda_ {r e c 1} \\big (| | I _ {c c} - I _ {c} | | _ {2} + | | I _ {s s} - I _ {s} | | _ {2} \\big) \\\\ + \\lambda_ {r e c 2} \\sum_ {l = 1} ^ {L} \\left(\\left\\| \\phi_ {l} \\left(I _ {c c}\\right) - \\phi_ {l} \\left(I _ {c}\\right) \\right\\| _ {2} + \\left\\| \\phi_ {l} \\left(I _ {s s}\\right) - \\phi_ {l} \\left(I _ {s}\\right) \\right\\| _ {2}\\right), \\tag {8} \\\\ \\end{array}", + "image_path": "254a629f8cfff93b8953a1ecc1c90cc379cceae655012e7323c4f5304148a832.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 242, + 546, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 242, + 546, + 289 + ], + "spans": [ + { + "bbox": [ + 305, + 242, + 546, + 289 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 242, + 546, + 289 + ], + "type": "inline_equation", + "content": "I_{cc}" + }, + { + "bbox": [ + 305, + 242, + 546, + 289 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 242, + 546, + 289 + ], + "type": "inline_equation", + "content": "I_{ss}" + }, + { + "bbox": [ + 305, + 242, + 546, + 289 + ], + "type": "text", + "content": " are the reconstructed images when both the input content and style images are " + }, + { + "bbox": [ + 305, + 242, + 546, + 289 + ], + "type": "inline_equation", + "content": "I_{c}" + }, + { + "bbox": [ + 305, + 242, + 546, + 289 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 242, + 546, + 289 + ], + "type": "inline_equation", + "content": "I_{s}" + }, + { + "bbox": [ + 305, + 242, + 546, + 289 + ], + "type": "text", + "content": ", respectively. " + }, + { + "bbox": [ + 305, + 242, + 546, + 289 + ], + "type": "inline_equation", + "content": "\\phi_l" + }, + { + "bbox": [ + 305, + 242, + 546, + 289 + ], + "type": "text", + "content": " refers to the " + }, + { + "bbox": [ + 305, + 242, + 546, + 289 + ], + "type": "inline_equation", + "content": "l_{th}" + }, + { + "bbox": [ + 305, + 242, + 546, + 289 + ], + "type": "text", + "content": " layer in VGG. We chose features from Relu2_1, Relu3_1, Relu4_1 and Relu5_1 layers." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 289, + 545, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 289, + 545, + 324 + ], + "spans": [ + { + "bbox": [ + 305, + 289, + 545, + 324 + ], + "type": "text", + "content": "REMD Loss " + }, + { + "bbox": [ + 305, + 289, + 545, + 324 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text{REMD}}" + }, + { + "bbox": [ + 305, + 289, + 545, + 324 + ], + "type": "text", + "content": " [25] adapts the relaxed earth mover distance (REMD) to align the manifold surface of style features. It is formulated as:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 331, + 545, + 369 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 331, + 545, + 369 + ], + "spans": [ + { + "bbox": [ + 313, + 331, + 545, + 369 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {R E M D} = \\max \\left(\\frac {1}{W _ {s} H _ {s}} \\sum_ {i} \\min _ {j} C _ {i j}, \\frac {1}{W _ {c} H _ {c}} \\sum_ {j} \\min _ {i} C _ {i j}\\right), \\tag {9}", + "image_path": "d964e104ed5f9cb8fc2e7487abf59467b25977ab9fe0dc319efc2ca3a648203c.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 378, + 545, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 378, + 545, + 403 + ], + "spans": [ + { + "bbox": [ + 305, + 378, + 545, + 403 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 378, + 545, + 403 + ], + "type": "inline_equation", + "content": "C_{ij}" + }, + { + "bbox": [ + 305, + 378, + 545, + 403 + ], + "type": "text", + "content": " denotes the pair-wise cosine distance matrix between the " + }, + { + "bbox": [ + 305, + 378, + 545, + 403 + ], + "type": "inline_equation", + "content": "i_{th}" + }, + { + "bbox": [ + 305, + 378, + 545, + 403 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 378, + 545, + 403 + ], + "type": "inline_equation", + "content": "j_{th}" + }, + { + "bbox": [ + 305, + 378, + 545, + 403 + ], + "type": "text", + "content": " feature vector in " + }, + { + "bbox": [ + 305, + 378, + 545, + 403 + ], + "type": "inline_equation", + "content": "Z_{cs}" + }, + { + "bbox": [ + 305, + 378, + 545, + 403 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 378, + 545, + 403 + ], + "type": "inline_equation", + "content": "Z_{s}" + }, + { + "bbox": [ + 305, + 378, + 545, + 403 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 413, + 388, + 427 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 413, + 388, + 427 + ], + "spans": [ + { + "bbox": [ + 306, + 413, + 388, + 427 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 433, + 547, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 433, + 547, + 553 + ], + "spans": [ + { + "bbox": [ + 304, + 433, + 547, + 553 + ], + "type": "text", + "content": "We train our proposed method on content images from the MS-COCO [30] dataset, and style images from WikiArt [23] database. Each dataset has around 80k images. The training images are first resized to 512, and then " + }, + { + "bbox": [ + 304, + 433, + 547, + 553 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 304, + 433, + 547, + 553 + ], + "type": "text", + "content": " patches are randomly cropped from the images as inputs. Note that our model can be applied to images of any resolution at the testing stage. Our model is implemented by PyTorch [34]. The Adam [24] is adopted as the optimization solver. We train our model for 160k iterations with a batch size of 16. The learning rate is set to 0.0001." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 553, + 547, + 637 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 553, + 547, + 637 + ], + "spans": [ + { + "bbox": [ + 305, + 553, + 547, + 637 + ], + "type": "text", + "content": "The hyperparameters in loss functions are set to " + }, + { + "bbox": [ + 305, + 553, + 547, + 637 + ], + "type": "inline_equation", + "content": "\\lambda_{cont} = 1" + }, + { + "bbox": [ + 305, + 553, + 547, + 637 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 553, + 547, + 637 + ], + "type": "inline_equation", + "content": "\\lambda_{rec} = 1" + }, + { + "bbox": [ + 305, + 553, + 547, + 637 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 553, + 547, + 637 + ], + "type": "inline_equation", + "content": "\\lambda_{sty} = 1" + }, + { + "bbox": [ + 305, + 553, + 547, + 637 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 553, + 547, + 637 + ], + "type": "inline_equation", + "content": "\\lambda_{rec1} = 20" + }, + { + "bbox": [ + 305, + 553, + 547, + 637 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 553, + 547, + 637 + ], + "type": "inline_equation", + "content": "\\lambda_{rec2} = 0.5" + }, + { + "bbox": [ + 305, + 553, + 547, + 637 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 553, + 547, + 637 + ], + "type": "inline_equation", + "content": "\\lambda_{REMD} = 3" + }, + { + "bbox": [ + 305, + 553, + 547, + 637 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 305, + 553, + 547, + 637 + ], + "type": "inline_equation", + "content": "\\lambda_{adv} = 1" + }, + { + "bbox": [ + 305, + 553, + 547, + 637 + ], + "type": "text", + "content": ". The encoder is a pretrained VGG-16 network [40], whose parameters are fixed during model training. A multi-scale discriminator is adopted from [43]. We update the discriminator one time after two generator iterations." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 644, + 531, + 657 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 644, + 531, + 657 + ], + "spans": [ + { + "bbox": [ + 305, + 644, + 531, + 657 + ], + "type": "text", + "content": "4.1. Comparison with State-of-the-Art Methods" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 665, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 665, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 665, + 547, + 714 + ], + "type": "text", + "content": "Qualitative Evaluation. As shown in Figure 4, we present qualitative results of different style transfer methods i.e., AdaConv [2], DRB-GAN [48], statistics matching based method like AdaIN [15], attention based methods including" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10087" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 70, + 545, + 401 + ], + "blocks": [ + { + "bbox": [ + 49, + 70, + 545, + 401 + ], + "lines": [ + { + "bbox": [ + 49, + 70, + 545, + 401 + ], + "spans": [ + { + "bbox": [ + 49, + 70, + 545, + 401 + ], + "type": "image", + "image_path": "d6b6fb1168881785c745bb9d5457e39f4a919107b0f5b2bdedf7cd1275be5f9e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 176, + 403, + 416, + 413 + ], + "lines": [ + { + "bbox": [ + 176, + 403, + 416, + 413 + ], + "spans": [ + { + "bbox": [ + 176, + 403, + 416, + 413 + ], + "type": "text", + "content": "Figure 4. Qualitative performance comparison on stylized results." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 47, + 440, + 548, + 494 + ], + "blocks": [ + { + "bbox": [ + 46, + 416, + 546, + 438 + ], + "lines": [ + { + "bbox": [ + 46, + 416, + 546, + 438 + ], + "spans": [ + { + "bbox": [ + 46, + 416, + 546, + 438 + ], + "type": "text", + "content": "Table 2. Quantitative comparison with state-of-the-art methods. We compute the average style loss and the LPIPS score of different methods to indicate how well the style and content are transferred." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 47, + 440, + 548, + 494 + ], + "lines": [ + { + "bbox": [ + 47, + 440, + 548, + 494 + ], + "spans": [ + { + "bbox": [ + 47, + 440, + 548, + 494 + ], + "type": "table", + "html": "
MethodAdaIN'17LST'19AvatarNet'18SANet'19IEC'21DRB-GAN'21AdaAttN'21MAST'21AdaConv'21StrTr²²Ours
Sty Loss↓1.772.675.911.411.811.511.14-1.041.070.98
LPIPS ↓0.370.330.340.360.310.330.320.320.420.330.30
", + "image_path": "a579c9f6a830248f4fa65b410024d3e406f631b3f7cf1710acc6dbfcca2ac82a.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 501, + 287, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 501, + 287, + 574 + ], + "spans": [ + { + "bbox": [ + 46, + 501, + 287, + 574 + ], + "type": "text", + "content": "AdaAttN [31] and IEC [5], and feature modification methods like " + }, + { + "bbox": [ + 46, + 501, + 287, + 574 + ], + "type": "inline_equation", + "content": "\\mathrm{StrTr}^2" + }, + { + "bbox": [ + 46, + 501, + 287, + 574 + ], + "type": "text", + "content": " [8] and MAST [16]. For a fair comparison, we deploy all competing methods for style transfer on images of the smaller dimension resized to 512 while the aspect ratio is preserved. Note that we use the public released code and follow the default configurations for testing." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "content": "The comparison in Figure 4 shows the outperformance of our method in terms of visual quality. These images produced by our method faithfully reflect the style characters (e.g., stroke sizes and colors) with no artifact in the regions, and most importantly, they preserve the structural similarity of the content images. On the contrary, AdaIN [15] and MAST [16] fail to generate sharp details and fine strokes. AdaConv [2] yields distorted patterns as it cannot always recover the original style patterns. We also observe nonnegligible artificial structures in those images obtained by " + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathrm{StrTr}^2" + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "content": " [8], DRB-GAN [48] and AdaIN [15]. These meth" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 502, + 547, + 562 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 502, + 547, + 562 + ], + "spans": [ + { + "bbox": [ + 304, + 502, + 547, + 562 + ], + "type": "text", + "content": "ods struggle to preserve the consistency in semantic regions such as the sky. In addition, AdaAttN [31] and IEC [5] and MAST [16] tend to overly preserve the structural similarity and fail to transfer the style to the content image, which makes the results look like the content images." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "content": "Quantitative Evaluation. (1) Style Loss. Following WCT [28], we adopt the style loss to measure the style consistency between the generated stylizations and the style references. The results of different methods are reported in Table 2. As we can observe, our method achieves the lowest style loss, which indicates that our method mostly transfers the style information to the output. (2) LPIPS. We conduct LPIPS to measure the stability and consistency of rendered video clips by following IEC [5]. This metric is to compute the average perceptual distances between consecutive frames and the lower LPIPS score indicates a better stable and consistent performance. We synthesize 10 video clips" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "10088" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 70, + 547, + 205 + ], + "blocks": [ + { + "bbox": [ + 49, + 70, + 547, + 205 + ], + "lines": [ + { + "bbox": [ + 49, + 70, + 547, + 205 + ], + "spans": [ + { + "bbox": [ + 49, + 70, + 547, + 205 + ], + "type": "image", + "image_path": "f232a4ce0e872f74b2d993bccf2b7954e25677987aa41a6f536de27315883cf3.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 207, + 546, + 231 + ], + "lines": [ + { + "bbox": [ + 46, + 207, + 546, + 231 + ], + "spans": [ + { + "bbox": [ + 46, + 207, + 546, + 231 + ], + "type": "text", + "content": "Figure 5. Qualitative performance comparison on stylized results of different model variants. The results of SANet are also listed as reference. Please zoom in to observe the detailed difference." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 56, + 240, + 279, + 353 + ], + "blocks": [ + { + "bbox": [ + 56, + 240, + 279, + 353 + ], + "lines": [ + { + "bbox": [ + 56, + 240, + 279, + 353 + ], + "spans": [ + { + "bbox": [ + 56, + 240, + 279, + 353 + ], + "type": "image", + "image_path": "ff832659753253a2c706d1da2144ef11e4deaba740d36ceabefefb850353fd9f.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 354, + 287, + 376 + ], + "lines": [ + { + "bbox": [ + 47, + 354, + 287, + 376 + ], + "spans": [ + { + "bbox": [ + 47, + 354, + 287, + 376 + ], + "type": "text", + "content": "Figure 6. Effectiveness of the Content-based Gating Module (CGM). The results of AdaAttN are also listed as reference." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 93, + 383, + 240, + 481 + ], + "blocks": [ + { + "bbox": [ + 93, + 383, + 240, + 481 + ], + "lines": [ + { + "bbox": [ + 93, + 383, + 240, + 481 + ], + "spans": [ + { + "bbox": [ + 93, + 383, + 240, + 481 + ], + "type": "image", + "image_path": "5d87ca800903838f16dca8eda18032ccfc8e8071b3f73514cccafeeee581c732.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 482, + 288, + 528 + ], + "lines": [ + { + "bbox": [ + 46, + 482, + 288, + 528 + ], + "spans": [ + { + "bbox": [ + 46, + 482, + 288, + 528 + ], + "type": "text", + "content": "Figure 7. Impact of grouped shuffling: we randomly take 100 content-style pairs to create stylizations. From their feature maps extracted by VGG network, we measure the mean activation value channel-wisely and report the overall distribution." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 542, + 287, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 542, + 287, + 567 + ], + "spans": [ + { + "bbox": [ + 46, + 542, + 287, + 567 + ], + "type": "text", + "content": "for each method. In Table 2 we observe that our approach produces the lowest LPIPS score among all methods." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": "Efficiency Analysis. In Table 1, we compare the inference time of different methods on image resolutions of " + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": ". All experiments are conducted using a single Tesla V100 GPU. Our method can achieve 25 fps on " + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": " images, which is comparable with SOTA methods such as AdaAttN and IEC. It worth pointing out that the operation of our style kernel takes FLOPs cost of " + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "inline_equation", + "content": "H_{c} \\times W_{c} \\times C_{in} \\times (k + k + 1)" + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": " while vanilla convolution operation has FLOPS cost of " + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "inline_equation", + "content": "H_{c} \\times W_{c} \\times C_{out} \\times (C_{in} \\times k \\times k + 1)" + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": ". In Table 3, we compare the inference time given different kernel sizes. Note we set " + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "inline_equation", + "content": "k = 3" + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": " as a trade-off between the efficiency and performance." + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 313, + 253, + 536, + 314 + ], + "blocks": [ + { + "bbox": [ + 335, + 241, + 515, + 251 + ], + "lines": [ + { + "bbox": [ + 335, + 241, + 515, + 251 + ], + "spans": [ + { + "bbox": [ + 335, + 241, + 515, + 251 + ], + "type": "text", + "content": "Table 3. Results of different sizes of style kernel." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 313, + 253, + 536, + 314 + ], + "lines": [ + { + "bbox": [ + 313, + 253, + 536, + 314 + ], + "spans": [ + { + "bbox": [ + 313, + 253, + 536, + 314 + ], + "type": "table", + "html": "
SettingSty Loss↓LPIPS ↓T256 ↓T512 ↓
k=11.040.300.0150.034
k=30.980.300.0170.035
k=50.970.310.0210.044
", + "image_path": "cd95f33141491ba1d20f07b8a904be8a131ae0509d87c0b5ee7468965a8b040d.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 320, + 400, + 335 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 320, + 400, + 335 + ], + "spans": [ + { + "bbox": [ + 306, + 320, + 400, + 335 + ], + "type": "text", + "content": "4.2. Ablation Study" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 339, + 545, + 364 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 339, + 545, + 364 + ], + "spans": [ + { + "bbox": [ + 305, + 339, + 545, + 364 + ], + "type": "text", + "content": "We conduct ablation studies to highlight the effectiveness of different modeling components used by our method." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 366, + 546, + 463 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 366, + 546, + 463 + ], + "spans": [ + { + "bbox": [ + 305, + 366, + 546, + 463 + ], + "type": "text", + "content": "Effectiveness of Style Kernel. This module works to fully explore the point-wise semantic structure correlation to modulate local content features for better artistic style transfer. As shown in Figure 5, our dynamic style kernels make it possible to transfer both the globally aggregated content- style aligned features to local regions in the content images. This ensures our new scheme \"style kernel\" works well on consistent stylization with well preserved structure." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 465, + 545, + 562 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 465, + 545, + 562 + ], + "spans": [ + { + "bbox": [ + 305, + 465, + 545, + 562 + ], + "type": "text", + "content": "Effectiveness of Grouped Shuffling. To verify this module, we report the statistic distribution of activation strength in Table 7. The distribution gap between the results and real artworks is significantly reduced via using grouped shuffling. Without using GS module, the model fails to produce stylizations consistent to the style reference as shown in Figure 5. This demonstrates that the GS shrinks the statistic gap between the generated images and the style images." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 563, + 545, + 660 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 563, + 545, + 660 + ], + "spans": [ + { + "bbox": [ + 304, + 563, + 545, + 660 + ], + "type": "text", + "content": "Effectiveness of CGM. We summarized the results of our model w/ and w/o CGM in Figure 6. The model w/o CGM produces images containing regions with corrupted patterns and the stylization is not consistent to the style reference. While our model w/ CGM faithfully preserves the completeness of semantic regions. This is because our CGM aims to select focusing regions, where query points can aggregate style information from fairly correlated nodes." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 668, + 410, + 679 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 668, + 410, + 679 + ], + "spans": [ + { + "bbox": [ + 306, + 668, + 410, + 679 + ], + "type": "text", + "content": "4.3. More Discussions" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "content": "Generalization of CGM. Our content-based gating modulation can be flexibly deployed as a plug-in module. To ver-" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10089" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 70, + 120, + 207 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 120, + 207 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 120, + 207 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 120, + 207 + ], + "type": "image", + "image_path": "641f9ab3d2660407056cf5a96f53936841ba51fe2ceabe9f174671452cde4b4f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 83, + 209, + 107, + 217 + ], + "lines": [ + { + "bbox": [ + 83, + 209, + 107, + 217 + ], + "spans": [ + { + "bbox": [ + 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+ }, + { + "bbox": [ + 64, + 353, + 112, + 361 + ], + "lines": [ + { + "bbox": [ + 64, + 353, + 112, + 361 + ], + "spans": [ + { + "bbox": [ + 64, + 353, + 112, + 361 + ], + "type": "text", + "content": "Content & Style" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 364, + 287, + 396 + ], + "lines": [ + { + "bbox": [ + 46, + 364, + 287, + 396 + ], + "spans": [ + { + "bbox": [ + 46, + 364, + 287, + 396 + ], + "type": "text", + "content": "Figure 9. Comparisons on video style transfer. The 1st column lists 2 frames from a video clip as content images. The style image is at the bottom-right corner." + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 129, + 250, + 206, + 351 + ], + "blocks": [ + { + "bbox": [ + 129, + 250, + 206, + 351 + ], + "lines": [ + { + "bbox": [ + 129, + 250, + 206, + 351 + ], + "spans": [ + { + "bbox": [ + 129, + 250, + 206, + 351 + ], + "type": "image", + "image_path": "59a41d33b03310aaa22a29584e4e3e94e28edab51d9ccbdd89704498296b02c8.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 156, + 353, + 172, + 361 + ], + "lines": [ + { + "bbox": [ + 156, + 353, + 172, + 361 + ], + "spans": [ + { + "bbox": [ + 156, + 353, + 172, + 361 + ], + "type": "text", + "content": "Ours" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 207, + 250, + 285, + 351 + ], + "blocks": [ + { + "bbox": [ + 207, + 250, + 285, + 351 + ], + "lines": [ + { + "bbox": [ + 207, + 250, + 285, + 351 + ], + "spans": [ + { + "bbox": [ + 207, + 250, + 285, + 351 + ], + "type": "image", + "image_path": "73c4cc5df329188124e3cfcf8af80b33c2bb2e0fca6e726e30df02d28e1d34ff.jpg" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 227, + 353, + 260, + 361 + ], + "lines": [ + { + "bbox": [ + 227, + 353, + 260, + 361 + ], + "spans": [ + { + "bbox": [ + 227, + 353, + 260, + 361 + ], + "type": "text", + "content": "DRB-GAN" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_caption" + } + ], + "index": 19 + }, + { + "bbox": [ + 46, + 407, + 287, + 537 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 407, + 287, + 537 + ], + "spans": [ + { + "bbox": [ + 46, + 407, + 287, + 537 + ], + "type": "text", + "content": "if the generalization, we conduct experiments by replacing the attention module in SANet and IEC with our CGM module. The refactored models are denoted as SANet + CGM and IEC + CGM. We train these models with the default settings and compare the performances in Figure 8. We can observe there are nonneglectable artifacts and distorted regions in the results of original SANet and IEC. By plugging-in our CGM, the artifacts are removed and the semantic regions are well preserved. This further proves the effectiveness of our CGM in aggregating semantically consistent information." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 46, + 541, + 287, + 650 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 541, + 287, + 650 + ], + "spans": [ + { + "bbox": [ + 46, + 541, + 287, + 650 + ], + "type": "text", + "content": "Real-world Video Style Transfer. To verify the performance on real-world video stylization, we collect a 1080P video clip consist of 1377 images and compare our method with DRB-GAN [48]. As shown in Figure 9, our approach outperforms existing style transfer methods in terms of style consistency and stability. This can be attributed to the fact that our style kernels are good at transferring the globally aggregated and locally semantic-aligned style features to local regions." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "text", + "content": "Social Impact and Future Work. Our model achieves impressive image stylizations with well preserved content structure and consistent style characteristics, as shown in Figure 10. This can definitely benefit our society. In the future, we will incorporate text information for text condi" + } + ] + } + ], + "index": 24 + }, + { + "type": "image", + "bbox": [ + 318, + 249, + 467, + 430 + ], + "blocks": [ + { + "bbox": [ + 46, + 220, + 545, + 243 + ], + "lines": [ + { + "bbox": [ + 46, + 220, + 545, + 243 + ], + "spans": [ + { + "bbox": [ + 46, + 220, + 545, + 243 + ], + "type": "text", + "content": "Figure 8. Generalization of our Content-based Gating Module (CGM). By replacing the attention module in SANet and IEC with our CGM, the artifacts and distorted regions in the results of original SANet and IEC are removed and the semantic regions are well preserved." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 318, + 249, + 467, + 430 + ], + "lines": [ + { + "bbox": [ + 318, + 249, + 467, + 430 + ], + "spans": [ + { + "bbox": [ + 318, + 249, + 467, + 430 + ], + "type": "image", + "image_path": "50b63598938ed7f852beed901fd876d7e02e8a6bf1df8870b4aaa7b0502b46c0.jpg" + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 383, + 432, + 399, + 440 + ], + "lines": [ + { + "bbox": [ + 383, + 432, + 399, + 440 + ], + "spans": [ + { + "bbox": [ + 383, + 432, + 399, + 440 + ], + "type": "text", + "content": "Ours" + } + ] + } + ], + "index": 26, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 306, + 443, + 545, + 465 + ], + "lines": [ + { + "bbox": [ + 306, + 443, + 545, + 465 + ], + "spans": [ + { + "bbox": [ + 306, + 443, + 545, + 465 + ], + "type": "text", + "content": "Figure 10. Demonstration of the performance of our method in terms of style consistency and structural similarity." + } + ] + } + ], + "index": 30, + "angle": 0, + "type": "image_caption" + } + ], + "index": 25 + }, + { + "type": "image", + "bbox": [ + 469, + 250, + 534, + 340 + ], + "blocks": [ + { + "bbox": [ + 469, + 250, + 534, + 340 + ], + "lines": [ + { + "bbox": [ + 469, + 250, + 534, + 340 + ], + "spans": [ + { + "bbox": [ + 469, + 250, + 534, + 340 + ], + "type": "image", + "image_path": "fb7885e43e8ffb8cf351d96e7369ff28a07e00438a44c54e4849428448612b40.jpg" + } + ] + } + ], + "index": 27, + "angle": 0, + "type": "image_body" + } + ], + "index": 27 + }, + { + "type": "image", + "bbox": [ + 469, + 341, + 534, + 430 + ], + "blocks": [ + { + "bbox": [ + 469, + 341, + 534, + 430 + ], + "lines": [ + { + "bbox": [ + 469, + 341, + 534, + 430 + ], + "spans": [ + { + "bbox": [ + 469, + 341, + 534, + 430 + ], + "type": "image", + "image_path": "7d497f3e307bdf49abe266035da881092573f73c9331a27ccbd21564cdb76dac.jpg" + } + ] + } + ], + "index": 28, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 495, + 432, + 511, + 441 + ], + "lines": [ + { + "bbox": [ + 495, + 432, + 511, + 441 + ], + "spans": [ + { + "bbox": [ + 495, + 432, + 511, + 441 + ], + "type": "text", + "content": "Style" + } + ] + } + ], + "index": 29, + "angle": 0, + "type": "image_caption" + } + ], + "index": 28 + }, + { + "bbox": [ + 306, + 472, + 406, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 472, + 406, + 484 + ], + "spans": [ + { + "bbox": [ + 306, + 472, + 406, + 484 + ], + "type": "text", + "content": "tioned image stylization." + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 306, + 495, + 378, + 507 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 495, + 378, + 507 + ], + "spans": [ + { + "bbox": [ + 306, + 495, + 378, + 507 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 304, + 515, + 545, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 515, + 545, + 658 + ], + "spans": [ + { + "bbox": [ + 304, + 515, + 545, + 658 + ], + "type": "text", + "content": "In this paper, we present a new scheme \"style kernel\" for artistic style transfer. Our method learns an attention map with focusing regions using the proposed content-based gating operator. The style feature is then aligned to match the semantics in the content feature based on the learned attention map. In the style kernel generation module, the dynamic parameters \"style kernel\" are learned from the content-style aligned feature and then applied to modulate the content feature for style transfer. Extensive experimental results demonstrate the remarkable performance of our model in generating synthetic style images with better quality than the state-of-the-art." + } + ] + } + ], + "index": 33 + }, + { + "bbox": [ + 306, + 670, + 403, + 683 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 670, + 403, + 683 + ], + "spans": [ + { + "bbox": [ + 306, + 670, + 403, + 683 + ], + "type": "text", + "content": "Acknowledgement" + } + ] + } + ], + "index": 34 + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": "This research was sponsored by Prof. Yongwei Nie's Natural Science Foundation of China (62072191)." + } + ] + } + ], + "index": 35 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10090" + } + ] + } + ], + "index": 36 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 144 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 144 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 144 + ], + "type": "text", + "content": "[1] Nicolas Carion, Francisco Massa, Gabriel Synnaeve, Nicolas Usunier, Alexander Kirillov, and Sergey Zagoruyko. 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In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 2482-2491, 2019. 3" + } + ] + } + ], + "index": 26 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "10092" + } + ] + } + ], + "index": 28 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Learning Emotion Representations From Verbal and Nonverbal Communication/73b56492-ee9f-4305-8379-ca00142aa516_content_list.json b/2023/Learning Emotion Representations From Verbal and Nonverbal Communication/73b56492-ee9f-4305-8379-ca00142aa516_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..e2dc1293518456fc886eee0d44bfa92184f60aab --- /dev/null +++ b/2023/Learning Emotion Representations From Verbal and Nonverbal Communication/73b56492-ee9f-4305-8379-ca00142aa516_content_list.json @@ -0,0 +1,1772 @@ +[ + { + "type": "text", + "text": "Learning Emotion Representations from Verbal and Nonverbal Communication", + "text_level": 1, + "bbox": [ + 81, + 130, + 887, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Sitao Zhang* Yimu Pan* James Z. Wang \nThe Pennsylvania State University, University Park, Pennsylvania, USA \n{sbz5211,ymp5078,jwang}@psu.edu", + "bbox": [ + 199, + 180, + 769, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 268, + 313, + 284 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Emotion understanding is an essential but highly challenging component of artificial general intelligence. The absence of extensive annotated datasets has significantly impeded advancements in this field. We present EmotionCLIP, the first pre-training paradigm to extract visual emotion representations from verbal and nonverbal communication using only uncurated data. Compared to numerical labels or descriptions used in previous methods, communication naturally contains emotion information. Furthermore, acquiring emotion representations from communication is more congruent with the human learning process. We guide EmotionCLIP to attend to nonverbal emotion cues through subject-aware context encoding and verbal emotion cues using sentiment-guided contrastive learning. Extensive experiments validates the effectiveness and transferability of EmotionCLIP. Using merely linear-probe evaluation protocol, EmotionCLIP outperforms the state-of-the-art supervised visual emotion recognition methods and rivals many multimodal approaches across various benchmarks. We anticipate that the advent of EmotionCLIP will address the prevailing issue of data scarcity in emotion understanding, thereby fostering progress in related domains. The code and pre-trained models are available at https://github.com/Xeaver/EmotionCLIP.", + "bbox": [ + 76, + 301, + 473, + 662 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 696, + 209, + 710 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "If artificial intelligence (AI) can be equipped with emotional intelligence (EQ), it will be a significant step toward developing the next generation of artificial general intelligence [46, 92]. The combination of emotion and intelligence distinguishes humans from other animals. The ability to understand, use, and express emotions will significantly facilitate the interaction of AI with humans and the environment [20, 48-50], making it the foundation for a wide variety of HCI [3], robotics [11], and autonomous driving [31] applications.", + "bbox": [ + 75, + 722, + 468, + 875 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/09120afb63ac282c8370e218736934497c1794fd15e9bd4037a88d71a9ebfba4.jpg", + "image_caption": [ + "Categorical Label: Shocked Regretful 0 1 0 0 0 1 0 0 0", + "Figure 1. Emotions emerge naturally in human communication through verbal and nonverbal cues. The rich semantic details within the expression can hardly be represented by human-annotated categorical labels and descriptions in current datasets." + ], + "image_footnote": [ + "Description: An old man is chatting with his son while eating at a restaurant.", + "Conversation: \n- Dad. Who is Dede? \n- Jesus. She was the love of my life and I was too stupid to realized it. I lost her because of something so dumb." + ], + "bbox": [ + 511, + 268, + 880, + 402 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Artificial emotional intelligence (AEI) research is still in its nascency [30, 73]. The recent emergence of pretrained models in CV [10, 24, 62] and NLP [7, 16, 33, 68] domains has ushered in a new era of research in related subjects. By training on large-scale unlabeled data in a self-supervised manner, the model learns nontrivial representations that generalize to downstream tasks [42, 62]. Unfortunately, such a technique remains absent from AEI research. The conventional approaches in visual emotion understanding have no choice but to train models from scratch, or leverage models from less-relevant domains [27, 66], suffering from data scarcity [29, 45]. The lack of pre-trained models greatly limits the development of AEI research.", + "bbox": [ + 496, + 580, + 892, + 776 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Research in neuroscience and psychology offers insights for addressing this problem. Extending from the capabilities that have been coded genetically, humans learn emotional expressions through daily interaction and communication as early as when they are infants. It has been shown that both vision [58] and language [41] play crucial roles in this learning process. By absorbing and imitating expressions from others, humans eventually master the necessary", + "bbox": [ + 496, + 779, + 893, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*equal contribution", + "bbox": [ + 94, + 887, + 200, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "18993", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "feelings to comprehend emotional states by observing and analyzing facial expressions, body movements, contextual environments, etc.", + "bbox": [ + 75, + 90, + 468, + 135 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Inspired by how humans comprehend emotions, we propose a new paradigm for emotion understanding that learn directly from human communication. The core of our idea is to explore the consistency between verbal and nonverbal affective cues in daily communication. Fig. 1 shows how communication reveals emotion. Our method that learns from communication is not only aligned with the human learning process but also has several advantages:", + "bbox": [ + 75, + 137, + 467, + 258 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "1) Our method bypasses the problems in emotion data collection by leveraging uncurated data from daily communication. Existing emotion understanding datasets are mainly annotated using crowdsourcing [29, 45, 77]. For image classification tasks, it is straightforward for annotators to agree on an image's label due to the fact that the label is determined by certain low-level visual characteristics. However, crowdsourcing participants usually have lower consensus on producing emotion annotations due to the subjectivity and subtlety of affective labels [90]. This phenomenon makes it extremely difficult to collect accurate emotion annotations on a large scale. Our approach does not rely on human annotations, allowing us to benefit from nearly unlimited web data.", + "bbox": [ + 75, + 260, + 467, + 470 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2) Our use of verbal expressions preserves fine-grained semantics to the greatest extent possible. Limited by the data collection strategy, existing datasets usually only contain annotations for a limited number of emotion categories, which is far from covering the space of human emotional expression [86]. Moreover, the categorical labels commonly used in existing datasets fail to precisely represent the magnitude or intensity of a certain emotion.", + "bbox": [ + 75, + 473, + 467, + 592 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3) Our approach provides a way to directly model expressed emotion. Ideally, AEI should identify the individual's emotional state, i.e., the emotion the person desires to express. Unfortunately, it is nearly impossible to collect data on this type of \"expressed emotion\" on a large scale. Instead, the current practice is to collect data on \"perceived emotion\" to approximate the person's actual emotional state, which inevitably introduces noise and bias to labels.", + "bbox": [ + 75, + 594, + 467, + 729 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In general, learning directly from how humans express themselves is a promising alternative that gives a far broader source of supervision and a more comprehensive representation. This strategy is closely analogous to the human learning process and provides an efficient solution for extracting emotion representations from uncurated data.", + "bbox": [ + 75, + 731, + 467, + 821 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We summarize our main contributions as follows:", + "bbox": [ + 96, + 824, + 431, + 837 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We introduce EmotionCLIP, the first vision-language pre-training paradigm using uncurated data to the visual emotion understanding domain.", + "- We propose two techniques to guide the model to cap" + ], + "bbox": [ + 94, + 839, + 467, + 898 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ture salient emotional expressions from human verbal and nonverbal communication.", + "bbox": [ + 529, + 90, + 888, + 119 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- Extensive experiments and analysis demonstrate the superiority and transferability of our method on various downstream datasets in emotion understanding.", + "bbox": [ + 517, + 121, + 888, + 165 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 180, + 640, + 195 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Emotion Recognition from Visual Clues. Facial expression recognition [19, 38, 69] has been well studied in the field of emotion recognition, mainly because faces are not only expressive but also easy to model. Handcrafted features have been developed to describe different facial expressions [13, 43, 74]. Recently, deep learning-based approaches have begun to emerge [38]. Principal research focuses on the design of novel modules for conventional network architectures [88], distinct loss functions for facial tasks [15, 71, 85], and addressing label uncertainties [8, 80].", + "bbox": [ + 496, + 205, + 890, + 356 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recently, with the growing interest in recognizing emotion in the wild, the focus of research has gradually shifted to modeling body language [21, 45, 59] and context [29, 53, 54]. Several datasets for understanding human emotional states in unconstrained environments have been proposed [5, 60, 77]; Kosti et al. [29] and Yu et al. [45] established the first benchmark for image and video data, respectively. Follow-up work mainly focuses on context-aware emotion recognition, which usually adopts a multi-branch structure where one branch focuses on the face or body and the other focuses on capturing context [12, 34, 53, 59]. Moreover, some approaches take into account temporal causality [54] or represent context information via graphs [96]. To the best of our knowledge, there are no pre-trained models or effective methods for leveraging unlabeled data in the domain of visual emotion recognition.", + "bbox": [ + 496, + 357, + 890, + 598 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Vision-Language Pre-training. Visual-language pretraining has achieved remarkable progress recently. CLIP [62] demonstrated the feasibility of using contrastive learning [10, 56] to learn transferable and powerful visual representations from large-scale image-text pairs [72]. Many follow-up approaches have been proposed to transfer the pre-trained model to downstream tasks [22, 97, 100] or leverage the scheme for different domains [37, 57, 64, 83, 98]. A line of research endeavors to expand CLIP for general video understanding [26, 35, 40, 44, 55, 82, 87]. The majority of the effort focuses on fine-tuning datasets with textual annotations [27, 32, 39]. However, not only are these curated annotations challenging to obtain, but they also limit the model's potential in various applications. Another line of work [36, 87] extends the image-level pre-training by utilizing unlabeled narrated videos [2, 52], similar to ours. However, we aim to learn abstract emotion representations rather than low-level visual patterns, which are beyond the reach of current models. EmotionNet [84] and its sequel [99], which likewise seeks to learn visual emotion repre", + "bbox": [ + 496, + 598, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "18994", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/8447b9a880c03f8b45ef7ce5b3882f649e8278342e7062f38d3ebff1dd2ab3ee.jpg", + "image_caption": [ + "Figure 2. Illustration of EmotionCLIP. For nonverbal communication, subject and context information is modeled by a frame encoder and further aggregated into video-level representations by a temporal encoder. For verbal communication, textual information is encoded as text representations and sentiment scores by a text encoder and sentiment analysis model, respectively. The model learns emotion representations under sentiment guidance in a contrastive manner, by exploring the consistency of verbal and nonverbal communication." + ], + "image_footnote": [], + "bbox": [ + 117, + 87, + 851, + 319 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "sentations, are connected to ours. However, their primary focus is on the images' stimuli rather than the recognition of human emotional expressions in the wild.", + "bbox": [ + 75, + 412, + 470, + 458 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 76, + 474, + 212, + 493 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our core idea is to learn directly from human communication how they express their emotions, by exploring the consistency between their verbal and nonverbal expressions [41]. We tackle this learning task under the vision-language contrastive learning framework [62], that is, the model is expected to learn consistent emotion representations from the verbal expressions (e.g., utterance and dialogue) and nonverbal expressions (e.g., facial expression, body language, and contextual environment) of the same individuals. We give a brief introduction of our data collection procedure in Sec. 3.1 before presenting the overview of EmotionCLIP in Sec. 3.2. We further discuss how the model is guided to learn emotion-relevant representations from the nonverbal perspective in Sec. 3.3, and from the verbal perspective in Sec. 3.4. Please see Appendix for details of the dataset and implementations.", + "bbox": [ + 75, + 501, + 470, + 743 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Data Collection", + "text_level": 1, + "bbox": [ + 76, + 755, + 233, + 768 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Publicly available large-scale vision-and-language datasets do not provide desired verbal and nonverbal information because they either comprise only captions of low-level visual elements [2, 72] or instructions of actions [52]. The captions mostly contain a brief description of the scene or activity, which is insufficient to reveal the underlying emotions; the instruction videos rarely include humans in the scene or express neutral emotions, which fail", + "bbox": [ + 75, + 779, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "to provide supervision signals for emotion understanding. To overcome such problems, we gather a large-scale video-and-text paired dataset. More specifically, the videos are TV series, while the texts are the corresponding closed captions. We collected 3,613 TV series from YouTube, which is equivalent to around a million raw video clips. We processed them using the off-the-shelf models to group the words in closed caption into complete sentences [23], tag each sentence with a sentiment score [68], and extract human bounding boxes [79].", + "bbox": [ + 496, + 412, + 893, + 564 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Overview of EmotionCLIP", + "text_level": 1, + "bbox": [ + 500, + 574, + 743, + 589 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Fig. 2 presents an overview of our approach. We follow the wildly adopted vision-language contrastive learning paradigm [62] where two separate branches are used to encode visual inputs (i.e., nonverbal expressions) and textual inputs (i.e., verbal expressions), respectively.", + "bbox": [ + 496, + 598, + 890, + 672 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Video Encoding. The visual branch of EmotionCLIP takes two inputs, including a sequence of RGB frames $X_{v}$ and a sequence of binary masks $X_{m}$ . The binary mask has the same shape as the frame and corresponds to the frame one-to-one, indicating the location of the subject within the frame. The backbone of the subject-aware frame encoder $f_{i}$ is a Vision Transformer [17]. In particular, it extracts $m$ non-overlapping image patches from the frame and projects them into 1D tokens $z_{i} \\in \\mathbb{R}^{d}$ . The sequence of tokens passed to the following Transformer encoder [76] is $\\mathbf{z} = [z_{1}, \\dots, z_{m}, z_{cls}, z_{hmn}]$ , where $z_{cls}, z_{hmn}$ are two additional learnable tokens. The mask $X_{m}$ is converted to an array of indices $P$ indicating the image patches containing the subject. The frame encoder further encodes $\\mathbf{z}, P$ into a frame-level representation. All frame representations are normalized by the average of the raw data.", + "bbox": [ + 496, + 674, + 892, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "18995", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/a78f6735b1cf9c161c14e068857d0348624ba3606b2dcc103632f1080ad56e30.jpg", + "image_caption": [ + "Figure 3. The traditional approaches (left) ignore the dependencies between context and subject, and encode a portion of the image redundantly. The proposed approaches (right two diagrams) efficiently model the subject and context in a synchronous way." + ], + "image_footnote": [], + "bbox": [ + 81, + 87, + 470, + 184 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "tions are then passed into the temporal encoder $f_{p}$ to produce a video-level representation as $v = f_{v}(\\mathbf{z}, P)$ , where $f_{v} = f_{p} \\circ f_{i}$ and $v \\in \\mathbb{R}^{d}$ .", + "bbox": [ + 75, + 282, + 468, + 330 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Text Encoding. The textual branch of EmotionCLIP takes sentences $X_{t}$ as inputs. The text encoder $f_{t}$ is a Transformer [16] with the architecture modification described in [63], and the sentiment model $f_{s}$ is a pre-trained sentiment analysis model [68] that is frozen during training. The input text is encoded by both models as $t = f_{t}(X_{t})$ and $s = f_{s}(X_{t})$ , where $t \\in \\mathbb{R}^{d}$ is the representation of the text and $s \\in \\mathbb{R}^{7}$ is the pseudo sentiment score.", + "bbox": [ + 75, + 332, + 468, + 454 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Training Objective. The training objective is to learn the correspondence between visual inputs and textual inputs by minimizing the sentiment-guided contrastive loss $\\mathcal{L}$ .", + "bbox": [ + 75, + 457, + 468, + 502 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We discuss the details of the proposed subject-aware encoding approaches in Sec. 3.3 and the sentiment-guided contrastive learning framework in Sec. 3.4.", + "bbox": [ + 75, + 505, + 468, + 551 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Subject-Aware Context Encoding", + "text_level": 1, + "bbox": [ + 76, + 571, + 369, + 588 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Context encoding is an important part of emotion understanding, especially in unconstrained environments, as it has been widely shown in psychology that emotional processes cannot be interpreted without context [47, 51, 65]. We intend to guide the model to focus on the interaction between the subject of interest and context. As shown in Fig. 3, the cropped character and the whole image are usually encoded by two separate networks and fused at the ends [34, 53, 59]. This approach is inflexible and inefficient since it overlooks the dependency between subject and context and encodes redundant image portions. Following this line of thought, we propose two potential subject-aware context encoding strategies, i.e., subject-aware attention masking (SAAM) and subject-aware prompting (SAP). The former can be regarded as an efficient implementation of the traditional two-stream approach but avoids the problem of redundant encoding. The latter is a novel encoding strategy that enables adaptive modeling of the interaction between the context and the subject by providing necessary prompts.", + "bbox": [ + 75, + 598, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Subject-Aware Attention Masking. The canonical attention module [76] in a Transformer is defined as:", + "bbox": [ + 498, + 90, + 890, + 121 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {A t t e n t i o n} (\\mathbf {Q}, \\mathbf {K}, \\mathbf {V}) = \\mathrm {s o f t m a x} \\left(\\frac {\\mathbf {Q} \\mathbf {K} ^ {\\top}}{\\sqrt {d}}\\right) \\mathbf {V}. \\qquad (1)\n$$\n", + "text_format": "latex", + "bbox": [ + 526, + 131, + 890, + 167 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We model the context and subject in a synchronous way by modifying the attention module to", + "bbox": [ + 498, + 175, + 890, + 205 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$\\mathbf{Attention}^{*}(\\mathbf{Q},\\mathbf{K},\\mathbf{V},\\mathbf{U}) =$", + "bbox": [ + 500, + 215, + 691, + 233 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\underbrace {\\operatorname {s o f t m a x} \\left(\\frac {\\mathbf {Q K} ^ {\\top}}{\\sqrt {d}}\\right) (\\mathbf {J} - \\mathbf {A}) \\mathbf {V}} _ {\\text {c o n t e x t}} + \\underbrace {\\operatorname {s o f t m a x} \\left(\\frac {\\mathbf {Q K} ^ {\\top}}{\\sqrt {d}}\\right) \\mathbf {A U V}} _ {\\text {s u b j e c t}},\n$$\n", + "text_format": "latex", + "bbox": [ + 501, + 234, + 906, + 306 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{J}$ is a matrix with all ones, $\\mathbf{A}$ is a learnable parameters containing values in range [0, 1], and $\\mathbf{U}$ is a weight matrix constructed using $P$ . Intuitively, we shift $\\mathbf{A}$ amount of attention from a total of $\\mathbf{J}$ amount of attention from the context to the subject. To partition the $\\mathbf{A}$ amount of attention to all image patches containing subject, we compute $\\mathbf{U}$ as the following:", + "bbox": [ + 496, + 319, + 890, + 426 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {U} = \\operatorname {s o f t m a x} \\left(\\frac {\\mathbf {Q} \\mathbf {K} ^ {\\top} + \\mathbf {M}}{\\sqrt {d}}\\right). \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 586, + 435, + 890, + 470 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The masking matrix $\\mathbf{M}$ is defined as:", + "bbox": [ + 500, + 479, + 746, + 494 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {M} = \\left[ \\begin{array}{l l} \\mathbf {M} ^ {(1)} & \\mathbf {M} ^ {(2)} \\\\ \\mathbf {M} ^ {(3)} & \\mathbf {M} ^ {(4)} \\end{array} \\right], \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 614, + 505, + 890, + 541 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{M}^{(1)} = \\mathbf{0}_{(m + 1)\\times (m + 1)}$ , $\\mathbf{M}^{(4)} = \\mathbf{0}_{1\\times 1}$ , $\\mathbf{M}_{i\\notin P}^{(2)} = \\mathbf{M}_{i\\notin P}^{(3)} = -\\infty$ , $\\mathbf{M}_{(m + 1)}^{(3)} = -\\infty$ , and all other entries are zero. Intuitively, $\\mathbf{M}^{(2)}$ and $\\mathbf{M}^{(3)}$ represent the attention between all image patches $z_{i}$ and the human token $z_{hmn}$ to model the subject stream; we mask out all attention between non-human patches and the human token. Moreover, we mask out attention from $z_{hmn}$ to $z_{cls}$ , $\\mathbf{M}_{(m + 1)}^{(3)}$ , to ensure $z_{hmn}$ only encodes the subject.", + "bbox": [ + 496, + 551, + 890, + 686 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Subject-Aware Prompting. Prompting is a parameter-free method that restricts the output space of the model by shaping inputs. In our case, we hope to prompt the model to distinguish between the context and the subject. A recent visual prompting method, CPT [89], provides such a prompt by altering the original image, i.e., imposing colored boxes on objects of interest. It shows that a Transformer is able to locate objects with the help of positional hints. However, introducing artifacts on pixel space may not be optimal as it causes large domain shifts. To address this issue, we propose to construct prompts in the latent space based on positional embeddings, considering that they are inherently designed as indicative information. Formally, let $e_i$ be", + "bbox": [ + 496, + 704, + 892, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "18996", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "the positional embedding corresponding to the patch token $z_{i}$ , and $P$ are the indicator set of the subject location. The prompting token is designed as $z_{hmn} = \\sum_{i\\in P}e_{i}$ .", + "bbox": [ + 76, + 90, + 468, + 137 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We argue the sum of positional embeddings is enough to provide hints about the subject location. The previous study [78] demonstrates a Transformer treats all tokens without positional embedding uniformly but with positional embedding differently. This result shows positional embeddings play a vital role in guiding model attention.", + "bbox": [ + 75, + 138, + 467, + 227 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Sentiment-Guided Contrastive Learning", + "text_level": 1, + "bbox": [ + 76, + 239, + 421, + 257 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We train the model to learn emotion representations from verbal and nonverbal expressions in a contrastive manner. In the traditional contrastive setting, the model is forced to repel all negative pairs except the only positive one. However, many expressions in daily communication indeed have the same semantics from an emotional perspective. Contrasting these undesirable negative pairs encourages the model to learn spurious relations. This problem comes from false negatives, i.e., the affectively similar samples are treated as negatives. We address this issue by introducing a trained sentiment analysis model [68] from the NLP domain for the suppression of false negatives, thereby guiding our model to capture emotion-related concepts from verbal expressions. Specifically, we propose a sentiment-guided contrastive loss:", + "bbox": [ + 75, + 263, + 468, + 489 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {S N C E} (v, t, s) = - \\sum_ {i \\in B} \\left(\\log \\frac {\\exp \\left(v _ {i} \\cdot t _ {i} / \\tau\\right)}{\\sum_ {j \\in B} \\exp \\left(v _ {i} \\cdot t _ {j} / \\tau - w _ {i , j}\\right)}\\right), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 500, + 470, + 568 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $B$ is a batch. The reweighting term $w_{i,j}$ is defined as", + "bbox": [ + 76, + 569, + 467, + 585 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nw _ {i, j} = \\left\\{ \\begin{array}{l l} \\beta \\cdot \\mathrm {K L} \\left(s _ {i} \\| s _ {j}\\right) ^ {- 1} & i \\neq j \\\\ 0 & i = j \\end{array} , \\right. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 150, + 598, + 468, + 638 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\beta$ is a hyper-parameter for controlling the reweighting strength. The total loss is defined as:", + "bbox": [ + 76, + 647, + 467, + 676 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\frac {1}{2 | B |} \\left(\\operatorname {S N C E} (v, t, s) + \\operatorname {S N C E} (t, v, s)\\right). \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 119, + 689, + 468, + 720 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As shown in Fig. 4, the false negative sample with similar emotion to the positive sample is greatly suppressed, while other negatives are not affected. Note that when $i \\neq j$ but $s_i = s_j$ , we have $w_{i,j} = \\infty$ , which is equivalent to removing $j$ th sample from the negative pairs; when $s_i$ and $s_j$ are very different, $w_{i,j}$ is negligible; we set $w_{i,i} = 0$ to not affect the true positive pair. Since $s$ is the sentiment score, the sentiment-related differences are emphasized and weighted more during training. Therefore, the proposed contrastive loss is expected to provide cleaner supervision signals for learning emotion-related representations.", + "bbox": [ + 75, + 734, + 467, + 900 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/8f3810a750c1bda701f236a17b4560227387a6797f7bc95ba0ebd0f5b4c50795.jpg", + "image_caption": [ + "Figure 4. A sample batch where both the positive pair (green) and the false negative pair (red) exist. The green bar and gray bar represent the similarity between all text and the positive video before and after reweighting." + ], + "image_footnote": [], + "bbox": [ + 542, + 89, + 851, + 191 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments and Results", + "text_level": 1, + "bbox": [ + 500, + 289, + 733, + 306 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We first introduce the datasets for evaluation in Sec. 4.1 before analyzing various components of EmotionCLIP in Sec. 4.2. Then, we compare EmotionCLIP with the state-of-the-art methods on various datasets in Sec. 4.3. Please see Appendix for more experimental results.", + "bbox": [ + 496, + 315, + 890, + 391 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Datasets and Evaluation Metrics", + "text_level": 1, + "bbox": [ + 500, + 402, + 785, + 417 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We evaluate the performance of EmotionCLIP on a variety of recently published challenging benchmarks, including four video datasets and an image dataset. The annotations of these datasets are mainly based on three physiological models: Ekman's basic emotion theory [18] (7 discrete categories), the fine-grained emotion model [14] (26 discrete categories), and the Valence-Arousal-Dominance emotion model [67] (3 continuous dimensions). The evaluation metrics are consistent with previous methods.", + "bbox": [ + 496, + 428, + 890, + 563 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "BoLD [45] is a dataset for understanding human body language in the wild, consisting of 9,827 video clips and 13,239 instances, in which each instance is annotated with 26 discrete categories and VAD dimensions.", + "bbox": [ + 496, + 564, + 890, + 625 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "MovieGraphs [77] is a dataset for understanding human-centric situations consisting of graph-based annotations on social events that appeared in 51 popular movies. Each graph comprises multiple types of nodes to represent actors' emotional and physical attributes, as well as their relationships and interactions. Following the preprocessing and evaluation protocol proposed in previous work [29, 54], we extract relevant emotion attributes from the graphs and group them into 26 discrete emotion categories.", + "bbox": [ + 496, + 626, + 890, + 762 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "MELD [60] is an extension to the EmotionLines [9], which is an emotion corpus of multi-party conversations initially proposed in the NLP domain. It offers the same dialogue examples as EmotionLines and includes audio and visual modalities along with the text. It contains around 1,400 dialogues and 13,000 utterances from the Friends tv show, where each example is annotated with 7 discrete categories.", + "bbox": [ + 496, + 763, + 890, + 869 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Liris-Accede [5] is a dataset that contains videos from a set of 160 professionally made and amateur movies covering a", + "bbox": [ + 496, + 869, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "18997", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/40d63f0f8f5d1d94725a908853a2c05b9409e1cbdd8a1ad2c8c0f4b83efdda2c.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
mAPAUCR2
EmotionCLIP (vanilla)21.9768.850.130
+ SAAM21.53-0.4468.56-0.290.137+0.007
+ SAP22.28+0.3169.06+0.210.131+0.001
+ SAP & SNCE22.51+0.5469.30+0.450.133+0.003
", + "bbox": [ + 81, + 88, + 467, + 179 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Component-wise analysis of our method on BoLD.", + "bbox": [ + 94, + 189, + 450, + 204 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "variety of themes. Valence and arousal scores are provided continuously (i.e., every second) along movies.", + "bbox": [ + 75, + 232, + 467, + 262 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Emotic [29] is an image dataset for emotion recognition in context, comprising 23,571 images of 34,320 annotated individuals in unconstrained real-world environments. Each subject is annotated with 26 discrete categories.", + "bbox": [ + 75, + 263, + 467, + 324 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 335, + 230, + 351 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2.1 Analysis of Subject-Aware Context Encoding", + "text_level": 1, + "bbox": [ + 76, + 359, + 444, + 376 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this series of experiments, we start with a vanilla model and analyze it by adding various subject-aware approaches. As shown in Table 1, decent results can be achieved in downstream tasks using the vanilla EmotionCLIP. This result supports our argument that models can learn non-trivial emotion representations from human verbal and nonverbal expressions by matching them together.", + "bbox": [ + 75, + 383, + 467, + 489 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The SAP achieves better results and improves over the baseline by a reasonable margin. This improvement demonstrates the design of SAP can incorporate location-specific information to guide the model in acquiring target-related content without impacting global information modeling.", + "bbox": [ + 75, + 491, + 467, + 566 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Additionally, we note that the model with SAAM yields mediocre performance. As discussed earlier, SAAM can be regarded as an efficient implementation of the multi-stream strategy in the Transformer. This outcome suggests that the multi-stream strategy, commonly used in previous methods, may not be optimal. To rule out the possibility of fusion at inappropriate layers, we explore the impact of different fusion positions by applying SAAM up to a certain layer in the Transformer. It shows that the performance change does not correlate to the fusion layer change, and SAAM consistently underperforms SAP, irrespective of the fusion location. This finding implies that imposing hard masks on the model's attention may introduce unanticipated biases, while adaptively modeling context-subject interaction is more reasonable. In subsequent experiments and discussions, we use SAP as the standard implementation, unless otherwise stated.", + "bbox": [ + 75, + 566, + 467, + 823 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Qualitative Analysis. SAP offers merely a positional hint, as opposed to the mandatory attention-shifting in SAAM. Since the purpose of SAP is to ensure subject-aware encoding, it is necessary to understand if the attention guidance is appropriate. We analyze SAP by plotting HMN token's", + "bbox": [ + 75, + 824, + 467, + 901 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/c6558b422b7149909814c5c136af8266fbe74e67e72b6d63006017dec2f5c7eb.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 524, + 90, + 867, + 157 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/28632e2c704fc78be6d795cf563f03bb0f96333d28648357f77972d2593e7405.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 524, + 160, + 867, + 227 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/293bd745b96ca8868e1fe6b26ac7d00f47b249a61b77355c2b2c7baff86022a1.jpg", + "image_caption": [ + "Figure 5. Attention weights for the HMN token from layer 1-4 (left to right) of the frame encoder in one trained network. Each row represents one frame. The green and yellow spots are the high-attention areas." + ], + "image_footnote": [], + "bbox": [ + 524, + 231, + 867, + 297 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "attention to all patches on the image. As shown in Fig. 5, HMN tokens first focus on random locations, but gradually turn their attention to the subject (i.e., the person with a bounding box) as we move to later layers, demonstrating that SAP offers sufficient guidance to the network attention.", + "bbox": [ + 498, + 395, + 890, + 472 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2.2 Analysis of Sentiment-Guided Contrastive Learning", + "text_level": 1, + "bbox": [ + 500, + 496, + 890, + 526 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We first compare models trained with different $\\beta$ , the hyperparameter used to control the strength of reweighting in SNCE. Note that the training objective is equivalent to the vanilla infoNCE loss [56] when $\\beta$ is set to zero. As $\\beta$ increases, more negative samples within the batch are suppressed. As shown in Table 1 and Fig. 6, reweighting with appropriate strength can significantly increase the performance of the model as it guides the direction of learning by eliminating some significant false negatives. However, an excessively large $\\beta$ can hinder the training of the model, which is within expectation. First, the sentiment scores used in the reweighting process are weak pseudo-labels provided by a pre-trained sentiment analysis model, which is not entirely reliable and accurate. Second, previous work has clearly demonstrated that batch size has a decisive impact on self-supervised learning [10, 24, 62]. A too-large $\\beta$ will cause too many negative samples to be suppressed, reducing the effective batch size and thus hindering the learning process.", + "bbox": [ + 496, + 537, + 890, + 823 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Qualitative Analysis. We show how the text expressing different emotions are treated by our sentiment-guided loss. Given a positive pair, the logits are the scaled similarities between texts and the positive video; the model is penalized on large logits unless it is associated with the positive text.", + "bbox": [ + 496, + 824, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "18998", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/4f1e56460446254646ec6f22bc1f96dae39d3e225cd5118bcaebcc52dd3bbea6.jpg", + "image_caption": [ + "Figure 6. The effect of varying the strength of reweighting in SNCE. The larger the $\\beta$ , the stronger the suppression of negative samples." + ], + "image_footnote": [], + "bbox": [ + 81, + 89, + 467, + 193 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/53714f00fed92bc67d801adccd9e115e23a9ff32a337d793682476912c0b471a.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
TextLogit
I'm sorry to keep you any longer than is necessary. (positive sample)10.65
I'm sorry Tom couldn't join us.12.6 → -697
I hate to say it guys but it's getting late.9.81 → -97.6
I still say it was a wild idea.13.8 → 13.6
Well, that was truly fascinating.15.2 → 15.0
", + "bbox": [ + 81, + 263, + 465, + 381 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "As shown in Table 2, the texts in the second and third rows provide undesired contributions to the loss as they express similar emotions as the positive sample. After reweighting, false negatives (2nd and 3rd) are effectively eliminated while true negatives (4th and 5th) are negligibly affected.", + "bbox": [ + 75, + 474, + 468, + 551 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2.3 Analysis of Model Implementation", + "text_level": 1, + "bbox": [ + 76, + 571, + 372, + 588 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The frame and text encoders of our model are initialized with the image-text pre-training weights from CLIP [62]. Research in neural science has demonstrated the necessity of basic visual and language understanding capabilities for learning high-level emotional semantics [58, 70]. To validate the effectiveness of using image-text pre-training for weight initialization, we evaluate variants with different implementations.", + "bbox": [ + 75, + 597, + 468, + 717 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We first consider encoders with random initialization. As shown in Table 3, the model's performance drops sharply when training from scratch. This result is within expectation for two reasons. From an engineering perspective, previous works have demonstrated the necessity of using pretraining weights for large video models [1, 6] and vision-language models [35, 55]. From a cognitive point of view, it is nearly infeasible to learn abstract concepts directly without basic comprehension skills [58]; if the model cannot recognize people, it is impossible to understand body language and facial expressions properly.", + "bbox": [ + 75, + 719, + 468, + 885 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We then consider frozen encoders with pre-training", + "bbox": [ + 96, + 885, + 468, + 901 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/0f4d99b2076a98958eb64d1af45a86176d04325b9e6f62703f38efd6a41cd057.jpg", + "table_caption": [ + "Table 2. An example batch containing both false negative and true negative samples. The logits represent the similarity between every text input and the positive video from a random epoch during training. $\\rightarrow$ represents the sentiment-guided reweighting process." + ], + "table_footnote": [], + "table_body": "
Text EncoderFrame EncoderTemporal EncodermAPAUC
✓✓-22.5169.30
-✓-12.43–45%54.96–21%
---11.02–51%50.28–27%
✗✓-13.40–40%57.38–17%
✗✗-18.43–18%65.08–6.0%
✓✓○21.17–5.9%68.74–0.8%
", + "bbox": [ + 504, + 88, + 890, + 236 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3. Ablation study on different model implementations. $\\checkmark$ means trainable, initialization with pre-training weights. $x$ means frozen, initialization with pre-training weights. - means trainable, random initialization. $\\circ$ means no parameters.", + "bbox": [ + 496, + 246, + 893, + 303 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "weights. This is a standard paradigm for video-language understanding that trains models with offline extracted features [36, 87]. As shown in Table 3, our model with variants using fixed encoders performs worse compared with the model using trainable encoders. This reflects the fact that affective tasks rely on visual and verbal semantics differently from low-level vision tasks, which is what CLIP and its successors overlooked [40].", + "bbox": [ + 496, + 330, + 890, + 450 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We study the effect of the temporal encoder. We consider a variant where the temporal encoder is replaced by a mean pooling layer that simply averages the features of all frames. As shown in Table 3, the performance gap is obvious compared with the baseline. This phenomenon suggests that temporal dependency plays a vital role in emotion representations.", + "bbox": [ + 496, + 453, + 892, + 558 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Comparison with the State of the Art", + "text_level": 1, + "bbox": [ + 498, + 571, + 821, + 588 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Based on our previous ablation experiments, we choose the model with SAP and SNCE as the default implementation and compare it with the state-of-the-art. In addition, we also compare with VideoCLIP [87] and X-CLIP [55], both of which are state-of-the-art vision-language pre-training models for general video recognition purposes. To evaluate the quality of learned representations, we follow the practice in CLIP [62] and use linear-probe evaluation protocol [10, 24] for vision-language pre-training models.", + "bbox": [ + 496, + 597, + 890, + 733 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "BoLD. As shown in Table 4a, EmotionCLIP substantially outperforms the state-of-the-art supervised learning methods on the challenging 26-class emotion classification task and achieves comparable results on continuous emotion regression. It is worth noting that a complex multi-stream model is used in [59] to integrate the human body and context information, while we achieve better results with a single-stream structure using RGB information only. This difference reflects that the subject-aware approach we designed models the relationship between the subject and context. We also notice that other vision-language-based meth", + "bbox": [ + 496, + 734, + 892, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "18999", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/acb03214215724aebb905828cc539c800eddb390c7fed43aa4b2cca9cf7c724c.jpg", + "table_caption": [ + "(a) BoLD [45]" + ], + "table_footnote": [], + "table_body": "
MethodmAP ↑AUC ↑R2 ↑
Supervised
ST-GCN [94]12.6355.960.044
TSN [81]17.0262.700.095
Filntis et al. [21]16.5662.660.092
Pikoulis et al. [59]19.2966.820.149
Linear-Eval
VideoCLIP [87]11.1951.23-5.11
X-CLIP [55]13.2656.86-0.03
EmotionCLIP22.5169.300.133
", + "bbox": [ + 78, + 106, + 361, + 247 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/d00b36d40397078be8b679849d8de6ec0e42012bb339e2c9d2f5300d190c2bbb.jpg", + "table_caption": [ + "(c) Emotic [29]" + ], + "table_footnote": [], + "table_body": "
MethodmAP ↑AUC ↑
Supervised
CAER-Net [34]20.84-
Affective Graph [96]28.42-
Fusion Model [29]29.45-
EmotiCon (GCN) [53]32.03-
EmotiCon (Depth) [53]35.48-
Linear-Eval
VideoCLIP [87]19.9256.31
X-CLIP [55]22.8061.31
EmotionCLIP32.9171.41
", + "bbox": [ + 367, + 106, + 620, + 258 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/066921443c558b2a3d3e921194e83d1df136733d74d0e4d283f21487a613ca50.jpg", + "table_caption": [ + "(e) Liris-Accede [5]" + ], + "table_footnote": [], + "table_body": "
MethodV. MSE ↓A. MSE ↓
Supervised
Quan et al. [61]0.1150.171
Ko et al. [28]0.1020.149
*CERTH-ITI [4]0.1170.138
*THUHCSI [25]0.0920.140
*Yi et al. [91]0.0900.136
*GLA [75]0.0840.133
*Zhao et al. [95]0.0710.137
*Affect2MM [54]0.0680.128
Linear-Eval
VideoCLIP [87]0.1420.151
X-CLIP [55]0.1330.246
EmotionCLIP0.0960.155
", + "bbox": [ + 630, + 106, + 890, + 294 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/8f5491b6d60b599e3d95aa3a0ddc3d896c7ee433d0372350a13e7d98ef036adc.jpg", + "table_caption": [ + "(b) MovieGraphs [77]" + ], + "table_footnote": [], + "table_body": "
MethodVal Acc ↑Test Acc ↑
Supervised
EmotionNet [84]35.6027.90
*Affect2MM [54]39.8830.58
Linear-Eval
VideoCLIP [87]29.9123.44
X-CLIP [55]29.0623.58
EmotionCLIP41.6032.35
", + "bbox": [ + 78, + 292, + 359, + 410 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/4ffee297480e13f1dcfc49b76fdc6d352f13a40dcc6fe6eb70b73fb311cccf65.jpg", + "table_caption": [ + "(d) MELD [60]" + ], + "table_footnote": [], + "table_body": "
MethodAcc ↑W. F1 ↑
Supervised
M2FNet (Visual) [12]45.6332.44
*M2FNet [12]67.8566.71
Linear-Eval
VideoCLIP [87]45.1932.06
X-CLIP [55]38.3132.46
EmotionCLIP48.2834.59
", + "bbox": [ + 367, + 292, + 620, + 410 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/6fe67ce636b79a0fc4726148683f30e5a7771e8a06fb86b6d62991dff8259244.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
AbbreviationMeaning
A. MSEArousal MSE
V. MSEValence MSE
W. F1Weighted F1
Acc.Top-1 Accuracy
↓Lower is better
↑Higher is better
", + "bbox": [ + 630, + 311, + 890, + 410 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 4. Comparisons to the state-of-the-art across multiple datasets. Methods marked with * use multimodal inputs, i.e., audio and text. Bold numbers indicate the best results achieved using visual inputs only.", + "bbox": [ + 75, + 422, + 890, + 450 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ods perform poorly on emotion recognition tasks, although they are designed for general video understanding purposes. This phenomenon is largely attributed to the lack of proper guidance; the model can only learn low-level visual patterns and fails to capture semantic and emotional information.", + "bbox": [ + 75, + 477, + 468, + 551 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "MovieGraphs. As shown in Table 4b, EmotionCLIP substantially outperforms the best vision-based method and even surpasses Affect2MM [54], a powerful multimodal approach that uses audio and text descriptions in addition to visual information. Instead, other vision-language pretraining models are still far from supervised methods.", + "bbox": [ + 75, + 551, + 468, + 643 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "MELD. EmotionCLIP performs well on MELD as shown in Table 4d; it achieves comparable results to the state-of-the-art vision-based methods. It is worth noting that this dataset is extended from an NLP dataset, so the visual data is noisier than the original text data. In fact, according to the ablation experiments in [12], it is possible to achieve an accuracy of $67.24\\%$ using only text, while adding visual modality information only improves the accuracy by about $0.5\\%$ . This result explains why our method significantly lags behind multimodal methods using text inputs.", + "bbox": [ + 75, + 643, + 468, + 794 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Liris-Accede. As shown in Table 4e, EmotionCLIP achieves promising results using visual inputs only. It even competes with many multimodal approaches that are benefited from the use of audio features [93].", + "bbox": [ + 75, + 794, + 468, + 854 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Emotic. As shown in Table 4c, EmotionCLIP outperforms all RGB-based supervised methods while other vision-language models perform poorly. The improvement of [53]", + "bbox": [ + 75, + 854, + 468, + 901 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "is attributable to the use of additional depth information. This result demonstrates the capability of EmotionCLIP in learning relevant features from complex environments.", + "bbox": [ + 496, + 477, + 890, + 523 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 537, + 617, + 553 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The pre-training methodology, which has brought about significant advancements in numerous CV and NLP domains, has not yet been employed in AEI research. We address this void by introducing EmotionCLIP, the first vision-language pre-training framework that circumvents the need for curated data and annotations. Our study establishes the viability of acquiring generalized emotion representations directly from human communication, thereby considerably broadening the horizons of current AEI research. The emergence of this pre-training paradigm offers an alternative solution to data scarcity, paving the way for a myriad of potential applications. We anticipate that our work will stimulate further investigation in this area and contribute to the evolution of more adaptable and efficacious approaches for affective computing.", + "bbox": [ + 496, + 563, + 890, + 790 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments. This research was supported by generous gifts from the Amazon Research Awards program. The work used computational resources from the Advanced Cyberinfrastructure Coordination Ecosystem: Services & Support (ACCESS) program, which is supported by National Science Foundation.", + "bbox": [ + 496, + 809, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "19000", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Anurag Arnab, Mostafa Dehghani, Georg Heigold, Chen Sun, Mario Lucic, and Cordelia Schmid. Vivit: A video vision transformer. In ICCV, pages 6836-6846, 2021. 7", + "[2] Max Bain, Arsha Nagrani, Gül Varol, and Andrew Zisserman. Frozen in time: A joint video and image encoder for end-to-end retrieval. 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IJCV, 130(9):2337-2348, 2022. 2" + ], + "bbox": [ + 503, + 92, + 890, + 460 + ], + "page_idx": 11 + }, + { + "type": "page_number", + "text": "19004", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 11 + } +] \ No newline at end of file diff --git a/2023/Learning Emotion Representations From Verbal and Nonverbal Communication/73b56492-ee9f-4305-8379-ca00142aa516_model.json b/2023/Learning Emotion Representations From Verbal and Nonverbal Communication/73b56492-ee9f-4305-8379-ca00142aa516_model.json new file mode 100644 index 0000000000000000000000000000000000000000..7a3ae201ae7c38632b79abd60e625e5dda8a7685 --- /dev/null +++ b/2023/Learning Emotion Representations From Verbal and Nonverbal Communication/73b56492-ee9f-4305-8379-ca00142aa516_model.json @@ -0,0 +1,2897 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.082, + 0.131, + 0.888, + 0.154 + ], + "angle": 0, + "content": "Learning Emotion Representations from Verbal and Nonverbal Communication" + }, + { + "type": "text", + "bbox": [ + 0.2, + 0.181, + 0.77, + 0.234 + ], + "angle": 0, + "content": "Sitao Zhang* Yimu Pan* James Z. Wang \nThe Pennsylvania State University, University Park, Pennsylvania, USA \n{sbz5211,ymp5078,jwang}@psu.edu" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.269, + 0.314, + 0.285 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.302, + 0.474, + 0.664 + ], + "angle": 0, + "content": "Emotion understanding is an essential but highly challenging component of artificial general intelligence. The absence of extensive annotated datasets has significantly impeded advancements in this field. We present EmotionCLIP, the first pre-training paradigm to extract visual emotion representations from verbal and nonverbal communication using only uncurated data. Compared to numerical labels or descriptions used in previous methods, communication naturally contains emotion information. Furthermore, acquiring emotion representations from communication is more congruent with the human learning process. We guide EmotionCLIP to attend to nonverbal emotion cues through subject-aware context encoding and verbal emotion cues using sentiment-guided contrastive learning. Extensive experiments validates the effectiveness and transferability of EmotionCLIP. Using merely linear-probe evaluation protocol, EmotionCLIP outperforms the state-of-the-art supervised visual emotion recognition methods and rivals many multimodal approaches across various benchmarks. We anticipate that the advent of EmotionCLIP will address the prevailing issue of data scarcity in emotion understanding, thereby fostering progress in related domains. The code and pre-trained models are available at https://github.com/Xeaver/EmotionCLIP." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.697, + 0.21, + 0.712 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.723, + 0.47, + 0.875 + ], + "angle": 0, + "content": "If artificial intelligence (AI) can be equipped with emotional intelligence (EQ), it will be a significant step toward developing the next generation of artificial general intelligence [46, 92]. The combination of emotion and intelligence distinguishes humans from other animals. The ability to understand, use, and express emotions will significantly facilitate the interaction of AI with humans and the environment [20, 48-50], making it the foundation for a wide variety of HCI [3], robotics [11], and autonomous driving [31] applications." + }, + { + "type": "image", + "bbox": [ + 0.513, + 0.269, + 0.882, + 0.403 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.516, + 0.408, + 0.65, + 0.441 + ], + "angle": 0, + "content": "Categorical Label: Shocked Regretful 0 1 0 0 0 1 0 0 0" + }, + { + "type": "image_footnote", + "bbox": [ + 0.516, + 0.444, + 0.687, + 0.474 + ], + "angle": 0, + "content": "Description: An old man is chatting with his son while eating at a restaurant." + }, + { + "type": "image_footnote", + "bbox": [ + 0.703, + 0.414, + 0.865, + 0.474 + ], + "angle": 0, + "content": "Conversation: \n- Dad. Who is Dede? \n- Jesus. She was the love of my life and I was too stupid to realized it. I lost her because of something so dumb." + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.493, + 0.892, + 0.549 + ], + "angle": 0, + "content": "Figure 1. Emotions emerge naturally in human communication through verbal and nonverbal cues. The rich semantic details within the expression can hardly be represented by human-annotated categorical labels and descriptions in current datasets." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.581, + 0.893, + 0.777 + ], + "angle": 0, + "content": "Artificial emotional intelligence (AEI) research is still in its nascency [30, 73]. The recent emergence of pretrained models in CV [10, 24, 62] and NLP [7, 16, 33, 68] domains has ushered in a new era of research in related subjects. By training on large-scale unlabeled data in a self-supervised manner, the model learns nontrivial representations that generalize to downstream tasks [42, 62]. Unfortunately, such a technique remains absent from AEI research. The conventional approaches in visual emotion understanding have no choice but to train models from scratch, or leverage models from less-relevant domains [27, 66], suffering from data scarcity [29, 45]. The lack of pre-trained models greatly limits the development of AEI research." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Research in neuroscience and psychology offers insights for addressing this problem. Extending from the capabilities that have been coded genetically, humans learn emotional expressions through daily interaction and communication as early as when they are infants. It has been shown that both vision [58] and language [41] play crucial roles in this learning process. By absorbing and imitating expressions from others, humans eventually master the necessary" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.888, + 0.202, + 0.9 + ], + "angle": 0, + "content": "*equal contribution" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18993" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.136 + ], + "angle": 0, + "content": "feelings to comprehend emotional states by observing and analyzing facial expressions, body movements, contextual environments, etc." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.138, + 0.468, + 0.259 + ], + "angle": 0, + "content": "Inspired by how humans comprehend emotions, we propose a new paradigm for emotion understanding that learn directly from human communication. The core of our idea is to explore the consistency between verbal and nonverbal affective cues in daily communication. Fig. 1 shows how communication reveals emotion. Our method that learns from communication is not only aligned with the human learning process but also has several advantages:" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.261, + 0.468, + 0.472 + ], + "angle": 0, + "content": "1) Our method bypasses the problems in emotion data collection by leveraging uncurated data from daily communication. Existing emotion understanding datasets are mainly annotated using crowdsourcing [29, 45, 77]. For image classification tasks, it is straightforward for annotators to agree on an image's label due to the fact that the label is determined by certain low-level visual characteristics. However, crowdsourcing participants usually have lower consensus on producing emotion annotations due to the subjectivity and subtlety of affective labels [90]. This phenomenon makes it extremely difficult to collect accurate emotion annotations on a large scale. Our approach does not rely on human annotations, allowing us to benefit from nearly unlimited web data." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.474, + 0.468, + 0.593 + ], + "angle": 0, + "content": "2) Our use of verbal expressions preserves fine-grained semantics to the greatest extent possible. Limited by the data collection strategy, existing datasets usually only contain annotations for a limited number of emotion categories, which is far from covering the space of human emotional expression [86]. Moreover, the categorical labels commonly used in existing datasets fail to precisely represent the magnitude or intensity of a certain emotion." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.595, + 0.468, + 0.73 + ], + "angle": 0, + "content": "3) Our approach provides a way to directly model expressed emotion. Ideally, AEI should identify the individual's emotional state, i.e., the emotion the person desires to express. Unfortunately, it is nearly impossible to collect data on this type of \"expressed emotion\" on a large scale. Instead, the current practice is to collect data on \"perceived emotion\" to approximate the person's actual emotional state, which inevitably introduces noise and bias to labels." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.732, + 0.468, + 0.822 + ], + "angle": 0, + "content": "In general, learning directly from how humans express themselves is a promising alternative that gives a far broader source of supervision and a more comprehensive representation. This strategy is closely analogous to the human learning process and provides an efficient solution for extracting emotion representations from uncurated data." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.825, + 0.433, + 0.838 + ], + "angle": 0, + "content": "We summarize our main contributions as follows:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.84, + 0.468, + 0.884 + ], + "angle": 0, + "content": "- We introduce EmotionCLIP, the first vision-language pre-training paradigm using uncurated data to the visual emotion understanding domain." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.887, + 0.468, + 0.9 + ], + "angle": 0, + "content": "- We propose two techniques to guide the model to cap" + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.84, + 0.468, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.531, + 0.092, + 0.89, + 0.12 + ], + "angle": 0, + "content": "ture salient emotional expressions from human verbal and nonverbal communication." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.122, + 0.89, + 0.166 + ], + "angle": 0, + "content": "- Extensive experiments and analysis demonstrate the superiority and transferability of our method on various downstream datasets in emotion understanding." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.181, + 0.642, + 0.196 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.206, + 0.892, + 0.357 + ], + "angle": 0, + "content": "Emotion Recognition from Visual Clues. Facial expression recognition [19, 38, 69] has been well studied in the field of emotion recognition, mainly because faces are not only expressive but also easy to model. Handcrafted features have been developed to describe different facial expressions [13, 43, 74]. Recently, deep learning-based approaches have begun to emerge [38]. Principal research focuses on the design of novel modules for conventional network architectures [88], distinct loss functions for facial tasks [15, 71, 85], and addressing label uncertainties [8, 80]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.358, + 0.892, + 0.599 + ], + "angle": 0, + "content": "Recently, with the growing interest in recognizing emotion in the wild, the focus of research has gradually shifted to modeling body language [21, 45, 59] and context [29, 53, 54]. Several datasets for understanding human emotional states in unconstrained environments have been proposed [5, 60, 77]; Kosti et al. [29] and Yu et al. [45] established the first benchmark for image and video data, respectively. Follow-up work mainly focuses on context-aware emotion recognition, which usually adopts a multi-branch structure where one branch focuses on the face or body and the other focuses on capturing context [12, 34, 53, 59]. Moreover, some approaches take into account temporal causality [54] or represent context information via graphs [96]. To the best of our knowledge, there are no pre-trained models or effective methods for leveraging unlabeled data in the domain of visual emotion recognition." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Vision-Language Pre-training. Visual-language pretraining has achieved remarkable progress recently. CLIP [62] demonstrated the feasibility of using contrastive learning [10, 56] to learn transferable and powerful visual representations from large-scale image-text pairs [72]. Many follow-up approaches have been proposed to transfer the pre-trained model to downstream tasks [22, 97, 100] or leverage the scheme for different domains [37, 57, 64, 83, 98]. A line of research endeavors to expand CLIP for general video understanding [26, 35, 40, 44, 55, 82, 87]. The majority of the effort focuses on fine-tuning datasets with textual annotations [27, 32, 39]. However, not only are these curated annotations challenging to obtain, but they also limit the model's potential in various applications. Another line of work [36, 87] extends the image-level pre-training by utilizing unlabeled narrated videos [2, 52], similar to ours. However, we aim to learn abstract emotion representations rather than low-level visual patterns, which are beyond the reach of current models. EmotionNet [84] and its sequel [99], which likewise seeks to learn visual emotion repre" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.956 + ], + "angle": 0, + "content": "18994" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.118, + 0.088, + 0.852, + 0.32 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.33, + 0.895, + 0.388 + ], + "angle": 0, + "content": "Figure 2. Illustration of EmotionCLIP. For nonverbal communication, subject and context information is modeled by a frame encoder and further aggregated into video-level representations by a temporal encoder. For verbal communication, textual information is encoded as text representations and sentiment scores by a text encoder and sentiment analysis model, respectively. The model learns emotion representations under sentiment guidance in a contrastive manner, by exploring the consistency of verbal and nonverbal communication." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.413, + 0.471, + 0.459 + ], + "angle": 0, + "content": "sentations, are connected to ours. However, their primary focus is on the images' stimuli rather than the recognition of human emotional expressions in the wild." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.475, + 0.214, + 0.494 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.502, + 0.471, + 0.744 + ], + "angle": 0, + "content": "Our core idea is to learn directly from human communication how they express their emotions, by exploring the consistency between their verbal and nonverbal expressions [41]. We tackle this learning task under the vision-language contrastive learning framework [62], that is, the model is expected to learn consistent emotion representations from the verbal expressions (e.g., utterance and dialogue) and nonverbal expressions (e.g., facial expression, body language, and contextual environment) of the same individuals. We give a brief introduction of our data collection procedure in Sec. 3.1 before presenting the overview of EmotionCLIP in Sec. 3.2. We further discuss how the model is guided to learn emotion-relevant representations from the nonverbal perspective in Sec. 3.3, and from the verbal perspective in Sec. 3.4. Please see Appendix for details of the dataset and implementations." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.756, + 0.235, + 0.77 + ], + "angle": 0, + "content": "3.1. Data Collection" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Publicly available large-scale vision-and-language datasets do not provide desired verbal and nonverbal information because they either comprise only captions of low-level visual elements [2, 72] or instructions of actions [52]. The captions mostly contain a brief description of the scene or activity, which is insufficient to reveal the underlying emotions; the instruction videos rarely include humans in the scene or express neutral emotions, which fail" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.413, + 0.895, + 0.565 + ], + "angle": 0, + "content": "to provide supervision signals for emotion understanding. To overcome such problems, we gather a large-scale video-and-text paired dataset. More specifically, the videos are TV series, while the texts are the corresponding closed captions. We collected 3,613 TV series from YouTube, which is equivalent to around a million raw video clips. We processed them using the off-the-shelf models to group the words in closed caption into complete sentences [23], tag each sentence with a sentiment score [68], and extract human bounding boxes [79]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.575, + 0.744, + 0.59 + ], + "angle": 0, + "content": "3.2. Overview of EmotionCLIP" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.892, + 0.674 + ], + "angle": 0, + "content": "Fig. 2 presents an overview of our approach. We follow the wildly adopted vision-language contrastive learning paradigm [62] where two separate branches are used to encode visual inputs (i.e., nonverbal expressions) and textual inputs (i.e., verbal expressions), respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Video Encoding. The visual branch of EmotionCLIP takes two inputs, including a sequence of RGB frames \\(X_{v}\\) and a sequence of binary masks \\(X_{m}\\). The binary mask has the same shape as the frame and corresponds to the frame one-to-one, indicating the location of the subject within the frame. The backbone of the subject-aware frame encoder \\(f_{i}\\) is a Vision Transformer [17]. In particular, it extracts \\(m\\) non-overlapping image patches from the frame and projects them into 1D tokens \\(z_{i} \\in \\mathbb{R}^{d}\\). The sequence of tokens passed to the following Transformer encoder [76] is \\(\\mathbf{z} = [z_{1}, \\dots, z_{m}, z_{cls}, z_{hmn}]\\), where \\(z_{cls}, z_{hmn}\\) are two additional learnable tokens. The mask \\(X_{m}\\) is converted to an array of indices \\(P\\) indicating the image patches containing the subject. The frame encoder further encodes \\(\\mathbf{z}, P\\) into a frame-level representation. All frame representations are normalized by the average of the raw data." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18995" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.088, + 0.472, + 0.185 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.194, + 0.47, + 0.251 + ], + "angle": 0, + "content": "Figure 3. The traditional approaches (left) ignore the dependencies between context and subject, and encode a portion of the image redundantly. The proposed approaches (right two diagrams) efficiently model the subject and context in a synchronous way." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.284, + 0.47, + 0.331 + ], + "angle": 0, + "content": "tions are then passed into the temporal encoder \\( f_{p} \\) to produce a video-level representation as \\( v = f_{v}(\\mathbf{z}, P) \\), where \\( f_{v} = f_{p} \\circ f_{i} \\) and \\( v \\in \\mathbb{R}^{d} \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.333, + 0.469, + 0.455 + ], + "angle": 0, + "content": "Text Encoding. The textual branch of EmotionCLIP takes sentences \\( X_{t} \\) as inputs. The text encoder \\( f_{t} \\) is a Transformer [16] with the architecture modification described in [63], and the sentiment model \\( f_{s} \\) is a pre-trained sentiment analysis model [68] that is frozen during training. The input text is encoded by both models as \\( t = f_{t}(X_{t}) \\) and \\( s = f_{s}(X_{t}) \\), where \\( t \\in \\mathbb{R}^{d} \\) is the representation of the text and \\( s \\in \\mathbb{R}^{7} \\) is the pseudo sentiment score." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.458, + 0.469, + 0.503 + ], + "angle": 0, + "content": "Training Objective. The training objective is to learn the correspondence between visual inputs and textual inputs by minimizing the sentiment-guided contrastive loss \\(\\mathcal{L}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.506, + 0.469, + 0.552 + ], + "angle": 0, + "content": "We discuss the details of the proposed subject-aware encoding approaches in Sec. 3.3 and the sentiment-guided contrastive learning framework in Sec. 3.4." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.572, + 0.37, + 0.589 + ], + "angle": 0, + "content": "3.3. Subject-Aware Context Encoding" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.599, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Context encoding is an important part of emotion understanding, especially in unconstrained environments, as it has been widely shown in psychology that emotional processes cannot be interpreted without context [47, 51, 65]. We intend to guide the model to focus on the interaction between the subject of interest and context. As shown in Fig. 3, the cropped character and the whole image are usually encoded by two separate networks and fused at the ends [34, 53, 59]. This approach is inflexible and inefficient since it overlooks the dependency between subject and context and encodes redundant image portions. Following this line of thought, we propose two potential subject-aware context encoding strategies, i.e., subject-aware attention masking (SAAM) and subject-aware prompting (SAP). The former can be regarded as an efficient implementation of the traditional two-stream approach but avoids the problem of redundant encoding. The latter is a novel encoding strategy that enables adaptive modeling of the interaction between the context and the subject by providing necessary prompts." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.122 + ], + "angle": 0, + "content": "Subject-Aware Attention Masking. The canonical attention module [76] in a Transformer is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.527, + 0.132, + 0.892, + 0.168 + ], + "angle": 0, + "content": "\\[\n\\mathrm {A t t e n t i o n} (\\mathbf {Q}, \\mathbf {K}, \\mathbf {V}) = \\mathrm {s o f t m a x} \\left(\\frac {\\mathbf {Q} \\mathbf {K} ^ {\\top}}{\\sqrt {d}}\\right) \\mathbf {V}. \\qquad (1)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.176, + 0.892, + 0.207 + ], + "angle": 0, + "content": "We model the context and subject in a synchronous way by modifying the attention module to" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.217, + 0.692, + 0.234 + ], + "angle": 0, + "content": "\\(\\mathbf{Attention}^{*}(\\mathbf{Q},\\mathbf{K},\\mathbf{V},\\mathbf{U}) =\\)" + }, + { + "type": "equation", + "bbox": [ + 0.502, + 0.236, + 0.907, + 0.308 + ], + "angle": 0, + "content": "\\[\n\\underbrace {\\operatorname {s o f t m a x} \\left(\\frac {\\mathbf {Q K} ^ {\\top}}{\\sqrt {d}}\\right) (\\mathbf {J} - \\mathbf {A}) \\mathbf {V}} _ {\\text {c o n t e x t}} + \\underbrace {\\operatorname {s o f t m a x} \\left(\\frac {\\mathbf {Q K} ^ {\\top}}{\\sqrt {d}}\\right) \\mathbf {A U V}} _ {\\text {s u b j e c t}},\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.32, + 0.892, + 0.427 + ], + "angle": 0, + "content": "where \\(\\mathbf{J}\\) is a matrix with all ones, \\(\\mathbf{A}\\) is a learnable parameters containing values in range [0, 1], and \\(\\mathbf{U}\\) is a weight matrix constructed using \\(P\\). Intuitively, we shift \\(\\mathbf{A}\\) amount of attention from a total of \\(\\mathbf{J}\\) amount of attention from the context to the subject. To partition the \\(\\mathbf{A}\\) amount of attention to all image patches containing subject, we compute \\(\\mathbf{U}\\) as the following:" + }, + { + "type": "equation", + "bbox": [ + 0.587, + 0.436, + 0.892, + 0.471 + ], + "angle": 0, + "content": "\\[\n\\mathbf {U} = \\operatorname {s o f t m a x} \\left(\\frac {\\mathbf {Q} \\mathbf {K} ^ {\\top} + \\mathbf {M}}{\\sqrt {d}}\\right). \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.481, + 0.747, + 0.496 + ], + "angle": 0, + "content": "The masking matrix \\(\\mathbf{M}\\) is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.615, + 0.506, + 0.892, + 0.542 + ], + "angle": 0, + "content": "\\[\n\\mathbf {M} = \\left[ \\begin{array}{l l} \\mathbf {M} ^ {(1)} & \\mathbf {M} ^ {(2)} \\\\ \\mathbf {M} ^ {(3)} & \\mathbf {M} ^ {(4)} \\end{array} \\right], \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.553, + 0.892, + 0.688 + ], + "angle": 0, + "content": "where \\(\\mathbf{M}^{(1)} = \\mathbf{0}_{(m + 1)\\times (m + 1)}\\), \\(\\mathbf{M}^{(4)} = \\mathbf{0}_{1\\times 1}\\), \\(\\mathbf{M}_{i\\notin P}^{(2)} = \\mathbf{M}_{i\\notin P}^{(3)} = -\\infty\\), \\(\\mathbf{M}_{(m + 1)}^{(3)} = -\\infty\\), and all other entries are zero. Intuitively, \\(\\mathbf{M}^{(2)}\\) and \\(\\mathbf{M}^{(3)}\\) represent the attention between all image patches \\(z_{i}\\) and the human token \\(z_{hmn}\\) to model the subject stream; we mask out all attention between non-human patches and the human token. Moreover, we mask out attention from \\(z_{hmn}\\) to \\(z_{cls}\\), \\(\\mathbf{M}_{(m + 1)}^{(3)}\\), to ensure \\(z_{hmn}\\) only encodes the subject." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Subject-Aware Prompting. Prompting is a parameter-free method that restricts the output space of the model by shaping inputs. In our case, we hope to prompt the model to distinguish between the context and the subject. A recent visual prompting method, CPT [89], provides such a prompt by altering the original image, i.e., imposing colored boxes on objects of interest. It shows that a Transformer is able to locate objects with the help of positional hints. However, introducing artifacts on pixel space may not be optimal as it causes large domain shifts. To address this issue, we propose to construct prompts in the latent space based on positional embeddings, considering that they are inherently designed as indicative information. Formally, let \\( e_i \\) be" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18996" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.138 + ], + "angle": 0, + "content": "the positional embedding corresponding to the patch token \\( z_{i} \\), and \\( P \\) are the indicator set of the subject location. The prompting token is designed as \\( z_{hmn} = \\sum_{i\\in P}e_{i} \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.139, + 0.468, + 0.228 + ], + "angle": 0, + "content": "We argue the sum of positional embeddings is enough to provide hints about the subject location. The previous study [78] demonstrates a Transformer treats all tokens without positional embedding uniformly but with positional embedding differently. This result shows positional embeddings play a vital role in guiding model attention." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.241, + 0.423, + 0.258 + ], + "angle": 0, + "content": "3.4. Sentiment-Guided Contrastive Learning" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.265, + 0.47, + 0.491 + ], + "angle": 0, + "content": "We train the model to learn emotion representations from verbal and nonverbal expressions in a contrastive manner. In the traditional contrastive setting, the model is forced to repel all negative pairs except the only positive one. However, many expressions in daily communication indeed have the same semantics from an emotional perspective. Contrasting these undesirable negative pairs encourages the model to learn spurious relations. This problem comes from false negatives, i.e., the affectively similar samples are treated as negatives. We address this issue by introducing a trained sentiment analysis model [68] from the NLP domain for the suppression of false negatives, thereby guiding our model to capture emotion-related concepts from verbal expressions. Specifically, we propose a sentiment-guided contrastive loss:" + }, + { + "type": "equation", + "bbox": [ + 0.077, + 0.501, + 0.472, + 0.569 + ], + "angle": 0, + "content": "\\[\n\\operatorname {S N C E} (v, t, s) = - \\sum_ {i \\in B} \\left(\\log \\frac {\\exp \\left(v _ {i} \\cdot t _ {i} / \\tau\\right)}{\\sum_ {j \\in B} \\exp \\left(v _ {i} \\cdot t _ {j} / \\tau - w _ {i , j}\\right)}\\right), \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.57, + 0.468, + 0.586 + ], + "angle": 0, + "content": "where \\(B\\) is a batch. The reweighting term \\(w_{i,j}\\) is defined as" + }, + { + "type": "equation", + "bbox": [ + 0.151, + 0.599, + 0.47, + 0.64 + ], + "angle": 0, + "content": "\\[\nw _ {i, j} = \\left\\{ \\begin{array}{l l} \\beta \\cdot \\mathrm {K L} \\left(s _ {i} \\| s _ {j}\\right) ^ {- 1} & i \\neq j \\\\ 0 & i = j \\end{array} , \\right. \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.648, + 0.468, + 0.678 + ], + "angle": 0, + "content": "where \\(\\beta\\) is a hyper-parameter for controlling the reweighting strength. The total loss is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.12, + 0.69, + 0.47, + 0.722 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\frac {1}{2 | B |} \\left(\\operatorname {S N C E} (v, t, s) + \\operatorname {S N C E} (t, v, s)\\right). \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.468, + 0.901 + ], + "angle": 0, + "content": "As shown in Fig. 4, the false negative sample with similar emotion to the positive sample is greatly suppressed, while other negatives are not affected. Note that when \\( i \\neq j \\) but \\( s_i = s_j \\), we have \\( w_{i,j} = \\infty \\), which is equivalent to removing \\( j \\)th sample from the negative pairs; when \\( s_i \\) and \\( s_j \\) are very different, \\( w_{i,j} \\) is negligible; we set \\( w_{i,i} = 0 \\) to not affect the true positive pair. Since \\( s \\) is the sentiment score, the sentiment-related differences are emphasized and weighted more during training. Therefore, the proposed contrastive loss is expected to provide cleaner supervision signals for learning emotion-related representations." + }, + { + "type": "image", + "bbox": [ + 0.543, + 0.09, + 0.852, + 0.193 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.206, + 0.892, + 0.263 + ], + "angle": 0, + "content": "Figure 4. A sample batch where both the positive pair (green) and the false negative pair (red) exist. The green bar and gray bar represent the similarity between all text and the positive video before and after reweighting." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.29, + 0.734, + 0.307 + ], + "angle": 0, + "content": "4. Experiments and Results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.316, + 0.892, + 0.392 + ], + "angle": 0, + "content": "We first introduce the datasets for evaluation in Sec. 4.1 before analyzing various components of EmotionCLIP in Sec. 4.2. Then, we compare EmotionCLIP with the state-of-the-art methods on various datasets in Sec. 4.3. Please see Appendix for more experimental results." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.404, + 0.787, + 0.419 + ], + "angle": 0, + "content": "4.1. Datasets and Evaluation Metrics" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.429, + 0.892, + 0.564 + ], + "angle": 0, + "content": "We evaluate the performance of EmotionCLIP on a variety of recently published challenging benchmarks, including four video datasets and an image dataset. The annotations of these datasets are mainly based on three physiological models: Ekman's basic emotion theory [18] (7 discrete categories), the fine-grained emotion model [14] (26 discrete categories), and the Valence-Arousal-Dominance emotion model [67] (3 continuous dimensions). The evaluation metrics are consistent with previous methods." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.565, + 0.892, + 0.626 + ], + "angle": 0, + "content": "BoLD [45] is a dataset for understanding human body language in the wild, consisting of 9,827 video clips and 13,239 instances, in which each instance is annotated with 26 discrete categories and VAD dimensions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.627, + 0.892, + 0.763 + ], + "angle": 0, + "content": "MovieGraphs [77] is a dataset for understanding human-centric situations consisting of graph-based annotations on social events that appeared in 51 popular movies. Each graph comprises multiple types of nodes to represent actors' emotional and physical attributes, as well as their relationships and interactions. Following the preprocessing and evaluation protocol proposed in previous work [29, 54], we extract relevant emotion attributes from the graphs and group them into 26 discrete emotion categories." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.764, + 0.892, + 0.87 + ], + "angle": 0, + "content": "MELD [60] is an extension to the EmotionLines [9], which is an emotion corpus of multi-party conversations initially proposed in the NLP domain. It offers the same dialogue examples as EmotionLines and includes audio and visual modalities along with the text. It contains around 1,400 dialogues and 13,000 utterances from the Friends tv show, where each example is annotated with 7 discrete categories." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Liris-Accede [5] is a dataset that contains videos from a set of 160 professionally made and amateur movies covering a" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18997" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.089, + 0.468, + 0.18 + ], + "angle": 0, + "content": "
mAPAUCR2
EmotionCLIP (vanilla)21.9768.850.130
+ SAAM21.53-0.4468.56-0.290.137+0.007
+ SAP22.28+0.3169.06+0.210.131+0.001
+ SAP & SNCE22.51+0.5469.30+0.450.133+0.003
" + }, + { + "type": "table_caption", + "bbox": [ + 0.095, + 0.19, + 0.452, + 0.205 + ], + "angle": 0, + "content": "Table 1. Component-wise analysis of our method on BoLD." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.233, + 0.468, + 0.263 + ], + "angle": 0, + "content": "variety of themes. Valence and arousal scores are provided continuously (i.e., every second) along movies." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.264, + 0.468, + 0.325 + ], + "angle": 0, + "content": "Emotic [29] is an image dataset for emotion recognition in context, comprising 23,571 images of 34,320 annotated individuals in unconstrained real-world environments. Each subject is annotated with 26 discrete categories." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.336, + 0.231, + 0.352 + ], + "angle": 0, + "content": "4.2. Ablation Study" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.36, + 0.445, + 0.377 + ], + "angle": 0, + "content": "4.2.1 Analysis of Subject-Aware Context Encoding" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.385, + 0.468, + 0.491 + ], + "angle": 0, + "content": "In this series of experiments, we start with a vanilla model and analyze it by adding various subject-aware approaches. As shown in Table 1, decent results can be achieved in downstream tasks using the vanilla EmotionCLIP. This result supports our argument that models can learn non-trivial emotion representations from human verbal and nonverbal expressions by matching them together." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.492, + 0.468, + 0.568 + ], + "angle": 0, + "content": "The SAP achieves better results and improves over the baseline by a reasonable margin. This improvement demonstrates the design of SAP can incorporate location-specific information to guide the model in acquiring target-related content without impacting global information modeling." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.568, + 0.468, + 0.824 + ], + "angle": 0, + "content": "Additionally, we note that the model with SAAM yields mediocre performance. As discussed earlier, SAAM can be regarded as an efficient implementation of the multi-stream strategy in the Transformer. This outcome suggests that the multi-stream strategy, commonly used in previous methods, may not be optimal. To rule out the possibility of fusion at inappropriate layers, we explore the impact of different fusion positions by applying SAAM up to a certain layer in the Transformer. It shows that the performance change does not correlate to the fusion layer change, and SAAM consistently underperforms SAP, irrespective of the fusion location. This finding implies that imposing hard masks on the model's attention may introduce unanticipated biases, while adaptively modeling context-subject interaction is more reasonable. In subsequent experiments and discussions, we use SAP as the standard implementation, unless otherwise stated." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.468, + 0.902 + ], + "angle": 0, + "content": "Qualitative Analysis. SAP offers merely a positional hint, as opposed to the mandatory attention-shifting in SAAM. Since the purpose of SAP is to ensure subject-aware encoding, it is necessary to understand if the attention guidance is appropriate. We analyze SAP by plotting HMN token's" + }, + { + "type": "image", + "bbox": [ + 0.525, + 0.091, + 0.869, + 0.158 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.525, + 0.161, + 0.869, + 0.228 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.526, + 0.232, + 0.869, + 0.299 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.311, + 0.892, + 0.368 + ], + "angle": 0, + "content": "Figure 5. Attention weights for the HMN token from layer 1-4 (left to right) of the frame encoder in one trained network. Each row represents one frame. The green and yellow spots are the high-attention areas." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.396, + 0.892, + 0.473 + ], + "angle": 0, + "content": "attention to all patches on the image. As shown in Fig. 5, HMN tokens first focus on random locations, but gradually turn their attention to the subject (i.e., the person with a bounding box) as we move to later layers, demonstrating that SAP offers sufficient guidance to the network attention." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.497, + 0.891, + 0.527 + ], + "angle": 0, + "content": "4.2.2 Analysis of Sentiment-Guided Contrastive Learning" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.538, + 0.892, + 0.824 + ], + "angle": 0, + "content": "We first compare models trained with different \\(\\beta\\), the hyperparameter used to control the strength of reweighting in SNCE. Note that the training objective is equivalent to the vanilla infoNCE loss [56] when \\(\\beta\\) is set to zero. As \\(\\beta\\) increases, more negative samples within the batch are suppressed. As shown in Table 1 and Fig. 6, reweighting with appropriate strength can significantly increase the performance of the model as it guides the direction of learning by eliminating some significant false negatives. However, an excessively large \\(\\beta\\) can hinder the training of the model, which is within expectation. First, the sentiment scores used in the reweighting process are weak pseudo-labels provided by a pre-trained sentiment analysis model, which is not entirely reliable and accurate. Second, previous work has clearly demonstrated that batch size has a decisive impact on self-supervised learning [10, 24, 62]. A too-large \\(\\beta\\) will cause too many negative samples to be suppressed, reducing the effective batch size and thus hindering the learning process." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Qualitative Analysis. We show how the text expressing different emotions are treated by our sentiment-guided loss. Given a positive pair, the logits are the scaled similarities between texts and the positive video; the model is penalized on large logits unless it is associated with the positive text." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18998" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.09, + 0.468, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.207, + 0.471, + 0.25 + ], + "angle": 0, + "content": "Figure 6. The effect of varying the strength of reweighting in SNCE. The larger the \\(\\beta\\), the stronger the suppression of negative samples." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.265, + 0.466, + 0.382 + ], + "angle": 0, + "content": "
TextLogit
I'm sorry to keep you any longer than is necessary. (positive sample)10.65
I'm sorry Tom couldn't join us.12.6 → -697
I hate to say it guys but it's getting late.9.81 → -97.6
I still say it was a wild idea.13.8 → 13.6
Well, that was truly fascinating.15.2 → 15.0
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.392, + 0.47, + 0.45 + ], + "angle": 0, + "content": "Table 2. An example batch containing both false negative and true negative samples. The logits represent the similarity between every text input and the positive video from a random epoch during training. \\(\\rightarrow\\) represents the sentiment-guided reweighting process." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.476, + 0.47, + 0.553 + ], + "angle": 0, + "content": "As shown in Table 2, the texts in the second and third rows provide undesired contributions to the loss as they express similar emotions as the positive sample. After reweighting, false negatives (2nd and 3rd) are effectively eliminated while true negatives (4th and 5th) are negligibly affected." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.573, + 0.373, + 0.589 + ], + "angle": 0, + "content": "4.2.3 Analysis of Model Implementation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.598, + 0.47, + 0.718 + ], + "angle": 0, + "content": "The frame and text encoders of our model are initialized with the image-text pre-training weights from CLIP [62]. Research in neural science has demonstrated the necessity of basic visual and language understanding capabilities for learning high-level emotional semantics [58, 70]. To validate the effectiveness of using image-text pre-training for weight initialization, we evaluate variants with different implementations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.47, + 0.886 + ], + "angle": 0, + "content": "We first consider encoders with random initialization. As shown in Table 3, the model's performance drops sharply when training from scratch. This result is within expectation for two reasons. From an engineering perspective, previous works have demonstrated the necessity of using pretraining weights for large video models [1, 6] and vision-language models [35, 55]. From a cognitive point of view, it is nearly infeasible to learn abstract concepts directly without basic comprehension skills [58]; if the model cannot recognize people, it is impossible to understand body language and facial expressions properly." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.886, + 0.47, + 0.902 + ], + "angle": 0, + "content": "We then consider frozen encoders with pre-training" + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.089, + 0.891, + 0.237 + ], + "angle": 0, + "content": "
Text EncoderFrame EncoderTemporal EncodermAPAUC
✓✓-22.5169.30
-✓-12.43–45%54.96–21%
---11.02–51%50.28–27%
✗✓-13.40–40%57.38–17%
✗✗-18.43–18%65.08–6.0%
✓✓○21.17–5.9%68.74–0.8%
" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.247, + 0.894, + 0.304 + ], + "angle": 0, + "content": "Table 3. Ablation study on different model implementations. \\(\\checkmark\\) means trainable, initialization with pre-training weights. \\(x\\) means frozen, initialization with pre-training weights. - means trainable, random initialization. \\(\\circ\\) means no parameters." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.332, + 0.892, + 0.452 + ], + "angle": 0, + "content": "weights. This is a standard paradigm for video-language understanding that trains models with offline extracted features [36, 87]. As shown in Table 3, our model with variants using fixed encoders performs worse compared with the model using trainable encoders. This reflects the fact that affective tasks rely on visual and verbal semantics differently from low-level vision tasks, which is what CLIP and its successors overlooked [40]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.454, + 0.893, + 0.559 + ], + "angle": 0, + "content": "We study the effect of the temporal encoder. We consider a variant where the temporal encoder is replaced by a mean pooling layer that simply averages the features of all frames. As shown in Table 3, the performance gap is obvious compared with the baseline. This phenomenon suggests that temporal dependency plays a vital role in emotion representations." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.573, + 0.822, + 0.589 + ], + "angle": 0, + "content": "4.3. Comparison with the State of the Art" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.598, + 0.892, + 0.734 + ], + "angle": 0, + "content": "Based on our previous ablation experiments, we choose the model with SAP and SNCE as the default implementation and compare it with the state-of-the-art. In addition, we also compare with VideoCLIP [87] and X-CLIP [55], both of which are state-of-the-art vision-language pre-training models for general video recognition purposes. To evaluate the quality of learned representations, we follow the practice in CLIP [62] and use linear-probe evaluation protocol [10, 24] for vision-language pre-training models." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.893, + 0.901 + ], + "angle": 0, + "content": "BoLD. As shown in Table 4a, EmotionCLIP substantially outperforms the state-of-the-art supervised learning methods on the challenging 26-class emotion classification task and achieves comparable results on continuous emotion regression. It is worth noting that a complex multi-stream model is used in [59] to integrate the human body and context information, while we achieve better results with a single-stream structure using RGB information only. This difference reflects that the subject-aware approach we designed models the relationship between the subject and context. We also notice that other vision-language-based meth" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "18999" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.182, + 0.093, + 0.26, + 0.105 + ], + "angle": 0, + "content": "(a) BoLD [45]" + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.107, + 0.362, + 0.248 + ], + "angle": 0, + "content": "
MethodmAP ↑AUC ↑R2 ↑
Supervised
ST-GCN [94]12.6355.960.044
TSN [81]17.0262.700.095
Filntis et al. [21]16.5662.660.092
Pikoulis et al. [59]19.2966.820.149
Linear-Eval
VideoCLIP [87]11.1951.23-5.11
X-CLIP [55]13.2656.86-0.03
EmotionCLIP22.5169.300.133
" + }, + { + "type": "table_caption", + "bbox": [ + 0.455, + 0.094, + 0.537, + 0.105 + ], + "angle": 0, + "content": "(c) Emotic [29]" + }, + { + "type": "table", + "bbox": [ + 0.369, + 0.107, + 0.622, + 0.26 + ], + "angle": 0, + "content": "
MethodmAP ↑AUC ↑
Supervised
CAER-Net [34]20.84-
Affective Graph [96]28.42-
Fusion Model [29]29.45-
EmotiCon (GCN) [53]32.03-
EmotiCon (Depth) [53]35.48-
Linear-Eval
VideoCLIP [87]19.9256.31
X-CLIP [55]22.8061.31
EmotionCLIP32.9171.41
" + }, + { + "type": "table_caption", + "bbox": [ + 0.707, + 0.094, + 0.814, + 0.105 + ], + "angle": 0, + "content": "(e) Liris-Accede [5]" + }, + { + "type": "table", + "bbox": [ + 0.631, + 0.107, + 0.892, + 0.295 + ], + "angle": 0, + "content": "
MethodV. MSE ↓A. MSE ↓
Supervised
Quan et al. [61]0.1150.171
Ko et al. [28]0.1020.149
*CERTH-ITI [4]0.1170.138
*THUHCSI [25]0.0920.140
*Yi et al. [91]0.0900.136
*GLA [75]0.0840.133
*Zhao et al. [95]0.0710.137
*Affect2MM [54]0.0680.128
Linear-Eval
VideoCLIP [87]0.1420.151
X-CLIP [55]0.1330.246
EmotionCLIP0.0960.155
" + }, + { + "type": "table_caption", + "bbox": [ + 0.162, + 0.281, + 0.279, + 0.293 + ], + "angle": 0, + "content": "(b) MovieGraphs [77]" + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.294, + 0.361, + 0.411 + ], + "angle": 0, + "content": "
MethodVal Acc ↑Test Acc ↑
Supervised
EmotionNet [84]35.6027.90
*Affect2MM [54]39.8830.58
Linear-Eval
VideoCLIP [87]29.9123.44
X-CLIP [55]29.0623.58
EmotionCLIP41.6032.35
" + }, + { + "type": "table_caption", + "bbox": [ + 0.455, + 0.281, + 0.537, + 0.293 + ], + "angle": 0, + "content": "(d) MELD [60]" + }, + { + "type": "table", + "bbox": [ + 0.369, + 0.294, + 0.622, + 0.411 + ], + "angle": 0, + "content": "
MethodAcc ↑W. F1 ↑
Supervised
M2FNet (Visual) [12]45.6332.44
*M2FNet [12]67.8566.71
Linear-Eval
VideoCLIP [87]45.1932.06
X-CLIP [55]38.3132.46
EmotionCLIP48.2834.59
" + }, + { + "type": "table", + "bbox": [ + 0.631, + 0.312, + 0.891, + 0.411 + ], + "angle": 0, + "content": "
AbbreviationMeaning
A. MSEArousal MSE
V. MSEValence MSE
W. F1Weighted F1
Acc.Top-1 Accuracy
↓Lower is better
↑Higher is better
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.423, + 0.892, + 0.452 + ], + "angle": 0, + "content": "Table 4. Comparisons to the state-of-the-art across multiple datasets. Methods marked with * use multimodal inputs, i.e., audio and text. Bold numbers indicate the best results achieved using visual inputs only." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.478, + 0.469, + 0.553 + ], + "angle": 0, + "content": "ods perform poorly on emotion recognition tasks, although they are designed for general video understanding purposes. This phenomenon is largely attributed to the lack of proper guidance; the model can only learn low-level visual patterns and fails to capture semantic and emotional information." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.553, + 0.469, + 0.644 + ], + "angle": 0, + "content": "MovieGraphs. As shown in Table 4b, EmotionCLIP substantially outperforms the best vision-based method and even surpasses Affect2MM [54], a powerful multimodal approach that uses audio and text descriptions in addition to visual information. Instead, other vision-language pretraining models are still far from supervised methods." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.644, + 0.469, + 0.795 + ], + "angle": 0, + "content": "MELD. EmotionCLIP performs well on MELD as shown in Table 4d; it achieves comparable results to the state-of-the-art vision-based methods. It is worth noting that this dataset is extended from an NLP dataset, so the visual data is noisier than the original text data. In fact, according to the ablation experiments in [12], it is possible to achieve an accuracy of \\(67.24\\%\\) using only text, while adding visual modality information only improves the accuracy by about \\(0.5\\%\\). This result explains why our method significantly lags behind multimodal methods using text inputs." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.469, + 0.855 + ], + "angle": 0, + "content": "Liris-Accede. As shown in Table 4e, EmotionCLIP achieves promising results using visual inputs only. It even competes with many multimodal approaches that are benefited from the use of audio features [93]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.469, + 0.902 + ], + "angle": 0, + "content": "Emotic. As shown in Table 4c, EmotionCLIP outperforms all RGB-based supervised methods while other vision-language models perform poorly. The improvement of [53]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.478, + 0.892, + 0.525 + ], + "angle": 0, + "content": "is attributable to the use of additional depth information. This result demonstrates the capability of EmotionCLIP in learning relevant features from complex environments." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.538, + 0.619, + 0.554 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.564, + 0.892, + 0.791 + ], + "angle": 0, + "content": "The pre-training methodology, which has brought about significant advancements in numerous CV and NLP domains, has not yet been employed in AEI research. We address this void by introducing EmotionCLIP, the first vision-language pre-training framework that circumvents the need for curated data and annotations. Our study establishes the viability of acquiring generalized emotion representations directly from human communication, thereby considerably broadening the horizons of current AEI research. The emergence of this pre-training paradigm offers an alternative solution to data scarcity, paving the way for a myriad of potential applications. We anticipate that our work will stimulate further investigation in this area and contribute to the evolution of more adaptable and efficacious approaches for affective computing." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Acknowledgments. This research was supported by generous gifts from the Amazon Research Awards program. The work used computational resources from the Advanced Cyberinfrastructure Coordination Ecosystem: Services & Support (ACCESS) program, which is supported by National Science Foundation." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19000" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.105 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.096, + 0.116, + 0.468, + 0.157 + ], + "angle": 0, + "content": "[1] Anurag Arnab, Mostafa Dehghani, Georg Heigold, Chen Sun, Mario Lucic, and Cordelia Schmid. Vivit: A video vision transformer. In ICCV, pages 6836-6846, 2021. 7" + }, + { + "type": "ref_text", + "bbox": [ + 0.096, + 0.159, + 0.468, + 0.211 + ], + "angle": 0, + "content": "[2] Max Bain, Arsha Nagrani, Gül Varol, and Andrew Zisserman. Frozen in time: A joint video and image encoder for end-to-end retrieval. 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Wang +The Pennsylvania State University, University Park, Pennsylvania, USA +{sbz5211,ymp5078,jwang}@psu.edu + +# Abstract + +Emotion understanding is an essential but highly challenging component of artificial general intelligence. The absence of extensive annotated datasets has significantly impeded advancements in this field. We present EmotionCLIP, the first pre-training paradigm to extract visual emotion representations from verbal and nonverbal communication using only uncurated data. Compared to numerical labels or descriptions used in previous methods, communication naturally contains emotion information. Furthermore, acquiring emotion representations from communication is more congruent with the human learning process. We guide EmotionCLIP to attend to nonverbal emotion cues through subject-aware context encoding and verbal emotion cues using sentiment-guided contrastive learning. Extensive experiments validates the effectiveness and transferability of EmotionCLIP. Using merely linear-probe evaluation protocol, EmotionCLIP outperforms the state-of-the-art supervised visual emotion recognition methods and rivals many multimodal approaches across various benchmarks. We anticipate that the advent of EmotionCLIP will address the prevailing issue of data scarcity in emotion understanding, thereby fostering progress in related domains. The code and pre-trained models are available at https://github.com/Xeaver/EmotionCLIP. + +# 1. Introduction + +If artificial intelligence (AI) can be equipped with emotional intelligence (EQ), it will be a significant step toward developing the next generation of artificial general intelligence [46, 92]. The combination of emotion and intelligence distinguishes humans from other animals. The ability to understand, use, and express emotions will significantly facilitate the interaction of AI with humans and the environment [20, 48-50], making it the foundation for a wide variety of HCI [3], robotics [11], and autonomous driving [31] applications. + +Categorical Label: Shocked Regretful 0 1 0 0 0 1 0 0 0 +Figure 1. Emotions emerge naturally in human communication through verbal and nonverbal cues. The rich semantic details within the expression can hardly be represented by human-annotated categorical labels and descriptions in current datasets. +![](images/09120afb63ac282c8370e218736934497c1794fd15e9bd4037a88d71a9ebfba4.jpg) +Description: An old man is chatting with his son while eating at a restaurant. +Conversation: +- Dad. Who is Dede? +- Jesus. She was the love of my life and I was too stupid to realized it. I lost her because of something so dumb. + +Artificial emotional intelligence (AEI) research is still in its nascency [30, 73]. The recent emergence of pretrained models in CV [10, 24, 62] and NLP [7, 16, 33, 68] domains has ushered in a new era of research in related subjects. By training on large-scale unlabeled data in a self-supervised manner, the model learns nontrivial representations that generalize to downstream tasks [42, 62]. Unfortunately, such a technique remains absent from AEI research. The conventional approaches in visual emotion understanding have no choice but to train models from scratch, or leverage models from less-relevant domains [27, 66], suffering from data scarcity [29, 45]. The lack of pre-trained models greatly limits the development of AEI research. + +Research in neuroscience and psychology offers insights for addressing this problem. Extending from the capabilities that have been coded genetically, humans learn emotional expressions through daily interaction and communication as early as when they are infants. It has been shown that both vision [58] and language [41] play crucial roles in this learning process. By absorbing and imitating expressions from others, humans eventually master the necessary + +feelings to comprehend emotional states by observing and analyzing facial expressions, body movements, contextual environments, etc. + +Inspired by how humans comprehend emotions, we propose a new paradigm for emotion understanding that learn directly from human communication. The core of our idea is to explore the consistency between verbal and nonverbal affective cues in daily communication. Fig. 1 shows how communication reveals emotion. Our method that learns from communication is not only aligned with the human learning process but also has several advantages: + +1) Our method bypasses the problems in emotion data collection by leveraging uncurated data from daily communication. Existing emotion understanding datasets are mainly annotated using crowdsourcing [29, 45, 77]. For image classification tasks, it is straightforward for annotators to agree on an image's label due to the fact that the label is determined by certain low-level visual characteristics. However, crowdsourcing participants usually have lower consensus on producing emotion annotations due to the subjectivity and subtlety of affective labels [90]. This phenomenon makes it extremely difficult to collect accurate emotion annotations on a large scale. Our approach does not rely on human annotations, allowing us to benefit from nearly unlimited web data. + +2) Our use of verbal expressions preserves fine-grained semantics to the greatest extent possible. Limited by the data collection strategy, existing datasets usually only contain annotations for a limited number of emotion categories, which is far from covering the space of human emotional expression [86]. Moreover, the categorical labels commonly used in existing datasets fail to precisely represent the magnitude or intensity of a certain emotion. + +3) Our approach provides a way to directly model expressed emotion. Ideally, AEI should identify the individual's emotional state, i.e., the emotion the person desires to express. Unfortunately, it is nearly impossible to collect data on this type of "expressed emotion" on a large scale. Instead, the current practice is to collect data on "perceived emotion" to approximate the person's actual emotional state, which inevitably introduces noise and bias to labels. + +In general, learning directly from how humans express themselves is a promising alternative that gives a far broader source of supervision and a more comprehensive representation. This strategy is closely analogous to the human learning process and provides an efficient solution for extracting emotion representations from uncurated data. + +We summarize our main contributions as follows: + +- We introduce EmotionCLIP, the first vision-language pre-training paradigm using uncurated data to the visual emotion understanding domain. +- We propose two techniques to guide the model to cap + +ture salient emotional expressions from human verbal and nonverbal communication. + +- Extensive experiments and analysis demonstrate the superiority and transferability of our method on various downstream datasets in emotion understanding. + +# 2. Related Work + +Emotion Recognition from Visual Clues. Facial expression recognition [19, 38, 69] has been well studied in the field of emotion recognition, mainly because faces are not only expressive but also easy to model. Handcrafted features have been developed to describe different facial expressions [13, 43, 74]. Recently, deep learning-based approaches have begun to emerge [38]. Principal research focuses on the design of novel modules for conventional network architectures [88], distinct loss functions for facial tasks [15, 71, 85], and addressing label uncertainties [8, 80]. + +Recently, with the growing interest in recognizing emotion in the wild, the focus of research has gradually shifted to modeling body language [21, 45, 59] and context [29, 53, 54]. Several datasets for understanding human emotional states in unconstrained environments have been proposed [5, 60, 77]; Kosti et al. [29] and Yu et al. [45] established the first benchmark for image and video data, respectively. Follow-up work mainly focuses on context-aware emotion recognition, which usually adopts a multi-branch structure where one branch focuses on the face or body and the other focuses on capturing context [12, 34, 53, 59]. Moreover, some approaches take into account temporal causality [54] or represent context information via graphs [96]. To the best of our knowledge, there are no pre-trained models or effective methods for leveraging unlabeled data in the domain of visual emotion recognition. + +Vision-Language Pre-training. Visual-language pretraining has achieved remarkable progress recently. CLIP [62] demonstrated the feasibility of using contrastive learning [10, 56] to learn transferable and powerful visual representations from large-scale image-text pairs [72]. Many follow-up approaches have been proposed to transfer the pre-trained model to downstream tasks [22, 97, 100] or leverage the scheme for different domains [37, 57, 64, 83, 98]. A line of research endeavors to expand CLIP for general video understanding [26, 35, 40, 44, 55, 82, 87]. The majority of the effort focuses on fine-tuning datasets with textual annotations [27, 32, 39]. However, not only are these curated annotations challenging to obtain, but they also limit the model's potential in various applications. Another line of work [36, 87] extends the image-level pre-training by utilizing unlabeled narrated videos [2, 52], similar to ours. However, we aim to learn abstract emotion representations rather than low-level visual patterns, which are beyond the reach of current models. EmotionNet [84] and its sequel [99], which likewise seeks to learn visual emotion repre + +![](images/8447b9a880c03f8b45ef7ce5b3882f649e8278342e7062f38d3ebff1dd2ab3ee.jpg) +Figure 2. Illustration of EmotionCLIP. For nonverbal communication, subject and context information is modeled by a frame encoder and further aggregated into video-level representations by a temporal encoder. For verbal communication, textual information is encoded as text representations and sentiment scores by a text encoder and sentiment analysis model, respectively. The model learns emotion representations under sentiment guidance in a contrastive manner, by exploring the consistency of verbal and nonverbal communication. + +sentations, are connected to ours. However, their primary focus is on the images' stimuli rather than the recognition of human emotional expressions in the wild. + +# 3. Methodology + +Our core idea is to learn directly from human communication how they express their emotions, by exploring the consistency between their verbal and nonverbal expressions [41]. We tackle this learning task under the vision-language contrastive learning framework [62], that is, the model is expected to learn consistent emotion representations from the verbal expressions (e.g., utterance and dialogue) and nonverbal expressions (e.g., facial expression, body language, and contextual environment) of the same individuals. We give a brief introduction of our data collection procedure in Sec. 3.1 before presenting the overview of EmotionCLIP in Sec. 3.2. We further discuss how the model is guided to learn emotion-relevant representations from the nonverbal perspective in Sec. 3.3, and from the verbal perspective in Sec. 3.4. Please see Appendix for details of the dataset and implementations. + +# 3.1. Data Collection + +Publicly available large-scale vision-and-language datasets do not provide desired verbal and nonverbal information because they either comprise only captions of low-level visual elements [2, 72] or instructions of actions [52]. The captions mostly contain a brief description of the scene or activity, which is insufficient to reveal the underlying emotions; the instruction videos rarely include humans in the scene or express neutral emotions, which fail + +to provide supervision signals for emotion understanding. To overcome such problems, we gather a large-scale video-and-text paired dataset. More specifically, the videos are TV series, while the texts are the corresponding closed captions. We collected 3,613 TV series from YouTube, which is equivalent to around a million raw video clips. We processed them using the off-the-shelf models to group the words in closed caption into complete sentences [23], tag each sentence with a sentiment score [68], and extract human bounding boxes [79]. + +# 3.2. Overview of EmotionCLIP + +Fig. 2 presents an overview of our approach. We follow the wildly adopted vision-language contrastive learning paradigm [62] where two separate branches are used to encode visual inputs (i.e., nonverbal expressions) and textual inputs (i.e., verbal expressions), respectively. + +Video Encoding. The visual branch of EmotionCLIP takes two inputs, including a sequence of RGB frames $X_{v}$ and a sequence of binary masks $X_{m}$ . The binary mask has the same shape as the frame and corresponds to the frame one-to-one, indicating the location of the subject within the frame. The backbone of the subject-aware frame encoder $f_{i}$ is a Vision Transformer [17]. In particular, it extracts $m$ non-overlapping image patches from the frame and projects them into 1D tokens $z_{i} \in \mathbb{R}^{d}$ . The sequence of tokens passed to the following Transformer encoder [76] is $\mathbf{z} = [z_{1}, \dots, z_{m}, z_{cls}, z_{hmn}]$ , where $z_{cls}, z_{hmn}$ are two additional learnable tokens. The mask $X_{m}$ is converted to an array of indices $P$ indicating the image patches containing the subject. The frame encoder further encodes $\mathbf{z}, P$ into a frame-level representation. All frame representations are normalized by the average of the raw data. + +![](images/a78f6735b1cf9c161c14e068857d0348624ba3606b2dcc103632f1080ad56e30.jpg) +Figure 3. The traditional approaches (left) ignore the dependencies between context and subject, and encode a portion of the image redundantly. The proposed approaches (right two diagrams) efficiently model the subject and context in a synchronous way. + +tions are then passed into the temporal encoder $f_{p}$ to produce a video-level representation as $v = f_{v}(\mathbf{z}, P)$ , where $f_{v} = f_{p} \circ f_{i}$ and $v \in \mathbb{R}^{d}$ . + +Text Encoding. The textual branch of EmotionCLIP takes sentences $X_{t}$ as inputs. The text encoder $f_{t}$ is a Transformer [16] with the architecture modification described in [63], and the sentiment model $f_{s}$ is a pre-trained sentiment analysis model [68] that is frozen during training. The input text is encoded by both models as $t = f_{t}(X_{t})$ and $s = f_{s}(X_{t})$ , where $t \in \mathbb{R}^{d}$ is the representation of the text and $s \in \mathbb{R}^{7}$ is the pseudo sentiment score. + +Training Objective. The training objective is to learn the correspondence between visual inputs and textual inputs by minimizing the sentiment-guided contrastive loss $\mathcal{L}$ . + +We discuss the details of the proposed subject-aware encoding approaches in Sec. 3.3 and the sentiment-guided contrastive learning framework in Sec. 3.4. + +# 3.3. Subject-Aware Context Encoding + +Context encoding is an important part of emotion understanding, especially in unconstrained environments, as it has been widely shown in psychology that emotional processes cannot be interpreted without context [47, 51, 65]. We intend to guide the model to focus on the interaction between the subject of interest and context. As shown in Fig. 3, the cropped character and the whole image are usually encoded by two separate networks and fused at the ends [34, 53, 59]. This approach is inflexible and inefficient since it overlooks the dependency between subject and context and encodes redundant image portions. Following this line of thought, we propose two potential subject-aware context encoding strategies, i.e., subject-aware attention masking (SAAM) and subject-aware prompting (SAP). The former can be regarded as an efficient implementation of the traditional two-stream approach but avoids the problem of redundant encoding. The latter is a novel encoding strategy that enables adaptive modeling of the interaction between the context and the subject by providing necessary prompts. + +Subject-Aware Attention Masking. The canonical attention module [76] in a Transformer is defined as: + +$$ +\mathrm {A t t e n t i o n} (\mathbf {Q}, \mathbf {K}, \mathbf {V}) = \mathrm {s o f t m a x} \left(\frac {\mathbf {Q} \mathbf {K} ^ {\top}}{\sqrt {d}}\right) \mathbf {V}. \qquad (1) +$$ + +We model the context and subject in a synchronous way by modifying the attention module to + +$\mathbf{Attention}^{*}(\mathbf{Q},\mathbf{K},\mathbf{V},\mathbf{U}) =$ + +$$ +\underbrace {\operatorname {s o f t m a x} \left(\frac {\mathbf {Q K} ^ {\top}}{\sqrt {d}}\right) (\mathbf {J} - \mathbf {A}) \mathbf {V}} _ {\text {c o n t e x t}} + \underbrace {\operatorname {s o f t m a x} \left(\frac {\mathbf {Q K} ^ {\top}}{\sqrt {d}}\right) \mathbf {A U V}} _ {\text {s u b j e c t}}, +$$ + +where $\mathbf{J}$ is a matrix with all ones, $\mathbf{A}$ is a learnable parameters containing values in range [0, 1], and $\mathbf{U}$ is a weight matrix constructed using $P$ . Intuitively, we shift $\mathbf{A}$ amount of attention from a total of $\mathbf{J}$ amount of attention from the context to the subject. To partition the $\mathbf{A}$ amount of attention to all image patches containing subject, we compute $\mathbf{U}$ as the following: + +$$ +\mathbf {U} = \operatorname {s o f t m a x} \left(\frac {\mathbf {Q} \mathbf {K} ^ {\top} + \mathbf {M}}{\sqrt {d}}\right). \tag {3} +$$ + +The masking matrix $\mathbf{M}$ is defined as: + +$$ +\mathbf {M} = \left[ \begin{array}{l l} \mathbf {M} ^ {(1)} & \mathbf {M} ^ {(2)} \\ \mathbf {M} ^ {(3)} & \mathbf {M} ^ {(4)} \end{array} \right], \tag {4} +$$ + +where $\mathbf{M}^{(1)} = \mathbf{0}_{(m + 1)\times (m + 1)}$ , $\mathbf{M}^{(4)} = \mathbf{0}_{1\times 1}$ , $\mathbf{M}_{i\notin P}^{(2)} = \mathbf{M}_{i\notin P}^{(3)} = -\infty$ , $\mathbf{M}_{(m + 1)}^{(3)} = -\infty$ , and all other entries are zero. Intuitively, $\mathbf{M}^{(2)}$ and $\mathbf{M}^{(3)}$ represent the attention between all image patches $z_{i}$ and the human token $z_{hmn}$ to model the subject stream; we mask out all attention between non-human patches and the human token. Moreover, we mask out attention from $z_{hmn}$ to $z_{cls}$ , $\mathbf{M}_{(m + 1)}^{(3)}$ , to ensure $z_{hmn}$ only encodes the subject. + +Subject-Aware Prompting. Prompting is a parameter-free method that restricts the output space of the model by shaping inputs. In our case, we hope to prompt the model to distinguish between the context and the subject. A recent visual prompting method, CPT [89], provides such a prompt by altering the original image, i.e., imposing colored boxes on objects of interest. It shows that a Transformer is able to locate objects with the help of positional hints. However, introducing artifacts on pixel space may not be optimal as it causes large domain shifts. To address this issue, we propose to construct prompts in the latent space based on positional embeddings, considering that they are inherently designed as indicative information. Formally, let $e_i$ be + +the positional embedding corresponding to the patch token $z_{i}$ , and $P$ are the indicator set of the subject location. The prompting token is designed as $z_{hmn} = \sum_{i\in P}e_{i}$ . + +We argue the sum of positional embeddings is enough to provide hints about the subject location. The previous study [78] demonstrates a Transformer treats all tokens without positional embedding uniformly but with positional embedding differently. This result shows positional embeddings play a vital role in guiding model attention. + +# 3.4. Sentiment-Guided Contrastive Learning + +We train the model to learn emotion representations from verbal and nonverbal expressions in a contrastive manner. In the traditional contrastive setting, the model is forced to repel all negative pairs except the only positive one. However, many expressions in daily communication indeed have the same semantics from an emotional perspective. Contrasting these undesirable negative pairs encourages the model to learn spurious relations. This problem comes from false negatives, i.e., the affectively similar samples are treated as negatives. We address this issue by introducing a trained sentiment analysis model [68] from the NLP domain for the suppression of false negatives, thereby guiding our model to capture emotion-related concepts from verbal expressions. Specifically, we propose a sentiment-guided contrastive loss: + +$$ +\operatorname {S N C E} (v, t, s) = - \sum_ {i \in B} \left(\log \frac {\exp \left(v _ {i} \cdot t _ {i} / \tau\right)}{\sum_ {j \in B} \exp \left(v _ {i} \cdot t _ {j} / \tau - w _ {i , j}\right)}\right), \tag {5} +$$ + +where $B$ is a batch. The reweighting term $w_{i,j}$ is defined as + +$$ +w _ {i, j} = \left\{ \begin{array}{l l} \beta \cdot \mathrm {K L} \left(s _ {i} \| s _ {j}\right) ^ {- 1} & i \neq j \\ 0 & i = j \end{array} , \right. \tag {6} +$$ + +where $\beta$ is a hyper-parameter for controlling the reweighting strength. The total loss is defined as: + +$$ +\mathcal {L} = \frac {1}{2 | B |} \left(\operatorname {S N C E} (v, t, s) + \operatorname {S N C E} (t, v, s)\right). \tag {7} +$$ + +As shown in Fig. 4, the false negative sample with similar emotion to the positive sample is greatly suppressed, while other negatives are not affected. Note that when $i \neq j$ but $s_i = s_j$ , we have $w_{i,j} = \infty$ , which is equivalent to removing $j$ th sample from the negative pairs; when $s_i$ and $s_j$ are very different, $w_{i,j}$ is negligible; we set $w_{i,i} = 0$ to not affect the true positive pair. Since $s$ is the sentiment score, the sentiment-related differences are emphasized and weighted more during training. Therefore, the proposed contrastive loss is expected to provide cleaner supervision signals for learning emotion-related representations. + +![](images/8f3810a750c1bda701f236a17b4560227387a6797f7bc95ba0ebd0f5b4c50795.jpg) +Figure 4. A sample batch where both the positive pair (green) and the false negative pair (red) exist. The green bar and gray bar represent the similarity between all text and the positive video before and after reweighting. + +# 4. Experiments and Results + +We first introduce the datasets for evaluation in Sec. 4.1 before analyzing various components of EmotionCLIP in Sec. 4.2. Then, we compare EmotionCLIP with the state-of-the-art methods on various datasets in Sec. 4.3. Please see Appendix for more experimental results. + +# 4.1. Datasets and Evaluation Metrics + +We evaluate the performance of EmotionCLIP on a variety of recently published challenging benchmarks, including four video datasets and an image dataset. The annotations of these datasets are mainly based on three physiological models: Ekman's basic emotion theory [18] (7 discrete categories), the fine-grained emotion model [14] (26 discrete categories), and the Valence-Arousal-Dominance emotion model [67] (3 continuous dimensions). The evaluation metrics are consistent with previous methods. + +BoLD [45] is a dataset for understanding human body language in the wild, consisting of 9,827 video clips and 13,239 instances, in which each instance is annotated with 26 discrete categories and VAD dimensions. + +MovieGraphs [77] is a dataset for understanding human-centric situations consisting of graph-based annotations on social events that appeared in 51 popular movies. Each graph comprises multiple types of nodes to represent actors' emotional and physical attributes, as well as their relationships and interactions. Following the preprocessing and evaluation protocol proposed in previous work [29, 54], we extract relevant emotion attributes from the graphs and group them into 26 discrete emotion categories. + +MELD [60] is an extension to the EmotionLines [9], which is an emotion corpus of multi-party conversations initially proposed in the NLP domain. It offers the same dialogue examples as EmotionLines and includes audio and visual modalities along with the text. It contains around 1,400 dialogues and 13,000 utterances from the Friends tv show, where each example is annotated with 7 discrete categories. + +Liris-Accede [5] is a dataset that contains videos from a set of 160 professionally made and amateur movies covering a + +
mAPAUCR2
EmotionCLIP (vanilla)21.9768.850.130
+ SAAM21.53-0.4468.56-0.290.137+0.007
+ SAP22.28+0.3169.06+0.210.131+0.001
+ SAP & SNCE22.51+0.5469.30+0.450.133+0.003
+ +Table 1. Component-wise analysis of our method on BoLD. + +variety of themes. Valence and arousal scores are provided continuously (i.e., every second) along movies. + +Emotic [29] is an image dataset for emotion recognition in context, comprising 23,571 images of 34,320 annotated individuals in unconstrained real-world environments. Each subject is annotated with 26 discrete categories. + +# 4.2. Ablation Study + +# 4.2.1 Analysis of Subject-Aware Context Encoding + +In this series of experiments, we start with a vanilla model and analyze it by adding various subject-aware approaches. As shown in Table 1, decent results can be achieved in downstream tasks using the vanilla EmotionCLIP. This result supports our argument that models can learn non-trivial emotion representations from human verbal and nonverbal expressions by matching them together. + +The SAP achieves better results and improves over the baseline by a reasonable margin. This improvement demonstrates the design of SAP can incorporate location-specific information to guide the model in acquiring target-related content without impacting global information modeling. + +Additionally, we note that the model with SAAM yields mediocre performance. As discussed earlier, SAAM can be regarded as an efficient implementation of the multi-stream strategy in the Transformer. This outcome suggests that the multi-stream strategy, commonly used in previous methods, may not be optimal. To rule out the possibility of fusion at inappropriate layers, we explore the impact of different fusion positions by applying SAAM up to a certain layer in the Transformer. It shows that the performance change does not correlate to the fusion layer change, and SAAM consistently underperforms SAP, irrespective of the fusion location. This finding implies that imposing hard masks on the model's attention may introduce unanticipated biases, while adaptively modeling context-subject interaction is more reasonable. In subsequent experiments and discussions, we use SAP as the standard implementation, unless otherwise stated. + +Qualitative Analysis. SAP offers merely a positional hint, as opposed to the mandatory attention-shifting in SAAM. Since the purpose of SAP is to ensure subject-aware encoding, it is necessary to understand if the attention guidance is appropriate. We analyze SAP by plotting HMN token's + +![](images/c6558b422b7149909814c5c136af8266fbe74e67e72b6d63006017dec2f5c7eb.jpg) + +![](images/28632e2c704fc78be6d795cf563f03bb0f96333d28648357f77972d2593e7405.jpg) + +![](images/293bd745b96ca8868e1fe6b26ac7d00f47b249a61b77355c2b2c7baff86022a1.jpg) +Figure 5. Attention weights for the HMN token from layer 1-4 (left to right) of the frame encoder in one trained network. Each row represents one frame. The green and yellow spots are the high-attention areas. + +attention to all patches on the image. As shown in Fig. 5, HMN tokens first focus on random locations, but gradually turn their attention to the subject (i.e., the person with a bounding box) as we move to later layers, demonstrating that SAP offers sufficient guidance to the network attention. + +# 4.2.2 Analysis of Sentiment-Guided Contrastive Learning + +We first compare models trained with different $\beta$ , the hyperparameter used to control the strength of reweighting in SNCE. Note that the training objective is equivalent to the vanilla infoNCE loss [56] when $\beta$ is set to zero. As $\beta$ increases, more negative samples within the batch are suppressed. As shown in Table 1 and Fig. 6, reweighting with appropriate strength can significantly increase the performance of the model as it guides the direction of learning by eliminating some significant false negatives. However, an excessively large $\beta$ can hinder the training of the model, which is within expectation. First, the sentiment scores used in the reweighting process are weak pseudo-labels provided by a pre-trained sentiment analysis model, which is not entirely reliable and accurate. Second, previous work has clearly demonstrated that batch size has a decisive impact on self-supervised learning [10, 24, 62]. A too-large $\beta$ will cause too many negative samples to be suppressed, reducing the effective batch size and thus hindering the learning process. + +Qualitative Analysis. We show how the text expressing different emotions are treated by our sentiment-guided loss. Given a positive pair, the logits are the scaled similarities between texts and the positive video; the model is penalized on large logits unless it is associated with the positive text. + +![](images/4f1e56460446254646ec6f22bc1f96dae39d3e225cd5118bcaebcc52dd3bbea6.jpg) +Figure 6. The effect of varying the strength of reweighting in SNCE. The larger the $\beta$ , the stronger the suppression of negative samples. + +
TextLogit
I'm sorry to keep you any longer than is necessary. (positive sample)10.65
I'm sorry Tom couldn't join us.12.6 → -697
I hate to say it guys but it's getting late.9.81 → -97.6
I still say it was a wild idea.13.8 → 13.6
Well, that was truly fascinating.15.2 → 15.0
+ +As shown in Table 2, the texts in the second and third rows provide undesired contributions to the loss as they express similar emotions as the positive sample. After reweighting, false negatives (2nd and 3rd) are effectively eliminated while true negatives (4th and 5th) are negligibly affected. + +# 4.2.3 Analysis of Model Implementation + +The frame and text encoders of our model are initialized with the image-text pre-training weights from CLIP [62]. Research in neural science has demonstrated the necessity of basic visual and language understanding capabilities for learning high-level emotional semantics [58, 70]. To validate the effectiveness of using image-text pre-training for weight initialization, we evaluate variants with different implementations. + +We first consider encoders with random initialization. As shown in Table 3, the model's performance drops sharply when training from scratch. This result is within expectation for two reasons. From an engineering perspective, previous works have demonstrated the necessity of using pretraining weights for large video models [1, 6] and vision-language models [35, 55]. From a cognitive point of view, it is nearly infeasible to learn abstract concepts directly without basic comprehension skills [58]; if the model cannot recognize people, it is impossible to understand body language and facial expressions properly. + +We then consider frozen encoders with pre-training + +Table 2. An example batch containing both false negative and true negative samples. The logits represent the similarity between every text input and the positive video from a random epoch during training. $\rightarrow$ represents the sentiment-guided reweighting process. + +
Text EncoderFrame EncoderTemporal EncodermAPAUC
✓✓-22.5169.30
-✓-12.43–45%54.96–21%
---11.02–51%50.28–27%
✗✓-13.40–40%57.38–17%
✗✗-18.43–18%65.08–6.0%
✓✓○21.17–5.9%68.74–0.8%
+ +Table 3. Ablation study on different model implementations. $\checkmark$ means trainable, initialization with pre-training weights. $x$ means frozen, initialization with pre-training weights. - means trainable, random initialization. $\circ$ means no parameters. + +weights. This is a standard paradigm for video-language understanding that trains models with offline extracted features [36, 87]. As shown in Table 3, our model with variants using fixed encoders performs worse compared with the model using trainable encoders. This reflects the fact that affective tasks rely on visual and verbal semantics differently from low-level vision tasks, which is what CLIP and its successors overlooked [40]. + +We study the effect of the temporal encoder. We consider a variant where the temporal encoder is replaced by a mean pooling layer that simply averages the features of all frames. As shown in Table 3, the performance gap is obvious compared with the baseline. This phenomenon suggests that temporal dependency plays a vital role in emotion representations. + +# 4.3. Comparison with the State of the Art + +Based on our previous ablation experiments, we choose the model with SAP and SNCE as the default implementation and compare it with the state-of-the-art. In addition, we also compare with VideoCLIP [87] and X-CLIP [55], both of which are state-of-the-art vision-language pre-training models for general video recognition purposes. To evaluate the quality of learned representations, we follow the practice in CLIP [62] and use linear-probe evaluation protocol [10, 24] for vision-language pre-training models. + +BoLD. As shown in Table 4a, EmotionCLIP substantially outperforms the state-of-the-art supervised learning methods on the challenging 26-class emotion classification task and achieves comparable results on continuous emotion regression. It is worth noting that a complex multi-stream model is used in [59] to integrate the human body and context information, while we achieve better results with a single-stream structure using RGB information only. This difference reflects that the subject-aware approach we designed models the relationship between the subject and context. We also notice that other vision-language-based meth + +(a) BoLD [45] + +
MethodmAP ↑AUC ↑R2 ↑
Supervised
ST-GCN [94]12.6355.960.044
TSN [81]17.0262.700.095
Filntis et al. [21]16.5662.660.092
Pikoulis et al. [59]19.2966.820.149
Linear-Eval
VideoCLIP [87]11.1951.23-5.11
X-CLIP [55]13.2656.86-0.03
EmotionCLIP22.5169.300.133
+ +(c) Emotic [29] + +
MethodmAP ↑AUC ↑
Supervised
CAER-Net [34]20.84-
Affective Graph [96]28.42-
Fusion Model [29]29.45-
EmotiCon (GCN) [53]32.03-
EmotiCon (Depth) [53]35.48-
Linear-Eval
VideoCLIP [87]19.9256.31
X-CLIP [55]22.8061.31
EmotionCLIP32.9171.41
+ +(e) Liris-Accede [5] + +
MethodV. MSE ↓A. MSE ↓
Supervised
Quan et al. [61]0.1150.171
Ko et al. [28]0.1020.149
*CERTH-ITI [4]0.1170.138
*THUHCSI [25]0.0920.140
*Yi et al. [91]0.0900.136
*GLA [75]0.0840.133
*Zhao et al. [95]0.0710.137
*Affect2MM [54]0.0680.128
Linear-Eval
VideoCLIP [87]0.1420.151
X-CLIP [55]0.1330.246
EmotionCLIP0.0960.155
+ +(b) MovieGraphs [77] + +
MethodVal Acc ↑Test Acc ↑
Supervised
EmotionNet [84]35.6027.90
*Affect2MM [54]39.8830.58
Linear-Eval
VideoCLIP [87]29.9123.44
X-CLIP [55]29.0623.58
EmotionCLIP41.6032.35
+ +(d) MELD [60] + +
MethodAcc ↑W. F1 ↑
Supervised
M2FNet (Visual) [12]45.6332.44
*M2FNet [12]67.8566.71
Linear-Eval
VideoCLIP [87]45.1932.06
X-CLIP [55]38.3132.46
EmotionCLIP48.2834.59
+ +
AbbreviationMeaning
A. MSEArousal MSE
V. MSEValence MSE
W. F1Weighted F1
Acc.Top-1 Accuracy
↓Lower is better
↑Higher is better
+ +Table 4. Comparisons to the state-of-the-art across multiple datasets. Methods marked with * use multimodal inputs, i.e., audio and text. Bold numbers indicate the best results achieved using visual inputs only. + +ods perform poorly on emotion recognition tasks, although they are designed for general video understanding purposes. This phenomenon is largely attributed to the lack of proper guidance; the model can only learn low-level visual patterns and fails to capture semantic and emotional information. + +MovieGraphs. As shown in Table 4b, EmotionCLIP substantially outperforms the best vision-based method and even surpasses Affect2MM [54], a powerful multimodal approach that uses audio and text descriptions in addition to visual information. Instead, other vision-language pretraining models are still far from supervised methods. + +MELD. EmotionCLIP performs well on MELD as shown in Table 4d; it achieves comparable results to the state-of-the-art vision-based methods. It is worth noting that this dataset is extended from an NLP dataset, so the visual data is noisier than the original text data. In fact, according to the ablation experiments in [12], it is possible to achieve an accuracy of $67.24\%$ using only text, while adding visual modality information only improves the accuracy by about $0.5\%$ . This result explains why our method significantly lags behind multimodal methods using text inputs. + +Liris-Accede. As shown in Table 4e, EmotionCLIP achieves promising results using visual inputs only. It even competes with many multimodal approaches that are benefited from the use of audio features [93]. + +Emotic. As shown in Table 4c, EmotionCLIP outperforms all RGB-based supervised methods while other vision-language models perform poorly. The improvement of [53] + +is attributable to the use of additional depth information. This result demonstrates the capability of EmotionCLIP in learning relevant features from complex environments. + +# 5. Conclusion + +The pre-training methodology, which has brought about significant advancements in numerous CV and NLP domains, has not yet been employed in AEI research. We address this void by introducing EmotionCLIP, the first vision-language pre-training framework that circumvents the need for curated data and annotations. Our study establishes the viability of acquiring generalized emotion representations directly from human communication, thereby considerably broadening the horizons of current AEI research. The emergence of this pre-training paradigm offers an alternative solution to data scarcity, paving the way for a myriad of potential applications. We anticipate that our work will stimulate further investigation in this area and contribute to the evolution of more adaptable and efficacious approaches for affective computing. + +Acknowledgments. This research was supported by generous gifts from the Amazon Research Awards program. 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IJCV, 130(9):2337-2348, 2022. 2 \ No newline at end of file diff --git a/2023/Learning Emotion Representations From Verbal and Nonverbal Communication/images.zip b/2023/Learning Emotion Representations From Verbal and Nonverbal Communication/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..13fd992475cf1cc4dd7ef68c4d9d74a17232b2fe --- /dev/null +++ b/2023/Learning Emotion Representations From Verbal and Nonverbal Communication/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:9462f7c7ad96aaa9f21c269bc7da699e19ddb8ad38a4545161cba51def20bf1e +size 438336 diff --git a/2023/Learning Emotion Representations From Verbal and Nonverbal Communication/layout.json b/2023/Learning Emotion Representations From Verbal and Nonverbal Communication/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..a13bfafbfdbb5ba6745201c78930d794bac94658 --- /dev/null +++ b/2023/Learning Emotion Representations From Verbal and Nonverbal Communication/layout.json @@ -0,0 +1,10220 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 50, + 103, + 543, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 103, + 543, + 121 + ], + "spans": [ + { + "bbox": [ + 50, + 103, + 543, + 121 + ], + "type": "text", + "content": "Learning Emotion Representations from Verbal and Nonverbal Communication" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 122, + 143, + 471, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 122, + 143, + 471, + 185 + ], + "spans": [ + { + "bbox": [ + 122, + 143, + 471, + 185 + ], + "type": "text", + "content": "Sitao Zhang* Yimu Pan* James Z. Wang \nThe Pennsylvania State University, University Park, Pennsylvania, USA \n{sbz5211,ymp5078,jwang}@psu.edu" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "spans": [ + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 239, + 290, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 239, + 290, + 525 + ], + "spans": [ + { + "bbox": [ + 47, + 239, + 290, + 525 + ], + "type": "text", + "content": "Emotion understanding is an essential but highly challenging component of artificial general intelligence. The absence of extensive annotated datasets has significantly impeded advancements in this field. We present EmotionCLIP, the first pre-training paradigm to extract visual emotion representations from verbal and nonverbal communication using only uncurated data. Compared to numerical labels or descriptions used in previous methods, communication naturally contains emotion information. Furthermore, acquiring emotion representations from communication is more congruent with the human learning process. We guide EmotionCLIP to attend to nonverbal emotion cues through subject-aware context encoding and verbal emotion cues using sentiment-guided contrastive learning. Extensive experiments validates the effectiveness and transferability of EmotionCLIP. Using merely linear-probe evaluation protocol, EmotionCLIP outperforms the state-of-the-art supervised visual emotion recognition methods and rivals many multimodal approaches across various benchmarks. We anticipate that the advent of EmotionCLIP will address the prevailing issue of data scarcity in emotion understanding, thereby fostering progress in related domains. The code and pre-trained models are available at https://github.com/Xeaver/EmotionCLIP." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 552, + 128, + 563 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 552, + 128, + 563 + ], + "spans": [ + { + "bbox": [ + 47, + 552, + 128, + 563 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 572, + 287, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 572, + 287, + 693 + ], + "spans": [ + { + "bbox": [ + 46, + 572, + 287, + 693 + ], + "type": "text", + "content": "If artificial intelligence (AI) can be equipped with emotional intelligence (EQ), it will be a significant step toward developing the next generation of artificial general intelligence [46, 92]. The combination of emotion and intelligence distinguishes humans from other animals. The ability to understand, use, and express emotions will significantly facilitate the interaction of AI with humans and the environment [20, 48-50], making it the foundation for a wide variety of HCI [3], robotics [11], and autonomous driving [31] applications." + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 313, + 213, + 539, + 319 + ], + "blocks": [ + { + "bbox": [ + 313, + 213, + 539, + 319 + ], + "lines": [ + { + "bbox": [ + 313, + 213, + 539, + 319 + ], + "spans": [ + { + "bbox": [ + 313, + 213, + 539, + 319 + ], + "type": "image", + "image_path": "09120afb63ac282c8370e218736934497c1794fd15e9bd4037a88d71a9ebfba4.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 315, + 323, + 397, + 349 + ], + "lines": [ + { + "bbox": [ + 315, + 323, + 397, + 349 + ], + "spans": [ + { + "bbox": [ + 315, + 323, + 397, + 349 + ], + "type": "text", + "content": "Categorical Label: Shocked Regretful 0 1 0 0 0 1 0 0 0" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 315, + 351, + 420, + 375 + ], + "lines": [ + { + "bbox": [ + 315, + 351, + 420, + 375 + ], + "spans": [ + { + "bbox": [ + 315, + 351, + 420, + 375 + ], + "type": "text", + "content": "Description: An old man is chatting with his son while eating at a restaurant." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_footnote" + }, + { + "bbox": [ + 430, + 327, + 529, + 375 + ], + "lines": [ + { + "bbox": [ + 430, + 327, + 529, + 375 + ], + "spans": [ + { + "bbox": [ + 430, + 327, + 529, + 375 + ], + "type": "text", + "content": "Conversation: \n- Dad. Who is Dede? \n- Jesus. She was the love of my life and I was too stupid to realized it. I lost her because of something so dumb." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_footnote" + }, + { + "bbox": [ + 306, + 390, + 545, + 434 + ], + "lines": [ + { + "bbox": [ + 306, + 390, + 545, + 434 + ], + "spans": [ + { + "bbox": [ + 306, + 390, + 545, + 434 + ], + "type": "text", + "content": "Figure 1. Emotions emerge naturally in human communication through verbal and nonverbal cues. The rich semantic details within the expression can hardly be represented by human-annotated categorical labels and descriptions in current datasets." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 460, + 546, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 460, + 546, + 615 + ], + "spans": [ + { + "bbox": [ + 304, + 460, + 546, + 615 + ], + "type": "text", + "content": "Artificial emotional intelligence (AEI) research is still in its nascency [30, 73]. The recent emergence of pretrained models in CV [10, 24, 62] and NLP [7, 16, 33, 68] domains has ushered in a new era of research in related subjects. By training on large-scale unlabeled data in a self-supervised manner, the model learns nontrivial representations that generalize to downstream tasks [42, 62]. Unfortunately, such a technique remains absent from AEI research. The conventional approaches in visual emotion understanding have no choice but to train models from scratch, or leverage models from less-relevant domains [27, 66], suffering from data scarcity [29, 45]. The lack of pre-trained models greatly limits the development of AEI research." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "type": "text", + "content": "Research in neuroscience and psychology offers insights for addressing this problem. Extending from the capabilities that have been coded genetically, humans learn emotional expressions through daily interaction and communication as early as when they are infants. It has been shown that both vision [58] and language [41] play crucial roles in this learning process. By absorbing and imitating expressions from others, humans eventually master the necessary" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 703, + 123, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 703, + 123, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 703, + 123, + 712 + ], + "type": "text", + "content": "*equal contribution" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18993" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 107 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 107 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 107 + ], + "type": "text", + "content": "feelings to comprehend emotional states by observing and analyzing facial expressions, body movements, contextual environments, etc." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 109, + 286, + 205 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 109, + 286, + 205 + ], + "spans": [ + { + "bbox": [ + 46, + 109, + 286, + 205 + ], + "type": "text", + "content": "Inspired by how humans comprehend emotions, we propose a new paradigm for emotion understanding that learn directly from human communication. The core of our idea is to explore the consistency between verbal and nonverbal affective cues in daily communication. Fig. 1 shows how communication reveals emotion. Our method that learns from communication is not only aligned with the human learning process but also has several advantages:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 206, + 286, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 206, + 286, + 373 + ], + "spans": [ + { + "bbox": [ + 46, + 206, + 286, + 373 + ], + "type": "text", + "content": "1) Our method bypasses the problems in emotion data collection by leveraging uncurated data from daily communication. Existing emotion understanding datasets are mainly annotated using crowdsourcing [29, 45, 77]. For image classification tasks, it is straightforward for annotators to agree on an image's label due to the fact that the label is determined by certain low-level visual characteristics. However, crowdsourcing participants usually have lower consensus on producing emotion annotations due to the subjectivity and subtlety of affective labels [90]. This phenomenon makes it extremely difficult to collect accurate emotion annotations on a large scale. Our approach does not rely on human annotations, allowing us to benefit from nearly unlimited web data." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 375, + 286, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 375, + 286, + 469 + ], + "spans": [ + { + "bbox": [ + 46, + 375, + 286, + 469 + ], + "type": "text", + "content": "2) Our use of verbal expressions preserves fine-grained semantics to the greatest extent possible. Limited by the data collection strategy, existing datasets usually only contain annotations for a limited number of emotion categories, which is far from covering the space of human emotional expression [86]. Moreover, the categorical labels commonly used in existing datasets fail to precisely represent the magnitude or intensity of a certain emotion." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 471, + 286, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 471, + 286, + 578 + ], + "spans": [ + { + "bbox": [ + 46, + 471, + 286, + 578 + ], + "type": "text", + "content": "3) Our approach provides a way to directly model expressed emotion. Ideally, AEI should identify the individual's emotional state, i.e., the emotion the person desires to express. Unfortunately, it is nearly impossible to collect data on this type of \"expressed emotion\" on a large scale. Instead, the current practice is to collect data on \"perceived emotion\" to approximate the person's actual emotional state, which inevitably introduces noise and bias to labels." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 579, + 286, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 579, + 286, + 651 + ], + "spans": [ + { + "bbox": [ + 46, + 579, + 286, + 651 + ], + "type": "text", + "content": "In general, learning directly from how humans express themselves is a promising alternative that gives a far broader source of supervision and a more comprehensive representation. This strategy is closely analogous to the human learning process and provides an efficient solution for extracting emotion representations from uncurated data." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 59, + 653, + 264, + 663 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 653, + 264, + 663 + ], + "spans": [ + { + "bbox": [ + 59, + 653, + 264, + 663 + ], + "type": "text", + "content": "We summarize our main contributions as follows:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 58, + 665, + 286, + 712 + ], + "type": "list", + "angle": 0, + "index": 9, + "blocks": [ + { + "bbox": [ + 58, + 665, + 286, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 665, + 286, + 700 + ], + "spans": [ + { + "bbox": [ + 58, + 665, + 286, + 700 + ], + "type": "text", + "content": "- We introduce EmotionCLIP, the first vision-language pre-training paradigm using uncurated data to the visual emotion understanding domain." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 58, + 702, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 286, + 712 + ], + "type": "text", + "content": "- We propose two techniques to guide the model to cap" + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 324, + 72, + 544, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 324, + 72, + 544, + 95 + ], + "spans": [ + { + "bbox": [ + 324, + 72, + 544, + 95 + ], + "type": "text", + "content": "ture salient emotional expressions from human verbal and nonverbal communication." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 317, + 96, + 544, + 131 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 96, + 544, + 131 + ], + "spans": [ + { + "bbox": [ + 317, + 96, + 544, + 131 + ], + "type": "text", + "content": "- Extensive experiments and analysis demonstrate the superiority and transferability of our method on various downstream datasets in emotion understanding." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 143, + 392, + 155 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 143, + 392, + 155 + ], + "spans": [ + { + "bbox": [ + 306, + 143, + 392, + 155 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 163, + 545, + 282 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 163, + 545, + 282 + ], + "spans": [ + { + "bbox": [ + 304, + 163, + 545, + 282 + ], + "type": "text", + "content": "Emotion Recognition from Visual Clues. Facial expression recognition [19, 38, 69] has been well studied in the field of emotion recognition, mainly because faces are not only expressive but also easy to model. Handcrafted features have been developed to describe different facial expressions [13, 43, 74]. Recently, deep learning-based approaches have begun to emerge [38]. Principal research focuses on the design of novel modules for conventional network architectures [88], distinct loss functions for facial tasks [15, 71, 85], and addressing label uncertainties [8, 80]." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 283, + 545, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 283, + 545, + 474 + ], + "spans": [ + { + "bbox": [ + 304, + 283, + 545, + 474 + ], + "type": "text", + "content": "Recently, with the growing interest in recognizing emotion in the wild, the focus of research has gradually shifted to modeling body language [21, 45, 59] and context [29, 53, 54]. Several datasets for understanding human emotional states in unconstrained environments have been proposed [5, 60, 77]; Kosti et al. [29] and Yu et al. [45] established the first benchmark for image and video data, respectively. Follow-up work mainly focuses on context-aware emotion recognition, which usually adopts a multi-branch structure where one branch focuses on the face or body and the other focuses on capturing context [12, 34, 53, 59]. Moreover, some approaches take into account temporal causality [54] or represent context information via graphs [96]. To the best of our knowledge, there are no pre-trained models or effective methods for leveraging unlabeled data in the domain of visual emotion recognition." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 474, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 545, + 713 + ], + "type": "text", + "content": "Vision-Language Pre-training. Visual-language pretraining has achieved remarkable progress recently. CLIP [62] demonstrated the feasibility of using contrastive learning [10, 56] to learn transferable and powerful visual representations from large-scale image-text pairs [72]. Many follow-up approaches have been proposed to transfer the pre-trained model to downstream tasks [22, 97, 100] or leverage the scheme for different domains [37, 57, 64, 83, 98]. A line of research endeavors to expand CLIP for general video understanding [26, 35, 40, 44, 55, 82, 87]. The majority of the effort focuses on fine-tuning datasets with textual annotations [27, 32, 39]. However, not only are these curated annotations challenging to obtain, but they also limit the model's potential in various applications. Another line of work [36, 87] extends the image-level pre-training by utilizing unlabeled narrated videos [2, 52], similar to ours. However, we aim to learn abstract emotion representations rather than low-level visual patterns, which are beyond the reach of current models. EmotionNet [84] and its sequel [99], which likewise seeks to learn visual emotion repre" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18994" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 72, + 69, + 521, + 253 + ], + "blocks": [ + { + "bbox": [ + 72, + 69, + 521, + 253 + ], + "lines": [ + { + "bbox": [ + 72, + 69, + 521, + 253 + ], + "spans": [ + { + "bbox": [ + 72, + 69, + 521, + 253 + ], + "type": "image", + "image_path": "8447b9a880c03f8b45ef7ce5b3882f649e8278342e7062f38d3ebff1dd2ab3ee.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 261, + 547, + 307 + ], + "lines": [ + { + "bbox": [ + 46, + 261, + 547, + 307 + ], + "spans": [ + { + "bbox": [ + 46, + 261, + 547, + 307 + ], + "type": "text", + "content": "Figure 2. Illustration of EmotionCLIP. For nonverbal communication, subject and context information is modeled by a frame encoder and further aggregated into video-level representations by a temporal encoder. For verbal communication, textual information is encoded as text representations and sentiment scores by a text encoder and sentiment analysis model, respectively. The model learns emotion representations under sentiment guidance in a contrastive manner, by exploring the consistency of verbal and nonverbal communication." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 327, + 288, + 363 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 327, + 288, + 363 + ], + "spans": [ + { + "bbox": [ + 46, + 327, + 288, + 363 + ], + "type": "text", + "content": "sentations, are connected to ours. However, their primary focus is on the images' stimuli rather than the recognition of human emotional expressions in the wild." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 376, + 130, + 391 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 376, + 130, + 391 + ], + "spans": [ + { + "bbox": [ + 47, + 376, + 130, + 391 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 397, + 288, + 589 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 397, + 288, + 589 + ], + "spans": [ + { + "bbox": [ + 46, + 397, + 288, + 589 + ], + "type": "text", + "content": "Our core idea is to learn directly from human communication how they express their emotions, by exploring the consistency between their verbal and nonverbal expressions [41]. We tackle this learning task under the vision-language contrastive learning framework [62], that is, the model is expected to learn consistent emotion representations from the verbal expressions (e.g., utterance and dialogue) and nonverbal expressions (e.g., facial expression, body language, and contextual environment) of the same individuals. We give a brief introduction of our data collection procedure in Sec. 3.1 before presenting the overview of EmotionCLIP in Sec. 3.2. We further discuss how the model is guided to learn emotion-relevant representations from the nonverbal perspective in Sec. 3.3, and from the verbal perspective in Sec. 3.4. Please see Appendix for details of the dataset and implementations." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 598, + 143, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 598, + 143, + 609 + ], + "spans": [ + { + "bbox": [ + 47, + 598, + 143, + 609 + ], + "type": "text", + "content": "3.1. Data Collection" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "content": "Publicly available large-scale vision-and-language datasets do not provide desired verbal and nonverbal information because they either comprise only captions of low-level visual elements [2, 72] or instructions of actions [52]. The captions mostly contain a brief description of the scene or activity, which is insufficient to reveal the underlying emotions; the instruction videos rarely include humans in the scene or express neutral emotions, which fail" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 327, + 547, + 447 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 327, + 547, + 447 + ], + "spans": [ + { + "bbox": [ + 304, + 327, + 547, + 447 + ], + "type": "text", + "content": "to provide supervision signals for emotion understanding. To overcome such problems, we gather a large-scale video-and-text paired dataset. More specifically, the videos are TV series, while the texts are the corresponding closed captions. We collected 3,613 TV series from YouTube, which is equivalent to around a million raw video clips. We processed them using the off-the-shelf models to group the words in closed caption into complete sentences [23], tag each sentence with a sentiment score [68], and extract human bounding boxes [79]." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 455, + 455, + 467 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 455, + 455, + 467 + ], + "spans": [ + { + "bbox": [ + 306, + 455, + 455, + 467 + ], + "type": "text", + "content": "3.2. Overview of EmotionCLIP" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 474, + 545, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 545, + 533 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 545, + 533 + ], + "type": "text", + "content": "Fig. 2 presents an overview of our approach. We follow the wildly adopted vision-language contrastive learning paradigm [62] where two separate branches are used to encode visual inputs (i.e., nonverbal expressions) and textual inputs (i.e., verbal expressions), respectively." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 534, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 546, + 713 + ], + "type": "text", + "content": "Video Encoding. The visual branch of EmotionCLIP takes two inputs, including a sequence of RGB frames " + }, + { + "bbox": [ + 304, + 534, + 546, + 713 + ], + "type": "inline_equation", + "content": "X_{v}" + }, + { + "bbox": [ + 304, + 534, + 546, + 713 + ], + "type": "text", + "content": " and a sequence of binary masks " + }, + { + "bbox": [ + 304, + 534, + 546, + 713 + ], + "type": "inline_equation", + "content": "X_{m}" + }, + { + "bbox": [ + 304, + 534, + 546, + 713 + ], + "type": "text", + "content": ". The binary mask has the same shape as the frame and corresponds to the frame one-to-one, indicating the location of the subject within the frame. The backbone of the subject-aware frame encoder " + }, + { + "bbox": [ + 304, + 534, + 546, + 713 + ], + "type": "inline_equation", + "content": "f_{i}" + }, + { + "bbox": [ + 304, + 534, + 546, + 713 + ], + "type": "text", + "content": " is a Vision Transformer [17]. In particular, it extracts " + }, + { + "bbox": [ + 304, + 534, + 546, + 713 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 534, + 546, + 713 + ], + "type": "text", + "content": " non-overlapping image patches from the frame and projects them into 1D tokens " + }, + { + "bbox": [ + 304, + 534, + 546, + 713 + ], + "type": "inline_equation", + "content": "z_{i} \\in \\mathbb{R}^{d}" + }, + { + "bbox": [ + 304, + 534, + 546, + 713 + ], + "type": "text", + "content": ". The sequence of tokens passed to the following Transformer encoder [76] is " + }, + { + "bbox": [ + 304, + 534, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{z} = [z_{1}, \\dots, z_{m}, z_{cls}, z_{hmn}]" + }, + { + "bbox": [ + 304, + 534, + 546, + 713 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 534, + 546, + 713 + ], + "type": "inline_equation", + "content": "z_{cls}, z_{hmn}" + }, + { + "bbox": [ + 304, + 534, + 546, + 713 + ], + "type": "text", + "content": " are two additional learnable tokens. The mask " + }, + { + "bbox": [ + 304, + 534, + 546, + 713 + ], + "type": "inline_equation", + "content": "X_{m}" + }, + { + "bbox": [ + 304, + 534, + 546, + 713 + ], + "type": "text", + "content": " is converted to an array of indices " + }, + { + "bbox": [ + 304, + 534, + 546, + 713 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 304, + 534, + 546, + 713 + ], + "type": "text", + "content": " indicating the image patches containing the subject. The frame encoder further encodes " + }, + { + "bbox": [ + 304, + 534, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{z}, P" + }, + { + "bbox": [ + 304, + 534, + 546, + 713 + ], + "type": "text", + "content": " into a frame-level representation. All frame representations are normalized by the average of the raw data." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18995" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 69, + 288, + 146 + ], + "blocks": [ + { + "bbox": [ + 50, + 69, + 288, + 146 + ], + "lines": [ + { + "bbox": [ + 50, + 69, + 288, + 146 + ], + "spans": [ + { + "bbox": [ + 50, + 69, + 288, + 146 + ], + "type": "image", + "image_path": "a78f6735b1cf9c161c14e068857d0348624ba3606b2dcc103632f1080ad56e30.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 153, + 287, + 198 + ], + "lines": [ + { + "bbox": [ + 46, + 153, + 287, + 198 + ], + "spans": [ + { + "bbox": [ + 46, + 153, + 287, + 198 + ], + "type": "text", + "content": "Figure 3. The traditional approaches (left) ignore the dependencies between context and subject, and encode a portion of the image redundantly. The proposed approaches (right two diagrams) efficiently model the subject and context in a synchronous way." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 224, + 287, + 262 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 224, + 287, + 262 + ], + "spans": [ + { + "bbox": [ + 46, + 224, + 287, + 262 + ], + "type": "text", + "content": "tions are then passed into the temporal encoder " + }, + { + "bbox": [ + 46, + 224, + 287, + 262 + ], + "type": "inline_equation", + "content": "f_{p}" + }, + { + "bbox": [ + 46, + 224, + 287, + 262 + ], + "type": "text", + "content": " to produce a video-level representation as " + }, + { + "bbox": [ + 46, + 224, + 287, + 262 + ], + "type": "inline_equation", + "content": "v = f_{v}(\\mathbf{z}, P)" + }, + { + "bbox": [ + 46, + 224, + 287, + 262 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 224, + 287, + 262 + ], + "type": "inline_equation", + "content": "f_{v} = f_{p} \\circ f_{i}" + }, + { + "bbox": [ + 46, + 224, + 287, + 262 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 224, + 287, + 262 + ], + "type": "inline_equation", + "content": "v \\in \\mathbb{R}^{d}" + }, + { + "bbox": [ + 46, + 224, + 287, + 262 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 263, + 287, + 360 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 263, + 287, + 360 + ], + "spans": [ + { + "bbox": [ + 46, + 263, + 287, + 360 + ], + "type": "text", + "content": "Text Encoding. The textual branch of EmotionCLIP takes sentences " + }, + { + "bbox": [ + 46, + 263, + 287, + 360 + ], + "type": "inline_equation", + "content": "X_{t}" + }, + { + "bbox": [ + 46, + 263, + 287, + 360 + ], + "type": "text", + "content": " as inputs. The text encoder " + }, + { + "bbox": [ + 46, + 263, + 287, + 360 + ], + "type": "inline_equation", + "content": "f_{t}" + }, + { + "bbox": [ + 46, + 263, + 287, + 360 + ], + "type": "text", + "content": " is a Transformer [16] with the architecture modification described in [63], and the sentiment model " + }, + { + "bbox": [ + 46, + 263, + 287, + 360 + ], + "type": "inline_equation", + "content": "f_{s}" + }, + { + "bbox": [ + 46, + 263, + 287, + 360 + ], + "type": "text", + "content": " is a pre-trained sentiment analysis model [68] that is frozen during training. The input text is encoded by both models as " + }, + { + "bbox": [ + 46, + 263, + 287, + 360 + ], + "type": "inline_equation", + "content": "t = f_{t}(X_{t})" + }, + { + "bbox": [ + 46, + 263, + 287, + 360 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 263, + 287, + 360 + ], + "type": "inline_equation", + "content": "s = f_{s}(X_{t})" + }, + { + "bbox": [ + 46, + 263, + 287, + 360 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 263, + 287, + 360 + ], + "type": "inline_equation", + "content": "t \\in \\mathbb{R}^{d}" + }, + { + "bbox": [ + 46, + 263, + 287, + 360 + ], + "type": "text", + "content": " is the representation of the text and " + }, + { + "bbox": [ + 46, + 263, + 287, + 360 + ], + "type": "inline_equation", + "content": "s \\in \\mathbb{R}^{7}" + }, + { + "bbox": [ + 46, + 263, + 287, + 360 + ], + "type": "text", + "content": " is the pseudo sentiment score." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 362, + 287, + 398 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 362, + 287, + 398 + ], + "spans": [ + { + "bbox": [ + 46, + 362, + 287, + 398 + ], + "type": "text", + "content": "Training Objective. The training objective is to learn the correspondence between visual inputs and textual inputs by minimizing the sentiment-guided contrastive loss " + }, + { + "bbox": [ + 46, + 362, + 287, + 398 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 46, + 362, + 287, + 398 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 400, + 287, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 400, + 287, + 437 + ], + "spans": [ + { + "bbox": [ + 46, + 400, + 287, + 437 + ], + "type": "text", + "content": "We discuss the details of the proposed subject-aware encoding approaches in Sec. 3.3 and the sentiment-guided contrastive learning framework in Sec. 3.4." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 453, + 226, + 466 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 453, + 226, + 466 + ], + "spans": [ + { + "bbox": [ + 47, + 453, + 226, + 466 + ], + "type": "text", + "content": "3.3. Subject-Aware Context Encoding" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 474, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 474, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 474, + 287, + 713 + ], + "type": "text", + "content": "Context encoding is an important part of emotion understanding, especially in unconstrained environments, as it has been widely shown in psychology that emotional processes cannot be interpreted without context [47, 51, 65]. We intend to guide the model to focus on the interaction between the subject of interest and context. As shown in Fig. 3, the cropped character and the whole image are usually encoded by two separate networks and fused at the ends [34, 53, 59]. This approach is inflexible and inefficient since it overlooks the dependency between subject and context and encodes redundant image portions. Following this line of thought, we propose two potential subject-aware context encoding strategies, i.e., subject-aware attention masking (SAAM) and subject-aware prompting (SAP). The former can be regarded as an efficient implementation of the traditional two-stream approach but avoids the problem of redundant encoding. The latter is a novel encoding strategy that enables adaptive modeling of the interaction between the context and the subject by providing necessary prompts." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "content": "Subject-Aware Attention Masking. The canonical attention module [76] in a Transformer is defined as:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 322, + 104, + 545, + 133 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 322, + 104, + 545, + 133 + ], + "spans": [ + { + "bbox": [ + 322, + 104, + 545, + 133 + ], + "type": "interline_equation", + "content": "\\mathrm {A t t e n t i o n} (\\mathbf {Q}, \\mathbf {K}, \\mathbf {V}) = \\mathrm {s o f t m a x} \\left(\\frac {\\mathbf {Q} \\mathbf {K} ^ {\\top}}{\\sqrt {d}}\\right) \\mathbf {V}. \\qquad (1)", + "image_path": "e2519bcfd50f35afd220c003638261ef40d73000b8839e5276e369363ad3fb91.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 139, + 545, + 163 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 139, + 545, + 163 + ], + "spans": [ + { + "bbox": [ + 305, + 139, + 545, + 163 + ], + "type": "text", + "content": "We model the context and subject in a synchronous way by modifying the attention module to" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 171, + 423, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 171, + 423, + 185 + ], + "spans": [ + { + "bbox": [ + 306, + 171, + 423, + 185 + ], + "type": "inline_equation", + "content": "\\mathbf{Attention}^{*}(\\mathbf{Q},\\mathbf{K},\\mathbf{V},\\mathbf{U}) =" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 307, + 186, + 555, + 243 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 186, + 555, + 243 + ], + "spans": [ + { + "bbox": [ + 307, + 186, + 555, + 243 + ], + "type": "interline_equation", + "content": "\\underbrace {\\operatorname {s o f t m a x} \\left(\\frac {\\mathbf {Q K} ^ {\\top}}{\\sqrt {d}}\\right) (\\mathbf {J} - \\mathbf {A}) \\mathbf {V}} _ {\\text {c o n t e x t}} + \\underbrace {\\operatorname {s o f t m a x} \\left(\\frac {\\mathbf {Q K} ^ {\\top}}{\\sqrt {d}}\\right) \\mathbf {A U V}} _ {\\text {s u b j e c t}},", + "image_path": "a0009ffa1ce43543839ebeec359d985939a27cf7d41e6b50fa5841165ff0bda2.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 253, + 545, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 253, + 545, + 338 + ], + "spans": [ + { + "bbox": [ + 304, + 253, + 545, + 338 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 253, + 545, + 338 + ], + "type": "inline_equation", + "content": "\\mathbf{J}" + }, + { + "bbox": [ + 304, + 253, + 545, + 338 + ], + "type": "text", + "content": " is a matrix with all ones, " + }, + { + "bbox": [ + 304, + 253, + 545, + 338 + ], + "type": "inline_equation", + "content": "\\mathbf{A}" + }, + { + "bbox": [ + 304, + 253, + 545, + 338 + ], + "type": "text", + "content": " is a learnable parameters containing values in range [0, 1], and " + }, + { + "bbox": [ + 304, + 253, + 545, + 338 + ], + "type": "inline_equation", + "content": "\\mathbf{U}" + }, + { + "bbox": [ + 304, + 253, + 545, + 338 + ], + "type": "text", + "content": " is a weight matrix constructed using " + }, + { + "bbox": [ + 304, + 253, + 545, + 338 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 304, + 253, + 545, + 338 + ], + "type": "text", + "content": ". Intuitively, we shift " + }, + { + "bbox": [ + 304, + 253, + 545, + 338 + ], + "type": "inline_equation", + "content": "\\mathbf{A}" + }, + { + "bbox": [ + 304, + 253, + 545, + 338 + ], + "type": "text", + "content": " amount of attention from a total of " + }, + { + "bbox": [ + 304, + 253, + 545, + 338 + ], + "type": "inline_equation", + "content": "\\mathbf{J}" + }, + { + "bbox": [ + 304, + 253, + 545, + 338 + ], + "type": "text", + "content": " amount of attention from the context to the subject. To partition the " + }, + { + "bbox": [ + 304, + 253, + 545, + 338 + ], + "type": "inline_equation", + "content": "\\mathbf{A}" + }, + { + "bbox": [ + 304, + 253, + 545, + 338 + ], + "type": "text", + "content": " amount of attention to all image patches containing subject, we compute " + }, + { + "bbox": [ + 304, + 253, + 545, + 338 + ], + "type": "inline_equation", + "content": "\\mathbf{U}" + }, + { + "bbox": [ + 304, + 253, + 545, + 338 + ], + "type": "text", + "content": " as the following:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 359, + 345, + 545, + 373 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 359, + 345, + 545, + 373 + ], + "spans": [ + { + "bbox": [ + 359, + 345, + 545, + 373 + ], + "type": "interline_equation", + "content": "\\mathbf {U} = \\operatorname {s o f t m a x} \\left(\\frac {\\mathbf {Q} \\mathbf {K} ^ {\\top} + \\mathbf {M}}{\\sqrt {d}}\\right). \\tag {3}", + "image_path": "4b411817d8fa0c8e001b40ff5d6a9644d2bdfcce91db06285e54de160c3a1f07.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 380, + 457, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 380, + 457, + 392 + ], + "spans": [ + { + "bbox": [ + 306, + 380, + 457, + 392 + ], + "type": "text", + "content": "The masking matrix " + }, + { + "bbox": [ + 306, + 380, + 457, + 392 + ], + "type": "inline_equation", + "content": "\\mathbf{M}" + }, + { + "bbox": [ + 306, + 380, + 457, + 392 + ], + "type": "text", + "content": " is defined as:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 376, + 400, + 545, + 429 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 376, + 400, + 545, + 429 + ], + "spans": [ + { + "bbox": [ + 376, + 400, + 545, + 429 + ], + "type": "interline_equation", + "content": "\\mathbf {M} = \\left[ \\begin{array}{l l} \\mathbf {M} ^ {(1)} & \\mathbf {M} ^ {(2)} \\\\ \\mathbf {M} ^ {(3)} & \\mathbf {M} ^ {(4)} \\end{array} \\right], \\tag {4}", + "image_path": "7e5a7ea3bd28240e9bd164197e61b8045b88eaa97d683a8d00ffcb18bb823f97.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 437, + 545, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 437, + 545, + 544 + ], + "spans": [ + { + "bbox": [ + 304, + 437, + 545, + 544 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 437, + 545, + 544 + ], + "type": "inline_equation", + "content": "\\mathbf{M}^{(1)} = \\mathbf{0}_{(m + 1)\\times (m + 1)}" + }, + { + "bbox": [ + 304, + 437, + 545, + 544 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 437, + 545, + 544 + ], + "type": "inline_equation", + "content": "\\mathbf{M}^{(4)} = \\mathbf{0}_{1\\times 1}" + }, + { + "bbox": [ + 304, + 437, + 545, + 544 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 437, + 545, + 544 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_{i\\notin P}^{(2)} = \\mathbf{M}_{i\\notin P}^{(3)} = -\\infty" + }, + { + "bbox": [ + 304, + 437, + 545, + 544 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 437, + 545, + 544 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_{(m + 1)}^{(3)} = -\\infty" + }, + { + "bbox": [ + 304, + 437, + 545, + 544 + ], + "type": "text", + "content": ", and all other entries are zero. Intuitively, " + }, + { + "bbox": [ + 304, + 437, + 545, + 544 + ], + "type": "inline_equation", + "content": "\\mathbf{M}^{(2)}" + }, + { + "bbox": [ + 304, + 437, + 545, + 544 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 437, + 545, + 544 + ], + "type": "inline_equation", + "content": "\\mathbf{M}^{(3)}" + }, + { + "bbox": [ + 304, + 437, + 545, + 544 + ], + "type": "text", + "content": " represent the attention between all image patches " + }, + { + "bbox": [ + 304, + 437, + 545, + 544 + ], + "type": "inline_equation", + "content": "z_{i}" + }, + { + "bbox": [ + 304, + 437, + 545, + 544 + ], + "type": "text", + "content": " and the human token " + }, + { + "bbox": [ + 304, + 437, + 545, + 544 + ], + "type": "inline_equation", + "content": "z_{hmn}" + }, + { + "bbox": [ + 304, + 437, + 545, + 544 + ], + "type": "text", + "content": " to model the subject stream; we mask out all attention between non-human patches and the human token. Moreover, we mask out attention from " + }, + { + "bbox": [ + 304, + 437, + 545, + 544 + ], + "type": "inline_equation", + "content": "z_{hmn}" + }, + { + "bbox": [ + 304, + 437, + 545, + 544 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 437, + 545, + 544 + ], + "type": "inline_equation", + "content": "z_{cls}" + }, + { + "bbox": [ + 304, + 437, + 545, + 544 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 437, + 545, + 544 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_{(m + 1)}^{(3)}" + }, + { + "bbox": [ + 304, + 437, + 545, + 544 + ], + "type": "text", + "content": ", to ensure " + }, + { + "bbox": [ + 304, + 437, + 545, + 544 + ], + "type": "inline_equation", + "content": "z_{hmn}" + }, + { + "bbox": [ + 304, + 437, + 545, + 544 + ], + "type": "text", + "content": " only encodes the subject." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 558, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 546, + 713 + ], + "type": "text", + "content": "Subject-Aware Prompting. Prompting is a parameter-free method that restricts the output space of the model by shaping inputs. In our case, we hope to prompt the model to distinguish between the context and the subject. A recent visual prompting method, CPT [89], provides such a prompt by altering the original image, i.e., imposing colored boxes on objects of interest. It shows that a Transformer is able to locate objects with the help of positional hints. However, introducing artifacts on pixel space may not be optimal as it causes large domain shifts. To address this issue, we propose to construct prompts in the latent space based on positional embeddings, considering that they are inherently designed as indicative information. Formally, let " + }, + { + "bbox": [ + 304, + 558, + 546, + 713 + ], + "type": "inline_equation", + "content": "e_i" + }, + { + "bbox": [ + 304, + 558, + 546, + 713 + ], + "type": "text", + "content": " be" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18996" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "type": "text", + "content": "the positional embedding corresponding to the patch token " + }, + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "type": "inline_equation", + "content": "z_{i}" + }, + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "type": "text", + "content": " are the indicator set of the subject location. The prompting token is designed as " + }, + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "type": "inline_equation", + "content": "z_{hmn} = \\sum_{i\\in P}e_{i}" + }, + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 110, + 286, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 110, + 286, + 180 + ], + "spans": [ + { + "bbox": [ + 46, + 110, + 286, + 180 + ], + "type": "text", + "content": "We argue the sum of positional embeddings is enough to provide hints about the subject location. The previous study [78] demonstrates a Transformer treats all tokens without positional embedding uniformly but with positional embedding differently. This result shows positional embeddings play a vital role in guiding model attention." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 190, + 258, + 204 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 190, + 258, + 204 + ], + "spans": [ + { + "bbox": [ + 47, + 190, + 258, + 204 + ], + "type": "text", + "content": "3.4. Sentiment-Guided Contrastive Learning" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 209, + 287, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 209, + 287, + 388 + ], + "spans": [ + { + "bbox": [ + 46, + 209, + 287, + 388 + ], + "type": "text", + "content": "We train the model to learn emotion representations from verbal and nonverbal expressions in a contrastive manner. In the traditional contrastive setting, the model is forced to repel all negative pairs except the only positive one. However, many expressions in daily communication indeed have the same semantics from an emotional perspective. Contrasting these undesirable negative pairs encourages the model to learn spurious relations. This problem comes from false negatives, i.e., the affectively similar samples are treated as negatives. We address this issue by introducing a trained sentiment analysis model [68] from the NLP domain for the suppression of false negatives, thereby guiding our model to capture emotion-related concepts from verbal expressions. Specifically, we propose a sentiment-guided contrastive loss:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 396, + 288, + 450 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 396, + 288, + 450 + ], + "spans": [ + { + "bbox": [ + 47, + 396, + 288, + 450 + ], + "type": "interline_equation", + "content": "\\operatorname {S N C E} (v, t, s) = - \\sum_ {i \\in B} \\left(\\log \\frac {\\exp \\left(v _ {i} \\cdot t _ {i} / \\tau\\right)}{\\sum_ {j \\in B} \\exp \\left(v _ {i} \\cdot t _ {j} / \\tau - w _ {i , j}\\right)}\\right), \\tag {5}", + "image_path": "2a5f087523ce35cc2a1753df1bbb7393498771dffd8525ba9a2c721947b5bc8b.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 451, + 286, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 451, + 286, + 464 + ], + "spans": [ + { + "bbox": [ + 47, + 451, + 286, + 464 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 451, + 286, + 464 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 47, + 451, + 286, + 464 + ], + "type": "text", + "content": " is a batch. The reweighting term " + }, + { + "bbox": [ + 47, + 451, + 286, + 464 + ], + "type": "inline_equation", + "content": "w_{i,j}" + }, + { + "bbox": [ + 47, + 451, + 286, + 464 + ], + "type": "text", + "content": " is defined as" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 92, + 474, + 287, + 506 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 92, + 474, + 287, + 506 + ], + "spans": [ + { + "bbox": [ + 92, + 474, + 287, + 506 + ], + "type": "interline_equation", + "content": "w _ {i, j} = \\left\\{ \\begin{array}{l l} \\beta \\cdot \\mathrm {K L} \\left(s _ {i} \\| s _ {j}\\right) ^ {- 1} & i \\neq j \\\\ 0 & i = j \\end{array} , \\right. \\tag {6}", + "image_path": "089cca3646638c38b617ea516e89825900f56538b4e748e74267b8322e417321.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 513, + 286, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 513, + 286, + 536 + ], + "spans": [ + { + "bbox": [ + 47, + 513, + 286, + 536 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 513, + 286, + 536 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 47, + 513, + 286, + 536 + ], + "type": "text", + "content": " is a hyper-parameter for controlling the reweighting strength. The total loss is defined as:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 73, + 546, + 287, + 571 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 73, + 546, + 287, + 571 + ], + "spans": [ + { + "bbox": [ + 73, + 546, + 287, + 571 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\frac {1}{2 | B |} \\left(\\operatorname {S N C E} (v, t, s) + \\operatorname {S N C E} (t, v, s)\\right). \\tag {7}", + "image_path": "7e40958fe2ceac93d0b4b318537b6783265a5b626119c524fe7f50af88bd722d.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 582, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 286, + 713 + ], + "type": "text", + "content": "As shown in Fig. 4, the false negative sample with similar emotion to the positive sample is greatly suppressed, while other negatives are not affected. Note that when " + }, + { + "bbox": [ + 46, + 582, + 286, + 713 + ], + "type": "inline_equation", + "content": "i \\neq j" + }, + { + "bbox": [ + 46, + 582, + 286, + 713 + ], + "type": "text", + "content": " but " + }, + { + "bbox": [ + 46, + 582, + 286, + 713 + ], + "type": "inline_equation", + "content": "s_i = s_j" + }, + { + "bbox": [ + 46, + 582, + 286, + 713 + ], + "type": "text", + "content": ", we have " + }, + { + "bbox": [ + 46, + 582, + 286, + 713 + ], + "type": "inline_equation", + "content": "w_{i,j} = \\infty" + }, + { + "bbox": [ + 46, + 582, + 286, + 713 + ], + "type": "text", + "content": ", which is equivalent to removing " + }, + { + "bbox": [ + 46, + 582, + 286, + 713 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 582, + 286, + 713 + ], + "type": "text", + "content": "th sample from the negative pairs; when " + }, + { + "bbox": [ + 46, + 582, + 286, + 713 + ], + "type": "inline_equation", + "content": "s_i" + }, + { + "bbox": [ + 46, + 582, + 286, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 582, + 286, + 713 + ], + "type": "inline_equation", + "content": "s_j" + }, + { + "bbox": [ + 46, + 582, + 286, + 713 + ], + "type": "text", + "content": " are very different, " + }, + { + "bbox": [ + 46, + 582, + 286, + 713 + ], + "type": "inline_equation", + "content": "w_{i,j}" + }, + { + "bbox": [ + 46, + 582, + 286, + 713 + ], + "type": "text", + "content": " is negligible; we set " + }, + { + "bbox": [ + 46, + 582, + 286, + 713 + ], + "type": "inline_equation", + "content": "w_{i,i} = 0" + }, + { + "bbox": [ + 46, + 582, + 286, + 713 + ], + "type": "text", + "content": " to not affect the true positive pair. Since " + }, + { + "bbox": [ + 46, + 582, + 286, + 713 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 46, + 582, + 286, + 713 + ], + "type": "text", + "content": " is the sentiment score, the sentiment-related differences are emphasized and weighted more during training. Therefore, the proposed contrastive loss is expected to provide cleaner supervision signals for learning emotion-related representations." + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 332, + 71, + 521, + 152 + ], + "blocks": [ + { + "bbox": [ + 332, + 71, + 521, + 152 + ], + "lines": [ + { + "bbox": [ + 332, + 71, + 521, + 152 + ], + "spans": [ + { + "bbox": [ + 332, + 71, + 521, + 152 + ], + "type": "image", + "image_path": "8f3810a750c1bda701f236a17b4560227387a6797f7bc95ba0ebd0f5b4c50795.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 163, + 545, + 208 + ], + "lines": [ + { + "bbox": [ + 304, + 163, + 545, + 208 + ], + "spans": [ + { + "bbox": [ + 304, + 163, + 545, + 208 + ], + "type": "text", + "content": "Figure 4. A sample batch where both the positive pair (green) and the false negative pair (red) exist. The green bar and gray bar represent the similarity between all text and the positive video before and after reweighting." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 229, + 449, + 243 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 229, + 449, + 243 + ], + "spans": [ + { + "bbox": [ + 306, + 229, + 449, + 243 + ], + "type": "text", + "content": "4. Experiments and Results" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 250, + 545, + 310 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 250, + 545, + 310 + ], + "spans": [ + { + "bbox": [ + 304, + 250, + 545, + 310 + ], + "type": "text", + "content": "We first introduce the datasets for evaluation in Sec. 4.1 before analyzing various components of EmotionCLIP in Sec. 4.2. Then, we compare EmotionCLIP with the state-of-the-art methods on various datasets in Sec. 4.3. Please see Appendix for more experimental results." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 319, + 481, + 331 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 319, + 481, + 331 + ], + "spans": [ + { + "bbox": [ + 306, + 319, + 481, + 331 + ], + "type": "text", + "content": "4.1. Datasets and Evaluation Metrics" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 339, + 545, + 446 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 339, + 545, + 446 + ], + "spans": [ + { + "bbox": [ + 304, + 339, + 545, + 446 + ], + "type": "text", + "content": "We evaluate the performance of EmotionCLIP on a variety of recently published challenging benchmarks, including four video datasets and an image dataset. The annotations of these datasets are mainly based on three physiological models: Ekman's basic emotion theory [18] (7 discrete categories), the fine-grained emotion model [14] (26 discrete categories), and the Valence-Arousal-Dominance emotion model [67] (3 continuous dimensions). The evaluation metrics are consistent with previous methods." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 447, + 545, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 447, + 545, + 495 + ], + "spans": [ + { + "bbox": [ + 304, + 447, + 545, + 495 + ], + "type": "text", + "content": "BoLD [45] is a dataset for understanding human body language in the wild, consisting of 9,827 video clips and 13,239 instances, in which each instance is annotated with 26 discrete categories and VAD dimensions." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 496, + 545, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 496, + 545, + 604 + ], + "spans": [ + { + "bbox": [ + 304, + 496, + 545, + 604 + ], + "type": "text", + "content": "MovieGraphs [77] is a dataset for understanding human-centric situations consisting of graph-based annotations on social events that appeared in 51 popular movies. Each graph comprises multiple types of nodes to represent actors' emotional and physical attributes, as well as their relationships and interactions. Following the preprocessing and evaluation protocol proposed in previous work [29, 54], we extract relevant emotion attributes from the graphs and group them into 26 discrete emotion categories." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 605, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 689 + ], + "type": "text", + "content": "MELD [60] is an extension to the EmotionLines [9], which is an emotion corpus of multi-party conversations initially proposed in the NLP domain. It offers the same dialogue examples as EmotionLines and includes audio and visual modalities along with the text. It contains around 1,400 dialogues and 13,000 utterances from the Friends tv show, where each example is annotated with 7 discrete categories." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "text", + "content": "Liris-Accede [5] is a dataset that contains videos from a set of 160 professionally made and amateur movies covering a" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18997" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 70, + 286, + 142 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 286, + 142 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 286, + 142 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 286, + 142 + ], + "type": "table", + "html": "
mAPAUCR2
EmotionCLIP (vanilla)21.9768.850.130
+ SAAM21.53-0.4468.56-0.290.137+0.007
+ SAP22.28+0.3169.06+0.210.131+0.001
+ SAP & SNCE22.51+0.5469.30+0.450.133+0.003
", + "image_path": "40d63f0f8f5d1d94725a908853a2c05b9409e1cbdd8a1ad2c8c0f4b83efdda2c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 58, + 150, + 276, + 162 + ], + "lines": [ + { + "bbox": [ + 58, + 150, + 276, + 162 + ], + "spans": [ + { + "bbox": [ + 58, + 150, + 276, + 162 + ], + "type": "text", + "content": "Table 1. Component-wise analysis of our method on BoLD." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 184, + 286, + 208 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 184, + 286, + 208 + ], + "spans": [ + { + "bbox": [ + 46, + 184, + 286, + 208 + ], + "type": "text", + "content": "variety of themes. Valence and arousal scores are provided continuously (i.e., every second) along movies." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 209, + 286, + 257 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 209, + 286, + 257 + ], + "spans": [ + { + "bbox": [ + 46, + 209, + 286, + 257 + ], + "type": "text", + "content": "Emotic [29] is an image dataset for emotion recognition in context, comprising 23,571 images of 34,320 annotated individuals in unconstrained real-world environments. Each subject is annotated with 26 discrete categories." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 266, + 141, + 278 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 266, + 141, + 278 + ], + "spans": [ + { + "bbox": [ + 47, + 266, + 141, + 278 + ], + "type": "text", + "content": "4.2. Ablation Study" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 285, + 272, + 298 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 285, + 272, + 298 + ], + "spans": [ + { + "bbox": [ + 47, + 285, + 272, + 298 + ], + "type": "text", + "content": "4.2.1 Analysis of Subject-Aware Context Encoding" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 304, + 286, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 304, + 286, + 388 + ], + "spans": [ + { + "bbox": [ + 46, + 304, + 286, + 388 + ], + "type": "text", + "content": "In this series of experiments, we start with a vanilla model and analyze it by adding various subject-aware approaches. As shown in Table 1, decent results can be achieved in downstream tasks using the vanilla EmotionCLIP. This result supports our argument that models can learn non-trivial emotion representations from human verbal and nonverbal expressions by matching them together." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 389, + 286, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 389, + 286, + 449 + ], + "spans": [ + { + "bbox": [ + 46, + 389, + 286, + 449 + ], + "type": "text", + "content": "The SAP achieves better results and improves over the baseline by a reasonable margin. This improvement demonstrates the design of SAP can incorporate location-specific information to guide the model in acquiring target-related content without impacting global information modeling." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 449, + 286, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 449, + 286, + 652 + ], + "spans": [ + { + "bbox": [ + 46, + 449, + 286, + 652 + ], + "type": "text", + "content": "Additionally, we note that the model with SAAM yields mediocre performance. As discussed earlier, SAAM can be regarded as an efficient implementation of the multi-stream strategy in the Transformer. This outcome suggests that the multi-stream strategy, commonly used in previous methods, may not be optimal. To rule out the possibility of fusion at inappropriate layers, we explore the impact of different fusion positions by applying SAAM up to a certain layer in the Transformer. It shows that the performance change does not correlate to the fusion layer change, and SAAM consistently underperforms SAP, irrespective of the fusion location. This finding implies that imposing hard masks on the model's attention may introduce unanticipated biases, while adaptively modeling context-subject interaction is more reasonable. In subsequent experiments and discussions, we use SAP as the standard implementation, unless otherwise stated." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 653, + 286, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 286, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 286, + 714 + ], + "type": "text", + "content": "Qualitative Analysis. SAP offers merely a positional hint, as opposed to the mandatory attention-shifting in SAAM. Since the purpose of SAP is to ensure subject-aware encoding, it is necessary to understand if the attention guidance is appropriate. We analyze SAP by plotting HMN token's" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 321, + 72, + 531, + 125 + ], + "blocks": [ + { + "bbox": [ + 321, + 72, + 531, + 125 + ], + "lines": [ + { + "bbox": [ + 321, + 72, + 531, + 125 + ], + "spans": [ + { + "bbox": [ + 321, + 72, + 531, + 125 + ], + "type": "image", + "image_path": "c6558b422b7149909814c5c136af8266fbe74e67e72b6d63006017dec2f5c7eb.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 321, + 127, + 531, + 180 + ], + "blocks": [ + { + "bbox": [ + 321, + 127, + 531, + 180 + ], + "lines": [ + { + "bbox": [ + 321, + 127, + 531, + 180 + ], + "spans": [ + { + "bbox": [ + 321, + 127, + 531, + 180 + ], + "type": "image", + "image_path": "28632e2c704fc78be6d795cf563f03bb0f96333d28648357f77972d2593e7405.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 321, + 183, + 531, + 236 + ], + "blocks": [ + { + "bbox": [ + 321, + 183, + 531, + 236 + ], + "lines": [ + { + "bbox": [ + 321, + 183, + 531, + 236 + ], + "spans": [ + { + "bbox": [ + 321, + 183, + 531, + 236 + ], + "type": "image", + "image_path": "293bd745b96ca8868e1fe6b26ac7d00f47b249a61b77355c2b2c7baff86022a1.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 246, + 545, + 291 + ], + "lines": [ + { + "bbox": [ + 305, + 246, + 545, + 291 + ], + "spans": [ + { + "bbox": [ + 305, + 246, + 545, + 291 + ], + "type": "text", + "content": "Figure 5. Attention weights for the HMN token from layer 1-4 (left to right) of the frame encoder in one trained network. Each row represents one frame. The green and yellow spots are the high-attention areas." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 313, + 545, + 374 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 313, + 545, + 374 + ], + "spans": [ + { + "bbox": [ + 305, + 313, + 545, + 374 + ], + "type": "text", + "content": "attention to all patches on the image. As shown in Fig. 5, HMN tokens first focus on random locations, but gradually turn their attention to the subject (i.e., the person with a bounding box) as we move to later layers, demonstrating that SAP offers sufficient guidance to the network attention." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 393, + 545, + 417 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 393, + 545, + 417 + ], + "spans": [ + { + "bbox": [ + 306, + 393, + 545, + 417 + ], + "type": "text", + "content": "4.2.2 Analysis of Sentiment-Guided Contrastive Learning" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 426, + 545, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 426, + 545, + 652 + ], + "spans": [ + { + "bbox": [ + 304, + 426, + 545, + 652 + ], + "type": "text", + "content": "We first compare models trained with different " + }, + { + "bbox": [ + 304, + 426, + 545, + 652 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 426, + 545, + 652 + ], + "type": "text", + "content": ", the hyperparameter used to control the strength of reweighting in SNCE. Note that the training objective is equivalent to the vanilla infoNCE loss [56] when " + }, + { + "bbox": [ + 304, + 426, + 545, + 652 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 426, + 545, + 652 + ], + "type": "text", + "content": " is set to zero. As " + }, + { + "bbox": [ + 304, + 426, + 545, + 652 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 426, + 545, + 652 + ], + "type": "text", + "content": " increases, more negative samples within the batch are suppressed. As shown in Table 1 and Fig. 6, reweighting with appropriate strength can significantly increase the performance of the model as it guides the direction of learning by eliminating some significant false negatives. However, an excessively large " + }, + { + "bbox": [ + 304, + 426, + 545, + 652 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 426, + 545, + 652 + ], + "type": "text", + "content": " can hinder the training of the model, which is within expectation. First, the sentiment scores used in the reweighting process are weak pseudo-labels provided by a pre-trained sentiment analysis model, which is not entirely reliable and accurate. Second, previous work has clearly demonstrated that batch size has a decisive impact on self-supervised learning [10, 24, 62]. A too-large " + }, + { + "bbox": [ + 304, + 426, + 545, + 652 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 426, + 545, + 652 + ], + "type": "text", + "content": " will cause too many negative samples to be suppressed, reducing the effective batch size and thus hindering the learning process." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "content": "Qualitative Analysis. We show how the text expressing different emotions are treated by our sentiment-guided loss. Given a positive pair, the logits are the scaled similarities between texts and the positive video; the model is penalized on large logits unless it is associated with the positive text." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18998" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 71, + 286, + 153 + ], + "blocks": [ + { + "bbox": [ + 50, + 71, + 286, + 153 + ], + "lines": [ + { + "bbox": [ + 50, + 71, + 286, + 153 + ], + "spans": [ + { + "bbox": [ + 50, + 71, + 286, + 153 + ], + "type": "image", + "image_path": "4f1e56460446254646ec6f22bc1f96dae39d3e225cd5118bcaebcc52dd3bbea6.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 163, + 288, + 198 + ], + "lines": [ + { + "bbox": [ + 46, + 163, + 288, + 198 + ], + "spans": [ + { + "bbox": [ + 46, + 163, + 288, + 198 + ], + "type": "text", + "content": "Figure 6. The effect of varying the strength of reweighting in SNCE. The larger the " + }, + { + "bbox": [ + 46, + 163, + 288, + 198 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 163, + 288, + 198 + ], + "type": "text", + "content": ", the stronger the suppression of negative samples." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 50, + 209, + 285, + 302 + ], + "blocks": [ + { + "bbox": [ + 50, + 209, + 285, + 302 + ], + "lines": [ + { + "bbox": [ + 50, + 209, + 285, + 302 + ], + "spans": [ + { + "bbox": [ + 50, + 209, + 285, + 302 + ], + "type": "table", + "html": "
TextLogit
I'm sorry to keep you any longer than is necessary. (positive sample)10.65
I'm sorry Tom couldn't join us.12.6 → -697
I hate to say it guys but it's getting late.9.81 → -97.6
I still say it was a wild idea.13.8 → 13.6
Well, that was truly fascinating.15.2 → 15.0
", + "image_path": "53714f00fed92bc67d801adccd9e115e23a9ff32a337d793682476912c0b471a.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 376, + 287, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 376, + 287, + 437 + ], + "spans": [ + { + "bbox": [ + 46, + 376, + 287, + 437 + ], + "type": "text", + "content": "As shown in Table 2, the texts in the second and third rows provide undesired contributions to the loss as they express similar emotions as the positive sample. After reweighting, false negatives (2nd and 3rd) are effectively eliminated while true negatives (4th and 5th) are negligibly affected." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 453, + 228, + 466 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 453, + 228, + 466 + ], + "spans": [ + { + "bbox": [ + 47, + 453, + 228, + 466 + ], + "type": "text", + "content": "4.2.3 Analysis of Model Implementation" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 473, + 287, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 473, + 287, + 568 + ], + "spans": [ + { + "bbox": [ + 46, + 473, + 287, + 568 + ], + "type": "text", + "content": "The frame and text encoders of our model are initialized with the image-text pre-training weights from CLIP [62]. Research in neural science has demonstrated the necessity of basic visual and language understanding capabilities for learning high-level emotional semantics [58, 70]. To validate the effectiveness of using image-text pre-training for weight initialization, we evaluate variants with different implementations." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 570, + 287, + 701 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 287, + 701 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 287, + 701 + ], + "type": "text", + "content": "We first consider encoders with random initialization. As shown in Table 3, the model's performance drops sharply when training from scratch. This result is within expectation for two reasons. From an engineering perspective, previous works have demonstrated the necessity of using pretraining weights for large video models [1, 6] and vision-language models [35, 55]. From a cognitive point of view, it is nearly infeasible to learn abstract concepts directly without basic comprehension skills [58]; if the model cannot recognize people, it is impossible to understand body language and facial expressions properly." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 59, + 701, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 701, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 59, + 701, + 287, + 714 + ], + "type": "text", + "content": "We then consider frozen encoders with pre-training" + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 309, + 70, + 545, + 187 + ], + "blocks": [ + { + "bbox": [ + 46, + 310, + 287, + 356 + ], + "lines": [ + { + "bbox": [ + 46, + 310, + 287, + 356 + ], + "spans": [ + { + "bbox": [ + 46, + 310, + 287, + 356 + ], + "type": "text", + "content": "Table 2. An example batch containing both false negative and true negative samples. The logits represent the similarity between every text input and the positive video from a random epoch during training. " + }, + { + "bbox": [ + 46, + 310, + 287, + 356 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 46, + 310, + 287, + 356 + ], + "type": "text", + "content": " represents the sentiment-guided reweighting process." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 309, + 70, + 545, + 187 + ], + "lines": [ + { + "bbox": [ + 309, + 70, + 545, + 187 + ], + "spans": [ + { + "bbox": [ + 309, + 70, + 545, + 187 + ], + "type": "table", + "html": "
Text EncoderFrame EncoderTemporal EncodermAPAUC
✓✓-22.5169.30
-✓-12.43–45%54.96–21%
---11.02–51%50.28–27%
✗✓-13.40–40%57.38–17%
✗✗-18.43–18%65.08–6.0%
✓✓○21.17–5.9%68.74–0.8%
", + "image_path": "0f4d99b2076a98958eb64d1af45a86176d04325b9e6f62703f38efd6a41cd057.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 195, + 547, + 240 + ], + "lines": [ + { + "bbox": [ + 304, + 195, + 547, + 240 + ], + "spans": [ + { + "bbox": [ + 304, + 195, + 547, + 240 + ], + "type": "text", + "content": "Table 3. Ablation study on different model implementations. " + }, + { + "bbox": [ + 304, + 195, + 547, + 240 + ], + "type": "inline_equation", + "content": "\\checkmark" + }, + { + "bbox": [ + 304, + 195, + 547, + 240 + ], + "type": "text", + "content": " means trainable, initialization with pre-training weights. " + }, + { + "bbox": [ + 304, + 195, + 547, + 240 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 195, + 547, + 240 + ], + "type": "text", + "content": " means frozen, initialization with pre-training weights. - means trainable, random initialization. " + }, + { + "bbox": [ + 304, + 195, + 547, + 240 + ], + "type": "inline_equation", + "content": "\\circ" + }, + { + "bbox": [ + 304, + 195, + 547, + 240 + ], + "type": "text", + "content": " means no parameters." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 262, + 545, + 357 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 262, + 545, + 357 + ], + "spans": [ + { + "bbox": [ + 304, + 262, + 545, + 357 + ], + "type": "text", + "content": "weights. This is a standard paradigm for video-language understanding that trains models with offline extracted features [36, 87]. As shown in Table 3, our model with variants using fixed encoders performs worse compared with the model using trainable encoders. This reflects the fact that affective tasks rely on visual and verbal semantics differently from low-level vision tasks, which is what CLIP and its successors overlooked [40]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 359, + 546, + 442 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 359, + 546, + 442 + ], + "spans": [ + { + "bbox": [ + 304, + 359, + 546, + 442 + ], + "type": "text", + "content": "We study the effect of the temporal encoder. We consider a variant where the temporal encoder is replaced by a mean pooling layer that simply averages the features of all frames. As shown in Table 3, the performance gap is obvious compared with the baseline. This phenomenon suggests that temporal dependency plays a vital role in emotion representations." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 453, + 503, + 466 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 453, + 503, + 466 + ], + "spans": [ + { + "bbox": [ + 305, + 453, + 503, + 466 + ], + "type": "text", + "content": "4.3. Comparison with the State of the Art" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 473, + 545, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 473, + 545, + 581 + ], + "spans": [ + { + "bbox": [ + 304, + 473, + 545, + 581 + ], + "type": "text", + "content": "Based on our previous ablation experiments, we choose the model with SAP and SNCE as the default implementation and compare it with the state-of-the-art. In addition, we also compare with VideoCLIP [87] and X-CLIP [55], both of which are state-of-the-art vision-language pre-training models for general video recognition purposes. To evaluate the quality of learned representations, we follow the practice in CLIP [62] and use linear-probe evaluation protocol [10, 24] for vision-language pre-training models." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 582, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 546, + 713 + ], + "type": "text", + "content": "BoLD. As shown in Table 4a, EmotionCLIP substantially outperforms the state-of-the-art supervised learning methods on the challenging 26-class emotion classification task and achieves comparable results on continuous emotion regression. It is worth noting that a complex multi-stream model is used in [59] to integrate the human body and context information, while we achieve better results with a single-stream structure using RGB information only. This difference reflects that the subject-aware approach we designed models the relationship between the subject and context. We also notice that other vision-language-based meth" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "18999" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 84, + 221, + 196 + ], + "blocks": [ + { + "bbox": [ + 111, + 73, + 159, + 83 + ], + "lines": [ + { + "bbox": [ + 111, + 73, + 159, + 83 + ], + "spans": [ + { + "bbox": [ + 111, + 73, + 159, + 83 + ], + "type": "text", + "content": "(a) BoLD [45]" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 84, + 221, + 196 + ], + "lines": [ + { + "bbox": [ + 48, + 84, + 221, + 196 + ], + "spans": [ + { + "bbox": [ + 48, + 84, + 221, + 196 + ], + "type": "table", + "html": "
MethodmAP ↑AUC ↑R2 ↑
Supervised
ST-GCN [94]12.6355.960.044
TSN [81]17.0262.700.095
Filntis et al. [21]16.5662.660.092
Pikoulis et al. [59]19.2966.820.149
Linear-Eval
VideoCLIP [87]11.1951.23-5.11
X-CLIP [55]13.2656.86-0.03
EmotionCLIP22.5169.300.133
", + "image_path": "acb03214215724aebb905828cc539c800eddb390c7fed43aa4b2cca9cf7c724c.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 225, + 84, + 380, + 205 + ], + "blocks": [ + { + "bbox": [ + 278, + 74, + 328, + 83 + ], + "lines": [ + { + "bbox": [ + 278, + 74, + 328, + 83 + ], + "spans": [ + { + "bbox": [ + 278, + 74, + 328, + 83 + ], + "type": "text", + "content": "(c) Emotic [29]" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 225, + 84, + 380, + 205 + ], + "lines": [ + { + "bbox": [ + 225, + 84, + 380, + 205 + ], + "spans": [ + { + "bbox": [ + 225, + 84, + 380, + 205 + ], + "type": "table", + "html": "
MethodmAP ↑AUC ↑
Supervised
CAER-Net [34]20.84-
Affective Graph [96]28.42-
Fusion Model [29]29.45-
EmotiCon (GCN) [53]32.03-
EmotiCon (Depth) [53]35.48-
Linear-Eval
VideoCLIP [87]19.9256.31
X-CLIP [55]22.8061.31
EmotionCLIP32.9171.41
", + "image_path": "d00b36d40397078be8b679849d8de6ec0e42012bb339e2c9d2f5300d190c2bbb.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 386, + 84, + 545, + 233 + ], + "blocks": [ + { + "bbox": [ + 432, + 74, + 498, + 83 + ], + "lines": [ + { + "bbox": [ + 432, + 74, + 498, + 83 + ], + "spans": [ + { + "bbox": [ + 432, + 74, + 498, + 83 + ], + "type": "text", + "content": "(e) Liris-Accede [5]" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 386, + 84, + 545, + 233 + ], + "lines": [ + { + "bbox": [ + 386, + 84, + 545, + 233 + ], + "spans": [ + { + "bbox": [ + 386, + 84, + 545, + 233 + ], + "type": "table", + "html": "
MethodV. MSE ↓A. MSE ↓
Supervised
Quan et al. [61]0.1150.171
Ko et al. [28]0.1020.149
*CERTH-ITI [4]0.1170.138
*THUHCSI [25]0.0920.140
*Yi et al. [91]0.0900.136
*GLA [75]0.0840.133
*Zhao et al. [95]0.0710.137
*Affect2MM [54]0.0680.128
Linear-Eval
VideoCLIP [87]0.1420.151
X-CLIP [55]0.1330.246
EmotionCLIP0.0960.155
", + "image_path": "066921443c558b2a3d3e921194e83d1df136733d74d0e4d283f21487a613ca50.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 48, + 232, + 220, + 325 + ], + "blocks": [ + { + "bbox": [ + 99, + 222, + 170, + 232 + ], + "lines": [ + { + "bbox": [ + 99, + 222, + 170, + 232 + ], + "spans": [ + { + "bbox": [ + 99, + 222, + 170, + 232 + ], + "type": "text", + "content": "(b) MovieGraphs [77]" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 232, + 220, + 325 + ], + "lines": [ + { + "bbox": [ + 48, + 232, + 220, + 325 + ], + "spans": [ + { + "bbox": [ + 48, + 232, + 220, + 325 + ], + "type": "table", + "html": "
MethodVal Acc ↑Test Acc ↑
Supervised
EmotionNet [84]35.6027.90
*Affect2MM [54]39.8830.58
Linear-Eval
VideoCLIP [87]29.9123.44
X-CLIP [55]29.0623.58
EmotionCLIP41.6032.35
", + "image_path": "8f5491b6d60b599e3d95aa3a0ddc3d896c7ee433d0372350a13e7d98ef036adc.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 225, + 232, + 380, + 325 + ], + "blocks": [ + { + "bbox": [ + 278, + 222, + 328, + 232 + ], + "lines": [ + { + "bbox": [ + 278, + 222, + 328, + 232 + ], + "spans": [ + { + "bbox": [ + 278, + 222, + 328, + 232 + ], + "type": "text", + "content": "(d) MELD [60]" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 225, + 232, + 380, + 325 + ], + "lines": [ + { + "bbox": [ + 225, + 232, + 380, + 325 + ], + "spans": [ + { + "bbox": [ + 225, + 232, + 380, + 325 + ], + "type": "table", + "html": "
MethodAcc ↑W. F1 ↑
Supervised
M2FNet (Visual) [12]45.6332.44
*M2FNet [12]67.8566.71
Linear-Eval
VideoCLIP [87]45.1932.06
X-CLIP [55]38.3132.46
EmotionCLIP48.2834.59
", + "image_path": "4ffee297480e13f1dcfc49b76fdc6d352f13a40dcc6fe6eb70b73fb311cccf65.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 386, + 247, + 545, + 325 + ], + "blocks": [ + { + "bbox": [ + 386, + 247, + 545, + 325 + ], + "lines": [ + { + "bbox": [ + 386, + 247, + 545, + 325 + ], + "spans": [ + { + "bbox": [ + 386, + 247, + 545, + 325 + ], + "type": "table", + "html": "
AbbreviationMeaning
A. MSEArousal MSE
V. MSEValence MSE
W. F1Weighted F1
Acc.Top-1 Accuracy
↓Lower is better
↑Higher is better
", + "image_path": "6fe67ce636b79a0fc4726148683f30e5a7771e8a06fb86b6d62991dff8259244.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 335, + 545, + 357 + ], + "lines": [ + { + "bbox": [ + 46, + 335, + 545, + 357 + ], + "spans": [ + { + "bbox": [ + 46, + 335, + 545, + 357 + ], + "type": "text", + "content": "Table 4. Comparisons to the state-of-the-art across multiple datasets. Methods marked with * use multimodal inputs, i.e., audio and text. Bold numbers indicate the best results achieved using visual inputs only." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 378, + 287, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 378, + 287, + 437 + ], + "spans": [ + { + "bbox": [ + 46, + 378, + 287, + 437 + ], + "type": "text", + "content": "ods perform poorly on emotion recognition tasks, although they are designed for general video understanding purposes. This phenomenon is largely attributed to the lack of proper guidance; the model can only learn low-level visual patterns and fails to capture semantic and emotional information." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 437, + 287, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 437, + 287, + 510 + ], + "spans": [ + { + "bbox": [ + 46, + 437, + 287, + 510 + ], + "type": "text", + "content": "MovieGraphs. As shown in Table 4b, EmotionCLIP substantially outperforms the best vision-based method and even surpasses Affect2MM [54], a powerful multimodal approach that uses audio and text descriptions in addition to visual information. Instead, other vision-language pretraining models are still far from supervised methods." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 510, + 287, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 287, + 629 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 287, + 629 + ], + "type": "text", + "content": "MELD. EmotionCLIP performs well on MELD as shown in Table 4d; it achieves comparable results to the state-of-the-art vision-based methods. It is worth noting that this dataset is extended from an NLP dataset, so the visual data is noisier than the original text data. In fact, according to the ablation experiments in [12], it is possible to achieve an accuracy of " + }, + { + "bbox": [ + 46, + 510, + 287, + 629 + ], + "type": "inline_equation", + "content": "67.24\\%" + }, + { + "bbox": [ + 46, + 510, + 287, + 629 + ], + "type": "text", + "content": " using only text, while adding visual modality information only improves the accuracy by about " + }, + { + "bbox": [ + 46, + 510, + 287, + 629 + ], + "type": "inline_equation", + "content": "0.5\\%" + }, + { + "bbox": [ + 46, + 510, + 287, + 629 + ], + "type": "text", + "content": ". This result explains why our method significantly lags behind multimodal methods using text inputs." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 629, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 287, + 677 + ], + "type": "text", + "content": "Liris-Accede. As shown in Table 4e, EmotionCLIP achieves promising results using visual inputs only. It even competes with many multimodal approaches that are benefited from the use of audio features [93]." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "text", + "content": "Emotic. As shown in Table 4c, EmotionCLIP outperforms all RGB-based supervised methods while other vision-language models perform poorly. The improvement of [53]" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 378, + 545, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 378, + 545, + 415 + ], + "spans": [ + { + "bbox": [ + 304, + 378, + 545, + 415 + ], + "type": "text", + "content": "is attributable to the use of additional depth information. This result demonstrates the capability of EmotionCLIP in learning relevant features from complex environments." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 426, + 378, + 438 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 426, + 378, + 438 + ], + "spans": [ + { + "bbox": [ + 306, + 426, + 378, + 438 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 446, + 545, + 626 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 446, + 545, + 626 + ], + "spans": [ + { + "bbox": [ + 304, + 446, + 545, + 626 + ], + "type": "text", + "content": "The pre-training methodology, which has brought about significant advancements in numerous CV and NLP domains, has not yet been employed in AEI research. We address this void by introducing EmotionCLIP, the first vision-language pre-training framework that circumvents the need for curated data and annotations. Our study establishes the viability of acquiring generalized emotion representations directly from human communication, thereby considerably broadening the horizons of current AEI research. The emergence of this pre-training paradigm offers an alternative solution to data scarcity, paving the way for a myriad of potential applications. We anticipate that our work will stimulate further investigation in this area and contribute to the evolution of more adaptable and efficacious approaches for affective computing." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 641, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 545, + 712 + ], + "type": "text", + "content": "Acknowledgments. This research was supported by generous gifts from the Amazon Research Awards program. 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IJCV, 130(9):2337-2348, 2022. 2" + } + ] + } + ], + "index": 15 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "19004" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 11 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Learning Event Guided High Dynamic Range Video Reconstruction/33cfc19b-aa34-4b73-9613-d3bfaa3bfbaf_content_list.json b/2023/Learning Event Guided High Dynamic Range Video Reconstruction/33cfc19b-aa34-4b73-9613-d3bfaa3bfbaf_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..c6d5a1dd5f69723ffc18c57691e45d4e3ba38fe3 --- /dev/null +++ b/2023/Learning Event Guided High Dynamic Range Video Reconstruction/33cfc19b-aa34-4b73-9613-d3bfaa3bfbaf_content_list.json @@ -0,0 +1,1976 @@ +[ + { + "type": "text", + "text": "Learning Event Guided High Dynamic Range Video Reconstruction", + "text_level": 1, + "bbox": [ + 138, + 118, + 823, + 138 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Yixin Yang $^{1,2}$ Jin Han $^{3,4}$ Jinxiu Liang $^{1,2}$ Imari Sato $^{3,4}$ Boxin Shi $^{*1,2}$", + "bbox": [ + 215, + 148, + 751, + 167 + ], + "page_idx": 0 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "$^{1}$ National Key Laboratory for Multimedia Information Processing, School of Computer Science, Peking University", + "$^{2}$ National Engineering Research Center of Visual Technology, School of Computer Science, Peking University" + ], + "bbox": [ + 140, + 170, + 826, + 203 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "3 Graduate School of Information Science and Technology, The University of Tokyo 4 National Institute of Informatics {yangyixin93, cssherryliang, shiboxin}@pku.edu.cn {jinhan, imarik}@nii.ac.jp", + "bbox": [ + 132, + 205, + 834, + 239 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/9a36ac9f79a20c3b2d3f27796d8b5f8774a36f6edd01a048efadfdfd357499df.jpg", + "image_caption": [ + "(a) LDR images" + ], + "image_footnote": [], + "bbox": [ + 84, + 250, + 241, + 465 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c875a8cd190c8ac85f4bf579145d973ec3dd92c76a3f523ec55737b407e20190.jpg", + "image_caption": [ + "(b) Events" + ], + "image_footnote": [], + "bbox": [ + 245, + 250, + 401, + 465 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/ba3532f56f8f436872a75e6631d3bc8e6dcac18d737ac33addf072648b22e19f.jpg", + "image_caption": [ + "(c) E2VID [60]", + "Figure 1. Given hybrid inputs of (a) LDR video and (b) stacked events, the HDR video can be reconstructed using different methods shown in (c) E2VID [60], (d) Han et al. [24], and (e) the proposed HDRev-Net. The samples here are tested on synthetic data (top row) and real data (bottom row) respectively. The proposed method is able to generate the HDR video with more details and less flickering effects. Please view our project page for corresponding animations." + ], + "image_footnote": [], + "bbox": [ + 405, + 250, + 562, + 465 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/f6209c31ecd7982d88ab9121c52eaa9b2ea4cd43a9f770637ac8c98e2b6e2ceb.jpg", + "image_caption": [ + "(d) Han et al. [24]" + ], + "image_footnote": [], + "bbox": [ + 565, + 250, + 723, + 465 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/adc3d33b7afdd85ef86bb2407b9e20c0b02b3572f729de7b7f4a9532ccc3b1d1.jpg", + "image_caption": [ + "(e) Ours" + ], + "image_footnote": [], + "bbox": [ + 725, + 250, + 883, + 465 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 549, + 312, + 564 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Limited by the trade-off between frame rate and exposure time when capturing moving scenes with conventional cameras, frame based HDR video reconstruction suffers from scene-dependent exposure ratio balancing and ghosting artifacts. Event cameras provide an alternative visual representation with a much higher dynamic range and temporal resolution free from the above issues, which could be an effective guidance for HDR imaging from LDR videos. In this paper, we propose a multimodal learning framework for event guided HDR video reconstruction. In order to better leverage the knowledge of the same scene from the two modalities of visual signals, a multimodal representation alignment strategy to learn a shared latent space and a fusion module tailored to complementing two types of signals for different dynamic ranges in different regions are proposed. Temporal correlations are utilized recurrently to suppress the flickering effects in the reconstructed HDR video. The proposed HDRev-Net demonstrates state-of-the-art performance quantitatively and qualitatively for both synthetic and real-world data.", + "bbox": [ + 73, + 580, + 472, + 883 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 501, + 549, + 630, + 564 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The dynamic range of the real world usually exceeds what a conventional camera and 8-bit image can record by a large margin. High dynamic range (HDR) imaging, which expands the luminance range limited by low dynamic range (LDR) images or videos, is a broadly used technique with extensive applications in photography/videoography, video games, and high-end display.", + "bbox": [ + 496, + 573, + 890, + 680 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Most HDR imaging methods for conventional cameras rely on capturing and merging multiple snapshots with different exposure times [9, 49], which is challenging for capturing videos. There have been enduring efforts for sophisticated modification on conventional frame based cameras to capture multi-exposure sequences (nearly) simultaneously, e.g., beam splitting with three or more sensors [69, 70], temporally [7, 30, 32] or spatially [1, 8, 22, 28, 53, 54] varying exposure. Nevertheless, their abilities for HDR video reconstruction are limited by the trade-off between a higher frame rate (for a smooth viewing experience) and a higher dynamic range (for capturing details in dark regions with", + "bbox": [ + 496, + 680, + 892, + 862 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* Corresponding author", + "bbox": [ + 522, + 875, + 653, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "Project page: https://yixinyang-00.github.io/HDRev/", + "bbox": [ + 522, + 887, + 890, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "13924", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "prolonged exposure time). Moreover, the optimal exposure ratio between LDR frame sequences with different exposure settings is scene-dependent and temporally-varying, whose balancing is difficult for diverse scenes captured in videos. Even worse, moving objects or camera shaking during video capture can lead to ghosting effects in frames generated by long exposure shots. An HDR video could also be hallucinated from LDR inputs in a frame-by-frame manner by leveraging prior knowledge of tone-mapping operators [61] or data modeling powers of deep learning [11]. However, due to the highly ill-posed nature of the hallucination process, it inevitably leads to severe flickering effects.", + "bbox": [ + 75, + 90, + 472, + 272 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In recent years, the event camera [16] has drawn increasing attention of researchers, due to its advantages over conventional frame based ones in sensing fast motions and extended dynamic ranges (e.g., 120dB for DAVIS346). Unlike using multi-exposure frames, events recorded along with an LDR video encode HDR irradiance changes without sacrificing the frame rate/exposure time of the LDR video, which avoids ghosting artifacts as well, and is very promising as guidance for HDR video reconstruction.", + "bbox": [ + 75, + 273, + 472, + 411 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "However, integrating events with LDR video for HDR video reconstruction is challenging due to inconsistency between events and frames in three aspects: 1) Modality misalignment: Frames and events are completely different representations of visual information, and \"fusing\" them by first translating events into intensity values [60,80] like [24] often includes artifacts from solving the ill-posed event integration problem. 2) Dynamic range gap: Performing image/video reconstruction under the guidance of events [75], i.e., doubly integrating events as intensity changes within the exposure time [56,57], ignores the dynamic range clipping in the capturing process of LDR frames, which leads to uncertainties in under/over-exposed regions. 3) Texture mismatching: Regions with smooth textures and slow motion hardly produce effective event observations, which results in inconsistent textures among consecutive event stacks and flickering effects in the reconstructed videos.", + "bbox": [ + 75, + 412, + 472, + 670 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We propose HDRev-Net, a multimodal learning framework for event guided HDR video reconstruction to tackle the challenges by the following strategies: 1) To achieve multimodal representation alignment for the two modalities of the same scene, we propose a learning strategy to progressively project them onto a shared representation space. 2) To reliably complement information from the two modalities in over/under-exposed regions, the representations produced by the two modality-specific encoders are fused for an expressive joint representation using a confidence guided multimodal fusion module. 3) To effectively suppress the flickering effects, we utilize the temporal redundant information between consecutive frames and events via the proposed recurrent convolutional encoders.", + "bbox": [ + 75, + 671, + 472, + 883 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "As shown in Fig. 1, HDRev-Net can successfully fuse", + "bbox": [ + 96, + 885, + 470, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "LDR frames and events to obtain HDR frames with more details and less flickering effects. It demonstrates state-of-the-art HDR video reconstruction performance on both synthetic and real data by making the following contributions:", + "bbox": [ + 496, + 90, + 890, + 151 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We design a multimodal alignment strategy to bridge the gap between events and frames by aligning their representation in a shared latent space.", + "- We develop a confidence guided fusion module to complement HDR information from events and finer details from well-exposed regions in LDR frames.", + "- We utilize the temporal correlation from consecutive events and LDR frames in a recurrent fashion to alleviate the flickering effects for recovered HDR videos." + ], + "bbox": [ + 517, + 151, + 890, + 284 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 297, + 640, + 314 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Frame based HDR reconstruction. A typical technique for HDR image reconstruction is to merge a stack of bracketed exposure LDR images into an HDR one [9, 49]. Such an idea is also feasible for HDR video reconstruction. Many works [38, 48, 69, 70] proposed to use multiple sensors to capture LDR images with different exposures simultaneously. Besides, there are methods designing spatially varying sensors [1, 8, 22, 28, 53, 54, 71] or using coded exposure by alternating the shutter speed [7, 29, 30, 32, 43]. However, HDR information is obtained at the cost of lowering spatial or temporal resolution in these methods. Moreover, for dynamic scenes, camera shake and moving objects during exposure can lead to ghosting artifacts. To tackle this, recent works [45, 68, 77] introduced attention mechanisms to perform implicit alignment between frames. However, they still heavily rely on fine-grained similarities across frames, which is hard to be captured in varying exposures.", + "bbox": [ + 496, + 323, + 890, + 580 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To avoid ghosting artifacts, Banterle et al. [2] proposed inverse tone mapping to reconstruct the HDR image from a single LDR image, which attempted to hallucinate HDR information in over/under-exposure regions. More recently, many works [6,11,12,19,33,39-41,44,47] attempted to better perform inverse tone mapping via convolutional neural networks (CNNs). However, the problem of hallucinating the lost information in over/under-exposed regions without any physical guidance is too ill-posed to be reliably solved in varying real-world scenarios by these methods.", + "bbox": [ + 496, + 580, + 890, + 731 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Event based HDR reconstruction. Event cameras inherently have a higher dynamic range than conventional ones, which enable direct reconstruction of HDR frames from pure events. Early attempt [35] for intensity reconstruction from events was based on strict assumptions about the scene or motion, e.g., brightness constancy and global rotational movement. Other methods [3, 4] optimized a variational model to reconstruct intensity images. With the help of deep learning, Mostafavi et al. [51, 73] and Wang et al. [74] used generative adversarial networks (GANs) [21] to reconstruct images from events. Rebecq et al. [59, 60] and", + "bbox": [ + 496, + 734, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "13925", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Zou et al. [80] used recurrent convolutional blocks [10, 25] to maintain temporal consistency inside long event streams for video reconstruction. However, these methods suffer from flickering effects and cannot provide stable colored video reconstruction because stream-like events only record the quantized logarithmic irradiance changes of each pixel. It is highly ill-posed to directly reconstruct frames from events without any intensity information as references.", + "bbox": [ + 75, + 90, + 472, + 210 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Event guided HDR reconstruction. Conventional cameras record the irradiance within a limited dynamic range synchronously, while event cameras record the logarithmic irradiance change with a much higher dynamic range asynchronously. Event guided HDR reconstruction combines the best of the two worlds by considering hybrid input of events and frames for reconstructing HDR frames. Wang et al. [72] proposed a sparse learning method along with the integration method [56] to enhance the image quality. Han et al. [24] proposed to reconstruct HDR intensity maps from events first and then fused them with LDR frame in the intensity domain. It is also proposed to guide the fusion of bracketed exposure with events [50,64] for plausible results. However, blurry artifacts are also introduced by the longer exposure of bracketed images. All these works focused on the reconstruction of HDR images.", + "bbox": [ + 75, + 214, + 472, + 455 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For event guided video reconstruction, Wang et al. [75] integrated events to interpolate frames based on [56, 57] and handled the noise and artifacts under simplified assumption by a variant of Kalman filter. However, the integration model [56, 57] ignored the dynamic range clipping of LDR frames, which leads to uncertainties in under/over-exposed regions. In contrast, we propose to integrate the two modalities in a learned shared representation space by leveraging the data modeling power of deep learning.", + "bbox": [ + 75, + 455, + 472, + 592 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Proposed Method", + "text_level": 1, + "bbox": [ + 76, + 603, + 250, + 619 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Formulation", + "text_level": 1, + "bbox": [ + 76, + 628, + 210, + 642 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Event generation and stacking. An event camera triggers an event $e = (t, p, \\sigma)$ at pixel position $p = (p_x, p_y)^\\top$ and time $t$ with polarity $\\sigma \\in \\{-1, +1\\}$ , when the logarithmic change of irradiance $R$ since the last event at the pixel $p$ and time $t - \\delta t$ exceeds a dispatched threshold $\\theta$ :", + "bbox": [ + 75, + 651, + 468, + 727 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\| \\log R _ {t} ^ {(p)} - \\log R _ {t - \\delta t} ^ {(p)} \\right\\| \\geq \\theta . \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 176, + 733, + 468, + 753 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To process stream-like events using CNNs, we need to convert a stream of events into a fixed size tensor-like representation. We use voxel grid [79] that encodes temporal information in a $C$ -channel 3D-volume. By discretizing duration $\\Delta t = t_{K - 1} - t_0$ spanned by $K$ events into $C$ temporal bins, each event $e_k = (t_k,p_k,\\sigma_k)$ distributes its polarity $\\sigma_{k}$ to the two closest voxels as follows [60]:", + "bbox": [ + 75, + 758, + 470, + 864 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nE _ {t} ^ {(p)} = \\sum_ {p _ {k} = p} \\sigma_ {k} \\max (0, 1 - | t - \\tilde {t} _ {k} |), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 145, + 869, + 468, + 904 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\tilde{t}_k\\coloneqq \\frac{C - 1}{\\Delta t} (t_k - t_0)$ is the normalized timestamp.", + "bbox": [ + 498, + 89, + 870, + 108 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "LDR image formation. Given the irradiance $R$ and exposure time $\\Delta t$ , an HDR image can be represented as $I_{\\mathrm{HDR}} = R \\cdot \\Delta t$ . There are three steps to produce an LDR image: dynamic range clipping, tone mapping with a camera response function (CRF) $f_{\\mathrm{CRF}}$ , and quantization:", + "bbox": [ + 498, + 109, + 890, + 185 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nI _ {\\mathrm {L D R}} = \\left\\lfloor 2 5 5 \\cdot f _ {\\mathrm {C R F}} \\left(\\max \\left(\\min \\left(I _ {\\mathrm {H D R}}, 1\\right), 0\\right)\\right) \\right\\rfloor / 2 5 5. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 517, + 195, + 890, + 212 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To align the LDR image and events in the linear irradiance domain, we first convert the LDR image by:", + "bbox": [ + 498, + 222, + 890, + 252 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nL = f _ {\\mathrm {C R F}} ^ {- 1} \\left(I _ {\\mathrm {L D R}}\\right) / \\Delta t, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 622, + 261, + 890, + 280 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $f_{\\mathrm{CRF}}^{-1}$ is the inverse CRF. To ease the learning difficulty in regression of values in linear domain spanning a wide range, the range of $I_{\\mathrm{HDR}}$ are compressed by [31]:", + "bbox": [ + 498, + 287, + 890, + 335 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nH = \\frac {\\log (1 + \\mu I _ {\\mathrm {H D R}})}{\\log (1 + \\mu)}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 617, + 343, + 890, + 377 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mu$ controls the amount of compression.", + "bbox": [ + 500, + 385, + 800, + 400 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. HDRev-Net", + "text_level": 1, + "bbox": [ + 500, + 409, + 625, + 422 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given the stacked event sequence $\\mathbb{E} = \\{E_t\\}_{t=1}^T$ and the corresponding LDR frame sequence $\\mathbb{L} = \\{L_t\\}_{t=1}^T$ of length $T$ , our goal is to reconstruct the HDR frame sequence $\\mathbb{H} = \\{H_t\\}_{t=1}^T$ through a multimodal learning network $\\mathcal{F}$ dubbed HDRev-Net. As illustrated in Fig. 2, $\\mathcal{F}$ consists of two modality-specific encoders $\\mathcal{F}_{\\mathrm{L}}$ and $\\mathcal{F}_{\\mathrm{E}}$ for both temporal context encoding and multimodal representation alignment, confidence guided multimodal fusion module $\\mathcal{F}_{\\mathrm{fusion}}$ and decoder $\\mathcal{F}_{\\mathrm{H}}$ for HDR video reconstruction from latent representation. Our pipeline can be described as:", + "bbox": [ + 498, + 425, + 893, + 577 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbb {H} = \\mathcal {F} _ {\\mathrm {H}} \\left(\\mathcal {F} _ {\\text {f u s i o n}} \\left(\\mathcal {F} _ {\\mathrm {L}} (\\mathbb {L}), \\mathcal {F} _ {\\mathrm {E}} (\\mathbb {E})\\right). \\right. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 584, + 587, + 890, + 604 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Multimodal representation alignment. Events and LDR frames are two quite different modalities for representing visual information, whose fusion is non-trivial due to distinct low-level statistical properties and highly non-linear relationships between them. Non-learning approaches based on the explicit fusion model [56, 57] may lead to uncertainties in over-exposed regions, while using CNNs to predict HDR frames from the two modalities by direct concatenation or performing event-to-frame translation firstly is ill-posed, which does not consider the differences and complementarities between the two modalities.", + "bbox": [ + 498, + 613, + 890, + 779 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this paper, we propose to perform implicit fusion by an encoder-decoder network: learning to represent events and LDR frames in a shared latent space by two modality-specific encoders and then integrating them by a fusion module in the bottleneck layer. A straightforward solution is training the two encoders simultaneously for jointly decoding the latent representation into HDR frames. However, due to the modality gap between frames and events,", + "bbox": [ + 496, + 779, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "13926", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/eac4d8bfc70da7a55c6f31d4dab3d7173ecc61244cb45a2894f86156e163cf4f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 78, + 88, + 893, + 258 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "jointly performing intra-modality (LDR to HDR) and intermodality (event to HDR) reconstruction can lead to a trivial solution: predicting HDR frames from the LDR frames mostly, leaving almost all the stacked events ignored in the training process and heavily relying on LDR frames.", + "bbox": [ + 75, + 342, + 468, + 417 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To effectively utilize the properties of high dynamic range and high frame rate of events, we should find a shared representation space that can well express common and complementary information from events and LDR frames for the subsequent multimodal fusion. To achieve this, we propose a multi-stage approach: performing inter-modality reconstruction from events and then intra-modality reconstruction from LDR frames at first, then jointly training the two encoders and HDR decoder together.", + "bbox": [ + 75, + 417, + 468, + 551 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Specifically, the event encoder $\\mathcal{F}_{\\mathrm{E}}$ is pretrained to map the input events to a latent representation, which is then decoded to HDR frames by an HDR decoder $\\mathcal{F}_{\\mathrm{H}}$ :", + "bbox": [ + 75, + 553, + 468, + 599 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nF _ {\\mathrm {E}} = \\mathcal {F} _ {\\mathrm {E}} (\\mathbb {E}), \\quad \\mathbb {H} = \\mathcal {F} _ {\\mathrm {H}} \\left(F _ {\\mathrm {E}}\\right). \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 171, + 608, + 468, + 626 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In order to project the input LDR frames onto the same latent space for representation alignment, an LDR encoder $\\mathcal{F}_{\\mathrm{L}}$ is then trained with the parameters of $\\mathcal{F}_{\\mathrm{H}}$ fixed:", + "bbox": [ + 76, + 633, + 468, + 681 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nF _ {\\mathrm {L}} = \\mathcal {F} _ {\\mathrm {L}} (\\mathbb {L}), \\quad \\mathbb {H} = \\mathcal {F} _ {\\mathrm {H}} \\left(F _ {\\mathrm {L}}\\right). \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 171, + 694, + 468, + 710 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Thanks to the shared decoder $\\mathcal{F}_{\\mathrm{H}}$ , the representation of events and LDR frames are aligned in a shared latent space and can then be effectively fused by the proposed event guided HDR video reconstruction pipeline Eq. (6).", + "bbox": [ + 75, + 715, + 468, + 777 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Confidence guided multimodal fusion. As shown in Fig. 2, both manually designed confidence masks and learnable channel-wise attention are used for weighting the intermediate representation $F_{\\mathrm{L}}$ , $F_{\\mathrm{E}}$ along two separate dimensions, spatial and channel. The manually designed confidence masks emphasize more reliable regions and robustness to inherent noise in data. Intuitively, events are triggered on high contrast edges. The confidence mask for", + "bbox": [ + 75, + 779, + 470, + 901 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/f3199053240b2409ac7eada9e9657ed6724f87b87446054b530abc76187671d1.jpg", + "image_caption": [ + "Figure 2. Overview of the proposed HDRev-Net. For multimodal representation alignment, the hybrid inputs of stacked events $\\mathbb{E}$ and LDR frames $\\mathbb{L}$ are mapped onto a shared representation space by the modality-specific encoders $\\mathcal{F}_{\\mathrm{E}},\\mathcal{F}_{\\mathrm{L}}$ , in which recurrent connections are applied for temporal context encoding. Under the guidance of confidence masks $M_E$ and $M_L$ extracted from $\\mathbb{E}$ and $\\mathbb{L}$ , respectively, their latent representations $F_{\\mathrm{E}},F_{\\mathrm{L}}$ are then integrated into a joint one $F_{\\mathrm{H}}$ by the multimodal fusion module $\\mathcal{F}_{\\mathrm{fusion}}$ . The HDR decoder $\\mathcal{F}_{\\mathrm{H}}$ decodes $F_{\\mathrm{H}}$ into HDR frame sequence $\\mathbb{H}$ eventually.", + "(a) LDR image $L$" + ], + "image_footnote": [], + "bbox": [ + 506, + 333, + 651, + 416 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/5fb4ae7793ed76e39cf1cc1ad7e5238075e68950ea4d0017d46b45b23734816b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 660, + 333, + 767, + 416 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/262842ed992fedd9caeb85cede0fd4b6d4f07c61bf4896164af2bcf8d4b94376.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 777, + 333, + 885, + 416 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/80ce34af8ce554608cc3e24062b5454ab12e9cbb02d98a402d4bc2611d25aa72.jpg", + "image_caption": [ + "(d) LDR mask $M_{L}$", + "Figure 3. Visualization of the confidence masks (d) $M_{\\mathrm{L}}$ and (e) $M_{\\mathrm{E}}$ extracted from (a) LDR frame $L$ and events (b) $E$ , respectively. The HDR reconstruction results are (c) \"W/o fusion\" and (f) ours." + ], + "image_footnote": [], + "bbox": [ + 504, + 426, + 650, + 510 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/396149e1f7b7a11c24ebf7b89401d83af17295f5c1b8b10d086e0b04416e3c67.jpg", + "image_caption": [ + "(b) Event stack $E$", + "(e) Event mask $M_E$" + ], + "image_footnote": [], + "bbox": [ + 660, + 426, + 767, + 508 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/a8ffc4cd20af2bb0cde0b9bed5b0b6f285809ac003e805de1e320ad164989764.jpg", + "image_caption": [ + "(c) W/o fusion results", + "(f) Ours result" + ], + "image_footnote": [], + "bbox": [ + 777, + 426, + 885, + 508 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "events makes the fusion module pay more attention to such regions (an example is shown in Fig. 3 (e)). The confidence mask $M_{\\mathrm{E}}$ is defined as:", + "bbox": [ + 498, + 577, + 890, + 622 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nM _ {\\mathrm {E}} = \\min (G * | E |, 1), \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 614, + 635, + 890, + 652 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $*$ denotes the convolution operator; $G$ denotes a Gaussian kernel with variance 3 and support $21 \\times 21$ , which is used to propagate the influence of the sparsely distributed events to their neighboring regions.", + "bbox": [ + 496, + 665, + 890, + 724 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For LDR frames, irradiance in well-exposed regions is more reliable. The confidence mask $M_{\\mathrm{L}}$ for LDR frames (an example is shown in Fig. 3 (d)) is defined as:", + "bbox": [ + 496, + 724, + 890, + 771 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nM _ {\\mathrm {L}} = \\frac {0 . 5 - \\max (| L - 0 . 5 | , \\lambda - 0 . 5)}{1 - \\lambda}, \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 563, + 781, + 890, + 813 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\lambda$ is a hyper-parameter (set as 0.8 in our experiments) that defines the range of values in which reliable pixels lie.", + "bbox": [ + 496, + 824, + 890, + 854 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To guide the fusion of latent representation with a smaller spatial size, we propagate the values of the mask according to the receptive field of each pixel. Specifically,", + "bbox": [ + 496, + 854, + 890, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "13927", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/e6102812b1b62a88d0f9d466f38df7dd604584aff8520a7353d2831d264651e4.jpg", + "image_caption": [ + "Figure 4. Illustration of the recurrent connections in encoder $\\mathcal{F}_{\\mathrm{L}}$ (the same structure is used for $\\mathcal{F}_{\\mathrm{E}}$ )." + ], + "image_footnote": [], + "bbox": [ + 80, + 95, + 452, + 286 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "the confidence mask $M^{(l)}$ for reweighing the chosen bottleneck feature $F_{\\mathrm{E}}$ , $F_{\\mathrm{L}}$ outputted by the $l$ -th layer is defined by the following recursive rule:", + "bbox": [ + 75, + 327, + 470, + 375 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nM ^ {(0)} = M, \\quad M ^ {(l)} = G _ {K _ {l}} * M ^ {(l - 1)}, \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 145, + 382, + 468, + 402 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $G_{K_l}$ denotes a Gaussian kernel with variance 3 and support $K_{l}\\times K_{l}$ , whose size is the same as the $l$ -th convolutional layer. Given the confidence masks $M_{\\mathrm{L}}^{(l)},M_{\\mathrm{E}}^{(l)}$ , the spatially weighted features are obtained by:", + "bbox": [ + 75, + 412, + 468, + 476 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {F} _ {\\mathrm {L}} = F _ {\\mathrm {L}} \\cdot M _ {\\mathrm {L}} ^ {(l)}, \\quad \\tilde {F} _ {\\mathrm {E}} = F _ {\\mathrm {E}} \\cdot M _ {\\mathrm {E}} ^ {(l)}. \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 151, + 484, + 468, + 506 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To adaptively exchange information between $\\tilde{F}_{\\mathrm{L}}$ and $\\tilde{F}_{\\mathrm{E}}$ , they are concatenated and reweighted by a channel attention module [27] $\\mathcal{A}$ to obtain an integrated one $\\tilde{F}_{\\mathrm{H}}$ :", + "bbox": [ + 75, + 516, + 468, + 564 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {F} _ {\\mathrm {H}} = \\mathcal {A} ([ \\tilde {F} _ {\\mathrm {L}}, \\tilde {F} _ {\\mathrm {E}} ]). \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 207, + 571, + 468, + 592 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To better balance the contributions of different modalities, $\\tilde{F}_{\\mathrm{E}},\\tilde{F}_{\\mathrm{L}}$ are reweighted along all dimensions with the weighting maps extracted from $\\tilde{F}_{\\mathrm{H}}$ by weighting layers $\\mathcal{W}_{\\mathrm{L}}$ and $\\mathcal{W}_{\\mathrm{E}}$ . Then they are concatenated and fed into a convolutional blending layer $\\mathcal{B}$ to obtain the joint representation for HDR reconstruction:", + "bbox": [ + 75, + 601, + 468, + 691 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nF _ {\\mathrm {H}} = \\mathcal {B} \\left(\\left[ \\tilde {F} _ {\\mathrm {L}} \\odot \\mathcal {W} _ {\\mathrm {L}} \\left(\\tilde {F} _ {\\mathrm {H}}\\right), \\tilde {F} _ {\\mathrm {E}} \\odot \\mathcal {W} _ {\\mathrm {E}} \\left(\\tilde {F} _ {\\mathrm {H}}\\right) \\right]\\right). \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 133, + 700, + 468, + 720 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Temporal context encoding. To alleviate the flickering effects in the generated HDR videos caused by texture mismatching among consecutive event stacks, we exploit the temporal structure within the data via a recurrent convolutional encoder, as shown in Fig. 4. The temporal context encoders $\\mathcal{F}_{\\mathrm{E}},\\mathcal{F}_{\\mathrm{L}}$ learn modality-specific latent representations $F_{\\mathrm{E}},F_{\\mathrm{L}}$ by capturing their underlying temporal structures by a recurrent variant of the encoder in U-Net [62], in which each convolutional layer is replaced by the ConvLSTM [65]. At each timestamp, it outputs the internal state from its own input as well as the encoded past states from", + "bbox": [ + 75, + 734, + 470, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "its previous input. It can provide more consistent global features of each modality and alleviates flickering effects in the recovered HDR videos.", + "bbox": [ + 496, + 90, + 890, + 135 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The internal states not only preserve temporal correlation between consecutive frames to suppress the flickering effects but also reduce noise in both input modalities, especially in the under-exposed regions. Through the recurrent design of the encoders, the temporal complementary and redundant information through time can be well exploited in the learned latent representations of events and LDR frames for better HDR video reconstruction.", + "bbox": [ + 496, + 136, + 890, + 257 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Training", + "text_level": 1, + "bbox": [ + 500, + 266, + 604, + 282 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Dataset preparation. For the training of HDRev-Net, a large amount of triplets $(\\mathbb{E},\\mathbb{L},\\mathbb{H})$ are required. There are no readily available datasets containing these triplets nor HDR video datasets with satisfactory scale and quality. To synthesize such a dataset, we collect 733 HDR images from [13, 15, 17, 18, 26, 37, 55, 66, 76] and 110 videos with local motion from [13, 14, 34, 37]. For HDR images, 733 HDR videos with global motion are simulated by generated random camera motion trajectories [5]. From each frame sequence of these videos, the hybrid input of events and LDR frames are simulated by [58] and [12], respectively, like capturing with a virtual camera. To better simulate real LDR images, the LDR frames are generated with randomly sampled CRF, exposure time and Poisson-Gaussian noise [23] for each iteration during training. The event generator [58] also considered the normal distributed thresholds to bridge the gap between real and synthetic. There are a total of 26520 (global motion) + 63754 (local motion) = 90274 frames with a resolution of $240\\times 180$ for training and 5600 frames with a resolution of $256\\times 256$ for testing.", + "bbox": [ + 496, + 289, + 892, + 592 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Loss functions. To train the proposed framework, the loss function to be minimized is defined as:", + "bbox": [ + 496, + 595, + 890, + 625 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\alpha_ {1} \\mathcal {L} _ {\\mathrm {m s e}} + \\alpha_ {2} \\mathcal {L} _ {\\text {p e r c}} + \\alpha_ {3} \\mathcal {L} _ {\\text {c o l o r}}, \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 578, + 638, + 890, + 655 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\alpha_{1,2,3}$ are hyper-parameters for balancing different terms. Our goal is to reconstruct HDR frame sequence $\\{H_t\\}_{t=1}^T$ , while the prediction of the network $\\mathcal{F}$ is $\\{O_t\\}_{t=1}^T$ . The mean square error (MSE) loss $\\mathcal{L}_{\\mathrm{mse}}$ is defined as:", + "bbox": [ + 498, + 665, + 890, + 727 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {m s e}} = \\sum_ {t} \\left(\\left\\| H _ {t} - O _ {t} \\right\\| _ {2} ^ {2}\\right). \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 602, + 736, + 890, + 767 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The perceptual loss $\\mathcal{L}_{\\mathrm{perc}}$ is defined based on the feature maps extracted by the VGG-16 [67] network pre-trained on ImageNet [63]:", + "bbox": [ + 496, + 779, + 890, + 824 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {\\text {p e r c}} = \\sum_ {t} \\left(\\sum_ {l} \\left(\\| \\phi_ {l} \\left(H _ {t}\\right) - \\phi_ {l} \\left(O _ {t}\\right) \\| _ {2} ^ {2} \\right. \\right. \\tag {17} \\\\ \\left. + \\left\\| \\mathcal {G} _ {l} ^ {\\phi} (H _ {t}) - \\mathcal {G} _ {l} ^ {\\phi} (O _ {t}) \\| _ {2} ^ {2}\\right)\\right), \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 532, + 835, + 890, + 905 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "13928", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\phi_l$ denotes the feature map extracted from $l$ -th layer of VGG-16, $\\mathcal{G}_l^\\phi$ calculates the Gram matrix of $\\phi_l$ . The layer we use in our experiments is \"relu4_3\". To enforce the color appearance of the reconstructed HDR frames to match that in the ground truth, a color loss is defined as:", + "bbox": [ + 75, + 90, + 470, + 167 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {c o l o r}} = \\sum_ {t} \\left(\\| \\widetilde {H} _ {t} - \\widetilde {O} _ {t} \\| _ {2} ^ {2}\\right), \\tag {18}\n$$\n", + "text_format": "latex", + "bbox": [ + 179, + 172, + 468, + 204 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\widetilde{H} = G * H$ and $\\widetilde{O} = G * O$ are blurred from $H, O$ to eliminate texture and content.", + "bbox": [ + 75, + 210, + 468, + 242 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Other implementation details. We adopt a lightweight variant of recurrent U-Net with 2 downsampling layers in all experiments. The network is unrolled for $T = 6$ steps during training. It is implemented on the PyTorch framework and runs on an NVIDIA GeForce RTX 3080 GPU. We use ADAM [36] with default parameter setting for optimization. The batch size is set as 1. The learning rate was fixed to $10^{-5}$ in the earlier epochs and reduced to 0 in the last $40\\%$ epochs by the linear decay strategy. The number of epochs for pretraining Eq. (7), representation alignment Eq. (8), and training the whole pipeline Eq. (6) are set as 40, 5, 5, respectively. Xavier initialization [20] is used for network initialization. The hyper-parameters in the loss function Eq. (15) are set as $\\alpha_{1} = 30$ , $\\alpha_{2} = 5$ , $\\alpha_{3} = 10^{-3}$ . The hyper-parameter $\\mu$ for dynamic range compression Eq. (5) is set as 5000.", + "bbox": [ + 75, + 247, + 468, + 489 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 501, + 209, + 517 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We compare the proposed HDRev-Net to several state-of-the-art HDR imaging methods, including a frame based HDR image reconstruction method: Liu et al. [44]; the colored variant of an event based HDR reconstruction method: E2VID [60]; two event guided HDR image reconstruction methods: Han et al. [24] and eSL-Net [72]; and two-exposure-based methods [9, 42].", + "bbox": [ + 75, + 521, + 468, + 628 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Evaluation on synthetic data", + "text_level": 1, + "bbox": [ + 76, + 633, + 333, + 650 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Metrics. We adopt the HDR-VDP-3 (\"VDP\" for short), the updated version of HDR-VDP [46], to evaluate the quality of reconstructed HDR images frame by frame. For evaluating the quality of HDR videos, we use HDR-VQM [52] (\"VQM\" for short), which is computed based on a spatiotemporal analysis related to human eye fixation behavior during video viewing. We also adopt commonly used peak signal-to-noise ratio (PSNR), structural similarity (SSIM), and the perceptual error with learned perceptual image patch similarity (LPIPS) [78] metrics as reference.", + "bbox": [ + 75, + 652, + 468, + 805 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Results. The quantitative results are reported in Table 1. For the two-exposure-based method Li et al. [42], we only calculate the PSNR, SSIM, and LPIPS since it only output tone-mapped HDR images which can not be used to calculate VDP and VQM in the linear domain. We generate two-exposure frame sequences for all the two-exposure-based", + "bbox": [ + 75, + 809, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/71ab593284abe722002d3ff1a4cb3baaad7e3ad9000ce2da8e754f7e60085179.jpg", + "table_caption": [ + "Table 1. Comparisons on synthetic data. $\\uparrow (\\downarrow)$ means higher (lower) is better." + ], + "table_footnote": [], + "table_body": "
MethodsPSNR↑SSIM↑LPIPS↓VDP↑VQM↓
eSL-Net [72]16.5750.7130.4135.9030.467
E2VID [60]13.7340.5890.4514.1430.343
Liu et al. [44]23.1590.9010.1047.5430.107
Han et al. [24]20.6970.8610.2086.7090.243
Debevec et al. [9]23.5960.8770.2646.1920.264
Li et al. [42]20.6730.8900.151--
Ours24.0710.9280.1108.1080.103
", + "bbox": [ + 504, + 121, + 883, + 250 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "methods with an exposure ratio setting that takes a reasonable balance between the dynamic range covered and the details preserved. The proposed method outperforms existing methods in terms of all metrics.", + "bbox": [ + 496, + 261, + 890, + 320 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The visual quality comparisons are shown in Fig. $5^{1}$ . In over/under-exposed regions of the LDR input, most of the details have been lost due to dynamic range clipping. Both frame-based [44] and event-based [60] approaches cannot restore lost information to produce high-quality HDR images. In particular, E2VID [60] produces severe artifacts and distorted color in the reconstructed HDR frames. Han et al. [24] converted one modality into another explicitly (i.e., events to intensity) at first, which leads to stripe-like artifacts and cannot restore natural color appearance. eSL-Net [72] mainly focuses on LDR input and cannot fuse the two modalities well. The performance of Li et al. [42] heavily depends on the selected exposure ratio. As shown in Fig. $5^{2}$ , even with the optimal exposure ratio, the results of Li et al. presents insufficient details (e.g., on the stones and windows). In comparison, the HDRev-Net effectively fuses the two modalities of visual information and successfully recovers the lost details, with no need to balance the exposure ratio for varying scenes captured by videos.", + "bbox": [ + 496, + 321, + 892, + 609 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Evaluation on real data", + "text_level": 1, + "bbox": [ + 500, + 621, + 715, + 636 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Fig. 6 shows the reconstructed HDR frames on real-world scenarios captured by a hybrid-camera system. We build the hybrid camera system by using a beam-splitter to divide the incident light equivalently into two sensors, i.e., an event camera (DAVIS346 Color) and an industrial camera (FLIR Chameleon 3 Color). Both of them share a similar field of view (FoV). To achieve spatial alignment between the two sensors, we crop the corresponding part of RGB frames w.r.t. the event sensor. With synchronized triggering, the hybrid camera system is able to capture aligned LDR frames and events simultaneously.", + "bbox": [ + 496, + 645, + 890, + 811 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "As shown in the HDR frame reconstruction results of", + "bbox": [ + 517, + 813, + 892, + 827 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "1We provide results of one method per category due to the space limit. Please refer to the supplementary materials to complete reconstruction results on synthetic data.", + "bbox": [ + 498, + 838, + 890, + 875 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "2The detailed analysis to exposure ratios are shown in supplementary materials.", + "bbox": [ + 500, + 875, + 890, + 898 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "13929", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/a26668fdfa5a88645484e1d2c2df57a6c6241665026f5449215185ec4d594da8.jpg", + "image_caption": [ + "Figure 5. Visual quality comparisons on synthetic data. The Q-scores (higher the better) of VDP metrics are labeled in each image." + ], + "image_footnote": [], + "bbox": [ + 83, + 90, + 885, + 345 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4f3c841ad78485360b5f8daa9f7c3adb689f5c7bea954d4ab5736167dc5a115f.jpg", + "image_caption": [ + "Figure 6. Visual quality comparisons on real-world data. The test samples here are under- and over-exposure cases respectively." + ], + "image_footnote": [], + "bbox": [ + 81, + 371, + 890, + 604 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "real-world data in Fig. 6, HDRev-Net can reconstruct HDR frames with a wider dynamic range and more details.", + "bbox": [ + 75, + 635, + 468, + 666 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Results of HDR video reconstruction", + "text_level": 1, + "bbox": [ + 76, + 676, + 393, + 690 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The information lost in over/under-exposed regions of LDR frames is recorded in events. However, it is unstable for HDR video reconstruction since events are triggered with irradiance changes, rather than absolute values as in LDR frames. HDR video reconstruction in a frame-by-frame manner suffers from flickering effects since temporal connections between consecutive frames are not considered. In the proposed method, recurrent architectures are utilized in the encoders to better maintain the model temporal correlation between frames. Thanks to these components, the proposed HDRev-Net effectively suppresses the flickering effects in the reconstructed HDR videos3.", + "bbox": [ + 75, + 695, + 470, + 875 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Ablation study", + "text_level": 1, + "bbox": [ + 500, + 635, + 648, + 650 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To validate the effectiveness and necessity of the three components of the proposed HDRev-Net, we compare it with its three variants. The quantitative results are shown in Table 2, and the qualitative results are shown in Fig. 3, Fig. 7, Fig. 8, respectively.", + "bbox": [ + 496, + 655, + 890, + 731 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effectiveness of multimodal representation alignment technique. We compare the proposed multimodal representation alignment strategy with joint training the pipeline Eq. (6) in an end-to-end manner, which is denoted by \"Joint training\" in Table 2. It can be seen that a performance drop occurs when the three networks are jointly trained, especially in terms of PSNR. As shown in Fig. 7, there are severe halo artifacts in over-exposed regions of the LDR in the results of \"Joint\" training, especially the contours of the cables and the pylons. Due to the domain gap between LDR frames and stacked events, jointly training", + "bbox": [ + 496, + 734, + 892, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_footnote", + "text": "3Please refer to the supplementary video for details.", + "bbox": [ + 94, + 886, + 370, + 898 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "13930", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/4e056bfd335b473d78cb607aa8d221043513f71ea2664e86ffc02d301ed20e7b.jpg", + "table_caption": [ + "Table 2. Results of ablation study. $\\uparrow (\\downarrow)$ means higher (lower) is better." + ], + "table_footnote": [], + "table_body": "
SettingPSNR↑SSIM↑LPIPS↓VDP↑VQM↓
Joint training22.1850.9110.1627.8710.120
W/o fusion19.4360.8670.2147.0240.175
W/o LSTM21.4630.8910.1977.1660.173
Complete model24.0710.9280.1108.1080.103
", + "bbox": [ + 86, + 121, + 460, + 209 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e84d94e0ff01c233bf349cdf60afa73b1191f737a48a3978e580d723e1151eff.jpg", + "image_caption": [ + "LDR frame" + ], + "image_footnote": [], + "bbox": [ + 78, + 222, + 207, + 253 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/816cd9f9d18df0b162b739e26b8a1c8962dddb492a6c6d17232a9abee4216bc4.jpg", + "image_caption": [ + "Complete $H_{L}$" + ], + "image_footnote": [], + "bbox": [ + 210, + 222, + 336, + 253 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/57c87b2dfca74b19dd6c2bcb3ef36dff9d4f521fac4f6dfc4dd6ef5fcc364441.jpg", + "image_caption": [ + "Joint $H_{L}$" + ], + "image_footnote": [], + "bbox": [ + 341, + 222, + 468, + 253 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d7b11b8a839655befb9f56ef257f98bd332952ef1a9dea21f1856a5cce72cc51.jpg", + "image_caption": [ + "Events" + ], + "image_footnote": [], + "bbox": [ + 80, + 266, + 207, + 297 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/51011cc47425f256148bff18d64be4066de7725684e05a57d6808912ca8f3515.jpg", + "image_caption": [ + "Complete $H_{E}$" + ], + "image_footnote": [], + "bbox": [ + 210, + 266, + 336, + 297 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/fec65939e593bc161d05182552689a1b03fd090132b1799cefd0fbebdff07207.jpg", + "image_caption": [ + "Joint $H_{E}$" + ], + "image_footnote": [], + "bbox": [ + 341, + 266, + 468, + 297 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/9c23375d5e13591bd0d6ee770a0d49be2134bebe3b59352072d8d43a2b4a0c93.jpg", + "image_caption": [ + "Ground truth" + ], + "image_footnote": [], + "bbox": [ + 80, + 308, + 207, + 339 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3d3a7f1863a674d5fb580ed36e10da00cd6d3551f3f61de75be7f4624e801b8a.jpg", + "image_caption": [ + "Complete $H$" + ], + "image_footnote": [], + "bbox": [ + 210, + 308, + 336, + 339 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c0efbcc092ab2c1f0cfdaaca1484cd2377bd27f5eee3d1b8c870e8ce60d2b736.jpg", + "image_caption": [ + "Joint $H$" + ], + "image_footnote": [], + "bbox": [ + 341, + 308, + 468, + 339 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0265deb7681332976ed05e4122d30999a32c25ba63aefa537861d56cfce35660.jpg", + "image_caption": [ + "Figure 7. Comparisons between \"Joint\" training and \"Complete\" model. $H_{L}(H_{E})$ denotes the network output with encoder $F_{E}$ ( $F_{L}$ ) disabled by setting input to zero.", + "Figure 8. Comparison between \"W/o LSTM\" and \"Complete\" model. The results of consecutive frames are shown in eight columns. The animations are shown on our project page." + ], + "image_footnote": [], + "bbox": [ + 80, + 402, + 467, + 574 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "the whole pipeline cannot well utilize the HDR information in events, which is recorded in a different way from the intensity values in LDR frames.", + "bbox": [ + 75, + 625, + 468, + 670 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effectiveness of the confidence guided multimodal fusion module. To verify the effectiveness of the proposed confidence guided multimodal fusion module, we replace the fusion module with a convolution layer with kernel size $3 \\times 3$ and \"relu\" activation fed by concatenated $F_{\\mathrm{L}}, F_{\\mathrm{E}}$ in the \"W/o fusion\" variant. As shown in Table 2, its performance is worse than the proposed one in terms of all metrics. As shown in Fig. 3, the proposed module can better leverage the information from both modalities and reconstruct HDR images with more details (e.g., the details of the shrub at the lower-left and the texture of the mountain) and less artifact (e.g., the top-left corner). In comparison, the lost details in over-exposed regions cannot be well restored without the fusion module. The convolution layer lacks the ability to dynamically highlight local regions and feature maps that", + "bbox": [ + 75, + 674, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "provide more information from one of the two modalities, which makes the recovering of global characteristics such as color and brightness worse than the proposed one.", + "bbox": [ + 498, + 90, + 890, + 137 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effectiveness of the temporal context encoding module. We evaluate the contribution of the recurrent connections in the proposed temporal context encoders by removing them in a \"W/o LSTM\" variant. As shown in Table 2, it performs the worst due to the absence of recurrent connections, especially in terms of VQM that reflects the temporal quality of the reconstructed HDR videos. As shown in Fig. 8, information lost in the over-exposed switch (e.g., the flickering effects pointed out by the yellow arrows) can hardly be restored since there is no event at this timestamp. However, the complete model with recurrent connections can recover fine details and textures from the previous frame, which suppresses flickering effects effectively.", + "bbox": [ + 498, + 146, + 890, + 343 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 359, + 617, + 375 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we present a multimodal learning framework for reconstructing HDR videos from hybrid inputs of LDR videos and events. There are three components in the proposed method: a multimodal representation alignment strategy for aligning LDR frames and events in a learned shared latent space, a confidence guided multimodal fusion module for adaptively integrating complementary information from the two modalities, and a temporal context encoding module for suppressing the flickering effects by exploiting the temporal correlation between consecutive frames and stacked events. The effectiveness of the proposed method in the task of event guided HDR video reconstruction is verified by extensive experiments on both synthetic and real-world data.", + "bbox": [ + 498, + 381, + 890, + 592 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitations. The proposed method aims at HDR video reconstruction under the guidance of HDR information provided by events. However, events contain inherent noise distributed differently from that of frames, which can lead to artifacts in the reconstructed HDR video, especially in low-light conditions. Moreover, due to the requirement of aligned spatial resolution of the hybrid inputs and low resolution of the chosen event camera (DAVIS346C), the proposed method has a limited ability for high-resolution HDR video reconstruction. Replacing the chosen event camera with a higher resolution one(e.g., Prophesee EVK4-HD with a spatial resolution of $720 \\times 1280$ ) and better low-light perception might further improve the performance.", + "bbox": [ + 496, + 602, + 890, + 799 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement", + "text_level": 1, + "bbox": [ + 500, + 806, + 660, + 824 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was supported by National Key R&D Program of China (2021ZD0109803) and National Natural Science Foundation of China (Grant No. 62088102, 62136001). Jinxiu Liang was also supported by China Postdoctoral Science Foundation (Grant No. 2022M720236).", + "bbox": [ + 496, + 825, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "13931", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Cecilia Aguerrebere, Andres Almansa, Yann Gousseau, Julie Delon, and Pablo Muse. Single shot high dynamic range imaging using piecewise linear estimators. In Proc. of International Conference on Computational Photography, 2014. 1, 2", + "[2] Francesco Banterle, Patrick Ledda, Kurt Debattista, and Alan Chalmers. Inverse tone mapping. In Proc. of International Conference on Computer Graphics and Interactive Techniques, 2006. 2", + "[3] Patrick Bardow, Andrew J. Davison, and Stefan Leutenegger. 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Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.139, + 0.119, + 0.825, + 0.14 + ], + "angle": 0, + "content": "Learning Event Guided High Dynamic Range Video Reconstruction" + }, + { + "type": "text", + "bbox": [ + 0.216, + 0.15, + 0.753, + 0.169 + ], + "angle": 0, + "content": "Yixin Yang\\(^{1,2}\\) Jin Han\\(^{3,4}\\) Jinxiu Liang\\(^{1,2}\\) Imari Sato\\(^{3,4}\\) Boxin Shi\\(^{*1,2}\\)" + }, + { + "type": "text", + "bbox": [ + 0.141, + 0.171, + 0.827, + 0.187 + ], + "angle": 0, + "content": "\\(^{1}\\) National Key Laboratory for Multimedia Information Processing, School of Computer Science, Peking University" + }, + { + "type": "text", + "bbox": [ + 0.155, + 0.188, + 0.815, + 0.204 + ], + "angle": 0, + "content": "\\(^{2}\\) National Engineering Research Center of Visual Technology, School of Computer Science, Peking University" + }, + { + "type": "list", + "bbox": [ + 0.141, + 0.171, + 0.827, + 0.204 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.133, + 0.206, + 0.836, + 0.24 + ], + "angle": 0, + "content": "3 Graduate School of Information Science and Technology, The University of Tokyo 4 National Institute of Informatics {yangyixin93, cssherryliang, shiboxin}@pku.edu.cn {jinhan, imarik}@nii.ac.jp" + }, + { + "type": "image", + "bbox": [ + 0.086, + 0.251, + 0.243, + 0.466 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.121, + 0.468, + 0.208, + 0.479 + ], + "angle": 0, + "content": "(a) LDR images" + }, + { + "type": "image", + "bbox": [ + 0.246, + 0.251, + 0.403, + 0.466 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.297, + 0.468, + 0.354, + 0.479 + ], + "angle": 0, + "content": "(b) Events" + }, + { + "type": "image", + "bbox": [ + 0.406, + 0.251, + 0.563, + 0.466 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.444, + 0.468, + 0.526, + 0.479 + ], + "angle": 0, + "content": "(c) E2VID [60]" + }, + { + "type": "image", + "bbox": [ + 0.566, + 0.251, + 0.724, + 0.466 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.597, + 0.468, + 0.695, + 0.479 + ], + "angle": 0, + "content": "(d) Han et al. [24]" + }, + { + "type": "image", + "bbox": [ + 0.727, + 0.251, + 0.885, + 0.466 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.784, + 0.468, + 0.829, + 0.479 + ], + "angle": 0, + "content": "(e) Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.481, + 0.894, + 0.537 + ], + "angle": 0, + "content": "Figure 1. Given hybrid inputs of (a) LDR video and (b) stacked events, the HDR video can be reconstructed using different methods shown in (c) E2VID [60], (d) Han et al. [24], and (e) the proposed HDRev-Net. The samples here are tested on synthetic data (top row) and real data (bottom row) respectively. The proposed method is able to generate the HDR video with more details and less flickering effects. Please view our project page for corresponding animations." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.55, + 0.313, + 0.565 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.581, + 0.473, + 0.884 + ], + "angle": 0, + "content": "Limited by the trade-off between frame rate and exposure time when capturing moving scenes with conventional cameras, frame based HDR video reconstruction suffers from scene-dependent exposure ratio balancing and ghosting artifacts. Event cameras provide an alternative visual representation with a much higher dynamic range and temporal resolution free from the above issues, which could be an effective guidance for HDR imaging from LDR videos. In this paper, we propose a multimodal learning framework for event guided HDR video reconstruction. In order to better leverage the knowledge of the same scene from the two modalities of visual signals, a multimodal representation alignment strategy to learn a shared latent space and a fusion module tailored to complementing two types of signals for different dynamic ranges in different regions are proposed. Temporal correlations are utilized recurrently to suppress the flickering effects in the reconstructed HDR video. The proposed HDRev-Net demonstrates state-of-the-art performance quantitatively and qualitatively for both synthetic and real-world data." + }, + { + "type": "title", + "bbox": [ + 0.502, + 0.55, + 0.631, + 0.565 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.574, + 0.892, + 0.681 + ], + "angle": 0, + "content": "The dynamic range of the real world usually exceeds what a conventional camera and 8-bit image can record by a large margin. High dynamic range (HDR) imaging, which expands the luminance range limited by low dynamic range (LDR) images or videos, is a broadly used technique with extensive applications in photography/videoography, video games, and high-end display." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.681, + 0.893, + 0.863 + ], + "angle": 0, + "content": "Most HDR imaging methods for conventional cameras rely on capturing and merging multiple snapshots with different exposure times [9, 49], which is challenging for capturing videos. There have been enduring efforts for sophisticated modification on conventional frame based cameras to capture multi-exposure sequences (nearly) simultaneously, e.g., beam splitting with three or more sensors [69, 70], temporally [7, 30, 32] or spatially [1, 8, 22, 28, 53, 54] varying exposure. Nevertheless, their abilities for HDR video reconstruction are limited by the trade-off between a higher frame rate (for a smooth viewing experience) and a higher dynamic range (for capturing details in dark regions with" + }, + { + "type": "page_footnote", + "bbox": [ + 0.524, + 0.876, + 0.654, + 0.888 + ], + "angle": 0, + "content": "* Corresponding author" + }, + { + "type": "page_footnote", + "bbox": [ + 0.524, + 0.888, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Project page: https://yixinyang-00.github.io/HDRev/" + }, + { + "type": "list", + "bbox": [ + 0.524, + 0.876, + 0.892, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13924" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.273 + ], + "angle": 0, + "content": "prolonged exposure time). Moreover, the optimal exposure ratio between LDR frame sequences with different exposure settings is scene-dependent and temporally-varying, whose balancing is difficult for diverse scenes captured in videos. Even worse, moving objects or camera shaking during video capture can lead to ghosting effects in frames generated by long exposure shots. An HDR video could also be hallucinated from LDR inputs in a frame-by-frame manner by leveraging prior knowledge of tone-mapping operators [61] or data modeling powers of deep learning [11]. However, due to the highly ill-posed nature of the hallucination process, it inevitably leads to severe flickering effects." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.275, + 0.473, + 0.412 + ], + "angle": 0, + "content": "In recent years, the event camera [16] has drawn increasing attention of researchers, due to its advantages over conventional frame based ones in sensing fast motions and extended dynamic ranges (e.g., 120dB for DAVIS346). Unlike using multi-exposure frames, events recorded along with an LDR video encode HDR irradiance changes without sacrificing the frame rate/exposure time of the LDR video, which avoids ghosting artifacts as well, and is very promising as guidance for HDR video reconstruction." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.413, + 0.473, + 0.671 + ], + "angle": 0, + "content": "However, integrating events with LDR video for HDR video reconstruction is challenging due to inconsistency between events and frames in three aspects: 1) Modality misalignment: Frames and events are completely different representations of visual information, and \"fusing\" them by first translating events into intensity values [60,80] like [24] often includes artifacts from solving the ill-posed event integration problem. 2) Dynamic range gap: Performing image/video reconstruction under the guidance of events [75], i.e., doubly integrating events as intensity changes within the exposure time [56,57], ignores the dynamic range clipping in the capturing process of LDR frames, which leads to uncertainties in under/over-exposed regions. 3) Texture mismatching: Regions with smooth textures and slow motion hardly produce effective event observations, which results in inconsistent textures among consecutive event stacks and flickering effects in the reconstructed videos." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.672, + 0.473, + 0.884 + ], + "angle": 0, + "content": "We propose HDRev-Net, a multimodal learning framework for event guided HDR video reconstruction to tackle the challenges by the following strategies: 1) To achieve multimodal representation alignment for the two modalities of the same scene, we propose a learning strategy to progressively project them onto a shared representation space. 2) To reliably complement information from the two modalities in over/under-exposed regions, the representations produced by the two modality-specific encoders are fused for an expressive joint representation using a confidence guided multimodal fusion module. 3) To effectively suppress the flickering effects, we utilize the temporal redundant information between consecutive frames and events via the proposed recurrent convolutional encoders." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.886, + 0.472, + 0.902 + ], + "angle": 0, + "content": "As shown in Fig. 1, HDRev-Net can successfully fuse" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.152 + ], + "angle": 0, + "content": "LDR frames and events to obtain HDR frames with more details and less flickering effects. It demonstrates state-of-the-art HDR video reconstruction performance on both synthetic and real data by making the following contributions:" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.152, + 0.892, + 0.196 + ], + "angle": 0, + "content": "- We design a multimodal alignment strategy to bridge the gap between events and frames by aligning their representation in a shared latent space." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.197, + 0.892, + 0.24 + ], + "angle": 0, + "content": "- We develop a confidence guided fusion module to complement HDR information from events and finer details from well-exposed regions in LDR frames." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.241, + 0.892, + 0.285 + ], + "angle": 0, + "content": "- We utilize the temporal correlation from consecutive events and LDR frames in a recurrent fashion to alleviate the flickering effects for recovered HDR videos." + }, + { + "type": "list", + "bbox": [ + 0.518, + 0.152, + 0.892, + 0.285 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.299, + 0.642, + 0.315 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.324, + 0.892, + 0.581 + ], + "angle": 0, + "content": "Frame based HDR reconstruction. A typical technique for HDR image reconstruction is to merge a stack of bracketed exposure LDR images into an HDR one [9, 49]. Such an idea is also feasible for HDR video reconstruction. Many works [38, 48, 69, 70] proposed to use multiple sensors to capture LDR images with different exposures simultaneously. Besides, there are methods designing spatially varying sensors [1, 8, 22, 28, 53, 54, 71] or using coded exposure by alternating the shutter speed [7, 29, 30, 32, 43]. However, HDR information is obtained at the cost of lowering spatial or temporal resolution in these methods. Moreover, for dynamic scenes, camera shake and moving objects during exposure can lead to ghosting artifacts. To tackle this, recent works [45, 68, 77] introduced attention mechanisms to perform implicit alignment between frames. However, they still heavily rely on fine-grained similarities across frames, which is hard to be captured in varying exposures." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.581, + 0.892, + 0.732 + ], + "angle": 0, + "content": "To avoid ghosting artifacts, Banterle et al. [2] proposed inverse tone mapping to reconstruct the HDR image from a single LDR image, which attempted to hallucinate HDR information in over/under-exposure regions. More recently, many works [6,11,12,19,33,39-41,44,47] attempted to better perform inverse tone mapping via convolutional neural networks (CNNs). However, the problem of hallucinating the lost information in over/under-exposed regions without any physical guidance is too ill-posed to be reliably solved in varying real-world scenarios by these methods." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Event based HDR reconstruction. Event cameras inherently have a higher dynamic range than conventional ones, which enable direct reconstruction of HDR frames from pure events. Early attempt [35] for intensity reconstruction from events was based on strict assumptions about the scene or motion, e.g., brightness constancy and global rotational movement. Other methods [3, 4] optimized a variational model to reconstruct intensity images. With the help of deep learning, Mostafavi et al. [51, 73] and Wang et al. [74] used generative adversarial networks (GANs) [21] to reconstruct images from events. Rebecq et al. [59, 60] and" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13925" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.473, + 0.212 + ], + "angle": 0, + "content": "Zou et al. [80] used recurrent convolutional blocks [10, 25] to maintain temporal consistency inside long event streams for video reconstruction. However, these methods suffer from flickering effects and cannot provide stable colored video reconstruction because stream-like events only record the quantized logarithmic irradiance changes of each pixel. It is highly ill-posed to directly reconstruct frames from events without any intensity information as references." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.215, + 0.473, + 0.456 + ], + "angle": 0, + "content": "Event guided HDR reconstruction. Conventional cameras record the irradiance within a limited dynamic range synchronously, while event cameras record the logarithmic irradiance change with a much higher dynamic range asynchronously. Event guided HDR reconstruction combines the best of the two worlds by considering hybrid input of events and frames for reconstructing HDR frames. Wang et al. [72] proposed a sparse learning method along with the integration method [56] to enhance the image quality. Han et al. [24] proposed to reconstruct HDR intensity maps from events first and then fused them with LDR frame in the intensity domain. It is also proposed to guide the fusion of bracketed exposure with events [50,64] for plausible results. However, blurry artifacts are also introduced by the longer exposure of bracketed images. All these works focused on the reconstruction of HDR images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.457, + 0.473, + 0.593 + ], + "angle": 0, + "content": "For event guided video reconstruction, Wang et al. [75] integrated events to interpolate frames based on [56, 57] and handled the noise and artifacts under simplified assumption by a variant of Kalman filter. However, the integration model [56, 57] ignored the dynamic range clipping of LDR frames, which leads to uncertainties in under/over-exposed regions. In contrast, we propose to integrate the two modalities in a learned shared representation space by leveraging the data modeling power of deep learning." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.604, + 0.251, + 0.62 + ], + "angle": 0, + "content": "3. Proposed Method" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.629, + 0.212, + 0.643 + ], + "angle": 0, + "content": "3.1. Formulation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.652, + 0.47, + 0.728 + ], + "angle": 0, + "content": "Event generation and stacking. An event camera triggers an event \\( e = (t, p, \\sigma) \\) at pixel position \\( p = (p_x, p_y)^\\top \\) and time \\( t \\) with polarity \\( \\sigma \\in \\{-1, +1\\} \\), when the logarithmic change of irradiance \\( R \\) since the last event at the pixel \\( p \\) and time \\( t - \\delta t \\) exceeds a dispatched threshold \\( \\theta \\):" + }, + { + "type": "equation", + "bbox": [ + 0.177, + 0.734, + 0.47, + 0.755 + ], + "angle": 0, + "content": "\\[\n\\left\\| \\log R _ {t} ^ {(p)} - \\log R _ {t - \\delta t} ^ {(p)} \\right\\| \\geq \\theta . \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.76, + 0.471, + 0.866 + ], + "angle": 0, + "content": "To process stream-like events using CNNs, we need to convert a stream of events into a fixed size tensor-like representation. We use voxel grid [79] that encodes temporal information in a \\(C\\)-channel 3D-volume. By discretizing duration \\(\\Delta t = t_{K - 1} - t_0\\) spanned by \\(K\\) events into \\(C\\) temporal bins, each event \\(e_k = (t_k,p_k,\\sigma_k)\\) distributes its polarity \\(\\sigma_{k}\\) to the two closest voxels as follows [60]:" + }, + { + "type": "equation", + "bbox": [ + 0.146, + 0.871, + 0.47, + 0.905 + ], + "angle": 0, + "content": "\\[\nE _ {t} ^ {(p)} = \\sum_ {p _ {k} = p} \\sigma_ {k} \\max (0, 1 - | t - \\tilde {t} _ {k} |), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.09, + 0.872, + 0.109 + ], + "angle": 0, + "content": "where \\(\\tilde{t}_k\\coloneqq \\frac{C - 1}{\\Delta t} (t_k - t_0)\\) is the normalized timestamp." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.11, + 0.892, + 0.186 + ], + "angle": 0, + "content": "LDR image formation. Given the irradiance \\( R \\) and exposure time \\( \\Delta t \\), an HDR image can be represented as \\( I_{\\mathrm{HDR}} = R \\cdot \\Delta t \\). There are three steps to produce an LDR image: dynamic range clipping, tone mapping with a camera response function (CRF) \\( f_{\\mathrm{CRF}} \\), and quantization:" + }, + { + "type": "equation", + "bbox": [ + 0.518, + 0.196, + 0.892, + 0.213 + ], + "angle": 0, + "content": "\\[\nI _ {\\mathrm {L D R}} = \\left\\lfloor 2 5 5 \\cdot f _ {\\mathrm {C R F}} \\left(\\max \\left(\\min \\left(I _ {\\mathrm {H D R}}, 1\\right), 0\\right)\\right) \\right\\rfloor / 2 5 5. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.223, + 0.892, + 0.253 + ], + "angle": 0, + "content": "To align the LDR image and events in the linear irradiance domain, we first convert the LDR image by:" + }, + { + "type": "equation", + "bbox": [ + 0.624, + 0.262, + 0.892, + 0.281 + ], + "angle": 0, + "content": "\\[\nL = f _ {\\mathrm {C R F}} ^ {- 1} \\left(I _ {\\mathrm {L D R}}\\right) / \\Delta t, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.289, + 0.892, + 0.336 + ], + "angle": 0, + "content": "where \\( f_{\\mathrm{CRF}}^{-1} \\) is the inverse CRF. To ease the learning difficulty in regression of values in linear domain spanning a wide range, the range of \\( I_{\\mathrm{HDR}} \\) are compressed by [31]:" + }, + { + "type": "equation", + "bbox": [ + 0.619, + 0.344, + 0.892, + 0.378 + ], + "angle": 0, + "content": "\\[\nH = \\frac {\\log (1 + \\mu I _ {\\mathrm {H D R}})}{\\log (1 + \\mu)}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.386, + 0.801, + 0.401 + ], + "angle": 0, + "content": "where \\(\\mu\\) controls the amount of compression." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.41, + 0.627, + 0.424 + ], + "angle": 0, + "content": "3.2. HDRev-Net" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.426, + 0.894, + 0.578 + ], + "angle": 0, + "content": "Given the stacked event sequence \\(\\mathbb{E} = \\{E_t\\}_{t=1}^T\\) and the corresponding LDR frame sequence \\(\\mathbb{L} = \\{L_t\\}_{t=1}^T\\) of length \\(T\\), our goal is to reconstruct the HDR frame sequence \\(\\mathbb{H} = \\{H_t\\}_{t=1}^T\\) through a multimodal learning network \\(\\mathcal{F}\\) dubbed HDRev-Net. As illustrated in Fig. 2, \\(\\mathcal{F}\\) consists of two modality-specific encoders \\(\\mathcal{F}_{\\mathrm{L}}\\) and \\(\\mathcal{F}_{\\mathrm{E}}\\) for both temporal context encoding and multimodal representation alignment, confidence guided multimodal fusion module \\(\\mathcal{F}_{\\mathrm{fusion}}\\) and decoder \\(\\mathcal{F}_{\\mathrm{H}}\\) for HDR video reconstruction from latent representation. Our pipeline can be described as:" + }, + { + "type": "equation", + "bbox": [ + 0.586, + 0.588, + 0.892, + 0.605 + ], + "angle": 0, + "content": "\\[\n\\mathbb {H} = \\mathcal {F} _ {\\mathrm {H}} \\left(\\mathcal {F} _ {\\text {f u s i o n}} \\left(\\mathcal {F} _ {\\mathrm {L}} (\\mathbb {L}), \\mathcal {F} _ {\\mathrm {E}} (\\mathbb {E})\\right). \\right. \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.614, + 0.892, + 0.78 + ], + "angle": 0, + "content": "Multimodal representation alignment. Events and LDR frames are two quite different modalities for representing visual information, whose fusion is non-trivial due to distinct low-level statistical properties and highly non-linear relationships between them. Non-learning approaches based on the explicit fusion model [56, 57] may lead to uncertainties in over-exposed regions, while using CNNs to predict HDR frames from the two modalities by direct concatenation or performing event-to-frame translation firstly is ill-posed, which does not consider the differences and complementarities between the two modalities." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In this paper, we propose to perform implicit fusion by an encoder-decoder network: learning to represent events and LDR frames in a shared latent space by two modality-specific encoders and then integrating them by a fusion module in the bottleneck layer. A straightforward solution is training the two encoders simultaneously for jointly decoding the latent representation into HDR frames. However, due to the modality gap between frames and events," + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "13926" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.08, + 0.089, + 0.895, + 0.259 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.264, + 0.895, + 0.334 + ], + "angle": 0, + "content": "Figure 2. Overview of the proposed HDRev-Net. For multimodal representation alignment, the hybrid inputs of stacked events \\(\\mathbb{E}\\) and LDR frames \\(\\mathbb{L}\\) are mapped onto a shared representation space by the modality-specific encoders \\(\\mathcal{F}_{\\mathrm{E}},\\mathcal{F}_{\\mathrm{L}}\\) , in which recurrent connections are applied for temporal context encoding. Under the guidance of confidence masks \\(M_E\\) and \\(M_L\\) extracted from \\(\\mathbb{E}\\) and \\(\\mathbb{L}\\) , respectively, their latent representations \\(F_{\\mathrm{E}},F_{\\mathrm{L}}\\) are then integrated into a joint one \\(F_{\\mathrm{H}}\\) by the multimodal fusion module \\(\\mathcal{F}_{\\mathrm{fusion}}\\) . The HDR decoder \\(\\mathcal{F}_{\\mathrm{H}}\\) decodes \\(F_{\\mathrm{H}}\\) into HDR frame sequence \\(\\mathbb{H}\\) eventually." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.343, + 0.47, + 0.418 + ], + "angle": 0, + "content": "jointly performing intra-modality (LDR to HDR) and intermodality (event to HDR) reconstruction can lead to a trivial solution: predicting HDR frames from the LDR frames mostly, leaving almost all the stacked events ignored in the training process and heavily relying on LDR frames." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.418, + 0.47, + 0.553 + ], + "angle": 0, + "content": "To effectively utilize the properties of high dynamic range and high frame rate of events, we should find a shared representation space that can well express common and complementary information from events and LDR frames for the subsequent multimodal fusion. To achieve this, we propose a multi-stage approach: performing inter-modality reconstruction from events and then intra-modality reconstruction from LDR frames at first, then jointly training the two encoders and HDR decoder together." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.554, + 0.47, + 0.6 + ], + "angle": 0, + "content": "Specifically, the event encoder \\(\\mathcal{F}_{\\mathrm{E}}\\) is pretrained to map the input events to a latent representation, which is then decoded to HDR frames by an HDR decoder \\(\\mathcal{F}_{\\mathrm{H}}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.172, + 0.609, + 0.47, + 0.627 + ], + "angle": 0, + "content": "\\[\nF _ {\\mathrm {E}} = \\mathcal {F} _ {\\mathrm {E}} (\\mathbb {E}), \\quad \\mathbb {H} = \\mathcal {F} _ {\\mathrm {H}} \\left(F _ {\\mathrm {E}}\\right). \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.635, + 0.47, + 0.682 + ], + "angle": 0, + "content": "In order to project the input LDR frames onto the same latent space for representation alignment, an LDR encoder \\(\\mathcal{F}_{\\mathrm{L}}\\) is then trained with the parameters of \\(\\mathcal{F}_{\\mathrm{H}}\\) fixed:" + }, + { + "type": "equation", + "bbox": [ + 0.172, + 0.695, + 0.47, + 0.712 + ], + "angle": 0, + "content": "\\[\nF _ {\\mathrm {L}} = \\mathcal {F} _ {\\mathrm {L}} (\\mathbb {L}), \\quad \\mathbb {H} = \\mathcal {F} _ {\\mathrm {H}} \\left(F _ {\\mathrm {L}}\\right). \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.717, + 0.47, + 0.778 + ], + "angle": 0, + "content": "Thanks to the shared decoder \\(\\mathcal{F}_{\\mathrm{H}}\\), the representation of events and LDR frames are aligned in a shared latent space and can then be effectively fused by the proposed event guided HDR video reconstruction pipeline Eq. (6)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Confidence guided multimodal fusion. As shown in Fig. 2, both manually designed confidence masks and learnable channel-wise attention are used for weighting the intermediate representation \\( F_{\\mathrm{L}} \\), \\( F_{\\mathrm{E}} \\) along two separate dimensions, spatial and channel. The manually designed confidence masks emphasize more reliable regions and robustness to inherent noise in data. Intuitively, events are triggered on high contrast edges. The confidence mask for" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.334, + 0.653, + 0.417 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.562, + 0.417, + 0.64, + 0.427 + ], + "angle": 0, + "content": "(a) LDR image \\(L\\)" + }, + { + "type": "image", + "bbox": [ + 0.661, + 0.334, + 0.768, + 0.417 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.675, + 0.418, + 0.755, + 0.427 + ], + "angle": 0, + "content": "(b) Event stack \\(E\\)" + }, + { + "type": "image", + "bbox": [ + 0.778, + 0.334, + 0.886, + 0.417 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.783, + 0.418, + 0.882, + 0.427 + ], + "angle": 0, + "content": "(c) W/o fusion results" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.427, + 0.651, + 0.511 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.556, + 0.511, + 0.638, + 0.521 + ], + "angle": 0, + "content": "(d) LDR mask \\(M_{L}\\)" + }, + { + "type": "image", + "bbox": [ + 0.661, + 0.427, + 0.768, + 0.51 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.671, + 0.511, + 0.758, + 0.522 + ], + "angle": 0, + "content": "(e) Event mask \\(M_E\\)" + }, + { + "type": "image", + "bbox": [ + 0.778, + 0.427, + 0.886, + 0.51 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.799, + 0.511, + 0.865, + 0.521 + ], + "angle": 0, + "content": "(f) Ours result" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.526, + 0.892, + 0.568 + ], + "angle": 0, + "content": "Figure 3. Visualization of the confidence masks (d) \\( M_{\\mathrm{L}} \\) and (e) \\( M_{\\mathrm{E}} \\) extracted from (a) LDR frame \\( L \\) and events (b) \\( E \\), respectively. The HDR reconstruction results are (c) \"W/o fusion\" and (f) ours." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.578, + 0.892, + 0.623 + ], + "angle": 0, + "content": "events makes the fusion module pay more attention to such regions (an example is shown in Fig. 3 (e)). The confidence mask \\( M_{\\mathrm{E}} \\) is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.615, + 0.636, + 0.892, + 0.654 + ], + "angle": 0, + "content": "\\[\nM _ {\\mathrm {E}} = \\min (G * | E |, 1), \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.666, + 0.892, + 0.726 + ], + "angle": 0, + "content": "where \\(*\\) denotes the convolution operator; \\(G\\) denotes a Gaussian kernel with variance 3 and support \\(21 \\times 21\\), which is used to propagate the influence of the sparsely distributed events to their neighboring regions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.726, + 0.892, + 0.772 + ], + "angle": 0, + "content": "For LDR frames, irradiance in well-exposed regions is more reliable. The confidence mask \\( M_{\\mathrm{L}} \\) for LDR frames (an example is shown in Fig. 3 (d)) is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.565, + 0.782, + 0.892, + 0.814 + ], + "angle": 0, + "content": "\\[\nM _ {\\mathrm {L}} = \\frac {0 . 5 - \\max (| L - 0 . 5 | , \\lambda - 0 . 5)}{1 - \\lambda}, \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.892, + 0.855 + ], + "angle": 0, + "content": "where \\(\\lambda\\) is a hyper-parameter (set as 0.8 in our experiments) that defines the range of values in which reliable pixels lie." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.902 + ], + "angle": 0, + "content": "To guide the fusion of latent representation with a smaller spatial size, we propagate the values of the mask according to the receptive field of each pixel. Specifically," + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13927" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.096, + 0.454, + 0.287 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.291, + 0.468, + 0.32 + ], + "angle": 0, + "content": "Figure 4. Illustration of the recurrent connections in encoder \\(\\mathcal{F}_{\\mathrm{L}}\\) (the same structure is used for \\(\\mathcal{F}_{\\mathrm{E}}\\))." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.328, + 0.471, + 0.375 + ], + "angle": 0, + "content": "the confidence mask \\( M^{(l)} \\) for reweighing the chosen bottleneck feature \\( F_{\\mathrm{E}} \\), \\( F_{\\mathrm{L}} \\) outputted by the \\( l \\)-th layer is defined by the following recursive rule:" + }, + { + "type": "equation", + "bbox": [ + 0.146, + 0.383, + 0.47, + 0.403 + ], + "angle": 0, + "content": "\\[\nM ^ {(0)} = M, \\quad M ^ {(l)} = G _ {K _ {l}} * M ^ {(l - 1)}, \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.413, + 0.47, + 0.477 + ], + "angle": 0, + "content": "where \\( G_{K_l} \\) denotes a Gaussian kernel with variance 3 and support \\( K_{l}\\times K_{l} \\), whose size is the same as the \\( l \\)-th convolutional layer. Given the confidence masks \\( M_{\\mathrm{L}}^{(l)},M_{\\mathrm{E}}^{(l)} \\), the spatially weighted features are obtained by:" + }, + { + "type": "equation", + "bbox": [ + 0.153, + 0.485, + 0.47, + 0.507 + ], + "angle": 0, + "content": "\\[\n\\tilde {F} _ {\\mathrm {L}} = F _ {\\mathrm {L}} \\cdot M _ {\\mathrm {L}} ^ {(l)}, \\quad \\tilde {F} _ {\\mathrm {E}} = F _ {\\mathrm {E}} \\cdot M _ {\\mathrm {E}} ^ {(l)}. \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.517, + 0.47, + 0.565 + ], + "angle": 0, + "content": "To adaptively exchange information between \\(\\tilde{F}_{\\mathrm{L}}\\) and \\(\\tilde{F}_{\\mathrm{E}}\\), they are concatenated and reweighted by a channel attention module [27] \\(\\mathcal{A}\\) to obtain an integrated one \\(\\tilde{F}_{\\mathrm{H}}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.209, + 0.572, + 0.469, + 0.593 + ], + "angle": 0, + "content": "\\[\n\\tilde {F} _ {\\mathrm {H}} = \\mathcal {A} ([ \\tilde {F} _ {\\mathrm {L}}, \\tilde {F} _ {\\mathrm {E}} ]). \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.602, + 0.47, + 0.692 + ], + "angle": 0, + "content": "To better balance the contributions of different modalities, \\(\\tilde{F}_{\\mathrm{E}},\\tilde{F}_{\\mathrm{L}}\\) are reweighted along all dimensions with the weighting maps extracted from \\(\\tilde{F}_{\\mathrm{H}}\\) by weighting layers \\(\\mathcal{W}_{\\mathrm{L}}\\) and \\(\\mathcal{W}_{\\mathrm{E}}\\). Then they are concatenated and fed into a convolutional blending layer \\(\\mathcal{B}\\) to obtain the joint representation for HDR reconstruction:" + }, + { + "type": "equation", + "bbox": [ + 0.134, + 0.702, + 0.469, + 0.722 + ], + "angle": 0, + "content": "\\[\nF _ {\\mathrm {H}} = \\mathcal {B} \\left(\\left[ \\tilde {F} _ {\\mathrm {L}} \\odot \\mathcal {W} _ {\\mathrm {L}} \\left(\\tilde {F} _ {\\mathrm {H}}\\right), \\tilde {F} _ {\\mathrm {E}} \\odot \\mathcal {W} _ {\\mathrm {E}} \\left(\\tilde {F} _ {\\mathrm {H}}\\right) \\right]\\right). \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Temporal context encoding. To alleviate the flickering effects in the generated HDR videos caused by texture mismatching among consecutive event stacks, we exploit the temporal structure within the data via a recurrent convolutional encoder, as shown in Fig. 4. The temporal context encoders \\(\\mathcal{F}_{\\mathrm{E}},\\mathcal{F}_{\\mathrm{L}}\\) learn modality-specific latent representations \\(F_{\\mathrm{E}},F_{\\mathrm{L}}\\) by capturing their underlying temporal structures by a recurrent variant of the encoder in U-Net [62], in which each convolutional layer is replaced by the ConvLSTM [65]. At each timestamp, it outputs the internal state from its own input as well as the encoded past states from" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.136 + ], + "angle": 0, + "content": "its previous input. It can provide more consistent global features of each modality and alleviates flickering effects in the recovered HDR videos." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.137, + 0.892, + 0.258 + ], + "angle": 0, + "content": "The internal states not only preserve temporal correlation between consecutive frames to suppress the flickering effects but also reduce noise in both input modalities, especially in the under-exposed regions. Through the recurrent design of the encoders, the temporal complementary and redundant information through time can be well exploited in the learned latent representations of events and LDR frames for better HDR video reconstruction." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.267, + 0.605, + 0.284 + ], + "angle": 0, + "content": "3.3. Training" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.29, + 0.893, + 0.593 + ], + "angle": 0, + "content": "Dataset preparation. For the training of HDRev-Net, a large amount of triplets \\((\\mathbb{E},\\mathbb{L},\\mathbb{H})\\) are required. There are no readily available datasets containing these triplets nor HDR video datasets with satisfactory scale and quality. To synthesize such a dataset, we collect 733 HDR images from [13, 15, 17, 18, 26, 37, 55, 66, 76] and 110 videos with local motion from [13, 14, 34, 37]. For HDR images, 733 HDR videos with global motion are simulated by generated random camera motion trajectories [5]. From each frame sequence of these videos, the hybrid input of events and LDR frames are simulated by [58] and [12], respectively, like capturing with a virtual camera. To better simulate real LDR images, the LDR frames are generated with randomly sampled CRF, exposure time and Poisson-Gaussian noise [23] for each iteration during training. The event generator [58] also considered the normal distributed thresholds to bridge the gap between real and synthetic. There are a total of 26520 (global motion) + 63754 (local motion) = 90274 frames with a resolution of \\(240\\times 180\\) for training and 5600 frames with a resolution of \\(256\\times 256\\) for testing." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.596, + 0.892, + 0.626 + ], + "angle": 0, + "content": "Loss functions. To train the proposed framework, the loss function to be minimized is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.579, + 0.639, + 0.892, + 0.656 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\alpha_ {1} \\mathcal {L} _ {\\mathrm {m s e}} + \\alpha_ {2} \\mathcal {L} _ {\\text {p e r c}} + \\alpha_ {3} \\mathcal {L} _ {\\text {c o l o r}}, \\tag {15}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.666, + 0.892, + 0.728 + ], + "angle": 0, + "content": "where \\(\\alpha_{1,2,3}\\) are hyper-parameters for balancing different terms. Our goal is to reconstruct HDR frame sequence \\(\\{H_t\\}_{t=1}^T\\), while the prediction of the network \\(\\mathcal{F}\\) is \\(\\{O_t\\}_{t=1}^T\\). The mean square error (MSE) loss \\(\\mathcal{L}_{\\mathrm{mse}}\\) is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.604, + 0.737, + 0.892, + 0.768 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {m s e}} = \\sum_ {t} \\left(\\left\\| H _ {t} - O _ {t} \\right\\| _ {2} ^ {2}\\right). \\tag {16}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.825 + ], + "angle": 0, + "content": "The perceptual loss \\(\\mathcal{L}_{\\mathrm{perc}}\\) is defined based on the feature maps extracted by the VGG-16 [67] network pre-trained on ImageNet [63]:" + }, + { + "type": "equation", + "bbox": [ + 0.534, + 0.836, + 0.892, + 0.906 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {\\text {p e r c}} = \\sum_ {t} \\left(\\sum_ {l} \\left(\\| \\phi_ {l} \\left(H _ {t}\\right) - \\phi_ {l} \\left(O _ {t}\\right) \\| _ {2} ^ {2} \\right. \\right. \\tag {17} \\\\ \\left. + \\left\\| \\mathcal {G} _ {l} ^ {\\phi} (H _ {t}) - \\mathcal {G} _ {l} ^ {\\phi} (O _ {t}) \\| _ {2} ^ {2}\\right)\\right), \\\\ \\end{array}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13928" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.471, + 0.168 + ], + "angle": 0, + "content": "where \\(\\phi_l\\) denotes the feature map extracted from \\(l\\)-th layer of VGG-16, \\(\\mathcal{G}_l^\\phi\\) calculates the Gram matrix of \\(\\phi_l\\). The layer we use in our experiments is \"relu4_3\". To enforce the color appearance of the reconstructed HDR frames to match that in the ground truth, a color loss is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.18, + 0.173, + 0.47, + 0.205 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {c o l o r}} = \\sum_ {t} \\left(\\| \\widetilde {H} _ {t} - \\widetilde {O} _ {t} \\| _ {2} ^ {2}\\right), \\tag {18}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.212, + 0.469, + 0.243 + ], + "angle": 0, + "content": "where \\(\\widetilde{H} = G * H\\) and \\(\\widetilde{O} = G * O\\) are blurred from \\(H, O\\) to eliminate texture and content." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.248, + 0.47, + 0.491 + ], + "angle": 0, + "content": "Other implementation details. We adopt a lightweight variant of recurrent U-Net with 2 downsampling layers in all experiments. The network is unrolled for \\( T = 6 \\) steps during training. It is implemented on the PyTorch framework and runs on an NVIDIA GeForce RTX 3080 GPU. We use ADAM [36] with default parameter setting for optimization. The batch size is set as 1. The learning rate was fixed to \\( 10^{-5} \\) in the earlier epochs and reduced to 0 in the last \\( 40\\% \\) epochs by the linear decay strategy. The number of epochs for pretraining Eq. (7), representation alignment Eq. (8), and training the whole pipeline Eq. (6) are set as 40, 5, 5, respectively. Xavier initialization [20] is used for network initialization. The hyper-parameters in the loss function Eq. (15) are set as \\( \\alpha_{1} = 30 \\), \\( \\alpha_{2} = 5 \\), \\( \\alpha_{3} = 10^{-3} \\). The hyper-parameter \\( \\mu \\) for dynamic range compression Eq. (5) is set as 5000." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.502, + 0.21, + 0.518 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.522, + 0.469, + 0.629 + ], + "angle": 0, + "content": "We compare the proposed HDRev-Net to several state-of-the-art HDR imaging methods, including a frame based HDR image reconstruction method: Liu et al. [44]; the colored variant of an event based HDR reconstruction method: E2VID [60]; two event guided HDR image reconstruction methods: Han et al. [24] and eSL-Net [72]; and two-exposure-based methods [9, 42]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.635, + 0.334, + 0.651 + ], + "angle": 0, + "content": "4.1. Evaluation on synthetic data" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.654, + 0.469, + 0.806 + ], + "angle": 0, + "content": "Metrics. We adopt the HDR-VDP-3 (\"VDP\" for short), the updated version of HDR-VDP [46], to evaluate the quality of reconstructed HDR images frame by frame. For evaluating the quality of HDR videos, we use HDR-VQM [52] (\"VQM\" for short), which is computed based on a spatiotemporal analysis related to human eye fixation behavior during video viewing. We also adopt commonly used peak signal-to-noise ratio (PSNR), structural similarity (SSIM), and the perceptual error with learned perceptual image patch similarity (LPIPS) [78] metrics as reference." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Results. The quantitative results are reported in Table 1. For the two-exposure-based method Li et al. [42], we only calculate the PSNR, SSIM, and LPIPS since it only output tone-mapped HDR images which can not be used to calculate VDP and VQM in the linear domain. We generate two-exposure frame sequences for all the two-exposure-based" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.09, + 0.892, + 0.117 + ], + "angle": 0, + "content": "Table 1. Comparisons on synthetic data. \\(\\uparrow (\\downarrow)\\) means higher (lower) is better." + }, + { + "type": "table", + "bbox": [ + 0.506, + 0.122, + 0.885, + 0.251 + ], + "angle": 0, + "content": "
MethodsPSNR↑SSIM↑LPIPS↓VDP↑VQM↓
eSL-Net [72]16.5750.7130.4135.9030.467
E2VID [60]13.7340.5890.4514.1430.343
Liu et al. [44]23.1590.9010.1047.5430.107
Han et al. [24]20.6970.8610.2086.7090.243
Debevec et al. [9]23.5960.8770.2646.1920.264
Li et al. [42]20.6730.8900.151--
Ours24.0710.9280.1108.1080.103
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.262, + 0.892, + 0.321 + ], + "angle": 0, + "content": "methods with an exposure ratio setting that takes a reasonable balance between the dynamic range covered and the details preserved. The proposed method outperforms existing methods in terms of all metrics." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.322, + 0.893, + 0.61 + ], + "angle": 0, + "content": "The visual quality comparisons are shown in Fig. \\(5^{1}\\). In over/under-exposed regions of the LDR input, most of the details have been lost due to dynamic range clipping. Both frame-based [44] and event-based [60] approaches cannot restore lost information to produce high-quality HDR images. In particular, E2VID [60] produces severe artifacts and distorted color in the reconstructed HDR frames. Han et al. [24] converted one modality into another explicitly (i.e., events to intensity) at first, which leads to stripe-like artifacts and cannot restore natural color appearance. eSL-Net [72] mainly focuses on LDR input and cannot fuse the two modalities well. The performance of Li et al. [42] heavily depends on the selected exposure ratio. As shown in Fig. \\(5^{2}\\), even with the optimal exposure ratio, the results of Li et al. presents insufficient details (e.g., on the stones and windows). In comparison, the HDRev-Net effectively fuses the two modalities of visual information and successfully recovers the lost details, with no need to balance the exposure ratio for varying scenes captured by videos." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.622, + 0.716, + 0.637 + ], + "angle": 0, + "content": "4.2. Evaluation on real data" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.646, + 0.892, + 0.812 + ], + "angle": 0, + "content": "Fig. 6 shows the reconstructed HDR frames on real-world scenarios captured by a hybrid-camera system. We build the hybrid camera system by using a beam-splitter to divide the incident light equivalently into two sensors, i.e., an event camera (DAVIS346 Color) and an industrial camera (FLIR Chameleon 3 Color). Both of them share a similar field of view (FoV). To achieve spatial alignment between the two sensors, we crop the corresponding part of RGB frames w.r.t. the event sensor. With synchronized triggering, the hybrid camera system is able to capture aligned LDR frames and events simultaneously." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.814, + 0.893, + 0.828 + ], + "angle": 0, + "content": "As shown in the HDR frame reconstruction results of" + }, + { + "type": "page_footnote", + "bbox": [ + 0.499, + 0.839, + 0.892, + 0.875 + ], + "angle": 0, + "content": "1We provide results of one method per category due to the space limit. Please refer to the supplementary materials to complete reconstruction results on synthetic data." + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.876, + 0.892, + 0.9 + ], + "angle": 0, + "content": "2The detailed analysis to exposure ratios are shown in supplementary materials." + }, + { + "type": "list", + "bbox": [ + 0.499, + 0.839, + 0.892, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13929" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.092, + 0.887, + 0.346 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.097, + 0.348, + 0.871, + 0.363 + ], + "angle": 0, + "content": "Figure 5. Visual quality comparisons on synthetic data. The Q-scores (higher the better) of VDP metrics are labeled in each image." + }, + { + "type": "image", + "bbox": [ + 0.083, + 0.372, + 0.891, + 0.606 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.107, + 0.608, + 0.861, + 0.622 + ], + "angle": 0, + "content": "Figure 6. Visual quality comparisons on real-world data. The test samples here are under- and over-exposure cases respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.636, + 0.47, + 0.667 + ], + "angle": 0, + "content": "real-world data in Fig. 6, HDRev-Net can reconstruct HDR frames with a wider dynamic range and more details." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.677, + 0.395, + 0.691 + ], + "angle": 0, + "content": "4.3. Results of HDR video reconstruction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.696, + 0.471, + 0.876 + ], + "angle": 0, + "content": "The information lost in over/under-exposed regions of LDR frames is recorded in events. However, it is unstable for HDR video reconstruction since events are triggered with irradiance changes, rather than absolute values as in LDR frames. HDR video reconstruction in a frame-by-frame manner suffers from flickering effects since temporal connections between consecutive frames are not considered. In the proposed method, recurrent architectures are utilized in the encoders to better maintain the model temporal correlation between frames. Thanks to these components, the proposed HDRev-Net effectively suppresses the flickering effects in the reconstructed HDR videos3." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.636, + 0.65, + 0.651 + ], + "angle": 0, + "content": "4.4. Ablation study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.656, + 0.892, + 0.732 + ], + "angle": 0, + "content": "To validate the effectiveness and necessity of the three components of the proposed HDRev-Net, we compare it with its three variants. The quantitative results are shown in Table 2, and the qualitative results are shown in Fig. 3, Fig. 7, Fig. 8, respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Effectiveness of multimodal representation alignment technique. We compare the proposed multimodal representation alignment strategy with joint training the pipeline Eq. (6) in an end-to-end manner, which is denoted by \"Joint training\" in Table 2. It can be seen that a performance drop occurs when the three networks are jointly trained, especially in terms of PSNR. As shown in Fig. 7, there are severe halo artifacts in over-exposed regions of the LDR in the results of \"Joint\" training, especially the contours of the cables and the pylons. Due to the domain gap between LDR frames and stacked events, jointly training" + }, + { + "type": "page_footnote", + "bbox": [ + 0.095, + 0.887, + 0.371, + 0.9 + ], + "angle": 0, + "content": "3Please refer to the supplementary video for details." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "13930" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.09, + 0.47, + 0.117 + ], + "angle": 0, + "content": "Table 2. Results of ablation study. \\(\\uparrow (\\downarrow)\\) means higher (lower) is better." + }, + { + "type": "table", + "bbox": [ + 0.088, + 0.122, + 0.462, + 0.21 + ], + "angle": 0, + "content": "
SettingPSNR↑SSIM↑LPIPS↓VDP↑VQM↓
Joint training22.1850.9110.1627.8710.120
W/o fusion19.4360.8670.2147.0240.175
W/o LSTM21.4630.8910.1977.1660.173
Complete model24.0710.9280.1108.1080.103
" + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.223, + 0.208, + 0.255 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.117, + 0.256, + 0.169, + 0.265 + ], + "angle": 0, + "content": "LDR frame" + }, + { + "type": "image", + "bbox": [ + 0.211, + 0.223, + 0.338, + 0.255 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.245, + 0.256, + 0.303, + 0.266 + ], + "angle": 0, + "content": "Complete \\(H_{L}\\)" + }, + { + "type": "image", + "bbox": [ + 0.342, + 0.223, + 0.469, + 0.255 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.383, + 0.256, + 0.425, + 0.266 + ], + "angle": 0, + "content": "Joint \\(H_{L}\\)" + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.267, + 0.208, + 0.299 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.128, + 0.299, + 0.159, + 0.308 + ], + "angle": 0, + "content": "Events" + }, + { + "type": "image", + "bbox": [ + 0.211, + 0.267, + 0.338, + 0.299 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.245, + 0.299, + 0.303, + 0.308 + ], + "angle": 0, + "content": "Complete \\(H_{E}\\)" + }, + { + "type": "image", + "bbox": [ + 0.342, + 0.267, + 0.469, + 0.299 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.383, + 0.299, + 0.425, + 0.309 + ], + "angle": 0, + "content": "Joint \\(H_{E}\\)" + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.309, + 0.208, + 0.34 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.114, + 0.342, + 0.173, + 0.351 + ], + "angle": 0, + "content": "Ground truth" + }, + { + "type": "image", + "bbox": [ + 0.211, + 0.309, + 0.338, + 0.34 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.246, + 0.341, + 0.301, + 0.351 + ], + "angle": 0, + "content": "Complete \\(H\\)" + }, + { + "type": "image", + "bbox": [ + 0.342, + 0.309, + 0.469, + 0.34 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.387, + 0.341, + 0.421, + 0.351 + ], + "angle": 0, + "content": "Joint \\(H\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.353, + 0.469, + 0.395 + ], + "angle": 0, + "content": "Figure 7. Comparisons between \"Joint\" training and \"Complete\" model. \\( H_{L}(H_{E}) \\) denotes the network output with encoder \\( F_{E} \\) (\\( F_{L} \\)) disabled by setting input to zero." + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.404, + 0.468, + 0.575 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.577, + 0.469, + 0.618 + ], + "angle": 0, + "content": "Figure 8. Comparison between \"W/o LSTM\" and \"Complete\" model. The results of consecutive frames are shown in eight columns. The animations are shown on our project page." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.626, + 0.469, + 0.671 + ], + "angle": 0, + "content": "the whole pipeline cannot well utilize the HDR information in events, which is recorded in a different way from the intensity values in LDR frames." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.675, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Effectiveness of the confidence guided multimodal fusion module. To verify the effectiveness of the proposed confidence guided multimodal fusion module, we replace the fusion module with a convolution layer with kernel size \\(3 \\times 3\\) and \"relu\" activation fed by concatenated \\(F_{\\mathrm{L}}, F_{\\mathrm{E}}\\) in the \"W/o fusion\" variant. As shown in Table 2, its performance is worse than the proposed one in terms of all metrics. As shown in Fig. 3, the proposed module can better leverage the information from both modalities and reconstruct HDR images with more details (e.g., the details of the shrub at the lower-left and the texture of the mountain) and less artifact (e.g., the top-left corner). In comparison, the lost details in over-exposed regions cannot be well restored without the fusion module. The convolution layer lacks the ability to dynamically highlight local regions and feature maps that" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.138 + ], + "angle": 0, + "content": "provide more information from one of the two modalities, which makes the recovering of global characteristics such as color and brightness worse than the proposed one." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.147, + 0.892, + 0.344 + ], + "angle": 0, + "content": "Effectiveness of the temporal context encoding module. We evaluate the contribution of the recurrent connections in the proposed temporal context encoders by removing them in a \"W/o LSTM\" variant. As shown in Table 2, it performs the worst due to the absence of recurrent connections, especially in terms of VQM that reflects the temporal quality of the reconstructed HDR videos. As shown in Fig. 8, information lost in the over-exposed switch (e.g., the flickering effects pointed out by the yellow arrows) can hardly be restored since there is no event at this timestamp. However, the complete model with recurrent connections can recover fine details and textures from the previous frame, which suppresses flickering effects effectively." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.36, + 0.619, + 0.376 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.382, + 0.892, + 0.593 + ], + "angle": 0, + "content": "In this paper, we present a multimodal learning framework for reconstructing HDR videos from hybrid inputs of LDR videos and events. There are three components in the proposed method: a multimodal representation alignment strategy for aligning LDR frames and events in a learned shared latent space, a confidence guided multimodal fusion module for adaptively integrating complementary information from the two modalities, and a temporal context encoding module for suppressing the flickering effects by exploiting the temporal correlation between consecutive frames and stacked events. The effectiveness of the proposed method in the task of event guided HDR video reconstruction is verified by extensive experiments on both synthetic and real-world data." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.603, + 0.892, + 0.8 + ], + "angle": 0, + "content": "Limitations. The proposed method aims at HDR video reconstruction under the guidance of HDR information provided by events. However, events contain inherent noise distributed differently from that of frames, which can lead to artifacts in the reconstructed HDR video, especially in low-light conditions. Moreover, due to the requirement of aligned spatial resolution of the hybrid inputs and low resolution of the chosen event camera (DAVIS346C), the proposed method has a limited ability for high-resolution HDR video reconstruction. Replacing the chosen event camera with a higher resolution one(e.g., Prophesee EVK4-HD with a spatial resolution of \\(720 \\times 1280\\)) and better low-light perception might further improve the performance." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.808, + 0.661, + 0.825 + ], + "angle": 0, + "content": "Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.9 + ], + "angle": 0, + "content": "This work was supported by National Key R&D Program of China (2021ZD0109803) and National Natural Science Foundation of China (Grant No. 62088102, 62136001). Jinxiu Liang was also supported by China Postdoctoral Science Foundation (Grant No. 2022M720236)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "13931" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.184 + ], + "angle": 0, + "content": "[1] Cecilia Aguerrebere, Andres Almansa, Yann Gousseau, Julie Delon, and Pablo Muse. Single shot high dynamic range imaging using piecewise linear estimators. In Proc. of International Conference on Computational Photography, 2014. 1, 2" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.187, + 0.472, + 0.243 + ], + "angle": 0, + "content": "[2] Francesco Banterle, Patrick Ledda, Kurt Debattista, and Alan Chalmers. Inverse tone mapping. 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Given hybrid inputs of (a) LDR video and (b) stacked events, the HDR video can be reconstructed using different methods shown in (c) E2VID [60], (d) Han et al. [24], and (e) the proposed HDRev-Net. The samples here are tested on synthetic data (top row) and real data (bottom row) respectively. The proposed method is able to generate the HDR video with more details and less flickering effects. Please view our project page for corresponding animations. + +![](images/f6209c31ecd7982d88ab9121c52eaa9b2ea4cd43a9f770637ac8c98e2b6e2ceb.jpg) +(d) Han et al. [24] + +![](images/adc3d33b7afdd85ef86bb2407b9e20c0b02b3572f729de7b7f4a9532ccc3b1d1.jpg) +(e) Ours + +# Abstract + +Limited by the trade-off between frame rate and exposure time when capturing moving scenes with conventional cameras, frame based HDR video reconstruction suffers from scene-dependent exposure ratio balancing and ghosting artifacts. Event cameras provide an alternative visual representation with a much higher dynamic range and temporal resolution free from the above issues, which could be an effective guidance for HDR imaging from LDR videos. In this paper, we propose a multimodal learning framework for event guided HDR video reconstruction. In order to better leverage the knowledge of the same scene from the two modalities of visual signals, a multimodal representation alignment strategy to learn a shared latent space and a fusion module tailored to complementing two types of signals for different dynamic ranges in different regions are proposed. Temporal correlations are utilized recurrently to suppress the flickering effects in the reconstructed HDR video. The proposed HDRev-Net demonstrates state-of-the-art performance quantitatively and qualitatively for both synthetic and real-world data. + +# 1. Introduction + +The dynamic range of the real world usually exceeds what a conventional camera and 8-bit image can record by a large margin. High dynamic range (HDR) imaging, which expands the luminance range limited by low dynamic range (LDR) images or videos, is a broadly used technique with extensive applications in photography/videoography, video games, and high-end display. + +Most HDR imaging methods for conventional cameras rely on capturing and merging multiple snapshots with different exposure times [9, 49], which is challenging for capturing videos. There have been enduring efforts for sophisticated modification on conventional frame based cameras to capture multi-exposure sequences (nearly) simultaneously, e.g., beam splitting with three or more sensors [69, 70], temporally [7, 30, 32] or spatially [1, 8, 22, 28, 53, 54] varying exposure. Nevertheless, their abilities for HDR video reconstruction are limited by the trade-off between a higher frame rate (for a smooth viewing experience) and a higher dynamic range (for capturing details in dark regions with + +prolonged exposure time). Moreover, the optimal exposure ratio between LDR frame sequences with different exposure settings is scene-dependent and temporally-varying, whose balancing is difficult for diverse scenes captured in videos. Even worse, moving objects or camera shaking during video capture can lead to ghosting effects in frames generated by long exposure shots. An HDR video could also be hallucinated from LDR inputs in a frame-by-frame manner by leveraging prior knowledge of tone-mapping operators [61] or data modeling powers of deep learning [11]. However, due to the highly ill-posed nature of the hallucination process, it inevitably leads to severe flickering effects. + +In recent years, the event camera [16] has drawn increasing attention of researchers, due to its advantages over conventional frame based ones in sensing fast motions and extended dynamic ranges (e.g., 120dB for DAVIS346). Unlike using multi-exposure frames, events recorded along with an LDR video encode HDR irradiance changes without sacrificing the frame rate/exposure time of the LDR video, which avoids ghosting artifacts as well, and is very promising as guidance for HDR video reconstruction. + +However, integrating events with LDR video for HDR video reconstruction is challenging due to inconsistency between events and frames in three aspects: 1) Modality misalignment: Frames and events are completely different representations of visual information, and "fusing" them by first translating events into intensity values [60,80] like [24] often includes artifacts from solving the ill-posed event integration problem. 2) Dynamic range gap: Performing image/video reconstruction under the guidance of events [75], i.e., doubly integrating events as intensity changes within the exposure time [56,57], ignores the dynamic range clipping in the capturing process of LDR frames, which leads to uncertainties in under/over-exposed regions. 3) Texture mismatching: Regions with smooth textures and slow motion hardly produce effective event observations, which results in inconsistent textures among consecutive event stacks and flickering effects in the reconstructed videos. + +We propose HDRev-Net, a multimodal learning framework for event guided HDR video reconstruction to tackle the challenges by the following strategies: 1) To achieve multimodal representation alignment for the two modalities of the same scene, we propose a learning strategy to progressively project them onto a shared representation space. 2) To reliably complement information from the two modalities in over/under-exposed regions, the representations produced by the two modality-specific encoders are fused for an expressive joint representation using a confidence guided multimodal fusion module. 3) To effectively suppress the flickering effects, we utilize the temporal redundant information between consecutive frames and events via the proposed recurrent convolutional encoders. + +As shown in Fig. 1, HDRev-Net can successfully fuse + +LDR frames and events to obtain HDR frames with more details and less flickering effects. It demonstrates state-of-the-art HDR video reconstruction performance on both synthetic and real data by making the following contributions: + +- We design a multimodal alignment strategy to bridge the gap between events and frames by aligning their representation in a shared latent space. +- We develop a confidence guided fusion module to complement HDR information from events and finer details from well-exposed regions in LDR frames. +- We utilize the temporal correlation from consecutive events and LDR frames in a recurrent fashion to alleviate the flickering effects for recovered HDR videos. + +# 2. Related Work + +Frame based HDR reconstruction. A typical technique for HDR image reconstruction is to merge a stack of bracketed exposure LDR images into an HDR one [9, 49]. Such an idea is also feasible for HDR video reconstruction. Many works [38, 48, 69, 70] proposed to use multiple sensors to capture LDR images with different exposures simultaneously. Besides, there are methods designing spatially varying sensors [1, 8, 22, 28, 53, 54, 71] or using coded exposure by alternating the shutter speed [7, 29, 30, 32, 43]. However, HDR information is obtained at the cost of lowering spatial or temporal resolution in these methods. Moreover, for dynamic scenes, camera shake and moving objects during exposure can lead to ghosting artifacts. To tackle this, recent works [45, 68, 77] introduced attention mechanisms to perform implicit alignment between frames. However, they still heavily rely on fine-grained similarities across frames, which is hard to be captured in varying exposures. + +To avoid ghosting artifacts, Banterle et al. [2] proposed inverse tone mapping to reconstruct the HDR image from a single LDR image, which attempted to hallucinate HDR information in over/under-exposure regions. More recently, many works [6,11,12,19,33,39-41,44,47] attempted to better perform inverse tone mapping via convolutional neural networks (CNNs). However, the problem of hallucinating the lost information in over/under-exposed regions without any physical guidance is too ill-posed to be reliably solved in varying real-world scenarios by these methods. + +Event based HDR reconstruction. Event cameras inherently have a higher dynamic range than conventional ones, which enable direct reconstruction of HDR frames from pure events. Early attempt [35] for intensity reconstruction from events was based on strict assumptions about the scene or motion, e.g., brightness constancy and global rotational movement. Other methods [3, 4] optimized a variational model to reconstruct intensity images. With the help of deep learning, Mostafavi et al. [51, 73] and Wang et al. [74] used generative adversarial networks (GANs) [21] to reconstruct images from events. Rebecq et al. [59, 60] and + +Zou et al. [80] used recurrent convolutional blocks [10, 25] to maintain temporal consistency inside long event streams for video reconstruction. However, these methods suffer from flickering effects and cannot provide stable colored video reconstruction because stream-like events only record the quantized logarithmic irradiance changes of each pixel. It is highly ill-posed to directly reconstruct frames from events without any intensity information as references. + +Event guided HDR reconstruction. Conventional cameras record the irradiance within a limited dynamic range synchronously, while event cameras record the logarithmic irradiance change with a much higher dynamic range asynchronously. Event guided HDR reconstruction combines the best of the two worlds by considering hybrid input of events and frames for reconstructing HDR frames. Wang et al. [72] proposed a sparse learning method along with the integration method [56] to enhance the image quality. Han et al. [24] proposed to reconstruct HDR intensity maps from events first and then fused them with LDR frame in the intensity domain. It is also proposed to guide the fusion of bracketed exposure with events [50,64] for plausible results. However, blurry artifacts are also introduced by the longer exposure of bracketed images. All these works focused on the reconstruction of HDR images. + +For event guided video reconstruction, Wang et al. [75] integrated events to interpolate frames based on [56, 57] and handled the noise and artifacts under simplified assumption by a variant of Kalman filter. However, the integration model [56, 57] ignored the dynamic range clipping of LDR frames, which leads to uncertainties in under/over-exposed regions. In contrast, we propose to integrate the two modalities in a learned shared representation space by leveraging the data modeling power of deep learning. + +# 3. Proposed Method + +# 3.1. Formulation + +Event generation and stacking. An event camera triggers an event $e = (t, p, \sigma)$ at pixel position $p = (p_x, p_y)^\top$ and time $t$ with polarity $\sigma \in \{-1, +1\}$ , when the logarithmic change of irradiance $R$ since the last event at the pixel $p$ and time $t - \delta t$ exceeds a dispatched threshold $\theta$ : + +$$ +\left\| \log R _ {t} ^ {(p)} - \log R _ {t - \delta t} ^ {(p)} \right\| \geq \theta . \tag {1} +$$ + +To process stream-like events using CNNs, we need to convert a stream of events into a fixed size tensor-like representation. We use voxel grid [79] that encodes temporal information in a $C$ -channel 3D-volume. By discretizing duration $\Delta t = t_{K - 1} - t_0$ spanned by $K$ events into $C$ temporal bins, each event $e_k = (t_k,p_k,\sigma_k)$ distributes its polarity $\sigma_{k}$ to the two closest voxels as follows [60]: + +$$ +E _ {t} ^ {(p)} = \sum_ {p _ {k} = p} \sigma_ {k} \max (0, 1 - | t - \tilde {t} _ {k} |), \tag {2} +$$ + +where $\tilde{t}_k\coloneqq \frac{C - 1}{\Delta t} (t_k - t_0)$ is the normalized timestamp. + +LDR image formation. Given the irradiance $R$ and exposure time $\Delta t$ , an HDR image can be represented as $I_{\mathrm{HDR}} = R \cdot \Delta t$ . There are three steps to produce an LDR image: dynamic range clipping, tone mapping with a camera response function (CRF) $f_{\mathrm{CRF}}$ , and quantization: + +$$ +I _ {\mathrm {L D R}} = \left\lfloor 2 5 5 \cdot f _ {\mathrm {C R F}} \left(\max \left(\min \left(I _ {\mathrm {H D R}}, 1\right), 0\right)\right) \right\rfloor / 2 5 5. \tag {3} +$$ + +To align the LDR image and events in the linear irradiance domain, we first convert the LDR image by: + +$$ +L = f _ {\mathrm {C R F}} ^ {- 1} \left(I _ {\mathrm {L D R}}\right) / \Delta t, \tag {4} +$$ + +where $f_{\mathrm{CRF}}^{-1}$ is the inverse CRF. To ease the learning difficulty in regression of values in linear domain spanning a wide range, the range of $I_{\mathrm{HDR}}$ are compressed by [31]: + +$$ +H = \frac {\log (1 + \mu I _ {\mathrm {H D R}})}{\log (1 + \mu)}, \tag {5} +$$ + +where $\mu$ controls the amount of compression. + +# 3.2. HDRev-Net + +Given the stacked event sequence $\mathbb{E} = \{E_t\}_{t=1}^T$ and the corresponding LDR frame sequence $\mathbb{L} = \{L_t\}_{t=1}^T$ of length $T$ , our goal is to reconstruct the HDR frame sequence $\mathbb{H} = \{H_t\}_{t=1}^T$ through a multimodal learning network $\mathcal{F}$ dubbed HDRev-Net. As illustrated in Fig. 2, $\mathcal{F}$ consists of two modality-specific encoders $\mathcal{F}_{\mathrm{L}}$ and $\mathcal{F}_{\mathrm{E}}$ for both temporal context encoding and multimodal representation alignment, confidence guided multimodal fusion module $\mathcal{F}_{\mathrm{fusion}}$ and decoder $\mathcal{F}_{\mathrm{H}}$ for HDR video reconstruction from latent representation. Our pipeline can be described as: + +$$ +\mathbb {H} = \mathcal {F} _ {\mathrm {H}} \left(\mathcal {F} _ {\text {f u s i o n}} \left(\mathcal {F} _ {\mathrm {L}} (\mathbb {L}), \mathcal {F} _ {\mathrm {E}} (\mathbb {E})\right). \right. \tag {6} +$$ + +Multimodal representation alignment. Events and LDR frames are two quite different modalities for representing visual information, whose fusion is non-trivial due to distinct low-level statistical properties and highly non-linear relationships between them. Non-learning approaches based on the explicit fusion model [56, 57] may lead to uncertainties in over-exposed regions, while using CNNs to predict HDR frames from the two modalities by direct concatenation or performing event-to-frame translation firstly is ill-posed, which does not consider the differences and complementarities between the two modalities. + +In this paper, we propose to perform implicit fusion by an encoder-decoder network: learning to represent events and LDR frames in a shared latent space by two modality-specific encoders and then integrating them by a fusion module in the bottleneck layer. A straightforward solution is training the two encoders simultaneously for jointly decoding the latent representation into HDR frames. However, due to the modality gap between frames and events, + +![](images/eac4d8bfc70da7a55c6f31d4dab3d7173ecc61244cb45a2894f86156e163cf4f.jpg) + +jointly performing intra-modality (LDR to HDR) and intermodality (event to HDR) reconstruction can lead to a trivial solution: predicting HDR frames from the LDR frames mostly, leaving almost all the stacked events ignored in the training process and heavily relying on LDR frames. + +To effectively utilize the properties of high dynamic range and high frame rate of events, we should find a shared representation space that can well express common and complementary information from events and LDR frames for the subsequent multimodal fusion. To achieve this, we propose a multi-stage approach: performing inter-modality reconstruction from events and then intra-modality reconstruction from LDR frames at first, then jointly training the two encoders and HDR decoder together. + +Specifically, the event encoder $\mathcal{F}_{\mathrm{E}}$ is pretrained to map the input events to a latent representation, which is then decoded to HDR frames by an HDR decoder $\mathcal{F}_{\mathrm{H}}$ : + +$$ +F _ {\mathrm {E}} = \mathcal {F} _ {\mathrm {E}} (\mathbb {E}), \quad \mathbb {H} = \mathcal {F} _ {\mathrm {H}} \left(F _ {\mathrm {E}}\right). \tag {7} +$$ + +In order to project the input LDR frames onto the same latent space for representation alignment, an LDR encoder $\mathcal{F}_{\mathrm{L}}$ is then trained with the parameters of $\mathcal{F}_{\mathrm{H}}$ fixed: + +$$ +F _ {\mathrm {L}} = \mathcal {F} _ {\mathrm {L}} (\mathbb {L}), \quad \mathbb {H} = \mathcal {F} _ {\mathrm {H}} \left(F _ {\mathrm {L}}\right). \tag {8} +$$ + +Thanks to the shared decoder $\mathcal{F}_{\mathrm{H}}$ , the representation of events and LDR frames are aligned in a shared latent space and can then be effectively fused by the proposed event guided HDR video reconstruction pipeline Eq. (6). + +Confidence guided multimodal fusion. As shown in Fig. 2, both manually designed confidence masks and learnable channel-wise attention are used for weighting the intermediate representation $F_{\mathrm{L}}$ , $F_{\mathrm{E}}$ along two separate dimensions, spatial and channel. The manually designed confidence masks emphasize more reliable regions and robustness to inherent noise in data. Intuitively, events are triggered on high contrast edges. The confidence mask for + +![](images/f3199053240b2409ac7eada9e9657ed6724f87b87446054b530abc76187671d1.jpg) +Figure 2. Overview of the proposed HDRev-Net. For multimodal representation alignment, the hybrid inputs of stacked events $\mathbb{E}$ and LDR frames $\mathbb{L}$ are mapped onto a shared representation space by the modality-specific encoders $\mathcal{F}_{\mathrm{E}},\mathcal{F}_{\mathrm{L}}$ , in which recurrent connections are applied for temporal context encoding. Under the guidance of confidence masks $M_E$ and $M_L$ extracted from $\mathbb{E}$ and $\mathbb{L}$ , respectively, their latent representations $F_{\mathrm{E}},F_{\mathrm{L}}$ are then integrated into a joint one $F_{\mathrm{H}}$ by the multimodal fusion module $\mathcal{F}_{\mathrm{fusion}}$ . The HDR decoder $\mathcal{F}_{\mathrm{H}}$ decodes $F_{\mathrm{H}}$ into HDR frame sequence $\mathbb{H}$ eventually. +(a) LDR image $L$ + +![](images/5fb4ae7793ed76e39cf1cc1ad7e5238075e68950ea4d0017d46b45b23734816b.jpg) + +![](images/262842ed992fedd9caeb85cede0fd4b6d4f07c61bf4896164af2bcf8d4b94376.jpg) + +![](images/80ce34af8ce554608cc3e24062b5454ab12e9cbb02d98a402d4bc2611d25aa72.jpg) +(d) LDR mask $M_{L}$ +Figure 3. Visualization of the confidence masks (d) $M_{\mathrm{L}}$ and (e) $M_{\mathrm{E}}$ extracted from (a) LDR frame $L$ and events (b) $E$ , respectively. The HDR reconstruction results are (c) "W/o fusion" and (f) ours. + +![](images/396149e1f7b7a11c24ebf7b89401d83af17295f5c1b8b10d086e0b04416e3c67.jpg) +(b) Event stack $E$ +(e) Event mask $M_E$ + +![](images/a8ffc4cd20af2bb0cde0b9bed5b0b6f285809ac003e805de1e320ad164989764.jpg) +(c) W/o fusion results +(f) Ours result + +events makes the fusion module pay more attention to such regions (an example is shown in Fig. 3 (e)). The confidence mask $M_{\mathrm{E}}$ is defined as: + +$$ +M _ {\mathrm {E}} = \min (G * | E |, 1), \tag {9} +$$ + +where $*$ denotes the convolution operator; $G$ denotes a Gaussian kernel with variance 3 and support $21 \times 21$ , which is used to propagate the influence of the sparsely distributed events to their neighboring regions. + +For LDR frames, irradiance in well-exposed regions is more reliable. The confidence mask $M_{\mathrm{L}}$ for LDR frames (an example is shown in Fig. 3 (d)) is defined as: + +$$ +M _ {\mathrm {L}} = \frac {0 . 5 - \max (| L - 0 . 5 | , \lambda - 0 . 5)}{1 - \lambda}, \tag {10} +$$ + +where $\lambda$ is a hyper-parameter (set as 0.8 in our experiments) that defines the range of values in which reliable pixels lie. + +To guide the fusion of latent representation with a smaller spatial size, we propagate the values of the mask according to the receptive field of each pixel. Specifically, + +![](images/e6102812b1b62a88d0f9d466f38df7dd604584aff8520a7353d2831d264651e4.jpg) +Figure 4. Illustration of the recurrent connections in encoder $\mathcal{F}_{\mathrm{L}}$ (the same structure is used for $\mathcal{F}_{\mathrm{E}}$ ). + +the confidence mask $M^{(l)}$ for reweighing the chosen bottleneck feature $F_{\mathrm{E}}$ , $F_{\mathrm{L}}$ outputted by the $l$ -th layer is defined by the following recursive rule: + +$$ +M ^ {(0)} = M, \quad M ^ {(l)} = G _ {K _ {l}} * M ^ {(l - 1)}, \tag {11} +$$ + +where $G_{K_l}$ denotes a Gaussian kernel with variance 3 and support $K_{l}\times K_{l}$ , whose size is the same as the $l$ -th convolutional layer. Given the confidence masks $M_{\mathrm{L}}^{(l)},M_{\mathrm{E}}^{(l)}$ , the spatially weighted features are obtained by: + +$$ +\tilde {F} _ {\mathrm {L}} = F _ {\mathrm {L}} \cdot M _ {\mathrm {L}} ^ {(l)}, \quad \tilde {F} _ {\mathrm {E}} = F _ {\mathrm {E}} \cdot M _ {\mathrm {E}} ^ {(l)}. \tag {12} +$$ + +To adaptively exchange information between $\tilde{F}_{\mathrm{L}}$ and $\tilde{F}_{\mathrm{E}}$ , they are concatenated and reweighted by a channel attention module [27] $\mathcal{A}$ to obtain an integrated one $\tilde{F}_{\mathrm{H}}$ : + +$$ +\tilde {F} _ {\mathrm {H}} = \mathcal {A} ([ \tilde {F} _ {\mathrm {L}}, \tilde {F} _ {\mathrm {E}} ]). \tag {13} +$$ + +To better balance the contributions of different modalities, $\tilde{F}_{\mathrm{E}},\tilde{F}_{\mathrm{L}}$ are reweighted along all dimensions with the weighting maps extracted from $\tilde{F}_{\mathrm{H}}$ by weighting layers $\mathcal{W}_{\mathrm{L}}$ and $\mathcal{W}_{\mathrm{E}}$ . Then they are concatenated and fed into a convolutional blending layer $\mathcal{B}$ to obtain the joint representation for HDR reconstruction: + +$$ +F _ {\mathrm {H}} = \mathcal {B} \left(\left[ \tilde {F} _ {\mathrm {L}} \odot \mathcal {W} _ {\mathrm {L}} \left(\tilde {F} _ {\mathrm {H}}\right), \tilde {F} _ {\mathrm {E}} \odot \mathcal {W} _ {\mathrm {E}} \left(\tilde {F} _ {\mathrm {H}}\right) \right]\right). \tag {14} +$$ + +Temporal context encoding. To alleviate the flickering effects in the generated HDR videos caused by texture mismatching among consecutive event stacks, we exploit the temporal structure within the data via a recurrent convolutional encoder, as shown in Fig. 4. The temporal context encoders $\mathcal{F}_{\mathrm{E}},\mathcal{F}_{\mathrm{L}}$ learn modality-specific latent representations $F_{\mathrm{E}},F_{\mathrm{L}}$ by capturing their underlying temporal structures by a recurrent variant of the encoder in U-Net [62], in which each convolutional layer is replaced by the ConvLSTM [65]. At each timestamp, it outputs the internal state from its own input as well as the encoded past states from + +its previous input. It can provide more consistent global features of each modality and alleviates flickering effects in the recovered HDR videos. + +The internal states not only preserve temporal correlation between consecutive frames to suppress the flickering effects but also reduce noise in both input modalities, especially in the under-exposed regions. Through the recurrent design of the encoders, the temporal complementary and redundant information through time can be well exploited in the learned latent representations of events and LDR frames for better HDR video reconstruction. + +# 3.3. Training + +Dataset preparation. For the training of HDRev-Net, a large amount of triplets $(\mathbb{E},\mathbb{L},\mathbb{H})$ are required. There are no readily available datasets containing these triplets nor HDR video datasets with satisfactory scale and quality. To synthesize such a dataset, we collect 733 HDR images from [13, 15, 17, 18, 26, 37, 55, 66, 76] and 110 videos with local motion from [13, 14, 34, 37]. For HDR images, 733 HDR videos with global motion are simulated by generated random camera motion trajectories [5]. From each frame sequence of these videos, the hybrid input of events and LDR frames are simulated by [58] and [12], respectively, like capturing with a virtual camera. To better simulate real LDR images, the LDR frames are generated with randomly sampled CRF, exposure time and Poisson-Gaussian noise [23] for each iteration during training. The event generator [58] also considered the normal distributed thresholds to bridge the gap between real and synthetic. There are a total of 26520 (global motion) + 63754 (local motion) = 90274 frames with a resolution of $240\times 180$ for training and 5600 frames with a resolution of $256\times 256$ for testing. + +Loss functions. To train the proposed framework, the loss function to be minimized is defined as: + +$$ +\mathcal {L} = \alpha_ {1} \mathcal {L} _ {\mathrm {m s e}} + \alpha_ {2} \mathcal {L} _ {\text {p e r c}} + \alpha_ {3} \mathcal {L} _ {\text {c o l o r}}, \tag {15} +$$ + +where $\alpha_{1,2,3}$ are hyper-parameters for balancing different terms. Our goal is to reconstruct HDR frame sequence $\{H_t\}_{t=1}^T$ , while the prediction of the network $\mathcal{F}$ is $\{O_t\}_{t=1}^T$ . The mean square error (MSE) loss $\mathcal{L}_{\mathrm{mse}}$ is defined as: + +$$ +\mathcal {L} _ {\mathrm {m s e}} = \sum_ {t} \left(\left\| H _ {t} - O _ {t} \right\| _ {2} ^ {2}\right). \tag {16} +$$ + +The perceptual loss $\mathcal{L}_{\mathrm{perc}}$ is defined based on the feature maps extracted by the VGG-16 [67] network pre-trained on ImageNet [63]: + +$$ +\begin{array}{l} \mathcal {L} _ {\text {p e r c}} = \sum_ {t} \left(\sum_ {l} \left(\| \phi_ {l} \left(H _ {t}\right) - \phi_ {l} \left(O _ {t}\right) \| _ {2} ^ {2} \right. \right. \tag {17} \\ \left. + \left\| \mathcal {G} _ {l} ^ {\phi} (H _ {t}) - \mathcal {G} _ {l} ^ {\phi} (O _ {t}) \| _ {2} ^ {2}\right)\right), \\ \end{array} +$$ + +where $\phi_l$ denotes the feature map extracted from $l$ -th layer of VGG-16, $\mathcal{G}_l^\phi$ calculates the Gram matrix of $\phi_l$ . The layer we use in our experiments is "relu4_3". To enforce the color appearance of the reconstructed HDR frames to match that in the ground truth, a color loss is defined as: + +$$ +\mathcal {L} _ {\text {c o l o r}} = \sum_ {t} \left(\| \widetilde {H} _ {t} - \widetilde {O} _ {t} \| _ {2} ^ {2}\right), \tag {18} +$$ + +where $\widetilde{H} = G * H$ and $\widetilde{O} = G * O$ are blurred from $H, O$ to eliminate texture and content. + +Other implementation details. We adopt a lightweight variant of recurrent U-Net with 2 downsampling layers in all experiments. The network is unrolled for $T = 6$ steps during training. It is implemented on the PyTorch framework and runs on an NVIDIA GeForce RTX 3080 GPU. We use ADAM [36] with default parameter setting for optimization. The batch size is set as 1. The learning rate was fixed to $10^{-5}$ in the earlier epochs and reduced to 0 in the last $40\%$ epochs by the linear decay strategy. The number of epochs for pretraining Eq. (7), representation alignment Eq. (8), and training the whole pipeline Eq. (6) are set as 40, 5, 5, respectively. Xavier initialization [20] is used for network initialization. The hyper-parameters in the loss function Eq. (15) are set as $\alpha_{1} = 30$ , $\alpha_{2} = 5$ , $\alpha_{3} = 10^{-3}$ . The hyper-parameter $\mu$ for dynamic range compression Eq. (5) is set as 5000. + +# 4. Experiments + +We compare the proposed HDRev-Net to several state-of-the-art HDR imaging methods, including a frame based HDR image reconstruction method: Liu et al. [44]; the colored variant of an event based HDR reconstruction method: E2VID [60]; two event guided HDR image reconstruction methods: Han et al. [24] and eSL-Net [72]; and two-exposure-based methods [9, 42]. + +# 4.1. Evaluation on synthetic data + +Metrics. We adopt the HDR-VDP-3 ("VDP" for short), the updated version of HDR-VDP [46], to evaluate the quality of reconstructed HDR images frame by frame. For evaluating the quality of HDR videos, we use HDR-VQM [52] ("VQM" for short), which is computed based on a spatiotemporal analysis related to human eye fixation behavior during video viewing. We also adopt commonly used peak signal-to-noise ratio (PSNR), structural similarity (SSIM), and the perceptual error with learned perceptual image patch similarity (LPIPS) [78] metrics as reference. + +Results. The quantitative results are reported in Table 1. For the two-exposure-based method Li et al. [42], we only calculate the PSNR, SSIM, and LPIPS since it only output tone-mapped HDR images which can not be used to calculate VDP and VQM in the linear domain. We generate two-exposure frame sequences for all the two-exposure-based + +Table 1. Comparisons on synthetic data. $\uparrow (\downarrow)$ means higher (lower) is better. + +
MethodsPSNR↑SSIM↑LPIPS↓VDP↑VQM↓
eSL-Net [72]16.5750.7130.4135.9030.467
E2VID [60]13.7340.5890.4514.1430.343
Liu et al. [44]23.1590.9010.1047.5430.107
Han et al. [24]20.6970.8610.2086.7090.243
Debevec et al. [9]23.5960.8770.2646.1920.264
Li et al. [42]20.6730.8900.151--
Ours24.0710.9280.1108.1080.103
+ +methods with an exposure ratio setting that takes a reasonable balance between the dynamic range covered and the details preserved. The proposed method outperforms existing methods in terms of all metrics. + +The visual quality comparisons are shown in Fig. $5^{1}$ . In over/under-exposed regions of the LDR input, most of the details have been lost due to dynamic range clipping. Both frame-based [44] and event-based [60] approaches cannot restore lost information to produce high-quality HDR images. In particular, E2VID [60] produces severe artifacts and distorted color in the reconstructed HDR frames. Han et al. [24] converted one modality into another explicitly (i.e., events to intensity) at first, which leads to stripe-like artifacts and cannot restore natural color appearance. eSL-Net [72] mainly focuses on LDR input and cannot fuse the two modalities well. The performance of Li et al. [42] heavily depends on the selected exposure ratio. As shown in Fig. $5^{2}$ , even with the optimal exposure ratio, the results of Li et al. presents insufficient details (e.g., on the stones and windows). In comparison, the HDRev-Net effectively fuses the two modalities of visual information and successfully recovers the lost details, with no need to balance the exposure ratio for varying scenes captured by videos. + +# 4.2. Evaluation on real data + +Fig. 6 shows the reconstructed HDR frames on real-world scenarios captured by a hybrid-camera system. We build the hybrid camera system by using a beam-splitter to divide the incident light equivalently into two sensors, i.e., an event camera (DAVIS346 Color) and an industrial camera (FLIR Chameleon 3 Color). Both of them share a similar field of view (FoV). To achieve spatial alignment between the two sensors, we crop the corresponding part of RGB frames w.r.t. the event sensor. With synchronized triggering, the hybrid camera system is able to capture aligned LDR frames and events simultaneously. + +As shown in the HDR frame reconstruction results of + +![](images/a26668fdfa5a88645484e1d2c2df57a6c6241665026f5449215185ec4d594da8.jpg) +Figure 5. Visual quality comparisons on synthetic data. The Q-scores (higher the better) of VDP metrics are labeled in each image. + +![](images/4f3c841ad78485360b5f8daa9f7c3adb689f5c7bea954d4ab5736167dc5a115f.jpg) +Figure 6. Visual quality comparisons on real-world data. The test samples here are under- and over-exposure cases respectively. + +real-world data in Fig. 6, HDRev-Net can reconstruct HDR frames with a wider dynamic range and more details. + +# 4.3. Results of HDR video reconstruction + +The information lost in over/under-exposed regions of LDR frames is recorded in events. However, it is unstable for HDR video reconstruction since events are triggered with irradiance changes, rather than absolute values as in LDR frames. HDR video reconstruction in a frame-by-frame manner suffers from flickering effects since temporal connections between consecutive frames are not considered. In the proposed method, recurrent architectures are utilized in the encoders to better maintain the model temporal correlation between frames. Thanks to these components, the proposed HDRev-Net effectively suppresses the flickering effects in the reconstructed HDR videos3. + +# 4.4. Ablation study + +To validate the effectiveness and necessity of the three components of the proposed HDRev-Net, we compare it with its three variants. The quantitative results are shown in Table 2, and the qualitative results are shown in Fig. 3, Fig. 7, Fig. 8, respectively. + +Effectiveness of multimodal representation alignment technique. We compare the proposed multimodal representation alignment strategy with joint training the pipeline Eq. (6) in an end-to-end manner, which is denoted by "Joint training" in Table 2. It can be seen that a performance drop occurs when the three networks are jointly trained, especially in terms of PSNR. As shown in Fig. 7, there are severe halo artifacts in over-exposed regions of the LDR in the results of "Joint" training, especially the contours of the cables and the pylons. Due to the domain gap between LDR frames and stacked events, jointly training + +Table 2. Results of ablation study. $\uparrow (\downarrow)$ means higher (lower) is better. + +
SettingPSNR↑SSIM↑LPIPS↓VDP↑VQM↓
Joint training22.1850.9110.1627.8710.120
W/o fusion19.4360.8670.2147.0240.175
W/o LSTM21.4630.8910.1977.1660.173
Complete model24.0710.9280.1108.1080.103
+ +![](images/e84d94e0ff01c233bf349cdf60afa73b1191f737a48a3978e580d723e1151eff.jpg) +LDR frame + +![](images/816cd9f9d18df0b162b739e26b8a1c8962dddb492a6c6d17232a9abee4216bc4.jpg) +Complete $H_{L}$ + +![](images/57c87b2dfca74b19dd6c2bcb3ef36dff9d4f521fac4f6dfc4dd6ef5fcc364441.jpg) +Joint $H_{L}$ + +![](images/d7b11b8a839655befb9f56ef257f98bd332952ef1a9dea21f1856a5cce72cc51.jpg) +Events + +![](images/51011cc47425f256148bff18d64be4066de7725684e05a57d6808912ca8f3515.jpg) +Complete $H_{E}$ + +![](images/fec65939e593bc161d05182552689a1b03fd090132b1799cefd0fbebdff07207.jpg) +Joint $H_{E}$ + +![](images/9c23375d5e13591bd0d6ee770a0d49be2134bebe3b59352072d8d43a2b4a0c93.jpg) +Ground truth + +![](images/3d3a7f1863a674d5fb580ed36e10da00cd6d3551f3f61de75be7f4624e801b8a.jpg) +Complete $H$ + +![](images/c0efbcc092ab2c1f0cfdaaca1484cd2377bd27f5eee3d1b8c870e8ce60d2b736.jpg) +Joint $H$ + +![](images/0265deb7681332976ed05e4122d30999a32c25ba63aefa537861d56cfce35660.jpg) +Figure 7. Comparisons between "Joint" training and "Complete" model. $H_{L}(H_{E})$ denotes the network output with encoder $F_{E}$ ( $F_{L}$ ) disabled by setting input to zero. +Figure 8. Comparison between "W/o LSTM" and "Complete" model. The results of consecutive frames are shown in eight columns. The animations are shown on our project page. + +the whole pipeline cannot well utilize the HDR information in events, which is recorded in a different way from the intensity values in LDR frames. + +Effectiveness of the confidence guided multimodal fusion module. To verify the effectiveness of the proposed confidence guided multimodal fusion module, we replace the fusion module with a convolution layer with kernel size $3 \times 3$ and "relu" activation fed by concatenated $F_{\mathrm{L}}, F_{\mathrm{E}}$ in the "W/o fusion" variant. As shown in Table 2, its performance is worse than the proposed one in terms of all metrics. As shown in Fig. 3, the proposed module can better leverage the information from both modalities and reconstruct HDR images with more details (e.g., the details of the shrub at the lower-left and the texture of the mountain) and less artifact (e.g., the top-left corner). In comparison, the lost details in over-exposed regions cannot be well restored without the fusion module. The convolution layer lacks the ability to dynamically highlight local regions and feature maps that + +provide more information from one of the two modalities, which makes the recovering of global characteristics such as color and brightness worse than the proposed one. + +Effectiveness of the temporal context encoding module. We evaluate the contribution of the recurrent connections in the proposed temporal context encoders by removing them in a "W/o LSTM" variant. As shown in Table 2, it performs the worst due to the absence of recurrent connections, especially in terms of VQM that reflects the temporal quality of the reconstructed HDR videos. As shown in Fig. 8, information lost in the over-exposed switch (e.g., the flickering effects pointed out by the yellow arrows) can hardly be restored since there is no event at this timestamp. However, the complete model with recurrent connections can recover fine details and textures from the previous frame, which suppresses flickering effects effectively. + +# 5. Conclusion + +In this paper, we present a multimodal learning framework for reconstructing HDR videos from hybrid inputs of LDR videos and events. There are three components in the proposed method: a multimodal representation alignment strategy for aligning LDR frames and events in a learned shared latent space, a confidence guided multimodal fusion module for adaptively integrating complementary information from the two modalities, and a temporal context encoding module for suppressing the flickering effects by exploiting the temporal correlation between consecutive frames and stacked events. The effectiveness of the proposed method in the task of event guided HDR video reconstruction is verified by extensive experiments on both synthetic and real-world data. + +Limitations. The proposed method aims at HDR video reconstruction under the guidance of HDR information provided by events. However, events contain inherent noise distributed differently from that of frames, which can lead to artifacts in the reconstructed HDR video, especially in low-light conditions. Moreover, due to the requirement of aligned spatial resolution of the hybrid inputs and low resolution of the chosen event camera (DAVIS346C), the proposed method has a limited ability for high-resolution HDR video reconstruction. Replacing the chosen event camera with a higher resolution one(e.g., Prophesee EVK4-HD with a spatial resolution of $720 \times 1280$ ) and better low-light perception might further improve the performance. + +# Acknowledgement + +This work was supported by National Key R&D Program of China (2021ZD0109803) and National Natural Science Foundation of China (Grant No. 62088102, 62136001). Jinxiu Liang was also supported by China Postdoctoral Science Foundation (Grant No. 2022M720236). + +# References + +[1] Cecilia Aguerrebere, Andres Almansa, Yann Gousseau, Julie Delon, and Pablo Muse. Single shot high dynamic range imaging using piecewise linear estimators. 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} + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 271, + 370, + 321, + 379 + ], + "lines": [ + { + "bbox": [ + 271, + 370, + 321, + 379 + ], + "spans": [ + { + "bbox": [ + 271, + 370, + 321, + 379 + ], + "type": "text", + "content": "(c) E2VID [60]" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 380, + 547, + 425 + ], + "lines": [ + { + "bbox": [ + 46, + 380, + 547, + 425 + ], + "spans": [ + { + "bbox": [ + 46, + 380, + 547, + 425 + ], + "type": "text", + "content": "Figure 1. Given hybrid inputs of (a) LDR video and (b) stacked events, the HDR video can be reconstructed using different methods shown in (c) E2VID [60], (d) Han et al. [24], and (e) the proposed HDRev-Net. The samples here are tested on synthetic data (top row) and real data (bottom row) respectively. The proposed method is able to generate the HDR video with more details and less flickering effects. Please view our project page for corresponding animations." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 346, + 198, + 443, + 369 + ], + "blocks": [ + { + "bbox": [ + 346, + 198, + 443, + 369 + ], + "lines": [ + { + "bbox": [ + 346, + 198, + 443, + 369 + ], + "spans": [ + { + "bbox": [ + 346, + 198, + 443, + 369 + ], + "type": "image", + "image_path": "f6209c31ecd7982d88ab9121c52eaa9b2ea4cd43a9f770637ac8c98e2b6e2ceb.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 365, + 370, + 425, + 379 + ], + "lines": [ + { + "bbox": [ + 365, + 370, + 425, + 379 + ], + "spans": [ + { + "bbox": [ + 365, + 370, + 425, + 379 + ], + "type": "text", + "content": "(d) Han et al. [24]" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 444, + 198, + 541, + 369 + ], + "blocks": [ + { + "bbox": [ + 444, + 198, + 541, + 369 + ], + "lines": [ + { + "bbox": [ + 444, + 198, + 541, + 369 + ], + "spans": [ + { + "bbox": [ + 444, + 198, + 541, + 369 + ], + "type": "image", + "image_path": "adc3d33b7afdd85ef86bb2407b9e20c0b02b3572f729de7b7f4a9532ccc3b1d1.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 479, + 370, + 507, + 379 + ], + "lines": [ + { + "bbox": [ + 479, + 370, + 507, + 379 + ], + "spans": [ + { + "bbox": [ + 479, + 370, + 507, + 379 + ], + "type": "text", + "content": "(e) Ours" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 16 + }, + { + "bbox": [ + 143, + 435, + 191, + 447 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 435, + 191, + 447 + ], + "spans": [ + { + "bbox": [ + 143, + 435, + 191, + 447 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 45, + 460, + 289, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 460, + 289, + 700 + ], + "spans": [ + { + "bbox": [ + 45, + 460, + 289, + 700 + ], + "type": "text", + "content": "Limited by the trade-off between frame rate and exposure time when capturing moving scenes with conventional cameras, frame based HDR video reconstruction suffers from scene-dependent exposure ratio balancing and ghosting artifacts. Event cameras provide an alternative visual representation with a much higher dynamic range and temporal resolution free from the above issues, which could be an effective guidance for HDR imaging from LDR videos. In this paper, we propose a multimodal learning framework for event guided HDR video reconstruction. In order to better leverage the knowledge of the same scene from the two modalities of visual signals, a multimodal representation alignment strategy to learn a shared latent space and a fusion module tailored to complementing two types of signals for different dynamic ranges in different regions are proposed. Temporal correlations are utilized recurrently to suppress the flickering effects in the reconstructed HDR video. The proposed HDRev-Net demonstrates state-of-the-art performance quantitatively and qualitatively for both synthetic and real-world data." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 307, + 435, + 386, + 447 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 435, + 386, + 447 + ], + "spans": [ + { + "bbox": [ + 307, + 435, + 386, + 447 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 454, + 545, + 539 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 454, + 545, + 539 + ], + "spans": [ + { + "bbox": [ + 304, + 454, + 545, + 539 + ], + "type": "text", + "content": "The dynamic range of the real world usually exceeds what a conventional camera and 8-bit image can record by a large margin. High dynamic range (HDR) imaging, which expands the luminance range limited by low dynamic range (LDR) images or videos, is a broadly used technique with extensive applications in photography/videoography, video games, and high-end display." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 539, + 546, + 683 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 539, + 546, + 683 + ], + "spans": [ + { + "bbox": [ + 304, + 539, + 546, + 683 + ], + "type": "text", + "content": "Most HDR imaging methods for conventional cameras rely on capturing and merging multiple snapshots with different exposure times [9, 49], which is challenging for capturing videos. There have been enduring efforts for sophisticated modification on conventional frame based cameras to capture multi-exposure sequences (nearly) simultaneously, e.g., beam splitting with three or more sensors [69, 70], temporally [7, 30, 32] or spatially [1, 8, 22, 28, 53, 54] varying exposure. Nevertheless, their abilities for HDR video reconstruction are limited by the trade-off between a higher frame rate (for a smooth viewing experience) and a higher dynamic range (for capturing details in dark regions with" + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 320, + 693, + 400, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 693, + 400, + 703 + ], + "spans": [ + { + "bbox": [ + 320, + 693, + 400, + 703 + ], + "type": "text", + "content": "* Corresponding author" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 320, + 703, + 545, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 703, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 320, + 703, + 545, + 713 + ], + "type": "text", + "content": "Project page: https://yixinyang-00.github.io/HDRev/" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13924" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "text", + "content": "prolonged exposure time). Moreover, the optimal exposure ratio between LDR frame sequences with different exposure settings is scene-dependent and temporally-varying, whose balancing is difficult for diverse scenes captured in videos. Even worse, moving objects or camera shaking during video capture can lead to ghosting effects in frames generated by long exposure shots. An HDR video could also be hallucinated from LDR inputs in a frame-by-frame manner by leveraging prior knowledge of tone-mapping operators [61] or data modeling powers of deep learning [11]. However, due to the highly ill-posed nature of the hallucination process, it inevitably leads to severe flickering effects." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 217, + 289, + 326 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 217, + 289, + 326 + ], + "spans": [ + { + "bbox": [ + 46, + 217, + 289, + 326 + ], + "type": "text", + "content": "In recent years, the event camera [16] has drawn increasing attention of researchers, due to its advantages over conventional frame based ones in sensing fast motions and extended dynamic ranges (e.g., 120dB for DAVIS346). Unlike using multi-exposure frames, events recorded along with an LDR video encode HDR irradiance changes without sacrificing the frame rate/exposure time of the LDR video, which avoids ghosting artifacts as well, and is very promising as guidance for HDR video reconstruction." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 327, + 289, + 531 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 327, + 289, + 531 + ], + "spans": [ + { + "bbox": [ + 46, + 327, + 289, + 531 + ], + "type": "text", + "content": "However, integrating events with LDR video for HDR video reconstruction is challenging due to inconsistency between events and frames in three aspects: 1) Modality misalignment: Frames and events are completely different representations of visual information, and \"fusing\" them by first translating events into intensity values [60,80] like [24] often includes artifacts from solving the ill-posed event integration problem. 2) Dynamic range gap: Performing image/video reconstruction under the guidance of events [75], i.e., doubly integrating events as intensity changes within the exposure time [56,57], ignores the dynamic range clipping in the capturing process of LDR frames, which leads to uncertainties in under/over-exposed regions. 3) Texture mismatching: Regions with smooth textures and slow motion hardly produce effective event observations, which results in inconsistent textures among consecutive event stacks and flickering effects in the reconstructed videos." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 532, + 289, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 532, + 289, + 700 + ], + "spans": [ + { + "bbox": [ + 46, + 532, + 289, + 700 + ], + "type": "text", + "content": "We propose HDRev-Net, a multimodal learning framework for event guided HDR video reconstruction to tackle the challenges by the following strategies: 1) To achieve multimodal representation alignment for the two modalities of the same scene, we propose a learning strategy to progressively project them onto a shared representation space. 2) To reliably complement information from the two modalities in over/under-exposed regions, the representations produced by the two modality-specific encoders are fused for an expressive joint representation using a confidence guided multimodal fusion module. 3) To effectively suppress the flickering effects, we utilize the temporal redundant information between consecutive frames and events via the proposed recurrent convolutional encoders." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 59, + 701, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 701, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 59, + 701, + 288, + 714 + ], + "type": "text", + "content": "As shown in Fig. 1, HDRev-Net can successfully fuse" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": "LDR frames and events to obtain HDR frames with more details and less flickering effects. It demonstrates state-of-the-art HDR video reconstruction performance on both synthetic and real data by making the following contributions:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 317, + 120, + 545, + 225 + ], + "type": "list", + "angle": 0, + "index": 9, + "blocks": [ + { + "bbox": [ + 317, + 120, + 545, + 155 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 120, + 545, + 155 + ], + "spans": [ + { + "bbox": [ + 317, + 120, + 545, + 155 + ], + "type": "text", + "content": "- We design a multimodal alignment strategy to bridge the gap between events and frames by aligning their representation in a shared latent space." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 317, + 156, + 545, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 156, + 545, + 190 + ], + "spans": [ + { + "bbox": [ + 317, + 156, + 545, + 190 + ], + "type": "text", + "content": "- We develop a confidence guided fusion module to complement HDR information from events and finer details from well-exposed regions in LDR frames." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 317, + 190, + 545, + 225 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 190, + 545, + 225 + ], + "spans": [ + { + "bbox": [ + 317, + 190, + 545, + 225 + ], + "type": "text", + "content": "- We utilize the temporal correlation from consecutive events and LDR frames in a recurrent fashion to alleviate the flickering effects for recovered HDR videos." + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 236, + 392, + 249 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 236, + 392, + 249 + ], + "spans": [ + { + "bbox": [ + 306, + 236, + 392, + 249 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 256, + 545, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 256, + 545, + 460 + ], + "spans": [ + { + "bbox": [ + 304, + 256, + 545, + 460 + ], + "type": "text", + "content": "Frame based HDR reconstruction. A typical technique for HDR image reconstruction is to merge a stack of bracketed exposure LDR images into an HDR one [9, 49]. Such an idea is also feasible for HDR video reconstruction. Many works [38, 48, 69, 70] proposed to use multiple sensors to capture LDR images with different exposures simultaneously. Besides, there are methods designing spatially varying sensors [1, 8, 22, 28, 53, 54, 71] or using coded exposure by alternating the shutter speed [7, 29, 30, 32, 43]. However, HDR information is obtained at the cost of lowering spatial or temporal resolution in these methods. Moreover, for dynamic scenes, camera shake and moving objects during exposure can lead to ghosting artifacts. To tackle this, recent works [45, 68, 77] introduced attention mechanisms to perform implicit alignment between frames. However, they still heavily rely on fine-grained similarities across frames, which is hard to be captured in varying exposures." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 460, + 545, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 460, + 545, + 579 + ], + "spans": [ + { + "bbox": [ + 304, + 460, + 545, + 579 + ], + "type": "text", + "content": "To avoid ghosting artifacts, Banterle et al. [2] proposed inverse tone mapping to reconstruct the HDR image from a single LDR image, which attempted to hallucinate HDR information in over/under-exposure regions. More recently, many works [6,11,12,19,33,39-41,44,47] attempted to better perform inverse tone mapping via convolutional neural networks (CNNs). However, the problem of hallucinating the lost information in over/under-exposed regions without any physical guidance is too ill-posed to be reliably solved in varying real-world scenarios by these methods." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": "Event based HDR reconstruction. Event cameras inherently have a higher dynamic range than conventional ones, which enable direct reconstruction of HDR frames from pure events. Early attempt [35] for intensity reconstruction from events was based on strict assumptions about the scene or motion, e.g., brightness constancy and global rotational movement. Other methods [3, 4] optimized a variational model to reconstruct intensity images. With the help of deep learning, Mostafavi et al. [51, 73] and Wang et al. [74] used generative adversarial networks (GANs) [21] to reconstruct images from events. Rebecq et al. [59, 60] and" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13925" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "text", + "content": "Zou et al. [80] used recurrent convolutional blocks [10, 25] to maintain temporal consistency inside long event streams for video reconstruction. However, these methods suffer from flickering effects and cannot provide stable colored video reconstruction because stream-like events only record the quantized logarithmic irradiance changes of each pixel. It is highly ill-posed to directly reconstruct frames from events without any intensity information as references." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 170, + 289, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 170, + 289, + 361 + ], + "spans": [ + { + "bbox": [ + 46, + 170, + 289, + 361 + ], + "type": "text", + "content": "Event guided HDR reconstruction. Conventional cameras record the irradiance within a limited dynamic range synchronously, while event cameras record the logarithmic irradiance change with a much higher dynamic range asynchronously. Event guided HDR reconstruction combines the best of the two worlds by considering hybrid input of events and frames for reconstructing HDR frames. Wang et al. [72] proposed a sparse learning method along with the integration method [56] to enhance the image quality. Han et al. [24] proposed to reconstruct HDR intensity maps from events first and then fused them with LDR frame in the intensity domain. It is also proposed to guide the fusion of bracketed exposure with events [50,64] for plausible results. However, blurry artifacts are also introduced by the longer exposure of bracketed images. All these works focused on the reconstruction of HDR images." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 361, + 289, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 361, + 289, + 469 + ], + "spans": [ + { + "bbox": [ + 46, + 361, + 289, + 469 + ], + "type": "text", + "content": "For event guided video reconstruction, Wang et al. [75] integrated events to interpolate frames based on [56, 57] and handled the noise and artifacts under simplified assumption by a variant of Kalman filter. However, the integration model [56, 57] ignored the dynamic range clipping of LDR frames, which leads to uncertainties in under/over-exposed regions. In contrast, we propose to integrate the two modalities in a learned shared representation space by leveraging the data modeling power of deep learning." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 478, + 153, + 491 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 478, + 153, + 491 + ], + "spans": [ + { + "bbox": [ + 47, + 478, + 153, + 491 + ], + "type": "text", + "content": "3. Proposed Method" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 498, + 129, + 509 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 498, + 129, + 509 + ], + "spans": [ + { + "bbox": [ + 47, + 498, + 129, + 509 + ], + "type": "text", + "content": "3.1. Formulation" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 516, + 287, + 576 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 516, + 287, + 576 + ], + "spans": [ + { + "bbox": [ + 46, + 516, + 287, + 576 + ], + "type": "text", + "content": "Event generation and stacking. An event camera triggers an event " + }, + { + "bbox": [ + 46, + 516, + 287, + 576 + ], + "type": "inline_equation", + "content": "e = (t, p, \\sigma)" + }, + { + "bbox": [ + 46, + 516, + 287, + 576 + ], + "type": "text", + "content": " at pixel position " + }, + { + "bbox": [ + 46, + 516, + 287, + 576 + ], + "type": "inline_equation", + "content": "p = (p_x, p_y)^\\top" + }, + { + "bbox": [ + 46, + 516, + 287, + 576 + ], + "type": "text", + "content": " and time " + }, + { + "bbox": [ + 46, + 516, + 287, + 576 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 516, + 287, + 576 + ], + "type": "text", + "content": " with polarity " + }, + { + "bbox": [ + 46, + 516, + 287, + 576 + ], + "type": "inline_equation", + "content": "\\sigma \\in \\{-1, +1\\}" + }, + { + "bbox": [ + 46, + 516, + 287, + 576 + ], + "type": "text", + "content": ", when the logarithmic change of irradiance " + }, + { + "bbox": [ + 46, + 516, + 287, + 576 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 46, + 516, + 287, + 576 + ], + "type": "text", + "content": " since the last event at the pixel " + }, + { + "bbox": [ + 46, + 516, + 287, + 576 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 46, + 516, + 287, + 576 + ], + "type": "text", + "content": " and time " + }, + { + "bbox": [ + 46, + 516, + 287, + 576 + ], + "type": "inline_equation", + "content": "t - \\delta t" + }, + { + "bbox": [ + 46, + 516, + 287, + 576 + ], + "type": "text", + "content": " exceeds a dispatched threshold " + }, + { + "bbox": [ + 46, + 516, + 287, + 576 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 516, + 287, + 576 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 108, + 581, + 287, + 597 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 581, + 287, + 597 + ], + "spans": [ + { + "bbox": [ + 108, + 581, + 287, + 597 + ], + "type": "interline_equation", + "content": "\\left\\| \\log R _ {t} ^ {(p)} - \\log R _ {t - \\delta t} ^ {(p)} \\right\\| \\geq \\theta . \\tag {1}", + "image_path": "48a83a07cd47f4d95befdf068d1a11ffb5fbb2c41bb2c25121c380ac0727666d.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 601, + 288, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 601, + 288, + 685 + ], + "spans": [ + { + "bbox": [ + 46, + 601, + 288, + 685 + ], + "type": "text", + "content": "To process stream-like events using CNNs, we need to convert a stream of events into a fixed size tensor-like representation. We use voxel grid [79] that encodes temporal information in a " + }, + { + "bbox": [ + 46, + 601, + 288, + 685 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 601, + 288, + 685 + ], + "type": "text", + "content": "-channel 3D-volume. By discretizing duration " + }, + { + "bbox": [ + 46, + 601, + 288, + 685 + ], + "type": "inline_equation", + "content": "\\Delta t = t_{K - 1} - t_0" + }, + { + "bbox": [ + 46, + 601, + 288, + 685 + ], + "type": "text", + "content": " spanned by " + }, + { + "bbox": [ + 46, + 601, + 288, + 685 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 601, + 288, + 685 + ], + "type": "text", + "content": " events into " + }, + { + "bbox": [ + 46, + 601, + 288, + 685 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 601, + 288, + 685 + ], + "type": "text", + "content": " temporal bins, each event " + }, + { + "bbox": [ + 46, + 601, + 288, + 685 + ], + "type": "inline_equation", + "content": "e_k = (t_k,p_k,\\sigma_k)" + }, + { + "bbox": [ + 46, + 601, + 288, + 685 + ], + "type": "text", + "content": " distributes its polarity " + }, + { + "bbox": [ + 46, + 601, + 288, + 685 + ], + "type": "inline_equation", + "content": "\\sigma_{k}" + }, + { + "bbox": [ + 46, + 601, + 288, + 685 + ], + "type": "text", + "content": " to the two closest voxels as follows [60]:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 89, + 689, + 287, + 716 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 89, + 689, + 287, + 716 + ], + "spans": [ + { + "bbox": [ + 89, + 689, + 287, + 716 + ], + "type": "interline_equation", + "content": "E _ {t} ^ {(p)} = \\sum_ {p _ {k} = p} \\sigma_ {k} \\max (0, 1 - | t - \\tilde {t} _ {k} |), \\tag {2}", + "image_path": "3a2cb5b69b8b9bc0b6394052a528c57c95d3699792382bf0e518740b996ab4a9.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 71, + 533, + 86 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 71, + 533, + 86 + ], + "spans": [ + { + "bbox": [ + 305, + 71, + 533, + 86 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 71, + 533, + 86 + ], + "type": "inline_equation", + "content": "\\tilde{t}_k\\coloneqq \\frac{C - 1}{\\Delta t} (t_k - t_0)" + }, + { + "bbox": [ + 305, + 71, + 533, + 86 + ], + "type": "text", + "content": " is the normalized timestamp." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 87, + 545, + 147 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 87, + 545, + 147 + ], + "spans": [ + { + "bbox": [ + 305, + 87, + 545, + 147 + ], + "type": "text", + "content": "LDR image formation. Given the irradiance " + }, + { + "bbox": [ + 305, + 87, + 545, + 147 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 305, + 87, + 545, + 147 + ], + "type": "text", + "content": " and exposure time " + }, + { + "bbox": [ + 305, + 87, + 545, + 147 + ], + "type": "inline_equation", + "content": "\\Delta t" + }, + { + "bbox": [ + 305, + 87, + 545, + 147 + ], + "type": "text", + "content": ", an HDR image can be represented as " + }, + { + "bbox": [ + 305, + 87, + 545, + 147 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{HDR}} = R \\cdot \\Delta t" + }, + { + "bbox": [ + 305, + 87, + 545, + 147 + ], + "type": "text", + "content": ". There are three steps to produce an LDR image: dynamic range clipping, tone mapping with a camera response function (CRF) " + }, + { + "bbox": [ + 305, + 87, + 545, + 147 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{CRF}}" + }, + { + "bbox": [ + 305, + 87, + 545, + 147 + ], + "type": "text", + "content": ", and quantization:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 317, + 155, + 545, + 168 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 155, + 545, + 168 + ], + "spans": [ + { + "bbox": [ + 317, + 155, + 545, + 168 + ], + "type": "interline_equation", + "content": "I _ {\\mathrm {L D R}} = \\left\\lfloor 2 5 5 \\cdot f _ {\\mathrm {C R F}} \\left(\\max \\left(\\min \\left(I _ {\\mathrm {H D R}}, 1\\right), 0\\right)\\right) \\right\\rfloor / 2 5 5. \\tag {3}", + "image_path": "d5f3e80f7e230c0bbc1a997a4bdec0f6e89417de59da78bf747ecae54fc3b11c.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 176, + 545, + 200 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 176, + 545, + 200 + ], + "spans": [ + { + "bbox": [ + 305, + 176, + 545, + 200 + ], + "type": "text", + "content": "To align the LDR image and events in the linear irradiance domain, we first convert the LDR image by:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 381, + 207, + 545, + 222 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 381, + 207, + 545, + 222 + ], + "spans": [ + { + "bbox": [ + 381, + 207, + 545, + 222 + ], + "type": "interline_equation", + "content": "L = f _ {\\mathrm {C R F}} ^ {- 1} \\left(I _ {\\mathrm {L D R}}\\right) / \\Delta t, \\tag {4}", + "image_path": "375d121762d9d9d00e2adb33f7d99ad8cf4ee99258b623d3b0cec2e0c4eb3661.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 228, + 545, + 266 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 228, + 545, + 266 + ], + "spans": [ + { + "bbox": [ + 305, + 228, + 545, + 266 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 228, + 545, + 266 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{CRF}}^{-1}" + }, + { + "bbox": [ + 305, + 228, + 545, + 266 + ], + "type": "text", + "content": " is the inverse CRF. To ease the learning difficulty in regression of values in linear domain spanning a wide range, the range of " + }, + { + "bbox": [ + 305, + 228, + 545, + 266 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{HDR}}" + }, + { + "bbox": [ + 305, + 228, + 545, + 266 + ], + "type": "text", + "content": " are compressed by [31]:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 378, + 272, + 545, + 299 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 378, + 272, + 545, + 299 + ], + "spans": [ + { + "bbox": [ + 378, + 272, + 545, + 299 + ], + "type": "interline_equation", + "content": "H = \\frac {\\log (1 + \\mu I _ {\\mathrm {H D R}})}{\\log (1 + \\mu)}, \\tag {5}", + "image_path": "1ae267f78171fd34dd3d5b8fbcffd0b8f59098dfdab38bed6b1fc40b0510d4fe.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 305, + 490, + 317 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 305, + 490, + 317 + ], + "spans": [ + { + "bbox": [ + 306, + 305, + 490, + 317 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 305, + 490, + 317 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 306, + 305, + 490, + 317 + ], + "type": "text", + "content": " controls the amount of compression." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 324, + 383, + 335 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 324, + 383, + 335 + ], + "spans": [ + { + "bbox": [ + 306, + 324, + 383, + 335 + ], + "type": "text", + "content": "3.2. HDRev-Net" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 337, + 547, + 457 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 337, + 547, + 457 + ], + "spans": [ + { + "bbox": [ + 305, + 337, + 547, + 457 + ], + "type": "text", + "content": "Given the stacked event sequence " + }, + { + "bbox": [ + 305, + 337, + 547, + 457 + ], + "type": "inline_equation", + "content": "\\mathbb{E} = \\{E_t\\}_{t=1}^T" + }, + { + "bbox": [ + 305, + 337, + 547, + 457 + ], + "type": "text", + "content": " and the corresponding LDR frame sequence " + }, + { + "bbox": [ + 305, + 337, + 547, + 457 + ], + "type": "inline_equation", + "content": "\\mathbb{L} = \\{L_t\\}_{t=1}^T" + }, + { + "bbox": [ + 305, + 337, + 547, + 457 + ], + "type": "text", + "content": " of length " + }, + { + "bbox": [ + 305, + 337, + 547, + 457 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 305, + 337, + 547, + 457 + ], + "type": "text", + "content": ", our goal is to reconstruct the HDR frame sequence " + }, + { + "bbox": [ + 305, + 337, + 547, + 457 + ], + "type": "inline_equation", + "content": "\\mathbb{H} = \\{H_t\\}_{t=1}^T" + }, + { + "bbox": [ + 305, + 337, + 547, + 457 + ], + "type": "text", + "content": " through a multimodal learning network " + }, + { + "bbox": [ + 305, + 337, + 547, + 457 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 305, + 337, + 547, + 457 + ], + "type": "text", + "content": " dubbed HDRev-Net. As illustrated in Fig. 2, " + }, + { + "bbox": [ + 305, + 337, + 547, + 457 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 305, + 337, + 547, + 457 + ], + "type": "text", + "content": " consists of two modality-specific encoders " + }, + { + "bbox": [ + 305, + 337, + 547, + 457 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{\\mathrm{L}}" + }, + { + "bbox": [ + 305, + 337, + 547, + 457 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 337, + 547, + 457 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{\\mathrm{E}}" + }, + { + "bbox": [ + 305, + 337, + 547, + 457 + ], + "type": "text", + "content": " for both temporal context encoding and multimodal representation alignment, confidence guided multimodal fusion module " + }, + { + "bbox": [ + 305, + 337, + 547, + 457 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{\\mathrm{fusion}}" + }, + { + "bbox": [ + 305, + 337, + 547, + 457 + ], + "type": "text", + "content": " and decoder " + }, + { + "bbox": [ + 305, + 337, + 547, + 457 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{\\mathrm{H}}" + }, + { + "bbox": [ + 305, + 337, + 547, + 457 + ], + "type": "text", + "content": " for HDR video reconstruction from latent representation. Our pipeline can be described as:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 358, + 465, + 545, + 479 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 358, + 465, + 545, + 479 + ], + "spans": [ + { + "bbox": [ + 358, + 465, + 545, + 479 + ], + "type": "interline_equation", + "content": "\\mathbb {H} = \\mathcal {F} _ {\\mathrm {H}} \\left(\\mathcal {F} _ {\\text {f u s i o n}} \\left(\\mathcal {F} _ {\\mathrm {L}} (\\mathbb {L}), \\mathcal {F} _ {\\mathrm {E}} (\\mathbb {E})\\right). \\right. \\tag {6}", + "image_path": "9e2495f9b582a7849fc651ad5321fed0dcc43b1ad21a3a82f43bf78b6bac0706.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 486, + 545, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 486, + 545, + 617 + ], + "spans": [ + { + "bbox": [ + 305, + 486, + 545, + 617 + ], + "type": "text", + "content": "Multimodal representation alignment. Events and LDR frames are two quite different modalities for representing visual information, whose fusion is non-trivial due to distinct low-level statistical properties and highly non-linear relationships between them. Non-learning approaches based on the explicit fusion model [56, 57] may lead to uncertainties in over-exposed regions, while using CNNs to predict HDR frames from the two modalities by direct concatenation or performing event-to-frame translation firstly is ill-posed, which does not consider the differences and complementarities between the two modalities." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": "In this paper, we propose to perform implicit fusion by an encoder-decoder network: learning to represent events and LDR frames in a shared latent space by two modality-specific encoders and then integrating them by a fusion module in the bottleneck layer. A straightforward solution is training the two encoders simultaneously for jointly decoding the latent representation into HDR frames. However, due to the modality gap between frames and events," + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "13926" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 70, + 547, + 205 + ], + "blocks": [ + { + "bbox": [ + 48, + 70, + 547, + 205 + ], + "lines": [ + { + "bbox": [ + 48, + 70, + 547, + 205 + ], + "spans": [ + { + "bbox": [ + 48, + 70, + 547, + 205 + ], + "type": "image", + "image_path": "eac4d8bfc70da7a55c6f31d4dab3d7173ecc61244cb45a2894f86156e163cf4f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 271, + 287, + 331 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 271, + 287, + 331 + ], + "spans": [ + { + "bbox": [ + 46, + 271, + 287, + 331 + ], + "type": "text", + "content": "jointly performing intra-modality (LDR to HDR) and intermodality (event to HDR) reconstruction can lead to a trivial solution: predicting HDR frames from the LDR frames mostly, leaving almost all the stacked events ignored in the training process and heavily relying on LDR frames." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 331, + 287, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 331, + 287, + 437 + ], + "spans": [ + { + "bbox": [ + 46, + 331, + 287, + 437 + ], + "type": "text", + "content": "To effectively utilize the properties of high dynamic range and high frame rate of events, we should find a shared representation space that can well express common and complementary information from events and LDR frames for the subsequent multimodal fusion. To achieve this, we propose a multi-stage approach: performing inter-modality reconstruction from events and then intra-modality reconstruction from LDR frames at first, then jointly training the two encoders and HDR decoder together." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 438, + 287, + 475 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 438, + 287, + 475 + ], + "spans": [ + { + "bbox": [ + 46, + 438, + 287, + 475 + ], + "type": "text", + "content": "Specifically, the event encoder " + }, + { + "bbox": [ + 46, + 438, + 287, + 475 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{\\mathrm{E}}" + }, + { + "bbox": [ + 46, + 438, + 287, + 475 + ], + "type": "text", + "content": " is pretrained to map the input events to a latent representation, which is then decoded to HDR frames by an HDR decoder " + }, + { + "bbox": [ + 46, + 438, + 287, + 475 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{\\mathrm{H}}" + }, + { + "bbox": [ + 46, + 438, + 287, + 475 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 482, + 287, + 496 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 482, + 287, + 496 + ], + "spans": [ + { + "bbox": [ + 105, + 482, + 287, + 496 + ], + "type": "interline_equation", + "content": "F _ {\\mathrm {E}} = \\mathcal {F} _ {\\mathrm {E}} (\\mathbb {E}), \\quad \\mathbb {H} = \\mathcal {F} _ {\\mathrm {H}} \\left(F _ {\\mathrm {E}}\\right). \\tag {7}", + "image_path": "fe536e24c55c38cf6fc6f77f6c85974a1a301271fe70f5e9fe3703ba678a5cde.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 502, + 287, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 502, + 287, + 540 + ], + "spans": [ + { + "bbox": [ + 47, + 502, + 287, + 540 + ], + "type": "text", + "content": "In order to project the input LDR frames onto the same latent space for representation alignment, an LDR encoder " + }, + { + "bbox": [ + 47, + 502, + 287, + 540 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{\\mathrm{L}}" + }, + { + "bbox": [ + 47, + 502, + 287, + 540 + ], + "type": "text", + "content": " is then trained with the parameters of " + }, + { + "bbox": [ + 47, + 502, + 287, + 540 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{\\mathrm{H}}" + }, + { + "bbox": [ + 47, + 502, + 287, + 540 + ], + "type": "text", + "content": " fixed:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 550, + 287, + 563 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 550, + 287, + 563 + ], + "spans": [ + { + "bbox": [ + 105, + 550, + 287, + 563 + ], + "type": "interline_equation", + "content": "F _ {\\mathrm {L}} = \\mathcal {F} _ {\\mathrm {L}} (\\mathbb {L}), \\quad \\mathbb {H} = \\mathcal {F} _ {\\mathrm {H}} \\left(F _ {\\mathrm {L}}\\right). \\tag {8}", + "image_path": "149c4b4d3867a3417eeb095937d0d5743cabb6254a2d4fb447943fd95a268410.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 567, + 287, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 567, + 287, + 616 + ], + "spans": [ + { + "bbox": [ + 46, + 567, + 287, + 616 + ], + "type": "text", + "content": "Thanks to the shared decoder " + }, + { + "bbox": [ + 46, + 567, + 287, + 616 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{\\mathrm{H}}" + }, + { + "bbox": [ + 46, + 567, + 287, + 616 + ], + "type": "text", + "content": ", the representation of events and LDR frames are aligned in a shared latent space and can then be effectively fused by the proposed event guided HDR video reconstruction pipeline Eq. (6)." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "text", + "content": "Confidence guided multimodal fusion. As shown in Fig. 2, both manually designed confidence masks and learnable channel-wise attention are used for weighting the intermediate representation " + }, + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "inline_equation", + "content": "F_{\\mathrm{L}}" + }, + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "inline_equation", + "content": "F_{\\mathrm{E}}" + }, + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "text", + "content": " along two separate dimensions, spatial and channel. The manually designed confidence masks emphasize more reliable regions and robustness to inherent noise in data. Intuitively, events are triggered on high contrast edges. The confidence mask for" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 310, + 264, + 399, + 330 + ], + "blocks": [ + { + "bbox": [ + 46, + 209, + 547, + 264 + ], + "lines": [ + { + "bbox": [ + 46, + 209, + 547, + 264 + ], + "spans": [ + { + "bbox": [ + 46, + 209, + 547, + 264 + ], + "type": "text", + "content": "Figure 2. Overview of the proposed HDRev-Net. For multimodal representation alignment, the hybrid inputs of stacked events " + }, + { + "bbox": [ + 46, + 209, + 547, + 264 + ], + "type": "inline_equation", + "content": "\\mathbb{E}" + }, + { + "bbox": [ + 46, + 209, + 547, + 264 + ], + "type": "text", + "content": " and LDR frames " + }, + { + "bbox": [ + 46, + 209, + 547, + 264 + ], + "type": "inline_equation", + "content": "\\mathbb{L}" + }, + { + "bbox": [ + 46, + 209, + 547, + 264 + ], + "type": "text", + "content": " are mapped onto a shared representation space by the modality-specific encoders " + }, + { + "bbox": [ + 46, + 209, + 547, + 264 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{\\mathrm{E}},\\mathcal{F}_{\\mathrm{L}}" + }, + { + "bbox": [ + 46, + 209, + 547, + 264 + ], + "type": "text", + "content": " , in which recurrent connections are applied for temporal context encoding. Under the guidance of confidence masks " + }, + { + "bbox": [ + 46, + 209, + 547, + 264 + ], + "type": "inline_equation", + "content": "M_E" + }, + { + "bbox": [ + 46, + 209, + 547, + 264 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 209, + 547, + 264 + ], + "type": "inline_equation", + "content": "M_L" + }, + { + "bbox": [ + 46, + 209, + 547, + 264 + ], + "type": "text", + "content": " extracted from " + }, + { + "bbox": [ + 46, + 209, + 547, + 264 + ], + "type": "inline_equation", + "content": "\\mathbb{E}" + }, + { + "bbox": [ + 46, + 209, + 547, + 264 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 209, + 547, + 264 + ], + "type": "inline_equation", + "content": "\\mathbb{L}" + }, + { + "bbox": [ + 46, + 209, + 547, + 264 + ], + "type": "text", + "content": " , respectively, their latent representations " + }, + { + "bbox": [ + 46, + 209, + 547, + 264 + ], + "type": "inline_equation", + "content": "F_{\\mathrm{E}},F_{\\mathrm{L}}" + }, + { + "bbox": [ + 46, + 209, + 547, + 264 + ], + "type": "text", + "content": " are then integrated into a joint one " + }, + { + "bbox": [ + 46, + 209, + 547, + 264 + ], + "type": "inline_equation", + "content": "F_{\\mathrm{H}}" + }, + { + "bbox": [ + 46, + 209, + 547, + 264 + ], + "type": "text", + "content": " by the multimodal fusion module " + }, + { + "bbox": [ + 46, + 209, + 547, + 264 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{\\mathrm{fusion}}" + }, + { + "bbox": [ + 46, + 209, + 547, + 264 + ], + "type": "text", + "content": " . 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Visualization of the confidence masks (d) " + }, + { + "bbox": [ + 305, + 416, + 545, + 449 + ], + "type": "inline_equation", + "content": "M_{\\mathrm{L}}" + }, + { + "bbox": [ + 305, + 416, + 545, + 449 + ], + "type": "text", + "content": " and (e) " + }, + { + "bbox": [ + 305, + 416, + 545, + 449 + ], + "type": "inline_equation", + "content": "M_{\\mathrm{E}}" + }, + { + "bbox": [ + 305, + 416, + 545, + 449 + ], + "type": "text", + "content": " extracted from (a) LDR frame " + }, + { + "bbox": [ + 305, + 416, + 545, + 449 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 305, + 416, + 545, + 449 + ], + "type": "text", + "content": " and events (b) " + }, + { + "bbox": [ + 305, + 416, + 545, + 449 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 305, + 416, + 545, + 449 + ], + "type": "text", + "content": ", respectively. The HDR reconstruction results are (c) \"W/o fusion\" and (f) ours." + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_caption" + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 404, + 338, + 470, + 403 + ], + "blocks": [ + { + "bbox": [ + 413, + 331, + 462, + 338 + ], + "lines": [ + { + "bbox": [ + 413, + 331, + 462, + 338 + ], + "spans": [ + { + "bbox": [ + 413, + 331, + 462, + 338 + ], + "type": "text", + "content": "(b) Event stack " + }, + { + "bbox": [ + 413, + 331, + 462, + 338 + ], + "type": "inline_equation", + "content": "E" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 404, + 338, + 470, + 403 + ], + "lines": [ + { + "bbox": [ + 404, + 338, + 470, + 403 + ], + "spans": [ + { + "bbox": [ + 404, + 338, + 470, + 403 + ], + "type": "image", + "image_path": "396149e1f7b7a11c24ebf7b89401d83af17295f5c1b8b10d086e0b04416e3c67.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 410, + 404, + 463, + 413 + ], + "lines": [ + { + "bbox": [ + 410, + 404, + 463, + 413 + ], + "spans": [ + { + "bbox": [ + 410, + 404, + 463, + 413 + ], + "type": "text", + "content": "(e) Event mask " + }, + { + "bbox": [ + 410, + 404, + 463, + 413 + ], + "type": "inline_equation", + "content": "M_E" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + } + ], + "index": 18 + }, + { + "type": "image", + "bbox": [ + 476, + 338, + 542, + 403 + ], + "blocks": [ + { + "bbox": [ + 479, + 331, + 539, + 338 + ], + "lines": [ + { + "bbox": [ + 479, + 331, + 539, + 338 + ], + "spans": [ + { + "bbox": [ + 479, + 331, + 539, + 338 + ], + "type": "text", + "content": "(c) W/o fusion results" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 476, + 338, + 542, + 403 + ], + "lines": [ + { + "bbox": [ + 476, + 338, + 542, + 403 + ], + "spans": [ + { + "bbox": [ + 476, + 338, + 542, + 403 + ], + "type": "image", + "image_path": "a8ffc4cd20af2bb0cde0b9bed5b0b6f285809ac003e805de1e320ad164989764.jpg" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 488, + 404, + 529, + 412 + ], + "lines": [ + { + "bbox": [ + 488, + 404, + 529, + 412 + ], + "spans": [ + { + "bbox": [ + 488, + 404, + 529, + 412 + ], + "type": "text", + "content": "(f) Ours result" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_caption" + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 457, + 545, + 493 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 457, + 545, + 493 + ], + "spans": [ + { + "bbox": [ + 305, + 457, + 545, + 493 + ], + "type": "text", + "content": "events makes the fusion module pay more attention to such regions (an example is shown in Fig. 3 (e)). The confidence mask " + }, + { + "bbox": [ + 305, + 457, + 545, + 493 + ], + "type": "inline_equation", + "content": "M_{\\mathrm{E}}" + }, + { + "bbox": [ + 305, + 457, + 545, + 493 + ], + "type": "text", + "content": " is defined as:" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 376, + 503, + 545, + 517 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 376, + 503, + 545, + 517 + ], + "spans": [ + { + "bbox": [ + 376, + 503, + 545, + 517 + ], + "type": "interline_equation", + "content": "M _ {\\mathrm {E}} = \\min (G * | E |, 1), \\tag {9}", + "image_path": "98294ca0e548f5a618e3299812bd894cbbaed2c24ef1813407686784801ace49.jpg" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 527, + 545, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 527, + 545, + 574 + ], + "spans": [ + { + "bbox": [ + 304, + 527, + 545, + 574 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 527, + 545, + 574 + ], + "type": "inline_equation", + "content": "*" + }, + { + "bbox": [ + 304, + 527, + 545, + 574 + ], + "type": "text", + "content": " denotes the convolution operator; " + }, + { + "bbox": [ + 304, + 527, + 545, + 574 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 304, + 527, + 545, + 574 + ], + "type": "text", + "content": " denotes a Gaussian kernel with variance 3 and support " + }, + { + "bbox": [ + 304, + 527, + 545, + 574 + ], + "type": "inline_equation", + "content": "21 \\times 21" + }, + { + "bbox": [ + 304, + 527, + 545, + 574 + ], + "type": "text", + "content": ", which is used to propagate the influence of the sparsely distributed events to their neighboring regions." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 304, + 574, + 545, + 611 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 574, + 545, + 611 + ], + "spans": [ + { + "bbox": [ + 304, + 574, + 545, + 611 + ], + "type": "text", + "content": "For LDR frames, irradiance in well-exposed regions is more reliable. The confidence mask " + }, + { + "bbox": [ + 304, + 574, + 545, + 611 + ], + "type": "inline_equation", + "content": "M_{\\mathrm{L}}" + }, + { + "bbox": [ + 304, + 574, + 545, + 611 + ], + "type": "text", + "content": " for LDR frames (an example is shown in Fig. 3 (d)) is defined as:" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 345, + 619, + 545, + 644 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 345, + 619, + 545, + 644 + ], + "spans": [ + { + "bbox": [ + 345, + 619, + 545, + 644 + ], + "type": "interline_equation", + "content": "M _ {\\mathrm {L}} = \\frac {0 . 5 - \\max (| L - 0 . 5 | , \\lambda - 0 . 5)}{1 - \\lambda}, \\tag {10}", + "image_path": "d6b5489c45c78ed2ec58f002bb730d7b255c5eb82b257ce6d6b7bb06b4fd367b.jpg" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 304, + 653, + 545, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 545, + 677 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 545, + 677 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 653, + 545, + 677 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 304, + 653, + 545, + 677 + ], + "type": "text", + "content": " is a hyper-parameter (set as 0.8 in our experiments) that defines the range of values in which reliable pixels lie." + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 304, + 677, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 714 + ], + "type": "text", + "content": "To guide the fusion of latent representation with a smaller spatial size, we propagate the values of the mask according to the receptive field of each pixel. Specifically," + } + ] + } + ], + "index": 29 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13927" + } + ] + } + ], + "index": 30 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 76, + 277, + 227 + ], + "blocks": [ + { + "bbox": [ + 49, + 76, + 277, + 227 + ], + "lines": [ + { + "bbox": [ + 49, + 76, + 277, + 227 + ], + "spans": [ + { + "bbox": [ + 49, + 76, + 277, + 227 + ], + "type": "image", + "image_path": "e6102812b1b62a88d0f9d466f38df7dd604584aff8520a7353d2831d264651e4.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 230, + 286, + 253 + ], + "lines": [ + { + "bbox": [ + 46, + 230, + 286, + 253 + ], + "spans": [ + { + "bbox": [ + 46, + 230, + 286, + 253 + ], + "type": "text", + "content": "Figure 4. Illustration of the recurrent connections in encoder " + }, + { + "bbox": [ + 46, + 230, + 286, + 253 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{\\mathrm{L}}" + }, + { + "bbox": [ + 46, + 230, + 286, + 253 + ], + "type": "text", + "content": " (the same structure is used for " + }, + { + "bbox": [ + 46, + 230, + 286, + 253 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{\\mathrm{E}}" + }, + { + "bbox": [ + 46, + 230, + 286, + 253 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 259, + 288, + 297 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 259, + 288, + 297 + ], + "spans": [ + { + "bbox": [ + 46, + 259, + 288, + 297 + ], + "type": "text", + "content": "the confidence mask " + }, + { + "bbox": [ + 46, + 259, + 288, + 297 + ], + "type": "inline_equation", + "content": "M^{(l)}" + }, + { + "bbox": [ + 46, + 259, + 288, + 297 + ], + "type": "text", + "content": " for reweighing the chosen bottleneck feature " + }, + { + "bbox": [ + 46, + 259, + 288, + 297 + ], + "type": "inline_equation", + "content": "F_{\\mathrm{E}}" + }, + { + "bbox": [ + 46, + 259, + 288, + 297 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 259, + 288, + 297 + ], + "type": "inline_equation", + "content": "F_{\\mathrm{L}}" + }, + { + "bbox": [ + 46, + 259, + 288, + 297 + ], + "type": "text", + "content": " outputted by the " + }, + { + "bbox": [ + 46, + 259, + 288, + 297 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 46, + 259, + 288, + 297 + ], + "type": "text", + "content": "-th layer is defined by the following recursive rule:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 89, + 303, + 287, + 319 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 89, + 303, + 287, + 319 + ], + "spans": [ + { + "bbox": [ + 89, + 303, + 287, + 319 + ], + "type": "interline_equation", + "content": "M ^ {(0)} = M, \\quad M ^ {(l)} = G _ {K _ {l}} * M ^ {(l - 1)}, \\tag {11}", + "image_path": "fc29011b19dbbb961fb036b96c53ec32116f4af66d55bb04ed5a84c2c6eca8a6.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 327, + 287, + 377 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 327, + 287, + 377 + ], + "spans": [ + { + "bbox": [ + 46, + 327, + 287, + 377 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 327, + 287, + 377 + ], + "type": "inline_equation", + "content": "G_{K_l}" + }, + { + "bbox": [ + 46, + 327, + 287, + 377 + ], + "type": "text", + "content": " denotes a Gaussian kernel with variance 3 and support " + }, + { + "bbox": [ + 46, + 327, + 287, + 377 + ], + "type": "inline_equation", + "content": "K_{l}\\times K_{l}" + }, + { + "bbox": [ + 46, + 327, + 287, + 377 + ], + "type": "text", + "content": ", whose size is the same as the " + }, + { + "bbox": [ + 46, + 327, + 287, + 377 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 46, + 327, + 287, + 377 + ], + "type": "text", + "content": "-th convolutional layer. Given the confidence masks " + }, + { + "bbox": [ + 46, + 327, + 287, + 377 + ], + "type": "inline_equation", + "content": "M_{\\mathrm{L}}^{(l)},M_{\\mathrm{E}}^{(l)}" + }, + { + "bbox": [ + 46, + 327, + 287, + 377 + ], + "type": "text", + "content": ", the spatially weighted features are obtained by:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 93, + 384, + 287, + 401 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 93, + 384, + 287, + 401 + ], + "spans": [ + { + "bbox": [ + 93, + 384, + 287, + 401 + ], + "type": "interline_equation", + "content": "\\tilde {F} _ {\\mathrm {L}} = F _ {\\mathrm {L}} \\cdot M _ {\\mathrm {L}} ^ {(l)}, \\quad \\tilde {F} _ {\\mathrm {E}} = F _ {\\mathrm {E}} \\cdot M _ {\\mathrm {E}} ^ {(l)}. \\tag {12}", + "image_path": "73a9f20a05f09639f660d176b3daf55b66a07a022c17f4fe6ea50210d909b7de.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 409, + 287, + 447 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 409, + 287, + 447 + ], + "spans": [ + { + "bbox": [ + 46, + 409, + 287, + 447 + ], + "type": "text", + "content": "To adaptively exchange information between " + }, + { + "bbox": [ + 46, + 409, + 287, + 447 + ], + "type": "inline_equation", + "content": "\\tilde{F}_{\\mathrm{L}}" + }, + { + "bbox": [ + 46, + 409, + 287, + 447 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 409, + 287, + 447 + ], + "type": "inline_equation", + "content": "\\tilde{F}_{\\mathrm{E}}" + }, + { + "bbox": [ + 46, + 409, + 287, + 447 + ], + "type": "text", + "content": ", they are concatenated and reweighted by a channel attention module [27] " + }, + { + "bbox": [ + 46, + 409, + 287, + 447 + ], + "type": "inline_equation", + "content": "\\mathcal{A}" + }, + { + "bbox": [ + 46, + 409, + 287, + 447 + ], + "type": "text", + "content": " to obtain an integrated one " + }, + { + "bbox": [ + 46, + 409, + 287, + 447 + ], + "type": "inline_equation", + "content": "\\tilde{F}_{\\mathrm{H}}" + }, + { + "bbox": [ + 46, + 409, + 287, + 447 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 127, + 453, + 287, + 469 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 127, + 453, + 287, + 469 + ], + "spans": [ + { + "bbox": [ + 127, + 453, + 287, + 469 + ], + "type": "interline_equation", + "content": "\\tilde {F} _ {\\mathrm {H}} = \\mathcal {A} ([ \\tilde {F} _ {\\mathrm {L}}, \\tilde {F} _ {\\mathrm {E}} ]). \\tag {13}", + "image_path": "071f83cb51ab8befa0b47d819860fa52253223d0ce16a7a866dd1f9fc3c2ea81.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 476, + 287, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 476, + 287, + 548 + ], + "spans": [ + { + "bbox": [ + 46, + 476, + 287, + 548 + ], + "type": "text", + "content": "To better balance the contributions of different modalities, " + }, + { + "bbox": [ + 46, + 476, + 287, + 548 + ], + "type": "inline_equation", + "content": "\\tilde{F}_{\\mathrm{E}},\\tilde{F}_{\\mathrm{L}}" + }, + { + "bbox": [ + 46, + 476, + 287, + 548 + ], + "type": "text", + "content": " are reweighted along all dimensions with the weighting maps extracted from " + }, + { + "bbox": [ + 46, + 476, + 287, + 548 + ], + "type": "inline_equation", + "content": "\\tilde{F}_{\\mathrm{H}}" + }, + { + "bbox": [ + 46, + 476, + 287, + 548 + ], + "type": "text", + "content": " by weighting layers " + }, + { + "bbox": [ + 46, + 476, + 287, + 548 + ], + "type": "inline_equation", + "content": "\\mathcal{W}_{\\mathrm{L}}" + }, + { + "bbox": [ + 46, + 476, + 287, + 548 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 476, + 287, + 548 + ], + "type": "inline_equation", + "content": "\\mathcal{W}_{\\mathrm{E}}" + }, + { + "bbox": [ + 46, + 476, + 287, + 548 + ], + "type": "text", + "content": ". Then they are concatenated and fed into a convolutional blending layer " + }, + { + "bbox": [ + 46, + 476, + 287, + 548 + ], + "type": "inline_equation", + "content": "\\mathcal{B}" + }, + { + "bbox": [ + 46, + 476, + 287, + 548 + ], + "type": "text", + "content": " to obtain the joint representation for HDR reconstruction:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 82, + 555, + 287, + 571 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 82, + 555, + 287, + 571 + ], + "spans": [ + { + "bbox": [ + 82, + 555, + 287, + 571 + ], + "type": "interline_equation", + "content": "F _ {\\mathrm {H}} = \\mathcal {B} \\left(\\left[ \\tilde {F} _ {\\mathrm {L}} \\odot \\mathcal {W} _ {\\mathrm {L}} \\left(\\tilde {F} _ {\\mathrm {H}}\\right), \\tilde {F} _ {\\mathrm {E}} \\odot \\mathcal {W} _ {\\mathrm {E}} \\left(\\tilde {F} _ {\\mathrm {H}}\\right) \\right]\\right). \\tag {14}", + "image_path": "74e3beef7cf29d89b0f3ec0b858bdfb8179e483d0e5aefb9637cbbd64bd09f11.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "text", + "content": "Temporal context encoding. To alleviate the flickering effects in the generated HDR videos caused by texture mismatching among consecutive event stacks, we exploit the temporal structure within the data via a recurrent convolutional encoder, as shown in Fig. 4. The temporal context encoders " + }, + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{\\mathrm{E}},\\mathcal{F}_{\\mathrm{L}}" + }, + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "text", + "content": " learn modality-specific latent representations " + }, + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "inline_equation", + "content": "F_{\\mathrm{E}},F_{\\mathrm{L}}" + }, + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "text", + "content": " by capturing their underlying temporal structures by a recurrent variant of the encoder in U-Net [62], in which each convolutional layer is replaced by the ConvLSTM [65]. At each timestamp, it outputs the internal state from its own input as well as the encoded past states from" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 72, + 545, + 107 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 107 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 107 + ], + "type": "text", + "content": "its previous input. It can provide more consistent global features of each modality and alleviates flickering effects in the recovered HDR videos." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 108, + 545, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 108, + 545, + 204 + ], + "spans": [ + { + "bbox": [ + 304, + 108, + 545, + 204 + ], + "type": "text", + "content": "The internal states not only preserve temporal correlation between consecutive frames to suppress the flickering effects but also reduce noise in both input modalities, especially in the under-exposed regions. Through the recurrent design of the encoders, the temporal complementary and redundant information through time can be well exploited in the learned latent representations of events and LDR frames for better HDR video reconstruction." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 211, + 370, + 224 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 211, + 370, + 224 + ], + "spans": [ + { + "bbox": [ + 306, + 211, + 370, + 224 + ], + "type": "text", + "content": "3.3. Training" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 229, + 546, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 229, + 546, + 469 + ], + "spans": [ + { + "bbox": [ + 304, + 229, + 546, + 469 + ], + "type": "text", + "content": "Dataset preparation. For the training of HDRev-Net, a large amount of triplets " + }, + { + "bbox": [ + 304, + 229, + 546, + 469 + ], + "type": "inline_equation", + "content": "(\\mathbb{E},\\mathbb{L},\\mathbb{H})" + }, + { + "bbox": [ + 304, + 229, + 546, + 469 + ], + "type": "text", + "content": " are required. There are no readily available datasets containing these triplets nor HDR video datasets with satisfactory scale and quality. To synthesize such a dataset, we collect 733 HDR images from [13, 15, 17, 18, 26, 37, 55, 66, 76] and 110 videos with local motion from [13, 14, 34, 37]. For HDR images, 733 HDR videos with global motion are simulated by generated random camera motion trajectories [5]. From each frame sequence of these videos, the hybrid input of events and LDR frames are simulated by [58] and [12], respectively, like capturing with a virtual camera. To better simulate real LDR images, the LDR frames are generated with randomly sampled CRF, exposure time and Poisson-Gaussian noise [23] for each iteration during training. The event generator [58] also considered the normal distributed thresholds to bridge the gap between real and synthetic. There are a total of 26520 (global motion) + 63754 (local motion) = 90274 frames with a resolution of " + }, + { + "bbox": [ + 304, + 229, + 546, + 469 + ], + "type": "inline_equation", + "content": "240\\times 180" + }, + { + "bbox": [ + 304, + 229, + 546, + 469 + ], + "type": "text", + "content": " for training and 5600 frames with a resolution of " + }, + { + "bbox": [ + 304, + 229, + 546, + 469 + ], + "type": "inline_equation", + "content": "256\\times 256" + }, + { + "bbox": [ + 304, + 229, + 546, + 469 + ], + "type": "text", + "content": " for testing." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 472, + 545, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 472, + 545, + 495 + ], + "spans": [ + { + "bbox": [ + 304, + 472, + 545, + 495 + ], + "type": "text", + "content": "Loss functions. To train the proposed framework, the loss function to be minimized is defined as:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 354, + 506, + 545, + 519 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 354, + 506, + 545, + 519 + ], + "spans": [ + { + "bbox": [ + 354, + 506, + 545, + 519 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\alpha_ {1} \\mathcal {L} _ {\\mathrm {m s e}} + \\alpha_ {2} \\mathcal {L} _ {\\text {p e r c}} + \\alpha_ {3} \\mathcal {L} _ {\\text {c o l o r}}, \\tag {15}", + "image_path": "1c3ca30cfa81259f7db52ca829d602b143d8936e446c002a8da7c459ba713de7.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 527, + 545, + 576 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 527, + 545, + 576 + ], + "spans": [ + { + "bbox": [ + 305, + 527, + 545, + 576 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 527, + 545, + 576 + ], + "type": "inline_equation", + "content": "\\alpha_{1,2,3}" + }, + { + "bbox": [ + 305, + 527, + 545, + 576 + ], + "type": "text", + "content": " are hyper-parameters for balancing different terms. Our goal is to reconstruct HDR frame sequence " + }, + { + "bbox": [ + 305, + 527, + 545, + 576 + ], + "type": "inline_equation", + "content": "\\{H_t\\}_{t=1}^T" + }, + { + "bbox": [ + 305, + 527, + 545, + 576 + ], + "type": "text", + "content": ", while the prediction of the network " + }, + { + "bbox": [ + 305, + 527, + 545, + 576 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 305, + 527, + 545, + 576 + ], + "type": "text", + "content": " is " + }, + { + "bbox": [ + 305, + 527, + 545, + 576 + ], + "type": "inline_equation", + "content": "\\{O_t\\}_{t=1}^T" + }, + { + "bbox": [ + 305, + 527, + 545, + 576 + ], + "type": "text", + "content": ". The mean square error (MSE) loss " + }, + { + "bbox": [ + 305, + 527, + 545, + 576 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{mse}}" + }, + { + "bbox": [ + 305, + 527, + 545, + 576 + ], + "type": "text", + "content": " is defined as:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 369, + 583, + 545, + 608 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 369, + 583, + 545, + 608 + ], + "spans": [ + { + "bbox": [ + 369, + 583, + 545, + 608 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {m s e}} = \\sum_ {t} \\left(\\left\\| H _ {t} - O _ {t} \\right\\| _ {2} ^ {2}\\right). \\tag {16}", + "image_path": "008c83847a8c495610bd1826edd14ff477525294c315420097acbb8e029d1e9b.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 617, + 545, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 653 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 653 + ], + "type": "text", + "content": "The perceptual loss " + }, + { + "bbox": [ + 304, + 617, + 545, + 653 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{perc}}" + }, + { + "bbox": [ + 304, + 617, + 545, + 653 + ], + "type": "text", + "content": " is defined based on the feature maps extracted by the VGG-16 [67] network pre-trained on ImageNet [63]:" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 326, + 662, + 545, + 717 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 662, + 545, + 717 + ], + "spans": [ + { + "bbox": [ + 326, + 662, + 545, + 717 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {\\text {p e r c}} = \\sum_ {t} \\left(\\sum_ {l} \\left(\\| \\phi_ {l} \\left(H _ {t}\\right) - \\phi_ {l} \\left(O _ {t}\\right) \\| _ {2} ^ {2} \\right. \\right. \\tag {17} \\\\ \\left. + \\left\\| \\mathcal {G} _ {l} ^ {\\phi} (H _ {t}) - \\mathcal {G} _ {l} ^ {\\phi} (O _ {t}) \\| _ {2} ^ {2}\\right)\\right), \\\\ \\end{array}", + "image_path": "56e7812a2e8aa736642a5248d8723ce393dbd90ffa38fda9f278bc61461e3f33.jpg" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "13928" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 133 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 133 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 72, + 288, + 133 + ], + "type": "inline_equation", + "content": "\\phi_l" + }, + { + "bbox": [ + 46, + 72, + 288, + 133 + ], + "type": "text", + "content": " denotes the feature map extracted from " + }, + { + "bbox": [ + 46, + 72, + 288, + 133 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 46, + 72, + 288, + 133 + ], + "type": "text", + "content": "-th layer of VGG-16, " + }, + { + "bbox": [ + 46, + 72, + 288, + 133 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_l^\\phi" + }, + { + "bbox": [ + 46, + 72, + 288, + 133 + ], + "type": "text", + "content": " calculates the Gram matrix of " + }, + { + "bbox": [ + 46, + 72, + 288, + 133 + ], + "type": "inline_equation", + "content": "\\phi_l" + }, + { + "bbox": [ + 46, + 72, + 288, + 133 + ], + "type": "text", + "content": ". The layer we use in our experiments is \"relu4_3\". To enforce the color appearance of the reconstructed HDR frames to match that in the ground truth, a color loss is defined as:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 110, + 137, + 287, + 162 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 110, + 137, + 287, + 162 + ], + "spans": [ + { + "bbox": [ + 110, + 137, + 287, + 162 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {c o l o r}} = \\sum_ {t} \\left(\\| \\widetilde {H} _ {t} - \\widetilde {O} _ {t} \\| _ {2} ^ {2}\\right), \\tag {18}", + "image_path": "404d7786205f953b7c3c72a8539d575f1c63056071fb60b4e8cd9f62a1a13927.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 167, + 287, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 167, + 287, + 192 + ], + "spans": [ + { + "bbox": [ + 46, + 167, + 287, + 192 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 167, + 287, + 192 + ], + "type": "inline_equation", + "content": "\\widetilde{H} = G * H" + }, + { + "bbox": [ + 46, + 167, + 287, + 192 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 167, + 287, + 192 + ], + "type": "inline_equation", + "content": "\\widetilde{O} = G * O" + }, + { + "bbox": [ + 46, + 167, + 287, + 192 + ], + "type": "text", + "content": " are blurred from " + }, + { + "bbox": [ + 46, + 167, + 287, + 192 + ], + "type": "inline_equation", + "content": "H, O" + }, + { + "bbox": [ + 46, + 167, + 287, + 192 + ], + "type": "text", + "content": " to eliminate texture and content." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 196, + 287, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 196, + 287, + 388 + ], + "spans": [ + { + "bbox": [ + 46, + 196, + 287, + 388 + ], + "type": "text", + "content": "Other implementation details. We adopt a lightweight variant of recurrent U-Net with 2 downsampling layers in all experiments. The network is unrolled for " + }, + { + "bbox": [ + 46, + 196, + 287, + 388 + ], + "type": "inline_equation", + "content": "T = 6" + }, + { + "bbox": [ + 46, + 196, + 287, + 388 + ], + "type": "text", + "content": " steps during training. It is implemented on the PyTorch framework and runs on an NVIDIA GeForce RTX 3080 GPU. We use ADAM [36] with default parameter setting for optimization. The batch size is set as 1. The learning rate was fixed to " + }, + { + "bbox": [ + 46, + 196, + 287, + 388 + ], + "type": "inline_equation", + "content": "10^{-5}" + }, + { + "bbox": [ + 46, + 196, + 287, + 388 + ], + "type": "text", + "content": " in the earlier epochs and reduced to 0 in the last " + }, + { + "bbox": [ + 46, + 196, + 287, + 388 + ], + "type": "inline_equation", + "content": "40\\%" + }, + { + "bbox": [ + 46, + 196, + 287, + 388 + ], + "type": "text", + "content": " epochs by the linear decay strategy. The number of epochs for pretraining Eq. (7), representation alignment Eq. (8), and training the whole pipeline Eq. (6) are set as 40, 5, 5, respectively. Xavier initialization [20] is used for network initialization. The hyper-parameters in the loss function Eq. (15) are set as " + }, + { + "bbox": [ + 46, + 196, + 287, + 388 + ], + "type": "inline_equation", + "content": "\\alpha_{1} = 30" + }, + { + "bbox": [ + 46, + 196, + 287, + 388 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 196, + 287, + 388 + ], + "type": "inline_equation", + "content": "\\alpha_{2} = 5" + }, + { + "bbox": [ + 46, + 196, + 287, + 388 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 196, + 287, + 388 + ], + "type": "inline_equation", + "content": "\\alpha_{3} = 10^{-3}" + }, + { + "bbox": [ + 46, + 196, + 287, + 388 + ], + "type": "text", + "content": ". The hyper-parameter " + }, + { + "bbox": [ + 46, + 196, + 287, + 388 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 46, + 196, + 287, + 388 + ], + "type": "text", + "content": " for dynamic range compression Eq. (5) is set as 5000." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 397, + 128, + 410 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 397, + 128, + 410 + ], + "spans": [ + { + "bbox": [ + 47, + 397, + 128, + 410 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 413, + 287, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 413, + 287, + 498 + ], + "spans": [ + { + "bbox": [ + 46, + 413, + 287, + 498 + ], + "type": "text", + "content": "We compare the proposed HDRev-Net to several state-of-the-art HDR imaging methods, including a frame based HDR image reconstruction method: Liu et al. [44]; the colored variant of an event based HDR reconstruction method: E2VID [60]; two event guided HDR image reconstruction methods: Han et al. [24] and eSL-Net [72]; and two-exposure-based methods [9, 42]." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 502, + 204, + 515 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 502, + 204, + 515 + ], + "spans": [ + { + "bbox": [ + 47, + 502, + 204, + 515 + ], + "type": "text", + "content": "4.1. Evaluation on synthetic data" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 517, + 287, + 638 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 517, + 287, + 638 + ], + "spans": [ + { + "bbox": [ + 46, + 517, + 287, + 638 + ], + "type": "text", + "content": "Metrics. We adopt the HDR-VDP-3 (\"VDP\" for short), the updated version of HDR-VDP [46], to evaluate the quality of reconstructed HDR images frame by frame. For evaluating the quality of HDR videos, we use HDR-VQM [52] (\"VQM\" for short), which is computed based on a spatiotemporal analysis related to human eye fixation behavior during video viewing. We also adopt commonly used peak signal-to-noise ratio (PSNR), structural similarity (SSIM), and the perceptual error with learned perceptual image patch similarity (LPIPS) [78] metrics as reference." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "type": "text", + "content": "Results. The quantitative results are reported in Table 1. For the two-exposure-based method Li et al. [42], we only calculate the PSNR, SSIM, and LPIPS since it only output tone-mapped HDR images which can not be used to calculate VDP and VQM in the linear domain. We generate two-exposure frame sequences for all the two-exposure-based" + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 309, + 96, + 541, + 198 + ], + "blocks": [ + { + "bbox": [ + 305, + 71, + 545, + 92 + ], + "lines": [ + { + "bbox": [ + 305, + 71, + 545, + 92 + ], + "spans": [ + { + "bbox": [ + 305, + 71, + 545, + 92 + ], + "type": "text", + "content": "Table 1. Comparisons on synthetic data. " + }, + { + "bbox": [ + 305, + 71, + 545, + 92 + ], + "type": "inline_equation", + "content": "\\uparrow (\\downarrow)" + }, + { + "bbox": [ + 305, + 71, + 545, + 92 + ], + "type": "text", + "content": " means higher (lower) is better." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 309, + 96, + 541, + 198 + ], + "lines": [ + { + "bbox": [ + 309, + 96, + 541, + 198 + ], + "spans": [ + { + "bbox": [ + 309, + 96, + 541, + 198 + ], + "type": "table", + "html": "
MethodsPSNR↑SSIM↑LPIPS↓VDP↑VQM↓
eSL-Net [72]16.5750.7130.4135.9030.467
E2VID [60]13.7340.5890.4514.1430.343
Liu et al. [44]23.1590.9010.1047.5430.107
Han et al. [24]20.6970.8610.2086.7090.243
Debevec et al. [9]23.5960.8770.2646.1920.264
Li et al. [42]20.6730.8900.151--
Ours24.0710.9280.1108.1080.103
", + "image_path": "71ab593284abe722002d3ff1a4cb3baaad7e3ad9000ce2da8e754f7e60085179.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 207, + 545, + 254 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 207, + 545, + 254 + ], + "spans": [ + { + "bbox": [ + 304, + 207, + 545, + 254 + ], + "type": "text", + "content": "methods with an exposure ratio setting that takes a reasonable balance between the dynamic range covered and the details preserved. The proposed method outperforms existing methods in terms of all metrics." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 255, + 546, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 255, + 546, + 483 + ], + "spans": [ + { + "bbox": [ + 304, + 255, + 546, + 483 + ], + "type": "text", + "content": "The visual quality comparisons are shown in Fig. " + }, + { + "bbox": [ + 304, + 255, + 546, + 483 + ], + "type": "inline_equation", + "content": "5^{1}" + }, + { + "bbox": [ + 304, + 255, + 546, + 483 + ], + "type": "text", + "content": ". In over/under-exposed regions of the LDR input, most of the details have been lost due to dynamic range clipping. Both frame-based [44] and event-based [60] approaches cannot restore lost information to produce high-quality HDR images. In particular, E2VID [60] produces severe artifacts and distorted color in the reconstructed HDR frames. Han et al. [24] converted one modality into another explicitly (i.e., events to intensity) at first, which leads to stripe-like artifacts and cannot restore natural color appearance. eSL-Net [72] mainly focuses on LDR input and cannot fuse the two modalities well. The performance of Li et al. [42] heavily depends on the selected exposure ratio. As shown in Fig. " + }, + { + "bbox": [ + 304, + 255, + 546, + 483 + ], + "type": "inline_equation", + "content": "5^{2}" + }, + { + "bbox": [ + 304, + 255, + 546, + 483 + ], + "type": "text", + "content": ", even with the optimal exposure ratio, the results of Li et al. presents insufficient details (e.g., on the stones and windows). In comparison, the HDRev-Net effectively fuses the two modalities of visual information and successfully recovers the lost details, with no need to balance the exposure ratio for varying scenes captured by videos." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 492, + 438, + 504 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 492, + 438, + 504 + ], + "spans": [ + { + "bbox": [ + 306, + 492, + 438, + 504 + ], + "type": "text", + "content": "4.2. Evaluation on real data" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 511, + 545, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 511, + 545, + 643 + ], + "spans": [ + { + "bbox": [ + 304, + 511, + 545, + 643 + ], + "type": "text", + "content": "Fig. 6 shows the reconstructed HDR frames on real-world scenarios captured by a hybrid-camera system. We build the hybrid camera system by using a beam-splitter to divide the incident light equivalently into two sensors, i.e., an event camera (DAVIS346 Color) and an industrial camera (FLIR Chameleon 3 Color). Both of them share a similar field of view (FoV). To achieve spatial alignment between the two sensors, we crop the corresponding part of RGB frames w.r.t. the event sensor. With synchronized triggering, the hybrid camera system is able to capture aligned LDR frames and events simultaneously." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 317, + 644, + 546, + 655 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 644, + 546, + 655 + ], + "spans": [ + { + "bbox": [ + 317, + 644, + 546, + 655 + ], + "type": "text", + "content": "As shown in the HDR frame reconstruction results of" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 305, + 664, + 545, + 693 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 664, + 545, + 693 + ], + "spans": [ + { + "bbox": [ + 305, + 664, + 545, + 693 + ], + "type": "text", + "content": "1We provide results of one method per category due to the space limit. Please refer to the supplementary materials to complete reconstruction results on synthetic data." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 693, + 545, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 693, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 306, + 693, + 545, + 712 + ], + "type": "text", + "content": "2The detailed analysis to exposure ratios are shown in supplementary materials." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13929" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 72, + 542, + 274 + ], + "blocks": [ + { + "bbox": [ + 51, + 72, + 542, + 274 + ], + "lines": [ + { + "bbox": [ + 51, + 72, + 542, + 274 + ], + "spans": [ + { + "bbox": [ + 51, + 72, + 542, + 274 + ], + "type": "image", + "image_path": "a26668fdfa5a88645484e1d2c2df57a6c6241665026f5449215185ec4d594da8.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 59, + 275, + 533, + 287 + ], + "lines": [ + { + "bbox": [ + 59, + 275, + 533, + 287 + ], + "spans": [ + { + "bbox": [ + 59, + 275, + 533, + 287 + ], + "type": "text", + "content": "Figure 5. Visual quality comparisons on synthetic data. The Q-scores (higher the better) of VDP metrics are labeled in each image." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 50, + 294, + 545, + 479 + ], + "blocks": [ + { + "bbox": [ + 50, + 294, + 545, + 479 + ], + "lines": [ + { + "bbox": [ + 50, + 294, + 545, + 479 + ], + "spans": [ + { + "bbox": [ + 50, + 294, + 545, + 479 + ], + "type": "image", + "image_path": "4f3c841ad78485360b5f8daa9f7c3adb689f5c7bea954d4ab5736167dc5a115f.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 65, + 481, + 526, + 492 + ], + "lines": [ + { + "bbox": [ + 65, + 481, + 526, + 492 + ], + "spans": [ + { + "bbox": [ + 65, + 481, + 526, + 492 + ], + "type": "text", + "content": "Figure 6. Visual quality comparisons on real-world data. The test samples here are under- and over-exposure cases respectively." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 503, + 287, + 528 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 503, + 287, + 528 + ], + "spans": [ + { + "bbox": [ + 46, + 503, + 287, + 528 + ], + "type": "text", + "content": "real-world data in Fig. 6, HDRev-Net can reconstruct HDR frames with a wider dynamic range and more details." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 536, + 241, + 547 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 536, + 241, + 547 + ], + "spans": [ + { + "bbox": [ + 47, + 536, + 241, + 547 + ], + "type": "text", + "content": "4.3. Results of HDR video reconstruction" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 551, + 288, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 551, + 288, + 693 + ], + "spans": [ + { + "bbox": [ + 46, + 551, + 288, + 693 + ], + "type": "text", + "content": "The information lost in over/under-exposed regions of LDR frames is recorded in events. However, it is unstable for HDR video reconstruction since events are triggered with irradiance changes, rather than absolute values as in LDR frames. HDR video reconstruction in a frame-by-frame manner suffers from flickering effects since temporal connections between consecutive frames are not considered. In the proposed method, recurrent architectures are utilized in the encoders to better maintain the model temporal correlation between frames. Thanks to these components, the proposed HDRev-Net effectively suppresses the flickering effects in the reconstructed HDR videos3." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 503, + 397, + 515 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 503, + 397, + 515 + ], + "spans": [ + { + "bbox": [ + 306, + 503, + 397, + 515 + ], + "type": "text", + "content": "4.4. Ablation study" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 519, + 545, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 519, + 545, + 579 + ], + "spans": [ + { + "bbox": [ + 304, + 519, + 545, + 579 + ], + "type": "text", + "content": "To validate the effectiveness and necessity of the three components of the proposed HDRev-Net, we compare it with its three variants. The quantitative results are shown in Table 2, and the qualitative results are shown in Fig. 3, Fig. 7, Fig. 8, respectively." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 582, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 546, + 713 + ], + "type": "text", + "content": "Effectiveness of multimodal representation alignment technique. We compare the proposed multimodal representation alignment strategy with joint training the pipeline Eq. (6) in an end-to-end manner, which is denoted by \"Joint training\" in Table 2. It can be seen that a performance drop occurs when the three networks are jointly trained, especially in terms of PSNR. As shown in Fig. 7, there are severe halo artifacts in over-exposed regions of the LDR in the results of \"Joint\" training, especially the contours of the cables and the pylons. Due to the domain gap between LDR frames and stacked events, jointly training" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 58, + 702, + 227, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 227, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 227, + 712 + ], + "type": "text", + "content": "3Please refer to the supplementary video for details." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "13930" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 53, + 96, + 282, + 166 + ], + "blocks": [ + { + "bbox": [ + 47, + 71, + 287, + 92 + ], + "lines": [ + { + "bbox": [ + 47, + 71, + 287, + 92 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 287, + 92 + ], + "type": "text", + "content": "Table 2. Results of ablation study. " + }, + { + "bbox": [ + 47, + 71, + 287, + 92 + ], + "type": "inline_equation", + "content": "\\uparrow (\\downarrow)" + }, + { + "bbox": [ + 47, + 71, + 287, + 92 + ], + "type": "text", + "content": " means higher (lower) is better." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 53, + 96, + 282, + 166 + ], + "lines": [ + { + "bbox": [ + 53, + 96, + 282, + 166 + ], + "spans": [ + { + "bbox": [ + 53, + 96, + 282, + 166 + ], + "type": "table", + "html": "
SettingPSNR↑SSIM↑LPIPS↓VDP↑VQM↓
Joint training22.1850.9110.1627.8710.120
W/o fusion19.4360.8670.2147.0240.175
W/o LSTM21.4630.8910.1977.1660.173
Complete model24.0710.9280.1108.1080.103
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Comparisons between \"Joint\" training and \"Complete\" model. " + }, + { + "bbox": [ + 47, + 279, + 287, + 312 + ], + "type": "inline_equation", + "content": "H_{L}(H_{E})" + }, + { + "bbox": [ + 47, + 279, + 287, + 312 + ], + "type": "text", + "content": " denotes the network output with encoder " + }, + { + "bbox": [ + 47, + 279, + 287, + 312 + ], + "type": "inline_equation", + "content": "F_{E}" + }, + { + "bbox": [ + 47, + 279, + 287, + 312 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 47, + 279, + 287, + 312 + ], + "type": "inline_equation", + "content": "F_{L}" + }, + { + "bbox": [ + 47, + 279, + 287, + 312 + ], + "type": "text", + "content": ") disabled by setting input to zero." + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 49, + 319, + 286, + 455 + ], + "lines": [ + { + "bbox": [ + 49, + 319, + 286, + 455 + ], + "spans": [ + { + "bbox": [ + 49, + 319, + 286, + 455 + ], + "type": "image", + "image_path": "0265deb7681332976ed05e4122d30999a32c25ba63aefa537861d56cfce35660.jpg" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 456, + 287, + 489 + ], + "lines": [ + { + "bbox": [ + 47, + 456, + 287, + 489 + ], + "spans": [ + { + "bbox": [ + 47, + 456, + 287, + 489 + ], + "type": "text", + "content": "Figure 8. Comparison between \"W/o LSTM\" and \"Complete\" model. The results of consecutive frames are shown in eight columns. The animations are shown on our project page." + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_caption" + } + ], + "index": 21 + }, + { + "bbox": [ + 46, + 495, + 287, + 531 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 495, + 287, + 531 + ], + "spans": [ + { + "bbox": [ + 46, + 495, + 287, + 531 + ], + "type": "text", + "content": "the whole pipeline cannot well utilize the HDR information in events, which is recorded in a different way from the intensity values in LDR frames." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 46, + 534, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 534, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 534, + 287, + 713 + ], + "type": "text", + "content": "Effectiveness of the confidence guided multimodal fusion module. To verify the effectiveness of the proposed confidence guided multimodal fusion module, we replace the fusion module with a convolution layer with kernel size " + }, + { + "bbox": [ + 46, + 534, + 287, + 713 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 46, + 534, + 287, + 713 + ], + "type": "text", + "content": " and \"relu\" activation fed by concatenated " + }, + { + "bbox": [ + 46, + 534, + 287, + 713 + ], + "type": "inline_equation", + "content": "F_{\\mathrm{L}}, F_{\\mathrm{E}}" + }, + { + "bbox": [ + 46, + 534, + 287, + 713 + ], + "type": "text", + "content": " in the \"W/o fusion\" variant. As shown in Table 2, its performance is worse than the proposed one in terms of all metrics. As shown in Fig. 3, the proposed module can better leverage the information from both modalities and reconstruct HDR images with more details (e.g., the details of the shrub at the lower-left and the texture of the mountain) and less artifact (e.g., the top-left corner). In comparison, the lost details in over-exposed regions cannot be well restored without the fusion module. The convolution layer lacks the ability to dynamically highlight local regions and feature maps that" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "content": "provide more information from one of the two modalities, which makes the recovering of global characteristics such as color and brightness worse than the proposed one." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 305, + 116, + 545, + 272 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 116, + 545, + 272 + ], + "spans": [ + { + "bbox": [ + 305, + 116, + 545, + 272 + ], + "type": "text", + "content": "Effectiveness of the temporal context encoding module. We evaluate the contribution of the recurrent connections in the proposed temporal context encoders by removing them in a \"W/o LSTM\" variant. As shown in Table 2, it performs the worst due to the absence of recurrent connections, especially in terms of VQM that reflects the temporal quality of the reconstructed HDR videos. As shown in Fig. 8, information lost in the over-exposed switch (e.g., the flickering effects pointed out by the yellow arrows) can hardly be restored since there is no event at this timestamp. However, the complete model with recurrent connections can recover fine details and textures from the previous frame, which suppresses flickering effects effectively." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 306, + 285, + 378, + 297 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 285, + 378, + 297 + ], + "spans": [ + { + "bbox": [ + 306, + 285, + 378, + 297 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 305, + 302, + 545, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 302, + 545, + 469 + ], + "spans": [ + { + "bbox": [ + 305, + 302, + 545, + 469 + ], + "type": "text", + "content": "In this paper, we present a multimodal learning framework for reconstructing HDR videos from hybrid inputs of LDR videos and events. There are three components in the proposed method: a multimodal representation alignment strategy for aligning LDR frames and events in a learned shared latent space, a confidence guided multimodal fusion module for adaptively integrating complementary information from the two modalities, and a temporal context encoding module for suppressing the flickering effects by exploiting the temporal correlation between consecutive frames and stacked events. The effectiveness of the proposed method in the task of event guided HDR video reconstruction is verified by extensive experiments on both synthetic and real-world data." + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 304, + 477, + 545, + 633 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 477, + 545, + 633 + ], + "spans": [ + { + "bbox": [ + 304, + 477, + 545, + 633 + ], + "type": "text", + "content": "Limitations. The proposed method aims at HDR video reconstruction under the guidance of HDR information provided by events. However, events contain inherent noise distributed differently from that of frames, which can lead to artifacts in the reconstructed HDR video, especially in low-light conditions. Moreover, due to the requirement of aligned spatial resolution of the hybrid inputs and low resolution of the chosen event camera (DAVIS346C), the proposed method has a limited ability for high-resolution HDR video reconstruction. Replacing the chosen event camera with a higher resolution one(e.g., Prophesee EVK4-HD with a spatial resolution of " + }, + { + "bbox": [ + 304, + 477, + 545, + 633 + ], + "type": "inline_equation", + "content": "720 \\times 1280" + }, + { + "bbox": [ + 304, + 477, + 545, + 633 + ], + "type": "text", + "content": ") and better low-light perception might further improve the performance." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 306, + 639, + 404, + 653 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 639, + 404, + 653 + ], + "spans": [ + { + "bbox": [ + 306, + 639, + 404, + 653 + ], + "type": "text", + "content": "Acknowledgement" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 304, + 654, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 712 + ], + "type": "text", + "content": "This work was supported by National Key R&D Program of China (2021ZD0109803) and National Natural Science Foundation of China (Grant No. 62088102, 62136001). 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In Proc. of Computer Vision and Pattern Recognition, 2021. 2, 3" + } + ] + } + ], + "index": 22 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "13934" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Learning Expressive Prompting With Residuals for Vision Transformers/4b3a492c-f313-415e-8ace-beb325209ff5_content_list.json b/2023/Learning Expressive Prompting With Residuals for Vision Transformers/4b3a492c-f313-415e-8ace-beb325209ff5_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..347a06d57446e0c23b14cecdec608804cc649488 --- /dev/null +++ b/2023/Learning Expressive Prompting With Residuals for Vision Transformers/4b3a492c-f313-415e-8ace-beb325209ff5_content_list.json @@ -0,0 +1,1373 @@ +[ + { + "type": "text", + "text": "Learning Expressive Prompting With Residuals for Vision Transformers", + "text_level": 1, + "bbox": [ + 120, + 130, + 849, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Rajshekhar Das $^{1,2*}$ , Yonatan Dukler $^{2}$ , Avinash Ravichandran $^{2**}$ , Ashwin Swaminathan $^{2}$ Carnegie Mellon University $^{1}$ AWS AI Labs $^{2}$", + "bbox": [ + 138, + 179, + 828, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "rajshekd@andrew.cmu.edu,dukler@amazon.com，swashwin@amazon.com", + "bbox": [ + 200, + 219, + 761, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 268, + 313, + 284 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Prompt learning is an efficient approach to adapt transformers by inserting learnable set of parameters into the input and intermediate representations of a pre-trained model. In this work, we present Expressive Prompts with Residuals (EXPRES) which modifies the prompt learning paradigm specifically for effective adaptation of vision transformers (ViT). Our method constructs downstream representations via learnable \"output\" tokens (shallow prompts), that are akin to the learned class tokens of the ViT. Further for better steering of the downstream representation processed by the frozen transformer, we introduce residual learnable tokens that are added to the output of various computations. We apply EXPRES for image classification and few-shot semantic segmentation, and show our method is capable of achieving state of the art prompt tuning on 3/3 categories of the VTAB benchmark. In addition to strong performance, we observe that our approach is an order of magnitude more prompt efficient than existing visual prompting baselines. We analytically show the computational benefits of our approach over weight space adaptation techniques like finetuning. Lastly we systematically corroborate the architectural design of our method via a series of ablation experiments.", + "bbox": [ + 75, + 300, + 473, + 648 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 675, + 209, + 690 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Scaling up of neural nets in the past few years has steadily improved performance on wide variety of downstream visual tasks. However, model adaptation is often necessary to achieve the best performance in downstream tasks like fine-grained recognition [89], semantic segmentation [8] or object recognition [34]. While traditional techniques like full-model finetuning have become the de-facto approach to adaptation, they are not well suited for many scenarios. For example, finetuning is susceptible to catastrophic forgetting [37] as it modifies model parameters without the knowledge of future domains, and potentially losing prior", + "bbox": [ + 75, + 700, + 468, + 867 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/8e217a44ee87e2e7710edd21f0dbc7ebfe37c360c49c7277dd2a0dca9a4a3f34.jpg", + "image_caption": [ + "Figure 1. Adapting large vision models is crucial to solving downstream tasks with wide variety of semantics (e.g., image classification, semantic segmentation etc.) as well as dataset sizes (few-shot, low-shot, full-shot). In this work, we propose a novel adaptation technique for large vision models that is capable of achieving the desired goal." + ], + "image_footnote": [], + "bbox": [ + 537, + 271, + 859, + 473 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "knowledge of current adaptation. Moreover, finetuning all of the model parameters of a large vision model with just a few training examples can lead to poor generalization. This is in contrast to human intelligence that is capable of solving wide variety of downstream tasks with extremely few exemplars.", + "bbox": [ + 496, + 597, + 892, + 686 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Motivated by the need for better adaptation, parameter efficient techniques like partial-finetuning or adapters [64, 101] have been developed to constructively adapt large models without significant parameter overhead. While serving as effective alternatives to finetuning, most parameter efficient techniques have been designed with convolutional architectures in mind. In light of recent works [15] that demonstrate that Vision Transformers are more suitable for scaling up than CNNs, designing adaptation techniques that exploit the Transformer architecture can be extremely useful. To that end, visual prompt tuning (VPT) [32] has been proposed as a way to constructively adapt transformers by introducing learnable tokens at every layer that interact with the patch and class tokens and are optimized together with a classi", + "bbox": [ + 496, + 688, + 893, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Work conducted while interning at AWS AI Labs.", + "bbox": [ + 99, + 875, + 372, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "**Work conducted while at AWS AI Labs.", + "bbox": [ + 99, + 887, + 330, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "3366", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "fier head. While being effective in practice, VPT allows only partial interactions between prompts and the remaining tokens, thus, leveraging only a part of the prompt capacity. Moreover, it often requires a large number of inserted prompts to achieve optimal performance but that significantly increases the computation costs due to the quadratic computational complexity of the self-attention layer.", + "bbox": [ + 75, + 90, + 468, + 196 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, we explore an alternate design to prompting motivated by the potential for greater prompt capacity. We propose ExPRes, an expressive prompt tuning method with residual tokens that inherits the strengths of parameter efficient adaptation while significantly improving downstream performance. Our prompt design is inspired by the two key observations - propagation of prompts by multilayered interaction with other tokens is crucial for strong capacity and learnable residual tokens can modulate the propagated prompts to favour task-specific relations (unlike in [32]). We first propagate shallow prompts through the encoder that are average pooled at the last layer to yield semantic image-level representations. Shallow prompts by themselves have limited capacity since they cannot specifically modulate token-token relations at higher layers. Therefore to harness the prompts, we add residual tokens to propagated prompts at various layerwise computations of the Transformer encoder including LayerNorm, self-attention and multi-head projection to facilitate layerwise modulation without increasing the number of prompts per layer. This results in enhanced prompt capacity at almost no additional computational cost.", + "bbox": [ + 75, + 198, + 470, + 527 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We empirically validate the effectiveness of our method on a variety of downstream tasks including fine-grained recognition and semantic segmentation. Our use of additional learnable parameters in the form of residual and shallow prompts allows the retention of prior knowledge in the form of frozen encoder weights while being extremely parameter efficient (prompts are $\\leq 1\\%$ of the total parameters). Thus, our method is highly suited for real world adaptation that requires information retention at low memory and computational overheads. Additionally, we show that in most cases we require fewer prompts than VPT to achieve the same or better performance, making it more suitable for limited data settings. Our main contributions can be summarized as follows:", + "bbox": [ + 75, + 530, + 468, + 741 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a novel prompting technique: EXPRES, that uses a combination of shallow and deep residual prompts to facilitate constructive adaptation to downstream tasks with limited labelled datasets.", + "- Our method significantly outperforms full-finetuning based adaptation by $4.6\\%$ on VTAB-1k. Moreover, our method outperforms state-of-the-art prompting approach [32] on the same benchmarks with significantly fewer prompts, suggesting that prompt design is cru" + ], + "bbox": [ + 94, + 753, + 467, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "cial to extracting more capacity at a given parameter/computational budget.", + "bbox": [ + 529, + 90, + 888, + 121 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- To the best of our knowledge, we are the first to demonstrate the effectiveness of prompting for diverse applications such as few-shot semantic segmentation. Our method outperforms strong adaptation baselines by $25\\%$ and achieves competitive performance with respect to language-assisted segmentation [40] despite training on significantly less data with dense annotations.", + "bbox": [ + 517, + 130, + 890, + 250 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related work", + "text_level": 1, + "bbox": [ + 500, + 271, + 635, + 286 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Large Vision Models: With the advent of Transformer models [80] and adoption to various computer vision tasks, including image classification [15, 51], object detection [7, 44], semantic and panoptic segmentation [76,85,102], video understanding [18, 25, 87] and few-shot learning [13], the scale of vision models have increased by orders of magnitude. Typically trained using large labelled data, either unimodal like ImageNet-21K [65] or multimodal, these models demonstrate superior performance on wide variety of visual tasks. Given their superior performance and much larger scale compared to ConvNets, the question of adapting such models efficiently becomes crucial. Motivated by the need, our work is primarily focussed on adaptation of Vision Transformers.", + "bbox": [ + 496, + 296, + 890, + 507 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Transfer Learning has been extensively studied for vision tasks in the context of ConvNets [105] and many techniques have been introduced including side tuning [101], residual adapter [63], bias tuning [6], etc. However, Transformer specific adaptation for visual tasks has received relatively less attention. At the same time, in the NLP domain, the dominance of large-scale pre-trained Transformer-based Large Language Models (LLM) [4, 11, 61], has paved way for many approaches [26, 29, 31] that efficiently fine-tune LLMs for different downstream NLP tasks [82, 83]. In this work we compare with the most representative methods for fair benchmarking. For example, Adapters [30] insert extra lightweight modules inside each Transformer layer. One adapter module generally consists of a linear down-projection, followed by a nonlinear activation function, and a linear up-projection, together with a residual connection [58, 59]. Instead of inserting new modules, [6] proposed to update the bias term and freeze the rest of backbone parameters when fine-tuning ConvNets. BitFit [3] applied this technique to Transformers and verified its effectiveness on LLM tuning. Through our experiments that we demonstrate that our method, EXPRESS provides a more effective way of adapting Transformers compared to prior approaches.", + "bbox": [ + 496, + 508, + 890, + 869 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Prompting: An alternative to traditional adaptation methods is prompting [48] - originally proposed as a way of", + "bbox": [ + 500, + 869, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "3367", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/9392da1658371cecf6c787ec7bd961fb94a933141e025545556014e1fbf648a9.jpg", + "image_caption": [ + "Figure 2. EXPRES Architecture in detail: EXPRES optimizes two types of prompts, shallow prompts (e.g., $p_i$ ) and residual prompts (e.g., $\\nabla_{LN,i}$ ), to construct task specific representation without updating the pretrained encoder weights. Each residual prompt is a learnable vector that is added to the output of various computations such as Layer Norm, Query-Key-Value projections, and linear projection after the MSA operation." + ], + "image_footnote": [], + "bbox": [ + 160, + 87, + 810, + 369 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "prepending language instruction to the input text so that a pre-trained LLM can \"understand\" the task. Through trial and error selection of appropriate prompts, GPT-3 shows strong generalization to downstream transfer learning tasks even in the few-shot or zero-shot settings [4]. This was followed up by other works on better prompt construction [33, 71]. Recent works [39, 43, 50] propose to treat the prompts as task-specific continuous vectors and directly optimize them via gradients during fine-tuning. Such approaches, named \"Prompt Tuning\" achieve performance comparable to finetuning but with $1000 \\times$ less parameters in some cases. Following the success in LLMs, prompt have also been adopted for vision-language models [22, 35, 60, 96, 103]. Nonetheless, all the above methods prompt the text encoders and hence are tied to language as input. However, many realistic visual tasks such as dense prediction may not be well aligned with the language modality. Thus, it becomes imperative to develop prompting approaches that can work in the visual modality. To that end, recent work on visual prompting [2, 10, 32, 66, 88] provides encouraging results. In particular, [32] demonstrate that even in the visual domain, adaptation based on continuous prompting can outperform finetuning, especially when the training datasets are small. Our work however shows that current prompting methods do not fully exploit the capacity of prompting for a vision transformer. Through a principled approach to prompting, we derive a more effective prompting technique that achieves state-of-the-art per", + "bbox": [ + 75, + 465, + 472, + 891 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "formance at much smaller computational overhead.", + "bbox": [ + 500, + 465, + 839, + 479 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Few-Shot Classification: Few-shot classification has received a lot of attention in recent years. While a variety of approaches [75] have been proposed, the most successful ones seek to transfer positive knowledge either by finetuning [1, 12, 79] or meta-learning [17, 19, 21, 24, 38, 62, 74, 77, 81]. Finetuning based few-shot learners can be viewed as specialists that perform well on the target domain [9, 27, 79], but suffer from catastrophic forgetting [70] on the base domain. Meta-learning approaches, on the other hand, can be seen as generalists that enjoy complete immunity against forgetting but at the cost of somewhat lower performance in the target domain. In this work, we propose EXPRES as a constructive adaptation technique that is immune to forgetting but at the same time benefits from task specific parameter tuning, thus, leveraging the best of both worlds. One of our key contribution is to demonstrate the transferability of Transformers from classification to dense prediction tasks (semantic segmentation) when adapted with EXPRES.", + "bbox": [ + 496, + 486, + 893, + 758 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Few-Shot Semantic Segmentation: This task was originally proposed in [68]. Most works after that follow the metric learning paradigm [14] with various novelties from improved support-query matching [47, 72, 95] to better optimization [46, 104], memory modules [90, 93], graph neural networks [84, 92, 99], and more [28, 42, 45, 52, 53, 78, 98, 106]. Some methods generate representative support prototypes with attention mechanism [20, 100], adaptive prototype learning [41, 57, 73], or various prototype generation", + "bbox": [ + 496, + 763, + 895, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "3368", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "techniques [49, 54, 86, 94]. In contrast, our approach directly adapts a model pretrained on image classification to few-shot semantic segmentation without intermediate pretraining on densely-annotated datasets.", + "bbox": [ + 75, + 90, + 468, + 151 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3. Approach", + "text_level": 1, + "bbox": [ + 76, + 167, + 184, + 184 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1. Preliminaries", + "text_level": 1, + "bbox": [ + 76, + 191, + 217, + 207 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Consider an input space $\\mathcal{X}$ and a categorical label set $\\mathcal{Y}$ where each class is represented via a one-hot encoding. A representation $\\mathcal{R} \\subset \\mathbb{R}^d$ of the input is defined by the composition of an augmentation function $\\mathcal{A}: \\mathcal{X} \\to \\mathcal{X}$ and an encoder model $E_{\\theta}: \\mathcal{X} \\to \\mathcal{R}$ , parameterized by $\\theta$ . The augmentation function is a composition of standard image transformations such as random cropping, horizontal flipping etc. A general recognition task $\\mathcal{T}$ can be defined in terms of a finite training set, $\\{(x_i, y_i)\\}_{i \\in \\mathcal{D}_{\\mathrm{train}}}^*$ and $N_c$ categories such that, $y_i \\in [N_c]$ . The goal, is to leverage a pretrained encoder, $E_{\\theta^*}$ and the training set to obtain a classifier for the task $\\mathcal{T}$ .", + "bbox": [ + 75, + 215, + 470, + 397 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Overview of Vision Transformers (ViT)", + "text_level": 1, + "bbox": [ + 76, + 409, + 413, + 424 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In a typical ViT, the image, $x \\in \\mathbb{R}^{h \\times w \\times 3}$ is uniformly divided into $N$ fixed-sized patches, each of which are projected to a $d$ -dimensional embedding and are added a positional embedding, resulting in a patch token $z_{n} \\in \\mathbb{R}^{d}$ . Additionally, a class token $z_{\\mathrm{cls}} \\in \\mathbb{R}^{d}$ is concatenated to the sequence of the patch tokens to form the input, $Z^0 \\in \\mathbb{R}^{(N + 1) \\times d}$ . Starting from layer $l = 0$ , the incoming activations at each layer, $z^{l - 1}$ are first normalized using LayerNorm (LN), and then processed by a multi-headed self-attention block (MSA) followed by an MLP block. At the last layer, the resulting class token is normalized to yield the final representation. The overall computations in a ViT encoder can be summarised as", + "bbox": [ + 75, + 431, + 468, + 628 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} Z ^ {0} = \\left[ z _ {\\mathrm {c l s}}, z _ {0}, \\dots , z _ {N - 1} \\right] \\\\ H ^ {l - 1} = \\operatorname {M S A} (\\operatorname {L N} (Z ^ {l - 1})) + Z ^ {l - 1} \\quad l = 0, \\dots , L - 1 \\\\ Z ^ {l} = \\operatorname {M L P} (\\operatorname {L N} (H ^ {l - 1})) + H ^ {l - 1} \\quad l = 0, \\dots , L - 1 \\\\ y = L N \\left(Z _ {\\mathrm {c l s}} ^ {L}\\right) \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 642, + 447, + 720 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $L$ represents the number of encoder layers. The multi-headed self-attention mechanism (MSA) abstracts patchwise representation by aggregating the right context at each layer. The context aggregation is facilitated by softmax attention that relies on patch-to-patch similarities and its parameters are governed by the pre-training task objective. During adaptation, however, the representations for downstream task might benefit from aggregating a slightly different context at each layer. Our prompt tuning approach facilitates task specific modulation of this context by augmenting and learning layerwise patch tokens.", + "bbox": [ + 75, + 734, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Expressive Prompt Tuning", + "text_level": 1, + "bbox": [ + 500, + 90, + 740, + 107 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "At the input layer of the ViT, we introduce prompt tokens, $P^0 \\in \\mathbb{R}^{M \\times d}$ which are $M$ parameterized vectors of dimension $d$ concatenated to the input token sequence, $Z^0$ , of the ViT. Input-level prompts, also referred to as shallow prompts, are propagated through the encoder together with the class and patch tokens such that at every layer, each token interacts with every other token through the self-attention layers. The propagated prompts at the last layer are average-pooled to obtain the final representation. The insertion and propagation of the prompts described above can be expressed as", + "bbox": [ + 496, + 113, + 893, + 280 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\tilde {Z} ^ {0} = \\left[ Z ^ {0} \\right| \\left| P ^ {0} \\right] \\tag {1} \\\\ \\tilde {H} ^ {l - 1} = \\operatorname {M S A} (\\operatorname {L N} (\\tilde {Z} ^ {l - 1})) + \\tilde {Z} ^ {l - 1} \\quad l = 0, \\dots , L - 1 \\\\ \\tilde {Z} ^ {l} = \\operatorname {M L P} (\\operatorname {L N} (\\tilde {H} ^ {l - 1})) + \\tilde {H} ^ {l - 1} \\quad l = 0, \\dots , L - 1 \\\\ Z ^ {L}, P ^ {L} = \\operatorname {c h u n k} \\left(\\tilde {Z} ^ {l}\\right) \\\\ \\tilde {y} = \\operatorname {A v g P o o l} \\left(P ^ {L}\\right) \\\\ y = L N (\\tilde {y}) \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 522, + 287, + 890, + 409 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "we use $||$ to denote the concatenation along the sequence axis and chunk to denote the splitting of the propagated sequence of length $N + M + 1$ into the $N + 1$ tokens and $M$ prompts. Shallow prompts are capable of modeling some of the desired token relations for a task. However, they have limited capacity due to the inability to alter for specific perlayer interactions with the class and image tokens.", + "bbox": [ + 496, + 417, + 890, + 523 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To enhance the prompt capacity, we introduce layer-wise residual prompts, $\\Delta^l\\in \\mathbb{R}^{M\\times d}$ that are added to the propagated prompts at various computations within the MSA block for an intermediate layer $l$ . This includes the output of attention LayerNorm, query-key-value projections and linear multi-head projection. We summarise the MSA computations at layer $l$ with $N_{h}$ heads and input $Z$", + "bbox": [ + 496, + 523, + 890, + 630 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} Z ^ {\\prime} = L N (Z) \\\\ Q _ {h} = Z ^ {\\prime} W _ {h} ^ {Q}; K _ {h} = Z ^ {\\prime} W _ {h} ^ {K}; V _ {h} = Z ^ {\\prime} W _ {h} ^ {V} \\\\ \\mathrm {g} _ {h} = \\text {A t t} \\left(Q _ {h}, K _ {h}, V _ {h}\\right) \\quad i = 1, \\dots , N _ {h} \\tag {2} \\\\ O = \\left[ \\mathbf {g} _ {1} \\right| | \\dots | | \\mathbf {g} _ {N _ {h}} \\rbrack W ^ {\\text {p r o j}} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 553, + 638, + 888, + 717 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "above $h$ is used to represent the head index of $W^{Q}, W^{K}, W^{V}$ and $W^{\\mathrm{proj}}$ denotes the projection matrix of the MSA block. The residually prompted computations can then be expressed as", + "bbox": [ + 498, + 726, + 893, + 786 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} Z ^ {\\prime} = L N (Z) + [ \\bar {\\mathbf {0}} | | \\boldsymbol {\\Delta} _ {\\mathbf {L N}} ] \\\\ \\tilde {Q} _ {h} = Q _ {h} + \\left[ \\bar {\\mathbf {0}} \\right| \\left| \\boldsymbol {\\Delta} _ {\\mathbf {Q}} \\right| \\\\ \\tilde {K} _ {h} = K _ {h} + [ \\mathbf {0} | | \\boldsymbol {\\Delta} _ {\\mathbf {K}} ] \\\\ \\tilde {V} _ {h} = V _ {h} + [ \\bar {\\mathbf {0}} | | \\boldsymbol {\\Delta} _ {\\mathbf {V}} ] \\\\ \\tilde {O} = O + \\left[ \\bar {\\mathbf {0}} \\right| | \\boldsymbol {\\Delta} _ {\\mathrm {p r o j}} ] \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 607, + 796, + 785, + 897 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "3369", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where the concatenation of $(N + 1) \\times d$ dimensional zero matrix, $\\bar{\\mathbf{0}}$ with the residual-prompts, signifies that the residuals $\\Delta$ are added only at the propagated prompt positions and not to the image patch or class token positions. The above residual computations occur at every layer with independently learned residual prompts, and we drop the layer indices in the equations for brevity. The overall EXPRES architecture is visualized in Figure 2.", + "bbox": [ + 75, + 90, + 472, + 212 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Interpreting Residual Prompting", + "text_level": 1, + "bbox": [ + 76, + 233, + 366, + 250 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We take a closer look at residual prompting for self-attention and interpret it's functionality. The Att operation in Eq. (2) facilitates weighted aggregation over all \"value\" tokens where the weights are computed using the \"query\" and a \"key\" tokens as $w_{ij} \\propto \\exp \\left( \\frac{q_i^T k_j}{\\sqrt{d / N_h}} \\right)$ . When prompted with residual tokens, the expression for the weights that aggregate information for a patch token $q_i$ can be factored as,", + "bbox": [ + 75, + 258, + 468, + 393 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\tilde {w} _ {i j} \\propto \\exp \\left(\\frac {q _ {i} ^ {T} \\left(k _ {j} + \\boldsymbol {\\Delta} _ {K , j}\\right)}{\\sqrt {d / N _ {h}}}\\right) \\\\ = \\exp \\left(\\frac {q _ {i} ^ {T} k _ {i}}{\\sqrt {d / N _ {h}}}\\right) \\exp \\left(\\frac {q _ {i} ^ {T} \\Delta_ {K , j}}{\\sqrt {d / N _ {h}}}\\right) \\tag {3} \\\\ = w _ {i j} * \\alpha_ {i j}. \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 135, + 412, + 468, + 516 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Based on Eq. (3), residual prompts facilitate task-specific reweighting of the attention weights independently at every layer, allowing the modulation of context aggregated per patch token. Such layerwise modulation can lead to better adaptation of the final representation compared to shallow prompting that restricts the modulation to the input layer. Moreover, the two-way interaction between prompts and patch tokens leads to greater flexibility than other forms of multilayered prompting [32, 67] that allow for only partial interaction. For instance, [32] restrict the prompts to act only as keys and never as queries.", + "bbox": [ + 75, + 534, + 468, + 700 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Residual prompt based attention reweighting is also interesting from parameter efficiency perspective as it circumvents the need for updating the attention weight matrices (done in finetuning approaches) to achieve the same goal of task specific adaptation. Specifically, each layer of a ViT consists of three attention weight matrices, each with $d \\times d$ dimensions, resulting in $\\mathcal{O}(d^2)$ learnable parameters. In contrast, each prompt is $d$ dimensional so, only $\\mathcal{O}(d)$ parameters need to be adapted even with $M$ prompts, where $M << d$ . We empirically validate that the high capacity as well as parameter efficiency of our prompting approach is crucial for achieving good adaptation performance in limited labelled data settings.", + "bbox": [ + 75, + 704, + 470, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5. Learning the Prompts", + "text_level": 1, + "bbox": [ + 500, + 90, + 705, + 107 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this work, we are mainly interested in two types of downstream tasks - image classification and semantic segmentation. To train the prompts for classification, we optimize a standard cross entropy loss with respect to the representation, $y$ in Eq. (1) and the corresponding ground-truth label, $y*$ . In the case of semantic segmentation, we adapt the model as well as the objective to perform dense predictions. At the final layer of the encoder, we extract the keys corresponding to the patch tokens and pass them through the classifier. The sequence outputs are then reshaped into a 2d map and resized to original image resolution using bilinear interpolation, resulting in a pixel wise prediction. Finally, to optimize the prompts with the classifier head, we use a dense cross entropy loss as follows", + "bbox": [ + 496, + 113, + 893, + 325 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\{p _ {m} ^ {*}\\right\\}, \\left\\{\\boldsymbol {\\Delta} ^ {*} \\right\\} = \\underset {\\left\\{p _ {m} \\right\\}, \\left\\{\\boldsymbol {\\Delta} \\right\\}, C} {\\arg \\min } \\sum_ {j \\in I _ {\\mathrm {c x t}}} \\sum_ {h, w} L _ {\\mathrm {C E}} \\left(y _ {j h w}, y _ {j h w} ^ {*}\\right)\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 335, + 875, + 368 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where, $h, w$ are used to index the spatial positions at the resolution, $H \\times W$ of the input image.", + "bbox": [ + 498, + 378, + 890, + 409 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 498, + 422, + 632, + 439 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We validate the effectiveness of EXPRES on a variety of benchmarks consisting of wide variety of tasks and dataset sizes. We also analyse the importance of various model components and design decisions.", + "bbox": [ + 496, + 446, + 893, + 507 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets: To evaluate EXPRES, we use two different benchmarks, VTAB-1k [97] and FGVC [32]. The VTAB-1k benchmark consists of 19 different visual classification tasks categorized under three groups: Natural - tasks with natural images captured with standard cameras; Specialized - tasks with images captured under specialized settings (medical and satellite imagery); and Structured - tasks that requires understanding scene geometry, like object distance. Each task-specific dataset contains 1000 training examples with varying number of samples per class, depending on the number of classes. For validation purposes and hyperparameter selection, we use a $800 - 200$ split of the training set and then train on all 1000 examples for final results, which are based on evaluation on the entire test set. The FGVC benchmark consists of the finegrained datasets including CUB [89], Oxford Flowers [55], Stanford Dogs [36] and Stanford Cars [23]. In conjunction with VTAB-1k, we use the FGVC datasets to conduct key ablation studies for EXPRES. A random $90 - 10$ split of each dataset is used for hyperparameter selection. For few shot segmentation, we use the standard PASCAL $-5^{\\mathrm{i}}$ [69] benchmark that was created from PASCAL VOC 2012 [16] with extra mask annotations for 20 object classes, evenly divided into 4 folds: $\\{5^i : i \\in \\{0,1,2,3\\}\\}$ . Following prior works for evaluation scheme, we randomly sample 1000 episodes per fold and report the average performance over all episodes", + "bbox": [ + 496, + 508, + 892, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "3370", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/7a9b1f2ea0c665a8ac90e84360cbdaf1c70ed38aa429035b1922f74954339b92.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
naturalspecializedstructured
CLEAR-100Caltech101DTDFlowers102PetsSVHNSun397MeanPatch CamelyonEuroSATResisc45RetinopathyMeanClevr/countClevr/distanceDMLabKITTI/distancedSprites/locationdSprites/orientationSmallNORB/azimuthSmallNORB/elevationMean
Linear63.485.063.297.086.336.651.068.9378.587.568.674.077.1634.330.633.255.412.520.09.619.226.84
MLP-263.284.860.597.685.934.147.867.7074.388.867.173.275.8645.231.631.855.730.924.616.623.332.47
MLP-363.884.762.397.484.732.549.267.8077.088.070.256.172.8347.832.832.358.112.921.215.224.830.62
MLP-559.384.459.996.184.430.946.865.9873.787.264.871.574.3150.832.331.556.47.520.814.420.429.23
MLP-953.180.553.995.182.624.443.761.9078.583.060.272.373.4947.527.928.954.06.217.710.816.226.15
Sidetune [101]60.760.853.695.566.734.935.358.2158.587.765.261.068.1227.622.631.351.78.214.49.821.823.41
Biastune [6]72.887.059.297.585.359.951.473.3078.791.672.969.878.2561.555.632.455.966.640.015.725.144.09
Adapter-25674.186.163.297.787.034.650.870.5076.388.073.170.576.9845.737.431.253.230.325.413.822.132.39
Adapter-6474.285.862.797.687.236.350.970.6576.387.573.770.977.1042.939.930.454.531.925.613.521.432.51
Adapter-874.285.762.797.887.236.450.770.6776.989.273.571.677.8045.241.831.156.430.424.613.222.033.09
Partial-166.885.962.597.385.537.650.669.4478.689.872.573.378.5341.534.333.961.031.332.816.322.434.17
FT-all68.987.764.397.286.987.438.875.8879.795.784.273.983.3656.358.641.765.557.546.725.729.147.64
VPT-shallow [32]77.786.962.697.587.374.551.276.8178.292.075.672.979.6650.558.640.567.168.736.120.234.146.98
VPT-deep [32]78.890.865.898.088.378.149.678.4881.896.183.468.482.4368.560.046.572.873.647.932.937.854.98
EXPRES (ours)78.089.668.898.788.981.951.979.784.896.280.974.284.066.560.446.577.678.049.526.135.355.0
", + "bbox": [ + 81, + 88, + 890, + 359 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/63ced1e4f6c23d23d7091eec95ce577209a7f556a55969d4f33ecb4af9cca9af.jpg", + "table_caption": [ + "Table 1. VTAB-1k benchmark: Per task adaptation results with ViT-B/16 model pretrained on ImageNet-21k.." + ], + "table_footnote": [], + "table_body": "
MethodIm-PreDense-PreBackbone50515253
SPNET [91]In-1k✓ResNet-10123.817.014.118.3
ZS3Net [5]In-1k✓ResNet-10140.839.439.333.6
LSEG [40]In-1k✓ViT-L/1661.363.643.141.0
LinearIn-21k-ViT-B/165.143.928.129.1
FT-allIn-21k-ViT-B/1618.331.927.923.2
BiastuneIn-21k-ViT-B/162.439.213.920.1
VPT-deep [32]In-21k-ViT-B/1633.456.249.847.7
EXPRES (Ours)In-21k-ViT-B/1641.860.252.451.4
", + "bbox": [ + 259, + 398, + 710, + 518 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. Five-Shot Semantic Segmentation on PASCAL - $5^{\\mathrm{i}}$ : Per fold adaptation results with ViT-B/16 model pretrained on ImageNet-21k.", + "bbox": [ + 75, + 529, + 892, + 556 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "of the corresponding fold. However, unlike prior works, we tune our EXPRES model on few-shot training examples and cross-validate the hyperparameters (e.g. number of prompts, $M$ ) on a validation set with fold-exclusive categories. In all our experiments, we use a reasonably small budget for hyperparameters (see supplementary) following recent studies [56] that highlight the likelihood of overoptimistic results in limited-labelled data settings due to excessive hyperparameter tuning on large validation sets.", + "bbox": [ + 75, + 585, + 468, + 719 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation Details: In all our experiments, we use a fixed encoder, ViT-B/16 pretrained on ImageNet-22K [65]. This model is effective on wide variety of tasks and allows direct comparison with prior works. For each downstream task, we train for a total 100 epochs with an initial warmup of 10 epochs. We use AdamW as our default optimizer with a suitable learning rate and fixed weight decay of $1e - 4$ . For VTAB-1k and FGVC experiments, we use a fixed batch size of 64. For segmentation experiments, since overall training set sizes are extremely small ( $\\leq 10$ images in total), we use the entire training set per batch. We use input image reso", + "bbox": [ + 75, + 720, + 470, + 888 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "lution of $224 \\times 224$ for classification tasks and $384 \\times 384$ for semantic segmentation tasks as dense prediction usually benefits from larger resolution. Since, ViT-B/16 is pretrained on standard $224 \\times 224$ resolution images, we use interpolated positional embeddings to accommodate larger resolutions in the case of segmentation. Finally, we use standard data augmentations for classification benchmarks i.e., Resize $\\rightarrow$ Random-Crop $\\rightarrow$ Horizontal-Flip during training and Resize $\\rightarrow$ Center-Crop during evaluation while for segmentation we only use Resize.", + "bbox": [ + 496, + 585, + 890, + 736 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation Metrics For classification experiments, we use accuracy as our performance metric. For evaluating segmentation masks, we use mean intersection over union (mIoU) that averages over the intersection over union curves per class.", + "bbox": [ + 496, + 738, + 893, + 814 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Main Results", + "text_level": 1, + "bbox": [ + 500, + 829, + 638, + 844 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We compare EXPRES with a number of commonly used adaptation techniques on VTAB-1k. The adaptation methods can be categorized as head-oriented, backbone-oriented", + "bbox": [ + 496, + 854, + 893, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "3371", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "and prompt-based. Under the first category, Linear only optimizes a linear classifier for the downstream task while MLP- $k$ uses a $k$ -layer multilayer perceptron (MLP) as the classifier head. As an example of the second category, Sidetune [101] uses features that are linearly interpolated between pretrained features and features from a \"side\" network trained on downstream data. While Biastune [6] adapts only the bias terms of an otherwise frozen backbone. Adapter- $d$ [30, 58, 59] introduces lightweight MLP modules inserted between Transformer layers. Partial- $k$ finetunes the last $k$ layers while keeping the rest of the backbone frozen, finally FT-all finetunes all the layers. VPT-shallow [32] additionally optimizes a linear classifier with the learnable input prompts propagated through the encoder. VPT-deep [32] introduces more capacity by replacing the propagated prompts with a new set of learnable prompts at each layer.", + "bbox": [ + 75, + 90, + 472, + 347 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "VTAB-1k Results (Table 1): Across all three splits of VTAB-1k, our method significantly outperforms the best head-oriented techniques: $+11\\%$ (natural), $+7\\%$ (specialized) and $+23\\%$ (structured). Similar trends hold even when comparing with the more powerful class of backbone-oriented techniques. While FT-all has been widely adopted as an effective technique for most adaptation scenarios, our method consistently outperforms it by a significant margin of $+4\\%$ (natural), $+1\\%$ (specialized) and $+7\\%$ (structured). Most interestingly our method even outperforms other powerful prompting techniques like VPT-deep on 12 (out of 19) datasets by a margin of about $+1\\%$ (natural), $+2\\%$ (specialized) and $+0.02\\%$ (structured). The performance gains are particularly impressive when considered from the perspective of computation vs performance tradeoff. Compared to VPT-deep that uses 53 prompts for natural and 108 prompts for structures, our method only requires 10 and 29 prompts for the respective splits. A more detailed summary is provided in the supplementary.", + "bbox": [ + 75, + 348, + 472, + 636 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Few-Shot Semantic Segmentation Without Dense Pretraining", + "text_level": 1, + "bbox": [ + 76, + 648, + 468, + 680 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We test the efficacy of EXPRES on a novel adaptation setup where the backbone, pretrained on classification tasks, is directly adapted for few-shot semantic segmentation task without additional training on large densely-annotated datasets. This is in contrast with most works that follow a two-stage pretraining procedure i.e., training on ImageNet-1k with image level labels followed by meta-learning on densely annotated datasets constructed from the train folds of PASCAL - $5^{\\mathrm{i}}$ . In contrast, we only perform the first stage pretraining on a sufficiently diverse dataset (ImageNet-21k in our case) with no meta-learning stage. During evaluation, each few-shot episode randomly samples a target image with a segmentation mask that assigns a label 1 to the pixels corresponding to one of the object cate", + "bbox": [ + 75, + 688, + 470, + 901 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3c8648be08dcc2a4acd015992e0b41ac8fbf1ee95850865d04d0248b3ee46a73.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 555, + 90, + 694, + 208 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5c4055773cecf3ec66ea5d9e829720502d21c9ca61f070f12afb9337f15ff43f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 699, + 90, + 838, + 208 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/73d0c0370ea4ef9cf588645ad89070c7d8a04fd592910493119024a6dc566729.jpg", + "image_caption": [ + "Figure 3. Prompt Propagation: Effect of propagating prompts with modulation upto a layer, $l = \\{2,\\dots ,12\\}$ of the ViT-B/16 encoder with total 12 layers. The datasets are sampled from the FGVC benchmark." + ], + "image_footnote": [], + "bbox": [ + 555, + 210, + 694, + 325 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4d74537b2d20cbd3489792118bbf48df87a3404194d63badcd6ec908147da441.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 699, + 210, + 838, + 325 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "gories in that image and a label 0 to remaining pixels (background). From the same object category, a set of five images are randomly sampled to form the training set where the mask of each image is annotated in the same way as the target. Our method as well as all baselines that perform meta-learning are optimized given a context set to yield a binary classifier for the target image. For dense representations, we use the last layer keys of the MSA-block as we found them to be more accurate than the typical MLP-block output. We observe that our method consistently outperforms the baselines (by $25\\%$ ) as well as other prompt techniques such as VPT-deep (by $5\\%$ ). Surprisingly, our method even outperforms [40] that leverages densely annotated datasets (training data per fold) with large language models for a second stage of pretraining. Specifically, on 2/4 folds, EXPRES outperforms [40] by $10\\%$ despite training on a significantly smaller densely-annotated dataset (five images). These results are particularly significant as they suggest that highly competitive results can be achieved with models pretrained on image classification. Consequently, results may be further improved by scaling up the image-level annotated datasets which are cheaper to scale than the densely annotated datasets. In the supplementary, we provide visualizations of the segmentation mask predictions by our method as well as Linear, FT-all and VPT-deep methods.", + "bbox": [ + 496, + 425, + 893, + 803 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Ablation Studies", + "text_level": 1, + "bbox": [ + 500, + 815, + 665, + 830 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We conduct extensive ablations to evaluate key design decisions used to develop EXPRES such as feature construction, residual prompting, number of prompts etc. For all ablations, we use the same ViT-B/16 backbone. When", + "bbox": [ + 496, + 839, + 893, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "3372", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/550875f4d1eceb067e3f167f7bd597c31282f462afe9bb9f4f7abf3a6afaeea0.jpg", + "image_caption": [ + "Figure 4. Residual Prompt Types: Evaluating the importance of different type of residual prompts on FGVC datasets." + ], + "image_footnote": [], + "bbox": [ + 158, + 85, + 803, + 215 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1645a6299075cc9d4a78cbb9571a2e0aa15f5073e114ef897a48546ffdea4f4e.jpg", + "image_caption": [ + "Figure 5. Computational Efficiency Plots: Comparing Accuracy vs Number of Prompts for VPT and EXPRES" + ], + "image_footnote": [], + "bbox": [ + 116, + 263, + 421, + 421 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "using FGVC datasets, we use only $10\\%$ of each dataset with official splits provided in [32].", + "bbox": [ + 75, + 492, + 468, + 522 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Prompt Propagation: We evaluate the importance of propagating prompts through the ViT-B/16 encoder with layerwise modulation. Specifically, upto a layer $l$ , we allow all tokens (patch, class and prompt) to attend to each other at every layer. Beyond $l$ , prompts are not allowed to interact with other tokens at all; they are simply projected by the value heads of MSA-block followed by MLP processing at every layer. In our experiments, we fix the number of prompts to 10 irrespective of the dataset. From Figure 3, we observe that downstream performance depends directly on the extent of prompt propagation with modulation: accuracy improves as more layers allow prompts to interact with other tokens. These results motivate our method, EXPRES, that facilitates finegrained layerwise modulation via residual tokens.", + "bbox": [ + 75, + 523, + 470, + 748 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Residual Prompt Type: In Figure 4 we evaluate the importance of different residual prompt types (one-at-a-time) including attention, LayerNorm $(LN)$ , query-key-value projections $(QKV)$ and linear multi-head projection $(Proj)$ . We also evaluate residual prompting in the MLP block: after LayerNorm $(LN,mlp)$ , first linear projection $(L1,mlp)$ and second linear projection $(L2,mlp)$ . We evaluate the composite effect of multiple prompt types within a computational block i.e., Att (MSA block) and MLP (MLP block). As a baseline, we provide the per-dataset results for shallow", + "bbox": [ + 75, + 750, + 472, + 901 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "prompting, referred to as None in the figure. The number of prompts at each layer are fixed at 10. We observe that, within the MSA block, adding residual prompts to LayerNorm and query-key-value projections yields the most improvements (3.5% and 2.8% on an average respectively) over None. Moreover, LayerNorm prompts in the MLP block are also more effective than prompting the two linear layers. Comparing blockwise performance, prompting the MSA block $(Att)$ yields significantly better performance (by 1.6%) than prompting the MLP block $(MLP)$ . The performance gap between $Att$ and $MLP$ highlights the importance of directly modulating layerwise interaction between tokens for better adaptation. Consequently, we use $Att$ as our default setting for all experiments.", + "bbox": [ + 496, + 267, + 893, + 479 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Computational Efficiency of Prompting: In prompting techniques, the primary computational overhead arises from the quadratic complexity (in number of tokens) of the transformer encoder. So to evaluate computation efficiency of prompting, we investigate the rate at which performance improves with number of prompts and provide comparisons between our method and VPT in Figure 5. We evaluate on two different datasets sampled from different categories of VTAB-1k. For a given accuracy, e.g. $58.5\\%$ on Clevr-Distance, EXPRES requires an order less prompts than VPT, resulting in 2 orders less computations. Overall EXPRES achieves higher optimal performance with far fewer prompts than VPT.", + "bbox": [ + 496, + 479, + 893, + 676 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 691, + 619, + 709 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this work we propose a novel prompting technique for adapting large vision models. Our method demonstrates strong performance across variety of downstream tasks with varying dataset sizes. 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In ACM MM, 2021. 3" + ], + "bbox": [ + 503, + 92, + 890, + 502 + ], + "page_idx": 11 + }, + { + "type": "page_number", + "text": "3377", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 11 + } +] \ No newline at end of file diff --git a/2023/Learning Expressive Prompting With Residuals for Vision Transformers/4b3a492c-f313-415e-8ace-beb325209ff5_model.json b/2023/Learning Expressive Prompting With Residuals for Vision Transformers/4b3a492c-f313-415e-8ace-beb325209ff5_model.json new file mode 100644 index 0000000000000000000000000000000000000000..e6f7973a0b77896ddb8db51ff7a8786b34b13c79 --- /dev/null +++ b/2023/Learning Expressive Prompting With Residuals for Vision Transformers/4b3a492c-f313-415e-8ace-beb325209ff5_model.json @@ -0,0 +1,2490 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.121, + 0.131, + 0.85, + 0.153 + ], + "angle": 0, + "content": "Learning Expressive Prompting With Residuals for Vision Transformers" + }, + { + "type": "text", + "bbox": [ + 0.139, + 0.18, + 0.83, + 0.217 + ], + "angle": 0, + "content": "Rajshekhar Das\\(^{1,2*}\\), Yonatan Dukler\\(^{2}\\), Avinash Ravichandran\\(^{2**}\\), Ashwin Swaminathan\\(^{2}\\) Carnegie Mellon University\\(^{1}\\) AWS AI Labs\\(^{2}\\)" + }, + { + "type": "text", + "bbox": [ + 0.202, + 0.22, + 0.763, + 0.234 + ], + "angle": 0, + "content": "rajshekd@andrew.cmu.edu,dukler@amazon.com，swashwin@amazon.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.269, + 0.314, + 0.285 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.301, + 0.474, + 0.65 + ], + "angle": 0, + "content": "Prompt learning is an efficient approach to adapt transformers by inserting learnable set of parameters into the input and intermediate representations of a pre-trained model. In this work, we present Expressive Prompts with Residuals (EXPRES) which modifies the prompt learning paradigm specifically for effective adaptation of vision transformers (ViT). Our method constructs downstream representations via learnable \"output\" tokens (shallow prompts), that are akin to the learned class tokens of the ViT. Further for better steering of the downstream representation processed by the frozen transformer, we introduce residual learnable tokens that are added to the output of various computations. We apply EXPRES for image classification and few-shot semantic segmentation, and show our method is capable of achieving state of the art prompt tuning on 3/3 categories of the VTAB benchmark. In addition to strong performance, we observe that our approach is an order of magnitude more prompt efficient than existing visual prompting baselines. We analytically show the computational benefits of our approach over weight space adaptation techniques like finetuning. Lastly we systematically corroborate the architectural design of our method via a series of ablation experiments." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.676, + 0.21, + 0.691 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.701, + 0.47, + 0.868 + ], + "angle": 0, + "content": "Scaling up of neural nets in the past few years has steadily improved performance on wide variety of downstream visual tasks. However, model adaptation is often necessary to achieve the best performance in downstream tasks like fine-grained recognition [89], semantic segmentation [8] or object recognition [34]. While traditional techniques like full-model finetuning have become the de-facto approach to adaptation, they are not well suited for many scenarios. For example, finetuning is susceptible to catastrophic forgetting [37] as it modifies model parameters without the knowledge of future domains, and potentially losing prior" + }, + { + "type": "image", + "bbox": [ + 0.539, + 0.272, + 0.86, + 0.474 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.486, + 0.893, + 0.57 + ], + "angle": 0, + "content": "Figure 1. Adapting large vision models is crucial to solving downstream tasks with wide variety of semantics (e.g., image classification, semantic segmentation etc.) as well as dataset sizes (few-shot, low-shot, full-shot). In this work, we propose a novel adaptation technique for large vision models that is capable of achieving the desired goal." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.598, + 0.893, + 0.688 + ], + "angle": 0, + "content": "knowledge of current adaptation. Moreover, finetuning all of the model parameters of a large vision model with just a few training examples can lead to poor generalization. This is in contrast to human intelligence that is capable of solving wide variety of downstream tasks with extremely few exemplars." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Motivated by the need for better adaptation, parameter efficient techniques like partial-finetuning or adapters [64, 101] have been developed to constructively adapt large models without significant parameter overhead. While serving as effective alternatives to finetuning, most parameter efficient techniques have been designed with convolutional architectures in mind. In light of recent works [15] that demonstrate that Vision Transformers are more suitable for scaling up than CNNs, designing adaptation techniques that exploit the Transformer architecture can be extremely useful. To that end, visual prompt tuning (VPT) [32] has been proposed as a way to constructively adapt transformers by introducing learnable tokens at every layer that interact with the patch and class tokens and are optimized together with a classi" + }, + { + "type": "page_footnote", + "bbox": [ + 0.1, + 0.875, + 0.374, + 0.888 + ], + "angle": 0, + "content": "*Work conducted while interning at AWS AI Labs." + }, + { + "type": "page_footnote", + "bbox": [ + 0.1, + 0.888, + 0.331, + 0.9 + ], + "angle": 0, + "content": "**Work conducted while at AWS AI Labs." + }, + { + "type": "list", + "bbox": [ + 0.1, + 0.875, + 0.374, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3366" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.198 + ], + "angle": 0, + "content": "fier head. While being effective in practice, VPT allows only partial interactions between prompts and the remaining tokens, thus, leveraging only a part of the prompt capacity. Moreover, it often requires a large number of inserted prompts to achieve optimal performance but that significantly increases the computation costs due to the quadratic computational complexity of the self-attention layer." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.199, + 0.471, + 0.529 + ], + "angle": 0, + "content": "In this work, we explore an alternate design to prompting motivated by the potential for greater prompt capacity. We propose ExPRes, an expressive prompt tuning method with residual tokens that inherits the strengths of parameter efficient adaptation while significantly improving downstream performance. Our prompt design is inspired by the two key observations - propagation of prompts by multilayered interaction with other tokens is crucial for strong capacity and learnable residual tokens can modulate the propagated prompts to favour task-specific relations (unlike in [32]). We first propagate shallow prompts through the encoder that are average pooled at the last layer to yield semantic image-level representations. Shallow prompts by themselves have limited capacity since they cannot specifically modulate token-token relations at higher layers. Therefore to harness the prompts, we add residual tokens to propagated prompts at various layerwise computations of the Transformer encoder including LayerNorm, self-attention and multi-head projection to facilitate layerwise modulation without increasing the number of prompts per layer. This results in enhanced prompt capacity at almost no additional computational cost." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.531, + 0.47, + 0.742 + ], + "angle": 0, + "content": "We empirically validate the effectiveness of our method on a variety of downstream tasks including fine-grained recognition and semantic segmentation. Our use of additional learnable parameters in the form of residual and shallow prompts allows the retention of prior knowledge in the form of frozen encoder weights while being extremely parameter efficient (prompts are \\(\\leq 1\\%\\) of the total parameters). Thus, our method is highly suited for real world adaptation that requires information retention at low memory and computational overheads. Additionally, we show that in most cases we require fewer prompts than VPT to achieve the same or better performance, making it more suitable for limited data settings. Our main contributions can be summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.754, + 0.468, + 0.813 + ], + "angle": 0, + "content": "- We propose a novel prompting technique: EXPRES, that uses a combination of shallow and deep residual prompts to facilitate constructive adaptation to downstream tasks with limited labelled datasets." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.826, + 0.468, + 0.901 + ], + "angle": 0, + "content": "- Our method significantly outperforms full-finetuning based adaptation by \\(4.6\\%\\) on VTAB-1k. Moreover, our method outperforms state-of-the-art prompting approach [32] on the same benchmarks with significantly fewer prompts, suggesting that prompt design is cru" + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.754, + 0.468, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.531, + 0.092, + 0.89, + 0.122 + ], + "angle": 0, + "content": "cial to extracting more capacity at a given parameter/computational budget." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.131, + 0.892, + 0.25 + ], + "angle": 0, + "content": "- To the best of our knowledge, we are the first to demonstrate the effectiveness of prompting for diverse applications such as few-shot semantic segmentation. Our method outperforms strong adaptation baselines by \\(25\\%\\) and achieves competitive performance with respect to language-assisted segmentation [40] despite training on significantly less data with dense annotations." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.272, + 0.637, + 0.287 + ], + "angle": 0, + "content": "2. Related work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.297, + 0.892, + 0.508 + ], + "angle": 0, + "content": "Large Vision Models: With the advent of Transformer models [80] and adoption to various computer vision tasks, including image classification [15, 51], object detection [7, 44], semantic and panoptic segmentation [76,85,102], video understanding [18, 25, 87] and few-shot learning [13], the scale of vision models have increased by orders of magnitude. Typically trained using large labelled data, either unimodal like ImageNet-21K [65] or multimodal, these models demonstrate superior performance on wide variety of visual tasks. Given their superior performance and much larger scale compared to ConvNets, the question of adapting such models efficiently becomes crucial. Motivated by the need, our work is primarily focussed on adaptation of Vision Transformers." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.509, + 0.892, + 0.87 + ], + "angle": 0, + "content": "Transfer Learning has been extensively studied for vision tasks in the context of ConvNets [105] and many techniques have been introduced including side tuning [101], residual adapter [63], bias tuning [6], etc. However, Transformer specific adaptation for visual tasks has received relatively less attention. At the same time, in the NLP domain, the dominance of large-scale pre-trained Transformer-based Large Language Models (LLM) [4, 11, 61], has paved way for many approaches [26, 29, 31] that efficiently fine-tune LLMs for different downstream NLP tasks [82, 83]. In this work we compare with the most representative methods for fair benchmarking. For example, Adapters [30] insert extra lightweight modules inside each Transformer layer. One adapter module generally consists of a linear down-projection, followed by a nonlinear activation function, and a linear up-projection, together with a residual connection [58, 59]. Instead of inserting new modules, [6] proposed to update the bias term and freeze the rest of backbone parameters when fine-tuning ConvNets. BitFit [3] applied this technique to Transformers and verified its effectiveness on LLM tuning. Through our experiments that we demonstrate that our method, EXPRESS provides a more effective way of adapting Transformers compared to prior approaches." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Prompting: An alternative to traditional adaptation methods is prompting [48] - originally proposed as a way of" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "3367" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.161, + 0.088, + 0.812, + 0.37 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.383, + 0.895, + 0.44 + ], + "angle": 0, + "content": "Figure 2. EXPRES Architecture in detail: EXPRES optimizes two types of prompts, shallow prompts (e.g., \\( p_i \\)) and residual prompts (e.g., \\( \\nabla_{LN,i} \\)), to construct task specific representation without updating the pretrained encoder weights. Each residual prompt is a learnable vector that is added to the output of various computations such as Layer Norm, Query-Key-Value projections, and linear projection after the MSA operation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.466, + 0.473, + 0.892 + ], + "angle": 0, + "content": "prepending language instruction to the input text so that a pre-trained LLM can \"understand\" the task. Through trial and error selection of appropriate prompts, GPT-3 shows strong generalization to downstream transfer learning tasks even in the few-shot or zero-shot settings [4]. This was followed up by other works on better prompt construction [33, 71]. Recent works [39, 43, 50] propose to treat the prompts as task-specific continuous vectors and directly optimize them via gradients during fine-tuning. Such approaches, named \"Prompt Tuning\" achieve performance comparable to finetuning but with \\(1000 \\times\\) less parameters in some cases. Following the success in LLMs, prompt have also been adopted for vision-language models [22, 35, 60, 96, 103]. Nonetheless, all the above methods prompt the text encoders and hence are tied to language as input. However, many realistic visual tasks such as dense prediction may not be well aligned with the language modality. Thus, it becomes imperative to develop prompting approaches that can work in the visual modality. To that end, recent work on visual prompting [2, 10, 32, 66, 88] provides encouraging results. In particular, [32] demonstrate that even in the visual domain, adaptation based on continuous prompting can outperform finetuning, especially when the training datasets are small. Our work however shows that current prompting methods do not fully exploit the capacity of prompting for a vision transformer. Through a principled approach to prompting, we derive a more effective prompting technique that achieves state-of-the-art per" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.466, + 0.84, + 0.481 + ], + "angle": 0, + "content": "formance at much smaller computational overhead." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.487, + 0.895, + 0.76 + ], + "angle": 0, + "content": "Few-Shot Classification: Few-shot classification has received a lot of attention in recent years. While a variety of approaches [75] have been proposed, the most successful ones seek to transfer positive knowledge either by finetuning [1, 12, 79] or meta-learning [17, 19, 21, 24, 38, 62, 74, 77, 81]. Finetuning based few-shot learners can be viewed as specialists that perform well on the target domain [9, 27, 79], but suffer from catastrophic forgetting [70] on the base domain. Meta-learning approaches, on the other hand, can be seen as generalists that enjoy complete immunity against forgetting but at the cost of somewhat lower performance in the target domain. In this work, we propose EXPRES as a constructive adaptation technique that is immune to forgetting but at the same time benefits from task specific parameter tuning, thus, leveraging the best of both worlds. One of our key contribution is to demonstrate the transferability of Transformers from classification to dense prediction tasks (semantic segmentation) when adapted with EXPRES." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.897, + 0.903 + ], + "angle": 0, + "content": "Few-Shot Semantic Segmentation: This task was originally proposed in [68]. Most works after that follow the metric learning paradigm [14] with various novelties from improved support-query matching [47, 72, 95] to better optimization [46, 104], memory modules [90, 93], graph neural networks [84, 92, 99], and more [28, 42, 45, 52, 53, 78, 98, 106]. Some methods generate representative support prototypes with attention mechanism [20, 100], adaptive prototype learning [41, 57, 73], or various prototype generation" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3368" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.152 + ], + "angle": 0, + "content": "techniques [49, 54, 86, 94]. In contrast, our approach directly adapts a model pretrained on image classification to few-shot semantic segmentation without intermediate pretraining on densely-annotated datasets." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.168, + 0.186, + 0.185 + ], + "angle": 0, + "content": "3. Approach" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.193, + 0.218, + 0.208 + ], + "angle": 0, + "content": "3.1. Preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.216, + 0.471, + 0.398 + ], + "angle": 0, + "content": "Consider an input space \\(\\mathcal{X}\\) and a categorical label set \\(\\mathcal{Y}\\) where each class is represented via a one-hot encoding. A representation \\(\\mathcal{R} \\subset \\mathbb{R}^d\\) of the input is defined by the composition of an augmentation function \\(\\mathcal{A}: \\mathcal{X} \\to \\mathcal{X}\\) and an encoder model \\(E_{\\theta}: \\mathcal{X} \\to \\mathcal{R}\\), parameterized by \\(\\theta\\). The augmentation function is a composition of standard image transformations such as random cropping, horizontal flipping etc. A general recognition task \\(\\mathcal{T}\\) can be defined in terms of a finite training set, \\(\\{(x_i, y_i)\\}_{i \\in \\mathcal{D}_{\\mathrm{train}}}^*\\) and \\(N_c\\) categories such that, \\(y_i \\in [N_c]\\). The goal, is to leverage a pretrained encoder, \\(E_{\\theta^*}\\) and the training set to obtain a classifier for the task \\(\\mathcal{T}\\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.41, + 0.414, + 0.425 + ], + "angle": 0, + "content": "3.2. Overview of Vision Transformers (ViT)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.432, + 0.47, + 0.629 + ], + "angle": 0, + "content": "In a typical ViT, the image, \\( x \\in \\mathbb{R}^{h \\times w \\times 3} \\) is uniformly divided into \\( N \\) fixed-sized patches, each of which are projected to a \\( d \\)-dimensional embedding and are added a positional embedding, resulting in a patch token \\( z_{n} \\in \\mathbb{R}^{d} \\). Additionally, a class token \\( z_{\\mathrm{cls}} \\in \\mathbb{R}^{d} \\) is concatenated to the sequence of the patch tokens to form the input, \\( Z^0 \\in \\mathbb{R}^{(N + 1) \\times d} \\). Starting from layer \\( l = 0 \\), the incoming activations at each layer, \\( z^{l - 1} \\) are first normalized using LayerNorm (LN), and then processed by a multi-headed self-attention block (MSA) followed by an MLP block. At the last layer, the resulting class token is normalized to yield the final representation. The overall computations in a ViT encoder can be summarised as" + }, + { + "type": "equation", + "bbox": [ + 0.101, + 0.643, + 0.448, + 0.722 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} Z ^ {0} = \\left[ z _ {\\mathrm {c l s}}, z _ {0}, \\dots , z _ {N - 1} \\right] \\\\ H ^ {l - 1} = \\operatorname {M S A} (\\operatorname {L N} (Z ^ {l - 1})) + Z ^ {l - 1} \\quad l = 0, \\dots , L - 1 \\\\ Z ^ {l} = \\operatorname {M L P} (\\operatorname {L N} (H ^ {l - 1})) + H ^ {l - 1} \\quad l = 0, \\dots , L - 1 \\\\ y = L N \\left(Z _ {\\mathrm {c l s}} ^ {L}\\right) \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.47, + 0.901 + ], + "angle": 0, + "content": "where \\( L \\) represents the number of encoder layers. The multi-headed self-attention mechanism (MSA) abstracts patchwise representation by aggregating the right context at each layer. The context aggregation is facilitated by softmax attention that relies on patch-to-patch similarities and its parameters are governed by the pre-training task objective. During adaptation, however, the representations for downstream task might benefit from aggregating a slightly different context at each layer. Our prompt tuning approach facilitates task specific modulation of this context by augmenting and learning layerwise patch tokens." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.091, + 0.741, + 0.108 + ], + "angle": 0, + "content": "3.3. Expressive Prompt Tuning" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.114, + 0.894, + 0.281 + ], + "angle": 0, + "content": "At the input layer of the ViT, we introduce prompt tokens, \\( P^0 \\in \\mathbb{R}^{M \\times d} \\) which are \\( M \\) parameterized vectors of dimension \\( d \\) concatenated to the input token sequence, \\( Z^0 \\), of the ViT. Input-level prompts, also referred to as shallow prompts, are propagated through the encoder together with the class and patch tokens such that at every layer, each token interacts with every other token through the self-attention layers. The propagated prompts at the last layer are average-pooled to obtain the final representation. The insertion and propagation of the prompts described above can be expressed as" + }, + { + "type": "equation", + "bbox": [ + 0.523, + 0.288, + 0.891, + 0.41 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\tilde {Z} ^ {0} = \\left[ Z ^ {0} \\right| \\left| P ^ {0} \\right] \\tag {1} \\\\ \\tilde {H} ^ {l - 1} = \\operatorname {M S A} (\\operatorname {L N} (\\tilde {Z} ^ {l - 1})) + \\tilde {Z} ^ {l - 1} \\quad l = 0, \\dots , L - 1 \\\\ \\tilde {Z} ^ {l} = \\operatorname {M L P} (\\operatorname {L N} (\\tilde {H} ^ {l - 1})) + \\tilde {H} ^ {l - 1} \\quad l = 0, \\dots , L - 1 \\\\ Z ^ {L}, P ^ {L} = \\operatorname {c h u n k} \\left(\\tilde {Z} ^ {l}\\right) \\\\ \\tilde {y} = \\operatorname {A v g P o o l} \\left(P ^ {L}\\right) \\\\ y = L N (\\tilde {y}) \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.419, + 0.892, + 0.524 + ], + "angle": 0, + "content": "we use \\(||\\) to denote the concatenation along the sequence axis and chunk to denote the splitting of the propagated sequence of length \\(N + M + 1\\) into the \\(N + 1\\) tokens and \\(M\\) prompts. Shallow prompts are capable of modeling some of the desired token relations for a task. However, they have limited capacity due to the inability to alter for specific perlayer interactions with the class and image tokens." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.524, + 0.892, + 0.631 + ], + "angle": 0, + "content": "To enhance the prompt capacity, we introduce layer-wise residual prompts, \\(\\Delta^l\\in \\mathbb{R}^{M\\times d}\\) that are added to the propagated prompts at various computations within the MSA block for an intermediate layer \\(l\\). This includes the output of attention LayerNorm, query-key-value projections and linear multi-head projection. We summarise the MSA computations at layer \\(l\\) with \\(N_{h}\\) heads and input \\(Z\\)" + }, + { + "type": "equation", + "bbox": [ + 0.554, + 0.64, + 0.89, + 0.718 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} Z ^ {\\prime} = L N (Z) \\\\ Q _ {h} = Z ^ {\\prime} W _ {h} ^ {Q}; K _ {h} = Z ^ {\\prime} W _ {h} ^ {K}; V _ {h} = Z ^ {\\prime} W _ {h} ^ {V} \\\\ \\mathrm {g} _ {h} = \\text {A t t} \\left(Q _ {h}, K _ {h}, V _ {h}\\right) \\quad i = 1, \\dots , N _ {h} \\tag {2} \\\\ O = \\left[ \\mathbf {g} _ {1} \\right| | \\dots | | \\mathbf {g} _ {N _ {h}} \\rbrack W ^ {\\text {p r o j}} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.727, + 0.894, + 0.787 + ], + "angle": 0, + "content": "above \\( h \\) is used to represent the head index of \\( W^{Q}, W^{K}, W^{V} \\) and \\( W^{\\mathrm{proj}} \\) denotes the projection matrix of the MSA block. The residually prompted computations can then be expressed as" + }, + { + "type": "equation", + "bbox": [ + 0.608, + 0.797, + 0.786, + 0.898 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} Z ^ {\\prime} = L N (Z) + [ \\bar {\\mathbf {0}} | | \\boldsymbol {\\Delta} _ {\\mathbf {L N}} ] \\\\ \\tilde {Q} _ {h} = Q _ {h} + \\left[ \\bar {\\mathbf {0}} \\right| \\left| \\boldsymbol {\\Delta} _ {\\mathbf {Q}} \\right| \\\\ \\tilde {K} _ {h} = K _ {h} + [ \\mathbf {0} | | \\boldsymbol {\\Delta} _ {\\mathbf {K}} ] \\\\ \\tilde {V} _ {h} = V _ {h} + [ \\bar {\\mathbf {0}} | | \\boldsymbol {\\Delta} _ {\\mathbf {V}} ] \\\\ \\tilde {O} = O + \\left[ \\bar {\\mathbf {0}} \\right| | \\boldsymbol {\\Delta} _ {\\mathrm {p r o j}} ] \\\\ \\end{array}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3369" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.213 + ], + "angle": 0, + "content": "where the concatenation of \\((N + 1) \\times d\\) dimensional zero matrix, \\(\\bar{\\mathbf{0}}\\) with the residual-prompts, signifies that the residuals \\(\\Delta\\) are added only at the propagated prompt positions and not to the image patch or class token positions. The above residual computations occur at every layer with independently learned residual prompts, and we drop the layer indices in the equations for brevity. The overall EXPRES architecture is visualized in Figure 2." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.234, + 0.367, + 0.25 + ], + "angle": 0, + "content": "3.4. Interpreting Residual Prompting" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.26, + 0.47, + 0.395 + ], + "angle": 0, + "content": "We take a closer look at residual prompting for self-attention and interpret it's functionality. The Att operation in Eq. (2) facilitates weighted aggregation over all \"value\" tokens where the weights are computed using the \"query\" and a \"key\" tokens as \\( w_{ij} \\propto \\exp \\left( \\frac{q_i^T k_j}{\\sqrt{d / N_h}} \\right) \\). When prompted with residual tokens, the expression for the weights that aggregate information for a patch token \\( q_i \\) can be factored as," + }, + { + "type": "equation", + "bbox": [ + 0.136, + 0.413, + 0.469, + 0.517 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\tilde {w} _ {i j} \\propto \\exp \\left(\\frac {q _ {i} ^ {T} \\left(k _ {j} + \\boldsymbol {\\Delta} _ {K , j}\\right)}{\\sqrt {d / N _ {h}}}\\right) \\\\ = \\exp \\left(\\frac {q _ {i} ^ {T} k _ {i}}{\\sqrt {d / N _ {h}}}\\right) \\exp \\left(\\frac {q _ {i} ^ {T} \\Delta_ {K , j}}{\\sqrt {d / N _ {h}}}\\right) \\tag {3} \\\\ = w _ {i j} * \\alpha_ {i j}. \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.535, + 0.47, + 0.702 + ], + "angle": 0, + "content": "Based on Eq. (3), residual prompts facilitate task-specific reweighting of the attention weights independently at every layer, allowing the modulation of context aggregated per patch token. Such layerwise modulation can lead to better adaptation of the final representation compared to shallow prompting that restricts the modulation to the input layer. Moreover, the two-way interaction between prompts and patch tokens leads to greater flexibility than other forms of multilayered prompting [32, 67] that allow for only partial interaction. For instance, [32] restrict the prompts to act only as keys and never as queries." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Residual prompt based attention reweighting is also interesting from parameter efficiency perspective as it circumvents the need for updating the attention weight matrices (done in finetuning approaches) to achieve the same goal of task specific adaptation. Specifically, each layer of a ViT consists of three attention weight matrices, each with \\( d \\times d \\) dimensions, resulting in \\( \\mathcal{O}(d^2) \\) learnable parameters. In contrast, each prompt is \\( d \\) dimensional so, only \\( \\mathcal{O}(d) \\) parameters need to be adapted even with \\( M \\) prompts, where \\( M << d \\). We empirically validate that the high capacity as well as parameter efficiency of our prompting approach is crucial for achieving good adaptation performance in limited labelled data settings." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.092, + 0.707, + 0.108 + ], + "angle": 0, + "content": "3.5. Learning the Prompts" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.114, + 0.895, + 0.326 + ], + "angle": 0, + "content": "In this work, we are mainly interested in two types of downstream tasks - image classification and semantic segmentation. To train the prompts for classification, we optimize a standard cross entropy loss with respect to the representation, \\( y \\) in Eq. (1) and the corresponding ground-truth label, \\( y* \\). In the case of semantic segmentation, we adapt the model as well as the objective to perform dense predictions. At the final layer of the encoder, we extract the keys corresponding to the patch tokens and pass them through the classifier. The sequence outputs are then reshaped into a 2d map and resized to original image resolution using bilinear interpolation, resulting in a pixel wise prediction. Finally, to optimize the prompts with the classifier head, we use a dense cross entropy loss as follows" + }, + { + "type": "equation", + "bbox": [ + 0.515, + 0.336, + 0.877, + 0.369 + ], + "angle": 0, + "content": "\\[\n\\left\\{p _ {m} ^ {*}\\right\\}, \\left\\{\\boldsymbol {\\Delta} ^ {*} \\right\\} = \\underset {\\left\\{p _ {m} \\right\\}, \\left\\{\\boldsymbol {\\Delta} \\right\\}, C} {\\arg \\min } \\sum_ {j \\in I _ {\\mathrm {c x t}}} \\sum_ {h, w} L _ {\\mathrm {C E}} \\left(y _ {j h w}, y _ {j h w} ^ {*}\\right)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.379, + 0.892, + 0.41 + ], + "angle": 0, + "content": "where, \\( h, w \\) are used to index the spatial positions at the resolution, \\( H \\times W \\) of the input image." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.423, + 0.633, + 0.44 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.448, + 0.894, + 0.508 + ], + "angle": 0, + "content": "We validate the effectiveness of EXPRES on a variety of benchmarks consisting of wide variety of tasks and dataset sizes. We also analyse the importance of various model components and design decisions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.509, + 0.893, + 0.902 + ], + "angle": 0, + "content": "Datasets: To evaluate EXPRES, we use two different benchmarks, VTAB-1k [97] and FGVC [32]. The VTAB-1k benchmark consists of 19 different visual classification tasks categorized under three groups: Natural - tasks with natural images captured with standard cameras; Specialized - tasks with images captured under specialized settings (medical and satellite imagery); and Structured - tasks that requires understanding scene geometry, like object distance. Each task-specific dataset contains 1000 training examples with varying number of samples per class, depending on the number of classes. For validation purposes and hyperparameter selection, we use a \\(800 - 200\\) split of the training set and then train on all 1000 examples for final results, which are based on evaluation on the entire test set. The FGVC benchmark consists of the finegrained datasets including CUB [89], Oxford Flowers [55], Stanford Dogs [36] and Stanford Cars [23]. In conjunction with VTAB-1k, we use the FGVC datasets to conduct key ablation studies for EXPRES. A random \\(90 - 10\\) split of each dataset is used for hyperparameter selection. For few shot segmentation, we use the standard PASCAL \\(-5^{\\mathrm{i}}\\) [69] benchmark that was created from PASCAL VOC 2012 [16] with extra mask annotations for 20 object classes, evenly divided into 4 folds: \\(\\{5^i : i \\in \\{0,1,2,3\\}\\}\\). Following prior works for evaluation scheme, we randomly sample 1000 episodes per fold and report the average performance over all episodes" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3370" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.089, + 0.891, + 0.361 + ], + "angle": 0, + "content": "
naturalspecializedstructured
CLEAR-100Caltech101DTDFlowers102PetsSVHNSun397MeanPatch CamelyonEuroSATResisc45RetinopathyMeanClevr/countClevr/distanceDMLabKITTI/distancedSprites/locationdSprites/orientationSmallNORB/azimuthSmallNORB/elevationMean
Linear63.485.063.297.086.336.651.068.9378.587.568.674.077.1634.330.633.255.412.520.09.619.226.84
MLP-263.284.860.597.685.934.147.867.7074.388.867.173.275.8645.231.631.855.730.924.616.623.332.47
MLP-363.884.762.397.484.732.549.267.8077.088.070.256.172.8347.832.832.358.112.921.215.224.830.62
MLP-559.384.459.996.184.430.946.865.9873.787.264.871.574.3150.832.331.556.47.520.814.420.429.23
MLP-953.180.553.995.182.624.443.761.9078.583.060.272.373.4947.527.928.954.06.217.710.816.226.15
Sidetune [101]60.760.853.695.566.734.935.358.2158.587.765.261.068.1227.622.631.351.78.214.49.821.823.41
Biastune [6]72.887.059.297.585.359.951.473.3078.791.672.969.878.2561.555.632.455.966.640.015.725.144.09
Adapter-25674.186.163.297.787.034.650.870.5076.388.073.170.576.9845.737.431.253.230.325.413.822.132.39
Adapter-6474.285.862.797.687.236.350.970.6576.387.573.770.977.1042.939.930.454.531.925.613.521.432.51
Adapter-874.285.762.797.887.236.450.770.6776.989.273.571.677.8045.241.831.156.430.424.613.222.033.09
Partial-166.885.962.597.385.537.650.669.4478.689.872.573.378.5341.534.333.961.031.332.816.322.434.17
FT-all68.987.764.397.286.987.438.875.8879.795.784.273.983.3656.358.641.765.557.546.725.729.147.64
VPT-shallow [32]77.786.962.697.587.374.551.276.8178.292.075.672.979.6650.558.640.567.168.736.120.234.146.98
VPT-deep [32]78.890.865.898.088.378.149.678.4881.896.183.468.482.4368.560.046.572.873.647.932.937.854.98
EXPRES (ours)78.089.668.898.788.981.951.979.784.896.280.974.284.066.560.446.577.678.049.526.135.355.0
" + }, + { + "type": "table_caption", + "bbox": [ + 0.154, + 0.371, + 0.816, + 0.385 + ], + "angle": 0, + "content": "Table 1. VTAB-1k benchmark: Per task adaptation results with ViT-B/16 model pretrained on ImageNet-21k.." + }, + { + "type": "table", + "bbox": [ + 0.261, + 0.399, + 0.712, + 0.52 + ], + "angle": 0, + "content": "
MethodIm-PreDense-PreBackbone50515253
SPNET [91]In-1k✓ResNet-10123.817.014.118.3
ZS3Net [5]In-1k✓ResNet-10140.839.439.333.6
LSEG [40]In-1k✓ViT-L/1661.363.643.141.0
LinearIn-21k-ViT-B/165.143.928.129.1
FT-allIn-21k-ViT-B/1618.331.927.923.2
BiastuneIn-21k-ViT-B/162.439.213.920.1
VPT-deep [32]In-21k-ViT-B/1633.456.249.847.7
EXPRES (Ours)In-21k-ViT-B/1641.860.252.451.4
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.53, + 0.893, + 0.558 + ], + "angle": 0, + "content": "Table 2. Five-Shot Semantic Segmentation on PASCAL - \\(5^{\\mathrm{i}}\\): Per fold adaptation results with ViT-B/16 model pretrained on ImageNet-21k." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.586, + 0.47, + 0.72 + ], + "angle": 0, + "content": "of the corresponding fold. However, unlike prior works, we tune our EXPRES model on few-shot training examples and cross-validate the hyperparameters (e.g. number of prompts, \\( M \\)) on a validation set with fold-exclusive categories. In all our experiments, we use a reasonably small budget for hyperparameters (see supplementary) following recent studies [56] that highlight the likelihood of overoptimistic results in limited-labelled data settings due to excessive hyperparameter tuning on large validation sets." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.722, + 0.471, + 0.889 + ], + "angle": 0, + "content": "Implementation Details: In all our experiments, we use a fixed encoder, ViT-B/16 pretrained on ImageNet-22K [65]. This model is effective on wide variety of tasks and allows direct comparison with prior works. For each downstream task, we train for a total 100 epochs with an initial warmup of 10 epochs. We use AdamW as our default optimizer with a suitable learning rate and fixed weight decay of \\(1e - 4\\). For VTAB-1k and FGVC experiments, we use a fixed batch size of 64. For segmentation experiments, since overall training set sizes are extremely small (\\(\\leq 10\\) images in total), we use the entire training set per batch. We use input image reso" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.586, + 0.892, + 0.737 + ], + "angle": 0, + "content": "lution of \\(224 \\times 224\\) for classification tasks and \\(384 \\times 384\\) for semantic segmentation tasks as dense prediction usually benefits from larger resolution. Since, ViT-B/16 is pretrained on standard \\(224 \\times 224\\) resolution images, we use interpolated positional embeddings to accommodate larger resolutions in the case of segmentation. Finally, we use standard data augmentations for classification benchmarks i.e., Resize \\(\\rightarrow\\) Random-Crop \\(\\rightarrow\\) Horizontal-Flip during training and Resize \\(\\rightarrow\\) Center-Crop during evaluation while for segmentation we only use Resize." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.739, + 0.894, + 0.815 + ], + "angle": 0, + "content": "Evaluation Metrics For classification experiments, we use accuracy as our performance metric. For evaluating segmentation masks, we use mean intersection over union (mIoU) that averages over the intersection over union curves per class." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.83, + 0.64, + 0.845 + ], + "angle": 0, + "content": "4.1. Main Results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.895, + 0.901 + ], + "angle": 0, + "content": "We compare EXPRES with a number of commonly used adaptation techniques on VTAB-1k. The adaptation methods can be categorized as head-oriented, backbone-oriented" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "3371" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.348 + ], + "angle": 0, + "content": "and prompt-based. Under the first category, Linear only optimizes a linear classifier for the downstream task while MLP-\\(k\\) uses a \\(k\\)-layer multilayer perceptron (MLP) as the classifier head. As an example of the second category, Sidetune [101] uses features that are linearly interpolated between pretrained features and features from a \"side\" network trained on downstream data. While Biastune [6] adapts only the bias terms of an otherwise frozen backbone. Adapter-\\(d\\) [30, 58, 59] introduces lightweight MLP modules inserted between Transformer layers. Partial-\\(k\\) finetunes the last \\(k\\) layers while keeping the rest of the backbone frozen, finally FT-all finetunes all the layers. VPT-shallow [32] additionally optimizes a linear classifier with the learnable input prompts propagated through the encoder. VPT-deep [32] introduces more capacity by replacing the propagated prompts with a new set of learnable prompts at each layer." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.349, + 0.473, + 0.637 + ], + "angle": 0, + "content": "VTAB-1k Results (Table 1): Across all three splits of VTAB-1k, our method significantly outperforms the best head-oriented techniques: \\(+11\\%\\) (natural), \\(+7\\%\\) (specialized) and \\(+23\\%\\) (structured). Similar trends hold even when comparing with the more powerful class of backbone-oriented techniques. While FT-all has been widely adopted as an effective technique for most adaptation scenarios, our method consistently outperforms it by a significant margin of \\(+4\\%\\) (natural), \\(+1\\%\\) (specialized) and \\(+7\\%\\) (structured). Most interestingly our method even outperforms other powerful prompting techniques like VPT-deep on 12 (out of 19) datasets by a margin of about \\(+1\\%\\) (natural), \\(+2\\%\\) (specialized) and \\(+0.02\\%\\) (structured). The performance gains are particularly impressive when considered from the perspective of computation vs performance tradeoff. Compared to VPT-deep that uses 53 prompts for natural and 108 prompts for structures, our method only requires 10 and 29 prompts for the respective splits. A more detailed summary is provided in the supplementary." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.65, + 0.47, + 0.681 + ], + "angle": 0, + "content": "4.2. Few-Shot Semantic Segmentation Without Dense Pretraining" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.471, + 0.902 + ], + "angle": 0, + "content": "We test the efficacy of EXPRES on a novel adaptation setup where the backbone, pretrained on classification tasks, is directly adapted for few-shot semantic segmentation task without additional training on large densely-annotated datasets. This is in contrast with most works that follow a two-stage pretraining procedure i.e., training on ImageNet-1k with image level labels followed by meta-learning on densely annotated datasets constructed from the train folds of PASCAL - \\(5^{\\mathrm{i}}\\). In contrast, we only perform the first stage pretraining on a sufficiently diverse dataset (ImageNet-21k in our case) with no meta-learning stage. During evaluation, each few-shot episode randomly samples a target image with a segmentation mask that assigns a label 1 to the pixels corresponding to one of the object cate" + }, + { + "type": "image", + "bbox": [ + 0.557, + 0.091, + 0.695, + 0.209 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.7, + 0.091, + 0.839, + 0.209 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.556, + 0.211, + 0.695, + 0.327 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.7, + 0.211, + 0.839, + 0.327 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.341, + 0.895, + 0.396 + ], + "angle": 0, + "content": "Figure 3. Prompt Propagation: Effect of propagating prompts with modulation upto a layer, \\( l = \\{2,\\dots ,12\\} \\) of the ViT-B/16 encoder with total 12 layers. The datasets are sampled from the FGVC benchmark." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.426, + 0.895, + 0.804 + ], + "angle": 0, + "content": "gories in that image and a label 0 to remaining pixels (background). From the same object category, a set of five images are randomly sampled to form the training set where the mask of each image is annotated in the same way as the target. Our method as well as all baselines that perform meta-learning are optimized given a context set to yield a binary classifier for the target image. For dense representations, we use the last layer keys of the MSA-block as we found them to be more accurate than the typical MLP-block output. We observe that our method consistently outperforms the baselines (by \\(25\\%\\)) as well as other prompt techniques such as VPT-deep (by \\(5\\%\\)). Surprisingly, our method even outperforms [40] that leverages densely annotated datasets (training data per fold) with large language models for a second stage of pretraining. Specifically, on 2/4 folds, EXPRES outperforms [40] by \\(10\\%\\) despite training on a significantly smaller densely-annotated dataset (five images). These results are particularly significant as they suggest that highly competitive results can be achieved with models pretrained on image classification. Consequently, results may be further improved by scaling up the image-level annotated datasets which are cheaper to scale than the densely annotated datasets. In the supplementary, we provide visualizations of the segmentation mask predictions by our method as well as Linear, FT-all and VPT-deep methods." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.816, + 0.666, + 0.832 + ], + "angle": 0, + "content": "4.3. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.895, + 0.901 + ], + "angle": 0, + "content": "We conduct extensive ablations to evaluate key design decisions used to develop EXPRES such as feature construction, residual prompting, number of prompts etc. For all ablations, we use the same ViT-B/16 backbone. When" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3372" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.16, + 0.087, + 0.805, + 0.216 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.132, + 0.227, + 0.837, + 0.243 + ], + "angle": 0, + "content": "Figure 4. Residual Prompt Types: Evaluating the importance of different type of residual prompts on FGVC datasets." + }, + { + "type": "image", + "bbox": [ + 0.117, + 0.264, + 0.422, + 0.422 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.438, + 0.47, + 0.466 + ], + "angle": 0, + "content": "Figure 5. Computational Efficiency Plots: Comparing Accuracy vs Number of Prompts for VPT and EXPRES" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.493, + 0.47, + 0.523 + ], + "angle": 0, + "content": "using FGVC datasets, we use only \\(10\\%\\) of each dataset with official splits provided in [32]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.524, + 0.471, + 0.749 + ], + "angle": 0, + "content": "Prompt Propagation: We evaluate the importance of propagating prompts through the ViT-B/16 encoder with layerwise modulation. Specifically, upto a layer \\( l \\), we allow all tokens (patch, class and prompt) to attend to each other at every layer. Beyond \\( l \\), prompts are not allowed to interact with other tokens at all; they are simply projected by the value heads of MSA-block followed by MLP processing at every layer. In our experiments, we fix the number of prompts to 10 irrespective of the dataset. From Figure 3, we observe that downstream performance depends directly on the extent of prompt propagation with modulation: accuracy improves as more layers allow prompts to interact with other tokens. These results motivate our method, EXPRES, that facilitates finegrained layerwise modulation via residual tokens." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.473, + 0.902 + ], + "angle": 0, + "content": "Residual Prompt Type: In Figure 4 we evaluate the importance of different residual prompt types (one-at-a-time) including attention, LayerNorm \\((LN)\\), query-key-value projections \\((QKV)\\) and linear multi-head projection \\((Proj)\\). We also evaluate residual prompting in the MLP block: after LayerNorm \\((LN,mlp)\\), first linear projection \\((L1,mlp)\\) and second linear projection \\((L2,mlp)\\). We evaluate the composite effect of multiple prompt types within a computational block i.e., Att (MSA block) and MLP (MLP block). As a baseline, we provide the per-dataset results for shallow" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.268, + 0.895, + 0.48 + ], + "angle": 0, + "content": "prompting, referred to as None in the figure. The number of prompts at each layer are fixed at 10. We observe that, within the MSA block, adding residual prompts to LayerNorm and query-key-value projections yields the most improvements (3.5% and 2.8% on an average respectively) over None. Moreover, LayerNorm prompts in the MLP block are also more effective than prompting the two linear layers. Comparing blockwise performance, prompting the MSA block \\((Att)\\) yields significantly better performance (by 1.6%) than prompting the MLP block \\((MLP)\\). The performance gap between \\(Att\\) and \\(MLP\\) highlights the importance of directly modulating layerwise interaction between tokens for better adaptation. Consequently, we use \\(Att\\) as our default setting for all experiments." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.481, + 0.895, + 0.678 + ], + "angle": 0, + "content": "Computational Efficiency of Prompting: In prompting techniques, the primary computational overhead arises from the quadratic complexity (in number of tokens) of the transformer encoder. So to evaluate computation efficiency of prompting, we investigate the rate at which performance improves with number of prompts and provide comparisons between our method and VPT in Figure 5. We evaluate on two different datasets sampled from different categories of VTAB-1k. For a given accuracy, e.g. \\(58.5\\%\\) on Clevr-Distance, EXPRES requires an order less prompts than VPT, resulting in 2 orders less computations. Overall EXPRES achieves higher optimal performance with far fewer prompts than VPT." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.693, + 0.62, + 0.71 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.895, + 0.903 + ], + "angle": 0, + "content": "In this work we propose a novel prompting technique for adapting large vision models. Our method demonstrates strong performance across variety of downstream tasks with varying dataset sizes. Further, our method outperforms commonly used finetuning approach as well as the recently proposed VPT method on standard benchmarks. We also demonstrate diverse adaptation ability of our method from classification to semantic segmentation tasks in the few-shot setting. Lastly, our method is more parameter efficient that existing weight-space and prompt based adaptation techniques. In the future, we plan to extend our method to additional settings including vision-language learning." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3373" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.175, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.093, + 0.117, + 0.47, + 0.158 + ], + "angle": 0, + "content": "[1] Arman Afrasiyabi, Jean-François Lalonde, and Christian Gagn'e. Associative alignment for few-shot image classification. In ECCV, 2020. 3" + }, + { + "type": "ref_text", + "bbox": [ + 0.093, + 0.16, + 0.47, + 0.202 + ], + "angle": 0, + "content": "[2] Hyojin Bahng, Ali Jahanian, Swami Sankaranarayanan, and Phillip Isola. 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In this work, we present Expressive Prompts with Residuals (EXPRES) which modifies the prompt learning paradigm specifically for effective adaptation of vision transformers (ViT). Our method constructs downstream representations via learnable "output" tokens (shallow prompts), that are akin to the learned class tokens of the ViT. Further for better steering of the downstream representation processed by the frozen transformer, we introduce residual learnable tokens that are added to the output of various computations. We apply EXPRES for image classification and few-shot semantic segmentation, and show our method is capable of achieving state of the art prompt tuning on 3/3 categories of the VTAB benchmark. In addition to strong performance, we observe that our approach is an order of magnitude more prompt efficient than existing visual prompting baselines. We analytically show the computational benefits of our approach over weight space adaptation techniques like finetuning. Lastly we systematically corroborate the architectural design of our method via a series of ablation experiments. + +# 1. Introduction + +Scaling up of neural nets in the past few years has steadily improved performance on wide variety of downstream visual tasks. However, model adaptation is often necessary to achieve the best performance in downstream tasks like fine-grained recognition [89], semantic segmentation [8] or object recognition [34]. While traditional techniques like full-model finetuning have become the de-facto approach to adaptation, they are not well suited for many scenarios. For example, finetuning is susceptible to catastrophic forgetting [37] as it modifies model parameters without the knowledge of future domains, and potentially losing prior + +![](images/8e217a44ee87e2e7710edd21f0dbc7ebfe37c360c49c7277dd2a0dca9a4a3f34.jpg) +Figure 1. Adapting large vision models is crucial to solving downstream tasks with wide variety of semantics (e.g., image classification, semantic segmentation etc.) as well as dataset sizes (few-shot, low-shot, full-shot). In this work, we propose a novel adaptation technique for large vision models that is capable of achieving the desired goal. + +knowledge of current adaptation. Moreover, finetuning all of the model parameters of a large vision model with just a few training examples can lead to poor generalization. This is in contrast to human intelligence that is capable of solving wide variety of downstream tasks with extremely few exemplars. + +Motivated by the need for better adaptation, parameter efficient techniques like partial-finetuning or adapters [64, 101] have been developed to constructively adapt large models without significant parameter overhead. While serving as effective alternatives to finetuning, most parameter efficient techniques have been designed with convolutional architectures in mind. In light of recent works [15] that demonstrate that Vision Transformers are more suitable for scaling up than CNNs, designing adaptation techniques that exploit the Transformer architecture can be extremely useful. To that end, visual prompt tuning (VPT) [32] has been proposed as a way to constructively adapt transformers by introducing learnable tokens at every layer that interact with the patch and class tokens and are optimized together with a classi + +fier head. While being effective in practice, VPT allows only partial interactions between prompts and the remaining tokens, thus, leveraging only a part of the prompt capacity. Moreover, it often requires a large number of inserted prompts to achieve optimal performance but that significantly increases the computation costs due to the quadratic computational complexity of the self-attention layer. + +In this work, we explore an alternate design to prompting motivated by the potential for greater prompt capacity. We propose ExPRes, an expressive prompt tuning method with residual tokens that inherits the strengths of parameter efficient adaptation while significantly improving downstream performance. Our prompt design is inspired by the two key observations - propagation of prompts by multilayered interaction with other tokens is crucial for strong capacity and learnable residual tokens can modulate the propagated prompts to favour task-specific relations (unlike in [32]). We first propagate shallow prompts through the encoder that are average pooled at the last layer to yield semantic image-level representations. Shallow prompts by themselves have limited capacity since they cannot specifically modulate token-token relations at higher layers. Therefore to harness the prompts, we add residual tokens to propagated prompts at various layerwise computations of the Transformer encoder including LayerNorm, self-attention and multi-head projection to facilitate layerwise modulation without increasing the number of prompts per layer. This results in enhanced prompt capacity at almost no additional computational cost. + +We empirically validate the effectiveness of our method on a variety of downstream tasks including fine-grained recognition and semantic segmentation. Our use of additional learnable parameters in the form of residual and shallow prompts allows the retention of prior knowledge in the form of frozen encoder weights while being extremely parameter efficient (prompts are $\leq 1\%$ of the total parameters). Thus, our method is highly suited for real world adaptation that requires information retention at low memory and computational overheads. Additionally, we show that in most cases we require fewer prompts than VPT to achieve the same or better performance, making it more suitable for limited data settings. Our main contributions can be summarized as follows: + +- We propose a novel prompting technique: EXPRES, that uses a combination of shallow and deep residual prompts to facilitate constructive adaptation to downstream tasks with limited labelled datasets. +- Our method significantly outperforms full-finetuning based adaptation by $4.6\%$ on VTAB-1k. Moreover, our method outperforms state-of-the-art prompting approach [32] on the same benchmarks with significantly fewer prompts, suggesting that prompt design is cru + +cial to extracting more capacity at a given parameter/computational budget. + +- To the best of our knowledge, we are the first to demonstrate the effectiveness of prompting for diverse applications such as few-shot semantic segmentation. Our method outperforms strong adaptation baselines by $25\%$ and achieves competitive performance with respect to language-assisted segmentation [40] despite training on significantly less data with dense annotations. + +# 2. Related work + +Large Vision Models: With the advent of Transformer models [80] and adoption to various computer vision tasks, including image classification [15, 51], object detection [7, 44], semantic and panoptic segmentation [76,85,102], video understanding [18, 25, 87] and few-shot learning [13], the scale of vision models have increased by orders of magnitude. Typically trained using large labelled data, either unimodal like ImageNet-21K [65] or multimodal, these models demonstrate superior performance on wide variety of visual tasks. Given their superior performance and much larger scale compared to ConvNets, the question of adapting such models efficiently becomes crucial. Motivated by the need, our work is primarily focussed on adaptation of Vision Transformers. + +Transfer Learning has been extensively studied for vision tasks in the context of ConvNets [105] and many techniques have been introduced including side tuning [101], residual adapter [63], bias tuning [6], etc. However, Transformer specific adaptation for visual tasks has received relatively less attention. At the same time, in the NLP domain, the dominance of large-scale pre-trained Transformer-based Large Language Models (LLM) [4, 11, 61], has paved way for many approaches [26, 29, 31] that efficiently fine-tune LLMs for different downstream NLP tasks [82, 83]. In this work we compare with the most representative methods for fair benchmarking. For example, Adapters [30] insert extra lightweight modules inside each Transformer layer. One adapter module generally consists of a linear down-projection, followed by a nonlinear activation function, and a linear up-projection, together with a residual connection [58, 59]. Instead of inserting new modules, [6] proposed to update the bias term and freeze the rest of backbone parameters when fine-tuning ConvNets. BitFit [3] applied this technique to Transformers and verified its effectiveness on LLM tuning. Through our experiments that we demonstrate that our method, EXPRESS provides a more effective way of adapting Transformers compared to prior approaches. + +Prompting: An alternative to traditional adaptation methods is prompting [48] - originally proposed as a way of + +![](images/9392da1658371cecf6c787ec7bd961fb94a933141e025545556014e1fbf648a9.jpg) +Figure 2. EXPRES Architecture in detail: EXPRES optimizes two types of prompts, shallow prompts (e.g., $p_i$ ) and residual prompts (e.g., $\nabla_{LN,i}$ ), to construct task specific representation without updating the pretrained encoder weights. Each residual prompt is a learnable vector that is added to the output of various computations such as Layer Norm, Query-Key-Value projections, and linear projection after the MSA operation. + +prepending language instruction to the input text so that a pre-trained LLM can "understand" the task. Through trial and error selection of appropriate prompts, GPT-3 shows strong generalization to downstream transfer learning tasks even in the few-shot or zero-shot settings [4]. This was followed up by other works on better prompt construction [33, 71]. Recent works [39, 43, 50] propose to treat the prompts as task-specific continuous vectors and directly optimize them via gradients during fine-tuning. Such approaches, named "Prompt Tuning" achieve performance comparable to finetuning but with $1000 \times$ less parameters in some cases. Following the success in LLMs, prompt have also been adopted for vision-language models [22, 35, 60, 96, 103]. Nonetheless, all the above methods prompt the text encoders and hence are tied to language as input. However, many realistic visual tasks such as dense prediction may not be well aligned with the language modality. Thus, it becomes imperative to develop prompting approaches that can work in the visual modality. To that end, recent work on visual prompting [2, 10, 32, 66, 88] provides encouraging results. In particular, [32] demonstrate that even in the visual domain, adaptation based on continuous prompting can outperform finetuning, especially when the training datasets are small. Our work however shows that current prompting methods do not fully exploit the capacity of prompting for a vision transformer. Through a principled approach to prompting, we derive a more effective prompting technique that achieves state-of-the-art per + +formance at much smaller computational overhead. + +Few-Shot Classification: Few-shot classification has received a lot of attention in recent years. While a variety of approaches [75] have been proposed, the most successful ones seek to transfer positive knowledge either by finetuning [1, 12, 79] or meta-learning [17, 19, 21, 24, 38, 62, 74, 77, 81]. Finetuning based few-shot learners can be viewed as specialists that perform well on the target domain [9, 27, 79], but suffer from catastrophic forgetting [70] on the base domain. Meta-learning approaches, on the other hand, can be seen as generalists that enjoy complete immunity against forgetting but at the cost of somewhat lower performance in the target domain. In this work, we propose EXPRES as a constructive adaptation technique that is immune to forgetting but at the same time benefits from task specific parameter tuning, thus, leveraging the best of both worlds. One of our key contribution is to demonstrate the transferability of Transformers from classification to dense prediction tasks (semantic segmentation) when adapted with EXPRES. + +Few-Shot Semantic Segmentation: This task was originally proposed in [68]. Most works after that follow the metric learning paradigm [14] with various novelties from improved support-query matching [47, 72, 95] to better optimization [46, 104], memory modules [90, 93], graph neural networks [84, 92, 99], and more [28, 42, 45, 52, 53, 78, 98, 106]. Some methods generate representative support prototypes with attention mechanism [20, 100], adaptive prototype learning [41, 57, 73], or various prototype generation + +techniques [49, 54, 86, 94]. In contrast, our approach directly adapts a model pretrained on image classification to few-shot semantic segmentation without intermediate pretraining on densely-annotated datasets. + +# 3. Approach + +# 3.1. Preliminaries + +Consider an input space $\mathcal{X}$ and a categorical label set $\mathcal{Y}$ where each class is represented via a one-hot encoding. A representation $\mathcal{R} \subset \mathbb{R}^d$ of the input is defined by the composition of an augmentation function $\mathcal{A}: \mathcal{X} \to \mathcal{X}$ and an encoder model $E_{\theta}: \mathcal{X} \to \mathcal{R}$ , parameterized by $\theta$ . The augmentation function is a composition of standard image transformations such as random cropping, horizontal flipping etc. A general recognition task $\mathcal{T}$ can be defined in terms of a finite training set, $\{(x_i, y_i)\}_{i \in \mathcal{D}_{\mathrm{train}}}^*$ and $N_c$ categories such that, $y_i \in [N_c]$ . The goal, is to leverage a pretrained encoder, $E_{\theta^*}$ and the training set to obtain a classifier for the task $\mathcal{T}$ . + +# 3.2. Overview of Vision Transformers (ViT) + +In a typical ViT, the image, $x \in \mathbb{R}^{h \times w \times 3}$ is uniformly divided into $N$ fixed-sized patches, each of which are projected to a $d$ -dimensional embedding and are added a positional embedding, resulting in a patch token $z_{n} \in \mathbb{R}^{d}$ . Additionally, a class token $z_{\mathrm{cls}} \in \mathbb{R}^{d}$ is concatenated to the sequence of the patch tokens to form the input, $Z^0 \in \mathbb{R}^{(N + 1) \times d}$ . Starting from layer $l = 0$ , the incoming activations at each layer, $z^{l - 1}$ are first normalized using LayerNorm (LN), and then processed by a multi-headed self-attention block (MSA) followed by an MLP block. At the last layer, the resulting class token is normalized to yield the final representation. The overall computations in a ViT encoder can be summarised as + +$$ +\begin{array}{l} Z ^ {0} = \left[ z _ {\mathrm {c l s}}, z _ {0}, \dots , z _ {N - 1} \right] \\ H ^ {l - 1} = \operatorname {M S A} (\operatorname {L N} (Z ^ {l - 1})) + Z ^ {l - 1} \quad l = 0, \dots , L - 1 \\ Z ^ {l} = \operatorname {M L P} (\operatorname {L N} (H ^ {l - 1})) + H ^ {l - 1} \quad l = 0, \dots , L - 1 \\ y = L N \left(Z _ {\mathrm {c l s}} ^ {L}\right) \\ \end{array} +$$ + +where $L$ represents the number of encoder layers. The multi-headed self-attention mechanism (MSA) abstracts patchwise representation by aggregating the right context at each layer. The context aggregation is facilitated by softmax attention that relies on patch-to-patch similarities and its parameters are governed by the pre-training task objective. During adaptation, however, the representations for downstream task might benefit from aggregating a slightly different context at each layer. Our prompt tuning approach facilitates task specific modulation of this context by augmenting and learning layerwise patch tokens. + +# 3.3. Expressive Prompt Tuning + +At the input layer of the ViT, we introduce prompt tokens, $P^0 \in \mathbb{R}^{M \times d}$ which are $M$ parameterized vectors of dimension $d$ concatenated to the input token sequence, $Z^0$ , of the ViT. Input-level prompts, also referred to as shallow prompts, are propagated through the encoder together with the class and patch tokens such that at every layer, each token interacts with every other token through the self-attention layers. The propagated prompts at the last layer are average-pooled to obtain the final representation. The insertion and propagation of the prompts described above can be expressed as + +$$ +\begin{array}{l} \tilde {Z} ^ {0} = \left[ Z ^ {0} \right| \left| P ^ {0} \right] \tag {1} \\ \tilde {H} ^ {l - 1} = \operatorname {M S A} (\operatorname {L N} (\tilde {Z} ^ {l - 1})) + \tilde {Z} ^ {l - 1} \quad l = 0, \dots , L - 1 \\ \tilde {Z} ^ {l} = \operatorname {M L P} (\operatorname {L N} (\tilde {H} ^ {l - 1})) + \tilde {H} ^ {l - 1} \quad l = 0, \dots , L - 1 \\ Z ^ {L}, P ^ {L} = \operatorname {c h u n k} \left(\tilde {Z} ^ {l}\right) \\ \tilde {y} = \operatorname {A v g P o o l} \left(P ^ {L}\right) \\ y = L N (\tilde {y}) \\ \end{array} +$$ + +we use $||$ to denote the concatenation along the sequence axis and chunk to denote the splitting of the propagated sequence of length $N + M + 1$ into the $N + 1$ tokens and $M$ prompts. Shallow prompts are capable of modeling some of the desired token relations for a task. However, they have limited capacity due to the inability to alter for specific perlayer interactions with the class and image tokens. + +To enhance the prompt capacity, we introduce layer-wise residual prompts, $\Delta^l\in \mathbb{R}^{M\times d}$ that are added to the propagated prompts at various computations within the MSA block for an intermediate layer $l$ . This includes the output of attention LayerNorm, query-key-value projections and linear multi-head projection. We summarise the MSA computations at layer $l$ with $N_{h}$ heads and input $Z$ + +$$ +\begin{array}{l} Z ^ {\prime} = L N (Z) \\ Q _ {h} = Z ^ {\prime} W _ {h} ^ {Q}; K _ {h} = Z ^ {\prime} W _ {h} ^ {K}; V _ {h} = Z ^ {\prime} W _ {h} ^ {V} \\ \mathrm {g} _ {h} = \text {A t t} \left(Q _ {h}, K _ {h}, V _ {h}\right) \quad i = 1, \dots , N _ {h} \tag {2} \\ O = \left[ \mathbf {g} _ {1} \right| | \dots | | \mathbf {g} _ {N _ {h}} \rbrack W ^ {\text {p r o j}} \\ \end{array} +$$ + +above $h$ is used to represent the head index of $W^{Q}, W^{K}, W^{V}$ and $W^{\mathrm{proj}}$ denotes the projection matrix of the MSA block. The residually prompted computations can then be expressed as + +$$ +\begin{array}{l} Z ^ {\prime} = L N (Z) + [ \bar {\mathbf {0}} | | \boldsymbol {\Delta} _ {\mathbf {L N}} ] \\ \tilde {Q} _ {h} = Q _ {h} + \left[ \bar {\mathbf {0}} \right| \left| \boldsymbol {\Delta} _ {\mathbf {Q}} \right| \\ \tilde {K} _ {h} = K _ {h} + [ \mathbf {0} | | \boldsymbol {\Delta} _ {\mathbf {K}} ] \\ \tilde {V} _ {h} = V _ {h} + [ \bar {\mathbf {0}} | | \boldsymbol {\Delta} _ {\mathbf {V}} ] \\ \tilde {O} = O + \left[ \bar {\mathbf {0}} \right| | \boldsymbol {\Delta} _ {\mathrm {p r o j}} ] \\ \end{array} +$$ + +where the concatenation of $(N + 1) \times d$ dimensional zero matrix, $\bar{\mathbf{0}}$ with the residual-prompts, signifies that the residuals $\Delta$ are added only at the propagated prompt positions and not to the image patch or class token positions. The above residual computations occur at every layer with independently learned residual prompts, and we drop the layer indices in the equations for brevity. The overall EXPRES architecture is visualized in Figure 2. + +# 3.4. Interpreting Residual Prompting + +We take a closer look at residual prompting for self-attention and interpret it's functionality. The Att operation in Eq. (2) facilitates weighted aggregation over all "value" tokens where the weights are computed using the "query" and a "key" tokens as $w_{ij} \propto \exp \left( \frac{q_i^T k_j}{\sqrt{d / N_h}} \right)$ . When prompted with residual tokens, the expression for the weights that aggregate information for a patch token $q_i$ can be factored as, + +$$ +\begin{array}{l} \tilde {w} _ {i j} \propto \exp \left(\frac {q _ {i} ^ {T} \left(k _ {j} + \boldsymbol {\Delta} _ {K , j}\right)}{\sqrt {d / N _ {h}}}\right) \\ = \exp \left(\frac {q _ {i} ^ {T} k _ {i}}{\sqrt {d / N _ {h}}}\right) \exp \left(\frac {q _ {i} ^ {T} \Delta_ {K , j}}{\sqrt {d / N _ {h}}}\right) \tag {3} \\ = w _ {i j} * \alpha_ {i j}. \\ \end{array} +$$ + +Based on Eq. (3), residual prompts facilitate task-specific reweighting of the attention weights independently at every layer, allowing the modulation of context aggregated per patch token. Such layerwise modulation can lead to better adaptation of the final representation compared to shallow prompting that restricts the modulation to the input layer. Moreover, the two-way interaction between prompts and patch tokens leads to greater flexibility than other forms of multilayered prompting [32, 67] that allow for only partial interaction. For instance, [32] restrict the prompts to act only as keys and never as queries. + +Residual prompt based attention reweighting is also interesting from parameter efficiency perspective as it circumvents the need for updating the attention weight matrices (done in finetuning approaches) to achieve the same goal of task specific adaptation. Specifically, each layer of a ViT consists of three attention weight matrices, each with $d \times d$ dimensions, resulting in $\mathcal{O}(d^2)$ learnable parameters. In contrast, each prompt is $d$ dimensional so, only $\mathcal{O}(d)$ parameters need to be adapted even with $M$ prompts, where $M << d$ . We empirically validate that the high capacity as well as parameter efficiency of our prompting approach is crucial for achieving good adaptation performance in limited labelled data settings. + +# 3.5. Learning the Prompts + +In this work, we are mainly interested in two types of downstream tasks - image classification and semantic segmentation. To train the prompts for classification, we optimize a standard cross entropy loss with respect to the representation, $y$ in Eq. (1) and the corresponding ground-truth label, $y*$ . In the case of semantic segmentation, we adapt the model as well as the objective to perform dense predictions. At the final layer of the encoder, we extract the keys corresponding to the patch tokens and pass them through the classifier. The sequence outputs are then reshaped into a 2d map and resized to original image resolution using bilinear interpolation, resulting in a pixel wise prediction. Finally, to optimize the prompts with the classifier head, we use a dense cross entropy loss as follows + +$$ +\left\{p _ {m} ^ {*}\right\}, \left\{\boldsymbol {\Delta} ^ {*} \right\} = \underset {\left\{p _ {m} \right\}, \left\{\boldsymbol {\Delta} \right\}, C} {\arg \min } \sum_ {j \in I _ {\mathrm {c x t}}} \sum_ {h, w} L _ {\mathrm {C E}} \left(y _ {j h w}, y _ {j h w} ^ {*}\right) +$$ + +where, $h, w$ are used to index the spatial positions at the resolution, $H \times W$ of the input image. + +# 4. Experiments + +We validate the effectiveness of EXPRES on a variety of benchmarks consisting of wide variety of tasks and dataset sizes. We also analyse the importance of various model components and design decisions. + +Datasets: To evaluate EXPRES, we use two different benchmarks, VTAB-1k [97] and FGVC [32]. The VTAB-1k benchmark consists of 19 different visual classification tasks categorized under three groups: Natural - tasks with natural images captured with standard cameras; Specialized - tasks with images captured under specialized settings (medical and satellite imagery); and Structured - tasks that requires understanding scene geometry, like object distance. Each task-specific dataset contains 1000 training examples with varying number of samples per class, depending on the number of classes. For validation purposes and hyperparameter selection, we use a $800 - 200$ split of the training set and then train on all 1000 examples for final results, which are based on evaluation on the entire test set. The FGVC benchmark consists of the finegrained datasets including CUB [89], Oxford Flowers [55], Stanford Dogs [36] and Stanford Cars [23]. In conjunction with VTAB-1k, we use the FGVC datasets to conduct key ablation studies for EXPRES. A random $90 - 10$ split of each dataset is used for hyperparameter selection. For few shot segmentation, we use the standard PASCAL $-5^{\mathrm{i}}$ [69] benchmark that was created from PASCAL VOC 2012 [16] with extra mask annotations for 20 object classes, evenly divided into 4 folds: $\{5^i : i \in \{0,1,2,3\}\}$ . Following prior works for evaluation scheme, we randomly sample 1000 episodes per fold and report the average performance over all episodes + +
naturalspecializedstructured
CLEAR-100Caltech101DTDFlowers102PetsSVHNSun397MeanPatch CamelyonEuroSATResisc45RetinopathyMeanClevr/countClevr/distanceDMLabKITTI/distancedSprites/locationdSprites/orientationSmallNORB/azimuthSmallNORB/elevationMean
Linear63.485.063.297.086.336.651.068.9378.587.568.674.077.1634.330.633.255.412.520.09.619.226.84
MLP-263.284.860.597.685.934.147.867.7074.388.867.173.275.8645.231.631.855.730.924.616.623.332.47
MLP-363.884.762.397.484.732.549.267.8077.088.070.256.172.8347.832.832.358.112.921.215.224.830.62
MLP-559.384.459.996.184.430.946.865.9873.787.264.871.574.3150.832.331.556.47.520.814.420.429.23
MLP-953.180.553.995.182.624.443.761.9078.583.060.272.373.4947.527.928.954.06.217.710.816.226.15
Sidetune [101]60.760.853.695.566.734.935.358.2158.587.765.261.068.1227.622.631.351.78.214.49.821.823.41
Biastune [6]72.887.059.297.585.359.951.473.3078.791.672.969.878.2561.555.632.455.966.640.015.725.144.09
Adapter-25674.186.163.297.787.034.650.870.5076.388.073.170.576.9845.737.431.253.230.325.413.822.132.39
Adapter-6474.285.862.797.687.236.350.970.6576.387.573.770.977.1042.939.930.454.531.925.613.521.432.51
Adapter-874.285.762.797.887.236.450.770.6776.989.273.571.677.8045.241.831.156.430.424.613.222.033.09
Partial-166.885.962.597.385.537.650.669.4478.689.872.573.378.5341.534.333.961.031.332.816.322.434.17
FT-all68.987.764.397.286.987.438.875.8879.795.784.273.983.3656.358.641.765.557.546.725.729.147.64
VPT-shallow [32]77.786.962.697.587.374.551.276.8178.292.075.672.979.6650.558.640.567.168.736.120.234.146.98
VPT-deep [32]78.890.865.898.088.378.149.678.4881.896.183.468.482.4368.560.046.572.873.647.932.937.854.98
EXPRES (ours)78.089.668.898.788.981.951.979.784.896.280.974.284.066.560.446.577.678.049.526.135.355.0
+ +Table 1. VTAB-1k benchmark: Per task adaptation results with ViT-B/16 model pretrained on ImageNet-21k.. + +
MethodIm-PreDense-PreBackbone50515253
SPNET [91]In-1k✓ResNet-10123.817.014.118.3
ZS3Net [5]In-1k✓ResNet-10140.839.439.333.6
LSEG [40]In-1k✓ViT-L/1661.363.643.141.0
LinearIn-21k-ViT-B/165.143.928.129.1
FT-allIn-21k-ViT-B/1618.331.927.923.2
BiastuneIn-21k-ViT-B/162.439.213.920.1
VPT-deep [32]In-21k-ViT-B/1633.456.249.847.7
EXPRES (Ours)In-21k-ViT-B/1641.860.252.451.4
+ +Table 2. Five-Shot Semantic Segmentation on PASCAL - $5^{\mathrm{i}}$ : Per fold adaptation results with ViT-B/16 model pretrained on ImageNet-21k. + +of the corresponding fold. However, unlike prior works, we tune our EXPRES model on few-shot training examples and cross-validate the hyperparameters (e.g. number of prompts, $M$ ) on a validation set with fold-exclusive categories. In all our experiments, we use a reasonably small budget for hyperparameters (see supplementary) following recent studies [56] that highlight the likelihood of overoptimistic results in limited-labelled data settings due to excessive hyperparameter tuning on large validation sets. + +Implementation Details: In all our experiments, we use a fixed encoder, ViT-B/16 pretrained on ImageNet-22K [65]. This model is effective on wide variety of tasks and allows direct comparison with prior works. For each downstream task, we train for a total 100 epochs with an initial warmup of 10 epochs. We use AdamW as our default optimizer with a suitable learning rate and fixed weight decay of $1e - 4$ . For VTAB-1k and FGVC experiments, we use a fixed batch size of 64. For segmentation experiments, since overall training set sizes are extremely small ( $\leq 10$ images in total), we use the entire training set per batch. We use input image reso + +lution of $224 \times 224$ for classification tasks and $384 \times 384$ for semantic segmentation tasks as dense prediction usually benefits from larger resolution. Since, ViT-B/16 is pretrained on standard $224 \times 224$ resolution images, we use interpolated positional embeddings to accommodate larger resolutions in the case of segmentation. Finally, we use standard data augmentations for classification benchmarks i.e., Resize $\rightarrow$ Random-Crop $\rightarrow$ Horizontal-Flip during training and Resize $\rightarrow$ Center-Crop during evaluation while for segmentation we only use Resize. + +Evaluation Metrics For classification experiments, we use accuracy as our performance metric. For evaluating segmentation masks, we use mean intersection over union (mIoU) that averages over the intersection over union curves per class. + +# 4.1. Main Results + +We compare EXPRES with a number of commonly used adaptation techniques on VTAB-1k. The adaptation methods can be categorized as head-oriented, backbone-oriented + +and prompt-based. Under the first category, Linear only optimizes a linear classifier for the downstream task while MLP- $k$ uses a $k$ -layer multilayer perceptron (MLP) as the classifier head. As an example of the second category, Sidetune [101] uses features that are linearly interpolated between pretrained features and features from a "side" network trained on downstream data. While Biastune [6] adapts only the bias terms of an otherwise frozen backbone. Adapter- $d$ [30, 58, 59] introduces lightweight MLP modules inserted between Transformer layers. Partial- $k$ finetunes the last $k$ layers while keeping the rest of the backbone frozen, finally FT-all finetunes all the layers. VPT-shallow [32] additionally optimizes a linear classifier with the learnable input prompts propagated through the encoder. VPT-deep [32] introduces more capacity by replacing the propagated prompts with a new set of learnable prompts at each layer. + +VTAB-1k Results (Table 1): Across all three splits of VTAB-1k, our method significantly outperforms the best head-oriented techniques: $+11\%$ (natural), $+7\%$ (specialized) and $+23\%$ (structured). Similar trends hold even when comparing with the more powerful class of backbone-oriented techniques. While FT-all has been widely adopted as an effective technique for most adaptation scenarios, our method consistently outperforms it by a significant margin of $+4\%$ (natural), $+1\%$ (specialized) and $+7\%$ (structured). Most interestingly our method even outperforms other powerful prompting techniques like VPT-deep on 12 (out of 19) datasets by a margin of about $+1\%$ (natural), $+2\%$ (specialized) and $+0.02\%$ (structured). The performance gains are particularly impressive when considered from the perspective of computation vs performance tradeoff. Compared to VPT-deep that uses 53 prompts for natural and 108 prompts for structures, our method only requires 10 and 29 prompts for the respective splits. A more detailed summary is provided in the supplementary. + +# 4.2. Few-Shot Semantic Segmentation Without Dense Pretraining + +We test the efficacy of EXPRES on a novel adaptation setup where the backbone, pretrained on classification tasks, is directly adapted for few-shot semantic segmentation task without additional training on large densely-annotated datasets. This is in contrast with most works that follow a two-stage pretraining procedure i.e., training on ImageNet-1k with image level labels followed by meta-learning on densely annotated datasets constructed from the train folds of PASCAL - $5^{\mathrm{i}}$ . In contrast, we only perform the first stage pretraining on a sufficiently diverse dataset (ImageNet-21k in our case) with no meta-learning stage. During evaluation, each few-shot episode randomly samples a target image with a segmentation mask that assigns a label 1 to the pixels corresponding to one of the object cate + +![](images/3c8648be08dcc2a4acd015992e0b41ac8fbf1ee95850865d04d0248b3ee46a73.jpg) + +![](images/5c4055773cecf3ec66ea5d9e829720502d21c9ca61f070f12afb9337f15ff43f.jpg) + +![](images/73d0c0370ea4ef9cf588645ad89070c7d8a04fd592910493119024a6dc566729.jpg) +Figure 3. Prompt Propagation: Effect of propagating prompts with modulation upto a layer, $l = \{2,\dots ,12\}$ of the ViT-B/16 encoder with total 12 layers. The datasets are sampled from the FGVC benchmark. + +![](images/4d74537b2d20cbd3489792118bbf48df87a3404194d63badcd6ec908147da441.jpg) + +gories in that image and a label 0 to remaining pixels (background). From the same object category, a set of five images are randomly sampled to form the training set where the mask of each image is annotated in the same way as the target. Our method as well as all baselines that perform meta-learning are optimized given a context set to yield a binary classifier for the target image. For dense representations, we use the last layer keys of the MSA-block as we found them to be more accurate than the typical MLP-block output. We observe that our method consistently outperforms the baselines (by $25\%$ ) as well as other prompt techniques such as VPT-deep (by $5\%$ ). Surprisingly, our method even outperforms [40] that leverages densely annotated datasets (training data per fold) with large language models for a second stage of pretraining. Specifically, on 2/4 folds, EXPRES outperforms [40] by $10\%$ despite training on a significantly smaller densely-annotated dataset (five images). These results are particularly significant as they suggest that highly competitive results can be achieved with models pretrained on image classification. Consequently, results may be further improved by scaling up the image-level annotated datasets which are cheaper to scale than the densely annotated datasets. In the supplementary, we provide visualizations of the segmentation mask predictions by our method as well as Linear, FT-all and VPT-deep methods. + +# 4.3. Ablation Studies + +We conduct extensive ablations to evaluate key design decisions used to develop EXPRES such as feature construction, residual prompting, number of prompts etc. For all ablations, we use the same ViT-B/16 backbone. When + +![](images/550875f4d1eceb067e3f167f7bd597c31282f462afe9bb9f4f7abf3a6afaeea0.jpg) +Figure 4. Residual Prompt Types: Evaluating the importance of different type of residual prompts on FGVC datasets. + +![](images/1645a6299075cc9d4a78cbb9571a2e0aa15f5073e114ef897a48546ffdea4f4e.jpg) +Figure 5. Computational Efficiency Plots: Comparing Accuracy vs Number of Prompts for VPT and EXPRES + +using FGVC datasets, we use only $10\%$ of each dataset with official splits provided in [32]. + +Prompt Propagation: We evaluate the importance of propagating prompts through the ViT-B/16 encoder with layerwise modulation. Specifically, upto a layer $l$ , we allow all tokens (patch, class and prompt) to attend to each other at every layer. Beyond $l$ , prompts are not allowed to interact with other tokens at all; they are simply projected by the value heads of MSA-block followed by MLP processing at every layer. In our experiments, we fix the number of prompts to 10 irrespective of the dataset. From Figure 3, we observe that downstream performance depends directly on the extent of prompt propagation with modulation: accuracy improves as more layers allow prompts to interact with other tokens. These results motivate our method, EXPRES, that facilitates finegrained layerwise modulation via residual tokens. + +Residual Prompt Type: In Figure 4 we evaluate the importance of different residual prompt types (one-at-a-time) including attention, LayerNorm $(LN)$ , query-key-value projections $(QKV)$ and linear multi-head projection $(Proj)$ . We also evaluate residual prompting in the MLP block: after LayerNorm $(LN,mlp)$ , first linear projection $(L1,mlp)$ and second linear projection $(L2,mlp)$ . We evaluate the composite effect of multiple prompt types within a computational block i.e., Att (MSA block) and MLP (MLP block). As a baseline, we provide the per-dataset results for shallow + +prompting, referred to as None in the figure. The number of prompts at each layer are fixed at 10. We observe that, within the MSA block, adding residual prompts to LayerNorm and query-key-value projections yields the most improvements (3.5% and 2.8% on an average respectively) over None. Moreover, LayerNorm prompts in the MLP block are also more effective than prompting the two linear layers. Comparing blockwise performance, prompting the MSA block $(Att)$ yields significantly better performance (by 1.6%) than prompting the MLP block $(MLP)$ . The performance gap between $Att$ and $MLP$ highlights the importance of directly modulating layerwise interaction between tokens for better adaptation. Consequently, we use $Att$ as our default setting for all experiments. + +Computational Efficiency of Prompting: In prompting techniques, the primary computational overhead arises from the quadratic complexity (in number of tokens) of the transformer encoder. So to evaluate computation efficiency of prompting, we investigate the rate at which performance improves with number of prompts and provide comparisons between our method and VPT in Figure 5. We evaluate on two different datasets sampled from different categories of VTAB-1k. For a given accuracy, e.g. $58.5\%$ on Clevr-Distance, EXPRES requires an order less prompts than VPT, resulting in 2 orders less computations. Overall EXPRES achieves higher optimal performance with far fewer prompts than VPT. + +# 5. Conclusion + +In this work we propose a novel prompting technique for adapting large vision models. Our method demonstrates strong performance across variety of downstream tasks with varying dataset sizes. Further, our method outperforms commonly used finetuning approach as well as the recently proposed VPT method on standard benchmarks. We also demonstrate diverse adaptation ability of our method from classification to semantic segmentation tasks in the few-shot setting. Lastly, our method is more parameter efficient that existing weight-space and prompt based adaptation techniques. 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In ACM MM, 2021. 3 \ No newline at end of file diff --git a/2023/Learning Expressive Prompting With Residuals for Vision Transformers/images.zip b/2023/Learning Expressive Prompting With Residuals for Vision Transformers/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..3fdefd30cbbf6f002562fb74eb4d723b809deb0e --- /dev/null +++ b/2023/Learning Expressive Prompting With Residuals for Vision Transformers/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:efbfe73edc727c04a447406c9a94e35a64abfbba7e5025d2c7fbf0e65bcf3179 +size 412207 diff --git a/2023/Learning Expressive Prompting With Residuals for Vision Transformers/layout.json b/2023/Learning Expressive Prompting With Residuals for Vision Transformers/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..d011aefe52cbcd5ff83111c18074b7b3ea2b1025 --- /dev/null +++ b/2023/Learning Expressive Prompting With Residuals for Vision Transformers/layout.json @@ -0,0 +1,9674 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 74, + 103, + 520, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 74, + 103, + 520, + 121 + ], + "spans": [ + { + "bbox": [ + 74, + 103, + 520, + 121 + ], + "type": "text", + "content": "Learning Expressive Prompting With Residuals for Vision Transformers" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 85, + 142, + 507, + 171 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 142, + 507, + 171 + ], + "spans": [ + { + "bbox": [ + 85, + 142, + 507, + 171 + ], + "type": "text", + "content": "Rajshekhar Das" + }, + { + "bbox": [ + 85, + 142, + 507, + 171 + ], + "type": "inline_equation", + "content": "^{1,2*}" + }, + { + "bbox": [ + 85, + 142, + 507, + 171 + ], + "type": "text", + "content": ", Yonatan Dukler" + }, + { + "bbox": [ + 85, + 142, + 507, + 171 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 85, + 142, + 507, + 171 + ], + "type": "text", + "content": ", Avinash Ravichandran" + }, + { + "bbox": [ + 85, + 142, + 507, + 171 + ], + "type": "inline_equation", + "content": "^{2**}" + }, + { + "bbox": [ + 85, + 142, + 507, + 171 + ], + "type": "text", + "content": ", Ashwin Swaminathan" + }, + { + "bbox": [ + 85, + 142, + 507, + 171 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 85, + 142, + 507, + 171 + ], + "type": "text", + "content": " Carnegie Mellon University" + }, + { + "bbox": [ + 85, + 142, + 507, + 171 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 85, + 142, + 507, + 171 + ], + "type": "text", + "content": " AWS AI Labs" + }, + { + "bbox": [ + 85, + 142, + 507, + 171 + ], + "type": "inline_equation", + "content": "^{2}" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 123, + 174, + 466, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 123, + 174, + 466, + 185 + ], + "spans": [ + { + "bbox": [ + 123, + 174, + 466, + 185 + ], + "type": "text", + "content": "rajshekd@andrew.cmu.edu,dukler@amazon.com，swashwin@amazon.com" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "spans": [ + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 238, + 290, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 238, + 290, + 514 + ], + "spans": [ + { + "bbox": [ + 46, + 238, + 290, + 514 + ], + "type": "text", + "content": "Prompt learning is an efficient approach to adapt transformers by inserting learnable set of parameters into the input and intermediate representations of a pre-trained model. In this work, we present Expressive Prompts with Residuals (EXPRES) which modifies the prompt learning paradigm specifically for effective adaptation of vision transformers (ViT). Our method constructs downstream representations via learnable \"output\" tokens (shallow prompts), that are akin to the learned class tokens of the ViT. Further for better steering of the downstream representation processed by the frozen transformer, we introduce residual learnable tokens that are added to the output of various computations. We apply EXPRES for image classification and few-shot semantic segmentation, and show our method is capable of achieving state of the art prompt tuning on 3/3 categories of the VTAB benchmark. In addition to strong performance, we observe that our approach is an order of magnitude more prompt efficient than existing visual prompting baselines. We analytically show the computational benefits of our approach over weight space adaptation techniques like finetuning. Lastly we systematically corroborate the architectural design of our method via a series of ablation experiments." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 535, + 128, + 547 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 535, + 128, + 547 + ], + "spans": [ + { + "bbox": [ + 47, + 535, + 128, + 547 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 555, + 287, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 555, + 287, + 687 + ], + "spans": [ + { + "bbox": [ + 46, + 555, + 287, + 687 + ], + "type": "text", + "content": "Scaling up of neural nets in the past few years has steadily improved performance on wide variety of downstream visual tasks. However, model adaptation is often necessary to achieve the best performance in downstream tasks like fine-grained recognition [89], semantic segmentation [8] or object recognition [34]. While traditional techniques like full-model finetuning have become the de-facto approach to adaptation, they are not well suited for many scenarios. For example, finetuning is susceptible to catastrophic forgetting [37] as it modifies model parameters without the knowledge of future domains, and potentially losing prior" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 329, + 215, + 526, + 375 + ], + "blocks": [ + { + "bbox": [ + 329, + 215, + 526, + 375 + ], + "lines": [ + { + "bbox": [ + 329, + 215, + 526, + 375 + ], + "spans": [ + { + "bbox": [ + 329, + 215, + 526, + 375 + ], + "type": "image", + "image_path": "8e217a44ee87e2e7710edd21f0dbc7ebfe37c360c49c7277dd2a0dca9a4a3f34.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 384, + 546, + 451 + ], + "lines": [ + { + "bbox": [ + 305, + 384, + 546, + 451 + ], + "spans": [ + { + "bbox": [ + 305, + 384, + 546, + 451 + ], + "type": "text", + "content": "Figure 1. Adapting large vision models is crucial to solving downstream tasks with wide variety of semantics (e.g., image classification, semantic segmentation etc.) as well as dataset sizes (few-shot, low-shot, full-shot). In this work, we propose a novel adaptation technique for large vision models that is capable of achieving the desired goal." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 473, + 546, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 473, + 546, + 544 + ], + "spans": [ + { + "bbox": [ + 304, + 473, + 546, + 544 + ], + "type": "text", + "content": "knowledge of current adaptation. Moreover, finetuning all of the model parameters of a large vision model with just a few training examples can lead to poor generalization. This is in contrast to human intelligence that is capable of solving wide variety of downstream tasks with extremely few exemplars." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 545, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 547, + 713 + ], + "type": "text", + "content": "Motivated by the need for better adaptation, parameter efficient techniques like partial-finetuning or adapters [64, 101] have been developed to constructively adapt large models without significant parameter overhead. While serving as effective alternatives to finetuning, most parameter efficient techniques have been designed with convolutional architectures in mind. In light of recent works [15] that demonstrate that Vision Transformers are more suitable for scaling up than CNNs, designing adaptation techniques that exploit the Transformer architecture can be extremely useful. To that end, visual prompt tuning (VPT) [32] has been proposed as a way to constructively adapt transformers by introducing learnable tokens at every layer that interact with the patch and class tokens and are optimized together with a classi" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 61, + 693, + 228, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 693, + 228, + 703 + ], + "spans": [ + { + "bbox": [ + 61, + 693, + 228, + 703 + ], + "type": "text", + "content": "*Work conducted while interning at AWS AI Labs." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 61, + 703, + 202, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 703, + 202, + 712 + ], + "spans": [ + { + "bbox": [ + 61, + 703, + 202, + 712 + ], + "type": "text", + "content": "**Work conducted while at AWS AI Labs." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3366" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "type": "text", + "content": "fier head. While being effective in practice, VPT allows only partial interactions between prompts and the remaining tokens, thus, leveraging only a part of the prompt capacity. Moreover, it often requires a large number of inserted prompts to achieve optimal performance but that significantly increases the computation costs due to the quadratic computational complexity of the self-attention layer." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 157, + 288, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 157, + 288, + 418 + ], + "spans": [ + { + "bbox": [ + 46, + 157, + 288, + 418 + ], + "type": "text", + "content": "In this work, we explore an alternate design to prompting motivated by the potential for greater prompt capacity. We propose ExPRes, an expressive prompt tuning method with residual tokens that inherits the strengths of parameter efficient adaptation while significantly improving downstream performance. Our prompt design is inspired by the two key observations - propagation of prompts by multilayered interaction with other tokens is crucial for strong capacity and learnable residual tokens can modulate the propagated prompts to favour task-specific relations (unlike in [32]). We first propagate shallow prompts through the encoder that are average pooled at the last layer to yield semantic image-level representations. Shallow prompts by themselves have limited capacity since they cannot specifically modulate token-token relations at higher layers. Therefore to harness the prompts, we add residual tokens to propagated prompts at various layerwise computations of the Transformer encoder including LayerNorm, self-attention and multi-head projection to facilitate layerwise modulation without increasing the number of prompts per layer. This results in enhanced prompt capacity at almost no additional computational cost." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 420, + 287, + 587 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 420, + 287, + 587 + ], + "spans": [ + { + "bbox": [ + 46, + 420, + 287, + 587 + ], + "type": "text", + "content": "We empirically validate the effectiveness of our method on a variety of downstream tasks including fine-grained recognition and semantic segmentation. Our use of additional learnable parameters in the form of residual and shallow prompts allows the retention of prior knowledge in the form of frozen encoder weights while being extremely parameter efficient (prompts are " + }, + { + "bbox": [ + 46, + 420, + 287, + 587 + ], + "type": "inline_equation", + "content": "\\leq 1\\%" + }, + { + "bbox": [ + 46, + 420, + 287, + 587 + ], + "type": "text", + "content": " of the total parameters). Thus, our method is highly suited for real world adaptation that requires information retention at low memory and computational overheads. Additionally, we show that in most cases we require fewer prompts than VPT to achieve the same or better performance, making it more suitable for limited data settings. Our main contributions can be summarized as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 58, + 597, + 286, + 713 + ], + "type": "list", + "angle": 0, + "index": 5, + "blocks": [ + { + "bbox": [ + 59, + 597, + 286, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 597, + 286, + 643 + ], + "spans": [ + { + "bbox": [ + 59, + 597, + 286, + 643 + ], + "type": "text", + "content": "- We propose a novel prompting technique: EXPRES, that uses a combination of shallow and deep residual prompts to facilitate constructive adaptation to downstream tasks with limited labelled datasets." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 58, + 654, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 654, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 654, + 286, + 713 + ], + "type": "text", + "content": "- Our method significantly outperforms full-finetuning based adaptation by " + }, + { + "bbox": [ + 58, + 654, + 286, + 713 + ], + "type": "inline_equation", + "content": "4.6\\%" + }, + { + "bbox": [ + 58, + 654, + 286, + 713 + ], + "type": "text", + "content": " on VTAB-1k. Moreover, our method outperforms state-of-the-art prompting approach [32] on the same benchmarks with significantly fewer prompts, suggesting that prompt design is cru" + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 324, + 72, + 544, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 324, + 72, + 544, + 96 + ], + "spans": [ + { + "bbox": [ + 324, + 72, + 544, + 96 + ], + "type": "text", + "content": "cial to extracting more capacity at a given parameter/computational budget." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 317, + 103, + 545, + 198 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 103, + 545, + 198 + ], + "spans": [ + { + "bbox": [ + 317, + 103, + 545, + 198 + ], + "type": "text", + "content": "- To the best of our knowledge, we are the first to demonstrate the effectiveness of prompting for diverse applications such as few-shot semantic segmentation. Our method outperforms strong adaptation baselines by " + }, + { + "bbox": [ + 317, + 103, + 545, + 198 + ], + "type": "inline_equation", + "content": "25\\%" + }, + { + "bbox": [ + 317, + 103, + 545, + 198 + ], + "type": "text", + "content": " and achieves competitive performance with respect to language-assisted segmentation [40] despite training on significantly less data with dense annotations." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 215, + 389, + 227 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 215, + 389, + 227 + ], + "spans": [ + { + "bbox": [ + 306, + 215, + 389, + 227 + ], + "type": "text", + "content": "2. Related work" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 235, + 545, + 402 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 235, + 545, + 402 + ], + "spans": [ + { + "bbox": [ + 304, + 235, + 545, + 402 + ], + "type": "text", + "content": "Large Vision Models: With the advent of Transformer models [80] and adoption to various computer vision tasks, including image classification [15, 51], object detection [7, 44], semantic and panoptic segmentation [76,85,102], video understanding [18, 25, 87] and few-shot learning [13], the scale of vision models have increased by orders of magnitude. Typically trained using large labelled data, either unimodal like ImageNet-21K [65] or multimodal, these models demonstrate superior performance on wide variety of visual tasks. Given their superior performance and much larger scale compared to ConvNets, the question of adapting such models efficiently becomes crucial. Motivated by the need, our work is primarily focussed on adaptation of Vision Transformers." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 403, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 403, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 403, + 545, + 689 + ], + "type": "text", + "content": "Transfer Learning has been extensively studied for vision tasks in the context of ConvNets [105] and many techniques have been introduced including side tuning [101], residual adapter [63], bias tuning [6], etc. However, Transformer specific adaptation for visual tasks has received relatively less attention. At the same time, in the NLP domain, the dominance of large-scale pre-trained Transformer-based Large Language Models (LLM) [4, 11, 61], has paved way for many approaches [26, 29, 31] that efficiently fine-tune LLMs for different downstream NLP tasks [82, 83]. In this work we compare with the most representative methods for fair benchmarking. For example, Adapters [30] insert extra lightweight modules inside each Transformer layer. One adapter module generally consists of a linear down-projection, followed by a nonlinear activation function, and a linear up-projection, together with a residual connection [58, 59]. Instead of inserting new modules, [6] proposed to update the bias term and freeze the rest of backbone parameters when fine-tuning ConvNets. BitFit [3] applied this technique to Transformers and verified its effectiveness on LLM tuning. Through our experiments that we demonstrate that our method, EXPRESS provides a more effective way of adapting Transformers compared to prior approaches." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": "Prompting: An alternative to traditional adaptation methods is prompting [48] - originally proposed as a way of" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3367" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 98, + 69, + 496, + 293 + ], + "blocks": [ + { + "bbox": [ + 98, + 69, + 496, + 293 + ], + "lines": [ + { + "bbox": [ + 98, + 69, + 496, + 293 + ], + "spans": [ + { + "bbox": [ + 98, + 69, + 496, + 293 + ], + "type": "image", + "image_path": "9392da1658371cecf6c787ec7bd961fb94a933141e025545556014e1fbf648a9.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 303, + 547, + 348 + ], + "lines": [ + { + "bbox": [ + 46, + 303, + 547, + 348 + ], + "spans": [ + { + "bbox": [ + 46, + 303, + 547, + 348 + ], + "type": "text", + "content": "Figure 2. EXPRES Architecture in detail: EXPRES optimizes two types of prompts, shallow prompts (e.g., " + }, + { + "bbox": [ + 46, + 303, + 547, + 348 + ], + "type": "inline_equation", + "content": "p_i" + }, + { + "bbox": [ + 46, + 303, + 547, + 348 + ], + "type": "text", + "content": ") and residual prompts (e.g., " + }, + { + "bbox": [ + 46, + 303, + 547, + 348 + ], + "type": "inline_equation", + "content": "\\nabla_{LN,i}" + }, + { + "bbox": [ + 46, + 303, + 547, + 348 + ], + "type": "text", + "content": "), to construct task specific representation without updating the pretrained encoder weights. Each residual prompt is a learnable vector that is added to the output of various computations such as Layer Norm, Query-Key-Value projections, and linear projection after the MSA operation." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 369, + 289, + 706 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 369, + 289, + 706 + ], + "spans": [ + { + "bbox": [ + 46, + 369, + 289, + 706 + ], + "type": "text", + "content": "prepending language instruction to the input text so that a pre-trained LLM can \"understand\" the task. Through trial and error selection of appropriate prompts, GPT-3 shows strong generalization to downstream transfer learning tasks even in the few-shot or zero-shot settings [4]. This was followed up by other works on better prompt construction [33, 71]. Recent works [39, 43, 50] propose to treat the prompts as task-specific continuous vectors and directly optimize them via gradients during fine-tuning. Such approaches, named \"Prompt Tuning\" achieve performance comparable to finetuning but with " + }, + { + "bbox": [ + 46, + 369, + 289, + 706 + ], + "type": "inline_equation", + "content": "1000 \\times" + }, + { + "bbox": [ + 46, + 369, + 289, + 706 + ], + "type": "text", + "content": " less parameters in some cases. Following the success in LLMs, prompt have also been adopted for vision-language models [22, 35, 60, 96, 103]. Nonetheless, all the above methods prompt the text encoders and hence are tied to language as input. However, many realistic visual tasks such as dense prediction may not be well aligned with the language modality. Thus, it becomes imperative to develop prompting approaches that can work in the visual modality. To that end, recent work on visual prompting [2, 10, 32, 66, 88] provides encouraging results. In particular, [32] demonstrate that even in the visual domain, adaptation based on continuous prompting can outperform finetuning, especially when the training datasets are small. Our work however shows that current prompting methods do not fully exploit the capacity of prompting for a vision transformer. Through a principled approach to prompting, we derive a more effective prompting technique that achieves state-of-the-art per" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 306, + 369, + 514, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 369, + 514, + 380 + ], + "spans": [ + { + "bbox": [ + 306, + 369, + 514, + 380 + ], + "type": "text", + "content": "formance at much smaller computational overhead." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 385, + 547, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 385, + 547, + 601 + ], + "spans": [ + { + "bbox": [ + 304, + 385, + 547, + 601 + ], + "type": "text", + "content": "Few-Shot Classification: Few-shot classification has received a lot of attention in recent years. While a variety of approaches [75] have been proposed, the most successful ones seek to transfer positive knowledge either by finetuning [1, 12, 79] or meta-learning [17, 19, 21, 24, 38, 62, 74, 77, 81]. Finetuning based few-shot learners can be viewed as specialists that perform well on the target domain [9, 27, 79], but suffer from catastrophic forgetting [70] on the base domain. Meta-learning approaches, on the other hand, can be seen as generalists that enjoy complete immunity against forgetting but at the cost of somewhat lower performance in the target domain. In this work, we propose EXPRES as a constructive adaptation technique that is immune to forgetting but at the same time benefits from task specific parameter tuning, thus, leveraging the best of both worlds. One of our key contribution is to demonstrate the transferability of Transformers from classification to dense prediction tasks (semantic segmentation) when adapted with EXPRES." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 605, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 548, + 715 + ], + "type": "text", + "content": "Few-Shot Semantic Segmentation: This task was originally proposed in [68]. Most works after that follow the metric learning paradigm [14] with various novelties from improved support-query matching [47, 72, 95] to better optimization [46, 104], memory modules [90, 93], graph neural networks [84, 92, 99], and more [28, 42, 45, 52, 53, 78, 98, 106]. Some methods generate representative support prototypes with attention mechanism [20, 100], adaptive prototype learning [41, 57, 73], or various prototype generation" + } + ] + } + ], + "index": 5 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3368" + } + ] + } + ], + "index": 6 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": "techniques [49, 54, 86, 94]. In contrast, our approach directly adapts a model pretrained on image classification to few-shot semantic segmentation without intermediate pretraining on densely-annotated datasets." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 133, + 113, + 146 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 133, + 113, + 146 + ], + "spans": [ + { + "bbox": [ + 47, + 133, + 113, + 146 + ], + "type": "text", + "content": "3. Approach" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 152, + 133, + 164 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 152, + 133, + 164 + ], + "spans": [ + { + "bbox": [ + 47, + 152, + 133, + 164 + ], + "type": "text", + "content": "3.1. Preliminaries" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 171, + 288, + 315 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 171, + 288, + 315 + ], + "spans": [ + { + "bbox": [ + 46, + 171, + 288, + 315 + ], + "type": "text", + "content": "Consider an input space " + }, + { + "bbox": [ + 46, + 171, + 288, + 315 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 46, + 171, + 288, + 315 + ], + "type": "text", + "content": " and a categorical label set " + }, + { + "bbox": [ + 46, + 171, + 288, + 315 + ], + "type": "inline_equation", + "content": "\\mathcal{Y}" + }, + { + "bbox": [ + 46, + 171, + 288, + 315 + ], + "type": "text", + "content": " where each class is represented via a one-hot encoding. A representation " + }, + { + "bbox": [ + 46, + 171, + 288, + 315 + ], + "type": "inline_equation", + "content": "\\mathcal{R} \\subset \\mathbb{R}^d" + }, + { + "bbox": [ + 46, + 171, + 288, + 315 + ], + "type": "text", + "content": " of the input is defined by the composition of an augmentation function " + }, + { + "bbox": [ + 46, + 171, + 288, + 315 + ], + "type": "inline_equation", + "content": "\\mathcal{A}: \\mathcal{X} \\to \\mathcal{X}" + }, + { + "bbox": [ + 46, + 171, + 288, + 315 + ], + "type": "text", + "content": " and an encoder model " + }, + { + "bbox": [ + 46, + 171, + 288, + 315 + ], + "type": "inline_equation", + "content": "E_{\\theta}: \\mathcal{X} \\to \\mathcal{R}" + }, + { + "bbox": [ + 46, + 171, + 288, + 315 + ], + "type": "text", + "content": ", parameterized by " + }, + { + "bbox": [ + 46, + 171, + 288, + 315 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 171, + 288, + 315 + ], + "type": "text", + "content": ". The augmentation function is a composition of standard image transformations such as random cropping, horizontal flipping etc. A general recognition task " + }, + { + "bbox": [ + 46, + 171, + 288, + 315 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 46, + 171, + 288, + 315 + ], + "type": "text", + "content": " can be defined in terms of a finite training set, " + }, + { + "bbox": [ + 46, + 171, + 288, + 315 + ], + "type": "inline_equation", + "content": "\\{(x_i, y_i)\\}_{i \\in \\mathcal{D}_{\\mathrm{train}}}^*" + }, + { + "bbox": [ + 46, + 171, + 288, + 315 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 171, + 288, + 315 + ], + "type": "inline_equation", + "content": "N_c" + }, + { + "bbox": [ + 46, + 171, + 288, + 315 + ], + "type": "text", + "content": " categories such that, " + }, + { + "bbox": [ + 46, + 171, + 288, + 315 + ], + "type": "inline_equation", + "content": "y_i \\in [N_c]" + }, + { + "bbox": [ + 46, + 171, + 288, + 315 + ], + "type": "text", + "content": ". The goal, is to leverage a pretrained encoder, " + }, + { + "bbox": [ + 46, + 171, + 288, + 315 + ], + "type": "inline_equation", + "content": "E_{\\theta^*}" + }, + { + "bbox": [ + 46, + 171, + 288, + 315 + ], + "type": "text", + "content": " and the training set to obtain a classifier for the task " + }, + { + "bbox": [ + 46, + 171, + 288, + 315 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 46, + 171, + 288, + 315 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 324, + 253, + 336 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 324, + 253, + 336 + ], + "spans": [ + { + "bbox": [ + 47, + 324, + 253, + 336 + ], + "type": "text", + "content": "3.2. Overview of Vision Transformers (ViT)" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 342, + 287, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 342, + 287, + 498 + ], + "spans": [ + { + "bbox": [ + 46, + 342, + 287, + 498 + ], + "type": "text", + "content": "In a typical ViT, the image, " + }, + { + "bbox": [ + 46, + 342, + 287, + 498 + ], + "type": "inline_equation", + "content": "x \\in \\mathbb{R}^{h \\times w \\times 3}" + }, + { + "bbox": [ + 46, + 342, + 287, + 498 + ], + "type": "text", + "content": " is uniformly divided into " + }, + { + "bbox": [ + 46, + 342, + 287, + 498 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 342, + 287, + 498 + ], + "type": "text", + "content": " fixed-sized patches, each of which are projected to a " + }, + { + "bbox": [ + 46, + 342, + 287, + 498 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 342, + 287, + 498 + ], + "type": "text", + "content": "-dimensional embedding and are added a positional embedding, resulting in a patch token " + }, + { + "bbox": [ + 46, + 342, + 287, + 498 + ], + "type": "inline_equation", + "content": "z_{n} \\in \\mathbb{R}^{d}" + }, + { + "bbox": [ + 46, + 342, + 287, + 498 + ], + "type": "text", + "content": ". Additionally, a class token " + }, + { + "bbox": [ + 46, + 342, + 287, + 498 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{cls}} \\in \\mathbb{R}^{d}" + }, + { + "bbox": [ + 46, + 342, + 287, + 498 + ], + "type": "text", + "content": " is concatenated to the sequence of the patch tokens to form the input, " + }, + { + "bbox": [ + 46, + 342, + 287, + 498 + ], + "type": "inline_equation", + "content": "Z^0 \\in \\mathbb{R}^{(N + 1) \\times d}" + }, + { + "bbox": [ + 46, + 342, + 287, + 498 + ], + "type": "text", + "content": ". Starting from layer " + }, + { + "bbox": [ + 46, + 342, + 287, + 498 + ], + "type": "inline_equation", + "content": "l = 0" + }, + { + "bbox": [ + 46, + 342, + 287, + 498 + ], + "type": "text", + "content": ", the incoming activations at each layer, " + }, + { + "bbox": [ + 46, + 342, + 287, + 498 + ], + "type": "inline_equation", + "content": "z^{l - 1}" + }, + { + "bbox": [ + 46, + 342, + 287, + 498 + ], + "type": "text", + "content": " are first normalized using LayerNorm (LN), and then processed by a multi-headed self-attention block (MSA) followed by an MLP block. At the last layer, the resulting class token is normalized to yield the final representation. The overall computations in a ViT encoder can be summarised as" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 61, + 509, + 274, + 571 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 509, + 274, + 571 + ], + "spans": [ + { + "bbox": [ + 61, + 509, + 274, + 571 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} Z ^ {0} = \\left[ z _ {\\mathrm {c l s}}, z _ {0}, \\dots , z _ {N - 1} \\right] \\\\ H ^ {l - 1} = \\operatorname {M S A} (\\operatorname {L N} (Z ^ {l - 1})) + Z ^ {l - 1} \\quad l = 0, \\dots , L - 1 \\\\ Z ^ {l} = \\operatorname {M L P} (\\operatorname {L N} (H ^ {l - 1})) + H ^ {l - 1} \\quad l = 0, \\dots , L - 1 \\\\ y = L N \\left(Z _ {\\mathrm {c l s}} ^ {L}\\right) \\\\ \\end{array}", + "image_path": "7757d72d8716811f2b7fd2b7b18d6882a5e98e238038d0ae77a4e35bf7187a7c.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "text", + "content": " represents the number of encoder layers. The multi-headed self-attention mechanism (MSA) abstracts patchwise representation by aggregating the right context at each layer. The context aggregation is facilitated by softmax attention that relies on patch-to-patch similarities and its parameters are governed by the pre-training task objective. During adaptation, however, the representations for downstream task might benefit from aggregating a slightly different context at each layer. Our prompt tuning approach facilitates task specific modulation of this context by augmenting and learning layerwise patch tokens." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 72, + 453, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 453, + 85 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 453, + 85 + ], + "type": "text", + "content": "3.3. Expressive Prompt Tuning" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 90, + 547, + 222 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 90, + 547, + 222 + ], + "spans": [ + { + "bbox": [ + 304, + 90, + 547, + 222 + ], + "type": "text", + "content": "At the input layer of the ViT, we introduce prompt tokens, " + }, + { + "bbox": [ + 304, + 90, + 547, + 222 + ], + "type": "inline_equation", + "content": "P^0 \\in \\mathbb{R}^{M \\times d}" + }, + { + "bbox": [ + 304, + 90, + 547, + 222 + ], + "type": "text", + "content": " which are " + }, + { + "bbox": [ + 304, + 90, + 547, + 222 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 90, + 547, + 222 + ], + "type": "text", + "content": " parameterized vectors of dimension " + }, + { + "bbox": [ + 304, + 90, + 547, + 222 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 90, + 547, + 222 + ], + "type": "text", + "content": " concatenated to the input token sequence, " + }, + { + "bbox": [ + 304, + 90, + 547, + 222 + ], + "type": "inline_equation", + "content": "Z^0" + }, + { + "bbox": [ + 304, + 90, + 547, + 222 + ], + "type": "text", + "content": ", of the ViT. Input-level prompts, also referred to as shallow prompts, are propagated through the encoder together with the class and patch tokens such that at every layer, each token interacts with every other token through the self-attention layers. The propagated prompts at the last layer are average-pooled to obtain the final representation. The insertion and propagation of the prompts described above can be expressed as" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 320, + 228, + 545, + 324 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 228, + 545, + 324 + ], + "spans": [ + { + "bbox": [ + 320, + 228, + 545, + 324 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\tilde {Z} ^ {0} = \\left[ Z ^ {0} \\right| \\left| P ^ {0} \\right] \\tag {1} \\\\ \\tilde {H} ^ {l - 1} = \\operatorname {M S A} (\\operatorname {L N} (\\tilde {Z} ^ {l - 1})) + \\tilde {Z} ^ {l - 1} \\quad l = 0, \\dots , L - 1 \\\\ \\tilde {Z} ^ {l} = \\operatorname {M L P} (\\operatorname {L N} (\\tilde {H} ^ {l - 1})) + \\tilde {H} ^ {l - 1} \\quad l = 0, \\dots , L - 1 \\\\ Z ^ {L}, P ^ {L} = \\operatorname {c h u n k} \\left(\\tilde {Z} ^ {l}\\right) \\\\ \\tilde {y} = \\operatorname {A v g P o o l} \\left(P ^ {L}\\right) \\\\ y = L N (\\tilde {y}) \\\\ \\end{array}", + "image_path": "47fd40cfbad7670ba6d88646410eb44123cd27211b0f5aa902f27bc232ac7926.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 331, + 545, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 331, + 545, + 415 + ], + "spans": [ + { + "bbox": [ + 304, + 331, + 545, + 415 + ], + "type": "text", + "content": "we use " + }, + { + "bbox": [ + 304, + 331, + 545, + 415 + ], + "type": "inline_equation", + "content": "||" + }, + { + "bbox": [ + 304, + 331, + 545, + 415 + ], + "type": "text", + "content": " to denote the concatenation along the sequence axis and chunk to denote the splitting of the propagated sequence of length " + }, + { + "bbox": [ + 304, + 331, + 545, + 415 + ], + "type": "inline_equation", + "content": "N + M + 1" + }, + { + "bbox": [ + 304, + 331, + 545, + 415 + ], + "type": "text", + "content": " into the " + }, + { + "bbox": [ + 304, + 331, + 545, + 415 + ], + "type": "inline_equation", + "content": "N + 1" + }, + { + "bbox": [ + 304, + 331, + 545, + 415 + ], + "type": "text", + "content": " tokens and " + }, + { + "bbox": [ + 304, + 331, + 545, + 415 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 331, + 545, + 415 + ], + "type": "text", + "content": " prompts. Shallow prompts are capable of modeling some of the desired token relations for a task. However, they have limited capacity due to the inability to alter for specific perlayer interactions with the class and image tokens." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 415, + 545, + 499 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 415, + 545, + 499 + ], + "spans": [ + { + "bbox": [ + 304, + 415, + 545, + 499 + ], + "type": "text", + "content": "To enhance the prompt capacity, we introduce layer-wise residual prompts, " + }, + { + "bbox": [ + 304, + 415, + 545, + 499 + ], + "type": "inline_equation", + "content": "\\Delta^l\\in \\mathbb{R}^{M\\times d}" + }, + { + "bbox": [ + 304, + 415, + 545, + 499 + ], + "type": "text", + "content": " that are added to the propagated prompts at various computations within the MSA block for an intermediate layer " + }, + { + "bbox": [ + 304, + 415, + 545, + 499 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 304, + 415, + 545, + 499 + ], + "type": "text", + "content": ". This includes the output of attention LayerNorm, query-key-value projections and linear multi-head projection. We summarise the MSA computations at layer " + }, + { + "bbox": [ + 304, + 415, + 545, + 499 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 304, + 415, + 545, + 499 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 304, + 415, + 545, + 499 + ], + "type": "inline_equation", + "content": "N_{h}" + }, + { + "bbox": [ + 304, + 415, + 545, + 499 + ], + "type": "text", + "content": " heads and input " + }, + { + "bbox": [ + 304, + 415, + 545, + 499 + ], + "type": "inline_equation", + "content": "Z" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 339, + 506, + 544, + 568 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 339, + 506, + 544, + 568 + ], + "spans": [ + { + "bbox": [ + 339, + 506, + 544, + 568 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} Z ^ {\\prime} = L N (Z) \\\\ Q _ {h} = Z ^ {\\prime} W _ {h} ^ {Q}; K _ {h} = Z ^ {\\prime} W _ {h} ^ {K}; V _ {h} = Z ^ {\\prime} W _ {h} ^ {V} \\\\ \\mathrm {g} _ {h} = \\text {A t t} \\left(Q _ {h}, K _ {h}, V _ {h}\\right) \\quad i = 1, \\dots , N _ {h} \\tag {2} \\\\ O = \\left[ \\mathbf {g} _ {1} \\right| | \\dots | | \\mathbf {g} _ {N _ {h}} \\rbrack W ^ {\\text {p r o j}} \\\\ \\end{array}", + "image_path": "0770c1bce820d0864adf18152cb1693519d4f1393a0bf5f2ff254bfbf630f941.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 575, + 547, + 623 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 575, + 547, + 623 + ], + "spans": [ + { + "bbox": [ + 305, + 575, + 547, + 623 + ], + "type": "text", + "content": "above " + }, + { + "bbox": [ + 305, + 575, + 547, + 623 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 305, + 575, + 547, + 623 + ], + "type": "text", + "content": " is used to represent the head index of " + }, + { + "bbox": [ + 305, + 575, + 547, + 623 + ], + "type": "inline_equation", + "content": "W^{Q}, W^{K}, W^{V}" + }, + { + "bbox": [ + 305, + 575, + 547, + 623 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 575, + 547, + 623 + ], + "type": "inline_equation", + "content": "W^{\\mathrm{proj}}" + }, + { + "bbox": [ + 305, + 575, + 547, + 623 + ], + "type": "text", + "content": " denotes the projection matrix of the MSA block. The residually prompted computations can then be expressed as" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 372, + 631, + 481, + 711 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 372, + 631, + 481, + 711 + ], + "spans": [ + { + "bbox": [ + 372, + 631, + 481, + 711 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} Z ^ {\\prime} = L N (Z) + [ \\bar {\\mathbf {0}} | | \\boldsymbol {\\Delta} _ {\\mathbf {L N}} ] \\\\ \\tilde {Q} _ {h} = Q _ {h} + \\left[ \\bar {\\mathbf {0}} \\right| \\left| \\boldsymbol {\\Delta} _ {\\mathbf {Q}} \\right| \\\\ \\tilde {K} _ {h} = K _ {h} + [ \\mathbf {0} | | \\boldsymbol {\\Delta} _ {\\mathbf {K}} ] \\\\ \\tilde {V} _ {h} = V _ {h} + [ \\bar {\\mathbf {0}} | | \\boldsymbol {\\Delta} _ {\\mathbf {V}} ] \\\\ \\tilde {O} = O + \\left[ \\bar {\\mathbf {0}} \\right| | \\boldsymbol {\\Delta} _ {\\mathrm {p r o j}} ] \\\\ \\end{array}", + "image_path": "22c6df568b7240ef6b6056f6fe191a3a7c1d87744d852f0f31d516c6882e035f.jpg" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3369" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "content": "where the concatenation of " + }, + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "inline_equation", + "content": "(N + 1) \\times d" + }, + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "content": " dimensional zero matrix, " + }, + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "inline_equation", + "content": "\\bar{\\mathbf{0}}" + }, + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "content": " with the residual-prompts, signifies that the residuals " + }, + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "inline_equation", + "content": "\\Delta" + }, + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "content": " are added only at the propagated prompt positions and not to the image patch or class token positions. The above residual computations occur at every layer with independently learned residual prompts, and we drop the layer indices in the equations for brevity. The overall EXPRES architecture is visualized in Figure 2." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 185, + 224, + 198 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 185, + 224, + 198 + ], + "spans": [ + { + "bbox": [ + 47, + 185, + 224, + 198 + ], + "type": "text", + "content": "3.4. Interpreting Residual Prompting" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 205, + 287, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 205, + 287, + 312 + ], + "spans": [ + { + "bbox": [ + 46, + 205, + 287, + 312 + ], + "type": "text", + "content": "We take a closer look at residual prompting for self-attention and interpret it's functionality. The Att operation in Eq. (2) facilitates weighted aggregation over all \"value\" tokens where the weights are computed using the \"query\" and a \"key\" tokens as " + }, + { + "bbox": [ + 46, + 205, + 287, + 312 + ], + "type": "inline_equation", + "content": "w_{ij} \\propto \\exp \\left( \\frac{q_i^T k_j}{\\sqrt{d / N_h}} \\right)" + }, + { + "bbox": [ + 46, + 205, + 287, + 312 + ], + "type": "text", + "content": ". When prompted with residual tokens, the expression for the weights that aggregate information for a patch token " + }, + { + "bbox": [ + 46, + 205, + 287, + 312 + ], + "type": "inline_equation", + "content": "q_i" + }, + { + "bbox": [ + 46, + 205, + 287, + 312 + ], + "type": "text", + "content": " can be factored as," + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 83, + 327, + 287, + 409 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 327, + 287, + 409 + ], + "spans": [ + { + "bbox": [ + 83, + 327, + 287, + 409 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\tilde {w} _ {i j} \\propto \\exp \\left(\\frac {q _ {i} ^ {T} \\left(k _ {j} + \\boldsymbol {\\Delta} _ {K , j}\\right)}{\\sqrt {d / N _ {h}}}\\right) \\\\ = \\exp \\left(\\frac {q _ {i} ^ {T} k _ {i}}{\\sqrt {d / N _ {h}}}\\right) \\exp \\left(\\frac {q _ {i} ^ {T} \\Delta_ {K , j}}{\\sqrt {d / N _ {h}}}\\right) \\tag {3} \\\\ = w _ {i j} * \\alpha_ {i j}. \\\\ \\end{array}", + "image_path": "cbc9e6ca91b289b8033b821bd6e42face3f22fd1016cc02d8fbd8a0f460ef9c9.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 423, + 287, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 423, + 287, + 555 + ], + "spans": [ + { + "bbox": [ + 46, + 423, + 287, + 555 + ], + "type": "text", + "content": "Based on Eq. (3), residual prompts facilitate task-specific reweighting of the attention weights independently at every layer, allowing the modulation of context aggregated per patch token. Such layerwise modulation can lead to better adaptation of the final representation compared to shallow prompting that restricts the modulation to the input layer. Moreover, the two-way interaction between prompts and patch tokens leads to greater flexibility than other forms of multilayered prompting [32, 67] that allow for only partial interaction. For instance, [32] restrict the prompts to act only as keys and never as queries." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "text", + "content": "Residual prompt based attention reweighting is also interesting from parameter efficiency perspective as it circumvents the need for updating the attention weight matrices (done in finetuning approaches) to achieve the same goal of task specific adaptation. Specifically, each layer of a ViT consists of three attention weight matrices, each with " + }, + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "inline_equation", + "content": "d \\times d" + }, + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "text", + "content": " dimensions, resulting in " + }, + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(d^2)" + }, + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "text", + "content": " learnable parameters. In contrast, each prompt is " + }, + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "text", + "content": " dimensional so, only " + }, + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(d)" + }, + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "text", + "content": " parameters need to be adapted even with " + }, + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "text", + "content": " prompts, where " + }, + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "inline_equation", + "content": "M << d" + }, + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "text", + "content": ". We empirically validate that the high capacity as well as parameter efficiency of our prompting approach is crucial for achieving good adaptation performance in limited labelled data settings." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 72, + 432, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 432, + 85 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 432, + 85 + ], + "type": "text", + "content": "3.5. Learning the Prompts" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 90, + 547, + 258 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 90, + 547, + 258 + ], + "spans": [ + { + "bbox": [ + 304, + 90, + 547, + 258 + ], + "type": "text", + "content": "In this work, we are mainly interested in two types of downstream tasks - image classification and semantic segmentation. To train the prompts for classification, we optimize a standard cross entropy loss with respect to the representation, " + }, + { + "bbox": [ + 304, + 90, + 547, + 258 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 304, + 90, + 547, + 258 + ], + "type": "text", + "content": " in Eq. (1) and the corresponding ground-truth label, " + }, + { + "bbox": [ + 304, + 90, + 547, + 258 + ], + "type": "inline_equation", + "content": "y*" + }, + { + "bbox": [ + 304, + 90, + 547, + 258 + ], + "type": "text", + "content": ". In the case of semantic segmentation, we adapt the model as well as the objective to perform dense predictions. At the final layer of the encoder, we extract the keys corresponding to the patch tokens and pass them through the classifier. The sequence outputs are then reshaped into a 2d map and resized to original image resolution using bilinear interpolation, resulting in a pixel wise prediction. Finally, to optimize the prompts with the classifier head, we use a dense cross entropy loss as follows" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 315, + 266, + 536, + 292 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 266, + 536, + 292 + ], + "spans": [ + { + "bbox": [ + 315, + 266, + 536, + 292 + ], + "type": "interline_equation", + "content": "\\left\\{p _ {m} ^ {*}\\right\\}, \\left\\{\\boldsymbol {\\Delta} ^ {*} \\right\\} = \\underset {\\left\\{p _ {m} \\right\\}, \\left\\{\\boldsymbol {\\Delta} \\right\\}, C} {\\arg \\min } \\sum_ {j \\in I _ {\\mathrm {c x t}}} \\sum_ {h, w} L _ {\\mathrm {C E}} \\left(y _ {j h w}, y _ {j h w} ^ {*}\\right)", + "image_path": "82c80c55045ba4488af05b0bd7278d736ca2cbcd5845546b31649b135b80099d.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 300, + 545, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 300, + 545, + 324 + ], + "spans": [ + { + "bbox": [ + 305, + 300, + 545, + 324 + ], + "type": "text", + "content": "where, " + }, + { + "bbox": [ + 305, + 300, + 545, + 324 + ], + "type": "inline_equation", + "content": "h, w" + }, + { + "bbox": [ + 305, + 300, + 545, + 324 + ], + "type": "text", + "content": " are used to index the spatial positions at the resolution, " + }, + { + "bbox": [ + 305, + 300, + 545, + 324 + ], + "type": "inline_equation", + "content": "H \\times W" + }, + { + "bbox": [ + 305, + 300, + 545, + 324 + ], + "type": "text", + "content": " of the input image." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 335, + 387, + 348 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 335, + 387, + 348 + ], + "spans": [ + { + "bbox": [ + 305, + 335, + 387, + 348 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 354, + 547, + 402 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 354, + 547, + 402 + ], + "spans": [ + { + "bbox": [ + 304, + 354, + 547, + 402 + ], + "type": "text", + "content": "We validate the effectiveness of EXPRES on a variety of benchmarks consisting of wide variety of tasks and dataset sizes. We also analyse the importance of various model components and design decisions." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 403, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 403, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 403, + 546, + 714 + ], + "type": "text", + "content": "Datasets: To evaluate EXPRES, we use two different benchmarks, VTAB-1k [97] and FGVC [32]. The VTAB-1k benchmark consists of 19 different visual classification tasks categorized under three groups: Natural - tasks with natural images captured with standard cameras; Specialized - tasks with images captured under specialized settings (medical and satellite imagery); and Structured - tasks that requires understanding scene geometry, like object distance. Each task-specific dataset contains 1000 training examples with varying number of samples per class, depending on the number of classes. For validation purposes and hyperparameter selection, we use a " + }, + { + "bbox": [ + 304, + 403, + 546, + 714 + ], + "type": "inline_equation", + "content": "800 - 200" + }, + { + "bbox": [ + 304, + 403, + 546, + 714 + ], + "type": "text", + "content": " split of the training set and then train on all 1000 examples for final results, which are based on evaluation on the entire test set. The FGVC benchmark consists of the finegrained datasets including CUB [89], Oxford Flowers [55], Stanford Dogs [36] and Stanford Cars [23]. In conjunction with VTAB-1k, we use the FGVC datasets to conduct key ablation studies for EXPRES. A random " + }, + { + "bbox": [ + 304, + 403, + 546, + 714 + ], + "type": "inline_equation", + "content": "90 - 10" + }, + { + "bbox": [ + 304, + 403, + 546, + 714 + ], + "type": "text", + "content": " split of each dataset is used for hyperparameter selection. For few shot segmentation, we use the standard PASCAL " + }, + { + "bbox": [ + 304, + 403, + 546, + 714 + ], + "type": "inline_equation", + "content": "-5^{\\mathrm{i}}" + }, + { + "bbox": [ + 304, + 403, + 546, + 714 + ], + "type": "text", + "content": " [69] benchmark that was created from PASCAL VOC 2012 [16] with extra mask annotations for 20 object classes, evenly divided into 4 folds: " + }, + { + "bbox": [ + 304, + 403, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\{5^i : i \\in \\{0,1,2,3\\}\\}" + }, + { + "bbox": [ + 304, + 403, + 546, + 714 + ], + "type": "text", + "content": ". Following prior works for evaluation scheme, we randomly sample 1000 episodes per fold and report the average performance over all episodes" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3370" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 70, + 545, + 285 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 545, + 285 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 545, + 285 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 545, + 285 + ], + "type": "table", + "html": "
naturalspecializedstructured
CLEAR-100Caltech101DTDFlowers102PetsSVHNSun397MeanPatch CamelyonEuroSATResisc45RetinopathyMeanClevr/countClevr/distanceDMLabKITTI/distancedSprites/locationdSprites/orientationSmallNORB/azimuthSmallNORB/elevationMean
Linear63.485.063.297.086.336.651.068.9378.587.568.674.077.1634.330.633.255.412.520.09.619.226.84
MLP-263.284.860.597.685.934.147.867.7074.388.867.173.275.8645.231.631.855.730.924.616.623.332.47
MLP-363.884.762.397.484.732.549.267.8077.088.070.256.172.8347.832.832.358.112.921.215.224.830.62
MLP-559.384.459.996.184.430.946.865.9873.787.264.871.574.3150.832.331.556.47.520.814.420.429.23
MLP-953.180.553.995.182.624.443.761.9078.583.060.272.373.4947.527.928.954.06.217.710.816.226.15
Sidetune [101]60.760.853.695.566.734.935.358.2158.587.765.261.068.1227.622.631.351.78.214.49.821.823.41
Biastune [6]72.887.059.297.585.359.951.473.3078.791.672.969.878.2561.555.632.455.966.640.015.725.144.09
Adapter-25674.186.163.297.787.034.650.870.5076.388.073.170.576.9845.737.431.253.230.325.413.822.132.39
Adapter-6474.285.862.797.687.236.350.970.6576.387.573.770.977.1042.939.930.454.531.925.613.521.432.51
Adapter-874.285.762.797.887.236.450.770.6776.989.273.571.677.8045.241.831.156.430.424.613.222.033.09
Partial-166.885.962.597.385.537.650.669.4478.689.872.573.378.5341.534.333.961.031.332.816.322.434.17
FT-all68.987.764.397.286.987.438.875.8879.795.784.273.983.3656.358.641.765.557.546.725.729.147.64
VPT-shallow [32]77.786.962.697.587.374.551.276.8178.292.075.672.979.6650.558.640.567.168.736.120.234.146.98
VPT-deep [32]78.890.865.898.088.378.149.678.4881.896.183.468.482.4368.560.046.572.873.647.932.937.854.98
EXPRES (ours)78.089.668.898.788.981.951.979.784.896.280.974.284.066.560.446.577.678.049.526.135.355.0
", + "image_path": "7a9b1f2ea0c665a8ac90e84360cbdaf1c70ed38aa429035b1922f74954339b92.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 159, + 316, + 435, + 411 + ], + "blocks": [ + { + "bbox": [ + 94, + 293, + 499, + 304 + ], + "lines": [ + { + "bbox": [ + 94, + 293, + 499, + 304 + ], + "spans": [ + { + "bbox": [ + 94, + 293, + 499, + 304 + ], + "type": "text", + "content": "Table 1. VTAB-1k benchmark: Per task adaptation results with ViT-B/16 model pretrained on ImageNet-21k.." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 159, + 316, + 435, + 411 + ], + "lines": [ + { + "bbox": [ + 159, + 316, + 435, + 411 + ], + "spans": [ + { + "bbox": [ + 159, + 316, + 435, + 411 + ], + "type": "table", + "html": "
MethodIm-PreDense-PreBackbone50515253
SPNET [91]In-1k✓ResNet-10123.817.014.118.3
ZS3Net [5]In-1k✓ResNet-10140.839.439.333.6
LSEG [40]In-1k✓ViT-L/1661.363.643.141.0
LinearIn-21k-ViT-B/165.143.928.129.1
FT-allIn-21k-ViT-B/1618.331.927.923.2
BiastuneIn-21k-ViT-B/162.439.213.920.1
VPT-deep [32]In-21k-ViT-B/1633.456.249.847.7
EXPRES (Ours)In-21k-ViT-B/1641.860.252.451.4
", + "image_path": "63ced1e4f6c23d23d7091eec95ce577209a7f556a55969d4f33ecb4af9cca9af.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 419, + 546, + 441 + ], + "lines": [ + { + "bbox": [ + 46, + 419, + 546, + 441 + ], + "spans": [ + { + "bbox": [ + 46, + 419, + 546, + 441 + ], + "type": "text", + "content": "Table 2. Five-Shot Semantic Segmentation on PASCAL - " + }, + { + "bbox": [ + 46, + 419, + 546, + 441 + ], + "type": "inline_equation", + "content": "5^{\\mathrm{i}}" + }, + { + "bbox": [ + 46, + 419, + 546, + 441 + ], + "type": "text", + "content": ": Per fold adaptation results with ViT-B/16 model pretrained on ImageNet-21k." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 464, + 287, + 570 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 464, + 287, + 570 + ], + "spans": [ + { + "bbox": [ + 46, + 464, + 287, + 570 + ], + "type": "text", + "content": "of the corresponding fold. However, unlike prior works, we tune our EXPRES model on few-shot training examples and cross-validate the hyperparameters (e.g. number of prompts, " + }, + { + "bbox": [ + 46, + 464, + 287, + 570 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 464, + 287, + 570 + ], + "type": "text", + "content": ") on a validation set with fold-exclusive categories. In all our experiments, we use a reasonably small budget for hyperparameters (see supplementary) following recent studies [56] that highlight the likelihood of overoptimistic results in limited-labelled data settings due to excessive hyperparameter tuning on large validation sets." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 571, + 288, + 704 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 571, + 288, + 704 + ], + "spans": [ + { + "bbox": [ + 46, + 571, + 288, + 704 + ], + "type": "text", + "content": "Implementation Details: In all our experiments, we use a fixed encoder, ViT-B/16 pretrained on ImageNet-22K [65]. This model is effective on wide variety of tasks and allows direct comparison with prior works. For each downstream task, we train for a total 100 epochs with an initial warmup of 10 epochs. We use AdamW as our default optimizer with a suitable learning rate and fixed weight decay of " + }, + { + "bbox": [ + 46, + 571, + 288, + 704 + ], + "type": "inline_equation", + "content": "1e - 4" + }, + { + "bbox": [ + 46, + 571, + 288, + 704 + ], + "type": "text", + "content": ". For VTAB-1k and FGVC experiments, we use a fixed batch size of 64. For segmentation experiments, since overall training set sizes are extremely small (" + }, + { + "bbox": [ + 46, + 571, + 288, + 704 + ], + "type": "inline_equation", + "content": "\\leq 10" + }, + { + "bbox": [ + 46, + 571, + 288, + 704 + ], + "type": "text", + "content": " images in total), we use the entire training set per batch. We use input image reso" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 464, + 545, + 583 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 464, + 545, + 583 + ], + "spans": [ + { + "bbox": [ + 304, + 464, + 545, + 583 + ], + "type": "text", + "content": "lution of " + }, + { + "bbox": [ + 304, + 464, + 545, + 583 + ], + "type": "inline_equation", + "content": "224 \\times 224" + }, + { + "bbox": [ + 304, + 464, + 545, + 583 + ], + "type": "text", + "content": " for classification tasks and " + }, + { + "bbox": [ + 304, + 464, + 545, + 583 + ], + "type": "inline_equation", + "content": "384 \\times 384" + }, + { + "bbox": [ + 304, + 464, + 545, + 583 + ], + "type": "text", + "content": " for semantic segmentation tasks as dense prediction usually benefits from larger resolution. Since, ViT-B/16 is pretrained on standard " + }, + { + "bbox": [ + 304, + 464, + 545, + 583 + ], + "type": "inline_equation", + "content": "224 \\times 224" + }, + { + "bbox": [ + 304, + 464, + 545, + 583 + ], + "type": "text", + "content": " resolution images, we use interpolated positional embeddings to accommodate larger resolutions in the case of segmentation. Finally, we use standard data augmentations for classification benchmarks i.e., Resize " + }, + { + "bbox": [ + 304, + 464, + 545, + 583 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 304, + 464, + 545, + 583 + ], + "type": "text", + "content": " Random-Crop " + }, + { + "bbox": [ + 304, + 464, + 545, + 583 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 304, + 464, + 545, + 583 + ], + "type": "text", + "content": " Horizontal-Flip during training and Resize " + }, + { + "bbox": [ + 304, + 464, + 545, + 583 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 304, + 464, + 545, + 583 + ], + "type": "text", + "content": " Center-Crop during evaluation while for segmentation we only use Resize." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 585, + 547, + 645 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 585, + 547, + 645 + ], + "spans": [ + { + "bbox": [ + 304, + 585, + 547, + 645 + ], + "type": "text", + "content": "Evaluation Metrics For classification experiments, we use accuracy as our performance metric. For evaluating segmentation masks, we use mean intersection over union (mIoU) that averages over the intersection over union curves per class." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 657, + 391, + 669 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 657, + 391, + 669 + ], + "spans": [ + { + "bbox": [ + 306, + 657, + 391, + 669 + ], + "type": "text", + "content": "4.1. Main Results" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "type": "text", + "content": "We compare EXPRES with a number of commonly used adaptation techniques on VTAB-1k. The adaptation methods can be categorized as head-oriented, backbone-oriented" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "3371" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 275 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 275 + ], + "type": "text", + "content": "and prompt-based. Under the first category, Linear only optimizes a linear classifier for the downstream task while MLP-" + }, + { + "bbox": [ + 46, + 72, + 289, + 275 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 72, + 289, + 275 + ], + "type": "text", + "content": " uses a " + }, + { + "bbox": [ + 46, + 72, + 289, + 275 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 72, + 289, + 275 + ], + "type": "text", + "content": "-layer multilayer perceptron (MLP) as the classifier head. As an example of the second category, Sidetune [101] uses features that are linearly interpolated between pretrained features and features from a \"side\" network trained on downstream data. While Biastune [6] adapts only the bias terms of an otherwise frozen backbone. Adapter-" + }, + { + "bbox": [ + 46, + 72, + 289, + 275 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 72, + 289, + 275 + ], + "type": "text", + "content": " [30, 58, 59] introduces lightweight MLP modules inserted between Transformer layers. Partial-" + }, + { + "bbox": [ + 46, + 72, + 289, + 275 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 72, + 289, + 275 + ], + "type": "text", + "content": " finetunes the last " + }, + { + "bbox": [ + 46, + 72, + 289, + 275 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 72, + 289, + 275 + ], + "type": "text", + "content": " layers while keeping the rest of the backbone frozen, finally FT-all finetunes all the layers. VPT-shallow [32] additionally optimizes a linear classifier with the learnable input prompts propagated through the encoder. VPT-deep [32] introduces more capacity by replacing the propagated prompts with a new set of learnable prompts at each layer." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 276, + 289, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 276, + 289, + 504 + ], + "spans": [ + { + "bbox": [ + 46, + 276, + 289, + 504 + ], + "type": "text", + "content": "VTAB-1k Results (Table 1): Across all three splits of VTAB-1k, our method significantly outperforms the best head-oriented techniques: " + }, + { + "bbox": [ + 46, + 276, + 289, + 504 + ], + "type": "inline_equation", + "content": "+11\\%" + }, + { + "bbox": [ + 46, + 276, + 289, + 504 + ], + "type": "text", + "content": " (natural), " + }, + { + "bbox": [ + 46, + 276, + 289, + 504 + ], + "type": "inline_equation", + "content": "+7\\%" + }, + { + "bbox": [ + 46, + 276, + 289, + 504 + ], + "type": "text", + "content": " (specialized) and " + }, + { + "bbox": [ + 46, + 276, + 289, + 504 + ], + "type": "inline_equation", + "content": "+23\\%" + }, + { + "bbox": [ + 46, + 276, + 289, + 504 + ], + "type": "text", + "content": " (structured). Similar trends hold even when comparing with the more powerful class of backbone-oriented techniques. While FT-all has been widely adopted as an effective technique for most adaptation scenarios, our method consistently outperforms it by a significant margin of " + }, + { + "bbox": [ + 46, + 276, + 289, + 504 + ], + "type": "inline_equation", + "content": "+4\\%" + }, + { + "bbox": [ + 46, + 276, + 289, + 504 + ], + "type": "text", + "content": " (natural), " + }, + { + "bbox": [ + 46, + 276, + 289, + 504 + ], + "type": "inline_equation", + "content": "+1\\%" + }, + { + "bbox": [ + 46, + 276, + 289, + 504 + ], + "type": "text", + "content": " (specialized) and " + }, + { + "bbox": [ + 46, + 276, + 289, + 504 + ], + "type": "inline_equation", + "content": "+7\\%" + }, + { + "bbox": [ + 46, + 276, + 289, + 504 + ], + "type": "text", + "content": " (structured). Most interestingly our method even outperforms other powerful prompting techniques like VPT-deep on 12 (out of 19) datasets by a margin of about " + }, + { + "bbox": [ + 46, + 276, + 289, + 504 + ], + "type": "inline_equation", + "content": "+1\\%" + }, + { + "bbox": [ + 46, + 276, + 289, + 504 + ], + "type": "text", + "content": " (natural), " + }, + { + "bbox": [ + 46, + 276, + 289, + 504 + ], + "type": "inline_equation", + "content": "+2\\%" + }, + { + "bbox": [ + 46, + 276, + 289, + 504 + ], + "type": "text", + "content": " (specialized) and " + }, + { + "bbox": [ + 46, + 276, + 289, + 504 + ], + "type": "inline_equation", + "content": "+0.02\\%" + }, + { + "bbox": [ + 46, + 276, + 289, + 504 + ], + "type": "text", + "content": " (structured). The performance gains are particularly impressive when considered from the perspective of computation vs performance tradeoff. Compared to VPT-deep that uses 53 prompts for natural and 108 prompts for structures, our method only requires 10 and 29 prompts for the respective splits. A more detailed summary is provided in the supplementary." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 514, + 287, + 539 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 514, + 287, + 539 + ], + "spans": [ + { + "bbox": [ + 47, + 514, + 287, + 539 + ], + "type": "text", + "content": "4.2. Few-Shot Semantic Segmentation Without Dense Pretraining" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "text", + "content": "We test the efficacy of EXPRES on a novel adaptation setup where the backbone, pretrained on classification tasks, is directly adapted for few-shot semantic segmentation task without additional training on large densely-annotated datasets. This is in contrast with most works that follow a two-stage pretraining procedure i.e., training on ImageNet-1k with image level labels followed by meta-learning on densely annotated datasets constructed from the train folds of PASCAL - " + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "inline_equation", + "content": "5^{\\mathrm{i}}" + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "text", + "content": ". In contrast, we only perform the first stage pretraining on a sufficiently diverse dataset (ImageNet-21k in our case) with no meta-learning stage. During evaluation, each few-shot episode randomly samples a target image with a segmentation mask that assigns a label 1 to the pixels corresponding to one of the object cate" + } + ] + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 340, + 72, + 425, + 165 + ], + "blocks": [ + { + "bbox": [ + 340, + 72, + 425, + 165 + ], + "lines": [ + { + "bbox": [ + 340, + 72, + 425, + 165 + ], + "spans": [ + { + "bbox": [ + 340, + 72, + 425, + 165 + ], + "type": "image", + "image_path": "3c8648be08dcc2a4acd015992e0b41ac8fbf1ee95850865d04d0248b3ee46a73.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 428, + 72, + 513, + 165 + ], + "blocks": [ + { + "bbox": [ + 428, + 72, + 513, + 165 + ], + "lines": [ + { + "bbox": [ + 428, + 72, + 513, + 165 + ], + "spans": [ + { + "bbox": [ + 428, + 72, + 513, + 165 + ], + "type": "image", + "image_path": "5c4055773cecf3ec66ea5d9e829720502d21c9ca61f070f12afb9337f15ff43f.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 340, + 167, + 425, + 258 + ], + "blocks": [ + { + "bbox": [ + 340, + 167, + 425, + 258 + ], + "lines": [ + { + "bbox": [ + 340, + 167, + 425, + 258 + ], + "spans": [ + { + "bbox": [ + 340, + 167, + 425, + 258 + ], + "type": "image", + "image_path": "73d0c0370ea4ef9cf588645ad89070c7d8a04fd592910493119024a6dc566729.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 270, + 547, + 313 + ], + "lines": [ + { + "bbox": [ + 304, + 270, + 547, + 313 + ], + "spans": [ + { + "bbox": [ + 304, + 270, + 547, + 313 + ], + "type": "text", + "content": "Figure 3. Prompt Propagation: Effect of propagating prompts with modulation upto a layer, " + }, + { + "bbox": [ + 304, + 270, + 547, + 313 + ], + "type": "inline_equation", + "content": "l = \\{2,\\dots ,12\\}" + }, + { + "bbox": [ + 304, + 270, + 547, + 313 + ], + "type": "text", + "content": " of the ViT-B/16 encoder with total 12 layers. The datasets are sampled from the FGVC benchmark." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 428, + 167, + 513, + 258 + ], + "blocks": [ + { + "bbox": [ + 428, + 167, + 513, + 258 + ], + "lines": [ + { + "bbox": [ + 428, + 167, + 513, + 258 + ], + "spans": [ + { + "bbox": [ + 428, + 167, + 513, + 258 + ], + "type": "image", + "image_path": "4d74537b2d20cbd3489792118bbf48df87a3404194d63badcd6ec908147da441.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 337, + 547, + 636 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 337, + 547, + 636 + ], + "spans": [ + { + "bbox": [ + 304, + 337, + 547, + 636 + ], + "type": "text", + "content": "gories in that image and a label 0 to remaining pixels (background). From the same object category, a set of five images are randomly sampled to form the training set where the mask of each image is annotated in the same way as the target. Our method as well as all baselines that perform meta-learning are optimized given a context set to yield a binary classifier for the target image. For dense representations, we use the last layer keys of the MSA-block as we found them to be more accurate than the typical MLP-block output. We observe that our method consistently outperforms the baselines (by " + }, + { + "bbox": [ + 304, + 337, + 547, + 636 + ], + "type": "inline_equation", + "content": "25\\%" + }, + { + "bbox": [ + 304, + 337, + 547, + 636 + ], + "type": "text", + "content": ") as well as other prompt techniques such as VPT-deep (by " + }, + { + "bbox": [ + 304, + 337, + 547, + 636 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 304, + 337, + 547, + 636 + ], + "type": "text", + "content": "). Surprisingly, our method even outperforms [40] that leverages densely annotated datasets (training data per fold) with large language models for a second stage of pretraining. Specifically, on 2/4 folds, EXPRES outperforms [40] by " + }, + { + "bbox": [ + 304, + 337, + 547, + 636 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 304, + 337, + 547, + 636 + ], + "type": "text", + "content": " despite training on a significantly smaller densely-annotated dataset (five images). These results are particularly significant as they suggest that highly competitive results can be achieved with models pretrained on image classification. Consequently, results may be further improved by scaling up the image-level annotated datasets which are cheaper to scale than the densely annotated datasets. In the supplementary, we provide visualizations of the segmentation mask predictions by our method as well as Linear, FT-all and VPT-deep methods." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 646, + 407, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 646, + 407, + 658 + ], + "spans": [ + { + "bbox": [ + 306, + 646, + 407, + 658 + ], + "type": "text", + "content": "4.3. Ablation Studies" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "content": "We conduct extensive ablations to evaluate key design decisions used to develop EXPRES such as feature construction, residual prompting, number of prompts etc. For all ablations, we use the same ViT-B/16 backbone. When" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3372" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 97, + 68, + 492, + 171 + ], + "blocks": [ + { + "bbox": [ + 97, + 68, + 492, + 171 + ], + "lines": [ + { + "bbox": [ + 97, + 68, + 492, + 171 + ], + "spans": [ + { + "bbox": [ + 97, + 68, + 492, + 171 + ], + "type": "image", + "image_path": "550875f4d1eceb067e3f167f7bd597c31282f462afe9bb9f4f7abf3a6afaeea0.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 80, + 179, + 512, + 192 + ], + "lines": [ + { + "bbox": [ + 80, + 179, + 512, + 192 + ], + "spans": [ + { + "bbox": [ + 80, + 179, + 512, + 192 + ], + "type": "text", + "content": "Figure 4. Residual Prompt Types: Evaluating the importance of different type of residual prompts on FGVC datasets." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 71, + 209, + 258, + 334 + ], + "blocks": [ + { + "bbox": [ + 71, + 209, + 258, + 334 + ], + "lines": [ + { + "bbox": [ + 71, + 209, + 258, + 334 + ], + "spans": [ + { + "bbox": [ + 71, + 209, + 258, + 334 + ], + "type": "image", + "image_path": "1645a6299075cc9d4a78cbb9571a2e0aa15f5073e114ef897a48546ffdea4f4e.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 346, + 287, + 369 + ], + "lines": [ + { + "bbox": [ + 47, + 346, + 287, + 369 + ], + "spans": [ + { + "bbox": [ + 47, + 346, + 287, + 369 + ], + "type": "text", + "content": "Figure 5. Computational Efficiency Plots: Comparing Accuracy vs Number of Prompts for VPT and EXPRES" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 390, + 287, + 414 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 390, + 287, + 414 + ], + "spans": [ + { + "bbox": [ + 46, + 390, + 287, + 414 + ], + "type": "text", + "content": "using FGVC datasets, we use only " + }, + { + "bbox": [ + 46, + 390, + 287, + 414 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 46, + 390, + 287, + 414 + ], + "type": "text", + "content": " of each dataset with official splits provided in [32]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 415, + 288, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 415, + 288, + 593 + ], + "spans": [ + { + "bbox": [ + 46, + 415, + 288, + 593 + ], + "type": "text", + "content": "Prompt Propagation: We evaluate the importance of propagating prompts through the ViT-B/16 encoder with layerwise modulation. Specifically, upto a layer " + }, + { + "bbox": [ + 46, + 415, + 288, + 593 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 46, + 415, + 288, + 593 + ], + "type": "text", + "content": ", we allow all tokens (patch, class and prompt) to attend to each other at every layer. Beyond " + }, + { + "bbox": [ + 46, + 415, + 288, + 593 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 46, + 415, + 288, + 593 + ], + "type": "text", + "content": ", prompts are not allowed to interact with other tokens at all; they are simply projected by the value heads of MSA-block followed by MLP processing at every layer. In our experiments, we fix the number of prompts to 10 irrespective of the dataset. From Figure 3, we observe that downstream performance depends directly on the extent of prompt propagation with modulation: accuracy improves as more layers allow prompts to interact with other tokens. These results motivate our method, EXPRES, that facilitates finegrained layerwise modulation via residual tokens." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 594, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 289, + 714 + ], + "type": "text", + "content": "Residual Prompt Type: In Figure 4 we evaluate the importance of different residual prompt types (one-at-a-time) including attention, LayerNorm " + }, + { + "bbox": [ + 46, + 594, + 289, + 714 + ], + "type": "inline_equation", + "content": "(LN)" + }, + { + "bbox": [ + 46, + 594, + 289, + 714 + ], + "type": "text", + "content": ", query-key-value projections " + }, + { + "bbox": [ + 46, + 594, + 289, + 714 + ], + "type": "inline_equation", + "content": "(QKV)" + }, + { + "bbox": [ + 46, + 594, + 289, + 714 + ], + "type": "text", + "content": " and linear multi-head projection " + }, + { + "bbox": [ + 46, + 594, + 289, + 714 + ], + "type": "inline_equation", + "content": "(Proj)" + }, + { + "bbox": [ + 46, + 594, + 289, + 714 + ], + "type": "text", + "content": ". We also evaluate residual prompting in the MLP block: after LayerNorm " + }, + { + "bbox": [ + 46, + 594, + 289, + 714 + ], + "type": "inline_equation", + "content": "(LN,mlp)" + }, + { + "bbox": [ + 46, + 594, + 289, + 714 + ], + "type": "text", + "content": ", first linear projection " + }, + { + "bbox": [ + 46, + 594, + 289, + 714 + ], + "type": "inline_equation", + "content": "(L1,mlp)" + }, + { + "bbox": [ + 46, + 594, + 289, + 714 + ], + "type": "text", + "content": " and second linear projection " + }, + { + "bbox": [ + 46, + 594, + 289, + 714 + ], + "type": "inline_equation", + "content": "(L2,mlp)" + }, + { + "bbox": [ + 46, + 594, + 289, + 714 + ], + "type": "text", + "content": ". We evaluate the composite effect of multiple prompt types within a computational block i.e., Att (MSA block) and MLP (MLP block). As a baseline, we provide the per-dataset results for shallow" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 212, + 547, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 212, + 547, + 380 + ], + "spans": [ + { + "bbox": [ + 304, + 212, + 547, + 380 + ], + "type": "text", + "content": "prompting, referred to as None in the figure. The number of prompts at each layer are fixed at 10. We observe that, within the MSA block, adding residual prompts to LayerNorm and query-key-value projections yields the most improvements (3.5% and 2.8% on an average respectively) over None. Moreover, LayerNorm prompts in the MLP block are also more effective than prompting the two linear layers. Comparing blockwise performance, prompting the MSA block " + }, + { + "bbox": [ + 304, + 212, + 547, + 380 + ], + "type": "inline_equation", + "content": "(Att)" + }, + { + "bbox": [ + 304, + 212, + 547, + 380 + ], + "type": "text", + "content": " yields significantly better performance (by 1.6%) than prompting the MLP block " + }, + { + "bbox": [ + 304, + 212, + 547, + 380 + ], + "type": "inline_equation", + "content": "(MLP)" + }, + { + "bbox": [ + 304, + 212, + 547, + 380 + ], + "type": "text", + "content": ". The performance gap between " + }, + { + "bbox": [ + 304, + 212, + 547, + 380 + ], + "type": "inline_equation", + "content": "Att" + }, + { + "bbox": [ + 304, + 212, + 547, + 380 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 212, + 547, + 380 + ], + "type": "inline_equation", + "content": "MLP" + }, + { + "bbox": [ + 304, + 212, + 547, + 380 + ], + "type": "text", + "content": " highlights the importance of directly modulating layerwise interaction between tokens for better adaptation. Consequently, we use " + }, + { + "bbox": [ + 304, + 212, + 547, + 380 + ], + "type": "inline_equation", + "content": "Att" + }, + { + "bbox": [ + 304, + 212, + 547, + 380 + ], + "type": "text", + "content": " as our default setting for all experiments." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 380, + 547, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 380, + 547, + 536 + ], + "spans": [ + { + "bbox": [ + 304, + 380, + 547, + 536 + ], + "type": "text", + "content": "Computational Efficiency of Prompting: In prompting techniques, the primary computational overhead arises from the quadratic complexity (in number of tokens) of the transformer encoder. So to evaluate computation efficiency of prompting, we investigate the rate at which performance improves with number of prompts and provide comparisons between our method and VPT in Figure 5. We evaluate on two different datasets sampled from different categories of VTAB-1k. For a given accuracy, e.g. " + }, + { + "bbox": [ + 304, + 380, + 547, + 536 + ], + "type": "inline_equation", + "content": "58.5\\%" + }, + { + "bbox": [ + 304, + 380, + 547, + 536 + ], + "type": "text", + "content": " on Clevr-Distance, EXPRES requires an order less prompts than VPT, resulting in 2 orders less computations. Overall EXPRES achieves higher optimal performance with far fewer prompts than VPT." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 548, + 379, + 562 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 548, + 379, + 562 + ], + "spans": [ + { + "bbox": [ + 306, + 548, + 379, + 562 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "content": "In this work we propose a novel prompting technique for adapting large vision models. Our method demonstrates strong performance across variety of downstream tasks with varying dataset sizes. Further, our method outperforms commonly used finetuning approach as well as the recently proposed VPT method on standard benchmarks. We also demonstrate diverse adaptation ability of our method from classification to semantic segmentation tasks in the few-shot setting. Lastly, our method is more parameter efficient that existing weight-space and prompt based adaptation techniques. In the future, we plan to extend our method to additional settings including vision-language learning." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3373" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 53, + 92, + 287, + 713 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 56, + 92, + 287, + 125 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 92, + 287, + 125 + ], + "spans": [ + { + "bbox": [ + 56, + 92, + 287, + 125 + ], + "type": "text", + "content": "[1] Arman Afrasiyabi, Jean-François Lalonde, and Christian Gagn'e. 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In ACM MM, 2021. 3" + } + ] + } + ], + "index": 23 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3377" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 11 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Learning Federated Visual Prompt in Null Space for MRI Reconstruction/20f20c2b-43db-4f5b-b2e9-0c30622bc0bc_content_list.json b/2023/Learning Federated Visual Prompt in Null Space for MRI Reconstruction/20f20c2b-43db-4f5b-b2e9-0c30622bc0bc_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..8d2220145b323fcf22493b718e2d61fde777e016 --- /dev/null +++ b/2023/Learning Federated Visual Prompt in Null Space for MRI Reconstruction/20f20c2b-43db-4f5b-b2e9-0c30622bc0bc_content_list.json @@ -0,0 +1,1645 @@ +[ + { + "type": "text", + "text": "Learning Federated Visual Prompt in Null Space for MRI Reconstruction", + "text_level": 1, + "bbox": [ + 112, + 130, + 854, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Chun-Mei Feng $^{1}$ Bangjun Li $^{2}$ Xinxing Xu $^{1,*}$ Yong Liu $^{1,*}$ Huazhu Fu $^{1}$ Wangmeng Zuo $^{3}$", + "bbox": [ + 107, + 179, + 861, + 199 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ Institute of High Performance Computing (IHPC),", + "bbox": [ + 281, + 198, + 686, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Agency for Science, Technology and Research (A*STAR), Singapore", + "bbox": [ + 210, + 217, + 759, + 234 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{2}$ School of Information Science and Engineering, Shangdong University, China", + "bbox": [ + 174, + 234, + 795, + 251 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{3}$ Harbin Institute of Technology, Harbin, China", + "bbox": [ + 299, + 252, + 669, + 268 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "strawberry.feng0304@gmail.com, {xuxinx, liuyong}@ihpc.a-star.edu.sg", + "bbox": [ + 192, + 272, + 774, + 287 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "https://github.com/chunmeifeng/FedPR", + "bbox": [ + 318, + 289, + 640, + 303 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 339, + 312, + 354 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Federated Magnetic Resonance Imaging (MRI) reconstruction enables multiple hospitals to collaborate distributedly without aggregating local data, thereby protecting patient privacy. However, the data heterogeneity caused by different MRI protocols, insufficient local training data, and limited communication bandwidth inevitably impair global model convergence and updating. In this paper, we propose a new algorithm, FedPR, to learn federated visual prompts in the null space of global prompt for MRI reconstruction. FedPR is a new federated paradigm that adopts a powerful pre-trained model while only learning and communicating the prompts with few learnable parameters, thereby significantly reducing communication costs and achieving competitive performance on limited local data. Moreover, to deal with catastrophic forgetting caused by data heterogeneity, FedPR also updates efficient federated visual prompts that project the local prompts into an approximate null space of the global prompt, thereby suppressing the interference of gradients on the server performance. Extensive experiments on federated MRI show that FedPR significantly outperforms state-of-the-art FL algorithms with $< 6\\%$ of communication costs when given the limited amount of local training data.", + "bbox": [ + 76, + 371, + 473, + 719 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 744, + 209, + 760 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Federated Magnetic Resonance Imaging (MRI) reconstruction enables multiple hospitals to train a powerful global model in a distributed manner without sharing private data [7, 9, 13]. In federated MRI, each client (i.e., hospital) uses its local computing power, memory, and private data to train local models independently, while the server aggregates all the local models in each communica", + "bbox": [ + 76, + 770, + 468, + 876 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c71ee1f0e0c0da547bb5107eee89af8d5c027e4bc0621d3cd973d689967ad3a4.jpg", + "image_caption": [ + "Figure 1. Illustration of the three key issues in federated MRI." + ], + "image_footnote": [], + "bbox": [ + 540, + 320, + 854, + 481 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tion round and distributes the global model to each client again [26].", + "bbox": [ + 498, + 506, + 890, + 536 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Existing federated MRI reconstruction techniques usually improve federated learning (FL) by enhancing the aggregation process [9] and reducing the local parameter's variance [5, 13]. Such techniques require a large communication bandwidth and sufficient local training data. However, federated MRI often faces two issues, insufficient amount of local training data due to the difficulty of acquiring the ground-truth of MRI reconstruction [10, 11, 12] and limited communication bandwidth due to unbalanced regional development (see Fig. 1). To cope with the issue, pre-trained models have exhibited superior performance, and have shown to close the gap between federated and centralized performance [3, 28]. However, since the model parameters need to be shared between the client and the server for updating, the large number of parameters of pre-trained models will result in a huge communication cost. On contrary, prompt tuning has recently been suggested as a new fine-tuning paradigm by freezing the models and only learning a small number of learnable parameters in the input space [15, 31, 32]. Benefited from pre-trained models, only parameter-efficient prompts are required in learning and communication, and prompt tuning can be conducted with a limited number of samples, making it very appealing in tackling the above two issues (i.e.,", + "bbox": [ + 496, + 537, + 892, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author.", + "bbox": [ + 94, + 887, + 220, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "8064", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$\\mathbf{1}$ and $\\mathbf{2}$ ) in federated MRI.", + "text_level": 1, + "bbox": [ + 76, + 90, + 264, + 104 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Besides, there is another critical issue for federated MRI, i.e., ⑧ catastrophic forgetting, caused by data heterogeneity due to the different imaging protocols of MRI scanners adopted by different clients [9, 39] (see Fig. 1). In the local update, the global model from the prior round tends to be overfitted to the local training data, leading to catastrophic forgetting. Analogous to continual learning, several techniques have been presented by introducing proper regularization terms in local models [4, 33, 39] or retaining previously acquired knowledge by knowledge distillation [14, 35, 38]. However, these strategies require seeking a balance between multiple losses and relying on proxy datasets. Instead, Adam-NSC mitigates catastrophic forgetting in continual learning with a new network parameter update rule, i.e., forces the network update to lie in the approximate null space of the input features of previous tasks at each layer [36]. However, the null space at feature level is built upon large local training data, which generally cannot be satisfied in federated MRI, i.e., the issue ①. Taking the issues ① and ⑧ into account, we suggest to optimize local prompts in the approximate null space of global prompts instead of input features, thereby preventing the loss of previously gained global knowledge.", + "bbox": [ + 76, + 106, + 468, + 454 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In a nutshell, we explore a new FL paradigm, i.e., FedPR, to learn federated visual prompts for MRI reconstruction. To begin with, we pre-train the model on a large-scale public dataset. Given limited amount of local training data, visual prompt tuning is adopted to learn local prompts in a distributed manner. For the issues 1 and 2, federated visual prompts are introduced to learn a strong global model, where only local and global prompts are learnable and communicated. As for the issue 3, we perform singular value decomposition (SVD) on the uncentered covariance matrix of global prompts to obtain the approximate null space. FedPR tunes only the local parameters in the null space of global prompts, thereby well preserving the prior knowledge of previous rounds and resulting in low communication costs. In particular, FedPR achieves a $>4.5$ dB gain in PSNR with less than $6\\%$ of communication costs. To sum up, our contributions are as follows:", + "bbox": [ + 76, + 455, + 468, + 710 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a federated visual prompt algorithm, FedPR, to solve the three key issues in federated MRI. By leveraging powerful pre-trained models and freezing backbone networks in FL, only a small amount of parameters in the input space are trainable, thereby reducing communication costs.", + "- We explore how to alleviate catastrophic forgetting in FL while reducing communication costs. By optimizing local parameters only in the null space of global prompts, FedPR well preserves the previously acquired global knowledge in each round, maintaining competitive performance with only a few local data." + ], + "bbox": [ + 76, + 719, + 467, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- We evaluate the performance of FedPR for federated MRI reconstruction. In comparison to the state-of-the-art FL methods, FedPR achieves superior performance in complex scenarios, e.g., less local data, lower communication costs, and faster convergence.", + "bbox": [ + 500, + 90, + 890, + 167 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 183, + 640, + 199 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Federated MRI Reconstruction. MRI reconstruction refers to reconstructing images without aliasing artifacts from undersampled $k$ -space data [6, 8, 12, 37, 41]. However, existing MRI reconstruction techniques are based on large-scale paired data, which is not only labor-intensive but also violates patient privacy [9]. Driven by these realistic problems, a few FL-based methods for MRI reconstruction have been proposed [5, 9, 13]. Guo et al. reduced data heterogeneity by iteratively aligning the data distribution between source and target clients [13]. Feng et al. proposed a personalized FL reconstruction scheme and introduced a weighted contrast regularization term to correct the update direction of global generalization [9]. However, these schemes either require frequent communication or are built on a large amount of local data. As a result, these techniques will produce sub-optimal solutions for MRI reconstruction when there is limited bandwidth and insufficient local training data. In contrast to these works, we build a federated MRI model upon a strong pre-trained model by updating and communicating only a small portion of parameters for each client using limited local data, achieving competitive results.", + "bbox": [ + 496, + 205, + 890, + 535 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Catastrophic Forgetting in FL. Due to the heterogeneous data distributions of different tasks in continual learning, when the network is fitted to the current task, the model parameters typically deviate from the areas where the previous knowledge is expected to be preserved [17]. Therefore, catastrophic forgetting is a fundamental challenge of continual learning. Similarly, catastrophic forgetting also affects FL [14, 19, 39]. When the client receives the global model and continues to update locally, it will cause the global model to forget the knowledge of the previous round due to the data heterogeneity across clients [19]. As a result, existing FL techniques that address catastrophic forgetting are designed by referring to continual learning. For example, knowledge distillation-based FL methods maintain previously gained knowledge, but this method strongly relies on proxy data [14, 35, 38]; regularization-based FL methods regularize locally trained parameters, but they require finding a compromise between loss terms [4, 33, 39]. All these studies are built on classification tasks and cannot be directly extended to MRI reconstruction. Inspired by the success of null space in continual learning [18, 23, 36], we try to update the local prompt in the approximate null space of global prompts, thereby preserving the knowledge acquired by the global model in the previous round and avoid", + "bbox": [ + 496, + 537, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "8065", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/49dbd40481e5ce7b8ff62315081544b4713a640ddea149e3ef9744b02a6a8735.jpg", + "image_caption": [ + "(a) Initialization and local update" + ], + "image_footnote": [], + "bbox": [ + 99, + 79, + 297, + 281 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/e7f3fbb295c11848b735f213b931378776230d91d272f1a754168f05a481c7a5.jpg", + "image_caption": [ + "(b) Federated visual prompt", + "(c) Server update", + "Figure 2. Illustration of our FedPR method. (a) For each client, the backbone model is pre-trained on massive data and fine-tuned via prompt (see Sec. 3.2). (b) Federated visual prompt is executed by updating the local prompt of each client only in the approximate null space of global prompts while preserving the previously acquired global knowledge (see Sec. 3.3). (c) Server update by aggregating local prompts." + ], + "image_footnote": [], + "bbox": [ + 323, + 78, + 874, + 282 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "ing catastrophic forgetting.", + "bbox": [ + 76, + 364, + 261, + 378 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Prompt Learning. Prompt tuning was initially proposed to enable pre-trained language models to \"understand\" downstream tasks by adding trainable tokens to the input text [24]. For example, Jia et al. achieved good performance on downstream tasks by introducing a small number of learnable tokens into the input space and keeping the backbone frozen [15]. Hyojin et al. suggested to modify pixel space for the frozen visual models [2]. Nie et al. proposed a unified prompt tuning framework that performs on different CNN and transformer-based architectures by training only a few additional parameters [29]. Although these works have made progress on various visual tasks, prompt is still limited to centralized systems, and the effectiveness of prompt in distributed framework remains uninvestigated. Therefore, this work focuses on how to learn a federated visual prompt to effectively tackle the three key problems in federated MRI reconstruction, i.e., the issues ①-③.", + "bbox": [ + 75, + 378, + 473, + 636 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 76, + 643, + 212, + 660 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Federated MRI Reconstruction", + "text_level": 1, + "bbox": [ + 76, + 664, + 354, + 679 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "MRI reconstruction is an inverse problem of recovering an artifact-free image $\\mathbf{y}$ from its undersampled observation $\\mathbf{x}$ that can reduce the online collection time and improve the patient experience [34, 37, 40]. Formally, such undersampling process can be expressed as", + "bbox": [ + 75, + 683, + 468, + 758 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {x} = \\mathcal {F} ^ {- 1} (\\mathcal {M} \\odot \\mathcal {F} (\\mathbf {y}) + \\epsilon), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 174, + 760, + 468, + 777 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathcal{F}$ is multi-dimensional Fourier transform, $\\epsilon$ is the measurement noise, and $\\mathcal{M}$ is the binary mask operator to undersample the data points in the Fourier space.", + "bbox": [ + 75, + 779, + 468, + 824 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The centralized approach violates patient privacy protection roles because it requires collecting large amounts of training data from different hospitals. As a remedy, Federated MRI has been suggested by deploying MRI reconstruction in a distributed manner [9, 13]. Suppose there are $K$", + "bbox": [ + 75, + 825, + 470, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "hospitals (local clients). The private data of all hospitals can be expressed as $\\mathcal{D} = \\{\\mathcal{D}^1,\\mathcal{D}^2,\\dots ,\\mathcal{D}^K\\}$ , where each contains limited pairs of undersampled samples $\\mathbf{x}_i$ and fully-sampled images $\\mathbf{y}_i$ . Federated MRI aims to learn a global model from the whole dataset $\\mathcal{D}$ in a distributed manner, which can be described as", + "bbox": [ + 496, + 364, + 892, + 453 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\arg \\min _ {\\boldsymbol {w}} \\mathcal {L} (\\boldsymbol {w}) = \\sum_ {k = 1} ^ {K} \\frac {| \\mathcal {D} ^ {k} |}{| \\mathcal {D} |} \\mathcal {L} _ {k} (\\boldsymbol {w}), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 580, + 455, + 890, + 496 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $|\\mathcal{D}|$ denotes the number of samples in $\\mathcal{D}$ , and $\\mathcal{L}_k(\\boldsymbol{w})$ is the empirical loss of client $k$ ,", + "bbox": [ + 496, + 498, + 890, + 527 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {k} (\\boldsymbol {w}) = \\mathbf {E} _ {(\\mathbf {x}, \\mathbf {y}) \\in \\mathcal {D} ^ {k}} \\ell_ {k} (f (\\mathbf {x}; \\boldsymbol {w})) \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 576, + 532, + 890, + 549 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\ell_{k}$ represents the local loss for MRI reconstruction, e.g., $L_{1}$ loss. After training, the reconstructed image $\\hat{\\mathbf{y}}$ can be produced by $f(\\mathbf{x};\\boldsymbol {w})$", + "bbox": [ + 496, + 553, + 893, + 599 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Learning Federated Prompt", + "text_level": 1, + "bbox": [ + 500, + 607, + 751, + 625 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As mentioned in Sec. 1, there are three key issues, i.e., 1-3, with the existing federated MRI algorithms. To tackle the issue 2, we freeze the backbone of the pre-trained model while only tuning and communicating a few learnable parameters for the clients and server. More importantly, it enables the model to achieve very competitive results on limited local data, thereby providing an effective solution to issue 1.", + "bbox": [ + 496, + 628, + 890, + 747 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As shown in Fig. 2, given a pre-trained model with parameters $\\theta$ , we introduce a set of continuous embeddings $P = \\{p_1, p_2, \\dots, p_l\\}$ as the prompts in the input space of each layer [15], where $l$ is the number of prompts. Thus, the overall parameters can be expressed as $\\boldsymbol{w} = \\{P, \\theta\\}$ . Suppose there are $Z$ rounds of communication, each round contains $T$ local updates. During the local update, for the $k$ -th client, only the client-specific prompts $P_k$ are learnable and communicated while the backbone network is frozen. Therefore, Eq. (2) can be rewritten as:", + "bbox": [ + 496, + 750, + 892, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "8066", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/6aa9308d7a76fd86981d6b134000b925c23644744698cfa3c78ccc22175d3b80.jpg", + "image_caption": [ + "Figure 3. Illustration of federated visual prompt for updating local prompts in the null space of global prompts." + ], + "image_footnote": [], + "bbox": [ + 78, + 78, + 472, + 287 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {P} _ {k} = \\arg \\min _ {\\boldsymbol {P}} \\mathcal {L} (\\boldsymbol {P}) = \\sum_ {k = 1} ^ {K} \\frac {\\left| \\mathcal {D} ^ {k} \\right|}{\\left| \\mathcal {D} \\right|} \\mathcal {L} _ {k} (\\boldsymbol {P}), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 135, + 340, + 468, + 381 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where the empirical loss for prompt tuning of client $k$ can be expressed as", + "bbox": [ + 76, + 382, + 468, + 411 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {k} (\\boldsymbol {P}) = \\mathbf {E} _ {(\\mathbf {x}, \\mathbf {y}) \\in \\mathcal {D} ^ {k}} \\ell_ {k} (f (\\mathbf {x}; \\boldsymbol {P}, \\boldsymbol {\\theta})). \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 145, + 414, + 468, + 431 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Benefited from pre-trained models, federated prompt tuning can be both parameter- and communication-efficient and effective in achieving competitive results with a small amount of local data, thereby serving as a favorable solution to the issues 1 and 2.", + "bbox": [ + 76, + 436, + 468, + 511 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Local Update Step: In each communication round $z = \\{1,2,\\dots,Z\\}$ , the clients are optimized using the following update rules with a learning rate of $\\eta_{k}$ :", + "bbox": [ + 76, + 512, + 468, + 558 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {P} _ {k} ^ {z, t + 1} \\leftarrow \\boldsymbol {P} _ {k} ^ {z, t} - \\eta_ {k} \\nabla \\ell_ {k} \\left(\\mathbf {x} ^ {k}; \\boldsymbol {P} _ {k} ^ {z, t}\\right), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 145, + 560, + 468, + 580 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $t$ denotes the $t$ -th update of the local clients.", + "bbox": [ + 76, + 580, + 413, + 595 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Server Update Step: After a round of local updates, all participating clients send their updated prompts $\\pmb{P}_{k}^{z}$ to the server performing aggregation. Such process can be expressed as follows", + "bbox": [ + 76, + 595, + 468, + 655 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {P} _ {g} ^ {z + 1} \\leftarrow \\sum_ {k = 1} ^ {K} \\frac {\\left| \\mathcal {D} ^ {k} \\right|}{\\left| \\mathcal {D} \\right|} \\mathbf {P} _ {k} ^ {z}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 194, + 648, + 468, + 690 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $P_{g}^{z + 1}$ denotes the global prompts of round $z + 1$ . To sum up, the issue $\\mathbf{0}$ can be largely mitigated because there are only a small number of learnable parameters $P$ communicated between the server and local clients. After $Z$ rounds of communication, we can get a robust global model parameterized by $P_{g}$ without sharing local private data.", + "bbox": [ + 76, + 691, + 468, + 784 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Local Updating in Prompting Null Space", + "text_level": 1, + "bbox": [ + 76, + 791, + 426, + 808 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The local update mechanism in Eq. (6), however, suffers from the issue ⑧, i.e., catastrophic forgetting, due to data heterogeneity of different clients. Inspired by the continual learning method Adam-NSC [36] that sequentially optimizes network parameters in the null space at feature level, we suggest to optimize the local model in the null space of", + "bbox": [ + 76, + 810, + 470, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Algorithm 1: FedPR", + "text_level": 1, + "bbox": [ + 509, + 94, + 653, + 109 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Input: Private datasets from $K$ clients: $\\mathcal{D}^1, \\mathcal{D}^2, \\ldots, \\mathcal{D}^K$ , local updates $T$ , communication rounds $Z$ , pre-trained model parameters $\\theta$ , prompt embeddings $P$ , learning rate $\\eta$ , hyperparameter $\\gamma$ ;", + "bbox": [ + 519, + 112, + 864, + 186 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1 // ServerExecution:", + "2 Initialize global prompt $P_{g}$ with parameters $\\theta$", + "3 for each communication round $z\\in \\{1,2,\\dots,Z\\}$ do" + ], + "bbox": [ + 506, + 188, + 859, + 232 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "4 for each client $k\\in \\{1,2,\\dots K\\}$ in parallel do 5 $\\begin{array}{rl} & P_k^z\\gets P_g^z;\\\\ & \\hat{P}_k^z\\gets \\mathrm{LocalUpdate}(k,P_k^z); \\end{array}$ 6", + "7 end" + ], + "bbox": [ + 506, + 233, + 849, + 295 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "8 $P_{g}^{z + 1}\\gets \\sum_{k = 1}^{K}\\frac{|\\mathcal{D}^{k}|}{|\\mathcal{D}|}\\hat{P}_{k}^{z};$", + "9 Compute the uncentered covariance matrix:" + ], + "bbox": [ + 506, + 297, + 833, + 334 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "10 $\\pmb{\\Sigma}_{g}^{z + 1} = \\left(\\pmb{P}_{g}^{z + 1}\\right)^{\\top}\\pmb{P}_{g}^{z + 1};$", + "11 Approximate the null space of $\\Sigma_g^{z + 1}$", + "12 $\\pmb{\\Sigma}_{g}^{z + 1} = \\pmb{U}^{z + 1}\\pmb{\\Lambda}^{z + 1}\\left(\\pmb{U}^{z + 1}\\right)^{\\top};$", + "13 Select the smallest diagonal singular values of $\\Lambda_2^{z + 1}$ with the ratio of $\\gamma$", + "14 Get $\\pmb{U}_2^{z + 1}$ corresponding to $\\Lambda_2^{z + 1}$" + ], + "bbox": [ + 503, + 335, + 849, + 434 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "15 end", + "16 return $P_{g}^{z + 1}$", + "17 // LocalUpdate $(k, P_k)$ :", + "18 for each local epoch $t \\in \\{1, 2, \\dots, T\\}$ do", + "19 Get the updated parameters $\\Delta P_k^z$ :", + "20 $|\\Delta P_k^z = U_2^{z + 1}\\left(U_2^{z + 1}\\right)^\\top P_k^z;$", + "21 $\\hat{P}_k^{z,t + 1}\\gets P_k^{z,t} - \\eta_k\\Delta P_k^{z,t};$", + "22 end", + "23 return $\\hat{P}_k^z$" + ], + "bbox": [ + 501, + 436, + 782, + 582 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "global prompts. Specifically, we train the local model in the approximate null space of the global prompts in a distributed way, preventing knowledge outside the local distribution from being overwritten and resulting in catastrophic forgetting. In comparison to [36], approximating the null space of global prompts instead of features does not require a large amount of local data and not increase the communication cost, thus offering a feasible way to tackle the three issues 1-8 in federated MRI.", + "bbox": [ + 496, + 619, + 890, + 755 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As shown in Fig. 3, we first compute the uncentered covariance matrix of $z + 1$ round global prompt $P_g^{z + 1}$ by", + "bbox": [ + 498, + 758, + 890, + 790 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {\\Sigma} _ {g} ^ {z + 1} = \\left(\\boldsymbol {P} _ {g} ^ {z + 1}\\right) ^ {\\top} \\boldsymbol {P} _ {g} ^ {z + 1}. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 609, + 797, + 890, + 818 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Then, we find the approximate null space of $\\Sigma_{g}^{z + 1}$ by apply SVD to it", + "bbox": [ + 498, + 824, + 890, + 854 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {\\Sigma} _ {g} ^ {z + 1} = \\boldsymbol {U} ^ {z + 1} \\boldsymbol {\\Lambda} ^ {z + 1} \\left(\\boldsymbol {U} ^ {z + 1}\\right) ^ {\\top}, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 589, + 864, + 890, + 885 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where", + "bbox": [ + 500, + 886, + 545, + 898 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "8067", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {U} ^ {z + 1} = \\left[ \\boldsymbol {U} _ {1} ^ {z + 1}, \\boldsymbol {U} _ {2} ^ {z + 1} \\right], \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 174, + 121, + 467, + 143 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {\\Lambda} ^ {z + 1} = \\left[ \\begin{array}{c c} \\boldsymbol {\\Lambda} _ {1} ^ {z + 1} & 0 \\\\ 0 & \\boldsymbol {\\Lambda} _ {2} ^ {z + 1} \\end{array} \\right].\n$$\n", + "text_format": "latex", + "bbox": [ + 174, + 142, + 364, + 176 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Here $U_{1}^{z + 1}$ are the singular vectors corresponding to the large singular values in $\\Lambda_1^{z + 1}$ [36]. According to principal component analysis (PCA), $U_{1}^{z + 1}$ can be considered as principal components, which contain the global knowledge that has been captured in the previous round. Thus, we have $\\Sigma_g^{z + 1} \\approx U_1^{z + 1}\\Lambda_1^{z + 1}\\left(U_1^{z + 1}\\right)^\\top$ . And the range space of $U_{2}^{z + 1}$ can be denoted as the approximate null space of $\\Sigma_g^{z + 1}$ [36]. In our implementation, we introduce a $\\gamma \\%$ to control $U_{2}^{z + 1}$ by selecting the last $\\gamma \\%$ of singular values in $\\Lambda_2^{z + 1}$ to constitute $U_{2}^{z + 1}$ .", + "bbox": [ + 76, + 178, + 468, + 333 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To tackle the issue $\\bullet$ , $P_{k}^{z}$ can be projected into the approximate null space of $\\Sigma_{g}^{z + 1}$ to get the updated parameters, while the principal components $U_{1}^{z + 1}$ containing the global knowledge from the previous round are preserved. Thus, the updated parameters $\\Delta P_{k}^{z}$ can be optimized in the null space of $\\Sigma_{g}^{z + 1}$ by", + "bbox": [ + 76, + 334, + 468, + 428 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\Delta \\boldsymbol {P} _ {k} ^ {z} = \\boldsymbol {U} _ {2} ^ {z + 1} \\left(\\boldsymbol {U} _ {2} ^ {z + 1}\\right) ^ {\\top} \\boldsymbol {P} _ {k} ^ {z}, \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 174, + 429, + 468, + 449 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\boldsymbol{U}_2^{t+1}(\\boldsymbol{U}_2^{t+1})^\\top$ is the projection operator [27]. Formally, the local update step of Eq. (6) can be rewritten as", + "bbox": [ + 76, + 452, + 468, + 484 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\boldsymbol {P}} _ {k} ^ {z, t + 1} \\leftarrow \\boldsymbol {P} _ {k} ^ {z, t} - \\eta_ {k} \\Delta \\boldsymbol {P} _ {k} ^ {z, t}. \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 174, + 489, + 468, + 508 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The detailed FedPR algorithm is given in Algorithm 1.", + "bbox": [ + 76, + 511, + 437, + 526 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 541, + 209, + 556 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 76, + 565, + 266, + 580 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implementation Details. Our method is trained by Pytorch with one NVIDIA Tesla V100 GPU and 32GB of memory. We use Adam as the optimizer, with a momentum of 0.9 and weight decay of 0.0005. The models are trained with 50 communication rounds and 10 local epochs for each round. We set the batch size and initial learning rate to 8 and $1 \\times 10^{-1}$ , respectively. The hyperparameter $\\gamma$ is empirically set to $80\\%$ . The prompt embeddings are added with a size of $8 \\times 20 \\times 256$ .", + "bbox": [ + 75, + 584, + 468, + 718 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets. We use fastMRI1, the largest publicly available MRI dataset, to train the pre-training model, with Swin Transformers and a standard ConvNet head serving as the backbone of our experiments [25]. We note that the mean and std of BN layer in the head are also shared with the server to update the original statistical properties. For the clients, we employ four datasets with a size of $320 \\times 320$ , including FeTS2 [30], $\\mathbf{IXI}^3$ [1], and two clinical datasets,", + "bbox": [ + 75, + 719, + 468, + 840 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "to comprise our local data. In our experiments, we divide them into 15 clients according to the acquiring institutions, i.e., FeTS is divided into 10 clients with only 120, 304, 304, 240, 160, 160, 280, 224, 264, and 184 images, respectively; IXI is divided into 3 clients with only 360, 328, and 296 images, respectively; two clinical datasets collected from the United Imaging Healthcare uMR 790 scanner and 3T Siemens Magnetom Skyra system form two clients with 432 and 360 images, respectively. The input data of each client employs a $1D$ random sampling pattern with $3 \\times$ acceleration. We note that our clients have only a small number of images. In comparison, FedMRI [9] and FL-MRCM [13] require thousands to tens of thousands of images. For In-Federation evaluation, we divide each dataset with a ratio of $7:3$ for local train/test. For Out-of-Federation evaluation, we use the test set of FeTS as our test set because it comes from a separate institution with a quite different distribution.", + "bbox": [ + 500, + 90, + 890, + 362 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Baselines. To demonstrate the effectiveness of our proposed method, we compare it with three categories of methods, including: a) SingleSet, a single model that each client is trained with their local data without FL; b) Centralized, a single model that is trained with the combination of all the local data, which serves as the upper-bound of FL models; and c) eight state-of-the-art FL algorithms, including: (1) FedAvg [26], a classical FL algorithm that is trained by averaging parameters of all the participating clients; (2) FedBN [22], a FL algorithm that alleviates the client-shift by using batch normalization on each local client; (3) FedProx [21], a FL algorithm that applies a proximal term to the local objective function; (4) SCAFFOLD [16], a FL algorithm that uses control variates to correct the client-drift; (5) MOON [20], a FL algorithm that utilizes the similarity between model representations to correct the local update; (6) FedReg [39], a FL algorithm that regularizes locally trained parameters with the loss on generated pseudo data to alleviate knowledge forgetting; (7) FL-MRCM [13], a federated MRI algorithm that aligns the latent features between the source and target clients; and (8) FedMRI [9], a federated MRI algorithm that preserves the client-specific properties to improve the FL performance. For a fair comparison, we adopt Swin Transformers and a standard ConvNet head as the reconstruction network for each client among all the baselines.", + "bbox": [ + 498, + 363, + 890, + 755 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Comparison with State-of-the-arts", + "text_level": 1, + "bbox": [ + 500, + 761, + 799, + 776 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In-Federation Performance. The first subtable of Table 1 provides a comprehensive evaluation of the In-Federation setting with regards to various FL algorithms, where SingleSet indicates that each client is trained to use their local data without FL, and Centralized indicates that all the local datasets are gathered, which serves as the upper-bound of FL models. Ours (w. Pro) and Ours (Full) are the variants of our method that only with prompts and", + "bbox": [ + 498, + 779, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_footnote", + "text": "1https://fastmri.org/. \n2https://www.synapse.org/#!Synapse:syn28546456/ \nwiki/. \n3https://brain-developmentment.org/", + "bbox": [ + 76, + 849, + 467, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "8068", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/38b4ba2d41976359cd561ae8d8f6faba2bf4d9542b12664a8e7229a4ea0babf0.jpg", + "table_caption": [ + "Table 1. Quantitative comparison of state-of-the-art FL methods with regard to In-Federation and Out-of-Federation scenarios, where # Com.cost is the communication cost, Ub indicates the upper-bound of FL algorithms, ↑ and ↓ indicate increments and decrements compared with FedAvg (w. FFt). Detailed analyses are provided in Sec. 4.2." + ], + "table_footnote": [], + "table_body": "
Method# Com.costIn-FederationOut-of-Federation
PSNRSSIMNMSEPSNRSSIMNMSE
SingleSet18.43 M28.79(3.35)↓0.805(0.099)↓0.021(0.011)↓28.92(2.15)↓0.808(0.091)↓0.032(0.011)↓
Centralized (Ub)18.43 M36.71(4.57)↑0.947(0.044)↑0.009(0.005)↑35.73(4.66)↑0.940(0.041)↑0.008(0.013)↑
FedAvg (w. FFt) [26]18.43 M32.14(0.00)0.903(0.000)0.010(0.000)31.07(0.00)0.899(0.000)0.021(0.000)
FedBN [22]18.40 M28.31(3.83)↓0.817(0.086)↓0.044(0.034)↓25.65(5.42)↓0.731(0.186)↓0.080(0.059)↓
FedProx [21]18.43 M32.84(0.70)↑0.901(0.002)↑0.010(0.000)31.98(0.91)↑0.905(0.006)↑0.018(0.003)↑
SCAFFOLD [16]18.43 M33.08(0.94)↑0.914(0.010)↑0.009(0.001)↑32.20(1.13)↑0.915(0.016)↑0.018(0.003)↑
MOON [20]18.43 M34.06(1.92)↑0.927(0.023)↑0.008(0.002)↑31.16(0.09)↑0.907(0.008)↑0.023(0.002)↓
FedReg [39]18.43 M33.29(1.15)↑0.890(0.013)↑0.009(0.001)↑32.41(1.34)↑0.907(0.008)↑0.017(0.004)↑
FL-MRCM [13]18.43 M33.60(1.46)↑0.922(0.019)↑0.013(0.003)↓32.72(1.65)↑0.911(0.012)↑0.016(0.005)↑
FedMRI [9]17.46 M33.35(1.21)↑0.923(0.020)↑0.014(0.004)↓32.00(0.93)↑0.914(0.015)↑0.019(0.002)↑
Ours (w. Pro)0.11 M35.29(3.15)↑0.927(0.024)↑0.009(0.001)↑34.65(3.58)↑0.921(0.022)↑0.010(0.011)↑
Ours (Full)0.11 M36.43(4.30)↑0.945(0.042)↑0.007(0.003)↑35.60(4.53)↑0.939(0.040)↑0.008(0.013)↑
", + "bbox": [ + 76, + 132, + 898, + 358 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "our full method that with both prompts and the null space mechanism. FedAvg (w. FfIt) [26] indicates the FedAvg algorithm while employing the pretrained model on the local side and full fine-tuning with all the participating clients. For a fair comparison, we retrain them on the two different scenarios with their default parameters and report their optimal results. All the competing methods are pretrained with Swin Transformers on fastMRI and fully fine-tuned with 50 communication rounds and 10 local epochs because they all converge before round 50. To assess the difference between a pair of methods, we use the paired Student's $t$ -test to demonstrate that all results were at the 0.001 level of statistical significance.", + "bbox": [ + 75, + 366, + 472, + 561 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "From Table 1, Ours (w. Pro) is superior to the competing FL methods in terms of PSNR, SSIM, and NMSE. In comparison to FedAvg (w. FFt), Ours (w. Pro) increases the PSNR results from 32.14 dB to 35.29 dB and the SSIM results from 0.903 to 0.927, because the FedAvg (w. FFt) is prone to overfitting when the local data is limited (i.e., issue ①) even though FedAvg (w. FFt) also employ the pretrained model on the local side. However, the method of freezing backbone networks that only fine-tune prompts is consistent with the mechanism of personalized FL, e.g., FedMRI, which divides the local network into a shared global generalized representation and a locally client-specific representation. More importantly, the number of training parameters and communication cost of Ours (w. Pro) is only $6\\%$ of FedAvg (w. FFt). Moreover, even compared to FedReg [39], which aims to address catastrophic forgetting in FL, our method still achieves $9.43\\%$ improvement in terms of PSNR. Furthermore, the reconstruction results of our proposed method are almost on par with the Centralized results (upper bound), i.e., PSNR: 36.71 dB vs. 36.41 dB, and SSIM: 0.947 vs. 0.945.", + "bbox": [ + 75, + 564, + 472, + 881 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In contrast, SingleSet has the lowest results, even though", + "bbox": [ + 96, + 885, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "it is also fine-tuned on the pre-trained model, as it cannot solve non-i.i.d. problems. For the classical federated MRI methods, FL-MRCM [13] and FedMRI [9], they lead to poor reconstruction performance when the number of local clients is large and the amount of local data is insufficient. Furthermore, other FL algorithms are either designed for data heterogeneity problems or for catastrophic forgetting problems. They have not considered the clinical issues of federated MRI, i.e., issues ①-③, causing it to produce less accurate reconstructions. These findings confirm our core idea that the three issues of federated MRI can be relieved by learning a federated visual prompt with our federated MRI paradigm. In addition, we visualize the reconstructed images and the corresponding error maps for all the competing methods in the first two rows of Fig. 4. The fewer textures in the error map, the better the reconstruction. It is obvious from the error map in Fig. 4 that our method can significantly reduce the reconstruction error.", + "bbox": [ + 496, + 366, + 893, + 638 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Out-of-Federation Performance. The second subtable of Table 1 provides quantitative evaluations under the Out-of-Federation scenario of various FL algorithms. Since the testing distribution in the Out-of-Federation scenario is unseen by the training distribution, the overall results of the Out-of-Federation scenario are slightly lower than those of In-Federation. However, our method still achieves the best performance in terms of the reconstruction results on the three metrics, i.e., Ours (Full) improves PSNR values from 31.07 dB to 35.60 dB, raises SSIM values from 0.899 to 0.939, and decreases NMSE values from 0.021 to 0.008. Notably, our method even achieves comparable results to the Centralized (Upper-bound) method, i.e., PSNR: 35.73 dB vs. 35.60 dB, SSIM: 0.940 vs. 0.939 and NMSE: 0.008 vs. 0.008. That is, our method suffers the least from the issue $\\Theta$ among all competing", + "bbox": [ + 496, + 643, + 895, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "8069", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/8dec8839b1b3e7c96b688dafff4eacc26d54a6b2c4c0a20b9710f9979fbbb0ae.jpg", + "image_caption": [ + "Figure 4. Qualitative comparison of different algorithms in terms of reconstruction images and error maps with corresponding quantitative measurements in PSNR/SSIM under In-Federation and Out-of-Federation scenarios. The less texture in the error map, the better reconstruction quality." + ], + "image_footnote": [], + "bbox": [ + 86, + 69, + 883, + 324 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "algorithms. These results support our core idea that learning federated visual prompts in the null space of global prompts can alleviate the three key issues in federated MRI while achieving competitive performance on limited local data. In addition, we show the qualitative evaluation results for the Out-of-Federation scenario in the second rows of Fig. 4, which visualizes the high-precision results of our method. As can be seen from this figure, our method provides comparable effects to the Centralized one, with clear details of tissue texture and boundaries.", + "bbox": [ + 75, + 376, + 472, + 526 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Ablation Studies", + "text_level": 1, + "bbox": [ + 76, + 534, + 241, + 547 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Catastrophic Forgetting vs. Local Updates. The catastrophic forgetting (i.e., issue ⑧) of federated MRI is caused by data heterogeneity due to different imaging protocols. As a result, more local updates will cause the local model to deviate from the global optimal solution. Here, we explore whether more local epochs cause the model to forget previously acquired global knowledge. In other words, it needs to be explored whether our proposed method can force local mitigation of this forgetting. Thus, we record the reconstruction results in terms of PSNR, SSIM, and NMSE for different numbers of local epochs in Fig. 5 (a). From this figure, in comparison to FedAvg (w. FFt) [26], increasing the local epoch does not greatly affect the accuracy of our method, i.e., Ours (w. Pro), and Ours (Full). In particular, as the number of local epochs increases, the performance of our method gradually stabilizes. In contrast, when the number of local epochs is too large, the reconstruction accuracy of FedAvg (w. FFt) will be reduced because it will gradually deviate from the global knowledge area. As a result, the result indicates that our method can learn without forgetting global knowledge over more local epochs.", + "bbox": [ + 75, + 551, + 468, + 868 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Analysis of Ratio $\\gamma\\%$ . As we mentioned in Sec. 3.3, the ratio $\\gamma\\%$ of the smallest singular values in $\\Lambda_2^{z+1}$ controls", + "bbox": [ + 75, + 869, + 468, + 901 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "the size of the approximate null space in global prompts. That is, the larger the $\\gamma\\%$ , the smaller the area of knowledge preservation. However, the area of knowledge preservation contains the global knowledge from the previous round, which is expected to be unchanged. To analyze the knowledge preservation capability that a good federated MRI framework should have, we discuss the reconstruction accuracy for different $\\gamma\\%$ values with regard to two scenarios in Fig. 6. It can be seen from this figure that, with the increase in $\\gamma\\%$ values, the reconstruction accuracy gradually increases. However, when $\\gamma\\% = 100\\%$ , the reconstruction accuracy drops rapidly. This is because when the knowledge preservation area is reduced to zero, fitting on the local distribution leads to forgetting the out-of-local distribution, i.e., the issue ⑧. Additionally, we can observe from Fig. 6 that roughly $40\\%$ of the area comprises previously acquired global knowledge because our method obtains the highest results at this point. Following [36], we use the proportion of the sum of singular values of $\\Lambda_{2}^{z+1}$ in the sum of singular values of $\\Lambda^{z+1}$ to verify the rationality of the approximation. We find that the proportion in each layer is smaller than $10^{-7}$ . That is, the sum of the smallest singular values $U_{2}^{z+1}$ can be ignored, thereby making it reasonable to approximate the null space through the spatial range of $U_{2}^{z+1}$ . Interestingly, our method only performs local updates in the approximate null space of global prompts, which greatly improves the stability of the model and thus prevents catastrophic forgetting, i.e., the issue ⑧.", + "bbox": [ + 496, + 376, + 892, + 800 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Communication Efficiency Analysis. Our primal interest is to learn a federated visual prompt that enables FL to perform well with less local data, lower communication cost, and faster convergence. Here, we investigate the communication efficiency of our proposed method in terms of communication cost and different communication rounds,", + "bbox": [ + 496, + 809, + 893, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "8070", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7e307877201c91a044cf86407d07c34d151582b2a02296805a0db976d3f69d2f.jpg", + "image_caption": [ + "In-Federation" + ], + "image_footnote": [], + "bbox": [ + 91, + 94, + 269, + 205 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ca71fa696f4ddd914119772483ba8a74ad5ea82e362e3c1dbdb622eee6e6c609.jpg", + "image_caption": [ + "Out-of-Federation" + ], + "image_footnote": [], + "bbox": [ + 271, + 95, + 465, + 205 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/5261998a6589c859352cbc7bc2d402fc919dd34bf9e2f4d760778f02ab5877fb.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 86, + 210, + 269, + 321 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c0db5db5d46b2426709c6420931e391b1ad39b6b958f2bf95fa5b67649f9e9d1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 271, + 210, + 464, + 321 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/daa6abb2286a7d6cd939c67a4525685a0ba8603d6354d9d2d1a64e64761a2904.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 86, + 325, + 271, + 459 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/cac29961ae468f0cab6374cb1c4398d6c753d40969e6d5818099a2e23d762f10.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 274, + 327, + 465, + 459 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a092321e18a27012f6668f742c46d2c04c32176a4dfe51b809c337b590af6fb7.jpg", + "image_caption": [ + "In-Federation" + ], + "image_footnote": [], + "bbox": [ + 493, + 95, + 686, + 204 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/5e996a3cdccf67b1924dc264e24c4edd048b73eedeba800ae48d998122390dbf.jpg", + "image_caption": [ + "Out-of-Federation" + ], + "image_footnote": [], + "bbox": [ + 694, + 95, + 877, + 204 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1e903308383565e73ef6f8b38d8590906f1dc3eda97c6de36449546bd3d2df4b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 493, + 208, + 678, + 320 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e96643dea33a387e2e53c34335067bfb085fa2f84ec1cdfe62e13816b39b876a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 686, + 210, + 877, + 320 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/5808f11a2b64f8d904f7f73e0b43b87e93e9f628f0cbca66730ba7a4246269fe.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 491, + 327, + 684, + 455 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b31e9e7058cbe4c86c069188532002f87f8eaa4680d48c13dfff3c8f32e31927.jpg", + "image_caption": [ + "(b)" + ], + "image_footnote": [], + "bbox": [ + 686, + 328, + 874, + 459 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8b6514d70fac09cda504ff90ab0228e87da68f5c64d1830c0c654a282a091266.jpg", + "image_caption": [ + "Figure 5. Reconstruction accuracy of FedAvg (w. FFt), Ours (w. Pro), and Ours (Full) versus (a) local epochs and (b) communication rounds under In-Federation and Out-of-Federation scenarios.", + "Figure 6. Analysis of the ratio $\\gamma \\%$ of the approximate null space in terms of PSNR, SSIM, and NMSE." + ], + "image_footnote": [], + "bbox": [ + 86, + 507, + 455, + 589 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "respectively. As shown in Table 1, the proposed method only requires $0.11\\mathrm{M}$ of communication, which is $6\\%$ of the others, thereby addressing the issue $\\mathbf{2}$ . However, although the classical federated MRI algorithms FL-MRCM [13] and FedMRI [9] can also achieve good accuracy, they ignored this clinical issue of federated MRI. Additionally, the reconstruction accuracy of FedAvg (w. FFt) [26], Ours (w. Pro), and Ours (Full) under different communication rounds is recorded in Fig. 5 (b), where the number of the local epochs is fixed at 10 for each method. As can be seen from the figure, our method converges within 10 rounds, while FedAvg (w. FFt) [26] converges after 30 rounds. Especially under the mechanism of updating the local prompts in the approximate null space of global prompts, our method provides higher reconstruction results. This is because our federated prompt learning mechanism prevents overfitting caused by the limited amount of local training data and offers a personalized scheme for each client. The results in Fig. 5 (b)", + "bbox": [ + 75, + 628, + 472, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "confirm that our method provides the highest communication efficiency even on limited local data, thus relieving the issues 1 and 2.", + "bbox": [ + 498, + 516, + 890, + 561 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 574, + 617, + 590 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This paper presented a federated visual prompt learning method, FedPR, to tackle the three issues in federated MRI reconstruction, i.e., limited communication bandwidth, insufficient local training data, and catastrophic forgetting. Benefiting from a powerful pre-trained model, our FedPR only learns prompts with a small number of learnable parameters. Additionally, FedPR greatly mitigates catastrophic forgetting by updating local prompts only in the approximate null space of global prompts, thereby preventing knowledge outside the local distribution from being overwritten. Experiments under In-Federation and Out-of-Federation scenarios demonstrate the superiority of FedPR in relieving the three issues of federated MRI reconstruction.", + "bbox": [ + 496, + 597, + 890, + 806 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements: This work was supported by the Agency for Science, Technology and Research (A*STAR) AME Programmatic Funds (Grant Number: A20H4b0141). This work was also supported by the AI Singapore Tech Challenge (Open-Theme) Funding Scheme (Award No.: AISG2-TC-2021-003).", + "bbox": [ + 496, + 809, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "8071", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 90, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] brain-development.org.", + "[2] Hyojin Bahng, Ali Jahanian, Swami Sankaranarayanan, and Phillip Isola. Exploring visual prompts for adapting large-scale models, 2022.", + "[3] Hong-You Chen, Cheng-Hao Tu, Ziwei Li, Han-Wei Shen, and Wei-Lun Chao. On pre-training for federated learning. arXiv preprint arXiv:2206.11488, 2022.", + "[4] Jiahua Dong, Lixu Wang, Zhen Fang, Gan Sun, Shichao Xu, Xiao Wang, and Qi Zhu. Federated class-incremental learning. 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In Proceedings of the IEEE/CVF Conference" + ], + "bbox": [ + 78, + 90, + 468, + 892 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "on Computer Vision and Pattern Recognition, pages 2049-2058, 2019.", + "bbox": [ + 535, + 93, + 890, + 119 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "8073", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Learning Federated Visual Prompt in Null Space for MRI Reconstruction/20f20c2b-43db-4f5b-b2e9-0c30622bc0bc_model.json b/2023/Learning Federated Visual Prompt in Null Space for MRI Reconstruction/20f20c2b-43db-4f5b-b2e9-0c30622bc0bc_model.json new file mode 100644 index 0000000000000000000000000000000000000000..652a0a92a88b06022ad01d63257903f3121a5326 --- /dev/null +++ b/2023/Learning Federated Visual Prompt in Null Space for MRI Reconstruction/20f20c2b-43db-4f5b-b2e9-0c30622bc0bc_model.json @@ -0,0 +1,2376 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.114, + 0.131, + 0.856, + 0.153 + ], + "angle": 0, + "content": "Learning Federated Visual Prompt in Null Space for MRI Reconstruction" + }, + { + "type": "text", + "bbox": [ + 0.108, + 0.18, + 0.862, + 0.2 + ], + "angle": 0, + "content": "Chun-Mei Feng\\(^{1}\\) Bangjun Li\\(^{2}\\) Xinxing Xu\\(^{1,*}\\) Yong Liu\\(^{1,*}\\) Huazhu Fu\\(^{1}\\) Wangmeng Zuo\\(^{3}\\)" + }, + { + "type": "text", + "bbox": [ + 0.282, + 0.199, + 0.687, + 0.217 + ], + "angle": 0, + "content": "\\(^{1}\\)Institute of High Performance Computing (IHPC)," + }, + { + "type": "text", + "bbox": [ + 0.212, + 0.218, + 0.76, + 0.235 + ], + "angle": 0, + "content": "Agency for Science, Technology and Research (A*STAR), Singapore" + }, + { + "type": "text", + "bbox": [ + 0.175, + 0.235, + 0.797, + 0.252 + ], + "angle": 0, + "content": "\\(^{2}\\)School of Information Science and Engineering, Shangdong University, China" + }, + { + "type": "text", + "bbox": [ + 0.3, + 0.253, + 0.671, + 0.27 + ], + "angle": 0, + "content": "\\(^{3}\\)Harbin Institute of Technology, Harbin, China" + }, + { + "type": "text", + "bbox": [ + 0.194, + 0.273, + 0.776, + 0.288 + ], + "angle": 0, + "content": "strawberry.feng0304@gmail.com, {xuxinx, liuyong}@ihpc.a-star.edu.sg" + }, + { + "type": "text", + "bbox": [ + 0.32, + 0.29, + 0.642, + 0.304 + ], + "angle": 0, + "content": "https://github.com/chunmeifeng/FedPR" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.34, + 0.313, + 0.355 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.372, + 0.474, + 0.72 + ], + "angle": 0, + "content": "Federated Magnetic Resonance Imaging (MRI) reconstruction enables multiple hospitals to collaborate distributedly without aggregating local data, thereby protecting patient privacy. However, the data heterogeneity caused by different MRI protocols, insufficient local training data, and limited communication bandwidth inevitably impair global model convergence and updating. In this paper, we propose a new algorithm, FedPR, to learn federated visual prompts in the null space of global prompt for MRI reconstruction. FedPR is a new federated paradigm that adopts a powerful pre-trained model while only learning and communicating the prompts with few learnable parameters, thereby significantly reducing communication costs and achieving competitive performance on limited local data. Moreover, to deal with catastrophic forgetting caused by data heterogeneity, FedPR also updates efficient federated visual prompts that project the local prompts into an approximate null space of the global prompt, thereby suppressing the interference of gradients on the server performance. Extensive experiments on federated MRI show that FedPR significantly outperforms state-of-the-art FL algorithms with \\(< 6\\%\\) of communication costs when given the limited amount of local training data." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.745, + 0.21, + 0.761 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.771, + 0.47, + 0.877 + ], + "angle": 0, + "content": "Federated Magnetic Resonance Imaging (MRI) reconstruction enables multiple hospitals to train a powerful global model in a distributed manner without sharing private data [7, 9, 13]. In federated MRI, each client (i.e., hospital) uses its local computing power, memory, and private data to train local models independently, while the server aggregates all the local models in each communica" + }, + { + "type": "image", + "bbox": [ + 0.541, + 0.321, + 0.856, + 0.482 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.505, + 0.486, + 0.885, + 0.501 + ], + "angle": 0, + "content": "Figure 1. Illustration of the three key issues in federated MRI." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.507, + 0.892, + 0.537 + ], + "angle": 0, + "content": "tion round and distributes the global model to each client again [26]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.539, + 0.893, + 0.903 + ], + "angle": 0, + "content": "Existing federated MRI reconstruction techniques usually improve federated learning (FL) by enhancing the aggregation process [9] and reducing the local parameter's variance [5, 13]. Such techniques require a large communication bandwidth and sufficient local training data. However, federated MRI often faces two issues, insufficient amount of local training data due to the difficulty of acquiring the ground-truth of MRI reconstruction [10, 11, 12] and limited communication bandwidth due to unbalanced regional development (see Fig. 1). To cope with the issue, pre-trained models have exhibited superior performance, and have shown to close the gap between federated and centralized performance [3, 28]. However, since the model parameters need to be shared between the client and the server for updating, the large number of parameters of pre-trained models will result in a huge communication cost. On contrary, prompt tuning has recently been suggested as a new fine-tuning paradigm by freezing the models and only learning a small number of learnable parameters in the input space [15, 31, 32]. Benefited from pre-trained models, only parameter-efficient prompts are required in learning and communication, and prompt tuning can be conducted with a limited number of samples, making it very appealing in tackling the above two issues (i.e.," + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.888, + 0.222, + 0.9 + ], + "angle": 0, + "content": "*Corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8064" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.092, + 0.265, + 0.106 + ], + "angle": 0, + "content": "\\(\\mathbf{1}\\) and \\(\\mathbf{2}\\) ) in federated MRI." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.107, + 0.47, + 0.455 + ], + "angle": 0, + "content": "Besides, there is another critical issue for federated MRI, i.e., ⑧ catastrophic forgetting, caused by data heterogeneity due to the different imaging protocols of MRI scanners adopted by different clients [9, 39] (see Fig. 1). In the local update, the global model from the prior round tends to be overfitted to the local training data, leading to catastrophic forgetting. Analogous to continual learning, several techniques have been presented by introducing proper regularization terms in local models [4, 33, 39] or retaining previously acquired knowledge by knowledge distillation [14, 35, 38]. However, these strategies require seeking a balance between multiple losses and relying on proxy datasets. Instead, Adam-NSC mitigates catastrophic forgetting in continual learning with a new network parameter update rule, i.e., forces the network update to lie in the approximate null space of the input features of previous tasks at each layer [36]. However, the null space at feature level is built upon large local training data, which generally cannot be satisfied in federated MRI, i.e., the issue ①. Taking the issues ① and ⑧ into account, we suggest to optimize local prompts in the approximate null space of global prompts instead of input features, thereby preventing the loss of previously gained global knowledge." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.456, + 0.47, + 0.712 + ], + "angle": 0, + "content": "In a nutshell, we explore a new FL paradigm, i.e., FedPR, to learn federated visual prompts for MRI reconstruction. To begin with, we pre-train the model on a large-scale public dataset. Given limited amount of local training data, visual prompt tuning is adopted to learn local prompts in a distributed manner. For the issues 1 and 2, federated visual prompts are introduced to learn a strong global model, where only local and global prompts are learnable and communicated. As for the issue 3, we perform singular value decomposition (SVD) on the uncentered covariance matrix of global prompts to obtain the approximate null space. FedPR tunes only the local parameters in the null space of global prompts, thereby well preserving the prior knowledge of previous rounds and resulting in low communication costs. In particular, FedPR achieves a \\(>4.5\\) dB gain in PSNR with less than \\(6\\%\\) of communication costs. To sum up, our contributions are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.72, + 0.468, + 0.809 + ], + "angle": 0, + "content": "- We propose a federated visual prompt algorithm, FedPR, to solve the three key issues in federated MRI. By leveraging powerful pre-trained models and freezing backbone networks in FL, only a small amount of parameters in the input space are trainable, thereby reducing communication costs." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.811, + 0.468, + 0.901 + ], + "angle": 0, + "content": "- We explore how to alleviate catastrophic forgetting in FL while reducing communication costs. By optimizing local parameters only in the null space of global prompts, FedPR well preserves the previously acquired global knowledge in each round, maintaining competitive performance with only a few local data." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.72, + 0.468, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.892, + 0.168 + ], + "angle": 0, + "content": "- We evaluate the performance of FedPR for federated MRI reconstruction. In comparison to the state-of-the-art FL methods, FedPR achieves superior performance in complex scenarios, e.g., less local data, lower communication costs, and faster convergence." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.184, + 0.642, + 0.2 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.207, + 0.892, + 0.536 + ], + "angle": 0, + "content": "Federated MRI Reconstruction. MRI reconstruction refers to reconstructing images without aliasing artifacts from undersampled \\(k\\)-space data [6, 8, 12, 37, 41]. However, existing MRI reconstruction techniques are based on large-scale paired data, which is not only labor-intensive but also violates patient privacy [9]. Driven by these realistic problems, a few FL-based methods for MRI reconstruction have been proposed [5, 9, 13]. Guo et al. reduced data heterogeneity by iteratively aligning the data distribution between source and target clients [13]. Feng et al. proposed a personalized FL reconstruction scheme and introduced a weighted contrast regularization term to correct the update direction of global generalization [9]. However, these schemes either require frequent communication or are built on a large amount of local data. As a result, these techniques will produce sub-optimal solutions for MRI reconstruction when there is limited bandwidth and insufficient local training data. In contrast to these works, we build a federated MRI model upon a strong pre-trained model by updating and communicating only a small portion of parameters for each client using limited local data, achieving competitive results." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.539, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Catastrophic Forgetting in FL. Due to the heterogeneous data distributions of different tasks in continual learning, when the network is fitted to the current task, the model parameters typically deviate from the areas where the previous knowledge is expected to be preserved [17]. Therefore, catastrophic forgetting is a fundamental challenge of continual learning. Similarly, catastrophic forgetting also affects FL [14, 19, 39]. When the client receives the global model and continues to update locally, it will cause the global model to forget the knowledge of the previous round due to the data heterogeneity across clients [19]. As a result, existing FL techniques that address catastrophic forgetting are designed by referring to continual learning. For example, knowledge distillation-based FL methods maintain previously gained knowledge, but this method strongly relies on proxy data [14, 35, 38]; regularization-based FL methods regularize locally trained parameters, but they require finding a compromise between loss terms [4, 33, 39]. All these studies are built on classification tasks and cannot be directly extended to MRI reconstruction. Inspired by the success of null space in continual learning [18, 23, 36], we try to update the local prompt in the approximate null space of global prompts, thereby preserving the knowledge acquired by the global model in the previous round and avoid" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8065" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.1, + 0.08, + 0.298, + 0.282 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.106, + 0.286, + 0.293, + 0.298 + ], + "angle": 0, + "content": "(a) Initialization and local update" + }, + { + "type": "image", + "bbox": [ + 0.324, + 0.079, + 0.875, + 0.283 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.359, + 0.286, + 0.518, + 0.299 + ], + "angle": 0, + "content": "(b) Federated visual prompt" + }, + { + "type": "image_caption", + "bbox": [ + 0.681, + 0.285, + 0.783, + 0.298 + ], + "angle": 0, + "content": "(c) Server update" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.305, + 0.894, + 0.361 + ], + "angle": 0, + "content": "Figure 2. Illustration of our FedPR method. (a) For each client, the backbone model is pre-trained on massive data and fine-tuned via prompt (see Sec. 3.2). (b) Federated visual prompt is executed by updating the local prompt of each client only in the approximate null space of global prompts while preserving the previously acquired global knowledge (see Sec. 3.3). (c) Server update by aggregating local prompts." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.365, + 0.262, + 0.38 + ], + "angle": 0, + "content": "ing catastrophic forgetting." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.38, + 0.474, + 0.637 + ], + "angle": 0, + "content": "Prompt Learning. Prompt tuning was initially proposed to enable pre-trained language models to \"understand\" downstream tasks by adding trainable tokens to the input text [24]. For example, Jia et al. achieved good performance on downstream tasks by introducing a small number of learnable tokens into the input space and keeping the backbone frozen [15]. Hyojin et al. suggested to modify pixel space for the frozen visual models [2]. Nie et al. proposed a unified prompt tuning framework that performs on different CNN and transformer-based architectures by training only a few additional parameters [29]. Although these works have made progress on various visual tasks, prompt is still limited to centralized systems, and the effectiveness of prompt in distributed framework remains uninvestigated. Therefore, this work focuses on how to learn a federated visual prompt to effectively tackle the three key problems in federated MRI reconstruction, i.e., the issues ①-③." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.645, + 0.214, + 0.661 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.665, + 0.355, + 0.68 + ], + "angle": 0, + "content": "3.1. Federated MRI Reconstruction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.684, + 0.47, + 0.759 + ], + "angle": 0, + "content": "MRI reconstruction is an inverse problem of recovering an artifact-free image \\( \\mathbf{y} \\) from its undersampled observation \\( \\mathbf{x} \\) that can reduce the online collection time and improve the patient experience [34, 37, 40]. Formally, such undersampling process can be expressed as" + }, + { + "type": "equation", + "bbox": [ + 0.176, + 0.761, + 0.47, + 0.778 + ], + "angle": 0, + "content": "\\[\n\\mathbf {x} = \\mathcal {F} ^ {- 1} (\\mathcal {M} \\odot \\mathcal {F} (\\mathbf {y}) + \\epsilon), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.47, + 0.825 + ], + "angle": 0, + "content": "where \\(\\mathcal{F}\\) is multi-dimensional Fourier transform, \\(\\epsilon\\) is the measurement noise, and \\(\\mathcal{M}\\) is the binary mask operator to undersample the data points in the Fourier space." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.471, + 0.901 + ], + "angle": 0, + "content": "The centralized approach violates patient privacy protection roles because it requires collecting large amounts of training data from different hospitals. As a remedy, Federated MRI has been suggested by deploying MRI reconstruction in a distributed manner [9, 13]. Suppose there are \\(K\\)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.365, + 0.893, + 0.454 + ], + "angle": 0, + "content": "hospitals (local clients). The private data of all hospitals can be expressed as \\(\\mathcal{D} = \\{\\mathcal{D}^1,\\mathcal{D}^2,\\dots ,\\mathcal{D}^K\\}\\), where each contains limited pairs of undersampled samples \\(\\mathbf{x}_i\\) and fully-sampled images \\(\\mathbf{y}_i\\). Federated MRI aims to learn a global model from the whole dataset \\(\\mathcal{D}\\) in a distributed manner, which can be described as" + }, + { + "type": "equation", + "bbox": [ + 0.581, + 0.456, + 0.892, + 0.497 + ], + "angle": 0, + "content": "\\[\n\\arg \\min _ {\\boldsymbol {w}} \\mathcal {L} (\\boldsymbol {w}) = \\sum_ {k = 1} ^ {K} \\frac {| \\mathcal {D} ^ {k} |}{| \\mathcal {D} |} \\mathcal {L} _ {k} (\\boldsymbol {w}), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.499, + 0.892, + 0.529 + ], + "angle": 0, + "content": "where \\(|\\mathcal{D}|\\) denotes the number of samples in \\(\\mathcal{D}\\), and \\(\\mathcal{L}_k(\\boldsymbol{w})\\) is the empirical loss of client \\(k\\)," + }, + { + "type": "equation", + "bbox": [ + 0.577, + 0.533, + 0.892, + 0.55 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {k} (\\boldsymbol {w}) = \\mathbf {E} _ {(\\mathbf {x}, \\mathbf {y}) \\in \\mathcal {D} ^ {k}} \\ell_ {k} (f (\\mathbf {x}; \\boldsymbol {w})) \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.554, + 0.894, + 0.6 + ], + "angle": 0, + "content": "where \\(\\ell_{k}\\) represents the local loss for MRI reconstruction, e.g., \\(L_{1}\\) loss. After training, the reconstructed image \\(\\hat{\\mathbf{y}}\\) can be produced by \\(f(\\mathbf{x};\\boldsymbol {w})\\)" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.608, + 0.753, + 0.625 + ], + "angle": 0, + "content": "3.2. Learning Federated Prompt" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.892, + 0.748 + ], + "angle": 0, + "content": "As mentioned in Sec. 1, there are three key issues, i.e., 1-3, with the existing federated MRI algorithms. To tackle the issue 2, we freeze the backbone of the pre-trained model while only tuning and communicating a few learnable parameters for the clients and server. More importantly, it enables the model to achieve very competitive results on limited local data, thereby providing an effective solution to issue 1." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.893, + 0.901 + ], + "angle": 0, + "content": "As shown in Fig. 2, given a pre-trained model with parameters \\(\\theta\\), we introduce a set of continuous embeddings \\(P = \\{p_1, p_2, \\dots, p_l\\}\\) as the prompts in the input space of each layer [15], where \\(l\\) is the number of prompts. Thus, the overall parameters can be expressed as \\(\\boldsymbol{w} = \\{P, \\theta\\}\\). Suppose there are \\(Z\\) rounds of communication, each round contains \\(T\\) local updates. During the local update, for the \\(k\\)-th client, only the client-specific prompts \\(P_k\\) are learnable and communicated while the backbone network is frozen. Therefore, Eq. (2) can be rewritten as:" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8066" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.079, + 0.079, + 0.473, + 0.288 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.292, + 0.471, + 0.322 + ], + "angle": 0, + "content": "Figure 3. Illustration of federated visual prompt for updating local prompts in the null space of global prompts." + }, + { + "type": "equation", + "bbox": [ + 0.137, + 0.341, + 0.47, + 0.382 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {P} _ {k} = \\arg \\min _ {\\boldsymbol {P}} \\mathcal {L} (\\boldsymbol {P}) = \\sum_ {k = 1} ^ {K} \\frac {\\left| \\mathcal {D} ^ {k} \\right|}{\\left| \\mathcal {D} \\right|} \\mathcal {L} _ {k} (\\boldsymbol {P}), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.383, + 0.47, + 0.412 + ], + "angle": 0, + "content": "where the empirical loss for prompt tuning of client \\( k \\) can be expressed as" + }, + { + "type": "equation", + "bbox": [ + 0.147, + 0.415, + 0.47, + 0.433 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {k} (\\boldsymbol {P}) = \\mathbf {E} _ {(\\mathbf {x}, \\mathbf {y}) \\in \\mathcal {D} ^ {k}} \\ell_ {k} (f (\\mathbf {x}; \\boldsymbol {P}, \\boldsymbol {\\theta})). \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.438, + 0.47, + 0.512 + ], + "angle": 0, + "content": "Benefited from pre-trained models, federated prompt tuning can be both parameter- and communication-efficient and effective in achieving competitive results with a small amount of local data, thereby serving as a favorable solution to the issues 1 and 2." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.513, + 0.47, + 0.559 + ], + "angle": 0, + "content": "Local Update Step: In each communication round \\( z = \\{1,2,\\dots,Z\\} \\), the clients are optimized using the following update rules with a learning rate of \\( \\eta_{k} \\):" + }, + { + "type": "equation", + "bbox": [ + 0.147, + 0.561, + 0.469, + 0.581 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {P} _ {k} ^ {z, t + 1} \\leftarrow \\boldsymbol {P} _ {k} ^ {z, t} - \\eta_ {k} \\nabla \\ell_ {k} \\left(\\mathbf {x} ^ {k}; \\boldsymbol {P} _ {k} ^ {z, t}\\right), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.582, + 0.414, + 0.597 + ], + "angle": 0, + "content": "where \\(t\\) denotes the \\(t\\)-th update of the local clients." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.597, + 0.47, + 0.656 + ], + "angle": 0, + "content": "Server Update Step: After a round of local updates, all participating clients send their updated prompts \\( \\pmb{P}_{k}^{z} \\) to the server performing aggregation. Such process can be expressed as follows" + }, + { + "type": "equation", + "bbox": [ + 0.196, + 0.65, + 0.469, + 0.691 + ], + "angle": 0, + "content": "\\[\n\\mathbf {P} _ {g} ^ {z + 1} \\leftarrow \\sum_ {k = 1} ^ {K} \\frac {\\left| \\mathcal {D} ^ {k} \\right|}{\\left| \\mathcal {D} \\right|} \\mathbf {P} _ {k} ^ {z}, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.692, + 0.47, + 0.785 + ], + "angle": 0, + "content": "where \\( P_{g}^{z + 1} \\) denotes the global prompts of round \\( z + 1 \\). To sum up, the issue \\( \\mathbf{0} \\) can be largely mitigated because there are only a small number of learnable parameters \\( P \\) communicated between the server and local clients. After \\( Z \\) rounds of communication, we can get a robust global model parameterized by \\( P_{g} \\) without sharing local private data." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.792, + 0.427, + 0.809 + ], + "angle": 0, + "content": "3.3. Local Updating in Prompting Null Space" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.811, + 0.471, + 0.902 + ], + "angle": 0, + "content": "The local update mechanism in Eq. (6), however, suffers from the issue ⑧, i.e., catastrophic forgetting, due to data heterogeneity of different clients. Inspired by the continual learning method Adam-NSC [36] that sequentially optimizes network parameters in the null space at feature level, we suggest to optimize the local model in the null space of" + }, + { + "type": "title", + "bbox": [ + 0.51, + 0.095, + 0.655, + 0.11 + ], + "angle": 0, + "content": "Algorithm 1: FedPR" + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.113, + 0.866, + 0.188 + ], + "angle": 0, + "content": "Input: Private datasets from \\(K\\) clients: \\(\\mathcal{D}^1, \\mathcal{D}^2, \\ldots, \\mathcal{D}^K\\), local updates \\(T\\), communication rounds \\(Z\\), pre-trained model parameters \\(\\theta\\), prompt embeddings \\(P\\), learning rate \\(\\eta\\), hyperparameter \\(\\gamma\\);" + }, + { + "type": "text", + "bbox": [ + 0.508, + 0.189, + 0.66, + 0.202 + ], + "angle": 0, + "content": "1 // ServerExecution:" + }, + { + "type": "text", + "bbox": [ + 0.508, + 0.203, + 0.829, + 0.218 + ], + "angle": 0, + "content": "2 Initialize global prompt \\(P_{g}\\) with parameters \\(\\theta\\)" + }, + { + "type": "text", + "bbox": [ + 0.508, + 0.218, + 0.86, + 0.233 + ], + "angle": 0, + "content": "3 for each communication round \\(z\\in \\{1,2,\\dots,Z\\}\\) do" + }, + { + "type": "list", + "bbox": [ + 0.508, + 0.189, + 0.86, + 0.233 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.507, + 0.234, + 0.85, + 0.282 + ], + "angle": 0, + "content": "4 for each client \\(k\\in \\{1,2,\\dots K\\}\\) in parallel do 5 \\(\\begin{array}{rl} & P_k^z\\gets P_g^z;\\\\ & \\hat{P}_k^z\\gets \\mathrm{LocalUpdate}(k,P_k^z); \\end{array}\\) 6" + }, + { + "type": "text", + "bbox": [ + 0.508, + 0.284, + 0.577, + 0.296 + ], + "angle": 0, + "content": "7 end" + }, + { + "type": "list", + "bbox": [ + 0.507, + 0.234, + 0.85, + 0.296 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.508, + 0.298, + 0.715, + 0.321 + ], + "angle": 0, + "content": "8 \\(P_{g}^{z + 1}\\gets \\sum_{k = 1}^{K}\\frac{|\\mathcal{D}^{k}|}{|\\mathcal{D}|}\\hat{P}_{k}^{z};\\)" + }, + { + "type": "text", + "bbox": [ + 0.507, + 0.322, + 0.834, + 0.335 + ], + "angle": 0, + "content": "9 Compute the uncentered covariance matrix:" + }, + { + "type": "list", + "bbox": [ + 0.507, + 0.298, + 0.834, + 0.335 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.337, + 0.716, + 0.354 + ], + "angle": 0, + "content": "10 \\(\\pmb{\\Sigma}_{g}^{z + 1} = \\left(\\pmb{P}_{g}^{z + 1}\\right)^{\\top}\\pmb{P}_{g}^{z + 1};\\)" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.354, + 0.793, + 0.371 + ], + "angle": 0, + "content": "11 Approximate the null space of \\(\\Sigma_g^{z + 1}\\)" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.371, + 0.757, + 0.388 + ], + "angle": 0, + "content": "12 \\(\\pmb{\\Sigma}_{g}^{z + 1} = \\pmb{U}^{z + 1}\\pmb{\\Lambda}^{z + 1}\\left(\\pmb{U}^{z + 1}\\right)^{\\top};\\)" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.388, + 0.851, + 0.419 + ], + "angle": 0, + "content": "13 Select the smallest diagonal singular values of \\(\\Lambda_2^{z + 1}\\) with the ratio of \\(\\gamma\\)" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.419, + 0.775, + 0.435 + ], + "angle": 0, + "content": "14 Get \\(\\pmb{U}_2^{z + 1}\\) corresponding to \\(\\Lambda_2^{z + 1}\\)" + }, + { + "type": "list", + "bbox": [ + 0.504, + 0.337, + 0.851, + 0.435 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.503, + 0.437, + 0.551, + 0.449 + ], + "angle": 0, + "content": "15 end" + }, + { + "type": "text", + "bbox": [ + 0.503, + 0.45, + 0.605, + 0.468 + ], + "angle": 0, + "content": "16 return \\(P_{g}^{z + 1}\\)" + }, + { + "type": "text", + "bbox": [ + 0.503, + 0.468, + 0.684, + 0.483 + ], + "angle": 0, + "content": "17 // LocalUpdate \\((k, P_k)\\):" + }, + { + "type": "text", + "bbox": [ + 0.503, + 0.483, + 0.783, + 0.498 + ], + "angle": 0, + "content": "18 for each local epoch \\(t \\in \\{1, 2, \\dots, T\\}\\) do" + }, + { + "type": "text", + "bbox": [ + 0.503, + 0.499, + 0.772, + 0.514 + ], + "angle": 0, + "content": "19 Get the updated parameters \\(\\Delta P_k^z\\):" + }, + { + "type": "text", + "bbox": [ + 0.503, + 0.514, + 0.74, + 0.531 + ], + "angle": 0, + "content": "20 \\(|\\Delta P_k^z = U_2^{z + 1}\\left(U_2^{z + 1}\\right)^\\top P_k^z;\\)" + }, + { + "type": "text", + "bbox": [ + 0.503, + 0.531, + 0.742, + 0.549 + ], + "angle": 0, + "content": "21 \\(\\hat{P}_k^{z,t + 1}\\gets P_k^{z,t} - \\eta_k\\Delta P_k^{z,t};\\)" + }, + { + "type": "text", + "bbox": [ + 0.503, + 0.549, + 0.55, + 0.562 + ], + "angle": 0, + "content": "22 end" + }, + { + "type": "text", + "bbox": [ + 0.503, + 0.565, + 0.589, + 0.583 + ], + "angle": 0, + "content": "23 return \\(\\hat{P}_k^z\\)" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.437, + 0.783, + 0.583 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.62, + 0.892, + 0.756 + ], + "angle": 0, + "content": "global prompts. Specifically, we train the local model in the approximate null space of the global prompts in a distributed way, preventing knowledge outside the local distribution from being overwritten and resulting in catastrophic forgetting. In comparison to [36], approximating the null space of global prompts instead of features does not require a large amount of local data and not increase the communication cost, thus offering a feasible way to tackle the three issues 1-8 in federated MRI." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.759, + 0.892, + 0.791 + ], + "angle": 0, + "content": "As shown in Fig. 3, we first compute the uncentered covariance matrix of \\( z + 1 \\) round global prompt \\( P_g^{z + 1} \\) by" + }, + { + "type": "equation", + "bbox": [ + 0.61, + 0.798, + 0.892, + 0.819 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {\\Sigma} _ {g} ^ {z + 1} = \\left(\\boldsymbol {P} _ {g} ^ {z + 1}\\right) ^ {\\top} \\boldsymbol {P} _ {g} ^ {z + 1}. \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.825, + 0.892, + 0.855 + ], + "angle": 0, + "content": "Then, we find the approximate null space of \\(\\Sigma_{g}^{z + 1}\\) by apply SVD to it" + }, + { + "type": "equation", + "bbox": [ + 0.59, + 0.865, + 0.892, + 0.886 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {\\Sigma} _ {g} ^ {z + 1} = \\boldsymbol {U} ^ {z + 1} \\boldsymbol {\\Lambda} ^ {z + 1} \\left(\\boldsymbol {U} ^ {z + 1}\\right) ^ {\\top}, \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.887, + 0.546, + 0.899 + ], + "angle": 0, + "content": "where" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8067" + } + ], + [ + { + "type": "equation", + "bbox": [ + 0.175, + 0.122, + 0.468, + 0.145 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {U} ^ {z + 1} = \\left[ \\boldsymbol {U} _ {1} ^ {z + 1}, \\boldsymbol {U} _ {2} ^ {z + 1} \\right], \\tag {10}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.175, + 0.143, + 0.366, + 0.177 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {\\Lambda} ^ {z + 1} = \\left[ \\begin{array}{c c} \\boldsymbol {\\Lambda} _ {1} ^ {z + 1} & 0 \\\\ 0 & \\boldsymbol {\\Lambda} _ {2} ^ {z + 1} \\end{array} \\right].\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.179, + 0.47, + 0.334 + ], + "angle": 0, + "content": "Here \\( U_{1}^{z + 1} \\) are the singular vectors corresponding to the large singular values in \\( \\Lambda_1^{z + 1} \\) [36]. According to principal component analysis (PCA), \\( U_{1}^{z + 1} \\) can be considered as principal components, which contain the global knowledge that has been captured in the previous round. Thus, we have \\( \\Sigma_g^{z + 1} \\approx U_1^{z + 1}\\Lambda_1^{z + 1}\\left(U_1^{z + 1}\\right)^\\top \\). And the range space of \\( U_{2}^{z + 1} \\) can be denoted as the approximate null space of \\( \\Sigma_g^{z + 1} \\) [36]. In our implementation, we introduce a \\( \\gamma \\% \\) to control \\( U_{2}^{z + 1} \\) by selecting the last \\( \\gamma \\% \\) of singular values in \\( \\Lambda_2^{z + 1} \\) to constitute \\( U_{2}^{z + 1} \\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.335, + 0.469, + 0.429 + ], + "angle": 0, + "content": "To tackle the issue \\( \\bullet \\), \\( P_{k}^{z} \\) can be projected into the approximate null space of \\( \\Sigma_{g}^{z + 1} \\) to get the updated parameters, while the principal components \\( U_{1}^{z + 1} \\) containing the global knowledge from the previous round are preserved. Thus, the updated parameters \\( \\Delta P_{k}^{z} \\) can be optimized in the null space of \\( \\Sigma_{g}^{z + 1} \\) by" + }, + { + "type": "equation", + "bbox": [ + 0.175, + 0.43, + 0.469, + 0.45 + ], + "angle": 0, + "content": "\\[\n\\Delta \\boldsymbol {P} _ {k} ^ {z} = \\boldsymbol {U} _ {2} ^ {z + 1} \\left(\\boldsymbol {U} _ {2} ^ {z + 1}\\right) ^ {\\top} \\boldsymbol {P} _ {k} ^ {z}, \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.453, + 0.469, + 0.485 + ], + "angle": 0, + "content": "where \\( \\boldsymbol{U}_2^{t+1}(\\boldsymbol{U}_2^{t+1})^\\top \\) is the projection operator [27]. Formally, the local update step of Eq. (6) can be rewritten as" + }, + { + "type": "equation", + "bbox": [ + 0.175, + 0.49, + 0.469, + 0.51 + ], + "angle": 0, + "content": "\\[\n\\hat {\\boldsymbol {P}} _ {k} ^ {z, t + 1} \\leftarrow \\boldsymbol {P} _ {k} ^ {z, t} - \\eta_ {k} \\Delta \\boldsymbol {P} _ {k} ^ {z, t}. \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.512, + 0.438, + 0.527 + ], + "angle": 0, + "content": "The detailed FedPR algorithm is given in Algorithm 1." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.542, + 0.21, + 0.558 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.566, + 0.267, + 0.582 + ], + "angle": 0, + "content": "4.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.585, + 0.469, + 0.719 + ], + "angle": 0, + "content": "Implementation Details. Our method is trained by Pytorch with one NVIDIA Tesla V100 GPU and 32GB of memory. We use Adam as the optimizer, with a momentum of 0.9 and weight decay of 0.0005. The models are trained with 50 communication rounds and 10 local epochs for each round. We set the batch size and initial learning rate to 8 and \\(1 \\times 10^{-1}\\), respectively. The hyperparameter \\(\\gamma\\) is empirically set to \\(80\\%\\). The prompt embeddings are added with a size of \\(8 \\times 20 \\times 256\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.469, + 0.841 + ], + "angle": 0, + "content": "Datasets. We use fastMRI1, the largest publicly available MRI dataset, to train the pre-training model, with Swin Transformers and a standard ConvNet head serving as the backbone of our experiments [25]. We note that the mean and std of BN layer in the head are also shared with the server to update the original statistical properties. For the clients, we employ four datasets with a size of \\(320 \\times 320\\), including FeTS2 [30], \\(\\mathbf{IXI}^3\\) [1], and two clinical datasets," + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.892, + 0.363 + ], + "angle": 0, + "content": "to comprise our local data. In our experiments, we divide them into 15 clients according to the acquiring institutions, i.e., FeTS is divided into 10 clients with only 120, 304, 304, 240, 160, 160, 280, 224, 264, and 184 images, respectively; IXI is divided into 3 clients with only 360, 328, and 296 images, respectively; two clinical datasets collected from the United Imaging Healthcare uMR 790 scanner and 3T Siemens Magnetom Skyra system form two clients with 432 and 360 images, respectively. The input data of each client employs a \\(1D\\) random sampling pattern with \\(3 \\times\\) acceleration. We note that our clients have only a small number of images. In comparison, FedMRI [9] and FL-MRCM [13] require thousands to tens of thousands of images. For In-Federation evaluation, we divide each dataset with a ratio of \\(7:3\\) for local train/test. For Out-of-Federation evaluation, we use the test set of FeTS as our test set because it comes from a separate institution with a quite different distribution." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.364, + 0.892, + 0.756 + ], + "angle": 0, + "content": "Baselines. To demonstrate the effectiveness of our proposed method, we compare it with three categories of methods, including: a) SingleSet, a single model that each client is trained with their local data without FL; b) Centralized, a single model that is trained with the combination of all the local data, which serves as the upper-bound of FL models; and c) eight state-of-the-art FL algorithms, including: (1) FedAvg [26], a classical FL algorithm that is trained by averaging parameters of all the participating clients; (2) FedBN [22], a FL algorithm that alleviates the client-shift by using batch normalization on each local client; (3) FedProx [21], a FL algorithm that applies a proximal term to the local objective function; (4) SCAFFOLD [16], a FL algorithm that uses control variates to correct the client-drift; (5) MOON [20], a FL algorithm that utilizes the similarity between model representations to correct the local update; (6) FedReg [39], a FL algorithm that regularizes locally trained parameters with the loss on generated pseudo data to alleviate knowledge forgetting; (7) FL-MRCM [13], a federated MRI algorithm that aligns the latent features between the source and target clients; and (8) FedMRI [9], a federated MRI algorithm that preserves the client-specific properties to improve the FL performance. For a fair comparison, we adopt Swin Transformers and a standard ConvNet head as the reconstruction network for each client among all the baselines." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.762, + 0.8, + 0.777 + ], + "angle": 0, + "content": "4.2. Comparison with State-of-the-arts" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.78, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In-Federation Performance. The first subtable of Table 1 provides a comprehensive evaluation of the In-Federation setting with regards to various FL algorithms, where SingleSet indicates that each client is trained to use their local data without FL, and Centralized indicates that all the local datasets are gathered, which serves as the upper-bound of FL models. Ours (w. Pro) and Ours (Full) are the variants of our method that only with prompts and" + }, + { + "type": "page_footnote", + "bbox": [ + 0.078, + 0.85, + 0.468, + 0.901 + ], + "angle": 0, + "content": "1https://fastmri.org/. \n2https://www.synapse.org/#!Synapse:syn28546456/ \nwiki/. \n3https://brain-developmentment.org/" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8068" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.09, + 0.894, + 0.131 + ], + "angle": 0, + "content": "Table 1. Quantitative comparison of state-of-the-art FL methods with regard to In-Federation and Out-of-Federation scenarios, where # Com.cost is the communication cost, Ub indicates the upper-bound of FL algorithms, ↑ and ↓ indicate increments and decrements compared with FedAvg (w. FFt). Detailed analyses are provided in Sec. 4.2." + }, + { + "type": "table", + "bbox": [ + 0.078, + 0.133, + 0.9, + 0.359 + ], + "angle": 0, + "content": "
Method# Com.costIn-FederationOut-of-Federation
PSNRSSIMNMSEPSNRSSIMNMSE
SingleSet18.43 M28.79(3.35)↓0.805(0.099)↓0.021(0.011)↓28.92(2.15)↓0.808(0.091)↓0.032(0.011)↓
Centralized (Ub)18.43 M36.71(4.57)↑0.947(0.044)↑0.009(0.005)↑35.73(4.66)↑0.940(0.041)↑0.008(0.013)↑
FedAvg (w. FFt) [26]18.43 M32.14(0.00)0.903(0.000)0.010(0.000)31.07(0.00)0.899(0.000)0.021(0.000)
FedBN [22]18.40 M28.31(3.83)↓0.817(0.086)↓0.044(0.034)↓25.65(5.42)↓0.731(0.186)↓0.080(0.059)↓
FedProx [21]18.43 M32.84(0.70)↑0.901(0.002)↑0.010(0.000)31.98(0.91)↑0.905(0.006)↑0.018(0.003)↑
SCAFFOLD [16]18.43 M33.08(0.94)↑0.914(0.010)↑0.009(0.001)↑32.20(1.13)↑0.915(0.016)↑0.018(0.003)↑
MOON [20]18.43 M34.06(1.92)↑0.927(0.023)↑0.008(0.002)↑31.16(0.09)↑0.907(0.008)↑0.023(0.002)↓
FedReg [39]18.43 M33.29(1.15)↑0.890(0.013)↑0.009(0.001)↑32.41(1.34)↑0.907(0.008)↑0.017(0.004)↑
FL-MRCM [13]18.43 M33.60(1.46)↑0.922(0.019)↑0.013(0.003)↓32.72(1.65)↑0.911(0.012)↑0.016(0.005)↑
FedMRI [9]17.46 M33.35(1.21)↑0.923(0.020)↑0.014(0.004)↓32.00(0.93)↑0.914(0.015)↑0.019(0.002)↑
Ours (w. Pro)0.11 M35.29(3.15)↑0.927(0.024)↑0.009(0.001)↑34.65(3.58)↑0.921(0.022)↑0.010(0.011)↑
Ours (Full)0.11 M36.43(4.30)↑0.945(0.042)↑0.007(0.003)↑35.60(4.53)↑0.939(0.040)↑0.008(0.013)↑
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.367, + 0.473, + 0.563 + ], + "angle": 0, + "content": "our full method that with both prompts and the null space mechanism. FedAvg (w. FfIt) [26] indicates the FedAvg algorithm while employing the pretrained model on the local side and full fine-tuning with all the participating clients. For a fair comparison, we retrain them on the two different scenarios with their default parameters and report their optimal results. All the competing methods are pretrained with Swin Transformers on fastMRI and fully fine-tuned with 50 communication rounds and 10 local epochs because they all converge before round 50. To assess the difference between a pair of methods, we use the paired Student's \\(t\\)-test to demonstrate that all results were at the 0.001 level of statistical significance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.565, + 0.473, + 0.882 + ], + "angle": 0, + "content": "From Table 1, Ours (w. Pro) is superior to the competing FL methods in terms of PSNR, SSIM, and NMSE. In comparison to FedAvg (w. FFt), Ours (w. Pro) increases the PSNR results from 32.14 dB to 35.29 dB and the SSIM results from 0.903 to 0.927, because the FedAvg (w. FFt) is prone to overfitting when the local data is limited (i.e., issue ①) even though FedAvg (w. FFt) also employ the pretrained model on the local side. However, the method of freezing backbone networks that only fine-tune prompts is consistent with the mechanism of personalized FL, e.g., FedMRI, which divides the local network into a shared global generalized representation and a locally client-specific representation. More importantly, the number of training parameters and communication cost of Ours (w. Pro) is only \\(6\\%\\) of FedAvg (w. FFt). Moreover, even compared to FedReg [39], which aims to address catastrophic forgetting in FL, our method still achieves \\(9.43\\%\\) improvement in terms of PSNR. Furthermore, the reconstruction results of our proposed method are almost on par with the Centralized results (upper bound), i.e., PSNR: 36.71 dB vs. 36.41 dB, and SSIM: 0.947 vs. 0.945." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.886, + 0.47, + 0.901 + ], + "angle": 0, + "content": "In contrast, SingleSet has the lowest results, even though" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.367, + 0.895, + 0.639 + ], + "angle": 0, + "content": "it is also fine-tuned on the pre-trained model, as it cannot solve non-i.i.d. problems. For the classical federated MRI methods, FL-MRCM [13] and FedMRI [9], they lead to poor reconstruction performance when the number of local clients is large and the amount of local data is insufficient. Furthermore, other FL algorithms are either designed for data heterogeneity problems or for catastrophic forgetting problems. They have not considered the clinical issues of federated MRI, i.e., issues ①-③, causing it to produce less accurate reconstructions. These findings confirm our core idea that the three issues of federated MRI can be relieved by learning a federated visual prompt with our federated MRI paradigm. In addition, we visualize the reconstructed images and the corresponding error maps for all the competing methods in the first two rows of Fig. 4. The fewer textures in the error map, the better the reconstruction. It is obvious from the error map in Fig. 4 that our method can significantly reduce the reconstruction error." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.896, + 0.903 + ], + "angle": 0, + "content": "Out-of-Federation Performance. The second subtable of Table 1 provides quantitative evaluations under the Out-of-Federation scenario of various FL algorithms. Since the testing distribution in the Out-of-Federation scenario is unseen by the training distribution, the overall results of the Out-of-Federation scenario are slightly lower than those of In-Federation. However, our method still achieves the best performance in terms of the reconstruction results on the three metrics, i.e., Ours (Full) improves PSNR values from 31.07 dB to 35.60 dB, raises SSIM values from 0.899 to 0.939, and decreases NMSE values from 0.021 to 0.008. Notably, our method even achieves comparable results to the Centralized (Upper-bound) method, i.e., PSNR: 35.73 dB vs. 35.60 dB, SSIM: 0.940 vs. 0.939 and NMSE: 0.008 vs. 0.008. That is, our method suffers the least from the issue \\(\\Theta\\) among all competing" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "8069" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.088, + 0.07, + 0.885, + 0.325 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.328, + 0.893, + 0.37 + ], + "angle": 0, + "content": "Figure 4. Qualitative comparison of different algorithms in terms of reconstruction images and error maps with corresponding quantitative measurements in PSNR/SSIM under In-Federation and Out-of-Federation scenarios. The less texture in the error map, the better reconstruction quality." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.377, + 0.473, + 0.527 + ], + "angle": 0, + "content": "algorithms. These results support our core idea that learning federated visual prompts in the null space of global prompts can alleviate the three key issues in federated MRI while achieving competitive performance on limited local data. In addition, we show the qualitative evaluation results for the Out-of-Federation scenario in the second rows of Fig. 4, which visualizes the high-precision results of our method. As can be seen from this figure, our method provides comparable effects to the Centralized one, with clear details of tissue texture and boundaries." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.535, + 0.242, + 0.549 + ], + "angle": 0, + "content": "4.3. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.552, + 0.47, + 0.869 + ], + "angle": 0, + "content": "Catastrophic Forgetting vs. Local Updates. The catastrophic forgetting (i.e., issue ⑧) of federated MRI is caused by data heterogeneity due to different imaging protocols. As a result, more local updates will cause the local model to deviate from the global optimal solution. Here, we explore whether more local epochs cause the model to forget previously acquired global knowledge. In other words, it needs to be explored whether our proposed method can force local mitigation of this forgetting. Thus, we record the reconstruction results in terms of PSNR, SSIM, and NMSE for different numbers of local epochs in Fig. 5 (a). From this figure, in comparison to FedAvg (w. FFt) [26], increasing the local epoch does not greatly affect the accuracy of our method, i.e., Ours (w. Pro), and Ours (Full). In particular, as the number of local epochs increases, the performance of our method gradually stabilizes. In contrast, when the number of local epochs is too large, the reconstruction accuracy of FedAvg (w. FFt) will be reduced because it will gradually deviate from the global knowledge area. As a result, the result indicates that our method can learn without forgetting global knowledge over more local epochs." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Analysis of Ratio \\(\\gamma\\%\\). As we mentioned in Sec. 3.3, the ratio \\(\\gamma\\%\\) of the smallest singular values in \\(\\Lambda_2^{z+1}\\) controls" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.377, + 0.893, + 0.801 + ], + "angle": 0, + "content": "the size of the approximate null space in global prompts. That is, the larger the \\(\\gamma\\%\\), the smaller the area of knowledge preservation. However, the area of knowledge preservation contains the global knowledge from the previous round, which is expected to be unchanged. To analyze the knowledge preservation capability that a good federated MRI framework should have, we discuss the reconstruction accuracy for different \\(\\gamma\\%\\) values with regard to two scenarios in Fig. 6. It can be seen from this figure that, with the increase in \\(\\gamma\\%\\) values, the reconstruction accuracy gradually increases. However, when \\(\\gamma\\% = 100\\%\\), the reconstruction accuracy drops rapidly. This is because when the knowledge preservation area is reduced to zero, fitting on the local distribution leads to forgetting the out-of-local distribution, i.e., the issue ⑧. Additionally, we can observe from Fig. 6 that roughly \\(40\\%\\) of the area comprises previously acquired global knowledge because our method obtains the highest results at this point. Following [36], we use the proportion of the sum of singular values of \\(\\Lambda_{2}^{z+1}\\) in the sum of singular values of \\(\\Lambda^{z+1}\\) to verify the rationality of the approximation. We find that the proportion in each layer is smaller than \\(10^{-7}\\). That is, the sum of the smallest singular values \\(U_{2}^{z+1}\\) can be ignored, thereby making it reasonable to approximate the null space through the spatial range of \\(U_{2}^{z+1}\\). Interestingly, our method only performs local updates in the approximate null space of global prompts, which greatly improves the stability of the model and thus prevents catastrophic forgetting, i.e., the issue ⑧." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Communication Efficiency Analysis. Our primal interest is to learn a federated visual prompt that enables FL to perform well with less local data, lower communication cost, and faster convergence. Here, we investigate the communication efficiency of our proposed method in terms of communication cost and different communication rounds," + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8070" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.153, + 0.083, + 0.227, + 0.094 + ], + "angle": 0, + "content": "In-Federation" + }, + { + "type": "image", + "bbox": [ + 0.092, + 0.095, + 0.27, + 0.206 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.333, + 0.083, + 0.43, + 0.094 + ], + "angle": 0, + "content": "Out-of-Federation" + }, + { + "type": "image", + "bbox": [ + 0.272, + 0.096, + 0.467, + 0.206 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.212, + 0.271, + 0.322 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.272, + 0.212, + 0.465, + 0.322 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.087, + 0.327, + 0.272, + 0.46 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.275, + 0.328, + 0.467, + 0.46 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.277, + 0.463, + 0.297, + 0.475 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image_caption", + "bbox": [ + 0.558, + 0.083, + 0.632, + 0.093 + ], + "angle": 0, + "content": "In-Federation" + }, + { + "type": "image", + "bbox": [ + 0.495, + 0.096, + 0.687, + 0.205 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.744, + 0.083, + 0.84, + 0.094 + ], + "angle": 0, + "content": "Out-of-Federation" + }, + { + "type": "image", + "bbox": [ + 0.695, + 0.096, + 0.878, + 0.205 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.495, + 0.209, + 0.679, + 0.321 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.687, + 0.212, + 0.879, + 0.321 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.493, + 0.328, + 0.686, + 0.457 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.687, + 0.329, + 0.875, + 0.46 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.696, + 0.463, + 0.714, + 0.475 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.478, + 0.893, + 0.504 + ], + "angle": 0, + "content": "Figure 5. Reconstruction accuracy of FedAvg (w. FFt), Ours (w. Pro), and Ours (Full) versus (a) local epochs and (b) communication rounds under In-Federation and Out-of-Federation scenarios." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.508, + 0.457, + 0.59 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.593, + 0.47, + 0.62 + ], + "angle": 0, + "content": "Figure 6. Analysis of the ratio \\(\\gamma \\%\\) of the approximate null space in terms of PSNR, SSIM, and NMSE." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.629, + 0.473, + 0.903 + ], + "angle": 0, + "content": "respectively. As shown in Table 1, the proposed method only requires \\(0.11\\mathrm{M}\\) of communication, which is \\(6\\%\\) of the others, thereby addressing the issue \\(\\mathbf{2}\\). However, although the classical federated MRI algorithms FL-MRCM [13] and FedMRI [9] can also achieve good accuracy, they ignored this clinical issue of federated MRI. Additionally, the reconstruction accuracy of FedAvg (w. FFt) [26], Ours (w. Pro), and Ours (Full) under different communication rounds is recorded in Fig. 5 (b), where the number of the local epochs is fixed at 10 for each method. As can be seen from the figure, our method converges within 10 rounds, while FedAvg (w. FFt) [26] converges after 30 rounds. Especially under the mechanism of updating the local prompts in the approximate null space of global prompts, our method provides higher reconstruction results. This is because our federated prompt learning mechanism prevents overfitting caused by the limited amount of local training data and offers a personalized scheme for each client. The results in Fig. 5 (b)" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.517, + 0.892, + 0.562 + ], + "angle": 0, + "content": "confirm that our method provides the highest communication efficiency even on limited local data, thus relieving the issues 1 and 2." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.575, + 0.619, + 0.591 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.598, + 0.892, + 0.807 + ], + "angle": 0, + "content": "This paper presented a federated visual prompt learning method, FedPR, to tackle the three issues in federated MRI reconstruction, i.e., limited communication bandwidth, insufficient local training data, and catastrophic forgetting. Benefiting from a powerful pre-trained model, our FedPR only learns prompts with a small number of learnable parameters. Additionally, FedPR greatly mitigates catastrophic forgetting by updating local prompts only in the approximate null space of global prompts, thereby preventing knowledge outside the local distribution from being overwritten. Experiments under In-Federation and Out-of-Federation scenarios demonstrate the superiority of FedPR in relieving the three issues of federated MRI reconstruction." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Acknowledgements: This work was supported by the Agency for Science, Technology and Research (A*STAR) AME Programmatic Funds (Grant Number: A20H4b0141). This work was also supported by the AI Singapore Tech Challenge (Open-Theme) Funding Scheme (Award No.: AISG2-TC-2021-003)." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "8071" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.091, + 0.174, + 0.105 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.252, + 0.129 + ], + "angle": 0, + "content": "[1] brain-development.org." + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.129, + 0.469, + 0.168 + ], + "angle": 0, + "content": "[2] Hyojin Bahng, Ali Jahanian, Swami Sankaranarayanan, and Phillip Isola. Exploring visual prompts for adapting large-scale models, 2022." + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.169, + 0.469, + 0.209 + ], + "angle": 0, + "content": "[3] Hong-You Chen, Cheng-Hao Tu, Ziwei Li, Han-Wei Shen, and Wei-Lun Chao. 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In Proceedings of the IEEE/CVF Conference" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.47, + 0.893 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.536, + 0.094, + 0.892, + 0.12 + ], + "angle": 0, + "content": "on Computer Vision and Pattern Recognition, pages 2049-2058, 2019." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.515, + 0.956 + ], + "angle": 0, + "content": "8073" + } + ] +] \ No newline at end of file diff --git a/2023/Learning Federated Visual Prompt in Null Space for MRI Reconstruction/20f20c2b-43db-4f5b-b2e9-0c30622bc0bc_origin.pdf b/2023/Learning Federated Visual Prompt in Null Space for MRI Reconstruction/20f20c2b-43db-4f5b-b2e9-0c30622bc0bc_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..0b3de9b1dfecc70a629f52c2da545a577873147c --- /dev/null +++ b/2023/Learning Federated Visual Prompt in Null Space for MRI Reconstruction/20f20c2b-43db-4f5b-b2e9-0c30622bc0bc_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:3c6c8754149f4d2851d6b3121024c28602c01e5f2e6e297f2125c8aaf80ab0b5 +size 2239139 diff --git a/2023/Learning Federated Visual Prompt in Null Space for MRI Reconstruction/full.md b/2023/Learning Federated Visual Prompt in Null Space for MRI Reconstruction/full.md new file mode 100644 index 0000000000000000000000000000000000000000..e1b172e30d3f558460c27988fac50a24abcb99db --- /dev/null +++ b/2023/Learning Federated Visual Prompt in Null Space for MRI Reconstruction/full.md @@ -0,0 +1,336 @@ +# Learning Federated Visual Prompt in Null Space for MRI Reconstruction + +Chun-Mei Feng $^{1}$ Bangjun Li $^{2}$ Xinxing Xu $^{1,*}$ Yong Liu $^{1,*}$ Huazhu Fu $^{1}$ Wangmeng Zuo $^{3}$ + +$^{1}$ Institute of High Performance Computing (IHPC), + +Agency for Science, Technology and Research (A*STAR), Singapore + +$^{2}$ School of Information Science and Engineering, Shangdong University, China + +$^{3}$ Harbin Institute of Technology, Harbin, China + +strawberry.feng0304@gmail.com, {xuxinx, liuyong}@ihpc.a-star.edu.sg + +https://github.com/chunmeifeng/FedPR + +# Abstract + +Federated Magnetic Resonance Imaging (MRI) reconstruction enables multiple hospitals to collaborate distributedly without aggregating local data, thereby protecting patient privacy. However, the data heterogeneity caused by different MRI protocols, insufficient local training data, and limited communication bandwidth inevitably impair global model convergence and updating. In this paper, we propose a new algorithm, FedPR, to learn federated visual prompts in the null space of global prompt for MRI reconstruction. FedPR is a new federated paradigm that adopts a powerful pre-trained model while only learning and communicating the prompts with few learnable parameters, thereby significantly reducing communication costs and achieving competitive performance on limited local data. Moreover, to deal with catastrophic forgetting caused by data heterogeneity, FedPR also updates efficient federated visual prompts that project the local prompts into an approximate null space of the global prompt, thereby suppressing the interference of gradients on the server performance. Extensive experiments on federated MRI show that FedPR significantly outperforms state-of-the-art FL algorithms with $< 6\%$ of communication costs when given the limited amount of local training data. + +# 1. Introduction + +Federated Magnetic Resonance Imaging (MRI) reconstruction enables multiple hospitals to train a powerful global model in a distributed manner without sharing private data [7, 9, 13]. In federated MRI, each client (i.e., hospital) uses its local computing power, memory, and private data to train local models independently, while the server aggregates all the local models in each communica + +![](images/c71ee1f0e0c0da547bb5107eee89af8d5c027e4bc0621d3cd973d689967ad3a4.jpg) +Figure 1. Illustration of the three key issues in federated MRI. + +tion round and distributes the global model to each client again [26]. + +Existing federated MRI reconstruction techniques usually improve federated learning (FL) by enhancing the aggregation process [9] and reducing the local parameter's variance [5, 13]. Such techniques require a large communication bandwidth and sufficient local training data. However, federated MRI often faces two issues, insufficient amount of local training data due to the difficulty of acquiring the ground-truth of MRI reconstruction [10, 11, 12] and limited communication bandwidth due to unbalanced regional development (see Fig. 1). To cope with the issue, pre-trained models have exhibited superior performance, and have shown to close the gap between federated and centralized performance [3, 28]. However, since the model parameters need to be shared between the client and the server for updating, the large number of parameters of pre-trained models will result in a huge communication cost. On contrary, prompt tuning has recently been suggested as a new fine-tuning paradigm by freezing the models and only learning a small number of learnable parameters in the input space [15, 31, 32]. Benefited from pre-trained models, only parameter-efficient prompts are required in learning and communication, and prompt tuning can be conducted with a limited number of samples, making it very appealing in tackling the above two issues (i.e., + +# $\mathbf{1}$ and $\mathbf{2}$ ) in federated MRI. + +Besides, there is another critical issue for federated MRI, i.e., ⑧ catastrophic forgetting, caused by data heterogeneity due to the different imaging protocols of MRI scanners adopted by different clients [9, 39] (see Fig. 1). In the local update, the global model from the prior round tends to be overfitted to the local training data, leading to catastrophic forgetting. Analogous to continual learning, several techniques have been presented by introducing proper regularization terms in local models [4, 33, 39] or retaining previously acquired knowledge by knowledge distillation [14, 35, 38]. However, these strategies require seeking a balance between multiple losses and relying on proxy datasets. Instead, Adam-NSC mitigates catastrophic forgetting in continual learning with a new network parameter update rule, i.e., forces the network update to lie in the approximate null space of the input features of previous tasks at each layer [36]. However, the null space at feature level is built upon large local training data, which generally cannot be satisfied in federated MRI, i.e., the issue ①. Taking the issues ① and ⑧ into account, we suggest to optimize local prompts in the approximate null space of global prompts instead of input features, thereby preventing the loss of previously gained global knowledge. + +In a nutshell, we explore a new FL paradigm, i.e., FedPR, to learn federated visual prompts for MRI reconstruction. To begin with, we pre-train the model on a large-scale public dataset. Given limited amount of local training data, visual prompt tuning is adopted to learn local prompts in a distributed manner. For the issues 1 and 2, federated visual prompts are introduced to learn a strong global model, where only local and global prompts are learnable and communicated. As for the issue 3, we perform singular value decomposition (SVD) on the uncentered covariance matrix of global prompts to obtain the approximate null space. FedPR tunes only the local parameters in the null space of global prompts, thereby well preserving the prior knowledge of previous rounds and resulting in low communication costs. In particular, FedPR achieves a $>4.5$ dB gain in PSNR with less than $6\%$ of communication costs. To sum up, our contributions are as follows: + +- We propose a federated visual prompt algorithm, FedPR, to solve the three key issues in federated MRI. By leveraging powerful pre-trained models and freezing backbone networks in FL, only a small amount of parameters in the input space are trainable, thereby reducing communication costs. +- We explore how to alleviate catastrophic forgetting in FL while reducing communication costs. By optimizing local parameters only in the null space of global prompts, FedPR well preserves the previously acquired global knowledge in each round, maintaining competitive performance with only a few local data. + +- We evaluate the performance of FedPR for federated MRI reconstruction. In comparison to the state-of-the-art FL methods, FedPR achieves superior performance in complex scenarios, e.g., less local data, lower communication costs, and faster convergence. + +# 2. Related Work + +Federated MRI Reconstruction. MRI reconstruction refers to reconstructing images without aliasing artifacts from undersampled $k$ -space data [6, 8, 12, 37, 41]. However, existing MRI reconstruction techniques are based on large-scale paired data, which is not only labor-intensive but also violates patient privacy [9]. Driven by these realistic problems, a few FL-based methods for MRI reconstruction have been proposed [5, 9, 13]. Guo et al. reduced data heterogeneity by iteratively aligning the data distribution between source and target clients [13]. Feng et al. proposed a personalized FL reconstruction scheme and introduced a weighted contrast regularization term to correct the update direction of global generalization [9]. However, these schemes either require frequent communication or are built on a large amount of local data. As a result, these techniques will produce sub-optimal solutions for MRI reconstruction when there is limited bandwidth and insufficient local training data. In contrast to these works, we build a federated MRI model upon a strong pre-trained model by updating and communicating only a small portion of parameters for each client using limited local data, achieving competitive results. + +Catastrophic Forgetting in FL. Due to the heterogeneous data distributions of different tasks in continual learning, when the network is fitted to the current task, the model parameters typically deviate from the areas where the previous knowledge is expected to be preserved [17]. Therefore, catastrophic forgetting is a fundamental challenge of continual learning. Similarly, catastrophic forgetting also affects FL [14, 19, 39]. When the client receives the global model and continues to update locally, it will cause the global model to forget the knowledge of the previous round due to the data heterogeneity across clients [19]. As a result, existing FL techniques that address catastrophic forgetting are designed by referring to continual learning. For example, knowledge distillation-based FL methods maintain previously gained knowledge, but this method strongly relies on proxy data [14, 35, 38]; regularization-based FL methods regularize locally trained parameters, but they require finding a compromise between loss terms [4, 33, 39]. All these studies are built on classification tasks and cannot be directly extended to MRI reconstruction. Inspired by the success of null space in continual learning [18, 23, 36], we try to update the local prompt in the approximate null space of global prompts, thereby preserving the knowledge acquired by the global model in the previous round and avoid + +![](images/49dbd40481e5ce7b8ff62315081544b4713a640ddea149e3ef9744b02a6a8735.jpg) +(a) Initialization and local update + +![](images/e7f3fbb295c11848b735f213b931378776230d91d272f1a754168f05a481c7a5.jpg) +(b) Federated visual prompt +(c) Server update +Figure 2. Illustration of our FedPR method. (a) For each client, the backbone model is pre-trained on massive data and fine-tuned via prompt (see Sec. 3.2). (b) Federated visual prompt is executed by updating the local prompt of each client only in the approximate null space of global prompts while preserving the previously acquired global knowledge (see Sec. 3.3). (c) Server update by aggregating local prompts. + +ing catastrophic forgetting. + +Prompt Learning. Prompt tuning was initially proposed to enable pre-trained language models to "understand" downstream tasks by adding trainable tokens to the input text [24]. For example, Jia et al. achieved good performance on downstream tasks by introducing a small number of learnable tokens into the input space and keeping the backbone frozen [15]. Hyojin et al. suggested to modify pixel space for the frozen visual models [2]. Nie et al. proposed a unified prompt tuning framework that performs on different CNN and transformer-based architectures by training only a few additional parameters [29]. Although these works have made progress on various visual tasks, prompt is still limited to centralized systems, and the effectiveness of prompt in distributed framework remains uninvestigated. Therefore, this work focuses on how to learn a federated visual prompt to effectively tackle the three key problems in federated MRI reconstruction, i.e., the issues ①-③. + +# 3. Methodology + +# 3.1. Federated MRI Reconstruction + +MRI reconstruction is an inverse problem of recovering an artifact-free image $\mathbf{y}$ from its undersampled observation $\mathbf{x}$ that can reduce the online collection time and improve the patient experience [34, 37, 40]. Formally, such undersampling process can be expressed as + +$$ +\mathbf {x} = \mathcal {F} ^ {- 1} (\mathcal {M} \odot \mathcal {F} (\mathbf {y}) + \epsilon), \tag {1} +$$ + +where $\mathcal{F}$ is multi-dimensional Fourier transform, $\epsilon$ is the measurement noise, and $\mathcal{M}$ is the binary mask operator to undersample the data points in the Fourier space. + +The centralized approach violates patient privacy protection roles because it requires collecting large amounts of training data from different hospitals. As a remedy, Federated MRI has been suggested by deploying MRI reconstruction in a distributed manner [9, 13]. Suppose there are $K$ + +hospitals (local clients). The private data of all hospitals can be expressed as $\mathcal{D} = \{\mathcal{D}^1,\mathcal{D}^2,\dots ,\mathcal{D}^K\}$ , where each contains limited pairs of undersampled samples $\mathbf{x}_i$ and fully-sampled images $\mathbf{y}_i$ . Federated MRI aims to learn a global model from the whole dataset $\mathcal{D}$ in a distributed manner, which can be described as + +$$ +\arg \min _ {\boldsymbol {w}} \mathcal {L} (\boldsymbol {w}) = \sum_ {k = 1} ^ {K} \frac {| \mathcal {D} ^ {k} |}{| \mathcal {D} |} \mathcal {L} _ {k} (\boldsymbol {w}), \tag {2} +$$ + +where $|\mathcal{D}|$ denotes the number of samples in $\mathcal{D}$ , and $\mathcal{L}_k(\boldsymbol{w})$ is the empirical loss of client $k$ , + +$$ +\mathcal {L} _ {k} (\boldsymbol {w}) = \mathbf {E} _ {(\mathbf {x}, \mathbf {y}) \in \mathcal {D} ^ {k}} \ell_ {k} (f (\mathbf {x}; \boldsymbol {w})) \tag {3} +$$ + +where $\ell_{k}$ represents the local loss for MRI reconstruction, e.g., $L_{1}$ loss. After training, the reconstructed image $\hat{\mathbf{y}}$ can be produced by $f(\mathbf{x};\boldsymbol {w})$ + +# 3.2. Learning Federated Prompt + +As mentioned in Sec. 1, there are three key issues, i.e., 1-3, with the existing federated MRI algorithms. To tackle the issue 2, we freeze the backbone of the pre-trained model while only tuning and communicating a few learnable parameters for the clients and server. More importantly, it enables the model to achieve very competitive results on limited local data, thereby providing an effective solution to issue 1. + +As shown in Fig. 2, given a pre-trained model with parameters $\theta$ , we introduce a set of continuous embeddings $P = \{p_1, p_2, \dots, p_l\}$ as the prompts in the input space of each layer [15], where $l$ is the number of prompts. Thus, the overall parameters can be expressed as $\boldsymbol{w} = \{P, \theta\}$ . Suppose there are $Z$ rounds of communication, each round contains $T$ local updates. During the local update, for the $k$ -th client, only the client-specific prompts $P_k$ are learnable and communicated while the backbone network is frozen. Therefore, Eq. (2) can be rewritten as: + +![](images/6aa9308d7a76fd86981d6b134000b925c23644744698cfa3c78ccc22175d3b80.jpg) +Figure 3. Illustration of federated visual prompt for updating local prompts in the null space of global prompts. + +$$ +\boldsymbol {P} _ {k} = \arg \min _ {\boldsymbol {P}} \mathcal {L} (\boldsymbol {P}) = \sum_ {k = 1} ^ {K} \frac {\left| \mathcal {D} ^ {k} \right|}{\left| \mathcal {D} \right|} \mathcal {L} _ {k} (\boldsymbol {P}), \tag {4} +$$ + +where the empirical loss for prompt tuning of client $k$ can be expressed as + +$$ +\mathcal {L} _ {k} (\boldsymbol {P}) = \mathbf {E} _ {(\mathbf {x}, \mathbf {y}) \in \mathcal {D} ^ {k}} \ell_ {k} (f (\mathbf {x}; \boldsymbol {P}, \boldsymbol {\theta})). \tag {5} +$$ + +Benefited from pre-trained models, federated prompt tuning can be both parameter- and communication-efficient and effective in achieving competitive results with a small amount of local data, thereby serving as a favorable solution to the issues 1 and 2. + +Local Update Step: In each communication round $z = \{1,2,\dots,Z\}$ , the clients are optimized using the following update rules with a learning rate of $\eta_{k}$ : + +$$ +\boldsymbol {P} _ {k} ^ {z, t + 1} \leftarrow \boldsymbol {P} _ {k} ^ {z, t} - \eta_ {k} \nabla \ell_ {k} \left(\mathbf {x} ^ {k}; \boldsymbol {P} _ {k} ^ {z, t}\right), \tag {6} +$$ + +where $t$ denotes the $t$ -th update of the local clients. + +Server Update Step: After a round of local updates, all participating clients send their updated prompts $\pmb{P}_{k}^{z}$ to the server performing aggregation. Such process can be expressed as follows + +$$ +\mathbf {P} _ {g} ^ {z + 1} \leftarrow \sum_ {k = 1} ^ {K} \frac {\left| \mathcal {D} ^ {k} \right|}{\left| \mathcal {D} \right|} \mathbf {P} _ {k} ^ {z}, \tag {7} +$$ + +where $P_{g}^{z + 1}$ denotes the global prompts of round $z + 1$ . To sum up, the issue $\mathbf{0}$ can be largely mitigated because there are only a small number of learnable parameters $P$ communicated between the server and local clients. After $Z$ rounds of communication, we can get a robust global model parameterized by $P_{g}$ without sharing local private data. + +# 3.3. Local Updating in Prompting Null Space + +The local update mechanism in Eq. (6), however, suffers from the issue ⑧, i.e., catastrophic forgetting, due to data heterogeneity of different clients. Inspired by the continual learning method Adam-NSC [36] that sequentially optimizes network parameters in the null space at feature level, we suggest to optimize the local model in the null space of + +# Algorithm 1: FedPR + +Input: Private datasets from $K$ clients: $\mathcal{D}^1, \mathcal{D}^2, \ldots, \mathcal{D}^K$ , local updates $T$ , communication rounds $Z$ , pre-trained model parameters $\theta$ , prompt embeddings $P$ , learning rate $\eta$ , hyperparameter $\gamma$ ; + +1 // ServerExecution: +2 Initialize global prompt $P_{g}$ with parameters $\theta$ +3 for each communication round $z\in \{1,2,\dots,Z\}$ do + +4 for each client $k\in \{1,2,\dots K\}$ in parallel do 5 $\begin{array}{rl} & P_k^z\gets P_g^z;\\ & \hat{P}_k^z\gets \mathrm{LocalUpdate}(k,P_k^z); \end{array}$ 6 +7 end + +8 $P_{g}^{z + 1}\gets \sum_{k = 1}^{K}\frac{|\mathcal{D}^{k}|}{|\mathcal{D}|}\hat{P}_{k}^{z};$ +9 Compute the uncentered covariance matrix: + +10 $\pmb{\Sigma}_{g}^{z + 1} = \left(\pmb{P}_{g}^{z + 1}\right)^{\top}\pmb{P}_{g}^{z + 1};$ +11 Approximate the null space of $\Sigma_g^{z + 1}$ +12 $\pmb{\Sigma}_{g}^{z + 1} = \pmb{U}^{z + 1}\pmb{\Lambda}^{z + 1}\left(\pmb{U}^{z + 1}\right)^{\top};$ +13 Select the smallest diagonal singular values of $\Lambda_2^{z + 1}$ with the ratio of $\gamma$ +14 Get $\pmb{U}_2^{z + 1}$ corresponding to $\Lambda_2^{z + 1}$ + +15 end +16 return $P_{g}^{z + 1}$ +17 // LocalUpdate $(k, P_k)$ : +18 for each local epoch $t \in \{1, 2, \dots, T\}$ do +19 Get the updated parameters $\Delta P_k^z$ : +20 $|\Delta P_k^z = U_2^{z + 1}\left(U_2^{z + 1}\right)^\top P_k^z;$ +21 $\hat{P}_k^{z,t + 1}\gets P_k^{z,t} - \eta_k\Delta P_k^{z,t};$ +22 end +23 return $\hat{P}_k^z$ + +global prompts. Specifically, we train the local model in the approximate null space of the global prompts in a distributed way, preventing knowledge outside the local distribution from being overwritten and resulting in catastrophic forgetting. In comparison to [36], approximating the null space of global prompts instead of features does not require a large amount of local data and not increase the communication cost, thus offering a feasible way to tackle the three issues 1-8 in federated MRI. + +As shown in Fig. 3, we first compute the uncentered covariance matrix of $z + 1$ round global prompt $P_g^{z + 1}$ by + +$$ +\boldsymbol {\Sigma} _ {g} ^ {z + 1} = \left(\boldsymbol {P} _ {g} ^ {z + 1}\right) ^ {\top} \boldsymbol {P} _ {g} ^ {z + 1}. \tag {8} +$$ + +Then, we find the approximate null space of $\Sigma_{g}^{z + 1}$ by apply SVD to it + +$$ +\boldsymbol {\Sigma} _ {g} ^ {z + 1} = \boldsymbol {U} ^ {z + 1} \boldsymbol {\Lambda} ^ {z + 1} \left(\boldsymbol {U} ^ {z + 1}\right) ^ {\top}, \tag {9} +$$ + +where + +$$ +\boldsymbol {U} ^ {z + 1} = \left[ \boldsymbol {U} _ {1} ^ {z + 1}, \boldsymbol {U} _ {2} ^ {z + 1} \right], \tag {10} +$$ + +$$ +\boldsymbol {\Lambda} ^ {z + 1} = \left[ \begin{array}{c c} \boldsymbol {\Lambda} _ {1} ^ {z + 1} & 0 \\ 0 & \boldsymbol {\Lambda} _ {2} ^ {z + 1} \end{array} \right]. +$$ + +Here $U_{1}^{z + 1}$ are the singular vectors corresponding to the large singular values in $\Lambda_1^{z + 1}$ [36]. According to principal component analysis (PCA), $U_{1}^{z + 1}$ can be considered as principal components, which contain the global knowledge that has been captured in the previous round. Thus, we have $\Sigma_g^{z + 1} \approx U_1^{z + 1}\Lambda_1^{z + 1}\left(U_1^{z + 1}\right)^\top$ . And the range space of $U_{2}^{z + 1}$ can be denoted as the approximate null space of $\Sigma_g^{z + 1}$ [36]. In our implementation, we introduce a $\gamma \%$ to control $U_{2}^{z + 1}$ by selecting the last $\gamma \%$ of singular values in $\Lambda_2^{z + 1}$ to constitute $U_{2}^{z + 1}$ . + +To tackle the issue $\bullet$ , $P_{k}^{z}$ can be projected into the approximate null space of $\Sigma_{g}^{z + 1}$ to get the updated parameters, while the principal components $U_{1}^{z + 1}$ containing the global knowledge from the previous round are preserved. Thus, the updated parameters $\Delta P_{k}^{z}$ can be optimized in the null space of $\Sigma_{g}^{z + 1}$ by + +$$ +\Delta \boldsymbol {P} _ {k} ^ {z} = \boldsymbol {U} _ {2} ^ {z + 1} \left(\boldsymbol {U} _ {2} ^ {z + 1}\right) ^ {\top} \boldsymbol {P} _ {k} ^ {z}, \tag {11} +$$ + +where $\boldsymbol{U}_2^{t+1}(\boldsymbol{U}_2^{t+1})^\top$ is the projection operator [27]. Formally, the local update step of Eq. (6) can be rewritten as + +$$ +\hat {\boldsymbol {P}} _ {k} ^ {z, t + 1} \leftarrow \boldsymbol {P} _ {k} ^ {z, t} - \eta_ {k} \Delta \boldsymbol {P} _ {k} ^ {z, t}. \tag {12} +$$ + +The detailed FedPR algorithm is given in Algorithm 1. + +# 4. Experiments + +# 4.1. Experimental Setup + +Implementation Details. Our method is trained by Pytorch with one NVIDIA Tesla V100 GPU and 32GB of memory. We use Adam as the optimizer, with a momentum of 0.9 and weight decay of 0.0005. The models are trained with 50 communication rounds and 10 local epochs for each round. We set the batch size and initial learning rate to 8 and $1 \times 10^{-1}$ , respectively. The hyperparameter $\gamma$ is empirically set to $80\%$ . The prompt embeddings are added with a size of $8 \times 20 \times 256$ . + +Datasets. We use fastMRI1, the largest publicly available MRI dataset, to train the pre-training model, with Swin Transformers and a standard ConvNet head serving as the backbone of our experiments [25]. We note that the mean and std of BN layer in the head are also shared with the server to update the original statistical properties. For the clients, we employ four datasets with a size of $320 \times 320$ , including FeTS2 [30], $\mathbf{IXI}^3$ [1], and two clinical datasets, + +to comprise our local data. In our experiments, we divide them into 15 clients according to the acquiring institutions, i.e., FeTS is divided into 10 clients with only 120, 304, 304, 240, 160, 160, 280, 224, 264, and 184 images, respectively; IXI is divided into 3 clients with only 360, 328, and 296 images, respectively; two clinical datasets collected from the United Imaging Healthcare uMR 790 scanner and 3T Siemens Magnetom Skyra system form two clients with 432 and 360 images, respectively. The input data of each client employs a $1D$ random sampling pattern with $3 \times$ acceleration. We note that our clients have only a small number of images. In comparison, FedMRI [9] and FL-MRCM [13] require thousands to tens of thousands of images. For In-Federation evaluation, we divide each dataset with a ratio of $7:3$ for local train/test. For Out-of-Federation evaluation, we use the test set of FeTS as our test set because it comes from a separate institution with a quite different distribution. + +Baselines. To demonstrate the effectiveness of our proposed method, we compare it with three categories of methods, including: a) SingleSet, a single model that each client is trained with their local data without FL; b) Centralized, a single model that is trained with the combination of all the local data, which serves as the upper-bound of FL models; and c) eight state-of-the-art FL algorithms, including: (1) FedAvg [26], a classical FL algorithm that is trained by averaging parameters of all the participating clients; (2) FedBN [22], a FL algorithm that alleviates the client-shift by using batch normalization on each local client; (3) FedProx [21], a FL algorithm that applies a proximal term to the local objective function; (4) SCAFFOLD [16], a FL algorithm that uses control variates to correct the client-drift; (5) MOON [20], a FL algorithm that utilizes the similarity between model representations to correct the local update; (6) FedReg [39], a FL algorithm that regularizes locally trained parameters with the loss on generated pseudo data to alleviate knowledge forgetting; (7) FL-MRCM [13], a federated MRI algorithm that aligns the latent features between the source and target clients; and (8) FedMRI [9], a federated MRI algorithm that preserves the client-specific properties to improve the FL performance. For a fair comparison, we adopt Swin Transformers and a standard ConvNet head as the reconstruction network for each client among all the baselines. + +# 4.2. Comparison with State-of-the-arts + +In-Federation Performance. The first subtable of Table 1 provides a comprehensive evaluation of the In-Federation setting with regards to various FL algorithms, where SingleSet indicates that each client is trained to use their local data without FL, and Centralized indicates that all the local datasets are gathered, which serves as the upper-bound of FL models. Ours (w. Pro) and Ours (Full) are the variants of our method that only with prompts and + +Table 1. Quantitative comparison of state-of-the-art FL methods with regard to In-Federation and Out-of-Federation scenarios, where # Com.cost is the communication cost, Ub indicates the upper-bound of FL algorithms, ↑ and ↓ indicate increments and decrements compared with FedAvg (w. FFt). Detailed analyses are provided in Sec. 4.2. + +
Method# Com.costIn-FederationOut-of-Federation
PSNRSSIMNMSEPSNRSSIMNMSE
SingleSet18.43 M28.79(3.35)↓0.805(0.099)↓0.021(0.011)↓28.92(2.15)↓0.808(0.091)↓0.032(0.011)↓
Centralized (Ub)18.43 M36.71(4.57)↑0.947(0.044)↑0.009(0.005)↑35.73(4.66)↑0.940(0.041)↑0.008(0.013)↑
FedAvg (w. FFt) [26]18.43 M32.14(0.00)0.903(0.000)0.010(0.000)31.07(0.00)0.899(0.000)0.021(0.000)
FedBN [22]18.40 M28.31(3.83)↓0.817(0.086)↓0.044(0.034)↓25.65(5.42)↓0.731(0.186)↓0.080(0.059)↓
FedProx [21]18.43 M32.84(0.70)↑0.901(0.002)↑0.010(0.000)31.98(0.91)↑0.905(0.006)↑0.018(0.003)↑
SCAFFOLD [16]18.43 M33.08(0.94)↑0.914(0.010)↑0.009(0.001)↑32.20(1.13)↑0.915(0.016)↑0.018(0.003)↑
MOON [20]18.43 M34.06(1.92)↑0.927(0.023)↑0.008(0.002)↑31.16(0.09)↑0.907(0.008)↑0.023(0.002)↓
FedReg [39]18.43 M33.29(1.15)↑0.890(0.013)↑0.009(0.001)↑32.41(1.34)↑0.907(0.008)↑0.017(0.004)↑
FL-MRCM [13]18.43 M33.60(1.46)↑0.922(0.019)↑0.013(0.003)↓32.72(1.65)↑0.911(0.012)↑0.016(0.005)↑
FedMRI [9]17.46 M33.35(1.21)↑0.923(0.020)↑0.014(0.004)↓32.00(0.93)↑0.914(0.015)↑0.019(0.002)↑
Ours (w. Pro)0.11 M35.29(3.15)↑0.927(0.024)↑0.009(0.001)↑34.65(3.58)↑0.921(0.022)↑0.010(0.011)↑
Ours (Full)0.11 M36.43(4.30)↑0.945(0.042)↑0.007(0.003)↑35.60(4.53)↑0.939(0.040)↑0.008(0.013)↑
+ +our full method that with both prompts and the null space mechanism. FedAvg (w. FfIt) [26] indicates the FedAvg algorithm while employing the pretrained model on the local side and full fine-tuning with all the participating clients. For a fair comparison, we retrain them on the two different scenarios with their default parameters and report their optimal results. All the competing methods are pretrained with Swin Transformers on fastMRI and fully fine-tuned with 50 communication rounds and 10 local epochs because they all converge before round 50. To assess the difference between a pair of methods, we use the paired Student's $t$ -test to demonstrate that all results were at the 0.001 level of statistical significance. + +From Table 1, Ours (w. Pro) is superior to the competing FL methods in terms of PSNR, SSIM, and NMSE. In comparison to FedAvg (w. FFt), Ours (w. Pro) increases the PSNR results from 32.14 dB to 35.29 dB and the SSIM results from 0.903 to 0.927, because the FedAvg (w. FFt) is prone to overfitting when the local data is limited (i.e., issue ①) even though FedAvg (w. FFt) also employ the pretrained model on the local side. However, the method of freezing backbone networks that only fine-tune prompts is consistent with the mechanism of personalized FL, e.g., FedMRI, which divides the local network into a shared global generalized representation and a locally client-specific representation. More importantly, the number of training parameters and communication cost of Ours (w. Pro) is only $6\%$ of FedAvg (w. FFt). Moreover, even compared to FedReg [39], which aims to address catastrophic forgetting in FL, our method still achieves $9.43\%$ improvement in terms of PSNR. Furthermore, the reconstruction results of our proposed method are almost on par with the Centralized results (upper bound), i.e., PSNR: 36.71 dB vs. 36.41 dB, and SSIM: 0.947 vs. 0.945. + +In contrast, SingleSet has the lowest results, even though + +it is also fine-tuned on the pre-trained model, as it cannot solve non-i.i.d. problems. For the classical federated MRI methods, FL-MRCM [13] and FedMRI [9], they lead to poor reconstruction performance when the number of local clients is large and the amount of local data is insufficient. Furthermore, other FL algorithms are either designed for data heterogeneity problems or for catastrophic forgetting problems. They have not considered the clinical issues of federated MRI, i.e., issues ①-③, causing it to produce less accurate reconstructions. These findings confirm our core idea that the three issues of federated MRI can be relieved by learning a federated visual prompt with our federated MRI paradigm. In addition, we visualize the reconstructed images and the corresponding error maps for all the competing methods in the first two rows of Fig. 4. The fewer textures in the error map, the better the reconstruction. It is obvious from the error map in Fig. 4 that our method can significantly reduce the reconstruction error. + +Out-of-Federation Performance. The second subtable of Table 1 provides quantitative evaluations under the Out-of-Federation scenario of various FL algorithms. Since the testing distribution in the Out-of-Federation scenario is unseen by the training distribution, the overall results of the Out-of-Federation scenario are slightly lower than those of In-Federation. However, our method still achieves the best performance in terms of the reconstruction results on the three metrics, i.e., Ours (Full) improves PSNR values from 31.07 dB to 35.60 dB, raises SSIM values from 0.899 to 0.939, and decreases NMSE values from 0.021 to 0.008. Notably, our method even achieves comparable results to the Centralized (Upper-bound) method, i.e., PSNR: 35.73 dB vs. 35.60 dB, SSIM: 0.940 vs. 0.939 and NMSE: 0.008 vs. 0.008. That is, our method suffers the least from the issue $\Theta$ among all competing + +![](images/8dec8839b1b3e7c96b688dafff4eacc26d54a6b2c4c0a20b9710f9979fbbb0ae.jpg) +Figure 4. Qualitative comparison of different algorithms in terms of reconstruction images and error maps with corresponding quantitative measurements in PSNR/SSIM under In-Federation and Out-of-Federation scenarios. The less texture in the error map, the better reconstruction quality. + +algorithms. These results support our core idea that learning federated visual prompts in the null space of global prompts can alleviate the three key issues in federated MRI while achieving competitive performance on limited local data. In addition, we show the qualitative evaluation results for the Out-of-Federation scenario in the second rows of Fig. 4, which visualizes the high-precision results of our method. As can be seen from this figure, our method provides comparable effects to the Centralized one, with clear details of tissue texture and boundaries. + +# 4.3. Ablation Studies + +Catastrophic Forgetting vs. Local Updates. The catastrophic forgetting (i.e., issue ⑧) of federated MRI is caused by data heterogeneity due to different imaging protocols. As a result, more local updates will cause the local model to deviate from the global optimal solution. Here, we explore whether more local epochs cause the model to forget previously acquired global knowledge. In other words, it needs to be explored whether our proposed method can force local mitigation of this forgetting. Thus, we record the reconstruction results in terms of PSNR, SSIM, and NMSE for different numbers of local epochs in Fig. 5 (a). From this figure, in comparison to FedAvg (w. FFt) [26], increasing the local epoch does not greatly affect the accuracy of our method, i.e., Ours (w. Pro), and Ours (Full). In particular, as the number of local epochs increases, the performance of our method gradually stabilizes. In contrast, when the number of local epochs is too large, the reconstruction accuracy of FedAvg (w. FFt) will be reduced because it will gradually deviate from the global knowledge area. As a result, the result indicates that our method can learn without forgetting global knowledge over more local epochs. + +Analysis of Ratio $\gamma\%$ . As we mentioned in Sec. 3.3, the ratio $\gamma\%$ of the smallest singular values in $\Lambda_2^{z+1}$ controls + +the size of the approximate null space in global prompts. That is, the larger the $\gamma\%$ , the smaller the area of knowledge preservation. However, the area of knowledge preservation contains the global knowledge from the previous round, which is expected to be unchanged. To analyze the knowledge preservation capability that a good federated MRI framework should have, we discuss the reconstruction accuracy for different $\gamma\%$ values with regard to two scenarios in Fig. 6. It can be seen from this figure that, with the increase in $\gamma\%$ values, the reconstruction accuracy gradually increases. However, when $\gamma\% = 100\%$ , the reconstruction accuracy drops rapidly. This is because when the knowledge preservation area is reduced to zero, fitting on the local distribution leads to forgetting the out-of-local distribution, i.e., the issue ⑧. Additionally, we can observe from Fig. 6 that roughly $40\%$ of the area comprises previously acquired global knowledge because our method obtains the highest results at this point. Following [36], we use the proportion of the sum of singular values of $\Lambda_{2}^{z+1}$ in the sum of singular values of $\Lambda^{z+1}$ to verify the rationality of the approximation. We find that the proportion in each layer is smaller than $10^{-7}$ . That is, the sum of the smallest singular values $U_{2}^{z+1}$ can be ignored, thereby making it reasonable to approximate the null space through the spatial range of $U_{2}^{z+1}$ . Interestingly, our method only performs local updates in the approximate null space of global prompts, which greatly improves the stability of the model and thus prevents catastrophic forgetting, i.e., the issue ⑧. + +Communication Efficiency Analysis. Our primal interest is to learn a federated visual prompt that enables FL to perform well with less local data, lower communication cost, and faster convergence. Here, we investigate the communication efficiency of our proposed method in terms of communication cost and different communication rounds, + +![](images/7e307877201c91a044cf86407d07c34d151582b2a02296805a0db976d3f69d2f.jpg) +In-Federation + +![](images/ca71fa696f4ddd914119772483ba8a74ad5ea82e362e3c1dbdb622eee6e6c609.jpg) +Out-of-Federation + +![](images/5261998a6589c859352cbc7bc2d402fc919dd34bf9e2f4d760778f02ab5877fb.jpg) + +![](images/c0db5db5d46b2426709c6420931e391b1ad39b6b958f2bf95fa5b67649f9e9d1.jpg) + +![](images/daa6abb2286a7d6cd939c67a4525685a0ba8603d6354d9d2d1a64e64761a2904.jpg) +(a) + +![](images/cac29961ae468f0cab6374cb1c4398d6c753d40969e6d5818099a2e23d762f10.jpg) + +![](images/a092321e18a27012f6668f742c46d2c04c32176a4dfe51b809c337b590af6fb7.jpg) +In-Federation + +![](images/5e996a3cdccf67b1924dc264e24c4edd048b73eedeba800ae48d998122390dbf.jpg) +Out-of-Federation + +![](images/1e903308383565e73ef6f8b38d8590906f1dc3eda97c6de36449546bd3d2df4b.jpg) + +![](images/e96643dea33a387e2e53c34335067bfb085fa2f84ec1cdfe62e13816b39b876a.jpg) + +![](images/5808f11a2b64f8d904f7f73e0b43b87e93e9f628f0cbca66730ba7a4246269fe.jpg) + +![](images/b31e9e7058cbe4c86c069188532002f87f8eaa4680d48c13dfff3c8f32e31927.jpg) +(b) + +![](images/8b6514d70fac09cda504ff90ab0228e87da68f5c64d1830c0c654a282a091266.jpg) +Figure 5. Reconstruction accuracy of FedAvg (w. FFt), Ours (w. Pro), and Ours (Full) versus (a) local epochs and (b) communication rounds under In-Federation and Out-of-Federation scenarios. +Figure 6. Analysis of the ratio $\gamma \%$ of the approximate null space in terms of PSNR, SSIM, and NMSE. + +respectively. As shown in Table 1, the proposed method only requires $0.11\mathrm{M}$ of communication, which is $6\%$ of the others, thereby addressing the issue $\mathbf{2}$ . However, although the classical federated MRI algorithms FL-MRCM [13] and FedMRI [9] can also achieve good accuracy, they ignored this clinical issue of federated MRI. Additionally, the reconstruction accuracy of FedAvg (w. FFt) [26], Ours (w. Pro), and Ours (Full) under different communication rounds is recorded in Fig. 5 (b), where the number of the local epochs is fixed at 10 for each method. As can be seen from the figure, our method converges within 10 rounds, while FedAvg (w. FFt) [26] converges after 30 rounds. Especially under the mechanism of updating the local prompts in the approximate null space of global prompts, our method provides higher reconstruction results. This is because our federated prompt learning mechanism prevents overfitting caused by the limited amount of local training data and offers a personalized scheme for each client. The results in Fig. 5 (b) + +confirm that our method provides the highest communication efficiency even on limited local data, thus relieving the issues 1 and 2. + +# 5. Conclusion + +This paper presented a federated visual prompt learning method, FedPR, to tackle the three issues in federated MRI reconstruction, i.e., limited communication bandwidth, insufficient local training data, and catastrophic forgetting. Benefiting from a powerful pre-trained model, our FedPR only learns prompts with a small number of learnable parameters. Additionally, FedPR greatly mitigates catastrophic forgetting by updating local prompts only in the approximate null space of global prompts, thereby preventing knowledge outside the local distribution from being overwritten. Experiments under In-Federation and Out-of-Federation scenarios demonstrate the superiority of FedPR in relieving the three issues of federated MRI reconstruction. + +Acknowledgements: This work was supported by the Agency for Science, Technology and Research (A*STAR) AME Programmatic Funds (Grant Number: A20H4b0141). This work was also supported by the AI Singapore Tech Challenge (Open-Theme) Funding Scheme (Award No.: AISG2-TC-2021-003). + +# References + +[1] brain-development.org. +[2] Hyojin Bahng, Ali Jahanian, Swami Sankaranarayanan, and Phillip Isola. Exploring visual prompts for adapting large-scale models, 2022. +[3] Hong-You Chen, Cheng-Hao Tu, Ziwei Li, Han-Wei Shen, and Wei-Lun Chao. 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Engineering, Shangdong University, China" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 183, + 200, + 410, + 213 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 183, + 200, + 410, + 213 + ], + "spans": [ + { + "bbox": [ + 183, + 200, + 410, + 213 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 183, + 200, + 410, + 213 + ], + "type": "text", + "content": "Harbin Institute of Technology, Harbin, China" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 118, + 216, + 474, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 118, + 216, + 474, + 228 + ], + "spans": [ + { + "bbox": [ + 118, + 216, + 474, + 228 + ], + "type": "text", + "content": "strawberry.feng0304@gmail.com, {xuxinx, liuyong}@ihpc.a-star.edu.sg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 195, + 229, + 392, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 195, + 229, + 392, + 240 + ], + "spans": [ + { + "bbox": [ + 195, + 229, + 392, + 240 + ], + "type": "text", + "content": "https://github.com/chunmeifeng/FedPR" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 143, + 269, + 191, + 281 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 269, + 191, + 281 + ], + "spans": [ + { + "bbox": [ + 143, + 269, + 191, + 281 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 294, + 290, + 570 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 294, + 290, + 570 + ], + "spans": [ + { + "bbox": [ + 47, + 294, + 290, + 570 + ], + "type": "text", + "content": "Federated Magnetic Resonance Imaging (MRI) reconstruction enables multiple hospitals to collaborate distributedly without aggregating local data, thereby protecting patient privacy. However, the data heterogeneity caused by different MRI protocols, insufficient local training data, and limited communication bandwidth inevitably impair global model convergence and updating. In this paper, we propose a new algorithm, FedPR, to learn federated visual prompts in the null space of global prompt for MRI reconstruction. FedPR is a new federated paradigm that adopts a powerful pre-trained model while only learning and communicating the prompts with few learnable parameters, thereby significantly reducing communication costs and achieving competitive performance on limited local data. Moreover, to deal with catastrophic forgetting caused by data heterogeneity, FedPR also updates efficient federated visual prompts that project the local prompts into an approximate null space of the global prompt, thereby suppressing the interference of gradients on the server performance. Extensive experiments on federated MRI show that FedPR significantly outperforms state-of-the-art FL algorithms with " + }, + { + "bbox": [ + 47, + 294, + 290, + 570 + ], + "type": "inline_equation", + "content": "< 6\\%" + }, + { + "bbox": [ + 47, + 294, + 290, + 570 + ], + "type": "text", + "content": " of communication costs when given the limited amount of local training data." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 590, + 128, + 602 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 590, + 128, + 602 + ], + "spans": [ + { + "bbox": [ + 47, + 590, + 128, + 602 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 610, + 287, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 610, + 287, + 694 + ], + "spans": [ + { + "bbox": [ + 47, + 610, + 287, + 694 + ], + "type": "text", + "content": "Federated Magnetic Resonance Imaging (MRI) reconstruction enables multiple hospitals to train a powerful global model in a distributed manner without sharing private data [7, 9, 13]. In federated MRI, each client (i.e., hospital) uses its local computing power, memory, and private data to train local models independently, while the server aggregates all the local models in each communica" + } + ] + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 331, + 254, + 523, + 381 + ], + "blocks": [ + { + "bbox": [ + 331, + 254, + 523, + 381 + ], + "lines": [ + { + "bbox": [ + 331, + 254, + 523, + 381 + ], + "spans": [ + { + "bbox": [ + 331, + 254, + 523, + 381 + ], + "type": "image", + "image_path": "c71ee1f0e0c0da547bb5107eee89af8d5c027e4bc0621d3cd973d689967ad3a4.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 309, + 384, + 541, + 396 + ], + "lines": [ + { + "bbox": [ + 309, + 384, + 541, + 396 + ], + "spans": [ + { + "bbox": [ + 309, + 384, + 541, + 396 + ], + "type": "text", + "content": "Figure 1. Illustration of the three key issues in federated MRI." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 401, + 545, + 425 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 401, + 545, + 425 + ], + "spans": [ + { + "bbox": [ + 305, + 401, + 545, + 425 + ], + "type": "text", + "content": "tion round and distributes the global model to each client again [26]." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 426, + 546, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 426, + 546, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 426, + 546, + 715 + ], + "type": "text", + "content": "Existing federated MRI reconstruction techniques usually improve federated learning (FL) by enhancing the aggregation process [9] and reducing the local parameter's variance [5, 13]. Such techniques require a large communication bandwidth and sufficient local training data. However, federated MRI often faces two issues, insufficient amount of local training data due to the difficulty of acquiring the ground-truth of MRI reconstruction [10, 11, 12] and limited communication bandwidth due to unbalanced regional development (see Fig. 1). To cope with the issue, pre-trained models have exhibited superior performance, and have shown to close the gap between federated and centralized performance [3, 28]. However, since the model parameters need to be shared between the client and the server for updating, the large number of parameters of pre-trained models will result in a huge communication cost. On contrary, prompt tuning has recently been suggested as a new fine-tuning paradigm by freezing the models and only learning a small number of learnable parameters in the input space [15, 31, 32]. Benefited from pre-trained models, only parameter-efficient prompts are required in learning and communication, and prompt tuning can be conducted with a limited number of samples, making it very appealing in tackling the above two issues (i.e.," + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 703, + 135, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 703, + 135, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 703, + 135, + 712 + ], + "type": "text", + "content": "*Corresponding author." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8064" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 162, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 162, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 162, + 83 + ], + "type": "inline_equation", + "content": "\\mathbf{1}" + }, + { + "bbox": [ + 47, + 72, + 162, + 83 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 72, + 162, + 83 + ], + "type": "inline_equation", + "content": "\\mathbf{2}" + }, + { + "bbox": [ + 47, + 72, + 162, + 83 + ], + "type": "text", + "content": " ) in federated MRI." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 84, + 287, + 360 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 84, + 287, + 360 + ], + "spans": [ + { + "bbox": [ + 47, + 84, + 287, + 360 + ], + "type": "text", + "content": "Besides, there is another critical issue for federated MRI, i.e., ⑧ catastrophic forgetting, caused by data heterogeneity due to the different imaging protocols of MRI scanners adopted by different clients [9, 39] (see Fig. 1). In the local update, the global model from the prior round tends to be overfitted to the local training data, leading to catastrophic forgetting. Analogous to continual learning, several techniques have been presented by introducing proper regularization terms in local models [4, 33, 39] or retaining previously acquired knowledge by knowledge distillation [14, 35, 38]. However, these strategies require seeking a balance between multiple losses and relying on proxy datasets. Instead, Adam-NSC mitigates catastrophic forgetting in continual learning with a new network parameter update rule, i.e., forces the network update to lie in the approximate null space of the input features of previous tasks at each layer [36]. However, the null space at feature level is built upon large local training data, which generally cannot be satisfied in federated MRI, i.e., the issue ①. Taking the issues ① and ⑧ into account, we suggest to optimize local prompts in the approximate null space of global prompts instead of input features, thereby preventing the loss of previously gained global knowledge." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 361, + 287, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 361, + 287, + 563 + ], + "spans": [ + { + "bbox": [ + 47, + 361, + 287, + 563 + ], + "type": "text", + "content": "In a nutshell, we explore a new FL paradigm, i.e., FedPR, to learn federated visual prompts for MRI reconstruction. To begin with, we pre-train the model on a large-scale public dataset. Given limited amount of local training data, visual prompt tuning is adopted to learn local prompts in a distributed manner. For the issues 1 and 2, federated visual prompts are introduced to learn a strong global model, where only local and global prompts are learnable and communicated. As for the issue 3, we perform singular value decomposition (SVD) on the uncentered covariance matrix of global prompts to obtain the approximate null space. FedPR tunes only the local parameters in the null space of global prompts, thereby well preserving the prior knowledge of previous rounds and resulting in low communication costs. In particular, FedPR achieves a " + }, + { + "bbox": [ + 47, + 361, + 287, + 563 + ], + "type": "inline_equation", + "content": ">4.5" + }, + { + "bbox": [ + 47, + 361, + 287, + 563 + ], + "type": "text", + "content": " dB gain in PSNR with less than " + }, + { + "bbox": [ + 47, + 361, + 287, + 563 + ], + "type": "inline_equation", + "content": "6\\%" + }, + { + "bbox": [ + 47, + 361, + 287, + 563 + ], + "type": "text", + "content": " of communication costs. To sum up, our contributions are as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 570, + 286, + 713 + ], + "type": "list", + "angle": 0, + "index": 5, + "blocks": [ + { + "bbox": [ + 47, + 570, + 286, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 570, + 286, + 640 + ], + "spans": [ + { + "bbox": [ + 47, + 570, + 286, + 640 + ], + "type": "text", + "content": "- We propose a federated visual prompt algorithm, FedPR, to solve the three key issues in federated MRI. By leveraging powerful pre-trained models and freezing backbone networks in FL, only a small amount of parameters in the input space are trainable, thereby reducing communication costs." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 642, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 642, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 642, + 286, + 713 + ], + "type": "text", + "content": "- We explore how to alleviate catastrophic forgetting in FL while reducing communication costs. By optimizing local parameters only in the null space of global prompts, FedPR well preserves the previously acquired global knowledge in each round, maintaining competitive performance with only a few local data." + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 72, + 545, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 545, + 133 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 545, + 133 + ], + "type": "text", + "content": "- We evaluate the performance of FedPR for federated MRI reconstruction. In comparison to the state-of-the-art FL methods, FedPR achieves superior performance in complex scenarios, e.g., less local data, lower communication costs, and faster convergence." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 145, + 392, + 158 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 145, + 392, + 158 + ], + "spans": [ + { + "bbox": [ + 306, + 145, + 392, + 158 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 163, + 545, + 424 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 163, + 545, + 424 + ], + "spans": [ + { + "bbox": [ + 304, + 163, + 545, + 424 + ], + "type": "text", + "content": "Federated MRI Reconstruction. MRI reconstruction refers to reconstructing images without aliasing artifacts from undersampled " + }, + { + "bbox": [ + 304, + 163, + 545, + 424 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 163, + 545, + 424 + ], + "type": "text", + "content": "-space data [6, 8, 12, 37, 41]. However, existing MRI reconstruction techniques are based on large-scale paired data, which is not only labor-intensive but also violates patient privacy [9]. Driven by these realistic problems, a few FL-based methods for MRI reconstruction have been proposed [5, 9, 13]. Guo et al. reduced data heterogeneity by iteratively aligning the data distribution between source and target clients [13]. Feng et al. proposed a personalized FL reconstruction scheme and introduced a weighted contrast regularization term to correct the update direction of global generalization [9]. However, these schemes either require frequent communication or are built on a large amount of local data. As a result, these techniques will produce sub-optimal solutions for MRI reconstruction when there is limited bandwidth and insufficient local training data. In contrast to these works, we build a federated MRI model upon a strong pre-trained model by updating and communicating only a small portion of parameters for each client using limited local data, achieving competitive results." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 426, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 426, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 426, + 545, + 713 + ], + "type": "text", + "content": "Catastrophic Forgetting in FL. Due to the heterogeneous data distributions of different tasks in continual learning, when the network is fitted to the current task, the model parameters typically deviate from the areas where the previous knowledge is expected to be preserved [17]. Therefore, catastrophic forgetting is a fundamental challenge of continual learning. Similarly, catastrophic forgetting also affects FL [14, 19, 39]. When the client receives the global model and continues to update locally, it will cause the global model to forget the knowledge of the previous round due to the data heterogeneity across clients [19]. As a result, existing FL techniques that address catastrophic forgetting are designed by referring to continual learning. For example, knowledge distillation-based FL methods maintain previously gained knowledge, but this method strongly relies on proxy data [14, 35, 38]; regularization-based FL methods regularize locally trained parameters, but they require finding a compromise between loss terms [4, 33, 39]. All these studies are built on classification tasks and cannot be directly extended to MRI reconstruction. Inspired by the success of null space in continual learning [18, 23, 36], we try to update the local prompt in the approximate null space of global prompts, thereby preserving the knowledge acquired by the global model in the previous round and avoid" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8065" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 63, + 182, + 223 + ], + "blocks": [ + { + "bbox": [ + 61, + 63, + 182, + 223 + ], + "lines": [ + { + "bbox": [ + 61, + 63, + 182, + 223 + ], + "spans": [ + { + "bbox": [ + 61, + 63, + 182, + 223 + ], + "type": "image", + "image_path": "49dbd40481e5ce7b8ff62315081544b4713a640ddea149e3ef9744b02a6a8735.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 64, + 226, + 179, + 236 + ], + "lines": [ + { + "bbox": [ + 64, + 226, + 179, + 236 + ], + "spans": [ + { + "bbox": [ + 64, + 226, + 179, + 236 + ], + "type": "text", + "content": "(a) Initialization and local update" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 198, + 62, + 535, + 224 + ], + "blocks": [ + { + "bbox": [ + 198, + 62, + 535, + 224 + ], + "lines": [ + { + "bbox": [ + 198, + 62, + 535, + 224 + ], + "spans": [ + { + "bbox": [ + 198, + 62, + 535, + 224 + ], + "type": "image", + "image_path": "e7f3fbb295c11848b735f213b931378776230d91d272f1a754168f05a481c7a5.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 219, + 226, + 317, + 236 + ], + "lines": [ + { + "bbox": [ + 219, + 226, + 317, + 236 + ], + "spans": [ + { + "bbox": [ + 219, + 226, + 317, + 236 + ], + "type": "text", + "content": "(b) Federated visual prompt" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 416, + 225, + 479, + 236 + ], + "lines": [ + { + "bbox": [ + 416, + 225, + 479, + 236 + ], + "spans": [ + { + "bbox": [ + 416, + 225, + 479, + 236 + ], + "type": "text", + "content": "(c) Server update" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 241, + 547, + 285 + ], + "lines": [ + { + "bbox": [ + 46, + 241, + 547, + 285 + ], + "spans": [ + { + "bbox": [ + 46, + 241, + 547, + 285 + ], + "type": "text", + "content": "Figure 2. Illustration of our FedPR method. (a) For each client, the backbone model is pre-trained on massive data and fine-tuned via prompt (see Sec. 3.2). (b) Federated visual prompt is executed by updating the local prompt of each client only in the approximate null space of global prompts while preserving the previously acquired global knowledge (see Sec. 3.3). (c) Server update by aggregating local prompts." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 289, + 160, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 289, + 160, + 300 + ], + "spans": [ + { + "bbox": [ + 47, + 289, + 160, + 300 + ], + "type": "text", + "content": "ing catastrophic forgetting." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 300, + 290, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 300, + 290, + 504 + ], + "spans": [ + { + "bbox": [ + 46, + 300, + 290, + 504 + ], + "type": "text", + "content": "Prompt Learning. Prompt tuning was initially proposed to enable pre-trained language models to \"understand\" downstream tasks by adding trainable tokens to the input text [24]. For example, Jia et al. achieved good performance on downstream tasks by introducing a small number of learnable tokens into the input space and keeping the backbone frozen [15]. Hyojin et al. suggested to modify pixel space for the frozen visual models [2]. Nie et al. proposed a unified prompt tuning framework that performs on different CNN and transformer-based architectures by training only a few additional parameters [29]. Although these works have made progress on various visual tasks, prompt is still limited to centralized systems, and the effectiveness of prompt in distributed framework remains uninvestigated. Therefore, this work focuses on how to learn a federated visual prompt to effectively tackle the three key problems in federated MRI reconstruction, i.e., the issues ①-③." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 510, + 130, + 523 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 510, + 130, + 523 + ], + "spans": [ + { + "bbox": [ + 47, + 510, + 130, + 523 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 526, + 217, + 538 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 526, + 217, + 538 + ], + "spans": [ + { + "bbox": [ + 47, + 526, + 217, + 538 + ], + "type": "text", + "content": "3.1. Federated MRI Reconstruction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 541, + 287, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 541, + 287, + 601 + ], + "spans": [ + { + "bbox": [ + 46, + 541, + 287, + 601 + ], + "type": "text", + "content": "MRI reconstruction is an inverse problem of recovering an artifact-free image " + }, + { + "bbox": [ + 46, + 541, + 287, + 601 + ], + "type": "inline_equation", + "content": "\\mathbf{y}" + }, + { + "bbox": [ + 46, + 541, + 287, + 601 + ], + "type": "text", + "content": " from its undersampled observation " + }, + { + "bbox": [ + 46, + 541, + 287, + 601 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 46, + 541, + 287, + 601 + ], + "type": "text", + "content": " that can reduce the online collection time and improve the patient experience [34, 37, 40]. Formally, such undersampling process can be expressed as" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 107, + 602, + 287, + 616 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 602, + 287, + 616 + ], + "spans": [ + { + "bbox": [ + 107, + 602, + 287, + 616 + ], + "type": "interline_equation", + "content": "\\mathbf {x} = \\mathcal {F} ^ {- 1} (\\mathcal {M} \\odot \\mathcal {F} (\\mathbf {y}) + \\epsilon), \\tag {1}", + "image_path": "6c9542bf3ad7c5660bec4656d7fa35103e2d415a13b078a1097f859bdc1d7da9.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 617, + 287, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 287, + 653 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 287, + 653 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 617, + 287, + 653 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 46, + 617, + 287, + 653 + ], + "type": "text", + "content": " is multi-dimensional Fourier transform, " + }, + { + "bbox": [ + 46, + 617, + 287, + 653 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 46, + 617, + 287, + 653 + ], + "type": "text", + "content": " is the measurement noise, and " + }, + { + "bbox": [ + 46, + 617, + 287, + 653 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 46, + 617, + 287, + 653 + ], + "type": "text", + "content": " is the binary mask operator to undersample the data points in the Fourier space." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 654, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 288, + 713 + ], + "type": "text", + "content": "The centralized approach violates patient privacy protection roles because it requires collecting large amounts of training data from different hospitals. As a remedy, Federated MRI has been suggested by deploying MRI reconstruction in a distributed manner [9, 13]. Suppose there are " + }, + { + "bbox": [ + 46, + 654, + 288, + 713 + ], + "type": "inline_equation", + "content": "K" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 289, + 546, + 359 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 289, + 546, + 359 + ], + "spans": [ + { + "bbox": [ + 304, + 289, + 546, + 359 + ], + "type": "text", + "content": "hospitals (local clients). The private data of all hospitals can be expressed as " + }, + { + "bbox": [ + 304, + 289, + 546, + 359 + ], + "type": "inline_equation", + "content": "\\mathcal{D} = \\{\\mathcal{D}^1,\\mathcal{D}^2,\\dots ,\\mathcal{D}^K\\}" + }, + { + "bbox": [ + 304, + 289, + 546, + 359 + ], + "type": "text", + "content": ", where each contains limited pairs of undersampled samples " + }, + { + "bbox": [ + 304, + 289, + 546, + 359 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i" + }, + { + "bbox": [ + 304, + 289, + 546, + 359 + ], + "type": "text", + "content": " and fully-sampled images " + }, + { + "bbox": [ + 304, + 289, + 546, + 359 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_i" + }, + { + "bbox": [ + 304, + 289, + 546, + 359 + ], + "type": "text", + "content": ". Federated MRI aims to learn a global model from the whole dataset " + }, + { + "bbox": [ + 304, + 289, + 546, + 359 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 304, + 289, + 546, + 359 + ], + "type": "text", + "content": " in a distributed manner, which can be described as" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 355, + 361, + 545, + 393 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 355, + 361, + 545, + 393 + ], + "spans": [ + { + "bbox": [ + 355, + 361, + 545, + 393 + ], + "type": "interline_equation", + "content": "\\arg \\min _ {\\boldsymbol {w}} \\mathcal {L} (\\boldsymbol {w}) = \\sum_ {k = 1} ^ {K} \\frac {| \\mathcal {D} ^ {k} |}{| \\mathcal {D} |} \\mathcal {L} _ {k} (\\boldsymbol {w}), \\tag {2}", + "image_path": "30e41bb8e7633e2c1cb013c18fb67bf106f5593c8d7e5ab313e32859375592ff.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 395, + 545, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 395, + 545, + 418 + ], + "spans": [ + { + "bbox": [ + 304, + 395, + 545, + 418 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 395, + 545, + 418 + ], + "type": "inline_equation", + "content": "|\\mathcal{D}|" + }, + { + "bbox": [ + 304, + 395, + 545, + 418 + ], + "type": "text", + "content": " denotes the number of samples in " + }, + { + "bbox": [ + 304, + 395, + 545, + 418 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 304, + 395, + 545, + 418 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 395, + 545, + 418 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_k(\\boldsymbol{w})" + }, + { + "bbox": [ + 304, + 395, + 545, + 418 + ], + "type": "text", + "content": " is the empirical loss of client " + }, + { + "bbox": [ + 304, + 395, + 545, + 418 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 395, + 545, + 418 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 353, + 422, + 545, + 435 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 353, + 422, + 545, + 435 + ], + "spans": [ + { + "bbox": [ + 353, + 422, + 545, + 435 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {k} (\\boldsymbol {w}) = \\mathbf {E} _ {(\\mathbf {x}, \\mathbf {y}) \\in \\mathcal {D} ^ {k}} \\ell_ {k} (f (\\mathbf {x}; \\boldsymbol {w})) \\tag {3}", + "image_path": "273444f2327b348692a7cf8d175fca522a13ae75a0cc0c64df7ba38124276e72.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 438, + 547, + 475 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 438, + 547, + 475 + ], + "spans": [ + { + "bbox": [ + 304, + 438, + 547, + 475 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 438, + 547, + 475 + ], + "type": "inline_equation", + "content": "\\ell_{k}" + }, + { + "bbox": [ + 304, + 438, + 547, + 475 + ], + "type": "text", + "content": " represents the local loss for MRI reconstruction, e.g., " + }, + { + "bbox": [ + 304, + 438, + 547, + 475 + ], + "type": "inline_equation", + "content": "L_{1}" + }, + { + "bbox": [ + 304, + 438, + 547, + 475 + ], + "type": "text", + "content": " loss. After training, the reconstructed image " + }, + { + "bbox": [ + 304, + 438, + 547, + 475 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{y}}" + }, + { + "bbox": [ + 304, + 438, + 547, + 475 + ], + "type": "text", + "content": " can be produced by " + }, + { + "bbox": [ + 304, + 438, + 547, + 475 + ], + "type": "inline_equation", + "content": "f(\\mathbf{x};\\boldsymbol {w})" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 481, + 460, + 495 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 481, + 460, + 495 + ], + "spans": [ + { + "bbox": [ + 306, + 481, + 460, + 495 + ], + "type": "text", + "content": "3.2. Learning Federated Prompt" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 498, + 545, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 545, + 592 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 545, + 592 + ], + "type": "text", + "content": "As mentioned in Sec. 1, there are three key issues, i.e., 1-3, with the existing federated MRI algorithms. To tackle the issue 2, we freeze the backbone of the pre-trained model while only tuning and communicating a few learnable parameters for the clients and server. More importantly, it enables the model to achieve very competitive results on limited local data, thereby providing an effective solution to issue 1." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "text", + "content": "As shown in Fig. 2, given a pre-trained model with parameters " + }, + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "text", + "content": ", we introduce a set of continuous embeddings " + }, + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "inline_equation", + "content": "P = \\{p_1, p_2, \\dots, p_l\\}" + }, + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "text", + "content": " as the prompts in the input space of each layer [15], where " + }, + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "text", + "content": " is the number of prompts. Thus, the overall parameters can be expressed as " + }, + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\boldsymbol{w} = \\{P, \\theta\\}" + }, + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "text", + "content": ". Suppose there are " + }, + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "text", + "content": " rounds of communication, each round contains " + }, + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "text", + "content": " local updates. During the local update, for the " + }, + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "text", + "content": "-th client, only the client-specific prompts " + }, + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "inline_equation", + "content": "P_k" + }, + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "text", + "content": " are learnable and communicated while the backbone network is frozen. Therefore, Eq. (2) can be rewritten as:" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8066" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 62, + 289, + 228 + ], + "blocks": [ + { + "bbox": [ + 48, + 62, + 289, + 228 + ], + "lines": [ + { + "bbox": [ + 48, + 62, + 289, + 228 + ], + "spans": [ + { + "bbox": [ + 48, + 62, + 289, + 228 + ], + "type": "image", + "image_path": "6aa9308d7a76fd86981d6b134000b925c23644744698cfa3c78ccc22175d3b80.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 231, + 288, + 255 + ], + "lines": [ + { + "bbox": [ + 47, + 231, + 288, + 255 + ], + "spans": [ + { + "bbox": [ + 47, + 231, + 288, + 255 + ], + "type": "text", + "content": "Figure 3. Illustration of federated visual prompt for updating local prompts in the null space of global prompts." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 83, + 270, + 287, + 302 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 270, + 287, + 302 + ], + "spans": [ + { + "bbox": [ + 83, + 270, + 287, + 302 + ], + "type": "interline_equation", + "content": "\\boldsymbol {P} _ {k} = \\arg \\min _ {\\boldsymbol {P}} \\mathcal {L} (\\boldsymbol {P}) = \\sum_ {k = 1} ^ {K} \\frac {\\left| \\mathcal {D} ^ {k} \\right|}{\\left| \\mathcal {D} \\right|} \\mathcal {L} _ {k} (\\boldsymbol {P}), \\tag {4}", + "image_path": "63fd08af8318e3c8479ebe706d49ca24c43824c51c868a16ab8e69eac19e900e.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 303, + 287, + 326 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 303, + 287, + 326 + ], + "spans": [ + { + "bbox": [ + 47, + 303, + 287, + 326 + ], + "type": "text", + "content": "where the empirical loss for prompt tuning of client " + }, + { + "bbox": [ + 47, + 303, + 287, + 326 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 47, + 303, + 287, + 326 + ], + "type": "text", + "content": " can be expressed as" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 89, + 328, + 287, + 342 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 89, + 328, + 287, + 342 + ], + "spans": [ + { + "bbox": [ + 89, + 328, + 287, + 342 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {k} (\\boldsymbol {P}) = \\mathbf {E} _ {(\\mathbf {x}, \\mathbf {y}) \\in \\mathcal {D} ^ {k}} \\ell_ {k} (f (\\mathbf {x}; \\boldsymbol {P}, \\boldsymbol {\\theta})). \\tag {5}", + "image_path": "b9c46612c7cd6158efd10e361a19b3d22a26ae266fd49eb0fd19e9675ff44039.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 346, + 287, + 405 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 346, + 287, + 405 + ], + "spans": [ + { + "bbox": [ + 47, + 346, + 287, + 405 + ], + "type": "text", + "content": "Benefited from pre-trained models, federated prompt tuning can be both parameter- and communication-efficient and effective in achieving competitive results with a small amount of local data, thereby serving as a favorable solution to the issues 1 and 2." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 406, + 287, + 442 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 406, + 287, + 442 + ], + "spans": [ + { + "bbox": [ + 47, + 406, + 287, + 442 + ], + "type": "text", + "content": "Local Update Step: In each communication round " + }, + { + "bbox": [ + 47, + 406, + 287, + 442 + ], + "type": "inline_equation", + "content": "z = \\{1,2,\\dots,Z\\}" + }, + { + "bbox": [ + 47, + 406, + 287, + 442 + ], + "type": "text", + "content": ", the clients are optimized using the following update rules with a learning rate of " + }, + { + "bbox": [ + 47, + 406, + 287, + 442 + ], + "type": "inline_equation", + "content": "\\eta_{k}" + }, + { + "bbox": [ + 47, + 406, + 287, + 442 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 89, + 444, + 287, + 460 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 89, + 444, + 287, + 460 + ], + "spans": [ + { + "bbox": [ + 89, + 444, + 287, + 460 + ], + "type": "interline_equation", + "content": "\\boldsymbol {P} _ {k} ^ {z, t + 1} \\leftarrow \\boldsymbol {P} _ {k} ^ {z, t} - \\eta_ {k} \\nabla \\ell_ {k} \\left(\\mathbf {x} ^ {k}; \\boldsymbol {P} _ {k} ^ {z, t}\\right), \\tag {6}", + "image_path": "962945a230712aee96bf8c7c1222631f8ba5efc72ca384cdd0ff65a3345cffed.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 460, + 253, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 460, + 253, + 472 + ], + "spans": [ + { + "bbox": [ + 47, + 460, + 253, + 472 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 460, + 253, + 472 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 47, + 460, + 253, + 472 + ], + "type": "text", + "content": " denotes the " + }, + { + "bbox": [ + 47, + 460, + 253, + 472 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 47, + 460, + 253, + 472 + ], + "type": "text", + "content": "-th update of the local clients." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 472, + 287, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 472, + 287, + 519 + ], + "spans": [ + { + "bbox": [ + 47, + 472, + 287, + 519 + ], + "type": "text", + "content": "Server Update Step: After a round of local updates, all participating clients send their updated prompts " + }, + { + "bbox": [ + 47, + 472, + 287, + 519 + ], + "type": "inline_equation", + "content": "\\pmb{P}_{k}^{z}" + }, + { + "bbox": [ + 47, + 472, + 287, + 519 + ], + "type": "text", + "content": " to the server performing aggregation. Such process can be expressed as follows" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 119, + 514, + 287, + 547 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 119, + 514, + 287, + 547 + ], + "spans": [ + { + "bbox": [ + 119, + 514, + 287, + 547 + ], + "type": "interline_equation", + "content": "\\mathbf {P} _ {g} ^ {z + 1} \\leftarrow \\sum_ {k = 1} ^ {K} \\frac {\\left| \\mathcal {D} ^ {k} \\right|}{\\left| \\mathcal {D} \\right|} \\mathbf {P} _ {k} ^ {z}, \\tag {7}", + "image_path": "f65d04d3733149f31fab8d72d25f3f215ebc42668b50148295826927fca0605e.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 548, + 287, + 621 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 548, + 287, + 621 + ], + "spans": [ + { + "bbox": [ + 47, + 548, + 287, + 621 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 548, + 287, + 621 + ], + "type": "inline_equation", + "content": "P_{g}^{z + 1}" + }, + { + "bbox": [ + 47, + 548, + 287, + 621 + ], + "type": "text", + "content": " denotes the global prompts of round " + }, + { + "bbox": [ + 47, + 548, + 287, + 621 + ], + "type": "inline_equation", + "content": "z + 1" + }, + { + "bbox": [ + 47, + 548, + 287, + 621 + ], + "type": "text", + "content": ". To sum up, the issue " + }, + { + "bbox": [ + 47, + 548, + 287, + 621 + ], + "type": "inline_equation", + "content": "\\mathbf{0}" + }, + { + "bbox": [ + 47, + 548, + 287, + 621 + ], + "type": "text", + "content": " can be largely mitigated because there are only a small number of learnable parameters " + }, + { + "bbox": [ + 47, + 548, + 287, + 621 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 47, + 548, + 287, + 621 + ], + "type": "text", + "content": " communicated between the server and local clients. After " + }, + { + "bbox": [ + 47, + 548, + 287, + 621 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 47, + 548, + 287, + 621 + ], + "type": "text", + "content": " rounds of communication, we can get a robust global model parameterized by " + }, + { + "bbox": [ + 47, + 548, + 287, + 621 + ], + "type": "inline_equation", + "content": "P_{g}" + }, + { + "bbox": [ + 47, + 548, + 287, + 621 + ], + "type": "text", + "content": " without sharing local private data." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 627, + 261, + 640 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 627, + 261, + 640 + ], + "spans": [ + { + "bbox": [ + 47, + 627, + 261, + 640 + ], + "type": "text", + "content": "3.3. Local Updating in Prompting Null Space" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 642, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 642, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 642, + 288, + 714 + ], + "type": "text", + "content": "The local update mechanism in Eq. (6), however, suffers from the issue ⑧, i.e., catastrophic forgetting, due to data heterogeneity of different clients. Inspired by the continual learning method Adam-NSC [36] that sequentially optimizes network parameters in the null space at feature level, we suggest to optimize the local model in the null space of" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 312, + 75, + 400, + 87 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 75, + 400, + 87 + ], + "spans": [ + { + "bbox": [ + 312, + 75, + 400, + 87 + ], + "type": "text", + "content": "Algorithm 1: FedPR" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 318, + 89, + 529, + 148 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 89, + 529, + 148 + ], + "spans": [ + { + "bbox": [ + 318, + 89, + 529, + 148 + ], + "type": "text", + "content": "Input: Private datasets from " + }, + { + "bbox": [ + 318, + 89, + 529, + 148 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 318, + 89, + 529, + 148 + ], + "type": "text", + "content": " clients: " + }, + { + "bbox": [ + 318, + 89, + 529, + 148 + ], + "type": "inline_equation", + "content": "\\mathcal{D}^1, \\mathcal{D}^2, \\ldots, \\mathcal{D}^K" + }, + { + "bbox": [ + 318, + 89, + 529, + 148 + ], + "type": "text", + "content": ", local updates " + }, + { + "bbox": [ + 318, + 89, + 529, + 148 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 318, + 89, + 529, + 148 + ], + "type": "text", + "content": ", communication rounds " + }, + { + "bbox": [ + 318, + 89, + 529, + 148 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 318, + 89, + 529, + 148 + ], + "type": "text", + "content": ", pre-trained model parameters " + }, + { + "bbox": [ + 318, + 89, + 529, + 148 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 318, + 89, + 529, + 148 + ], + "type": "text", + "content": ", prompt embeddings " + }, + { + "bbox": [ + 318, + 89, + 529, + 148 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 318, + 89, + 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Specifically, we train the local model in the approximate null space of the global prompts in a distributed way, preventing knowledge outside the local distribution from being overwritten and resulting in catastrophic forgetting. In comparison to [36], approximating the null space of global prompts instead of features does not require a large amount of local data and not increase the communication cost, thus offering a feasible way to tackle the three issues 1-8 in federated MRI." + } + ] + } + ], + "index": 42 + }, + { + "bbox": [ + 305, + 601, + 545, + 626 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 601, + 545, + 626 + ], + "spans": [ + { + "bbox": [ + 305, + 601, + 545, + 626 + ], + "type": "text", + "content": "As shown in Fig. 3, we first compute the uncentered covariance matrix of " + }, + { + "bbox": [ + 305, + 601, + 545, + 626 + ], + "type": "inline_equation", + "content": "z + 1" + }, + { + "bbox": [ + 305, + 601, + 545, + 626 + ], + "type": "text", + "content": " round global prompt " + }, + { + "bbox": [ + 305, + 601, + 545, + 626 + ], + "type": "inline_equation", + "content": "P_g^{z + 1}" + }, + { + "bbox": [ + 305, + 601, + 545, + 626 + ], + "type": "text", + 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According to principal component analysis (PCA), " + }, + { + "bbox": [ + 47, + 141, + 287, + 264 + ], + "type": "inline_equation", + "content": "U_{1}^{z + 1}" + }, + { + "bbox": [ + 47, + 141, + 287, + 264 + ], + "type": "text", + "content": " can be considered as principal components, which contain the global knowledge that has been captured in the previous round. Thus, we have " + }, + { + "bbox": [ + 47, + 141, + 287, + 264 + ], + "type": "inline_equation", + "content": "\\Sigma_g^{z + 1} \\approx U_1^{z + 1}\\Lambda_1^{z + 1}\\left(U_1^{z + 1}\\right)^\\top" + }, + { + "bbox": [ + 47, + 141, + 287, + 264 + ], + "type": "text", + "content": ". And the range space of " + }, + { + "bbox": [ + 47, + 141, + 287, + 264 + ], + "type": "inline_equation", + "content": "U_{2}^{z + 1}" + }, + { + "bbox": [ + 47, + 141, + 287, + 264 + ], + "type": "text", + "content": " can be denoted as the approximate null space of " + }, + { + "bbox": [ + 47, + 141, + 287, + 264 + ], + "type": "inline_equation", + "content": "\\Sigma_g^{z + 1}" + }, + { + "bbox": [ + 47, + 141, + 287, + 264 + ], + "type": "text", + "content": " [36]. In our implementation, we introduce a " + }, + { + "bbox": [ + 47, + 141, + 287, + 264 + ], + "type": "inline_equation", + "content": "\\gamma \\%" + }, + { + "bbox": [ + 47, + 141, + 287, + 264 + ], + "type": "text", + "content": " to control " + }, + { + "bbox": [ + 47, + 141, + 287, + 264 + ], + "type": "inline_equation", + "content": "U_{2}^{z + 1}" + }, + { + "bbox": [ + 47, + 141, + 287, + 264 + ], + "type": "text", + "content": " by selecting the last " + }, + { + "bbox": [ + 47, + 141, + 287, + 264 + ], + "type": "inline_equation", + "content": "\\gamma \\%" + }, + { + "bbox": [ + 47, + 141, + 287, + 264 + ], + "type": "text", + "content": " of singular values in " + }, + { + "bbox": [ + 47, + 141, + 287, + 264 + ], + "type": "inline_equation", + "content": "\\Lambda_2^{z + 1}" + }, + { + "bbox": [ + 47, + 141, + 287, + 264 + ], + "type": "text", + "content": " to constitute " + }, + { + "bbox": [ + 47, + 141, + 287, + 264 + ], + "type": "inline_equation", + "content": "U_{2}^{z + 1}" + }, + { + "bbox": [ + 47, + 141, + 287, + 264 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 265, + 287, + 339 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 265, + 287, + 339 + ], + "spans": [ + { + "bbox": [ + 47, + 265, + 287, + 339 + ], + "type": "text", + "content": "To tackle the issue " + }, + { + "bbox": [ + 47, + 265, + 287, + 339 + ], + "type": "inline_equation", + "content": "\\bullet" + }, + { + "bbox": [ + 47, + 265, + 287, + 339 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 265, + 287, + 339 + ], + "type": "inline_equation", + "content": "P_{k}^{z}" + }, + { + "bbox": [ + 47, + 265, + 287, + 339 + ], + "type": "text", + "content": " can be projected into the approximate null space of " + }, + { + "bbox": [ + 47, + 265, + 287, + 339 + ], + "type": "inline_equation", + "content": "\\Sigma_{g}^{z + 1}" + }, + { + "bbox": [ + 47, + 265, + 287, + 339 + ], + "type": "text", + "content": " to get the updated parameters, while the principal components " + }, + { + "bbox": [ + 47, + 265, + 287, + 339 + ], + "type": "inline_equation", + "content": "U_{1}^{z + 1}" + }, + { + "bbox": [ + 47, + 265, + 287, + 339 + ], + "type": "text", + "content": " containing the global knowledge from the previous round are preserved. Thus, the updated parameters " + }, + { + "bbox": [ + 47, + 265, + 287, + 339 + ], + "type": "inline_equation", + "content": "\\Delta P_{k}^{z}" + }, + { + "bbox": [ + 47, + 265, + 287, + 339 + ], + "type": "text", + "content": " can be optimized in the null space of " + }, + { + "bbox": [ + 47, + 265, + 287, + 339 + ], + "type": "inline_equation", + "content": "\\Sigma_{g}^{z + 1}" + }, + { + "bbox": [ + 47, + 265, + 287, + 339 + ], + "type": "text", + "content": " by" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 107, + 340, + 287, + 356 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 340, + 287, + 356 + ], + "spans": [ + { + "bbox": [ + 107, + 340, + 287, + 356 + ], + "type": "interline_equation", + "content": "\\Delta \\boldsymbol {P} _ {k} ^ {z} = \\boldsymbol {U} _ {2} ^ {z + 1} \\left(\\boldsymbol {U} _ {2} ^ {z + 1}\\right) ^ {\\top} \\boldsymbol {P} _ {k} ^ {z}, \\tag {11}", + "image_path": "56b9d180e63879910e1bcc58e82d9a8472562c19c5e650d8814cf91e9acdb648.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 358, + 287, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 358, + 287, + 384 + ], + "spans": [ + { + "bbox": [ + 47, + 358, + 287, + 384 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 358, + 287, + 384 + ], + "type": "inline_equation", + "content": "\\boldsymbol{U}_2^{t+1}(\\boldsymbol{U}_2^{t+1})^\\top" + }, + { + "bbox": [ + 47, + 358, + 287, + 384 + ], + "type": "text", + "content": " is the projection operator [27]. Formally, the local update step of Eq. (6) can be rewritten as" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 107, + 388, + 287, + 403 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 388, + 287, + 403 + ], + "spans": [ + { + "bbox": [ + 107, + 388, + 287, + 403 + ], + "type": "interline_equation", + "content": "\\hat {\\boldsymbol {P}} _ {k} ^ {z, t + 1} \\leftarrow \\boldsymbol {P} _ {k} ^ {z, t} - \\eta_ {k} \\Delta \\boldsymbol {P} _ {k} ^ {z, t}. \\tag {12}", + "image_path": "07e94d415e14ee745cd6bbdf762187957c1856d4d50f7449e4dc4da64997955c.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 405, + 268, + 417 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 405, + 268, + 417 + ], + "spans": [ + { + "bbox": [ + 47, + 405, + 268, + 417 + ], + "type": "text", + "content": "The detailed FedPR algorithm is given in Algorithm 1." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 429, + 128, + 441 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 429, + 128, + 441 + ], + "spans": [ + { + "bbox": [ + 47, + 429, + 128, + 441 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 448, + 163, + 460 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 448, + 163, + 460 + ], + "spans": [ + { + "bbox": [ + 47, + 448, + 163, + 460 + ], + "type": "text", + "content": "4.1. Experimental Setup" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 463, + 287, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 463, + 287, + 569 + ], + "spans": [ + { + "bbox": [ + 46, + 463, + 287, + 569 + ], + "type": "text", + "content": "Implementation Details. Our method is trained by Pytorch with one NVIDIA Tesla V100 GPU and 32GB of memory. We use Adam as the optimizer, with a momentum of 0.9 and weight decay of 0.0005. The models are trained with 50 communication rounds and 10 local epochs for each round. We set the batch size and initial learning rate to 8 and " + }, + { + "bbox": [ + 46, + 463, + 287, + 569 + ], + "type": "inline_equation", + "content": "1 \\times 10^{-1}" + }, + { + "bbox": [ + 46, + 463, + 287, + 569 + ], + "type": "text", + "content": ", respectively. The hyperparameter " + }, + { + "bbox": [ + 46, + 463, + 287, + 569 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 46, + 463, + 287, + 569 + ], + "type": "text", + "content": " is empirically set to " + }, + { + "bbox": [ + 46, + 463, + 287, + 569 + ], + "type": "inline_equation", + "content": "80\\%" + }, + { + "bbox": [ + 46, + 463, + 287, + 569 + ], + "type": "text", + "content": ". The prompt embeddings are added with a size of " + }, + { + "bbox": [ + 46, + 463, + 287, + 569 + ], + "type": "inline_equation", + "content": "8 \\times 20 \\times 256" + }, + { + "bbox": [ + 46, + 463, + 287, + 569 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 570, + 287, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 287, + 666 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 287, + 666 + ], + "type": "text", + "content": "Datasets. We use fastMRI1, the largest publicly available MRI dataset, to train the pre-training model, with Swin Transformers and a standard ConvNet head serving as the backbone of our experiments [25]. We note that the mean and std of BN layer in the head are also shared with the server to update the original statistical properties. For the clients, we employ four datasets with a size of " + }, + { + "bbox": [ + 46, + 570, + 287, + 666 + ], + "type": "inline_equation", + "content": "320 \\times 320" + }, + { + "bbox": [ + 46, + 570, + 287, + 666 + ], + "type": "text", + "content": ", including FeTS2 [30], " + }, + { + "bbox": [ + 46, + 570, + 287, + 666 + ], + "type": "inline_equation", + "content": "\\mathbf{IXI}^3" + }, + { + "bbox": [ + 46, + 570, + 287, + 666 + ], + "type": "text", + "content": " [1], and two clinical datasets," + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 72, + 545, + 287 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 545, + 287 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 545, + 287 + ], + "type": "text", + "content": "to comprise our local data. In our experiments, we divide them into 15 clients according to the acquiring institutions, i.e., FeTS is divided into 10 clients with only 120, 304, 304, 240, 160, 160, 280, 224, 264, and 184 images, respectively; IXI is divided into 3 clients with only 360, 328, and 296 images, respectively; two clinical datasets collected from the United Imaging Healthcare uMR 790 scanner and 3T Siemens Magnetom Skyra system form two clients with 432 and 360 images, respectively. The input data of each client employs a " + }, + { + "bbox": [ + 306, + 72, + 545, + 287 + ], + "type": "inline_equation", + "content": "1D" + }, + { + "bbox": [ + 306, + 72, + 545, + 287 + ], + "type": "text", + "content": " random sampling pattern with " + }, + { + "bbox": [ + 306, + 72, + 545, + 287 + ], + "type": "inline_equation", + "content": "3 \\times" + }, + { + "bbox": [ + 306, + 72, + 545, + 287 + ], + "type": "text", + "content": " acceleration. We note that our clients have only a small number of images. In comparison, FedMRI [9] and FL-MRCM [13] require thousands to tens of thousands of images. For In-Federation evaluation, we divide each dataset with a ratio of " + }, + { + "bbox": [ + 306, + 72, + 545, + 287 + ], + "type": "inline_equation", + "content": "7:3" + }, + { + "bbox": [ + 306, + 72, + 545, + 287 + ], + "type": "text", + "content": " for local train/test. For Out-of-Federation evaluation, we use the test set of FeTS as our test set because it comes from a separate institution with a quite different distribution." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 288, + 545, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 288, + 545, + 598 + ], + "spans": [ + { + "bbox": [ + 305, + 288, + 545, + 598 + ], + "type": "text", + "content": "Baselines. To demonstrate the effectiveness of our proposed method, we compare it with three categories of methods, including: a) SingleSet, a single model that each client is trained with their local data without FL; b) Centralized, a single model that is trained with the combination of all the local data, which serves as the upper-bound of FL models; and c) eight state-of-the-art FL algorithms, including: (1) FedAvg [26], a classical FL algorithm that is trained by averaging parameters of all the participating clients; (2) FedBN [22], a FL algorithm that alleviates the client-shift by using batch normalization on each local client; (3) FedProx [21], a FL algorithm that applies a proximal term to the local objective function; (4) SCAFFOLD [16], a FL algorithm that uses control variates to correct the client-drift; (5) MOON [20], a FL algorithm that utilizes the similarity between model representations to correct the local update; (6) FedReg [39], a FL algorithm that regularizes locally trained parameters with the loss on generated pseudo data to alleviate knowledge forgetting; (7) FL-MRCM [13], a federated MRI algorithm that aligns the latent features between the source and target clients; and (8) FedMRI [9], a federated MRI algorithm that preserves the client-specific properties to improve the FL performance. For a fair comparison, we adopt Swin Transformers and a standard ConvNet head as the reconstruction network for each client among all the baselines." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 603, + 489, + 615 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 603, + 489, + 615 + ], + "spans": [ + { + "bbox": [ + 306, + 603, + 489, + 615 + ], + "type": "text", + "content": "4.2. Comparison with State-of-the-arts" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 617, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 617, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 617, + 545, + 713 + ], + "type": "text", + "content": "In-Federation Performance. The first subtable of Table 1 provides a comprehensive evaluation of the In-Federation setting with regards to various FL algorithms, where SingleSet indicates that each client is trained to use their local data without FL, and Centralized indicates that all the local datasets are gathered, which serves as the upper-bound of FL models. Ours (w. Pro) and Ours (Full) are the variants of our method that only with prompts and" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 47, + 673, + 286, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 673, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 673, + 286, + 713 + ], + "type": "text", + "content": "1https://fastmri.org/. \n2https://www.synapse.org/#!Synapse:syn28546456/ \nwiki/. \n3https://brain-developmentment.org/" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8068" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 47, + 105, + 550, + 284 + ], + "blocks": [ + { + "bbox": [ + 46, + 71, + 547, + 103 + ], + "lines": [ + { + "bbox": [ + 46, + 71, + 547, + 103 + ], + "spans": [ + { + "bbox": [ + 46, + 71, + 547, + 103 + ], + "type": "text", + "content": "Table 1. Quantitative comparison of state-of-the-art FL methods with regard to In-Federation and Out-of-Federation scenarios, where # Com.cost is the communication cost, Ub indicates the upper-bound of FL algorithms, ↑ and ↓ indicate increments and decrements compared with FedAvg (w. FFt). Detailed analyses are provided in Sec. 4.2." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 47, + 105, + 550, + 284 + ], + "lines": [ + { + "bbox": [ + 47, + 105, + 550, + 284 + ], + "spans": [ + { + "bbox": [ + 47, + 105, + 550, + 284 + ], + "type": "table", + "html": "
Method# Com.costIn-FederationOut-of-Federation
PSNRSSIMNMSEPSNRSSIMNMSE
SingleSet18.43 M28.79(3.35)↓0.805(0.099)↓0.021(0.011)↓28.92(2.15)↓0.808(0.091)↓0.032(0.011)↓
Centralized (Ub)18.43 M36.71(4.57)↑0.947(0.044)↑0.009(0.005)↑35.73(4.66)↑0.940(0.041)↑0.008(0.013)↑
FedAvg (w. FFt) [26]18.43 M32.14(0.00)0.903(0.000)0.010(0.000)31.07(0.00)0.899(0.000)0.021(0.000)
FedBN [22]18.40 M28.31(3.83)↓0.817(0.086)↓0.044(0.034)↓25.65(5.42)↓0.731(0.186)↓0.080(0.059)↓
FedProx [21]18.43 M32.84(0.70)↑0.901(0.002)↑0.010(0.000)31.98(0.91)↑0.905(0.006)↑0.018(0.003)↑
SCAFFOLD [16]18.43 M33.08(0.94)↑0.914(0.010)↑0.009(0.001)↑32.20(1.13)↑0.915(0.016)↑0.018(0.003)↑
MOON [20]18.43 M34.06(1.92)↑0.927(0.023)↑0.008(0.002)↑31.16(0.09)↑0.907(0.008)↑0.023(0.002)↓
FedReg [39]18.43 M33.29(1.15)↑0.890(0.013)↑0.009(0.001)↑32.41(1.34)↑0.907(0.008)↑0.017(0.004)↑
FL-MRCM [13]18.43 M33.60(1.46)↑0.922(0.019)↑0.013(0.003)↓32.72(1.65)↑0.911(0.012)↑0.016(0.005)↑
FedMRI [9]17.46 M33.35(1.21)↑0.923(0.020)↑0.014(0.004)↓32.00(0.93)↑0.914(0.015)↑0.019(0.002)↑
Ours (w. Pro)0.11 M35.29(3.15)↑0.927(0.024)↑0.009(0.001)↑34.65(3.58)↑0.921(0.022)↑0.010(0.011)↑
Ours (Full)0.11 M36.43(4.30)↑0.945(0.042)↑0.007(0.003)↑35.60(4.53)↑0.939(0.040)↑0.008(0.013)↑
", + "image_path": "38b4ba2d41976359cd561ae8d8f6faba2bf4d9542b12664a8e7229a4ea0babf0.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 290, + 289, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 290, + 289, + 445 + ], + "spans": [ + { + "bbox": [ + 46, + 290, + 289, + 445 + ], + "type": "text", + "content": "our full method that with both prompts and the null space mechanism. FedAvg (w. FfIt) [26] indicates the FedAvg algorithm while employing the pretrained model on the local side and full fine-tuning with all the participating clients. For a fair comparison, we retrain them on the two different scenarios with their default parameters and report their optimal results. All the competing methods are pretrained with Swin Transformers on fastMRI and fully fine-tuned with 50 communication rounds and 10 local epochs because they all converge before round 50. To assess the difference between a pair of methods, we use the paired Student's " + }, + { + "bbox": [ + 46, + 290, + 289, + 445 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 290, + 289, + 445 + ], + "type": "text", + "content": "-test to demonstrate that all results were at the 0.001 level of statistical significance." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 447, + 289, + 698 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 447, + 289, + 698 + ], + "spans": [ + { + "bbox": [ + 46, + 447, + 289, + 698 + ], + "type": "text", + "content": "From Table 1, Ours (w. Pro) is superior to the competing FL methods in terms of PSNR, SSIM, and NMSE. In comparison to FedAvg (w. FFt), Ours (w. Pro) increases the PSNR results from 32.14 dB to 35.29 dB and the SSIM results from 0.903 to 0.927, because the FedAvg (w. FFt) is prone to overfitting when the local data is limited (i.e., issue ①) even though FedAvg (w. FFt) also employ the pretrained model on the local side. However, the method of freezing backbone networks that only fine-tune prompts is consistent with the mechanism of personalized FL, e.g., FedMRI, which divides the local network into a shared global generalized representation and a locally client-specific representation. More importantly, the number of training parameters and communication cost of Ours (w. Pro) is only " + }, + { + "bbox": [ + 46, + 447, + 289, + 698 + ], + "type": "inline_equation", + "content": "6\\%" + }, + { + "bbox": [ + 46, + 447, + 289, + 698 + ], + "type": "text", + "content": " of FedAvg (w. FFt). Moreover, even compared to FedReg [39], which aims to address catastrophic forgetting in FL, our method still achieves " + }, + { + "bbox": [ + 46, + 447, + 289, + 698 + ], + "type": "inline_equation", + "content": "9.43\\%" + }, + { + "bbox": [ + 46, + 447, + 289, + 698 + ], + "type": "text", + "content": " improvement in terms of PSNR. Furthermore, the reconstruction results of our proposed method are almost on par with the Centralized results (upper bound), i.e., PSNR: 36.71 dB vs. 36.41 dB, and SSIM: 0.947 vs. 0.945." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 59, + 701, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 701, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 59, + 701, + 287, + 713 + ], + "type": "text", + "content": "In contrast, SingleSet has the lowest results, even though" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 290, + 547, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 290, + 547, + 506 + ], + "spans": [ + { + "bbox": [ + 304, + 290, + 547, + 506 + ], + "type": "text", + "content": "it is also fine-tuned on the pre-trained model, as it cannot solve non-i.i.d. problems. For the classical federated MRI methods, FL-MRCM [13] and FedMRI [9], they lead to poor reconstruction performance when the number of local clients is large and the amount of local data is insufficient. Furthermore, other FL algorithms are either designed for data heterogeneity problems or for catastrophic forgetting problems. They have not considered the clinical issues of federated MRI, i.e., issues ①-③, causing it to produce less accurate reconstructions. These findings confirm our core idea that the three issues of federated MRI can be relieved by learning a federated visual prompt with our federated MRI paradigm. In addition, we visualize the reconstructed images and the corresponding error maps for all the competing methods in the first two rows of Fig. 4. The fewer textures in the error map, the better the reconstruction. It is obvious from the error map in Fig. 4 that our method can significantly reduce the reconstruction error." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 510, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 548, + 715 + ], + "type": "text", + "content": "Out-of-Federation Performance. The second subtable of Table 1 provides quantitative evaluations under the Out-of-Federation scenario of various FL algorithms. Since the testing distribution in the Out-of-Federation scenario is unseen by the training distribution, the overall results of the Out-of-Federation scenario are slightly lower than those of In-Federation. However, our method still achieves the best performance in terms of the reconstruction results on the three metrics, i.e., Ours (Full) improves PSNR values from 31.07 dB to 35.60 dB, raises SSIM values from 0.899 to 0.939, and decreases NMSE values from 0.021 to 0.008. Notably, our method even achieves comparable results to the Centralized (Upper-bound) method, i.e., PSNR: 35.73 dB vs. 35.60 dB, SSIM: 0.940 vs. 0.939 and NMSE: 0.008 vs. 0.008. That is, our method suffers the least from the issue " + }, + { + "bbox": [ + 304, + 510, + 548, + 715 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 304, + 510, + 548, + 715 + ], + "type": "text", + "content": " among all competing" + } + ] + } + ], + "index": 6 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8069" + } + ] + } + ], + "index": 7 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 55, + 541, + 257 + ], + "blocks": [ + { + "bbox": [ + 53, + 55, + 541, + 257 + ], + "lines": [ + { + "bbox": [ + 53, + 55, + 541, + 257 + ], + "spans": [ + { + "bbox": [ + 53, + 55, + 541, + 257 + ], + "type": "image", + "image_path": "8dec8839b1b3e7c96b688dafff4eacc26d54a6b2c4c0a20b9710f9979fbbb0ae.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 259, + 546, + 293 + ], + "lines": [ + { + "bbox": [ + 46, + 259, + 546, + 293 + ], + "spans": [ + { + "bbox": [ + 46, + 259, + 546, + 293 + ], + "type": "text", + "content": "Figure 4. Qualitative comparison of different algorithms in terms of reconstruction images and error maps with corresponding quantitative measurements in PSNR/SSIM under In-Federation and Out-of-Federation scenarios. The less texture in the error map, the better reconstruction quality." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 298, + 289, + 417 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 298, + 289, + 417 + ], + "spans": [ + { + "bbox": [ + 46, + 298, + 289, + 417 + ], + "type": "text", + "content": "algorithms. These results support our core idea that learning federated visual prompts in the null space of global prompts can alleviate the three key issues in federated MRI while achieving competitive performance on limited local data. In addition, we show the qualitative evaluation results for the Out-of-Federation scenario in the second rows of Fig. 4, which visualizes the high-precision results of our method. As can be seen from this figure, our method provides comparable effects to the Centralized one, with clear details of tissue texture and boundaries." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 423, + 148, + 434 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 423, + 148, + 434 + ], + "spans": [ + { + "bbox": [ + 47, + 423, + 148, + 434 + ], + "type": "text", + "content": "4.3. Ablation Studies" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 437, + 287, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 437, + 287, + 688 + ], + "spans": [ + { + "bbox": [ + 46, + 437, + 287, + 688 + ], + "type": "text", + "content": "Catastrophic Forgetting vs. Local Updates. The catastrophic forgetting (i.e., issue ⑧) of federated MRI is caused by data heterogeneity due to different imaging protocols. As a result, more local updates will cause the local model to deviate from the global optimal solution. Here, we explore whether more local epochs cause the model to forget previously acquired global knowledge. In other words, it needs to be explored whether our proposed method can force local mitigation of this forgetting. Thus, we record the reconstruction results in terms of PSNR, SSIM, and NMSE for different numbers of local epochs in Fig. 5 (a). From this figure, in comparison to FedAvg (w. FFt) [26], increasing the local epoch does not greatly affect the accuracy of our method, i.e., Ours (w. Pro), and Ours (Full). In particular, as the number of local epochs increases, the performance of our method gradually stabilizes. In contrast, when the number of local epochs is too large, the reconstruction accuracy of FedAvg (w. FFt) will be reduced because it will gradually deviate from the global knowledge area. As a result, the result indicates that our method can learn without forgetting global knowledge over more local epochs." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "content": "Analysis of Ratio " + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\gamma\\%" + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "content": ". As we mentioned in Sec. 3.3, the ratio " + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\gamma\\%" + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "content": " of the smallest singular values in " + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\Lambda_2^{z+1}" + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "content": " controls" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 298, + 546, + 634 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 298, + 546, + 634 + ], + "spans": [ + { + "bbox": [ + 304, + 298, + 546, + 634 + ], + "type": "text", + "content": "the size of the approximate null space in global prompts. That is, the larger the " + }, + { + "bbox": [ + 304, + 298, + 546, + 634 + ], + "type": "inline_equation", + "content": "\\gamma\\%" + }, + { + "bbox": [ + 304, + 298, + 546, + 634 + ], + "type": "text", + "content": ", the smaller the area of knowledge preservation. However, the area of knowledge preservation contains the global knowledge from the previous round, which is expected to be unchanged. To analyze the knowledge preservation capability that a good federated MRI framework should have, we discuss the reconstruction accuracy for different " + }, + { + "bbox": [ + 304, + 298, + 546, + 634 + ], + "type": "inline_equation", + "content": "\\gamma\\%" + }, + { + "bbox": [ + 304, + 298, + 546, + 634 + ], + "type": "text", + "content": " values with regard to two scenarios in Fig. 6. It can be seen from this figure that, with the increase in " + }, + { + "bbox": [ + 304, + 298, + 546, + 634 + ], + "type": "inline_equation", + "content": "\\gamma\\%" + }, + { + "bbox": [ + 304, + 298, + 546, + 634 + ], + "type": "text", + "content": " values, the reconstruction accuracy gradually increases. However, when " + }, + { + "bbox": [ + 304, + 298, + 546, + 634 + ], + "type": "inline_equation", + "content": "\\gamma\\% = 100\\%" + }, + { + "bbox": [ + 304, + 298, + 546, + 634 + ], + "type": "text", + "content": ", the reconstruction accuracy drops rapidly. This is because when the knowledge preservation area is reduced to zero, fitting on the local distribution leads to forgetting the out-of-local distribution, i.e., the issue ⑧. Additionally, we can observe from Fig. 6 that roughly " + }, + { + "bbox": [ + 304, + 298, + 546, + 634 + ], + "type": "inline_equation", + "content": "40\\%" + }, + { + "bbox": [ + 304, + 298, + 546, + 634 + ], + "type": "text", + "content": " of the area comprises previously acquired global knowledge because our method obtains the highest results at this point. Following [36], we use the proportion of the sum of singular values of " + }, + { + "bbox": [ + 304, + 298, + 546, + 634 + ], + "type": "inline_equation", + "content": "\\Lambda_{2}^{z+1}" + }, + { + "bbox": [ + 304, + 298, + 546, + 634 + ], + "type": "text", + "content": " in the sum of singular values of " + }, + { + "bbox": [ + 304, + 298, + 546, + 634 + ], + "type": "inline_equation", + "content": "\\Lambda^{z+1}" + }, + { + "bbox": [ + 304, + 298, + 546, + 634 + ], + "type": "text", + "content": " to verify the rationality of the approximation. We find that the proportion in each layer is smaller than " + }, + { + "bbox": [ + 304, + 298, + 546, + 634 + ], + "type": "inline_equation", + "content": "10^{-7}" + }, + { + "bbox": [ + 304, + 298, + 546, + 634 + ], + "type": "text", + "content": ". That is, the sum of the smallest singular values " + }, + { + "bbox": [ + 304, + 298, + 546, + 634 + ], + "type": "inline_equation", + "content": "U_{2}^{z+1}" + }, + { + "bbox": [ + 304, + 298, + 546, + 634 + ], + "type": "text", + "content": " can be ignored, thereby making it reasonable to approximate the null space through the spatial range of " + }, + { + "bbox": [ + 304, + 298, + 546, + 634 + ], + "type": "inline_equation", + "content": "U_{2}^{z+1}" + }, + { + "bbox": [ + 304, + 298, + 546, + 634 + ], + "type": "text", + "content": ". Interestingly, our method only performs local updates in the approximate null space of global prompts, which greatly improves the stability of the model and thus prevents catastrophic forgetting, i.e., the issue ⑧." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 641, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 547, + 713 + ], + "type": "text", + "content": "Communication Efficiency Analysis. Our primal interest is to learn a federated visual prompt that enables FL to perform well with less local data, lower communication cost, and faster convergence. Here, we investigate the communication efficiency of our proposed method in terms of communication cost and different communication rounds," + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8070" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 75, + 165, + 163 + ], + "blocks": [ + { + "bbox": [ + 93, + 65, + 138, + 74 + ], + "lines": [ + { + "bbox": [ + 93, + 65, + 138, + 74 + ], + "spans": [ + { + "bbox": [ + 93, + 65, + 138, + 74 + ], + "type": "text", + "content": "In-Federation" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 56, + 75, + 165, + 163 + ], + "lines": [ + { + 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Reconstruction accuracy of FedAvg (w. FFt), Ours (w. Pro), and Ours (Full) versus (a) local epochs and (b) communication rounds under In-Federation and Out-of-Federation scenarios." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 53, + 402, + 279, + 467 + ], + "lines": [ + { + "bbox": [ + 53, + 402, + 279, + 467 + ], + "spans": [ + { + "bbox": [ + 53, + 402, + 279, + 467 + ], + "type": "image", + "image_path": "8b6514d70fac09cda504ff90ab0228e87da68f5c64d1830c0c654a282a091266.jpg" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 469, + 287, + 491 + ], + "lines": [ + { + "bbox": [ + 46, + 469, + 287, + 491 + ], + "spans": [ + { + "bbox": [ + 46, + 469, + 287, + 491 + ], + "type": "text", + "content": "Figure 6. Analysis of the ratio " + }, + { + "bbox": [ + 46, + 469, + 287, + 491 + ], + "type": "inline_equation", + "content": "\\gamma \\%" + }, + { + "bbox": [ + 46, + 469, + 287, + 491 + ], + "type": "text", + "content": " of the approximate null space in terms of PSNR, SSIM, and NMSE." + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_caption" + } + ], + "index": 19 + }, + { + "bbox": [ + 46, + 498, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 289, + 715 + ], + "type": "text", + "content": "respectively. As shown in Table 1, the proposed method only requires " + }, + { + "bbox": [ + 46, + 498, + 289, + 715 + ], + "type": "inline_equation", + "content": "0.11\\mathrm{M}" + }, + { + "bbox": [ + 46, + 498, + 289, + 715 + ], + "type": "text", + "content": " of communication, which is " + }, + { + "bbox": [ + 46, + 498, + 289, + 715 + ], + "type": "inline_equation", + "content": "6\\%" + }, + { + "bbox": [ + 46, + 498, + 289, + 715 + ], + "type": "text", + "content": " of the others, thereby addressing the issue " + }, + { + "bbox": [ + 46, + 498, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{2}" + }, + { + "bbox": [ + 46, + 498, + 289, + 715 + ], + "type": "text", + "content": ". However, although the classical federated MRI algorithms FL-MRCM [13] and FedMRI [9] can also achieve good accuracy, they ignored this clinical issue of federated MRI. Additionally, the reconstruction accuracy of FedAvg (w. FFt) [26], Ours (w. Pro), and Ours (Full) under different communication rounds is recorded in Fig. 5 (b), where the number of the local epochs is fixed at 10 for each method. As can be seen from the figure, our method converges within 10 rounds, while FedAvg (w. FFt) [26] converges after 30 rounds. Especially under the mechanism of updating the local prompts in the approximate null space of global prompts, our method provides higher reconstruction results. This is because our federated prompt learning mechanism prevents overfitting caused by the limited amount of local training data and offers a personalized scheme for each client. The results in Fig. 5 (b)" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 305, + 409, + 545, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 409, + 545, + 445 + ], + "spans": [ + { + "bbox": [ + 305, + 409, + 545, + 445 + ], + "type": "text", + "content": "confirm that our method provides the highest communication efficiency even on limited local data, thus relieving the issues 1 and 2." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 306, + 455, + 378, + 468 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 455, + 378, + 468 + ], + "spans": [ + { + "bbox": [ + 306, + 455, + 378, + 468 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 473, + 545, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 473, + 545, + 639 + ], + "spans": [ + { + "bbox": [ + 304, + 473, + 545, + 639 + ], + "type": "text", + "content": "This paper presented a federated visual prompt learning method, FedPR, to tackle the three issues in federated MRI reconstruction, i.e., limited communication bandwidth, insufficient local training data, and catastrophic forgetting. Benefiting from a powerful pre-trained model, our FedPR only learns prompts with a small number of learnable parameters. Additionally, FedPR greatly mitigates catastrophic forgetting by updating local prompts only in the approximate null space of global prompts, thereby preventing knowledge outside the local distribution from being overwritten. Experiments under In-Federation and Out-of-Federation scenarios demonstrate the superiority of FedPR in relieving the three issues of federated MRI reconstruction." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 641, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 545, + 712 + ], + "type": "text", + "content": "Acknowledgements: This work was supported by the Agency for Science, Technology and Research (A*STAR) AME Programmatic Funds (Grant Number: A20H4b0141). 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Recently, the meta-learning based label correction strategy is widely adopted to tackle this problem via identifying and correcting potential noisy labels with the help of a small set of clean validation data. Although training with purified labels can effectively improve performance, solving the meta-learning problem inevitably involves a nested loop of bi-level optimization between model weights and hyper-parameters (i.e., label distribution). As compromise, previous methods resort to a coupled learning process with alternating update. In this paper, we empirically find such simultaneous optimization over both model weights and label distribution can not achieve an optimal routine, consequently limiting the representation ability of backbone and accuracy of corrected labels. From this observation, a novel multi-stage label purifier named DMLP is proposed. DMLP decouples the label correction process into label-free representation learning and a simple meta label purifier. In this way, DMLP can focus on extracting discriminative feature and label correction in two distinctive stages. DMLP is a plug-and-play label purifier, the purified labels can be directly reused in naive end-to-end network retraining or other robust learning methods, where state-of-the-art results are obtained on several synthetic and real-world noisy datasets, especially under high noise levels. Code is available at https://github.com/yuanpengtu/DMLP.", + "bbox": [ + 75, + 354, + 473, + 777 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 806, + 209, + 821 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Deep learning has achieved significant progress on various recognition tasks. The key to its success is the availabil", + "bbox": [ + 76, + 833, + 472, + 864 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/e3936704b0d16aaab9a514b36ed00d4a9038cb15ea5b7a85501d3d45013cff1e.jpg", + "image_caption": [ + "Figure 1. (a) Traditional coupled alternating update to solve meta label purification problem, and (b) the proposed DMLP method that decouples the label purification process into representation learning and a simple non-nested meta label purifier." + ], + "image_footnote": [], + "bbox": [ + 532, + 321, + 856, + 536 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ity of large-scale datasets with reliable annotations. Collecting such datasets, however, is time-consuming and expensive. Easy ways to obtain labeled data, such as web crawling [31], inevitably yield samples with noisy labels, which is not appropriate to be directly utilized to train DNN since these complex models are vulnerable to memorize noisy labels [2].", + "bbox": [ + 496, + 608, + 893, + 700 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Towards this problem, numerous Learning with Noisy Label (LNL) approaches were proposed. Classical LNL methods focus on identifying the noisy samples and reducing their effect on parameter updates by abandoning [12] or assigning smaller importance. However, when it comes to extremely noisy and complex scenarios, such scheme struggles since there is no sufficient clean data to train a discriminative classifier. Therefore, label correction approaches are proposed to augment clean training samples by revising noisy labels to underlying correct ones. Among them, meta-learning based approaches [9, 16, 25] achieve state-of-the-art performance via resorting to a small clean validation set and taking noisy labels as hyper-parameters, which provides sound guidance", + "bbox": [ + 496, + 704, + 895, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* Equal contribution.", + "bbox": [ + 99, + 875, + 214, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Corresponding author.", + "bbox": [ + 99, + 887, + 230, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "19934", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "toward underlying label distribution of clean samples. However, such meta purification inevitably involves a nested bi-level optimization problem on both model weight and hyper-parameters (shown as Fig. 1 (a)), which is computationally infeasible. As a compromise, the alternating update between model weights and hyper-parameters is adopted to optimize the objective [9, 16, 25], leading to a coupled solution for representation learning and label purification.", + "bbox": [ + 75, + 90, + 470, + 210 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Empirical observation. Intuitively, alternate optimization over a large search space (model weight and hyperparameters) may lead to sub-optimal solutions. To investigate how such approximation affects results in robust learning, we conduct empirical analysis on CIFAR-10 [14] with recent label purification methods MLC [41] and MSLC [9], which consist of a deep model and a meta label correction network, and make observation as Fig. 2.", + "bbox": [ + 75, + 214, + 470, + 335 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- Coupled optimization hinders quality of corrected labels. We first compare the Coupled meta corrector MLC with its extremely Decoupled variant where the model weights are first optimized for 70 epochs with noisy labels and get fixed, then labels are purified with the guidance of validation set. We adopt the accuracy of corrected label to measure the performance of purification. From Fig. 2 (a), we can clearly observe that compared with Decoupled counterpart, joint optimization yields inferior correction performance, and these miscorrection will reversely affect the representation learning in coupled optimization.", + "bbox": [ + 75, + 337, + 470, + 503 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- Coupled optimization hinders representation ability. We investigate the representation quality by evaluating the linear prob accuracy [6] of extracted feature in Fig. 2 (b). We find the representation quality of Coupled training is much worse at the beginning, which leads to slow and unstable representation learning in the later stage. To further investigate the effect on representation learning, we also resort to a well pretrained backbone with self-supervised learning [5] as initialization, recent research [40] shows pretrained representation is substantially helpful for LNL framework. However, we find this conclusion does not strictly hold for coupled meta label correctors. As shown in Fig. 2 (c), by comparing the classification accuracy from classifier of MLC/MSLC, we observe the pretrained model only brings marginal improvement if model weights is still coupled with hyper-parameters. In contrast, when the weight of backbone is fixed and decoupled from the label purification and classifier, the improvement becomes more significant.", + "bbox": [ + 75, + 506, + 470, + 777 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Decoupled Meta Purification. From the observation above, we find the decoupling between model weights and hyperparameters of meta correctors is essential to label accuracy and final results. Therefore, in this paper, we aim at detaching the meta label purification from representation learning and designing a simple meta label purifier which is more friendly to optimization of label distribution problem than existing complex meta networks [9, 41]. Hence", + "bbox": [ + 75, + 780, + 470, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "we propose a general multi-stage label correction strategy, named Decoupled Meta Label Purifier (DMLP). The core of DMLP is a meta-learning based label purifier, however, to avoid solving the bi-level optimization with a coupled solution, DMLP decouples this process into self-supervised representation learning and a linear meta-learner to fit underlying correct label distribution (illustrated as Fig. 1 (b)), thus simplifies the label purification stage as a single-level optimization problem. The simple meta-learner is carefully designed with two mutually reinforcing correcting processes, named intrinsic primary correction (IPC) and extrinsic auxiliary correction (EAC) respectively. IPC plays the role of purifying labels in a global sense at a steady pace, while EAC targets at accelerating the purification process via looking ahead (i.e., training with) the updated labels from IPC. The two processes can enhance the ability of each other and form a positive loop of label correction. Our DMLP framework is flexible for application, the purified labels can either be directly applied for naive end-to-end network retraining, or exploited to boost the performance of existing LNL frameworks. Extensive experiments conducted on mainstream benchmarks, including synthetic (noisy versions of CIFAR) and real-world (Clothing1M) datasets, demonstrate the superiority of DMLP. In a nutshell, the key contributions of this paper include:", + "bbox": [ + 496, + 90, + 893, + 468 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We analyze the necessity of decoupled optimization for label correction in robust learning, based on which we propose DMLP, a flexible and novel multi-stage label purifier that solves bi-level meta-learning problem with a decoupled manner, which consists of representation learning and non-nested meta label purification;", + "- In DMLP, a novel non-nested meta label purifier equipped with two correctors, IPC and EAC is proposed. IPC is a global and steady corrector, while EAC accelerates the correction process via training with the updated labels from IPC. The two processes form a positive training loop to learn more accurate label distribution;", + "- Deep models trained with purified labels from DMLP achieve state-of-the-art results on several synthetic and real-world noisy datasets across various types and levels of label noise, especially under high noise levels. Extensive ablation studies are provided to verify the effectiveness." + ], + "bbox": [ + 496, + 469, + 893, + 726 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 500, + 739, + 650, + 753 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The existing LNL approaches that are related to our work can be coarsely categorized into two groups: noisy sample detection and label correction.", + "bbox": [ + 496, + 763, + 893, + 808 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Noisy sample detection methods aim to identify and reduce the importance of suspicious false-labeled samples during training. The detected noisy samples are abandoned [12, 23], assigned with smaller weights via a sample re-weight training scheme [20, 37], or used to formulate a semi-supervised learning problem by throwing away the", + "bbox": [ + 496, + 810, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "19935", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/8a50c9cb329dbdebc1218cb7e70137130b7bdedfbd2aafd074a359b75750c040.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 96, + 89, + 336, + 251 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/98d6b66e344d31d229eb5d5f3ff924c2997373e6d6e6b55d843eca7a3d232509.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 348, + 88, + 589, + 251 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/d0abbb336eeae71722088e95b43213f527a7ae5db69bbc1c3d8b0ecdc0c83187.jpg", + "image_caption": [ + "Figure 2. The corrected label accuracy (a) and linear probe accuracy of representations (b) between coupled [41] and decoupled label correction schemes during training under $50\\%$ and $90\\%$ symmetric label noise on CIFAR-10. (c) investigates the effect of representation learning on 'Ori'-original coupled network training from scratch, 'SimCLR-Coupled'-initialization with stronger self-supervised pretrained weights and 'SimCLR-Decoupled'-further fix the pretrained backbone during label purification." + ], + "image_footnote": [], + "bbox": [ + 598, + 88, + 869, + 252 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "labels while keeping the unlabeled data [15,38]. These methods show robustness under certain noise levels, but struggle when it comes to extremely noisy and complex scenarios since there is no sufficient clean data to train a classifier.", + "bbox": [ + 75, + 311, + 470, + 372 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Label correction approaches attempt to augment the training set by finding and correcting noisy labels to their underlying true ones. To do so, some works [22] try to estimate the noise transition matrix. However, these methods usually assume that the noise type is class-dependent, which may be inappropriate for more complex noise settings, such as real-world noisy datasets [31]. Some other works resort to exploiting the prediction of the network, both soft [1, 13, 24, 35] and hard [27, 28] label correction schemes are designed. However, the predictions of overparameterized backbone network can be unreliable since it tends to fluctuate during training in the presence of false-labeled data ([38]). Another line of works utilize robust representations learned via unsupervised contrastive learning methods [11, 17, 38, 40] to eliminate the interference of noisy labels, which provides a reliable initialization of deep models. Recently, meta-learning based methods [9, 16, 25, 41] show great potential towards LNL problems with the help of a small clean validation set to provide sound guidance toward underlying label distribution of clean sample. However, these approaches involves a bi-level optimization problem on model weights and hyper-parameters, which is too computationally expensive to optimize. As a compromise, the one-step approximation is commonly adopted [9, 41] to convert the nested objective into a coupled update procedure between model weights and hyper-parameters, leading to sub-optimal performance.", + "bbox": [ + 75, + 393, + 472, + 803 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Accordingly, DMLP belongs to the label correction group via meta-learning strategy, but unlike previous meta-learning based methods [9,41], the learning process on model weights and labels are decoupled into individual stages within DMLP. Next, we will introduce the proposed DMLP in detail.", + "bbox": [ + 75, + 824, + 470, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 500, + 310, + 589, + 324 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Decoupled Solution to Meta Label Purification", + "text_level": 1, + "bbox": [ + 500, + 335, + 890, + 351 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For convenience, notations within DMLP are clarified first. The noisy training dataset is denoted as $D_{t} = \\{(x_{i},y_{i})|1\\leq i\\leq N_{t}\\}$ , where $x_{i}\\in \\mathbb{R}^{H\\times W\\times 3},y_{i}\\in \\{0,1\\}^{c}$ are the image and corrupted label of the $i$ -th instance, $c$ is the class number. Similarly, a small clean validation dataset is denoted as $D_{v} = \\{(x_{i},y_{i})|1\\leq i\\leq N_{v}\\}$ . $N$ denotes the dataset size, and $N_{v}\\ll N_{t}$ . The subscripts $t,v$ represent the data is from training set or validation set.", + "bbox": [ + 498, + 358, + 890, + 479 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Typical meta-learning based purification requires solving a bi-level optimization problem on both model weights and hyper-parameters with objective:", + "bbox": [ + 498, + 479, + 890, + 525 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\theta_ {\\alpha}} E _ {(x _ {v}, y _ {v}) \\in D _ {v}} \\mathcal {L} _ {v a l} (x _ {v}, y _ {v}; w ^ {*} (\\theta_ {\\alpha})), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 563, + 532, + 890, + 561 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "s.t. $w^{*}(\\theta_{\\alpha}) = \\arg \\min_{w}E_{(x_{t},y_{t})\\in D_{t}}\\mathcal{L}_{train}(x_{t},y_{t};w,\\theta_{\\alpha}),$", + "bbox": [ + 509, + 556, + 866, + 575 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $w$ and $\\theta_{\\alpha}$ denote the model weights and the meta hyper-parameters respectively. In the classical label purification pipeline, $\\theta_{\\alpha}$ is reparameterized as a function of noisy label distribution, i.e. $\\theta_{\\alpha} = g(y_{t})$ . $\\mathcal{L}_{val}$ and $\\mathcal{L}_{train}$ are the loss function on different datasets. Since both loss terms are not analytical and involve complicated forward pass of DNN, solving the nested optimization objective is computationally expensive. Meanwhile, alternating one-step approximation [9, 25] cannot guarantee that the optimization direction is optimal due to coupled update.", + "bbox": [ + 496, + 590, + 893, + 739 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In contrast, in order to avoid coupled optimization over the large searching space of network parameters $w$ , we reformulate the meta-learning objective in DMLP as:", + "bbox": [ + 498, + 741, + 893, + 786 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {y t} E _ {(x _ {v}, y _ {v}) \\in D _ {v}} \\mathcal {L} _ {v a l} (\\mathbf {f} _ {v}, y _ {v}; w ^ {*} (y _ {t})),\n$$\n", + "text_format": "latex", + "bbox": [ + 578, + 792, + 815, + 814 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "s.t. $w^{*}(y_{t}) = \\arg \\min_{w}E_{(x_{t},y_{t})\\in D_{t}}\\mathcal{L}_{train}(\\mathbf{f}_{t},y_{t};w),$ (2)", + "bbox": [ + 529, + 818, + 890, + 837 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {f} _ {t} = G (x _ {t}; \\theta_ {G} ^ {*}), \\quad \\mathbf {f} _ {v} = G (x _ {v}; \\theta_ {G} ^ {*}),\n$$\n", + "text_format": "latex", + "bbox": [ + 594, + 840, + 813, + 856 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where a pretrained feature extractor $G:\\mathbb{R}^{H\\times W\\times 3}\\to \\mathbb{R}^d$ is designed to extract $d$ -dimensional image representation $\\mathbf{f}$ . In", + "bbox": [ + 498, + 869, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "19936", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/a7e95151bab114d7a4aac1c6a529e125d8c61f7985059abfff42eecedcaad516.jpg", + "image_caption": [ + "Figure 3. The overall framework of DMLP. (a) Decoupled meta label purification (Sec. 3.2). (b) The purified labels can be applied in normal network retraining (CE) or other LNL loss (Sec. 3.3)." + ], + "image_footnote": [], + "bbox": [ + 102, + 90, + 867, + 250 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "order to obtain representation of high quality, these extracted features are utilized in a contrastive self-supervised learning framework [5, 6] to update the parameters $\\theta_{G}$ as pretraining without noisy labels. Subsequently, the established feature extractor $\\mathbf{f} = G(x; \\theta_{G}^{*})$ can learn a noise-agnostic descriptor of image data, which is also highly separable in high dimensional feature space [38]. In this manner, we detach the representation learning from noisy label correction, while keeping strong separability of features.", + "bbox": [ + 75, + 282, + 472, + 417 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Further, since the feature is representative and separable, the loss term $\\mathcal{L}_{train}$ and $\\mathcal{L}_{val}$ can be formulated with simple risk estimation functions (e.g. linear discrimination) instead of complex DNN forward pass, making it possible to solve the problem of Eq. (2) in a non-nested manner with an analytical solution, which will be introduced in Sec. 3.2.", + "bbox": [ + 75, + 419, + 473, + 508 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Non-nested Meta Label Purifier", + "text_level": 1, + "bbox": [ + 76, + 530, + 357, + 544 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To solve the purification problem of Eq. (2), we propose two mutually reinforced solutions to seek purified training labels as shown in Fig. 3, the intrinsic primary correction (IPC) and extrinsic auxiliary correction (EAC) processes.", + "bbox": [ + 75, + 553, + 468, + 613 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Intrinsic Primary Correction. IPC aims at performing global-wise label purification at a slow and steady pace. Specifically, as shown in Fig. 3 (a), the features and labels of a batch of $b$ training data are gathered into matrix $F_{t} \\in \\mathbb{R}^{b \\times d}$ and $Y_{t} \\in \\mathbb{R}^{b \\times c}$ as:", + "bbox": [ + 75, + 614, + 470, + 689 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nF _ {t} = [ \\mathbf {f} _ {t, 1}, \\mathbf {f} _ {t, 2}, \\dots , \\mathbf {f} _ {t, b} ] ^ {T}, Y _ {t} = [ y _ {t, 1}, y _ {t, 2}, \\dots , y _ {t, b} ] ^ {T}. (3)\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 698, + 472, + 718 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Since the feature descriptors are representative, we assume there exists a simple linear estimation transform $w \\in \\mathbb{R}^{d \\times c}$ , which accurately predict the categorical distribution with ridge regression:", + "bbox": [ + 75, + 724, + 472, + 786 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {w} \\mathcal {L} _ {t r a i n} (F _ {t}, Y _ {t}; w) = \\| \\sigma (\\alpha Y _ {t}) - F _ {t} w \\| ^ {2} + \\lambda \\| w \\| ^ {2}, (4)\n$$\n", + "text_format": "latex", + "bbox": [ + 94, + 794, + 472, + 816 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\sigma(\\cdot)$ is the softmax function along the categorical dimension to meet the normalization constraint, and $\\alpha$ is a scaling factor. By solving the linear regression problem of Eq. (4) through least square method (see supplementary material for details), we can obtain its closed-form solution", + "bbox": [ + 75, + 824, + 472, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$w^{*}(Y_{t})$ on the training batch $(F_{t},Y_{t})$ and derive its optimal prediction via linear regression on samples $\\mathbf{f}_{v,i}$ from validation set $D_{v}$ :", + "bbox": [ + 496, + 282, + 893, + 329 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} y _ {v, i} ^ {\\prime} (Y _ {t}) = w ^ {*} (Y _ {t}) ^ {T} \\mathbf {f} _ {v, i} \\\\ = \\sigma \\left(\\alpha Y _ {t}\\right) ^ {T} F _ {t} \\left(F _ {t} ^ {T} F _ {t} + \\lambda I\\right) ^ {- 1} \\mathbf {f} _ {v, i}. \\tag {5} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 542, + 339, + 893, + 383 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Intuitively, the discrepancy between the predicted results $y_{v,i}^{\\prime}$ and the ground truth labels $y_{v,i}$ of $D_v$ is due to the potential noise from $Y_{t}$ , therefore we take the prediction discrepancy as objective for label purification:", + "bbox": [ + 496, + 393, + 892, + 455 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {v a l}} \\left(Y _ {t}\\right) = \\frac {1}{N _ {v}} \\sum_ {i = 1} ^ {N _ {v}} \\left| \\left| y _ {v, i} ^ {\\prime} \\left(Y _ {t}\\right) - y _ {v, i} \\right| \\right| ^ {2} + \\mathcal {H} \\left(y _ {v, i} ^ {\\prime} \\left(Y _ {t}\\right)\\right), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 465, + 892, + 502 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{H}(\\cdot)$ represents the entropy of input distribution as a regularization term to sharpen the predicted label distribution as [35]. With Eq. (5) and Eq. (6), the validation loss can be expressed analytically by training labels $Y_{t}$ in a batch, thus the noisy labels can be corrected steadily with correction rate $\\eta_{I}$ by the gradient back-propagated from Eq. (6) as", + "bbox": [ + 496, + 512, + 893, + 603 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nY _ {t} ^ {p + 1} := Y _ {t} ^ {p} - \\eta_ {I} \\nabla \\left(\\mathcal {L} _ {\\text {v a l}} \\left(Y _ {t} ^ {p}\\right)\\right). \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 591, + 613, + 892, + 630 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Extrinsic Auxiliary Correction. To accelerate the label correction process, an external correction process is further proposed. Specifically, an accompanied linear classifier $C(\\cdot; w_c): \\mathbb{R}^d \\to \\mathbb{R}^c$ with learnable parameter $w_c$ is trained along with the updated labels from IPC:", + "bbox": [ + 496, + 641, + 893, + 717 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {c}} \\left(w _ {c}\\right) = \\mathcal {L} _ {\\mathrm {c e}} \\left(C \\left(\\mathbf {f} _ {t}; w _ {c}\\right), y ^ {\\prime} _ {t}\\right) + \\mathcal {H} \\left(C \\left(\\mathbf {f} _ {t}; w _ {c}\\right)\\right), \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 549, + 727, + 892, + 743 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $y_{t}^{\\prime}$ is the updated training label from IPC, and $\\mathcal{L}_{\\mathrm{ce}}$ denotes the cross entropy loss function. Since the accompanied linear classifier is intrinsically robust to noisy labels in $y_{t}^{\\prime}$ [24], it can quickly achieve high correction accuracy. With this intuition, the predicted results of the classifier $C(\\mathbf{f}_t;w_c)$ are used to correct labels periodically, specifically, the update rule of $Y_{t}$ switches to momentum update (i.e., EMA) every $T$ iterations:", + "bbox": [ + 496, + 753, + 893, + 875 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nY _ {t} ^ {p + 1} := \\left(1 - \\eta_ {E}\\right) Y _ {t} ^ {p} + \\eta_ {E} C \\left(F _ {t}; w _ {c}\\right) \\quad \\text {i f} \\quad p = n T, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 531, + 883, + 892, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "19937", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/6dacc3da1fe0948e1466271bcc1c542f133a548168581be6743066d876cf780b.jpg", + "table_caption": [ + "Table 1. Comparison with state-of-the-art methods on CIFAR-10/100 datasets with symmetric noise. \"CE\" is the standard ConvNet trained with Cross-Entropy loss in an end-to-end manner. \"Classifier\" means adopts the pre-trained SimCLR features to re-train a linear classifier. \"Val\" denotes using a small clean validation set. DivideMix* denotes training DivideMix with the same validation set as additional data." + ], + "table_footnote": [], + "table_body": "
Dataset\nMethodValNoise ratioCIFAR-10CIFAR-100
20%50%80%90%20%50%80%90%
Cross-Entropy (CE)XBest86.879.462.942.762.046.719.910.1
Last82.757.926.116.861.837.38.83.5
Co-teaching+ [36]XBest89.585.767.447.965.651.827.913.7
Last88.284.145.530.164.145.315.58.8
PENCIL [35]XBest92.489.177.558.969.457.531.115.3
Last92.088.776.558.268.156.420.78.8
REED [38]XBest95.895.694.393.676.773.066.959.6
Last95.795.494.193.576.572.266.559.4
Sel-CL+ [18]XBest95.593.989.281.976.572.459.648.8
Last95.193.388.781.676.172.059.248.6
MOIT+ [21]XBest94.191.881.174.775.970.647.641.8
Last93.891.380.674.075.270.146.941.2
C2D-DivideMix [40]XBest96.395.294.493.578.676.467.758.7
Last96.295.194.193.478.376.067.458.4
DivideMix [15]XBest96.194.693.276.077.374.660.231.5
Last95.794.492.975.476.974.259.631.0
Meta-Learning [16]✓Best92.989.377.458.768.559.242.419.5
Last92.088.876.158.367.758.040.114.3
MLC [41]✓Best92.688.177.467.966.852.721.815.0
Last91.887.577.167.066.552.418.914.2
MSLC [9]✓Best93.489.969.856.172.565.424.316.7
Last93.389.468.855.272.064.920.514.6
DivideMix* [15]✓Best96.194.993.677.377.774.860.732.5
Last95.994.693.076.577.174.360.532.2
DMLP-Naive✓Best94.794.293.592.872.768.063.561.3
Last94.294.093.292.072.367.463.260.9
DMLP-DivideMix✓Best96.395.894.594.379.976.868.665.8
Last96.295.694.394.079.476.168.565.4
", + "bbox": [ + 114, + 132, + 849, + 609 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $T$ and $\\eta_{E}$ are the period and momentum for update, and $n$ is an arbitrary positive integer to denote the $n$ -th time of EAC update. In a global sense, after $T$ iterations of training, EAC can quickly achieve locally optimal label estimation by mimic of gradually updated labels from IPC, which reversely facilitates the label correction of IPC by providing cleaner training labels. Subsequently, IPC and EAC form a positive loop and mutually improve the quality of label correction of each other.", + "bbox": [ + 75, + 621, + 470, + 755 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Application of DMLP", + "text_level": 1, + "bbox": [ + 76, + 768, + 282, + 786 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The DMLP is a flexible label purifier, the corrected training labels $y_{t}^{*}$ can be applied in different ways in robust learning scenarios, as shown in Fig. 3.", + "bbox": [ + 75, + 792, + 470, + 839 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Naive classification network with DMLP. In a simple and direct manner, we can take the purified labels to retrain a neural network with simple cross-entropy loss (CE), here we term this simple application as DMLP-Naive.", + "bbox": [ + 75, + 839, + 470, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "LNL framework boosted by DMLP. Considering that there may still be a small number of noisy or miscorrected labels after purification, another effective way to apply DMLP is to take the purified labels as new training samples for the existing LNL framework. In this work, we extend some classic frameworks [12, 15, 19, 30] with DMLP, and the boosted LNL methods are denoted with prefix of “DMLP-” (e.g. DMLP-DivideMix, DMLP-ELR+, etc.)", + "bbox": [ + 496, + 621, + 893, + 742 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 758, + 633, + 776 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Experimental Settings", + "text_level": 1, + "bbox": [ + 500, + 785, + 705, + 801 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "CIFAR-10/100. For the self-supervised pre-training stage, we adopt the popular SimCLR algorithm [5] with ResNet as the backbone network. Classifiers in meta-learner are trained for 100 epochs with the Adam optimizer. For the final DivideMix algorithm, ResNet18 is adopted for a fair comparison. $\\eta_{I}$ and $\\eta_{E}$ are set as 0.01 and 1.0 respec", + "bbox": [ + 496, + 809, + 893, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "19938", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/6ed94261b20711a005f33ed3ba27094d44fee201e72f48b8dbf5942244fa31cb.jpg", + "table_caption": [ + "Table 2. Evaluation results with asymmetric noise of different noisy ratio on CIFAR-10. \"Validation\" denotes the method exploits a small clean validation set." + ], + "table_footnote": [], + "table_body": "
MethodValidationNoisy ratio
20%40%
Joint-Optim [28]X92.891.7
PENCIL [35]X92.491.2
M-correction [1]X-86.3
Iterative-CV [4]X-88.0
DivideMix [15]X93.493.4
REED [38]X95.092.3
C2D-DivideMix [40]X93.893.4
Sel-CL+ [18]X95.293.4
GCE [11]X87.378.1
RRL [17]X-92.4
Zhang, et al. [39]✓92.790.2
Meta-Learning [16]✓-88.6
MSLC [9]✓94.491.6
DMLP-Naive✓94.693.9
DMLP-DivideMix✓95.295.0
", + "bbox": [ + 102, + 132, + 436, + 396 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/dea745c271f4fa8eaad6055196f0b11c40749ada49bfd181211c44d556391630.jpg", + "table_caption": [ + "Table 3. Top-1 testing accuracy on Clothing-1M testset. \"Validation\" denotes using the validation provided by [31]." + ], + "table_footnote": [], + "table_body": "
MethodValidationTop-1 Accuracy
PENCIL [35]X73.49
DivideMix [15]X74.76
RRL [17]X74.90
GCE [11]X73.30
C2D-DivideMix [40]X74.30
REED [38]X75.81
Meta-Learning [16]✓73.47
Self-Learning [13]✓76.44
MLC [41]✓75.78
MSLC [9]✓74.02
Meta-Cleaner [10]✓72.50
Meta-Weight [8]✓73.72
FaMUS [34]✓74.40
MSLG [7]✓76.02
DMLP-Naive✓77.77
DMLP-DivideMix✓78.23
", + "bbox": [ + 112, + 433, + 426, + 691 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "tively. The scaling factor $\\alpha$ is set as 1.0. To ensure fair evaluation, we follow previous meta-learning based LNL methods [8, 9] to randomly separate 1,000 images as the clean validation set for CIFAR-10/100 [14], leaving the rest as training samples. We strictly follow the protocol in [12] to generate label noise. Specifically, symmetric noise is generated by replacing labels with one of the other classes uniformly, while the labels in asymmetric noise are disturbed to their similar classes to simulate label noise in real-world scenarios. Our experiments are conducted under different noisy rates: $\\pi \\in \\{20\\%, 50\\%, 80\\%, 90\\% \\}$ for symmetric and $\\pi \\in \\{20\\%, 40\\% \\}$ for asymmetric noises.", + "bbox": [ + 75, + 702, + 468, + 883 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Clothing1M. For the first stage on the Clothing1M [32],", + "bbox": [ + 96, + 885, + 470, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "the ResNet50 is trained with the official MoCo-v2 [6] to fully leverage its advantages on large-scale datasets. Afterward, the meta-learner is trained for 50 epochs. For DMLP-DivideMix, ResNet50 is adopted and initialized with weights from previous stages and trained for 80 epochs. Due to the space constraint, we put more detailed experimental settings and descriptions of each compared LNL method in our supplementary materials.", + "bbox": [ + 496, + 90, + 893, + 212 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Experimental Results", + "text_level": 1, + "bbox": [ + 500, + 224, + 702, + 239 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Comparison with state-of-the-art methods. We compare our method with multiple recent competitive methods on CIFAR-10/100 under various noisy settings (detailed descriptions of these methods are provided in the supplementary materials). Both test accuracy of the best and last epoch are reported. As shown in Table 1, the simple DMLP-Naive can already achieve competitive results to most methods, the superiority is more obvious in extremely noisy cases, further, the DMLP-DivideMix achieves state-of-the-art performance across all the settings. It is worth noting that directly utilizing the validation data to train DvldeMix (i.e., DivideMix*) only brings marginal improvement, while when equipped with the purified labels by DMLP, significant improvements are obtained, indicating that DMLP is effective in terms of utilizing validation set towards LNL problem. On the other hand, though there exist other meta-learning methods utilizing validation set [9, 16, 41], DMLP shows great advantages over them. It is also noticeable that compared with the original DivideMix, the purified version of DMLP-DivideMix achieves better results by a large margin, indicating that the purified label from our approach is more friendly to boost LNL frameworks. Table 2 shows comparison with the recent methods on asymmetric noisy CIFAR-10 dataset. DMLP-DivideMix outperforms REED by $0.2\\%$ and $2.7\\%$ under different noisy ratios and obtains greater improvements over the rest methods, demonstrating the ability of DMLP in handling harder semantic-related noise. Finally, DMLP-based methods suffer less from increasing noisy ratio than other competitors, indicating its robustness to variant noisy levels.", + "bbox": [ + 496, + 248, + 893, + 686 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Furthermore, we also evaluate DMLP on the large-scale real-world noisy dataset Clothing1M. As shown in Table 3, simple DMLP-Naive can outperform all other methods by a large margin, and DMLP-DivideMix further improves the accuracy by about $0.46\\%$ . The results indicate that DMLP is more suitable for noise from real-world situations.", + "bbox": [ + 496, + 688, + 893, + 779 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Label correction accuracy. Fig. 4 compares the label accuracy after correction in our meta-learner against coupled label purifiers MLC and MSLC on CIFAR-10. Specifically, the one-hot form of the corrected pseudo-labels is compared with the ground truth for evaluation. As Fig. 4 shows, labels can be rapidly corrected to accuracy over $92\\%$ in low noise cases. For severe label noise, DMLP can still improve label accuracy similar to low-noise settings. The overall corrected", + "bbox": [ + 496, + 779, + 893, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "19939", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/772f657cc08ea091cfd2d424f81c70ac198ac81803bdd461b011e8d69516a2fa.jpg", + "table_caption": [ + "Table 4. Comparison between the LNL methods and their DMLP applications with symmetric noise on CIFAR-10/100. Specifically, the 9-layer CNN is adopted as the backbone network of Co-teaching." + ], + "table_footnote": [], + "table_body": "
Dataset\nMethod/Noise ratioCIFAR-10CIFAR-100
20%50%80%90%20%50%80%90%
Co-teaching [12]Best82.673.024.014.650.538.211.84.9
Last81.972.623.511.750.338.011.34.3
DMLP-Co-teachingBest85.885.885.484.651.249.848.145.3
Last85.685.685.384.551.049.347.845.1
CDR [30]Best90.485.047.212.363.339.529.28.0
Last82.749.416.610.162.939.59.74.5
DMLP-CDRBest91.491.291.290.269.264.861.458.5
Last91.290.890.689.368.364.361.157.9
ELR+ [19]Best94.693.891.175.277.572.458.230.8
Last94.493.790.573.576.272.256.830.6
DMLP-ELR+Best94.994.193.092.577.873.663.960.5
Last94.694.092.792.177.173.463.660.5
", + "bbox": [ + 155, + 119, + 807, + 339 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/611b5fd0a0d8f77049fbce68fb27a5e20e8408ea09db054299683e99434221ad.jpg", + "image_caption": [ + "Figure 4. Comparison of corrected label accuracy under symmetric-20% (left), symmetric-80% (right) noise settings on CIFAR-10. Label accuracy within DMLP is superior against other competitors across all noise settings (More detailed experimental results can be found in the supplementary material)." + ], + "image_footnote": [], + "bbox": [ + 76, + 349, + 272, + 472 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b8fa7779cb5b86beb572d1c55558d363158f6d0541a1b6ba3cbc553365374cd6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 272, + 349, + 467, + 472 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Generality of DMLP. To validate the generalization ability of DMLP, other than DivideMix, another three popular LNL methods, $\\mathrm{ELR + }$ [19], Co-teaching [12], and CDR [30] are further adopted to work collaboratively with purified labels of DMLP. As shown in Table 4, all the applications of DMLP perform consistently better over their corresponding baselines, and the improvement becomes more significant when it comes to high-level noise cases. It is worth noting that since CDR highly relies on the early stopping technique, it suffers from a severe memorization effect in the training process, leading to a discrepancy between best results and last performance. In contrast, when training CDR with our purified labels, this discrepancy almost disappears, demonstrating the labels output by DMLP have a better quality to suppress the memorization effect, thus alleviating the reliance on early stopping. Therefore, the results indicate that the purified labels of DMLP are friendly to boost LNL frameworks. More detailed experimental results can be found in the supplementary materials.", + "bbox": [ + 75, + 551, + 470, + 838 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Ablation Studies", + "text_level": 1, + "bbox": [ + 76, + 847, + 240, + 862 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Analysis on different label correction process. We explore the influence of IPC and EAC on the performance", + "bbox": [ + 75, + 869, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/69a4c72ee05b9a859588f735d055eeda25975e88d559a0be2ae82e98980054e1.jpg", + "table_caption": [ + "Table 5. Ablation study for the effectiveness of IPC and EAC in DMLP-Naive on CIFAR-10." + ], + "table_footnote": [], + "table_body": "
ComponentCIFAR-10Clothing
IPCEAC20%50%80%90%1M
X✓Best93.793.391.167.476.5
Last93.092.990.666.576.1
✓XBest87.885.779.976.076.8
Last87.285.579.475.476.5
✓✓Best94.794.293.592.877.7
Last94.294.093.292.077.6
", + "bbox": [ + 501, + 382, + 901, + 516 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "of DMLP-Naive in Table 5, when one of the process is excluded, the updated labels from the other are applied to retrain a new model. It is observed that EAC performs well in low noise cases due to its intrinsic robustness, as the noise ratio increases, the performance drops rapidly. On the other hand, IPC is more robust to high-level noise, but there exists a large gap compared with the full DMLP pipeline due to its slow optimization process. In contrast, when IPC and EAC work collaboratively, DMLP can achieve optimal results.", + "bbox": [ + 496, + 532, + 893, + 670 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparison against other coupled purifiers with pretraining. To solely evaluate the influence of decoupled purification, we train two coupled meta label correction methods MLC and MSLC with the same self-supervised pretrained weights and apply their corrected labels to naive training or DivideMix for fair comparisons. As shown in Table. 6, though self-supervised weights can marginally boost the performance of coupled label correctors, there still exists a large gap between their performance and DMLP, especially for high noisy cases. Moreover, when further applying the corrected labels to mainstream LNL framework DivideMix, our method can also consistently outperform the coupled counterparts across all the noisy settings, demonstrating our corrected labels are of better quality. Therefore, these results verify that the superiority mainly attributes to decoupled", + "bbox": [ + 496, + 674, + 893, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "19940", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/4b2b5e4eb1095426612675b764895dd07c9464908ac71067fca87d899413d868.jpg", + "table_caption": [ + "Table 6. Comparison with coupled meta label correction methods MLC [41] and MSLC [9] on CIFAR-10. \" *\" denotes training with SimCLR pretrained ResNet-18." + ], + "table_footnote": [], + "table_body": "
MethodNoisy ratio
20%50%80%90%
MLC*Best91.886.277.672.9
Last91.685.977.572.6
MSLC*Best92.087.778.067.8
Last92.087.577.967.3
DMLP-Naive*Best94.093.793.192.3
Last93.993.492.991.9
MLC*-DivideMixBest95.394.093.086.6
Last95.093.692.786.5
MSLC*-DivideMixBest95.794.993.883.0
Last95.594.893.182.8
DMLP*-DivideMixBest96.395.694.193.8
Last96.095.294.093.6
", + "bbox": [ + 116, + 132, + 426, + 351 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/67f634355c1b3beefb8828decdbaee609e1fadd070162b700f55605628810108.jpg", + "table_caption": [ + "Table 7. Investigation of the validation set size $\\tau$ on Clothing1M." + ], + "table_footnote": [], + "table_body": "
τ10%20%30%40%50%100%
Accuracy (%)75.5076.4076.6177.0077.3077.31
", + "bbox": [ + 93, + 380, + 446, + 425 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "label correction instead of self-supervised pretraining.", + "bbox": [ + 76, + 431, + 436, + 446 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effect of different feature representation for purification. The quality of features plays a crucial role in the label correction process of DMLP since the distribution of learned features is closely related to the rationality behind the linear estimation assumption in high-dimensional space. Therefore, we study the influence of different features on performance. Specifically, two types of features are investigated, including features from the ResNet-18/50 which load the self-supervised pre-trained weights. As the results in Table 8 show, the features from the ResNet-18 lead to slightly poor performance, while it brings performance improvements when using features from self-supervised ResNet-50. This observation indicates that although feature representation of higher quality benefits the purification results, DMLP is not very sensitive to the representation ability of input feature.", + "bbox": [ + 75, + 446, + 468, + 672 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effect of validation size. We examine how the number of validation set affects performance. Specifically, validation sizes from $10\\%$ to $100\\%$ of the whole validation set are evaluated on Clothing1M for DMLP-Naive. As shown in Table 7, DMLP-Naive achieves similar performance regardless of the validation size $N_v$ , demonstrating DMLP is not sensitive to the number of images. It is worth noting that even using only $10\\%$ of the validation set (around $0.1\\%$ of training data), DMLP-Naive still achieves high accuracy and outperforms most methods in Table.3, indicating that the effectiveness of DMLP is not heavily relied on validation size.", + "bbox": [ + 75, + 674, + 470, + 838 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Performance under extremely noisy setting. In an extremely noisy scenario where all labels in the training set are unreliable except the given clean validation set, the LNL problem is converted into a semi-supervised learning prob", + "bbox": [ + 75, + 839, + 470, + 901 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/5aa726ed83e920e6b8e16249f8f9400884acae9c27d511e88915409d968169eb.jpg", + "table_caption": [ + "Table 8. Ablation study for adopting different features in DMLP-Naive on CIFAR-10, where \"R18/50\" denote \"ResNet-18/50\" and \"M/S\" represent \"MoCo/SimCLR\"." + ], + "table_footnote": [], + "table_body": "
Feature SourceNoisy ratio
20%50%80%90%
R18 (M)Best93.893.392.290.4
Last93.792.792.190.0
R18 (S)Best94.093.793.192.3
Last93.993.492.991.9
R50 (S)Best94.794.293.592.8
Last94.294.093.292.0
", + "bbox": [ + 568, + 132, + 821, + 257 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/97454c353760e8dd0685ac3848cc7c3fff17f9fc0a559b075738c525af23ea06.jpg", + "table_caption": [ + "Table 9. Comparison between recent semi-supervised methods and DMLP-DivideMix on CIFAR-10/100 with $100\\%$ noisy ratio." + ], + "table_footnote": [], + "table_body": "
MethodCIFAR-10CIFAR-100
MeanTeacher83.031.0
MixMatch87.957.7
FixMatch88.156.3
UDA88.256.1
Ours91.760.1
", + "bbox": [ + 584, + 295, + 803, + 388 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "lem, therefore we further compare DMLP-DivideMix with some state-of-the-art semi-supervised learning algorithms, including MeanTeacher [29], MixMatch [3], FixMatch [26] and UDA [33], under the $100\\%$ symmetric noise case on CIFAR-10 and CIFAR-100. From the results in Table 9, DMLP-DivideMix performs optimally among all methods when using the validation set as labeled samples, indicating the proposed method is potential for broader applications.", + "bbox": [ + 496, + 400, + 893, + 521 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 534, + 617, + 550 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we propose a flexible and novel multi-stage robust learning approach termed as DMLP. The core of DMLP is a carefully-designed meta-learning based label purifier, which decouples the complex bi-level optimization problem into representation and label distribution learning, thus helping the meta-learner focus on correcting noisy labels in a faster and more precise manner even under extremely noisy scenarios. Further, DMLP can be applied either for naive retraining on noisy data or assistance of existing LNL methods to boost performance. Extensive experiments conducted on several synthetic and real-world noisy datasets verify the superiority of the proposed method.", + "bbox": [ + 496, + 560, + 893, + 741 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement", + "text_level": 1, + "bbox": [ + 500, + 753, + 660, + 771 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was supported by National Natural Science Fund of China (62076184, 61976158, 61976160, 62076182, 62276190), in part by Fundamental Research Funds for the Central Universities and State Key Laboratory of Integrated Services Networks (Xidian University), in part by Shanghai Innovation Action Project of Science and Technology (20511100700) and Shanghai Natural Science Foundation (22ZR1466700).", + "bbox": [ + 496, + 779, + 893, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "19941", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Eric Arazo, Diego Ortego, Paul Albert, Noel E O'Connor, and Kevin McGuinness. 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In Association for the Advancement of Artificial Intelligence (AAAI), 2021." + ], + "bbox": [ + 78, + 90, + 470, + 768 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "19943", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Learning From Noisy Labels With Decoupled Meta Label Purifier/39f5cc23-28da-4792-9a48-41c37b920aca_model.json b/2023/Learning From Noisy Labels With Decoupled Meta Label Purifier/39f5cc23-28da-4792-9a48-41c37b920aca_model.json new file mode 100644 index 0000000000000000000000000000000000000000..bfc06d7d65cb8f6e36f12ea0e6b0eb20e5f4a68a --- /dev/null +++ b/2023/Learning From Noisy Labels With Decoupled Meta Label Purifier/39f5cc23-28da-4792-9a48-41c37b920aca_model.json @@ -0,0 +1,1980 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.159, + 0.131, + 0.815, + 0.154 + ], + "angle": 0, + "content": "Learning from Noisy Labels with Decoupled Meta Label Purifier" + }, + { + "type": "text", + "bbox": [ + 0.199, + 0.18, + 0.771, + 0.218 + ], + "angle": 0, + "content": "Yuanpeng \\(\\mathrm{Tu}^{1*}\\) Boshen Zhang\\(^{2*}\\) Yuxi Li\\(^{2*}\\) Liang Liu\\(^{2}\\) Jian Li\\(^{2}\\) Yabiao Wang\\(^{2}\\) Chengjie Wang\\(^{2,3\\dagger}\\) Cai Rong Zhao\\(^{1\\dagger}\\)" + }, + { + "type": "text", + "bbox": [ + 0.175, + 0.218, + 0.796, + 0.253 + ], + "angle": 0, + "content": "\\(^{1}\\)Dept. of Electronic and Information Engineering, Tongji Univeristy, Shanghai \\(^{2}\\)YouTu Lab, Tencent, Shanghai, \\(^{3}\\)Shanghai Jiao Tong University" + }, + { + "type": "text", + "bbox": [ + 0.327, + 0.255, + 0.646, + 0.269 + ], + "angle": 0, + "content": "{2030809，zhaocairong}@tongji.edu.cn" + }, + { + "type": "text", + "bbox": [ + 0.141, + 0.273, + 0.831, + 0.287 + ], + "angle": 0, + "content": "{boshenzhang, yukiyxli, leoneliu, swordli, caseywang, jasoncjwang}@tencent.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.322, + 0.314, + 0.339 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.355, + 0.474, + 0.779 + ], + "angle": 0, + "content": "Training deep neural networks (DNN) with noisy labels is challenging since DNN can easily memorize inaccurate labels, leading to poor generalization ability. Recently, the meta-learning based label correction strategy is widely adopted to tackle this problem via identifying and correcting potential noisy labels with the help of a small set of clean validation data. Although training with purified labels can effectively improve performance, solving the meta-learning problem inevitably involves a nested loop of bi-level optimization between model weights and hyper-parameters (i.e., label distribution). As compromise, previous methods resort to a coupled learning process with alternating update. In this paper, we empirically find such simultaneous optimization over both model weights and label distribution can not achieve an optimal routine, consequently limiting the representation ability of backbone and accuracy of corrected labels. From this observation, a novel multi-stage label purifier named DMLP is proposed. DMLP decouples the label correction process into label-free representation learning and a simple meta label purifier. In this way, DMLP can focus on extracting discriminative feature and label correction in two distinctive stages. DMLP is a plug-and-play label purifier, the purified labels can be directly reused in naive end-to-end network retraining or other robust learning methods, where state-of-the-art results are obtained on several synthetic and real-world noisy datasets, especially under high noise levels. Code is available at https://github.com/yuanpengtu/DMLP." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.808, + 0.21, + 0.823 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.834, + 0.473, + 0.865 + ], + "angle": 0, + "content": "Deep learning has achieved significant progress on various recognition tasks. The key to its success is the availabil" + }, + { + "type": "image", + "bbox": [ + 0.533, + 0.323, + 0.857, + 0.537 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.541, + 0.895, + 0.598 + ], + "angle": 0, + "content": "Figure 1. (a) Traditional coupled alternating update to solve meta label purification problem, and (b) the proposed DMLP method that decouples the label purification process into representation learning and a simple non-nested meta label purifier." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.609, + 0.895, + 0.701 + ], + "angle": 0, + "content": "ity of large-scale datasets with reliable annotations. Collecting such datasets, however, is time-consuming and expensive. Easy ways to obtain labeled data, such as web crawling [31], inevitably yield samples with noisy labels, which is not appropriate to be directly utilized to train DNN since these complex models are vulnerable to memorize noisy labels [2]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.896, + 0.903 + ], + "angle": 0, + "content": "Towards this problem, numerous Learning with Noisy Label (LNL) approaches were proposed. Classical LNL methods focus on identifying the noisy samples and reducing their effect on parameter updates by abandoning [12] or assigning smaller importance. However, when it comes to extremely noisy and complex scenarios, such scheme struggles since there is no sufficient clean data to train a discriminative classifier. Therefore, label correction approaches are proposed to augment clean training samples by revising noisy labels to underlying correct ones. Among them, meta-learning based approaches [9, 16, 25] achieve state-of-the-art performance via resorting to a small clean validation set and taking noisy labels as hyper-parameters, which provides sound guidance" + }, + { + "type": "page_footnote", + "bbox": [ + 0.1, + 0.876, + 0.215, + 0.888 + ], + "angle": 0, + "content": "* Equal contribution." + }, + { + "type": "page_footnote", + "bbox": [ + 0.1, + 0.888, + 0.232, + 0.901 + ], + "angle": 0, + "content": "† Corresponding author." + }, + { + "type": "list", + "bbox": [ + 0.1, + 0.876, + 0.232, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "19934" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.471, + 0.212 + ], + "angle": 0, + "content": "toward underlying label distribution of clean samples. However, such meta purification inevitably involves a nested bi-level optimization problem on both model weight and hyper-parameters (shown as Fig. 1 (a)), which is computationally infeasible. As a compromise, the alternating update between model weights and hyper-parameters is adopted to optimize the objective [9, 16, 25], leading to a coupled solution for representation learning and label purification." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.215, + 0.471, + 0.336 + ], + "angle": 0, + "content": "Empirical observation. Intuitively, alternate optimization over a large search space (model weight and hyperparameters) may lead to sub-optimal solutions. To investigate how such approximation affects results in robust learning, we conduct empirical analysis on CIFAR-10 [14] with recent label purification methods MLC [41] and MSLC [9], which consist of a deep model and a meta label correction network, and make observation as Fig. 2." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.338, + 0.472, + 0.504 + ], + "angle": 0, + "content": "- Coupled optimization hinders quality of corrected labels. We first compare the Coupled meta corrector MLC with its extremely Decoupled variant where the model weights are first optimized for 70 epochs with noisy labels and get fixed, then labels are purified with the guidance of validation set. We adopt the accuracy of corrected label to measure the performance of purification. From Fig. 2 (a), we can clearly observe that compared with Decoupled counterpart, joint optimization yields inferior correction performance, and these miscorrection will reversely affect the representation learning in coupled optimization." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.507, + 0.472, + 0.779 + ], + "angle": 0, + "content": "- Coupled optimization hinders representation ability. We investigate the representation quality by evaluating the linear prob accuracy [6] of extracted feature in Fig. 2 (b). We find the representation quality of Coupled training is much worse at the beginning, which leads to slow and unstable representation learning in the later stage. To further investigate the effect on representation learning, we also resort to a well pretrained backbone with self-supervised learning [5] as initialization, recent research [40] shows pretrained representation is substantially helpful for LNL framework. However, we find this conclusion does not strictly hold for coupled meta label correctors. As shown in Fig. 2 (c), by comparing the classification accuracy from classifier of MLC/MSLC, we observe the pretrained model only brings marginal improvement if model weights is still coupled with hyper-parameters. In contrast, when the weight of backbone is fixed and decoupled from the label purification and classifier, the improvement becomes more significant." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.472, + 0.903 + ], + "angle": 0, + "content": "Decoupled Meta Purification. From the observation above, we find the decoupling between model weights and hyperparameters of meta correctors is essential to label accuracy and final results. Therefore, in this paper, we aim at detaching the meta label purification from representation learning and designing a simple meta label purifier which is more friendly to optimization of label distribution problem than existing complex meta networks [9, 41]. Hence" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.469 + ], + "angle": 0, + "content": "we propose a general multi-stage label correction strategy, named Decoupled Meta Label Purifier (DMLP). The core of DMLP is a meta-learning based label purifier, however, to avoid solving the bi-level optimization with a coupled solution, DMLP decouples this process into self-supervised representation learning and a linear meta-learner to fit underlying correct label distribution (illustrated as Fig. 1 (b)), thus simplifies the label purification stage as a single-level optimization problem. The simple meta-learner is carefully designed with two mutually reinforcing correcting processes, named intrinsic primary correction (IPC) and extrinsic auxiliary correction (EAC) respectively. IPC plays the role of purifying labels in a global sense at a steady pace, while EAC targets at accelerating the purification process via looking ahead (i.e., training with) the updated labels from IPC. The two processes can enhance the ability of each other and form a positive loop of label correction. Our DMLP framework is flexible for application, the purified labels can either be directly applied for naive end-to-end network retraining, or exploited to boost the performance of existing LNL frameworks. Extensive experiments conducted on mainstream benchmarks, including synthetic (noisy versions of CIFAR) and real-world (Clothing1M) datasets, demonstrate the superiority of DMLP. In a nutshell, the key contributions of this paper include:" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.47, + 0.895, + 0.56 + ], + "angle": 0, + "content": "- We analyze the necessity of decoupled optimization for label correction in robust learning, based on which we propose DMLP, a flexible and novel multi-stage label purifier that solves bi-level meta-learning problem with a decoupled manner, which consists of representation learning and non-nested meta label purification;" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.56, + 0.895, + 0.649 + ], + "angle": 0, + "content": "- In DMLP, a novel non-nested meta label purifier equipped with two correctors, IPC and EAC is proposed. IPC is a global and steady corrector, while EAC accelerates the correction process via training with the updated labels from IPC. The two processes form a positive training loop to learn more accurate label distribution;" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.65, + 0.895, + 0.727 + ], + "angle": 0, + "content": "- Deep models trained with purified labels from DMLP achieve state-of-the-art results on several synthetic and real-world noisy datasets across various types and levels of label noise, especially under high noise levels. Extensive ablation studies are provided to verify the effectiveness." + }, + { + "type": "list", + "bbox": [ + 0.498, + 0.47, + 0.895, + 0.727 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.74, + 0.651, + 0.755 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.894, + 0.809 + ], + "angle": 0, + "content": "The existing LNL approaches that are related to our work can be coarsely categorized into two groups: noisy sample detection and label correction." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Noisy sample detection methods aim to identify and reduce the importance of suspicious false-labeled samples during training. The detected noisy samples are abandoned [12, 23], assigned with smaller weights via a sample re-weight training scheme [20, 37], or used to formulate a semi-supervised learning problem by throwing away the" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "19935" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.098, + 0.09, + 0.337, + 0.252 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.349, + 0.089, + 0.59, + 0.252 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.599, + 0.089, + 0.87, + 0.253 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.253, + 0.894, + 0.308 + ], + "angle": 0, + "content": "Figure 2. The corrected label accuracy (a) and linear probe accuracy of representations (b) between coupled [41] and decoupled label correction schemes during training under \\(50\\%\\) and \\(90\\%\\) symmetric label noise on CIFAR-10. (c) investigates the effect of representation learning on 'Ori'-original coupled network training from scratch, 'SimCLR-Coupled'-initialization with stronger self-supervised pretrained weights and 'SimCLR-Decoupled'-further fix the pretrained backbone during label purification." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.313, + 0.471, + 0.373 + ], + "angle": 0, + "content": "labels while keeping the unlabeled data [15,38]. These methods show robustness under certain noise levels, but struggle when it comes to extremely noisy and complex scenarios since there is no sufficient clean data to train a classifier." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.395, + 0.473, + 0.804 + ], + "angle": 0, + "content": "Label correction approaches attempt to augment the training set by finding and correcting noisy labels to their underlying true ones. To do so, some works [22] try to estimate the noise transition matrix. However, these methods usually assume that the noise type is class-dependent, which may be inappropriate for more complex noise settings, such as real-world noisy datasets [31]. Some other works resort to exploiting the prediction of the network, both soft [1, 13, 24, 35] and hard [27, 28] label correction schemes are designed. However, the predictions of overparameterized backbone network can be unreliable since it tends to fluctuate during training in the presence of false-labeled data ([38]). Another line of works utilize robust representations learned via unsupervised contrastive learning methods [11, 17, 38, 40] to eliminate the interference of noisy labels, which provides a reliable initialization of deep models. Recently, meta-learning based methods [9, 16, 25, 41] show great potential towards LNL problems with the help of a small clean validation set to provide sound guidance toward underlying label distribution of clean sample. However, these approaches involves a bi-level optimization problem on model weights and hyper-parameters, which is too computationally expensive to optimize. As a compromise, the one-step approximation is commonly adopted [9, 41] to convert the nested objective into a coupled update procedure between model weights and hyper-parameters, leading to sub-optimal performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.472, + 0.901 + ], + "angle": 0, + "content": "Accordingly, DMLP belongs to the label correction group via meta-learning strategy, but unlike previous meta-learning based methods [9,41], the learning process on model weights and labels are decoupled into individual stages within DMLP. Next, we will introduce the proposed DMLP in detail." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.311, + 0.591, + 0.325 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.336, + 0.892, + 0.352 + ], + "angle": 0, + "content": "3.1. Decoupled Solution to Meta Label Purification" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.359, + 0.892, + 0.48 + ], + "angle": 0, + "content": "For convenience, notations within DMLP are clarified first. The noisy training dataset is denoted as \\(D_{t} = \\{(x_{i},y_{i})|1\\leq i\\leq N_{t}\\}\\), where \\(x_{i}\\in \\mathbb{R}^{H\\times W\\times 3},y_{i}\\in \\{0,1\\}^{c}\\) are the image and corrupted label of the \\(i\\)-th instance, \\(c\\) is the class number. Similarly, a small clean validation dataset is denoted as \\(D_{v} = \\{(x_{i},y_{i})|1\\leq i\\leq N_{v}\\}\\). \\(N\\) denotes the dataset size, and \\(N_{v}\\ll N_{t}\\). The subscripts \\(t,v\\) represent the data is from training set or validation set." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.48, + 0.892, + 0.526 + ], + "angle": 0, + "content": "Typical meta-learning based purification requires solving a bi-level optimization problem on both model weights and hyper-parameters with objective:" + }, + { + "type": "equation", + "bbox": [ + 0.565, + 0.533, + 0.892, + 0.562 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\theta_ {\\alpha}} E _ {(x _ {v}, y _ {v}) \\in D _ {v}} \\mathcal {L} _ {v a l} (x _ {v}, y _ {v}; w ^ {*} (\\theta_ {\\alpha})), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.558, + 0.867, + 0.577 + ], + "angle": 0, + "content": "s.t. \\(w^{*}(\\theta_{\\alpha}) = \\arg \\min_{w}E_{(x_{t},y_{t})\\in D_{t}}\\mathcal{L}_{train}(x_{t},y_{t};w,\\theta_{\\alpha}),\\)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.591, + 0.894, + 0.741 + ], + "angle": 0, + "content": "where \\( w \\) and \\( \\theta_{\\alpha} \\) denote the model weights and the meta hyper-parameters respectively. In the classical label purification pipeline, \\( \\theta_{\\alpha} \\) is reparameterized as a function of noisy label distribution, i.e. \\( \\theta_{\\alpha} = g(y_{t}) \\). \\( \\mathcal{L}_{val} \\) and \\( \\mathcal{L}_{train} \\) are the loss function on different datasets. Since both loss terms are not analytical and involve complicated forward pass of DNN, solving the nested optimization objective is computationally expensive. Meanwhile, alternating one-step approximation [9, 25] cannot guarantee that the optimization direction is optimal due to coupled update." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.742, + 0.894, + 0.787 + ], + "angle": 0, + "content": "In contrast, in order to avoid coupled optimization over the large searching space of network parameters \\( w \\), we reformulate the meta-learning objective in DMLP as:" + }, + { + "type": "equation", + "bbox": [ + 0.58, + 0.794, + 0.816, + 0.815 + ], + "angle": 0, + "content": "\\[\n\\min _ {y t} E _ {(x _ {v}, y _ {v}) \\in D _ {v}} \\mathcal {L} _ {v a l} (\\mathbf {f} _ {v}, y _ {v}; w ^ {*} (y _ {t})),\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.531, + 0.819, + 0.892, + 0.838 + ], + "angle": 0, + "content": "s.t. \\(w^{*}(y_{t}) = \\arg \\min_{w}E_{(x_{t},y_{t})\\in D_{t}}\\mathcal{L}_{train}(\\mathbf{f}_{t},y_{t};w),\\) (2)" + }, + { + "type": "equation", + "bbox": [ + 0.596, + 0.842, + 0.815, + 0.857 + ], + "angle": 0, + "content": "\\[\n\\mathbf {f} _ {t} = G (x _ {t}; \\theta_ {G} ^ {*}), \\quad \\mathbf {f} _ {v} = G (x _ {v}; \\theta_ {G} ^ {*}),\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.87, + 0.892, + 0.901 + ], + "angle": 0, + "content": "where a pretrained feature extractor \\(G:\\mathbb{R}^{H\\times W\\times 3}\\to \\mathbb{R}^d\\) is designed to extract \\(d\\)-dimensional image representation \\(\\mathbf{f}\\). In" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19936" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.104, + 0.092, + 0.868, + 0.25 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.251, + 0.895, + 0.278 + ], + "angle": 0, + "content": "Figure 3. The overall framework of DMLP. (a) Decoupled meta label purification (Sec. 3.2). (b) The purified labels can be applied in normal network retraining (CE) or other LNL loss (Sec. 3.3)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.284, + 0.473, + 0.419 + ], + "angle": 0, + "content": "order to obtain representation of high quality, these extracted features are utilized in a contrastive self-supervised learning framework [5, 6] to update the parameters \\(\\theta_{G}\\) as pretraining without noisy labels. Subsequently, the established feature extractor \\(\\mathbf{f} = G(x; \\theta_{G}^{*})\\) can learn a noise-agnostic descriptor of image data, which is also highly separable in high dimensional feature space [38]. In this manner, we detach the representation learning from noisy label correction, while keeping strong separability of features." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.42, + 0.474, + 0.51 + ], + "angle": 0, + "content": "Further, since the feature is representative and separable, the loss term \\(\\mathcal{L}_{train}\\) and \\(\\mathcal{L}_{val}\\) can be formulated with simple risk estimation functions (e.g. linear discrimination) instead of complex DNN forward pass, making it possible to solve the problem of Eq. (2) in a non-nested manner with an analytical solution, which will be introduced in Sec. 3.2." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.531, + 0.358, + 0.545 + ], + "angle": 0, + "content": "3.2. Non-nested Meta Label Purifier" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.554, + 0.47, + 0.614 + ], + "angle": 0, + "content": "To solve the purification problem of Eq. (2), we propose two mutually reinforced solutions to seek purified training labels as shown in Fig. 3, the intrinsic primary correction (IPC) and extrinsic auxiliary correction (EAC) processes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.615, + 0.472, + 0.69 + ], + "angle": 0, + "content": "Intrinsic Primary Correction. IPC aims at performing global-wise label purification at a slow and steady pace. Specifically, as shown in Fig. 3 (a), the features and labels of a batch of \\( b \\) training data are gathered into matrix \\( F_{t} \\in \\mathbb{R}^{b \\times d} \\) and \\( Y_{t} \\in \\mathbb{R}^{b \\times c} \\) as:" + }, + { + "type": "equation", + "bbox": [ + 0.091, + 0.699, + 0.473, + 0.719 + ], + "angle": 0, + "content": "\\[\nF _ {t} = [ \\mathbf {f} _ {t, 1}, \\mathbf {f} _ {t, 2}, \\dots , \\mathbf {f} _ {t, b} ] ^ {T}, Y _ {t} = [ y _ {t, 1}, y _ {t, 2}, \\dots , y _ {t, b} ] ^ {T}. (3)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.726, + 0.473, + 0.787 + ], + "angle": 0, + "content": "Since the feature descriptors are representative, we assume there exists a simple linear estimation transform \\( w \\in \\mathbb{R}^{d \\times c} \\), which accurately predict the categorical distribution with ridge regression:" + }, + { + "type": "equation", + "bbox": [ + 0.095, + 0.795, + 0.473, + 0.817 + ], + "angle": 0, + "content": "\\[\n\\min _ {w} \\mathcal {L} _ {t r a i n} (F _ {t}, Y _ {t}; w) = \\| \\sigma (\\alpha Y _ {t}) - F _ {t} w \\| ^ {2} + \\lambda \\| w \\| ^ {2}, (4)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.473, + 0.901 + ], + "angle": 0, + "content": "where \\(\\sigma(\\cdot)\\) is the softmax function along the categorical dimension to meet the normalization constraint, and \\(\\alpha\\) is a scaling factor. By solving the linear regression problem of Eq. (4) through least square method (see supplementary material for details), we can obtain its closed-form solution" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.283, + 0.895, + 0.33 + ], + "angle": 0, + "content": "\\(w^{*}(Y_{t})\\) on the training batch \\((F_{t},Y_{t})\\) and derive its optimal prediction via linear regression on samples \\(\\mathbf{f}_{v,i}\\) from validation set \\(D_{v}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.543, + 0.34, + 0.894, + 0.384 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} y _ {v, i} ^ {\\prime} (Y _ {t}) = w ^ {*} (Y _ {t}) ^ {T} \\mathbf {f} _ {v, i} \\\\ = \\sigma \\left(\\alpha Y _ {t}\\right) ^ {T} F _ {t} \\left(F _ {t} ^ {T} F _ {t} + \\lambda I\\right) ^ {- 1} \\mathbf {f} _ {v, i}. \\tag {5} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.394, + 0.893, + 0.456 + ], + "angle": 0, + "content": "Intuitively, the discrepancy between the predicted results \\( y_{v,i}^{\\prime} \\) and the ground truth labels \\( y_{v,i} \\) of \\( D_v \\) is due to the potential noise from \\( Y_{t} \\), therefore we take the prediction discrepancy as objective for label purification:" + }, + { + "type": "equation", + "bbox": [ + 0.515, + 0.466, + 0.893, + 0.503 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {v a l}} \\left(Y _ {t}\\right) = \\frac {1}{N _ {v}} \\sum_ {i = 1} ^ {N _ {v}} \\left| \\left| y _ {v, i} ^ {\\prime} \\left(Y _ {t}\\right) - y _ {v, i} \\right| \\right| ^ {2} + \\mathcal {H} \\left(y _ {v, i} ^ {\\prime} \\left(Y _ {t}\\right)\\right), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.513, + 0.894, + 0.604 + ], + "angle": 0, + "content": "where \\(\\mathcal{H}(\\cdot)\\) represents the entropy of input distribution as a regularization term to sharpen the predicted label distribution as [35]. With Eq. (5) and Eq. (6), the validation loss can be expressed analytically by training labels \\(Y_{t}\\) in a batch, thus the noisy labels can be corrected steadily with correction rate \\(\\eta_{I}\\) by the gradient back-propagated from Eq. (6) as" + }, + { + "type": "equation", + "bbox": [ + 0.592, + 0.614, + 0.893, + 0.631 + ], + "angle": 0, + "content": "\\[\nY _ {t} ^ {p + 1} := Y _ {t} ^ {p} - \\eta_ {I} \\nabla \\left(\\mathcal {L} _ {\\text {v a l}} \\left(Y _ {t} ^ {p}\\right)\\right). \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.642, + 0.895, + 0.718 + ], + "angle": 0, + "content": "Extrinsic Auxiliary Correction. To accelerate the label correction process, an external correction process is further proposed. Specifically, an accompanied linear classifier \\( C(\\cdot; w_c): \\mathbb{R}^d \\to \\mathbb{R}^c \\) with learnable parameter \\( w_c \\) is trained along with the updated labels from IPC:" + }, + { + "type": "equation", + "bbox": [ + 0.55, + 0.728, + 0.893, + 0.744 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {c}} \\left(w _ {c}\\right) = \\mathcal {L} _ {\\mathrm {c e}} \\left(C \\left(\\mathbf {f} _ {t}; w _ {c}\\right), y ^ {\\prime} _ {t}\\right) + \\mathcal {H} \\left(C \\left(\\mathbf {f} _ {t}; w _ {c}\\right)\\right), \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.754, + 0.895, + 0.876 + ], + "angle": 0, + "content": "where \\( y_{t}^{\\prime} \\) is the updated training label from IPC, and \\( \\mathcal{L}_{\\mathrm{ce}} \\) denotes the cross entropy loss function. Since the accompanied linear classifier is intrinsically robust to noisy labels in \\( y_{t}^{\\prime} \\) [24], it can quickly achieve high correction accuracy. With this intuition, the predicted results of the classifier \\( C(\\mathbf{f}_t;w_c) \\) are used to correct labels periodically, specifically, the update rule of \\( Y_{t} \\) switches to momentum update (i.e., EMA) every \\( T \\) iterations:" + }, + { + "type": "equation", + "bbox": [ + 0.532, + 0.885, + 0.893, + 0.902 + ], + "angle": 0, + "content": "\\[\nY _ {t} ^ {p + 1} := \\left(1 - \\eta_ {E}\\right) Y _ {t} ^ {p} + \\eta_ {E} C \\left(F _ {t}; w _ {c}\\right) \\quad \\text {i f} \\quad p = n T, \\tag {9}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19937" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.075, + 0.089, + 0.895, + 0.132 + ], + "angle": 0, + "content": "Table 1. Comparison with state-of-the-art methods on CIFAR-10/100 datasets with symmetric noise. \"CE\" is the standard ConvNet trained with Cross-Entropy loss in an end-to-end manner. \"Classifier\" means adopts the pre-trained SimCLR features to re-train a linear classifier. \"Val\" denotes using a small clean validation set. DivideMix* denotes training DivideMix with the same validation set as additional data." + }, + { + "type": "table", + "bbox": [ + 0.115, + 0.133, + 0.85, + 0.611 + ], + "angle": 0, + "content": "
Dataset\nMethodValNoise ratioCIFAR-10CIFAR-100
20%50%80%90%20%50%80%90%
Cross-Entropy (CE)XBest86.879.462.942.762.046.719.910.1
Last82.757.926.116.861.837.38.83.5
Co-teaching+ [36]XBest89.585.767.447.965.651.827.913.7
Last88.284.145.530.164.145.315.58.8
PENCIL [35]XBest92.489.177.558.969.457.531.115.3
Last92.088.776.558.268.156.420.78.8
REED [38]XBest95.895.694.393.676.773.066.959.6
Last95.795.494.193.576.572.266.559.4
Sel-CL+ [18]XBest95.593.989.281.976.572.459.648.8
Last95.193.388.781.676.172.059.248.6
MOIT+ [21]XBest94.191.881.174.775.970.647.641.8
Last93.891.380.674.075.270.146.941.2
C2D-DivideMix [40]XBest96.395.294.493.578.676.467.758.7
Last96.295.194.193.478.376.067.458.4
DivideMix [15]XBest96.194.693.276.077.374.660.231.5
Last95.794.492.975.476.974.259.631.0
Meta-Learning [16]✓Best92.989.377.458.768.559.242.419.5
Last92.088.876.158.367.758.040.114.3
MLC [41]✓Best92.688.177.467.966.852.721.815.0
Last91.887.577.167.066.552.418.914.2
MSLC [9]✓Best93.489.969.856.172.565.424.316.7
Last93.389.468.855.272.064.920.514.6
DivideMix* [15]✓Best96.194.993.677.377.774.860.732.5
Last95.994.693.076.577.174.360.532.2
DMLP-Naive✓Best94.794.293.592.872.768.063.561.3
Last94.294.093.292.072.367.463.260.9
DMLP-DivideMix✓Best96.395.894.594.379.976.868.665.8
Last96.295.694.394.079.476.168.565.4
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.622, + 0.472, + 0.756 + ], + "angle": 0, + "content": "where \\(T\\) and \\(\\eta_{E}\\) are the period and momentum for update, and \\(n\\) is an arbitrary positive integer to denote the \\(n\\)-th time of EAC update. In a global sense, after \\(T\\) iterations of training, EAC can quickly achieve locally optimal label estimation by mimic of gradually updated labels from IPC, which reversely facilitates the label correction of IPC by providing cleaner training labels. Subsequently, IPC and EAC form a positive loop and mutually improve the quality of label correction of each other." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.769, + 0.283, + 0.787 + ], + "angle": 0, + "content": "3.3. Application of DMLP" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.794, + 0.471, + 0.84 + ], + "angle": 0, + "content": "The DMLP is a flexible label purifier, the corrected training labels \\( y_{t}^{*} \\) can be applied in different ways in robust learning scenarios, as shown in Fig. 3." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Naive classification network with DMLP. In a simple and direct manner, we can take the purified labels to retrain a neural network with simple cross-entropy loss (CE), here we term this simple application as DMLP-Naive." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.622, + 0.895, + 0.743 + ], + "angle": 0, + "content": "LNL framework boosted by DMLP. Considering that there may still be a small number of noisy or miscorrected labels after purification, another effective way to apply DMLP is to take the purified labels as new training samples for the existing LNL framework. In this work, we extend some classic frameworks [12, 15, 19, 30] with DMLP, and the boosted LNL methods are denoted with prefix of “DMLP-” (e.g. DMLP-DivideMix, DMLP-ELR+, etc.)" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.76, + 0.634, + 0.777 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.786, + 0.707, + 0.803 + ], + "angle": 0, + "content": "4.1. Experimental Settings" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.895, + 0.903 + ], + "angle": 0, + "content": "CIFAR-10/100. For the self-supervised pre-training stage, we adopt the popular SimCLR algorithm [5] with ResNet as the backbone network. Classifiers in meta-learner are trained for 100 epochs with the Adam optimizer. For the final DivideMix algorithm, ResNet18 is adopted for a fair comparison. \\(\\eta_{I}\\) and \\(\\eta_{E}\\) are set as 0.01 and 1.0 respec" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "19938" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.472, + 0.13 + ], + "angle": 0, + "content": "Table 2. Evaluation results with asymmetric noise of different noisy ratio on CIFAR-10. \"Validation\" denotes the method exploits a small clean validation set." + }, + { + "type": "table", + "bbox": [ + 0.104, + 0.133, + 0.437, + 0.397 + ], + "angle": 0, + "content": "
MethodValidationNoisy ratio
20%40%
Joint-Optim [28]X92.891.7
PENCIL [35]X92.491.2
M-correction [1]X-86.3
Iterative-CV [4]X-88.0
DivideMix [15]X93.493.4
REED [38]X95.092.3
C2D-DivideMix [40]X93.893.4
Sel-CL+ [18]X95.293.4
GCE [11]X87.378.1
RRL [17]X-92.4
Zhang, et al. [39]✓92.790.2
Meta-Learning [16]✓-88.6
MSLC [9]✓94.491.6
DMLP-Naive✓94.693.9
DMLP-DivideMix✓95.295.0
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.406, + 0.472, + 0.433 + ], + "angle": 0, + "content": "Table 3. Top-1 testing accuracy on Clothing-1M testset. \"Validation\" denotes using the validation provided by [31]." + }, + { + "type": "table", + "bbox": [ + 0.114, + 0.434, + 0.428, + 0.692 + ], + "angle": 0, + "content": "
MethodValidationTop-1 Accuracy
PENCIL [35]X73.49
DivideMix [15]X74.76
RRL [17]X74.90
GCE [11]X73.30
C2D-DivideMix [40]X74.30
REED [38]X75.81
Meta-Learning [16]✓73.47
Self-Learning [13]✓76.44
MLC [41]✓75.78
MSLC [9]✓74.02
Meta-Cleaner [10]✓72.50
Meta-Weight [8]✓73.72
FaMUS [34]✓74.40
MSLG [7]✓76.02
DMLP-Naive✓77.77
DMLP-DivideMix✓78.23
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.703, + 0.47, + 0.884 + ], + "angle": 0, + "content": "tively. The scaling factor \\(\\alpha\\) is set as 1.0. To ensure fair evaluation, we follow previous meta-learning based LNL methods [8, 9] to randomly separate 1,000 images as the clean validation set for CIFAR-10/100 [14], leaving the rest as training samples. We strictly follow the protocol in [12] to generate label noise. Specifically, symmetric noise is generated by replacing labels with one of the other classes uniformly, while the labels in asymmetric noise are disturbed to their similar classes to simulate label noise in real-world scenarios. Our experiments are conducted under different noisy rates: \\(\\pi \\in \\{20\\%, 50\\%, 80\\%, 90\\% \\}\\) for symmetric and \\(\\pi \\in \\{20\\%, 40\\% \\}\\) for asymmetric noises." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.886, + 0.472, + 0.902 + ], + "angle": 0, + "content": "Clothing1M. For the first stage on the Clothing1M [32]," + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.213 + ], + "angle": 0, + "content": "the ResNet50 is trained with the official MoCo-v2 [6] to fully leverage its advantages on large-scale datasets. Afterward, the meta-learner is trained for 50 epochs. For DMLP-DivideMix, ResNet50 is adopted and initialized with weights from previous stages and trained for 80 epochs. Due to the space constraint, we put more detailed experimental settings and descriptions of each compared LNL method in our supplementary materials." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.225, + 0.704, + 0.241 + ], + "angle": 0, + "content": "4.2. Experimental Results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.249, + 0.895, + 0.687 + ], + "angle": 0, + "content": "Comparison with state-of-the-art methods. We compare our method with multiple recent competitive methods on CIFAR-10/100 under various noisy settings (detailed descriptions of these methods are provided in the supplementary materials). Both test accuracy of the best and last epoch are reported. As shown in Table 1, the simple DMLP-Naive can already achieve competitive results to most methods, the superiority is more obvious in extremely noisy cases, further, the DMLP-DivideMix achieves state-of-the-art performance across all the settings. It is worth noting that directly utilizing the validation data to train DvldeMix (i.e., DivideMix*) only brings marginal improvement, while when equipped with the purified labels by DMLP, significant improvements are obtained, indicating that DMLP is effective in terms of utilizing validation set towards LNL problem. On the other hand, though there exist other meta-learning methods utilizing validation set [9, 16, 41], DMLP shows great advantages over them. It is also noticeable that compared with the original DivideMix, the purified version of DMLP-DivideMix achieves better results by a large margin, indicating that the purified label from our approach is more friendly to boost LNL frameworks. Table 2 shows comparison with the recent methods on asymmetric noisy CIFAR-10 dataset. DMLP-DivideMix outperforms REED by \\(0.2\\%\\) and \\(2.7\\%\\) under different noisy ratios and obtains greater improvements over the rest methods, demonstrating the ability of DMLP in handling harder semantic-related noise. Finally, DMLP-based methods suffer less from increasing noisy ratio than other competitors, indicating its robustness to variant noisy levels." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.894, + 0.78 + ], + "angle": 0, + "content": "Furthermore, we also evaluate DMLP on the large-scale real-world noisy dataset Clothing1M. As shown in Table 3, simple DMLP-Naive can outperform all other methods by a large margin, and DMLP-DivideMix further improves the accuracy by about \\(0.46\\%\\). The results indicate that DMLP is more suitable for noise from real-world situations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Label correction accuracy. Fig. 4 compares the label accuracy after correction in our meta-learner against coupled label purifiers MLC and MSLC on CIFAR-10. Specifically, the one-hot form of the corrected pseudo-labels is compared with the ground truth for evaluation. As Fig. 4 shows, labels can be rapidly corrected to accuracy over \\(92\\%\\) in low noise cases. For severe label noise, DMLP can still improve label accuracy similar to low-noise settings. The overall corrected" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "19939" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.892, + 0.118 + ], + "angle": 0, + "content": "Table 4. Comparison between the LNL methods and their DMLP applications with symmetric noise on CIFAR-10/100. Specifically, the 9-layer CNN is adopted as the backbone network of Co-teaching." + }, + { + "type": "table", + "bbox": [ + 0.156, + 0.12, + 0.808, + 0.34 + ], + "angle": 0, + "content": "
Dataset\nMethod/Noise ratioCIFAR-10CIFAR-100
20%50%80%90%20%50%80%90%
Co-teaching [12]Best82.673.024.014.650.538.211.84.9
Last81.972.623.511.750.338.011.34.3
DMLP-Co-teachingBest85.885.885.484.651.249.848.145.3
Last85.685.685.384.551.049.347.845.1
CDR [30]Best90.485.047.212.363.339.529.28.0
Last82.749.416.610.162.939.59.74.5
DMLP-CDRBest91.491.291.290.269.264.861.458.5
Last91.290.890.689.368.364.361.157.9
ELR+ [19]Best94.693.891.175.277.572.458.230.8
Last94.493.790.573.576.272.256.830.6
DMLP-ELR+Best94.994.193.092.577.873.663.960.5
Last94.694.092.792.177.173.463.660.5
" + }, + { + "type": "image", + "bbox": [ + 0.078, + 0.351, + 0.273, + 0.473 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.274, + 0.351, + 0.468, + 0.473 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.478, + 0.472, + 0.552 + ], + "angle": 0, + "content": "Figure 4. Comparison of corrected label accuracy under symmetric-20% (left), symmetric-80% (right) noise settings on CIFAR-10. Label accuracy within DMLP is superior against other competitors across all noise settings (More detailed experimental results can be found in the supplementary material)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.552, + 0.472, + 0.839 + ], + "angle": 0, + "content": "Generality of DMLP. To validate the generalization ability of DMLP, other than DivideMix, another three popular LNL methods, \\(\\mathrm{ELR + }\\) [19], Co-teaching [12], and CDR [30] are further adopted to work collaboratively with purified labels of DMLP. As shown in Table 4, all the applications of DMLP perform consistently better over their corresponding baselines, and the improvement becomes more significant when it comes to high-level noise cases. It is worth noting that since CDR highly relies on the early stopping technique, it suffers from a severe memorization effect in the training process, leading to a discrepancy between best results and last performance. In contrast, when training CDR with our purified labels, this discrepancy almost disappears, demonstrating the labels output by DMLP have a better quality to suppress the memorization effect, thus alleviating the reliance on early stopping. Therefore, the results indicate that the purified labels of DMLP are friendly to boost LNL frameworks. More detailed experimental results can be found in the supplementary materials." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.848, + 0.241, + 0.863 + ], + "angle": 0, + "content": "4.3. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Analysis on different label correction process. We explore the influence of IPC and EAC on the performance" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.353, + 0.892, + 0.38 + ], + "angle": 0, + "content": "Table 5. Ablation study for the effectiveness of IPC and EAC in DMLP-Naive on CIFAR-10." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.383, + 0.903, + 0.517 + ], + "angle": 0, + "content": "
ComponentCIFAR-10Clothing
IPCEAC20%50%80%90%1M
X✓Best93.793.391.167.476.5
Last93.092.990.666.576.1
✓XBest87.885.779.976.076.8
Last87.285.579.475.476.5
✓✓Best94.794.293.592.877.7
Last94.294.093.292.077.6
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.534, + 0.894, + 0.671 + ], + "angle": 0, + "content": "of DMLP-Naive in Table 5, when one of the process is excluded, the updated labels from the other are applied to retrain a new model. It is observed that EAC performs well in low noise cases due to its intrinsic robustness, as the noise ratio increases, the performance drops rapidly. On the other hand, IPC is more robust to high-level noise, but there exists a large gap compared with the full DMLP pipeline due to its slow optimization process. In contrast, when IPC and EAC work collaboratively, DMLP can achieve optimal results." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Comparison against other coupled purifiers with pretraining. To solely evaluate the influence of decoupled purification, we train two coupled meta label correction methods MLC and MSLC with the same self-supervised pretrained weights and apply their corrected labels to naive training or DivideMix for fair comparisons. As shown in Table. 6, though self-supervised weights can marginally boost the performance of coupled label correctors, there still exists a large gap between their performance and DMLP, especially for high noisy cases. Moreover, when further applying the corrected labels to mainstream LNL framework DivideMix, our method can also consistently outperform the coupled counterparts across all the noisy settings, demonstrating our corrected labels are of better quality. Therefore, these results verify that the superiority mainly attributes to decoupled" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19940" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.472, + 0.131 + ], + "angle": 0, + "content": "Table 6. Comparison with coupled meta label correction methods MLC [41] and MSLC [9] on CIFAR-10. \" *\" denotes training with SimCLR pretrained ResNet-18." + }, + { + "type": "table", + "bbox": [ + 0.117, + 0.133, + 0.428, + 0.352 + ], + "angle": 0, + "content": "
MethodNoisy ratio
20%50%80%90%
MLC*Best91.886.277.672.9
Last91.685.977.572.6
MSLC*Best92.087.778.067.8
Last92.087.577.967.3
DMLP-Naive*Best94.093.793.192.3
Last93.993.492.991.9
MLC*-DivideMixBest95.394.093.086.6
Last95.093.692.786.5
MSLC*-DivideMixBest95.794.993.883.0
Last95.594.893.182.8
DMLP*-DivideMixBest96.395.694.193.8
Last96.095.294.093.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.08, + 0.365, + 0.466, + 0.379 + ], + "angle": 0, + "content": "Table 7. Investigation of the validation set size \\( \\tau \\) on Clothing1M." + }, + { + "type": "table", + "bbox": [ + 0.094, + 0.381, + 0.447, + 0.426 + ], + "angle": 0, + "content": "
τ10%20%30%40%50%100%
Accuracy (%)75.5076.4076.6177.0077.3077.31
" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.433, + 0.437, + 0.447 + ], + "angle": 0, + "content": "label correction instead of self-supervised pretraining." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.448, + 0.47, + 0.674 + ], + "angle": 0, + "content": "Effect of different feature representation for purification. The quality of features plays a crucial role in the label correction process of DMLP since the distribution of learned features is closely related to the rationality behind the linear estimation assumption in high-dimensional space. Therefore, we study the influence of different features on performance. Specifically, two types of features are investigated, including features from the ResNet-18/50 which load the self-supervised pre-trained weights. As the results in Table 8 show, the features from the ResNet-18 lead to slightly poor performance, while it brings performance improvements when using features from self-supervised ResNet-50. This observation indicates that although feature representation of higher quality benefits the purification results, DMLP is not very sensitive to the representation ability of input feature." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.675, + 0.471, + 0.839 + ], + "angle": 0, + "content": "Effect of validation size. We examine how the number of validation set affects performance. Specifically, validation sizes from \\(10\\%\\) to \\(100\\%\\) of the whole validation set are evaluated on Clothing1M for DMLP-Naive. As shown in Table 7, DMLP-Naive achieves similar performance regardless of the validation size \\(N_v\\), demonstrating DMLP is not sensitive to the number of images. It is worth noting that even using only \\(10\\%\\) of the validation set (around \\(0.1\\%\\) of training data), DMLP-Naive still achieves high accuracy and outperforms most methods in Table.3, indicating that the effectiveness of DMLP is not heavily relied on validation size." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.472, + 0.902 + ], + "angle": 0, + "content": "Performance under extremely noisy setting. In an extremely noisy scenario where all labels in the training set are unreliable except the given clean validation set, the LNL problem is converted into a semi-supervised learning prob" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.089, + 0.894, + 0.131 + ], + "angle": 0, + "content": "Table 8. Ablation study for adopting different features in DMLP-Naive on CIFAR-10, where \"R18/50\" denote \"ResNet-18/50\" and \"M/S\" represent \"MoCo/SimCLR\"." + }, + { + "type": "table", + "bbox": [ + 0.569, + 0.133, + 0.822, + 0.258 + ], + "angle": 0, + "content": "
Feature SourceNoisy ratio
20%50%80%90%
R18 (M)Best93.893.392.290.4
Last93.792.792.190.0
R18 (S)Best94.093.793.192.3
Last93.993.492.991.9
R50 (S)Best94.794.293.592.8
Last94.294.093.292.0
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.266, + 0.892, + 0.294 + ], + "angle": 0, + "content": "Table 9. Comparison between recent semi-supervised methods and DMLP-DivideMix on CIFAR-10/100 with \\(100\\%\\) noisy ratio." + }, + { + "type": "table", + "bbox": [ + 0.585, + 0.296, + 0.805, + 0.39 + ], + "angle": 0, + "content": "
MethodCIFAR-10CIFAR-100
MeanTeacher83.031.0
MixMatch87.957.7
FixMatch88.156.3
UDA88.256.1
Ours91.760.1
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.401, + 0.895, + 0.522 + ], + "angle": 0, + "content": "lem, therefore we further compare DMLP-DivideMix with some state-of-the-art semi-supervised learning algorithms, including MeanTeacher [29], MixMatch [3], FixMatch [26] and UDA [33], under the \\(100\\%\\) symmetric noise case on CIFAR-10 and CIFAR-100. From the results in Table 9, DMLP-DivideMix performs optimally among all methods when using the validation set as labeled samples, indicating the proposed method is potential for broader applications." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.535, + 0.619, + 0.551 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.561, + 0.895, + 0.742 + ], + "angle": 0, + "content": "In this paper, we propose a flexible and novel multi-stage robust learning approach termed as DMLP. The core of DMLP is a carefully-designed meta-learning based label purifier, which decouples the complex bi-level optimization problem into representation and label distribution learning, thus helping the meta-learner focus on correcting noisy labels in a faster and more precise manner even under extremely noisy scenarios. Further, DMLP can be applied either for naive retraining on noisy data or assistance of existing LNL methods to boost performance. Extensive experiments conducted on several synthetic and real-world noisy datasets verify the superiority of the proposed method." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.755, + 0.661, + 0.772 + ], + "angle": 0, + "content": "Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.895, + 0.901 + ], + "angle": 0, + "content": "This work was supported by National Natural Science Fund of China (62076184, 61976158, 61976160, 62076182, 62276190), in part by Fundamental Research Funds for the Central Universities and State Key Laboratory of Integrated Services Networks (Xidian University), in part by Shanghai Innovation Action Project of Science and Technology (20511100700) and Shanghai Natural Science Foundation (22ZR1466700)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "19941" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.171 + ], + "angle": 0, + "content": "[1] Eric Arazo, Diego Ortego, Paul Albert, Noel E O'Connor, and Kevin McGuinness. 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Recently, the meta-learning based label correction strategy is widely adopted to tackle this problem via identifying and correcting potential noisy labels with the help of a small set of clean validation data. Although training with purified labels can effectively improve performance, solving the meta-learning problem inevitably involves a nested loop of bi-level optimization between model weights and hyper-parameters (i.e., label distribution). As compromise, previous methods resort to a coupled learning process with alternating update. In this paper, we empirically find such simultaneous optimization over both model weights and label distribution can not achieve an optimal routine, consequently limiting the representation ability of backbone and accuracy of corrected labels. From this observation, a novel multi-stage label purifier named DMLP is proposed. DMLP decouples the label correction process into label-free representation learning and a simple meta label purifier. In this way, DMLP can focus on extracting discriminative feature and label correction in two distinctive stages. DMLP is a plug-and-play label purifier, the purified labels can be directly reused in naive end-to-end network retraining or other robust learning methods, where state-of-the-art results are obtained on several synthetic and real-world noisy datasets, especially under high noise levels. Code is available at https://github.com/yuanpengtu/DMLP. + +# 1. Introduction + +Deep learning has achieved significant progress on various recognition tasks. The key to its success is the availabil + +![](images/e3936704b0d16aaab9a514b36ed00d4a9038cb15ea5b7a85501d3d45013cff1e.jpg) +Figure 1. (a) Traditional coupled alternating update to solve meta label purification problem, and (b) the proposed DMLP method that decouples the label purification process into representation learning and a simple non-nested meta label purifier. + +ity of large-scale datasets with reliable annotations. Collecting such datasets, however, is time-consuming and expensive. Easy ways to obtain labeled data, such as web crawling [31], inevitably yield samples with noisy labels, which is not appropriate to be directly utilized to train DNN since these complex models are vulnerable to memorize noisy labels [2]. + +Towards this problem, numerous Learning with Noisy Label (LNL) approaches were proposed. Classical LNL methods focus on identifying the noisy samples and reducing their effect on parameter updates by abandoning [12] or assigning smaller importance. However, when it comes to extremely noisy and complex scenarios, such scheme struggles since there is no sufficient clean data to train a discriminative classifier. Therefore, label correction approaches are proposed to augment clean training samples by revising noisy labels to underlying correct ones. Among them, meta-learning based approaches [9, 16, 25] achieve state-of-the-art performance via resorting to a small clean validation set and taking noisy labels as hyper-parameters, which provides sound guidance + +toward underlying label distribution of clean samples. However, such meta purification inevitably involves a nested bi-level optimization problem on both model weight and hyper-parameters (shown as Fig. 1 (a)), which is computationally infeasible. As a compromise, the alternating update between model weights and hyper-parameters is adopted to optimize the objective [9, 16, 25], leading to a coupled solution for representation learning and label purification. + +Empirical observation. Intuitively, alternate optimization over a large search space (model weight and hyperparameters) may lead to sub-optimal solutions. To investigate how such approximation affects results in robust learning, we conduct empirical analysis on CIFAR-10 [14] with recent label purification methods MLC [41] and MSLC [9], which consist of a deep model and a meta label correction network, and make observation as Fig. 2. + +- Coupled optimization hinders quality of corrected labels. We first compare the Coupled meta corrector MLC with its extremely Decoupled variant where the model weights are first optimized for 70 epochs with noisy labels and get fixed, then labels are purified with the guidance of validation set. We adopt the accuracy of corrected label to measure the performance of purification. From Fig. 2 (a), we can clearly observe that compared with Decoupled counterpart, joint optimization yields inferior correction performance, and these miscorrection will reversely affect the representation learning in coupled optimization. + +- Coupled optimization hinders representation ability. We investigate the representation quality by evaluating the linear prob accuracy [6] of extracted feature in Fig. 2 (b). We find the representation quality of Coupled training is much worse at the beginning, which leads to slow and unstable representation learning in the later stage. To further investigate the effect on representation learning, we also resort to a well pretrained backbone with self-supervised learning [5] as initialization, recent research [40] shows pretrained representation is substantially helpful for LNL framework. However, we find this conclusion does not strictly hold for coupled meta label correctors. As shown in Fig. 2 (c), by comparing the classification accuracy from classifier of MLC/MSLC, we observe the pretrained model only brings marginal improvement if model weights is still coupled with hyper-parameters. In contrast, when the weight of backbone is fixed and decoupled from the label purification and classifier, the improvement becomes more significant. + +Decoupled Meta Purification. From the observation above, we find the decoupling between model weights and hyperparameters of meta correctors is essential to label accuracy and final results. Therefore, in this paper, we aim at detaching the meta label purification from representation learning and designing a simple meta label purifier which is more friendly to optimization of label distribution problem than existing complex meta networks [9, 41]. Hence + +we propose a general multi-stage label correction strategy, named Decoupled Meta Label Purifier (DMLP). The core of DMLP is a meta-learning based label purifier, however, to avoid solving the bi-level optimization with a coupled solution, DMLP decouples this process into self-supervised representation learning and a linear meta-learner to fit underlying correct label distribution (illustrated as Fig. 1 (b)), thus simplifies the label purification stage as a single-level optimization problem. The simple meta-learner is carefully designed with two mutually reinforcing correcting processes, named intrinsic primary correction (IPC) and extrinsic auxiliary correction (EAC) respectively. IPC plays the role of purifying labels in a global sense at a steady pace, while EAC targets at accelerating the purification process via looking ahead (i.e., training with) the updated labels from IPC. The two processes can enhance the ability of each other and form a positive loop of label correction. Our DMLP framework is flexible for application, the purified labels can either be directly applied for naive end-to-end network retraining, or exploited to boost the performance of existing LNL frameworks. Extensive experiments conducted on mainstream benchmarks, including synthetic (noisy versions of CIFAR) and real-world (Clothing1M) datasets, demonstrate the superiority of DMLP. In a nutshell, the key contributions of this paper include: + +- We analyze the necessity of decoupled optimization for label correction in robust learning, based on which we propose DMLP, a flexible and novel multi-stage label purifier that solves bi-level meta-learning problem with a decoupled manner, which consists of representation learning and non-nested meta label purification; +- In DMLP, a novel non-nested meta label purifier equipped with two correctors, IPC and EAC is proposed. IPC is a global and steady corrector, while EAC accelerates the correction process via training with the updated labels from IPC. The two processes form a positive training loop to learn more accurate label distribution; +- Deep models trained with purified labels from DMLP achieve state-of-the-art results on several synthetic and real-world noisy datasets across various types and levels of label noise, especially under high noise levels. Extensive ablation studies are provided to verify the effectiveness. + +# 2. Related Works + +The existing LNL approaches that are related to our work can be coarsely categorized into two groups: noisy sample detection and label correction. + +Noisy sample detection methods aim to identify and reduce the importance of suspicious false-labeled samples during training. The detected noisy samples are abandoned [12, 23], assigned with smaller weights via a sample re-weight training scheme [20, 37], or used to formulate a semi-supervised learning problem by throwing away the + +![](images/8a50c9cb329dbdebc1218cb7e70137130b7bdedfbd2aafd074a359b75750c040.jpg) + +![](images/98d6b66e344d31d229eb5d5f3ff924c2997373e6d6e6b55d843eca7a3d232509.jpg) + +![](images/d0abbb336eeae71722088e95b43213f527a7ae5db69bbc1c3d8b0ecdc0c83187.jpg) +Figure 2. The corrected label accuracy (a) and linear probe accuracy of representations (b) between coupled [41] and decoupled label correction schemes during training under $50\%$ and $90\%$ symmetric label noise on CIFAR-10. (c) investigates the effect of representation learning on 'Ori'-original coupled network training from scratch, 'SimCLR-Coupled'-initialization with stronger self-supervised pretrained weights and 'SimCLR-Decoupled'-further fix the pretrained backbone during label purification. + +labels while keeping the unlabeled data [15,38]. These methods show robustness under certain noise levels, but struggle when it comes to extremely noisy and complex scenarios since there is no sufficient clean data to train a classifier. + +Label correction approaches attempt to augment the training set by finding and correcting noisy labels to their underlying true ones. To do so, some works [22] try to estimate the noise transition matrix. However, these methods usually assume that the noise type is class-dependent, which may be inappropriate for more complex noise settings, such as real-world noisy datasets [31]. Some other works resort to exploiting the prediction of the network, both soft [1, 13, 24, 35] and hard [27, 28] label correction schemes are designed. However, the predictions of overparameterized backbone network can be unreliable since it tends to fluctuate during training in the presence of false-labeled data ([38]). Another line of works utilize robust representations learned via unsupervised contrastive learning methods [11, 17, 38, 40] to eliminate the interference of noisy labels, which provides a reliable initialization of deep models. Recently, meta-learning based methods [9, 16, 25, 41] show great potential towards LNL problems with the help of a small clean validation set to provide sound guidance toward underlying label distribution of clean sample. However, these approaches involves a bi-level optimization problem on model weights and hyper-parameters, which is too computationally expensive to optimize. As a compromise, the one-step approximation is commonly adopted [9, 41] to convert the nested objective into a coupled update procedure between model weights and hyper-parameters, leading to sub-optimal performance. + +Accordingly, DMLP belongs to the label correction group via meta-learning strategy, but unlike previous meta-learning based methods [9,41], the learning process on model weights and labels are decoupled into individual stages within DMLP. Next, we will introduce the proposed DMLP in detail. + +# 3. Method + +# 3.1. Decoupled Solution to Meta Label Purification + +For convenience, notations within DMLP are clarified first. The noisy training dataset is denoted as $D_{t} = \{(x_{i},y_{i})|1\leq i\leq N_{t}\}$ , where $x_{i}\in \mathbb{R}^{H\times W\times 3},y_{i}\in \{0,1\}^{c}$ are the image and corrupted label of the $i$ -th instance, $c$ is the class number. Similarly, a small clean validation dataset is denoted as $D_{v} = \{(x_{i},y_{i})|1\leq i\leq N_{v}\}$ . $N$ denotes the dataset size, and $N_{v}\ll N_{t}$ . The subscripts $t,v$ represent the data is from training set or validation set. + +Typical meta-learning based purification requires solving a bi-level optimization problem on both model weights and hyper-parameters with objective: + +$$ +\min _ {\theta_ {\alpha}} E _ {(x _ {v}, y _ {v}) \in D _ {v}} \mathcal {L} _ {v a l} (x _ {v}, y _ {v}; w ^ {*} (\theta_ {\alpha})), \tag {1} +$$ + +s.t. $w^{*}(\theta_{\alpha}) = \arg \min_{w}E_{(x_{t},y_{t})\in D_{t}}\mathcal{L}_{train}(x_{t},y_{t};w,\theta_{\alpha}),$ + +where $w$ and $\theta_{\alpha}$ denote the model weights and the meta hyper-parameters respectively. In the classical label purification pipeline, $\theta_{\alpha}$ is reparameterized as a function of noisy label distribution, i.e. $\theta_{\alpha} = g(y_{t})$ . $\mathcal{L}_{val}$ and $\mathcal{L}_{train}$ are the loss function on different datasets. Since both loss terms are not analytical and involve complicated forward pass of DNN, solving the nested optimization objective is computationally expensive. Meanwhile, alternating one-step approximation [9, 25] cannot guarantee that the optimization direction is optimal due to coupled update. + +In contrast, in order to avoid coupled optimization over the large searching space of network parameters $w$ , we reformulate the meta-learning objective in DMLP as: + +$$ +\min _ {y t} E _ {(x _ {v}, y _ {v}) \in D _ {v}} \mathcal {L} _ {v a l} (\mathbf {f} _ {v}, y _ {v}; w ^ {*} (y _ {t})), +$$ + +s.t. $w^{*}(y_{t}) = \arg \min_{w}E_{(x_{t},y_{t})\in D_{t}}\mathcal{L}_{train}(\mathbf{f}_{t},y_{t};w),$ (2) + +$$ +\mathbf {f} _ {t} = G (x _ {t}; \theta_ {G} ^ {*}), \quad \mathbf {f} _ {v} = G (x _ {v}; \theta_ {G} ^ {*}), +$$ + +where a pretrained feature extractor $G:\mathbb{R}^{H\times W\times 3}\to \mathbb{R}^d$ is designed to extract $d$ -dimensional image representation $\mathbf{f}$ . In + +![](images/a7e95151bab114d7a4aac1c6a529e125d8c61f7985059abfff42eecedcaad516.jpg) +Figure 3. The overall framework of DMLP. (a) Decoupled meta label purification (Sec. 3.2). (b) The purified labels can be applied in normal network retraining (CE) or other LNL loss (Sec. 3.3). + +order to obtain representation of high quality, these extracted features are utilized in a contrastive self-supervised learning framework [5, 6] to update the parameters $\theta_{G}$ as pretraining without noisy labels. Subsequently, the established feature extractor $\mathbf{f} = G(x; \theta_{G}^{*})$ can learn a noise-agnostic descriptor of image data, which is also highly separable in high dimensional feature space [38]. In this manner, we detach the representation learning from noisy label correction, while keeping strong separability of features. + +Further, since the feature is representative and separable, the loss term $\mathcal{L}_{train}$ and $\mathcal{L}_{val}$ can be formulated with simple risk estimation functions (e.g. linear discrimination) instead of complex DNN forward pass, making it possible to solve the problem of Eq. (2) in a non-nested manner with an analytical solution, which will be introduced in Sec. 3.2. + +# 3.2. Non-nested Meta Label Purifier + +To solve the purification problem of Eq. (2), we propose two mutually reinforced solutions to seek purified training labels as shown in Fig. 3, the intrinsic primary correction (IPC) and extrinsic auxiliary correction (EAC) processes. + +Intrinsic Primary Correction. IPC aims at performing global-wise label purification at a slow and steady pace. Specifically, as shown in Fig. 3 (a), the features and labels of a batch of $b$ training data are gathered into matrix $F_{t} \in \mathbb{R}^{b \times d}$ and $Y_{t} \in \mathbb{R}^{b \times c}$ as: + +$$ +F _ {t} = [ \mathbf {f} _ {t, 1}, \mathbf {f} _ {t, 2}, \dots , \mathbf {f} _ {t, b} ] ^ {T}, Y _ {t} = [ y _ {t, 1}, y _ {t, 2}, \dots , y _ {t, b} ] ^ {T}. (3) +$$ + +Since the feature descriptors are representative, we assume there exists a simple linear estimation transform $w \in \mathbb{R}^{d \times c}$ , which accurately predict the categorical distribution with ridge regression: + +$$ +\min _ {w} \mathcal {L} _ {t r a i n} (F _ {t}, Y _ {t}; w) = \| \sigma (\alpha Y _ {t}) - F _ {t} w \| ^ {2} + \lambda \| w \| ^ {2}, (4) +$$ + +where $\sigma(\cdot)$ is the softmax function along the categorical dimension to meet the normalization constraint, and $\alpha$ is a scaling factor. By solving the linear regression problem of Eq. (4) through least square method (see supplementary material for details), we can obtain its closed-form solution + +$w^{*}(Y_{t})$ on the training batch $(F_{t},Y_{t})$ and derive its optimal prediction via linear regression on samples $\mathbf{f}_{v,i}$ from validation set $D_{v}$ : + +$$ +\begin{array}{l} y _ {v, i} ^ {\prime} (Y _ {t}) = w ^ {*} (Y _ {t}) ^ {T} \mathbf {f} _ {v, i} \\ = \sigma \left(\alpha Y _ {t}\right) ^ {T} F _ {t} \left(F _ {t} ^ {T} F _ {t} + \lambda I\right) ^ {- 1} \mathbf {f} _ {v, i}. \tag {5} \\ \end{array} +$$ + +Intuitively, the discrepancy between the predicted results $y_{v,i}^{\prime}$ and the ground truth labels $y_{v,i}$ of $D_v$ is due to the potential noise from $Y_{t}$ , therefore we take the prediction discrepancy as objective for label purification: + +$$ +\mathcal {L} _ {\text {v a l}} \left(Y _ {t}\right) = \frac {1}{N _ {v}} \sum_ {i = 1} ^ {N _ {v}} \left| \left| y _ {v, i} ^ {\prime} \left(Y _ {t}\right) - y _ {v, i} \right| \right| ^ {2} + \mathcal {H} \left(y _ {v, i} ^ {\prime} \left(Y _ {t}\right)\right), \tag {6} +$$ + +where $\mathcal{H}(\cdot)$ represents the entropy of input distribution as a regularization term to sharpen the predicted label distribution as [35]. With Eq. (5) and Eq. (6), the validation loss can be expressed analytically by training labels $Y_{t}$ in a batch, thus the noisy labels can be corrected steadily with correction rate $\eta_{I}$ by the gradient back-propagated from Eq. (6) as + +$$ +Y _ {t} ^ {p + 1} := Y _ {t} ^ {p} - \eta_ {I} \nabla \left(\mathcal {L} _ {\text {v a l}} \left(Y _ {t} ^ {p}\right)\right). \tag {7} +$$ + +Extrinsic Auxiliary Correction. To accelerate the label correction process, an external correction process is further proposed. Specifically, an accompanied linear classifier $C(\cdot; w_c): \mathbb{R}^d \to \mathbb{R}^c$ with learnable parameter $w_c$ is trained along with the updated labels from IPC: + +$$ +\mathcal {L} _ {\mathrm {c}} \left(w _ {c}\right) = \mathcal {L} _ {\mathrm {c e}} \left(C \left(\mathbf {f} _ {t}; w _ {c}\right), y ^ {\prime} _ {t}\right) + \mathcal {H} \left(C \left(\mathbf {f} _ {t}; w _ {c}\right)\right), \tag {8} +$$ + +where $y_{t}^{\prime}$ is the updated training label from IPC, and $\mathcal{L}_{\mathrm{ce}}$ denotes the cross entropy loss function. Since the accompanied linear classifier is intrinsically robust to noisy labels in $y_{t}^{\prime}$ [24], it can quickly achieve high correction accuracy. With this intuition, the predicted results of the classifier $C(\mathbf{f}_t;w_c)$ are used to correct labels periodically, specifically, the update rule of $Y_{t}$ switches to momentum update (i.e., EMA) every $T$ iterations: + +$$ +Y _ {t} ^ {p + 1} := \left(1 - \eta_ {E}\right) Y _ {t} ^ {p} + \eta_ {E} C \left(F _ {t}; w _ {c}\right) \quad \text {i f} \quad p = n T, \tag {9} +$$ + +Table 1. Comparison with state-of-the-art methods on CIFAR-10/100 datasets with symmetric noise. "CE" is the standard ConvNet trained with Cross-Entropy loss in an end-to-end manner. "Classifier" means adopts the pre-trained SimCLR features to re-train a linear classifier. "Val" denotes using a small clean validation set. DivideMix* denotes training DivideMix with the same validation set as additional data. + +
Dataset +MethodValNoise ratioCIFAR-10CIFAR-100
20%50%80%90%20%50%80%90%
Cross-Entropy (CE)XBest86.879.462.942.762.046.719.910.1
Last82.757.926.116.861.837.38.83.5
Co-teaching+ [36]XBest89.585.767.447.965.651.827.913.7
Last88.284.145.530.164.145.315.58.8
PENCIL [35]XBest92.489.177.558.969.457.531.115.3
Last92.088.776.558.268.156.420.78.8
REED [38]XBest95.895.694.393.676.773.066.959.6
Last95.795.494.193.576.572.266.559.4
Sel-CL+ [18]XBest95.593.989.281.976.572.459.648.8
Last95.193.388.781.676.172.059.248.6
MOIT+ [21]XBest94.191.881.174.775.970.647.641.8
Last93.891.380.674.075.270.146.941.2
C2D-DivideMix [40]XBest96.395.294.493.578.676.467.758.7
Last96.295.194.193.478.376.067.458.4
DivideMix [15]XBest96.194.693.276.077.374.660.231.5
Last95.794.492.975.476.974.259.631.0
Meta-Learning [16]✓Best92.989.377.458.768.559.242.419.5
Last92.088.876.158.367.758.040.114.3
MLC [41]✓Best92.688.177.467.966.852.721.815.0
Last91.887.577.167.066.552.418.914.2
MSLC [9]✓Best93.489.969.856.172.565.424.316.7
Last93.389.468.855.272.064.920.514.6
DivideMix* [15]✓Best96.194.993.677.377.774.860.732.5
Last95.994.693.076.577.174.360.532.2
DMLP-Naive✓Best94.794.293.592.872.768.063.561.3
Last94.294.093.292.072.367.463.260.9
DMLP-DivideMix✓Best96.395.894.594.379.976.868.665.8
Last96.295.694.394.079.476.168.565.4
+ +where $T$ and $\eta_{E}$ are the period and momentum for update, and $n$ is an arbitrary positive integer to denote the $n$ -th time of EAC update. In a global sense, after $T$ iterations of training, EAC can quickly achieve locally optimal label estimation by mimic of gradually updated labels from IPC, which reversely facilitates the label correction of IPC by providing cleaner training labels. Subsequently, IPC and EAC form a positive loop and mutually improve the quality of label correction of each other. + +# 3.3. Application of DMLP + +The DMLP is a flexible label purifier, the corrected training labels $y_{t}^{*}$ can be applied in different ways in robust learning scenarios, as shown in Fig. 3. + +Naive classification network with DMLP. In a simple and direct manner, we can take the purified labels to retrain a neural network with simple cross-entropy loss (CE), here we term this simple application as DMLP-Naive. + +LNL framework boosted by DMLP. Considering that there may still be a small number of noisy or miscorrected labels after purification, another effective way to apply DMLP is to take the purified labels as new training samples for the existing LNL framework. In this work, we extend some classic frameworks [12, 15, 19, 30] with DMLP, and the boosted LNL methods are denoted with prefix of “DMLP-” (e.g. DMLP-DivideMix, DMLP-ELR+, etc.) + +# 4. Experiments + +# 4.1. Experimental Settings + +CIFAR-10/100. For the self-supervised pre-training stage, we adopt the popular SimCLR algorithm [5] with ResNet as the backbone network. Classifiers in meta-learner are trained for 100 epochs with the Adam optimizer. For the final DivideMix algorithm, ResNet18 is adopted for a fair comparison. $\eta_{I}$ and $\eta_{E}$ are set as 0.01 and 1.0 respec + +Table 2. Evaluation results with asymmetric noise of different noisy ratio on CIFAR-10. "Validation" denotes the method exploits a small clean validation set. + +
MethodValidationNoisy ratio
20%40%
Joint-Optim [28]X92.891.7
PENCIL [35]X92.491.2
M-correction [1]X-86.3
Iterative-CV [4]X-88.0
DivideMix [15]X93.493.4
REED [38]X95.092.3
C2D-DivideMix [40]X93.893.4
Sel-CL+ [18]X95.293.4
GCE [11]X87.378.1
RRL [17]X-92.4
Zhang, et al. [39]✓92.790.2
Meta-Learning [16]✓-88.6
MSLC [9]✓94.491.6
DMLP-Naive✓94.693.9
DMLP-DivideMix✓95.295.0
+ +Table 3. Top-1 testing accuracy on Clothing-1M testset. "Validation" denotes using the validation provided by [31]. + +
MethodValidationTop-1 Accuracy
PENCIL [35]X73.49
DivideMix [15]X74.76
RRL [17]X74.90
GCE [11]X73.30
C2D-DivideMix [40]X74.30
REED [38]X75.81
Meta-Learning [16]✓73.47
Self-Learning [13]✓76.44
MLC [41]✓75.78
MSLC [9]✓74.02
Meta-Cleaner [10]✓72.50
Meta-Weight [8]✓73.72
FaMUS [34]✓74.40
MSLG [7]✓76.02
DMLP-Naive✓77.77
DMLP-DivideMix✓78.23
+ +tively. The scaling factor $\alpha$ is set as 1.0. To ensure fair evaluation, we follow previous meta-learning based LNL methods [8, 9] to randomly separate 1,000 images as the clean validation set for CIFAR-10/100 [14], leaving the rest as training samples. We strictly follow the protocol in [12] to generate label noise. Specifically, symmetric noise is generated by replacing labels with one of the other classes uniformly, while the labels in asymmetric noise are disturbed to their similar classes to simulate label noise in real-world scenarios. Our experiments are conducted under different noisy rates: $\pi \in \{20\%, 50\%, 80\%, 90\% \}$ for symmetric and $\pi \in \{20\%, 40\% \}$ for asymmetric noises. + +Clothing1M. For the first stage on the Clothing1M [32], + +the ResNet50 is trained with the official MoCo-v2 [6] to fully leverage its advantages on large-scale datasets. Afterward, the meta-learner is trained for 50 epochs. For DMLP-DivideMix, ResNet50 is adopted and initialized with weights from previous stages and trained for 80 epochs. Due to the space constraint, we put more detailed experimental settings and descriptions of each compared LNL method in our supplementary materials. + +# 4.2. Experimental Results + +Comparison with state-of-the-art methods. We compare our method with multiple recent competitive methods on CIFAR-10/100 under various noisy settings (detailed descriptions of these methods are provided in the supplementary materials). Both test accuracy of the best and last epoch are reported. As shown in Table 1, the simple DMLP-Naive can already achieve competitive results to most methods, the superiority is more obvious in extremely noisy cases, further, the DMLP-DivideMix achieves state-of-the-art performance across all the settings. It is worth noting that directly utilizing the validation data to train DvldeMix (i.e., DivideMix*) only brings marginal improvement, while when equipped with the purified labels by DMLP, significant improvements are obtained, indicating that DMLP is effective in terms of utilizing validation set towards LNL problem. On the other hand, though there exist other meta-learning methods utilizing validation set [9, 16, 41], DMLP shows great advantages over them. It is also noticeable that compared with the original DivideMix, the purified version of DMLP-DivideMix achieves better results by a large margin, indicating that the purified label from our approach is more friendly to boost LNL frameworks. Table 2 shows comparison with the recent methods on asymmetric noisy CIFAR-10 dataset. DMLP-DivideMix outperforms REED by $0.2\%$ and $2.7\%$ under different noisy ratios and obtains greater improvements over the rest methods, demonstrating the ability of DMLP in handling harder semantic-related noise. Finally, DMLP-based methods suffer less from increasing noisy ratio than other competitors, indicating its robustness to variant noisy levels. + +Furthermore, we also evaluate DMLP on the large-scale real-world noisy dataset Clothing1M. As shown in Table 3, simple DMLP-Naive can outperform all other methods by a large margin, and DMLP-DivideMix further improves the accuracy by about $0.46\%$ . The results indicate that DMLP is more suitable for noise from real-world situations. + +Label correction accuracy. Fig. 4 compares the label accuracy after correction in our meta-learner against coupled label purifiers MLC and MSLC on CIFAR-10. Specifically, the one-hot form of the corrected pseudo-labels is compared with the ground truth for evaluation. As Fig. 4 shows, labels can be rapidly corrected to accuracy over $92\%$ in low noise cases. For severe label noise, DMLP can still improve label accuracy similar to low-noise settings. The overall corrected + +Table 4. Comparison between the LNL methods and their DMLP applications with symmetric noise on CIFAR-10/100. Specifically, the 9-layer CNN is adopted as the backbone network of Co-teaching. + +
Dataset +Method/Noise ratioCIFAR-10CIFAR-100
20%50%80%90%20%50%80%90%
Co-teaching [12]Best82.673.024.014.650.538.211.84.9
Last81.972.623.511.750.338.011.34.3
DMLP-Co-teachingBest85.885.885.484.651.249.848.145.3
Last85.685.685.384.551.049.347.845.1
CDR [30]Best90.485.047.212.363.339.529.28.0
Last82.749.416.610.162.939.59.74.5
DMLP-CDRBest91.491.291.290.269.264.861.458.5
Last91.290.890.689.368.364.361.157.9
ELR+ [19]Best94.693.891.175.277.572.458.230.8
Last94.493.790.573.576.272.256.830.6
DMLP-ELR+Best94.994.193.092.577.873.663.960.5
Last94.694.092.792.177.173.463.660.5
+ +![](images/611b5fd0a0d8f77049fbce68fb27a5e20e8408ea09db054299683e99434221ad.jpg) +Figure 4. Comparison of corrected label accuracy under symmetric-20% (left), symmetric-80% (right) noise settings on CIFAR-10. Label accuracy within DMLP is superior against other competitors across all noise settings (More detailed experimental results can be found in the supplementary material). + +![](images/b8fa7779cb5b86beb572d1c55558d363158f6d0541a1b6ba3cbc553365374cd6.jpg) + +Generality of DMLP. To validate the generalization ability of DMLP, other than DivideMix, another three popular LNL methods, $\mathrm{ELR + }$ [19], Co-teaching [12], and CDR [30] are further adopted to work collaboratively with purified labels of DMLP. As shown in Table 4, all the applications of DMLP perform consistently better over their corresponding baselines, and the improvement becomes more significant when it comes to high-level noise cases. It is worth noting that since CDR highly relies on the early stopping technique, it suffers from a severe memorization effect in the training process, leading to a discrepancy between best results and last performance. In contrast, when training CDR with our purified labels, this discrepancy almost disappears, demonstrating the labels output by DMLP have a better quality to suppress the memorization effect, thus alleviating the reliance on early stopping. Therefore, the results indicate that the purified labels of DMLP are friendly to boost LNL frameworks. More detailed experimental results can be found in the supplementary materials. + +# 4.3. Ablation Studies + +Analysis on different label correction process. We explore the influence of IPC and EAC on the performance + +Table 5. Ablation study for the effectiveness of IPC and EAC in DMLP-Naive on CIFAR-10. + +
ComponentCIFAR-10Clothing
IPCEAC20%50%80%90%1M
X✓Best93.793.391.167.476.5
Last93.092.990.666.576.1
✓XBest87.885.779.976.076.8
Last87.285.579.475.476.5
✓✓Best94.794.293.592.877.7
Last94.294.093.292.077.6
+ +of DMLP-Naive in Table 5, when one of the process is excluded, the updated labels from the other are applied to retrain a new model. It is observed that EAC performs well in low noise cases due to its intrinsic robustness, as the noise ratio increases, the performance drops rapidly. On the other hand, IPC is more robust to high-level noise, but there exists a large gap compared with the full DMLP pipeline due to its slow optimization process. In contrast, when IPC and EAC work collaboratively, DMLP can achieve optimal results. + +Comparison against other coupled purifiers with pretraining. To solely evaluate the influence of decoupled purification, we train two coupled meta label correction methods MLC and MSLC with the same self-supervised pretrained weights and apply their corrected labels to naive training or DivideMix for fair comparisons. As shown in Table. 6, though self-supervised weights can marginally boost the performance of coupled label correctors, there still exists a large gap between their performance and DMLP, especially for high noisy cases. Moreover, when further applying the corrected labels to mainstream LNL framework DivideMix, our method can also consistently outperform the coupled counterparts across all the noisy settings, demonstrating our corrected labels are of better quality. Therefore, these results verify that the superiority mainly attributes to decoupled + +Table 6. Comparison with coupled meta label correction methods MLC [41] and MSLC [9] on CIFAR-10. " *" denotes training with SimCLR pretrained ResNet-18. + +
MethodNoisy ratio
20%50%80%90%
MLC*Best91.886.277.672.9
Last91.685.977.572.6
MSLC*Best92.087.778.067.8
Last92.087.577.967.3
DMLP-Naive*Best94.093.793.192.3
Last93.993.492.991.9
MLC*-DivideMixBest95.394.093.086.6
Last95.093.692.786.5
MSLC*-DivideMixBest95.794.993.883.0
Last95.594.893.182.8
DMLP*-DivideMixBest96.395.694.193.8
Last96.095.294.093.6
+ +Table 7. Investigation of the validation set size $\tau$ on Clothing1M. + +
τ10%20%30%40%50%100%
Accuracy (%)75.5076.4076.6177.0077.3077.31
+ +label correction instead of self-supervised pretraining. + +Effect of different feature representation for purification. The quality of features plays a crucial role in the label correction process of DMLP since the distribution of learned features is closely related to the rationality behind the linear estimation assumption in high-dimensional space. Therefore, we study the influence of different features on performance. Specifically, two types of features are investigated, including features from the ResNet-18/50 which load the self-supervised pre-trained weights. As the results in Table 8 show, the features from the ResNet-18 lead to slightly poor performance, while it brings performance improvements when using features from self-supervised ResNet-50. This observation indicates that although feature representation of higher quality benefits the purification results, DMLP is not very sensitive to the representation ability of input feature. + +Effect of validation size. We examine how the number of validation set affects performance. Specifically, validation sizes from $10\%$ to $100\%$ of the whole validation set are evaluated on Clothing1M for DMLP-Naive. As shown in Table 7, DMLP-Naive achieves similar performance regardless of the validation size $N_v$ , demonstrating DMLP is not sensitive to the number of images. It is worth noting that even using only $10\%$ of the validation set (around $0.1\%$ of training data), DMLP-Naive still achieves high accuracy and outperforms most methods in Table.3, indicating that the effectiveness of DMLP is not heavily relied on validation size. + +Performance under extremely noisy setting. In an extremely noisy scenario where all labels in the training set are unreliable except the given clean validation set, the LNL problem is converted into a semi-supervised learning prob + +Table 8. Ablation study for adopting different features in DMLP-Naive on CIFAR-10, where "R18/50" denote "ResNet-18/50" and "M/S" represent "MoCo/SimCLR". + +
Feature SourceNoisy ratio
20%50%80%90%
R18 (M)Best93.893.392.290.4
Last93.792.792.190.0
R18 (S)Best94.093.793.192.3
Last93.993.492.991.9
R50 (S)Best94.794.293.592.8
Last94.294.093.292.0
+ +Table 9. Comparison between recent semi-supervised methods and DMLP-DivideMix on CIFAR-10/100 with $100\%$ noisy ratio. + +
MethodCIFAR-10CIFAR-100
MeanTeacher83.031.0
MixMatch87.957.7
FixMatch88.156.3
UDA88.256.1
Ours91.760.1
+ +lem, therefore we further compare DMLP-DivideMix with some state-of-the-art semi-supervised learning algorithms, including MeanTeacher [29], MixMatch [3], FixMatch [26] and UDA [33], under the $100\%$ symmetric noise case on CIFAR-10 and CIFAR-100. From the results in Table 9, DMLP-DivideMix performs optimally among all methods when using the validation set as labeled samples, indicating the proposed method is potential for broader applications. + +# 5. Conclusion + +In this paper, we propose a flexible and novel multi-stage robust learning approach termed as DMLP. The core of DMLP is a carefully-designed meta-learning based label purifier, which decouples the complex bi-level optimization problem into representation and label distribution learning, thus helping the meta-learner focus on correcting noisy labels in a faster and more precise manner even under extremely noisy scenarios. Further, DMLP can be applied either for naive retraining on noisy data or assistance of existing LNL methods to boost performance. Extensive experiments conducted on several synthetic and real-world noisy datasets verify the superiority of the proposed method. + +# Acknowledgement + +This work was supported by National Natural Science Fund of China (62076184, 61976158, 61976160, 62076182, 62276190), in part by Fundamental Research Funds for the Central Universities and State Key Laboratory of Integrated Services Networks (Xidian University), in part by Shanghai Innovation Action Project of Science and Technology (20511100700) and Shanghai Natural Science Foundation (22ZR1466700). + +# References + +[1] Eric Arazo, Diego Ortego, Paul Albert, Noel E O'Connor, and Kevin McGuinness. Unsupervised label noise modeling and loss correction. In Proc. 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Springer, 2023. +[38] Hui Zhang and Quanming Yao. Decoupling representation and classifier for noisy label learning. arXiv preprint arXiv:2011.08145, 2020. +[39] Z. Zhang, H. Zhang, S. Arik, H. Lee, and T. Pfister. Distilling effective supervision from severe label noise. In Proc. IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2020. +[40] Evgenii Zheltonozhskii, Chaim Baskin, Avi Mendelson, Alex M Bronstein, and Or Litany. Contrast to divide: Self-supervised pre-training for learning with noisy labels. In Proc. IEEE/CVF Winter Conference on Applications of Computer Vision (WACV), pages 1657-1667, 2022. +[41] Guoqing Zheng, Ahmed Hassan Awadallah, and Susan Dumas. Meta label correction for noisy label learning. 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"content": "Abstract" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 281, + 290, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 281, + 290, + 616 + ], + "spans": [ + { + "bbox": [ + 46, + 281, + 290, + 616 + ], + "type": "text", + "content": "Training deep neural networks (DNN) with noisy labels is challenging since DNN can easily memorize inaccurate labels, leading to poor generalization ability. Recently, the meta-learning based label correction strategy is widely adopted to tackle this problem via identifying and correcting potential noisy labels with the help of a small set of clean validation data. Although training with purified labels can effectively improve performance, solving the meta-learning problem inevitably involves a nested loop of bi-level optimization between model weights and hyper-parameters (i.e., label distribution). As compromise, previous methods resort to a coupled learning process with alternating update. In this paper, we empirically find such simultaneous optimization over both model weights and label distribution can not achieve an optimal routine, consequently limiting the representation ability of backbone and accuracy of corrected labels. From this observation, a novel multi-stage label purifier named DMLP is proposed. DMLP decouples the label correction process into label-free representation learning and a simple meta label purifier. In this way, DMLP can focus on extracting discriminative feature and label correction in two distinctive stages. DMLP is a plug-and-play label purifier, the purified labels can be directly reused in naive end-to-end network retraining or other robust learning methods, where state-of-the-art results are obtained on several synthetic and real-world noisy datasets, especially under high noise levels. Code is available at https://github.com/yuanpengtu/DMLP." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 639, + 128, + 651 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 639, + 128, + 651 + ], + "spans": [ + { + "bbox": [ + 47, + 639, + 128, + 651 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 660, + 289, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 660, + 289, + 685 + ], + "spans": [ + { + "bbox": [ + 47, + 660, + 289, + 685 + ], + "type": "text", + "content": "Deep learning has achieved significant progress on various recognition tasks. The key to its success is the availabil" + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 326, + 255, + 524, + 425 + ], + "blocks": [ + { + "bbox": [ + 326, + 255, + 524, + 425 + ], + "lines": [ + { + "bbox": [ + 326, + 255, + 524, + 425 + ], + "spans": [ + { + "bbox": [ + 326, + 255, + 524, + 425 + ], + "type": "image", + "image_path": "e3936704b0d16aaab9a514b36ed00d4a9038cb15ea5b7a85501d3d45013cff1e.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 428, + 547, + 473 + ], + "lines": [ + { + "bbox": [ + 305, + 428, + 547, + 473 + ], + "spans": [ + { + "bbox": [ + 305, + 428, + 547, + 473 + ], + "type": "text", + "content": "Figure 1. (a) Traditional coupled alternating update to solve meta label purification problem, and (b) the proposed DMLP method that decouples the label purification process into representation learning and a simple non-nested meta label purifier." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 482, + 547, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 482, + 547, + 555 + ], + "spans": [ + { + "bbox": [ + 304, + 482, + 547, + 555 + ], + "type": "text", + "content": "ity of large-scale datasets with reliable annotations. Collecting such datasets, however, is time-consuming and expensive. Easy ways to obtain labeled data, such as web crawling [31], inevitably yield samples with noisy labels, which is not appropriate to be directly utilized to train DNN since these complex models are vulnerable to memorize noisy labels [2]." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 558, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 548, + 715 + ], + "type": "text", + "content": "Towards this problem, numerous Learning with Noisy Label (LNL) approaches were proposed. Classical LNL methods focus on identifying the noisy samples and reducing their effect on parameter updates by abandoning [12] or assigning smaller importance. However, when it comes to extremely noisy and complex scenarios, such scheme struggles since there is no sufficient clean data to train a discriminative classifier. Therefore, label correction approaches are proposed to augment clean training samples by revising noisy labels to underlying correct ones. Among them, meta-learning based approaches [9, 16, 25] achieve state-of-the-art performance via resorting to a small clean validation set and taking noisy labels as hyper-parameters, which provides sound guidance" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 61, + 693, + 131, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 693, + 131, + 703 + ], + "spans": [ + { + "bbox": [ + 61, + 693, + 131, + 703 + ], + "type": "text", + "content": "* Equal contribution." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 61, + 703, + 141, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 703, + 141, + 713 + ], + "spans": [ + { + "bbox": [ + 61, + 703, + 141, + 713 + ], + "type": "text", + "content": "† Corresponding author." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "19934" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 167 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 167 + ], + "type": "text", + "content": "toward underlying label distribution of clean samples. However, such meta purification inevitably involves a nested bi-level optimization problem on both model weight and hyper-parameters (shown as Fig. 1 (a)), which is computationally infeasible. As a compromise, the alternating update between model weights and hyper-parameters is adopted to optimize the objective [9, 16, 25], leading to a coupled solution for representation learning and label purification." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 170, + 288, + 266 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 170, + 288, + 266 + ], + "spans": [ + { + "bbox": [ + 46, + 170, + 288, + 266 + ], + "type": "text", + "content": "Empirical observation. Intuitively, alternate optimization over a large search space (model weight and hyperparameters) may lead to sub-optimal solutions. To investigate how such approximation affects results in robust learning, we conduct empirical analysis on CIFAR-10 [14] with recent label purification methods MLC [41] and MSLC [9], which consist of a deep model and a meta label correction network, and make observation as Fig. 2." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 267, + 288, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 267, + 288, + 399 + ], + "spans": [ + { + "bbox": [ + 46, + 267, + 288, + 399 + ], + "type": "text", + "content": "- Coupled optimization hinders quality of corrected labels. We first compare the Coupled meta corrector MLC with its extremely Decoupled variant where the model weights are first optimized for 70 epochs with noisy labels and get fixed, then labels are purified with the guidance of validation set. We adopt the accuracy of corrected label to measure the performance of purification. From Fig. 2 (a), we can clearly observe that compared with Decoupled counterpart, joint optimization yields inferior correction performance, and these miscorrection will reversely affect the representation learning in coupled optimization." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 401, + 288, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 401, + 288, + 616 + ], + "spans": [ + { + "bbox": [ + 46, + 401, + 288, + 616 + ], + "type": "text", + "content": "- Coupled optimization hinders representation ability. We investigate the representation quality by evaluating the linear prob accuracy [6] of extracted feature in Fig. 2 (b). We find the representation quality of Coupled training is much worse at the beginning, which leads to slow and unstable representation learning in the later stage. To further investigate the effect on representation learning, we also resort to a well pretrained backbone with self-supervised learning [5] as initialization, recent research [40] shows pretrained representation is substantially helpful for LNL framework. However, we find this conclusion does not strictly hold for coupled meta label correctors. As shown in Fig. 2 (c), by comparing the classification accuracy from classifier of MLC/MSLC, we observe the pretrained model only brings marginal improvement if model weights is still coupled with hyper-parameters. In contrast, when the weight of backbone is fixed and decoupled from the label purification and classifier, the improvement becomes more significant." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 618, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 618, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 618, + 288, + 715 + ], + "type": "text", + "content": "Decoupled Meta Purification. From the observation above, we find the decoupling between model weights and hyperparameters of meta correctors is essential to label accuracy and final results. Therefore, in this paper, we aim at detaching the meta label purification from representation learning and designing a simple meta label purifier which is more friendly to optimization of label distribution problem than existing complex meta networks [9, 41]. Hence" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 72, + 547, + 371 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 371 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 371 + ], + "type": "text", + "content": "we propose a general multi-stage label correction strategy, named Decoupled Meta Label Purifier (DMLP). The core of DMLP is a meta-learning based label purifier, however, to avoid solving the bi-level optimization with a coupled solution, DMLP decouples this process into self-supervised representation learning and a linear meta-learner to fit underlying correct label distribution (illustrated as Fig. 1 (b)), thus simplifies the label purification stage as a single-level optimization problem. The simple meta-learner is carefully designed with two mutually reinforcing correcting processes, named intrinsic primary correction (IPC) and extrinsic auxiliary correction (EAC) respectively. IPC plays the role of purifying labels in a global sense at a steady pace, while EAC targets at accelerating the purification process via looking ahead (i.e., training with) the updated labels from IPC. The two processes can enhance the ability of each other and form a positive loop of label correction. Our DMLP framework is flexible for application, the purified labels can either be directly applied for naive end-to-end network retraining, or exploited to boost the performance of existing LNL frameworks. Extensive experiments conducted on mainstream benchmarks, including synthetic (noisy versions of CIFAR) and real-world (Clothing1M) datasets, demonstrate the superiority of DMLP. In a nutshell, the key contributions of this paper include:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 372, + 547, + 575 + ], + "type": "list", + "angle": 0, + "index": 9, + "blocks": [ + { + "bbox": [ + 304, + 372, + 547, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 372, + 547, + 443 + ], + "spans": [ + { + "bbox": [ + 304, + 372, + 547, + 443 + ], + "type": "text", + "content": "- We analyze the necessity of decoupled optimization for label correction in robust learning, based on which we propose DMLP, a flexible and novel multi-stage label purifier that solves bi-level meta-learning problem with a decoupled manner, which consists of representation learning and non-nested meta label purification;" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 443, + 547, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 443, + 547, + 514 + ], + "spans": [ + { + "bbox": [ + 304, + 443, + 547, + 514 + ], + "type": "text", + "content": "- In DMLP, a novel non-nested meta label purifier equipped with two correctors, IPC and EAC is proposed. IPC is a global and steady corrector, while EAC accelerates the correction process via training with the updated labels from IPC. The two processes form a positive training loop to learn more accurate label distribution;" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 514, + 547, + 575 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 514, + 547, + 575 + ], + "spans": [ + { + "bbox": [ + 304, + 514, + 547, + 575 + ], + "type": "text", + "content": "- Deep models trained with purified labels from DMLP achieve state-of-the-art results on several synthetic and real-world noisy datasets across various types and levels of label noise, especially under high noise levels. Extensive ablation studies are provided to verify the effectiveness." + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 586, + 398, + 597 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 586, + 398, + 597 + ], + "spans": [ + { + "bbox": [ + 306, + 586, + 398, + 597 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 605, + 547, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 547, + 640 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 547, + 640 + ], + "type": "text", + "content": "The existing LNL approaches that are related to our work can be coarsely categorized into two groups: noisy sample detection and label correction." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "type": "text", + "content": "Noisy sample detection methods aim to identify and reduce the importance of suspicious false-labeled samples during training. The detected noisy samples are abandoned [12, 23], assigned with smaller weights via a sample re-weight training scheme [20, 37], or used to formulate a semi-supervised learning problem by throwing away the" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "19935" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 59, + 71, + 206, + 199 + ], + "blocks": [ + { + "bbox": [ + 59, + 71, + 206, + 199 + ], + "lines": [ + { + "bbox": [ + 59, + 71, + 206, + 199 + ], + "spans": [ + { + "bbox": [ + 59, + 71, + 206, + 199 + ], + "type": "image", + "image_path": "8a50c9cb329dbdebc1218cb7e70137130b7bdedfbd2aafd074a359b75750c040.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 213, + 70, + 361, + 199 + ], + "blocks": [ + { + "bbox": [ + 213, + 70, + 361, + 199 + ], + "lines": [ + { + "bbox": [ + 213, + 70, + 361, + 199 + ], + "spans": [ + { + "bbox": [ + 213, + 70, + 361, + 199 + ], + "type": "image", + "image_path": "98d6b66e344d31d229eb5d5f3ff924c2997373e6d6e6b55d843eca7a3d232509.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 366, + 70, + 532, + 200 + ], + "blocks": [ + { + "bbox": [ + 366, + 70, + 532, + 200 + ], + "lines": [ + { + "bbox": [ + 366, + 70, + 532, + 200 + ], + "spans": [ + { + "bbox": [ + 366, + 70, + 532, + 200 + ], + "type": "image", + "image_path": "d0abbb336eeae71722088e95b43213f527a7ae5db69bbc1c3d8b0ecdc0c83187.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 200, + 547, + 243 + ], + "lines": [ + { + "bbox": [ + 46, + 200, + 547, + 243 + ], + "spans": [ + { + "bbox": [ + 46, + 200, + 547, + 243 + ], + "type": "text", + "content": "Figure 2. The corrected label accuracy (a) and linear probe accuracy of representations (b) between coupled [41] and decoupled label correction schemes during training under " + }, + { + "bbox": [ + 46, + 200, + 547, + 243 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 46, + 200, + 547, + 243 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 200, + 547, + 243 + ], + "type": "inline_equation", + "content": "90\\%" + }, + { + "bbox": [ + 46, + 200, + 547, + 243 + ], + "type": "text", + "content": " symmetric label noise on CIFAR-10. (c) investigates the effect of representation learning on 'Ori'-original coupled network training from scratch, 'SimCLR-Coupled'-initialization with stronger self-supervised pretrained weights and 'SimCLR-Decoupled'-further fix the pretrained backbone during label purification." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 247, + 288, + 295 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 247, + 288, + 295 + ], + "spans": [ + { + "bbox": [ + 46, + 247, + 288, + 295 + ], + "type": "text", + "content": "labels while keeping the unlabeled data [15,38]. These methods show robustness under certain noise levels, but struggle when it comes to extremely noisy and complex scenarios since there is no sufficient clean data to train a classifier." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 312, + 289, + 636 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 312, + 289, + 636 + ], + "spans": [ + { + "bbox": [ + 46, + 312, + 289, + 636 + ], + "type": "text", + "content": "Label correction approaches attempt to augment the training set by finding and correcting noisy labels to their underlying true ones. To do so, some works [22] try to estimate the noise transition matrix. However, these methods usually assume that the noise type is class-dependent, which may be inappropriate for more complex noise settings, such as real-world noisy datasets [31]. Some other works resort to exploiting the prediction of the network, both soft [1, 13, 24, 35] and hard [27, 28] label correction schemes are designed. However, the predictions of overparameterized backbone network can be unreliable since it tends to fluctuate during training in the presence of false-labeled data ([38]). Another line of works utilize robust representations learned via unsupervised contrastive learning methods [11, 17, 38, 40] to eliminate the interference of noisy labels, which provides a reliable initialization of deep models. Recently, meta-learning based methods [9, 16, 25, 41] show great potential towards LNL problems with the help of a small clean validation set to provide sound guidance toward underlying label distribution of clean sample. However, these approaches involves a bi-level optimization problem on model weights and hyper-parameters, which is too computationally expensive to optimize. As a compromise, the one-step approximation is commonly adopted [9, 41] to convert the nested objective into a coupled update procedure between model weights and hyper-parameters, leading to sub-optimal performance." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 653, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 288, + 713 + ], + "type": "text", + "content": "Accordingly, DMLP belongs to the label correction group via meta-learning strategy, but unlike previous meta-learning based methods [9,41], the learning process on model weights and labels are decoupled into individual stages within DMLP. Next, we will introduce the proposed DMLP in detail." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 246, + 361, + 257 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 246, + 361, + 257 + ], + "spans": [ + { + "bbox": [ + 306, + 246, + 361, + 257 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 266, + 545, + 278 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 266, + 545, + 278 + ], + "spans": [ + { + "bbox": [ + 306, + 266, + 545, + 278 + ], + "type": "text", + "content": "3.1. Decoupled Solution to Meta Label Purification" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 284, + 545, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 284, + 545, + 380 + ], + "spans": [ + { + "bbox": [ + 305, + 284, + 545, + 380 + ], + "type": "text", + "content": "For convenience, notations within DMLP are clarified first. The noisy training dataset is denoted as " + }, + { + "bbox": [ + 305, + 284, + 545, + 380 + ], + "type": "inline_equation", + "content": "D_{t} = \\{(x_{i},y_{i})|1\\leq i\\leq N_{t}\\}" + }, + { + "bbox": [ + 305, + 284, + 545, + 380 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 305, + 284, + 545, + 380 + ], + "type": "inline_equation", + "content": "x_{i}\\in \\mathbb{R}^{H\\times W\\times 3},y_{i}\\in \\{0,1\\}^{c}" + }, + { + "bbox": [ + 305, + 284, + 545, + 380 + ], + "type": "text", + "content": " are the image and corrupted label of the " + }, + { + "bbox": [ + 305, + 284, + 545, + 380 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 305, + 284, + 545, + 380 + ], + "type": "text", + "content": "-th instance, " + }, + { + "bbox": [ + 305, + 284, + 545, + 380 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 305, + 284, + 545, + 380 + ], + "type": "text", + "content": " is the class number. Similarly, a small clean validation dataset is denoted as " + }, + { + "bbox": [ + 305, + 284, + 545, + 380 + ], + "type": "inline_equation", + "content": "D_{v} = \\{(x_{i},y_{i})|1\\leq i\\leq N_{v}\\}" + }, + { + "bbox": [ + 305, + 284, + 545, + 380 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 305, + 284, + 545, + 380 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 305, + 284, + 545, + 380 + ], + "type": "text", + "content": " denotes the dataset size, and " + }, + { + "bbox": [ + 305, + 284, + 545, + 380 + ], + "type": "inline_equation", + "content": "N_{v}\\ll N_{t}" + }, + { + "bbox": [ + 305, + 284, + 545, + 380 + ], + "type": "text", + "content": ". The subscripts " + }, + { + "bbox": [ + 305, + 284, + 545, + 380 + ], + "type": "inline_equation", + "content": "t,v" + }, + { + "bbox": [ + 305, + 284, + 545, + 380 + ], + "type": "text", + "content": " represent the data is from training set or validation set." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 380, + 545, + 416 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 380, + 545, + 416 + ], + "spans": [ + { + "bbox": [ + 305, + 380, + 545, + 416 + ], + "type": "text", + "content": "Typical meta-learning based purification requires solving a bi-level optimization problem on both model weights and hyper-parameters with objective:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 345, + 422, + 545, + 445 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 345, + 422, + 545, + 445 + ], + "spans": [ + { + "bbox": [ + 345, + 422, + 545, + 445 + ], + "type": "interline_equation", + "content": "\\min _ {\\theta_ {\\alpha}} E _ {(x _ {v}, y _ {v}) \\in D _ {v}} \\mathcal {L} _ {v a l} (x _ {v}, y _ {v}; w ^ {*} (\\theta_ {\\alpha})), \\tag {1}", + "image_path": "157dd849764bbdfd1b131e9f43fb85fc33317de144fe4bb106b53a0e7b22223d.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 312, + 441, + 530, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 441, + 530, + 456 + ], + "spans": [ + { + "bbox": [ + 312, + 441, + 530, + 456 + ], + "type": "text", + "content": "s.t. " + }, + { + "bbox": [ + 312, + 441, + 530, + 456 + ], + "type": "inline_equation", + "content": "w^{*}(\\theta_{\\alpha}) = \\arg \\min_{w}E_{(x_{t},y_{t})\\in D_{t}}\\mathcal{L}_{train}(x_{t},y_{t};w,\\theta_{\\alpha})," + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 468, + 547, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 468, + 547, + 586 + ], + "spans": [ + { + "bbox": [ + 304, + 468, + 547, + 586 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 468, + 547, + 586 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 304, + 468, + 547, + 586 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 468, + 547, + 586 + ], + "type": "inline_equation", + "content": "\\theta_{\\alpha}" + }, + { + "bbox": [ + 304, + 468, + 547, + 586 + ], + "type": "text", + "content": " denote the model weights and the meta hyper-parameters respectively. In the classical label purification pipeline, " + }, + { + "bbox": [ + 304, + 468, + 547, + 586 + ], + "type": "inline_equation", + "content": "\\theta_{\\alpha}" + }, + { + "bbox": [ + 304, + 468, + 547, + 586 + ], + "type": "text", + "content": " is reparameterized as a function of noisy label distribution, i.e. " + }, + { + "bbox": [ + 304, + 468, + 547, + 586 + ], + "type": "inline_equation", + "content": "\\theta_{\\alpha} = g(y_{t})" + }, + { + "bbox": [ + 304, + 468, + 547, + 586 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 468, + 547, + 586 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{val}" + }, + { + "bbox": [ + 304, + 468, + 547, + 586 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 468, + 547, + 586 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{train}" + }, + { + "bbox": [ + 304, + 468, + 547, + 586 + ], + "type": "text", + "content": " are the loss function on different datasets. Since both loss terms are not analytical and involve complicated forward pass of DNN, solving the nested optimization objective is computationally expensive. Meanwhile, alternating one-step approximation [9, 25] cannot guarantee that the optimization direction is optimal due to coupled update." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 587, + 547, + 623 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 587, + 547, + 623 + ], + "spans": [ + { + "bbox": [ + 305, + 587, + 547, + 623 + ], + "type": "text", + "content": "In contrast, in order to avoid coupled optimization over the large searching space of network parameters " + }, + { + "bbox": [ + 305, + 587, + 547, + 623 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 305, + 587, + 547, + 623 + ], + "type": "text", + "content": ", we reformulate the meta-learning objective in DMLP as:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 354, + 628, + 499, + 645 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 354, + 628, + 499, + 645 + ], + "spans": [ + { + "bbox": [ + 354, + 628, + 499, + 645 + ], + "type": "interline_equation", + "content": "\\min _ {y t} E _ {(x _ {v}, y _ {v}) \\in D _ {v}} \\mathcal {L} _ {v a l} (\\mathbf {f} _ {v}, y _ {v}; w ^ {*} (y _ {t})),", + "image_path": "00b9ebc671db014f49d2d6d27d3b4dcf161da08fa3c2bd247ced298356ad3aa2.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 324, + 648, + 545, + 663 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 324, + 648, + 545, + 663 + ], + "spans": [ + { + "bbox": [ + 324, + 648, + 545, + 663 + ], + "type": "text", + "content": "s.t. " + }, + { + "bbox": [ + 324, + 648, + 545, + 663 + ], + "type": "inline_equation", + "content": "w^{*}(y_{t}) = \\arg \\min_{w}E_{(x_{t},y_{t})\\in D_{t}}\\mathcal{L}_{train}(\\mathbf{f}_{t},y_{t};w)," + }, + { + "bbox": [ + 324, + 648, + 545, + 663 + ], + "type": "text", + "content": " (2)" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 364, + 666, + 498, + 678 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 364, + 666, + 498, + 678 + ], + "spans": [ + { + "bbox": [ + 364, + 666, + 498, + 678 + ], + "type": "interline_equation", + "content": "\\mathbf {f} _ {t} = G (x _ {t}; \\theta_ {G} ^ {*}), \\quad \\mathbf {f} _ {v} = G (x _ {v}; \\theta_ {G} ^ {*}),", + "image_path": "51d40eaa46871c7b998490681ac05142130327126f98e8927ec9165aaad3e67a.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": "where a pretrained feature extractor " + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "inline_equation", + "content": "G:\\mathbb{R}^{H\\times W\\times 3}\\to \\mathbb{R}^d" + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": " is designed to extract " + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": "-dimensional image representation " + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{f}" + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": ". In" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19936" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 63, + 72, + 531, + 198 + ], + "blocks": [ + { + "bbox": [ + 63, + 72, + 531, + 198 + ], + "lines": [ + { + "bbox": [ + 63, + 72, + 531, + 198 + ], + "spans": [ + { + "bbox": [ + 63, + 72, + 531, + 198 + ], + "type": "image", + "image_path": "a7e95151bab114d7a4aac1c6a529e125d8c61f7985059abfff42eecedcaad516.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 198, + 547, + 220 + ], + "lines": [ + { + "bbox": [ + 46, + 198, + 547, + 220 + ], + "spans": [ + { + "bbox": [ + 46, + 198, + 547, + 220 + ], + "type": "text", + "content": "Figure 3. The overall framework of DMLP. (a) Decoupled meta label purification (Sec. 3.2). (b) The purified labels can be applied in normal network retraining (CE) or other LNL loss (Sec. 3.3)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 224, + 289, + 331 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 224, + 289, + 331 + ], + "spans": [ + { + "bbox": [ + 46, + 224, + 289, + 331 + ], + "type": "text", + "content": "order to obtain representation of high quality, these extracted features are utilized in a contrastive self-supervised learning framework [5, 6] to update the parameters " + }, + { + "bbox": [ + 46, + 224, + 289, + 331 + ], + "type": "inline_equation", + "content": "\\theta_{G}" + }, + { + "bbox": [ + 46, + 224, + 289, + 331 + ], + "type": "text", + "content": " as pretraining without noisy labels. Subsequently, the established feature extractor " + }, + { + "bbox": [ + 46, + 224, + 289, + 331 + ], + "type": "inline_equation", + "content": "\\mathbf{f} = G(x; \\theta_{G}^{*})" + }, + { + "bbox": [ + 46, + 224, + 289, + 331 + ], + "type": "text", + "content": " can learn a noise-agnostic descriptor of image data, which is also highly separable in high dimensional feature space [38]. In this manner, we detach the representation learning from noisy label correction, while keeping strong separability of features." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 332, + 290, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 332, + 290, + 403 + ], + "spans": [ + { + "bbox": [ + 46, + 332, + 290, + 403 + ], + "type": "text", + "content": "Further, since the feature is representative and separable, the loss term " + }, + { + "bbox": [ + 46, + 332, + 290, + 403 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{train}" + }, + { + "bbox": [ + 46, + 332, + 290, + 403 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 332, + 290, + 403 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{val}" + }, + { + "bbox": [ + 46, + 332, + 290, + 403 + ], + "type": "text", + "content": " can be formulated with simple risk estimation functions (e.g. linear discrimination) instead of complex DNN forward pass, making it possible to solve the problem of Eq. (2) in a non-nested manner with an analytical solution, which will be introduced in Sec. 3.2." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 420, + 219, + 431 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 420, + 219, + 431 + ], + "spans": [ + { + "bbox": [ + 47, + 420, + 219, + 431 + ], + "type": "text", + "content": "3.2. Non-nested Meta Label Purifier" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 438, + 287, + 486 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 438, + 287, + 486 + ], + "spans": [ + { + "bbox": [ + 46, + 438, + 287, + 486 + ], + "type": "text", + "content": "To solve the purification problem of Eq. (2), we propose two mutually reinforced solutions to seek purified training labels as shown in Fig. 3, the intrinsic primary correction (IPC) and extrinsic auxiliary correction (EAC) processes." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 487, + 288, + 546 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 487, + 288, + 546 + ], + "spans": [ + { + "bbox": [ + 46, + 487, + 288, + 546 + ], + "type": "text", + "content": "Intrinsic Primary Correction. IPC aims at performing global-wise label purification at a slow and steady pace. Specifically, as shown in Fig. 3 (a), the features and labels of a batch of " + }, + { + "bbox": [ + 46, + 487, + 288, + 546 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 46, + 487, + 288, + 546 + ], + "type": "text", + "content": " training data are gathered into matrix " + }, + { + "bbox": [ + 46, + 487, + 288, + 546 + ], + "type": "inline_equation", + "content": "F_{t} \\in \\mathbb{R}^{b \\times d}" + }, + { + "bbox": [ + 46, + 487, + 288, + 546 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 487, + 288, + 546 + ], + "type": "inline_equation", + "content": "Y_{t} \\in \\mathbb{R}^{b \\times c}" + }, + { + "bbox": [ + 46, + 487, + 288, + 546 + ], + "type": "text", + "content": " as:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 553, + 289, + 569 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 553, + 289, + 569 + ], + "spans": [ + { + "bbox": [ + 55, + 553, + 289, + 569 + ], + "type": "interline_equation", + "content": "F _ {t} = [ \\mathbf {f} _ {t, 1}, \\mathbf {f} _ {t, 2}, \\dots , \\mathbf {f} _ {t, b} ] ^ {T}, Y _ {t} = [ y _ {t, 1}, y _ {t, 2}, \\dots , y _ {t, b} ] ^ {T}. (3)", + "image_path": "3526d6bcfbceb426e1500f7449c13775c8f3878be4fcc34a6009f7308f7ecb7d.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 574, + 289, + 623 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 574, + 289, + 623 + ], + "spans": [ + { + "bbox": [ + 46, + 574, + 289, + 623 + ], + "type": "text", + "content": "Since the feature descriptors are representative, we assume there exists a simple linear estimation transform " + }, + { + "bbox": [ + 46, + 574, + 289, + 623 + ], + "type": "inline_equation", + "content": "w \\in \\mathbb{R}^{d \\times c}" + }, + { + "bbox": [ + 46, + 574, + 289, + 623 + ], + "type": "text", + "content": ", which accurately predict the categorical distribution with ridge regression:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 58, + 629, + 289, + 647 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 629, + 289, + 647 + ], + "spans": [ + { + "bbox": [ + 58, + 629, + 289, + 647 + ], + "type": "interline_equation", + "content": "\\min _ {w} \\mathcal {L} _ {t r a i n} (F _ {t}, Y _ {t}; w) = \\| \\sigma (\\alpha Y _ {t}) - F _ {t} w \\| ^ {2} + \\lambda \\| w \\| ^ {2}, (4)", + "image_path": "4c8aee3ae3c80a3b53c684efb93e9f5c9cfa0df67e0ce4a80434324ee4153b04.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 653, + 289, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 289, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 289, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 653, + 289, + 713 + ], + "type": "inline_equation", + "content": "\\sigma(\\cdot)" + }, + { + "bbox": [ + 46, + 653, + 289, + 713 + ], + "type": "text", + "content": " is the softmax function along the categorical dimension to meet the normalization constraint, and " + }, + { + "bbox": [ + 46, + 653, + 289, + 713 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 653, + 289, + 713 + ], + "type": "text", + "content": " is a scaling factor. By solving the linear regression problem of Eq. (4) through least square method (see supplementary material for details), we can obtain its closed-form solution" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 224, + 547, + 261 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 224, + 547, + 261 + ], + "spans": [ + { + "bbox": [ + 304, + 224, + 547, + 261 + ], + "type": "inline_equation", + "content": "w^{*}(Y_{t})" + }, + { + "bbox": [ + 304, + 224, + 547, + 261 + ], + "type": "text", + "content": " on the training batch " + }, + { + "bbox": [ + 304, + 224, + 547, + 261 + ], + "type": "inline_equation", + "content": "(F_{t},Y_{t})" + }, + { + "bbox": [ + 304, + 224, + 547, + 261 + ], + "type": "text", + "content": " and derive its optimal prediction via linear regression on samples " + }, + { + "bbox": [ + 304, + 224, + 547, + 261 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_{v,i}" + }, + { + "bbox": [ + 304, + 224, + 547, + 261 + ], + "type": "text", + "content": " from validation set " + }, + { + "bbox": [ + 304, + 224, + 547, + 261 + ], + "type": "inline_equation", + "content": "D_{v}" + }, + { + "bbox": [ + 304, + 224, + 547, + 261 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 332, + 269, + 547, + 304 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 332, + 269, + 547, + 304 + ], + "spans": [ + { + "bbox": [ + 332, + 269, + 547, + 304 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} y _ {v, i} ^ {\\prime} (Y _ {t}) = w ^ {*} (Y _ {t}) ^ {T} \\mathbf {f} _ {v, i} \\\\ = \\sigma \\left(\\alpha Y _ {t}\\right) ^ {T} F _ {t} \\left(F _ {t} ^ {T} F _ {t} + \\lambda I\\right) ^ {- 1} \\mathbf {f} _ {v, i}. \\tag {5} \\\\ \\end{array}", + "image_path": "d654b8f1159c834011f8dd0189636898372adb643bb372afc5066e314322f039.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 312, + 546, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 312, + 546, + 361 + ], + "spans": [ + { + "bbox": [ + 304, + 312, + 546, + 361 + ], + "type": "text", + "content": "Intuitively, the discrepancy between the predicted results " + }, + { + "bbox": [ + 304, + 312, + 546, + 361 + ], + "type": "inline_equation", + "content": "y_{v,i}^{\\prime}" + }, + { + "bbox": [ + 304, + 312, + 546, + 361 + ], + "type": "text", + "content": " and the ground truth labels " + }, + { + "bbox": [ + 304, + 312, + 546, + 361 + ], + "type": "inline_equation", + "content": "y_{v,i}" + }, + { + "bbox": [ + 304, + 312, + 546, + 361 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 304, + 312, + 546, + 361 + ], + "type": "inline_equation", + "content": "D_v" + }, + { + "bbox": [ + 304, + 312, + 546, + 361 + ], + "type": "text", + "content": " is due to the potential noise from " + }, + { + "bbox": [ + 304, + 312, + 546, + 361 + ], + "type": "inline_equation", + "content": "Y_{t}" + }, + { + "bbox": [ + 304, + 312, + 546, + 361 + ], + "type": "text", + "content": ", therefore we take the prediction discrepancy as objective for label purification:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 315, + 369, + 546, + 398 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 369, + 546, + 398 + ], + "spans": [ + { + "bbox": [ + 315, + 369, + 546, + 398 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {v a l}} \\left(Y _ {t}\\right) = \\frac {1}{N _ {v}} \\sum_ {i = 1} ^ {N _ {v}} \\left| \\left| y _ {v, i} ^ {\\prime} \\left(Y _ {t}\\right) - y _ {v, i} \\right| \\right| ^ {2} + \\mathcal {H} \\left(y _ {v, i} ^ {\\prime} \\left(Y _ {t}\\right)\\right), \\tag {6}", + "image_path": "02892fd9a17b0b25f7998e06fe096bc3cb69768564a97cc18529f4984dea6be3.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 406, + 547, + 478 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 406, + 547, + 478 + ], + "spans": [ + { + "bbox": [ + 304, + 406, + 547, + 478 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 406, + 547, + 478 + ], + "type": "inline_equation", + "content": "\\mathcal{H}(\\cdot)" + }, + { + "bbox": [ + 304, + 406, + 547, + 478 + ], + "type": "text", + "content": " represents the entropy of input distribution as a regularization term to sharpen the predicted label distribution as [35]. With Eq. (5) and Eq. (6), the validation loss can be expressed analytically by training labels " + }, + { + "bbox": [ + 304, + 406, + 547, + 478 + ], + "type": "inline_equation", + "content": "Y_{t}" + }, + { + "bbox": [ + 304, + 406, + 547, + 478 + ], + "type": "text", + "content": " in a batch, thus the noisy labels can be corrected steadily with correction rate " + }, + { + "bbox": [ + 304, + 406, + 547, + 478 + ], + "type": "inline_equation", + "content": "\\eta_{I}" + }, + { + "bbox": [ + 304, + 406, + 547, + 478 + ], + "type": "text", + "content": " by the gradient back-propagated from Eq. (6) as" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 362, + 486, + 546, + 499 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 362, + 486, + 546, + 499 + ], + "spans": [ + { + "bbox": [ + 362, + 486, + 546, + 499 + ], + "type": "interline_equation", + "content": "Y _ {t} ^ {p + 1} := Y _ {t} ^ {p} - \\eta_ {I} \\nabla \\left(\\mathcal {L} _ {\\text {v a l}} \\left(Y _ {t} ^ {p}\\right)\\right). \\tag {7}", + "image_path": "4a8e90384d43232fcfb362d08c597d5f54b0793e1dd9fb5aab84609e25fe39ee.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 508, + 547, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 508, + 547, + 568 + ], + "spans": [ + { + "bbox": [ + 304, + 508, + 547, + 568 + ], + "type": "text", + "content": "Extrinsic Auxiliary Correction. To accelerate the label correction process, an external correction process is further proposed. Specifically, an accompanied linear classifier " + }, + { + "bbox": [ + 304, + 508, + 547, + 568 + ], + "type": "inline_equation", + "content": "C(\\cdot; w_c): \\mathbb{R}^d \\to \\mathbb{R}^c" + }, + { + "bbox": [ + 304, + 508, + 547, + 568 + ], + "type": "text", + "content": " with learnable parameter " + }, + { + "bbox": [ + 304, + 508, + 547, + 568 + ], + "type": "inline_equation", + "content": "w_c" + }, + { + "bbox": [ + 304, + 508, + 547, + 568 + ], + "type": "text", + "content": " is trained along with the updated labels from IPC:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 336, + 576, + 546, + 589 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 336, + 576, + 546, + 589 + ], + "spans": [ + { + "bbox": [ + 336, + 576, + 546, + 589 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {c}} \\left(w _ {c}\\right) = \\mathcal {L} _ {\\mathrm {c e}} \\left(C \\left(\\mathbf {f} _ {t}; w _ {c}\\right), y ^ {\\prime} _ {t}\\right) + \\mathcal {H} \\left(C \\left(\\mathbf {f} _ {t}; w _ {c}\\right)\\right), \\tag {8}", + "image_path": "aceec7b4967133f41549e8bb016d72f1a7e9214ccc162518b7dc9f40f920b97c.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 597, + 547, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 597, + 547, + 693 + ], + "spans": [ + { + "bbox": [ + 304, + 597, + 547, + 693 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 597, + 547, + 693 + ], + "type": "inline_equation", + "content": "y_{t}^{\\prime}" + }, + { + "bbox": [ + 304, + 597, + 547, + 693 + ], + "type": "text", + "content": " is the updated training label from IPC, and " + }, + { + "bbox": [ + 304, + 597, + 547, + 693 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{ce}}" + }, + { + "bbox": [ + 304, + 597, + 547, + 693 + ], + "type": "text", + "content": " denotes the cross entropy loss function. Since the accompanied linear classifier is intrinsically robust to noisy labels in " + }, + { + "bbox": [ + 304, + 597, + 547, + 693 + ], + "type": "inline_equation", + "content": "y_{t}^{\\prime}" + }, + { + "bbox": [ + 304, + 597, + 547, + 693 + ], + "type": "text", + "content": " [24], it can quickly achieve high correction accuracy. With this intuition, the predicted results of the classifier " + }, + { + "bbox": [ + 304, + 597, + 547, + 693 + ], + "type": "inline_equation", + "content": "C(\\mathbf{f}_t;w_c)" + }, + { + "bbox": [ + 304, + 597, + 547, + 693 + ], + "type": "text", + "content": " are used to correct labels periodically, specifically, the update rule of " + }, + { + "bbox": [ + 304, + 597, + 547, + 693 + ], + "type": "inline_equation", + "content": "Y_{t}" + }, + { + "bbox": [ + 304, + 597, + 547, + 693 + ], + "type": "text", + "content": " switches to momentum update (i.e., EMA) every " + }, + { + "bbox": [ + 304, + 597, + 547, + 693 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 597, + 547, + 693 + ], + "type": "text", + "content": " iterations:" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 325, + 700, + 546, + 714 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 325, + 700, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 325, + 700, + 546, + 714 + ], + "type": "interline_equation", + "content": "Y _ {t} ^ {p + 1} := \\left(1 - \\eta_ {E}\\right) Y _ {t} ^ {p} + \\eta_ {E} C \\left(F _ {t}; w _ {c}\\right) \\quad \\text {i f} \\quad p = n T, \\tag {9}", + "image_path": "d78ad5575be3ee1fefd137e8696a21d8e53dfb9ab798eccaa1c137ed9df02463.jpg" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "19937" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 70, + 105, + 520, + 483 + ], + "blocks": [ + { + "bbox": [ + 45, + 70, + 547, + 104 + ], + "lines": [ + { + "bbox": [ + 45, + 70, + 547, + 104 + ], + "spans": [ + { + "bbox": [ + 45, + 70, + 547, + 104 + ], + "type": "text", + "content": "Table 1. Comparison with state-of-the-art methods on CIFAR-10/100 datasets with symmetric noise. \"CE\" is the standard ConvNet trained with Cross-Entropy loss in an end-to-end manner. \"Classifier\" means adopts the pre-trained SimCLR features to re-train a linear classifier. \"Val\" denotes using a small clean validation set. DivideMix* denotes training DivideMix with the same validation set as additional data." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 70, + 105, + 520, + 483 + ], + "lines": [ + { + "bbox": [ + 70, + 105, + 520, + 483 + ], + "spans": [ + { + "bbox": [ + 70, + 105, + 520, + 483 + ], + "type": "table", + "html": "
Dataset\nMethodValNoise ratioCIFAR-10CIFAR-100
20%50%80%90%20%50%80%90%
Cross-Entropy (CE)XBest86.879.462.942.762.046.719.910.1
Last82.757.926.116.861.837.38.83.5
Co-teaching+ [36]XBest89.585.767.447.965.651.827.913.7
Last88.284.145.530.164.145.315.58.8
PENCIL [35]XBest92.489.177.558.969.457.531.115.3
Last92.088.776.558.268.156.420.78.8
REED [38]XBest95.895.694.393.676.773.066.959.6
Last95.795.494.193.576.572.266.559.4
Sel-CL+ [18]XBest95.593.989.281.976.572.459.648.8
Last95.193.388.781.676.172.059.248.6
MOIT+ [21]XBest94.191.881.174.775.970.647.641.8
Last93.891.380.674.075.270.146.941.2
C2D-DivideMix [40]XBest96.395.294.493.578.676.467.758.7
Last96.295.194.193.478.376.067.458.4
DivideMix [15]XBest96.194.693.276.077.374.660.231.5
Last95.794.492.975.476.974.259.631.0
Meta-Learning [16]✓Best92.989.377.458.768.559.242.419.5
Last92.088.876.158.367.758.040.114.3
MLC [41]✓Best92.688.177.467.966.852.721.815.0
Last91.887.577.167.066.552.418.914.2
MSLC [9]✓Best93.489.969.856.172.565.424.316.7
Last93.389.468.855.272.064.920.514.6
DivideMix* [15]✓Best96.194.993.677.377.774.860.732.5
Last95.994.693.076.577.174.360.532.2
DMLP-Naive✓Best94.794.293.592.872.768.063.561.3
Last94.294.093.292.072.367.463.260.9
DMLP-DivideMix✓Best96.395.894.594.379.976.868.665.8
Last96.295.694.394.079.476.168.565.4
", + "image_path": "6dacc3da1fe0948e1466271bcc1c542f133a548168581be6743066d876cf780b.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 492, + 288, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 492, + 288, + 598 + ], + "spans": [ + { + "bbox": [ + 46, + 492, + 288, + 598 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 492, + 288, + 598 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 492, + 288, + 598 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 492, + 288, + 598 + ], + "type": "inline_equation", + "content": "\\eta_{E}" + }, + { + "bbox": [ + 46, + 492, + 288, + 598 + ], + "type": "text", + "content": " are the period and momentum for update, and " + }, + { + "bbox": [ + 46, + 492, + 288, + 598 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 492, + 288, + 598 + ], + "type": "text", + "content": " is an arbitrary positive integer to denote the " + }, + { + "bbox": [ + 46, + 492, + 288, + 598 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 492, + 288, + 598 + ], + "type": "text", + "content": "-th time of EAC update. In a global sense, after " + }, + { + "bbox": [ + 46, + 492, + 288, + 598 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 492, + 288, + 598 + ], + "type": "text", + "content": " iterations of training, EAC can quickly achieve locally optimal label estimation by mimic of gradually updated labels from IPC, which reversely facilitates the label correction of IPC by providing cleaner training labels. Subsequently, IPC and EAC form a positive loop and mutually improve the quality of label correction of each other." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 609, + 173, + 623 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 609, + 173, + 623 + ], + "spans": [ + { + "bbox": [ + 47, + 609, + 173, + 623 + ], + "type": "text", + "content": "3.3. Application of DMLP" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 628, + 288, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 628, + 288, + 665 + ], + "spans": [ + { + "bbox": [ + 46, + 628, + 288, + 665 + ], + "type": "text", + "content": "The DMLP is a flexible label purifier, the corrected training labels " + }, + { + "bbox": [ + 46, + 628, + 288, + 665 + ], + "type": "inline_equation", + "content": "y_{t}^{*}" + }, + { + "bbox": [ + 46, + 628, + 288, + 665 + ], + "type": "text", + "content": " can be applied in different ways in robust learning scenarios, as shown in Fig. 3." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": "Naive classification network with DMLP. In a simple and direct manner, we can take the purified labels to retrain a neural network with simple cross-entropy loss (CE), here we term this simple application as DMLP-Naive." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 492, + 547, + 588 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 492, + 547, + 588 + ], + "spans": [ + { + "bbox": [ + 304, + 492, + 547, + 588 + ], + "type": "text", + "content": "LNL framework boosted by DMLP. Considering that there may still be a small number of noisy or miscorrected labels after purification, another effective way to apply DMLP is to take the purified labels as new training samples for the existing LNL framework. In this work, we extend some classic frameworks [12, 15, 19, 30] with DMLP, and the boosted LNL methods are denoted with prefix of “DMLP-” (e.g. DMLP-DivideMix, DMLP-ELR+, etc.)" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 601, + 388, + 615 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 601, + 388, + 615 + ], + "spans": [ + { + "bbox": [ + 306, + 601, + 388, + 615 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 622, + 432, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 622, + 432, + 635 + ], + "spans": [ + { + "bbox": [ + 306, + 622, + 432, + 635 + ], + "type": "text", + "content": "4.1. Experimental Settings" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "content": "CIFAR-10/100. For the self-supervised pre-training stage, we adopt the popular SimCLR algorithm [5] with ResNet as the backbone network. Classifiers in meta-learner are trained for 100 epochs with the Adam optimizer. For the final DivideMix algorithm, ResNet18 is adopted for a fair comparison. " + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\eta_{I}" + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\eta_{E}" + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "content": " are set as 0.01 and 1.0 respec" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "19938" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 63, + 105, + 267, + 314 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 288, + 102 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 288, + 102 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 288, + 102 + ], + "type": "text", + "content": "Table 2. Evaluation results with asymmetric noise of different noisy ratio on CIFAR-10. \"Validation\" denotes the method exploits a small clean validation set." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 63, + 105, + 267, + 314 + ], + "lines": [ + { + "bbox": [ + 63, + 105, + 267, + 314 + ], + "spans": [ + { + "bbox": [ + 63, + 105, + 267, + 314 + ], + "type": "table", + "html": "
MethodValidationNoisy ratio
20%40%
Joint-Optim [28]X92.891.7
PENCIL [35]X92.491.2
M-correction [1]X-86.3
Iterative-CV [4]X-88.0
DivideMix [15]X93.493.4
REED [38]X95.092.3
C2D-DivideMix [40]X93.893.4
Sel-CL+ [18]X95.293.4
GCE [11]X87.378.1
RRL [17]X-92.4
Zhang, et al. [39]✓92.790.2
Meta-Learning [16]✓-88.6
MSLC [9]✓94.491.6
DMLP-Naive✓94.693.9
DMLP-DivideMix✓95.295.0
", + "image_path": "6ed94261b20711a005f33ed3ba27094d44fee201e72f48b8dbf5942244fa31cb.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 69, + 343, + 261, + 548 + ], + "blocks": [ + { + "bbox": [ + 47, + 321, + 288, + 342 + ], + "lines": [ + { + "bbox": [ + 47, + 321, + 288, + 342 + ], + "spans": [ + { + "bbox": [ + 47, + 321, + 288, + 342 + ], + "type": "text", + "content": "Table 3. Top-1 testing accuracy on Clothing-1M testset. \"Validation\" denotes using the validation provided by [31]." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 69, + 343, + 261, + 548 + ], + "lines": [ + { + "bbox": [ + 69, + 343, + 261, + 548 + ], + "spans": [ + { + "bbox": [ + 69, + 343, + 261, + 548 + ], + "type": "table", + "html": "
MethodValidationTop-1 Accuracy
PENCIL [35]X73.49
DivideMix [15]X74.76
RRL [17]X74.90
GCE [11]X73.30
C2D-DivideMix [40]X74.30
REED [38]X75.81
Meta-Learning [16]✓73.47
Self-Learning [13]✓76.44
MLC [41]✓75.78
MSLC [9]✓74.02
Meta-Cleaner [10]✓72.50
Meta-Weight [8]✓73.72
FaMUS [34]✓74.40
MSLG [7]✓76.02
DMLP-Naive✓77.77
DMLP-DivideMix✓78.23
", + "image_path": "dea745c271f4fa8eaad6055196f0b11c40749ada49bfd181211c44d556391630.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 556, + 287, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 556, + 287, + 700 + ], + "spans": [ + { + "bbox": [ + 46, + 556, + 287, + 700 + ], + "type": "text", + "content": "tively. The scaling factor " + }, + { + "bbox": [ + 46, + 556, + 287, + 700 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 556, + 287, + 700 + ], + "type": "text", + "content": " is set as 1.0. To ensure fair evaluation, we follow previous meta-learning based LNL methods [8, 9] to randomly separate 1,000 images as the clean validation set for CIFAR-10/100 [14], leaving the rest as training samples. We strictly follow the protocol in [12] to generate label noise. Specifically, symmetric noise is generated by replacing labels with one of the other classes uniformly, while the labels in asymmetric noise are disturbed to their similar classes to simulate label noise in real-world scenarios. Our experiments are conducted under different noisy rates: " + }, + { + "bbox": [ + 46, + 556, + 287, + 700 + ], + "type": "inline_equation", + "content": "\\pi \\in \\{20\\%, 50\\%, 80\\%, 90\\% \\}" + }, + { + "bbox": [ + 46, + 556, + 287, + 700 + ], + "type": "text", + "content": " for symmetric and " + }, + { + "bbox": [ + 46, + 556, + 287, + 700 + ], + "type": "inline_equation", + "content": "\\pi \\in \\{20\\%, 40\\% \\}" + }, + { + "bbox": [ + 46, + 556, + 287, + 700 + ], + "type": "text", + "content": " for asymmetric noises." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 59, + 701, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 701, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 59, + 701, + 288, + 714 + ], + "type": "text", + "content": "Clothing1M. For the first stage on the Clothing1M [32]," + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 547, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 168 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 168 + ], + "type": "text", + "content": "the ResNet50 is trained with the official MoCo-v2 [6] to fully leverage its advantages on large-scale datasets. Afterward, the meta-learner is trained for 50 epochs. For DMLP-DivideMix, ResNet50 is adopted and initialized with weights from previous stages and trained for 80 epochs. Due to the space constraint, we put more detailed experimental settings and descriptions of each compared LNL method in our supplementary materials." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 178, + 430, + 190 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 178, + 430, + 190 + ], + "spans": [ + { + "bbox": [ + 306, + 178, + 430, + 190 + ], + "type": "text", + "content": "4.2. Experimental Results" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 197, + 547, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 197, + 547, + 544 + ], + "spans": [ + { + "bbox": [ + 304, + 197, + 547, + 544 + ], + "type": "text", + "content": "Comparison with state-of-the-art methods. We compare our method with multiple recent competitive methods on CIFAR-10/100 under various noisy settings (detailed descriptions of these methods are provided in the supplementary materials). Both test accuracy of the best and last epoch are reported. As shown in Table 1, the simple DMLP-Naive can already achieve competitive results to most methods, the superiority is more obvious in extremely noisy cases, further, the DMLP-DivideMix achieves state-of-the-art performance across all the settings. It is worth noting that directly utilizing the validation data to train DvldeMix (i.e., DivideMix*) only brings marginal improvement, while when equipped with the purified labels by DMLP, significant improvements are obtained, indicating that DMLP is effective in terms of utilizing validation set towards LNL problem. On the other hand, though there exist other meta-learning methods utilizing validation set [9, 16, 41], DMLP shows great advantages over them. It is also noticeable that compared with the original DivideMix, the purified version of DMLP-DivideMix achieves better results by a large margin, indicating that the purified label from our approach is more friendly to boost LNL frameworks. Table 2 shows comparison with the recent methods on asymmetric noisy CIFAR-10 dataset. DMLP-DivideMix outperforms REED by " + }, + { + "bbox": [ + 304, + 197, + 547, + 544 + ], + "type": "inline_equation", + "content": "0.2\\%" + }, + { + "bbox": [ + 304, + 197, + 547, + 544 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 197, + 547, + 544 + ], + "type": "inline_equation", + "content": "2.7\\%" + }, + { + "bbox": [ + 304, + 197, + 547, + 544 + ], + "type": "text", + "content": " under different noisy ratios and obtains greater improvements over the rest methods, demonstrating the ability of DMLP in handling harder semantic-related noise. Finally, DMLP-based methods suffer less from increasing noisy ratio than other competitors, indicating its robustness to variant noisy levels." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 545, + 547, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 547, + 617 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 547, + 617 + ], + "type": "text", + "content": "Furthermore, we also evaluate DMLP on the large-scale real-world noisy dataset Clothing1M. As shown in Table 3, simple DMLP-Naive can outperform all other methods by a large margin, and DMLP-DivideMix further improves the accuracy by about " + }, + { + "bbox": [ + 304, + 545, + 547, + 617 + ], + "type": "inline_equation", + "content": "0.46\\%" + }, + { + "bbox": [ + 304, + 545, + 547, + 617 + ], + "type": "text", + "content": ". The results indicate that DMLP is more suitable for noise from real-world situations." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "text", + "content": "Label correction accuracy. Fig. 4 compares the label accuracy after correction in our meta-learner against coupled label purifiers MLC and MSLC on CIFAR-10. Specifically, the one-hot form of the corrected pseudo-labels is compared with the ground truth for evaluation. As Fig. 4 shows, labels can be rapidly corrected to accuracy over " + }, + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "inline_equation", + "content": "92\\%" + }, + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "text", + "content": " in low noise cases. For severe label noise, DMLP can still improve label accuracy similar to low-noise settings. The overall corrected" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "19939" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 95, + 95, + 494, + 269 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 545, + 93 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 545, + 93 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 545, + 93 + ], + "type": "text", + "content": "Table 4. Comparison between the LNL methods and their DMLP applications with symmetric noise on CIFAR-10/100. Specifically, the 9-layer CNN is adopted as the backbone network of Co-teaching." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 95, + 95, + 494, + 269 + ], + "lines": [ + { + "bbox": [ + 95, + 95, + 494, + 269 + ], + "spans": [ + { + "bbox": [ + 95, + 95, + 494, + 269 + ], + "type": "table", + "html": "
Dataset\nMethod/Noise ratioCIFAR-10CIFAR-100
20%50%80%90%20%50%80%90%
Co-teaching [12]Best82.673.024.014.650.538.211.84.9
Last81.972.623.511.750.338.011.34.3
DMLP-Co-teachingBest85.885.885.484.651.249.848.145.3
Last85.685.685.384.551.049.347.845.1
CDR [30]Best90.485.047.212.363.339.529.28.0
Last82.749.416.610.162.939.59.74.5
DMLP-CDRBest91.491.291.290.269.264.861.458.5
Last91.290.890.689.368.364.361.157.9
ELR+ [19]Best94.693.891.175.277.572.458.230.8
Last94.493.790.573.576.272.256.830.6
DMLP-ELR+Best94.994.193.092.577.873.663.960.5
Last94.694.092.792.177.173.463.660.5
", + "image_path": "772f657cc08ea091cfd2d424f81c70ac198ac81803bdd461b011e8d69516a2fa.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 47, + 277, + 167, + 374 + ], + "blocks": [ + { + "bbox": [ + 47, + 277, + 167, + 374 + ], + "lines": [ + { + "bbox": [ + 47, + 277, + 167, + 374 + ], + "spans": [ + { + "bbox": [ + 47, + 277, + 167, + 374 + ], + "type": "image", + "image_path": "611b5fd0a0d8f77049fbce68fb27a5e20e8408ea09db054299683e99434221ad.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 378, + 288, + 437 + ], + "lines": [ + { + "bbox": [ + 46, + 378, + 288, + 437 + ], + "spans": [ + { + "bbox": [ + 46, + 378, + 288, + 437 + ], + "type": "text", + "content": "Figure 4. Comparison of corrected label accuracy under symmetric-20% (left), symmetric-80% (right) noise settings on CIFAR-10. Label accuracy within DMLP is superior against other competitors across all noise settings (More detailed experimental results can be found in the supplementary material)." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 167, + 277, + 286, + 374 + ], + "blocks": [ + { + "bbox": [ + 167, + 277, + 286, + 374 + ], + "lines": [ + { + "bbox": [ + 167, + 277, + 286, + 374 + ], + "spans": [ + { + "bbox": [ + 167, + 277, + 286, + 374 + ], + "type": "image", + "image_path": "b8fa7779cb5b86beb572d1c55558d363158f6d0541a1b6ba3cbc553365374cd6.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 437, + 288, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 437, + 288, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 437, + 288, + 664 + ], + "type": "text", + "content": "Generality of DMLP. To validate the generalization ability of DMLP, other than DivideMix, another three popular LNL methods, " + }, + { + "bbox": [ + 46, + 437, + 288, + 664 + ], + "type": "inline_equation", + "content": "\\mathrm{ELR + }" + }, + { + "bbox": [ + 46, + 437, + 288, + 664 + ], + "type": "text", + "content": " [19], Co-teaching [12], and CDR [30] are further adopted to work collaboratively with purified labels of DMLP. As shown in Table 4, all the applications of DMLP perform consistently better over their corresponding baselines, and the improvement becomes more significant when it comes to high-level noise cases. It is worth noting that since CDR highly relies on the early stopping technique, it suffers from a severe memorization effect in the training process, leading to a discrepancy between best results and last performance. In contrast, when training CDR with our purified labels, this discrepancy almost disappears, demonstrating the labels output by DMLP have a better quality to suppress the memorization effect, thus alleviating the reliance on early stopping. Therefore, the results indicate that the purified labels of DMLP are friendly to boost LNL frameworks. More detailed experimental results can be found in the supplementary materials." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 671, + 147, + 683 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 671, + 147, + 683 + ], + "spans": [ + { + "bbox": [ + 47, + 671, + 147, + 683 + ], + "type": "text", + "content": "4.3. Ablation Studies" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "type": "text", + "content": "Analysis on different label correction process. We explore the influence of IPC and EAC on the performance" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 307, + 303, + 552, + 409 + ], + "blocks": [ + { + "bbox": [ + 305, + 279, + 545, + 300 + ], + "lines": [ + { + "bbox": [ + 305, + 279, + 545, + 300 + ], + "spans": [ + { + "bbox": [ + 305, + 279, + 545, + 300 + ], + "type": "text", + "content": "Table 5. Ablation study for the effectiveness of IPC and EAC in DMLP-Naive on CIFAR-10." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 303, + 552, + 409 + ], + "lines": [ + { + "bbox": [ + 307, + 303, + 552, + 409 + ], + "spans": [ + { + "bbox": [ + 307, + 303, + 552, + 409 + ], + "type": "table", + "html": "
ComponentCIFAR-10Clothing
IPCEAC20%50%80%90%1M
X✓Best93.793.391.167.476.5
Last93.092.990.666.576.1
✓XBest87.885.779.976.076.8
Last87.285.579.475.476.5
✓✓Best94.794.293.592.877.7
Last94.294.093.292.077.6
", + "image_path": "69a4c72ee05b9a859588f735d055eeda25975e88d559a0be2ae82e98980054e1.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 422, + 547, + 531 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 422, + 547, + 531 + ], + "spans": [ + { + "bbox": [ + 304, + 422, + 547, + 531 + ], + "type": "text", + "content": "of DMLP-Naive in Table 5, when one of the process is excluded, the updated labels from the other are applied to retrain a new model. It is observed that EAC performs well in low noise cases due to its intrinsic robustness, as the noise ratio increases, the performance drops rapidly. On the other hand, IPC is more robust to high-level noise, but there exists a large gap compared with the full DMLP pipeline due to its slow optimization process. In contrast, when IPC and EAC work collaboratively, DMLP can achieve optimal results." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 547, + 714 + ], + "type": "text", + "content": "Comparison against other coupled purifiers with pretraining. To solely evaluate the influence of decoupled purification, we train two coupled meta label correction methods MLC and MSLC with the same self-supervised pretrained weights and apply their corrected labels to naive training or DivideMix for fair comparisons. As shown in Table. 6, though self-supervised weights can marginally boost the performance of coupled label correctors, there still exists a large gap between their performance and DMLP, especially for high noisy cases. Moreover, when further applying the corrected labels to mainstream LNL framework DivideMix, our method can also consistently outperform the coupled counterparts across all the noisy settings, demonstrating our corrected labels are of better quality. Therefore, these results verify that the superiority mainly attributes to decoupled" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19940" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 71, + 105, + 261, + 278 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 288, + 103 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 288, + 103 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 288, + 103 + ], + "type": "text", + "content": "Table 6. Comparison with coupled meta label correction methods MLC [41] and MSLC [9] on CIFAR-10. \" *\" denotes training with SimCLR pretrained ResNet-18." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 71, + 105, + 261, + 278 + ], + "lines": [ + { + "bbox": [ + 71, + 105, + 261, + 278 + ], + "spans": [ + { + "bbox": [ + 71, + 105, + 261, + 278 + ], + "type": "table", + "html": "
MethodNoisy ratio
20%50%80%90%
MLC*Best91.886.277.672.9
Last91.685.977.572.6
MSLC*Best92.087.778.067.8
Last92.087.577.967.3
DMLP-Naive*Best94.093.793.192.3
Last93.993.492.991.9
MLC*-DivideMixBest95.394.093.086.6
Last95.093.692.786.5
MSLC*-DivideMixBest95.794.993.883.0
Last95.594.893.182.8
DMLP*-DivideMixBest96.395.694.193.8
Last96.095.294.093.6
", + "image_path": "4b2b5e4eb1095426612675b764895dd07c9464908ac71067fca87d899413d868.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 57, + 301, + 273, + 337 + ], + "blocks": [ + { + "bbox": [ + 48, + 289, + 285, + 300 + ], + "lines": [ + { + "bbox": [ + 48, + 289, + 285, + 300 + ], + "spans": [ + { + "bbox": [ + 48, + 289, + 285, + 300 + ], + "type": "text", + "content": "Table 7. Investigation of the validation set size " + }, + { + "bbox": [ + 48, + 289, + 285, + 300 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 48, + 289, + 285, + 300 + ], + "type": "text", + "content": " on Clothing1M." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 57, + 301, + 273, + 337 + ], + "lines": [ + { + "bbox": [ + 57, + 301, + 273, + 337 + ], + "spans": [ + { + "bbox": [ + 57, + 301, + 273, + 337 + ], + "type": "table", + "html": "
τ10%20%30%40%50%100%
Accuracy (%)75.5076.4076.6177.0077.3077.31
", + "image_path": "67f634355c1b3beefb8828decdbaee609e1fadd070162b700f55605628810108.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 342, + 267, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 342, + 267, + 354 + ], + "spans": [ + { + "bbox": [ + 47, + 342, + 267, + 354 + ], + "type": "text", + "content": "label correction instead of self-supervised pretraining." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 354, + 287, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 354, + 287, + 533 + ], + "spans": [ + { + "bbox": [ + 46, + 354, + 287, + 533 + ], + "type": "text", + "content": "Effect of different feature representation for purification. The quality of features plays a crucial role in the label correction process of DMLP since the distribution of learned features is closely related to the rationality behind the linear estimation assumption in high-dimensional space. Therefore, we study the influence of different features on performance. Specifically, two types of features are investigated, including features from the ResNet-18/50 which load the self-supervised pre-trained weights. As the results in Table 8 show, the features from the ResNet-18 lead to slightly poor performance, while it brings performance improvements when using features from self-supervised ResNet-50. This observation indicates that although feature representation of higher quality benefits the purification results, DMLP is not very sensitive to the representation ability of input feature." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 534, + 288, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 534, + 288, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 534, + 288, + 664 + ], + "type": "text", + "content": "Effect of validation size. We examine how the number of validation set affects performance. Specifically, validation sizes from " + }, + { + "bbox": [ + 46, + 534, + 288, + 664 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 46, + 534, + 288, + 664 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 534, + 288, + 664 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 46, + 534, + 288, + 664 + ], + "type": "text", + "content": " of the whole validation set are evaluated on Clothing1M for DMLP-Naive. As shown in Table 7, DMLP-Naive achieves similar performance regardless of the validation size " + }, + { + "bbox": [ + 46, + 534, + 288, + 664 + ], + "type": "inline_equation", + "content": "N_v" + }, + { + "bbox": [ + 46, + 534, + 288, + 664 + ], + "type": "text", + "content": ", demonstrating DMLP is not sensitive to the number of images. It is worth noting that even using only " + }, + { + "bbox": [ + 46, + 534, + 288, + 664 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 46, + 534, + 288, + 664 + ], + "type": "text", + "content": " of the validation set (around " + }, + { + "bbox": [ + 46, + 534, + 288, + 664 + ], + "type": "inline_equation", + "content": "0.1\\%" + }, + { + "bbox": [ + 46, + 534, + 288, + 664 + ], + "type": "text", + "content": " of training data), DMLP-Naive still achieves high accuracy and outperforms most methods in Table.3, indicating that the effectiveness of DMLP is not heavily relied on validation size." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "content": "Performance under extremely noisy setting. In an extremely noisy scenario where all labels in the training set are unreliable except the given clean validation set, the LNL problem is converted into a semi-supervised learning prob" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 348, + 105, + 503, + 204 + ], + "blocks": [ + { + "bbox": [ + 305, + 70, + 547, + 103 + ], + "lines": [ + { + "bbox": [ + 305, + 70, + 547, + 103 + ], + "spans": [ + { + "bbox": [ + 305, + 70, + 547, + 103 + ], + "type": "text", + "content": "Table 8. Ablation study for adopting different features in DMLP-Naive on CIFAR-10, where \"R18/50\" denote \"ResNet-18/50\" and \"M/S\" represent \"MoCo/SimCLR\"." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 348, + 105, + 503, + 204 + ], + "lines": [ + { + "bbox": [ + 348, + 105, + 503, + 204 + ], + "spans": [ + { + "bbox": [ + 348, + 105, + 503, + 204 + ], + "type": "table", + "html": "
Feature SourceNoisy ratio
20%50%80%90%
R18 (M)Best93.893.392.290.4
Last93.792.792.190.0
R18 (S)Best94.093.793.192.3
Last93.993.492.991.9
R50 (S)Best94.794.293.592.8
Last94.294.093.292.0
", + "image_path": "5aa726ed83e920e6b8e16249f8f9400884acae9c27d511e88915409d968169eb.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 358, + 234, + 492, + 308 + ], + "blocks": [ + { + "bbox": [ + 305, + 210, + 545, + 232 + ], + "lines": [ + { + "bbox": [ + 305, + 210, + 545, + 232 + ], + "spans": [ + { + "bbox": [ + 305, + 210, + 545, + 232 + ], + "type": "text", + "content": "Table 9. Comparison between recent semi-supervised methods and DMLP-DivideMix on CIFAR-10/100 with " + }, + { + "bbox": [ + 305, + 210, + 545, + 232 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 305, + 210, + 545, + 232 + ], + "type": "text", + "content": " noisy ratio." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 358, + 234, + 492, + 308 + ], + "lines": [ + { + "bbox": [ + 358, + 234, + 492, + 308 + ], + "spans": [ + { + "bbox": [ + 358, + 234, + 492, + 308 + ], + "type": "table", + "html": "
MethodCIFAR-10CIFAR-100
MeanTeacher83.031.0
MixMatch87.957.7
FixMatch88.156.3
UDA88.256.1
Ours91.760.1
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From the results in Table 9, DMLP-DivideMix performs optimally among all methods when using the validation set as labeled samples, indicating the proposed method is potential for broader applications." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 423, + 378, + 436 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 423, + 378, + 436 + ], + "spans": [ + { + "bbox": [ + 306, + 423, + 378, + 436 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 444, + 547, + 587 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 444, + 547, + 587 + ], + "spans": [ + { + "bbox": [ + 304, + 444, + 547, + 587 + ], + "type": "text", + "content": "In this paper, we propose a flexible and novel multi-stage robust learning approach termed as DMLP. The core of DMLP is a carefully-designed meta-learning based label purifier, which decouples the complex bi-level optimization problem into representation and label distribution learning, thus helping the meta-learner focus on correcting noisy labels in a faster and more precise manner even under extremely noisy scenarios. Further, DMLP can be applied either for naive retraining on noisy data or assistance of existing LNL methods to boost performance. Extensive experiments conducted on several synthetic and real-world noisy datasets verify the superiority of the proposed method." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 597, + 404, + 611 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 597, + 404, + 611 + ], + "spans": [ + { + "bbox": [ + 306, + 597, + 404, + 611 + ], + "type": "text", + "content": "Acknowledgement" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "text", + "content": "This work was supported by National Natural Science Fund of China (62076184, 61976158, 61976160, 62076182, 62276190), in part by Fundamental Research Funds for the Central Universities and State Key Laboratory of Integrated Services Networks (Xidian University), in part by Shanghai Innovation Action Project of Science and Technology (20511100700) and Shanghai Natural Science Foundation (22ZR1466700)." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19941" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 17, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "text", + "content": "[1] Eric Arazo, Diego Ortego, Paul Albert, Noel E O'Connor, and Kevin McGuinness. 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Given the same visual stimuli, people's attention is driven by both salient visual cues and their own inherent preferences. Knowledge of visual preferences not only facilitates understanding of fine-grained attention patterns of diverse users, but also has the potential of benefiting the development of customized applications. Nevertheless, existing saliency models typically limit their scope to attention as it applies to the general population and ignore the variability between users' behaviors. In this paper, we identify the critical roles of visual preferences in attention modeling, and for the first time study the problem of user-aware saliency modeling. Our work aims to advance attention research from three distinct perspectives: (1) We present a new model with the flexibility to capture attention patterns of various combinations of users, so that we can adaptively predict personalized attention, user group attention, and general saliency at the same time with one single model; (2) To augment models with knowledge about the composition of attention from different users, we further propose a principled learning method to understand visual attention in a progressive manner; and (3) We carry out extensive analyses on publicly available saliency datasets to shed light on the roles of visual preferences. Experimental results on diverse stimuli, including naturalistic images and web pages, demonstrate the advantages of our method in capturing the distinct visual behaviors of different users and the general saliency of visual stimuli.", + "bbox": [ + 75, + 361, + 473, + 770 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 796, + 209, + 811 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "With the pervasiveness of a visual attention network in the brain, attention has become an important interface for understanding people's behavioral patterns. A collection", + "bbox": [ + 75, + 821, + 468, + 867 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/eead546da9b281f2b6ac20767720c3088d04552717e1979121cf20afc8e43947.jpg", + "image_caption": [ + "Figure 1. A hierarchy for user-aware saliency modeling, where each level focuses on a different perspective of attention." + ], + "image_footnote": [], + "bbox": [ + 500, + 325, + 893, + 526 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "of studies focus on leveraging human attention to optimize graphical designs [7, 16, 36], web page layouts [8, 37, 45], and user experience in immersive environments [22, 38, 44]. They demonstrate its usefulness for a broad range of applications, and more importantly, highlight the intertwined nature between attention and users' preferences [11]. As shown in Figure 1, attention modeling can be formulated as a hierarchy of tasks, i.e., from a sophisticated understanding of individuals' behaviors (personalized attention), to modeling the visual behaviors of larger groups (user-group attention), and the saliency of visual stimuli (general saliency). With the great diversity in attentional behaviors among different groups (e.g., attention of users with diverse characteristics, children vs elderly, male vs female, etc.), knowledge of visual preferences can play an essential role in enabling a more fine-grained understanding of attention.", + "bbox": [ + 496, + 597, + 892, + 838 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To accurately capture human attention on visual stimuli, considerable efforts have been placed on building saliency prediction models [10, 19, 21, 29, 30]. While achieving optimistic results for modeling attention of the general popu", + "bbox": [ + 496, + 839, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Work done during an internship at Google Research.", + "bbox": [ + 94, + 875, + 379, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Corresponding author", + "bbox": [ + 96, + 887, + 220, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "2701", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "lation, there are two key challenges remaining largely unresolved: (1) Existing models ignore the variability of users' visual behaviors, and hence do not have the ability to identify fine-grained attention patterns of distinct users; and (2) Apart from the shortage of models for user-aware saliency modeling, there has also been no attempt to formulate a training paradigm to understand the composition of attention, which hampers the integration of attention from diverse users. To fill the gap, we concentrate on a new research problem for modeling attention of adaptively selected users, and tackle the challenge with a new computational model together with a progressive learning method.", + "bbox": [ + 75, + 90, + 472, + 272 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "At the heart of our saliency model is the incorporation of visual preferences with personalized filters and adaptive user masks. Unlike conventional methods designed for predicting a single saliency map representing attention of all users, it takes advantage of personalized filters to encode individuals' attention patterns. The attention patterns are adaptively integrated based on a user mask indicating the presence of users in the current sample, which enables attention prediction for various combinations of users. The aforementioned paradigm serves as the foundation for bridging individuals' preferences with visual saliency, and augments models with more abundant information about fine-grained visual behaviors. It not only shows promise in modeling attention of specific users, but also benefits the inference of the general saliency.", + "bbox": [ + 75, + 273, + 472, + 498 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "A key challenge in user-aware saliency modeling is the lack of understanding when aggregating attention from diverse users. The issue becomes more critical when further considering the joint effects of stimuli and user preferences on visual attention [11], where the former factor may overshadow the impacts of the latter one, leading to difficulties in capturing the variability of users' attention. Inspired by human learning that acquires knowledge through a set of carefully designed curricula [2], we propose to tackle the aforementioned issues with a progressive learning approach. The essence of our method is to encourage a model to learn the composition of attention from a dynamic set of users, from individuals to user groups representing the general population. Through optimizing on dynamically evolving annotations, it provides opportunities for models to learn both the unique attention patterns of different users and the saliency of visual stimuli.", + "bbox": [ + 75, + 500, + 472, + 755 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To summarize, our major contributions are as follows:", + "bbox": [ + 96, + 755, + 454, + 770 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We identify the significance of characterizing visual preferences for attention modeling, and develop a novel model that can predict attention of various users.", + "- We present a progressive learning method to understand the composition of attention and capture its variability between different users.", + "We perform extensive experiments and analyses to in" + ], + "bbox": [ + 94, + 777, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "vestigate the roles of visual preferences on tackling the challenges of user-aware and general saliency, and addressing the issues of incomplete users. Results demonstrate that user-aware saliency modeling is advantageous in all the above three aspects.", + "bbox": [ + 531, + 90, + 890, + 167 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 500, + 180, + 650, + 196 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our work is most related to previous efforts on visual saliency prediction, which make contributions in both data collection and computational modeling.", + "bbox": [ + 498, + 205, + 890, + 251 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Saliency prediction datasets. With the overarching goal of facilitating the development of attention modeling methods, many studies have contributed saliency prediction datasets with diverse visual stimuli. The pioneering work [25] presents a gaze estimation dataset for naturalistic images together with an online benchmark [24]. Several subsequent studies propose to characterize images into finer categories based on visual scenes [3], visual semantics [41], or sentiments [14]. To overcome the difficulties of large-scale data collection, Jiang et al. [23] use mouse-tracking as a substitute for gaze estimation and construct currently the largest saliency prediction dataset. In addition to the aforementioned works that study attention on naturalistic images, several studies focus on attention for broader types of visual stimuli, including graphical designs [7, 16, 36], web pages [8, 37, 45], and immersive environments [22, 38, 44]. There are also attempts that go beyond attention collected during free-viewing, and study goal-directed attention when performing various tasks such as driving [1] and visual reasoning [9]. These data efforts enable the developments of a series of computational methods for attention modeling.", + "bbox": [ + 496, + 251, + 892, + 566 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Saliency prediction models. To estimate attention distribution on different visual stimuli, a large body of research concentrates on building saliency prediction models. Early studies leverage handcrafted features that encode high- and low-level visual cues [5,17,20,40]. More recent approaches opt to automatically learn discriminative features based on deep neural networks. In particular, Huang et al. [19] utilize a convolution neural network (CNN) with multi-scale inputs to model the coarse-to-fine semantics. Kümmerer et al. [28] demonstrate the usefulness of deep features learned from image recognition for saliency prediction. Cornia et al. [10] develop a recurrent neural network to iteratively refine the visual features for saliency prediction. Jia et al. [21] augment model with rich visual semantics extracted from multiple levels of a CNN. Lou et al. [30] investigate the effectiveness of vision Transformers [13] for saliency prediction. Apart from the studies on general saliency prediction, a few works [32, 42, 43] attempt to tackle the problem of personalized saliency, which involves predicting attention of different users on naturalistic images. They adopt a simplified setting which only takes into account individuals' attention and assumes that the general saliency maps are given", + "bbox": [ + 496, + 569, + 893, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "2702", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/ced0a2328c238da104a51282616c9d620f3bd8eedf792dcc90a3de5cd20e0652.jpg", + "image_caption": [ + "Evolution of ground truth throughout the progressive learning procedure", + "Figure 2. An overview of the proposed framework. The top figure illustrates the architectural design of our saliency model for predicting attention of diverse users, while the bottom one outlines our progressive learning method for understanding the composition of attention." + ], + "image_footnote": [], + "bbox": [ + 119, + 85, + 851, + 402 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "as inputs. While showing usefulness in capturing visual attention, the aforementioned methods either consider only attention aggregated from all users (i.e., general saliency) or rely on assumptions that are inapplicable to less-constrained real-world scenarios. They also utilize diverse paradigms for modeling different types of attention, which prevents a joint reasoning on the variability of users' visual behaviors.", + "bbox": [ + 75, + 484, + 468, + 589 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our study differentiates from prior research in three key aspects: (1) We identify the significance of visual preferences for attention modeling, and for the first time tackle the challenge of user-aware saliency modeling. The new problem unifies previous studies on general and personalized saliency prediction, with the number of users being a dynamic factor; (2) Without imposing constraints on inputs (e.g., availability of general saliency maps [32,42,43] and naturalistic images as visual stimuli [10, 21, 28]), our model directly infers attention from visual stimuli and is able to generalize to broader scenarios (e.g., naturalistic images and web pages); and (3) In addition to a novel computational model, we also present a progressive learning approach to understand the composition of attention and capture the variability of attention.", + "bbox": [ + 75, + 589, + 468, + 816 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 76, + 829, + 210, + 847 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Attention modeling would benefit from the knowledge about individuals' visual preferences and the capability to adaptively integrate them. This section presents an integral", + "bbox": [ + 76, + 854, + 468, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "framework consisting of two important components: (1) A new saliency prediction model that encodes visual preferences and dynamically predicts attention patterns of diverse combinations of users (Section 3.1), and (2) A principled approach for learning the composition of attention in a progressive manner (Section 3.2).", + "bbox": [ + 498, + 484, + 892, + 575 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Encoding Visual Preferences with Personalized Filters", + "text_level": 1, + "bbox": [ + 500, + 587, + 890, + 619 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "A primary goal of our study is to endow models with the flexibility to predict attention for various users. We tackle the challenge with a new model paradigm that leverages a collection of personalized filters to identify individuals' visual preferences, and decomposes the overall attention patterns into fine-grained ones for different users. The key differentiators of our model lie in its (1) applicability to broader scenarios (e.g., from general saliency to attention of diverse users) and (2) flexibility to different settings (e.g., without assuming the availability of general saliency maps).", + "bbox": [ + 496, + 627, + 892, + 779 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Figure 2 (top) provides an overview of the proposed model. The principal idea behind our model is to take advantage of personalized filters to encode attention patterns of different users, and adaptively incorporate them based on the selection of users. Specifically, we build our model on top of the state-of-the-art EML-Net [21], which is a top-performing model on the MIT saliency benchmark [24]. Given an input image, our model extracts multi-scale fea", + "bbox": [ + 496, + 780, + 893, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "2703", + "bbox": [ + 482, + 944, + 514, + 957 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "tures from different layers of a convolutional neural network pretrained on ImageNet [12], encoding both high- and low-level visual cues. The raw features of different scales $V_{t} \\in \\mathbb{R}^{D \\times H \\times W}$ ( $D, H$ and $W$ correspond to the feature channel, height, and width, $t$ denotes index for scales) are processed independently with their corresponding attention decoders $f_{t}^{\\alpha}$ consisting of a sequence of convolutional and upsampling layers (see Section 4.1 for details), and then the decoded attention features $V_{t}^{\\alpha}$ are aggregated across all scales to form the unregularized attention maps $S^{raw}$ :", + "bbox": [ + 75, + 90, + 472, + 243 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nV _ {t} ^ {\\alpha} = f _ {t} ^ {\\alpha} (V _ {t}) \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 223, + 251, + 468, + 268 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nS ^ {r a w} = \\sum_ {t} V _ {t} ^ {\\alpha} \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 217, + 287, + 468, + 319 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Different from conventional methods [10, 19, 21, 28] that directly predict a single saliency map for the general population (i.e., $S^{raw} \\in \\mathbb{R}^{H \\times W}$ ), our method takes into account discriminative attention patterns of each individual user (i.e., $S^{raw} \\in \\mathbb{R}^{N \\times H \\times W}$ , where $N$ is the total number of users). We achieve the goal by expanding the filters in the last convolutional layer of each attention decoder, i.e., from a single filter to $N$ personalized filters. To adaptively predict the visual attention for various combinations of users, our model takes in a user mask $M$ in addition to the visual stimuli as input. The user mask is a binary vector $M \\in [0,1]^N$ representing the presence of users, where $M_n = 1$ implies that attention of the $n^{th}$ user is considered in the current sample. It plays the role as an indicator for integrating the unregularized attention maps from the selected users and generating the final saliency map $S \\in \\mathbb{R}^{H \\times W}$ :", + "bbox": [ + 75, + 323, + 472, + 566 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nS = \\operatorname {s o f t m a x} \\left(\\sum_ {n} M _ {n} \\cdot S _ {n} ^ {\\text {r a w}}\\right) \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 166, + 574, + 468, + 604 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\cdot$ denotes the element-wise multiplication.", + "bbox": [ + 76, + 612, + 398, + 627 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To bridge individuals' visual preferences with the overall attention, we optimize our model with supervision on both the intermediate per-user predictions and the final output. We follow [10] and define the loss function $L_{sal}$ as a combination of saliency metrics including Normalized Scanpath Saliency [33], Correlation Coefficient [31] and KL-Divergence [27] (see [10] and our supplementary materials). For per-user supervision, we apply a softmax activation function independently on unregularized attention map of each user to obtain their corresponding predictions:", + "bbox": [ + 75, + 628, + 468, + 779 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nS _ {n} ^ {\\text {u s e r}} = \\operatorname {s o f t m a x} \\left(S _ {n} ^ {\\text {r a w}}\\right) \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 184, + 787, + 468, + 806 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Our overall objective simultaneously optimizes both the intermediate per-user predictions and the final output:", + "bbox": [ + 75, + 813, + 468, + 844 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} L = L _ {s a l} (S, S a l, F i x) \\\\ + \\lambda \\sum_ {n} L _ {s a l} \\left(S _ {n} ^ {\\text {u s e r}}, S a l _ {n} ^ {\\text {u s e r}}, F i x _ {n} ^ {\\text {u s e r}}\\right) \\tag {5} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 135, + 852, + 468, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $Sal$ and $Fix$ are the ground truth saliency and fixation maps aggregated from selected users, $Sal_{n}^{user}$ and $Fix_{n}^{user}$ are those for individual user $n$ . Note that only users selected in the user mask (i.e., $M_{n} = 1$ ) will be considered for optimization. $\\lambda$ is the balancing factor.", + "bbox": [ + 498, + 90, + 890, + 167 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The aforementioned model illustrates a general paradigm for connecting user preferences and visual saliency. It serves as the foundation for user-aware saliency modeling, and supports the development of our progressive learning method, as detailed in the next subsection.", + "bbox": [ + 496, + 167, + 890, + 243 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Learning the Composition of Attention", + "text_level": 1, + "bbox": [ + 498, + 255, + 834, + 271 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Visual attention is driven by both salient regions that most people find attractive and individuals' unique interests. Understanding how to incorporate attention patterns of different users is an important challenge for user-aware saliency modeling. Without such knowledge, a model can overfit to attention driven by visual stimuli, and has difficulties learning the variability of users' attention. For instance, as there exists a considerable overlap between attention of different users, a model can exploit such a shortcut and predict an averaged attention map (of all users) regardless of the selection of users (see supplementary materials). To tackle the challenge, we propose a principled learning method that augments our saliency model with understanding of the composition of attention.", + "bbox": [ + 496, + 279, + 890, + 489 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Drawing inspirations from human learning, which is highly organized and based on curricula that gradually introduce diverse concepts, our method emphasizes progressive learning with dynamically evolving objectives. As illustrated in Figure 2 (bottom), it can be viewed as a three-phase training procedure: (1) As the initial step of learning, the model is encouraged to establish the correspondence between personalized modules and individuals' visual preference; (2) Later on, in the second phase, it is driven to take advantage of the learned preferences and construct saliency maps for diverse selections of users; (3) In the final phase, we allow the model to refine its prediction on attention of broader users, unifying personalized [42] and general saliency prediction [23, 25, 41]. Instead of dividing the learning into three separate stages (e.g., with a sequence of pretraining and fine-tuning), we instantiate the aforementioned paradigm by manipulating the characteristics of training samples throughout the learning process. Specifically, we first sample the number of users K from a specific range, and then randomly select of fixations K users (with a uniform distribution) to construct the ground truth fixation and saliency maps on the fly.", + "bbox": [ + 496, + 491, + 892, + 824 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Through controlling the number of users sampled among different training epochs, our method allows a continuous and progressive learning of the composition of attention: (1) We start with annotations from a small number of users (e.g., 1-4 users) and adaptively optimizing different compo", + "bbox": [ + 496, + 825, + 893, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "2704", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "nents of the networks (e.g., personalized filters indicated by the input user masks), which allows the model to encode individuals' visual preferences. It also attenuates the effects of overfitting to attention driven by visual stimuli, as the model has no access to annotations from all users and thus can not exploit the correlation between individuals' attention and the averaged one; (2) With the progress of training, we gradually increase both the lower and the upper bounds for sampling range of K (e.g., from 1-4 to 5-9 users). Note that the users are randomly selected on a sample basis for every training iteration (i.e., one sample in a single batch). The scheme facilitates understanding of how to combine visual preferences of each individual to the attention patterns of different user groups; (3) During the last several training epochs, we fix the bounds for sampling to relatively large values (e.g., $80\\% - 100\\%$ users), allowing the refinement of predictions for the general saliency.", + "bbox": [ + 75, + 90, + 472, + 347 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our learning paradigm enables a smooth transition from individuals' preferences to attention of a broad range of users. Together with the proposed model, our full method shows promise in capturing attention of both diverse users (Section 4.2) and the general population (Section 4.3)", + "bbox": [ + 75, + 347, + 470, + 425 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiment", + "text_level": 1, + "bbox": [ + 76, + 435, + 202, + 453 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we present the implementation details (Section 4.1), and carry out extensive experiments to study the effectiveness of the proposed framework. Our experiments and analyses aim to shed light on the following research questions that have yet to be answered:", + "bbox": [ + 75, + 460, + 468, + 536 + ], + "page_idx": 4 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Does learning the composition of attention help capture attention of diverse users? (Section 4.2)", + "- Are visual preferences beneficial for general saliency prediction? (Section 4.3)", + "- Can user-aware saliency modeling overcome the issues of incomplete users? (Section 4.4)" + ], + "bbox": [ + 94, + 542, + 467, + 650 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We also include additional analyses and ablation studies in the supplementary materials.", + "bbox": [ + 75, + 657, + 467, + 686 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Implementation", + "text_level": 1, + "bbox": [ + 76, + 696, + 236, + 710 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Dataset. We demonstrate the effectiveness of our method with two types of visual stimuli, i.e., naturalistic images and web pages. Since most saliency datasets only offer aggregated fixation annotations, we choose two publicly available saliency datasets, OSIE [39, 41] and FiWI [37], as our testbeds, which provide per-user annotations for user-aware saliency modeling. OSIE contains eye-tracking data collected on 700 naturalistic images with rich semantics. We use the version collected in [39], which has more diverse attention patterns from 32 users (about 14 users are presented with each sample) due to their less constrained experimental settings. FiWI is a popular eye-tracking dataset", + "bbox": [ + 75, + 719, + 472, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "for web pages, which contains data from 11 users on 149 samples. We also conduct experiments on the recently introduced web page saliency dataset [8] with 450 samples, and report the results in our supplementary materials.", + "bbox": [ + 496, + 90, + 890, + 151 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Evaluation. Saliency prediction is typically evaluated with multiple metrics [6]. Following [8, 19, 21, 30], we adopt seven popular saliency metrics, including Normalized Scanpath Saliency (NSS) [33], KL-Divergence (KLD) [27], Similarity (SIM) [35], Correlation Coefficient (CC) [31], Area Under the ROC Curve (AUC) [15], AUC-Judd [25], and shuffled AUC (sAUC) [4]. For the OSIE dataset, we follow [41], and randomly split the samples into 600 and 100 for training and evaluation, respectively. In terms of the FiWI dataset, following [37] and [8], we consider two evaluation settings, including 5-fold cross-validation and evaluation with fixed training/test sets. Besides estimating the capability of our method on capturing the attention patterns of diverse users (Section 4.2), we also study its usefulness on general saliency prediction (Section 4.3).", + "bbox": [ + 496, + 152, + 892, + 378 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Model Configuration. We build our method on the state-of-the-art EML-Net [21] saliency model. We use ResNet-50 [18] as the backbone, which is pretrained on ImageNet classification [12] and offers profound understanding of visual semantics. To show the generalizability of our method, we also experiment with a different saliency model (i.e., a variation of SimpleNet [34], see the supplementary materials). Multi-scale features are extracted from 4 layers, where each corresponds to the end of a block inside the backbone. The features are processed with a set of attention decoders, where the decoder of each scale contains two consecutive convolutional layers with 16 and N filters (N is the number of users), and an upsampling layer that rescales features to have the same spatial resolution as the image.", + "bbox": [ + 496, + 380, + 892, + 590 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Training. Following [10], we train models for 50 epochs with batch size 10 using the Adam optimizer [26]. $\\lambda$ factor in equation (5) is empirically set to 0.2. Learning rate is initially set to $10^{-4}$ , and decayed by a factor of 0.8 for every 10 epochs. For our learning approach proposed in Section 3.2, we set the initial bounds to [1, 4] and [1, 6] for FiWI and OSIE, respectively, and increase both the upper and lower bounds by 2 every 10 epochs. The bounds are fixed to [9, 11] and [11, 15] for FiWI and OSIE after reaching the corresponding values. The aforementioned hyperparameters are determined based on 5-fold cross-validation. For a fair comparison with the state-of-the-art [8, 37] and a more flexible setting, we do not pretrain our models on external saliency datasets like the SALICON [23] dataset.", + "bbox": [ + 496, + 592, + 893, + 803 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Does Learning the Composition of Attention Help Capture Attention of Diverse Users?", + "text_level": 1, + "bbox": [ + 498, + 815, + 890, + 847 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We first study the effectiveness of our method for capturing the visual preferences of diverse users. Specifically, we randomly sample K users $(\\mathrm{K} = 1,3,5)$ for each evaluation", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "2705", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/b0aea0daf15427a03c67ad5b50cf9070fa8f87b6ed0b19913a913f11e0492e77.jpg", + "image_caption": [ + "Figure 3. Qualitative results for predicting attention of diverse users. We show results for two different user groups for each sample, and also consider variable numbers of users $K = 1, 3, 5$ . Note that EML-Net is user-agnostic and predicts the same result for two groups." + ], + "image_footnote": [], + "bbox": [ + 117, + 88, + 851, + 502 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "image, and estimate the predictions with ground truth annotations aggregated from the selected users. We repeat the procedure 5 times to reduce the variance of results, and report the average performance. Following [41] and [37], we use fixed training/test splits on the OSIE dataset and perform 5-fold cross-validation on the FiWI dataset. We compare our full method (Ours) with three approaches, including the user-agnostic EML-Net baseline [21], an ensemble of EML-Net trained on individual users (Single-user, with one model for each user), and our model without incorporating progressive learning (Ours*). Three key observations can be made on the results reported in Table 1 and Table 2:", + "bbox": [ + 75, + 566, + 472, + 748 + ], + "page_idx": 5 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- There exist considerable discrepancies between general and user-aware saliency modeling. Despite the inter-user agreement on visual attention, the user-agnostic EML-Net achieves inferior performance on both datasets, especially FiWI with web pages associated with richer semantics and more diverse viewing behaviors. The observation highlights the significance of visual preferences for attention modeling.", + "- Learning how to integrate attention is important" + ], + "bbox": [ + 94, + 756, + 472, + 901 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/1af4641ab3091d639ec012b52ef667d6262d5481f8902e6abdcbe912153389c7.jpg", + "table_caption": [ + "Table 1. User-aware saliency results on FiWI [37]." + ], + "table_footnote": [], + "table_body": "
K=1K=3K=5
NSSCCNSSCCNSSCC
EML-Net1.4810.3071.5060.4541.4980.519
Single-user1.9620.3731.7490.5181.7450.591
Ours*1.9080.3661.7850.5261.7840.609
Ours2.0590.3921.8290.5401.8150.620
", + "bbox": [ + 504, + 589, + 885, + 708 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/20f70185c7db8085a376160303c6e724924ff50657906e6c07c1633876807b9f.jpg", + "table_caption": [ + "Table 2. User-aware saliency results on OSIE data [39]." + ], + "table_footnote": [], + "table_body": "
K=1K=3K=5
NSSCCNSSCCNSSCC
EML-Net1.7550.3671.7630.5321.7180.594
Single-user1.4560.3141.5650.4921.5740.566
Ours*1.6400.2941.7680.5371.8120.625
Ours1.8090.3101.8090.5501.8260.629
", + "bbox": [ + 504, + 744, + 885, + 864 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "2706", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/93d8a4269b6504884dd4d83916a3325051aac025734918025e4bb6e87b7dc9b8.jpg", + "table_caption": [ + "Table 3. General saliency results on FiWI data [37]." + ], + "table_footnote": [], + "table_body": "
NSSKLDCCAUC-JuddsAUC
DeepGaze II1.229-0.4880.7970.625
SAM-ResNet1.246-0.5950.7910.673
UMSI0.938-0.4570.7550.675
AGD-F1.606-0.7350.7670.748
EML-Net1.6530.6030.6610.8470.675
EML-Net+SALICON1.7220.5670.6890.8480.697
Ours1.7520.5640.6990.8510.704
", + "bbox": [ + 81, + 114, + 460, + 256 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/1aaaa552c532807beb229cb8fdbf6f10f83861e3b9deeb59f0479f93f071e118.jpg", + "table_caption": [ + "Table 4. General saliency results on OSIE data [39]." + ], + "table_footnote": [], + "table_body": "
NSSKLDSIMCCAUC
SALICON1.6410.5750.6000.6850.846
SAM-ResNet1.8110.4800.6480.7580.860
UMSI1.7880.5130.6310.7460.856
EML-Net1.7370.5370.6190.7170.854
Ours1.8400.5060.6520.7610.860
", + "bbox": [ + 81, + 294, + 460, + 424 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "for capturing visual preferences. A key component of our framework is the progressive learning method for understanding the composition of attention. According to the comparative results between our methods with and without progressive learning, it helps models better identify the attentional preferences of both individuals (i.e., $\\mathrm{K} = 1$ ) and user groups (i.e., $\\mathrm{K} = 3$ , 5). As illustrated in Figure 3, unlike EML-Net and our method without progressive learning (Ours*) that fail to capture the visual preferences and generate similar attention maps regardless of the selection of users, our full method is able to predict attention maps that accurately reflect the regions of interest of diverse users.", + "bbox": [ + 107, + 450, + 468, + 648 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "- Additive ensemble falls short of modeling user-aware attention. Training one model for each user offers a straightforward way to model user preferences, and slightly outperforms our method without progressive learning when considering individuals' attention (i.e., $\\mathrm{K} = 1$ ) on FiWI. However, without learning how to integrate attention, it lacks the capability to predict attention maps with multiple users and is outperformed by our full method across all settings. Additionally, such an additive ensemble also fails to benefit general saliency prediction due to its high computational overhead and the inability to jointly consider attention of different users (see our supplementary materials).", + "bbox": [ + 96, + 659, + 468, + 857 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "These observations highlight the significance of modeling visual preferences and the composition of attention, and", + "bbox": [ + 76, + 869, + 468, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "demonstrate the advantages of our method for user-aware saliency modeling. While we do not consider demographic information in this study, our method is general and can be extended to broader scenarios for customized applications. For instance, instead of developing personalized filters, we can cluster users based on certain criteria (e.g., gender, age, personal interest) and optimize models to predict attentional preferences of users of specific characteristics.", + "bbox": [ + 496, + 90, + 890, + 212 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Are Visual Preferences Beneficial for General Saliency Prediction?", + "text_level": 1, + "bbox": [ + 498, + 222, + 890, + 253 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "General saliency prediction focuses on attention aggregated from all users, and yet little attention has been paid to the diversity of attention patterns between users. In this subsection, we further investigate if knowledge of visual preferences is beneficial for the task. We compare our user-aware method with six state-of-the-art models, including SALICON [19], Deep Gaze II [28], SAM [10], EML-Net [21], UMSI [16], and AGD-F [8]. For a fair comparison, we adopt the training and test sets provided in [8] for evaluation on FiWI dataset. Table 3 and Table 4 report results on the FiWI [37] and OSIE [39, 41] datasets.", + "bbox": [ + 496, + 261, + 890, + 426 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Compared to the EML-Net baseline, our model that takes into account visual preferences shows consistent improvements among all settings. Its performance is also competitive against existing state-of-the-art. As illustrated in Figure 4, the performance gain of our method can be attributed to the capability to capture fine-grained attention patterns (i.e., focuses on the man, little girls, and woman in the three examples, respectively) in addition to the salient regions attended by the majority of users (i.e., text, the food, and the boy). Moreover, the advantages of our method is also a result of increased data efficiency. Comparative results show that it outperforms EML-Net pretrained on the SALICON [23] dataset with 15000 images (EML-Net+SALICON), despite only relying on training samples in the FiWI dataset with 149 images. Such a unique feature can play an important role in generalizing towards domains with diverse characteristics (e.g., web page vs naturalistic image), where suitable data for pretraining is not necessarily available.", + "bbox": [ + 496, + 428, + 890, + 700 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Can User-aware Saliency Modeling Overcome the Issues of Incomplete Users?", + "text_level": 1, + "bbox": [ + 498, + 710, + 890, + 741 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Collecting human behavioral data demands stringent paradigms, and building large attention datasets has been challenging for decades [23]. As a result, it is common for saliency datasets to have samples associated with incomplete users. For instance, there are 32 users recruited in [39], while only about 14 users are presented for each sample. Different from prior works [19, 21, 28, 30] that overlook the issue, we examine if knowledge of visual preferences can be helpful for tackling the problem.", + "bbox": [ + 496, + 750, + 890, + 883 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Specifically, we randomly drop $K^{*}$ users for each train-", + "bbox": [ + 517, + 885, + 890, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "2707", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/69082e2a8dd2ecd2806c3d856af0d8e10f6054c2e66c5fcef5df54b90dab185b.jpg", + "image_caption": [ + "Figure 4. Qualitative results for general saliency prediction." + ], + "image_footnote": [], + "bbox": [ + 179, + 88, + 795, + 354 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/d74b38a46a5ca0f5f154573a9beec12a6c2fec6b9353607b49dd9dfe72c9d035.jpg", + "table_caption": [ + "Table 5. Results for saliency prediction with incomplete users on seen and unseen images." + ], + "table_footnote": [], + "table_body": "
K=1K=3K=5Unseen
NSSCCNSSCCNSSCCNSSCC
K* = 5EML-Net1.7330.3591.7190.5181.7120.5891.6160.601
Ours1.7590.3411.7810.5301.7970.6141.6980.632
K* = 7EML-Net1.6620.3421.6590.5011.6580.5731.5840.551
Ours1.7230.3301.7340.5121.7390.5941.7080.589
", + "bbox": [ + 181, + 417, + 781, + 550 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ing sample in the FiWI dataset, and consider two evaluation settings: (1) attention of missing users on seen samples (we use different numbers of missing users, i.e., $\\mathrm{K} = 1, 3, 5$ ), and (2) attention of all users on unseen test samples (i.e., Unseen). The first setting is particularly useful for scenarios where we are interested in comparing users' preferences. On the other hand, the second setting aims to study models' robustness against the scarcity of annotations.", + "bbox": [ + 75, + 573, + 468, + 695 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "According to comparative results reported in Table 5, the proposed user-aware method is advantageous in both evaluation settings. Despite the slightly lower CC scores for individuals' attention $(\\mathrm{K} = 1)$ on seen images, it achieves considerable improvements among all other evaluation settings. This is likely because predictions from the user-agnostic EML-Net tend to have a broader coverage, which is favored by CC metric emphasizing the overall distribution. Differently, our method has the capability to more accurately attend to regions of interest of different users, resulting in higher NSS scores as well as CC scores for more users. It also makes better use of the available data, and is more robust against the scarcity of annotations (i.e., higher general", + "bbox": [ + 75, + 703, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ization performance on unseen images).", + "bbox": [ + 500, + 574, + 764, + 589 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 603, + 619, + 618 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This paper identifies the critical roles of user preferences in visual attention, and for the first time tackles the challenge of user-aware saliency modeling. It unifies the conventional tasks for predicting general and personalized attention, and proposes an integral framework that jointly solves attention modeling for individual users, different groups of users, and the general population. By making progress with both a novel saliency prediction model and a progressive learning method, our framework illustrates a principled paradigm for establishing the connections between user preferences and visual saliency. Experimental results in diverse settings demonstrate the advantages of the proposed method in inferring the attention patterns of a variety of users, and highlights the significance of incorporating the variability of attention. We hope that our study can open new avenues for attention research, and benefit the development of new applications based on user-aware saliency models.", + "bbox": [ + 496, + 628, + 893, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "2708", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Stefano Alletto, Andrea Palazzi, Francesco Solera, Simone Calderara, and Rita Cucchiara. Dr(eye)ve: A dataset for attention-based tasks with applications to autonomous and assisted driving. In CVPR workshop, pages 54-60, 2016. 2", + "[2] Yoshua Bengio, Jérôme Louradour, Ronan Collobert, and Jason Weston. Curriculum learning. In ICML, page 41-48, 2009. 2", + "[3] Ali Borji and Laurent Itti. Cat2000: A large scale fixation dataset for boosting saliency research. 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Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.145, + 0.131, + 0.826, + 0.154 + ], + "angle": 0, + "content": "Learning from Unique Perspectives: User-aware Saliency Modeling" + }, + { + "type": "text", + "bbox": [ + 0.22, + 0.182, + 0.305, + 0.198 + ], + "angle": 0, + "content": "Shi Chen*" + }, + { + "type": "text", + "bbox": [ + 0.163, + 0.2, + 0.357, + 0.216 + ], + "angle": 0, + "content": "University of Minnesota" + }, + { + "type": "text", + "bbox": [ + 0.188, + 0.22, + 0.332, + 0.233 + ], + "angle": 0, + "content": "chen4595@umn.edu" + }, + { + "type": "text", + "bbox": [ + 0.218, + 0.242, + 0.297, + 0.26 + ], + "angle": 0, + "content": "Xinyu Ye" + }, + { + "type": "text", + "bbox": [ + 0.227, + 0.261, + 0.288, + 0.277 + ], + "angle": 0, + "content": "Google" + }, + { + "type": "text", + "bbox": [ + 0.176, + 0.281, + 0.339, + 0.294 + ], + "angle": 0, + "content": "yexinyu@google.com" + }, + { + "type": "text", + "bbox": [ + 0.404, + 0.182, + 0.59, + 0.2 + ], + "angle": 0, + "content": "Nachiappan Valliappan" + }, + { + "type": "text", + "bbox": [ + 0.428, + 0.2, + 0.566, + 0.218 + ], + "angle": 0, + "content": "Google Research" + }, + { + "type": "text", + "bbox": [ + 0.434, + 0.22, + 0.562, + 0.234 + ], + "angle": 0, + "content": "nac@google.com" + }, + { + "type": "text", + "bbox": [ + 0.421, + 0.242, + 0.53, + 0.259 + ], + "angle": 0, + "content": "Kai Kohlhoff" + }, + { + "type": "text", + "bbox": [ + 0.406, + 0.261, + 0.543, + 0.278 + ], + "angle": 0, + "content": "Google Research" + }, + { + "type": "text", + "bbox": [ + 0.389, + 0.28, + 0.56, + 0.294 + ], + "angle": 0, + "content": "kohlhoff@google.com" + }, + { + "type": "text", + "bbox": [ + 0.669, + 0.182, + 0.776, + 0.198 + ], + "angle": 0, + "content": "Shaolei Shen" + }, + { + "type": "text", + "bbox": [ + 0.692, + 0.2, + 0.753, + 0.217 + ], + "angle": 0, + "content": "Google" + }, + { + "type": "text", + "bbox": [ + 0.638, + 0.22, + 0.809, + 0.234 + ], + "angle": 0, + "content": "shaoleis@google.com" + }, + { + "type": "text", + "bbox": [ + 0.655, + 0.241, + 0.756, + 0.26 + ], + "angle": 0, + "content": "Junfeng He†" + }, + { + "type": "text", + "bbox": [ + 0.633, + 0.261, + 0.771, + 0.278 + ], + "angle": 0, + "content": "Google Research" + }, + { + "type": "text", + "bbox": [ + 0.612, + 0.281, + 0.79, + 0.295 + ], + "angle": 0, + "content": "junfenghe@google.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.329, + 0.313, + 0.345 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.362, + 0.474, + 0.771 + ], + "angle": 0, + "content": "Everyone is unique. Given the same visual stimuli, people's attention is driven by both salient visual cues and their own inherent preferences. Knowledge of visual preferences not only facilitates understanding of fine-grained attention patterns of diverse users, but also has the potential of benefiting the development of customized applications. Nevertheless, existing saliency models typically limit their scope to attention as it applies to the general population and ignore the variability between users' behaviors. In this paper, we identify the critical roles of visual preferences in attention modeling, and for the first time study the problem of user-aware saliency modeling. Our work aims to advance attention research from three distinct perspectives: (1) We present a new model with the flexibility to capture attention patterns of various combinations of users, so that we can adaptively predict personalized attention, user group attention, and general saliency at the same time with one single model; (2) To augment models with knowledge about the composition of attention from different users, we further propose a principled learning method to understand visual attention in a progressive manner; and (3) We carry out extensive analyses on publicly available saliency datasets to shed light on the roles of visual preferences. Experimental results on diverse stimuli, including naturalistic images and web pages, demonstrate the advantages of our method in capturing the distinct visual behaviors of different users and the general saliency of visual stimuli." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.797, + 0.21, + 0.812 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.822, + 0.47, + 0.868 + ], + "angle": 0, + "content": "With the pervasiveness of a visual attention network in the brain, attention has become an important interface for understanding people's behavioral patterns. A collection" + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.327, + 0.895, + 0.527 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.54, + 0.893, + 0.569 + ], + "angle": 0, + "content": "Figure 1. A hierarchy for user-aware saliency modeling, where each level focuses on a different perspective of attention." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.598, + 0.893, + 0.839 + ], + "angle": 0, + "content": "of studies focus on leveraging human attention to optimize graphical designs [7, 16, 36], web page layouts [8, 37, 45], and user experience in immersive environments [22, 38, 44]. They demonstrate its usefulness for a broad range of applications, and more importantly, highlight the intertwined nature between attention and users' preferences [11]. As shown in Figure 1, attention modeling can be formulated as a hierarchy of tasks, i.e., from a sophisticated understanding of individuals' behaviors (personalized attention), to modeling the visual behaviors of larger groups (user-group attention), and the saliency of visual stimuli (general saliency). With the great diversity in attentional behaviors among different groups (e.g., attention of users with diverse characteristics, children vs elderly, male vs female, etc.), knowledge of visual preferences can play an essential role in enabling a more fine-grained understanding of attention." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.894, + 0.903 + ], + "angle": 0, + "content": "To accurately capture human attention on visual stimuli, considerable efforts have been placed on building saliency prediction models [10, 19, 21, 29, 30]. While achieving optimistic results for modeling attention of the general popu" + }, + { + "type": "page_footnote", + "bbox": [ + 0.095, + 0.875, + 0.38, + 0.888 + ], + "angle": 0, + "content": "*Work done during an internship at Google Research." + }, + { + "type": "page_footnote", + "bbox": [ + 0.098, + 0.888, + 0.221, + 0.9 + ], + "angle": 0, + "content": "† Corresponding author" + }, + { + "type": "list", + "bbox": [ + 0.095, + 0.875, + 0.38, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "2701" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.273 + ], + "angle": 0, + "content": "lation, there are two key challenges remaining largely unresolved: (1) Existing models ignore the variability of users' visual behaviors, and hence do not have the ability to identify fine-grained attention patterns of distinct users; and (2) Apart from the shortage of models for user-aware saliency modeling, there has also been no attempt to formulate a training paradigm to understand the composition of attention, which hampers the integration of attention from diverse users. To fill the gap, we concentrate on a new research problem for modeling attention of adaptively selected users, and tackle the challenge with a new computational model together with a progressive learning method." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.274, + 0.473, + 0.499 + ], + "angle": 0, + "content": "At the heart of our saliency model is the incorporation of visual preferences with personalized filters and adaptive user masks. Unlike conventional methods designed for predicting a single saliency map representing attention of all users, it takes advantage of personalized filters to encode individuals' attention patterns. The attention patterns are adaptively integrated based on a user mask indicating the presence of users in the current sample, which enables attention prediction for various combinations of users. The aforementioned paradigm serves as the foundation for bridging individuals' preferences with visual saliency, and augments models with more abundant information about fine-grained visual behaviors. It not only shows promise in modeling attention of specific users, but also benefits the inference of the general saliency." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.5, + 0.473, + 0.756 + ], + "angle": 0, + "content": "A key challenge in user-aware saliency modeling is the lack of understanding when aggregating attention from diverse users. The issue becomes more critical when further considering the joint effects of stimuli and user preferences on visual attention [11], where the former factor may overshadow the impacts of the latter one, leading to difficulties in capturing the variability of users' attention. Inspired by human learning that acquires knowledge through a set of carefully designed curricula [2], we propose to tackle the aforementioned issues with a progressive learning approach. The essence of our method is to encourage a model to learn the composition of attention from a dynamic set of users, from individuals to user groups representing the general population. Through optimizing on dynamically evolving annotations, it provides opportunities for models to learn both the unique attention patterns of different users and the saliency of visual stimuli." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.756, + 0.455, + 0.771 + ], + "angle": 0, + "content": "To summarize, our major contributions are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.778, + 0.469, + 0.824 + ], + "angle": 0, + "content": "- We identify the significance of characterizing visual preferences for attention modeling, and develop a novel model that can predict attention of various users." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.832, + 0.469, + 0.877 + ], + "angle": 0, + "content": "- We present a progressive learning method to understand the composition of attention and capture its variability between different users." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.886, + 0.469, + 0.901 + ], + "angle": 0, + "content": "We perform extensive experiments and analyses to in" + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.778, + 0.469, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.532, + 0.092, + 0.892, + 0.168 + ], + "angle": 0, + "content": "vestigate the roles of visual preferences on tackling the challenges of user-aware and general saliency, and addressing the issues of incomplete users. Results demonstrate that user-aware saliency modeling is advantageous in all the above three aspects." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.181, + 0.651, + 0.197 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.207, + 0.892, + 0.252 + ], + "angle": 0, + "content": "Our work is most related to previous efforts on visual saliency prediction, which make contributions in both data collection and computational modeling." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.252, + 0.893, + 0.568 + ], + "angle": 0, + "content": "Saliency prediction datasets. With the overarching goal of facilitating the development of attention modeling methods, many studies have contributed saliency prediction datasets with diverse visual stimuli. The pioneering work [25] presents a gaze estimation dataset for naturalistic images together with an online benchmark [24]. Several subsequent studies propose to characterize images into finer categories based on visual scenes [3], visual semantics [41], or sentiments [14]. To overcome the difficulties of large-scale data collection, Jiang et al. [23] use mouse-tracking as a substitute for gaze estimation and construct currently the largest saliency prediction dataset. In addition to the aforementioned works that study attention on naturalistic images, several studies focus on attention for broader types of visual stimuli, including graphical designs [7, 16, 36], web pages [8, 37, 45], and immersive environments [22, 38, 44]. There are also attempts that go beyond attention collected during free-viewing, and study goal-directed attention when performing various tasks such as driving [1] and visual reasoning [9]. These data efforts enable the developments of a series of computational methods for attention modeling." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.57, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Saliency prediction models. To estimate attention distribution on different visual stimuli, a large body of research concentrates on building saliency prediction models. Early studies leverage handcrafted features that encode high- and low-level visual cues [5,17,20,40]. More recent approaches opt to automatically learn discriminative features based on deep neural networks. In particular, Huang et al. [19] utilize a convolution neural network (CNN) with multi-scale inputs to model the coarse-to-fine semantics. Kümmerer et al. [28] demonstrate the usefulness of deep features learned from image recognition for saliency prediction. Cornia et al. [10] develop a recurrent neural network to iteratively refine the visual features for saliency prediction. Jia et al. [21] augment model with rich visual semantics extracted from multiple levels of a CNN. Lou et al. [30] investigate the effectiveness of vision Transformers [13] for saliency prediction. Apart from the studies on general saliency prediction, a few works [32, 42, 43] attempt to tackle the problem of personalized saliency, which involves predicting attention of different users on naturalistic images. They adopt a simplified setting which only takes into account individuals' attention and assumes that the general saliency maps are given" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2702" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.12, + 0.087, + 0.852, + 0.403 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.288, + 0.405, + 0.69, + 0.419 + ], + "angle": 0, + "content": "Evolution of ground truth throughout the progressive learning procedure" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.43, + 0.893, + 0.459 + ], + "angle": 0, + "content": "Figure 2. An overview of the proposed framework. The top figure illustrates the architectural design of our saliency model for predicting attention of diverse users, while the bottom one outlines our progressive learning method for understanding the composition of attention." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.485, + 0.469, + 0.59 + ], + "angle": 0, + "content": "as inputs. While showing usefulness in capturing visual attention, the aforementioned methods either consider only attention aggregated from all users (i.e., general saliency) or rely on assumptions that are inapplicable to less-constrained real-world scenarios. They also utilize diverse paradigms for modeling different types of attention, which prevents a joint reasoning on the variability of users' visual behaviors." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.59, + 0.47, + 0.818 + ], + "angle": 0, + "content": "Our study differentiates from prior research in three key aspects: (1) We identify the significance of visual preferences for attention modeling, and for the first time tackle the challenge of user-aware saliency modeling. The new problem unifies previous studies on general and personalized saliency prediction, with the number of users being a dynamic factor; (2) Without imposing constraints on inputs (e.g., availability of general saliency maps [32,42,43] and naturalistic images as visual stimuli [10, 21, 28]), our model directly infers attention from visual stimuli and is able to generalize to broader scenarios (e.g., naturalistic images and web pages); and (3) In addition to a novel computational model, we also present a progressive learning approach to understand the composition of attention and capture the variability of attention." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.83, + 0.212, + 0.848 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Attention modeling would benefit from the knowledge about individuals' visual preferences and the capability to adaptively integrate them. This section presents an integral" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.485, + 0.893, + 0.577 + ], + "angle": 0, + "content": "framework consisting of two important components: (1) A new saliency prediction model that encodes visual preferences and dynamically predicts attention patterns of diverse combinations of users (Section 3.1), and (2) A principled approach for learning the composition of attention in a progressive manner (Section 3.2)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.588, + 0.892, + 0.62 + ], + "angle": 0, + "content": "3.1. Encoding Visual Preferences with Personalized Filters" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.628, + 0.893, + 0.78 + ], + "angle": 0, + "content": "A primary goal of our study is to endow models with the flexibility to predict attention for various users. We tackle the challenge with a new model paradigm that leverages a collection of personalized filters to identify individuals' visual preferences, and decomposes the overall attention patterns into fine-grained ones for different users. The key differentiators of our model lie in its (1) applicability to broader scenarios (e.g., from general saliency to attention of diverse users) and (2) flexibility to different settings (e.g., without assuming the availability of general saliency maps)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.781, + 0.894, + 0.902 + ], + "angle": 0, + "content": "Figure 2 (top) provides an overview of the proposed model. The principal idea behind our model is to take advantage of personalized filters to encode attention patterns of different users, and adaptively incorporate them based on the selection of users. Specifically, we build our model on top of the state-of-the-art EML-Net [21], which is a top-performing model on the MIT saliency benchmark [24]. Given an input image, our model extracts multi-scale fea" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.958 + ], + "angle": 0, + "content": "2703" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.244 + ], + "angle": 0, + "content": "tures from different layers of a convolutional neural network pretrained on ImageNet [12], encoding both high- and low-level visual cues. The raw features of different scales \\( V_{t} \\in \\mathbb{R}^{D \\times H \\times W} \\) (\\( D, H \\) and \\( W \\) correspond to the feature channel, height, and width, \\( t \\) denotes index for scales) are processed independently with their corresponding attention decoders \\( f_{t}^{\\alpha} \\) consisting of a sequence of convolutional and upsampling layers (see Section 4.1 for details), and then the decoded attention features \\( V_{t}^{\\alpha} \\) are aggregated across all scales to form the unregularized attention maps \\( S^{raw} \\):" + }, + { + "type": "equation", + "bbox": [ + 0.225, + 0.252, + 0.47, + 0.27 + ], + "angle": 0, + "content": "\\[\nV _ {t} ^ {\\alpha} = f _ {t} ^ {\\alpha} (V _ {t}) \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.218, + 0.289, + 0.47, + 0.32 + ], + "angle": 0, + "content": "\\[\nS ^ {r a w} = \\sum_ {t} V _ {t} ^ {\\alpha} \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.324, + 0.473, + 0.567 + ], + "angle": 0, + "content": "Different from conventional methods [10, 19, 21, 28] that directly predict a single saliency map for the general population (i.e., \\( S^{raw} \\in \\mathbb{R}^{H \\times W} \\)), our method takes into account discriminative attention patterns of each individual user (i.e., \\( S^{raw} \\in \\mathbb{R}^{N \\times H \\times W} \\), where \\( N \\) is the total number of users). We achieve the goal by expanding the filters in the last convolutional layer of each attention decoder, i.e., from a single filter to \\( N \\) personalized filters. To adaptively predict the visual attention for various combinations of users, our model takes in a user mask \\( M \\) in addition to the visual stimuli as input. The user mask is a binary vector \\( M \\in [0,1]^N \\) representing the presence of users, where \\( M_n = 1 \\) implies that attention of the \\( n^{th} \\) user is considered in the current sample. It plays the role as an indicator for integrating the unregularized attention maps from the selected users and generating the final saliency map \\( S \\in \\mathbb{R}^{H \\times W} \\):" + }, + { + "type": "equation", + "bbox": [ + 0.167, + 0.575, + 0.47, + 0.605 + ], + "angle": 0, + "content": "\\[\nS = \\operatorname {s o f t m a x} \\left(\\sum_ {n} M _ {n} \\cdot S _ {n} ^ {\\text {r a w}}\\right) \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.613, + 0.4, + 0.628 + ], + "angle": 0, + "content": "where \\(\\cdot\\) denotes the element-wise multiplication." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.629, + 0.47, + 0.78 + ], + "angle": 0, + "content": "To bridge individuals' visual preferences with the overall attention, we optimize our model with supervision on both the intermediate per-user predictions and the final output. We follow [10] and define the loss function \\( L_{sal} \\) as a combination of saliency metrics including Normalized Scanpath Saliency [33], Correlation Coefficient [31] and KL-Divergence [27] (see [10] and our supplementary materials). For per-user supervision, we apply a softmax activation function independently on unregularized attention map of each user to obtain their corresponding predictions:" + }, + { + "type": "equation", + "bbox": [ + 0.185, + 0.788, + 0.47, + 0.807 + ], + "angle": 0, + "content": "\\[\nS _ {n} ^ {\\text {u s e r}} = \\operatorname {s o f t m a x} \\left(S _ {n} ^ {\\text {r a w}}\\right) \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.814, + 0.47, + 0.845 + ], + "angle": 0, + "content": "Our overall objective simultaneously optimizes both the intermediate per-user predictions and the final output:" + }, + { + "type": "equation", + "bbox": [ + 0.136, + 0.853, + 0.469, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} L = L _ {s a l} (S, S a l, F i x) \\\\ + \\lambda \\sum_ {n} L _ {s a l} \\left(S _ {n} ^ {\\text {u s e r}}, S a l _ {n} ^ {\\text {u s e r}}, F i x _ {n} ^ {\\text {u s e r}}\\right) \\tag {5} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.168 + ], + "angle": 0, + "content": "where \\( Sal \\) and \\( Fix \\) are the ground truth saliency and fixation maps aggregated from selected users, \\( Sal_{n}^{user} \\) and \\( Fix_{n}^{user} \\) are those for individual user \\( n \\). Note that only users selected in the user mask (i.e., \\( M_{n} = 1 \\)) will be considered for optimization. \\( \\lambda \\) is the balancing factor." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.169, + 0.892, + 0.244 + ], + "angle": 0, + "content": "The aforementioned model illustrates a general paradigm for connecting user preferences and visual saliency. It serves as the foundation for user-aware saliency modeling, and supports the development of our progressive learning method, as detailed in the next subsection." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.256, + 0.836, + 0.272 + ], + "angle": 0, + "content": "3.2. Learning the Composition of Attention" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.28, + 0.892, + 0.491 + ], + "angle": 0, + "content": "Visual attention is driven by both salient regions that most people find attractive and individuals' unique interests. Understanding how to incorporate attention patterns of different users is an important challenge for user-aware saliency modeling. Without such knowledge, a model can overfit to attention driven by visual stimuli, and has difficulties learning the variability of users' attention. For instance, as there exists a considerable overlap between attention of different users, a model can exploit such a shortcut and predict an averaged attention map (of all users) regardless of the selection of users (see supplementary materials). To tackle the challenge, we propose a principled learning method that augments our saliency model with understanding of the composition of attention." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.492, + 0.893, + 0.825 + ], + "angle": 0, + "content": "Drawing inspirations from human learning, which is highly organized and based on curricula that gradually introduce diverse concepts, our method emphasizes progressive learning with dynamically evolving objectives. As illustrated in Figure 2 (bottom), it can be viewed as a three-phase training procedure: (1) As the initial step of learning, the model is encouraged to establish the correspondence between personalized modules and individuals' visual preference; (2) Later on, in the second phase, it is driven to take advantage of the learned preferences and construct saliency maps for diverse selections of users; (3) In the final phase, we allow the model to refine its prediction on attention of broader users, unifying personalized [42] and general saliency prediction [23, 25, 41]. Instead of dividing the learning into three separate stages (e.g., with a sequence of pretraining and fine-tuning), we instantiate the aforementioned paradigm by manipulating the characteristics of training samples throughout the learning process. Specifically, we first sample the number of users K from a specific range, and then randomly select of fixations K users (with a uniform distribution) to construct the ground truth fixation and saliency maps on the fly." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.894, + 0.902 + ], + "angle": 0, + "content": "Through controlling the number of users sampled among different training epochs, our method allows a continuous and progressive learning of the composition of attention: (1) We start with annotations from a small number of users (e.g., 1-4 users) and adaptively optimizing different compo" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2704" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.348 + ], + "angle": 0, + "content": "nents of the networks (e.g., personalized filters indicated by the input user masks), which allows the model to encode individuals' visual preferences. It also attenuates the effects of overfitting to attention driven by visual stimuli, as the model has no access to annotations from all users and thus can not exploit the correlation between individuals' attention and the averaged one; (2) With the progress of training, we gradually increase both the lower and the upper bounds for sampling range of K (e.g., from 1-4 to 5-9 users). Note that the users are randomly selected on a sample basis for every training iteration (i.e., one sample in a single batch). The scheme facilitates understanding of how to combine visual preferences of each individual to the attention patterns of different user groups; (3) During the last several training epochs, we fix the bounds for sampling to relatively large values (e.g., \\(80\\% - 100\\%\\) users), allowing the refinement of predictions for the general saliency." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.348, + 0.472, + 0.426 + ], + "angle": 0, + "content": "Our learning paradigm enables a smooth transition from individuals' preferences to attention of a broad range of users. Together with the proposed model, our full method shows promise in capturing attention of both diverse users (Section 4.2) and the general population (Section 4.3)" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.436, + 0.203, + 0.454 + ], + "angle": 0, + "content": "4. Experiment" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.461, + 0.47, + 0.537 + ], + "angle": 0, + "content": "In this section, we present the implementation details (Section 4.1), and carry out extensive experiments to study the effectiveness of the proposed framework. Our experiments and analyses aim to shed light on the following research questions that have yet to be answered:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.544, + 0.468, + 0.573 + ], + "angle": 0, + "content": "- Does learning the composition of attention help capture attention of diverse users? (Section 4.2)" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.583, + 0.468, + 0.613 + ], + "angle": 0, + "content": "- Are visual preferences beneficial for general saliency prediction? (Section 4.3)" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.622, + 0.468, + 0.651 + ], + "angle": 0, + "content": "- Can user-aware saliency modeling overcome the issues of incomplete users? (Section 4.4)" + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.544, + 0.468, + 0.651 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.659, + 0.468, + 0.688 + ], + "angle": 0, + "content": "We also include additional analyses and ablation studies in the supplementary materials." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.697, + 0.238, + 0.712 + ], + "angle": 0, + "content": "4.1. Implementation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Dataset. We demonstrate the effectiveness of our method with two types of visual stimuli, i.e., naturalistic images and web pages. Since most saliency datasets only offer aggregated fixation annotations, we choose two publicly available saliency datasets, OSIE [39, 41] and FiWI [37], as our testbeds, which provide per-user annotations for user-aware saliency modeling. OSIE contains eye-tracking data collected on 700 naturalistic images with rich semantics. We use the version collected in [39], which has more diverse attention patterns from 32 users (about 14 users are presented with each sample) due to their less constrained experimental settings. FiWI is a popular eye-tracking dataset" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.152 + ], + "angle": 0, + "content": "for web pages, which contains data from 11 users on 149 samples. We also conduct experiments on the recently introduced web page saliency dataset [8] with 450 samples, and report the results in our supplementary materials." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.153, + 0.893, + 0.379 + ], + "angle": 0, + "content": "Evaluation. Saliency prediction is typically evaluated with multiple metrics [6]. Following [8, 19, 21, 30], we adopt seven popular saliency metrics, including Normalized Scanpath Saliency (NSS) [33], KL-Divergence (KLD) [27], Similarity (SIM) [35], Correlation Coefficient (CC) [31], Area Under the ROC Curve (AUC) [15], AUC-Judd [25], and shuffled AUC (sAUC) [4]. For the OSIE dataset, we follow [41], and randomly split the samples into 600 and 100 for training and evaluation, respectively. In terms of the FiWI dataset, following [37] and [8], we consider two evaluation settings, including 5-fold cross-validation and evaluation with fixed training/test sets. Besides estimating the capability of our method on capturing the attention patterns of diverse users (Section 4.2), we also study its usefulness on general saliency prediction (Section 4.3)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.381, + 0.893, + 0.592 + ], + "angle": 0, + "content": "Model Configuration. We build our method on the state-of-the-art EML-Net [21] saliency model. We use ResNet-50 [18] as the backbone, which is pretrained on ImageNet classification [12] and offers profound understanding of visual semantics. To show the generalizability of our method, we also experiment with a different saliency model (i.e., a variation of SimpleNet [34], see the supplementary materials). Multi-scale features are extracted from 4 layers, where each corresponds to the end of a block inside the backbone. The features are processed with a set of attention decoders, where the decoder of each scale contains two consecutive convolutional layers with 16 and N filters (N is the number of users), and an upsampling layer that rescales features to have the same spatial resolution as the image." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.593, + 0.894, + 0.804 + ], + "angle": 0, + "content": "Training. Following [10], we train models for 50 epochs with batch size 10 using the Adam optimizer [26]. \\(\\lambda\\) factor in equation (5) is empirically set to 0.2. Learning rate is initially set to \\(10^{-4}\\), and decayed by a factor of 0.8 for every 10 epochs. For our learning approach proposed in Section 3.2, we set the initial bounds to [1, 4] and [1, 6] for FiWI and OSIE, respectively, and increase both the upper and lower bounds by 2 every 10 epochs. The bounds are fixed to [9, 11] and [11, 15] for FiWI and OSIE after reaching the corresponding values. The aforementioned hyperparameters are determined based on 5-fold cross-validation. For a fair comparison with the state-of-the-art [8, 37] and a more flexible setting, we do not pretrain our models on external saliency datasets like the SALICON [23] dataset." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.816, + 0.892, + 0.848 + ], + "angle": 0, + "content": "4.2. Does Learning the Composition of Attention Help Capture Attention of Diverse Users?" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We first study the effectiveness of our method for capturing the visual preferences of diverse users. Specifically, we randomly sample K users \\((\\mathrm{K} = 1,3,5)\\) for each evaluation" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2705" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.118, + 0.089, + 0.852, + 0.503 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.512, + 0.895, + 0.542 + ], + "angle": 0, + "content": "Figure 3. Qualitative results for predicting attention of diverse users. We show results for two different user groups for each sample, and also consider variable numbers of users \\( K = 1, 3, 5 \\). Note that EML-Net is user-agnostic and predicts the same result for two groups." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.567, + 0.473, + 0.749 + ], + "angle": 0, + "content": "image, and estimate the predictions with ground truth annotations aggregated from the selected users. We repeat the procedure 5 times to reduce the variance of results, and report the average performance. Following [41] and [37], we use fixed training/test splits on the OSIE dataset and perform 5-fold cross-validation on the FiWI dataset. We compare our full method (Ours) with three approaches, including the user-agnostic EML-Net baseline [21], an ensemble of EML-Net trained on individual users (Single-user, with one model for each user), and our model without incorporating progressive learning (Ours*). Three key observations can be made on the results reported in Table 1 and Table 2:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.757, + 0.473, + 0.879 + ], + "angle": 0, + "content": "- There exist considerable discrepancies between general and user-aware saliency modeling. Despite the inter-user agreement on visual attention, the user-agnostic EML-Net achieves inferior performance on both datasets, especially FiWI with web pages associated with richer semantics and more diverse viewing behaviors. The observation highlights the significance of visual preferences for attention modeling." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.886, + 0.472, + 0.902 + ], + "angle": 0, + "content": "- Learning how to integrate attention is important" + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.757, + 0.473, + 0.902 + ], + "angle": 0, + "content": null + }, + { + "type": "table_caption", + "bbox": [ + 0.545, + 0.565, + 0.847, + 0.58 + ], + "angle": 0, + "content": "Table 1. User-aware saliency results on FiWI [37]." + }, + { + "type": "table", + "bbox": [ + 0.506, + 0.59, + 0.887, + 0.709 + ], + "angle": 0, + "content": "
K=1K=3K=5
NSSCCNSSCCNSSCC
EML-Net1.4810.3071.5060.4541.4980.519
Single-user1.9620.3731.7490.5181.7450.591
Ours*1.9080.3661.7850.5261.7840.609
Ours2.0590.3921.8290.5401.8150.620
" + }, + { + "type": "table_caption", + "bbox": [ + 0.53, + 0.72, + 0.862, + 0.735 + ], + "angle": 0, + "content": "Table 2. User-aware saliency results on OSIE data [39]." + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.745, + 0.887, + 0.865 + ], + "angle": 0, + "content": "
K=1K=3K=5
NSSCCNSSCCNSSCC
EML-Net1.7550.3671.7630.5321.7180.594
Single-user1.4560.3141.5650.4921.5740.566
Ours*1.6400.2941.7680.5371.8120.625
Ours1.8090.3101.8090.5501.8260.629
" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2706" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.119, + 0.09, + 0.427, + 0.104 + ], + "angle": 0, + "content": "Table 3. General saliency results on FiWI data [37]." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.115, + 0.462, + 0.257 + ], + "angle": 0, + "content": "
NSSKLDCCAUC-JuddsAUC
DeepGaze II1.229-0.4880.7970.625
SAM-ResNet1.246-0.5950.7910.673
UMSI0.938-0.4570.7550.675
AGD-F1.606-0.7350.7670.748
EML-Net1.6530.6030.6610.8470.675
EML-Net+SALICON1.7220.5670.6890.8480.697
Ours1.7520.5640.6990.8510.704
" + }, + { + "type": "table_caption", + "bbox": [ + 0.119, + 0.27, + 0.428, + 0.284 + ], + "angle": 0, + "content": "Table 4. General saliency results on OSIE data [39]." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.295, + 0.462, + 0.425 + ], + "angle": 0, + "content": "
NSSKLDSIMCCAUC
SALICON1.6410.5750.6000.6850.846
SAM-ResNet1.8110.4800.6480.7580.860
UMSI1.7880.5130.6310.7460.856
EML-Net1.7370.5370.6190.7170.854
Ours1.8400.5060.6520.7610.860
" + }, + { + "type": "text", + "bbox": [ + 0.108, + 0.452, + 0.47, + 0.649 + ], + "angle": 0, + "content": "for capturing visual preferences. A key component of our framework is the progressive learning method for understanding the composition of attention. According to the comparative results between our methods with and without progressive learning, it helps models better identify the attentional preferences of both individuals (i.e., \\( \\mathrm{K} = 1 \\)) and user groups (i.e., \\( \\mathrm{K} = 3 \\), 5). As illustrated in Figure 3, unlike EML-Net and our method without progressive learning (Ours*) that fail to capture the visual preferences and generate similar attention maps regardless of the selection of users, our full method is able to predict attention maps that accurately reflect the regions of interest of diverse users." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.66, + 0.47, + 0.858 + ], + "angle": 0, + "content": "- Additive ensemble falls short of modeling user-aware attention. Training one model for each user offers a straightforward way to model user preferences, and slightly outperforms our method without progressive learning when considering individuals' attention (i.e., \\( \\mathrm{K} = 1 \\)) on FiWI. However, without learning how to integrate attention, it lacks the capability to predict attention maps with multiple users and is outperformed by our full method across all settings. Additionally, such an additive ensemble also fails to benefit general saliency prediction due to its high computational overhead and the inability to jointly consider attention of different users (see our supplementary materials)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.47, + 0.903 + ], + "angle": 0, + "content": "These observations highlight the significance of modeling visual preferences and the composition of attention, and" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.213 + ], + "angle": 0, + "content": "demonstrate the advantages of our method for user-aware saliency modeling. While we do not consider demographic information in this study, our method is general and can be extended to broader scenarios for customized applications. For instance, instead of developing personalized filters, we can cluster users based on certain criteria (e.g., gender, age, personal interest) and optimize models to predict attentional preferences of users of specific characteristics." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.223, + 0.892, + 0.254 + ], + "angle": 0, + "content": "4.3. Are Visual Preferences Beneficial for General Saliency Prediction?" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.262, + 0.892, + 0.428 + ], + "angle": 0, + "content": "General saliency prediction focuses on attention aggregated from all users, and yet little attention has been paid to the diversity of attention patterns between users. In this subsection, we further investigate if knowledge of visual preferences is beneficial for the task. We compare our user-aware method with six state-of-the-art models, including SALICON [19], Deep Gaze II [28], SAM [10], EML-Net [21], UMSI [16], and AGD-F [8]. For a fair comparison, we adopt the training and test sets provided in [8] for evaluation on FiWI dataset. Table 3 and Table 4 report results on the FiWI [37] and OSIE [39, 41] datasets." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.429, + 0.892, + 0.701 + ], + "angle": 0, + "content": "Compared to the EML-Net baseline, our model that takes into account visual preferences shows consistent improvements among all settings. Its performance is also competitive against existing state-of-the-art. As illustrated in Figure 4, the performance gain of our method can be attributed to the capability to capture fine-grained attention patterns (i.e., focuses on the man, little girls, and woman in the three examples, respectively) in addition to the salient regions attended by the majority of users (i.e., text, the food, and the boy). Moreover, the advantages of our method is also a result of increased data efficiency. Comparative results show that it outperforms EML-Net pretrained on the SALICON [23] dataset with 15000 images (EML-Net+SALICON), despite only relying on training samples in the FiWI dataset with 149 images. Such a unique feature can play an important role in generalizing towards domains with diverse characteristics (e.g., web page vs naturalistic image), where suitable data for pretraining is not necessarily available." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.711, + 0.892, + 0.742 + ], + "angle": 0, + "content": "4.4. Can User-aware Saliency Modeling Overcome the Issues of Incomplete Users?" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.885 + ], + "angle": 0, + "content": "Collecting human behavioral data demands stringent paradigms, and building large attention datasets has been challenging for decades [23]. As a result, it is common for saliency datasets to have samples associated with incomplete users. For instance, there are 32 users recruited in [39], while only about 14 users are presented for each sample. Different from prior works [19, 21, 28, 30] that overlook the issue, we examine if knowledge of visual preferences can be helpful for tackling the problem." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.886, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Specifically, we randomly drop \\( K^{*} \\) users for each train-" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2707" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.18, + 0.089, + 0.797, + 0.355 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.307, + 0.364, + 0.663, + 0.379 + ], + "angle": 0, + "content": "Figure 4. Qualitative results for general saliency prediction." + }, + { + "type": "table_caption", + "bbox": [ + 0.218, + 0.393, + 0.751, + 0.408 + ], + "angle": 0, + "content": "Table 5. Results for saliency prediction with incomplete users on seen and unseen images." + }, + { + "type": "table", + "bbox": [ + 0.182, + 0.418, + 0.782, + 0.551 + ], + "angle": 0, + "content": "
K=1K=3K=5Unseen
NSSCCNSSCCNSSCCNSSCC
K* = 5EML-Net1.7330.3591.7190.5181.7120.5891.6160.601
Ours1.7590.3411.7810.5301.7970.6141.6980.632
K* = 7EML-Net1.6620.3421.6590.5011.6580.5731.5840.551
Ours1.7230.3301.7340.5121.7390.5941.7080.589
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.574, + 0.47, + 0.696 + ], + "angle": 0, + "content": "ing sample in the FiWI dataset, and consider two evaluation settings: (1) attention of missing users on seen samples (we use different numbers of missing users, i.e., \\( \\mathrm{K} = 1, 3, 5 \\)), and (2) attention of all users on unseen test samples (i.e., Unseen). The first setting is particularly useful for scenarios where we are interested in comparing users' preferences. On the other hand, the second setting aims to study models' robustness against the scarcity of annotations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.704, + 0.471, + 0.903 + ], + "angle": 0, + "content": "According to comparative results reported in Table 5, the proposed user-aware method is advantageous in both evaluation settings. Despite the slightly lower CC scores for individuals' attention \\((\\mathrm{K} = 1)\\) on seen images, it achieves considerable improvements among all other evaluation settings. This is likely because predictions from the user-agnostic EML-Net tend to have a broader coverage, which is favored by CC metric emphasizing the overall distribution. Differently, our method has the capability to more accurately attend to regions of interest of different users, resulting in higher NSS scores as well as CC scores for more users. It also makes better use of the available data, and is more robust against the scarcity of annotations (i.e., higher general" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.575, + 0.766, + 0.59 + ], + "angle": 0, + "content": "ization performance on unseen images)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.604, + 0.62, + 0.619 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.895, + 0.903 + ], + "angle": 0, + "content": "This paper identifies the critical roles of user preferences in visual attention, and for the first time tackles the challenge of user-aware saliency modeling. It unifies the conventional tasks for predicting general and personalized attention, and proposes an integral framework that jointly solves attention modeling for individual users, different groups of users, and the general population. By making progress with both a novel saliency prediction model and a progressive learning method, our framework illustrates a principled paradigm for establishing the connections between user preferences and visual saliency. Experimental results in diverse settings demonstrate the advantages of the proposed method in inferring the attention patterns of a variety of users, and highlights the significance of incorporating the variability of attention. We hope that our study can open new avenues for attention research, and benefit the development of new applications based on user-aware saliency models." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2708" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.175, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.171 + ], + "angle": 0, + "content": "[1] Stefano Alletto, Andrea Palazzi, Francesco Solera, Simone Calderara, and Rita Cucchiara. Dr(eye)ve: A dataset for attention-based tasks with applications to autonomous and assisted driving. In CVPR workshop, pages 54-60, 2016. 2" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.172, + 0.47, + 0.211 + ], + "angle": 0, + "content": "[2] Yoshua Bengio, Jérôme Louradour, Ronan Collobert, and Jason Weston. Curriculum learning. 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In ECCV, pages 300-316, 2018. 1, 2" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.468, + 0.743 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.517, + 0.956 + ], + "angle": 0, + "content": "2710" + } + ] +] \ No newline at end of file diff --git a/2023/Learning From Unique Perspectives_ User-Aware Saliency Modeling/f7bfd1c8-4126-4d0a-afcb-ecafb59d0e63_origin.pdf b/2023/Learning From Unique Perspectives_ User-Aware Saliency Modeling/f7bfd1c8-4126-4d0a-afcb-ecafb59d0e63_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..9d7346d39626bbbbf98f897a3d71c2455f350490 --- /dev/null +++ b/2023/Learning From Unique Perspectives_ User-Aware Saliency Modeling/f7bfd1c8-4126-4d0a-afcb-ecafb59d0e63_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:d2c34f9161665351729744cb166def1960bd2a2c62a2ddb76f6513e198db2464 +size 8622911 diff --git a/2023/Learning From Unique Perspectives_ User-Aware Saliency Modeling/full.md b/2023/Learning From Unique Perspectives_ User-Aware Saliency Modeling/full.md new file mode 100644 index 0000000000000000000000000000000000000000..ea76fedabf0a41fa6e818f1790b8cad6873f6627 --- /dev/null +++ b/2023/Learning From Unique Perspectives_ User-Aware Saliency Modeling/full.md @@ -0,0 +1,277 @@ +# Learning from Unique Perspectives: User-aware Saliency Modeling + +Shi Chen* + +University of Minnesota + +chen4595@umn.edu + +Xinyu Ye + +Google + +yexinyu@google.com + +Nachiappan Valliappan + +Google Research + +nac@google.com + +Kai Kohlhoff + +Google Research + +kohlhoff@google.com + +Shaolei Shen + +Google + +shaoleis@google.com + +Junfeng He† + +Google Research + +junfenghe@google.com + +# Abstract + +Everyone is unique. Given the same visual stimuli, people's attention is driven by both salient visual cues and their own inherent preferences. Knowledge of visual preferences not only facilitates understanding of fine-grained attention patterns of diverse users, but also has the potential of benefiting the development of customized applications. Nevertheless, existing saliency models typically limit their scope to attention as it applies to the general population and ignore the variability between users' behaviors. In this paper, we identify the critical roles of visual preferences in attention modeling, and for the first time study the problem of user-aware saliency modeling. Our work aims to advance attention research from three distinct perspectives: (1) We present a new model with the flexibility to capture attention patterns of various combinations of users, so that we can adaptively predict personalized attention, user group attention, and general saliency at the same time with one single model; (2) To augment models with knowledge about the composition of attention from different users, we further propose a principled learning method to understand visual attention in a progressive manner; and (3) We carry out extensive analyses on publicly available saliency datasets to shed light on the roles of visual preferences. Experimental results on diverse stimuli, including naturalistic images and web pages, demonstrate the advantages of our method in capturing the distinct visual behaviors of different users and the general saliency of visual stimuli. + +# 1. Introduction + +With the pervasiveness of a visual attention network in the brain, attention has become an important interface for understanding people's behavioral patterns. A collection + +![](images/eead546da9b281f2b6ac20767720c3088d04552717e1979121cf20afc8e43947.jpg) +Figure 1. A hierarchy for user-aware saliency modeling, where each level focuses on a different perspective of attention. + +of studies focus on leveraging human attention to optimize graphical designs [7, 16, 36], web page layouts [8, 37, 45], and user experience in immersive environments [22, 38, 44]. They demonstrate its usefulness for a broad range of applications, and more importantly, highlight the intertwined nature between attention and users' preferences [11]. As shown in Figure 1, attention modeling can be formulated as a hierarchy of tasks, i.e., from a sophisticated understanding of individuals' behaviors (personalized attention), to modeling the visual behaviors of larger groups (user-group attention), and the saliency of visual stimuli (general saliency). With the great diversity in attentional behaviors among different groups (e.g., attention of users with diverse characteristics, children vs elderly, male vs female, etc.), knowledge of visual preferences can play an essential role in enabling a more fine-grained understanding of attention. + +To accurately capture human attention on visual stimuli, considerable efforts have been placed on building saliency prediction models [10, 19, 21, 29, 30]. While achieving optimistic results for modeling attention of the general popu + +lation, there are two key challenges remaining largely unresolved: (1) Existing models ignore the variability of users' visual behaviors, and hence do not have the ability to identify fine-grained attention patterns of distinct users; and (2) Apart from the shortage of models for user-aware saliency modeling, there has also been no attempt to formulate a training paradigm to understand the composition of attention, which hampers the integration of attention from diverse users. To fill the gap, we concentrate on a new research problem for modeling attention of adaptively selected users, and tackle the challenge with a new computational model together with a progressive learning method. + +At the heart of our saliency model is the incorporation of visual preferences with personalized filters and adaptive user masks. Unlike conventional methods designed for predicting a single saliency map representing attention of all users, it takes advantage of personalized filters to encode individuals' attention patterns. The attention patterns are adaptively integrated based on a user mask indicating the presence of users in the current sample, which enables attention prediction for various combinations of users. The aforementioned paradigm serves as the foundation for bridging individuals' preferences with visual saliency, and augments models with more abundant information about fine-grained visual behaviors. It not only shows promise in modeling attention of specific users, but also benefits the inference of the general saliency. + +A key challenge in user-aware saliency modeling is the lack of understanding when aggregating attention from diverse users. The issue becomes more critical when further considering the joint effects of stimuli and user preferences on visual attention [11], where the former factor may overshadow the impacts of the latter one, leading to difficulties in capturing the variability of users' attention. Inspired by human learning that acquires knowledge through a set of carefully designed curricula [2], we propose to tackle the aforementioned issues with a progressive learning approach. The essence of our method is to encourage a model to learn the composition of attention from a dynamic set of users, from individuals to user groups representing the general population. Through optimizing on dynamically evolving annotations, it provides opportunities for models to learn both the unique attention patterns of different users and the saliency of visual stimuli. + +To summarize, our major contributions are as follows: + +- We identify the significance of characterizing visual preferences for attention modeling, and develop a novel model that can predict attention of various users. +- We present a progressive learning method to understand the composition of attention and capture its variability between different users. +We perform extensive experiments and analyses to in + +vestigate the roles of visual preferences on tackling the challenges of user-aware and general saliency, and addressing the issues of incomplete users. Results demonstrate that user-aware saliency modeling is advantageous in all the above three aspects. + +# 2. Related Works + +Our work is most related to previous efforts on visual saliency prediction, which make contributions in both data collection and computational modeling. + +Saliency prediction datasets. With the overarching goal of facilitating the development of attention modeling methods, many studies have contributed saliency prediction datasets with diverse visual stimuli. The pioneering work [25] presents a gaze estimation dataset for naturalistic images together with an online benchmark [24]. Several subsequent studies propose to characterize images into finer categories based on visual scenes [3], visual semantics [41], or sentiments [14]. To overcome the difficulties of large-scale data collection, Jiang et al. [23] use mouse-tracking as a substitute for gaze estimation and construct currently the largest saliency prediction dataset. In addition to the aforementioned works that study attention on naturalistic images, several studies focus on attention for broader types of visual stimuli, including graphical designs [7, 16, 36], web pages [8, 37, 45], and immersive environments [22, 38, 44]. There are also attempts that go beyond attention collected during free-viewing, and study goal-directed attention when performing various tasks such as driving [1] and visual reasoning [9]. These data efforts enable the developments of a series of computational methods for attention modeling. + +Saliency prediction models. To estimate attention distribution on different visual stimuli, a large body of research concentrates on building saliency prediction models. Early studies leverage handcrafted features that encode high- and low-level visual cues [5,17,20,40]. More recent approaches opt to automatically learn discriminative features based on deep neural networks. In particular, Huang et al. [19] utilize a convolution neural network (CNN) with multi-scale inputs to model the coarse-to-fine semantics. Kümmerer et al. [28] demonstrate the usefulness of deep features learned from image recognition for saliency prediction. Cornia et al. [10] develop a recurrent neural network to iteratively refine the visual features for saliency prediction. Jia et al. [21] augment model with rich visual semantics extracted from multiple levels of a CNN. Lou et al. [30] investigate the effectiveness of vision Transformers [13] for saliency prediction. Apart from the studies on general saliency prediction, a few works [32, 42, 43] attempt to tackle the problem of personalized saliency, which involves predicting attention of different users on naturalistic images. They adopt a simplified setting which only takes into account individuals' attention and assumes that the general saliency maps are given + +![](images/ced0a2328c238da104a51282616c9d620f3bd8eedf792dcc90a3de5cd20e0652.jpg) +Evolution of ground truth throughout the progressive learning procedure +Figure 2. An overview of the proposed framework. The top figure illustrates the architectural design of our saliency model for predicting attention of diverse users, while the bottom one outlines our progressive learning method for understanding the composition of attention. + +as inputs. While showing usefulness in capturing visual attention, the aforementioned methods either consider only attention aggregated from all users (i.e., general saliency) or rely on assumptions that are inapplicable to less-constrained real-world scenarios. They also utilize diverse paradigms for modeling different types of attention, which prevents a joint reasoning on the variability of users' visual behaviors. + +Our study differentiates from prior research in three key aspects: (1) We identify the significance of visual preferences for attention modeling, and for the first time tackle the challenge of user-aware saliency modeling. The new problem unifies previous studies on general and personalized saliency prediction, with the number of users being a dynamic factor; (2) Without imposing constraints on inputs (e.g., availability of general saliency maps [32,42,43] and naturalistic images as visual stimuli [10, 21, 28]), our model directly infers attention from visual stimuli and is able to generalize to broader scenarios (e.g., naturalistic images and web pages); and (3) In addition to a novel computational model, we also present a progressive learning approach to understand the composition of attention and capture the variability of attention. + +# 3. Methodology + +Attention modeling would benefit from the knowledge about individuals' visual preferences and the capability to adaptively integrate them. This section presents an integral + +framework consisting of two important components: (1) A new saliency prediction model that encodes visual preferences and dynamically predicts attention patterns of diverse combinations of users (Section 3.1), and (2) A principled approach for learning the composition of attention in a progressive manner (Section 3.2). + +# 3.1. Encoding Visual Preferences with Personalized Filters + +A primary goal of our study is to endow models with the flexibility to predict attention for various users. We tackle the challenge with a new model paradigm that leverages a collection of personalized filters to identify individuals' visual preferences, and decomposes the overall attention patterns into fine-grained ones for different users. The key differentiators of our model lie in its (1) applicability to broader scenarios (e.g., from general saliency to attention of diverse users) and (2) flexibility to different settings (e.g., without assuming the availability of general saliency maps). + +Figure 2 (top) provides an overview of the proposed model. The principal idea behind our model is to take advantage of personalized filters to encode attention patterns of different users, and adaptively incorporate them based on the selection of users. Specifically, we build our model on top of the state-of-the-art EML-Net [21], which is a top-performing model on the MIT saliency benchmark [24]. Given an input image, our model extracts multi-scale fea + +tures from different layers of a convolutional neural network pretrained on ImageNet [12], encoding both high- and low-level visual cues. The raw features of different scales $V_{t} \in \mathbb{R}^{D \times H \times W}$ ( $D, H$ and $W$ correspond to the feature channel, height, and width, $t$ denotes index for scales) are processed independently with their corresponding attention decoders $f_{t}^{\alpha}$ consisting of a sequence of convolutional and upsampling layers (see Section 4.1 for details), and then the decoded attention features $V_{t}^{\alpha}$ are aggregated across all scales to form the unregularized attention maps $S^{raw}$ : + +$$ +V _ {t} ^ {\alpha} = f _ {t} ^ {\alpha} (V _ {t}) \tag {1} +$$ + +$$ +S ^ {r a w} = \sum_ {t} V _ {t} ^ {\alpha} \tag {2} +$$ + +Different from conventional methods [10, 19, 21, 28] that directly predict a single saliency map for the general population (i.e., $S^{raw} \in \mathbb{R}^{H \times W}$ ), our method takes into account discriminative attention patterns of each individual user (i.e., $S^{raw} \in \mathbb{R}^{N \times H \times W}$ , where $N$ is the total number of users). We achieve the goal by expanding the filters in the last convolutional layer of each attention decoder, i.e., from a single filter to $N$ personalized filters. To adaptively predict the visual attention for various combinations of users, our model takes in a user mask $M$ in addition to the visual stimuli as input. The user mask is a binary vector $M \in [0,1]^N$ representing the presence of users, where $M_n = 1$ implies that attention of the $n^{th}$ user is considered in the current sample. It plays the role as an indicator for integrating the unregularized attention maps from the selected users and generating the final saliency map $S \in \mathbb{R}^{H \times W}$ : + +$$ +S = \operatorname {s o f t m a x} \left(\sum_ {n} M _ {n} \cdot S _ {n} ^ {\text {r a w}}\right) \tag {3} +$$ + +where $\cdot$ denotes the element-wise multiplication. + +To bridge individuals' visual preferences with the overall attention, we optimize our model with supervision on both the intermediate per-user predictions and the final output. We follow [10] and define the loss function $L_{sal}$ as a combination of saliency metrics including Normalized Scanpath Saliency [33], Correlation Coefficient [31] and KL-Divergence [27] (see [10] and our supplementary materials). For per-user supervision, we apply a softmax activation function independently on unregularized attention map of each user to obtain their corresponding predictions: + +$$ +S _ {n} ^ {\text {u s e r}} = \operatorname {s o f t m a x} \left(S _ {n} ^ {\text {r a w}}\right) \tag {4} +$$ + +Our overall objective simultaneously optimizes both the intermediate per-user predictions and the final output: + +$$ +\begin{array}{l} L = L _ {s a l} (S, S a l, F i x) \\ + \lambda \sum_ {n} L _ {s a l} \left(S _ {n} ^ {\text {u s e r}}, S a l _ {n} ^ {\text {u s e r}}, F i x _ {n} ^ {\text {u s e r}}\right) \tag {5} \\ \end{array} +$$ + +where $Sal$ and $Fix$ are the ground truth saliency and fixation maps aggregated from selected users, $Sal_{n}^{user}$ and $Fix_{n}^{user}$ are those for individual user $n$ . Note that only users selected in the user mask (i.e., $M_{n} = 1$ ) will be considered for optimization. $\lambda$ is the balancing factor. + +The aforementioned model illustrates a general paradigm for connecting user preferences and visual saliency. It serves as the foundation for user-aware saliency modeling, and supports the development of our progressive learning method, as detailed in the next subsection. + +# 3.2. Learning the Composition of Attention + +Visual attention is driven by both salient regions that most people find attractive and individuals' unique interests. Understanding how to incorporate attention patterns of different users is an important challenge for user-aware saliency modeling. Without such knowledge, a model can overfit to attention driven by visual stimuli, and has difficulties learning the variability of users' attention. For instance, as there exists a considerable overlap between attention of different users, a model can exploit such a shortcut and predict an averaged attention map (of all users) regardless of the selection of users (see supplementary materials). To tackle the challenge, we propose a principled learning method that augments our saliency model with understanding of the composition of attention. + +Drawing inspirations from human learning, which is highly organized and based on curricula that gradually introduce diverse concepts, our method emphasizes progressive learning with dynamically evolving objectives. As illustrated in Figure 2 (bottom), it can be viewed as a three-phase training procedure: (1) As the initial step of learning, the model is encouraged to establish the correspondence between personalized modules and individuals' visual preference; (2) Later on, in the second phase, it is driven to take advantage of the learned preferences and construct saliency maps for diverse selections of users; (3) In the final phase, we allow the model to refine its prediction on attention of broader users, unifying personalized [42] and general saliency prediction [23, 25, 41]. Instead of dividing the learning into three separate stages (e.g., with a sequence of pretraining and fine-tuning), we instantiate the aforementioned paradigm by manipulating the characteristics of training samples throughout the learning process. Specifically, we first sample the number of users K from a specific range, and then randomly select of fixations K users (with a uniform distribution) to construct the ground truth fixation and saliency maps on the fly. + +Through controlling the number of users sampled among different training epochs, our method allows a continuous and progressive learning of the composition of attention: (1) We start with annotations from a small number of users (e.g., 1-4 users) and adaptively optimizing different compo + +nents of the networks (e.g., personalized filters indicated by the input user masks), which allows the model to encode individuals' visual preferences. It also attenuates the effects of overfitting to attention driven by visual stimuli, as the model has no access to annotations from all users and thus can not exploit the correlation between individuals' attention and the averaged one; (2) With the progress of training, we gradually increase both the lower and the upper bounds for sampling range of K (e.g., from 1-4 to 5-9 users). Note that the users are randomly selected on a sample basis for every training iteration (i.e., one sample in a single batch). The scheme facilitates understanding of how to combine visual preferences of each individual to the attention patterns of different user groups; (3) During the last several training epochs, we fix the bounds for sampling to relatively large values (e.g., $80\% - 100\%$ users), allowing the refinement of predictions for the general saliency. + +Our learning paradigm enables a smooth transition from individuals' preferences to attention of a broad range of users. Together with the proposed model, our full method shows promise in capturing attention of both diverse users (Section 4.2) and the general population (Section 4.3) + +# 4. Experiment + +In this section, we present the implementation details (Section 4.1), and carry out extensive experiments to study the effectiveness of the proposed framework. Our experiments and analyses aim to shed light on the following research questions that have yet to be answered: + +- Does learning the composition of attention help capture attention of diverse users? (Section 4.2) +- Are visual preferences beneficial for general saliency prediction? (Section 4.3) +- Can user-aware saliency modeling overcome the issues of incomplete users? (Section 4.4) + +We also include additional analyses and ablation studies in the supplementary materials. + +# 4.1. Implementation + +Dataset. We demonstrate the effectiveness of our method with two types of visual stimuli, i.e., naturalistic images and web pages. Since most saliency datasets only offer aggregated fixation annotations, we choose two publicly available saliency datasets, OSIE [39, 41] and FiWI [37], as our testbeds, which provide per-user annotations for user-aware saliency modeling. OSIE contains eye-tracking data collected on 700 naturalistic images with rich semantics. We use the version collected in [39], which has more diverse attention patterns from 32 users (about 14 users are presented with each sample) due to their less constrained experimental settings. FiWI is a popular eye-tracking dataset + +for web pages, which contains data from 11 users on 149 samples. We also conduct experiments on the recently introduced web page saliency dataset [8] with 450 samples, and report the results in our supplementary materials. + +Evaluation. Saliency prediction is typically evaluated with multiple metrics [6]. Following [8, 19, 21, 30], we adopt seven popular saliency metrics, including Normalized Scanpath Saliency (NSS) [33], KL-Divergence (KLD) [27], Similarity (SIM) [35], Correlation Coefficient (CC) [31], Area Under the ROC Curve (AUC) [15], AUC-Judd [25], and shuffled AUC (sAUC) [4]. For the OSIE dataset, we follow [41], and randomly split the samples into 600 and 100 for training and evaluation, respectively. In terms of the FiWI dataset, following [37] and [8], we consider two evaluation settings, including 5-fold cross-validation and evaluation with fixed training/test sets. Besides estimating the capability of our method on capturing the attention patterns of diverse users (Section 4.2), we also study its usefulness on general saliency prediction (Section 4.3). + +Model Configuration. We build our method on the state-of-the-art EML-Net [21] saliency model. We use ResNet-50 [18] as the backbone, which is pretrained on ImageNet classification [12] and offers profound understanding of visual semantics. To show the generalizability of our method, we also experiment with a different saliency model (i.e., a variation of SimpleNet [34], see the supplementary materials). Multi-scale features are extracted from 4 layers, where each corresponds to the end of a block inside the backbone. The features are processed with a set of attention decoders, where the decoder of each scale contains two consecutive convolutional layers with 16 and N filters (N is the number of users), and an upsampling layer that rescales features to have the same spatial resolution as the image. + +Training. Following [10], we train models for 50 epochs with batch size 10 using the Adam optimizer [26]. $\lambda$ factor in equation (5) is empirically set to 0.2. Learning rate is initially set to $10^{-4}$ , and decayed by a factor of 0.8 for every 10 epochs. For our learning approach proposed in Section 3.2, we set the initial bounds to [1, 4] and [1, 6] for FiWI and OSIE, respectively, and increase both the upper and lower bounds by 2 every 10 epochs. The bounds are fixed to [9, 11] and [11, 15] for FiWI and OSIE after reaching the corresponding values. The aforementioned hyperparameters are determined based on 5-fold cross-validation. For a fair comparison with the state-of-the-art [8, 37] and a more flexible setting, we do not pretrain our models on external saliency datasets like the SALICON [23] dataset. + +# 4.2. Does Learning the Composition of Attention Help Capture Attention of Diverse Users? + +We first study the effectiveness of our method for capturing the visual preferences of diverse users. Specifically, we randomly sample K users $(\mathrm{K} = 1,3,5)$ for each evaluation + +![](images/b0aea0daf15427a03c67ad5b50cf9070fa8f87b6ed0b19913a913f11e0492e77.jpg) +Figure 3. Qualitative results for predicting attention of diverse users. We show results for two different user groups for each sample, and also consider variable numbers of users $K = 1, 3, 5$ . Note that EML-Net is user-agnostic and predicts the same result for two groups. + +image, and estimate the predictions with ground truth annotations aggregated from the selected users. We repeat the procedure 5 times to reduce the variance of results, and report the average performance. Following [41] and [37], we use fixed training/test splits on the OSIE dataset and perform 5-fold cross-validation on the FiWI dataset. We compare our full method (Ours) with three approaches, including the user-agnostic EML-Net baseline [21], an ensemble of EML-Net trained on individual users (Single-user, with one model for each user), and our model without incorporating progressive learning (Ours*). Three key observations can be made on the results reported in Table 1 and Table 2: + +- There exist considerable discrepancies between general and user-aware saliency modeling. Despite the inter-user agreement on visual attention, the user-agnostic EML-Net achieves inferior performance on both datasets, especially FiWI with web pages associated with richer semantics and more diverse viewing behaviors. The observation highlights the significance of visual preferences for attention modeling. +- Learning how to integrate attention is important + +Table 1. User-aware saliency results on FiWI [37]. + +
K=1K=3K=5
NSSCCNSSCCNSSCC
EML-Net1.4810.3071.5060.4541.4980.519
Single-user1.9620.3731.7490.5181.7450.591
Ours*1.9080.3661.7850.5261.7840.609
Ours2.0590.3921.8290.5401.8150.620
+ +Table 2. User-aware saliency results on OSIE data [39]. + +
K=1K=3K=5
NSSCCNSSCCNSSCC
EML-Net1.7550.3671.7630.5321.7180.594
Single-user1.4560.3141.5650.4921.5740.566
Ours*1.6400.2941.7680.5371.8120.625
Ours1.8090.3101.8090.5501.8260.629
+ +Table 3. General saliency results on FiWI data [37]. + +
NSSKLDCCAUC-JuddsAUC
DeepGaze II1.229-0.4880.7970.625
SAM-ResNet1.246-0.5950.7910.673
UMSI0.938-0.4570.7550.675
AGD-F1.606-0.7350.7670.748
EML-Net1.6530.6030.6610.8470.675
EML-Net+SALICON1.7220.5670.6890.8480.697
Ours1.7520.5640.6990.8510.704
+ +Table 4. General saliency results on OSIE data [39]. + +
NSSKLDSIMCCAUC
SALICON1.6410.5750.6000.6850.846
SAM-ResNet1.8110.4800.6480.7580.860
UMSI1.7880.5130.6310.7460.856
EML-Net1.7370.5370.6190.7170.854
Ours1.8400.5060.6520.7610.860
+ +for capturing visual preferences. A key component of our framework is the progressive learning method for understanding the composition of attention. According to the comparative results between our methods with and without progressive learning, it helps models better identify the attentional preferences of both individuals (i.e., $\mathrm{K} = 1$ ) and user groups (i.e., $\mathrm{K} = 3$ , 5). As illustrated in Figure 3, unlike EML-Net and our method without progressive learning (Ours*) that fail to capture the visual preferences and generate similar attention maps regardless of the selection of users, our full method is able to predict attention maps that accurately reflect the regions of interest of diverse users. + +- Additive ensemble falls short of modeling user-aware attention. Training one model for each user offers a straightforward way to model user preferences, and slightly outperforms our method without progressive learning when considering individuals' attention (i.e., $\mathrm{K} = 1$ ) on FiWI. However, without learning how to integrate attention, it lacks the capability to predict attention maps with multiple users and is outperformed by our full method across all settings. Additionally, such an additive ensemble also fails to benefit general saliency prediction due to its high computational overhead and the inability to jointly consider attention of different users (see our supplementary materials). + +These observations highlight the significance of modeling visual preferences and the composition of attention, and + +demonstrate the advantages of our method for user-aware saliency modeling. While we do not consider demographic information in this study, our method is general and can be extended to broader scenarios for customized applications. For instance, instead of developing personalized filters, we can cluster users based on certain criteria (e.g., gender, age, personal interest) and optimize models to predict attentional preferences of users of specific characteristics. + +# 4.3. Are Visual Preferences Beneficial for General Saliency Prediction? + +General saliency prediction focuses on attention aggregated from all users, and yet little attention has been paid to the diversity of attention patterns between users. In this subsection, we further investigate if knowledge of visual preferences is beneficial for the task. We compare our user-aware method with six state-of-the-art models, including SALICON [19], Deep Gaze II [28], SAM [10], EML-Net [21], UMSI [16], and AGD-F [8]. For a fair comparison, we adopt the training and test sets provided in [8] for evaluation on FiWI dataset. Table 3 and Table 4 report results on the FiWI [37] and OSIE [39, 41] datasets. + +Compared to the EML-Net baseline, our model that takes into account visual preferences shows consistent improvements among all settings. Its performance is also competitive against existing state-of-the-art. As illustrated in Figure 4, the performance gain of our method can be attributed to the capability to capture fine-grained attention patterns (i.e., focuses on the man, little girls, and woman in the three examples, respectively) in addition to the salient regions attended by the majority of users (i.e., text, the food, and the boy). Moreover, the advantages of our method is also a result of increased data efficiency. Comparative results show that it outperforms EML-Net pretrained on the SALICON [23] dataset with 15000 images (EML-Net+SALICON), despite only relying on training samples in the FiWI dataset with 149 images. Such a unique feature can play an important role in generalizing towards domains with diverse characteristics (e.g., web page vs naturalistic image), where suitable data for pretraining is not necessarily available. + +# 4.4. Can User-aware Saliency Modeling Overcome the Issues of Incomplete Users? + +Collecting human behavioral data demands stringent paradigms, and building large attention datasets has been challenging for decades [23]. As a result, it is common for saliency datasets to have samples associated with incomplete users. For instance, there are 32 users recruited in [39], while only about 14 users are presented for each sample. Different from prior works [19, 21, 28, 30] that overlook the issue, we examine if knowledge of visual preferences can be helpful for tackling the problem. + +Specifically, we randomly drop $K^{*}$ users for each train- + +![](images/69082e2a8dd2ecd2806c3d856af0d8e10f6054c2e66c5fcef5df54b90dab185b.jpg) +Figure 4. Qualitative results for general saliency prediction. + +Table 5. Results for saliency prediction with incomplete users on seen and unseen images. + +
K=1K=3K=5Unseen
NSSCCNSSCCNSSCCNSSCC
K* = 5EML-Net1.7330.3591.7190.5181.7120.5891.6160.601
Ours1.7590.3411.7810.5301.7970.6141.6980.632
K* = 7EML-Net1.6620.3421.6590.5011.6580.5731.5840.551
Ours1.7230.3301.7340.5121.7390.5941.7080.589
+ +ing sample in the FiWI dataset, and consider two evaluation settings: (1) attention of missing users on seen samples (we use different numbers of missing users, i.e., $\mathrm{K} = 1, 3, 5$ ), and (2) attention of all users on unseen test samples (i.e., Unseen). The first setting is particularly useful for scenarios where we are interested in comparing users' preferences. On the other hand, the second setting aims to study models' robustness against the scarcity of annotations. + +According to comparative results reported in Table 5, the proposed user-aware method is advantageous in both evaluation settings. Despite the slightly lower CC scores for individuals' attention $(\mathrm{K} = 1)$ on seen images, it achieves considerable improvements among all other evaluation settings. This is likely because predictions from the user-agnostic EML-Net tend to have a broader coverage, which is favored by CC metric emphasizing the overall distribution. Differently, our method has the capability to more accurately attend to regions of interest of different users, resulting in higher NSS scores as well as CC scores for more users. It also makes better use of the available data, and is more robust against the scarcity of annotations (i.e., higher general + +ization performance on unseen images). + +# 5. Conclusion + +This paper identifies the critical roles of user preferences in visual attention, and for the first time tackles the challenge of user-aware saliency modeling. It unifies the conventional tasks for predicting general and personalized attention, and proposes an integral framework that jointly solves attention modeling for individual users, different groups of users, and the general population. By making progress with both a novel saliency prediction model and a progressive learning method, our framework illustrates a principled paradigm for establishing the connections between user preferences and visual saliency. 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610 + ], + "type": "text", + "content": "Everyone is unique. Given the same visual stimuli, people's attention is driven by both salient visual cues and their own inherent preferences. Knowledge of visual preferences not only facilitates understanding of fine-grained attention patterns of diverse users, but also has the potential of benefiting the development of customized applications. Nevertheless, existing saliency models typically limit their scope to attention as it applies to the general population and ignore the variability between users' behaviors. In this paper, we identify the critical roles of visual preferences in attention modeling, and for the first time study the problem of user-aware saliency modeling. Our work aims to advance attention research from three distinct perspectives: (1) We present a new model with the flexibility to capture attention patterns of various combinations of users, so that we can adaptively predict personalized attention, user group attention, and general saliency at the same time with one single model; (2) To augment models with knowledge about the composition of attention from different users, we further propose a principled learning method to understand visual attention in a progressive manner; and (3) We carry out extensive analyses on publicly available saliency datasets to shed light on the roles of visual preferences. Experimental results on diverse stimuli, including naturalistic images and web pages, demonstrate the advantages of our method in capturing the distinct visual behaviors of different users and the general saliency of visual stimuli." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 47, + 631, + 128, + 643 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 631, + 128, + 643 + ], + "spans": [ + { + "bbox": [ + 47, + 631, + 128, + 643 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 46, + 651, + 287, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 651, + 287, + 687 + ], + "spans": [ + { + "bbox": [ + 46, + 651, + 287, + 687 + ], + "type": "text", + "content": "With the pervasiveness of a visual attention network in the brain, attention has become an important interface for understanding people's behavioral patterns. A collection" + } + ] + } + ], + "index": 24 + }, + { + "type": "image", + "bbox": [ + 306, + 258, + 547, + 417 + ], + "blocks": [ + { + "bbox": [ + 306, + 258, + 547, + 417 + ], + "lines": [ + { + "bbox": [ + 306, + 258, + 547, + 417 + ], + "spans": [ + { + "bbox": [ + 306, + 258, + 547, + 417 + ], + "type": "image", + "image_path": "eead546da9b281f2b6ac20767720c3088d04552717e1979121cf20afc8e43947.jpg" + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 427, + 546, + 450 + ], + "lines": [ + { + "bbox": [ + 305, + 427, + 546, + 450 + ], + "spans": [ + { + "bbox": [ + 305, + 427, + 546, + 450 + ], + "type": "text", + "content": "Figure 1. A hierarchy for user-aware saliency modeling, where each level focuses on a different perspective of attention." + } + ] + } + ], + "index": 26, + "angle": 0, + "type": "image_caption" + } + ], + "index": 25 + }, + { + "bbox": [ + 304, + 473, + 546, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 473, + 546, + 664 + ], + "spans": [ + { + "bbox": [ + 304, + 473, + 546, + 664 + ], + "type": "text", + "content": "of studies focus on leveraging human attention to optimize graphical designs [7, 16, 36], web page layouts [8, 37, 45], and user experience in immersive environments [22, 38, 44]. They demonstrate its usefulness for a broad range of applications, and more importantly, highlight the intertwined nature between attention and users' preferences [11]. As shown in Figure 1, attention modeling can be formulated as a hierarchy of tasks, i.e., from a sophisticated understanding of individuals' behaviors (personalized attention), to modeling the visual behaviors of larger groups (user-group attention), and the saliency of visual stimuli (general saliency). With the great diversity in attentional behaviors among different groups (e.g., attention of users with diverse characteristics, children vs elderly, male vs female, etc.), knowledge of visual preferences can play an essential role in enabling a more fine-grained understanding of attention." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "content": "To accurately capture human attention on visual stimuli, considerable efforts have been placed on building saliency prediction models [10, 19, 21, 29, 30]. While achieving optimistic results for modeling attention of the general popu" + } + ] + } + ], + "index": 28 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 693, + 232, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 693, + 232, + 703 + ], + "spans": [ + { + "bbox": [ + 58, + 693, + 232, + 703 + ], + "type": "text", + "content": "*Work done during an internship at Google Research." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 59, + 703, + 135, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 703, + 135, + 712 + ], + "spans": [ + { + "bbox": [ + 59, + 703, + 135, + 712 + ], + "type": "text", + "content": "† Corresponding author" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "2701" + } + ] + } + ], + "index": 32 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "text", + "content": "lation, there are two key challenges remaining largely unresolved: (1) Existing models ignore the variability of users' visual behaviors, and hence do not have the ability to identify fine-grained attention patterns of distinct users; and (2) Apart from the shortage of models for user-aware saliency modeling, there has also been no attempt to formulate a training paradigm to understand the composition of attention, which hampers the integration of attention from diverse users. To fill the gap, we concentrate on a new research problem for modeling attention of adaptively selected users, and tackle the challenge with a new computational model together with a progressive learning method." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 217, + 289, + 395 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 217, + 289, + 395 + ], + "spans": [ + { + "bbox": [ + 46, + 217, + 289, + 395 + ], + "type": "text", + "content": "At the heart of our saliency model is the incorporation of visual preferences with personalized filters and adaptive user masks. Unlike conventional methods designed for predicting a single saliency map representing attention of all users, it takes advantage of personalized filters to encode individuals' attention patterns. The attention patterns are adaptively integrated based on a user mask indicating the presence of users in the current sample, which enables attention prediction for various combinations of users. The aforementioned paradigm serves as the foundation for bridging individuals' preferences with visual saliency, and augments models with more abundant information about fine-grained visual behaviors. It not only shows promise in modeling attention of specific users, but also benefits the inference of the general saliency." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 396, + 289, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 396, + 289, + 598 + ], + "spans": [ + { + "bbox": [ + 46, + 396, + 289, + 598 + ], + "type": "text", + "content": "A key challenge in user-aware saliency modeling is the lack of understanding when aggregating attention from diverse users. The issue becomes more critical when further considering the joint effects of stimuli and user preferences on visual attention [11], where the former factor may overshadow the impacts of the latter one, leading to difficulties in capturing the variability of users' attention. Inspired by human learning that acquires knowledge through a set of carefully designed curricula [2], we propose to tackle the aforementioned issues with a progressive learning approach. The essence of our method is to encourage a model to learn the composition of attention from a dynamic set of users, from individuals to user groups representing the general population. Through optimizing on dynamically evolving annotations, it provides opportunities for models to learn both the unique attention patterns of different users and the saliency of visual stimuli." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 59, + 598, + 278, + 610 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 598, + 278, + 610 + ], + "spans": [ + { + "bbox": [ + 59, + 598, + 278, + 610 + ], + "type": "text", + "content": "To summarize, our major contributions are as follows:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 58, + 616, + 287, + 713 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 58, + 616, + 287, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 616, + 287, + 652 + ], + "spans": [ + { + "bbox": [ + 58, + 616, + 287, + 652 + ], + "type": "text", + "content": "- We identify the significance of characterizing visual preferences for attention modeling, and develop a novel model that can predict attention of various users." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 58, + 658, + 287, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 658, + 287, + 694 + ], + "spans": [ + { + "bbox": [ + 58, + 658, + 287, + 694 + ], + "type": "text", + "content": "- We present a progressive learning method to understand the composition of attention and capture its variability between different users." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 58, + 701, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 701, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 701, + 287, + 713 + ], + "type": "text", + "content": "We perform extensive experiments and analyses to in" + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 325, + 72, + 545, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 325, + 72, + 545, + 133 + ], + "spans": [ + { + "bbox": [ + 325, + 72, + 545, + 133 + ], + "type": "text", + "content": "vestigate the roles of visual preferences on tackling the challenges of user-aware and general saliency, and addressing the issues of incomplete users. Results demonstrate that user-aware saliency modeling is advantageous in all the above three aspects." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 143, + 398, + 156 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 143, + 398, + 156 + ], + "spans": [ + { + "bbox": [ + 306, + 143, + 398, + 156 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 163, + 545, + 199 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 163, + 545, + 199 + ], + "spans": [ + { + "bbox": [ + 305, + 163, + 545, + 199 + ], + "type": "text", + "content": "Our work is most related to previous efforts on visual saliency prediction, which make contributions in both data collection and computational modeling." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 199, + 546, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 199, + 546, + 449 + ], + "spans": [ + { + "bbox": [ + 304, + 199, + 546, + 449 + ], + "type": "text", + "content": "Saliency prediction datasets. With the overarching goal of facilitating the development of attention modeling methods, many studies have contributed saliency prediction datasets with diverse visual stimuli. The pioneering work [25] presents a gaze estimation dataset for naturalistic images together with an online benchmark [24]. Several subsequent studies propose to characterize images into finer categories based on visual scenes [3], visual semantics [41], or sentiments [14]. To overcome the difficulties of large-scale data collection, Jiang et al. [23] use mouse-tracking as a substitute for gaze estimation and construct currently the largest saliency prediction dataset. In addition to the aforementioned works that study attention on naturalistic images, several studies focus on attention for broader types of visual stimuli, including graphical designs [7, 16, 36], web pages [8, 37, 45], and immersive environments [22, 38, 44]. There are also attempts that go beyond attention collected during free-viewing, and study goal-directed attention when performing various tasks such as driving [1] and visual reasoning [9]. These data efforts enable the developments of a series of computational methods for attention modeling." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 451, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 451, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 451, + 547, + 714 + ], + "type": "text", + "content": "Saliency prediction models. To estimate attention distribution on different visual stimuli, a large body of research concentrates on building saliency prediction models. Early studies leverage handcrafted features that encode high- and low-level visual cues [5,17,20,40]. More recent approaches opt to automatically learn discriminative features based on deep neural networks. In particular, Huang et al. [19] utilize a convolution neural network (CNN) with multi-scale inputs to model the coarse-to-fine semantics. Kümmerer et al. [28] demonstrate the usefulness of deep features learned from image recognition for saliency prediction. Cornia et al. [10] develop a recurrent neural network to iteratively refine the visual features for saliency prediction. Jia et al. [21] augment model with rich visual semantics extracted from multiple levels of a CNN. Lou et al. [30] investigate the effectiveness of vision Transformers [13] for saliency prediction. Apart from the studies on general saliency prediction, a few works [32, 42, 43] attempt to tackle the problem of personalized saliency, which involves predicting attention of different users on naturalistic images. They adopt a simplified setting which only takes into account individuals' attention and assumes that the general saliency maps are given" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2702" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 73, + 68, + 521, + 319 + ], + "blocks": [ + { + "bbox": [ + 73, + 68, + 521, + 319 + ], + "lines": [ + { + "bbox": [ + 73, + 68, + 521, + 319 + ], + "spans": [ + { + "bbox": [ + 73, + 68, + 521, + 319 + ], + "type": "image", + "image_path": "ced0a2328c238da104a51282616c9d620f3bd8eedf792dcc90a3de5cd20e0652.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 176, + 320, + 422, + 331 + ], + "lines": [ + { + "bbox": [ + 176, + 320, + 422, + 331 + ], + "spans": [ + { + "bbox": [ + 176, + 320, + 422, + 331 + ], + "type": "text", + "content": "Evolution of ground truth throughout the progressive learning procedure" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 340, + 546, + 363 + ], + "lines": [ + { + "bbox": [ + 46, + 340, + 546, + 363 + ], + "spans": [ + { + "bbox": [ + 46, + 340, + 546, + 363 + ], + "type": "text", + "content": "Figure 2. An overview of the proposed framework. The top figure illustrates the architectural design of our saliency model for predicting attention of diverse users, while the bottom one outlines our progressive learning method for understanding the composition of attention." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 384, + 287, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 384, + 287, + 467 + ], + "spans": [ + { + "bbox": [ + 46, + 384, + 287, + 467 + ], + "type": "text", + "content": "as inputs. While showing usefulness in capturing visual attention, the aforementioned methods either consider only attention aggregated from all users (i.e., general saliency) or rely on assumptions that are inapplicable to less-constrained real-world scenarios. They also utilize diverse paradigms for modeling different types of attention, which prevents a joint reasoning on the variability of users' visual behaviors." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 467, + 287, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 467, + 287, + 647 + ], + "spans": [ + { + "bbox": [ + 46, + 467, + 287, + 647 + ], + "type": "text", + "content": "Our study differentiates from prior research in three key aspects: (1) We identify the significance of visual preferences for attention modeling, and for the first time tackle the challenge of user-aware saliency modeling. The new problem unifies previous studies on general and personalized saliency prediction, with the number of users being a dynamic factor; (2) Without imposing constraints on inputs (e.g., availability of general saliency maps [32,42,43] and naturalistic images as visual stimuli [10, 21, 28]), our model directly infers attention from visual stimuli and is able to generalize to broader scenarios (e.g., naturalistic images and web pages); and (3) In addition to a novel computational model, we also present a progressive learning approach to understand the composition of attention and capture the variability of attention." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 657, + 129, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 657, + 129, + 671 + ], + "spans": [ + { + "bbox": [ + 47, + 657, + 129, + 671 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "text", + "content": "Attention modeling would benefit from the knowledge about individuals' visual preferences and the capability to adaptively integrate them. This section presents an integral" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 384, + 546, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 384, + 546, + 456 + ], + "spans": [ + { + "bbox": [ + 305, + 384, + 546, + 456 + ], + "type": "text", + "content": "framework consisting of two important components: (1) A new saliency prediction model that encodes visual preferences and dynamically predicts attention patterns of diverse combinations of users (Section 3.1), and (2) A principled approach for learning the composition of attention in a progressive manner (Section 3.2)." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 465, + 545, + 491 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 465, + 545, + 491 + ], + "spans": [ + { + "bbox": [ + 306, + 465, + 545, + 491 + ], + "type": "text", + "content": "3.1. Encoding Visual Preferences with Personalized Filters" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 497, + 546, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 497, + 546, + 617 + ], + "spans": [ + { + "bbox": [ + 304, + 497, + 546, + 617 + ], + "type": "text", + "content": "A primary goal of our study is to endow models with the flexibility to predict attention for various users. We tackle the challenge with a new model paradigm that leverages a collection of personalized filters to identify individuals' visual preferences, and decomposes the overall attention patterns into fine-grained ones for different users. The key differentiators of our model lie in its (1) applicability to broader scenarios (e.g., from general saliency to attention of diverse users) and (2) flexibility to different settings (e.g., without assuming the availability of general saliency maps)." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 618, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 618, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 618, + 547, + 714 + ], + "type": "text", + "content": "Figure 2 (top) provides an overview of the proposed model. The principal idea behind our model is to take advantage of personalized filters to encode attention patterns of different users, and adaptively incorporate them based on the selection of users. Specifically, we build our model on top of the state-of-the-art EML-Net [21], which is a top-performing model on the MIT saliency benchmark [24]. Given an input image, our model extracts multi-scale fea" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 758 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 758 + ], + "type": "text", + "content": "2703" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "text", + "content": "tures from different layers of a convolutional neural network pretrained on ImageNet [12], encoding both high- and low-level visual cues. The raw features of different scales " + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "inline_equation", + "content": "V_{t} \\in \\mathbb{R}^{D \\times H \\times W}" + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "inline_equation", + "content": "D, H" + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "text", + "content": " correspond to the feature channel, height, and width, " + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "text", + "content": " denotes index for scales) are processed independently with their corresponding attention decoders " + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "inline_equation", + "content": "f_{t}^{\\alpha}" + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "text", + "content": " consisting of a sequence of convolutional and upsampling layers (see Section 4.1 for details), and then the decoded attention features " + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "inline_equation", + "content": "V_{t}^{\\alpha}" + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "text", + "content": " are aggregated across all scales to form the unregularized attention maps " + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "inline_equation", + "content": "S^{raw}" + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 137, + 199, + 287, + 213 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 137, + 199, + 287, + 213 + ], + "spans": [ + { + "bbox": [ + 137, + 199, + 287, + 213 + ], + "type": "interline_equation", + "content": "V _ {t} ^ {\\alpha} = f _ {t} ^ {\\alpha} (V _ {t}) \\tag {1}", + "image_path": "924e1b1e33124f1ccab3276a6a35c2a506e1706bfc9051deaccbcd5b76efe897.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 133, + 228, + 287, + 253 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 133, + 228, + 287, + 253 + ], + "spans": [ + { + "bbox": [ + 133, + 228, + 287, + 253 + ], + "type": "interline_equation", + "content": "S ^ {r a w} = \\sum_ {t} V _ {t} ^ {\\alpha} \\tag {2}", + "image_path": "38245fca6053f189b8c653660b25e3dfc318749953b2e68e61219cb063555ae8.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 256, + 289, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 256, + 289, + 449 + ], + "spans": [ + { + "bbox": [ + 46, + 256, + 289, + 449 + ], + "type": "text", + "content": "Different from conventional methods [10, 19, 21, 28] that directly predict a single saliency map for the general population (i.e., " + }, + { + "bbox": [ + 46, + 256, + 289, + 449 + ], + "type": "inline_equation", + "content": "S^{raw} \\in \\mathbb{R}^{H \\times W}" + }, + { + "bbox": [ + 46, + 256, + 289, + 449 + ], + "type": "text", + "content": "), our method takes into account discriminative attention patterns of each individual user (i.e., " + }, + { + "bbox": [ + 46, + 256, + 289, + 449 + ], + "type": "inline_equation", + "content": "S^{raw} \\in \\mathbb{R}^{N \\times H \\times W}" + }, + { + "bbox": [ + 46, + 256, + 289, + 449 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 256, + 289, + 449 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 256, + 289, + 449 + ], + "type": "text", + "content": " is the total number of users). We achieve the goal by expanding the filters in the last convolutional layer of each attention decoder, i.e., from a single filter to " + }, + { + "bbox": [ + 46, + 256, + 289, + 449 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 256, + 289, + 449 + ], + "type": "text", + "content": " personalized filters. To adaptively predict the visual attention for various combinations of users, our model takes in a user mask " + }, + { + "bbox": [ + 46, + 256, + 289, + 449 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 256, + 289, + 449 + ], + "type": "text", + "content": " in addition to the visual stimuli as input. The user mask is a binary vector " + }, + { + "bbox": [ + 46, + 256, + 289, + 449 + ], + "type": "inline_equation", + "content": "M \\in [0,1]^N" + }, + { + "bbox": [ + 46, + 256, + 289, + 449 + ], + "type": "text", + "content": " representing the presence of users, where " + }, + { + "bbox": [ + 46, + 256, + 289, + 449 + ], + "type": "inline_equation", + "content": "M_n = 1" + }, + { + "bbox": [ + 46, + 256, + 289, + 449 + ], + "type": "text", + "content": " implies that attention of the " + }, + { + "bbox": [ + 46, + 256, + 289, + 449 + ], + "type": "inline_equation", + "content": "n^{th}" + }, + { + "bbox": [ + 46, + 256, + 289, + 449 + ], + "type": "text", + "content": " user is considered in the current sample. It plays the role as an indicator for integrating the unregularized attention maps from the selected users and generating the final saliency map " + }, + { + "bbox": [ + 46, + 256, + 289, + 449 + ], + "type": "inline_equation", + "content": "S \\in \\mathbb{R}^{H \\times W}" + }, + { + "bbox": [ + 46, + 256, + 289, + 449 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 102, + 455, + 287, + 479 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 102, + 455, + 287, + 479 + ], + "spans": [ + { + "bbox": [ + 102, + 455, + 287, + 479 + ], + "type": "interline_equation", + "content": "S = \\operatorname {s o f t m a x} \\left(\\sum_ {n} M _ {n} \\cdot S _ {n} ^ {\\text {r a w}}\\right) \\tag {3}", + "image_path": "9c335a4af27cb9ddb08ec1ca7c513da2ff8193c778bbd34bf3287a69984838e2.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 485, + 244, + 497 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 485, + 244, + 497 + ], + "spans": [ + { + "bbox": [ + 47, + 485, + 244, + 497 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 485, + 244, + 497 + ], + "type": "inline_equation", + "content": "\\cdot" + }, + { + "bbox": [ + 47, + 485, + 244, + 497 + ], + "type": "text", + "content": " denotes the element-wise multiplication." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 498, + 287, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 287, + 617 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 287, + 617 + ], + "type": "text", + "content": "To bridge individuals' visual preferences with the overall attention, we optimize our model with supervision on both the intermediate per-user predictions and the final output. We follow [10] and define the loss function " + }, + { + "bbox": [ + 46, + 498, + 287, + 617 + ], + "type": "inline_equation", + "content": "L_{sal}" + }, + { + "bbox": [ + 46, + 498, + 287, + 617 + ], + "type": "text", + "content": " as a combination of saliency metrics including Normalized Scanpath Saliency [33], Correlation Coefficient [31] and KL-Divergence [27] (see [10] and our supplementary materials). For per-user supervision, we apply a softmax activation function independently on unregularized attention map of each user to obtain their corresponding predictions:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 113, + 624, + 287, + 639 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 113, + 624, + 287, + 639 + ], + "spans": [ + { + "bbox": [ + 113, + 624, + 287, + 639 + ], + "type": "interline_equation", + "content": "S _ {n} ^ {\\text {u s e r}} = \\operatorname {s o f t m a x} \\left(S _ {n} ^ {\\text {r a w}}\\right) \\tag {4}", + "image_path": "cad882a5e8001e7524d2490d6e96d312304fccc2a181a6aadd25793abed8fa94.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 644, + 287, + 669 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 644, + 287, + 669 + ], + "spans": [ + { + "bbox": [ + 46, + 644, + 287, + 669 + ], + "type": "text", + "content": "Our overall objective simultaneously optimizes both the intermediate per-user predictions and the final output:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 83, + 675, + 287, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 675, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 83, + 675, + 287, + 715 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} L = L _ {s a l} (S, S a l, F i x) \\\\ + \\lambda \\sum_ {n} L _ {s a l} \\left(S _ {n} ^ {\\text {u s e r}}, S a l _ {n} ^ {\\text {u s e r}}, F i x _ {n} ^ {\\text {u s e r}}\\right) \\tag {5} \\\\ \\end{array}", + "image_path": "1223b852f7e70fe4b5cb1ae7a3342668774a0c819bc0bc98b2524c81aeedf850.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 72, + 545, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 133 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 133 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 72, + 545, + 133 + ], + "type": "inline_equation", + "content": "Sal" + }, + { + "bbox": [ + 305, + 72, + 545, + 133 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 72, + 545, + 133 + ], + "type": "inline_equation", + "content": "Fix" + }, + { + "bbox": [ + 305, + 72, + 545, + 133 + ], + "type": "text", + "content": " are the ground truth saliency and fixation maps aggregated from selected users, " + }, + { + "bbox": [ + 305, + 72, + 545, + 133 + ], + "type": "inline_equation", + "content": "Sal_{n}^{user}" + }, + { + "bbox": [ + 305, + 72, + 545, + 133 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 72, + 545, + 133 + ], + "type": "inline_equation", + "content": "Fix_{n}^{user}" + }, + { + "bbox": [ + 305, + 72, + 545, + 133 + ], + "type": "text", + "content": " are those for individual user " + }, + { + "bbox": [ + 305, + 72, + 545, + 133 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 305, + 72, + 545, + 133 + ], + "type": "text", + "content": ". Note that only users selected in the user mask (i.e., " + }, + { + "bbox": [ + 305, + 72, + 545, + 133 + ], + "type": "inline_equation", + "content": "M_{n} = 1" + }, + { + "bbox": [ + 305, + 72, + 545, + 133 + ], + "type": "text", + "content": ") will be considered for optimization. " + }, + { + "bbox": [ + 305, + 72, + 545, + 133 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 305, + 72, + 545, + 133 + ], + "type": "text", + "content": " is the balancing factor." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 133, + 545, + 193 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 133, + 545, + 193 + ], + "spans": [ + { + "bbox": [ + 304, + 133, + 545, + 193 + ], + "type": "text", + "content": "The aforementioned model illustrates a general paradigm for connecting user preferences and visual saliency. It serves as the foundation for user-aware saliency modeling, and supports the development of our progressive learning method, as detailed in the next subsection." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 202, + 511, + 215 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 202, + 511, + 215 + ], + "spans": [ + { + "bbox": [ + 305, + 202, + 511, + 215 + ], + "type": "text", + "content": "3.2. Learning the Composition of Attention" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 221, + 545, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 221, + 545, + 388 + ], + "spans": [ + { + "bbox": [ + 304, + 221, + 545, + 388 + ], + "type": "text", + "content": "Visual attention is driven by both salient regions that most people find attractive and individuals' unique interests. Understanding how to incorporate attention patterns of different users is an important challenge for user-aware saliency modeling. Without such knowledge, a model can overfit to attention driven by visual stimuli, and has difficulties learning the variability of users' attention. For instance, as there exists a considerable overlap between attention of different users, a model can exploit such a shortcut and predict an averaged attention map (of all users) regardless of the selection of users (see supplementary materials). To tackle the challenge, we propose a principled learning method that augments our saliency model with understanding of the composition of attention." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 389, + 546, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 389, + 546, + 653 + ], + "spans": [ + { + "bbox": [ + 304, + 389, + 546, + 653 + ], + "type": "text", + "content": "Drawing inspirations from human learning, which is highly organized and based on curricula that gradually introduce diverse concepts, our method emphasizes progressive learning with dynamically evolving objectives. As illustrated in Figure 2 (bottom), it can be viewed as a three-phase training procedure: (1) As the initial step of learning, the model is encouraged to establish the correspondence between personalized modules and individuals' visual preference; (2) Later on, in the second phase, it is driven to take advantage of the learned preferences and construct saliency maps for diverse selections of users; (3) In the final phase, we allow the model to refine its prediction on attention of broader users, unifying personalized [42] and general saliency prediction [23, 25, 41]. Instead of dividing the learning into three separate stages (e.g., with a sequence of pretraining and fine-tuning), we instantiate the aforementioned paradigm by manipulating the characteristics of training samples throughout the learning process. Specifically, we first sample the number of users K from a specific range, and then randomly select of fixations K users (with a uniform distribution) to construct the ground truth fixation and saliency maps on the fly." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 654, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 547, + 714 + ], + "type": "text", + "content": "Through controlling the number of users sampled among different training epochs, our method allows a continuous and progressive learning of the composition of attention: (1) We start with annotations from a small number of users (e.g., 1-4 users) and adaptively optimizing different compo" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2704" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 275 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 275 + ], + "type": "text", + "content": "nents of the networks (e.g., personalized filters indicated by the input user masks), which allows the model to encode individuals' visual preferences. It also attenuates the effects of overfitting to attention driven by visual stimuli, as the model has no access to annotations from all users and thus can not exploit the correlation between individuals' attention and the averaged one; (2) With the progress of training, we gradually increase both the lower and the upper bounds for sampling range of K (e.g., from 1-4 to 5-9 users). Note that the users are randomly selected on a sample basis for every training iteration (i.e., one sample in a single batch). The scheme facilitates understanding of how to combine visual preferences of each individual to the attention patterns of different user groups; (3) During the last several training epochs, we fix the bounds for sampling to relatively large values (e.g., " + }, + { + "bbox": [ + 46, + 72, + 289, + 275 + ], + "type": "inline_equation", + "content": "80\\% - 100\\%" + }, + { + "bbox": [ + 46, + 72, + 289, + 275 + ], + "type": "text", + "content": " users), allowing the refinement of predictions for the general saliency." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 275, + 288, + 337 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 275, + 288, + 337 + ], + "spans": [ + { + "bbox": [ + 46, + 275, + 288, + 337 + ], + "type": "text", + "content": "Our learning paradigm enables a smooth transition from individuals' preferences to attention of a broad range of users. Together with the proposed model, our full method shows promise in capturing attention of both diverse users (Section 4.2) and the general population (Section 4.3)" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 345, + 124, + 359 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 345, + 124, + 359 + ], + "spans": [ + { + "bbox": [ + 47, + 345, + 124, + 359 + ], + "type": "text", + "content": "4. Experiment" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 365, + 287, + 425 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 365, + 287, + 425 + ], + "spans": [ + { + "bbox": [ + 46, + 365, + 287, + 425 + ], + "type": "text", + "content": "In this section, we present the implementation details (Section 4.1), and carry out extensive experiments to study the effectiveness of the proposed framework. Our experiments and analyses aim to shed light on the following research questions that have yet to be answered:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 58, + 430, + 286, + 515 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 58, + 430, + 286, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 430, + 286, + 453 + ], + "spans": [ + { + "bbox": [ + 58, + 430, + 286, + 453 + ], + "type": "text", + "content": "- Does learning the composition of attention help capture attention of diverse users? (Section 4.2)" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 58, + 461, + 286, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 461, + 286, + 485 + ], + "spans": [ + { + "bbox": [ + 58, + 461, + 286, + 485 + ], + "type": "text", + "content": "- Are visual preferences beneficial for general saliency prediction? (Section 4.3)" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 58, + 492, + 286, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 492, + 286, + 515 + ], + "spans": [ + { + "bbox": [ + 58, + 492, + 286, + 515 + ], + "type": "text", + "content": "- Can user-aware saliency modeling overcome the issues of incomplete users? (Section 4.4)" + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 46, + 521, + 286, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 286, + 544 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 286, + 544 + ], + "type": "text", + "content": "We also include additional analyses and ablation studies in the supplementary materials." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 552, + 145, + 563 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 552, + 145, + 563 + ], + "spans": [ + { + "bbox": [ + 47, + 552, + 145, + 563 + ], + "type": "text", + "content": "4.1. Implementation" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "text", + "content": "Dataset. We demonstrate the effectiveness of our method with two types of visual stimuli, i.e., naturalistic images and web pages. Since most saliency datasets only offer aggregated fixation annotations, we choose two publicly available saliency datasets, OSIE [39, 41] and FiWI [37], as our testbeds, which provide per-user annotations for user-aware saliency modeling. OSIE contains eye-tracking data collected on 700 naturalistic images with rich semantics. We use the version collected in [39], which has more diverse attention patterns from 32 users (about 14 users are presented with each sample) due to their less constrained experimental settings. FiWI is a popular eye-tracking dataset" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": "for web pages, which contains data from 11 users on 149 samples. We also conduct experiments on the recently introduced web page saliency dataset [8] with 450 samples, and report the results in our supplementary materials." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 121, + 546, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 121, + 546, + 300 + ], + "spans": [ + { + "bbox": [ + 304, + 121, + 546, + 300 + ], + "type": "text", + "content": "Evaluation. Saliency prediction is typically evaluated with multiple metrics [6]. Following [8, 19, 21, 30], we adopt seven popular saliency metrics, including Normalized Scanpath Saliency (NSS) [33], KL-Divergence (KLD) [27], Similarity (SIM) [35], Correlation Coefficient (CC) [31], Area Under the ROC Curve (AUC) [15], AUC-Judd [25], and shuffled AUC (sAUC) [4]. For the OSIE dataset, we follow [41], and randomly split the samples into 600 and 100 for training and evaluation, respectively. In terms of the FiWI dataset, following [37] and [8], we consider two evaluation settings, including 5-fold cross-validation and evaluation with fixed training/test sets. Besides estimating the capability of our method on capturing the attention patterns of diverse users (Section 4.2), we also study its usefulness on general saliency prediction (Section 4.3)." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 301, + 546, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 301, + 546, + 468 + ], + "spans": [ + { + "bbox": [ + 304, + 301, + 546, + 468 + ], + "type": "text", + "content": "Model Configuration. We build our method on the state-of-the-art EML-Net [21] saliency model. We use ResNet-50 [18] as the backbone, which is pretrained on ImageNet classification [12] and offers profound understanding of visual semantics. To show the generalizability of our method, we also experiment with a different saliency model (i.e., a variation of SimpleNet [34], see the supplementary materials). Multi-scale features are extracted from 4 layers, where each corresponds to the end of a block inside the backbone. The features are processed with a set of attention decoders, where the decoder of each scale contains two consecutive convolutional layers with 16 and N filters (N is the number of users), and an upsampling layer that rescales features to have the same spatial resolution as the image." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 469, + 547, + 636 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 469, + 547, + 636 + ], + "spans": [ + { + "bbox": [ + 304, + 469, + 547, + 636 + ], + "type": "text", + "content": "Training. Following [10], we train models for 50 epochs with batch size 10 using the Adam optimizer [26]. " + }, + { + "bbox": [ + 304, + 469, + 547, + 636 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 304, + 469, + 547, + 636 + ], + "type": "text", + "content": " factor in equation (5) is empirically set to 0.2. Learning rate is initially set to " + }, + { + "bbox": [ + 304, + 469, + 547, + 636 + ], + "type": "inline_equation", + "content": "10^{-4}" + }, + { + "bbox": [ + 304, + 469, + 547, + 636 + ], + "type": "text", + "content": ", and decayed by a factor of 0.8 for every 10 epochs. For our learning approach proposed in Section 3.2, we set the initial bounds to [1, 4] and [1, 6] for FiWI and OSIE, respectively, and increase both the upper and lower bounds by 2 every 10 epochs. The bounds are fixed to [9, 11] and [11, 15] for FiWI and OSIE after reaching the corresponding values. The aforementioned hyperparameters are determined based on 5-fold cross-validation. For a fair comparison with the state-of-the-art [8, 37] and a more flexible setting, we do not pretrain our models on external saliency datasets like the SALICON [23] dataset." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 646, + 545, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 646, + 545, + 671 + ], + "spans": [ + { + "bbox": [ + 305, + 646, + 545, + 671 + ], + "type": "text", + "content": "4.2. Does Learning the Composition of Attention Help Capture Attention of Diverse Users?" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": "We first study the effectiveness of our method for capturing the visual preferences of diverse users. Specifically, we randomly sample K users " + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "inline_equation", + "content": "(\\mathrm{K} = 1,3,5)" + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": " for each evaluation" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2705" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 72, + 70, + 521, + 398 + ], + "blocks": [ + { + "bbox": [ + 72, + 70, + 521, + 398 + ], + "lines": [ + { + "bbox": [ + 72, + 70, + 521, + 398 + ], + "spans": [ + { + "bbox": [ + 72, + 70, + 521, + 398 + ], + "type": "image", + "image_path": "b0aea0daf15427a03c67ad5b50cf9070fa8f87b6ed0b19913a913f11e0492e77.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 405, + 547, + 429 + ], + "lines": [ + { + "bbox": [ + 46, + 405, + 547, + 429 + ], + "spans": [ + { + "bbox": [ + 46, + 405, + 547, + 429 + ], + "type": "text", + "content": "Figure 3. Qualitative results for predicting attention of diverse users. We show results for two different user groups for each sample, and also consider variable numbers of users " + }, + { + "bbox": [ + 46, + 405, + 547, + 429 + ], + "type": "inline_equation", + "content": "K = 1, 3, 5" + }, + { + "bbox": [ + 46, + 405, + 547, + 429 + ], + "type": "text", + "content": ". Note that EML-Net is user-agnostic and predicts the same result for two groups." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 449, + 289, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 449, + 289, + 593 + ], + "spans": [ + { + "bbox": [ + 46, + 449, + 289, + 593 + ], + "type": "text", + "content": "image, and estimate the predictions with ground truth annotations aggregated from the selected users. We repeat the procedure 5 times to reduce the variance of results, and report the average performance. Following [41] and [37], we use fixed training/test splits on the OSIE dataset and perform 5-fold cross-validation on the FiWI dataset. We compare our full method (Ours) with three approaches, including the user-agnostic EML-Net baseline [21], an ensemble of EML-Net trained on individual users (Single-user, with one model for each user), and our model without incorporating progressive learning (Ours*). Three key observations can be made on the results reported in Table 1 and Table 2:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 58, + 599, + 289, + 714 + ], + "type": "list", + "angle": 0, + "index": 5, + "blocks": [ + { + "bbox": [ + 58, + 599, + 289, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 599, + 289, + 696 + ], + "spans": [ + { + "bbox": [ + 58, + 599, + 289, + 696 + ], + "type": "text", + "content": "- There exist considerable discrepancies between general and user-aware saliency modeling. Despite the inter-user agreement on visual attention, the user-agnostic EML-Net achieves inferior performance on both datasets, especially FiWI with web pages associated with richer semantics and more diverse viewing behaviors. The observation highlights the significance of visual preferences for attention modeling." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 58, + 701, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 701, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 58, + 701, + 288, + 714 + ], + "type": "text", + "content": "- Learning how to integrate attention is important" + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "text" + }, + { + "type": "table", + "bbox": [ + 309, + 467, + 542, + 561 + ], + "blocks": [ + { + "bbox": [ + 333, + 447, + 518, + 459 + ], + "lines": [ + { + "bbox": [ + 333, + 447, + 518, + 459 + ], + "spans": [ + { + "bbox": [ + 333, + 447, + 518, + 459 + ], + "type": "text", + "content": "Table 1. User-aware saliency results on FiWI [37]." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 309, + 467, + 542, + 561 + ], + "lines": [ + { + "bbox": [ + 309, + 467, + 542, + 561 + ], + "spans": [ + { + "bbox": [ + 309, + 467, + 542, + 561 + ], + "type": "table", + "html": "
K=1K=3K=5
NSSCCNSSCCNSSCC
EML-Net1.4810.3071.5060.4541.4980.519
Single-user1.9620.3731.7490.5181.7450.591
Ours*1.9080.3661.7850.5261.7840.609
Ours2.0590.3921.8290.5401.8150.620
", + "image_path": "1af4641ab3091d639ec012b52ef667d6262d5481f8902e6abdcbe912153389c7.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 309, + 590, + 542, + 685 + ], + "blocks": [ + { + "bbox": [ + 324, + 570, + 527, + 582 + ], + "lines": [ + { + "bbox": [ + 324, + 570, + 527, + 582 + ], + "spans": [ + { + "bbox": [ + 324, + 570, + 527, + 582 + ], + "type": "text", + "content": "Table 2. User-aware saliency results on OSIE data [39]." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 309, + 590, + 542, + 685 + ], + "lines": [ + { + "bbox": [ + 309, + 590, + 542, + 685 + ], + "spans": [ + { + "bbox": [ + 309, + 590, + 542, + 685 + ], + "type": "table", + "html": "
K=1K=3K=5
NSSCCNSSCCNSSCC
EML-Net1.7550.3671.7630.5321.7180.594
Single-user1.4560.3141.5650.4921.5740.566
Ours*1.6400.2941.7680.5371.8120.625
Ours1.8090.3101.8090.5501.8260.629
", + "image_path": "20f70185c7db8085a376160303c6e724924ff50657906e6c07c1633876807b9f.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2706" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 91, + 282, + 203 + ], + "blocks": [ + { + "bbox": [ + 72, + 71, + 261, + 82 + ], + "lines": [ + { + "bbox": [ + 72, + 71, + 261, + 82 + ], + "spans": [ + { + "bbox": [ + 72, + 71, + 261, + 82 + ], + "type": "text", + "content": "Table 3. General saliency results on FiWI data [37]." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 91, + 282, + 203 + ], + "lines": [ + { + "bbox": [ + 50, + 91, + 282, + 203 + ], + "spans": [ + { + "bbox": [ + 50, + 91, + 282, + 203 + ], + "type": "table", + "html": "
NSSKLDCCAUC-JuddsAUC
DeepGaze II1.229-0.4880.7970.625
SAM-ResNet1.246-0.5950.7910.673
UMSI0.938-0.4570.7550.675
AGD-F1.606-0.7350.7670.748
EML-Net1.6530.6030.6610.8470.675
EML-Net+SALICON1.7220.5670.6890.8480.697
Ours1.7520.5640.6990.8510.704
", + "image_path": "93d8a4269b6504884dd4d83916a3325051aac025734918025e4bb6e87b7dc9b8.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 50, + 233, + 282, + 336 + ], + "blocks": [ + { + "bbox": [ + 72, + 213, + 261, + 224 + ], + "lines": [ + { + "bbox": [ + 72, + 213, + 261, + 224 + ], + "spans": [ + { + "bbox": [ + 72, + 213, + 261, + 224 + ], + "type": "text", + "content": "Table 4. General saliency results on OSIE data [39]." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 233, + 282, + 336 + ], + "lines": [ + { + "bbox": [ + 50, + 233, + 282, + 336 + ], + "spans": [ + { + "bbox": [ + 50, + 233, + 282, + 336 + ], + "type": "table", + "html": "
NSSKLDSIMCCAUC
SALICON1.6410.5750.6000.6850.846
SAM-ResNet1.8110.4800.6480.7580.860
UMSI1.7880.5130.6310.7460.856
EML-Net1.7370.5370.6190.7170.854
Ours1.8400.5060.6520.7610.860
", + "image_path": "1aaaa552c532807beb229cb8fdbf6f10f83861e3b9deeb59f0479f93f071e118.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 66, + 357, + 287, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 357, + 287, + 514 + ], + "spans": [ + { + "bbox": [ + 66, + 357, + 287, + 514 + ], + "type": "text", + "content": "for capturing visual preferences. A key component of our framework is the progressive learning method for understanding the composition of attention. According to the comparative results between our methods with and without progressive learning, it helps models better identify the attentional preferences of both individuals (i.e., " + }, + { + "bbox": [ + 66, + 357, + 287, + 514 + ], + "type": "inline_equation", + "content": "\\mathrm{K} = 1" + }, + { + "bbox": [ + 66, + 357, + 287, + 514 + ], + "type": "text", + "content": ") and user groups (i.e., " + }, + { + "bbox": [ + 66, + 357, + 287, + 514 + ], + "type": "inline_equation", + "content": "\\mathrm{K} = 3" + }, + { + "bbox": [ + 66, + 357, + 287, + 514 + ], + "type": "text", + "content": ", 5). As illustrated in Figure 3, unlike EML-Net and our method without progressive learning (Ours*) that fail to capture the visual preferences and generate similar attention maps regardless of the selection of users, our full method is able to predict attention maps that accurately reflect the regions of interest of diverse users." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 59, + 522, + 287, + 679 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 522, + 287, + 679 + ], + "spans": [ + { + "bbox": [ + 59, + 522, + 287, + 679 + ], + "type": "text", + "content": "- Additive ensemble falls short of modeling user-aware attention. Training one model for each user offers a straightforward way to model user preferences, and slightly outperforms our method without progressive learning when considering individuals' attention (i.e., " + }, + { + "bbox": [ + 59, + 522, + 287, + 679 + ], + "type": "inline_equation", + "content": "\\mathrm{K} = 1" + }, + { + "bbox": [ + 59, + 522, + 287, + 679 + ], + "type": "text", + "content": ") on FiWI. However, without learning how to integrate attention, it lacks the capability to predict attention maps with multiple users and is outperformed by our full method across all settings. Additionally, such an additive ensemble also fails to benefit general saliency prediction due to its high computational overhead and the inability to jointly consider attention of different users (see our supplementary materials)." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "content": "These observations highlight the significance of modeling visual preferences and the composition of attention, and" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "text", + "content": "demonstrate the advantages of our method for user-aware saliency modeling. While we do not consider demographic information in this study, our method is general and can be extended to broader scenarios for customized applications. For instance, instead of developing personalized filters, we can cluster users based on certain criteria (e.g., gender, age, personal interest) and optimize models to predict attentional preferences of users of specific characteristics." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 176, + 545, + 201 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 176, + 545, + 201 + ], + "spans": [ + { + "bbox": [ + 305, + 176, + 545, + 201 + ], + "type": "text", + "content": "4.3. Are Visual Preferences Beneficial for General Saliency Prediction?" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 207, + 545, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 207, + 545, + 338 + ], + "spans": [ + { + "bbox": [ + 304, + 207, + 545, + 338 + ], + "type": "text", + "content": "General saliency prediction focuses on attention aggregated from all users, and yet little attention has been paid to the diversity of attention patterns between users. In this subsection, we further investigate if knowledge of visual preferences is beneficial for the task. We compare our user-aware method with six state-of-the-art models, including SALICON [19], Deep Gaze II [28], SAM [10], EML-Net [21], UMSI [16], and AGD-F [8]. For a fair comparison, we adopt the training and test sets provided in [8] for evaluation on FiWI dataset. Table 3 and Table 4 report results on the FiWI [37] and OSIE [39, 41] datasets." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 339, + 545, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 339, + 545, + 555 + ], + "spans": [ + { + "bbox": [ + 304, + 339, + 545, + 555 + ], + "type": "text", + "content": "Compared to the EML-Net baseline, our model that takes into account visual preferences shows consistent improvements among all settings. Its performance is also competitive against existing state-of-the-art. As illustrated in Figure 4, the performance gain of our method can be attributed to the capability to capture fine-grained attention patterns (i.e., focuses on the man, little girls, and woman in the three examples, respectively) in addition to the salient regions attended by the majority of users (i.e., text, the food, and the boy). Moreover, the advantages of our method is also a result of increased data efficiency. Comparative results show that it outperforms EML-Net pretrained on the SALICON [23] dataset with 15000 images (EML-Net+SALICON), despite only relying on training samples in the FiWI dataset with 149 images. Such a unique feature can play an important role in generalizing towards domains with diverse characteristics (e.g., web page vs naturalistic image), where suitable data for pretraining is not necessarily available." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 563, + 545, + 587 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 563, + 545, + 587 + ], + "spans": [ + { + "bbox": [ + 305, + 563, + 545, + 587 + ], + "type": "text", + "content": "4.4. Can User-aware Saliency Modeling Overcome the Issues of Incomplete Users?" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 594, + 545, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 700 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 700 + ], + "type": "text", + "content": "Collecting human behavioral data demands stringent paradigms, and building large attention datasets has been challenging for decades [23]. As a result, it is common for saliency datasets to have samples associated with incomplete users. For instance, there are 32 users recruited in [39], while only about 14 users are presented for each sample. Different from prior works [19, 21, 28, 30] that overlook the issue, we examine if knowledge of visual preferences can be helpful for tackling the problem." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "type": "text", + "content": "Specifically, we randomly drop " + }, + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "type": "inline_equation", + "content": "K^{*}" + }, + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "type": "text", + "content": " users for each train-" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2707" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 110, + 70, + 487, + 281 + ], + "blocks": [ + { + "bbox": [ + 110, + 70, + 487, + 281 + ], + "lines": [ + { + "bbox": [ + 110, + 70, + 487, + 281 + ], + "spans": [ + { + "bbox": [ + 110, + 70, + 487, + 281 + ], + "type": "image", + "image_path": "69082e2a8dd2ecd2806c3d856af0d8e10f6054c2e66c5fcef5df54b90dab185b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 187, + 288, + 405, + 300 + ], + "lines": [ + { + "bbox": [ + 187, + 288, + 405, + 300 + ], + "spans": [ + { + "bbox": [ + 187, + 288, + 405, + 300 + ], + "type": "text", + "content": "Figure 4. Qualitative results for general saliency prediction." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 111, + 331, + 478, + 436 + ], + "blocks": [ + { + "bbox": [ + 133, + 311, + 459, + 323 + ], + "lines": [ + { + "bbox": [ + 133, + 311, + 459, + 323 + ], + "spans": [ + { + "bbox": [ + 133, + 311, + 459, + 323 + ], + "type": "text", + "content": "Table 5. Results for saliency prediction with incomplete users on seen and unseen images." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 111, + 331, + 478, + 436 + ], + "lines": [ + { + "bbox": [ + 111, + 331, + 478, + 436 + ], + "spans": [ + { + "bbox": [ + 111, + 331, + 478, + 436 + ], + "type": "table", + "html": "
K=1K=3K=5Unseen
NSSCCNSSCCNSSCCNSSCC
K* = 5EML-Net1.7330.3591.7190.5181.7120.5891.6160.601
Ours1.7590.3411.7810.5301.7970.6141.6980.632
K* = 7EML-Net1.6620.3421.6590.5011.6580.5731.5840.551
Ours1.7230.3301.7340.5121.7390.5941.7080.589
", + "image_path": "d74b38a46a5ca0f5f154573a9beec12a6c2fec6b9353607b49dd9dfe72c9d035.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 454, + 287, + 551 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 454, + 287, + 551 + ], + "spans": [ + { + "bbox": [ + 46, + 454, + 287, + 551 + ], + "type": "text", + "content": "ing sample in the FiWI dataset, and consider two evaluation settings: (1) attention of missing users on seen samples (we use different numbers of missing users, i.e., " + }, + { + "bbox": [ + 46, + 454, + 287, + 551 + ], + "type": "inline_equation", + "content": "\\mathrm{K} = 1, 3, 5" + }, + { + "bbox": [ + 46, + 454, + 287, + 551 + ], + "type": "text", + "content": "), and (2) attention of all users on unseen test samples (i.e., Unseen). The first setting is particularly useful for scenarios where we are interested in comparing users' preferences. On the other hand, the second setting aims to study models' robustness against the scarcity of annotations." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 557, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 557, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 557, + 288, + 715 + ], + "type": "text", + "content": "According to comparative results reported in Table 5, the proposed user-aware method is advantageous in both evaluation settings. Despite the slightly lower CC scores for individuals' attention " + }, + { + "bbox": [ + 46, + 557, + 288, + 715 + ], + "type": "inline_equation", + "content": "(\\mathrm{K} = 1)" + }, + { + "bbox": [ + 46, + 557, + 288, + 715 + ], + "type": "text", + "content": " on seen images, it achieves considerable improvements among all other evaluation settings. This is likely because predictions from the user-agnostic EML-Net tend to have a broader coverage, which is favored by CC metric emphasizing the overall distribution. Differently, our method has the capability to more accurately attend to regions of interest of different users, resulting in higher NSS scores as well as CC scores for more users. It also makes better use of the available data, and is more robust against the scarcity of annotations (i.e., higher general" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 455, + 468, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 455, + 468, + 467 + ], + "spans": [ + { + "bbox": [ + 306, + 455, + 468, + 467 + ], + "type": "text", + "content": "ization performance on unseen images)." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 478, + 379, + 490 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 478, + 379, + 490 + ], + "spans": [ + { + "bbox": [ + 306, + 478, + 379, + 490 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 498, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 547, + 715 + ], + "type": "text", + "content": "This paper identifies the critical roles of user preferences in visual attention, and for the first time tackles the challenge of user-aware saliency modeling. It unifies the conventional tasks for predicting general and personalized attention, and proposes an integral framework that jointly solves attention modeling for individual users, different groups of users, and the general population. By making progress with both a novel saliency prediction model and a progressive learning method, our framework illustrates a principled paradigm for establishing the connections between user preferences and visual saliency. Experimental results in diverse settings demonstrate the advantages of the proposed method in inferring the attention patterns of a variety of users, and highlights the significance of incorporating the variability of attention. We hope that our study can open new avenues for attention research, and benefit the development of new applications based on user-aware saliency models." + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2708" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 713 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "text", + "content": "[1] Stefano Alletto, Andrea Palazzi, Francesco Solera, Simone Calderara, and Rita Cucchiara. 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Results obtained with TBSRN [7], TATT [41] and our approach on the segments of Chinese text image cropped from a real low-resolution invoice and a signboard. Both baselines are re-trained with elaborated degradations as in BSRGAN [75] and Real-ESRGAN [66]." + ], + "image_footnote": [], + "bbox": [ + 511, + 253, + 890, + 405 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 467, + 312, + 482 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Blind text image super-resolution (SR) is challenging as one needs to cope with diverse font styles and unknown degradation. To address the problem, existing methods perform character recognition in parallel to regularize the SR task, either through a loss constraint or intermediate feature condition. Nonetheless, the high-level prior could still fail when encountering severe degradation. The problem is further compounded given characters of complex structures, e.g., Chinese characters that combine multiple pictographic or ideographic symbols into a single character. In this work, we present a novel prior that focuses more on the character structure. In particular, we learn to encapsulate rich and diverse structures in a StyleGAN and exploit such generative structure priors for restoration. To restrict the generative space of StyleGAN so that it obeys the structure of characters yet remains flexible in handling different font styles, we store the discrete features for each character in a codebook. The code subsequently drives the StyleGAN to generate high-resolution structural details to aid text SR. Compared to priors based on character recognition, the proposed structure prior exerts stronger character-specific guidance to restore faithful and precise strokes of a designated character. Extensive experiments on synthetic and real datasets demonstrate the compelling performance of the proposed generative structure prior in facilitating robust text SR. Our code is available at https://github.com/csxmli2016/MARCONet.", + "bbox": [ + 75, + 491, + 473, + 898 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 501, + 467, + 630, + 482 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Blind text super-resolution (SR) aims at restoring a high-resolution (HR) image from a low-resolution (LR) text image that is corrupted by unknown degradation. The problem is relatively less explored than SR of natural and face images.", + "bbox": [ + 496, + 489, + 892, + 549 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "This seemingly easy task actually possesses many unique challenges. In particular, each character owns its unique structure. A suboptimal restoration that destroys the structure with, e.g., distorted, missing or additional strokes, is easily perceptible and may alter the meaning of the original word. The task becomes more difficult when dealing with writing systems such as Chinese, Kanji and Hanja characters, in which the patterns of thousands of characters vary in complex ways and are mostly composed of different subunits (or compound ideographs). A slight deviation in strokes, say '太' and '大' carries entirely different meanings. The problem becomes more intricate given the different typefaces. In addition, complex and unknown degradation make the data-driven convolutional neural networks (CNNs) incapable of generalizing well to real-world degraded observations.", + "bbox": [ + 496, + 551, + 893, + 777 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To ameliorate the difficulties in blind text SR, especially in retaining the unique structure of each character, recent studies design new loss functions to constrain SR results semantically close to the high-resolution (HR) groundtruth [7,8,45,50,79], or incorporate the recognition prior into the intermediate features [40, 41, 44]. Figure 1 shows several representative results of these two types of methods, i.e., TB-SRN [7] that applies content-aware constraint and TATT [41]", + "bbox": [ + 496, + 779, + 895, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "10103", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "that embeds the recognition prior into the SR process. The results are not satisfactory despite the models were retrained with data synthesized with sophisticated degradation models, i.e., BSRGAN [75] and Real-ESRGAN [66]. TBSRN and TATT perform well when the LR character has fewer strokes. However, they both fail to generate the desired structures when the character is composed of complex strokes, e.g., the 4, 6, 8, 11-th characters in (a). The results suggest that high-level recognition prior cannot well benefit the SR task in restoring faithful and accurate structures.", + "bbox": [ + 75, + 90, + 472, + 241 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "When dealing with complex characters, we can identify some commonly used strokes as constituents of characters or their subparts. These obvious structural regularities have not been studied thoroughly in the literature. In particular, most existing text SR studies [7, 40, 41, 45, 50, 79] focus on scene text images that are presented in different view perspectives or arranged in irregular patterns. In contrast, our goal is to explore structural regularities specific to complex characters and investigate an effective way to exploit the prior. The investigation has practical values in many applications, including the restoration of old printed media (e.g., newspapers or books) for digitalization and preservation, and the enhancement of captions in digital media.", + "bbox": [ + 75, + 244, + 472, + 441 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The key idea of our solution is to mine structure prior from a generative network, and use the prior to facilitate blind SR of text images. To capture the structure prior of characters, we train a StyleGAN to generate characters of different styles. As our intent is not to generate infinite and non-repetitive results, we restrict the generative space of StyleGAN to obey the structure of characters by constraining the generation with a codebook. Specifically, the codebook stores the discrete code of each character, and each code serves as a constant to StyleGAN for generating a specific high-resolution character. The font style is governed by the $\\mathcal{W}$ latent space of StyleGAN. Once the character StyleGAN is trained, we can extract its intermediate features serving as the generative structure prior, which encapsulates the intrinsic structure and style of the LR character.", + "bbox": [ + 75, + 443, + 472, + 670 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Using the prior for text SR can be conveniently achieved through an additional Transformer-based encoder and a text SR network that accepts prior. In particular, given a text image that constitutes multiple characters (e.g., Figure 1), we use a Transformer-based encoder to predict the font style, character bounding boxes, and their respective indexes in the codebook jointly. The codebook indexes drive the structure prior generation for each character. In the text SR network, each LR character is super-resolved, guided by the respective priors that are aligned using their bounding boxes.", + "bbox": [ + 75, + 671, + 472, + 824 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Experiments demonstrate that our design can generate robust and consistent structure priors for diverse and severely degraded text input. With the embedded structure prior, our approach performs superior against state-of-the-art methods in generating photo-realistic text results and shows excellent", + "bbox": [ + 75, + 824, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "generalization to real-world LR text images. While our study mainly employs Chinese characters as examples, the proposed method can be readily extended to characters of other languages. We call our approach as MARCONet. The main contributions are summarized as follows:", + "bbox": [ + 496, + 90, + 893, + 167 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We show that blind SR task, especially for characters with complex structures, can be restored by using their structure prior encapsulated in a generative network.", + "- We present a viable way of learning such generative structure prior through reformulating a StyleGAN by replacing its single constant with discrete codes that represent different characters.", + "- To retrieve the prior accurately, we propose a Transformer-based encoder to jointly predict the font styles, character bounding boxes and their indexes in codebook from the LR input." + ], + "bbox": [ + 517, + 167, + 890, + 334 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 345, + 640, + 363 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Blind Image SR. Blind image SR is challenging due to the complex mixture of unknown degradations. Recent studies address the problem from two aspects, i.e., degradation estimation [3, 19, 38, 39, 62] and establishing more realistic training data [4, 28, 33, 66, 70, 75]. The former paradigm mainly focuses on estimating degradation model parameters and then applies non-blind SR methods, e.g., ZSSR [57]. The latter builds training pairs either through capturing real-world LR and HR pairs [4, 70] or designing elaborate degradation models that imitate real-world degradation [28, 33, 66, 75]. Since characters in text images have specific and semantic structures, we show that a good restoration performance cannot be achieved by merely using elaborately designed degradation models.", + "bbox": [ + 496, + 371, + 893, + 583 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Text Image SR. Text image SR has been studied for many years. In traditional methods, maximum a posterior (MAP) [5] and Bayesian framework [9] are exploited for super-resolving text images. These earlier approaches are incapable of generating high-quality results. Dong et al. [13] adopt CNNs (i.e., SRCNN [12]) for text image SR and achieve promising results in the ICDAR 2015 competition [49]. Xu et al. [72] adopt a Generative Adversarial Network (GAN) [17] to learn category-specific prior for face and text images SR, along with the supervision from a multi-class GAN loss. Mou et al. [44] propose to plug a SR unit into the recognition process of degraded text images. Wang et al. [64] introduce the first real-world text SR pairs (i.e., TextZoom), which are cropped from RealSR [4] and SRRAW [77]. They also present a sequential residual block by incorporating Bi-directional LSTM to capture the sequential information for low-level reconstruction. Both RealSR and SRRAW are captured by different digital cameras with different focal lengths, aiming to collect natural LR/HR pairs in real-world scenarios. The setting is not designed specifically for text images. We observe that most HR text images", + "bbox": [ + 496, + 583, + 895, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "10104", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "in TextZoom are limited in clarity, which could limit the SR performance when taking them as ground-truth.", + "bbox": [ + 76, + 90, + 468, + 121 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Text SR benefits from prior and auxiliary constraints. Quan et al. [51] recover text images in a cascade model by predicting the high-frequency information. Chen et al. [7] propose Transformer-based position-aware and content-aware modules to emphasize the position and the content of each character. Analogously, Nakaune et al. [45] and Qin et al. [50] respectively present the structure-aware loss and content-perceptual constraint for learning detailed structural skeletons. Zhao et al. [78] propose a parallel contextual attention network to learn sequence-dependent features for bringing more high-frequency information into text reconstruction. Zhao et al. [79] exploit linguistic, recognition and visual clues to jointly boost the SR performance. Chen et al. [8] propose a stroke-aware framework by concentrating on stroke-level internal structures. Ma et al. [41] introduce text recognition prior to text reconstruction with a Transformer-based module, leveraging the global attention mechanism. They also embed categorical text priors in the encoder and employ multi-stage refinement to progressively enhance low-resolution images [40].", + "bbox": [ + 75, + 128, + 472, + 431 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Many methods above employ recognition information either as a loss function on the SR results [7, 8, 50, 79] or as intermediate SR features for providing high-level guidance [40, 41]. Albeit the high-level recognition prior helps improve the text recognition ability, it is limited in providing accurate structure and style guidance, especially for certain texts with complex structures. In this study, we show that generative structure prior benefits high-quality guidance to restore the faithful structure of LR characters.", + "bbox": [ + 75, + 439, + 472, + 575 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Generative Structure Prior in Image SR. Image structure prior is proven effective in many low-level vision tasks, e.g., depth image enhancement [21, 27, 37], image inpainting [11, 46, 52], and image restoration [10, 35, 36, 47]. Most recently, by using generative structure priors obtained from pre-trained StyleGANs [30, 31] or codebooks [15], blind face restoration has achieved tremendous improvement [6, 22, 34, 65, 69, 73], suggesting the apparent advantage of such prior over other methods in generating photo-realistic textures. Our study is inspired by the success of these approaches. Nevertheless, crafting a suitable structural prior for text images are harder than face images. This is because each character has its unique strokes, but may have a vast variety of font styles. Any distorted, missing or additional strokes easily change their semantic layout that is easily perceptible, and worsens their actual meaning (see Figure 1). All of these challenges aggravate the difficulties for learning a generative structure prior for the text SR task. In this study, we show an effective way of learning such prior through replacing the constant input of StyleGAN with a discrete codebook, while controlling the font style via the $\\mathcal{W}$ space.", + "bbox": [ + 75, + 583, + 472, + 901 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/17169bbb912c04f587ae6c3095542eebd27198c4c059b3acd23576f88c151726.jpg", + "image_caption": [ + "Figure 2. Pre-training generative structure prior for each character. The codebook stores the discrete code of each character, and each code serves as a constant to StyleGAN for generating a specific high-resolution character. The intermediate features encapsulate the generative structure prior and will be used for guiding text SR." + ], + "image_footnote": [], + "bbox": [ + 526, + 82, + 867, + 186 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 500, + 272, + 635, + 289 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "A GAN model can well capture the intrinsic structure prior for a category by training the model on abundant images of the same category. Many image restoration tasks [6,20,42,48,65,73] have shown the benefits of using such generative priors for restoring photo-realistic details from LR inputs despite severe and complex degradation. Previous studies mainly use the prior for face restoration, while its application to text SR is under-explored. In this paper, we propose MARCONet, the first attempt to eMbed generative stRuCture priOr for blind text SR. The proposed pipeline is depicted in Figure 3. It mainly contains three parts, 1) the prediction of font style, character bounding boxes and their indexes in codebook based on a given LR input, 2) the generation of the structure prior for each character, 3) the SR framework that takes the generative structure prior as guidance for restoration. Next, we first describe the approach to obtain the generative structure prior for each character, followed by the way to employ such prior for the text SR.", + "bbox": [ + 496, + 297, + 893, + 570 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Pre-training of Generative Structure Prior", + "text_level": 1, + "bbox": [ + 500, + 578, + 862, + 594 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The original StyleGANs [30, 31] take a learnable constant as input, and control the style of output image through the $w \\in \\mathcal{W}$ space, which is a projection from the initial latent space $z \\in \\mathcal{Z}$ . Layer-wise noise is also introduced to support stochastic variation on fine-grained details. To better capture the structure of text images, we remove the layer-wise noise and replace the single constant with discrete codes that represent different characters (see details in Figure 2).", + "bbox": [ + 496, + 602, + 893, + 720 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We denote each character code as $c \\in \\{C_i\\}_{i=1}^M$ , where $C$ is the codebook that stores all the character features. Each code is learnable, with a size of $1 \\times 1 \\times 512$ . Following CRNN [56], the cardinality of codebook $M$ is set to 6736, a size covering simplified Chinese characters, English letters, and numbers. The retrofitted StyleGAN is defined as:", + "bbox": [ + 496, + 722, + 893, + 813 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {S} ^ {c} = G (c, \\mathcal {F} (z); \\Theta_ {G}) = G (c, w; \\Theta_ {G}), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 573, + 818, + 892, + 835 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathcal{F}$ represents the network that maps $z$ to $w$ , and $\\Theta_G$ is the model parameters of StyleGAN. For generalizing to different scenarios, we simplify the structure image $S^c$ with pixel values $\\in \\{0,1\\}$ (see the output in Figure 2). The struc", + "bbox": [ + 496, + 839, + 893, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "10105", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/e7d50faef30a02e067e145f865c675e5ecfe7fa4e31126df0288700cba61f00f.jpg", + "image_caption": [ + "Figure 3. Overview of our MARCONet. It contains three parts, i.e., (i) Transformer encoder for predicting the font style, classification and bounding boxes of each character from LR input, (ii) structure prior generation with pre-trained StyleGAN for generating reliable structure prior for each character, and (iii) the SR process for reconstructing the SR output with the incorporation of each characters' structure prior." + ], + "image_footnote": [], + "bbox": [ + 122, + 84, + 848, + 330 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "ture prior $\\mathcal{P}^c$ used in this work is the intermediate features from $G$ in Eqn. (1), and can be formulated as:", + "bbox": [ + 75, + 391, + 470, + 421 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {P} ^ {c} = G _ {i} (c, w; \\Theta_ {G}), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 205, + 426, + 468, + 441 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $G_{i}$ represents the output features from $i$ -th layer of $G$ .", + "bbox": [ + 75, + 448, + 470, + 463 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The training of the character StyleGAN can be done on synthetic images yet with satisfying generalization ability to real-world texts. In particular, the PIL package1 is adopted to synthesize high-resolution character images with hundreds of font styles (see examples in the suppl.). We also augment the diversity with random translations, font sizes and slight affine transformation. Different from the original StyleGANs that adopt only adversarial loss [17], we introduce an additional recognition loss derived from a pre-trained Transformer-based recognizer as regularization. Once learned, each learnable code $c$ well captures the distinctive features of each character and $w \\in \\mathcal{W}$ can control the font styles of the output image. In the following, we will describe the approach to extract the structure prior for each character in a given LR text image.", + "bbox": [ + 75, + 464, + 470, + 690 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Transformer Encoder", + "text_level": 1, + "bbox": [ + 76, + 700, + 282, + 715 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "A LR text image usually is composed of several characters. To derive the generative structure prior for each character, first, we need to obtain the font style $w$ of the LR characters. Second, the indexes of each character in the codebook and their bounding boxes are also necessary for aligning the structure prior with each LR character. To this end, we adopt a Transformer-based encoder to jointly predict the needed information. Transformer [61] is chosen so that we can better capture the dependency across different characters in the input image.", + "bbox": [ + 75, + 724, + 468, + 876 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Learning to predict the font style $w$ is similar to learning-based GAN inversion [2, 54, 60, 63], where the Transformer network serves as an encoder. It is observed that the Transformer-based encoder achieves satisfactory inversion, achieving reconstruction with low distortion and of high quality [25]. Note that characters in one text image generally have the same font style. So we use one linear layer to map the features of all characters to a single prediction $(w)$ , which is shared with all the characters in the same LR image. We also use a similar structure as $w$ prediction to carry out the regression and classification of the bounding boxes and code indexes. These three sub-tasks share the same Transformer encoder (i.e., ViT [14]) and a CNN backbone (i.e., ResNet45 [24]). Positional encoding is incorporated to inject positions of features in the sequence.", + "bbox": [ + 504, + 391, + 893, + 618 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The font style prediction branch is optimized with the gradient from StyleGAN. Since the input text image has unconstrained numbers of characters, we adopt CTC loss [18] for recognition. The loss is proposed to solve the alignment between predicted and target labels and is widely used in scene text recognition tasks. As for the learning of character bounding boxes regression, we adopt a linear combination of the Smooth $L_{1}$ loss [16] and the generalized IoU loss [53]. The ground-truth boxes of each character can be obtained when synthesizing the training images with PIL package. The gradient from the latter text SR network can further benefit the learning process of the whole Transformer encoder.", + "bbox": [ + 496, + 619, + 893, + 801 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Text Super-resolution Network", + "text_level": 1, + "bbox": [ + 500, + 815, + 772, + 830 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Network Architecture. With the Transformer encoder, we can obtain the font style $w$ , classification label (i.e., index in codebook), and the bounding box for each character in the LR input. Then, the corresponding high-quality generative", + "bbox": [ + 496, + 839, + 893, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_footnote", + "text": "$^{1}$ https://python-pillow.org/", + "bbox": [ + 94, + 886, + 238, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "10106", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/09a5a31c549c2a7145a686f178c962d85aae3dfe2be0f611c405e1ab6e3bc319.jpg", + "image_caption": [ + "Figure 4. Details of the structure prior transform module. Each LR character is cropped and aligned by using the bounding boxes, and is super-resolved with the guidance of their structure prior." + ], + "image_footnote": [], + "bbox": [ + 102, + 84, + 444, + 323 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "structure prior $\\mathcal{P}^c$ for each character can be generated with $w$ and the selected code $c$ through the pre-trained StyleGAN in Eqn. (2) (see the character structure prior in Figure 3). In this section, we describe how to use them for the text SR task. First, a simple UNet [55] is stacked upon the ResNet45 to extract the LR features. Then, the generative structure prior of each character is embedded into their LR characters through a structure prior transform module. The process is shown in Figure 4 (more details can be found in the suppl.). For the LR features, we adopt the detected bounding boxes to crop and align each LR character by RoIAlign operation [23]. For each character, AdaIN [26] is adopted to normalize the prior's distribution, and spatial feature transformation [67] is subsequently employed to predict the affine parameters, which are applied on the LR character features. The reverse RoIAlign is finally used to paste the enhanced features back to their original locations. The structure prior transform module is adopted at two scales $s\\in \\{32,64\\}$ , allowing our MARCONet to remain high fidelity with different degradation. A Conv-ReLU-ResBlock based CNN module is stacked to generate the final SR result.", + "bbox": [ + 75, + 383, + 472, + 700 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Learning Objective. We minimize the differences between the SR results $\\hat{I}_{SR}$ and HR ground-truth $I_{HR}$ on both the pixel and perceptual domains [29]:", + "bbox": [ + 76, + 702, + 470, + 748 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {r e c} = \\left\\| \\hat {I} _ {S R} - I _ {H R} \\right\\| _ {1} + \\sum_ {i = 1} ^ {4} \\frac {\\lambda_ {p e r}}{\\mathcal {C} _ {i} \\mathcal {H} _ {i} \\mathcal {W} _ {i}} \\left\\| \\Phi_ {i} (\\hat {I} _ {S R}) - \\Phi_ {i} (I _ {H R}) \\right\\| _ {1}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 84, + 753, + 468, + 789 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{C}_i$ , $\\mathcal{H}_i$ and $\\mathcal{W}_i$ are the feature dimensions from the $i$ -th convolution layer of the pre-trained VGG-19 model $\\Phi$ [58]. $\\lambda_{per}$ is the trade-off parameter and is set to 0.05. The loss $\\mathcal{L}_{rec}$ is applied to the whole text image.", + "bbox": [ + 76, + 792, + 468, + 854 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Adversarial loss [17] $\\mathcal{L}_{adv}$ is also added to improve visual quality. Instead of constraining on the whole image as in Eqn. (3), $\\mathcal{L}_{adv}$ is performed on each cropped character image", + "bbox": [ + 76, + 854, + 468, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "together with its corresponding structure image as additional conditions [43]. To be specific, the concatenation of HR character image $I_{HR}^{c}$ and its structure image $S_{HR}^{c}$ is expected to be classified as Real, while the concatenation of SR character image $\\hat{I}_{SR}^{c}$ and its structure image $S_{SR}^{c}$ is recognized as Fake. Note that $S_{HR}^{c}$ is the binarized version of $I_{HR}^{c}$ , which represents the ground-truth structure, and $S_{SR}^{c}$ is obtained from Eqn. (1) with $w$ and $c$ predicted from LR input. Such design allows us to better constrain the embedding of generative structure prior into the SR results. The hinge version of adversarial loss [74] for each character is defined as:", + "bbox": [ + 496, + 90, + 893, + 257 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {D} = - \\mathbb {E} \\left[ \\min \\left(0, - 1 + D \\left(I _ {H R} ^ {c}, S _ {H R} ^ {c}\\right)\\right) \\right] - \\mathbb {E} \\left[ \\min \\left(0, - 1 - D \\left(\\hat {I} _ {S R} ^ {c}, S _ {S R} ^ {c}\\right)\\right) \\right],\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 263, + 893, + 281 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {G} = - \\mathbb {E} \\left[ D \\left(\\hat {I} _ {S R} ^ {c}, \\mathcal {S} _ {S R} ^ {c}\\right) \\right]. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 620, + 284, + 890, + 301 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Finally, we use the $L_{1}$ loss on structure image $\\mathcal{S}^c$ in the text SR training stage to further fine-tune $w$ and code $c$ in codebook. For each character, this constraint is defined as:", + "bbox": [ + 496, + 308, + 890, + 354 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {s t r} = \\left\\| \\mathcal {S} _ {S R} ^ {c} - \\mathcal {S} _ {H R} ^ {c} \\right\\| _ {1}. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 624, + 359, + 890, + 375 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "With these learning objectives, the whole framework of MARCONet is optimized in an end-to-end manner.", + "bbox": [ + 496, + 380, + 893, + 411 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 422, + 633, + 440 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Training Data. In this work, we take Chinese characters as our initial exploration for super-resolving complex characters but with regularity. The same method can be extended to other languages by retraining the framework with specific data. Since a text image is usually composed of several characters, here we use the Chinese corpus from Xu et al. [71], which contains tens of millions of common items. We also collect 182 font families to introduce diverse structures. PIL toolbox is adopted to synthesize these text images, rendered with random RGB values, font sizes and locations. The text background is obtained from DIV2K [1] and Flickr2K [59] datasets, in which each image is randomly cropped and upsampled to $\\times 4\\sim 16$ to synthesize the complex background. With this toolbox, we can obtain the HR text images $I_{HR}$ , together with the classification label, bounding box and the ground-truth structure image $S_{HR}^{c}$ of each character. The degradation pipeline presented in BSRGAN [75] and Real-ESRGAN [66] are applied online to degrade the HR image to LR input (see input in Figure 3). Since each text image usually contains varying numbers of characters, we pad zeros to the width dimension to keep the structure unchanged.", + "bbox": [ + 496, + 446, + 893, + 763 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implementation Details. The training of the whole MARCONet and the pre-training for generative structure prior are conducted on a server with four Tesla V100 GPUs. The batch size is set to 2 and 16, respectively. We employ Adam [32] as the optimizer. The initial learning rate $lr$ is set to $1e - 4$ and decreased by 0.5 when $\\mathcal{L}_{rec}$ reaches a stable range on the validation set. The $lr$ for StyleGAN in the text SR training stage is set to $1e - 6$ for fine-tuning. The height of HR images is set to 128. Color jittering [80] is used to increase", + "bbox": [ + 496, + 765, + 893, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "10107", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/05be199feca5a9bfbf15527fc1a6c007dd522e6bbb0f636f5b65ec62611e56bc.jpg", + "image_caption": [ + "Figure 5. Visual comparison on $\\times 2$ (1\\~2 columns) and $\\times 4$ (3\\~4 columns) SR. The stroke details are best viewed by zooming in." + ], + "image_footnote": [], + "bbox": [ + 124, + 78, + 305, + 284 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/b5c8c8c3c992fdae0e04d7cac547f6c8e6708ea025b6a608c0499f18336669bf.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 307, + 78, + 542, + 282 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/2cabfbfc1adc0c4b5db5941e05ade02c2d715f0ee47938749a274bdc551cf3ef.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 542, + 78, + 694, + 284 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/177fa6f33977f954dd09e72fac03ca5e7d66caca143aa430c743dc976a6f5237.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 694, + 78, + 843, + 284 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/387fcc5ee8efdf7202f90380a306e539d233dd445f79453b23d4349d41980585.jpg", + "table_caption": [ + "Table 1. Quantitative comparison on $\\times 2$ and $\\times 4\\mathrm{{SR}}$ ." + ], + "table_footnote": [], + "table_body": "
Methods×2×4
PSNR↑SSIM↑LPIPS↓Acc.↑PSNR↑SSIM↑LPIPS↓Acc.↑
SRCNN [12]23.34.868.09582.1719.56.750.21871.41
ESRGAN [68]23.72.891.08583.2519.86.778.20472.12
TSRN [64]24.27.893.09485.8220.67.782.20176.94
TBSRN [7]25.62.906.07492.3721.07.794.18684.32
TATT [41]25.84.907.07393.2621.49.800.18585.17
Ours28.32.941.03399.1624.04.873.09692.53
", + "bbox": [ + 78, + 338, + 470, + 446 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "image diversity. It takes two days for pre-training StyleGAN and nearly four days for training the whole MARCONet.", + "bbox": [ + 75, + 458, + 468, + 488 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Baselines. Since there are few works studying the problem of these types of text images on SR task, we compare with two types of methods following TATT [41], i.e., general image SR (i.e., SRCNN [12], ESRGAN [68]) and recent text image SR (i.e., TSRN [64], TBSRN [7] and TATT [41]). For a fair comparison, we modify their codes to handle $\\times 2$ and $\\times 4$ SR tasks, and carefully retrain them with the same training data as Ours. In particular, the retrained TBSRN adopts the ground-truth text and bounding boxes for its pretrained content-aware and position-aware modules. As for TATT, we also use the ground-truth text to pre-train its TPG module. We report the quantitative and qualitative results on our synthetic dataset, which contains 1,000 LR/HR pairs for $\\times 2$ and $\\times 4$ tasks, respectively. These LR inputs are injected with random noise, blurring and JPEG compression, to simulate real-world degradation. We also provide the results on real-world text images collected from different sources. More results can be found in the suppl.", + "bbox": [ + 75, + 489, + 468, + 761 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Quantitative Comparison", + "text_level": 1, + "bbox": [ + 76, + 770, + 308, + 787 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1 summarizes the PSNR, SSIM and LPIPS [76] of different methods on the synthetic dataset. An additional pre-trained CRNN [56] is used to compute the recognition accuracy of SR results (Acc.), serving as an auxiliary indicator for the restoration performance. Note that the synthetic data is non-trivial given its low quality. Without specifically designed components for text images, general SR methods", + "bbox": [ + 75, + 794, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "perform poorly as expected. By incorporating the recognition information, both TBSRN [7] and TATT [41] show obvious improvement, especially in retaining the semantic layout of character for recognition (see Acc. columns). Our method achieves the best quantitative results and outperforms others with a large margin (e.g., 2.5 dB higher than the second-best method on average). Even with severe degradation (i.e., $\\times 4$ ), our method still attains favorable performance, which can be ascribed to the effectiveness of the learned generative structure prior for each character.", + "bbox": [ + 496, + 318, + 893, + 469 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Qualitative Comparison", + "text_level": 1, + "bbox": [ + 498, + 478, + 720, + 494 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Figure 5 shows the visual comparison on our synthetic LR images for $\\times 2$ and $\\times 4$ tasks. With careful retraining, competing methods perform favorably when the LR input has slight degradation, but they are not able to recover the unique structure of characters with complex strokes. When the degradation turns more severe, all of them fail to restore satisfactory results (see the last column). The results yielded by TBSRN [7] and TATT [41] suggest that high-level recognition constraints bring limited benefit to the SR task, especially in coping with diverse and complex font structures and styles. With the guidance of characters' generative structure prior, our method shows compelling results that exhibit more consistent structures with ground-truth (GT). It is interesting to observe the strong performance of MARCONet in restoring heavily degraded LR input that is challenging for humans to recognize (last column of Figure 5).", + "bbox": [ + 496, + 501, + 893, + 742 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Apart from the evaluation on synthetic LR input, we also evaluate our method on real-world LR text images. We collect real-world LR text images from different sources, e.g., invoices, license plates, scanned documents, road signs, plaques, video captions, and scene texts from TextZoom [64]. Each text region is cropped by $\\mathrm{CnSTD}^2$ . We compare with two competing methods, i.e., TBSRN [7] and TATT [41], which are specifically designed for text images and achieve the top quantitative results in Table 1. The results are shown", + "bbox": [ + 496, + 743, + 893, + 878 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "$^{2}$ https://github.com/breezeedeus/CnSTD", + "bbox": [ + 516, + 886, + 728, + 898 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "10108", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/cce5c68a6860a978ed4574feea5a37d7a72d289a11c6f7564d65a68b865fc8ba.jpg", + "image_caption": [ + "Figure 6. Visual comparison on real-world LR text images, including invoice, license plate, scanned document, road sign, plaque, etc." + ], + "image_footnote": [], + "bbox": [ + 137, + 78, + 830, + 452 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "in Figure 6. Benefiting from our synthetic training data, the competing methods achieve comparable performance on these characters with simple structures, even for LR inputs corrupted by unknown and complex degradation. The positive results suggest that our synthetic HR text images are of high quality and well-suited as ground-truth for the SR task. The usage of degradation models from BSRGAN [75] and Real-ESRGAN [66] further benefits these methods in synthesizing realistic LR inputs. However, both of these two methods fail to generate plausible results when the LR character is degraded severely or contains complex structures. In contrast, with the proposed generative structure prior, our method achieves the best performance, not only in visual quality, but also in the generation of accurate structures.", + "bbox": [ + 75, + 484, + 473, + 696 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 709, + 232, + 726 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Analyses of $\\mathcal{W}$ Space. The $\\mathcal{W}$ space controls the style of a character's structure prior. Figure 7 shows the structure image $S_{SR}^{c}$ from our StyleGAN with $w\\in \\mathcal{W}$ and character indexes predicted from the LR input. One can observe that $w$ can well capture the manifold of font styles, e.g., the thickness of different font families (1-st column) and different font sizes and locations (2-nd column). We also interpolate two $w$ from different LR inputs and demonstrate their results in the $3\\sim 5$ rows. One can see that the generated structures change smoothly, indicating that $w$ in our framework also has the editable ability like the original StyleGAN. Finally,", + "bbox": [ + 75, + 734, + 472, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "we use the predicted $w$ from a real-world LR video frame (The Dream of the Red Chamber) and explore font style transfer. Even though the LR input contains a traditional Chinese character and the font family does not exist in our training data, our predicted $w$ can well capture its style and successfully transfer it to other characters. Besides, the $w$ latent and character code $c$ are disentangled, judging from the good separation of roles between the $w$ and $c$ in style control and storing the unique structure for each character.", + "bbox": [ + 496, + 484, + 893, + 621 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Analyses of Variants. Here we consider the following variants to evaluate each part of our MARCONet, 1) Ours $(UNet)$ & Ours $(UNet^{\\dagger})$ : only taking ResNet45 and UNet to perform the SR task and increasing its model parameters, respectively, 2) Ours (CRNN) & Ours (PSP): replacing our Transformer-based character classification and $w$ inversion branches with CRNN [56] and PSP encoder [54], respectively, 3) Ours $(D^{-})$ : only taking the SR and HR images as input of discriminator without concatenating their structure images, 4) Ours $(w / o S)$ : removing StyleGAN and directly incorporating the code $c$ on each LR character features through spatial affine transformation, 5) Ours $(w / o C)$ : removing codebook and directly taking each LR character features into a pre-trained StyleGAN that produces colored output like GFPGAN [65], 6) Ours (#32) & Ours (#64): only using the structure prior transform module on feature sizes of either $32 \\times 32$ or $64 \\times 64$ . Their performance on our synthetic test set is shown in Table 2 and Figure 8. We can observe", + "bbox": [ + 496, + 628, + 895, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "10109", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c883fe39ae803d3bfe151e28331dbb34771946ce3de864516131f2cb560cdc2a.jpg", + "image_caption": [ + "Figure 7. The $\\mathcal{W}$ space in StyleGAN controls the font style of characters. The 1-st and 7-th rows are LR input. The 2-nd and 6-th rows are output of StyleGAN with $w$ and code indexes from their LR input. The remaining rows are the interpolation results of $w$ from two LR inputs." + ], + "image_footnote": [], + "bbox": [ + 127, + 78, + 375, + 329 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/fd00eabebcc0dc241e083d9c1aae0c416446f51291a6a29e1fe5c0a0a385f656.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 377, + 78, + 650, + 329 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ed5a75e65ae181afc2d420fa9915d8238d90f73981f52d58342375646f2b0118.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 651, + 78, + 841, + 329 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/99ab50dccca87e9882254ee1702b31a2c57aa0fd74f6f0010c6c19fdf54cad6d.jpg", + "table_caption": [ + "Table 2. Comparison of different variants of the proposed method." + ], + "table_footnote": [], + "table_body": "
Variants×2×4
PSNR↑SSIM↑LPIPS↓Acc.↑PSNR↑SSIM↑LPIPS↓Acc.↑
Ours (UNet)23.69.890.09482.6319.84.777.20971.96
Ours (UNet†)23.71.891.09282.7419.87.778.20372.16
Ours (CRNN)28.00.931.03498.8723.98.871.10192.41
Ours (PSP)28.04.932.03599.0723.99.871.09992.49
Ours (D-)28.29.940.03499.1123.94.870.09892.48
Ours (w/o S)25.86.907.07494.6421.57.802.18286.63
Ours (w/o C)25.53.905.04192.2521.39.798.12883.71
Ours (#32)28.16.937.03998.8623.96.870.10192.16
Ours (#64)28.30.940.03599.1024.02.872.09992.33
Ours (Full)28.32.941.03399.1624.04.873.09692.53
", + "bbox": [ + 78, + 391, + 468, + 551 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "that a) Ours (UNet) and Ours $(UNet^{\\dagger})$ perform on par with general SR methods, and indicate that a mere increase in model capacity would not bring significant performance improvement; b) the Transformer-based encoder is more effective than CRNN [56] and PSP encoder [54], which may be caused by the global attention and thus contribute better to the classification and GAN inversion tasks. It is observed that Ours (CRNN) sometimes makes wrong predictions on character. While the SR leads to a clear image, the character loses its actual semantic layout (see red box in Figure 8); c) the concatenation of structure image on discriminator is beneficial for emphasizing the structure prior more on LR input and thus boosting the final SR result; d) by removing StyleGAN and codebook, Ours $(w / o S)$ and Ours $(w / o C)$ show obvious inferior results, indicating that codebook can benefit the recognition accuracy while StyleGAN contributes more on the visual quality (e.g., LPIPS); e) Ours (#64) has slightly better results than Ours (#32) but both of them are inferior to Ours (Full) that deploys a multi-scale structure prior transform module. From these analyses, we conclude that the Transformer-based encoder, codebook, StyleGAN and multi-scale structure prior transform module are all crucial", + "bbox": [ + 75, + 568, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d3e51e4657c5930b1ae78e22b1c03551c9a25db6ace27e70a71d29194c5b1dcd.jpg", + "image_caption": [ + "Figure 8. Visual comparison of different variants." + ], + "image_footnote": [], + "bbox": [ + 509, + 377, + 883, + 588 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "for achieving good performance in Ours (Full).", + "bbox": [ + 500, + 618, + 812, + 633 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 647, + 617, + 662 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this work, we made the first attempt to embed the generative structure prior for blind SR of text images. The combination of a codebook for storing distinctive character-specific codes and a retrofitted StyleGAN for controlling font style cope well with complicated structures, high similarity between characters, and a great variety of font styles. We have shown that such structure prior is beneficial for super-resolving LR text images, even for those with severe degradation. We can potentially extend it to other text-related tasks, e.g., text image completion for ancient documents, font style transformation, and few-shot font generation.", + "bbox": [ + 496, + 672, + 893, + 837 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement. This study is supported under the RIE2020 Industry Alignment Fund - Industry Collaboration Projects (IAF-ICP) Funding Initiative, as well as cash and in-kind contribution from the industry partner(s).", + "bbox": [ + 496, + 839, + 893, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "10110", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Eirikur Agustsson and Radu Timofte. NTIRE 2017 challenge on single image super-resolution: Dataset and study. In CVPRW, 2017. 5", + "[2] Yuval Alaluf, Omer Tov, Ron Mokady, Rinon Gal, and Amit Bermano. Hyperstyle: StyleGAN inversion with hypernetworks for real image editing. In CVPR, 2022. 4", + "[3] Sefi Bell-Kligler, Assaf Shocher, and Michal Irani. Blind super-resolution kernel estimation using an internal-GAN. 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In ECCV, 2020. 5" + ], + "bbox": [ + 78, + 90, + 470, + 431 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "10113", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Learning Generative Structure Prior for Blind Text Image Super-Resolution/be24eaf6-c383-4655-bacc-0e5ade4d218b_model.json b/2023/Learning Generative Structure Prior for Blind Text Image Super-Resolution/be24eaf6-c383-4655-bacc-0e5ade4d218b_model.json new file mode 100644 index 0000000000000000000000000000000000000000..ae2c495de7009e89429366668b90cdda655cdb4b --- /dev/null +++ b/2023/Learning Generative Structure Prior for Blind Text Image Super-Resolution/be24eaf6-c383-4655-bacc-0e5ade4d218b_model.json @@ -0,0 +1,2334 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.105, + 0.118, + 0.867, + 0.14 + ], + "angle": 0, + "content": "Learning Generative Structure Prior for Blind Text Image Super-resolution" + }, + { + "type": "text", + "bbox": [ + 0.235, + 0.177, + 0.348, + 0.195 + ], + "angle": 0, + "content": "Xiaoming Li" + }, + { + "type": "text", + "bbox": [ + 0.383, + 0.178, + 0.519, + 0.195 + ], + "angle": 0, + "content": "Wangmeng Zuo" + }, + { + "type": "text", + "bbox": [ + 0.554, + 0.177, + 0.733, + 0.196 + ], + "angle": 0, + "content": "Chen Change Loy1(⊗)" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.196, + 0.512, + 0.213 + ], + "angle": 0, + "content": "\\(^{1}\\)S-Lab, Nanyang Technological University" + }, + { + "type": "text", + "bbox": [ + 0.548, + 0.196, + 0.8, + 0.214 + ], + "angle": 0, + "content": "\\(^{2}\\)Harbin Institute of Technology" + }, + { + "type": "text", + "bbox": [ + 0.24, + 0.217, + 0.386, + 0.23 + ], + "angle": 0, + "content": "csxml@gmail.com" + }, + { + "type": "text", + "bbox": [ + 0.411, + 0.217, + 0.555, + 0.23 + ], + "angle": 0, + "content": "wmzuo@hit.edu.cn" + }, + { + "type": "text", + "bbox": [ + 0.581, + 0.217, + 0.725, + 0.23 + ], + "angle": 0, + "content": "ccloy@ntu.edu.sg" + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.254, + 0.51, + 0.401 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.115, + 0.407, + 0.493, + 0.421 + ], + "angle": 0, + "content": "(a) A real-world LR text image cropped from a Chinese invoice" + }, + { + "type": "image", + "bbox": [ + 0.513, + 0.254, + 0.891, + 0.406 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.529, + 0.407, + 0.872, + 0.422 + ], + "angle": 0, + "content": "(b) A real-world LR text image cropped from a signboard" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.424, + 0.895, + 0.453 + ], + "angle": 0, + "content": "Figure 1. Results obtained with TBSRN [7], TATT [41] and our approach on the segments of Chinese text image cropped from a real low-resolution invoice and a signboard. Both baselines are re-trained with elaborated degradations as in BSRGAN [75] and Real-ESRGAN [66]." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.468, + 0.313, + 0.483 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.492, + 0.474, + 0.899 + ], + "angle": 0, + "content": "Blind text image super-resolution (SR) is challenging as one needs to cope with diverse font styles and unknown degradation. To address the problem, existing methods perform character recognition in parallel to regularize the SR task, either through a loss constraint or intermediate feature condition. Nonetheless, the high-level prior could still fail when encountering severe degradation. The problem is further compounded given characters of complex structures, e.g., Chinese characters that combine multiple pictographic or ideographic symbols into a single character. In this work, we present a novel prior that focuses more on the character structure. In particular, we learn to encapsulate rich and diverse structures in a StyleGAN and exploit such generative structure priors for restoration. To restrict the generative space of StyleGAN so that it obeys the structure of characters yet remains flexible in handling different font styles, we store the discrete features for each character in a codebook. The code subsequently drives the StyleGAN to generate high-resolution structural details to aid text SR. Compared to priors based on character recognition, the proposed structure prior exerts stronger character-specific guidance to restore faithful and precise strokes of a designated character. Extensive experiments on synthetic and real datasets demonstrate the compelling performance of the proposed generative structure prior in facilitating robust text SR. Our code is available at https://github.com/csxmli2016/MARCONet." + }, + { + "type": "title", + "bbox": [ + 0.502, + 0.468, + 0.631, + 0.483 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.49, + 0.893, + 0.55 + ], + "angle": 0, + "content": "Blind text super-resolution (SR) aims at restoring a high-resolution (HR) image from a low-resolution (LR) text image that is corrupted by unknown degradation. The problem is relatively less explored than SR of natural and face images." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.552, + 0.895, + 0.779 + ], + "angle": 0, + "content": "This seemingly easy task actually possesses many unique challenges. In particular, each character owns its unique structure. A suboptimal restoration that destroys the structure with, e.g., distorted, missing or additional strokes, is easily perceptible and may alter the meaning of the original word. The task becomes more difficult when dealing with writing systems such as Chinese, Kanji and Hanja characters, in which the patterns of thousands of characters vary in complex ways and are mostly composed of different subunits (or compound ideographs). A slight deviation in strokes, say '太' and '大' carries entirely different meanings. The problem becomes more intricate given the different typefaces. In addition, complex and unknown degradation make the data-driven convolutional neural networks (CNNs) incapable of generalizing well to real-world degraded observations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.896, + 0.902 + ], + "angle": 0, + "content": "To ameliorate the difficulties in blind text SR, especially in retaining the unique structure of each character, recent studies design new loss functions to constrain SR results semantically close to the high-resolution (HR) groundtruth [7,8,45,50,79], or incorporate the recognition prior into the intermediate features [40, 41, 44]. Figure 1 shows several representative results of these two types of methods, i.e., TB-SRN [7] that applies content-aware constraint and TATT [41]" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10103" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.242 + ], + "angle": 0, + "content": "that embeds the recognition prior into the SR process. The results are not satisfactory despite the models were retrained with data synthesized with sophisticated degradation models, i.e., BSRGAN [75] and Real-ESRGAN [66]. TBSRN and TATT perform well when the LR character has fewer strokes. However, they both fail to generate the desired structures when the character is composed of complex strokes, e.g., the 4, 6, 8, 11-th characters in (a). The results suggest that high-level recognition prior cannot well benefit the SR task in restoring faithful and accurate structures." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.245, + 0.473, + 0.442 + ], + "angle": 0, + "content": "When dealing with complex characters, we can identify some commonly used strokes as constituents of characters or their subparts. These obvious structural regularities have not been studied thoroughly in the literature. In particular, most existing text SR studies [7, 40, 41, 45, 50, 79] focus on scene text images that are presented in different view perspectives or arranged in irregular patterns. In contrast, our goal is to explore structural regularities specific to complex characters and investigate an effective way to exploit the prior. The investigation has practical values in many applications, including the restoration of old printed media (e.g., newspapers or books) for digitalization and preservation, and the enhancement of captions in digital media." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.444, + 0.473, + 0.671 + ], + "angle": 0, + "content": "The key idea of our solution is to mine structure prior from a generative network, and use the prior to facilitate blind SR of text images. To capture the structure prior of characters, we train a StyleGAN to generate characters of different styles. As our intent is not to generate infinite and non-repetitive results, we restrict the generative space of StyleGAN to obey the structure of characters by constraining the generation with a codebook. Specifically, the codebook stores the discrete code of each character, and each code serves as a constant to StyleGAN for generating a specific high-resolution character. The font style is governed by the \\(\\mathcal{W}\\) latent space of StyleGAN. Once the character StyleGAN is trained, we can extract its intermediate features serving as the generative structure prior, which encapsulates the intrinsic structure and style of the LR character." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.672, + 0.473, + 0.825 + ], + "angle": 0, + "content": "Using the prior for text SR can be conveniently achieved through an additional Transformer-based encoder and a text SR network that accepts prior. In particular, given a text image that constitutes multiple characters (e.g., Figure 1), we use a Transformer-based encoder to predict the font style, character bounding boxes, and their respective indexes in the codebook jointly. The codebook indexes drive the structure prior generation for each character. In the text SR network, each LR character is super-resolved, guided by the respective priors that are aligned using their bounding boxes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Experiments demonstrate that our design can generate robust and consistent structure priors for diverse and severely degraded text input. With the embedded structure prior, our approach performs superior against state-of-the-art methods in generating photo-realistic text results and shows excellent" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.168 + ], + "angle": 0, + "content": "generalization to real-world LR text images. While our study mainly employs Chinese characters as examples, the proposed method can be readily extended to characters of other languages. We call our approach as MARCONet. The main contributions are summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.168, + 0.892, + 0.214 + ], + "angle": 0, + "content": "- We show that blind SR task, especially for characters with complex structures, can be restored by using their structure prior encapsulated in a generative network." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.214, + 0.892, + 0.273 + ], + "angle": 0, + "content": "- We present a viable way of learning such generative structure prior through reformulating a StyleGAN by replacing its single constant with discrete codes that represent different characters." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.274, + 0.892, + 0.335 + ], + "angle": 0, + "content": "- To retrieve the prior accurately, we propose a Transformer-based encoder to jointly predict the font styles, character bounding boxes and their indexes in codebook from the LR input." + }, + { + "type": "list", + "bbox": [ + 0.518, + 0.168, + 0.892, + 0.335 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.347, + 0.642, + 0.364 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.372, + 0.895, + 0.584 + ], + "angle": 0, + "content": "Blind Image SR. Blind image SR is challenging due to the complex mixture of unknown degradations. Recent studies address the problem from two aspects, i.e., degradation estimation [3, 19, 38, 39, 62] and establishing more realistic training data [4, 28, 33, 66, 70, 75]. The former paradigm mainly focuses on estimating degradation model parameters and then applies non-blind SR methods, e.g., ZSSR [57]. The latter builds training pairs either through capturing real-world LR and HR pairs [4, 70] or designing elaborate degradation models that imitate real-world degradation [28, 33, 66, 75]. Since characters in text images have specific and semantic structures, we show that a good restoration performance cannot be achieved by merely using elaborately designed degradation models." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.584, + 0.897, + 0.903 + ], + "angle": 0, + "content": "Text Image SR. Text image SR has been studied for many years. In traditional methods, maximum a posterior (MAP) [5] and Bayesian framework [9] are exploited for super-resolving text images. These earlier approaches are incapable of generating high-quality results. Dong et al. [13] adopt CNNs (i.e., SRCNN [12]) for text image SR and achieve promising results in the ICDAR 2015 competition [49]. Xu et al. [72] adopt a Generative Adversarial Network (GAN) [17] to learn category-specific prior for face and text images SR, along with the supervision from a multi-class GAN loss. Mou et al. [44] propose to plug a SR unit into the recognition process of degraded text images. Wang et al. [64] introduce the first real-world text SR pairs (i.e., TextZoom), which are cropped from RealSR [4] and SRRAW [77]. They also present a sequential residual block by incorporating Bi-directional LSTM to capture the sequential information for low-level reconstruction. Both RealSR and SRRAW are captured by different digital cameras with different focal lengths, aiming to collect natural LR/HR pairs in real-world scenarios. The setting is not designed specifically for text images. We observe that most HR text images" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "10104" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.091, + 0.47, + 0.122 + ], + "angle": 0, + "content": "in TextZoom are limited in clarity, which could limit the SR performance when taking them as ground-truth." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.129, + 0.473, + 0.433 + ], + "angle": 0, + "content": "Text SR benefits from prior and auxiliary constraints. Quan et al. [51] recover text images in a cascade model by predicting the high-frequency information. Chen et al. [7] propose Transformer-based position-aware and content-aware modules to emphasize the position and the content of each character. Analogously, Nakaune et al. [45] and Qin et al. [50] respectively present the structure-aware loss and content-perceptual constraint for learning detailed structural skeletons. Zhao et al. [78] propose a parallel contextual attention network to learn sequence-dependent features for bringing more high-frequency information into text reconstruction. Zhao et al. [79] exploit linguistic, recognition and visual clues to jointly boost the SR performance. Chen et al. [8] propose a stroke-aware framework by concentrating on stroke-level internal structures. Ma et al. [41] introduce text recognition prior to text reconstruction with a Transformer-based module, leveraging the global attention mechanism. They also embed categorical text priors in the encoder and employ multi-stage refinement to progressively enhance low-resolution images [40]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.44, + 0.473, + 0.576 + ], + "angle": 0, + "content": "Many methods above employ recognition information either as a loss function on the SR results [7, 8, 50, 79] or as intermediate SR features for providing high-level guidance [40, 41]. Albeit the high-level recognition prior helps improve the text recognition ability, it is limited in providing accurate structure and style guidance, especially for certain texts with complex structures. In this study, we show that generative structure prior benefits high-quality guidance to restore the faithful structure of LR characters." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.584, + 0.473, + 0.902 + ], + "angle": 0, + "content": "Generative Structure Prior in Image SR. Image structure prior is proven effective in many low-level vision tasks, e.g., depth image enhancement [21, 27, 37], image inpainting [11, 46, 52], and image restoration [10, 35, 36, 47]. Most recently, by using generative structure priors obtained from pre-trained StyleGANs [30, 31] or codebooks [15], blind face restoration has achieved tremendous improvement [6, 22, 34, 65, 69, 73], suggesting the apparent advantage of such prior over other methods in generating photo-realistic textures. Our study is inspired by the success of these approaches. Nevertheless, crafting a suitable structural prior for text images are harder than face images. This is because each character has its unique strokes, but may have a vast variety of font styles. Any distorted, missing or additional strokes easily change their semantic layout that is easily perceptible, and worsens their actual meaning (see Figure 1). All of these challenges aggravate the difficulties for learning a generative structure prior for the text SR task. In this study, we show an effective way of learning such prior through replacing the constant input of StyleGAN with a discrete codebook, while controlling the font style via the \\(\\mathcal{W}\\) space." + }, + { + "type": "image", + "bbox": [ + 0.527, + 0.083, + 0.868, + 0.187 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.193, + 0.895, + 0.264 + ], + "angle": 0, + "content": "Figure 2. Pre-training generative structure prior for each character. The codebook stores the discrete code of each character, and each code serves as a constant to StyleGAN for generating a specific high-resolution character. The intermediate features encapsulate the generative structure prior and will be used for guiding text SR." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.273, + 0.637, + 0.29 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.298, + 0.895, + 0.571 + ], + "angle": 0, + "content": "A GAN model can well capture the intrinsic structure prior for a category by training the model on abundant images of the same category. Many image restoration tasks [6,20,42,48,65,73] have shown the benefits of using such generative priors for restoring photo-realistic details from LR inputs despite severe and complex degradation. Previous studies mainly use the prior for face restoration, while its application to text SR is under-explored. In this paper, we propose MARCONet, the first attempt to eMbed generative stRuCture priOr for blind text SR. The proposed pipeline is depicted in Figure 3. It mainly contains three parts, 1) the prediction of font style, character bounding boxes and their indexes in codebook based on a given LR input, 2) the generation of the structure prior for each character, 3) the SR framework that takes the generative structure prior as guidance for restoration. Next, we first describe the approach to obtain the generative structure prior for each character, followed by the way to employ such prior for the text SR." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.579, + 0.864, + 0.595 + ], + "angle": 0, + "content": "3.1. Pre-training of Generative Structure Prior" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.603, + 0.894, + 0.722 + ], + "angle": 0, + "content": "The original StyleGANs [30, 31] take a learnable constant as input, and control the style of output image through the \\( w \\in \\mathcal{W} \\) space, which is a projection from the initial latent space \\( z \\in \\mathcal{Z} \\). Layer-wise noise is also introduced to support stochastic variation on fine-grained details. To better capture the structure of text images, we remove the layer-wise noise and replace the single constant with discrete codes that represent different characters (see details in Figure 2)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.723, + 0.894, + 0.814 + ], + "angle": 0, + "content": "We denote each character code as \\( c \\in \\{C_i\\}_{i=1}^M \\), where \\( C \\) is the codebook that stores all the character features. Each code is learnable, with a size of \\( 1 \\times 1 \\times 512 \\). Following CRNN [56], the cardinality of codebook \\( M \\) is set to 6736, a size covering simplified Chinese characters, English letters, and numbers. The retrofitted StyleGAN is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.574, + 0.819, + 0.893, + 0.836 + ], + "angle": 0, + "content": "\\[\n\\mathcal {S} ^ {c} = G (c, \\mathcal {F} (z); \\Theta_ {G}) = G (c, w; \\Theta_ {G}), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.895, + 0.902 + ], + "angle": 0, + "content": "where \\(\\mathcal{F}\\) represents the network that maps \\(z\\) to \\(w\\), and \\(\\Theta_G\\) is the model parameters of StyleGAN. For generalizing to different scenarios, we simplify the structure image \\(S^c\\) with pixel values \\(\\in \\{0,1\\}\\) (see the output in Figure 2). The struc" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10105" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.123, + 0.085, + 0.849, + 0.331 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.339, + 0.895, + 0.381 + ], + "angle": 0, + "content": "Figure 3. Overview of our MARCONet. It contains three parts, i.e., (i) Transformer encoder for predicting the font style, classification and bounding boxes of each character from LR input, (ii) structure prior generation with pre-trained StyleGAN for generating reliable structure prior for each character, and (iii) the SR process for reconstructing the SR output with the incorporation of each characters' structure prior." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.392, + 0.471, + 0.422 + ], + "angle": 0, + "content": "ture prior \\(\\mathcal{P}^c\\) used in this work is the intermediate features from \\(G\\) in Eqn. (1), and can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.207, + 0.428, + 0.47, + 0.443 + ], + "angle": 0, + "content": "\\[\n\\mathcal {P} ^ {c} = G _ {i} (c, w; \\Theta_ {G}), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.449, + 0.471, + 0.464 + ], + "angle": 0, + "content": "where \\( G_{i} \\) represents the output features from \\( i \\)-th layer of \\( G \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.465, + 0.472, + 0.691 + ], + "angle": 0, + "content": "The training of the character StyleGAN can be done on synthetic images yet with satisfying generalization ability to real-world texts. In particular, the PIL package1 is adopted to synthesize high-resolution character images with hundreds of font styles (see examples in the suppl.). We also augment the diversity with random translations, font sizes and slight affine transformation. Different from the original StyleGANs that adopt only adversarial loss [17], we introduce an additional recognition loss derived from a pre-trained Transformer-based recognizer as regularization. Once learned, each learnable code \\( c \\) well captures the distinctive features of each character and \\( w \\in \\mathcal{W} \\) can control the font styles of the output image. In the following, we will describe the approach to extract the structure prior for each character in a given LR text image." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.702, + 0.283, + 0.716 + ], + "angle": 0, + "content": "3.2. Transformer Encoder" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.725, + 0.47, + 0.877 + ], + "angle": 0, + "content": "A LR text image usually is composed of several characters. To derive the generative structure prior for each character, first, we need to obtain the font style \\( w \\) of the LR characters. Second, the indexes of each character in the codebook and their bounding boxes are also necessary for aligning the structure prior with each LR character. To this end, we adopt a Transformer-based encoder to jointly predict the needed information. Transformer [61] is chosen so that we can better capture the dependency across different characters in the input image." + }, + { + "type": "text", + "bbox": [ + 0.506, + 0.392, + 0.895, + 0.619 + ], + "angle": 0, + "content": "Learning to predict the font style \\( w \\) is similar to learning-based GAN inversion [2, 54, 60, 63], where the Transformer network serves as an encoder. It is observed that the Transformer-based encoder achieves satisfactory inversion, achieving reconstruction with low distortion and of high quality [25]. Note that characters in one text image generally have the same font style. So we use one linear layer to map the features of all characters to a single prediction \\( (w) \\), which is shared with all the characters in the same LR image. We also use a similar structure as \\( w \\) prediction to carry out the regression and classification of the bounding boxes and code indexes. These three sub-tasks share the same Transformer encoder (i.e., ViT [14]) and a CNN backbone (i.e., ResNet45 [24]). Positional encoding is incorporated to inject positions of features in the sequence." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.62, + 0.895, + 0.802 + ], + "angle": 0, + "content": "The font style prediction branch is optimized with the gradient from StyleGAN. Since the input text image has unconstrained numbers of characters, we adopt CTC loss [18] for recognition. The loss is proposed to solve the alignment between predicted and target labels and is widely used in scene text recognition tasks. As for the learning of character bounding boxes regression, we adopt a linear combination of the Smooth \\( L_{1} \\) loss [16] and the generalized IoU loss [53]. The ground-truth boxes of each character can be obtained when synthesizing the training images with PIL package. The gradient from the latter text SR network can further benefit the learning process of the whole Transformer encoder." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.816, + 0.774, + 0.832 + ], + "angle": 0, + "content": "3.3. Text Super-resolution Network" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.894, + 0.903 + ], + "angle": 0, + "content": "Network Architecture. With the Transformer encoder, we can obtain the font style \\( w \\), classification label (i.e., index in codebook), and the bounding box for each character in the LR input. Then, the corresponding high-quality generative" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.24, + 0.901 + ], + "angle": 0, + "content": "\\(^{1}\\)https://python-pillow.org/" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "10106" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.104, + 0.085, + 0.445, + 0.324 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.329, + 0.471, + 0.372 + ], + "angle": 0, + "content": "Figure 4. Details of the structure prior transform module. Each LR character is cropped and aligned by using the bounding boxes, and is super-resolved with the guidance of their structure prior." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.385, + 0.473, + 0.701 + ], + "angle": 0, + "content": "structure prior \\(\\mathcal{P}^c\\) for each character can be generated with \\(w\\) and the selected code \\(c\\) through the pre-trained StyleGAN in Eqn. (2) (see the character structure prior in Figure 3). In this section, we describe how to use them for the text SR task. First, a simple UNet [55] is stacked upon the ResNet45 to extract the LR features. Then, the generative structure prior of each character is embedded into their LR characters through a structure prior transform module. The process is shown in Figure 4 (more details can be found in the suppl.). For the LR features, we adopt the detected bounding boxes to crop and align each LR character by RoIAlign operation [23]. For each character, AdaIN [26] is adopted to normalize the prior's distribution, and spatial feature transformation [67] is subsequently employed to predict the affine parameters, which are applied on the LR character features. The reverse RoIAlign is finally used to paste the enhanced features back to their original locations. The structure prior transform module is adopted at two scales \\(s\\in \\{32,64\\}\\), allowing our MARCONet to remain high fidelity with different degradation. A Conv-ReLU-ResBlock based CNN module is stacked to generate the final SR result." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.703, + 0.471, + 0.749 + ], + "angle": 0, + "content": "Learning Objective. We minimize the differences between the SR results \\(\\hat{I}_{SR}\\) and HR ground-truth \\(I_{HR}\\) on both the pixel and perceptual domains [29]:" + }, + { + "type": "equation", + "bbox": [ + 0.085, + 0.755, + 0.47, + 0.79 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {r e c} = \\left\\| \\hat {I} _ {S R} - I _ {H R} \\right\\| _ {1} + \\sum_ {i = 1} ^ {4} \\frac {\\lambda_ {p e r}}{\\mathcal {C} _ {i} \\mathcal {H} _ {i} \\mathcal {W} _ {i}} \\left\\| \\Phi_ {i} (\\hat {I} _ {S R}) - \\Phi_ {i} (I _ {H R}) \\right\\| _ {1}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.794, + 0.469, + 0.855 + ], + "angle": 0, + "content": "where \\(\\mathcal{C}_i\\), \\(\\mathcal{H}_i\\) and \\(\\mathcal{W}_i\\) are the feature dimensions from the \\(i\\)-th convolution layer of the pre-trained VGG-19 model \\(\\Phi\\) [58]. \\(\\lambda_{per}\\) is the trade-off parameter and is set to 0.05. The loss \\(\\mathcal{L}_{rec}\\) is applied to the whole text image." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Adversarial loss [17] \\(\\mathcal{L}_{adv}\\) is also added to improve visual quality. Instead of constraining on the whole image as in Eqn. (3), \\(\\mathcal{L}_{adv}\\) is performed on each cropped character image" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.258 + ], + "angle": 0, + "content": "together with its corresponding structure image as additional conditions [43]. To be specific, the concatenation of HR character image \\( I_{HR}^{c} \\) and its structure image \\( S_{HR}^{c} \\) is expected to be classified as Real, while the concatenation of SR character image \\( \\hat{I}_{SR}^{c} \\) and its structure image \\( S_{SR}^{c} \\) is recognized as Fake. Note that \\( S_{HR}^{c} \\) is the binarized version of \\( I_{HR}^{c} \\), which represents the ground-truth structure, and \\( S_{SR}^{c} \\) is obtained from Eqn. (1) with \\( w \\) and \\( c \\) predicted from LR input. Such design allows us to better constrain the embedding of generative structure prior into the SR results. The hinge version of adversarial loss [74] for each character is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.5, + 0.265, + 0.895, + 0.282 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {D} = - \\mathbb {E} \\left[ \\min \\left(0, - 1 + D \\left(I _ {H R} ^ {c}, S _ {H R} ^ {c}\\right)\\right) \\right] - \\mathbb {E} \\left[ \\min \\left(0, - 1 - D \\left(\\hat {I} _ {S R} ^ {c}, S _ {S R} ^ {c}\\right)\\right) \\right],\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.622, + 0.285, + 0.892, + 0.302 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {G} = - \\mathbb {E} \\left[ D \\left(\\hat {I} _ {S R} ^ {c}, \\mathcal {S} _ {S R} ^ {c}\\right) \\right]. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.309, + 0.892, + 0.355 + ], + "angle": 0, + "content": "Finally, we use the \\(L_{1}\\) loss on structure image \\(\\mathcal{S}^c\\) in the text SR training stage to further fine-tune \\(w\\) and code \\(c\\) in codebook. For each character, this constraint is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.625, + 0.36, + 0.892, + 0.376 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {s t r} = \\left\\| \\mathcal {S} _ {S R} ^ {c} - \\mathcal {S} _ {H R} ^ {c} \\right\\| _ {1}. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.381, + 0.894, + 0.412 + ], + "angle": 0, + "content": "With these learning objectives, the whole framework of MARCONet is optimized in an end-to-end manner." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.424, + 0.634, + 0.441 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.448, + 0.895, + 0.765 + ], + "angle": 0, + "content": "Training Data. In this work, we take Chinese characters as our initial exploration for super-resolving complex characters but with regularity. The same method can be extended to other languages by retraining the framework with specific data. Since a text image is usually composed of several characters, here we use the Chinese corpus from Xu et al. [71], which contains tens of millions of common items. We also collect 182 font families to introduce diverse structures. PIL toolbox is adopted to synthesize these text images, rendered with random RGB values, font sizes and locations. The text background is obtained from DIV2K [1] and Flickr2K [59] datasets, in which each image is randomly cropped and upsampled to \\(\\times 4\\sim 16\\) to synthesize the complex background. With this toolbox, we can obtain the HR text images \\(I_{HR}\\), together with the classification label, bounding box and the ground-truth structure image \\(S_{HR}^{c}\\) of each character. The degradation pipeline presented in BSRGAN [75] and Real-ESRGAN [66] are applied online to degrade the HR image to LR input (see input in Figure 3). Since each text image usually contains varying numbers of characters, we pad zeros to the width dimension to keep the structure unchanged." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.766, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Implementation Details. The training of the whole MARCONet and the pre-training for generative structure prior are conducted on a server with four Tesla V100 GPUs. The batch size is set to 2 and 16, respectively. We employ Adam [32] as the optimizer. The initial learning rate \\( lr \\) is set to \\( 1e - 4 \\) and decreased by 0.5 when \\( \\mathcal{L}_{rec} \\) reaches a stable range on the validation set. The \\( lr \\) for StyleGAN in the text SR training stage is set to \\( 1e - 6 \\) for fine-tuning. The height of HR images is set to 128. Color jittering [80] is used to increase" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10107" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.125, + 0.079, + 0.307, + 0.285 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.308, + 0.079, + 0.543, + 0.284 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.543, + 0.079, + 0.695, + 0.285 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.696, + 0.079, + 0.844, + 0.285 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.097, + 0.293, + 0.871, + 0.308 + ], + "angle": 0, + "content": "Figure 5. Visual comparison on \\(\\times 2\\) (1\\~2 columns) and \\(\\times 4\\) (3\\~4 columns) SR. The stroke details are best viewed by zooming in." + }, + { + "type": "table_caption", + "bbox": [ + 0.116, + 0.32, + 0.43, + 0.334 + ], + "angle": 0, + "content": "Table 1. Quantitative comparison on \\( \\times 2 \\) and \\( \\times 4\\mathrm{{SR}} \\) ." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.339, + 0.472, + 0.448 + ], + "angle": 0, + "content": "
Methods×2×4
PSNR↑SSIM↑LPIPS↓Acc.↑PSNR↑SSIM↑LPIPS↓Acc.↑
SRCNN [12]23.34.868.09582.1719.56.750.21871.41
ESRGAN [68]23.72.891.08583.2519.86.778.20472.12
TSRN [64]24.27.893.09485.8220.67.782.20176.94
TBSRN [7]25.62.906.07492.3721.07.794.18684.32
TATT [41]25.84.907.07393.2621.49.800.18585.17
Ours28.32.941.03399.1624.04.873.09692.53
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.459, + 0.469, + 0.489 + ], + "angle": 0, + "content": "image diversity. It takes two days for pre-training StyleGAN and nearly four days for training the whole MARCONet." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.49, + 0.47, + 0.762 + ], + "angle": 0, + "content": "Baselines. Since there are few works studying the problem of these types of text images on SR task, we compare with two types of methods following TATT [41], i.e., general image SR (i.e., SRCNN [12], ESRGAN [68]) and recent text image SR (i.e., TSRN [64], TBSRN [7] and TATT [41]). For a fair comparison, we modify their codes to handle \\(\\times 2\\) and \\(\\times 4\\) SR tasks, and carefully retrain them with the same training data as Ours. In particular, the retrained TBSRN adopts the ground-truth text and bounding boxes for its pretrained content-aware and position-aware modules. As for TATT, we also use the ground-truth text to pre-train its TPG module. We report the quantitative and qualitative results on our synthetic dataset, which contains 1,000 LR/HR pairs for \\(\\times 2\\) and \\(\\times 4\\) tasks, respectively. These LR inputs are injected with random noise, blurring and JPEG compression, to simulate real-world degradation. We also provide the results on real-world text images collected from different sources. More results can be found in the suppl." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.771, + 0.31, + 0.789 + ], + "angle": 0, + "content": "4.1. Quantitative Comparison" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Table 1 summarizes the PSNR, SSIM and LPIPS [76] of different methods on the synthetic dataset. An additional pre-trained CRNN [56] is used to compute the recognition accuracy of SR results (Acc.), serving as an auxiliary indicator for the restoration performance. Note that the synthetic data is non-trivial given its low quality. Without specifically designed components for text images, general SR methods" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.319, + 0.895, + 0.47 + ], + "angle": 0, + "content": "perform poorly as expected. By incorporating the recognition information, both TBSRN [7] and TATT [41] show obvious improvement, especially in retaining the semantic layout of character for recognition (see Acc. columns). Our method achieves the best quantitative results and outperforms others with a large margin (e.g., 2.5 dB higher than the second-best method on average). Even with severe degradation (i.e., \\(\\times 4\\)), our method still attains favorable performance, which can be ascribed to the effectiveness of the learned generative structure prior for each character." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.479, + 0.722, + 0.495 + ], + "angle": 0, + "content": "4.2. Qualitative Comparison" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.502, + 0.895, + 0.743 + ], + "angle": 0, + "content": "Figure 5 shows the visual comparison on our synthetic LR images for \\(\\times 2\\) and \\(\\times 4\\) tasks. With careful retraining, competing methods perform favorably when the LR input has slight degradation, but they are not able to recover the unique structure of characters with complex strokes. When the degradation turns more severe, all of them fail to restore satisfactory results (see the last column). The results yielded by TBSRN [7] and TATT [41] suggest that high-level recognition constraints bring limited benefit to the SR task, especially in coping with diverse and complex font structures and styles. With the guidance of characters' generative structure prior, our method shows compelling results that exhibit more consistent structures with ground-truth (GT). It is interesting to observe the strong performance of MARCONet in restoring heavily degraded LR input that is challenging for humans to recognize (last column of Figure 5)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.744, + 0.895, + 0.879 + ], + "angle": 0, + "content": "Apart from the evaluation on synthetic LR input, we also evaluate our method on real-world LR text images. We collect real-world LR text images from different sources, e.g., invoices, license plates, scanned documents, road signs, plaques, video captions, and scene texts from TextZoom [64]. Each text region is cropped by \\(\\mathrm{CnSTD}^2\\). We compare with two competing methods, i.e., TBSRN [7] and TATT [41], which are specifically designed for text images and achieve the top quantitative results in Table 1. The results are shown" + }, + { + "type": "page_footnote", + "bbox": [ + 0.517, + 0.887, + 0.729, + 0.9 + ], + "angle": 0, + "content": "\\(^{2}\\)https://github.com/breezeedeus/CnSTD" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10108" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.138, + 0.079, + 0.831, + 0.453 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.459, + 0.879, + 0.473 + ], + "angle": 0, + "content": "Figure 6. Visual comparison on real-world LR text images, including invoice, license plate, scanned document, road sign, plaque, etc." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.485, + 0.474, + 0.698 + ], + "angle": 0, + "content": "in Figure 6. Benefiting from our synthetic training data, the competing methods achieve comparable performance on these characters with simple structures, even for LR inputs corrupted by unknown and complex degradation. The positive results suggest that our synthetic HR text images are of high quality and well-suited as ground-truth for the SR task. The usage of degradation models from BSRGAN [75] and Real-ESRGAN [66] further benefits these methods in synthesizing realistic LR inputs. However, both of these two methods fail to generate plausible results when the LR character is degraded severely or contains complex structures. In contrast, with the proposed generative structure prior, our method achieves the best performance, not only in visual quality, but also in the generation of accurate structures." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.71, + 0.233, + 0.727 + ], + "angle": 0, + "content": "4.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Analyses of \\(\\mathcal{W}\\) Space. The \\(\\mathcal{W}\\) space controls the style of a character's structure prior. Figure 7 shows the structure image \\(S_{SR}^{c}\\) from our StyleGAN with \\(w\\in \\mathcal{W}\\) and character indexes predicted from the LR input. One can observe that \\(w\\) can well capture the manifold of font styles, e.g., the thickness of different font families (1-st column) and different font sizes and locations (2-nd column). We also interpolate two \\(w\\) from different LR inputs and demonstrate their results in the \\(3\\sim 5\\) rows. One can see that the generated structures change smoothly, indicating that \\(w\\) in our framework also has the editable ability like the original StyleGAN. Finally," + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.485, + 0.895, + 0.622 + ], + "angle": 0, + "content": "we use the predicted \\( w \\) from a real-world LR video frame (The Dream of the Red Chamber) and explore font style transfer. Even though the LR input contains a traditional Chinese character and the font family does not exist in our training data, our predicted \\( w \\) can well capture its style and successfully transfer it to other characters. Besides, the \\( w \\) latent and character code \\( c \\) are disentangled, judging from the good separation of roles between the \\( w \\) and \\( c \\) in style control and storing the unique structure for each character." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.897, + 0.902 + ], + "angle": 0, + "content": "Analyses of Variants. Here we consider the following variants to evaluate each part of our MARCONet, 1) Ours \\((UNet)\\) & Ours \\((UNet^{\\dagger})\\): only taking ResNet45 and UNet to perform the SR task and increasing its model parameters, respectively, 2) Ours (CRNN) & Ours (PSP): replacing our Transformer-based character classification and \\(w\\) inversion branches with CRNN [56] and PSP encoder [54], respectively, 3) Ours \\((D^{-})\\): only taking the SR and HR images as input of discriminator without concatenating their structure images, 4) Ours \\((w / o S)\\): removing StyleGAN and directly incorporating the code \\(c\\) on each LR character features through spatial affine transformation, 5) Ours \\((w / o C)\\): removing codebook and directly taking each LR character features into a pre-trained StyleGAN that produces colored output like GFPGAN [65], 6) Ours (#32) & Ours (#64): only using the structure prior transform module on feature sizes of either \\(32 \\times 32\\) or \\(64 \\times 64\\). Their performance on our synthetic test set is shown in Table 2 and Figure 8. We can observe" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "10109" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.129, + 0.079, + 0.377, + 0.33 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.379, + 0.079, + 0.651, + 0.33 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.653, + 0.079, + 0.842, + 0.33 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.337, + 0.892, + 0.365 + ], + "angle": 0, + "content": "Figure 7. The \\(\\mathcal{W}\\) space in StyleGAN controls the font style of characters. The 1-st and 7-th rows are LR input. The 2-nd and 6-th rows are output of StyleGAN with \\(w\\) and code indexes from their LR input. The remaining rows are the interpolation results of \\(w\\) from two LR inputs." + }, + { + "type": "table_caption", + "bbox": [ + 0.078, + 0.375, + 0.468, + 0.388 + ], + "angle": 0, + "content": "Table 2. Comparison of different variants of the proposed method." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.392, + 0.469, + 0.552 + ], + "angle": 0, + "content": "
Variants×2×4
PSNR↑SSIM↑LPIPS↓Acc.↑PSNR↑SSIM↑LPIPS↓Acc.↑
Ours (UNet)23.69.890.09482.6319.84.777.20971.96
Ours (UNet†)23.71.891.09282.7419.87.778.20372.16
Ours (CRNN)28.00.931.03498.8723.98.871.10192.41
Ours (PSP)28.04.932.03599.0723.99.871.09992.49
Ours (D-)28.29.940.03499.1123.94.870.09892.48
Ours (w/o S)25.86.907.07494.6421.57.802.18286.63
Ours (w/o C)25.53.905.04192.2521.39.798.12883.71
Ours (#32)28.16.937.03998.8623.96.870.10192.16
Ours (#64)28.30.940.03599.1024.02.872.09992.33
Ours (Full)28.32.941.03399.1624.04.873.09692.53
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.569, + 0.47, + 0.901 + ], + "angle": 0, + "content": "that a) Ours (UNet) and Ours \\((UNet^{\\dagger})\\) perform on par with general SR methods, and indicate that a mere increase in model capacity would not bring significant performance improvement; b) the Transformer-based encoder is more effective than CRNN [56] and PSP encoder [54], which may be caused by the global attention and thus contribute better to the classification and GAN inversion tasks. It is observed that Ours (CRNN) sometimes makes wrong predictions on character. While the SR leads to a clear image, the character loses its actual semantic layout (see red box in Figure 8); c) the concatenation of structure image on discriminator is beneficial for emphasizing the structure prior more on LR input and thus boosting the final SR result; d) by removing StyleGAN and codebook, Ours \\((w / o S)\\) and Ours \\((w / o C)\\) show obvious inferior results, indicating that codebook can benefit the recognition accuracy while StyleGAN contributes more on the visual quality (e.g., LPIPS); e) Ours (#64) has slightly better results than Ours (#32) but both of them are inferior to Ours (Full) that deploys a multi-scale structure prior transform module. From these analyses, we conclude that the Transformer-based encoder, codebook, StyleGAN and multi-scale structure prior transform module are all crucial" + }, + { + "type": "image", + "bbox": [ + 0.511, + 0.378, + 0.884, + 0.589 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.548, + 0.593, + 0.842, + 0.607 + ], + "angle": 0, + "content": "Figure 8. Visual comparison of different variants." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.619, + 0.813, + 0.634 + ], + "angle": 0, + "content": "for achieving good performance in Ours (Full)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.648, + 0.618, + 0.663 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.673, + 0.894, + 0.838 + ], + "angle": 0, + "content": "In this work, we made the first attempt to embed the generative structure prior for blind SR of text images. The combination of a codebook for storing distinctive character-specific codes and a retrofitted StyleGAN for controlling font style cope well with complicated structures, high similarity between characters, and a great variety of font styles. We have shown that such structure prior is beneficial for super-resolving LR text images, even for those with severe degradation. We can potentially extend it to other text-related tasks, e.g., text image completion for ancient documents, font style transformation, and few-shot font generation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Acknowledgement. This study is supported under the RIE2020 Industry Alignment Fund - Industry Collaboration Projects (IAF-ICP) Funding Initiative, as well as cash and in-kind contribution from the industry partner(s)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10110" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.471, + 0.156 + ], + "angle": 0, + "content": "[1] Eirikur Agustsson and Radu Timofte. NTIRE 2017 challenge on single image super-resolution: Dataset and study. In CVPRW, 2017. 5" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.159, + 0.472, + 0.2 + ], + "angle": 0, + "content": "[2] Yuval Alaluf, Omer Tov, Ron Mokady, Rinon Gal, and Amit Bermano. Hyperstyle: StyleGAN inversion with hypernetworks for real image editing. 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Results obtained with TBSRN [7], TATT [41] and our approach on the segments of Chinese text image cropped from a real low-resolution invoice and a signboard. Both baselines are re-trained with elaborated degradations as in BSRGAN [75] and Real-ESRGAN [66]. + +# Abstract + +Blind text image super-resolution (SR) is challenging as one needs to cope with diverse font styles and unknown degradation. To address the problem, existing methods perform character recognition in parallel to regularize the SR task, either through a loss constraint or intermediate feature condition. Nonetheless, the high-level prior could still fail when encountering severe degradation. The problem is further compounded given characters of complex structures, e.g., Chinese characters that combine multiple pictographic or ideographic symbols into a single character. In this work, we present a novel prior that focuses more on the character structure. In particular, we learn to encapsulate rich and diverse structures in a StyleGAN and exploit such generative structure priors for restoration. To restrict the generative space of StyleGAN so that it obeys the structure of characters yet remains flexible in handling different font styles, we store the discrete features for each character in a codebook. The code subsequently drives the StyleGAN to generate high-resolution structural details to aid text SR. Compared to priors based on character recognition, the proposed structure prior exerts stronger character-specific guidance to restore faithful and precise strokes of a designated character. Extensive experiments on synthetic and real datasets demonstrate the compelling performance of the proposed generative structure prior in facilitating robust text SR. Our code is available at https://github.com/csxmli2016/MARCONet. + +# 1. Introduction + +Blind text super-resolution (SR) aims at restoring a high-resolution (HR) image from a low-resolution (LR) text image that is corrupted by unknown degradation. The problem is relatively less explored than SR of natural and face images. + +This seemingly easy task actually possesses many unique challenges. In particular, each character owns its unique structure. A suboptimal restoration that destroys the structure with, e.g., distorted, missing or additional strokes, is easily perceptible and may alter the meaning of the original word. The task becomes more difficult when dealing with writing systems such as Chinese, Kanji and Hanja characters, in which the patterns of thousands of characters vary in complex ways and are mostly composed of different subunits (or compound ideographs). A slight deviation in strokes, say '太' and '大' carries entirely different meanings. The problem becomes more intricate given the different typefaces. In addition, complex and unknown degradation make the data-driven convolutional neural networks (CNNs) incapable of generalizing well to real-world degraded observations. + +To ameliorate the difficulties in blind text SR, especially in retaining the unique structure of each character, recent studies design new loss functions to constrain SR results semantically close to the high-resolution (HR) groundtruth [7,8,45,50,79], or incorporate the recognition prior into the intermediate features [40, 41, 44]. Figure 1 shows several representative results of these two types of methods, i.e., TB-SRN [7] that applies content-aware constraint and TATT [41] + +that embeds the recognition prior into the SR process. The results are not satisfactory despite the models were retrained with data synthesized with sophisticated degradation models, i.e., BSRGAN [75] and Real-ESRGAN [66]. TBSRN and TATT perform well when the LR character has fewer strokes. However, they both fail to generate the desired structures when the character is composed of complex strokes, e.g., the 4, 6, 8, 11-th characters in (a). The results suggest that high-level recognition prior cannot well benefit the SR task in restoring faithful and accurate structures. + +When dealing with complex characters, we can identify some commonly used strokes as constituents of characters or their subparts. These obvious structural regularities have not been studied thoroughly in the literature. In particular, most existing text SR studies [7, 40, 41, 45, 50, 79] focus on scene text images that are presented in different view perspectives or arranged in irregular patterns. In contrast, our goal is to explore structural regularities specific to complex characters and investigate an effective way to exploit the prior. The investigation has practical values in many applications, including the restoration of old printed media (e.g., newspapers or books) for digitalization and preservation, and the enhancement of captions in digital media. + +The key idea of our solution is to mine structure prior from a generative network, and use the prior to facilitate blind SR of text images. To capture the structure prior of characters, we train a StyleGAN to generate characters of different styles. As our intent is not to generate infinite and non-repetitive results, we restrict the generative space of StyleGAN to obey the structure of characters by constraining the generation with a codebook. Specifically, the codebook stores the discrete code of each character, and each code serves as a constant to StyleGAN for generating a specific high-resolution character. The font style is governed by the $\mathcal{W}$ latent space of StyleGAN. Once the character StyleGAN is trained, we can extract its intermediate features serving as the generative structure prior, which encapsulates the intrinsic structure and style of the LR character. + +Using the prior for text SR can be conveniently achieved through an additional Transformer-based encoder and a text SR network that accepts prior. In particular, given a text image that constitutes multiple characters (e.g., Figure 1), we use a Transformer-based encoder to predict the font style, character bounding boxes, and their respective indexes in the codebook jointly. The codebook indexes drive the structure prior generation for each character. In the text SR network, each LR character is super-resolved, guided by the respective priors that are aligned using their bounding boxes. + +Experiments demonstrate that our design can generate robust and consistent structure priors for diverse and severely degraded text input. With the embedded structure prior, our approach performs superior against state-of-the-art methods in generating photo-realistic text results and shows excellent + +generalization to real-world LR text images. While our study mainly employs Chinese characters as examples, the proposed method can be readily extended to characters of other languages. We call our approach as MARCONet. The main contributions are summarized as follows: + +- We show that blind SR task, especially for characters with complex structures, can be restored by using their structure prior encapsulated in a generative network. +- We present a viable way of learning such generative structure prior through reformulating a StyleGAN by replacing its single constant with discrete codes that represent different characters. +- To retrieve the prior accurately, we propose a Transformer-based encoder to jointly predict the font styles, character bounding boxes and their indexes in codebook from the LR input. + +# 2. Related Work + +Blind Image SR. Blind image SR is challenging due to the complex mixture of unknown degradations. Recent studies address the problem from two aspects, i.e., degradation estimation [3, 19, 38, 39, 62] and establishing more realistic training data [4, 28, 33, 66, 70, 75]. The former paradigm mainly focuses on estimating degradation model parameters and then applies non-blind SR methods, e.g., ZSSR [57]. The latter builds training pairs either through capturing real-world LR and HR pairs [4, 70] or designing elaborate degradation models that imitate real-world degradation [28, 33, 66, 75]. Since characters in text images have specific and semantic structures, we show that a good restoration performance cannot be achieved by merely using elaborately designed degradation models. + +Text Image SR. Text image SR has been studied for many years. In traditional methods, maximum a posterior (MAP) [5] and Bayesian framework [9] are exploited for super-resolving text images. These earlier approaches are incapable of generating high-quality results. Dong et al. [13] adopt CNNs (i.e., SRCNN [12]) for text image SR and achieve promising results in the ICDAR 2015 competition [49]. Xu et al. [72] adopt a Generative Adversarial Network (GAN) [17] to learn category-specific prior for face and text images SR, along with the supervision from a multi-class GAN loss. Mou et al. [44] propose to plug a SR unit into the recognition process of degraded text images. Wang et al. [64] introduce the first real-world text SR pairs (i.e., TextZoom), which are cropped from RealSR [4] and SRRAW [77]. They also present a sequential residual block by incorporating Bi-directional LSTM to capture the sequential information for low-level reconstruction. Both RealSR and SRRAW are captured by different digital cameras with different focal lengths, aiming to collect natural LR/HR pairs in real-world scenarios. The setting is not designed specifically for text images. We observe that most HR text images + +in TextZoom are limited in clarity, which could limit the SR performance when taking them as ground-truth. + +Text SR benefits from prior and auxiliary constraints. Quan et al. [51] recover text images in a cascade model by predicting the high-frequency information. Chen et al. [7] propose Transformer-based position-aware and content-aware modules to emphasize the position and the content of each character. Analogously, Nakaune et al. [45] and Qin et al. [50] respectively present the structure-aware loss and content-perceptual constraint for learning detailed structural skeletons. Zhao et al. [78] propose a parallel contextual attention network to learn sequence-dependent features for bringing more high-frequency information into text reconstruction. Zhao et al. [79] exploit linguistic, recognition and visual clues to jointly boost the SR performance. Chen et al. [8] propose a stroke-aware framework by concentrating on stroke-level internal structures. Ma et al. [41] introduce text recognition prior to text reconstruction with a Transformer-based module, leveraging the global attention mechanism. They also embed categorical text priors in the encoder and employ multi-stage refinement to progressively enhance low-resolution images [40]. + +Many methods above employ recognition information either as a loss function on the SR results [7, 8, 50, 79] or as intermediate SR features for providing high-level guidance [40, 41]. Albeit the high-level recognition prior helps improve the text recognition ability, it is limited in providing accurate structure and style guidance, especially for certain texts with complex structures. In this study, we show that generative structure prior benefits high-quality guidance to restore the faithful structure of LR characters. + +Generative Structure Prior in Image SR. Image structure prior is proven effective in many low-level vision tasks, e.g., depth image enhancement [21, 27, 37], image inpainting [11, 46, 52], and image restoration [10, 35, 36, 47]. Most recently, by using generative structure priors obtained from pre-trained StyleGANs [30, 31] or codebooks [15], blind face restoration has achieved tremendous improvement [6, 22, 34, 65, 69, 73], suggesting the apparent advantage of such prior over other methods in generating photo-realistic textures. Our study is inspired by the success of these approaches. Nevertheless, crafting a suitable structural prior for text images are harder than face images. This is because each character has its unique strokes, but may have a vast variety of font styles. Any distorted, missing or additional strokes easily change their semantic layout that is easily perceptible, and worsens their actual meaning (see Figure 1). All of these challenges aggravate the difficulties for learning a generative structure prior for the text SR task. In this study, we show an effective way of learning such prior through replacing the constant input of StyleGAN with a discrete codebook, while controlling the font style via the $\mathcal{W}$ space. + +![](images/17169bbb912c04f587ae6c3095542eebd27198c4c059b3acd23576f88c151726.jpg) +Figure 2. Pre-training generative structure prior for each character. The codebook stores the discrete code of each character, and each code serves as a constant to StyleGAN for generating a specific high-resolution character. The intermediate features encapsulate the generative structure prior and will be used for guiding text SR. + +# 3. Methodology + +A GAN model can well capture the intrinsic structure prior for a category by training the model on abundant images of the same category. Many image restoration tasks [6,20,42,48,65,73] have shown the benefits of using such generative priors for restoring photo-realistic details from LR inputs despite severe and complex degradation. Previous studies mainly use the prior for face restoration, while its application to text SR is under-explored. In this paper, we propose MARCONet, the first attempt to eMbed generative stRuCture priOr for blind text SR. The proposed pipeline is depicted in Figure 3. It mainly contains three parts, 1) the prediction of font style, character bounding boxes and their indexes in codebook based on a given LR input, 2) the generation of the structure prior for each character, 3) the SR framework that takes the generative structure prior as guidance for restoration. Next, we first describe the approach to obtain the generative structure prior for each character, followed by the way to employ such prior for the text SR. + +# 3.1. Pre-training of Generative Structure Prior + +The original StyleGANs [30, 31] take a learnable constant as input, and control the style of output image through the $w \in \mathcal{W}$ space, which is a projection from the initial latent space $z \in \mathcal{Z}$ . Layer-wise noise is also introduced to support stochastic variation on fine-grained details. To better capture the structure of text images, we remove the layer-wise noise and replace the single constant with discrete codes that represent different characters (see details in Figure 2). + +We denote each character code as $c \in \{C_i\}_{i=1}^M$ , where $C$ is the codebook that stores all the character features. Each code is learnable, with a size of $1 \times 1 \times 512$ . Following CRNN [56], the cardinality of codebook $M$ is set to 6736, a size covering simplified Chinese characters, English letters, and numbers. The retrofitted StyleGAN is defined as: + +$$ +\mathcal {S} ^ {c} = G (c, \mathcal {F} (z); \Theta_ {G}) = G (c, w; \Theta_ {G}), \tag {1} +$$ + +where $\mathcal{F}$ represents the network that maps $z$ to $w$ , and $\Theta_G$ is the model parameters of StyleGAN. For generalizing to different scenarios, we simplify the structure image $S^c$ with pixel values $\in \{0,1\}$ (see the output in Figure 2). The struc + +![](images/e7d50faef30a02e067e145f865c675e5ecfe7fa4e31126df0288700cba61f00f.jpg) +Figure 3. Overview of our MARCONet. It contains three parts, i.e., (i) Transformer encoder for predicting the font style, classification and bounding boxes of each character from LR input, (ii) structure prior generation with pre-trained StyleGAN for generating reliable structure prior for each character, and (iii) the SR process for reconstructing the SR output with the incorporation of each characters' structure prior. + +ture prior $\mathcal{P}^c$ used in this work is the intermediate features from $G$ in Eqn. (1), and can be formulated as: + +$$ +\mathcal {P} ^ {c} = G _ {i} (c, w; \Theta_ {G}), \tag {2} +$$ + +where $G_{i}$ represents the output features from $i$ -th layer of $G$ . + +The training of the character StyleGAN can be done on synthetic images yet with satisfying generalization ability to real-world texts. In particular, the PIL package1 is adopted to synthesize high-resolution character images with hundreds of font styles (see examples in the suppl.). We also augment the diversity with random translations, font sizes and slight affine transformation. Different from the original StyleGANs that adopt only adversarial loss [17], we introduce an additional recognition loss derived from a pre-trained Transformer-based recognizer as regularization. Once learned, each learnable code $c$ well captures the distinctive features of each character and $w \in \mathcal{W}$ can control the font styles of the output image. In the following, we will describe the approach to extract the structure prior for each character in a given LR text image. + +# 3.2. Transformer Encoder + +A LR text image usually is composed of several characters. To derive the generative structure prior for each character, first, we need to obtain the font style $w$ of the LR characters. Second, the indexes of each character in the codebook and their bounding boxes are also necessary for aligning the structure prior with each LR character. To this end, we adopt a Transformer-based encoder to jointly predict the needed information. Transformer [61] is chosen so that we can better capture the dependency across different characters in the input image. + +Learning to predict the font style $w$ is similar to learning-based GAN inversion [2, 54, 60, 63], where the Transformer network serves as an encoder. It is observed that the Transformer-based encoder achieves satisfactory inversion, achieving reconstruction with low distortion and of high quality [25]. Note that characters in one text image generally have the same font style. So we use one linear layer to map the features of all characters to a single prediction $(w)$ , which is shared with all the characters in the same LR image. We also use a similar structure as $w$ prediction to carry out the regression and classification of the bounding boxes and code indexes. These three sub-tasks share the same Transformer encoder (i.e., ViT [14]) and a CNN backbone (i.e., ResNet45 [24]). Positional encoding is incorporated to inject positions of features in the sequence. + +The font style prediction branch is optimized with the gradient from StyleGAN. Since the input text image has unconstrained numbers of characters, we adopt CTC loss [18] for recognition. The loss is proposed to solve the alignment between predicted and target labels and is widely used in scene text recognition tasks. As for the learning of character bounding boxes regression, we adopt a linear combination of the Smooth $L_{1}$ loss [16] and the generalized IoU loss [53]. The ground-truth boxes of each character can be obtained when synthesizing the training images with PIL package. The gradient from the latter text SR network can further benefit the learning process of the whole Transformer encoder. + +# 3.3. Text Super-resolution Network + +Network Architecture. With the Transformer encoder, we can obtain the font style $w$ , classification label (i.e., index in codebook), and the bounding box for each character in the LR input. Then, the corresponding high-quality generative + +![](images/09a5a31c549c2a7145a686f178c962d85aae3dfe2be0f611c405e1ab6e3bc319.jpg) +Figure 4. Details of the structure prior transform module. Each LR character is cropped and aligned by using the bounding boxes, and is super-resolved with the guidance of their structure prior. + +structure prior $\mathcal{P}^c$ for each character can be generated with $w$ and the selected code $c$ through the pre-trained StyleGAN in Eqn. (2) (see the character structure prior in Figure 3). In this section, we describe how to use them for the text SR task. First, a simple UNet [55] is stacked upon the ResNet45 to extract the LR features. Then, the generative structure prior of each character is embedded into their LR characters through a structure prior transform module. The process is shown in Figure 4 (more details can be found in the suppl.). For the LR features, we adopt the detected bounding boxes to crop and align each LR character by RoIAlign operation [23]. For each character, AdaIN [26] is adopted to normalize the prior's distribution, and spatial feature transformation [67] is subsequently employed to predict the affine parameters, which are applied on the LR character features. The reverse RoIAlign is finally used to paste the enhanced features back to their original locations. The structure prior transform module is adopted at two scales $s\in \{32,64\}$ , allowing our MARCONet to remain high fidelity with different degradation. A Conv-ReLU-ResBlock based CNN module is stacked to generate the final SR result. + +Learning Objective. We minimize the differences between the SR results $\hat{I}_{SR}$ and HR ground-truth $I_{HR}$ on both the pixel and perceptual domains [29]: + +$$ +\mathcal {L} _ {r e c} = \left\| \hat {I} _ {S R} - I _ {H R} \right\| _ {1} + \sum_ {i = 1} ^ {4} \frac {\lambda_ {p e r}}{\mathcal {C} _ {i} \mathcal {H} _ {i} \mathcal {W} _ {i}} \left\| \Phi_ {i} (\hat {I} _ {S R}) - \Phi_ {i} (I _ {H R}) \right\| _ {1}, \tag {3} +$$ + +where $\mathcal{C}_i$ , $\mathcal{H}_i$ and $\mathcal{W}_i$ are the feature dimensions from the $i$ -th convolution layer of the pre-trained VGG-19 model $\Phi$ [58]. $\lambda_{per}$ is the trade-off parameter and is set to 0.05. The loss $\mathcal{L}_{rec}$ is applied to the whole text image. + +Adversarial loss [17] $\mathcal{L}_{adv}$ is also added to improve visual quality. Instead of constraining on the whole image as in Eqn. (3), $\mathcal{L}_{adv}$ is performed on each cropped character image + +together with its corresponding structure image as additional conditions [43]. To be specific, the concatenation of HR character image $I_{HR}^{c}$ and its structure image $S_{HR}^{c}$ is expected to be classified as Real, while the concatenation of SR character image $\hat{I}_{SR}^{c}$ and its structure image $S_{SR}^{c}$ is recognized as Fake. Note that $S_{HR}^{c}$ is the binarized version of $I_{HR}^{c}$ , which represents the ground-truth structure, and $S_{SR}^{c}$ is obtained from Eqn. (1) with $w$ and $c$ predicted from LR input. Such design allows us to better constrain the embedding of generative structure prior into the SR results. The hinge version of adversarial loss [74] for each character is defined as: + +$$ +\mathcal {L} _ {D} = - \mathbb {E} \left[ \min \left(0, - 1 + D \left(I _ {H R} ^ {c}, S _ {H R} ^ {c}\right)\right) \right] - \mathbb {E} \left[ \min \left(0, - 1 - D \left(\hat {I} _ {S R} ^ {c}, S _ {S R} ^ {c}\right)\right) \right], +$$ + +$$ +\mathcal {L} _ {G} = - \mathbb {E} \left[ D \left(\hat {I} _ {S R} ^ {c}, \mathcal {S} _ {S R} ^ {c}\right) \right]. \tag {4} +$$ + +Finally, we use the $L_{1}$ loss on structure image $\mathcal{S}^c$ in the text SR training stage to further fine-tune $w$ and code $c$ in codebook. For each character, this constraint is defined as: + +$$ +\mathcal {L} _ {s t r} = \left\| \mathcal {S} _ {S R} ^ {c} - \mathcal {S} _ {H R} ^ {c} \right\| _ {1}. \tag {5} +$$ + +With these learning objectives, the whole framework of MARCONet is optimized in an end-to-end manner. + +# 4. Experiments + +Training Data. In this work, we take Chinese characters as our initial exploration for super-resolving complex characters but with regularity. The same method can be extended to other languages by retraining the framework with specific data. Since a text image is usually composed of several characters, here we use the Chinese corpus from Xu et al. [71], which contains tens of millions of common items. We also collect 182 font families to introduce diverse structures. PIL toolbox is adopted to synthesize these text images, rendered with random RGB values, font sizes and locations. The text background is obtained from DIV2K [1] and Flickr2K [59] datasets, in which each image is randomly cropped and upsampled to $\times 4\sim 16$ to synthesize the complex background. With this toolbox, we can obtain the HR text images $I_{HR}$ , together with the classification label, bounding box and the ground-truth structure image $S_{HR}^{c}$ of each character. The degradation pipeline presented in BSRGAN [75] and Real-ESRGAN [66] are applied online to degrade the HR image to LR input (see input in Figure 3). Since each text image usually contains varying numbers of characters, we pad zeros to the width dimension to keep the structure unchanged. + +Implementation Details. The training of the whole MARCONet and the pre-training for generative structure prior are conducted on a server with four Tesla V100 GPUs. The batch size is set to 2 and 16, respectively. We employ Adam [32] as the optimizer. The initial learning rate $lr$ is set to $1e - 4$ and decreased by 0.5 when $\mathcal{L}_{rec}$ reaches a stable range on the validation set. The $lr$ for StyleGAN in the text SR training stage is set to $1e - 6$ for fine-tuning. The height of HR images is set to 128. Color jittering [80] is used to increase + +![](images/05be199feca5a9bfbf15527fc1a6c007dd522e6bbb0f636f5b65ec62611e56bc.jpg) +Figure 5. Visual comparison on $\times 2$ (1\~2 columns) and $\times 4$ (3\~4 columns) SR. The stroke details are best viewed by zooming in. + +![](images/b5c8c8c3c992fdae0e04d7cac547f6c8e6708ea025b6a608c0499f18336669bf.jpg) + +![](images/2cabfbfc1adc0c4b5db5941e05ade02c2d715f0ee47938749a274bdc551cf3ef.jpg) + +![](images/177fa6f33977f954dd09e72fac03ca5e7d66caca143aa430c743dc976a6f5237.jpg) + +Table 1. Quantitative comparison on $\times 2$ and $\times 4\mathrm{{SR}}$ . + +
Methods×2×4
PSNR↑SSIM↑LPIPS↓Acc.↑PSNR↑SSIM↑LPIPS↓Acc.↑
SRCNN [12]23.34.868.09582.1719.56.750.21871.41
ESRGAN [68]23.72.891.08583.2519.86.778.20472.12
TSRN [64]24.27.893.09485.8220.67.782.20176.94
TBSRN [7]25.62.906.07492.3721.07.794.18684.32
TATT [41]25.84.907.07393.2621.49.800.18585.17
Ours28.32.941.03399.1624.04.873.09692.53
+ +image diversity. It takes two days for pre-training StyleGAN and nearly four days for training the whole MARCONet. + +Baselines. Since there are few works studying the problem of these types of text images on SR task, we compare with two types of methods following TATT [41], i.e., general image SR (i.e., SRCNN [12], ESRGAN [68]) and recent text image SR (i.e., TSRN [64], TBSRN [7] and TATT [41]). For a fair comparison, we modify their codes to handle $\times 2$ and $\times 4$ SR tasks, and carefully retrain them with the same training data as Ours. In particular, the retrained TBSRN adopts the ground-truth text and bounding boxes for its pretrained content-aware and position-aware modules. As for TATT, we also use the ground-truth text to pre-train its TPG module. We report the quantitative and qualitative results on our synthetic dataset, which contains 1,000 LR/HR pairs for $\times 2$ and $\times 4$ tasks, respectively. These LR inputs are injected with random noise, blurring and JPEG compression, to simulate real-world degradation. We also provide the results on real-world text images collected from different sources. More results can be found in the suppl. + +# 4.1. Quantitative Comparison + +Table 1 summarizes the PSNR, SSIM and LPIPS [76] of different methods on the synthetic dataset. An additional pre-trained CRNN [56] is used to compute the recognition accuracy of SR results (Acc.), serving as an auxiliary indicator for the restoration performance. Note that the synthetic data is non-trivial given its low quality. Without specifically designed components for text images, general SR methods + +perform poorly as expected. By incorporating the recognition information, both TBSRN [7] and TATT [41] show obvious improvement, especially in retaining the semantic layout of character for recognition (see Acc. columns). Our method achieves the best quantitative results and outperforms others with a large margin (e.g., 2.5 dB higher than the second-best method on average). Even with severe degradation (i.e., $\times 4$ ), our method still attains favorable performance, which can be ascribed to the effectiveness of the learned generative structure prior for each character. + +# 4.2. Qualitative Comparison + +Figure 5 shows the visual comparison on our synthetic LR images for $\times 2$ and $\times 4$ tasks. With careful retraining, competing methods perform favorably when the LR input has slight degradation, but they are not able to recover the unique structure of characters with complex strokes. When the degradation turns more severe, all of them fail to restore satisfactory results (see the last column). The results yielded by TBSRN [7] and TATT [41] suggest that high-level recognition constraints bring limited benefit to the SR task, especially in coping with diverse and complex font structures and styles. With the guidance of characters' generative structure prior, our method shows compelling results that exhibit more consistent structures with ground-truth (GT). It is interesting to observe the strong performance of MARCONet in restoring heavily degraded LR input that is challenging for humans to recognize (last column of Figure 5). + +Apart from the evaluation on synthetic LR input, we also evaluate our method on real-world LR text images. We collect real-world LR text images from different sources, e.g., invoices, license plates, scanned documents, road signs, plaques, video captions, and scene texts from TextZoom [64]. Each text region is cropped by $\mathrm{CnSTD}^2$ . We compare with two competing methods, i.e., TBSRN [7] and TATT [41], which are specifically designed for text images and achieve the top quantitative results in Table 1. The results are shown + +![](images/cce5c68a6860a978ed4574feea5a37d7a72d289a11c6f7564d65a68b865fc8ba.jpg) +Figure 6. Visual comparison on real-world LR text images, including invoice, license plate, scanned document, road sign, plaque, etc. + +in Figure 6. Benefiting from our synthetic training data, the competing methods achieve comparable performance on these characters with simple structures, even for LR inputs corrupted by unknown and complex degradation. The positive results suggest that our synthetic HR text images are of high quality and well-suited as ground-truth for the SR task. The usage of degradation models from BSRGAN [75] and Real-ESRGAN [66] further benefits these methods in synthesizing realistic LR inputs. However, both of these two methods fail to generate plausible results when the LR character is degraded severely or contains complex structures. In contrast, with the proposed generative structure prior, our method achieves the best performance, not only in visual quality, but also in the generation of accurate structures. + +# 4.3. Ablation Study + +Analyses of $\mathcal{W}$ Space. The $\mathcal{W}$ space controls the style of a character's structure prior. Figure 7 shows the structure image $S_{SR}^{c}$ from our StyleGAN with $w\in \mathcal{W}$ and character indexes predicted from the LR input. One can observe that $w$ can well capture the manifold of font styles, e.g., the thickness of different font families (1-st column) and different font sizes and locations (2-nd column). We also interpolate two $w$ from different LR inputs and demonstrate their results in the $3\sim 5$ rows. One can see that the generated structures change smoothly, indicating that $w$ in our framework also has the editable ability like the original StyleGAN. Finally, + +we use the predicted $w$ from a real-world LR video frame (The Dream of the Red Chamber) and explore font style transfer. Even though the LR input contains a traditional Chinese character and the font family does not exist in our training data, our predicted $w$ can well capture its style and successfully transfer it to other characters. Besides, the $w$ latent and character code $c$ are disentangled, judging from the good separation of roles between the $w$ and $c$ in style control and storing the unique structure for each character. + +Analyses of Variants. Here we consider the following variants to evaluate each part of our MARCONet, 1) Ours $(UNet)$ & Ours $(UNet^{\dagger})$ : only taking ResNet45 and UNet to perform the SR task and increasing its model parameters, respectively, 2) Ours (CRNN) & Ours (PSP): replacing our Transformer-based character classification and $w$ inversion branches with CRNN [56] and PSP encoder [54], respectively, 3) Ours $(D^{-})$ : only taking the SR and HR images as input of discriminator without concatenating their structure images, 4) Ours $(w / o S)$ : removing StyleGAN and directly incorporating the code $c$ on each LR character features through spatial affine transformation, 5) Ours $(w / o C)$ : removing codebook and directly taking each LR character features into a pre-trained StyleGAN that produces colored output like GFPGAN [65], 6) Ours (#32) & Ours (#64): only using the structure prior transform module on feature sizes of either $32 \times 32$ or $64 \times 64$ . Their performance on our synthetic test set is shown in Table 2 and Figure 8. We can observe + +![](images/c883fe39ae803d3bfe151e28331dbb34771946ce3de864516131f2cb560cdc2a.jpg) +Figure 7. The $\mathcal{W}$ space in StyleGAN controls the font style of characters. The 1-st and 7-th rows are LR input. The 2-nd and 6-th rows are output of StyleGAN with $w$ and code indexes from their LR input. The remaining rows are the interpolation results of $w$ from two LR inputs. + +![](images/fd00eabebcc0dc241e083d9c1aae0c416446f51291a6a29e1fe5c0a0a385f656.jpg) + +![](images/ed5a75e65ae181afc2d420fa9915d8238d90f73981f52d58342375646f2b0118.jpg) + +Table 2. Comparison of different variants of the proposed method. + +
Variants×2×4
PSNR↑SSIM↑LPIPS↓Acc.↑PSNR↑SSIM↑LPIPS↓Acc.↑
Ours (UNet)23.69.890.09482.6319.84.777.20971.96
Ours (UNet†)23.71.891.09282.7419.87.778.20372.16
Ours (CRNN)28.00.931.03498.8723.98.871.10192.41
Ours (PSP)28.04.932.03599.0723.99.871.09992.49
Ours (D-)28.29.940.03499.1123.94.870.09892.48
Ours (w/o S)25.86.907.07494.6421.57.802.18286.63
Ours (w/o C)25.53.905.04192.2521.39.798.12883.71
Ours (#32)28.16.937.03998.8623.96.870.10192.16
Ours (#64)28.30.940.03599.1024.02.872.09992.33
Ours (Full)28.32.941.03399.1624.04.873.09692.53
+ +that a) Ours (UNet) and Ours $(UNet^{\dagger})$ perform on par with general SR methods, and indicate that a mere increase in model capacity would not bring significant performance improvement; b) the Transformer-based encoder is more effective than CRNN [56] and PSP encoder [54], which may be caused by the global attention and thus contribute better to the classification and GAN inversion tasks. It is observed that Ours (CRNN) sometimes makes wrong predictions on character. While the SR leads to a clear image, the character loses its actual semantic layout (see red box in Figure 8); c) the concatenation of structure image on discriminator is beneficial for emphasizing the structure prior more on LR input and thus boosting the final SR result; d) by removing StyleGAN and codebook, Ours $(w / o S)$ and Ours $(w / o C)$ show obvious inferior results, indicating that codebook can benefit the recognition accuracy while StyleGAN contributes more on the visual quality (e.g., LPIPS); e) Ours (#64) has slightly better results than Ours (#32) but both of them are inferior to Ours (Full) that deploys a multi-scale structure prior transform module. From these analyses, we conclude that the Transformer-based encoder, codebook, StyleGAN and multi-scale structure prior transform module are all crucial + +![](images/d3e51e4657c5930b1ae78e22b1c03551c9a25db6ace27e70a71d29194c5b1dcd.jpg) +Figure 8. Visual comparison of different variants. + +for achieving good performance in Ours (Full). + +# 5. Conclusion + +In this work, we made the first attempt to embed the generative structure prior for blind SR of text images. The combination of a codebook for storing distinctive character-specific codes and a retrofitted StyleGAN for controlling font style cope well with complicated structures, high similarity between characters, and a great variety of font styles. We have shown that such structure prior is beneficial for super-resolving LR text images, even for those with severe degradation. We can potentially extend it to other text-related tasks, e.g., text image completion for ancient documents, font style transformation, and few-shot font generation. + +Acknowledgement. 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In ECCV, 2020. 5 \ No newline at end of file diff --git a/2023/Learning Generative Structure Prior for Blind Text Image Super-Resolution/images.zip b/2023/Learning Generative Structure Prior for Blind Text Image Super-Resolution/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..36d06f8940f7dbfa3f87e776400f16a64f86b247 --- /dev/null +++ b/2023/Learning Generative Structure Prior for Blind Text Image Super-Resolution/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:f715b966ef70c2942c1ac870217c18847efbcc43697dabc92b88fd3b827bc367 +size 986049 diff --git a/2023/Learning Generative Structure Prior for Blind Text Image Super-Resolution/layout.json b/2023/Learning Generative Structure Prior for Blind Text Image Super-Resolution/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..7ed3b4800d193cefc1daaca8b4bd3e5300b7251f --- /dev/null +++ b/2023/Learning Generative Structure Prior for Blind Text Image 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+ 201, + 312, + 317 + ], + "blocks": [ + { + "bbox": [ + 48, + 201, + 312, + 317 + ], + "lines": [ + { + "bbox": [ + 48, + 201, + 312, + 317 + ], + "spans": [ + { + "bbox": [ + 48, + 201, + 312, + 317 + ], + "type": "image", + "image_path": "466893e9af6dc1b2210461344024164f4205ec286ea9669a51a9d399719040aa.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 70, + 322, + 301, + 333 + ], + "lines": [ + { + "bbox": [ + 70, + 322, + 301, + 333 + ], + "spans": [ + { + "bbox": [ + 70, + 322, + 301, + 333 + ], + "type": "text", + "content": "(a) A real-world LR text image cropped from a Chinese invoice" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 313, + 201, + 545, + 321 + ], + "blocks": [ + { + "bbox": [ + 313, + 201, + 545, + 321 + ], + "lines": [ + { + "bbox": [ + 313, + 201, + 545, + 321 + ], + "spans": [ + { + "bbox": [ + 313, + 201, + 545, + 321 + ], + "type": "image", + "image_path": "e18d2a4378079ffa59de1d750ac456c4afe7c5525e11703e6ca50352457ff512.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 323, + 322, + 533, + 334 + ], + "lines": [ + { + "bbox": [ + 323, + 322, + 533, + 334 + ], + "spans": [ + { + "bbox": [ + 323, + 322, + 533, + 334 + ], + "type": "text", + "content": "(b) A real-world LR text image cropped from a signboard" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 335, + 547, + 358 + ], + "lines": [ + { + "bbox": [ + 46, + 335, + 547, + 358 + ], + "spans": [ + { + "bbox": [ + 46, + 335, + 547, + 358 + ], + "type": "text", + "content": "Figure 1. Results obtained with TBSRN [7], TATT [41] and our approach on the segments of Chinese text image cropped from a real low-resolution invoice and a signboard. Both baselines are re-trained with elaborated degradations as in BSRGAN [75] and Real-ESRGAN [66]." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 143, + 370, + 191, + 382 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 370, + 191, + 382 + ], + "spans": [ + { + "bbox": [ + 143, + 370, + 191, + 382 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 46, + 389, + 290, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 389, + 290, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 389, + 290, + 712 + ], + "type": "text", + "content": "Blind text image super-resolution (SR) is challenging as one needs to cope with diverse font styles and unknown degradation. To address the problem, existing methods perform character recognition in parallel to regularize the SR task, either through a loss constraint or intermediate feature condition. Nonetheless, the high-level prior could still fail when encountering severe degradation. The problem is further compounded given characters of complex structures, e.g., Chinese characters that combine multiple pictographic or ideographic symbols into a single character. In this work, we present a novel prior that focuses more on the character structure. In particular, we learn to encapsulate rich and diverse structures in a StyleGAN and exploit such generative structure priors for restoration. To restrict the generative space of StyleGAN so that it obeys the structure of characters yet remains flexible in handling different font styles, we store the discrete features for each character in a codebook. The code subsequently drives the StyleGAN to generate high-resolution structural details to aid text SR. Compared to priors based on character recognition, the proposed structure prior exerts stronger character-specific guidance to restore faithful and precise strokes of a designated character. Extensive experiments on synthetic and real datasets demonstrate the compelling performance of the proposed generative structure prior in facilitating robust text SR. Our code is available at https://github.com/csxmli2016/MARCONet." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 307, + 370, + 386, + 382 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 370, + 386, + 382 + ], + "spans": [ + { + "bbox": [ + 307, + 370, + 386, + 382 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 388, + 546, + 435 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 388, + 546, + 435 + ], + "spans": [ + { + "bbox": [ + 304, + 388, + 546, + 435 + ], + "type": "text", + "content": "Blind text super-resolution (SR) aims at restoring a high-resolution (HR) image from a low-resolution (LR) text image that is corrupted by unknown degradation. The problem is relatively less explored than SR of natural and face images." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 437, + 547, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 437, + 547, + 616 + ], + "spans": [ + { + "bbox": [ + 304, + 437, + 547, + 616 + ], + "type": "text", + "content": "This seemingly easy task actually possesses many unique challenges. In particular, each character owns its unique structure. A suboptimal restoration that destroys the structure with, e.g., distorted, missing or additional strokes, is easily perceptible and may alter the meaning of the original word. The task becomes more difficult when dealing with writing systems such as Chinese, Kanji and Hanja characters, in which the patterns of thousands of characters vary in complex ways and are mostly composed of different subunits (or compound ideographs). A slight deviation in strokes, say '太' and '大' carries entirely different meanings. The problem becomes more intricate given the different typefaces. In addition, complex and unknown degradation make the data-driven convolutional neural networks (CNNs) incapable of generalizing well to real-world degraded observations." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 617, + 548, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 548, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 548, + 714 + ], + "type": "text", + "content": "To ameliorate the difficulties in blind text SR, especially in retaining the unique structure of each character, recent studies design new loss functions to constrain SR results semantically close to the high-resolution (HR) groundtruth [7,8,45,50,79], or incorporate the recognition prior into the intermediate features [40, 41, 44]. Figure 1 shows several representative results of these two types of methods, i.e., TB-SRN [7] that applies content-aware constraint and TATT [41]" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10103" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "text", + "content": "that embeds the recognition prior into the SR process. The results are not satisfactory despite the models were retrained with data synthesized with sophisticated degradation models, i.e., BSRGAN [75] and Real-ESRGAN [66]. TBSRN and TATT perform well when the LR character has fewer strokes. However, they both fail to generate the desired structures when the character is composed of complex strokes, e.g., the 4, 6, 8, 11-th characters in (a). The results suggest that high-level recognition prior cannot well benefit the SR task in restoring faithful and accurate structures." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 194, + 289, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 194, + 289, + 350 + ], + "spans": [ + { + "bbox": [ + 46, + 194, + 289, + 350 + ], + "type": "text", + "content": "When dealing with complex characters, we can identify some commonly used strokes as constituents of characters or their subparts. These obvious structural regularities have not been studied thoroughly in the literature. In particular, most existing text SR studies [7, 40, 41, 45, 50, 79] focus on scene text images that are presented in different view perspectives or arranged in irregular patterns. In contrast, our goal is to explore structural regularities specific to complex characters and investigate an effective way to exploit the prior. The investigation has practical values in many applications, including the restoration of old printed media (e.g., newspapers or books) for digitalization and preservation, and the enhancement of captions in digital media." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 351, + 289, + 531 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 351, + 289, + 531 + ], + "spans": [ + { + "bbox": [ + 46, + 351, + 289, + 531 + ], + "type": "text", + "content": "The key idea of our solution is to mine structure prior from a generative network, and use the prior to facilitate blind SR of text images. To capture the structure prior of characters, we train a StyleGAN to generate characters of different styles. As our intent is not to generate infinite and non-repetitive results, we restrict the generative space of StyleGAN to obey the structure of characters by constraining the generation with a codebook. Specifically, the codebook stores the discrete code of each character, and each code serves as a constant to StyleGAN for generating a specific high-resolution character. The font style is governed by the " + }, + { + "bbox": [ + 46, + 351, + 289, + 531 + ], + "type": "inline_equation", + "content": "\\mathcal{W}" + }, + { + "bbox": [ + 46, + 351, + 289, + 531 + ], + "type": "text", + "content": " latent space of StyleGAN. Once the character StyleGAN is trained, we can extract its intermediate features serving as the generative structure prior, which encapsulates the intrinsic structure and style of the LR character." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 532, + 289, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 532, + 289, + 653 + ], + "spans": [ + { + "bbox": [ + 46, + 532, + 289, + 653 + ], + "type": "text", + "content": "Using the prior for text SR can be conveniently achieved through an additional Transformer-based encoder and a text SR network that accepts prior. In particular, given a text image that constitutes multiple characters (e.g., Figure 1), we use a Transformer-based encoder to predict the font style, character bounding boxes, and their respective indexes in the codebook jointly. The codebook indexes drive the structure prior generation for each character. In the text SR network, each LR character is super-resolved, guided by the respective priors that are aligned using their bounding boxes." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 653, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 289, + 715 + ], + "type": "text", + "content": "Experiments demonstrate that our design can generate robust and consistent structure priors for diverse and severely degraded text input. With the embedded structure prior, our approach performs superior against state-of-the-art methods in generating photo-realistic text results and shows excellent" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "text", + "content": "generalization to real-world LR text images. While our study mainly employs Chinese characters as examples, the proposed method can be readily extended to characters of other languages. We call our approach as MARCONet. The main contributions are summarized as follows:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 317, + 133, + 545, + 265 + ], + "type": "list", + "angle": 0, + "index": 9, + "blocks": [ + { + "bbox": [ + 317, + 133, + 545, + 169 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 133, + 545, + 169 + ], + "spans": [ + { + "bbox": [ + 317, + 133, + 545, + 169 + ], + "type": "text", + "content": "- We show that blind SR task, especially for characters with complex structures, can be restored by using their structure prior encapsulated in a generative network." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 317, + 169, + 545, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 169, + 545, + 216 + ], + "spans": [ + { + "bbox": [ + 317, + 169, + 545, + 216 + ], + "type": "text", + "content": "- We present a viable way of learning such generative structure prior through reformulating a StyleGAN by replacing its single constant with discrete codes that represent different characters." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 317, + 217, + 545, + 265 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 217, + 545, + 265 + ], + "spans": [ + { + "bbox": [ + 317, + 217, + 545, + 265 + ], + "type": "text", + "content": "- To retrieve the prior accurately, we propose a Transformer-based encoder to jointly predict the font styles, character bounding boxes and their indexes in codebook from the LR input." + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 274, + 392, + 288 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 274, + 392, + 288 + ], + "spans": [ + { + "bbox": [ + 306, + 274, + 392, + 288 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 294, + 547, + 462 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 294, + 547, + 462 + ], + "spans": [ + { + "bbox": [ + 304, + 294, + 547, + 462 + ], + "type": "text", + "content": "Blind Image SR. Blind image SR is challenging due to the complex mixture of unknown degradations. Recent studies address the problem from two aspects, i.e., degradation estimation [3, 19, 38, 39, 62] and establishing more realistic training data [4, 28, 33, 66, 70, 75]. The former paradigm mainly focuses on estimating degradation model parameters and then applies non-blind SR methods, e.g., ZSSR [57]. The latter builds training pairs either through capturing real-world LR and HR pairs [4, 70] or designing elaborate degradation models that imitate real-world degradation [28, 33, 66, 75]. Since characters in text images have specific and semantic structures, we show that a good restoration performance cannot be achieved by merely using elaborately designed degradation models." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 462, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 462, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 462, + 548, + 715 + ], + "type": "text", + "content": "Text Image SR. Text image SR has been studied for many years. In traditional methods, maximum a posterior (MAP) [5] and Bayesian framework [9] are exploited for super-resolving text images. These earlier approaches are incapable of generating high-quality results. Dong et al. [13] adopt CNNs (i.e., SRCNN [12]) for text image SR and achieve promising results in the ICDAR 2015 competition [49]. Xu et al. [72] adopt a Generative Adversarial Network (GAN) [17] to learn category-specific prior for face and text images SR, along with the supervision from a multi-class GAN loss. Mou et al. [44] propose to plug a SR unit into the recognition process of degraded text images. Wang et al. [64] introduce the first real-world text SR pairs (i.e., TextZoom), which are cropped from RealSR [4] and SRRAW [77]. They also present a sequential residual block by incorporating Bi-directional LSTM to capture the sequential information for low-level reconstruction. Both RealSR and SRRAW are captured by different digital cameras with different focal lengths, aiming to collect natural LR/HR pairs in real-world scenarios. The setting is not designed specifically for text images. We observe that most HR text images" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "10104" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "content": "in TextZoom are limited in clarity, which could limit the SR performance when taking them as ground-truth." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 102, + 289, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 102, + 289, + 342 + ], + "spans": [ + { + "bbox": [ + 46, + 102, + 289, + 342 + ], + "type": "text", + "content": "Text SR benefits from prior and auxiliary constraints. Quan et al. [51] recover text images in a cascade model by predicting the high-frequency information. Chen et al. [7] propose Transformer-based position-aware and content-aware modules to emphasize the position and the content of each character. Analogously, Nakaune et al. [45] and Qin et al. [50] respectively present the structure-aware loss and content-perceptual constraint for learning detailed structural skeletons. Zhao et al. [78] propose a parallel contextual attention network to learn sequence-dependent features for bringing more high-frequency information into text reconstruction. Zhao et al. [79] exploit linguistic, recognition and visual clues to jointly boost the SR performance. Chen et al. [8] propose a stroke-aware framework by concentrating on stroke-level internal structures. Ma et al. [41] introduce text recognition prior to text reconstruction with a Transformer-based module, leveraging the global attention mechanism. They also embed categorical text priors in the encoder and employ multi-stage refinement to progressively enhance low-resolution images [40]." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 348, + 289, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 348, + 289, + 456 + ], + "spans": [ + { + "bbox": [ + 46, + 348, + 289, + 456 + ], + "type": "text", + "content": "Many methods above employ recognition information either as a loss function on the SR results [7, 8, 50, 79] or as intermediate SR features for providing high-level guidance [40, 41]. Albeit the high-level recognition prior helps improve the text recognition ability, it is limited in providing accurate structure and style guidance, especially for certain texts with complex structures. In this study, we show that generative structure prior benefits high-quality guidance to restore the faithful structure of LR characters." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 462, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 462, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 462, + 289, + 714 + ], + "type": "text", + "content": "Generative Structure Prior in Image SR. Image structure prior is proven effective in many low-level vision tasks, e.g., depth image enhancement [21, 27, 37], image inpainting [11, 46, 52], and image restoration [10, 35, 36, 47]. Most recently, by using generative structure priors obtained from pre-trained StyleGANs [30, 31] or codebooks [15], blind face restoration has achieved tremendous improvement [6, 22, 34, 65, 69, 73], suggesting the apparent advantage of such prior over other methods in generating photo-realistic textures. Our study is inspired by the success of these approaches. Nevertheless, crafting a suitable structural prior for text images are harder than face images. This is because each character has its unique strokes, but may have a vast variety of font styles. Any distorted, missing or additional strokes easily change their semantic layout that is easily perceptible, and worsens their actual meaning (see Figure 1). All of these challenges aggravate the difficulties for learning a generative structure prior for the text SR task. In this study, we show an effective way of learning such prior through replacing the constant input of StyleGAN with a discrete codebook, while controlling the font style via the " + }, + { + "bbox": [ + 46, + 462, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{W}" + }, + { + "bbox": [ + 46, + 462, + 289, + 714 + ], + "type": "text", + "content": " space." + } + ] + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 322, + 65, + 531, + 148 + ], + "blocks": [ + { + "bbox": [ + 322, + 65, + 531, + 148 + ], + "lines": [ + { + "bbox": [ + 322, + 65, + 531, + 148 + ], + "spans": [ + { + "bbox": [ + 322, + 65, + 531, + 148 + ], + "type": "image", + "image_path": "17169bbb912c04f587ae6c3095542eebd27198c4c059b3acd23576f88c151726.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 152, + 547, + 209 + ], + "lines": [ + { + "bbox": [ + 304, + 152, + 547, + 209 + ], + "spans": [ + { + "bbox": [ + 304, + 152, + 547, + 209 + ], + "type": "text", + "content": "Figure 2. Pre-training generative structure prior for each character. The codebook stores the discrete code of each character, and each code serves as a constant to StyleGAN for generating a specific high-resolution character. The intermediate features encapsulate the generative structure prior and will be used for guiding text SR." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 216, + 389, + 229 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 216, + 389, + 229 + ], + "spans": [ + { + "bbox": [ + 306, + 216, + 389, + 229 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 236, + 547, + 452 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 236, + 547, + 452 + ], + "spans": [ + { + "bbox": [ + 304, + 236, + 547, + 452 + ], + "type": "text", + "content": "A GAN model can well capture the intrinsic structure prior for a category by training the model on abundant images of the same category. Many image restoration tasks [6,20,42,48,65,73] have shown the benefits of using such generative priors for restoring photo-realistic details from LR inputs despite severe and complex degradation. Previous studies mainly use the prior for face restoration, while its application to text SR is under-explored. In this paper, we propose MARCONet, the first attempt to eMbed generative stRuCture priOr for blind text SR. The proposed pipeline is depicted in Figure 3. It mainly contains three parts, 1) the prediction of font style, character bounding boxes and their indexes in codebook based on a given LR input, 2) the generation of the structure prior for each character, 3) the SR framework that takes the generative structure prior as guidance for restoration. Next, we first describe the approach to obtain the generative structure prior for each character, followed by the way to employ such prior for the text SR." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 458, + 528, + 471 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 458, + 528, + 471 + ], + "spans": [ + { + "bbox": [ + 306, + 458, + 528, + 471 + ], + "type": "text", + "content": "3.1. Pre-training of Generative Structure Prior" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 477, + 547, + 571 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 477, + 547, + 571 + ], + "spans": [ + { + "bbox": [ + 304, + 477, + 547, + 571 + ], + "type": "text", + "content": "The original StyleGANs [30, 31] take a learnable constant as input, and control the style of output image through the " + }, + { + "bbox": [ + 304, + 477, + 547, + 571 + ], + "type": "inline_equation", + "content": "w \\in \\mathcal{W}" + }, + { + "bbox": [ + 304, + 477, + 547, + 571 + ], + "type": "text", + "content": " space, which is a projection from the initial latent space " + }, + { + "bbox": [ + 304, + 477, + 547, + 571 + ], + "type": "inline_equation", + "content": "z \\in \\mathcal{Z}" + }, + { + "bbox": [ + 304, + 477, + 547, + 571 + ], + "type": "text", + "content": ". Layer-wise noise is also introduced to support stochastic variation on fine-grained details. To better capture the structure of text images, we remove the layer-wise noise and replace the single constant with discrete codes that represent different characters (see details in Figure 2)." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 572, + 547, + 644 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 572, + 547, + 644 + ], + "spans": [ + { + "bbox": [ + 304, + 572, + 547, + 644 + ], + "type": "text", + "content": "We denote each character code as " + }, + { + "bbox": [ + 304, + 572, + 547, + 644 + ], + "type": "inline_equation", + "content": "c \\in \\{C_i\\}_{i=1}^M" + }, + { + "bbox": [ + 304, + 572, + 547, + 644 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 572, + 547, + 644 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 304, + 572, + 547, + 644 + ], + "type": "text", + "content": " is the codebook that stores all the character features. Each code is learnable, with a size of " + }, + { + "bbox": [ + 304, + 572, + 547, + 644 + ], + "type": "inline_equation", + "content": "1 \\times 1 \\times 512" + }, + { + "bbox": [ + 304, + 572, + 547, + 644 + ], + "type": "text", + "content": ". Following CRNN [56], the cardinality of codebook " + }, + { + "bbox": [ + 304, + 572, + 547, + 644 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 572, + 547, + 644 + ], + "type": "text", + "content": " is set to 6736, a size covering simplified Chinese characters, English letters, and numbers. The retrofitted StyleGAN is defined as:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 351, + 648, + 546, + 662 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 351, + 648, + 546, + 662 + ], + "spans": [ + { + "bbox": [ + 351, + 648, + 546, + 662 + ], + "type": "interline_equation", + "content": "\\mathcal {S} ^ {c} = G (c, \\mathcal {F} (z); \\Theta_ {G}) = G (c, w; \\Theta_ {G}), \\tag {1}", + "image_path": "2898d8fd8df7c4285d97cdaae3b4159cb082cb1b31e65c1b8fe416df4fd1fb62.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 665, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 665, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 304, + 665, + 547, + 714 + ], + "type": "text", + "content": " represents the network that maps " + }, + { + "bbox": [ + 304, + 665, + 547, + 714 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 304, + 665, + 547, + 714 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 665, + 547, + 714 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 304, + 665, + 547, + 714 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 665, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\Theta_G" + }, + { + "bbox": [ + 304, + 665, + 547, + 714 + ], + "type": "text", + "content": " is the model parameters of StyleGAN. For generalizing to different scenarios, we simplify the structure image " + }, + { + "bbox": [ + 304, + 665, + 547, + 714 + ], + "type": "inline_equation", + "content": "S^c" + }, + { + "bbox": [ + 304, + 665, + 547, + 714 + ], + "type": "text", + "content": " with pixel values " + }, + { + "bbox": [ + 304, + 665, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\in \\{0,1\\}" + }, + { + "bbox": [ + 304, + 665, + 547, + 714 + ], + "type": "text", + "content": " (see the output in Figure 2). The struc" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10105" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 75, + 67, + 519, + 262 + ], + "blocks": [ + { + "bbox": [ + 75, + 67, + 519, + 262 + ], + "lines": [ + { + "bbox": [ + 75, + 67, + 519, + 262 + ], + "spans": [ + { + "bbox": [ + 75, + 67, + 519, + 262 + ], + "type": "image", + "image_path": "e7d50faef30a02e067e145f865c675e5ecfe7fa4e31126df0288700cba61f00f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 268, + 547, + 301 + ], + "lines": [ + { + "bbox": [ + 46, + 268, + 547, + 301 + ], + "spans": [ + { + "bbox": [ + 46, + 268, + 547, + 301 + ], + "type": "text", + "content": "Figure 3. Overview of our MARCONet. It contains three parts, i.e., (i) Transformer encoder for predicting the font style, classification and bounding boxes of each character from LR input, (ii) structure prior generation with pre-trained StyleGAN for generating reliable structure prior for each character, and (iii) the SR process for reconstructing the SR output with the incorporation of each characters' structure prior." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 310, + 288, + 334 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 310, + 288, + 334 + ], + "spans": [ + { + "bbox": [ + 46, + 310, + 288, + 334 + ], + "type": "text", + "content": "ture prior " + }, + { + "bbox": [ + 46, + 310, + 288, + 334 + ], + "type": "inline_equation", + "content": "\\mathcal{P}^c" + }, + { + "bbox": [ + 46, + 310, + 288, + 334 + ], + "type": "text", + "content": " used in this work is the intermediate features from " + }, + { + "bbox": [ + 46, + 310, + 288, + 334 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 46, + 310, + 288, + 334 + ], + "type": "text", + "content": " in Eqn. (1), and can be formulated as:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 126, + 338, + 287, + 350 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 126, + 338, + 287, + 350 + ], + "spans": [ + { + "bbox": [ + 126, + 338, + 287, + 350 + ], + "type": "interline_equation", + "content": "\\mathcal {P} ^ {c} = G _ {i} (c, w; \\Theta_ {G}), \\tag {2}", + "image_path": "26434cd7f195e07ba7a822ef07b1fbfc3e0aeabdae1b9a3ad05002ea4da04c9e.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 355, + 288, + 367 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 355, + 288, + 367 + ], + "spans": [ + { + "bbox": [ + 46, + 355, + 288, + 367 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 355, + 288, + 367 + ], + "type": "inline_equation", + "content": "G_{i}" + }, + { + "bbox": [ + 46, + 355, + 288, + 367 + ], + "type": "text", + "content": " represents the output features from " + }, + { + "bbox": [ + 46, + 355, + 288, + 367 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 355, + 288, + 367 + ], + "type": "text", + "content": "-th layer of " + }, + { + "bbox": [ + 46, + 355, + 288, + 367 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 46, + 355, + 288, + 367 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 368, + 288, + 547 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 368, + 288, + 547 + ], + "spans": [ + { + "bbox": [ + 46, + 368, + 288, + 547 + ], + "type": "text", + "content": "The training of the character StyleGAN can be done on synthetic images yet with satisfying generalization ability to real-world texts. In particular, the PIL package1 is adopted to synthesize high-resolution character images with hundreds of font styles (see examples in the suppl.). We also augment the diversity with random translations, font sizes and slight affine transformation. Different from the original StyleGANs that adopt only adversarial loss [17], we introduce an additional recognition loss derived from a pre-trained Transformer-based recognizer as regularization. Once learned, each learnable code " + }, + { + "bbox": [ + 46, + 368, + 288, + 547 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 368, + 288, + 547 + ], + "type": "text", + "content": " well captures the distinctive features of each character and " + }, + { + "bbox": [ + 46, + 368, + 288, + 547 + ], + "type": "inline_equation", + "content": "w \\in \\mathcal{W}" + }, + { + "bbox": [ + 46, + 368, + 288, + 547 + ], + "type": "text", + "content": " can control the font styles of the output image. In the following, we will describe the approach to extract the structure prior for each character in a given LR text image." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 555, + 173, + 567 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 555, + 173, + 567 + ], + "spans": [ + { + "bbox": [ + 47, + 555, + 173, + 567 + ], + "type": "text", + "content": "3.2. Transformer Encoder" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 574, + 287, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 574, + 287, + 694 + ], + "spans": [ + { + "bbox": [ + 46, + 574, + 287, + 694 + ], + "type": "text", + "content": "A LR text image usually is composed of several characters. To derive the generative structure prior for each character, first, we need to obtain the font style " + }, + { + "bbox": [ + 46, + 574, + 287, + 694 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 46, + 574, + 287, + 694 + ], + "type": "text", + "content": " of the LR characters. Second, the indexes of each character in the codebook and their bounding boxes are also necessary for aligning the structure prior with each LR character. To this end, we adopt a Transformer-based encoder to jointly predict the needed information. Transformer [61] is chosen so that we can better capture the dependency across different characters in the input image." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 309, + 310, + 547, + 490 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 310, + 547, + 490 + ], + "spans": [ + { + "bbox": [ + 309, + 310, + 547, + 490 + ], + "type": "text", + "content": "Learning to predict the font style " + }, + { + "bbox": [ + 309, + 310, + 547, + 490 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 309, + 310, + 547, + 490 + ], + "type": "text", + "content": " is similar to learning-based GAN inversion [2, 54, 60, 63], where the Transformer network serves as an encoder. It is observed that the Transformer-based encoder achieves satisfactory inversion, achieving reconstruction with low distortion and of high quality [25]. Note that characters in one text image generally have the same font style. So we use one linear layer to map the features of all characters to a single prediction " + }, + { + "bbox": [ + 309, + 310, + 547, + 490 + ], + "type": "inline_equation", + "content": "(w)" + }, + { + "bbox": [ + 309, + 310, + 547, + 490 + ], + "type": "text", + "content": ", which is shared with all the characters in the same LR image. We also use a similar structure as " + }, + { + "bbox": [ + 309, + 310, + 547, + 490 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 309, + 310, + 547, + 490 + ], + "type": "text", + "content": " prediction to carry out the regression and classification of the bounding boxes and code indexes. These three sub-tasks share the same Transformer encoder (i.e., ViT [14]) and a CNN backbone (i.e., ResNet45 [24]). Positional encoding is incorporated to inject positions of features in the sequence." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 491, + 547, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 491, + 547, + 635 + ], + "spans": [ + { + "bbox": [ + 304, + 491, + 547, + 635 + ], + "type": "text", + "content": "The font style prediction branch is optimized with the gradient from StyleGAN. Since the input text image has unconstrained numbers of characters, we adopt CTC loss [18] for recognition. The loss is proposed to solve the alignment between predicted and target labels and is widely used in scene text recognition tasks. As for the learning of character bounding boxes regression, we adopt a linear combination of the Smooth " + }, + { + "bbox": [ + 304, + 491, + 547, + 635 + ], + "type": "inline_equation", + "content": "L_{1}" + }, + { + "bbox": [ + 304, + 491, + 547, + 635 + ], + "type": "text", + "content": " loss [16] and the generalized IoU loss [53]. The ground-truth boxes of each character can be obtained when synthesizing the training images with PIL package. The gradient from the latter text SR network can further benefit the learning process of the whole Transformer encoder." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 646, + 473, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 646, + 473, + 658 + ], + "spans": [ + { + "bbox": [ + 306, + 646, + 473, + 658 + ], + "type": "text", + "content": "3.3. Text Super-resolution Network" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "content": "Network Architecture. With the Transformer encoder, we can obtain the font style " + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "content": ", classification label (i.e., index in codebook), and the bounding box for each character in the LR input. Then, the corresponding high-quality generative" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 58, + 702, + 146, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 146, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 146, + 713 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 58, + 702, + 146, + 713 + ], + "type": "text", + "content": "https://python-pillow.org/" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "10106" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 63, + 67, + 272, + 256 + ], + "blocks": [ + { + "bbox": [ + 63, + 67, + 272, + 256 + ], + "lines": [ + { + "bbox": [ + 63, + 67, + 272, + 256 + ], + "spans": [ + { + "bbox": [ + 63, + 67, + 272, + 256 + ], + "type": "image", + "image_path": "09a5a31c549c2a7145a686f178c962d85aae3dfe2be0f611c405e1ab6e3bc319.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 260, + 288, + 294 + ], + "lines": [ + { + "bbox": [ + 46, + 260, + 288, + 294 + ], + "spans": [ + { + "bbox": [ + 46, + 260, + 288, + 294 + ], + "type": "text", + "content": "Figure 4. Details of the structure prior transform module. Each LR character is cropped and aligned by using the bounding boxes, and is super-resolved with the guidance of their structure prior." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 304, + 289, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 304, + 289, + 555 + ], + "spans": [ + { + "bbox": [ + 46, + 304, + 289, + 555 + ], + "type": "text", + "content": "structure prior " + }, + { + "bbox": [ + 46, + 304, + 289, + 555 + ], + "type": "inline_equation", + "content": "\\mathcal{P}^c" + }, + { + "bbox": [ + 46, + 304, + 289, + 555 + ], + "type": "text", + "content": " for each character can be generated with " + }, + { + "bbox": [ + 46, + 304, + 289, + 555 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 46, + 304, + 289, + 555 + ], + "type": "text", + "content": " and the selected code " + }, + { + "bbox": [ + 46, + 304, + 289, + 555 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 304, + 289, + 555 + ], + "type": "text", + "content": " through the pre-trained StyleGAN in Eqn. (2) (see the character structure prior in Figure 3). In this section, we describe how to use them for the text SR task. First, a simple UNet [55] is stacked upon the ResNet45 to extract the LR features. Then, the generative structure prior of each character is embedded into their LR characters through a structure prior transform module. The process is shown in Figure 4 (more details can be found in the suppl.). For the LR features, we adopt the detected bounding boxes to crop and align each LR character by RoIAlign operation [23]. For each character, AdaIN [26] is adopted to normalize the prior's distribution, and spatial feature transformation [67] is subsequently employed to predict the affine parameters, which are applied on the LR character features. The reverse RoIAlign is finally used to paste the enhanced features back to their original locations. The structure prior transform module is adopted at two scales " + }, + { + "bbox": [ + 46, + 304, + 289, + 555 + ], + "type": "inline_equation", + "content": "s\\in \\{32,64\\}" + }, + { + "bbox": [ + 46, + 304, + 289, + 555 + ], + "type": "text", + "content": ", allowing our MARCONet to remain high fidelity with different degradation. A Conv-ReLU-ResBlock based CNN module is stacked to generate the final SR result." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 556, + 288, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 556, + 288, + 593 + ], + "spans": [ + { + "bbox": [ + 47, + 556, + 288, + 593 + ], + "type": "text", + "content": "Learning Objective. We minimize the differences between the SR results " + }, + { + "bbox": [ + 47, + 556, + 288, + 593 + ], + "type": "inline_equation", + "content": "\\hat{I}_{SR}" + }, + { + "bbox": [ + 47, + 556, + 288, + 593 + ], + "type": "text", + "content": " and HR ground-truth " + }, + { + "bbox": [ + 47, + 556, + 288, + 593 + ], + "type": "inline_equation", + "content": "I_{HR}" + }, + { + "bbox": [ + 47, + 556, + 288, + 593 + ], + "type": "text", + "content": " on both the pixel and perceptual domains [29]:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 52, + 597, + 287, + 625 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 597, + 287, + 625 + ], + "spans": [ + { + "bbox": [ + 52, + 597, + 287, + 625 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {r e c} = \\left\\| \\hat {I} _ {S R} - I _ {H R} \\right\\| _ {1} + \\sum_ {i = 1} ^ {4} \\frac {\\lambda_ {p e r}}{\\mathcal {C} _ {i} \\mathcal {H} _ {i} \\mathcal {W} _ {i}} \\left\\| \\Phi_ {i} (\\hat {I} _ {S R}) - \\Phi_ {i} (I _ {H R}) \\right\\| _ {1}, \\tag {3}", + "image_path": "f7491cec4250fe5a24d22c439b724f83c85540e8c057c7eab3af2a7fa67613ea.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 628, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 628, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 47, + 628, + 287, + 677 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 628, + 287, + 677 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_i" + }, + { + "bbox": [ + 47, + 628, + 287, + 677 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 628, + 287, + 677 + ], + "type": "inline_equation", + "content": "\\mathcal{H}_i" + }, + { + "bbox": [ + 47, + 628, + 287, + 677 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 628, + 287, + 677 + ], + "type": "inline_equation", + "content": "\\mathcal{W}_i" + }, + { + "bbox": [ + 47, + 628, + 287, + 677 + ], + "type": "text", + "content": " are the feature dimensions from the " + }, + { + "bbox": [ + 47, + 628, + 287, + 677 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 47, + 628, + 287, + 677 + ], + "type": "text", + "content": "-th convolution layer of the pre-trained VGG-19 model " + }, + { + "bbox": [ + 47, + 628, + 287, + 677 + ], + "type": "inline_equation", + "content": "\\Phi" + }, + { + "bbox": [ + 47, + 628, + 287, + 677 + ], + "type": "text", + "content": " [58]. " + }, + { + "bbox": [ + 47, + 628, + 287, + 677 + ], + "type": "inline_equation", + "content": "\\lambda_{per}" + }, + { + "bbox": [ + 47, + 628, + 287, + 677 + ], + "type": "text", + "content": " is the trade-off parameter and is set to 0.05. The loss " + }, + { + "bbox": [ + 47, + 628, + 287, + 677 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{rec}" + }, + { + "bbox": [ + 47, + 628, + 287, + 677 + ], + "type": "text", + "content": " is applied to the whole text image." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "text", + "content": "Adversarial loss [17] " + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{adv}" + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "text", + "content": " is also added to improve visual quality. Instead of constraining on the whole image as in Eqn. (3), " + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{adv}" + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "text", + "content": " is performed on each cropped character image" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 547, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 204 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 204 + ], + "type": "text", + "content": "together with its corresponding structure image as additional conditions [43]. To be specific, the concatenation of HR character image " + }, + { + "bbox": [ + 304, + 72, + 547, + 204 + ], + "type": "inline_equation", + "content": "I_{HR}^{c}" + }, + { + "bbox": [ + 304, + 72, + 547, + 204 + ], + "type": "text", + "content": " and its structure image " + }, + { + "bbox": [ + 304, + 72, + 547, + 204 + ], + "type": "inline_equation", + "content": "S_{HR}^{c}" + }, + { + "bbox": [ + 304, + 72, + 547, + 204 + ], + "type": "text", + "content": " is expected to be classified as Real, while the concatenation of SR character image " + }, + { + "bbox": [ + 304, + 72, + 547, + 204 + ], + "type": "inline_equation", + "content": "\\hat{I}_{SR}^{c}" + }, + { + "bbox": [ + 304, + 72, + 547, + 204 + ], + "type": "text", + "content": " and its structure image " + }, + { + "bbox": [ + 304, + 72, + 547, + 204 + ], + "type": "inline_equation", + "content": "S_{SR}^{c}" + }, + { + "bbox": [ + 304, + 72, + 547, + 204 + ], + "type": "text", + "content": " is recognized as Fake. Note that " + }, + { + "bbox": [ + 304, + 72, + 547, + 204 + ], + "type": "inline_equation", + "content": "S_{HR}^{c}" + }, + { + "bbox": [ + 304, + 72, + 547, + 204 + ], + "type": "text", + "content": " is the binarized version of " + }, + { + "bbox": [ + 304, + 72, + 547, + 204 + ], + "type": "inline_equation", + "content": "I_{HR}^{c}" + }, + { + "bbox": [ + 304, + 72, + 547, + 204 + ], + "type": "text", + "content": ", which represents the ground-truth structure, and " + }, + { + "bbox": [ + 304, + 72, + 547, + 204 + ], + "type": "inline_equation", + "content": "S_{SR}^{c}" + }, + { + "bbox": [ + 304, + 72, + 547, + 204 + ], + "type": "text", + "content": " is obtained from Eqn. (1) with " + }, + { + "bbox": [ + 304, + 72, + 547, + 204 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 304, + 72, + 547, + 204 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 72, + 547, + 204 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 72, + 547, + 204 + ], + "type": "text", + "content": " predicted from LR input. Such design allows us to better constrain the embedding of generative structure prior into the SR results. The hinge version of adversarial loss [74] for each character is defined as:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 209, + 547, + 223 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 209, + 547, + 223 + ], + "spans": [ + { + "bbox": [ + 306, + 209, + 547, + 223 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {D} = - \\mathbb {E} \\left[ \\min \\left(0, - 1 + D \\left(I _ {H R} ^ {c}, S _ {H R} ^ {c}\\right)\\right) \\right] - \\mathbb {E} \\left[ \\min \\left(0, - 1 - D \\left(\\hat {I} _ {S R} ^ {c}, S _ {S R} ^ {c}\\right)\\right) \\right],", + "image_path": "6c5268bbb4ce4ba30b3b08a3d250ccc14c85f7b156299132f33ead9098b47151.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 380, + 225, + 545, + 239 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 380, + 225, + 545, + 239 + ], + "spans": [ + { + "bbox": [ + 380, + 225, + 545, + 239 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {G} = - \\mathbb {E} \\left[ D \\left(\\hat {I} _ {S R} ^ {c}, \\mathcal {S} _ {S R} ^ {c}\\right) \\right]. \\tag {4}", + "image_path": "e87ca36f66f595b31b34c1562bbdb075495f41134ddb87b4994ad781c3adb9d7.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 244, + 545, + 281 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 244, + 545, + 281 + ], + "spans": [ + { + "bbox": [ + 304, + 244, + 545, + 281 + ], + "type": "text", + "content": "Finally, we use the " + }, + { + "bbox": [ + 304, + 244, + 545, + 281 + ], + "type": "inline_equation", + "content": "L_{1}" + }, + { + "bbox": [ + 304, + 244, + 545, + 281 + ], + "type": "text", + "content": " loss on structure image " + }, + { + "bbox": [ + 304, + 244, + 545, + 281 + ], + "type": "inline_equation", + "content": "\\mathcal{S}^c" + }, + { + "bbox": [ + 304, + 244, + 545, + 281 + ], + "type": "text", + "content": " in the text SR training stage to further fine-tune " + }, + { + "bbox": [ + 304, + 244, + 545, + 281 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 304, + 244, + 545, + 281 + ], + "type": "text", + "content": " and code " + }, + { + "bbox": [ + 304, + 244, + 545, + 281 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 244, + 545, + 281 + ], + "type": "text", + "content": " in codebook. For each character, this constraint is defined as:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 382, + 285, + 545, + 297 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 382, + 285, + 545, + 297 + ], + "spans": [ + { + "bbox": [ + 382, + 285, + 545, + 297 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {s t r} = \\left\\| \\mathcal {S} _ {S R} ^ {c} - \\mathcal {S} _ {H R} ^ {c} \\right\\| _ {1}. \\tag {5}", + "image_path": "49e78045c47c7580243dd659db5b27812b0606c80074d62cca1577bb587a21be.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 301, + 547, + 326 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 301, + 547, + 326 + ], + "spans": [ + { + "bbox": [ + 304, + 301, + 547, + 326 + ], + "type": "text", + "content": "With these learning objectives, the whole framework of MARCONet is optimized in an end-to-end manner." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 335, + 388, + 349 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 335, + 388, + 349 + ], + "spans": [ + { + "bbox": [ + 306, + 335, + 388, + 349 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 354, + 547, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 354, + 547, + 605 + ], + "spans": [ + { + "bbox": [ + 304, + 354, + 547, + 605 + ], + "type": "text", + "content": "Training Data. In this work, we take Chinese characters as our initial exploration for super-resolving complex characters but with regularity. The same method can be extended to other languages by retraining the framework with specific data. Since a text image is usually composed of several characters, here we use the Chinese corpus from Xu et al. [71], which contains tens of millions of common items. We also collect 182 font families to introduce diverse structures. PIL toolbox is adopted to synthesize these text images, rendered with random RGB values, font sizes and locations. The text background is obtained from DIV2K [1] and Flickr2K [59] datasets, in which each image is randomly cropped and upsampled to " + }, + { + "bbox": [ + 304, + 354, + 547, + 605 + ], + "type": "inline_equation", + "content": "\\times 4\\sim 16" + }, + { + "bbox": [ + 304, + 354, + 547, + 605 + ], + "type": "text", + "content": " to synthesize the complex background. With this toolbox, we can obtain the HR text images " + }, + { + "bbox": [ + 304, + 354, + 547, + 605 + ], + "type": "inline_equation", + "content": "I_{HR}" + }, + { + "bbox": [ + 304, + 354, + 547, + 605 + ], + "type": "text", + "content": ", together with the classification label, bounding box and the ground-truth structure image " + }, + { + "bbox": [ + 304, + 354, + 547, + 605 + ], + "type": "inline_equation", + "content": "S_{HR}^{c}" + }, + { + "bbox": [ + 304, + 354, + 547, + 605 + ], + "type": "text", + "content": " of each character. The degradation pipeline presented in BSRGAN [75] and Real-ESRGAN [66] are applied online to degrade the HR image to LR input (see input in Figure 3). Since each text image usually contains varying numbers of characters, we pad zeros to the width dimension to keep the structure unchanged." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 606, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 606, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 606, + 547, + 713 + ], + "type": "text", + "content": "Implementation Details. The training of the whole MARCONet and the pre-training for generative structure prior are conducted on a server with four Tesla V100 GPUs. The batch size is set to 2 and 16, respectively. We employ Adam [32] as the optimizer. The initial learning rate " + }, + { + "bbox": [ + 304, + 606, + 547, + 713 + ], + "type": "inline_equation", + "content": "lr" + }, + { + "bbox": [ + 304, + 606, + 547, + 713 + ], + "type": "text", + "content": " is set to " + }, + { + "bbox": [ + 304, + 606, + 547, + 713 + ], + "type": "inline_equation", + "content": "1e - 4" + }, + { + "bbox": [ + 304, + 606, + 547, + 713 + ], + "type": "text", + "content": " and decreased by 0.5 when " + }, + { + "bbox": [ + 304, + 606, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{rec}" + }, + { + "bbox": [ + 304, + 606, + 547, + 713 + ], + "type": "text", + "content": " reaches a stable range on the validation set. The " + }, + { + "bbox": [ + 304, + 606, + 547, + 713 + ], + "type": "inline_equation", + "content": "lr" + }, + { + "bbox": [ + 304, + 606, + 547, + 713 + ], + "type": "text", + "content": " for StyleGAN in the text SR training stage is set to " + }, + { + "bbox": [ + 304, + 606, + 547, + 713 + ], + "type": "inline_equation", + "content": "1e - 6" + }, + { + "bbox": [ + 304, + 606, + 547, + 713 + ], + "type": "text", + "content": " for fine-tuning. The height of HR images is set to 128. Color jittering [80] is used to increase" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10107" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 76, + 62, + 187, + 225 + ], + "blocks": [ + { + "bbox": [ + 76, + 62, + 187, + 225 + ], + "lines": [ + { + "bbox": [ + 76, + 62, + 187, + 225 + ], + "spans": [ + { + "bbox": [ + 76, + 62, + 187, + 225 + ], + "type": "image", + "image_path": "05be199feca5a9bfbf15527fc1a6c007dd522e6bbb0f636f5b65ec62611e56bc.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 59, + 232, + 533, + 243 + ], + "lines": [ + { + "bbox": [ + 59, + 232, + 533, + 243 + ], + "spans": [ + { + "bbox": [ + 59, + 232, + 533, + 243 + ], + "type": "text", + "content": "Figure 5. Visual comparison on " + }, + { + "bbox": [ + 59, + 232, + 533, + 243 + ], + "type": "inline_equation", + "content": "\\times 2" + }, + { + "bbox": [ + 59, + 232, + 533, + 243 + ], + "type": "text", + "content": " (1\\~2 columns) and " + }, + { + "bbox": [ + 59, + 232, + 533, + 243 + ], + "type": "inline_equation", + "content": "\\times 4" + }, + { + "bbox": [ + 59, + 232, + 533, + 243 + ], + "type": "text", + "content": " (3\\~4 columns) SR. The stroke details are best viewed by zooming in." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 188, + 62, + 332, + 224 + ], + "blocks": [ + { + "bbox": [ + 188, + 62, + 332, + 224 + ], + "lines": [ + { + "bbox": [ + 188, + 62, + 332, + 224 + ], + "spans": [ + { + "bbox": [ + 188, + 62, + 332, + 224 + ], + "type": "image", + "image_path": "b5c8c8c3c992fdae0e04d7cac547f6c8e6708ea025b6a608c0499f18336669bf.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 332, + 62, + 425, + 225 + ], + "blocks": [ + { + "bbox": [ + 332, + 62, + 425, + 225 + ], + "lines": [ + { + "bbox": [ + 332, + 62, + 425, + 225 + ], + "spans": [ + { + "bbox": [ + 332, + 62, + 425, + 225 + ], + "type": "image", + "image_path": "2cabfbfc1adc0c4b5db5941e05ade02c2d715f0ee47938749a274bdc551cf3ef.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 425, + 62, + 516, + 225 + ], + "blocks": [ + { + "bbox": [ + 425, + 62, + 516, + 225 + ], + "lines": [ + { + "bbox": [ + 425, + 62, + 516, + 225 + ], + "spans": [ + { + "bbox": [ + 425, + 62, + 516, + 225 + ], + "type": "image", + "image_path": "177fa6f33977f954dd09e72fac03ca5e7d66caca143aa430c743dc976a6f5237.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 48, + 268, + 288, + 354 + ], + "blocks": [ + { + "bbox": [ + 70, + 253, + 263, + 264 + ], + "lines": [ + { + "bbox": [ + 70, + 253, + 263, + 264 + ], + "spans": [ + { + "bbox": [ + 70, + 253, + 263, + 264 + ], + "type": "text", + "content": "Table 1. Quantitative comparison on " + }, + { + "bbox": [ + 70, + 253, + 263, + 264 + ], + "type": "inline_equation", + "content": "\\times 2" + }, + { + "bbox": [ + 70, + 253, + 263, + 264 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 70, + 253, + 263, + 264 + ], + "type": "inline_equation", + "content": "\\times 4\\mathrm{{SR}}" + }, + { + "bbox": [ + 70, + 253, + 263, + 264 + ], + "type": "text", + "content": " ." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 268, + 288, + 354 + ], + "lines": [ + { + "bbox": [ + 48, + 268, + 288, + 354 + ], + "spans": [ + { + "bbox": [ + 48, + 268, + 288, + 354 + ], + "type": "table", + "html": "
Methods×2×4
PSNR↑SSIM↑LPIPS↓Acc.↑PSNR↑SSIM↑LPIPS↓Acc.↑
SRCNN [12]23.34.868.09582.1719.56.750.21871.41
ESRGAN [68]23.72.891.08583.2519.86.778.20472.12
TSRN [64]24.27.893.09485.8220.67.782.20176.94
TBSRN [7]25.62.906.07492.3721.07.794.18684.32
TATT [41]25.84.907.07393.2621.49.800.18585.17
Ours28.32.941.03399.1624.04.873.09692.53
", + "image_path": "387fcc5ee8efdf7202f90380a306e539d233dd445f79453b23d4349d41980585.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 363, + 287, + 387 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 363, + 287, + 387 + ], + "spans": [ + { + "bbox": [ + 46, + 363, + 287, + 387 + ], + "type": "text", + "content": "image diversity. It takes two days for pre-training StyleGAN and nearly four days for training the whole MARCONet." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 388, + 287, + 603 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 388, + 287, + 603 + ], + "spans": [ + { + "bbox": [ + 46, + 388, + 287, + 603 + ], + "type": "text", + "content": "Baselines. Since there are few works studying the problem of these types of text images on SR task, we compare with two types of methods following TATT [41], i.e., general image SR (i.e., SRCNN [12], ESRGAN [68]) and recent text image SR (i.e., TSRN [64], TBSRN [7] and TATT [41]). For a fair comparison, we modify their codes to handle " + }, + { + "bbox": [ + 46, + 388, + 287, + 603 + ], + "type": "inline_equation", + "content": "\\times 2" + }, + { + "bbox": [ + 46, + 388, + 287, + 603 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 388, + 287, + 603 + ], + "type": "inline_equation", + "content": "\\times 4" + }, + { + "bbox": [ + 46, + 388, + 287, + 603 + ], + "type": "text", + "content": " SR tasks, and carefully retrain them with the same training data as Ours. In particular, the retrained TBSRN adopts the ground-truth text and bounding boxes for its pretrained content-aware and position-aware modules. As for TATT, we also use the ground-truth text to pre-train its TPG module. We report the quantitative and qualitative results on our synthetic dataset, which contains 1,000 LR/HR pairs for " + }, + { + "bbox": [ + 46, + 388, + 287, + 603 + ], + "type": "inline_equation", + "content": "\\times 2" + }, + { + "bbox": [ + 46, + 388, + 287, + 603 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 388, + 287, + 603 + ], + "type": "inline_equation", + "content": "\\times 4" + }, + { + "bbox": [ + 46, + 388, + 287, + 603 + ], + "type": "text", + "content": " tasks, respectively. These LR inputs are injected with random noise, blurring and JPEG compression, to simulate real-world degradation. We also provide the results on real-world text images collected from different sources. More results can be found in the suppl." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 610, + 189, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 610, + 189, + 624 + ], + "spans": [ + { + "bbox": [ + 47, + 610, + 189, + 624 + ], + "type": "text", + "content": "4.1. Quantitative Comparison" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "content": "Table 1 summarizes the PSNR, SSIM and LPIPS [76] of different methods on the synthetic dataset. An additional pre-trained CRNN [56] is used to compute the recognition accuracy of SR results (Acc.), serving as an auxiliary indicator for the restoration performance. Note that the synthetic data is non-trivial given its low quality. Without specifically designed components for text images, general SR methods" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 252, + 547, + 372 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 252, + 547, + 372 + ], + "spans": [ + { + "bbox": [ + 304, + 252, + 547, + 372 + ], + "type": "text", + "content": "perform poorly as expected. By incorporating the recognition information, both TBSRN [7] and TATT [41] show obvious improvement, especially in retaining the semantic layout of character for recognition (see Acc. columns). Our method achieves the best quantitative results and outperforms others with a large margin (e.g., 2.5 dB higher than the second-best method on average). Even with severe degradation (i.e., " + }, + { + "bbox": [ + 304, + 252, + 547, + 372 + ], + "type": "inline_equation", + "content": "\\times 4" + }, + { + "bbox": [ + 304, + 252, + 547, + 372 + ], + "type": "text", + "content": "), our method still attains favorable performance, which can be ascribed to the effectiveness of the learned generative structure prior for each character." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 379, + 441, + 392 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 379, + 441, + 392 + ], + "spans": [ + { + "bbox": [ + 305, + 379, + 441, + 392 + ], + "type": "text", + "content": "4.2. Qualitative Comparison" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 397, + 547, + 588 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 397, + 547, + 588 + ], + "spans": [ + { + "bbox": [ + 304, + 397, + 547, + 588 + ], + "type": "text", + "content": "Figure 5 shows the visual comparison on our synthetic LR images for " + }, + { + "bbox": [ + 304, + 397, + 547, + 588 + ], + "type": "inline_equation", + "content": "\\times 2" + }, + { + "bbox": [ + 304, + 397, + 547, + 588 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 397, + 547, + 588 + ], + "type": "inline_equation", + "content": "\\times 4" + }, + { + "bbox": [ + 304, + 397, + 547, + 588 + ], + "type": "text", + "content": " tasks. With careful retraining, competing methods perform favorably when the LR input has slight degradation, but they are not able to recover the unique structure of characters with complex strokes. When the degradation turns more severe, all of them fail to restore satisfactory results (see the last column). The results yielded by TBSRN [7] and TATT [41] suggest that high-level recognition constraints bring limited benefit to the SR task, especially in coping with diverse and complex font structures and styles. With the guidance of characters' generative structure prior, our method shows compelling results that exhibit more consistent structures with ground-truth (GT). It is interesting to observe the strong performance of MARCONet in restoring heavily degraded LR input that is challenging for humans to recognize (last column of Figure 5)." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 589, + 547, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 589, + 547, + 696 + ], + "spans": [ + { + "bbox": [ + 304, + 589, + 547, + 696 + ], + "type": "text", + "content": "Apart from the evaluation on synthetic LR input, we also evaluate our method on real-world LR text images. We collect real-world LR text images from different sources, e.g., invoices, license plates, scanned documents, road signs, plaques, video captions, and scene texts from TextZoom [64]. Each text region is cropped by " + }, + { + "bbox": [ + 304, + 589, + 547, + 696 + ], + "type": "inline_equation", + "content": "\\mathrm{CnSTD}^2" + }, + { + "bbox": [ + 304, + 589, + 547, + 696 + ], + "type": "text", + "content": ". We compare with two competing methods, i.e., TBSRN [7] and TATT [41], which are specifically designed for text images and achieve the top quantitative results in Table 1. The results are shown" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 316, + 702, + 446, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 702, + 446, + 712 + ], + "spans": [ + { + "bbox": [ + 316, + 702, + 446, + 712 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 316, + 702, + 446, + 712 + ], + "type": "text", + "content": "https://github.com/breezeedeus/CnSTD" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10108" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 84, + 62, + 508, + 358 + ], + "blocks": [ + { + "bbox": [ + 84, + 62, + 508, + 358 + ], + "lines": [ + { + "bbox": [ + 84, + 62, + 508, + 358 + ], + "spans": [ + { + "bbox": [ + 84, + 62, + 508, + 358 + ], + "type": "image", + "image_path": "cce5c68a6860a978ed4574feea5a37d7a72d289a11c6f7564d65a68b865fc8ba.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 363, + 537, + 374 + ], + "lines": [ + { + "bbox": [ + 54, + 363, + 537, + 374 + ], + "spans": [ + { + "bbox": [ + 54, + 363, + 537, + 374 + ], + "type": "text", + "content": "Figure 6. Visual comparison on real-world LR text images, including invoice, license plate, scanned document, road sign, plaque, etc." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 384, + 290, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 384, + 290, + 552 + ], + "spans": [ + { + "bbox": [ + 46, + 384, + 290, + 552 + ], + "type": "text", + "content": "in Figure 6. Benefiting from our synthetic training data, the competing methods achieve comparable performance on these characters with simple structures, even for LR inputs corrupted by unknown and complex degradation. The positive results suggest that our synthetic HR text images are of high quality and well-suited as ground-truth for the SR task. The usage of degradation models from BSRGAN [75] and Real-ESRGAN [66] further benefits these methods in synthesizing realistic LR inputs. However, both of these two methods fail to generate plausible results when the LR character is degraded severely or contains complex structures. In contrast, with the proposed generative structure prior, our method achieves the best performance, not only in visual quality, but also in the generation of accurate structures." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 562, + 142, + 575 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 562, + 142, + 575 + ], + "spans": [ + { + "bbox": [ + 47, + 562, + 142, + 575 + ], + "type": "text", + "content": "4.3. Ablation Study" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "content": "Analyses of " + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{W}" + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "content": " Space. The " + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{W}" + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "content": " space controls the style of a character's structure prior. Figure 7 shows the structure image " + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "inline_equation", + "content": "S_{SR}^{c}" + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "content": " from our StyleGAN with " + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "inline_equation", + "content": "w\\in \\mathcal{W}" + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "content": " and character indexes predicted from the LR input. One can observe that " + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "content": " can well capture the manifold of font styles, e.g., the thickness of different font families (1-st column) and different font sizes and locations (2-nd column). We also interpolate two " + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "content": " from different LR inputs and demonstrate their results in the " + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "inline_equation", + "content": "3\\sim 5" + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "content": " rows. One can see that the generated structures change smoothly, indicating that " + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "content": " in our framework also has the editable ability like the original StyleGAN. Finally," + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 384, + 547, + 492 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 384, + 547, + 492 + ], + "spans": [ + { + "bbox": [ + 304, + 384, + 547, + 492 + ], + "type": "text", + "content": "we use the predicted " + }, + { + "bbox": [ + 304, + 384, + 547, + 492 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 304, + 384, + 547, + 492 + ], + "type": "text", + "content": " from a real-world LR video frame (The Dream of the Red Chamber) and explore font style transfer. Even though the LR input contains a traditional Chinese character and the font family does not exist in our training data, our predicted " + }, + { + "bbox": [ + 304, + 384, + 547, + 492 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 304, + 384, + 547, + 492 + ], + "type": "text", + "content": " can well capture its style and successfully transfer it to other characters. Besides, the " + }, + { + "bbox": [ + 304, + 384, + 547, + 492 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 304, + 384, + 547, + 492 + ], + "type": "text", + "content": " latent and character code " + }, + { + "bbox": [ + 304, + 384, + 547, + 492 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 384, + 547, + 492 + ], + "type": "text", + "content": " are disentangled, judging from the good separation of roles between the " + }, + { + "bbox": [ + 304, + 384, + 547, + 492 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 304, + 384, + 547, + 492 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 384, + 547, + 492 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 384, + 547, + 492 + ], + "type": "text", + "content": " in style control and storing the unique structure for each character." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 498, + 548, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 548, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 548, + 714 + ], + "type": "text", + "content": "Analyses of Variants. Here we consider the following variants to evaluate each part of our MARCONet, 1) Ours " + }, + { + "bbox": [ + 304, + 498, + 548, + 714 + ], + "type": "inline_equation", + "content": "(UNet)" + }, + { + "bbox": [ + 304, + 498, + 548, + 714 + ], + "type": "text", + "content": " & Ours " + }, + { + "bbox": [ + 304, + 498, + 548, + 714 + ], + "type": "inline_equation", + "content": "(UNet^{\\dagger})" + }, + { + "bbox": [ + 304, + 498, + 548, + 714 + ], + "type": "text", + "content": ": only taking ResNet45 and UNet to perform the SR task and increasing its model parameters, respectively, 2) Ours (CRNN) & Ours (PSP): replacing our Transformer-based character classification and " + }, + { + "bbox": [ + 304, + 498, + 548, + 714 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 304, + 498, + 548, + 714 + ], + "type": "text", + "content": " inversion branches with CRNN [56] and PSP encoder [54], respectively, 3) Ours " + }, + { + "bbox": [ + 304, + 498, + 548, + 714 + ], + "type": "inline_equation", + "content": "(D^{-})" + }, + { + "bbox": [ + 304, + 498, + 548, + 714 + ], + "type": "text", + "content": ": only taking the SR and HR images as input of discriminator without concatenating their structure images, 4) Ours " + }, + { + "bbox": [ + 304, + 498, + 548, + 714 + ], + "type": "inline_equation", + "content": "(w / o S)" + }, + { + "bbox": [ + 304, + 498, + 548, + 714 + ], + "type": "text", + "content": ": removing StyleGAN and directly incorporating the code " + }, + { + "bbox": [ + 304, + 498, + 548, + 714 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 498, + 548, + 714 + ], + "type": "text", + "content": " on each LR character features through spatial affine transformation, 5) Ours " + }, + { + "bbox": [ + 304, + 498, + 548, + 714 + ], + "type": "inline_equation", + "content": "(w / o C)" + }, + { + "bbox": [ + 304, + 498, + 548, + 714 + ], + "type": "text", + "content": ": removing codebook and directly taking each LR character features into a pre-trained StyleGAN that produces colored output like GFPGAN [65], 6) Ours (#32) & Ours (#64): only using the structure prior transform module on feature sizes of either " + }, + { + "bbox": [ + 304, + 498, + 548, + 714 + ], + "type": "inline_equation", + "content": "32 \\times 32" + }, + { + "bbox": [ + 304, + 498, + 548, + 714 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 304, + 498, + 548, + 714 + ], + "type": "inline_equation", + "content": "64 \\times 64" + }, + { + "bbox": [ + 304, + 498, + 548, + 714 + ], + "type": "text", + "content": ". Their performance on our synthetic test set is shown in Table 2 and Figure 8. We can observe" + } + ] + } + ], + "index": 6 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "10109" + } + ] + } + ], + "index": 7 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 78, + 62, + 230, + 261 + ], + "blocks": [ + { + "bbox": [ + 78, + 62, + 230, + 261 + ], + "lines": [ + { + "bbox": [ + 78, + 62, + 230, + 261 + ], + "spans": [ + { + "bbox": [ + 78, + 62, + 230, + 261 + ], + "type": "image", + "image_path": "c883fe39ae803d3bfe151e28331dbb34771946ce3de864516131f2cb560cdc2a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 266, + 545, + 289 + ], + "lines": [ + { + "bbox": [ + 46, + 266, + 545, + 289 + ], + "spans": [ + { + "bbox": [ + 46, + 266, + 545, + 289 + ], + "type": "text", + "content": "Figure 7. The " + }, + { + "bbox": [ + 46, + 266, + 545, + 289 + ], + "type": "inline_equation", + "content": "\\mathcal{W}" + }, + { + "bbox": [ + 46, + 266, + 545, + 289 + ], + "type": "text", + "content": " space in StyleGAN controls the font style of characters. The 1-st and 7-th rows are LR input. The 2-nd and 6-th rows are output of StyleGAN with " + }, + { + "bbox": [ + 46, + 266, + 545, + 289 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 46, + 266, + 545, + 289 + ], + "type": "text", + "content": " and code indexes from their LR input. The remaining rows are the interpolation results of " + }, + { + "bbox": [ + 46, + 266, + 545, + 289 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 46, + 266, + 545, + 289 + ], + "type": "text", + "content": " from two LR inputs." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 231, + 62, + 398, + 261 + ], + "blocks": [ + { + "bbox": [ + 231, + 62, + 398, + 261 + ], + "lines": [ + { + "bbox": [ + 231, + 62, + 398, + 261 + ], + "spans": [ + { + "bbox": [ + 231, + 62, + 398, + 261 + ], + "type": "image", + "image_path": "fd00eabebcc0dc241e083d9c1aae0c416446f51291a6a29e1fe5c0a0a385f656.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 399, + 62, + 515, + 261 + ], + "blocks": [ + { + "bbox": [ + 399, + 62, + 515, + 261 + ], + "lines": [ + { + "bbox": [ + 399, + 62, + 515, + 261 + ], + "spans": [ + { + "bbox": [ + 399, + 62, + 515, + 261 + ], + "type": "image", + "image_path": "ed5a75e65ae181afc2d420fa9915d8238d90f73981f52d58342375646f2b0118.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 48, + 310, + 287, + 437 + ], + "blocks": [ + { + "bbox": [ + 47, + 297, + 286, + 307 + ], + "lines": [ + { + "bbox": [ + 47, + 297, + 286, + 307 + ], + "spans": [ + { + "bbox": [ + 47, + 297, + 286, + 307 + ], + "type": "text", + "content": "Table 2. Comparison of different variants of the proposed method." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 310, + 287, + 437 + ], + "lines": [ + { + "bbox": [ + 48, + 310, + 287, + 437 + ], + "spans": [ + { + "bbox": [ + 48, + 310, + 287, + 437 + ], + "type": "table", + "html": "
Variants×2×4
PSNR↑SSIM↑LPIPS↓Acc.↑PSNR↑SSIM↑LPIPS↓Acc.↑
Ours (UNet)23.69.890.09482.6319.84.777.20971.96
Ours (UNet†)23.71.891.09282.7419.87.778.20372.16
Ours (CRNN)28.00.931.03498.8723.98.871.10192.41
Ours (PSP)28.04.932.03599.0723.99.871.09992.49
Ours (D-)28.29.940.03499.1123.94.870.09892.48
Ours (w/o S)25.86.907.07494.6421.57.802.18286.63
Ours (w/o C)25.53.905.04192.2521.39.798.12883.71
Ours (#32)28.16.937.03998.8623.96.870.10192.16
Ours (#64)28.30.940.03599.1024.02.872.09992.33
Ours (Full)28.32.941.03399.1624.04.873.09692.53
", + "image_path": "99ab50dccca87e9882254ee1702b31a2c57aa0fd74f6f0010c6c19fdf54cad6d.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 450, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 450, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 450, + 287, + 713 + ], + "type": "text", + "content": "that a) Ours (UNet) and Ours " + }, + { + "bbox": [ + 46, + 450, + 287, + 713 + ], + "type": "inline_equation", + "content": "(UNet^{\\dagger})" + }, + { + "bbox": [ + 46, + 450, + 287, + 713 + ], + "type": "text", + "content": " perform on par with general SR methods, and indicate that a mere increase in model capacity would not bring significant performance improvement; b) the Transformer-based encoder is more effective than CRNN [56] and PSP encoder [54], which may be caused by the global attention and thus contribute better to the classification and GAN inversion tasks. It is observed that Ours (CRNN) sometimes makes wrong predictions on character. While the SR leads to a clear image, the character loses its actual semantic layout (see red box in Figure 8); c) the concatenation of structure image on discriminator is beneficial for emphasizing the structure prior more on LR input and thus boosting the final SR result; d) by removing StyleGAN and codebook, Ours " + }, + { + "bbox": [ + 46, + 450, + 287, + 713 + ], + "type": "inline_equation", + "content": "(w / o S)" + }, + { + "bbox": [ + 46, + 450, + 287, + 713 + ], + "type": "text", + "content": " and Ours " + }, + { + "bbox": [ + 46, + 450, + 287, + 713 + ], + "type": "inline_equation", + "content": "(w / o C)" + }, + { + "bbox": [ + 46, + 450, + 287, + 713 + ], + "type": "text", + "content": " show obvious inferior results, indicating that codebook can benefit the recognition accuracy while StyleGAN contributes more on the visual quality (e.g., LPIPS); e) Ours (#64) has slightly better results than Ours (#32) but both of them are inferior to Ours (Full) that deploys a multi-scale structure prior transform module. From these analyses, we conclude that the Transformer-based encoder, codebook, StyleGAN and multi-scale structure prior transform module are all crucial" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 312, + 299, + 541, + 466 + ], + "blocks": [ + { + "bbox": [ + 312, + 299, + 541, + 466 + ], + "lines": [ + { + "bbox": [ + 312, + 299, + 541, + 466 + ], + "spans": [ + { + "bbox": [ + 312, + 299, + 541, + 466 + ], + "type": "image", + "image_path": "d3e51e4657c5930b1ae78e22b1c03551c9a25db6ace27e70a71d29194c5b1dcd.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 335, + 469, + 515, + 480 + ], + "lines": [ + { + "bbox": [ + 335, + 469, + 515, + 480 + ], + "spans": [ + { + "bbox": [ + 335, + 469, + 515, + 480 + ], + "type": "text", + "content": "Figure 8. Visual comparison of different variants." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 490, + 497, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 490, + 497, + 502 + ], + "spans": [ + { + "bbox": [ + 306, + 490, + 497, + 502 + ], + "type": "text", + "content": "for achieving good performance in Ours (Full)." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 513, + 378, + 525 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 513, + 378, + 525 + ], + "spans": [ + { + "bbox": [ + 306, + 513, + 378, + 525 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 533, + 547, + 663 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 547, + 663 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 547, + 663 + ], + "type": "text", + "content": "In this work, we made the first attempt to embed the generative structure prior for blind SR of text images. The combination of a codebook for storing distinctive character-specific codes and a retrofitted StyleGAN for controlling font style cope well with complicated structures, high similarity between characters, and a great variety of font styles. We have shown that such structure prior is beneficial for super-resolving LR text images, even for those with severe degradation. We can potentially extend it to other text-related tasks, e.g., text image completion for ancient documents, font style transformation, and few-shot font generation." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "content": "Acknowledgement. This study is supported under the RIE2020 Industry Alignment Fund - Industry Collaboration Projects (IAF-ICP) Funding Initiative, as well as cash and in-kind contribution from the industry partner(s)." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10110" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 712 + ], + "type": "list", + "angle": 0, + "index": 19, + "blocks": [ + { + "bbox": [ + 53, + 91, + 288, + 123 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 288, + 123 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 288, + 123 + ], + "type": "text", + "content": "[1] Eirikur Agustsson and Radu Timofte. 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However, the need for large-scale scene datasets can impede scalability and further improvements. This paper explores an alternative learning method by leveraging a lightweight and publicly available type of 3D data in the form of CAD models. We construct a 3D space with geometric-aware alignment where the similarity in this space reflects the geometric similarity of CAD models based on the Chamfer distance. The acquired geometric-aware properties are then induced into 2D features, which boost performance on downstream tasks more effectively than existing RGB-CAD approaches. Our technique is not limited to paired RGB-CAD datasets. By training exclusively on pseudo pairs generated from CAD-based reconstruction methods, we enhance the performance of SOTA 2D pre-trained models that use ResNet-50 or ViT-B backbones on various 2D understanding tasks. We also achieve comparable results to SOTA methods trained on scene scans on four tasks in NYUv2, SUNRGB-D, indoor ADE20k, and indoor/outdoor COCO, despite using lightweight CAD models or pseudo data. Please visit our page: https://", + "bbox": [ + 76, + 325, + 473, + 689 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "//GeoAware2dRepUsingCAD.github.io/", + "bbox": [ + 78, + 689, + 349, + 700 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 78, + 737, + 207, + 752 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recent 2D visual representation learning approaches, such as contrastive learning [3, 6, 10, 17, 28] or masked autoencoder [20], are widely used to tackle various problems in computer vision due to their ability to encode rich visual features. While these methods have shown exceptional results on 2D image classification, they still have shortcomings in other 2D understanding tasks that involve instance-level reasoning. Prior research [25] also shows that models pre-trained using image augmentations [8,21] or supervised", + "bbox": [ + 76, + 763, + 468, + 902 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/68a9afe9805c7f178efb03c903f64007cac465bf3828961fe44392f555e6ef81.jpg", + "image_caption": [ + "Figure 1. Overview concept of our solution. We leverage CAD models to train a joint 2D-3D space such that images of objects with similar shapes, based on the Chamfer distance, are attracted to each other, while images with different shapes are separated. This results in a continuous geometric-aware space where the distance between two points reflects their geometric similarity, which could be utilized for downstream 2D object understanding tasks." + ], + "image_footnote": [], + "bbox": [ + 511, + 290, + 880, + 551 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "labels [13] could not deliver satisfactory results when applied to downstream tasks such as semantic segmentation, instance segmentation, and object detection [12, 42].", + "bbox": [ + 498, + 667, + 890, + 714 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To alleviate this, Hou et al. [25] proposed to learn 3D geometric priors, such as view-invariance, from 3D data and transfer the learned priors to 2D representations. In particular, their model is first pre-trained on ScanNet [12], a database of multi-view RGB-D scans, using contrastive learning and later used as initialization for fine-tuning networks on downstream tasks. Chen et al. [5] further extend this work by utilizing additional priors through learning to group nearby points that refer to the same object part from 3D scenes.", + "bbox": [ + 496, + 715, + 892, + 866 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The key concept of their introduced new paradigm is to share useful 3D priors from 3D data with 2D representa", + "bbox": [ + 500, + 869, + 890, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "21371", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tions. However, previous studies have investigated mostly 3D priors related to viewpoint invariance from 3D scene datasets, which are often limited in size and scene variations due to the laborious data collecting and labeling process [24]. This scarcity of large-scale 3D data also limits the number of available 3D priors for learning the invariance, hence hindering further performance gains. This paper questions whether there are other effective 3D priors for 2D downstream tasks and whether they can be learned from other forms of 3D data that are lighter and easier to obtain.", + "bbox": [ + 75, + 90, + 472, + 242 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We begin our exploration by considering how to learn an embedding space that maps together images with the same or similar geometries. One solution is to learn from images that share the same 3D model, which inspires our interest in CAD models. Unlike 3D scenes, CAD models are lightweight, publicly available, and can be easily aligned with RGB images via web scraping or human annotation [2]. There exist studies that jointly learn 2D and 3D CAD representation for other CAD-related tasks, e.g., 3D classification [1,27]. However, their 2D features, which are derived from augmentation-based CAD features, are insufficient to be directly applied to 2D object understanding tasks—they can group images with similar geometries but struggle to learn the distinctions between object categories.", + "bbox": [ + 75, + 244, + 472, + 457 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We argue that useful geometric-aware representations should account for both similarities and differences in object geometry. Our key idea is to acquire such features by imitating the Chamfer distance between 3D objects in our embedding space and inducing this derived geometric awareness in our learned 2D representation. In particular, we learn our space by attracting the encoded features of geometrically similar CAD models in the mini-batch based on the Chamfer distance and repelling those with lower similarities. In contrast to other methods trained on supervised discrete signals like object labels or through 3D augmentations, our method produces a continuous 3D space that better captures the similarity and difference in geometry (see Section 5.1). In addition, we employ augmentation-based contrastive learning [6] to learn other useful visual feature properties, such as translation and color invariances. This results in a 2D representation in a 2D-3D space that contains rich visual information and strong geometric-aware properties, as shown in Fig. 1, which can be leveraged to improve 2D object understanding tasks.", + "bbox": [ + 75, + 459, + 472, + 762 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To match our geometric-aware CAD features with corresponding 2D features, a paired RGB-CAD dataset, such as Pix3D [45], is required. However, by leveraging recent techniques [19, 31] that can reconstruct a CAD model from an input image, it is possible to generate pseudo CAD models for any images and use them to learn our method without a paired dataset. Adapting this pseudo-pair generation to other techniques that rely on scene scans is significantly harder, as synthesizing full 3D scenes with reasonable detail", + "bbox": [ + 75, + 763, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "remains harder than reconstructing individual objects.", + "bbox": [ + 498, + 90, + 854, + 106 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We demonstrate the effectiveness of our geometric-aware 2D representation in Fig. 2. Our features can group and differentiate objects based on their categories or subcategories, leading to improved performance on multiple 2D object understanding tasks using both ResNet-50 [23] and ViT-B [29] backbones. Our method trained on a pseudopair dataset also yields superior results over DINO [3] and MAE [20]. Remarkably, we also surpass a state-of-the-art method, Pri3D [25] without using any 3D scene scans in the following tasks: (i) semantic segmentation using NYUv2 [42] and indoor ADE20k [54]; (ii) object detection and instance segmentation using NYUv2 and in/outdoor COCO [35]; (iii) object retrieval using Pix3D [45].", + "bbox": [ + 496, + 107, + 890, + 301 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To summarize, our contributions are as follows.", + "bbox": [ + 517, + 303, + 834, + 316 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We present a simple yet effective approach to inducing geometric-aware properties in 2D representation using lightweight CAD models. These can be either ground truth from RGB-CAD datasets or generated pseudo CAD pairs based on 2D-only data.", + "- We propose training objectives to learn a 2D-3D embedding space where feature similarity reflects geometric similarity based on the Chamfer distance.", + "- We enhance the performance of SOTA 2D representation learning techniques on four 2D object understanding tasks and achieve competitive results to SOTA that require 3D scene scans across five datasets, in both settings that use real or pseudo-RGB-CAD datasets." + ], + "bbox": [ + 517, + 316, + 890, + 516 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related works", + "text_level": 1, + "bbox": [ + 500, + 527, + 643, + 542 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2D Representation Learning. Contrastive learning [49] has continuously shown improvements in various downstream tasks. Its main concept is to maximize a similarity score between two different views (e.g., two different augmentations of the same instance [6, 9, 10, 17, 21], two instances with the same label [28], or two different encoders [3, 7]). Meanwhile, learning representation in autoencoder fashion [20] also has recently demonstrated a performance boost from contrastive learning works.", + "bbox": [ + 496, + 553, + 890, + 688 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "This paper shows that these 2D representation learning methods could not provide geometric-aware properties, which are critical in object understanding tasks.", + "bbox": [ + 496, + 689, + 890, + 734 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3D Representation Learning requires specific network architecture for extracting features based on an input's data structure (e.g., rendered images [44], point clouds [39, 46], or meshes [15, 16]). These architectures can encode geometric information of each 3D shape into representations with a deep understanding of shape structure. Later, contrastive learning in 3D, such as point cloud augmentation [52], or multiple modalities [1, 53], showed their improvement in 3D classification, retrieval, and part segmentation problems. Concurrently, 3D reconstruction techniques [11, 14, 37] also deliver promising results in similar tasks.", + "bbox": [ + 496, + 734, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "21372", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/c1158c3436b75be9708460bf079194afc0a4a29aaa00fbb2378c30da4ca57ab8.jpg", + "image_caption": [ + "Figure 2. Visualization of the pairwise cosine similarity between the learned representations of objects from each method. The bright color indicates higher similarity. The first row shows the similarity scores of all validation images in Pix3D [45] dataset, sorted by object category and subcategory (i.e., object models). The second row zooms in on a single category (Sofa) from the first row. Our method shows a better grouping of the same sofa than others, especially SimCLR [6] and SupCon [28], which can hardly differentiate between each sofa type. CrossPoint [1] and SupCon (fine), unlike others, can group the same sofa but fail to separate sofas from other categories in the first row. Surprisingly, MAE [20] also delivers visual features without subcategory awareness. Compared to SimCLR, Ours (pseudo) provides distinguishable features (with darker colors) between each sofa type. Additional studies on Ours (pseudo) are provided in Appendix B." + ], + "image_footnote": [], + "bbox": [ + 83, + 88, + 883, + 272 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this paper, we adapt the encoded 3D features with rich geometric information to share the ability to recognize geometric similarities in each object to 2D representations.", + "bbox": [ + 76, + 386, + 470, + 431 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Multimodal Representation Learning gains attraction due to its ability to share modality-specific contexts. CLIP [40] facilitates various vision-language tasks by contrastive learning on text-image data. Similarly, 2D-3D representation learning transfers geometric information from 3D to 2D features [5, 25, 36]. Pri3D [25] introduces a contrastive learning method on multi-view RGB frames and 3D scene scans [12]. These modal pairs allow them to learn view and 3D priors in 2D features and achieve impressive 2D indoor scene understanding performance. Later, SetInfoNCE [5] improves upon Pri3D by fine-tuning the Pri3D pre-trained model using additional 3D priors, e.g., sets of nearby points referring to the same object part, generated from training scans. While these studies have focused on scene scans, this paper demonstrates that geometric priors from CAD models can achieve comparable or better object understanding than learning on 3D scenes.", + "bbox": [ + 75, + 431, + 468, + 686 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Some studies, e.g., CrossPoint [1, 27], have been conducted to share visual context to guide CAD features (2D $\\rightarrow$ 3D). Their learned 2D features, on the other hand, fail to discriminate object categories, resulting in poor object understanding results. We then investigate a more efficient method of learning and sharing modality-specific context from CAD to RGB without hurting 2D task performance.", + "bbox": [ + 75, + 688, + 468, + 794 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2D-3D Object Matching has been studied for searching or generating a 3D model of objects appearing in a given image. [19, 30-32] use existing CAD databases to train an RGB-CAD retrieval and alignment module in a multi-task learning fashion using a given set of ground truths (e.g., camera intrinsic, depth map, mask, or pose parameters). [26, 34] utilize category labels to guide a joint RGB-CAD", + "bbox": [ + 75, + 795, + 470, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "space for 2D-3D retrieval tasks. Another approach is to reconstruct a 3D model from the image directly [16, 18, 47]. However, the generated 3D may be less realistic than retrieving human-designed 3D from the databases.", + "bbox": [ + 496, + 386, + 890, + 446 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We utilize these works to generate CAD pairs for our pre-training RGB images. Learning representation on just pseudo-RGB-CAD pairs can surpass SOTA competitors.", + "bbox": [ + 496, + 449, + 893, + 494 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Proposed method", + "text_level": 1, + "bbox": [ + 500, + 518, + 669, + 535 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our goal is to construct a pre-trained model that can provide a 2D representation $\\mathbf{z}_i^!$ of an input image $I_{i}$ with useful geometric priors to enhance 2D object understanding. Unlike prior works [5,25], we aim to learn the representations without 3D scene scans using other efficient alternatives.", + "bbox": [ + 496, + 546, + 890, + 622 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We propose a novel approach that can obtain such geometric priors from a lightweight and publicly available type of 3D data in the form of CAD models, while retaining discriminative representations for 2D tasks. Given an image $I_{i}$ and its associated CAD model $G_{i}$ , our solution constructs a 2D-3D embedding space with strong geometric-aware properties by learning CAD features $\\mathbf{z}_{i}^{\\mathrm{G}} = f^{\\mathrm{G}}(G_{i})$ along with rich visual information from 2D features $\\mathbf{z}_{i}^{\\mathrm{I}} = f^{\\mathrm{I}}(I_{i})$ . We show that the acquired 2D representations, where their feature similarity reflects geometric similarity, are more effective than solely relying on standard augmentation invariant CAD features and perform almost as effectively as 3D priors from scene scans on common 2D understanding tasks. The overview of our proposed framework is shown in Fig. 3.", + "bbox": [ + 496, + 625, + 892, + 851 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "An extension to training our model on generated RGB-CAD pairs is further introduced in order to learn geometric-aware representations using just RGB training data.", + "bbox": [ + 496, + 854, + 890, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "21373", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/f81051a1ad6e9320d56d629dc8ee2b92513827b249b80b14b7fe386dd626e426.jpg", + "image_caption": [ + "Figure 3. Our pre-training strategy. We learn 2D representations on a joint 2D-3D space from RGB-CAD pairs based on three loss functions. $L_{\\mathrm{GEO}}$ focuses on learning CAD features from two similar CAD models mined from Chamfer distance, $L_{\\mathrm{IMG}}$ focuses on learning visual differences between two image augmentations, and $L_{\\mathrm{CROSS}}$ shares geometric awareness from CAD features to 2D representation." + ], + "image_footnote": [], + "bbox": [ + 96, + 87, + 872, + 315 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1. Training objectives", + "text_level": 1, + "bbox": [ + 76, + 375, + 261, + 391 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The core idea of our training objective is to share two modality-specific contexts, i.e., strong geometric-aware properties from $\\mathbf{z}_i^{\\mathrm{G}}\\in \\mathbf{z}^{\\mathrm{G}}$ and rich visual information from $\\mathbf{z}_i^{\\mathrm{I}}\\in \\mathbf{z}^{\\mathrm{I}}$ , in the joint 2D-3D embedding space by training on RGB-CAD pairs $(I,G)$ . To achieve this objective, we use three loss functions: $L_{\\mathrm{GEO}}$ , $L_{\\mathrm{IMG}}$ , and $L_{\\mathrm{CROSS}}$ . The first loss $L_{\\mathrm{GEO}}$ helps the 3D encoder $f^{\\mathrm{G}}(\\cdot)$ construct a geometric-aware embedding space, such that CAD models in $G$ with similar shapes, based on the Chamfer distance, are located near each other. The second loss $L_{\\mathrm{IMG}}$ helps the 2D encoder $f^{\\mathrm{I}}(\\cdot)$ learn useful visual representation properties, e.g., translation and color invariance from $I$ . The third loss $L_{\\mathrm{CROSS}}$ enforces the consistency between $\\mathbf{z}_i^{\\mathrm{G}}$ and $\\mathbf{z}_i^{\\mathrm{I}}$ for each $(I_i,G_i)$ pair. Finally, the multi-task loss function is", + "bbox": [ + 75, + 398, + 473, + 612 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL = L _ {\\text {G E O}} + L _ {\\text {I M G}} + L _ {\\text {C R O S S}}. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 176, + 621, + 468, + 638 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Detailed explanations of the three components are given in the following subsections.", + "bbox": [ + 75, + 647, + 468, + 678 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1.1 Geometric-aware CAD features", + "text_level": 1, + "bbox": [ + 76, + 695, + 352, + 709 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We first explain how $L_{\\mathrm{GEO}}$ provides geometric awareness to our features. Given $(I_i, G_i)$ , we use $G_i$ to train $f^{\\mathrm{G}}(\\cdot)$ for extracting a geometric context $\\mathbf{z}_i^{\\mathrm{G}}$ of each pair. We process each $G_i$ by converting it to a point cloud and use DGCNN [46] as $f^{\\mathrm{G}}(\\cdot)$ to capture local and global point cloud structure information, resulting in an encoded feature $\\mathbf{z}_i^{\\mathrm{G}}$ .", + "bbox": [ + 75, + 719, + 468, + 825 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To learn the space, we follow a common contrastive learning strategy by maximizing the similarity between $\\mathbf{z}_i^{\\mathrm{G}}$ and the encoded feature $\\mathbf{z}^{+}$ of each positive term in a minibatch. However, instead of selecting $\\mathbf{z}^{+}$ based on object labels or augmentations as is commonly done, we select $\\mathbf{z}^{+}$", + "bbox": [ + 75, + 825, + 470, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "based on a geometric-based similarity function, the Chamfer distance.", + "bbox": [ + 496, + 376, + 890, + 404 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We calculate pairwise Chamfer distances across a minibatch and select $K$ point clouds with the lowest distances to be the positive terms for each $G_{i}$ in the loss function. We call this process Chamfer mining. The set of encoded positive terms is referred to as $P(\\mathbf{z}_i^{\\mathrm{G}})$ . Finally, the contrastive loss is given as", + "bbox": [ + 496, + 405, + 890, + 489 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\mathrm {G E O}} = \\frac {1}{N K} \\sum_ {i = 1} ^ {N} \\sum_ {\\mathbf {z} ^ {+} \\in P \\left(\\mathbf {z} _ {i} ^ {\\mathrm {G}}\\right)} - \\log \\frac {\\exp \\left(\\mathbf {z} _ {i} ^ {\\mathrm {G}} \\cdot \\mathbf {z} ^ {+} / \\tau\\right)}{\\sum_ {\\mathbf {z} ^ {-} \\in \\mathbf {z} ^ {\\mathrm {G}} \\backslash \\left\\{\\mathbf {z} _ {i} ^ {\\mathrm {G}} \\right\\}} \\exp \\left(\\mathbf {z} _ {i} ^ {\\mathrm {G}} \\cdot \\mathbf {z} ^ {-} / \\tau\\right)}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 504, + 496, + 890, + 549 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $N$ is the batch size and $\\tau$ is a tunable temperature parameter. Using $\\mathbf{z}^{+}$ based on the Chamfer distance better captures the similarity and difference in 3D geometry and benefits 2D representation than other choices, e.g., 3D augmentation or category labels, which will be discussed later in Section 5.5 and Appendix B.", + "bbox": [ + 496, + 550, + 890, + 642 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1.2 Learning to discriminate 2D visual features", + "text_level": 1, + "bbox": [ + 498, + 657, + 856, + 672 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Translation and color invariance are crucial in many vision problems [17]. Learning them along with geometric-aware properties potentially yields better results.", + "bbox": [ + 496, + 681, + 890, + 726 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To acquire these invariances, we define the second function $L_{\\mathrm{IMG}}$ by following a common practice in 2D representation learning. In particular, we use SimCLR [6] and learn to discriminate between two different augmentations of $I_{i}$ (i.e., $I_{i}$ and $I_{i}^{+}$ ):", + "bbox": [ + 496, + 726, + 890, + 797 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\mathrm {I M G}} = l _ {\\mathrm {I M G}} \\left(\\mathbf {z} ^ {\\mathrm {I}}, \\mathbf {z} ^ {\\mathrm {I +}}\\right) + l _ {\\mathrm {I M G}} \\left(\\mathbf {z} ^ {\\mathrm {I +}}, \\mathbf {z} ^ {\\mathrm {I}}\\right),\n$$\n", + "text_format": "latex", + "bbox": [ + 544, + 805, + 761, + 823 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nl _ {\\mathrm {I M G}} \\left(\\mathbf {z} ^ {\\mathrm {I}}, \\mathbf {z} ^ {\\mathrm {I} +}\\right) = \\frac {1}{2 N} \\sum_ {i = 1} ^ {N} - \\log \\frac {\\exp \\left(\\mathbf {z} _ {i} ^ {\\mathrm {I}} \\cdot \\mathbf {z} _ {i} ^ {\\mathrm {I} +} / \\tau\\right)}{\\sum_ {\\mathbf {z} ^ {-} \\in \\mathbf {z} ^ {\\mathrm {I}} \\cup \\mathbf {z} ^ {\\mathrm {I} +} \\backslash \\left\\{\\mathbf {z} _ {i} ^ {\\mathrm {I}} \\right\\}} \\exp \\left(\\mathbf {z} _ {i} ^ {\\mathrm {I}} \\cdot \\mathbf {z} ^ {-} / \\tau\\right)}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 498, + 825, + 892, + 876 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{z}_i^{1 + }\\in \\mathbf{z}^{1 + }$ is an encoded feature of $I_{i}^{+}$", + "bbox": [ + 500, + 883, + 795, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "21374", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1.3 Cross-modal sharing the properties on the joint 2D-3D space", + "text_level": 1, + "bbox": [ + 76, + 90, + 468, + 121 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The third function $L_{\\mathrm{CROSS}}$ aligns the geometric-aware features $\\mathbf{z}^{\\mathrm{G}}$ with the 2D features $\\mathbf{z}^{\\mathrm{I}}$ by constructing a common 2D-3D space for the two encoders, $f^{\\mathrm{G}}(\\cdot)$ and $f^{\\mathrm{I}}(\\cdot)$ . To this end, we use cross-modal contrastive learning loss as a training objective as follows:", + "bbox": [ + 76, + 128, + 467, + 199 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} L _ {\\mathrm {C R O S S}} = l _ {\\mathrm {C R O S S}} \\left(\\mathbf {z} ^ {\\mathrm {I}}, \\mathbf {z} ^ {\\mathrm {G}}\\right) + l _ {\\mathrm {C R O S S}} \\left(\\mathbf {z} ^ {\\mathrm {G}}, \\mathbf {z} ^ {\\mathrm {I}}\\right), \\\\ l _ {\\text {C R O S S}} \\left(\\mathbf {z} ^ {\\mathrm {I}}, \\mathbf {z} ^ {\\mathrm {G}}\\right) = \\frac {1}{2 N} \\sum_ {i = 1} ^ {N} - \\log \\frac {\\exp \\left(\\mathbf {z} _ {i} ^ {\\mathrm {I}} \\cdot \\mathbf {z} _ {i} ^ {\\mathrm {G}} / \\tau\\right)}{\\sum_ {\\mathbf {z} ^ {-} \\in \\mathbf {z} ^ {\\mathrm {G}} \\backslash \\left\\{\\mathbf {z} _ {i} ^ {\\mathrm {G}} \\right\\}} \\exp \\left(\\mathbf {z} _ {i} ^ {\\mathrm {I}} \\cdot \\mathbf {z} ^ {-} / \\tau\\right)}. \\tag {4} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 88, + 212, + 468, + 281 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Sharing $\\mathbf{z}^{\\mathrm{G}}$ from $L_{\\mathrm{GEO}}$ with $\\mathbf{z}^{\\mathrm{l}}$ from $L_{\\mathrm{IMG}}$ on $L_{\\mathrm{CROSS}}$ using $L$ results in a $f^{1}(\\cdot)$ that can produce 2D representation with useful geometric and visual priors that show superior fin-tuning performance in the experimental section.", + "bbox": [ + 76, + 292, + 468, + 353 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.2. Learning geometric-aware representation on non-paired RGB datasets", + "text_level": 1, + "bbox": [ + 76, + 362, + 468, + 393 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Training a model to induce geometric-aware properties in 2D representation using Eq. (2) and Eq. (4) requires RGB-CAD pairs $(I, G)$ . However, obtaining such paired datasets is a cumbersome problem in every cross-modal learning framework. To address this, we propose to utilize 2D-3D object matching techniques, e.g., [16, 19, 30, 31, 47], to generate pseudo-pair of images and its associated 3D models, $(I_i, G_i')$ , which can be used for training instead of the real pairs. Our experiments show that these pseudo pairs still help induce geometric-aware properties in our representations, resulting in better performance on 2D object understanding tasks, compared to state-of-the-art 2D representation learning approaches.", + "bbox": [ + 75, + 400, + 468, + 597 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experimental setup", + "text_level": 1, + "bbox": [ + 76, + 611, + 264, + 628 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Pre-training details", + "text_level": 1, + "bbox": [ + 76, + 635, + 263, + 651 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We use ResNet-50 [23] or ViT-B [29] initialized with supervised pre-trained ImageNet weights for the 2D encoder and use DGCNN [46] for the 3D encoder. We choose $\\tau = 0.07$ for all equations and $K = 3$ in Eq. (2). Modality-specific projection heads are used for both 2D and 3D encoders to produce feature vectors $z^{\\mathrm{IMG}}$ and $z^{\\mathrm{GEO}}$ used in Eq. (1). Each head consists of two linear layers of sizes 1024 and 512, where the first one has ReLU activation. We pre-trained the model on the NVIDIA A100 GPU with a batch size of 256, then neglected the projection heads and retained only the 2D encoder for fine-tuning with downstream tasks. More details are given in Appendix A.", + "bbox": [ + 75, + 657, + 468, + 839 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For the pre-train dataset, we use Pix3D [45] with the S1 train-test split [16]. This dataset consists of 10,069 paired RGB images of indoor scene furniture (e.g., bed, chair, sofa) and corresponding CAD models (subcategories) with", + "bbox": [ + 75, + 839, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "a total of 395 shapes. We preprocessed each CAD model by uniform sampling random points to generate point clouds consisting of $N = 1024$ and applied point translation, rotation, and jittering to them. For RGB images, we applied the same augmentation strategy as [6] by randomly cropping an image into a size of $224 \\times 224$ , then randomly applying horizontal flipping, color jittering, grayscale, and Gaussian blurring to the images.", + "bbox": [ + 496, + 90, + 890, + 212 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Pseudo-pair generation setup", + "text_level": 1, + "bbox": [ + 498, + 232, + 761, + 248 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We utilized a state-of-the-art 3D shape retrieval model, ROCA [19], to generate a pseudo CAD model for any RGB image in indoor scene domains. ROCA was trained on Scan2CAD dataset [2] containing RGB-D frames of indoor scenes and annotated CAD models for each object in each frame. The Mask-RCNN [22] is employed to detect objects in an input image and generate bounding boxes of those detected ones. The feature of each bounding box will be further used in the ROCA retrieval module for predicting its associated CAD model listed in the ShapeNet [4] database.", + "bbox": [ + 496, + 258, + 890, + 409 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The pairing for each RGB input was selected based on a predicted CAD model of the largest detected bounding box. See Appendix G for more ablation studies on pair generation. Later in the experiment section, we compare our model trained on RGB images from Pix3D dataset [45] and pseudo CAD pairs generated by ROCA with competitors.", + "bbox": [ + 496, + 412, + 890, + 503 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Baseline competitors", + "text_level": 1, + "bbox": [ + 498, + 523, + 694, + 539 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "All competitors except SupImg and Pri3D were initialized using pre-trained ImageNet weights and subsequently trained on Pix3D to ensure evaluation fairness.", + "bbox": [ + 496, + 550, + 890, + 595 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Supervised ImageNet Pre-training (SupImg) [13] represents the base performance of a pre-trained model without additional training on indoor scene datasets.", + "bbox": [ + 496, + 599, + 890, + 643 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "SimCLR [6] and SupCon [28] provide the results when learning 2D representation on augmented RGB images (SimCLR), object categories (SupCon), or subcategories (SupCon (Fine)) in a CNN backbone.", + "bbox": [ + 496, + 648, + 890, + 708 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "CrossPoint [1] shows the performance of existing CAD-RGB representation learning. Note that this work has not been studied for solving 2D object understanding tasks.", + "bbox": [ + 496, + 712, + 890, + 757 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Pri3D [25] and Set-InfoNCE [5] are state-of-the-art geometric-aware 2D representation learning works trained on multi-view RGB frames and 3D scans of ScanNet [12] dataset. Note that Set-InfoNCE did not publicly share their code, so we can only compare the results to their reported statistics on ScanNet [12] and NYUv2 [42] datasets.", + "bbox": [ + 496, + 761, + 890, + 851 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "DINO [3] and MAE [20] are state-of-the-art 2D representation learning models based on Vision Transformer (ViT) [29] architectures.", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "21375", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Experimental results", + "text_level": 1, + "bbox": [ + 76, + 89, + 276, + 107 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Properties of our learned features", + "text_level": 1, + "bbox": [ + 76, + 114, + 372, + 131 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluating geometric-aware properties. Fig. 2 visualizes the pairwise cosine similarities between each encoded feature of objects from the Pix3D validation split. The representations were encoded with the 2D encoder (without a projection head) of each approach.", + "bbox": [ + 76, + 138, + 468, + 214 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Our representations have high similarity scores for images with the same geometry (intra-subcategory) and others with the same object category (intra-category), while none of the competitors could reflect two properties at the same time. More visualizations from other categories and other competitors are provided in Appendix B.", + "bbox": [ + 75, + 214, + 468, + 305 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "One interesting aspect is that our representations also well capture the differences across inter-category and inter-subcategory samples. We acquire better mean intra and inter-category similarity scores than the self-supervised baselines, as shown in Fig. 4. Furthermore, Ours (pseudo) yields similar findings, particularly for inter-category. An additional study in Appendix B also demonstrates that Ours (pseudo) has better discrimination in inter-subcategory features. These geometric-aware properties in our learned representation lead to improved 2D object understanding performance in further subsections.", + "bbox": [ + 75, + 305, + 468, + 470 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/dec816489b57275f8fa313bd278708b09d58e89b57fda05fe1e885f9422e8ed4.jpg", + "image_caption": [ + "Figure 4. Distribution of pairwise cosine similarity score among intra and inter-category samples. Our representations learned by $L_{\\mathrm{GEO}}$ based on the Chamfer distance have the highest mean score (vertical dashed lines) within intra-category samples and also have the lowest score in the inter-category scenario." + ], + "image_footnote": [], + "bbox": [ + 86, + 472, + 459, + 622 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Object localization. We study whether our model can generalize to images with multiple objects, even though it was trained on a dataset of single objects. Fig. 5 shows that our learned features from the ViT-B backbone can be used for roughly localizing patches associated with object categories without fine-tuning. More details and results are provided in Appendix C. This property may arise from how our loss function encourages learning discriminative part features, which are useful for classifying, localizing, and segmenting multiple objects demonstrated in our subsequent experiments. This similar behavior is also observed in other 2D self-supervised models [3] trained on single-object datasets (e.g., ImageNet [13]).", + "bbox": [ + 75, + 704, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/f2d823514a3cee9e7a3747f1295546ffbfa1a8d9706077ef673aa63bf3ef9936.jpg", + "image_caption": [ + "Figure 5. We compute the feature similarity between each patch in an unseen input image and the mean global feature of learned images in each category using models with a ViT-B backbone. Without fine-tuning, our model can identify the table and roughly localize patches associated with the chairs in the image by using the category of the most similar mean global feature of each patch." + ], + "image_footnote": [], + "bbox": [ + 506, + 75, + 888, + 169 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. 2D Semantic segmentation", + "text_level": 1, + "bbox": [ + 500, + 271, + 740, + 287 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1 compares fine-tuning results in semantic segmentation tasks with other competitors. Following [5, 25], we train a U-Net [41] with residual connections for predicting segmentation masks with cross-entropy loss. The encoder part of U-Net is ResNet-50, while the decoder is conv layers with bi-linear interpolation. For ViT-B, we follow [20] by using UPerNet [51] as a segmentation head.", + "bbox": [ + 496, + 297, + 890, + 404 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We employ two variants of mean intersection-over-union (mIoU) for the evaluation metric. The first mIoU, initially implemented by Pri3D [25], does not include pixels that were incorrectly predicted to be ignored classes (e.g., background) as a false positive in mIoU computation. In comparison, our revised mIoU includes these pixels to avoid model cheating by predicting more ignored classes. The experiments were conducted on NYUv2 [42], ScanNet [12], indoor ADE20k [54], and indoor SUNRGB-D [43] datasets. We filtered ADE20k to include only indoor scenes and ignored previously omitted classes in an NYUv2 setting following the prior work [25] for SUNRGB-D. More details on our split are provided in Appendix D.", + "bbox": [ + 496, + 407, + 892, + 604 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "When pre-trained on non-paired RGB datasets, Ours (pseudo) outperforms all 2D competitors in both architectures, including DINO [3] and MAE [20]. For 2D-3D competitors, we win against Pri3D and achieve very competitive results to Set-InfoNCE in NYUv2 by only -0.16 in mIoU [25]. We also outperform Pri3D in ADE20k by +1.01 for the original and +0.79 for the pseudo version. The qualitative results are shown in Fig. 6 and Appendix E.", + "bbox": [ + 496, + 606, + 890, + 729 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For ScanNet and SUNRGB-D datasets, Pri3D and SetInfoNCE perform better than ours. This might be because their models were trained directly on ScanNet 3D scans. Some images in SUNRGB-D also appear similar to those in ScanNet, as both datasets sampled RGB-D frames from recorded videos at a high frame-per-second rate. Nonetheless, even without 3D ScanNet, our method still achieves comparable results to Pri3D (-0.17).", + "bbox": [ + 496, + 729, + 890, + 852 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Additionally, in Appendix F, we present results obtained by increasing the pre-training data, which allows us to surpass Set-InfoNCE on NYUv2 without real 3D pairs.", + "bbox": [ + 496, + 854, + 890, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "21376", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/d5c9ffb0300bd9f77f7d6ad0cf97704e2a8dcf6c2ce9cba217fc09138aa50af8.jpg", + "table_caption": [ + "Table 1. Semantic segmentation results on four popular benchmark datasets. For both ResNet-50 (RN50) and ViT-B architectures, our approaches have better mIoU than 2D representation learning baselines. (*) denotes scores from the methods that were directly pre-trained on 2D and 3D data of ScanNet dataset. We win against Pri3D in NYUv2 and ADE20k without requiring 3D scene scans." + ], + "table_footnote": [], + "table_body": "
Arch.GT pairMethod3DNYUv2ScanNetindoor ADE20kSUNRGB-D
mIoUmIoU [25]mIoUmIoU [25]mIoUmIoU [25]mIoUmIoU [25]
RN502D onlySupImg-47.0450.049.1255.737.5239.6947.9663.12
SimCLR-47.9453.3249.9156.3438.1939.5648.5163.00
SupCon-48.4954.1650.5956.5737.9640.1348.1365.01
SupCon (fine)-47.3453.4549.8156.2237.8739.9248.0563.13
pseudoOurs (pseudo)CAD49.4654.6250.7756.7639.1340.4349.1365.45
2D-3DCrossPointCAD46.0449.1847.2654.0236.5537.8847.1562.77
Pri3Dscene49.5254.754.72*61.7*38.3439.1750.0266.65
Set-InfoNCEscene-55.4-63.1*----
OursCAD49.7755.2451.0357.1239.3540.8649.8565.95
ViT-B2D onlySupImg-49.4455.5963.9359.7242.7844.3851.2666.45
DINO-52.1457.2462.5458.1341.7243.4150.5266.12
MAE-50.1055.6662.2358.9542.9644.9652.2267.87
pseudoOurs (pseudo)CAD52.4758.0264.4960.7343.0245.3752.5369.59
2D-3DOursCAD53.058.6765.2760.9543.1245.8252.9669.69
", + "bbox": [ + 114, + 133, + 844, + 348 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b7fecadc9068005cd319a67c4ca592794581485ee3b55aaf0cc393ed45288d42.jpg", + "image_caption": [ + "Figure 6. Qualitative results on NYUv2 [42] semantic segmentation. Our methods yield better segmentation results when labeling a scene is challenging due to color or lighting. The geometric priors in our learned representations boost understanding of each scene." + ], + "image_footnote": [], + "bbox": [ + 106, + 349, + 859, + 611 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3.2D Instance segmentation and object detection", + "text_level": 1, + "bbox": [ + 76, + 648, + 470, + 666 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Indoor scenes. We show how our features improve instance segmentation and object detection results in Table 2. Similar to [25], we use Mask-RCNN [22] with ResNet-50 encoder, implemented on Detectron2 [48] framework for both tasks. For ViT-B, we resize input images to $224 \\times 224$ and follow [33] by using Mask-RCNN as the detection head. All backbones were initialized by the pre-trained weights of our model or competitors'. Following [5,25], we use NYUv2 [42] dataset and a well-known detection benchmark, COCO dataset, with Average Precision (AP) as the metric. We filtered COCO images to include only indoor objects. Details on the selected classes are in Appendix D.", + "bbox": [ + 75, + 672, + 468, + 854 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Our method outperforms state-of-the-art 2D and 2D-3D competitors in all settings. Ours (pseudo) achieves competitive scores against Pri3D and Set-InfoNCE in NYUv2 and", + "bbox": [ + 75, + 854, + 470, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "beats Pri3D in COCO without ground truth 3D pairs.", + "bbox": [ + 498, + 650, + 849, + 665 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Outdoor scenes. We also pre-trained our model on PAS-CAL3D+ [50] dataset, which contains objects such as vehicles and furniture in both indoor and outdoor scenes, and evaluated the model on another subset of COCO images called outdoor COCO. Further dataset details are provided in Appendix D. Our method leads to similar improvements in AP as observed in the indoor-only settings.", + "bbox": [ + 496, + 666, + 890, + 772 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.4. Experiments on 2D retrieval", + "text_level": 1, + "bbox": [ + 500, + 785, + 754, + 801 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3 shows the retrieval performance on Pix3D [45] by fine-tuning the pre-trained model on coarse-grained (category) and fine-grained (subcategory) labels of objects. The 2D encoder was fine-tuned along with an additional retrieval head, consisting of two linear layers of sizes 1024 and 512 with ReLU applied only to the first layer. All", + "bbox": [ + 496, + 809, + 892, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "21377", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/9be909d71dee3101eb0cd45c3ee2eeb225cd88e1cf978791e6f327ae2d39083b.jpg", + "table_caption": [ + "Table 2. Object detection and instance segmentation performance. We outperform competitors for all datasets." + ], + "table_footnote": [], + "table_body": "
Arch. SizeGT pairMethod3DNYUv2indoor COCOoutdoor COCO
Object Det.Instance segm.Object Det.Instance seg.Object Det.Instance seg.
AP50AP75APAP50AP75APAP50AP75APAP50AP75APAP50AP75APAP50AP75
RN50 4802D onlySupImg-29.917.316.825.113.913.441.7824.2123.7039.1623.3522.6146.0926.9828.0842.4523.3423.92
SimCLR-32.8120.1519.2429.1015.9715.6243.6326.4625.4540.8724.7923.8648.1528.7530.4044.3125.0124.99
SupCon-33.2320.3619.6329.4416.1615.8343.6626.3425.3240.8424.5323.7547.8928.6730.2944.1624.6324.97
SupCon (fine)-32.5619.7418.9229.0616.1115.7443.5825.9525.2140.6524.2223.6645.0127.9026.5941.9725.6124.66
pseudoOurs (pseudo)CAD34.4520.2719.7229.6416.2416.1343.7426.4725.4840.9224.7723.91------
2D-3DCrossPointCAD28.4215.9415.2224.4913.3213.1140.2522.7822.2638.5421.9220.8043.2224.5725.6039.7521.9321.11
Pri3Dscene34.020.419.429.516.315.843.4926.4025.2240.7124.7223.61------
Set-InfoNCEscene34.620.519.729.716.316.5-----------
OursCAD34.8520.8920.1230.0316.5116.8444.1126.7825.6941.0224.9124.0849.0329.8031.6245.2325.9025.85
ViT-B 2242D onlySupImg-34.4019.2419.0628.4214.0514.9731.4520.6319.4129.7718.7317.8233.5623.1921.8131.6819.5218.11
DINO-33.0318.6217.9126.8214.5614.7327.7016.2415.8725.7814.8614.7632.5722.1320.6129.8618.0717.66
MAE-35.9219.3019.2429.8816.0115.8231.5420.5919.3329.9218.6517.8336.9724.5123.1233.6720.1519.46
pseudoOurs (pseudo)CAD36.2419.7819.7230.1015.9416.0531.7820.7419.4630.0119.0717.94------
2D-3DOursCAD36.3119.9119.9430.3016.1616.2732.0221.0419.6730.1619.0218.0937.7424.9223.4234.1320.4919.89
", + "bbox": [ + 86, + 104, + 874, + 299 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/260d1d3fda4c375c01eb0c53b679b125ddb4860c499dc1ae6c2004949de06295.jpg", + "table_caption": [ + "Table 3. Retrieval performance on Pix3D [45]. Our method outperforms all competitors in all situations." + ], + "table_footnote": [], + "table_body": "
Arch.GT PairMethod3DCoarse R@1Fine R@1
RN502D onlySupImg-78.8551.18
SimCLR-80.0455.01
SupCon-81.3252.39
SupCon (fine)-79.9555.84
pseudoOurs (pseudo)CAD81.7456.71
2D-3DCrossPointCAD75.9748.09
Pri3Dscene79.7251.63
OursCAD82.8858.97
ViT-B2D onlySupImg-84.0464.17
DINO-84.5965.48
MAE-83.7962.00
pseudoOurs (pseudo)CAD86.1666.40
2D-3DOursCAD86.3267.23
", + "bbox": [ + 84, + 340, + 454, + 513 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/99d5996f48bbb7bf32973e6bdfacab0b1ae38403d41548f349a3a3e939bb3890.jpg", + "table_caption": [ + "Table 4. Effects on losses and positive mining choices. Training on three losses simultaneously yields the best performance in mIoU. At the same time, choosing the Chamfer Distance (CD) as a positive mining choice in $L_{\\mathrm{GEO}}$ also wins against the others." + ], + "table_footnote": [], + "table_body": "
LIMGLGEOLCROSSPos.NYUv2ADE20k
-✓✓CD48.2337.71
✓-✓-48.4638.47
✓---47.9438.19
--✓-47.0237.43
✓✓✓Sup49.4839.12
✓✓✓Aug49.1438.65
✓✓✓CD49.7739.35
", + "bbox": [ + 106, + 582, + 434, + 699 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "retrieval models were trained using supervised contrastive loss [28] with $\\tau = 0.07$ . Our methods outperform all competitors in all architectures.", + "bbox": [ + 75, + 714, + 467, + 760 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.5. Ablation studies", + "text_level": 1, + "bbox": [ + 76, + 770, + 236, + 784 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "All ablation experiments are evaluated on NYUv2 and ADE20k semantic segmentation tasks using our revised mIoU metric on ResNet-50 architecture.", + "bbox": [ + 76, + 794, + 467, + 838 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effects on losses and positive mining choices Table 4 shows the effects of three loss choices (i.e., $L_{\\mathrm{IMG}}$ , $L_{\\mathrm{GEO}}$ , and $L_{\\mathrm{CROSS}}$ ) and three different choices of the positive point cloud using in Eq. (2), including using object categories", + "bbox": [ + 75, + 839, + 467, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "(Sup), point cloud augmentation (Aug), and Chamfer distance (CD). We found that training three loss functions simultaneously notably improves mIoU from training single or dual losses. While in the positive choice study, our selected Chamfer distance achieves the best mIoU.", + "bbox": [ + 496, + 313, + 890, + 388 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effects on $K$ selected positive point clouds. We studied the best number of $K$ in Eq. (2). Fig. 7 reveals that $K = 3$ can achieve the best mIoU among the others. Using a lower $K$ leads to lower mIoU, similar to a higher $K$ . This is probably because higher $K$ has more chance to select false positive samples due to higher Chamfer distances, which means that the selected samples might have a much different shape than the anchor $\\mathbf{z}_i^G$ .", + "bbox": [ + 496, + 388, + 890, + 510 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3596632e824760fc9c5158432ababfcaec07fafe05d16f13b3d359d78a87532c.jpg", + "image_caption": [ + "Figure 7. Effect of varying $K$ selected positive point clouds. $K = 3$ has the best mIoU." + ], + "image_footnote": [], + "bbox": [ + 524, + 518, + 867, + 580 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Limitations and Discussion", + "text_level": 1, + "bbox": [ + 500, + 618, + 750, + 633 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Using CAD models for inducing geometric-aware properties in 2D representation via Chamfer distance shows significantly enhanced 2D object understanding results that are almost as effective as 3D priors from scene scans. This finding remains true when we train our model on generated pseudo-RGB-CAD pairs, allowing us to beat SOTA 2D competitors without the need for paired datasets. However, the performance of the pseudo-pair generator currently hinders our results. As seen in Fig. 2 and 4, features trained on pseudo pairs cannot clearly categorize intra-subcategory images. We observe that this is due to an improper CAD pair assignment; more information is given in Appendix B. Nonetheless, generating or retrieving 3D models from a single image is still more tractable than scene scans and shows progressive performance improvement [38]. This enables harnessing the massive-scale RGB data and generalizing beyond domains with paired data (See Appendix F).", + "bbox": [ + 496, + 643, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "21378", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Mohamed Afham, Isuru Dissanayake, Dinithi Dissanayake, Amaya Dharmasiri, Kanchana Thilakarathna, and Ranga Rodrigo. Crosspoint: Self-supervised cross-modal contrastive learning for 3d point cloud understanding. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 9902-9912, June 2022. 2, 3, 5", + "[2] Armen Avetisyan, Manuel Dahnert, Angela Dai, Manolis Savva, Angel X Chang, and Matthias Nießner. Scan2cad: Learning cad model alignment in rgb-d scans. 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Unified perceptual parsing for scene understand-" + ], + "bbox": [ + 501, + 90, + 892, + 900 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "21380", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 9 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "ing. In Proceedings of the European conference on computer vision (ECCV), pages 418-434, 2018. 6", + "[52] Saining Xie, Jiatao Gu, Demi Guo, Charles R Qi, Leonidas Guibas, and Or Litany. Pointcontrast: Unsupervised pretraining for 3d point cloud understanding. In European conference on computer vision, pages 574-591. Springer, 2020. 2", + "[53] Zaiwei Zhang, Rohit Girdhar, Armand Joulin, and Ishan Misra. Self-supervised pretraining of 3d features on any point-cloud. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 10252-10263, 2021. 2", + "[54] Bolei Zhou, Hang Zhao, Xavier Puig, Sanja Fidler, Adela Barriuso, and Antonio Torralba. Scene parsing through ade20k dataset. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 633-641, 2017. 2, 6" + ], + "bbox": [ + 78, + 90, + 468, + 330 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "21381", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Learning Geometric-Aware Properties in 2D Representation Using Lightweight CAD Models, or Zero Real 3D Pairs/17e7e6f9-e779-4537-89d2-408c0b6a8259_model.json b/2023/Learning Geometric-Aware Properties in 2D Representation Using Lightweight CAD Models, or Zero Real 3D Pairs/17e7e6f9-e779-4537-89d2-408c0b6a8259_model.json new file mode 100644 index 0000000000000000000000000000000000000000..b8b65627f2278411a5d3487bbd62f752b8848a35 --- /dev/null +++ b/2023/Learning Geometric-Aware Properties in 2D Representation Using Lightweight CAD Models, or Zero Real 3D Pairs/17e7e6f9-e779-4537-89d2-408c0b6a8259_model.json @@ -0,0 +1,2224 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.088, + 0.13, + 0.885, + 0.175 + ], + "angle": 0, + "content": "Learning Geometric-aware Properties in 2D Representation Using Lightweight CAD Models, or Zero Real 3D Pairs" + }, + { + "type": "text", + "bbox": [ + 0.164, + 0.205, + 0.378, + 0.222 + ], + "angle": 0, + "content": "Pattaramanee Arsomngern" + }, + { + "type": "text", + "bbox": [ + 0.424, + 0.205, + 0.564, + 0.222 + ], + "angle": 0, + "content": "Sarana Nutanong" + }, + { + "type": "text", + "bbox": [ + 0.41, + 0.223, + 0.562, + 0.239 + ], + "angle": 0, + "content": "VISTEC, Thailand" + }, + { + "type": "text", + "bbox": [ + 0.612, + 0.205, + 0.806, + 0.222 + ], + "angle": 0, + "content": "Supasorn Suwajanakorn" + }, + { + "type": "text", + "bbox": [ + 0.241, + 0.242, + 0.724, + 0.257 + ], + "angle": 0, + "content": "{pattaramanee.a_s19, snutanon, supasorn.s}@vistec.ac.th" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.292, + 0.314, + 0.308 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.326, + 0.474, + 0.69 + ], + "angle": 0, + "content": "Cross-modal training using 2D-3D paired datasets, such as those containing multi-view images and 3D scene scans, presents an effective way to enhance 2D scene understanding by introducing geometric and view-invariance priors into 2D features. However, the need for large-scale scene datasets can impede scalability and further improvements. This paper explores an alternative learning method by leveraging a lightweight and publicly available type of 3D data in the form of CAD models. We construct a 3D space with geometric-aware alignment where the similarity in this space reflects the geometric similarity of CAD models based on the Chamfer distance. The acquired geometric-aware properties are then induced into 2D features, which boost performance on downstream tasks more effectively than existing RGB-CAD approaches. Our technique is not limited to paired RGB-CAD datasets. By training exclusively on pseudo pairs generated from CAD-based reconstruction methods, we enhance the performance of SOTA 2D pre-trained models that use ResNet-50 or ViT-B backbones on various 2D understanding tasks. We also achieve comparable results to SOTA methods trained on scene scans on four tasks in NYUv2, SUNRGB-D, indoor ADE20k, and indoor/outdoor COCO, despite using lightweight CAD models or pseudo data. Please visit our page: https://" + }, + { + "type": "text", + "bbox": [ + 0.079, + 0.69, + 0.35, + 0.702 + ], + "angle": 0, + "content": "//GeoAware2dRepUsingCAD.github.io/" + }, + { + "type": "title", + "bbox": [ + 0.079, + 0.738, + 0.208, + 0.753 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.765, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Recent 2D visual representation learning approaches, such as contrastive learning [3, 6, 10, 17, 28] or masked autoencoder [20], are widely used to tackle various problems in computer vision due to their ability to encode rich visual features. While these methods have shown exceptional results on 2D image classification, they still have shortcomings in other 2D understanding tasks that involve instance-level reasoning. Prior research [25] also shows that models pre-trained using image augmentations [8,21] or supervised" + }, + { + "type": "image", + "bbox": [ + 0.513, + 0.291, + 0.882, + 0.553 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.558, + 0.892, + 0.656 + ], + "angle": 0, + "content": "Figure 1. Overview concept of our solution. We leverage CAD models to train a joint 2D-3D space such that images of objects with similar shapes, based on the Chamfer distance, are attracted to each other, while images with different shapes are separated. This results in a continuous geometric-aware space where the distance between two points reflects their geometric similarity, which could be utilized for downstream 2D object understanding tasks." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.669, + 0.892, + 0.715 + ], + "angle": 0, + "content": "labels [13] could not deliver satisfactory results when applied to downstream tasks such as semantic segmentation, instance segmentation, and object detection [12, 42]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.717, + 0.893, + 0.867 + ], + "angle": 0, + "content": "To alleviate this, Hou et al. [25] proposed to learn 3D geometric priors, such as view-invariance, from 3D data and transfer the learned priors to 2D representations. In particular, their model is first pre-trained on ScanNet [12], a database of multi-view RGB-D scans, using contrastive learning and later used as initialization for fine-tuning networks on downstream tasks. Chen et al. [5] further extend this work by utilizing additional priors through learning to group nearby points that refer to the same object part from 3D scenes." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "The key concept of their introduced new paradigm is to share useful 3D priors from 3D data with 2D representa" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "21371" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.243 + ], + "angle": 0, + "content": "tions. However, previous studies have investigated mostly 3D priors related to viewpoint invariance from 3D scene datasets, which are often limited in size and scene variations due to the laborious data collecting and labeling process [24]. This scarcity of large-scale 3D data also limits the number of available 3D priors for learning the invariance, hence hindering further performance gains. This paper questions whether there are other effective 3D priors for 2D downstream tasks and whether they can be learned from other forms of 3D data that are lighter and easier to obtain." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.246, + 0.473, + 0.458 + ], + "angle": 0, + "content": "We begin our exploration by considering how to learn an embedding space that maps together images with the same or similar geometries. One solution is to learn from images that share the same 3D model, which inspires our interest in CAD models. Unlike 3D scenes, CAD models are lightweight, publicly available, and can be easily aligned with RGB images via web scraping or human annotation [2]. There exist studies that jointly learn 2D and 3D CAD representation for other CAD-related tasks, e.g., 3D classification [1,27]. However, their 2D features, which are derived from augmentation-based CAD features, are insufficient to be directly applied to 2D object understanding tasks—they can group images with similar geometries but struggle to learn the distinctions between object categories." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.46, + 0.473, + 0.763 + ], + "angle": 0, + "content": "We argue that useful geometric-aware representations should account for both similarities and differences in object geometry. Our key idea is to acquire such features by imitating the Chamfer distance between 3D objects in our embedding space and inducing this derived geometric awareness in our learned 2D representation. In particular, we learn our space by attracting the encoded features of geometrically similar CAD models in the mini-batch based on the Chamfer distance and repelling those with lower similarities. In contrast to other methods trained on supervised discrete signals like object labels or through 3D augmentations, our method produces a continuous 3D space that better captures the similarity and difference in geometry (see Section 5.1). In addition, we employ augmentation-based contrastive learning [6] to learn other useful visual feature properties, such as translation and color invariances. This results in a 2D representation in a 2D-3D space that contains rich visual information and strong geometric-aware properties, as shown in Fig. 1, which can be leveraged to improve 2D object understanding tasks." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.473, + 0.903 + ], + "angle": 0, + "content": "To match our geometric-aware CAD features with corresponding 2D features, a paired RGB-CAD dataset, such as Pix3D [45], is required. However, by leveraging recent techniques [19, 31] that can reconstruct a CAD model from an input image, it is possible to generate pseudo CAD models for any images and use them to learn our method without a paired dataset. Adapting this pseudo-pair generation to other techniques that rely on scene scans is significantly harder, as synthesizing full 3D scenes with reasonable detail" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.856, + 0.107 + ], + "angle": 0, + "content": "remains harder than reconstructing individual objects." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.108, + 0.892, + 0.303 + ], + "angle": 0, + "content": "We demonstrate the effectiveness of our geometric-aware 2D representation in Fig. 2. Our features can group and differentiate objects based on their categories or subcategories, leading to improved performance on multiple 2D object understanding tasks using both ResNet-50 [23] and ViT-B [29] backbones. Our method trained on a pseudopair dataset also yields superior results over DINO [3] and MAE [20]. Remarkably, we also surpass a state-of-the-art method, Pri3D [25] without using any 3D scene scans in the following tasks: (i) semantic segmentation using NYUv2 [42] and indoor ADE20k [54]; (ii) object detection and instance segmentation using NYUv2 and in/outdoor COCO [35]; (iii) object retrieval using Pix3D [45]." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.304, + 0.835, + 0.317 + ], + "angle": 0, + "content": "To summarize, our contributions are as follows." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.318, + 0.892, + 0.395 + ], + "angle": 0, + "content": "- We present a simple yet effective approach to inducing geometric-aware properties in 2D representation using lightweight CAD models. These can be either ground truth from RGB-CAD datasets or generated pseudo CAD pairs based on 2D-only data." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.395, + 0.892, + 0.44 + ], + "angle": 0, + "content": "- We propose training objectives to learn a 2D-3D embedding space where feature similarity reflects geometric similarity based on the Chamfer distance." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.442, + 0.892, + 0.517 + ], + "angle": 0, + "content": "- We enhance the performance of SOTA 2D representation learning techniques on four 2D object understanding tasks and achieve competitive results to SOTA that require 3D scene scans across five datasets, in both settings that use real or pseudo-RGB-CAD datasets." + }, + { + "type": "list", + "bbox": [ + 0.518, + 0.318, + 0.892, + 0.517 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.529, + 0.645, + 0.544 + ], + "angle": 0, + "content": "2. Related works" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.554, + 0.892, + 0.689 + ], + "angle": 0, + "content": "2D Representation Learning. Contrastive learning [49] has continuously shown improvements in various downstream tasks. Its main concept is to maximize a similarity score between two different views (e.g., two different augmentations of the same instance [6, 9, 10, 17, 21], two instances with the same label [28], or two different encoders [3, 7]). Meanwhile, learning representation in autoencoder fashion [20] also has recently demonstrated a performance boost from contrastive learning works." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.69, + 0.892, + 0.735 + ], + "angle": 0, + "content": "This paper shows that these 2D representation learning methods could not provide geometric-aware properties, which are critical in object understanding tasks." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.901 + ], + "angle": 0, + "content": "3D Representation Learning requires specific network architecture for extracting features based on an input's data structure (e.g., rendered images [44], point clouds [39, 46], or meshes [15, 16]). These architectures can encode geometric information of each 3D shape into representations with a deep understanding of shape structure. Later, contrastive learning in 3D, such as point cloud augmentation [52], or multiple modalities [1, 53], showed their improvement in 3D classification, retrieval, and part segmentation problems. Concurrently, 3D reconstruction techniques [11, 14, 37] also deliver promising results in similar tasks." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "21372" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.089, + 0.885, + 0.273 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.276, + 0.895, + 0.374 + ], + "angle": 0, + "content": "Figure 2. Visualization of the pairwise cosine similarity between the learned representations of objects from each method. The bright color indicates higher similarity. The first row shows the similarity scores of all validation images in Pix3D [45] dataset, sorted by object category and subcategory (i.e., object models). The second row zooms in on a single category (Sofa) from the first row. Our method shows a better grouping of the same sofa than others, especially SimCLR [6] and SupCon [28], which can hardly differentiate between each sofa type. CrossPoint [1] and SupCon (fine), unlike others, can group the same sofa but fail to separate sofas from other categories in the first row. Surprisingly, MAE [20] also delivers visual features without subcategory awareness. Compared to SimCLR, Ours (pseudo) provides distinguishable features (with darker colors) between each sofa type. Additional studies on Ours (pseudo) are provided in Appendix B." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.387, + 0.471, + 0.432 + ], + "angle": 0, + "content": "In this paper, we adapt the encoded 3D features with rich geometric information to share the ability to recognize geometric similarities in each object to 2D representations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.433, + 0.47, + 0.688 + ], + "angle": 0, + "content": "Multimodal Representation Learning gains attraction due to its ability to share modality-specific contexts. CLIP [40] facilitates various vision-language tasks by contrastive learning on text-image data. Similarly, 2D-3D representation learning transfers geometric information from 3D to 2D features [5, 25, 36]. Pri3D [25] introduces a contrastive learning method on multi-view RGB frames and 3D scene scans [12]. These modal pairs allow them to learn view and 3D priors in 2D features and achieve impressive 2D indoor scene understanding performance. Later, SetInfoNCE [5] improves upon Pri3D by fine-tuning the Pri3D pre-trained model using additional 3D priors, e.g., sets of nearby points referring to the same object part, generated from training scans. While these studies have focused on scene scans, this paper demonstrates that geometric priors from CAD models can achieve comparable or better object understanding than learning on 3D scenes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.47, + 0.795 + ], + "angle": 0, + "content": "Some studies, e.g., CrossPoint [1, 27], have been conducted to share visual context to guide CAD features (2D \\(\\rightarrow\\) 3D). Their learned 2D features, on the other hand, fail to discriminate object categories, resulting in poor object understanding results. We then investigate a more efficient method of learning and sharing modality-specific context from CAD to RGB without hurting 2D task performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.471, + 0.902 + ], + "angle": 0, + "content": "2D-3D Object Matching has been studied for searching or generating a 3D model of objects appearing in a given image. [19, 30-32] use existing CAD databases to train an RGB-CAD retrieval and alignment module in a multi-task learning fashion using a given set of ground truths (e.g., camera intrinsic, depth map, mask, or pose parameters). [26, 34] utilize category labels to guide a joint RGB-CAD" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.387, + 0.892, + 0.448 + ], + "angle": 0, + "content": "space for 2D-3D retrieval tasks. Another approach is to reconstruct a 3D model from the image directly [16, 18, 47]. However, the generated 3D may be less realistic than retrieving human-designed 3D from the databases." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.45, + 0.894, + 0.496 + ], + "angle": 0, + "content": "We utilize these works to generate CAD pairs for our pre-training RGB images. Learning representation on just pseudo-RGB-CAD pairs can surpass SOTA competitors." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.519, + 0.671, + 0.536 + ], + "angle": 0, + "content": "3. Proposed method" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.547, + 0.892, + 0.623 + ], + "angle": 0, + "content": "Our goal is to construct a pre-trained model that can provide a 2D representation \\(\\mathbf{z}_i^!\\) of an input image \\(I_{i}\\) with useful geometric priors to enhance 2D object understanding. Unlike prior works [5,25], we aim to learn the representations without 3D scene scans using other efficient alternatives." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.626, + 0.893, + 0.852 + ], + "angle": 0, + "content": "We propose a novel approach that can obtain such geometric priors from a lightweight and publicly available type of 3D data in the form of CAD models, while retaining discriminative representations for 2D tasks. Given an image \\( I_{i} \\) and its associated CAD model \\( G_{i} \\), our solution constructs a 2D-3D embedding space with strong geometric-aware properties by learning CAD features \\( \\mathbf{z}_{i}^{\\mathrm{G}} = f^{\\mathrm{G}}(G_{i}) \\) along with rich visual information from 2D features \\( \\mathbf{z}_{i}^{\\mathrm{I}} = f^{\\mathrm{I}}(I_{i}) \\). We show that the acquired 2D representations, where their feature similarity reflects geometric similarity, are more effective than solely relying on standard augmentation invariant CAD features and perform almost as effectively as 3D priors from scene scans on common 2D understanding tasks. The overview of our proposed framework is shown in Fig. 3." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.902 + ], + "angle": 0, + "content": "An extension to training our model on generated RGB-CAD pairs is further introduced in order to learn geometric-aware representations using just RGB training data." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "21373" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.098, + 0.088, + 0.873, + 0.316 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.323, + 0.895, + 0.368 + ], + "angle": 0, + "content": "Figure 3. Our pre-training strategy. We learn 2D representations on a joint 2D-3D space from RGB-CAD pairs based on three loss functions. \\( L_{\\mathrm{GEO}} \\) focuses on learning CAD features from two similar CAD models mined from Chamfer distance, \\( L_{\\mathrm{IMG}} \\) focuses on learning visual differences between two image augmentations, and \\( L_{\\mathrm{CROSS}} \\) shares geometric awareness from CAD features to 2D representation." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.376, + 0.262, + 0.392 + ], + "angle": 0, + "content": "3.1. Training objectives" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.399, + 0.474, + 0.613 + ], + "angle": 0, + "content": "The core idea of our training objective is to share two modality-specific contexts, i.e., strong geometric-aware properties from \\(\\mathbf{z}_i^{\\mathrm{G}}\\in \\mathbf{z}^{\\mathrm{G}}\\) and rich visual information from \\(\\mathbf{z}_i^{\\mathrm{I}}\\in \\mathbf{z}^{\\mathrm{I}}\\), in the joint 2D-3D embedding space by training on RGB-CAD pairs \\((I,G)\\). To achieve this objective, we use three loss functions: \\(L_{\\mathrm{GEO}}\\), \\(L_{\\mathrm{IMG}}\\), and \\(L_{\\mathrm{CROSS}}\\). The first loss \\(L_{\\mathrm{GEO}}\\) helps the 3D encoder \\(f^{\\mathrm{G}}(\\cdot)\\) construct a geometric-aware embedding space, such that CAD models in \\(G\\) with similar shapes, based on the Chamfer distance, are located near each other. The second loss \\(L_{\\mathrm{IMG}}\\) helps the 2D encoder \\(f^{\\mathrm{I}}(\\cdot)\\) learn useful visual representation properties, e.g., translation and color invariance from \\(I\\). The third loss \\(L_{\\mathrm{CROSS}}\\) enforces the consistency between \\(\\mathbf{z}_i^{\\mathrm{G}}\\) and \\(\\mathbf{z}_i^{\\mathrm{I}}\\) for each \\((I_i,G_i)\\) pair. Finally, the multi-task loss function is" + }, + { + "type": "equation", + "bbox": [ + 0.178, + 0.622, + 0.47, + 0.639 + ], + "angle": 0, + "content": "\\[\nL = L _ {\\text {G E O}} + L _ {\\text {I M G}} + L _ {\\text {C R O S S}}. \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.648, + 0.47, + 0.679 + ], + "angle": 0, + "content": "Detailed explanations of the three components are given in the following subsections." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.696, + 0.353, + 0.71 + ], + "angle": 0, + "content": "3.1.1 Geometric-aware CAD features" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.47, + 0.826 + ], + "angle": 0, + "content": "We first explain how \\( L_{\\mathrm{GEO}} \\) provides geometric awareness to our features. Given \\( (I_i, G_i) \\), we use \\( G_i \\) to train \\( f^{\\mathrm{G}}(\\cdot) \\) for extracting a geometric context \\( \\mathbf{z}_i^{\\mathrm{G}} \\) of each pair. We process each \\( G_i \\) by converting it to a point cloud and use DGCNN [46] as \\( f^{\\mathrm{G}}(\\cdot) \\) to capture local and global point cloud structure information, resulting in an encoded feature \\( \\mathbf{z}_i^{\\mathrm{G}} \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.471, + 0.902 + ], + "angle": 0, + "content": "To learn the space, we follow a common contrastive learning strategy by maximizing the similarity between \\(\\mathbf{z}_i^{\\mathrm{G}}\\) and the encoded feature \\(\\mathbf{z}^{+}\\) of each positive term in a minibatch. However, instead of selecting \\(\\mathbf{z}^{+}\\) based on object labels or augmentations as is commonly done, we select \\(\\mathbf{z}^{+}\\)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.377, + 0.891, + 0.405 + ], + "angle": 0, + "content": "based on a geometric-based similarity function, the Chamfer distance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.406, + 0.892, + 0.49 + ], + "angle": 0, + "content": "We calculate pairwise Chamfer distances across a minibatch and select \\(K\\) point clouds with the lowest distances to be the positive terms for each \\(G_{i}\\) in the loss function. We call this process Chamfer mining. The set of encoded positive terms is referred to as \\(P(\\mathbf{z}_i^{\\mathrm{G}})\\). Finally, the contrastive loss is given as" + }, + { + "type": "equation", + "bbox": [ + 0.506, + 0.497, + 0.892, + 0.55 + ], + "angle": 0, + "content": "\\[\nL _ {\\mathrm {G E O}} = \\frac {1}{N K} \\sum_ {i = 1} ^ {N} \\sum_ {\\mathbf {z} ^ {+} \\in P \\left(\\mathbf {z} _ {i} ^ {\\mathrm {G}}\\right)} - \\log \\frac {\\exp \\left(\\mathbf {z} _ {i} ^ {\\mathrm {G}} \\cdot \\mathbf {z} ^ {+} / \\tau\\right)}{\\sum_ {\\mathbf {z} ^ {-} \\in \\mathbf {z} ^ {\\mathrm {G}} \\backslash \\left\\{\\mathbf {z} _ {i} ^ {\\mathrm {G}} \\right\\}} \\exp \\left(\\mathbf {z} _ {i} ^ {\\mathrm {G}} \\cdot \\mathbf {z} ^ {-} / \\tau\\right)}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.551, + 0.892, + 0.643 + ], + "angle": 0, + "content": "where \\(N\\) is the batch size and \\(\\tau\\) is a tunable temperature parameter. Using \\(\\mathbf{z}^{+}\\) based on the Chamfer distance better captures the similarity and difference in 3D geometry and benefits 2D representation than other choices, e.g., 3D augmentation or category labels, which will be discussed later in Section 5.5 and Appendix B." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.659, + 0.857, + 0.674 + ], + "angle": 0, + "content": "3.1.2 Learning to discriminate 2D visual features" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.682, + 0.892, + 0.727 + ], + "angle": 0, + "content": "Translation and color invariance are crucial in many vision problems [17]. Learning them along with geometric-aware properties potentially yields better results." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.727, + 0.892, + 0.799 + ], + "angle": 0, + "content": "To acquire these invariances, we define the second function \\(L_{\\mathrm{IMG}}\\) by following a common practice in 2D representation learning. In particular, we use SimCLR [6] and learn to discriminate between two different augmentations of \\(I_{i}\\) (i.e., \\(I_{i}\\) and \\(I_{i}^{+}\\)):" + }, + { + "type": "equation", + "bbox": [ + 0.545, + 0.806, + 0.762, + 0.824 + ], + "angle": 0, + "content": "\\[\nL _ {\\mathrm {I M G}} = l _ {\\mathrm {I M G}} \\left(\\mathbf {z} ^ {\\mathrm {I}}, \\mathbf {z} ^ {\\mathrm {I +}}\\right) + l _ {\\mathrm {I M G}} \\left(\\mathbf {z} ^ {\\mathrm {I +}}, \\mathbf {z} ^ {\\mathrm {I}}\\right),\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.499, + 0.826, + 0.893, + 0.877 + ], + "angle": 0, + "content": "\\[\nl _ {\\mathrm {I M G}} \\left(\\mathbf {z} ^ {\\mathrm {I}}, \\mathbf {z} ^ {\\mathrm {I} +}\\right) = \\frac {1}{2 N} \\sum_ {i = 1} ^ {N} - \\log \\frac {\\exp \\left(\\mathbf {z} _ {i} ^ {\\mathrm {I}} \\cdot \\mathbf {z} _ {i} ^ {\\mathrm {I} +} / \\tau\\right)}{\\sum_ {\\mathbf {z} ^ {-} \\in \\mathbf {z} ^ {\\mathrm {I}} \\cup \\mathbf {z} ^ {\\mathrm {I} +} \\backslash \\left\\{\\mathbf {z} _ {i} ^ {\\mathrm {I}} \\right\\}} \\exp \\left(\\mathbf {z} _ {i} ^ {\\mathrm {I}} \\cdot \\mathbf {z} ^ {-} / \\tau\\right)}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.885, + 0.796, + 0.903 + ], + "angle": 0, + "content": "where \\(\\mathbf{z}_i^{1 + }\\in \\mathbf{z}^{1 + }\\) is an encoded feature of \\(I_{i}^{+}\\)" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "21374" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.122 + ], + "angle": 0, + "content": "3.1.3 Cross-modal sharing the properties on the joint 2D-3D space" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.129, + 0.468, + 0.2 + ], + "angle": 0, + "content": "The third function \\( L_{\\mathrm{CROSS}} \\) aligns the geometric-aware features \\( \\mathbf{z}^{\\mathrm{G}} \\) with the 2D features \\( \\mathbf{z}^{\\mathrm{I}} \\) by constructing a common 2D-3D space for the two encoders, \\( f^{\\mathrm{G}}(\\cdot) \\) and \\( f^{\\mathrm{I}}(\\cdot) \\). To this end, we use cross-modal contrastive learning loss as a training objective as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.089, + 0.213, + 0.469, + 0.282 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} L _ {\\mathrm {C R O S S}} = l _ {\\mathrm {C R O S S}} \\left(\\mathbf {z} ^ {\\mathrm {I}}, \\mathbf {z} ^ {\\mathrm {G}}\\right) + l _ {\\mathrm {C R O S S}} \\left(\\mathbf {z} ^ {\\mathrm {G}}, \\mathbf {z} ^ {\\mathrm {I}}\\right), \\\\ l _ {\\text {C R O S S}} \\left(\\mathbf {z} ^ {\\mathrm {I}}, \\mathbf {z} ^ {\\mathrm {G}}\\right) = \\frac {1}{2 N} \\sum_ {i = 1} ^ {N} - \\log \\frac {\\exp \\left(\\mathbf {z} _ {i} ^ {\\mathrm {I}} \\cdot \\mathbf {z} _ {i} ^ {\\mathrm {G}} / \\tau\\right)}{\\sum_ {\\mathbf {z} ^ {-} \\in \\mathbf {z} ^ {\\mathrm {G}} \\backslash \\left\\{\\mathbf {z} _ {i} ^ {\\mathrm {G}} \\right\\}} \\exp \\left(\\mathbf {z} _ {i} ^ {\\mathrm {I}} \\cdot \\mathbf {z} ^ {-} / \\tau\\right)}. \\tag {4} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.293, + 0.469, + 0.354 + ], + "angle": 0, + "content": "Sharing \\(\\mathbf{z}^{\\mathrm{G}}\\) from \\(L_{\\mathrm{GEO}}\\) with \\(\\mathbf{z}^{\\mathrm{l}}\\) from \\(L_{\\mathrm{IMG}}\\) on \\(L_{\\mathrm{CROSS}}\\) using \\(L\\) results in a \\(f^{1}(\\cdot)\\) that can produce 2D representation with useful geometric and visual priors that show superior fin-tuning performance in the experimental section." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.363, + 0.469, + 0.395 + ], + "angle": 0, + "content": "3.2. Learning geometric-aware representation on non-paired RGB datasets" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.401, + 0.469, + 0.598 + ], + "angle": 0, + "content": "Training a model to induce geometric-aware properties in 2D representation using Eq. (2) and Eq. (4) requires RGB-CAD pairs \\((I, G)\\). However, obtaining such paired datasets is a cumbersome problem in every cross-modal learning framework. To address this, we propose to utilize 2D-3D object matching techniques, e.g., [16, 19, 30, 31, 47], to generate pseudo-pair of images and its associated 3D models, \\((I_i, G_i')\\), which can be used for training instead of the real pairs. Our experiments show that these pseudo pairs still help induce geometric-aware properties in our representations, resulting in better performance on 2D object understanding tasks, compared to state-of-the-art 2D representation learning approaches." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.612, + 0.266, + 0.629 + ], + "angle": 0, + "content": "4. Experimental setup" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.636, + 0.264, + 0.652 + ], + "angle": 0, + "content": "4.1. Pre-training details" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.659, + 0.469, + 0.84 + ], + "angle": 0, + "content": "We use ResNet-50 [23] or ViT-B [29] initialized with supervised pre-trained ImageNet weights for the 2D encoder and use DGCNN [46] for the 3D encoder. We choose \\(\\tau = 0.07\\) for all equations and \\(K = 3\\) in Eq. (2). Modality-specific projection heads are used for both 2D and 3D encoders to produce feature vectors \\(z^{\\mathrm{IMG}}\\) and \\(z^{\\mathrm{GEO}}\\) used in Eq. (1). Each head consists of two linear layers of sizes 1024 and 512, where the first one has ReLU activation. We pre-trained the model on the NVIDIA A100 GPU with a batch size of 256, then neglected the projection heads and retained only the 2D encoder for fine-tuning with downstream tasks. More details are given in Appendix A." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.469, + 0.901 + ], + "angle": 0, + "content": "For the pre-train dataset, we use Pix3D [45] with the S1 train-test split [16]. This dataset consists of 10,069 paired RGB images of indoor scene furniture (e.g., bed, chair, sofa) and corresponding CAD models (subcategories) with" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.213 + ], + "angle": 0, + "content": "a total of 395 shapes. We preprocessed each CAD model by uniform sampling random points to generate point clouds consisting of \\( N = 1024 \\) and applied point translation, rotation, and jittering to them. For RGB images, we applied the same augmentation strategy as [6] by randomly cropping an image into a size of \\( 224 \\times 224 \\), then randomly applying horizontal flipping, color jittering, grayscale, and Gaussian blurring to the images." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.233, + 0.762, + 0.249 + ], + "angle": 0, + "content": "4.2. Pseudo-pair generation setup" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.259, + 0.892, + 0.41 + ], + "angle": 0, + "content": "We utilized a state-of-the-art 3D shape retrieval model, ROCA [19], to generate a pseudo CAD model for any RGB image in indoor scene domains. ROCA was trained on Scan2CAD dataset [2] containing RGB-D frames of indoor scenes and annotated CAD models for each object in each frame. The Mask-RCNN [22] is employed to detect objects in an input image and generate bounding boxes of those detected ones. The feature of each bounding box will be further used in the ROCA retrieval module for predicting its associated CAD model listed in the ShapeNet [4] database." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.414, + 0.892, + 0.504 + ], + "angle": 0, + "content": "The pairing for each RGB input was selected based on a predicted CAD model of the largest detected bounding box. See Appendix G for more ablation studies on pair generation. Later in the experiment section, we compare our model trained on RGB images from Pix3D dataset [45] and pseudo CAD pairs generated by ROCA with competitors." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.524, + 0.696, + 0.54 + ], + "angle": 0, + "content": "4.3. Baseline competitors" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.551, + 0.892, + 0.596 + ], + "angle": 0, + "content": "All competitors except SupImg and Pri3D were initialized using pre-trained ImageNet weights and subsequently trained on Pix3D to ensure evaluation fairness." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.6, + 0.892, + 0.645 + ], + "angle": 0, + "content": "Supervised ImageNet Pre-training (SupImg) [13] represents the base performance of a pre-trained model without additional training on indoor scene datasets." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.649, + 0.892, + 0.709 + ], + "angle": 0, + "content": "SimCLR [6] and SupCon [28] provide the results when learning 2D representation on augmented RGB images (SimCLR), object categories (SupCon), or subcategories (SupCon (Fine)) in a CNN backbone." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.713, + 0.892, + 0.758 + ], + "angle": 0, + "content": "CrossPoint [1] shows the performance of existing CAD-RGB representation learning. Note that this work has not been studied for solving 2D object understanding tasks." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.762, + 0.892, + 0.852 + ], + "angle": 0, + "content": "Pri3D [25] and Set-InfoNCE [5] are state-of-the-art geometric-aware 2D representation learning works trained on multi-view RGB frames and 3D scans of ScanNet [12] dataset. Note that Set-InfoNCE did not publicly share their code, so we can only compare the results to their reported statistics on ScanNet [12] and NYUv2 [42] datasets." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "DINO [3] and MAE [20] are state-of-the-art 2D representation learning models based on Vision Transformer (ViT) [29] architectures." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "21375" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.09, + 0.277, + 0.108 + ], + "angle": 0, + "content": "5. Experimental results" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.115, + 0.373, + 0.132 + ], + "angle": 0, + "content": "5.1. Properties of our learned features" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.139, + 0.47, + 0.215 + ], + "angle": 0, + "content": "Evaluating geometric-aware properties. Fig. 2 visualizes the pairwise cosine similarities between each encoded feature of objects from the Pix3D validation split. The representations were encoded with the 2D encoder (without a projection head) of each approach." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.215, + 0.47, + 0.306 + ], + "angle": 0, + "content": "Our representations have high similarity scores for images with the same geometry (intra-subcategory) and others with the same object category (intra-category), while none of the competitors could reflect two properties at the same time. More visualizations from other categories and other competitors are provided in Appendix B." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.306, + 0.47, + 0.472 + ], + "angle": 0, + "content": "One interesting aspect is that our representations also well capture the differences across inter-category and inter-subcategory samples. We acquire better mean intra and inter-category similarity scores than the self-supervised baselines, as shown in Fig. 4. Furthermore, Ours (pseudo) yields similar findings, particularly for inter-category. An additional study in Appendix B also demonstrates that Ours (pseudo) has better discrimination in inter-subcategory features. These geometric-aware properties in our learned representation lead to improved 2D object understanding performance in further subsections." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.473, + 0.46, + 0.623 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.624, + 0.47, + 0.695 + ], + "angle": 0, + "content": "Figure 4. Distribution of pairwise cosine similarity score among intra and inter-category samples. Our representations learned by \\( L_{\\mathrm{GEO}} \\) based on the Chamfer distance have the highest mean score (vertical dashed lines) within intra-category samples and also have the lowest score in the inter-category scenario." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Object localization. We study whether our model can generalize to images with multiple objects, even though it was trained on a dataset of single objects. Fig. 5 shows that our learned features from the ViT-B backbone can be used for roughly localizing patches associated with object categories without fine-tuning. More details and results are provided in Appendix C. This property may arise from how our loss function encourages learning discriminative part features, which are useful for classifying, localizing, and segmenting multiple objects demonstrated in our subsequent experiments. This similar behavior is also observed in other 2D self-supervised models [3] trained on single-object datasets (e.g., ImageNet [13])." + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.077, + 0.889, + 0.17 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.172, + 0.892, + 0.256 + ], + "angle": 0, + "content": "Figure 5. We compute the feature similarity between each patch in an unseen input image and the mean global feature of learned images in each category using models with a ViT-B backbone. Without fine-tuning, our model can identify the table and roughly localize patches associated with the chairs in the image by using the category of the most similar mean global feature of each patch." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.272, + 0.741, + 0.289 + ], + "angle": 0, + "content": "5.2. 2D Semantic segmentation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.299, + 0.892, + 0.405 + ], + "angle": 0, + "content": "Table 1 compares fine-tuning results in semantic segmentation tasks with other competitors. Following [5, 25], we train a U-Net [41] with residual connections for predicting segmentation masks with cross-entropy loss. The encoder part of U-Net is ResNet-50, while the decoder is conv layers with bi-linear interpolation. For ViT-B, we follow [20] by using UPerNet [51] as a segmentation head." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.408, + 0.893, + 0.605 + ], + "angle": 0, + "content": "We employ two variants of mean intersection-over-union (mIoU) for the evaluation metric. The first mIoU, initially implemented by Pri3D [25], does not include pixels that were incorrectly predicted to be ignored classes (e.g., background) as a false positive in mIoU computation. In comparison, our revised mIoU includes these pixels to avoid model cheating by predicting more ignored classes. The experiments were conducted on NYUv2 [42], ScanNet [12], indoor ADE20k [54], and indoor SUNRGB-D [43] datasets. We filtered ADE20k to include only indoor scenes and ignored previously omitted classes in an NYUv2 setting following the prior work [25] for SUNRGB-D. More details on our split are provided in Appendix D." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.607, + 0.892, + 0.73 + ], + "angle": 0, + "content": "When pre-trained on non-paired RGB datasets, Ours (pseudo) outperforms all 2D competitors in both architectures, including DINO [3] and MAE [20]. For 2D-3D competitors, we win against Pri3D and achieve very competitive results to Set-InfoNCE in NYUv2 by only -0.16 in mIoU [25]. We also outperform Pri3D in ADE20k by +1.01 for the original and +0.79 for the pseudo version. The qualitative results are shown in Fig. 6 and Appendix E." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.731, + 0.892, + 0.853 + ], + "angle": 0, + "content": "For ScanNet and SUNRGB-D datasets, Pri3D and SetInfoNCE perform better than ours. This might be because their models were trained directly on ScanNet 3D scans. Some images in SUNRGB-D also appear similar to those in ScanNet, as both datasets sampled RGB-D frames from recorded videos at a high frame-per-second rate. Nonetheless, even without 3D ScanNet, our method still achieves comparable results to Pri3D (-0.17)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Additionally, in Appendix F, we present results obtained by increasing the pre-training data, which allows us to surpass Set-InfoNCE on NYUv2 without real 3D pairs." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "21376" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.895, + 0.132 + ], + "angle": 0, + "content": "Table 1. Semantic segmentation results on four popular benchmark datasets. For both ResNet-50 (RN50) and ViT-B architectures, our approaches have better mIoU than 2D representation learning baselines. (*) denotes scores from the methods that were directly pre-trained on 2D and 3D data of ScanNet dataset. We win against Pri3D in NYUv2 and ADE20k without requiring 3D scene scans." + }, + { + "type": "table", + "bbox": [ + 0.115, + 0.134, + 0.846, + 0.349 + ], + "angle": 0, + "content": "
Arch.GT pairMethod3DNYUv2ScanNetindoor ADE20kSUNRGB-D
mIoUmIoU [25]mIoUmIoU [25]mIoUmIoU [25]mIoUmIoU [25]
RN502D onlySupImg-47.0450.049.1255.737.5239.6947.9663.12
SimCLR-47.9453.3249.9156.3438.1939.5648.5163.00
SupCon-48.4954.1650.5956.5737.9640.1348.1365.01
SupCon (fine)-47.3453.4549.8156.2237.8739.9248.0563.13
pseudoOurs (pseudo)CAD49.4654.6250.7756.7639.1340.4349.1365.45
2D-3DCrossPointCAD46.0449.1847.2654.0236.5537.8847.1562.77
Pri3Dscene49.5254.754.72*61.7*38.3439.1750.0266.65
Set-InfoNCEscene-55.4-63.1*----
OursCAD49.7755.2451.0357.1239.3540.8649.8565.95
ViT-B2D onlySupImg-49.4455.5963.9359.7242.7844.3851.2666.45
DINO-52.1457.2462.5458.1341.7243.4150.5266.12
MAE-50.1055.6662.2358.9542.9644.9652.2267.87
pseudoOurs (pseudo)CAD52.4758.0264.4960.7343.0245.3752.5369.59
2D-3DOursCAD53.058.6765.2760.9543.1245.8252.9669.69
" + }, + { + "type": "image", + "bbox": [ + 0.107, + 0.351, + 0.861, + 0.612 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.613, + 0.893, + 0.643 + ], + "angle": 0, + "content": "Figure 6. Qualitative results on NYUv2 [42] semantic segmentation. Our methods yield better segmentation results when labeling a scene is challenging due to color or lighting. The geometric priors in our learned representations boost understanding of each scene." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.65, + 0.471, + 0.667 + ], + "angle": 0, + "content": "5.3.2D Instance segmentation and object detection" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.674, + 0.47, + 0.856 + ], + "angle": 0, + "content": "Indoor scenes. We show how our features improve instance segmentation and object detection results in Table 2. Similar to [25], we use Mask-RCNN [22] with ResNet-50 encoder, implemented on Detectron2 [48] framework for both tasks. For ViT-B, we resize input images to \\(224 \\times 224\\) and follow [33] by using Mask-RCNN as the detection head. All backbones were initialized by the pre-trained weights of our model or competitors'. Following [5,25], we use NYUv2 [42] dataset and a well-known detection benchmark, COCO dataset, with Average Precision (AP) as the metric. We filtered COCO images to include only indoor objects. Details on the selected classes are in Appendix D." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Our method outperforms state-of-the-art 2D and 2D-3D competitors in all settings. Ours (pseudo) achieves competitive scores against Pri3D and Set-InfoNCE in NYUv2 and" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.651, + 0.85, + 0.666 + ], + "angle": 0, + "content": "beats Pri3D in COCO without ground truth 3D pairs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.667, + 0.892, + 0.773 + ], + "angle": 0, + "content": "Outdoor scenes. We also pre-trained our model on PAS-CAL3D+ [50] dataset, which contains objects such as vehicles and furniture in both indoor and outdoor scenes, and evaluated the model on another subset of COCO images called outdoor COCO. Further dataset details are provided in Appendix D. Our method leads to similar improvements in AP as observed in the indoor-only settings." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.786, + 0.755, + 0.802 + ], + "angle": 0, + "content": "5.4. Experiments on 2D retrieval" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Table 3 shows the retrieval performance on Pix3D [45] by fine-tuning the pre-trained model on coarse-grained (category) and fine-grained (subcategory) labels of objects. The 2D encoder was fine-tuned along with an additional retrieval head, consisting of two linear layers of sizes 1024 and 512 with ReLU applied only to the first layer. All" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "21377" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.146, + 0.09, + 0.82, + 0.104 + ], + "angle": 0, + "content": "Table 2. Object detection and instance segmentation performance. We outperform competitors for all datasets." + }, + { + "type": "table", + "bbox": [ + 0.088, + 0.106, + 0.875, + 0.3 + ], + "angle": 0, + "content": "
Arch. SizeGT pairMethod3DNYUv2indoor COCOoutdoor COCO
Object Det.Instance segm.Object Det.Instance seg.Object Det.Instance seg.
AP50AP75APAP50AP75APAP50AP75APAP50AP75APAP50AP75APAP50AP75
RN50 4802D onlySupImg-29.917.316.825.113.913.441.7824.2123.7039.1623.3522.6146.0926.9828.0842.4523.3423.92
SimCLR-32.8120.1519.2429.1015.9715.6243.6326.4625.4540.8724.7923.8648.1528.7530.4044.3125.0124.99
SupCon-33.2320.3619.6329.4416.1615.8343.6626.3425.3240.8424.5323.7547.8928.6730.2944.1624.6324.97
SupCon (fine)-32.5619.7418.9229.0616.1115.7443.5825.9525.2140.6524.2223.6645.0127.9026.5941.9725.6124.66
pseudoOurs (pseudo)CAD34.4520.2719.7229.6416.2416.1343.7426.4725.4840.9224.7723.91------
2D-3DCrossPointCAD28.4215.9415.2224.4913.3213.1140.2522.7822.2638.5421.9220.8043.2224.5725.6039.7521.9321.11
Pri3Dscene34.020.419.429.516.315.843.4926.4025.2240.7124.7223.61------
Set-InfoNCEscene34.620.519.729.716.316.5-----------
OursCAD34.8520.8920.1230.0316.5116.8444.1126.7825.6941.0224.9124.0849.0329.8031.6245.2325.9025.85
ViT-B 2242D onlySupImg-34.4019.2419.0628.4214.0514.9731.4520.6319.4129.7718.7317.8233.5623.1921.8131.6819.5218.11
DINO-33.0318.6217.9126.8214.5614.7327.7016.2415.8725.7814.8614.7632.5722.1320.6129.8618.0717.66
MAE-35.9219.3019.2429.8816.0115.8231.5420.5919.3329.9218.6517.8336.9724.5123.1233.6720.1519.46
pseudoOurs (pseudo)CAD36.2419.7819.7230.1015.9416.0531.7820.7419.4630.0119.0717.94------
2D-3DOursCAD36.3119.9119.9430.3016.1616.2732.0221.0419.6730.1619.0218.0937.7424.9223.4234.1320.4919.89
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.313, + 0.468, + 0.339 + ], + "angle": 0, + "content": "Table 3. Retrieval performance on Pix3D [45]. Our method outperforms all competitors in all situations." + }, + { + "type": "table", + "bbox": [ + 0.085, + 0.341, + 0.455, + 0.515 + ], + "angle": 0, + "content": "
Arch.GT PairMethod3DCoarse R@1Fine R@1
RN502D onlySupImg-78.8551.18
SimCLR-80.0455.01
SupCon-81.3252.39
SupCon (fine)-79.9555.84
pseudoOurs (pseudo)CAD81.7456.71
2D-3DCrossPointCAD75.9748.09
Pri3Dscene79.7251.63
OursCAD82.8858.97
ViT-B2D onlySupImg-84.0464.17
DINO-84.5965.48
MAE-83.7962.00
pseudoOurs (pseudo)CAD86.1666.40
2D-3DOursCAD86.3267.23
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.524, + 0.468, + 0.58 + ], + "angle": 0, + "content": "Table 4. Effects on losses and positive mining choices. Training on three losses simultaneously yields the best performance in mIoU. At the same time, choosing the Chamfer Distance (CD) as a positive mining choice in \\( L_{\\mathrm{GEO}} \\) also wins against the others." + }, + { + "type": "table", + "bbox": [ + 0.107, + 0.583, + 0.435, + 0.7 + ], + "angle": 0, + "content": "
LIMGLGEOLCROSSPos.NYUv2ADE20k
-✓✓CD48.2337.71
✓-✓-48.4638.47
✓---47.9438.19
--✓-47.0237.43
✓✓✓Sup49.4839.12
✓✓✓Aug49.1438.65
✓✓✓CD49.7739.35
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.715, + 0.468, + 0.761 + ], + "angle": 0, + "content": "retrieval models were trained using supervised contrastive loss [28] with \\(\\tau = 0.07\\). Our methods outperform all competitors in all architectures." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.771, + 0.238, + 0.785 + ], + "angle": 0, + "content": "5.5. Ablation studies" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.795, + 0.468, + 0.839 + ], + "angle": 0, + "content": "All ablation experiments are evaluated on NYUv2 and ADE20k semantic segmentation tasks using our revised mIoU metric on ResNet-50 architecture." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Effects on losses and positive mining choices Table 4 shows the effects of three loss choices (i.e., \\(L_{\\mathrm{IMG}}\\), \\(L_{\\mathrm{GEO}}\\), and \\(L_{\\mathrm{CROSS}}\\)) and three different choices of the positive point cloud using in Eq. (2), including using object categories" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.314, + 0.892, + 0.389 + ], + "angle": 0, + "content": "(Sup), point cloud augmentation (Aug), and Chamfer distance (CD). We found that training three loss functions simultaneously notably improves mIoU from training single or dual losses. While in the positive choice study, our selected Chamfer distance achieves the best mIoU." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.39, + 0.892, + 0.511 + ], + "angle": 0, + "content": "Effects on \\(K\\) selected positive point clouds. We studied the best number of \\(K\\) in Eq. (2). Fig. 7 reveals that \\(K = 3\\) can achieve the best mIoU among the others. Using a lower \\(K\\) leads to lower mIoU, similar to a higher \\(K\\). This is probably because higher \\(K\\) has more chance to select false positive samples due to higher Chamfer distances, which means that the selected samples might have a much different shape than the anchor \\(\\mathbf{z}_i^G\\)." + }, + { + "type": "image", + "bbox": [ + 0.525, + 0.519, + 0.868, + 0.582 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.584, + 0.89, + 0.611 + ], + "angle": 0, + "content": "Figure 7. Effect of varying \\( K \\) selected positive point clouds. \\( K = 3 \\) has the best mIoU." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.619, + 0.75, + 0.634 + ], + "angle": 0, + "content": "6. Limitations and Discussion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Using CAD models for inducing geometric-aware properties in 2D representation via Chamfer distance shows significantly enhanced 2D object understanding results that are almost as effective as 3D priors from scene scans. This finding remains true when we train our model on generated pseudo-RGB-CAD pairs, allowing us to beat SOTA 2D competitors without the need for paired datasets. However, the performance of the pseudo-pair generator currently hinders our results. As seen in Fig. 2 and 4, features trained on pseudo pairs cannot clearly categorize intra-subcategory images. We observe that this is due to an improper CAD pair assignment; more information is given in Appendix B. Nonetheless, generating or retrieving 3D models from a single image is still more tractable than scene scans and shows progressive performance improvement [38]. This enables harnessing the massive-scale RGB data and generalizing beyond domains with paired data (See Appendix F)." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "21378" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.105 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.198 + ], + "angle": 0, + "content": "[1] Mohamed Afham, Isuru Dissanayake, Dinithi Dissanayake, Amaya Dharmasiri, Kanchana Thilakarathna, and Ranga Rodrigo. Crosspoint: Self-supervised cross-modal contrastive learning for 3d point cloud understanding. 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In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 633-641, 2017. 2, 6" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.47, + 0.331 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.518, + 0.956 + ], + "angle": 0, + "content": "21381" + } + ] +] \ No newline at end of file diff --git a/2023/Learning Geometric-Aware Properties in 2D Representation Using Lightweight CAD Models, or Zero Real 3D Pairs/17e7e6f9-e779-4537-89d2-408c0b6a8259_origin.pdf b/2023/Learning Geometric-Aware Properties in 2D Representation Using Lightweight CAD Models, or Zero Real 3D Pairs/17e7e6f9-e779-4537-89d2-408c0b6a8259_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..79d6961fe756b5941972801cd1bf92056967b129 --- /dev/null +++ b/2023/Learning Geometric-Aware Properties in 2D Representation Using Lightweight CAD Models, or Zero Real 3D Pairs/17e7e6f9-e779-4537-89d2-408c0b6a8259_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:b917921627afbf91419043f56e3473b49dc7f13858f4ff6a7f290299122abe6e +size 7187203 diff --git a/2023/Learning Geometric-Aware Properties in 2D Representation Using Lightweight CAD Models, or Zero Real 3D Pairs/full.md b/2023/Learning Geometric-Aware Properties in 2D Representation Using Lightweight CAD Models, or Zero Real 3D Pairs/full.md new file mode 100644 index 0000000000000000000000000000000000000000..10a762eb6064ddf1f5375dcd9e251231d577a4ea --- /dev/null +++ b/2023/Learning Geometric-Aware Properties in 2D Representation Using Lightweight CAD Models, or Zero Real 3D Pairs/full.md @@ -0,0 +1,312 @@ +# Learning Geometric-aware Properties in 2D Representation Using Lightweight CAD Models, or Zero Real 3D Pairs + +Pattaramanee Arsomngern + +Sarana Nutanong + +VISTEC, Thailand + +Supasorn Suwajanakorn + +{pattaramanee.a_s19, snutanon, supasorn.s}@vistec.ac.th + +# Abstract + +Cross-modal training using 2D-3D paired datasets, such as those containing multi-view images and 3D scene scans, presents an effective way to enhance 2D scene understanding by introducing geometric and view-invariance priors into 2D features. However, the need for large-scale scene datasets can impede scalability and further improvements. This paper explores an alternative learning method by leveraging a lightweight and publicly available type of 3D data in the form of CAD models. We construct a 3D space with geometric-aware alignment where the similarity in this space reflects the geometric similarity of CAD models based on the Chamfer distance. The acquired geometric-aware properties are then induced into 2D features, which boost performance on downstream tasks more effectively than existing RGB-CAD approaches. Our technique is not limited to paired RGB-CAD datasets. By training exclusively on pseudo pairs generated from CAD-based reconstruction methods, we enhance the performance of SOTA 2D pre-trained models that use ResNet-50 or ViT-B backbones on various 2D understanding tasks. We also achieve comparable results to SOTA methods trained on scene scans on four tasks in NYUv2, SUNRGB-D, indoor ADE20k, and indoor/outdoor COCO, despite using lightweight CAD models or pseudo data. Please visit our page: https:// + +//GeoAware2dRepUsingCAD.github.io/ + +# 1. Introduction + +Recent 2D visual representation learning approaches, such as contrastive learning [3, 6, 10, 17, 28] or masked autoencoder [20], are widely used to tackle various problems in computer vision due to their ability to encode rich visual features. While these methods have shown exceptional results on 2D image classification, they still have shortcomings in other 2D understanding tasks that involve instance-level reasoning. Prior research [25] also shows that models pre-trained using image augmentations [8,21] or supervised + +![](images/68a9afe9805c7f178efb03c903f64007cac465bf3828961fe44392f555e6ef81.jpg) +Figure 1. Overview concept of our solution. We leverage CAD models to train a joint 2D-3D space such that images of objects with similar shapes, based on the Chamfer distance, are attracted to each other, while images with different shapes are separated. This results in a continuous geometric-aware space where the distance between two points reflects their geometric similarity, which could be utilized for downstream 2D object understanding tasks. + +labels [13] could not deliver satisfactory results when applied to downstream tasks such as semantic segmentation, instance segmentation, and object detection [12, 42]. + +To alleviate this, Hou et al. [25] proposed to learn 3D geometric priors, such as view-invariance, from 3D data and transfer the learned priors to 2D representations. In particular, their model is first pre-trained on ScanNet [12], a database of multi-view RGB-D scans, using contrastive learning and later used as initialization for fine-tuning networks on downstream tasks. Chen et al. [5] further extend this work by utilizing additional priors through learning to group nearby points that refer to the same object part from 3D scenes. + +The key concept of their introduced new paradigm is to share useful 3D priors from 3D data with 2D representa + +tions. However, previous studies have investigated mostly 3D priors related to viewpoint invariance from 3D scene datasets, which are often limited in size and scene variations due to the laborious data collecting and labeling process [24]. This scarcity of large-scale 3D data also limits the number of available 3D priors for learning the invariance, hence hindering further performance gains. This paper questions whether there are other effective 3D priors for 2D downstream tasks and whether they can be learned from other forms of 3D data that are lighter and easier to obtain. + +We begin our exploration by considering how to learn an embedding space that maps together images with the same or similar geometries. One solution is to learn from images that share the same 3D model, which inspires our interest in CAD models. Unlike 3D scenes, CAD models are lightweight, publicly available, and can be easily aligned with RGB images via web scraping or human annotation [2]. There exist studies that jointly learn 2D and 3D CAD representation for other CAD-related tasks, e.g., 3D classification [1,27]. However, their 2D features, which are derived from augmentation-based CAD features, are insufficient to be directly applied to 2D object understanding tasks—they can group images with similar geometries but struggle to learn the distinctions between object categories. + +We argue that useful geometric-aware representations should account for both similarities and differences in object geometry. Our key idea is to acquire such features by imitating the Chamfer distance between 3D objects in our embedding space and inducing this derived geometric awareness in our learned 2D representation. In particular, we learn our space by attracting the encoded features of geometrically similar CAD models in the mini-batch based on the Chamfer distance and repelling those with lower similarities. In contrast to other methods trained on supervised discrete signals like object labels or through 3D augmentations, our method produces a continuous 3D space that better captures the similarity and difference in geometry (see Section 5.1). In addition, we employ augmentation-based contrastive learning [6] to learn other useful visual feature properties, such as translation and color invariances. This results in a 2D representation in a 2D-3D space that contains rich visual information and strong geometric-aware properties, as shown in Fig. 1, which can be leveraged to improve 2D object understanding tasks. + +To match our geometric-aware CAD features with corresponding 2D features, a paired RGB-CAD dataset, such as Pix3D [45], is required. However, by leveraging recent techniques [19, 31] that can reconstruct a CAD model from an input image, it is possible to generate pseudo CAD models for any images and use them to learn our method without a paired dataset. Adapting this pseudo-pair generation to other techniques that rely on scene scans is significantly harder, as synthesizing full 3D scenes with reasonable detail + +remains harder than reconstructing individual objects. + +We demonstrate the effectiveness of our geometric-aware 2D representation in Fig. 2. Our features can group and differentiate objects based on their categories or subcategories, leading to improved performance on multiple 2D object understanding tasks using both ResNet-50 [23] and ViT-B [29] backbones. Our method trained on a pseudopair dataset also yields superior results over DINO [3] and MAE [20]. Remarkably, we also surpass a state-of-the-art method, Pri3D [25] without using any 3D scene scans in the following tasks: (i) semantic segmentation using NYUv2 [42] and indoor ADE20k [54]; (ii) object detection and instance segmentation using NYUv2 and in/outdoor COCO [35]; (iii) object retrieval using Pix3D [45]. + +To summarize, our contributions are as follows. + +- We present a simple yet effective approach to inducing geometric-aware properties in 2D representation using lightweight CAD models. These can be either ground truth from RGB-CAD datasets or generated pseudo CAD pairs based on 2D-only data. +- We propose training objectives to learn a 2D-3D embedding space where feature similarity reflects geometric similarity based on the Chamfer distance. +- We enhance the performance of SOTA 2D representation learning techniques on four 2D object understanding tasks and achieve competitive results to SOTA that require 3D scene scans across five datasets, in both settings that use real or pseudo-RGB-CAD datasets. + +# 2. Related works + +2D Representation Learning. Contrastive learning [49] has continuously shown improvements in various downstream tasks. Its main concept is to maximize a similarity score between two different views (e.g., two different augmentations of the same instance [6, 9, 10, 17, 21], two instances with the same label [28], or two different encoders [3, 7]). Meanwhile, learning representation in autoencoder fashion [20] also has recently demonstrated a performance boost from contrastive learning works. + +This paper shows that these 2D representation learning methods could not provide geometric-aware properties, which are critical in object understanding tasks. + +3D Representation Learning requires specific network architecture for extracting features based on an input's data structure (e.g., rendered images [44], point clouds [39, 46], or meshes [15, 16]). These architectures can encode geometric information of each 3D shape into representations with a deep understanding of shape structure. Later, contrastive learning in 3D, such as point cloud augmentation [52], or multiple modalities [1, 53], showed their improvement in 3D classification, retrieval, and part segmentation problems. Concurrently, 3D reconstruction techniques [11, 14, 37] also deliver promising results in similar tasks. + +![](images/c1158c3436b75be9708460bf079194afc0a4a29aaa00fbb2378c30da4ca57ab8.jpg) +Figure 2. Visualization of the pairwise cosine similarity between the learned representations of objects from each method. The bright color indicates higher similarity. The first row shows the similarity scores of all validation images in Pix3D [45] dataset, sorted by object category and subcategory (i.e., object models). The second row zooms in on a single category (Sofa) from the first row. Our method shows a better grouping of the same sofa than others, especially SimCLR [6] and SupCon [28], which can hardly differentiate between each sofa type. CrossPoint [1] and SupCon (fine), unlike others, can group the same sofa but fail to separate sofas from other categories in the first row. Surprisingly, MAE [20] also delivers visual features without subcategory awareness. Compared to SimCLR, Ours (pseudo) provides distinguishable features (with darker colors) between each sofa type. Additional studies on Ours (pseudo) are provided in Appendix B. + +In this paper, we adapt the encoded 3D features with rich geometric information to share the ability to recognize geometric similarities in each object to 2D representations. + +Multimodal Representation Learning gains attraction due to its ability to share modality-specific contexts. CLIP [40] facilitates various vision-language tasks by contrastive learning on text-image data. Similarly, 2D-3D representation learning transfers geometric information from 3D to 2D features [5, 25, 36]. Pri3D [25] introduces a contrastive learning method on multi-view RGB frames and 3D scene scans [12]. These modal pairs allow them to learn view and 3D priors in 2D features and achieve impressive 2D indoor scene understanding performance. Later, SetInfoNCE [5] improves upon Pri3D by fine-tuning the Pri3D pre-trained model using additional 3D priors, e.g., sets of nearby points referring to the same object part, generated from training scans. While these studies have focused on scene scans, this paper demonstrates that geometric priors from CAD models can achieve comparable or better object understanding than learning on 3D scenes. + +Some studies, e.g., CrossPoint [1, 27], have been conducted to share visual context to guide CAD features (2D $\rightarrow$ 3D). Their learned 2D features, on the other hand, fail to discriminate object categories, resulting in poor object understanding results. We then investigate a more efficient method of learning and sharing modality-specific context from CAD to RGB without hurting 2D task performance. + +2D-3D Object Matching has been studied for searching or generating a 3D model of objects appearing in a given image. [19, 30-32] use existing CAD databases to train an RGB-CAD retrieval and alignment module in a multi-task learning fashion using a given set of ground truths (e.g., camera intrinsic, depth map, mask, or pose parameters). [26, 34] utilize category labels to guide a joint RGB-CAD + +space for 2D-3D retrieval tasks. Another approach is to reconstruct a 3D model from the image directly [16, 18, 47]. However, the generated 3D may be less realistic than retrieving human-designed 3D from the databases. + +We utilize these works to generate CAD pairs for our pre-training RGB images. Learning representation on just pseudo-RGB-CAD pairs can surpass SOTA competitors. + +# 3. Proposed method + +Our goal is to construct a pre-trained model that can provide a 2D representation $\mathbf{z}_i^!$ of an input image $I_{i}$ with useful geometric priors to enhance 2D object understanding. Unlike prior works [5,25], we aim to learn the representations without 3D scene scans using other efficient alternatives. + +We propose a novel approach that can obtain such geometric priors from a lightweight and publicly available type of 3D data in the form of CAD models, while retaining discriminative representations for 2D tasks. Given an image $I_{i}$ and its associated CAD model $G_{i}$ , our solution constructs a 2D-3D embedding space with strong geometric-aware properties by learning CAD features $\mathbf{z}_{i}^{\mathrm{G}} = f^{\mathrm{G}}(G_{i})$ along with rich visual information from 2D features $\mathbf{z}_{i}^{\mathrm{I}} = f^{\mathrm{I}}(I_{i})$ . We show that the acquired 2D representations, where their feature similarity reflects geometric similarity, are more effective than solely relying on standard augmentation invariant CAD features and perform almost as effectively as 3D priors from scene scans on common 2D understanding tasks. The overview of our proposed framework is shown in Fig. 3. + +An extension to training our model on generated RGB-CAD pairs is further introduced in order to learn geometric-aware representations using just RGB training data. + +![](images/f81051a1ad6e9320d56d629dc8ee2b92513827b249b80b14b7fe386dd626e426.jpg) +Figure 3. Our pre-training strategy. We learn 2D representations on a joint 2D-3D space from RGB-CAD pairs based on three loss functions. $L_{\mathrm{GEO}}$ focuses on learning CAD features from two similar CAD models mined from Chamfer distance, $L_{\mathrm{IMG}}$ focuses on learning visual differences between two image augmentations, and $L_{\mathrm{CROSS}}$ shares geometric awareness from CAD features to 2D representation. + +# 3.1. Training objectives + +The core idea of our training objective is to share two modality-specific contexts, i.e., strong geometric-aware properties from $\mathbf{z}_i^{\mathrm{G}}\in \mathbf{z}^{\mathrm{G}}$ and rich visual information from $\mathbf{z}_i^{\mathrm{I}}\in \mathbf{z}^{\mathrm{I}}$ , in the joint 2D-3D embedding space by training on RGB-CAD pairs $(I,G)$ . To achieve this objective, we use three loss functions: $L_{\mathrm{GEO}}$ , $L_{\mathrm{IMG}}$ , and $L_{\mathrm{CROSS}}$ . The first loss $L_{\mathrm{GEO}}$ helps the 3D encoder $f^{\mathrm{G}}(\cdot)$ construct a geometric-aware embedding space, such that CAD models in $G$ with similar shapes, based on the Chamfer distance, are located near each other. The second loss $L_{\mathrm{IMG}}$ helps the 2D encoder $f^{\mathrm{I}}(\cdot)$ learn useful visual representation properties, e.g., translation and color invariance from $I$ . The third loss $L_{\mathrm{CROSS}}$ enforces the consistency between $\mathbf{z}_i^{\mathrm{G}}$ and $\mathbf{z}_i^{\mathrm{I}}$ for each $(I_i,G_i)$ pair. Finally, the multi-task loss function is + +$$ +L = L _ {\text {G E O}} + L _ {\text {I M G}} + L _ {\text {C R O S S}}. \tag {1} +$$ + +Detailed explanations of the three components are given in the following subsections. + +# 3.1.1 Geometric-aware CAD features + +We first explain how $L_{\mathrm{GEO}}$ provides geometric awareness to our features. Given $(I_i, G_i)$ , we use $G_i$ to train $f^{\mathrm{G}}(\cdot)$ for extracting a geometric context $\mathbf{z}_i^{\mathrm{G}}$ of each pair. We process each $G_i$ by converting it to a point cloud and use DGCNN [46] as $f^{\mathrm{G}}(\cdot)$ to capture local and global point cloud structure information, resulting in an encoded feature $\mathbf{z}_i^{\mathrm{G}}$ . + +To learn the space, we follow a common contrastive learning strategy by maximizing the similarity between $\mathbf{z}_i^{\mathrm{G}}$ and the encoded feature $\mathbf{z}^{+}$ of each positive term in a minibatch. However, instead of selecting $\mathbf{z}^{+}$ based on object labels or augmentations as is commonly done, we select $\mathbf{z}^{+}$ + +based on a geometric-based similarity function, the Chamfer distance. + +We calculate pairwise Chamfer distances across a minibatch and select $K$ point clouds with the lowest distances to be the positive terms for each $G_{i}$ in the loss function. We call this process Chamfer mining. The set of encoded positive terms is referred to as $P(\mathbf{z}_i^{\mathrm{G}})$ . Finally, the contrastive loss is given as + +$$ +L _ {\mathrm {G E O}} = \frac {1}{N K} \sum_ {i = 1} ^ {N} \sum_ {\mathbf {z} ^ {+} \in P \left(\mathbf {z} _ {i} ^ {\mathrm {G}}\right)} - \log \frac {\exp \left(\mathbf {z} _ {i} ^ {\mathrm {G}} \cdot \mathbf {z} ^ {+} / \tau\right)}{\sum_ {\mathbf {z} ^ {-} \in \mathbf {z} ^ {\mathrm {G}} \backslash \left\{\mathbf {z} _ {i} ^ {\mathrm {G}} \right\}} \exp \left(\mathbf {z} _ {i} ^ {\mathrm {G}} \cdot \mathbf {z} ^ {-} / \tau\right)}, \tag {2} +$$ + +where $N$ is the batch size and $\tau$ is a tunable temperature parameter. Using $\mathbf{z}^{+}$ based on the Chamfer distance better captures the similarity and difference in 3D geometry and benefits 2D representation than other choices, e.g., 3D augmentation or category labels, which will be discussed later in Section 5.5 and Appendix B. + +# 3.1.2 Learning to discriminate 2D visual features + +Translation and color invariance are crucial in many vision problems [17]. Learning them along with geometric-aware properties potentially yields better results. + +To acquire these invariances, we define the second function $L_{\mathrm{IMG}}$ by following a common practice in 2D representation learning. In particular, we use SimCLR [6] and learn to discriminate between two different augmentations of $I_{i}$ (i.e., $I_{i}$ and $I_{i}^{+}$ ): + +$$ +L _ {\mathrm {I M G}} = l _ {\mathrm {I M G}} \left(\mathbf {z} ^ {\mathrm {I}}, \mathbf {z} ^ {\mathrm {I +}}\right) + l _ {\mathrm {I M G}} \left(\mathbf {z} ^ {\mathrm {I +}}, \mathbf {z} ^ {\mathrm {I}}\right), +$$ + +$$ +l _ {\mathrm {I M G}} \left(\mathbf {z} ^ {\mathrm {I}}, \mathbf {z} ^ {\mathrm {I} +}\right) = \frac {1}{2 N} \sum_ {i = 1} ^ {N} - \log \frac {\exp \left(\mathbf {z} _ {i} ^ {\mathrm {I}} \cdot \mathbf {z} _ {i} ^ {\mathrm {I} +} / \tau\right)}{\sum_ {\mathbf {z} ^ {-} \in \mathbf {z} ^ {\mathrm {I}} \cup \mathbf {z} ^ {\mathrm {I} +} \backslash \left\{\mathbf {z} _ {i} ^ {\mathrm {I}} \right\}} \exp \left(\mathbf {z} _ {i} ^ {\mathrm {I}} \cdot \mathbf {z} ^ {-} / \tau\right)}, \tag {3} +$$ + +where $\mathbf{z}_i^{1 + }\in \mathbf{z}^{1 + }$ is an encoded feature of $I_{i}^{+}$ + +# 3.1.3 Cross-modal sharing the properties on the joint 2D-3D space + +The third function $L_{\mathrm{CROSS}}$ aligns the geometric-aware features $\mathbf{z}^{\mathrm{G}}$ with the 2D features $\mathbf{z}^{\mathrm{I}}$ by constructing a common 2D-3D space for the two encoders, $f^{\mathrm{G}}(\cdot)$ and $f^{\mathrm{I}}(\cdot)$ . To this end, we use cross-modal contrastive learning loss as a training objective as follows: + +$$ +\begin{array}{l} L _ {\mathrm {C R O S S}} = l _ {\mathrm {C R O S S}} \left(\mathbf {z} ^ {\mathrm {I}}, \mathbf {z} ^ {\mathrm {G}}\right) + l _ {\mathrm {C R O S S}} \left(\mathbf {z} ^ {\mathrm {G}}, \mathbf {z} ^ {\mathrm {I}}\right), \\ l _ {\text {C R O S S}} \left(\mathbf {z} ^ {\mathrm {I}}, \mathbf {z} ^ {\mathrm {G}}\right) = \frac {1}{2 N} \sum_ {i = 1} ^ {N} - \log \frac {\exp \left(\mathbf {z} _ {i} ^ {\mathrm {I}} \cdot \mathbf {z} _ {i} ^ {\mathrm {G}} / \tau\right)}{\sum_ {\mathbf {z} ^ {-} \in \mathbf {z} ^ {\mathrm {G}} \backslash \left\{\mathbf {z} _ {i} ^ {\mathrm {G}} \right\}} \exp \left(\mathbf {z} _ {i} ^ {\mathrm {I}} \cdot \mathbf {z} ^ {-} / \tau\right)}. \tag {4} \\ \end{array} +$$ + +Sharing $\mathbf{z}^{\mathrm{G}}$ from $L_{\mathrm{GEO}}$ with $\mathbf{z}^{\mathrm{l}}$ from $L_{\mathrm{IMG}}$ on $L_{\mathrm{CROSS}}$ using $L$ results in a $f^{1}(\cdot)$ that can produce 2D representation with useful geometric and visual priors that show superior fin-tuning performance in the experimental section. + +# 3.2. Learning geometric-aware representation on non-paired RGB datasets + +Training a model to induce geometric-aware properties in 2D representation using Eq. (2) and Eq. (4) requires RGB-CAD pairs $(I, G)$ . However, obtaining such paired datasets is a cumbersome problem in every cross-modal learning framework. To address this, we propose to utilize 2D-3D object matching techniques, e.g., [16, 19, 30, 31, 47], to generate pseudo-pair of images and its associated 3D models, $(I_i, G_i')$ , which can be used for training instead of the real pairs. Our experiments show that these pseudo pairs still help induce geometric-aware properties in our representations, resulting in better performance on 2D object understanding tasks, compared to state-of-the-art 2D representation learning approaches. + +# 4. Experimental setup + +# 4.1. Pre-training details + +We use ResNet-50 [23] or ViT-B [29] initialized with supervised pre-trained ImageNet weights for the 2D encoder and use DGCNN [46] for the 3D encoder. We choose $\tau = 0.07$ for all equations and $K = 3$ in Eq. (2). Modality-specific projection heads are used for both 2D and 3D encoders to produce feature vectors $z^{\mathrm{IMG}}$ and $z^{\mathrm{GEO}}$ used in Eq. (1). Each head consists of two linear layers of sizes 1024 and 512, where the first one has ReLU activation. We pre-trained the model on the NVIDIA A100 GPU with a batch size of 256, then neglected the projection heads and retained only the 2D encoder for fine-tuning with downstream tasks. More details are given in Appendix A. + +For the pre-train dataset, we use Pix3D [45] with the S1 train-test split [16]. This dataset consists of 10,069 paired RGB images of indoor scene furniture (e.g., bed, chair, sofa) and corresponding CAD models (subcategories) with + +a total of 395 shapes. We preprocessed each CAD model by uniform sampling random points to generate point clouds consisting of $N = 1024$ and applied point translation, rotation, and jittering to them. For RGB images, we applied the same augmentation strategy as [6] by randomly cropping an image into a size of $224 \times 224$ , then randomly applying horizontal flipping, color jittering, grayscale, and Gaussian blurring to the images. + +# 4.2. Pseudo-pair generation setup + +We utilized a state-of-the-art 3D shape retrieval model, ROCA [19], to generate a pseudo CAD model for any RGB image in indoor scene domains. ROCA was trained on Scan2CAD dataset [2] containing RGB-D frames of indoor scenes and annotated CAD models for each object in each frame. The Mask-RCNN [22] is employed to detect objects in an input image and generate bounding boxes of those detected ones. The feature of each bounding box will be further used in the ROCA retrieval module for predicting its associated CAD model listed in the ShapeNet [4] database. + +The pairing for each RGB input was selected based on a predicted CAD model of the largest detected bounding box. See Appendix G for more ablation studies on pair generation. Later in the experiment section, we compare our model trained on RGB images from Pix3D dataset [45] and pseudo CAD pairs generated by ROCA with competitors. + +# 4.3. Baseline competitors + +All competitors except SupImg and Pri3D were initialized using pre-trained ImageNet weights and subsequently trained on Pix3D to ensure evaluation fairness. + +Supervised ImageNet Pre-training (SupImg) [13] represents the base performance of a pre-trained model without additional training on indoor scene datasets. + +SimCLR [6] and SupCon [28] provide the results when learning 2D representation on augmented RGB images (SimCLR), object categories (SupCon), or subcategories (SupCon (Fine)) in a CNN backbone. + +CrossPoint [1] shows the performance of existing CAD-RGB representation learning. Note that this work has not been studied for solving 2D object understanding tasks. + +Pri3D [25] and Set-InfoNCE [5] are state-of-the-art geometric-aware 2D representation learning works trained on multi-view RGB frames and 3D scans of ScanNet [12] dataset. Note that Set-InfoNCE did not publicly share their code, so we can only compare the results to their reported statistics on ScanNet [12] and NYUv2 [42] datasets. + +DINO [3] and MAE [20] are state-of-the-art 2D representation learning models based on Vision Transformer (ViT) [29] architectures. + +# 5. Experimental results + +# 5.1. Properties of our learned features + +Evaluating geometric-aware properties. Fig. 2 visualizes the pairwise cosine similarities between each encoded feature of objects from the Pix3D validation split. The representations were encoded with the 2D encoder (without a projection head) of each approach. + +Our representations have high similarity scores for images with the same geometry (intra-subcategory) and others with the same object category (intra-category), while none of the competitors could reflect two properties at the same time. More visualizations from other categories and other competitors are provided in Appendix B. + +One interesting aspect is that our representations also well capture the differences across inter-category and inter-subcategory samples. We acquire better mean intra and inter-category similarity scores than the self-supervised baselines, as shown in Fig. 4. Furthermore, Ours (pseudo) yields similar findings, particularly for inter-category. An additional study in Appendix B also demonstrates that Ours (pseudo) has better discrimination in inter-subcategory features. These geometric-aware properties in our learned representation lead to improved 2D object understanding performance in further subsections. + +![](images/dec816489b57275f8fa313bd278708b09d58e89b57fda05fe1e885f9422e8ed4.jpg) +Figure 4. Distribution of pairwise cosine similarity score among intra and inter-category samples. Our representations learned by $L_{\mathrm{GEO}}$ based on the Chamfer distance have the highest mean score (vertical dashed lines) within intra-category samples and also have the lowest score in the inter-category scenario. + +Object localization. We study whether our model can generalize to images with multiple objects, even though it was trained on a dataset of single objects. Fig. 5 shows that our learned features from the ViT-B backbone can be used for roughly localizing patches associated with object categories without fine-tuning. More details and results are provided in Appendix C. This property may arise from how our loss function encourages learning discriminative part features, which are useful for classifying, localizing, and segmenting multiple objects demonstrated in our subsequent experiments. This similar behavior is also observed in other 2D self-supervised models [3] trained on single-object datasets (e.g., ImageNet [13]). + +![](images/f2d823514a3cee9e7a3747f1295546ffbfa1a8d9706077ef673aa63bf3ef9936.jpg) +Figure 5. We compute the feature similarity between each patch in an unseen input image and the mean global feature of learned images in each category using models with a ViT-B backbone. Without fine-tuning, our model can identify the table and roughly localize patches associated with the chairs in the image by using the category of the most similar mean global feature of each patch. + +# 5.2. 2D Semantic segmentation + +Table 1 compares fine-tuning results in semantic segmentation tasks with other competitors. Following [5, 25], we train a U-Net [41] with residual connections for predicting segmentation masks with cross-entropy loss. The encoder part of U-Net is ResNet-50, while the decoder is conv layers with bi-linear interpolation. For ViT-B, we follow [20] by using UPerNet [51] as a segmentation head. + +We employ two variants of mean intersection-over-union (mIoU) for the evaluation metric. The first mIoU, initially implemented by Pri3D [25], does not include pixels that were incorrectly predicted to be ignored classes (e.g., background) as a false positive in mIoU computation. In comparison, our revised mIoU includes these pixels to avoid model cheating by predicting more ignored classes. The experiments were conducted on NYUv2 [42], ScanNet [12], indoor ADE20k [54], and indoor SUNRGB-D [43] datasets. We filtered ADE20k to include only indoor scenes and ignored previously omitted classes in an NYUv2 setting following the prior work [25] for SUNRGB-D. More details on our split are provided in Appendix D. + +When pre-trained on non-paired RGB datasets, Ours (pseudo) outperforms all 2D competitors in both architectures, including DINO [3] and MAE [20]. For 2D-3D competitors, we win against Pri3D and achieve very competitive results to Set-InfoNCE in NYUv2 by only -0.16 in mIoU [25]. We also outperform Pri3D in ADE20k by +1.01 for the original and +0.79 for the pseudo version. The qualitative results are shown in Fig. 6 and Appendix E. + +For ScanNet and SUNRGB-D datasets, Pri3D and SetInfoNCE perform better than ours. This might be because their models were trained directly on ScanNet 3D scans. Some images in SUNRGB-D also appear similar to those in ScanNet, as both datasets sampled RGB-D frames from recorded videos at a high frame-per-second rate. Nonetheless, even without 3D ScanNet, our method still achieves comparable results to Pri3D (-0.17). + +Additionally, in Appendix F, we present results obtained by increasing the pre-training data, which allows us to surpass Set-InfoNCE on NYUv2 without real 3D pairs. + +Table 1. Semantic segmentation results on four popular benchmark datasets. For both ResNet-50 (RN50) and ViT-B architectures, our approaches have better mIoU than 2D representation learning baselines. (*) denotes scores from the methods that were directly pre-trained on 2D and 3D data of ScanNet dataset. We win against Pri3D in NYUv2 and ADE20k without requiring 3D scene scans. + +
Arch.GT pairMethod3DNYUv2ScanNetindoor ADE20kSUNRGB-D
mIoUmIoU [25]mIoUmIoU [25]mIoUmIoU [25]mIoUmIoU [25]
RN502D onlySupImg-47.0450.049.1255.737.5239.6947.9663.12
SimCLR-47.9453.3249.9156.3438.1939.5648.5163.00
SupCon-48.4954.1650.5956.5737.9640.1348.1365.01
SupCon (fine)-47.3453.4549.8156.2237.8739.9248.0563.13
pseudoOurs (pseudo)CAD49.4654.6250.7756.7639.1340.4349.1365.45
2D-3DCrossPointCAD46.0449.1847.2654.0236.5537.8847.1562.77
Pri3Dscene49.5254.754.72*61.7*38.3439.1750.0266.65
Set-InfoNCEscene-55.4-63.1*----
OursCAD49.7755.2451.0357.1239.3540.8649.8565.95
ViT-B2D onlySupImg-49.4455.5963.9359.7242.7844.3851.2666.45
DINO-52.1457.2462.5458.1341.7243.4150.5266.12
MAE-50.1055.6662.2358.9542.9644.9652.2267.87
pseudoOurs (pseudo)CAD52.4758.0264.4960.7343.0245.3752.5369.59
2D-3DOursCAD53.058.6765.2760.9543.1245.8252.9669.69
+ +![](images/b7fecadc9068005cd319a67c4ca592794581485ee3b55aaf0cc393ed45288d42.jpg) +Figure 6. Qualitative results on NYUv2 [42] semantic segmentation. Our methods yield better segmentation results when labeling a scene is challenging due to color or lighting. The geometric priors in our learned representations boost understanding of each scene. + +# 5.3.2D Instance segmentation and object detection + +Indoor scenes. We show how our features improve instance segmentation and object detection results in Table 2. Similar to [25], we use Mask-RCNN [22] with ResNet-50 encoder, implemented on Detectron2 [48] framework for both tasks. For ViT-B, we resize input images to $224 \times 224$ and follow [33] by using Mask-RCNN as the detection head. All backbones were initialized by the pre-trained weights of our model or competitors'. Following [5,25], we use NYUv2 [42] dataset and a well-known detection benchmark, COCO dataset, with Average Precision (AP) as the metric. We filtered COCO images to include only indoor objects. Details on the selected classes are in Appendix D. + +Our method outperforms state-of-the-art 2D and 2D-3D competitors in all settings. Ours (pseudo) achieves competitive scores against Pri3D and Set-InfoNCE in NYUv2 and + +beats Pri3D in COCO without ground truth 3D pairs. + +Outdoor scenes. We also pre-trained our model on PAS-CAL3D+ [50] dataset, which contains objects such as vehicles and furniture in both indoor and outdoor scenes, and evaluated the model on another subset of COCO images called outdoor COCO. Further dataset details are provided in Appendix D. Our method leads to similar improvements in AP as observed in the indoor-only settings. + +# 5.4. Experiments on 2D retrieval + +Table 3 shows the retrieval performance on Pix3D [45] by fine-tuning the pre-trained model on coarse-grained (category) and fine-grained (subcategory) labels of objects. The 2D encoder was fine-tuned along with an additional retrieval head, consisting of two linear layers of sizes 1024 and 512 with ReLU applied only to the first layer. All + +Table 2. Object detection and instance segmentation performance. We outperform competitors for all datasets. + +
Arch. SizeGT pairMethod3DNYUv2indoor COCOoutdoor COCO
Object Det.Instance segm.Object Det.Instance seg.Object Det.Instance seg.
AP50AP75APAP50AP75APAP50AP75APAP50AP75APAP50AP75APAP50AP75
RN50 4802D onlySupImg-29.917.316.825.113.913.441.7824.2123.7039.1623.3522.6146.0926.9828.0842.4523.3423.92
SimCLR-32.8120.1519.2429.1015.9715.6243.6326.4625.4540.8724.7923.8648.1528.7530.4044.3125.0124.99
SupCon-33.2320.3619.6329.4416.1615.8343.6626.3425.3240.8424.5323.7547.8928.6730.2944.1624.6324.97
SupCon (fine)-32.5619.7418.9229.0616.1115.7443.5825.9525.2140.6524.2223.6645.0127.9026.5941.9725.6124.66
pseudoOurs (pseudo)CAD34.4520.2719.7229.6416.2416.1343.7426.4725.4840.9224.7723.91------
2D-3DCrossPointCAD28.4215.9415.2224.4913.3213.1140.2522.7822.2638.5421.9220.8043.2224.5725.6039.7521.9321.11
Pri3Dscene34.020.419.429.516.315.843.4926.4025.2240.7124.7223.61------
Set-InfoNCEscene34.620.519.729.716.316.5-----------
OursCAD34.8520.8920.1230.0316.5116.8444.1126.7825.6941.0224.9124.0849.0329.8031.6245.2325.9025.85
ViT-B 2242D onlySupImg-34.4019.2419.0628.4214.0514.9731.4520.6319.4129.7718.7317.8233.5623.1921.8131.6819.5218.11
DINO-33.0318.6217.9126.8214.5614.7327.7016.2415.8725.7814.8614.7632.5722.1320.6129.8618.0717.66
MAE-35.9219.3019.2429.8816.0115.8231.5420.5919.3329.9218.6517.8336.9724.5123.1233.6720.1519.46
pseudoOurs (pseudo)CAD36.2419.7819.7230.1015.9416.0531.7820.7419.4630.0119.0717.94------
2D-3DOursCAD36.3119.9119.9430.3016.1616.2732.0221.0419.6730.1619.0218.0937.7424.9223.4234.1320.4919.89
+ +Table 3. Retrieval performance on Pix3D [45]. Our method outperforms all competitors in all situations. + +
Arch.GT PairMethod3DCoarse R@1Fine R@1
RN502D onlySupImg-78.8551.18
SimCLR-80.0455.01
SupCon-81.3252.39
SupCon (fine)-79.9555.84
pseudoOurs (pseudo)CAD81.7456.71
2D-3DCrossPointCAD75.9748.09
Pri3Dscene79.7251.63
OursCAD82.8858.97
ViT-B2D onlySupImg-84.0464.17
DINO-84.5965.48
MAE-83.7962.00
pseudoOurs (pseudo)CAD86.1666.40
2D-3DOursCAD86.3267.23
+ +Table 4. Effects on losses and positive mining choices. Training on three losses simultaneously yields the best performance in mIoU. At the same time, choosing the Chamfer Distance (CD) as a positive mining choice in $L_{\mathrm{GEO}}$ also wins against the others. + +
LIMGLGEOLCROSSPos.NYUv2ADE20k
-✓✓CD48.2337.71
✓-✓-48.4638.47
✓---47.9438.19
--✓-47.0237.43
✓✓✓Sup49.4839.12
✓✓✓Aug49.1438.65
✓✓✓CD49.7739.35
+ +retrieval models were trained using supervised contrastive loss [28] with $\tau = 0.07$ . Our methods outperform all competitors in all architectures. + +# 5.5. Ablation studies + +All ablation experiments are evaluated on NYUv2 and ADE20k semantic segmentation tasks using our revised mIoU metric on ResNet-50 architecture. + +Effects on losses and positive mining choices Table 4 shows the effects of three loss choices (i.e., $L_{\mathrm{IMG}}$ , $L_{\mathrm{GEO}}$ , and $L_{\mathrm{CROSS}}$ ) and three different choices of the positive point cloud using in Eq. (2), including using object categories + +(Sup), point cloud augmentation (Aug), and Chamfer distance (CD). We found that training three loss functions simultaneously notably improves mIoU from training single or dual losses. While in the positive choice study, our selected Chamfer distance achieves the best mIoU. + +Effects on $K$ selected positive point clouds. We studied the best number of $K$ in Eq. (2). Fig. 7 reveals that $K = 3$ can achieve the best mIoU among the others. Using a lower $K$ leads to lower mIoU, similar to a higher $K$ . This is probably because higher $K$ has more chance to select false positive samples due to higher Chamfer distances, which means that the selected samples might have a much different shape than the anchor $\mathbf{z}_i^G$ . + +![](images/3596632e824760fc9c5158432ababfcaec07fafe05d16f13b3d359d78a87532c.jpg) +Figure 7. Effect of varying $K$ selected positive point clouds. $K = 3$ has the best mIoU. + +# 6. Limitations and Discussion + +Using CAD models for inducing geometric-aware properties in 2D representation via Chamfer distance shows significantly enhanced 2D object understanding results that are almost as effective as 3D priors from scene scans. This finding remains true when we train our model on generated pseudo-RGB-CAD pairs, allowing us to beat SOTA 2D competitors without the need for paired datasets. 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In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 633-641, 2017. 2, 6 \ No newline at end of file diff --git a/2023/Learning Geometric-Aware Properties in 2D Representation Using Lightweight CAD Models, or Zero Real 3D Pairs/images.zip b/2023/Learning Geometric-Aware Properties in 2D Representation Using Lightweight CAD Models, or Zero Real 3D Pairs/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..d58ad1ccab056b3904db4888a03a87e2822de733 --- /dev/null +++ b/2023/Learning Geometric-Aware Properties in 2D Representation Using Lightweight CAD Models, or Zero Real 3D Pairs/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:55311f9caa5aa4e21bd68ea6881eaace56bcec18a511c8d64b860c5c2580c588 +size 817530 diff --git a/2023/Learning Geometric-Aware Properties in 2D Representation Using Lightweight CAD Models, or Zero Real 3D Pairs/layout.json b/2023/Learning Geometric-Aware Properties in 2D Representation Using Lightweight CAD Models, or Zero Real 3D Pairs/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..02fd269ddeb468c9266ddcca29d9f498f26714a9 --- /dev/null +++ b/2023/Learning Geometric-Aware Properties in 2D Representation Using Lightweight CAD Models, or Zero Real 3D Pairs/layout.json @@ -0,0 +1,8454 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 53, + 102, + 541, + 138 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 102, + 541, + 138 + ], + "spans": [ + { + "bbox": [ + 53, + 102, + 541, + 138 + ], + "type": "text", + "content": "Learning Geometric-aware Properties in 2D Representation Using Lightweight CAD Models, or Zero Real 3D Pairs" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 100, + 162, + 231, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 100, + 162, + 231, + 175 + ], + "spans": [ + { + "bbox": [ + 100, + 162, + 231, + 175 + ], + "type": "text", + "content": "Pattaramanee Arsomngern" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 259, + 162, + 345, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 259, + 162, + 345, + 175 + ], + "spans": [ + { + "bbox": [ + 259, + 162, + 345, + 175 + ], + "type": "text", + "content": "Sarana Nutanong" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 250, + 176, + 343, + 189 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 250, + 176, + 343, + 189 + ], + "spans": [ + { + "bbox": [ + 250, + 176, + 343, + 189 + ], + "type": "text", + "content": "VISTEC, Thailand" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 374, + 162, + 493, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 374, + 162, + 493, + 175 + ], + "spans": [ + { + "bbox": [ + 374, + 162, + 493, + 175 + ], + "type": "text", + "content": "Supasorn Suwajanakorn" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 147, + 191, + 443, + 203 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 147, + 191, + 443, + 203 + ], + "spans": [ + { + "bbox": [ + 147, + 191, + 443, + 203 + ], + "type": "text", + "content": "{pattaramanee.a_s19, snutanon, supasorn.s}@vistec.ac.th" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 143, + 231, + 192, + 243 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 231, + 192, + 243 + ], + "spans": [ + { + "bbox": [ + 143, + 231, + 192, + 243 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 258, + 290, + 546 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 258, + 290, + 546 + ], + "spans": [ + { + "bbox": [ + 47, + 258, + 290, + 546 + ], + "type": "text", + "content": "Cross-modal training using 2D-3D paired datasets, such as those containing multi-view images and 3D scene scans, presents an effective way to enhance 2D scene understanding by introducing geometric and view-invariance priors into 2D features. However, the need for large-scale scene datasets can impede scalability and further improvements. This paper explores an alternative learning method by leveraging a lightweight and publicly available type of 3D data in the form of CAD models. We construct a 3D space with geometric-aware alignment where the similarity in this space reflects the geometric similarity of CAD models based on the Chamfer distance. The acquired geometric-aware properties are then induced into 2D features, which boost performance on downstream tasks more effectively than existing RGB-CAD approaches. Our technique is not limited to paired RGB-CAD datasets. By training exclusively on pseudo pairs generated from CAD-based reconstruction methods, we enhance the performance of SOTA 2D pre-trained models that use ResNet-50 or ViT-B backbones on various 2D understanding tasks. We also achieve comparable results to SOTA methods trained on scene scans on four tasks in NYUv2, SUNRGB-D, indoor ADE20k, and indoor/outdoor COCO, despite using lightweight CAD models or pseudo data. Please visit our page: https://" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 48, + 546, + 214, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 546, + 214, + 555 + ], + "spans": [ + { + "bbox": [ + 48, + 546, + 214, + 555 + ], + "type": "text", + "content": "//GeoAware2dRepUsingCAD.github.io/" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 48, + 584, + 127, + 596 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 584, + 127, + 596 + ], + "spans": [ + { + "bbox": [ + 48, + 584, + 127, + 596 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 605, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 605, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 605, + 287, + 715 + ], + "type": "text", + "content": "Recent 2D visual representation learning approaches, such as contrastive learning [3, 6, 10, 17, 28] or masked autoencoder [20], are widely used to tackle various problems in computer vision due to their ability to encode rich visual features. While these methods have shown exceptional results on 2D image classification, they still have shortcomings in other 2D understanding tasks that involve instance-level reasoning. Prior research [25] also shows that models pre-trained using image augmentations [8,21] or supervised" + } + ] + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 313, + 230, + 539, + 437 + ], + "blocks": [ + { + "bbox": [ + 313, + 230, + 539, + 437 + ], + "lines": [ + { + "bbox": [ + 313, + 230, + 539, + 437 + ], + "spans": [ + { + "bbox": [ + 313, + 230, + 539, + 437 + ], + "type": "image", + "image_path": "68a9afe9805c7f178efb03c903f64007cac465bf3828961fe44392f555e6ef81.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 441, + 545, + 519 + ], + "lines": [ + { + "bbox": [ + 305, + 441, + 545, + 519 + ], + "spans": [ + { + "bbox": [ + 305, + 441, + 545, + 519 + ], + "type": "text", + "content": "Figure 1. Overview concept of our solution. We leverage CAD models to train a joint 2D-3D space such that images of objects with similar shapes, based on the Chamfer distance, are attracted to each other, while images with different shapes are separated. This results in a continuous geometric-aware space where the distance between two points reflects their geometric similarity, which could be utilized for downstream 2D object understanding tasks." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 529, + 545, + 566 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 529, + 545, + 566 + ], + "spans": [ + { + "bbox": [ + 305, + 529, + 545, + 566 + ], + "type": "text", + "content": "labels [13] could not deliver satisfactory results when applied to downstream tasks such as semantic segmentation, instance segmentation, and object detection [12, 42]." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 567, + 546, + 686 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 567, + 546, + 686 + ], + "spans": [ + { + "bbox": [ + 304, + 567, + 546, + 686 + ], + "type": "text", + "content": "To alleviate this, Hou et al. [25] proposed to learn 3D geometric priors, such as view-invariance, from 3D data and transfer the learned priors to 2D representations. In particular, their model is first pre-trained on ScanNet [12], a database of multi-view RGB-D scans, using contrastive learning and later used as initialization for fine-tuning networks on downstream tasks. Chen et al. [5] further extend this work by utilizing additional priors through learning to group nearby points that refer to the same object part from 3D scenes." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "content": "The key concept of their introduced new paradigm is to share useful 3D priors from 3D data with 2D representa" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21371" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 192 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 192 + ], + "type": "text", + "content": "tions. However, previous studies have investigated mostly 3D priors related to viewpoint invariance from 3D scene datasets, which are often limited in size and scene variations due to the laborious data collecting and labeling process [24]. This scarcity of large-scale 3D data also limits the number of available 3D priors for learning the invariance, hence hindering further performance gains. This paper questions whether there are other effective 3D priors for 2D downstream tasks and whether they can be learned from other forms of 3D data that are lighter and easier to obtain." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 194, + 289, + 362 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 194, + 289, + 362 + ], + "spans": [ + { + "bbox": [ + 46, + 194, + 289, + 362 + ], + "type": "text", + "content": "We begin our exploration by considering how to learn an embedding space that maps together images with the same or similar geometries. One solution is to learn from images that share the same 3D model, which inspires our interest in CAD models. Unlike 3D scenes, CAD models are lightweight, publicly available, and can be easily aligned with RGB images via web scraping or human annotation [2]. There exist studies that jointly learn 2D and 3D CAD representation for other CAD-related tasks, e.g., 3D classification [1,27]. However, their 2D features, which are derived from augmentation-based CAD features, are insufficient to be directly applied to 2D object understanding tasks—they can group images with similar geometries but struggle to learn the distinctions between object categories." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 364, + 289, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 364, + 289, + 604 + ], + "spans": [ + { + "bbox": [ + 46, + 364, + 289, + 604 + ], + "type": "text", + "content": "We argue that useful geometric-aware representations should account for both similarities and differences in object geometry. Our key idea is to acquire such features by imitating the Chamfer distance between 3D objects in our embedding space and inducing this derived geometric awareness in our learned 2D representation. In particular, we learn our space by attracting the encoded features of geometrically similar CAD models in the mini-batch based on the Chamfer distance and repelling those with lower similarities. In contrast to other methods trained on supervised discrete signals like object labels or through 3D augmentations, our method produces a continuous 3D space that better captures the similarity and difference in geometry (see Section 5.1). In addition, we employ augmentation-based contrastive learning [6] to learn other useful visual feature properties, such as translation and color invariances. This results in a 2D representation in a 2D-3D space that contains rich visual information and strong geometric-aware properties, as shown in Fig. 1, which can be leveraged to improve 2D object understanding tasks." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 605, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 289, + 715 + ], + "type": "text", + "content": "To match our geometric-aware CAD features with corresponding 2D features, a paired RGB-CAD dataset, such as Pix3D [45], is required. However, by leveraging recent techniques [19, 31] that can reconstruct a CAD model from an input image, it is possible to generate pseudo CAD models for any images and use them to learn our method without a paired dataset. Adapting this pseudo-pair generation to other techniques that rely on scene scans is significantly harder, as synthesizing full 3D scenes with reasonable detail" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 305, + 72, + 523, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 523, + 84 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 523, + 84 + ], + "type": "text", + "content": "remains harder than reconstructing individual objects." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 85, + 545, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 85, + 545, + 239 + ], + "spans": [ + { + "bbox": [ + 304, + 85, + 545, + 239 + ], + "type": "text", + "content": "We demonstrate the effectiveness of our geometric-aware 2D representation in Fig. 2. Our features can group and differentiate objects based on their categories or subcategories, leading to improved performance on multiple 2D object understanding tasks using both ResNet-50 [23] and ViT-B [29] backbones. Our method trained on a pseudopair dataset also yields superior results over DINO [3] and MAE [20]. Remarkably, we also surpass a state-of-the-art method, Pri3D [25] without using any 3D scene scans in the following tasks: (i) semantic segmentation using NYUv2 [42] and indoor ADE20k [54]; (ii) object detection and instance segmentation using NYUv2 and in/outdoor COCO [35]; (iii) object retrieval using Pix3D [45]." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 317, + 240, + 511, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 240, + 511, + 251 + ], + "spans": [ + { + "bbox": [ + 317, + 240, + 511, + 251 + ], + "type": "text", + "content": "To summarize, our contributions are as follows." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 317, + 251, + 545, + 409 + ], + "type": "list", + "angle": 0, + "index": 10, + "blocks": [ + { + "bbox": [ + 317, + 251, + 545, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 251, + 545, + 312 + ], + "spans": [ + { + "bbox": [ + 317, + 251, + 545, + 312 + ], + "type": "text", + "content": "- We present a simple yet effective approach to inducing geometric-aware properties in 2D representation using lightweight CAD models. These can be either ground truth from RGB-CAD datasets or generated pseudo CAD pairs based on 2D-only data." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 317, + 312, + 545, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 312, + 545, + 348 + ], + "spans": [ + { + "bbox": [ + 317, + 312, + 545, + 348 + ], + "type": "text", + "content": "- We propose training objectives to learn a 2D-3D embedding space where feature similarity reflects geometric similarity based on the Chamfer distance." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 317, + 350, + 545, + 409 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 350, + 545, + 409 + ], + "spans": [ + { + "bbox": [ + 317, + 350, + 545, + 409 + ], + "type": "text", + "content": "- We enhance the performance of SOTA 2D representation learning techniques on four 2D object understanding tasks and achieve competitive results to SOTA that require 3D scene scans across five datasets, in both settings that use real or pseudo-RGB-CAD datasets." + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 418, + 394, + 430 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 418, + 394, + 430 + ], + "spans": [ + { + "bbox": [ + 306, + 418, + 394, + 430 + ], + "type": "text", + "content": "2. Related works" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 438, + 545, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 438, + 545, + 545 + ], + "spans": [ + { + "bbox": [ + 304, + 438, + 545, + 545 + ], + "type": "text", + "content": "2D Representation Learning. Contrastive learning [49] has continuously shown improvements in various downstream tasks. Its main concept is to maximize a similarity score between two different views (e.g., two different augmentations of the same instance [6, 9, 10, 17, 21], two instances with the same label [28], or two different encoders [3, 7]). Meanwhile, learning representation in autoencoder fashion [20] also has recently demonstrated a performance boost from contrastive learning works." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 546, + 545, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 546, + 545, + 582 + ], + "spans": [ + { + "bbox": [ + 304, + 546, + 545, + 582 + ], + "type": "text", + "content": "This paper shows that these 2D representation learning methods could not provide geometric-aware properties, which are critical in object understanding tasks." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": "3D Representation Learning requires specific network architecture for extracting features based on an input's data structure (e.g., rendered images [44], point clouds [39, 46], or meshes [15, 16]). These architectures can encode geometric information of each 3D shape into representations with a deep understanding of shape structure. Later, contrastive learning in 3D, such as point cloud augmentation [52], or multiple modalities [1, 53], showed their improvement in 3D classification, retrieval, and part segmentation problems. Concurrently, 3D reconstruction techniques [11, 14, 37] also deliver promising results in similar tasks." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "21372" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 70, + 541, + 216 + ], + "blocks": [ + { + "bbox": [ + 51, + 70, + 541, + 216 + ], + "lines": [ + { + "bbox": [ + 51, + 70, + 541, + 216 + ], + "spans": [ + { + "bbox": [ + 51, + 70, + 541, + 216 + ], + "type": "image", + "image_path": "c1158c3436b75be9708460bf079194afc0a4a29aaa00fbb2378c30da4ca57ab8.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 218, + 547, + 296 + ], + "lines": [ + { + "bbox": [ + 46, + 218, + 547, + 296 + ], + "spans": [ + { + "bbox": [ + 46, + 218, + 547, + 296 + ], + "type": "text", + "content": "Figure 2. Visualization of the pairwise cosine similarity between the learned representations of objects from each method. The bright color indicates higher similarity. The first row shows the similarity scores of all validation images in Pix3D [45] dataset, sorted by object category and subcategory (i.e., object models). The second row zooms in on a single category (Sofa) from the first row. Our method shows a better grouping of the same sofa than others, especially SimCLR [6] and SupCon [28], which can hardly differentiate between each sofa type. CrossPoint [1] and SupCon (fine), unlike others, can group the same sofa but fail to separate sofas from other categories in the first row. Surprisingly, MAE [20] also delivers visual features without subcategory awareness. Compared to SimCLR, Ours (pseudo) provides distinguishable features (with darker colors) between each sofa type. Additional studies on Ours (pseudo) are provided in Appendix B." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 306, + 288, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 306, + 288, + 342 + ], + "spans": [ + { + "bbox": [ + 47, + 306, + 288, + 342 + ], + "type": "text", + "content": "In this paper, we adapt the encoded 3D features with rich geometric information to share the ability to recognize geometric similarities in each object to 2D representations." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 342, + 287, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 342, + 287, + 544 + ], + "spans": [ + { + "bbox": [ + 46, + 342, + 287, + 544 + ], + "type": "text", + "content": "Multimodal Representation Learning gains attraction due to its ability to share modality-specific contexts. CLIP [40] facilitates various vision-language tasks by contrastive learning on text-image data. Similarly, 2D-3D representation learning transfers geometric information from 3D to 2D features [5, 25, 36]. Pri3D [25] introduces a contrastive learning method on multi-view RGB frames and 3D scene scans [12]. These modal pairs allow them to learn view and 3D priors in 2D features and achieve impressive 2D indoor scene understanding performance. Later, SetInfoNCE [5] improves upon Pri3D by fine-tuning the Pri3D pre-trained model using additional 3D priors, e.g., sets of nearby points referring to the same object part, generated from training scans. While these studies have focused on scene scans, this paper demonstrates that geometric priors from CAD models can achieve comparable or better object understanding than learning on 3D scenes." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 545, + 287, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 287, + 629 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 287, + 629 + ], + "type": "text", + "content": "Some studies, e.g., CrossPoint [1, 27], have been conducted to share visual context to guide CAD features (2D " + }, + { + "bbox": [ + 46, + 545, + 287, + 629 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 46, + 545, + 287, + 629 + ], + "type": "text", + "content": " 3D). Their learned 2D features, on the other hand, fail to discriminate object categories, resulting in poor object understanding results. We then investigate a more efficient method of learning and sharing modality-specific context from CAD to RGB without hurting 2D task performance." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "text", + "content": "2D-3D Object Matching has been studied for searching or generating a 3D model of objects appearing in a given image. [19, 30-32] use existing CAD databases to train an RGB-CAD retrieval and alignment module in a multi-task learning fashion using a given set of ground truths (e.g., camera intrinsic, depth map, mask, or pose parameters). [26, 34] utilize category labels to guide a joint RGB-CAD" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 306, + 545, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 306, + 545, + 354 + ], + "spans": [ + { + "bbox": [ + 304, + 306, + 545, + 354 + ], + "type": "text", + "content": "space for 2D-3D retrieval tasks. Another approach is to reconstruct a 3D model from the image directly [16, 18, 47]. However, the generated 3D may be less realistic than retrieving human-designed 3D from the databases." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 356, + 547, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 356, + 547, + 392 + ], + "spans": [ + { + "bbox": [ + 304, + 356, + 547, + 392 + ], + "type": "text", + "content": "We utilize these works to generate CAD pairs for our pre-training RGB images. Learning representation on just pseudo-RGB-CAD pairs can surpass SOTA competitors." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 411, + 410, + 424 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 411, + 410, + 424 + ], + "spans": [ + { + "bbox": [ + 306, + 411, + 410, + 424 + ], + "type": "text", + "content": "3. Proposed method" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 433, + 545, + 493 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 433, + 545, + 493 + ], + "spans": [ + { + "bbox": [ + 304, + 433, + 545, + 493 + ], + "type": "text", + "content": "Our goal is to construct a pre-trained model that can provide a 2D representation " + }, + { + "bbox": [ + 304, + 433, + 545, + 493 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_i^!" + }, + { + "bbox": [ + 304, + 433, + 545, + 493 + ], + "type": "text", + "content": " of an input image " + }, + { + "bbox": [ + 304, + 433, + 545, + 493 + ], + "type": "inline_equation", + "content": "I_{i}" + }, + { + "bbox": [ + 304, + 433, + 545, + 493 + ], + "type": "text", + "content": " with useful geometric priors to enhance 2D object understanding. Unlike prior works [5,25], we aim to learn the representations without 3D scene scans using other efficient alternatives." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 495, + 546, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 495, + 546, + 674 + ], + "spans": [ + { + "bbox": [ + 304, + 495, + 546, + 674 + ], + "type": "text", + "content": "We propose a novel approach that can obtain such geometric priors from a lightweight and publicly available type of 3D data in the form of CAD models, while retaining discriminative representations for 2D tasks. Given an image " + }, + { + "bbox": [ + 304, + 495, + 546, + 674 + ], + "type": "inline_equation", + "content": "I_{i}" + }, + { + "bbox": [ + 304, + 495, + 546, + 674 + ], + "type": "text", + "content": " and its associated CAD model " + }, + { + "bbox": [ + 304, + 495, + 546, + 674 + ], + "type": "inline_equation", + "content": "G_{i}" + }, + { + "bbox": [ + 304, + 495, + 546, + 674 + ], + "type": "text", + "content": ", our solution constructs a 2D-3D embedding space with strong geometric-aware properties by learning CAD features " + }, + { + "bbox": [ + 304, + 495, + 546, + 674 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{i}^{\\mathrm{G}} = f^{\\mathrm{G}}(G_{i})" + }, + { + "bbox": [ + 304, + 495, + 546, + 674 + ], + "type": "text", + "content": " along with rich visual information from 2D features " + }, + { + "bbox": [ + 304, + 495, + 546, + 674 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{i}^{\\mathrm{I}} = f^{\\mathrm{I}}(I_{i})" + }, + { + "bbox": [ + 304, + 495, + 546, + 674 + ], + "type": "text", + "content": ". We show that the acquired 2D representations, where their feature similarity reflects geometric similarity, are more effective than solely relying on standard augmentation invariant CAD features and perform almost as effectively as 3D priors from scene scans on common 2D understanding tasks. The overview of our proposed framework is shown in Fig. 3." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 677, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 714 + ], + "type": "text", + "content": "An extension to training our model on generated RGB-CAD pairs is further introduced in order to learn geometric-aware representations using just RGB training data." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "21373" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 59, + 69, + 534, + 250 + ], + "blocks": [ + { + "bbox": [ + 59, + 69, + 534, + 250 + ], + "lines": [ + { + "bbox": [ + 59, + 69, + 534, + 250 + ], + "spans": [ + { + "bbox": [ + 59, + 69, + 534, + 250 + ], + "type": "image", + "image_path": "f81051a1ad6e9320d56d629dc8ee2b92513827b249b80b14b7fe386dd626e426.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 255, + 547, + 291 + ], + "lines": [ + { + "bbox": [ + 46, + 255, + 547, + 291 + ], + "spans": [ + { + "bbox": [ + 46, + 255, + 547, + 291 + ], + "type": "text", + "content": "Figure 3. Our pre-training strategy. We learn 2D representations on a joint 2D-3D space from RGB-CAD pairs based on three loss functions. " + }, + { + "bbox": [ + 46, + 255, + 547, + 291 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{GEO}}" + }, + { + "bbox": [ + 46, + 255, + 547, + 291 + ], + "type": "text", + "content": " focuses on learning CAD features from two similar CAD models mined from Chamfer distance, " + }, + { + "bbox": [ + 46, + 255, + 547, + 291 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{IMG}}" + }, + { + "bbox": [ + 46, + 255, + 547, + 291 + ], + "type": "text", + "content": " focuses on learning visual differences between two image augmentations, and " + }, + { + "bbox": [ + 46, + 255, + 547, + 291 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{CROSS}}" + }, + { + "bbox": [ + 46, + 255, + 547, + 291 + ], + "type": "text", + "content": " shares geometric awareness from CAD features to 2D representation." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 297, + 160, + 310 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 297, + 160, + 310 + ], + "spans": [ + { + "bbox": [ + 47, + 297, + 160, + 310 + ], + "type": "text", + "content": "3.1. Training objectives" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 316, + 290, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 316, + 290, + 485 + ], + "spans": [ + { + "bbox": [ + 46, + 316, + 290, + 485 + ], + "type": "text", + "content": "The core idea of our training objective is to share two modality-specific contexts, i.e., strong geometric-aware properties from " + }, + { + "bbox": [ + 46, + 316, + 290, + 485 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_i^{\\mathrm{G}}\\in \\mathbf{z}^{\\mathrm{G}}" + }, + { + "bbox": [ + 46, + 316, + 290, + 485 + ], + "type": "text", + "content": " and rich visual information from " + }, + { + "bbox": [ + 46, + 316, + 290, + 485 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_i^{\\mathrm{I}}\\in \\mathbf{z}^{\\mathrm{I}}" + }, + { + "bbox": [ + 46, + 316, + 290, + 485 + ], + "type": "text", + "content": ", in the joint 2D-3D embedding space by training on RGB-CAD pairs " + }, + { + "bbox": [ + 46, + 316, + 290, + 485 + ], + "type": "inline_equation", + "content": "(I,G)" + }, + { + "bbox": [ + 46, + 316, + 290, + 485 + ], + "type": "text", + "content": ". To achieve this objective, we use three loss functions: " + }, + { + "bbox": [ + 46, + 316, + 290, + 485 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{GEO}}" + }, + { + "bbox": [ + 46, + 316, + 290, + 485 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 316, + 290, + 485 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{IMG}}" + }, + { + "bbox": [ + 46, + 316, + 290, + 485 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 316, + 290, + 485 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{CROSS}}" + }, + { + "bbox": [ + 46, + 316, + 290, + 485 + ], + "type": "text", + "content": ". The first loss " + }, + { + "bbox": [ + 46, + 316, + 290, + 485 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{GEO}}" + }, + { + "bbox": [ + 46, + 316, + 290, + 485 + ], + "type": "text", + "content": " helps the 3D encoder " + }, + { + "bbox": [ + 46, + 316, + 290, + 485 + ], + "type": "inline_equation", + "content": "f^{\\mathrm{G}}(\\cdot)" + }, + { + "bbox": [ + 46, + 316, + 290, + 485 + ], + "type": "text", + "content": " construct a geometric-aware embedding space, such that CAD models in " + }, + { + "bbox": [ + 46, + 316, + 290, + 485 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 46, + 316, + 290, + 485 + ], + "type": "text", + "content": " with similar shapes, based on the Chamfer distance, are located near each other. The second loss " + }, + { + "bbox": [ + 46, + 316, + 290, + 485 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{IMG}}" + }, + { + "bbox": [ + 46, + 316, + 290, + 485 + ], + "type": "text", + "content": " helps the 2D encoder " + }, + { + "bbox": [ + 46, + 316, + 290, + 485 + ], + "type": "inline_equation", + "content": "f^{\\mathrm{I}}(\\cdot)" + }, + { + "bbox": [ + 46, + 316, + 290, + 485 + ], + "type": "text", + "content": " learn useful visual representation properties, e.g., translation and color invariance from " + }, + { + "bbox": [ + 46, + 316, + 290, + 485 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 46, + 316, + 290, + 485 + ], + "type": "text", + "content": ". The third loss " + }, + { + "bbox": [ + 46, + 316, + 290, + 485 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{CROSS}}" + }, + { + "bbox": [ + 46, + 316, + 290, + 485 + ], + "type": "text", + "content": " enforces the consistency between " + }, + { + "bbox": [ + 46, + 316, + 290, + 485 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_i^{\\mathrm{G}}" + }, + { + "bbox": [ + 46, + 316, + 290, + 485 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 316, + 290, + 485 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_i^{\\mathrm{I}}" + }, + { + "bbox": [ + 46, + 316, + 290, + 485 + ], + "type": "text", + "content": " for each " + }, + { + "bbox": [ + 46, + 316, + 290, + 485 + ], + "type": "inline_equation", + "content": "(I_i,G_i)" + }, + { + "bbox": [ + 46, + 316, + 290, + 485 + ], + "type": "text", + "content": " pair. Finally, the multi-task loss function is" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 108, + 492, + 287, + 506 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 492, + 287, + 506 + ], + "spans": [ + { + "bbox": [ + 108, + 492, + 287, + 506 + ], + "type": "interline_equation", + "content": "L = L _ {\\text {G E O}} + L _ {\\text {I M G}} + L _ {\\text {C R O S S}}. \\tag {1}", + "image_path": "343bc01c4df4042dcb4f1a4c2f52bf5c983c469f40f3ed3cb49d1c9315996511.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 513, + 287, + 537 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 513, + 287, + 537 + ], + "spans": [ + { + "bbox": [ + 46, + 513, + 287, + 537 + ], + "type": "text", + "content": "Detailed explanations of the three components are given in the following subsections." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 551, + 216, + 562 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 551, + 216, + 562 + ], + "spans": [ + { + "bbox": [ + 47, + 551, + 216, + 562 + ], + "type": "text", + "content": "3.1.1 Geometric-aware CAD features" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 570, + 287, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 287, + 654 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 287, + 654 + ], + "type": "text", + "content": "We first explain how " + }, + { + "bbox": [ + 46, + 570, + 287, + 654 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{GEO}}" + }, + { + "bbox": [ + 46, + 570, + 287, + 654 + ], + "type": "text", + "content": " provides geometric awareness to our features. Given " + }, + { + "bbox": [ + 46, + 570, + 287, + 654 + ], + "type": "inline_equation", + "content": "(I_i, G_i)" + }, + { + "bbox": [ + 46, + 570, + 287, + 654 + ], + "type": "text", + "content": ", we use " + }, + { + "bbox": [ + 46, + 570, + 287, + 654 + ], + "type": "inline_equation", + "content": "G_i" + }, + { + "bbox": [ + 46, + 570, + 287, + 654 + ], + "type": "text", + "content": " to train " + }, + { + "bbox": [ + 46, + 570, + 287, + 654 + ], + "type": "inline_equation", + "content": "f^{\\mathrm{G}}(\\cdot)" + }, + { + "bbox": [ + 46, + 570, + 287, + 654 + ], + "type": "text", + "content": " for extracting a geometric context " + }, + { + "bbox": [ + 46, + 570, + 287, + 654 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_i^{\\mathrm{G}}" + }, + { + "bbox": [ + 46, + 570, + 287, + 654 + ], + "type": "text", + "content": " of each pair. We process each " + }, + { + "bbox": [ + 46, + 570, + 287, + 654 + ], + "type": "inline_equation", + "content": "G_i" + }, + { + "bbox": [ + 46, + 570, + 287, + 654 + ], + "type": "text", + "content": " by converting it to a point cloud and use DGCNN [46] as " + }, + { + "bbox": [ + 46, + 570, + 287, + 654 + ], + "type": "inline_equation", + "content": "f^{\\mathrm{G}}(\\cdot)" + }, + { + "bbox": [ + 46, + 570, + 287, + 654 + ], + "type": "text", + "content": " to capture local and global point cloud structure information, resulting in an encoded feature " + }, + { + "bbox": [ + 46, + 570, + 287, + 654 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_i^{\\mathrm{G}}" + }, + { + "bbox": [ + 46, + 570, + 287, + 654 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 654, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 288, + 714 + ], + "type": "text", + "content": "To learn the space, we follow a common contrastive learning strategy by maximizing the similarity between " + }, + { + "bbox": [ + 46, + 654, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_i^{\\mathrm{G}}" + }, + { + "bbox": [ + 46, + 654, + 288, + 714 + ], + "type": "text", + "content": " and the encoded feature " + }, + { + "bbox": [ + 46, + 654, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{z}^{+}" + }, + { + "bbox": [ + 46, + 654, + 288, + 714 + ], + "type": "text", + "content": " of each positive term in a minibatch. However, instead of selecting " + }, + { + "bbox": [ + 46, + 654, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{z}^{+}" + }, + { + "bbox": [ + 46, + 654, + 288, + 714 + ], + "type": "text", + "content": " based on object labels or augmentations as is commonly done, we select " + }, + { + "bbox": [ + 46, + 654, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{z}^{+}" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 298, + 545, + 320 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 298, + 545, + 320 + ], + "spans": [ + { + "bbox": [ + 304, + 298, + 545, + 320 + ], + "type": "text", + "content": "based on a geometric-based similarity function, the Chamfer distance." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 321, + 545, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 321, + 545, + 388 + ], + "spans": [ + { + "bbox": [ + 304, + 321, + 545, + 388 + ], + "type": "text", + "content": "We calculate pairwise Chamfer distances across a minibatch and select " + }, + { + "bbox": [ + 304, + 321, + 545, + 388 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 321, + 545, + 388 + ], + "type": "text", + "content": " point clouds with the lowest distances to be the positive terms for each " + }, + { + "bbox": [ + 304, + 321, + 545, + 388 + ], + "type": "inline_equation", + "content": "G_{i}" + }, + { + "bbox": [ + 304, + 321, + 545, + 388 + ], + "type": "text", + "content": " in the loss function. We call this process Chamfer mining. The set of encoded positive terms is referred to as " + }, + { + "bbox": [ + 304, + 321, + 545, + 388 + ], + "type": "inline_equation", + "content": "P(\\mathbf{z}_i^{\\mathrm{G}})" + }, + { + "bbox": [ + 304, + 321, + 545, + 388 + ], + "type": "text", + "content": ". Finally, the contrastive loss is given as" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 309, + 393, + 545, + 435 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 393, + 545, + 435 + ], + "spans": [ + { + "bbox": [ + 309, + 393, + 545, + 435 + ], + "type": "interline_equation", + "content": "L _ {\\mathrm {G E O}} = \\frac {1}{N K} \\sum_ {i = 1} ^ {N} \\sum_ {\\mathbf {z} ^ {+} \\in P \\left(\\mathbf {z} _ {i} ^ {\\mathrm {G}}\\right)} - \\log \\frac {\\exp \\left(\\mathbf {z} _ {i} ^ {\\mathrm {G}} \\cdot \\mathbf {z} ^ {+} / \\tau\\right)}{\\sum_ {\\mathbf {z} ^ {-} \\in \\mathbf {z} ^ {\\mathrm {G}} \\backslash \\left\\{\\mathbf {z} _ {i} ^ {\\mathrm {G}} \\right\\}} \\exp \\left(\\mathbf {z} _ {i} ^ {\\mathrm {G}} \\cdot \\mathbf {z} ^ {-} / \\tau\\right)}, \\tag {2}", + "image_path": "61b2c8ca84a5c6f5075e9bd84dce38c716508afd422831ef7b1399dab40adcf7.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 436, + 545, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 436, + 545, + 509 + ], + "spans": [ + { + "bbox": [ + 304, + 436, + 545, + 509 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 436, + 545, + 509 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 436, + 545, + 509 + ], + "type": "text", + "content": " is the batch size and " + }, + { + "bbox": [ + 304, + 436, + 545, + 509 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 436, + 545, + 509 + ], + "type": "text", + "content": " is a tunable temperature parameter. Using " + }, + { + "bbox": [ + 304, + 436, + 545, + 509 + ], + "type": "inline_equation", + "content": "\\mathbf{z}^{+}" + }, + { + "bbox": [ + 304, + 436, + 545, + 509 + ], + "type": "text", + "content": " based on the Chamfer distance better captures the similarity and difference in 3D geometry and benefits 2D representation than other choices, e.g., 3D augmentation or category labels, which will be discussed later in Section 5.5 and Appendix B." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 521, + 524, + 533 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 521, + 524, + 533 + ], + "spans": [ + { + "bbox": [ + 305, + 521, + 524, + 533 + ], + "type": "text", + "content": "3.1.2 Learning to discriminate 2D visual features" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 540, + 545, + 575 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 540, + 545, + 575 + ], + "spans": [ + { + "bbox": [ + 304, + 540, + 545, + 575 + ], + "type": "text", + "content": "Translation and color invariance are crucial in many vision problems [17]. Learning them along with geometric-aware properties potentially yields better results." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 575, + 545, + 632 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 575, + 545, + 632 + ], + "spans": [ + { + "bbox": [ + 304, + 575, + 545, + 632 + ], + "type": "text", + "content": "To acquire these invariances, we define the second function " + }, + { + "bbox": [ + 304, + 575, + 545, + 632 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{IMG}}" + }, + { + "bbox": [ + 304, + 575, + 545, + 632 + ], + "type": "text", + "content": " by following a common practice in 2D representation learning. In particular, we use SimCLR [6] and learn to discriminate between two different augmentations of " + }, + { + "bbox": [ + 304, + 575, + 545, + 632 + ], + "type": "inline_equation", + "content": "I_{i}" + }, + { + "bbox": [ + 304, + 575, + 545, + 632 + ], + "type": "text", + "content": " (i.e., " + }, + { + "bbox": [ + 304, + 575, + 545, + 632 + ], + "type": "inline_equation", + "content": "I_{i}" + }, + { + "bbox": [ + 304, + 575, + 545, + 632 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 575, + 545, + 632 + ], + "type": "inline_equation", + "content": "I_{i}^{+}" + }, + { + "bbox": [ + 304, + 575, + 545, + 632 + ], + "type": "text", + "content": "):" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 333, + 638, + 466, + 652 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 333, + 638, + 466, + 652 + ], + "spans": [ + { + "bbox": [ + 333, + 638, + 466, + 652 + ], + "type": "interline_equation", + "content": "L _ {\\mathrm {I M G}} = l _ {\\mathrm {I M G}} \\left(\\mathbf {z} ^ {\\mathrm {I}}, \\mathbf {z} ^ {\\mathrm {I +}}\\right) + l _ {\\mathrm {I M G}} \\left(\\mathbf {z} ^ {\\mathrm {I +}}, \\mathbf {z} ^ {\\mathrm {I}}\\right),", + "image_path": "847b1edfc575a3d150a9b2e76429978404faf9c588c14a4c8fdc4004064bb838.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 654, + 546, + 694 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 654, + 546, + 694 + ], + "spans": [ + { + "bbox": [ + 305, + 654, + 546, + 694 + ], + "type": "interline_equation", + "content": "l _ {\\mathrm {I M G}} \\left(\\mathbf {z} ^ {\\mathrm {I}}, \\mathbf {z} ^ {\\mathrm {I} +}\\right) = \\frac {1}{2 N} \\sum_ {i = 1} ^ {N} - \\log \\frac {\\exp \\left(\\mathbf {z} _ {i} ^ {\\mathrm {I}} \\cdot \\mathbf {z} _ {i} ^ {\\mathrm {I} +} / \\tau\\right)}{\\sum_ {\\mathbf {z} ^ {-} \\in \\mathbf {z} ^ {\\mathrm {I}} \\cup \\mathbf {z} ^ {\\mathrm {I} +} \\backslash \\left\\{\\mathbf {z} _ {i} ^ {\\mathrm {I}} \\right\\}} \\exp \\left(\\mathbf {z} _ {i} ^ {\\mathrm {I}} \\cdot \\mathbf {z} ^ {-} / \\tau\\right)}, \\tag {3}", + "image_path": "291559416db036766fde2c7e8daabba06e77161e1696c97253b5e82b36e37eaf.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 700, + 487, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 700, + 487, + 715 + ], + "spans": [ + { + "bbox": [ + 306, + 700, + 487, + 715 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 700, + 487, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_i^{1 + }\\in \\mathbf{z}^{1 + }" + }, + { + "bbox": [ + 306, + 700, + 487, + 715 + ], + "type": "text", + "content": " is an encoded feature of " + }, + { + "bbox": [ + 306, + 700, + 487, + 715 + ], + "type": "inline_equation", + "content": "I_{i}^{+}" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "21374" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "content": "3.1.3 Cross-modal sharing the properties on the joint 2D-3D space" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 102, + 286, + 158 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 102, + 286, + 158 + ], + "spans": [ + { + "bbox": [ + 47, + 102, + 286, + 158 + ], + "type": "text", + "content": "The third function " + }, + { + "bbox": [ + 47, + 102, + 286, + 158 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{CROSS}}" + }, + { + "bbox": [ + 47, + 102, + 286, + 158 + ], + "type": "text", + "content": " aligns the geometric-aware features " + }, + { + "bbox": [ + 47, + 102, + 286, + 158 + ], + "type": "inline_equation", + "content": "\\mathbf{z}^{\\mathrm{G}}" + }, + { + "bbox": [ + 47, + 102, + 286, + 158 + ], + "type": "text", + "content": " with the 2D features " + }, + { + "bbox": [ + 47, + 102, + 286, + 158 + ], + "type": "inline_equation", + "content": "\\mathbf{z}^{\\mathrm{I}}" + }, + { + "bbox": [ + 47, + 102, + 286, + 158 + ], + "type": "text", + "content": " by constructing a common 2D-3D space for the two encoders, " + }, + { + "bbox": [ + 47, + 102, + 286, + 158 + ], + "type": "inline_equation", + "content": "f^{\\mathrm{G}}(\\cdot)" + }, + { + "bbox": [ + 47, + 102, + 286, + 158 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 102, + 286, + 158 + ], + "type": "inline_equation", + "content": "f^{\\mathrm{I}}(\\cdot)" + }, + { + "bbox": [ + 47, + 102, + 286, + 158 + ], + "type": "text", + "content": ". To this end, we use cross-modal contrastive learning loss as a training objective as follows:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 54, + 168, + 287, + 223 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 168, + 287, + 223 + ], + "spans": [ + { + "bbox": [ + 54, + 168, + 287, + 223 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} L _ {\\mathrm {C R O S S}} = l _ {\\mathrm {C R O S S}} \\left(\\mathbf {z} ^ {\\mathrm {I}}, \\mathbf {z} ^ {\\mathrm {G}}\\right) + l _ {\\mathrm {C R O S S}} \\left(\\mathbf {z} ^ {\\mathrm {G}}, \\mathbf {z} ^ {\\mathrm {I}}\\right), \\\\ l _ {\\text {C R O S S}} \\left(\\mathbf {z} ^ {\\mathrm {I}}, \\mathbf {z} ^ {\\mathrm {G}}\\right) = \\frac {1}{2 N} \\sum_ {i = 1} ^ {N} - \\log \\frac {\\exp \\left(\\mathbf {z} _ {i} ^ {\\mathrm {I}} \\cdot \\mathbf {z} _ {i} ^ {\\mathrm {G}} / \\tau\\right)}{\\sum_ {\\mathbf {z} ^ {-} \\in \\mathbf {z} ^ {\\mathrm {G}} \\backslash \\left\\{\\mathbf {z} _ {i} ^ {\\mathrm {G}} \\right\\}} \\exp \\left(\\mathbf {z} _ {i} ^ {\\mathrm {I}} \\cdot \\mathbf {z} ^ {-} / \\tau\\right)}. \\tag {4} \\\\ \\end{array}", + "image_path": "68deef260c655e0ce74aa55f66179fdc4bc0b5cb8f407d1b3bb86cfe03ff5c34.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 232, + 287, + 280 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 232, + 287, + 280 + ], + "spans": [ + { + "bbox": [ + 47, + 232, + 287, + 280 + ], + "type": "text", + "content": "Sharing " + }, + { + "bbox": [ + 47, + 232, + 287, + 280 + ], + "type": "inline_equation", + "content": "\\mathbf{z}^{\\mathrm{G}}" + }, + { + "bbox": [ + 47, + 232, + 287, + 280 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 47, + 232, + 287, + 280 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{GEO}}" + }, + { + "bbox": [ + 47, + 232, + 287, + 280 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 47, + 232, + 287, + 280 + ], + "type": "inline_equation", + "content": "\\mathbf{z}^{\\mathrm{l}}" + }, + { + "bbox": [ + 47, + 232, + 287, + 280 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 47, + 232, + 287, + 280 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{IMG}}" + }, + { + "bbox": [ + 47, + 232, + 287, + 280 + ], + "type": "text", + "content": " on " + }, + { + "bbox": [ + 47, + 232, + 287, + 280 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{CROSS}}" + }, + { + "bbox": [ + 47, + 232, + 287, + 280 + ], + "type": "text", + "content": " using " + }, + { + "bbox": [ + 47, + 232, + 287, + 280 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 47, + 232, + 287, + 280 + ], + "type": "text", + "content": " results in a " + }, + { + "bbox": [ + 47, + 232, + 287, + 280 + ], + "type": "inline_equation", + "content": "f^{1}(\\cdot)" + }, + { + "bbox": [ + 47, + 232, + 287, + 280 + ], + "type": "text", + "content": " that can produce 2D representation with useful geometric and visual priors that show superior fin-tuning performance in the experimental section." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 287, + 287, + 312 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 287, + 287, + 312 + ], + "spans": [ + { + "bbox": [ + 47, + 287, + 287, + 312 + ], + "type": "text", + "content": "3.2. Learning geometric-aware representation on non-paired RGB datasets" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 317, + 287, + 473 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 317, + 287, + 473 + ], + "spans": [ + { + "bbox": [ + 46, + 317, + 287, + 473 + ], + "type": "text", + "content": "Training a model to induce geometric-aware properties in 2D representation using Eq. (2) and Eq. (4) requires RGB-CAD pairs " + }, + { + "bbox": [ + 46, + 317, + 287, + 473 + ], + "type": "inline_equation", + "content": "(I, G)" + }, + { + "bbox": [ + 46, + 317, + 287, + 473 + ], + "type": "text", + "content": ". However, obtaining such paired datasets is a cumbersome problem in every cross-modal learning framework. To address this, we propose to utilize 2D-3D object matching techniques, e.g., [16, 19, 30, 31, 47], to generate pseudo-pair of images and its associated 3D models, " + }, + { + "bbox": [ + 46, + 317, + 287, + 473 + ], + "type": "inline_equation", + "content": "(I_i, G_i')" + }, + { + "bbox": [ + 46, + 317, + 287, + 473 + ], + "type": "text", + "content": ", which can be used for training instead of the real pairs. Our experiments show that these pseudo pairs still help induce geometric-aware properties in our representations, resulting in better performance on 2D object understanding tasks, compared to state-of-the-art 2D representation learning approaches." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 484, + 162, + 498 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 484, + 162, + 498 + ], + "spans": [ + { + "bbox": [ + 47, + 484, + 162, + 498 + ], + "type": "text", + "content": "4. Experimental setup" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 503, + 161, + 516 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 503, + 161, + 516 + ], + "spans": [ + { + "bbox": [ + 47, + 503, + 161, + 516 + ], + "type": "text", + "content": "4.1. Pre-training details" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 521, + 287, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 287, + 665 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 287, + 665 + ], + "type": "text", + "content": "We use ResNet-50 [23] or ViT-B [29] initialized with supervised pre-trained ImageNet weights for the 2D encoder and use DGCNN [46] for the 3D encoder. We choose " + }, + { + "bbox": [ + 46, + 521, + 287, + 665 + ], + "type": "inline_equation", + "content": "\\tau = 0.07" + }, + { + "bbox": [ + 46, + 521, + 287, + 665 + ], + "type": "text", + "content": " for all equations and " + }, + { + "bbox": [ + 46, + 521, + 287, + 665 + ], + "type": "inline_equation", + "content": "K = 3" + }, + { + "bbox": [ + 46, + 521, + 287, + 665 + ], + "type": "text", + "content": " in Eq. (2). Modality-specific projection heads are used for both 2D and 3D encoders to produce feature vectors " + }, + { + "bbox": [ + 46, + 521, + 287, + 665 + ], + "type": "inline_equation", + "content": "z^{\\mathrm{IMG}}" + }, + { + "bbox": [ + 46, + 521, + 287, + 665 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 521, + 287, + 665 + ], + "type": "inline_equation", + "content": "z^{\\mathrm{GEO}}" + }, + { + "bbox": [ + 46, + 521, + 287, + 665 + ], + "type": "text", + "content": " used in Eq. (1). Each head consists of two linear layers of sizes 1024 and 512, where the first one has ReLU activation. We pre-trained the model on the NVIDIA A100 GPU with a batch size of 256, then neglected the projection heads and retained only the 2D encoder for fine-tuning with downstream tasks. More details are given in Appendix A." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "content": "For the pre-train dataset, we use Pix3D [45] with the S1 train-test split [16]. This dataset consists of 10,069 paired RGB images of indoor scene furniture (e.g., bed, chair, sofa) and corresponding CAD models (subcategories) with" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "text", + "content": "a total of 395 shapes. We preprocessed each CAD model by uniform sampling random points to generate point clouds consisting of " + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "inline_equation", + "content": "N = 1024" + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "text", + "content": " and applied point translation, rotation, and jittering to them. For RGB images, we applied the same augmentation strategy as [6] by randomly cropping an image into a size of " + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "inline_equation", + "content": "224 \\times 224" + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "text", + "content": ", then randomly applying horizontal flipping, color jittering, grayscale, and Gaussian blurring to the images." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 184, + 466, + 197 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 184, + 466, + 197 + ], + "spans": [ + { + "bbox": [ + 305, + 184, + 466, + 197 + ], + "type": "text", + "content": "4.2. Pseudo-pair generation setup" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 205, + 545, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 205, + 545, + 324 + ], + "spans": [ + { + "bbox": [ + 304, + 205, + 545, + 324 + ], + "type": "text", + "content": "We utilized a state-of-the-art 3D shape retrieval model, ROCA [19], to generate a pseudo CAD model for any RGB image in indoor scene domains. ROCA was trained on Scan2CAD dataset [2] containing RGB-D frames of indoor scenes and annotated CAD models for each object in each frame. The Mask-RCNN [22] is employed to detect objects in an input image and generate bounding boxes of those detected ones. The feature of each bounding box will be further used in the ROCA retrieval module for predicting its associated CAD model listed in the ShapeNet [4] database." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 327, + 545, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 327, + 545, + 399 + ], + "spans": [ + { + "bbox": [ + 304, + 327, + 545, + 399 + ], + "type": "text", + "content": "The pairing for each RGB input was selected based on a predicted CAD model of the largest detected bounding box. See Appendix G for more ablation studies on pair generation. Later in the experiment section, we compare our model trained on RGB images from Pix3D dataset [45] and pseudo CAD pairs generated by ROCA with competitors." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 415, + 425, + 427 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 415, + 425, + 427 + ], + "spans": [ + { + "bbox": [ + 305, + 415, + 425, + 427 + ], + "type": "text", + "content": "4.3. Baseline competitors" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 436, + 545, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 436, + 545, + 472 + ], + "spans": [ + { + "bbox": [ + 304, + 436, + 545, + 472 + ], + "type": "text", + "content": "All competitors except SupImg and Pri3D were initialized using pre-trained ImageNet weights and subsequently trained on Pix3D to ensure evaluation fairness." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 475, + 545, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 475, + 545, + 510 + ], + "spans": [ + { + "bbox": [ + 304, + 475, + 545, + 510 + ], + "type": "text", + "content": "Supervised ImageNet Pre-training (SupImg) [13] represents the base performance of a pre-trained model without additional training on indoor scene datasets." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 514, + 545, + 561 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 514, + 545, + 561 + ], + "spans": [ + { + "bbox": [ + 304, + 514, + 545, + 561 + ], + "type": "text", + "content": "SimCLR [6] and SupCon [28] provide the results when learning 2D representation on augmented RGB images (SimCLR), object categories (SupCon), or subcategories (SupCon (Fine)) in a CNN backbone." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 564, + 545, + 600 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 564, + 545, + 600 + ], + "spans": [ + { + "bbox": [ + 304, + 564, + 545, + 600 + ], + "type": "text", + "content": "CrossPoint [1] shows the performance of existing CAD-RGB representation learning. Note that this work has not been studied for solving 2D object understanding tasks." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 603, + 545, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 603, + 545, + 674 + ], + "spans": [ + { + "bbox": [ + 304, + 603, + 545, + 674 + ], + "type": "text", + "content": "Pri3D [25] and Set-InfoNCE [5] are state-of-the-art geometric-aware 2D representation learning works trained on multi-view RGB frames and 3D scans of ScanNet [12] dataset. Note that Set-InfoNCE did not publicly share their code, so we can only compare the results to their reported statistics on ScanNet [12] and NYUv2 [42] datasets." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": "DINO [3] and MAE [20] are state-of-the-art 2D representation learning models based on Vision Transformer (ViT) [29] architectures." + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21375" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 71, + 169, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 71, + 169, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 169, + 85 + ], + "type": "text", + "content": "5. Experimental results" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 91, + 228, + 104 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 91, + 228, + 104 + ], + "spans": [ + { + "bbox": [ + 47, + 91, + 228, + 104 + ], + "type": "text", + "content": "5.1. Properties of our learned features" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 110, + 287, + 170 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 110, + 287, + 170 + ], + "spans": [ + { + "bbox": [ + 47, + 110, + 287, + 170 + ], + "type": "text", + "content": "Evaluating geometric-aware properties. Fig. 2 visualizes the pairwise cosine similarities between each encoded feature of objects from the Pix3D validation split. The representations were encoded with the 2D encoder (without a projection head) of each approach." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 170, + 287, + 242 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 170, + 287, + 242 + ], + "spans": [ + { + "bbox": [ + 46, + 170, + 287, + 242 + ], + "type": "text", + "content": "Our representations have high similarity scores for images with the same geometry (intra-subcategory) and others with the same object category (intra-category), while none of the competitors could reflect two properties at the same time. More visualizations from other categories and other competitors are provided in Appendix B." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 242, + 287, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 242, + 287, + 373 + ], + "spans": [ + { + "bbox": [ + 46, + 242, + 287, + 373 + ], + "type": "text", + "content": "One interesting aspect is that our representations also well capture the differences across inter-category and inter-subcategory samples. We acquire better mean intra and inter-category similarity scores than the self-supervised baselines, as shown in Fig. 4. Furthermore, Ours (pseudo) yields similar findings, particularly for inter-category. An additional study in Appendix B also demonstrates that Ours (pseudo) has better discrimination in inter-subcategory features. These geometric-aware properties in our learned representation lead to improved 2D object understanding performance in further subsections." + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 53, + 374, + 281, + 493 + ], + "blocks": [ + { + "bbox": [ + 53, + 374, + 281, + 493 + ], + "lines": [ + { + "bbox": [ + 53, + 374, + 281, + 493 + ], + "spans": [ + { + "bbox": [ + 53, + 374, + 281, + 493 + ], + "type": "image", + "image_path": "dec816489b57275f8fa313bd278708b09d58e89b57fda05fe1e885f9422e8ed4.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 494, + 287, + 550 + ], + "lines": [ + { + "bbox": [ + 46, + 494, + 287, + 550 + ], + "spans": [ + { + "bbox": [ + 46, + 494, + 287, + 550 + ], + "type": "text", + "content": "Figure 4. Distribution of pairwise cosine similarity score among intra and inter-category samples. Our representations learned by " + }, + { + "bbox": [ + 46, + 494, + 287, + 550 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{GEO}}" + }, + { + "bbox": [ + 46, + 494, + 287, + 550 + ], + "type": "text", + "content": " based on the Chamfer distance have the highest mean score (vertical dashed lines) within intra-category samples and also have the lowest score in the inter-category scenario." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "text", + "content": "Object localization. We study whether our model can generalize to images with multiple objects, even though it was trained on a dataset of single objects. Fig. 5 shows that our learned features from the ViT-B backbone can be used for roughly localizing patches associated with object categories without fine-tuning. More details and results are provided in Appendix C. This property may arise from how our loss function encourages learning discriminative part features, which are useful for classifying, localizing, and segmenting multiple objects demonstrated in our subsequent experiments. This similar behavior is also observed in other 2D self-supervised models [3] trained on single-object datasets (e.g., ImageNet [13])." + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 310, + 60, + 544, + 134 + ], + "blocks": [ + { + "bbox": [ + 310, + 60, + 544, + 134 + ], + "lines": [ + { + "bbox": [ + 310, + 60, + 544, + 134 + ], + "spans": [ + { + "bbox": [ + 310, + 60, + 544, + 134 + ], + "type": "image", + "image_path": "f2d823514a3cee9e7a3747f1295546ffbfa1a8d9706077ef673aa63bf3ef9936.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 136, + 545, + 202 + ], + "lines": [ + { + "bbox": [ + 304, + 136, + 545, + 202 + ], + "spans": [ + { + "bbox": [ + 304, + 136, + 545, + 202 + ], + "type": "text", + "content": "Figure 5. We compute the feature similarity between each patch in an unseen input image and the mean global feature of learned images in each category using models with a ViT-B backbone. Without fine-tuning, our model can identify the table and roughly localize patches associated with the chairs in the image by using the category of the most similar mean global feature of each patch." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 215, + 453, + 228 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 215, + 453, + 228 + ], + "spans": [ + { + "bbox": [ + 306, + 215, + 453, + 228 + ], + "type": "text", + "content": "5.2. 2D Semantic segmentation" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 236, + 545, + 320 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 236, + 545, + 320 + ], + "spans": [ + { + "bbox": [ + 304, + 236, + 545, + 320 + ], + "type": "text", + "content": "Table 1 compares fine-tuning results in semantic segmentation tasks with other competitors. Following [5, 25], we train a U-Net [41] with residual connections for predicting segmentation masks with cross-entropy loss. The encoder part of U-Net is ResNet-50, while the decoder is conv layers with bi-linear interpolation. For ViT-B, we follow [20] by using UPerNet [51] as a segmentation head." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 323, + 546, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 323, + 546, + 479 + ], + "spans": [ + { + "bbox": [ + 304, + 323, + 546, + 479 + ], + "type": "text", + "content": "We employ two variants of mean intersection-over-union (mIoU) for the evaluation metric. The first mIoU, initially implemented by Pri3D [25], does not include pixels that were incorrectly predicted to be ignored classes (e.g., background) as a false positive in mIoU computation. In comparison, our revised mIoU includes these pixels to avoid model cheating by predicting more ignored classes. The experiments were conducted on NYUv2 [42], ScanNet [12], indoor ADE20k [54], and indoor SUNRGB-D [43] datasets. We filtered ADE20k to include only indoor scenes and ignored previously omitted classes in an NYUv2 setting following the prior work [25] for SUNRGB-D. More details on our split are provided in Appendix D." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 480, + 545, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 480, + 545, + 578 + ], + "spans": [ + { + "bbox": [ + 304, + 480, + 545, + 578 + ], + "type": "text", + "content": "When pre-trained on non-paired RGB datasets, Ours (pseudo) outperforms all 2D competitors in both architectures, including DINO [3] and MAE [20]. For 2D-3D competitors, we win against Pri3D and achieve very competitive results to Set-InfoNCE in NYUv2 by only -0.16 in mIoU [25]. We also outperform Pri3D in ADE20k by +1.01 for the original and +0.79 for the pseudo version. The qualitative results are shown in Fig. 6 and Appendix E." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 578, + 545, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 578, + 545, + 675 + ], + "spans": [ + { + "bbox": [ + 304, + 578, + 545, + 675 + ], + "type": "text", + "content": "For ScanNet and SUNRGB-D datasets, Pri3D and SetInfoNCE perform better than ours. This might be because their models were trained directly on ScanNet 3D scans. Some images in SUNRGB-D also appear similar to those in ScanNet, as both datasets sampled RGB-D frames from recorded videos at a high frame-per-second rate. Nonetheless, even without 3D ScanNet, our method still achieves comparable results to Pri3D (-0.17)." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 677, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 714 + ], + "type": "text", + "content": "Additionally, in Appendix F, we present results obtained by increasing the pre-training data, which allows us to surpass Set-InfoNCE on NYUv2 without real 3D pairs." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "21376" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 70, + 106, + 517, + 276 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 547, + 104 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 547, + 104 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 547, + 104 + ], + "type": "text", + "content": "Table 1. Semantic segmentation results on four popular benchmark datasets. For both ResNet-50 (RN50) and ViT-B architectures, our approaches have better mIoU than 2D representation learning baselines. (*) denotes scores from the methods that were directly pre-trained on 2D and 3D data of ScanNet dataset. We win against Pri3D in NYUv2 and ADE20k without requiring 3D scene scans." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 70, + 106, + 517, + 276 + ], + "lines": [ + { + "bbox": [ + 70, + 106, + 517, + 276 + ], + "spans": [ + { + "bbox": [ + 70, + 106, + 517, + 276 + ], + "type": "table", + "html": "
Arch.GT pairMethod3DNYUv2ScanNetindoor ADE20kSUNRGB-D
mIoUmIoU [25]mIoUmIoU [25]mIoUmIoU [25]mIoUmIoU [25]
RN502D onlySupImg-47.0450.049.1255.737.5239.6947.9663.12
SimCLR-47.9453.3249.9156.3438.1939.5648.5163.00
SupCon-48.4954.1650.5956.5737.9640.1348.1365.01
SupCon (fine)-47.3453.4549.8156.2237.8739.9248.0563.13
pseudoOurs (pseudo)CAD49.4654.6250.7756.7639.1340.4349.1365.45
2D-3DCrossPointCAD46.0449.1847.2654.0236.5537.8847.1562.77
Pri3Dscene49.5254.754.72*61.7*38.3439.1750.0266.65
Set-InfoNCEscene-55.4-63.1*----
OursCAD49.7755.2451.0357.1239.3540.8649.8565.95
ViT-B2D onlySupImg-49.4455.5963.9359.7242.7844.3851.2666.45
DINO-52.1457.2462.5458.1341.7243.4150.5266.12
MAE-50.1055.6662.2358.9542.9644.9652.2267.87
pseudoOurs (pseudo)CAD52.4758.0264.4960.7343.0245.3752.5369.59
2D-3DOursCAD53.058.6765.2760.9543.1245.8252.9669.69
", + "image_path": "d5c9ffb0300bd9f77f7d6ad0cf97704e2a8dcf6c2ce9cba217fc09138aa50af8.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 65, + 277, + 526, + 484 + ], + "blocks": [ + { + "bbox": [ + 65, + 277, + 526, + 484 + ], + "lines": [ + { + "bbox": [ + 65, + 277, + 526, + 484 + ], + "spans": [ + { + "bbox": [ + 65, + 277, + 526, + 484 + ], + "type": "image", + "image_path": "b7fecadc9068005cd319a67c4ca592794581485ee3b55aaf0cc393ed45288d42.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 485, + 546, + 509 + ], + "lines": [ + { + "bbox": [ + 46, + 485, + 546, + 509 + ], + "spans": [ + { + "bbox": [ + 46, + 485, + 546, + 509 + ], + "type": "text", + "content": "Figure 6. Qualitative results on NYUv2 [42] semantic segmentation. Our methods yield better segmentation results when labeling a scene is challenging due to color or lighting. The geometric priors in our learned representations boost understanding of each scene." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 514, + 288, + 528 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 514, + 288, + 528 + ], + "spans": [ + { + "bbox": [ + 47, + 514, + 288, + 528 + ], + "type": "text", + "content": "5.3.2D Instance segmentation and object detection" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 533, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 533, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 533, + 287, + 677 + ], + "type": "text", + "content": "Indoor scenes. We show how our features improve instance segmentation and object detection results in Table 2. Similar to [25], we use Mask-RCNN [22] with ResNet-50 encoder, implemented on Detectron2 [48] framework for both tasks. For ViT-B, we resize input images to " + }, + { + "bbox": [ + 46, + 533, + 287, + 677 + ], + "type": "inline_equation", + "content": "224 \\times 224" + }, + { + "bbox": [ + 46, + 533, + 287, + 677 + ], + "type": "text", + "content": " and follow [33] by using Mask-RCNN as the detection head. All backbones were initialized by the pre-trained weights of our model or competitors'. Following [5,25], we use NYUv2 [42] dataset and a well-known detection benchmark, COCO dataset, with Average Precision (AP) as the metric. We filtered COCO images to include only indoor objects. Details on the selected classes are in Appendix D." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 677, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 288, + 713 + ], + "type": "text", + "content": "Our method outperforms state-of-the-art 2D and 2D-3D competitors in all settings. Ours (pseudo) achieves competitive scores against Pri3D and Set-InfoNCE in NYUv2 and" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 515, + 520, + 527 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 515, + 520, + 527 + ], + "spans": [ + { + "bbox": [ + 305, + 515, + 520, + 527 + ], + "type": "text", + "content": "beats Pri3D in COCO without ground truth 3D pairs." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 528, + 545, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 528, + 545, + 612 + ], + "spans": [ + { + "bbox": [ + 304, + 528, + 545, + 612 + ], + "type": "text", + "content": "Outdoor scenes. We also pre-trained our model on PAS-CAL3D+ [50] dataset, which contains objects such as vehicles and furniture in both indoor and outdoor scenes, and evaluated the model on another subset of COCO images called outdoor COCO. Further dataset details are provided in Appendix D. Our method leads to similar improvements in AP as observed in the indoor-only settings." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 622, + 462, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 622, + 462, + 635 + ], + "spans": [ + { + "bbox": [ + 306, + 622, + 462, + 635 + ], + "type": "text", + "content": "5.4. Experiments on 2D retrieval" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 641, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 546, + 713 + ], + "type": "text", + "content": "Table 3 shows the retrieval performance on Pix3D [45] by fine-tuning the pre-trained model on coarse-grained (category) and fine-grained (subcategory) labels of objects. The 2D encoder was fine-tuned along with an additional retrieval head, consisting of two linear layers of sizes 1024 and 512 with ReLU applied only to the first layer. All" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "21377" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 53, + 83, + 535, + 237 + ], + "blocks": [ + { + "bbox": [ + 89, + 71, + 501, + 82 + ], + "lines": [ + { + "bbox": [ + 89, + 71, + 501, + 82 + ], + "spans": [ + { + "bbox": [ + 89, + 71, + 501, + 82 + ], + "type": "text", + "content": "Table 2. Object detection and instance segmentation performance. We outperform competitors for all datasets." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 53, + 83, + 535, + 237 + ], + "lines": [ + { + "bbox": [ + 53, + 83, + 535, + 237 + ], + "spans": [ + { + "bbox": [ + 53, + 83, + 535, + 237 + ], + "type": "table", + "html": "
Arch. SizeGT pairMethod3DNYUv2indoor COCOoutdoor COCO
Object Det.Instance segm.Object Det.Instance seg.Object Det.Instance seg.
AP50AP75APAP50AP75APAP50AP75APAP50AP75APAP50AP75APAP50AP75
RN50 4802D onlySupImg-29.917.316.825.113.913.441.7824.2123.7039.1623.3522.6146.0926.9828.0842.4523.3423.92
SimCLR-32.8120.1519.2429.1015.9715.6243.6326.4625.4540.8724.7923.8648.1528.7530.4044.3125.0124.99
SupCon-33.2320.3619.6329.4416.1615.8343.6626.3425.3240.8424.5323.7547.8928.6730.2944.1624.6324.97
SupCon (fine)-32.5619.7418.9229.0616.1115.7443.5825.9525.2140.6524.2223.6645.0127.9026.5941.9725.6124.66
pseudoOurs (pseudo)CAD34.4520.2719.7229.6416.2416.1343.7426.4725.4840.9224.7723.91------
2D-3DCrossPointCAD28.4215.9415.2224.4913.3213.1140.2522.7822.2638.5421.9220.8043.2224.5725.6039.7521.9321.11
Pri3Dscene34.020.419.429.516.315.843.4926.4025.2240.7124.7223.61------
Set-InfoNCEscene34.620.519.729.716.316.5-----------
OursCAD34.8520.8920.1230.0316.5116.8444.1126.7825.6941.0224.9124.0849.0329.8031.6245.2325.9025.85
ViT-B 2242D onlySupImg-34.4019.2419.0628.4214.0514.9731.4520.6319.4129.7718.7317.8233.5623.1921.8131.6819.5218.11
DINO-33.0318.6217.9126.8214.5614.7327.7016.2415.8725.7814.8614.7632.5722.1320.6129.8618.0717.66
MAE-35.9219.3019.2429.8816.0115.8231.5420.5919.3329.9218.6517.8336.9724.5123.1233.6720.1519.46
pseudoOurs (pseudo)CAD36.2419.7819.7230.1015.9416.0531.7820.7419.4630.0119.0717.94------
2D-3DOursCAD36.3119.9119.9430.3016.1616.2732.0221.0419.6730.1619.0218.0937.7424.9223.4234.1320.4919.89
", + "image_path": "9be909d71dee3101eb0cd45c3ee2eeb225cd88e1cf978791e6f327ae2d39083b.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 52, + 270, + 278, + 407 + ], + "blocks": [ + { + "bbox": [ + 47, + 247, + 286, + 268 + ], + "lines": [ + { + "bbox": [ + 47, + 247, + 286, + 268 + ], + "spans": [ + { + "bbox": [ + 47, + 247, + 286, + 268 + ], + "type": "text", + "content": "Table 3. Retrieval performance on Pix3D [45]. Our method outperforms all competitors in all situations." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 52, + 270, + 278, + 407 + ], + "lines": [ + { + "bbox": [ + 52, + 270, + 278, + 407 + ], + "spans": [ + { + "bbox": [ + 52, + 270, + 278, + 407 + ], + "type": "table", + "html": "
Arch.GT PairMethod3DCoarse R@1Fine R@1
RN502D onlySupImg-78.8551.18
SimCLR-80.0455.01
SupCon-81.3252.39
SupCon (fine)-79.9555.84
pseudoOurs (pseudo)CAD81.7456.71
2D-3DCrossPointCAD75.9748.09
Pri3Dscene79.7251.63
OursCAD82.8858.97
ViT-B2D onlySupImg-84.0464.17
DINO-84.5965.48
MAE-83.7962.00
pseudoOurs (pseudo)CAD86.1666.40
2D-3DOursCAD86.3267.23
", + "image_path": "260d1d3fda4c375c01eb0c53b679b125ddb4860c499dc1ae6c2004949de06295.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 65, + 461, + 266, + 554 + ], + "blocks": [ + { + "bbox": [ + 46, + 415, + 286, + 459 + ], + "lines": [ + { + "bbox": [ + 46, + 415, + 286, + 459 + ], + "spans": [ + { + "bbox": [ + 46, + 415, + 286, + 459 + ], + "type": "text", + "content": "Table 4. Effects on losses and positive mining choices. Training on three losses simultaneously yields the best performance in mIoU. At the same time, choosing the Chamfer Distance (CD) as a positive mining choice in " + }, + { + "bbox": [ + 46, + 415, + 286, + 459 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{GEO}}" + }, + { + "bbox": [ + 46, + 415, + 286, + 459 + ], + "type": "text", + "content": " also wins against the others." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 65, + 461, + 266, + 554 + ], + "lines": [ + { + "bbox": [ + 65, + 461, + 266, + 554 + ], + "spans": [ + { + "bbox": [ + 65, + 461, + 266, + 554 + ], + "type": "table", + "html": "
LIMGLGEOLCROSSPos.NYUv2ADE20k
-✓✓CD48.2337.71
✓-✓-48.4638.47
✓---47.9438.19
--✓-47.0237.43
✓✓✓Sup49.4839.12
✓✓✓Aug49.1438.65
✓✓✓CD49.7739.35
", + "image_path": "99d5996f48bbb7bf32973e6bdfacab0b1ae38403d41548f349a3a3e939bb3890.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 566, + 286, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 566, + 286, + 602 + ], + "spans": [ + { + "bbox": [ + 46, + 566, + 286, + 602 + ], + "type": "text", + "content": "retrieval models were trained using supervised contrastive loss [28] with " + }, + { + "bbox": [ + 46, + 566, + 286, + 602 + ], + "type": "inline_equation", + "content": "\\tau = 0.07" + }, + { + "bbox": [ + 46, + 566, + 286, + 602 + ], + "type": "text", + "content": ". Our methods outperform all competitors in all architectures." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 610, + 145, + 621 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 610, + 145, + 621 + ], + "spans": [ + { + "bbox": [ + 47, + 610, + 145, + 621 + ], + "type": "text", + "content": "5.5. Ablation studies" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 629, + 286, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 629, + 286, + 664 + ], + "spans": [ + { + "bbox": [ + 47, + 629, + 286, + 664 + ], + "type": "text", + "content": "All ablation experiments are evaluated on NYUv2 and ADE20k semantic segmentation tasks using our revised mIoU metric on ResNet-50 architecture." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 665, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 286, + 713 + ], + "type": "text", + "content": "Effects on losses and positive mining choices Table 4 shows the effects of three loss choices (i.e., " + }, + { + "bbox": [ + 46, + 665, + 286, + 713 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{IMG}}" + }, + { + "bbox": [ + 46, + 665, + 286, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 665, + 286, + 713 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{GEO}}" + }, + { + "bbox": [ + 46, + 665, + 286, + 713 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 665, + 286, + 713 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{CROSS}}" + }, + { + "bbox": [ + 46, + 665, + 286, + 713 + ], + "type": "text", + "content": ") and three different choices of the positive point cloud using in Eq. (2), including using object categories" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 248, + 545, + 308 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 248, + 545, + 308 + ], + "spans": [ + { + "bbox": [ + 304, + 248, + 545, + 308 + ], + "type": "text", + "content": "(Sup), point cloud augmentation (Aug), and Chamfer distance (CD). We found that training three loss functions simultaneously notably improves mIoU from training single or dual losses. While in the positive choice study, our selected Chamfer distance achieves the best mIoU." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 308, + 545, + 404 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 308, + 545, + 404 + ], + "spans": [ + { + "bbox": [ + 304, + 308, + 545, + 404 + ], + "type": "text", + "content": "Effects on " + }, + { + "bbox": [ + 304, + 308, + 545, + 404 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 308, + 545, + 404 + ], + "type": "text", + "content": " selected positive point clouds. We studied the best number of " + }, + { + "bbox": [ + 304, + 308, + 545, + 404 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 308, + 545, + 404 + ], + "type": "text", + "content": " in Eq. (2). Fig. 7 reveals that " + }, + { + "bbox": [ + 304, + 308, + 545, + 404 + ], + "type": "inline_equation", + "content": "K = 3" + }, + { + "bbox": [ + 304, + 308, + 545, + 404 + ], + "type": "text", + "content": " can achieve the best mIoU among the others. Using a lower " + }, + { + "bbox": [ + 304, + 308, + 545, + 404 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 308, + 545, + 404 + ], + "type": "text", + "content": " leads to lower mIoU, similar to a higher " + }, + { + "bbox": [ + 304, + 308, + 545, + 404 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 308, + 545, + 404 + ], + "type": "text", + "content": ". This is probably because higher " + }, + { + "bbox": [ + 304, + 308, + 545, + 404 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 308, + 545, + 404 + ], + "type": "text", + "content": " has more chance to select false positive samples due to higher Chamfer distances, which means that the selected samples might have a much different shape than the anchor " + }, + { + "bbox": [ + 304, + 308, + 545, + 404 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_i^G" + }, + { + "bbox": [ + 304, + 308, + 545, + 404 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 321, + 411, + 531, + 460 + ], + "blocks": [ + { + "bbox": [ + 321, + 411, + 531, + 460 + ], + "lines": [ + { + "bbox": [ + 321, + 411, + 531, + 460 + ], + "spans": [ + { + "bbox": [ + 321, + 411, + 531, + 460 + ], + "type": "image", + "image_path": "3596632e824760fc9c5158432ababfcaec07fafe05d16f13b3d359d78a87532c.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 462, + 544, + 483 + ], + "lines": [ + { + "bbox": [ + 306, + 462, + 544, + 483 + ], + "spans": [ + { + "bbox": [ + 306, + 462, + 544, + 483 + ], + "type": "text", + "content": "Figure 7. Effect of varying " + }, + { + "bbox": [ + 306, + 462, + 544, + 483 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 306, + 462, + 544, + 483 + ], + "type": "text", + "content": " selected positive point clouds. " + }, + { + "bbox": [ + 306, + 462, + 544, + 483 + ], + "type": "inline_equation", + "content": "K = 3" + }, + { + "bbox": [ + 306, + 462, + 544, + 483 + ], + "type": "text", + "content": " has the best mIoU." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 490, + 459, + 502 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 490, + 459, + 502 + ], + "spans": [ + { + "bbox": [ + 306, + 490, + 459, + 502 + ], + "type": "text", + "content": "6. Limitations and Discussion" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "text", + "content": "Using CAD models for inducing geometric-aware properties in 2D representation via Chamfer distance shows significantly enhanced 2D object understanding results that are almost as effective as 3D priors from scene scans. This finding remains true when we train our model on generated pseudo-RGB-CAD pairs, allowing us to beat SOTA 2D competitors without the need for paired datasets. However, the performance of the pseudo-pair generator currently hinders our results. As seen in Fig. 2 and 4, features trained on pseudo pairs cannot clearly categorize intra-subcategory images. We observe that this is due to an improper CAD pair assignment; more information is given in Appendix B. Nonetheless, generating or retrieving 3D models from a single image is still more tractable than scene scans and shows progressive performance improvement [38]. This enables harnessing the massive-scale RGB data and generalizing beyond domains with paired data (See Appendix F)." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21378" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 156 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 156 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 156 + ], + "type": "text", + "content": "[1] Mohamed Afham, Isuru Dissanayake, Dinithi Dissanayake, Amaya Dharmasiri, Kanchana Thilakarathna, and Ranga Rodrigo. 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In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 633-641, 2017. 2, 6" + } + ] + } + ], + "index": 3 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "21381" + } + ] + } + ], + "index": 5 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Learning Geometry-Aware Representations by Sketching/f80a6701-d163-4c1c-a5df-2e5aa49a37e5_content_list.json b/2023/Learning Geometry-Aware Representations by Sketching/f80a6701-d163-4c1c-a5df-2e5aa49a37e5_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..290cfc380a44e4a625449f18da2b7c3060e5772e --- /dev/null +++ b/2023/Learning Geometry-Aware Representations by Sketching/f80a6701-d163-4c1c-a5df-2e5aa49a37e5_content_list.json @@ -0,0 +1,1753 @@ +[ + { + "type": "text", + "text": "Learning Geometry-aware Representations by Sketching", + "text_level": 1, + "bbox": [ + 197, + 130, + 772, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Hyundo Lee, Inwoo Hwang, Hyunsung Go, Won-Seok Choi, Kibeom Kim, Byoung-Tak Zhang AI Institute, Seoul National University", + "bbox": [ + 107, + 180, + 859, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{hdlee, iwhwang, hsgo, wchoi, kbkim, btzhang}@bi.snu.ac.kr", + "bbox": [ + 225, + 219, + 738, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 268, + 313, + 284 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Understanding geometric concepts, such as distance and shape, is essential for understanding the real world and also for many vision tasks. To incorporate such information into a visual representation of a scene, we propose learning to represent the scene by sketching, inspired by human behavior. Our method, coined Learning by Sketching (LBS), learns to convert an image into a set of colored strokes that explicitly incorporate the geometric information of the scene in a single inference step without requiring a sketch dataset. A sketch is then generated from the strokes where CLIP-based perceptual loss maintains a semantic similarity between the sketch and the image. We show theoretically that sketching is equivariant with respect to arbitrary affine transformations and thus provably preserves geometric information. Experimental results show that LBS substantially improves the performance of object attribute classification on the unlabeled CLEVR dataset, domain transfer between CLEVR and STL-10 datasets, and for diverse downstream tasks, confirming that LBS provides rich geometric information.", + "bbox": [ + 75, + 300, + 473, + 603 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 632, + 209, + 648 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Since geometric principles form the bedrock of our physical world, many real-world scenarios involve geometric concepts such as position, shape, distance, and orientation. For example, grabbing an object requires estimating its shape and relative distance. Understanding geometric concepts is also essential for numerous vision tasks such as image segmentation, visual reasoning, and pose estimation [27]. Thus, it is crucial to learn a visual representation of the image that can preserve such information [76], which we call geometry-aware representation.", + "bbox": [ + 75, + 657, + 468, + 809 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "However, there is still a challenge in learning geometry-aware representations in a compact way that can be useful for various downstream tasks. Previous approaches have focused on capturing geometric features of an image in a 2D grid structure, using methods such as handcrafted feature extraction [2, 4, 14, 31], segmentation maps [21, 57], or", + "bbox": [ + 75, + 810, + 470, + 902 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/acb59d35df6f7bc2e3430296b492e7e7e1744cb30a0210c7a994b08e09f0bdcf.jpg", + "image_caption": [ + "Figure 1. Overview of LBS, which aims to generate sketches that accurately reflect the geometric information of an image. A sketch consists of a set of strokes represented by a parameterized vector that specifies curve, color, and thickness. We leverage it as a geometry-aware representation for various downstream tasks." + ], + "image_footnote": [], + "bbox": [ + 514, + 268, + 874, + 438 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "convolution features [36, 55]. Although these methods are widely applicable to various domains, they often lack compactness based on a high-level understanding of the scene and tend to prioritize nuisance features such as the background. Another line of work proposes architectures that guarantee to preserve geometric structure [12, 13, 23, 58, 73] or disentangle prominent factors in the data [8, 28, 39, 51]. Although these methods can represent geometric concepts in a compact latent space, they are typically designed to learn features that are specific to a particular domain and often face challenges in generalizing to other domains [64].", + "bbox": [ + 496, + 537, + 890, + 703 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this study, we present a novel approach to learning geometry-aware representations via sketching. Sketching, which is the process of converting the salient features of an image into a set of color-coded strokes, as illustrated in Figure 1, is the primary means by which humans represent images while preserving their geometry. Our key idea is that sketches can be a compact, high-level representation of an image that accurately reflects geometric information. Sketching requires a high-level understanding of the scene, as it aims to capture the most salient features of the image and abstract them into a limited number of strokes. In addition, a sketch can be represented as a set of parameters by replacing each stroke with parametric curves. Sketch-", + "bbox": [ + 496, + 704, + 892, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "23315", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/76d1e600a6daaab19456fc30889477324598309ccd191d694be2599883e9f568.jpg", + "image_caption": [ + "Figure 2. Examples of how sketches capture essential geometric concepts such as shape, size, orientation, curvature, and local distortion. The control points of each stroke compactly represent the local geometric information of the corresponding region in the sketch. The strokes as a whole maintain the geometric structure of the entire image under various transformations in the image domain." + ], + "image_footnote": [], + "bbox": [ + 84, + 94, + 869, + 289 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ing has also been linked to how people learn geometric concepts [66]. Based on these properties, we directly use strokes as a geometry-aware representation and utilize them for downstream tasks. Under the theoretical framework of geometric deep learning [3], we conduct theoretical analysis to validate the effectiveness of strokes as a representation and prove their ability to preserve affine transformations.", + "bbox": [ + 75, + 356, + 468, + 462 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To validate our hypothesis, we introduce Learning by Sketching (LBS), a method that generates abstract sketches coherent with the geometry of an input image. Our model is distinct from existing sketch generation methods as it does not require a sketch dataset for training, which often has limited abstraction or fails to accurately reflect geometric information. Instead, LBS learns to convert an image into a set of colored Bezier curves that explicitly represent the geometric concepts of the input image. To teach the style of sketching, we use perceptual loss based on the CLIP model [59, 68], which measures both semantic and geometric similarities between images and generated sketches. We propose a progressive optimization process that predicts how strokes will be optimized from their initial positions through CLIP-based perceptual loss to generate abstract sketches in a single inference step. As a result, LBS generates a representation that reflects visual understanding in a single inference step, without requiring a sketch dataset. This produces highly explainable representations through sketches, as illustrated in Figure 2.", + "bbox": [ + 75, + 462, + 468, + 763 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We conduct experimental analyses to evaluate the effectiveness of our approach, learning by sketching, by addressing multiple research questions in various downstream tasks, including: (i) describing the relationships between geometric primitives, (ii) demonstrating simple spatial reasoning ability by conveying global and local geometric information, (iii) containing general geometric information shared across different domains, and (iv) improving performance on FG-SBIR, a traditional sketch task.", + "bbox": [ + 75, + 763, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related work", + "text_level": 1, + "bbox": [ + 500, + 354, + 635, + 371 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Geometry-aware representation learning", + "text_level": 1, + "bbox": [ + 500, + 383, + 849, + 400 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Previous studies that aim to capture geometric information within the data can be categorized into two approaches: Firstly, explicitly capturing the geometric information with features on the image space, and secondly, inducing a compact feature vector that preserves the geometric structure of the data.", + "bbox": [ + 498, + 410, + 892, + 500 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Features on image space. The most straightforward approach to representing geometric structures in images is to establish features directly on the image space, i.e., to define features on the 2D grid structure. Approaches that utilize this method include those that employ traditional edge detection algorithms [4, 35, 74, 75], low-level convolutional features [36, 68], and segmentation maps [49, 57, 61]. However, these features are unsuitable for conversion into compact vector representations for downstream tasks. Alternative approaches include utilizing hand-crafted feature detection algorithms [2, 14, 31, 62], clustering specific areas of an image into superpixels [21, 32], and representing the relationships between specific areas as a graph [15, 65]. Our approach is primarily notable for its ability to capture the most salient image features through an overall understanding of the scene, resulting in a concise representation.", + "bbox": [ + 496, + 503, + 892, + 746 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Geometric deep learning. Research has also been conducted to develop informative and compact representations that preserve geometric structures in a latent vector space. One representative method is geometric deep learning [3], which involves preserving the geometric properties of an image by learning an invariant (i.e., maintaining the output identically) or an equivariant representation (i.e., there exists an operator acting on the feature space corresponding to the transformations) with respect to geometric transformations. Steerable networks [12, 13, 23, 73] extend the", + "bbox": [ + 496, + 750, + 893, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "23316", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "translation equivariance of CNNs to a larger group of symmetries and introduce an efficient weight-sharing architecture. However, designing their architecture requires complex analytic solutions, and they are constrained to particular transformations [37]. Another approach is to disentangle factors of variation into distinct latent subspaces [8, 28, 39, 40, 51, 58, 70]. However, these methods face difficulties in handling changing factors of variation [64] and therefore struggle to generalize to arbitrary geometric transformations. Sketching, in contrast to these methods, can naturally ensure equivariance with respect to geometric transformations by being defined on the image space. In Sec. 3 we show that strokes can be equivariant with respect to arbitrary affine transformations.", + "bbox": [ + 75, + 90, + 472, + 303 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Sketch generation methods", + "text_level": 1, + "bbox": [ + 76, + 315, + 321, + 330 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Human-drawn sketches are widely used as valuable descriptions in various applications, including image retrieval [16, 47, 78], modeling 3D shapes and surfaces [25, 42, 43, 45], and image editing [33, 56, 69, 71]. Unfortunately, previous works that aim to learn sketching or drawing mostly endeavor to generate artistic works, rather than focusing on its applicability [19, 24, 30, 48, 52, 83].", + "bbox": [ + 75, + 339, + 468, + 445 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Sketch generation models often rely on explicit sketch datasets to follow the style of human drawings [5, 10, 46, 60, 67, 82]. However, many existing datasets are not designed to preserve geometric information [7, 20, 63] or contain sketches without sophisticated image abstraction, resembling simple edge detection [1, 72]. This presents challenges for sketch models to accurately abstract an image while preserving its geometries. Without sketch datasets, stroke-based rendering methods usually minimize the reconstruction loss which is related to the pixel-wise distance, which promotes learning in the style of painting [19, 30, 48, 52, 53, 81, 83]. There have also been studies that attempt to capture the geometric and semantic features of a scene through imitating the style of line drawing [6, 44, 77]. However, these methods require numerous strokes to cover the whole canvas, primarily focusing on the superfluous background instead of salient features.", + "bbox": [ + 75, + 446, + 472, + 703 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Abstract sketches for representation. Only a few works aim to generate sketches for the sake of representing an image with a limited number of strokes. Learning to Draw (LtD) [54] creates a representative sketch of an image and uses it as a communication channel between agents. While it primarily focuses on communicating with a specific receiver, we aim to leverage strokes as a general representation for various downstream tasks. CLIPasso [68] utilizes the capabilities of CLIP [59], a neural network trained on images paired with text, to synthesize abstract sketches by maintaining both semantic and geometric attributes. Generating representations with this method, however, is impractical due to its reliance on an optimization-based approach", + "bbox": [ + 75, + 704, + 472, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "that is extremely time consuming and numerically unstable. In contrast, our method generates a sketch of an image in a single inference step after training, and is relatively more stable and suitable as a representation.", + "bbox": [ + 496, + 90, + 890, + 151 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Mathematical framework", + "text_level": 1, + "bbox": [ + 498, + 162, + 741, + 180 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we present our theoretical analysis on how sketches can facilitate geometry-aware representation. We begin with a formal definition of sketch and strokes. We then introduce a mathematical framework based on geometric deep learning, which aims to impose the geometric prior on the learned feature.1 Finally, we show that with a loss function that satisfies certain conditions, strokes can be equivariant with respect to arbitrary affine transformations and thus preserve geometric information.", + "bbox": [ + 496, + 188, + 890, + 325 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Preliminaries and notations", + "text_level": 1, + "bbox": [ + 498, + 332, + 750, + 347 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We consider an image $I \\in \\mathcal{I}$ as signals on a physical domain $\\Omega$ , which maps pixel coordinates to the $C$ color channels, i.e., $I: \\Omega \\to \\mathbb{R}^C$ . Although $\\Omega$ is a 2D grid space for the real image, we assume $\\Omega$ as a homogeneous space, where each border is connected to the opposite side.", + "bbox": [ + 496, + 354, + 890, + 430 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Stroke and sketch. A stroke is a tuple $p = (t, c, w)$ composed of $k$ control points $t \\in \\Omega^k$ , color $c \\in [0,1]^C$ , and thickness $w \\in [0,1]$ of the Bézier curve. A rendering process $r: \\mathcal{P} \\to S(\\subset \\mathcal{I})$ converts a set of $n$ strokes $\\pmb{p} = \\{p^{(1)}, \\dots, p^{(n)}\\} \\in \\mathcal{P}$ into the corresponding image (see Appendix D for further details), which we denote as sketch $S = r(\\pmb{p}) \\in S$ . Let $f: \\mathcal{I} \\to \\mathcal{P}$ be the embedding function which maps an image to a set of strokes. We denote $f(I) \\in \\mathcal{P}$ and $[r \\circ f](I) \\in S$ respectively as a stroke representation and a sketch representation of the image $I$ w.r.t $f$ . To generate a sketch that accurately reflects the given image, we adopt a metric function $\\mathcal{L}: \\mathcal{I} \\times S \\to \\mathbb{R}$ that measures the distance between the image and the sketch.", + "bbox": [ + 496, + 431, + 892, + 627 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Definition 1. We denote $S_{I} = \\arg \\min_{S\\in \\mathcal{S}}\\mathcal{L}(I,S)$ as an optimal sketch representation of $I$ .", + "bbox": [ + 496, + 633, + 890, + 664 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Geometry-aware representation. We denote $\\mathcal{G}$ as a group of geometric transformations that acts on points in $\\Omega$ (see Appendix E for definitions). For example, $\\mathcal{G}$ could be a group of translation or rotation. $\\rho$ is a group representation of $g\\in \\mathcal{G}$ such that $\\rho (g)$ is a linear operator which acts on $\\mathcal{I}$ , i.e., $[ \\rho (g)I ] ( u ) = I ( g ^ { - 1 } u )$ for $u\\in \\Omega$", + "bbox": [ + 496, + 670, + 890, + 762 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Definition 2. $f(I)$ is a geometry-aware representation of $I$ with respect to $\\mathcal{G}$ if there exists a group representation $\\rho'$ such that $f(\\rho(g)I) = \\rho'(g)f(I)$ for $\\forall I \\in \\mathcal{I}$ and $\\forall g \\in \\mathcal{G}$ .", + "bbox": [ + 496, + 767, + 893, + 814 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this case, we say $f$ is a $\\mathcal{G}$ -equivariant map, and the symmetry of $\\mathcal{G}$ is preserved by $f$ . For example, a convolution operator is a translation-equivariant map since the feature of the shifted image is equal to the shifted feature of", + "bbox": [ + 496, + 819, + 893, + 878 + ], + "page_idx": 2 + }, + { + "type": "page_footnote", + "text": "See [3] for the extensive review.", + "bbox": [ + 517, + 886, + 696, + 898 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "23317", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/e8ce89e563b6225adcd168ef774be80bae3e9b4f72a518784d8868d6538ec32c.jpg", + "image_caption": [ + "Figure 3. Visualization of the overall architecture of LBS. (a) A CNN-based encoder extracts the feature of the image. (b) Initial strokes are updated repeatedly with a stroke generator based on a Transformer decoder. For the progressive optimization process, intermediate strokes are extracted from each intermediate layer. (c) The rasterized sketch and stroke embedding $z_{h}$ are generated from the strokes. Features derived from the CNN encoder, strokes, and stroke embedding are combined to form the final representation, $z_{LBS+}$ ." + ], + "image_footnote": [], + "bbox": [ + 101, + 88, + 861, + 305 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "the original image. In other words, the convolution operator preserves the symmetry of the translation and produces a geometry-aware representation with respect to it.", + "bbox": [ + 75, + 383, + 470, + 429 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Geometry-aware representations by sketching", + "text_level": 1, + "bbox": [ + 76, + 436, + 465, + 452 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We now show that stroke representation is a geometry-aware representation with respect to arbitrary affine transformations. Refer to Appendix E for detailed proofs.", + "bbox": [ + 75, + 459, + 468, + 506 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Proposition 1. If $\\mathcal{L}(\\rho(g)I, \\rho(g)S) = \\lambda(g)\\mathcal{L}(I, S)$ where $\\lambda : \\mathcal{G} \\to \\mathbb{R}^+$ exists, and there exists a unique $f^*$ such that $[r \\circ f^*](I) = S_I$ for $\\forall I \\in \\mathcal{I}$ , then $f^*(I)$ is a geometry-aware representation w.r.t. affine transformations $\\mathcal{A}$ .", + "bbox": [ + 76, + 510, + 470, + 571 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Prop. 1 states the conditions for $f$ to be an $\\mathcal{A}$ -equivariant map. Therefore, by designing stroke representations to be injective for $r$ , and optimizing $f$ to minimize $\\mathcal{L}$ subject to the conditions outlined in Prop. 1, $f$ generates a geometry-aware representation with respect to arbitrary affine transformations. In the next section, we propose an architecture and a loss function that satisfy these conditions.", + "bbox": [ + 75, + 575, + 468, + 681 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Method", + "text_level": 1, + "bbox": [ + 76, + 694, + 168, + 709 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We describe our model LBS, which provides geometry-aware representations from strokes by learning to generate a sketch in a short inference time without using a sketch dataset. We introduce an objective function and techniques for training LBS. We then propose a stroke embedding network that aggregates information of whole strokes. Hereafter, we use the terms \"sketch\" and \"image\" to denote realized sketch $S(\\Omega)$ and realized image $I(\\Omega)$ for simplicity.", + "bbox": [ + 75, + 719, + 468, + 840 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Learning by Sketching (LBS)", + "text_level": 1, + "bbox": [ + 76, + 847, + 338, + 863 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "LBS aims to generate a set of strokes to sketch the image and extract geometric information with color for down-", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "stream tasks. To achieve the goal, we design a stroke generator by referring to Transformer-based sketch generation models [48,60].", + "bbox": [ + 496, + 383, + 890, + 429 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Architecture. As shown in Fig. 3, LBS generates a set of strokes from trainable parameters, which are denoted as initial strokes. Our stroke generator uses Transformer decoder layers and incorporates image features from a CNN encoder (ResNet18 is used in this paper). Then, 2-layer MLP decoders decode a set of $n$ strokes from the output of the Transformer decoder. Each stroke contains four control points that parameterize a cubic Bezier curve, as well as color and thickness information. The sketch of an image is then created by rasterizing the generated set of strokes using a differentiable rasterizer [53]. For a detailed description of our architecture, please refer to Appendix C.", + "bbox": [ + 496, + 429, + 892, + 611 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Representation of LBS. The primary output of LBS is a set of strokes $\\pmb{p}$ , and a geometry-aware representation is obtained by using the flattened vector of the strokes $z_{p} = (p^{(1)},\\dots,p^{(n)})$ . To complement information that may not be encoded with strokes such as texture, we concatenate $z_{p}$ with the image features $z_{e}$ from the CNN encoder with global average pooling. The resulting concatenated representation is denoted as $z_{LBS}$ . In addition, we can combine this with representation $z_{h}$ that aggregates the entire stroke, the result of which we denote as $z_{LBS+}$ . Further details can be found in Sec. 4.4. The final representation space of LBS is as follows:", + "bbox": [ + 496, + 611, + 893, + 790 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nz _ {L B S} = \\left(z _ {e}, z _ {p}\\right), \\quad z _ {L B S +} = \\left(z _ {e}, z _ {p}, z _ {h}\\right). \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 553, + 804, + 890, + 821 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. CLIP-based perceptual loss function", + "text_level": 1, + "bbox": [ + 500, + 832, + 815, + 848 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As discussed in Sec. 3.2, proper $\\mathcal{L}$ must be given to train a geometry-aware representation of an image. To this end, we adopt CLIP-based perceptual loss to measure the sim", + "bbox": [ + 500, + 854, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "23318", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/659d2d001fb14f4c82237891847c7c65030ece67e44ccedbc8d278b716f3c0fc.jpg", + "image_caption": [ + "Figure 4. Visualization of the progressive optimization process. Strokes initialized from the saliency map are optimized using the gradient of $\\mathcal{L}_{\\text{percept}}$ until convergence and stored in a total of $L$ intermediate steps denoted by $\\pmb{p}_{gt,l}$ . Then, the stroke generator is trained through $\\mathcal{L}_{\\text{guide}}$ to progressively predict each intermediate stroke $\\pmb{p}_l$ from $\\pmb{p}_{gt,l}$ ." + ], + "image_footnote": [], + "bbox": [ + 81, + 88, + 457, + 256 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "ilarity between the sketch and the input image in terms of both geometric and semantic differences [68]. To generate a sketch that is semantically similar to the input image, it should minimize the distance on the embedding space of the CLIP model $f_{C}$ as follows:", + "bbox": [ + 75, + 369, + 470, + 445 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {s e m a n t i c}} = \\sum_ {A \\in \\mathcal {A}} \\phi (A (I), A (S)), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 158, + 455, + 468, + 488 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{A}$ is the group of affine transformations and $\\phi$ is the cosine similarity of the CLIP embeddings, i.e., $\\phi (x,y) = \\cos (f_C(x),f_C(y))$ . In addition, it compares low-level features of the sketch and the input image to estimate the geometric similarity as follows:", + "bbox": [ + 75, + 500, + 468, + 575 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {g e o m e t r i c}} = \\sum_ {A \\in \\mathcal {A}} \\sum_ {i} \\phi_ {i} (A (I), A (S)), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 140, + 585, + 468, + 619 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\phi_{i}$ is the $\\mathcal{L}_2$ distance of the embeddings from the $i$ -th intermediate layer of the CLIP model, i.e., $\\phi_{i}(x,y) = \\| f_{C,i}(x) - f_{C,i}(y)\\|_{2}^{2}$ . Specifically, we used $i\\in \\{3,4\\}$ with the ResNet101 CLIP model, proposed as [68]. The final perceptual loss is as follows:", + "bbox": [ + 76, + 628, + 468, + 705 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {p e r c e p t}} = \\mathcal {L} _ {\\text {g e o m e t r i c}} + \\lambda_ {s} \\cdot \\mathcal {L} _ {\\text {s e m a n t i c}}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 137, + 718, + 468, + 734 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "with $\\lambda_{s} = 0.1$ as a hyperparameter.", + "bbox": [ + 76, + 746, + 313, + 762 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Training with progressive optimization process", + "text_level": 1, + "bbox": [ + 76, + 771, + 468, + 787 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Abstracting an image into a sketch requires high-level reasoning, and predicting the corresponding stroke parameters in a single inference step is a delicate process. Although CLIPasso [68] addresses these problems via an optimization-based approach, its time-consuming properties ( $\\sim 2$ min per image) make it impractical as a representation. Moreover, as CLIPasso reported that the changes", + "bbox": [ + 75, + 795, + 470, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "in initial strokes significantly impacted the final results, directly optimizing each stroke through the optimizer for thousands of steps leads to highly variable results and numerical instability.", + "bbox": [ + 496, + 90, + 890, + 151 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To generate a stable representation within a single inference step, we modify the optimization-based approach of CLIPasso and utilize it as desirable guidance for the stroke generator, which we call the guidance stroke and denote as $\\pmb{p}_{gt}$ . To ensure high-quality sketch generation, each intermediate layer of the stroke generator is guided by strokes obtained at the corresponding intermediate step of the optimization process instead of relying solely on the final outcome. This process, depicted in Fig. 4, involves progressively updating strokes from the previous layer, which can be modeled by residual blocks from the Transformer architecture. By decomposing the prediction of the entire optimization process into predicting changes in relatively short intervals for each intermediate layer, our approach leads to better-quality sketches.", + "bbox": [ + 496, + 152, + 892, + 377 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "However, the process through which CLIPasso initializes strokes via stochastic sampling from the saliency map results in unstable outcomes. To address this issue, we select initialized strokes deterministically by selecting the most salient regions from the saliency map in a greedy manner. The color of the stroke is determined during the initialization step by referencing the corresponding region in the original image. More details are described in Appendix A.", + "bbox": [ + 496, + 378, + 890, + 498 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To ensure that the guidance loss is invariant to the permutation of the order of each stroke, we use the Hungarian algorithm [41] which is widely used for the assignment problem. The guidance loss is as follows:", + "bbox": [ + 496, + 500, + 890, + 559 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {g u i d e}} = \\sum_ {l = 1} ^ {L} \\min _ {\\sigma} \\sum_ {i = 1} ^ {n} \\mathcal {L} _ {1} \\left(p _ {g t, l} ^ {(i)}, p _ {l} ^ {(\\sigma (i))}\\right), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 560, + 566, + 890, + 609 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\sigma$ is a permutation of the stroke index, and $p_l^{(i)}$ is the $i$ -th decoded stroke from the $l$ -th intermediate layer with $L$ layers in total. $\\mathcal{L}_1$ is the L1 distance, and $p_{gt,l}^{(i)}$ is the guidance stroke corresponding to $p_l^{(\\sigma(i))}$ .", + "bbox": [ + 498, + 619, + 890, + 689 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.4. Stroke embedding network", + "text_level": 1, + "bbox": [ + 500, + 696, + 745, + 712 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As strokes primarily express localized and fine-grained details, they can be less suitable for representing coarse-grained information. To address this, we offer an additional representation that combines full strokes through a stroke embedding network. Stroke embedding network $h: \\mathcal{P} \\to \\mathcal{Z}_h$ maps the set of $n$ strokes into embedding space $\\mathcal{Z}_h$ . Since the rasterized sketch is invariant to the stroke indices (except for contact point between strokes), we followed the permutation invariant model from DeepSets [80] to generate stroke embedding. The choice of the loss function $\\mathcal{L}_{embed}$ to train $z_h \\in \\mathcal{Z}_h$ is unconstrained (e.g., Cross-Entropy or InfoNCE loss in our paper). During the training", + "bbox": [ + 496, + 719, + 892, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "23319", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "phase, the gradient from $h$ is also passed to $f$ to capture coarse-grained information.", + "bbox": [ + 75, + 90, + 468, + 119 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The final objective is as follows:", + "bbox": [ + 96, + 121, + 313, + 136 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {L B S} = \\mathcal {L} _ {\\text {p e r c e p t}} + \\lambda_ {g} \\cdot \\mathcal {L} _ {\\text {g u i d e}} + \\lambda_ {e} \\cdot \\mathcal {L} _ {\\text {e m b e d}}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 104, + 148, + 468, + 167 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\lambda_{g}$ and $\\lambda_{e}$ are hyperparameters (for specific values, refer to Appendix C).", + "bbox": [ + 75, + 178, + 468, + 209 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 76, + 223, + 209, + 239 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Research questions and task designs", + "text_level": 1, + "bbox": [ + 76, + 248, + 390, + 265 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We investigate the effectiveness and generalizability of our approach by designing multiple research questions, as well as corresponding downstream tasks for each question. Detailed information about each experimental setup is described in Appendix B.", + "bbox": [ + 75, + 271, + 468, + 348 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "RQ1. Effects of equivariance: What is the benefit of equivariant representation, and does LBS achieve it?", + "text_level": 1, + "bbox": [ + 75, + 349, + 468, + 380 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "From the definition of equivariance, we expect that an equivariant model with respect to geometric transformation would have generalization capability for augmented images with transformation. To verify this, we conduct experiments on the Rotated MNIST (rotMNIST) dataset [22], which consists of rotated images from the MNIST dataset. We rotate images by $30^{\\circ}$ and $45^{\\circ}$ for training and classify the digit of images rotated by $0^{\\circ}$ and $90^{\\circ}$ to evaluate whether LBS generalizes the information from the training domain to the test domain. To verify that our model satisfies equivariance outside the training domain, we classify the rotation and reflection between an original image and the same image rotated with an interval of $90^{\\circ}$ and horizontally flipped.", + "bbox": [ + 75, + 381, + 468, + 577 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "RQ2. Effects on geometric primitives and concepts: How well does LBS represent geometric primitives and understand their conceptual relationships?", + "text_level": 1, + "bbox": [ + 75, + 580, + 468, + 625 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To evaluate whether LBS is suitable for representing geometric primitives and concepts, we perform a classification task on the Geoclidean dataset [29]. The Geoclidean dataset consists of realized images from a concept of Euclidean geometry, e.g., black parallel lines on a white background. Geoclidean is divided into two categories: Geoclidean-Elements and Geoclidean-Constraints, visualized in Fig. 7 on Appendix B. By providing a limited training set consisting of only 10 images per concept, we evaluate whether LBS can effectively learn the high-level relationships between each primitive and generalize them across different examples by classifying the concept of the test image.", + "bbox": [ + 75, + 626, + 468, + 806 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "RQ3. Local geometric information and spatial reasoning: How effectively does LBS reflect local geometric information and extend it to spatial reasoning tasks?", + "text_level": 1, + "bbox": [ + 75, + 809, + 468, + 854 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We validate whether LBS can reflect the local geometric information of each object in a synthetic photo dataset consisting of multiple objects, using the CLEVR dataset [34].", + "bbox": [ + 75, + 854, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/b799f4139f9d108e57e75e730c277dfca4599b8544ec54d5b6dccf3e526a49ba.jpg", + "table_caption": [ + "Table 1. Quantitative results of LBS and the baselines evaluated on the corresponding tasks on the rotMNIST and Geoclidean." + ], + "table_footnote": [], + "table_body": "
La-\nbelMethodrotMNIST (30°, 45°)Geoclidean
0°, 90°RotationConstraintsElements
✓CE62.72±1.8973.14±0.3553.89±1.5870.57±4.29
SupCon [38]65.25±1.0573.37±0.2042.41±3.1655.83±4.28
LtD-diff [54]60.09±1.1628.91±2.1557.26±2.1969.47±2.11
E(2)-CNN [73]85.12±0.1777.00±0.3971.03±1.9469.28±1.46
LBS (CE)65.00±3.3275.81±0.3050.01±1.5881.06±3.14
XSimCLR [9]47.66±0.4172.96±0.8432.04±0.6465.14±4.11
β-TCVAE [8]37.84±1.0660.14±0.3217.18±1.3533.82±1.64
GeoSSL [55]--18.66±3.3333.47±2.80
HoG [14]25.4264.9423.8252.05
LBS47.31±2.5370.02±0.6447.43±1.3481.34±0.16
", + "bbox": [ + 501, + 128, + 890, + 287 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We train our model with very limited descriptions, where the label for the entire scene is provided as the rightmost object or without any descriptions at all. We validate the effectiveness of our representation by evaluating its ability to successfully classify attributes that are not provided as labels, such as determining the color of the leftmost object. Additionally, we test its ability to perform simple spatial reasoning, such as shifting the rightmost object and inferring the attribute of the current rightmost object.", + "bbox": [ + 496, + 301, + 890, + 438 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "RQ4. Domain transfer: Can the geometric concepts of LBS trained in a specific domain be extended to other domains?", + "text_level": 1, + "bbox": [ + 498, + 441, + 893, + 484 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To investigate whether the learned representation within a specific image domain provides meaningful geometric information across other domains, we evaluate the model by shifting the distribution from the STL-10 [11] dataset to CLEVR and vice versa. Evaluation in the STL-10 dataset is conducted through object classification.", + "bbox": [ + 496, + 486, + 890, + 577 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "RQ5. Traditional sketch tasks: Does geometry-aware representation from LBS help in traditional FG-SBIR tasks?", + "text_level": 1, + "bbox": [ + 498, + 580, + 890, + 609 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We assess the impact of geometry-aware representations acquired by LBS on a conventional sketch task by evaluating them with the fine-grained sketch-based image retrieval (FG-SBIR) task on the QMUL-ShoeV2 Dataset [78]. The aim of FG-SBIR is to match a given sketch of a shoe to its corresponding photo image. Since geometric information is essential for distinguishing each shoe, we investigate whether leveraging representations from LBS can improve performance on the FG-SBIR task.", + "bbox": [ + 496, + 609, + 890, + 744 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Experimental setup", + "text_level": 1, + "bbox": [ + 500, + 756, + 687, + 772 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation details. As samples from rotMNIST and Geoclidean can be directly represented with a few strokes, we replace $\\mathcal{L}_{\\text {percept }}$ and $\\mathcal{L}_{\\text {guide }}$ with $\\mathcal{L}_1$ loss, which does not rely on a pre-trained CLIP model. For the STL-10 dataset, providing mask information for the background with U2-Net [57] improves the quality of generated sketches. For $\\mathcal{L}_{\\text {embed }}$ , we use Cross-Entropy loss for supervised training which we denote as LBS (CE) in Tab. 1, 2 and", + "bbox": [ + 496, + 779, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "23320", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/13a09efb8eb5a5fce085986016988eb37582f2c4e3f3d774de6f909dca529205.jpg", + "table_caption": [ + "Table 2. Quantitative results on CLEVR dataset for labeled and unlabeled settings and for CLIP and HoG features. RC, LC, BC refer to inferring the color of the rightmost, leftmost, bottommost object, and Size, Shape, Material refer to inferring the size, shape, material of the rightmost object, respectively. Third refers to inferring the color of the third object from the right, and Shift refers to predicting the color of the rightmost object after shifting the initial rightmost object to the left by 0.15 times the image width." + ], + "table_footnote": [], + "table_body": "
LabelMethodRCLCBCSizeShapeMaterialThirdShift
✓CE98.71±0.1076.72±0.8676.02±0.9092.51±0.4049.97±0.2964.38±1.9040.66±0.2062.06±1.62
SupCon [38]98.75±0.0863.82±2.3666.04±2.6591.88±0.3749.15±0.8559.20±0.5737.93±0.2756.05±2.56
LtD-diff [54]62.29±0.4814.01±0.4215.84±0.4363.98±3.3843.96±3.0554.47±0.4516.47±0.5917.21±0.29
E(2)-CNN [73]98.50±0.1070.10±1.1573.51±2.5089.84±0.4645.85±0.9363.05±0.5941.95±0.1859.29±0.91
LBS (CE)97.49±0.2281.79±0.2784.09±0.8493.22±0.2970.03±0.6886.84±0.5438.23±0.2551.56±0.16
×SimCLR [9]60.61±1.2463.89±2.3563.77±2.2983.35±0.6041.95±0.3351.66±0.2433.42±0.5543.05±0.55
E(2)-CNN [73]53.50±7.3054.60±7.3455.52±7.6083.52±1.5642.06±1.1253.04±2.8130.74±2.8438.03±4.44
β-TCVAE [8]17.09±0.2017.50±0.3320.04±0.7171.27±0.1036.30±0.1056.11±0.1315.38±0.1916.35±0.18
GeoSSL [55]20.16±0.6320.54±0.8721.61±0.6773.79±0.7844.08±1.1054.54±2.9415.39±0.1616.94±0.34
DefGrid [21]73.81±0.9173.96±1.0273.38±0.8081.50±0.2246.34±0.7768.65±1.1724.90±0.2736.28±0.13
LBS84.31±0.0880.47±0.7883.00±0.3992.66±0.4170.01±0.5385.52±0.4337.41±0.2949.32±0.17
CLIP [59]37.3939.154.9877.5166.9172.6634.7534.80
HoG [14]56.8349.6958.6981.7361.1468.3824.2833.25
", + "bbox": [ + 116, + 155, + 849, + 359 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/e7641237a9cb8482a098b16f8b1369b47a58d52a0ea783d84622f43c96e67114.jpg", + "table_caption": [ + "Table 3. Quantitative results of models trained on STL-10 dataset and evaluated on CLEVR dataset." + ], + "table_footnote": [], + "table_body": "
DatasetMethodRCLCBCSizeShapeMaterialThirdShift
STL-10↓CLEVRLtD [54]18.70±0.0219.15±0.7721.69±1.0573.13±3.2147.88±1.1359.11±2.3416.47±0.5917.21±0.29
SimCLR [9]26.97±0.2826.26±0.8838.88±0.1982.33±0.6456.88±1.2377.39±0.3523.45±0.3524.95±0.17
E(2)-CNN [73]26.82±2.2325.40±1.2039.30±2.8079.48±0.7153.54±0.8472.18±0.3423.35±1.0124.80±1.08
β-TCVAE [8]17.04±0.7618.46±2.3618.88±1.1471.32±0.6737.14±0.1256.81±0.2615.63±1.3516.43±0.38
GeoSSL [55]14.41±0.5514.73±0.1114.37±0.6677.47±5.1748.10±1.9055.63±2.8613.71±0.4513.63±0.13
DefGrid [21]66.74±1.1068.60±0.0868.35±0.8278.97±0.2940.92±0.4462.98±1.3123.48±0.4933.07±0.52
LBS53.87±2.7253.85±2.2061.84±2.2392.46±0.6259.52±0.4580.06±1.2930.75±0.4139.95±1.15
", + "bbox": [ + 117, + 398, + 849, + 513 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/f3348e18ed0ba3afb631e652ce883977e6ba86807ffb5a473fc5d773aa6096ab.jpg", + "table_caption": [ + "Table 4. Quantitative results of models trained on CLEVR dataset and evaluated on STL-10 dataset classification." + ], + "table_footnote": [], + "table_body": "
DatasetLabeledUnlabeled
MethodAccuracyMethodAccuracy
CLEVR↓STL-10CE46.15±0.12SimCLR [9]41.68±0.05
SupCon [38]43.41±0.36β-TCVAE [8]27.35±0.38
LtD-diff [54]50.81±0.67GeoSSL [55]35.93±0.96
E(2)-CNN [73]45.19±0.84E(2)-CNN [73]38.50±0.49
LBS (CE)56.48±0.89DefGrid [21]33.13±0.17
LBS55.35±0.18
", + "bbox": [ + 80, + 569, + 467, + 679 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4. For the unlabeled setting, the model is trained without $\\mathcal{L}_{embed}$ and is denoted LBS with no parentheses. For evaluation, we use $z_{LBS+}$ for LBS (CE), and $z_{LBS}$ for LBS. All evaluations are performed with the common protocol of linear classification. For more detailed information on our implementation, please refer to Appendix C.", + "bbox": [ + 75, + 694, + 468, + 784 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Baselines. We compare our models with:", + "bbox": [ + 76, + 785, + 352, + 800 + ], + "page_idx": 6 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Models which only use image encoder: trained with Cross-Entropy, SimCLR [9], or SupCon loss [38].", + "- Equivariance models: E(2)-Equivariant Steerable CNNs (E(2)-CNN) [73], and work by Novotny et al., denoted as GeoSSL [55].", + "- Disentanglement model: $\\beta$ -TCVAE [8]." + ], + "bbox": [ + 94, + 806, + 467, + 900 + ], + "page_idx": 6 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Sketch model for communication between agents: Learning to Draw (LtD) [54]", + "- Grid-based superpixel model: DefGrid [21]", + "- Handcrafted feature descriptor: HoG [14].", + "- Pre-trained CLIP model used for training LBS." + ], + "bbox": [ + 517, + 532, + 888, + 608 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Results and analysis", + "text_level": 1, + "bbox": [ + 500, + 618, + 691, + 633 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Analysis on RQ1 and RQ2: Tab. 1 shows the experimental results for RQ1 and RQ2, which can be summarized as: (a) Providing a strong inductive bias for equivariance, as shown in the case of E(2)-CNN, leads to good performance on the tasks of RQ1. While LBS outperformed LtD-diff, which also utilizes a sketch-based approach, it requires additional validation and refinement. (b) For RQ2, LBS performs substantially better than the other baselines except for the supervised setting on Geoclidean-Constraints, showing that it successfully captures geometric concepts. In particular, Geoclidean-Elements perform better when trained without labels. (c) Disentanglement methods and handcrafted features offer less informative features for both tasks.", + "bbox": [ + 496, + 641, + 890, + 835 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Analysis on RQ3: Tab. 2 summarizes the experiments conducted on the CLEVR dataset, demonstrating that LBS provides valuable information for tasks of RQ3. The key observations from Tab. 2 are: (a) While the baselines in the", + "bbox": [ + 496, + 839, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "23321", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/2c9730bb69dde4ea1876181663c87565fcf3a3b58ff158abbeefd54405121110.jpg", + "table_caption": [ + "Table 5. Top-1 and Top-10 accuracy on QMUL-Shoe-v2 dataset, using Triplet Loss for $\\mathcal{L}_{embed}$ in LBS." + ], + "table_footnote": [], + "table_body": "
MethodRepTop-1Top-10
LBS (Triplet)zLBS+40.8±4.1988.3±1.76
ze30.8±3.8977.8±3.89
Tripletze32.5±1.7380.0±4.36
", + "bbox": [ + 133, + 125, + 406, + 190 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "supervised setting struggle to generalize on unlearned attributes, LBS (CE) can provide more general information. (b) The results of LBS show a larger performance gap in the unlabeled setting, with its performance being almost as good as LBS (CE). (c) Embeddings from pre-trained CLIP perform less effectively than unlabeled baselines, such as SimCLR, on tasks related to local geometry. Also, handcrafted features yielded limited effectiveness. (d) Methods that focus on preserving global transformations and disentanglement are not effective in environments of RQ3.", + "bbox": [ + 75, + 217, + 470, + 368 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Analysis on RQ4: Tabs. 3 and 4 summarize the results for shifting domains from STL-10 to CLEVR, and vice versa. As shown in Fig. 11 on Appendix I, LBS trained on STL-10 can successfully describe scenes from CLEVR, while LBS trained on CLEVR can abstractly depict natural images from STL-10, leading to substantially high classification accuracy. These results indicate that learning geometric information, such as position and curvature, by sketching salient parts of a scene successfully induces learning of general features across domains. Furthermore, LtD-diff, which also utilizes a sketch-based approach, demonstrated good performance in transferring CLEVR to STL-10.", + "bbox": [ + 75, + 375, + 468, + 556 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Analysis on RQ5: Tab. 5 presents the results for the FG-SBIR task. Compared to the baseline trained without sketching, LBS can accurately predict the corresponding shoe during the test phase. The huge drop in performance upon removing strokes and stroke embedding from $z_{LBS+}$ indicates that the geometry-aware representation provided by LBS is also valuable for traditional sketch tasks.", + "bbox": [ + 75, + 563, + 468, + 670 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.4. Comparisons with stroke-based methods", + "text_level": 1, + "bbox": [ + 76, + 691, + 424, + 708 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Tab. 6 compares LBS to other stroke-based generation methods on STL-10 dataset, and Fig. 5 visualizes the results of each method. The evaluation is based solely on strokes, and LBSonly uses $z_{p}$ as a representation. LBS ( $\\mathcal{L}_{\\text{percept}}$ ) achieved superior results compared to LBS ( $\\mathcal{L}_1$ ) and the Paint Transformer [48] based on $\\mathcal{L}_1$ loss. We also compare our results to CLIPasso modified to use our deterministic initialization process, suggesting that strokes generated from CLIPasso may not be suitable as a representation. LtD-diff, which generates sketches to solve a communication game, often omits important geometric and color information, resulting in low performance.", + "bbox": [ + 75, + 719, + 470, + 901 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/4283d4e975956dc976373604f5d21b3060104e09069ac69c7c257189391fed2e.jpg", + "table_caption": [ + "Table 6. Comparison between stroke-based generation methods." + ], + "table_footnote": [], + "table_body": "
RCBCSizeShapeMaterial
LtD-diff [54]18.7021.6973.1347.8859.11
Paint [48]51.9660.4077.3544.3070.02
CLIPasso [68]12.5513.5555.3535.4050.00
LBS (L1)34.4357.8178.3240.9961.59
LBS (Lpercept)55.1560.6390.1451.2376.16
", + "bbox": [ + 516, + 109, + 869, + 200 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/40b28f7b4f829fc9c4f298b97fdd99fdcb5a8747450c02c5237e6d380a161c75.jpg", + "image_caption": [ + "Image" + ], + "image_footnote": [], + "bbox": [ + 550, + 215, + 638, + 284 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/5079b595f71bd5bf05ba88d1122beef86c26ba739a0daa37438fbfeab8294b6e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 651, + 215, + 736, + 282 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c1e78f89ce9b879d04293557e74151e33a2917b704e58a2601b8a87fa160227b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 751, + 215, + 838, + 282 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/294718abd7aa9d3b0a1dfb5ef008de731d41fae507cd82a0a93e14066a6b0d0e.jpg", + "image_caption": [ + "CLIPasso", + "Figure 5. Comparisons to other stroke-based methods. LBS encodes both the geometric and semantic information." + ], + "image_footnote": [], + "bbox": [ + 550, + 295, + 637, + 362 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f6ca962c5db510c9b03283a6e47584f237198c2f20702026d3e5348aef5e991e.jpg", + "image_caption": [ + "LBS $(\\mathcal{L}_{percept})$", + "LtD-diff" + ], + "image_footnote": [], + "bbox": [ + 651, + 295, + 736, + 362 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6aa3c1ddf294f05add07b2e376097960a930fe16ca6a354dbd988b5adcf81a84.jpg", + "image_caption": [ + "LBS $(\\mathcal{L}_1)$", + "Paint Transformer" + ], + "image_footnote": [], + "bbox": [ + 751, + 295, + 838, + 362 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 422, + 617, + 436 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We propose a novel representation learning perspective through sketching, a visual expression that retains geometric information. By considering the mathematical concept of equivariance, we provide a formal definition of sketch and stroke, and prove that strokes can preserve the information of arbitrary affine transformations. Our sketch generation model, LBS, minimizes CLIP-based perceptual loss and supports the idea that sketches can effectively convey geometric information. The experiments shed light on the potential benefits of leveraging the process of sketching to represent high-level geometric information explicitly. These benefits include learning equivariant representations, understanding geometric concepts, improving spatial reasoning abilities, and acquiring general geometric information across different domains.", + "bbox": [ + 496, + 448, + 890, + 674 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Still, there are several limitations to our method. The training process of LBS relies on pre-trained CLIP and optionally U2-Net, and requires generating guidance strokes through a time-consuming optimization-based process. Moreover, while our work has demonstrated the theoretical strengths of sketching in terms of equivariance, a clearer methodology and further experimental analysis are needed to fully achieve this potential. Future work should address these issues and extend the methodology, focusing on scalability and including more complex and realistic tasks.", + "bbox": [ + 496, + 676, + 890, + 828 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement This work was partly supported by the Korean government (2021-0-02068-AIHub/25%, 2021-0-01343-GSAI/25%, 2022-0-00951-LBA/25%, 2022-0-00953-PICA/25%).", + "bbox": [ + 496, + 839, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "23322", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Pablo Arbelaez, Michael Maire, Charless Fowlkes, and Jitendra Malik. Contour detection and hierarchical image segmentation. IEEE Trans. Pattern Anal. Mach. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 15689-15698, 2021. 3" + ], + "bbox": [ + 78, + 90, + 470, + 316 + ], + "page_idx": 11 + }, + { + "type": "page_number", + "text": "23326", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 11 + } +] \ No newline at end of file diff --git a/2023/Learning Geometry-Aware Representations by Sketching/f80a6701-d163-4c1c-a5df-2e5aa49a37e5_model.json b/2023/Learning Geometry-Aware Representations by Sketching/f80a6701-d163-4c1c-a5df-2e5aa49a37e5_model.json new file mode 100644 index 0000000000000000000000000000000000000000..4698df364373ab07a636ca08bbe6076a344d48dc --- /dev/null +++ b/2023/Learning Geometry-Aware Representations by Sketching/f80a6701-d163-4c1c-a5df-2e5aa49a37e5_model.json @@ -0,0 +1,2765 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.198, + 0.131, + 0.773, + 0.154 + ], + "angle": 0, + "content": "Learning Geometry-aware Representations by Sketching" + }, + { + "type": "text", + "bbox": [ + 0.109, + 0.181, + 0.86, + 0.217 + ], + "angle": 0, + "content": "Hyundo Lee, Inwoo Hwang, Hyunsung Go, Won-Seok Choi, Kibeom Kim, Byoung-Tak Zhang AI Institute, Seoul National University" + }, + { + "type": "text", + "bbox": [ + 0.227, + 0.22, + 0.74, + 0.234 + ], + "angle": 0, + "content": "{hdlee, iwhwang, hsgo, wchoi, kbkim, btzhang}@bi.snu.ac.kr" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.269, + 0.314, + 0.285 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.301, + 0.474, + 0.604 + ], + "angle": 0, + "content": "Understanding geometric concepts, such as distance and shape, is essential for understanding the real world and also for many vision tasks. To incorporate such information into a visual representation of a scene, we propose learning to represent the scene by sketching, inspired by human behavior. Our method, coined Learning by Sketching (LBS), learns to convert an image into a set of colored strokes that explicitly incorporate the geometric information of the scene in a single inference step without requiring a sketch dataset. A sketch is then generated from the strokes where CLIP-based perceptual loss maintains a semantic similarity between the sketch and the image. We show theoretically that sketching is equivariant with respect to arbitrary affine transformations and thus provably preserves geometric information. Experimental results show that LBS substantially improves the performance of object attribute classification on the unlabeled CLEVR dataset, domain transfer between CLEVR and STL-10 datasets, and for diverse downstream tasks, confirming that LBS provides rich geometric information." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.633, + 0.21, + 0.649 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.659, + 0.47, + 0.81 + ], + "angle": 0, + "content": "Since geometric principles form the bedrock of our physical world, many real-world scenarios involve geometric concepts such as position, shape, distance, and orientation. For example, grabbing an object requires estimating its shape and relative distance. Understanding geometric concepts is also essential for numerous vision tasks such as image segmentation, visual reasoning, and pose estimation [27]. Thus, it is crucial to learn a visual representation of the image that can preserve such information [76], which we call geometry-aware representation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.471, + 0.903 + ], + "angle": 0, + "content": "However, there is still a challenge in learning geometry-aware representations in a compact way that can be useful for various downstream tasks. Previous approaches have focused on capturing geometric features of an image in a 2D grid structure, using methods such as handcrafted feature extraction [2, 4, 14, 31], segmentation maps [21, 57], or" + }, + { + "type": "image", + "bbox": [ + 0.516, + 0.269, + 0.875, + 0.439 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.448, + 0.895, + 0.519 + ], + "angle": 0, + "content": "Figure 1. Overview of LBS, which aims to generate sketches that accurately reflect the geometric information of an image. A sketch consists of a set of strokes represented by a parameterized vector that specifies curve, color, and thickness. We leverage it as a geometry-aware representation for various downstream tasks." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.538, + 0.892, + 0.704 + ], + "angle": 0, + "content": "convolution features [36, 55]. Although these methods are widely applicable to various domains, they often lack compactness based on a high-level understanding of the scene and tend to prioritize nuisance features such as the background. Another line of work proposes architectures that guarantee to preserve geometric structure [12, 13, 23, 58, 73] or disentangle prominent factors in the data [8, 28, 39, 51]. Although these methods can represent geometric concepts in a compact latent space, they are typically designed to learn features that are specific to a particular domain and often face challenges in generalizing to other domains [64]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.893, + 0.902 + ], + "angle": 0, + "content": "In this study, we present a novel approach to learning geometry-aware representations via sketching. Sketching, which is the process of converting the salient features of an image into a set of color-coded strokes, as illustrated in Figure 1, is the primary means by which humans represent images while preserving their geometry. Our key idea is that sketches can be a compact, high-level representation of an image that accurately reflects geometric information. Sketching requires a high-level understanding of the scene, as it aims to capture the most salient features of the image and abstract them into a limited number of strokes. In addition, a sketch can be represented as a set of parameters by replacing each stroke with parametric curves. Sketch-" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "23315" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.086, + 0.095, + 0.87, + 0.29 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.295, + 0.893, + 0.339 + ], + "angle": 0, + "content": "Figure 2. Examples of how sketches capture essential geometric concepts such as shape, size, orientation, curvature, and local distortion. The control points of each stroke compactly represent the local geometric information of the corresponding region in the sketch. The strokes as a whole maintain the geometric structure of the entire image under various transformations in the image domain." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.357, + 0.47, + 0.463 + ], + "angle": 0, + "content": "ing has also been linked to how people learn geometric concepts [66]. Based on these properties, we directly use strokes as a geometry-aware representation and utilize them for downstream tasks. Under the theoretical framework of geometric deep learning [3], we conduct theoretical analysis to validate the effectiveness of strokes as a representation and prove their ability to preserve affine transformations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.463, + 0.47, + 0.765 + ], + "angle": 0, + "content": "To validate our hypothesis, we introduce Learning by Sketching (LBS), a method that generates abstract sketches coherent with the geometry of an input image. Our model is distinct from existing sketch generation methods as it does not require a sketch dataset for training, which often has limited abstraction or fails to accurately reflect geometric information. Instead, LBS learns to convert an image into a set of colored Bezier curves that explicitly represent the geometric concepts of the input image. To teach the style of sketching, we use perceptual loss based on the CLIP model [59, 68], which measures both semantic and geometric similarities between images and generated sketches. We propose a progressive optimization process that predicts how strokes will be optimized from their initial positions through CLIP-based perceptual loss to generate abstract sketches in a single inference step. As a result, LBS generates a representation that reflects visual understanding in a single inference step, without requiring a sketch dataset. This produces highly explainable representations through sketches, as illustrated in Figure 2." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.47, + 0.901 + ], + "angle": 0, + "content": "We conduct experimental analyses to evaluate the effectiveness of our approach, learning by sketching, by addressing multiple research questions in various downstream tasks, including: (i) describing the relationships between geometric primitives, (ii) demonstrating simple spatial reasoning ability by conveying global and local geometric information, (iii) containing general geometric information shared across different domains, and (iv) improving performance on FG-SBIR, a traditional sketch task." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.356, + 0.637, + 0.372 + ], + "angle": 0, + "content": "2. Related work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.385, + 0.851, + 0.401 + ], + "angle": 0, + "content": "2.1. Geometry-aware representation learning" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.411, + 0.893, + 0.501 + ], + "angle": 0, + "content": "Previous studies that aim to capture geometric information within the data can be categorized into two approaches: Firstly, explicitly capturing the geometric information with features on the image space, and secondly, inducing a compact feature vector that preserves the geometric structure of the data." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.505, + 0.893, + 0.747 + ], + "angle": 0, + "content": "Features on image space. The most straightforward approach to representing geometric structures in images is to establish features directly on the image space, i.e., to define features on the 2D grid structure. Approaches that utilize this method include those that employ traditional edge detection algorithms [4, 35, 74, 75], low-level convolutional features [36, 68], and segmentation maps [49, 57, 61]. However, these features are unsuitable for conversion into compact vector representations for downstream tasks. Alternative approaches include utilizing hand-crafted feature detection algorithms [2, 14, 31, 62], clustering specific areas of an image into superpixels [21, 32], and representing the relationships between specific areas as a graph [15, 65]. Our approach is primarily notable for its ability to capture the most salient image features through an overall understanding of the scene, resulting in a concise representation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Geometric deep learning. Research has also been conducted to develop informative and compact representations that preserve geometric structures in a latent vector space. One representative method is geometric deep learning [3], which involves preserving the geometric properties of an image by learning an invariant (i.e., maintaining the output identically) or an equivariant representation (i.e., there exists an operator acting on the feature space corresponding to the transformations) with respect to geometric transformations. Steerable networks [12, 13, 23, 73] extend the" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "23316" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.304 + ], + "angle": 0, + "content": "translation equivariance of CNNs to a larger group of symmetries and introduce an efficient weight-sharing architecture. However, designing their architecture requires complex analytic solutions, and they are constrained to particular transformations [37]. Another approach is to disentangle factors of variation into distinct latent subspaces [8, 28, 39, 40, 51, 58, 70]. However, these methods face difficulties in handling changing factors of variation [64] and therefore struggle to generalize to arbitrary geometric transformations. Sketching, in contrast to these methods, can naturally ensure equivariance with respect to geometric transformations by being defined on the image space. In Sec. 3 we show that strokes can be equivariant with respect to arbitrary affine transformations." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.316, + 0.322, + 0.332 + ], + "angle": 0, + "content": "2.2. Sketch generation methods" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.34, + 0.47, + 0.446 + ], + "angle": 0, + "content": "Human-drawn sketches are widely used as valuable descriptions in various applications, including image retrieval [16, 47, 78], modeling 3D shapes and surfaces [25, 42, 43, 45], and image editing [33, 56, 69, 71]. Unfortunately, previous works that aim to learn sketching or drawing mostly endeavor to generate artistic works, rather than focusing on its applicability [19, 24, 30, 48, 52, 83]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.447, + 0.473, + 0.704 + ], + "angle": 0, + "content": "Sketch generation models often rely on explicit sketch datasets to follow the style of human drawings [5, 10, 46, 60, 67, 82]. However, many existing datasets are not designed to preserve geometric information [7, 20, 63] or contain sketches without sophisticated image abstraction, resembling simple edge detection [1, 72]. This presents challenges for sketch models to accurately abstract an image while preserving its geometries. Without sketch datasets, stroke-based rendering methods usually minimize the reconstruction loss which is related to the pixel-wise distance, which promotes learning in the style of painting [19, 30, 48, 52, 53, 81, 83]. There have also been studies that attempt to capture the geometric and semantic features of a scene through imitating the style of line drawing [6, 44, 77]. However, these methods require numerous strokes to cover the whole canvas, primarily focusing on the superfluous background instead of salient features." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.473, + 0.902 + ], + "angle": 0, + "content": "Abstract sketches for representation. Only a few works aim to generate sketches for the sake of representing an image with a limited number of strokes. Learning to Draw (LtD) [54] creates a representative sketch of an image and uses it as a communication channel between agents. While it primarily focuses on communicating with a specific receiver, we aim to leverage strokes as a general representation for various downstream tasks. CLIPasso [68] utilizes the capabilities of CLIP [59], a neural network trained on images paired with text, to synthesize abstract sketches by maintaining both semantic and geometric attributes. Generating representations with this method, however, is impractical due to its reliance on an optimization-based approach" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.152 + ], + "angle": 0, + "content": "that is extremely time consuming and numerically unstable. In contrast, our method generates a sketch of an image in a single inference step after training, and is relatively more stable and suitable as a representation." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.164, + 0.742, + 0.181 + ], + "angle": 0, + "content": "3. Mathematical framework" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.189, + 0.892, + 0.326 + ], + "angle": 0, + "content": "In this section, we present our theoretical analysis on how sketches can facilitate geometry-aware representation. We begin with a formal definition of sketch and strokes. We then introduce a mathematical framework based on geometric deep learning, which aims to impose the geometric prior on the learned feature.1 Finally, we show that with a loss function that satisfies certain conditions, strokes can be equivariant with respect to arbitrary affine transformations and thus preserve geometric information." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.333, + 0.75, + 0.348 + ], + "angle": 0, + "content": "3.1. Preliminaries and notations" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.356, + 0.892, + 0.431 + ], + "angle": 0, + "content": "We consider an image \\(I \\in \\mathcal{I}\\) as signals on a physical domain \\(\\Omega\\), which maps pixel coordinates to the \\(C\\) color channels, i.e., \\(I: \\Omega \\to \\mathbb{R}^C\\). Although \\(\\Omega\\) is a 2D grid space for the real image, we assume \\(\\Omega\\) as a homogeneous space, where each border is connected to the opposite side." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.432, + 0.893, + 0.628 + ], + "angle": 0, + "content": "Stroke and sketch. A stroke is a tuple \\( p = (t, c, w) \\) composed of \\( k \\) control points \\( t \\in \\Omega^k \\), color \\( c \\in [0,1]^C \\), and thickness \\( w \\in [0,1] \\) of the Bézier curve. A rendering process \\( r: \\mathcal{P} \\to S(\\subset \\mathcal{I}) \\) converts a set of \\( n \\) strokes \\( \\pmb{p} = \\{p^{(1)}, \\dots, p^{(n)}\\} \\in \\mathcal{P} \\) into the corresponding image (see Appendix D for further details), which we denote as sketch \\( S = r(\\pmb{p}) \\in S \\). Let \\( f: \\mathcal{I} \\to \\mathcal{P} \\) be the embedding function which maps an image to a set of strokes. We denote \\( f(I) \\in \\mathcal{P} \\) and \\( [r \\circ f](I) \\in S \\) respectively as a stroke representation and a sketch representation of the image \\( I \\) w.r.t \\( f \\). To generate a sketch that accurately reflects the given image, we adopt a metric function \\( \\mathcal{L}: \\mathcal{I} \\times S \\to \\mathbb{R} \\) that measures the distance between the image and the sketch." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.634, + 0.892, + 0.665 + ], + "angle": 0, + "content": "Definition 1. We denote \\( S_{I} = \\arg \\min_{S\\in \\mathcal{S}}\\mathcal{L}(I,S) \\) as an optimal sketch representation of \\( I \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.671, + 0.892, + 0.763 + ], + "angle": 0, + "content": "Geometry-aware representation. We denote \\(\\mathcal{G}\\) as a group of geometric transformations that acts on points in \\(\\Omega\\) (see Appendix E for definitions). For example, \\(\\mathcal{G}\\) could be a group of translation or rotation. \\(\\rho\\) is a group representation of \\(g\\in \\mathcal{G}\\) such that \\(\\rho (g)\\) is a linear operator which acts on \\(\\mathcal{I}\\), i.e., \\([ \\rho (g)I ] ( u ) = I ( g ^ { - 1 } u )\\) for \\(u\\in \\Omega\\)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.768, + 0.895, + 0.815 + ], + "angle": 0, + "content": "Definition 2. \\( f(I) \\) is a geometry-aware representation of \\( I \\) with respect to \\( \\mathcal{G} \\) if there exists a group representation \\( \\rho' \\) such that \\( f(\\rho(g)I) = \\rho'(g)f(I) \\) for \\( \\forall I \\in \\mathcal{I} \\) and \\( \\forall g \\in \\mathcal{G} \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.82, + 0.895, + 0.88 + ], + "angle": 0, + "content": "In this case, we say \\( f \\) is a \\( \\mathcal{G} \\)-equivariant map, and the symmetry of \\( \\mathcal{G} \\) is preserved by \\( f \\). For example, a convolution operator is a translation-equivariant map since the feature of the shifted image is equal to the shifted feature of" + }, + { + "type": "page_footnote", + "bbox": [ + 0.518, + 0.887, + 0.697, + 0.9 + ], + "angle": 0, + "content": "See [3] for the extensive review." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "23317" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.102, + 0.089, + 0.862, + 0.306 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.312, + 0.895, + 0.37 + ], + "angle": 0, + "content": "Figure 3. Visualization of the overall architecture of LBS. (a) A CNN-based encoder extracts the feature of the image. (b) Initial strokes are updated repeatedly with a stroke generator based on a Transformer decoder. For the progressive optimization process, intermediate strokes are extracted from each intermediate layer. (c) The rasterized sketch and stroke embedding \\( z_{h} \\) are generated from the strokes. Features derived from the CNN encoder, strokes, and stroke embedding are combined to form the final representation, \\( z_{LBS+} \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.385, + 0.471, + 0.43 + ], + "angle": 0, + "content": "the original image. In other words, the convolution operator preserves the symmetry of the translation and produces a geometry-aware representation with respect to it." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.437, + 0.467, + 0.453 + ], + "angle": 0, + "content": "3.2. Geometry-aware representations by sketching" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.46, + 0.47, + 0.507 + ], + "angle": 0, + "content": "We now show that stroke representation is a geometry-aware representation with respect to arbitrary affine transformations. Refer to Appendix E for detailed proofs." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.511, + 0.471, + 0.573 + ], + "angle": 0, + "content": "Proposition 1. If \\(\\mathcal{L}(\\rho(g)I, \\rho(g)S) = \\lambda(g)\\mathcal{L}(I, S)\\) where \\(\\lambda : \\mathcal{G} \\to \\mathbb{R}^+\\) exists, and there exists a unique \\(f^*\\) such that \\([r \\circ f^*](I) = S_I\\) for \\(\\forall I \\in \\mathcal{I}\\), then \\(f^*(I)\\) is a geometry-aware representation w.r.t. affine transformations \\(\\mathcal{A}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.577, + 0.47, + 0.683 + ], + "angle": 0, + "content": "Prop. 1 states the conditions for \\( f \\) to be an \\( \\mathcal{A} \\)-equivariant map. Therefore, by designing stroke representations to be injective for \\( r \\), and optimizing \\( f \\) to minimize \\( \\mathcal{L} \\) subject to the conditions outlined in Prop. 1, \\( f \\) generates a geometry-aware representation with respect to arbitrary affine transformations. In the next section, we propose an architecture and a loss function that satisfy these conditions." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.695, + 0.169, + 0.71 + ], + "angle": 0, + "content": "4. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.469, + 0.841 + ], + "angle": 0, + "content": "We describe our model LBS, which provides geometry-aware representations from strokes by learning to generate a sketch in a short inference time without using a sketch dataset. We introduce an objective function and techniques for training LBS. We then propose a stroke embedding network that aggregates information of whole strokes. Hereafter, we use the terms \"sketch\" and \"image\" to denote realized sketch \\( S(\\Omega) \\) and realized image \\( I(\\Omega) \\) for simplicity." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.848, + 0.339, + 0.864 + ], + "angle": 0, + "content": "4.1. Learning by Sketching (LBS)" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.47, + 0.901 + ], + "angle": 0, + "content": "LBS aims to generate a set of strokes to sketch the image and extract geometric information with color for down-" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.385, + 0.892, + 0.43 + ], + "angle": 0, + "content": "stream tasks. To achieve the goal, we design a stroke generator by referring to Transformer-based sketch generation models [48,60]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.43, + 0.893, + 0.612 + ], + "angle": 0, + "content": "Architecture. As shown in Fig. 3, LBS generates a set of strokes from trainable parameters, which are denoted as initial strokes. Our stroke generator uses Transformer decoder layers and incorporates image features from a CNN encoder (ResNet18 is used in this paper). Then, 2-layer MLP decoders decode a set of \\( n \\) strokes from the output of the Transformer decoder. Each stroke contains four control points that parameterize a cubic Bezier curve, as well as color and thickness information. The sketch of an image is then created by rasterizing the generated set of strokes using a differentiable rasterizer [53]. For a detailed description of our architecture, please refer to Appendix C." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.612, + 0.894, + 0.791 + ], + "angle": 0, + "content": "Representation of LBS. The primary output of LBS is a set of strokes \\( \\pmb{p} \\), and a geometry-aware representation is obtained by using the flattened vector of the strokes \\( z_{p} = (p^{(1)},\\dots,p^{(n)}) \\). To complement information that may not be encoded with strokes such as texture, we concatenate \\( z_{p} \\) with the image features \\( z_{e} \\) from the CNN encoder with global average pooling. The resulting concatenated representation is denoted as \\( z_{LBS} \\). In addition, we can combine this with representation \\( z_{h} \\) that aggregates the entire stroke, the result of which we denote as \\( z_{LBS+} \\). Further details can be found in Sec. 4.4. The final representation space of LBS is as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.555, + 0.805, + 0.892, + 0.822 + ], + "angle": 0, + "content": "\\[\nz _ {L B S} = \\left(z _ {e}, z _ {p}\\right), \\quad z _ {L B S +} = \\left(z _ {e}, z _ {p}, z _ {h}\\right). \\tag {1}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.833, + 0.816, + 0.849 + ], + "angle": 0, + "content": "4.2. CLIP-based perceptual loss function" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "As discussed in Sec. 3.2, proper \\(\\mathcal{L}\\) must be given to train a geometry-aware representation of an image. To this end, we adopt CLIP-based perceptual loss to measure the sim" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "23318" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.089, + 0.458, + 0.257 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.269, + 0.473, + 0.354 + ], + "angle": 0, + "content": "Figure 4. Visualization of the progressive optimization process. Strokes initialized from the saliency map are optimized using the gradient of \\(\\mathcal{L}_{\\text{percept}}\\) until convergence and stored in a total of \\(L\\) intermediate steps denoted by \\(\\pmb{p}_{gt,l}\\). Then, the stroke generator is trained through \\(\\mathcal{L}_{\\text{guide}}\\) to progressively predict each intermediate stroke \\(\\pmb{p}_l\\) from \\(\\pmb{p}_{gt,l}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.37, + 0.472, + 0.446 + ], + "angle": 0, + "content": "ilarity between the sketch and the input image in terms of both geometric and semantic differences [68]. To generate a sketch that is semantically similar to the input image, it should minimize the distance on the embedding space of the CLIP model \\( f_{C} \\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.159, + 0.456, + 0.47, + 0.489 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {s e m a n t i c}} = \\sum_ {A \\in \\mathcal {A}} \\phi (A (I), A (S)), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.5, + 0.47, + 0.576 + ], + "angle": 0, + "content": "where \\(\\mathcal{A}\\) is the group of affine transformations and \\(\\phi\\) is the cosine similarity of the CLIP embeddings, i.e., \\(\\phi (x,y) = \\cos (f_C(x),f_C(y))\\). In addition, it compares low-level features of the sketch and the input image to estimate the geometric similarity as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.141, + 0.587, + 0.47, + 0.62 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {g e o m e t r i c}} = \\sum_ {A \\in \\mathcal {A}} \\sum_ {i} \\phi_ {i} (A (I), A (S)), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.63, + 0.47, + 0.706 + ], + "angle": 0, + "content": "where \\(\\phi_{i}\\) is the \\(\\mathcal{L}_2\\) distance of the embeddings from the \\(i\\)-th intermediate layer of the CLIP model, i.e., \\(\\phi_{i}(x,y) = \\| f_{C,i}(x) - f_{C,i}(y)\\|_{2}^{2}\\). Specifically, we used \\(i\\in \\{3,4\\}\\) with the ResNet101 CLIP model, proposed as [68]. The final perceptual loss is as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.138, + 0.719, + 0.47, + 0.736 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {p e r c e p t}} = \\mathcal {L} _ {\\text {g e o m e t r i c}} + \\lambda_ {s} \\cdot \\mathcal {L} _ {\\text {s e m a n t i c}}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.747, + 0.314, + 0.763 + ], + "angle": 0, + "content": "with \\(\\lambda_{s} = 0.1\\) as a hyperparameter." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.772, + 0.47, + 0.789 + ], + "angle": 0, + "content": "4.3. Training with progressive optimization process" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Abstracting an image into a sketch requires high-level reasoning, and predicting the corresponding stroke parameters in a single inference step is a delicate process. Although CLIPasso [68] addresses these problems via an optimization-based approach, its time-consuming properties (\\(\\sim 2\\) min per image) make it impractical as a representation. Moreover, as CLIPasso reported that the changes" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.152 + ], + "angle": 0, + "content": "in initial strokes significantly impacted the final results, directly optimizing each stroke through the optimizer for thousands of steps leads to highly variable results and numerical instability." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.153, + 0.893, + 0.378 + ], + "angle": 0, + "content": "To generate a stable representation within a single inference step, we modify the optimization-based approach of CLIPasso and utilize it as desirable guidance for the stroke generator, which we call the guidance stroke and denote as \\( \\pmb{p}_{gt} \\). To ensure high-quality sketch generation, each intermediate layer of the stroke generator is guided by strokes obtained at the corresponding intermediate step of the optimization process instead of relying solely on the final outcome. This process, depicted in Fig. 4, involves progressively updating strokes from the previous layer, which can be modeled by residual blocks from the Transformer architecture. By decomposing the prediction of the entire optimization process into predicting changes in relatively short intervals for each intermediate layer, our approach leads to better-quality sketches." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.379, + 0.892, + 0.499 + ], + "angle": 0, + "content": "However, the process through which CLIPasso initializes strokes via stochastic sampling from the saliency map results in unstable outcomes. To address this issue, we select initialized strokes deterministically by selecting the most salient regions from the saliency map in a greedy manner. The color of the stroke is determined during the initialization step by referencing the corresponding region in the original image. More details are described in Appendix A." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.5, + 0.892, + 0.56 + ], + "angle": 0, + "content": "To ensure that the guidance loss is invariant to the permutation of the order of each stroke, we use the Hungarian algorithm [41] which is widely used for the assignment problem. The guidance loss is as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.562, + 0.568, + 0.892, + 0.61 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {g u i d e}} = \\sum_ {l = 1} ^ {L} \\min _ {\\sigma} \\sum_ {i = 1} ^ {n} \\mathcal {L} _ {1} \\left(p _ {g t, l} ^ {(i)}, p _ {l} ^ {(\\sigma (i))}\\right), \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.62, + 0.892, + 0.69 + ], + "angle": 0, + "content": "where \\(\\sigma\\) is a permutation of the stroke index, and \\(p_l^{(i)}\\) is the \\(i\\)-th decoded stroke from the \\(l\\)-th intermediate layer with \\(L\\) layers in total. \\(\\mathcal{L}_1\\) is the L1 distance, and \\(p_{gt,l}^{(i)}\\) is the guidance stroke corresponding to \\(p_l^{(\\sigma(i))}\\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.697, + 0.746, + 0.713 + ], + "angle": 0, + "content": "4.4. Stroke embedding network" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.893, + 0.902 + ], + "angle": 0, + "content": "As strokes primarily express localized and fine-grained details, they can be less suitable for representing coarse-grained information. To address this, we offer an additional representation that combines full strokes through a stroke embedding network. Stroke embedding network \\( h: \\mathcal{P} \\to \\mathcal{Z}_h \\) maps the set of \\( n \\) strokes into embedding space \\( \\mathcal{Z}_h \\). Since the rasterized sketch is invariant to the stroke indices (except for contact point between strokes), we followed the permutation invariant model from DeepSets [80] to generate stroke embedding. The choice of the loss function \\( \\mathcal{L}_{embed} \\) to train \\( z_h \\in \\mathcal{Z}_h \\) is unconstrained (e.g., Cross-Entropy or InfoNCE loss in our paper). During the training" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "23319" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.121 + ], + "angle": 0, + "content": "phase, the gradient from \\( h \\) is also passed to \\( f \\) to capture coarse-grained information." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.122, + 0.314, + 0.137 + ], + "angle": 0, + "content": "The final objective is as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.106, + 0.15, + 0.469, + 0.168 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {L B S} = \\mathcal {L} _ {\\text {p e r c e p t}} + \\lambda_ {g} \\cdot \\mathcal {L} _ {\\text {g u i d e}} + \\lambda_ {e} \\cdot \\mathcal {L} _ {\\text {e m b e d}}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.179, + 0.469, + 0.21 + ], + "angle": 0, + "content": "where \\(\\lambda_{g}\\) and \\(\\lambda_{e}\\) are hyperparameters (for specific values, refer to Appendix C)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.224, + 0.21, + 0.24 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.249, + 0.392, + 0.266 + ], + "angle": 0, + "content": "5.1. Research questions and task designs" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.272, + 0.47, + 0.349 + ], + "angle": 0, + "content": "We investigate the effectiveness and generalizability of our approach by designing multiple research questions, as well as corresponding downstream tasks for each question. Detailed information about each experimental setup is described in Appendix B." + }, + { + "type": "title", + "bbox": [ + 0.076, + 0.351, + 0.469, + 0.381 + ], + "angle": 0, + "content": "RQ1. Effects of equivariance: What is the benefit of equivariant representation, and does LBS achieve it?" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.382, + 0.47, + 0.578 + ], + "angle": 0, + "content": "From the definition of equivariance, we expect that an equivariant model with respect to geometric transformation would have generalization capability for augmented images with transformation. To verify this, we conduct experiments on the Rotated MNIST (rotMNIST) dataset [22], which consists of rotated images from the MNIST dataset. We rotate images by \\(30^{\\circ}\\) and \\(45^{\\circ}\\) for training and classify the digit of images rotated by \\(0^{\\circ}\\) and \\(90^{\\circ}\\) to evaluate whether LBS generalizes the information from the training domain to the test domain. To verify that our model satisfies equivariance outside the training domain, we classify the rotation and reflection between an original image and the same image rotated with an interval of \\(90^{\\circ}\\) and horizontally flipped." + }, + { + "type": "title", + "bbox": [ + 0.076, + 0.581, + 0.469, + 0.626 + ], + "angle": 0, + "content": "RQ2. Effects on geometric primitives and concepts: How well does LBS represent geometric primitives and understand their conceptual relationships?" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.627, + 0.47, + 0.808 + ], + "angle": 0, + "content": "To evaluate whether LBS is suitable for representing geometric primitives and concepts, we perform a classification task on the Geoclidean dataset [29]. The Geoclidean dataset consists of realized images from a concept of Euclidean geometry, e.g., black parallel lines on a white background. Geoclidean is divided into two categories: Geoclidean-Elements and Geoclidean-Constraints, visualized in Fig. 7 on Appendix B. By providing a limited training set consisting of only 10 images per concept, we evaluate whether LBS can effectively learn the high-level relationships between each primitive and generalize them across different examples by classifying the concept of the test image." + }, + { + "type": "title", + "bbox": [ + 0.076, + 0.81, + 0.469, + 0.856 + ], + "angle": 0, + "content": "RQ3. Local geometric information and spatial reasoning: How effectively does LBS reflect local geometric information and extend it to spatial reasoning tasks?" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.469, + 0.901 + ], + "angle": 0, + "content": "We validate whether LBS can reflect the local geometric information of each object in a synthetic photo dataset consisting of multiple objects, using the CLEVR dataset [34]." + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.09, + 0.892, + 0.118 + ], + "angle": 0, + "content": "Table 1. Quantitative results of LBS and the baselines evaluated on the corresponding tasks on the rotMNIST and Geoclidean." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.129, + 0.892, + 0.289 + ], + "angle": 0, + "content": "
La-\nbelMethodrotMNIST (30°, 45°)Geoclidean
0°, 90°RotationConstraintsElements
✓CE62.72±1.8973.14±0.3553.89±1.5870.57±4.29
SupCon [38]65.25±1.0573.37±0.2042.41±3.1655.83±4.28
LtD-diff [54]60.09±1.1628.91±2.1557.26±2.1969.47±2.11
E(2)-CNN [73]85.12±0.1777.00±0.3971.03±1.9469.28±1.46
LBS (CE)65.00±3.3275.81±0.3050.01±1.5881.06±3.14
XSimCLR [9]47.66±0.4172.96±0.8432.04±0.6465.14±4.11
β-TCVAE [8]37.84±1.0660.14±0.3217.18±1.3533.82±1.64
GeoSSL [55]--18.66±3.3333.47±2.80
HoG [14]25.4264.9423.8252.05
LBS47.31±2.5370.02±0.6447.43±1.3481.34±0.16
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.303, + 0.892, + 0.439 + ], + "angle": 0, + "content": "We train our model with very limited descriptions, where the label for the entire scene is provided as the rightmost object or without any descriptions at all. We validate the effectiveness of our representation by evaluating its ability to successfully classify attributes that are not provided as labels, such as determining the color of the leftmost object. Additionally, we test its ability to perform simple spatial reasoning, such as shifting the rightmost object and inferring the attribute of the current rightmost object." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.442, + 0.894, + 0.485 + ], + "angle": 0, + "content": "RQ4. Domain transfer: Can the geometric concepts of LBS trained in a specific domain be extended to other domains?" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.487, + 0.892, + 0.578 + ], + "angle": 0, + "content": "To investigate whether the learned representation within a specific image domain provides meaningful geometric information across other domains, we evaluate the model by shifting the distribution from the STL-10 [11] dataset to CLEVR and vice versa. Evaluation in the STL-10 dataset is conducted through object classification." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.581, + 0.892, + 0.611 + ], + "angle": 0, + "content": "RQ5. Traditional sketch tasks: Does geometry-aware representation from LBS help in traditional FG-SBIR tasks?" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.611, + 0.892, + 0.746 + ], + "angle": 0, + "content": "We assess the impact of geometry-aware representations acquired by LBS on a conventional sketch task by evaluating them with the fine-grained sketch-based image retrieval (FG-SBIR) task on the QMUL-ShoeV2 Dataset [78]. The aim of FG-SBIR is to match a given sketch of a shoe to its corresponding photo image. Since geometric information is essential for distinguishing each shoe, we investigate whether leveraging representations from LBS can improve performance on the FG-SBIR task." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.757, + 0.688, + 0.773 + ], + "angle": 0, + "content": "5.2. Experimental setup" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Implementation details. As samples from rotMNIST and Geoclidean can be directly represented with a few strokes, we replace \\(\\mathcal{L}_{\\text {percept }}\\) and \\(\\mathcal{L}_{\\text {guide }}\\) with \\(\\mathcal{L}_1\\) loss, which does not rely on a pre-trained CLIP model. For the STL-10 dataset, providing mask information for the background with U2-Net [57] improves the quality of generated sketches. For \\(\\mathcal{L}_{\\text {embed }}\\), we use Cross-Entropy loss for supervised training which we denote as LBS (CE) in Tab. 1, 2 and" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "23320" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.895, + 0.149 + ], + "angle": 0, + "content": "Table 2. Quantitative results on CLEVR dataset for labeled and unlabeled settings and for CLIP and HoG features. RC, LC, BC refer to inferring the color of the rightmost, leftmost, bottommost object, and Size, Shape, Material refer to inferring the size, shape, material of the rightmost object, respectively. Third refers to inferring the color of the third object from the right, and Shift refers to predicting the color of the rightmost object after shifting the initial rightmost object to the left by 0.15 times the image width." + }, + { + "type": "table", + "bbox": [ + 0.117, + 0.156, + 0.851, + 0.361 + ], + "angle": 0, + "content": "
LabelMethodRCLCBCSizeShapeMaterialThirdShift
✓CE98.71±0.1076.72±0.8676.02±0.9092.51±0.4049.97±0.2964.38±1.9040.66±0.2062.06±1.62
SupCon [38]98.75±0.0863.82±2.3666.04±2.6591.88±0.3749.15±0.8559.20±0.5737.93±0.2756.05±2.56
LtD-diff [54]62.29±0.4814.01±0.4215.84±0.4363.98±3.3843.96±3.0554.47±0.4516.47±0.5917.21±0.29
E(2)-CNN [73]98.50±0.1070.10±1.1573.51±2.5089.84±0.4645.85±0.9363.05±0.5941.95±0.1859.29±0.91
LBS (CE)97.49±0.2281.79±0.2784.09±0.8493.22±0.2970.03±0.6886.84±0.5438.23±0.2551.56±0.16
×SimCLR [9]60.61±1.2463.89±2.3563.77±2.2983.35±0.6041.95±0.3351.66±0.2433.42±0.5543.05±0.55
E(2)-CNN [73]53.50±7.3054.60±7.3455.52±7.6083.52±1.5642.06±1.1253.04±2.8130.74±2.8438.03±4.44
β-TCVAE [8]17.09±0.2017.50±0.3320.04±0.7171.27±0.1036.30±0.1056.11±0.1315.38±0.1916.35±0.18
GeoSSL [55]20.16±0.6320.54±0.8721.61±0.6773.79±0.7844.08±1.1054.54±2.9415.39±0.1616.94±0.34
DefGrid [21]73.81±0.9173.96±1.0273.38±0.8081.50±0.2246.34±0.7768.65±1.1724.90±0.2736.28±0.13
LBS84.31±0.0880.47±0.7883.00±0.3992.66±0.4170.01±0.5385.52±0.4337.41±0.2949.32±0.17
CLIP [59]37.3939.154.9877.5166.9172.6634.7534.80
HoG [14]56.8349.6958.6981.7361.1468.3824.2833.25
" + }, + { + "type": "table_caption", + "bbox": [ + 0.189, + 0.374, + 0.78, + 0.388 + ], + "angle": 0, + "content": "Table 3. Quantitative results of models trained on STL-10 dataset and evaluated on CLEVR dataset." + }, + { + "type": "table", + "bbox": [ + 0.118, + 0.399, + 0.851, + 0.514 + ], + "angle": 0, + "content": "
DatasetMethodRCLCBCSizeShapeMaterialThirdShift
STL-10↓CLEVRLtD [54]18.70±0.0219.15±0.7721.69±1.0573.13±3.2147.88±1.1359.11±2.3416.47±0.5917.21±0.29
SimCLR [9]26.97±0.2826.26±0.8838.88±0.1982.33±0.6456.88±1.2377.39±0.3523.45±0.3524.95±0.17
E(2)-CNN [73]26.82±2.2325.40±1.2039.30±2.8079.48±0.7153.54±0.8472.18±0.3423.35±1.0124.80±1.08
β-TCVAE [8]17.04±0.7618.46±2.3618.88±1.1471.32±0.6737.14±0.1256.81±0.2615.63±1.3516.43±0.38
GeoSSL [55]14.41±0.5514.73±0.1114.37±0.6677.47±5.1748.10±1.9055.63±2.8613.71±0.4513.63±0.13
DefGrid [21]66.74±1.1068.60±0.0868.35±0.8278.97±0.2940.92±0.4462.98±1.3123.48±0.4933.07±0.52
LBS53.87±2.7253.85±2.2061.84±2.2392.46±0.6259.52±0.4580.06±1.2930.75±0.4139.95±1.15
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.53, + 0.47, + 0.558 + ], + "angle": 0, + "content": "Table 4. Quantitative results of models trained on CLEVR dataset and evaluated on STL-10 dataset classification." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.57, + 0.468, + 0.68 + ], + "angle": 0, + "content": "
DatasetLabeledUnlabeled
MethodAccuracyMethodAccuracy
CLEVR↓STL-10CE46.15±0.12SimCLR [9]41.68±0.05
SupCon [38]43.41±0.36β-TCVAE [8]27.35±0.38
LtD-diff [54]50.81±0.67GeoSSL [55]35.93±0.96
E(2)-CNN [73]45.19±0.84E(2)-CNN [73]38.50±0.49
LBS (CE)56.48±0.89DefGrid [21]33.13±0.17
LBS55.35±0.18
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.695, + 0.47, + 0.785 + ], + "angle": 0, + "content": "4. For the unlabeled setting, the model is trained without \\(\\mathcal{L}_{embed}\\) and is denoted LBS with no parentheses. For evaluation, we use \\(z_{LBS+}\\) for LBS (CE), and \\(z_{LBS}\\) for LBS. All evaluations are performed with the common protocol of linear classification. For more detailed information on our implementation, please refer to Appendix C." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.786, + 0.354, + 0.801 + ], + "angle": 0, + "content": "Baselines. We compare our models with:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.807, + 0.468, + 0.837 + ], + "angle": 0, + "content": "- Models which only use image encoder: trained with Cross-Entropy, SimCLR [9], or SupCon loss [38]." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.839, + 0.468, + 0.884 + ], + "angle": 0, + "content": "- Equivariance models: E(2)-Equivariant Steerable CNNs (E(2)-CNN) [73], and work by Novotny et al., denoted as GeoSSL [55]." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.886, + 0.374, + 0.901 + ], + "angle": 0, + "content": "- Disentanglement model: \\(\\beta\\)-TCVAE [8]." + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.807, + 0.468, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.533, + 0.89, + 0.563 + ], + "angle": 0, + "content": "- Sketch model for communication between agents: Learning to Draw (LtD) [54]" + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.563, + 0.822, + 0.578 + ], + "angle": 0, + "content": "- Grid-based superpixel model: DefGrid [21]" + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.579, + 0.813, + 0.593 + ], + "angle": 0, + "content": "- Handcrafted feature descriptor: HoG [14]." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.594, + 0.842, + 0.609 + ], + "angle": 0, + "content": "- Pre-trained CLIP model used for training LBS." + }, + { + "type": "list", + "bbox": [ + 0.518, + 0.533, + 0.89, + 0.609 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.619, + 0.692, + 0.634 + ], + "angle": 0, + "content": "5.3. Results and analysis" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.642, + 0.892, + 0.837 + ], + "angle": 0, + "content": "Analysis on RQ1 and RQ2: Tab. 1 shows the experimental results for RQ1 and RQ2, which can be summarized as: (a) Providing a strong inductive bias for equivariance, as shown in the case of E(2)-CNN, leads to good performance on the tasks of RQ1. While LBS outperformed LtD-diff, which also utilizes a sketch-based approach, it requires additional validation and refinement. (b) For RQ2, LBS performs substantially better than the other baselines except for the supervised setting on Geoclidean-Constraints, showing that it successfully captures geometric concepts. In particular, Geoclidean-Elements perform better when trained without labels. (c) Disentanglement methods and handcrafted features offer less informative features for both tasks." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Analysis on RQ3: Tab. 2 summarizes the experiments conducted on the CLEVR dataset, demonstrating that LBS provides valuable information for tasks of RQ3. The key observations from Tab. 2 are: (a) While the baselines in the" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.946, + 0.518, + 0.957 + ], + "angle": 0, + "content": "23321" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.47, + 0.118 + ], + "angle": 0, + "content": "Table 5. Top-1 and Top-10 accuracy on QMUL-Shoe-v2 dataset, using Triplet Loss for \\( \\mathcal{L}_{embed} \\) in LBS." + }, + { + "type": "table", + "bbox": [ + 0.134, + 0.126, + 0.408, + 0.191 + ], + "angle": 0, + "content": "
MethodRepTop-1Top-10
LBS (Triplet)zLBS+40.8±4.1988.3±1.76
ze30.8±3.8977.8±3.89
Tripletze32.5±1.7380.0±4.36
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.218, + 0.471, + 0.369 + ], + "angle": 0, + "content": "supervised setting struggle to generalize on unlearned attributes, LBS (CE) can provide more general information. (b) The results of LBS show a larger performance gap in the unlabeled setting, with its performance being almost as good as LBS (CE). (c) Embeddings from pre-trained CLIP perform less effectively than unlabeled baselines, such as SimCLR, on tasks related to local geometry. Also, handcrafted features yielded limited effectiveness. (d) Methods that focus on preserving global transformations and disentanglement are not effective in environments of RQ3." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.376, + 0.47, + 0.557 + ], + "angle": 0, + "content": "Analysis on RQ4: Tabs. 3 and 4 summarize the results for shifting domains from STL-10 to CLEVR, and vice versa. As shown in Fig. 11 on Appendix I, LBS trained on STL-10 can successfully describe scenes from CLEVR, while LBS trained on CLEVR can abstractly depict natural images from STL-10, leading to substantially high classification accuracy. These results indicate that learning geometric information, such as position and curvature, by sketching salient parts of a scene successfully induces learning of general features across domains. Furthermore, LtD-diff, which also utilizes a sketch-based approach, demonstrated good performance in transferring CLEVR to STL-10." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.564, + 0.47, + 0.671 + ], + "angle": 0, + "content": "Analysis on RQ5: Tab. 5 presents the results for the FG-SBIR task. Compared to the baseline trained without sketching, LBS can accurately predict the corresponding shoe during the test phase. The huge drop in performance upon removing strokes and stroke embedding from \\( z_{LBS+} \\) indicates that the geometry-aware representation provided by LBS is also valuable for traditional sketch tasks." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.692, + 0.426, + 0.709 + ], + "angle": 0, + "content": "5.4. Comparisons with stroke-based methods" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Tab. 6 compares LBS to other stroke-based generation methods on STL-10 dataset, and Fig. 5 visualizes the results of each method. The evaluation is based solely on strokes, and LBSonly uses \\( z_{p} \\) as a representation. LBS (\\( \\mathcal{L}_{\\text{percept}} \\)) achieved superior results compared to LBS (\\( \\mathcal{L}_1 \\)) and the Paint Transformer [48] based on \\( \\mathcal{L}_1 \\) loss. We also compare our results to CLIPasso modified to use our deterministic initialization process, suggesting that strokes generated from CLIPasso may not be suitable as a representation. LtD-diff, which generates sketches to solve a communication game, often omits important geometric and color information, resulting in low performance." + }, + { + "type": "table_caption", + "bbox": [ + 0.506, + 0.089, + 0.885, + 0.104 + ], + "angle": 0, + "content": "Table 6. Comparison between stroke-based generation methods." + }, + { + "type": "table", + "bbox": [ + 0.517, + 0.111, + 0.87, + 0.201 + ], + "angle": 0, + "content": "
RCBCSizeShapeMaterial
LtD-diff [54]18.7021.6973.1347.8859.11
Paint [48]51.9660.4077.3544.3070.02
CLIPasso [68]12.5513.5555.3535.4050.00
LBS (L1)34.4357.8178.3240.9961.59
LBS (Lpercept)55.1560.6390.1451.2376.16
" + }, + { + "type": "image", + "bbox": [ + 0.551, + 0.217, + 0.64, + 0.285 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.576, + 0.285, + 0.61, + 0.296 + ], + "angle": 0, + "content": "Image" + }, + { + "type": "image", + "bbox": [ + 0.652, + 0.217, + 0.738, + 0.284 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.662, + 0.285, + 0.732, + 0.297 + ], + "angle": 0, + "content": "LBS \\((\\mathcal{L}_{percept})\\)" + }, + { + "type": "image", + "bbox": [ + 0.753, + 0.217, + 0.839, + 0.284 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.771, + 0.285, + 0.819, + 0.296 + ], + "angle": 0, + "content": "LBS \\((\\mathcal{L}_1)\\)" + }, + { + "type": "image", + "bbox": [ + 0.551, + 0.296, + 0.638, + 0.363 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.568, + 0.364, + 0.621, + 0.374 + ], + "angle": 0, + "content": "CLIPasso" + }, + { + "type": "image", + "bbox": [ + 0.652, + 0.296, + 0.738, + 0.363 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.672, + 0.364, + 0.718, + 0.374 + ], + "angle": 0, + "content": "LtD-diff" + }, + { + "type": "image", + "bbox": [ + 0.753, + 0.296, + 0.839, + 0.363 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.746, + 0.364, + 0.846, + 0.374 + ], + "angle": 0, + "content": "Paint Transformer" + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.379, + 0.892, + 0.407 + ], + "angle": 0, + "content": "Figure 5. Comparisons to other stroke-based methods. LBS encodes both the geometric and semantic information." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.423, + 0.619, + 0.438 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.449, + 0.892, + 0.675 + ], + "angle": 0, + "content": "We propose a novel representation learning perspective through sketching, a visual expression that retains geometric information. By considering the mathematical concept of equivariance, we provide a formal definition of sketch and stroke, and prove that strokes can preserve the information of arbitrary affine transformations. Our sketch generation model, LBS, minimizes CLIP-based perceptual loss and supports the idea that sketches can effectively convey geometric information. The experiments shed light on the potential benefits of leveraging the process of sketching to represent high-level geometric information explicitly. These benefits include learning equivariant representations, understanding geometric concepts, improving spatial reasoning abilities, and acquiring general geometric information across different domains." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.677, + 0.892, + 0.829 + ], + "angle": 0, + "content": "Still, there are several limitations to our method. The training process of LBS relies on pre-trained CLIP and optionally U2-Net, and requires generating guidance strokes through a time-consuming optimization-based process. Moreover, while our work has demonstrated the theoretical strengths of sketching in terms of equivariance, a clearer methodology and further experimental analysis are needed to fully achieve this potential. Future work should address these issues and extend the methodology, focusing on scalability and including more complex and realistic tasks." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Acknowledgement This work was partly supported by the Korean government (2021-0-02068-AIHub/25%, 2021-0-01343-GSAI/25%, 2022-0-00951-LBA/25%, 2022-0-00953-PICA/25%)." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "23322" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.175, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.171 + ], + "angle": 0, + "content": "[1] Pablo Arbelaez, Michael Maire, Charless Fowlkes, and Jitendra Malik. Contour detection and hierarchical image segmentation. IEEE Trans. Pattern Anal. Mach. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 15689-15698, 2021. 3" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.471, + 0.318 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "23326" + } + ] +] \ No newline at end of file diff --git a/2023/Learning Geometry-Aware Representations by Sketching/f80a6701-d163-4c1c-a5df-2e5aa49a37e5_origin.pdf b/2023/Learning Geometry-Aware Representations by Sketching/f80a6701-d163-4c1c-a5df-2e5aa49a37e5_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..b1b308ebe91e6c8ec07c6ede62c9d2562558a19a --- /dev/null +++ b/2023/Learning Geometry-Aware Representations by Sketching/f80a6701-d163-4c1c-a5df-2e5aa49a37e5_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:7debad0b44b3dc082b83ea6ad2b91f464e79aafbe8367c03931c0e4782c65f80 +size 1553068 diff --git a/2023/Learning Geometry-Aware Representations by Sketching/full.md b/2023/Learning Geometry-Aware Representations by Sketching/full.md new file mode 100644 index 0000000000000000000000000000000000000000..0ead0a5d7f1d34ecab8cf6b80d155f7349196c4c --- /dev/null +++ b/2023/Learning Geometry-Aware Representations by Sketching/full.md @@ -0,0 +1,368 @@ +# Learning Geometry-aware Representations by Sketching + +Hyundo Lee, Inwoo Hwang, Hyunsung Go, Won-Seok Choi, Kibeom Kim, Byoung-Tak Zhang AI Institute, Seoul National University + +{hdlee, iwhwang, hsgo, wchoi, kbkim, btzhang}@bi.snu.ac.kr + +# Abstract + +Understanding geometric concepts, such as distance and shape, is essential for understanding the real world and also for many vision tasks. To incorporate such information into a visual representation of a scene, we propose learning to represent the scene by sketching, inspired by human behavior. Our method, coined Learning by Sketching (LBS), learns to convert an image into a set of colored strokes that explicitly incorporate the geometric information of the scene in a single inference step without requiring a sketch dataset. A sketch is then generated from the strokes where CLIP-based perceptual loss maintains a semantic similarity between the sketch and the image. We show theoretically that sketching is equivariant with respect to arbitrary affine transformations and thus provably preserves geometric information. Experimental results show that LBS substantially improves the performance of object attribute classification on the unlabeled CLEVR dataset, domain transfer between CLEVR and STL-10 datasets, and for diverse downstream tasks, confirming that LBS provides rich geometric information. + +# 1. Introduction + +Since geometric principles form the bedrock of our physical world, many real-world scenarios involve geometric concepts such as position, shape, distance, and orientation. For example, grabbing an object requires estimating its shape and relative distance. Understanding geometric concepts is also essential for numerous vision tasks such as image segmentation, visual reasoning, and pose estimation [27]. Thus, it is crucial to learn a visual representation of the image that can preserve such information [76], which we call geometry-aware representation. + +However, there is still a challenge in learning geometry-aware representations in a compact way that can be useful for various downstream tasks. Previous approaches have focused on capturing geometric features of an image in a 2D grid structure, using methods such as handcrafted feature extraction [2, 4, 14, 31], segmentation maps [21, 57], or + +![](images/acb59d35df6f7bc2e3430296b492e7e7e1744cb30a0210c7a994b08e09f0bdcf.jpg) +Figure 1. Overview of LBS, which aims to generate sketches that accurately reflect the geometric information of an image. A sketch consists of a set of strokes represented by a parameterized vector that specifies curve, color, and thickness. We leverage it as a geometry-aware representation for various downstream tasks. + +convolution features [36, 55]. Although these methods are widely applicable to various domains, they often lack compactness based on a high-level understanding of the scene and tend to prioritize nuisance features such as the background. Another line of work proposes architectures that guarantee to preserve geometric structure [12, 13, 23, 58, 73] or disentangle prominent factors in the data [8, 28, 39, 51]. Although these methods can represent geometric concepts in a compact latent space, they are typically designed to learn features that are specific to a particular domain and often face challenges in generalizing to other domains [64]. + +In this study, we present a novel approach to learning geometry-aware representations via sketching. Sketching, which is the process of converting the salient features of an image into a set of color-coded strokes, as illustrated in Figure 1, is the primary means by which humans represent images while preserving their geometry. Our key idea is that sketches can be a compact, high-level representation of an image that accurately reflects geometric information. Sketching requires a high-level understanding of the scene, as it aims to capture the most salient features of the image and abstract them into a limited number of strokes. In addition, a sketch can be represented as a set of parameters by replacing each stroke with parametric curves. Sketch- + +![](images/76d1e600a6daaab19456fc30889477324598309ccd191d694be2599883e9f568.jpg) +Figure 2. Examples of how sketches capture essential geometric concepts such as shape, size, orientation, curvature, and local distortion. The control points of each stroke compactly represent the local geometric information of the corresponding region in the sketch. The strokes as a whole maintain the geometric structure of the entire image under various transformations in the image domain. + +ing has also been linked to how people learn geometric concepts [66]. Based on these properties, we directly use strokes as a geometry-aware representation and utilize them for downstream tasks. Under the theoretical framework of geometric deep learning [3], we conduct theoretical analysis to validate the effectiveness of strokes as a representation and prove their ability to preserve affine transformations. + +To validate our hypothesis, we introduce Learning by Sketching (LBS), a method that generates abstract sketches coherent with the geometry of an input image. Our model is distinct from existing sketch generation methods as it does not require a sketch dataset for training, which often has limited abstraction or fails to accurately reflect geometric information. Instead, LBS learns to convert an image into a set of colored Bezier curves that explicitly represent the geometric concepts of the input image. To teach the style of sketching, we use perceptual loss based on the CLIP model [59, 68], which measures both semantic and geometric similarities between images and generated sketches. We propose a progressive optimization process that predicts how strokes will be optimized from their initial positions through CLIP-based perceptual loss to generate abstract sketches in a single inference step. As a result, LBS generates a representation that reflects visual understanding in a single inference step, without requiring a sketch dataset. This produces highly explainable representations through sketches, as illustrated in Figure 2. + +We conduct experimental analyses to evaluate the effectiveness of our approach, learning by sketching, by addressing multiple research questions in various downstream tasks, including: (i) describing the relationships between geometric primitives, (ii) demonstrating simple spatial reasoning ability by conveying global and local geometric information, (iii) containing general geometric information shared across different domains, and (iv) improving performance on FG-SBIR, a traditional sketch task. + +# 2. Related work + +# 2.1. Geometry-aware representation learning + +Previous studies that aim to capture geometric information within the data can be categorized into two approaches: Firstly, explicitly capturing the geometric information with features on the image space, and secondly, inducing a compact feature vector that preserves the geometric structure of the data. + +Features on image space. The most straightforward approach to representing geometric structures in images is to establish features directly on the image space, i.e., to define features on the 2D grid structure. Approaches that utilize this method include those that employ traditional edge detection algorithms [4, 35, 74, 75], low-level convolutional features [36, 68], and segmentation maps [49, 57, 61]. However, these features are unsuitable for conversion into compact vector representations for downstream tasks. Alternative approaches include utilizing hand-crafted feature detection algorithms [2, 14, 31, 62], clustering specific areas of an image into superpixels [21, 32], and representing the relationships between specific areas as a graph [15, 65]. Our approach is primarily notable for its ability to capture the most salient image features through an overall understanding of the scene, resulting in a concise representation. + +Geometric deep learning. Research has also been conducted to develop informative and compact representations that preserve geometric structures in a latent vector space. One representative method is geometric deep learning [3], which involves preserving the geometric properties of an image by learning an invariant (i.e., maintaining the output identically) or an equivariant representation (i.e., there exists an operator acting on the feature space corresponding to the transformations) with respect to geometric transformations. Steerable networks [12, 13, 23, 73] extend the + +translation equivariance of CNNs to a larger group of symmetries and introduce an efficient weight-sharing architecture. However, designing their architecture requires complex analytic solutions, and they are constrained to particular transformations [37]. Another approach is to disentangle factors of variation into distinct latent subspaces [8, 28, 39, 40, 51, 58, 70]. However, these methods face difficulties in handling changing factors of variation [64] and therefore struggle to generalize to arbitrary geometric transformations. Sketching, in contrast to these methods, can naturally ensure equivariance with respect to geometric transformations by being defined on the image space. In Sec. 3 we show that strokes can be equivariant with respect to arbitrary affine transformations. + +# 2.2. Sketch generation methods + +Human-drawn sketches are widely used as valuable descriptions in various applications, including image retrieval [16, 47, 78], modeling 3D shapes and surfaces [25, 42, 43, 45], and image editing [33, 56, 69, 71]. Unfortunately, previous works that aim to learn sketching or drawing mostly endeavor to generate artistic works, rather than focusing on its applicability [19, 24, 30, 48, 52, 83]. + +Sketch generation models often rely on explicit sketch datasets to follow the style of human drawings [5, 10, 46, 60, 67, 82]. However, many existing datasets are not designed to preserve geometric information [7, 20, 63] or contain sketches without sophisticated image abstraction, resembling simple edge detection [1, 72]. This presents challenges for sketch models to accurately abstract an image while preserving its geometries. Without sketch datasets, stroke-based rendering methods usually minimize the reconstruction loss which is related to the pixel-wise distance, which promotes learning in the style of painting [19, 30, 48, 52, 53, 81, 83]. There have also been studies that attempt to capture the geometric and semantic features of a scene through imitating the style of line drawing [6, 44, 77]. However, these methods require numerous strokes to cover the whole canvas, primarily focusing on the superfluous background instead of salient features. + +Abstract sketches for representation. Only a few works aim to generate sketches for the sake of representing an image with a limited number of strokes. Learning to Draw (LtD) [54] creates a representative sketch of an image and uses it as a communication channel between agents. While it primarily focuses on communicating with a specific receiver, we aim to leverage strokes as a general representation for various downstream tasks. CLIPasso [68] utilizes the capabilities of CLIP [59], a neural network trained on images paired with text, to synthesize abstract sketches by maintaining both semantic and geometric attributes. Generating representations with this method, however, is impractical due to its reliance on an optimization-based approach + +that is extremely time consuming and numerically unstable. In contrast, our method generates a sketch of an image in a single inference step after training, and is relatively more stable and suitable as a representation. + +# 3. Mathematical framework + +In this section, we present our theoretical analysis on how sketches can facilitate geometry-aware representation. We begin with a formal definition of sketch and strokes. We then introduce a mathematical framework based on geometric deep learning, which aims to impose the geometric prior on the learned feature.1 Finally, we show that with a loss function that satisfies certain conditions, strokes can be equivariant with respect to arbitrary affine transformations and thus preserve geometric information. + +# 3.1. Preliminaries and notations + +We consider an image $I \in \mathcal{I}$ as signals on a physical domain $\Omega$ , which maps pixel coordinates to the $C$ color channels, i.e., $I: \Omega \to \mathbb{R}^C$ . Although $\Omega$ is a 2D grid space for the real image, we assume $\Omega$ as a homogeneous space, where each border is connected to the opposite side. + +Stroke and sketch. A stroke is a tuple $p = (t, c, w)$ composed of $k$ control points $t \in \Omega^k$ , color $c \in [0,1]^C$ , and thickness $w \in [0,1]$ of the Bézier curve. A rendering process $r: \mathcal{P} \to S(\subset \mathcal{I})$ converts a set of $n$ strokes $\pmb{p} = \{p^{(1)}, \dots, p^{(n)}\} \in \mathcal{P}$ into the corresponding image (see Appendix D for further details), which we denote as sketch $S = r(\pmb{p}) \in S$ . Let $f: \mathcal{I} \to \mathcal{P}$ be the embedding function which maps an image to a set of strokes. We denote $f(I) \in \mathcal{P}$ and $[r \circ f](I) \in S$ respectively as a stroke representation and a sketch representation of the image $I$ w.r.t $f$ . To generate a sketch that accurately reflects the given image, we adopt a metric function $\mathcal{L}: \mathcal{I} \times S \to \mathbb{R}$ that measures the distance between the image and the sketch. + +Definition 1. We denote $S_{I} = \arg \min_{S\in \mathcal{S}}\mathcal{L}(I,S)$ as an optimal sketch representation of $I$ . + +Geometry-aware representation. We denote $\mathcal{G}$ as a group of geometric transformations that acts on points in $\Omega$ (see Appendix E for definitions). For example, $\mathcal{G}$ could be a group of translation or rotation. $\rho$ is a group representation of $g\in \mathcal{G}$ such that $\rho (g)$ is a linear operator which acts on $\mathcal{I}$ , i.e., $[ \rho (g)I ] ( u ) = I ( g ^ { - 1 } u )$ for $u\in \Omega$ + +Definition 2. $f(I)$ is a geometry-aware representation of $I$ with respect to $\mathcal{G}$ if there exists a group representation $\rho'$ such that $f(\rho(g)I) = \rho'(g)f(I)$ for $\forall I \in \mathcal{I}$ and $\forall g \in \mathcal{G}$ . + +In this case, we say $f$ is a $\mathcal{G}$ -equivariant map, and the symmetry of $\mathcal{G}$ is preserved by $f$ . For example, a convolution operator is a translation-equivariant map since the feature of the shifted image is equal to the shifted feature of + +![](images/e8ce89e563b6225adcd168ef774be80bae3e9b4f72a518784d8868d6538ec32c.jpg) +Figure 3. Visualization of the overall architecture of LBS. (a) A CNN-based encoder extracts the feature of the image. (b) Initial strokes are updated repeatedly with a stroke generator based on a Transformer decoder. For the progressive optimization process, intermediate strokes are extracted from each intermediate layer. (c) The rasterized sketch and stroke embedding $z_{h}$ are generated from the strokes. Features derived from the CNN encoder, strokes, and stroke embedding are combined to form the final representation, $z_{LBS+}$ . + +the original image. In other words, the convolution operator preserves the symmetry of the translation and produces a geometry-aware representation with respect to it. + +# 3.2. Geometry-aware representations by sketching + +We now show that stroke representation is a geometry-aware representation with respect to arbitrary affine transformations. Refer to Appendix E for detailed proofs. + +Proposition 1. If $\mathcal{L}(\rho(g)I, \rho(g)S) = \lambda(g)\mathcal{L}(I, S)$ where $\lambda : \mathcal{G} \to \mathbb{R}^+$ exists, and there exists a unique $f^*$ such that $[r \circ f^*](I) = S_I$ for $\forall I \in \mathcal{I}$ , then $f^*(I)$ is a geometry-aware representation w.r.t. affine transformations $\mathcal{A}$ . + +Prop. 1 states the conditions for $f$ to be an $\mathcal{A}$ -equivariant map. Therefore, by designing stroke representations to be injective for $r$ , and optimizing $f$ to minimize $\mathcal{L}$ subject to the conditions outlined in Prop. 1, $f$ generates a geometry-aware representation with respect to arbitrary affine transformations. In the next section, we propose an architecture and a loss function that satisfy these conditions. + +# 4. Method + +We describe our model LBS, which provides geometry-aware representations from strokes by learning to generate a sketch in a short inference time without using a sketch dataset. We introduce an objective function and techniques for training LBS. We then propose a stroke embedding network that aggregates information of whole strokes. Hereafter, we use the terms "sketch" and "image" to denote realized sketch $S(\Omega)$ and realized image $I(\Omega)$ for simplicity. + +# 4.1. Learning by Sketching (LBS) + +LBS aims to generate a set of strokes to sketch the image and extract geometric information with color for down- + +stream tasks. To achieve the goal, we design a stroke generator by referring to Transformer-based sketch generation models [48,60]. + +Architecture. As shown in Fig. 3, LBS generates a set of strokes from trainable parameters, which are denoted as initial strokes. Our stroke generator uses Transformer decoder layers and incorporates image features from a CNN encoder (ResNet18 is used in this paper). Then, 2-layer MLP decoders decode a set of $n$ strokes from the output of the Transformer decoder. Each stroke contains four control points that parameterize a cubic Bezier curve, as well as color and thickness information. The sketch of an image is then created by rasterizing the generated set of strokes using a differentiable rasterizer [53]. For a detailed description of our architecture, please refer to Appendix C. + +Representation of LBS. The primary output of LBS is a set of strokes $\pmb{p}$ , and a geometry-aware representation is obtained by using the flattened vector of the strokes $z_{p} = (p^{(1)},\dots,p^{(n)})$ . To complement information that may not be encoded with strokes such as texture, we concatenate $z_{p}$ with the image features $z_{e}$ from the CNN encoder with global average pooling. The resulting concatenated representation is denoted as $z_{LBS}$ . In addition, we can combine this with representation $z_{h}$ that aggregates the entire stroke, the result of which we denote as $z_{LBS+}$ . Further details can be found in Sec. 4.4. The final representation space of LBS is as follows: + +$$ +z _ {L B S} = \left(z _ {e}, z _ {p}\right), \quad z _ {L B S +} = \left(z _ {e}, z _ {p}, z _ {h}\right). \tag {1} +$$ + +# 4.2. CLIP-based perceptual loss function + +As discussed in Sec. 3.2, proper $\mathcal{L}$ must be given to train a geometry-aware representation of an image. To this end, we adopt CLIP-based perceptual loss to measure the sim + +![](images/659d2d001fb14f4c82237891847c7c65030ece67e44ccedbc8d278b716f3c0fc.jpg) +Figure 4. Visualization of the progressive optimization process. Strokes initialized from the saliency map are optimized using the gradient of $\mathcal{L}_{\text{percept}}$ until convergence and stored in a total of $L$ intermediate steps denoted by $\pmb{p}_{gt,l}$ . Then, the stroke generator is trained through $\mathcal{L}_{\text{guide}}$ to progressively predict each intermediate stroke $\pmb{p}_l$ from $\pmb{p}_{gt,l}$ . + +ilarity between the sketch and the input image in terms of both geometric and semantic differences [68]. To generate a sketch that is semantically similar to the input image, it should minimize the distance on the embedding space of the CLIP model $f_{C}$ as follows: + +$$ +\mathcal {L} _ {\text {s e m a n t i c}} = \sum_ {A \in \mathcal {A}} \phi (A (I), A (S)), \tag {2} +$$ + +where $\mathcal{A}$ is the group of affine transformations and $\phi$ is the cosine similarity of the CLIP embeddings, i.e., $\phi (x,y) = \cos (f_C(x),f_C(y))$ . In addition, it compares low-level features of the sketch and the input image to estimate the geometric similarity as follows: + +$$ +\mathcal {L} _ {\text {g e o m e t r i c}} = \sum_ {A \in \mathcal {A}} \sum_ {i} \phi_ {i} (A (I), A (S)), \tag {3} +$$ + +where $\phi_{i}$ is the $\mathcal{L}_2$ distance of the embeddings from the $i$ -th intermediate layer of the CLIP model, i.e., $\phi_{i}(x,y) = \| f_{C,i}(x) - f_{C,i}(y)\|_{2}^{2}$ . Specifically, we used $i\in \{3,4\}$ with the ResNet101 CLIP model, proposed as [68]. The final perceptual loss is as follows: + +$$ +\mathcal {L} _ {\text {p e r c e p t}} = \mathcal {L} _ {\text {g e o m e t r i c}} + \lambda_ {s} \cdot \mathcal {L} _ {\text {s e m a n t i c}}, \tag {4} +$$ + +with $\lambda_{s} = 0.1$ as a hyperparameter. + +# 4.3. Training with progressive optimization process + +Abstracting an image into a sketch requires high-level reasoning, and predicting the corresponding stroke parameters in a single inference step is a delicate process. Although CLIPasso [68] addresses these problems via an optimization-based approach, its time-consuming properties ( $\sim 2$ min per image) make it impractical as a representation. Moreover, as CLIPasso reported that the changes + +in initial strokes significantly impacted the final results, directly optimizing each stroke through the optimizer for thousands of steps leads to highly variable results and numerical instability. + +To generate a stable representation within a single inference step, we modify the optimization-based approach of CLIPasso and utilize it as desirable guidance for the stroke generator, which we call the guidance stroke and denote as $\pmb{p}_{gt}$ . To ensure high-quality sketch generation, each intermediate layer of the stroke generator is guided by strokes obtained at the corresponding intermediate step of the optimization process instead of relying solely on the final outcome. This process, depicted in Fig. 4, involves progressively updating strokes from the previous layer, which can be modeled by residual blocks from the Transformer architecture. By decomposing the prediction of the entire optimization process into predicting changes in relatively short intervals for each intermediate layer, our approach leads to better-quality sketches. + +However, the process through which CLIPasso initializes strokes via stochastic sampling from the saliency map results in unstable outcomes. To address this issue, we select initialized strokes deterministically by selecting the most salient regions from the saliency map in a greedy manner. The color of the stroke is determined during the initialization step by referencing the corresponding region in the original image. More details are described in Appendix A. + +To ensure that the guidance loss is invariant to the permutation of the order of each stroke, we use the Hungarian algorithm [41] which is widely used for the assignment problem. The guidance loss is as follows: + +$$ +\mathcal {L} _ {\text {g u i d e}} = \sum_ {l = 1} ^ {L} \min _ {\sigma} \sum_ {i = 1} ^ {n} \mathcal {L} _ {1} \left(p _ {g t, l} ^ {(i)}, p _ {l} ^ {(\sigma (i))}\right), \tag {5} +$$ + +where $\sigma$ is a permutation of the stroke index, and $p_l^{(i)}$ is the $i$ -th decoded stroke from the $l$ -th intermediate layer with $L$ layers in total. $\mathcal{L}_1$ is the L1 distance, and $p_{gt,l}^{(i)}$ is the guidance stroke corresponding to $p_l^{(\sigma(i))}$ . + +# 4.4. Stroke embedding network + +As strokes primarily express localized and fine-grained details, they can be less suitable for representing coarse-grained information. To address this, we offer an additional representation that combines full strokes through a stroke embedding network. Stroke embedding network $h: \mathcal{P} \to \mathcal{Z}_h$ maps the set of $n$ strokes into embedding space $\mathcal{Z}_h$ . Since the rasterized sketch is invariant to the stroke indices (except for contact point between strokes), we followed the permutation invariant model from DeepSets [80] to generate stroke embedding. The choice of the loss function $\mathcal{L}_{embed}$ to train $z_h \in \mathcal{Z}_h$ is unconstrained (e.g., Cross-Entropy or InfoNCE loss in our paper). During the training + +phase, the gradient from $h$ is also passed to $f$ to capture coarse-grained information. + +The final objective is as follows: + +$$ +\mathcal {L} _ {L B S} = \mathcal {L} _ {\text {p e r c e p t}} + \lambda_ {g} \cdot \mathcal {L} _ {\text {g u i d e}} + \lambda_ {e} \cdot \mathcal {L} _ {\text {e m b e d}}, \tag {6} +$$ + +where $\lambda_{g}$ and $\lambda_{e}$ are hyperparameters (for specific values, refer to Appendix C). + +# 5. Experiments + +# 5.1. Research questions and task designs + +We investigate the effectiveness and generalizability of our approach by designing multiple research questions, as well as corresponding downstream tasks for each question. Detailed information about each experimental setup is described in Appendix B. + +# RQ1. Effects of equivariance: What is the benefit of equivariant representation, and does LBS achieve it? + +From the definition of equivariance, we expect that an equivariant model with respect to geometric transformation would have generalization capability for augmented images with transformation. To verify this, we conduct experiments on the Rotated MNIST (rotMNIST) dataset [22], which consists of rotated images from the MNIST dataset. We rotate images by $30^{\circ}$ and $45^{\circ}$ for training and classify the digit of images rotated by $0^{\circ}$ and $90^{\circ}$ to evaluate whether LBS generalizes the information from the training domain to the test domain. To verify that our model satisfies equivariance outside the training domain, we classify the rotation and reflection between an original image and the same image rotated with an interval of $90^{\circ}$ and horizontally flipped. + +# RQ2. Effects on geometric primitives and concepts: How well does LBS represent geometric primitives and understand their conceptual relationships? + +To evaluate whether LBS is suitable for representing geometric primitives and concepts, we perform a classification task on the Geoclidean dataset [29]. The Geoclidean dataset consists of realized images from a concept of Euclidean geometry, e.g., black parallel lines on a white background. Geoclidean is divided into two categories: Geoclidean-Elements and Geoclidean-Constraints, visualized in Fig. 7 on Appendix B. By providing a limited training set consisting of only 10 images per concept, we evaluate whether LBS can effectively learn the high-level relationships between each primitive and generalize them across different examples by classifying the concept of the test image. + +# RQ3. Local geometric information and spatial reasoning: How effectively does LBS reflect local geometric information and extend it to spatial reasoning tasks? + +We validate whether LBS can reflect the local geometric information of each object in a synthetic photo dataset consisting of multiple objects, using the CLEVR dataset [34]. + +Table 1. Quantitative results of LBS and the baselines evaluated on the corresponding tasks on the rotMNIST and Geoclidean. + +
La- +belMethodrotMNIST (30°, 45°)Geoclidean
0°, 90°RotationConstraintsElements
✓CE62.72±1.8973.14±0.3553.89±1.5870.57±4.29
SupCon [38]65.25±1.0573.37±0.2042.41±3.1655.83±4.28
LtD-diff [54]60.09±1.1628.91±2.1557.26±2.1969.47±2.11
E(2)-CNN [73]85.12±0.1777.00±0.3971.03±1.9469.28±1.46
LBS (CE)65.00±3.3275.81±0.3050.01±1.5881.06±3.14
XSimCLR [9]47.66±0.4172.96±0.8432.04±0.6465.14±4.11
β-TCVAE [8]37.84±1.0660.14±0.3217.18±1.3533.82±1.64
GeoSSL [55]--18.66±3.3333.47±2.80
HoG [14]25.4264.9423.8252.05
LBS47.31±2.5370.02±0.6447.43±1.3481.34±0.16
+ +We train our model with very limited descriptions, where the label for the entire scene is provided as the rightmost object or without any descriptions at all. We validate the effectiveness of our representation by evaluating its ability to successfully classify attributes that are not provided as labels, such as determining the color of the leftmost object. Additionally, we test its ability to perform simple spatial reasoning, such as shifting the rightmost object and inferring the attribute of the current rightmost object. + +# RQ4. Domain transfer: Can the geometric concepts of LBS trained in a specific domain be extended to other domains? + +To investigate whether the learned representation within a specific image domain provides meaningful geometric information across other domains, we evaluate the model by shifting the distribution from the STL-10 [11] dataset to CLEVR and vice versa. Evaluation in the STL-10 dataset is conducted through object classification. + +# RQ5. Traditional sketch tasks: Does geometry-aware representation from LBS help in traditional FG-SBIR tasks? + +We assess the impact of geometry-aware representations acquired by LBS on a conventional sketch task by evaluating them with the fine-grained sketch-based image retrieval (FG-SBIR) task on the QMUL-ShoeV2 Dataset [78]. The aim of FG-SBIR is to match a given sketch of a shoe to its corresponding photo image. Since geometric information is essential for distinguishing each shoe, we investigate whether leveraging representations from LBS can improve performance on the FG-SBIR task. + +# 5.2. Experimental setup + +Implementation details. As samples from rotMNIST and Geoclidean can be directly represented with a few strokes, we replace $\mathcal{L}_{\text {percept }}$ and $\mathcal{L}_{\text {guide }}$ with $\mathcal{L}_1$ loss, which does not rely on a pre-trained CLIP model. For the STL-10 dataset, providing mask information for the background with U2-Net [57] improves the quality of generated sketches. For $\mathcal{L}_{\text {embed }}$ , we use Cross-Entropy loss for supervised training which we denote as LBS (CE) in Tab. 1, 2 and + +Table 2. Quantitative results on CLEVR dataset for labeled and unlabeled settings and for CLIP and HoG features. RC, LC, BC refer to inferring the color of the rightmost, leftmost, bottommost object, and Size, Shape, Material refer to inferring the size, shape, material of the rightmost object, respectively. Third refers to inferring the color of the third object from the right, and Shift refers to predicting the color of the rightmost object after shifting the initial rightmost object to the left by 0.15 times the image width. + +
LabelMethodRCLCBCSizeShapeMaterialThirdShift
✓CE98.71±0.1076.72±0.8676.02±0.9092.51±0.4049.97±0.2964.38±1.9040.66±0.2062.06±1.62
SupCon [38]98.75±0.0863.82±2.3666.04±2.6591.88±0.3749.15±0.8559.20±0.5737.93±0.2756.05±2.56
LtD-diff [54]62.29±0.4814.01±0.4215.84±0.4363.98±3.3843.96±3.0554.47±0.4516.47±0.5917.21±0.29
E(2)-CNN [73]98.50±0.1070.10±1.1573.51±2.5089.84±0.4645.85±0.9363.05±0.5941.95±0.1859.29±0.91
LBS (CE)97.49±0.2281.79±0.2784.09±0.8493.22±0.2970.03±0.6886.84±0.5438.23±0.2551.56±0.16
×SimCLR [9]60.61±1.2463.89±2.3563.77±2.2983.35±0.6041.95±0.3351.66±0.2433.42±0.5543.05±0.55
E(2)-CNN [73]53.50±7.3054.60±7.3455.52±7.6083.52±1.5642.06±1.1253.04±2.8130.74±2.8438.03±4.44
β-TCVAE [8]17.09±0.2017.50±0.3320.04±0.7171.27±0.1036.30±0.1056.11±0.1315.38±0.1916.35±0.18
GeoSSL [55]20.16±0.6320.54±0.8721.61±0.6773.79±0.7844.08±1.1054.54±2.9415.39±0.1616.94±0.34
DefGrid [21]73.81±0.9173.96±1.0273.38±0.8081.50±0.2246.34±0.7768.65±1.1724.90±0.2736.28±0.13
LBS84.31±0.0880.47±0.7883.00±0.3992.66±0.4170.01±0.5385.52±0.4337.41±0.2949.32±0.17
CLIP [59]37.3939.154.9877.5166.9172.6634.7534.80
HoG [14]56.8349.6958.6981.7361.1468.3824.2833.25
+ +Table 3. Quantitative results of models trained on STL-10 dataset and evaluated on CLEVR dataset. + +
DatasetMethodRCLCBCSizeShapeMaterialThirdShift
STL-10↓CLEVRLtD [54]18.70±0.0219.15±0.7721.69±1.0573.13±3.2147.88±1.1359.11±2.3416.47±0.5917.21±0.29
SimCLR [9]26.97±0.2826.26±0.8838.88±0.1982.33±0.6456.88±1.2377.39±0.3523.45±0.3524.95±0.17
E(2)-CNN [73]26.82±2.2325.40±1.2039.30±2.8079.48±0.7153.54±0.8472.18±0.3423.35±1.0124.80±1.08
β-TCVAE [8]17.04±0.7618.46±2.3618.88±1.1471.32±0.6737.14±0.1256.81±0.2615.63±1.3516.43±0.38
GeoSSL [55]14.41±0.5514.73±0.1114.37±0.6677.47±5.1748.10±1.9055.63±2.8613.71±0.4513.63±0.13
DefGrid [21]66.74±1.1068.60±0.0868.35±0.8278.97±0.2940.92±0.4462.98±1.3123.48±0.4933.07±0.52
LBS53.87±2.7253.85±2.2061.84±2.2392.46±0.6259.52±0.4580.06±1.2930.75±0.4139.95±1.15
+ +Table 4. Quantitative results of models trained on CLEVR dataset and evaluated on STL-10 dataset classification. + +
DatasetLabeledUnlabeled
MethodAccuracyMethodAccuracy
CLEVR↓STL-10CE46.15±0.12SimCLR [9]41.68±0.05
SupCon [38]43.41±0.36β-TCVAE [8]27.35±0.38
LtD-diff [54]50.81±0.67GeoSSL [55]35.93±0.96
E(2)-CNN [73]45.19±0.84E(2)-CNN [73]38.50±0.49
LBS (CE)56.48±0.89DefGrid [21]33.13±0.17
LBS55.35±0.18
+ +4. For the unlabeled setting, the model is trained without $\mathcal{L}_{embed}$ and is denoted LBS with no parentheses. For evaluation, we use $z_{LBS+}$ for LBS (CE), and $z_{LBS}$ for LBS. All evaluations are performed with the common protocol of linear classification. For more detailed information on our implementation, please refer to Appendix C. + +Baselines. We compare our models with: + +- Models which only use image encoder: trained with Cross-Entropy, SimCLR [9], or SupCon loss [38]. +- Equivariance models: E(2)-Equivariant Steerable CNNs (E(2)-CNN) [73], and work by Novotny et al., denoted as GeoSSL [55]. +- Disentanglement model: $\beta$ -TCVAE [8]. + +- Sketch model for communication between agents: Learning to Draw (LtD) [54] +- Grid-based superpixel model: DefGrid [21] +- Handcrafted feature descriptor: HoG [14]. +- Pre-trained CLIP model used for training LBS. + +# 5.3. Results and analysis + +Analysis on RQ1 and RQ2: Tab. 1 shows the experimental results for RQ1 and RQ2, which can be summarized as: (a) Providing a strong inductive bias for equivariance, as shown in the case of E(2)-CNN, leads to good performance on the tasks of RQ1. While LBS outperformed LtD-diff, which also utilizes a sketch-based approach, it requires additional validation and refinement. (b) For RQ2, LBS performs substantially better than the other baselines except for the supervised setting on Geoclidean-Constraints, showing that it successfully captures geometric concepts. In particular, Geoclidean-Elements perform better when trained without labels. (c) Disentanglement methods and handcrafted features offer less informative features for both tasks. + +Analysis on RQ3: Tab. 2 summarizes the experiments conducted on the CLEVR dataset, demonstrating that LBS provides valuable information for tasks of RQ3. The key observations from Tab. 2 are: (a) While the baselines in the + +Table 5. Top-1 and Top-10 accuracy on QMUL-Shoe-v2 dataset, using Triplet Loss for $\mathcal{L}_{embed}$ in LBS. + +
MethodRepTop-1Top-10
LBS (Triplet)zLBS+40.8±4.1988.3±1.76
ze30.8±3.8977.8±3.89
Tripletze32.5±1.7380.0±4.36
+ +supervised setting struggle to generalize on unlearned attributes, LBS (CE) can provide more general information. (b) The results of LBS show a larger performance gap in the unlabeled setting, with its performance being almost as good as LBS (CE). (c) Embeddings from pre-trained CLIP perform less effectively than unlabeled baselines, such as SimCLR, on tasks related to local geometry. Also, handcrafted features yielded limited effectiveness. (d) Methods that focus on preserving global transformations and disentanglement are not effective in environments of RQ3. + +Analysis on RQ4: Tabs. 3 and 4 summarize the results for shifting domains from STL-10 to CLEVR, and vice versa. As shown in Fig. 11 on Appendix I, LBS trained on STL-10 can successfully describe scenes from CLEVR, while LBS trained on CLEVR can abstractly depict natural images from STL-10, leading to substantially high classification accuracy. These results indicate that learning geometric information, such as position and curvature, by sketching salient parts of a scene successfully induces learning of general features across domains. Furthermore, LtD-diff, which also utilizes a sketch-based approach, demonstrated good performance in transferring CLEVR to STL-10. + +Analysis on RQ5: Tab. 5 presents the results for the FG-SBIR task. Compared to the baseline trained without sketching, LBS can accurately predict the corresponding shoe during the test phase. The huge drop in performance upon removing strokes and stroke embedding from $z_{LBS+}$ indicates that the geometry-aware representation provided by LBS is also valuable for traditional sketch tasks. + +# 5.4. Comparisons with stroke-based methods + +Tab. 6 compares LBS to other stroke-based generation methods on STL-10 dataset, and Fig. 5 visualizes the results of each method. The evaluation is based solely on strokes, and LBSonly uses $z_{p}$ as a representation. LBS ( $\mathcal{L}_{\text{percept}}$ ) achieved superior results compared to LBS ( $\mathcal{L}_1$ ) and the Paint Transformer [48] based on $\mathcal{L}_1$ loss. We also compare our results to CLIPasso modified to use our deterministic initialization process, suggesting that strokes generated from CLIPasso may not be suitable as a representation. LtD-diff, which generates sketches to solve a communication game, often omits important geometric and color information, resulting in low performance. + +Table 6. Comparison between stroke-based generation methods. + +
RCBCSizeShapeMaterial
LtD-diff [54]18.7021.6973.1347.8859.11
Paint [48]51.9660.4077.3544.3070.02
CLIPasso [68]12.5513.5555.3535.4050.00
LBS (L1)34.4357.8178.3240.9961.59
LBS (Lpercept)55.1560.6390.1451.2376.16
+ +![](images/40b28f7b4f829fc9c4f298b97fdd99fdcb5a8747450c02c5237e6d380a161c75.jpg) +Image + +![](images/5079b595f71bd5bf05ba88d1122beef86c26ba739a0daa37438fbfeab8294b6e.jpg) + +![](images/c1e78f89ce9b879d04293557e74151e33a2917b704e58a2601b8a87fa160227b.jpg) + +![](images/294718abd7aa9d3b0a1dfb5ef008de731d41fae507cd82a0a93e14066a6b0d0e.jpg) +CLIPasso +Figure 5. Comparisons to other stroke-based methods. LBS encodes both the geometric and semantic information. + +![](images/f6ca962c5db510c9b03283a6e47584f237198c2f20702026d3e5348aef5e991e.jpg) +LBS $(\mathcal{L}_{percept})$ +LtD-diff + +![](images/6aa3c1ddf294f05add07b2e376097960a930fe16ca6a354dbd988b5adcf81a84.jpg) +LBS $(\mathcal{L}_1)$ +Paint Transformer + +# 6. Conclusion + +We propose a novel representation learning perspective through sketching, a visual expression that retains geometric information. By considering the mathematical concept of equivariance, we provide a formal definition of sketch and stroke, and prove that strokes can preserve the information of arbitrary affine transformations. Our sketch generation model, LBS, minimizes CLIP-based perceptual loss and supports the idea that sketches can effectively convey geometric information. The experiments shed light on the potential benefits of leveraging the process of sketching to represent high-level geometric information explicitly. These benefits include learning equivariant representations, understanding geometric concepts, improving spatial reasoning abilities, and acquiring general geometric information across different domains. + +Still, there are several limitations to our method. The training process of LBS relies on pre-trained CLIP and optionally U2-Net, and requires generating guidance strokes through a time-consuming optimization-based process. Moreover, while our work has demonstrated the theoretical strengths of sketching in terms of equivariance, a clearer methodology and further experimental analysis are needed to fully achieve this potential. Future work should address these issues and extend the methodology, focusing on scalability and including more complex and realistic tasks. + +Acknowledgement This work was partly supported by the Korean government (2021-0-02068-AIHub/25%, 2021-0-01343-GSAI/25%, 2022-0-00951-LBA/25%, 2022-0-00953-PICA/25%). + +# References + +[1] Pablo Arbelaez, Michael Maire, Charless Fowlkes, and Jitendra Malik. Contour detection and hierarchical image segmentation. IEEE Trans. Pattern Anal. Mach. Intell., 33(5):898-916, May 2011. 3 +[2] Hilton Bristow, Jack Valmadre, and Simon Lucey. Dense semantic correspondence where every pixel is a classifier. In Proceedings of the IEEE International Conference on Computer Vision, pages 4024-4031, 2015. 1, 2 +[3] Michael M. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 15689-15698, 2021. 3 \ No newline at end of file diff --git a/2023/Learning Geometry-Aware Representations by Sketching/images.zip b/2023/Learning Geometry-Aware Representations by Sketching/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..0b1b53ea14f9ca421bd27d22e8d3745261c81165 --- /dev/null +++ b/2023/Learning Geometry-Aware Representations by Sketching/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:0515f2bfec849ded33dd5cd4fa9d6f73cf00c64833661aefd373fff5fbde3383 +size 577204 diff --git a/2023/Learning Geometry-Aware Representations by Sketching/layout.json b/2023/Learning Geometry-Aware Representations by Sketching/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..ce90158d3e97c7fa16f168755759c800dd8554a5 --- /dev/null +++ b/2023/Learning Geometry-Aware Representations by Sketching/layout.json @@ -0,0 +1,10858 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 121, + 103, + 473, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 121, + 103, + 473, + 121 + ], + "spans": [ + { + "bbox": [ + 121, + 103, + 473, + 121 + ], + "type": "text", + "content": "Learning Geometry-aware Representations by Sketching" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 66, + 143, + 526, + 171 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 143, + 526, + 171 + ], + "spans": [ + { + "bbox": [ + 66, + 143, + 526, + 171 + ], + "type": "text", + "content": "Hyundo Lee, Inwoo Hwang, Hyunsung Go, Won-Seok Choi, Kibeom Kim, Byoung-Tak Zhang AI Institute, Seoul National University" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 138, + 174, + 452, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 138, + 174, + 452, + 185 + ], + "spans": [ + { + "bbox": [ + 138, + 174, + 452, + 185 + ], + "type": "text", + "content": "{hdlee, iwhwang, hsgo, wchoi, kbkim, btzhang}@bi.snu.ac.kr" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "spans": [ + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 238, + 290, + 478 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 238, + 290, + 478 + ], + "spans": [ + { + "bbox": [ + 46, + 238, + 290, + 478 + ], + "type": "text", + "content": "Understanding geometric concepts, such as distance and shape, is essential for understanding the real world and also for many vision tasks. To incorporate such information into a visual representation of a scene, we propose learning to represent the scene by sketching, inspired by human behavior. Our method, coined Learning by Sketching (LBS), learns to convert an image into a set of colored strokes that explicitly incorporate the geometric information of the scene in a single inference step without requiring a sketch dataset. A sketch is then generated from the strokes where CLIP-based perceptual loss maintains a semantic similarity between the sketch and the image. We show theoretically that sketching is equivariant with respect to arbitrary affine transformations and thus provably preserves geometric information. Experimental results show that LBS substantially improves the performance of object attribute classification on the unlabeled CLEVR dataset, domain transfer between CLEVR and STL-10 datasets, and for diverse downstream tasks, confirming that LBS provides rich geometric information." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 501, + 128, + 514 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 501, + 128, + 514 + ], + "spans": [ + { + "bbox": [ + 47, + 501, + 128, + 514 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 521, + 287, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 287, + 641 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 287, + 641 + ], + "type": "text", + "content": "Since geometric principles form the bedrock of our physical world, many real-world scenarios involve geometric concepts such as position, shape, distance, and orientation. For example, grabbing an object requires estimating its shape and relative distance. Understanding geometric concepts is also essential for numerous vision tasks such as image segmentation, visual reasoning, and pose estimation [27]. Thus, it is crucial to learn a visual representation of the image that can preserve such information [76], which we call geometry-aware representation." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 642, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 288, + 715 + ], + "type": "text", + "content": "However, there is still a challenge in learning geometry-aware representations in a compact way that can be useful for various downstream tasks. Previous approaches have focused on capturing geometric features of an image in a 2D grid structure, using methods such as handcrafted feature extraction [2, 4, 14, 31], segmentation maps [21, 57], or" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 315, + 213, + 535, + 347 + ], + "blocks": [ + { + "bbox": [ + 315, + 213, + 535, + 347 + ], + "lines": [ + { + "bbox": [ + 315, + 213, + 535, + 347 + ], + "spans": [ + { + "bbox": [ + 315, + 213, + 535, + 347 + ], + "type": "image", + "image_path": "acb59d35df6f7bc2e3430296b492e7e7e1744cb30a0210c7a994b08e09f0bdcf.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 354, + 547, + 411 + ], + "lines": [ + { + "bbox": [ + 304, + 354, + 547, + 411 + ], + "spans": [ + { + "bbox": [ + 304, + 354, + 547, + 411 + ], + "type": "text", + "content": "Figure 1. Overview of LBS, which aims to generate sketches that accurately reflect the geometric information of an image. A sketch consists of a set of strokes represented by a parameterized vector that specifies curve, color, and thickness. We leverage it as a geometry-aware representation for various downstream tasks." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 426, + 545, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 426, + 545, + 557 + ], + "spans": [ + { + "bbox": [ + 304, + 426, + 545, + 557 + ], + "type": "text", + "content": "convolution features [36, 55]. Although these methods are widely applicable to various domains, they often lack compactness based on a high-level understanding of the scene and tend to prioritize nuisance features such as the background. Another line of work proposes architectures that guarantee to preserve geometric structure [12, 13, 23, 58, 73] or disentangle prominent factors in the data [8, 28, 39, 51]. Although these methods can represent geometric concepts in a compact latent space, they are typically designed to learn features that are specific to a particular domain and often face challenges in generalizing to other domains [64]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 558, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 546, + 714 + ], + "type": "text", + "content": "In this study, we present a novel approach to learning geometry-aware representations via sketching. Sketching, which is the process of converting the salient features of an image into a set of color-coded strokes, as illustrated in Figure 1, is the primary means by which humans represent images while preserving their geometry. Our key idea is that sketches can be a compact, high-level representation of an image that accurately reflects geometric information. Sketching requires a high-level understanding of the scene, as it aims to capture the most salient features of the image and abstract them into a limited number of strokes. In addition, a sketch can be represented as a set of parameters by replacing each stroke with parametric curves. Sketch-" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "23315" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 52, + 75, + 532, + 229 + ], + "blocks": [ + { + "bbox": [ + 52, + 75, + 532, + 229 + ], + "lines": [ + { + "bbox": [ + 52, + 75, + 532, + 229 + ], + "spans": [ + { + "bbox": [ + 52, + 75, + 532, + 229 + ], + "type": "image", + "image_path": "76d1e600a6daaab19456fc30889477324598309ccd191d694be2599883e9f568.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 233, + 546, + 268 + ], + "lines": [ + { + "bbox": [ + 46, + 233, + 546, + 268 + ], + "spans": [ + { + "bbox": [ + 46, + 233, + 546, + 268 + ], + "type": "text", + "content": "Figure 2. Examples of how sketches capture essential geometric concepts such as shape, size, orientation, curvature, and local distortion. The control points of each stroke compactly represent the local geometric information of the corresponding region in the sketch. The strokes as a whole maintain the geometric structure of the entire image under various transformations in the image domain." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 282, + 287, + 366 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 282, + 287, + 366 + ], + "spans": [ + { + "bbox": [ + 46, + 282, + 287, + 366 + ], + "type": "text", + "content": "ing has also been linked to how people learn geometric concepts [66]. Based on these properties, we directly use strokes as a geometry-aware representation and utilize them for downstream tasks. Under the theoretical framework of geometric deep learning [3], we conduct theoretical analysis to validate the effectiveness of strokes as a representation and prove their ability to preserve affine transformations." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 366, + 287, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 366, + 287, + 605 + ], + "spans": [ + { + "bbox": [ + 46, + 366, + 287, + 605 + ], + "type": "text", + "content": "To validate our hypothesis, we introduce Learning by Sketching (LBS), a method that generates abstract sketches coherent with the geometry of an input image. Our model is distinct from existing sketch generation methods as it does not require a sketch dataset for training, which often has limited abstraction or fails to accurately reflect geometric information. Instead, LBS learns to convert an image into a set of colored Bezier curves that explicitly represent the geometric concepts of the input image. To teach the style of sketching, we use perceptual loss based on the CLIP model [59, 68], which measures both semantic and geometric similarities between images and generated sketches. We propose a progressive optimization process that predicts how strokes will be optimized from their initial positions through CLIP-based perceptual loss to generate abstract sketches in a single inference step. As a result, LBS generates a representation that reflects visual understanding in a single inference step, without requiring a sketch dataset. This produces highly explainable representations through sketches, as illustrated in Figure 2." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "content": "We conduct experimental analyses to evaluate the effectiveness of our approach, learning by sketching, by addressing multiple research questions in various downstream tasks, including: (i) describing the relationships between geometric primitives, (ii) demonstrating simple spatial reasoning ability by conveying global and local geometric information, (iii) containing general geometric information shared across different domains, and (iv) improving performance on FG-SBIR, a traditional sketch task." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 281, + 389, + 294 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 281, + 389, + 294 + ], + "spans": [ + { + "bbox": [ + 306, + 281, + 389, + 294 + ], + "type": "text", + "content": "2. Related work" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 304, + 520, + 317 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 304, + 520, + 317 + ], + "spans": [ + { + "bbox": [ + 306, + 304, + 520, + 317 + ], + "type": "text", + "content": "2.1. Geometry-aware representation learning" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 325, + 546, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 325, + 546, + 396 + ], + "spans": [ + { + "bbox": [ + 305, + 325, + 546, + 396 + ], + "type": "text", + "content": "Previous studies that aim to capture geometric information within the data can be categorized into two approaches: Firstly, explicitly capturing the geometric information with features on the image space, and secondly, inducing a compact feature vector that preserves the geometric structure of the data." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 399, + 546, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 399, + 546, + 591 + ], + "spans": [ + { + "bbox": [ + 304, + 399, + 546, + 591 + ], + "type": "text", + "content": "Features on image space. The most straightforward approach to representing geometric structures in images is to establish features directly on the image space, i.e., to define features on the 2D grid structure. Approaches that utilize this method include those that employ traditional edge detection algorithms [4, 35, 74, 75], low-level convolutional features [36, 68], and segmentation maps [49, 57, 61]. However, these features are unsuitable for conversion into compact vector representations for downstream tasks. Alternative approaches include utilizing hand-crafted feature detection algorithms [2, 14, 31, 62], clustering specific areas of an image into superpixels [21, 32], and representing the relationships between specific areas as a graph [15, 65]. Our approach is primarily notable for its ability to capture the most salient image features through an overall understanding of the scene, resulting in a concise representation." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "text", + "content": "Geometric deep learning. Research has also been conducted to develop informative and compact representations that preserve geometric structures in a latent vector space. One representative method is geometric deep learning [3], which involves preserving the geometric properties of an image by learning an invariant (i.e., maintaining the output identically) or an equivariant representation (i.e., there exists an operator acting on the feature space corresponding to the transformations) with respect to geometric transformations. Steerable networks [12, 13, 23, 73] extend the" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "23316" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "text", + "content": "translation equivariance of CNNs to a larger group of symmetries and introduce an efficient weight-sharing architecture. However, designing their architecture requires complex analytic solutions, and they are constrained to particular transformations [37]. Another approach is to disentangle factors of variation into distinct latent subspaces [8, 28, 39, 40, 51, 58, 70]. However, these methods face difficulties in handling changing factors of variation [64] and therefore struggle to generalize to arbitrary geometric transformations. Sketching, in contrast to these methods, can naturally ensure equivariance with respect to geometric transformations by being defined on the image space. In Sec. 3 we show that strokes can be equivariant with respect to arbitrary affine transformations." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 250, + 197, + 262 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 250, + 197, + 262 + ], + "spans": [ + { + "bbox": [ + 47, + 250, + 197, + 262 + ], + "type": "text", + "content": "2.2. Sketch generation methods" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 269, + 287, + 353 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 269, + 287, + 353 + ], + "spans": [ + { + "bbox": [ + 46, + 269, + 287, + 353 + ], + "type": "text", + "content": "Human-drawn sketches are widely used as valuable descriptions in various applications, including image retrieval [16, 47, 78], modeling 3D shapes and surfaces [25, 42, 43, 45], and image editing [33, 56, 69, 71]. Unfortunately, previous works that aim to learn sketching or drawing mostly endeavor to generate artistic works, rather than focusing on its applicability [19, 24, 30, 48, 52, 83]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 354, + 289, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 354, + 289, + 557 + ], + "spans": [ + { + "bbox": [ + 46, + 354, + 289, + 557 + ], + "type": "text", + "content": "Sketch generation models often rely on explicit sketch datasets to follow the style of human drawings [5, 10, 46, 60, 67, 82]. However, many existing datasets are not designed to preserve geometric information [7, 20, 63] or contain sketches without sophisticated image abstraction, resembling simple edge detection [1, 72]. This presents challenges for sketch models to accurately abstract an image while preserving its geometries. Without sketch datasets, stroke-based rendering methods usually minimize the reconstruction loss which is related to the pixel-wise distance, which promotes learning in the style of painting [19, 30, 48, 52, 53, 81, 83]. There have also been studies that attempt to capture the geometric and semantic features of a scene through imitating the style of line drawing [6, 44, 77]. However, these methods require numerous strokes to cover the whole canvas, primarily focusing on the superfluous background instead of salient features." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 558, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 289, + 714 + ], + "type": "text", + "content": "Abstract sketches for representation. Only a few works aim to generate sketches for the sake of representing an image with a limited number of strokes. Learning to Draw (LtD) [54] creates a representative sketch of an image and uses it as a communication channel between agents. While it primarily focuses on communicating with a specific receiver, we aim to leverage strokes as a general representation for various downstream tasks. CLIPasso [68] utilizes the capabilities of CLIP [59], a neural network trained on images paired with text, to synthesize abstract sketches by maintaining both semantic and geometric attributes. Generating representations with this method, however, is impractical due to its reliance on an optimization-based approach" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": "that is extremely time consuming and numerically unstable. In contrast, our method generates a sketch of an image in a single inference step after training, and is relatively more stable and suitable as a representation." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 129, + 454, + 143 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 129, + 454, + 143 + ], + "spans": [ + { + "bbox": [ + 305, + 129, + 454, + 143 + ], + "type": "text", + "content": "3. Mathematical framework" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 149, + 545, + 258 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 149, + 545, + 258 + ], + "spans": [ + { + "bbox": [ + 304, + 149, + 545, + 258 + ], + "type": "text", + "content": "In this section, we present our theoretical analysis on how sketches can facilitate geometry-aware representation. We begin with a formal definition of sketch and strokes. We then introduce a mathematical framework based on geometric deep learning, which aims to impose the geometric prior on the learned feature.1 Finally, we show that with a loss function that satisfies certain conditions, strokes can be equivariant with respect to arbitrary affine transformations and thus preserve geometric information." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 263, + 459, + 275 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 263, + 459, + 275 + ], + "spans": [ + { + "bbox": [ + 305, + 263, + 459, + 275 + ], + "type": "text", + "content": "3.1. Preliminaries and notations" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 281, + 545, + 341 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 281, + 545, + 341 + ], + "spans": [ + { + "bbox": [ + 304, + 281, + 545, + 341 + ], + "type": "text", + "content": "We consider an image " + }, + { + "bbox": [ + 304, + 281, + 545, + 341 + ], + "type": "inline_equation", + "content": "I \\in \\mathcal{I}" + }, + { + "bbox": [ + 304, + 281, + 545, + 341 + ], + "type": "text", + "content": " as signals on a physical domain " + }, + { + "bbox": [ + 304, + 281, + 545, + 341 + ], + "type": "inline_equation", + "content": "\\Omega" + }, + { + "bbox": [ + 304, + 281, + 545, + 341 + ], + "type": "text", + "content": ", which maps pixel coordinates to the " + }, + { + "bbox": [ + 304, + 281, + 545, + 341 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 304, + 281, + 545, + 341 + ], + "type": "text", + "content": " color channels, i.e., " + }, + { + "bbox": [ + 304, + 281, + 545, + 341 + ], + "type": "inline_equation", + "content": "I: \\Omega \\to \\mathbb{R}^C" + }, + { + "bbox": [ + 304, + 281, + 545, + 341 + ], + "type": "text", + "content": ". Although " + }, + { + "bbox": [ + 304, + 281, + 545, + 341 + ], + "type": "inline_equation", + "content": "\\Omega" + }, + { + "bbox": [ + 304, + 281, + 545, + 341 + ], + "type": "text", + "content": " is a 2D grid space for the real image, we assume " + }, + { + "bbox": [ + 304, + 281, + 545, + 341 + ], + "type": "inline_equation", + "content": "\\Omega" + }, + { + "bbox": [ + 304, + 281, + 545, + 341 + ], + "type": "text", + "content": " as a homogeneous space, where each border is connected to the opposite side." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 342, + 546, + 497 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 342, + 546, + 497 + ], + "spans": [ + { + "bbox": [ + 304, + 342, + 546, + 497 + ], + "type": "text", + "content": "Stroke and sketch. A stroke is a tuple " + }, + { + "bbox": [ + 304, + 342, + 546, + 497 + ], + "type": "inline_equation", + "content": "p = (t, c, w)" + }, + { + "bbox": [ + 304, + 342, + 546, + 497 + ], + "type": "text", + "content": " composed of " + }, + { + "bbox": [ + 304, + 342, + 546, + 497 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 342, + 546, + 497 + ], + "type": "text", + "content": " control points " + }, + { + "bbox": [ + 304, + 342, + 546, + 497 + ], + "type": "inline_equation", + "content": "t \\in \\Omega^k" + }, + { + "bbox": [ + 304, + 342, + 546, + 497 + ], + "type": "text", + "content": ", color " + }, + { + "bbox": [ + 304, + 342, + 546, + 497 + ], + "type": "inline_equation", + "content": "c \\in [0,1]^C" + }, + { + "bbox": [ + 304, + 342, + 546, + 497 + ], + "type": "text", + "content": ", and thickness " + }, + { + "bbox": [ + 304, + 342, + 546, + 497 + ], + "type": "inline_equation", + "content": "w \\in [0,1]" + }, + { + "bbox": [ + 304, + 342, + 546, + 497 + ], + "type": "text", + "content": " of the Bézier curve. A rendering process " + }, + { + "bbox": [ + 304, + 342, + 546, + 497 + ], + "type": "inline_equation", + "content": "r: \\mathcal{P} \\to S(\\subset \\mathcal{I})" + }, + { + "bbox": [ + 304, + 342, + 546, + 497 + ], + "type": "text", + "content": " converts a set of " + }, + { + "bbox": [ + 304, + 342, + 546, + 497 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 342, + 546, + 497 + ], + "type": "text", + "content": " strokes " + }, + { + "bbox": [ + 304, + 342, + 546, + 497 + ], + "type": "inline_equation", + "content": "\\pmb{p} = \\{p^{(1)}, \\dots, p^{(n)}\\} \\in \\mathcal{P}" + }, + { + "bbox": [ + 304, + 342, + 546, + 497 + ], + "type": "text", + "content": " into the corresponding image (see Appendix D for further details), which we denote as sketch " + }, + { + "bbox": [ + 304, + 342, + 546, + 497 + ], + "type": "inline_equation", + "content": "S = r(\\pmb{p}) \\in S" + }, + { + "bbox": [ + 304, + 342, + 546, + 497 + ], + "type": "text", + "content": ". Let " + }, + { + "bbox": [ + 304, + 342, + 546, + 497 + ], + "type": "inline_equation", + "content": "f: \\mathcal{I} \\to \\mathcal{P}" + }, + { + "bbox": [ + 304, + 342, + 546, + 497 + ], + "type": "text", + "content": " be the embedding function which maps an image to a set of strokes. We denote " + }, + { + "bbox": [ + 304, + 342, + 546, + 497 + ], + "type": "inline_equation", + "content": "f(I) \\in \\mathcal{P}" + }, + { + "bbox": [ + 304, + 342, + 546, + 497 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 342, + 546, + 497 + ], + "type": "inline_equation", + "content": "[r \\circ f](I) \\in S" + }, + { + "bbox": [ + 304, + 342, + 546, + 497 + ], + "type": "text", + "content": " respectively as a stroke representation and a sketch representation of the image " + }, + { + "bbox": [ + 304, + 342, + 546, + 497 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 304, + 342, + 546, + 497 + ], + "type": "text", + "content": " w.r.t " + }, + { + "bbox": [ + 304, + 342, + 546, + 497 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 342, + 546, + 497 + ], + "type": "text", + "content": ". To generate a sketch that accurately reflects the given image, we adopt a metric function " + }, + { + "bbox": [ + 304, + 342, + 546, + 497 + ], + "type": "inline_equation", + "content": "\\mathcal{L}: \\mathcal{I} \\times S \\to \\mathbb{R}" + }, + { + "bbox": [ + 304, + 342, + 546, + 497 + ], + "type": "text", + "content": " that measures the distance between the image and the sketch." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 502, + 545, + 526 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 502, + 545, + 526 + ], + "spans": [ + { + "bbox": [ + 304, + 502, + 545, + 526 + ], + "type": "text", + "content": "Definition 1. We denote " + }, + { + "bbox": [ + 304, + 502, + 545, + 526 + ], + "type": "inline_equation", + "content": "S_{I} = \\arg \\min_{S\\in \\mathcal{S}}\\mathcal{L}(I,S)" + }, + { + "bbox": [ + 304, + 502, + 545, + 526 + ], + "type": "text", + "content": " as an optimal sketch representation of " + }, + { + "bbox": [ + 304, + 502, + 545, + 526 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 304, + 502, + 545, + 526 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 531, + 545, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 531, + 545, + 604 + ], + "spans": [ + { + "bbox": [ + 304, + 531, + 545, + 604 + ], + "type": "text", + "content": "Geometry-aware representation. We denote " + }, + { + "bbox": [ + 304, + 531, + 545, + 604 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 304, + 531, + 545, + 604 + ], + "type": "text", + "content": " as a group of geometric transformations that acts on points in " + }, + { + "bbox": [ + 304, + 531, + 545, + 604 + ], + "type": "inline_equation", + "content": "\\Omega" + }, + { + "bbox": [ + 304, + 531, + 545, + 604 + ], + "type": "text", + "content": " (see Appendix E for definitions). For example, " + }, + { + "bbox": [ + 304, + 531, + 545, + 604 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 304, + 531, + 545, + 604 + ], + "type": "text", + "content": " could be a group of translation or rotation. " + }, + { + "bbox": [ + 304, + 531, + 545, + 604 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 304, + 531, + 545, + 604 + ], + "type": "text", + "content": " is a group representation of " + }, + { + "bbox": [ + 304, + 531, + 545, + 604 + ], + "type": "inline_equation", + "content": "g\\in \\mathcal{G}" + }, + { + "bbox": [ + 304, + 531, + 545, + 604 + ], + "type": "text", + "content": " such that " + }, + { + "bbox": [ + 304, + 531, + 545, + 604 + ], + "type": "inline_equation", + "content": "\\rho (g)" + }, + { + "bbox": [ + 304, + 531, + 545, + 604 + ], + "type": "text", + "content": " is a linear operator which acts on " + }, + { + "bbox": [ + 304, + 531, + 545, + 604 + ], + "type": "inline_equation", + "content": "\\mathcal{I}" + }, + { + "bbox": [ + 304, + 531, + 545, + 604 + ], + "type": "text", + "content": ", i.e., " + }, + { + "bbox": [ + 304, + 531, + 545, + 604 + ], + "type": "inline_equation", + "content": "[ \\rho (g)I ] ( u ) = I ( g ^ { - 1 } u )" + }, + { + "bbox": [ + 304, + 531, + 545, + 604 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 304, + 531, + 545, + 604 + ], + "type": "inline_equation", + "content": "u\\in \\Omega" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 608, + 547, + 645 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 608, + 547, + 645 + ], + "spans": [ + { + "bbox": [ + 304, + 608, + 547, + 645 + ], + "type": "text", + "content": "Definition 2. " + }, + { + "bbox": [ + 304, + 608, + 547, + 645 + ], + "type": "inline_equation", + "content": "f(I)" + }, + { + "bbox": [ + 304, + 608, + 547, + 645 + ], + "type": "text", + "content": " is a geometry-aware representation of " + }, + { + "bbox": [ + 304, + 608, + 547, + 645 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 304, + 608, + 547, + 645 + ], + "type": "text", + "content": " with respect to " + }, + { + "bbox": [ + 304, + 608, + 547, + 645 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 304, + 608, + 547, + 645 + ], + "type": "text", + "content": " if there exists a group representation " + }, + { + "bbox": [ + 304, + 608, + 547, + 645 + ], + "type": "inline_equation", + "content": "\\rho'" + }, + { + "bbox": [ + 304, + 608, + 547, + 645 + ], + "type": "text", + "content": " such that " + }, + { + "bbox": [ + 304, + 608, + 547, + 645 + ], + "type": "inline_equation", + "content": "f(\\rho(g)I) = \\rho'(g)f(I)" + }, + { + "bbox": [ + 304, + 608, + 547, + 645 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 304, + 608, + 547, + 645 + ], + "type": "inline_equation", + "content": "\\forall I \\in \\mathcal{I}" + }, + { + "bbox": [ + 304, + 608, + 547, + 645 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 608, + 547, + 645 + ], + "type": "inline_equation", + "content": "\\forall g \\in \\mathcal{G}" + }, + { + "bbox": [ + 304, + 608, + 547, + 645 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 649, + 547, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 649, + 547, + 696 + ], + "spans": [ + { + "bbox": [ + 304, + 649, + 547, + 696 + ], + "type": "text", + "content": "In this case, we say " + }, + { + "bbox": [ + 304, + 649, + 547, + 696 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 649, + 547, + 696 + ], + "type": "text", + "content": " is a " + }, + { + "bbox": [ + 304, + 649, + 547, + 696 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 304, + 649, + 547, + 696 + ], + "type": "text", + "content": "-equivariant map, and the symmetry of " + }, + { + "bbox": [ + 304, + 649, + 547, + 696 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 304, + 649, + 547, + 696 + ], + "type": "text", + "content": " is preserved by " + }, + { + "bbox": [ + 304, + 649, + 547, + 696 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 649, + 547, + 696 + ], + "type": "text", + "content": ". For example, a convolution operator is a translation-equivariant map since the feature of the shifted image is equal to the shifted feature of" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 317, + 702, + 426, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 702, + 426, + 712 + ], + "spans": [ + { + "bbox": [ + 317, + 702, + 426, + 712 + ], + "type": "text", + "content": "See [3] for the extensive review." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "23317" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 62, + 70, + 527, + 242 + ], + "blocks": [ + { + "bbox": [ + 62, + 70, + 527, + 242 + ], + "lines": [ + { + "bbox": [ + 62, + 70, + 527, + 242 + ], + "spans": [ + { + "bbox": [ + 62, + 70, + 527, + 242 + ], + "type": "image", + "image_path": "e8ce89e563b6225adcd168ef774be80bae3e9b4f72a518784d8868d6538ec32c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 247, + 547, + 293 + ], + "lines": [ + { + "bbox": [ + 46, + 247, + 547, + 293 + ], + "spans": [ + { + "bbox": [ + 46, + 247, + 547, + 293 + ], + "type": "text", + "content": "Figure 3. Visualization of the overall architecture of LBS. (a) A CNN-based encoder extracts the feature of the image. (b) Initial strokes are updated repeatedly with a stroke generator based on a Transformer decoder. For the progressive optimization process, intermediate strokes are extracted from each intermediate layer. (c) The rasterized sketch and stroke embedding " + }, + { + "bbox": [ + 46, + 247, + 547, + 293 + ], + "type": "inline_equation", + "content": "z_{h}" + }, + { + "bbox": [ + 46, + 247, + 547, + 293 + ], + "type": "text", + "content": " are generated from the strokes. Features derived from the CNN encoder, strokes, and stroke embedding are combined to form the final representation, " + }, + { + "bbox": [ + 46, + 247, + 547, + 293 + ], + "type": "inline_equation", + "content": "z_{LBS+}" + }, + { + "bbox": [ + 46, + 247, + 547, + 293 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 304, + 288, + 340 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 304, + 288, + 340 + ], + "spans": [ + { + "bbox": [ + 46, + 304, + 288, + 340 + ], + "type": "text", + "content": "the original image. In other words, the convolution operator preserves the symmetry of the translation and produces a geometry-aware representation with respect to it." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 346, + 285, + 358 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 346, + 285, + 358 + ], + "spans": [ + { + "bbox": [ + 47, + 346, + 285, + 358 + ], + "type": "text", + "content": "3.2. Geometry-aware representations by sketching" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 364, + 287, + 401 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 364, + 287, + 401 + ], + "spans": [ + { + "bbox": [ + 46, + 364, + 287, + 401 + ], + "type": "text", + "content": "We now show that stroke representation is a geometry-aware representation with respect to arbitrary affine transformations. Refer to Appendix E for detailed proofs." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 404, + 288, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 404, + 288, + 453 + ], + "spans": [ + { + "bbox": [ + 47, + 404, + 288, + 453 + ], + "type": "text", + "content": "Proposition 1. If " + }, + { + "bbox": [ + 47, + 404, + 288, + 453 + ], + "type": "inline_equation", + "content": "\\mathcal{L}(\\rho(g)I, \\rho(g)S) = \\lambda(g)\\mathcal{L}(I, S)" + }, + { + "bbox": [ + 47, + 404, + 288, + 453 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 47, + 404, + 288, + 453 + ], + "type": "inline_equation", + "content": "\\lambda : \\mathcal{G} \\to \\mathbb{R}^+" + }, + { + "bbox": [ + 47, + 404, + 288, + 453 + ], + "type": "text", + "content": " exists, and there exists a unique " + }, + { + "bbox": [ + 47, + 404, + 288, + 453 + ], + "type": "inline_equation", + "content": "f^*" + }, + { + "bbox": [ + 47, + 404, + 288, + 453 + ], + "type": "text", + "content": " such that " + }, + { + "bbox": [ + 47, + 404, + 288, + 453 + ], + "type": "inline_equation", + "content": "[r \\circ f^*](I) = S_I" + }, + { + "bbox": [ + 47, + 404, + 288, + 453 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 47, + 404, + 288, + 453 + ], + "type": "inline_equation", + "content": "\\forall I \\in \\mathcal{I}" + }, + { + "bbox": [ + 47, + 404, + 288, + 453 + ], + "type": "text", + "content": ", then " + }, + { + "bbox": [ + 47, + 404, + 288, + 453 + ], + "type": "inline_equation", + "content": "f^*(I)" + }, + { + "bbox": [ + 47, + 404, + 288, + 453 + ], + "type": "text", + "content": " is a geometry-aware representation w.r.t. affine transformations " + }, + { + "bbox": [ + 47, + 404, + 288, + 453 + ], + "type": "inline_equation", + "content": "\\mathcal{A}" + }, + { + "bbox": [ + 47, + 404, + 288, + 453 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 456, + 287, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 456, + 287, + 540 + ], + "spans": [ + { + "bbox": [ + 46, + 456, + 287, + 540 + ], + "type": "text", + "content": "Prop. 1 states the conditions for " + }, + { + "bbox": [ + 46, + 456, + 287, + 540 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 456, + 287, + 540 + ], + "type": "text", + "content": " to be an " + }, + { + "bbox": [ + 46, + 456, + 287, + 540 + ], + "type": "inline_equation", + "content": "\\mathcal{A}" + }, + { + "bbox": [ + 46, + 456, + 287, + 540 + ], + "type": "text", + "content": "-equivariant map. Therefore, by designing stroke representations to be injective for " + }, + { + "bbox": [ + 46, + 456, + 287, + 540 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 46, + 456, + 287, + 540 + ], + "type": "text", + "content": ", and optimizing " + }, + { + "bbox": [ + 46, + 456, + 287, + 540 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 456, + 287, + 540 + ], + "type": "text", + "content": " to minimize " + }, + { + "bbox": [ + 46, + 456, + 287, + 540 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 46, + 456, + 287, + 540 + ], + "type": "text", + "content": " subject to the conditions outlined in Prop. 1, " + }, + { + "bbox": [ + 46, + 456, + 287, + 540 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 456, + 287, + 540 + ], + "type": "text", + "content": " generates a geometry-aware representation with respect to arbitrary affine transformations. In the next section, we propose an architecture and a loss function that satisfy these conditions." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 550, + 103, + 562 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 550, + 103, + 562 + ], + "spans": [ + { + "bbox": [ + 47, + 550, + 103, + 562 + ], + "type": "text", + "content": "4. Method" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 570, + 287, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 287, + 666 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 287, + 666 + ], + "type": "text", + "content": "We describe our model LBS, which provides geometry-aware representations from strokes by learning to generate a sketch in a short inference time without using a sketch dataset. We introduce an objective function and techniques for training LBS. We then propose a stroke embedding network that aggregates information of whole strokes. Hereafter, we use the terms \"sketch\" and \"image\" to denote realized sketch " + }, + { + "bbox": [ + 46, + 570, + 287, + 666 + ], + "type": "inline_equation", + "content": "S(\\Omega)" + }, + { + "bbox": [ + 46, + 570, + 287, + 666 + ], + "type": "text", + "content": " and realized image " + }, + { + "bbox": [ + 46, + 570, + 287, + 666 + ], + "type": "inline_equation", + "content": "I(\\Omega)" + }, + { + "bbox": [ + 46, + 570, + 287, + 666 + ], + "type": "text", + "content": " for simplicity." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 671, + 207, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 671, + 207, + 684 + ], + "spans": [ + { + "bbox": [ + 47, + 671, + 207, + 684 + ], + "type": "text", + "content": "4.1. Learning by Sketching (LBS)" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "LBS aims to generate a set of strokes to sketch the image and extract geometric information with color for down-" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 304, + 545, + 340 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 304, + 545, + 340 + ], + "spans": [ + { + "bbox": [ + 304, + 304, + 545, + 340 + ], + "type": "text", + "content": "stream tasks. To achieve the goal, we design a stroke generator by referring to Transformer-based sketch generation models [48,60]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 340, + 546, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 340, + 546, + 484 + ], + "spans": [ + { + "bbox": [ + 304, + 340, + 546, + 484 + ], + "type": "text", + "content": "Architecture. As shown in Fig. 3, LBS generates a set of strokes from trainable parameters, which are denoted as initial strokes. Our stroke generator uses Transformer decoder layers and incorporates image features from a CNN encoder (ResNet18 is used in this paper). Then, 2-layer MLP decoders decode a set of " + }, + { + "bbox": [ + 304, + 340, + 546, + 484 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 340, + 546, + 484 + ], + "type": "text", + "content": " strokes from the output of the Transformer decoder. Each stroke contains four control points that parameterize a cubic Bezier curve, as well as color and thickness information. The sketch of an image is then created by rasterizing the generated set of strokes using a differentiable rasterizer [53]. For a detailed description of our architecture, please refer to Appendix C." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 484, + 547, + 626 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 484, + 547, + 626 + ], + "spans": [ + { + "bbox": [ + 304, + 484, + 547, + 626 + ], + "type": "text", + "content": "Representation of LBS. The primary output of LBS is a set of strokes " + }, + { + "bbox": [ + 304, + 484, + 547, + 626 + ], + "type": "inline_equation", + "content": "\\pmb{p}" + }, + { + "bbox": [ + 304, + 484, + 547, + 626 + ], + "type": "text", + "content": ", and a geometry-aware representation is obtained by using the flattened vector of the strokes " + }, + { + "bbox": [ + 304, + 484, + 547, + 626 + ], + "type": "inline_equation", + "content": "z_{p} = (p^{(1)},\\dots,p^{(n)})" + }, + { + "bbox": [ + 304, + 484, + 547, + 626 + ], + "type": "text", + "content": ". To complement information that may not be encoded with strokes such as texture, we concatenate " + }, + { + "bbox": [ + 304, + 484, + 547, + 626 + ], + "type": "inline_equation", + "content": "z_{p}" + }, + { + "bbox": [ + 304, + 484, + 547, + 626 + ], + "type": "text", + "content": " with the image features " + }, + { + "bbox": [ + 304, + 484, + 547, + 626 + ], + "type": "inline_equation", + "content": "z_{e}" + }, + { + "bbox": [ + 304, + 484, + 547, + 626 + ], + "type": "text", + "content": " from the CNN encoder with global average pooling. The resulting concatenated representation is denoted as " + }, + { + "bbox": [ + 304, + 484, + 547, + 626 + ], + "type": "inline_equation", + "content": "z_{LBS}" + }, + { + "bbox": [ + 304, + 484, + 547, + 626 + ], + "type": "text", + "content": ". In addition, we can combine this with representation " + }, + { + "bbox": [ + 304, + 484, + 547, + 626 + ], + "type": "inline_equation", + "content": "z_{h}" + }, + { + "bbox": [ + 304, + 484, + 547, + 626 + ], + "type": "text", + "content": " that aggregates the entire stroke, the result of which we denote as " + }, + { + "bbox": [ + 304, + 484, + 547, + 626 + ], + "type": "inline_equation", + "content": "z_{LBS+}" + }, + { + "bbox": [ + 304, + 484, + 547, + 626 + ], + "type": "text", + "content": ". Further details can be found in Sec. 4.4. The final representation space of LBS is as follows:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 339, + 637, + 545, + 651 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 339, + 637, + 545, + 651 + ], + "spans": [ + { + "bbox": [ + 339, + 637, + 545, + 651 + ], + "type": "interline_equation", + "content": "z _ {L B S} = \\left(z _ {e}, z _ {p}\\right), \\quad z _ {L B S +} = \\left(z _ {e}, z _ {p}, z _ {h}\\right). \\tag {1}", + "image_path": "c5ae6ab79ebda59e9a1208beb2461d9474ea88eae2025f4531b814a7ce09bbe4.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 659, + 499, + 672 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 659, + 499, + 672 + ], + "spans": [ + { + "bbox": [ + 306, + 659, + 499, + 672 + ], + "type": "text", + "content": "4.2. CLIP-based perceptual loss function" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 677, + 545, + 713 + ], + "type": "text", + "content": "As discussed in Sec. 3.2, proper " + }, + { + "bbox": [ + 306, + 677, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 306, + 677, + 545, + 713 + ], + "type": "text", + "content": " must be given to train a geometry-aware representation of an image. To this end, we adopt CLIP-based perceptual loss to measure the sim" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23318" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 70, + 280, + 203 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 280, + 203 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 280, + 203 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 280, + 203 + ], + "type": "image", + "image_path": "659d2d001fb14f4c82237891847c7c65030ece67e44ccedbc8d278b716f3c0fc.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 213, + 289, + 280 + ], + "lines": [ + { + "bbox": [ + 46, + 213, + 289, + 280 + ], + "spans": [ + { + "bbox": [ + 46, + 213, + 289, + 280 + ], + "type": "text", + "content": "Figure 4. Visualization of the progressive optimization process. Strokes initialized from the saliency map are optimized using the gradient of " + }, + { + "bbox": [ + 46, + 213, + 289, + 280 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text{percept}}" + }, + { + "bbox": [ + 46, + 213, + 289, + 280 + ], + "type": "text", + "content": " until convergence and stored in a total of " + }, + { + "bbox": [ + 46, + 213, + 289, + 280 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 213, + 289, + 280 + ], + "type": "text", + "content": " intermediate steps denoted by " + }, + { + "bbox": [ + 46, + 213, + 289, + 280 + ], + "type": "inline_equation", + "content": "\\pmb{p}_{gt,l}" + }, + { + "bbox": [ + 46, + 213, + 289, + 280 + ], + "type": "text", + "content": ". Then, the stroke generator is trained through " + }, + { + "bbox": [ + 46, + 213, + 289, + 280 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text{guide}}" + }, + { + "bbox": [ + 46, + 213, + 289, + 280 + ], + "type": "text", + "content": " to progressively predict each intermediate stroke " + }, + { + "bbox": [ + 46, + 213, + 289, + 280 + ], + "type": "inline_equation", + "content": "\\pmb{p}_l" + }, + { + "bbox": [ + 46, + 213, + 289, + 280 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 46, + 213, + 289, + 280 + ], + "type": "inline_equation", + "content": "\\pmb{p}_{gt,l}" + }, + { + "bbox": [ + 46, + 213, + 289, + 280 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 293, + 288, + 353 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 293, + 288, + 353 + ], + "spans": [ + { + "bbox": [ + 46, + 293, + 288, + 353 + ], + "type": "text", + "content": "ilarity between the sketch and the input image in terms of both geometric and semantic differences [68]. To generate a sketch that is semantically similar to the input image, it should minimize the distance on the embedding space of the CLIP model " + }, + { + "bbox": [ + 46, + 293, + 288, + 353 + ], + "type": "inline_equation", + "content": "f_{C}" + }, + { + "bbox": [ + 46, + 293, + 288, + 353 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 97, + 361, + 287, + 387 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 97, + 361, + 287, + 387 + ], + "spans": [ + { + "bbox": [ + 97, + 361, + 287, + 387 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {s e m a n t i c}} = \\sum_ {A \\in \\mathcal {A}} \\phi (A (I), A (S)), \\tag {2}", + "image_path": "805fb38ba2d84de09a4c6abaaa06df0f29da9eeef5477bf73e734735bf0b8e89.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 396, + 287, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 396, + 287, + 456 + ], + "spans": [ + { + "bbox": [ + 46, + 396, + 287, + 456 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 396, + 287, + 456 + ], + "type": "inline_equation", + "content": "\\mathcal{A}" + }, + { + "bbox": [ + 46, + 396, + 287, + 456 + ], + "type": "text", + "content": " is the group of affine transformations and " + }, + { + "bbox": [ + 46, + 396, + 287, + 456 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 46, + 396, + 287, + 456 + ], + "type": "text", + "content": " is the cosine similarity of the CLIP embeddings, i.e., " + }, + { + "bbox": [ + 46, + 396, + 287, + 456 + ], + "type": "inline_equation", + "content": "\\phi (x,y) = \\cos (f_C(x),f_C(y))" + }, + { + "bbox": [ + 46, + 396, + 287, + 456 + ], + "type": "text", + "content": ". In addition, it compares low-level features of the sketch and the input image to estimate the geometric similarity as follows:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 86, + 464, + 287, + 491 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 464, + 287, + 491 + ], + "spans": [ + { + "bbox": [ + 86, + 464, + 287, + 491 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {g e o m e t r i c}} = \\sum_ {A \\in \\mathcal {A}} \\sum_ {i} \\phi_ {i} (A (I), A (S)), \\tag {3}", + "image_path": "9c0bf9c91f28866908c8c4a3043423f573b1044c2d78dd5b881cbc6dafa2c1c1.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 498, + 287, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 498, + 287, + 559 + ], + "spans": [ + { + "bbox": [ + 47, + 498, + 287, + 559 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 498, + 287, + 559 + ], + "type": "inline_equation", + "content": "\\phi_{i}" + }, + { + "bbox": [ + 47, + 498, + 287, + 559 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 47, + 498, + 287, + 559 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_2" + }, + { + "bbox": [ + 47, + 498, + 287, + 559 + ], + "type": "text", + "content": " distance of the embeddings from the " + }, + { + "bbox": [ + 47, + 498, + 287, + 559 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 47, + 498, + 287, + 559 + ], + "type": "text", + "content": "-th intermediate layer of the CLIP model, i.e., " + }, + { + "bbox": [ + 47, + 498, + 287, + 559 + ], + "type": "inline_equation", + "content": "\\phi_{i}(x,y) = \\| f_{C,i}(x) - f_{C,i}(y)\\|_{2}^{2}" + }, + { + "bbox": [ + 47, + 498, + 287, + 559 + ], + "type": "text", + "content": ". Specifically, we used " + }, + { + "bbox": [ + 47, + 498, + 287, + 559 + ], + "type": "inline_equation", + "content": "i\\in \\{3,4\\}" + }, + { + "bbox": [ + 47, + 498, + 287, + 559 + ], + "type": "text", + "content": " with the ResNet101 CLIP model, proposed as [68]. The final perceptual loss is as follows:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 84, + 569, + 287, + 582 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 84, + 569, + 287, + 582 + ], + "spans": [ + { + "bbox": [ + 84, + 569, + 287, + 582 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {p e r c e p t}} = \\mathcal {L} _ {\\text {g e o m e t r i c}} + \\lambda_ {s} \\cdot \\mathcal {L} _ {\\text {s e m a n t i c}}, \\tag {4}", + "image_path": "513685149dedca65b0c5ec395f07322474a1ec33696cdba00d6302dabcb5ab04.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 591, + 192, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 591, + 192, + 604 + ], + "spans": [ + { + "bbox": [ + 47, + 591, + 192, + 604 + ], + "type": "text", + "content": "with " + }, + { + "bbox": [ + 47, + 591, + 192, + 604 + ], + "type": "inline_equation", + "content": "\\lambda_{s} = 0.1" + }, + { + "bbox": [ + 47, + 591, + 192, + 604 + ], + "type": "text", + "content": " as a hyperparameter." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 611, + 287, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 611, + 287, + 624 + ], + "spans": [ + { + "bbox": [ + 47, + 611, + 287, + 624 + ], + "type": "text", + "content": "4.3. Training with progressive optimization process" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "text", + "content": "Abstracting an image into a sketch requires high-level reasoning, and predicting the corresponding stroke parameters in a single inference step is a delicate process. Although CLIPasso [68] addresses these problems via an optimization-based approach, its time-consuming properties (" + }, + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\sim 2" + }, + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "text", + "content": " min per image) make it impractical as a representation. Moreover, as CLIPasso reported that the changes" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": "in initial strokes significantly impacted the final results, directly optimizing each stroke through the optimizer for thousands of steps leads to highly variable results and numerical instability." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 121, + 546, + 299 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 121, + 546, + 299 + ], + "spans": [ + { + "bbox": [ + 304, + 121, + 546, + 299 + ], + "type": "text", + "content": "To generate a stable representation within a single inference step, we modify the optimization-based approach of CLIPasso and utilize it as desirable guidance for the stroke generator, which we call the guidance stroke and denote as " + }, + { + "bbox": [ + 304, + 121, + 546, + 299 + ], + "type": "inline_equation", + "content": "\\pmb{p}_{gt}" + }, + { + "bbox": [ + 304, + 121, + 546, + 299 + ], + "type": "text", + "content": ". To ensure high-quality sketch generation, each intermediate layer of the stroke generator is guided by strokes obtained at the corresponding intermediate step of the optimization process instead of relying solely on the final outcome. This process, depicted in Fig. 4, involves progressively updating strokes from the previous layer, which can be modeled by residual blocks from the Transformer architecture. By decomposing the prediction of the entire optimization process into predicting changes in relatively short intervals for each intermediate layer, our approach leads to better-quality sketches." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 300, + 545, + 395 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 300, + 545, + 395 + ], + "spans": [ + { + "bbox": [ + 304, + 300, + 545, + 395 + ], + "type": "text", + "content": "However, the process through which CLIPasso initializes strokes via stochastic sampling from the saliency map results in unstable outcomes. To address this issue, we select initialized strokes deterministically by selecting the most salient regions from the saliency map in a greedy manner. The color of the stroke is determined during the initialization step by referencing the corresponding region in the original image. More details are described in Appendix A." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 396, + 545, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 396, + 545, + 443 + ], + "spans": [ + { + "bbox": [ + 304, + 396, + 545, + 443 + ], + "type": "text", + "content": "To ensure that the guidance loss is invariant to the permutation of the order of each stroke, we use the Hungarian algorithm [41] which is widely used for the assignment problem. The guidance loss is as follows:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 343, + 449, + 545, + 483 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 343, + 449, + 545, + 483 + ], + "spans": [ + { + "bbox": [ + 343, + 449, + 545, + 483 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {g u i d e}} = \\sum_ {l = 1} ^ {L} \\min _ {\\sigma} \\sum_ {i = 1} ^ {n} \\mathcal {L} _ {1} \\left(p _ {g t, l} ^ {(i)}, p _ {l} ^ {(\\sigma (i))}\\right), \\tag {5}", + "image_path": "d21a673122a2d9493af070d858a85bc64528d35c37250912977807929d55b28c.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 491, + 545, + 546 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 491, + 545, + 546 + ], + "spans": [ + { + "bbox": [ + 305, + 491, + 545, + 546 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 491, + 545, + 546 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 305, + 491, + 545, + 546 + ], + "type": "text", + "content": " is a permutation of the stroke index, and " + }, + { + "bbox": [ + 305, + 491, + 545, + 546 + ], + "type": "inline_equation", + "content": "p_l^{(i)}" + }, + { + "bbox": [ + 305, + 491, + 545, + 546 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 305, + 491, + 545, + 546 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 305, + 491, + 545, + 546 + ], + "type": "text", + "content": "-th decoded stroke from the " + }, + { + "bbox": [ + 305, + 491, + 545, + 546 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 305, + 491, + 545, + 546 + ], + "type": "text", + "content": "-th intermediate layer with " + }, + { + "bbox": [ + 305, + 491, + 545, + 546 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 305, + 491, + 545, + 546 + ], + "type": "text", + "content": " layers in total. " + }, + { + "bbox": [ + 305, + 491, + 545, + 546 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_1" + }, + { + "bbox": [ + 305, + 491, + 545, + 546 + ], + "type": "text", + "content": " is the L1 distance, and " + }, + { + "bbox": [ + 305, + 491, + 545, + 546 + ], + "type": "inline_equation", + "content": "p_{gt,l}^{(i)}" + }, + { + "bbox": [ + 305, + 491, + 545, + 546 + ], + "type": "text", + "content": " is the guidance stroke corresponding to " + }, + { + "bbox": [ + 305, + 491, + 545, + 546 + ], + "type": "inline_equation", + "content": "p_l^{(\\sigma(i))}" + }, + { + "bbox": [ + 305, + 491, + 545, + 546 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 552, + 456, + 564 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 552, + 456, + 564 + ], + "spans": [ + { + "bbox": [ + 306, + 552, + 456, + 564 + ], + "type": "text", + "content": "4.4. Stroke embedding network" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 570, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 546, + 714 + ], + "type": "text", + "content": "As strokes primarily express localized and fine-grained details, they can be less suitable for representing coarse-grained information. To address this, we offer an additional representation that combines full strokes through a stroke embedding network. Stroke embedding network " + }, + { + "bbox": [ + 304, + 570, + 546, + 714 + ], + "type": "inline_equation", + "content": "h: \\mathcal{P} \\to \\mathcal{Z}_h" + }, + { + "bbox": [ + 304, + 570, + 546, + 714 + ], + "type": "text", + "content": " maps the set of " + }, + { + "bbox": [ + 304, + 570, + 546, + 714 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 570, + 546, + 714 + ], + "type": "text", + "content": " strokes into embedding space " + }, + { + "bbox": [ + 304, + 570, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}_h" + }, + { + "bbox": [ + 304, + 570, + 546, + 714 + ], + "type": "text", + "content": ". Since the rasterized sketch is invariant to the stroke indices (except for contact point between strokes), we followed the permutation invariant model from DeepSets [80] to generate stroke embedding. The choice of the loss function " + }, + { + "bbox": [ + 304, + 570, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{embed}" + }, + { + "bbox": [ + 304, + 570, + 546, + 714 + ], + "type": "text", + "content": " to train " + }, + { + "bbox": [ + 304, + 570, + 546, + 714 + ], + "type": "inline_equation", + "content": "z_h \\in \\mathcal{Z}_h" + }, + { + "bbox": [ + 304, + 570, + 546, + 714 + ], + "type": "text", + "content": " is unconstrained (e.g., Cross-Entropy or InfoNCE loss in our paper). During the training" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "23319" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "content": "phase, the gradient from " + }, + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "content": " is also passed to " + }, + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "content": " to capture coarse-grained information." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 59, + 96, + 192, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 96, + 192, + 108 + ], + "spans": [ + { + "bbox": [ + 59, + 96, + 192, + 108 + ], + "type": "text", + "content": "The final objective is as follows:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 64, + 118, + 287, + 133 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 64, + 118, + 287, + 133 + ], + "spans": [ + { + "bbox": [ + 64, + 118, + 287, + 133 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {L B S} = \\mathcal {L} _ {\\text {p e r c e p t}} + \\lambda_ {g} \\cdot \\mathcal {L} _ {\\text {g u i d e}} + \\lambda_ {e} \\cdot \\mathcal {L} _ {\\text {e m b e d}}, \\tag {6}", + "image_path": "c164e28dda38561e42c62b43a261fa03c828ca2011f0bdece0bf350f5e63f5f1.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 141, + 287, + 166 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 141, + 287, + 166 + ], + "spans": [ + { + "bbox": [ + 46, + 141, + 287, + 166 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 141, + 287, + 166 + ], + "type": "inline_equation", + "content": "\\lambda_{g}" + }, + { + "bbox": [ + 46, + 141, + 287, + 166 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 141, + 287, + 166 + ], + "type": "inline_equation", + "content": "\\lambda_{e}" + }, + { + "bbox": [ + 46, + 141, + 287, + 166 + ], + "type": "text", + "content": " are hyperparameters (for specific values, refer to Appendix C)." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 177, + 128, + 190 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 177, + 128, + 190 + ], + "spans": [ + { + "bbox": [ + 47, + 177, + 128, + 190 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 197, + 239, + 210 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 197, + 239, + 210 + ], + "spans": [ + { + "bbox": [ + 47, + 197, + 239, + 210 + ], + "type": "text", + "content": "5.1. Research questions and task designs" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 215, + 287, + 276 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 215, + 287, + 276 + ], + "spans": [ + { + "bbox": [ + 46, + 215, + 287, + 276 + ], + "type": "text", + "content": "We investigate the effectiveness and generalizability of our approach by designing multiple research questions, as well as corresponding downstream tasks for each question. Detailed information about each experimental setup is described in Appendix B." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 277, + 287, + 301 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 277, + 287, + 301 + ], + "spans": [ + { + "bbox": [ + 46, + 277, + 287, + 301 + ], + "type": "text", + "content": "RQ1. Effects of equivariance: What is the benefit of equivariant representation, and does LBS achieve it?" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 302, + 287, + 457 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 302, + 287, + 457 + ], + "spans": [ + { + "bbox": [ + 46, + 302, + 287, + 457 + ], + "type": "text", + "content": "From the definition of equivariance, we expect that an equivariant model with respect to geometric transformation would have generalization capability for augmented images with transformation. To verify this, we conduct experiments on the Rotated MNIST (rotMNIST) dataset [22], which consists of rotated images from the MNIST dataset. We rotate images by " + }, + { + "bbox": [ + 46, + 302, + 287, + 457 + ], + "type": "inline_equation", + "content": "30^{\\circ}" + }, + { + "bbox": [ + 46, + 302, + 287, + 457 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 302, + 287, + 457 + ], + "type": "inline_equation", + "content": "45^{\\circ}" + }, + { + "bbox": [ + 46, + 302, + 287, + 457 + ], + "type": "text", + "content": " for training and classify the digit of images rotated by " + }, + { + "bbox": [ + 46, + 302, + 287, + 457 + ], + "type": "inline_equation", + "content": "0^{\\circ}" + }, + { + "bbox": [ + 46, + 302, + 287, + 457 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 302, + 287, + 457 + ], + "type": "inline_equation", + "content": "90^{\\circ}" + }, + { + "bbox": [ + 46, + 302, + 287, + 457 + ], + "type": "text", + "content": " to evaluate whether LBS generalizes the information from the training domain to the test domain. To verify that our model satisfies equivariance outside the training domain, we classify the rotation and reflection between an original image and the same image rotated with an interval of " + }, + { + "bbox": [ + 46, + 302, + 287, + 457 + ], + "type": "inline_equation", + "content": "90^{\\circ}" + }, + { + "bbox": [ + 46, + 302, + 287, + 457 + ], + "type": "text", + "content": " and horizontally flipped." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 460, + 287, + 495 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 460, + 287, + 495 + ], + "spans": [ + { + "bbox": [ + 46, + 460, + 287, + 495 + ], + "type": "text", + "content": "RQ2. Effects on geometric primitives and concepts: How well does LBS represent geometric primitives and understand their conceptual relationships?" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 496, + 287, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 496, + 287, + 639 + ], + "spans": [ + { + "bbox": [ + 46, + 496, + 287, + 639 + ], + "type": "text", + "content": "To evaluate whether LBS is suitable for representing geometric primitives and concepts, we perform a classification task on the Geoclidean dataset [29]. The Geoclidean dataset consists of realized images from a concept of Euclidean geometry, e.g., black parallel lines on a white background. Geoclidean is divided into two categories: Geoclidean-Elements and Geoclidean-Constraints, visualized in Fig. 7 on Appendix B. By providing a limited training set consisting of only 10 images per concept, we evaluate whether LBS can effectively learn the high-level relationships between each primitive and generalize them across different examples by classifying the concept of the test image." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 641, + 287, + 677 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 287, + 677 + ], + "type": "text", + "content": "RQ3. Local geometric information and spatial reasoning: How effectively does LBS reflect local geometric information and extend it to spatial reasoning tasks?" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": "We validate whether LBS can reflect the local geometric information of each object in a synthetic photo dataset consisting of multiple objects, using the CLEVR dataset [34]." + } + ] + } + ], + "index": 12 + }, + { + "type": "table", + "bbox": [ + 307, + 102, + 545, + 228 + ], + "blocks": [ + { + "bbox": [ + 305, + 71, + 545, + 93 + ], + "lines": [ + { + "bbox": [ + 305, + 71, + 545, + 93 + ], + "spans": [ + { + "bbox": [ + 305, + 71, + 545, + 93 + ], + "type": "text", + "content": "Table 1. Quantitative results of LBS and the baselines evaluated on the corresponding tasks on the rotMNIST and Geoclidean." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 102, + 545, + 228 + ], + "lines": [ + { + "bbox": [ + 307, + 102, + 545, + 228 + ], + "spans": [ + { + "bbox": [ + 307, + 102, + 545, + 228 + ], + "type": "table", + "html": "
La-\nbelMethodrotMNIST (30°, 45°)Geoclidean
0°, 90°RotationConstraintsElements
✓CE62.72±1.8973.14±0.3553.89±1.5870.57±4.29
SupCon [38]65.25±1.0573.37±0.2042.41±3.1655.83±4.28
LtD-diff [54]60.09±1.1628.91±2.1557.26±2.1969.47±2.11
E(2)-CNN [73]85.12±0.1777.00±0.3971.03±1.9469.28±1.46
LBS (CE)65.00±3.3275.81±0.3050.01±1.5881.06±3.14
XSimCLR [9]47.66±0.4172.96±0.8432.04±0.6465.14±4.11
β-TCVAE [8]37.84±1.0660.14±0.3217.18±1.3533.82±1.64
GeoSSL [55]--18.66±3.3333.47±2.80
HoG [14]25.4264.9423.8252.05
LBS47.31±2.5370.02±0.6447.43±1.3481.34±0.16
", + "image_path": "b799f4139f9d108e57e75e730c277dfca4599b8544ec54d5b6dccf3e526a49ba.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "table_body" + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 239, + 545, + 347 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 239, + 545, + 347 + ], + "spans": [ + { + "bbox": [ + 304, + 239, + 545, + 347 + ], + "type": "text", + "content": "We train our model with very limited descriptions, where the label for the entire scene is provided as the rightmost object or without any descriptions at all. We validate the effectiveness of our representation by evaluating its ability to successfully classify attributes that are not provided as labels, such as determining the color of the leftmost object. Additionally, we test its ability to perform simple spatial reasoning, such as shifting the rightmost object and inferring the attribute of the current rightmost object." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 350, + 547, + 384 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 350, + 547, + 384 + ], + "spans": [ + { + "bbox": [ + 305, + 350, + 547, + 384 + ], + "type": "text", + "content": "RQ4. Domain transfer: Can the geometric concepts of LBS trained in a specific domain be extended to other domains?" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 385, + 545, + 457 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 385, + 545, + 457 + ], + "spans": [ + { + "bbox": [ + 304, + 385, + 545, + 457 + ], + "type": "text", + "content": "To investigate whether the learned representation within a specific image domain provides meaningful geometric information across other domains, we evaluate the model by shifting the distribution from the STL-10 [11] dataset to CLEVR and vice versa. Evaluation in the STL-10 dataset is conducted through object classification." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 460, + 545, + 483 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 460, + 545, + 483 + ], + "spans": [ + { + "bbox": [ + 305, + 460, + 545, + 483 + ], + "type": "text", + "content": "RQ5. Traditional sketch tasks: Does geometry-aware representation from LBS help in traditional FG-SBIR tasks?" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 483, + 545, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 483, + 545, + 590 + ], + "spans": [ + { + "bbox": [ + 304, + 483, + 545, + 590 + ], + "type": "text", + "content": "We assess the impact of geometry-aware representations acquired by LBS on a conventional sketch task by evaluating them with the fine-grained sketch-based image retrieval (FG-SBIR) task on the QMUL-ShoeV2 Dataset [78]. The aim of FG-SBIR is to match a given sketch of a shoe to its corresponding photo image. Since geometric information is essential for distinguishing each shoe, we investigate whether leveraging representations from LBS can improve performance on the FG-SBIR task." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 599, + 421, + 612 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 599, + 421, + 612 + ], + "spans": [ + { + "bbox": [ + 306, + 599, + 421, + 612 + ], + "type": "text", + "content": "5.2. Experimental setup" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": "Implementation details. As samples from rotMNIST and Geoclidean can be directly represented with a few strokes, we replace " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text {percept }}" + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text {guide }}" + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_1" + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": " loss, which does not rely on a pre-trained CLIP model. For the STL-10 dataset, providing mask information for the background with U2-Net [57] improves the quality of generated sketches. For " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text {embed }}" + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": ", we use Cross-Entropy loss for supervised training which we denote as LBS (CE) in Tab. 1, 2 and" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "23320" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 71, + 123, + 520, + 285 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 547, + 118 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 547, + 118 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 547, + 118 + ], + "type": "text", + "content": "Table 2. Quantitative results on CLEVR dataset for labeled and unlabeled settings and for CLIP and HoG features. RC, LC, BC refer to inferring the color of the rightmost, leftmost, bottommost object, and Size, Shape, Material refer to inferring the size, shape, material of the rightmost object, respectively. Third refers to inferring the color of the third object from the right, and Shift refers to predicting the color of the rightmost object after shifting the initial rightmost object to the left by 0.15 times the image width." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 71, + 123, + 520, + 285 + ], + "lines": [ + { + "bbox": [ + 71, + 123, + 520, + 285 + ], + "spans": [ + { + "bbox": [ + 71, + 123, + 520, + 285 + ], + "type": "table", + "html": "
LabelMethodRCLCBCSizeShapeMaterialThirdShift
✓CE98.71±0.1076.72±0.8676.02±0.9092.51±0.4049.97±0.2964.38±1.9040.66±0.2062.06±1.62
SupCon [38]98.75±0.0863.82±2.3666.04±2.6591.88±0.3749.15±0.8559.20±0.5737.93±0.2756.05±2.56
LtD-diff [54]62.29±0.4814.01±0.4215.84±0.4363.98±3.3843.96±3.0554.47±0.4516.47±0.5917.21±0.29
E(2)-CNN [73]98.50±0.1070.10±1.1573.51±2.5089.84±0.4645.85±0.9363.05±0.5941.95±0.1859.29±0.91
LBS (CE)97.49±0.2281.79±0.2784.09±0.8493.22±0.2970.03±0.6886.84±0.5438.23±0.2551.56±0.16
×SimCLR [9]60.61±1.2463.89±2.3563.77±2.2983.35±0.6041.95±0.3351.66±0.2433.42±0.5543.05±0.55
E(2)-CNN [73]53.50±7.3054.60±7.3455.52±7.6083.52±1.5642.06±1.1253.04±2.8130.74±2.8438.03±4.44
β-TCVAE [8]17.09±0.2017.50±0.3320.04±0.7171.27±0.1036.30±0.1056.11±0.1315.38±0.1916.35±0.18
GeoSSL [55]20.16±0.6320.54±0.8721.61±0.6773.79±0.7844.08±1.1054.54±2.9415.39±0.1616.94±0.34
DefGrid [21]73.81±0.9173.96±1.0273.38±0.8081.50±0.2246.34±0.7768.65±1.1724.90±0.2736.28±0.13
LBS84.31±0.0880.47±0.7883.00±0.3992.66±0.4170.01±0.5385.52±0.4337.41±0.2949.32±0.17
CLIP [59]37.3939.154.9877.5166.9172.6634.7534.80
HoG [14]56.8349.6958.6981.7361.1468.3824.2833.25
", + "image_path": "13a09efb8eb5a5fce085986016988eb37582f2c4e3f3d774de6f909dca529205.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 72, + 316, + 520, + 407 + ], + "blocks": [ + { + "bbox": [ + 115, + 296, + 477, + 307 + ], + "lines": [ + { + "bbox": [ + 115, + 296, + 477, + 307 + ], + "spans": [ + { + "bbox": [ + 115, + 296, + 477, + 307 + ], + "type": "text", + "content": "Table 3. Quantitative results of models trained on STL-10 dataset and evaluated on CLEVR dataset." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 72, + 316, + 520, + 407 + ], + "lines": [ + { + "bbox": [ + 72, + 316, + 520, + 407 + ], + "spans": [ + { + "bbox": [ + 72, + 316, + 520, + 407 + ], + "type": "table", + "html": "
DatasetMethodRCLCBCSizeShapeMaterialThirdShift
STL-10↓CLEVRLtD [54]18.70±0.0219.15±0.7721.69±1.0573.13±3.2147.88±1.1359.11±2.3416.47±0.5917.21±0.29
SimCLR [9]26.97±0.2826.26±0.8838.88±0.1982.33±0.6456.88±1.2377.39±0.3523.45±0.3524.95±0.17
E(2)-CNN [73]26.82±2.2325.40±1.2039.30±2.8079.48±0.7153.54±0.8472.18±0.3423.35±1.0124.80±1.08
β-TCVAE [8]17.04±0.7618.46±2.3618.88±1.1471.32±0.6737.14±0.1256.81±0.2615.63±1.3516.43±0.38
GeoSSL [55]14.41±0.5514.73±0.1114.37±0.6677.47±5.1748.10±1.9055.63±2.8613.71±0.4513.63±0.13
DefGrid [21]66.74±1.1068.60±0.0868.35±0.8278.97±0.2940.92±0.4462.98±1.3123.48±0.4933.07±0.52
LBS53.87±2.7253.85±2.2061.84±2.2392.46±0.6259.52±0.4580.06±1.2930.75±0.4139.95±1.15
", + "image_path": "e7641237a9cb8482a098b16f8b1369b47a58d52a0ea783d84622f43c96e67114.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 49, + 451, + 286, + 538 + ], + "blocks": [ + { + "bbox": [ + 47, + 419, + 287, + 441 + ], + "lines": [ + { + "bbox": [ + 47, + 419, + 287, + 441 + ], + "spans": [ + { + "bbox": [ + 47, + 419, + 287, + 441 + ], + "type": "text", + "content": "Table 4. Quantitative results of models trained on CLEVR dataset and evaluated on STL-10 dataset classification." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 49, + 451, + 286, + 538 + ], + "lines": [ + { + "bbox": [ + 49, + 451, + 286, + 538 + ], + "spans": [ + { + "bbox": [ + 49, + 451, + 286, + 538 + ], + "type": "table", + "html": "
DatasetLabeledUnlabeled
MethodAccuracyMethodAccuracy
CLEVR↓STL-10CE46.15±0.12SimCLR [9]41.68±0.05
SupCon [38]43.41±0.36β-TCVAE [8]27.35±0.38
LtD-diff [54]50.81±0.67GeoSSL [55]35.93±0.96
E(2)-CNN [73]45.19±0.84E(2)-CNN [73]38.50±0.49
LBS (CE)56.48±0.89DefGrid [21]33.13±0.17
LBS55.35±0.18
", + "image_path": "f3348e18ed0ba3afb631e652ce883977e6ba86807ffb5a473fc5d773aa6096ab.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 550, + 287, + 621 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 550, + 287, + 621 + ], + "spans": [ + { + "bbox": [ + 46, + 550, + 287, + 621 + ], + "type": "text", + "content": "4. For the unlabeled setting, the model is trained without " + }, + { + "bbox": [ + 46, + 550, + 287, + 621 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{embed}" + }, + { + "bbox": [ + 46, + 550, + 287, + 621 + ], + "type": "text", + "content": " and is denoted LBS with no parentheses. For evaluation, we use " + }, + { + "bbox": [ + 46, + 550, + 287, + 621 + ], + "type": "inline_equation", + "content": "z_{LBS+}" + }, + { + "bbox": [ + 46, + 550, + 287, + 621 + ], + "type": "text", + "content": " for LBS (CE), and " + }, + { + "bbox": [ + 46, + 550, + 287, + 621 + ], + "type": "inline_equation", + "content": "z_{LBS}" + }, + { + "bbox": [ + 46, + 550, + 287, + 621 + ], + "type": "text", + "content": " for LBS. All evaluations are performed with the common protocol of linear classification. For more detailed information on our implementation, please refer to Appendix C." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 622, + 216, + 634 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 622, + 216, + 634 + ], + "spans": [ + { + "bbox": [ + 47, + 622, + 216, + 634 + ], + "type": "text", + "content": "Baselines. We compare our models with:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 58, + 639, + 286, + 713 + ], + "type": "list", + "angle": 0, + "index": 11, + "blocks": [ + { + "bbox": [ + 58, + 639, + 286, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 639, + 286, + 662 + ], + "spans": [ + { + "bbox": [ + 58, + 639, + 286, + 662 + ], + "type": "text", + "content": "- Models which only use image encoder: trained with Cross-Entropy, SimCLR [9], or SupCon loss [38]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 58, + 664, + 286, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 664, + 286, + 700 + ], + "spans": [ + { + "bbox": [ + 58, + 664, + 286, + 700 + ], + "type": "text", + "content": "- Equivariance models: E(2)-Equivariant Steerable CNNs (E(2)-CNN) [73], and work by Novotny et al., denoted as GeoSSL [55]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 58, + 701, + 228, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 701, + 228, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 701, + 228, + 713 + ], + "type": "text", + "content": "- Disentanglement model: " + }, + { + "bbox": [ + 58, + 701, + 228, + 713 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 58, + 701, + 228, + 713 + ], + "type": "text", + "content": "-TCVAE [8]." + } + ] + } + ], + "index": 10 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 317, + 422, + 544, + 482 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 317, + 422, + 544, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 422, + 544, + 445 + ], + "spans": [ + { + "bbox": [ + 317, + 422, + 544, + 445 + ], + "type": "text", + "content": "- Sketch model for communication between agents: Learning to Draw (LtD) [54]" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 317, + 445, + 503, + 457 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 445, + 503, + 457 + ], + "spans": [ + { + "bbox": [ + 317, + 445, + 503, + 457 + ], + "type": "text", + "content": "- Grid-based superpixel model: DefGrid [21]" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 318, + 458, + 497, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 458, + 497, + 469 + ], + "spans": [ + { + "bbox": [ + 318, + 458, + 497, + 469 + ], + "type": "text", + "content": "- Handcrafted feature descriptor: HoG [14]." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 318, + 470, + 515, + 482 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 470, + 515, + 482 + ], + "spans": [ + { + "bbox": [ + 318, + 470, + 515, + 482 + ], + "type": "text", + "content": "- Pre-trained CLIP model used for training LBS." + } + ] + } + ], + "index": 15 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 490, + 423, + 502 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 490, + 423, + 502 + ], + "spans": [ + { + "bbox": [ + 306, + 490, + 423, + 502 + ], + "type": "text", + "content": "5.3. Results and analysis" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 508, + 545, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 508, + 545, + 662 + ], + "spans": [ + { + "bbox": [ + 304, + 508, + 545, + 662 + ], + "type": "text", + "content": "Analysis on RQ1 and RQ2: Tab. 1 shows the experimental results for RQ1 and RQ2, which can be summarized as: (a) Providing a strong inductive bias for equivariance, as shown in the case of E(2)-CNN, leads to good performance on the tasks of RQ1. While LBS outperformed LtD-diff, which also utilizes a sketch-based approach, it requires additional validation and refinement. (b) For RQ2, LBS performs substantially better than the other baselines except for the supervised setting on Geoclidean-Constraints, showing that it successfully captures geometric concepts. In particular, Geoclidean-Elements perform better when trained without labels. (c) Disentanglement methods and handcrafted features offer less informative features for both tasks." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "Analysis on RQ3: Tab. 2 summarizes the experiments conducted on the CLEVR dataset, demonstrating that LBS provides valuable information for tasks of RQ3. The key observations from Tab. 2 are: (a) While the baselines in the" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "23321" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 82, + 99, + 249, + 151 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 287, + 93 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 287, + 93 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 287, + 93 + ], + "type": "text", + "content": "Table 5. Top-1 and Top-10 accuracy on QMUL-Shoe-v2 dataset, using Triplet Loss for " + }, + { + "bbox": [ + 47, + 70, + 287, + 93 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{embed}" + }, + { + "bbox": [ + 47, + 70, + 287, + 93 + ], + "type": "text", + "content": " in LBS." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 82, + 99, + 249, + 151 + ], + "lines": [ + { + "bbox": [ + 82, + 99, + 249, + 151 + ], + "spans": [ + { + "bbox": [ + 82, + 99, + 249, + 151 + ], + "type": "table", + "html": "
MethodRepTop-1Top-10
LBS (Triplet)zLBS+40.8±4.1988.3±1.76
ze30.8±3.8977.8±3.89
Tripletze32.5±1.7380.0±4.36
", + "image_path": "2c9730bb69dde4ea1876181663c87565fcf3a3b58ff158abbeefd54405121110.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 172, + 288, + 292 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 172, + 288, + 292 + ], + "spans": [ + { + "bbox": [ + 46, + 172, + 288, + 292 + ], + "type": "text", + "content": "supervised setting struggle to generalize on unlearned attributes, LBS (CE) can provide more general information. (b) The results of LBS show a larger performance gap in the unlabeled setting, with its performance being almost as good as LBS (CE). (c) Embeddings from pre-trained CLIP perform less effectively than unlabeled baselines, such as SimCLR, on tasks related to local geometry. Also, handcrafted features yielded limited effectiveness. (d) Methods that focus on preserving global transformations and disentanglement are not effective in environments of RQ3." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 297, + 287, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 297, + 287, + 441 + ], + "spans": [ + { + "bbox": [ + 46, + 297, + 287, + 441 + ], + "type": "text", + "content": "Analysis on RQ4: Tabs. 3 and 4 summarize the results for shifting domains from STL-10 to CLEVR, and vice versa. As shown in Fig. 11 on Appendix I, LBS trained on STL-10 can successfully describe scenes from CLEVR, while LBS trained on CLEVR can abstractly depict natural images from STL-10, leading to substantially high classification accuracy. These results indicate that learning geometric information, such as position and curvature, by sketching salient parts of a scene successfully induces learning of general features across domains. Furthermore, LtD-diff, which also utilizes a sketch-based approach, demonstrated good performance in transferring CLEVR to STL-10." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 446, + 287, + 531 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 446, + 287, + 531 + ], + "spans": [ + { + "bbox": [ + 46, + 446, + 287, + 531 + ], + "type": "text", + "content": "Analysis on RQ5: Tab. 5 presents the results for the FG-SBIR task. Compared to the baseline trained without sketching, LBS can accurately predict the corresponding shoe during the test phase. The huge drop in performance upon removing strokes and stroke embedding from " + }, + { + "bbox": [ + 46, + 446, + 287, + 531 + ], + "type": "inline_equation", + "content": "z_{LBS+}" + }, + { + "bbox": [ + 46, + 446, + 287, + 531 + ], + "type": "text", + "content": " indicates that the geometry-aware representation provided by LBS is also valuable for traditional sketch tasks." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 548, + 260, + 561 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 548, + 260, + 561 + ], + "spans": [ + { + "bbox": [ + 47, + 548, + 260, + 561 + ], + "type": "text", + "content": "5.4. Comparisons with stroke-based methods" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": "Tab. 6 compares LBS to other stroke-based generation methods on STL-10 dataset, and Fig. 5 visualizes the results of each method. The evaluation is based solely on strokes, and LBSonly uses " + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "inline_equation", + "content": "z_{p}" + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": " as a representation. LBS (" + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text{percept}}" + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": ") achieved superior results compared to LBS (" + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_1" + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": ") and the Paint Transformer [48] based on " + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_1" + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": " loss. We also compare our results to CLIPasso modified to use our deterministic initialization process, suggesting that strokes generated from CLIPasso may not be suitable as a representation. LtD-diff, which generates sketches to solve a communication game, often omits important geometric and color information, resulting in low performance." + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 316, + 87, + 532, + 159 + ], + "blocks": [ + { + "bbox": [ + 309, + 70, + 541, + 82 + ], + "lines": [ + { + "bbox": [ + 309, + 70, + 541, + 82 + ], + "spans": [ + { + "bbox": [ + 309, + 70, + 541, + 82 + ], + "type": "text", + "content": "Table 6. Comparison between stroke-based generation methods." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 316, + 87, + 532, + 159 + ], + "lines": [ + { + "bbox": [ + 316, + 87, + 532, + 159 + ], + "spans": [ + { + "bbox": [ + 316, + 87, + 532, + 159 + ], + "type": "table", + "html": "
RCBCSizeShapeMaterial
LtD-diff [54]18.7021.6973.1347.8859.11
Paint [48]51.9660.4077.3544.3070.02
CLIPasso [68]12.5513.5555.3535.4050.00
LBS (L1)34.4357.8178.3240.9961.59
LBS (Lpercept)55.1560.6390.1451.2376.16
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Comparisons to other stroke-based methods. LBS encodes both the geometric and semantic information." + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 399, + 234, + 451, + 287 + ], + "blocks": [ + { + "bbox": [ + 405, + 225, + 447, + 235 + ], + "lines": [ + { + "bbox": [ + 405, + 225, + 447, + 235 + ], + "spans": [ + { + "bbox": [ + 405, + 225, + 447, + 235 + ], + "type": "text", + "content": "LBS " + }, + { + "bbox": [ + 405, + 225, + 447, + 235 + ], + "type": "inline_equation", + "content": "(\\mathcal{L}_{percept})" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 399, + 234, + 451, + 287 + ], + "lines": [ + { + "bbox": [ + 399, + 234, + 451, + 287 + ], + "spans": [ + { + "bbox": [ + 399, + 234, + 451, + 287 + ], + "type": "image", + "image_path": "f6ca962c5db510c9b03283a6e47584f237198c2f20702026d3e5348aef5e991e.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 411, + 288, + 439, + 296 + ], + "lines": [ + { + "bbox": [ + 411, + 288, + 439, + 296 + ], + "spans": [ + { + "bbox": [ + 411, + 288, + 439, + 296 + ], + "type": "text", + "content": "LtD-diff" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 460, + 234, + 513, + 287 + ], + "blocks": [ + { + "bbox": [ + 471, + 225, + 501, + 234 + ], + "lines": [ + { + "bbox": [ + 471, + 225, + 501, + 234 + ], + "spans": [ + { + "bbox": [ + 471, + 225, + 501, + 234 + ], + "type": "text", + "content": "LBS " + }, + { + "bbox": [ + 471, + 225, + 501, + 234 + ], + "type": "inline_equation", + "content": "(\\mathcal{L}_1)" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 460, + 234, + 513, + 287 + ], + "lines": [ + { + "bbox": [ + 460, + 234, + 513, + 287 + ], + "spans": [ + { + "bbox": [ + 460, + 234, + 513, + 287 + ], + "type": "image", + "image_path": "6aa3c1ddf294f05add07b2e376097960a930fe16ca6a354dbd988b5adcf81a84.jpg" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 456, + 288, + 517, + 296 + ], + "lines": [ + { + "bbox": [ + 456, + 288, + 517, + 296 + ], + "spans": [ + { + "bbox": [ + 456, + 288, + 517, + 296 + ], + "type": "text", + "content": "Paint Transformer" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_caption" + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 335, + 378, + 346 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 335, + 378, + 346 + ], + "spans": [ + { + "bbox": [ + 306, + 335, + 378, + 346 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 355, + 545, + 534 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 355, + 545, + 534 + ], + "spans": [ + { + "bbox": [ + 304, + 355, + 545, + 534 + ], + "type": "text", + "content": "We propose a novel representation learning perspective through sketching, a visual expression that retains geometric information. By considering the mathematical concept of equivariance, we provide a formal definition of sketch and stroke, and prove that strokes can preserve the information of arbitrary affine transformations. Our sketch generation model, LBS, minimizes CLIP-based perceptual loss and supports the idea that sketches can effectively convey geometric information. The experiments shed light on the potential benefits of leveraging the process of sketching to represent high-level geometric information explicitly. These benefits include learning equivariant representations, understanding geometric concepts, improving spatial reasoning abilities, and acquiring general geometric information across different domains." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 536, + 545, + 656 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 536, + 545, + 656 + ], + "spans": [ + { + "bbox": [ + 304, + 536, + 545, + 656 + ], + "type": "text", + "content": "Still, there are several limitations to our method. The training process of LBS relies on pre-trained CLIP and optionally U2-Net, and requires generating guidance strokes through a time-consuming optimization-based process. Moreover, while our work has demonstrated the theoretical strengths of sketching in terms of equivariance, a clearer methodology and further experimental analysis are needed to fully achieve this potential. Future work should address these issues and extend the methodology, focusing on scalability and including more complex and realistic tasks." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "Acknowledgement This work was partly supported by the Korean government (2021-0-02068-AIHub/25%, 2021-0-01343-GSAI/25%, 2022-0-00951-LBA/25%, 2022-0-00953-PICA/25%)." + } + ] + } + ], + "index": 25 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23322" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 91, + 288, + 715 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "text", + "content": "[1] Pablo Arbelaez, Michael Maire, Charless Fowlkes, and Jitendra Malik. 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Unlike previous methods that perform scene-aware mesh optimization, we propose to first estimate absolute position and dense scene contacts with a sparse 3D CNN, and later enhance a pretrained human mesh recovery network by cross-attention with the derived 3D scene cues. Joint learning on images and scene geometry enables our method to reduce the ambiguity caused by depth and occlusion, resulting in more reasonable global postures and contacts. Encoding scene-aware cues in the network also allows the proposed method to be optimization-free, and opens up the opportunity for real-time applications. The experiments show that the proposed network is capable of recovering accurate and physically-plausible meshes by a single forward pass and outperforms state-of-the-art methods in terms of both accuracy and speed. Code is available on our project page: https://zju3dv.github.io/sahmr/.", + "bbox": [ + 75, + 287, + 473, + 561 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 622, + 209, + 638 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Monocular human mesh recovery (HMR), i.e., estimating pose and shape parameters of a parametric human model from a single image, has gained significant attention in recent years. To better capture and understand human behaviors, many recent works [1-5] propose to address the problem of scene-aware HMR which involves human-scene interaction constraints when recovering human meshes, given the 3D geometry of the scene scanned by range sensors [5-7], as well as the camera pose of the input image relative to the scene, which may enable more applications in video surveillance, household robots, and motion analysis in gyms and clinics.", + "bbox": [ + 75, + 647, + 468, + 828 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Most existing methods propose using scene-aware optimization to fit the human mesh into a pre-scanned scene. They optimize a parametric human model iteratively, e.g.,", + "bbox": [ + 76, + 829, + 468, + 876 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/ff8689aef3051835a559618c047a54bbb709eb57d294c089a468cf06b8166aa5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 521, + 255, + 696, + 390 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/b31c8e031c8754726b90b80ff317948b89d7b82f7876b132f86b180a9b6610b9.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 697, + 255, + 870, + 390 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/0d2904060809c3847866cd385c6e3dda838ad97e09f2cccd312294c013adfebd.jpg", + "image_caption": [ + "Input", + "Figure 1. Comparison between the optimization-based method and the proposed method. Optimization-based methods typically fit a parametric human model iteratively by minimizing 2D reprojection error and scene conflicts. In contrast, the proposed method utilizes a single forward pass of the network to estimate the global position (blue ball), contact scene points (colored scene points), and a scene-aware human mesh. This design leads to improvements in both efficiency and accuracy." + ], + "image_footnote": [], + "bbox": [ + 521, + 392, + 696, + 526 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/fc60ca6c1f19c0ea866075dfdbe1d088155ccc1e0fe075cbfc598548392ed96b.jpg", + "image_caption": [ + "Prediction" + ], + "image_footnote": [], + "bbox": [ + 697, + 392, + 870, + 526 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "SMPL [8], to minimize scene penetration, chamfer distance of contact regions, and the 3D-2D re-projection error. However, optimization tends to be slow at inference time and is sensitive to initialization and hyperparameters, failing to respond in low-latency applications. As illustrated in Fig. 1, an optimization-based method PROX [5] takes 18.4s to fit a human model into the scene, while the incorrect position and pose still occur.", + "bbox": [ + 496, + 700, + 893, + 823 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recent works [9-13] propose to recover human mesh with neural networks trained on large-scale datasets [14-17]. Specifically, the networks learn a mapping from an input image to a human mesh in the canonical coordinates. Applying these methods in the scene-aware HMR", + "bbox": [ + 498, + 824, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "†Corresponding author.", + "bbox": [ + 102, + 886, + 228, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "17038", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "task still requires post-processing optimization, where the global translation and the human poses are refined in accordance with the given scene. However, the monocular prediction is conditioned on the input image solely, omitting the joint distribution of human pose and scene geometry, and therefore tends to suffer from depth ambiguity and occlusion. As a result, the optimization-based post-processing could be easily deteriorated by the erroneous initial poses and may even worsen the initial prediction.", + "bbox": [ + 75, + 90, + 472, + 226 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, we propose a Scene-Aware Human Mesh Recovery network (SA-HMR), the first learning-based approach that predicts the absolute position and mesh of a human in the scene by a single forward pass. The overall pipeline is illustrated in Fig. 2. Given the input image and scene point cloud, we first use a sparse 3D CNN to estimate dense scene contacts and absolute human position, where the scene contact estimation is treated as a point cloud labeling task, and the human position prediction is presented as a voting vector field refinement task. The predicted dense contact points are centered by the human position and passed to a scene network in the human mesh recovery step. Specifically, we enhance a pretrained monocular HMR network METRO [12] by cross-attention with the proposed scene network in parallel. In this way, SA-HMR learns a joint distribution of human pose and scene geometry, resulting in more reasonable postures, contacts, and global positions, as illustrated in Fig. 1. Learning scene-aware cues in the network also avoids scene-aware optimization as post-processing and achieves fast inference speed.", + "bbox": [ + 75, + 227, + 472, + 527 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We evaluate the proposed method on the RICH [6] and PROX [5] datasets of indoor and outdoor scenes. The experimental results show that SA-HMR is not only effective in recovering absolute positions and meshes that are in accordance with the given scene, but also significantly faster than the optimization-based baselines.", + "bbox": [ + 75, + 529, + 472, + 619 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, we make the following contributions:", + "bbox": [ + 96, + 619, + 429, + 633 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- The first optimization-free framework for scene-aware human mesh recovery from a single image and a prescanned scene.", + "- The cross-attention design for enhancing a pretrained HMR network with a parallel scene network, enabling joint learning on the human pose and scene geometry.", + "- Superior performance compared to optimization-based baselines in terms of both accuracy and speed." + ], + "bbox": [ + 96, + 643, + 468, + 781 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 794, + 218, + 810 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Monocular Human Mesh Recovery. Most existing approaches formulate the monocular HMR task as recovering the mesh of statistical human body models, e.g. SMPL and SMPL-X [8, 18, 19], where recent works can be divided into optimization-based and learning-based approaches.", + "bbox": [ + 75, + 825, + 468, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The optimization-based approaches fit a parametric human model by minimizing the 3D-2D re-projection error of body joints and energy terms of heuristic priors iteratively, which are represented by SMPLify [20] that fits SMPL [8]. More recently, SMPLify-X [19] proposes a variational pose prior and fits a more expressive SMPL-X. PoseNDF [21] proposes to represent the manifold of plausible human poses with a neural field. While optimization-based methods are general in their mathematical formulation, they are usually sensitive to hyperparameters and require much time for inference.", + "bbox": [ + 496, + 90, + 890, + 256 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The learning-based methods utilize deep neural networks to predict either the parameters [9, 10, 22, 23] or the mesh vertices [11-13] of the SMPL model. HMR [9] is the pioneering work in predicting SMPL parameters, and SPIN [10] improves upon it using an optimization loop. For predicting SMPL mesh vertices, GraphCMR [11] deforms a template human mesh using graph neural network, while METRO [12] uses transformers, and [13] uses graph hierarchy to further improve the performance. However, for scene-aware HMR, the vertices of the human and scene meshes in contact are close in Euclidean space, making methods that regress parameters unsuitable due to errors that accumulate along the kinematic chains. Therefore, the proposed method is built on the works that predict mesh vertices. More details can be found in Sec. 3.", + "bbox": [ + 496, + 260, + 890, + 486 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Scene-aware Human Mesh Recovery. PROX [5] is a seminal work that uses scene constraints to reduce the depth and occlusion ambiguity in monocular HMR. It achieves this by adding two energy terms of human-scene contact and penetration in the optimization process [19]. In addition, scene-aware pose generative models [2, 24] can also be used as prior terms in the scene-aware HMR task. Other recent works in this area include MoCapDeform [4], which considers deformable scene objects, LEMO [1], which uses temporal information, and HULC [3], which uses consecutive frames and dense contacts prediction on both the scene and human body. In contrast to these works, the proposed method is optimization-free and requires only a single forward pass.", + "bbox": [ + 496, + 494, + 890, + 708 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In a broader topic of capturing humans in a scene-aware manner, [25-27] propose using a simulator and dynamic model, where a pre-defined agent is controlled to interact with the scene, and [28,29] consider human-object arrangement by first predicting the human and object and then performing global optimization.", + "bbox": [ + 496, + 710, + 890, + 801 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Attention in Transformers. Attention is a key mechanism in Transformers [30]. It allows a set of query features to fuse the most relevant information from another set of key-value features. When query and key-value features come from the same source, it is called self-attention, otherwise cross-attention. In HMR, METRO [12] uses self-attention to re", + "bbox": [ + 496, + 809, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "17039", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/099d627c6371e6f265ecdb14d5cbd081cb6e5e1014f1544beefc162ca88ddb90.jpg", + "image_caption": [ + "1. Human Root and Scene Contacts" + ], + "image_footnote": [], + "bbox": [ + 99, + 126, + 454, + 262 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/1344a1eae09f2a30ed5ac3fb1109504220a94f08a5adf1ec816b0a392fd9cffe.jpg", + "image_caption": [ + "2. Scene-aware Human Mesh Recovery", + "Figure 2. Overview of the proposed SA-HMR. 1. The human root and scene contact estimation module (Sec. 3.2) that first predicts the initial root and then refines the root with 3D scene cues using a sparse 3D CNN. The module also predicts contact labels [5] for each scene point. Please refer to Sec. 3.2 for a detailed definition of the 3D feature construction module. 2. The scene-aware human mesh recovery module (Sec. 3.3) that enhances the pretrained METRO [12] network with a parallel scene network. The scene network takes the predicted contact scene points as input, and uses cross-attention to pass messages to the intermediate features of the METRO network." + ], + "image_footnote": [], + "bbox": [ + 457, + 119, + 867, + 262 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "duce occlusion ambiguity by establishing non-local feature exchange between visible and invisible parts of a template human mesh. In feature matching, SuperGlue [31] uses cross-attention to make the corresponding image features more similar. Predator [32] uses cross-attention in matching two sets of point clouds.", + "bbox": [ + 75, + 372, + 468, + 462 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Inspired by feature matching, the proposed method uses cross-attention to potentially make the features of the human and scene that are in contact more similar, resulting in better contact and more reasonable postures.", + "bbox": [ + 76, + 463, + 468, + 525 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methods", + "text_level": 1, + "bbox": [ + 76, + 540, + 174, + 556 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given a calibrated image and a pre-scanned scene point cloud (Sec. 3.1), SA-HMR first estimates the absolute human root position and scene contacts (Sec. 3.2), and then recovers the human mesh with the contact points by enhancing a pretrained METRO network (Sec. 3.3). An overview of the proposed method is presented in Fig. 2.", + "bbox": [ + 75, + 566, + 468, + 657 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Preliminaries", + "text_level": 1, + "bbox": [ + 76, + 669, + 217, + 684 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Human Representation. We use SMPL [8] as the human representation. The SMPL is a parametric model that uses the body joint rotations, root translation, and body shape coefficients to compute the body mesh. Following [11, 12], we directly predict the SMPL mesh vertices $V = \\mathbb{R}^{6890 \\times 3}$ , and use H36M [14] joint regression matrix $M \\in \\mathbb{R}^{14 \\times 6890}$ to compute 3D joints $J \\in \\mathbb{R}^{14 \\times 3}$ from the vertices for quantitative evaluation, $J = MV$ .", + "bbox": [ + 75, + 698, + 468, + 819 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Scene and Image Representation. We assume that the scene is pre-scanned with range sensors, as in RICH [6] and PROX [5], and the image is calibrated and localized in the scene, i.e. with known intrinsic and extrinsic parameters $\\{(f,c_x,c_y),(R_c,t_c)\\}$ . Following METRO [12], we detect", + "bbox": [ + 76, + 825, + 468, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "a squared bounding box around the target human and resize the cropped region as the input image $I \\in \\mathbb{R}^{224 \\times 224 \\times 3}$ . Based on the camera parameters and the bounding box, we select scene points that fall within the visual frustum as the input scene point cloud $S \\in \\mathbb{R}^{N_S \\times 3}$ .", + "bbox": [ + 496, + 372, + 890, + 448 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Human-Scene Contact. Following PROX [5], we use seven regions of the SMPL mesh that are most likely to be contacted. The details are provided in the supplementary material. Using these seven categories and one for not being in contact, we perform a segmentation task on the scene point cloud.", + "bbox": [ + 496, + 452, + 892, + 544 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Human Root and Scene Contacts", + "text_level": 1, + "bbox": [ + 500, + 551, + 790, + 566 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given an image $I$ bounding the human, we propose using a 2D convolutional neural network (CNN) to extract image features $F$ and predict the initial human root $r$ . Based on the scene points $S$ , we unproject the image features $F$ to 3D, resulting in $\\hat{F}$ . Additionally, we calculate point-wise offset vectors $O$ that point from a voxelized scene point cloud to the initial root. By taking $\\hat{F}$ and $O$ as input, a sparse 3D CNN predicts the segmentation of scene contacts and the refined offsets, which are then converted to the refined human root $r^{*}$ . An overview of this process is presented in the left column of Fig. 2.", + "bbox": [ + 496, + 574, + 890, + 742 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Initial Root. We predict the initial root $r = (X, Y, Z)$ in a 2.5D manner following SMAP [33]. Specifically, we use a CNN to predict the 2D heatmap and a normalized depth map of the root. Then, the 2D position $(x, y)$ is obtained by applying argmax to the heatmap, and the corresponding normalized depth value $\\tilde{Z}$ is retrieved from the depth map. Finally, using the intrinsic parameters $f, c_x, c_y$ and image size $w$ , the 3D root position is computed:", + "bbox": [ + 496, + 744, + 892, + 867 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nZ = \\tilde {Z} \\frac {f}{w} \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 661, + 875, + 890, + 905 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "17040", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/9c4f56bb248248a8ca505d924665a8e26221b1c570ae623579dab2c31146c233.jpg", + "image_caption": [ + "Figure 3. 3D feature construction. We voxelize a scene point cloud to a sparse volume. The initial feature of each voxel consists of two parts, which are the offset vector pointing from the voxel center to the human root and the unprojected image features." + ], + "image_footnote": [], + "bbox": [ + 117, + 88, + 429, + 220 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nX = \\frac {x - c _ {x}}{f} \\cdot Z, \\quad Y = \\frac {y - c _ {y}}{f} \\cdot Z \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 151, + 310, + 468, + 340 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "From our observation, estimating $(x,y)$ achieves good results with a mean squared error of fewer than two pixels across datasets. However, estimating $\\tilde{Z}$ is relatively challenging, possibly due to the variations in human shapes.", + "bbox": [ + 75, + 344, + 468, + 405 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3D Feature Construction. Based on the initial root $r$ and image features $F$ , we construct the 3D features on the voxelized scene point cloud, which is illustrated in Fig. 3.", + "bbox": [ + 75, + 409, + 468, + 454 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "First, we select regions of interest around the initial root $r$ in the point cloud. Specifically, we treat $r$ as an anchor and keep points within a radius $\\gamma_1$ . Since $Z$ has more uncertainty than $(x,y)$ , we sample two additional anchors along the z-axis, whose distance to $r$ is $\\gamma_2$ . Next, we construct a sparse volume $\\bar{S}$ by voxelizing these points with voxel size $s_{vox}$ , where the center of each voxel is denoted as $\\bar{s}_i$ .", + "bbox": [ + 75, + 455, + 468, + 559 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For each voxel $i$ , the feature consists of the offset vector $o_i$ and the unprojected image feature $\\hat{f}_i$ . Specifically, $o_i$ is a vector pointing from the voxel center to the human root:", + "bbox": [ + 76, + 561, + 468, + 606 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\no _ {i} = r - \\bar {s} _ {i} \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 230, + 616, + 468, + 630 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$\\hat{f}$ is computed by projecting voxel center $\\bar{s}_i$ onto the image using camera parameters and bilinearly sampling the image feature map $F$ .", + "bbox": [ + 75, + 638, + 468, + 684 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Estimating Refined Root and Scene Contacts. We use sparse 3D CNN [34] to process the constructed 3D features and learn to improve the root estimation and predict the scene contacts. Specifically, the output of each voxel includes an updated offset vector $o_i^*$ , confidence $c_i$ , and segmentation indicating the contact category. We compute the refined root $r^*$ :", + "bbox": [ + 75, + 689, + 468, + 794 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nr ^ {*} = \\sum_ {i} c _ {i} \\cdot \\left(o _ {i} ^ {*} + \\bar {s} _ {i}\\right). \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 192, + 801, + 468, + 832 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "There are 8 categories of contact points, including 7 most probable regions on the body that would be contacted [5] and 1 category of not being in contact. We take the category of the highest score as the prediction for the voxel and", + "bbox": [ + 75, + 839, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/65c2791949dd0be2029cae1f86dc4c878a3b9f06a416235b0672e7d8c902d622.jpg", + "image_caption": [ + "Figure 4. Enhancing METRO with a parallel network. The orange parts are the original METRO [12] network, where the residual connection and positional encoding are omitted for simplicity. The blue parts are the proposed parallel network which takes predicted contact scene points as input. The yellow parts indicate feature interaction between METRO and the parallel network." + ], + "image_footnote": [], + "bbox": [ + 509, + 87, + 867, + 362 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "set the dense point cloud belonging to the voxel with that category. The contact points $\\hat{S}_{seg3d} \\in \\mathbb{R}^{\\hat{N}_S \\times 3}$ serve as the input for the mesh recovery module.", + "bbox": [ + 498, + 484, + 890, + 532 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Scene-aware Human Mesh Recovery", + "text_level": 1, + "bbox": [ + 500, + 545, + 816, + 561 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Since the training data of scene-aware human mesh recovery is limited, we build our model upon a network named METRO [12] that is pre-trained on large-scale data of monocular human mesh recovery. METRO processes feature based on the self-attention mechanism, and our approach enhances METRO by adding a parallel scene network, which provides a cross-attention-based mechanism that enables METRO to notice important scene details and achieve scene-aware human mesh recovery.", + "bbox": [ + 496, + 569, + 890, + 705 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "METRO consists of a CNN backbone and multiple Transformer encoders. It first extracts global CNN features, then combines the feature to the vertices of a zero posed SMPL mesh, and finally predicts a posed mesh with shape through the transformers. The part of the transformer is illustrated in the orange part of Fig. 4.", + "bbox": [ + 496, + 710, + 890, + 801 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Enhancing METRO with Cross-Attention. We improve METRO with a scene network, which makes the predicted human vertices to be close to the corresponding contact scene points $\\hat{S}_{seg3d}$ (Sec. 3.2).", + "bbox": [ + 496, + 808, + 890, + 869 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As illustrated in Fig. 4, we add a parallel network, which has a similar architecture as the transformer of METRO,", + "bbox": [ + 498, + 869, + 890, + 898 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "17041", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/52c52e3d1e59a88b64ba968f1f625c9b54cc63dfa00acc5a85974ce5bacdf5b8.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 99, + 88, + 207, + 256 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/46fa9aad8b9fd7b602a2235cc527bf00715c49bb2400fc499929e272cbf20f56.jpg", + "image_caption": [ + "(b)" + ], + "image_footnote": [], + "bbox": [ + 210, + 88, + 320, + 255 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/d05cdefacc22f054e018275653bef8ef306d3842d9561b63d4f134fa48aae402.jpg", + "image_caption": [ + "(c)", + "Figure 5. Visualization of the cross-attention from a body vertex (blue point) to the predicted dense scene contacts (white points). (a) The image and the predicted dense scene contacts. (b) The hand vertex is in contact with the scene according to the image, and its feature is similar to the nearby scene point features, enabling the final vertex prediction to be close to the corresponding scene surface. (c) The arm vertex is not in contact with the scene, where feature similarities tend to be evenly distributed. The feature similarities are normalized to the same range of $0 \\rightarrow 1$ ." + ], + "image_footnote": [], + "bbox": [ + 323, + 88, + 447, + 256 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "to extract features of scene contact points and output the point positions like an autoencoder. Specifically, we first use METRO's CNN backbone to extract the image feature and map it to a set of vertex tokens by a fully-connected layer. In METRO, these tokens are directly concatenated with the positions of initial human vertices. However, the number of scene contact points is not the same as the tokens', and there is no one-to-one correspondence between them. To resolve this issue, we perform the average pooling to vertex tokens based on the contact categories defined on the SMPL mesh vertices [5], resulting in 7 tokens. Then, we append each scene contact point with the corresponding aggregated token based on the predicted category in Sec. 3.2. Intuitively, this helps the cross-attention to focus on the semantically corresponding parts. To be invariant to the global translation, the scene contact points are zero-centered by the predicted root $r^*$ .", + "bbox": [ + 75, + 431, + 468, + 688 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Motivated by recent feature matching methods [31, 32], we propose to use cross-attention to pass features from scene contact points to human vertices. The cross-attention and self-attention share the same underlying mechanism, both of which first compute the similarity of query and key, and then use the weighted sum to fuse features. When the query and key are from the same source features, it is self-attention, and otherwise is cross-attention. In practice, we use linear attention operator [35] to improve efficiency. A visualization of cross attention over human vertices and scene points is in Fig. 5. The detailed network architecture is provided in the supplementary material.", + "bbox": [ + 75, + 688, + 468, + 869 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Note that, we use a weight-sharing regressor layer with METRO, which regresses from point-wise features to point", + "bbox": [ + 76, + 869, + 470, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "position $(x,y,z)$ . Therefore, to get a similar $(x,y,z)$ , the input features of this layer should also be similar. This strategy implicitly aligns the features of human vertices and scene points when their final predictions are near in 3D space, thus facilitating the cross-attention to find correspondences between human vertices and scene points.", + "bbox": [ + 496, + 90, + 890, + 181 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Training Loss", + "text_level": 1, + "bbox": [ + 500, + 191, + 643, + 207 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Root and Contact. The loss function $L_{\\mathrm{RC}}$ for the root and contact estimation is defined as:", + "bbox": [ + 498, + 219, + 890, + 250 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\mathrm {R C}} = L _ {\\mathrm {R 2 D}} + w _ {\\mathrm {R Z}} \\cdot L _ {\\mathrm {R Z}} + L _ {\\mathrm {R O V}} + L _ {\\mathrm {R 3 D}} + L _ {\\mathrm {C}} \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 524, + 261, + 890, + 277 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $L_{\\mathrm{R2D}}$ is the MSE loss on the root heatmap; $L_{\\mathrm{RZ}}$ , $L_{\\mathrm{ROV}}$ , and $L_{\\mathrm{R3D}}$ are the L1 losses on the relative depth, offset vectors, and the 3D root, respectively; $L_{\\mathrm{C}}$ is the cross-entropy loss for contact categories of voxel points, where we additionally train an auxiliary task of 2D contact segmentation similar to the voxel points.", + "bbox": [ + 498, + 289, + 890, + 378 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Human Mesh Recovery. The loss function $L_{\\mathrm{HMR}}$ for the mesh recovery is defined as:", + "bbox": [ + 498, + 383, + 890, + 414 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\mathrm {H M R}} = L _ {\\mathrm {V}} + L _ {\\mathrm {J}} + L _ {\\mathrm {C P}} + L _ {\\mathrm {G V}} \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 586, + 426, + 890, + 441 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $L_{\\mathrm{V}}$ , $L_{\\mathrm{J}}$ , $L_{\\mathrm{CP}}$ , and $L_{\\mathrm{GV}}$ are the L1 losses on the translation-aligned human vertices, human joints, reconstructed contact points, and global human vertices, respectively. More details are in the supplementary material.", + "bbox": [ + 496, + 454, + 890, + 513 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5. Implementation Details", + "text_level": 1, + "bbox": [ + 500, + 523, + 718, + 539 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We train two modules separately. For the root and contact module, the CNN is HRNet-stride-4 [36] with METRO initialization, the sparse 3D CNN is SPVCNN [34, 37] with random initialization. We use linear layers to align intermediate feature dimensions. $\\gamma_{1}$ is $1.25\\mathrm{m}$ , $\\gamma_{2}$ is $0.5\\mathrm{m}$ , $s_{vox}$ is $5^{3}cm^{3}$ , and $w_{\\mathrm{RZ}}$ is 10. The contact threshold is $7\\mathrm{cm}$ . We flip images for augmentation. The module is trained with an initial learning rate of $3.75\\mathrm{e - 5}$ and a batch size of 24. It converges after 30 epochs of training on one V100 GPU. For the mesh recovery module, the METRO network is initialized as pretrained and the scene network is randomly initialized. The initial learning rate is $7.5\\mathrm{e - 6}$ and the batch size is 24. It converges after 30 epochs of training.", + "bbox": [ + 496, + 547, + 890, + 743 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 756, + 633, + 773 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Datasets", + "text_level": 1, + "bbox": [ + 500, + 781, + 601, + 796 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We train and evaluate the proposed method on RICH [6] and PROX [5] datasets separately.", + "bbox": [ + 500, + 804, + 890, + 835 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "RICH [6] captures multi-view video sequences in 6 outdoor and 2 indoor scenes. It provides images, reconstructed bodies, scene scans, and human-scene contact labels annotated on SMPL vertices. We skip frames including multiple", + "bbox": [ + 498, + 839, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "17042", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/b6333eb4a224c4b357df69b177e46d1fec709ba7f835109192cf83ccaf1e984c.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodLearning-basedOptimizationScene-awareG-MPJE↓G-MPV\\( \\downarrow \\)PenE↓ConFE↓MPJPE↓MPVE↓
Dataset GT [6]✓✓//9.810.8//
SMPLify-X [19]✓482.0483.735.743.4166.9177.6
PROX [5]✓✓390.1397.215.524.1164.1175.8
POSA [2]✓✓427.8434.021.127.0177.2188.4
PLACE [38]✓✓395.9403.016.124.8163.8175.4
METRO \\( [12]^† + SA-Opt \\) [6, 29]✓✓✓563.1561.37.414.8102.7112.8
METRO [12]✓678.6679.452.256.9129.6134.5
METRO \\( [12]^† \\)✓511.7509.733.637.698.8107.9
SA-HMR✓✓264.6272.714.919.093.9103.0
", + "bbox": [ + 99, + 88, + 870, + 229 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "subjects, remove the first 45 frames of each video to avoid static starting pose, and skip frames where the subjects' 2D bounding boxes are not inside the images. Then we down-sample the train / val / test splits to $2/1/1$ fps, resulting in 15360 / 3823 / 3316 frames.", + "bbox": [ + 75, + 306, + 470, + 383 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "PROX [5] captures monocular RGBD videos in 12 indoor scenes. We use RGB images and scene scans. It is a challenging dataset where severe occlusions exist in most frames. We use the qualitative set for training and the quantitative set for testing. In order to get better training annotations, we additionally use HuMoR [26] which utilizes motion prior and optimizes a sequence of frames. Then, we manually remove the failed frames that are not consistent with the images and scenes. Finally, the training split contains 4852 frames.", + "bbox": [ + 75, + 388, + 470, + 541 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Metrics", + "text_level": 1, + "bbox": [ + 76, + 554, + 171, + 569 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We evaluate quantitatively in terms of human mesh recovery and human-scene contact.", + "bbox": [ + 75, + 579, + 468, + 609 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Human Mesh Recovery. We report the Global Mean-Per-Joint-Position-Error (G-MPJPE) and Global Mean-Per-Vertex-Error (G-MPVE) in the scene coordinate system, which calculates the average L2 distances between predicted and ground truth joints/vertices. Additionally, we report the translation-aligned metrics MPJPE and MPVE.", + "bbox": [ + 75, + 614, + 468, + 707 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Human-scene Contact. We report the Penetration Error (PenE) and Contact Failure Error (ConFE). PenE measures the total distance that SMPL vertices penetrate the scene mesh:", + "bbox": [ + 75, + 712, + 468, + 772 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {P e n E} = \\sum_ {i = 1} ^ {V} \\mathbb {1} _ {x < 0} [ s d f (v _ {i}, \\mathcal {S}) ] \\cdot | s d f (v _ {i}, \\mathcal {S}) |, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 125, + 784, + 468, + 828 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $V$ is the number of SMPL vertices, $sdf(v_{i},\\mathcal{S})$ is the signed distance from vertex $v$ to scene $\\mathcal{S}$ , and $\\mathbb{1}_{x < 0}[\\cdot ]$ is an indicator function that returns 1 when the condition is met, and 0 otherwise. ConFE measures contact quality when the", + "bbox": [ + 75, + 839, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/b99416d4c8f7db2a806dbb934bc2bffe090a2ac6019459cdfd6d05902a5dc8a9.jpg", + "table_caption": [ + "Table 1. Evaluation on the RICH [6] dataset. METRO† indicates that the model is finetuned on the dataset. SA-Opt indicates scene-aware optimization, with contact estimation from BSTRO [6] and loss formulation from PROX [5] and PHOSA [29]. The proposed SA-HMR achieves the overall best results and is significantly faster than the methods that require optimization." + ], + "table_footnote": [], + "table_body": "
MethodG-MPJPE↓G-MPVE↓PenE↓MPJPE↓MPVE↓
Dataset GT [5]//9.6//
SMPLify-X [19]216.0222.649.3100.7112.8
PROX [5]172.0178.510.7101.1114.0
POSA [2]172.3180.916.6108.5119.4
PLACE [38]168.1176.712.3100.8113.7
METRO [12]283.2277.762.4137.0147.2
METRO [12]†265.6262.767.5117.1128.5
SA-HMR150.4160.026.9111.1122.5
", + "bbox": [ + 504, + 304, + 888, + 431 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. Evaluation on the PROX [5] dataset. The proposed method achieves the best performance in global metrics.", + "bbox": [ + 498, + 441, + 892, + 470 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "ground truth contact label is available:", + "bbox": [ + 500, + 494, + 754, + 511 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\operatorname {C o n F E} = \\sum_ {i = 1} ^ {V} \\left(C _ {g t} \\left(v _ {i}\\right) \\cdot | s d f \\left(v _ {i}, \\mathcal {S}\\right) |\\right. \\\\ + \\left(1 - C _ {g t} \\left(v _ {i}\\right)\\right) \\cdot \\mathbb {1} _ {x < 0} [ s d f \\left(v _ {i}, \\mathcal {S}\\right) ] \\cdot | s d f \\left(v _ {i}, \\mathcal {S}\\right) |), \\tag {8} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 503, + 518, + 890, + 595 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $C_{gt}(v)$ equals 1 if $v$ is labeled as in contact, and 0 otherwise. In order to obtain a good result of ConFE, the body vertices in contact should be close to the scene surface, while vertices not in contact should avoid penetration.", + "bbox": [ + 496, + 606, + 892, + 667 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Main Results", + "text_level": 1, + "bbox": [ + 500, + 676, + 638, + 691 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Baselines. Optimization: SMPLify-X [19] uses RGB only, PROX [5] extends it with losses of human-scene contact and penetration, POSA [2] and PLACE [38] extend PROX with scene-aware pose priors, and METRO $[12]^{\\dagger} + \\mathrm{SA}$ -Opt stands for post-processing a finetuned METRO with scene-aware optimization, which will be explained later. Learning-based: METRO predicts canonical human mesh vertices and a weak-perspective camera. We solve the transformation from human to camera coordinate by minimizing joint re-projection error with a PnP solver [39]. The $\\mathrm{METRO}^{\\dagger}$ is finetuned with the same training protocol as SA-HMR.", + "bbox": [ + 496, + 703, + 892, + 869 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Since METRO does not consider scenes, we additionally optimize the global pose and scale by minimizing", + "bbox": [ + 498, + 869, + 892, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "17043", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/db44f28439336681346481cfdef3fc59823a63f43e380e048220b1416a46bf0c.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
DatasetInitial RtErrRefined RtErrFinal RtErr
RICH510.8284.7246.5
PROX364.2132.3111.8
", + "bbox": [ + 130, + 88, + 416, + 140 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "scene-aware losses, including re-projection error, human-scene penetration, contact distance [6], and ordinal depth error [29], following the key ideas of PROX and PHOSA [29], which is denoted as $\\mathrm{METRO}^{\\dagger} + \\mathrm{SA}$ -Opt.", + "bbox": [ + 75, + 205, + 468, + 267 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results. For the RICH dataset, Tab. 1 shows that SA-HMR notably outperforms other baselines in terms of the G-MPJPE and G-MPVE by a significant margin, demonstrating the effectiveness of the proposed pipeline. The joint learning on both image and scene geometry also improves the metrics of local pose and human-scene contact. We use open-sourced code for SMPLify-X and PROX, and implement POSA and PLACE upon PROX. Optimization methods approximately cost 18s for a single fitting, which is much slower compared to 0.2s of SA-HMR. We provide qualitative results comparing to baselines in Fig. 6.", + "bbox": [ + 75, + 271, + 468, + 436 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "For the PROX dataset, SA-HMR outperforms all baselines in terms of global accuracy as illustrated in Tab. 2. Since the pseudo ground truth of the training set is still not of high quality, as well as a domain gap exists in the test set where the subject wears a MoCap suit, our method falls a little behind in local accuracy and scene penetration. And we do not report ConFE, since the ground truth contact label is not available. Nevertheless, the clear improvement compared to the most relevant model $\\mathrm{METRO}^{\\dagger}$ has demonstrated the effectiveness of the proposed method.", + "bbox": [ + 75, + 438, + 468, + 588 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We also observe that while considering the scene geometry is critical for estimating the global position and improving physical plausibility, it may not fully resolve the ambiguity of the local pose, where multiple physically plausible solutions may still exist. For example, the RGB-only method SMPLify-X and the scene-aware method PROX perform similarly in MPJPE and MPVE.", + "bbox": [ + 75, + 589, + 468, + 694 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 705, + 228, + 722 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Root and Contact Module. Tab. 3 shows that the predicted human root position is improved progressively by the refinement and scene-aware HMR modules, where the initial prediction [33] is improved $44\\% / 52\\%$ in RICH, and $64\\% / 69\\%$ in PROX. The offset representation helps to improve erroneous initial root prediction that is not consistent with the scene surface. For scene contact estimation, the precision / recall is $0.57 / 0.53$ on RICH, and $0.45 / 0.24$ on PROX. We observe that the contacts are difficult to predict, which aligns with the conclusion of a recent work HULC [3]. More visualizations are presented in Fig. 7.", + "bbox": [ + 75, + 734, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/653186934dc684e3b6b64766e20d4fe1420e4ca07a30745da6c2a4385bae5d17.jpg", + "table_caption": [ + "Table 3. Ablation study of root estimation. The human root position errors (RtErr) in mm are reported." + ], + "table_footnote": [], + "table_body": "
MethodG-MPJPEG-MPVEMPJPEMPVECErr↓
w/o parallel304.8312.998.5108.910.2
Ours264.6272.793.9103.08.9
", + "bbox": [ + 501, + 88, + 888, + 138 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/d6720a6825d2ebba357df454eeb9cf52b513635aa06c3ccfc21c9ec72017073e.jpg", + "table_caption": [ + "Table 4. Ablation study of the parallel network on the RICH dataset. The compared variant fuses features of contact points at the early stage." + ], + "table_footnote": [], + "table_body": "
RootContactMPJPEMPVECErr↓
//98.8107.910.5
Est.Est.93.9103.08.9
GTEst.89.298.17.9
Est.GT90.499.28.3
GTGT76.784.65.2
", + "bbox": [ + 571, + 204, + 821, + 291 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 5. Ablation study of the scene-aware mesh recovery module. We validate the upper bound of the proposed method on the RICH dataset.", + "bbox": [ + 498, + 301, + 890, + 342 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Mesh Recovery Module. As shown in Tab. 4, the parallel network that uses cross-attention outperforms a variant that fuses the pointnet features of the contact points to the METRO network in the early stage. The CErr indicates the error of contact mesh vertices in the translation-aligned coordinates. In Tab. 5, we validate the upper bound of the mesh recovery module. We replace the intermediate estimation of root and contact, and find a steady improvement in the pose and shape accuracy.", + "bbox": [ + 496, + 368, + 890, + 505 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Running Time. SA-HMR runs at 170 ms with a peak memory cost of 1852 MB for a $224 \\times 224$ image and a scene point cloud of 2 cm resolution on a V100 GPU. Specifically, the root and contact module takes 92 ms (CNN 50 ms, SPVCNN 42 ms), the mesh recovery module takes 75 ms (CNN 49 ms, Transformer 26 ms), and the intermediate processing takes 3 ms.", + "bbox": [ + 496, + 508, + 890, + 614 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 628, + 617, + 643 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "This work addresses the challenge of estimating the human mesh from an RGB image with the consideration of the scene geometry. Our key idea is to inject 3D scene cues into a monocular human mesh recovery network to recover the absolute human pose and shape in the scene. To this end, our approach first predicts the 3D human location and dense human-scene contacts with a sparse 3D CNN. We then develop a transformer to extract features from contact scene points and feed them into the pose estimation network using cross-attention. Experiments demonstrate that our approach achieves state-of-the-art performance on the RICH and PROX datasets.", + "bbox": [ + 496, + 652, + 890, + 834 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Acknowledgement. This work was supported by the Key Research Project of Zhejiang Lab (No. K2022PG1BB01), NSFC (No. 62172364), and Information Technology Center and State Key Lab of CAD&CG, Zhejiang University.", + "bbox": [ + 496, + 839, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "17044", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2d1fa03337d55309cd2aaae9b2bc6d054b3b66eb6f519940c98c34c1f26e6a21.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 93, + 87, + 220, + 186 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/5ad35535b77f781d28f6a9386efcf6ee88559c726e16e5f1dc0c1be6cde2a7a7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 225, + 88, + 352, + 186 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/97323ca0895074e21e3ac1b4c3d4b5fdc1e8f21656655b36e6fc38727bc1e1e5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ 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"image_caption": [ + "Image" + ], + "image_footnote": [], + "bbox": [ + 94, + 497, + 220, + 595 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/037da32f8f7c2c091bc3279fc59d04f8c5bfac3c20cd3d1f3548475194514e24.jpg", + "image_caption": [ + "PROX" + ], + "image_footnote": [], + "bbox": [ + 225, + 497, + 352, + 595 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/10d50eb2c62c3a91bd63bf30e36c832a25e92731a489132f58cc551cd178c0c7.jpg", + "image_caption": [ + "METRO" + ], + "image_footnote": [], + "bbox": [ + 357, + 497, + 483, + 595 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/05d21c6883002efc84c2ed9ff8668431979fdce01f8c4717e98a579fc7af296b.jpg", + "image_caption": [ + "METRO† + SA-Opt" + ], + "image_footnote": [], + "bbox": [ + 486, + 497, + 614, + 595 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/13878a5eddeb1f6eff18cd029cab93f0dd5431acd4f6ff25bbe9e8889dc7def1.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 617, + 497, + 745, + 595 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/2c305b503d2e504dab1f693bfcf7adfe48d042223234f930d439629e10c2eeff.jpg", + "image_caption": [ + "GroundTruth" + ], + "image_footnote": [], + "bbox": [ + 750, + 497, + 875, + 595 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/5571b3957704ef1625dfc3406a9ad65ab0b095f5e863220deba4b25cc58c62fa.jpg", + "image_caption": [ + "Figure 6. Qualitative results on the RICH [6] dataset. We compare the proposed method to PROX [5], finetuned METRO [12], finetuned METRO with scene-aware optimization, and ground truth. The leftmost column shows the input images. The proposed method recovers the global positions and human-scene contact more accurately because of the 3D learning on human root refinement and dense scene contact labeling tasks.", + "Root & Contact", + "Figure 7. Qualitative visualization of the estimated root locations and dense scene contacts. In both examples, the estimated contact points provide accurate position and scene structure for the following step of mesh recovery. The reconstructed human mesh is in good contact with the corresponding scene regions." + ], + "image_footnote": [], + "bbox": [ + 94, + 702, + 220, + 800 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8372d6878066b2829c2d9bf4235093ab6983f43c5fb888895324fdb691a7e71a.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 225, + 702, + 352, + 800 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/5d9f46cc9baa01aaf59215d1b71b148c07f91366feecb691eb80f50c26038b8f.jpg", + "image_caption": [ + "GroundTruth" + ], + "image_footnote": [], + "bbox": [ + 357, + 702, + 483, + 800 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/01fbd4a33c10fad547ac8704043c45b553f945021618d4f2aace0ba17db43d10.jpg", + "image_caption": [ + "Root & Contact" + ], + "image_footnote": [], + "bbox": [ + 486, + 702, + 614, + 800 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f63e5d8142b08010df889569cea4aa0ea07311c01d2033caf12963ebb2bc25d1.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 617, + 702, + 745, + 800 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/06a399853a426b34da89706616de3d217df436668717c9b807085a0b144c3b52.jpg", + "image_caption": [ + "GroundTruth" + ], + "image_footnote": [], + "bbox": [ + 750, + 702, + 875, + 800 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "17045", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Siwei Zhang, Yan Zhang, Federica Bogo, Marc Pollefeys, and Siyu Tang. 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Dr. Dobb's Journal of Software Tools, 2000. 6" + ], + "bbox": [ + 78, + 90, + 468, + 518 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "17047", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Learning Human Mesh Recovery in 3D Scenes/76a14e05-6adf-4600-8709-b0e5b9fb7b40_model.json b/2023/Learning Human Mesh Recovery in 3D Scenes/76a14e05-6adf-4600-8709-b0e5b9fb7b40_model.json new file mode 100644 index 0000000000000000000000000000000000000000..6c6ce46d0340fa0ebb22758c871b2a39ad842d58 --- /dev/null +++ b/2023/Learning Human Mesh Recovery in 3D Scenes/76a14e05-6adf-4600-8709-b0e5b9fb7b40_model.json @@ -0,0 +1,2596 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.25, + 0.131, + 0.723, + 0.154 + ], + "angle": 0, + "content": "Learning Human Mesh Recovery in 3D Scenes" + }, + { + "type": "text", + "bbox": [ + 0.152, + 0.181, + 0.817, + 0.224 + ], + "angle": 0, + "content": "Zehong Shen Zhi Cen Sida Peng Qing Shuai Hujun Bao Xiaowei Zhou† \nState Key Lab of CAD&CG, Zhejiang University" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.257, + 0.314, + 0.273 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.289, + 0.474, + 0.562 + ], + "angle": 0, + "content": "We present a novel method for recovering the absolute pose and shape of a human in a pre-scanned scene given a single image. Unlike previous methods that perform scene-aware mesh optimization, we propose to first estimate absolute position and dense scene contacts with a sparse 3D CNN, and later enhance a pretrained human mesh recovery network by cross-attention with the derived 3D scene cues. Joint learning on images and scene geometry enables our method to reduce the ambiguity caused by depth and occlusion, resulting in more reasonable global postures and contacts. Encoding scene-aware cues in the network also allows the proposed method to be optimization-free, and opens up the opportunity for real-time applications. The experiments show that the proposed network is capable of recovering accurate and physically-plausible meshes by a single forward pass and outperforms state-of-the-art methods in terms of both accuracy and speed. Code is available on our project page: https://zju3dv.github.io/sahmr/." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.623, + 0.21, + 0.639 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.648, + 0.47, + 0.829 + ], + "angle": 0, + "content": "Monocular human mesh recovery (HMR), i.e., estimating pose and shape parameters of a parametric human model from a single image, has gained significant attention in recent years. To better capture and understand human behaviors, many recent works [1-5] propose to address the problem of scene-aware HMR which involves human-scene interaction constraints when recovering human meshes, given the 3D geometry of the scene scanned by range sensors [5-7], as well as the camera pose of the input image relative to the scene, which may enable more applications in video surveillance, household robots, and motion analysis in gyms and clinics." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.83, + 0.47, + 0.877 + ], + "angle": 0, + "content": "Most existing methods propose using scene-aware optimization to fit the human mesh into a pre-scanned scene. They optimize a parametric human model iteratively, e.g.," + }, + { + "type": "image", + "bbox": [ + 0.522, + 0.256, + 0.697, + 0.391 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.698, + 0.256, + 0.872, + 0.391 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.522, + 0.393, + 0.697, + 0.527 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.591, + 0.534, + 0.625, + 0.546 + ], + "angle": 0, + "content": "Input" + }, + { + "type": "image", + "bbox": [ + 0.698, + 0.393, + 0.872, + 0.527 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.753, + 0.534, + 0.815, + 0.545 + ], + "angle": 0, + "content": "Prediction" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.56, + 0.895, + 0.673 + ], + "angle": 0, + "content": "Figure 1. Comparison between the optimization-based method and the proposed method. Optimization-based methods typically fit a parametric human model iteratively by minimizing 2D reprojection error and scene conflicts. In contrast, the proposed method utilizes a single forward pass of the network to estimate the global position (blue ball), contact scene points (colored scene points), and a scene-aware human mesh. This design leads to improvements in both efficiency and accuracy." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.702, + 0.894, + 0.824 + ], + "angle": 0, + "content": "SMPL [8], to minimize scene penetration, chamfer distance of contact regions, and the 3D-2D re-projection error. However, optimization tends to be slow at inference time and is sensitive to initialization and hyperparameters, failing to respond in low-latency applications. As illustrated in Fig. 1, an optimization-based method PROX [5] takes 18.4s to fit a human model into the scene, while the incorrect position and pose still occur." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.825, + 0.894, + 0.903 + ], + "angle": 0, + "content": "Recent works [9-13] propose to recover human mesh with neural networks trained on large-scale datasets [14-17]. Specifically, the networks learn a mapping from an input image to a human mesh in the canonical coordinates. Applying these methods in the scene-aware HMR" + }, + { + "type": "page_footnote", + "bbox": [ + 0.103, + 0.887, + 0.23, + 0.901 + ], + "angle": 0, + "content": "†Corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "17038" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.227 + ], + "angle": 0, + "content": "task still requires post-processing optimization, where the global translation and the human poses are refined in accordance with the given scene. However, the monocular prediction is conditioned on the input image solely, omitting the joint distribution of human pose and scene geometry, and therefore tends to suffer from depth ambiguity and occlusion. As a result, the optimization-based post-processing could be easily deteriorated by the erroneous initial poses and may even worsen the initial prediction." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.228, + 0.473, + 0.529 + ], + "angle": 0, + "content": "In this work, we propose a Scene-Aware Human Mesh Recovery network (SA-HMR), the first learning-based approach that predicts the absolute position and mesh of a human in the scene by a single forward pass. The overall pipeline is illustrated in Fig. 2. Given the input image and scene point cloud, we first use a sparse 3D CNN to estimate dense scene contacts and absolute human position, where the scene contact estimation is treated as a point cloud labeling task, and the human position prediction is presented as a voting vector field refinement task. The predicted dense contact points are centered by the human position and passed to a scene network in the human mesh recovery step. Specifically, we enhance a pretrained monocular HMR network METRO [12] by cross-attention with the proposed scene network in parallel. In this way, SA-HMR learns a joint distribution of human pose and scene geometry, resulting in more reasonable postures, contacts, and global positions, as illustrated in Fig. 1. Learning scene-aware cues in the network also avoids scene-aware optimization as post-processing and achieves fast inference speed." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.53, + 0.473, + 0.62 + ], + "angle": 0, + "content": "We evaluate the proposed method on the RICH [6] and PROX [5] datasets of indoor and outdoor scenes. The experimental results show that SA-HMR is not only effective in recovering absolute positions and meshes that are in accordance with the given scene, but also significantly faster than the optimization-based baselines." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.621, + 0.431, + 0.635 + ], + "angle": 0, + "content": "In summary, we make the following contributions:" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.644, + 0.469, + 0.688 + ], + "angle": 0, + "content": "- The first optimization-free framework for scene-aware human mesh recovery from a single image and a prescanned scene." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.698, + 0.469, + 0.743 + ], + "angle": 0, + "content": "- The cross-attention design for enhancing a pretrained HMR network with a parallel scene network, enabling joint learning on the human pose and scene geometry." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.752, + 0.469, + 0.782 + ], + "angle": 0, + "content": "- Superior performance compared to optimization-based baselines in terms of both accuracy and speed." + }, + { + "type": "list", + "bbox": [ + 0.097, + 0.644, + 0.469, + 0.782 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.795, + 0.22, + 0.811 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Monocular Human Mesh Recovery. Most existing approaches formulate the monocular HMR task as recovering the mesh of statistical human body models, e.g. SMPL and SMPL-X [8, 18, 19], where recent works can be divided into optimization-based and learning-based approaches." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.257 + ], + "angle": 0, + "content": "The optimization-based approaches fit a parametric human model by minimizing the 3D-2D re-projection error of body joints and energy terms of heuristic priors iteratively, which are represented by SMPLify [20] that fits SMPL [8]. More recently, SMPLify-X [19] proposes a variational pose prior and fits a more expressive SMPL-X. PoseNDF [21] proposes to represent the manifold of plausible human poses with a neural field. While optimization-based methods are general in their mathematical formulation, they are usually sensitive to hyperparameters and require much time for inference." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.261, + 0.892, + 0.487 + ], + "angle": 0, + "content": "The learning-based methods utilize deep neural networks to predict either the parameters [9, 10, 22, 23] or the mesh vertices [11-13] of the SMPL model. HMR [9] is the pioneering work in predicting SMPL parameters, and SPIN [10] improves upon it using an optimization loop. For predicting SMPL mesh vertices, GraphCMR [11] deforms a template human mesh using graph neural network, while METRO [12] uses transformers, and [13] uses graph hierarchy to further improve the performance. However, for scene-aware HMR, the vertices of the human and scene meshes in contact are close in Euclidean space, making methods that regress parameters unsuitable due to errors that accumulate along the kinematic chains. Therefore, the proposed method is built on the works that predict mesh vertices. More details can be found in Sec. 3." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.496, + 0.892, + 0.709 + ], + "angle": 0, + "content": "Scene-aware Human Mesh Recovery. PROX [5] is a seminal work that uses scene constraints to reduce the depth and occlusion ambiguity in monocular HMR. It achieves this by adding two energy terms of human-scene contact and penetration in the optimization process [19]. In addition, scene-aware pose generative models [2, 24] can also be used as prior terms in the scene-aware HMR task. Other recent works in this area include MoCapDeform [4], which considers deformable scene objects, LEMO [1], which uses temporal information, and HULC [3], which uses consecutive frames and dense contacts prediction on both the scene and human body. In contrast to these works, the proposed method is optimization-free and requires only a single forward pass." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.711, + 0.892, + 0.802 + ], + "angle": 0, + "content": "In a broader topic of capturing humans in a scene-aware manner, [25-27] propose using a simulator and dynamic model, where a pre-defined agent is controlled to interact with the scene, and [28,29] consider human-object arrangement by first predicting the human and object and then performing global optimization." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Attention in Transformers. Attention is a key mechanism in Transformers [30]. It allows a set of query features to fuse the most relevant information from another set of key-value features. When query and key-value features come from the same source, it is called self-attention, otherwise cross-attention. In HMR, METRO [12] uses self-attention to re" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "17039" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.135, + 0.1, + 0.419, + 0.115 + ], + "angle": 0, + "content": "1. Human Root and Scene Contacts" + }, + { + "type": "image", + "bbox": [ + 0.101, + 0.127, + 0.455, + 0.263 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.505, + 0.1, + 0.82, + 0.117 + ], + "angle": 0, + "content": "2. Scene-aware Human Mesh Recovery" + }, + { + "type": "image", + "bbox": [ + 0.458, + 0.12, + 0.868, + 0.263 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.276, + 0.894, + 0.348 + ], + "angle": 0, + "content": "Figure 2. Overview of the proposed SA-HMR. 1. The human root and scene contact estimation module (Sec. 3.2) that first predicts the initial root and then refines the root with 3D scene cues using a sparse 3D CNN. The module also predicts contact labels [5] for each scene point. Please refer to Sec. 3.2 for a detailed definition of the 3D feature construction module. 2. The scene-aware human mesh recovery module (Sec. 3.3) that enhances the pretrained METRO [12] network with a parallel scene network. The scene network takes the predicted contact scene points as input, and uses cross-attention to pass messages to the intermediate features of the METRO network." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.373, + 0.469, + 0.463 + ], + "angle": 0, + "content": "duce occlusion ambiguity by establishing non-local feature exchange between visible and invisible parts of a template human mesh. In feature matching, SuperGlue [31] uses cross-attention to make the corresponding image features more similar. Predator [32] uses cross-attention in matching two sets of point clouds." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.464, + 0.47, + 0.526 + ], + "angle": 0, + "content": "Inspired by feature matching, the proposed method uses cross-attention to potentially make the features of the human and scene that are in contact more similar, resulting in better contact and more reasonable postures." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.541, + 0.176, + 0.557 + ], + "angle": 0, + "content": "3. Methods" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.567, + 0.47, + 0.658 + ], + "angle": 0, + "content": "Given a calibrated image and a pre-scanned scene point cloud (Sec. 3.1), SA-HMR first estimates the absolute human root position and scene contacts (Sec. 3.2), and then recovers the human mesh with the contact points by enhancing a pretrained METRO network (Sec. 3.3). An overview of the proposed method is presented in Fig. 2." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.67, + 0.218, + 0.685 + ], + "angle": 0, + "content": "3.1. Preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.699, + 0.469, + 0.82 + ], + "angle": 0, + "content": "Human Representation. We use SMPL [8] as the human representation. The SMPL is a parametric model that uses the body joint rotations, root translation, and body shape coefficients to compute the body mesh. Following [11, 12], we directly predict the SMPL mesh vertices \\( V = \\mathbb{R}^{6890 \\times 3} \\), and use H36M [14] joint regression matrix \\( M \\in \\mathbb{R}^{14 \\times 6890} \\) to compute 3D joints \\( J \\in \\mathbb{R}^{14 \\times 3} \\) from the vertices for quantitative evaluation, \\( J = MV \\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.826, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Scene and Image Representation. We assume that the scene is pre-scanned with range sensors, as in RICH [6] and PROX [5], and the image is calibrated and localized in the scene, i.e. with known intrinsic and extrinsic parameters \\(\\{(f,c_x,c_y),(R_c,t_c)\\}\\). Following METRO [12], we detect" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.373, + 0.892, + 0.449 + ], + "angle": 0, + "content": "a squared bounding box around the target human and resize the cropped region as the input image \\(I \\in \\mathbb{R}^{224 \\times 224 \\times 3}\\). Based on the camera parameters and the bounding box, we select scene points that fall within the visual frustum as the input scene point cloud \\(S \\in \\mathbb{R}^{N_S \\times 3}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.453, + 0.893, + 0.545 + ], + "angle": 0, + "content": "Human-Scene Contact. Following PROX [5], we use seven regions of the SMPL mesh that are most likely to be contacted. The details are provided in the supplementary material. Using these seven categories and one for not being in contact, we perform a segmentation task on the scene point cloud." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.552, + 0.792, + 0.567 + ], + "angle": 0, + "content": "3.2. Human Root and Scene Contacts" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.575, + 0.892, + 0.743 + ], + "angle": 0, + "content": "Given an image \\(I\\) bounding the human, we propose using a 2D convolutional neural network (CNN) to extract image features \\(F\\) and predict the initial human root \\(r\\). Based on the scene points \\(S\\), we unproject the image features \\(F\\) to 3D, resulting in \\(\\hat{F}\\). Additionally, we calculate point-wise offset vectors \\(O\\) that point from a voxelized scene point cloud to the initial root. By taking \\(\\hat{F}\\) and \\(O\\) as input, a sparse 3D CNN predicts the segmentation of scene contacts and the refined offsets, which are then converted to the refined human root \\(r^{*}\\). An overview of this process is presented in the left column of Fig. 2." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.746, + 0.893, + 0.868 + ], + "angle": 0, + "content": "Initial Root. We predict the initial root \\( r = (X, Y, Z) \\) in a 2.5D manner following SMAP [33]. Specifically, we use a CNN to predict the 2D heatmap and a normalized depth map of the root. Then, the 2D position \\( (x, y) \\) is obtained by applying argmax to the heatmap, and the corresponding normalized depth value \\( \\tilde{Z} \\) is retrieved from the depth map. Finally, using the intrinsic parameters \\( f, c_x, c_y \\) and image size \\( w \\), the 3D root position is computed:" + }, + { + "type": "equation", + "bbox": [ + 0.662, + 0.876, + 0.892, + 0.906 + ], + "angle": 0, + "content": "\\[\nZ = \\tilde {Z} \\frac {f}{w} \\tag {1}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "17040" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.118, + 0.089, + 0.43, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.234, + 0.471, + 0.292 + ], + "angle": 0, + "content": "Figure 3. 3D feature construction. We voxelize a scene point cloud to a sparse volume. The initial feature of each voxel consists of two parts, which are the offset vector pointing from the voxel center to the human root and the unprojected image features." + }, + { + "type": "equation", + "bbox": [ + 0.152, + 0.311, + 0.47, + 0.342 + ], + "angle": 0, + "content": "\\[\nX = \\frac {x - c _ {x}}{f} \\cdot Z, \\quad Y = \\frac {y - c _ {y}}{f} \\cdot Z \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.345, + 0.47, + 0.406 + ], + "angle": 0, + "content": "From our observation, estimating \\((x,y)\\) achieves good results with a mean squared error of fewer than two pixels across datasets. However, estimating \\(\\tilde{Z}\\) is relatively challenging, possibly due to the variations in human shapes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.41, + 0.469, + 0.455 + ], + "angle": 0, + "content": "3D Feature Construction. Based on the initial root \\( r \\) and image features \\( F \\), we construct the 3D features on the voxelized scene point cloud, which is illustrated in Fig. 3." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.456, + 0.469, + 0.56 + ], + "angle": 0, + "content": "First, we select regions of interest around the initial root \\( r \\) in the point cloud. Specifically, we treat \\( r \\) as an anchor and keep points within a radius \\( \\gamma_1 \\). Since \\( Z \\) has more uncertainty than \\( (x,y) \\), we sample two additional anchors along the z-axis, whose distance to \\( r \\) is \\( \\gamma_2 \\). Next, we construct a sparse volume \\( \\bar{S} \\) by voxelizing these points with voxel size \\( s_{vox} \\), where the center of each voxel is denoted as \\( \\bar{s}_i \\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.562, + 0.47, + 0.607 + ], + "angle": 0, + "content": "For each voxel \\(i\\), the feature consists of the offset vector \\(o_i\\) and the unprojected image feature \\(\\hat{f}_i\\). Specifically, \\(o_i\\) is a vector pointing from the voxel center to the human root:" + }, + { + "type": "equation", + "bbox": [ + 0.232, + 0.617, + 0.469, + 0.631 + ], + "angle": 0, + "content": "\\[\no _ {i} = r - \\bar {s} _ {i} \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.639, + 0.469, + 0.685 + ], + "angle": 0, + "content": "\\(\\hat{f}\\) is computed by projecting voxel center \\(\\bar{s}_i\\) onto the image using camera parameters and bilinearly sampling the image feature map \\(F\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.69, + 0.469, + 0.795 + ], + "angle": 0, + "content": "Estimating Refined Root and Scene Contacts. We use sparse 3D CNN [34] to process the constructed 3D features and learn to improve the root estimation and predict the scene contacts. Specifically, the output of each voxel includes an updated offset vector \\( o_i^* \\), confidence \\( c_i \\), and segmentation indicating the contact category. We compute the refined root \\( r^* \\):" + }, + { + "type": "equation", + "bbox": [ + 0.193, + 0.802, + 0.469, + 0.833 + ], + "angle": 0, + "content": "\\[\nr ^ {*} = \\sum_ {i} c _ {i} \\cdot \\left(o _ {i} ^ {*} + \\bar {s} _ {i}\\right). \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.47, + 0.902 + ], + "angle": 0, + "content": "There are 8 categories of contact points, including 7 most probable regions on the body that would be contacted [5] and 1 category of not being in contact. We take the category of the highest score as the prediction for the voxel and" + }, + { + "type": "image", + "bbox": [ + 0.511, + 0.088, + 0.868, + 0.363 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.373, + 0.892, + 0.457 + ], + "angle": 0, + "content": "Figure 4. Enhancing METRO with a parallel network. The orange parts are the original METRO [12] network, where the residual connection and positional encoding are omitted for simplicity. The blue parts are the proposed parallel network which takes predicted contact scene points as input. The yellow parts indicate feature interaction between METRO and the parallel network." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.486, + 0.892, + 0.534 + ], + "angle": 0, + "content": "set the dense point cloud belonging to the voxel with that category. The contact points \\(\\hat{S}_{seg3d} \\in \\mathbb{R}^{\\hat{N}_S \\times 3}\\) serve as the input for the mesh recovery module." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.546, + 0.818, + 0.563 + ], + "angle": 0, + "content": "3.3. Scene-aware Human Mesh Recovery" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.57, + 0.892, + 0.707 + ], + "angle": 0, + "content": "Since the training data of scene-aware human mesh recovery is limited, we build our model upon a network named METRO [12] that is pre-trained on large-scale data of monocular human mesh recovery. METRO processes feature based on the self-attention mechanism, and our approach enhances METRO by adding a parallel scene network, which provides a cross-attention-based mechanism that enables METRO to notice important scene details and achieve scene-aware human mesh recovery." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.712, + 0.892, + 0.803 + ], + "angle": 0, + "content": "METRO consists of a CNN backbone and multiple Transformer encoders. It first extracts global CNN features, then combines the feature to the vertices of a zero posed SMPL mesh, and finally predicts a posed mesh with shape through the transformers. The part of the transformer is illustrated in the orange part of Fig. 4." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.809, + 0.892, + 0.87 + ], + "angle": 0, + "content": "Enhancing METRO with Cross-Attention. We improve METRO with a scene network, which makes the predicted human vertices to be close to the corresponding contact scene points \\(\\hat{S}_{seg3d}\\) (Sec. 3.2)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.9 + ], + "angle": 0, + "content": "As illustrated in Fig. 4, we add a parallel network, which has a similar architecture as the transformer of METRO," + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "17041" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.1, + 0.089, + 0.209, + 0.257 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.148, + 0.258, + 0.16, + 0.267 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.212, + 0.089, + 0.321, + 0.256 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.26, + 0.258, + 0.274, + 0.267 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image", + "bbox": [ + 0.325, + 0.089, + 0.448, + 0.257 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.373, + 0.258, + 0.385, + 0.267 + ], + "angle": 0, + "content": "(c)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.28, + 0.473, + 0.406 + ], + "angle": 0, + "content": "Figure 5. Visualization of the cross-attention from a body vertex (blue point) to the predicted dense scene contacts (white points). (a) The image and the predicted dense scene contacts. (b) The hand vertex is in contact with the scene according to the image, and its feature is similar to the nearby scene point features, enabling the final vertex prediction to be close to the corresponding scene surface. (c) The arm vertex is not in contact with the scene, where feature similarities tend to be evenly distributed. The feature similarities are normalized to the same range of \\(0 \\rightarrow 1\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.433, + 0.47, + 0.689 + ], + "angle": 0, + "content": "to extract features of scene contact points and output the point positions like an autoencoder. Specifically, we first use METRO's CNN backbone to extract the image feature and map it to a set of vertex tokens by a fully-connected layer. In METRO, these tokens are directly concatenated with the positions of initial human vertices. However, the number of scene contact points is not the same as the tokens', and there is no one-to-one correspondence between them. To resolve this issue, we perform the average pooling to vertex tokens based on the contact categories defined on the SMPL mesh vertices [5], resulting in 7 tokens. Then, we append each scene contact point with the corresponding aggregated token based on the predicted category in Sec. 3.2. Intuitively, this helps the cross-attention to focus on the semantically corresponding parts. To be invariant to the global translation, the scene contact points are zero-centered by the predicted root \\( r^* \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.47, + 0.87 + ], + "angle": 0, + "content": "Motivated by recent feature matching methods [31, 32], we propose to use cross-attention to pass features from scene contact points to human vertices. The cross-attention and self-attention share the same underlying mechanism, both of which first compute the similarity of query and key, and then use the weighted sum to fuse features. When the query and key are from the same source features, it is self-attention, and otherwise is cross-attention. In practice, we use linear attention operator [35] to improve efficiency. A visualization of cross attention over human vertices and scene points is in Fig. 5. The detailed network architecture is provided in the supplementary material." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Note that, we use a weight-sharing regressor layer with METRO, which regresses from point-wise features to point" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.183 + ], + "angle": 0, + "content": "position \\((x,y,z)\\). Therefore, to get a similar \\((x,y,z)\\), the input features of this layer should also be similar. This strategy implicitly aligns the features of human vertices and scene points when their final predictions are near in 3D space, thus facilitating the cross-attention to find correspondences between human vertices and scene points." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.192, + 0.644, + 0.208 + ], + "angle": 0, + "content": "3.4. Training Loss" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.22, + 0.892, + 0.25 + ], + "angle": 0, + "content": "Root and Contact. The loss function \\( L_{\\mathrm{RC}} \\) for the root and contact estimation is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.526, + 0.262, + 0.892, + 0.278 + ], + "angle": 0, + "content": "\\[\nL _ {\\mathrm {R C}} = L _ {\\mathrm {R 2 D}} + w _ {\\mathrm {R Z}} \\cdot L _ {\\mathrm {R Z}} + L _ {\\mathrm {R O V}} + L _ {\\mathrm {R 3 D}} + L _ {\\mathrm {C}} \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.29, + 0.892, + 0.38 + ], + "angle": 0, + "content": "where \\( L_{\\mathrm{R2D}} \\) is the MSE loss on the root heatmap; \\( L_{\\mathrm{RZ}} \\), \\( L_{\\mathrm{ROV}} \\), and \\( L_{\\mathrm{R3D}} \\) are the L1 losses on the relative depth, offset vectors, and the 3D root, respectively; \\( L_{\\mathrm{C}} \\) is the cross-entropy loss for contact categories of voxel points, where we additionally train an auxiliary task of 2D contact segmentation similar to the voxel points." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.385, + 0.892, + 0.415 + ], + "angle": 0, + "content": "Human Mesh Recovery. The loss function \\( L_{\\mathrm{HMR}} \\) for the mesh recovery is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.588, + 0.428, + 0.892, + 0.443 + ], + "angle": 0, + "content": "\\[\nL _ {\\mathrm {H M R}} = L _ {\\mathrm {V}} + L _ {\\mathrm {J}} + L _ {\\mathrm {C P}} + L _ {\\mathrm {G V}} \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.455, + 0.892, + 0.515 + ], + "angle": 0, + "content": "where \\( L_{\\mathrm{V}} \\), \\( L_{\\mathrm{J}} \\), \\( L_{\\mathrm{CP}} \\), and \\( L_{\\mathrm{GV}} \\) are the L1 losses on the translation-aligned human vertices, human joints, reconstructed contact points, and global human vertices, respectively. More details are in the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.524, + 0.719, + 0.54 + ], + "angle": 0, + "content": "3.5. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.548, + 0.892, + 0.744 + ], + "angle": 0, + "content": "We train two modules separately. For the root and contact module, the CNN is HRNet-stride-4 [36] with METRO initialization, the sparse 3D CNN is SPVCNN [34, 37] with random initialization. We use linear layers to align intermediate feature dimensions. \\(\\gamma_{1}\\) is \\(1.25\\mathrm{m}\\), \\(\\gamma_{2}\\) is \\(0.5\\mathrm{m}\\), \\(s_{vox}\\) is \\(5^{3}cm^{3}\\), and \\(w_{\\mathrm{RZ}}\\) is 10. The contact threshold is \\(7\\mathrm{cm}\\). We flip images for augmentation. The module is trained with an initial learning rate of \\(3.75\\mathrm{e - 5}\\) and a batch size of 24. It converges after 30 epochs of training on one V100 GPU. For the mesh recovery module, the METRO network is initialized as pretrained and the scene network is randomly initialized. The initial learning rate is \\(7.5\\mathrm{e - 6}\\) and the batch size is 24. It converges after 30 epochs of training." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.757, + 0.634, + 0.774 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.782, + 0.602, + 0.797 + ], + "angle": 0, + "content": "4.1. Datasets" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.805, + 0.892, + 0.836 + ], + "angle": 0, + "content": "We train and evaluate the proposed method on RICH [6] and PROX [5] datasets separately." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "RICH [6] captures multi-view video sequences in 6 outdoor and 2 indoor scenes. It provides images, reconstructed bodies, scene scans, and human-scene contact labels annotated on SMPL vertices. We skip frames including multiple" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "17042" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.1, + 0.089, + 0.872, + 0.23 + ], + "angle": 0, + "content": "
MethodLearning-basedOptimizationScene-awareG-MPJE↓G-MPV\\( \\downarrow \\)PenE↓ConFE↓MPJPE↓MPVE↓
Dataset GT [6]✓✓//9.810.8//
SMPLify-X [19]✓482.0483.735.743.4166.9177.6
PROX [5]✓✓390.1397.215.524.1164.1175.8
POSA [2]✓✓427.8434.021.127.0177.2188.4
PLACE [38]✓✓395.9403.016.124.8163.8175.4
METRO \\( [12]^† + SA-Opt \\) [6, 29]✓✓✓563.1561.37.414.8102.7112.8
METRO [12]✓678.6679.452.256.9129.6134.5
METRO \\( [12]^† \\)✓511.7509.733.637.698.8107.9
SA-HMR✓✓264.6272.714.919.093.9103.0
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.239, + 0.895, + 0.285 + ], + "angle": 0, + "content": "Table 1. Evaluation on the RICH [6] dataset. METRO† indicates that the model is finetuned on the dataset. SA-Opt indicates scene-aware optimization, with contact estimation from BSTRO [6] and loss formulation from PROX [5] and PHOSA [29]. The proposed SA-HMR achieves the overall best results and is significantly faster than the methods that require optimization." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.308, + 0.471, + 0.385 + ], + "angle": 0, + "content": "subjects, remove the first 45 frames of each video to avoid static starting pose, and skip frames where the subjects' 2D bounding boxes are not inside the images. Then we down-sample the train / val / test splits to \\(2/1/1\\) fps, resulting in 15360 / 3823 / 3316 frames." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.39, + 0.471, + 0.542 + ], + "angle": 0, + "content": "PROX [5] captures monocular RGBD videos in 12 indoor scenes. We use RGB images and scene scans. It is a challenging dataset where severe occlusions exist in most frames. We use the qualitative set for training and the quantitative set for testing. In order to get better training annotations, we additionally use HuMoR [26] which utilizes motion prior and optimizes a sequence of frames. Then, we manually remove the failed frames that are not consistent with the images and scenes. Finally, the training split contains 4852 frames." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.555, + 0.173, + 0.57 + ], + "angle": 0, + "content": "4.2. Metrics" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.58, + 0.47, + 0.611 + ], + "angle": 0, + "content": "We evaluate quantitatively in terms of human mesh recovery and human-scene contact." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.616, + 0.47, + 0.708 + ], + "angle": 0, + "content": "Human Mesh Recovery. We report the Global Mean-Per-Joint-Position-Error (G-MPJPE) and Global Mean-Per-Vertex-Error (G-MPVE) in the scene coordinate system, which calculates the average L2 distances between predicted and ground truth joints/vertices. Additionally, we report the translation-aligned metrics MPJPE and MPVE." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.713, + 0.47, + 0.773 + ], + "angle": 0, + "content": "Human-scene Contact. We report the Penetration Error (PenE) and Contact Failure Error (ConFE). PenE measures the total distance that SMPL vertices penetrate the scene mesh:" + }, + { + "type": "equation", + "bbox": [ + 0.127, + 0.785, + 0.47, + 0.829 + ], + "angle": 0, + "content": "\\[\n\\operatorname {P e n E} = \\sum_ {i = 1} ^ {V} \\mathbb {1} _ {x < 0} [ s d f (v _ {i}, \\mathcal {S}) ] \\cdot | s d f (v _ {i}, \\mathcal {S}) |, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.903 + ], + "angle": 0, + "content": "where \\(V\\) is the number of SMPL vertices, \\(sdf(v_{i},\\mathcal{S})\\) is the signed distance from vertex \\(v\\) to scene \\(\\mathcal{S}\\), and \\(\\mathbb{1}_{x < 0}[\\cdot ]\\) is an indicator function that returns 1 when the condition is met, and 0 otherwise. ConFE measures contact quality when the" + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.305, + 0.89, + 0.432 + ], + "angle": 0, + "content": "
MethodG-MPJPE↓G-MPVE↓PenE↓MPJPE↓MPVE↓
Dataset GT [5]//9.6//
SMPLify-X [19]216.0222.649.3100.7112.8
PROX [5]172.0178.510.7101.1114.0
POSA [2]172.3180.916.6108.5119.4
PLACE [38]168.1176.712.3100.8113.7
METRO [12]283.2277.762.4137.0147.2
METRO [12]†265.6262.767.5117.1128.5
SA-HMR150.4160.026.9111.1122.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.442, + 0.893, + 0.471 + ], + "angle": 0, + "content": "Table 2. Evaluation on the PROX [5] dataset. The proposed method achieves the best performance in global metrics." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.496, + 0.756, + 0.512 + ], + "angle": 0, + "content": "ground truth contact label is available:" + }, + { + "type": "equation", + "bbox": [ + 0.504, + 0.52, + 0.891, + 0.597 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\operatorname {C o n F E} = \\sum_ {i = 1} ^ {V} \\left(C _ {g t} \\left(v _ {i}\\right) \\cdot | s d f \\left(v _ {i}, \\mathcal {S}\\right) |\\right. \\\\ + \\left(1 - C _ {g t} \\left(v _ {i}\\right)\\right) \\cdot \\mathbb {1} _ {x < 0} [ s d f \\left(v _ {i}, \\mathcal {S}\\right) ] \\cdot | s d f \\left(v _ {i}, \\mathcal {S}\\right) |), \\tag {8} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.607, + 0.893, + 0.669 + ], + "angle": 0, + "content": "where \\( C_{gt}(v) \\) equals 1 if \\( v \\) is labeled as in contact, and 0 otherwise. In order to obtain a good result of ConFE, the body vertices in contact should be close to the scene surface, while vertices not in contact should avoid penetration." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.677, + 0.64, + 0.692 + ], + "angle": 0, + "content": "4.3. Main Results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.893, + 0.871 + ], + "angle": 0, + "content": "Baselines. Optimization: SMPLify-X [19] uses RGB only, PROX [5] extends it with losses of human-scene contact and penetration, POSA [2] and PLACE [38] extend PROX with scene-aware pose priors, and METRO \\([12]^{\\dagger} + \\mathrm{SA}\\) -Opt stands for post-processing a finetuned METRO with scene-aware optimization, which will be explained later. Learning-based: METRO predicts canonical human mesh vertices and a weak-perspective camera. We solve the transformation from human to camera coordinate by minimizing joint re-projection error with a PnP solver [39]. The \\(\\mathrm{METRO}^{\\dagger}\\) is finetuned with the same training protocol as SA-HMR." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.893, + 0.903 + ], + "angle": 0, + "content": "Since METRO does not consider scenes, we additionally optimize the global pose and scale by minimizing" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17043" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.131, + 0.089, + 0.418, + 0.141 + ], + "angle": 0, + "content": "
DatasetInitial RtErrRefined RtErrFinal RtErr
RICH510.8284.7246.5
PROX364.2132.3111.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.151, + 0.47, + 0.18 + ], + "angle": 0, + "content": "Table 3. Ablation study of root estimation. The human root position errors (RtErr) in mm are reported." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.207, + 0.469, + 0.268 + ], + "angle": 0, + "content": "scene-aware losses, including re-projection error, human-scene penetration, contact distance [6], and ordinal depth error [29], following the key ideas of PROX and PHOSA [29], which is denoted as \\(\\mathrm{METRO}^{\\dagger} + \\mathrm{SA}\\)-Opt." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.272, + 0.469, + 0.438 + ], + "angle": 0, + "content": "Results. For the RICH dataset, Tab. 1 shows that SA-HMR notably outperforms other baselines in terms of the G-MPJPE and G-MPVE by a significant margin, demonstrating the effectiveness of the proposed pipeline. The joint learning on both image and scene geometry also improves the metrics of local pose and human-scene contact. We use open-sourced code for SMPLify-X and PROX, and implement POSA and PLACE upon PROX. Optimization methods approximately cost 18s for a single fitting, which is much slower compared to 0.2s of SA-HMR. We provide qualitative results comparing to baselines in Fig. 6." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.439, + 0.469, + 0.589 + ], + "angle": 0, + "content": "For the PROX dataset, SA-HMR outperforms all baselines in terms of global accuracy as illustrated in Tab. 2. Since the pseudo ground truth of the training set is still not of high quality, as well as a domain gap exists in the test set where the subject wears a MoCap suit, our method falls a little behind in local accuracy and scene penetration. And we do not report ConFE, since the ground truth contact label is not available. Nevertheless, the clear improvement compared to the most relevant model \\(\\mathrm{METRO}^{\\dagger}\\) has demonstrated the effectiveness of the proposed method." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.59, + 0.469, + 0.695 + ], + "angle": 0, + "content": "We also observe that while considering the scene geometry is critical for estimating the global position and improving physical plausibility, it may not fully resolve the ambiguity of the local pose, where multiple physically plausible solutions may still exist. For example, the RGB-only method SMPLify-X and the scene-aware method PROX perform similarly in MPJPE and MPVE." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.706, + 0.229, + 0.723 + ], + "angle": 0, + "content": "4.4. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Root and Contact Module. Tab. 3 shows that the predicted human root position is improved progressively by the refinement and scene-aware HMR modules, where the initial prediction [33] is improved \\(44\\% / 52\\%\\) in RICH, and \\(64\\% / 69\\%\\) in PROX. The offset representation helps to improve erroneous initial root prediction that is not consistent with the scene surface. For scene contact estimation, the precision / recall is \\(0.57 / 0.53\\) on RICH, and \\(0.45 / 0.24\\) on PROX. We observe that the contacts are difficult to predict, which aligns with the conclusion of a recent work HULC [3]. More visualizations are presented in Fig. 7." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.089, + 0.89, + 0.14 + ], + "angle": 0, + "content": "
MethodG-MPJPEG-MPVEMPJPEMPVECErr↓
w/o parallel304.8312.998.5108.910.2
Ours264.6272.793.9103.08.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.149, + 0.892, + 0.192 + ], + "angle": 0, + "content": "Table 4. Ablation study of the parallel network on the RICH dataset. The compared variant fuses features of contact points at the early stage." + }, + { + "type": "table", + "bbox": [ + 0.572, + 0.205, + 0.822, + 0.292 + ], + "angle": 0, + "content": "
RootContactMPJPEMPVECErr↓
//98.8107.910.5
Est.Est.93.9103.08.9
GTEst.89.298.17.9
Est.GT90.499.28.3
GTGT76.784.65.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.302, + 0.892, + 0.343 + ], + "angle": 0, + "content": "Table 5. Ablation study of the scene-aware mesh recovery module. We validate the upper bound of the proposed method on the RICH dataset." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.369, + 0.892, + 0.506 + ], + "angle": 0, + "content": "Mesh Recovery Module. As shown in Tab. 4, the parallel network that uses cross-attention outperforms a variant that fuses the pointnet features of the contact points to the METRO network in the early stage. The CErr indicates the error of contact mesh vertices in the translation-aligned coordinates. In Tab. 5, we validate the upper bound of the mesh recovery module. We replace the intermediate estimation of root and contact, and find a steady improvement in the pose and shape accuracy." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.51, + 0.892, + 0.616 + ], + "angle": 0, + "content": "Running Time. SA-HMR runs at 170 ms with a peak memory cost of 1852 MB for a \\(224 \\times 224\\) image and a scene point cloud of 2 cm resolution on a V100 GPU. Specifically, the root and contact module takes 92 ms (CNN 50 ms, SPVCNN 42 ms), the mesh recovery module takes 75 ms (CNN 49 ms, Transformer 26 ms), and the intermediate processing takes 3 ms." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.629, + 0.619, + 0.644 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.654, + 0.892, + 0.835 + ], + "angle": 0, + "content": "This work addresses the challenge of estimating the human mesh from an RGB image with the consideration of the scene geometry. Our key idea is to inject 3D scene cues into a monocular human mesh recovery network to recover the absolute human pose and shape in the scene. To this end, our approach first predicts the 3D human location and dense human-scene contacts with a sparse 3D CNN. We then develop a transformer to extract features from contact scene points and feed them into the pose estimation network using cross-attention. Experiments demonstrate that our approach achieves state-of-the-art performance on the RICH and PROX datasets." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Acknowledgement. This work was supported by the Key Research Project of Zhejiang Lab (No. K2022PG1BB01), NSFC (No. 62172364), and Information Technology Center and State Key Lab of CAD&CG, Zhejiang University." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17044" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.094, + 0.088, + 0.222, + 0.187 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.226, + 0.089, + 0.353, + 0.187 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.358, + 0.089, + 0.484, + 0.187 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.489, + 0.089, + 0.616, + 0.187 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.62, + 0.089, + 0.746, + 0.187 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.75, + 0.089, + 0.877, + 0.187 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.096, + 0.19, + 0.222, + 0.289 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.226, + 0.193, + 0.353, + 0.289 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.358, + 0.194, + 0.483, + 0.289 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.488, + 0.194, + 0.615, + 0.289 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.619, + 0.194, + 0.746, + 0.289 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.75, + 0.194, + 0.876, + 0.289 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.096, + 0.293, + 0.222, + 0.392 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.226, + 0.295, + 0.353, + 0.392 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.358, + 0.295, + 0.484, + 0.392 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.489, + 0.295, + 0.615, + 0.392 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.619, + 0.295, + 0.746, + 0.392 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.75, + 0.295, + 0.877, + 0.392 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.096, + 0.396, + 0.222, + 0.494 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.226, + 0.396, + 0.353, + 0.493 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.358, + 0.396, + 0.483, + 0.493 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.488, + 0.396, + 0.615, + 0.493 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.619, + 0.396, + 0.746, + 0.493 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.75, + 0.396, + 0.877, + 0.494 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.096, + 0.498, + 0.222, + 0.596 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.141, + 0.605, + 0.176, + 0.617 + ], + "angle": 0, + "content": "Image" + }, + { + "type": "image", + "bbox": [ + 0.226, + 0.498, + 0.353, + 0.596 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.271, + 0.605, + 0.306, + 0.616 + ], + "angle": 0, + "content": "PROX" + }, + { + "type": "image", + "bbox": [ + 0.358, + 0.498, + 0.484, + 0.596 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.399, + 0.603, + 0.444, + 0.616 + ], + "angle": 0, + "content": "METRO" + }, + { + "type": "image", + "bbox": [ + 0.488, + 0.498, + 0.615, + 0.596 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.505, + 0.603, + 0.599, + 0.617 + ], + "angle": 0, + "content": "METRO† + SA-Opt" + }, + { + "type": "image", + "bbox": [ + 0.619, + 0.498, + 0.746, + 0.596 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.669, + 0.605, + 0.696, + 0.616 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image", + "bbox": [ + 0.75, + 0.498, + 0.877, + 0.596 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.78, + 0.605, + 0.845, + 0.616 + ], + "angle": 0, + "content": "GroundTruth" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.63, + 0.895, + 0.687 + ], + "angle": 0, + "content": "Figure 6. Qualitative results on the RICH [6] dataset. We compare the proposed method to PROX [5], finetuned METRO [12], finetuned METRO with scene-aware optimization, and ground truth. The leftmost column shows the input images. The proposed method recovers the global positions and human-scene contact more accurately because of the 3D learning on human root refinement and dense scene contact labeling tasks." + }, + { + "type": "image", + "bbox": [ + 0.095, + 0.703, + 0.222, + 0.801 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.119, + 0.808, + 0.198, + 0.819 + ], + "angle": 0, + "content": "Root & Contact" + }, + { + "type": "image", + "bbox": [ + 0.226, + 0.703, + 0.353, + 0.801 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.274, + 0.808, + 0.301, + 0.819 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image", + "bbox": [ + 0.358, + 0.703, + 0.484, + 0.801 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.388, + 0.808, + 0.452, + 0.819 + ], + "angle": 0, + "content": "GroundTruth" + }, + { + "type": "image", + "bbox": [ + 0.488, + 0.703, + 0.615, + 0.801 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.515, + 0.808, + 0.593, + 0.819 + ], + "angle": 0, + "content": "Root & Contact" + }, + { + "type": "image", + "bbox": [ + 0.619, + 0.703, + 0.746, + 0.801 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.668, + 0.808, + 0.696, + 0.819 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image", + "bbox": [ + 0.75, + 0.703, + 0.877, + 0.801 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.783, + 0.808, + 0.847, + 0.819 + ], + "angle": 0, + "content": "GroundTruth" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.833, + 0.895, + 0.876 + ], + "angle": 0, + "content": "Figure 7. Qualitative visualization of the estimated root locations and dense scene contacts. In both examples, the estimated contact points provide accurate position and scene structure for the following step of mesh recovery. The reconstructed human mesh is in good contact with the corresponding scene regions." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17045" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.468, + 0.156 + ], + "angle": 0, + "content": "[1] Siwei Zhang, Yan Zhang, Federica Bogo, Marc Pollefeys, and Siyu Tang. Learning motion priors for 4d human body capture in 3d scenes. 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Unlike previous methods that perform scene-aware mesh optimization, we propose to first estimate absolute position and dense scene contacts with a sparse 3D CNN, and later enhance a pretrained human mesh recovery network by cross-attention with the derived 3D scene cues. Joint learning on images and scene geometry enables our method to reduce the ambiguity caused by depth and occlusion, resulting in more reasonable global postures and contacts. Encoding scene-aware cues in the network also allows the proposed method to be optimization-free, and opens up the opportunity for real-time applications. The experiments show that the proposed network is capable of recovering accurate and physically-plausible meshes by a single forward pass and outperforms state-of-the-art methods in terms of both accuracy and speed. Code is available on our project page: https://zju3dv.github.io/sahmr/. + +# 1. Introduction + +Monocular human mesh recovery (HMR), i.e., estimating pose and shape parameters of a parametric human model from a single image, has gained significant attention in recent years. To better capture and understand human behaviors, many recent works [1-5] propose to address the problem of scene-aware HMR which involves human-scene interaction constraints when recovering human meshes, given the 3D geometry of the scene scanned by range sensors [5-7], as well as the camera pose of the input image relative to the scene, which may enable more applications in video surveillance, household robots, and motion analysis in gyms and clinics. + +Most existing methods propose using scene-aware optimization to fit the human mesh into a pre-scanned scene. They optimize a parametric human model iteratively, e.g., + +![](images/ff8689aef3051835a559618c047a54bbb709eb57d294c089a468cf06b8166aa5.jpg) + +![](images/b31c8e031c8754726b90b80ff317948b89d7b82f7876b132f86b180a9b6610b9.jpg) + +![](images/0d2904060809c3847866cd385c6e3dda838ad97e09f2cccd312294c013adfebd.jpg) +Input +Figure 1. Comparison between the optimization-based method and the proposed method. Optimization-based methods typically fit a parametric human model iteratively by minimizing 2D reprojection error and scene conflicts. In contrast, the proposed method utilizes a single forward pass of the network to estimate the global position (blue ball), contact scene points (colored scene points), and a scene-aware human mesh. This design leads to improvements in both efficiency and accuracy. + +![](images/fc60ca6c1f19c0ea866075dfdbe1d088155ccc1e0fe075cbfc598548392ed96b.jpg) +Prediction + +SMPL [8], to minimize scene penetration, chamfer distance of contact regions, and the 3D-2D re-projection error. However, optimization tends to be slow at inference time and is sensitive to initialization and hyperparameters, failing to respond in low-latency applications. As illustrated in Fig. 1, an optimization-based method PROX [5] takes 18.4s to fit a human model into the scene, while the incorrect position and pose still occur. + +Recent works [9-13] propose to recover human mesh with neural networks trained on large-scale datasets [14-17]. Specifically, the networks learn a mapping from an input image to a human mesh in the canonical coordinates. Applying these methods in the scene-aware HMR + +task still requires post-processing optimization, where the global translation and the human poses are refined in accordance with the given scene. However, the monocular prediction is conditioned on the input image solely, omitting the joint distribution of human pose and scene geometry, and therefore tends to suffer from depth ambiguity and occlusion. As a result, the optimization-based post-processing could be easily deteriorated by the erroneous initial poses and may even worsen the initial prediction. + +In this work, we propose a Scene-Aware Human Mesh Recovery network (SA-HMR), the first learning-based approach that predicts the absolute position and mesh of a human in the scene by a single forward pass. The overall pipeline is illustrated in Fig. 2. Given the input image and scene point cloud, we first use a sparse 3D CNN to estimate dense scene contacts and absolute human position, where the scene contact estimation is treated as a point cloud labeling task, and the human position prediction is presented as a voting vector field refinement task. The predicted dense contact points are centered by the human position and passed to a scene network in the human mesh recovery step. Specifically, we enhance a pretrained monocular HMR network METRO [12] by cross-attention with the proposed scene network in parallel. In this way, SA-HMR learns a joint distribution of human pose and scene geometry, resulting in more reasonable postures, contacts, and global positions, as illustrated in Fig. 1. Learning scene-aware cues in the network also avoids scene-aware optimization as post-processing and achieves fast inference speed. + +We evaluate the proposed method on the RICH [6] and PROX [5] datasets of indoor and outdoor scenes. The experimental results show that SA-HMR is not only effective in recovering absolute positions and meshes that are in accordance with the given scene, but also significantly faster than the optimization-based baselines. + +In summary, we make the following contributions: + +- The first optimization-free framework for scene-aware human mesh recovery from a single image and a prescanned scene. +- The cross-attention design for enhancing a pretrained HMR network with a parallel scene network, enabling joint learning on the human pose and scene geometry. +- Superior performance compared to optimization-based baselines in terms of both accuracy and speed. + +# 2. Related Work + +Monocular Human Mesh Recovery. Most existing approaches formulate the monocular HMR task as recovering the mesh of statistical human body models, e.g. SMPL and SMPL-X [8, 18, 19], where recent works can be divided into optimization-based and learning-based approaches. + +The optimization-based approaches fit a parametric human model by minimizing the 3D-2D re-projection error of body joints and energy terms of heuristic priors iteratively, which are represented by SMPLify [20] that fits SMPL [8]. More recently, SMPLify-X [19] proposes a variational pose prior and fits a more expressive SMPL-X. PoseNDF [21] proposes to represent the manifold of plausible human poses with a neural field. While optimization-based methods are general in their mathematical formulation, they are usually sensitive to hyperparameters and require much time for inference. + +The learning-based methods utilize deep neural networks to predict either the parameters [9, 10, 22, 23] or the mesh vertices [11-13] of the SMPL model. HMR [9] is the pioneering work in predicting SMPL parameters, and SPIN [10] improves upon it using an optimization loop. For predicting SMPL mesh vertices, GraphCMR [11] deforms a template human mesh using graph neural network, while METRO [12] uses transformers, and [13] uses graph hierarchy to further improve the performance. However, for scene-aware HMR, the vertices of the human and scene meshes in contact are close in Euclidean space, making methods that regress parameters unsuitable due to errors that accumulate along the kinematic chains. Therefore, the proposed method is built on the works that predict mesh vertices. More details can be found in Sec. 3. + +Scene-aware Human Mesh Recovery. PROX [5] is a seminal work that uses scene constraints to reduce the depth and occlusion ambiguity in monocular HMR. It achieves this by adding two energy terms of human-scene contact and penetration in the optimization process [19]. In addition, scene-aware pose generative models [2, 24] can also be used as prior terms in the scene-aware HMR task. Other recent works in this area include MoCapDeform [4], which considers deformable scene objects, LEMO [1], which uses temporal information, and HULC [3], which uses consecutive frames and dense contacts prediction on both the scene and human body. In contrast to these works, the proposed method is optimization-free and requires only a single forward pass. + +In a broader topic of capturing humans in a scene-aware manner, [25-27] propose using a simulator and dynamic model, where a pre-defined agent is controlled to interact with the scene, and [28,29] consider human-object arrangement by first predicting the human and object and then performing global optimization. + +Attention in Transformers. Attention is a key mechanism in Transformers [30]. It allows a set of query features to fuse the most relevant information from another set of key-value features. When query and key-value features come from the same source, it is called self-attention, otherwise cross-attention. In HMR, METRO [12] uses self-attention to re + +![](images/099d627c6371e6f265ecdb14d5cbd081cb6e5e1014f1544beefc162ca88ddb90.jpg) +1. Human Root and Scene Contacts + +![](images/1344a1eae09f2a30ed5ac3fb1109504220a94f08a5adf1ec816b0a392fd9cffe.jpg) +2. Scene-aware Human Mesh Recovery +Figure 2. Overview of the proposed SA-HMR. 1. The human root and scene contact estimation module (Sec. 3.2) that first predicts the initial root and then refines the root with 3D scene cues using a sparse 3D CNN. The module also predicts contact labels [5] for each scene point. Please refer to Sec. 3.2 for a detailed definition of the 3D feature construction module. 2. The scene-aware human mesh recovery module (Sec. 3.3) that enhances the pretrained METRO [12] network with a parallel scene network. The scene network takes the predicted contact scene points as input, and uses cross-attention to pass messages to the intermediate features of the METRO network. + +duce occlusion ambiguity by establishing non-local feature exchange between visible and invisible parts of a template human mesh. In feature matching, SuperGlue [31] uses cross-attention to make the corresponding image features more similar. Predator [32] uses cross-attention in matching two sets of point clouds. + +Inspired by feature matching, the proposed method uses cross-attention to potentially make the features of the human and scene that are in contact more similar, resulting in better contact and more reasonable postures. + +# 3. Methods + +Given a calibrated image and a pre-scanned scene point cloud (Sec. 3.1), SA-HMR first estimates the absolute human root position and scene contacts (Sec. 3.2), and then recovers the human mesh with the contact points by enhancing a pretrained METRO network (Sec. 3.3). An overview of the proposed method is presented in Fig. 2. + +# 3.1. Preliminaries + +Human Representation. We use SMPL [8] as the human representation. The SMPL is a parametric model that uses the body joint rotations, root translation, and body shape coefficients to compute the body mesh. Following [11, 12], we directly predict the SMPL mesh vertices $V = \mathbb{R}^{6890 \times 3}$ , and use H36M [14] joint regression matrix $M \in \mathbb{R}^{14 \times 6890}$ to compute 3D joints $J \in \mathbb{R}^{14 \times 3}$ from the vertices for quantitative evaluation, $J = MV$ . + +Scene and Image Representation. We assume that the scene is pre-scanned with range sensors, as in RICH [6] and PROX [5], and the image is calibrated and localized in the scene, i.e. with known intrinsic and extrinsic parameters $\{(f,c_x,c_y),(R_c,t_c)\}$ . Following METRO [12], we detect + +a squared bounding box around the target human and resize the cropped region as the input image $I \in \mathbb{R}^{224 \times 224 \times 3}$ . Based on the camera parameters and the bounding box, we select scene points that fall within the visual frustum as the input scene point cloud $S \in \mathbb{R}^{N_S \times 3}$ . + +Human-Scene Contact. Following PROX [5], we use seven regions of the SMPL mesh that are most likely to be contacted. The details are provided in the supplementary material. Using these seven categories and one for not being in contact, we perform a segmentation task on the scene point cloud. + +# 3.2. Human Root and Scene Contacts + +Given an image $I$ bounding the human, we propose using a 2D convolutional neural network (CNN) to extract image features $F$ and predict the initial human root $r$ . Based on the scene points $S$ , we unproject the image features $F$ to 3D, resulting in $\hat{F}$ . Additionally, we calculate point-wise offset vectors $O$ that point from a voxelized scene point cloud to the initial root. By taking $\hat{F}$ and $O$ as input, a sparse 3D CNN predicts the segmentation of scene contacts and the refined offsets, which are then converted to the refined human root $r^{*}$ . An overview of this process is presented in the left column of Fig. 2. + +Initial Root. We predict the initial root $r = (X, Y, Z)$ in a 2.5D manner following SMAP [33]. Specifically, we use a CNN to predict the 2D heatmap and a normalized depth map of the root. Then, the 2D position $(x, y)$ is obtained by applying argmax to the heatmap, and the corresponding normalized depth value $\tilde{Z}$ is retrieved from the depth map. Finally, using the intrinsic parameters $f, c_x, c_y$ and image size $w$ , the 3D root position is computed: + +$$ +Z = \tilde {Z} \frac {f}{w} \tag {1} +$$ + +![](images/9c4f56bb248248a8ca505d924665a8e26221b1c570ae623579dab2c31146c233.jpg) +Figure 3. 3D feature construction. We voxelize a scene point cloud to a sparse volume. The initial feature of each voxel consists of two parts, which are the offset vector pointing from the voxel center to the human root and the unprojected image features. + +$$ +X = \frac {x - c _ {x}}{f} \cdot Z, \quad Y = \frac {y - c _ {y}}{f} \cdot Z \tag {2} +$$ + +From our observation, estimating $(x,y)$ achieves good results with a mean squared error of fewer than two pixels across datasets. However, estimating $\tilde{Z}$ is relatively challenging, possibly due to the variations in human shapes. + +3D Feature Construction. Based on the initial root $r$ and image features $F$ , we construct the 3D features on the voxelized scene point cloud, which is illustrated in Fig. 3. + +First, we select regions of interest around the initial root $r$ in the point cloud. Specifically, we treat $r$ as an anchor and keep points within a radius $\gamma_1$ . Since $Z$ has more uncertainty than $(x,y)$ , we sample two additional anchors along the z-axis, whose distance to $r$ is $\gamma_2$ . Next, we construct a sparse volume $\bar{S}$ by voxelizing these points with voxel size $s_{vox}$ , where the center of each voxel is denoted as $\bar{s}_i$ . + +For each voxel $i$ , the feature consists of the offset vector $o_i$ and the unprojected image feature $\hat{f}_i$ . Specifically, $o_i$ is a vector pointing from the voxel center to the human root: + +$$ +o _ {i} = r - \bar {s} _ {i} \tag {3} +$$ + +$\hat{f}$ is computed by projecting voxel center $\bar{s}_i$ onto the image using camera parameters and bilinearly sampling the image feature map $F$ . + +Estimating Refined Root and Scene Contacts. We use sparse 3D CNN [34] to process the constructed 3D features and learn to improve the root estimation and predict the scene contacts. Specifically, the output of each voxel includes an updated offset vector $o_i^*$ , confidence $c_i$ , and segmentation indicating the contact category. We compute the refined root $r^*$ : + +$$ +r ^ {*} = \sum_ {i} c _ {i} \cdot \left(o _ {i} ^ {*} + \bar {s} _ {i}\right). \tag {4} +$$ + +There are 8 categories of contact points, including 7 most probable regions on the body that would be contacted [5] and 1 category of not being in contact. We take the category of the highest score as the prediction for the voxel and + +![](images/65c2791949dd0be2029cae1f86dc4c878a3b9f06a416235b0672e7d8c902d622.jpg) +Figure 4. Enhancing METRO with a parallel network. The orange parts are the original METRO [12] network, where the residual connection and positional encoding are omitted for simplicity. The blue parts are the proposed parallel network which takes predicted contact scene points as input. The yellow parts indicate feature interaction between METRO and the parallel network. + +set the dense point cloud belonging to the voxel with that category. The contact points $\hat{S}_{seg3d} \in \mathbb{R}^{\hat{N}_S \times 3}$ serve as the input for the mesh recovery module. + +# 3.3. Scene-aware Human Mesh Recovery + +Since the training data of scene-aware human mesh recovery is limited, we build our model upon a network named METRO [12] that is pre-trained on large-scale data of monocular human mesh recovery. METRO processes feature based on the self-attention mechanism, and our approach enhances METRO by adding a parallel scene network, which provides a cross-attention-based mechanism that enables METRO to notice important scene details and achieve scene-aware human mesh recovery. + +METRO consists of a CNN backbone and multiple Transformer encoders. It first extracts global CNN features, then combines the feature to the vertices of a zero posed SMPL mesh, and finally predicts a posed mesh with shape through the transformers. The part of the transformer is illustrated in the orange part of Fig. 4. + +Enhancing METRO with Cross-Attention. We improve METRO with a scene network, which makes the predicted human vertices to be close to the corresponding contact scene points $\hat{S}_{seg3d}$ (Sec. 3.2). + +As illustrated in Fig. 4, we add a parallel network, which has a similar architecture as the transformer of METRO, + +![](images/52c52e3d1e59a88b64ba968f1f625c9b54cc63dfa00acc5a85974ce5bacdf5b8.jpg) +(a) + +![](images/46fa9aad8b9fd7b602a2235cc527bf00715c49bb2400fc499929e272cbf20f56.jpg) +(b) + +![](images/d05cdefacc22f054e018275653bef8ef306d3842d9561b63d4f134fa48aae402.jpg) +(c) +Figure 5. Visualization of the cross-attention from a body vertex (blue point) to the predicted dense scene contacts (white points). (a) The image and the predicted dense scene contacts. (b) The hand vertex is in contact with the scene according to the image, and its feature is similar to the nearby scene point features, enabling the final vertex prediction to be close to the corresponding scene surface. (c) The arm vertex is not in contact with the scene, where feature similarities tend to be evenly distributed. The feature similarities are normalized to the same range of $0 \rightarrow 1$ . + +to extract features of scene contact points and output the point positions like an autoencoder. Specifically, we first use METRO's CNN backbone to extract the image feature and map it to a set of vertex tokens by a fully-connected layer. In METRO, these tokens are directly concatenated with the positions of initial human vertices. However, the number of scene contact points is not the same as the tokens', and there is no one-to-one correspondence between them. To resolve this issue, we perform the average pooling to vertex tokens based on the contact categories defined on the SMPL mesh vertices [5], resulting in 7 tokens. Then, we append each scene contact point with the corresponding aggregated token based on the predicted category in Sec. 3.2. Intuitively, this helps the cross-attention to focus on the semantically corresponding parts. To be invariant to the global translation, the scene contact points are zero-centered by the predicted root $r^*$ . + +Motivated by recent feature matching methods [31, 32], we propose to use cross-attention to pass features from scene contact points to human vertices. The cross-attention and self-attention share the same underlying mechanism, both of which first compute the similarity of query and key, and then use the weighted sum to fuse features. When the query and key are from the same source features, it is self-attention, and otherwise is cross-attention. In practice, we use linear attention operator [35] to improve efficiency. A visualization of cross attention over human vertices and scene points is in Fig. 5. The detailed network architecture is provided in the supplementary material. + +Note that, we use a weight-sharing regressor layer with METRO, which regresses from point-wise features to point + +position $(x,y,z)$ . Therefore, to get a similar $(x,y,z)$ , the input features of this layer should also be similar. This strategy implicitly aligns the features of human vertices and scene points when their final predictions are near in 3D space, thus facilitating the cross-attention to find correspondences between human vertices and scene points. + +# 3.4. Training Loss + +Root and Contact. The loss function $L_{\mathrm{RC}}$ for the root and contact estimation is defined as: + +$$ +L _ {\mathrm {R C}} = L _ {\mathrm {R 2 D}} + w _ {\mathrm {R Z}} \cdot L _ {\mathrm {R Z}} + L _ {\mathrm {R O V}} + L _ {\mathrm {R 3 D}} + L _ {\mathrm {C}} \tag {5} +$$ + +where $L_{\mathrm{R2D}}$ is the MSE loss on the root heatmap; $L_{\mathrm{RZ}}$ , $L_{\mathrm{ROV}}$ , and $L_{\mathrm{R3D}}$ are the L1 losses on the relative depth, offset vectors, and the 3D root, respectively; $L_{\mathrm{C}}$ is the cross-entropy loss for contact categories of voxel points, where we additionally train an auxiliary task of 2D contact segmentation similar to the voxel points. + +Human Mesh Recovery. The loss function $L_{\mathrm{HMR}}$ for the mesh recovery is defined as: + +$$ +L _ {\mathrm {H M R}} = L _ {\mathrm {V}} + L _ {\mathrm {J}} + L _ {\mathrm {C P}} + L _ {\mathrm {G V}} \tag {6} +$$ + +where $L_{\mathrm{V}}$ , $L_{\mathrm{J}}$ , $L_{\mathrm{CP}}$ , and $L_{\mathrm{GV}}$ are the L1 losses on the translation-aligned human vertices, human joints, reconstructed contact points, and global human vertices, respectively. More details are in the supplementary material. + +# 3.5. Implementation Details + +We train two modules separately. For the root and contact module, the CNN is HRNet-stride-4 [36] with METRO initialization, the sparse 3D CNN is SPVCNN [34, 37] with random initialization. We use linear layers to align intermediate feature dimensions. $\gamma_{1}$ is $1.25\mathrm{m}$ , $\gamma_{2}$ is $0.5\mathrm{m}$ , $s_{vox}$ is $5^{3}cm^{3}$ , and $w_{\mathrm{RZ}}$ is 10. The contact threshold is $7\mathrm{cm}$ . We flip images for augmentation. The module is trained with an initial learning rate of $3.75\mathrm{e - 5}$ and a batch size of 24. It converges after 30 epochs of training on one V100 GPU. For the mesh recovery module, the METRO network is initialized as pretrained and the scene network is randomly initialized. The initial learning rate is $7.5\mathrm{e - 6}$ and the batch size is 24. It converges after 30 epochs of training. + +# 4. Experiments + +# 4.1. Datasets + +We train and evaluate the proposed method on RICH [6] and PROX [5] datasets separately. + +RICH [6] captures multi-view video sequences in 6 outdoor and 2 indoor scenes. It provides images, reconstructed bodies, scene scans, and human-scene contact labels annotated on SMPL vertices. We skip frames including multiple + +
MethodLearning-basedOptimizationScene-awareG-MPJE↓G-MPV\( \downarrow \)PenE↓ConFE↓MPJPE↓MPVE↓
Dataset GT [6]✓✓//9.810.8//
SMPLify-X [19]✓482.0483.735.743.4166.9177.6
PROX [5]✓✓390.1397.215.524.1164.1175.8
POSA [2]✓✓427.8434.021.127.0177.2188.4
PLACE [38]✓✓395.9403.016.124.8163.8175.4
METRO \( [12]^† + SA-Opt \) [6, 29]✓✓✓563.1561.37.414.8102.7112.8
METRO [12]✓678.6679.452.256.9129.6134.5
METRO \( [12]^† \)✓511.7509.733.637.698.8107.9
SA-HMR✓✓264.6272.714.919.093.9103.0
+ +subjects, remove the first 45 frames of each video to avoid static starting pose, and skip frames where the subjects' 2D bounding boxes are not inside the images. Then we down-sample the train / val / test splits to $2/1/1$ fps, resulting in 15360 / 3823 / 3316 frames. + +PROX [5] captures monocular RGBD videos in 12 indoor scenes. We use RGB images and scene scans. It is a challenging dataset where severe occlusions exist in most frames. We use the qualitative set for training and the quantitative set for testing. In order to get better training annotations, we additionally use HuMoR [26] which utilizes motion prior and optimizes a sequence of frames. Then, we manually remove the failed frames that are not consistent with the images and scenes. Finally, the training split contains 4852 frames. + +# 4.2. Metrics + +We evaluate quantitatively in terms of human mesh recovery and human-scene contact. + +Human Mesh Recovery. We report the Global Mean-Per-Joint-Position-Error (G-MPJPE) and Global Mean-Per-Vertex-Error (G-MPVE) in the scene coordinate system, which calculates the average L2 distances between predicted and ground truth joints/vertices. Additionally, we report the translation-aligned metrics MPJPE and MPVE. + +Human-scene Contact. We report the Penetration Error (PenE) and Contact Failure Error (ConFE). PenE measures the total distance that SMPL vertices penetrate the scene mesh: + +$$ +\operatorname {P e n E} = \sum_ {i = 1} ^ {V} \mathbb {1} _ {x < 0} [ s d f (v _ {i}, \mathcal {S}) ] \cdot | s d f (v _ {i}, \mathcal {S}) |, \tag {7} +$$ + +where $V$ is the number of SMPL vertices, $sdf(v_{i},\mathcal{S})$ is the signed distance from vertex $v$ to scene $\mathcal{S}$ , and $\mathbb{1}_{x < 0}[\cdot ]$ is an indicator function that returns 1 when the condition is met, and 0 otherwise. ConFE measures contact quality when the + +Table 1. Evaluation on the RICH [6] dataset. METRO† indicates that the model is finetuned on the dataset. SA-Opt indicates scene-aware optimization, with contact estimation from BSTRO [6] and loss formulation from PROX [5] and PHOSA [29]. The proposed SA-HMR achieves the overall best results and is significantly faster than the methods that require optimization. + +
MethodG-MPJPE↓G-MPVE↓PenE↓MPJPE↓MPVE↓
Dataset GT [5]//9.6//
SMPLify-X [19]216.0222.649.3100.7112.8
PROX [5]172.0178.510.7101.1114.0
POSA [2]172.3180.916.6108.5119.4
PLACE [38]168.1176.712.3100.8113.7
METRO [12]283.2277.762.4137.0147.2
METRO [12]†265.6262.767.5117.1128.5
SA-HMR150.4160.026.9111.1122.5
+ +Table 2. Evaluation on the PROX [5] dataset. The proposed method achieves the best performance in global metrics. + +ground truth contact label is available: + +$$ +\begin{array}{l} \operatorname {C o n F E} = \sum_ {i = 1} ^ {V} \left(C _ {g t} \left(v _ {i}\right) \cdot | s d f \left(v _ {i}, \mathcal {S}\right) |\right. \\ + \left(1 - C _ {g t} \left(v _ {i}\right)\right) \cdot \mathbb {1} _ {x < 0} [ s d f \left(v _ {i}, \mathcal {S}\right) ] \cdot | s d f \left(v _ {i}, \mathcal {S}\right) |), \tag {8} \\ \end{array} +$$ + +where $C_{gt}(v)$ equals 1 if $v$ is labeled as in contact, and 0 otherwise. In order to obtain a good result of ConFE, the body vertices in contact should be close to the scene surface, while vertices not in contact should avoid penetration. + +# 4.3. Main Results + +Baselines. Optimization: SMPLify-X [19] uses RGB only, PROX [5] extends it with losses of human-scene contact and penetration, POSA [2] and PLACE [38] extend PROX with scene-aware pose priors, and METRO $[12]^{\dagger} + \mathrm{SA}$ -Opt stands for post-processing a finetuned METRO with scene-aware optimization, which will be explained later. Learning-based: METRO predicts canonical human mesh vertices and a weak-perspective camera. We solve the transformation from human to camera coordinate by minimizing joint re-projection error with a PnP solver [39]. The $\mathrm{METRO}^{\dagger}$ is finetuned with the same training protocol as SA-HMR. + +Since METRO does not consider scenes, we additionally optimize the global pose and scale by minimizing + +
DatasetInitial RtErrRefined RtErrFinal RtErr
RICH510.8284.7246.5
PROX364.2132.3111.8
+ +scene-aware losses, including re-projection error, human-scene penetration, contact distance [6], and ordinal depth error [29], following the key ideas of PROX and PHOSA [29], which is denoted as $\mathrm{METRO}^{\dagger} + \mathrm{SA}$ -Opt. + +Results. For the RICH dataset, Tab. 1 shows that SA-HMR notably outperforms other baselines in terms of the G-MPJPE and G-MPVE by a significant margin, demonstrating the effectiveness of the proposed pipeline. The joint learning on both image and scene geometry also improves the metrics of local pose and human-scene contact. We use open-sourced code for SMPLify-X and PROX, and implement POSA and PLACE upon PROX. Optimization methods approximately cost 18s for a single fitting, which is much slower compared to 0.2s of SA-HMR. We provide qualitative results comparing to baselines in Fig. 6. + +For the PROX dataset, SA-HMR outperforms all baselines in terms of global accuracy as illustrated in Tab. 2. Since the pseudo ground truth of the training set is still not of high quality, as well as a domain gap exists in the test set where the subject wears a MoCap suit, our method falls a little behind in local accuracy and scene penetration. And we do not report ConFE, since the ground truth contact label is not available. Nevertheless, the clear improvement compared to the most relevant model $\mathrm{METRO}^{\dagger}$ has demonstrated the effectiveness of the proposed method. + +We also observe that while considering the scene geometry is critical for estimating the global position and improving physical plausibility, it may not fully resolve the ambiguity of the local pose, where multiple physically plausible solutions may still exist. For example, the RGB-only method SMPLify-X and the scene-aware method PROX perform similarly in MPJPE and MPVE. + +# 4.4. Ablation Study + +Root and Contact Module. Tab. 3 shows that the predicted human root position is improved progressively by the refinement and scene-aware HMR modules, where the initial prediction [33] is improved $44\% / 52\%$ in RICH, and $64\% / 69\%$ in PROX. The offset representation helps to improve erroneous initial root prediction that is not consistent with the scene surface. For scene contact estimation, the precision / recall is $0.57 / 0.53$ on RICH, and $0.45 / 0.24$ on PROX. We observe that the contacts are difficult to predict, which aligns with the conclusion of a recent work HULC [3]. More visualizations are presented in Fig. 7. + +Table 3. Ablation study of root estimation. The human root position errors (RtErr) in mm are reported. + +
MethodG-MPJPEG-MPVEMPJPEMPVECErr↓
w/o parallel304.8312.998.5108.910.2
Ours264.6272.793.9103.08.9
+ +Table 4. Ablation study of the parallel network on the RICH dataset. The compared variant fuses features of contact points at the early stage. + +
RootContactMPJPEMPVECErr↓
//98.8107.910.5
Est.Est.93.9103.08.9
GTEst.89.298.17.9
Est.GT90.499.28.3
GTGT76.784.65.2
+ +Table 5. Ablation study of the scene-aware mesh recovery module. We validate the upper bound of the proposed method on the RICH dataset. + +Mesh Recovery Module. As shown in Tab. 4, the parallel network that uses cross-attention outperforms a variant that fuses the pointnet features of the contact points to the METRO network in the early stage. The CErr indicates the error of contact mesh vertices in the translation-aligned coordinates. In Tab. 5, we validate the upper bound of the mesh recovery module. We replace the intermediate estimation of root and contact, and find a steady improvement in the pose and shape accuracy. + +Running Time. SA-HMR runs at 170 ms with a peak memory cost of 1852 MB for a $224 \times 224$ image and a scene point cloud of 2 cm resolution on a V100 GPU. Specifically, the root and contact module takes 92 ms (CNN 50 ms, SPVCNN 42 ms), the mesh recovery module takes 75 ms (CNN 49 ms, Transformer 26 ms), and the intermediate processing takes 3 ms. + +# 5. Conclusion + +This work addresses the challenge of estimating the human mesh from an RGB image with the consideration of the scene geometry. Our key idea is to inject 3D scene cues into a monocular human mesh recovery network to recover the absolute human pose and shape in the scene. To this end, our approach first predicts the 3D human location and dense human-scene contacts with a sparse 3D CNN. We then develop a transformer to extract features from contact scene points and feed them into the pose estimation network using cross-attention. Experiments demonstrate that our approach achieves state-of-the-art performance on the RICH and PROX datasets. + +Acknowledgement. This work was supported by the Key Research Project of Zhejiang Lab (No. K2022PG1BB01), NSFC (No. 62172364), and Information Technology Center and State Key Lab of CAD&CG, Zhejiang University. + +![](images/2d1fa03337d55309cd2aaae9b2bc6d054b3b66eb6f519940c98c34c1f26e6a21.jpg) + +![](images/5ad35535b77f781d28f6a9386efcf6ee88559c726e16e5f1dc0c1be6cde2a7a7.jpg) + +![](images/97323ca0895074e21e3ac1b4c3d4b5fdc1e8f21656655b36e6fc38727bc1e1e5.jpg) + +![](images/3faba6a71431a23dc68f551ff24cd652232bed70c9be0ba22e8df9f57e501f5a.jpg) + +![](images/73bb95413668605418bd6370f7a3d512f01098e97db11be0616e5d8f187ac4a0.jpg) + +![](images/da6874eba4f0e4504b2dc9d8d7f75483badff0d9315ea5d409608018bc1c758b.jpg) + +![](images/3b061224069cad54e8341188cf501eb014de0f7faccf352c77872d4cade89dd6.jpg) + +![](images/141d6daa40a573e1fddfc4524ebe191fbfdea87eda0212b793b661cc3d0aebb0.jpg) + +![](images/babf688cede582e9f6c4e2a3f5c287f97bdaba92f6bf9b938c46731dabff83c2.jpg) + +![](images/f2c70e890fae86e9796b9a91c0fe99be9f2f9615c11fe51f540b721c1eb55b6d.jpg) + +![](images/34a037781e6c55b637532c5cd20b3504060d48285c140a74c6aa97a2272c342b.jpg) + +![](images/f696b9ce1002404c3bbe0ecf562be3d7e75c383cc6ef699a495458ffc4204dcf.jpg) + +![](images/19c7b38496fd79c6c9ed5940bacaf2173f52587ae17538619ee64ef35b2a9ac4.jpg) + +![](images/06b53b029829367b676d2b870d8b40929202854b208070ae4f79190449d31e4a.jpg) + +![](images/a6d6979efc75ffb0416f8013d50b670a1271fcf6ed1cf754fb2c192157f73655.jpg) + +![](images/32e62b603f7f8f73a1e1311a91b4de4c57bdcdc43691150c1ad1f413f2244d1a.jpg) + +![](images/7a82fdc6338d5b5e892fbee8dea37d4c5b3853f4ee5b8804eac0650675d92312.jpg) + +![](images/382aaada2acb8e2fb66e2c33fdeafd76ed1e994df9afa894b434fceff7d71495.jpg) + +![](images/81d47976b5216aa2a5ff73dbe33a962c405c585e6b5bf91ff998e0929fdad1bd.jpg) + +![](images/d05f2215e45c726c1329f665fa7b1ab800e9fe46ee087b2ee60764451573b95c.jpg) + +![](images/65d31747494d28ca377e69f9031b284839f9cdfe8a81b4f32143de1f9ca83b1c.jpg) + +![](images/be4e49d57cc1bd64a7e56ce303279cd9d21a1b5b96e848829a2175208d050bef.jpg) + +![](images/cda21a98f3af00e12f8b40e290ccac0a8a4d88711a44b91f906b44681e807e81.jpg) + +![](images/dc53376c0dbb8d5c99c50464533e25e041dcd2836748e761ee65667ba860c149.jpg) + +![](images/58ee558df178da3f416c930e65c41e4e7eba958d84aa4e3b0ac22ae813cc4b6e.jpg) +Image + +![](images/037da32f8f7c2c091bc3279fc59d04f8c5bfac3c20cd3d1f3548475194514e24.jpg) +PROX + +![](images/10d50eb2c62c3a91bd63bf30e36c832a25e92731a489132f58cc551cd178c0c7.jpg) +METRO + +![](images/05d21c6883002efc84c2ed9ff8668431979fdce01f8c4717e98a579fc7af296b.jpg) +METRO† + SA-Opt + +![](images/13878a5eddeb1f6eff18cd029cab93f0dd5431acd4f6ff25bbe9e8889dc7def1.jpg) +Ours + +![](images/2c305b503d2e504dab1f693bfcf7adfe48d042223234f930d439629e10c2eeff.jpg) +GroundTruth + +![](images/5571b3957704ef1625dfc3406a9ad65ab0b095f5e863220deba4b25cc58c62fa.jpg) +Figure 6. Qualitative results on the RICH [6] dataset. We compare the proposed method to PROX [5], finetuned METRO [12], finetuned METRO with scene-aware optimization, and ground truth. The leftmost column shows the input images. The proposed method recovers the global positions and human-scene contact more accurately because of the 3D learning on human root refinement and dense scene contact labeling tasks. +Root & Contact +Figure 7. Qualitative visualization of the estimated root locations and dense scene contacts. In both examples, the estimated contact points provide accurate position and scene structure for the following step of mesh recovery. The reconstructed human mesh is in good contact with the corresponding scene regions. + +![](images/8372d6878066b2829c2d9bf4235093ab6983f43c5fb888895324fdb691a7e71a.jpg) +Ours + +![](images/5d9f46cc9baa01aaf59215d1b71b148c07f91366feecb691eb80f50c26038b8f.jpg) +GroundTruth + +![](images/01fbd4a33c10fad547ac8704043c45b553f945021618d4f2aace0ba17db43d10.jpg) +Root & Contact + +![](images/f63e5d8142b08010df889569cea4aa0ea07311c01d2033caf12963ebb2bc25d1.jpg) +Ours + +![](images/06a399853a426b34da89706616de3d217df436668717c9b807085a0b144c3b52.jpg) +GroundTruth + +# References + +[1] Siwei Zhang, Yan Zhang, Federica Bogo, Marc Pollefeys, and Siyu Tang. Learning motion priors for 4d human body capture in 3d scenes. In ICCV, 2021. 1, 2 +[2] Mohamed Hassan, Partha Ghosh, Joachim Tesch, Dimitrios Tzionas, and Michael J. Black. Populating 3d scenes by learning human-scene interaction. 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Attention is all you need. In NeurIPS, 2017. 2 + +[31] Paul-Edouard Sarlin, Daniel DeTone, Tomasz Malisiewicz, and Andrew Rabinovich. Superglue: Learning feature matching with graph neural networks. In CVPR, 2020. 3, 5 +[32] Shengyu Huang, Zan Gojcic, Mikhail Usvyatsov, Andreas Wieser, and Konrad Schindler. Predator: Registration of 3d point clouds with low overlap. In CVPR, 2021. 3, 5 +[33] Jianan Zhen, Qi Fang, Jiaming Sun, Wentao Liu, Wei Jiang, Hujun Bao, and Xiaowei Zhou. SMAP: Single-shot multiperson absolute 3d pose estimation. In ECCV, 2020. 3, 7 +[34] Haotian Tang, Zhijian Liu, Shengyu Zhao, Yujun Lin, Ji Lin, Hanrui Wang, and Song Han. Searching efficient 3d architectures with sparse point-voxel convolution. In ECCV, 2020. 4, 5 +[35] Angelos Katharopoulos, Apoorv Vyas, Nikolaos Pappas, and François Fleuret. Transformers are rnns: Fast autoregressive transformers with linear attention. In ICML, 2020. 5 +[36] Ke Sun, Bin Xiao, Dong Liu, and Jingdong Wang. Deep high-resolution representation learning for human pose estimation. In CVPR, 2019. 5 +[37] Haotian Tang, Zhijian Liu, Xiuyu Li, Yujun Lin, and Song Han. TorchSparse: Efficient Point Cloud Inference Engine. In MLSys, 2022. 5 +[38] Siwei Zhang, Yan Zhang, Qianli Ma, Michael J. Black, and Siyu Tang. PLACE: Proximity learning of articulation and contact in 3d environments. In 3DV, 2020. 6 +[39] G. Bradski. The OpenCV Library. Dr. Dobb's Journal of Software Tools, 2000. 6 \ No newline at end of file diff --git a/2023/Learning Human Mesh Recovery in 3D Scenes/images.zip b/2023/Learning Human Mesh Recovery in 3D Scenes/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..09b08280d8272b994dc78813856880fd69334073 --- /dev/null +++ b/2023/Learning Human Mesh Recovery in 3D Scenes/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:4df036379dc5ca7cd7d2030dc1f53d07004e9b4a9797b58dcbbe96590e213ee5 +size 602262 diff --git a/2023/Learning Human Mesh Recovery in 3D Scenes/layout.json b/2023/Learning Human Mesh Recovery in 3D Scenes/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..fad928563c7254904c987e3b482ac84fc8c94db7 --- /dev/null +++ b/2023/Learning Human Mesh Recovery in 3D Scenes/layout.json @@ -0,0 +1,10189 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 153, + 103, + 442, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 153, + 103, + 442, + 121 + ], + "spans": [ + { + "bbox": [ + 153, + 103, + 442, + 121 + ], + "type": "text", + "content": "Learning Human Mesh Recovery in 3D Scenes" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 93, + 143, + 500, + 177 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 93, + 143, + 500, + 177 + ], + "spans": [ + { + "bbox": [ + 93, + 143, + 500, + 177 + ], + "type": "text", + "content": "Zehong Shen Zhi Cen Sida Peng Qing Shuai Hujun Bao Xiaowei Zhou† \nState Key Lab of CAD&CG, Zhejiang University" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 143, + 203, + 192, + 216 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 203, + 192, + 216 + ], + "spans": [ + { + "bbox": [ + 143, + 203, + 192, + 216 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 228, + 290, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 228, + 290, + 445 + ], + "spans": [ + { + "bbox": [ + 46, + 228, + 290, + 445 + ], + "type": "text", + "content": "We present a novel method for recovering the absolute pose and shape of a human in a pre-scanned scene given a single image. Unlike previous methods that perform scene-aware mesh optimization, we propose to first estimate absolute position and dense scene contacts with a sparse 3D CNN, and later enhance a pretrained human mesh recovery network by cross-attention with the derived 3D scene cues. Joint learning on images and scene geometry enables our method to reduce the ambiguity caused by depth and occlusion, resulting in more reasonable global postures and contacts. Encoding scene-aware cues in the network also allows the proposed method to be optimization-free, and opens up the opportunity for real-time applications. The experiments show that the proposed network is capable of recovering accurate and physically-plausible meshes by a single forward pass and outperforms state-of-the-art methods in terms of both accuracy and speed. Code is available on our project page: https://zju3dv.github.io/sahmr/." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 493, + 128, + 506 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 493, + 128, + 506 + ], + "spans": [ + { + "bbox": [ + 47, + 493, + 128, + 506 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 513, + 287, + 656 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 513, + 287, + 656 + ], + "spans": [ + { + "bbox": [ + 46, + 513, + 287, + 656 + ], + "type": "text", + "content": "Monocular human mesh recovery (HMR), i.e., estimating pose and shape parameters of a parametric human model from a single image, has gained significant attention in recent years. To better capture and understand human behaviors, many recent works [1-5] propose to address the problem of scene-aware HMR which involves human-scene interaction constraints when recovering human meshes, given the 3D geometry of the scene scanned by range sensors [5-7], as well as the camera pose of the input image relative to the scene, which may enable more applications in video surveillance, household robots, and motion analysis in gyms and clinics." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 657, + 287, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 657, + 287, + 694 + ], + "spans": [ + { + "bbox": [ + 47, + 657, + 287, + 694 + ], + "type": "text", + "content": "Most existing methods propose using scene-aware optimization to fit the human mesh into a pre-scanned scene. 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Comparison between the optimization-based method and the proposed method. Optimization-based methods typically fit a parametric human model iteratively by minimizing 2D reprojection error and scene conflicts. In contrast, the proposed method utilizes a single forward pass of the network to estimate the global position (blue ball), contact scene points (colored scene points), and a scene-aware human mesh. This design leads to improvements in both efficiency and accuracy." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 427, + 311, + 533, + 417 + ], + "blocks": [ + { + "bbox": [ + 427, + 311, + 533, + 417 + ], + "lines": [ + { + "bbox": [ + 427, + 311, + 533, + 417 + ], + "spans": [ + { + "bbox": [ + 427, + 311, + 533, + 417 + ], + "type": "image", + "image_path": "fc60ca6c1f19c0ea866075dfdbe1d088155ccc1e0fe075cbfc598548392ed96b.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 460, + 422, + 498, + 431 + ], + "lines": [ + { + "bbox": [ + 460, + 422, + 498, + 431 + ], + "spans": [ + { + "bbox": [ + 460, + 422, + 498, + 431 + ], + "type": "text", + "content": "Prediction" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 555, + 547, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 555, + 547, + 652 + ], + "spans": [ + { + "bbox": [ + 304, + 555, + 547, + 652 + ], + "type": "text", + "content": "SMPL [8], to minimize scene penetration, chamfer distance of contact regions, and the 3D-2D re-projection error. However, optimization tends to be slow at inference time and is sensitive to initialization and hyperparameters, failing to respond in low-latency applications. As illustrated in Fig. 1, an optimization-based method PROX [5] takes 18.4s to fit a human model into the scene, while the incorrect position and pose still occur." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 653, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 653, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 653, + 547, + 715 + ], + "type": "text", + "content": "Recent works [9-13] propose to recover human mesh with neural networks trained on large-scale datasets [14-17]. Specifically, the networks learn a mapping from an input image to a human mesh in the canonical coordinates. 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Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 63, + 702, + 140, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 702, + 140, + 713 + ], + "spans": [ + { + "bbox": [ + 63, + 702, + 140, + 713 + ], + "type": "text", + "content": "†Corresponding author." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "17038" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 179 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 179 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 179 + ], + "type": "text", + "content": "task still requires post-processing optimization, where the global translation and the human poses are refined in accordance with the given scene. However, the monocular prediction is conditioned on the input image solely, omitting the joint distribution of human pose and scene geometry, and therefore tends to suffer from depth ambiguity and occlusion. As a result, the optimization-based post-processing could be easily deteriorated by the erroneous initial poses and may even worsen the initial prediction." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 180, + 289, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 180, + 289, + 418 + ], + "spans": [ + { + "bbox": [ + 46, + 180, + 289, + 418 + ], + "type": "text", + "content": "In this work, we propose a Scene-Aware Human Mesh Recovery network (SA-HMR), the first learning-based approach that predicts the absolute position and mesh of a human in the scene by a single forward pass. The overall pipeline is illustrated in Fig. 2. Given the input image and scene point cloud, we first use a sparse 3D CNN to estimate dense scene contacts and absolute human position, where the scene contact estimation is treated as a point cloud labeling task, and the human position prediction is presented as a voting vector field refinement task. The predicted dense contact points are centered by the human position and passed to a scene network in the human mesh recovery step. Specifically, we enhance a pretrained monocular HMR network METRO [12] by cross-attention with the proposed scene network in parallel. In this way, SA-HMR learns a joint distribution of human pose and scene geometry, resulting in more reasonable postures, contacts, and global positions, as illustrated in Fig. 1. Learning scene-aware cues in the network also avoids scene-aware optimization as post-processing and achieves fast inference speed." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 419, + 289, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 419, + 289, + 491 + ], + "spans": [ + { + "bbox": [ + 46, + 419, + 289, + 491 + ], + "type": "text", + "content": "We evaluate the proposed method on the RICH [6] and PROX [5] datasets of indoor and outdoor scenes. The experimental results show that SA-HMR is not only effective in recovering absolute positions and meshes that are in accordance with the given scene, but also significantly faster than the optimization-based baselines." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 59, + 491, + 263, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 491, + 263, + 502 + ], + "spans": [ + { + "bbox": [ + 59, + 491, + 263, + 502 + ], + "type": "text", + "content": "In summary, we make the following contributions:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 59, + 510, + 287, + 619 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 59, + 510, + 287, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 510, + 287, + 544 + ], + "spans": [ + { + "bbox": [ + 59, + 510, + 287, + 544 + ], + "type": "text", + "content": "- The first optimization-free framework for scene-aware human mesh recovery from a single image and a prescanned scene." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 59, + 552, + 287, + 588 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 552, + 287, + 588 + ], + "spans": [ + { + "bbox": [ + 59, + 552, + 287, + 588 + ], + "type": "text", + "content": "- The cross-attention design for enhancing a pretrained HMR network with a parallel scene network, enabling joint learning on the human pose and scene geometry." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 59, + 595, + 287, + 619 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 595, + 287, + 619 + ], + "spans": [ + { + "bbox": [ + 59, + 595, + 287, + 619 + ], + "type": "text", + "content": "- Superior performance compared to optimization-based baselines in terms of both accuracy and speed." + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 629, + 134, + 642 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 629, + 134, + 642 + ], + "spans": [ + { + "bbox": [ + 47, + 629, + 134, + 642 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 654, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 287, + 715 + ], + "type": "text", + "content": "Monocular Human Mesh Recovery. Most existing approaches formulate the monocular HMR task as recovering the mesh of statistical human body models, e.g. SMPL and SMPL-X [8, 18, 19], where recent works can be divided into optimization-based and learning-based approaches." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 72, + 545, + 203 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 203 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 203 + ], + "type": "text", + "content": "The optimization-based approaches fit a parametric human model by minimizing the 3D-2D re-projection error of body joints and energy terms of heuristic priors iteratively, which are represented by SMPLify [20] that fits SMPL [8]. More recently, SMPLify-X [19] proposes a variational pose prior and fits a more expressive SMPL-X. PoseNDF [21] proposes to represent the manifold of plausible human poses with a neural field. While optimization-based methods are general in their mathematical formulation, they are usually sensitive to hyperparameters and require much time for inference." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 206, + 545, + 385 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 206, + 545, + 385 + ], + "spans": [ + { + "bbox": [ + 304, + 206, + 545, + 385 + ], + "type": "text", + "content": "The learning-based methods utilize deep neural networks to predict either the parameters [9, 10, 22, 23] or the mesh vertices [11-13] of the SMPL model. HMR [9] is the pioneering work in predicting SMPL parameters, and SPIN [10] improves upon it using an optimization loop. For predicting SMPL mesh vertices, GraphCMR [11] deforms a template human mesh using graph neural network, while METRO [12] uses transformers, and [13] uses graph hierarchy to further improve the performance. However, for scene-aware HMR, the vertices of the human and scene meshes in contact are close in Euclidean space, making methods that regress parameters unsuitable due to errors that accumulate along the kinematic chains. Therefore, the proposed method is built on the works that predict mesh vertices. More details can be found in Sec. 3." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 392, + 545, + 561 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 392, + 545, + 561 + ], + "spans": [ + { + "bbox": [ + 304, + 392, + 545, + 561 + ], + "type": "text", + "content": "Scene-aware Human Mesh Recovery. PROX [5] is a seminal work that uses scene constraints to reduce the depth and occlusion ambiguity in monocular HMR. It achieves this by adding two energy terms of human-scene contact and penetration in the optimization process [19]. In addition, scene-aware pose generative models [2, 24] can also be used as prior terms in the scene-aware HMR task. Other recent works in this area include MoCapDeform [4], which considers deformable scene objects, LEMO [1], which uses temporal information, and HULC [3], which uses consecutive frames and dense contacts prediction on both the scene and human body. In contrast to these works, the proposed method is optimization-free and requires only a single forward pass." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 563, + 545, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 563, + 545, + 635 + ], + "spans": [ + { + "bbox": [ + 304, + 563, + 545, + 635 + ], + "type": "text", + "content": "In a broader topic of capturing humans in a scene-aware manner, [25-27] propose using a simulator and dynamic model, where a pre-defined agent is controlled to interact with the scene, and [28,29] consider human-object arrangement by first predicting the human and object and then performing global optimization." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "content": "Attention in Transformers. Attention is a key mechanism in Transformers [30]. It allows a set of query features to fuse the most relevant information from another set of key-value features. When query and key-value features come from the same source, it is called self-attention, otherwise cross-attention. In HMR, METRO [12] uses self-attention to re" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "17039" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 100, + 278, + 208 + ], + "blocks": [ + { + "bbox": [ + 82, + 79, + 256, + 91 + ], + "lines": [ + { + "bbox": [ + 82, + 79, + 256, + 91 + ], + "spans": [ + { + "bbox": [ + 82, + 79, + 256, + 91 + ], + "type": "text", + "content": "1. Human Root and Scene Contacts" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 61, + 100, + 278, + 208 + ], + "lines": [ + { + "bbox": [ + 61, + 100, + 278, + 208 + ], + "spans": [ + { + "bbox": [ + 61, + 100, + 278, + 208 + ], + "type": "image", + "image_path": "099d627c6371e6f265ecdb14d5cbd081cb6e5e1014f1544beefc162ca88ddb90.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 280, + 95, + 531, + 208 + ], + "blocks": [ + { + "bbox": [ + 309, + 79, + 501, + 92 + ], + "lines": [ + { + "bbox": [ + 309, + 79, + 501, + 92 + ], + "spans": [ + { + "bbox": [ + 309, + 79, + 501, + 92 + ], + "type": "text", + "content": "2. Scene-aware Human Mesh Recovery" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 280, + 95, + 531, + 208 + ], + "lines": [ + { + "bbox": [ + 280, + 95, + 531, + 208 + ], + "spans": [ + { + "bbox": [ + 280, + 95, + 531, + 208 + ], + "type": "image", + "image_path": "1344a1eae09f2a30ed5ac3fb1109504220a94f08a5adf1ec816b0a392fd9cffe.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 218, + 547, + 275 + ], + "lines": [ + { + "bbox": [ + 46, + 218, + 547, + 275 + ], + "spans": [ + { + "bbox": [ + 46, + 218, + 547, + 275 + ], + "type": "text", + "content": "Figure 2. Overview of the proposed SA-HMR. 1. The human root and scene contact estimation module (Sec. 3.2) that first predicts the initial root and then refines the root with 3D scene cues using a sparse 3D CNN. The module also predicts contact labels [5] for each scene point. Please refer to Sec. 3.2 for a detailed definition of the 3D feature construction module. 2. The scene-aware human mesh recovery module (Sec. 3.3) that enhances the pretrained METRO [12] network with a parallel scene network. The scene network takes the predicted contact scene points as input, and uses cross-attention to pass messages to the intermediate features of the METRO network." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 295, + 287, + 366 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 295, + 287, + 366 + ], + "spans": [ + { + "bbox": [ + 46, + 295, + 287, + 366 + ], + "type": "text", + "content": "duce occlusion ambiguity by establishing non-local feature exchange between visible and invisible parts of a template human mesh. In feature matching, SuperGlue [31] uses cross-attention to make the corresponding image features more similar. Predator [32] uses cross-attention in matching two sets of point clouds." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 367, + 287, + 416 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 367, + 287, + 416 + ], + "spans": [ + { + "bbox": [ + 47, + 367, + 287, + 416 + ], + "type": "text", + "content": "Inspired by feature matching, the proposed method uses cross-attention to potentially make the features of the human and scene that are in contact more similar, resulting in better contact and more reasonable postures." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 428, + 107, + 441 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 428, + 107, + 441 + ], + "spans": [ + { + "bbox": [ + 47, + 428, + 107, + 441 + ], + "type": "text", + "content": "3. Methods" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 449, + 287, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 449, + 287, + 521 + ], + "spans": [ + { + "bbox": [ + 46, + 449, + 287, + 521 + ], + "type": "text", + "content": "Given a calibrated image and a pre-scanned scene point cloud (Sec. 3.1), SA-HMR first estimates the absolute human root position and scene contacts (Sec. 3.2), and then recovers the human mesh with the contact points by enhancing a pretrained METRO network (Sec. 3.3). An overview of the proposed method is presented in Fig. 2." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 530, + 133, + 542 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 530, + 133, + 542 + ], + "spans": [ + { + "bbox": [ + 47, + 530, + 133, + 542 + ], + "type": "text", + "content": "3.1. Preliminaries" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 553, + 287, + 649 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 553, + 287, + 649 + ], + "spans": [ + { + "bbox": [ + 46, + 553, + 287, + 649 + ], + "type": "text", + "content": "Human Representation. We use SMPL [8] as the human representation. The SMPL is a parametric model that uses the body joint rotations, root translation, and body shape coefficients to compute the body mesh. Following [11, 12], we directly predict the SMPL mesh vertices " + }, + { + "bbox": [ + 46, + 553, + 287, + 649 + ], + "type": "inline_equation", + "content": "V = \\mathbb{R}^{6890 \\times 3}" + }, + { + "bbox": [ + 46, + 553, + 287, + 649 + ], + "type": "text", + "content": ", and use H36M [14] joint regression matrix " + }, + { + "bbox": [ + 46, + 553, + 287, + 649 + ], + "type": "inline_equation", + "content": "M \\in \\mathbb{R}^{14 \\times 6890}" + }, + { + "bbox": [ + 46, + 553, + 287, + 649 + ], + "type": "text", + "content": " to compute 3D joints " + }, + { + "bbox": [ + 46, + 553, + 287, + 649 + ], + "type": "inline_equation", + "content": "J \\in \\mathbb{R}^{14 \\times 3}" + }, + { + "bbox": [ + 46, + 553, + 287, + 649 + ], + "type": "text", + "content": " from the vertices for quantitative evaluation, " + }, + { + "bbox": [ + 46, + 553, + 287, + 649 + ], + "type": "inline_equation", + "content": "J = MV" + }, + { + "bbox": [ + 46, + 553, + 287, + 649 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 654, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 654, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 654, + 287, + 715 + ], + "type": "text", + "content": "Scene and Image Representation. We assume that the scene is pre-scanned with range sensors, as in RICH [6] and PROX [5], and the image is calibrated and localized in the scene, i.e. with known intrinsic and extrinsic parameters " + }, + { + "bbox": [ + 47, + 654, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\{(f,c_x,c_y),(R_c,t_c)\\}" + }, + { + "bbox": [ + 47, + 654, + 287, + 715 + ], + "type": "text", + "content": ". Following METRO [12], we detect" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 295, + 545, + 355 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 295, + 545, + 355 + ], + "spans": [ + { + "bbox": [ + 304, + 295, + 545, + 355 + ], + "type": "text", + "content": "a squared bounding box around the target human and resize the cropped region as the input image " + }, + { + "bbox": [ + 304, + 295, + 545, + 355 + ], + "type": "inline_equation", + "content": "I \\in \\mathbb{R}^{224 \\times 224 \\times 3}" + }, + { + "bbox": [ + 304, + 295, + 545, + 355 + ], + "type": "text", + "content": ". Based on the camera parameters and the bounding box, we select scene points that fall within the visual frustum as the input scene point cloud " + }, + { + "bbox": [ + 304, + 295, + 545, + 355 + ], + "type": "inline_equation", + "content": "S \\in \\mathbb{R}^{N_S \\times 3}" + }, + { + "bbox": [ + 304, + 295, + 545, + 355 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 358, + 546, + 431 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 358, + 546, + 431 + ], + "spans": [ + { + "bbox": [ + 304, + 358, + 546, + 431 + ], + "type": "text", + "content": "Human-Scene Contact. Following PROX [5], we use seven regions of the SMPL mesh that are most likely to be contacted. The details are provided in the supplementary material. Using these seven categories and one for not being in contact, we perform a segmentation task on the scene point cloud." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 437, + 484, + 449 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 437, + 484, + 449 + ], + "spans": [ + { + "bbox": [ + 306, + 437, + 484, + 449 + ], + "type": "text", + "content": "3.2. Human Root and Scene Contacts" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 455, + 545, + 588 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 455, + 545, + 588 + ], + "spans": [ + { + "bbox": [ + 304, + 455, + 545, + 588 + ], + "type": "text", + "content": "Given an image " + }, + { + "bbox": [ + 304, + 455, + 545, + 588 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 304, + 455, + 545, + 588 + ], + "type": "text", + "content": " bounding the human, we propose using a 2D convolutional neural network (CNN) to extract image features " + }, + { + "bbox": [ + 304, + 455, + 545, + 588 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 304, + 455, + 545, + 588 + ], + "type": "text", + "content": " and predict the initial human root " + }, + { + "bbox": [ + 304, + 455, + 545, + 588 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 304, + 455, + 545, + 588 + ], + "type": "text", + "content": ". Based on the scene points " + }, + { + "bbox": [ + 304, + 455, + 545, + 588 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 455, + 545, + 588 + ], + "type": "text", + "content": ", we unproject the image features " + }, + { + "bbox": [ + 304, + 455, + 545, + 588 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 304, + 455, + 545, + 588 + ], + "type": "text", + "content": " to 3D, resulting in " + }, + { + "bbox": [ + 304, + 455, + 545, + 588 + ], + "type": "inline_equation", + "content": "\\hat{F}" + }, + { + "bbox": [ + 304, + 455, + 545, + 588 + ], + "type": "text", + "content": ". Additionally, we calculate point-wise offset vectors " + }, + { + "bbox": [ + 304, + 455, + 545, + 588 + ], + "type": "inline_equation", + "content": "O" + }, + { + "bbox": [ + 304, + 455, + 545, + 588 + ], + "type": "text", + "content": " that point from a voxelized scene point cloud to the initial root. By taking " + }, + { + "bbox": [ + 304, + 455, + 545, + 588 + ], + "type": "inline_equation", + "content": "\\hat{F}" + }, + { + "bbox": [ + 304, + 455, + 545, + 588 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 455, + 545, + 588 + ], + "type": "inline_equation", + "content": "O" + }, + { + "bbox": [ + 304, + 455, + 545, + 588 + ], + "type": "text", + "content": " as input, a sparse 3D CNN predicts the segmentation of scene contacts and the refined offsets, which are then converted to the refined human root " + }, + { + "bbox": [ + 304, + 455, + 545, + 588 + ], + "type": "inline_equation", + "content": "r^{*}" + }, + { + "bbox": [ + 304, + 455, + 545, + 588 + ], + "type": "text", + "content": ". An overview of this process is presented in the left column of Fig. 2." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 590, + 546, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 590, + 546, + 687 + ], + "spans": [ + { + "bbox": [ + 304, + 590, + 546, + 687 + ], + "type": "text", + "content": "Initial Root. We predict the initial root " + }, + { + "bbox": [ + 304, + 590, + 546, + 687 + ], + "type": "inline_equation", + "content": "r = (X, Y, Z)" + }, + { + "bbox": [ + 304, + 590, + 546, + 687 + ], + "type": "text", + "content": " in a 2.5D manner following SMAP [33]. Specifically, we use a CNN to predict the 2D heatmap and a normalized depth map of the root. Then, the 2D position " + }, + { + "bbox": [ + 304, + 590, + 546, + 687 + ], + "type": "inline_equation", + "content": "(x, y)" + }, + { + "bbox": [ + 304, + 590, + 546, + 687 + ], + "type": "text", + "content": " is obtained by applying argmax to the heatmap, and the corresponding normalized depth value " + }, + { + "bbox": [ + 304, + 590, + 546, + 687 + ], + "type": "inline_equation", + "content": "\\tilde{Z}" + }, + { + "bbox": [ + 304, + 590, + 546, + 687 + ], + "type": "text", + "content": " is retrieved from the depth map. Finally, using the intrinsic parameters " + }, + { + "bbox": [ + 304, + 590, + 546, + 687 + ], + "type": "inline_equation", + "content": "f, c_x, c_y" + }, + { + "bbox": [ + 304, + 590, + 546, + 687 + ], + "type": "text", + "content": " and image size " + }, + { + "bbox": [ + 304, + 590, + 546, + 687 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 304, + 590, + 546, + 687 + ], + "type": "text", + "content": ", the 3D root position is computed:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 405, + 693, + 545, + 717 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 405, + 693, + 545, + 717 + ], + "spans": [ + { + "bbox": [ + 405, + 693, + 545, + 717 + ], + "type": "interline_equation", + "content": "Z = \\tilde {Z} \\frac {f}{w} \\tag {1}", + "image_path": "d0c045856e042c870a6d507808e7a175a995568aebf2345c747a37966a5c054c.jpg" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "17040" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 72, + 70, + 263, + 175 + ], + "blocks": [ + { + "bbox": [ + 72, + 70, + 263, + 175 + ], + "lines": [ + { + "bbox": [ + 72, + 70, + 263, + 175 + ], + "spans": [ + { + "bbox": [ + 72, + 70, + 263, + 175 + ], + "type": "image", + "image_path": "9c4f56bb248248a8ca505d924665a8e26221b1c570ae623579dab2c31146c233.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 185, + 288, + 231 + ], + "lines": [ + { + "bbox": [ + 46, + 185, + 288, + 231 + ], + "spans": [ + { + "bbox": [ + 46, + 185, + 288, + 231 + ], + "type": "text", + "content": "Figure 3. 3D feature construction. We voxelize a scene point cloud to a sparse volume. The initial feature of each voxel consists of two parts, which are the offset vector pointing from the voxel center to the human root and the unprojected image features." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 93, + 246, + 287, + 270 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 93, + 246, + 287, + 270 + ], + "spans": [ + { + "bbox": [ + 93, + 246, + 287, + 270 + ], + "type": "interline_equation", + "content": "X = \\frac {x - c _ {x}}{f} \\cdot Z, \\quad Y = \\frac {y - c _ {y}}{f} \\cdot Z \\tag {2}", + "image_path": "2ed6a5564f2a1a116a9e6652af1c8f1464c30389ff425ab3b998b8ca3f3a1206.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 273, + 287, + 321 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 273, + 287, + 321 + ], + "spans": [ + { + "bbox": [ + 46, + 273, + 287, + 321 + ], + "type": "text", + "content": "From our observation, estimating " + }, + { + "bbox": [ + 46, + 273, + 287, + 321 + ], + "type": "inline_equation", + "content": "(x,y)" + }, + { + "bbox": [ + 46, + 273, + 287, + 321 + ], + "type": "text", + "content": " achieves good results with a mean squared error of fewer than two pixels across datasets. However, estimating " + }, + { + "bbox": [ + 46, + 273, + 287, + 321 + ], + "type": "inline_equation", + "content": "\\tilde{Z}" + }, + { + "bbox": [ + 46, + 273, + 287, + 321 + ], + "type": "text", + "content": " is relatively challenging, possibly due to the variations in human shapes." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 324, + 287, + 360 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 324, + 287, + 360 + ], + "spans": [ + { + "bbox": [ + 46, + 324, + 287, + 360 + ], + "type": "text", + "content": "3D Feature Construction. Based on the initial root " + }, + { + "bbox": [ + 46, + 324, + 287, + 360 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 46, + 324, + 287, + 360 + ], + "type": "text", + "content": " and image features " + }, + { + "bbox": [ + 46, + 324, + 287, + 360 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 46, + 324, + 287, + 360 + ], + "type": "text", + "content": ", we construct the 3D features on the voxelized scene point cloud, which is illustrated in Fig. 3." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 361, + 287, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 361, + 287, + 443 + ], + "spans": [ + { + "bbox": [ + 46, + 361, + 287, + 443 + ], + "type": "text", + "content": "First, we select regions of interest around the initial root " + }, + { + "bbox": [ + 46, + 361, + 287, + 443 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 46, + 361, + 287, + 443 + ], + "type": "text", + "content": " in the point cloud. Specifically, we treat " + }, + { + "bbox": [ + 46, + 361, + 287, + 443 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 46, + 361, + 287, + 443 + ], + "type": "text", + "content": " as an anchor and keep points within a radius " + }, + { + "bbox": [ + 46, + 361, + 287, + 443 + ], + "type": "inline_equation", + "content": "\\gamma_1" + }, + { + "bbox": [ + 46, + 361, + 287, + 443 + ], + "type": "text", + "content": ". Since " + }, + { + "bbox": [ + 46, + 361, + 287, + 443 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 46, + 361, + 287, + 443 + ], + "type": "text", + "content": " has more uncertainty than " + }, + { + "bbox": [ + 46, + 361, + 287, + 443 + ], + "type": "inline_equation", + "content": "(x,y)" + }, + { + "bbox": [ + 46, + 361, + 287, + 443 + ], + "type": "text", + "content": ", we sample two additional anchors along the z-axis, whose distance to " + }, + { + "bbox": [ + 46, + 361, + 287, + 443 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 46, + 361, + 287, + 443 + ], + "type": "text", + "content": " is " + }, + { + "bbox": [ + 46, + 361, + 287, + 443 + ], + "type": "inline_equation", + "content": "\\gamma_2" + }, + { + "bbox": [ + 46, + 361, + 287, + 443 + ], + "type": "text", + "content": ". Next, we construct a sparse volume " + }, + { + "bbox": [ + 46, + 361, + 287, + 443 + ], + "type": "inline_equation", + "content": "\\bar{S}" + }, + { + "bbox": [ + 46, + 361, + 287, + 443 + ], + "type": "text", + "content": " by voxelizing these points with voxel size " + }, + { + "bbox": [ + 46, + 361, + 287, + 443 + ], + "type": "inline_equation", + "content": "s_{vox}" + }, + { + "bbox": [ + 46, + 361, + 287, + 443 + ], + "type": "text", + "content": ", where the center of each voxel is denoted as " + }, + { + "bbox": [ + 46, + 361, + 287, + 443 + ], + "type": "inline_equation", + "content": "\\bar{s}_i" + }, + { + "bbox": [ + 46, + 361, + 287, + 443 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 445, + 287, + 480 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 445, + 287, + 480 + ], + "spans": [ + { + "bbox": [ + 47, + 445, + 287, + 480 + ], + "type": "text", + "content": "For each voxel " + }, + { + "bbox": [ + 47, + 445, + 287, + 480 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 47, + 445, + 287, + 480 + ], + "type": "text", + "content": ", the feature consists of the offset vector " + }, + { + "bbox": [ + 47, + 445, + 287, + 480 + ], + "type": "inline_equation", + "content": "o_i" + }, + { + "bbox": [ + 47, + 445, + 287, + 480 + ], + "type": "text", + "content": " and the unprojected image feature " + }, + { + "bbox": [ + 47, + 445, + 287, + 480 + ], + "type": "inline_equation", + "content": "\\hat{f}_i" + }, + { + "bbox": [ + 47, + 445, + 287, + 480 + ], + "type": "text", + "content": ". Specifically, " + }, + { + "bbox": [ + 47, + 445, + 287, + 480 + ], + "type": "inline_equation", + "content": "o_i" + }, + { + "bbox": [ + 47, + 445, + 287, + 480 + ], + "type": "text", + "content": " is a vector pointing from the voxel center to the human root:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 141, + 488, + 287, + 499 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 488, + 287, + 499 + ], + "spans": [ + { + "bbox": [ + 141, + 488, + 287, + 499 + ], + "type": "interline_equation", + "content": "o _ {i} = r - \\bar {s} _ {i} \\tag {3}", + "image_path": "2669e94cd862d137c52567b616a92fadf7c2cefc47c54e030c8f9469292451e2.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 506, + 287, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 506, + 287, + 542 + ], + "spans": [ + { + "bbox": [ + 46, + 506, + 287, + 542 + ], + "type": "inline_equation", + "content": "\\hat{f}" + }, + { + "bbox": [ + 46, + 506, + 287, + 542 + ], + "type": "text", + "content": " is computed by projecting voxel center " + }, + { + "bbox": [ + 46, + 506, + 287, + 542 + ], + "type": "inline_equation", + "content": "\\bar{s}_i" + }, + { + "bbox": [ + 46, + 506, + 287, + 542 + ], + "type": "text", + "content": " onto the image using camera parameters and bilinearly sampling the image feature map " + }, + { + "bbox": [ + 46, + 506, + 287, + 542 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 46, + 506, + 287, + 542 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 546, + 287, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 546, + 287, + 629 + ], + "spans": [ + { + "bbox": [ + 46, + 546, + 287, + 629 + ], + "type": "text", + "content": "Estimating Refined Root and Scene Contacts. We use sparse 3D CNN [34] to process the constructed 3D features and learn to improve the root estimation and predict the scene contacts. Specifically, the output of each voxel includes an updated offset vector " + }, + { + "bbox": [ + 46, + 546, + 287, + 629 + ], + "type": "inline_equation", + "content": "o_i^*" + }, + { + "bbox": [ + 46, + 546, + 287, + 629 + ], + "type": "text", + "content": ", confidence " + }, + { + "bbox": [ + 46, + 546, + 287, + 629 + ], + "type": "inline_equation", + "content": "c_i" + }, + { + "bbox": [ + 46, + 546, + 287, + 629 + ], + "type": "text", + "content": ", and segmentation indicating the contact category. We compute the refined root " + }, + { + "bbox": [ + 46, + 546, + 287, + 629 + ], + "type": "inline_equation", + "content": "r^*" + }, + { + "bbox": [ + 46, + 546, + 287, + 629 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 118, + 635, + 287, + 659 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 118, + 635, + 287, + 659 + ], + "spans": [ + { + "bbox": [ + 118, + 635, + 287, + 659 + ], + "type": "interline_equation", + "content": "r ^ {*} = \\sum_ {i} c _ {i} \\cdot \\left(o _ {i} ^ {*} + \\bar {s} _ {i}\\right). \\tag {4}", + "image_path": "e378c7b13deca120105d2c3e61c59b52bcad27c8a98edb039e1b7ec4074f9bf4.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "content": "There are 8 categories of contact points, including 7 most probable regions on the body that would be contacted [5] and 1 category of not being in contact. We take the category of the highest score as the prediction for the voxel and" + } + ] + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 312, + 69, + 531, + 287 + ], + "blocks": [ + { + "bbox": [ + 312, + 69, + 531, + 287 + ], + "lines": [ + { + "bbox": [ + 312, + 69, + 531, + 287 + ], + "spans": [ + { + "bbox": [ + 312, + 69, + 531, + 287 + ], + "type": "image", + "image_path": "65c2791949dd0be2029cae1f86dc4c878a3b9f06a416235b0672e7d8c902d622.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 295, + 545, + 361 + ], + "lines": [ + { + "bbox": [ + 305, + 295, + 545, + 361 + ], + "spans": [ + { + "bbox": [ + 305, + 295, + 545, + 361 + ], + "type": "text", + "content": "Figure 4. Enhancing METRO with a parallel network. The orange parts are the original METRO [12] network, where the residual connection and positional encoding are omitted for simplicity. The blue parts are the proposed parallel network which takes predicted contact scene points as input. The yellow parts indicate feature interaction between METRO and the parallel network." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 384, + 545, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 384, + 545, + 422 + ], + "spans": [ + { + "bbox": [ + 305, + 384, + 545, + 422 + ], + "type": "text", + "content": "set the dense point cloud belonging to the voxel with that category. The contact points " + }, + { + "bbox": [ + 305, + 384, + 545, + 422 + ], + "type": "inline_equation", + "content": "\\hat{S}_{seg3d} \\in \\mathbb{R}^{\\hat{N}_S \\times 3}" + }, + { + "bbox": [ + 305, + 384, + 545, + 422 + ], + "type": "text", + "content": " serve as the input for the mesh recovery module." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 432, + 500, + 445 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 432, + 500, + 445 + ], + "spans": [ + { + "bbox": [ + 306, + 432, + 500, + 445 + ], + "type": "text", + "content": "3.3. Scene-aware Human Mesh Recovery" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 451, + 545, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 451, + 545, + 559 + ], + "spans": [ + { + "bbox": [ + 304, + 451, + 545, + 559 + ], + "type": "text", + "content": "Since the training data of scene-aware human mesh recovery is limited, we build our model upon a network named METRO [12] that is pre-trained on large-scale data of monocular human mesh recovery. METRO processes feature based on the self-attention mechanism, and our approach enhances METRO by adding a parallel scene network, which provides a cross-attention-based mechanism that enables METRO to notice important scene details and achieve scene-aware human mesh recovery." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 563, + 545, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 563, + 545, + 635 + ], + "spans": [ + { + "bbox": [ + 304, + 563, + 545, + 635 + ], + "type": "text", + "content": "METRO consists of a CNN backbone and multiple Transformer encoders. It first extracts global CNN features, then combines the feature to the vertices of a zero posed SMPL mesh, and finally predicts a posed mesh with shape through the transformers. The part of the transformer is illustrated in the orange part of Fig. 4." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 640, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 640, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 640, + 545, + 689 + ], + "type": "text", + "content": "Enhancing METRO with Cross-Attention. We improve METRO with a scene network, which makes the predicted human vertices to be close to the corresponding contact scene points " + }, + { + "bbox": [ + 304, + 640, + 545, + 689 + ], + "type": "inline_equation", + "content": "\\hat{S}_{seg3d}" + }, + { + "bbox": [ + 304, + 640, + 545, + 689 + ], + "type": "text", + "content": " (Sec. 3.2)." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 689, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 712 + ], + "type": "text", + "content": "As illustrated in Fig. 4, we add a parallel network, which has a similar architecture as the transformer of METRO," + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17041" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 70, + 127, + 203 + ], + "blocks": [ + { + "bbox": [ + 61, + 70, + 127, + 203 + ], + "lines": [ + { + "bbox": [ + 61, + 70, + 127, + 203 + ], + "spans": [ + { + "bbox": [ + 61, + 70, + 127, + 203 + ], + "type": "image", + "image_path": "52c52e3d1e59a88b64ba968f1f625c9b54cc63dfa00acc5a85974ce5bacdf5b8.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 90, + 204, + 97, + 211 + ], + "lines": [ + { + "bbox": [ + 90, + 204, + 97, + 211 + ], + "spans": [ + { + "bbox": [ + 90, + 204, + 97, + 211 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 129, + 70, + 196, + 202 + ], + "blocks": [ + { + "bbox": [ + 129, + 70, + 196, + 202 + ], + "lines": [ + { + "bbox": [ + 129, + 70, + 196, + 202 + ], + "spans": [ + { + "bbox": [ + 129, + 70, + 196, + 202 + ], + "type": "image", + "image_path": "46fa9aad8b9fd7b602a2235cc527bf00715c49bb2400fc499929e272cbf20f56.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 159, + 204, + 167, + 211 + ], + "lines": [ + { + "bbox": [ + 159, + 204, + 167, + 211 + ], + "spans": [ + { + "bbox": [ + 159, + 204, + 167, + 211 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 198, + 70, + 274, + 203 + ], + "blocks": [ + { + "bbox": [ + 198, + 70, + 274, + 203 + ], + "lines": [ + { + "bbox": [ + 198, + 70, + 274, + 203 + ], + "spans": [ + { + "bbox": [ + 198, + 70, + 274, + 203 + ], + "type": "image", + "image_path": "d05cdefacc22f054e018275653bef8ef306d3842d9561b63d4f134fa48aae402.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 228, + 204, + 235, + 211 + ], + "lines": [ + { + "bbox": [ + 228, + 204, + 235, + 211 + ], + "spans": [ + { + "bbox": [ + 228, + 204, + 235, + 211 + ], + "type": "text", + "content": "(c)" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 221, + 289, + 321 + ], + "lines": [ + { + "bbox": [ + 46, + 221, + 289, + 321 + ], + "spans": [ + { + "bbox": [ + 46, + 221, + 289, + 321 + ], + "type": "text", + "content": "Figure 5. Visualization of the cross-attention from a body vertex (blue point) to the predicted dense scene contacts (white points). (a) The image and the predicted dense scene contacts. (b) The hand vertex is in contact with the scene according to the image, and its feature is similar to the nearby scene point features, enabling the final vertex prediction to be close to the corresponding scene surface. (c) The arm vertex is not in contact with the scene, where feature similarities tend to be evenly distributed. The feature similarities are normalized to the same range of " + }, + { + "bbox": [ + 46, + 221, + 289, + 321 + ], + "type": "inline_equation", + "content": "0 \\rightarrow 1" + }, + { + "bbox": [ + 46, + 221, + 289, + 321 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 342, + 287, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 342, + 287, + 545 + ], + "spans": [ + { + "bbox": [ + 46, + 342, + 287, + 545 + ], + "type": "text", + "content": "to extract features of scene contact points and output the point positions like an autoencoder. Specifically, we first use METRO's CNN backbone to extract the image feature and map it to a set of vertex tokens by a fully-connected layer. In METRO, these tokens are directly concatenated with the positions of initial human vertices. However, the number of scene contact points is not the same as the tokens', and there is no one-to-one correspondence between them. To resolve this issue, we perform the average pooling to vertex tokens based on the contact categories defined on the SMPL mesh vertices [5], resulting in 7 tokens. Then, we append each scene contact point with the corresponding aggregated token based on the predicted category in Sec. 3.2. Intuitively, this helps the cross-attention to focus on the semantically corresponding parts. To be invariant to the global translation, the scene contact points are zero-centered by the predicted root " + }, + { + "bbox": [ + 46, + 342, + 287, + 545 + ], + "type": "inline_equation", + "content": "r^*" + }, + { + "bbox": [ + 46, + 342, + 287, + 545 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 545, + 287, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 287, + 689 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 287, + 689 + ], + "type": "text", + "content": "Motivated by recent feature matching methods [31, 32], we propose to use cross-attention to pass features from scene contact points to human vertices. The cross-attention and self-attention share the same underlying mechanism, both of which first compute the similarity of query and key, and then use the weighted sum to fuse features. When the query and key are from the same source features, it is self-attention, and otherwise is cross-attention. In practice, we use linear attention operator [35] to improve efficiency. A visualization of cross attention over human vertices and scene points is in Fig. 5. The detailed network architecture is provided in the supplementary material." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "type": "text", + "content": "Note that, we use a weight-sharing regressor layer with METRO, which regresses from point-wise features to point" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": "position " + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "inline_equation", + "content": "(x,y,z)" + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": ". Therefore, to get a similar " + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "inline_equation", + "content": "(x,y,z)" + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": ", the input features of this layer should also be similar. This strategy implicitly aligns the features of human vertices and scene points when their final predictions are near in 3D space, thus facilitating the cross-attention to find correspondences between human vertices and scene points." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 152, + 394, + 164 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 152, + 394, + 164 + ], + "spans": [ + { + "bbox": [ + 306, + 152, + 394, + 164 + ], + "type": "text", + "content": "3.4. Training Loss" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 174, + 545, + 198 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 174, + 545, + 198 + ], + "spans": [ + { + "bbox": [ + 305, + 174, + 545, + 198 + ], + "type": "text", + "content": "Root and Contact. The loss function " + }, + { + "bbox": [ + 305, + 174, + 545, + 198 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{RC}}" + }, + { + "bbox": [ + 305, + 174, + 545, + 198 + ], + "type": "text", + "content": " for the root and contact estimation is defined as:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 321, + 207, + 545, + 220 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 207, + 545, + 220 + ], + "spans": [ + { + "bbox": [ + 321, + 207, + 545, + 220 + ], + "type": "interline_equation", + "content": "L _ {\\mathrm {R C}} = L _ {\\mathrm {R 2 D}} + w _ {\\mathrm {R Z}} \\cdot L _ {\\mathrm {R Z}} + L _ {\\mathrm {R O V}} + L _ {\\mathrm {R 3 D}} + L _ {\\mathrm {C}} \\tag {5}", + "image_path": "a939ccb05ba5f6c51b7dd192fb387cf20da6327aebe4b65b0100a623d6e52d35.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 229, + 545, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 229, + 545, + 300 + ], + "spans": [ + { + "bbox": [ + 305, + 229, + 545, + 300 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 229, + 545, + 300 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{R2D}}" + }, + { + "bbox": [ + 305, + 229, + 545, + 300 + ], + "type": "text", + "content": " is the MSE loss on the root heatmap; " + }, + { + "bbox": [ + 305, + 229, + 545, + 300 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{RZ}}" + }, + { + "bbox": [ + 305, + 229, + 545, + 300 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 229, + 545, + 300 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{ROV}}" + }, + { + "bbox": [ + 305, + 229, + 545, + 300 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 305, + 229, + 545, + 300 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{R3D}}" + }, + { + "bbox": [ + 305, + 229, + 545, + 300 + ], + "type": "text", + "content": " are the L1 losses on the relative depth, offset vectors, and the 3D root, respectively; " + }, + { + "bbox": [ + 305, + 229, + 545, + 300 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{C}}" + }, + { + "bbox": [ + 305, + 229, + 545, + 300 + ], + "type": "text", + "content": " is the cross-entropy loss for contact categories of voxel points, where we additionally train an auxiliary task of 2D contact segmentation similar to the voxel points." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 304, + 545, + 328 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 304, + 545, + 328 + ], + "spans": [ + { + "bbox": [ + 305, + 304, + 545, + 328 + ], + "type": "text", + "content": "Human Mesh Recovery. The loss function " + }, + { + "bbox": [ + 305, + 304, + 545, + 328 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{HMR}}" + }, + { + "bbox": [ + 305, + 304, + 545, + 328 + ], + "type": "text", + "content": " for the mesh recovery is defined as:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 359, + 338, + 545, + 350 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 359, + 338, + 545, + 350 + ], + "spans": [ + { + "bbox": [ + 359, + 338, + 545, + 350 + ], + "type": "interline_equation", + "content": "L _ {\\mathrm {H M R}} = L _ {\\mathrm {V}} + L _ {\\mathrm {J}} + L _ {\\mathrm {C P}} + L _ {\\mathrm {G V}} \\tag {6}", + "image_path": "aa50193f3b64f5fa67cc75af9ccca56b691daa6dc001ea96ec384d6c8175e2e4.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 360, + 545, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 360, + 545, + 407 + ], + "spans": [ + { + "bbox": [ + 304, + 360, + 545, + 407 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 360, + 545, + 407 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{V}}" + }, + { + "bbox": [ + 304, + 360, + 545, + 407 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 360, + 545, + 407 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{J}}" + }, + { + "bbox": [ + 304, + 360, + 545, + 407 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 360, + 545, + 407 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{CP}}" + }, + { + "bbox": [ + 304, + 360, + 545, + 407 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 360, + 545, + 407 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{GV}}" + }, + { + "bbox": [ + 304, + 360, + 545, + 407 + ], + "type": "text", + "content": " are the L1 losses on the translation-aligned human vertices, human joints, reconstructed contact points, and global human vertices, respectively. More details are in the supplementary material." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 415, + 440, + 427 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 415, + 440, + 427 + ], + "spans": [ + { + "bbox": [ + 306, + 415, + 440, + 427 + ], + "type": "text", + "content": "3.5. Implementation Details" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 434, + 545, + 589 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 434, + 545, + 589 + ], + "spans": [ + { + "bbox": [ + 304, + 434, + 545, + 589 + ], + "type": "text", + "content": "We train two modules separately. For the root and contact module, the CNN is HRNet-stride-4 [36] with METRO initialization, the sparse 3D CNN is SPVCNN [34, 37] with random initialization. We use linear layers to align intermediate feature dimensions. " + }, + { + "bbox": [ + 304, + 434, + 545, + 589 + ], + "type": "inline_equation", + "content": "\\gamma_{1}" + }, + { + "bbox": [ + 304, + 434, + 545, + 589 + ], + "type": "text", + "content": " is " + }, + { + "bbox": [ + 304, + 434, + 545, + 589 + ], + "type": "inline_equation", + "content": "1.25\\mathrm{m}" + }, + { + "bbox": [ + 304, + 434, + 545, + 589 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 434, + 545, + 589 + ], + "type": "inline_equation", + "content": "\\gamma_{2}" + }, + { + "bbox": [ + 304, + 434, + 545, + 589 + ], + "type": "text", + "content": " is " + }, + { + "bbox": [ + 304, + 434, + 545, + 589 + ], + "type": "inline_equation", + "content": "0.5\\mathrm{m}" + }, + { + "bbox": [ + 304, + 434, + 545, + 589 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 434, + 545, + 589 + ], + "type": "inline_equation", + "content": "s_{vox}" + }, + { + "bbox": [ + 304, + 434, + 545, + 589 + ], + "type": "text", + "content": " is " + }, + { + "bbox": [ + 304, + 434, + 545, + 589 + ], + "type": "inline_equation", + "content": "5^{3}cm^{3}" + }, + { + "bbox": [ + 304, + 434, + 545, + 589 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 434, + 545, + 589 + ], + "type": "inline_equation", + "content": "w_{\\mathrm{RZ}}" + }, + { + "bbox": [ + 304, + 434, + 545, + 589 + ], + "type": "text", + "content": " is 10. The contact threshold is " + }, + { + "bbox": [ + 304, + 434, + 545, + 589 + ], + "type": "inline_equation", + "content": "7\\mathrm{cm}" + }, + { + "bbox": [ + 304, + 434, + 545, + 589 + ], + "type": "text", + "content": ". We flip images for augmentation. The module is trained with an initial learning rate of " + }, + { + "bbox": [ + 304, + 434, + 545, + 589 + ], + "type": "inline_equation", + "content": "3.75\\mathrm{e - 5}" + }, + { + "bbox": [ + 304, + 434, + 545, + 589 + ], + "type": "text", + "content": " and a batch size of 24. It converges after 30 epochs of training on one V100 GPU. For the mesh recovery module, the METRO network is initialized as pretrained and the scene network is randomly initialized. The initial learning rate is " + }, + { + "bbox": [ + 304, + 434, + 545, + 589 + ], + "type": "inline_equation", + "content": "7.5\\mathrm{e - 6}" + }, + { + "bbox": [ + 304, + 434, + 545, + 589 + ], + "type": "text", + "content": " and the batch size is 24. It converges after 30 epochs of training." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 599, + 388, + 613 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 599, + 388, + 613 + ], + "spans": [ + { + "bbox": [ + 306, + 599, + 388, + 613 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 619, + 368, + 631 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 619, + 368, + 631 + ], + "spans": [ + { + "bbox": [ + 306, + 619, + 368, + 631 + ], + "type": "text", + "content": "4.1. Datasets" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 637, + 545, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 637, + 545, + 662 + ], + "spans": [ + { + "bbox": [ + 306, + 637, + 545, + 662 + ], + "type": "text", + "content": "We train and evaluate the proposed method on RICH [6] and PROX [5] datasets separately." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "type": "text", + "content": "RICH [6] captures multi-view video sequences in 6 outdoor and 2 indoor scenes. It provides images, reconstructed bodies, scene scans, and human-scene contact labels annotated on SMPL vertices. We skip frames including multiple" + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "17042" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 61, + 70, + 533, + 182 + ], + "blocks": [ + { + "bbox": [ + 61, + 70, + 533, + 182 + ], + "lines": [ + { + "bbox": [ + 61, + 70, + 533, + 182 + ], + "spans": [ + { + "bbox": [ + 61, + 70, + 533, + 182 + ], + "type": "table", + "html": "
MethodLearning-basedOptimizationScene-awareG-MPJE↓G-MPV\\( \\downarrow \\)PenE↓ConFE↓MPJPE↓MPVE↓
Dataset GT [6]✓✓//9.810.8//
SMPLify-X [19]✓482.0483.735.743.4166.9177.6
PROX [5]✓✓390.1397.215.524.1164.1175.8
POSA [2]✓✓427.8434.021.127.0177.2188.4
PLACE [38]✓✓395.9403.016.124.8163.8175.4
METRO \\( [12]^† + SA-Opt \\) [6, 29]✓✓✓563.1561.37.414.8102.7112.8
METRO [12]✓678.6679.452.256.9129.6134.5
METRO \\( [12]^† \\)✓511.7509.733.637.698.8107.9
SA-HMR✓✓264.6272.714.919.093.9103.0
", + "image_path": "b6333eb4a224c4b357df69b177e46d1fec709ba7f835109192cf83ccaf1e984c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 243, + 288, + 304 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 243, + 288, + 304 + ], + "spans": [ + { + "bbox": [ + 46, + 243, + 288, + 304 + ], + "type": "text", + "content": "subjects, remove the first 45 frames of each video to avoid static starting pose, and skip frames where the subjects' 2D bounding boxes are not inside the images. Then we down-sample the train / val / test splits to " + }, + { + "bbox": [ + 46, + 243, + 288, + 304 + ], + "type": "inline_equation", + "content": "2/1/1" + }, + { + "bbox": [ + 46, + 243, + 288, + 304 + ], + "type": "text", + "content": " fps, resulting in 15360 / 3823 / 3316 frames." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 308, + 288, + 429 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 308, + 288, + 429 + ], + "spans": [ + { + "bbox": [ + 46, + 308, + 288, + 429 + ], + "type": "text", + "content": "PROX [5] captures monocular RGBD videos in 12 indoor scenes. We use RGB images and scene scans. It is a challenging dataset where severe occlusions exist in most frames. We use the qualitative set for training and the quantitative set for testing. In order to get better training annotations, we additionally use HuMoR [26] which utilizes motion prior and optimizes a sequence of frames. Then, we manually remove the failed frames that are not consistent with the images and scenes. Finally, the training split contains 4852 frames." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 439, + 105, + 451 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 439, + 105, + 451 + ], + "spans": [ + { + "bbox": [ + 47, + 439, + 105, + 451 + ], + "type": "text", + "content": "4.2. Metrics" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 459, + 287, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 459, + 287, + 483 + ], + "spans": [ + { + "bbox": [ + 46, + 459, + 287, + 483 + ], + "type": "text", + "content": "We evaluate quantitatively in terms of human mesh recovery and human-scene contact." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 487, + 287, + 560 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 487, + 287, + 560 + ], + "spans": [ + { + "bbox": [ + 46, + 487, + 287, + 560 + ], + "type": "text", + "content": "Human Mesh Recovery. We report the Global Mean-Per-Joint-Position-Error (G-MPJPE) and Global Mean-Per-Vertex-Error (G-MPVE) in the scene coordinate system, which calculates the average L2 distances between predicted and ground truth joints/vertices. Additionally, we report the translation-aligned metrics MPJPE and MPVE." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 564, + 287, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 564, + 287, + 612 + ], + "spans": [ + { + "bbox": [ + 46, + 564, + 287, + 612 + ], + "type": "text", + "content": "Human-scene Contact. We report the Penetration Error (PenE) and Contact Failure Error (ConFE). PenE measures the total distance that SMPL vertices penetrate the scene mesh:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 77, + 621, + 287, + 656 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 621, + 287, + 656 + ], + "spans": [ + { + "bbox": [ + 77, + 621, + 287, + 656 + ], + "type": "interline_equation", + "content": "\\operatorname {P e n E} = \\sum_ {i = 1} ^ {V} \\mathbb {1} _ {x < 0} [ s d f (v _ {i}, \\mathcal {S}) ] \\cdot | s d f (v _ {i}, \\mathcal {S}) |, \\tag {7}", + "image_path": "fd8c54c65592000da61a3dd5d38e872eab2dbe96e07d82188cae806bcd01cd15.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": " is the number of SMPL vertices, " + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "inline_equation", + "content": "sdf(v_{i},\\mathcal{S})" + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": " is the signed distance from vertex " + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": " to scene " + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{S}" + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathbb{1}_{x < 0}[\\cdot ]" + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": " is an indicator function that returns 1 when the condition is met, and 0 otherwise. ConFE measures contact quality when the" + } + ] + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 309, + 241, + 544, + 342 + ], + "blocks": [ + { + "bbox": [ + 46, + 189, + 547, + 225 + ], + "lines": [ + { + "bbox": [ + 46, + 189, + 547, + 225 + ], + "spans": [ + { + "bbox": [ + 46, + 189, + 547, + 225 + ], + "type": "text", + "content": "Table 1. Evaluation on the RICH [6] dataset. METRO† indicates that the model is finetuned on the dataset. SA-Opt indicates scene-aware optimization, with contact estimation from BSTRO [6] and loss formulation from PROX [5] and PHOSA [29]. The proposed SA-HMR achieves the overall best results and is significantly faster than the methods that require optimization." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 309, + 241, + 544, + 342 + ], + "lines": [ + { + "bbox": [ + 309, + 241, + 544, + 342 + ], + "spans": [ + { + "bbox": [ + 309, + 241, + 544, + 342 + ], + "type": "table", + "html": "
MethodG-MPJPE↓G-MPVE↓PenE↓MPJPE↓MPVE↓
Dataset GT [5]//9.6//
SMPLify-X [19]216.0222.649.3100.7112.8
PROX [5]172.0178.510.7101.1114.0
POSA [2]172.3180.916.6108.5119.4
PLACE [38]168.1176.712.3100.8113.7
METRO [12]283.2277.762.4137.0147.2
METRO [12]†265.6262.767.5117.1128.5
SA-HMR150.4160.026.9111.1122.5
", + "image_path": "b99416d4c8f7db2a806dbb934bc2bffe090a2ac6019459cdfd6d05902a5dc8a9.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 350, + 546, + 373 + ], + "lines": [ + { + "bbox": [ + 305, + 350, + 546, + 373 + ], + "spans": [ + { + "bbox": [ + 305, + 350, + 546, + 373 + ], + "type": "text", + "content": "Table 2. Evaluation on the PROX [5] dataset. The proposed method achieves the best performance in global metrics." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 306, + 392, + 462, + 405 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 392, + 462, + 405 + ], + "spans": [ + { + "bbox": [ + 306, + 392, + 462, + 405 + ], + "type": "text", + "content": "ground truth contact label is available:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 308, + 411, + 545, + 472 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 411, + 545, + 472 + ], + "spans": [ + { + "bbox": [ + 308, + 411, + 545, + 472 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\operatorname {C o n F E} = \\sum_ {i = 1} ^ {V} \\left(C _ {g t} \\left(v _ {i}\\right) \\cdot | s d f \\left(v _ {i}, \\mathcal {S}\\right) |\\right. \\\\ + \\left(1 - C _ {g t} \\left(v _ {i}\\right)\\right) \\cdot \\mathbb {1} _ {x < 0} [ s d f \\left(v _ {i}, \\mathcal {S}\\right) ] \\cdot | s d f \\left(v _ {i}, \\mathcal {S}\\right) |), \\tag {8} \\\\ \\end{array}", + "image_path": "3412f0bd3dbf10cae97a6d7dfdb31d35c1eba5f712cec9417d063f15ba1466bc.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 480, + 546, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 480, + 546, + 529 + ], + "spans": [ + { + "bbox": [ + 304, + 480, + 546, + 529 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 480, + 546, + 529 + ], + "type": "inline_equation", + "content": "C_{gt}(v)" + }, + { + "bbox": [ + 304, + 480, + 546, + 529 + ], + "type": "text", + "content": " equals 1 if " + }, + { + "bbox": [ + 304, + 480, + 546, + 529 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 304, + 480, + 546, + 529 + ], + "type": "text", + "content": " is labeled as in contact, and 0 otherwise. In order to obtain a good result of ConFE, the body vertices in contact should be close to the scene surface, while vertices not in contact should avoid penetration." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 536, + 391, + 548 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 536, + 391, + 548 + ], + "spans": [ + { + "bbox": [ + 306, + 536, + 391, + 548 + ], + "type": "text", + "content": "4.3. Main Results" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 557, + 546, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 546, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 546, + 689 + ], + "type": "text", + "content": "Baselines. Optimization: SMPLify-X [19] uses RGB only, PROX [5] extends it with losses of human-scene contact and penetration, POSA [2] and PLACE [38] extend PROX with scene-aware pose priors, and METRO " + }, + { + "bbox": [ + 304, + 557, + 546, + 689 + ], + "type": "inline_equation", + "content": "[12]^{\\dagger} + \\mathrm{SA}" + }, + { + "bbox": [ + 304, + 557, + 546, + 689 + ], + "type": "text", + "content": " -Opt stands for post-processing a finetuned METRO with scene-aware optimization, which will be explained later. Learning-based: METRO predicts canonical human mesh vertices and a weak-perspective camera. We solve the transformation from human to camera coordinate by minimizing joint re-projection error with a PnP solver [39]. The " + }, + { + "bbox": [ + 304, + 557, + 546, + 689 + ], + "type": "inline_equation", + "content": "\\mathrm{METRO}^{\\dagger}" + }, + { + "bbox": [ + 304, + 557, + 546, + 689 + ], + "type": "text", + "content": " is finetuned with the same training protocol as SA-HMR." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 689, + 546, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 546, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 546, + 715 + ], + "type": "text", + "content": "Since METRO does not consider scenes, we additionally optimize the global pose and scale by minimizing" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17043" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 80, + 70, + 255, + 111 + ], + "blocks": [ + { + "bbox": [ + 80, + 70, + 255, + 111 + ], + "lines": [ + { + "bbox": [ + 80, + 70, + 255, + 111 + ], + "spans": [ + { + "bbox": [ + 80, + 70, + 255, + 111 + ], + "type": "table", + "html": "
DatasetInitial RtErrRefined RtErrFinal RtErr
RICH510.8284.7246.5
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For the RICH dataset, Tab. 1 shows that SA-HMR notably outperforms other baselines in terms of the G-MPJPE and G-MPVE by a significant margin, demonstrating the effectiveness of the proposed pipeline. The joint learning on both image and scene geometry also improves the metrics of local pose and human-scene contact. We use open-sourced code for SMPLify-X and PROX, and implement POSA and PLACE upon PROX. Optimization methods approximately cost 18s for a single fitting, which is much slower compared to 0.2s of SA-HMR. We provide qualitative results comparing to baselines in Fig. 6." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 347, + 287, + 466 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 347, + 287, + 466 + ], + "spans": [ + { + "bbox": [ + 46, + 347, + 287, + 466 + ], + "type": "text", + "content": "For the PROX dataset, SA-HMR outperforms all baselines in terms of global accuracy as illustrated in Tab. 2. Since the pseudo ground truth of the training set is still not of high quality, as well as a domain gap exists in the test set where the subject wears a MoCap suit, our method falls a little behind in local accuracy and scene penetration. And we do not report ConFE, since the ground truth contact label is not available. Nevertheless, the clear improvement compared to the most relevant model " + }, + { + "bbox": [ + 46, + 347, + 287, + 466 + ], + "type": "inline_equation", + "content": "\\mathrm{METRO}^{\\dagger}" + }, + { + "bbox": [ + 46, + 347, + 287, + 466 + ], + "type": "text", + "content": " has demonstrated the effectiveness of the proposed method." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 467, + 287, + 550 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 467, + 287, + 550 + ], + "spans": [ + { + "bbox": [ + 46, + 467, + 287, + 550 + ], + "type": "text", + "content": "We also observe that while considering the scene geometry is critical for estimating the global position and improving physical plausibility, it may not fully resolve the ambiguity of the local pose, where multiple physically plausible solutions may still exist. For example, the RGB-only method SMPLify-X and the scene-aware method PROX perform similarly in MPJPE and MPVE." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 559, + 140, + 572 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 559, + 140, + 572 + ], + "spans": [ + { + "bbox": [ + 47, + 559, + 140, + 572 + ], + "type": "text", + "content": "4.4. Ablation Study" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "text", + "content": "Root and Contact Module. Tab. 3 shows that the predicted human root position is improved progressively by the refinement and scene-aware HMR modules, where the initial prediction [33] is improved " + }, + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "inline_equation", + "content": "44\\% / 52\\%" + }, + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "text", + "content": " in RICH, and " + }, + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "inline_equation", + "content": "64\\% / 69\\%" + }, + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "text", + "content": " in PROX. The offset representation helps to improve erroneous initial root prediction that is not consistent with the scene surface. For scene contact estimation, the precision / recall is " + }, + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "inline_equation", + "content": "0.57 / 0.53" + }, + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "text", + "content": " on RICH, and " + }, + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "inline_equation", + "content": "0.45 / 0.24" + }, + { + "bbox": [ + 46, + 582, + 287, + 713 + ], + "type": "text", + "content": " on PROX. We observe that the contacts are difficult to predict, which aligns with the conclusion of a recent work HULC [3]. More visualizations are presented in Fig. 7." + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 307, + 70, + 544, + 110 + ], + "blocks": [ + { + "bbox": [ + 47, + 119, + 287, + 142 + ], + "lines": [ + { + "bbox": [ + 47, + 119, + 287, + 142 + ], + "spans": [ + { + "bbox": [ + 47, + 119, + 287, + 142 + ], + "type": "text", + "content": "Table 3. Ablation study of root estimation. The human root position errors (RtErr) in mm are reported." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 70, + 544, + 110 + ], + "lines": [ + { + "bbox": [ + 307, + 70, + 544, + 110 + ], + "spans": [ + { + "bbox": [ + 307, + 70, + 544, + 110 + ], + "type": "table", + "html": "
MethodG-MPJPEG-MPVEMPJPEMPVECErr↓
w/o parallel304.8312.998.5108.910.2
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RootContactMPJPEMPVECErr↓
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As shown in Tab. 4, the parallel network that uses cross-attention outperforms a variant that fuses the pointnet features of the contact points to the METRO network in the early stage. The CErr indicates the error of contact mesh vertices in the translation-aligned coordinates. In Tab. 5, we validate the upper bound of the mesh recovery module. We replace the intermediate estimation of root and contact, and find a steady improvement in the pose and shape accuracy." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 403, + 545, + 487 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 403, + 545, + 487 + ], + "spans": [ + { + "bbox": [ + 304, + 403, + 545, + 487 + ], + "type": "text", + "content": "Running Time. SA-HMR runs at 170 ms with a peak memory cost of 1852 MB for a " + }, + { + "bbox": [ + 304, + 403, + 545, + 487 + ], + "type": "inline_equation", + "content": "224 \\times 224" + }, + { + "bbox": [ + 304, + 403, + 545, + 487 + ], + "type": "text", + "content": " image and a scene point cloud of 2 cm resolution on a V100 GPU. Specifically, the root and contact module takes 92 ms (CNN 50 ms, SPVCNN 42 ms), the mesh recovery module takes 75 ms (CNN 49 ms, Transformer 26 ms), and the intermediate processing takes 3 ms." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 498, + 378, + 510 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 498, + 378, + 510 + ], + "spans": [ + { + "bbox": [ + 306, + 498, + 378, + 510 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 517, + 545, + 661 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 517, + 545, + 661 + ], + "spans": [ + { + "bbox": [ + 304, + 517, + 545, + 661 + ], + "type": "text", + "content": "This work addresses the challenge of estimating the human mesh from an RGB image with the consideration of the scene geometry. Our key idea is to inject 3D scene cues into a monocular human mesh recovery network to recover the absolute human pose and shape in the scene. To this end, our approach first predicts the 3D human location and dense human-scene contacts with a sparse 3D CNN. We then develop a transformer to extract features from contact scene points and feed them into the pose estimation network using cross-attention. Experiments demonstrate that our approach achieves state-of-the-art performance on the RICH and PROX datasets." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "Acknowledgement. This work was supported by the Key Research Project of Zhejiang Lab (No. K2022PG1BB01), NSFC (No. 62172364), and Information Technology Center and State Key Lab of CAD&CG, Zhejiang University." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17044" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 57, + 69, + 135, + 148 + ], + "blocks": [ + { + "bbox": [ + 57, + 69, + 135, + 148 + ], + "lines": [ + { + "bbox": [ + 57, + 69, + 135, + 148 + ], + "spans": [ + { + "bbox": [ + 57, + 69, + 135, + 148 + ], + "type": "image", + "image_path": "2d1fa03337d55309cd2aaae9b2bc6d054b3b66eb6f519940c98c34c1f26e6a21.jpg" + } + ] + } + ], + 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Qualitative results on the RICH [6] dataset. We compare the proposed method to PROX [5], finetuned METRO [12], finetuned METRO with scene-aware optimization, and ground truth. The leftmost column shows the input images. The proposed method recovers the global positions and human-scene contact more accurately because of the 3D learning on human root refinement and dense scene contact labeling tasks." + } + ] + } + ], + "index": 36, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 58, + 556, + 135, + 634 + ], + "lines": [ + { + "bbox": [ + 58, + 556, + 135, + 634 + ], + "spans": [ + { + "bbox": [ + 58, + 556, + 135, + 634 + ], + "type": "image", + "image_path": "5571b3957704ef1625dfc3406a9ad65ab0b095f5e863220deba4b25cc58c62fa.jpg" + } + ] + } + ], + "index": 37, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 72, + 639, + 121, + 648 + ], + "lines": [ + { + "bbox": [ + 72, + 639, + 121, + 648 + ], + "spans": [ + { + "bbox": [ + 72, + 639, + 121, + 648 + ], + "type": "text", + "content": "Root & Contact" + } + ] + } + ], + "index": 38, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 659, + 547, + 693 + ], + "lines": [ + { + "bbox": [ + 46, + 659, + 547, + 693 + ], + "spans": [ + { + "bbox": [ + 46, + 659, + 547, + 693 + ], + "type": "text", + "content": "Figure 7. Qualitative visualization of the estimated root locations and dense scene contacts. In both examples, the estimated contact points provide accurate position and scene structure for the following step of mesh recovery. 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Dr. Dobb's Journal of Software Tools, 2000. 6" + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17047" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Learning Human-to-Robot Handovers From Point Clouds/336c5a3d-faa8-45f9-8aaa-bb35d62132fd_content_list.json b/2023/Learning Human-to-Robot Handovers From Point Clouds/336c5a3d-faa8-45f9-8aaa-bb35d62132fd_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..a10233f54732006abc116f0c162d5c0b2820ba5a --- /dev/null +++ b/2023/Learning Human-to-Robot Handovers From Point Clouds/336c5a3d-faa8-45f9-8aaa-bb35d62132fd_content_list.json @@ -0,0 +1,1310 @@ +[ + { + "type": "text", + "text": "Learning Human-to-Robot Handovers from Point Clouds", + "text_level": 1, + "bbox": [ + 194, + 130, + 774, + 151 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Sammy Christen1,2* \nOtmar Hilliges1", + "bbox": [ + 171, + 179, + 339, + 217 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Wei Yang² Dieter Fox²,³", + "bbox": [ + 418, + 180, + 542, + 214 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Claudia Pérez-D'Arpino² Yu-Wei Chao²", + "bbox": [ + 591, + 180, + 795, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ ETH Zurich $^{2}$ NVIDIA $^{3}$ University of Washington", + "bbox": [ + 261, + 226, + 702, + 244 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{sammy.christen, otmar.hilliges}@inf.ethz.ch {weiy, claudiap, dieterf, ychao}@nvidia.com", + "bbox": [ + 140, + 244, + 828, + 258 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/9886bba537c4f0425fb12a9319a6d5d8a38f0d4dbef4e30a59cf7a7970b69b62.jpg", + "image_caption": [ + "Figure 1. We introduce a framework to learn human-to-robot handover policies from point cloud input. Our policies take input from a wrist mounted camera and directly generate action output for the robot's end effector. We train our policies in a simulated handover environment, and evaluate on unseen handover motion and poses. We further transfer the model across physics simulators and to a real robotic platform." + ], + "image_footnote": [], + "bbox": [ + 102, + 277, + 864, + 479 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 547, + 313, + 563 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We propose the first framework to learn control policies for vision-based human-to-robot handovers, a critical task for human-robot interaction. While research in Embodied AI has made significant progress in training robot agents in simulated environments, interacting with humans remains challenging due to the difficulties of simulating humans. Fortunately, recent research has developed realistic simulated environments for human-to-robot handovers. Leveraging this result, we introduce a method that is trained with a human-in-the-loop via a two-stage teacher-student framework that uses motion and grasp planning, reinforcement learning, and self-supervision. We show significant performance gains over baselines on a simulation benchmark, sim-to-sim transfer and sim-to-real transfer. Video and code are available at https://handover-sim2real.github.io.", + "bbox": [ + 73, + 571, + 470, + 799 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 823, + 207, + 838 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Handling over objects between humans and robots is an important tasks for human-robot interaction (HRI) [35]. It", + "bbox": [ + 76, + 848, + 468, + 878 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "allows robots to assist humans in daily collaborative activities, such as helping to prepare a meal, or to exchange tools and parts with human collaborators in manufacturing settings. To complete these tasks successfully and safely, intricate coordination between human and robot is required. This is challenging, because the robot has to react to human behavior, while only having access to sparse sensory inputs such as a single camera with limited field of view. Therefore, a need for methods that solve interactive tasks such as handovers purely from vision input arises.", + "bbox": [ + 496, + 549, + 890, + 700 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Bootstrapping robot training in the real world can be unsafe and time-consuming. Therefore, recent trends in Embodied AI have focused on training agents to act and interact in simulated (sim) environments [11, 12, 19, 43, 45, 46, 51]. With advances in rendering and physics simulation, models have been trained to map raw sensory input to action output, and can even be directly transferred from simulation to the real world [2, 42]. Many successes have been achieved particularly around the suite of tasks of robot navigation, manipulation, or a combination of both. In contrast to these areas, little progress has been made around tasks pertained to HRI. This is largely hindered by the challenges in embedding realistic human agents in these environments, since", + "bbox": [ + 496, + 704, + 892, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*This work was done during an internship at NVIDIA.", + "bbox": [ + 94, + 886, + 383, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "9654", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "modeling and simulating realistic humans is challenging.", + "bbox": [ + 76, + 90, + 454, + 107 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Despite the challenges, an increasing number of works have attempted to embed realistic human agents in simulated environments [6, 9, 16, 36-38, 48]. Notably, a recent work has introduced a simulation environment (\"Handover-Sim\") for human-to-robot handover (H2R) [6]. To ensure a realistic human handover motion, they use a large motion capture dataset [7] to drive the movements of a virtual human in simulation. However, despite the great potential for training robots, the work of [6] only evaluates off-the-shelf models from prior work, and has not explored any policy training with humans in the loop in their environment.", + "bbox": [ + 75, + 108, + 468, + 273 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We aim to close this gap by introducing a vision-based learning framework for H2R handovers that is trained with a human-in-the-loop (see Fig. 1). In particular, we propose a novel mixed imitation learning (IL) and reinforcement learning (RL) based approach, trained by interacting with the humans in HandoverSim. Our approach draws inspiration from a recent method for learning polices for grasping static objects from point clouds [50], but proposes several key changes to address the challenges in H2R handovers. In contrast to static object grasping, where the policy only requires object information, we additionally encode human hand information in the policy's input. Also, compared to static grasping without a human, we explicitly take human collisions into account in the supervision of training. Finally, the key distinction between static object grasping and handovers is the dynamic nature of the hand and object during handover. To excel on the task, the robot needs to react to dynamic human behavior. Prior work typically relies on open-loop motion planners [49] to generate expert demonstrations, which may result in suboptimal supervision for dynamic cases. To this end, we propose a two-stage training framework. In the first stage, we fix the humans to be stationary and train an RL policy that is partially guided by expert demonstrations obtained from a motion and grasp planner. In the second stage, we finetune the RL policy in the original dynamic setting where the human and robot move simultaneously. Instead of relying on a planner, we propose a self-supervision scheme, where the pre-trained RL policy serves as a teacher to the downstream policy.", + "bbox": [ + 75, + 276, + 472, + 715 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We evaluate our method in three \"worlds\" (see Fig. 1). First, we evaluate on the \"native\" test scenes in HandoverSim [6], which use the same backend physics simulator (Bullet [10]) as training but unseen handover motions from the simulated humans. Next, we perform sim-to-sim evaluation on the test scenes implemented with a different physics simulator (Isaac Gym [29]). Lastly, we investigate sim-to-real transfer by evaluating polices on a real robotic system and demonstrate the benefits of our method.", + "bbox": [ + 75, + 717, + 468, + 852 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We contribute: i) the first framework to train human-to-robot handover tasks from vision input with a human-in-the-loop, ii) a novel teacher-student method to train in the", + "bbox": [ + 76, + 854, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "setting of a jointly moving human and robot, iii) an empirical evaluation showing that our approach outperforms baselines on the HandoverSim benchmark, iv) transfer experiments indicating that our method leads to more robust sim-to-sim and sim-to-real transfer compared to baselines.", + "bbox": [ + 498, + 90, + 890, + 167 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 181, + 640, + 198 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Human-to-Robot Handovers Encouraging progress in hand and object pose estimation [22, 26, 27] has been achieved, aided by the introduction of large hand-object interaction datasets [5, 7, 17, 20, 21, 28, 32, 47, 54, 55]. These developments enable applying model-based grasp planning [3,4,31], a well-studied approach in which full pose estimation and tracking are needed, to H2R handovers [7, 41]. However, these methods require the 3D shape models of the object and cannot handle unseen objects. Alternatively, some recent works [13, 30, 40, 52, 53] achieve H2R handover by employing learning-based grasp planners to generate grasps for novel objects from raw vision inputs such as images or point clouds [33, 34]. While promising results have been shown, these methods work only on an open-loop sequential setting in which the human hand has to stay still once the robot starts to move [40], or need complex hand-designed cost functions for grasp selection [52] and robot motion planning [30, 53] for reactive handovers, which requires expertise in robot motion and control. Hence, these methods are difficult to reproduce and deploy to new environments. Progress towards dynamic simultaneous motion has been shown by a learning-based method [48], using state inputs, leaving an open challenge for training policies that receive visual input directly. In contrast, we propose to learn control policies together with grasp prediction for handovers in an end-to-end manner from segmented point clouds with a deep neural net. To facilitate easy and fair comparisons among different handover methods, [6] propose a physics-simulated environment with diverse objects and realistic human handover behavior collected by a mocap system [7]. They provide benchmark results of several previous handover systems, including a learning-based grasping policy trained with static objects [50]. However, learning a safe and efficient handover policy is not trivial with a human-in-the-loop, which we address in this work.", + "bbox": [ + 496, + 208, + 893, + 739 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Policy Learning for Grasping Object grasping is an essential skill for many robot tasks, including handovers. Prior works usually generate grasp poses given a known 3D object geometry such as object shape or pose [3,4,31], which is nontrivial to obtain from real-world sensory input such as images or point clouds. To overcome this, recent works train deep neural networks to predict grasps from sensor data [25] and compute trajectories to reach the predicted grasp pose. Though 3D object geometry is no longer needed, the feasibility is not guaranteed since the grasp", + "bbox": [ + 496, + 750, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "9655", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "prediction and trajectory planning are computed separately. Some recent works directly learn grasping policies given raw sensor data. [24] propose a self-supervised RL framework based on RGB images to learn a deep Q-function from real-world grasps. To improve data efficiency, [44] use a low-cost handheld device to collect grasping demonstrations with a wrist-mounted camera. They train an RL-based 6-DoF closed-loop grasping policy with these demonstrations. [50] combines imitation learning from expert data with RL to learn a control policy for object grasping from point clouds. Although this method performs well in HandoverSim [6] when the human hand is not moving, it has difficulty coordinating with a dynamic human hand since the policy is learned with static objects. Instead, our policy is directly learned from large-scale dynamic hand-object trajectories obtained from the real world. To facilitate the training for the dynamic case, we propose a two-stage teacher-student framework, that is conceptually inspired by [8], which has been proven critical through experiments.", + "bbox": [ + 75, + 90, + 472, + 380 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Background", + "text_level": 1, + "bbox": [ + 76, + 398, + 205, + 414 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Reinforcement Learning", + "text_level": 1, + "bbox": [ + 76, + 424, + 302, + 441 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "MDP We formalize RL as a Markov Decision Process (MDP), that consists of a 5-tuple $\\mathcal{M} = (\\mathcal{S},\\mathcal{A},\\mathcal{R},\\mathcal{T},\\gamma)$ where $\\mathcal{S}$ is the state space, $\\mathcal{A}$ the action space, $\\mathcal{R}$ a scalar reward function, $\\mathcal{T}$ a transition function that maps state-action pairs to distributions over states, and $\\gamma$ a discount factor. The goal is to find a policy that maximizes the long-term reward: $\\pi^{*} = \\arg \\max_{\\pi}\\mathbb{E}\\sum_{t = 0}^{t = T}\\gamma^{t}\\mathcal{R}(\\mathbf{s}_{t})$ , with $\\mathbf{s}_t\\sim \\mathcal{T}(\\mathbf{s}_{t - 1},\\mathbf{a}_{t - 1})$ and $\\mathbf{a}_{t - 1}\\sim \\pi (\\mathbf{s}_{t - 1})$ .", + "bbox": [ + 75, + 449, + 468, + 571 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Learning Algorithm In this work, we use TD3 [18], a common algorithm for continuous control. It is an actor-critic method, which consists of a policy $\\pi_{\\theta}(\\mathbf{s})$ (actor) and a Q-function approximator $Q_{\\phi}(\\mathbf{s},\\mathbf{a})$ (critic) that predicts the expected return from a state-action pair. Both are represented by neural networks with parameters $\\theta$ and $\\phi$ . TD3 is off-policy, and hence there is a replay buffer in which training transitions are stored. During training, both the actor and critic are updated using samples from the buffer. To update the critic, we minimize the Bellman error:", + "bbox": [ + 75, + 599, + 468, + 751 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\mathrm {B E}} (\\phi) = \\mathbb {E} _ {\\mathcal {M}} \\left[ \\left(Q _ {\\phi} \\left(\\mathbf {s} _ {t}, \\mathbf {a} _ {t}\\right) - r \\left(\\mathbf {s} _ {t}, \\mathbf {a} _ {t}\\right) + \\gamma Q _ {\\phi} \\left(\\mathbf {s} _ {t + 1}, \\mathbf {a} _ {t + 1}\\right)\\right) ^ {2} \\right] \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 78, + 766, + 467, + 804 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For the actor network, the policy parameters are trained to maximize the Q-values:", + "bbox": [ + 76, + 806, + 467, + 837 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\mathrm {D D P G}} (\\theta) = \\mathbb {E} _ {\\boldsymbol {\\pi}} \\left[ Q _ {\\phi} \\left(\\mathbf {s} _ {t}, \\mathbf {a} _ {t}\\right) \\mid \\mathbf {s} _ {t}, \\mathbf {a} _ {t} = \\boldsymbol {\\pi} _ {\\theta} \\left(\\mathbf {s} _ {t}\\right) \\right] \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 122, + 853, + 467, + 869 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For more details, we refer the reader to [18].", + "bbox": [ + 76, + 885, + 370, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. HandoverSim Benchmark", + "text_level": 1, + "bbox": [ + 500, + 90, + 736, + 104 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "HandoverSim [6] is a benchmark for evaluating H2R handover policies in simulation. The task setting consists of a tabletop with different objects, a Panda 7DoF robotic arm with a gripper and a wrist-mounted RGB-D camera, and a simulated human hand. The task starts with the human grasping an object and moving it to a handover pose. The robot should move to the object and grasp it. The task is successful if the object has been grasped from the human without collision and brought to a designated position without dropping. To accurately model the human, trajectories from the DexYCB dataset [7], which comprises a large amount of human-object interaction sequences, are replayed in simulation. Several baselines [49,50,52] are provided for comparison. The setup in HandoverSim has only been used for handover performance evaluation purposes, whereas in this work we utilize it as a learning environment.", + "bbox": [ + 496, + 113, + 890, + 356 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Method", + "text_level": 1, + "bbox": [ + 500, + 371, + 589, + 386 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The overall pipeline is depicted in Fig. 2 and consists of three different modules: perception, vision-based control, and the handover environment. The perception module receives egocentric visual information from the handover environment and processes it into segmented point clouds. The vision-based control module receives the point clouds and predicts the next action for the robot and whether to approach or to grasp the object. This information is passed to the handover environment, which updates the robot state and sends the new visual information to the perception module. Note that the input to our method comes from the wrist-mounted camera, i.e., there is no explicit information, such as object or hand pose, provided to the agent. We will now explain each of the modules of our method in more detail.", + "bbox": [ + 496, + 397, + 890, + 608 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.1. Handover Environment", + "text_level": 1, + "bbox": [ + 500, + 619, + 718, + 633 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We split the handover task into two distinct phases (see Fig. 2). First, during the approaching phase, the robot moves to a pre-grasp pose that is close to the object by running the learned control policy $\\pi$ . A learned grasp predictor $\\sigma$ continuously computes a grasp probability to determine when the system can proceed to the second phase. Once the pre-grasp pose is reached and the grasp prediction is confident to take over the object from the human, the task will switch to the grasping phase, in which the end-effector moves forward to the final grasp pose in open-loop fashion and closes the gripper to grasp the object. Finally, after object grasping, the robot follows a predetermined trajectory to retract to a base position and complete the episode. This task logic is used in both our simulation environment and the real robot deployment. Sequencing based on a pre-grasp pose is widely used in literature for dynamic grasping [1].", + "bbox": [ + 496, + 643, + 890, + 885 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We follow the HandoverSim task setup [6], where the hu", + "bbox": [ + 519, + 885, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "9656", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/01cbbf0223db88902fe482b9b742b9bf23145af4c5b25e7e5681fac1f4ba7531.jpg", + "image_caption": [ + "Figure 2. Method Overview. The Perception module takes egocentric RGB-D and segmentation images from the environment and outputs a hand/object segmented point cloud. Next, the segmented point cloud is passed to the Vision-based Control module and processed by PointNet++ [39] to obtain a lower-dimensional representation. This embedding is used as input to both the control policy and the grasp predictor. Each task episode in the Handover Environment follows two phases: during the approaching phase, the robot moves towards a pre-grasp pose, driven by the control policy $\\pi$ that outputs end-effector actions a. A learned grasp predictor monitors the motion and determines when the robot should switch into the grasping phase, which follows the steps: 1. moving the gripper forward from a pre-grasp to a grasping pose 2. closing the gripper 3. retracting the object to a designated location, after which the episode ends." + ], + "image_footnote": [], + "bbox": [ + 120, + 93, + 859, + 294 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "man hand and objects are simulated by replaying data from the DexYCB dataset [7] (see Sec. 3.2). First, actions a in the form of the next 6DoF end-effector pose (translation and rotation) are received from the policy $\\pi (\\mathbf{a}|\\mathbf{s})$ . We then convert the end-effector pose into a target robot configuration using inverse kinematics. Thereafter, we use PD-controllers to compute torques, which are applied to the robot. Finally, the visual information is rendered from the robot's wrist-mounted RGB-D camera and sent to the perception module.", + "bbox": [ + 75, + 416, + 470, + 553 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. Perception", + "text_level": 1, + "bbox": [ + 76, + 563, + 197, + 579 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Our policy network takes a segmented hand and object point cloud as input. In the handover environment, we first render an egocentric RGB-D image from the wrist camera. Then we obtain the object point cloud $\\mathbf{p}_o$ and hand point cloud $\\mathbf{p}_h$ by overlaying the ground-truth segmentation mask with the RGB-D image. Since the hand and object may not always be visible from the current egocentric view, we keep track of the last available point clouds. The latest available point clouds are then sent to the control module.", + "bbox": [ + 75, + 587, + 470, + 723 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.3. Vision-Based Control", + "text_level": 1, + "bbox": [ + 76, + 733, + 277, + 748 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Input Representation Depending on the amount of points contained in the hand point cloud $\\mathbf{p}_h$ and object point cloud $\\mathbf{p}_o$ , we down- or upsample them into constant size. Next, we concatenate the two point clouds into a single point cloud $\\mathbf{p}$ and add two one-hot-encoded vectors to indicate the locations of object and hand points within $\\mathbf{p}$ . We then encode the point cloud into a lower dimensional representation $\\psi(\\mathbf{p})$ by passing it through PointNet++ [39]. Finally, the lower dimensional encoding $\\psi(\\mathbf{p})$ is passed on to the control policy $\\pi$ and the grasp prediction network $\\sigma$ .", + "bbox": [ + 75, + 757, + 470, + 909 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Control Policy The policy network $\\pi(\\mathbf{a}|\\psi(\\mathbf{p}))$ is a small, two-layered MLP that takes the PointNet++ embedding as input state ( $\\mathbf{s} = \\psi(\\mathbf{p})$ ) and predicts actions $\\mathbf{a}$ that correspond to the change in 6DoF end-effector pose. These are passed on to the handover environment.", + "bbox": [ + 496, + 416, + 893, + 492 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Grasp Prediction We introduce a grasp prediction network $\\sigma(\\psi(\\mathbf{p}))$ that predicts when the robot should switch from approaching to executing the grasping motion (cf. Fig. 2). We model grasp prediction as a binary classification task. The input corresponds to the PointNet++ embedding $\\psi(\\mathbf{p})$ , which is fed through a 3-layered MLP. The output is a probability that indicates the likelihood of a successful grasp given the current point cloud feature. If the probability is above a tunable threshold, we execute an open-loop grasping motion. The model is trained offline with pre-grasp poses attained from [15]. We augment the dataset by adding random noise to pre-grasp poses. To determine the labels, we initialize the robot with the pre-grasp poses in the physics simulation and execute the forward grasping motion. The label is one if the grasp is successful, and zero otherwise. We use a binary cross-entropy loss for training.", + "bbox": [ + 496, + 503, + 892, + 744 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.4. Two-Stage Teacher-Student Training", + "text_level": 1, + "bbox": [ + 498, + 755, + 818, + 771 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We aim at training a handover policy capable of moving simultaneously with the human. Training this policy directly in the setting of dynamic motion is challenging because expert demonstrations with open-loop planners to guide training can only be obtained when the human is stationary. A key contribution of our work is a two-stage training scheme for handovers that incrementally trains the policy to alleviate this challenge. In the first stage, we pretrain", + "bbox": [ + 496, + 780, + 890, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "9657", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/ed7c431eb9c3aab692d4b4ddf1c254d12f68f3ac96ab0e504786df70595c0c5e.jpg", + "image_caption": [ + "Figure 3. Training Procedure. In the pretraining stage (top left box), the human hand is stationary. We alternate between collecting expert demonstrations via motion planning and exploration data with the RL policy $\\pi_{\\mathrm{pre}}$ . Transitions $\\mathbf{d}$ are stored in a replay buffer $\\mathcal{D}$ . During training (green box, right), a batch of randomly sampled transitions from the replay buffer is passed through PointNet++ and the actor and critic networks. In the finetuning stage (bottom left box), the human and robot move concurrently. The expert motion planner is replaced by the expert policy $\\pi_{\\mathrm{exp}}$ , which shares the weights of the pretrained policy $\\pi_{\\mathrm{pre}}$ . This policy network will be kept frozen for the rest of training and serves as a regularizer for the RL agent. The RL agent's actor network $\\pi_{*}$ and critic network $Q_{*}$ are also initialized with the weights of pretrained agent's networks, but the model will be updated during finetuning. In this stage, transitions are stored in a new replay buffer $\\mathcal{D}_{*}$ . Data is sampled solely from this buffer during finetuning." + ], + "image_footnote": [], + "bbox": [ + 99, + 89, + 872, + 321 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "in a setting where the robot only starts moving once the human has stopped (sequential). This pretrained policy is further finetuned in the second stage in which the human and robot move simultaneously (simultaneous).", + "bbox": [ + 75, + 467, + 470, + 527 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Pretraining in Sequential Setting In the sequential setting, the robot starts moving once the human has come to a stop (see Fig. 3, top left). To grasp the object from the stationary human hand, we leverage motion planning to provide expert demonstrations. During data collection, we alternate between motion planning and RL-based exploration. In both cases, we store the transitions $\\mathbf{d}_t = \\{\\mathbf{p}_t,\\mathbf{a}_t,\\mathbf{g}_t,\\mathbf{r}_t,\\mathbf{p}_{t + 1},\\mathbf{e}_t\\}$ in a replay buffer $\\mathcal{D}$ , from which we sample during network training. The term $\\mathbf{p}_t$ and $\\mathbf{p}_{t + 1}$ indicate the point cloud and the next point cloud, $\\mathbf{a}_t$ the action, $\\mathbf{g}_t$ the pre-grasp goal pose, $\\mathbf{r}_t$ the reward, and $\\mathbf{e}_t$ an indicator of whether the transition is from the expert.", + "bbox": [ + 75, + 537, + 468, + 718 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Inspired by [50], we collect expert trajectories with the OMG planner [49] that leverages ground-truth states. Note that some expert trajectories generated by the planner result in collision with the hand, which is why we introduce an offline pre-filtering scheme. We first parse the ACRONYM dataset [14] for potential grasps. We then run collision checking to filter out grasps where the robot and human hand collide. For the set of remaining collision-free grasps, we plan trajectories to grasp the object and execute them in open-loop fashion. On the other hand, the RL policy $\\pi_{\\mathrm{pre}}$ explores the environment and receives a sparse reward, i.e., the reward is one if the task is completed successfully, oth-", + "bbox": [ + 75, + 719, + 470, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "erwise zero. Hence, collisions with the human will get implicitly penalized by not receiving any positive reward.", + "bbox": [ + 498, + 467, + 890, + 498 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Finetuning in Simultaneous Setting In this setting, the human and robot move at the same time. Hence, we cannot rely on motion and grasp planning to guide the policy. On the other hand, simply taking the pre-trained policy $\\pi_{\\mathrm{pre}}$ from the sequential setting and continue training it without an expert leads to an immediate drop in performance. Hence, we introduce a self-supervision scheme for stability reasons, i.e., we want to keep the finetuning policy close to the pre-trained policy. To this end, we replace the expert planner from the sequential setting by an expert policy $\\pi_{\\mathrm{exp}}$ , which is initialized with the weights of the pre-trained policy $\\pi_{\\mathrm{pre}}$ that already provides a reasonable prior policy (see Fig. 3 bottom left). Therefore, we have two policies: i) the expert policy $\\pi_{\\mathrm{exp}}$ as proxy for the motion and grasping planner. We freeze the network weights of this policy, ii) the finetuning policy $\\pi_*$ and critic $Q_*$ , which are initialized with the weights of the pre-trained policy $\\pi_{\\mathrm{pre}}$ and critic $Q_{\\mathrm{pre}}$ , respectively. We proceed to train these two networks using the loss functions which we describe next.", + "bbox": [ + 496, + 503, + 892, + 792 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Network Training During training, we sample a batch of random transitions from the replay buffer $\\mathcal{D}$ . The policy network is trained using a combination of behavior cloning, RL-based losses and an auxiliary objective. In particular, the policy is updated using the following loss function:", + "bbox": [ + 496, + 799, + 893, + 876 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL (\\theta) = \\lambda L _ {\\mathrm {B C}} + (1 - \\lambda) L _ {\\mathrm {D D P G}} + L _ {\\mathrm {A U X}}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 560, + 885, + 892, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "9658", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/f5f34e9dbd6e31da3134eb39e85b3a6b23b4b85e152d1285f8b6a034f2a885c4.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
success (%)mean accum time (s)failure (%)
execplantotalcontactdroptimeouttotal
SequentialOMG Planner [49] †62.508.3091.4149.72227.788.331.3937.50
Yang et al. [52] †64.584.8640.0364.90017.3611.816.2535.42
GA-DDPG [50]50.007.1390.1427.2814.8619.4425.6950.00
GA-DDPG [50] finetuned57.186.3240.0866.4116.4827.089.2642.82
Ours75.237.7430.1777.9229.2613.432.0824.77
Simult.GA-DDPG [50]36.814.6640.1324.7969.0325.0029.1763.19
GA-DDPG [50] finetuned54.864.8320.0824.9146.7126.3912.0445.14
Ours68.756.2320.1786.4118.8017.824.6331.25
", + "bbox": [ + 140, + 88, + 826, + 233 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. HandoverSim Benchmark Evaluation. Comparison of our method against various baselines from the HandoverSim benchmark [6]. In the sequential setting, we find that our baseline achieves better overall success rates than the baselines. In the simultaneous setting, we outperform the applicable baselines by large margins. The results for our method are averaged across 3 random seeds. $\\dagger$ : both methods [49, 52] are evaluated with ground-truth states in [6] and thus are not directly comparable with ours.", + "bbox": [ + 75, + 241, + 890, + 297 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $L_{\\mathrm{BC}}$ is a behavior cloning loss that keeps the policy close to the expert policy, $L_{\\mathrm{DDPG}}$ is the standard actor-critic loss described in Eq. 2, and $L_{\\mathrm{AUX}}$ is an auxiliary objective that predicts the grasping goal pose of the end-effector. The coefficient $\\lambda$ balances the behavior cloning and the RL objective. The critic loss is defined as:", + "bbox": [ + 75, + 311, + 470, + 402 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nL (\\phi) = L _ {\\mathrm {B E}} + L _ {\\mathrm {A U X}}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 199, + 410, + 468, + 426 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $L_{\\mathrm{BE}}$ indicates the Bellman error from Eq. 1 and $L_{\\mathrm{AUX}}$ is the same auxiliary loss used in Eq. 3. We refer the reader to supplementary material or [50] for more details.", + "bbox": [ + 75, + 429, + 468, + 474 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 76, + 488, + 209, + 505 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We first evaluate our approach in simulation using the HandoverSim benchmark (Sec. 5.1). Next, we investigate the performance of sim-to-sim transfer by evaluating the trained models on the test environments powered by a different physics engine (Sec. 5.2). Finally, we apply the trained model to a real-world robotic system and analyze the performance of sim-to-real transfer (Sec. 5.3).", + "bbox": [ + 75, + 513, + 468, + 619 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Simulation Evaluation", + "text_level": 1, + "bbox": [ + 76, + 628, + 285, + 643 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Setup HandoverSim [6] contains 1,000 unique H2R handover scenes divided into train, val, and test splits. Each scene contains a unique human handover motion. We evaluate on the \"s0\" setup which contains 720 training and 144 testing scenes. See the supp. material for evaluations on unseen objects, subjects, and handedness. Following the evaluation of GA-DDPG [50] in [6], we consider two settings: (1) the \"sequential\" setting where the robot is allowed to move only after the human hand reaches the handover location and remains static there (i.e., \"hold\" in [6]), and (2) the \"simultaneous\" setting where the robot is allowed to move from the beginning of the episode (i.e., \"w/o hold\" in [6]).", + "bbox": [ + 75, + 651, + 468, + 834 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Metrics We follow the evaluation protocol in Handover-Sim [6]. A handover is considered successful if the robot grasps the object from the human hand and moves it to a designated location. A failure is claimed and the episode", + "bbox": [ + 75, + 839, + 468, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "is terminated if any of the following three conditions occur: (1) the robot collides with the hand (contact), (2) the robot drops the object (drop), or (3) a maximum time limit is reached (timeout). Besides efficacy, the benchmark also reports efficiency in time. The time metric is further broken down into (1) the execution time (exec), i.e., the time to physically move the robot, and (2) the planning time (plan), i.e., the time spent on running the policy. All reported metrics are averaged over the rollouts on the test scenes.", + "bbox": [ + 496, + 311, + 890, + 448 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Baselines Our primary baseline is GA-DDPG [50]. Besides comparing with the original model (i.e., trained in [50] for table-top grasping and evaluated in [6]), we additionally compare with a variant finetuned on HandoverSim (\"GA-DDPG [50] finetuned\"). For completeness, we also include two other baselines from [6]: \"OMG Planner [49]\" and \"Yang et al. [52]\". However, both of them are evaluated with ground-truth state input in [6] and thus are not directly comparable with our method.", + "bbox": [ + 496, + 455, + 890, + 592 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Results Tab. 1 reports the evaluation results on the test scenes. In the sequential setting, our method significantly outperforms all the baselines in terms of success rate, even compared to methods that use state-based input. Our method is slightly slower on average than GA-DDDPG in terms of total time needed for handovers. In the simultaneous setting, our method clearly outperforms GA-DDDPG, which has low success rates. Qualitatively, we observe that GA-DDDPG directly tries to grasp the object from the user while it is still moving, while our method follows the hand and finds a feasible grasp once the hand has come to a stop, resulting in a trade-off on the overall execution time. We provide a qualitative example of this behavior in Fig. 4 (a) and in the supplementary video. We also refer to the supp. material for a discussion of limitations and a robustness analysis of our pipeline under noisy observations.", + "bbox": [ + 496, + 599, + 890, + 843 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Ablations We evaluate our design choices in an ablation study and report the results in Tab. 2. We analyze the vision backbone by replacing PointNet++ with a ResNet18 [23]", + "bbox": [ + 496, + 854, + 890, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "9659", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/64a3e89bf357d7361f049fd3f4bd7b992e71dcd8bb2ac1d9b051d4fc6821445e.jpg", + "image_caption": [ + "Figure 4. Qualitative results. We provide a comparison to show our methods' advantages over GA-DDPG [50]. (a) Our method reacts to the moving human, while the baseline tries to go for a grasp directly, which leads to collision. (b) In the sim-to-sim transfer, we often find that the baseline does not find a grasp on the object. (c) In the sim-to-real experiment, GA-DDPG usually tries to get to a grasp directly, while our method adjusts the gripper into a stable grasping pose first. See the video in supp. material for more qualitative examples." + ], + "image_footnote": [], + "bbox": [ + 117, + 87, + 849, + 614 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/e8cb21c6eae268c5767a8b1f66eee86a3238403b0930d44f13d3ccaafbe0c3f4.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Ablation Study
success (%)failure (%)
contactdroptimeout
w/ RGBDM + ResNet1834.106.2045.8013.90
w/ third person view60.429,9525.693.94
w/o hand point cloud59.0324.0711.585.32
w/o aux prediction70.6010.6516.202.54
w/o standoff52.557.8736.802.78
w/o finetuning73.389.0313.893.70
Ours75.239.2613.432.08
w/o finetuning simul.62.2711.8120.375.56
Ours simul.68.758.817.824.63
", + "bbox": [ + 94, + 686, + 444, + 821 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2. Ablation. We ablate the vision backbone, hand perception, and egocentric view. We also study the effect of finetuning, the auxiliary prediction, and splitting the task into two phases. All design choices are crucial aspects of our method with regards to overall performance. Results are averaged over 3 random seeds.", + "bbox": [ + 75, + 825, + 472, + 898 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "that processes the RGB and depth/segmentation (DM) images. Similar to the findings in GA-DDPG, the PointNet++ backbone performs better. Next, we train our method from third person view instead of egocentric view and without active hand segmentation ( $w/o$ hand point cloud), i.e., the policy only perceives the object point cloud but not the hand point cloud. We also ablate the auxiliary prediction ( $w/o$ aux prediction) and evaluate a variant that directly learns to approach and grasp the object instead of using the two task phases of approaching and grasping ( $w/o$ standoff). Lastly, we compare against our pretrained model, which was only trained in the sequential setting without finetuning ( $w/o$ finetuning). We find that the ablated components comprise important elements of our method. The results indicate an in-", + "bbox": [ + 496, + 689, + 890, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "9660", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/7229d3e298e96557ddd4043c4caa0cc830273b6fbe00079b46bfc077e9e0bb0b.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Sim-to-Sim
success (%)failure (%)
contactdroptimeout
SequentialGA-DDPG [50]19.444.8647.2228.47
GA-DDPG [50] finetuned11.816.2568.7513.19
Ours44.219.4940.515.79
Ours w/o grasp54.407.8733.344.40
Simult.GA-DDPG [50]11.1115.9748.6124.31
GA-DDPG [50] finetuned16.679.7263.899.72
Ours39.589.0343.757.64
Ours w/o grasp pred.47.9210.6535.885.56
", + "bbox": [ + 96, + 88, + 444, + 205 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "creased amount of hand collision or object drop in all ablations. A closer analysis in the simultaneous setting shows that our finetuned model outperforms the pretrained model.", + "bbox": [ + 76, + 265, + 468, + 310 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.2. Sim-to-Sim Transfer", + "text_level": 1, + "bbox": [ + 76, + 320, + 272, + 335 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Instead of directly transferring to the real world, we first evaluate the robustness of the models by transferring them to a different physics simulator. We re-implement the HandoverSim environment following the mechanism presented in [6] except for replacing the backend physics engine from Bullet [10] to Isaac Gym [29]. We then evaluate the models trained on the original Bullet-based environment on the test scenes powered by Isaac Gym. The results are presented in Tab. 3. We observe a significant drop for GA-DDPG on the success rates (i.e., to below $20\\%$ ) in both settings. Qualitatively, we see that grasps are often either missed completely or only partially grasped (see Fig. 4 (b)). On the other hand, our method is able to retain higher success rates. Expectedly, it also suffers from a loss in performance. We analyze the influence of our grasp predictor on transfer performance and compare against a variant where we execute the grasping motion after a fixed amount of time (Ours w/o grasp pred.), which will leave the robot enough time to find a pre-grasp pose. Part of the performance drop is caused by the grasp predictor initiating the grasping phase at the wrong time, which can be improved upon in future work.", + "bbox": [ + 75, + 343, + 468, + 661 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.3. Sim-to-Real Transfer", + "text_level": 1, + "bbox": [ + 76, + 671, + 276, + 686 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Finally, we deploy the models trained in HandoverSim on a real robotic platform. We follow the perception pipeline used in [50,52] to generate segmented hand and object point clouds for the policy, and use the output to update the end effector's target position. We compare our method against GA-DDPG [50] with two sets of experiments: (1) a pilot study with controlled handover poses and (2) a user evaluation with free-form handovers. For experimental details and the full results, please see the supp. material.", + "bbox": [ + 75, + 695, + 468, + 830 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Pilot Study We first conduct a pilot study with two subjects. The subjects are instructed to handover 10 objects from HandoverSim by grasping and presenting the objects in controlled poses. For each object, we test with 6 poses", + "bbox": [ + 75, + 839, + 468, + 902 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/c084d54b07da6323c39a5e13eade3d491270622da35c6a443873d360369b15ef.jpg", + "table_caption": [ + "Table 3. Sim-to-Sim Experiment. We evaluate sim-to-sim transfer of the learning-based method to Isaac Gym [29], Our method shows better transfer capabilities than GA-DDPG [50]." + ], + "table_footnote": [], + "table_body": "
Subject 1Subject 2
GA-DDPG [50]OursGA-DDPG [50]Ours
011_banana3 / 66 / 66 / 65 / 6
037_scissors2 / 65 / 63 / 65 / 6
006_mustard_bottle1 / 63 / 62 / 64 / 6
024_bowl3 / 64 / 63 / 63 / 6
040_large Marker0 / 64 / 64 / 65 / 6
003_cracker_box3 / 62 / 60 / 62 / 6
052extra_large_clamp1 / 64 / 65 / 65 / 6
008_pudding_box3 / 66 / 64 / 64 / 6
010_potted_meat_can2 / 62 / 63 / 64 / 6
021_bleach_cleanser3 / 65 / 63 / 64 / 6
total21 / 6041 / 6033 / 6041 / 60
", + "bbox": [ + 517, + 88, + 867, + 241 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 4. Sim-to-Real Experiment. Success rates of the pilot study. Our method outperforms GA-DDPG [50] for both subjects.", + "bbox": [ + 500, + 250, + 890, + 277 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "(3 poses for each hand) with varying object orientation and varying amount of hand occlusion, resulting in 60 poses per subject. The same set of poses are used in testing both our model and GA-DDPG [50]. The success rates are shown Tab. 4. Results indicate that our method outperforms GA-DDPG [50] for both subjects on the overall success rate (i.e., 41/60 versus 21/60 for Subject 1). Qualitatively, we observe that GA-DDPG [50] tends to fail more from unstable grasping as well as hand collision. Fig. 4 (c) shows two examples of the real world handover trials.", + "bbox": [ + 496, + 305, + 890, + 455 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "User Evaluation We further recruited 6 users to compare the two methods and collected feedback from a questionnaire with Likert-scale and open-ended questions. In contrast to the pilot study, we asked the users to handover the 10 objects in ways that are most comfortable to them. We repeated the same experimental process for both methods, and counterbalanced the order to avoid bias. From participants' feedback, the majority agreed that the timing of our method is more appropriate and our method can adjust between different object poses better. The interpretability of the robot's motion was also acknowledged by their comments. Please see the supp. material for more details.", + "bbox": [ + 496, + 467, + 890, + 648 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 665, + 617, + 680 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this work, we have presented a learning-based framework for human-to-robot handovers from vision input with a simulated human-in-the-loop. We have introduced a two-stage teacher-student training procedure. In our experiments we have shown that our method outperforms baselines by a significant margin on the HandoverSim benchmark [6]. Furthermore, we have demonstrated that our approach is more robust when transferring to a different physics simulator and a real robotic system.", + "bbox": [ + 496, + 691, + 890, + 827 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements We thank Tao Chen and Adithyavairavan Murali for laying the groundwork, Lirui Wang for the help with GA-DDPG, and Mert Albaba, Christoph Gebhardt, Thomas Langerak and Juan Zarate for their feedback on the manuscript.", + "bbox": [ + 496, + 844, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "9661", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Iretiayo Akinola, Jingxi Xu, Shuran Song, and Peter K Allen. Dynamic grasping with reachability and motion awareness. 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Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.195, + 0.131, + 0.776, + 0.152 + ], + "angle": 0, + "content": "Learning Human-to-Robot Handovers from Point Clouds" + }, + { + "type": "text", + "bbox": [ + 0.173, + 0.18, + 0.341, + 0.218 + ], + "angle": 0, + "content": "Sammy Christen1,2* \nOtmar Hilliges1" + }, + { + "type": "text", + "bbox": [ + 0.419, + 0.181, + 0.543, + 0.215 + ], + "angle": 0, + "content": "Wei Yang² Dieter Fox²,³" + }, + { + "type": "text", + "bbox": [ + 0.593, + 0.181, + 0.796, + 0.216 + ], + "angle": 0, + "content": "Claudia Pérez-D'Arpino² Yu-Wei Chao²" + }, + { + "type": "text", + "bbox": [ + 0.262, + 0.227, + 0.704, + 0.246 + ], + "angle": 0, + "content": "\\(^{1}\\)ETH Zurich \\(^{2}\\)NVIDIA \\(^{3}\\)University of Washington" + }, + { + "type": "text", + "bbox": [ + 0.141, + 0.246, + 0.83, + 0.26 + ], + "angle": 0, + "content": "{sammy.christen, otmar.hilliges}@inf.ethz.ch {weiy, claudiap, dieterf, ychao}@nvidia.com" + }, + { + "type": "image", + "bbox": [ + 0.104, + 0.279, + 0.866, + 0.48 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.493, + 0.893, + 0.536 + ], + "angle": 0, + "content": "Figure 1. We introduce a framework to learn human-to-robot handover policies from point cloud input. Our policies take input from a wrist mounted camera and directly generate action output for the robot's end effector. We train our policies in a simulated handover environment, and evaluate on unseen handover motion and poses. We further transfer the model across physics simulators and to a real robotic platform." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.549, + 0.314, + 0.564 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.573, + 0.471, + 0.8 + ], + "angle": 0, + "content": "We propose the first framework to learn control policies for vision-based human-to-robot handovers, a critical task for human-robot interaction. While research in Embodied AI has made significant progress in training robot agents in simulated environments, interacting with humans remains challenging due to the difficulties of simulating humans. Fortunately, recent research has developed realistic simulated environments for human-to-robot handovers. Leveraging this result, we introduce a method that is trained with a human-in-the-loop via a two-stage teacher-student framework that uses motion and grasp planning, reinforcement learning, and self-supervision. We show significant performance gains over baselines on a simulation benchmark, sim-to-sim transfer and sim-to-real transfer. Video and code are available at https://handover-sim2real.github.io." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.824, + 0.209, + 0.839 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.849, + 0.47, + 0.88 + ], + "angle": 0, + "content": "Handling over objects between humans and robots is an important tasks for human-robot interaction (HRI) [35]. It" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.385, + 0.901 + ], + "angle": 0, + "content": "*This work was done during an internship at NVIDIA." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.55, + 0.892, + 0.701 + ], + "angle": 0, + "content": "allows robots to assist humans in daily collaborative activities, such as helping to prepare a meal, or to exchange tools and parts with human collaborators in manufacturing settings. To complete these tasks successfully and safely, intricate coordination between human and robot is required. This is challenging, because the robot has to react to human behavior, while only having access to sparse sensory inputs such as a single camera with limited field of view. Therefore, a need for methods that solve interactive tasks such as handovers purely from vision input arises." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Bootstrapping robot training in the real world can be unsafe and time-consuming. Therefore, recent trends in Embodied AI have focused on training agents to act and interact in simulated (sim) environments [11, 12, 19, 43, 45, 46, 51]. With advances in rendering and physics simulation, models have been trained to map raw sensory input to action output, and can even be directly transferred from simulation to the real world [2, 42]. Many successes have been achieved particularly around the suite of tasks of robot navigation, manipulation, or a combination of both. In contrast to these areas, little progress has been made around tasks pertained to HRI. This is largely hindered by the challenges in embedding realistic human agents in these environments, since" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "9654" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.455, + 0.108 + ], + "angle": 0, + "content": "modeling and simulating realistic humans is challenging." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.109, + 0.47, + 0.275 + ], + "angle": 0, + "content": "Despite the challenges, an increasing number of works have attempted to embed realistic human agents in simulated environments [6, 9, 16, 36-38, 48]. Notably, a recent work has introduced a simulation environment (\"Handover-Sim\") for human-to-robot handover (H2R) [6]. To ensure a realistic human handover motion, they use a large motion capture dataset [7] to drive the movements of a virtual human in simulation. However, despite the great potential for training robots, the work of [6] only evaluates off-the-shelf models from prior work, and has not explored any policy training with humans in the loop in their environment." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.277, + 0.473, + 0.716 + ], + "angle": 0, + "content": "We aim to close this gap by introducing a vision-based learning framework for H2R handovers that is trained with a human-in-the-loop (see Fig. 1). In particular, we propose a novel mixed imitation learning (IL) and reinforcement learning (RL) based approach, trained by interacting with the humans in HandoverSim. Our approach draws inspiration from a recent method for learning polices for grasping static objects from point clouds [50], but proposes several key changes to address the challenges in H2R handovers. In contrast to static object grasping, where the policy only requires object information, we additionally encode human hand information in the policy's input. Also, compared to static grasping without a human, we explicitly take human collisions into account in the supervision of training. Finally, the key distinction between static object grasping and handovers is the dynamic nature of the hand and object during handover. To excel on the task, the robot needs to react to dynamic human behavior. Prior work typically relies on open-loop motion planners [49] to generate expert demonstrations, which may result in suboptimal supervision for dynamic cases. To this end, we propose a two-stage training framework. In the first stage, we fix the humans to be stationary and train an RL policy that is partially guided by expert demonstrations obtained from a motion and grasp planner. In the second stage, we finetune the RL policy in the original dynamic setting where the human and robot move simultaneously. Instead of relying on a planner, we propose a self-supervision scheme, where the pre-trained RL policy serves as a teacher to the downstream policy." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.718, + 0.47, + 0.853 + ], + "angle": 0, + "content": "We evaluate our method in three \"worlds\" (see Fig. 1). First, we evaluate on the \"native\" test scenes in HandoverSim [6], which use the same backend physics simulator (Bullet [10]) as training but unseen handover motions from the simulated humans. Next, we perform sim-to-sim evaluation on the test scenes implemented with a different physics simulator (Isaac Gym [29]). Lastly, we investigate sim-to-real transfer by evaluating polices on a real robotic system and demonstrate the benefits of our method." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.47, + 0.901 + ], + "angle": 0, + "content": "We contribute: i) the first framework to train human-to-robot handover tasks from vision input with a human-in-the-loop, ii) a novel teacher-student method to train in the" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.168 + ], + "angle": 0, + "content": "setting of a jointly moving human and robot, iii) an empirical evaluation showing that our approach outperforms baselines on the HandoverSim benchmark, iv) transfer experiments indicating that our method leads to more robust sim-to-sim and sim-to-real transfer compared to baselines." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.183, + 0.642, + 0.199 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.209, + 0.895, + 0.74 + ], + "angle": 0, + "content": "Human-to-Robot Handovers Encouraging progress in hand and object pose estimation [22, 26, 27] has been achieved, aided by the introduction of large hand-object interaction datasets [5, 7, 17, 20, 21, 28, 32, 47, 54, 55]. These developments enable applying model-based grasp planning [3,4,31], a well-studied approach in which full pose estimation and tracking are needed, to H2R handovers [7, 41]. However, these methods require the 3D shape models of the object and cannot handle unseen objects. Alternatively, some recent works [13, 30, 40, 52, 53] achieve H2R handover by employing learning-based grasp planners to generate grasps for novel objects from raw vision inputs such as images or point clouds [33, 34]. While promising results have been shown, these methods work only on an open-loop sequential setting in which the human hand has to stay still once the robot starts to move [40], or need complex hand-designed cost functions for grasp selection [52] and robot motion planning [30, 53] for reactive handovers, which requires expertise in robot motion and control. Hence, these methods are difficult to reproduce and deploy to new environments. Progress towards dynamic simultaneous motion has been shown by a learning-based method [48], using state inputs, leaving an open challenge for training policies that receive visual input directly. In contrast, we propose to learn control policies together with grasp prediction for handovers in an end-to-end manner from segmented point clouds with a deep neural net. To facilitate easy and fair comparisons among different handover methods, [6] propose a physics-simulated environment with diverse objects and realistic human handover behavior collected by a mocap system [7]. They provide benchmark results of several previous handover systems, including a learning-based grasping policy trained with static objects [50]. However, learning a safe and efficient handover policy is not trivial with a human-in-the-loop, which we address in this work." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Policy Learning for Grasping Object grasping is an essential skill for many robot tasks, including handovers. Prior works usually generate grasp poses given a known 3D object geometry such as object shape or pose [3,4,31], which is nontrivial to obtain from real-world sensory input such as images or point clouds. To overcome this, recent works train deep neural networks to predict grasps from sensor data [25] and compute trajectories to reach the predicted grasp pose. Though 3D object geometry is no longer needed, the feasibility is not guaranteed since the grasp" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "9655" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.381 + ], + "angle": 0, + "content": "prediction and trajectory planning are computed separately. Some recent works directly learn grasping policies given raw sensor data. [24] propose a self-supervised RL framework based on RGB images to learn a deep Q-function from real-world grasps. To improve data efficiency, [44] use a low-cost handheld device to collect grasping demonstrations with a wrist-mounted camera. They train an RL-based 6-DoF closed-loop grasping policy with these demonstrations. [50] combines imitation learning from expert data with RL to learn a control policy for object grasping from point clouds. Although this method performs well in HandoverSim [6] when the human hand is not moving, it has difficulty coordinating with a dynamic human hand since the policy is learned with static objects. Instead, our policy is directly learned from large-scale dynamic hand-object trajectories obtained from the real world. To facilitate the training for the dynamic case, we propose a two-stage teacher-student framework, that is conceptually inspired by [8], which has been proven critical through experiments." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.399, + 0.206, + 0.415 + ], + "angle": 0, + "content": "3. Background" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.425, + 0.303, + 0.442 + ], + "angle": 0, + "content": "3.1. Reinforcement Learning" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.45, + 0.47, + 0.573 + ], + "angle": 0, + "content": "MDP We formalize RL as a Markov Decision Process (MDP), that consists of a 5-tuple \\(\\mathcal{M} = (\\mathcal{S},\\mathcal{A},\\mathcal{R},\\mathcal{T},\\gamma)\\) where \\(\\mathcal{S}\\) is the state space, \\(\\mathcal{A}\\) the action space, \\(\\mathcal{R}\\) a scalar reward function, \\(\\mathcal{T}\\) a transition function that maps state-action pairs to distributions over states, and \\(\\gamma\\) a discount factor. The goal is to find a policy that maximizes the long-term reward: \\(\\pi^{*} = \\arg \\max_{\\pi}\\mathbb{E}\\sum_{t = 0}^{t = T}\\gamma^{t}\\mathcal{R}(\\mathbf{s}_{t})\\), with \\(\\mathbf{s}_t\\sim \\mathcal{T}(\\mathbf{s}_{t - 1},\\mathbf{a}_{t - 1})\\) and \\(\\mathbf{a}_{t - 1}\\sim \\pi (\\mathbf{s}_{t - 1})\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.601, + 0.47, + 0.752 + ], + "angle": 0, + "content": "Learning Algorithm In this work, we use TD3 [18], a common algorithm for continuous control. It is an actor-critic method, which consists of a policy \\(\\pi_{\\theta}(\\mathbf{s})\\) (actor) and a Q-function approximator \\(Q_{\\phi}(\\mathbf{s},\\mathbf{a})\\) (critic) that predicts the expected return from a state-action pair. Both are represented by neural networks with parameters \\(\\theta\\) and \\(\\phi\\). TD3 is off-policy, and hence there is a replay buffer in which training transitions are stored. During training, both the actor and critic are updated using samples from the buffer. To update the critic, we minimize the Bellman error:" + }, + { + "type": "equation", + "bbox": [ + 0.08, + 0.767, + 0.468, + 0.805 + ], + "angle": 0, + "content": "\\[\nL _ {\\mathrm {B E}} (\\phi) = \\mathbb {E} _ {\\mathcal {M}} \\left[ \\left(Q _ {\\phi} \\left(\\mathbf {s} _ {t}, \\mathbf {a} _ {t}\\right) - r \\left(\\mathbf {s} _ {t}, \\mathbf {a} _ {t}\\right) + \\gamma Q _ {\\phi} \\left(\\mathbf {s} _ {t + 1}, \\mathbf {a} _ {t + 1}\\right)\\right) ^ {2} \\right] \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.808, + 0.468, + 0.838 + ], + "angle": 0, + "content": "For the actor network, the policy parameters are trained to maximize the Q-values:" + }, + { + "type": "equation", + "bbox": [ + 0.124, + 0.854, + 0.468, + 0.871 + ], + "angle": 0, + "content": "\\[\nL _ {\\mathrm {D D P G}} (\\theta) = \\mathbb {E} _ {\\boldsymbol {\\pi}} \\left[ Q _ {\\phi} \\left(\\mathbf {s} _ {t}, \\mathbf {a} _ {t}\\right) \\mid \\mathbf {s} _ {t}, \\mathbf {a} _ {t} = \\boldsymbol {\\pi} _ {\\theta} \\left(\\mathbf {s} _ {t}\\right) \\right] \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.886, + 0.371, + 0.901 + ], + "angle": 0, + "content": "For more details, we refer the reader to [18]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.091, + 0.738, + 0.106 + ], + "angle": 0, + "content": "3.2. HandoverSim Benchmark" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.114, + 0.892, + 0.357 + ], + "angle": 0, + "content": "HandoverSim [6] is a benchmark for evaluating H2R handover policies in simulation. The task setting consists of a tabletop with different objects, a Panda 7DoF robotic arm with a gripper and a wrist-mounted RGB-D camera, and a simulated human hand. The task starts with the human grasping an object and moving it to a handover pose. The robot should move to the object and grasp it. The task is successful if the object has been grasped from the human without collision and brought to a designated position without dropping. To accurately model the human, trajectories from the DexYCB dataset [7], which comprises a large amount of human-object interaction sequences, are replayed in simulation. Several baselines [49,50,52] are provided for comparison. The setup in HandoverSim has only been used for handover performance evaluation purposes, whereas in this work we utilize it as a learning environment." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.372, + 0.591, + 0.387 + ], + "angle": 0, + "content": "4. Method" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.398, + 0.892, + 0.609 + ], + "angle": 0, + "content": "The overall pipeline is depicted in Fig. 2 and consists of three different modules: perception, vision-based control, and the handover environment. The perception module receives egocentric visual information from the handover environment and processes it into segmented point clouds. The vision-based control module receives the point clouds and predicts the next action for the robot and whether to approach or to grasp the object. This information is passed to the handover environment, which updates the robot state and sends the new visual information to the perception module. Note that the input to our method comes from the wrist-mounted camera, i.e., there is no explicit information, such as object or hand pose, provided to the agent. We will now explain each of the modules of our method in more detail." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.62, + 0.719, + 0.635 + ], + "angle": 0, + "content": "4.1. Handover Environment" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.892, + 0.886 + ], + "angle": 0, + "content": "We split the handover task into two distinct phases (see Fig. 2). First, during the approaching phase, the robot moves to a pre-grasp pose that is close to the object by running the learned control policy \\(\\pi\\). A learned grasp predictor \\(\\sigma\\) continuously computes a grasp probability to determine when the system can proceed to the second phase. Once the pre-grasp pose is reached and the grasp prediction is confident to take over the object from the human, the task will switch to the grasping phase, in which the end-effector moves forward to the final grasp pose in open-loop fashion and closes the gripper to grasp the object. Finally, after object grasping, the robot follows a predetermined trajectory to retract to a base position and complete the episode. This task logic is used in both our simulation environment and the real robot deployment. Sequencing based on a pre-grasp pose is widely used in literature for dynamic grasping [1]." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.886, + 0.891, + 0.901 + ], + "angle": 0, + "content": "We follow the HandoverSim task setup [6], where the hu" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.957 + ], + "angle": 0, + "content": "9656" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.122, + 0.094, + 0.861, + 0.295 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.304, + 0.895, + 0.404 + ], + "angle": 0, + "content": "Figure 2. Method Overview. The Perception module takes egocentric RGB-D and segmentation images from the environment and outputs a hand/object segmented point cloud. Next, the segmented point cloud is passed to the Vision-based Control module and processed by PointNet++ [39] to obtain a lower-dimensional representation. This embedding is used as input to both the control policy and the grasp predictor. Each task episode in the Handover Environment follows two phases: during the approaching phase, the robot moves towards a pre-grasp pose, driven by the control policy \\(\\pi\\) that outputs end-effector actions a. A learned grasp predictor monitors the motion and determines when the robot should switch into the grasping phase, which follows the steps: 1. moving the gripper forward from a pre-grasp to a grasping pose 2. closing the gripper 3. retracting the object to a designated location, after which the episode ends." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.417, + 0.471, + 0.554 + ], + "angle": 0, + "content": "man hand and objects are simulated by replaying data from the DexYCB dataset [7] (see Sec. 3.2). First, actions a in the form of the next 6DoF end-effector pose (translation and rotation) are received from the policy \\(\\pi (\\mathbf{a}|\\mathbf{s})\\). We then convert the end-effector pose into a target robot configuration using inverse kinematics. Thereafter, we use PD-controllers to compute torques, which are applied to the robot. Finally, the visual information is rendered from the robot's wrist-mounted RGB-D camera and sent to the perception module." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.564, + 0.199, + 0.58 + ], + "angle": 0, + "content": "4.2. Perception" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.588, + 0.471, + 0.724 + ], + "angle": 0, + "content": "Our policy network takes a segmented hand and object point cloud as input. In the handover environment, we first render an egocentric RGB-D image from the wrist camera. Then we obtain the object point cloud \\(\\mathbf{p}_o\\) and hand point cloud \\(\\mathbf{p}_h\\) by overlaying the ground-truth segmentation mask with the RGB-D image. Since the hand and object may not always be visible from the current egocentric view, we keep track of the last available point clouds. The latest available point clouds are then sent to the control module." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.734, + 0.279, + 0.749 + ], + "angle": 0, + "content": "4.3. Vision-Based Control" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.758, + 0.471, + 0.91 + ], + "angle": 0, + "content": "Input Representation Depending on the amount of points contained in the hand point cloud \\(\\mathbf{p}_h\\) and object point cloud \\(\\mathbf{p}_o\\), we down- or upsample them into constant size. Next, we concatenate the two point clouds into a single point cloud \\(\\mathbf{p}\\) and add two one-hot-encoded vectors to indicate the locations of object and hand points within \\(\\mathbf{p}\\). We then encode the point cloud into a lower dimensional representation \\(\\psi(\\mathbf{p})\\) by passing it through PointNet++ [39]. Finally, the lower dimensional encoding \\(\\psi(\\mathbf{p})\\) is passed on to the control policy \\(\\pi\\) and the grasp prediction network \\(\\sigma\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.417, + 0.895, + 0.493 + ], + "angle": 0, + "content": "Control Policy The policy network \\(\\pi(\\mathbf{a}|\\psi(\\mathbf{p}))\\) is a small, two-layered MLP that takes the PointNet++ embedding as input state (\\(\\mathbf{s} = \\psi(\\mathbf{p})\\)) and predicts actions \\(\\mathbf{a}\\) that correspond to the change in 6DoF end-effector pose. These are passed on to the handover environment." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.504, + 0.893, + 0.746 + ], + "angle": 0, + "content": "Grasp Prediction We introduce a grasp prediction network \\(\\sigma(\\psi(\\mathbf{p}))\\) that predicts when the robot should switch from approaching to executing the grasping motion (cf. Fig. 2). We model grasp prediction as a binary classification task. The input corresponds to the PointNet++ embedding \\(\\psi(\\mathbf{p})\\), which is fed through a 3-layered MLP. The output is a probability that indicates the likelihood of a successful grasp given the current point cloud feature. If the probability is above a tunable threshold, we execute an open-loop grasping motion. The model is trained offline with pre-grasp poses attained from [15]. We augment the dataset by adding random noise to pre-grasp poses. To determine the labels, we initialize the robot with the pre-grasp poses in the physics simulation and execute the forward grasping motion. The label is one if the grasp is successful, and zero otherwise. We use a binary cross-entropy loss for training." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.756, + 0.82, + 0.772 + ], + "angle": 0, + "content": "4.4. Two-Stage Teacher-Student Training" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.781, + 0.892, + 0.903 + ], + "angle": 0, + "content": "We aim at training a handover policy capable of moving simultaneously with the human. Training this policy directly in the setting of dynamic motion is challenging because expert demonstrations with open-loop planners to guide training can only be obtained when the human is stationary. A key contribution of our work is a two-stage training scheme for handovers that incrementally trains the policy to alleviate this challenge. In the first stage, we pretrain" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "9657" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.101, + 0.09, + 0.874, + 0.322 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.336, + 0.896, + 0.449 + ], + "angle": 0, + "content": "Figure 3. Training Procedure. In the pretraining stage (top left box), the human hand is stationary. We alternate between collecting expert demonstrations via motion planning and exploration data with the RL policy \\(\\pi_{\\mathrm{pre}}\\). Transitions \\(\\mathbf{d}\\) are stored in a replay buffer \\(\\mathcal{D}\\). During training (green box, right), a batch of randomly sampled transitions from the replay buffer is passed through PointNet++ and the actor and critic networks. In the finetuning stage (bottom left box), the human and robot move concurrently. The expert motion planner is replaced by the expert policy \\(\\pi_{\\mathrm{exp}}\\), which shares the weights of the pretrained policy \\(\\pi_{\\mathrm{pre}}\\). This policy network will be kept frozen for the rest of training and serves as a regularizer for the RL agent. The RL agent's actor network \\(\\pi_{*}\\) and critic network \\(Q_{*}\\) are also initialized with the weights of pretrained agent's networks, but the model will be updated during finetuning. In this stage, transitions are stored in a new replay buffer \\(\\mathcal{D}_{*}\\). Data is sampled solely from this buffer during finetuning." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.468, + 0.471, + 0.529 + ], + "angle": 0, + "content": "in a setting where the robot only starts moving once the human has stopped (sequential). This pretrained policy is further finetuned in the second stage in which the human and robot move simultaneously (simultaneous)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.539, + 0.47, + 0.719 + ], + "angle": 0, + "content": "Pretraining in Sequential Setting In the sequential setting, the robot starts moving once the human has come to a stop (see Fig. 3, top left). To grasp the object from the stationary human hand, we leverage motion planning to provide expert demonstrations. During data collection, we alternate between motion planning and RL-based exploration. In both cases, we store the transitions \\(\\mathbf{d}_t = \\{\\mathbf{p}_t,\\mathbf{a}_t,\\mathbf{g}_t,\\mathbf{r}_t,\\mathbf{p}_{t + 1},\\mathbf{e}_t\\}\\) in a replay buffer \\(\\mathcal{D}\\), from which we sample during network training. The term \\(\\mathbf{p}_t\\) and \\(\\mathbf{p}_{t + 1}\\) indicate the point cloud and the next point cloud, \\(\\mathbf{a}_t\\) the action, \\(\\mathbf{g}_t\\) the pre-grasp goal pose, \\(\\mathbf{r}_t\\) the reward, and \\(\\mathbf{e}_t\\) an indicator of whether the transition is from the expert." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Inspired by [50], we collect expert trajectories with the OMG planner [49] that leverages ground-truth states. Note that some expert trajectories generated by the planner result in collision with the hand, which is why we introduce an offline pre-filtering scheme. We first parse the ACRONYM dataset [14] for potential grasps. We then run collision checking to filter out grasps where the robot and human hand collide. For the set of remaining collision-free grasps, we plan trajectories to grasp the object and execute them in open-loop fashion. On the other hand, the RL policy \\(\\pi_{\\mathrm{pre}}\\) explores the environment and receives a sparse reward, i.e., the reward is one if the task is completed successfully, oth-" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.468, + 0.892, + 0.499 + ], + "angle": 0, + "content": "erwise zero. Hence, collisions with the human will get implicitly penalized by not receiving any positive reward." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.505, + 0.893, + 0.793 + ], + "angle": 0, + "content": "Finetuning in Simultaneous Setting In this setting, the human and robot move at the same time. Hence, we cannot rely on motion and grasp planning to guide the policy. On the other hand, simply taking the pre-trained policy \\(\\pi_{\\mathrm{pre}}\\) from the sequential setting and continue training it without an expert leads to an immediate drop in performance. Hence, we introduce a self-supervision scheme for stability reasons, i.e., we want to keep the finetuning policy close to the pre-trained policy. To this end, we replace the expert planner from the sequential setting by an expert policy \\(\\pi_{\\mathrm{exp}}\\), which is initialized with the weights of the pre-trained policy \\(\\pi_{\\mathrm{pre}}\\) that already provides a reasonable prior policy (see Fig. 3 bottom left). Therefore, we have two policies: i) the expert policy \\(\\pi_{\\mathrm{exp}}\\) as proxy for the motion and grasping planner. We freeze the network weights of this policy, ii) the finetuning policy \\(\\pi_*\\) and critic \\(Q_*\\), which are initialized with the weights of the pre-trained policy \\(\\pi_{\\mathrm{pre}}\\) and critic \\(Q_{\\mathrm{pre}}\\), respectively. We proceed to train these two networks using the loss functions which we describe next." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.8, + 0.895, + 0.877 + ], + "angle": 0, + "content": "Network Training During training, we sample a batch of random transitions from the replay buffer \\(\\mathcal{D}\\). The policy network is trained using a combination of behavior cloning, RL-based losses and an auxiliary objective. In particular, the policy is updated using the following loss function:" + }, + { + "type": "equation", + "bbox": [ + 0.561, + 0.886, + 0.893, + 0.903 + ], + "angle": 0, + "content": "\\[\nL (\\theta) = \\lambda L _ {\\mathrm {B C}} + (1 - \\lambda) L _ {\\mathrm {D D P G}} + L _ {\\mathrm {A U X}}, \\tag {3}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "9658" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.141, + 0.089, + 0.828, + 0.234 + ], + "angle": 0, + "content": "
success (%)mean accum time (s)failure (%)
execplantotalcontactdroptimeouttotal
SequentialOMG Planner [49] †62.508.3091.4149.72227.788.331.3937.50
Yang et al. [52] †64.584.8640.0364.90017.3611.816.2535.42
GA-DDPG [50]50.007.1390.1427.2814.8619.4425.6950.00
GA-DDPG [50] finetuned57.186.3240.0866.4116.4827.089.2642.82
Ours75.237.7430.1777.9229.2613.432.0824.77
Simult.GA-DDPG [50]36.814.6640.1324.7969.0325.0029.1763.19
GA-DDPG [50] finetuned54.864.8320.0824.9146.7126.3912.0445.14
Ours68.756.2320.1786.4118.8017.824.6331.25
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.242, + 0.892, + 0.298 + ], + "angle": 0, + "content": "Table 1. HandoverSim Benchmark Evaluation. Comparison of our method against various baselines from the HandoverSim benchmark [6]. In the sequential setting, we find that our baseline achieves better overall success rates than the baselines. In the simultaneous setting, we outperform the applicable baselines by large margins. The results for our method are averaged across 3 random seeds. \\(\\dagger\\): both methods [49, 52] are evaluated with ground-truth states in [6] and thus are not directly comparable with ours." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.313, + 0.471, + 0.404 + ], + "angle": 0, + "content": "where \\( L_{\\mathrm{BC}} \\) is a behavior cloning loss that keeps the policy close to the expert policy, \\( L_{\\mathrm{DDPG}} \\) is the standard actor-critic loss described in Eq. 2, and \\( L_{\\mathrm{AUX}} \\) is an auxiliary objective that predicts the grasping goal pose of the end-effector. The coefficient \\( \\lambda \\) balances the behavior cloning and the RL objective. The critic loss is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.2, + 0.411, + 0.47, + 0.427 + ], + "angle": 0, + "content": "\\[\nL (\\phi) = L _ {\\mathrm {B E}} + L _ {\\mathrm {A U X}}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.43, + 0.47, + 0.476 + ], + "angle": 0, + "content": "where \\( L_{\\mathrm{BE}} \\) indicates the Bellman error from Eq. 1 and \\( L_{\\mathrm{AUX}} \\) is the same auxiliary loss used in Eq. 3. We refer the reader to supplementary material or [50] for more details." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.489, + 0.21, + 0.506 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.514, + 0.47, + 0.62 + ], + "angle": 0, + "content": "We first evaluate our approach in simulation using the HandoverSim benchmark (Sec. 5.1). Next, we investigate the performance of sim-to-sim transfer by evaluating the trained models on the test environments powered by a different physics engine (Sec. 5.2). Finally, we apply the trained model to a real-world robotic system and analyze the performance of sim-to-real transfer (Sec. 5.3)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.629, + 0.287, + 0.644 + ], + "angle": 0, + "content": "5.1. Simulation Evaluation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.652, + 0.47, + 0.835 + ], + "angle": 0, + "content": "Setup HandoverSim [6] contains 1,000 unique H2R handover scenes divided into train, val, and test splits. Each scene contains a unique human handover motion. We evaluate on the \"s0\" setup which contains 720 training and 144 testing scenes. See the supp. material for evaluations on unseen objects, subjects, and handedness. Following the evaluation of GA-DDPG [50] in [6], we consider two settings: (1) the \"sequential\" setting where the robot is allowed to move only after the human hand reaches the handover location and remains static there (i.e., \"hold\" in [6]), and (2) the \"simultaneous\" setting where the robot is allowed to move from the beginning of the episode (i.e., \"w/o hold\" in [6])." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Metrics We follow the evaluation protocol in Handover-Sim [6]. A handover is considered successful if the robot grasps the object from the human hand and moves it to a designated location. A failure is claimed and the episode" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.313, + 0.892, + 0.449 + ], + "angle": 0, + "content": "is terminated if any of the following three conditions occur: (1) the robot collides with the hand (contact), (2) the robot drops the object (drop), or (3) a maximum time limit is reached (timeout). Besides efficacy, the benchmark also reports efficiency in time. The time metric is further broken down into (1) the execution time (exec), i.e., the time to physically move the robot, and (2) the planning time (plan), i.e., the time spent on running the policy. All reported metrics are averaged over the rollouts on the test scenes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.457, + 0.892, + 0.593 + ], + "angle": 0, + "content": "Baselines Our primary baseline is GA-DDPG [50]. Besides comparing with the original model (i.e., trained in [50] for table-top grasping and evaluated in [6]), we additionally compare with a variant finetuned on HandoverSim (\"GA-DDPG [50] finetuned\"). For completeness, we also include two other baselines from [6]: \"OMG Planner [49]\" and \"Yang et al. [52]\". However, both of them are evaluated with ground-truth state input in [6] and thus are not directly comparable with our method." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.601, + 0.892, + 0.844 + ], + "angle": 0, + "content": "Results Tab. 1 reports the evaluation results on the test scenes. In the sequential setting, our method significantly outperforms all the baselines in terms of success rate, even compared to methods that use state-based input. Our method is slightly slower on average than GA-DDDPG in terms of total time needed for handovers. In the simultaneous setting, our method clearly outperforms GA-DDDPG, which has low success rates. Qualitatively, we observe that GA-DDDPG directly tries to grasp the object from the user while it is still moving, while our method follows the hand and finds a feasible grasp once the hand has come to a stop, resulting in a trade-off on the overall execution time. We provide a qualitative example of this behavior in Fig. 4 (a) and in the supplementary video. We also refer to the supp. material for a discussion of limitations and a robustness analysis of our pipeline under noisy observations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.903 + ], + "angle": 0, + "content": "Ablations We evaluate our design choices in an ablation study and report the results in Tab. 2. We analyze the vision backbone by replacing PointNet++ with a ResNet18 [23]" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "9659" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.118, + 0.088, + 0.85, + 0.616 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.623, + 0.895, + 0.681 + ], + "angle": 0, + "content": "Figure 4. Qualitative results. We provide a comparison to show our methods' advantages over GA-DDPG [50]. (a) Our method reacts to the moving human, while the baseline tries to go for a grasp directly, which leads to collision. (b) In the sim-to-sim transfer, we often find that the baseline does not find a grasp on the object. (c) In the sim-to-real experiment, GA-DDPG usually tries to get to a grasp directly, while our method adjusts the gripper into a stable grasping pose first. See the video in supp. material for more qualitative examples." + }, + { + "type": "table", + "bbox": [ + 0.096, + 0.687, + 0.446, + 0.823 + ], + "angle": 0, + "content": "
Ablation Study
success (%)failure (%)
contactdroptimeout
w/ RGBDM + ResNet1834.106.2045.8013.90
w/ third person view60.429,9525.693.94
w/o hand point cloud59.0324.0711.585.32
w/o aux prediction70.6010.6516.202.54
w/o standoff52.557.8736.802.78
w/o finetuning73.389.0313.893.70
Ours75.239.2613.432.08
w/o finetuning simul.62.2711.8120.375.56
Ours simul.68.758.817.824.63
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.827, + 0.473, + 0.899 + ], + "angle": 0, + "content": "Table 2. Ablation. We ablate the vision backbone, hand perception, and egocentric view. We also study the effect of finetuning, the auxiliary prediction, and splitting the task into two phases. All design choices are crucial aspects of our method with regards to overall performance. Results are averaged over 3 random seeds." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.69, + 0.892, + 0.903 + ], + "angle": 0, + "content": "that processes the RGB and depth/segmentation (DM) images. Similar to the findings in GA-DDPG, the PointNet++ backbone performs better. Next, we train our method from third person view instead of egocentric view and without active hand segmentation (\\(w/o\\) hand point cloud), i.e., the policy only perceives the object point cloud but not the hand point cloud. We also ablate the auxiliary prediction (\\(w/o\\) aux prediction) and evaluate a variant that directly learns to approach and grasp the object instead of using the two task phases of approaching and grasping (\\(w/o\\) standoff). Lastly, we compare against our pretrained model, which was only trained in the sequential setting without finetuning (\\(w/o\\) finetuning). We find that the ablated components comprise important elements of our method. The results indicate an in-" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "9660" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.097, + 0.089, + 0.445, + 0.207 + ], + "angle": 0, + "content": "
Sim-to-Sim
success (%)failure (%)
contactdroptimeout
SequentialGA-DDPG [50]19.444.8647.2228.47
GA-DDPG [50] finetuned11.816.2568.7513.19
Ours44.219.4940.515.79
Ours w/o grasp54.407.8733.344.40
Simult.GA-DDPG [50]11.1115.9748.6124.31
GA-DDPG [50] finetuned16.679.7263.899.72
Ours39.589.0343.757.64
Ours w/o grasp pred.47.9210.6535.885.56
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.211, + 0.47, + 0.253 + ], + "angle": 0, + "content": "Table 3. Sim-to-Sim Experiment. We evaluate sim-to-sim transfer of the learning-based method to Isaac Gym [29], Our method shows better transfer capabilities than GA-DDPG [50]." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.266, + 0.469, + 0.311 + ], + "angle": 0, + "content": "creased amount of hand collision or object drop in all ablations. A closer analysis in the simultaneous setting shows that our finetuned model outperforms the pretrained model." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.321, + 0.273, + 0.336 + ], + "angle": 0, + "content": "5.2. Sim-to-Sim Transfer" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.344, + 0.47, + 0.662 + ], + "angle": 0, + "content": "Instead of directly transferring to the real world, we first evaluate the robustness of the models by transferring them to a different physics simulator. We re-implement the HandoverSim environment following the mechanism presented in [6] except for replacing the backend physics engine from Bullet [10] to Isaac Gym [29]. We then evaluate the models trained on the original Bullet-based environment on the test scenes powered by Isaac Gym. The results are presented in Tab. 3. We observe a significant drop for GA-DDPG on the success rates (i.e., to below \\(20\\%\\)) in both settings. Qualitatively, we see that grasps are often either missed completely or only partially grasped (see Fig. 4 (b)). On the other hand, our method is able to retain higher success rates. Expectedly, it also suffers from a loss in performance. We analyze the influence of our grasp predictor on transfer performance and compare against a variant where we execute the grasping motion after a fixed amount of time (Ours w/o grasp pred.), which will leave the robot enough time to find a pre-grasp pose. Part of the performance drop is caused by the grasp predictor initiating the grasping phase at the wrong time, which can be improved upon in future work." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.672, + 0.277, + 0.687 + ], + "angle": 0, + "content": "5.3. Sim-to-Real Transfer" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.696, + 0.469, + 0.832 + ], + "angle": 0, + "content": "Finally, we deploy the models trained in HandoverSim on a real robotic platform. We follow the perception pipeline used in [50,52] to generate segmented hand and object point clouds for the policy, and use the output to update the end effector's target position. We compare our method against GA-DDPG [50] with two sets of experiments: (1) a pilot study with controlled handover poses and (2) a user evaluation with free-form handovers. For experimental details and the full results, please see the supp. material." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Pilot Study We first conduct a pilot study with two subjects. The subjects are instructed to handover 10 objects from HandoverSim by grasping and presenting the objects in controlled poses. For each object, we test with 6 poses" + }, + { + "type": "table", + "bbox": [ + 0.518, + 0.089, + 0.868, + 0.242 + ], + "angle": 0, + "content": "
Subject 1Subject 2
GA-DDPG [50]OursGA-DDPG [50]Ours
011_banana3 / 66 / 66 / 65 / 6
037_scissors2 / 65 / 63 / 65 / 6
006_mustard_bottle1 / 63 / 62 / 64 / 6
024_bowl3 / 64 / 63 / 63 / 6
040_large Marker0 / 64 / 64 / 65 / 6
003_cracker_box3 / 62 / 60 / 62 / 6
052extra_large_clamp1 / 64 / 65 / 65 / 6
008_pudding_box3 / 66 / 64 / 64 / 6
010_potted_meat_can2 / 62 / 63 / 64 / 6
021_bleach_cleanser3 / 65 / 63 / 64 / 6
total21 / 6041 / 6033 / 6041 / 60
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.25, + 0.892, + 0.278 + ], + "angle": 0, + "content": "Table 4. Sim-to-Real Experiment. Success rates of the pilot study. Our method outperforms GA-DDPG [50] for both subjects." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.306, + 0.892, + 0.457 + ], + "angle": 0, + "content": "(3 poses for each hand) with varying object orientation and varying amount of hand occlusion, resulting in 60 poses per subject. The same set of poses are used in testing both our model and GA-DDPG [50]. The success rates are shown Tab. 4. Results indicate that our method outperforms GA-DDPG [50] for both subjects on the overall success rate (i.e., 41/60 versus 21/60 for Subject 1). Qualitatively, we observe that GA-DDPG [50] tends to fail more from unstable grasping as well as hand collision. Fig. 4 (c) shows two examples of the real world handover trials." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.468, + 0.892, + 0.65 + ], + "angle": 0, + "content": "User Evaluation We further recruited 6 users to compare the two methods and collected feedback from a questionnaire with Likert-scale and open-ended questions. In contrast to the pilot study, we asked the users to handover the 10 objects in ways that are most comfortable to them. We repeated the same experimental process for both methods, and counterbalanced the order to avoid bias. From participants' feedback, the majority agreed that the timing of our method is more appropriate and our method can adjust between different object poses better. The interpretability of the robot's motion was also acknowledged by their comments. Please see the supp. material for more details." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.666, + 0.618, + 0.681 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.692, + 0.892, + 0.828 + ], + "angle": 0, + "content": "In this work, we have presented a learning-based framework for human-to-robot handovers from vision input with a simulated human-in-the-loop. We have introduced a two-stage teacher-student training procedure. In our experiments we have shown that our method outperforms baselines by a significant margin on the HandoverSim benchmark [6]. Furthermore, we have demonstrated that our approach is more robust when transferring to a different physics simulator and a real robotic system." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.845, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Acknowledgements We thank Tao Chen and Adithyavairavan Murali for laying the groundwork, Lirui Wang for the help with GA-DDPG, and Mert Albaba, Christoph Gebhardt, Thomas Langerak and Juan Zarate for their feedback on the manuscript." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "9661" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.171 + ], + "angle": 0, + "content": "[1] Iretiayo Akinola, Jingxi Xu, Shuran Song, and Peter K Allen. Dynamic grasping with reachability and motion awareness. 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We introduce a framework to learn human-to-robot handover policies from point cloud input. Our policies take input from a wrist mounted camera and directly generate action output for the robot's end effector. We train our policies in a simulated handover environment, and evaluate on unseen handover motion and poses. We further transfer the model across physics simulators and to a real robotic platform. + +# Abstract + +We propose the first framework to learn control policies for vision-based human-to-robot handovers, a critical task for human-robot interaction. While research in Embodied AI has made significant progress in training robot agents in simulated environments, interacting with humans remains challenging due to the difficulties of simulating humans. Fortunately, recent research has developed realistic simulated environments for human-to-robot handovers. Leveraging this result, we introduce a method that is trained with a human-in-the-loop via a two-stage teacher-student framework that uses motion and grasp planning, reinforcement learning, and self-supervision. We show significant performance gains over baselines on a simulation benchmark, sim-to-sim transfer and sim-to-real transfer. Video and code are available at https://handover-sim2real.github.io. + +# 1. Introduction + +Handling over objects between humans and robots is an important tasks for human-robot interaction (HRI) [35]. It + +allows robots to assist humans in daily collaborative activities, such as helping to prepare a meal, or to exchange tools and parts with human collaborators in manufacturing settings. To complete these tasks successfully and safely, intricate coordination between human and robot is required. This is challenging, because the robot has to react to human behavior, while only having access to sparse sensory inputs such as a single camera with limited field of view. Therefore, a need for methods that solve interactive tasks such as handovers purely from vision input arises. + +Bootstrapping robot training in the real world can be unsafe and time-consuming. Therefore, recent trends in Embodied AI have focused on training agents to act and interact in simulated (sim) environments [11, 12, 19, 43, 45, 46, 51]. With advances in rendering and physics simulation, models have been trained to map raw sensory input to action output, and can even be directly transferred from simulation to the real world [2, 42]. Many successes have been achieved particularly around the suite of tasks of robot navigation, manipulation, or a combination of both. In contrast to these areas, little progress has been made around tasks pertained to HRI. This is largely hindered by the challenges in embedding realistic human agents in these environments, since + +modeling and simulating realistic humans is challenging. + +Despite the challenges, an increasing number of works have attempted to embed realistic human agents in simulated environments [6, 9, 16, 36-38, 48]. Notably, a recent work has introduced a simulation environment ("Handover-Sim") for human-to-robot handover (H2R) [6]. To ensure a realistic human handover motion, they use a large motion capture dataset [7] to drive the movements of a virtual human in simulation. However, despite the great potential for training robots, the work of [6] only evaluates off-the-shelf models from prior work, and has not explored any policy training with humans in the loop in their environment. + +We aim to close this gap by introducing a vision-based learning framework for H2R handovers that is trained with a human-in-the-loop (see Fig. 1). In particular, we propose a novel mixed imitation learning (IL) and reinforcement learning (RL) based approach, trained by interacting with the humans in HandoverSim. Our approach draws inspiration from a recent method for learning polices for grasping static objects from point clouds [50], but proposes several key changes to address the challenges in H2R handovers. In contrast to static object grasping, where the policy only requires object information, we additionally encode human hand information in the policy's input. Also, compared to static grasping without a human, we explicitly take human collisions into account in the supervision of training. Finally, the key distinction between static object grasping and handovers is the dynamic nature of the hand and object during handover. To excel on the task, the robot needs to react to dynamic human behavior. Prior work typically relies on open-loop motion planners [49] to generate expert demonstrations, which may result in suboptimal supervision for dynamic cases. To this end, we propose a two-stage training framework. In the first stage, we fix the humans to be stationary and train an RL policy that is partially guided by expert demonstrations obtained from a motion and grasp planner. In the second stage, we finetune the RL policy in the original dynamic setting where the human and robot move simultaneously. Instead of relying on a planner, we propose a self-supervision scheme, where the pre-trained RL policy serves as a teacher to the downstream policy. + +We evaluate our method in three "worlds" (see Fig. 1). First, we evaluate on the "native" test scenes in HandoverSim [6], which use the same backend physics simulator (Bullet [10]) as training but unseen handover motions from the simulated humans. Next, we perform sim-to-sim evaluation on the test scenes implemented with a different physics simulator (Isaac Gym [29]). Lastly, we investigate sim-to-real transfer by evaluating polices on a real robotic system and demonstrate the benefits of our method. + +We contribute: i) the first framework to train human-to-robot handover tasks from vision input with a human-in-the-loop, ii) a novel teacher-student method to train in the + +setting of a jointly moving human and robot, iii) an empirical evaluation showing that our approach outperforms baselines on the HandoverSim benchmark, iv) transfer experiments indicating that our method leads to more robust sim-to-sim and sim-to-real transfer compared to baselines. + +# 2. Related Work + +Human-to-Robot Handovers Encouraging progress in hand and object pose estimation [22, 26, 27] has been achieved, aided by the introduction of large hand-object interaction datasets [5, 7, 17, 20, 21, 28, 32, 47, 54, 55]. These developments enable applying model-based grasp planning [3,4,31], a well-studied approach in which full pose estimation and tracking are needed, to H2R handovers [7, 41]. However, these methods require the 3D shape models of the object and cannot handle unseen objects. Alternatively, some recent works [13, 30, 40, 52, 53] achieve H2R handover by employing learning-based grasp planners to generate grasps for novel objects from raw vision inputs such as images or point clouds [33, 34]. While promising results have been shown, these methods work only on an open-loop sequential setting in which the human hand has to stay still once the robot starts to move [40], or need complex hand-designed cost functions for grasp selection [52] and robot motion planning [30, 53] for reactive handovers, which requires expertise in robot motion and control. Hence, these methods are difficult to reproduce and deploy to new environments. Progress towards dynamic simultaneous motion has been shown by a learning-based method [48], using state inputs, leaving an open challenge for training policies that receive visual input directly. In contrast, we propose to learn control policies together with grasp prediction for handovers in an end-to-end manner from segmented point clouds with a deep neural net. To facilitate easy and fair comparisons among different handover methods, [6] propose a physics-simulated environment with diverse objects and realistic human handover behavior collected by a mocap system [7]. They provide benchmark results of several previous handover systems, including a learning-based grasping policy trained with static objects [50]. However, learning a safe and efficient handover policy is not trivial with a human-in-the-loop, which we address in this work. + +Policy Learning for Grasping Object grasping is an essential skill for many robot tasks, including handovers. Prior works usually generate grasp poses given a known 3D object geometry such as object shape or pose [3,4,31], which is nontrivial to obtain from real-world sensory input such as images or point clouds. To overcome this, recent works train deep neural networks to predict grasps from sensor data [25] and compute trajectories to reach the predicted grasp pose. Though 3D object geometry is no longer needed, the feasibility is not guaranteed since the grasp + +prediction and trajectory planning are computed separately. Some recent works directly learn grasping policies given raw sensor data. [24] propose a self-supervised RL framework based on RGB images to learn a deep Q-function from real-world grasps. To improve data efficiency, [44] use a low-cost handheld device to collect grasping demonstrations with a wrist-mounted camera. They train an RL-based 6-DoF closed-loop grasping policy with these demonstrations. [50] combines imitation learning from expert data with RL to learn a control policy for object grasping from point clouds. Although this method performs well in HandoverSim [6] when the human hand is not moving, it has difficulty coordinating with a dynamic human hand since the policy is learned with static objects. Instead, our policy is directly learned from large-scale dynamic hand-object trajectories obtained from the real world. To facilitate the training for the dynamic case, we propose a two-stage teacher-student framework, that is conceptually inspired by [8], which has been proven critical through experiments. + +# 3. Background + +# 3.1. Reinforcement Learning + +MDP We formalize RL as a Markov Decision Process (MDP), that consists of a 5-tuple $\mathcal{M} = (\mathcal{S},\mathcal{A},\mathcal{R},\mathcal{T},\gamma)$ where $\mathcal{S}$ is the state space, $\mathcal{A}$ the action space, $\mathcal{R}$ a scalar reward function, $\mathcal{T}$ a transition function that maps state-action pairs to distributions over states, and $\gamma$ a discount factor. The goal is to find a policy that maximizes the long-term reward: $\pi^{*} = \arg \max_{\pi}\mathbb{E}\sum_{t = 0}^{t = T}\gamma^{t}\mathcal{R}(\mathbf{s}_{t})$ , with $\mathbf{s}_t\sim \mathcal{T}(\mathbf{s}_{t - 1},\mathbf{a}_{t - 1})$ and $\mathbf{a}_{t - 1}\sim \pi (\mathbf{s}_{t - 1})$ . + +Learning Algorithm In this work, we use TD3 [18], a common algorithm for continuous control. It is an actor-critic method, which consists of a policy $\pi_{\theta}(\mathbf{s})$ (actor) and a Q-function approximator $Q_{\phi}(\mathbf{s},\mathbf{a})$ (critic) that predicts the expected return from a state-action pair. Both are represented by neural networks with parameters $\theta$ and $\phi$ . TD3 is off-policy, and hence there is a replay buffer in which training transitions are stored. During training, both the actor and critic are updated using samples from the buffer. To update the critic, we minimize the Bellman error: + +$$ +L _ {\mathrm {B E}} (\phi) = \mathbb {E} _ {\mathcal {M}} \left[ \left(Q _ {\phi} \left(\mathbf {s} _ {t}, \mathbf {a} _ {t}\right) - r \left(\mathbf {s} _ {t}, \mathbf {a} _ {t}\right) + \gamma Q _ {\phi} \left(\mathbf {s} _ {t + 1}, \mathbf {a} _ {t + 1}\right)\right) ^ {2} \right] \tag {1} +$$ + +For the actor network, the policy parameters are trained to maximize the Q-values: + +$$ +L _ {\mathrm {D D P G}} (\theta) = \mathbb {E} _ {\boldsymbol {\pi}} \left[ Q _ {\phi} \left(\mathbf {s} _ {t}, \mathbf {a} _ {t}\right) \mid \mathbf {s} _ {t}, \mathbf {a} _ {t} = \boldsymbol {\pi} _ {\theta} \left(\mathbf {s} _ {t}\right) \right] \tag {2} +$$ + +For more details, we refer the reader to [18]. + +# 3.2. HandoverSim Benchmark + +HandoverSim [6] is a benchmark for evaluating H2R handover policies in simulation. The task setting consists of a tabletop with different objects, a Panda 7DoF robotic arm with a gripper and a wrist-mounted RGB-D camera, and a simulated human hand. The task starts with the human grasping an object and moving it to a handover pose. The robot should move to the object and grasp it. The task is successful if the object has been grasped from the human without collision and brought to a designated position without dropping. To accurately model the human, trajectories from the DexYCB dataset [7], which comprises a large amount of human-object interaction sequences, are replayed in simulation. Several baselines [49,50,52] are provided for comparison. The setup in HandoverSim has only been used for handover performance evaluation purposes, whereas in this work we utilize it as a learning environment. + +# 4. Method + +The overall pipeline is depicted in Fig. 2 and consists of three different modules: perception, vision-based control, and the handover environment. The perception module receives egocentric visual information from the handover environment and processes it into segmented point clouds. The vision-based control module receives the point clouds and predicts the next action for the robot and whether to approach or to grasp the object. This information is passed to the handover environment, which updates the robot state and sends the new visual information to the perception module. Note that the input to our method comes from the wrist-mounted camera, i.e., there is no explicit information, such as object or hand pose, provided to the agent. We will now explain each of the modules of our method in more detail. + +# 4.1. Handover Environment + +We split the handover task into two distinct phases (see Fig. 2). First, during the approaching phase, the robot moves to a pre-grasp pose that is close to the object by running the learned control policy $\pi$ . A learned grasp predictor $\sigma$ continuously computes a grasp probability to determine when the system can proceed to the second phase. Once the pre-grasp pose is reached and the grasp prediction is confident to take over the object from the human, the task will switch to the grasping phase, in which the end-effector moves forward to the final grasp pose in open-loop fashion and closes the gripper to grasp the object. Finally, after object grasping, the robot follows a predetermined trajectory to retract to a base position and complete the episode. This task logic is used in both our simulation environment and the real robot deployment. Sequencing based on a pre-grasp pose is widely used in literature for dynamic grasping [1]. + +We follow the HandoverSim task setup [6], where the hu + +![](images/01cbbf0223db88902fe482b9b742b9bf23145af4c5b25e7e5681fac1f4ba7531.jpg) +Figure 2. Method Overview. The Perception module takes egocentric RGB-D and segmentation images from the environment and outputs a hand/object segmented point cloud. Next, the segmented point cloud is passed to the Vision-based Control module and processed by PointNet++ [39] to obtain a lower-dimensional representation. This embedding is used as input to both the control policy and the grasp predictor. Each task episode in the Handover Environment follows two phases: during the approaching phase, the robot moves towards a pre-grasp pose, driven by the control policy $\pi$ that outputs end-effector actions a. A learned grasp predictor monitors the motion and determines when the robot should switch into the grasping phase, which follows the steps: 1. moving the gripper forward from a pre-grasp to a grasping pose 2. closing the gripper 3. retracting the object to a designated location, after which the episode ends. + +man hand and objects are simulated by replaying data from the DexYCB dataset [7] (see Sec. 3.2). First, actions a in the form of the next 6DoF end-effector pose (translation and rotation) are received from the policy $\pi (\mathbf{a}|\mathbf{s})$ . We then convert the end-effector pose into a target robot configuration using inverse kinematics. Thereafter, we use PD-controllers to compute torques, which are applied to the robot. Finally, the visual information is rendered from the robot's wrist-mounted RGB-D camera and sent to the perception module. + +# 4.2. Perception + +Our policy network takes a segmented hand and object point cloud as input. In the handover environment, we first render an egocentric RGB-D image from the wrist camera. Then we obtain the object point cloud $\mathbf{p}_o$ and hand point cloud $\mathbf{p}_h$ by overlaying the ground-truth segmentation mask with the RGB-D image. Since the hand and object may not always be visible from the current egocentric view, we keep track of the last available point clouds. The latest available point clouds are then sent to the control module. + +# 4.3. Vision-Based Control + +Input Representation Depending on the amount of points contained in the hand point cloud $\mathbf{p}_h$ and object point cloud $\mathbf{p}_o$ , we down- or upsample them into constant size. Next, we concatenate the two point clouds into a single point cloud $\mathbf{p}$ and add two one-hot-encoded vectors to indicate the locations of object and hand points within $\mathbf{p}$ . We then encode the point cloud into a lower dimensional representation $\psi(\mathbf{p})$ by passing it through PointNet++ [39]. Finally, the lower dimensional encoding $\psi(\mathbf{p})$ is passed on to the control policy $\pi$ and the grasp prediction network $\sigma$ . + +Control Policy The policy network $\pi(\mathbf{a}|\psi(\mathbf{p}))$ is a small, two-layered MLP that takes the PointNet++ embedding as input state ( $\mathbf{s} = \psi(\mathbf{p})$ ) and predicts actions $\mathbf{a}$ that correspond to the change in 6DoF end-effector pose. These are passed on to the handover environment. + +Grasp Prediction We introduce a grasp prediction network $\sigma(\psi(\mathbf{p}))$ that predicts when the robot should switch from approaching to executing the grasping motion (cf. Fig. 2). We model grasp prediction as a binary classification task. The input corresponds to the PointNet++ embedding $\psi(\mathbf{p})$ , which is fed through a 3-layered MLP. The output is a probability that indicates the likelihood of a successful grasp given the current point cloud feature. If the probability is above a tunable threshold, we execute an open-loop grasping motion. The model is trained offline with pre-grasp poses attained from [15]. We augment the dataset by adding random noise to pre-grasp poses. To determine the labels, we initialize the robot with the pre-grasp poses in the physics simulation and execute the forward grasping motion. The label is one if the grasp is successful, and zero otherwise. We use a binary cross-entropy loss for training. + +# 4.4. Two-Stage Teacher-Student Training + +We aim at training a handover policy capable of moving simultaneously with the human. Training this policy directly in the setting of dynamic motion is challenging because expert demonstrations with open-loop planners to guide training can only be obtained when the human is stationary. A key contribution of our work is a two-stage training scheme for handovers that incrementally trains the policy to alleviate this challenge. In the first stage, we pretrain + +![](images/ed7c431eb9c3aab692d4b4ddf1c254d12f68f3ac96ab0e504786df70595c0c5e.jpg) +Figure 3. Training Procedure. In the pretraining stage (top left box), the human hand is stationary. We alternate between collecting expert demonstrations via motion planning and exploration data with the RL policy $\pi_{\mathrm{pre}}$ . Transitions $\mathbf{d}$ are stored in a replay buffer $\mathcal{D}$ . During training (green box, right), a batch of randomly sampled transitions from the replay buffer is passed through PointNet++ and the actor and critic networks. In the finetuning stage (bottom left box), the human and robot move concurrently. The expert motion planner is replaced by the expert policy $\pi_{\mathrm{exp}}$ , which shares the weights of the pretrained policy $\pi_{\mathrm{pre}}$ . This policy network will be kept frozen for the rest of training and serves as a regularizer for the RL agent. The RL agent's actor network $\pi_{*}$ and critic network $Q_{*}$ are also initialized with the weights of pretrained agent's networks, but the model will be updated during finetuning. In this stage, transitions are stored in a new replay buffer $\mathcal{D}_{*}$ . Data is sampled solely from this buffer during finetuning. + +in a setting where the robot only starts moving once the human has stopped (sequential). This pretrained policy is further finetuned in the second stage in which the human and robot move simultaneously (simultaneous). + +Pretraining in Sequential Setting In the sequential setting, the robot starts moving once the human has come to a stop (see Fig. 3, top left). To grasp the object from the stationary human hand, we leverage motion planning to provide expert demonstrations. During data collection, we alternate between motion planning and RL-based exploration. In both cases, we store the transitions $\mathbf{d}_t = \{\mathbf{p}_t,\mathbf{a}_t,\mathbf{g}_t,\mathbf{r}_t,\mathbf{p}_{t + 1},\mathbf{e}_t\}$ in a replay buffer $\mathcal{D}$ , from which we sample during network training. The term $\mathbf{p}_t$ and $\mathbf{p}_{t + 1}$ indicate the point cloud and the next point cloud, $\mathbf{a}_t$ the action, $\mathbf{g}_t$ the pre-grasp goal pose, $\mathbf{r}_t$ the reward, and $\mathbf{e}_t$ an indicator of whether the transition is from the expert. + +Inspired by [50], we collect expert trajectories with the OMG planner [49] that leverages ground-truth states. Note that some expert trajectories generated by the planner result in collision with the hand, which is why we introduce an offline pre-filtering scheme. We first parse the ACRONYM dataset [14] for potential grasps. We then run collision checking to filter out grasps where the robot and human hand collide. For the set of remaining collision-free grasps, we plan trajectories to grasp the object and execute them in open-loop fashion. On the other hand, the RL policy $\pi_{\mathrm{pre}}$ explores the environment and receives a sparse reward, i.e., the reward is one if the task is completed successfully, oth- + +erwise zero. Hence, collisions with the human will get implicitly penalized by not receiving any positive reward. + +Finetuning in Simultaneous Setting In this setting, the human and robot move at the same time. Hence, we cannot rely on motion and grasp planning to guide the policy. On the other hand, simply taking the pre-trained policy $\pi_{\mathrm{pre}}$ from the sequential setting and continue training it without an expert leads to an immediate drop in performance. Hence, we introduce a self-supervision scheme for stability reasons, i.e., we want to keep the finetuning policy close to the pre-trained policy. To this end, we replace the expert planner from the sequential setting by an expert policy $\pi_{\mathrm{exp}}$ , which is initialized with the weights of the pre-trained policy $\pi_{\mathrm{pre}}$ that already provides a reasonable prior policy (see Fig. 3 bottom left). Therefore, we have two policies: i) the expert policy $\pi_{\mathrm{exp}}$ as proxy for the motion and grasping planner. We freeze the network weights of this policy, ii) the finetuning policy $\pi_*$ and critic $Q_*$ , which are initialized with the weights of the pre-trained policy $\pi_{\mathrm{pre}}$ and critic $Q_{\mathrm{pre}}$ , respectively. We proceed to train these two networks using the loss functions which we describe next. + +Network Training During training, we sample a batch of random transitions from the replay buffer $\mathcal{D}$ . The policy network is trained using a combination of behavior cloning, RL-based losses and an auxiliary objective. In particular, the policy is updated using the following loss function: + +$$ +L (\theta) = \lambda L _ {\mathrm {B C}} + (1 - \lambda) L _ {\mathrm {D D P G}} + L _ {\mathrm {A U X}}, \tag {3} +$$ + +
success (%)mean accum time (s)failure (%)
execplantotalcontactdroptimeouttotal
SequentialOMG Planner [49] †62.508.3091.4149.72227.788.331.3937.50
Yang et al. [52] †64.584.8640.0364.90017.3611.816.2535.42
GA-DDPG [50]50.007.1390.1427.2814.8619.4425.6950.00
GA-DDPG [50] finetuned57.186.3240.0866.4116.4827.089.2642.82
Ours75.237.7430.1777.9229.2613.432.0824.77
Simult.GA-DDPG [50]36.814.6640.1324.7969.0325.0029.1763.19
GA-DDPG [50] finetuned54.864.8320.0824.9146.7126.3912.0445.14
Ours68.756.2320.1786.4118.8017.824.6331.25
+ +Table 1. HandoverSim Benchmark Evaluation. Comparison of our method against various baselines from the HandoverSim benchmark [6]. In the sequential setting, we find that our baseline achieves better overall success rates than the baselines. In the simultaneous setting, we outperform the applicable baselines by large margins. The results for our method are averaged across 3 random seeds. $\dagger$ : both methods [49, 52] are evaluated with ground-truth states in [6] and thus are not directly comparable with ours. + +where $L_{\mathrm{BC}}$ is a behavior cloning loss that keeps the policy close to the expert policy, $L_{\mathrm{DDPG}}$ is the standard actor-critic loss described in Eq. 2, and $L_{\mathrm{AUX}}$ is an auxiliary objective that predicts the grasping goal pose of the end-effector. The coefficient $\lambda$ balances the behavior cloning and the RL objective. The critic loss is defined as: + +$$ +L (\phi) = L _ {\mathrm {B E}} + L _ {\mathrm {A U X}}, \tag {4} +$$ + +where $L_{\mathrm{BE}}$ indicates the Bellman error from Eq. 1 and $L_{\mathrm{AUX}}$ is the same auxiliary loss used in Eq. 3. We refer the reader to supplementary material or [50] for more details. + +# 5. Experiments + +We first evaluate our approach in simulation using the HandoverSim benchmark (Sec. 5.1). Next, we investigate the performance of sim-to-sim transfer by evaluating the trained models on the test environments powered by a different physics engine (Sec. 5.2). Finally, we apply the trained model to a real-world robotic system and analyze the performance of sim-to-real transfer (Sec. 5.3). + +# 5.1. Simulation Evaluation + +Setup HandoverSim [6] contains 1,000 unique H2R handover scenes divided into train, val, and test splits. Each scene contains a unique human handover motion. We evaluate on the "s0" setup which contains 720 training and 144 testing scenes. See the supp. material for evaluations on unseen objects, subjects, and handedness. Following the evaluation of GA-DDPG [50] in [6], we consider two settings: (1) the "sequential" setting where the robot is allowed to move only after the human hand reaches the handover location and remains static there (i.e., "hold" in [6]), and (2) the "simultaneous" setting where the robot is allowed to move from the beginning of the episode (i.e., "w/o hold" in [6]). + +Metrics We follow the evaluation protocol in Handover-Sim [6]. A handover is considered successful if the robot grasps the object from the human hand and moves it to a designated location. A failure is claimed and the episode + +is terminated if any of the following three conditions occur: (1) the robot collides with the hand (contact), (2) the robot drops the object (drop), or (3) a maximum time limit is reached (timeout). Besides efficacy, the benchmark also reports efficiency in time. The time metric is further broken down into (1) the execution time (exec), i.e., the time to physically move the robot, and (2) the planning time (plan), i.e., the time spent on running the policy. All reported metrics are averaged over the rollouts on the test scenes. + +Baselines Our primary baseline is GA-DDPG [50]. Besides comparing with the original model (i.e., trained in [50] for table-top grasping and evaluated in [6]), we additionally compare with a variant finetuned on HandoverSim ("GA-DDPG [50] finetuned"). For completeness, we also include two other baselines from [6]: "OMG Planner [49]" and "Yang et al. [52]". However, both of them are evaluated with ground-truth state input in [6] and thus are not directly comparable with our method. + +Results Tab. 1 reports the evaluation results on the test scenes. In the sequential setting, our method significantly outperforms all the baselines in terms of success rate, even compared to methods that use state-based input. Our method is slightly slower on average than GA-DDDPG in terms of total time needed for handovers. In the simultaneous setting, our method clearly outperforms GA-DDDPG, which has low success rates. Qualitatively, we observe that GA-DDDPG directly tries to grasp the object from the user while it is still moving, while our method follows the hand and finds a feasible grasp once the hand has come to a stop, resulting in a trade-off on the overall execution time. We provide a qualitative example of this behavior in Fig. 4 (a) and in the supplementary video. We also refer to the supp. material for a discussion of limitations and a robustness analysis of our pipeline under noisy observations. + +Ablations We evaluate our design choices in an ablation study and report the results in Tab. 2. We analyze the vision backbone by replacing PointNet++ with a ResNet18 [23] + +![](images/64a3e89bf357d7361f049fd3f4bd7b992e71dcd8bb2ac1d9b051d4fc6821445e.jpg) +Figure 4. Qualitative results. We provide a comparison to show our methods' advantages over GA-DDPG [50]. (a) Our method reacts to the moving human, while the baseline tries to go for a grasp directly, which leads to collision. (b) In the sim-to-sim transfer, we often find that the baseline does not find a grasp on the object. (c) In the sim-to-real experiment, GA-DDPG usually tries to get to a grasp directly, while our method adjusts the gripper into a stable grasping pose first. See the video in supp. material for more qualitative examples. + +
Ablation Study
success (%)failure (%)
contactdroptimeout
w/ RGBDM + ResNet1834.106.2045.8013.90
w/ third person view60.429,9525.693.94
w/o hand point cloud59.0324.0711.585.32
w/o aux prediction70.6010.6516.202.54
w/o standoff52.557.8736.802.78
w/o finetuning73.389.0313.893.70
Ours75.239.2613.432.08
w/o finetuning simul.62.2711.8120.375.56
Ours simul.68.758.817.824.63
+ +Table 2. Ablation. We ablate the vision backbone, hand perception, and egocentric view. We also study the effect of finetuning, the auxiliary prediction, and splitting the task into two phases. All design choices are crucial aspects of our method with regards to overall performance. Results are averaged over 3 random seeds. + +that processes the RGB and depth/segmentation (DM) images. Similar to the findings in GA-DDPG, the PointNet++ backbone performs better. Next, we train our method from third person view instead of egocentric view and without active hand segmentation ( $w/o$ hand point cloud), i.e., the policy only perceives the object point cloud but not the hand point cloud. We also ablate the auxiliary prediction ( $w/o$ aux prediction) and evaluate a variant that directly learns to approach and grasp the object instead of using the two task phases of approaching and grasping ( $w/o$ standoff). Lastly, we compare against our pretrained model, which was only trained in the sequential setting without finetuning ( $w/o$ finetuning). We find that the ablated components comprise important elements of our method. The results indicate an in- + +
Sim-to-Sim
success (%)failure (%)
contactdroptimeout
SequentialGA-DDPG [50]19.444.8647.2228.47
GA-DDPG [50] finetuned11.816.2568.7513.19
Ours44.219.4940.515.79
Ours w/o grasp54.407.8733.344.40
Simult.GA-DDPG [50]11.1115.9748.6124.31
GA-DDPG [50] finetuned16.679.7263.899.72
Ours39.589.0343.757.64
Ours w/o grasp pred.47.9210.6535.885.56
+ +creased amount of hand collision or object drop in all ablations. A closer analysis in the simultaneous setting shows that our finetuned model outperforms the pretrained model. + +# 5.2. Sim-to-Sim Transfer + +Instead of directly transferring to the real world, we first evaluate the robustness of the models by transferring them to a different physics simulator. We re-implement the HandoverSim environment following the mechanism presented in [6] except for replacing the backend physics engine from Bullet [10] to Isaac Gym [29]. We then evaluate the models trained on the original Bullet-based environment on the test scenes powered by Isaac Gym. The results are presented in Tab. 3. We observe a significant drop for GA-DDPG on the success rates (i.e., to below $20\%$ ) in both settings. Qualitatively, we see that grasps are often either missed completely or only partially grasped (see Fig. 4 (b)). On the other hand, our method is able to retain higher success rates. Expectedly, it also suffers from a loss in performance. We analyze the influence of our grasp predictor on transfer performance and compare against a variant where we execute the grasping motion after a fixed amount of time (Ours w/o grasp pred.), which will leave the robot enough time to find a pre-grasp pose. Part of the performance drop is caused by the grasp predictor initiating the grasping phase at the wrong time, which can be improved upon in future work. + +# 5.3. Sim-to-Real Transfer + +Finally, we deploy the models trained in HandoverSim on a real robotic platform. We follow the perception pipeline used in [50,52] to generate segmented hand and object point clouds for the policy, and use the output to update the end effector's target position. We compare our method against GA-DDPG [50] with two sets of experiments: (1) a pilot study with controlled handover poses and (2) a user evaluation with free-form handovers. For experimental details and the full results, please see the supp. material. + +Pilot Study We first conduct a pilot study with two subjects. The subjects are instructed to handover 10 objects from HandoverSim by grasping and presenting the objects in controlled poses. For each object, we test with 6 poses + +Table 3. Sim-to-Sim Experiment. We evaluate sim-to-sim transfer of the learning-based method to Isaac Gym [29], Our method shows better transfer capabilities than GA-DDPG [50]. + +
Subject 1Subject 2
GA-DDPG [50]OursGA-DDPG [50]Ours
011_banana3 / 66 / 66 / 65 / 6
037_scissors2 / 65 / 63 / 65 / 6
006_mustard_bottle1 / 63 / 62 / 64 / 6
024_bowl3 / 64 / 63 / 63 / 6
040_large Marker0 / 64 / 64 / 65 / 6
003_cracker_box3 / 62 / 60 / 62 / 6
052extra_large_clamp1 / 64 / 65 / 65 / 6
008_pudding_box3 / 66 / 64 / 64 / 6
010_potted_meat_can2 / 62 / 63 / 64 / 6
021_bleach_cleanser3 / 65 / 63 / 64 / 6
total21 / 6041 / 6033 / 6041 / 60
+ +Table 4. Sim-to-Real Experiment. Success rates of the pilot study. Our method outperforms GA-DDPG [50] for both subjects. + +(3 poses for each hand) with varying object orientation and varying amount of hand occlusion, resulting in 60 poses per subject. The same set of poses are used in testing both our model and GA-DDPG [50]. The success rates are shown Tab. 4. Results indicate that our method outperforms GA-DDPG [50] for both subjects on the overall success rate (i.e., 41/60 versus 21/60 for Subject 1). Qualitatively, we observe that GA-DDPG [50] tends to fail more from unstable grasping as well as hand collision. Fig. 4 (c) shows two examples of the real world handover trials. + +User Evaluation We further recruited 6 users to compare the two methods and collected feedback from a questionnaire with Likert-scale and open-ended questions. In contrast to the pilot study, we asked the users to handover the 10 objects in ways that are most comfortable to them. We repeated the same experimental process for both methods, and counterbalanced the order to avoid bias. From participants' feedback, the majority agreed that the timing of our method is more appropriate and our method can adjust between different object poses better. The interpretability of the robot's motion was also acknowledged by their comments. Please see the supp. material for more details. + +# 6. Conclusion + +In this work, we have presented a learning-based framework for human-to-robot handovers from vision input with a simulated human-in-the-loop. We have introduced a two-stage teacher-student training procedure. In our experiments we have shown that our method outperforms baselines by a significant margin on the HandoverSim benchmark [6]. Furthermore, we have demonstrated that our approach is more robust when transferring to a different physics simulator and a real robotic system. + +Acknowledgements We thank Tao Chen and Adithyavairavan Murali for laying the groundwork, Lirui Wang for the help with GA-DDPG, and Mert Albaba, Christoph Gebhardt, Thomas Langerak and Juan Zarate for their feedback on the manuscript. + +# References + +[1] Iretiayo Akinola, Jingxi Xu, Shuran Song, and Peter K Allen. Dynamic grasping with reachability and motion awareness. In IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2021. 3 +[2] Peter Anderson, Ayush Shrivastava, Joanne Truong, Arjun Majumdar, Devi Parikh, Dhruv Batra, and Stefan Lee. Sim-to-real transfer for vision-and-language navigation. In Conference on Robot Learning (CoRL), 2021. 1 +[3] Antonio Bicchi and Vijay Kumar. Robotic grasping and contact: A review. 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We introduce a framework to learn human-to-robot handover policies from point cloud input. Our policies take input from a wrist mounted camera and directly generate action output for the robot's end effector. We train our policies in a simulated handover environment, and evaluate on unseen handover motion and poses. We further transfer the model across physics simulators and to a real robotic platform." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 143, + 434, + 192, + 446 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 434, + 192, + 446 + ], + "spans": [ + { + "bbox": [ + 143, + 434, + 192, + 446 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 45, + 453, + 288, + 633 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 453, + 288, + 633 + ], + "spans": [ + { + "bbox": [ + 45, + 453, + 288, + 633 + ], + "type": "text", + "content": "We propose the first framework to learn control policies for vision-based human-to-robot handovers, a critical task for human-robot interaction. While research in Embodied AI has made significant progress in training robot agents in simulated environments, interacting with humans remains challenging due to the difficulties of simulating humans. Fortunately, recent research has developed realistic simulated environments for human-to-robot handovers. Leveraging this result, we introduce a method that is trained with a human-in-the-loop via a two-stage teacher-student framework that uses motion and grasp planning, reinforcement learning, and self-supervision. We show significant performance gains over baselines on a simulation benchmark, sim-to-sim transfer and sim-to-real transfer. Video and code are available at https://handover-sim2real.github.io." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 652, + 127, + 664 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 652, + 127, + 664 + ], + "spans": [ + { + "bbox": [ + 47, + 652, + 127, + 664 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 672, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 672, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 47, + 672, + 287, + 696 + ], + "type": "text", + "content": "Handling over objects between humans and robots is an important tasks for human-robot interaction (HRI) [35]. It" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 435, + 545, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 435, + 545, + 555 + ], + "spans": [ + { + "bbox": [ + 304, + 435, + 545, + 555 + ], + "type": "text", + "content": "allows robots to assist humans in daily collaborative activities, such as helping to prepare a meal, or to exchange tools and parts with human collaborators in manufacturing settings. To complete these tasks successfully and safely, intricate coordination between human and robot is required. This is challenging, because the robot has to react to human behavior, while only having access to sparse sensory inputs such as a single camera with limited field of view. Therefore, a need for methods that solve interactive tasks such as handovers purely from vision input arises." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 558, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 546, + 713 + ], + "type": "text", + "content": "Bootstrapping robot training in the real world can be unsafe and time-consuming. Therefore, recent trends in Embodied AI have focused on training agents to act and interact in simulated (sim) environments [11, 12, 19, 43, 45, 46, 51]. With advances in rendering and physics simulation, models have been trained to map raw sensory input to action output, and can even be directly transferred from simulation to the real world [2, 42]. Many successes have been achieved particularly around the suite of tasks of robot navigation, manipulation, or a combination of both. In contrast to these areas, little progress has been made around tasks pertained to HRI. This is largely hindered by the challenges in embedding realistic human agents in these environments, since" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 235, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 235, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 235, + 713 + ], + "type": "text", + "content": "*This work was done during an internship at NVIDIA." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "9654" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 278, + 85 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 278, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 278, + 85 + ], + "type": "text", + "content": "modeling and simulating realistic humans is challenging." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 86, + 287, + 217 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 86, + 287, + 217 + ], + "spans": [ + { + "bbox": [ + 46, + 86, + 287, + 217 + ], + "type": "text", + "content": "Despite the challenges, an increasing number of works have attempted to embed realistic human agents in simulated environments [6, 9, 16, 36-38, 48]. Notably, a recent work has introduced a simulation environment (\"Handover-Sim\") for human-to-robot handover (H2R) [6]. To ensure a realistic human handover motion, they use a large motion capture dataset [7] to drive the movements of a virtual human in simulation. However, despite the great potential for training robots, the work of [6] only evaluates off-the-shelf models from prior work, and has not explored any policy training with humans in the loop in their environment." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 219, + 289, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 219, + 289, + 567 + ], + "spans": [ + { + "bbox": [ + 46, + 219, + 289, + 567 + ], + "type": "text", + "content": "We aim to close this gap by introducing a vision-based learning framework for H2R handovers that is trained with a human-in-the-loop (see Fig. 1). In particular, we propose a novel mixed imitation learning (IL) and reinforcement learning (RL) based approach, trained by interacting with the humans in HandoverSim. Our approach draws inspiration from a recent method for learning polices for grasping static objects from point clouds [50], but proposes several key changes to address the challenges in H2R handovers. In contrast to static object grasping, where the policy only requires object information, we additionally encode human hand information in the policy's input. Also, compared to static grasping without a human, we explicitly take human collisions into account in the supervision of training. Finally, the key distinction between static object grasping and handovers is the dynamic nature of the hand and object during handover. To excel on the task, the robot needs to react to dynamic human behavior. Prior work typically relies on open-loop motion planners [49] to generate expert demonstrations, which may result in suboptimal supervision for dynamic cases. To this end, we propose a two-stage training framework. In the first stage, we fix the humans to be stationary and train an RL policy that is partially guided by expert demonstrations obtained from a motion and grasp planner. In the second stage, we finetune the RL policy in the original dynamic setting where the human and robot move simultaneously. Instead of relying on a planner, we propose a self-supervision scheme, where the pre-trained RL policy serves as a teacher to the downstream policy." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 568, + 287, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 568, + 287, + 675 + ], + "spans": [ + { + "bbox": [ + 46, + 568, + 287, + 675 + ], + "type": "text", + "content": "We evaluate our method in three \"worlds\" (see Fig. 1). First, we evaluate on the \"native\" test scenes in HandoverSim [6], which use the same backend physics simulator (Bullet [10]) as training but unseen handover motions from the simulated humans. Next, we perform sim-to-sim evaluation on the test scenes implemented with a different physics simulator (Isaac Gym [29]). Lastly, we investigate sim-to-real transfer by evaluating polices on a real robotic system and demonstrate the benefits of our method." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "content": "We contribute: i) the first framework to train human-to-robot handover tasks from vision input with a human-in-the-loop, ii) a novel teacher-student method to train in the" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 305, + 72, + 545, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 133 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 133 + ], + "type": "text", + "content": "setting of a jointly moving human and robot, iii) an empirical evaluation showing that our approach outperforms baselines on the HandoverSim benchmark, iv) transfer experiments indicating that our method leads to more robust sim-to-sim and sim-to-real transfer compared to baselines." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 144, + 392, + 157 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 144, + 392, + 157 + ], + "spans": [ + { + "bbox": [ + 306, + 144, + 392, + 157 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 165, + 547, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 165, + 547, + 586 + ], + "spans": [ + { + "bbox": [ + 304, + 165, + 547, + 586 + ], + "type": "text", + "content": "Human-to-Robot Handovers Encouraging progress in hand and object pose estimation [22, 26, 27] has been achieved, aided by the introduction of large hand-object interaction datasets [5, 7, 17, 20, 21, 28, 32, 47, 54, 55]. These developments enable applying model-based grasp planning [3,4,31], a well-studied approach in which full pose estimation and tracking are needed, to H2R handovers [7, 41]. However, these methods require the 3D shape models of the object and cannot handle unseen objects. Alternatively, some recent works [13, 30, 40, 52, 53] achieve H2R handover by employing learning-based grasp planners to generate grasps for novel objects from raw vision inputs such as images or point clouds [33, 34]. While promising results have been shown, these methods work only on an open-loop sequential setting in which the human hand has to stay still once the robot starts to move [40], or need complex hand-designed cost functions for grasp selection [52] and robot motion planning [30, 53] for reactive handovers, which requires expertise in robot motion and control. Hence, these methods are difficult to reproduce and deploy to new environments. Progress towards dynamic simultaneous motion has been shown by a learning-based method [48], using state inputs, leaving an open challenge for training policies that receive visual input directly. In contrast, we propose to learn control policies together with grasp prediction for handovers in an end-to-end manner from segmented point clouds with a deep neural net. To facilitate easy and fair comparisons among different handover methods, [6] propose a physics-simulated environment with diverse objects and realistic human handover behavior collected by a mocap system [7]. They provide benchmark results of several previous handover systems, including a learning-based grasping policy trained with static objects [50]. However, learning a safe and efficient handover policy is not trivial with a human-in-the-loop, which we address in this work." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "content": "Policy Learning for Grasping Object grasping is an essential skill for many robot tasks, including handovers. Prior works usually generate grasp poses given a known 3D object geometry such as object shape or pose [3,4,31], which is nontrivial to obtain from real-world sensory input such as images or point clouds. To overcome this, recent works train deep neural networks to predict grasps from sensor data [25] and compute trajectories to reach the predicted grasp pose. Though 3D object geometry is no longer needed, the feasibility is not guaranteed since the grasp" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "9655" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 301 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 301 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 301 + ], + "type": "text", + "content": "prediction and trajectory planning are computed separately. Some recent works directly learn grasping policies given raw sensor data. [24] propose a self-supervised RL framework based on RGB images to learn a deep Q-function from real-world grasps. To improve data efficiency, [44] use a low-cost handheld device to collect grasping demonstrations with a wrist-mounted camera. They train an RL-based 6-DoF closed-loop grasping policy with these demonstrations. [50] combines imitation learning from expert data with RL to learn a control policy for object grasping from point clouds. Although this method performs well in HandoverSim [6] when the human hand is not moving, it has difficulty coordinating with a dynamic human hand since the policy is learned with static objects. Instead, our policy is directly learned from large-scale dynamic hand-object trajectories obtained from the real world. To facilitate the training for the dynamic case, we propose a two-stage teacher-student framework, that is conceptually inspired by [8], which has been proven critical through experiments." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 316, + 126, + 328 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 316, + 126, + 328 + ], + "spans": [ + { + "bbox": [ + 47, + 316, + 126, + 328 + ], + "type": "text", + "content": "3. Background" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 336, + 185, + 350 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 336, + 185, + 350 + ], + "spans": [ + { + "bbox": [ + 47, + 336, + 185, + 350 + ], + "type": "text", + "content": "3.1. Reinforcement Learning" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 356, + 287, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 356, + 287, + 453 + ], + "spans": [ + { + "bbox": [ + 46, + 356, + 287, + 453 + ], + "type": "text", + "content": "MDP We formalize RL as a Markov Decision Process (MDP), that consists of a 5-tuple " + }, + { + "bbox": [ + 46, + 356, + 287, + 453 + ], + "type": "inline_equation", + "content": "\\mathcal{M} = (\\mathcal{S},\\mathcal{A},\\mathcal{R},\\mathcal{T},\\gamma)" + }, + { + "bbox": [ + 46, + 356, + 287, + 453 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 46, + 356, + 287, + 453 + ], + "type": "inline_equation", + "content": "\\mathcal{S}" + }, + { + "bbox": [ + 46, + 356, + 287, + 453 + ], + "type": "text", + "content": " is the state space, " + }, + { + "bbox": [ + 46, + 356, + 287, + 453 + ], + "type": "inline_equation", + "content": "\\mathcal{A}" + }, + { + "bbox": [ + 46, + 356, + 287, + 453 + ], + "type": "text", + "content": " the action space, " + }, + { + "bbox": [ + 46, + 356, + 287, + 453 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 46, + 356, + 287, + 453 + ], + "type": "text", + "content": " a scalar reward function, " + }, + { + "bbox": [ + 46, + 356, + 287, + 453 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 46, + 356, + 287, + 453 + ], + "type": "text", + "content": " a transition function that maps state-action pairs to distributions over states, and " + }, + { + "bbox": [ + 46, + 356, + 287, + 453 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 46, + 356, + 287, + 453 + ], + "type": "text", + "content": " a discount factor. The goal is to find a policy that maximizes the long-term reward: " + }, + { + "bbox": [ + 46, + 356, + 287, + 453 + ], + "type": "inline_equation", + "content": "\\pi^{*} = \\arg \\max_{\\pi}\\mathbb{E}\\sum_{t = 0}^{t = T}\\gamma^{t}\\mathcal{R}(\\mathbf{s}_{t})" + }, + { + "bbox": [ + 46, + 356, + 287, + 453 + ], + "type": "text", + "content": ", with " + }, + { + "bbox": [ + 46, + 356, + 287, + 453 + ], + "type": "inline_equation", + "content": "\\mathbf{s}_t\\sim \\mathcal{T}(\\mathbf{s}_{t - 1},\\mathbf{a}_{t - 1})" + }, + { + "bbox": [ + 46, + 356, + 287, + 453 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 356, + 287, + 453 + ], + "type": "inline_equation", + "content": "\\mathbf{a}_{t - 1}\\sim \\pi (\\mathbf{s}_{t - 1})" + }, + { + "bbox": [ + 46, + 356, + 287, + 453 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 475, + 287, + 595 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 475, + 287, + 595 + ], + "spans": [ + { + "bbox": [ + 46, + 475, + 287, + 595 + ], + "type": "text", + "content": "Learning Algorithm In this work, we use TD3 [18], a common algorithm for continuous control. It is an actor-critic method, which consists of a policy " + }, + { + "bbox": [ + 46, + 475, + 287, + 595 + ], + "type": "inline_equation", + "content": "\\pi_{\\theta}(\\mathbf{s})" + }, + { + "bbox": [ + 46, + 475, + 287, + 595 + ], + "type": "text", + "content": " (actor) and a Q-function approximator " + }, + { + "bbox": [ + 46, + 475, + 287, + 595 + ], + "type": "inline_equation", + "content": "Q_{\\phi}(\\mathbf{s},\\mathbf{a})" + }, + { + "bbox": [ + 46, + 475, + 287, + 595 + ], + "type": "text", + "content": " (critic) that predicts the expected return from a state-action pair. Both are represented by neural networks with parameters " + }, + { + "bbox": [ + 46, + 475, + 287, + 595 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 475, + 287, + 595 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 475, + 287, + 595 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 46, + 475, + 287, + 595 + ], + "type": "text", + "content": ". TD3 is off-policy, and hence there is a replay buffer in which training transitions are stored. During training, both the actor and critic are updated using samples from the buffer. To update the critic, we minimize the Bellman error:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 48, + 607, + 286, + 637 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 607, + 286, + 637 + ], + "spans": [ + { + "bbox": [ + 48, + 607, + 286, + 637 + ], + "type": "interline_equation", + "content": "L _ {\\mathrm {B E}} (\\phi) = \\mathbb {E} _ {\\mathcal {M}} \\left[ \\left(Q _ {\\phi} \\left(\\mathbf {s} _ {t}, \\mathbf {a} _ {t}\\right) - r \\left(\\mathbf {s} _ {t}, \\mathbf {a} _ {t}\\right) + \\gamma Q _ {\\phi} \\left(\\mathbf {s} _ {t + 1}, \\mathbf {a} _ {t + 1}\\right)\\right) ^ {2} \\right] \\tag {1}", + "image_path": "4e1f42e33b920865fbc52e0b05fdb2a319ea623457921c99796f730039cd0942.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 639, + 286, + 663 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 639, + 286, + 663 + ], + "spans": [ + { + "bbox": [ + 47, + 639, + 286, + 663 + ], + "type": "text", + "content": "For the actor network, the policy parameters are trained to maximize the Q-values:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 75, + 676, + 286, + 689 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 75, + 676, + 286, + 689 + ], + "spans": [ + { + "bbox": [ + 75, + 676, + 286, + 689 + ], + "type": "interline_equation", + "content": "L _ {\\mathrm {D D P G}} (\\theta) = \\mathbb {E} _ {\\boldsymbol {\\pi}} \\left[ Q _ {\\phi} \\left(\\mathbf {s} _ {t}, \\mathbf {a} _ {t}\\right) \\mid \\mathbf {s} _ {t}, \\mathbf {a} _ {t} = \\boldsymbol {\\pi} _ {\\theta} \\left(\\mathbf {s} _ {t}\\right) \\right] \\tag {2}", + "image_path": "09fbfb1cc844c3a92a76b0b495c595814b2f585e7a13e96ce831b6aceeb24013.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 701, + 227, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 701, + 227, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 701, + 227, + 713 + ], + "type": "text", + "content": "For more details, we refer the reader to [18]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 72, + 451, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 451, + 83 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 451, + 83 + ], + "type": "text", + "content": "3.2. HandoverSim Benchmark" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 90, + 545, + 282 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 90, + 545, + 282 + ], + "spans": [ + { + "bbox": [ + 304, + 90, + 545, + 282 + ], + "type": "text", + "content": "HandoverSim [6] is a benchmark for evaluating H2R handover policies in simulation. The task setting consists of a tabletop with different objects, a Panda 7DoF robotic arm with a gripper and a wrist-mounted RGB-D camera, and a simulated human hand. The task starts with the human grasping an object and moving it to a handover pose. The robot should move to the object and grasp it. The task is successful if the object has been grasped from the human without collision and brought to a designated position without dropping. To accurately model the human, trajectories from the DexYCB dataset [7], which comprises a large amount of human-object interaction sequences, are replayed in simulation. Several baselines [49,50,52] are provided for comparison. The setup in HandoverSim has only been used for handover performance evaluation purposes, whereas in this work we utilize it as a learning environment." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 294, + 361, + 306 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 294, + 361, + 306 + ], + "spans": [ + { + "bbox": [ + 306, + 294, + 361, + 306 + ], + "type": "text", + "content": "4. Method" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 315, + 545, + 482 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 315, + 545, + 482 + ], + "spans": [ + { + "bbox": [ + 304, + 315, + 545, + 482 + ], + "type": "text", + "content": "The overall pipeline is depicted in Fig. 2 and consists of three different modules: perception, vision-based control, and the handover environment. The perception module receives egocentric visual information from the handover environment and processes it into segmented point clouds. The vision-based control module receives the point clouds and predicts the next action for the robot and whether to approach or to grasp the object. This information is passed to the handover environment, which updates the robot state and sends the new visual information to the perception module. Note that the input to our method comes from the wrist-mounted camera, i.e., there is no explicit information, such as object or hand pose, provided to the agent. We will now explain each of the modules of our method in more detail." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 491, + 440, + 502 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 491, + 440, + 502 + ], + "spans": [ + { + "bbox": [ + 306, + 491, + 440, + 502 + ], + "type": "text", + "content": "4.1. Handover Environment" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 510, + 545, + 701 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 545, + 701 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 545, + 701 + ], + "type": "text", + "content": "We split the handover task into two distinct phases (see Fig. 2). First, during the approaching phase, the robot moves to a pre-grasp pose that is close to the object by running the learned control policy " + }, + { + "bbox": [ + 304, + 510, + 545, + 701 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 304, + 510, + 545, + 701 + ], + "type": "text", + "content": ". A learned grasp predictor " + }, + { + "bbox": [ + 304, + 510, + 545, + 701 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 304, + 510, + 545, + 701 + ], + "type": "text", + "content": " continuously computes a grasp probability to determine when the system can proceed to the second phase. Once the pre-grasp pose is reached and the grasp prediction is confident to take over the object from the human, the task will switch to the grasping phase, in which the end-effector moves forward to the final grasp pose in open-loop fashion and closes the gripper to grasp the object. Finally, after object grasping, the robot follows a predetermined trajectory to retract to a base position and complete the episode. This task logic is used in both our simulation environment and the real robot deployment. Sequencing based on a pre-grasp pose is widely used in literature for dynamic grasping [1]." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 318, + 701, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 701, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 318, + 701, + 545, + 713 + ], + "type": "text", + "content": "We follow the HandoverSim task setup [6], where the hu" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "9656" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 74, + 74, + 526, + 233 + ], + "blocks": [ + { + "bbox": [ + 74, + 74, + 526, + 233 + ], + "lines": [ + { + "bbox": [ + 74, + 74, + 526, + 233 + ], + "spans": [ + { + "bbox": [ + 74, + 74, + 526, + 233 + ], + "type": "image", + "image_path": "01cbbf0223db88902fe482b9b742b9bf23145af4c5b25e7e5681fac1f4ba7531.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 240, + 547, + 319 + ], + "lines": [ + { + "bbox": [ + 46, + 240, + 547, + 319 + ], + "spans": [ + { + "bbox": [ + 46, + 240, + 547, + 319 + ], + "type": "text", + "content": "Figure 2. Method Overview. The Perception module takes egocentric RGB-D and segmentation images from the environment and outputs a hand/object segmented point cloud. Next, the segmented point cloud is passed to the Vision-based Control module and processed by PointNet++ [39] to obtain a lower-dimensional representation. This embedding is used as input to both the control policy and the grasp predictor. Each task episode in the Handover Environment follows two phases: during the approaching phase, the robot moves towards a pre-grasp pose, driven by the control policy " + }, + { + "bbox": [ + 46, + 240, + 547, + 319 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 46, + 240, + 547, + 319 + ], + "type": "text", + "content": " that outputs end-effector actions a. A learned grasp predictor monitors the motion and determines when the robot should switch into the grasping phase, which follows the steps: 1. moving the gripper forward from a pre-grasp to a grasping pose 2. closing the gripper 3. retracting the object to a designated location, after which the episode ends." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 330, + 288, + 438 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 330, + 288, + 438 + ], + "spans": [ + { + "bbox": [ + 46, + 330, + 288, + 438 + ], + "type": "text", + "content": "man hand and objects are simulated by replaying data from the DexYCB dataset [7] (see Sec. 3.2). First, actions a in the form of the next 6DoF end-effector pose (translation and rotation) are received from the policy " + }, + { + "bbox": [ + 46, + 330, + 288, + 438 + ], + "type": "inline_equation", + "content": "\\pi (\\mathbf{a}|\\mathbf{s})" + }, + { + "bbox": [ + 46, + 330, + 288, + 438 + ], + "type": "text", + "content": ". We then convert the end-effector pose into a target robot configuration using inverse kinematics. Thereafter, we use PD-controllers to compute torques, which are applied to the robot. Finally, the visual information is rendered from the robot's wrist-mounted RGB-D camera and sent to the perception module." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 446, + 121, + 459 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 446, + 121, + 459 + ], + "spans": [ + { + "bbox": [ + 47, + 446, + 121, + 459 + ], + "type": "text", + "content": "4.2. Perception" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 465, + 288, + 573 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 465, + 288, + 573 + ], + "spans": [ + { + "bbox": [ + 46, + 465, + 288, + 573 + ], + "type": "text", + "content": "Our policy network takes a segmented hand and object point cloud as input. In the handover environment, we first render an egocentric RGB-D image from the wrist camera. Then we obtain the object point cloud " + }, + { + "bbox": [ + 46, + 465, + 288, + 573 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_o" + }, + { + "bbox": [ + 46, + 465, + 288, + 573 + ], + "type": "text", + "content": " and hand point cloud " + }, + { + "bbox": [ + 46, + 465, + 288, + 573 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_h" + }, + { + "bbox": [ + 46, + 465, + 288, + 573 + ], + "type": "text", + "content": " by overlaying the ground-truth segmentation mask with the RGB-D image. Since the hand and object may not always be visible from the current egocentric view, we keep track of the last available point clouds. The latest available point clouds are then sent to the control module." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 581, + 170, + 593 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 581, + 170, + 593 + ], + "spans": [ + { + "bbox": [ + 47, + 581, + 170, + 593 + ], + "type": "text", + "content": "4.3. Vision-Based Control" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 600, + 288, + 720 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 600, + 288, + 720 + ], + "spans": [ + { + "bbox": [ + 46, + 600, + 288, + 720 + ], + "type": "text", + "content": "Input Representation Depending on the amount of points contained in the hand point cloud " + }, + { + "bbox": [ + 46, + 600, + 288, + 720 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_h" + }, + { + "bbox": [ + 46, + 600, + 288, + 720 + ], + "type": "text", + "content": " and object point cloud " + }, + { + "bbox": [ + 46, + 600, + 288, + 720 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_o" + }, + { + "bbox": [ + 46, + 600, + 288, + 720 + ], + "type": "text", + "content": ", we down- or upsample them into constant size. Next, we concatenate the two point clouds into a single point cloud " + }, + { + "bbox": [ + 46, + 600, + 288, + 720 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 46, + 600, + 288, + 720 + ], + "type": "text", + "content": " and add two one-hot-encoded vectors to indicate the locations of object and hand points within " + }, + { + "bbox": [ + 46, + 600, + 288, + 720 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 46, + 600, + 288, + 720 + ], + "type": "text", + "content": ". We then encode the point cloud into a lower dimensional representation " + }, + { + "bbox": [ + 46, + 600, + 288, + 720 + ], + "type": "inline_equation", + "content": "\\psi(\\mathbf{p})" + }, + { + "bbox": [ + 46, + 600, + 288, + 720 + ], + "type": "text", + "content": " by passing it through PointNet++ [39]. Finally, the lower dimensional encoding " + }, + { + "bbox": [ + 46, + 600, + 288, + 720 + ], + "type": "inline_equation", + "content": "\\psi(\\mathbf{p})" + }, + { + "bbox": [ + 46, + 600, + 288, + 720 + ], + "type": "text", + "content": " is passed on to the control policy " + }, + { + "bbox": [ + 46, + 600, + 288, + 720 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 46, + 600, + 288, + 720 + ], + "type": "text", + "content": " and the grasp prediction network " + }, + { + "bbox": [ + 46, + 600, + 288, + 720 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 46, + 600, + 288, + 720 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 330, + 547, + 390 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 330, + 547, + 390 + ], + "spans": [ + { + "bbox": [ + 304, + 330, + 547, + 390 + ], + "type": "text", + "content": "Control Policy The policy network " + }, + { + "bbox": [ + 304, + 330, + 547, + 390 + ], + "type": "inline_equation", + "content": "\\pi(\\mathbf{a}|\\psi(\\mathbf{p}))" + }, + { + "bbox": [ + 304, + 330, + 547, + 390 + ], + "type": "text", + "content": " is a small, two-layered MLP that takes the PointNet++ embedding as input state (" + }, + { + "bbox": [ + 304, + 330, + 547, + 390 + ], + "type": "inline_equation", + "content": "\\mathbf{s} = \\psi(\\mathbf{p})" + }, + { + "bbox": [ + 304, + 330, + 547, + 390 + ], + "type": "text", + "content": ") and predicts actions " + }, + { + "bbox": [ + 304, + 330, + 547, + 390 + ], + "type": "inline_equation", + "content": "\\mathbf{a}" + }, + { + "bbox": [ + 304, + 330, + 547, + 390 + ], + "type": "text", + "content": " that correspond to the change in 6DoF end-effector pose. These are passed on to the handover environment." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 399, + 546, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 399, + 546, + 590 + ], + "spans": [ + { + "bbox": [ + 304, + 399, + 546, + 590 + ], + "type": "text", + "content": "Grasp Prediction We introduce a grasp prediction network " + }, + { + "bbox": [ + 304, + 399, + 546, + 590 + ], + "type": "inline_equation", + "content": "\\sigma(\\psi(\\mathbf{p}))" + }, + { + "bbox": [ + 304, + 399, + 546, + 590 + ], + "type": "text", + "content": " that predicts when the robot should switch from approaching to executing the grasping motion (cf. Fig. 2). We model grasp prediction as a binary classification task. The input corresponds to the PointNet++ embedding " + }, + { + "bbox": [ + 304, + 399, + 546, + 590 + ], + "type": "inline_equation", + "content": "\\psi(\\mathbf{p})" + }, + { + "bbox": [ + 304, + 399, + 546, + 590 + ], + "type": "text", + "content": ", which is fed through a 3-layered MLP. The output is a probability that indicates the likelihood of a successful grasp given the current point cloud feature. If the probability is above a tunable threshold, we execute an open-loop grasping motion. The model is trained offline with pre-grasp poses attained from [15]. We augment the dataset by adding random noise to pre-grasp poses. To determine the labels, we initialize the robot with the pre-grasp poses in the physics simulation and execute the forward grasping motion. The label is one if the grasp is successful, and zero otherwise. We use a binary cross-entropy loss for training." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 598, + 501, + 611 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 598, + 501, + 611 + ], + "spans": [ + { + "bbox": [ + 305, + 598, + 501, + 611 + ], + "type": "text", + "content": "4.4. Two-Stage Teacher-Student Training" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 618, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 618, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 618, + 545, + 715 + ], + "type": "text", + "content": "We aim at training a handover policy capable of moving simultaneously with the human. Training this policy directly in the setting of dynamic motion is challenging because expert demonstrations with open-loop planners to guide training can only be obtained when the human is stationary. A key contribution of our work is a two-stage training scheme for handovers that incrementally trains the policy to alleviate this challenge. In the first stage, we pretrain" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "9657" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 71, + 534, + 255 + ], + "blocks": [ + { + "bbox": [ + 61, + 71, + 534, + 255 + ], + "lines": [ + { + "bbox": [ + 61, + 71, + 534, + 255 + ], + "spans": [ + { + "bbox": [ + 61, + 71, + 534, + 255 + ], + "type": "image", + "image_path": "ed7c431eb9c3aab692d4b4ddf1c254d12f68f3ac96ab0e504786df70595c0c5e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 266, + 548, + 355 + ], + "lines": [ + { + "bbox": [ + 46, + 266, + 548, + 355 + ], + "spans": [ + { + "bbox": [ + 46, + 266, + 548, + 355 + ], + "type": "text", + "content": "Figure 3. Training Procedure. In the pretraining stage (top left box), the human hand is stationary. We alternate between collecting expert demonstrations via motion planning and exploration data with the RL policy " + }, + { + "bbox": [ + 46, + 266, + 548, + 355 + ], + "type": "inline_equation", + "content": "\\pi_{\\mathrm{pre}}" + }, + { + "bbox": [ + 46, + 266, + 548, + 355 + ], + "type": "text", + "content": ". Transitions " + }, + { + "bbox": [ + 46, + 266, + 548, + 355 + ], + "type": "inline_equation", + "content": "\\mathbf{d}" + }, + { + "bbox": [ + 46, + 266, + 548, + 355 + ], + "type": "text", + "content": " are stored in a replay buffer " + }, + { + "bbox": [ + 46, + 266, + 548, + 355 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 46, + 266, + 548, + 355 + ], + "type": "text", + "content": ". During training (green box, right), a batch of randomly sampled transitions from the replay buffer is passed through PointNet++ and the actor and critic networks. In the finetuning stage (bottom left box), the human and robot move concurrently. The expert motion planner is replaced by the expert policy " + }, + { + "bbox": [ + 46, + 266, + 548, + 355 + ], + "type": "inline_equation", + "content": "\\pi_{\\mathrm{exp}}" + }, + { + "bbox": [ + 46, + 266, + 548, + 355 + ], + "type": "text", + "content": ", which shares the weights of the pretrained policy " + }, + { + "bbox": [ + 46, + 266, + 548, + 355 + ], + "type": "inline_equation", + "content": "\\pi_{\\mathrm{pre}}" + }, + { + "bbox": [ + 46, + 266, + 548, + 355 + ], + "type": "text", + "content": ". This policy network will be kept frozen for the rest of training and serves as a regularizer for the RL agent. The RL agent's actor network " + }, + { + "bbox": [ + 46, + 266, + 548, + 355 + ], + "type": "inline_equation", + "content": "\\pi_{*}" + }, + { + "bbox": [ + 46, + 266, + 548, + 355 + ], + "type": "text", + "content": " and critic network " + }, + { + "bbox": [ + 46, + 266, + 548, + 355 + ], + "type": "inline_equation", + "content": "Q_{*}" + }, + { + "bbox": [ + 46, + 266, + 548, + 355 + ], + "type": "text", + "content": " are also initialized with the weights of pretrained agent's networks, but the model will be updated during finetuning. In this stage, transitions are stored in a new replay buffer " + }, + { + "bbox": [ + 46, + 266, + 548, + 355 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{*}" + }, + { + "bbox": [ + 46, + 266, + 548, + 355 + ], + "type": "text", + "content": ". Data is sampled solely from this buffer during finetuning." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 370, + 288, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 370, + 288, + 418 + ], + "spans": [ + { + "bbox": [ + 46, + 370, + 288, + 418 + ], + "type": "text", + "content": "in a setting where the robot only starts moving once the human has stopped (sequential). This pretrained policy is further finetuned in the second stage in which the human and robot move simultaneously (simultaneous)." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 426, + 287, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 426, + 287, + 569 + ], + "spans": [ + { + "bbox": [ + 46, + 426, + 287, + 569 + ], + "type": "text", + "content": "Pretraining in Sequential Setting In the sequential setting, the robot starts moving once the human has come to a stop (see Fig. 3, top left). To grasp the object from the stationary human hand, we leverage motion planning to provide expert demonstrations. During data collection, we alternate between motion planning and RL-based exploration. In both cases, we store the transitions " + }, + { + "bbox": [ + 46, + 426, + 287, + 569 + ], + "type": "inline_equation", + "content": "\\mathbf{d}_t = \\{\\mathbf{p}_t,\\mathbf{a}_t,\\mathbf{g}_t,\\mathbf{r}_t,\\mathbf{p}_{t + 1},\\mathbf{e}_t\\}" + }, + { + "bbox": [ + 46, + 426, + 287, + 569 + ], + "type": "text", + "content": " in a replay buffer " + }, + { + "bbox": [ + 46, + 426, + 287, + 569 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 46, + 426, + 287, + 569 + ], + "type": "text", + "content": ", from which we sample during network training. The term " + }, + { + "bbox": [ + 46, + 426, + 287, + 569 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_t" + }, + { + "bbox": [ + 46, + 426, + 287, + 569 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 426, + 287, + 569 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_{t + 1}" + }, + { + "bbox": [ + 46, + 426, + 287, + 569 + ], + "type": "text", + "content": " indicate the point cloud and the next point cloud, " + }, + { + "bbox": [ + 46, + 426, + 287, + 569 + ], + "type": "inline_equation", + "content": "\\mathbf{a}_t" + }, + { + "bbox": [ + 46, + 426, + 287, + 569 + ], + "type": "text", + "content": " the action, " + }, + { + "bbox": [ + 46, + 426, + 287, + 569 + ], + "type": "inline_equation", + "content": "\\mathbf{g}_t" + }, + { + "bbox": [ + 46, + 426, + 287, + 569 + ], + "type": "text", + "content": " the pre-grasp goal pose, " + }, + { + "bbox": [ + 46, + 426, + 287, + 569 + ], + "type": "inline_equation", + "content": "\\mathbf{r}_t" + }, + { + "bbox": [ + 46, + 426, + 287, + 569 + ], + "type": "text", + "content": " the reward, and " + }, + { + "bbox": [ + 46, + 426, + 287, + 569 + ], + "type": "inline_equation", + "content": "\\mathbf{e}_t" + }, + { + "bbox": [ + 46, + 426, + 287, + 569 + ], + "type": "text", + "content": " an indicator of whether the transition is from the expert." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": "Inspired by [50], we collect expert trajectories with the OMG planner [49] that leverages ground-truth states. Note that some expert trajectories generated by the planner result in collision with the hand, which is why we introduce an offline pre-filtering scheme. We first parse the ACRONYM dataset [14] for potential grasps. We then run collision checking to filter out grasps where the robot and human hand collide. For the set of remaining collision-free grasps, we plan trajectories to grasp the object and execute them in open-loop fashion. On the other hand, the RL policy " + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\pi_{\\mathrm{pre}}" + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": " explores the environment and receives a sparse reward, i.e., the reward is one if the task is completed successfully, oth-" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 305, + 370, + 545, + 395 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 370, + 545, + 395 + ], + "spans": [ + { + "bbox": [ + 305, + 370, + 545, + 395 + ], + "type": "text", + "content": "erwise zero. Hence, collisions with the human will get implicitly penalized by not receiving any positive reward." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 399, + 546, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 399, + 546, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 399, + 546, + 628 + ], + "type": "text", + "content": "Finetuning in Simultaneous Setting In this setting, the human and robot move at the same time. Hence, we cannot rely on motion and grasp planning to guide the policy. On the other hand, simply taking the pre-trained policy " + }, + { + "bbox": [ + 304, + 399, + 546, + 628 + ], + "type": "inline_equation", + "content": "\\pi_{\\mathrm{pre}}" + }, + { + "bbox": [ + 304, + 399, + 546, + 628 + ], + "type": "text", + "content": " from the sequential setting and continue training it without an expert leads to an immediate drop in performance. Hence, we introduce a self-supervision scheme for stability reasons, i.e., we want to keep the finetuning policy close to the pre-trained policy. To this end, we replace the expert planner from the sequential setting by an expert policy " + }, + { + "bbox": [ + 304, + 399, + 546, + 628 + ], + "type": "inline_equation", + "content": "\\pi_{\\mathrm{exp}}" + }, + { + "bbox": [ + 304, + 399, + 546, + 628 + ], + "type": "text", + "content": ", which is initialized with the weights of the pre-trained policy " + }, + { + "bbox": [ + 304, + 399, + 546, + 628 + ], + "type": "inline_equation", + "content": "\\pi_{\\mathrm{pre}}" + }, + { + "bbox": [ + 304, + 399, + 546, + 628 + ], + "type": "text", + "content": " that already provides a reasonable prior policy (see Fig. 3 bottom left). Therefore, we have two policies: i) the expert policy " + }, + { + "bbox": [ + 304, + 399, + 546, + 628 + ], + "type": "inline_equation", + "content": "\\pi_{\\mathrm{exp}}" + }, + { + "bbox": [ + 304, + 399, + 546, + 628 + ], + "type": "text", + "content": " as proxy for the motion and grasping planner. We freeze the network weights of this policy, ii) the finetuning policy " + }, + { + "bbox": [ + 304, + 399, + 546, + 628 + ], + "type": "inline_equation", + "content": "\\pi_*" + }, + { + "bbox": [ + 304, + 399, + 546, + 628 + ], + "type": "text", + "content": " and critic " + }, + { + "bbox": [ + 304, + 399, + 546, + 628 + ], + "type": "inline_equation", + "content": "Q_*" + }, + { + "bbox": [ + 304, + 399, + 546, + 628 + ], + "type": "text", + "content": ", which are initialized with the weights of the pre-trained policy " + }, + { + "bbox": [ + 304, + 399, + 546, + 628 + ], + "type": "inline_equation", + "content": "\\pi_{\\mathrm{pre}}" + }, + { + "bbox": [ + 304, + 399, + 546, + 628 + ], + "type": "text", + "content": " and critic " + }, + { + "bbox": [ + 304, + 399, + 546, + 628 + ], + "type": "inline_equation", + "content": "Q_{\\mathrm{pre}}" + }, + { + "bbox": [ + 304, + 399, + 546, + 628 + ], + "type": "text", + "content": ", respectively. We proceed to train these two networks using the loss functions which we describe next." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 633, + 547, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 633, + 547, + 694 + ], + "spans": [ + { + "bbox": [ + 304, + 633, + 547, + 694 + ], + "type": "text", + "content": "Network Training During training, we sample a batch of random transitions from the replay buffer " + }, + { + "bbox": [ + 304, + 633, + 547, + 694 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 304, + 633, + 547, + 694 + ], + "type": "text", + "content": ". The policy network is trained using a combination of behavior cloning, RL-based losses and an auxiliary objective. In particular, the policy is updated using the following loss function:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 343, + 701, + 546, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 343, + 701, + 546, + 715 + ], + "spans": [ + { + "bbox": [ + 343, + 701, + 546, + 715 + ], + "type": "interline_equation", + "content": "L (\\theta) = \\lambda L _ {\\mathrm {B C}} + (1 - \\lambda) L _ {\\mathrm {D D P G}} + L _ {\\mathrm {A U X}}, \\tag {3}", + "image_path": "b1846bc4bf441627ffdead3b36be7fcd73e86beb4c3c8d28b12a9f9b1cb975ba.jpg" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "9658" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 86, + 70, + 506, + 185 + ], + "blocks": [ + { + "bbox": [ + 86, + 70, + 506, + 185 + ], + "lines": [ + { + "bbox": [ + 86, + 70, + 506, + 185 + ], + "spans": [ + { + "bbox": [ + 86, + 70, + 506, + 185 + ], + "type": "table", + "html": "
success (%)mean accum time (s)failure (%)
execplantotalcontactdroptimeouttotal
SequentialOMG Planner [49] †62.508.3091.4149.72227.788.331.3937.50
Yang et al. [52] †64.584.8640.0364.90017.3611.816.2535.42
GA-DDPG [50]50.007.1390.1427.2814.8619.4425.6950.00
GA-DDPG [50] finetuned57.186.3240.0866.4116.4827.089.2642.82
Ours75.237.7430.1777.9229.2613.432.0824.77
Simult.GA-DDPG [50]36.814.6640.1324.7969.0325.0029.1763.19
GA-DDPG [50] finetuned54.864.8320.0824.9146.7126.3912.0445.14
Ours68.756.2320.1786.4118.8017.824.6331.25
", + "image_path": "f5f34e9dbd6e31da3134eb39e85b3a6b23b4b85e152d1285f8b6a034f2a885c4.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 191, + 545, + 236 + ], + "lines": [ + { + "bbox": [ + 46, + 191, + 545, + 236 + ], + "spans": [ + { + "bbox": [ + 46, + 191, + 545, + 236 + ], + "type": "text", + "content": "Table 1. HandoverSim Benchmark Evaluation. Comparison of our method against various baselines from the HandoverSim benchmark [6]. In the sequential setting, we find that our baseline achieves better overall success rates than the baselines. In the simultaneous setting, we outperform the applicable baselines by large margins. The results for our method are averaged across 3 random seeds. " + }, + { + "bbox": [ + 46, + 191, + 545, + 236 + ], + "type": "inline_equation", + "content": "\\dagger" + }, + { + "bbox": [ + 46, + 191, + 545, + 236 + ], + "type": "text", + "content": ": both methods [49, 52] are evaluated with ground-truth states in [6] and thus are not directly comparable with ours." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 247, + 288, + 319 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 247, + 288, + 319 + ], + "spans": [ + { + "bbox": [ + 46, + 247, + 288, + 319 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 247, + 288, + 319 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{BC}}" + }, + { + "bbox": [ + 46, + 247, + 288, + 319 + ], + "type": "text", + "content": " is a behavior cloning loss that keeps the policy close to the expert policy, " + }, + { + "bbox": [ + 46, + 247, + 288, + 319 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{DDPG}}" + }, + { + "bbox": [ + 46, + 247, + 288, + 319 + ], + "type": "text", + "content": " is the standard actor-critic loss described in Eq. 2, and " + }, + { + "bbox": [ + 46, + 247, + 288, + 319 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{AUX}}" + }, + { + "bbox": [ + 46, + 247, + 288, + 319 + ], + "type": "text", + "content": " is an auxiliary objective that predicts the grasping goal pose of the end-effector. The coefficient " + }, + { + "bbox": [ + 46, + 247, + 288, + 319 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 46, + 247, + 288, + 319 + ], + "type": "text", + "content": " balances the behavior cloning and the RL objective. The critic loss is defined as:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 122, + 325, + 287, + 338 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 122, + 325, + 287, + 338 + ], + "spans": [ + { + "bbox": [ + 122, + 325, + 287, + 338 + ], + "type": "interline_equation", + "content": "L (\\phi) = L _ {\\mathrm {B E}} + L _ {\\mathrm {A U X}}, \\tag {4}", + "image_path": "d03be03a1e0834e0fbbfd86d13696289654f973427b52dff64b2dd4a23fa95e0.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 340, + 287, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 340, + 287, + 376 + ], + "spans": [ + { + "bbox": [ + 46, + 340, + 287, + 376 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 340, + 287, + 376 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{BE}}" + }, + { + "bbox": [ + 46, + 340, + 287, + 376 + ], + "type": "text", + "content": " indicates the Bellman error from Eq. 1 and " + }, + { + "bbox": [ + 46, + 340, + 287, + 376 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{AUX}}" + }, + { + "bbox": [ + 46, + 340, + 287, + 376 + ], + "type": "text", + "content": " is the same auxiliary loss used in Eq. 3. We refer the reader to supplementary material or [50] for more details." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 387, + 128, + 400 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 387, + 128, + 400 + ], + "spans": [ + { + "bbox": [ + 47, + 387, + 128, + 400 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 407, + 287, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 407, + 287, + 491 + ], + "spans": [ + { + "bbox": [ + 46, + 407, + 287, + 491 + ], + "type": "text", + "content": "We first evaluate our approach in simulation using the HandoverSim benchmark (Sec. 5.1). Next, we investigate the performance of sim-to-sim transfer by evaluating the trained models on the test environments powered by a different physics engine (Sec. 5.2). Finally, we apply the trained model to a real-world robotic system and analyze the performance of sim-to-real transfer (Sec. 5.3)." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 498, + 175, + 510 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 498, + 175, + 510 + ], + "spans": [ + { + "bbox": [ + 47, + 498, + 175, + 510 + ], + "type": "text", + "content": "5.1. Simulation Evaluation" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 516, + 287, + 661 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 516, + 287, + 661 + ], + "spans": [ + { + "bbox": [ + 46, + 516, + 287, + 661 + ], + "type": "text", + "content": "Setup HandoverSim [6] contains 1,000 unique H2R handover scenes divided into train, val, and test splits. Each scene contains a unique human handover motion. We evaluate on the \"s0\" setup which contains 720 training and 144 testing scenes. See the supp. material for evaluations on unseen objects, subjects, and handedness. Following the evaluation of GA-DDPG [50] in [6], we consider two settings: (1) the \"sequential\" setting where the robot is allowed to move only after the human hand reaches the handover location and remains static there (i.e., \"hold\" in [6]), and (2) the \"simultaneous\" setting where the robot is allowed to move from the beginning of the episode (i.e., \"w/o hold\" in [6])." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 665, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 715 + ], + "type": "text", + "content": "Metrics We follow the evaluation protocol in Handover-Sim [6]. A handover is considered successful if the robot grasps the object from the human hand and moves it to a designated location. A failure is claimed and the episode" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 247, + 545, + 355 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 247, + 545, + 355 + ], + "spans": [ + { + "bbox": [ + 304, + 247, + 545, + 355 + ], + "type": "text", + "content": "is terminated if any of the following three conditions occur: (1) the robot collides with the hand (contact), (2) the robot drops the object (drop), or (3) a maximum time limit is reached (timeout). Besides efficacy, the benchmark also reports efficiency in time. The time metric is further broken down into (1) the execution time (exec), i.e., the time to physically move the robot, and (2) the planning time (plan), i.e., the time spent on running the policy. All reported metrics are averaged over the rollouts on the test scenes." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 361, + 545, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 361, + 545, + 469 + ], + "spans": [ + { + "bbox": [ + 304, + 361, + 545, + 469 + ], + "type": "text", + "content": "Baselines Our primary baseline is GA-DDPG [50]. Besides comparing with the original model (i.e., trained in [50] for table-top grasping and evaluated in [6]), we additionally compare with a variant finetuned on HandoverSim (\"GA-DDPG [50] finetuned\"). For completeness, we also include two other baselines from [6]: \"OMG Planner [49]\" and \"Yang et al. [52]\". However, both of them are evaluated with ground-truth state input in [6] and thus are not directly comparable with our method." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 475, + 545, + 668 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 475, + 545, + 668 + ], + "spans": [ + { + "bbox": [ + 304, + 475, + 545, + 668 + ], + "type": "text", + "content": "Results Tab. 1 reports the evaluation results on the test scenes. In the sequential setting, our method significantly outperforms all the baselines in terms of success rate, even compared to methods that use state-based input. Our method is slightly slower on average than GA-DDDPG in terms of total time needed for handovers. In the simultaneous setting, our method clearly outperforms GA-DDDPG, which has low success rates. Qualitatively, we observe that GA-DDDPG directly tries to grasp the object from the user while it is still moving, while our method follows the hand and finds a feasible grasp once the hand has come to a stop, resulting in a trade-off on the overall execution time. We provide a qualitative example of this behavior in Fig. 4 (a) and in the supplementary video. We also refer to the supp. material for a discussion of limitations and a robustness analysis of our pipeline under noisy observations." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 677, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 715 + ], + "type": "text", + "content": "Ablations We evaluate our design choices in an ablation study and report the results in Tab. 2. We analyze the vision backbone by replacing PointNet++ with a ResNet18 [23]" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "9659" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 72, + 69, + 520, + 487 + ], + "blocks": [ + { + "bbox": [ + 72, + 69, + 520, + 487 + ], + "lines": [ + { + "bbox": [ + 72, + 69, + 520, + 487 + ], + "spans": [ + { + "bbox": [ + 72, + 69, + 520, + 487 + ], + "type": "image", + "image_path": "64a3e89bf357d7361f049fd3f4bd7b992e71dcd8bb2ac1d9b051d4fc6821445e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 493, + 547, + 539 + ], + "lines": [ + { + "bbox": [ + 46, + 493, + 547, + 539 + ], + "spans": [ + { + "bbox": [ + 46, + 493, + 547, + 539 + ], + "type": "text", + "content": "Figure 4. Qualitative results. We provide a comparison to show our methods' advantages over GA-DDPG [50]. (a) Our method reacts to the moving human, while the baseline tries to go for a grasp directly, which leads to collision. (b) In the sim-to-sim transfer, we often find that the baseline does not find a grasp on the object. (c) In the sim-to-real experiment, GA-DDPG usually tries to get to a grasp directly, while our method adjusts the gripper into a stable grasping pose first. See the video in supp. material for more qualitative examples." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 58, + 544, + 272, + 651 + ], + "blocks": [ + { + "bbox": [ + 58, + 544, + 272, + 651 + ], + "lines": [ + { + "bbox": [ + 58, + 544, + 272, + 651 + ], + "spans": [ + { + "bbox": [ + 58, + 544, + 272, + 651 + ], + "type": "table", + "html": "
Ablation Study
success (%)failure (%)
contactdroptimeout
w/ RGBDM + ResNet1834.106.2045.8013.90
w/ third person view60.429,9525.693.94
w/o hand point cloud59.0324.0711.585.32
w/o aux prediction70.6010.6516.202.54
w/o standoff52.557.8736.802.78
w/o finetuning73.389.0313.893.70
Ours75.239.2613.432.08
w/o finetuning simul.62.2711.8120.375.56
Ours simul.68.758.817.824.63
", + "image_path": "e8cb21c6eae268c5767a8b1f66eee86a3238403b0930d44f13d3ccaafbe0c3f4.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 654, + 289, + 712 + ], + "lines": [ + { + "bbox": [ + 46, + 654, + 289, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 289, + 712 + ], + "type": "text", + "content": "Table 2. Ablation. We ablate the vision backbone, hand perception, and egocentric view. We also study the effect of finetuning, the auxiliary prediction, and splitting the task into two phases. All design choices are crucial aspects of our method with regards to overall performance. Results are averaged over 3 random seeds." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 546, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 546, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 546, + 545, + 715 + ], + "type": "text", + "content": "that processes the RGB and depth/segmentation (DM) images. Similar to the findings in GA-DDPG, the PointNet++ backbone performs better. Next, we train our method from third person view instead of egocentric view and without active hand segmentation (" + }, + { + "bbox": [ + 304, + 546, + 545, + 715 + ], + "type": "inline_equation", + "content": "w/o" + }, + { + "bbox": [ + 304, + 546, + 545, + 715 + ], + "type": "text", + "content": " hand point cloud), i.e., the policy only perceives the object point cloud but not the hand point cloud. We also ablate the auxiliary prediction (" + }, + { + "bbox": [ + 304, + 546, + 545, + 715 + ], + "type": "inline_equation", + "content": "w/o" + }, + { + "bbox": [ + 304, + 546, + 545, + 715 + ], + "type": "text", + "content": " aux prediction) and evaluate a variant that directly learns to approach and grasp the object instead of using the two task phases of approaching and grasping (" + }, + { + "bbox": [ + 304, + 546, + 545, + 715 + ], + "type": "inline_equation", + "content": "w/o" + }, + { + "bbox": [ + 304, + 546, + 545, + 715 + ], + "type": "text", + "content": " standoff). Lastly, we compare against our pretrained model, which was only trained in the sequential setting without finetuning (" + }, + { + "bbox": [ + 304, + 546, + 545, + 715 + ], + "type": "inline_equation", + "content": "w/o" + }, + { + "bbox": [ + 304, + 546, + 545, + 715 + ], + "type": "text", + "content": " finetuning). We find that the ablated components comprise important elements of our method. The results indicate an in-" + } + ] + } + ], + "index": 4 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "9660" + } + ] + } + ], + "index": 5 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 59, + 70, + 272, + 163 + ], + "blocks": [ + { + "bbox": [ + 59, + 70, + 272, + 163 + ], + "lines": [ + { + "bbox": [ + 59, + 70, + 272, + 163 + ], + "spans": [ + { + "bbox": [ + 59, + 70, + 272, + 163 + ], + "type": "table", + "html": "
Sim-to-Sim
success (%)failure (%)
contactdroptimeout
SequentialGA-DDPG [50]19.444.8647.2228.47
GA-DDPG [50] finetuned11.816.2568.7513.19
Ours44.219.4940.515.79
Ours w/o grasp54.407.8733.344.40
Simult.GA-DDPG [50]11.1115.9748.6124.31
GA-DDPG [50] finetuned16.679.7263.899.72
Ours39.589.0343.757.64
Ours w/o grasp pred.47.9210.6535.885.56
", + "image_path": "7229d3e298e96557ddd4043c4caa0cc830273b6fbe00079b46bfc077e9e0bb0b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 210, + 287, + 246 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 210, + 287, + 246 + ], + "spans": [ + { + "bbox": [ + 47, + 210, + 287, + 246 + ], + "type": "text", + "content": "creased amount of hand collision or object drop in all ablations. A closer analysis in the simultaneous setting shows that our finetuned model outperforms the pretrained model." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 254, + 167, + 266 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 254, + 167, + 266 + ], + "spans": [ + { + "bbox": [ + 47, + 254, + 167, + 266 + ], + "type": "text", + "content": "5.2. Sim-to-Sim Transfer" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 272, + 287, + 524 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 272, + 287, + 524 + ], + "spans": [ + { + "bbox": [ + 46, + 272, + 287, + 524 + ], + "type": "text", + "content": "Instead of directly transferring to the real world, we first evaluate the robustness of the models by transferring them to a different physics simulator. We re-implement the HandoverSim environment following the mechanism presented in [6] except for replacing the backend physics engine from Bullet [10] to Isaac Gym [29]. We then evaluate the models trained on the original Bullet-based environment on the test scenes powered by Isaac Gym. The results are presented in Tab. 3. We observe a significant drop for GA-DDPG on the success rates (i.e., to below " + }, + { + "bbox": [ + 46, + 272, + 287, + 524 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 46, + 272, + 287, + 524 + ], + "type": "text", + "content": ") in both settings. Qualitatively, we see that grasps are often either missed completely or only partially grasped (see Fig. 4 (b)). On the other hand, our method is able to retain higher success rates. Expectedly, it also suffers from a loss in performance. We analyze the influence of our grasp predictor on transfer performance and compare against a variant where we execute the grasping motion after a fixed amount of time (Ours w/o grasp pred.), which will leave the robot enough time to find a pre-grasp pose. Part of the performance drop is caused by the grasp predictor initiating the grasping phase at the wrong time, which can be improved upon in future work." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 532, + 169, + 544 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 532, + 169, + 544 + ], + "spans": [ + { + "bbox": [ + 47, + 532, + 169, + 544 + ], + "type": "text", + "content": "5.3. Sim-to-Real Transfer" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 551, + 287, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 551, + 287, + 658 + ], + "spans": [ + { + "bbox": [ + 46, + 551, + 287, + 658 + ], + "type": "text", + "content": "Finally, we deploy the models trained in HandoverSim on a real robotic platform. We follow the perception pipeline used in [50,52] to generate segmented hand and object point clouds for the policy, and use the output to update the end effector's target position. We compare our method against GA-DDPG [50] with two sets of experiments: (1) a pilot study with controlled handover poses and (2) a user evaluation with free-form handovers. For experimental details and the full results, please see the supp. material." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 665, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 715 + ], + "type": "text", + "content": "Pilot Study We first conduct a pilot study with two subjects. The subjects are instructed to handover 10 objects from HandoverSim by grasping and presenting the objects in controlled poses. For each object, we test with 6 poses" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 317, + 70, + 531, + 191 + ], + "blocks": [ + { + "bbox": [ + 47, + 167, + 287, + 200 + ], + "lines": [ + { + "bbox": [ + 47, + 167, + 287, + 200 + ], + "spans": [ + { + "bbox": [ + 47, + 167, + 287, + 200 + ], + "type": "text", + "content": "Table 3. Sim-to-Sim Experiment. We evaluate sim-to-sim transfer of the learning-based method to Isaac Gym [29], Our method shows better transfer capabilities than GA-DDPG [50]." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 317, + 70, + 531, + 191 + ], + "lines": [ + { + "bbox": [ + 317, + 70, + 531, + 191 + ], + "spans": [ + { + "bbox": [ + 317, + 70, + 531, + 191 + ], + "type": "table", + "html": "
Subject 1Subject 2
GA-DDPG [50]OursGA-DDPG [50]Ours
011_banana3 / 66 / 66 / 65 / 6
037_scissors2 / 65 / 63 / 65 / 6
006_mustard_bottle1 / 63 / 62 / 64 / 6
024_bowl3 / 64 / 63 / 63 / 6
040_large Marker0 / 64 / 64 / 65 / 6
003_cracker_box3 / 62 / 60 / 62 / 6
052extra_large_clamp1 / 64 / 65 / 65 / 6
008_pudding_box3 / 66 / 64 / 64 / 6
010_potted_meat_can2 / 62 / 63 / 64 / 6
021_bleach_cleanser3 / 65 / 63 / 64 / 6
total21 / 6041 / 6033 / 6041 / 60
", + "image_path": "c084d54b07da6323c39a5e13eade3d491270622da35c6a443873d360369b15ef.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 198, + 545, + 220 + ], + "lines": [ + { + "bbox": [ + 306, + 198, + 545, + 220 + ], + "spans": [ + { + "bbox": [ + 306, + 198, + 545, + 220 + ], + "type": "text", + "content": "Table 4. Sim-to-Real Experiment. Success rates of the pilot study. Our method outperforms GA-DDPG [50] for both subjects." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 242, + 545, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 242, + 545, + 361 + ], + "spans": [ + { + "bbox": [ + 304, + 242, + 545, + 361 + ], + "type": "text", + "content": "(3 poses for each hand) with varying object orientation and varying amount of hand occlusion, resulting in 60 poses per subject. The same set of poses are used in testing both our model and GA-DDPG [50]. The success rates are shown Tab. 4. Results indicate that our method outperforms GA-DDPG [50] for both subjects on the overall success rate (i.e., 41/60 versus 21/60 for Subject 1). Qualitatively, we observe that GA-DDPG [50] tends to fail more from unstable grasping as well as hand collision. Fig. 4 (c) shows two examples of the real world handover trials." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 370, + 545, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 370, + 545, + 514 + ], + "spans": [ + { + "bbox": [ + 304, + 370, + 545, + 514 + ], + "type": "text", + "content": "User Evaluation We further recruited 6 users to compare the two methods and collected feedback from a questionnaire with Likert-scale and open-ended questions. In contrast to the pilot study, we asked the users to handover the 10 objects in ways that are most comfortable to them. We repeated the same experimental process for both methods, and counterbalanced the order to avoid bias. From participants' feedback, the majority agreed that the timing of our method is more appropriate and our method can adjust between different object poses better. The interpretability of the robot's motion was also acknowledged by their comments. Please see the supp. material for more details." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 527, + 378, + 539 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 527, + 378, + 539 + ], + "spans": [ + { + "bbox": [ + 306, + 527, + 378, + 539 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 548, + 545, + 655 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 548, + 545, + 655 + ], + "spans": [ + { + "bbox": [ + 304, + 548, + 545, + 655 + ], + "type": "text", + "content": "In this work, we have presented a learning-based framework for human-to-robot handovers from vision input with a simulated human-in-the-loop. We have introduced a two-stage teacher-student training procedure. In our experiments we have shown that our method outperforms baselines by a significant margin on the HandoverSim benchmark [6]. Furthermore, we have demonstrated that our approach is more robust when transferring to a different physics simulator and a real robotic system." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 669, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 669, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 669, + 545, + 713 + ], + "type": "text", + "content": "Acknowledgements We thank Tao Chen and Adithyavairavan Murali for laying the groundwork, Lirui Wang for the help with GA-DDPG, and Mert Albaba, Christoph Gebhardt, Thomas Langerak and Juan Zarate for their feedback on the manuscript." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "9661" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "text", + "content": "[1] Iretiayo Akinola, Jingxi Xu, Shuran Song, and Peter K Allen. 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In IEEE/CVF International Conference on Computer Vision (ICCV), 2021. 2" + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "text", + "content": "9664" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Learning Imbalanced Data With Vision Transformers/2c5c04d7-db27-4f72-9591-822af7466068_content_list.json b/2023/Learning Imbalanced Data With Vision Transformers/2c5c04d7-db27-4f72-9591-822af7466068_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..acae284066e8b0fa50f769ec3327fb3b9623411c --- /dev/null +++ b/2023/Learning Imbalanced Data With Vision Transformers/2c5c04d7-db27-4f72-9591-822af7466068_content_list.json @@ -0,0 +1,1599 @@ +[ + { + "type": "text", + "text": "Learning Imbalanced Data with Vision Transformers", + "text_level": 1, + "bbox": [ + 215, + 130, + 754, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Zhengzhuo Xu Ruikang Liu Shuo Yang Zenghao Chai Chun Yuan† Shenzhen International Graduate School, Tsinghua University, China", + "bbox": [ + 158, + 179, + 805, + 217 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{xzzthu, liuruikang.cs, ysss9264, zenghaochai}@gmail.com yuanc@sz.tsinghua.edu.cn", + "bbox": [ + 111, + 219, + 851, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 268, + 313, + 284 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The real-world data tends to be heavily imbalanced and severely skew the data-driven deep neural networks, which makes Long-Tailed Recognition (LTR) a massive challenging task. Existing LTR methods seldom train Vision Transformers (ViTs) with Long-Tailed (LT) data, while the off-the-shelf pretrain weight of ViTs always leads to unfair comparisons. In this paper, we systematically investigate the ViTs' performance in LTR and propose LiVT to train ViTs from scratch only with LT data. With the observation that ViTs suffer more severe LTR problems, we conduct Masked Generative Pretraining (MGP) to learn generalized features. With ample and solid evidence, we show that MGP is more robust than supervised manners. Although Binary Cross Entropy (BCE) loss performs well with ViTs, it struggles on the LTR tasks. We further propose the balanced BCE to ameliorate it with strong theoretical groundings. Specially, we derive the unbiased extension of Sigmoid and compensate extra logit margins for deploying it. Our Bal-BCE contributes to the quick convergence of ViTs in just a few epochs. Extensive experiments demonstrate that with MGP and Bal-BCE, LiVT successfully trains ViTs well without any additional data and outperforms comparable state-of-the-art methods significantly, e.g., our ViT-B achieves $81.0\\%$ Top-1 accuracy in iNaturalist 2018 without bells and whistles. Code is available at https://github.com/XuZhengzhuo/LiVT.", + "bbox": [ + 75, + 300, + 473, + 694 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 723, + 209, + 739 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "With the vast success in the computer vision field, Vision Transformers (ViTs) [15, 43] get increasingly popular and have been widely used in visual recognition [15], detection [5], and video analysis [16]. These models are heavily dependent on large-scale and balanced data to avoid overfitting [39, 52, 82]. However, real-world data usually confronts severe class-imbalance problems, i.e., most labels (tail) are associated with limited instances while a few categories (head) occupy dominant samples. The models simply classify images into head classes for lower error because the", + "bbox": [ + 75, + 750, + 468, + 901 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/6eb455689ff51af9ee53c56a0a9d2cdbb08eecaf302e6ee1a740bfd9afb6377a.jpg", + "image_caption": [ + "Figure 1. Top-1 Acc v.s. Model Size on ImageNet-LT dataset. We choose the Tiny / Small / Base / Large ViT and multi-expert approaches. R50 represents the ResNet50 model. ViT-Base gets lower Acc than ResNet50 when trained in a supervised manner." + ], + "image_footnote": [], + "bbox": [ + 498, + 263, + 867, + 449 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "head always overwhelms tail ones in LTR. The data paucity also results in the model overfitting on the tail with unaccepted generalization. The aforementioned problems make Long Tail Recognition (LTR) a challenging task.", + "bbox": [ + 496, + 522, + 892, + 582 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Numerous papers [4, 13, 22, 34, 35, 44, 70] handle the LTR problem with traditional supervised cross-entropy learning based on ResNet [20] or its derivatives [68]. Some methods use ViTs with pretrained weights on ImageNet [52] (or larger datasets), which leads to unfair comparisons with additional data, e.g. on ImageNet-LT (a subset of ImageNet-1K) benchmark. Moreover, there are still limited explorations on the utilization of Long-Tailed (LT) data to train ViTs effectively. Therefore, in this paper, we try to train ViTs from scratch with LT data. We observe that it is particularly difficult to train ViT with LT labels' supervision. As Tab. 1 shows, ViTs degrade heavily when training data become skewed. ViT-B is much worse than ResNet50 with the same CE training manner (c.f. Fig. 1). One reasonable explanation is that ViTs require longer training to learn the inductive bias, while CNNs offer the built-in translation invariance implicitly. Yet another one lies in the label statistical bias in the LTR datasets, which confuses models to make predictions with an inherent bias to the head [12, 47]. The well-trained ViTs have to overcome the above plights simultaneously to avoid falling into dilemmas.", + "bbox": [ + 496, + 583, + 893, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "15793", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Inspired by decoupling [29], many methods [9, 12, 60, 80, 83] attempt to enhance feature extraction in supervised manners like mixup [74] / remix [9], or Self-Supervised Learning (SSL) like Contrastive Learning (CL) [7, 19]. Liu et al. [41] claim that SSL representations are more robust to class imbalance than supervised ones, which inspires us to train ViTs with SSL. However, CL is quite challenging for extensive memory requisition and converge difficulties [8], where more explorations are required to work well with ViTs in LTR. In contrast, we propose to Learn imbalanced data with ViTs (LiVT) by Masked Generative Pretraining (MGP) and Balanced Fine Tuning (BFT).", + "bbox": [ + 75, + 90, + 472, + 271 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Firstly, LiVT adopts MGP to enhance ViTs' feature extraction, which has been proven effective on BeiT [2] and MAE [18]. It reconstructs the masked region of images with an extra lightweight decoder. We observe that MGP is stable with ViTs and robust enough to LT data with empirical evidence. Despite the label distribution, the comparable number of training images will bring similar feature extraction ability, which greatly alleviates the toxic effect of LT labels [26]. Meanwhile, the training is accelerated by masked tokens with acceptable memory requisition.", + "bbox": [ + 75, + 272, + 472, + 422 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Secondly, LiVT trains the downstream head with rebalancing strategies to utilize annotation information, which is consistent with [29, 35, 80]. Generally, Binary Cross-Entropy (BCE) loss performs better than Cross-Entropy loss when collaborating with ViTs [55]. However, it fails to catch up with widely adopted Balanced Cross-Entropy (Bal-CE) loss and shows severe training instability in LTR. We propose the Balanced BCE (Bal-BCE) loss to revise the mismatch margins given by Bal-CE. Detailed and solid theoretical derivations are provided from Bayesian theory. Our Bal-BCE ameliorates BCE by a large margin and achieves state-of-the-art (SOTA) performance with ViTs.", + "bbox": [ + 75, + 422, + 472, + 604 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Extensive experiments show that LiVT learns LT data more efficiently and outperforms vanilla ViT [15], DeiT III [55], and MAE [18] remarkably. As detailed comparisons in Fig. 1, LiVT achieves SOTA on ImageNet-LT with affordable parameters, despite that ImageNet-LT is a relatively small dataset for ViTs. The ViT-Small [55] also achieves outstanding performance compared to ResNet50. Our key contributions are summarized as follows.", + "bbox": [ + 75, + 604, + 472, + 724 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- To our best knowledge, we are the first to investigate training ViTs from scratch with LT data systematically.", + "- We pinpoint that the masked generative pretraining is robust to LT data, which avoids the toxic influence of imbalanced labels on feature learning.", + "- With a solid theoretical grounding, we propose the balanced version of BCE loss (Bal-BCE), which improves the vanilla BCE by a large margin in LTR.", + "- We propose LiVT recipe to train ViTs from scratch, and the performance of LiVT achieves state-of-the-art across various benchmarks for long-tailed recognition." + ], + "bbox": [ + 94, + 727, + 467, + 900 + ], + "page_idx": 1 + }, + { + "type": "table", + "img_path": "images/ecdff1f4cf005665a3ce41f8095fadc04eed7bf6b076d388ba927deab026df06.jpg", + "table_caption": [ + "Table 1. Top-1 accuracy (\\%) of different recipes to train ViT-B-16 from scratch on ImageNet-LT/BAL. All perform much worse on LT than BAL. See descriptions of LT & BAL in section 5.1." + ], + "table_footnote": [], + "table_body": "
DatasetViTΔDeiT IIIΔMAEΔ
ImageNet-BAL38.7-67.2-69.2-
ImageNet-LT31.6-7.048.4-18.854.5-14.7
", + "bbox": [ + 503, + 142, + 893, + 196 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 203, + 640, + 219 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Long-tailed Visual Recognition", + "text_level": 1, + "bbox": [ + 500, + 231, + 774, + 247 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We roughly divide LTR progress into three groups.", + "bbox": [ + 517, + 257, + 854, + 273 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Rebalancing strategies adjust each class contribution with delicate designs. Re-sampling methods adopt class-wise sampling rate to learn balanced networks [13, 35, 62, 72, 81]. More sophisticated approaches replenish few-shot samples with the help of many-shot ones [9, 10, 31, 49, 70, 78]. The re-weighting proposals modify the loss function by adjusting class weights [1, 13, 38, 50, 53, 54, 80] to assign different weights to samples or enlarging logit margins [4, 22, 35, 47, 51, 70, 75, 77] to learn more challenging and sparse classes. However, the rebalancing strategies are always at the cost of many-shot accuracy inevitably.", + "bbox": [ + 496, + 275, + 890, + 441 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Multi-Expert networks alleviate the LTR problem with single expert learning and knowledge aggregation [3, 21, 25, 33, 34, 37, 61, 67, 77, 81]. LFME [67] trains experts with the subsets with a lower imbalance ratio and aggregate via knowledge distillation. TADE [77] learns three classifiers with the different test labels prior based on Logit Adjustment [47] and optimizes classifiers' output weights by contrastive learning [7]. NCL [34] collaboratively learns multiple experts together to reduce tail uncertainty. However, it is still heuristic to design expert individual training and knowledge aggregation manners. The overly complex models also make training difficult and limit the inference speed.", + "bbox": [ + 496, + 444, + 892, + 626 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Multi-stage training is another effective training strategy for LTR. Cao et al. [4] propose to learn features at first and defer re-weighting in the second stage. Kang et al. [29] further decouples the representation and classifier learning separately, where the classifier is trained with re-balancing strategies just in the second stage. Some works [9, 70, 80] adopt more approaches, e.g., mixup [74] or remix [9], to improve features in the first stage. More recently, Contristive Learning (CL) [7, 19] is gaining increasing concern. Kang et al. [28] exploit to learn balanced feature representations by CL to bypass the influence of imbalanced labels. However, it is more effective to adopt Supervised Contristive Learning (SCL) to utilize the labels [60, 71]. With SCL, SO-TAs [12, 27, 36, 83] all adopt the Bal-CE loss [22, 47, 51, 70] to train the classifier for better performance. Masked Generative learning [6, 14, 18] is another effective feature learning method. However, there is still limited research on it in the community of LTR.", + "bbox": [ + 496, + 628, + 893, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "15794", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Vision Transformers", + "text_level": 1, + "bbox": [ + 76, + 90, + 272, + 104 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Current observations and conclusions are mostly based on ResNets [20, 68]. Most recently, ViT [15] has shown extraordinary performance after pre-training on large-scale and balanced datasets. Swin transformer [43] proposes a hierarchical transformer with shift windows to bring greater efficiency. DeiT [55] introduces a simple but effective recipe to train ViT with limited data. BeiT [2] trains ViT with the idea of Mask Language Models. MAE [18] further reduces the computation complexity with a lightweight decoder and higher mask ratio. Although RAC [45] adopts ViTs with pretrained checkpoints, there is limited research to train ViTs from scratch on long-tailed datasets.", + "bbox": [ + 75, + 113, + 472, + 297 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Preliminaries", + "text_level": 1, + "bbox": [ + 76, + 308, + 215, + 324 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Task Definition", + "text_level": 1, + "bbox": [ + 76, + 333, + 230, + 348 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "With a $N$ -sample and $C$ -class dataset $\\mathcal{D} = \\{\\mathcal{X}, \\mathcal{Y}\\}$ , we note each instance $\\mathbf{x}_i \\in \\mathcal{X} := \\{\\mathbf{x}_1, \\dots, \\mathbf{x}_N\\}$ and corresponding $\\mathbf{y}_i \\in \\mathcal{Y} := \\{\\mathbf{y}_1, \\dots, \\mathbf{y}_N\\}$ , where each $\\mathbf{y}_i \\in \\mathcal{C} := \\{1, \\dots, C\\}$ . In long-tailed visual recognition, each category $\\mathcal{C}_i$ has a different instance number $n_i = |\\mathcal{C}_i|$ and we set $\\gamma = n_{max} / n_{min}$ to measure how skewed the long-tailed dataset is. We train the model $\\mathcal{M} := \\{\\mathcal{F}_{\\theta_f}, \\mathcal{W}_{\\theta_w}\\}$ with $\\mathcal{D}$ which contains a feature encoder $\\mathcal{F}_{\\theta_f}$ and a classifier $\\mathcal{W}_{\\theta_w}$ . Besides, we consider a lightweight decoder $\\mathcal{D}_{\\theta_d}$ for mask autoencoder architecture. For an input image $\\mathbf{x}$ , the encoder extracts the feature representation $\\mathbf{v} := \\mathcal{F}(\\mathbf{x} | \\theta_f) \\in \\mathbb{R}^d$ , the classifier gives the logits $\\mathbf{z} := \\mathcal{W}(\\mathbf{v} | \\theta_w) \\in \\mathbb{R}^c$ and the decoder reconstructs original image $\\hat{\\mathbf{x}} := \\mathcal{D}(\\mathbf{v} | \\theta_d) \\in \\mathbb{R}^{H \\times W \\times 3}$ . The $d / H / W$ is feature dimension / resized height / resized width, respectively.", + "bbox": [ + 75, + 356, + 472, + 583 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Balanced Cross-entropy", + "text_level": 1, + "bbox": [ + 76, + 592, + 297, + 609 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Here, we revisit the balanced softmax and corresponding Balanced Cross-Entropy (BalCE) loss [22,34,47,51,70,83], which has been widely adopted in LTR. Consider the standard softmax operation and cross-entropy loss:", + "bbox": [ + 76, + 616, + 468, + 676 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {\\mathrm {C E}} \\left(\\mathcal {M} \\left(\\mathbf {x} \\mid \\theta_ {f}, \\theta_ {w}\\right), \\mathbf {y} _ {i}\\right) = - \\log \\left(p \\left(\\mathbf {y} _ {i} \\mid \\mathbf {x}; \\theta_ {f}, \\theta_ {w}\\right)\\right) \\\\ = - \\log \\left[ e ^ {z _ {\\mathbf {y} _ {i}}} / \\sum_ {\\mathbf {y} _ {j} \\in \\mathcal {Y}} e ^ {z _ {\\mathbf {y} _ {j}}} \\right] = \\log \\left[ 1 + \\sum_ {\\mathbf {y} _ {j} \\neq \\mathbf {y} _ {i}} e ^ {\\mathbf {z} _ {\\mathbf {y} _ {j}} - \\mathbf {z} _ {\\mathbf {y} _ {i}}} \\right]. \\tag {1} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 84, + 686, + 468, + 741 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "If we take the class instance number $n_{\\mathbf{y}_i}$ into account for softmax [51], we have the balanced cross-entropy loss:", + "bbox": [ + 76, + 752, + 468, + 782 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {\\mathrm {B a l - C E}} \\left(\\mathcal {M} \\left(\\mathbf {x} \\mid \\theta_ {f}, \\theta_ {w}\\right), \\mathbf {y} _ {i}\\right) = - \\log \\left(p \\left(\\mathbf {y} _ {i} \\mid \\mathbf {x}; \\theta_ {f}, \\theta_ {w}\\right)\\right) \\\\ = - \\log \\left[ \\frac {n _ {\\mathbf {y} _ {i}} e ^ {z _ {\\mathbf {y} _ {i}}}}{\\sum_ {\\mathbf {y} _ {j} \\in \\mathcal {Y}} n _ {\\mathbf {y} _ {j}} e ^ {z _ {\\mathbf {y} _ {j}}}} \\right] \\tag {2} \\\\ = \\log [ 1 + \\sum_ {\\mathbf {y} _ {j} \\neq \\mathbf {y} _ {i}} e ^ {\\log n _ {\\mathbf {y} _ {j}} - \\log n _ {\\mathbf {y} _ {i}}} \\cdot e ^ {\\mathbf {z} _ {\\mathbf {y} _ {j}} - \\mathbf {z} _ {\\mathbf {y} _ {i}}} ]. \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 792, + 468, + 883 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Theorem 1. Logit Bias of Balanced CE. Let $\\pi_{\\mathbf{y}_i} = n_{\\mathbf{y}_i} / N$ be the training label $\\mathbf{y}_i$ distribution. If we implement the balanced cross-entropy loss via logit adjustment, the bias item of logit $\\mathbf{z}_{\\mathbf{y}_i}$ will be $\\mathcal{B}_{\\mathbf{y}_i}^{\\mathrm{ce}} = \\log \\pi_{\\mathbf{y}_i}$ , i.e.,", + "bbox": [ + 498, + 90, + 890, + 156 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {\\mathrm {B a l - C E}} = \\log \\left[ 1 + \\sum_ {\\mathbf {y} _ {j} \\neq \\mathbf {y} _ {i}} e ^ {\\log n _ {\\mathbf {y} _ {j}} - \\log n _ {\\mathbf {y} _ {i}}} \\cdot e ^ {\\mathbf {z} _ {\\mathbf {y} _ {j}} - \\mathbf {z} _ {\\mathbf {y} _ {i}}} \\right] \\\\ = \\log [ 1 + \\sum_ {\\mathbf {y} _ {j} \\neq \\mathbf {y} _ {i}} e ^ {(\\mathbf {z} _ {\\mathbf {y} _ {j}} + \\log n _ {\\mathbf {y} _ {j}}) - (\\mathbf {z} _ {\\mathbf {y} _ {i}} + \\log n _ {\\mathbf {y} _ {i}})} ] \\tag {3} \\\\ = \\log [ 1 + \\sum_ {\\mathbf {y} _ {j} \\neq \\mathbf {y} _ {i}} e ^ {(\\mathbf {z} _ {\\mathbf {y} _ {j}} + \\log \\pi_ {\\mathbf {y} _ {j}}) - (\\mathbf {z} _ {\\mathbf {y} _ {i}} + \\log \\pi_ {\\mathbf {y} _ {i}})} ]. \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 509, + 175, + 890, + 284 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Proof. See subsection 5.1 from [47] or detail derivation in the Appendix from the Bayesian Theorem perspective.", + "bbox": [ + 498, + 290, + 890, + 319 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Bal-CE loss strengthens the tail instance's contributions while suppressing bias to the head, which alleviates the LTR problem effectively. However, the $\\mathcal{B}_{\\mathbf{y}_i}^{\\mathrm{ce}}$ in Thm.1 fails to work well when collaborating with BCE, where More analysis is required to build a balanced version BCE loss.", + "bbox": [ + 498, + 320, + 890, + 396 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Methodology", + "text_level": 1, + "bbox": [ + 500, + 407, + 635, + 424 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we introduce our LiVT in two stages. In section 4.1, we revisit the generative masked auto-encoder as our first stage. Then, we propose the novel balanced sigmoid and corresponding binary cross entropy to collaborate with ViTs in section 4.2. Eventually, we summarize our whole pipeline in section 4.3.", + "bbox": [ + 498, + 431, + 890, + 523 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.1. Masked Generative Pretraining", + "text_level": 1, + "bbox": [ + 500, + 530, + 779, + 546 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Inspired by BeiT [2] and MAE [18], we pretrain feature encoder $\\mathcal{F}_{\\theta_f}$ via MGP for its training efficiency and label irrelevance. MGP trains the encoder parameters $\\theta_{f}$ with high ratio masked images and reconstructs the original image by a lightweight decoder $\\mathcal{D}_{\\theta_d}$ .", + "bbox": [ + 498, + 553, + 890, + 630 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathbf {x}} = \\mathcal {D} _ {\\theta_ {d}} \\left(\\mathcal {F} _ {\\theta_ {f}} (\\mathbf {M} \\odot \\mathbf {x})\\right), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 604, + 635, + 890, + 652 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathbf{M} \\in \\{0,1\\}^{H \\times W}$ is a random patch-wise binary mask. Then, we optimize $\\theta_{f}, \\theta_{d}$ end-to-end via minimizing the mean squared error between $\\mathbf{x}$ and $\\hat{\\mathbf{x}}$ .", + "bbox": [ + 498, + 657, + 890, + 703 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We adopt MGP for two reasons: 1) It is difficult to train ViTs directly with label supervision (see plain ViT-B performance in Fig. 1) for its convergence difficulty and computation requirement. The DeiT III [55] is hard to catch up with SOTAs in LTR, even with more training epochs, stronger data augmentation, and larger model sizes. 2) The feature extraction ability of MGP is affected slightly by class instance number, compared with previous mixup-based supervision [29,35,80], CL [60] or SCL [12,27,36,83]. Even pretraining on LTR datasets, the transfer performance of MGP is on par with that trained on balanced datasets with comparable total training instances. See transfer results in Tab. 5 and more visualization in Appendix.", + "bbox": [ + 498, + 704, + 890, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "15795", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.2. Balanced Fine Tuning", + "text_level": 1, + "bbox": [ + 76, + 90, + 282, + 107 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In the Balanced Fine-Tuning (BFT) phase, softmax + CE loss has been the standard paradigm for utilizing annotated labels. However, recent research [42, 55, 65] pinpoint that Binary Cross-Entropy (BCE) loss works much well with ViTs and is more convenient when employed with mixup-manners [42, 73, 74], which can be written as:", + "bbox": [ + 75, + 114, + 468, + 205 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {\\mathrm {B C E}} = - \\sum_ {\\mathbf {y} _ {i} \\in \\mathcal {C}} w _ {\\mathbf {y} _ {i}} [ \\mathbb {1} (\\mathbf {y} _ {i}) \\cdot \\log \\sigma (\\mathbf {z} _ {\\mathbf {y} _ {i}}) \\tag {5} \\\\ \\left. + \\left(1 - \\mathbb {1} \\left(\\mathbf {y} _ {i}\\right)\\right) \\cdot \\log \\left(1 - \\sigma \\left(\\mathbf {z} _ {\\mathbf {y} _ {i}}\\right)\\right) \\right], \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 96, + 218, + 468, + 272 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\sigma (x) = 1 / (1 + e^{-x})$ indicates the sigmoid operation.", + "bbox": [ + 76, + 286, + 468, + 301 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In LTR, Balanced CE (Eq. 2) improves original CE (Eq. 1) remarkably. However, we observe that it is not directly applicable when it comes to BCE. The logit bias $\\mathcal{B}_{\\mathbf{y}_i}$ in Thm. 1 leads to an even worse situation. Here, we claim that the proper bias of BCE shall be revised as Thm. 2 when collaborating with BCE in LTR.", + "bbox": [ + 75, + 301, + 468, + 393 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Theorem 2. Logit Bias of Balanced BCE. Let $\\pi_{\\mathbf{y}_i} = n_{\\mathbf{y}_i} / N$ be the class $\\mathbf{y}_i$ distribution. If we implement the balanced binary cross-entropy loss via logit adjustment, the bias item of logit $\\mathbf{z}_{\\mathbf{y}_i}$ will be $\\mathcal{B}_{\\mathbf{y}_i}^{\\mathrm{bce}} = \\log \\pi_{\\mathbf{y}_i} - \\log (1 - \\pi_{\\mathbf{y}_i})$ ,", + "bbox": [ + 76, + 406, + 468, + 470 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {\\text {B a l - B C E}} = - \\sum_ {\\mathbf {y} _ {i} \\in \\mathcal {C}} w _ {i} [ \\mathbb {1} (\\mathbf {y} _ {i}) \\cdot \\log \\frac {1}{1 + e ^ {- [ \\mathbf {z} _ {\\mathbf {y} _ {i}} + \\log \\pi_ {\\mathbf {y} _ {i}} - \\log (1 - \\pi_ {\\mathbf {y} _ {i}}) ]}} \\\\ + (1 - \\mathbb {1} (\\mathbf {y} _ {i})) \\cdot \\log (1 - \\frac {1}{1 + e ^ {- [ \\mathbf {z} _ {\\mathbf {y} _ {i}} + \\log \\pi_ {\\mathbf {y} _ {i}} - \\log (1 - \\pi_ {\\mathbf {y} _ {i}}) ]}}) ] \\tag {6} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 487, + 496, + 569 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Proof. We regard Binary CE as $C$ binary classification loss. Hence, for the class $\\mathbf{y}_i$ , $\\pi_{\\mathbf{y}_i}$ indicates positive samples proportion and $1 - \\pi_{\\mathbf{y}_i}$ indicates negative ones. Here, we start by revising the sigmoid activation function:", + "bbox": [ + 76, + 570, + 468, + 631 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\sigma \\left(\\mathbf {z} _ {\\mathbf {y} _ {i}}\\right) = \\frac {1}{1 + e ^ {- \\mathbf {z} _ {\\mathbf {y} _ {i}}}} = \\frac {e ^ {0}}{e ^ {0} + e ^ {- \\mathbf {z} _ {\\mathbf {y} _ {i}}}} = \\frac {e ^ {\\mathbf {z} _ {\\mathbf {y} _ {i}}}}{e ^ {\\mathbf {z} _ {\\mathbf {y} _ {i}}} + e ^ {0}} \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 643, + 468, + 676 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "If we view Eq. 7 as the binary version of softmax, $e^x (e^0)$ will be the normalized probability to indicate yes (no). Similar to Eq. 2, we use instance number to balance sigmoid:", + "bbox": [ + 76, + 690, + 468, + 736 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\hat {\\sigma} \\left(\\mathbf {z} _ {\\mathbf {y} _ {i}}\\right) = \\frac {n _ {\\mathbf {y} _ {i}} \\cdot e ^ {\\mathbf {z} _ {\\mathbf {y} _ {i}}}}{n _ {\\mathbf {y} _ {i}} \\cdot e ^ {\\mathbf {z} _ {\\mathbf {y} _ {i}}} + (N - n _ {\\mathbf {y} _ {i}}) \\cdot e ^ {0}} \\\\ = \\frac {\\pi_ {\\mathbf {y} _ {i}} \\cdot e ^ {\\mathbf {z} _ {\\mathbf {y} _ {i}}}}{\\pi_ {\\mathbf {y} _ {i}} \\cdot e ^ {\\mathbf {z} _ {\\mathbf {y} _ {i}}} + \\left(1 - \\pi_ {\\mathbf {y} _ {i}}\\right) \\cdot e ^ {0}} \\tag {8} \\\\ = \\frac {1}{1 + \\frac {1 - \\pi_ {\\mathbf {y} _ {i}}}{\\pi_ {\\mathbf {y} _ {i}}} \\cdot e ^ {- \\mathbf {z} _ {\\mathbf {y} _ {i}}}} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 142, + 748, + 468, + 857 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Considering the log-sum-exp trick for numerical stability, we change the weight of $e^{-\\mathbf{z}_{\\mathbf{y}_i}}$ to the bias term of $\\mathbf{z}_{\\mathbf{y}_i}$ :", + "bbox": [ + 76, + 869, + 468, + 902 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\hat {\\sigma} (\\mathbf {z} _ {\\mathbf {y} _ {i}}) = \\frac {1}{1 + \\frac {1 - \\pi_ {\\mathbf {y} _ {i}}}{\\pi_ {\\mathbf {y} _ {i}}} \\cdot e ^ {- \\mathbf {z} _ {\\mathbf {y} _ {i}}}} = \\frac {1}{1 + e ^ {- \\mathbf {z} _ {\\mathbf {y} _ {i}} + \\log \\frac {1 - \\pi_ {\\mathbf {y} _ {i}}}{\\pi_ {\\mathbf {y} _ {i}}}}} \\\\ = \\frac {1}{1 + e ^ {- \\mathbf {z} _ {\\mathbf {y} _ {i}} + \\log (1 - \\pi_ {\\mathbf {y} _ {i}}) - \\log \\pi_ {\\mathbf {y} _ {i}}}} \\tag {9} \\\\ = \\frac {1}{1 + e ^ {- [ {\\bf z _ {y}} _ {i} + \\log \\pi_ {{\\bf y} _ {i}} - \\log (1 - \\pi_ {{\\bf y} _ {i}}) ]}} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 509, + 113, + 890, + 219 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Hence, we derive the bias item of logit $\\mathbf{z}_i$ shall be $\\mathcal{B}_{\\mathbf{y}_i}^{\\mathrm{bce}} = \\log \\pi_{\\mathbf{y}_i} - \\log (1 - \\pi_{\\mathbf{y}_i})$ . If we bring Eq. 9 into Binary CE (Eq. 5), we will get the Balanced Binary CE as Eq. 6.", + "bbox": [ + 498, + 229, + 890, + 276 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "□", + "bbox": [ + 874, + 277, + 890, + 290 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Interpretation. With the additional $-\\log (1 - \\pi_{\\mathbf{y}_i})$ , $\\mathcal{B}_{\\mathbf{y}_i}^{\\mathrm{bce}}$ keeps consistent character with $\\mathcal{B}_{\\mathbf{y}_i}^{\\mathrm{ce}}$ w.r.t. $\\pi_{\\mathbf{y}_i}$ . Similar to $\\mathcal{B}_{\\mathbf{y}_i}^{\\mathrm{ce}}$ , it enlarges the margins to increase the difficulty of the tail (smaller $\\pi_{\\mathbf{y}_i}$ ). However, $\\mathcal{B}_{\\mathbf{y}_i}^{\\mathrm{bce}}$ further reduces the head (larger $\\pi_{\\mathbf{y}_i}$ ) inter-class distances with larger positive values. Notice that BCE is not class-wise mutually exclusive, and the smaller head inter-class distance helps the networks focus more on the tail's contributions. See visualizations and more in-depth analysis in Appendix.", + "bbox": [ + 498, + 291, + 890, + 429 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Through Bayesian theory [70], we can further extend the proposed Balanced BCE if the test distribution is available as $\\pi^t$ , which can be summarized as the following theorem:", + "bbox": [ + 498, + 429, + 890, + 474 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Theorem 3. Logit Bias of Balanced BCE with Test Prior. Let $\\pi_{\\mathbf{y}_i}^s$ and $\\pi_{\\mathbf{y}_i}^t$ be the label $\\mathbf{y}_i$ training and test distribution. If we implement the balanced cross-entropy loss via logit adjustment, the bias item of logit $\\mathbf{z}_{\\mathbf{y}_i}$ will be:", + "bbox": [ + 500, + 484, + 890, + 546 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {B} _ {\\mathbf {y} _ {i}} ^ {\\mathrm {b c e}} = \\left(\\log \\pi_ {\\mathbf {y} _ {i}} ^ {s} - \\log \\pi_ {\\mathbf {y} _ {i}} ^ {t}\\right) - \\left(\\log \\left(1 - \\pi_ {\\mathbf {y} _ {i}} ^ {s}\\right) - \\log \\left(1 - \\pi_ {\\mathbf {y} _ {i}} ^ {t}\\right)\\right)\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 556, + 901, + 577 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Proof. See detailed derivation in Appendix.", + "bbox": [ + 500, + 585, + 787, + 602 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Notice that for the balanced test dataset, $\\pi_{\\mathbf{y}_i}^t = 1 / C$ . Hence, the logit bias in Thm.3 will be:", + "bbox": [ + 498, + 612, + 888, + 642 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {B} _ {\\mathbf {y} _ {i}} ^ {\\mathrm {b c e}} = \\left(\\log \\pi_ {\\mathbf {y} _ {i}} ^ {\\mathrm {s}} - \\log 1 / C\\right) - \\left(\\log \\left(1 - \\pi_ {\\mathbf {y} _ {i}} ^ {\\mathrm {s}}\\right) - \\log \\left(\\frac {C - 1}{C}\\right)\\right) \\\\ = \\log \\pi_ {\\mathbf {y} _ {i}} ^ {s} - \\log \\left(1 - \\pi_ {\\mathbf {y} _ {i}} ^ {s}\\right) + \\log (C - 1) \\tag {10} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 652, + 900, + 714 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Compared with the conclusion of Thm. 2, we get an extra term $\\log (C - 1)$ . From the convex objectives optimization view, there is no expected difference between Thm. 2 and Eq. 10. However, it will increase ViTs' training stability remarkably, especially when the class number $C$ gets larger.", + "bbox": [ + 498, + 715, + 890, + 791 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.3. Pipeline", + "text_level": 1, + "bbox": [ + 500, + 801, + 598, + 816 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We describe LiVT training pipeline precisely in Alg. 1, which can be divided into two stages, i.e., MGP and BFT. Specifically, in the MGP stage, we adopt simple data augmentation $\\mathcal{A}_{pt}$ and more training epochs $T_{pt}$ to update the parameters of $\\mathcal{F}$ and $\\mathcal{D}$ . In the BFT stage, the decoder $\\mathcal{D}$", + "bbox": [ + 498, + 824, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "15796", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Algorithm 1 LiVT Training Pipeline." + ], + "code_body": "Input: $\\mathcal{D},\\mathcal{F},\\mathcal{W},\\mathcal{D},T_{pt},T_{ft},A_{pt},A_{ft},\\pi_{\\mathbf{y}_i},\\tau$ \nOutput: Optimized $\\theta_f,\\theta_w$ \n1: Initialize $\\theta_f,\\theta_d$ randomly. MGP Stage \n2: for $t = 1$ to $T_{pt}$ do \n3: for $\\{\\mathbf{x},\\mathbf{y}\\}$ sampled from $\\mathcal{D}$ do \n4: $\\mathbf{x}:= \\mathcal{A}_{pt}(\\mathbf{x})$ \n5: $\\hat{\\mathbf{x}} = \\mathcal{D}(\\mathcal{F}(\\mathbf{M}\\odot \\mathbf{x}\\mid \\theta_f)\\mid \\theta_d)$ \n6: $\\mathcal{L}_{MSE}(\\hat{\\mathbf{x}},\\mathbf{x}) = ||\\hat{\\mathbf{x}} -\\mathbf{x}||_2$ \n7: $\\{\\theta_f,\\theta_d\\} \\gets \\{\\theta_f,\\theta_d\\} -\\alpha \\nabla_{\\{\\theta_f,\\theta_d\\}}\\cdot \\mathcal{L}_{MSE}(\\hat{\\mathbf{x}},\\mathbf{x})$ \n8: end for \n9: end for \n10: Initialize $\\theta_w$ randomly. BFT Stage \n11: Calculate logit bias $\\mathcal{B}_{\\mathbf{y}_i}^{\\mathrm{bce}}$ via Eq. 10. \n12: for $t = 1$ to $T_{ft}$ do \n13: for $\\{\\mathbf{x},\\mathbf{y}\\}$ sampled from $\\mathcal{D}$ do \n14: $\\mathbf{x}:= \\mathcal{A}_{ft}(\\mathbf{x})$ \n15: $\\mathbf{v} = \\mathcal{F}(\\mathbf{x}\\mid \\theta_f)$ \n16: $\\mathbf{z} = \\mathcal{W}(\\mathbf{v}\\mid \\theta_w) + \\tau \\cdot \\mathcal{B}^{\\mathrm{bce}}$ \n17: Calculate $\\mathcal{L}_{BCE}$ via Eq. 5 with calibrated z. \n18: $\\{\\theta_f,\\theta_w\\} \\leftarrow \\{\\theta_f,\\theta_w\\} -\\alpha \\nabla_{\\{\\theta_f,\\theta_w\\}}\\cdot \\mathcal{L}_{BCE}$ \n19: end for \n20: end for", + "bbox": [ + 78, + 109, + 468, + 523 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "is discarded. We adopt more general data augmentations $\\mathcal{A}_{ft}$ to finetune a few epochs $T_{ft}$ . As shown in Alg. 1 Line 16, we add a hyper-parameter $\\tau$ to control the influence of the proposed bias. It is worth noticing that the proposed logit bias will add negligible computational costs. With Balanced Binary CE loss, we further optimize the parameters of $\\mathcal{F}$ and $\\mathcal{W}$ to achieve satisfying networks.", + "bbox": [ + 75, + 531, + 472, + 638 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Experiment", + "text_level": 1, + "bbox": [ + 76, + 652, + 200, + 671 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.1. Datasets", + "text_level": 1, + "bbox": [ + 76, + 679, + 179, + 694 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "CIFAR-10/100-LT are created from the original CIFAR datasets [32], where $\\gamma$ controls the data imbalance degree. Following previous works [4, 12, 70, 81], we employ imbalance factors $\\{100, 10\\}$ in our experiments. ImageNet-LT/BAL are both the subsets of popular ImageNet [52]. The LT version [44] ( $\\gamma = 256$ ) is selected following the Pareto distribution with power value $\\alpha = 6$ , which contains $115.8\\mathrm{K}$ images from 1,000 categories. We build the BAL version ( $\\gamma = 1$ ) by sampling 116 images per category to exploit how ViTs perform given a similar number of training images. Notice that both LT and BAL adopt the same validation dataset. iNaturalist 2018 [57, 63] (iNat18 for short) is a species classification dataset, which contains $437.5\\mathrm{K}$", + "bbox": [ + 75, + 703, + 472, + 902 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/8c5e5c4344343fb01f9291f5de05ecd5c4480aedd12d7e428cc70bbefb418aa2.jpg", + "table_caption": [ + "Table 2. Top-1 accuracy $(\\%)$ of ResNet50 on ImageNet-LT. $\\dagger$ indicates results with ResNeXt50. $*$ training with 384 resolution." + ], + "table_footnote": [], + "table_body": "
MethodRef.ManyMed.FewAcc
CE [13]CVPR 1964.033.85.841.6
LDAM [4]NeurIPS 1960.446.930.749.8
c-RT [29]ICLR 2061.846.227.349.6
τ-Norm [29]ICLR 2059.146.930.749.4
Causal [54]NeurIPS 2062.748.831.651.8
Logit Adj. [47]ICLR 2161.147.527.650.1
RIDE(4E)† [61]ICLR 2168.353.535.956.8
MiSLAS [80]CVPR 2162.950.734.352.7
DisAlign [75]CVPR 2161.352.231.452.9
ACE† [3]ICCV 2171.754.623.556.6
PaCo† [12]ICCV 2168.056.437.258.2
TADE† [77]ICCV 2166.557.043.558.8
TSC [36]CVPR 2263.549.730.452.4
GCL [35]CVPR 2263.052.737.154.5
TLC [33]CVPR 2268.955.740.855.1
BCL† [83]CVPR 2267.654.636.657.2
NCL [34]CVPR 2267.355.439.057.7
SAFA [23]ECCV 2263.849.933.453.1
DOC [58]ECCV 2265.152.834.255.0
DLSA [69]ECCV 2267.854.538.857.5
ViT-B training from scratch
ViT [15]ICLR 2150.523.56.931.6
MAE [18]CVPR 2274.748.219.454.5
DeiT [55]ECCV 2270.440.912.848.4
LiVT73.656.441.060.9
LiVT *76.459.742.763.8
", + "bbox": [ + 503, + 128, + 890, + 489 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "images from 8,142 categories and suffers from extremely LTR problem $(\\gamma = 512)$ . Places-LT is a synthetic long-tail variant of the large-scale scene classification dataset Places [82]. With 62.5K images from 365 categories, its class cardinality ranges from 5 to 4,980 $(\\gamma = 996)$ . All datasets adopt the official validation images for fair comparisons. See detailed dataset information in Appendix.", + "bbox": [ + 496, + 498, + 890, + 604 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.2. Implement Details", + "text_level": 1, + "bbox": [ + 498, + 618, + 679, + 635 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For image classification on main benchmarks, we adopt ViT-Base-16 [15] as the backbone and ViT-Tiny / Small [55] ViT-Large [15] for the ablation study. All models are trained with AdamW optimizer [46] with $\\beta s = \\{0.9, 0.95\\}$ . The effective batch size is 4,096 (MGP) / 1,024 (BFT). Vanilla ViTs [15], DeiT III [55] and MAE [18] are all trained 800 epochs because ViTs require longer training time to converge. Following previous work [18], LiVT is pretrained 800 epochs with the mask ratio 0.75 and finetuned 100(50) epochs for ViT-T/S/B(L). We train all models with RandAug(9, 0.5) [11], mixup (0.8) and cutmix (1.0). All experiments set $\\tau \\equiv 1$ . For fair comparisons, we re-implement [4, 13, 22, 50, 51] with ViTs in the same settings. Following [44], we report Top-1 accuracy and three groups' accuracy: Many-shot ( $>100$ images), Medium-shot ( $20\\sim 100$ images) and Few-shot ( $<20$ images). Besides, we report the Expected Calibration Error (ECE) and Maximum Cali", + "bbox": [ + 496, + 643, + 893, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "15797", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/9192638162a3463dd8ae95059a3aeb13678d7581a680903d2420d5c9a8579175.jpg", + "table_caption": [ + "Table 3. Top-1 accuracy $(\\%)$ of ResNet50 on iNaturalist 2018. $\\ast$ training with 384 resolution." + ], + "table_footnote": [ + "bration Error (MCE) to quantify the predictive uncertainty [17]. See detailed implementation settings in Appendix." + ], + "table_body": "
MethodRef.ManyMed.FewAcc
CE [13]CVPR 1972.263.057.261.7
OLTR [44]CVPR 1959.064.164.963.9
c-RT [29]ICLR 2069.066.063.265.2
τ-Norm [29]ICLR 2065.665.365.965.6
LWS [29]ICLR 2065.066.365.565.9
BBN [81]CVPR 2061.873.666.969.6
BS [51]ICLR 2170.070.269.970.0
RIDE(4E) [61]ICLR 2170.972.573.172.6
DisAlign [75]CVPR 2169.071.170.270.6
MiSLAS [80]CVPR 2173.272.470.471.6
DiVE [21]ICCV 2170.670.067.669.1
ACE(4E) [3]ICCV 21---72.9
TADE [77]ICCV 2174.472.573.172.9
PaCo [12]ICCV 2170.472.873.673.2
ALA [79]AAAI 2271.370.870.470.7
TSC [36]CVPR 2272.670.667.869.7
LTR-WD [1]CVPR 2271.270.469.770.2
GCL [35]CVPR 2267.571.371.571.0
BCL [83]CVPR 2266.771.070.770.4
NCL [34]CVPR 2272.074.973.874.2
DOC [58]ECCV 2272.871.770.071.0
DLSA [69]ECCV 22---72.8
ViT-B training from scratch
ViT [15]ICLR 2165.455.350.954.6
MAE [18]CVPR 2279.670.865.069.4
DeiT [55]ECCV 2272.962.855.861.0
LiVT-78.976.574.876.1
LiVT*-83.281.579.781.0
", + "bbox": [ + 80, + 128, + 470, + 539 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.3. Comparison with Prior Arts", + "text_level": 1, + "bbox": [ + 76, + 594, + 331, + 611 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We conduct comprehensive experiments with ViT-B-16 on ImageNet-LT, iNat18, and Place-LT benchmarks. LiVT successfully trains it from scratch without any additional data pretraining and outperforms ResNet50, ResNeXt50 and ResNet152 conspicuously.", + "bbox": [ + 75, + 619, + 468, + 696 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Comparison on ImageNet-LT. Tab. 2 shows the experimental comparison results with recent SOTA methods on ImageNet-LT. The training resolution of LiVT is $224 / 224$ for MGP/BFT. Based on the model ensemble, multi-expert methods like RIDE [61], TADE [77], and NCL [34] exhibit powerful preference with heavier model size compared to baseline. The CL-based methods (PaCo [12], TSC [36], BCL [83]) also achieve satisfying results with larger batches and longer training epochs. However, our LiVT has shown superior performance without bells and whistles and outperforms them consistently on all metrics while training ViTs from scratch. Notice that LiVT gains more performance $(63.8\\%)$ vs $60.9\\%$ with higher image resolu", + "bbox": [ + 75, + 704, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/32088e2edec3853945604b33fac36d4ab91df39f8ffc668bf12470b78ae7c39e.jpg", + "table_caption": [ + "Table 4. Top-1 accuracy $(\\%)$ of ResNet152 (with ImageNet-1K pretrained weight) on Places-LT. $\\ast$ training with 384 resolution." + ], + "table_footnote": [ + "Table 5. The transfer performance of ViT-B (resolution $224\\times 224$ ) on iNat18 dataset. D-PT represents the pretrain datasets. BAL and LT have similar amounts of data and contribute to similar transfer performance, which means MGP is robust to data distribution." + ], + "table_body": "
MethodRef.ManyMed.FewAcc
CE [13]CVPR 1945.727.38.230.2
Focal [38]ICCV 1741.134.822.434.6
Range [76]CVPR 1741.135.423.235.1
OLTR [44]CVPR 1944.737.025.335.9
FSA [10]ECCV 2042.837.522.736.4
LWS [29]ICLR 2040.639.128.637.6
Causal [54]NeurIPS 2023.835.840.432.4
BS [51]NeurIPS 2042.039.330.538.6
DisAlign [75]CVPR 2140.442.430.139.3
LADE [22]CVPR 2142.839.031.238.8
RSG [59]CVPR 2141.941.432.039.3
TADE [77]ICCV 2143.142.433.240.9
PaCo [12]ICCV 2136.147.935.341.2
ALA [79]AAAI 2243.940.132.940.1
NCL [34]CVPR 22---41.8
BF [24]CVPR 2244.043.133.741.6
CKT [48]CVPR 2241.641.435.140.2
GCL [35]CVPR 22---40.6
Bread [40]ECCV 2240.641.033.439.3
ViT-B training from scratch
MAE [18]CVPR 2248.924.68.730.3
DeiT [55]ECCV 2251.631.09.434.2
LiVT-48.140.627.540.8
LiVT*-50.742.427.942.6
", + "bbox": [ + 503, + 128, + 893, + 494 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/1b4e1076c1a4421d81439128e85bc1c2a7a1a028aa85899a595746d4ea01f2af.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
D-PTLossManyMed.FewAccECEMCE
BALCE63.757.152.455.91.23.4
LTCE64.557.552.756.41.23.1
BALBal-BCE53.358.860.759.00.81.6
LTBal-BCE56.560.861.660.71.02.9
", + "bbox": [ + 503, + 566, + 890, + 650 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "tion in the BFT stage, which is consistent with the observations in [43, 55, 56]. Notice that LiVT improves the iNat18 dataset most significantly because BCE mitigates fine-grained problems as well [64].", + "bbox": [ + 498, + 657, + 890, + 718 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Comparison on iNaturalist 2018. Tab. 3 lists experimental results on iNaturalist 2018. The training resolution of LiVT is 128 / 224 for MGP/BFT. LiVT consistently surpasses recent SOTA methods like PcCo [12], NCL [34] and DLSA [69]. Unlike most LTR methods, our LiVT improves all groups' Acc without sacrificing many-shot performance. Compared to ensemble NCL $(3\\times)$ , LiVT surpasses it by $1.9\\%$ (6.8% higher resolution) with comparable model size, which verifies the effectiveness of LiVT.", + "bbox": [ + 496, + 726, + 890, + 861 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Comparison on Places-LT. Tab. 4 summarizes the experimental results on Places-LT. All LTR proposals adopt", + "bbox": [ + 498, + 869, + 890, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "15798", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/403f922404bc249811609a910a69e7fdd93ecb9b668f0fee452a0ad66b5669b3.jpg", + "table_caption": [ + "Table 6. Ablation study of the proposed bias (c.f. Eq. 10) on CE / BCE. All models are trained on ImageNet-LT with the same settings. Our Bal-BCE ameliorates the original BCE by a large margin in all aspects, which is consistent with CE and Bal-CE." + ], + "table_footnote": [], + "table_body": "
ModelSizeLossMany ↑Med. ↑Few ↑Acc ↑ECE ↓MCE ↓
ViT-Tiny [55]5.7MCE56.129.210.537.03.76.1
Bal-CE48.8 (-7.3)39.2 (+10.0)28.1 (+17.6)41.4 (+4.4)2.6 (-1.1)4.6 (-1.6)
BCE42.111.10.921.62.98.6
Bal-BCE50.6 (+8.4)37.2 (+26.1)26.1 (+25.2)40.8 (+19.2)3.1 (+0.1)6.8 (-1.8)
ViT-Small [55]22MCE68.943.117.349.54.79.2
Bal-CE62.7 (-6.2)52.0 (+8.9)36.3 (+19.0)54.0 (+4.5)0.9 (-3.8)2.4 (-6.8)
BCE62.430.68.439.85.711.1
Bal-BCE65.8 (+3.4)50.6 (+20.0)32.9 (+24.6)54.1 (+14.2)4.8 (-0.9)9.0 (-2.2)
ViT-Base [15]86MCE74.748.219.454.55.16.8
Bal-CE70.5 (-4.3)56.8 (+8.6)43.7 (+24.3)60.1 (+5.6)3.7 (-1.4)4.9 (-1.9)
BCE73.746.515.652.45.67.9
Bal-BCE73.6 (-0.1)55.8 (+9.3)41.0 (+25.4)60.9 (+8.6)2.4 (-3.1)3.2 (-4.7)
ViT-Large [15]304MCE77.351.521.757.43.67.4
Bal-CE72.7 (-4.5)60.1 (+8.6)41.9 (+20.3)62.1 (+4.8)2.1 (-1.5)4.2 (-3.2)
BCE74.746.717.053.48.415.9
Bal-BCE75.3 (+0.6)58.8 (+12.1)37.5 (+20.5)62.6 (+9.2)6.6 (-1.8)14.8 (-1.1)
", + "bbox": [ + 138, + 122, + 831, + 378 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ResNet152 pre-trained on ImageNet-1K. For fair comparisons, we conduct MGP at ImageNet-1K and BFT at PlacesLT. As illustrated in Tab. 4, LiVT obtains satisfying performance compared with previous SOTAs. Notice that PlacesLT has limited instances compared to iNat18 (437.5K) and ImageNet-1K (1M). Considering both Tab. 3 and Tab. 4 results, we observe that ViTs, which benefit from large-scale data, are limited in this case. However, our LiVT performs the best even in such data paucity situations.", + "bbox": [ + 75, + 388, + 472, + 525 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.4. Further Analysis", + "text_level": 1, + "bbox": [ + 76, + 541, + 243, + 556 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Robustness of MGP. The performance results in Tab. 1 have shown that MGP is more robust to learning label irrelevant features than supervised methods. For deeper observations, we show the transfer results in Tab. 5. Concretely, we conduct MGP on ImageNet-LT / ImageNet-BAL (See section 5.1) and BFT on iNat18 with resolution 224. Regardless of the data distribution of the MGP dataset, both BAL and LT achieve quite similar performance in terms of all evaluated metrics on iNat18. If we further compare the reported results with Tab. 3, we will draw the conclusion that the training instance number plays the key role in LiVT instead of the label distribution, which is clearly different from previous SCL [12,83] methods. We show more reconstruction visualization given by LT / BAL in Appendix.", + "bbox": [ + 75, + 573, + 468, + 785 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effectiveness of Proposed Bias. To learn balanced ViTs, we propose Bal-BCE with a simple yet effective logit bias (c.f. Eq. 10). To validate its effectiveness, we conduct the ablation study and compare it with the most popular rebalance loss, i.e., Bal-CE. As shown in Tab. 6, the new logit bias boosts vanilla BCE significantly with lower ECE on four ViT backbones, which is consistent with the behavior", + "bbox": [ + 75, + 794, + 470, + 900 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f8a95414ed46ebc65973315109fc718192d2a485dddee37f754a70ccd8fdb17b.jpg", + "image_caption": [ + "Figure 2. Training loss and Top-1% accuracy of ViT-S on iNaturalist 2018 dataset. Solid and dot lines represent the accuracy and training loss, respectively. All models adopt the same settings and random seed except for loss type." + ], + "image_footnote": [], + "bbox": [ + 501, + 385, + 893, + 571 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "of Bal-CE. It is worth noticing that CE generally performs better than BCE in LTR scenarios, which is different from the conclusion in balanced datasets [55]. However, our BalBCE alleviates it remarkably and outperforms Bal-CE in most cases. In addition, Bal-BCE shows more satisfying numerical stability and faster convergence. See Bal-BCE in Fig. 2. for detailed illustrations.", + "bbox": [ + 496, + 643, + 893, + 751 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "For comprehensive comparisons, we re-implement recent rebalancing strategies in our BFT stage and show the results of ViT-B on CIFAR-LT in Tab. 7. Without loss of fairness, we conduct MGP on ImageNet-1K because the resolution $(32\\times 32)$ of CIFAR is too small to mask for ViT-B-16. We do not reproduce the CL-based (conflict to MGP) and ensemble (memory limitation) methods. We also give up some ingenious rebalancing methods for loss NaN during training. As shown in Tab. 7, the proposed Bal-BCE", + "bbox": [ + 496, + 763, + 893, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "15799", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/bc0187475fb32e0ebaf0b214202da9076a6c0628403872cb2ae7f4c00e0d1f8b.jpg", + "table_caption": [ + "Table 7. Ablation study of rebalancing strategies on ViT-B." + ], + "table_footnote": [], + "table_body": "
MethodCIFAR-10-LTCIFAR-100-LT
γ1001010010
CE [13]79.289.550.966.1
CB [13]82.089.952.066.8
LDAM [4]78.688.652.5666.1
LADE [22]68.881.756.768.2
IB [50]75.479.250.851.6
Bal-CE [51]84.490.756.868.1
Bal-BCE (ours)86.391.358.269.2
", + "bbox": [ + 98, + 114, + 446, + 234 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "achieves the best results, which firmly manifests its effectiveness. Notice that some methods are not consistent with their performance on ResNet, which means some exquisite designs may not generalize well on ViTs.", + "bbox": [ + 75, + 241, + 468, + 301 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Hyper-Parameter Analysis. In Alg. 1 Line 11, we add a hyper-parameter $\\tau$ to adjust our proposed bias (Eq. 10). We further present in-depth investigations on the influence of $\\tau$ . Similar to the aforementioned settings with plain augmentations, we conduct the ablation study on CIFAR-100-LT with MGP on ImageNet-1K and show the results in Fig.3. The few-shot accuracy gets obvious amelioration when $\\tau$ gets larger, which is consistent with our explanations in section 4.2. The best overall accuracy is obtained around 1, which inspires us to set $\\tau \\equiv 1$ in LiVT for all experiments by default. Besides, the ECE gets smaller with increasing $\\tau$ , which means that the proposed bias guides ViTs to be the calibrated models with Fisher Consistency ensured [47].", + "bbox": [ + 75, + 309, + 468, + 505 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Discussion", + "text_level": 1, + "bbox": [ + 76, + 520, + 191, + 536 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Why train from scratch? Previous ViTs papers are all based on pretrained weights from ImageNet-1K or ImageNet-22K and thus may lead to unfair comparisons with LTR methods, which are all trained from scratch. It is difficult to conclude that the intriguing performance mainly benefits from their proposals. Our approach provides a strong baseline to verify proposals' effectiveness with ViTs. It's also instructive to train plain ViTs for areas where data exhibits severe domain gaps. From the original intention of the LTR task, the core is to learn more large-scale imbalanced data effectively. Our work provides a feasible way to utilize more real-world LT (labels or attributes) data without expensive artificial balancing to achieve better representation learning.", + "bbox": [ + 75, + 553, + 468, + 750 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "How we extend MAE. We empirically prove that masked autoencoder learns generalized features even with imbalanced data, which is quite different from other self-supervised manners like CL [7] and SCL [30]. Extensive experiments on ImageNet-LT/BAL show that the instance number is more crucial than balanced annotation. We further propose the balanced binary cross-entropy loss to build our LiVT and achieve a new SOTA in LTR.", + "bbox": [ + 75, + 757, + 467, + 876 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitations. One limitation is that LiVT can not be de", + "bbox": [ + 76, + 885, + 467, + 898 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/81d4417f9ab195409a45ac4fa3326dbf67c8f21c3333b2a686d3d5251e5ef1c0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 514, + 92, + 883, + 255 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f55cb4b5a8e15969bea715d57f9f2bf98ddaea7f958246d1f0532530bea0d8f5.jpg", + "image_caption": [ + "Figure 3. Performance of ViT-B with different $\\tau$ on CIFAR-100-LT. A bigger $\\tau$ results in better few-shot performance." + ], + "image_footnote": [], + "bbox": [ + 511, + 257, + 883, + 422 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ployed in an end-to-end manner. An intuitive idea is two branches learning to optimize the decoder and classifier simultaneously, like BBN [81] or PaCo [12]. However, the heavily masked image prevents effective classification, while dynamic mask ratios exacerbate memory limitations.", + "bbox": [ + 498, + 464, + 890, + 541 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 551, + 617, + 566 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we propose to Learn imbalanced data with Vision Transformers (LiVT), which consists of Masked Generative Pretraining (MGP) and Balanced Fine Tuning (BFT). MGP is based on our empirical insight that it guides ViTs to learn more generalized features on long-tailed datasets compared to supervised or contrastive paradigms. BFT is based on the theoretical analysis of Binary Cross-Entropy (BCE) in the imbalanced scenario. We propose the balanced BCE to learn unbiased ViTs by compensating extra logit margins. Bal-BCE ameliorates BCE significantly and surpasses the powerful and widely adopted Balanced Cross-Entropy loss when cooperating with ViTs. Extensive experiments on large-scale datasets demonstrate that LiVT successfully trains ViTs without any additional data and achieves a new state-of-the-art for long-tail recognition.", + "bbox": [ + 496, + 577, + 890, + 803 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement", + "text_level": 1, + "bbox": [ + 500, + 815, + 660, + 832 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was supported by the National Key R&D Program of China (2022YFB4701400/4701402), SZSTC Grant (JCYJ 20190809172201639, WDZC20200820200655001), Shenzhen Key Laboratory (ZDSYS20210623092001004).", + "bbox": [ + 498, + 839, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "15800", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 106 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Shaden Alshammari, Yu-Xiong Wang, Deva Ramanan, and Shu Kong. 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In CVPR, pages 6908-6917, 2022. 2, 3, 5, 6, 7" + ], + "bbox": [ + 501, + 90, + 892, + 556 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "15803", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Learning Imbalanced Data With Vision Transformers/2c5c04d7-db27-4f72-9591-822af7466068_model.json b/2023/Learning Imbalanced Data With Vision Transformers/2c5c04d7-db27-4f72-9591-822af7466068_model.json new file mode 100644 index 0000000000000000000000000000000000000000..156b257b4d31d7a353e32419085ef40c9806e77a --- /dev/null +++ b/2023/Learning Imbalanced Data With Vision Transformers/2c5c04d7-db27-4f72-9591-822af7466068_model.json @@ -0,0 +1,2521 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.217, + 0.131, + 0.756, + 0.154 + ], + "angle": 0, + "content": "Learning Imbalanced Data with Vision Transformers" + }, + { + "type": "text", + "bbox": [ + 0.16, + 0.18, + 0.807, + 0.218 + ], + "angle": 0, + "content": "Zhengzhuo Xu Ruikang Liu Shuo Yang Zenghao Chai Chun Yuan† Shenzhen International Graduate School, Tsinghua University, China" + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.22, + 0.852, + 0.234 + ], + "angle": 0, + "content": "{xzzthu, liuruikang.cs, ysss9264, zenghaochai}@gmail.com yuanc@sz.tsinghua.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.269, + 0.314, + 0.285 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.301, + 0.474, + 0.695 + ], + "angle": 0, + "content": "The real-world data tends to be heavily imbalanced and severely skew the data-driven deep neural networks, which makes Long-Tailed Recognition (LTR) a massive challenging task. Existing LTR methods seldom train Vision Transformers (ViTs) with Long-Tailed (LT) data, while the off-the-shelf pretrain weight of ViTs always leads to unfair comparisons. In this paper, we systematically investigate the ViTs' performance in LTR and propose LiVT to train ViTs from scratch only with LT data. With the observation that ViTs suffer more severe LTR problems, we conduct Masked Generative Pretraining (MGP) to learn generalized features. With ample and solid evidence, we show that MGP is more robust than supervised manners. Although Binary Cross Entropy (BCE) loss performs well with ViTs, it struggles on the LTR tasks. We further propose the balanced BCE to ameliorate it with strong theoretical groundings. Specially, we derive the unbiased extension of Sigmoid and compensate extra logit margins for deploying it. Our Bal-BCE contributes to the quick convergence of ViTs in just a few epochs. Extensive experiments demonstrate that with MGP and Bal-BCE, LiVT successfully trains ViTs well without any additional data and outperforms comparable state-of-the-art methods significantly, e.g., our ViT-B achieves \\(81.0\\%\\) Top-1 accuracy in iNaturalist 2018 without bells and whistles. Code is available at https://github.com/XuZhengzhuo/LiVT." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.724, + 0.21, + 0.74 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.47, + 0.902 + ], + "angle": 0, + "content": "With the vast success in the computer vision field, Vision Transformers (ViTs) [15, 43] get increasingly popular and have been widely used in visual recognition [15], detection [5], and video analysis [16]. These models are heavily dependent on large-scale and balanced data to avoid overfitting [39, 52, 82]. However, real-world data usually confronts severe class-imbalance problems, i.e., most labels (tail) are associated with limited instances while a few categories (head) occupy dominant samples. The models simply classify images into head classes for lower error because the" + }, + { + "type": "image", + "bbox": [ + 0.499, + 0.265, + 0.868, + 0.45 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.459, + 0.895, + 0.515 + ], + "angle": 0, + "content": "Figure 1. Top-1 Acc v.s. Model Size on ImageNet-LT dataset. We choose the Tiny / Small / Base / Large ViT and multi-expert approaches. R50 represents the ResNet50 model. ViT-Base gets lower Acc than ResNet50 when trained in a supervised manner." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.523, + 0.893, + 0.583 + ], + "angle": 0, + "content": "head always overwhelms tail ones in LTR. The data paucity also results in the model overfitting on the tail with unaccepted generalization. The aforementioned problems make Long Tail Recognition (LTR) a challenging task." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.584, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Numerous papers [4, 13, 22, 34, 35, 44, 70] handle the LTR problem with traditional supervised cross-entropy learning based on ResNet [20] or its derivatives [68]. Some methods use ViTs with pretrained weights on ImageNet [52] (or larger datasets), which leads to unfair comparisons with additional data, e.g. on ImageNet-LT (a subset of ImageNet-1K) benchmark. Moreover, there are still limited explorations on the utilization of Long-Tailed (LT) data to train ViTs effectively. Therefore, in this paper, we try to train ViTs from scratch with LT data. We observe that it is particularly difficult to train ViT with LT labels' supervision. As Tab. 1 shows, ViTs degrade heavily when training data become skewed. ViT-B is much worse than ResNet50 with the same CE training manner (c.f. Fig. 1). One reasonable explanation is that ViTs require longer training to learn the inductive bias, while CNNs offer the built-in translation invariance implicitly. Yet another one lies in the label statistical bias in the LTR datasets, which confuses models to make predictions with an inherent bias to the head [12, 47]. The well-trained ViTs have to overcome the above plights simultaneously to avoid falling into dilemmas." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15793" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.272 + ], + "angle": 0, + "content": "Inspired by decoupling [29], many methods [9, 12, 60, 80, 83] attempt to enhance feature extraction in supervised manners like mixup [74] / remix [9], or Self-Supervised Learning (SSL) like Contrastive Learning (CL) [7, 19]. Liu et al. [41] claim that SSL representations are more robust to class imbalance than supervised ones, which inspires us to train ViTs with SSL. However, CL is quite challenging for extensive memory requisition and converge difficulties [8], where more explorations are required to work well with ViTs in LTR. In contrast, we propose to Learn imbalanced data with ViTs (LiVT) by Masked Generative Pretraining (MGP) and Balanced Fine Tuning (BFT)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.273, + 0.473, + 0.424 + ], + "angle": 0, + "content": "Firstly, LiVT adopts MGP to enhance ViTs' feature extraction, which has been proven effective on BeiT [2] and MAE [18]. It reconstructs the masked region of images with an extra lightweight decoder. We observe that MGP is stable with ViTs and robust enough to LT data with empirical evidence. Despite the label distribution, the comparable number of training images will bring similar feature extraction ability, which greatly alleviates the toxic effect of LT labels [26]. Meanwhile, the training is accelerated by masked tokens with acceptable memory requisition." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.424, + 0.473, + 0.605 + ], + "angle": 0, + "content": "Secondly, LiVT trains the downstream head with rebalancing strategies to utilize annotation information, which is consistent with [29, 35, 80]. Generally, Binary Cross-Entropy (BCE) loss performs better than Cross-Entropy loss when collaborating with ViTs [55]. However, it fails to catch up with widely adopted Balanced Cross-Entropy (Bal-CE) loss and shows severe training instability in LTR. We propose the Balanced BCE (Bal-BCE) loss to revise the mismatch margins given by Bal-CE. Detailed and solid theoretical derivations are provided from Bayesian theory. Our Bal-BCE ameliorates BCE by a large margin and achieves state-of-the-art (SOTA) performance with ViTs." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.605, + 0.473, + 0.726 + ], + "angle": 0, + "content": "Extensive experiments show that LiVT learns LT data more efficiently and outperforms vanilla ViT [15], DeiT III [55], and MAE [18] remarkably. As detailed comparisons in Fig. 1, LiVT achieves SOTA on ImageNet-LT with affordable parameters, despite that ImageNet-LT is a relatively small dataset for ViTs. The ViT-Small [55] also achieves outstanding performance compared to ResNet50. Our key contributions are summarized as follows." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.728, + 0.468, + 0.758 + ], + "angle": 0, + "content": "- To our best knowledge, we are the first to investigate training ViTs from scratch with LT data systematically." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.761, + 0.468, + 0.806 + ], + "angle": 0, + "content": "- We pinpoint that the masked generative pretraining is robust to LT data, which avoids the toxic influence of imbalanced labels on feature learning." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.808, + 0.468, + 0.853 + ], + "angle": 0, + "content": "- With a solid theoretical grounding, we propose the balanced version of BCE loss (Bal-BCE), which improves the vanilla BCE by a large margin in LTR." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.856, + 0.468, + 0.901 + ], + "angle": 0, + "content": "- We propose LiVT recipe to train ViTs from scratch, and the performance of LiVT achieves state-of-the-art across various benchmarks for long-tailed recognition." + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.728, + 0.468, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.089, + 0.895, + 0.132 + ], + "angle": 0, + "content": "Table 1. Top-1 accuracy (\\%) of different recipes to train ViT-B-16 from scratch on ImageNet-LT/BAL. All perform much worse on LT than BAL. See descriptions of LT & BAL in section 5.1." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.143, + 0.895, + 0.198 + ], + "angle": 0, + "content": "
DatasetViTΔDeiT IIIΔMAEΔ
ImageNet-BAL38.7-67.2-69.2-
ImageNet-LT31.6-7.048.4-18.854.5-14.7
" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.204, + 0.642, + 0.22 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.232, + 0.776, + 0.248 + ], + "angle": 0, + "content": "2.1. Long-tailed Visual Recognition" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.258, + 0.856, + 0.274 + ], + "angle": 0, + "content": "We roughly divide LTR progress into three groups." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.276, + 0.892, + 0.442 + ], + "angle": 0, + "content": "Rebalancing strategies adjust each class contribution with delicate designs. Re-sampling methods adopt class-wise sampling rate to learn balanced networks [13, 35, 62, 72, 81]. More sophisticated approaches replenish few-shot samples with the help of many-shot ones [9, 10, 31, 49, 70, 78]. The re-weighting proposals modify the loss function by adjusting class weights [1, 13, 38, 50, 53, 54, 80] to assign different weights to samples or enlarging logit margins [4, 22, 35, 47, 51, 70, 75, 77] to learn more challenging and sparse classes. However, the rebalancing strategies are always at the cost of many-shot accuracy inevitably." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.445, + 0.893, + 0.627 + ], + "angle": 0, + "content": "Multi-Expert networks alleviate the LTR problem with single expert learning and knowledge aggregation [3, 21, 25, 33, 34, 37, 61, 67, 77, 81]. LFME [67] trains experts with the subsets with a lower imbalance ratio and aggregate via knowledge distillation. TADE [77] learns three classifiers with the different test labels prior based on Logit Adjustment [47] and optimizes classifiers' output weights by contrastive learning [7]. NCL [34] collaboratively learns multiple experts together to reduce tail uncertainty. However, it is still heuristic to design expert individual training and knowledge aggregation manners. The overly complex models also make training difficult and limit the inference speed." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Multi-stage training is another effective training strategy for LTR. Cao et al. [4] propose to learn features at first and defer re-weighting in the second stage. Kang et al. [29] further decouples the representation and classifier learning separately, where the classifier is trained with re-balancing strategies just in the second stage. Some works [9, 70, 80] adopt more approaches, e.g., mixup [74] or remix [9], to improve features in the first stage. More recently, Contristive Learning (CL) [7, 19] is gaining increasing concern. Kang et al. [28] exploit to learn balanced feature representations by CL to bypass the influence of imbalanced labels. However, it is more effective to adopt Supervised Contristive Learning (SCL) to utilize the labels [60, 71]. With SCL, SO-TAs [12, 27, 36, 83] all adopt the Bal-CE loss [22, 47, 51, 70] to train the classifier for better performance. Masked Generative learning [6, 14, 18] is another effective feature learning method. However, there is still limited research on it in the community of LTR." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "15794" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.091, + 0.273, + 0.106 + ], + "angle": 0, + "content": "2.2. Vision Transformers" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.114, + 0.473, + 0.298 + ], + "angle": 0, + "content": "Current observations and conclusions are mostly based on ResNets [20, 68]. Most recently, ViT [15] has shown extraordinary performance after pre-training on large-scale and balanced datasets. Swin transformer [43] proposes a hierarchical transformer with shift windows to bring greater efficiency. DeiT [55] introduces a simple but effective recipe to train ViT with limited data. BeiT [2] trains ViT with the idea of Mask Language Models. MAE [18] further reduces the computation complexity with a lightweight decoder and higher mask ratio. Although RAC [45] adopts ViTs with pretrained checkpoints, there is limited research to train ViTs from scratch on long-tailed datasets." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.309, + 0.216, + 0.325 + ], + "angle": 0, + "content": "3. Preliminaries" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.334, + 0.232, + 0.349 + ], + "angle": 0, + "content": "3.1. Task Definition" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.357, + 0.473, + 0.584 + ], + "angle": 0, + "content": "With a \\(N\\)-sample and \\(C\\)-class dataset \\(\\mathcal{D} = \\{\\mathcal{X}, \\mathcal{Y}\\}\\), we note each instance \\(\\mathbf{x}_i \\in \\mathcal{X} := \\{\\mathbf{x}_1, \\dots, \\mathbf{x}_N\\}\\) and corresponding \\(\\mathbf{y}_i \\in \\mathcal{Y} := \\{\\mathbf{y}_1, \\dots, \\mathbf{y}_N\\}\\), where each \\(\\mathbf{y}_i \\in \\mathcal{C} := \\{1, \\dots, C\\}\\). In long-tailed visual recognition, each category \\(\\mathcal{C}_i\\) has a different instance number \\(n_i = |\\mathcal{C}_i|\\) and we set \\(\\gamma = n_{max} / n_{min}\\) to measure how skewed the long-tailed dataset is. We train the model \\(\\mathcal{M} := \\{\\mathcal{F}_{\\theta_f}, \\mathcal{W}_{\\theta_w}\\}\\) with \\(\\mathcal{D}\\) which contains a feature encoder \\(\\mathcal{F}_{\\theta_f}\\) and a classifier \\(\\mathcal{W}_{\\theta_w}\\). Besides, we consider a lightweight decoder \\(\\mathcal{D}_{\\theta_d}\\) for mask autoencoder architecture. For an input image \\(\\mathbf{x}\\), the encoder extracts the feature representation \\(\\mathbf{v} := \\mathcal{F}(\\mathbf{x} | \\theta_f) \\in \\mathbb{R}^d\\), the classifier gives the logits \\(\\mathbf{z} := \\mathcal{W}(\\mathbf{v} | \\theta_w) \\in \\mathbb{R}^c\\) and the decoder reconstructs original image \\(\\hat{\\mathbf{x}} := \\mathcal{D}(\\mathbf{v} | \\theta_d) \\in \\mathbb{R}^{H \\times W \\times 3}\\). The \\(d / H / W\\) is feature dimension / resized height / resized width, respectively." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.593, + 0.299, + 0.61 + ], + "angle": 0, + "content": "3.2. Balanced Cross-entropy" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.617, + 0.47, + 0.678 + ], + "angle": 0, + "content": "Here, we revisit the balanced softmax and corresponding Balanced Cross-Entropy (BalCE) loss [22,34,47,51,70,83], which has been widely adopted in LTR. Consider the standard softmax operation and cross-entropy loss:" + }, + { + "type": "equation", + "bbox": [ + 0.086, + 0.688, + 0.469, + 0.742 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {\\mathrm {C E}} \\left(\\mathcal {M} \\left(\\mathbf {x} \\mid \\theta_ {f}, \\theta_ {w}\\right), \\mathbf {y} _ {i}\\right) = - \\log \\left(p \\left(\\mathbf {y} _ {i} \\mid \\mathbf {x}; \\theta_ {f}, \\theta_ {w}\\right)\\right) \\\\ = - \\log \\left[ e ^ {z _ {\\mathbf {y} _ {i}}} / \\sum_ {\\mathbf {y} _ {j} \\in \\mathcal {Y}} e ^ {z _ {\\mathbf {y} _ {j}}} \\right] = \\log \\left[ 1 + \\sum_ {\\mathbf {y} _ {j} \\neq \\mathbf {y} _ {i}} e ^ {\\mathbf {z} _ {\\mathbf {y} _ {j}} - \\mathbf {z} _ {\\mathbf {y} _ {i}}} \\right]. \\tag {1} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.753, + 0.47, + 0.784 + ], + "angle": 0, + "content": "If we take the class instance number \\( n_{\\mathbf{y}_i} \\) into account for softmax [51], we have the balanced cross-entropy loss:" + }, + { + "type": "equation", + "bbox": [ + 0.091, + 0.794, + 0.469, + 0.885 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {\\mathrm {B a l - C E}} \\left(\\mathcal {M} \\left(\\mathbf {x} \\mid \\theta_ {f}, \\theta_ {w}\\right), \\mathbf {y} _ {i}\\right) = - \\log \\left(p \\left(\\mathbf {y} _ {i} \\mid \\mathbf {x}; \\theta_ {f}, \\theta_ {w}\\right)\\right) \\\\ = - \\log \\left[ \\frac {n _ {\\mathbf {y} _ {i}} e ^ {z _ {\\mathbf {y} _ {i}}}}{\\sum_ {\\mathbf {y} _ {j} \\in \\mathcal {Y}} n _ {\\mathbf {y} _ {j}} e ^ {z _ {\\mathbf {y} _ {j}}}} \\right] \\tag {2} \\\\ = \\log [ 1 + \\sum_ {\\mathbf {y} _ {j} \\neq \\mathbf {y} _ {i}} e ^ {\\log n _ {\\mathbf {y} _ {j}} - \\log n _ {\\mathbf {y} _ {i}}} \\cdot e ^ {\\mathbf {z} _ {\\mathbf {y} _ {j}} - \\mathbf {z} _ {\\mathbf {y} _ {i}}} ]. \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.091, + 0.892, + 0.157 + ], + "angle": 0, + "content": "Theorem 1. Logit Bias of Balanced CE. Let \\(\\pi_{\\mathbf{y}_i} = n_{\\mathbf{y}_i} / N\\) be the training label \\(\\mathbf{y}_i\\) distribution. If we implement the balanced cross-entropy loss via logit adjustment, the bias item of logit \\(\\mathbf{z}_{\\mathbf{y}_i}\\) will be \\(\\mathcal{B}_{\\mathbf{y}_i}^{\\mathrm{ce}} = \\log \\pi_{\\mathbf{y}_i}\\), i.e.," + }, + { + "type": "equation", + "bbox": [ + 0.51, + 0.176, + 0.891, + 0.285 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {\\mathrm {B a l - C E}} = \\log \\left[ 1 + \\sum_ {\\mathbf {y} _ {j} \\neq \\mathbf {y} _ {i}} e ^ {\\log n _ {\\mathbf {y} _ {j}} - \\log n _ {\\mathbf {y} _ {i}}} \\cdot e ^ {\\mathbf {z} _ {\\mathbf {y} _ {j}} - \\mathbf {z} _ {\\mathbf {y} _ {i}}} \\right] \\\\ = \\log [ 1 + \\sum_ {\\mathbf {y} _ {j} \\neq \\mathbf {y} _ {i}} e ^ {(\\mathbf {z} _ {\\mathbf {y} _ {j}} + \\log n _ {\\mathbf {y} _ {j}}) - (\\mathbf {z} _ {\\mathbf {y} _ {i}} + \\log n _ {\\mathbf {y} _ {i}})} ] \\tag {3} \\\\ = \\log [ 1 + \\sum_ {\\mathbf {y} _ {j} \\neq \\mathbf {y} _ {i}} e ^ {(\\mathbf {z} _ {\\mathbf {y} _ {j}} + \\log \\pi_ {\\mathbf {y} _ {j}}) - (\\mathbf {z} _ {\\mathbf {y} _ {i}} + \\log \\pi_ {\\mathbf {y} _ {i}})} ]. \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.291, + 0.892, + 0.32 + ], + "angle": 0, + "content": "Proof. See subsection 5.1 from [47] or detail derivation in the Appendix from the Bayesian Theorem perspective." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.321, + 0.892, + 0.397 + ], + "angle": 0, + "content": "Bal-CE loss strengthens the tail instance's contributions while suppressing bias to the head, which alleviates the LTR problem effectively. However, the \\(\\mathcal{B}_{\\mathbf{y}_i}^{\\mathrm{ce}}\\) in Thm.1 fails to work well when collaborating with BCE, where More analysis is required to build a balanced version BCE loss." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.408, + 0.636, + 0.425 + ], + "angle": 0, + "content": "4. Methodology" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.433, + 0.892, + 0.524 + ], + "angle": 0, + "content": "In this section, we introduce our LiVT in two stages. In section 4.1, we revisit the generative masked auto-encoder as our first stage. Then, we propose the novel balanced sigmoid and corresponding binary cross entropy to collaborate with ViTs in section 4.2. Eventually, we summarize our whole pipeline in section 4.3." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.531, + 0.78, + 0.547 + ], + "angle": 0, + "content": "4.1. Masked Generative Pretraining" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.554, + 0.892, + 0.631 + ], + "angle": 0, + "content": "Inspired by BeiT [2] and MAE [18], we pretrain feature encoder \\(\\mathcal{F}_{\\theta_f}\\) via MGP for its training efficiency and label irrelevance. MGP trains the encoder parameters \\(\\theta_{f}\\) with high ratio masked images and reconstructs the original image by a lightweight decoder \\(\\mathcal{D}_{\\theta_d}\\)." + }, + { + "type": "equation", + "bbox": [ + 0.606, + 0.636, + 0.891, + 0.654 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathbf {x}} = \\mathcal {D} _ {\\theta_ {d}} \\left(\\mathcal {F} _ {\\theta_ {f}} (\\mathbf {M} \\odot \\mathbf {x})\\right), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.659, + 0.891, + 0.704 + ], + "angle": 0, + "content": "where \\(\\mathbf{M} \\in \\{0,1\\}^{H \\times W}\\) is a random patch-wise binary mask. Then, we optimize \\(\\theta_{f}, \\theta_{d}\\) end-to-end via minimizing the mean squared error between \\(\\mathbf{x}\\) and \\(\\hat{\\mathbf{x}}\\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.705, + 0.892, + 0.902 + ], + "angle": 0, + "content": "We adopt MGP for two reasons: 1) It is difficult to train ViTs directly with label supervision (see plain ViT-B performance in Fig. 1) for its convergence difficulty and computation requirement. The DeiT III [55] is hard to catch up with SOTAs in LTR, even with more training epochs, stronger data augmentation, and larger model sizes. 2) The feature extraction ability of MGP is affected slightly by class instance number, compared with previous mixup-based supervision [29,35,80], CL [60] or SCL [12,27,36,83]. Even pretraining on LTR datasets, the transfer performance of MGP is on par with that trained on balanced datasets with comparable total training instances. See transfer results in Tab. 5 and more visualization in Appendix." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15795" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.077, + 0.091, + 0.283, + 0.108 + ], + "angle": 0, + "content": "4.2. Balanced Fine Tuning" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.115, + 0.47, + 0.206 + ], + "angle": 0, + "content": "In the Balanced Fine-Tuning (BFT) phase, softmax + CE loss has been the standard paradigm for utilizing annotated labels. However, recent research [42, 55, 65] pinpoint that Binary Cross-Entropy (BCE) loss works much well with ViTs and is more convenient when employed with mixup-manners [42, 73, 74], which can be written as:" + }, + { + "type": "equation", + "bbox": [ + 0.097, + 0.219, + 0.469, + 0.273 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {\\mathrm {B C E}} = - \\sum_ {\\mathbf {y} _ {i} \\in \\mathcal {C}} w _ {\\mathbf {y} _ {i}} [ \\mathbb {1} (\\mathbf {y} _ {i}) \\cdot \\log \\sigma (\\mathbf {z} _ {\\mathbf {y} _ {i}}) \\tag {5} \\\\ \\left. + \\left(1 - \\mathbb {1} \\left(\\mathbf {y} _ {i}\\right)\\right) \\cdot \\log \\left(1 - \\sigma \\left(\\mathbf {z} _ {\\mathbf {y} _ {i}}\\right)\\right) \\right], \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.287, + 0.469, + 0.302 + ], + "angle": 0, + "content": "where \\(\\sigma (x) = 1 / (1 + e^{-x})\\) indicates the sigmoid operation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.303, + 0.469, + 0.395 + ], + "angle": 0, + "content": "In LTR, Balanced CE (Eq. 2) improves original CE (Eq. 1) remarkably. However, we observe that it is not directly applicable when it comes to BCE. The logit bias \\(\\mathcal{B}_{\\mathbf{y}_i}\\) in Thm. 1 leads to an even worse situation. Here, we claim that the proper bias of BCE shall be revised as Thm. 2 when collaborating with BCE in LTR." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.407, + 0.47, + 0.471 + ], + "angle": 0, + "content": "Theorem 2. Logit Bias of Balanced BCE. Let \\(\\pi_{\\mathbf{y}_i} = n_{\\mathbf{y}_i} / N\\) be the class \\(\\mathbf{y}_i\\) distribution. If we implement the balanced binary cross-entropy loss via logit adjustment, the bias item of logit \\(\\mathbf{z}_{\\mathbf{y}_i}\\) will be \\(\\mathcal{B}_{\\mathbf{y}_i}^{\\mathrm{bce}} = \\log \\pi_{\\mathbf{y}_i} - \\log (1 - \\pi_{\\mathbf{y}_i})\\)," + }, + { + "type": "equation", + "bbox": [ + 0.077, + 0.488, + 0.498, + 0.57 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {\\text {B a l - B C E}} = - \\sum_ {\\mathbf {y} _ {i} \\in \\mathcal {C}} w _ {i} [ \\mathbb {1} (\\mathbf {y} _ {i}) \\cdot \\log \\frac {1}{1 + e ^ {- [ \\mathbf {z} _ {\\mathbf {y} _ {i}} + \\log \\pi_ {\\mathbf {y} _ {i}} - \\log (1 - \\pi_ {\\mathbf {y} _ {i}}) ]}} \\\\ + (1 - \\mathbb {1} (\\mathbf {y} _ {i})) \\cdot \\log (1 - \\frac {1}{1 + e ^ {- [ \\mathbf {z} _ {\\mathbf {y} _ {i}} + \\log \\pi_ {\\mathbf {y} _ {i}} - \\log (1 - \\pi_ {\\mathbf {y} _ {i}}) ]}}) ] \\tag {6} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.571, + 0.469, + 0.632 + ], + "angle": 0, + "content": "Proof. We regard Binary CE as \\(C\\) binary classification loss. Hence, for the class \\(\\mathbf{y}_i\\), \\(\\pi_{\\mathbf{y}_i}\\) indicates positive samples proportion and \\(1 - \\pi_{\\mathbf{y}_i}\\) indicates negative ones. Here, we start by revising the sigmoid activation function:" + }, + { + "type": "equation", + "bbox": [ + 0.1, + 0.645, + 0.469, + 0.677 + ], + "angle": 0, + "content": "\\[\n\\sigma \\left(\\mathbf {z} _ {\\mathbf {y} _ {i}}\\right) = \\frac {1}{1 + e ^ {- \\mathbf {z} _ {\\mathbf {y} _ {i}}}} = \\frac {e ^ {0}}{e ^ {0} + e ^ {- \\mathbf {z} _ {\\mathbf {y} _ {i}}}} = \\frac {e ^ {\\mathbf {z} _ {\\mathbf {y} _ {i}}}}{e ^ {\\mathbf {z} _ {\\mathbf {y} _ {i}}} + e ^ {0}} \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.691, + 0.469, + 0.737 + ], + "angle": 0, + "content": "If we view Eq. 7 as the binary version of softmax, \\( e^x (e^0) \\) will be the normalized probability to indicate yes (no). Similar to Eq. 2, we use instance number to balance sigmoid:" + }, + { + "type": "equation", + "bbox": [ + 0.143, + 0.749, + 0.469, + 0.858 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\hat {\\sigma} \\left(\\mathbf {z} _ {\\mathbf {y} _ {i}}\\right) = \\frac {n _ {\\mathbf {y} _ {i}} \\cdot e ^ {\\mathbf {z} _ {\\mathbf {y} _ {i}}}}{n _ {\\mathbf {y} _ {i}} \\cdot e ^ {\\mathbf {z} _ {\\mathbf {y} _ {i}}} + (N - n _ {\\mathbf {y} _ {i}}) \\cdot e ^ {0}} \\\\ = \\frac {\\pi_ {\\mathbf {y} _ {i}} \\cdot e ^ {\\mathbf {z} _ {\\mathbf {y} _ {i}}}}{\\pi_ {\\mathbf {y} _ {i}} \\cdot e ^ {\\mathbf {z} _ {\\mathbf {y} _ {i}}} + \\left(1 - \\pi_ {\\mathbf {y} _ {i}}\\right) \\cdot e ^ {0}} \\tag {8} \\\\ = \\frac {1}{1 + \\frac {1 - \\pi_ {\\mathbf {y} _ {i}}}{\\pi_ {\\mathbf {y} _ {i}}} \\cdot e ^ {- \\mathbf {z} _ {\\mathbf {y} _ {i}}}} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.903 + ], + "angle": 0, + "content": "Considering the log-sum-exp trick for numerical stability, we change the weight of \\( e^{-\\mathbf{z}_{\\mathbf{y}_i}} \\) to the bias term of \\( \\mathbf{z}_{\\mathbf{y}_i} \\):" + }, + { + "type": "equation", + "bbox": [ + 0.511, + 0.114, + 0.892, + 0.22 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\hat {\\sigma} (\\mathbf {z} _ {\\mathbf {y} _ {i}}) = \\frac {1}{1 + \\frac {1 - \\pi_ {\\mathbf {y} _ {i}}}{\\pi_ {\\mathbf {y} _ {i}}} \\cdot e ^ {- \\mathbf {z} _ {\\mathbf {y} _ {i}}}} = \\frac {1}{1 + e ^ {- \\mathbf {z} _ {\\mathbf {y} _ {i}} + \\log \\frac {1 - \\pi_ {\\mathbf {y} _ {i}}}{\\pi_ {\\mathbf {y} _ {i}}}}} \\\\ = \\frac {1}{1 + e ^ {- \\mathbf {z} _ {\\mathbf {y} _ {i}} + \\log (1 - \\pi_ {\\mathbf {y} _ {i}}) - \\log \\pi_ {\\mathbf {y} _ {i}}}} \\tag {9} \\\\ = \\frac {1}{1 + e ^ {- [ {\\bf z _ {y}} _ {i} + \\log \\pi_ {{\\bf y} _ {i}} - \\log (1 - \\pi_ {{\\bf y} _ {i}}) ]}} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.231, + 0.892, + 0.277 + ], + "angle": 0, + "content": "Hence, we derive the bias item of logit \\(\\mathbf{z}_i\\) shall be \\(\\mathcal{B}_{\\mathbf{y}_i}^{\\mathrm{bce}} = \\log \\pi_{\\mathbf{y}_i} - \\log (1 - \\pi_{\\mathbf{y}_i})\\). If we bring Eq. 9 into Binary CE (Eq. 5), we will get the Balanced Binary CE as Eq. 6." + }, + { + "type": "text", + "bbox": [ + 0.875, + 0.278, + 0.892, + 0.291 + ], + "angle": 0, + "content": "□" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.292, + 0.892, + 0.43 + ], + "angle": 0, + "content": "Interpretation. With the additional \\(-\\log (1 - \\pi_{\\mathbf{y}_i})\\), \\(\\mathcal{B}_{\\mathbf{y}_i}^{\\mathrm{bce}}\\) keeps consistent character with \\(\\mathcal{B}_{\\mathbf{y}_i}^{\\mathrm{ce}}\\) w.r.t. \\(\\pi_{\\mathbf{y}_i}\\). Similar to \\(\\mathcal{B}_{\\mathbf{y}_i}^{\\mathrm{ce}}\\), it enlarges the margins to increase the difficulty of the tail (smaller \\(\\pi_{\\mathbf{y}_i}\\)). However, \\(\\mathcal{B}_{\\mathbf{y}_i}^{\\mathrm{bce}}\\) further reduces the head (larger \\(\\pi_{\\mathbf{y}_i}\\)) inter-class distances with larger positive values. Notice that BCE is not class-wise mutually exclusive, and the smaller head inter-class distance helps the networks focus more on the tail's contributions. See visualizations and more in-depth analysis in Appendix." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.43, + 0.892, + 0.476 + ], + "angle": 0, + "content": "Through Bayesian theory [70], we can further extend the proposed Balanced BCE if the test distribution is available as \\(\\pi^t\\), which can be summarized as the following theorem:" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.486, + 0.892, + 0.547 + ], + "angle": 0, + "content": "Theorem 3. Logit Bias of Balanced BCE with Test Prior. Let \\(\\pi_{\\mathbf{y}_i}^s\\) and \\(\\pi_{\\mathbf{y}_i}^t\\) be the label \\(\\mathbf{y}_i\\) training and test distribution. If we implement the balanced cross-entropy loss via logit adjustment, the bias item of logit \\(\\mathbf{z}_{\\mathbf{y}_i}\\) will be:" + }, + { + "type": "equation", + "bbox": [ + 0.5, + 0.557, + 0.902, + 0.578 + ], + "angle": 0, + "content": "\\[\n\\mathcal {B} _ {\\mathbf {y} _ {i}} ^ {\\mathrm {b c e}} = \\left(\\log \\pi_ {\\mathbf {y} _ {i}} ^ {s} - \\log \\pi_ {\\mathbf {y} _ {i}} ^ {t}\\right) - \\left(\\log \\left(1 - \\pi_ {\\mathbf {y} _ {i}} ^ {s}\\right) - \\log \\left(1 - \\pi_ {\\mathbf {y} _ {i}} ^ {t}\\right)\\right)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.587, + 0.789, + 0.603 + ], + "angle": 0, + "content": "Proof. See detailed derivation in Appendix." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.613, + 0.89, + 0.643 + ], + "angle": 0, + "content": "Notice that for the balanced test dataset, \\(\\pi_{\\mathbf{y}_i}^t = 1 / C\\). Hence, the logit bias in Thm.3 will be:" + }, + { + "type": "equation", + "bbox": [ + 0.5, + 0.654, + 0.901, + 0.715 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {B} _ {\\mathbf {y} _ {i}} ^ {\\mathrm {b c e}} = \\left(\\log \\pi_ {\\mathbf {y} _ {i}} ^ {\\mathrm {s}} - \\log 1 / C\\right) - \\left(\\log \\left(1 - \\pi_ {\\mathbf {y} _ {i}} ^ {\\mathrm {s}}\\right) - \\log \\left(\\frac {C - 1}{C}\\right)\\right) \\\\ = \\log \\pi_ {\\mathbf {y} _ {i}} ^ {s} - \\log \\left(1 - \\pi_ {\\mathbf {y} _ {i}} ^ {s}\\right) + \\log (C - 1) \\tag {10} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.717, + 0.892, + 0.792 + ], + "angle": 0, + "content": "Compared with the conclusion of Thm. 2, we get an extra term \\(\\log (C - 1)\\). From the convex objectives optimization view, there is no expected difference between Thm. 2 and Eq. 10. However, it will increase ViTs' training stability remarkably, especially when the class number \\(C\\) gets larger." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.802, + 0.599, + 0.818 + ], + "angle": 0, + "content": "4.3. Pipeline" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.825, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We describe LiVT training pipeline precisely in Alg. 1, which can be divided into two stages, i.e., MGP and BFT. Specifically, in the MGP stage, we adopt simple data augmentation \\(\\mathcal{A}_{pt}\\) and more training epochs \\(T_{pt}\\) to update the parameters of \\(\\mathcal{F}\\) and \\(\\mathcal{D}\\). In the BFT stage, the decoder \\(\\mathcal{D}\\)" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15796" + } + ], + [ + { + "type": "code_caption", + "bbox": [ + 0.08, + 0.092, + 0.327, + 0.107 + ], + "angle": 0, + "content": "Algorithm 1 LiVT Training Pipeline." + }, + { + "type": "algorithm", + "bbox": [ + 0.08, + 0.11, + 0.47, + 0.524 + ], + "angle": 0, + "content": "Input: \\(\\mathcal{D},\\mathcal{F},\\mathcal{W},\\mathcal{D},T_{pt},T_{ft},A_{pt},A_{ft},\\pi_{\\mathbf{y}_i},\\tau\\) \nOutput: Optimized \\(\\theta_f,\\theta_w\\) \n1: Initialize \\(\\theta_f,\\theta_d\\) randomly. MGP Stage \n2: for \\(t = 1\\) to \\(T_{pt}\\) do \n3: for \\(\\{\\mathbf{x},\\mathbf{y}\\}\\) sampled from \\(\\mathcal{D}\\) do \n4: \\(\\mathbf{x}:= \\mathcal{A}_{pt}(\\mathbf{x})\\) \n5: \\(\\hat{\\mathbf{x}} = \\mathcal{D}(\\mathcal{F}(\\mathbf{M}\\odot \\mathbf{x}\\mid \\theta_f)\\mid \\theta_d)\\) \n6: \\(\\mathcal{L}_{MSE}(\\hat{\\mathbf{x}},\\mathbf{x}) = ||\\hat{\\mathbf{x}} -\\mathbf{x}||_2\\) \n7: \\(\\{\\theta_f,\\theta_d\\} \\gets \\{\\theta_f,\\theta_d\\} -\\alpha \\nabla_{\\{\\theta_f,\\theta_d\\}}\\cdot \\mathcal{L}_{MSE}(\\hat{\\mathbf{x}},\\mathbf{x})\\) \n8: end for \n9: end for \n10: Initialize \\(\\theta_w\\) randomly. BFT Stage \n11: Calculate logit bias \\(\\mathcal{B}_{\\mathbf{y}_i}^{\\mathrm{bce}}\\) via Eq. 10. \n12: for \\(t = 1\\) to \\(T_{ft}\\) do \n13: for \\(\\{\\mathbf{x},\\mathbf{y}\\}\\) sampled from \\(\\mathcal{D}\\) do \n14: \\(\\mathbf{x}:= \\mathcal{A}_{ft}(\\mathbf{x})\\) \n15: \\(\\mathbf{v} = \\mathcal{F}(\\mathbf{x}\\mid \\theta_f)\\) \n16: \\(\\mathbf{z} = \\mathcal{W}(\\mathbf{v}\\mid \\theta_w) + \\tau \\cdot \\mathcal{B}^{\\mathrm{bce}}\\) \n17: Calculate \\(\\mathcal{L}_{BCE}\\) via Eq. 5 with calibrated z. \n18: \\(\\{\\theta_f,\\theta_w\\} \\leftarrow \\{\\theta_f,\\theta_w\\} -\\alpha \\nabla_{\\{\\theta_f,\\theta_w\\}}\\cdot \\mathcal{L}_{BCE}\\) \n19: end for \n20: end for" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.532, + 0.473, + 0.64 + ], + "angle": 0, + "content": "is discarded. We adopt more general data augmentations \\(\\mathcal{A}_{ft}\\) to finetune a few epochs \\(T_{ft}\\). As shown in Alg. 1 Line 16, we add a hyper-parameter \\(\\tau\\) to control the influence of the proposed bias. It is worth noticing that the proposed logit bias will add negligible computational costs. With Balanced Binary CE loss, we further optimize the parameters of \\(\\mathcal{F}\\) and \\(\\mathcal{W}\\) to achieve satisfying networks." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.654, + 0.202, + 0.672 + ], + "angle": 0, + "content": "5. Experiment" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.68, + 0.18, + 0.695 + ], + "angle": 0, + "content": "5.1. Datasets" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.704, + 0.473, + 0.903 + ], + "angle": 0, + "content": "CIFAR-10/100-LT are created from the original CIFAR datasets [32], where \\(\\gamma\\) controls the data imbalance degree. Following previous works [4, 12, 70, 81], we employ imbalance factors \\(\\{100, 10\\}\\) in our experiments. ImageNet-LT/BAL are both the subsets of popular ImageNet [52]. The LT version [44] (\\(\\gamma = 256\\)) is selected following the Pareto distribution with power value \\(\\alpha = 6\\), which contains \\(115.8\\mathrm{K}\\) images from 1,000 categories. We build the BAL version (\\(\\gamma = 1\\)) by sampling 116 images per category to exploit how ViTs perform given a similar number of training images. Notice that both LT and BAL adopt the same validation dataset. iNaturalist 2018 [57, 63] (iNat18 for short) is a species classification dataset, which contains \\(437.5\\mathrm{K}\\)" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.089, + 0.892, + 0.118 + ], + "angle": 0, + "content": "Table 2. Top-1 accuracy \\((\\%)\\) of ResNet50 on ImageNet-LT. \\(\\dagger\\) indicates results with ResNeXt50. \\(*\\) training with 384 resolution." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.129, + 0.892, + 0.491 + ], + "angle": 0, + "content": "
MethodRef.ManyMed.FewAcc
CE [13]CVPR 1964.033.85.841.6
LDAM [4]NeurIPS 1960.446.930.749.8
c-RT [29]ICLR 2061.846.227.349.6
τ-Norm [29]ICLR 2059.146.930.749.4
Causal [54]NeurIPS 2062.748.831.651.8
Logit Adj. [47]ICLR 2161.147.527.650.1
RIDE(4E)† [61]ICLR 2168.353.535.956.8
MiSLAS [80]CVPR 2162.950.734.352.7
DisAlign [75]CVPR 2161.352.231.452.9
ACE† [3]ICCV 2171.754.623.556.6
PaCo† [12]ICCV 2168.056.437.258.2
TADE† [77]ICCV 2166.557.043.558.8
TSC [36]CVPR 2263.549.730.452.4
GCL [35]CVPR 2263.052.737.154.5
TLC [33]CVPR 2268.955.740.855.1
BCL† [83]CVPR 2267.654.636.657.2
NCL [34]CVPR 2267.355.439.057.7
SAFA [23]ECCV 2263.849.933.453.1
DOC [58]ECCV 2265.152.834.255.0
DLSA [69]ECCV 2267.854.538.857.5
ViT-B training from scratch
ViT [15]ICLR 2150.523.56.931.6
MAE [18]CVPR 2274.748.219.454.5
DeiT [55]ECCV 2270.440.912.848.4
LiVT73.656.441.060.9
LiVT *76.459.742.763.8
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.499, + 0.892, + 0.606 + ], + "angle": 0, + "content": "images from 8,142 categories and suffers from extremely LTR problem \\((\\gamma = 512)\\). Places-LT is a synthetic long-tail variant of the large-scale scene classification dataset Places [82]. With 62.5K images from 365 categories, its class cardinality ranges from 5 to 4,980 \\((\\gamma = 996)\\). All datasets adopt the official validation images for fair comparisons. See detailed dataset information in Appendix." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.619, + 0.68, + 0.636 + ], + "angle": 0, + "content": "5.2. Implement Details" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.895, + 0.902 + ], + "angle": 0, + "content": "For image classification on main benchmarks, we adopt ViT-Base-16 [15] as the backbone and ViT-Tiny / Small [55] ViT-Large [15] for the ablation study. All models are trained with AdamW optimizer [46] with \\(\\beta s = \\{0.9, 0.95\\}\\). The effective batch size is 4,096 (MGP) / 1,024 (BFT). Vanilla ViTs [15], DeiT III [55] and MAE [18] are all trained 800 epochs because ViTs require longer training time to converge. Following previous work [18], LiVT is pretrained 800 epochs with the mask ratio 0.75 and finetuned 100(50) epochs for ViT-T/S/B(L). We train all models with RandAug(9, 0.5) [11], mixup (0.8) and cutmix (1.0). All experiments set \\(\\tau \\equiv 1\\). For fair comparisons, we re-implement [4, 13, 22, 50, 51] with ViTs in the same settings. Following [44], we report Top-1 accuracy and three groups' accuracy: Many-shot (\\(>100\\) images), Medium-shot (\\(20\\sim 100\\) images) and Few-shot (\\(<20\\) images). Besides, we report the Expected Calibration Error (ECE) and Maximum Cali" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "15797" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.47, + 0.118 + ], + "angle": 0, + "content": "Table 3. Top-1 accuracy \\((\\%)\\) of ResNet50 on iNaturalist 2018. \\(\\ast\\) training with 384 resolution." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.13, + 0.472, + 0.54 + ], + "angle": 0, + "content": "
MethodRef.ManyMed.FewAcc
CE [13]CVPR 1972.263.057.261.7
OLTR [44]CVPR 1959.064.164.963.9
c-RT [29]ICLR 2069.066.063.265.2
τ-Norm [29]ICLR 2065.665.365.965.6
LWS [29]ICLR 2065.066.365.565.9
BBN [81]CVPR 2061.873.666.969.6
BS [51]ICLR 2170.070.269.970.0
RIDE(4E) [61]ICLR 2170.972.573.172.6
DisAlign [75]CVPR 2169.071.170.270.6
MiSLAS [80]CVPR 2173.272.470.471.6
DiVE [21]ICCV 2170.670.067.669.1
ACE(4E) [3]ICCV 21---72.9
TADE [77]ICCV 2174.472.573.172.9
PaCo [12]ICCV 2170.472.873.673.2
ALA [79]AAAI 2271.370.870.470.7
TSC [36]CVPR 2272.670.667.869.7
LTR-WD [1]CVPR 2271.270.469.770.2
GCL [35]CVPR 2267.571.371.571.0
BCL [83]CVPR 2266.771.070.770.4
NCL [34]CVPR 2272.074.973.874.2
DOC [58]ECCV 2272.871.770.071.0
DLSA [69]ECCV 22---72.8
ViT-B training from scratch
ViT [15]ICLR 2165.455.350.954.6
MAE [18]CVPR 2279.670.865.069.4
DeiT [55]ECCV 2272.962.855.861.0
LiVT-78.976.574.876.1
LiVT*-83.281.579.781.0
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.077, + 0.549, + 0.47, + 0.581 + ], + "angle": 0, + "content": "bration Error (MCE) to quantify the predictive uncertainty [17]. See detailed implementation settings in Appendix." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.595, + 0.333, + 0.612 + ], + "angle": 0, + "content": "5.3. Comparison with Prior Arts" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.62, + 0.47, + 0.697 + ], + "angle": 0, + "content": "We conduct comprehensive experiments with ViT-B-16 on ImageNet-LT, iNat18, and Place-LT benchmarks. LiVT successfully trains it from scratch without any additional data pretraining and outperforms ResNet50, ResNeXt50 and ResNet152 conspicuously." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Comparison on ImageNet-LT. Tab. 2 shows the experimental comparison results with recent SOTA methods on ImageNet-LT. The training resolution of LiVT is \\(224 / 224\\) for MGP/BFT. Based on the model ensemble, multi-expert methods like RIDE [61], TADE [77], and NCL [34] exhibit powerful preference with heavier model size compared to baseline. The CL-based methods (PaCo [12], TSC [36], BCL [83]) also achieve satisfying results with larger batches and longer training epochs. However, our LiVT has shown superior performance without bells and whistles and outperforms them consistently on all metrics while training ViTs from scratch. Notice that LiVT gains more performance \\((63.8\\%)\\) vs \\(60.9\\%\\) with higher image resolu" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.089, + 0.892, + 0.119 + ], + "angle": 0, + "content": "Table 4. Top-1 accuracy \\((\\%)\\) of ResNet152 (with ImageNet-1K pretrained weight) on Places-LT. \\(\\ast\\) training with 384 resolution." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.13, + 0.895, + 0.495 + ], + "angle": 0, + "content": "
MethodRef.ManyMed.FewAcc
CE [13]CVPR 1945.727.38.230.2
Focal [38]ICCV 1741.134.822.434.6
Range [76]CVPR 1741.135.423.235.1
OLTR [44]CVPR 1944.737.025.335.9
FSA [10]ECCV 2042.837.522.736.4
LWS [29]ICLR 2040.639.128.637.6
Causal [54]NeurIPS 2023.835.840.432.4
BS [51]NeurIPS 2042.039.330.538.6
DisAlign [75]CVPR 2140.442.430.139.3
LADE [22]CVPR 2142.839.031.238.8
RSG [59]CVPR 2141.941.432.039.3
TADE [77]ICCV 2143.142.433.240.9
PaCo [12]ICCV 2136.147.935.341.2
ALA [79]AAAI 2243.940.132.940.1
NCL [34]CVPR 22---41.8
BF [24]CVPR 2244.043.133.741.6
CKT [48]CVPR 2241.641.435.140.2
GCL [35]CVPR 22---40.6
Bread [40]ECCV 2240.641.033.439.3
ViT-B training from scratch
MAE [18]CVPR 2248.924.68.730.3
DeiT [55]ECCV 2251.631.09.434.2
LiVT-48.140.627.540.8
LiVT*-50.742.427.942.6
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.499, + 0.499, + 0.892, + 0.556 + ], + "angle": 0, + "content": "Table 5. The transfer performance of ViT-B (resolution \\(224\\times 224\\)) on iNat18 dataset. D-PT represents the pretrain datasets. BAL and LT have similar amounts of data and contribute to similar transfer performance, which means MGP is robust to data distribution." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.568, + 0.892, + 0.651 + ], + "angle": 0, + "content": "
D-PTLossManyMed.FewAccECEMCE
BALCE63.757.152.455.91.23.4
LTCE64.557.552.756.41.23.1
BALBal-BCE53.358.860.759.00.81.6
LTBal-BCE56.560.861.660.71.02.9
" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.658, + 0.892, + 0.719 + ], + "angle": 0, + "content": "tion in the BFT stage, which is consistent with the observations in [43, 55, 56]. Notice that LiVT improves the iNat18 dataset most significantly because BCE mitigates fine-grained problems as well [64]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.727, + 0.892, + 0.862 + ], + "angle": 0, + "content": "Comparison on iNaturalist 2018. Tab. 3 lists experimental results on iNaturalist 2018. The training resolution of LiVT is 128 / 224 for MGP/BFT. LiVT consistently surpasses recent SOTA methods like PcCo [12], NCL [34] and DLSA [69]. Unlike most LTR methods, our LiVT improves all groups' Acc without sacrificing many-shot performance. Compared to ensemble NCL \\((3\\times)\\), LiVT surpasses it by \\(1.9\\%\\) (6.8% higher resolution) with comparable model size, which verifies the effectiveness of LiVT." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.903 + ], + "angle": 0, + "content": "Comparison on Places-LT. Tab. 4 summarizes the experimental results on Places-LT. All LTR proposals adopt" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15798" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.892, + 0.118 + ], + "angle": 0, + "content": "Table 6. Ablation study of the proposed bias (c.f. Eq. 10) on CE / BCE. All models are trained on ImageNet-LT with the same settings. Our Bal-BCE ameliorates the original BCE by a large margin in all aspects, which is consistent with CE and Bal-CE." + }, + { + "type": "table", + "bbox": [ + 0.14, + 0.123, + 0.833, + 0.379 + ], + "angle": 0, + "content": "
ModelSizeLossMany ↑Med. ↑Few ↑Acc ↑ECE ↓MCE ↓
ViT-Tiny [55]5.7MCE56.129.210.537.03.76.1
Bal-CE48.8 (-7.3)39.2 (+10.0)28.1 (+17.6)41.4 (+4.4)2.6 (-1.1)4.6 (-1.6)
BCE42.111.10.921.62.98.6
Bal-BCE50.6 (+8.4)37.2 (+26.1)26.1 (+25.2)40.8 (+19.2)3.1 (+0.1)6.8 (-1.8)
ViT-Small [55]22MCE68.943.117.349.54.79.2
Bal-CE62.7 (-6.2)52.0 (+8.9)36.3 (+19.0)54.0 (+4.5)0.9 (-3.8)2.4 (-6.8)
BCE62.430.68.439.85.711.1
Bal-BCE65.8 (+3.4)50.6 (+20.0)32.9 (+24.6)54.1 (+14.2)4.8 (-0.9)9.0 (-2.2)
ViT-Base [15]86MCE74.748.219.454.55.16.8
Bal-CE70.5 (-4.3)56.8 (+8.6)43.7 (+24.3)60.1 (+5.6)3.7 (-1.4)4.9 (-1.9)
BCE73.746.515.652.45.67.9
Bal-BCE73.6 (-0.1)55.8 (+9.3)41.0 (+25.4)60.9 (+8.6)2.4 (-3.1)3.2 (-4.7)
ViT-Large [15]304MCE77.351.521.757.43.67.4
Bal-CE72.7 (-4.5)60.1 (+8.6)41.9 (+20.3)62.1 (+4.8)2.1 (-1.5)4.2 (-3.2)
BCE74.746.717.053.48.415.9
Bal-BCE75.3 (+0.6)58.8 (+12.1)37.5 (+20.5)62.6 (+9.2)6.6 (-1.8)14.8 (-1.1)
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.389, + 0.473, + 0.526 + ], + "angle": 0, + "content": "ResNet152 pre-trained on ImageNet-1K. For fair comparisons, we conduct MGP at ImageNet-1K and BFT at PlacesLT. As illustrated in Tab. 4, LiVT obtains satisfying performance compared with previous SOTAs. Notice that PlacesLT has limited instances compared to iNat18 (437.5K) and ImageNet-1K (1M). Considering both Tab. 3 and Tab. 4 results, we observe that ViTs, which benefit from large-scale data, are limited in this case. However, our LiVT performs the best even in such data paucity situations." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.542, + 0.245, + 0.558 + ], + "angle": 0, + "content": "5.4. Further Analysis" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.574, + 0.47, + 0.786 + ], + "angle": 0, + "content": "Robustness of MGP. The performance results in Tab. 1 have shown that MGP is more robust to learning label irrelevant features than supervised methods. For deeper observations, we show the transfer results in Tab. 5. Concretely, we conduct MGP on ImageNet-LT / ImageNet-BAL (See section 5.1) and BFT on iNat18 with resolution 224. Regardless of the data distribution of the MGP dataset, both BAL and LT achieve quite similar performance in terms of all evaluated metrics on iNat18. If we further compare the reported results with Tab. 3, we will draw the conclusion that the training instance number plays the key role in LiVT instead of the label distribution, which is clearly different from previous SCL [12,83] methods. We show more reconstruction visualization given by LT / BAL in Appendix." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Effectiveness of Proposed Bias. To learn balanced ViTs, we propose Bal-BCE with a simple yet effective logit bias (c.f. Eq. 10). To validate its effectiveness, we conduct the ablation study and compare it with the most popular rebalance loss, i.e., Bal-CE. As shown in Tab. 6, the new logit bias boosts vanilla BCE significantly with lower ECE on four ViT backbones, which is consistent with the behavior" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.386, + 0.895, + 0.573 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.582, + 0.892, + 0.639 + ], + "angle": 0, + "content": "Figure 2. Training loss and Top-1% accuracy of ViT-S on iNaturalist 2018 dataset. Solid and dot lines represent the accuracy and training loss, respectively. All models adopt the same settings and random seed except for loss type." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.645, + 0.894, + 0.752 + ], + "angle": 0, + "content": "of Bal-CE. It is worth noticing that CE generally performs better than BCE in LTR scenarios, which is different from the conclusion in balanced datasets [55]. However, our BalBCE alleviates it remarkably and outperforms Bal-CE in most cases. In addition, Bal-BCE shows more satisfying numerical stability and faster convergence. See Bal-BCE in Fig. 2. for detailed illustrations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.895, + 0.903 + ], + "angle": 0, + "content": "For comprehensive comparisons, we re-implement recent rebalancing strategies in our BFT stage and show the results of ViT-B on CIFAR-LT in Tab. 7. Without loss of fairness, we conduct MGP on ImageNet-1K because the resolution \\((32\\times 32)\\) of CIFAR is too small to mask for ViT-B-16. We do not reproduce the CL-based (conflict to MGP) and ensemble (memory limitation) methods. We also give up some ingenious rebalancing methods for loss NaN during training. As shown in Tab. 7, the proposed Bal-BCE" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "15799" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.098, + 0.09, + 0.447, + 0.103 + ], + "angle": 0, + "content": "Table 7. Ablation study of rebalancing strategies on ViT-B." + }, + { + "type": "table", + "bbox": [ + 0.099, + 0.115, + 0.447, + 0.235 + ], + "angle": 0, + "content": "
MethodCIFAR-10-LTCIFAR-100-LT
γ1001010010
CE [13]79.289.550.966.1
CB [13]82.089.952.066.8
LDAM [4]78.688.652.5666.1
LADE [22]68.881.756.768.2
IB [50]75.479.250.851.6
Bal-CE [51]84.490.756.868.1
Bal-BCE (ours)86.391.358.269.2
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.242, + 0.47, + 0.303 + ], + "angle": 0, + "content": "achieves the best results, which firmly manifests its effectiveness. Notice that some methods are not consistent with their performance on ResNet, which means some exquisite designs may not generalize well on ViTs." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.31, + 0.47, + 0.506 + ], + "angle": 0, + "content": "Hyper-Parameter Analysis. In Alg. 1 Line 11, we add a hyper-parameter \\(\\tau\\) to adjust our proposed bias (Eq. 10). We further present in-depth investigations on the influence of \\(\\tau\\). Similar to the aforementioned settings with plain augmentations, we conduct the ablation study on CIFAR-100-LT with MGP on ImageNet-1K and show the results in Fig.3. The few-shot accuracy gets obvious amelioration when \\(\\tau\\) gets larger, which is consistent with our explanations in section 4.2. The best overall accuracy is obtained around 1, which inspires us to set \\(\\tau \\equiv 1\\) in LiVT for all experiments by default. Besides, the ECE gets smaller with increasing \\(\\tau\\), which means that the proposed bias guides ViTs to be the calibrated models with Fisher Consistency ensured [47]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.521, + 0.192, + 0.537 + ], + "angle": 0, + "content": "6. Discussion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.554, + 0.47, + 0.751 + ], + "angle": 0, + "content": "Why train from scratch? Previous ViTs papers are all based on pretrained weights from ImageNet-1K or ImageNet-22K and thus may lead to unfair comparisons with LTR methods, which are all trained from scratch. It is difficult to conclude that the intriguing performance mainly benefits from their proposals. Our approach provides a strong baseline to verify proposals' effectiveness with ViTs. It's also instructive to train plain ViTs for areas where data exhibits severe domain gaps. From the original intention of the LTR task, the core is to learn more large-scale imbalanced data effectively. Our work provides a feasible way to utilize more real-world LT (labels or attributes) data without expensive artificial balancing to achieve better representation learning." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.758, + 0.468, + 0.877 + ], + "angle": 0, + "content": "How we extend MAE. We empirically prove that masked autoencoder learns generalized features even with imbalanced data, which is quite different from other self-supervised manners like CL [7] and SCL [30]. Extensive experiments on ImageNet-LT/BAL show that the instance number is more crucial than balanced annotation. We further propose the balanced binary cross-entropy loss to build our LiVT and achieve a new SOTA in LTR." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.886, + 0.468, + 0.9 + ], + "angle": 0, + "content": "Limitations. One limitation is that LiVT can not be de" + }, + { + "type": "image", + "bbox": [ + 0.515, + 0.093, + 0.885, + 0.256 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.513, + 0.258, + 0.885, + 0.424 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.429, + 0.892, + 0.457 + ], + "angle": 0, + "content": "Figure 3. Performance of ViT-B with different \\(\\tau\\) on CIFAR-100-LT. A bigger \\(\\tau\\) results in better few-shot performance." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.465, + 0.892, + 0.542 + ], + "angle": 0, + "content": "ployed in an end-to-end manner. An intuitive idea is two branches learning to optimize the decoder and classifier simultaneously, like BBN [81] or PaCo [12]. However, the heavily masked image prevents effective classification, while dynamic mask ratios exacerbate memory limitations." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.552, + 0.619, + 0.568 + ], + "angle": 0, + "content": "7. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.578, + 0.892, + 0.804 + ], + "angle": 0, + "content": "In this paper, we propose to Learn imbalanced data with Vision Transformers (LiVT), which consists of Masked Generative Pretraining (MGP) and Balanced Fine Tuning (BFT). MGP is based on our empirical insight that it guides ViTs to learn more generalized features on long-tailed datasets compared to supervised or contrastive paradigms. BFT is based on the theoretical analysis of Binary Cross-Entropy (BCE) in the imbalanced scenario. We propose the balanced BCE to learn unbiased ViTs by compensating extra logit margins. Bal-BCE ameliorates BCE significantly and surpasses the powerful and widely adopted Balanced Cross-Entropy loss when cooperating with ViTs. Extensive experiments on large-scale datasets demonstrate that LiVT successfully trains ViTs without any additional data and achieves a new state-of-the-art for long-tail recognition." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.816, + 0.661, + 0.833 + ], + "angle": 0, + "content": "Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "This work was supported by the National Key R&D Program of China (2022YFB4701400/4701402), SZSTC Grant (JCYJ 20190809172201639, WDZC20200820200655001), Shenzhen Key Laboratory (ZDSYS20210623092001004)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15800" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.175, + 0.107 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.156 + ], + "angle": 0, + "content": "[1] Shaden Alshammari, Yu-Xiong Wang, Deva Ramanan, and Shu Kong. 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In CVPR, pages 6908-6917, 2022. 2, 3, 5, 6, 7" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.092, + 0.893, + 0.557 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.956 + ], + "angle": 0, + "content": "15803" + } + ] +] \ No newline at end of file diff --git a/2023/Learning Imbalanced Data With Vision Transformers/2c5c04d7-db27-4f72-9591-822af7466068_origin.pdf b/2023/Learning Imbalanced Data With Vision Transformers/2c5c04d7-db27-4f72-9591-822af7466068_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..e0f9c5522e5d5dd4f260d1ca9a5925f97ad74df4 --- /dev/null +++ b/2023/Learning Imbalanced Data With Vision Transformers/2c5c04d7-db27-4f72-9591-822af7466068_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:32485d3ba07b78bf4f84adad826346e8226a94fe6d749010b76b659ec1d7aa61 +size 1019551 diff --git a/2023/Learning Imbalanced Data With Vision Transformers/full.md b/2023/Learning Imbalanced Data With Vision Transformers/full.md new file mode 100644 index 0000000000000000000000000000000000000000..a777ad0c287155405cf2e1b24b3fe0c32cf5bc01 --- /dev/null +++ b/2023/Learning Imbalanced Data With Vision Transformers/full.md @@ -0,0 +1,372 @@ +# Learning Imbalanced Data with Vision Transformers + +Zhengzhuo Xu Ruikang Liu Shuo Yang Zenghao Chai Chun Yuan† Shenzhen International Graduate School, Tsinghua University, China + +{xzzthu, liuruikang.cs, ysss9264, zenghaochai}@gmail.com yuanc@sz.tsinghua.edu.cn + +# Abstract + +The real-world data tends to be heavily imbalanced and severely skew the data-driven deep neural networks, which makes Long-Tailed Recognition (LTR) a massive challenging task. Existing LTR methods seldom train Vision Transformers (ViTs) with Long-Tailed (LT) data, while the off-the-shelf pretrain weight of ViTs always leads to unfair comparisons. In this paper, we systematically investigate the ViTs' performance in LTR and propose LiVT to train ViTs from scratch only with LT data. With the observation that ViTs suffer more severe LTR problems, we conduct Masked Generative Pretraining (MGP) to learn generalized features. With ample and solid evidence, we show that MGP is more robust than supervised manners. Although Binary Cross Entropy (BCE) loss performs well with ViTs, it struggles on the LTR tasks. We further propose the balanced BCE to ameliorate it with strong theoretical groundings. Specially, we derive the unbiased extension of Sigmoid and compensate extra logit margins for deploying it. Our Bal-BCE contributes to the quick convergence of ViTs in just a few epochs. Extensive experiments demonstrate that with MGP and Bal-BCE, LiVT successfully trains ViTs well without any additional data and outperforms comparable state-of-the-art methods significantly, e.g., our ViT-B achieves $81.0\%$ Top-1 accuracy in iNaturalist 2018 without bells and whistles. Code is available at https://github.com/XuZhengzhuo/LiVT. + +# 1. Introduction + +With the vast success in the computer vision field, Vision Transformers (ViTs) [15, 43] get increasingly popular and have been widely used in visual recognition [15], detection [5], and video analysis [16]. These models are heavily dependent on large-scale and balanced data to avoid overfitting [39, 52, 82]. However, real-world data usually confronts severe class-imbalance problems, i.e., most labels (tail) are associated with limited instances while a few categories (head) occupy dominant samples. The models simply classify images into head classes for lower error because the + +![](images/6eb455689ff51af9ee53c56a0a9d2cdbb08eecaf302e6ee1a740bfd9afb6377a.jpg) +Figure 1. Top-1 Acc v.s. Model Size on ImageNet-LT dataset. We choose the Tiny / Small / Base / Large ViT and multi-expert approaches. R50 represents the ResNet50 model. ViT-Base gets lower Acc than ResNet50 when trained in a supervised manner. + +head always overwhelms tail ones in LTR. The data paucity also results in the model overfitting on the tail with unaccepted generalization. The aforementioned problems make Long Tail Recognition (LTR) a challenging task. + +Numerous papers [4, 13, 22, 34, 35, 44, 70] handle the LTR problem with traditional supervised cross-entropy learning based on ResNet [20] or its derivatives [68]. Some methods use ViTs with pretrained weights on ImageNet [52] (or larger datasets), which leads to unfair comparisons with additional data, e.g. on ImageNet-LT (a subset of ImageNet-1K) benchmark. Moreover, there are still limited explorations on the utilization of Long-Tailed (LT) data to train ViTs effectively. Therefore, in this paper, we try to train ViTs from scratch with LT data. We observe that it is particularly difficult to train ViT with LT labels' supervision. As Tab. 1 shows, ViTs degrade heavily when training data become skewed. ViT-B is much worse than ResNet50 with the same CE training manner (c.f. Fig. 1). One reasonable explanation is that ViTs require longer training to learn the inductive bias, while CNNs offer the built-in translation invariance implicitly. Yet another one lies in the label statistical bias in the LTR datasets, which confuses models to make predictions with an inherent bias to the head [12, 47]. The well-trained ViTs have to overcome the above plights simultaneously to avoid falling into dilemmas. + +Inspired by decoupling [29], many methods [9, 12, 60, 80, 83] attempt to enhance feature extraction in supervised manners like mixup [74] / remix [9], or Self-Supervised Learning (SSL) like Contrastive Learning (CL) [7, 19]. Liu et al. [41] claim that SSL representations are more robust to class imbalance than supervised ones, which inspires us to train ViTs with SSL. However, CL is quite challenging for extensive memory requisition and converge difficulties [8], where more explorations are required to work well with ViTs in LTR. In contrast, we propose to Learn imbalanced data with ViTs (LiVT) by Masked Generative Pretraining (MGP) and Balanced Fine Tuning (BFT). + +Firstly, LiVT adopts MGP to enhance ViTs' feature extraction, which has been proven effective on BeiT [2] and MAE [18]. It reconstructs the masked region of images with an extra lightweight decoder. We observe that MGP is stable with ViTs and robust enough to LT data with empirical evidence. Despite the label distribution, the comparable number of training images will bring similar feature extraction ability, which greatly alleviates the toxic effect of LT labels [26]. Meanwhile, the training is accelerated by masked tokens with acceptable memory requisition. + +Secondly, LiVT trains the downstream head with rebalancing strategies to utilize annotation information, which is consistent with [29, 35, 80]. Generally, Binary Cross-Entropy (BCE) loss performs better than Cross-Entropy loss when collaborating with ViTs [55]. However, it fails to catch up with widely adopted Balanced Cross-Entropy (Bal-CE) loss and shows severe training instability in LTR. We propose the Balanced BCE (Bal-BCE) loss to revise the mismatch margins given by Bal-CE. Detailed and solid theoretical derivations are provided from Bayesian theory. Our Bal-BCE ameliorates BCE by a large margin and achieves state-of-the-art (SOTA) performance with ViTs. + +Extensive experiments show that LiVT learns LT data more efficiently and outperforms vanilla ViT [15], DeiT III [55], and MAE [18] remarkably. As detailed comparisons in Fig. 1, LiVT achieves SOTA on ImageNet-LT with affordable parameters, despite that ImageNet-LT is a relatively small dataset for ViTs. The ViT-Small [55] also achieves outstanding performance compared to ResNet50. Our key contributions are summarized as follows. + +- To our best knowledge, we are the first to investigate training ViTs from scratch with LT data systematically. +- We pinpoint that the masked generative pretraining is robust to LT data, which avoids the toxic influence of imbalanced labels on feature learning. +- With a solid theoretical grounding, we propose the balanced version of BCE loss (Bal-BCE), which improves the vanilla BCE by a large margin in LTR. +- We propose LiVT recipe to train ViTs from scratch, and the performance of LiVT achieves state-of-the-art across various benchmarks for long-tailed recognition. + +Table 1. Top-1 accuracy (\%) of different recipes to train ViT-B-16 from scratch on ImageNet-LT/BAL. All perform much worse on LT than BAL. See descriptions of LT & BAL in section 5.1. + +
DatasetViTΔDeiT IIIΔMAEΔ
ImageNet-BAL38.7-67.2-69.2-
ImageNet-LT31.6-7.048.4-18.854.5-14.7
+ +# 2. Related Work + +# 2.1. Long-tailed Visual Recognition + +We roughly divide LTR progress into three groups. + +Rebalancing strategies adjust each class contribution with delicate designs. Re-sampling methods adopt class-wise sampling rate to learn balanced networks [13, 35, 62, 72, 81]. More sophisticated approaches replenish few-shot samples with the help of many-shot ones [9, 10, 31, 49, 70, 78]. The re-weighting proposals modify the loss function by adjusting class weights [1, 13, 38, 50, 53, 54, 80] to assign different weights to samples or enlarging logit margins [4, 22, 35, 47, 51, 70, 75, 77] to learn more challenging and sparse classes. However, the rebalancing strategies are always at the cost of many-shot accuracy inevitably. + +Multi-Expert networks alleviate the LTR problem with single expert learning and knowledge aggregation [3, 21, 25, 33, 34, 37, 61, 67, 77, 81]. LFME [67] trains experts with the subsets with a lower imbalance ratio and aggregate via knowledge distillation. TADE [77] learns three classifiers with the different test labels prior based on Logit Adjustment [47] and optimizes classifiers' output weights by contrastive learning [7]. NCL [34] collaboratively learns multiple experts together to reduce tail uncertainty. However, it is still heuristic to design expert individual training and knowledge aggregation manners. The overly complex models also make training difficult and limit the inference speed. + +Multi-stage training is another effective training strategy for LTR. Cao et al. [4] propose to learn features at first and defer re-weighting in the second stage. Kang et al. [29] further decouples the representation and classifier learning separately, where the classifier is trained with re-balancing strategies just in the second stage. Some works [9, 70, 80] adopt more approaches, e.g., mixup [74] or remix [9], to improve features in the first stage. More recently, Contristive Learning (CL) [7, 19] is gaining increasing concern. Kang et al. [28] exploit to learn balanced feature representations by CL to bypass the influence of imbalanced labels. However, it is more effective to adopt Supervised Contristive Learning (SCL) to utilize the labels [60, 71]. With SCL, SO-TAs [12, 27, 36, 83] all adopt the Bal-CE loss [22, 47, 51, 70] to train the classifier for better performance. Masked Generative learning [6, 14, 18] is another effective feature learning method. However, there is still limited research on it in the community of LTR. + +# 2.2. Vision Transformers + +Current observations and conclusions are mostly based on ResNets [20, 68]. Most recently, ViT [15] has shown extraordinary performance after pre-training on large-scale and balanced datasets. Swin transformer [43] proposes a hierarchical transformer with shift windows to bring greater efficiency. DeiT [55] introduces a simple but effective recipe to train ViT with limited data. BeiT [2] trains ViT with the idea of Mask Language Models. MAE [18] further reduces the computation complexity with a lightweight decoder and higher mask ratio. Although RAC [45] adopts ViTs with pretrained checkpoints, there is limited research to train ViTs from scratch on long-tailed datasets. + +# 3. Preliminaries + +# 3.1. Task Definition + +With a $N$ -sample and $C$ -class dataset $\mathcal{D} = \{\mathcal{X}, \mathcal{Y}\}$ , we note each instance $\mathbf{x}_i \in \mathcal{X} := \{\mathbf{x}_1, \dots, \mathbf{x}_N\}$ and corresponding $\mathbf{y}_i \in \mathcal{Y} := \{\mathbf{y}_1, \dots, \mathbf{y}_N\}$ , where each $\mathbf{y}_i \in \mathcal{C} := \{1, \dots, C\}$ . In long-tailed visual recognition, each category $\mathcal{C}_i$ has a different instance number $n_i = |\mathcal{C}_i|$ and we set $\gamma = n_{max} / n_{min}$ to measure how skewed the long-tailed dataset is. We train the model $\mathcal{M} := \{\mathcal{F}_{\theta_f}, \mathcal{W}_{\theta_w}\}$ with $\mathcal{D}$ which contains a feature encoder $\mathcal{F}_{\theta_f}$ and a classifier $\mathcal{W}_{\theta_w}$ . Besides, we consider a lightweight decoder $\mathcal{D}_{\theta_d}$ for mask autoencoder architecture. For an input image $\mathbf{x}$ , the encoder extracts the feature representation $\mathbf{v} := \mathcal{F}(\mathbf{x} | \theta_f) \in \mathbb{R}^d$ , the classifier gives the logits $\mathbf{z} := \mathcal{W}(\mathbf{v} | \theta_w) \in \mathbb{R}^c$ and the decoder reconstructs original image $\hat{\mathbf{x}} := \mathcal{D}(\mathbf{v} | \theta_d) \in \mathbb{R}^{H \times W \times 3}$ . The $d / H / W$ is feature dimension / resized height / resized width, respectively. + +# 3.2. Balanced Cross-entropy + +Here, we revisit the balanced softmax and corresponding Balanced Cross-Entropy (BalCE) loss [22,34,47,51,70,83], which has been widely adopted in LTR. Consider the standard softmax operation and cross-entropy loss: + +$$ +\begin{array}{l} \mathcal {L} _ {\mathrm {C E}} \left(\mathcal {M} \left(\mathbf {x} \mid \theta_ {f}, \theta_ {w}\right), \mathbf {y} _ {i}\right) = - \log \left(p \left(\mathbf {y} _ {i} \mid \mathbf {x}; \theta_ {f}, \theta_ {w}\right)\right) \\ = - \log \left[ e ^ {z _ {\mathbf {y} _ {i}}} / \sum_ {\mathbf {y} _ {j} \in \mathcal {Y}} e ^ {z _ {\mathbf {y} _ {j}}} \right] = \log \left[ 1 + \sum_ {\mathbf {y} _ {j} \neq \mathbf {y} _ {i}} e ^ {\mathbf {z} _ {\mathbf {y} _ {j}} - \mathbf {z} _ {\mathbf {y} _ {i}}} \right]. \tag {1} \\ \end{array} +$$ + +If we take the class instance number $n_{\mathbf{y}_i}$ into account for softmax [51], we have the balanced cross-entropy loss: + +$$ +\begin{array}{l} \mathcal {L} _ {\mathrm {B a l - C E}} \left(\mathcal {M} \left(\mathbf {x} \mid \theta_ {f}, \theta_ {w}\right), \mathbf {y} _ {i}\right) = - \log \left(p \left(\mathbf {y} _ {i} \mid \mathbf {x}; \theta_ {f}, \theta_ {w}\right)\right) \\ = - \log \left[ \frac {n _ {\mathbf {y} _ {i}} e ^ {z _ {\mathbf {y} _ {i}}}}{\sum_ {\mathbf {y} _ {j} \in \mathcal {Y}} n _ {\mathbf {y} _ {j}} e ^ {z _ {\mathbf {y} _ {j}}}} \right] \tag {2} \\ = \log [ 1 + \sum_ {\mathbf {y} _ {j} \neq \mathbf {y} _ {i}} e ^ {\log n _ {\mathbf {y} _ {j}} - \log n _ {\mathbf {y} _ {i}}} \cdot e ^ {\mathbf {z} _ {\mathbf {y} _ {j}} - \mathbf {z} _ {\mathbf {y} _ {i}}} ]. \\ \end{array} +$$ + +Theorem 1. Logit Bias of Balanced CE. Let $\pi_{\mathbf{y}_i} = n_{\mathbf{y}_i} / N$ be the training label $\mathbf{y}_i$ distribution. If we implement the balanced cross-entropy loss via logit adjustment, the bias item of logit $\mathbf{z}_{\mathbf{y}_i}$ will be $\mathcal{B}_{\mathbf{y}_i}^{\mathrm{ce}} = \log \pi_{\mathbf{y}_i}$ , i.e., + +$$ +\begin{array}{l} \mathcal {L} _ {\mathrm {B a l - C E}} = \log \left[ 1 + \sum_ {\mathbf {y} _ {j} \neq \mathbf {y} _ {i}} e ^ {\log n _ {\mathbf {y} _ {j}} - \log n _ {\mathbf {y} _ {i}}} \cdot e ^ {\mathbf {z} _ {\mathbf {y} _ {j}} - \mathbf {z} _ {\mathbf {y} _ {i}}} \right] \\ = \log [ 1 + \sum_ {\mathbf {y} _ {j} \neq \mathbf {y} _ {i}} e ^ {(\mathbf {z} _ {\mathbf {y} _ {j}} + \log n _ {\mathbf {y} _ {j}}) - (\mathbf {z} _ {\mathbf {y} _ {i}} + \log n _ {\mathbf {y} _ {i}})} ] \tag {3} \\ = \log [ 1 + \sum_ {\mathbf {y} _ {j} \neq \mathbf {y} _ {i}} e ^ {(\mathbf {z} _ {\mathbf {y} _ {j}} + \log \pi_ {\mathbf {y} _ {j}}) - (\mathbf {z} _ {\mathbf {y} _ {i}} + \log \pi_ {\mathbf {y} _ {i}})} ]. \\ \end{array} +$$ + +Proof. See subsection 5.1 from [47] or detail derivation in the Appendix from the Bayesian Theorem perspective. + +Bal-CE loss strengthens the tail instance's contributions while suppressing bias to the head, which alleviates the LTR problem effectively. However, the $\mathcal{B}_{\mathbf{y}_i}^{\mathrm{ce}}$ in Thm.1 fails to work well when collaborating with BCE, where More analysis is required to build a balanced version BCE loss. + +# 4. Methodology + +In this section, we introduce our LiVT in two stages. In section 4.1, we revisit the generative masked auto-encoder as our first stage. Then, we propose the novel balanced sigmoid and corresponding binary cross entropy to collaborate with ViTs in section 4.2. Eventually, we summarize our whole pipeline in section 4.3. + +# 4.1. Masked Generative Pretraining + +Inspired by BeiT [2] and MAE [18], we pretrain feature encoder $\mathcal{F}_{\theta_f}$ via MGP for its training efficiency and label irrelevance. MGP trains the encoder parameters $\theta_{f}$ with high ratio masked images and reconstructs the original image by a lightweight decoder $\mathcal{D}_{\theta_d}$ . + +$$ +\hat {\mathbf {x}} = \mathcal {D} _ {\theta_ {d}} \left(\mathcal {F} _ {\theta_ {f}} (\mathbf {M} \odot \mathbf {x})\right), \tag {4} +$$ + +where $\mathbf{M} \in \{0,1\}^{H \times W}$ is a random patch-wise binary mask. Then, we optimize $\theta_{f}, \theta_{d}$ end-to-end via minimizing the mean squared error between $\mathbf{x}$ and $\hat{\mathbf{x}}$ . + +We adopt MGP for two reasons: 1) It is difficult to train ViTs directly with label supervision (see plain ViT-B performance in Fig. 1) for its convergence difficulty and computation requirement. The DeiT III [55] is hard to catch up with SOTAs in LTR, even with more training epochs, stronger data augmentation, and larger model sizes. 2) The feature extraction ability of MGP is affected slightly by class instance number, compared with previous mixup-based supervision [29,35,80], CL [60] or SCL [12,27,36,83]. Even pretraining on LTR datasets, the transfer performance of MGP is on par with that trained on balanced datasets with comparable total training instances. See transfer results in Tab. 5 and more visualization in Appendix. + +# 4.2. Balanced Fine Tuning + +In the Balanced Fine-Tuning (BFT) phase, softmax + CE loss has been the standard paradigm for utilizing annotated labels. However, recent research [42, 55, 65] pinpoint that Binary Cross-Entropy (BCE) loss works much well with ViTs and is more convenient when employed with mixup-manners [42, 73, 74], which can be written as: + +$$ +\begin{array}{l} \mathcal {L} _ {\mathrm {B C E}} = - \sum_ {\mathbf {y} _ {i} \in \mathcal {C}} w _ {\mathbf {y} _ {i}} [ \mathbb {1} (\mathbf {y} _ {i}) \cdot \log \sigma (\mathbf {z} _ {\mathbf {y} _ {i}}) \tag {5} \\ \left. + \left(1 - \mathbb {1} \left(\mathbf {y} _ {i}\right)\right) \cdot \log \left(1 - \sigma \left(\mathbf {z} _ {\mathbf {y} _ {i}}\right)\right) \right], \\ \end{array} +$$ + +where $\sigma (x) = 1 / (1 + e^{-x})$ indicates the sigmoid operation. + +In LTR, Balanced CE (Eq. 2) improves original CE (Eq. 1) remarkably. However, we observe that it is not directly applicable when it comes to BCE. The logit bias $\mathcal{B}_{\mathbf{y}_i}$ in Thm. 1 leads to an even worse situation. Here, we claim that the proper bias of BCE shall be revised as Thm. 2 when collaborating with BCE in LTR. + +Theorem 2. Logit Bias of Balanced BCE. Let $\pi_{\mathbf{y}_i} = n_{\mathbf{y}_i} / N$ be the class $\mathbf{y}_i$ distribution. If we implement the balanced binary cross-entropy loss via logit adjustment, the bias item of logit $\mathbf{z}_{\mathbf{y}_i}$ will be $\mathcal{B}_{\mathbf{y}_i}^{\mathrm{bce}} = \log \pi_{\mathbf{y}_i} - \log (1 - \pi_{\mathbf{y}_i})$ , + +$$ +\begin{array}{l} \mathcal {L} _ {\text {B a l - B C E}} = - \sum_ {\mathbf {y} _ {i} \in \mathcal {C}} w _ {i} [ \mathbb {1} (\mathbf {y} _ {i}) \cdot \log \frac {1}{1 + e ^ {- [ \mathbf {z} _ {\mathbf {y} _ {i}} + \log \pi_ {\mathbf {y} _ {i}} - \log (1 - \pi_ {\mathbf {y} _ {i}}) ]}} \\ + (1 - \mathbb {1} (\mathbf {y} _ {i})) \cdot \log (1 - \frac {1}{1 + e ^ {- [ \mathbf {z} _ {\mathbf {y} _ {i}} + \log \pi_ {\mathbf {y} _ {i}} - \log (1 - \pi_ {\mathbf {y} _ {i}}) ]}}) ] \tag {6} \\ \end{array} +$$ + +Proof. We regard Binary CE as $C$ binary classification loss. Hence, for the class $\mathbf{y}_i$ , $\pi_{\mathbf{y}_i}$ indicates positive samples proportion and $1 - \pi_{\mathbf{y}_i}$ indicates negative ones. Here, we start by revising the sigmoid activation function: + +$$ +\sigma \left(\mathbf {z} _ {\mathbf {y} _ {i}}\right) = \frac {1}{1 + e ^ {- \mathbf {z} _ {\mathbf {y} _ {i}}}} = \frac {e ^ {0}}{e ^ {0} + e ^ {- \mathbf {z} _ {\mathbf {y} _ {i}}}} = \frac {e ^ {\mathbf {z} _ {\mathbf {y} _ {i}}}}{e ^ {\mathbf {z} _ {\mathbf {y} _ {i}}} + e ^ {0}} \tag {7} +$$ + +If we view Eq. 7 as the binary version of softmax, $e^x (e^0)$ will be the normalized probability to indicate yes (no). Similar to Eq. 2, we use instance number to balance sigmoid: + +$$ +\begin{array}{l} \hat {\sigma} \left(\mathbf {z} _ {\mathbf {y} _ {i}}\right) = \frac {n _ {\mathbf {y} _ {i}} \cdot e ^ {\mathbf {z} _ {\mathbf {y} _ {i}}}}{n _ {\mathbf {y} _ {i}} \cdot e ^ {\mathbf {z} _ {\mathbf {y} _ {i}}} + (N - n _ {\mathbf {y} _ {i}}) \cdot e ^ {0}} \\ = \frac {\pi_ {\mathbf {y} _ {i}} \cdot e ^ {\mathbf {z} _ {\mathbf {y} _ {i}}}}{\pi_ {\mathbf {y} _ {i}} \cdot e ^ {\mathbf {z} _ {\mathbf {y} _ {i}}} + \left(1 - \pi_ {\mathbf {y} _ {i}}\right) \cdot e ^ {0}} \tag {8} \\ = \frac {1}{1 + \frac {1 - \pi_ {\mathbf {y} _ {i}}}{\pi_ {\mathbf {y} _ {i}}} \cdot e ^ {- \mathbf {z} _ {\mathbf {y} _ {i}}}} \\ \end{array} +$$ + +Considering the log-sum-exp trick for numerical stability, we change the weight of $e^{-\mathbf{z}_{\mathbf{y}_i}}$ to the bias term of $\mathbf{z}_{\mathbf{y}_i}$ : + +$$ +\begin{array}{l} \hat {\sigma} (\mathbf {z} _ {\mathbf {y} _ {i}}) = \frac {1}{1 + \frac {1 - \pi_ {\mathbf {y} _ {i}}}{\pi_ {\mathbf {y} _ {i}}} \cdot e ^ {- \mathbf {z} _ {\mathbf {y} _ {i}}}} = \frac {1}{1 + e ^ {- \mathbf {z} _ {\mathbf {y} _ {i}} + \log \frac {1 - \pi_ {\mathbf {y} _ {i}}}{\pi_ {\mathbf {y} _ {i}}}}} \\ = \frac {1}{1 + e ^ {- \mathbf {z} _ {\mathbf {y} _ {i}} + \log (1 - \pi_ {\mathbf {y} _ {i}}) - \log \pi_ {\mathbf {y} _ {i}}}} \tag {9} \\ = \frac {1}{1 + e ^ {- [ {\bf z _ {y}} _ {i} + \log \pi_ {{\bf y} _ {i}} - \log (1 - \pi_ {{\bf y} _ {i}}) ]}} \\ \end{array} +$$ + +Hence, we derive the bias item of logit $\mathbf{z}_i$ shall be $\mathcal{B}_{\mathbf{y}_i}^{\mathrm{bce}} = \log \pi_{\mathbf{y}_i} - \log (1 - \pi_{\mathbf{y}_i})$ . If we bring Eq. 9 into Binary CE (Eq. 5), we will get the Balanced Binary CE as Eq. 6. + +□ + +Interpretation. With the additional $-\log (1 - \pi_{\mathbf{y}_i})$ , $\mathcal{B}_{\mathbf{y}_i}^{\mathrm{bce}}$ keeps consistent character with $\mathcal{B}_{\mathbf{y}_i}^{\mathrm{ce}}$ w.r.t. $\pi_{\mathbf{y}_i}$ . Similar to $\mathcal{B}_{\mathbf{y}_i}^{\mathrm{ce}}$ , it enlarges the margins to increase the difficulty of the tail (smaller $\pi_{\mathbf{y}_i}$ ). However, $\mathcal{B}_{\mathbf{y}_i}^{\mathrm{bce}}$ further reduces the head (larger $\pi_{\mathbf{y}_i}$ ) inter-class distances with larger positive values. Notice that BCE is not class-wise mutually exclusive, and the smaller head inter-class distance helps the networks focus more on the tail's contributions. See visualizations and more in-depth analysis in Appendix. + +Through Bayesian theory [70], we can further extend the proposed Balanced BCE if the test distribution is available as $\pi^t$ , which can be summarized as the following theorem: + +Theorem 3. Logit Bias of Balanced BCE with Test Prior. Let $\pi_{\mathbf{y}_i}^s$ and $\pi_{\mathbf{y}_i}^t$ be the label $\mathbf{y}_i$ training and test distribution. If we implement the balanced cross-entropy loss via logit adjustment, the bias item of logit $\mathbf{z}_{\mathbf{y}_i}$ will be: + +$$ +\mathcal {B} _ {\mathbf {y} _ {i}} ^ {\mathrm {b c e}} = \left(\log \pi_ {\mathbf {y} _ {i}} ^ {s} - \log \pi_ {\mathbf {y} _ {i}} ^ {t}\right) - \left(\log \left(1 - \pi_ {\mathbf {y} _ {i}} ^ {s}\right) - \log \left(1 - \pi_ {\mathbf {y} _ {i}} ^ {t}\right)\right) +$$ + +Proof. See detailed derivation in Appendix. + +Notice that for the balanced test dataset, $\pi_{\mathbf{y}_i}^t = 1 / C$ . Hence, the logit bias in Thm.3 will be: + +$$ +\begin{array}{l} \mathcal {B} _ {\mathbf {y} _ {i}} ^ {\mathrm {b c e}} = \left(\log \pi_ {\mathbf {y} _ {i}} ^ {\mathrm {s}} - \log 1 / C\right) - \left(\log \left(1 - \pi_ {\mathbf {y} _ {i}} ^ {\mathrm {s}}\right) - \log \left(\frac {C - 1}{C}\right)\right) \\ = \log \pi_ {\mathbf {y} _ {i}} ^ {s} - \log \left(1 - \pi_ {\mathbf {y} _ {i}} ^ {s}\right) + \log (C - 1) \tag {10} \\ \end{array} +$$ + +Compared with the conclusion of Thm. 2, we get an extra term $\log (C - 1)$ . From the convex objectives optimization view, there is no expected difference between Thm. 2 and Eq. 10. However, it will increase ViTs' training stability remarkably, especially when the class number $C$ gets larger. + +# 4.3. Pipeline + +We describe LiVT training pipeline precisely in Alg. 1, which can be divided into two stages, i.e., MGP and BFT. Specifically, in the MGP stage, we adopt simple data augmentation $\mathcal{A}_{pt}$ and more training epochs $T_{pt}$ to update the parameters of $\mathcal{F}$ and $\mathcal{D}$ . In the BFT stage, the decoder $\mathcal{D}$ + +Algorithm 1 LiVT Training Pipeline. +Input: $\mathcal{D},\mathcal{F},\mathcal{W},\mathcal{D},T_{pt},T_{ft},A_{pt},A_{ft},\pi_{\mathbf{y}_i},\tau$ +Output: Optimized $\theta_f,\theta_w$ +1: Initialize $\theta_f,\theta_d$ randomly. MGP Stage +2: for $t = 1$ to $T_{pt}$ do +3: for $\{\mathbf{x},\mathbf{y}\}$ sampled from $\mathcal{D}$ do +4: $\mathbf{x}:= \mathcal{A}_{pt}(\mathbf{x})$ +5: $\hat{\mathbf{x}} = \mathcal{D}(\mathcal{F}(\mathbf{M}\odot \mathbf{x}\mid \theta_f)\mid \theta_d)$ +6: $\mathcal{L}_{MSE}(\hat{\mathbf{x}},\mathbf{x}) = ||\hat{\mathbf{x}} -\mathbf{x}||_2$ +7: $\{\theta_f,\theta_d\} \gets \{\theta_f,\theta_d\} -\alpha \nabla_{\{\theta_f,\theta_d\}}\cdot \mathcal{L}_{MSE}(\hat{\mathbf{x}},\mathbf{x})$ +8: end for +9: end for +10: Initialize $\theta_w$ randomly. BFT Stage +11: Calculate logit bias $\mathcal{B}_{\mathbf{y}_i}^{\mathrm{bce}}$ via Eq. 10. +12: for $t = 1$ to $T_{ft}$ do +13: for $\{\mathbf{x},\mathbf{y}\}$ sampled from $\mathcal{D}$ do +14: $\mathbf{x}:= \mathcal{A}_{ft}(\mathbf{x})$ +15: $\mathbf{v} = \mathcal{F}(\mathbf{x}\mid \theta_f)$ +16: $\mathbf{z} = \mathcal{W}(\mathbf{v}\mid \theta_w) + \tau \cdot \mathcal{B}^{\mathrm{bce}}$ +17: Calculate $\mathcal{L}_{BCE}$ via Eq. 5 with calibrated z. +18: $\{\theta_f,\theta_w\} \leftarrow \{\theta_f,\theta_w\} -\alpha \nabla_{\{\theta_f,\theta_w\}}\cdot \mathcal{L}_{BCE}$ +19: end for +20: end for + +is discarded. We adopt more general data augmentations $\mathcal{A}_{ft}$ to finetune a few epochs $T_{ft}$ . As shown in Alg. 1 Line 16, we add a hyper-parameter $\tau$ to control the influence of the proposed bias. It is worth noticing that the proposed logit bias will add negligible computational costs. With Balanced Binary CE loss, we further optimize the parameters of $\mathcal{F}$ and $\mathcal{W}$ to achieve satisfying networks. + +# 5. Experiment + +# 5.1. Datasets + +CIFAR-10/100-LT are created from the original CIFAR datasets [32], where $\gamma$ controls the data imbalance degree. Following previous works [4, 12, 70, 81], we employ imbalance factors $\{100, 10\}$ in our experiments. ImageNet-LT/BAL are both the subsets of popular ImageNet [52]. The LT version [44] ( $\gamma = 256$ ) is selected following the Pareto distribution with power value $\alpha = 6$ , which contains $115.8\mathrm{K}$ images from 1,000 categories. We build the BAL version ( $\gamma = 1$ ) by sampling 116 images per category to exploit how ViTs perform given a similar number of training images. Notice that both LT and BAL adopt the same validation dataset. iNaturalist 2018 [57, 63] (iNat18 for short) is a species classification dataset, which contains $437.5\mathrm{K}$ + +Table 2. Top-1 accuracy $(\%)$ of ResNet50 on ImageNet-LT. $\dagger$ indicates results with ResNeXt50. $*$ training with 384 resolution. + +
MethodRef.ManyMed.FewAcc
CE [13]CVPR 1964.033.85.841.6
LDAM [4]NeurIPS 1960.446.930.749.8
c-RT [29]ICLR 2061.846.227.349.6
τ-Norm [29]ICLR 2059.146.930.749.4
Causal [54]NeurIPS 2062.748.831.651.8
Logit Adj. [47]ICLR 2161.147.527.650.1
RIDE(4E)† [61]ICLR 2168.353.535.956.8
MiSLAS [80]CVPR 2162.950.734.352.7
DisAlign [75]CVPR 2161.352.231.452.9
ACE† [3]ICCV 2171.754.623.556.6
PaCo† [12]ICCV 2168.056.437.258.2
TADE† [77]ICCV 2166.557.043.558.8
TSC [36]CVPR 2263.549.730.452.4
GCL [35]CVPR 2263.052.737.154.5
TLC [33]CVPR 2268.955.740.855.1
BCL† [83]CVPR 2267.654.636.657.2
NCL [34]CVPR 2267.355.439.057.7
SAFA [23]ECCV 2263.849.933.453.1
DOC [58]ECCV 2265.152.834.255.0
DLSA [69]ECCV 2267.854.538.857.5
ViT-B training from scratch
ViT [15]ICLR 2150.523.56.931.6
MAE [18]CVPR 2274.748.219.454.5
DeiT [55]ECCV 2270.440.912.848.4
LiVT73.656.441.060.9
LiVT *76.459.742.763.8
+ +images from 8,142 categories and suffers from extremely LTR problem $(\gamma = 512)$ . Places-LT is a synthetic long-tail variant of the large-scale scene classification dataset Places [82]. With 62.5K images from 365 categories, its class cardinality ranges from 5 to 4,980 $(\gamma = 996)$ . All datasets adopt the official validation images for fair comparisons. See detailed dataset information in Appendix. + +# 5.2. Implement Details + +For image classification on main benchmarks, we adopt ViT-Base-16 [15] as the backbone and ViT-Tiny / Small [55] ViT-Large [15] for the ablation study. All models are trained with AdamW optimizer [46] with $\beta s = \{0.9, 0.95\}$ . The effective batch size is 4,096 (MGP) / 1,024 (BFT). Vanilla ViTs [15], DeiT III [55] and MAE [18] are all trained 800 epochs because ViTs require longer training time to converge. Following previous work [18], LiVT is pretrained 800 epochs with the mask ratio 0.75 and finetuned 100(50) epochs for ViT-T/S/B(L). We train all models with RandAug(9, 0.5) [11], mixup (0.8) and cutmix (1.0). All experiments set $\tau \equiv 1$ . For fair comparisons, we re-implement [4, 13, 22, 50, 51] with ViTs in the same settings. Following [44], we report Top-1 accuracy and three groups' accuracy: Many-shot ( $>100$ images), Medium-shot ( $20\sim 100$ images) and Few-shot ( $<20$ images). Besides, we report the Expected Calibration Error (ECE) and Maximum Cali + +Table 3. Top-1 accuracy $(\%)$ of ResNet50 on iNaturalist 2018. $\ast$ training with 384 resolution. + +
MethodRef.ManyMed.FewAcc
CE [13]CVPR 1972.263.057.261.7
OLTR [44]CVPR 1959.064.164.963.9
c-RT [29]ICLR 2069.066.063.265.2
τ-Norm [29]ICLR 2065.665.365.965.6
LWS [29]ICLR 2065.066.365.565.9
BBN [81]CVPR 2061.873.666.969.6
BS [51]ICLR 2170.070.269.970.0
RIDE(4E) [61]ICLR 2170.972.573.172.6
DisAlign [75]CVPR 2169.071.170.270.6
MiSLAS [80]CVPR 2173.272.470.471.6
DiVE [21]ICCV 2170.670.067.669.1
ACE(4E) [3]ICCV 21---72.9
TADE [77]ICCV 2174.472.573.172.9
PaCo [12]ICCV 2170.472.873.673.2
ALA [79]AAAI 2271.370.870.470.7
TSC [36]CVPR 2272.670.667.869.7
LTR-WD [1]CVPR 2271.270.469.770.2
GCL [35]CVPR 2267.571.371.571.0
BCL [83]CVPR 2266.771.070.770.4
NCL [34]CVPR 2272.074.973.874.2
DOC [58]ECCV 2272.871.770.071.0
DLSA [69]ECCV 22---72.8
ViT-B training from scratch
ViT [15]ICLR 2165.455.350.954.6
MAE [18]CVPR 2279.670.865.069.4
DeiT [55]ECCV 2272.962.855.861.0
LiVT-78.976.574.876.1
LiVT*-83.281.579.781.0
+ +bration Error (MCE) to quantify the predictive uncertainty [17]. See detailed implementation settings in Appendix. + +# 5.3. Comparison with Prior Arts + +We conduct comprehensive experiments with ViT-B-16 on ImageNet-LT, iNat18, and Place-LT benchmarks. LiVT successfully trains it from scratch without any additional data pretraining and outperforms ResNet50, ResNeXt50 and ResNet152 conspicuously. + +Comparison on ImageNet-LT. Tab. 2 shows the experimental comparison results with recent SOTA methods on ImageNet-LT. The training resolution of LiVT is $224 / 224$ for MGP/BFT. Based on the model ensemble, multi-expert methods like RIDE [61], TADE [77], and NCL [34] exhibit powerful preference with heavier model size compared to baseline. The CL-based methods (PaCo [12], TSC [36], BCL [83]) also achieve satisfying results with larger batches and longer training epochs. However, our LiVT has shown superior performance without bells and whistles and outperforms them consistently on all metrics while training ViTs from scratch. Notice that LiVT gains more performance $(63.8\%)$ vs $60.9\%$ with higher image resolu + +Table 4. Top-1 accuracy $(\%)$ of ResNet152 (with ImageNet-1K pretrained weight) on Places-LT. $\ast$ training with 384 resolution. + +
MethodRef.ManyMed.FewAcc
CE [13]CVPR 1945.727.38.230.2
Focal [38]ICCV 1741.134.822.434.6
Range [76]CVPR 1741.135.423.235.1
OLTR [44]CVPR 1944.737.025.335.9
FSA [10]ECCV 2042.837.522.736.4
LWS [29]ICLR 2040.639.128.637.6
Causal [54]NeurIPS 2023.835.840.432.4
BS [51]NeurIPS 2042.039.330.538.6
DisAlign [75]CVPR 2140.442.430.139.3
LADE [22]CVPR 2142.839.031.238.8
RSG [59]CVPR 2141.941.432.039.3
TADE [77]ICCV 2143.142.433.240.9
PaCo [12]ICCV 2136.147.935.341.2
ALA [79]AAAI 2243.940.132.940.1
NCL [34]CVPR 22---41.8
BF [24]CVPR 2244.043.133.741.6
CKT [48]CVPR 2241.641.435.140.2
GCL [35]CVPR 22---40.6
Bread [40]ECCV 2240.641.033.439.3
ViT-B training from scratch
MAE [18]CVPR 2248.924.68.730.3
DeiT [55]ECCV 2251.631.09.434.2
LiVT-48.140.627.540.8
LiVT*-50.742.427.942.6
+ +Table 5. The transfer performance of ViT-B (resolution $224\times 224$ ) on iNat18 dataset. D-PT represents the pretrain datasets. BAL and LT have similar amounts of data and contribute to similar transfer performance, which means MGP is robust to data distribution. + +
D-PTLossManyMed.FewAccECEMCE
BALCE63.757.152.455.91.23.4
LTCE64.557.552.756.41.23.1
BALBal-BCE53.358.860.759.00.81.6
LTBal-BCE56.560.861.660.71.02.9
+ +tion in the BFT stage, which is consistent with the observations in [43, 55, 56]. Notice that LiVT improves the iNat18 dataset most significantly because BCE mitigates fine-grained problems as well [64]. + +Comparison on iNaturalist 2018. Tab. 3 lists experimental results on iNaturalist 2018. The training resolution of LiVT is 128 / 224 for MGP/BFT. LiVT consistently surpasses recent SOTA methods like PcCo [12], NCL [34] and DLSA [69]. Unlike most LTR methods, our LiVT improves all groups' Acc without sacrificing many-shot performance. Compared to ensemble NCL $(3\times)$ , LiVT surpasses it by $1.9\%$ (6.8% higher resolution) with comparable model size, which verifies the effectiveness of LiVT. + +Comparison on Places-LT. Tab. 4 summarizes the experimental results on Places-LT. All LTR proposals adopt + +Table 6. Ablation study of the proposed bias (c.f. Eq. 10) on CE / BCE. All models are trained on ImageNet-LT with the same settings. Our Bal-BCE ameliorates the original BCE by a large margin in all aspects, which is consistent with CE and Bal-CE. + +
ModelSizeLossMany ↑Med. ↑Few ↑Acc ↑ECE ↓MCE ↓
ViT-Tiny [55]5.7MCE56.129.210.537.03.76.1
Bal-CE48.8 (-7.3)39.2 (+10.0)28.1 (+17.6)41.4 (+4.4)2.6 (-1.1)4.6 (-1.6)
BCE42.111.10.921.62.98.6
Bal-BCE50.6 (+8.4)37.2 (+26.1)26.1 (+25.2)40.8 (+19.2)3.1 (+0.1)6.8 (-1.8)
ViT-Small [55]22MCE68.943.117.349.54.79.2
Bal-CE62.7 (-6.2)52.0 (+8.9)36.3 (+19.0)54.0 (+4.5)0.9 (-3.8)2.4 (-6.8)
BCE62.430.68.439.85.711.1
Bal-BCE65.8 (+3.4)50.6 (+20.0)32.9 (+24.6)54.1 (+14.2)4.8 (-0.9)9.0 (-2.2)
ViT-Base [15]86MCE74.748.219.454.55.16.8
Bal-CE70.5 (-4.3)56.8 (+8.6)43.7 (+24.3)60.1 (+5.6)3.7 (-1.4)4.9 (-1.9)
BCE73.746.515.652.45.67.9
Bal-BCE73.6 (-0.1)55.8 (+9.3)41.0 (+25.4)60.9 (+8.6)2.4 (-3.1)3.2 (-4.7)
ViT-Large [15]304MCE77.351.521.757.43.67.4
Bal-CE72.7 (-4.5)60.1 (+8.6)41.9 (+20.3)62.1 (+4.8)2.1 (-1.5)4.2 (-3.2)
BCE74.746.717.053.48.415.9
Bal-BCE75.3 (+0.6)58.8 (+12.1)37.5 (+20.5)62.6 (+9.2)6.6 (-1.8)14.8 (-1.1)
+ +ResNet152 pre-trained on ImageNet-1K. For fair comparisons, we conduct MGP at ImageNet-1K and BFT at PlacesLT. As illustrated in Tab. 4, LiVT obtains satisfying performance compared with previous SOTAs. Notice that PlacesLT has limited instances compared to iNat18 (437.5K) and ImageNet-1K (1M). Considering both Tab. 3 and Tab. 4 results, we observe that ViTs, which benefit from large-scale data, are limited in this case. However, our LiVT performs the best even in such data paucity situations. + +# 5.4. Further Analysis + +Robustness of MGP. The performance results in Tab. 1 have shown that MGP is more robust to learning label irrelevant features than supervised methods. For deeper observations, we show the transfer results in Tab. 5. Concretely, we conduct MGP on ImageNet-LT / ImageNet-BAL (See section 5.1) and BFT on iNat18 with resolution 224. Regardless of the data distribution of the MGP dataset, both BAL and LT achieve quite similar performance in terms of all evaluated metrics on iNat18. If we further compare the reported results with Tab. 3, we will draw the conclusion that the training instance number plays the key role in LiVT instead of the label distribution, which is clearly different from previous SCL [12,83] methods. We show more reconstruction visualization given by LT / BAL in Appendix. + +Effectiveness of Proposed Bias. To learn balanced ViTs, we propose Bal-BCE with a simple yet effective logit bias (c.f. Eq. 10). To validate its effectiveness, we conduct the ablation study and compare it with the most popular rebalance loss, i.e., Bal-CE. As shown in Tab. 6, the new logit bias boosts vanilla BCE significantly with lower ECE on four ViT backbones, which is consistent with the behavior + +![](images/f8a95414ed46ebc65973315109fc718192d2a485dddee37f754a70ccd8fdb17b.jpg) +Figure 2. Training loss and Top-1% accuracy of ViT-S on iNaturalist 2018 dataset. Solid and dot lines represent the accuracy and training loss, respectively. All models adopt the same settings and random seed except for loss type. + +of Bal-CE. It is worth noticing that CE generally performs better than BCE in LTR scenarios, which is different from the conclusion in balanced datasets [55]. However, our BalBCE alleviates it remarkably and outperforms Bal-CE in most cases. In addition, Bal-BCE shows more satisfying numerical stability and faster convergence. See Bal-BCE in Fig. 2. for detailed illustrations. + +For comprehensive comparisons, we re-implement recent rebalancing strategies in our BFT stage and show the results of ViT-B on CIFAR-LT in Tab. 7. Without loss of fairness, we conduct MGP on ImageNet-1K because the resolution $(32\times 32)$ of CIFAR is too small to mask for ViT-B-16. We do not reproduce the CL-based (conflict to MGP) and ensemble (memory limitation) methods. We also give up some ingenious rebalancing methods for loss NaN during training. As shown in Tab. 7, the proposed Bal-BCE + +Table 7. Ablation study of rebalancing strategies on ViT-B. + +
MethodCIFAR-10-LTCIFAR-100-LT
γ1001010010
CE [13]79.289.550.966.1
CB [13]82.089.952.066.8
LDAM [4]78.688.652.5666.1
LADE [22]68.881.756.768.2
IB [50]75.479.250.851.6
Bal-CE [51]84.490.756.868.1
Bal-BCE (ours)86.391.358.269.2
+ +achieves the best results, which firmly manifests its effectiveness. Notice that some methods are not consistent with their performance on ResNet, which means some exquisite designs may not generalize well on ViTs. + +Hyper-Parameter Analysis. In Alg. 1 Line 11, we add a hyper-parameter $\tau$ to adjust our proposed bias (Eq. 10). We further present in-depth investigations on the influence of $\tau$ . Similar to the aforementioned settings with plain augmentations, we conduct the ablation study on CIFAR-100-LT with MGP on ImageNet-1K and show the results in Fig.3. The few-shot accuracy gets obvious amelioration when $\tau$ gets larger, which is consistent with our explanations in section 4.2. The best overall accuracy is obtained around 1, which inspires us to set $\tau \equiv 1$ in LiVT for all experiments by default. Besides, the ECE gets smaller with increasing $\tau$ , which means that the proposed bias guides ViTs to be the calibrated models with Fisher Consistency ensured [47]. + +# 6. Discussion + +Why train from scratch? Previous ViTs papers are all based on pretrained weights from ImageNet-1K or ImageNet-22K and thus may lead to unfair comparisons with LTR methods, which are all trained from scratch. It is difficult to conclude that the intriguing performance mainly benefits from their proposals. Our approach provides a strong baseline to verify proposals' effectiveness with ViTs. It's also instructive to train plain ViTs for areas where data exhibits severe domain gaps. From the original intention of the LTR task, the core is to learn more large-scale imbalanced data effectively. Our work provides a feasible way to utilize more real-world LT (labels or attributes) data without expensive artificial balancing to achieve better representation learning. + +How we extend MAE. We empirically prove that masked autoencoder learns generalized features even with imbalanced data, which is quite different from other self-supervised manners like CL [7] and SCL [30]. Extensive experiments on ImageNet-LT/BAL show that the instance number is more crucial than balanced annotation. We further propose the balanced binary cross-entropy loss to build our LiVT and achieve a new SOTA in LTR. + +Limitations. One limitation is that LiVT can not be de + +![](images/81d4417f9ab195409a45ac4fa3326dbf67c8f21c3333b2a686d3d5251e5ef1c0.jpg) + +![](images/f55cb4b5a8e15969bea715d57f9f2bf98ddaea7f958246d1f0532530bea0d8f5.jpg) +Figure 3. Performance of ViT-B with different $\tau$ on CIFAR-100-LT. A bigger $\tau$ results in better few-shot performance. + +ployed in an end-to-end manner. An intuitive idea is two branches learning to optimize the decoder and classifier simultaneously, like BBN [81] or PaCo [12]. However, the heavily masked image prevents effective classification, while dynamic mask ratios exacerbate memory limitations. + +# 7. Conclusion + +In this paper, we propose to Learn imbalanced data with Vision Transformers (LiVT), which consists of Masked Generative Pretraining (MGP) and Balanced Fine Tuning (BFT). MGP is based on our empirical insight that it guides ViTs to learn more generalized features on long-tailed datasets compared to supervised or contrastive paradigms. BFT is based on the theoretical analysis of Binary Cross-Entropy (BCE) in the imbalanced scenario. We propose the balanced BCE to learn unbiased ViTs by compensating extra logit margins. Bal-BCE ameliorates BCE significantly and surpasses the powerful and widely adopted Balanced Cross-Entropy loss when cooperating with ViTs. Extensive experiments on large-scale datasets demonstrate that LiVT successfully trains ViTs without any additional data and achieves a new state-of-the-art for long-tail recognition. + +# Acknowledgement + +This work was supported by the National Key R&D Program of China (2022YFB4701400/4701402), SZSTC Grant (JCYJ 20190809172201639, WDZC20200820200655001), Shenzhen Key Laboratory (ZDSYS20210623092001004). + +# References + +[1] Shaden Alshammari, Yu-Xiong Wang, Deva Ramanan, and Shu Kong. Long-tailed recognition via weight balancing. In CVPR, pages 6897-6907, 2022. 2, 6 +[2] Hangbo Bao, Li Dong, Songhao Piao, and Furu Wei. BEit: BERT pre-training of image transformers. In ICLR, 2022. 2, 3 +[3] Jiarui Cai, Yizhou Wang, Jenq-Neng Hwang, et al. Ace: Ally complementary experts for solving long-tailed recognition in one-shot. In ICCV, pages 112-121, 2021. 2, 5, 6 +[4] Kaidi Cao, Colin Wei, Adrien Gaidon, Nikos Arechiga, and Tengyu Ma. 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In CVPR, pages 6908-6917, 2022. 2, 3, 5, 6, 7 \ No newline at end of file diff --git a/2023/Learning Imbalanced Data With Vision Transformers/images.zip b/2023/Learning Imbalanced Data With Vision Transformers/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..413ede79371c9d168c8cdeb245919e495b0916f5 --- /dev/null +++ b/2023/Learning Imbalanced Data With Vision Transformers/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:6844b9fade56610b53f074c59f84ca8c9e7fe24c6a5bec712c9af27840bad62c +size 786983 diff --git a/2023/Learning Imbalanced Data With Vision Transformers/layout.json b/2023/Learning Imbalanced Data With Vision Transformers/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..11dbda129d07ec0557cbf04fbb4f83ba193175f4 --- /dev/null +++ b/2023/Learning Imbalanced Data With Vision Transformers/layout.json @@ -0,0 +1,10248 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 132, + 103, + 462, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 132, + 103, + 462, + 121 + ], + "spans": [ + { + "bbox": [ + 132, + 103, + 462, + 121 + ], + "type": "text", + "content": "Learning Imbalanced Data with Vision Transformers" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 97, + 142, + 493, + 172 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 97, + 142, + 493, + 172 + ], + "spans": [ + { + "bbox": [ + 97, + 142, + 493, + 172 + ], + "type": "text", + "content": "Zhengzhuo Xu Ruikang Liu Shuo Yang Zenghao Chai Chun Yuan† Shenzhen International Graduate School, Tsinghua University, China" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 68, + 174, + 521, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 174, + 521, + 185 + ], + "spans": [ + { + "bbox": [ + 68, + 174, + 521, + 185 + ], + "type": "text", + "content": "{xzzthu, liuruikang.cs, ysss9264, zenghaochai}@gmail.com yuanc@sz.tsinghua.edu.cn" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "spans": [ + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 238, + 290, + 550 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 238, + 290, + 550 + ], + "spans": [ + { + "bbox": [ + 46, + 238, + 290, + 550 + ], + "type": "text", + "content": "The real-world data tends to be heavily imbalanced and severely skew the data-driven deep neural networks, which makes Long-Tailed Recognition (LTR) a massive challenging task. Existing LTR methods seldom train Vision Transformers (ViTs) with Long-Tailed (LT) data, while the off-the-shelf pretrain weight of ViTs always leads to unfair comparisons. In this paper, we systematically investigate the ViTs' performance in LTR and propose LiVT to train ViTs from scratch only with LT data. With the observation that ViTs suffer more severe LTR problems, we conduct Masked Generative Pretraining (MGP) to learn generalized features. With ample and solid evidence, we show that MGP is more robust than supervised manners. Although Binary Cross Entropy (BCE) loss performs well with ViTs, it struggles on the LTR tasks. We further propose the balanced BCE to ameliorate it with strong theoretical groundings. Specially, we derive the unbiased extension of Sigmoid and compensate extra logit margins for deploying it. Our Bal-BCE contributes to the quick convergence of ViTs in just a few epochs. Extensive experiments demonstrate that with MGP and Bal-BCE, LiVT successfully trains ViTs well without any additional data and outperforms comparable state-of-the-art methods significantly, e.g., our ViT-B achieves " + }, + { + "bbox": [ + 46, + 238, + 290, + 550 + ], + "type": "inline_equation", + "content": "81.0\\%" + }, + { + "bbox": [ + 46, + 238, + 290, + 550 + ], + "type": "text", + "content": " Top-1 accuracy in iNaturalist 2018 without bells and whistles. Code is available at https://github.com/XuZhengzhuo/LiVT." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 573, + 128, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 573, + 128, + 586 + ], + "spans": [ + { + "bbox": [ + 47, + 573, + 128, + 586 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 594, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 287, + 714 + ], + "type": "text", + "content": "With the vast success in the computer vision field, Vision Transformers (ViTs) [15, 43] get increasingly popular and have been widely used in visual recognition [15], detection [5], and video analysis [16]. These models are heavily dependent on large-scale and balanced data to avoid overfitting [39, 52, 82]. However, real-world data usually confronts severe class-imbalance problems, i.e., most labels (tail) are associated with limited instances while a few categories (head) occupy dominant samples. The models simply classify images into head classes for lower error because the" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 305, + 209, + 531, + 356 + ], + "blocks": [ + { + "bbox": [ + 305, + 209, + 531, + 356 + ], + "lines": [ + { + "bbox": [ + 305, + 209, + 531, + 356 + ], + "spans": [ + { + "bbox": [ + 305, + 209, + 531, + 356 + ], + "type": "image", + "image_path": "6eb455689ff51af9ee53c56a0a9d2cdbb08eecaf302e6ee1a740bfd9afb6377a.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 363, + 547, + 407 + ], + "lines": [ + { + "bbox": [ + 304, + 363, + 547, + 407 + ], + "spans": [ + { + "bbox": [ + 304, + 363, + 547, + 407 + ], + "type": "text", + "content": "Figure 1. Top-1 Acc v.s. Model Size on ImageNet-LT dataset. We choose the Tiny / Small / Base / Large ViT and multi-expert approaches. R50 represents the ResNet50 model. ViT-Base gets lower Acc than ResNet50 when trained in a supervised manner." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 414, + 546, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 414, + 546, + 461 + ], + "spans": [ + { + "bbox": [ + 304, + 414, + 546, + 461 + ], + "type": "text", + "content": "head always overwhelms tail ones in LTR. The data paucity also results in the model overfitting on the tail with unaccepted generalization. The aforementioned problems make Long Tail Recognition (LTR) a challenging task." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 462, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 462, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 462, + 547, + 714 + ], + "type": "text", + "content": "Numerous papers [4, 13, 22, 34, 35, 44, 70] handle the LTR problem with traditional supervised cross-entropy learning based on ResNet [20] or its derivatives [68]. Some methods use ViTs with pretrained weights on ImageNet [52] (or larger datasets), which leads to unfair comparisons with additional data, e.g. on ImageNet-LT (a subset of ImageNet-1K) benchmark. Moreover, there are still limited explorations on the utilization of Long-Tailed (LT) data to train ViTs effectively. Therefore, in this paper, we try to train ViTs from scratch with LT data. We observe that it is particularly difficult to train ViT with LT labels' supervision. As Tab. 1 shows, ViTs degrade heavily when training data become skewed. ViT-B is much worse than ResNet50 with the same CE training manner (c.f. Fig. 1). One reasonable explanation is that ViTs require longer training to learn the inductive bias, while CNNs offer the built-in translation invariance implicitly. Yet another one lies in the label statistical bias in the LTR datasets, which confuses models to make predictions with an inherent bias to the head [12, 47]. The well-trained ViTs have to overcome the above plights simultaneously to avoid falling into dilemmas." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15793" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "type": "text", + "content": "Inspired by decoupling [29], many methods [9, 12, 60, 80, 83] attempt to enhance feature extraction in supervised manners like mixup [74] / remix [9], or Self-Supervised Learning (SSL) like Contrastive Learning (CL) [7, 19]. Liu et al. [41] claim that SSL representations are more robust to class imbalance than supervised ones, which inspires us to train ViTs with SSL. However, CL is quite challenging for extensive memory requisition and converge difficulties [8], where more explorations are required to work well with ViTs in LTR. In contrast, we propose to Learn imbalanced data with ViTs (LiVT) by Masked Generative Pretraining (MGP) and Balanced Fine Tuning (BFT)." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 216, + 289, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 216, + 289, + 335 + ], + "spans": [ + { + "bbox": [ + 46, + 216, + 289, + 335 + ], + "type": "text", + "content": "Firstly, LiVT adopts MGP to enhance ViTs' feature extraction, which has been proven effective on BeiT [2] and MAE [18]. It reconstructs the masked region of images with an extra lightweight decoder. We observe that MGP is stable with ViTs and robust enough to LT data with empirical evidence. Despite the label distribution, the comparable number of training images will bring similar feature extraction ability, which greatly alleviates the toxic effect of LT labels [26]. Meanwhile, the training is accelerated by masked tokens with acceptable memory requisition." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 335, + 289, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 335, + 289, + 479 + ], + "spans": [ + { + "bbox": [ + 46, + 335, + 289, + 479 + ], + "type": "text", + "content": "Secondly, LiVT trains the downstream head with rebalancing strategies to utilize annotation information, which is consistent with [29, 35, 80]. Generally, Binary Cross-Entropy (BCE) loss performs better than Cross-Entropy loss when collaborating with ViTs [55]. However, it fails to catch up with widely adopted Balanced Cross-Entropy (Bal-CE) loss and shows severe training instability in LTR. We propose the Balanced BCE (Bal-BCE) loss to revise the mismatch margins given by Bal-CE. Detailed and solid theoretical derivations are provided from Bayesian theory. Our Bal-BCE ameliorates BCE by a large margin and achieves state-of-the-art (SOTA) performance with ViTs." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 479, + 289, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 479, + 289, + 574 + ], + "spans": [ + { + "bbox": [ + 46, + 479, + 289, + 574 + ], + "type": "text", + "content": "Extensive experiments show that LiVT learns LT data more efficiently and outperforms vanilla ViT [15], DeiT III [55], and MAE [18] remarkably. As detailed comparisons in Fig. 1, LiVT achieves SOTA on ImageNet-LT with affordable parameters, despite that ImageNet-LT is a relatively small dataset for ViTs. The ViT-Small [55] also achieves outstanding performance compared to ResNet50. Our key contributions are summarized as follows." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 58, + 576, + 286, + 713 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 58, + 576, + 286, + 600 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 576, + 286, + 600 + ], + "spans": [ + { + "bbox": [ + 58, + 576, + 286, + 600 + ], + "type": "text", + "content": "- To our best knowledge, we are the first to investigate training ViTs from scratch with LT data systematically." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 58, + 602, + 286, + 638 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 602, + 286, + 638 + ], + "spans": [ + { + "bbox": [ + 58, + 602, + 286, + 638 + ], + "type": "text", + "content": "- We pinpoint that the masked generative pretraining is robust to LT data, which avoids the toxic influence of imbalanced labels on feature learning." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 58, + 639, + 286, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 639, + 286, + 675 + ], + "spans": [ + { + "bbox": [ + 58, + 639, + 286, + 675 + ], + "type": "text", + "content": "- With a solid theoretical grounding, we propose the balanced version of BCE loss (Bal-BCE), which improves the vanilla BCE by a large margin in LTR." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 58, + 677, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 677, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 677, + 286, + 713 + ], + "type": "text", + "content": "- We propose LiVT recipe to train ViTs from scratch, and the performance of LiVT achieves state-of-the-art across various benchmarks for long-tailed recognition." + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "type": "table", + "bbox": [ + 308, + 113, + 547, + 156 + ], + "blocks": [ + { + "bbox": [ + 305, + 70, + 547, + 104 + ], + "lines": [ + { + "bbox": [ + 305, + 70, + 547, + 104 + ], + "spans": [ + { + "bbox": [ + 305, + 70, + 547, + 104 + ], + "type": "text", + "content": "Table 1. Top-1 accuracy (\\%) of different recipes to train ViT-B-16 from scratch on ImageNet-LT/BAL. All perform much worse on LT than BAL. See descriptions of LT & BAL in section 5.1." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 113, + 547, + 156 + ], + "lines": [ + { + "bbox": [ + 308, + 113, + 547, + 156 + ], + "spans": [ + { + "bbox": [ + 308, + 113, + 547, + 156 + ], + "type": "table", + "html": "
DatasetViTΔDeiT IIIΔMAEΔ
ImageNet-BAL38.7-67.2-69.2-
ImageNet-LT31.6-7.048.4-18.854.5-14.7
", + "image_path": "ecdff1f4cf005665a3ce41f8095fadc04eed7bf6b076d388ba927deab026df06.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 161, + 392, + 174 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 161, + 392, + 174 + ], + "spans": [ + { + "bbox": [ + 306, + 161, + 392, + 174 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 183, + 474, + 196 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 183, + 474, + 196 + ], + "spans": [ + { + "bbox": [ + 306, + 183, + 474, + 196 + ], + "type": "text", + "content": "2.1. Long-tailed Visual Recognition" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 317, + 204, + 523, + 217 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 204, + 523, + 217 + ], + "spans": [ + { + "bbox": [ + 317, + 204, + 523, + 217 + ], + "type": "text", + "content": "We roughly divide LTR progress into three groups." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 218, + 545, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 218, + 545, + 350 + ], + "spans": [ + { + "bbox": [ + 304, + 218, + 545, + 350 + ], + "type": "text", + "content": "Rebalancing strategies adjust each class contribution with delicate designs. Re-sampling methods adopt class-wise sampling rate to learn balanced networks [13, 35, 62, 72, 81]. More sophisticated approaches replenish few-shot samples with the help of many-shot ones [9, 10, 31, 49, 70, 78]. The re-weighting proposals modify the loss function by adjusting class weights [1, 13, 38, 50, 53, 54, 80] to assign different weights to samples or enlarging logit margins [4, 22, 35, 47, 51, 70, 75, 77] to learn more challenging and sparse classes. However, the rebalancing strategies are always at the cost of many-shot accuracy inevitably." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 352, + 546, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 352, + 546, + 496 + ], + "spans": [ + { + "bbox": [ + 304, + 352, + 546, + 496 + ], + "type": "text", + "content": "Multi-Expert networks alleviate the LTR problem with single expert learning and knowledge aggregation [3, 21, 25, 33, 34, 37, 61, 67, 77, 81]. LFME [67] trains experts with the subsets with a lower imbalance ratio and aggregate via knowledge distillation. TADE [77] learns three classifiers with the different test labels prior based on Logit Adjustment [47] and optimizes classifiers' output weights by contrastive learning [7]. NCL [34] collaboratively learns multiple experts together to reduce tail uncertainty. However, it is still heuristic to design expert individual training and knowledge aggregation manners. The overly complex models also make training difficult and limit the inference speed." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 498, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 547, + 713 + ], + "type": "text", + "content": "Multi-stage training is another effective training strategy for LTR. Cao et al. [4] propose to learn features at first and defer re-weighting in the second stage. Kang et al. [29] further decouples the representation and classifier learning separately, where the classifier is trained with re-balancing strategies just in the second stage. Some works [9, 70, 80] adopt more approaches, e.g., mixup [74] or remix [9], to improve features in the first stage. More recently, Contristive Learning (CL) [7, 19] is gaining increasing concern. Kang et al. [28] exploit to learn balanced feature representations by CL to bypass the influence of imbalanced labels. However, it is more effective to adopt Supervised Contristive Learning (SCL) to utilize the labels [60, 71]. With SCL, SO-TAs [12, 27, 36, 83] all adopt the Bal-CE loss [22, 47, 51, 70] to train the classifier for better performance. Masked Generative learning [6, 14, 18] is another effective feature learning method. However, there is still limited research on it in the community of LTR." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "15794" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 167, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 167, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 167, + 83 + ], + "type": "text", + "content": "2.2. Vision Transformers" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 90, + 289, + 236 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 90, + 289, + 236 + ], + "spans": [ + { + "bbox": [ + 46, + 90, + 289, + 236 + ], + "type": "text", + "content": "Current observations and conclusions are mostly based on ResNets [20, 68]. Most recently, ViT [15] has shown extraordinary performance after pre-training on large-scale and balanced datasets. Swin transformer [43] proposes a hierarchical transformer with shift windows to bring greater efficiency. DeiT [55] introduces a simple but effective recipe to train ViT with limited data. BeiT [2] trains ViT with the idea of Mask Language Models. MAE [18] further reduces the computation complexity with a lightweight decoder and higher mask ratio. Although RAC [45] adopts ViTs with pretrained checkpoints, there is limited research to train ViTs from scratch on long-tailed datasets." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 244, + 132, + 257 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 244, + 132, + 257 + ], + "spans": [ + { + "bbox": [ + 47, + 244, + 132, + 257 + ], + "type": "text", + "content": "3. Preliminaries" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 264, + 141, + 276 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 264, + 141, + 276 + ], + "spans": [ + { + "bbox": [ + 47, + 264, + 141, + 276 + ], + "type": "text", + "content": "3.1. Task Definition" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 282, + 289, + 462 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 282, + 289, + 462 + ], + "spans": [ + { + "bbox": [ + 46, + 282, + 289, + 462 + ], + "type": "text", + "content": "With a " + }, + { + "bbox": [ + 46, + 282, + 289, + 462 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 282, + 289, + 462 + ], + "type": "text", + "content": "-sample and " + }, + { + "bbox": [ + 46, + 282, + 289, + 462 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 282, + 289, + 462 + ], + "type": "text", + "content": "-class dataset " + }, + { + "bbox": [ + 46, + 282, + 289, + 462 + ], + "type": "inline_equation", + "content": "\\mathcal{D} = \\{\\mathcal{X}, \\mathcal{Y}\\}" + }, + { + "bbox": [ + 46, + 282, + 289, + 462 + ], + "type": "text", + "content": ", we note each instance " + }, + { + "bbox": [ + 46, + 282, + 289, + 462 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i \\in \\mathcal{X} := \\{\\mathbf{x}_1, \\dots, \\mathbf{x}_N\\}" + }, + { + "bbox": [ + 46, + 282, + 289, + 462 + ], + "type": "text", + "content": " and corresponding " + }, + { + "bbox": [ + 46, + 282, + 289, + 462 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_i \\in \\mathcal{Y} := \\{\\mathbf{y}_1, \\dots, \\mathbf{y}_N\\}" + }, + { + "bbox": [ + 46, + 282, + 289, + 462 + ], + "type": "text", + "content": ", where each " + }, + { + "bbox": [ + 46, + 282, + 289, + 462 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_i \\in \\mathcal{C} := \\{1, \\dots, C\\}" + }, + { + "bbox": [ + 46, + 282, + 289, + 462 + ], + "type": "text", + "content": ". In long-tailed visual recognition, each category " + }, + { + "bbox": [ + 46, + 282, + 289, + 462 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_i" + }, + { + "bbox": [ + 46, + 282, + 289, + 462 + ], + "type": "text", + "content": " has a different instance number " + }, + { + "bbox": [ + 46, + 282, + 289, + 462 + ], + "type": "inline_equation", + "content": "n_i = |\\mathcal{C}_i|" + }, + { + "bbox": [ + 46, + 282, + 289, + 462 + ], + "type": "text", + "content": " and we set " + }, + { + "bbox": [ + 46, + 282, + 289, + 462 + ], + "type": "inline_equation", + "content": "\\gamma = n_{max} / n_{min}" + }, + { + "bbox": [ + 46, + 282, + 289, + 462 + ], + "type": "text", + "content": " to measure how skewed the long-tailed dataset is. We train the model " + }, + { + "bbox": [ + 46, + 282, + 289, + 462 + ], + "type": "inline_equation", + "content": "\\mathcal{M} := \\{\\mathcal{F}_{\\theta_f}, \\mathcal{W}_{\\theta_w}\\}" + }, + { + "bbox": [ + 46, + 282, + 289, + 462 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 46, + 282, + 289, + 462 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 46, + 282, + 289, + 462 + ], + "type": "text", + "content": " which contains a feature encoder " + }, + { + "bbox": [ + 46, + 282, + 289, + 462 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{\\theta_f}" + }, + { + "bbox": [ + 46, + 282, + 289, + 462 + ], + "type": "text", + "content": " and a classifier " + }, + { + "bbox": [ + 46, + 282, + 289, + 462 + ], + "type": "inline_equation", + "content": "\\mathcal{W}_{\\theta_w}" + }, + { + "bbox": [ + 46, + 282, + 289, + 462 + ], + "type": "text", + "content": ". Besides, we consider a lightweight decoder " + }, + { + "bbox": [ + 46, + 282, + 289, + 462 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\theta_d}" + }, + { + "bbox": [ + 46, + 282, + 289, + 462 + ], + "type": "text", + "content": " for mask autoencoder architecture. For an input image " + }, + { + "bbox": [ + 46, + 282, + 289, + 462 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 46, + 282, + 289, + 462 + ], + "type": "text", + "content": ", the encoder extracts the feature representation " + }, + { + "bbox": [ + 46, + 282, + 289, + 462 + ], + "type": "inline_equation", + "content": "\\mathbf{v} := \\mathcal{F}(\\mathbf{x} | \\theta_f) \\in \\mathbb{R}^d" + }, + { + "bbox": [ + 46, + 282, + 289, + 462 + ], + "type": "text", + "content": ", the classifier gives the logits " + }, + { + "bbox": [ + 46, + 282, + 289, + 462 + ], + "type": "inline_equation", + "content": "\\mathbf{z} := \\mathcal{W}(\\mathbf{v} | \\theta_w) \\in \\mathbb{R}^c" + }, + { + "bbox": [ + 46, + 282, + 289, + 462 + ], + "type": "text", + "content": " and the decoder reconstructs original image " + }, + { + "bbox": [ + 46, + 282, + 289, + 462 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{x}} := \\mathcal{D}(\\mathbf{v} | \\theta_d) \\in \\mathbb{R}^{H \\times W \\times 3}" + }, + { + "bbox": [ + 46, + 282, + 289, + 462 + ], + "type": "text", + "content": ". The " + }, + { + "bbox": [ + 46, + 282, + 289, + 462 + ], + "type": "inline_equation", + "content": "d / H / W" + }, + { + "bbox": [ + 46, + 282, + 289, + 462 + ], + "type": "text", + "content": " is feature dimension / resized height / resized width, respectively." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 469, + 182, + 483 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 469, + 182, + 483 + ], + "spans": [ + { + "bbox": [ + 47, + 469, + 182, + 483 + ], + "type": "text", + "content": "3.2. Balanced Cross-entropy" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 488, + 287, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 488, + 287, + 536 + ], + "spans": [ + { + "bbox": [ + 47, + 488, + 287, + 536 + ], + "type": "text", + "content": "Here, we revisit the balanced softmax and corresponding Balanced Cross-Entropy (BalCE) loss [22,34,47,51,70,83], which has been widely adopted in LTR. Consider the standard softmax operation and cross-entropy loss:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 52, + 544, + 287, + 587 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 544, + 287, + 587 + ], + "spans": [ + { + "bbox": [ + 52, + 544, + 287, + 587 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {\\mathrm {C E}} \\left(\\mathcal {M} \\left(\\mathbf {x} \\mid \\theta_ {f}, \\theta_ {w}\\right), \\mathbf {y} _ {i}\\right) = - \\log \\left(p \\left(\\mathbf {y} _ {i} \\mid \\mathbf {x}; \\theta_ {f}, \\theta_ {w}\\right)\\right) \\\\ = - \\log \\left[ e ^ {z _ {\\mathbf {y} _ {i}}} / \\sum_ {\\mathbf {y} _ {j} \\in \\mathcal {Y}} e ^ {z _ {\\mathbf {y} _ {j}}} \\right] = \\log \\left[ 1 + \\sum_ {\\mathbf {y} _ {j} \\neq \\mathbf {y} _ {i}} e ^ {\\mathbf {z} _ {\\mathbf {y} _ {j}} - \\mathbf {z} _ {\\mathbf {y} _ {i}}} \\right]. \\tag {1} \\\\ \\end{array}", + "image_path": "acdcaac978b2d8f9e041d84e6770ca5248bf56defdaee48d7d3e973dd11147be.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 596, + 287, + 620 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 596, + 287, + 620 + ], + "spans": [ + { + "bbox": [ + 47, + 596, + 287, + 620 + ], + "type": "text", + "content": "If we take the class instance number " + }, + { + "bbox": [ + 47, + 596, + 287, + 620 + ], + "type": "inline_equation", + "content": "n_{\\mathbf{y}_i}" + }, + { + "bbox": [ + 47, + 596, + 287, + 620 + ], + "type": "text", + "content": " into account for softmax [51], we have the balanced cross-entropy loss:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 628, + 287, + 700 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 628, + 287, + 700 + ], + "spans": [ + { + "bbox": [ + 55, + 628, + 287, + 700 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {\\mathrm {B a l - C E}} \\left(\\mathcal {M} \\left(\\mathbf {x} \\mid \\theta_ {f}, \\theta_ {w}\\right), \\mathbf {y} _ {i}\\right) = - \\log \\left(p \\left(\\mathbf {y} _ {i} \\mid \\mathbf {x}; \\theta_ {f}, \\theta_ {w}\\right)\\right) \\\\ = - \\log \\left[ \\frac {n _ {\\mathbf {y} _ {i}} e ^ {z _ {\\mathbf {y} _ {i}}}}{\\sum_ {\\mathbf {y} _ {j} \\in \\mathcal {Y}} n _ {\\mathbf {y} _ {j}} e ^ {z _ {\\mathbf {y} _ {j}}}} \\right] \\tag {2} \\\\ = \\log [ 1 + \\sum_ {\\mathbf {y} _ {j} \\neq \\mathbf {y} _ {i}} e ^ {\\log n _ {\\mathbf {y} _ {j}} - \\log n _ {\\mathbf {y} _ {i}}} \\cdot e ^ {\\mathbf {z} _ {\\mathbf {y} _ {j}} - \\mathbf {z} _ {\\mathbf {y} _ {i}}} ]. \\\\ \\end{array}", + "image_path": "816e82649e06a02798b4f95d9d7a06ce3389cbc242b8bd89f481623f5d30c9ba.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 72, + 545, + 124 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 124 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 124 + ], + "type": "text", + "content": "Theorem 1. Logit Bias of Balanced CE. Let " + }, + { + "bbox": [ + 305, + 72, + 545, + 124 + ], + "type": "inline_equation", + "content": "\\pi_{\\mathbf{y}_i} = n_{\\mathbf{y}_i} / N" + }, + { + "bbox": [ + 305, + 72, + 545, + 124 + ], + "type": "text", + "content": " be the training label " + }, + { + "bbox": [ + 305, + 72, + 545, + 124 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_i" + }, + { + "bbox": [ + 305, + 72, + 545, + 124 + ], + "type": "text", + "content": " distribution. If we implement the balanced cross-entropy loss via logit adjustment, the bias item of logit " + }, + { + "bbox": [ + 305, + 72, + 545, + 124 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{\\mathbf{y}_i}" + }, + { + "bbox": [ + 305, + 72, + 545, + 124 + ], + "type": "text", + "content": " will be " + }, + { + "bbox": [ + 305, + 72, + 545, + 124 + ], + "type": "inline_equation", + "content": "\\mathcal{B}_{\\mathbf{y}_i}^{\\mathrm{ce}} = \\log \\pi_{\\mathbf{y}_i}" + }, + { + "bbox": [ + 305, + 72, + 545, + 124 + ], + "type": "text", + "content": ", i.e.," + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 312, + 139, + 545, + 225 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 139, + 545, + 225 + ], + "spans": [ + { + "bbox": [ + 312, + 139, + 545, + 225 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {\\mathrm {B a l - C E}} = \\log \\left[ 1 + \\sum_ {\\mathbf {y} _ {j} \\neq \\mathbf {y} _ {i}} e ^ {\\log n _ {\\mathbf {y} _ {j}} - \\log n _ {\\mathbf {y} _ {i}}} \\cdot e ^ {\\mathbf {z} _ {\\mathbf {y} _ {j}} - \\mathbf {z} _ {\\mathbf {y} _ {i}}} \\right] \\\\ = \\log [ 1 + \\sum_ {\\mathbf {y} _ {j} \\neq \\mathbf {y} _ {i}} e ^ {(\\mathbf {z} _ {\\mathbf {y} _ {j}} + \\log n _ {\\mathbf {y} _ {j}}) - (\\mathbf {z} _ {\\mathbf {y} _ {i}} + \\log n _ {\\mathbf {y} _ {i}})} ] \\tag {3} \\\\ = \\log [ 1 + \\sum_ {\\mathbf {y} _ {j} \\neq \\mathbf {y} _ {i}} e ^ {(\\mathbf {z} _ {\\mathbf {y} _ {j}} + \\log \\pi_ {\\mathbf {y} _ {j}}) - (\\mathbf {z} _ {\\mathbf {y} _ {i}} + \\log \\pi_ {\\mathbf {y} _ {i}})} ]. \\\\ \\end{array}", + "image_path": "d828369802920914c69ef56e5f908dbc3401c5812b71d65d644316ee2ef9ef3b.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 230, + 545, + 253 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 230, + 545, + 253 + ], + "spans": [ + { + "bbox": [ + 305, + 230, + 545, + 253 + ], + "type": "text", + "content": "Proof. See subsection 5.1 from [47] or detail derivation in the Appendix from the Bayesian Theorem perspective." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 254, + 545, + 314 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 254, + 545, + 314 + ], + "spans": [ + { + "bbox": [ + 305, + 254, + 545, + 314 + ], + "type": "text", + "content": "Bal-CE loss strengthens the tail instance's contributions while suppressing bias to the head, which alleviates the LTR problem effectively. However, the " + }, + { + "bbox": [ + 305, + 254, + 545, + 314 + ], + "type": "inline_equation", + "content": "\\mathcal{B}_{\\mathbf{y}_i}^{\\mathrm{ce}}" + }, + { + "bbox": [ + 305, + 254, + 545, + 314 + ], + "type": "text", + "content": " in Thm.1 fails to work well when collaborating with BCE, where More analysis is required to build a balanced version BCE loss." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 323, + 389, + 336 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 323, + 389, + 336 + ], + "spans": [ + { + "bbox": [ + 306, + 323, + 389, + 336 + ], + "type": "text", + "content": "4. Methodology" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 342, + 545, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 342, + 545, + 415 + ], + "spans": [ + { + "bbox": [ + 305, + 342, + 545, + 415 + ], + "type": "text", + "content": "In this section, we introduce our LiVT in two stages. In section 4.1, we revisit the generative masked auto-encoder as our first stage. Then, we propose the novel balanced sigmoid and corresponding binary cross entropy to collaborate with ViTs in section 4.2. Eventually, we summarize our whole pipeline in section 4.3." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 420, + 477, + 433 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 420, + 477, + 433 + ], + "spans": [ + { + "bbox": [ + 306, + 420, + 477, + 433 + ], + "type": "text", + "content": "4.1. Masked Generative Pretraining" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 438, + 545, + 499 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 438, + 545, + 499 + ], + "spans": [ + { + "bbox": [ + 305, + 438, + 545, + 499 + ], + "type": "text", + "content": "Inspired by BeiT [2] and MAE [18], we pretrain feature encoder " + }, + { + "bbox": [ + 305, + 438, + 545, + 499 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{\\theta_f}" + }, + { + "bbox": [ + 305, + 438, + 545, + 499 + ], + "type": "text", + "content": " via MGP for its training efficiency and label irrelevance. MGP trains the encoder parameters " + }, + { + "bbox": [ + 305, + 438, + 545, + 499 + ], + "type": "inline_equation", + "content": "\\theta_{f}" + }, + { + "bbox": [ + 305, + 438, + 545, + 499 + ], + "type": "text", + "content": " with high ratio masked images and reconstructs the original image by a lightweight decoder " + }, + { + "bbox": [ + 305, + 438, + 545, + 499 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\theta_d}" + }, + { + "bbox": [ + 305, + 438, + 545, + 499 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 370, + 503, + 545, + 517 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 370, + 503, + 545, + 517 + ], + "spans": [ + { + "bbox": [ + 370, + 503, + 545, + 517 + ], + "type": "interline_equation", + "content": "\\hat {\\mathbf {x}} = \\mathcal {D} _ {\\theta_ {d}} \\left(\\mathcal {F} _ {\\theta_ {f}} (\\mathbf {M} \\odot \\mathbf {x})\\right), \\tag {4}", + "image_path": "f8a6c7001ef5f042ca8c6bea11c59aa2b0ca02547e381dd82dfc1c11e5a8d761.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 521, + 545, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 521, + 545, + 557 + ], + "spans": [ + { + "bbox": [ + 305, + 521, + 545, + 557 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 521, + 545, + 557 + ], + "type": "inline_equation", + "content": "\\mathbf{M} \\in \\{0,1\\}^{H \\times W}" + }, + { + "bbox": [ + 305, + 521, + 545, + 557 + ], + "type": "text", + "content": " is a random patch-wise binary mask. Then, we optimize " + }, + { + "bbox": [ + 305, + 521, + 545, + 557 + ], + "type": "inline_equation", + "content": "\\theta_{f}, \\theta_{d}" + }, + { + "bbox": [ + 305, + 521, + 545, + 557 + ], + "type": "text", + "content": " end-to-end via minimizing the mean squared error between " + }, + { + "bbox": [ + 305, + 521, + 545, + 557 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 305, + 521, + 545, + 557 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 521, + 545, + 557 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{x}}" + }, + { + "bbox": [ + 305, + 521, + 545, + 557 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 558, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 558, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 558, + 545, + 714 + ], + "type": "text", + "content": "We adopt MGP for two reasons: 1) It is difficult to train ViTs directly with label supervision (see plain ViT-B performance in Fig. 1) for its convergence difficulty and computation requirement. The DeiT III [55] is hard to catch up with SOTAs in LTR, even with more training epochs, stronger data augmentation, and larger model sizes. 2) The feature extraction ability of MGP is affected slightly by class instance number, compared with previous mixup-based supervision [29,35,80], CL [60] or SCL [12,27,36,83]. Even pretraining on LTR datasets, the transfer performance of MGP is on par with that trained on balanced datasets with comparable total training instances. See transfer results in Tab. 5 and more visualization in Appendix." + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15795" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 173, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 173, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 173, + 85 + ], + "type": "text", + "content": "4.2. Balanced Fine Tuning" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 91, + 287, + 163 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 91, + 287, + 163 + ], + "spans": [ + { + "bbox": [ + 46, + 91, + 287, + 163 + ], + "type": "text", + "content": "In the Balanced Fine-Tuning (BFT) phase, softmax + CE loss has been the standard paradigm for utilizing annotated labels. However, recent research [42, 55, 65] pinpoint that Binary Cross-Entropy (BCE) loss works much well with ViTs and is more convenient when employed with mixup-manners [42, 73, 74], which can be written as:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 59, + 173, + 287, + 216 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 173, + 287, + 216 + ], + "spans": [ + { + "bbox": [ + 59, + 173, + 287, + 216 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {\\mathrm {B C E}} = - \\sum_ {\\mathbf {y} _ {i} \\in \\mathcal {C}} w _ {\\mathbf {y} _ {i}} [ \\mathbb {1} (\\mathbf {y} _ {i}) \\cdot \\log \\sigma (\\mathbf {z} _ {\\mathbf {y} _ {i}}) \\tag {5} \\\\ \\left. + \\left(1 - \\mathbb {1} \\left(\\mathbf {y} _ {i}\\right)\\right) \\cdot \\log \\left(1 - \\sigma \\left(\\mathbf {z} _ {\\mathbf {y} _ {i}}\\right)\\right) \\right], \\\\ \\end{array}", + "image_path": "53488e735a45c1f4022f6455b8a51e3b4dde95221d968252c012e33db3ac9eda.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 227, + 287, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 227, + 287, + 239 + ], + "spans": [ + { + "bbox": [ + 47, + 227, + 287, + 239 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 227, + 287, + 239 + ], + "type": "inline_equation", + "content": "\\sigma (x) = 1 / (1 + e^{-x})" + }, + { + "bbox": [ + 47, + 227, + 287, + 239 + ], + "type": "text", + "content": " indicates the sigmoid operation." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 239, + 287, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 239, + 287, + 312 + ], + "spans": [ + { + "bbox": [ + 46, + 239, + 287, + 312 + ], + "type": "text", + "content": "In LTR, Balanced CE (Eq. 2) improves original CE (Eq. 1) remarkably. However, we observe that it is not directly applicable when it comes to BCE. The logit bias " + }, + { + "bbox": [ + 46, + 239, + 287, + 312 + ], + "type": "inline_equation", + "content": "\\mathcal{B}_{\\mathbf{y}_i}" + }, + { + "bbox": [ + 46, + 239, + 287, + 312 + ], + "type": "text", + "content": " in Thm. 1 leads to an even worse situation. Here, we claim that the proper bias of BCE shall be revised as Thm. 2 when collaborating with BCE in LTR." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 322, + 287, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 322, + 287, + 373 + ], + "spans": [ + { + "bbox": [ + 47, + 322, + 287, + 373 + ], + "type": "text", + "content": "Theorem 2. Logit Bias of Balanced BCE. Let " + }, + { + "bbox": [ + 47, + 322, + 287, + 373 + ], + "type": "inline_equation", + "content": "\\pi_{\\mathbf{y}_i} = n_{\\mathbf{y}_i} / N" + }, + { + "bbox": [ + 47, + 322, + 287, + 373 + ], + "type": "text", + "content": " be the class " + }, + { + "bbox": [ + 47, + 322, + 287, + 373 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_i" + }, + { + "bbox": [ + 47, + 322, + 287, + 373 + ], + "type": "text", + "content": " distribution. If we implement the balanced binary cross-entropy loss via logit adjustment, the bias item of logit " + }, + { + "bbox": [ + 47, + 322, + 287, + 373 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{\\mathbf{y}_i}" + }, + { + "bbox": [ + 47, + 322, + 287, + 373 + ], + "type": "text", + "content": " will be " + }, + { + "bbox": [ + 47, + 322, + 287, + 373 + ], + "type": "inline_equation", + "content": "\\mathcal{B}_{\\mathbf{y}_i}^{\\mathrm{bce}} = \\log \\pi_{\\mathbf{y}_i} - \\log (1 - \\pi_{\\mathbf{y}_i})" + }, + { + "bbox": [ + 47, + 322, + 287, + 373 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 386, + 304, + 451 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 386, + 304, + 451 + ], + "spans": [ + { + "bbox": [ + 47, + 386, + 304, + 451 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {\\text {B a l - B C E}} = - \\sum_ {\\mathbf {y} _ {i} \\in \\mathcal {C}} w _ {i} [ \\mathbb {1} (\\mathbf {y} _ {i}) \\cdot \\log \\frac {1}{1 + e ^ {- [ \\mathbf {z} _ {\\mathbf {y} _ {i}} + \\log \\pi_ {\\mathbf {y} _ {i}} - \\log (1 - \\pi_ {\\mathbf {y} _ {i}}) ]}} \\\\ + (1 - \\mathbb {1} (\\mathbf {y} _ {i})) \\cdot \\log (1 - \\frac {1}{1 + e ^ {- [ \\mathbf {z} _ {\\mathbf {y} _ {i}} + \\log \\pi_ {\\mathbf {y} _ {i}} - \\log (1 - \\pi_ {\\mathbf {y} _ {i}}) ]}}) ] \\tag {6} \\\\ \\end{array}", + "image_path": "32764b1a95908425070f49cbe9e369572ad41b540a871ef3583b67093dccec94.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 452, + 287, + 500 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 452, + 287, + 500 + ], + "spans": [ + { + "bbox": [ + 47, + 452, + 287, + 500 + ], + "type": "text", + "content": "Proof. We regard Binary CE as " + }, + { + "bbox": [ + 47, + 452, + 287, + 500 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 47, + 452, + 287, + 500 + ], + "type": "text", + "content": " binary classification loss. Hence, for the class " + }, + { + "bbox": [ + 47, + 452, + 287, + 500 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_i" + }, + { + "bbox": [ + 47, + 452, + 287, + 500 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 452, + 287, + 500 + ], + "type": "inline_equation", + "content": "\\pi_{\\mathbf{y}_i}" + }, + { + "bbox": [ + 47, + 452, + 287, + 500 + ], + "type": "text", + "content": " indicates positive samples proportion and " + }, + { + "bbox": [ + 47, + 452, + 287, + 500 + ], + "type": "inline_equation", + "content": "1 - \\pi_{\\mathbf{y}_i}" + }, + { + "bbox": [ + 47, + 452, + 287, + 500 + ], + "type": "text", + "content": " indicates negative ones. Here, we start by revising the sigmoid activation function:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 61, + 510, + 287, + 536 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 510, + 287, + 536 + ], + "spans": [ + { + "bbox": [ + 61, + 510, + 287, + 536 + ], + "type": "interline_equation", + "content": "\\sigma \\left(\\mathbf {z} _ {\\mathbf {y} _ {i}}\\right) = \\frac {1}{1 + e ^ {- \\mathbf {z} _ {\\mathbf {y} _ {i}}}} = \\frac {e ^ {0}}{e ^ {0} + e ^ {- \\mathbf {z} _ {\\mathbf {y} _ {i}}}} = \\frac {e ^ {\\mathbf {z} _ {\\mathbf {y} _ {i}}}}{e ^ {\\mathbf {z} _ {\\mathbf {y} _ {i}}} + e ^ {0}} \\tag {7}", + "image_path": "0881915f35d4ba37d874b615206bbdac59adf8bbf2183c9dd1c5e1ccc70ac1c3.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 547, + 287, + 583 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 547, + 287, + 583 + ], + "spans": [ + { + "bbox": [ + 47, + 547, + 287, + 583 + ], + "type": "text", + "content": "If we view Eq. 7 as the binary version of softmax, " + }, + { + "bbox": [ + 47, + 547, + 287, + 583 + ], + "type": "inline_equation", + "content": "e^x (e^0)" + }, + { + "bbox": [ + 47, + 547, + 287, + 583 + ], + "type": "text", + "content": " will be the normalized probability to indicate yes (no). Similar to Eq. 2, we use instance number to balance sigmoid:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 87, + 593, + 287, + 679 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 87, + 593, + 287, + 679 + ], + "spans": [ + { + "bbox": [ + 87, + 593, + 287, + 679 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\hat {\\sigma} \\left(\\mathbf {z} _ {\\mathbf {y} _ {i}}\\right) = \\frac {n _ {\\mathbf {y} _ {i}} \\cdot e ^ {\\mathbf {z} _ {\\mathbf {y} _ {i}}}}{n _ {\\mathbf {y} _ {i}} \\cdot e ^ {\\mathbf {z} _ {\\mathbf {y} _ {i}}} + (N - n _ {\\mathbf {y} _ {i}}) \\cdot e ^ {0}} \\\\ = \\frac {\\pi_ {\\mathbf {y} _ {i}} \\cdot e ^ {\\mathbf {z} _ {\\mathbf {y} _ {i}}}}{\\pi_ {\\mathbf {y} _ {i}} \\cdot e ^ {\\mathbf {z} _ {\\mathbf {y} _ {i}}} + \\left(1 - \\pi_ {\\mathbf {y} _ {i}}\\right) \\cdot e ^ {0}} \\tag {8} \\\\ = \\frac {1}{1 + \\frac {1 - \\pi_ {\\mathbf {y} _ {i}}}{\\pi_ {\\mathbf {y} _ {i}}} \\cdot e ^ {- \\mathbf {z} _ {\\mathbf {y} _ {i}}}} \\\\ \\end{array}", + "image_path": "17649e6a90181c66b82d938033408684d529735f3eb2d0c466d8ace522e0ac2b.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "content": "Considering the log-sum-exp trick for numerical stability, we change the weight of " + }, + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "inline_equation", + "content": "e^{-\\mathbf{z}_{\\mathbf{y}_i}}" + }, + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "content": " to the bias term of " + }, + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{\\mathbf{y}_i}" + }, + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 312, + 90, + 545, + 174 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 90, + 545, + 174 + ], + "spans": [ + { + "bbox": [ + 312, + 90, + 545, + 174 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\hat {\\sigma} (\\mathbf {z} _ {\\mathbf {y} _ {i}}) = \\frac {1}{1 + \\frac {1 - \\pi_ {\\mathbf {y} _ {i}}}{\\pi_ {\\mathbf {y} _ {i}}} \\cdot e ^ {- \\mathbf {z} _ {\\mathbf {y} _ {i}}}} = \\frac {1}{1 + e ^ {- \\mathbf {z} _ {\\mathbf {y} _ {i}} + \\log \\frac {1 - \\pi_ {\\mathbf {y} _ {i}}}{\\pi_ {\\mathbf {y} _ {i}}}}} \\\\ = \\frac {1}{1 + e ^ {- \\mathbf {z} _ {\\mathbf {y} _ {i}} + \\log (1 - \\pi_ {\\mathbf {y} _ {i}}) - \\log \\pi_ {\\mathbf {y} _ {i}}}} \\tag {9} \\\\ = \\frac {1}{1 + e ^ {- [ {\\bf z _ {y}} _ {i} + \\log \\pi_ {{\\bf y} _ {i}} - \\log (1 - \\pi_ {{\\bf y} _ {i}}) ]}} \\\\ \\end{array}", + "image_path": "814a530d14cbe3850944f4d229a7938726a681a55f0f188ae5430a3d02dc43bb.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 182, + 545, + 219 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 182, + 545, + 219 + ], + "spans": [ + { + "bbox": [ + 305, + 182, + 545, + 219 + ], + "type": "text", + "content": "Hence, we derive the bias item of logit " + }, + { + "bbox": [ + 305, + 182, + 545, + 219 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_i" + }, + { + "bbox": [ + 305, + 182, + 545, + 219 + ], + "type": "text", + "content": " shall be " + }, + { + "bbox": [ + 305, + 182, + 545, + 219 + ], + "type": "inline_equation", + "content": "\\mathcal{B}_{\\mathbf{y}_i}^{\\mathrm{bce}} = \\log \\pi_{\\mathbf{y}_i} - \\log (1 - \\pi_{\\mathbf{y}_i})" + }, + { + "bbox": [ + 305, + 182, + 545, + 219 + ], + "type": "text", + "content": ". If we bring Eq. 9 into Binary CE (Eq. 5), we will get the Balanced Binary CE as Eq. 6." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 535, + 220, + 545, + 230 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 535, + 220, + 545, + 230 + ], + "spans": [ + { + "bbox": [ + 535, + 220, + 545, + 230 + ], + "type": "text", + "content": "□" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 231, + 545, + 340 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 231, + 545, + 340 + ], + "spans": [ + { + "bbox": [ + 305, + 231, + 545, + 340 + ], + "type": "text", + "content": "Interpretation. With the additional " + }, + { + "bbox": [ + 305, + 231, + 545, + 340 + ], + "type": "inline_equation", + "content": "-\\log (1 - \\pi_{\\mathbf{y}_i})" + }, + { + "bbox": [ + 305, + 231, + 545, + 340 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 231, + 545, + 340 + ], + "type": "inline_equation", + "content": "\\mathcal{B}_{\\mathbf{y}_i}^{\\mathrm{bce}}" + }, + { + "bbox": [ + 305, + 231, + 545, + 340 + ], + "type": "text", + "content": " keeps consistent character with " + }, + { + "bbox": [ + 305, + 231, + 545, + 340 + ], + "type": "inline_equation", + "content": "\\mathcal{B}_{\\mathbf{y}_i}^{\\mathrm{ce}}" + }, + { + "bbox": [ + 305, + 231, + 545, + 340 + ], + "type": "text", + "content": " w.r.t. " + }, + { + "bbox": [ + 305, + 231, + 545, + 340 + ], + "type": "inline_equation", + "content": "\\pi_{\\mathbf{y}_i}" + }, + { + "bbox": [ + 305, + 231, + 545, + 340 + ], + "type": "text", + "content": ". Similar to " + }, + { + "bbox": [ + 305, + 231, + 545, + 340 + ], + "type": "inline_equation", + "content": "\\mathcal{B}_{\\mathbf{y}_i}^{\\mathrm{ce}}" + }, + { + "bbox": [ + 305, + 231, + 545, + 340 + ], + "type": "text", + "content": ", it enlarges the margins to increase the difficulty of the tail (smaller " + }, + { + "bbox": [ + 305, + 231, + 545, + 340 + ], + "type": "inline_equation", + "content": "\\pi_{\\mathbf{y}_i}" + }, + { + "bbox": [ + 305, + 231, + 545, + 340 + ], + "type": "text", + "content": "). However, " + }, + { + "bbox": [ + 305, + 231, + 545, + 340 + ], + "type": "inline_equation", + "content": "\\mathcal{B}_{\\mathbf{y}_i}^{\\mathrm{bce}}" + }, + { + "bbox": [ + 305, + 231, + 545, + 340 + ], + "type": "text", + "content": " further reduces the head (larger " + }, + { + "bbox": [ + 305, + 231, + 545, + 340 + ], + "type": "inline_equation", + "content": "\\pi_{\\mathbf{y}_i}" + }, + { + "bbox": [ + 305, + 231, + 545, + 340 + ], + "type": "text", + "content": ") inter-class distances with larger positive values. Notice that BCE is not class-wise mutually exclusive, and the smaller head inter-class distance helps the networks focus more on the tail's contributions. See visualizations and more in-depth analysis in Appendix." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 340, + 545, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 340, + 545, + 376 + ], + "spans": [ + { + "bbox": [ + 305, + 340, + 545, + 376 + ], + "type": "text", + "content": "Through Bayesian theory [70], we can further extend the proposed Balanced BCE if the test distribution is available as " + }, + { + "bbox": [ + 305, + 340, + 545, + 376 + ], + "type": "inline_equation", + "content": "\\pi^t" + }, + { + "bbox": [ + 305, + 340, + 545, + 376 + ], + "type": "text", + "content": ", which can be summarized as the following theorem:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 384, + 545, + 433 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 384, + 545, + 433 + ], + "spans": [ + { + "bbox": [ + 306, + 384, + 545, + 433 + ], + "type": "text", + "content": "Theorem 3. Logit Bias of Balanced BCE with Test Prior. Let " + }, + { + "bbox": [ + 306, + 384, + 545, + 433 + ], + "type": "inline_equation", + "content": "\\pi_{\\mathbf{y}_i}^s" + }, + { + "bbox": [ + 306, + 384, + 545, + 433 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 384, + 545, + 433 + ], + "type": "inline_equation", + "content": "\\pi_{\\mathbf{y}_i}^t" + }, + { + "bbox": [ + 306, + 384, + 545, + 433 + ], + "type": "text", + "content": " be the label " + }, + { + "bbox": [ + 306, + 384, + 545, + 433 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_i" + }, + { + "bbox": [ + 306, + 384, + 545, + 433 + ], + "type": "text", + "content": " training and test distribution. If we implement the balanced cross-entropy loss via logit adjustment, the bias item of logit " + }, + { + "bbox": [ + 306, + 384, + 545, + 433 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{\\mathbf{y}_i}" + }, + { + "bbox": [ + 306, + 384, + 545, + 433 + ], + "type": "text", + "content": " will be:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 441, + 552, + 457 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 441, + 552, + 457 + ], + "spans": [ + { + "bbox": [ + 306, + 441, + 552, + 457 + ], + "type": "interline_equation", + "content": "\\mathcal {B} _ {\\mathbf {y} _ {i}} ^ {\\mathrm {b c e}} = \\left(\\log \\pi_ {\\mathbf {y} _ {i}} ^ {s} - \\log \\pi_ {\\mathbf {y} _ {i}} ^ {t}\\right) - \\left(\\log \\left(1 - \\pi_ {\\mathbf {y} _ {i}} ^ {s}\\right) - \\log \\left(1 - \\pi_ {\\mathbf {y} _ {i}} ^ {t}\\right)\\right)", + "image_path": "b4b812d2f61cd3ab9dc00af0fb0f21b8cdda1e1d6f881a616d1fe4bd9753bb3d.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 464, + 482, + 477 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 464, + 482, + 477 + ], + "spans": [ + { + "bbox": [ + 306, + 464, + 482, + 477 + ], + "type": "text", + "content": "Proof. See detailed derivation in Appendix." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 485, + 544, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 485, + 544, + 509 + ], + "spans": [ + { + "bbox": [ + 305, + 485, + 544, + 509 + ], + "type": "text", + "content": "Notice that for the balanced test dataset, " + }, + { + "bbox": [ + 305, + 485, + 544, + 509 + ], + "type": "inline_equation", + "content": "\\pi_{\\mathbf{y}_i}^t = 1 / C" + }, + { + "bbox": [ + 305, + 485, + 544, + 509 + ], + "type": "text", + "content": ". Hence, the logit bias in Thm.3 will be:" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 517, + 551, + 566 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 517, + 551, + 566 + ], + "spans": [ + { + "bbox": [ + 306, + 517, + 551, + 566 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {B} _ {\\mathbf {y} _ {i}} ^ {\\mathrm {b c e}} = \\left(\\log \\pi_ {\\mathbf {y} _ {i}} ^ {\\mathrm {s}} - \\log 1 / C\\right) - \\left(\\log \\left(1 - \\pi_ {\\mathbf {y} _ {i}} ^ {\\mathrm {s}}\\right) - \\log \\left(\\frac {C - 1}{C}\\right)\\right) \\\\ = \\log \\pi_ {\\mathbf {y} _ {i}} ^ {s} - \\log \\left(1 - \\pi_ {\\mathbf {y} _ {i}} ^ {s}\\right) + \\log (C - 1) \\tag {10} \\\\ \\end{array}", + "image_path": "661edb7be0c73aebe2924e60b4501a24fcdf8b72c194f55a9fa388602dc167dc.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 305, + 567, + 545, + 627 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 567, + 545, + 627 + ], + "spans": [ + { + "bbox": [ + 305, + 567, + 545, + 627 + ], + "type": "text", + "content": "Compared with the conclusion of Thm. 2, we get an extra term " + }, + { + "bbox": [ + 305, + 567, + 545, + 627 + ], + "type": "inline_equation", + "content": "\\log (C - 1)" + }, + { + "bbox": [ + 305, + 567, + 545, + 627 + ], + "type": "text", + "content": ". From the convex objectives optimization view, there is no expected difference between Thm. 2 and Eq. 10. However, it will increase ViTs' training stability remarkably, especially when the class number " + }, + { + "bbox": [ + 305, + 567, + 545, + 627 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 305, + 567, + 545, + 627 + ], + "type": "text", + "content": " gets larger." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 306, + 635, + 366, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 635, + 366, + 647 + ], + "spans": [ + { + "bbox": [ + 306, + 635, + 366, + 647 + ], + "type": "text", + "content": "4.3. Pipeline" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 305, + 653, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 653, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 653, + 545, + 713 + ], + "type": "text", + "content": "We describe LiVT training pipeline precisely in Alg. 1, which can be divided into two stages, i.e., MGP and BFT. Specifically, in the MGP stage, we adopt simple data augmentation " + }, + { + "bbox": [ + 305, + 653, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{A}_{pt}" + }, + { + "bbox": [ + 305, + 653, + 545, + 713 + ], + "type": "text", + "content": " and more training epochs " + }, + { + "bbox": [ + 305, + 653, + 545, + 713 + ], + "type": "inline_equation", + "content": "T_{pt}" + }, + { + "bbox": [ + 305, + 653, + 545, + 713 + ], + "type": "text", + "content": " to update the parameters of " + }, + { + "bbox": [ + 305, + 653, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 305, + 653, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 653, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 305, + 653, + 545, + 713 + ], + "type": "text", + "content": ". In the BFT stage, the decoder " + }, + { + "bbox": [ + 305, + 653, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15796" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "code", + "bbox": [ + 48, + 87, + 287, + 415 + ], + "blocks": [ + { + "bbox": [ + 48, + 72, + 200, + 84 + ], + "lines": [ + { + "bbox": [ + 48, + 72, + 200, + 84 + ], + "spans": [ + { + "bbox": [ + 48, + 72, + 200, + 84 + ], + "type": "text", + "content": "Algorithm 1 LiVT Training Pipeline." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 48, + 87, + 287, + 415 + ], + "lines": [ + { + "bbox": [ + 48, + 87, + 287, + 415 + ], + "spans": [ + { + "bbox": [ + 48, + 87, + 287, + 415 + ], + "type": "text", + "content": "Input: " + }, + { + "bbox": [ + 48, + 87, + 287, + 415 + ], + "type": "inline_equation", + "content": "\\mathcal{D},\\mathcal{F},\\mathcal{W},\\mathcal{D},T_{pt},T_{ft},A_{pt},A_{ft},\\pi_{\\mathbf{y}_i},\\tau" + }, + { + "bbox": [ + 48, + 87, + 287, + 415 + ], + "type": "text", + "content": " \nOutput: Optimized " + }, + { + "bbox": [ + 48, + 87, + 287, + 415 + ], + "type": "inline_equation", + "content": "\\theta_f,\\theta_w" + }, + { + "bbox": [ + 48, + 87, + 287, + 415 + ], + "type": "text", + "content": " \n1: Initialize " + }, + { + "bbox": [ + 48, + 87, + 287, + 415 + ], + "type": "inline_equation", + "content": "\\theta_f,\\theta_d" + }, + { + "bbox": [ + 48, + 87, + 287, + 415 + ], + "type": "text", + "content": " randomly. MGP Stage \n2: for " + }, + { + "bbox": [ + 48, + 87, + 287, + 415 + ], + "type": "inline_equation", + "content": "t = 1" + }, + { + "bbox": [ + 48, + 87, + 287, + 415 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 48, + 87, + 287, + 415 + ], + "type": "inline_equation", + "content": "T_{pt}" + }, + { + "bbox": [ + 48, + 87, + 287, + 415 + ], + "type": "text", + "content": " do \n3: for " + }, + { + "bbox": [ + 48, + 87, + 287, + 415 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{x},\\mathbf{y}\\}" + }, + { + "bbox": [ + 48, + 87, + 287, + 415 + ], + "type": "text", + "content": " sampled from " + }, + { + "bbox": [ + 48, + 87, + 287, + 415 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 48, + 87, + 287, + 415 + ], + "type": "text", + "content": " do \n4: " + }, + { + "bbox": [ + 48, + 87, + 287, + 415 + ], + "type": "inline_equation", + "content": "\\mathbf{x}:= \\mathcal{A}_{pt}(\\mathbf{x})" + }, + { + "bbox": [ + 48, + 87, + 287, + 415 + ], + "type": "text", + "content": " \n5: " + }, + { + "bbox": [ + 48, + 87, + 287, + 415 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{x}} = \\mathcal{D}(\\mathcal{F}(\\mathbf{M}\\odot \\mathbf{x}\\mid \\theta_f)\\mid \\theta_d)" + }, + { + "bbox": [ + 48, + 87, + 287, + 415 + ], + "type": "text", + "content": " \n6: " + }, + { + "bbox": [ + 48, + 87, + 287, + 415 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{MSE}(\\hat{\\mathbf{x}},\\mathbf{x}) = ||\\hat{\\mathbf{x}} -\\mathbf{x}||_2" + }, + { + "bbox": [ + 48, + 87, + 287, + 415 + ], + "type": "text", + "content": " \n7: " + }, + { + "bbox": [ + 48, + 87, + 287, + 415 + ], + "type": "inline_equation", + "content": "\\{\\theta_f,\\theta_d\\} \\gets \\{\\theta_f,\\theta_d\\} -\\alpha \\nabla_{\\{\\theta_f,\\theta_d\\}}\\cdot \\mathcal{L}_{MSE}(\\hat{\\mathbf{x}},\\mathbf{x})" + }, + { + "bbox": [ + 48, + 87, + 287, + 415 + ], + "type": "text", + "content": " \n8: end for \n9: end for \n10: Initialize " + }, + { + "bbox": [ + 48, + 87, + 287, + 415 + ], + "type": "inline_equation", + "content": "\\theta_w" + }, + { + "bbox": [ + 48, + 87, + 287, + 415 + ], + "type": "text", + "content": " randomly. BFT Stage \n11: Calculate logit bias " + }, + { + "bbox": [ + 48, + 87, + 287, + 415 + ], + "type": "inline_equation", + "content": "\\mathcal{B}_{\\mathbf{y}_i}^{\\mathrm{bce}}" + }, + { + "bbox": [ + 48, + 87, + 287, + 415 + ], + "type": "text", + "content": " via Eq. 10. \n12: for " + }, + { + "bbox": [ + 48, + 87, + 287, + 415 + ], + "type": "inline_equation", + "content": "t = 1" + }, + { + "bbox": [ + 48, + 87, + 287, + 415 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 48, + 87, + 287, + 415 + ], + "type": "inline_equation", + "content": "T_{ft}" + }, + { + "bbox": [ + 48, + 87, + 287, + 415 + ], + "type": "text", + "content": " do \n13: for " + }, + { + "bbox": [ + 48, + 87, + 287, + 415 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{x},\\mathbf{y}\\}" + }, + { + "bbox": [ + 48, + 87, + 287, + 415 + ], + "type": "text", + "content": " sampled from " + }, + { + "bbox": [ + 48, + 87, + 287, + 415 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 48, + 87, + 287, + 415 + ], + "type": "text", + "content": " do \n14: " + }, + { + "bbox": [ + 48, + 87, + 287, + 415 + ], + "type": "inline_equation", + "content": "\\mathbf{x}:= \\mathcal{A}_{ft}(\\mathbf{x})" + }, + { + "bbox": [ + 48, + 87, + 287, + 415 + ], + "type": "text", + "content": " \n15: " + }, + { + "bbox": [ + 48, + 87, + 287, + 415 + ], + "type": "inline_equation", + "content": "\\mathbf{v} = \\mathcal{F}(\\mathbf{x}\\mid \\theta_f)" + }, + { + "bbox": [ + 48, + 87, + 287, + 415 + ], + "type": "text", + "content": " \n16: " + }, + { + "bbox": [ + 48, + 87, + 287, + 415 + ], + "type": "inline_equation", + "content": "\\mathbf{z} = \\mathcal{W}(\\mathbf{v}\\mid \\theta_w) + \\tau \\cdot \\mathcal{B}^{\\mathrm{bce}}" + }, + { + "bbox": [ + 48, + 87, + 287, + 415 + ], + "type": "text", + "content": " \n17: Calculate " + }, + { + "bbox": [ + 48, + 87, + 287, + 415 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{BCE}" + }, + { + "bbox": [ + 48, + 87, + 287, + 415 + ], + "type": "text", + "content": " via Eq. 5 with calibrated z. \n18: " + }, + { + "bbox": [ + 48, + 87, + 287, + 415 + ], + "type": "inline_equation", + "content": "\\{\\theta_f,\\theta_w\\} \\leftarrow \\{\\theta_f,\\theta_w\\} -\\alpha \\nabla_{\\{\\theta_f,\\theta_w\\}}\\cdot \\mathcal{L}_{BCE}" + }, + { + "bbox": [ + 48, + 87, + 287, + 415 + ], + "type": "text", + "content": " \n19: end for \n20: end for" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "code_body" + } + ], + "index": 1, + "sub_type": "algorithm" + }, + { + "bbox": [ + 46, + 421, + 289, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 421, + 289, + 506 + ], + "spans": [ + { + "bbox": [ + 46, + 421, + 289, + 506 + ], + "type": "text", + "content": "is discarded. We adopt more general data augmentations " + }, + { + "bbox": [ + 46, + 421, + 289, + 506 + ], + "type": "inline_equation", + "content": "\\mathcal{A}_{ft}" + }, + { + "bbox": [ + 46, + 421, + 289, + 506 + ], + "type": "text", + "content": " to finetune a few epochs " + }, + { + "bbox": [ + 46, + 421, + 289, + 506 + ], + "type": "inline_equation", + "content": "T_{ft}" + }, + { + "bbox": [ + 46, + 421, + 289, + 506 + ], + "type": "text", + "content": ". As shown in Alg. 1 Line 16, we add a hyper-parameter " + }, + { + "bbox": [ + 46, + 421, + 289, + 506 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 46, + 421, + 289, + 506 + ], + "type": "text", + "content": " to control the influence of the proposed bias. It is worth noticing that the proposed logit bias will add negligible computational costs. With Balanced Binary CE loss, we further optimize the parameters of " + }, + { + "bbox": [ + 46, + 421, + 289, + 506 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 46, + 421, + 289, + 506 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 421, + 289, + 506 + ], + "type": "inline_equation", + "content": "\\mathcal{W}" + }, + { + "bbox": [ + 46, + 421, + 289, + 506 + ], + "type": "text", + "content": " to achieve satisfying networks." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 517, + 123, + 532 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 517, + 123, + 532 + ], + "spans": [ + { + "bbox": [ + 47, + 517, + 123, + 532 + ], + "type": "text", + "content": "5. Experiment" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 538, + 110, + 550 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 538, + 110, + 550 + ], + "spans": [ + { + "bbox": [ + 47, + 538, + 110, + 550 + ], + "type": "text", + "content": "5.1. Datasets" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 557, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 557, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 557, + 289, + 715 + ], + "type": "text", + "content": "CIFAR-10/100-LT are created from the original CIFAR datasets [32], where " + }, + { + "bbox": [ + 46, + 557, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 46, + 557, + 289, + 715 + ], + "type": "text", + "content": " controls the data imbalance degree. Following previous works [4, 12, 70, 81], we employ imbalance factors " + }, + { + "bbox": [ + 46, + 557, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\{100, 10\\}" + }, + { + "bbox": [ + 46, + 557, + 289, + 715 + ], + "type": "text", + "content": " in our experiments. ImageNet-LT/BAL are both the subsets of popular ImageNet [52]. The LT version [44] (" + }, + { + "bbox": [ + 46, + 557, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\gamma = 256" + }, + { + "bbox": [ + 46, + 557, + 289, + 715 + ], + "type": "text", + "content": ") is selected following the Pareto distribution with power value " + }, + { + "bbox": [ + 46, + 557, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\alpha = 6" + }, + { + "bbox": [ + 46, + 557, + 289, + 715 + ], + "type": "text", + "content": ", which contains " + }, + { + "bbox": [ + 46, + 557, + 289, + 715 + ], + "type": "inline_equation", + "content": "115.8\\mathrm{K}" + }, + { + "bbox": [ + 46, + 557, + 289, + 715 + ], + "type": "text", + "content": " images from 1,000 categories. We build the BAL version (" + }, + { + "bbox": [ + 46, + 557, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\gamma = 1" + }, + { + "bbox": [ + 46, + 557, + 289, + 715 + ], + "type": "text", + "content": ") by sampling 116 images per category to exploit how ViTs perform given a similar number of training images. Notice that both LT and BAL adopt the same validation dataset. iNaturalist 2018 [57, 63] (iNat18 for short) is a species classification dataset, which contains " + }, + { + "bbox": [ + 46, + 557, + 289, + 715 + ], + "type": "inline_equation", + "content": "437.5\\mathrm{K}" + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 308, + 102, + 545, + 388 + ], + "blocks": [ + { + "bbox": [ + 305, + 70, + 545, + 93 + ], + "lines": [ + { + "bbox": [ + 305, + 70, + 545, + 93 + ], + "spans": [ + { + "bbox": [ + 305, + 70, + 545, + 93 + ], + "type": "text", + "content": "Table 2. Top-1 accuracy " + }, + { + "bbox": [ + 305, + 70, + 545, + 93 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 305, + 70, + 545, + 93 + ], + "type": "text", + "content": " of ResNet50 on ImageNet-LT. " + }, + { + "bbox": [ + 305, + 70, + 545, + 93 + ], + "type": "inline_equation", + "content": "\\dagger" + }, + { + "bbox": [ + 305, + 70, + 545, + 93 + ], + "type": "text", + "content": " indicates results with ResNeXt50. " + }, + { + "bbox": [ + 305, + 70, + 545, + 93 + ], + "type": "inline_equation", + "content": "*" + }, + { + "bbox": [ + 305, + 70, + 545, + 93 + ], + "type": "text", + "content": " training with 384 resolution." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 102, + 545, + 388 + ], + "lines": [ + { + "bbox": [ + 308, + 102, + 545, + 388 + ], + "spans": [ + { + "bbox": [ + 308, + 102, + 545, + 388 + ], + "type": "table", + "html": "
MethodRef.ManyMed.FewAcc
CE [13]CVPR 1964.033.85.841.6
LDAM [4]NeurIPS 1960.446.930.749.8
c-RT [29]ICLR 2061.846.227.349.6
τ-Norm [29]ICLR 2059.146.930.749.4
Causal [54]NeurIPS 2062.748.831.651.8
Logit Adj. [47]ICLR 2161.147.527.650.1
RIDE(4E)† [61]ICLR 2168.353.535.956.8
MiSLAS [80]CVPR 2162.950.734.352.7
DisAlign [75]CVPR 2161.352.231.452.9
ACE† [3]ICCV 2171.754.623.556.6
PaCo† [12]ICCV 2168.056.437.258.2
TADE† [77]ICCV 2166.557.043.558.8
TSC [36]CVPR 2263.549.730.452.4
GCL [35]CVPR 2263.052.737.154.5
TLC [33]CVPR 2268.955.740.855.1
BCL† [83]CVPR 2267.654.636.657.2
NCL [34]CVPR 2267.355.439.057.7
SAFA [23]ECCV 2263.849.933.453.1
DOC [58]ECCV 2265.152.834.255.0
DLSA [69]ECCV 2267.854.538.857.5
ViT-B training from scratch
ViT [15]ICLR 2150.523.56.931.6
MAE [18]CVPR 2274.748.219.454.5
DeiT [55]ECCV 2270.440.912.848.4
LiVT73.656.441.060.9
LiVT *76.459.742.763.8
", + "image_path": "8c5e5c4344343fb01f9291f5de05ecd5c4480aedd12d7e428cc70bbefb418aa2.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 395, + 545, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 395, + 545, + 479 + ], + "spans": [ + { + "bbox": [ + 304, + 395, + 545, + 479 + ], + "type": "text", + "content": "images from 8,142 categories and suffers from extremely LTR problem " + }, + { + "bbox": [ + 304, + 395, + 545, + 479 + ], + "type": "inline_equation", + "content": "(\\gamma = 512)" + }, + { + "bbox": [ + 304, + 395, + 545, + 479 + ], + "type": "text", + "content": ". Places-LT is a synthetic long-tail variant of the large-scale scene classification dataset Places [82]. With 62.5K images from 365 categories, its class cardinality ranges from 5 to 4,980 " + }, + { + "bbox": [ + 304, + 395, + 545, + 479 + ], + "type": "inline_equation", + "content": "(\\gamma = 996)" + }, + { + "bbox": [ + 304, + 395, + 545, + 479 + ], + "type": "text", + "content": ". All datasets adopt the official validation images for fair comparisons. See detailed dataset information in Appendix." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 490, + 416, + 503 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 490, + 416, + 503 + ], + "spans": [ + { + "bbox": [ + 305, + 490, + 416, + 503 + ], + "type": "text", + "content": "5.2. Implement Details" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 510, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 547, + 714 + ], + "type": "text", + "content": "For image classification on main benchmarks, we adopt ViT-Base-16 [15] as the backbone and ViT-Tiny / Small [55] ViT-Large [15] for the ablation study. All models are trained with AdamW optimizer [46] with " + }, + { + "bbox": [ + 304, + 510, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\beta s = \\{0.9, 0.95\\}" + }, + { + "bbox": [ + 304, + 510, + 547, + 714 + ], + "type": "text", + "content": ". The effective batch size is 4,096 (MGP) / 1,024 (BFT). Vanilla ViTs [15], DeiT III [55] and MAE [18] are all trained 800 epochs because ViTs require longer training time to converge. Following previous work [18], LiVT is pretrained 800 epochs with the mask ratio 0.75 and finetuned 100(50) epochs for ViT-T/S/B(L). We train all models with RandAug(9, 0.5) [11], mixup (0.8) and cutmix (1.0). All experiments set " + }, + { + "bbox": [ + 304, + 510, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\tau \\equiv 1" + }, + { + "bbox": [ + 304, + 510, + 547, + 714 + ], + "type": "text", + "content": ". For fair comparisons, we re-implement [4, 13, 22, 50, 51] with ViTs in the same settings. Following [44], we report Top-1 accuracy and three groups' accuracy: Many-shot (" + }, + { + "bbox": [ + 304, + 510, + 547, + 714 + ], + "type": "inline_equation", + "content": ">100" + }, + { + "bbox": [ + 304, + 510, + 547, + 714 + ], + "type": "text", + "content": " images), Medium-shot (" + }, + { + "bbox": [ + 304, + 510, + 547, + 714 + ], + "type": "inline_equation", + "content": "20\\sim 100" + }, + { + "bbox": [ + 304, + 510, + 547, + 714 + ], + "type": "text", + "content": " images) and Few-shot (" + }, + { + "bbox": [ + 304, + 510, + 547, + 714 + ], + "type": "inline_equation", + "content": "<20" + }, + { + "bbox": [ + 304, + 510, + 547, + 714 + ], + "type": "text", + "content": " images). Besides, we report the Expected Calibration Error (ECE) and Maximum Cali" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "15797" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 49, + 102, + 288, + 427 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 287, + 93 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 287, + 93 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 287, + 93 + ], + "type": "text", + "content": "Table 3. Top-1 accuracy " + }, + { + "bbox": [ + 47, + 70, + 287, + 93 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 47, + 70, + 287, + 93 + ], + "type": "text", + "content": " of ResNet50 on iNaturalist 2018. " + }, + { + "bbox": [ + 47, + 70, + 287, + 93 + ], + "type": "inline_equation", + "content": "\\ast" + }, + { + "bbox": [ + 47, + 70, + 287, + 93 + ], + "type": "text", + "content": " training with 384 resolution." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 49, + 102, + 288, + 427 + ], + "lines": [ + { + "bbox": [ + 49, + 102, + 288, + 427 + ], + "spans": [ + { + "bbox": [ + 49, + 102, + 288, + 427 + ], + "type": "table", + "html": "
MethodRef.ManyMed.FewAcc
CE [13]CVPR 1972.263.057.261.7
OLTR [44]CVPR 1959.064.164.963.9
c-RT [29]ICLR 2069.066.063.265.2
τ-Norm [29]ICLR 2065.665.365.965.6
LWS [29]ICLR 2065.066.365.565.9
BBN [81]CVPR 2061.873.666.969.6
BS [51]ICLR 2170.070.269.970.0
RIDE(4E) [61]ICLR 2170.972.573.172.6
DisAlign [75]CVPR 2169.071.170.270.6
MiSLAS [80]CVPR 2173.272.470.471.6
DiVE [21]ICCV 2170.670.067.669.1
ACE(4E) [3]ICCV 21---72.9
TADE [77]ICCV 2174.472.573.172.9
PaCo [12]ICCV 2170.472.873.673.2
ALA [79]AAAI 2271.370.870.470.7
TSC [36]CVPR 2272.670.667.869.7
LTR-WD [1]CVPR 2271.270.469.770.2
GCL [35]CVPR 2267.571.371.571.0
BCL [83]CVPR 2266.771.070.770.4
NCL [34]CVPR 2272.074.973.874.2
DOC [58]ECCV 2272.871.770.071.0
DLSA [69]ECCV 22---72.8
ViT-B training from scratch
ViT [15]ICLR 2165.455.350.954.6
MAE [18]CVPR 2279.670.865.069.4
DeiT [55]ECCV 2272.962.855.861.0
LiVT-78.976.574.876.1
LiVT*-83.281.579.781.0
", + "image_path": "9192638162a3463dd8ae95059a3aeb13678d7581a680903d2420d5c9a8579175.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 47, + 434, + 287, + 460 + ], + "lines": [ + { + "bbox": [ + 47, + 434, + 287, + 460 + ], + "spans": [ + { + "bbox": [ + 47, + 434, + 287, + 460 + ], + "type": "text", + "content": "bration Error (MCE) to quantify the predictive uncertainty [17]. See detailed implementation settings in Appendix." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 471, + 203, + 484 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 471, + 203, + 484 + ], + "spans": [ + { + "bbox": [ + 47, + 471, + 203, + 484 + ], + "type": "text", + "content": "5.3. Comparison with Prior Arts" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 491, + 287, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 491, + 287, + 552 + ], + "spans": [ + { + "bbox": [ + 46, + 491, + 287, + 552 + ], + "type": "text", + "content": "We conduct comprehensive experiments with ViT-B-16 on ImageNet-LT, iNat18, and Place-LT benchmarks. LiVT successfully trains it from scratch without any additional data pretraining and outperforms ResNet50, ResNeXt50 and ResNet152 conspicuously." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "text", + "content": "Comparison on ImageNet-LT. Tab. 2 shows the experimental comparison results with recent SOTA methods on ImageNet-LT. The training resolution of LiVT is " + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "inline_equation", + "content": "224 / 224" + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "text", + "content": " for MGP/BFT. Based on the model ensemble, multi-expert methods like RIDE [61], TADE [77], and NCL [34] exhibit powerful preference with heavier model size compared to baseline. The CL-based methods (PaCo [12], TSC [36], BCL [83]) also achieve satisfying results with larger batches and longer training epochs. However, our LiVT has shown superior performance without bells and whistles and outperforms them consistently on all metrics while training ViTs from scratch. Notice that LiVT gains more performance " + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "inline_equation", + "content": "(63.8\\%)" + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "text", + "content": " vs " + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "inline_equation", + "content": "60.9\\%" + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "text", + "content": " with higher image resolu" + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 308, + 102, + 547, + 392 + ], + "blocks": [ + { + "bbox": [ + 305, + 70, + 545, + 94 + ], + "lines": [ + { + "bbox": [ + 305, + 70, + 545, + 94 + ], + "spans": [ + { + "bbox": [ + 305, + 70, + 545, + 94 + ], + "type": "text", + "content": "Table 4. Top-1 accuracy " + }, + { + "bbox": [ + 305, + 70, + 545, + 94 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 305, + 70, + 545, + 94 + ], + "type": "text", + "content": " of ResNet152 (with ImageNet-1K pretrained weight) on Places-LT. " + }, + { + "bbox": [ + 305, + 70, + 545, + 94 + ], + "type": "inline_equation", + "content": "\\ast" + }, + { + "bbox": [ + 305, + 70, + 545, + 94 + ], + "type": "text", + "content": " training with 384 resolution." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 102, + 547, + 392 + ], + "lines": [ + { + "bbox": [ + 308, + 102, + 547, + 392 + ], + "spans": [ + { + "bbox": [ + 308, + 102, + 547, + 392 + ], + "type": "table", + "html": "
MethodRef.ManyMed.FewAcc
CE [13]CVPR 1945.727.38.230.2
Focal [38]ICCV 1741.134.822.434.6
Range [76]CVPR 1741.135.423.235.1
OLTR [44]CVPR 1944.737.025.335.9
FSA [10]ECCV 2042.837.522.736.4
LWS [29]ICLR 2040.639.128.637.6
Causal [54]NeurIPS 2023.835.840.432.4
BS [51]NeurIPS 2042.039.330.538.6
DisAlign [75]CVPR 2140.442.430.139.3
LADE [22]CVPR 2142.839.031.238.8
RSG [59]CVPR 2141.941.432.039.3
TADE [77]ICCV 2143.142.433.240.9
PaCo [12]ICCV 2136.147.935.341.2
ALA [79]AAAI 2243.940.132.940.1
NCL [34]CVPR 22---41.8
BF [24]CVPR 2244.043.133.741.6
CKT [48]CVPR 2241.641.435.140.2
GCL [35]CVPR 22---40.6
Bread [40]ECCV 2240.641.033.439.3
ViT-B training from scratch
MAE [18]CVPR 2248.924.68.730.3
DeiT [55]ECCV 2251.631.09.434.2
LiVT-48.140.627.540.8
LiVT*-50.742.427.942.6
", + "image_path": "32088e2edec3853945604b33fac36d4ab91df39f8ffc668bf12470b78ae7c39e.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 305, + 395, + 545, + 440 + ], + "lines": [ + { + "bbox": [ + 305, + 395, + 545, + 440 + ], + "spans": [ + { + "bbox": [ + 305, + 395, + 545, + 440 + ], + "type": "text", + "content": "Table 5. The transfer performance of ViT-B (resolution " + }, + { + "bbox": [ + 305, + 395, + 545, + 440 + ], + "type": "inline_equation", + "content": "224\\times 224" + }, + { + "bbox": [ + 305, + 395, + 545, + 440 + ], + "type": "text", + "content": ") on iNat18 dataset. D-PT represents the pretrain datasets. BAL and LT have similar amounts of data and contribute to similar transfer performance, which means MGP is robust to data distribution." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 308, + 449, + 545, + 515 + ], + "blocks": [ + { + "bbox": [ + 308, + 449, + 545, + 515 + ], + "lines": [ + { + "bbox": [ + 308, + 449, + 545, + 515 + ], + "spans": [ + { + "bbox": [ + 308, + 449, + 545, + 515 + ], + "type": "table", + "html": "
D-PTLossManyMed.FewAccECEMCE
BALCE63.757.152.455.91.23.4
LTCE64.557.552.756.41.23.1
BALBal-BCE53.358.860.759.00.81.6
LTBal-BCE56.560.861.660.71.02.9
", + "image_path": "1b4e1076c1a4421d81439128e85bc1c2a7a1a028aa85899a595746d4ea01f2af.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 521, + 545, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 521, + 545, + 569 + ], + "spans": [ + { + "bbox": [ + 305, + 521, + 545, + 569 + ], + "type": "text", + "content": "tion in the BFT stage, which is consistent with the observations in [43, 55, 56]. Notice that LiVT improves the iNat18 dataset most significantly because BCE mitigates fine-grained problems as well [64]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 575, + 545, + 682 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 575, + 545, + 682 + ], + "spans": [ + { + "bbox": [ + 304, + 575, + 545, + 682 + ], + "type": "text", + "content": "Comparison on iNaturalist 2018. Tab. 3 lists experimental results on iNaturalist 2018. The training resolution of LiVT is 128 / 224 for MGP/BFT. LiVT consistently surpasses recent SOTA methods like PcCo [12], NCL [34] and DLSA [69]. Unlike most LTR methods, our LiVT improves all groups' Acc without sacrificing many-shot performance. Compared to ensemble NCL " + }, + { + "bbox": [ + 304, + 575, + 545, + 682 + ], + "type": "inline_equation", + "content": "(3\\times)" + }, + { + "bbox": [ + 304, + 575, + 545, + 682 + ], + "type": "text", + "content": ", LiVT surpasses it by " + }, + { + "bbox": [ + 304, + 575, + 545, + 682 + ], + "type": "inline_equation", + "content": "1.9\\%" + }, + { + "bbox": [ + 304, + 575, + 545, + 682 + ], + "type": "text", + "content": " (6.8% higher resolution) with comparable model size, which verifies the effectiveness of LiVT." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 689, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 715 + ], + "type": "text", + "content": "Comparison on Places-LT. Tab. 4 summarizes the experimental results on Places-LT. All LTR proposals adopt" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15798" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 85, + 97, + 509, + 300 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 545, + 93 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 545, + 93 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 545, + 93 + ], + "type": "text", + "content": "Table 6. Ablation study of the proposed bias (c.f. Eq. 10) on CE / BCE. All models are trained on ImageNet-LT with the same settings. Our Bal-BCE ameliorates the original BCE by a large margin in all aspects, which is consistent with CE and Bal-CE." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 85, + 97, + 509, + 300 + ], + "lines": [ + { + "bbox": [ + 85, + 97, + 509, + 300 + ], + "spans": [ + { + "bbox": [ + 85, + 97, + 509, + 300 + ], + "type": "table", + "html": "
ModelSizeLossMany ↑Med. ↑Few ↑Acc ↑ECE ↓MCE ↓
ViT-Tiny [55]5.7MCE56.129.210.537.03.76.1
Bal-CE48.8 (-7.3)39.2 (+10.0)28.1 (+17.6)41.4 (+4.4)2.6 (-1.1)4.6 (-1.6)
BCE42.111.10.921.62.98.6
Bal-BCE50.6 (+8.4)37.2 (+26.1)26.1 (+25.2)40.8 (+19.2)3.1 (+0.1)6.8 (-1.8)
ViT-Small [55]22MCE68.943.117.349.54.79.2
Bal-CE62.7 (-6.2)52.0 (+8.9)36.3 (+19.0)54.0 (+4.5)0.9 (-3.8)2.4 (-6.8)
BCE62.430.68.439.85.711.1
Bal-BCE65.8 (+3.4)50.6 (+20.0)32.9 (+24.6)54.1 (+14.2)4.8 (-0.9)9.0 (-2.2)
ViT-Base [15]86MCE74.748.219.454.55.16.8
Bal-CE70.5 (-4.3)56.8 (+8.6)43.7 (+24.3)60.1 (+5.6)3.7 (-1.4)4.9 (-1.9)
BCE73.746.515.652.45.67.9
Bal-BCE73.6 (-0.1)55.8 (+9.3)41.0 (+25.4)60.9 (+8.6)2.4 (-3.1)3.2 (-4.7)
ViT-Large [15]304MCE77.351.521.757.43.67.4
Bal-CE72.7 (-4.5)60.1 (+8.6)41.9 (+20.3)62.1 (+4.8)2.1 (-1.5)4.2 (-3.2)
BCE74.746.717.053.48.415.9
Bal-BCE75.3 (+0.6)58.8 (+12.1)37.5 (+20.5)62.6 (+9.2)6.6 (-1.8)14.8 (-1.1)
", + "image_path": "403f922404bc249811609a910a69e7fdd93ecb9b668f0fee452a0ad66b5669b3.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 308, + 289, + 416 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 308, + 289, + 416 + ], + "spans": [ + { + "bbox": [ + 46, + 308, + 289, + 416 + ], + "type": "text", + "content": "ResNet152 pre-trained on ImageNet-1K. For fair comparisons, we conduct MGP at ImageNet-1K and BFT at PlacesLT. As illustrated in Tab. 4, LiVT obtains satisfying performance compared with previous SOTAs. Notice that PlacesLT has limited instances compared to iNat18 (437.5K) and ImageNet-1K (1M). Considering both Tab. 3 and Tab. 4 results, we observe that ViTs, which benefit from large-scale data, are limited in this case. However, our LiVT performs the best even in such data paucity situations." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 429, + 149, + 441 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 429, + 149, + 441 + ], + "spans": [ + { + "bbox": [ + 47, + 429, + 149, + 441 + ], + "type": "text", + "content": "5.4. Further Analysis" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 454, + 287, + 622 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 454, + 287, + 622 + ], + "spans": [ + { + "bbox": [ + 46, + 454, + 287, + 622 + ], + "type": "text", + "content": "Robustness of MGP. The performance results in Tab. 1 have shown that MGP is more robust to learning label irrelevant features than supervised methods. For deeper observations, we show the transfer results in Tab. 5. Concretely, we conduct MGP on ImageNet-LT / ImageNet-BAL (See section 5.1) and BFT on iNat18 with resolution 224. Regardless of the data distribution of the MGP dataset, both BAL and LT achieve quite similar performance in terms of all evaluated metrics on iNat18. If we further compare the reported results with Tab. 3, we will draw the conclusion that the training instance number plays the key role in LiVT instead of the label distribution, which is clearly different from previous SCL [12,83] methods. We show more reconstruction visualization given by LT / BAL in Appendix." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 629, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 288, + 713 + ], + "type": "text", + "content": "Effectiveness of Proposed Bias. To learn balanced ViTs, we propose Bal-BCE with a simple yet effective logit bias (c.f. Eq. 10). To validate its effectiveness, we conduct the ablation study and compare it with the most popular rebalance loss, i.e., Bal-CE. As shown in Tab. 6, the new logit bias boosts vanilla BCE significantly with lower ECE on four ViT backbones, which is consistent with the behavior" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 307, + 305, + 547, + 453 + ], + "blocks": [ + { + "bbox": [ + 307, + 305, + 547, + 453 + ], + "lines": [ + { + "bbox": [ + 307, + 305, + 547, + 453 + ], + "spans": [ + { + "bbox": [ + 307, + 305, + 547, + 453 + ], + "type": "image", + "image_path": "f8a95414ed46ebc65973315109fc718192d2a485dddee37f754a70ccd8fdb17b.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 460, + 545, + 506 + ], + "lines": [ + { + "bbox": [ + 304, + 460, + 545, + 506 + ], + "spans": [ + { + "bbox": [ + 304, + 460, + 545, + 506 + ], + "type": "text", + "content": "Figure 2. Training loss and Top-1% accuracy of ViT-S on iNaturalist 2018 dataset. Solid and dot lines represent the accuracy and training loss, respectively. All models adopt the same settings and random seed except for loss type." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 510, + 547, + 595 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 547, + 595 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 547, + 595 + ], + "type": "text", + "content": "of Bal-CE. It is worth noticing that CE generally performs better than BCE in LTR scenarios, which is different from the conclusion in balanced datasets [55]. However, our BalBCE alleviates it remarkably and outperforms Bal-CE in most cases. In addition, Bal-BCE shows more satisfying numerical stability and faster convergence. See Bal-BCE in Fig. 2. for detailed illustrations." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": "For comprehensive comparisons, we re-implement recent rebalancing strategies in our BFT stage and show the results of ViT-B on CIFAR-LT in Tab. 7. Without loss of fairness, we conduct MGP on ImageNet-1K because the resolution " + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "inline_equation", + "content": "(32\\times 32)" + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": " of CIFAR is too small to mask for ViT-B-16. We do not reproduce the CL-based (conflict to MGP) and ensemble (memory limitation) methods. We also give up some ingenious rebalancing methods for loss NaN during training. As shown in Tab. 7, the proposed Bal-BCE" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "15799" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 60, + 91, + 273, + 186 + ], + "blocks": [ + { + "bbox": [ + 59, + 71, + 273, + 81 + ], + "lines": [ + { + "bbox": [ + 59, + 71, + 273, + 81 + ], + "spans": [ + { + "bbox": [ + 59, + 71, + 273, + 81 + ], + "type": "text", + "content": "Table 7. Ablation study of rebalancing strategies on ViT-B." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 60, + 91, + 273, + 186 + ], + "lines": [ + { + "bbox": [ + 60, + 91, + 273, + 186 + ], + "spans": [ + { + "bbox": [ + 60, + 91, + 273, + 186 + ], + "type": "table", + "html": "
MethodCIFAR-10-LTCIFAR-100-LT
γ1001010010
CE [13]79.289.550.966.1
CB [13]82.089.952.066.8
LDAM [4]78.688.652.5666.1
LADE [22]68.881.756.768.2
IB [50]75.479.250.851.6
Bal-CE [51]84.490.756.868.1
Bal-BCE (ours)86.391.358.269.2
", + "image_path": "bc0187475fb32e0ebaf0b214202da9076a6c0628403872cb2ae7f4c00e0d1f8b.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 191, + 287, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 191, + 287, + 239 + ], + "spans": [ + { + "bbox": [ + 46, + 191, + 287, + 239 + ], + "type": "text", + "content": "achieves the best results, which firmly manifests its effectiveness. Notice that some methods are not consistent with their performance on ResNet, which means some exquisite designs may not generalize well on ViTs." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 245, + 287, + 400 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 245, + 287, + 400 + ], + "spans": [ + { + "bbox": [ + 46, + 245, + 287, + 400 + ], + "type": "text", + "content": "Hyper-Parameter Analysis. In Alg. 1 Line 11, we add a hyper-parameter " + }, + { + "bbox": [ + 46, + 245, + 287, + 400 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 46, + 245, + 287, + 400 + ], + "type": "text", + "content": " to adjust our proposed bias (Eq. 10). We further present in-depth investigations on the influence of " + }, + { + "bbox": [ + 46, + 245, + 287, + 400 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 46, + 245, + 287, + 400 + ], + "type": "text", + "content": ". Similar to the aforementioned settings with plain augmentations, we conduct the ablation study on CIFAR-100-LT with MGP on ImageNet-1K and show the results in Fig.3. The few-shot accuracy gets obvious amelioration when " + }, + { + "bbox": [ + 46, + 245, + 287, + 400 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 46, + 245, + 287, + 400 + ], + "type": "text", + "content": " gets larger, which is consistent with our explanations in section 4.2. The best overall accuracy is obtained around 1, which inspires us to set " + }, + { + "bbox": [ + 46, + 245, + 287, + 400 + ], + "type": "inline_equation", + "content": "\\tau \\equiv 1" + }, + { + "bbox": [ + 46, + 245, + 287, + 400 + ], + "type": "text", + "content": " in LiVT for all experiments by default. Besides, the ECE gets smaller with increasing " + }, + { + "bbox": [ + 46, + 245, + 287, + 400 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 46, + 245, + 287, + 400 + ], + "type": "text", + "content": ", which means that the proposed bias guides ViTs to be the calibrated models with Fisher Consistency ensured [47]." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 412, + 117, + 425 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 412, + 117, + 425 + ], + "spans": [ + { + "bbox": [ + 47, + 412, + 117, + 425 + ], + "type": "text", + "content": "6. Discussion" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 438, + 287, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 438, + 287, + 594 + ], + "spans": [ + { + "bbox": [ + 46, + 438, + 287, + 594 + ], + "type": "text", + "content": "Why train from scratch? Previous ViTs papers are all based on pretrained weights from ImageNet-1K or ImageNet-22K and thus may lead to unfair comparisons with LTR methods, which are all trained from scratch. It is difficult to conclude that the intriguing performance mainly benefits from their proposals. Our approach provides a strong baseline to verify proposals' effectiveness with ViTs. It's also instructive to train plain ViTs for areas where data exhibits severe domain gaps. From the original intention of the LTR task, the core is to learn more large-scale imbalanced data effectively. Our work provides a feasible way to utilize more real-world LT (labels or attributes) data without expensive artificial balancing to achieve better representation learning." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 600, + 286, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 600, + 286, + 694 + ], + "spans": [ + { + "bbox": [ + 46, + 600, + 286, + 694 + ], + "type": "text", + "content": "How we extend MAE. We empirically prove that masked autoencoder learns generalized features even with imbalanced data, which is quite different from other self-supervised manners like CL [7] and SCL [30]. Extensive experiments on ImageNet-LT/BAL show that the instance number is more crucial than balanced annotation. We further propose the balanced binary cross-entropy loss to build our LiVT and achieve a new SOTA in LTR." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 701, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 701, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 47, + 701, + 286, + 712 + ], + "type": "text", + "content": "Limitations. One limitation is that LiVT can not be de" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 315, + 73, + 541, + 202 + ], + "blocks": [ + { + "bbox": [ + 315, + 73, + 541, + 202 + ], + "lines": [ + { + "bbox": [ + 315, + 73, + 541, + 202 + ], + "spans": [ + { + "bbox": [ + 315, + 73, + 541, + 202 + ], + "type": "image", + "image_path": "81d4417f9ab195409a45ac4fa3326dbf67c8f21c3333b2a686d3d5251e5ef1c0.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 313, + 204, + 541, + 335 + ], + "blocks": [ + { + "bbox": [ + 313, + 204, + 541, + 335 + ], + "lines": [ + { + "bbox": [ + 313, + 204, + 541, + 335 + ], + "spans": [ + { + "bbox": [ + 313, + 204, + 541, + 335 + ], + "type": "image", + "image_path": "f55cb4b5a8e15969bea715d57f9f2bf98ddaea7f958246d1f0532530bea0d8f5.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 339, + 545, + 361 + ], + "lines": [ + { + "bbox": [ + 305, + 339, + 545, + 361 + ], + "spans": [ + { + "bbox": [ + 305, + 339, + 545, + 361 + ], + "type": "text", + "content": "Figure 3. Performance of ViT-B with different " + }, + { + "bbox": [ + 305, + 339, + 545, + 361 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 305, + 339, + 545, + 361 + ], + "type": "text", + "content": " on CIFAR-100-LT. A bigger " + }, + { + "bbox": [ + 305, + 339, + 545, + 361 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 305, + 339, + 545, + 361 + ], + "type": "text", + "content": " results in better few-shot performance." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 368, + 545, + 429 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 368, + 545, + 429 + ], + "spans": [ + { + "bbox": [ + 305, + 368, + 545, + 429 + ], + "type": "text", + "content": "ployed in an end-to-end manner. An intuitive idea is two branches learning to optimize the decoder and classifier simultaneously, like BBN [81] or PaCo [12]. However, the heavily masked image prevents effective classification, while dynamic mask ratios exacerbate memory limitations." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 437, + 378, + 449 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 437, + 378, + 449 + ], + "spans": [ + { + "bbox": [ + 306, + 437, + 378, + 449 + ], + "type": "text", + "content": "7. Conclusion" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 457, + 545, + 636 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 457, + 545, + 636 + ], + "spans": [ + { + "bbox": [ + 304, + 457, + 545, + 636 + ], + "type": "text", + "content": "In this paper, we propose to Learn imbalanced data with Vision Transformers (LiVT), which consists of Masked Generative Pretraining (MGP) and Balanced Fine Tuning (BFT). MGP is based on our empirical insight that it guides ViTs to learn more generalized features on long-tailed datasets compared to supervised or contrastive paradigms. BFT is based on the theoretical analysis of Binary Cross-Entropy (BCE) in the imbalanced scenario. We propose the balanced BCE to learn unbiased ViTs by compensating extra logit margins. Bal-BCE ameliorates BCE significantly and surpasses the powerful and widely adopted Balanced Cross-Entropy loss when cooperating with ViTs. Extensive experiments on large-scale datasets demonstrate that LiVT successfully trains ViTs without any additional data and achieves a new state-of-the-art for long-tail recognition." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 646, + 404, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 646, + 404, + 659 + ], + "spans": [ + { + "bbox": [ + 306, + 646, + 404, + 659 + ], + "type": "text", + "content": "Acknowledgement" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "type": "text", + "content": "This work was supported by the National Key R&D Program of China (2022YFB4701400/4701402), SZSTC Grant (JCYJ 20190809172201639, WDZC20200820200655001), Shenzhen Key Laboratory (ZDSYS20210623092001004)." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15800" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 716 + ], + "type": "list", + "angle": 0, + "index": 17, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "type": "text", + "content": "[1] Shaden Alshammari, Yu-Xiong Wang, Deva Ramanan, and Shu Kong. 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